diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/FormalAssociatedAction.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/FormalAssociatedAction.lean index 17e095e893b684c7340a6fe382ed71425bed8076..f366192b4eb3de1f75f70ea0cd2cf16f0a69de95 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/FormalAssociatedAction.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/FormalAssociatedAction.lean @@ -1,77 +1,77 @@ -import OAI.RepresentationTheory.RestrictedTilting.FormalSectionAction -import OAI.RepresentationTheory.RestrictedTilting.AssociatedPlaneJet -import OAI.RepresentationTheory.RestrictedTilting.NumeratorAction -import OAI.RepresentationTheory.RestrictedTilting.CompletionCoefficients -import OAI.RepresentationTheory.RestrictedTilting.CompletedCoordinates - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory -open scoped TensorProduct BigOperators Pointwise -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (ι : Type u) [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) -variable (P : Matrix ι ι (Polynomial k)) -variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) -variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) -local notation "N" => associatedSectionsSubmodule k ι ρ -local notation "A" => MvPolynomial (Fin 2) k -local notation "I" => MvPolynomial.idealOfVars (Fin 2) k -local notation "σ" => associatedSectionsRepresentation k ι ρ -local notation "hσ" => associatedSections_planeCompatible k ι ρ -local notation "W" => associatedNumeratorLinear k ι ρ P hP d hd -variable [Module.Finite k ((associatedSectionsSubmodule k ι ρ) ⧸ - planeJetRelation (M := associatedSectionsSubmodule k ι ρ) k 1)] -local notation "T" => planeJetFD k σ hσ 1 - -noncomputable def formalAssociatedCoordinates - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) (v : T) : - ι → planeCompletion k := completedCoordinates I W (formalPlaneSection k σ hσ s hs v) - -omit [Infinite k] in -lemma linePolynomial_cleared (p : Polynomial k) (t : k) (d : ℕ) : - linePolynomial k (clearedPolynomial p (MvPolynomial.C t) ((MvPolynomial.X 0 : A)^2) d) = - clearedLineAction k p t d := by - rw [map_clearedPolynomial] - simp [linePolynomial, clearedLineAction] - -omit [Infinite k] in -lemma formalLineMap_cleared (p : Polynomial k) (t : k) (d : ℕ) : - formalLineMap k (algebraMap A (planeCompletion k) - (clearedPolynomial p (MvPolynomial.C t) ((MvPolynomial.X 0 : A)^2) d)) = - clearedPolynomial p (algebraMap k (PowerSeries k) t) ((PowerSeries.X : PowerSeries k)^2) d := by - change formalLineMap k ((IsScalarTower.toAlgHom k A (planeCompletion k)) _) = _ - rw [map_clearedPolynomial, map_clearedPolynomial] - simp only [IsScalarTower.toAlgHom_apply, map_pow, formalLineMap_X] - congr 1 - rw [MvPolynomial.C_eq_algebraMap, ← IsScalarTower.algebraMap_apply, - AlgHom.commutes] - -lemma formalAssociatedCoordinates_unipotent - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (t : k) (v : T) (i : ι) : - (PowerSeries.X : PowerSeries k)^(2*d) * formalLineMap k - (formalAssociatedCoordinates k ι ρ P hP d hd s hs ((planeJetFD k σ hσ 1).ρ (unipotent k t) v) i) = - ∑ j, clearedPolynomial (P i j) (algebraMap k (PowerSeries k) t) - ((PowerSeries.X : PowerSeries k)^2) d * formalLineMap k - (formalAssociatedCoordinates k ι ρ P hP d hd s hs v j) := by - let F : N →ₗ[A] A := (MvPolynomial.X 0 : A)^(2*d) • (LinearMap.proj i).comp W - let G : N →ₗ[A] A := ∑ j, clearedPolynomial (P i j) (MvPolynomial.C t) - ((MvPolynomial.X 0 : A)^2) d • (LinearMap.proj j).comp W - have he : ∀ f : N, linePolynomial k (F (σ (unipotent k t) f)) = linePolynomial k (G f) := by - intro f - simpa only [F,G,LinearMap.smul_apply,LinearMap.sum_apply,LinearMap.comp_apply, - LinearMap.proj_apply,smul_eq_mul,map_mul,map_pow,map_sum, - show linePolynomial k (MvPolynomial.X 0) = Polynomial.X from by simp [linePolynomial], - linePolynomial_cleared] using associatedNumerator_line_unipotent k ι ρ P hP d hd t f i - have h := formalPlaneSection_line_action k σ hσ s hs (unipotent k t) F G he v - simp only [F,G,completion_map_smul, LinearMap.sum_apply, completion_self_smul, map_mul, map_sum, - map_pow, formalLineMap_X, formalLineMap_cleared] at h - simpa only [formalAssociatedCoordinates, completedCoordinates_apply] using h -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.FormalSectionAction +import OAI.RepresentationTheory.RestrictedTilting.AssociatedPlaneJet +import OAI.RepresentationTheory.RestrictedTilting.NumeratorAction +import OAI.RepresentationTheory.RestrictedTilting.CompletionCoefficients +import OAI.RepresentationTheory.RestrictedTilting.CompletedCoordinates + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory +open scoped TensorProduct BigOperators Pointwise +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (ι : Type u) [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) +variable (P : Matrix ι ι (Polynomial k)) +variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) +variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) +local notation "N" => associatedSectionsSubmodule k ι ρ +local notation "A" => MvPolynomial (Fin 2) k +local notation "I" => MvPolynomial.idealOfVars (Fin 2) k +local notation "σ" => associatedSectionsRepresentation k ι ρ +local notation "hσ" => associatedSections_planeCompatible k ι ρ +local notation "W" => associatedNumeratorLinear k ι ρ P hP d hd +variable [Module.Finite k ((associatedSectionsSubmodule k ι ρ) ⧸ + planeJetRelation (M := associatedSectionsSubmodule k ι ρ) k 1)] +local notation "T" => planeJetFD k σ hσ 1 + +noncomputable def formalAssociatedCoordinates + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) (v : T) : + ι → planeCompletion k := completedCoordinates I W (formalPlaneSection k σ hσ s hs v) + +omit [Infinite k] in +lemma linePolynomial_cleared (p : Polynomial k) (t : k) (d : ℕ) : + linePolynomial k (clearedPolynomial p (MvPolynomial.C t) ((MvPolynomial.X 0 : A)^2) d) = + clearedLineAction k p t d := by + rw [map_clearedPolynomial] + simp [linePolynomial, clearedLineAction] + +omit [Infinite k] in +lemma formalLineMap_cleared (p : Polynomial k) (t : k) (d : ℕ) : + formalLineMap k (algebraMap A (planeCompletion k) + (clearedPolynomial p (MvPolynomial.C t) ((MvPolynomial.X 0 : A)^2) d)) = + clearedPolynomial p (algebraMap k (PowerSeries k) t) ((PowerSeries.X : PowerSeries k)^2) d := by + change formalLineMap k ((IsScalarTower.toAlgHom k A (planeCompletion k)) _) = _ + rw [map_clearedPolynomial, map_clearedPolynomial] + simp only [IsScalarTower.toAlgHom_apply, map_pow, formalLineMap_X] + congr 1 + rw [MvPolynomial.C_eq_algebraMap, ← IsScalarTower.algebraMap_apply, + AlgHom.commutes] + +lemma formalAssociatedCoordinates_unipotent + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (t : k) (v : T) (i : ι) : + (PowerSeries.X : PowerSeries k)^(2*d) * formalLineMap k + (formalAssociatedCoordinates k ι ρ P hP d hd s hs ((planeJetFD k σ hσ 1).ρ (unipotent k t) v) i) = + ∑ j, clearedPolynomial (P i j) (algebraMap k (PowerSeries k) t) + ((PowerSeries.X : PowerSeries k)^2) d * formalLineMap k + (formalAssociatedCoordinates k ι ρ P hP d hd s hs v j) := by + let F : N →ₗ[A] A := (MvPolynomial.X 0 : A)^(2*d) • (LinearMap.proj i).comp W + let G : N →ₗ[A] A := ∑ j, clearedPolynomial (P i j) (MvPolynomial.C t) + ((MvPolynomial.X 0 : A)^2) d • (LinearMap.proj j).comp W + have he : ∀ f : N, linePolynomial k (F (σ (unipotent k t) f)) = linePolynomial k (G f) := by + intro f + simpa only [F,G,LinearMap.smul_apply,LinearMap.sum_apply,LinearMap.comp_apply, + LinearMap.proj_apply,smul_eq_mul,map_mul,map_pow,map_sum, + show linePolynomial k (MvPolynomial.X 0) = Polynomial.X from by simp [linePolynomial], + linePolynomial_cleared] using associatedNumerator_line_unipotent k ι ρ P hP d hd t f i + have h := formalPlaneSection_line_action k σ hσ s hs (unipotent k t) F G he v + simp only [F,G,completion_map_smul, LinearMap.sum_apply, completion_self_smul, map_mul, map_sum, + map_pow, formalLineMap_X, formalLineMap_cleared] at h + simpa only [formalAssociatedCoordinates, completedCoordinates_apply] using h +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/FormalAssociatedIso.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/FormalAssociatedIso.lean index 7729d084eeb9d264b85c15e1c2bc69a2e212fd32..fb70028a2604dcb4cb4da0fd5c03ec3e73020c55 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/FormalAssociatedIso.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/FormalAssociatedIso.lean @@ -1,100 +1,100 @@ -import OAI.RepresentationTheory.RestrictedTilting.FormalAssociatedAction - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory Matrix -open scoped TensorProduct BigOperators Pointwise -universe u -variable (k : Type u) [Field k] [Infinite k] -attribute [local instance 1100] HahnSeries.instAlgebra -variable (ι : Type u) [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) -variable (P : Matrix ι ι (Polynomial k)) -variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) -variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) -local notation "N" => associatedSectionsSubmodule k ι ρ -local notation "A" => MvPolynomial (Fin 2) k -local notation "I" => MvPolynomial.idealOfVars (Fin 2) k -local notation "H" => planeCompletion k -local notation "K" => LaurentSeries k -local notation "σ" => associatedSectionsRepresentation k ι ρ -local notation "hσ" => associatedSections_planeCompatible k ι ρ -local notation "W" => associatedNumeratorLinear k ι ρ P hP d hd -local notation "Z" => associatedDenominatorLinear k ι ρ P hP d hd -local notation "hx" => And.left (associatedSections_regular k ι ρ P hP) -local notation "hy" => And.right (associatedSections_regular k ι ρ P hP) -variable [Module.Finite k ((associatedSectionsSubmodule k ι ρ) ⧸ - planeJetRelation (M := associatedSectionsSubmodule k ι ρ) k 1)] -local notation "T" => planeJetFD k σ hσ 1 - -omit [Infinite k] in -lemma ofPowerSeriesAlg_apply_eq (f : PowerSeries k) : - (HahnSeries.ofPowerSeriesAlg ℤ k) f = HahnSeries.ofPowerSeries ℤ k f := rfl - -noncomputable def formalLineParameter : K := - HahnSeries.ofPowerSeries ℤ k PowerSeries.X - -omit [Infinite k] in -lemma formalLineParameter_ne_zero : formalLineParameter k ≠ 0 := by - intro hz - apply PowerSeries.X_ne_zero (R := k) - exact HahnSeries.ofPowerSeries_injective (hz.trans (map_zero _).symm) - -noncomputable def associatedFieldTrivialization - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) : (K ⊗[k] T) ≃ₗ[K] (ι → K) := by - letI : Algebra H K := (formalLineFieldMap k).toRingHom.toAlgebra - exact fieldCoordinateTrivialization (formalPlaneTrivialization k σ hσ s hs0 hs hx hy) - (completedCoordinates I W) (completedDenominator I Z) - (algebraMap A H ((MvPolynomial.X 0)^ (d+d))) - (completedCoordinates_denominator I W Z _ (associatedNumerator_denominator k ι ρ P hP d hd)) - (completedDenominator_coordinates I W Z _ (associatedDenominator_numerator k ι ρ P hP d hd)) - (by - change formalLineFieldMap k (algebraMap A H ((MvPolynomial.X 0)^(d+d))) ≠ 0 - rw [map_pow, map_pow] - exact pow_ne_zero _ (formalLineFieldMap_X_ne_zero k)) - -lemma associatedFieldTrivialization_one - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (v : T) (i : ι) : - associatedFieldTrivialization k ι ρ P hP d hd s hs0 hs (1 ⊗ₜ[k] v) i = - HahnSeries.ofPowerSeries ℤ k - (formalLineMap k (formalAssociatedCoordinates k ι ρ P hP d hd s hs v i)) := by - let : Algebra H K := (formalLineFieldMap k).toRingHom.toAlgebra - dsimp only [associatedFieldTrivialization] - rw [fieldCoordinateTrivialization_one, formalPlaneTrivialization_one_tmul] - rfl - -lemma associatedFieldTrivialization_unipotent_one - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (t : k) (v : T) : - associatedFieldTrivialization k ι ρ P hP d hd s hs0 hs - (1 ⊗ₜ[k] ((planeJetFD k σ hσ 1).ρ (unipotent k t) v)) = - polynomialMatrixEval P (algebraMap k K t / (formalLineParameter k)^2) *ᵥ - associatedFieldTrivialization k ι ρ P hP d hd s hs0 hs (1 ⊗ₜ[k] v) := by - apply funext - intro i - have he := congrArg (HahnSeries.ofPowerSeriesAlg ℤ k) - (formalAssociatedCoordinates_unipotent k ι ρ P hP d hd s hs t v i) - simp only [map_mul, map_pow, map_sum] at he - have hc (j : ι) : (HahnSeries.ofPowerSeriesAlg ℤ k) - (clearedPolynomial (P i j) (algebraMap k (PowerSeries k) t) - ((PowerSeries.X : PowerSeries k)^2) d) = - (formalLineParameter k)^(2*d) * - Polynomial.aeval (algebraMap k K t / (formalLineParameter k)^2) (P i j) := by - have hc := clearedPolynomial_eval (HahnSeries.ofPowerSeriesAlg ℤ k) (P i j) - (algebraMap k (PowerSeries k) t) ((PowerSeries.X : PowerSeries k)^2) d (hd i j) - (by - rw [map_pow] - exact pow_ne_zero 2 (formalLineParameter_ne_zero k)) - simpa only [map_pow, AlgHom.commutes, ofPowerSeriesAlg_apply_eq, formalLineParameter, ← pow_mul, div_eq_mul_inv] using hc - simp only [hc, mul_assoc, ← Finset.mul_sum] at he - apply mul_left_cancel₀ (pow_ne_zero (2*d) (formalLineParameter_ne_zero k)) - simpa only [associatedFieldTrivialization_one, Matrix.mulVec, dotProduct, polynomialMatrixEval, - formalLineParameter, ofPowerSeriesAlg_apply_eq] using he -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.FormalAssociatedAction + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory Matrix +open scoped TensorProduct BigOperators Pointwise +universe u +variable (k : Type u) [Field k] [Infinite k] +attribute [local instance 1100] HahnSeries.instAlgebra +variable (ι : Type u) [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) +variable (P : Matrix ι ι (Polynomial k)) +variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) +variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) +local notation "N" => associatedSectionsSubmodule k ι ρ +local notation "A" => MvPolynomial (Fin 2) k +local notation "I" => MvPolynomial.idealOfVars (Fin 2) k +local notation "H" => planeCompletion k +local notation "K" => LaurentSeries k +local notation "σ" => associatedSectionsRepresentation k ι ρ +local notation "hσ" => associatedSections_planeCompatible k ι ρ +local notation "W" => associatedNumeratorLinear k ι ρ P hP d hd +local notation "Z" => associatedDenominatorLinear k ι ρ P hP d hd +local notation "hx" => And.left (associatedSections_regular k ι ρ P hP) +local notation "hy" => And.right (associatedSections_regular k ι ρ P hP) +variable [Module.Finite k ((associatedSectionsSubmodule k ι ρ) ⧸ + planeJetRelation (M := associatedSectionsSubmodule k ι ρ) k 1)] +local notation "T" => planeJetFD k σ hσ 1 + +omit [Infinite k] in +lemma ofPowerSeriesAlg_apply_eq (f : PowerSeries k) : + (HahnSeries.ofPowerSeriesAlg ℤ k) f = HahnSeries.ofPowerSeries ℤ k f := rfl + +noncomputable def formalLineParameter : K := + HahnSeries.ofPowerSeries ℤ k PowerSeries.X + +omit [Infinite k] in +lemma formalLineParameter_ne_zero : formalLineParameter k ≠ 0 := by + intro hz + apply PowerSeries.X_ne_zero (R := k) + exact HahnSeries.ofPowerSeries_injective (hz.trans (map_zero _).symm) + +noncomputable def associatedFieldTrivialization + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) : (K ⊗[k] T) ≃ₗ[K] (ι → K) := by + letI : Algebra H K := (formalLineFieldMap k).toRingHom.toAlgebra + exact fieldCoordinateTrivialization (formalPlaneTrivialization k σ hσ s hs0 hs hx hy) + (completedCoordinates I W) (completedDenominator I Z) + (algebraMap A H ((MvPolynomial.X 0)^ (d+d))) + (completedCoordinates_denominator I W Z _ (associatedNumerator_denominator k ι ρ P hP d hd)) + (completedDenominator_coordinates I W Z _ (associatedDenominator_numerator k ι ρ P hP d hd)) + (by + change formalLineFieldMap k (algebraMap A H ((MvPolynomial.X 0)^(d+d))) ≠ 0 + rw [map_pow, map_pow] + exact pow_ne_zero _ (formalLineFieldMap_X_ne_zero k)) + +lemma associatedFieldTrivialization_one + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (v : T) (i : ι) : + associatedFieldTrivialization k ι ρ P hP d hd s hs0 hs (1 ⊗ₜ[k] v) i = + HahnSeries.ofPowerSeries ℤ k + (formalLineMap k (formalAssociatedCoordinates k ι ρ P hP d hd s hs v i)) := by + let : Algebra H K := (formalLineFieldMap k).toRingHom.toAlgebra + dsimp only [associatedFieldTrivialization] + rw [fieldCoordinateTrivialization_one, formalPlaneTrivialization_one_tmul] + rfl + +lemma associatedFieldTrivialization_unipotent_one + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (t : k) (v : T) : + associatedFieldTrivialization k ι ρ P hP d hd s hs0 hs + (1 ⊗ₜ[k] ((planeJetFD k σ hσ 1).ρ (unipotent k t) v)) = + polynomialMatrixEval P (algebraMap k K t / (formalLineParameter k)^2) *ᵥ + associatedFieldTrivialization k ι ρ P hP d hd s hs0 hs (1 ⊗ₜ[k] v) := by + apply funext + intro i + have he := congrArg (HahnSeries.ofPowerSeriesAlg ℤ k) + (formalAssociatedCoordinates_unipotent k ι ρ P hP d hd s hs t v i) + simp only [map_mul, map_pow, map_sum] at he + have hc (j : ι) : (HahnSeries.ofPowerSeriesAlg ℤ k) + (clearedPolynomial (P i j) (algebraMap k (PowerSeries k) t) + ((PowerSeries.X : PowerSeries k)^2) d) = + (formalLineParameter k)^(2*d) * + Polynomial.aeval (algebraMap k K t / (formalLineParameter k)^2) (P i j) := by + have hc := clearedPolynomial_eval (HahnSeries.ofPowerSeriesAlg ℤ k) (P i j) + (algebraMap k (PowerSeries k) t) ((PowerSeries.X : PowerSeries k)^2) d (hd i j) + (by + rw [map_pow] + exact pow_ne_zero 2 (formalLineParameter_ne_zero k)) + simpa only [map_pow, AlgHom.commutes, ofPowerSeriesAlg_apply_eq, formalLineParameter, ← pow_mul, div_eq_mul_inv] using hc + simp only [hc, mul_assoc, ← Finset.mul_sum] at he + apply mul_left_cancel₀ (pow_ne_zero (2*d) (formalLineParameter_ne_zero k)) + simpa only [associatedFieldTrivialization_one, Matrix.mulVec, dotProduct, polynomialMatrixEval, + formalLineParameter, ofPowerSeriesAlg_apply_eq] using he +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/FormalLine.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/FormalLine.lean index 270b2f197a68bc821dd5efd937bd07d04c5daade..6ce58ec2ac8581b89c983f307e412771eb6890b7 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/FormalLine.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/FormalLine.lean @@ -1,92 +1,92 @@ -import Mathlib - -namespace OAI - -namespace FiberFunctorProof -open scoped TensorProduct -universe u -variable (k : Type u) [Field k] -attribute [local instance 1100] HahnSeries.instAlgebra - -abbrev planeCompletion := AdicCompletion (MvPolynomial.idealOfVars (Fin 2) k) - (MvPolynomial (Fin 2) k) - - -def formalLineEmbedding : Unit ↪ Fin 2 := ⟨fun _ => 0, fun a b _ => Subsingleton.elim a b⟩ - -noncomputable def formalLineMap : planeCompletion k →ₐ[k] PowerSeries k := - (MvPowerSeries.killCompl (formalLineEmbedding)).comp - ((MvPowerSeries.toAdicCompletionAlgEquiv (Fin 2) k).symm.restrictScalars k).toAlgHom - - - -noncomputable def formalLineFieldMap : planeCompletion k →ₐ[k] LaurentSeries k := - (HahnSeries.ofPowerSeriesAlg ℤ k).comp (formalLineMap k) - -lemma formalLineMap_poly : - (formalLineMap k).comp (IsScalarTower.toAlgHom k (MvPolynomial (Fin 2) k) (planeCompletion k)) = - MvPolynomial.aeval (fun i : Fin 2 => if i = 0 then (PowerSeries.X : PowerSeries k) else 0) := by - ext i : 1 - change MvPowerSeries.killCompl (formalLineEmbedding) - ((MvPowerSeries.toAdicCompletionAlgEquiv (Fin 2) k).symm - (algebraMap (MvPolynomial (Fin 2) k) (planeCompletion k) (MvPolynomial.X i))) = _ - rw [AlgEquiv.commutes] - rw [MvPowerSeries.algebraMap_apply', MvPolynomial.coe_X, MvPowerSeries.map_X] - fin_cases i - · simp only [MvPolynomial.aeval_X] - change MvPowerSeries.killCompl (R := k) formalLineEmbedding (MvPowerSeries.X 0) = PowerSeries.X - exact MvPowerSeries.killCompl_X (R := k) (e := formalLineEmbedding) () - · rw [MvPowerSeries.killCompl_X_eq_zero] - · simp - · rintro ⟨u,hu⟩ - exact Fin.zero_ne_one (show (0 : Fin 2) = 1 from hu) - -@[simp] lemma formalLineMap_of (P : MvPolynomial (Fin 2) k) : - formalLineMap k (algebraMap (MvPolynomial (Fin 2) k) (planeCompletion k) P) = - MvPolynomial.aeval (fun i : Fin 2 => if i = 0 then (PowerSeries.X : PowerSeries k) else 0) P := - congrArg (fun f : MvPolynomial (Fin 2) k →ₐ[k] PowerSeries k => f P) (formalLineMap_poly k) - -@[simp] lemma formalLineMap_X : - formalLineMap k (algebraMap (MvPolynomial (Fin 2) k) (planeCompletion k) (MvPolynomial.X 0)) = - PowerSeries.X := by simp - -@[simp] lemma formalLineMap_Y : - formalLineMap k (algebraMap (MvPolynomial (Fin 2) k) (planeCompletion k) (MvPolynomial.X 1)) = 0 := by - simp - -lemma formalLineFieldMap_X_ne_zero : - formalLineFieldMap k (algebraMap (MvPolynomial (Fin 2) k) (planeCompletion k) - (MvPolynomial.X 0)) ≠ 0 := by - change HahnSeries.ofPowerSeries ℤ k (formalLineMap k _) ≠ 0 - rw [formalLineMap_X] - intro hz - apply PowerSeries.X_ne_zero (R := k) - exact (HahnSeries.ofPowerSeries_injective (Γ := ℤ) (R := k)) - (hz.trans (map_zero _).symm) - - - -lemma formalLineMap_coeff_eq (n : ℕ) (x y : planeCompletion k) - (h : x.val (n+1) = y.val (n+1)) : - PowerSeries.coeff n (formalLineMap k x) = PowerSeries.coeff n (formalLineMap k y) := by - change MvPowerSeries.coeff (Finsupp.single () n) - (MvPowerSeries.killCompl (formalLineEmbedding) ((MvPowerSeries.toAdicCompletionAlgEquiv (Fin 2) k).symm x)) = - MvPowerSeries.coeff (Finsupp.single () n) - (MvPowerSeries.killCompl (formalLineEmbedding) ((MvPowerSeries.toAdicCompletionAlgEquiv (Fin 2) k).symm y)) - simp only [MvPowerSeries.coeff_killCompl, Finsupp.embDomain_single] - change MvPowerSeries.coeff (Finsupp.single (0 : Fin 2) n) - ((MvPowerSeries.toAdicCompletionAlgEquiv (Fin 2) k).symm x) = - MvPowerSeries.coeff (Finsupp.single (0 : Fin 2) n) - ((MvPowerSeries.toAdicCompletionAlgEquiv (Fin 2) k).symm y) - simp only [MvPowerSeries.toAdicCompletionAlgEquiv_symm_apply, - MvPowerSeries.coeff_toAdicCompletionInv] - apply congrArg (fun polynomial : MvPolynomial (Fin 2) k => - polynomial.coeff (Finsupp.single (0 : Fin 2) n)) - have h' : x.val ((Finsupp.single (0 : Fin 2) n).degree + 1) = - y.val ((Finsupp.single (0 : Fin 2) n).degree + 1) := by - rw [Finsupp.degree_single] - exact h - exact congrArg Quotient.out h' -end FiberFunctorProof - -end OAI +import Mathlib + +namespace OAI + +namespace FiberFunctorProof +open scoped TensorProduct +universe u +variable (k : Type u) [Field k] +attribute [local instance 1100] HahnSeries.instAlgebra + +abbrev planeCompletion := AdicCompletion (MvPolynomial.idealOfVars (Fin 2) k) + (MvPolynomial (Fin 2) k) + + +def formalLineEmbedding : Unit ↪ Fin 2 := ⟨fun _ => 0, fun a b _ => Subsingleton.elim a b⟩ + +noncomputable def formalLineMap : planeCompletion k →ₐ[k] PowerSeries k := + (MvPowerSeries.killCompl (formalLineEmbedding)).comp + ((MvPowerSeries.toAdicCompletionAlgEquiv (Fin 2) k).symm.restrictScalars k).toAlgHom + + + +noncomputable def formalLineFieldMap : planeCompletion k →ₐ[k] LaurentSeries k := + (HahnSeries.ofPowerSeriesAlg ℤ k).comp (formalLineMap k) + +lemma formalLineMap_poly : + (formalLineMap k).comp (IsScalarTower.toAlgHom k (MvPolynomial (Fin 2) k) (planeCompletion k)) = + MvPolynomial.aeval (fun i : Fin 2 => if i = 0 then (PowerSeries.X : PowerSeries k) else 0) := by + ext i : 1 + change MvPowerSeries.killCompl (formalLineEmbedding) + ((MvPowerSeries.toAdicCompletionAlgEquiv (Fin 2) k).symm + (algebraMap (MvPolynomial (Fin 2) k) (planeCompletion k) (MvPolynomial.X i))) = _ + rw [AlgEquiv.commutes] + rw [MvPowerSeries.algebraMap_apply', MvPolynomial.coe_X, MvPowerSeries.map_X] + fin_cases i + · simp only [MvPolynomial.aeval_X] + change MvPowerSeries.killCompl (R := k) formalLineEmbedding (MvPowerSeries.X 0) = PowerSeries.X + exact MvPowerSeries.killCompl_X (R := k) (e := formalLineEmbedding) () + · rw [MvPowerSeries.killCompl_X_eq_zero] + · simp + · rintro ⟨u,hu⟩ + exact Fin.zero_ne_one (show (0 : Fin 2) = 1 from hu) + +@[simp] lemma formalLineMap_of (P : MvPolynomial (Fin 2) k) : + formalLineMap k (algebraMap (MvPolynomial (Fin 2) k) (planeCompletion k) P) = + MvPolynomial.aeval (fun i : Fin 2 => if i = 0 then (PowerSeries.X : PowerSeries k) else 0) P := + congrArg (fun f : MvPolynomial (Fin 2) k →ₐ[k] PowerSeries k => f P) (formalLineMap_poly k) + +@[simp] lemma formalLineMap_X : + formalLineMap k (algebraMap (MvPolynomial (Fin 2) k) (planeCompletion k) (MvPolynomial.X 0)) = + PowerSeries.X := by simp + +@[simp] lemma formalLineMap_Y : + formalLineMap k (algebraMap (MvPolynomial (Fin 2) k) (planeCompletion k) (MvPolynomial.X 1)) = 0 := by + simp + +lemma formalLineFieldMap_X_ne_zero : + formalLineFieldMap k (algebraMap (MvPolynomial (Fin 2) k) (planeCompletion k) + (MvPolynomial.X 0)) ≠ 0 := by + change HahnSeries.ofPowerSeries ℤ k (formalLineMap k _) ≠ 0 + rw [formalLineMap_X] + intro hz + apply PowerSeries.X_ne_zero (R := k) + exact (HahnSeries.ofPowerSeries_injective (Γ := ℤ) (R := k)) + (hz.trans (map_zero _).symm) + + + +lemma formalLineMap_coeff_eq (n : ℕ) (x y : planeCompletion k) + (h : x.val (n+1) = y.val (n+1)) : + PowerSeries.coeff n (formalLineMap k x) = PowerSeries.coeff n (formalLineMap k y) := by + change MvPowerSeries.coeff (Finsupp.single () n) + (MvPowerSeries.killCompl (formalLineEmbedding) ((MvPowerSeries.toAdicCompletionAlgEquiv (Fin 2) k).symm x)) = + MvPowerSeries.coeff (Finsupp.single () n) + (MvPowerSeries.killCompl (formalLineEmbedding) ((MvPowerSeries.toAdicCompletionAlgEquiv (Fin 2) k).symm y)) + simp only [MvPowerSeries.coeff_killCompl, Finsupp.embDomain_single] + change MvPowerSeries.coeff (Finsupp.single (0 : Fin 2) n) + ((MvPowerSeries.toAdicCompletionAlgEquiv (Fin 2) k).symm x) = + MvPowerSeries.coeff (Finsupp.single (0 : Fin 2) n) + ((MvPowerSeries.toAdicCompletionAlgEquiv (Fin 2) k).symm y) + simp only [MvPowerSeries.toAdicCompletionAlgEquiv_symm_apply, + MvPowerSeries.coeff_toAdicCompletionInv] + apply congrArg (fun polynomial : MvPolynomial (Fin 2) k => + polynomial.coeff (Finsupp.single (0 : Fin 2) n)) + have h' : x.val ((Finsupp.single (0 : Fin 2) n).degree + 1) = + y.val ((Finsupp.single (0 : Fin 2) n).degree + 1) := by + rw [Finsupp.degree_single] + exact h + exact congrArg Quotient.out h' +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/FormalLineContinuity.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/FormalLineContinuity.lean index 85e276b5348fa8306b79673cc6a6619b8dd9d5ef..0302652d11eeb862ec33fcdfacfcba0bf9b4965b 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/FormalLineContinuity.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/FormalLineContinuity.lean @@ -1,50 +1,50 @@ -import OAI.RepresentationTheory.RestrictedTilting.FormalLine -import OAI.RepresentationTheory.RestrictedTilting.ClearedPolynomial - -namespace OAI - -namespace FiberFunctorProof -universe u -variable (k : Type u) [Field k] -local notation "A" => MvPolynomial (Fin 2) k -local notation "I" => MvPolynomial.idealOfVars (Fin 2) k - -lemma formalLineMap_of_linePolynomial (P : A) : - formalLineMap k (AdicCompletion.of I A P) = - Polynomial.aeval (PowerSeries.X : PowerSeries k) (linePolynomial k P) := by - change formalLineMap k (algebraMap A (planeCompletion k) P) = _ - rw [formalLineMap_of] - have he : (Polynomial.aeval (PowerSeries.X : PowerSeries k)).comp (linePolynomial k) = - MvPolynomial.aeval (fun i : Fin 2 => if i = 0 then PowerSeries.X else 0) := by - ext i - simp only [AlgHom.comp_apply, linePolynomial, MvPolynomial.aeval_X] - split_ifs <;> simp - exact congrArg (fun f : A →ₐ[k] PowerSeries k => f P) he.symm - -variable {M : Type u} [AddCommGroup M] [Module (MvPolynomial (Fin 2) k) M] - - - -lemma formalLine_map_eq_of_representatives - (F G : M →ₗ[A] A) (x y : AdicCompletion I M) - (h : ∀ n : ℕ, ∃ v w : M, - x.val (n+1) = (AdicCompletion.of I M v).val (n+1) ∧ - y.val (n+1) = (AdicCompletion.of I M w).val (n+1) ∧ - linePolynomial k (F v) = linePolynomial k (G w)) : - formalLineMap k (AdicCompletion.map I F x) = - formalLineMap k (AdicCompletion.map I G y) := by - ext n - obtain ⟨v,w,hv,hw,he⟩ := h n - have hF : (AdicCompletion.map I F x).val (n+1) = - (AdicCompletion.of I A (F v)).val (n+1) := by - rw [← AdicCompletion.map_of] - simp only [AdicCompletion.map_val_apply, hv] - have hG : (AdicCompletion.map I G y).val (n+1) = - (AdicCompletion.of I A (G w)).val (n+1) := by - rw [← AdicCompletion.map_of] - simp only [AdicCompletion.map_val_apply, hw] - rw [formalLineMap_coeff_eq k n _ _ hF, formalLineMap_coeff_eq k n _ _ hG, - formalLineMap_of_linePolynomial, formalLineMap_of_linePolynomial, he] -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.FormalLine +import OAI.RepresentationTheory.RestrictedTilting.ClearedPolynomial + +namespace OAI + +namespace FiberFunctorProof +universe u +variable (k : Type u) [Field k] +local notation "A" => MvPolynomial (Fin 2) k +local notation "I" => MvPolynomial.idealOfVars (Fin 2) k + +lemma formalLineMap_of_linePolynomial (P : A) : + formalLineMap k (AdicCompletion.of I A P) = + Polynomial.aeval (PowerSeries.X : PowerSeries k) (linePolynomial k P) := by + change formalLineMap k (algebraMap A (planeCompletion k) P) = _ + rw [formalLineMap_of] + have he : (Polynomial.aeval (PowerSeries.X : PowerSeries k)).comp (linePolynomial k) = + MvPolynomial.aeval (fun i : Fin 2 => if i = 0 then PowerSeries.X else 0) := by + ext i + simp only [AlgHom.comp_apply, linePolynomial, MvPolynomial.aeval_X] + split_ifs <;> simp + exact congrArg (fun f : A →ₐ[k] PowerSeries k => f P) he.symm + +variable {M : Type u} [AddCommGroup M] [Module (MvPolynomial (Fin 2) k) M] + + + +lemma formalLine_map_eq_of_representatives + (F G : M →ₗ[A] A) (x y : AdicCompletion I M) + (h : ∀ n : ℕ, ∃ v w : M, + x.val (n+1) = (AdicCompletion.of I M v).val (n+1) ∧ + y.val (n+1) = (AdicCompletion.of I M w).val (n+1) ∧ + linePolynomial k (F v) = linePolynomial k (G w)) : + formalLineMap k (AdicCompletion.map I F x) = + formalLineMap k (AdicCompletion.map I G y) := by + ext n + obtain ⟨v,w,hv,hw,he⟩ := h n + have hF : (AdicCompletion.map I F x).val (n+1) = + (AdicCompletion.of I A (F v)).val (n+1) := by + rw [← AdicCompletion.map_of] + simp only [AdicCompletion.map_val_apply, hv] + have hG : (AdicCompletion.map I G y).val (n+1) = + (AdicCompletion.of I A (G w)).val (n+1) := by + rw [← AdicCompletion.map_of] + simp only [AdicCompletion.map_val_apply, hw] + rw [formalLineMap_coeff_eq k n _ _ hF, formalLineMap_coeff_eq k n _ _ hG, + formalLineMap_of_linePolynomial, formalLineMap_of_linePolynomial, he] +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/FormalSectionAction.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/FormalSectionAction.lean index f6a692b7e27496efc5d206a437e5a878cb1f3579..19c3e364278f965954c5484c1afebd72c871cd1e 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/FormalSectionAction.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/FormalSectionAction.lean @@ -1,37 +1,37 @@ -import OAI.RepresentationTheory.RestrictedTilting.FormalSections -import OAI.RepresentationTheory.RestrictedTilting.FormalLineContinuity - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory -open scoped TensorProduct -universe u -variable (k : Type u) [Field k] -variable {M : Type u} [AddCommGroup M] [Module k M] - [Module (MvPolynomial (Fin 2) k) M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] - [Module.Finite k (M ⧸ planeJetRelation (M := M) k 1)] -variable (σ : Representation k (SL2 k) M) (hσ : PlaneCompatible k σ) -local notation "A" => MvPolynomial (Fin 2) k -local notation "I" => MvPolynomial.idealOfVars (Fin 2) k -local notation "T" => planeJetFD k σ hσ 1 - -lemma formalPlaneSection_line_action - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (g : SL2 k) (F G : M →ₗ[A] A) - (he : ∀ v, linePolynomial k (F (σ g v)) = linePolynomial k (G v)) (t : T) : - formalLineMap k (AdicCompletion.map I F (formalPlaneSection k σ hσ s hs ((planeJetFD k σ hσ 1).ρ g t))) = - formalLineMap k (AdicCompletion.map I G (formalPlaneSection k σ hσ s hs t)) := by - apply formalLine_map_eq_of_representatives - intro n - obtain ⟨v,hv⟩ := (planeJetRelation (M := M) k (n+1)).mkQ_surjective (fdrepLinear k (s n) t) - refine ⟨σ g v, v, ?_, ?_, he v⟩ - · rw [formalPlaneSection_equivariant, ← hv] - rfl - · change planeJetAdicEquiv k (n+1) (fdrepLinear k (s n) t) = _ - rw [← hv] - rfl -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.FormalSections +import OAI.RepresentationTheory.RestrictedTilting.FormalLineContinuity + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory +open scoped TensorProduct +universe u +variable (k : Type u) [Field k] +variable {M : Type u} [AddCommGroup M] [Module k M] + [Module (MvPolynomial (Fin 2) k) M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] + [Module.Finite k (M ⧸ planeJetRelation (M := M) k 1)] +variable (σ : Representation k (SL2 k) M) (hσ : PlaneCompatible k σ) +local notation "A" => MvPolynomial (Fin 2) k +local notation "I" => MvPolynomial.idealOfVars (Fin 2) k +local notation "T" => planeJetFD k σ hσ 1 + +lemma formalPlaneSection_line_action + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (g : SL2 k) (F G : M →ₗ[A] A) + (he : ∀ v, linePolynomial k (F (σ g v)) = linePolynomial k (G v)) (t : T) : + formalLineMap k (AdicCompletion.map I F (formalPlaneSection k σ hσ s hs ((planeJetFD k σ hσ 1).ρ g t))) = + formalLineMap k (AdicCompletion.map I G (formalPlaneSection k σ hσ s hs t)) := by + apply formalLine_map_eq_of_representatives + intro n + obtain ⟨v,hv⟩ := (planeJetRelation (M := M) k (n+1)).mkQ_surjective (fdrepLinear k (s n) t) + refine ⟨σ g v, v, ?_, ?_, he v⟩ + · rw [formalPlaneSection_equivariant, ← hv] + rfl + · change planeJetAdicEquiv k (n+1) (fdrepLinear k (s n) t) = _ + rw [← hv] + rfl +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/FormalSections.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/FormalSections.lean index 1f611c6383844a2ff56b5a0d375dd43ef92cbbae..3f047f97e0b021e4f4f1037f7c4c857b9262a41c 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/FormalSections.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/FormalSections.lean @@ -1,169 +1,169 @@ -import OAI.RepresentationTheory.RestrictedTilting.FiniteJetMaps -import OAI.RepresentationTheory.RestrictedTilting.CompletionTriviality - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory -open scoped TensorProduct Pointwise -universe u -variable (k : Type u) [Field k] -variable {M : Type u} [AddCommGroup M] [Module k M] - [Module (MvPolynomial (Fin 2) k) M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] - [Module.Finite k (M ⧸ planeJetRelation (M := M) k 1)] -variable (σ : Representation k (SL2 k) M) (hσ : PlaneCompatible k σ) -local notation "A" => MvPolynomial (Fin 2) k -local notation "I" => MvPolynomial.idealOfVars (Fin 2) k -local notation "T" => planeJetFD k σ hσ 1 - -noncomputable def adicPlaneSections - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) : - (j : ℕ) → T →ₗ[k] M ⧸ (I^j • (⊤ : Submodule A M)) - | 0 => 0 - | j+1 => (planeJetAdicEquiv k (j+1)).toLinearMap ∘ₗ fdrepLinear k (s j) - -lemma adicPlaneSections_succ - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (j : ℕ) (t : T) : - AdicCompletion.transitionMap I M (Nat.le_succ j) (adicPlaneSections k σ hσ s (j+1) t) = - adicPlaneSections k σ hσ s j t := by - cases j with - | zero => - have : Subsingleton (M ⧸ (I^0 • (⊤ : Submodule A M))) := by - rw [pow_zero, Submodule.one_smul] - infer_instance - exact Subsingleton.elim _ _ - | succ j => - change AdicCompletion.transitionMap I M (Nat.le_succ (j+1)) - (planeJetAdicEquiv k (j+2) (fdrepLinear k (s (j+1)) t)) = - planeJetAdicEquiv k (j+1) (fdrepLinear k (s j) t) - trans planeJetAdicEquiv k (j+1) - (planeJetTransition k (j+1) (fdrepLinear k (s (j+1)) t)) - · exact planeJetAdicEquiv_transition k (j+1) _ - apply congrArg - exact congrArg (fun f : T ⟶ planeJetFD k σ hσ (j+1) => fdrepLinear k f t) (hs j) - -lemma adicPlaneSections_transition - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (m n : ℕ) (h : m ≤ n) (t : T) : - AdicCompletion.transitionMap I M h (adicPlaneSections k σ hσ s n t) = - adicPlaneSections k σ hσ s m t := by - exact (Submodule.eq_factor_of_eq_factor_succ - (fun _ _ h => Submodule.pow_smul_top_le I M h) - (fun j => adicPlaneSections k σ hσ s j t) - (fun j => (adicPlaneSections_succ k σ hσ s hs j t).symm) h).symm - -lemma adicPlaneSections_origin - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) (t : T) : - adicPlaneSections k σ hσ s 1 t = planeJetAdicEquiv k 1 t := by - change planeJetAdicEquiv k 1 (fdrepLinear k (s 0) t) = _ - rw [hs0] - rfl - -lemma adicPlaneSections_bijective - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : A) • m)) - (hy : ∀ v n : M, (MvPolynomial.X 1 : A) • v = (MvPolynomial.X 0 : A) • n → - ∃ w : M, v = (MvPolynomial.X 0 : A) • w) (j : ℕ) : - Function.Bijective (polynomialJetExtend j (adicPlaneSections k σ hσ s j)) := by - cases j with - | zero => - have : Subsingleton (M ⧸ (I^0 • (⊤ : Submodule A M))) := by - rw [pow_zero, Submodule.one_smul]; infer_instance - have : Subsingleton ((A ⊗[k] T) ⧸ (I^0 • (⊤ : Submodule A (A ⊗[k] T)))) := by - rw [pow_zero, Submodule.one_smul]; infer_instance - exact ⟨fun _ _ _ => Subsingleton.elim _ _, fun z => ⟨0, Subsingleton.elim _ _⟩⟩ - | succ j => - let q : M →ₗ[k] T := (planeJetRelation k 1).mkQ - let r : (M ⧸ (I^(j+1) • (⊤ : Submodule A M))) →ₗ[k] T := - (planeJetAdicEquiv k 1).symm.toLinearMap ∘ₗ - (AdicCompletion.transitionMap I M (Nat.succ_le_succ (Nat.zero_le j))).restrictScalars k - apply polynomialJetExtend_bijective (j+1) q _ r - · intro n - change (Submodule.Quotient.mk n : M ⧸ planeJetRelation k 1) = 0 ↔ _ - rw [Submodule.Quotient.mk_eq_zero] - simp only [planeJetRelation, Submodule.restrictScalars_mem, jetRelation_one] - · intro n; rfl - · ext t - change (planeJetAdicEquiv k 1).symm - (AdicCompletion.transitionMap I M (Nat.succ_le_succ (Nat.zero_le j)) (adicPlaneSections k σ hσ s (j+1) t)) = t - rw [adicPlaneSections_transition k σ hσ s hs, adicPlaneSections_origin k σ hσ s hs0] - exact (planeJetAdicEquiv k 1).symm_apply_apply t - · exact hx - · exact hy - - -noncomputable def formalPlaneSection - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) : - T →ₗ[k] AdicCompletion I M where - toFun t := ⟨fun j => adicPlaneSections k σ hσ s j t, - fun {_ _} h => adicPlaneSections_transition k σ hσ s hs _ _ h t⟩ - map_add' a b := by ext j; exact map_add _ _ _ - map_smul' c a := by ext j; exact map_smul _ _ _ - - - -lemma formalPlaneSection_equivariant - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (g : SL2 k) (j : ℕ) (t : T) : - (formalPlaneSection k σ hσ s hs ((planeJetFD k σ hσ 1).ρ g t)).val (j+1) = - planeJetAdicEquiv k (j+1) - ((planeJetFD k σ hσ (j+1)).ρ g (fdrepLinear k (s j) t)) := by - change planeJetAdicEquiv k (j+1) (fdrepLinear k (s j) ((planeJetFD k σ hσ 1).ρ g t)) = _ - exact congrArg (planeJetAdicEquiv k (j+1)) (fdrepLinear_comm k (s j) g t) - - - -noncomputable def formalPlaneTrivialization - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : A) • m)) - (hy : ∀ v n : M, (MvPolynomial.X 1 : A) • v = (MvPolynomial.X 0 : A) • n → - ∃ w : M, v = (MvPolynomial.X 0 : A) • w) : - (AdicCompletion I A) ⊗[k] T ≃ₗ[AdicCompletion I A] AdicCompletion I M := - (TensorProduct.AlgebraTensorModule.cancelBaseChange k A - (AdicCompletion I A) (AdicCompletion I A) T).symm ≪≫ₗ - AdicCompletion.ofTensorProductEquivOfFiniteNoetherian I (A ⊗[k] T) ≪≫ₗ - LinearEquiv.ofBijective - (completionOfJetMaps I (fun j => polynomialJetExtend j (adicPlaneSections k σ hσ s j)) - (fun m n h z => polynomialJetExtend_transition m n h _ _ - (adicPlaneSections_transition k σ hσ s hs m n h) z)) - (completionOfJetMaps_bijective I _ _ (adicPlaneSections_bijective k σ hσ s hs0 hs hx hy)) - -lemma formalPlaneTrivialization_one_tmul - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : A) • m)) - (hy : ∀ v n : M, (MvPolynomial.X 1 : A) • v = (MvPolynomial.X 0 : A) • n → - ∃ w : M, v = (MvPolynomial.X 0 : A) • w) (t : T) : - formalPlaneTrivialization k σ hσ s hs0 hs hx hy (1 ⊗ₜ[k] t) = - formalPlaneSection k σ hσ s hs t := by - simp only [formalPlaneTrivialization, LinearEquiv.trans_apply, - TensorProduct.AlgebraTensorModule.cancelBaseChange_symm_tmul, - AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply, - AdicCompletion.ofTensorProduct_tmul, one_smul] - apply AdicCompletion.ext - intro j - change polynomialJetExtend j (adicPlaneSections k σ hσ s j) - (Submodule.Quotient.mk ((1 : A) ⊗ₜ[k] t)) = adicPlaneSections k σ hσ s j t - rw [polynomialJetExtend_mk_tmul, one_smul] - - - -theorem exists_formalPlaneTrivialization [Infinite k] - (hr : IsRational k σ) - (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : A) • m)) - (hy : ∀ v n : M, (MvPolynomial.X 1 : A) • v = (MvPolynomial.X 0 : A) • n → - ∃ w : M, v = (MvPolynomial.X 0 : A) • w) - (hT : IsTilting k T) : - Nonempty ((AdicCompletion I A) ⊗[k] T ≃ₗ[AdicCompletion I A] AdicCompletion I M) := by - obtain ⟨s,hs0,hs⟩ := compatible_planeJet_sections k σ hσ hr hx hy hT - exact ⟨formalPlaneTrivialization k σ hσ s hs0 hs hx hy⟩ -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.FiniteJetMaps +import OAI.RepresentationTheory.RestrictedTilting.CompletionTriviality + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory +open scoped TensorProduct Pointwise +universe u +variable (k : Type u) [Field k] +variable {M : Type u} [AddCommGroup M] [Module k M] + [Module (MvPolynomial (Fin 2) k) M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] + [Module.Finite k (M ⧸ planeJetRelation (M := M) k 1)] +variable (σ : Representation k (SL2 k) M) (hσ : PlaneCompatible k σ) +local notation "A" => MvPolynomial (Fin 2) k +local notation "I" => MvPolynomial.idealOfVars (Fin 2) k +local notation "T" => planeJetFD k σ hσ 1 + +noncomputable def adicPlaneSections + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) : + (j : ℕ) → T →ₗ[k] M ⧸ (I^j • (⊤ : Submodule A M)) + | 0 => 0 + | j+1 => (planeJetAdicEquiv k (j+1)).toLinearMap ∘ₗ fdrepLinear k (s j) + +lemma adicPlaneSections_succ + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (j : ℕ) (t : T) : + AdicCompletion.transitionMap I M (Nat.le_succ j) (adicPlaneSections k σ hσ s (j+1) t) = + adicPlaneSections k σ hσ s j t := by + cases j with + | zero => + have : Subsingleton (M ⧸ (I^0 • (⊤ : Submodule A M))) := by + rw [pow_zero, Submodule.one_smul] + infer_instance + exact Subsingleton.elim _ _ + | succ j => + change AdicCompletion.transitionMap I M (Nat.le_succ (j+1)) + (planeJetAdicEquiv k (j+2) (fdrepLinear k (s (j+1)) t)) = + planeJetAdicEquiv k (j+1) (fdrepLinear k (s j) t) + trans planeJetAdicEquiv k (j+1) + (planeJetTransition k (j+1) (fdrepLinear k (s (j+1)) t)) + · exact planeJetAdicEquiv_transition k (j+1) _ + apply congrArg + exact congrArg (fun f : T ⟶ planeJetFD k σ hσ (j+1) => fdrepLinear k f t) (hs j) + +lemma adicPlaneSections_transition + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (m n : ℕ) (h : m ≤ n) (t : T) : + AdicCompletion.transitionMap I M h (adicPlaneSections k σ hσ s n t) = + adicPlaneSections k σ hσ s m t := by + exact (Submodule.eq_factor_of_eq_factor_succ + (fun _ _ h => Submodule.pow_smul_top_le I M h) + (fun j => adicPlaneSections k σ hσ s j t) + (fun j => (adicPlaneSections_succ k σ hσ s hs j t).symm) h).symm + +lemma adicPlaneSections_origin + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) (t : T) : + adicPlaneSections k σ hσ s 1 t = planeJetAdicEquiv k 1 t := by + change planeJetAdicEquiv k 1 (fdrepLinear k (s 0) t) = _ + rw [hs0] + rfl + +lemma adicPlaneSections_bijective + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : A) • m)) + (hy : ∀ v n : M, (MvPolynomial.X 1 : A) • v = (MvPolynomial.X 0 : A) • n → + ∃ w : M, v = (MvPolynomial.X 0 : A) • w) (j : ℕ) : + Function.Bijective (polynomialJetExtend j (adicPlaneSections k σ hσ s j)) := by + cases j with + | zero => + have : Subsingleton (M ⧸ (I^0 • (⊤ : Submodule A M))) := by + rw [pow_zero, Submodule.one_smul]; infer_instance + have : Subsingleton ((A ⊗[k] T) ⧸ (I^0 • (⊤ : Submodule A (A ⊗[k] T)))) := by + rw [pow_zero, Submodule.one_smul]; infer_instance + exact ⟨fun _ _ _ => Subsingleton.elim _ _, fun z => ⟨0, Subsingleton.elim _ _⟩⟩ + | succ j => + let q : M →ₗ[k] T := (planeJetRelation k 1).mkQ + let r : (M ⧸ (I^(j+1) • (⊤ : Submodule A M))) →ₗ[k] T := + (planeJetAdicEquiv k 1).symm.toLinearMap ∘ₗ + (AdicCompletion.transitionMap I M (Nat.succ_le_succ (Nat.zero_le j))).restrictScalars k + apply polynomialJetExtend_bijective (j+1) q _ r + · intro n + change (Submodule.Quotient.mk n : M ⧸ planeJetRelation k 1) = 0 ↔ _ + rw [Submodule.Quotient.mk_eq_zero] + simp only [planeJetRelation, Submodule.restrictScalars_mem, jetRelation_one] + · intro n; rfl + · ext t + change (planeJetAdicEquiv k 1).symm + (AdicCompletion.transitionMap I M (Nat.succ_le_succ (Nat.zero_le j)) (adicPlaneSections k σ hσ s (j+1) t)) = t + rw [adicPlaneSections_transition k σ hσ s hs, adicPlaneSections_origin k σ hσ s hs0] + exact (planeJetAdicEquiv k 1).symm_apply_apply t + · exact hx + · exact hy + + +noncomputable def formalPlaneSection + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) : + T →ₗ[k] AdicCompletion I M where + toFun t := ⟨fun j => adicPlaneSections k σ hσ s j t, + fun {_ _} h => adicPlaneSections_transition k σ hσ s hs _ _ h t⟩ + map_add' a b := by ext j; exact map_add _ _ _ + map_smul' c a := by ext j; exact map_smul _ _ _ + + + +lemma formalPlaneSection_equivariant + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (g : SL2 k) (j : ℕ) (t : T) : + (formalPlaneSection k σ hσ s hs ((planeJetFD k σ hσ 1).ρ g t)).val (j+1) = + planeJetAdicEquiv k (j+1) + ((planeJetFD k σ hσ (j+1)).ρ g (fdrepLinear k (s j) t)) := by + change planeJetAdicEquiv k (j+1) (fdrepLinear k (s j) ((planeJetFD k σ hσ 1).ρ g t)) = _ + exact congrArg (planeJetAdicEquiv k (j+1)) (fdrepLinear_comm k (s j) g t) + + + +noncomputable def formalPlaneTrivialization + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : A) • m)) + (hy : ∀ v n : M, (MvPolynomial.X 1 : A) • v = (MvPolynomial.X 0 : A) • n → + ∃ w : M, v = (MvPolynomial.X 0 : A) • w) : + (AdicCompletion I A) ⊗[k] T ≃ₗ[AdicCompletion I A] AdicCompletion I M := + (TensorProduct.AlgebraTensorModule.cancelBaseChange k A + (AdicCompletion I A) (AdicCompletion I A) T).symm ≪≫ₗ + AdicCompletion.ofTensorProductEquivOfFiniteNoetherian I (A ⊗[k] T) ≪≫ₗ + LinearEquiv.ofBijective + (completionOfJetMaps I (fun j => polynomialJetExtend j (adicPlaneSections k σ hσ s j)) + (fun m n h z => polynomialJetExtend_transition m n h _ _ + (adicPlaneSections_transition k σ hσ s hs m n h) z)) + (completionOfJetMaps_bijective I _ _ (adicPlaneSections_bijective k σ hσ s hs0 hs hx hy)) + +lemma formalPlaneTrivialization_one_tmul + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : A) • m)) + (hy : ∀ v n : M, (MvPolynomial.X 1 : A) • v = (MvPolynomial.X 0 : A) • n → + ∃ w : M, v = (MvPolynomial.X 0 : A) • w) (t : T) : + formalPlaneTrivialization k σ hσ s hs0 hs hx hy (1 ⊗ₜ[k] t) = + formalPlaneSection k σ hσ s hs t := by + simp only [formalPlaneTrivialization, LinearEquiv.trans_apply, + TensorProduct.AlgebraTensorModule.cancelBaseChange_symm_tmul, + AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply, + AdicCompletion.ofTensorProduct_tmul, one_smul] + apply AdicCompletion.ext + intro j + change polynomialJetExtend j (adicPlaneSections k σ hσ s j) + (Submodule.Quotient.mk ((1 : A) ⊗ₜ[k] t)) = adicPlaneSections k σ hσ s j t + rw [polynomialJetExtend_mk_tmul, one_smul] + + + +theorem exists_formalPlaneTrivialization [Infinite k] + (hr : IsRational k σ) + (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : A) • m)) + (hy : ∀ v n : M, (MvPolynomial.X 1 : A) • v = (MvPolynomial.X 0 : A) • n → + ∃ w : M, v = (MvPolynomial.X 0 : A) • w) + (hT : IsTilting k T) : + Nonempty ((AdicCompletion I A) ⊗[k] T ≃ₗ[AdicCompletion I A] AdicCompletion I M) := by + obtain ⟨s,hs0,hs⟩ := compatible_planeJet_sections k σ hσ hr hx hy hT + exact ⟨formalPlaneTrivialization k σ hσ s hs0 hs hx hy⟩ +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/FrobeniusTensor.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/FrobeniusTensor.lean index d7bdd8ae88d4a48dbc157803384fb1d6552c2bf0..301ea2f7d5605da59fb459f36c65807915ac95a5 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/FrobeniusTensor.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/FrobeniusTensor.lean @@ -1,226 +1,226 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.SteinbergDuality -import OAI.RepresentationTheory.RestrictedTilting.TensorLimits - -namespace OAI - -/-! Binary Frobenius multiplication and Steinberg twists of filtrations. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section -open scoped TensorProduct -universe u -variable (k : Type u) [Field k] - -lemma expand_homogeneous {n : ℕ} (p : ℕ) - (f : MvPolynomial (Fin 2) k) (hf : f.IsHomogeneous n) : - (MvPolynomial.expand p f).IsHomogeneous (p*n) := by - exact hf.aeval (fun i => MvPolynomial.X i ^ p) - (fun i => by simpa using (MvPolynomial.isHomogeneous_X k i).pow p) - -noncomputable def binaryFrobeniusMultiply (p b : ℕ) : - Binary k (p-1) ⊗[k] Binary k b →ₗ[k] Binary k (p-1+p*b) := - TensorProduct.lift - { toFun := fun f => - { toFun := fun g => ⟨f.val * MvPolynomial.expand p g.val, - f.property.mul (expand_homogeneous k p g.val g.property)⟩ - map_add' := by intro g h; apply Subtype.ext; simp [mul_add] - map_smul' := by intro c g; apply Subtype.ext; simp } - map_add' := by intro f g; ext h : 1; apply Subtype.ext; simp [add_mul] - map_smul' := by intro c f; ext g : 1; apply Subtype.ext; simp } - -@[simp] lemma binaryFrobeniusMultiply_tmul (p b : ℕ) - (f : Binary k (p-1)) (g : Binary k b) : - (binaryFrobeniusMultiply k p b (f ⊗ₜ[k] g)).val = - f.val * MvPolynomial.expand p g.val := rfl - -lemma binaryFrobeniusMultiply_surjective (p b : ℕ) (hp : 0 < p) : - Function.Surjective (binaryFrobeniusMultiply k p b) := by - rw [← LinearMap.range_eq_top] - apply top_unique - rw [← (binaryBasis k (p-1+p*b)).span_eq] - apply Submodule.span_le.mpr - rintro _ ⟨i,rfl⟩ - have hj : i.val % p < p := Nat.mod_lt _ hp - have hil : i.val < p*(b+1) := by have := i.isLt; nlinarith [Nat.sub_add_cancel hp] - have hl : i.val / p < b+1 := (Nat.div_lt_iff_lt_mul hp).mpr (by simpa [mul_comm] using hil) - let j : Fin (p-1+1) := ⟨i.val % p, by omega⟩ - let l : Fin (b+1) := ⟨i.val / p, hl⟩ - refine ⟨binaryBasis k (p-1) j ⊗ₜ[k] binaryBasis k b l, ?_⟩ - apply Subtype.ext - simp only [binaryFrobeniusMultiply_tmul, binaryBasis_apply, map_mul, map_pow, - MvPolynomial.expand_X, ← pow_mul] - rw [mul_mul_mul_comm, ← pow_add, ← pow_add] - have hi : j.val + p*l.val = i.val := Nat.mod_add_div _ _ - have hnot : l.val ≤ b := by omega - have h₁ : (p-1-j.val) + p*(b-l.val) = p-1+p*b-i.val := by - rw [Nat.mul_sub_left_distrib] - have hpj : j.val ≤ p-1 := by dsimp [j]; omega - have hpb : p*l.val ≤ p*b := Nat.mul_le_mul_left _ hnot - omega - rw [h₁, hi] - -lemma binaryFrobeniusMultiply_bijective (p b : ℕ) (hp : 0 < p) : - Function.Bijective (binaryFrobeniusMultiply k p b) := by - have he : Module.finrank k (Binary k (p-1) ⊗[k] Binary k b) = - Module.finrank k (Binary k (p-1+p*b)) := by - rw [Module.finrank_tensorProduct, binaryBasis_finrank, binaryBasis_finrank, - binaryBasis_finrank] - nlinarith [Nat.sub_add_cancel hp] - constructor - · apply (LinearMap.injective_iff_surjective_of_finrank_eq_finrank (K := k) - (V := Binary k (p-1) ⊗[k] Binary k b) (V₂ := Binary k (p-1+p*b)) - he (f := binaryFrobeniusMultiply k p b)).mpr - exact binaryFrobeniusMultiply_surjective k p b hp - · exact binaryFrobeniusMultiply_surjective k p b hp - -variable (p : ℕ) [Fact p.Prime] [CharP k p] - -noncomputable def frobeniusSL2 : SL2 k →* SL2 k := - Matrix.SpecialLinearGroup.map (frobenius k p) - -lemma dualMatrix_frobeniusSL2 (g : SL2 k) : - dualMatrix k (frobeniusSL2 k p g) = - (frobenius k p).mapMatrix (dualMatrix k g) := by - change ((↑((frobeniusSL2 k p g)⁻¹) : Matrix (Fin 2) (Fin 2) k)).transpose = _ - rw [← map_inv] - rfl - -lemma linearChange_expand (A : Matrix (Fin 2) (Fin 2) k) (f : MvPolynomial (Fin 2) k) : - linearChange A (MvPolynomial.expand p f) = - MvPolynomial.expand p (linearChange ((frobenius k p).mapMatrix A) f) := by - have he : (linearChange A).comp (MvPolynomial.expand p) = - (MvPolynomial.expand p).comp (linearChange ((frobenius k p).mapMatrix A)) := by - ext i : 1 - simp [Fin.sum_univ_two, add_pow_char, mul_pow, frobenius_def, map_pow] - exact AlgHom.congr_fun he f - -lemma binaryFrobeniusMultiply_intertwines (b : ℕ) (g : SL2 k) - (z : Binary k (p-1) ⊗[k] Binary k b) : - binaryFrobeniusMultiply k p b - (Representation.tprod (costandard k (p-1)).ρ - ((costandard k b).ρ.comp (frobeniusSL2 k p)) g z) = - (costandard k (p-1+p*b)).ρ g (binaryFrobeniusMultiply k p b z) := by - change binaryFrobeniusMultiply k p b - (TensorProduct.map (homogeneousRepresentation (p-1) (dualMatrix k g)) - (homogeneousRepresentation b (dualMatrix k (frobeniusSL2 k p g))) z) = - homogeneousRepresentation (p-1+p*b) (dualMatrix k g) (binaryFrobeniusMultiply k p b z) - induction z using TensorProduct.inductionOn with - | add z w hz hw => simp only [map_add, hz, hw] - | tmul f h => - apply Subtype.ext - change linearChange (dualMatrix k g) f.val * - MvPolynomial.expand p (linearChange (dualMatrix k (frobeniusSL2 k p g)) h.val) = - linearChange (dualMatrix k g) (f.val * MvPolynomial.expand p h.val) - rw [map_mul, dualMatrix_frobeniusSL2, linearChange_expand] - -end - -universe u -variable (k : Type u) [Field k] -variable (p : ℕ) [Fact p.Prime] [CharP k p] - - -noncomputable def frobeniusTwist : FDRep k (SL2 k) ⥤ FDRep k (SL2 k) := - Action.res (FGModuleCat k) (frobeniusSL2 k p) - -instance : (frobeniusTwist k p).Additive where - map_add := by intros; rfl - -lemma frobeniusTwist_shortExact (S : ShortComplex (FDRep k (SL2 k))) - (hS : S.ShortExact) : (S.map (frobeniusTwist k p)).ShortExact := by - have := hS.mono_f - have := hS.epi_g - exact fdrep_shortExact k _ (fdrep_injective k S.f) (fdrep_surjective k S.g) - (fdrep_exact k (S := S) hS.exact) - -noncomputable def frobeniusCostandardHom (b : ℕ) : - costandard k (p-1) ⊗ (frobeniusTwist k p).obj (costandard k b) ⟶ - costandard k (p-1+p*b) := - fdrepHom k (binaryFrobeniusMultiply k p b) (binaryFrobeniusMultiply_intertwines k p b) - -noncomputable def frobeniusCostandardIso (b : ℕ) : - costandard k (p-1) ⊗ (frobeniusTwist k p).obj (costandard k b) ≅ - costandard k (p-1+p*b) := by - let f := frobeniusCostandardHom k p b - have : IsIso f := fdrepHom_isIso_of_bijective k f - (binaryFrobeniusMultiply_bijective k p b (Fact.out : p.Prime).pos) - exact asIso f - - - -theorem HasGoodFiltration.steinberg_frobenius {A : FDRep k (SL2 k)} - (hA : HasGoodFiltration k A) : - HasGoodFiltration k (costandard k (p-1) ⊗ (frobeniusTwist k p).obj A) := by - induction hA with - | zero A hA => - exact .zero _ ((tensorLeft (costandard k (p-1))).map_isZero - ((frobeniusTwist k p).map_isZero hA)) - | @step A B n f g w hS hA ih => - let F := tensorLeft (costandard k (p-1)) - let := tensorLeft_preservesFiniteLimits (costandard k (p-1)) - let := tensorLeft_preservesFiniteColimits (costandard k (p-1)) - have hT := (frobeniusTwist_shortExact k p _ hS).map_of_exact F - have hc := (costandard_hasGoodFiltration k (p-1+p*n)).of_iso k - (frobeniusCostandardIso k p n).symm - exact ih.extension k hc _ _ _ hT - - -lemma IsRational.frobenius {M : Type u} [AddCommGroup M] [Module k M] - (ρ : Representation k (SL2 k) M) (hρ : IsRational k ρ) : - IsRational k (ρ.comp (frobeniusSL2 k p)) := by - intro v l - obtain ⟨P,hP⟩ := hρ v l - refine ⟨MvPolynomial.expand p P, fun g => ?_⟩ - change l (ρ (frobeniusSL2 k p g) v) = _ - rw [hP] - change MvPolynomial.eval₂ (RingHom.id k) (fun ij => (g ij.1 ij.2)^p) P = - MvPolynomial.eval₂ (RingHom.id k) (fun ij => g ij.1 ij.2) (MvPolynomial.expand p P) - rw [MvPolynomial.eval₂_expand] - rfl - -noncomputable def frobeniusDualIso (A : FDRep k (SL2 k)) : - ((frobeniusTwist k p).obj A)ᘁ ≅ (frobeniusTwist k p).obj Aᘁ := by - let f : ((frobeniusTwist k p).obj A)ᘁ ⟶ (frobeniusTwist k p).obj Aᘁ := - fdrepHom k LinearMap.id (by - intro g l - change Module.Dual k A at l - rw [fdrep_dual_repr] - change Representation.dual (A.ρ.comp (frobeniusSL2 k p)) g l = - Aᘁ.ρ (frobeniusSL2 k p g) l - rw [fdrep_dual_repr] - apply LinearMap.ext - intro x - change l (A.ρ (frobeniusSL2 k p (g⁻¹)) x) = l (A.ρ ((frobeniusSL2 k p g)⁻¹) x) - rw [map_inv]) - have : IsIso f := fdrepHom_isIso_of_bijective k f Function.bijective_id - exact asIso f - -variable [Infinite k] - - -theorem IsTilting.steinberg_frobenius {A : FDRep k (SL2 k)} (hA : IsTilting k A) : - IsTilting k (costandard k (p-1) ⊗ (frobeniusTwist k p).obj A) := by - have hr : IsRational k ((frobeniusTwist k p).obj A).ρ := - IsRational.frobenius k p A.ρ hA.1 - have hrt : IsRational k (costandard k (p-1) ⊗ (frobeniusTwist k p).obj A).ρ := - IsRational.tensor k (costandard k (p-1)).ρ ((frobeniusTwist k p).obj A).ρ - (costandard_rational k (p-1)) hr - refine ⟨hrt, hA.2.1.steinberg_frobenius k p, ?_⟩ - obtain ⟨hs⟩ := costandard_self_dual_of_choose_ne_zero k (p-1) - (fun i => choose_cast_ne_zero_of_lt_char k p - (by have := (Fact.out : p.Prime).pos; omega) (by have := i.isLt; omega)) - let e : (costandard k (p-1) ⊗ (frobeniusTwist k p).obj A)ᘁ ≅ - costandard k (p-1) ⊗ (frobeniusTwist k p).obj Aᘁ := - rightDualTensorIso _ _ ≪≫ (tensorIso (frobeniusDualIso k p A) hs) ≪≫ - (β_ _ _) - exact (hA.2.2.steinberg_frobenius k p).of_iso k e.symm - -end FiberFunctorProof -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.SteinbergDuality +import OAI.RepresentationTheory.RestrictedTilting.TensorLimits + +namespace OAI + +/-! Binary Frobenius multiplication and Steinberg twists of filtrations. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section +open scoped TensorProduct +universe u +variable (k : Type u) [Field k] + +lemma expand_homogeneous {n : ℕ} (p : ℕ) + (f : MvPolynomial (Fin 2) k) (hf : f.IsHomogeneous n) : + (MvPolynomial.expand p f).IsHomogeneous (p*n) := by + exact hf.aeval (fun i => MvPolynomial.X i ^ p) + (fun i => by simpa using (MvPolynomial.isHomogeneous_X k i).pow p) + +noncomputable def binaryFrobeniusMultiply (p b : ℕ) : + Binary k (p-1) ⊗[k] Binary k b →ₗ[k] Binary k (p-1+p*b) := + TensorProduct.lift + { toFun := fun f => + { toFun := fun g => ⟨f.val * MvPolynomial.expand p g.val, + f.property.mul (expand_homogeneous k p g.val g.property)⟩ + map_add' := by intro g h; apply Subtype.ext; simp [mul_add] + map_smul' := by intro c g; apply Subtype.ext; simp } + map_add' := by intro f g; ext h : 1; apply Subtype.ext; simp [add_mul] + map_smul' := by intro c f; ext g : 1; apply Subtype.ext; simp } + +@[simp] lemma binaryFrobeniusMultiply_tmul (p b : ℕ) + (f : Binary k (p-1)) (g : Binary k b) : + (binaryFrobeniusMultiply k p b (f ⊗ₜ[k] g)).val = + f.val * MvPolynomial.expand p g.val := rfl + +lemma binaryFrobeniusMultiply_surjective (p b : ℕ) (hp : 0 < p) : + Function.Surjective (binaryFrobeniusMultiply k p b) := by + rw [← LinearMap.range_eq_top] + apply top_unique + rw [← (binaryBasis k (p-1+p*b)).span_eq] + apply Submodule.span_le.mpr + rintro _ ⟨i,rfl⟩ + have hj : i.val % p < p := Nat.mod_lt _ hp + have hil : i.val < p*(b+1) := by have := i.isLt; nlinarith [Nat.sub_add_cancel hp] + have hl : i.val / p < b+1 := (Nat.div_lt_iff_lt_mul hp).mpr (by simpa [mul_comm] using hil) + let j : Fin (p-1+1) := ⟨i.val % p, by omega⟩ + let l : Fin (b+1) := ⟨i.val / p, hl⟩ + refine ⟨binaryBasis k (p-1) j ⊗ₜ[k] binaryBasis k b l, ?_⟩ + apply Subtype.ext + simp only [binaryFrobeniusMultiply_tmul, binaryBasis_apply, map_mul, map_pow, + MvPolynomial.expand_X, ← pow_mul] + rw [mul_mul_mul_comm, ← pow_add, ← pow_add] + have hi : j.val + p*l.val = i.val := Nat.mod_add_div _ _ + have hnot : l.val ≤ b := by omega + have h₁ : (p-1-j.val) + p*(b-l.val) = p-1+p*b-i.val := by + rw [Nat.mul_sub_left_distrib] + have hpj : j.val ≤ p-1 := by dsimp [j]; omega + have hpb : p*l.val ≤ p*b := Nat.mul_le_mul_left _ hnot + omega + rw [h₁, hi] + +lemma binaryFrobeniusMultiply_bijective (p b : ℕ) (hp : 0 < p) : + Function.Bijective (binaryFrobeniusMultiply k p b) := by + have he : Module.finrank k (Binary k (p-1) ⊗[k] Binary k b) = + Module.finrank k (Binary k (p-1+p*b)) := by + rw [Module.finrank_tensorProduct, binaryBasis_finrank, binaryBasis_finrank, + binaryBasis_finrank] + nlinarith [Nat.sub_add_cancel hp] + constructor + · apply (LinearMap.injective_iff_surjective_of_finrank_eq_finrank (K := k) + (V := Binary k (p-1) ⊗[k] Binary k b) (V₂ := Binary k (p-1+p*b)) + he (f := binaryFrobeniusMultiply k p b)).mpr + exact binaryFrobeniusMultiply_surjective k p b hp + · exact binaryFrobeniusMultiply_surjective k p b hp + +variable (p : ℕ) [Fact p.Prime] [CharP k p] + +noncomputable def frobeniusSL2 : SL2 k →* SL2 k := + Matrix.SpecialLinearGroup.map (frobenius k p) + +lemma dualMatrix_frobeniusSL2 (g : SL2 k) : + dualMatrix k (frobeniusSL2 k p g) = + (frobenius k p).mapMatrix (dualMatrix k g) := by + change ((↑((frobeniusSL2 k p g)⁻¹) : Matrix (Fin 2) (Fin 2) k)).transpose = _ + rw [← map_inv] + rfl + +lemma linearChange_expand (A : Matrix (Fin 2) (Fin 2) k) (f : MvPolynomial (Fin 2) k) : + linearChange A (MvPolynomial.expand p f) = + MvPolynomial.expand p (linearChange ((frobenius k p).mapMatrix A) f) := by + have he : (linearChange A).comp (MvPolynomial.expand p) = + (MvPolynomial.expand p).comp (linearChange ((frobenius k p).mapMatrix A)) := by + ext i : 1 + simp [Fin.sum_univ_two, add_pow_char, mul_pow, frobenius_def, map_pow] + exact AlgHom.congr_fun he f + +lemma binaryFrobeniusMultiply_intertwines (b : ℕ) (g : SL2 k) + (z : Binary k (p-1) ⊗[k] Binary k b) : + binaryFrobeniusMultiply k p b + (Representation.tprod (costandard k (p-1)).ρ + ((costandard k b).ρ.comp (frobeniusSL2 k p)) g z) = + (costandard k (p-1+p*b)).ρ g (binaryFrobeniusMultiply k p b z) := by + change binaryFrobeniusMultiply k p b + (TensorProduct.map (homogeneousRepresentation (p-1) (dualMatrix k g)) + (homogeneousRepresentation b (dualMatrix k (frobeniusSL2 k p g))) z) = + homogeneousRepresentation (p-1+p*b) (dualMatrix k g) (binaryFrobeniusMultiply k p b z) + induction z using TensorProduct.inductionOn with + | add z w hz hw => simp only [map_add, hz, hw] + | tmul f h => + apply Subtype.ext + change linearChange (dualMatrix k g) f.val * + MvPolynomial.expand p (linearChange (dualMatrix k (frobeniusSL2 k p g)) h.val) = + linearChange (dualMatrix k g) (f.val * MvPolynomial.expand p h.val) + rw [map_mul, dualMatrix_frobeniusSL2, linearChange_expand] + +end + +universe u +variable (k : Type u) [Field k] +variable (p : ℕ) [Fact p.Prime] [CharP k p] + + +noncomputable def frobeniusTwist : FDRep k (SL2 k) ⥤ FDRep k (SL2 k) := + Action.res (FGModuleCat k) (frobeniusSL2 k p) + +instance : (frobeniusTwist k p).Additive where + map_add := by intros; rfl + +lemma frobeniusTwist_shortExact (S : ShortComplex (FDRep k (SL2 k))) + (hS : S.ShortExact) : (S.map (frobeniusTwist k p)).ShortExact := by + have := hS.mono_f + have := hS.epi_g + exact fdrep_shortExact k _ (fdrep_injective k S.f) (fdrep_surjective k S.g) + (fdrep_exact k (S := S) hS.exact) + +noncomputable def frobeniusCostandardHom (b : ℕ) : + costandard k (p-1) ⊗ (frobeniusTwist k p).obj (costandard k b) ⟶ + costandard k (p-1+p*b) := + fdrepHom k (binaryFrobeniusMultiply k p b) (binaryFrobeniusMultiply_intertwines k p b) + +noncomputable def frobeniusCostandardIso (b : ℕ) : + costandard k (p-1) ⊗ (frobeniusTwist k p).obj (costandard k b) ≅ + costandard k (p-1+p*b) := by + let f := frobeniusCostandardHom k p b + have : IsIso f := fdrepHom_isIso_of_bijective k f + (binaryFrobeniusMultiply_bijective k p b (Fact.out : p.Prime).pos) + exact asIso f + + + +theorem HasGoodFiltration.steinberg_frobenius {A : FDRep k (SL2 k)} + (hA : HasGoodFiltration k A) : + HasGoodFiltration k (costandard k (p-1) ⊗ (frobeniusTwist k p).obj A) := by + induction hA with + | zero A hA => + exact .zero _ ((tensorLeft (costandard k (p-1))).map_isZero + ((frobeniusTwist k p).map_isZero hA)) + | @step A B n f g w hS hA ih => + let F := tensorLeft (costandard k (p-1)) + let := tensorLeft_preservesFiniteLimits (costandard k (p-1)) + let := tensorLeft_preservesFiniteColimits (costandard k (p-1)) + have hT := (frobeniusTwist_shortExact k p _ hS).map_of_exact F + have hc := (costandard_hasGoodFiltration k (p-1+p*n)).of_iso k + (frobeniusCostandardIso k p n).symm + exact ih.extension k hc _ _ _ hT + + +lemma IsRational.frobenius {M : Type u} [AddCommGroup M] [Module k M] + (ρ : Representation k (SL2 k) M) (hρ : IsRational k ρ) : + IsRational k (ρ.comp (frobeniusSL2 k p)) := by + intro v l + obtain ⟨P,hP⟩ := hρ v l + refine ⟨MvPolynomial.expand p P, fun g => ?_⟩ + change l (ρ (frobeniusSL2 k p g) v) = _ + rw [hP] + change MvPolynomial.eval₂ (RingHom.id k) (fun ij => (g ij.1 ij.2)^p) P = + MvPolynomial.eval₂ (RingHom.id k) (fun ij => g ij.1 ij.2) (MvPolynomial.expand p P) + rw [MvPolynomial.eval₂_expand] + rfl + +noncomputable def frobeniusDualIso (A : FDRep k (SL2 k)) : + ((frobeniusTwist k p).obj A)ᘁ ≅ (frobeniusTwist k p).obj Aᘁ := by + let f : ((frobeniusTwist k p).obj A)ᘁ ⟶ (frobeniusTwist k p).obj Aᘁ := + fdrepHom k LinearMap.id (by + intro g l + change Module.Dual k A at l + rw [fdrep_dual_repr] + change Representation.dual (A.ρ.comp (frobeniusSL2 k p)) g l = + Aᘁ.ρ (frobeniusSL2 k p g) l + rw [fdrep_dual_repr] + apply LinearMap.ext + intro x + change l (A.ρ (frobeniusSL2 k p (g⁻¹)) x) = l (A.ρ ((frobeniusSL2 k p g)⁻¹) x) + rw [map_inv]) + have : IsIso f := fdrepHom_isIso_of_bijective k f Function.bijective_id + exact asIso f + +variable [Infinite k] + + +theorem IsTilting.steinberg_frobenius {A : FDRep k (SL2 k)} (hA : IsTilting k A) : + IsTilting k (costandard k (p-1) ⊗ (frobeniusTwist k p).obj A) := by + have hr : IsRational k ((frobeniusTwist k p).obj A).ρ := + IsRational.frobenius k p A.ρ hA.1 + have hrt : IsRational k (costandard k (p-1) ⊗ (frobeniusTwist k p).obj A).ρ := + IsRational.tensor k (costandard k (p-1)).ρ ((frobeniusTwist k p).obj A).ρ + (costandard_rational k (p-1)) hr + refine ⟨hrt, hA.2.1.steinberg_frobenius k p, ?_⟩ + obtain ⟨hs⟩ := costandard_self_dual_of_choose_ne_zero k (p-1) + (fun i => choose_cast_ne_zero_of_lt_char k p + (by have := (Fact.out : p.Prime).pos; omega) (by have := i.isLt; omega)) + let e : (costandard k (p-1) ⊗ (frobeniusTwist k p).obj A)ᘁ ≅ + costandard k (p-1) ⊗ (frobeniusTwist k p).obj Aᘁ := + rightDualTensorIso _ _ ≪≫ (tensorIso (frobeniusDualIso k p A) hs) ≪≫ + (β_ _ _) + exact (hA.2.2.steinberg_frobenius k p).of_iso k e.symm + +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/GeneratedStableKernel.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/GeneratedStableKernel.lean index f87f49874851786476e35f18892caea6021d1dc4..00004498dad9314690d6ae13997176f195fd1cb3 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/GeneratedStableKernel.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/GeneratedStableKernel.lean @@ -1,117 +1,117 @@ -import OAI.RepresentationTheory.RestrictedTilting.TiltingCovers -import OAI.RepresentationTheory.RestrictedTilting.SteinbergSpan -import OAI.RepresentationTheory.RestrictedTilting.BoundedStableFaithfulness - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (p r : ℕ) [Fact p.Prime] [CharP k p] -variable (l : (Fin r → ZMod p) →+ k) (hl : Function.Injective l) - - -def StableFaithfulPair (A B : FDRep k (SL2 k)) : Prop := - ∀ (f : A ⟶ B), FactorsThroughProjective ((restrictElementary k p r l).map f) → - f ∈ steinbergSpan k p r A B - -omit [Infinite k] [CharP k p] in -lemma StableFaithfulPair.iso_left {A A' B : FDRep k (SL2 k)} - (h : StableFaithfulPair k p r l A B) (e : A ≅ A') : - StableFaithfulPair k p r l A' B := by - intro f hf - have hg : FactorsThroughProjective ((restrictElementary k p r l).map (e.hom ≫ f)) := by - rw [Functor.map_comp] - exact hf.precomp _ - have H := steinbergSpan.precomp k p r e.inv _ (h _ hg) - simpa using H - -omit [Infinite k] [CharP k p] in -lemma StableFaithfulPair.iso_right {A B B' : FDRep k (SL2 k)} - (h : StableFaithfulPair k p r l A B) (e : B ≅ B') : - StableFaithfulPair k p r l A B' := by - intro f hf - have hg : FactorsThroughProjective ((restrictElementary k p r l).map (f ≫ e.inv)) := by - rw [Functor.map_comp] - exact hf.postcomp _ - have H := steinbergSpan.postcomp k p r _ e.hom (h _ hg) - simpa using H - -omit [Infinite k] [CharP k p] in -lemma StableFaithfulPair.prod_left {A A' B : FDRep k (SL2 k)} - (h : StableFaithfulPair k p r l A B) (h' : StableFaithfulPair k p r l A' B) : - StableFaithfulPair k p r l (repProduct k A A') B := by - intro f hf - have h₁ : FactorsThroughProjective - ((restrictElementary k p r l).map (repInl k A A' ≫ f)) := by - rw [Functor.map_comp]; exact hf.precomp _ - have h₂ : FactorsThroughProjective - ((restrictElementary k p r l).map (repInr k A A' ≫ f)) := by - rw [Functor.map_comp]; exact hf.precomp _ - have H := (steinbergSpan k p r _ B).add_mem - (steinbergSpan.precomp k p r (repFst k A A') _ (h _ h₁)) - (steinbergSpan.precomp k p r (repSnd k A A') _ (h' _ h₂)) - have he : (repFst k A A' ≫ repInl k A A' + repSnd k A A' ≫ repInr k A A') ≫ f = f := by - rw [repProduct_decomposition, Category.id_comp] - rw [Preadditive.add_comp, Category.assoc, Category.assoc] at he - rwa [he] at H - -omit [Infinite k] [CharP k p] in -lemma StableFaithfulPair.prod_right {A B B' : FDRep k (SL2 k)} - (h : StableFaithfulPair k p r l A B) (h' : StableFaithfulPair k p r l A B') : - StableFaithfulPair k p r l A (repProduct k B B') := by - intro f hf - have h₁ : FactorsThroughProjective - ((restrictElementary k p r l).map (f ≫ repFst k B B')) := by - rw [Functor.map_comp]; exact hf.postcomp _ - have h₂ : FactorsThroughProjective - ((restrictElementary k p r l).map (f ≫ repSnd k B B')) := by - rw [Functor.map_comp]; exact hf.postcomp _ - have H := (steinbergSpan k p r A _).add_mem - (steinbergSpan.postcomp k p r _ (repInl k B B') (h _ h₁)) - (steinbergSpan.postcomp k p r _ (repInr k B B') (h' _ h₂)) - have he : f ≫ (repFst k B B' ≫ repInl k B B' + repSnd k B B' ≫ repInr k B B') = f := by - rw [repProduct_decomposition, Category.comp_id] - rw [Preadditive.comp_add, ← Category.assoc, ← Category.assoc] at he - rwa [he] at H - -include hl - -omit [CharP k p] in -lemma generated_stable_kernel {A B : FDRep k (SL2 k)} - (hA : SteinbergGenerated k p r A) (hB : SteinbergGenerated k p r B) : - StableFaithfulPair k p r l A B := by - induction hA generalizing B with - | low A hA a ha hw => - induction hB with - | low B hB b hb hw' => - intro f hf - have hz := low_weight_projective_factor_zero p r l hl A B hA.1 hB.1 a b hw hw' - (by omega) f hf - rw [hz] - exact (steinbergSpan k p r A B).zero_mem - | high X hX => exact fun f _ => steinbergSpan_of_high_right k p r X hX f - | of_iso hB e ih => exact ih.iso_right k p r l e - | prod hB hB' ih ih' => exact ih.prod_right k p r l ih' - | high X hX => exact fun f _ => steinbergSpan_of_high_left k p r X hX f - | of_iso hA e ih => exact (ih hB).iso_left k p r l e - | prod hA hA' ih ih' => exact (ih hB).prod_left k p r l (ih' hB) - - -theorem tilting_projective_factor_mem_steinbergSpan (hr : 1 ≤ r) - (A B : FDRep k (SL2 k)) (hA : IsTilting k A) (hB : IsTilting k B) - (f : A ⟶ B) (hf : FactorsThroughProjective ((restrictElementary k p r l).map f)) : - f ∈ steinbergSpan k p r A B := by - obtain ⟨P,a,s,ha,hP⟩ := tilting_retract_generated k p r hr A hA - obtain ⟨Q,b,t,hb,hQ⟩ := tilting_retract_generated k p r hr B hB - have hg : FactorsThroughProjective ((restrictElementary k p r l).map (a ≫ f ≫ t)) := by - simp only [Functor.map_comp] - exact (hf.precomp _).postcomp _ - have H := generated_stable_kernel k p r l hl hP hQ _ hg - have H' := steinbergSpan.postcomp k p r _ b (steinbergSpan.precomp k p r s _ H) - simp only [Category.assoc] at H' - rwa [← Category.assoc s a, ha, Category.id_comp, hb, Category.comp_id] at H' -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.TiltingCovers +import OAI.RepresentationTheory.RestrictedTilting.SteinbergSpan +import OAI.RepresentationTheory.RestrictedTilting.BoundedStableFaithfulness + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (p r : ℕ) [Fact p.Prime] [CharP k p] +variable (l : (Fin r → ZMod p) →+ k) (hl : Function.Injective l) + + +def StableFaithfulPair (A B : FDRep k (SL2 k)) : Prop := + ∀ (f : A ⟶ B), FactorsThroughProjective ((restrictElementary k p r l).map f) → + f ∈ steinbergSpan k p r A B + +omit [Infinite k] [CharP k p] in +lemma StableFaithfulPair.iso_left {A A' B : FDRep k (SL2 k)} + (h : StableFaithfulPair k p r l A B) (e : A ≅ A') : + StableFaithfulPair k p r l A' B := by + intro f hf + have hg : FactorsThroughProjective ((restrictElementary k p r l).map (e.hom ≫ f)) := by + rw [Functor.map_comp] + exact hf.precomp _ + have H := steinbergSpan.precomp k p r e.inv _ (h _ hg) + simpa using H + +omit [Infinite k] [CharP k p] in +lemma StableFaithfulPair.iso_right {A B B' : FDRep k (SL2 k)} + (h : StableFaithfulPair k p r l A B) (e : B ≅ B') : + StableFaithfulPair k p r l A B' := by + intro f hf + have hg : FactorsThroughProjective ((restrictElementary k p r l).map (f ≫ e.inv)) := by + rw [Functor.map_comp] + exact hf.postcomp _ + have H := steinbergSpan.postcomp k p r _ e.hom (h _ hg) + simpa using H + +omit [Infinite k] [CharP k p] in +lemma StableFaithfulPair.prod_left {A A' B : FDRep k (SL2 k)} + (h : StableFaithfulPair k p r l A B) (h' : StableFaithfulPair k p r l A' B) : + StableFaithfulPair k p r l (repProduct k A A') B := by + intro f hf + have h₁ : FactorsThroughProjective + ((restrictElementary k p r l).map (repInl k A A' ≫ f)) := by + rw [Functor.map_comp]; exact hf.precomp _ + have h₂ : FactorsThroughProjective + ((restrictElementary k p r l).map (repInr k A A' ≫ f)) := by + rw [Functor.map_comp]; exact hf.precomp _ + have H := (steinbergSpan k p r _ B).add_mem + (steinbergSpan.precomp k p r (repFst k A A') _ (h _ h₁)) + (steinbergSpan.precomp k p r (repSnd k A A') _ (h' _ h₂)) + have he : (repFst k A A' ≫ repInl k A A' + repSnd k A A' ≫ repInr k A A') ≫ f = f := by + rw [repProduct_decomposition, Category.id_comp] + rw [Preadditive.add_comp, Category.assoc, Category.assoc] at he + rwa [he] at H + +omit [Infinite k] [CharP k p] in +lemma StableFaithfulPair.prod_right {A B B' : FDRep k (SL2 k)} + (h : StableFaithfulPair k p r l A B) (h' : StableFaithfulPair k p r l A B') : + StableFaithfulPair k p r l A (repProduct k B B') := by + intro f hf + have h₁ : FactorsThroughProjective + ((restrictElementary k p r l).map (f ≫ repFst k B B')) := by + rw [Functor.map_comp]; exact hf.postcomp _ + have h₂ : FactorsThroughProjective + ((restrictElementary k p r l).map (f ≫ repSnd k B B')) := by + rw [Functor.map_comp]; exact hf.postcomp _ + have H := (steinbergSpan k p r A _).add_mem + (steinbergSpan.postcomp k p r _ (repInl k B B') (h _ h₁)) + (steinbergSpan.postcomp k p r _ (repInr k B B') (h' _ h₂)) + have he : f ≫ (repFst k B B' ≫ repInl k B B' + repSnd k B B' ≫ repInr k B B') = f := by + rw [repProduct_decomposition, Category.comp_id] + rw [Preadditive.comp_add, ← Category.assoc, ← Category.assoc] at he + rwa [he] at H + +include hl + +omit [CharP k p] in +lemma generated_stable_kernel {A B : FDRep k (SL2 k)} + (hA : SteinbergGenerated k p r A) (hB : SteinbergGenerated k p r B) : + StableFaithfulPair k p r l A B := by + induction hA generalizing B with + | low A hA a ha hw => + induction hB with + | low B hB b hb hw' => + intro f hf + have hz := low_weight_projective_factor_zero p r l hl A B hA.1 hB.1 a b hw hw' + (by omega) f hf + rw [hz] + exact (steinbergSpan k p r A B).zero_mem + | high X hX => exact fun f _ => steinbergSpan_of_high_right k p r X hX f + | of_iso hB e ih => exact ih.iso_right k p r l e + | prod hB hB' ih ih' => exact ih.prod_right k p r l ih' + | high X hX => exact fun f _ => steinbergSpan_of_high_left k p r X hX f + | of_iso hA e ih => exact (ih hB).iso_left k p r l e + | prod hA hA' ih ih' => exact (ih hB).prod_left k p r l (ih' hB) + + +theorem tilting_projective_factor_mem_steinbergSpan (hr : 1 ≤ r) + (A B : FDRep k (SL2 k)) (hA : IsTilting k A) (hB : IsTilting k B) + (f : A ⟶ B) (hf : FactorsThroughProjective ((restrictElementary k p r l).map f)) : + f ∈ steinbergSpan k p r A B := by + obtain ⟨P,a,s,ha,hP⟩ := tilting_retract_generated k p r hr A hA + obtain ⟨Q,b,t,hb,hQ⟩ := tilting_retract_generated k p r hr B hB + have hg : FactorsThroughProjective ((restrictElementary k p r l).map (a ≫ f ≫ t)) := by + simp only [Functor.map_comp] + exact (hf.precomp _).postcomp _ + have H := generated_stable_kernel k p r l hl hP hQ _ hg + have H' := steinbergSpan.postcomp k p r _ b (steinbergSpan.precomp k p r s _ H) + simp only [Category.assoc] at H' + rwa [← Category.assoc s a, ha, Category.id_comp, hb, Category.comp_id] at H' +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/GlobalLattices.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/GlobalLattices.lean index a972c1c15d558ed9a99b1af72ca0d87f9803cb3a..5a629dff1894f0c0f2ff4e90325185a417ddd355 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/GlobalLattices.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/GlobalLattices.lean @@ -1,323 +1,323 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.OriginCoordinates - -namespace OAI - -/-! Fraction charts, global lattices and finite origin quotients. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section -variable (k : Type*) [Field k] -abbrev planeFractionField := FractionRing (MvPolynomial (Fin 2) k) - -noncomputable instance planeCoordinateRing_gcd : GCDMonoid (MvPolynomial (Fin 2) k) := - UniqueFactorizationMonoid.toGCDMonoid _ - -lemma planeCoordinates_relPrime : - IsRelPrime (MvPolynomial.X (0 : Fin 2) : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) := by - apply (MvPolynomial.X_prime (R := k) (i := (0 : Fin 2))).irreducible.isRelPrime_iff_not_dvd.mpr - intro h - exact (by decide : (0 : Fin 2) ≠ 1) (MvPolynomial.X_dvd_X.mp h) - -lemma planeFractionCoordinate_ne_zero (i : Fin 2) : - algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) (MvPolynomial.X i) ≠ 0 := - fun h => MvPolynomial.X_ne_zero i - ((FaithfulSMul.algebraMap_injective _ _) (h.trans (map_zero _).symm)) - -noncomputable def planeChartToFraction (i : Fin 2) : - planeCoordinateChart k i →ₐ[k] planeFractionField k := - IsLocalization.Away.liftAlgHom (MvPolynomial.X i : MvPolynomial (Fin 2) k) - (f := IsScalarTower.toAlgHom k (MvPolynomial (Fin 2) k) (planeFractionField k)) - (isUnit_iff_ne_zero.mpr (planeFractionCoordinate_ne_zero k i)) - -lemma planeChartToFraction_algebraMap (i : Fin 2) (P : MvPolynomial (Fin 2) k) : - planeChartToFraction k i - (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i) P) = - algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) P := - IsLocalization.Away.lift_eq _ (isUnit_iff_ne_zero.mpr (planeFractionCoordinate_ne_zero k i)) _ - -lemma planeChartToFraction_injective (i : Fin 2) : - Function.Injective (planeChartToFraction k i) := by - apply (IsLocalization.injective_iff_map_algebraMap_eq - (Submonoid.powers (MvPolynomial.X i : MvPolynomial (Fin 2) k)) - (planeChartToFraction k i).toRingHom).mpr - intro P Q - constructor - · exact congrArg (planeChartToFraction k i) - · intro h - have h' : algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) P = - algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) Q := by - simpa only [AlgHom.toRingHom_eq_coe, RingHom.coe_coe, planeChartToFraction_algebraMap] using h - exact congrArg (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i)) - ((FaithfulSMul.algebraMap_injective _ _) h') - -noncomputable def planeChartToFractionLinear (i : Fin 2) : - planeCoordinateChart k i →ₗ[MvPolynomial (Fin 2) k] planeFractionField k where - toFun := planeChartToFraction k i - map_add' := (planeChartToFraction k i).map_add - map_smul' := by - intro P f - simp only [Algebra.smul_def, map_mul, planeChartToFraction_algebraMap, - RingHom.id_apply] - -noncomputable def planeOverlapToFraction : planeOverlapRing k →ₐ[k] planeFractionField k := - IsLocalization.Away.liftAlgHom (MvPolynomial.X 0 * MvPolynomial.X 1 : MvPolynomial (Fin 2) k) - (f := IsScalarTower.toAlgHom k (MvPolynomial (Fin 2) k) (planeFractionField k)) - (isUnit_iff_ne_zero.mpr (by - change algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) - (MvPolynomial.X 0 * MvPolynomial.X 1) ≠ 0 - rw [map_mul] - exact mul_ne_zero (planeFractionCoordinate_ne_zero k 0) (planeFractionCoordinate_ne_zero k 1))) - -lemma planeOverlapToFraction_algebraMap (P : MvPolynomial (Fin 2) k) : - planeOverlapToFraction k - (algebraMap (MvPolynomial (Fin 2) k) (planeOverlapRing k) P) = - algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) P := by - unfold planeOverlapToFraction - rw [IsLocalization.Away.liftAlgHom_apply, IsLocalization.Away.lift_eq] - rfl - -lemma planeChartToFraction_overlap (i : Fin 2) (f : planeCoordinateChart k i) : - planeOverlapToFraction k (planeChartToOverlap k i f) = planeChartToFraction k i f := by - have h : (planeOverlapToFraction k).toRingHom.comp (planeChartToOverlap k i).toRingHom = - (planeChartToFraction k i).toRingHom := by - apply IsLocalization.ringHom_ext - (Submonoid.powers (MvPolynomial.X i : MvPolynomial (Fin 2) k)) - apply RingHom.ext - intro P - simp only [RingHom.comp_apply, AlgHom.toRingHom_eq_coe, RingHom.coe_coe, - planeChartToOverlap_algebraMap, planeChartToFraction_algebraMap, - planeOverlapToFraction_algebraMap] - exact RingHom.congr_fun h f - -noncomputable def planeOverlapInverse : planeOverlapRing k := - IsLocalization.Away.invSelf (MvPolynomial.X 0 * MvPolynomial.X 1 : MvPolynomial (Fin 2) k) - -lemma planeOverlapInverse_evaluation (x : planeTorusPoints k) : - planeOverlapEvaluation k (planeOverlapInverse k) x = (x.val 0 * x.val 1)⁻¹ := by - have h := congrFun (congrArg (planeOverlapEvaluation k) - (IsLocalization.Away.mul_invSelf (S := planeOverlapRing k) - (MvPolynomial.X 0 * MvPolynomial.X 1 : MvPolynomial (Fin 2) k))) x - simp only [map_mul, map_one, Pi.mul_apply, Pi.one_apply, - planeOverlapEvaluation_algebraMap, planeTorusEvaluation_apply, - MvPolynomial.eval_X] at h - exact mul_left_cancel₀ (mul_ne_zero (x.property 0) (x.property 1)) - (h.trans (mul_inv_cancel₀ (mul_ne_zero (x.property 0) (x.property 1))).symm) - -lemma planeOverlapInverse_fraction : - planeOverlapToFraction k (planeOverlapInverse k) = - (algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) - (MvPolynomial.X 0 * MvPolynomial.X 1))⁻¹ := by - have h := congrArg (planeOverlapToFraction k) - (IsLocalization.Away.mul_invSelf (S := planeOverlapRing k) - (MvPolynomial.X 0 * MvPolynomial.X 1 : MvPolynomial (Fin 2) k)) - simp only [map_mul, map_one, planeOverlapToFraction_algebraMap] at h - have hn : algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) - (MvPolynomial.X 0 * MvPolynomial.X 1) ≠ 0 := by - rw [map_mul] - exact mul_ne_zero (planeFractionCoordinate_ne_zero k 0) (planeFractionCoordinate_ne_zero k 1) - apply mul_left_cancel₀ hn - rw [mul_inv_cancel₀ hn] - simpa only [map_mul, planeOverlapInverse] using h - -variable {ι : Type*} [Fintype ι] [DecidableEq ι] - -omit [DecidableEq ι] in -lemma planeChartVector_mem (a : Fin 2) (f : ι → planeCoordinateChart k a) : - (fun i => planeChartToFraction k a (f i)) ∈ - powerLocalization (MvPolynomial.X a : MvPolynomial (Fin 2) k) coordinateLattice := by - obtain ⟨s,hs⟩ := IsLocalization.exist_integer_multiples - (Submonoid.powers (MvPolynomial.X a : MvPolynomial (Fin 2) k)) Finset.univ f - obtain ⟨n,hn⟩ := s.property - refine ⟨n, (mem_coordinateLattice _).mpr fun i => ?_⟩ - obtain ⟨b,hb⟩ := hs i (Finset.mem_univ i) - refine ⟨b,?_⟩ - have h := congrArg (planeChartToFraction k a) hb - rw [planeChartToFraction_algebraMap] at h - change _ = planeChartToFraction k a (s.val • f i) at h - rw [← hn] at h - exact h.trans ((planeChartToFractionLinear k a).map_smul (MvPolynomial.X a ^ n) (f i)) - -variable [Infinite k] -variable (P : Matrix ι ι (Polynomial k)) - -omit [DecidableEq ι] in -lemma planeChartPair_fraction_relation - (f₀ : ι → planeCoordinateChart k 0) (f₁ : ι → planeCoordinateChart k 1) - (hf : ∀ x : planeTorusPoints k, - (fun j => planeChartEvaluation k 1 (f₁ j) x) = - (polynomialMatrixEval P ((x.val 0 * x.val 1)⁻¹)).mulVec - (fun j => planeChartEvaluation k 0 (f₀ j) x)) : - (fun i => planeChartToFraction k 1 (f₁ i)) = - (polynomialMatrixEval P ((algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) - (MvPolynomial.X 0 * MvPolynomial.X 1))⁻¹)).mulVec - (fun i => planeChartToFraction k 0 (f₀ i)) := by - have hov (i : ι) : planeChartToOverlap k 1 (f₁ i) = - ∑ j, Polynomial.aeval (planeOverlapInverse k) (P i j) * planeChartToOverlap k 0 (f₀ j) := by - apply planeOverlapEvaluation_injective k - funext x - let ev : planeOverlapRing k →ₐ[k] k := - (Pi.evalAlgHom k _ x).comp (planeOverlapEvaluation k) - change ev (planeChartToOverlap k 1 (f₁ i)) = ev _ - simp only [map_sum, map_mul, map_aeval_polynomial] - change planeOverlapEvaluation k (planeChartToOverlap k 1 (f₁ i)) x = - ∑ j, Polynomial.aeval (planeOverlapEvaluation k (planeOverlapInverse k) x) (P i j) * - planeOverlapEvaluation k (planeChartToOverlap k 0 (f₀ j)) x - simp only [planeChartToOverlap_evaluation, planeOverlapInverse_evaluation] - exact congrFun (hf x) i - funext i - have h := congrArg (planeOverlapToFraction k) (hov i) - simpa only [map_sum, map_mul, map_aeval_polynomial, planeChartToFraction_overlap, - planeOverlapInverse_fraction, Matrix.mulVec, dotProduct, polynomialMatrixEval] using h - -variable (h0 : polynomialMatrixEval P (0 : k) = 1) - (hadd : ∀ s t : k, polynomialMatrixEval P (s+t) = - polynomialMatrixEval P s * polynomialMatrixEval P t) - -noncomputable def planeGlobalTransition : - (ι → planeFractionField k) ≃ₗ[planeFractionField k] (ι → planeFractionField k) := - polynomialActionEquiv P h0 hadd - (-(algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) - (MvPolynomial.X 0 * MvPolynomial.X 1))⁻¹) - -noncomputable def planeGlobalLattice : - Submodule (MvPolynomial (Fin 2) k) (ι → planeFractionField k) := - gluedLattice (MvPolynomial.X 0) (MvPolynomial.X 1) (planeGlobalTransition k P h0 hadd) - -omit [Infinite k] in -lemma planeFraction_product_ne_zero : - algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) - (MvPolynomial.X 0 * MvPolynomial.X 1) ≠ 0 := by - rw [map_mul] - exact mul_ne_zero (planeFractionCoordinate_ne_zero k 0) (planeFractionCoordinate_ne_zero k 1) - -lemma planeGlobalTransition_denominator (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : - ∀ v ∈ coordinateLattice (R := MvPolynomial (Fin 2) k), - (MvPolynomial.X 0 * MvPolynomial.X 1 : MvPolynomial (Fin 2) k)^d • - planeGlobalTransition k P h0 hadd v ∈ coordinateLattice (R := MvPolynomial (Fin 2) k) := - polynomialAction_denominator P h0 hadd _ (planeFraction_product_ne_zero k) d hd - -lemma planeGlobalLattice_finite (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : - Module.Finite (MvPolynomial (Fin 2) k) (planeGlobalLattice k P h0 hadd) := - gluedLattice_finite _ _ (MvPolynomial.X_ne_zero 0) (planeCoordinates_relPrime k) _ d - (planeGlobalTransition_denominator k P h0 hadd d hd) - -lemma planeChartPair_mem_globalLattice - (f₀ : ι → planeCoordinateChart k 0) (f₁ : ι → planeCoordinateChart k 1) - (hf : ∀ x : planeTorusPoints k, - (fun j => planeChartEvaluation k 1 (f₁ j) x) = - (polynomialMatrixEval P ((x.val 0 * x.val 1)⁻¹)).mulVec - (fun j => planeChartEvaluation k 0 (f₀ j) x)) : - (fun i => planeChartToFraction k 0 (f₀ i)) ∈ planeGlobalLattice k P h0 hadd := by - constructor - · exact planeChartVector_mem k 0 f₀ - · refine ⟨fun i => planeChartToFraction k 1 (f₁ i), planeChartVector_mem k 1 f₁, ?_⟩ - have h := planeChartPair_fraction_relation k P f₀ f₁ hf - change planeGlobalTransition k P h0 hadd (fun i => planeChartToFraction k 1 (f₁ i)) = _ - rw [h] - change (polynomialMatrixEval P (-_)).mulVec ((polynomialMatrixEval P _).mulVec _) = _ - rw [Matrix.mulVec_mulVec, ← polynomialMatrixEval_add P hadd, neg_add_cancel, - polynomialMatrixEval_zero P h0, Matrix.one_mulVec] - -end - -section -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (ι : Type u) [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) -variable (P : Matrix ι ι (Polynomial k)) -variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) - -omit [Infinite k] in -include hP in -lemma associatedPolynomial_zero : polynomialMatrixEval P (0 : k) = 1 := by - rw [hP] - change LinearMap.toMatrix' (ρ 1) = 1 - rw [map_one] - exact LinearMap.toMatrix'_one - -omit [Infinite k] in -include hP in -lemma associatedPolynomial_add (s t : k) : polynomialMatrixEval P (s+t) = - polynomialMatrixEval P s * polynomialMatrixEval P t := by - rw [hP, hP, hP] - change LinearMap.toMatrix' (ρ (Multiplicative.ofAdd s * Multiplicative.ofAdd t)) = _ - rw [map_mul, LinearMap.toMatrix'_mul] - -noncomputable def associatedFractionChart : - (associatedSectionsSubmodule k ι ρ) →ₗ[MvPolynomial (Fin 2) k] - (ι → planeFractionField k) := - (LinearMap.pi fun i => (planeChartToFractionLinear k 0).comp - (LinearMap.proj i)).comp (associatedXChartPolynomial k ι ρ) - -omit [Fintype ι] [DecidableEq ι] in -lemma associatedFractionChart_injective : Function.Injective (associatedFractionChart k ι ρ) := by - intro f g h - apply associatedXChart_injective k ι ρ - funext i - exact planeChartToFraction_injective k 0 (congrFun h i) - -lemma associatedFractionChart_mem (f : associatedSectionsSubmodule k ι ρ) : - associatedFractionChart k ι ρ f ∈ planeGlobalLattice k P - (associatedPolynomial_zero k ι ρ P hP) (associatedPolynomial_add k ι ρ P hP) := by - apply planeChartPair_mem_globalLattice k P _ _ - (associatedXChart k ι ρ f) (associatedYChart k ι ρ f) - intro x - rw [hP, LinearMap.toMatrix'_mulVec] - exact associatedCharts_transition k ι ρ f x - -include hP in - - -theorem associatedSections_finite (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : - Module.Finite (MvPolynomial (Fin 2) k) (associatedSectionsSubmodule k ι ρ) := by - let L := planeGlobalLattice k P - (associatedPolynomial_zero k ι ρ P hP) (associatedPolynomial_add k ι ρ P hP) - let : Module.Finite (MvPolynomial (Fin 2) k) L := - planeGlobalLattice_finite k P _ _ d hd - let f := (associatedFractionChart k ι ρ).codRestrict L - (associatedFractionChart_mem k ι ρ P hP) - exact Module.Finite.of_injective f fun a b h => - associatedFractionChart_injective k ι ρ (congrArg Subtype.val h) - -end - -variable {k M σ : Type*} [Field k] [AddCommGroup M] [Module k M] - [Module (MvPolynomial σ k) M] [IsScalarTower k (MvPolynomial σ k) M] - -lemma originQuotient_polynomial_smul (N : Submodule k M) - (hX : ∀ (i : σ) (m : M), (MvPolynomial.X i : MvPolynomial σ k) • m ∈ N) - (P : MvPolynomial σ k) (m : M) : - N.mkQ (P • m) = MvPolynomial.constantCoeff P • N.mkQ m := by - induction P using MvPolynomial.induction_on with - | C a => - rw [MvPolynomial.constantCoeff_C] - change N.mkQ (algebraMap k (MvPolynomial σ k) a • m) = a • N.mkQ m - rw [algebraMap_smul, map_smul] - | add P Q hP hQ => simp only [add_smul, map_add, hP, hQ] - | mul_X P i _ => - rw [mul_comm, mul_smul] - have hz : N.mkQ ((MvPolynomial.X i : MvPolynomial σ k) • (P • m)) = 0 := - (Submodule.Quotient.mk_eq_zero N).mpr (hX i (P • m)) - simpa using hz - - - -theorem originQuotient_finite (N : Submodule k M) - (hX : ∀ (i : σ) (m : M), (MvPolynomial.X i : MvPolynomial σ k) • m ∈ N) - [Module.Finite (MvPolynomial σ k) M] : Module.Finite k (M ⧸ N) := by - let f : M →ₛₗ[MvPolynomial.constantCoeff] (M ⧸ N) := - { toFun := N.mkQ - map_add' := N.mkQ.map_add - map_smul' := originQuotient_polynomial_smul N hX } - exact Module.Finite.of_surjective f N.mkQ_surjective - -end FiberFunctorProof -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.OriginCoordinates + +namespace OAI + +/-! Fraction charts, global lattices and finite origin quotients. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section +variable (k : Type*) [Field k] +abbrev planeFractionField := FractionRing (MvPolynomial (Fin 2) k) + +noncomputable instance planeCoordinateRing_gcd : GCDMonoid (MvPolynomial (Fin 2) k) := + UniqueFactorizationMonoid.toGCDMonoid _ + +lemma planeCoordinates_relPrime : + IsRelPrime (MvPolynomial.X (0 : Fin 2) : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) := by + apply (MvPolynomial.X_prime (R := k) (i := (0 : Fin 2))).irreducible.isRelPrime_iff_not_dvd.mpr + intro h + exact (by decide : (0 : Fin 2) ≠ 1) (MvPolynomial.X_dvd_X.mp h) + +lemma planeFractionCoordinate_ne_zero (i : Fin 2) : + algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) (MvPolynomial.X i) ≠ 0 := + fun h => MvPolynomial.X_ne_zero i + ((FaithfulSMul.algebraMap_injective _ _) (h.trans (map_zero _).symm)) + +noncomputable def planeChartToFraction (i : Fin 2) : + planeCoordinateChart k i →ₐ[k] planeFractionField k := + IsLocalization.Away.liftAlgHom (MvPolynomial.X i : MvPolynomial (Fin 2) k) + (f := IsScalarTower.toAlgHom k (MvPolynomial (Fin 2) k) (planeFractionField k)) + (isUnit_iff_ne_zero.mpr (planeFractionCoordinate_ne_zero k i)) + +lemma planeChartToFraction_algebraMap (i : Fin 2) (P : MvPolynomial (Fin 2) k) : + planeChartToFraction k i + (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i) P) = + algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) P := + IsLocalization.Away.lift_eq _ (isUnit_iff_ne_zero.mpr (planeFractionCoordinate_ne_zero k i)) _ + +lemma planeChartToFraction_injective (i : Fin 2) : + Function.Injective (planeChartToFraction k i) := by + apply (IsLocalization.injective_iff_map_algebraMap_eq + (Submonoid.powers (MvPolynomial.X i : MvPolynomial (Fin 2) k)) + (planeChartToFraction k i).toRingHom).mpr + intro P Q + constructor + · exact congrArg (planeChartToFraction k i) + · intro h + have h' : algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) P = + algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) Q := by + simpa only [AlgHom.toRingHom_eq_coe, RingHom.coe_coe, planeChartToFraction_algebraMap] using h + exact congrArg (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i)) + ((FaithfulSMul.algebraMap_injective _ _) h') + +noncomputable def planeChartToFractionLinear (i : Fin 2) : + planeCoordinateChart k i →ₗ[MvPolynomial (Fin 2) k] planeFractionField k where + toFun := planeChartToFraction k i + map_add' := (planeChartToFraction k i).map_add + map_smul' := by + intro P f + simp only [Algebra.smul_def, map_mul, planeChartToFraction_algebraMap, + RingHom.id_apply] + +noncomputable def planeOverlapToFraction : planeOverlapRing k →ₐ[k] planeFractionField k := + IsLocalization.Away.liftAlgHom (MvPolynomial.X 0 * MvPolynomial.X 1 : MvPolynomial (Fin 2) k) + (f := IsScalarTower.toAlgHom k (MvPolynomial (Fin 2) k) (planeFractionField k)) + (isUnit_iff_ne_zero.mpr (by + change algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) + (MvPolynomial.X 0 * MvPolynomial.X 1) ≠ 0 + rw [map_mul] + exact mul_ne_zero (planeFractionCoordinate_ne_zero k 0) (planeFractionCoordinate_ne_zero k 1))) + +lemma planeOverlapToFraction_algebraMap (P : MvPolynomial (Fin 2) k) : + planeOverlapToFraction k + (algebraMap (MvPolynomial (Fin 2) k) (planeOverlapRing k) P) = + algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) P := by + unfold planeOverlapToFraction + rw [IsLocalization.Away.liftAlgHom_apply, IsLocalization.Away.lift_eq] + rfl + +lemma planeChartToFraction_overlap (i : Fin 2) (f : planeCoordinateChart k i) : + planeOverlapToFraction k (planeChartToOverlap k i f) = planeChartToFraction k i f := by + have h : (planeOverlapToFraction k).toRingHom.comp (planeChartToOverlap k i).toRingHom = + (planeChartToFraction k i).toRingHom := by + apply IsLocalization.ringHom_ext + (Submonoid.powers (MvPolynomial.X i : MvPolynomial (Fin 2) k)) + apply RingHom.ext + intro P + simp only [RingHom.comp_apply, AlgHom.toRingHom_eq_coe, RingHom.coe_coe, + planeChartToOverlap_algebraMap, planeChartToFraction_algebraMap, + planeOverlapToFraction_algebraMap] + exact RingHom.congr_fun h f + +noncomputable def planeOverlapInverse : planeOverlapRing k := + IsLocalization.Away.invSelf (MvPolynomial.X 0 * MvPolynomial.X 1 : MvPolynomial (Fin 2) k) + +lemma planeOverlapInverse_evaluation (x : planeTorusPoints k) : + planeOverlapEvaluation k (planeOverlapInverse k) x = (x.val 0 * x.val 1)⁻¹ := by + have h := congrFun (congrArg (planeOverlapEvaluation k) + (IsLocalization.Away.mul_invSelf (S := planeOverlapRing k) + (MvPolynomial.X 0 * MvPolynomial.X 1 : MvPolynomial (Fin 2) k))) x + simp only [map_mul, map_one, Pi.mul_apply, Pi.one_apply, + planeOverlapEvaluation_algebraMap, planeTorusEvaluation_apply, + MvPolynomial.eval_X] at h + exact mul_left_cancel₀ (mul_ne_zero (x.property 0) (x.property 1)) + (h.trans (mul_inv_cancel₀ (mul_ne_zero (x.property 0) (x.property 1))).symm) + +lemma planeOverlapInverse_fraction : + planeOverlapToFraction k (planeOverlapInverse k) = + (algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) + (MvPolynomial.X 0 * MvPolynomial.X 1))⁻¹ := by + have h := congrArg (planeOverlapToFraction k) + (IsLocalization.Away.mul_invSelf (S := planeOverlapRing k) + (MvPolynomial.X 0 * MvPolynomial.X 1 : MvPolynomial (Fin 2) k)) + simp only [map_mul, map_one, planeOverlapToFraction_algebraMap] at h + have hn : algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) + (MvPolynomial.X 0 * MvPolynomial.X 1) ≠ 0 := by + rw [map_mul] + exact mul_ne_zero (planeFractionCoordinate_ne_zero k 0) (planeFractionCoordinate_ne_zero k 1) + apply mul_left_cancel₀ hn + rw [mul_inv_cancel₀ hn] + simpa only [map_mul, planeOverlapInverse] using h + +variable {ι : Type*} [Fintype ι] [DecidableEq ι] + +omit [DecidableEq ι] in +lemma planeChartVector_mem (a : Fin 2) (f : ι → planeCoordinateChart k a) : + (fun i => planeChartToFraction k a (f i)) ∈ + powerLocalization (MvPolynomial.X a : MvPolynomial (Fin 2) k) coordinateLattice := by + obtain ⟨s,hs⟩ := IsLocalization.exist_integer_multiples + (Submonoid.powers (MvPolynomial.X a : MvPolynomial (Fin 2) k)) Finset.univ f + obtain ⟨n,hn⟩ := s.property + refine ⟨n, (mem_coordinateLattice _).mpr fun i => ?_⟩ + obtain ⟨b,hb⟩ := hs i (Finset.mem_univ i) + refine ⟨b,?_⟩ + have h := congrArg (planeChartToFraction k a) hb + rw [planeChartToFraction_algebraMap] at h + change _ = planeChartToFraction k a (s.val • f i) at h + rw [← hn] at h + exact h.trans ((planeChartToFractionLinear k a).map_smul (MvPolynomial.X a ^ n) (f i)) + +variable [Infinite k] +variable (P : Matrix ι ι (Polynomial k)) + +omit [DecidableEq ι] in +lemma planeChartPair_fraction_relation + (f₀ : ι → planeCoordinateChart k 0) (f₁ : ι → planeCoordinateChart k 1) + (hf : ∀ x : planeTorusPoints k, + (fun j => planeChartEvaluation k 1 (f₁ j) x) = + (polynomialMatrixEval P ((x.val 0 * x.val 1)⁻¹)).mulVec + (fun j => planeChartEvaluation k 0 (f₀ j) x)) : + (fun i => planeChartToFraction k 1 (f₁ i)) = + (polynomialMatrixEval P ((algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) + (MvPolynomial.X 0 * MvPolynomial.X 1))⁻¹)).mulVec + (fun i => planeChartToFraction k 0 (f₀ i)) := by + have hov (i : ι) : planeChartToOverlap k 1 (f₁ i) = + ∑ j, Polynomial.aeval (planeOverlapInverse k) (P i j) * planeChartToOverlap k 0 (f₀ j) := by + apply planeOverlapEvaluation_injective k + funext x + let ev : planeOverlapRing k →ₐ[k] k := + (Pi.evalAlgHom k _ x).comp (planeOverlapEvaluation k) + change ev (planeChartToOverlap k 1 (f₁ i)) = ev _ + simp only [map_sum, map_mul, map_aeval_polynomial] + change planeOverlapEvaluation k (planeChartToOverlap k 1 (f₁ i)) x = + ∑ j, Polynomial.aeval (planeOverlapEvaluation k (planeOverlapInverse k) x) (P i j) * + planeOverlapEvaluation k (planeChartToOverlap k 0 (f₀ j)) x + simp only [planeChartToOverlap_evaluation, planeOverlapInverse_evaluation] + exact congrFun (hf x) i + funext i + have h := congrArg (planeOverlapToFraction k) (hov i) + simpa only [map_sum, map_mul, map_aeval_polynomial, planeChartToFraction_overlap, + planeOverlapInverse_fraction, Matrix.mulVec, dotProduct, polynomialMatrixEval] using h + +variable (h0 : polynomialMatrixEval P (0 : k) = 1) + (hadd : ∀ s t : k, polynomialMatrixEval P (s+t) = + polynomialMatrixEval P s * polynomialMatrixEval P t) + +noncomputable def planeGlobalTransition : + (ι → planeFractionField k) ≃ₗ[planeFractionField k] (ι → planeFractionField k) := + polynomialActionEquiv P h0 hadd + (-(algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) + (MvPolynomial.X 0 * MvPolynomial.X 1))⁻¹) + +noncomputable def planeGlobalLattice : + Submodule (MvPolynomial (Fin 2) k) (ι → planeFractionField k) := + gluedLattice (MvPolynomial.X 0) (MvPolynomial.X 1) (planeGlobalTransition k P h0 hadd) + +omit [Infinite k] in +lemma planeFraction_product_ne_zero : + algebraMap (MvPolynomial (Fin 2) k) (planeFractionField k) + (MvPolynomial.X 0 * MvPolynomial.X 1) ≠ 0 := by + rw [map_mul] + exact mul_ne_zero (planeFractionCoordinate_ne_zero k 0) (planeFractionCoordinate_ne_zero k 1) + +lemma planeGlobalTransition_denominator (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : + ∀ v ∈ coordinateLattice (R := MvPolynomial (Fin 2) k), + (MvPolynomial.X 0 * MvPolynomial.X 1 : MvPolynomial (Fin 2) k)^d • + planeGlobalTransition k P h0 hadd v ∈ coordinateLattice (R := MvPolynomial (Fin 2) k) := + polynomialAction_denominator P h0 hadd _ (planeFraction_product_ne_zero k) d hd + +lemma planeGlobalLattice_finite (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : + Module.Finite (MvPolynomial (Fin 2) k) (planeGlobalLattice k P h0 hadd) := + gluedLattice_finite _ _ (MvPolynomial.X_ne_zero 0) (planeCoordinates_relPrime k) _ d + (planeGlobalTransition_denominator k P h0 hadd d hd) + +lemma planeChartPair_mem_globalLattice + (f₀ : ι → planeCoordinateChart k 0) (f₁ : ι → planeCoordinateChart k 1) + (hf : ∀ x : planeTorusPoints k, + (fun j => planeChartEvaluation k 1 (f₁ j) x) = + (polynomialMatrixEval P ((x.val 0 * x.val 1)⁻¹)).mulVec + (fun j => planeChartEvaluation k 0 (f₀ j) x)) : + (fun i => planeChartToFraction k 0 (f₀ i)) ∈ planeGlobalLattice k P h0 hadd := by + constructor + · exact planeChartVector_mem k 0 f₀ + · refine ⟨fun i => planeChartToFraction k 1 (f₁ i), planeChartVector_mem k 1 f₁, ?_⟩ + have h := planeChartPair_fraction_relation k P f₀ f₁ hf + change planeGlobalTransition k P h0 hadd (fun i => planeChartToFraction k 1 (f₁ i)) = _ + rw [h] + change (polynomialMatrixEval P (-_)).mulVec ((polynomialMatrixEval P _).mulVec _) = _ + rw [Matrix.mulVec_mulVec, ← polynomialMatrixEval_add P hadd, neg_add_cancel, + polynomialMatrixEval_zero P h0, Matrix.one_mulVec] + +end + +section +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (ι : Type u) [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) +variable (P : Matrix ι ι (Polynomial k)) +variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) + +omit [Infinite k] in +include hP in +lemma associatedPolynomial_zero : polynomialMatrixEval P (0 : k) = 1 := by + rw [hP] + change LinearMap.toMatrix' (ρ 1) = 1 + rw [map_one] + exact LinearMap.toMatrix'_one + +omit [Infinite k] in +include hP in +lemma associatedPolynomial_add (s t : k) : polynomialMatrixEval P (s+t) = + polynomialMatrixEval P s * polynomialMatrixEval P t := by + rw [hP, hP, hP] + change LinearMap.toMatrix' (ρ (Multiplicative.ofAdd s * Multiplicative.ofAdd t)) = _ + rw [map_mul, LinearMap.toMatrix'_mul] + +noncomputable def associatedFractionChart : + (associatedSectionsSubmodule k ι ρ) →ₗ[MvPolynomial (Fin 2) k] + (ι → planeFractionField k) := + (LinearMap.pi fun i => (planeChartToFractionLinear k 0).comp + (LinearMap.proj i)).comp (associatedXChartPolynomial k ι ρ) + +omit [Fintype ι] [DecidableEq ι] in +lemma associatedFractionChart_injective : Function.Injective (associatedFractionChart k ι ρ) := by + intro f g h + apply associatedXChart_injective k ι ρ + funext i + exact planeChartToFraction_injective k 0 (congrFun h i) + +lemma associatedFractionChart_mem (f : associatedSectionsSubmodule k ι ρ) : + associatedFractionChart k ι ρ f ∈ planeGlobalLattice k P + (associatedPolynomial_zero k ι ρ P hP) (associatedPolynomial_add k ι ρ P hP) := by + apply planeChartPair_mem_globalLattice k P _ _ + (associatedXChart k ι ρ f) (associatedYChart k ι ρ f) + intro x + rw [hP, LinearMap.toMatrix'_mulVec] + exact associatedCharts_transition k ι ρ f x + +include hP in + + +theorem associatedSections_finite (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : + Module.Finite (MvPolynomial (Fin 2) k) (associatedSectionsSubmodule k ι ρ) := by + let L := planeGlobalLattice k P + (associatedPolynomial_zero k ι ρ P hP) (associatedPolynomial_add k ι ρ P hP) + let : Module.Finite (MvPolynomial (Fin 2) k) L := + planeGlobalLattice_finite k P _ _ d hd + let f := (associatedFractionChart k ι ρ).codRestrict L + (associatedFractionChart_mem k ι ρ P hP) + exact Module.Finite.of_injective f fun a b h => + associatedFractionChart_injective k ι ρ (congrArg Subtype.val h) + +end + +variable {k M σ : Type*} [Field k] [AddCommGroup M] [Module k M] + [Module (MvPolynomial σ k) M] [IsScalarTower k (MvPolynomial σ k) M] + +lemma originQuotient_polynomial_smul (N : Submodule k M) + (hX : ∀ (i : σ) (m : M), (MvPolynomial.X i : MvPolynomial σ k) • m ∈ N) + (P : MvPolynomial σ k) (m : M) : + N.mkQ (P • m) = MvPolynomial.constantCoeff P • N.mkQ m := by + induction P using MvPolynomial.induction_on with + | C a => + rw [MvPolynomial.constantCoeff_C] + change N.mkQ (algebraMap k (MvPolynomial σ k) a • m) = a • N.mkQ m + rw [algebraMap_smul, map_smul] + | add P Q hP hQ => simp only [add_smul, map_add, hP, hQ] + | mul_X P i _ => + rw [mul_comm, mul_smul] + have hz : N.mkQ ((MvPolynomial.X i : MvPolynomial σ k) • (P • m)) = 0 := + (Submodule.Quotient.mk_eq_zero N).mpr (hX i (P • m)) + simpa using hz + + + +theorem originQuotient_finite (N : Submodule k M) + (hX : ∀ (i : σ) (m : M), (MvPolynomial.X i : MvPolynomial σ k) • m ∈ N) + [Module.Finite (MvPolynomial σ k) M] : Module.Finite k (M ⧸ N) := by + let f : M →ₛₗ[MvPolynomial.constantCoeff] (M ⧸ N) := + { toFun := N.mkQ + map_add' := N.mkQ.map_add + map_smul' := originQuotient_polynomial_smul N hX } + exact Module.Finite.of_surjective f N.mkQ_surjective + +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/GoodKernel.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/GoodKernel.lean index 8080e7e67e47920a07e459670cc9939e83b16015..93bd5f907ab7f010be4e4635651afa90f34c4989 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/GoodKernel.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/GoodKernel.lean @@ -1,104 +1,104 @@ -import OAI.RepresentationTheory.RestrictedTilting.CompatibleJets - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -universe u -variable (k : Type u) [Field k] - - -def HasGoodKernel {P A : FDRep k (SL2 k)} (g : P ⟶ A) : Prop := - ∃ (K : FDRep k (SL2 k)) (i : K ⟶ P) (w : i ≫ g = 0), - (ShortComplex.mk i g w).ShortExact ∧ HasGoodFiltration k K - -lemma HasGoodKernel.epi {P A : FDRep k (SL2 k)} {g : P ⟶ A} - (h : HasGoodKernel k g) : Epi g := by - obtain ⟨K,i,w,hs,hK⟩ := h - exact hs.epi_g - -lemma fdrepKernel_shortExact {P A : FDRep k (SL2 k)} (g : P ⟶ A) - (hg : Function.Surjective (fdrepLinear k g)) : - (ShortComplex.mk (fdrepKernelι k g) g (by - apply fdrep_hom_ext k; intro x; exact x.property)).ShortExact := by - apply fdrep_shortExact k _ Subtype.val_injective hg - exact Submodule.range_subtype _ - -lemma HasGoodKernel.id (A : FDRep k (SL2 k)) : HasGoodKernel k (𝟙 A) := by - refine ⟨fdrepKernel k (𝟙 A), fdrepKernelι k (𝟙 A), ?_, ?_, ?_⟩ - · apply fdrep_hom_ext k; intro x; exact x.property - · exact fdrepKernel_shortExact k (𝟙 A) Function.surjective_id - · have : Subsingleton (fdrepKernel k (𝟙 A)) := by - apply subsingleton_of_forall_eq 0 - intro x - apply Subtype.ext - exact x.property - exact .zero _ (fdrep_isZero_of_subsingleton k _) - -lemma HasGoodKernel.comp {P A B : FDRep k (SL2 k)} {g : P ⟶ A} {h : A ⟶ B} - (hg : HasGoodKernel k g) (hh : HasGoodKernel k h) : HasGoodKernel k (g ≫ h) := by - obtain ⟨K,i,w,hS,hK⟩ := hg - obtain ⟨L,j,v,hT,hL⟩ := hh - obtain ⟨N,a,b,c,wab,wc,hN,hC⟩ := fdrep_splice k i g w hS j h v hT - exact ⟨N,c,wc,hC,hK.extension k hL a b wab hN⟩ - -lemma HasGoodKernel.tensor_right {P A : FDRep k (SL2 k)} {g : P ⟶ A} - (hg : HasGoodKernel k g) (B : FDRep k (SL2 k)) (hB : HasGoodFiltration k B) : - HasGoodKernel k ((tensorRight B).map g) := by - obtain ⟨K,i,w,hS,hK⟩ := hg - let := tensorRight_preservesFiniteLimits B - let := tensorRight_preservesFiniteColimits B - exact ⟨K ⊗ B, (tensorRight B).map i, (by rw [← Functor.map_comp, w, Functor.map_zero]), - hS.map_of_exact (tensorRight B), hK.tensor k hB⟩ - -lemma HasGoodKernel.split [Infinite k] {P A : FDRep k (SL2 k)} {g : P ⟶ A} - (hg : HasGoodKernel k g) (hP : IsRational k P.ρ) (hA : IsTilting k A) : - ∃ s : A ⟶ P, s ≫ g = 𝟙 A := by - obtain ⟨K,i,w,hS,hK⟩ := hg - exact good_weyl_extension_split k hK hA.2.2 P hP i g w hS - -lemma HasGoodKernel.of_isIso {P A : FDRep k (SL2 k)} (g : P ⟶ A) [IsIso g] : - HasGoodKernel k g := by - refine ⟨fdrepKernel k g, fdrepKernelι k g, ?_, ?_, ?_⟩ - · apply fdrep_hom_ext k; intro x; exact x.property - · exact fdrepKernel_shortExact k g (fdrep_surjective k g) - · have : Subsingleton (fdrepKernel k g) := by - apply subsingleton_of_forall_eq 0 - intro x - apply Subtype.ext - apply fdrep_injective k g - exact x.property.trans (map_zero _).symm - exact .zero _ (fdrep_isZero_of_subsingleton k _) - - -lemma costandardMultiply_goodKernel (a b : ℕ) : HasGoodKernel k (costandardMultiply k a b) := by - rcases a with _ | a - · have := costandardMultiply_isIso_of_zero k 0 b (Or.inl rfl) - exact HasGoodKernel.of_isIso k _ - · rcases b with _ | b - · have := costandardMultiply_isIso_of_zero k (a+1) 0 (Or.inr rfl) - exact HasGoodKernel.of_isIso k _ - · exact ⟨_, costandardDeterminant k a b, costandardDeterminant_multiply k a b, - costandardTensorSequence_shortExact k a b, costandard_tensor_hasGoodFiltration k a b⟩ - -lemma HasGoodKernel.kernel_good {P A : FDRep k (SL2 k)} {g : P ⟶ A} - (hg : HasGoodKernel k g) : HasGoodFiltration k (fdrepKernel k g) := by - obtain ⟨K,i,w,hS,hK⟩ := hg - have := hS.mono_f - let j := fdrepKernelLift k i g w - have hj : Function.Bijective (fdrepLinear k j) := by - constructor - · intro x y h - apply fdrep_injective k i - exact congrArg Subtype.val h - · intro x - have hx : x.val ∈ LinearMap.range (fdrepLinear k i) := by - rw [fdrep_exact k hS.exact] - exact x.property - obtain ⟨v,hv⟩ := hx - exact ⟨v,Subtype.ext hv⟩ - have := fdrepHom_isIso_of_bijective k j hj - exact hK.of_iso k (asIso j) -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.CompatibleJets + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +universe u +variable (k : Type u) [Field k] + + +def HasGoodKernel {P A : FDRep k (SL2 k)} (g : P ⟶ A) : Prop := + ∃ (K : FDRep k (SL2 k)) (i : K ⟶ P) (w : i ≫ g = 0), + (ShortComplex.mk i g w).ShortExact ∧ HasGoodFiltration k K + +lemma HasGoodKernel.epi {P A : FDRep k (SL2 k)} {g : P ⟶ A} + (h : HasGoodKernel k g) : Epi g := by + obtain ⟨K,i,w,hs,hK⟩ := h + exact hs.epi_g + +lemma fdrepKernel_shortExact {P A : FDRep k (SL2 k)} (g : P ⟶ A) + (hg : Function.Surjective (fdrepLinear k g)) : + (ShortComplex.mk (fdrepKernelι k g) g (by + apply fdrep_hom_ext k; intro x; exact x.property)).ShortExact := by + apply fdrep_shortExact k _ Subtype.val_injective hg + exact Submodule.range_subtype _ + +lemma HasGoodKernel.id (A : FDRep k (SL2 k)) : HasGoodKernel k (𝟙 A) := by + refine ⟨fdrepKernel k (𝟙 A), fdrepKernelι k (𝟙 A), ?_, ?_, ?_⟩ + · apply fdrep_hom_ext k; intro x; exact x.property + · exact fdrepKernel_shortExact k (𝟙 A) Function.surjective_id + · have : Subsingleton (fdrepKernel k (𝟙 A)) := by + apply subsingleton_of_forall_eq 0 + intro x + apply Subtype.ext + exact x.property + exact .zero _ (fdrep_isZero_of_subsingleton k _) + +lemma HasGoodKernel.comp {P A B : FDRep k (SL2 k)} {g : P ⟶ A} {h : A ⟶ B} + (hg : HasGoodKernel k g) (hh : HasGoodKernel k h) : HasGoodKernel k (g ≫ h) := by + obtain ⟨K,i,w,hS,hK⟩ := hg + obtain ⟨L,j,v,hT,hL⟩ := hh + obtain ⟨N,a,b,c,wab,wc,hN,hC⟩ := fdrep_splice k i g w hS j h v hT + exact ⟨N,c,wc,hC,hK.extension k hL a b wab hN⟩ + +lemma HasGoodKernel.tensor_right {P A : FDRep k (SL2 k)} {g : P ⟶ A} + (hg : HasGoodKernel k g) (B : FDRep k (SL2 k)) (hB : HasGoodFiltration k B) : + HasGoodKernel k ((tensorRight B).map g) := by + obtain ⟨K,i,w,hS,hK⟩ := hg + let := tensorRight_preservesFiniteLimits B + let := tensorRight_preservesFiniteColimits B + exact ⟨K ⊗ B, (tensorRight B).map i, (by rw [← Functor.map_comp, w, Functor.map_zero]), + hS.map_of_exact (tensorRight B), hK.tensor k hB⟩ + +lemma HasGoodKernel.split [Infinite k] {P A : FDRep k (SL2 k)} {g : P ⟶ A} + (hg : HasGoodKernel k g) (hP : IsRational k P.ρ) (hA : IsTilting k A) : + ∃ s : A ⟶ P, s ≫ g = 𝟙 A := by + obtain ⟨K,i,w,hS,hK⟩ := hg + exact good_weyl_extension_split k hK hA.2.2 P hP i g w hS + +lemma HasGoodKernel.of_isIso {P A : FDRep k (SL2 k)} (g : P ⟶ A) [IsIso g] : + HasGoodKernel k g := by + refine ⟨fdrepKernel k g, fdrepKernelι k g, ?_, ?_, ?_⟩ + · apply fdrep_hom_ext k; intro x; exact x.property + · exact fdrepKernel_shortExact k g (fdrep_surjective k g) + · have : Subsingleton (fdrepKernel k g) := by + apply subsingleton_of_forall_eq 0 + intro x + apply Subtype.ext + apply fdrep_injective k g + exact x.property.trans (map_zero _).symm + exact .zero _ (fdrep_isZero_of_subsingleton k _) + + +lemma costandardMultiply_goodKernel (a b : ℕ) : HasGoodKernel k (costandardMultiply k a b) := by + rcases a with _ | a + · have := costandardMultiply_isIso_of_zero k 0 b (Or.inl rfl) + exact HasGoodKernel.of_isIso k _ + · rcases b with _ | b + · have := costandardMultiply_isIso_of_zero k (a+1) 0 (Or.inr rfl) + exact HasGoodKernel.of_isIso k _ + · exact ⟨_, costandardDeterminant k a b, costandardDeterminant_multiply k a b, + costandardTensorSequence_shortExact k a b, costandard_tensor_hasGoodFiltration k a b⟩ + +lemma HasGoodKernel.kernel_good {P A : FDRep k (SL2 k)} {g : P ⟶ A} + (hg : HasGoodKernel k g) : HasGoodFiltration k (fdrepKernel k g) := by + obtain ⟨K,i,w,hS,hK⟩ := hg + have := hS.mono_f + let j := fdrepKernelLift k i g w + have hj : Function.Bijective (fdrepLinear k j) := by + constructor + · intro x y h + apply fdrep_injective k i + exact congrArg Subtype.val h + · intro x + have hx : x.val ∈ LinearMap.range (fdrepLinear k i) := by + rw [fdrep_exact k hS.exact] + exact x.property + obtain ⟨v,hv⟩ := hx + exact ⟨v,Subtype.ext hv⟩ + have := fdrepHom_isIso_of_bijective k j hj + exact hK.of_iso k (asIso j) +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/GoodKernelExtension.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/GoodKernelExtension.lean index 14ee11256d7be5d58fad65645c485cad0555830c..ff91dca6654262de0ab592802f92195571640621 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/GoodKernelExtension.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/GoodKernelExtension.lean @@ -1,101 +1,101 @@ -import OAI.RepresentationTheory.RestrictedTilting.GoodKernel -import OAI.RepresentationTheory.RestrictedTilting.RepProducts - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -universe u -variable (k : Type u) [Field k] - - -noncomputable def extensionCoverMap {A B P Q : FDRep k (SL2 k)} - (f : A ⟶ B) (a : P ⟶ A) (s : Q ⟶ B) : repProduct k P Q ⟶ B := - repFst k P Q ≫ a ≫ f + repSnd k P Q ≫ s - -lemma extensionCoverMap_goodKernel {A B C P Q : FDRep k (SL2 k)} - (f : A ⟶ B) (g : B ⟶ C) (w : f ≫ g = 0) - (hS : (ShortComplex.mk f g w).ShortExact) - (a : P ⟶ A) (q : Q ⟶ C) (ha : HasGoodKernel k a) (hq : HasGoodKernel k q) - (s : Q ⟶ B) (hs : s ≫ g = q) : - HasGoodKernel k (extensionCoverMap k f a s) := by - have := hS.mono_f - have := ha.epi k - have := hq.epi k - have hf := fdrep_injective k f - have hex := fdrep_exact k hS.exact - have hfg (x : A) : fdrepLinear k g (fdrepLinear k f x) = 0 := - congrArg (fun z => fdrepLinear k z x) w - have hsg (y : Q) : fdrepLinear k g (fdrepLinear k s y) = fdrepLinear k q y := - congrArg (fun z => fdrepLinear k z y) hs - let F := extensionCoverMap k f a s - have hF (x : repProduct k P Q) : fdrepLinear k F x = - fdrepLinear k f (fdrepLinear k a x.1) + fdrepLinear k s x.2 := rfl - have hFsurj : Function.Surjective (fdrepLinear k F) := by - intro b - obtain ⟨y,hy⟩ := fdrep_surjective k q (fdrepLinear k g b) - have hmem : b - fdrepLinear k s y ∈ LinearMap.range (fdrepLinear k f) := by - rw [hex] - change fdrepLinear k g (b - fdrepLinear k s y) = 0 - rw [map_sub, hsg, hy, sub_self] - obtain ⟨x,hx⟩ := hmem - obtain ⟨v,hv⟩ := fdrep_surjective k a x - refine ⟨(v,y), ?_⟩ - erw [hF, hv, hx, sub_add_cancel] - let K := fdrepKernel k F - let Ka := fdrepKernel k a - let Kq := fdrepKernel k q - have hker (x : K) : fdrepLinear k q x.val.2 = 0 := by - have h := congrArg (fdrepLinear k g) (show fdrepLinear k F x.val = 0 from x.property) - rw [hF, map_add, hfg, hsg, zero_add, map_zero] at h - exact h - let i : Ka ⟶ K := fdrepHom k - { toFun := fun x => ⟨(x.val,0), by - change fdrepLinear k F (x.val,0) = 0 - erw [hF, show fdrepLinear k a x.val = 0 from x.property, map_zero, map_zero, add_zero]⟩ - map_add' := by intros; apply Subtype.ext; exact Prod.ext rfl (zero_add _).symm - map_smul' := by intros; apply Subtype.ext; exact Prod.ext rfl (smul_zero _).symm } - (by intro t x; apply Subtype.ext; exact Prod.ext rfl (map_zero (Q.ρ t)).symm) - let j : K ⟶ Kq := fdrepHom k - { toFun := fun x => ⟨x.val.2, hker x⟩ - map_add' := by intros; rfl - map_smul' := by intros; rfl } - (by intros; rfl) - have wij : i ≫ j = 0 := by apply fdrep_hom_ext k; intro x; rfl - have hi : Function.Injective (fdrepLinear k i) := by - intro x y h - apply Subtype.ext - exact congrArg (fun z : K => z.val.1) h - have hj : Function.Surjective (fdrepLinear k j) := by - intro y - have hmem : fdrepLinear k s y.val ∈ LinearMap.range (fdrepLinear k f) := by - rw [hex] - change fdrepLinear k g (fdrepLinear k s y.val) = 0 - rw [hsg] - exact y.property - obtain ⟨x,hx⟩ := hmem - obtain ⟨v,hv⟩ := fdrep_surjective k a (-x) - have hvy : fdrepLinear k F (v,y.val) = 0 := by - erw [hF, hv, map_neg, hx, neg_add_cancel] - exact ⟨⟨(v,y.val),hvy⟩,rfl⟩ - have he : LinearMap.range (fdrepLinear k i) = LinearMap.ker (fdrepLinear k j) := by - ext x - constructor - · rintro ⟨y,rfl⟩; rfl - · intro hx - have hx2 : x.val.2 = 0 := congrArg Subtype.val (show fdrepLinear k j x = 0 from hx) - have hx1 : fdrepLinear k a x.val.1 = 0 := by - apply hf - have h := show fdrepLinear k F x.val = 0 from x.property - rw [hF, hx2, map_zero, add_zero] at h - exact h.trans (map_zero _).symm - refine ⟨⟨x.val.1,hx1⟩, ?_⟩ - apply Subtype.ext - exact Prod.ext rfl hx2.symm - have hK : HasGoodFiltration k K := - (ha.kernel_good k).extension k (hq.kernel_good k) i j wij (fdrep_shortExact k _ hi hj he) - exact ⟨K, fdrepKernelι k F, (by apply fdrep_hom_ext k; intro x; exact x.property), - fdrepKernel_shortExact k F hFsurj, hK⟩ -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.GoodKernel +import OAI.RepresentationTheory.RestrictedTilting.RepProducts + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +universe u +variable (k : Type u) [Field k] + + +noncomputable def extensionCoverMap {A B P Q : FDRep k (SL2 k)} + (f : A ⟶ B) (a : P ⟶ A) (s : Q ⟶ B) : repProduct k P Q ⟶ B := + repFst k P Q ≫ a ≫ f + repSnd k P Q ≫ s + +lemma extensionCoverMap_goodKernel {A B C P Q : FDRep k (SL2 k)} + (f : A ⟶ B) (g : B ⟶ C) (w : f ≫ g = 0) + (hS : (ShortComplex.mk f g w).ShortExact) + (a : P ⟶ A) (q : Q ⟶ C) (ha : HasGoodKernel k a) (hq : HasGoodKernel k q) + (s : Q ⟶ B) (hs : s ≫ g = q) : + HasGoodKernel k (extensionCoverMap k f a s) := by + have := hS.mono_f + have := ha.epi k + have := hq.epi k + have hf := fdrep_injective k f + have hex := fdrep_exact k hS.exact + have hfg (x : A) : fdrepLinear k g (fdrepLinear k f x) = 0 := + congrArg (fun z => fdrepLinear k z x) w + have hsg (y : Q) : fdrepLinear k g (fdrepLinear k s y) = fdrepLinear k q y := + congrArg (fun z => fdrepLinear k z y) hs + let F := extensionCoverMap k f a s + have hF (x : repProduct k P Q) : fdrepLinear k F x = + fdrepLinear k f (fdrepLinear k a x.1) + fdrepLinear k s x.2 := rfl + have hFsurj : Function.Surjective (fdrepLinear k F) := by + intro b + obtain ⟨y,hy⟩ := fdrep_surjective k q (fdrepLinear k g b) + have hmem : b - fdrepLinear k s y ∈ LinearMap.range (fdrepLinear k f) := by + rw [hex] + change fdrepLinear k g (b - fdrepLinear k s y) = 0 + rw [map_sub, hsg, hy, sub_self] + obtain ⟨x,hx⟩ := hmem + obtain ⟨v,hv⟩ := fdrep_surjective k a x + refine ⟨(v,y), ?_⟩ + erw [hF, hv, hx, sub_add_cancel] + let K := fdrepKernel k F + let Ka := fdrepKernel k a + let Kq := fdrepKernel k q + have hker (x : K) : fdrepLinear k q x.val.2 = 0 := by + have h := congrArg (fdrepLinear k g) (show fdrepLinear k F x.val = 0 from x.property) + rw [hF, map_add, hfg, hsg, zero_add, map_zero] at h + exact h + let i : Ka ⟶ K := fdrepHom k + { toFun := fun x => ⟨(x.val,0), by + change fdrepLinear k F (x.val,0) = 0 + erw [hF, show fdrepLinear k a x.val = 0 from x.property, map_zero, map_zero, add_zero]⟩ + map_add' := by intros; apply Subtype.ext; exact Prod.ext rfl (zero_add _).symm + map_smul' := by intros; apply Subtype.ext; exact Prod.ext rfl (smul_zero _).symm } + (by intro t x; apply Subtype.ext; exact Prod.ext rfl (map_zero (Q.ρ t)).symm) + let j : K ⟶ Kq := fdrepHom k + { toFun := fun x => ⟨x.val.2, hker x⟩ + map_add' := by intros; rfl + map_smul' := by intros; rfl } + (by intros; rfl) + have wij : i ≫ j = 0 := by apply fdrep_hom_ext k; intro x; rfl + have hi : Function.Injective (fdrepLinear k i) := by + intro x y h + apply Subtype.ext + exact congrArg (fun z : K => z.val.1) h + have hj : Function.Surjective (fdrepLinear k j) := by + intro y + have hmem : fdrepLinear k s y.val ∈ LinearMap.range (fdrepLinear k f) := by + rw [hex] + change fdrepLinear k g (fdrepLinear k s y.val) = 0 + rw [hsg] + exact y.property + obtain ⟨x,hx⟩ := hmem + obtain ⟨v,hv⟩ := fdrep_surjective k a (-x) + have hvy : fdrepLinear k F (v,y.val) = 0 := by + erw [hF, hv, map_neg, hx, neg_add_cancel] + exact ⟨⟨(v,y.val),hvy⟩,rfl⟩ + have he : LinearMap.range (fdrepLinear k i) = LinearMap.ker (fdrepLinear k j) := by + ext x + constructor + · rintro ⟨y,rfl⟩; rfl + · intro hx + have hx2 : x.val.2 = 0 := congrArg Subtype.val (show fdrepLinear k j x = 0 from hx) + have hx1 : fdrepLinear k a x.val.1 = 0 := by + apply hf + have h := show fdrepLinear k F x.val = 0 from x.property + rw [hF, hx2, map_zero, add_zero] at h + exact h.trans (map_zero _).symm + refine ⟨⟨x.val.1,hx1⟩, ?_⟩ + apply Subtype.ext + exact Prod.ext rfl hx2.symm + have hK : HasGoodFiltration k K := + (ha.kernel_good k).extension k (hq.kernel_good k) i j wij (fdrep_shortExact k _ hi hj he) + exact ⟨K, fdrepKernelι k F, (by apply fdrep_hom_ext k; intro x; exact x.property), + fdrepKernel_shortExact k F hFsurj, hK⟩ +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/IntertwinerDescent.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/IntertwinerDescent.lean index c7c419cfc99eb6829c04e768d607a6020dfa0b7e..998a5adab88817b982d3a20aa98e02c421266d02 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/IntertwinerDescent.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/IntertwinerDescent.lean @@ -1,94 +1,94 @@ -import Mathlib - -namespace OAI - - - -noncomputable section -open scoped BigOperators - -namespace FiberFunctorProof - - - -lemma invertible_linear_combination - {k K : Type*} [Field k] [Infinite k] [Field K] [Algebra k K] - {n ι : Type*} [Fintype n] [DecidableEq n] [Fintype ι] - (M : ι → Matrix n n k) (v : ι → K) - (hv : (∑ a : ι, v a • (M a).map (algebraMap k K)).det ≠ 0) : - ∃ c : ι → k, (∑ a : ι, c a • M a).det ≠ 0 := by - classical - let P : Matrix n n (MvPolynomial ι k) := - fun i j => ∑ a : ι, MvPolynomial.C (M a i j) * MvPolynomial.X a - have hP : P.det ≠ 0 := by - intro hzero - apply hv - have heval : P.map (MvPolynomial.eval₂Hom (algebraMap k K) v) = - ∑ a : ι, v a • (M a).map (algebraMap k K) := by - ext i j - simp only [Matrix.map_apply, Matrix.sum_apply, Matrix.smul_apply] - dsimp [P] - simp [mul_comm] - rw [← heval, ← RingHom.mapMatrix_apply, ← RingHom.map_det, hzero, map_zero] - have hex : ∃ c : ι → k, MvPolynomial.eval c P.det ≠ 0 := by - by_contra! h - apply hP - apply MvPolynomial.funext - intro c - simpa only [map_zero] using h c - obtain ⟨c, hc⟩ := hex - refine ⟨c, ?_⟩ - have heval : P.map (MvPolynomial.eval c) = ∑ a : ι, c a • M a := by - ext i j - simp only [Matrix.map_apply, Matrix.sum_apply, Matrix.smul_apply] - dsimp [P] - simp [mul_comm] - rwa [← heval, ← RingHom.mapMatrix_apply, ← RingHom.map_det] - - - -theorem intertwiner_descent - {k K : Type*} [Field k] [Infinite k] [Field K] [Algebra k K] - {n : Type*} [Fintype n] [DecidableEq n] {G : Type*} - (A B : G → Matrix n n k) - (C : Matrix n n K) (hC : C.det ≠ 0) - (h : ∀ g, (A g).map (algebraMap k K) * C = C * (B g).map (algebraMap k K)) : - ∃ D : Matrix n n k, D.det ≠ 0 ∧ ∀ g, A g * D = D * B g := by - classical - let W : Submodule k K := Submodule.span k (Set.range (fun ij : n × n => C ij.1 ij.2)) - have : FiniteDimensional k W := FiniteDimensional.span_of_finite k (Set.finite_range _) - let b := Module.finBasis k W - let V : Matrix n n W := fun i j => ⟨C i j, Submodule.subset_span ⟨(i, j), rfl⟩⟩ - let M : Fin (Module.finrank k W) → Matrix n n k := fun a i j => b.repr (V i j) a - have hrepr : C = ∑ a, (b a : K) • (M a).map (algebraMap k K) := by - ext i j - have heq := congrArg (fun x : W => (x : K)) (b.sum_repr (V i j)) - simp only [Matrix.sum_apply, Matrix.smul_apply, Matrix.map_apply] - change (V i j : K) = ∑ a, (b a : K) * algebraMap k K (b.repr (V i j) a) - simp only [Submodule.coe_sum, Submodule.coe_smul, Algebra.smul_def] at heq - exact heq.symm.trans (Finset.sum_congr rfl fun a _ => mul_comm _ _) - have hM : ∀ a g, A g * M a = M a * B g := by - intro a g - ext i j - have hW : ∑ l : n, A g i l • V l j = ∑ l : n, B g l j • V i l := by - apply Subtype.val_injective - have heq := congrArg (fun X : Matrix n n K => X i j) (h g) - simp only [Matrix.mul_apply, Matrix.map_apply] at heq - simp only [Submodule.coe_sum, Submodule.coe_smul, Algebra.smul_def] - exact heq.trans (Finset.sum_congr rfl fun l _ => mul_comm _ _) - have heq := congrArg (b.coord a) hW - simp only [Matrix.mul_apply] - simp only [map_sum, map_smul, smul_eq_mul, Module.Basis.coord_apply] at heq - exact heq.trans (Finset.sum_congr rfl fun l _ => mul_comm _ _) - have hcomb : (∑ a, (b a : K) • (M a).map (algebraMap k K)).det ≠ 0 := by - rwa [← hrepr] - obtain ⟨c, hc⟩ := invertible_linear_combination M (fun a => (b a : K)) hcomb - refine ⟨∑ a, c a • M a, hc, ?_⟩ - intro g - simp only [Matrix.mul_sum, Matrix.sum_mul, Matrix.mul_smul, Matrix.smul_mul, hM] - -end FiberFunctorProof - -end - -end OAI +import Mathlib + +namespace OAI + + + +noncomputable section +open scoped BigOperators + +namespace FiberFunctorProof + + + +lemma invertible_linear_combination + {k K : Type*} [Field k] [Infinite k] [Field K] [Algebra k K] + {n ι : Type*} [Fintype n] [DecidableEq n] [Fintype ι] + (M : ι → Matrix n n k) (v : ι → K) + (hv : (∑ a : ι, v a • (M a).map (algebraMap k K)).det ≠ 0) : + ∃ c : ι → k, (∑ a : ι, c a • M a).det ≠ 0 := by + classical + let P : Matrix n n (MvPolynomial ι k) := + fun i j => ∑ a : ι, MvPolynomial.C (M a i j) * MvPolynomial.X a + have hP : P.det ≠ 0 := by + intro hzero + apply hv + have heval : P.map (MvPolynomial.eval₂Hom (algebraMap k K) v) = + ∑ a : ι, v a • (M a).map (algebraMap k K) := by + ext i j + simp only [Matrix.map_apply, Matrix.sum_apply, Matrix.smul_apply] + dsimp [P] + simp [mul_comm] + rw [← heval, ← RingHom.mapMatrix_apply, ← RingHom.map_det, hzero, map_zero] + have hex : ∃ c : ι → k, MvPolynomial.eval c P.det ≠ 0 := by + by_contra! h + apply hP + apply MvPolynomial.funext + intro c + simpa only [map_zero] using h c + obtain ⟨c, hc⟩ := hex + refine ⟨c, ?_⟩ + have heval : P.map (MvPolynomial.eval c) = ∑ a : ι, c a • M a := by + ext i j + simp only [Matrix.map_apply, Matrix.sum_apply, Matrix.smul_apply] + dsimp [P] + simp [mul_comm] + rwa [← heval, ← RingHom.mapMatrix_apply, ← RingHom.map_det] + + + +theorem intertwiner_descent + {k K : Type*} [Field k] [Infinite k] [Field K] [Algebra k K] + {n : Type*} [Fintype n] [DecidableEq n] {G : Type*} + (A B : G → Matrix n n k) + (C : Matrix n n K) (hC : C.det ≠ 0) + (h : ∀ g, (A g).map (algebraMap k K) * C = C * (B g).map (algebraMap k K)) : + ∃ D : Matrix n n k, D.det ≠ 0 ∧ ∀ g, A g * D = D * B g := by + classical + let W : Submodule k K := Submodule.span k (Set.range (fun ij : n × n => C ij.1 ij.2)) + have : FiniteDimensional k W := FiniteDimensional.span_of_finite k (Set.finite_range _) + let b := Module.finBasis k W + let V : Matrix n n W := fun i j => ⟨C i j, Submodule.subset_span ⟨(i, j), rfl⟩⟩ + let M : Fin (Module.finrank k W) → Matrix n n k := fun a i j => b.repr (V i j) a + have hrepr : C = ∑ a, (b a : K) • (M a).map (algebraMap k K) := by + ext i j + have heq := congrArg (fun x : W => (x : K)) (b.sum_repr (V i j)) + simp only [Matrix.sum_apply, Matrix.smul_apply, Matrix.map_apply] + change (V i j : K) = ∑ a, (b a : K) * algebraMap k K (b.repr (V i j) a) + simp only [Submodule.coe_sum, Submodule.coe_smul, Algebra.smul_def] at heq + exact heq.symm.trans (Finset.sum_congr rfl fun a _ => mul_comm _ _) + have hM : ∀ a g, A g * M a = M a * B g := by + intro a g + ext i j + have hW : ∑ l : n, A g i l • V l j = ∑ l : n, B g l j • V i l := by + apply Subtype.val_injective + have heq := congrArg (fun X : Matrix n n K => X i j) (h g) + simp only [Matrix.mul_apply, Matrix.map_apply] at heq + simp only [Submodule.coe_sum, Submodule.coe_smul, Algebra.smul_def] + exact heq.trans (Finset.sum_congr rfl fun l _ => mul_comm _ _) + have heq := congrArg (b.coord a) hW + simp only [Matrix.mul_apply] + simp only [map_sum, map_smul, smul_eq_mul, Module.Basis.coord_apply] at heq + exact heq.trans (Finset.sum_congr rfl fun l _ => mul_comm _ _) + have hcomb : (∑ a, (b a : K) • (M a).map (algebraMap k K)).det ≠ 0 := by + rwa [← hrepr] + obtain ⟨c, hc⟩ := invertible_linear_combination M (fun a => (b a : K)) hcomb + refine ⟨∑ a, c a • M a, hc, ?_⟩ + intro g + simp only [Matrix.mul_sum, Matrix.sum_mul, Matrix.mul_smul, Matrix.smul_mul, hM] + +end FiberFunctorProof + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/JetRelations.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/JetRelations.lean index fb06738cc5a8531ddd31cb4ceaae926d836f088e..8e8f3cbf58bbb2aca0352a1908486d1b50ca8061 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/JetRelations.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/JetRelations.lean @@ -1,277 +1,277 @@ -import Mathlib - -namespace OAI - -/-! Binary sums, jet relations and their layer quotients. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -open scoped BigOperators Pointwise - -variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M] - - -def binarySum (x y : R) (n : ℕ) : (Fin (n+1) → M) →ₗ[R] M := - ∑ i : Fin (n+1), (x^i.val * y^(n-i.val)) • LinearMap.proj i - -lemma binarySum_apply (x y : R) (n : ℕ) (v : Fin (n+1) → M) : - binarySum x y n v = ∑ i : Fin (n+1), (x^i.val * y^(n-i.val)) • v i := by - simp [binarySum] - -lemma binarySum_zero (x y : R) (v : Fin 1 → M) : binarySum x y 0 v = v 0 := by - simp [binarySum_apply] - -lemma binarySum_succ (x y : R) (n : ℕ) (v : Fin (n+2) → M) : - binarySum x y (n+1) v = y^(n+1) • v 0 + x • binarySum x y n (fun i => v i.succ) := by - rw [binarySum_apply, Fin.sum_univ_succ, binarySum_apply, Finset.smul_sum] - simp only [Fin.val_zero, pow_zero, Nat.sub_zero, one_mul, Fin.val_succ, Nat.add_sub_add_right] - congr 1 - apply Finset.sum_congr rfl - intro i _ - rw [pow_succ, mul_comm (x^i.val) x, mul_assoc, mul_smul] - -lemma binarySum_single_zero (x y : R) (n : ℕ) (v : M) : - binarySum x y n (Pi.single 0 v) = y^n • v := by - classical - rw [binarySum_apply, Finset.sum_eq_single 0] - · simp - · intro i _ hi - simp [Pi.single_eq_of_ne hi] - · simp - - -def pairRelation (x y : R) : Submodule R M := - x • (⊤ : Submodule R M) ⊔ y • (⊤ : Submodule R M) - -lemma x_smul_mem_pairRelation (x y : R) (v : M) : x • v ∈ pairRelation x y := - (show x • (⊤ : Submodule R M) ≤ pairRelation x y from le_sup_left) - (Submodule.smul_mem_pointwise_smul v x ⊤ (by trivial)) - -lemma y_smul_mem_pairRelation (x y : R) (v : M) : y • v ∈ pairRelation x y := - (show y • (⊤ : Submodule R M) ≤ pairRelation x y from le_sup_right) - (Submodule.smul_mem_pointwise_smul v y ⊤ (by trivial)) - -lemma regular_pair_y_pow (x y : R) - (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) - (j : ℕ) (v n : M) (h : y^j • v = x • n) : ∃ w : M, v = x • w := by - induction j generalizing n with - | zero => exact ⟨n, by simpa using h⟩ - | succ j ih => - obtain ⟨w,hw⟩ := hy (y^j • v) n (by simpa only [pow_succ', mul_smul] using h) - exact ih w hw - - - -theorem binarySum_kernel_coefficients (x y : R) - (hx : Function.Injective (fun m : M => x • m)) - (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) - (j : ℕ) (v : Fin (j+1) → M) (hv : binarySum x y j v = 0) : - ∀ i, v i ∈ pairRelation x y := by - classical - induction j with - | zero => - intro i - have hi : i = 0 := Fin.ext (by omega) - rw [binarySum_zero] at hv - rw [hi, hv] - exact Submodule.zero_mem _ - | succ j ih => - have h0 : y^(j+1) • v 0 = x • (-binarySum x y j (fun i => v i.succ)) := by - rw [smul_neg] - exact eq_neg_of_add_eq_zero_left ((binarySum_succ x y j v) ▸ hv) - obtain ⟨w,hw⟩ := regular_pair_y_pow x y hy (j+1) (v 0) _ h0 - let v' : Fin (j+1) → M := (fun i => v i.succ) + Pi.single 0 (y • w) - have hv' : binarySum x y j v' = 0 := by - apply hx - change x • binarySum x y j v' = x • (0 : M) - rw [smul_zero] - have he : x • binarySum x y j v' = binarySum x y (j+1) v := by - change x • binarySum x y j ((fun i => v i.succ) + Pi.single 0 (y • w)) = _ - rw [map_add, binarySum_single_zero, smul_add, binarySum_succ, hw] - rw [smul_comm (y^(j+1)) x, ← mul_smul (y^j) y w, ← pow_succ] - exact add_comm _ _ - exact he.trans hv - have hc := ih v' hv' - intro i - refine Fin.cases ?_ (fun i => ?_) i - · rw [hw] - exact x_smul_mem_pairRelation x y w - · have hu : (Pi.single (0 : Fin (j+1)) (y • w) : Fin (j+1) → M) i ∈ pairRelation x y := by - by_cases hi : i = 0 - · subst i - simpa using y_smul_mem_pairRelation x y w - · simp [Pi.single_eq_of_ne hi] - have hh := (pairRelation (M := M) x y).sub_mem (hc i) hu - simpa only [v', Pi.add_apply, add_sub_cancel_right] using hh - -lemma binarySum_succ_last (x y : R) (n : ℕ) (v : Fin (n+2) → M) : - binarySum x y (n+1) v = y • binarySum x y n (fun i => v i.castSucc) + x^(n+1) • v (Fin.last _) := by - rw [binarySum_apply, Fin.sum_univ_castSucc, binarySum_apply, Finset.smul_sum] - simp only [Fin.val_last, Nat.sub_self, pow_zero, mul_one, Fin.val_castSucc] - congr 1 - apply Finset.sum_congr rfl - intro i _ - have hi : n+1-i.val = (n-i.val)+1 := by omega - rw [hi, pow_succ, ← mul_assoc, mul_comm (x^i.val * y^(n-i.val)) y, mul_smul] - -lemma binarySum_prepend_zero (x y : R) (n : ℕ) (v : Fin (n+1) → M) : - binarySum x y (n+1) (Fin.cons 0 v) = x • binarySum x y n v := by - rw [binarySum_succ] - simp - -lemma binarySum_append_zero (x y : R) (n : ℕ) (v : Fin (n+1) → M) : - binarySum x y (n+1) (Fin.snoc v 0) = y • binarySum x y n v := by - rw [binarySum_succ_last] - simp - - -def jetRelation (x y : R) (j : ℕ) : Submodule R M := (binarySum x y j).range - -lemma jetRelation_zero (x y : R) : jetRelation (M := M) x y 0 = ⊤ := by - apply LinearMap.range_eq_top.mpr - intro m - exact ⟨fun _ => m, binarySum_zero x y _⟩ - -lemma mem_pairRelation (x y : R) (m : M) : m ∈ pairRelation x y ↔ ∃ a b : M, m = x • a + y • b := by - constructor - · intro h - obtain ⟨a,ha,b,hb,rfl⟩ := Submodule.mem_sup.mp h - obtain ⟨a',_,rfl⟩ := (Submodule.mem_smul_pointwise_iff_exists a x ⊤).mp ha - obtain ⟨b',_,rfl⟩ := (Submodule.mem_smul_pointwise_iff_exists b y ⊤).mp hb - exact ⟨a',b',rfl⟩ - · rintro ⟨a,b,rfl⟩ - exact (pairRelation x y).add_mem (x_smul_mem_pairRelation x y a) (y_smul_mem_pairRelation x y b) - -lemma jetRelation_one (x y : R) : jetRelation (M := M) x y 1 = pairRelation x y := by - ext m - constructor - · rintro ⟨v,rfl⟩ - rw [binarySum_succ, binarySum_zero] - simpa only [Nat.zero_add, pow_one] using - (pairRelation x y).add_mem (y_smul_mem_pairRelation x y (v 0)) - (x_smul_mem_pairRelation x y (v (Fin.succ 0))) - · intro hm - obtain ⟨a,b,rfl⟩ := (mem_pairRelation x y m).mp hm - refine ⟨Fin.cons b (fun _ => a), ?_⟩ - rw [binarySum_succ, binarySum_zero] - simp [add_comm] - -lemma jetRelation_succ_le (x y : R) (j : ℕ) : - jetRelation (M := M) x y (j+1) ≤ jetRelation x y j := by - rintro m ⟨v,rfl⟩ - refine ⟨x • (fun i => v i.succ) + Pi.single 0 (y • v 0), ?_⟩ - rw [map_add, map_smul, binarySum_single_zero, binarySum_succ, ← mul_smul, ← pow_succ] - exact add_comm _ _ - -lemma binarySum_pairRelation (x y : R) (j : ℕ) (v : Fin (j+1) → M) - (hv : ∀ i, v i ∈ pairRelation x y) : - binarySum x y j v ∈ jetRelation x y (j+1) := by - classical - choose a b hab using fun i => (mem_pairRelation x y (v i)).mp (hv i) - have he : v = x • a + y • b := funext hab - rw [he, map_add, map_smul, map_smul] - apply (jetRelation x y (j+1)).add_mem - · exact ⟨Fin.cons 0 a, binarySum_prepend_zero x y j a⟩ - · exact ⟨Fin.snoc b 0, binarySum_append_zero x y j b⟩ - - - -theorem binarySum_mem_next_iff (x y : R) - (hx : Function.Injective (fun m : M => x • m)) - (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) - (j : ℕ) (v : Fin (j+1) → M) : - binarySum x y j v ∈ jetRelation x y (j+1) ↔ ∀ i, v i ∈ pairRelation x y := by - constructor - · rintro ⟨w,hw⟩ - let c : Fin (j+1) → M := x • (fun i => w i.succ) + Pi.single 0 (y • w 0) - have hc : ∀ i, c i ∈ pairRelation x y := by - intro i - apply (pairRelation x y).add_mem (x_smul_mem_pairRelation x y _) - classical - by_cases hi : i = 0 - · subst i - simp only [Pi.single_eq_same] - exact y_smul_mem_pairRelation x y _ - · simp [Pi.single_eq_of_ne hi] - have hbc : binarySum x y j c = binarySum x y (j+1) w := by - change binarySum x y j (x • (fun i => w i.succ) + Pi.single 0 (y • w 0)) = _ - rw [map_add, map_smul, binarySum_single_zero, binarySum_succ, ← mul_smul, ← pow_succ] - exact add_comm _ _ - have hz : binarySum x y j (v-c) = 0 := by rw [map_sub, hbc, hw, sub_self] - have hh := binarySum_kernel_coefficients x y hx hy j (v-c) hz - intro i - have hi := (pairRelation x y).add_mem (hh i) (hc i) - simpa only [Pi.sub_apply, sub_add_cancel] using hi - · exact binarySum_pairRelation x y j v - -abbrev jetLayer (x y : R) (j : ℕ) := - (jetRelation (M := M) x y j) ⧸ - ((jetRelation x y (j+1)).comap (jetRelation x y j).subtype) - -def jetLayerMap (x y : R) (j : ℕ) : (Fin (j+1) → M) →ₗ[R] jetLayer (M := M) x y j := - ((jetRelation x y (j+1)).comap (jetRelation x y j).subtype).mkQ.comp - (binarySum x y j).rangeRestrict - -lemma jetLayerMap_surjective (x y : R) (j : ℕ) : - Function.Surjective (jetLayerMap (M := M) x y j) := - ((jetRelation x y (j+1)).comap (jetRelation x y j).subtype).mkQ_surjective.comp - (by rintro ⟨m,v,rfl⟩; exact ⟨v,rfl⟩) - -lemma jetLayerMap_eq_zero_iff (x y : R) (j : ℕ) (v : Fin (j+1) → M) : - jetLayerMap x y j v = 0 ↔ binarySum x y j v ∈ jetRelation x y (j+1) := by - exact Submodule.Quotient.mk_eq_zero _ - -def originCoefficientMap (x y : R) (j : ℕ) : - (Fin (j+1) → M) →ₗ[R] (Fin (j+1) → (M ⧸ pairRelation (M := M) x y)) := - LinearMap.pi (fun i => (pairRelation x y).mkQ.comp (LinearMap.proj i)) - -lemma originCoefficientMap_surjective (x y : R) (j : ℕ) : - Function.Surjective (originCoefficientMap (M := M) x y j) := by - intro v - choose w hw using fun i => (pairRelation (M := M) x y).mkQ_surjective (v i) - exact ⟨w, funext hw⟩ - -lemma originCoefficientMap_eq_zero_iff (x y : R) (j : ℕ) (v : Fin (j+1) → M) : - originCoefficientMap x y j v = 0 ↔ ∀ i, v i ∈ pairRelation x y := by - constructor - · intro h i - exact (Submodule.Quotient.mk_eq_zero _).mp (congrFun h i) - · intro h - ext i - exact (Submodule.Quotient.mk_eq_zero _).mpr (h i) - -lemma jetLayerMap_ker (x y : R) - (hx : Function.Injective (fun m : M => x • m)) - (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) (j : ℕ) : - (jetLayerMap (M := M) x y j).ker = (originCoefficientMap x y j).ker := by - ext v - exact (jetLayerMap_eq_zero_iff x y j v).trans - ((binarySum_mem_next_iff x y hx hy j v).trans - (originCoefficientMap_eq_zero_iff x y j v).symm) - - - -noncomputable def jetLayerEquiv (x y : R) - (hx : Function.Injective (fun m : M => x • m)) - (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) (j : ℕ) : - (Fin (j+1) → (M ⧸ pairRelation (M := M) x y)) ≃ₗ[R] jetLayer (M := M) x y j := - ((originCoefficientMap x y j).quotKerEquivOfSurjective - (originCoefficientMap_surjective x y j)).symm ≪≫ₗ - (Submodule.quotEquivOfEq _ _ (jetLayerMap_ker x y hx hy j).symm) ≪≫ₗ - (jetLayerMap x y j).quotKerEquivOfSurjective (jetLayerMap_surjective x y j) - -lemma jetLayerEquiv_apply (x y : R) - (hx : Function.Injective (fun m : M => x • m)) - (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) - (j : ℕ) (v : Fin (j+1) → M) : - jetLayerEquiv x y hx hy j (originCoefficientMap x y j v) = jetLayerMap x y j v := by - simp only [jetLayerEquiv, LinearEquiv.trans_apply, - LinearMap.quotKerEquivOfSurjective_symm_apply, Submodule.quotEquivOfEq_mk, - LinearMap.quotKerEquivOfSurjective_apply_mk] -end FiberFunctorProof -end - -end OAI +import Mathlib + +namespace OAI + +/-! Binary sums, jet relations and their layer quotients. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +open scoped BigOperators Pointwise + +variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M] + + +def binarySum (x y : R) (n : ℕ) : (Fin (n+1) → M) →ₗ[R] M := + ∑ i : Fin (n+1), (x^i.val * y^(n-i.val)) • LinearMap.proj i + +lemma binarySum_apply (x y : R) (n : ℕ) (v : Fin (n+1) → M) : + binarySum x y n v = ∑ i : Fin (n+1), (x^i.val * y^(n-i.val)) • v i := by + simp [binarySum] + +lemma binarySum_zero (x y : R) (v : Fin 1 → M) : binarySum x y 0 v = v 0 := by + simp [binarySum_apply] + +lemma binarySum_succ (x y : R) (n : ℕ) (v : Fin (n+2) → M) : + binarySum x y (n+1) v = y^(n+1) • v 0 + x • binarySum x y n (fun i => v i.succ) := by + rw [binarySum_apply, Fin.sum_univ_succ, binarySum_apply, Finset.smul_sum] + simp only [Fin.val_zero, pow_zero, Nat.sub_zero, one_mul, Fin.val_succ, Nat.add_sub_add_right] + congr 1 + apply Finset.sum_congr rfl + intro i _ + rw [pow_succ, mul_comm (x^i.val) x, mul_assoc, mul_smul] + +lemma binarySum_single_zero (x y : R) (n : ℕ) (v : M) : + binarySum x y n (Pi.single 0 v) = y^n • v := by + classical + rw [binarySum_apply, Finset.sum_eq_single 0] + · simp + · intro i _ hi + simp [Pi.single_eq_of_ne hi] + · simp + + +def pairRelation (x y : R) : Submodule R M := + x • (⊤ : Submodule R M) ⊔ y • (⊤ : Submodule R M) + +lemma x_smul_mem_pairRelation (x y : R) (v : M) : x • v ∈ pairRelation x y := + (show x • (⊤ : Submodule R M) ≤ pairRelation x y from le_sup_left) + (Submodule.smul_mem_pointwise_smul v x ⊤ (by trivial)) + +lemma y_smul_mem_pairRelation (x y : R) (v : M) : y • v ∈ pairRelation x y := + (show y • (⊤ : Submodule R M) ≤ pairRelation x y from le_sup_right) + (Submodule.smul_mem_pointwise_smul v y ⊤ (by trivial)) + +lemma regular_pair_y_pow (x y : R) + (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) + (j : ℕ) (v n : M) (h : y^j • v = x • n) : ∃ w : M, v = x • w := by + induction j generalizing n with + | zero => exact ⟨n, by simpa using h⟩ + | succ j ih => + obtain ⟨w,hw⟩ := hy (y^j • v) n (by simpa only [pow_succ', mul_smul] using h) + exact ih w hw + + + +theorem binarySum_kernel_coefficients (x y : R) + (hx : Function.Injective (fun m : M => x • m)) + (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) + (j : ℕ) (v : Fin (j+1) → M) (hv : binarySum x y j v = 0) : + ∀ i, v i ∈ pairRelation x y := by + classical + induction j with + | zero => + intro i + have hi : i = 0 := Fin.ext (by omega) + rw [binarySum_zero] at hv + rw [hi, hv] + exact Submodule.zero_mem _ + | succ j ih => + have h0 : y^(j+1) • v 0 = x • (-binarySum x y j (fun i => v i.succ)) := by + rw [smul_neg] + exact eq_neg_of_add_eq_zero_left ((binarySum_succ x y j v) ▸ hv) + obtain ⟨w,hw⟩ := regular_pair_y_pow x y hy (j+1) (v 0) _ h0 + let v' : Fin (j+1) → M := (fun i => v i.succ) + Pi.single 0 (y • w) + have hv' : binarySum x y j v' = 0 := by + apply hx + change x • binarySum x y j v' = x • (0 : M) + rw [smul_zero] + have he : x • binarySum x y j v' = binarySum x y (j+1) v := by + change x • binarySum x y j ((fun i => v i.succ) + Pi.single 0 (y • w)) = _ + rw [map_add, binarySum_single_zero, smul_add, binarySum_succ, hw] + rw [smul_comm (y^(j+1)) x, ← mul_smul (y^j) y w, ← pow_succ] + exact add_comm _ _ + exact he.trans hv + have hc := ih v' hv' + intro i + refine Fin.cases ?_ (fun i => ?_) i + · rw [hw] + exact x_smul_mem_pairRelation x y w + · have hu : (Pi.single (0 : Fin (j+1)) (y • w) : Fin (j+1) → M) i ∈ pairRelation x y := by + by_cases hi : i = 0 + · subst i + simpa using y_smul_mem_pairRelation x y w + · simp [Pi.single_eq_of_ne hi] + have hh := (pairRelation (M := M) x y).sub_mem (hc i) hu + simpa only [v', Pi.add_apply, add_sub_cancel_right] using hh + +lemma binarySum_succ_last (x y : R) (n : ℕ) (v : Fin (n+2) → M) : + binarySum x y (n+1) v = y • binarySum x y n (fun i => v i.castSucc) + x^(n+1) • v (Fin.last _) := by + rw [binarySum_apply, Fin.sum_univ_castSucc, binarySum_apply, Finset.smul_sum] + simp only [Fin.val_last, Nat.sub_self, pow_zero, mul_one, Fin.val_castSucc] + congr 1 + apply Finset.sum_congr rfl + intro i _ + have hi : n+1-i.val = (n-i.val)+1 := by omega + rw [hi, pow_succ, ← mul_assoc, mul_comm (x^i.val * y^(n-i.val)) y, mul_smul] + +lemma binarySum_prepend_zero (x y : R) (n : ℕ) (v : Fin (n+1) → M) : + binarySum x y (n+1) (Fin.cons 0 v) = x • binarySum x y n v := by + rw [binarySum_succ] + simp + +lemma binarySum_append_zero (x y : R) (n : ℕ) (v : Fin (n+1) → M) : + binarySum x y (n+1) (Fin.snoc v 0) = y • binarySum x y n v := by + rw [binarySum_succ_last] + simp + + +def jetRelation (x y : R) (j : ℕ) : Submodule R M := (binarySum x y j).range + +lemma jetRelation_zero (x y : R) : jetRelation (M := M) x y 0 = ⊤ := by + apply LinearMap.range_eq_top.mpr + intro m + exact ⟨fun _ => m, binarySum_zero x y _⟩ + +lemma mem_pairRelation (x y : R) (m : M) : m ∈ pairRelation x y ↔ ∃ a b : M, m = x • a + y • b := by + constructor + · intro h + obtain ⟨a,ha,b,hb,rfl⟩ := Submodule.mem_sup.mp h + obtain ⟨a',_,rfl⟩ := (Submodule.mem_smul_pointwise_iff_exists a x ⊤).mp ha + obtain ⟨b',_,rfl⟩ := (Submodule.mem_smul_pointwise_iff_exists b y ⊤).mp hb + exact ⟨a',b',rfl⟩ + · rintro ⟨a,b,rfl⟩ + exact (pairRelation x y).add_mem (x_smul_mem_pairRelation x y a) (y_smul_mem_pairRelation x y b) + +lemma jetRelation_one (x y : R) : jetRelation (M := M) x y 1 = pairRelation x y := by + ext m + constructor + · rintro ⟨v,rfl⟩ + rw [binarySum_succ, binarySum_zero] + simpa only [Nat.zero_add, pow_one] using + (pairRelation x y).add_mem (y_smul_mem_pairRelation x y (v 0)) + (x_smul_mem_pairRelation x y (v (Fin.succ 0))) + · intro hm + obtain ⟨a,b,rfl⟩ := (mem_pairRelation x y m).mp hm + refine ⟨Fin.cons b (fun _ => a), ?_⟩ + rw [binarySum_succ, binarySum_zero] + simp [add_comm] + +lemma jetRelation_succ_le (x y : R) (j : ℕ) : + jetRelation (M := M) x y (j+1) ≤ jetRelation x y j := by + rintro m ⟨v,rfl⟩ + refine ⟨x • (fun i => v i.succ) + Pi.single 0 (y • v 0), ?_⟩ + rw [map_add, map_smul, binarySum_single_zero, binarySum_succ, ← mul_smul, ← pow_succ] + exact add_comm _ _ + +lemma binarySum_pairRelation (x y : R) (j : ℕ) (v : Fin (j+1) → M) + (hv : ∀ i, v i ∈ pairRelation x y) : + binarySum x y j v ∈ jetRelation x y (j+1) := by + classical + choose a b hab using fun i => (mem_pairRelation x y (v i)).mp (hv i) + have he : v = x • a + y • b := funext hab + rw [he, map_add, map_smul, map_smul] + apply (jetRelation x y (j+1)).add_mem + · exact ⟨Fin.cons 0 a, binarySum_prepend_zero x y j a⟩ + · exact ⟨Fin.snoc b 0, binarySum_append_zero x y j b⟩ + + + +theorem binarySum_mem_next_iff (x y : R) + (hx : Function.Injective (fun m : M => x • m)) + (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) + (j : ℕ) (v : Fin (j+1) → M) : + binarySum x y j v ∈ jetRelation x y (j+1) ↔ ∀ i, v i ∈ pairRelation x y := by + constructor + · rintro ⟨w,hw⟩ + let c : Fin (j+1) → M := x • (fun i => w i.succ) + Pi.single 0 (y • w 0) + have hc : ∀ i, c i ∈ pairRelation x y := by + intro i + apply (pairRelation x y).add_mem (x_smul_mem_pairRelation x y _) + classical + by_cases hi : i = 0 + · subst i + simp only [Pi.single_eq_same] + exact y_smul_mem_pairRelation x y _ + · simp [Pi.single_eq_of_ne hi] + have hbc : binarySum x y j c = binarySum x y (j+1) w := by + change binarySum x y j (x • (fun i => w i.succ) + Pi.single 0 (y • w 0)) = _ + rw [map_add, map_smul, binarySum_single_zero, binarySum_succ, ← mul_smul, ← pow_succ] + exact add_comm _ _ + have hz : binarySum x y j (v-c) = 0 := by rw [map_sub, hbc, hw, sub_self] + have hh := binarySum_kernel_coefficients x y hx hy j (v-c) hz + intro i + have hi := (pairRelation x y).add_mem (hh i) (hc i) + simpa only [Pi.sub_apply, sub_add_cancel] using hi + · exact binarySum_pairRelation x y j v + +abbrev jetLayer (x y : R) (j : ℕ) := + (jetRelation (M := M) x y j) ⧸ + ((jetRelation x y (j+1)).comap (jetRelation x y j).subtype) + +def jetLayerMap (x y : R) (j : ℕ) : (Fin (j+1) → M) →ₗ[R] jetLayer (M := M) x y j := + ((jetRelation x y (j+1)).comap (jetRelation x y j).subtype).mkQ.comp + (binarySum x y j).rangeRestrict + +lemma jetLayerMap_surjective (x y : R) (j : ℕ) : + Function.Surjective (jetLayerMap (M := M) x y j) := + ((jetRelation x y (j+1)).comap (jetRelation x y j).subtype).mkQ_surjective.comp + (by rintro ⟨m,v,rfl⟩; exact ⟨v,rfl⟩) + +lemma jetLayerMap_eq_zero_iff (x y : R) (j : ℕ) (v : Fin (j+1) → M) : + jetLayerMap x y j v = 0 ↔ binarySum x y j v ∈ jetRelation x y (j+1) := by + exact Submodule.Quotient.mk_eq_zero _ + +def originCoefficientMap (x y : R) (j : ℕ) : + (Fin (j+1) → M) →ₗ[R] (Fin (j+1) → (M ⧸ pairRelation (M := M) x y)) := + LinearMap.pi (fun i => (pairRelation x y).mkQ.comp (LinearMap.proj i)) + +lemma originCoefficientMap_surjective (x y : R) (j : ℕ) : + Function.Surjective (originCoefficientMap (M := M) x y j) := by + intro v + choose w hw using fun i => (pairRelation (M := M) x y).mkQ_surjective (v i) + exact ⟨w, funext hw⟩ + +lemma originCoefficientMap_eq_zero_iff (x y : R) (j : ℕ) (v : Fin (j+1) → M) : + originCoefficientMap x y j v = 0 ↔ ∀ i, v i ∈ pairRelation x y := by + constructor + · intro h i + exact (Submodule.Quotient.mk_eq_zero _).mp (congrFun h i) + · intro h + ext i + exact (Submodule.Quotient.mk_eq_zero _).mpr (h i) + +lemma jetLayerMap_ker (x y : R) + (hx : Function.Injective (fun m : M => x • m)) + (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) (j : ℕ) : + (jetLayerMap (M := M) x y j).ker = (originCoefficientMap x y j).ker := by + ext v + exact (jetLayerMap_eq_zero_iff x y j v).trans + ((binarySum_mem_next_iff x y hx hy j v).trans + (originCoefficientMap_eq_zero_iff x y j v).symm) + + + +noncomputable def jetLayerEquiv (x y : R) + (hx : Function.Injective (fun m : M => x • m)) + (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) (j : ℕ) : + (Fin (j+1) → (M ⧸ pairRelation (M := M) x y)) ≃ₗ[R] jetLayer (M := M) x y j := + ((originCoefficientMap x y j).quotKerEquivOfSurjective + (originCoefficientMap_surjective x y j)).symm ≪≫ₗ + (Submodule.quotEquivOfEq _ _ (jetLayerMap_ker x y hx hy j).symm) ≪≫ₗ + (jetLayerMap x y j).quotKerEquivOfSurjective (jetLayerMap_surjective x y j) + +lemma jetLayerEquiv_apply (x y : R) + (hx : Function.Injective (fun m : M => x • m)) + (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) + (j : ℕ) (v : Fin (j+1) → M) : + jetLayerEquiv x y hx hy j (originCoefficientMap x y j v) = jetLayerMap x y j v := by + simp only [jetLayerEquiv, LinearEquiv.trans_apply, + LinearMap.quotKerEquivOfSurjective_symm_apply, Submodule.quotEquivOfEq_mk, + LinearMap.quotKerEquivOfSurjective_apply_mk] +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/JetRepresentations.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/JetRepresentations.lean index 78238503f577324b9a2c32715bc5bd1da11c214b..cd97d33e5ae767926a9f134855854c88257f22d1 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/JetRepresentations.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/JetRepresentations.lean @@ -1,357 +1,357 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.JetRelations -import OAI.RepresentationTheory.RestrictedTilting.WeightBounds - -namespace OAI - -/-! Plane jet modules, homogeneous layers and equivariant inclusions. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -open scoped TensorProduct BigOperators Pointwise -universe u -variable (k : Type u) [Field k] -variable {M : Type u} [AddCommGroup M] [Module k M] - [Module (MvPolynomial (Fin 2) k) M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] - -noncomputable abbrev planeJetRelation (j : ℕ) : Submodule k M := - (jetRelation (M := M) (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) j).restrictScalars k - -noncomputable def jetMonomialBasis (j : ℕ) : - Module.Basis (Fin (j+1)) k (MvPolynomial.homogeneousSubmodule (Fin 2) k j) := - (binaryBasis k j).reindex Fin.revPerm - -lemma jetMonomialBasis_apply (j : ℕ) (i : Fin (j+1)) : - (jetMonomialBasis k j i).val = - (MvPolynomial.X 0 : MvPolynomial (Fin 2) k)^i.val * MvPolynomial.X 1^(j-i.val) := by - simp only [jetMonomialBasis, Module.Basis.reindex_apply, Fin.revPerm_symm, - Fin.revPerm_apply, binaryBasis_apply, Fin.val_rev] - congr 2 <;> omega - -lemma homogeneous_smul_mem_jet (j : ℕ) - (P : MvPolynomial.homogeneousSubmodule (Fin 2) k j) (v : M) : - P.val • v ∈ planeJetRelation (M := M) k j := by - have hp := (jetMonomialBasis k j).sum_repr P - have hv := congrArg (fun Q : MvPolynomial.homogeneousSubmodule (Fin 2) k j => Q.val • v) hp - have he : P.val • v = binarySum (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) j - (fun i => (jetMonomialBasis k j).repr P i • v) := by - rw [← hv, binarySum_apply] - simp only [Submodule.coe_sum, Submodule.coe_smul_of_tower, Finset.sum_smul, - jetMonomialBasis_apply, smul_assoc] - apply Finset.sum_congr rfl - intro i _ - exact smul_comm _ _ _ - exact ⟨_,he.symm⟩ - -lemma homogeneous_smul_pair_mem_next (j : ℕ) - (P : MvPolynomial.homogeneousSubmodule (Fin 2) k j) (v : M) - (hv : v ∈ planeJetRelation (M := M) k 1) : P.val • v ∈ planeJetRelation (M := M) k (j+1) := by - have hp := (jetMonomialBasis k j).sum_repr P - have he : P.val • v = binarySum (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) j - (fun i => (jetMonomialBasis k j).repr P i • v) := by - rw [← congrArg (fun Q : MvPolynomial.homogeneousSubmodule (Fin 2) k j => Q.val • v) hp, - binarySum_apply] - simp only [Submodule.coe_sum, Submodule.coe_smul_of_tower, Finset.sum_smul, - jetMonomialBasis_apply, smul_assoc] - apply Finset.sum_congr rfl - intro i _ - exact smul_comm _ _ _ - rw [he] - apply binarySum_pairRelation - intro i - change _ ∈ (jetRelation (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) 1).restrictScalars k at hv - have : (jetMonomialBasis k j).repr P i • v ∈ planeJetRelation (M := M) k 1 := - (planeJetRelation (M := M) k 1).smul_mem _ hv - simpa only [planeJetRelation, Submodule.restrictScalars_mem, jetRelation_one] using this - - -def PlaneCompatible (σ : Representation k (SL2 k) M) : Prop := - ∀ (g : SL2 k) (P : MvPolynomial (Fin 2) k) (v : M), - σ g (P • v) = linearChange (dualMatrix k g) P • σ g v - -lemma planeJetRelation_stable (σ : Representation k (SL2 k) M) - (hσ : PlaneCompatible k σ) (j : ℕ) (g : SL2 k) : - planeJetRelation (M := M) k j ≤ (planeJetRelation (M := M) k j).comap (σ g) := by - rintro m ⟨v,rfl⟩ - change σ g (binarySum (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) j v) ∈ planeJetRelation (M := M) k j - rw [binarySum_apply, map_sum] - apply (planeJetRelation (M := M) k j).sum_mem - intro i _ - rw [hσ] - have hh : ((MvPolynomial.X 0 : MvPolynomial (Fin 2) k)^i.val * - MvPolynomial.X 1^(j-i.val)).IsHomogeneous j := by - rw [← jetMonomialBasis_apply k j i] - exact (jetMonomialBasis k j i).property - exact homogeneous_smul_mem_jet k j - ⟨_, linearChange_homogeneous (dualMatrix k g) hh⟩ _ - -noncomputable def planeJetRep (σ : Representation k (SL2 k) M) - (hσ : PlaneCompatible k σ) (j : ℕ) : - Representation k (SL2 k) (M ⧸ planeJetRelation (M := M) k j) := - Representation.quotient σ (planeJetRelation (M := M) k j) (planeJetRelation_stable k σ hσ j) - -lemma planeJetRep_mk (σ : Representation k (SL2 k) M) - (hσ : PlaneCompatible k σ) (j : ℕ) (g : SL2 k) (v : M) : - planeJetRep k σ hσ j g ((planeJetRelation (M := M) k j).mkQ v) = - (planeJetRelation (M := M) k j).mkQ (σ g v) := rfl - -lemma planeJetRep_rational (σ : Representation k (SL2 k) M) - (hσ : PlaneCompatible k σ) (hr : IsRational k σ) (j : ℕ) : - IsRational k (planeJetRep k σ hσ j) := by - intro v l - obtain ⟨w, rfl⟩ := (planeJetRelation (M := M) k j).mkQ_surjective v - obtain ⟨P,hP⟩ := hr w (l.comp (planeJetRelation (M := M) k j).mkQ) - exact ⟨P,hP⟩ - -noncomputable abbrev planeJetLayerRelation (j : ℕ) : Submodule k (planeJetRelation (M := M) k j) := - (planeJetRelation (M := M) k (j+1)).comap (planeJetRelation (M := M) k j).subtype -noncomputable abbrev planeJetLayer (j : ℕ) := (planeJetRelation (M := M) k j) ⧸ planeJetLayerRelation (M := M) k j - -noncomputable def planeHomogeneousMultiply (j : ℕ) - (P : MvPolynomial.homogeneousSubmodule (Fin 2) k j) : M →ₗ[k] planeJetRelation (M := M) k j where - toFun v := ⟨P.val • v, homogeneous_smul_mem_jet k j P v⟩ - map_add' _ _ := Subtype.ext (smul_add _ _ _) - map_smul' _ _ := Subtype.ext (smul_comm _ _ _) - -noncomputable def planeLayerMul (j : ℕ) (P : MvPolynomial.homogeneousSubmodule (Fin 2) k j) : - M →ₗ[k] planeJetLayer (M := M) k j := - (planeJetLayerRelation (M := M) k j).mkQ.comp (planeHomogeneousMultiply k j P) - -lemma planeLayerMul_ker (j : ℕ) (P : MvPolynomial.homogeneousSubmodule (Fin 2) k j) : - planeJetRelation (M := M) k 1 ≤ (planeLayerMul k j P).ker := by - intro v hv - exact (Submodule.Quotient.mk_eq_zero _).mpr (homogeneous_smul_pair_mem_next k j P v hv) - -noncomputable def planeLayerBilinear (j : ℕ) : - (MvPolynomial.homogeneousSubmodule (Fin 2) k j) →ₗ[k] - ((M ⧸ planeJetRelation (M := M) k 1) →ₗ[k] planeJetLayer (M := M) k j) where - toFun P := (planeJetRelation (M := M) k 1).liftQ (planeLayerMul k j P) (planeLayerMul_ker k j P) - map_add' P Q := by - apply LinearMap.ext - intro t - obtain ⟨v,rfl⟩ := (planeJetRelation (M := M) k 1).mkQ_surjective t - change (planeJetLayerRelation (M := M) k j).mkQ _ = - (planeJetLayerRelation (M := M) k j).mkQ _ + (planeJetLayerRelation (M := M) k j).mkQ _ - rw [← map_add] - congr 1 - exact Subtype.ext (add_smul P.val Q.val v) - map_smul' a P := by - apply LinearMap.ext - intro t - obtain ⟨v,rfl⟩ := (planeJetRelation (M := M) k 1).mkQ_surjective t - change (planeJetLayerRelation (M := M) k j).mkQ _ = a • (planeJetLayerRelation (M := M) k j).mkQ _ - rw [← map_smul] - congr 1 - exact Subtype.ext (smul_assoc a P.val v) - -noncomputable def planeLayerMultiply (j : ℕ) : - (MvPolynomial.homogeneousSubmodule (Fin 2) k j) ⊗[k] - (M ⧸ planeJetRelation (M := M) k 1) →ₗ[k] planeJetLayer (M := M) k j := - TensorProduct.lift (planeLayerBilinear k j) - -lemma planeLayerMultiply_tmul_mk (j : ℕ) - (P : MvPolynomial.homogeneousSubmodule (Fin 2) k j) (v : M) : - planeLayerMultiply k j (P ⊗ₜ[k] (planeJetRelation (M := M) k 1).mkQ v) = - (planeJetLayerRelation (M := M) k j).mkQ ⟨P.val • v, homogeneous_smul_mem_jet k j P v⟩ := rfl - -lemma planeLayerMultiply_sum (j : ℕ) (v : Fin (j+1) → M) : - planeLayerMultiply k j (∑ i, jetMonomialBasis k j i ⊗ₜ[k] (planeJetRelation (M := M) k 1).mkQ (v i)) = - (planeJetLayerRelation (M := M) k j).mkQ - ⟨binarySum (MvPolynomial.X 0) (MvPolynomial.X 1) j v, ⟨v,rfl⟩⟩ := by - rw [map_sum] - simp only [planeLayerMultiply_tmul_mk, ← map_sum] - congr 1 - apply Subtype.ext - simp only [Submodule.coe_sum, jetMonomialBasis_apply, binarySum_apply] - -lemma tensor_basis_decomposition {H T : Type u} [AddCommGroup H] [Module k H] - [AddCommGroup T] [Module k T] {ι : Type*} [Fintype ι] - (b : Module.Basis ι k H) (z : H ⊗[k] T) : - ∃ v : ι → T, z = ∑ i, b i ⊗ₜ[k] v i := by - classical - induction z using TensorProduct.inductionOn with - | tmul h t => - refine ⟨fun i => b.repr h i • t, ?_⟩ - conv_lhs => rw [← b.sum_repr h, TensorProduct.sum_tmul] - apply Finset.sum_congr rfl - intro i _ - rw [TensorProduct.smul_tmul, TensorProduct.tmul_smul] - | add z w hz hw => - obtain ⟨v,rfl⟩ := hz - obtain ⟨w,rfl⟩ := hw - exact ⟨v+w, by simp only [Pi.add_apply, TensorProduct.tmul_add, Finset.sum_add_distrib]⟩ - -lemma planeLayerMultiply_surjective (j : ℕ) : - Function.Surjective (planeLayerMultiply (M := M) k j) := by - intro z - obtain ⟨⟨m,v,rfl⟩,rfl⟩ := (planeJetLayerRelation (M := M) k j).mkQ_surjective z - exact ⟨_, planeLayerMultiply_sum k j v⟩ - -lemma planeLayerMultiply_injective - (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • m)) - (hy : ∀ v n : M, (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) • v = - (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n → - ∃ w : M, v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • w) (j : ℕ) : - Function.Injective (planeLayerMultiply (M := M) k j) := by - have hzero : ∀ z, planeLayerMultiply (M := M) k j z = 0 → z = 0 := by - intro z hz - obtain ⟨v,rfl⟩ := tensor_basis_decomposition k (jetMonomialBasis k j) z - choose w hw using fun i => (planeJetRelation (M := M) k 1).mkQ_surjective (v i) - have he : v = fun i => (planeJetRelation (M := M) k 1).mkQ (w i) := funext fun i => (hw i).symm - rw [he, planeLayerMultiply_sum] at hz - have hm := (Submodule.Quotient.mk_eq_zero _).mp hz - have hc := (binarySum_mem_next_iff (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) - (MvPolynomial.X 1) hx hy j w).mp hm - have hv : ∀ i, v i = 0 := by - intro i - rw [← hw i] - apply (Submodule.Quotient.mk_eq_zero _).mpr - simpa only [planeJetRelation, Submodule.restrictScalars_mem, jetRelation_one] using hc i - simp only [hv, TensorProduct.tmul_zero, Finset.sum_const_zero] - intro a b hab - apply sub_eq_zero.mp - apply hzero - rw [map_sub,hab,sub_self] - -noncomputable def planeLayerEquiv - (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • m)) - (hy : ∀ v n : M, (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) • v = - (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n → - ∃ w : M, v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • w) (j : ℕ) : - (MvPolynomial.homogeneousSubmodule (Fin 2) k j) ⊗[k] - (M ⧸ planeJetRelation (M := M) k 1) ≃ₗ[k] planeJetLayer (M := M) k j := - LinearEquiv.ofBijective (planeLayerMultiply k j) - ⟨planeLayerMultiply_injective k hx hy j, planeLayerMultiply_surjective k j⟩ - -noncomputable def planeJetSubrep (σ : Representation k (SL2 k) M) - (hσ : PlaneCompatible k σ) (j : ℕ) : - Representation k (SL2 k) (planeJetRelation (M := M) k j) := - Representation.subrepresentation σ _ (planeJetRelation_stable k σ hσ j) - -lemma planeJetLayerRelation_stable (σ : Representation k (SL2 k) M) - (hσ : PlaneCompatible k σ) (j : ℕ) (g : SL2 k) : - planeJetLayerRelation (M := M) k j ≤ - (planeJetLayerRelation k j).comap (planeJetSubrep k σ hσ j g) := by - intro v hv - exact planeJetRelation_stable k σ hσ (j+1) g hv - -noncomputable def planeJetLayerRep (σ : Representation k (SL2 k) M) - (hσ : PlaneCompatible k σ) (j : ℕ) : - Representation k (SL2 k) (planeJetLayer (M := M) k j) := - Representation.quotient (planeJetSubrep k σ hσ j) _ - (planeJetLayerRelation_stable k σ hσ j) - -lemma planeLayerMultiply_intertwines (σ : Representation k (SL2 k) M) - (hσ : PlaneCompatible k σ) (j : ℕ) (g : SL2 k) - (z : (MvPolynomial.homogeneousSubmodule (Fin 2) k j) ⊗[k] - (M ⧸ planeJetRelation (M := M) k 1)) : - planeLayerMultiply (M := M) k j - (Representation.tprod ((homogeneousRepresentation j).comp (dualMatrix k)) - (planeJetRep k σ hσ 1) g z) = - planeJetLayerRep k σ hσ j g (planeLayerMultiply k j z) := by - induction z using TensorProduct.inductionOn with - | tmul P v => - obtain ⟨w,rfl⟩ := (planeJetRelation (M := M) k 1).mkQ_surjective v - simp only [Representation.tprod_apply, TensorProduct.map_tmul, - planeJetRep_mk, planeLayerMultiply_tmul_mk] - change (planeJetLayerRelation k j).mkQ ⟨_,_⟩ = - (planeJetLayerRelation k j).mkQ ⟨σ g (P.val • w),_⟩ - congr 1 - apply Subtype.ext - exact (hσ g P.val w).symm - | add x y hx hy => simp only [map_add, hx, hy] - -lemma planeLayer_finite [Module.Finite k (M ⧸ planeJetRelation (M := M) k 1)] (j : ℕ) : - Module.Finite k (planeJetLayer (M := M) k j) := - Module.Finite.of_surjective (planeLayerMultiply k j) (planeLayerMultiply_surjective k j) - -lemma planeJetRelation_succ_le (j : ℕ) : - planeJetRelation (M := M) k (j+1) ≤ planeJetRelation (M := M) k j := - jetRelation_succ_le (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) j - -lemma planeJetRelation_zero : planeJetRelation (M := M) k 0 = ⊤ := by - simp only [planeJetRelation, jetRelation_zero, Submodule.restrictScalars_top] - -noncomputable def planeJetTransition (j : ℕ) : - (M ⧸ planeJetRelation (M := M) k (j+1)) →ₗ[k] (M ⧸ planeJetRelation (M := M) k j) := - (planeJetRelation k (j+1)).mapQ (planeJetRelation k j) LinearMap.id - (planeJetRelation_succ_le k j) - -lemma planeJetTransition_mk (j : ℕ) (v : M) : - planeJetTransition k j ((planeJetRelation (M := M) k (j+1)).mkQ v) = - (planeJetRelation (M := M) k j).mkQ v := rfl - -lemma planeJetTransition_surjective (j : ℕ) : - Function.Surjective (planeJetTransition (M := M) k j) := by - intro v - obtain ⟨w,rfl⟩ := (planeJetRelation (M := M) k j).mkQ_surjective v - exact ⟨(planeJetRelation k (j+1)).mkQ w,rfl⟩ - -noncomputable def planeJetLayerInclusion (j : ℕ) : - planeJetLayer (M := M) k j →ₗ[k] (M ⧸ planeJetRelation (M := M) k (j+1)) := - (planeJetLayerRelation k j).liftQ - ((planeJetRelation k (j+1)).mkQ.comp (planeJetRelation k j).subtype) (by - intro v hv - exact (Submodule.Quotient.mk_eq_zero _).mpr hv) - -lemma planeJetLayerInclusion_mk (j : ℕ) (v : planeJetRelation (M := M) k j) : - planeJetLayerInclusion k j ((planeJetLayerRelation k j).mkQ v) = - (planeJetRelation (M := M) k (j+1)).mkQ v.val := rfl - -lemma planeJetLayerInclusion_injective (j : ℕ) : - Function.Injective (planeJetLayerInclusion (M := M) k j) := by - apply (LinearMap.ker_eq_bot (f := planeJetLayerInclusion (M := M) k j)).mp - apply (LinearMap.ker_eq_bot' (f := planeJetLayerInclusion (M := M) k j)).mpr - intro v hv - obtain ⟨w,rfl⟩ := (planeJetLayerRelation (M := M) k j).mkQ_surjective v - rw [planeJetLayerInclusion_mk] at hv - have hw : w.val ∈ planeJetRelation (M := M) k (j+1) := - (Submodule.Quotient.mk_eq_zero (planeJetRelation k (j+1))).mp hv - exact (Submodule.Quotient.mk_eq_zero _).mpr hw - -lemma planeJet_shortExact (j : ℕ) : - Function.Exact (planeJetLayerInclusion (M := M) k j) (planeJetTransition k j) := by - intro v - obtain ⟨w,rfl⟩ := (planeJetRelation (M := M) k (j+1)).mkQ_surjective v - constructor - · intro hw - have hj : w ∈ planeJetRelation (M := M) k j := (Submodule.Quotient.mk_eq_zero _).mp hw - exact ⟨(planeJetLayerRelation k j).mkQ ⟨w,hj⟩,rfl⟩ - · rintro ⟨z,hz⟩ - obtain ⟨t,rfl⟩ := (planeJetLayerRelation (M := M) k j).mkQ_surjective z - rw [← hz, planeJetLayerInclusion_mk, planeJetTransition_mk] - exact (Submodule.Quotient.mk_eq_zero _).mpr t.property - -lemma planeJet_finite [Module.Finite k (M ⧸ planeJetRelation (M := M) k 1)] (j : ℕ) : - Module.Finite k (M ⧸ planeJetRelation (M := M) k j) := by - induction j with - | zero => - rw [planeJetRelation_zero] - infer_instance - | succ j ih => - let := ih - let := planeLayer_finite (M := M) k j - exact Module.Finite.of_exact (planeJet_shortExact k j) (planeJetTransition_surjective k j) - -lemma planeJetTransition_intertwines (σ : Representation k (SL2 k) M) - (hσ : PlaneCompatible k σ) (j : ℕ) (g : SL2 k) - (v : M ⧸ planeJetRelation (M := M) k (j+1)) : - planeJetTransition k j (planeJetRep k σ hσ (j+1) g v) = - planeJetRep k σ hσ j g (planeJetTransition k j v) := by - obtain ⟨w,rfl⟩ := (planeJetRelation (M := M) k (j+1)).mkQ_surjective v - rfl - -lemma planeJetLayerInclusion_intertwines (σ : Representation k (SL2 k) M) - (hσ : PlaneCompatible k σ) (j : ℕ) (g : SL2 k) - (v : planeJetLayer (M := M) k j) : - planeJetLayerInclusion k j (planeJetLayerRep k σ hσ j g v) = - planeJetRep k σ hσ (j+1) g (planeJetLayerInclusion k j v) := by - obtain ⟨w,rfl⟩ := (planeJetLayerRelation (M := M) k j).mkQ_surjective v - rfl -end FiberFunctorProof -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.JetRelations +import OAI.RepresentationTheory.RestrictedTilting.WeightBounds + +namespace OAI + +/-! Plane jet modules, homogeneous layers and equivariant inclusions. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +open scoped TensorProduct BigOperators Pointwise +universe u +variable (k : Type u) [Field k] +variable {M : Type u} [AddCommGroup M] [Module k M] + [Module (MvPolynomial (Fin 2) k) M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] + +noncomputable abbrev planeJetRelation (j : ℕ) : Submodule k M := + (jetRelation (M := M) (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) j).restrictScalars k + +noncomputable def jetMonomialBasis (j : ℕ) : + Module.Basis (Fin (j+1)) k (MvPolynomial.homogeneousSubmodule (Fin 2) k j) := + (binaryBasis k j).reindex Fin.revPerm + +lemma jetMonomialBasis_apply (j : ℕ) (i : Fin (j+1)) : + (jetMonomialBasis k j i).val = + (MvPolynomial.X 0 : MvPolynomial (Fin 2) k)^i.val * MvPolynomial.X 1^(j-i.val) := by + simp only [jetMonomialBasis, Module.Basis.reindex_apply, Fin.revPerm_symm, + Fin.revPerm_apply, binaryBasis_apply, Fin.val_rev] + congr 2 <;> omega + +lemma homogeneous_smul_mem_jet (j : ℕ) + (P : MvPolynomial.homogeneousSubmodule (Fin 2) k j) (v : M) : + P.val • v ∈ planeJetRelation (M := M) k j := by + have hp := (jetMonomialBasis k j).sum_repr P + have hv := congrArg (fun Q : MvPolynomial.homogeneousSubmodule (Fin 2) k j => Q.val • v) hp + have he : P.val • v = binarySum (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) j + (fun i => (jetMonomialBasis k j).repr P i • v) := by + rw [← hv, binarySum_apply] + simp only [Submodule.coe_sum, Submodule.coe_smul_of_tower, Finset.sum_smul, + jetMonomialBasis_apply, smul_assoc] + apply Finset.sum_congr rfl + intro i _ + exact smul_comm _ _ _ + exact ⟨_,he.symm⟩ + +lemma homogeneous_smul_pair_mem_next (j : ℕ) + (P : MvPolynomial.homogeneousSubmodule (Fin 2) k j) (v : M) + (hv : v ∈ planeJetRelation (M := M) k 1) : P.val • v ∈ planeJetRelation (M := M) k (j+1) := by + have hp := (jetMonomialBasis k j).sum_repr P + have he : P.val • v = binarySum (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) j + (fun i => (jetMonomialBasis k j).repr P i • v) := by + rw [← congrArg (fun Q : MvPolynomial.homogeneousSubmodule (Fin 2) k j => Q.val • v) hp, + binarySum_apply] + simp only [Submodule.coe_sum, Submodule.coe_smul_of_tower, Finset.sum_smul, + jetMonomialBasis_apply, smul_assoc] + apply Finset.sum_congr rfl + intro i _ + exact smul_comm _ _ _ + rw [he] + apply binarySum_pairRelation + intro i + change _ ∈ (jetRelation (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) 1).restrictScalars k at hv + have : (jetMonomialBasis k j).repr P i • v ∈ planeJetRelation (M := M) k 1 := + (planeJetRelation (M := M) k 1).smul_mem _ hv + simpa only [planeJetRelation, Submodule.restrictScalars_mem, jetRelation_one] using this + + +def PlaneCompatible (σ : Representation k (SL2 k) M) : Prop := + ∀ (g : SL2 k) (P : MvPolynomial (Fin 2) k) (v : M), + σ g (P • v) = linearChange (dualMatrix k g) P • σ g v + +lemma planeJetRelation_stable (σ : Representation k (SL2 k) M) + (hσ : PlaneCompatible k σ) (j : ℕ) (g : SL2 k) : + planeJetRelation (M := M) k j ≤ (planeJetRelation (M := M) k j).comap (σ g) := by + rintro m ⟨v,rfl⟩ + change σ g (binarySum (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) j v) ∈ planeJetRelation (M := M) k j + rw [binarySum_apply, map_sum] + apply (planeJetRelation (M := M) k j).sum_mem + intro i _ + rw [hσ] + have hh : ((MvPolynomial.X 0 : MvPolynomial (Fin 2) k)^i.val * + MvPolynomial.X 1^(j-i.val)).IsHomogeneous j := by + rw [← jetMonomialBasis_apply k j i] + exact (jetMonomialBasis k j i).property + exact homogeneous_smul_mem_jet k j + ⟨_, linearChange_homogeneous (dualMatrix k g) hh⟩ _ + +noncomputable def planeJetRep (σ : Representation k (SL2 k) M) + (hσ : PlaneCompatible k σ) (j : ℕ) : + Representation k (SL2 k) (M ⧸ planeJetRelation (M := M) k j) := + Representation.quotient σ (planeJetRelation (M := M) k j) (planeJetRelation_stable k σ hσ j) + +lemma planeJetRep_mk (σ : Representation k (SL2 k) M) + (hσ : PlaneCompatible k σ) (j : ℕ) (g : SL2 k) (v : M) : + planeJetRep k σ hσ j g ((planeJetRelation (M := M) k j).mkQ v) = + (planeJetRelation (M := M) k j).mkQ (σ g v) := rfl + +lemma planeJetRep_rational (σ : Representation k (SL2 k) M) + (hσ : PlaneCompatible k σ) (hr : IsRational k σ) (j : ℕ) : + IsRational k (planeJetRep k σ hσ j) := by + intro v l + obtain ⟨w, rfl⟩ := (planeJetRelation (M := M) k j).mkQ_surjective v + obtain ⟨P,hP⟩ := hr w (l.comp (planeJetRelation (M := M) k j).mkQ) + exact ⟨P,hP⟩ + +noncomputable abbrev planeJetLayerRelation (j : ℕ) : Submodule k (planeJetRelation (M := M) k j) := + (planeJetRelation (M := M) k (j+1)).comap (planeJetRelation (M := M) k j).subtype +noncomputable abbrev planeJetLayer (j : ℕ) := (planeJetRelation (M := M) k j) ⧸ planeJetLayerRelation (M := M) k j + +noncomputable def planeHomogeneousMultiply (j : ℕ) + (P : MvPolynomial.homogeneousSubmodule (Fin 2) k j) : M →ₗ[k] planeJetRelation (M := M) k j where + toFun v := ⟨P.val • v, homogeneous_smul_mem_jet k j P v⟩ + map_add' _ _ := Subtype.ext (smul_add _ _ _) + map_smul' _ _ := Subtype.ext (smul_comm _ _ _) + +noncomputable def planeLayerMul (j : ℕ) (P : MvPolynomial.homogeneousSubmodule (Fin 2) k j) : + M →ₗ[k] planeJetLayer (M := M) k j := + (planeJetLayerRelation (M := M) k j).mkQ.comp (planeHomogeneousMultiply k j P) + +lemma planeLayerMul_ker (j : ℕ) (P : MvPolynomial.homogeneousSubmodule (Fin 2) k j) : + planeJetRelation (M := M) k 1 ≤ (planeLayerMul k j P).ker := by + intro v hv + exact (Submodule.Quotient.mk_eq_zero _).mpr (homogeneous_smul_pair_mem_next k j P v hv) + +noncomputable def planeLayerBilinear (j : ℕ) : + (MvPolynomial.homogeneousSubmodule (Fin 2) k j) →ₗ[k] + ((M ⧸ planeJetRelation (M := M) k 1) →ₗ[k] planeJetLayer (M := M) k j) where + toFun P := (planeJetRelation (M := M) k 1).liftQ (planeLayerMul k j P) (planeLayerMul_ker k j P) + map_add' P Q := by + apply LinearMap.ext + intro t + obtain ⟨v,rfl⟩ := (planeJetRelation (M := M) k 1).mkQ_surjective t + change (planeJetLayerRelation (M := M) k j).mkQ _ = + (planeJetLayerRelation (M := M) k j).mkQ _ + (planeJetLayerRelation (M := M) k j).mkQ _ + rw [← map_add] + congr 1 + exact Subtype.ext (add_smul P.val Q.val v) + map_smul' a P := by + apply LinearMap.ext + intro t + obtain ⟨v,rfl⟩ := (planeJetRelation (M := M) k 1).mkQ_surjective t + change (planeJetLayerRelation (M := M) k j).mkQ _ = a • (planeJetLayerRelation (M := M) k j).mkQ _ + rw [← map_smul] + congr 1 + exact Subtype.ext (smul_assoc a P.val v) + +noncomputable def planeLayerMultiply (j : ℕ) : + (MvPolynomial.homogeneousSubmodule (Fin 2) k j) ⊗[k] + (M ⧸ planeJetRelation (M := M) k 1) →ₗ[k] planeJetLayer (M := M) k j := + TensorProduct.lift (planeLayerBilinear k j) + +lemma planeLayerMultiply_tmul_mk (j : ℕ) + (P : MvPolynomial.homogeneousSubmodule (Fin 2) k j) (v : M) : + planeLayerMultiply k j (P ⊗ₜ[k] (planeJetRelation (M := M) k 1).mkQ v) = + (planeJetLayerRelation (M := M) k j).mkQ ⟨P.val • v, homogeneous_smul_mem_jet k j P v⟩ := rfl + +lemma planeLayerMultiply_sum (j : ℕ) (v : Fin (j+1) → M) : + planeLayerMultiply k j (∑ i, jetMonomialBasis k j i ⊗ₜ[k] (planeJetRelation (M := M) k 1).mkQ (v i)) = + (planeJetLayerRelation (M := M) k j).mkQ + ⟨binarySum (MvPolynomial.X 0) (MvPolynomial.X 1) j v, ⟨v,rfl⟩⟩ := by + rw [map_sum] + simp only [planeLayerMultiply_tmul_mk, ← map_sum] + congr 1 + apply Subtype.ext + simp only [Submodule.coe_sum, jetMonomialBasis_apply, binarySum_apply] + +lemma tensor_basis_decomposition {H T : Type u} [AddCommGroup H] [Module k H] + [AddCommGroup T] [Module k T] {ι : Type*} [Fintype ι] + (b : Module.Basis ι k H) (z : H ⊗[k] T) : + ∃ v : ι → T, z = ∑ i, b i ⊗ₜ[k] v i := by + classical + induction z using TensorProduct.inductionOn with + | tmul h t => + refine ⟨fun i => b.repr h i • t, ?_⟩ + conv_lhs => rw [← b.sum_repr h, TensorProduct.sum_tmul] + apply Finset.sum_congr rfl + intro i _ + rw [TensorProduct.smul_tmul, TensorProduct.tmul_smul] + | add z w hz hw => + obtain ⟨v,rfl⟩ := hz + obtain ⟨w,rfl⟩ := hw + exact ⟨v+w, by simp only [Pi.add_apply, TensorProduct.tmul_add, Finset.sum_add_distrib]⟩ + +lemma planeLayerMultiply_surjective (j : ℕ) : + Function.Surjective (planeLayerMultiply (M := M) k j) := by + intro z + obtain ⟨⟨m,v,rfl⟩,rfl⟩ := (planeJetLayerRelation (M := M) k j).mkQ_surjective z + exact ⟨_, planeLayerMultiply_sum k j v⟩ + +lemma planeLayerMultiply_injective + (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • m)) + (hy : ∀ v n : M, (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) • v = + (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n → + ∃ w : M, v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • w) (j : ℕ) : + Function.Injective (planeLayerMultiply (M := M) k j) := by + have hzero : ∀ z, planeLayerMultiply (M := M) k j z = 0 → z = 0 := by + intro z hz + obtain ⟨v,rfl⟩ := tensor_basis_decomposition k (jetMonomialBasis k j) z + choose w hw using fun i => (planeJetRelation (M := M) k 1).mkQ_surjective (v i) + have he : v = fun i => (planeJetRelation (M := M) k 1).mkQ (w i) := funext fun i => (hw i).symm + rw [he, planeLayerMultiply_sum] at hz + have hm := (Submodule.Quotient.mk_eq_zero _).mp hz + have hc := (binarySum_mem_next_iff (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) + (MvPolynomial.X 1) hx hy j w).mp hm + have hv : ∀ i, v i = 0 := by + intro i + rw [← hw i] + apply (Submodule.Quotient.mk_eq_zero _).mpr + simpa only [planeJetRelation, Submodule.restrictScalars_mem, jetRelation_one] using hc i + simp only [hv, TensorProduct.tmul_zero, Finset.sum_const_zero] + intro a b hab + apply sub_eq_zero.mp + apply hzero + rw [map_sub,hab,sub_self] + +noncomputable def planeLayerEquiv + (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • m)) + (hy : ∀ v n : M, (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) • v = + (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n → + ∃ w : M, v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • w) (j : ℕ) : + (MvPolynomial.homogeneousSubmodule (Fin 2) k j) ⊗[k] + (M ⧸ planeJetRelation (M := M) k 1) ≃ₗ[k] planeJetLayer (M := M) k j := + LinearEquiv.ofBijective (planeLayerMultiply k j) + ⟨planeLayerMultiply_injective k hx hy j, planeLayerMultiply_surjective k j⟩ + +noncomputable def planeJetSubrep (σ : Representation k (SL2 k) M) + (hσ : PlaneCompatible k σ) (j : ℕ) : + Representation k (SL2 k) (planeJetRelation (M := M) k j) := + Representation.subrepresentation σ _ (planeJetRelation_stable k σ hσ j) + +lemma planeJetLayerRelation_stable (σ : Representation k (SL2 k) M) + (hσ : PlaneCompatible k σ) (j : ℕ) (g : SL2 k) : + planeJetLayerRelation (M := M) k j ≤ + (planeJetLayerRelation k j).comap (planeJetSubrep k σ hσ j g) := by + intro v hv + exact planeJetRelation_stable k σ hσ (j+1) g hv + +noncomputable def planeJetLayerRep (σ : Representation k (SL2 k) M) + (hσ : PlaneCompatible k σ) (j : ℕ) : + Representation k (SL2 k) (planeJetLayer (M := M) k j) := + Representation.quotient (planeJetSubrep k σ hσ j) _ + (planeJetLayerRelation_stable k σ hσ j) + +lemma planeLayerMultiply_intertwines (σ : Representation k (SL2 k) M) + (hσ : PlaneCompatible k σ) (j : ℕ) (g : SL2 k) + (z : (MvPolynomial.homogeneousSubmodule (Fin 2) k j) ⊗[k] + (M ⧸ planeJetRelation (M := M) k 1)) : + planeLayerMultiply (M := M) k j + (Representation.tprod ((homogeneousRepresentation j).comp (dualMatrix k)) + (planeJetRep k σ hσ 1) g z) = + planeJetLayerRep k σ hσ j g (planeLayerMultiply k j z) := by + induction z using TensorProduct.inductionOn with + | tmul P v => + obtain ⟨w,rfl⟩ := (planeJetRelation (M := M) k 1).mkQ_surjective v + simp only [Representation.tprod_apply, TensorProduct.map_tmul, + planeJetRep_mk, planeLayerMultiply_tmul_mk] + change (planeJetLayerRelation k j).mkQ ⟨_,_⟩ = + (planeJetLayerRelation k j).mkQ ⟨σ g (P.val • w),_⟩ + congr 1 + apply Subtype.ext + exact (hσ g P.val w).symm + | add x y hx hy => simp only [map_add, hx, hy] + +lemma planeLayer_finite [Module.Finite k (M ⧸ planeJetRelation (M := M) k 1)] (j : ℕ) : + Module.Finite k (planeJetLayer (M := M) k j) := + Module.Finite.of_surjective (planeLayerMultiply k j) (planeLayerMultiply_surjective k j) + +lemma planeJetRelation_succ_le (j : ℕ) : + planeJetRelation (M := M) k (j+1) ≤ planeJetRelation (M := M) k j := + jetRelation_succ_le (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) j + +lemma planeJetRelation_zero : planeJetRelation (M := M) k 0 = ⊤ := by + simp only [planeJetRelation, jetRelation_zero, Submodule.restrictScalars_top] + +noncomputable def planeJetTransition (j : ℕ) : + (M ⧸ planeJetRelation (M := M) k (j+1)) →ₗ[k] (M ⧸ planeJetRelation (M := M) k j) := + (planeJetRelation k (j+1)).mapQ (planeJetRelation k j) LinearMap.id + (planeJetRelation_succ_le k j) + +lemma planeJetTransition_mk (j : ℕ) (v : M) : + planeJetTransition k j ((planeJetRelation (M := M) k (j+1)).mkQ v) = + (planeJetRelation (M := M) k j).mkQ v := rfl + +lemma planeJetTransition_surjective (j : ℕ) : + Function.Surjective (planeJetTransition (M := M) k j) := by + intro v + obtain ⟨w,rfl⟩ := (planeJetRelation (M := M) k j).mkQ_surjective v + exact ⟨(planeJetRelation k (j+1)).mkQ w,rfl⟩ + +noncomputable def planeJetLayerInclusion (j : ℕ) : + planeJetLayer (M := M) k j →ₗ[k] (M ⧸ planeJetRelation (M := M) k (j+1)) := + (planeJetLayerRelation k j).liftQ + ((planeJetRelation k (j+1)).mkQ.comp (planeJetRelation k j).subtype) (by + intro v hv + exact (Submodule.Quotient.mk_eq_zero _).mpr hv) + +lemma planeJetLayerInclusion_mk (j : ℕ) (v : planeJetRelation (M := M) k j) : + planeJetLayerInclusion k j ((planeJetLayerRelation k j).mkQ v) = + (planeJetRelation (M := M) k (j+1)).mkQ v.val := rfl + +lemma planeJetLayerInclusion_injective (j : ℕ) : + Function.Injective (planeJetLayerInclusion (M := M) k j) := by + apply (LinearMap.ker_eq_bot (f := planeJetLayerInclusion (M := M) k j)).mp + apply (LinearMap.ker_eq_bot' (f := planeJetLayerInclusion (M := M) k j)).mpr + intro v hv + obtain ⟨w,rfl⟩ := (planeJetLayerRelation (M := M) k j).mkQ_surjective v + rw [planeJetLayerInclusion_mk] at hv + have hw : w.val ∈ planeJetRelation (M := M) k (j+1) := + (Submodule.Quotient.mk_eq_zero (planeJetRelation k (j+1))).mp hv + exact (Submodule.Quotient.mk_eq_zero _).mpr hw + +lemma planeJet_shortExact (j : ℕ) : + Function.Exact (planeJetLayerInclusion (M := M) k j) (planeJetTransition k j) := by + intro v + obtain ⟨w,rfl⟩ := (planeJetRelation (M := M) k (j+1)).mkQ_surjective v + constructor + · intro hw + have hj : w ∈ planeJetRelation (M := M) k j := (Submodule.Quotient.mk_eq_zero _).mp hw + exact ⟨(planeJetLayerRelation k j).mkQ ⟨w,hj⟩,rfl⟩ + · rintro ⟨z,hz⟩ + obtain ⟨t,rfl⟩ := (planeJetLayerRelation (M := M) k j).mkQ_surjective z + rw [← hz, planeJetLayerInclusion_mk, planeJetTransition_mk] + exact (Submodule.Quotient.mk_eq_zero _).mpr t.property + +lemma planeJet_finite [Module.Finite k (M ⧸ planeJetRelation (M := M) k 1)] (j : ℕ) : + Module.Finite k (M ⧸ planeJetRelation (M := M) k j) := by + induction j with + | zero => + rw [planeJetRelation_zero] + infer_instance + | succ j ih => + let := ih + let := planeLayer_finite (M := M) k j + exact Module.Finite.of_exact (planeJet_shortExact k j) (planeJetTransition_surjective k j) + +lemma planeJetTransition_intertwines (σ : Representation k (SL2 k) M) + (hσ : PlaneCompatible k σ) (j : ℕ) (g : SL2 k) + (v : M ⧸ planeJetRelation (M := M) k (j+1)) : + planeJetTransition k j (planeJetRep k σ hσ (j+1) g v) = + planeJetRep k σ hσ j g (planeJetTransition k j v) := by + obtain ⟨w,rfl⟩ := (planeJetRelation (M := M) k (j+1)).mkQ_surjective v + rfl + +lemma planeJetLayerInclusion_intertwines (σ : Representation k (SL2 k) M) + (hσ : PlaneCompatible k σ) (j : ℕ) (g : SL2 k) + (v : planeJetLayer (M := M) k j) : + planeJetLayerInclusion k j (planeJetLayerRep k σ hσ j g v) = + planeJetRep k σ hσ (j+1) g (planeJetLayerInclusion k j v) := by + obtain ⟨w,rfl⟩ := (planeJetLayerRelation (M := M) k j).mkQ_surjective v + rfl +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/JetTriviality.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/JetTriviality.lean index c8ddfbeb3e48c74896dc754b78d0da7a784a9c4a..66becbfb6923753461a6da9fbae557c1228d599b 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/JetTriviality.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/JetTriviality.lean @@ -1,108 +1,108 @@ -import OAI.RepresentationTheory.RestrictedTilting.CompatibleJets - -namespace OAI - -namespace FiberFunctorProof -open scoped BigOperators Pointwise -section -variable {R M N : Type*} [CommRing R] [AddCommGroup M] [Module R M] - [AddCommGroup N] [Module R N] - -lemma map_binarySum (f : M →ₗ[R] N) (x y : R) (j : ℕ) (v : Fin (j+1) → M) : - f (binarySum x y j v) = binarySum x y j (f ∘ v) := by - simp only [binarySum_apply, map_sum, map_smul, Function.comp_apply] - -lemma jetRelation_map_le (f : M →ₗ[R] N) (x y : R) (j : ℕ) : - jetRelation x y j ≤ (jetRelation x y j).comap f := by - rintro m ⟨v,rfl⟩ - exact ⟨f ∘ v, (map_binarySum f x y j v).symm⟩ - - -def jetMap (f : M →ₗ[R] N) (x y : R) (j : ℕ) : - (M ⧸ jetRelation (M := M) x y j) →ₗ[R] (N ⧸ jetRelation (M := N) x y j) := - (jetRelation (M := M) x y j).mapQ (jetRelation (M := N) x y j) f (jetRelation_map_le f x y j) - -lemma jetMap_mk (f : M →ₗ[R] N) (x y : R) (j : ℕ) (m : M) : - jetMap f x y j ((jetRelation x y j).mkQ m) = (jetRelation x y j).mkQ (f m) := rfl - - - -lemma jetMap_surjective (f : M →ₗ[R] N) (x y : R) - (h0 : ∀ n : N, ∃ m : M, n - f m ∈ pairRelation x y) (j : ℕ) : - Function.Surjective (jetMap f x y j) := by - suffices H : ∀ n : N, ∃ m : M, n - f m ∈ jetRelation x y j by - intro z - obtain ⟨n,rfl⟩ := (jetRelation (M := N) x y j).mkQ_surjective z - obtain ⟨m,hm⟩ := H n - refine ⟨(jetRelation x y j).mkQ m, ?_⟩ - rw [jetMap_mk, ← sub_eq_zero, ← map_sub] - apply (Submodule.Quotient.mk_eq_zero _).mpr - simpa only [neg_sub] using (jetRelation x y j).neg_mem hm - induction j with - | zero => intro n; exact ⟨0, by rw [jetRelation_zero]; trivial⟩ - | succ j ih => - intro n - obtain ⟨m, v, hv⟩ := ih n - choose w hw using fun i => h0 (v i) - refine ⟨m + binarySum x y j w, ?_⟩ - have he : n - f (m + binarySum x y j w) = - binarySum x y j (v - f ∘ w) := by - rw [map_add, map_binarySum, map_sub, hv] - abel - rw [he] - exact binarySum_pairRelation x y j _ hw - - - -lemma jetMap_injective (f : M →ₗ[R] N) (x y : R) - (hx : Function.Injective (fun n : N => x • n)) - (hy : ∀ v n : N, y • v = x • n → ∃ w : N, v = x • w) - (h0 : ∀ m : M, f m ∈ pairRelation x y → m ∈ pairRelation x y) (j : ℕ) : - Function.Injective (jetMap f x y j) := by - have H : ∀ j (m : M), f m ∈ jetRelation x y j → m ∈ jetRelation x y j := by - intro j - induction j with - | zero => intros; rw [jetRelation_zero]; trivial - | succ j ih => - intro m hm - obtain ⟨v,rfl⟩ := ih m (jetRelation_succ_le x y j hm) - rw [map_binarySum] at hm - apply binarySum_pairRelation - intro i - exact h0 (v i) ((binarySum_mem_next_iff x y hx hy j (f ∘ v)).mp hm i) - apply (LinearMap.ker_eq_bot (f := jetMap f x y j)).mp - apply (LinearMap.ker_eq_bot' (f := jetMap f x y j)).mpr - intro z hz - obtain ⟨m,rfl⟩ := (jetRelation (M := M) x y j).mkQ_surjective z - rw [jetMap_mk] at hz - exact (Submodule.Quotient.mk_eq_zero _).mpr - (H j m ((Submodule.Quotient.mk_eq_zero _).mp hz)) - - - -theorem jetMap_bijective (f : M →ₗ[R] N) (x y : R) - (hx : Function.Injective (fun n : N => x • n)) - (hy : ∀ v n : N, y • v = x • n → ∃ w : N, v = x • w) - (h0 : Function.Bijective (jetMap f x y 1)) (j : ℕ) : - Function.Bijective (jetMap f x y j) := by - constructor - · apply jetMap_injective f x y hx hy - intro m hm - have hz : jetMap f x y 1 ((jetRelation x y 1).mkQ m) = 0 := by - rw [jetMap_mk] - apply (Submodule.Quotient.mk_eq_zero _).mpr - simpa only [jetRelation_one] using hm - have hm0 := h0.1 (hz.trans (map_zero _).symm) - simpa only [jetRelation_one] using (Submodule.Quotient.mk_eq_zero _).mp hm0 - · apply jetMap_surjective f x y - intro n - obtain ⟨z,hz⟩ := h0.2 ((jetRelation x y 1).mkQ n) - obtain ⟨m,rfl⟩ := (jetRelation x y 1).mkQ_surjective z - refine ⟨m, ?_⟩ - rw [jetMap_mk] at hz - have hh : (jetRelation x y 1).mkQ (n - f m) = 0 := by rw [map_sub, hz, sub_self] - simpa only [jetRelation_one] using (Submodule.Quotient.mk_eq_zero _).mp hh -end -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.CompatibleJets + +namespace OAI + +namespace FiberFunctorProof +open scoped BigOperators Pointwise +section +variable {R M N : Type*} [CommRing R] [AddCommGroup M] [Module R M] + [AddCommGroup N] [Module R N] + +lemma map_binarySum (f : M →ₗ[R] N) (x y : R) (j : ℕ) (v : Fin (j+1) → M) : + f (binarySum x y j v) = binarySum x y j (f ∘ v) := by + simp only [binarySum_apply, map_sum, map_smul, Function.comp_apply] + +lemma jetRelation_map_le (f : M →ₗ[R] N) (x y : R) (j : ℕ) : + jetRelation x y j ≤ (jetRelation x y j).comap f := by + rintro m ⟨v,rfl⟩ + exact ⟨f ∘ v, (map_binarySum f x y j v).symm⟩ + + +def jetMap (f : M →ₗ[R] N) (x y : R) (j : ℕ) : + (M ⧸ jetRelation (M := M) x y j) →ₗ[R] (N ⧸ jetRelation (M := N) x y j) := + (jetRelation (M := M) x y j).mapQ (jetRelation (M := N) x y j) f (jetRelation_map_le f x y j) + +lemma jetMap_mk (f : M →ₗ[R] N) (x y : R) (j : ℕ) (m : M) : + jetMap f x y j ((jetRelation x y j).mkQ m) = (jetRelation x y j).mkQ (f m) := rfl + + + +lemma jetMap_surjective (f : M →ₗ[R] N) (x y : R) + (h0 : ∀ n : N, ∃ m : M, n - f m ∈ pairRelation x y) (j : ℕ) : + Function.Surjective (jetMap f x y j) := by + suffices H : ∀ n : N, ∃ m : M, n - f m ∈ jetRelation x y j by + intro z + obtain ⟨n,rfl⟩ := (jetRelation (M := N) x y j).mkQ_surjective z + obtain ⟨m,hm⟩ := H n + refine ⟨(jetRelation x y j).mkQ m, ?_⟩ + rw [jetMap_mk, ← sub_eq_zero, ← map_sub] + apply (Submodule.Quotient.mk_eq_zero _).mpr + simpa only [neg_sub] using (jetRelation x y j).neg_mem hm + induction j with + | zero => intro n; exact ⟨0, by rw [jetRelation_zero]; trivial⟩ + | succ j ih => + intro n + obtain ⟨m, v, hv⟩ := ih n + choose w hw using fun i => h0 (v i) + refine ⟨m + binarySum x y j w, ?_⟩ + have he : n - f (m + binarySum x y j w) = + binarySum x y j (v - f ∘ w) := by + rw [map_add, map_binarySum, map_sub, hv] + abel + rw [he] + exact binarySum_pairRelation x y j _ hw + + + +lemma jetMap_injective (f : M →ₗ[R] N) (x y : R) + (hx : Function.Injective (fun n : N => x • n)) + (hy : ∀ v n : N, y • v = x • n → ∃ w : N, v = x • w) + (h0 : ∀ m : M, f m ∈ pairRelation x y → m ∈ pairRelation x y) (j : ℕ) : + Function.Injective (jetMap f x y j) := by + have H : ∀ j (m : M), f m ∈ jetRelation x y j → m ∈ jetRelation x y j := by + intro j + induction j with + | zero => intros; rw [jetRelation_zero]; trivial + | succ j ih => + intro m hm + obtain ⟨v,rfl⟩ := ih m (jetRelation_succ_le x y j hm) + rw [map_binarySum] at hm + apply binarySum_pairRelation + intro i + exact h0 (v i) ((binarySum_mem_next_iff x y hx hy j (f ∘ v)).mp hm i) + apply (LinearMap.ker_eq_bot (f := jetMap f x y j)).mp + apply (LinearMap.ker_eq_bot' (f := jetMap f x y j)).mpr + intro z hz + obtain ⟨m,rfl⟩ := (jetRelation (M := M) x y j).mkQ_surjective z + rw [jetMap_mk] at hz + exact (Submodule.Quotient.mk_eq_zero _).mpr + (H j m ((Submodule.Quotient.mk_eq_zero _).mp hz)) + + + +theorem jetMap_bijective (f : M →ₗ[R] N) (x y : R) + (hx : Function.Injective (fun n : N => x • n)) + (hy : ∀ v n : N, y • v = x • n → ∃ w : N, v = x • w) + (h0 : Function.Bijective (jetMap f x y 1)) (j : ℕ) : + Function.Bijective (jetMap f x y j) := by + constructor + · apply jetMap_injective f x y hx hy + intro m hm + have hz : jetMap f x y 1 ((jetRelation x y 1).mkQ m) = 0 := by + rw [jetMap_mk] + apply (Submodule.Quotient.mk_eq_zero _).mpr + simpa only [jetRelation_one] using hm + have hm0 := h0.1 (hz.trans (map_zero _).symm) + simpa only [jetRelation_one] using (Submodule.Quotient.mk_eq_zero _).mp hm0 + · apply jetMap_surjective f x y + intro n + obtain ⟨z,hz⟩ := h0.2 ((jetRelation x y 1).mkQ n) + obtain ⟨m,rfl⟩ := (jetRelation x y 1).mkQ_surjective z + refine ⟨m, ?_⟩ + rw [jetMap_mk] at hz + have hh : (jetRelation x y 1).mkQ (n - f m) = 0 := by rw [map_sub, hz, sub_self] + simpa only [jetRelation_one] using (Submodule.Quotient.mk_eq_zero _).mp hh +end +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeGluing.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeGluing.lean index 36bb81473a6be50f6e6a898959a8d750a5e0c117..b978933be4efc7ac6694f7598c63d2e9a0084893 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeGluing.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeGluing.lean @@ -1,313 +1,313 @@ -import Mathlib - -namespace OAI - -/-! Free intersections, power localizations and finite glued lattices. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators TensorProduct - -namespace FiberFunctorProof -section - -variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M] - -lemma tensor_span_pair (x y : R) (I : Ideal R) (hI : I = Ideal.span {x,y}) - (z : I ⊗[R] M) : - ∃ u v : M, z = (⟨x, by rw [hI]; exact Ideal.subset_span (by simp)⟩ : I) ⊗ₜ[R] u + - (⟨y, by rw [hI]; exact Ideal.subset_span (by simp)⟩ : I) ⊗ₜ[R] v := by - let ix : I := ⟨x, by rw [hI]; exact Ideal.subset_span (by simp)⟩ - let iy : I := ⟨y, by rw [hI]; exact Ideal.subset_span (by simp)⟩ - change ∃ u v, z = ix ⊗ₜ[R] u + iy ⊗ₜ[R] v - induction z using TensorProduct.inductionOn with - | tmul a m => - have ha : a.val ∈ Ideal.span {x,y} := hI ▸ a.property - obtain ⟨b,c,hbc⟩ := Ideal.mem_span_pair.mp ha - have heq : a = b • ix + c • iy := by - apply Subtype.ext - exact hbc.symm - refine ⟨b • m, c • m, ?_⟩ - rw [heq, TensorProduct.add_tmul, TensorProduct.smul_tmul, TensorProduct.smul_tmul] - | add a b ha hb => - obtain ⟨u,v,rfl⟩ := ha - obtain ⟨u',v',rfl⟩ := hb - exact ⟨u+u', v+v', by simp only [TensorProduct.tmul_add]; abel⟩ - - - -theorem free_of_two_generators [IsLocalRing R] [Module.FinitePresentation R M] - (x y : R) (hm : IsLocalRing.maximalIdeal R = Ideal.span {x,y}) - (hx : Function.Injective (fun m : M => x • m)) - (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) : - Module.Free R M := by - apply Module.free_of_maximalIdeal_rTensor_injective - apply LinearMap.ker_eq_bot.mp - apply LinearMap.ker_eq_bot'.mpr - intro z hz - let I := IsLocalRing.maximalIdeal R - let ix : I := ⟨x, by dsimp [I]; rw [hm]; exact Ideal.subset_span (by simp)⟩ - let iy : I := ⟨y, by dsimp [I]; rw [hm]; exact Ideal.subset_span (by simp)⟩ - obtain ⟨u,v,hz'⟩ := tensor_span_pair x y I hm z - change z = ix ⊗ₜ[R] u + iy ⊗ₜ[R] v at hz' - have huv : x • u + y • v = 0 := by - have h := congrArg (TensorProduct.lid R M) hz - rw [hz'] at h - simpa [LinearMap.rTensor_tmul, ix, iy] using h - have hv : y • v = x • (-u) := by - rw [smul_neg] - exact eq_neg_of_add_eq_zero_right huv - obtain ⟨w,hw⟩ := hy v (-u) hv - have hu : u = -(y • w) := by - apply hx - change x • u = x • (-(y • w)) - rw [smul_neg] - have := huv - rw [hw, smul_comm y x] at this - exact eq_neg_of_add_eq_zero_left this - rw [hz', hu, hw] - simp only [TensorProduct.tmul_neg, TensorProduct.tmul_smul, TensorProduct.smul_tmul'] - have heq : y • ix = x • iy := by - apply Subtype.ext - exact mul_comm y x - rw [heq] - exact neg_add_cancel _ - -end - -section - -variable {R K W : Type*} [CommRing R] [Field K] [Algebra R K] - [AddCommGroup W] [Module K W] [Module R W] [IsScalarTower R K W] - - - -theorem intersection_regular (A B : Submodule R W) (x y : R) - (hx : algebraMap R K x ≠ 0) (hy : algebraMap R K y ≠ 0) - (hA : ∀ v ∈ A, (algebraMap R K x)⁻¹ • v ∈ A) - (hB : ∀ v ∈ B, (algebraMap R K y)⁻¹ • v ∈ B) : - Function.Injective (fun m : ↥(A ⊓ B) => x • m) ∧ - ∀ v n : ↥(A ⊓ B), y • v = x • n → ∃ w : ↥(A ⊓ B), v = x • w := by - constructor - · intro a b hab - apply Subtype.ext - have h : (algebraMap R K x) • (a : W) = (algebraMap R K x) • (b : W) := by - simpa only [algebraMap_smul, Submodule.coe_smul] using congrArg Subtype.val hab - exact (smul_right_injective W hx) h - · intro v n hvn - have h : (algebraMap R K y) • (v : W) = (algebraMap R K x) • (n : W) := by - simpa only [algebraMap_smul, Submodule.coe_smul] using congrArg Subtype.val hvn - have hw : (algebraMap R K x)⁻¹ • (v : W) = - (algebraMap R K y)⁻¹ • (n : W) := by - apply (smul_right_injective W hx) - simp only [smul_inv_smul₀ hx] - rw [smul_comm, ← h, inv_smul_smul₀ hy] - refine ⟨⟨(algebraMap R K x)⁻¹ • (v : W), - hA v v.property.1, hw ▸ hB n n.property.2⟩, ?_⟩ - apply Subtype.ext - change (v : W) = x • ((algebraMap R K x)⁻¹ • (v : W)) - rw [← algebraMap_smul K x, smul_inv_smul₀ hx] - - - -theorem intersection_free [IsLocalRing R] - (A B : Submodule R W) [Module.FinitePresentation R ↥(A ⊓ B)] (x y : R) - (hm : IsLocalRing.maximalIdeal R = Ideal.span {x,y}) - (hx : algebraMap R K x ≠ 0) (hy : algebraMap R K y ≠ 0) - (hA : ∀ v ∈ A, (algebraMap R K x)⁻¹ • v ∈ A) - (hB : ∀ v ∈ B, (algebraMap R K y)⁻¹ • v ∈ B) : - Module.Free R ↥(A ⊓ B) := by - obtain ⟨h1,h2⟩ := intersection_regular A B x y hx hy hA hB - exact free_of_two_generators x y hm h1 h2 - -end - - - -section PowerLocalization -variable {R W : Type*} [CommRing R] [AddCommGroup W] [Module R W] - - -def powerLocalization (x : R) (L : Submodule R W) : Submodule R W where - carrier := {v | ∃ n : ℕ, x ^ n • v ∈ L} - zero_mem' := ⟨0, by simp⟩ - add_mem' := by - rintro a b ⟨n,hn⟩ ⟨m,hm⟩ - refine ⟨n+m, ?_⟩ - rw [smul_add, pow_add] - exact L.add_mem - (by rw [mul_comm, mul_smul]; exact L.smul_mem _ hn) - (by rw [mul_smul]; exact L.smul_mem _ hm) - smul_mem' := by - rintro c a ⟨n,hn⟩ - exact ⟨n, by rw [smul_comm]; exact L.smul_mem c hn⟩ - -lemma le_powerLocalization (x : R) (L : Submodule R W) : L ≤ powerLocalization x L := by - intro v hv - exact ⟨0, by simpa using hv⟩ - -lemma powerLocalization_mono (x : R) {L L' : Submodule R W} (h : L ≤ L') : - powerLocalization x L ≤ powerLocalization x L' := by - rintro v ⟨n,hn⟩ - exact ⟨n,h hn⟩ - -end PowerLocalization - -section Field -variable {R K W : Type*} [CommRing R] [Field K] [Algebra R K] - [AddCommGroup W] [Module K W] [Module R W] [IsScalarTower R K W] - -lemma powerLocalization_div (x : R) (L : Submodule R W) - (hx : algebraMap R K x ≠ 0) {v : W} (hv : v ∈ powerLocalization x L) : - (algebraMap R K x)⁻¹ • v ∈ powerLocalization x L := by - obtain ⟨n,hn⟩ := hv - refine ⟨n+1, ?_⟩ - rw [pow_succ, mul_smul, ← algebraMap_smul K x, smul_inv_smul₀ hx] - exact hn - -end Field - -section -variable {R K ι : Type*} [CommRing R] [Field K] [Algebra R K] - - -def coordinateMap : (ι → R) →ₗ[R] (ι → K) where - toFun v i := algebraMap R K (v i) - map_add' v w := by ext i; exact map_add _ _ _ - map_smul' c v := by ext i; simp [Algebra.smul_def] - -def coordinateLattice : Submodule R (ι → K) := - LinearMap.range (coordinateMap (R := R) (K := K) (ι := ι)) - -lemma mem_coordinateLattice (v : ι → K) : v ∈ coordinateLattice (R := R) ↔ - ∀ i, ∃ r : R, algebraMap R K r = v i := by - constructor - · rintro ⟨w,rfl⟩ i - exact ⟨w i,rfl⟩ - · intro hv - choose w hw using hv - exact ⟨w,funext hw⟩ - -instance coordinateLattice_finite [Finite ι] : - Module.Finite R (coordinateLattice (R := R) (K := K) (ι := ι)) := by - exact Module.Finite.range _ - - - -theorem coordinateLattice_intersection [IsDomain R] [GCDMonoid R] [IsFractionRing R K] - (x y : R) (hx : x ≠ 0) (hxy : IsRelPrime x y) : - powerLocalization x (coordinateLattice (R := R) (K := K) (ι := ι)) ⊓ - powerLocalization y (coordinateLattice (R := R) (K := K) (ι := ι)) = - coordinateLattice (R := R) (K := K) (ι := ι) := by - apply le_antisymm - · rintro v ⟨⟨n,hn⟩,⟨m,hm⟩⟩ - apply (mem_coordinateLattice v).mpr - intro i - obtain ⟨a,ha⟩ := (mem_coordinateLattice _).mp hn i - obtain ⟨b,hb⟩ := (mem_coordinateLattice _).mp hm i - have hinj : Function.Injective (algebraMap R K) := FaithfulSMul.algebraMap_injective R K - have hab : y ^ m * a = x ^ n * b := by - apply hinj - simp only [map_mul, ha, hb] - change algebraMap R K (y ^ m) * (x^n • v i) = - algebraMap R K (x ^ n) * (y^m • v i) - simp only [Algebra.smul_def] - ring - have hdiv : x ^ n ∣ a := - (hxy.pow (m := n) (n := m)).dvd_of_dvd_mul_left ⟨b, hab⟩ - obtain ⟨c,hc⟩ := hdiv - refine ⟨c, ?_⟩ - have hxn : algebraMap R K (x^n) ≠ 0 := by - exact fun h => pow_ne_zero n hx (hinj (h.trans (map_zero _).symm)) - apply mul_left_cancel₀ hxn - rw [← map_mul, ← hc, ha] - exact Algebra.smul_def _ _ - · exact le_inf (le_powerLocalization ..) (le_powerLocalization ..) - -end - -section -variable {R K ι : Type*} [CommRing R] [IsDomain R] [GCDMonoid R] - [Field K] [Algebra R K] [IsFractionRing R K] - - -def gluedLattice (x y : R) (P : (ι → K) ≃ₗ[K] (ι → K)) : Submodule R (ι → K) := - powerLocalization x coordinateLattice ⊓ - (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) - - - -lemma gluedLattice_bound (x y : R) (hx : x ≠ 0) (hxy : IsRelPrime x y) - (P : (ι → K) ≃ₗ[K] (ι → K)) (d : ℕ) - (hP : ∀ v ∈ coordinateLattice (R := R), (x*y)^d • P v ∈ coordinateLattice (R := R)) - {z : ι → K} (hz : z ∈ gluedLattice x y P) : - x^d • z ∈ coordinateLattice (R := R) := by - change z ∈ powerLocalization x coordinateLattice ∧ - z ∈ (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) at hz - rw [← coordinateLattice_intersection x y hx hxy] - constructor - · exact (powerLocalization x (coordinateLattice (R := R) (K := K) (ι := ι))).smul_mem (x^d) hz.1 - change ∃ m : ℕ, y^m • (x^d • z) ∈ coordinateLattice (R := R) - obtain ⟨v,hv,hvP⟩ := hz.2 - obtain ⟨m,hm⟩ := hv - refine ⟨d+m, ?_⟩ - have h := hP (y^m • v) hm - have hlin : P (y^m • v) = y^m • P v := (P.restrictScalars R).map_smul _ _ - rw [hlin, mul_pow, mul_smul] at h - change P v = z at hvP - rw [hvP, ← mul_smul (y^d) (y^m), ← pow_add, smul_comm (x^d)] at h - exact h - -theorem gluedLattice_finite [Finite ι] [IsNoetherianRing R] - (x y : R) (hx : x ≠ 0) (hxy : IsRelPrime x y) - (P : (ι → K) ≃ₗ[K] (ι → K)) (d : ℕ) - (hP : ∀ v ∈ coordinateLattice (R := R), (x*y)^d • P v ∈ coordinateLattice (R := R)) : - Module.Finite R (gluedLattice x y P) := by - let f : (ι → K) →ₗ[R] (ι → K) := - (algebraMap R K (x ^ d))⁻¹ • LinearMap.id - let L := (coordinateLattice (R := R) (K := K) (ι := ι)).map f - have hle : gluedLattice x y P ≤ L := by - intro z hz - refine ⟨x^d • z, gluedLattice_bound x y hx hxy P d hP hz, ?_⟩ - change (algebraMap R K (x^d))⁻¹ • (x^d • z) = z - rw [← algebraMap_smul K (x^d), inv_smul_smul₀] - exact fun h => pow_ne_zero d hx - ((FaithfulSMul.algebraMap_injective R K) (h.trans (map_zero _).symm)) - exact Module.Finite.of_injective (Submodule.inclusion hle) (Submodule.inclusion_injective hle) - -end - -variable {R K ι : Type*} [CommRing R] [IsDomain R] [GCDMonoid R] - [Field K] [Algebra R K] [IsFractionRing R K] - - - -theorem gluedLattice_free [Finite ι] [IsNoetherianRing R] [IsLocalRing R] - (x y : R) (hx : x ≠ 0) (hy : y ≠ 0) (hxy : IsRelPrime x y) - (hm : IsLocalRing.maximalIdeal R = Ideal.span {x,y}) - (P : (ι → K) ≃ₗ[K] (ι → K)) (d : ℕ) - (hP : ∀ v ∈ coordinateLattice (R := R), (x*y)^d • P v ∈ coordinateLattice (R := R)) : - Module.Free R (gluedLattice x y P) := by - have hinj := FaithfulSMul.algebraMap_injective R K - have hxK : algebraMap R K x ≠ 0 := fun h => hx (hinj (h.trans (map_zero _).symm)) - have hyK : algebraMap R K y ≠ 0 := fun h => hy (hinj (h.trans (map_zero _).symm)) - have : Module.Finite R (gluedLattice x y P) := gluedLattice_finite x y hx hxy P d hP - have : Module.FinitePresentation R (gluedLattice x y P) := - Module.finitePresentation_of_finite R (gluedLattice x y P) - have hB : ∀ z ∈ (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R), - (algebraMap R K y)⁻¹ • z ∈ - (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) := by - rintro z ⟨v,hv,rfl⟩ - refine ⟨(algebraMap R K y)⁻¹ • v, powerLocalization_div y _ hyK hv, ?_⟩ - exact P.map_smul _ _ - have : Module.FinitePresentation R - ↥(powerLocalization x (coordinateLattice (R := R) (K := K) (ι := ι)) ⊓ - (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R)) := by - change Module.FinitePresentation R (gluedLattice x y P) - infer_instance - exact intersection_free _ _ x y hm hxK hyK (fun _ hv => powerLocalization_div x _ hxK hv) hB - -end FiberFunctorProof -end - -end OAI +import Mathlib + +namespace OAI + +/-! Free intersections, power localizations and finite glued lattices. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators TensorProduct + +namespace FiberFunctorProof +section + +variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M] + +lemma tensor_span_pair (x y : R) (I : Ideal R) (hI : I = Ideal.span {x,y}) + (z : I ⊗[R] M) : + ∃ u v : M, z = (⟨x, by rw [hI]; exact Ideal.subset_span (by simp)⟩ : I) ⊗ₜ[R] u + + (⟨y, by rw [hI]; exact Ideal.subset_span (by simp)⟩ : I) ⊗ₜ[R] v := by + let ix : I := ⟨x, by rw [hI]; exact Ideal.subset_span (by simp)⟩ + let iy : I := ⟨y, by rw [hI]; exact Ideal.subset_span (by simp)⟩ + change ∃ u v, z = ix ⊗ₜ[R] u + iy ⊗ₜ[R] v + induction z using TensorProduct.inductionOn with + | tmul a m => + have ha : a.val ∈ Ideal.span {x,y} := hI ▸ a.property + obtain ⟨b,c,hbc⟩ := Ideal.mem_span_pair.mp ha + have heq : a = b • ix + c • iy := by + apply Subtype.ext + exact hbc.symm + refine ⟨b • m, c • m, ?_⟩ + rw [heq, TensorProduct.add_tmul, TensorProduct.smul_tmul, TensorProduct.smul_tmul] + | add a b ha hb => + obtain ⟨u,v,rfl⟩ := ha + obtain ⟨u',v',rfl⟩ := hb + exact ⟨u+u', v+v', by simp only [TensorProduct.tmul_add]; abel⟩ + + + +theorem free_of_two_generators [IsLocalRing R] [Module.FinitePresentation R M] + (x y : R) (hm : IsLocalRing.maximalIdeal R = Ideal.span {x,y}) + (hx : Function.Injective (fun m : M => x • m)) + (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) : + Module.Free R M := by + apply Module.free_of_maximalIdeal_rTensor_injective + apply LinearMap.ker_eq_bot.mp + apply LinearMap.ker_eq_bot'.mpr + intro z hz + let I := IsLocalRing.maximalIdeal R + let ix : I := ⟨x, by dsimp [I]; rw [hm]; exact Ideal.subset_span (by simp)⟩ + let iy : I := ⟨y, by dsimp [I]; rw [hm]; exact Ideal.subset_span (by simp)⟩ + obtain ⟨u,v,hz'⟩ := tensor_span_pair x y I hm z + change z = ix ⊗ₜ[R] u + iy ⊗ₜ[R] v at hz' + have huv : x • u + y • v = 0 := by + have h := congrArg (TensorProduct.lid R M) hz + rw [hz'] at h + simpa [LinearMap.rTensor_tmul, ix, iy] using h + have hv : y • v = x • (-u) := by + rw [smul_neg] + exact eq_neg_of_add_eq_zero_right huv + obtain ⟨w,hw⟩ := hy v (-u) hv + have hu : u = -(y • w) := by + apply hx + change x • u = x • (-(y • w)) + rw [smul_neg] + have := huv + rw [hw, smul_comm y x] at this + exact eq_neg_of_add_eq_zero_left this + rw [hz', hu, hw] + simp only [TensorProduct.tmul_neg, TensorProduct.tmul_smul, TensorProduct.smul_tmul'] + have heq : y • ix = x • iy := by + apply Subtype.ext + exact mul_comm y x + rw [heq] + exact neg_add_cancel _ + +end + +section + +variable {R K W : Type*} [CommRing R] [Field K] [Algebra R K] + [AddCommGroup W] [Module K W] [Module R W] [IsScalarTower R K W] + + + +theorem intersection_regular (A B : Submodule R W) (x y : R) + (hx : algebraMap R K x ≠ 0) (hy : algebraMap R K y ≠ 0) + (hA : ∀ v ∈ A, (algebraMap R K x)⁻¹ • v ∈ A) + (hB : ∀ v ∈ B, (algebraMap R K y)⁻¹ • v ∈ B) : + Function.Injective (fun m : ↥(A ⊓ B) => x • m) ∧ + ∀ v n : ↥(A ⊓ B), y • v = x • n → ∃ w : ↥(A ⊓ B), v = x • w := by + constructor + · intro a b hab + apply Subtype.ext + have h : (algebraMap R K x) • (a : W) = (algebraMap R K x) • (b : W) := by + simpa only [algebraMap_smul, Submodule.coe_smul] using congrArg Subtype.val hab + exact (smul_right_injective W hx) h + · intro v n hvn + have h : (algebraMap R K y) • (v : W) = (algebraMap R K x) • (n : W) := by + simpa only [algebraMap_smul, Submodule.coe_smul] using congrArg Subtype.val hvn + have hw : (algebraMap R K x)⁻¹ • (v : W) = + (algebraMap R K y)⁻¹ • (n : W) := by + apply (smul_right_injective W hx) + simp only [smul_inv_smul₀ hx] + rw [smul_comm, ← h, inv_smul_smul₀ hy] + refine ⟨⟨(algebraMap R K x)⁻¹ • (v : W), + hA v v.property.1, hw ▸ hB n n.property.2⟩, ?_⟩ + apply Subtype.ext + change (v : W) = x • ((algebraMap R K x)⁻¹ • (v : W)) + rw [← algebraMap_smul K x, smul_inv_smul₀ hx] + + + +theorem intersection_free [IsLocalRing R] + (A B : Submodule R W) [Module.FinitePresentation R ↥(A ⊓ B)] (x y : R) + (hm : IsLocalRing.maximalIdeal R = Ideal.span {x,y}) + (hx : algebraMap R K x ≠ 0) (hy : algebraMap R K y ≠ 0) + (hA : ∀ v ∈ A, (algebraMap R K x)⁻¹ • v ∈ A) + (hB : ∀ v ∈ B, (algebraMap R K y)⁻¹ • v ∈ B) : + Module.Free R ↥(A ⊓ B) := by + obtain ⟨h1,h2⟩ := intersection_regular A B x y hx hy hA hB + exact free_of_two_generators x y hm h1 h2 + +end + + + +section PowerLocalization +variable {R W : Type*} [CommRing R] [AddCommGroup W] [Module R W] + + +def powerLocalization (x : R) (L : Submodule R W) : Submodule R W where + carrier := {v | ∃ n : ℕ, x ^ n • v ∈ L} + zero_mem' := ⟨0, by simp⟩ + add_mem' := by + rintro a b ⟨n,hn⟩ ⟨m,hm⟩ + refine ⟨n+m, ?_⟩ + rw [smul_add, pow_add] + exact L.add_mem + (by rw [mul_comm, mul_smul]; exact L.smul_mem _ hn) + (by rw [mul_smul]; exact L.smul_mem _ hm) + smul_mem' := by + rintro c a ⟨n,hn⟩ + exact ⟨n, by rw [smul_comm]; exact L.smul_mem c hn⟩ + +lemma le_powerLocalization (x : R) (L : Submodule R W) : L ≤ powerLocalization x L := by + intro v hv + exact ⟨0, by simpa using hv⟩ + +lemma powerLocalization_mono (x : R) {L L' : Submodule R W} (h : L ≤ L') : + powerLocalization x L ≤ powerLocalization x L' := by + rintro v ⟨n,hn⟩ + exact ⟨n,h hn⟩ + +end PowerLocalization + +section Field +variable {R K W : Type*} [CommRing R] [Field K] [Algebra R K] + [AddCommGroup W] [Module K W] [Module R W] [IsScalarTower R K W] + +lemma powerLocalization_div (x : R) (L : Submodule R W) + (hx : algebraMap R K x ≠ 0) {v : W} (hv : v ∈ powerLocalization x L) : + (algebraMap R K x)⁻¹ • v ∈ powerLocalization x L := by + obtain ⟨n,hn⟩ := hv + refine ⟨n+1, ?_⟩ + rw [pow_succ, mul_smul, ← algebraMap_smul K x, smul_inv_smul₀ hx] + exact hn + +end Field + +section +variable {R K ι : Type*} [CommRing R] [Field K] [Algebra R K] + + +def coordinateMap : (ι → R) →ₗ[R] (ι → K) where + toFun v i := algebraMap R K (v i) + map_add' v w := by ext i; exact map_add _ _ _ + map_smul' c v := by ext i; simp [Algebra.smul_def] + +def coordinateLattice : Submodule R (ι → K) := + LinearMap.range (coordinateMap (R := R) (K := K) (ι := ι)) + +lemma mem_coordinateLattice (v : ι → K) : v ∈ coordinateLattice (R := R) ↔ + ∀ i, ∃ r : R, algebraMap R K r = v i := by + constructor + · rintro ⟨w,rfl⟩ i + exact ⟨w i,rfl⟩ + · intro hv + choose w hw using hv + exact ⟨w,funext hw⟩ + +instance coordinateLattice_finite [Finite ι] : + Module.Finite R (coordinateLattice (R := R) (K := K) (ι := ι)) := by + exact Module.Finite.range _ + + + +theorem coordinateLattice_intersection [IsDomain R] [GCDMonoid R] [IsFractionRing R K] + (x y : R) (hx : x ≠ 0) (hxy : IsRelPrime x y) : + powerLocalization x (coordinateLattice (R := R) (K := K) (ι := ι)) ⊓ + powerLocalization y (coordinateLattice (R := R) (K := K) (ι := ι)) = + coordinateLattice (R := R) (K := K) (ι := ι) := by + apply le_antisymm + · rintro v ⟨⟨n,hn⟩,⟨m,hm⟩⟩ + apply (mem_coordinateLattice v).mpr + intro i + obtain ⟨a,ha⟩ := (mem_coordinateLattice _).mp hn i + obtain ⟨b,hb⟩ := (mem_coordinateLattice _).mp hm i + have hinj : Function.Injective (algebraMap R K) := FaithfulSMul.algebraMap_injective R K + have hab : y ^ m * a = x ^ n * b := by + apply hinj + simp only [map_mul, ha, hb] + change algebraMap R K (y ^ m) * (x^n • v i) = + algebraMap R K (x ^ n) * (y^m • v i) + simp only [Algebra.smul_def] + ring + have hdiv : x ^ n ∣ a := + (hxy.pow (m := n) (n := m)).dvd_of_dvd_mul_left ⟨b, hab⟩ + obtain ⟨c,hc⟩ := hdiv + refine ⟨c, ?_⟩ + have hxn : algebraMap R K (x^n) ≠ 0 := by + exact fun h => pow_ne_zero n hx (hinj (h.trans (map_zero _).symm)) + apply mul_left_cancel₀ hxn + rw [← map_mul, ← hc, ha] + exact Algebra.smul_def _ _ + · exact le_inf (le_powerLocalization ..) (le_powerLocalization ..) + +end + +section +variable {R K ι : Type*} [CommRing R] [IsDomain R] [GCDMonoid R] + [Field K] [Algebra R K] [IsFractionRing R K] + + +def gluedLattice (x y : R) (P : (ι → K) ≃ₗ[K] (ι → K)) : Submodule R (ι → K) := + powerLocalization x coordinateLattice ⊓ + (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) + + + +lemma gluedLattice_bound (x y : R) (hx : x ≠ 0) (hxy : IsRelPrime x y) + (P : (ι → K) ≃ₗ[K] (ι → K)) (d : ℕ) + (hP : ∀ v ∈ coordinateLattice (R := R), (x*y)^d • P v ∈ coordinateLattice (R := R)) + {z : ι → K} (hz : z ∈ gluedLattice x y P) : + x^d • z ∈ coordinateLattice (R := R) := by + change z ∈ powerLocalization x coordinateLattice ∧ + z ∈ (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) at hz + rw [← coordinateLattice_intersection x y hx hxy] + constructor + · exact (powerLocalization x (coordinateLattice (R := R) (K := K) (ι := ι))).smul_mem (x^d) hz.1 + change ∃ m : ℕ, y^m • (x^d • z) ∈ coordinateLattice (R := R) + obtain ⟨v,hv,hvP⟩ := hz.2 + obtain ⟨m,hm⟩ := hv + refine ⟨d+m, ?_⟩ + have h := hP (y^m • v) hm + have hlin : P (y^m • v) = y^m • P v := (P.restrictScalars R).map_smul _ _ + rw [hlin, mul_pow, mul_smul] at h + change P v = z at hvP + rw [hvP, ← mul_smul (y^d) (y^m), ← pow_add, smul_comm (x^d)] at h + exact h + +theorem gluedLattice_finite [Finite ι] [IsNoetherianRing R] + (x y : R) (hx : x ≠ 0) (hxy : IsRelPrime x y) + (P : (ι → K) ≃ₗ[K] (ι → K)) (d : ℕ) + (hP : ∀ v ∈ coordinateLattice (R := R), (x*y)^d • P v ∈ coordinateLattice (R := R)) : + Module.Finite R (gluedLattice x y P) := by + let f : (ι → K) →ₗ[R] (ι → K) := + (algebraMap R K (x ^ d))⁻¹ • LinearMap.id + let L := (coordinateLattice (R := R) (K := K) (ι := ι)).map f + have hle : gluedLattice x y P ≤ L := by + intro z hz + refine ⟨x^d • z, gluedLattice_bound x y hx hxy P d hP hz, ?_⟩ + change (algebraMap R K (x^d))⁻¹ • (x^d • z) = z + rw [← algebraMap_smul K (x^d), inv_smul_smul₀] + exact fun h => pow_ne_zero d hx + ((FaithfulSMul.algebraMap_injective R K) (h.trans (map_zero _).symm)) + exact Module.Finite.of_injective (Submodule.inclusion hle) (Submodule.inclusion_injective hle) + +end + +variable {R K ι : Type*} [CommRing R] [IsDomain R] [GCDMonoid R] + [Field K] [Algebra R K] [IsFractionRing R K] + + + +theorem gluedLattice_free [Finite ι] [IsNoetherianRing R] [IsLocalRing R] + (x y : R) (hx : x ≠ 0) (hy : y ≠ 0) (hxy : IsRelPrime x y) + (hm : IsLocalRing.maximalIdeal R = Ideal.span {x,y}) + (P : (ι → K) ≃ₗ[K] (ι → K)) (d : ℕ) + (hP : ∀ v ∈ coordinateLattice (R := R), (x*y)^d • P v ∈ coordinateLattice (R := R)) : + Module.Free R (gluedLattice x y P) := by + have hinj := FaithfulSMul.algebraMap_injective R K + have hxK : algebraMap R K x ≠ 0 := fun h => hx (hinj (h.trans (map_zero _).symm)) + have hyK : algebraMap R K y ≠ 0 := fun h => hy (hinj (h.trans (map_zero _).symm)) + have : Module.Finite R (gluedLattice x y P) := gluedLattice_finite x y hx hxy P d hP + have : Module.FinitePresentation R (gluedLattice x y P) := + Module.finitePresentation_of_finite R (gluedLattice x y P) + have hB : ∀ z ∈ (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R), + (algebraMap R K y)⁻¹ • z ∈ + (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) := by + rintro z ⟨v,hv,rfl⟩ + refine ⟨(algebraMap R K y)⁻¹ • v, powerLocalization_div y _ hyK hv, ?_⟩ + exact P.map_smul _ _ + have : Module.FinitePresentation R + ↥(powerLocalization x (coordinateLattice (R := R) (K := K) (ι := ι)) ⊓ + (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R)) := by + change Module.FinitePresentation R (gluedLattice x y P) + infer_instance + exact intersection_free _ _ x y hm hxK hyK (fun _ hv => powerLocalization_div x _ hxK hv) hB + +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeLocalProjectivity.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeLocalProjectivity.lean index 6eff3046fd04ce620929def570503d598eb73ce9..0f2ce41ee1e525b27ef2dd3c2c9af292c537bf6d 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeLocalProjectivity.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeLocalProjectivity.lean @@ -1,28 +1,28 @@ -import OAI.RepresentationTheory.RestrictedTilting.BaseChangeProjective -import OAI.RepresentationTheory.RestrictedTilting.LatticeSwap - -namespace OAI - -namespace FiberFunctorProof -open scoped TensorProduct -variable {R K S ι : Type*} [CommRing R] [IsDomain R] [GCDMonoid R] - [Field K] [Algebra R K] [IsFractionRing R K] [Fintype ι] - [CommRing S] [Algebra R S] - - - -theorem gluedLattice_projective_baseChange (x y : R) (hx : x ≠ 0) - (hxy : IsRelPrime x y) (P : (ι → K) ≃ₗ[K] (ι → K)) (d e : ℕ) - (hP : ∀ v ∈ coordinateLattice (R := R), (x*y)^d • P v ∈ coordinateLattice (R := R)) - (hQ : ∀ v ∈ coordinateLattice (R := R), (x*y)^e • P.symm v ∈ coordinateLattice (R := R)) - (hu : IsUnit (algebraMap R S x)) : - Module.Projective S (S ⊗[R] gluedLattice x y P) := by - apply projective_baseChange_of_split_smul - (latticeNumerator x y hx hxy P d hP) (latticeDenominator x y P e hQ) (x^(d+e)) - · ext v : 1 - exact latticeDenominator_numerator x y hx hxy P d e hP hQ v - · simpa only [map_pow] using hu.pow (d+e) - -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.BaseChangeProjective +import OAI.RepresentationTheory.RestrictedTilting.LatticeSwap + +namespace OAI + +namespace FiberFunctorProof +open scoped TensorProduct +variable {R K S ι : Type*} [CommRing R] [IsDomain R] [GCDMonoid R] + [Field K] [Algebra R K] [IsFractionRing R K] [Fintype ι] + [CommRing S] [Algebra R S] + + + +theorem gluedLattice_projective_baseChange (x y : R) (hx : x ≠ 0) + (hxy : IsRelPrime x y) (P : (ι → K) ≃ₗ[K] (ι → K)) (d e : ℕ) + (hP : ∀ v ∈ coordinateLattice (R := R), (x*y)^d • P v ∈ coordinateLattice (R := R)) + (hQ : ∀ v ∈ coordinateLattice (R := R), (x*y)^e • P.symm v ∈ coordinateLattice (R := R)) + (hu : IsUnit (algebraMap R S x)) : + Module.Projective S (S ⊗[R] gluedLattice x y P) := by + apply projective_baseChange_of_split_smul + (latticeNumerator x y hx hxy P d hP) (latticeDenominator x y P e hQ) (x^(d+e)) + · ext v : 1 + exact latticeDenominator_numerator x y hx hxy P d e hP hQ v + · simpa only [map_pow] using hu.pow (d+e) + +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeNumerator.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeNumerator.lean index 1192c4fc29b687dc997b3b4c2cba33ba9918819b..efee8456bd3abda616cc06ada816573e70d3af26 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeNumerator.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeNumerator.lean @@ -1,76 +1,76 @@ -import OAI.RepresentationTheory.RestrictedTilting.Basic - -namespace OAI - -namespace FiberFunctorProof -section Numerator -variable {R K ι : Type*} [CommRing R] [IsDomain R] [GCDMonoid R] - [Field K] [Algebra R K] [IsFractionRing R K] - -omit [IsDomain R] [GCDMonoid R] in -lemma coordinateMap_injective : Function.Injective (coordinateMap (R := R) (K := K) (ι := ι)) := by - intro v w h - funext i - exact (FaithfulSMul.algebraMap_injective R K) (congrFun h i) - -noncomputable def coordinateEquiv : (ι → R) ≃ₗ[R] coordinateLattice (R := R) (K := K) (ι := ι) := - LinearEquiv.ofInjective (coordinateMap (R := R) (K := K) (ι := ι)) coordinateMap_injective - -omit [IsDomain R] [GCDMonoid R] in -lemma coordinateEquiv_apply (v : ι → R) : - (coordinateEquiv (K := K) v).val = coordinateMap v := rfl - -variable (x y : R) (hx : x ≠ 0) (hxy : IsRelPrime x y) - (P : (ι → K) ≃ₗ[K] (ι → K)) (d e : ℕ) - (hP : ∀ v ∈ coordinateLattice (R := R), (x*y)^d • P v ∈ coordinateLattice (R := R)) - (hQ : ∀ v ∈ coordinateLattice (R := R), (x*y)^e • P.symm v ∈ coordinateLattice (R := R)) - - - -noncomputable def latticeNumerator : gluedLattice x y P →ₗ[R] (ι → R) := - (coordinateEquiv (K := K)).symm.toLinearMap ∘ₗ - (((x^d) • (gluedLattice x y P).subtype).codRestrict _ - (fun z => gluedLattice_bound x y hx hxy P d hP z.property)) - -lemma latticeNumerator_coordinates (z : gluedLattice x y P) : - coordinateMap (latticeNumerator x y hx hxy P d hP z) = x^d • z.val := by - change (coordinateEquiv (K := K) - ((coordinateEquiv (K := K)).symm _)).val = _ - rw [LinearEquiv.apply_symm_apply] - rfl - -include hQ in -omit [IsDomain R] [GCDMonoid R] [IsFractionRing R K] in -lemma latticeDenominator_mem (v : ι → R) : - x^e • coordinateMap (K := K) v ∈ gluedLattice x y P := by - have hv : coordinateMap (K := K) v ∈ coordinateLattice (R := R) := ⟨v,rfl⟩ - constructor - · exact ⟨0, by simpa using (coordinateLattice (R := R)).smul_mem (x^e) hv⟩ - · refine ⟨x^e • P.symm (coordinateMap v), ⟨e, ?_⟩, ?_⟩ - · simpa only [mul_pow, mul_smul, smul_comm (y^e)] using hQ _ hv - · change P (x^e • P.symm (coordinateMap v)) = _ - rw [linearEquiv_map_base_smul, LinearEquiv.apply_symm_apply] - -noncomputable def latticeDenominator : (ι → R) →ₗ[R] gluedLattice x y P := - ((x^e) • coordinateMap (R := R) (K := K)).codRestrict _ - (latticeDenominator_mem x y P e hQ) - -lemma latticeNumerator_denominator (v : ι → R) : - latticeNumerator x y hx hxy P d hP (latticeDenominator x y P e hQ v) = - x^(d+e) • v := by - apply coordinateMap_injective (K := K) - rw [latticeNumerator_coordinates, map_smul] - change x^d • (x^e • coordinateMap v) = _ - rw [← mul_smul, ← pow_add] - -lemma latticeDenominator_numerator (z : gluedLattice x y P) : - latticeDenominator x y P e hQ (latticeNumerator x y hx hxy P d hP z) = - x^(d+e) • z := by - apply Subtype.ext - change x^e • coordinateMap (latticeNumerator x y hx hxy P d hP z) = x^(d+e) • z.val - rw [latticeNumerator_coordinates, ← mul_smul, ← pow_add, Nat.add_comm] - -end Numerator -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.Basic + +namespace OAI + +namespace FiberFunctorProof +section Numerator +variable {R K ι : Type*} [CommRing R] [IsDomain R] [GCDMonoid R] + [Field K] [Algebra R K] [IsFractionRing R K] + +omit [IsDomain R] [GCDMonoid R] in +lemma coordinateMap_injective : Function.Injective (coordinateMap (R := R) (K := K) (ι := ι)) := by + intro v w h + funext i + exact (FaithfulSMul.algebraMap_injective R K) (congrFun h i) + +noncomputable def coordinateEquiv : (ι → R) ≃ₗ[R] coordinateLattice (R := R) (K := K) (ι := ι) := + LinearEquiv.ofInjective (coordinateMap (R := R) (K := K) (ι := ι)) coordinateMap_injective + +omit [IsDomain R] [GCDMonoid R] in +lemma coordinateEquiv_apply (v : ι → R) : + (coordinateEquiv (K := K) v).val = coordinateMap v := rfl + +variable (x y : R) (hx : x ≠ 0) (hxy : IsRelPrime x y) + (P : (ι → K) ≃ₗ[K] (ι → K)) (d e : ℕ) + (hP : ∀ v ∈ coordinateLattice (R := R), (x*y)^d • P v ∈ coordinateLattice (R := R)) + (hQ : ∀ v ∈ coordinateLattice (R := R), (x*y)^e • P.symm v ∈ coordinateLattice (R := R)) + + + +noncomputable def latticeNumerator : gluedLattice x y P →ₗ[R] (ι → R) := + (coordinateEquiv (K := K)).symm.toLinearMap ∘ₗ + (((x^d) • (gluedLattice x y P).subtype).codRestrict _ + (fun z => gluedLattice_bound x y hx hxy P d hP z.property)) + +lemma latticeNumerator_coordinates (z : gluedLattice x y P) : + coordinateMap (latticeNumerator x y hx hxy P d hP z) = x^d • z.val := by + change (coordinateEquiv (K := K) + ((coordinateEquiv (K := K)).symm _)).val = _ + rw [LinearEquiv.apply_symm_apply] + rfl + +include hQ in +omit [IsDomain R] [GCDMonoid R] [IsFractionRing R K] in +lemma latticeDenominator_mem (v : ι → R) : + x^e • coordinateMap (K := K) v ∈ gluedLattice x y P := by + have hv : coordinateMap (K := K) v ∈ coordinateLattice (R := R) := ⟨v,rfl⟩ + constructor + · exact ⟨0, by simpa using (coordinateLattice (R := R)).smul_mem (x^e) hv⟩ + · refine ⟨x^e • P.symm (coordinateMap v), ⟨e, ?_⟩, ?_⟩ + · simpa only [mul_pow, mul_smul, smul_comm (y^e)] using hQ _ hv + · change P (x^e • P.symm (coordinateMap v)) = _ + rw [linearEquiv_map_base_smul, LinearEquiv.apply_symm_apply] + +noncomputable def latticeDenominator : (ι → R) →ₗ[R] gluedLattice x y P := + ((x^e) • coordinateMap (R := R) (K := K)).codRestrict _ + (latticeDenominator_mem x y P e hQ) + +lemma latticeNumerator_denominator (v : ι → R) : + latticeNumerator x y hx hxy P d hP (latticeDenominator x y P e hQ v) = + x^(d+e) • v := by + apply coordinateMap_injective (K := K) + rw [latticeNumerator_coordinates, map_smul] + change x^d • (x^e • coordinateMap v) = _ + rw [← mul_smul, ← pow_add] + +lemma latticeDenominator_numerator (z : gluedLattice x y P) : + latticeDenominator x y P e hQ (latticeNumerator x y hx hxy P d hP z) = + x^(d+e) • z := by + apply Subtype.ext + change x^e • coordinateMap (latticeNumerator x y hx hxy P d hP z) = x^(d+e) • z.val + rw [latticeNumerator_coordinates, ← mul_smul, ← pow_add, Nat.add_comm] + +end Numerator +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeSwap.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeSwap.lean index 38598cba0c6fdb3d62e8e0a6822c9ac3a612b7f3..9658ea145e1855771e11943c13ab3319a0a0909b 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeSwap.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/LatticeSwap.lean @@ -1,33 +1,33 @@ -import OAI.RepresentationTheory.RestrictedTilting.LatticeNumerator - -namespace OAI - -namespace FiberFunctorProof -variable {R K ι : Type*} [CommRing R] [IsDomain R] [GCDMonoid R] - [Field K] [Algebra R K] [IsFractionRing R K] - -omit [IsDomain R] [GCDMonoid R] [IsFractionRing R K] in -lemma lattice_swap_mem (x y : R) (P : (ι → K) ≃ₗ[K] (ι → K)) - {v : ι → K} (hv : v ∈ gluedLattice x y P) : - P.symm v ∈ gluedLattice y x P.symm := by - obtain ⟨h₁,w,h₂,hw⟩ := hv - change P w = v at hw - constructor - · simpa only [← hw, LinearEquiv.symm_apply_apply] using h₂ - · exact ⟨v,h₁,rfl⟩ - - - -noncomputable def latticeSwap (x y : R) (P : (ι → K) ≃ₗ[K] (ι → K)) : - gluedLattice x y P ≃ₗ[R] gluedLattice y x P.symm where - toFun v := ⟨P.symm v.val, lattice_swap_mem x y P v.property⟩ - invFun v := ⟨P v.val, by - simpa only [LinearEquiv.symm_symm] using lattice_swap_mem y x P.symm v.property⟩ - left_inv v := by apply Subtype.ext; exact P.apply_symm_apply v.val - right_inv v := by apply Subtype.ext; exact P.symm_apply_apply v.val - map_add' v w := by apply Subtype.ext; exact P.symm.map_add _ _ - map_smul' a v := by apply Subtype.ext; exact linearEquiv_map_base_smul P.symm a v.val - -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.LatticeNumerator + +namespace OAI + +namespace FiberFunctorProof +variable {R K ι : Type*} [CommRing R] [IsDomain R] [GCDMonoid R] + [Field K] [Algebra R K] [IsFractionRing R K] + +omit [IsDomain R] [GCDMonoid R] [IsFractionRing R K] in +lemma lattice_swap_mem (x y : R) (P : (ι → K) ≃ₗ[K] (ι → K)) + {v : ι → K} (hv : v ∈ gluedLattice x y P) : + P.symm v ∈ gluedLattice y x P.symm := by + obtain ⟨h₁,w,h₂,hw⟩ := hv + change P w = v at hw + constructor + · simpa only [← hw, LinearEquiv.symm_apply_apply] using h₂ + · exact ⟨v,h₁,rfl⟩ + + + +noncomputable def latticeSwap (x y : R) (P : (ι → K) ≃ₗ[K] (ι → K)) : + gluedLattice x y P ≃ₗ[R] gluedLattice y x P.symm where + toFun v := ⟨P.symm v.val, lattice_swap_mem x y P v.property⟩ + invFun v := ⟨P v.val, by + simpa only [LinearEquiv.symm_symm] using lattice_swap_mem y x P.symm v.property⟩ + left_inv v := by apply Subtype.ext; exact P.apply_symm_apply v.val + right_inv v := by apply Subtype.ext; exact P.symm_apply_apply v.val + map_add' v w := by apply Subtype.ext; exact P.symm.map_add _ _ + map_smul' a v := by apply Subtype.ext; exact linearEquiv_map_base_smul P.symm a v.val + +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/LaurentPolynomialSeparation.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/LaurentPolynomialSeparation.lean index 31df8b6d9702a8963639dd3ecb03f4fc227a22d1..a9c9537e5551f7c873673772f2c2a6b8b7b2fde0 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/LaurentPolynomialSeparation.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/LaurentPolynomialSeparation.lean @@ -1,71 +1,71 @@ -import Mathlib - -namespace OAI - -namespace FiberFunctorProof -open scoped LaurentPolynomial -section -variable {k L : Type*} [Field k] [Infinite k] [Field L] [Algebra k L] - -lemma polynomial_eq_of_base_evals (P Q : Polynomial L) - (h : ∀ t : k, P.eval (algebraMap k L t) = Q.eval (algebraMap k L t)) : P = Q := by - apply Polynomial.eq_of_infinite_eval_eq - apply (Set.infinite_range_of_injective (FaithfulSMul.algebraMap_injective k L)).mono - rintro _ ⟨t,rfl⟩ - exact h t - -lemma laurent_eq_zero_of_base_evals (P : LaurentPolynomial L) - (h : ∀ a : kˣ, - LaurentPolynomial.eval₂ (RingHom.id L) (Units.map (algebraMap k L) a) P = 0) : P = 0 := by - obtain ⟨n,p,hp⟩ := P.exists_T_pow - have hp0 : p = 0 := by - apply Polynomial.eq_of_infinite_eval_eq - apply (((Set.finite_singleton (0:k)).infinite_compl).image - (FaithfulSMul.algebraMap_injective k L).injOn).mono - rintro b ⟨a,ha,rfl⟩ - let x : kˣ := Units.mk0 a ha - have he := congrArg (LaurentPolynomial.eval₂ (RingHom.id L) - (Units.map (algebraMap k L) x)) hp - simp only [LaurentPolynomial.eval₂_toLaurent, map_mul, h x, zero_mul, - Polynomial.eval₂_id] at he - change p.eval (algebraMap k L a) = Polynomial.eval (algebraMap k L a) 0 - have hx : ((Units.map (algebraMap k L) x : Lˣ) : L) = algebraMap k L a := rfl - rw [hx] at he - simpa only [Polynomial.eval_zero] using he - rw [hp0, map_zero] at hp - exact (mul_eq_zero.mp hp.symm).resolve_right (IsUnit.ne_zero (LaurentPolynomial.isUnit_T n)) - -lemma laurent_eq_of_base_evals (P Q : LaurentPolynomial L) - (h : ∀ a : kˣ, - LaurentPolynomial.eval₂ (RingHom.id L) (Units.map (algebraMap k L) a) P = - LaurentPolynomial.eval₂ (RingHom.id L) (Units.map (algebraMap k L) a) Q) : P = Q := by - apply sub_eq_zero.mp - apply laurent_eq_zero_of_base_evals (k := k) - intro a - rw [map_sub, h a, sub_self] -lemma laurent_eq_of_evals (P Q : LaurentPolynomial k) - (h : ∀ a : kˣ, LaurentPolynomial.eval₂ (RingHom.id k) a P = - LaurentPolynomial.eval₂ (RingHom.id k) a Q) : P = Q := by - have hz (a : kˣ) : LaurentPolynomial.eval₂ (RingHom.id k) a (P-Q) = 0 := by - rw [map_sub, h a, sub_self] - obtain ⟨n,p,hp⟩ := (P-Q).exists_T_pow - have hp0 : p = 0 := by - apply Polynomial.eq_of_infinite_eval_eq - apply ((Set.finite_singleton (0:k)).infinite_compl).mono - intro a ha - let x : kˣ := Units.mk0 a ha - have he := congrArg (LaurentPolynomial.eval₂ (RingHom.id k) x) hp - simp only [LaurentPolynomial.eval₂_toLaurent, map_mul, hz x, zero_mul, - Polynomial.eval₂_id] at he - have hx : (x : k) = a := rfl - rw [hx] at he - change p.eval a = Polynomial.eval a 0 - simpa only [Polynomial.eval_zero] using he - rw [hp0, map_zero] at hp - exact sub_eq_zero.mp ((mul_eq_zero.mp hp.symm).resolve_right - (IsUnit.ne_zero (LaurentPolynomial.isUnit_T n))) - -end -end FiberFunctorProof - -end OAI +import Mathlib + +namespace OAI + +namespace FiberFunctorProof +open scoped LaurentPolynomial +section +variable {k L : Type*} [Field k] [Infinite k] [Field L] [Algebra k L] + +lemma polynomial_eq_of_base_evals (P Q : Polynomial L) + (h : ∀ t : k, P.eval (algebraMap k L t) = Q.eval (algebraMap k L t)) : P = Q := by + apply Polynomial.eq_of_infinite_eval_eq + apply (Set.infinite_range_of_injective (FaithfulSMul.algebraMap_injective k L)).mono + rintro _ ⟨t,rfl⟩ + exact h t + +lemma laurent_eq_zero_of_base_evals (P : LaurentPolynomial L) + (h : ∀ a : kˣ, + LaurentPolynomial.eval₂ (RingHom.id L) (Units.map (algebraMap k L) a) P = 0) : P = 0 := by + obtain ⟨n,p,hp⟩ := P.exists_T_pow + have hp0 : p = 0 := by + apply Polynomial.eq_of_infinite_eval_eq + apply (((Set.finite_singleton (0:k)).infinite_compl).image + (FaithfulSMul.algebraMap_injective k L).injOn).mono + rintro b ⟨a,ha,rfl⟩ + let x : kˣ := Units.mk0 a ha + have he := congrArg (LaurentPolynomial.eval₂ (RingHom.id L) + (Units.map (algebraMap k L) x)) hp + simp only [LaurentPolynomial.eval₂_toLaurent, map_mul, h x, zero_mul, + Polynomial.eval₂_id] at he + change p.eval (algebraMap k L a) = Polynomial.eval (algebraMap k L a) 0 + have hx : ((Units.map (algebraMap k L) x : Lˣ) : L) = algebraMap k L a := rfl + rw [hx] at he + simpa only [Polynomial.eval_zero] using he + rw [hp0, map_zero] at hp + exact (mul_eq_zero.mp hp.symm).resolve_right (IsUnit.ne_zero (LaurentPolynomial.isUnit_T n)) + +lemma laurent_eq_of_base_evals (P Q : LaurentPolynomial L) + (h : ∀ a : kˣ, + LaurentPolynomial.eval₂ (RingHom.id L) (Units.map (algebraMap k L) a) P = + LaurentPolynomial.eval₂ (RingHom.id L) (Units.map (algebraMap k L) a) Q) : P = Q := by + apply sub_eq_zero.mp + apply laurent_eq_zero_of_base_evals (k := k) + intro a + rw [map_sub, h a, sub_self] +lemma laurent_eq_of_evals (P Q : LaurentPolynomial k) + (h : ∀ a : kˣ, LaurentPolynomial.eval₂ (RingHom.id k) a P = + LaurentPolynomial.eval₂ (RingHom.id k) a Q) : P = Q := by + have hz (a : kˣ) : LaurentPolynomial.eval₂ (RingHom.id k) a (P-Q) = 0 := by + rw [map_sub, h a, sub_self] + obtain ⟨n,p,hp⟩ := (P-Q).exists_T_pow + have hp0 : p = 0 := by + apply Polynomial.eq_of_infinite_eval_eq + apply ((Set.finite_singleton (0:k)).infinite_compl).mono + intro a ha + let x : kˣ := Units.mk0 a ha + have he := congrArg (LaurentPolynomial.eval₂ (RingHom.id k) x) hp + simp only [LaurentPolynomial.eval₂_toLaurent, map_mul, hz x, zero_mul, + Polynomial.eval₂_id] at he + have hx : (x : k) = a := rfl + rw [hx] at he + change p.eval a = Polynomial.eval a 0 + simpa only [Polynomial.eval_zero] using he + rw [hp0, map_zero] at hp + exact sub_eq_zero.mp ((mul_eq_zero.mp hp.symm).resolve_right + (IsUnit.ne_zero (LaurentPolynomial.isUnit_T n))) + +end +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/LinearFormalComparison.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/LinearFormalComparison.lean index bebc93ddce8d549d01e0cb3c996633fbb052c52b..bdc63411c06cfed6c6ddb54103d3657726b3cbcd 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/LinearFormalComparison.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/LinearFormalComparison.lean @@ -1,85 +1,85 @@ -import OAI.RepresentationTheory.RestrictedTilting.MatrixFormalComparison -import OAI.RepresentationTheory.RestrictedTilting.CoordinateTensor - -namespace OAI - -namespace FiberFunctorProof -open Matrix -open scoped TensorProduct BigOperators -universe u v -variable {k : Type u} [Field k] [Infinite k] -variable {K : Type v} [Field K] [Algebra k K] -variable {ι : Type u} [Fintype ι] [DecidableEq ι] -variable {T : Type u} [AddCommGroup T] [Module k T] [Module.Finite k T] - -omit [Infinite k] in -lemma scalarCoordinates_one (v : ι → k) : - (TensorProduct.piScalarRight k K K ι) (1 ⊗ₜ[k] v) = fun i => algebraMap k K (v i) := by - simp only [TensorProduct.piScalarRight_apply, TensorProduct.piScalarRightHom_tmul, - Algebra.smul_def, mul_one] - -omit [Infinite k] in -lemma scalarCoordinates_symm_base (v : ι → k) : - (TensorProduct.piScalarRight k K K ι).symm (fun i => algebraMap k K (v i)) = 1 ⊗ₜ[k] v := by - rw [← scalarCoordinates_one, LinearEquiv.symm_apply_apply] - -omit [Infinite k] [DecidableEq ι] in -lemma eq_finrank_of_field_equiv (F : (K ⊗[k] T) ≃ₗ[K] (ι → K)) : - Module.finrank k T = Module.finrank k (ι → k) := by - rw [Module.finrank_fintype_fun_eq_card, ← Module.finrank_baseChange (R := K)] - exact F.finrank_eq.trans (Module.finrank_fintype_fun_eq_card K) - - - -theorem linear_formal_comparison - (ρ : Representation k (SL2 k) T) (hρ : IsRational k ρ) - (P : Matrix ι ι (Polynomial k)) (x : K) (hx : x ≠ 0) - (F : (K ⊗[k] T) ≃ₗ[K] (ι → K)) - (hF : ∀ t : k, ∀ v : T, - F (1 ⊗ₜ[k] ρ (unipotent k t) v) = - polynomialMatrixEval P (algebraMap k K t / x^2) *ᵥ F (1 ⊗ₜ[k] v)) : - ∃ E : T ≃ₗ[k] (ι → k), ∀ t : k, ∀ v : T, - E (ρ (unipotent k t) v) = polynomialMatrixEval P t *ᵥ E v := by - let e : T ≃ₗ[k] (ι → k) := LinearEquiv.ofFinrankEq T (ι → k) (eq_finrank_of_field_equiv F) - let τ := coordinateRepresentation k ρ e - have hτ : IsRational k τ := coordinateRepresentation_rational k ρ e hρ - let Q := TensorProduct.piScalarRight k K K ι - let C₀ : (ι → K) ≃ₗ[K] (ι → K) := Q.symm ≪≫ₗ e.symm.baseChange k K _ _ ≪≫ₗ F - let C := LinearMap.toMatrix' C₀.toLinearMap - have hC : C.det ≠ 0 := (C₀.isUnit_det (Pi.basisFun K ι) (Pi.basisFun K ι)).ne_zero - have hCv (v : ι → k) : C *ᵥ (fun i => algebraMap k K (v i)) = F (1 ⊗ₜ[k] e.symm v) := by - rw [LinearMap.toMatrix'_mulVec] - change F (e.symm.baseChange k K _ _ (Q.symm (fun i => algebraMap k K (v i)))) = _ - rw [scalarCoordinates_symm_base, LinearEquiv.baseChange_tmul] - have hCeq (t : k) : C * (LinearMap.toMatrix' (τ (unipotent k t))).map (algebraMap k K) = - polynomialMatrixEval P (algebraMap k K t / x^2) * C := by - apply Matrix.ext_of_mulVec_single - intro j - rw [← Matrix.mulVec_mulVec, ← Matrix.mulVec_mulVec] - have hsingle : (Pi.single j 1 : ι → K) = fun i => algebraMap k K ((Pi.single j 1 : ι → k) i) := by - funext i - simp [Pi.single_apply] - have hmap (B : Matrix ι ι k) (v : ι → k) : - B.map (algebraMap k K) *ᵥ (fun i => algebraMap k K (v i)) = - fun i => algebraMap k K ((B *ᵥ v) i) := by - funext i - exact (RingHom.map_mulVec (algebraMap k K) B v i).symm - rw [hsingle, hmap, hCv, hCv, LinearMap.toMatrix'_mulVec] - have heq : e.symm (τ (unipotent k t) (Pi.single j 1)) = - ρ (unipotent k t) (e.symm (Pi.single j 1)) := by - apply e.injective - rw [e.apply_symm_apply, coordinateRepresentation_equiv, e.apply_symm_apply] - rw [heq] - exact hF t _ - obtain ⟨D,hD,heD⟩ := matrix_formal_comparison τ hτ P x hx C hC hCeq - let E₀ := Matrix.toLinearEquiv (Pi.basisFun k ι) D (isUnit_iff_ne_zero.mpr hD) - have hE₀ (v : ι → k) : E₀ v = D *ᵥ v := by - rw [Matrix.toLinearEquiv_apply] - rfl - refine ⟨e.trans E₀, fun t v => ?_⟩ - simp only [LinearEquiv.trans_apply, hE₀, coordinateRepresentation_equiv] - rw [← LinearMap.toMatrix'_mulVec (τ (unipotent k t)), Matrix.mulVec_mulVec, - ← heD, ← Matrix.mulVec_mulVec] -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.MatrixFormalComparison +import OAI.RepresentationTheory.RestrictedTilting.CoordinateTensor + +namespace OAI + +namespace FiberFunctorProof +open Matrix +open scoped TensorProduct BigOperators +universe u v +variable {k : Type u} [Field k] [Infinite k] +variable {K : Type v} [Field K] [Algebra k K] +variable {ι : Type u} [Fintype ι] [DecidableEq ι] +variable {T : Type u} [AddCommGroup T] [Module k T] [Module.Finite k T] + +omit [Infinite k] in +lemma scalarCoordinates_one (v : ι → k) : + (TensorProduct.piScalarRight k K K ι) (1 ⊗ₜ[k] v) = fun i => algebraMap k K (v i) := by + simp only [TensorProduct.piScalarRight_apply, TensorProduct.piScalarRightHom_tmul, + Algebra.smul_def, mul_one] + +omit [Infinite k] in +lemma scalarCoordinates_symm_base (v : ι → k) : + (TensorProduct.piScalarRight k K K ι).symm (fun i => algebraMap k K (v i)) = 1 ⊗ₜ[k] v := by + rw [← scalarCoordinates_one, LinearEquiv.symm_apply_apply] + +omit [Infinite k] [DecidableEq ι] in +lemma eq_finrank_of_field_equiv (F : (K ⊗[k] T) ≃ₗ[K] (ι → K)) : + Module.finrank k T = Module.finrank k (ι → k) := by + rw [Module.finrank_fintype_fun_eq_card, ← Module.finrank_baseChange (R := K)] + exact F.finrank_eq.trans (Module.finrank_fintype_fun_eq_card K) + + + +theorem linear_formal_comparison + (ρ : Representation k (SL2 k) T) (hρ : IsRational k ρ) + (P : Matrix ι ι (Polynomial k)) (x : K) (hx : x ≠ 0) + (F : (K ⊗[k] T) ≃ₗ[K] (ι → K)) + (hF : ∀ t : k, ∀ v : T, + F (1 ⊗ₜ[k] ρ (unipotent k t) v) = + polynomialMatrixEval P (algebraMap k K t / x^2) *ᵥ F (1 ⊗ₜ[k] v)) : + ∃ E : T ≃ₗ[k] (ι → k), ∀ t : k, ∀ v : T, + E (ρ (unipotent k t) v) = polynomialMatrixEval P t *ᵥ E v := by + let e : T ≃ₗ[k] (ι → k) := LinearEquiv.ofFinrankEq T (ι → k) (eq_finrank_of_field_equiv F) + let τ := coordinateRepresentation k ρ e + have hτ : IsRational k τ := coordinateRepresentation_rational k ρ e hρ + let Q := TensorProduct.piScalarRight k K K ι + let C₀ : (ι → K) ≃ₗ[K] (ι → K) := Q.symm ≪≫ₗ e.symm.baseChange k K _ _ ≪≫ₗ F + let C := LinearMap.toMatrix' C₀.toLinearMap + have hC : C.det ≠ 0 := (C₀.isUnit_det (Pi.basisFun K ι) (Pi.basisFun K ι)).ne_zero + have hCv (v : ι → k) : C *ᵥ (fun i => algebraMap k K (v i)) = F (1 ⊗ₜ[k] e.symm v) := by + rw [LinearMap.toMatrix'_mulVec] + change F (e.symm.baseChange k K _ _ (Q.symm (fun i => algebraMap k K (v i)))) = _ + rw [scalarCoordinates_symm_base, LinearEquiv.baseChange_tmul] + have hCeq (t : k) : C * (LinearMap.toMatrix' (τ (unipotent k t))).map (algebraMap k K) = + polynomialMatrixEval P (algebraMap k K t / x^2) * C := by + apply Matrix.ext_of_mulVec_single + intro j + rw [← Matrix.mulVec_mulVec, ← Matrix.mulVec_mulVec] + have hsingle : (Pi.single j 1 : ι → K) = fun i => algebraMap k K ((Pi.single j 1 : ι → k) i) := by + funext i + simp [Pi.single_apply] + have hmap (B : Matrix ι ι k) (v : ι → k) : + B.map (algebraMap k K) *ᵥ (fun i => algebraMap k K (v i)) = + fun i => algebraMap k K ((B *ᵥ v) i) := by + funext i + exact (RingHom.map_mulVec (algebraMap k K) B v i).symm + rw [hsingle, hmap, hCv, hCv, LinearMap.toMatrix'_mulVec] + have heq : e.symm (τ (unipotent k t) (Pi.single j 1)) = + ρ (unipotent k t) (e.symm (Pi.single j 1)) := by + apply e.injective + rw [e.apply_symm_apply, coordinateRepresentation_equiv, e.apply_symm_apply] + rw [heq] + exact hF t _ + obtain ⟨D,hD,heD⟩ := matrix_formal_comparison τ hτ P x hx C hC hCeq + let E₀ := Matrix.toLinearEquiv (Pi.basisFun k ι) D (isUnit_iff_ne_zero.mpr hD) + have hE₀ (v : ι → k) : E₀ v = D *ᵥ v := by + rw [Matrix.toLinearEquiv_apply] + rfl + refine ⟨e.trans E₀, fun t v => ?_⟩ + simp only [LinearEquiv.trans_apply, hE₀, coordinateRepresentation_equiv] + rw [← LinearMap.toMatrix'_mulVec (τ (unipotent k t)), Matrix.mulVec_mulVec, + ← heD, ← Matrix.mulVec_mulVec] +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/LocalFreeness.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/LocalFreeness.lean index ef263fddf135c4b1a884d976ff6f9dc3557ef228..bf674cd436a12f2184793b0ec3c409543d607efa 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/LocalFreeness.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/LocalFreeness.lean @@ -1,139 +1,139 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.AssociatedLattices - -namespace OAI - -/-! Weak regularity and local freeness of associated sections. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section -open scoped Pointwise TensorProduct -open RingTheory.Sequence - -section -variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M] - -lemma weaklyRegular_pair_iff (x y : R) : - IsWeaklyRegular M [x,y] ↔ - Function.Injective (fun m : M => x • m) ∧ - ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w := by - rw [isWeaklyRegular_cons_iff, isWeaklyRegular_singleton_iff] - change IsSMulRegular M x ∧ IsSMulRegular (M ⧸ (x • (⊤ : Submodule R M))) y ↔ _ - rw [isSMulRegular_on_quot_iff_lsmul_comap_le] - constructor - · rintro ⟨hx,hy⟩ - refine ⟨hx, fun v n hn => ?_⟩ - have hv : v ∈ x • (⊤ : Submodule R M) := hy (by - change y • v ∈ x • (⊤ : Submodule R M) - rw [hn] - exact Submodule.smul_mem_pointwise_smul n x ⊤ (by trivial)) - obtain ⟨w,_,hw⟩ := (Submodule.mem_smul_pointwise_iff_exists _ _ _).mp hv - exact ⟨w,hw.symm⟩ - · rintro ⟨hx,hy⟩ - refine ⟨hx, ?_⟩ - intro v hv - obtain ⟨n,_,hn⟩ := (Submodule.mem_smul_pointwise_iff_exists _ _ _).mp hv - obtain ⟨w,hw⟩ := hy v n hn.symm - rw [hw] - exact Submodule.smul_mem_pointwise_smul w x ⊤ (by trivial) - -end - - - -theorem flat_baseChange_free {R S M : Type*} - [CommRing R] [CommRing S] [Algebra R S] [Module.Flat R S] - [IsLocalRing S] [IsNoetherianRing S] - [AddCommGroup M] [Module R M] [Module.Finite R M] - (x y : R) (hm : IsLocalRing.maximalIdeal S = - Ideal.span {algebraMap R S x, algebraMap R S y}) - (hx : Function.Injective (fun m : M => x • m)) - (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) : - Module.Free S (S ⊗[R] M) := by - have hr := (weaklyRegular_pair_iff x y).mpr ⟨hx,hy⟩ - have hS := hr.isWeaklyRegular_lTensor (M₂ := S) - obtain ⟨hxS,hyS⟩ := (weaklyRegular_pair_iff (M := S ⊗[R] M) x y).mp hS - let : Module.FinitePresentation S (S ⊗[R] M) := Module.finitePresentation_of_finite S _ - apply free_of_two_generators (algebraMap R S x) (algebraMap R S y) hm - · simpa only [algebraMap_smul] using hxS - · simpa only [algebraMap_smul] using hyS -end - -open scoped TensorProduct - -lemma gluedLattice_regular {R K ι : Type*} [CommRing R] [Field K] - [Algebra R K] [FaithfulSMul R K] (x y : R) (hx : x ≠ 0) (hy : y ≠ 0) - (P : (ι → K) ≃ₗ[K] (ι → K)) : - Function.Injective (fun m : gluedLattice x y P => x • m) ∧ - ∀ v n : gluedLattice x y P, y • v = x • n → - ∃ w : gluedLattice x y P, v = x • w := by - have hinj := FaithfulSMul.algebraMap_injective R K - have hxK : algebraMap R K x ≠ 0 := fun h => hx (hinj (h.trans (map_zero _).symm)) - have hyK : algebraMap R K y ≠ 0 := fun h => hy (hinj (h.trans (map_zero _).symm)) - have hB : ∀ z ∈ (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R), - (algebraMap R K y)⁻¹ • z ∈ - (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) := by - rintro z ⟨v,hv,rfl⟩ - refine ⟨(algebraMap R K y)⁻¹ • v, powerLocalization_div y _ hyK hv, ?_⟩ - exact P.map_smul _ _ - exact intersection_regular _ _ x y hxK hyK - (fun _ hv => powerLocalization_div x _ hxK hv) hB - -lemma regular_pair_equiv {R M N : Type*} [CommRing R] - [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N] - (e : M ≃ₗ[R] N) (x y : R) - (hx : Function.Injective (fun n : N => x • n)) - (hy : ∀ v n : N, y • v = x • n → ∃ w : N, v = x • w) : - Function.Injective (fun m : M => x • m) ∧ - ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w := by - constructor - · intro a b hab - apply e.injective - apply hx - simpa using congrArg e hab - · intro v n hn - obtain ⟨w,hw⟩ := hy (e v) (e n) (by simpa using congrArg e hn) - refine ⟨e.symm w, e.injective ?_⟩ - simpa using hw - -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (ι : Type u) [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) -variable (P : Matrix ι ι (Polynomial k)) -variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) - -include hP in - -theorem associatedSections_regular : - Function.Injective (fun m : associatedSectionsSubmodule k ι ρ => - (MvPolynomial.X (0 : Fin 2) : MvPolynomial (Fin 2) k) • m) ∧ - ∀ v n : associatedSectionsSubmodule k ι ρ, - (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) • v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n → - ∃ w : associatedSectionsSubmodule k ι ρ, v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • w := by - obtain ⟨hx,hy⟩ := gluedLattice_regular - (MvPolynomial.X (0 : Fin 2) : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) - (MvPolynomial.X_ne_zero 0) (MvPolynomial.X_ne_zero 1) - (planeGlobalTransition k P (associatedPolynomial_zero k ι ρ P hP) - (associatedPolynomial_add k ι ρ P hP)) - exact regular_pair_equiv (associatedLatticeEquiv k ι ρ P hP) _ _ hx hy - -include hP in - - -theorem associatedStalk_free (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : - Module.Free (planeOriginRing k) - ((planeOriginRing k) ⊗[MvPolynomial (Fin 2) k] (associatedSectionsSubmodule k ι ρ)) := by - let : Module.Finite (MvPolynomial (Fin 2) k) (associatedSectionsSubmodule k ι ρ) := - associatedSections_finite k ι ρ P hP d hd - obtain ⟨hx,hy⟩ := associatedSections_regular k ι ρ P hP - exact flat_baseChange_free (MvPolynomial.X 0) (MvPolynomial.X 1) - (planeOrigin_maximalIdeal k) hx hy -end FiberFunctorProof -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.AssociatedLattices + +namespace OAI + +/-! Weak regularity and local freeness of associated sections. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section +open scoped Pointwise TensorProduct +open RingTheory.Sequence + +section +variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M] + +lemma weaklyRegular_pair_iff (x y : R) : + IsWeaklyRegular M [x,y] ↔ + Function.Injective (fun m : M => x • m) ∧ + ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w := by + rw [isWeaklyRegular_cons_iff, isWeaklyRegular_singleton_iff] + change IsSMulRegular M x ∧ IsSMulRegular (M ⧸ (x • (⊤ : Submodule R M))) y ↔ _ + rw [isSMulRegular_on_quot_iff_lsmul_comap_le] + constructor + · rintro ⟨hx,hy⟩ + refine ⟨hx, fun v n hn => ?_⟩ + have hv : v ∈ x • (⊤ : Submodule R M) := hy (by + change y • v ∈ x • (⊤ : Submodule R M) + rw [hn] + exact Submodule.smul_mem_pointwise_smul n x ⊤ (by trivial)) + obtain ⟨w,_,hw⟩ := (Submodule.mem_smul_pointwise_iff_exists _ _ _).mp hv + exact ⟨w,hw.symm⟩ + · rintro ⟨hx,hy⟩ + refine ⟨hx, ?_⟩ + intro v hv + obtain ⟨n,_,hn⟩ := (Submodule.mem_smul_pointwise_iff_exists _ _ _).mp hv + obtain ⟨w,hw⟩ := hy v n hn.symm + rw [hw] + exact Submodule.smul_mem_pointwise_smul w x ⊤ (by trivial) + +end + + + +theorem flat_baseChange_free {R S M : Type*} + [CommRing R] [CommRing S] [Algebra R S] [Module.Flat R S] + [IsLocalRing S] [IsNoetherianRing S] + [AddCommGroup M] [Module R M] [Module.Finite R M] + (x y : R) (hm : IsLocalRing.maximalIdeal S = + Ideal.span {algebraMap R S x, algebraMap R S y}) + (hx : Function.Injective (fun m : M => x • m)) + (hy : ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w) : + Module.Free S (S ⊗[R] M) := by + have hr := (weaklyRegular_pair_iff x y).mpr ⟨hx,hy⟩ + have hS := hr.isWeaklyRegular_lTensor (M₂ := S) + obtain ⟨hxS,hyS⟩ := (weaklyRegular_pair_iff (M := S ⊗[R] M) x y).mp hS + let : Module.FinitePresentation S (S ⊗[R] M) := Module.finitePresentation_of_finite S _ + apply free_of_two_generators (algebraMap R S x) (algebraMap R S y) hm + · simpa only [algebraMap_smul] using hxS + · simpa only [algebraMap_smul] using hyS +end + +open scoped TensorProduct + +lemma gluedLattice_regular {R K ι : Type*} [CommRing R] [Field K] + [Algebra R K] [FaithfulSMul R K] (x y : R) (hx : x ≠ 0) (hy : y ≠ 0) + (P : (ι → K) ≃ₗ[K] (ι → K)) : + Function.Injective (fun m : gluedLattice x y P => x • m) ∧ + ∀ v n : gluedLattice x y P, y • v = x • n → + ∃ w : gluedLattice x y P, v = x • w := by + have hinj := FaithfulSMul.algebraMap_injective R K + have hxK : algebraMap R K x ≠ 0 := fun h => hx (hinj (h.trans (map_zero _).symm)) + have hyK : algebraMap R K y ≠ 0 := fun h => hy (hinj (h.trans (map_zero _).symm)) + have hB : ∀ z ∈ (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R), + (algebraMap R K y)⁻¹ • z ∈ + (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) := by + rintro z ⟨v,hv,rfl⟩ + refine ⟨(algebraMap R K y)⁻¹ • v, powerLocalization_div y _ hyK hv, ?_⟩ + exact P.map_smul _ _ + exact intersection_regular _ _ x y hxK hyK + (fun _ hv => powerLocalization_div x _ hxK hv) hB + +lemma regular_pair_equiv {R M N : Type*} [CommRing R] + [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N] + (e : M ≃ₗ[R] N) (x y : R) + (hx : Function.Injective (fun n : N => x • n)) + (hy : ∀ v n : N, y • v = x • n → ∃ w : N, v = x • w) : + Function.Injective (fun m : M => x • m) ∧ + ∀ v n : M, y • v = x • n → ∃ w : M, v = x • w := by + constructor + · intro a b hab + apply e.injective + apply hx + simpa using congrArg e hab + · intro v n hn + obtain ⟨w,hw⟩ := hy (e v) (e n) (by simpa using congrArg e hn) + refine ⟨e.symm w, e.injective ?_⟩ + simpa using hw + +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (ι : Type u) [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) +variable (P : Matrix ι ι (Polynomial k)) +variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) + +include hP in + +theorem associatedSections_regular : + Function.Injective (fun m : associatedSectionsSubmodule k ι ρ => + (MvPolynomial.X (0 : Fin 2) : MvPolynomial (Fin 2) k) • m) ∧ + ∀ v n : associatedSectionsSubmodule k ι ρ, + (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) • v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n → + ∃ w : associatedSectionsSubmodule k ι ρ, v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • w := by + obtain ⟨hx,hy⟩ := gluedLattice_regular + (MvPolynomial.X (0 : Fin 2) : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) + (MvPolynomial.X_ne_zero 0) (MvPolynomial.X_ne_zero 1) + (planeGlobalTransition k P (associatedPolynomial_zero k ι ρ P hP) + (associatedPolynomial_add k ι ρ P hP)) + exact regular_pair_equiv (associatedLatticeEquiv k ι ρ P hP) _ _ hx hy + +include hP in + + +theorem associatedStalk_free (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : + Module.Free (planeOriginRing k) + ((planeOriginRing k) ⊗[MvPolynomial (Fin 2) k] (associatedSectionsSubmodule k ι ρ)) := by + let : Module.Finite (MvPolynomial (Fin 2) k) (associatedSectionsSubmodule k ι ρ) := + associatedSections_finite k ι ρ P hP d hd + obtain ⟨hx,hy⟩ := associatedSections_regular k ι ρ P hP + exact flat_baseChange_free (MvPolynomial.X 0) (MvPolynomial.X 1) + (planeOrigin_maximalIdeal k) hx hy +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/LowDegreeTrace.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/LowDegreeTrace.lean index 46bac23a14e4d44845a7e19869b729f790c08add..1f6347d78dd6dc9a00da88140f86021c88c3f35e 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/LowDegreeTrace.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/LowDegreeTrace.lean @@ -1,49 +1,49 @@ -import Mathlib - -namespace OAI - -namespace FiberFunctorProof -open scoped BigOperators -universe u v -variable {k : Type u} [Field k] {E : Type v} [AddGroup E] [Fintype E] [DecidableEq E] - - - -lemma additive_lagrange_denominator (l : E →+ k) (a : E) : - (∏ b ∈ Finset.univ.erase a, (l a - l b)) = - ∏ b ∈ Finset.univ.erase 0, l b := by - classical - apply Finset.prod_equiv (Equiv.subLeft a) - · intro b - simp [Equiv.subLeft_apply, sub_eq_zero, eq_comm] - · intro b _ - simp - - - -theorem finite_additive_polynomial_sum_zero (l : E →+ k) (hl : Function.Injective l) - (P : Polynomial k) (hP : P.natDegree < Fintype.card E - 1) : - ∑ a : E, P.eval (l a) = 0 := by - classical - let c : k := ∏ b ∈ Finset.univ.erase (0 : E), l b - have hc : c ≠ 0 := by - apply Finset.prod_ne_zero_iff.mpr - intro a ha hz - have h := hl (show l a = l 0 by simpa using hz) - exact (Finset.mem_erase.mp ha).1 h - have hd : P.degree < (Finset.univ : Finset E).card := by - apply lt_of_le_of_lt Polynomial.degree_le_natDegree - exact_mod_cast (show P.natDegree < Fintype.card E by omega) - have he := Lagrange.coeff_eq_sum (s := Finset.univ) (v := l) hl.injOn hd - have hcoe : P.coeff ((Finset.univ : Finset E).card - 1) = 0 := - Polynomial.coeff_eq_zero_of_natDegree_lt (by simpa using hP) - rw [hcoe] at he - simp only [additive_lagrange_denominator, ← Finset.sum_div] at he - exact (div_eq_zero_iff.mp he.symm).resolve_right hc - -lemma finite_additive_power_sum_zero (l : E →+ k) (hl : Function.Injective l) - (n : ℕ) (hn : n < Fintype.card E - 1) : ∑ a : E, l a ^ n = 0 := by - simpa using finite_additive_polynomial_sum_zero l hl (Polynomial.X ^ n) (by simpa using hn) -end FiberFunctorProof - -end OAI +import Mathlib + +namespace OAI + +namespace FiberFunctorProof +open scoped BigOperators +universe u v +variable {k : Type u} [Field k] {E : Type v} [AddGroup E] [Fintype E] [DecidableEq E] + + + +lemma additive_lagrange_denominator (l : E →+ k) (a : E) : + (∏ b ∈ Finset.univ.erase a, (l a - l b)) = + ∏ b ∈ Finset.univ.erase 0, l b := by + classical + apply Finset.prod_equiv (Equiv.subLeft a) + · intro b + simp [Equiv.subLeft_apply, sub_eq_zero, eq_comm] + · intro b _ + simp + + + +theorem finite_additive_polynomial_sum_zero (l : E →+ k) (hl : Function.Injective l) + (P : Polynomial k) (hP : P.natDegree < Fintype.card E - 1) : + ∑ a : E, P.eval (l a) = 0 := by + classical + let c : k := ∏ b ∈ Finset.univ.erase (0 : E), l b + have hc : c ≠ 0 := by + apply Finset.prod_ne_zero_iff.mpr + intro a ha hz + have h := hl (show l a = l 0 by simpa using hz) + exact (Finset.mem_erase.mp ha).1 h + have hd : P.degree < (Finset.univ : Finset E).card := by + apply lt_of_le_of_lt Polynomial.degree_le_natDegree + exact_mod_cast (show P.natDegree < Fintype.card E by omega) + have he := Lagrange.coeff_eq_sum (s := Finset.univ) (v := l) hl.injOn hd + have hcoe : P.coeff ((Finset.univ : Finset E).card - 1) = 0 := + Polynomial.coeff_eq_zero_of_natDegree_lt (by simpa using hP) + rw [hcoe] at he + simp only [additive_lagrange_denominator, ← Finset.sum_div] at he + exact (div_eq_zero_iff.mp he.symm).resolve_right hc + +lemma finite_additive_power_sum_zero (l : E →+ k) (hl : Function.Injective l) + (n : ℕ) (hn : n < Fintype.card E - 1) : ∑ a : E, l a ^ n = 0 := by + simpa using finite_additive_polynomial_sum_zero l hl (Polynomial.X ^ n) (by simpa using hn) +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/Main.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/Main.lean index 86e67772993f1282e40da97d300a6637e9ecd220..f89bd639100afdb2897c3adc84e783f671f4a99a 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/Main.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/Main.lean @@ -1,89 +1,89 @@ -import OAI.RepresentationTheory.RestrictedTilting.AdicJets -import OAI.RepresentationTheory.RestrictedTilting.AssociatedBundle -import OAI.RepresentationTheory.RestrictedTilting.AssociatedFibre -import OAI.RepresentationTheory.RestrictedTilting.AssociatedNumerator -import OAI.RepresentationTheory.RestrictedTilting.AssociatedPlaneJet -import OAI.RepresentationTheory.RestrictedTilting.AssociatedProjective -import OAI.RepresentationTheory.RestrictedTilting.BaseChangeProjective -import OAI.RepresentationTheory.RestrictedTilting.BoundedOrigin -import OAI.RepresentationTheory.RestrictedTilting.BoundedOriginTarget -import OAI.RepresentationTheory.RestrictedTilting.BoundedStableFaithfulness -import OAI.RepresentationTheory.RestrictedTilting.BoundedUnipotentTilting -import OAI.RepresentationTheory.RestrictedTilting.BoundedWeightsFactors -import OAI.RepresentationTheory.RestrictedTilting.ClearedPolynomial -import OAI.RepresentationTheory.RestrictedTilting.CompatibleJets -import OAI.RepresentationTheory.RestrictedTilting.CompletedCoordinates -import OAI.RepresentationTheory.RestrictedTilting.CompletionCoefficients -import OAI.RepresentationTheory.RestrictedTilting.CompletionTriviality -import OAI.RepresentationTheory.RestrictedTilting.CoordinateTensor -import OAI.RepresentationTheory.RestrictedTilting.FaithfulTarget -import OAI.RepresentationTheory.RestrictedTilting.FiniteFreeTrace -import OAI.RepresentationTheory.RestrictedTilting.FiniteGenerator -import OAI.RepresentationTheory.RestrictedTilting.FiniteJetMaps -import OAI.RepresentationTheory.RestrictedTilting.FiniteSubgroupLift -import OAI.RepresentationTheory.RestrictedTilting.FormalAssociatedAction -import OAI.RepresentationTheory.RestrictedTilting.FormalAssociatedIso -import OAI.RepresentationTheory.RestrictedTilting.FormalLine -import OAI.RepresentationTheory.RestrictedTilting.FormalLineContinuity -import OAI.RepresentationTheory.RestrictedTilting.FormalSectionAction -import OAI.RepresentationTheory.RestrictedTilting.FormalSections -import OAI.RepresentationTheory.RestrictedTilting.GeneratedStableKernel -import OAI.RepresentationTheory.RestrictedTilting.GoodKernel -import OAI.RepresentationTheory.RestrictedTilting.GoodKernelExtension -import OAI.RepresentationTheory.RestrictedTilting.IntertwinerDescent -import OAI.RepresentationTheory.RestrictedTilting.JetTriviality -import OAI.RepresentationTheory.RestrictedTilting.LatticeLocalProjectivity -import OAI.RepresentationTheory.RestrictedTilting.LatticeNumerator -import OAI.RepresentationTheory.RestrictedTilting.LatticeSwap -import OAI.RepresentationTheory.RestrictedTilting.LaurentPolynomialSeparation -import OAI.RepresentationTheory.RestrictedTilting.LinearFormalComparison -import OAI.RepresentationTheory.RestrictedTilting.LowDegreeTrace -import OAI.RepresentationTheory.RestrictedTilting.Basic -import OAI.RepresentationTheory.RestrictedTilting.MatrixFormalComparison -import OAI.RepresentationTheory.RestrictedTilting.NormConverse -import OAI.RepresentationTheory.RestrictedTilting.NormDefinitions -import OAI.RepresentationTheory.RestrictedTilting.NormFree -import OAI.RepresentationTheory.RestrictedTilting.NormMaps -import OAI.RepresentationTheory.RestrictedTilting.NormProjectivity -import OAI.RepresentationTheory.RestrictedTilting.NumeratorAction -import OAI.RepresentationTheory.RestrictedTilting.PGroupInvariants -import OAI.RepresentationTheory.RestrictedTilting.PiPlaneOrigin -import OAI.RepresentationTheory.RestrictedTilting.PlaneFibre -import OAI.RepresentationTheory.RestrictedTilting.PlaneMatrixTensor -import OAI.RepresentationTheory.RestrictedTilting.PolynomialCovers -import OAI.RepresentationTheory.RestrictedTilting.PolynomialIntertwiner -import OAI.RepresentationTheory.RestrictedTilting.PolynomialJets -import OAI.RepresentationTheory.RestrictedTilting.ProjectiveFactor -import OAI.RepresentationTheory.RestrictedTilting.ProjectiveRegular -import OAI.RepresentationTheory.RestrictedTilting.RationalHomWeights -import OAI.RepresentationTheory.RestrictedTilting.RationalMatrices -import OAI.RepresentationTheory.RestrictedTilting.RegularSplitting -import OAI.RepresentationTheory.RestrictedTilting.RelativeTrace -import OAI.RepresentationTheory.RestrictedTilting.RepProducts -import OAI.RepresentationTheory.RestrictedTilting.RestrictedLift -import OAI.RepresentationTheory.RestrictedTilting.RestrictedTarget -import OAI.RepresentationTheory.RestrictedTilting.RestrictedTilting -import OAI.RepresentationTheory.RestrictedTilting.SmallGroupTrace -import OAI.RepresentationTheory.RestrictedTilting.SpecializeCompletion -import OAI.RepresentationTheory.RestrictedTilting.SplitRepresentation -import OAI.RepresentationTheory.RestrictedTilting.StableKernel -import OAI.RepresentationTheory.RestrictedTilting.StableRestriction -import OAI.RepresentationTheory.RestrictedTilting.SteinbergRegular -import OAI.RepresentationTheory.RestrictedTilting.SteinbergSpan -import OAI.RepresentationTheory.RestrictedTilting.TensorAssociatedAction -import OAI.RepresentationTheory.RestrictedTilting.TensorAssociatedIso -import OAI.RepresentationTheory.RestrictedTilting.TensorCoordinates -import OAI.RepresentationTheory.RestrictedTilting.TensorExactness -import OAI.RepresentationTheory.RestrictedTilting.TensorFormalComparison -import OAI.RepresentationTheory.RestrictedTilting.TensorNumerator -import OAI.RepresentationTheory.RestrictedTilting.TensorPlaneTilting -import OAI.RepresentationTheory.RestrictedTilting.TensorWeights -import OAI.RepresentationTheory.RestrictedTilting.ThetaTarget -import OAI.RepresentationTheory.RestrictedTilting.TiltingCovers -import OAI.RepresentationTheory.RestrictedTilting.TorusExtension -import OAI.RepresentationTheory.RestrictedTilting.TorusRelations -import OAI.RepresentationTheory.RestrictedTilting.TorusWeightProjection -import OAI.RepresentationTheory.RestrictedTilting.TraceFactor -import OAI.RepresentationTheory.RestrictedTilting.UnitAnnihilator -import OAI.RepresentationTheory.RestrictedTilting.UnitSimple -import OAI.RepresentationTheory.RestrictedTilting.XChartLineEval +import OAI.RepresentationTheory.RestrictedTilting.AdicJets +import OAI.RepresentationTheory.RestrictedTilting.AssociatedBundle +import OAI.RepresentationTheory.RestrictedTilting.AssociatedFibre +import OAI.RepresentationTheory.RestrictedTilting.AssociatedNumerator +import OAI.RepresentationTheory.RestrictedTilting.AssociatedPlaneJet +import OAI.RepresentationTheory.RestrictedTilting.AssociatedProjective +import OAI.RepresentationTheory.RestrictedTilting.BaseChangeProjective +import OAI.RepresentationTheory.RestrictedTilting.BoundedOrigin +import OAI.RepresentationTheory.RestrictedTilting.BoundedOriginTarget +import OAI.RepresentationTheory.RestrictedTilting.BoundedStableFaithfulness +import OAI.RepresentationTheory.RestrictedTilting.BoundedUnipotentTilting +import OAI.RepresentationTheory.RestrictedTilting.BoundedWeightsFactors +import OAI.RepresentationTheory.RestrictedTilting.ClearedPolynomial +import OAI.RepresentationTheory.RestrictedTilting.CompatibleJets +import OAI.RepresentationTheory.RestrictedTilting.CompletedCoordinates +import OAI.RepresentationTheory.RestrictedTilting.CompletionCoefficients +import OAI.RepresentationTheory.RestrictedTilting.CompletionTriviality +import OAI.RepresentationTheory.RestrictedTilting.CoordinateTensor +import OAI.RepresentationTheory.RestrictedTilting.FaithfulTarget +import OAI.RepresentationTheory.RestrictedTilting.FiniteFreeTrace +import OAI.RepresentationTheory.RestrictedTilting.FiniteGenerator +import OAI.RepresentationTheory.RestrictedTilting.FiniteJetMaps +import OAI.RepresentationTheory.RestrictedTilting.FiniteSubgroupLift +import OAI.RepresentationTheory.RestrictedTilting.FormalAssociatedAction +import OAI.RepresentationTheory.RestrictedTilting.FormalAssociatedIso +import OAI.RepresentationTheory.RestrictedTilting.FormalLine +import OAI.RepresentationTheory.RestrictedTilting.FormalLineContinuity +import OAI.RepresentationTheory.RestrictedTilting.FormalSectionAction +import OAI.RepresentationTheory.RestrictedTilting.FormalSections +import OAI.RepresentationTheory.RestrictedTilting.GeneratedStableKernel +import OAI.RepresentationTheory.RestrictedTilting.GoodKernel +import OAI.RepresentationTheory.RestrictedTilting.GoodKernelExtension +import OAI.RepresentationTheory.RestrictedTilting.IntertwinerDescent +import OAI.RepresentationTheory.RestrictedTilting.JetTriviality +import OAI.RepresentationTheory.RestrictedTilting.LatticeLocalProjectivity +import OAI.RepresentationTheory.RestrictedTilting.LatticeNumerator +import OAI.RepresentationTheory.RestrictedTilting.LatticeSwap +import OAI.RepresentationTheory.RestrictedTilting.LaurentPolynomialSeparation +import OAI.RepresentationTheory.RestrictedTilting.LinearFormalComparison +import OAI.RepresentationTheory.RestrictedTilting.LowDegreeTrace +import OAI.RepresentationTheory.RestrictedTilting.Basic +import OAI.RepresentationTheory.RestrictedTilting.MatrixFormalComparison +import OAI.RepresentationTheory.RestrictedTilting.NormConverse +import OAI.RepresentationTheory.RestrictedTilting.NormDefinitions +import OAI.RepresentationTheory.RestrictedTilting.NormFree +import OAI.RepresentationTheory.RestrictedTilting.NormMaps +import OAI.RepresentationTheory.RestrictedTilting.NormProjectivity +import OAI.RepresentationTheory.RestrictedTilting.NumeratorAction +import OAI.RepresentationTheory.RestrictedTilting.PGroupInvariants +import OAI.RepresentationTheory.RestrictedTilting.PiPlaneOrigin +import OAI.RepresentationTheory.RestrictedTilting.PlaneFibre +import OAI.RepresentationTheory.RestrictedTilting.PlaneMatrixTensor +import OAI.RepresentationTheory.RestrictedTilting.PolynomialCovers +import OAI.RepresentationTheory.RestrictedTilting.PolynomialIntertwiner +import OAI.RepresentationTheory.RestrictedTilting.PolynomialJets +import OAI.RepresentationTheory.RestrictedTilting.ProjectiveFactor +import OAI.RepresentationTheory.RestrictedTilting.ProjectiveRegular +import OAI.RepresentationTheory.RestrictedTilting.RationalHomWeights +import OAI.RepresentationTheory.RestrictedTilting.RationalMatrices +import OAI.RepresentationTheory.RestrictedTilting.RegularSplitting +import OAI.RepresentationTheory.RestrictedTilting.RelativeTrace +import OAI.RepresentationTheory.RestrictedTilting.RepProducts +import OAI.RepresentationTheory.RestrictedTilting.RestrictedLift +import OAI.RepresentationTheory.RestrictedTilting.RestrictedTarget +import OAI.RepresentationTheory.RestrictedTilting.RestrictedTilting +import OAI.RepresentationTheory.RestrictedTilting.SmallGroupTrace +import OAI.RepresentationTheory.RestrictedTilting.SpecializeCompletion +import OAI.RepresentationTheory.RestrictedTilting.SplitRepresentation +import OAI.RepresentationTheory.RestrictedTilting.StableKernel +import OAI.RepresentationTheory.RestrictedTilting.StableRestriction +import OAI.RepresentationTheory.RestrictedTilting.SteinbergRegular +import OAI.RepresentationTheory.RestrictedTilting.SteinbergSpan +import OAI.RepresentationTheory.RestrictedTilting.TensorAssociatedAction +import OAI.RepresentationTheory.RestrictedTilting.TensorAssociatedIso +import OAI.RepresentationTheory.RestrictedTilting.TensorCoordinates +import OAI.RepresentationTheory.RestrictedTilting.TensorExactness +import OAI.RepresentationTheory.RestrictedTilting.TensorFormalComparison +import OAI.RepresentationTheory.RestrictedTilting.TensorNumerator +import OAI.RepresentationTheory.RestrictedTilting.TensorPlaneTilting +import OAI.RepresentationTheory.RestrictedTilting.TensorWeights +import OAI.RepresentationTheory.RestrictedTilting.ThetaTarget +import OAI.RepresentationTheory.RestrictedTilting.TiltingCovers +import OAI.RepresentationTheory.RestrictedTilting.TorusExtension +import OAI.RepresentationTheory.RestrictedTilting.TorusRelations +import OAI.RepresentationTheory.RestrictedTilting.TorusWeightProjection +import OAI.RepresentationTheory.RestrictedTilting.TraceFactor +import OAI.RepresentationTheory.RestrictedTilting.UnitAnnihilator +import OAI.RepresentationTheory.RestrictedTilting.UnitSimple +import OAI.RepresentationTheory.RestrictedTilting.XChartLineEval diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/MatrixFormalComparison.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/MatrixFormalComparison.lean index 501d1aa7dd3bdb3a776a54d571ec0c5a6b47d2d0..aa1c13c27f29f828be4a8199d13379a26cf38260 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/MatrixFormalComparison.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/MatrixFormalComparison.lean @@ -1,50 +1,50 @@ -import OAI.RepresentationTheory.RestrictedTilting.TorusExtension -import OAI.RepresentationTheory.RestrictedTilting.PolynomialIntertwiner -import OAI.RepresentationTheory.RestrictedTilting.IntertwinerDescent - -namespace OAI - -namespace FiberFunctorProof -universe u v -variable {k : Type u} [Field k] [Infinite k] -variable {K : Type v} [Field K] [Algebra k K] -variable {ι : Type u} [Fintype ι] [DecidableEq ι] - - - -theorem matrix_formal_comparison - (ρ : Representation k (SL2 k) (ι → k)) (hρ : IsRational k ρ) - (P : Matrix ι ι (Polynomial k)) (x : K) (hx : x ≠ 0) - (C : Matrix ι ι K) (hC : C.det ≠ 0) - (h : ∀ t : k, C * (LinearMap.toMatrix' (ρ (unipotent k t))).map (algebraMap k K) = - polynomialMatrixEval P (algebraMap k K t / x^2) * C) : - ∃ D : Matrix ι ι k, D.det ≠ 0 ∧ ∀ t : k, - polynomialMatrixEval P t * D = D * LinearMap.toMatrix' (ρ (unipotent k t)) := by - let B := rationalUnipotentMatrix k ρ hρ - have hext : ∀ t : K, C * polynomialMatrixEval B t = polynomialMatrixEval P (t*(x^2)⁻¹)*C := by - apply polynomial_intertwiner_extension P B C ((x^2)⁻¹) - intro t - rw [polynomialMatrixEval_base] - have hB : polynomialMatrixEval B t = LinearMap.toMatrix' (ρ (unipotent k t)) := - eval_rationalUnipotentMatrix k ρ hρ t - rw [hB] - simpa only [div_eq_mul_inv] using h t - let xU : Kˣ := Units.mk0 x hx - let Q := torusMatrixAt ρ hρ xU - have hQ : Q.det ≠ 0 := torusMatrixAt_det_ne_zero ρ hρ xU - apply intertwiner_descent (fun t : k => polynomialMatrixEval P t) - (fun t : k => LinearMap.toMatrix' (ρ (unipotent k t))) (C*Q) - (by rw [Matrix.det_mul]; exact mul_ne_zero hC hQ) - intro t - have hh := hext (x^2 * algebraMap k K t) - have hp : (x^2 * algebraMap k K t) * (x^2)⁻¹ = algebraMap k K t := by - field_simp - rw [hp] at hh - rw [← polynomialMatrixEval_base, ← Matrix.mul_assoc, ← hh, Matrix.mul_assoc] - have hQt := torusMatrixAt_unipotent ρ hρ xU t - change Q * _ = polynomialMatrixEval B (x^2 * algebraMap k K t) * Q at hQt - rw [← hQt, Matrix.mul_assoc] - -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.TorusExtension +import OAI.RepresentationTheory.RestrictedTilting.PolynomialIntertwiner +import OAI.RepresentationTheory.RestrictedTilting.IntertwinerDescent + +namespace OAI + +namespace FiberFunctorProof +universe u v +variable {k : Type u} [Field k] [Infinite k] +variable {K : Type v} [Field K] [Algebra k K] +variable {ι : Type u} [Fintype ι] [DecidableEq ι] + + + +theorem matrix_formal_comparison + (ρ : Representation k (SL2 k) (ι → k)) (hρ : IsRational k ρ) + (P : Matrix ι ι (Polynomial k)) (x : K) (hx : x ≠ 0) + (C : Matrix ι ι K) (hC : C.det ≠ 0) + (h : ∀ t : k, C * (LinearMap.toMatrix' (ρ (unipotent k t))).map (algebraMap k K) = + polynomialMatrixEval P (algebraMap k K t / x^2) * C) : + ∃ D : Matrix ι ι k, D.det ≠ 0 ∧ ∀ t : k, + polynomialMatrixEval P t * D = D * LinearMap.toMatrix' (ρ (unipotent k t)) := by + let B := rationalUnipotentMatrix k ρ hρ + have hext : ∀ t : K, C * polynomialMatrixEval B t = polynomialMatrixEval P (t*(x^2)⁻¹)*C := by + apply polynomial_intertwiner_extension P B C ((x^2)⁻¹) + intro t + rw [polynomialMatrixEval_base] + have hB : polynomialMatrixEval B t = LinearMap.toMatrix' (ρ (unipotent k t)) := + eval_rationalUnipotentMatrix k ρ hρ t + rw [hB] + simpa only [div_eq_mul_inv] using h t + let xU : Kˣ := Units.mk0 x hx + let Q := torusMatrixAt ρ hρ xU + have hQ : Q.det ≠ 0 := torusMatrixAt_det_ne_zero ρ hρ xU + apply intertwiner_descent (fun t : k => polynomialMatrixEval P t) + (fun t : k => LinearMap.toMatrix' (ρ (unipotent k t))) (C*Q) + (by rw [Matrix.det_mul]; exact mul_ne_zero hC hQ) + intro t + have hh := hext (x^2 * algebraMap k K t) + have hp : (x^2 * algebraMap k K t) * (x^2)⁻¹ = algebraMap k K t := by + field_simp + rw [hp] at hh + rw [← polynomialMatrixEval_base, ← Matrix.mul_assoc, ← hh, Matrix.mul_assoc] + have hQt := torusMatrixAt_unipotent ρ hρ xU t + change Q * _ = polynomialMatrixEval B (x^2 * algebraMap k K t) * Q at hQt + rw [← hQt, Matrix.mul_assoc] + +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/NormConverse.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/NormConverse.lean index 8c2a89f4cbae4eea1e53d67dbedc386ca8098850..c0194044413cdc50f4a0fd81208b6fbe7127bb9e 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/NormConverse.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/NormConverse.lean @@ -1,96 +1,96 @@ -import OAI.RepresentationTheory.RestrictedTilting.NormMaps -import OAI.RepresentationTheory.RestrictedTilting.PGroupInvariants -import OAI.RepresentationTheory.RestrictedTilting.ProjectiveRegular -import OAI.RepresentationTheory.RestrictedTilting.SplitRepresentation - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory Representation -universe u -variable {k : Type u} [Field k] {p : ℕ} [Fact p.Prime] [CharP k p] -variable {G : Type u} [Group G] [Fintype G] -variable {V : Type u} [AddCommGroup V] [Module k V] - - - -lemma regular_map_injective (hG : IsPGroup p G) (ρ : Representation k G V) - (f : (Representation.leftRegular k G).IntertwiningMap ρ) - (hN : f ((Representation.leftRegular k G).norm (MonoidAlgebra.single 1 1)) ≠ 0) : - Function.Injective f := by - apply LinearMap.ker_eq_bot.mp - apply le_antisymm _ bot_le - intro x hx - change x = 0 - by_contra hx0 - have hxk : (⟨x,hx⟩ : f.ker.toSubmodule) ≠ 0 := fun h => hx0 (congrArg Subtype.val h) - obtain ⟨z,hz,hfix⟩ := pgroup_exists_invariant hG f.ker.toRepresentation ⟨x,hx⟩ hxk - have hval : (z : MonoidAlgebra k G) ≠ 0 := fun h => hz (Subtype.ext h) - have hzN := regular_invariant_eq (z : MonoidAlgebra k G) - (fun g => congrArg Subtype.val (hfix g)) - have hz0 : f (z : MonoidAlgebra k G) = 0 := z.property - have hc : (z : MonoidAlgebra k G).coeff 1 = 0 := by - rw [hzN, map_smul] at hz0 - exact (smul_eq_zero.mp hz0).resolve_right hN - apply hval - rw [hzN, hc, zero_smul] - - - -theorem projective_of_normSurjective (hG : IsPGroup p G) - [FiniteDimensional k V] (ρ : Representation k G V) (hρ : NormSurjective ρ) : - Projective (Rep.of ρ) := by - suffices H : ∀ n : ℕ, ∀ (M : Type u) [AddCommGroup M] [Module k M] - [FiniteDimensional k M], Module.finrank k M = n → - ∀ τ : Representation k G M, NormSurjective τ → Projective (Rep.of τ) by - exact H _ V rfl ρ hρ - intro n - induction n using Nat.strong_induction_on with - | h n ih => - intro M _ _ _ hdim τ hτ - cases subsingleton_or_nontrivial M with - | inl hs => - let := hs - constructor - intro E X f e he - refine ⟨0, ?_⟩ - rw [Limits.zero_comp] - apply Rep.hom_ext - apply IntertwiningMap.ext - ext m - rw [Subsingleton.elim m 0] - simp - | inr hnt => - let := hnt - obtain ⟨v,hv⟩ := exists_ne (0 : M) - obtain ⟨w,hw,hfix⟩ := pgroup_exists_invariant hG τ v hv - obtain ⟨m,hm⟩ := hτ w hfix - let f : (Representation.leftRegular k G).IntertwiningMap τ := - (Rep.leftRegularHom (Rep.of τ) m).hom - have hfm : f (MonoidAlgebra.single 1 1) = m := by simp [f] - have hfn : f ((Representation.leftRegular k G).norm (MonoidAlgebra.single 1 1)) ≠ 0 := by - rw [intertwining_norm f, hfm, hm] - exact hw - have hf := regular_map_injective hG τ f hfn - obtain ⟨s,hs⟩ := regular_split_of_injective τ f hf - let κ := s.ker.toRepresentation - have hκ : NormSurjective κ := - normSurjective_of_retract (kernelInclusion s) - (splitKernelProjection f s hs) (splitKernelProjection_inclusion f s hs) hτ - have hker : s.toLinearMap.ker ≠ ⊤ := by - intro htop - have hzero : s (f (MonoidAlgebra.single 1 1)) = 0 := by - exact (show f (MonoidAlgebra.single 1 1) ∈ s.toLinearMap.ker by rw [htop]; trivial) - have hsf : s (f (MonoidAlgebra.single 1 1)) = MonoidAlgebra.single 1 1 := - congr($(hs) (MonoidAlgebra.single 1 1)) - rw [hsf] at hzero - have hh := congrArg (fun v : MonoidAlgebra k G => v.coeff 1) hzero - simp at hh - have hlt : Module.finrank k s.ker.toSubmodule < n := by - rw [← hdim] - exact Submodule.finrank_lt hker - have hK : Projective (Rep.of κ) := ih _ hlt _ rfl κ hκ - exact projective_of_split_kernel f s hs (rep_leftRegular_projective k G) hK -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.NormMaps +import OAI.RepresentationTheory.RestrictedTilting.PGroupInvariants +import OAI.RepresentationTheory.RestrictedTilting.ProjectiveRegular +import OAI.RepresentationTheory.RestrictedTilting.SplitRepresentation + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory Representation +universe u +variable {k : Type u} [Field k] {p : ℕ} [Fact p.Prime] [CharP k p] +variable {G : Type u} [Group G] [Fintype G] +variable {V : Type u} [AddCommGroup V] [Module k V] + + + +lemma regular_map_injective (hG : IsPGroup p G) (ρ : Representation k G V) + (f : (Representation.leftRegular k G).IntertwiningMap ρ) + (hN : f ((Representation.leftRegular k G).norm (MonoidAlgebra.single 1 1)) ≠ 0) : + Function.Injective f := by + apply LinearMap.ker_eq_bot.mp + apply le_antisymm _ bot_le + intro x hx + change x = 0 + by_contra hx0 + have hxk : (⟨x,hx⟩ : f.ker.toSubmodule) ≠ 0 := fun h => hx0 (congrArg Subtype.val h) + obtain ⟨z,hz,hfix⟩ := pgroup_exists_invariant hG f.ker.toRepresentation ⟨x,hx⟩ hxk + have hval : (z : MonoidAlgebra k G) ≠ 0 := fun h => hz (Subtype.ext h) + have hzN := regular_invariant_eq (z : MonoidAlgebra k G) + (fun g => congrArg Subtype.val (hfix g)) + have hz0 : f (z : MonoidAlgebra k G) = 0 := z.property + have hc : (z : MonoidAlgebra k G).coeff 1 = 0 := by + rw [hzN, map_smul] at hz0 + exact (smul_eq_zero.mp hz0).resolve_right hN + apply hval + rw [hzN, hc, zero_smul] + + + +theorem projective_of_normSurjective (hG : IsPGroup p G) + [FiniteDimensional k V] (ρ : Representation k G V) (hρ : NormSurjective ρ) : + Projective (Rep.of ρ) := by + suffices H : ∀ n : ℕ, ∀ (M : Type u) [AddCommGroup M] [Module k M] + [FiniteDimensional k M], Module.finrank k M = n → + ∀ τ : Representation k G M, NormSurjective τ → Projective (Rep.of τ) by + exact H _ V rfl ρ hρ + intro n + induction n using Nat.strong_induction_on with + | h n ih => + intro M _ _ _ hdim τ hτ + cases subsingleton_or_nontrivial M with + | inl hs => + let := hs + constructor + intro E X f e he + refine ⟨0, ?_⟩ + rw [Limits.zero_comp] + apply Rep.hom_ext + apply IntertwiningMap.ext + ext m + rw [Subsingleton.elim m 0] + simp + | inr hnt => + let := hnt + obtain ⟨v,hv⟩ := exists_ne (0 : M) + obtain ⟨w,hw,hfix⟩ := pgroup_exists_invariant hG τ v hv + obtain ⟨m,hm⟩ := hτ w hfix + let f : (Representation.leftRegular k G).IntertwiningMap τ := + (Rep.leftRegularHom (Rep.of τ) m).hom + have hfm : f (MonoidAlgebra.single 1 1) = m := by simp [f] + have hfn : f ((Representation.leftRegular k G).norm (MonoidAlgebra.single 1 1)) ≠ 0 := by + rw [intertwining_norm f, hfm, hm] + exact hw + have hf := regular_map_injective hG τ f hfn + obtain ⟨s,hs⟩ := regular_split_of_injective τ f hf + let κ := s.ker.toRepresentation + have hκ : NormSurjective κ := + normSurjective_of_retract (kernelInclusion s) + (splitKernelProjection f s hs) (splitKernelProjection_inclusion f s hs) hτ + have hker : s.toLinearMap.ker ≠ ⊤ := by + intro htop + have hzero : s (f (MonoidAlgebra.single 1 1)) = 0 := by + exact (show f (MonoidAlgebra.single 1 1) ∈ s.toLinearMap.ker by rw [htop]; trivial) + have hsf : s (f (MonoidAlgebra.single 1 1)) = MonoidAlgebra.single 1 1 := + congr($(hs) (MonoidAlgebra.single 1 1)) + rw [hsf] at hzero + have hh := congrArg (fun v : MonoidAlgebra k G => v.coeff 1) hzero + simp at hh + have hlt : Module.finrank k s.ker.toSubmodule < n := by + rw [← hdim] + exact Submodule.finrank_lt hker + have hK : Projective (Rep.of κ) := ih _ hlt _ rfl κ hκ + exact projective_of_split_kernel f s hs (rep_leftRegular_projective k G) hK +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/NormDefinitions.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/NormDefinitions.lean index 0a6b332c433dec273d874498cae7777ab2bf3057..46d21f373c488750f0eababf134b522a344b78f1 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/NormDefinitions.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/NormDefinitions.lean @@ -1,39 +1,39 @@ -import Mathlib - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory Representation -universe u v -variable {k : Type u} [Field k] {G : Type v} [Group G] [Fintype G] -variable {V : Type u} [AddCommGroup V] [Module k V] - - -noncomputable def normToInvariants (ρ : Representation k G V) : V →ₗ[k] ρ.invariants := - ρ.norm.codRestrict _ (fun v g => ρ.self_norm_apply g v) - - -noncomputable def coinvariantNorm (ρ : Representation k G V) : - Coinvariants ρ →ₗ[k] ρ.invariants := - Coinvariants.lift ρ (normToInvariants ρ) (fun g => by - ext v - exact ρ.norm_self_apply g v) - -@[simp] theorem coinvariantNorm_mk (ρ : Representation k G V) (v : V) : - (coinvariantNorm ρ (Coinvariants.mk ρ v) : V) = ρ.norm v := rfl - - - -def NormProjectivityTheorem : Prop := - ∀ (k : Type u) [Field k] [IsAlgClosed k] (p : ℕ) [Fact p.Prime] [CharP k p], - (∀ (H : Type u) [Group H] [Fintype H], IsPGroup p H → - ∀ (M : Type u) [AddCommGroup M] [Module k M] [FiniteDimensional k M] - (ρ : Representation k H M), - Projective (Rep.of ρ) ↔ Function.Bijective (coinvariantNorm ρ)) ∧ - (∀ (G : Type u) [Group G] [Fintype G] - (M : Type u) [AddCommGroup M] [Module k M] [FiniteDimensional k M] - (ρ : Representation k G M), - Projective (Rep.of ρ) → Function.Bijective (coinvariantNorm ρ)) -end FiberFunctorProof - -end OAI +import Mathlib + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory Representation +universe u v +variable {k : Type u} [Field k] {G : Type v} [Group G] [Fintype G] +variable {V : Type u} [AddCommGroup V] [Module k V] + + +noncomputable def normToInvariants (ρ : Representation k G V) : V →ₗ[k] ρ.invariants := + ρ.norm.codRestrict _ (fun v g => ρ.self_norm_apply g v) + + +noncomputable def coinvariantNorm (ρ : Representation k G V) : + Coinvariants ρ →ₗ[k] ρ.invariants := + Coinvariants.lift ρ (normToInvariants ρ) (fun g => by + ext v + exact ρ.norm_self_apply g v) + +@[simp] theorem coinvariantNorm_mk (ρ : Representation k G V) (v : V) : + (coinvariantNorm ρ (Coinvariants.mk ρ v) : V) = ρ.norm v := rfl + + + +def NormProjectivityTheorem : Prop := + ∀ (k : Type u) [Field k] [IsAlgClosed k] (p : ℕ) [Fact p.Prime] [CharP k p], + (∀ (H : Type u) [Group H] [Fintype H], IsPGroup p H → + ∀ (M : Type u) [AddCommGroup M] [Module k M] [FiniteDimensional k M] + (ρ : Representation k H M), + Projective (Rep.of ρ) ↔ Function.Bijective (coinvariantNorm ρ)) ∧ + (∀ (G : Type u) [Group G] [Fintype G] + (M : Type u) [AddCommGroup M] [Module k M] [FiniteDimensional k M] + (ρ : Representation k G M), + Projective (Rep.of ρ) → Function.Bijective (coinvariantNorm ρ)) +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/NormFree.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/NormFree.lean index c3f5250701b0e1a4c004be85b7c6087a064a7e40..c86b486c15fd9db23abd8e19c964b0a37bcc9165 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/NormFree.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/NormFree.lean @@ -1,100 +1,100 @@ -import OAI.RepresentationTheory.RestrictedTilting.NormMaps - -namespace OAI - -namespace FiberFunctorProof -open Representation -universe u -variable {k : Type u} [Field k] {G : Type u} [Group G] [Fintype G] -variable (I : Type u) - - - -noncomputable def freeNormRepresentative : - (I →₀ MonoidAlgebra k G) →ₗ[k] (I →₀ MonoidAlgebra k G) := - Finsupp.mapRange.linearMap - ((MonoidAlgebra.lsingle 1).comp - ((Finsupp.lapply 1).comp (MonoidAlgebra.coeffLinearEquiv k).toLinearMap)) - -omit [Fintype G] in -@[simp] lemma freeNormRepresentative_apply (x : I →₀ MonoidAlgebra k G) (i : I) : - freeNormRepresentative I x i = MonoidAlgebra.single 1 ((x i).coeff 1) := rfl - -omit [Fintype G] in -lemma free_action_apply (g : G) (x : I →₀ MonoidAlgebra k G) (i : I) : - Representation.free k G I g x i = Representation.leftRegular k G g (x i) := by - classical - have H : (Finsupp.lapply i).comp (Representation.free k G I g) = - (Representation.leftRegular k G g).comp (Finsupp.lapply i) := by - apply Finsupp.lhom_ext - intro j v - simp only [LinearMap.comp_apply, Representation.finsupp_single, Finsupp.lapply_apply] - by_cases h : j = i - · subst j; simp - · simp [Ne.symm h] - exact congr($(H) x) - -lemma free_norm_apply (x : I →₀ MonoidAlgebra k G) (i : I) : - (Representation.free k G I).norm x i = (Representation.leftRegular k G).norm (x i) := by - classical - simp only [Representation.norm, LinearMap.sum_apply, Finsupp.finsetSum_apply, free_action_apply] - -lemma free_normRepresentative_invariant (x : I →₀ MonoidAlgebra k G) - (hx : ∀ g, Representation.free k G I g x = x) : - (Representation.free k G I).norm (freeNormRepresentative I x) = x := by - apply Finsupp.ext - intro i - rw [free_norm_apply, freeNormRepresentative_apply] - have hxi (g : G) : Representation.leftRegular k G g (x i) = x i := by - have hi := congrArg (fun v : I →₀ MonoidAlgebra k G => v i) (hx g) - simpa only [free_action_apply] using hi - have heq : MonoidAlgebra.single (1:G) ((x i).coeff 1) = - (x i).coeff 1 • MonoidAlgebra.single 1 (1 : k) := by simp - rw [heq, map_smul] - exact (regular_invariant_eq (x i) hxi).symm - -lemma free_normRepresentative_coinvariant : - (Coinvariants.mk (Representation.free k G I)).comp - ((freeNormRepresentative I).comp (Representation.free k G I).norm) = - Coinvariants.mk (Representation.free k G I) := by - classical - ext i g - have hn : (Representation.free k G I).norm (Finsupp.single i (MonoidAlgebra.single g (1:k))) = - Finsupp.single i ((Representation.leftRegular k G).norm (MonoidAlgebra.single g 1)) := by - simp only [Representation.norm, LinearMap.sum_apply, Representation.finsupp_single] - exact (map_sum (Finsupp.lsingle i : MonoidAlgebra k G →ₗ[k] (I →₀ MonoidAlgebra k G)) - (fun h => Representation.leftRegular k G h (MonoidAlgebra.single g 1)) Finset.univ).symm - have hone : ((Representation.leftRegular k G).norm (MonoidAlgebra.single g (1:k))).coeff 1 = 1 := by - rw [Representation.leftRegular_norm_apply] - simp [regular_norm_single_coeff] - have hrep : freeNormRepresentative I - (Finsupp.single i ((Representation.leftRegular k G).norm (MonoidAlgebra.single g (1:k)))) = - Finsupp.single i (MonoidAlgebra.single 1 1) := by - simp [freeNormRepresentative, hone] - change Coinvariants.mk _ (freeNormRepresentative I ((Representation.free k G I).norm - (Finsupp.single i (MonoidAlgebra.single g 1)))) = _ - rw [hn, hrep] - simpa [Representation.free_single_single] using - (Coinvariants.mk_self_apply (Representation.free k G I) g - (Finsupp.single i (MonoidAlgebra.single 1 (1:k)))).symm - - - -theorem free_norm_bijective : Function.Bijective - (coinvariantNorm (Representation.free k G I)) := by - constructor - · intro a b hab - obtain ⟨x,rfl⟩ := Coinvariants.mk_surjective _ a - obtain ⟨y,rfl⟩ := Coinvariants.mk_surjective _ b - have hn := congrArg Subtype.val hab - have hx := congr($(free_normRepresentative_coinvariant (k:=k) (G:=G) I) x) - have hy := congr($(free_normRepresentative_coinvariant (k:=k) (G:=G) I) y) - dsimp only [LinearMap.comp_apply] at hx hy - rw [← hx, ← hy] - exact congrArg (fun z => Coinvariants.mk _ (freeNormRepresentative I z)) hn - · apply (coinvariantNorm_surjective_iff _).2 - intro x hx - exact ⟨freeNormRepresentative I x, free_normRepresentative_invariant I x hx⟩ -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.NormMaps + +namespace OAI + +namespace FiberFunctorProof +open Representation +universe u +variable {k : Type u} [Field k] {G : Type u} [Group G] [Fintype G] +variable (I : Type u) + + + +noncomputable def freeNormRepresentative : + (I →₀ MonoidAlgebra k G) →ₗ[k] (I →₀ MonoidAlgebra k G) := + Finsupp.mapRange.linearMap + ((MonoidAlgebra.lsingle 1).comp + ((Finsupp.lapply 1).comp (MonoidAlgebra.coeffLinearEquiv k).toLinearMap)) + +omit [Fintype G] in +@[simp] lemma freeNormRepresentative_apply (x : I →₀ MonoidAlgebra k G) (i : I) : + freeNormRepresentative I x i = MonoidAlgebra.single 1 ((x i).coeff 1) := rfl + +omit [Fintype G] in +lemma free_action_apply (g : G) (x : I →₀ MonoidAlgebra k G) (i : I) : + Representation.free k G I g x i = Representation.leftRegular k G g (x i) := by + classical + have H : (Finsupp.lapply i).comp (Representation.free k G I g) = + (Representation.leftRegular k G g).comp (Finsupp.lapply i) := by + apply Finsupp.lhom_ext + intro j v + simp only [LinearMap.comp_apply, Representation.finsupp_single, Finsupp.lapply_apply] + by_cases h : j = i + · subst j; simp + · simp [Ne.symm h] + exact congr($(H) x) + +lemma free_norm_apply (x : I →₀ MonoidAlgebra k G) (i : I) : + (Representation.free k G I).norm x i = (Representation.leftRegular k G).norm (x i) := by + classical + simp only [Representation.norm, LinearMap.sum_apply, Finsupp.finsetSum_apply, free_action_apply] + +lemma free_normRepresentative_invariant (x : I →₀ MonoidAlgebra k G) + (hx : ∀ g, Representation.free k G I g x = x) : + (Representation.free k G I).norm (freeNormRepresentative I x) = x := by + apply Finsupp.ext + intro i + rw [free_norm_apply, freeNormRepresentative_apply] + have hxi (g : G) : Representation.leftRegular k G g (x i) = x i := by + have hi := congrArg (fun v : I →₀ MonoidAlgebra k G => v i) (hx g) + simpa only [free_action_apply] using hi + have heq : MonoidAlgebra.single (1:G) ((x i).coeff 1) = + (x i).coeff 1 • MonoidAlgebra.single 1 (1 : k) := by simp + rw [heq, map_smul] + exact (regular_invariant_eq (x i) hxi).symm + +lemma free_normRepresentative_coinvariant : + (Coinvariants.mk (Representation.free k G I)).comp + ((freeNormRepresentative I).comp (Representation.free k G I).norm) = + Coinvariants.mk (Representation.free k G I) := by + classical + ext i g + have hn : (Representation.free k G I).norm (Finsupp.single i (MonoidAlgebra.single g (1:k))) = + Finsupp.single i ((Representation.leftRegular k G).norm (MonoidAlgebra.single g 1)) := by + simp only [Representation.norm, LinearMap.sum_apply, Representation.finsupp_single] + exact (map_sum (Finsupp.lsingle i : MonoidAlgebra k G →ₗ[k] (I →₀ MonoidAlgebra k G)) + (fun h => Representation.leftRegular k G h (MonoidAlgebra.single g 1)) Finset.univ).symm + have hone : ((Representation.leftRegular k G).norm (MonoidAlgebra.single g (1:k))).coeff 1 = 1 := by + rw [Representation.leftRegular_norm_apply] + simp [regular_norm_single_coeff] + have hrep : freeNormRepresentative I + (Finsupp.single i ((Representation.leftRegular k G).norm (MonoidAlgebra.single g (1:k)))) = + Finsupp.single i (MonoidAlgebra.single 1 1) := by + simp [freeNormRepresentative, hone] + change Coinvariants.mk _ (freeNormRepresentative I ((Representation.free k G I).norm + (Finsupp.single i (MonoidAlgebra.single g 1)))) = _ + rw [hn, hrep] + simpa [Representation.free_single_single] using + (Coinvariants.mk_self_apply (Representation.free k G I) g + (Finsupp.single i (MonoidAlgebra.single 1 (1:k)))).symm + + + +theorem free_norm_bijective : Function.Bijective + (coinvariantNorm (Representation.free k G I)) := by + constructor + · intro a b hab + obtain ⟨x,rfl⟩ := Coinvariants.mk_surjective _ a + obtain ⟨y,rfl⟩ := Coinvariants.mk_surjective _ b + have hn := congrArg Subtype.val hab + have hx := congr($(free_normRepresentative_coinvariant (k:=k) (G:=G) I) x) + have hy := congr($(free_normRepresentative_coinvariant (k:=k) (G:=G) I) y) + dsimp only [LinearMap.comp_apply] at hx hy + rw [← hx, ← hy] + exact congrArg (fun z => Coinvariants.mk _ (freeNormRepresentative I z)) hn + · apply (coinvariantNorm_surjective_iff _).2 + intro x hx + exact ⟨freeNormRepresentative I x, free_normRepresentative_invariant I x hx⟩ +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/NormMaps.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/NormMaps.lean index a99af7805b30ec19b22153414b4292d885e73787..2d07e0063f81f92afb5a60de6d9ac6121b418944 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/NormMaps.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/NormMaps.lean @@ -1,58 +1,58 @@ -import OAI.RepresentationTheory.RestrictedTilting.NormDefinitions -import OAI.RepresentationTheory.RestrictedTilting.RegularSplitting - -namespace OAI - -namespace FiberFunctorProof -open Representation -universe u -variable {k : Type u} [Field k] {G : Type u} [Group G] [Fintype G] -variable {V W : Type u} [AddCommGroup V] [Module k V] [AddCommGroup W] [Module k W] - - -def NormSurjective (ρ : Representation k G V) : Prop := - ∀ w : V, (∀ g, ρ g w = w) → ∃ v, ρ.norm v = w - -lemma coinvariantNorm_surjective_iff (ρ : Representation k G V) : - Function.Surjective (coinvariantNorm ρ) ↔ NormSurjective ρ := by - constructor - · intro h w hw - obtain ⟨c,hc⟩ := h ⟨w,hw⟩ - obtain ⟨v,rfl⟩ := Coinvariants.mk_surjective ρ c - exact ⟨v,congrArg Subtype.val hc⟩ - · intro h w - obtain ⟨v,hv⟩ := h w w.property - exact ⟨Coinvariants.mk ρ v, Subtype.ext hv⟩ - -lemma normSurjective_of_retract {ρ : Representation k G V} {σ : Representation k G W} - (f : ρ.IntertwiningMap σ) (s : σ.IntertwiningMap ρ) - (h : s.comp f = IntertwiningMap.id ρ) (hσ : NormSurjective σ) : NormSurjective ρ := by - have hsf (v : V) : s (f v) = v := congr($(h) v) - intro w hw - obtain ⟨v,hv⟩ := hσ (f w) (fun g => by rw [← f.isIntertwining, hw g]) - exact ⟨s v, by rw [← intertwining_norm s, hv, hsf]⟩ - -lemma norm_bijective_of_retract {ρ : Representation k G V} {σ : Representation k G W} - (f : ρ.IntertwiningMap σ) (s : σ.IntertwiningMap ρ) - (h : s.comp f = IntertwiningMap.id ρ) - (hσ : Function.Bijective (coinvariantNorm σ)) : - Function.Bijective (coinvariantNorm ρ) := by - classical - have hsf (v : V) : s (f v) = v := congr($(h) v) - constructor - · intro a b hab - obtain ⟨v,rfl⟩ := Coinvariants.mk_surjective ρ a - obtain ⟨w,rfl⟩ := Coinvariants.mk_surjective ρ b - have hvw : ρ.norm v = ρ.norm w := congrArg Subtype.val hab - have hn : coinvariantNorm σ (Coinvariants.mk σ (f v)) = - coinvariantNorm σ (Coinvariants.mk σ (f w)) := by - apply Subtype.ext - change σ.norm (f v) = σ.norm (f w) - rw [← intertwining_norm f, ← intertwining_norm f, hvw] - have hc := congrArg (Coinvariants.map σ ρ s) (hσ.1 hn) - simpa only [Coinvariants.map_mk, hsf] using hc - · exact (coinvariantNorm_surjective_iff ρ).2 (normSurjective_of_retract f s h - ((coinvariantNorm_surjective_iff σ).1 hσ.2)) -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.NormDefinitions +import OAI.RepresentationTheory.RestrictedTilting.RegularSplitting + +namespace OAI + +namespace FiberFunctorProof +open Representation +universe u +variable {k : Type u} [Field k] {G : Type u} [Group G] [Fintype G] +variable {V W : Type u} [AddCommGroup V] [Module k V] [AddCommGroup W] [Module k W] + + +def NormSurjective (ρ : Representation k G V) : Prop := + ∀ w : V, (∀ g, ρ g w = w) → ∃ v, ρ.norm v = w + +lemma coinvariantNorm_surjective_iff (ρ : Representation k G V) : + Function.Surjective (coinvariantNorm ρ) ↔ NormSurjective ρ := by + constructor + · intro h w hw + obtain ⟨c,hc⟩ := h ⟨w,hw⟩ + obtain ⟨v,rfl⟩ := Coinvariants.mk_surjective ρ c + exact ⟨v,congrArg Subtype.val hc⟩ + · intro h w + obtain ⟨v,hv⟩ := h w w.property + exact ⟨Coinvariants.mk ρ v, Subtype.ext hv⟩ + +lemma normSurjective_of_retract {ρ : Representation k G V} {σ : Representation k G W} + (f : ρ.IntertwiningMap σ) (s : σ.IntertwiningMap ρ) + (h : s.comp f = IntertwiningMap.id ρ) (hσ : NormSurjective σ) : NormSurjective ρ := by + have hsf (v : V) : s (f v) = v := congr($(h) v) + intro w hw + obtain ⟨v,hv⟩ := hσ (f w) (fun g => by rw [← f.isIntertwining, hw g]) + exact ⟨s v, by rw [← intertwining_norm s, hv, hsf]⟩ + +lemma norm_bijective_of_retract {ρ : Representation k G V} {σ : Representation k G W} + (f : ρ.IntertwiningMap σ) (s : σ.IntertwiningMap ρ) + (h : s.comp f = IntertwiningMap.id ρ) + (hσ : Function.Bijective (coinvariantNorm σ)) : + Function.Bijective (coinvariantNorm ρ) := by + classical + have hsf (v : V) : s (f v) = v := congr($(h) v) + constructor + · intro a b hab + obtain ⟨v,rfl⟩ := Coinvariants.mk_surjective ρ a + obtain ⟨w,rfl⟩ := Coinvariants.mk_surjective ρ b + have hvw : ρ.norm v = ρ.norm w := congrArg Subtype.val hab + have hn : coinvariantNorm σ (Coinvariants.mk σ (f v)) = + coinvariantNorm σ (Coinvariants.mk σ (f w)) := by + apply Subtype.ext + change σ.norm (f v) = σ.norm (f w) + rw [← intertwining_norm f, ← intertwining_norm f, hvw] + have hc := congrArg (Coinvariants.map σ ρ s) (hσ.1 hn) + simpa only [Coinvariants.map_mk, hsf] using hc + · exact (coinvariantNorm_surjective_iff ρ).2 (normSurjective_of_retract f s h + ((coinvariantNorm_surjective_iff σ).1 hσ.2)) +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/NormProjectivity.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/NormProjectivity.lean index e8318ca7ede6fb6e1df70a69ef3a60e80750d210..318cb9471e9878c51680c319e323301c604ddb56 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/NormProjectivity.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/NormProjectivity.lean @@ -1,41 +1,41 @@ -import OAI.RepresentationTheory.RestrictedTilting.NormConverse -import OAI.RepresentationTheory.RestrictedTilting.NormFree - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory Representation -universe u -variable {k : Type u} [Field k] {G : Type u} [Group G] [Fintype G] -variable {V : Type u} [AddCommGroup V] [Module k V] - - - -theorem norm_bijective_of_projective (ρ : Representation k G V) - (hρ : Projective (Rep.of ρ)) : Function.Bijective (coinvariantNorm ρ) := by - let e : Rep.free k G V ⟶ Rep.of ρ := Rep.ofHom (Representation.freeLift ρ id) - have he : Function.Surjective e.hom := by - intro v - refine ⟨Finsupp.single v (MonoidAlgebra.single 1 1), ?_⟩ - simp [e] - let : Epi e := (Rep.epi_iff_surjective e).2 he - obtain ⟨s,hs⟩ := hρ.factors (𝟙 (Rep.of ρ)) e - apply norm_bijective_of_retract s.hom e.hom - · exact congrArg Rep.Hom.hom hs - · exact free_norm_bijective V - - - -theorem norm_projectivity : NormProjectivityTheorem.{u} := by - intro k _ _ p _ _ - constructor - · intro G _ _ hG V _ _ _ ρ - constructor - · exact norm_bijective_of_projective ρ - · intro h - exact projective_of_normSurjective hG ρ ((coinvariantNorm_surjective_iff ρ).1 h.2) - · intro G _ _ V _ _ _ ρ - exact norm_bijective_of_projective ρ -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.NormConverse +import OAI.RepresentationTheory.RestrictedTilting.NormFree + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory Representation +universe u +variable {k : Type u} [Field k] {G : Type u} [Group G] [Fintype G] +variable {V : Type u} [AddCommGroup V] [Module k V] + + + +theorem norm_bijective_of_projective (ρ : Representation k G V) + (hρ : Projective (Rep.of ρ)) : Function.Bijective (coinvariantNorm ρ) := by + let e : Rep.free k G V ⟶ Rep.of ρ := Rep.ofHom (Representation.freeLift ρ id) + have he : Function.Surjective e.hom := by + intro v + refine ⟨Finsupp.single v (MonoidAlgebra.single 1 1), ?_⟩ + simp [e] + let : Epi e := (Rep.epi_iff_surjective e).2 he + obtain ⟨s,hs⟩ := hρ.factors (𝟙 (Rep.of ρ)) e + apply norm_bijective_of_retract s.hom e.hom + · exact congrArg Rep.Hom.hom hs + · exact free_norm_bijective V + + + +theorem norm_projectivity : NormProjectivityTheorem.{u} := by + intro k _ _ p _ _ + constructor + · intro G _ _ hG V _ _ _ ρ + constructor + · exact norm_bijective_of_projective ρ + · intro h + exact projective_of_normSurjective hG ρ ((coinvariantNorm_surjective_iff ρ).1 h.2) + · intro G _ _ V _ _ _ ρ + exact norm_bijective_of_projective ρ +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/NumeratorAction.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/NumeratorAction.lean index 6de49439f7258ff209fb853bff5e3496e1bad380..8ec57ebda293c35b4609d899f71f52fc32a034a8 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/NumeratorAction.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/NumeratorAction.lean @@ -1,54 +1,54 @@ -import OAI.RepresentationTheory.RestrictedTilting.AssociatedNumerator -import OAI.RepresentationTheory.RestrictedTilting.XChartLineEval -import OAI.RepresentationTheory.RestrictedTilting.ClearedPolynomial - -namespace OAI - -namespace FiberFunctorProof -open scoped BigOperators -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (ι : Type u) [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) -variable (P : Matrix ι ι (Polynomial k)) -variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) -variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) -local notation "N" => associatedSectionsSubmodule k ι ρ -local notation "W" => associatedNumeratorLinear k ι ρ P hP d hd - -lemma associatedNumerator_line_eval (a : kˣ) (f : N) (i : ι) : - (linePolynomial k (W f i)).eval (a : k) = (a : k)^d * - regularVectorEvaluation k ι (diagonalTorus k a) f.val i := by - rw [linePolynomial_eval] - change planeLineEval k a (W f i) = _ - have h := congrArg (chartLineEval k a) (associatedNumeratorLinear_spec k ι ρ P hP d hd f i) - rw [chartLineEval_algebraMap, map_mul, map_pow, chartLineEval_coordinate] at h - simpa only [ite_true, congrFun (associatedXChart_line k ι ρ a f) i] using h - - - -lemma associatedNumerator_line_unipotent (t : k) (f : N) (i : ι) : - Polynomial.X^(2*d) * linePolynomial k - (W (associatedSectionsRepresentation k ι ρ (unipotent k t) f) i) = - ∑ j, clearedLineAction k (P i j) t d * linePolynomial k (W f j) := by - apply Polynomial.eq_of_infinite_eval_eq - apply (Set.finite_singleton (0 : k)).infinite_compl.mono - intro a ha - have ha0 : a ≠ 0 := ha - let u : kˣ := Units.mk0 a ha0 - change Polynomial.eval (u : k) _ = Polynomial.eval (u : k) _ - simp only [Polynomial.eval_mul, Polynomial.eval_pow, Polynomial.eval_X, - Polynomial.eval_finsetSum] - rw [associatedNumerator_line_eval k ι ρ P hP d hd, - associatedSections_line_unipotent k ι ρ u t f] - simp_rw [clearedLineAction_eval k _ t (u : k) d (hd i _) u.ne_zero, - associatedNumerator_line_eval k ι ρ P hP d hd u f] - rw [← LinearMap.toMatrix'_mulVec, ← hP] - simp only [polynomialMatrixEval, Matrix.mulVec, dotProduct, - Polynomial.aeval_def, Algebra.algebraMap_self, Polynomial.eval₂_id, Finset.mul_sum] - apply Finset.sum_congr rfl - intro j _ - ring -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.AssociatedNumerator +import OAI.RepresentationTheory.RestrictedTilting.XChartLineEval +import OAI.RepresentationTheory.RestrictedTilting.ClearedPolynomial + +namespace OAI + +namespace FiberFunctorProof +open scoped BigOperators +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (ι : Type u) [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) +variable (P : Matrix ι ι (Polynomial k)) +variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) +variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) +local notation "N" => associatedSectionsSubmodule k ι ρ +local notation "W" => associatedNumeratorLinear k ι ρ P hP d hd + +lemma associatedNumerator_line_eval (a : kˣ) (f : N) (i : ι) : + (linePolynomial k (W f i)).eval (a : k) = (a : k)^d * + regularVectorEvaluation k ι (diagonalTorus k a) f.val i := by + rw [linePolynomial_eval] + change planeLineEval k a (W f i) = _ + have h := congrArg (chartLineEval k a) (associatedNumeratorLinear_spec k ι ρ P hP d hd f i) + rw [chartLineEval_algebraMap, map_mul, map_pow, chartLineEval_coordinate] at h + simpa only [ite_true, congrFun (associatedXChart_line k ι ρ a f) i] using h + + + +lemma associatedNumerator_line_unipotent (t : k) (f : N) (i : ι) : + Polynomial.X^(2*d) * linePolynomial k + (W (associatedSectionsRepresentation k ι ρ (unipotent k t) f) i) = + ∑ j, clearedLineAction k (P i j) t d * linePolynomial k (W f j) := by + apply Polynomial.eq_of_infinite_eval_eq + apply (Set.finite_singleton (0 : k)).infinite_compl.mono + intro a ha + have ha0 : a ≠ 0 := ha + let u : kˣ := Units.mk0 a ha0 + change Polynomial.eval (u : k) _ = Polynomial.eval (u : k) _ + simp only [Polynomial.eval_mul, Polynomial.eval_pow, Polynomial.eval_X, + Polynomial.eval_finsetSum] + rw [associatedNumerator_line_eval k ι ρ P hP d hd, + associatedSections_line_unipotent k ι ρ u t f] + simp_rw [clearedLineAction_eval k _ t (u : k) d (hd i _) u.ne_zero, + associatedNumerator_line_eval k ι ρ P hP d hd u f] + rw [← LinearMap.toMatrix'_mulVec, ← hP] + simp only [polynomialMatrixEval, Matrix.mulVec, dotProduct, + Polynomial.aeval_def, Algebra.algebraMap_self, Polynomial.eval₂_id, Finset.mul_sum] + apply Finset.sum_congr rfl + intro j _ + ring +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/OriginCoordinates.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/OriginCoordinates.lean index fefd76f03fb76419d1c347a76226d429a6aa6485..38612f8365d631768744ed94ffe3138e155ceb1b 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/OriginCoordinates.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/OriginCoordinates.lean @@ -1,346 +1,346 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.ActionDenominators - -namespace OAI - -/-! Plane-origin coordinate rings, stalk lattices and overlap evaluation. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section - -variable (k : Type*) [Field k] - -abbrev planeCoordinateRing := MvPolynomial (Fin 2) k - -def planeOriginIdeal : Ideal (planeCoordinateRing k) := - RingHom.ker MvPolynomial.constantCoeff - -instance planeOriginIdeal_isMaximal : (planeOriginIdeal k).IsMaximal := - RingHom.ker_isMaximal_of_surjective MvPolynomial.constantCoeff - (fun a => ⟨MvPolynomial.C a, MvPolynomial.constantCoeff_C (Fin 2) a⟩) - -lemma planeOriginIdeal_eq_span : planeOriginIdeal k = - Ideal.span {MvPolynomial.X (0 : Fin 2), MvPolynomial.X (1 : Fin 2)} := by - have hvars : planeOriginIdeal k = MvPolynomial.idealOfVars (Fin 2) k := by - ext f - change f.coeff 0 = 0 ↔ f ∈ MvPolynomial.idealOfVars (Fin 2) k - have he := MvPolynomial.mem_pow_idealOfVars_iff' (R := k) (σ := Fin 2) 1 f - simpa only [pow_one, Nat.lt_one_iff, Finsupp.degree_eq_zero_iff, - forall_eq] using he.symm - rw [hvars, MvPolynomial.idealOfVars] - congr 1 - ext p - constructor - · rintro ⟨i,rfl⟩ - fin_cases i <;> simp - · rintro (rfl | rfl) - · exact ⟨0,rfl⟩ - · exact ⟨1,rfl⟩ - -abbrev planeOriginRing := Localization.AtPrime (planeOriginIdeal k) - -abbrev planeOriginCoordinate (i : Fin 2) : planeOriginRing k := - algebraMap (planeCoordinateRing k) (planeOriginRing k) (MvPolynomial.X i) - -lemma planeOriginCoordinate_ne_zero (i : Fin 2) : planeOriginCoordinate k i ≠ 0 := by - exact fun h => MvPolynomial.X_ne_zero i - ((IsLocalization.injective (planeOriginRing k) - (planeOriginIdeal k).primeCompl_le_nonZeroDivisors) (h.trans (map_zero _).symm)) - -lemma planeOrigin_maximalIdeal : IsLocalRing.maximalIdeal (planeOriginRing k) = - Ideal.span {planeOriginCoordinate k 0, planeOriginCoordinate k 1} := by - rw [← IsLocalization.AtPrime.map_eq_maximalIdeal (planeOriginIdeal k) (planeOriginRing k)] - calc - _ = Ideal.map (algebraMap (planeCoordinateRing k) (planeOriginRing k)) - (Ideal.span {MvPolynomial.X (0 : Fin 2), MvPolynomial.X (1 : Fin 2)}) := - congrArg (Ideal.map (algebraMap (planeCoordinateRing k) (planeOriginRing k))) - (planeOriginIdeal_eq_span k) - _ = _ := by - rw [Ideal.map_span] - simp only [Set.image_insert_eq, Set.image_singleton, planeOriginCoordinate] - -lemma planeOriginCoordinate_prime (i : Fin 2) : Prime (planeOriginCoordinate k i) := by - apply (IsLocalization.toLocalizationMap (planeOriginIdeal k).primeCompl - (planeOriginRing k)).map_prime (MvPolynomial.X_prime (i := i)) (planeOriginCoordinate_ne_zero k i) - change ¬ IsUnit (planeOriginCoordinate k i) - rw [IsLocalization.AtPrime.isUnit_to_map_iff (planeOriginRing k) (planeOriginIdeal k)] - change ¬ (MvPolynomial.X i : planeCoordinateRing k) ∉ planeOriginIdeal k - simp [planeOriginIdeal, RingHom.mem_ker] - -lemma planeOriginCoordinates_relPrime : - IsRelPrime (planeOriginCoordinate k 0) (planeOriginCoordinate k 1) := by - apply (planeOriginCoordinate_prime k 0).irreducible.isRelPrime_iff_not_dvd.mpr - intro h - obtain ⟨s,hs,hd⟩ := - (IsLocalization.toLocalizationMap (planeOriginIdeal k).primeCompl - (planeOriginRing k)).map_dvd_map.mp h - rcases (MvPolynomial.X_prime (R := k) (i := (0 : Fin 2))).dvd_or_dvd hd with ha | hb - · have hx : (MvPolynomial.X (0 : Fin 2) : planeCoordinateRing k) ∈ planeOriginIdeal k := by - simp [planeOriginIdeal, RingHom.mem_ker] - obtain ⟨a,rfl⟩ := ha - exact hs ((planeOriginIdeal k).mul_mem_right a hx) - · exact (by decide : (0 : Fin 2) ≠ 1) (MvPolynomial.X_dvd_X.mp hb) - -noncomputable instance planeOriginRing_gcd : GCDMonoid (planeOriginRing k) := - UniqueFactorizationMonoid.toGCDMonoid _ - -example : IsNoetherianRing (planeOriginRing k) := inferInstance -example : IsLocalRing (planeOriginRing k) := inferInstance - -end - -section PowerCharts -variable {R K ι : Type*} [CommRing R] [Field K] [Algebra R K] - -lemma linearEquiv_map_base_smul (P : (ι → K) ≃ₗ[K] (ι → K)) (a : R) (v : ι → K) : - P (a • v) = a • P v := - (P.restrictScalars R).map_smul a v - -lemma powerLocalization_idem (x : R) (L : Submodule R (ι → K)) : - powerLocalization x (powerLocalization x L) = powerLocalization x L := by - apply le_antisymm - · rintro v ⟨n,m,h⟩ - exact ⟨m+n, by simpa only [pow_add, mul_smul] using h⟩ - · exact le_powerLocalization _ _ - -lemma powerLocalization_equiv_map (x : R) (L : Submodule R (ι → K)) - (P : (ι → K) ≃ₗ[K] (ι → K)) : - powerLocalization x (L.map (P.toLinearMap.restrictScalars R)) = - (powerLocalization x L).map (P.toLinearMap.restrictScalars R) := by - apply le_antisymm - · rintro v ⟨n,w,hw,he⟩ - refine ⟨P.symm v, ⟨n, ?_⟩, P.apply_symm_apply v⟩ - have h : w = x^n • P.symm v := by - apply P.injective - change P w = x^n • v at he - simpa only [linearEquiv_map_base_smul, P.apply_symm_apply] using he - exact h ▸ hw - · rintro v ⟨w,⟨n,hn⟩,rfl⟩ - refine ⟨n,x^n • w,hn,?_⟩ - exact (P.restrictScalars R).map_smul _ _ - -end PowerCharts - -section -variable {R K ι : Type*} [CommRing R] [Field K] [Algebra R K] - - -theorem gluedLattice_xChart (x y : R) (P : (ι → K) ≃ₗ[K] (ι → K)) - (d : ℕ) (hP : ∀ v ∈ coordinateLattice (R := R), - (x*y)^d • P.symm v ∈ coordinateLattice (R := R)) : - powerLocalization x (gluedLattice x y P) = powerLocalization x coordinateLattice := by - apply le_antisymm - · exact (powerLocalization_mono x inf_le_left).trans (le_of_eq (powerLocalization_idem x _)) - · rintro v hv - obtain ⟨n,hn⟩ := hv - refine ⟨d+n, ?_⟩ - change x^(d+n) • v ∈ powerLocalization x coordinateLattice ∧ - x^(d+n) • v ∈ (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) - constructor - · exact ⟨0, by simpa only [pow_zero, one_smul, pow_add, mul_smul] using - (coordinateLattice (R := R)).smul_mem (x^d) hn⟩ - · refine ⟨x^(d+n) • P.symm v, ⟨d, ?_⟩, ?_⟩ - · have h := hP (x^n • v) hn - rw [linearEquiv_map_base_smul, mul_pow, mul_smul, - smul_comm (y^d), ← mul_smul, ← pow_add] at h - simpa only [smul_comm (y^d)] using h - · change P (x^(d+n) • P.symm v) = x^(d+n) • v - rw [linearEquiv_map_base_smul, P.apply_symm_apply] - - -theorem gluedLattice_yChart (x y : R) (P : (ι → K) ≃ₗ[K] (ι → K)) - (d : ℕ) (hP : ∀ v ∈ coordinateLattice (R := R), - (x*y)^d • P v ∈ coordinateLattice (R := R)) : - powerLocalization y (gluedLattice x y P) = - (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) := by - apply le_antisymm - · refine (powerLocalization_mono y inf_le_right).trans ?_ - rw [powerLocalization_equiv_map, powerLocalization_idem] - · rintro v ⟨w,⟨n,hn⟩,rfl⟩ - refine ⟨d+n, ?_⟩ - change y^(d+n) • P w ∈ powerLocalization x coordinateLattice ∧ - y^(d+n) • P w ∈ (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) - constructor - · refine ⟨d, ?_⟩ - have h := hP (y^n • w) hn - rw [linearEquiv_map_base_smul, mul_pow, mul_smul, - ← mul_smul (y^d), ← pow_add] at h - exact h - · refine ⟨y^(d+n) • w, ⟨0, ?_⟩, ?_⟩ - · simpa only [pow_zero, one_smul, pow_add, mul_smul] using - (coordinateLattice (R := R)).smul_mem (y^d) hn - · exact (P.restrictScalars R).map_smul _ _ - -end - -section - -variable {k ι : Type*} [Field k] [Infinite k] [Fintype ι] [DecidableEq ι] -variable (P : Matrix ι ι (Polynomial k)) - (h0 : polynomialMatrixEval P (0 : k) = 1) - (hadd : ∀ s t : k, polynomialMatrixEval P (s+t) = - polynomialMatrixEval P s * polynomialMatrixEval P t) - -abbrev planeOriginFractionField := FractionRing (planeCoordinateRing k) - -instance planeOriginFraction_tower : - IsScalarTower k (planeOriginRing k) (planeOriginFractionField (k := k)) := - IsScalarTower.to₁₃₄ k (planeCoordinateRing k) (planeOriginRing k) - (planeOriginFractionField (k := k)) - -instance planeOriginFraction_isFractionRing : - IsFractionRing (planeOriginRing k) (planeOriginFractionField (k := k)) := - IsFractionRing.isFractionRing_of_isLocalization (planeOriginIdeal k).primeCompl - (planeOriginRing k) (planeOriginFractionField (k := k)) - (planeOriginIdeal k).primeCompl_le_nonZeroDivisors - -noncomputable def planeStalkTransition : - (ι → planeOriginFractionField (k := k)) ≃ₗ[planeOriginFractionField (k := k)] - (ι → planeOriginFractionField (k := k)) := - polynomialActionEquiv P h0 hadd - (-(algebraMap (planeOriginRing k) (planeOriginFractionField (k := k)) - (planeOriginCoordinate k 0 * planeOriginCoordinate k 1))⁻¹) - - - -noncomputable def planeAssociatedLattice : - Submodule (planeOriginRing k) (ι → planeOriginFractionField (k := k)) := - gluedLattice (planeOriginCoordinate k 0) (planeOriginCoordinate k 1) - (planeStalkTransition P h0 hadd) - -omit [Infinite k] in -lemma planeOrigin_product_ne_zero : - algebraMap (planeOriginRing k) (planeOriginFractionField (k := k)) - (planeOriginCoordinate k 0 * planeOriginCoordinate k 1) ≠ 0 := by - have h := FaithfulSMul.algebraMap_injective (planeOriginRing k) - (planeOriginFractionField (k := k)) - exact fun hz => (mul_ne_zero (planeOriginCoordinate_ne_zero k 0) - (planeOriginCoordinate_ne_zero k 1)) (h (hz.trans (map_zero _).symm)) - -lemma planeStalkTransition_denominator (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : - ∀ v ∈ coordinateLattice (R := planeOriginRing k), - (planeOriginCoordinate k 0 * planeOriginCoordinate k 1)^d • - planeStalkTransition P h0 hadd v ∈ coordinateLattice (R := planeOriginRing k) := - polynomialAction_denominator P h0 hadd _ planeOrigin_product_ne_zero d hd - -lemma planeStalkTransition_symm_denominator (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : - ∀ v ∈ coordinateLattice (R := planeOriginRing k), - (planeOriginCoordinate k 0 * planeOriginCoordinate k 1)^d • - (planeStalkTransition P h0 hadd).symm v ∈ coordinateLattice (R := planeOriginRing k) := by - have h := polynomialAction_fraction_denominator (R := planeOriginRing k) - (K := planeOriginFractionField (k := k)) P h0 hadd 1 _ planeOrigin_product_ne_zero d hd - simpa only [planeStalkTransition, polynomialActionEquiv_symm, neg_neg, - map_one, one_mul] using h - - - -theorem planeAssociatedLattice_finite_free (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : - Module.Finite (planeOriginRing k) (planeAssociatedLattice P h0 hadd) ∧ - Module.Free (planeOriginRing k) (planeAssociatedLattice P h0 hadd) := by - constructor - · exact gluedLattice_finite _ _ (planeOriginCoordinate_ne_zero k 0) - (planeOriginCoordinates_relPrime k) _ d (planeStalkTransition_denominator P h0 hadd d hd) - · exact gluedLattice_free _ _ (planeOriginCoordinate_ne_zero k 0) - (planeOriginCoordinate_ne_zero k 1) (planeOriginCoordinates_relPrime k) - (planeOrigin_maximalIdeal k) _ d (planeStalkTransition_denominator P h0 hadd d hd) - -theorem planeAssociatedLattice_xChart (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : - powerLocalization (planeOriginCoordinate k 0) (planeAssociatedLattice P h0 hadd) = - powerLocalization (planeOriginCoordinate k 0) coordinateLattice := - gluedLattice_xChart _ _ _ d (planeStalkTransition_symm_denominator P h0 hadd d hd) - -theorem planeAssociatedLattice_yChart (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : - powerLocalization (planeOriginCoordinate k 1) (planeAssociatedLattice P h0 hadd) = - (powerLocalization (planeOriginCoordinate k 1) coordinateLattice).map - ((planeStalkTransition P h0 hadd).toLinearMap.restrictScalars (planeOriginRing k)) := - gluedLattice_yChart _ _ _ d (planeStalkTransition_denominator P h0 hadd d hd) - -end - -variable (k : Type*) [Field k] [Infinite k] - -abbrev planeOverlapRing := Localization.Away - ((MvPolynomial.X 0 : MvPolynomial (Fin 2) k) * MvPolynomial.X 1) - -omit [Infinite k] in -lemma planeTorusEvaluation_product_isUnit : - IsUnit (planeTorusEvaluation k - ((MvPolynomial.X 0 : MvPolynomial (Fin 2) k) * MvPolynomial.X 1)) := by - rw [map_mul] - exact (planeTorusEvaluation_X_isUnit k 0).mul (planeTorusEvaluation_X_isUnit k 1) - -noncomputable def planeOverlapEvaluation : - planeOverlapRing k →ₐ[k] (planeTorusPoints k → k) := - IsLocalization.Away.liftAlgHom _ (planeTorusEvaluation_product_isUnit k) - -omit [Infinite k] in -lemma planeOverlapEvaluation_algebraMap (P : MvPolynomial (Fin 2) k) : - planeOverlapEvaluation k (algebraMap (MvPolynomial (Fin 2) k) (planeOverlapRing k) P) = - planeTorusEvaluation k P := - IsLocalization.Away.lift_eq _ (planeTorusEvaluation_product_isUnit k) _ - -theorem planeOverlapEvaluation_injective : - Function.Injective (planeOverlapEvaluation k) := by - apply (IsLocalization.injective_iff_map_algebraMap_eq - (R := MvPolynomial (Fin 2) k) (S := planeOverlapRing k) - (Submonoid.powers (MvPolynomial.X 0 * MvPolynomial.X 1)) - (planeOverlapEvaluation k).toRingHom).mpr - intro P Q - constructor - · exact congrArg (planeOverlapEvaluation k) - · intro h - have h' : planeTorusEvaluation k P = planeTorusEvaluation k Q := by - simpa only [AlgHom.toRingHom_eq_coe, RingHom.coe_coe, - planeOverlapEvaluation_algebraMap] using h - exact congrArg (algebraMap (MvPolynomial (Fin 2) k) (planeOverlapRing k)) - (planeTorusEvaluation_injective k h') - -omit [Infinite k] in -lemma planeOverlapCoordinate_isUnit (i : Fin 2) : - IsUnit (algebraMap (MvPolynomial (Fin 2) k) (planeOverlapRing k) (MvPolynomial.X i)) := by - apply IsLocalization.Away.isUnit_of_dvd - (x := (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) * MvPolynomial.X 1) - fin_cases i - · exact dvd_mul_right _ _ - · exact dvd_mul_left _ _ - -noncomputable def planeChartToOverlap (i : Fin 2) : - planeCoordinateChart k i →ₐ[k] planeOverlapRing k := - IsLocalization.Away.liftAlgHom (MvPolynomial.X i : MvPolynomial (Fin 2) k) - (f := IsScalarTower.toAlgHom k (MvPolynomial (Fin 2) k) (planeOverlapRing k)) - (planeOverlapCoordinate_isUnit k i) - -omit [Infinite k] in -lemma planeChartToOverlap_algebraMap (i : Fin 2) (P : MvPolynomial (Fin 2) k) : - planeChartToOverlap k i - (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i) P) = - algebraMap (MvPolynomial (Fin 2) k) (planeOverlapRing k) P := - IsLocalization.Away.lift_eq _ (planeOverlapCoordinate_isUnit k i) _ - -omit [Infinite k] in -lemma planeChartToOverlap_evaluation (i : Fin 2) (f : planeCoordinateChart k i) : - planeOverlapEvaluation k (planeChartToOverlap k i f) = planeChartEvaluation k i f := by - have h : (planeOverlapEvaluation k).toRingHom.comp (planeChartToOverlap k i).toRingHom = - (planeChartEvaluation k i).toRingHom := by - apply IsLocalization.ringHom_ext - (Submonoid.powers (MvPolynomial.X i : MvPolynomial (Fin 2) k)) - apply RingHom.ext - intro P - simp only [RingHom.comp_apply, AlgHom.toRingHom_eq_coe, RingHom.coe_coe, - planeChartToOverlap_algebraMap, planeOverlapEvaluation_algebraMap, - planeChartEvaluation_algebraMap] - exact RingHom.congr_fun h f - -lemma planeChartToOverlap_injective (i : Fin 2) : Function.Injective (planeChartToOverlap k i) := by - intro f h he - apply planeChartEvaluation_injective k i - rw [← planeChartToOverlap_evaluation, ← planeChartToOverlap_evaluation, he] - -end FiberFunctorProof -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.ActionDenominators + +namespace OAI + +/-! Plane-origin coordinate rings, stalk lattices and overlap evaluation. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section + +variable (k : Type*) [Field k] + +abbrev planeCoordinateRing := MvPolynomial (Fin 2) k + +def planeOriginIdeal : Ideal (planeCoordinateRing k) := + RingHom.ker MvPolynomial.constantCoeff + +instance planeOriginIdeal_isMaximal : (planeOriginIdeal k).IsMaximal := + RingHom.ker_isMaximal_of_surjective MvPolynomial.constantCoeff + (fun a => ⟨MvPolynomial.C a, MvPolynomial.constantCoeff_C (Fin 2) a⟩) + +lemma planeOriginIdeal_eq_span : planeOriginIdeal k = + Ideal.span {MvPolynomial.X (0 : Fin 2), MvPolynomial.X (1 : Fin 2)} := by + have hvars : planeOriginIdeal k = MvPolynomial.idealOfVars (Fin 2) k := by + ext f + change f.coeff 0 = 0 ↔ f ∈ MvPolynomial.idealOfVars (Fin 2) k + have he := MvPolynomial.mem_pow_idealOfVars_iff' (R := k) (σ := Fin 2) 1 f + simpa only [pow_one, Nat.lt_one_iff, Finsupp.degree_eq_zero_iff, + forall_eq] using he.symm + rw [hvars, MvPolynomial.idealOfVars] + congr 1 + ext p + constructor + · rintro ⟨i,rfl⟩ + fin_cases i <;> simp + · rintro (rfl | rfl) + · exact ⟨0,rfl⟩ + · exact ⟨1,rfl⟩ + +abbrev planeOriginRing := Localization.AtPrime (planeOriginIdeal k) + +abbrev planeOriginCoordinate (i : Fin 2) : planeOriginRing k := + algebraMap (planeCoordinateRing k) (planeOriginRing k) (MvPolynomial.X i) + +lemma planeOriginCoordinate_ne_zero (i : Fin 2) : planeOriginCoordinate k i ≠ 0 := by + exact fun h => MvPolynomial.X_ne_zero i + ((IsLocalization.injective (planeOriginRing k) + (planeOriginIdeal k).primeCompl_le_nonZeroDivisors) (h.trans (map_zero _).symm)) + +lemma planeOrigin_maximalIdeal : IsLocalRing.maximalIdeal (planeOriginRing k) = + Ideal.span {planeOriginCoordinate k 0, planeOriginCoordinate k 1} := by + rw [← IsLocalization.AtPrime.map_eq_maximalIdeal (planeOriginIdeal k) (planeOriginRing k)] + calc + _ = Ideal.map (algebraMap (planeCoordinateRing k) (planeOriginRing k)) + (Ideal.span {MvPolynomial.X (0 : Fin 2), MvPolynomial.X (1 : Fin 2)}) := + congrArg (Ideal.map (algebraMap (planeCoordinateRing k) (planeOriginRing k))) + (planeOriginIdeal_eq_span k) + _ = _ := by + rw [Ideal.map_span] + simp only [Set.image_insert_eq, Set.image_singleton, planeOriginCoordinate] + +lemma planeOriginCoordinate_prime (i : Fin 2) : Prime (planeOriginCoordinate k i) := by + apply (IsLocalization.toLocalizationMap (planeOriginIdeal k).primeCompl + (planeOriginRing k)).map_prime (MvPolynomial.X_prime (i := i)) (planeOriginCoordinate_ne_zero k i) + change ¬ IsUnit (planeOriginCoordinate k i) + rw [IsLocalization.AtPrime.isUnit_to_map_iff (planeOriginRing k) (planeOriginIdeal k)] + change ¬ (MvPolynomial.X i : planeCoordinateRing k) ∉ planeOriginIdeal k + simp [planeOriginIdeal, RingHom.mem_ker] + +lemma planeOriginCoordinates_relPrime : + IsRelPrime (planeOriginCoordinate k 0) (planeOriginCoordinate k 1) := by + apply (planeOriginCoordinate_prime k 0).irreducible.isRelPrime_iff_not_dvd.mpr + intro h + obtain ⟨s,hs,hd⟩ := + (IsLocalization.toLocalizationMap (planeOriginIdeal k).primeCompl + (planeOriginRing k)).map_dvd_map.mp h + rcases (MvPolynomial.X_prime (R := k) (i := (0 : Fin 2))).dvd_or_dvd hd with ha | hb + · have hx : (MvPolynomial.X (0 : Fin 2) : planeCoordinateRing k) ∈ planeOriginIdeal k := by + simp [planeOriginIdeal, RingHom.mem_ker] + obtain ⟨a,rfl⟩ := ha + exact hs ((planeOriginIdeal k).mul_mem_right a hx) + · exact (by decide : (0 : Fin 2) ≠ 1) (MvPolynomial.X_dvd_X.mp hb) + +noncomputable instance planeOriginRing_gcd : GCDMonoid (planeOriginRing k) := + UniqueFactorizationMonoid.toGCDMonoid _ + +example : IsNoetherianRing (planeOriginRing k) := inferInstance +example : IsLocalRing (planeOriginRing k) := inferInstance + +end + +section PowerCharts +variable {R K ι : Type*} [CommRing R] [Field K] [Algebra R K] + +lemma linearEquiv_map_base_smul (P : (ι → K) ≃ₗ[K] (ι → K)) (a : R) (v : ι → K) : + P (a • v) = a • P v := + (P.restrictScalars R).map_smul a v + +lemma powerLocalization_idem (x : R) (L : Submodule R (ι → K)) : + powerLocalization x (powerLocalization x L) = powerLocalization x L := by + apply le_antisymm + · rintro v ⟨n,m,h⟩ + exact ⟨m+n, by simpa only [pow_add, mul_smul] using h⟩ + · exact le_powerLocalization _ _ + +lemma powerLocalization_equiv_map (x : R) (L : Submodule R (ι → K)) + (P : (ι → K) ≃ₗ[K] (ι → K)) : + powerLocalization x (L.map (P.toLinearMap.restrictScalars R)) = + (powerLocalization x L).map (P.toLinearMap.restrictScalars R) := by + apply le_antisymm + · rintro v ⟨n,w,hw,he⟩ + refine ⟨P.symm v, ⟨n, ?_⟩, P.apply_symm_apply v⟩ + have h : w = x^n • P.symm v := by + apply P.injective + change P w = x^n • v at he + simpa only [linearEquiv_map_base_smul, P.apply_symm_apply] using he + exact h ▸ hw + · rintro v ⟨w,⟨n,hn⟩,rfl⟩ + refine ⟨n,x^n • w,hn,?_⟩ + exact (P.restrictScalars R).map_smul _ _ + +end PowerCharts + +section +variable {R K ι : Type*} [CommRing R] [Field K] [Algebra R K] + + +theorem gluedLattice_xChart (x y : R) (P : (ι → K) ≃ₗ[K] (ι → K)) + (d : ℕ) (hP : ∀ v ∈ coordinateLattice (R := R), + (x*y)^d • P.symm v ∈ coordinateLattice (R := R)) : + powerLocalization x (gluedLattice x y P) = powerLocalization x coordinateLattice := by + apply le_antisymm + · exact (powerLocalization_mono x inf_le_left).trans (le_of_eq (powerLocalization_idem x _)) + · rintro v hv + obtain ⟨n,hn⟩ := hv + refine ⟨d+n, ?_⟩ + change x^(d+n) • v ∈ powerLocalization x coordinateLattice ∧ + x^(d+n) • v ∈ (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) + constructor + · exact ⟨0, by simpa only [pow_zero, one_smul, pow_add, mul_smul] using + (coordinateLattice (R := R)).smul_mem (x^d) hn⟩ + · refine ⟨x^(d+n) • P.symm v, ⟨d, ?_⟩, ?_⟩ + · have h := hP (x^n • v) hn + rw [linearEquiv_map_base_smul, mul_pow, mul_smul, + smul_comm (y^d), ← mul_smul, ← pow_add] at h + simpa only [smul_comm (y^d)] using h + · change P (x^(d+n) • P.symm v) = x^(d+n) • v + rw [linearEquiv_map_base_smul, P.apply_symm_apply] + + +theorem gluedLattice_yChart (x y : R) (P : (ι → K) ≃ₗ[K] (ι → K)) + (d : ℕ) (hP : ∀ v ∈ coordinateLattice (R := R), + (x*y)^d • P v ∈ coordinateLattice (R := R)) : + powerLocalization y (gluedLattice x y P) = + (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) := by + apply le_antisymm + · refine (powerLocalization_mono y inf_le_right).trans ?_ + rw [powerLocalization_equiv_map, powerLocalization_idem] + · rintro v ⟨w,⟨n,hn⟩,rfl⟩ + refine ⟨d+n, ?_⟩ + change y^(d+n) • P w ∈ powerLocalization x coordinateLattice ∧ + y^(d+n) • P w ∈ (powerLocalization y coordinateLattice).map (P.toLinearMap.restrictScalars R) + constructor + · refine ⟨d, ?_⟩ + have h := hP (y^n • w) hn + rw [linearEquiv_map_base_smul, mul_pow, mul_smul, + ← mul_smul (y^d), ← pow_add] at h + exact h + · refine ⟨y^(d+n) • w, ⟨0, ?_⟩, ?_⟩ + · simpa only [pow_zero, one_smul, pow_add, mul_smul] using + (coordinateLattice (R := R)).smul_mem (y^d) hn + · exact (P.restrictScalars R).map_smul _ _ + +end + +section + +variable {k ι : Type*} [Field k] [Infinite k] [Fintype ι] [DecidableEq ι] +variable (P : Matrix ι ι (Polynomial k)) + (h0 : polynomialMatrixEval P (0 : k) = 1) + (hadd : ∀ s t : k, polynomialMatrixEval P (s+t) = + polynomialMatrixEval P s * polynomialMatrixEval P t) + +abbrev planeOriginFractionField := FractionRing (planeCoordinateRing k) + +instance planeOriginFraction_tower : + IsScalarTower k (planeOriginRing k) (planeOriginFractionField (k := k)) := + IsScalarTower.to₁₃₄ k (planeCoordinateRing k) (planeOriginRing k) + (planeOriginFractionField (k := k)) + +instance planeOriginFraction_isFractionRing : + IsFractionRing (planeOriginRing k) (planeOriginFractionField (k := k)) := + IsFractionRing.isFractionRing_of_isLocalization (planeOriginIdeal k).primeCompl + (planeOriginRing k) (planeOriginFractionField (k := k)) + (planeOriginIdeal k).primeCompl_le_nonZeroDivisors + +noncomputable def planeStalkTransition : + (ι → planeOriginFractionField (k := k)) ≃ₗ[planeOriginFractionField (k := k)] + (ι → planeOriginFractionField (k := k)) := + polynomialActionEquiv P h0 hadd + (-(algebraMap (planeOriginRing k) (planeOriginFractionField (k := k)) + (planeOriginCoordinate k 0 * planeOriginCoordinate k 1))⁻¹) + + + +noncomputable def planeAssociatedLattice : + Submodule (planeOriginRing k) (ι → planeOriginFractionField (k := k)) := + gluedLattice (planeOriginCoordinate k 0) (planeOriginCoordinate k 1) + (planeStalkTransition P h0 hadd) + +omit [Infinite k] in +lemma planeOrigin_product_ne_zero : + algebraMap (planeOriginRing k) (planeOriginFractionField (k := k)) + (planeOriginCoordinate k 0 * planeOriginCoordinate k 1) ≠ 0 := by + have h := FaithfulSMul.algebraMap_injective (planeOriginRing k) + (planeOriginFractionField (k := k)) + exact fun hz => (mul_ne_zero (planeOriginCoordinate_ne_zero k 0) + (planeOriginCoordinate_ne_zero k 1)) (h (hz.trans (map_zero _).symm)) + +lemma planeStalkTransition_denominator (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : + ∀ v ∈ coordinateLattice (R := planeOriginRing k), + (planeOriginCoordinate k 0 * planeOriginCoordinate k 1)^d • + planeStalkTransition P h0 hadd v ∈ coordinateLattice (R := planeOriginRing k) := + polynomialAction_denominator P h0 hadd _ planeOrigin_product_ne_zero d hd + +lemma planeStalkTransition_symm_denominator (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : + ∀ v ∈ coordinateLattice (R := planeOriginRing k), + (planeOriginCoordinate k 0 * planeOriginCoordinate k 1)^d • + (planeStalkTransition P h0 hadd).symm v ∈ coordinateLattice (R := planeOriginRing k) := by + have h := polynomialAction_fraction_denominator (R := planeOriginRing k) + (K := planeOriginFractionField (k := k)) P h0 hadd 1 _ planeOrigin_product_ne_zero d hd + simpa only [planeStalkTransition, polynomialActionEquiv_symm, neg_neg, + map_one, one_mul] using h + + + +theorem planeAssociatedLattice_finite_free (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : + Module.Finite (planeOriginRing k) (planeAssociatedLattice P h0 hadd) ∧ + Module.Free (planeOriginRing k) (planeAssociatedLattice P h0 hadd) := by + constructor + · exact gluedLattice_finite _ _ (planeOriginCoordinate_ne_zero k 0) + (planeOriginCoordinates_relPrime k) _ d (planeStalkTransition_denominator P h0 hadd d hd) + · exact gluedLattice_free _ _ (planeOriginCoordinate_ne_zero k 0) + (planeOriginCoordinate_ne_zero k 1) (planeOriginCoordinates_relPrime k) + (planeOrigin_maximalIdeal k) _ d (planeStalkTransition_denominator P h0 hadd d hd) + +theorem planeAssociatedLattice_xChart (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : + powerLocalization (planeOriginCoordinate k 0) (planeAssociatedLattice P h0 hadd) = + powerLocalization (planeOriginCoordinate k 0) coordinateLattice := + gluedLattice_xChart _ _ _ d (planeStalkTransition_symm_denominator P h0 hadd d hd) + +theorem planeAssociatedLattice_yChart (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) : + powerLocalization (planeOriginCoordinate k 1) (planeAssociatedLattice P h0 hadd) = + (powerLocalization (planeOriginCoordinate k 1) coordinateLattice).map + ((planeStalkTransition P h0 hadd).toLinearMap.restrictScalars (planeOriginRing k)) := + gluedLattice_yChart _ _ _ d (planeStalkTransition_denominator P h0 hadd d hd) + +end + +variable (k : Type*) [Field k] [Infinite k] + +abbrev planeOverlapRing := Localization.Away + ((MvPolynomial.X 0 : MvPolynomial (Fin 2) k) * MvPolynomial.X 1) + +omit [Infinite k] in +lemma planeTorusEvaluation_product_isUnit : + IsUnit (planeTorusEvaluation k + ((MvPolynomial.X 0 : MvPolynomial (Fin 2) k) * MvPolynomial.X 1)) := by + rw [map_mul] + exact (planeTorusEvaluation_X_isUnit k 0).mul (planeTorusEvaluation_X_isUnit k 1) + +noncomputable def planeOverlapEvaluation : + planeOverlapRing k →ₐ[k] (planeTorusPoints k → k) := + IsLocalization.Away.liftAlgHom _ (planeTorusEvaluation_product_isUnit k) + +omit [Infinite k] in +lemma planeOverlapEvaluation_algebraMap (P : MvPolynomial (Fin 2) k) : + planeOverlapEvaluation k (algebraMap (MvPolynomial (Fin 2) k) (planeOverlapRing k) P) = + planeTorusEvaluation k P := + IsLocalization.Away.lift_eq _ (planeTorusEvaluation_product_isUnit k) _ + +theorem planeOverlapEvaluation_injective : + Function.Injective (planeOverlapEvaluation k) := by + apply (IsLocalization.injective_iff_map_algebraMap_eq + (R := MvPolynomial (Fin 2) k) (S := planeOverlapRing k) + (Submonoid.powers (MvPolynomial.X 0 * MvPolynomial.X 1)) + (planeOverlapEvaluation k).toRingHom).mpr + intro P Q + constructor + · exact congrArg (planeOverlapEvaluation k) + · intro h + have h' : planeTorusEvaluation k P = planeTorusEvaluation k Q := by + simpa only [AlgHom.toRingHom_eq_coe, RingHom.coe_coe, + planeOverlapEvaluation_algebraMap] using h + exact congrArg (algebraMap (MvPolynomial (Fin 2) k) (planeOverlapRing k)) + (planeTorusEvaluation_injective k h') + +omit [Infinite k] in +lemma planeOverlapCoordinate_isUnit (i : Fin 2) : + IsUnit (algebraMap (MvPolynomial (Fin 2) k) (planeOverlapRing k) (MvPolynomial.X i)) := by + apply IsLocalization.Away.isUnit_of_dvd + (x := (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) * MvPolynomial.X 1) + fin_cases i + · exact dvd_mul_right _ _ + · exact dvd_mul_left _ _ + +noncomputable def planeChartToOverlap (i : Fin 2) : + planeCoordinateChart k i →ₐ[k] planeOverlapRing k := + IsLocalization.Away.liftAlgHom (MvPolynomial.X i : MvPolynomial (Fin 2) k) + (f := IsScalarTower.toAlgHom k (MvPolynomial (Fin 2) k) (planeOverlapRing k)) + (planeOverlapCoordinate_isUnit k i) + +omit [Infinite k] in +lemma planeChartToOverlap_algebraMap (i : Fin 2) (P : MvPolynomial (Fin 2) k) : + planeChartToOverlap k i + (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i) P) = + algebraMap (MvPolynomial (Fin 2) k) (planeOverlapRing k) P := + IsLocalization.Away.lift_eq _ (planeOverlapCoordinate_isUnit k i) _ + +omit [Infinite k] in +lemma planeChartToOverlap_evaluation (i : Fin 2) (f : planeCoordinateChart k i) : + planeOverlapEvaluation k (planeChartToOverlap k i f) = planeChartEvaluation k i f := by + have h : (planeOverlapEvaluation k).toRingHom.comp (planeChartToOverlap k i).toRingHom = + (planeChartEvaluation k i).toRingHom := by + apply IsLocalization.ringHom_ext + (Submonoid.powers (MvPolynomial.X i : MvPolynomial (Fin 2) k)) + apply RingHom.ext + intro P + simp only [RingHom.comp_apply, AlgHom.toRingHom_eq_coe, RingHom.coe_coe, + planeChartToOverlap_algebraMap, planeOverlapEvaluation_algebraMap, + planeChartEvaluation_algebraMap] + exact RingHom.congr_fun h f + +lemma planeChartToOverlap_injective (i : Fin 2) : Function.Injective (planeChartToOverlap k i) := by + intro f h he + apply planeChartEvaluation_injective k i + rw [← planeChartToOverlap_evaluation, ← planeChartToOverlap_evaluation, he] + +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/PGroupInvariants.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/PGroupInvariants.lean index 067205f0249aba06bd20ce38471c35b9b364340b..76af826a59fda251e6541ee47465e70d5d1f09ec 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/PGroupInvariants.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/PGroupInvariants.lean @@ -1,58 +1,58 @@ -import Mathlib - -namespace OAI - -namespace FiberFunctorProof -open Representation -universe u v -variable {k : Type u} [Field k] {p : ℕ} [Fact p.Prime] [CharP k p] -variable {G : Type v} [Group G] [Finite G] -variable {V : Type u} [AddCommGroup V] [Module k V] - - - -theorem pgroup_exists_invariant (hG : IsPGroup p G) (ρ : Representation k G V) - (v : V) (hv : v ≠ 0) : ∃ w : V, w ≠ 0 ∧ ∀ g, ρ g w = w := by - classical - let : Algebra (ZMod p) k := ZMod.algebra k p - let : Module (ZMod p) V := Module.compHom V (algebraMap (ZMod p) k) - let : IsScalarTower (ZMod p) k V := IsScalarTower.of_algebraMap_smul fun _ _ => rfl - let W : Submodule (ZMod p) V := Submodule.span (ZMod p) (Set.range fun g : G => ρ g v) - have hvW : v ∈ W := by - apply Submodule.subset_span - exact ⟨1, by simp⟩ - have hstable (g : G) : W ≤ W.comap ((ρ g).restrictScalars (ZMod p)) := by - apply Submodule.span_le.mpr - rintro _ ⟨h,rfl⟩ - change ρ g (ρ h v) ∈ W - change (ρ g * ρ h) v ∈ W - rw [← map_mul] - exact Submodule.subset_span ⟨g*h,rfl⟩ - let σ : Representation (ZMod p) G W := - { toFun := fun g => ((ρ g).restrictScalars (ZMod p)).restrict (hstable g) - map_one' := by ext w; simp - map_mul' := by intro g h; ext w; simp [map_mul] } - let : Module.Finite (ZMod p) W := - Module.Finite.of_fg (Submodule.fg_span (Set.finite_range _)) - let : Finite W := Module.finite_of_finite (ZMod p) - have hnt : Nontrivial W := ⟨⟨⟨v,hvW⟩,0,fun h => hv (congrArg Subtype.val h)⟩⟩ - let := hnt - let : MulAction G W := { - smul g w := σ g w - one_smul := by intro w; change σ 1 w = w; simp - mul_smul := by intro g h w; change σ (g*h) w = σ g (σ h w); simp [map_mul] } - have hpW : p ∣ Nat.card W := by - let := Fintype.ofFinite W - rw [Nat.card_eq_fintype_card, Module.card_eq_pow_finrank (K := ZMod p), ZMod.card] - exact dvd_pow_self p (ne_of_gt (Module.finrank_pos (R := ZMod p) (M := W))) - obtain ⟨w,hw,hne⟩ := hG.exists_fixed_point_of_prime_dvd_card_of_fixed_point W hpW - (a := 0) (by intro g; change σ g 0 = 0; simp) - refine ⟨w,?_,?_⟩ - · intro h - apply hne - exact Subtype.ext h.symm - · intro g - exact congrArg Subtype.val (hw g) -end FiberFunctorProof - -end OAI +import Mathlib + +namespace OAI + +namespace FiberFunctorProof +open Representation +universe u v +variable {k : Type u} [Field k] {p : ℕ} [Fact p.Prime] [CharP k p] +variable {G : Type v} [Group G] [Finite G] +variable {V : Type u} [AddCommGroup V] [Module k V] + + + +theorem pgroup_exists_invariant (hG : IsPGroup p G) (ρ : Representation k G V) + (v : V) (hv : v ≠ 0) : ∃ w : V, w ≠ 0 ∧ ∀ g, ρ g w = w := by + classical + let : Algebra (ZMod p) k := ZMod.algebra k p + let : Module (ZMod p) V := Module.compHom V (algebraMap (ZMod p) k) + let : IsScalarTower (ZMod p) k V := IsScalarTower.of_algebraMap_smul fun _ _ => rfl + let W : Submodule (ZMod p) V := Submodule.span (ZMod p) (Set.range fun g : G => ρ g v) + have hvW : v ∈ W := by + apply Submodule.subset_span + exact ⟨1, by simp⟩ + have hstable (g : G) : W ≤ W.comap ((ρ g).restrictScalars (ZMod p)) := by + apply Submodule.span_le.mpr + rintro _ ⟨h,rfl⟩ + change ρ g (ρ h v) ∈ W + change (ρ g * ρ h) v ∈ W + rw [← map_mul] + exact Submodule.subset_span ⟨g*h,rfl⟩ + let σ : Representation (ZMod p) G W := + { toFun := fun g => ((ρ g).restrictScalars (ZMod p)).restrict (hstable g) + map_one' := by ext w; simp + map_mul' := by intro g h; ext w; simp [map_mul] } + let : Module.Finite (ZMod p) W := + Module.Finite.of_fg (Submodule.fg_span (Set.finite_range _)) + let : Finite W := Module.finite_of_finite (ZMod p) + have hnt : Nontrivial W := ⟨⟨⟨v,hvW⟩,0,fun h => hv (congrArg Subtype.val h)⟩⟩ + let := hnt + let : MulAction G W := { + smul g w := σ g w + one_smul := by intro w; change σ 1 w = w; simp + mul_smul := by intro g h w; change σ (g*h) w = σ g (σ h w); simp [map_mul] } + have hpW : p ∣ Nat.card W := by + let := Fintype.ofFinite W + rw [Nat.card_eq_fintype_card, Module.card_eq_pow_finrank (K := ZMod p), ZMod.card] + exact dvd_pow_self p (ne_of_gt (Module.finrank_pos (R := ZMod p) (M := W))) + obtain ⟨w,hw,hne⟩ := hG.exists_fixed_point_of_prime_dvd_card_of_fixed_point W hpW + (a := 0) (by intro g; change σ g 0 = 0; simp) + refine ⟨w,?_,?_⟩ + · intro h + apply hne + exact Subtype.ext h.symm + · intro g + exact congrArg Subtype.val (hw g) +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/PiPlaneOrigin.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/PiPlaneOrigin.lean index 28b447d5bf4b4cc1e9f8e110ce80d474fc502743..85b716972cc3b759b45abac95c59646702b13ce8 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/PiPlaneOrigin.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/PiPlaneOrigin.lean @@ -1,82 +1,82 @@ -import OAI.RepresentationTheory.RestrictedTilting.PlaneMatrixTensor - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory -open scoped BigOperators TensorProduct -universe u -variable (k : Type u) [Field k] -variable {β : Type u} [Fintype β] [DecidableEq β] -variable {M : Type u} [AddCommGroup M] [Module k M] - [Module (MvPolynomial (Fin 2) k) M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] -local notation "A" => MvPolynomial (Fin 2) k -local notation "pM" => planeJetRelation (M := M) k 1 -local notation "pPi" => planeJetRelation (M := β → M) k 1 - -noncomputable def piPlaneOriginMap : (β → M) →ₗ[k] (β → M ⧸ pM) := - LinearMap.pi fun i => (pM).mkQ.comp (LinearMap.proj i) - -omit [Fintype β] [DecidableEq β] in -lemma piPlaneOriginMap_apply (v : β → M) (i : β) : - piPlaneOriginMap k v i = (pM).mkQ (v i) := rfl - -omit [Fintype β] [DecidableEq β] in -lemma piPlaneOriginMap_surjective : Function.Surjective (piPlaneOriginMap (β := β) (M := M) k) := by - intro v - choose w hw using fun i => (pM).mkQ_surjective (v i) - exact ⟨w, funext hw⟩ - -lemma planeOrigin_mem_iff (v : M) : v ∈ pM ↔ - ∃ a b : M, v = (MvPolynomial.X 0 : A) • a + (MvPolynomial.X 1 : A) • b := by - change v ∈ jetRelation (MvPolynomial.X 0 : A) (MvPolynomial.X 1) 1 ↔ _ - rw [jetRelation_one, mem_pairRelation] - -omit [Fintype β] [DecidableEq β] in -lemma piPlaneOriginMap_ker : (piPlaneOriginMap (β := β) (M := M) k).ker = pPi := by - ext v - change piPlaneOriginMap k v = 0 ↔ v ∈ pPi - rw [planeOrigin_mem_iff] - constructor - · intro h - have hi (i : β) : v i ∈ pM := by - exact (Submodule.Quotient.mk_eq_zero pM).mp (congrFun h i) - choose a b hab using fun i => (planeOrigin_mem_iff k (v i)).mp (hi i) - exact ⟨a,b,funext hab⟩ - · rintro ⟨a,b,rfl⟩ - funext i - exact (Submodule.Quotient.mk_eq_zero pM).mpr - ((planeOrigin_mem_iff k _).mpr ⟨a i,b i,rfl⟩) - -noncomputable def piPlaneOriginEquiv : ((β → M) ⧸ pPi) ≃ₗ[k] (β → M ⧸ pM) := by - let f : (β → M) →ₗ[k] (β → M ⧸ pM) := piPlaneOriginMap (β := β) (M := M) k - let e : ((β → M) ⧸ f.ker) ≃ₗ[k] (β → M ⧸ pM) := - f.quotKerEquivOfSurjective (piPlaneOriginMap_surjective (β := β) (M := M) k) - exact (Submodule.quotEquivOfEq pPi f.ker (piPlaneOriginMap_ker (β := β) (M := M) k).symm).trans e - -omit [Fintype β] [DecidableEq β] in -lemma piPlaneOriginEquiv_mk (v : β → M) : - piPlaneOriginEquiv k ((pPi).mkQ v) = fun i => (pM).mkQ (v i) := rfl - -omit [DecidableEq β] in -lemma piPlaneOrigin_finite [Module.Finite k (M ⧸ pM)] : - Module.Finite k ((β → M) ⧸ pPi) := - Module.Finite.of_surjective (piPlaneOriginEquiv (β := β) (M := M) k).symm.toLinearMap - (piPlaneOriginEquiv k).symm.surjective - -variable (τ : Representation k (SL2 k) (β → k)) (σ : Representation k (SL2 k) M) - (hσ : PlaneCompatible k σ) - -lemma piPlaneOriginEquiv_intertwines (g : SL2 k) (v : (β → M) ⧸ pPi) : - piPlaneOriginEquiv k - (planeJetRep k (matrixTensorRepresentation τ σ) (matrixTensor_planeCompatible k τ σ hσ) 1 g v) = - matrixTensorRepresentation τ (planeJetRep k σ hσ 1) g (piPlaneOriginEquiv k v) := by - obtain ⟨v,rfl⟩ := (pPi).mkQ_surjective v - change piPlaneOriginEquiv k ((pPi).mkQ (matrixTensorRepresentation τ σ g v)) = _ - rw [piPlaneOriginEquiv_mk, piPlaneOriginEquiv_mk] - funext i - simp only [matrixTensorRepresentation_apply, map_sum, map_smul] - rfl -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.PlaneMatrixTensor + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory +open scoped BigOperators TensorProduct +universe u +variable (k : Type u) [Field k] +variable {β : Type u} [Fintype β] [DecidableEq β] +variable {M : Type u} [AddCommGroup M] [Module k M] + [Module (MvPolynomial (Fin 2) k) M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] +local notation "A" => MvPolynomial (Fin 2) k +local notation "pM" => planeJetRelation (M := M) k 1 +local notation "pPi" => planeJetRelation (M := β → M) k 1 + +noncomputable def piPlaneOriginMap : (β → M) →ₗ[k] (β → M ⧸ pM) := + LinearMap.pi fun i => (pM).mkQ.comp (LinearMap.proj i) + +omit [Fintype β] [DecidableEq β] in +lemma piPlaneOriginMap_apply (v : β → M) (i : β) : + piPlaneOriginMap k v i = (pM).mkQ (v i) := rfl + +omit [Fintype β] [DecidableEq β] in +lemma piPlaneOriginMap_surjective : Function.Surjective (piPlaneOriginMap (β := β) (M := M) k) := by + intro v + choose w hw using fun i => (pM).mkQ_surjective (v i) + exact ⟨w, funext hw⟩ + +lemma planeOrigin_mem_iff (v : M) : v ∈ pM ↔ + ∃ a b : M, v = (MvPolynomial.X 0 : A) • a + (MvPolynomial.X 1 : A) • b := by + change v ∈ jetRelation (MvPolynomial.X 0 : A) (MvPolynomial.X 1) 1 ↔ _ + rw [jetRelation_one, mem_pairRelation] + +omit [Fintype β] [DecidableEq β] in +lemma piPlaneOriginMap_ker : (piPlaneOriginMap (β := β) (M := M) k).ker = pPi := by + ext v + change piPlaneOriginMap k v = 0 ↔ v ∈ pPi + rw [planeOrigin_mem_iff] + constructor + · intro h + have hi (i : β) : v i ∈ pM := by + exact (Submodule.Quotient.mk_eq_zero pM).mp (congrFun h i) + choose a b hab using fun i => (planeOrigin_mem_iff k (v i)).mp (hi i) + exact ⟨a,b,funext hab⟩ + · rintro ⟨a,b,rfl⟩ + funext i + exact (Submodule.Quotient.mk_eq_zero pM).mpr + ((planeOrigin_mem_iff k _).mpr ⟨a i,b i,rfl⟩) + +noncomputable def piPlaneOriginEquiv : ((β → M) ⧸ pPi) ≃ₗ[k] (β → M ⧸ pM) := by + let f : (β → M) →ₗ[k] (β → M ⧸ pM) := piPlaneOriginMap (β := β) (M := M) k + let e : ((β → M) ⧸ f.ker) ≃ₗ[k] (β → M ⧸ pM) := + f.quotKerEquivOfSurjective (piPlaneOriginMap_surjective (β := β) (M := M) k) + exact (Submodule.quotEquivOfEq pPi f.ker (piPlaneOriginMap_ker (β := β) (M := M) k).symm).trans e + +omit [Fintype β] [DecidableEq β] in +lemma piPlaneOriginEquiv_mk (v : β → M) : + piPlaneOriginEquiv k ((pPi).mkQ v) = fun i => (pM).mkQ (v i) := rfl + +omit [DecidableEq β] in +lemma piPlaneOrigin_finite [Module.Finite k (M ⧸ pM)] : + Module.Finite k ((β → M) ⧸ pPi) := + Module.Finite.of_surjective (piPlaneOriginEquiv (β := β) (M := M) k).symm.toLinearMap + (piPlaneOriginEquiv k).symm.surjective + +variable (τ : Representation k (SL2 k) (β → k)) (σ : Representation k (SL2 k) M) + (hσ : PlaneCompatible k σ) + +lemma piPlaneOriginEquiv_intertwines (g : SL2 k) (v : (β → M) ⧸ pPi) : + piPlaneOriginEquiv k + (planeJetRep k (matrixTensorRepresentation τ σ) (matrixTensor_planeCompatible k τ σ hσ) 1 g v) = + matrixTensorRepresentation τ (planeJetRep k σ hσ 1) g (piPlaneOriginEquiv k v) := by + obtain ⟨v,rfl⟩ := (pPi).mkQ_surjective v + change piPlaneOriginEquiv k ((pPi).mkQ (matrixTensorRepresentation τ σ g v)) = _ + rw [piPlaneOriginEquiv_mk, piPlaneOriginEquiv_mk] + funext i + simp only [matrixTensorRepresentation_apply, map_sum, map_smul] + rfl +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/PlaneCharts.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/PlaneCharts.lean index 2b8f17da84e8c37f80a65641d0d4180c0ef40423..a27c639c3086b5dd2183d26c2e0a4b4015c11b84 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/PlaneCharts.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/PlaneCharts.lean @@ -1,270 +1,270 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.RegularTorus - -namespace OAI - -/-! Two plane sections, transition matrices and associated charts. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section -universe u -variable (k : Type u) [Field k] [Infinite k] - -noncomputable def planeXSection (x : planeTorusPoints k) : SL2 k := - ⟨!![x.val 0, 0; x.val 1, (x.val 0)⁻¹], by - simp [Matrix.det_fin_two, x.property 0]⟩ - -noncomputable def planeYSection (x : planeTorusPoints k) : SL2 k := - ⟨!![x.val 0, -(x.val 1)⁻¹; x.val 1, 0], by - simp [Matrix.det_fin_two, x.property 1]⟩ - -noncomputable def planeChartCoordinate (i j : Fin 2) : planeCoordinateChart k i := - algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i) (MvPolynomial.X j) - -noncomputable def planeChartInverse (i : Fin 2) : planeCoordinateChart k i := - IsLocalization.Away.invSelf (S := planeCoordinateChart k i) (MvPolynomial.X i : MvPolynomial (Fin 2) k) - -omit [Infinite k] in -lemma planeChartEvaluation_coordinate (i j : Fin 2) (x : planeTorusPoints k) : - planeChartEvaluation k i (planeChartCoordinate k i j) x = x.val j := by - rw [planeChartCoordinate, planeChartEvaluation_algebraMap, - planeTorusEvaluation_apply, MvPolynomial.eval_X] - -omit [Infinite k] in -lemma planeChartEvaluation_inverse (i : Fin 2) (x : planeTorusPoints k) : - planeChartEvaluation k i (planeChartInverse k i) x = (x.val i)⁻¹ := by - have hmul : planeChartCoordinate k i i * planeChartInverse k i = 1 := - IsLocalization.Away.mul_invSelf (S := planeCoordinateChart k i) (MvPolynomial.X i : MvPolynomial (Fin 2) k) - have h := congrFun (congrArg (planeChartEvaluation k i) hmul) x - simp only [map_mul, map_one, Pi.mul_apply, Pi.one_apply, - planeChartEvaluation_coordinate] at h - exact mul_left_cancel₀ (x.property i) (h.trans (mul_inv_cancel₀ (x.property i)).symm) - -noncomputable def planeXPolynomialChart : - MvPolynomial (Fin 2 × Fin 2) k →ₐ[k] planeCoordinateChart k 0 := - MvPolynomial.aeval (fun ij => - (!![planeChartCoordinate k 0 0, 0; - planeChartCoordinate k 0 1, planeChartInverse k 0]) ij.1 ij.2) - -noncomputable def planeYPolynomialChart : - MvPolynomial (Fin 2 × Fin 2) k →ₐ[k] planeCoordinateChart k 1 := - MvPolynomial.aeval (fun ij => - (!![planeChartCoordinate k 1 0, -planeChartInverse k 1; - planeChartCoordinate k 1 1, 0]) ij.1 ij.2) - -omit [Infinite k] in -lemma planeXPolynomialChart_evaluation (P : MvPolynomial (Fin 2 × Fin 2) k) - (x : planeTorusPoints k) : - planeChartEvaluation k 0 (planeXPolynomialChart k P) x = - coordinateEvaluation k P (planeXSection k x) := by - induction P using MvPolynomial.induction_on with - | C c => simp [planeXPolynomialChart, coordinateEvaluation] - | add P Q hp hq => simp only [map_add, Pi.add_apply, hp, hq] - | mul_X P i hp => - simp only [map_mul, Pi.mul_apply, hp] - congr 1 - rw [coordinateEvaluation_apply, MvPolynomial.eval_X] - rcases i with ⟨i,j⟩ - fin_cases i <;> fin_cases j <;> - simp [planeXPolynomialChart, planeXSection, - planeChartEvaluation_coordinate, planeChartEvaluation_inverse] - -omit [Infinite k] in -lemma planeYPolynomialChart_evaluation (P : MvPolynomial (Fin 2 × Fin 2) k) - (x : planeTorusPoints k) : - planeChartEvaluation k 1 (planeYPolynomialChart k P) x = - coordinateEvaluation k P (planeYSection k x) := by - induction P using MvPolynomial.induction_on with - | C c => simp [planeYPolynomialChart, coordinateEvaluation] - | add P Q hp hq => simp only [map_add, Pi.add_apply, hp, hq] - | mul_X P i hp => - simp only [map_mul, Pi.mul_apply, hp] - congr 1 - rw [coordinateEvaluation_apply, MvPolynomial.eval_X] - rcases i with ⟨i,j⟩ - fin_cases i <;> fin_cases j <;> - simp [planeYPolynomialChart, planeYSection, - planeChartEvaluation_coordinate, planeChartEvaluation_inverse] - -noncomputable def regularXChartValue (f : regularSL2Functions k) : planeCoordinateChart k 0 := - planeXPolynomialChart k f.property.choose - -omit [Infinite k] in -lemma regularXChartValue_evaluation (f : regularSL2Functions k) (x : planeTorusPoints k) : - planeChartEvaluation k 0 (regularXChartValue k f) x = f.val (planeXSection k x) := by - rw [regularXChartValue, planeXPolynomialChart_evaluation] - exact congrFun f.property.choose_spec _ - -noncomputable def regularXChart : regularSL2Functions k →ₐ[k] planeCoordinateChart k 0 where - toFun := regularXChartValue k - map_zero' := by - apply planeChartEvaluation_injective k 0 - ext x - rw [regularXChartValue_evaluation, map_zero] - rfl - map_one' := by - apply planeChartEvaluation_injective k 0 - ext x - rw [regularXChartValue_evaluation, map_one] - rfl - map_add' f h := by - apply planeChartEvaluation_injective k 0 - ext x - rw [map_add, Pi.add_apply, regularXChartValue_evaluation, - regularXChartValue_evaluation, regularXChartValue_evaluation] - rfl - map_mul' f h := by - apply planeChartEvaluation_injective k 0 - ext x - rw [map_mul, Pi.mul_apply, regularXChartValue_evaluation, - regularXChartValue_evaluation, regularXChartValue_evaluation] - rfl - commutes' a := by - apply planeChartEvaluation_injective k 0 - ext x - rw [regularXChartValue_evaluation, AlgHom.commutes] - rfl - -noncomputable def regularYChartValue (f : regularSL2Functions k) : planeCoordinateChart k 1 := - planeYPolynomialChart k f.property.choose - -omit [Infinite k] in -lemma regularYChartValue_evaluation (f : regularSL2Functions k) (x : planeTorusPoints k) : - planeChartEvaluation k 1 (regularYChartValue k f) x = f.val (planeYSection k x) := by - rw [regularYChartValue, planeYPolynomialChart_evaluation] - exact congrFun f.property.choose_spec _ - -noncomputable def regularYChart : regularSL2Functions k →ₐ[k] planeCoordinateChart k 1 where - toFun := regularYChartValue k - map_zero' := by - apply planeChartEvaluation_injective k 1 - ext x - rw [regularYChartValue_evaluation, map_zero] - rfl - map_one' := by - apply planeChartEvaluation_injective k 1 - ext x - rw [regularYChartValue_evaluation, map_one] - rfl - map_add' f h := by - apply planeChartEvaluation_injective k 1 - ext x - rw [map_add, Pi.add_apply, regularYChartValue_evaluation, - regularYChartValue_evaluation, regularYChartValue_evaluation] - rfl - map_mul' f h := by - apply planeChartEvaluation_injective k 1 - ext x - rw [map_mul, Pi.mul_apply, regularYChartValue_evaluation, - regularYChartValue_evaluation, regularYChartValue_evaluation] - rfl - commutes' a := by - apply planeChartEvaluation_injective k 1 - ext x - rw [regularYChartValue_evaluation, AlgHom.commutes] - rfl - -end - -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (ι : Type u) [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) - -omit [Infinite k] [Fintype ι] [DecidableEq ι] in -lemma planeSections_transition (x : planeTorusPoints k) : - planeYSection k x = planeXSection k x * unipotent k (-(x.val 0 * x.val 1)⁻¹) := by - apply Subtype.ext - ext i j - change _ = ((planeXSection k x : Matrix (Fin 2) (Fin 2) k) * - (unipotent k (-(x.val 0 * x.val 1)⁻¹) : Matrix (Fin 2) (Fin 2) k)) i j - fin_cases i <;> fin_cases j <;> - simp [planeXSection, planeYSection, unipotent, Matrix.mul_apply, - Fin.sum_univ_two, x.property] - field_simp [x.property 0, x.property 1] - -omit [Infinite k] [Fintype ι] [DecidableEq ι] in -lemma sl2_xSection_decomposition (g : SL2 k) (ha : g 0 0 ≠ 0) (hc : g 1 0 ≠ 0) : - g = planeXSection k ⟨fun i => g i 0, by intro i; fin_cases i; exact ha; exact hc⟩ * - unipotent k (g 0 1 / g 0 0) := by - have hd : g 0 0 * g 1 1 - g 0 1 * g 1 0 = 1 := by - simpa only [Matrix.det_fin_two] using g.property - apply Subtype.ext - ext i j - change (g : Matrix (Fin 2) (Fin 2) k) i j = - ((planeXSection k _ : Matrix (Fin 2) (Fin 2) k) * - (unipotent k (g 0 1 / g 0 0) : Matrix (Fin 2) (Fin 2) k)) i j - fin_cases i <;> fin_cases j <;> - simp [planeXSection, unipotent, Matrix.mul_apply, Fin.sum_univ_two] - · field_simp - · apply (mul_left_cancel₀ ha) - field_simp - linear_combination hd - -noncomputable def associatedXChart : - (associatedSectionsSubmodule k ι ρ) →ₗ[k] (ι → planeCoordinateChart k 0) where - toFun f i := regularXChart k (f.val i) - map_add' := by intro f h; funext i; exact map_add _ _ _ - map_smul' := by intro a f; funext i; exact (regularXChart k).toLinearMap.map_smul a (f.val i) - -noncomputable def associatedYChart : - (associatedSectionsSubmodule k ι ρ) →ₗ[k] (ι → planeCoordinateChart k 1) where - toFun f i := regularYChart k (f.val i) - map_add' := by intro f h; funext i; exact map_add _ _ _ - map_smul' := by intro a f; funext i; exact (regularYChart k).toLinearMap.map_smul a (f.val i) - -omit [Fintype ι] [DecidableEq ι] in -lemma associatedXChart_evaluation (f : associatedSectionsSubmodule k ι ρ) - (x : planeTorusPoints k) : - (fun i => planeChartEvaluation k 0 (associatedXChart k ι ρ f i) x) = - regularVectorEvaluation k ι (planeXSection k x) f.val := by - funext i - exact regularXChartValue_evaluation k (f.val i) x - -omit [Fintype ι] [DecidableEq ι] in -lemma associatedYChart_evaluation (f : associatedSectionsSubmodule k ι ρ) - (x : planeTorusPoints k) : - (fun i => planeChartEvaluation k 1 (associatedYChart k ι ρ f i) x) = - regularVectorEvaluation k ι (planeYSection k x) f.val := by - funext i - exact regularYChartValue_evaluation k (f.val i) x - -omit [Fintype ι] [DecidableEq ι] in -lemma associatedCharts_transition (f : associatedSectionsSubmodule k ι ρ) - (x : planeTorusPoints k) : - (fun i => planeChartEvaluation k 1 (associatedYChart k ι ρ f i) x) = - ρ (Multiplicative.ofAdd ((x.val 0 * x.val 1)⁻¹)) - (fun i => planeChartEvaluation k 0 (associatedXChart k ι ρ f i) x) := by - rw [associatedYChart_evaluation, associatedXChart_evaluation, planeSections_transition] - simpa only [neg_neg] using f.property (planeXSection k x) (-(x.val 0 * x.val 1)⁻¹) - -omit [Fintype ι] [DecidableEq ι] in -lemma associatedXChart_injective : Function.Injective (associatedXChart k ι ρ) := by - intro f h he - apply Subtype.ext - funext i - apply sub_eq_zero.mp - apply regularSL2_torus_dense k - intro g ha hc - let x : planeTorusPoints k := ⟨fun j => g j 0, by intro j; fin_cases j; exact ha; exact hc⟩ - have hf' : regularVectorEvaluation k ι (planeXSection k x) f.val = - regularVectorEvaluation k ι (planeXSection k x) h.val := by - rw [← associatedXChart_evaluation, ← associatedXChart_evaluation, he] - have heq := f.property (planeXSection k x) (g 0 1 / g 0 0) - have heq' := h.property (planeXSection k x) (g 0 1 / g 0 0) - rw [← sl2_xSection_decomposition k g ha hc, hf'] at heq - rw [← sl2_xSection_decomposition k g ha hc] at heq' - exact sub_eq_zero.mpr (congrFun (heq.trans heq'.symm) i) - -end FiberFunctorProof - - - -open scoped BigOperators -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.RegularTorus + +namespace OAI + +/-! Two plane sections, transition matrices and associated charts. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section +universe u +variable (k : Type u) [Field k] [Infinite k] + +noncomputable def planeXSection (x : planeTorusPoints k) : SL2 k := + ⟨!![x.val 0, 0; x.val 1, (x.val 0)⁻¹], by + simp [Matrix.det_fin_two, x.property 0]⟩ + +noncomputable def planeYSection (x : planeTorusPoints k) : SL2 k := + ⟨!![x.val 0, -(x.val 1)⁻¹; x.val 1, 0], by + simp [Matrix.det_fin_two, x.property 1]⟩ + +noncomputable def planeChartCoordinate (i j : Fin 2) : planeCoordinateChart k i := + algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i) (MvPolynomial.X j) + +noncomputable def planeChartInverse (i : Fin 2) : planeCoordinateChart k i := + IsLocalization.Away.invSelf (S := planeCoordinateChart k i) (MvPolynomial.X i : MvPolynomial (Fin 2) k) + +omit [Infinite k] in +lemma planeChartEvaluation_coordinate (i j : Fin 2) (x : planeTorusPoints k) : + planeChartEvaluation k i (planeChartCoordinate k i j) x = x.val j := by + rw [planeChartCoordinate, planeChartEvaluation_algebraMap, + planeTorusEvaluation_apply, MvPolynomial.eval_X] + +omit [Infinite k] in +lemma planeChartEvaluation_inverse (i : Fin 2) (x : planeTorusPoints k) : + planeChartEvaluation k i (planeChartInverse k i) x = (x.val i)⁻¹ := by + have hmul : planeChartCoordinate k i i * planeChartInverse k i = 1 := + IsLocalization.Away.mul_invSelf (S := planeCoordinateChart k i) (MvPolynomial.X i : MvPolynomial (Fin 2) k) + have h := congrFun (congrArg (planeChartEvaluation k i) hmul) x + simp only [map_mul, map_one, Pi.mul_apply, Pi.one_apply, + planeChartEvaluation_coordinate] at h + exact mul_left_cancel₀ (x.property i) (h.trans (mul_inv_cancel₀ (x.property i)).symm) + +noncomputable def planeXPolynomialChart : + MvPolynomial (Fin 2 × Fin 2) k →ₐ[k] planeCoordinateChart k 0 := + MvPolynomial.aeval (fun ij => + (!![planeChartCoordinate k 0 0, 0; + planeChartCoordinate k 0 1, planeChartInverse k 0]) ij.1 ij.2) + +noncomputable def planeYPolynomialChart : + MvPolynomial (Fin 2 × Fin 2) k →ₐ[k] planeCoordinateChart k 1 := + MvPolynomial.aeval (fun ij => + (!![planeChartCoordinate k 1 0, -planeChartInverse k 1; + planeChartCoordinate k 1 1, 0]) ij.1 ij.2) + +omit [Infinite k] in +lemma planeXPolynomialChart_evaluation (P : MvPolynomial (Fin 2 × Fin 2) k) + (x : planeTorusPoints k) : + planeChartEvaluation k 0 (planeXPolynomialChart k P) x = + coordinateEvaluation k P (planeXSection k x) := by + induction P using MvPolynomial.induction_on with + | C c => simp [planeXPolynomialChart, coordinateEvaluation] + | add P Q hp hq => simp only [map_add, Pi.add_apply, hp, hq] + | mul_X P i hp => + simp only [map_mul, Pi.mul_apply, hp] + congr 1 + rw [coordinateEvaluation_apply, MvPolynomial.eval_X] + rcases i with ⟨i,j⟩ + fin_cases i <;> fin_cases j <;> + simp [planeXPolynomialChart, planeXSection, + planeChartEvaluation_coordinate, planeChartEvaluation_inverse] + +omit [Infinite k] in +lemma planeYPolynomialChart_evaluation (P : MvPolynomial (Fin 2 × Fin 2) k) + (x : planeTorusPoints k) : + planeChartEvaluation k 1 (planeYPolynomialChart k P) x = + coordinateEvaluation k P (planeYSection k x) := by + induction P using MvPolynomial.induction_on with + | C c => simp [planeYPolynomialChart, coordinateEvaluation] + | add P Q hp hq => simp only [map_add, Pi.add_apply, hp, hq] + | mul_X P i hp => + simp only [map_mul, Pi.mul_apply, hp] + congr 1 + rw [coordinateEvaluation_apply, MvPolynomial.eval_X] + rcases i with ⟨i,j⟩ + fin_cases i <;> fin_cases j <;> + simp [planeYPolynomialChart, planeYSection, + planeChartEvaluation_coordinate, planeChartEvaluation_inverse] + +noncomputable def regularXChartValue (f : regularSL2Functions k) : planeCoordinateChart k 0 := + planeXPolynomialChart k f.property.choose + +omit [Infinite k] in +lemma regularXChartValue_evaluation (f : regularSL2Functions k) (x : planeTorusPoints k) : + planeChartEvaluation k 0 (regularXChartValue k f) x = f.val (planeXSection k x) := by + rw [regularXChartValue, planeXPolynomialChart_evaluation] + exact congrFun f.property.choose_spec _ + +noncomputable def regularXChart : regularSL2Functions k →ₐ[k] planeCoordinateChart k 0 where + toFun := regularXChartValue k + map_zero' := by + apply planeChartEvaluation_injective k 0 + ext x + rw [regularXChartValue_evaluation, map_zero] + rfl + map_one' := by + apply planeChartEvaluation_injective k 0 + ext x + rw [regularXChartValue_evaluation, map_one] + rfl + map_add' f h := by + apply planeChartEvaluation_injective k 0 + ext x + rw [map_add, Pi.add_apply, regularXChartValue_evaluation, + regularXChartValue_evaluation, regularXChartValue_evaluation] + rfl + map_mul' f h := by + apply planeChartEvaluation_injective k 0 + ext x + rw [map_mul, Pi.mul_apply, regularXChartValue_evaluation, + regularXChartValue_evaluation, regularXChartValue_evaluation] + rfl + commutes' a := by + apply planeChartEvaluation_injective k 0 + ext x + rw [regularXChartValue_evaluation, AlgHom.commutes] + rfl + +noncomputable def regularYChartValue (f : regularSL2Functions k) : planeCoordinateChart k 1 := + planeYPolynomialChart k f.property.choose + +omit [Infinite k] in +lemma regularYChartValue_evaluation (f : regularSL2Functions k) (x : planeTorusPoints k) : + planeChartEvaluation k 1 (regularYChartValue k f) x = f.val (planeYSection k x) := by + rw [regularYChartValue, planeYPolynomialChart_evaluation] + exact congrFun f.property.choose_spec _ + +noncomputable def regularYChart : regularSL2Functions k →ₐ[k] planeCoordinateChart k 1 where + toFun := regularYChartValue k + map_zero' := by + apply planeChartEvaluation_injective k 1 + ext x + rw [regularYChartValue_evaluation, map_zero] + rfl + map_one' := by + apply planeChartEvaluation_injective k 1 + ext x + rw [regularYChartValue_evaluation, map_one] + rfl + map_add' f h := by + apply planeChartEvaluation_injective k 1 + ext x + rw [map_add, Pi.add_apply, regularYChartValue_evaluation, + regularYChartValue_evaluation, regularYChartValue_evaluation] + rfl + map_mul' f h := by + apply planeChartEvaluation_injective k 1 + ext x + rw [map_mul, Pi.mul_apply, regularYChartValue_evaluation, + regularYChartValue_evaluation, regularYChartValue_evaluation] + rfl + commutes' a := by + apply planeChartEvaluation_injective k 1 + ext x + rw [regularYChartValue_evaluation, AlgHom.commutes] + rfl + +end + +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (ι : Type u) [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) + +omit [Infinite k] [Fintype ι] [DecidableEq ι] in +lemma planeSections_transition (x : planeTorusPoints k) : + planeYSection k x = planeXSection k x * unipotent k (-(x.val 0 * x.val 1)⁻¹) := by + apply Subtype.ext + ext i j + change _ = ((planeXSection k x : Matrix (Fin 2) (Fin 2) k) * + (unipotent k (-(x.val 0 * x.val 1)⁻¹) : Matrix (Fin 2) (Fin 2) k)) i j + fin_cases i <;> fin_cases j <;> + simp [planeXSection, planeYSection, unipotent, Matrix.mul_apply, + Fin.sum_univ_two, x.property] + field_simp [x.property 0, x.property 1] + +omit [Infinite k] [Fintype ι] [DecidableEq ι] in +lemma sl2_xSection_decomposition (g : SL2 k) (ha : g 0 0 ≠ 0) (hc : g 1 0 ≠ 0) : + g = planeXSection k ⟨fun i => g i 0, by intro i; fin_cases i; exact ha; exact hc⟩ * + unipotent k (g 0 1 / g 0 0) := by + have hd : g 0 0 * g 1 1 - g 0 1 * g 1 0 = 1 := by + simpa only [Matrix.det_fin_two] using g.property + apply Subtype.ext + ext i j + change (g : Matrix (Fin 2) (Fin 2) k) i j = + ((planeXSection k _ : Matrix (Fin 2) (Fin 2) k) * + (unipotent k (g 0 1 / g 0 0) : Matrix (Fin 2) (Fin 2) k)) i j + fin_cases i <;> fin_cases j <;> + simp [planeXSection, unipotent, Matrix.mul_apply, Fin.sum_univ_two] + · field_simp + · apply (mul_left_cancel₀ ha) + field_simp + linear_combination hd + +noncomputable def associatedXChart : + (associatedSectionsSubmodule k ι ρ) →ₗ[k] (ι → planeCoordinateChart k 0) where + toFun f i := regularXChart k (f.val i) + map_add' := by intro f h; funext i; exact map_add _ _ _ + map_smul' := by intro a f; funext i; exact (regularXChart k).toLinearMap.map_smul a (f.val i) + +noncomputable def associatedYChart : + (associatedSectionsSubmodule k ι ρ) →ₗ[k] (ι → planeCoordinateChart k 1) where + toFun f i := regularYChart k (f.val i) + map_add' := by intro f h; funext i; exact map_add _ _ _ + map_smul' := by intro a f; funext i; exact (regularYChart k).toLinearMap.map_smul a (f.val i) + +omit [Fintype ι] [DecidableEq ι] in +lemma associatedXChart_evaluation (f : associatedSectionsSubmodule k ι ρ) + (x : planeTorusPoints k) : + (fun i => planeChartEvaluation k 0 (associatedXChart k ι ρ f i) x) = + regularVectorEvaluation k ι (planeXSection k x) f.val := by + funext i + exact regularXChartValue_evaluation k (f.val i) x + +omit [Fintype ι] [DecidableEq ι] in +lemma associatedYChart_evaluation (f : associatedSectionsSubmodule k ι ρ) + (x : planeTorusPoints k) : + (fun i => planeChartEvaluation k 1 (associatedYChart k ι ρ f i) x) = + regularVectorEvaluation k ι (planeYSection k x) f.val := by + funext i + exact regularYChartValue_evaluation k (f.val i) x + +omit [Fintype ι] [DecidableEq ι] in +lemma associatedCharts_transition (f : associatedSectionsSubmodule k ι ρ) + (x : planeTorusPoints k) : + (fun i => planeChartEvaluation k 1 (associatedYChart k ι ρ f i) x) = + ρ (Multiplicative.ofAdd ((x.val 0 * x.val 1)⁻¹)) + (fun i => planeChartEvaluation k 0 (associatedXChart k ι ρ f i) x) := by + rw [associatedYChart_evaluation, associatedXChart_evaluation, planeSections_transition] + simpa only [neg_neg] using f.property (planeXSection k x) (-(x.val 0 * x.val 1)⁻¹) + +omit [Fintype ι] [DecidableEq ι] in +lemma associatedXChart_injective : Function.Injective (associatedXChart k ι ρ) := by + intro f h he + apply Subtype.ext + funext i + apply sub_eq_zero.mp + apply regularSL2_torus_dense k + intro g ha hc + let x : planeTorusPoints k := ⟨fun j => g j 0, by intro j; fin_cases j; exact ha; exact hc⟩ + have hf' : regularVectorEvaluation k ι (planeXSection k x) f.val = + regularVectorEvaluation k ι (planeXSection k x) h.val := by + rw [← associatedXChart_evaluation, ← associatedXChart_evaluation, he] + have heq := f.property (planeXSection k x) (g 0 1 / g 0 0) + have heq' := h.property (planeXSection k x) (g 0 1 / g 0 0) + rw [← sl2_xSection_decomposition k g ha hc, hf'] at heq + rw [← sl2_xSection_decomposition k g ha hc] at heq' + exact sub_eq_zero.mpr (congrFun (heq.trans heq'.symm) i) + +end FiberFunctorProof + + + +open scoped BigOperators +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/PlaneFibre.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/PlaneFibre.lean index 95909a9882f0a864e540b72b5bd14ea433668634..6c0e050bd02c31aaaaa8bb247040c205651e62f2 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/PlaneFibre.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/PlaneFibre.lean @@ -1,122 +1,122 @@ -import OAI.RepresentationTheory.RestrictedTilting.BoundedOriginTarget - -namespace OAI - -namespace FiberFunctorProof -open scoped Pointwise -universe u -noncomputable section -variable {k : Type u} [Field k] -local notation "A" => MvPolynomial (Fin 2) k -variable (M N : Type u) [AddCommGroup M] [Module k M] [Module (MvPolynomial (Fin 2) k) M] - [IsScalarTower k (MvPolynomial (Fin 2) k) M] [AddCommGroup N] [Module k N] [Module (MvPolynomial (Fin 2) k) N] [IsScalarTower k (MvPolynomial (Fin 2) k) N] - -abbrev planeFibreRelations (a : Fin 2 → k) : Submodule k M := - ((planePointIdeal a • (⊤ : Submodule A M))).restrictScalars k - -lemma planeFibre_mk_smul (a : Fin 2 → k) (P : A) (m : M) : - (planeFibreRelations M a).mkQ (P • m) = - MvPolynomial.eval a P • (planeFibreRelations M a).mkQ m := by - rw [← map_smul] - apply (Submodule.Quotient.eq _).mpr - change P • m - MvPolynomial.eval a P • m ∈ planePointIdeal a • (⊤ : Submodule A M) - have h : P - MvPolynomial.C (MvPolynomial.eval a P) ∈ planePointIdeal a := by - simp [planePointIdeal, RingHom.mem_ker] - convert Submodule.smul_mem_smul h (show m ∈ (⊤ : Submodule A M) from trivial) using 1 - simp only [sub_smul, MvPolynomial.C_eq_algebraMap, algebraMap_smul] - -lemma planeFibre_map_mem (a : Fin 2 → k) (f : M →ₗ[A] N) : - planeFibreRelations M a ≤ (planeFibreRelations N a).comap (f.restrictScalars k) := by - intro m hm - change f m ∈ planePointIdeal a • (⊤ : Submodule A N) - have hf : (planePointIdeal a • (⊤ : Submodule A M)).map f ≤ - planePointIdeal a • (⊤ : Submodule A N) := by - rw [Submodule.map_smul''] - exact smul_mono_right (planePointIdeal a) le_top - exact hf (Submodule.mem_map_of_mem hm) - -def planeFibreMap (a : Fin 2 → k) (f : M →ₗ[A] N) : - (M ⧸ planeFibreRelations M a) →ₗ[k] (N ⧸ planeFibreRelations N a) := - (planeFibreRelations M a).mapQ (planeFibreRelations N a) (f.restrictScalars k) - (planeFibre_map_mem M N a f) - -@[simp] lemma planeFibreMap_mk (a : Fin 2 → k) (f : M →ₗ[A] N) (m : M) : - planeFibreMap M N a f ((planeFibreRelations M a).mkQ m) = - (planeFibreRelations N a).mkQ (f m) := rfl - - - -def planeFibreEquivOfSplit (a : Fin 2 → k) (f : M →ₗ[A] N) (g : N →ₗ[A] M) - (s : A) (hs : MvPolynomial.eval a s = 1) - (hgf : ∀ m, g (f m) = s • m) (hfg : ∀ n, f (g n) = s • n) : - (M ⧸ planeFibreRelations M a) ≃ₗ[k] (N ⧸ planeFibreRelations N a) := - LinearEquiv.ofLinearMap (planeFibreMap M N a f) (planeFibreMap N M a g) - (by apply LinearMap.ext; intro n; obtain ⟨n,rfl⟩ := (planeFibreRelations N a).mkQ_surjective n - change (planeFibreRelations N a).mkQ (f (g n)) = (planeFibreRelations N a).mkQ n - rw [hfg, planeFibre_mk_smul, hs, one_smul]) - (by apply LinearMap.ext; intro m; obtain ⟨m,rfl⟩ := (planeFibreRelations M a).mkQ_surjective m - change (planeFibreRelations M a).mkQ (g (f m)) = (planeFibreRelations M a).mkQ m - rw [hgf, planeFibre_mk_smul, hs, one_smul]) - -variable (ι : Type u) [Fintype ι] [DecidableEq ι] - -def planeVectorEval (a : Fin 2 → k) : (ι → A) →ₗ[k] (ι → k) where - toFun v i := MvPolynomial.eval a (v i) - map_add' v w := by ext i; simp - map_smul' c v := by ext i; simp - -def planeVectorConstant : (ι → k) →ₗ[k] (ι → A) where - toFun v i := MvPolynomial.C (v i) - map_add' v w := by ext i; simp - map_smul' c v := by ext i; simp [MvPolynomial.C_mul, Algebra.smul_def] - -omit [Fintype ι] [DecidableEq ι] in -lemma planeVectorEval_relations (a : Fin 2 → k) : - planeFibreRelations (ι → A) a ≤ (planeVectorEval ι a).ker := by - intro v hv - change v ∈ planePointIdeal a • (⊤ : Submodule A (ι → A)) at hv - change planeVectorEval ι a v = 0 - refine Submodule.smul_induction_on hv ?_ ?_ - · intro r hr n hn - ext i - change MvPolynomial.eval a (r * n i) = 0 - have hr0 : MvPolynomial.eval a r = 0 := hr - simp [hr0] - · intro x y hx hy - simp only [map_add, hx, hy, add_zero] - -def planeFreeFibreEval (a : Fin 2 → k) : - ((ι → A) ⧸ planeFibreRelations (ι → A) a) →ₗ[k] (ι → k) := - (planeFibreRelations (ι → A) a).liftQ (planeVectorEval ι a) (planeVectorEval_relations ι a) - -lemma planeFreeFibre_constant_eval (a : Fin 2 → k) (v : ι → A) : - (planeFibreRelations (ι → A) a).mkQ (planeVectorConstant ι (planeVectorEval ι a v)) = - (planeFibreRelations (ι → A) a).mkQ v := by - apply (Submodule.Quotient.eq _).mpr - change planeVectorConstant ι (planeVectorEval ι a v) - v ∈ - planePointIdeal a • (⊤ : Submodule A (ι → A)) - have he : planeVectorConstant ι (planeVectorEval ι a v) - v = - ∑ i : ι, (MvPolynomial.C (MvPolynomial.eval a (v i)) - v i) • Pi.single i (1 : A) := by - ext j - simp [planeVectorConstant, planeVectorEval, Pi.single_apply] - rw [he] - apply Submodule.sum_mem - intro i hi - apply Submodule.smul_mem_smul _ (Submodule.mem_top) - simp [planePointIdeal, RingHom.mem_ker] - -def planeFreeFibreEquiv (a : Fin 2 → k) : - ((ι → A) ⧸ planeFibreRelations (ι → A) a) ≃ₗ[k] (ι → k) := - LinearEquiv.ofLinearMap (planeFreeFibreEval ι a) - ((planeFibreRelations (ι → A) a).mkQ.comp (planeVectorConstant ι)) - (by apply LinearMap.ext; intro v; ext i; simp [planeFreeFibreEval, planeVectorEval, planeVectorConstant]) - (by apply LinearMap.ext; intro v; obtain ⟨v,rfl⟩ := (planeFibreRelations (ι → A) a).mkQ_surjective v - exact planeFreeFibre_constant_eval ι a v) - -@[simp] lemma planeFreeFibreEquiv_mk (a : Fin 2 → k) (v : ι → A) : - planeFreeFibreEquiv ι a ((planeFibreRelations (ι → A) a).mkQ v) = planeVectorEval ι a v := rfl - -end -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.BoundedOriginTarget + +namespace OAI + +namespace FiberFunctorProof +open scoped Pointwise +universe u +noncomputable section +variable {k : Type u} [Field k] +local notation "A" => MvPolynomial (Fin 2) k +variable (M N : Type u) [AddCommGroup M] [Module k M] [Module (MvPolynomial (Fin 2) k) M] + [IsScalarTower k (MvPolynomial (Fin 2) k) M] [AddCommGroup N] [Module k N] [Module (MvPolynomial (Fin 2) k) N] [IsScalarTower k (MvPolynomial (Fin 2) k) N] + +abbrev planeFibreRelations (a : Fin 2 → k) : Submodule k M := + ((planePointIdeal a • (⊤ : Submodule A M))).restrictScalars k + +lemma planeFibre_mk_smul (a : Fin 2 → k) (P : A) (m : M) : + (planeFibreRelations M a).mkQ (P • m) = + MvPolynomial.eval a P • (planeFibreRelations M a).mkQ m := by + rw [← map_smul] + apply (Submodule.Quotient.eq _).mpr + change P • m - MvPolynomial.eval a P • m ∈ planePointIdeal a • (⊤ : Submodule A M) + have h : P - MvPolynomial.C (MvPolynomial.eval a P) ∈ planePointIdeal a := by + simp [planePointIdeal, RingHom.mem_ker] + convert Submodule.smul_mem_smul h (show m ∈ (⊤ : Submodule A M) from trivial) using 1 + simp only [sub_smul, MvPolynomial.C_eq_algebraMap, algebraMap_smul] + +lemma planeFibre_map_mem (a : Fin 2 → k) (f : M →ₗ[A] N) : + planeFibreRelations M a ≤ (planeFibreRelations N a).comap (f.restrictScalars k) := by + intro m hm + change f m ∈ planePointIdeal a • (⊤ : Submodule A N) + have hf : (planePointIdeal a • (⊤ : Submodule A M)).map f ≤ + planePointIdeal a • (⊤ : Submodule A N) := by + rw [Submodule.map_smul''] + exact smul_mono_right (planePointIdeal a) le_top + exact hf (Submodule.mem_map_of_mem hm) + +def planeFibreMap (a : Fin 2 → k) (f : M →ₗ[A] N) : + (M ⧸ planeFibreRelations M a) →ₗ[k] (N ⧸ planeFibreRelations N a) := + (planeFibreRelations M a).mapQ (planeFibreRelations N a) (f.restrictScalars k) + (planeFibre_map_mem M N a f) + +@[simp] lemma planeFibreMap_mk (a : Fin 2 → k) (f : M →ₗ[A] N) (m : M) : + planeFibreMap M N a f ((planeFibreRelations M a).mkQ m) = + (planeFibreRelations N a).mkQ (f m) := rfl + + + +def planeFibreEquivOfSplit (a : Fin 2 → k) (f : M →ₗ[A] N) (g : N →ₗ[A] M) + (s : A) (hs : MvPolynomial.eval a s = 1) + (hgf : ∀ m, g (f m) = s • m) (hfg : ∀ n, f (g n) = s • n) : + (M ⧸ planeFibreRelations M a) ≃ₗ[k] (N ⧸ planeFibreRelations N a) := + LinearEquiv.ofLinearMap (planeFibreMap M N a f) (planeFibreMap N M a g) + (by apply LinearMap.ext; intro n; obtain ⟨n,rfl⟩ := (planeFibreRelations N a).mkQ_surjective n + change (planeFibreRelations N a).mkQ (f (g n)) = (planeFibreRelations N a).mkQ n + rw [hfg, planeFibre_mk_smul, hs, one_smul]) + (by apply LinearMap.ext; intro m; obtain ⟨m,rfl⟩ := (planeFibreRelations M a).mkQ_surjective m + change (planeFibreRelations M a).mkQ (g (f m)) = (planeFibreRelations M a).mkQ m + rw [hgf, planeFibre_mk_smul, hs, one_smul]) + +variable (ι : Type u) [Fintype ι] [DecidableEq ι] + +def planeVectorEval (a : Fin 2 → k) : (ι → A) →ₗ[k] (ι → k) where + toFun v i := MvPolynomial.eval a (v i) + map_add' v w := by ext i; simp + map_smul' c v := by ext i; simp + +def planeVectorConstant : (ι → k) →ₗ[k] (ι → A) where + toFun v i := MvPolynomial.C (v i) + map_add' v w := by ext i; simp + map_smul' c v := by ext i; simp [MvPolynomial.C_mul, Algebra.smul_def] + +omit [Fintype ι] [DecidableEq ι] in +lemma planeVectorEval_relations (a : Fin 2 → k) : + planeFibreRelations (ι → A) a ≤ (planeVectorEval ι a).ker := by + intro v hv + change v ∈ planePointIdeal a • (⊤ : Submodule A (ι → A)) at hv + change planeVectorEval ι a v = 0 + refine Submodule.smul_induction_on hv ?_ ?_ + · intro r hr n hn + ext i + change MvPolynomial.eval a (r * n i) = 0 + have hr0 : MvPolynomial.eval a r = 0 := hr + simp [hr0] + · intro x y hx hy + simp only [map_add, hx, hy, add_zero] + +def planeFreeFibreEval (a : Fin 2 → k) : + ((ι → A) ⧸ planeFibreRelations (ι → A) a) →ₗ[k] (ι → k) := + (planeFibreRelations (ι → A) a).liftQ (planeVectorEval ι a) (planeVectorEval_relations ι a) + +lemma planeFreeFibre_constant_eval (a : Fin 2 → k) (v : ι → A) : + (planeFibreRelations (ι → A) a).mkQ (planeVectorConstant ι (planeVectorEval ι a v)) = + (planeFibreRelations (ι → A) a).mkQ v := by + apply (Submodule.Quotient.eq _).mpr + change planeVectorConstant ι (planeVectorEval ι a v) - v ∈ + planePointIdeal a • (⊤ : Submodule A (ι → A)) + have he : planeVectorConstant ι (planeVectorEval ι a v) - v = + ∑ i : ι, (MvPolynomial.C (MvPolynomial.eval a (v i)) - v i) • Pi.single i (1 : A) := by + ext j + simp [planeVectorConstant, planeVectorEval, Pi.single_apply] + rw [he] + apply Submodule.sum_mem + intro i hi + apply Submodule.smul_mem_smul _ (Submodule.mem_top) + simp [planePointIdeal, RingHom.mem_ker] + +def planeFreeFibreEquiv (a : Fin 2 → k) : + ((ι → A) ⧸ planeFibreRelations (ι → A) a) ≃ₗ[k] (ι → k) := + LinearEquiv.ofLinearMap (planeFreeFibreEval ι a) + ((planeFibreRelations (ι → A) a).mkQ.comp (planeVectorConstant ι)) + (by apply LinearMap.ext; intro v; ext i; simp [planeFreeFibreEval, planeVectorEval, planeVectorConstant]) + (by apply LinearMap.ext; intro v; obtain ⟨v,rfl⟩ := (planeFibreRelations (ι → A) a).mkQ_surjective v + exact planeFreeFibre_constant_eval ι a v) + +@[simp] lemma planeFreeFibreEquiv_mk (a : Fin 2 → k) (v : ι → A) : + planeFreeFibreEquiv ι a ((planeFibreRelations (ι → A) a).mkQ v) = planeVectorEval ι a v := rfl + +end +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/PlaneMatrixTensor.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/PlaneMatrixTensor.lean index 40d95acfd396932428a82fd9779f79b96ab1dc64..950160198892e18035c1959ca75b270cfb33fccd 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/PlaneMatrixTensor.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/PlaneMatrixTensor.lean @@ -1,115 +1,115 @@ -import OAI.RepresentationTheory.RestrictedTilting.CompatibleJets - -namespace OAI - -namespace FiberFunctorProof -open scoped BigOperators TensorProduct -universe u -section MatrixTensor -variable {k : Type u} [Field k] {G : Type u} [Monoid G] -variable {β : Type u} [Fintype β] [DecidableEq β] -variable {M : Type u} [AddCommGroup M] [Module k M] - -noncomputable def matrixTensorLinear (A : Matrix β β k) (f : M →ₗ[k] M) : - (β → M) →ₗ[k] (β → M) := - LinearMap.pi fun i => ∑ j, A i j • f.comp (LinearMap.proj j) - -omit [DecidableEq β] in -lemma matrixTensorLinear_apply (A : Matrix β β k) (f : M →ₗ[k] M) (v : β → M) (i : β) : - matrixTensorLinear A f v i = ∑ j, A i j • f (v j) := by - simp only [matrixTensorLinear, LinearMap.pi_apply, LinearMap.sum_apply, - LinearMap.smul_apply, LinearMap.comp_apply, LinearMap.proj_apply] - -lemma matrixTensorLinear_one : matrixTensorLinear (1 : Matrix β β k) (LinearMap.id : M →ₗ[k] M) = 1 := by - apply LinearMap.ext - intro v - funext i - simp [matrixTensorLinear_apply, Matrix.one_apply] - -omit [DecidableEq β] in -lemma matrixTensorLinear_mul (A B : Matrix β β k) (f g : M →ₗ[k] M) : - matrixTensorLinear (A*B) (f*g) = matrixTensorLinear A f * matrixTensorLinear B g := by - apply LinearMap.ext - intro v - funext i - simp only [Module.End.mul_apply, matrixTensorLinear_apply, Matrix.mul_apply, - Finset.sum_smul, map_sum, map_smul, Finset.smul_sum, smul_smul] - rw [Finset.sum_comm] - -noncomputable def matrixTensorRepresentation - (τ : Representation k G (β → k)) (σ : Representation k G M) : - Representation k G (β → M) where - toFun g := matrixTensorLinear (LinearMap.toMatrix' (τ g)) (σ g) - map_one' := by - simp only [map_one, LinearMap.toMatrix'_one] - exact matrixTensorLinear_one - map_mul' g h := by - simp only [map_mul, LinearMap.toMatrix'_mul, matrixTensorLinear_mul] - -lemma matrixTensorRepresentation_apply (τ : Representation k G (β → k)) - (σ : Representation k G M) (g : G) (v : β → M) (i : β) : - matrixTensorRepresentation τ σ g v i = ∑ j, LinearMap.toMatrix' (τ g) i j • σ g (v j) := - matrixTensorLinear_apply _ _ _ _ - -end MatrixTensor - -section PlaneTensor -variable (k : Type u) [Field k] -variable {β : Type u} [Fintype β] [DecidableEq β] -variable {M : Type u} [AddCommGroup M] [Module k M] -variable (τ : Representation k (SL2 k) (β → k)) (σ : Representation k (SL2 k) M) - -lemma matrixTensor_rational (hτ : IsRational k τ) (hσ : IsRational k σ) : - IsRational k (matrixTensorRepresentation τ σ) := by - classical - intro v l - choose P hP using fun (i j : β) => hτ (Pi.single j 1) (LinearMap.proj i) - choose Q hQ using fun (i j : β) => hσ (v j) (l.comp (LinearMap.single k (fun _ : β => M) i)) - refine ⟨∑ i, ∑ j, P i j * Q i j, fun g => ?_⟩ - have he : matrixTensorRepresentation τ σ g v = - ∑ i, ∑ j, LinearMap.toMatrix' (τ g) i j • - (LinearMap.single k (fun _ : β => M) i) (σ g (v j)) := by - calc - _ = ∑ i, (LinearMap.single k (fun _ : β => M) i) - (matrixTensorRepresentation τ σ g v i) := (Finset.univ_sum_single _).symm - _ = _ := by - simp only [matrixTensorRepresentation_apply, map_sum, map_smul] - rw [he] - simp only [map_sum, map_smul, smul_eq_mul, map_mul, ← hP, ← hQ, - LinearMap.comp_apply, LinearMap.toMatrix'_apply, LinearMap.proj_apply] - -variable [Module (MvPolynomial (Fin 2) k) M] - [IsScalarTower k (MvPolynomial (Fin 2) k) M] - -lemma matrixTensor_planeCompatible (hσ : PlaneCompatible k σ) : - PlaneCompatible k (matrixTensorRepresentation τ σ) := by - intro g P v - funext i - simp only [matrixTensorRepresentation_apply, Pi.smul_apply, Finset.smul_sum] - apply Finset.sum_congr rfl - intro j _ - rw [hσ] - exact smul_comm _ _ _ - -omit [Fintype β] [DecidableEq β] [Module k M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] in -lemma pi_regular_x - (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • m)) : - Function.Injective (fun m : β → M => (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • m) := by - intro v w h - funext i - exact hx (congrFun h i) - -omit [Fintype β] [DecidableEq β] [Module k M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] in -lemma pi_regular_y - (hy : ∀ v n : M, (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) • v = - (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n → ∃ w : M, v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • w) : - ∀ v n : β → M, (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) • v = - (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n → ∃ w : β → M, v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • w := by - intro v n h - choose w hw using fun i => hy (v i) (n i) (congrFun h i) - exact ⟨w, funext hw⟩ - -end PlaneTensor -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.CompatibleJets + +namespace OAI + +namespace FiberFunctorProof +open scoped BigOperators TensorProduct +universe u +section MatrixTensor +variable {k : Type u} [Field k] {G : Type u} [Monoid G] +variable {β : Type u} [Fintype β] [DecidableEq β] +variable {M : Type u} [AddCommGroup M] [Module k M] + +noncomputable def matrixTensorLinear (A : Matrix β β k) (f : M →ₗ[k] M) : + (β → M) →ₗ[k] (β → M) := + LinearMap.pi fun i => ∑ j, A i j • f.comp (LinearMap.proj j) + +omit [DecidableEq β] in +lemma matrixTensorLinear_apply (A : Matrix β β k) (f : M →ₗ[k] M) (v : β → M) (i : β) : + matrixTensorLinear A f v i = ∑ j, A i j • f (v j) := by + simp only [matrixTensorLinear, LinearMap.pi_apply, LinearMap.sum_apply, + LinearMap.smul_apply, LinearMap.comp_apply, LinearMap.proj_apply] + +lemma matrixTensorLinear_one : matrixTensorLinear (1 : Matrix β β k) (LinearMap.id : M →ₗ[k] M) = 1 := by + apply LinearMap.ext + intro v + funext i + simp [matrixTensorLinear_apply, Matrix.one_apply] + +omit [DecidableEq β] in +lemma matrixTensorLinear_mul (A B : Matrix β β k) (f g : M →ₗ[k] M) : + matrixTensorLinear (A*B) (f*g) = matrixTensorLinear A f * matrixTensorLinear B g := by + apply LinearMap.ext + intro v + funext i + simp only [Module.End.mul_apply, matrixTensorLinear_apply, Matrix.mul_apply, + Finset.sum_smul, map_sum, map_smul, Finset.smul_sum, smul_smul] + rw [Finset.sum_comm] + +noncomputable def matrixTensorRepresentation + (τ : Representation k G (β → k)) (σ : Representation k G M) : + Representation k G (β → M) where + toFun g := matrixTensorLinear (LinearMap.toMatrix' (τ g)) (σ g) + map_one' := by + simp only [map_one, LinearMap.toMatrix'_one] + exact matrixTensorLinear_one + map_mul' g h := by + simp only [map_mul, LinearMap.toMatrix'_mul, matrixTensorLinear_mul] + +lemma matrixTensorRepresentation_apply (τ : Representation k G (β → k)) + (σ : Representation k G M) (g : G) (v : β → M) (i : β) : + matrixTensorRepresentation τ σ g v i = ∑ j, LinearMap.toMatrix' (τ g) i j • σ g (v j) := + matrixTensorLinear_apply _ _ _ _ + +end MatrixTensor + +section PlaneTensor +variable (k : Type u) [Field k] +variable {β : Type u} [Fintype β] [DecidableEq β] +variable {M : Type u} [AddCommGroup M] [Module k M] +variable (τ : Representation k (SL2 k) (β → k)) (σ : Representation k (SL2 k) M) + +lemma matrixTensor_rational (hτ : IsRational k τ) (hσ : IsRational k σ) : + IsRational k (matrixTensorRepresentation τ σ) := by + classical + intro v l + choose P hP using fun (i j : β) => hτ (Pi.single j 1) (LinearMap.proj i) + choose Q hQ using fun (i j : β) => hσ (v j) (l.comp (LinearMap.single k (fun _ : β => M) i)) + refine ⟨∑ i, ∑ j, P i j * Q i j, fun g => ?_⟩ + have he : matrixTensorRepresentation τ σ g v = + ∑ i, ∑ j, LinearMap.toMatrix' (τ g) i j • + (LinearMap.single k (fun _ : β => M) i) (σ g (v j)) := by + calc + _ = ∑ i, (LinearMap.single k (fun _ : β => M) i) + (matrixTensorRepresentation τ σ g v i) := (Finset.univ_sum_single _).symm + _ = _ := by + simp only [matrixTensorRepresentation_apply, map_sum, map_smul] + rw [he] + simp only [map_sum, map_smul, smul_eq_mul, map_mul, ← hP, ← hQ, + LinearMap.comp_apply, LinearMap.toMatrix'_apply, LinearMap.proj_apply] + +variable [Module (MvPolynomial (Fin 2) k) M] + [IsScalarTower k (MvPolynomial (Fin 2) k) M] + +lemma matrixTensor_planeCompatible (hσ : PlaneCompatible k σ) : + PlaneCompatible k (matrixTensorRepresentation τ σ) := by + intro g P v + funext i + simp only [matrixTensorRepresentation_apply, Pi.smul_apply, Finset.smul_sum] + apply Finset.sum_congr rfl + intro j _ + rw [hσ] + exact smul_comm _ _ _ + +omit [Fintype β] [DecidableEq β] [Module k M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] in +lemma pi_regular_x + (hx : Function.Injective (fun m : M => (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • m)) : + Function.Injective (fun m : β → M => (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • m) := by + intro v w h + funext i + exact hx (congrFun h i) + +omit [Fintype β] [DecidableEq β] [Module k M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] in +lemma pi_regular_y + (hy : ∀ v n : M, (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) • v = + (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n → ∃ w : M, v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • w) : + ∀ v n : β → M, (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) • v = + (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n → ∃ w : β → M, v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • w := by + intro v n h + choose w hw using fun i => hy (v i) (n i) (congrFun h i) + exact ⟨w, funext hw⟩ + +end PlaneTensor +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialActions.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialActions.lean index 96495e167b386c11abc1e7c4b42e494806592c4f..205f653a37d61dc578d1e7a4d7de749fbc5cef49 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialActions.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialActions.lean @@ -1,398 +1,398 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.PlaneCharts - -namespace OAI - -/-! Polynomial additive actions and associated polynomial sections. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section -variable {k A B : Type*} [CommRing k] [CommRing A] [CommRing B] - [Algebra k A] [Algebra k B] - -lemma map_aeval_polynomial (f : A →ₐ[k] B) (a : A) (p : Polynomial k) : - f (Polynomial.aeval a p) = Polynomial.aeval (f a) p := by - have h : f.comp (Polynomial.aeval a) = Polynomial.aeval (f a) := by - ext - simp - exact AlgHom.congr_fun h p -end - -section -variable {k ι : Type*} [Field k] [Infinite k] [Fintype ι] [DecidableEq ι] - - -noncomputable def polynomialMatrixEval (P : Matrix ι ι (Polynomial k)) - {A : Type*} [CommRing A] [Algebra k A] (t : A) : Matrix ι ι A := - fun i j => Polynomial.aeval t (P i j) - -omit [Infinite k] [Fintype ι] [DecidableEq ι] in -lemma polynomialMatrixEval_map (P : Matrix ι ι (Polynomial k)) - {A B : Type*} [CommRing A] [CommRing B] [Algebra k A] [Algebra k B] - (f : A →ₐ[k] B) (t : A) : - (polynomialMatrixEval P t).map f = polynomialMatrixEval P (f t) := by - ext i j - exact map_aeval_polynomial f t (P i j) - -omit [DecidableEq ι] in - - -theorem polynomialMatrixEval_add (P : Matrix ι ι (Polynomial k)) - (hP : ∀ s t : k, polynomialMatrixEval P (s+t) = - polynomialMatrixEval P s * polynomialMatrixEval P t) - {A : Type*} [CommRing A] [Algebra k A] (s t : A) : - polynomialMatrixEval P (s+t) = polynomialMatrixEval P s * polynomialMatrixEval P t := by - let X : Fin 2 → MvPolynomial (Fin 2) k := MvPolynomial.X - have h : polynomialMatrixEval P (X 0 + X 1) = - polynomialMatrixEval P (X 0) * polynomialMatrixEval P (X 1) := by - apply Matrix.ext - intro i j - apply MvPolynomial.funext - intro a - change MvPolynomial.aeval a _ = MvPolynomial.aeval a _ - simp only [polynomialMatrixEval, Matrix.mul_apply, map_sum, map_mul, - map_aeval_polynomial, map_add, X, MvPolynomial.aeval_X] - exact congrArg (fun Q : Matrix ι ι k => Q i j) (hP (a 0) (a 1)) - have he := congrArg (fun Q : Matrix ι ι (MvPolynomial (Fin 2) k) => - Q.map (MvPolynomial.aeval ![s,t])) h - simpa only [polynomialMatrixEval_map, map_add, X, MvPolynomial.aeval_X, - Matrix.cons_val_zero, Matrix.cons_val_one, Matrix.map_mul] using he - -omit [Infinite k] [Fintype ι] in -lemma polynomialMatrixEval_zero (P : Matrix ι ι (Polynomial k)) - (hP : polynomialMatrixEval P (0 : k) = 1) - (A : Type*) [CommRing A] [Algebra k A] : - polynomialMatrixEval P (0 : A) = 1 := by - have he := congrArg (fun Q : Matrix ι ι k => Q.map (algebraMap k A)) hP - have hm (i j : ι) : algebraMap k A (polynomialMatrixEval P (0 : k) i j) = - polynomialMatrixEval P (0 : A) i j := by - simp [polynomialMatrixEval, Polynomial.aeval_def] - apply Matrix.ext - intro i j - have heij := congrArg (fun Q : Matrix ι ι A => Q i j) he - rw [Matrix.map_apply, hm] at heij - simpa [Matrix.map_apply, Matrix.one_apply] using heij - - - -noncomputable def polynomialAdditiveRepresentation - (P : Matrix ι ι (Polynomial k)) - (h0 : polynomialMatrixEval P (0 : k) = 1) - (hadd : ∀ s t : k, polynomialMatrixEval P (s+t) = - polynomialMatrixEval P s * polynomialMatrixEval P t) - (A : Type*) [CommRing A] [Algebra k A] : - Multiplicative A →* Matrix ι ι A where - toFun t := polynomialMatrixEval P t.toAdd - map_one' := polynomialMatrixEval_zero P h0 A - map_mul' s t := polynomialMatrixEval_add P hadd s.toAdd t.toAdd - -end - -section -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (ι : Type u) [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) - -omit [Infinite k] [Fintype ι] [DecidableEq ι] in -lemma additive_rep_apply_add (s t : k) (v : ι → k) : - ρ (Multiplicative.ofAdd (s+t)) v = - ρ (Multiplicative.ofAdd s) (ρ (Multiplicative.ofAdd t) v) := by - change ρ (Multiplicative.ofAdd s * Multiplicative.ofAdd t) v = _ - rw [map_mul] - rfl - -noncomputable def associatedLocalExpression (P : Matrix ι ι (Polynomial k)) - (a : Fin 2) (f : ι → planeCoordinateChart k a) (i : ι) : - regularCoordinateLocalization k a := - ∑ j, Polynomial.aeval - (-(algebraMap (regularSL2Functions k) (regularCoordinateLocalization k a) - (regularEntry k a 1)) * regularCoordinateInverse k a) (P i j) * - planeChartPullback k a (f j) - -omit [Infinite k] in -lemma associatedLocalExpression_evaluation (P : Matrix ι ι (Polynomial k)) - (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) - (a : Fin 2) (f : ι → planeCoordinateChart k a) (g : regularTorusPoints k) : - (fun i => regularLocalizationEvaluation k a (associatedLocalExpression k ι P a f i) g) = - ρ (Multiplicative.ofAdd (-(g.val a 1 / g.val a 0))) - (fun j => planeChartEvaluation k a (f j) (regularToPlaneTorus k g)) := by - have h := LinearMap.toMatrix'_mulVec - (ρ (Multiplicative.ofAdd (-(g.val a 1 / g.val a 0)))) - (fun j => planeChartEvaluation k a (f j) (regularToPlaneTorus k g)) - rw [← hP] at h - rw [← h] - funext i - let ev : regularCoordinateLocalization k a →ₐ[k] k := - (Pi.evalAlgHom k _ g).comp (regularLocalizationEvaluation k a) - change ev (associatedLocalExpression k ι P a f i) = _ - simp only [associatedLocalExpression, map_sum, map_mul, - map_aeval_polynomial (k := k) (A := regularCoordinateLocalization k a) (B := k) ev, - map_neg] - change (∑ j, Polynomial.aeval - (-(regularLocalizationEvaluation k a - (algebraMap (regularSL2Functions k) (regularCoordinateLocalization k a) - (regularEntry k a 1)) g) * - regularLocalizationEvaluation k a (regularCoordinateInverse k a) g) (P i j) * - regularLocalizationEvaluation k a (planeChartPullback k a (f j)) g) = _ - rw [regularLocalizationEvaluation_algebraMap] - change (∑ j, Polynomial.aeval - (-(regularEntry k a 1).val g.val * - regularLocalizationEvaluation k a (regularCoordinateInverse k a) g) (P i j) * - regularLocalizationEvaluation k a (planeChartPullback k a (f j)) g) = _ - simp only [regularEntry_apply, regularCoordinateInverse_evaluation, - planeChartPullback_evaluation, Matrix.mulVec, dotProduct, polynomialMatrixEval, - div_eq_mul_inv, neg_mul] - -noncomputable def associatedTorusValue (f : ι → planeCoordinateChart k 0) - (g : regularTorusPoints k) : ι → k := - ρ (Multiplicative.ofAdd (-(g.val 0 1 / g.val 0 0))) - (fun j => planeChartEvaluation k 0 (f j) (regularToPlaneTorus k g)) - -omit [Infinite k] in -lemma associatedChartPair_local_compatible - (P : Matrix ι ι (Polynomial k)) - (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) - (f₀ : ι → planeCoordinateChart k 0) (f₁ : ι → planeCoordinateChart k 1) - (hf : ∀ x : planeTorusPoints k, - (fun j => planeChartEvaluation k 1 (f₁ j) x) = - ρ (Multiplicative.ofAdd ((x.val 0 * x.val 1)⁻¹)) - (fun j => planeChartEvaluation k 0 (f₀ j) x)) (g : regularTorusPoints k) : - (fun i => regularLocalizationEvaluation k 1 (associatedLocalExpression k ι P 1 f₁ i) g) = - associatedTorusValue k ι ρ f₀ g := by - rw [associatedLocalExpression_evaluation k ι ρ P hP, hf, - ← additive_rep_apply_add] - unfold associatedTorusValue - congr 2 - change -(g.val 1 1 / g.val 1 0) + (g.val 0 0 * g.val 1 0)⁻¹ = - -(g.val 0 1 / g.val 0 0) - have hd : g.val 0 0 * g.val 1 1 - g.val 0 1 * g.val 1 0 = 1 := by - simpa only [Matrix.det_fin_two] using g.val.property - field_simp [g.property 0, g.property 1] - linear_combination -hd - -omit [Infinite k] [Fintype ι] [DecidableEq ι] in -lemma secondColumn_unipotent_mul (g : SL2 k) (t : k) (i : Fin 2) : - (g * unipotent k t) i 1 = g i 0 * t + g i 1 := by - change (((g : Matrix (Fin 2) (Fin 2) k) * - (unipotent k t : Matrix (Fin 2) (Fin 2) k)) i 1) = _ - simp [Matrix.mul_apply, Fin.sum_univ_two, unipotent] - -noncomputable def regularTorusRightUnipotent (g : regularTorusPoints k) (t : k) : - regularTorusPoints k := - ⟨g.val * unipotent k t, by intro i; rw [firstColumn_unipotent_mul]; exact g.property i⟩ - -omit [Infinite k] [Fintype ι] [DecidableEq ι] in -lemma associatedTorusValue_unipotent (f : ι → planeCoordinateChart k 0) - (g : regularTorusPoints k) (t : k) : - associatedTorusValue k ι ρ f (regularTorusRightUnipotent k g t) = - ρ (Multiplicative.ofAdd (-t)) (associatedTorusValue k ι ρ f g) := by - have hx : regularToPlaneTorus k (regularTorusRightUnipotent k g t) = - regularToPlaneTorus k g := by - apply Subtype.ext - funext i - exact firstColumn_unipotent_mul k g.val t i - unfold associatedTorusValue - rw [hx, ← additive_rep_apply_add] - apply congrArg (fun s : k => ρ (Multiplicative.ofAdd s) - (fun j => planeChartEvaluation k 0 (f j) (regularToPlaneTorus k g))) - change -((g.val * unipotent k t) 0 1 / (g.val * unipotent k t) 0 0) = _ - rw [secondColumn_unipotent_mul, firstColumn_unipotent_mul] - field_simp [g.property 0] - ring - -noncomputable def regularVectorCombination (L : (ι → k) →ₗ[k] (ι → k)) - (f : ι → regularSL2Functions k) (i : ι) : regularSL2Functions k := - ∑ j, (LinearMap.toMatrix' L i j) • f j - -omit [Infinite k] in -lemma regularVectorCombination_evaluation (L : (ι → k) →ₗ[k] (ι → k)) - (f : ι → regularSL2Functions k) (g : SL2 k) : - regularVectorEvaluation k ι g (regularVectorCombination k ι L f) = - L (regularVectorEvaluation k ι g f) := by - rw [← LinearMap.toMatrix'_mulVec L] - funext i - change (Subalgebra.val (regularSL2Functions k) - (∑ j, (LinearMap.toMatrix' L i j) • f j)) g = _ - simp only [map_sum, map_smul, Finset.sum_apply, Pi.smul_apply, - smul_eq_mul, Matrix.mulVec, dotProduct] - rfl - - - -theorem associatedChartPair_glue - (P : Matrix ι ι (Polynomial k)) - (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) - (f₀ : ι → planeCoordinateChart k 0) (f₁ : ι → planeCoordinateChart k 1) - (hf : ∀ x : planeTorusPoints k, - (fun j => planeChartEvaluation k 1 (f₁ j) x) = - ρ (Multiplicative.ofAdd ((x.val 0 * x.val 1)⁻¹)) - (fun j => planeChartEvaluation k 0 (f₀ j) x)) : - ∃ f : associatedSectionsSubmodule k ι ρ, - associatedXChart k ι ρ f = f₀ ∧ associatedYChart k ι ρ f = f₁ := by - have hg (i : ι) : ∃ f : regularSL2Functions k, - regularTorusRestriction k f = fun g => associatedTorusValue k ι ρ f₀ g i := by - apply regularTorus_glue k _ (associatedLocalExpression k ι P 0 f₀ i) - (associatedLocalExpression k ι P 1 f₁ i) - · funext g - exact congrFun (associatedLocalExpression_evaluation k ι ρ P hP 0 f₀ g) i - · funext g - exact congrFun (associatedChartPair_local_compatible k ι ρ P hP f₀ f₁ hf g) i - choose f hfg using hg - have hev (g : regularTorusPoints k) : regularVectorEvaluation k ι g.val f = - associatedTorusValue k ι ρ f₀ g := by - funext i - exact congrFun (hfg i) g - have hmem : f ∈ associatedSectionsSubmodule k ι ρ := by - intro g t - funext i - have hz : regularRightTranslation k (unipotent k t) (f i) - - regularVectorCombination k ι (ρ (Multiplicative.ofAdd (-t))) f i = 0 := by - apply regularSL2_torus_dense k - intro h ha hc - let h' : regularTorusPoints k := ⟨h, by intro j; fin_cases j; exact ha; exact hc⟩ - have he := associatedTorusValue_unipotent k ι ρ f₀ h' t - rw [← hev, ← hev] at he - have he' := congrFun he i - change (f i).val (h * unipotent k t) = _ at he' - change (f i).val (h * unipotent k t) - - (regularVectorCombination k ι (ρ (Multiplicative.ofAdd (-t))) f i).val h = 0 - rw [he'] - exact sub_eq_zero.mpr - (congrFun (regularVectorCombination_evaluation k ι - (ρ (Multiplicative.ofAdd (-t))) f h) i).symm - have he := congrArg (fun a : regularSL2Functions k => a.val g) (sub_eq_zero.mp hz) - change (f i).val (g * unipotent k t) = _ at he - exact he.trans (congrFun (regularVectorCombination_evaluation k ι - (ρ (Multiplicative.ofAdd (-t))) f g) i) - let F : associatedSectionsSubmodule k ι ρ := ⟨f,hmem⟩ - have hx : associatedXChart k ι ρ F = f₀ := by - funext i - apply planeChartEvaluation_injective k 0 - funext x - have he := hev ⟨planeXSection k x, by - intro j - fin_cases j <;> simpa [planeXSection] using x.property _⟩ - have hx' : regularToPlaneTorus k ⟨planeXSection k x, by - intro j; fin_cases j <;> simpa [planeXSection] using x.property _⟩ = x := by - apply Subtype.ext - funext j - fin_cases j <;> simp [regularToPlaneTorus, planeXSection] - unfold associatedTorusValue at he - rw [hx'] at he - change regularVectorEvaluation k ι (planeXSection k x) f = - ρ (Multiplicative.ofAdd (-(0 / x.val 0))) - (fun j => planeChartEvaluation k 0 (f₀ j) x) at he - simp only [zero_div, neg_zero] at he - change regularVectorEvaluation k ι (planeXSection k x) f = - ρ 1 (fun j => planeChartEvaluation k 0 (f₀ j) x) at he - rw [map_one] at he - exact (congrFun (associatedXChart_evaluation k ι ρ F x) i).trans (congrFun he i) - refine ⟨F,hx,?_⟩ - funext i - apply planeChartEvaluation_injective k 1 - funext x - have he := associatedCharts_transition k ι ρ F x - rw [hx, ← hf x] at he - exact congrFun he i - -end - -universe u -variable (k : Type u) [Field k] -variable (ι : Type u) [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) - -noncomputable instance regularPlaneAlgebra : - Algebra (MvPolynomial (Fin 2) k) (regularSL2Functions k) := - (regularPlane k).toRingHom.toAlgebra - -instance regularPlaneScalarTower : - IsScalarTower k (MvPolynomial (Fin 2) k) (regularSL2Functions k) := - IsScalarTower.of_algHom (regularPlane k) - -lemma regularPlane_algebraMap (P : MvPolynomial (Fin 2) k) : - algebraMap (MvPolynomial (Fin 2) k) (regularSL2Functions k) P = regularPlane k P := rfl - -omit [Fintype ι] [DecidableEq ι] in -lemma regularVector_plane_smul (P : MvPolynomial (Fin 2) k) - (f : ι → regularSL2Functions k) (g : SL2 k) : - regularVectorEvaluation k ι g (P • f) = - MvPolynomial.eval (fun i => g i 0) P • regularVectorEvaluation k ι g f := by - funext i - change (P • f i).val g = _ - rw [Algebra.smul_def, regularPlane_algebraMap] - change (regularPlane k P).val g * (f i).val g = _ - rw [regularPlane_evaluation] - rfl - -omit [Fintype ι] [DecidableEq ι] in -lemma associatedSections_plane_smul_mem (P : MvPolynomial (Fin 2) k) - (f : ι → regularSL2Functions k) (hf : f ∈ associatedSectionsSubmodule k ι ρ) : - P • f ∈ associatedSectionsSubmodule k ι ρ := by - intro g t - rw [regularVector_plane_smul, regularVector_plane_smul, hf, map_smul] - simp only [firstColumn_unipotent_mul] - -noncomputable def associatedPolynomialSections : - Submodule (MvPolynomial (Fin 2) k) (ι → regularSL2Functions k) where - carrier := associatedSectionsSubmodule k ι ρ - zero_mem' := (associatedSectionsSubmodule k ι ρ).zero_mem - add_mem' := (associatedSectionsSubmodule k ι ρ).add_mem - smul_mem' := associatedSections_plane_smul_mem k ι ρ - -noncomputable instance associatedSectionsAddCommGroup : - AddCommGroup (associatedSectionsSubmodule k ι ρ) := - Submodule.addCommGroup (associatedSectionsSubmodule k ι ρ) - -noncomputable instance (priority := 2000) associatedSectionsPolynomialSMul : - SMul (MvPolynomial (Fin 2) k) (associatedSectionsSubmodule k ι ρ) := - (Submodule.module (associatedPolynomialSections k ι ρ)).toSMul - -noncomputable instance (priority := 2000) associatedSectionsPolynomialModule : - Module (MvPolynomial (Fin 2) k) (associatedSectionsSubmodule k ι ρ) := - Submodule.module (associatedPolynomialSections k ι ρ) - -instance associatedSectionsScalarTower : - IsScalarTower k (MvPolynomial (Fin 2) k) (associatedSectionsSubmodule k ι ρ) where - smul_assoc a P f := Subtype.ext (smul_assoc a P f.val) - -variable [Infinite k] -noncomputable def associatedXChartPolynomial : - (associatedSectionsSubmodule k ι ρ) →ₗ[MvPolynomial (Fin 2) k] - (ι → planeCoordinateChart k 0) where - toFun := associatedXChart k ι ρ - map_add' := (associatedXChart k ι ρ).map_add - map_smul' := by - intro P f - funext i - apply planeChartEvaluation_injective k 0 - funext x - have he := congrFun (associatedXChart_evaluation k ι ρ (P • f) x) i - change _ = _ at he - rw [show (P • f).val = P • f.val from rfl, regularVector_plane_smul] at he - rw [he] - change MvPolynomial.eval (fun j => (planeXSection k x) j 0) P * - regularVectorEvaluation k ι (planeXSection k x) f.val i = - planeChartEvaluation k 0 (P • associatedXChart k ι ρ f i) x - rw [Algebra.smul_def, map_mul, planeChartEvaluation_algebraMap] - change _ = planeTorusEvaluation k P x * - planeChartEvaluation k 0 (associatedXChart k ι ρ f i) x - rw [planeTorusEvaluation_apply, congrFun (associatedXChart_evaluation k ι ρ f x) i] - congr 2 - apply congrArg MvPolynomial.eval - funext j - fin_cases j <;> simp [planeXSection] - -end FiberFunctorProof - - - -open scoped TensorProduct -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.PlaneCharts + +namespace OAI + +/-! Polynomial additive actions and associated polynomial sections. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section +variable {k A B : Type*} [CommRing k] [CommRing A] [CommRing B] + [Algebra k A] [Algebra k B] + +lemma map_aeval_polynomial (f : A →ₐ[k] B) (a : A) (p : Polynomial k) : + f (Polynomial.aeval a p) = Polynomial.aeval (f a) p := by + have h : f.comp (Polynomial.aeval a) = Polynomial.aeval (f a) := by + ext + simp + exact AlgHom.congr_fun h p +end + +section +variable {k ι : Type*} [Field k] [Infinite k] [Fintype ι] [DecidableEq ι] + + +noncomputable def polynomialMatrixEval (P : Matrix ι ι (Polynomial k)) + {A : Type*} [CommRing A] [Algebra k A] (t : A) : Matrix ι ι A := + fun i j => Polynomial.aeval t (P i j) + +omit [Infinite k] [Fintype ι] [DecidableEq ι] in +lemma polynomialMatrixEval_map (P : Matrix ι ι (Polynomial k)) + {A B : Type*} [CommRing A] [CommRing B] [Algebra k A] [Algebra k B] + (f : A →ₐ[k] B) (t : A) : + (polynomialMatrixEval P t).map f = polynomialMatrixEval P (f t) := by + ext i j + exact map_aeval_polynomial f t (P i j) + +omit [DecidableEq ι] in + + +theorem polynomialMatrixEval_add (P : Matrix ι ι (Polynomial k)) + (hP : ∀ s t : k, polynomialMatrixEval P (s+t) = + polynomialMatrixEval P s * polynomialMatrixEval P t) + {A : Type*} [CommRing A] [Algebra k A] (s t : A) : + polynomialMatrixEval P (s+t) = polynomialMatrixEval P s * polynomialMatrixEval P t := by + let X : Fin 2 → MvPolynomial (Fin 2) k := MvPolynomial.X + have h : polynomialMatrixEval P (X 0 + X 1) = + polynomialMatrixEval P (X 0) * polynomialMatrixEval P (X 1) := by + apply Matrix.ext + intro i j + apply MvPolynomial.funext + intro a + change MvPolynomial.aeval a _ = MvPolynomial.aeval a _ + simp only [polynomialMatrixEval, Matrix.mul_apply, map_sum, map_mul, + map_aeval_polynomial, map_add, X, MvPolynomial.aeval_X] + exact congrArg (fun Q : Matrix ι ι k => Q i j) (hP (a 0) (a 1)) + have he := congrArg (fun Q : Matrix ι ι (MvPolynomial (Fin 2) k) => + Q.map (MvPolynomial.aeval ![s,t])) h + simpa only [polynomialMatrixEval_map, map_add, X, MvPolynomial.aeval_X, + Matrix.cons_val_zero, Matrix.cons_val_one, Matrix.map_mul] using he + +omit [Infinite k] [Fintype ι] in +lemma polynomialMatrixEval_zero (P : Matrix ι ι (Polynomial k)) + (hP : polynomialMatrixEval P (0 : k) = 1) + (A : Type*) [CommRing A] [Algebra k A] : + polynomialMatrixEval P (0 : A) = 1 := by + have he := congrArg (fun Q : Matrix ι ι k => Q.map (algebraMap k A)) hP + have hm (i j : ι) : algebraMap k A (polynomialMatrixEval P (0 : k) i j) = + polynomialMatrixEval P (0 : A) i j := by + simp [polynomialMatrixEval, Polynomial.aeval_def] + apply Matrix.ext + intro i j + have heij := congrArg (fun Q : Matrix ι ι A => Q i j) he + rw [Matrix.map_apply, hm] at heij + simpa [Matrix.map_apply, Matrix.one_apply] using heij + + + +noncomputable def polynomialAdditiveRepresentation + (P : Matrix ι ι (Polynomial k)) + (h0 : polynomialMatrixEval P (0 : k) = 1) + (hadd : ∀ s t : k, polynomialMatrixEval P (s+t) = + polynomialMatrixEval P s * polynomialMatrixEval P t) + (A : Type*) [CommRing A] [Algebra k A] : + Multiplicative A →* Matrix ι ι A where + toFun t := polynomialMatrixEval P t.toAdd + map_one' := polynomialMatrixEval_zero P h0 A + map_mul' s t := polynomialMatrixEval_add P hadd s.toAdd t.toAdd + +end + +section +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (ι : Type u) [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) + +omit [Infinite k] [Fintype ι] [DecidableEq ι] in +lemma additive_rep_apply_add (s t : k) (v : ι → k) : + ρ (Multiplicative.ofAdd (s+t)) v = + ρ (Multiplicative.ofAdd s) (ρ (Multiplicative.ofAdd t) v) := by + change ρ (Multiplicative.ofAdd s * Multiplicative.ofAdd t) v = _ + rw [map_mul] + rfl + +noncomputable def associatedLocalExpression (P : Matrix ι ι (Polynomial k)) + (a : Fin 2) (f : ι → planeCoordinateChart k a) (i : ι) : + regularCoordinateLocalization k a := + ∑ j, Polynomial.aeval + (-(algebraMap (regularSL2Functions k) (regularCoordinateLocalization k a) + (regularEntry k a 1)) * regularCoordinateInverse k a) (P i j) * + planeChartPullback k a (f j) + +omit [Infinite k] in +lemma associatedLocalExpression_evaluation (P : Matrix ι ι (Polynomial k)) + (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) + (a : Fin 2) (f : ι → planeCoordinateChart k a) (g : regularTorusPoints k) : + (fun i => regularLocalizationEvaluation k a (associatedLocalExpression k ι P a f i) g) = + ρ (Multiplicative.ofAdd (-(g.val a 1 / g.val a 0))) + (fun j => planeChartEvaluation k a (f j) (regularToPlaneTorus k g)) := by + have h := LinearMap.toMatrix'_mulVec + (ρ (Multiplicative.ofAdd (-(g.val a 1 / g.val a 0)))) + (fun j => planeChartEvaluation k a (f j) (regularToPlaneTorus k g)) + rw [← hP] at h + rw [← h] + funext i + let ev : regularCoordinateLocalization k a →ₐ[k] k := + (Pi.evalAlgHom k _ g).comp (regularLocalizationEvaluation k a) + change ev (associatedLocalExpression k ι P a f i) = _ + simp only [associatedLocalExpression, map_sum, map_mul, + map_aeval_polynomial (k := k) (A := regularCoordinateLocalization k a) (B := k) ev, + map_neg] + change (∑ j, Polynomial.aeval + (-(regularLocalizationEvaluation k a + (algebraMap (regularSL2Functions k) (regularCoordinateLocalization k a) + (regularEntry k a 1)) g) * + regularLocalizationEvaluation k a (regularCoordinateInverse k a) g) (P i j) * + regularLocalizationEvaluation k a (planeChartPullback k a (f j)) g) = _ + rw [regularLocalizationEvaluation_algebraMap] + change (∑ j, Polynomial.aeval + (-(regularEntry k a 1).val g.val * + regularLocalizationEvaluation k a (regularCoordinateInverse k a) g) (P i j) * + regularLocalizationEvaluation k a (planeChartPullback k a (f j)) g) = _ + simp only [regularEntry_apply, regularCoordinateInverse_evaluation, + planeChartPullback_evaluation, Matrix.mulVec, dotProduct, polynomialMatrixEval, + div_eq_mul_inv, neg_mul] + +noncomputable def associatedTorusValue (f : ι → planeCoordinateChart k 0) + (g : regularTorusPoints k) : ι → k := + ρ (Multiplicative.ofAdd (-(g.val 0 1 / g.val 0 0))) + (fun j => planeChartEvaluation k 0 (f j) (regularToPlaneTorus k g)) + +omit [Infinite k] in +lemma associatedChartPair_local_compatible + (P : Matrix ι ι (Polynomial k)) + (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) + (f₀ : ι → planeCoordinateChart k 0) (f₁ : ι → planeCoordinateChart k 1) + (hf : ∀ x : planeTorusPoints k, + (fun j => planeChartEvaluation k 1 (f₁ j) x) = + ρ (Multiplicative.ofAdd ((x.val 0 * x.val 1)⁻¹)) + (fun j => planeChartEvaluation k 0 (f₀ j) x)) (g : regularTorusPoints k) : + (fun i => regularLocalizationEvaluation k 1 (associatedLocalExpression k ι P 1 f₁ i) g) = + associatedTorusValue k ι ρ f₀ g := by + rw [associatedLocalExpression_evaluation k ι ρ P hP, hf, + ← additive_rep_apply_add] + unfold associatedTorusValue + congr 2 + change -(g.val 1 1 / g.val 1 0) + (g.val 0 0 * g.val 1 0)⁻¹ = + -(g.val 0 1 / g.val 0 0) + have hd : g.val 0 0 * g.val 1 1 - g.val 0 1 * g.val 1 0 = 1 := by + simpa only [Matrix.det_fin_two] using g.val.property + field_simp [g.property 0, g.property 1] + linear_combination -hd + +omit [Infinite k] [Fintype ι] [DecidableEq ι] in +lemma secondColumn_unipotent_mul (g : SL2 k) (t : k) (i : Fin 2) : + (g * unipotent k t) i 1 = g i 0 * t + g i 1 := by + change (((g : Matrix (Fin 2) (Fin 2) k) * + (unipotent k t : Matrix (Fin 2) (Fin 2) k)) i 1) = _ + simp [Matrix.mul_apply, Fin.sum_univ_two, unipotent] + +noncomputable def regularTorusRightUnipotent (g : regularTorusPoints k) (t : k) : + regularTorusPoints k := + ⟨g.val * unipotent k t, by intro i; rw [firstColumn_unipotent_mul]; exact g.property i⟩ + +omit [Infinite k] [Fintype ι] [DecidableEq ι] in +lemma associatedTorusValue_unipotent (f : ι → planeCoordinateChart k 0) + (g : regularTorusPoints k) (t : k) : + associatedTorusValue k ι ρ f (regularTorusRightUnipotent k g t) = + ρ (Multiplicative.ofAdd (-t)) (associatedTorusValue k ι ρ f g) := by + have hx : regularToPlaneTorus k (regularTorusRightUnipotent k g t) = + regularToPlaneTorus k g := by + apply Subtype.ext + funext i + exact firstColumn_unipotent_mul k g.val t i + unfold associatedTorusValue + rw [hx, ← additive_rep_apply_add] + apply congrArg (fun s : k => ρ (Multiplicative.ofAdd s) + (fun j => planeChartEvaluation k 0 (f j) (regularToPlaneTorus k g))) + change -((g.val * unipotent k t) 0 1 / (g.val * unipotent k t) 0 0) = _ + rw [secondColumn_unipotent_mul, firstColumn_unipotent_mul] + field_simp [g.property 0] + ring + +noncomputable def regularVectorCombination (L : (ι → k) →ₗ[k] (ι → k)) + (f : ι → regularSL2Functions k) (i : ι) : regularSL2Functions k := + ∑ j, (LinearMap.toMatrix' L i j) • f j + +omit [Infinite k] in +lemma regularVectorCombination_evaluation (L : (ι → k) →ₗ[k] (ι → k)) + (f : ι → regularSL2Functions k) (g : SL2 k) : + regularVectorEvaluation k ι g (regularVectorCombination k ι L f) = + L (regularVectorEvaluation k ι g f) := by + rw [← LinearMap.toMatrix'_mulVec L] + funext i + change (Subalgebra.val (regularSL2Functions k) + (∑ j, (LinearMap.toMatrix' L i j) • f j)) g = _ + simp only [map_sum, map_smul, Finset.sum_apply, Pi.smul_apply, + smul_eq_mul, Matrix.mulVec, dotProduct] + rfl + + + +theorem associatedChartPair_glue + (P : Matrix ι ι (Polynomial k)) + (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) + (f₀ : ι → planeCoordinateChart k 0) (f₁ : ι → planeCoordinateChart k 1) + (hf : ∀ x : planeTorusPoints k, + (fun j => planeChartEvaluation k 1 (f₁ j) x) = + ρ (Multiplicative.ofAdd ((x.val 0 * x.val 1)⁻¹)) + (fun j => planeChartEvaluation k 0 (f₀ j) x)) : + ∃ f : associatedSectionsSubmodule k ι ρ, + associatedXChart k ι ρ f = f₀ ∧ associatedYChart k ι ρ f = f₁ := by + have hg (i : ι) : ∃ f : regularSL2Functions k, + regularTorusRestriction k f = fun g => associatedTorusValue k ι ρ f₀ g i := by + apply regularTorus_glue k _ (associatedLocalExpression k ι P 0 f₀ i) + (associatedLocalExpression k ι P 1 f₁ i) + · funext g + exact congrFun (associatedLocalExpression_evaluation k ι ρ P hP 0 f₀ g) i + · funext g + exact congrFun (associatedChartPair_local_compatible k ι ρ P hP f₀ f₁ hf g) i + choose f hfg using hg + have hev (g : regularTorusPoints k) : regularVectorEvaluation k ι g.val f = + associatedTorusValue k ι ρ f₀ g := by + funext i + exact congrFun (hfg i) g + have hmem : f ∈ associatedSectionsSubmodule k ι ρ := by + intro g t + funext i + have hz : regularRightTranslation k (unipotent k t) (f i) - + regularVectorCombination k ι (ρ (Multiplicative.ofAdd (-t))) f i = 0 := by + apply regularSL2_torus_dense k + intro h ha hc + let h' : regularTorusPoints k := ⟨h, by intro j; fin_cases j; exact ha; exact hc⟩ + have he := associatedTorusValue_unipotent k ι ρ f₀ h' t + rw [← hev, ← hev] at he + have he' := congrFun he i + change (f i).val (h * unipotent k t) = _ at he' + change (f i).val (h * unipotent k t) - + (regularVectorCombination k ι (ρ (Multiplicative.ofAdd (-t))) f i).val h = 0 + rw [he'] + exact sub_eq_zero.mpr + (congrFun (regularVectorCombination_evaluation k ι + (ρ (Multiplicative.ofAdd (-t))) f h) i).symm + have he := congrArg (fun a : regularSL2Functions k => a.val g) (sub_eq_zero.mp hz) + change (f i).val (g * unipotent k t) = _ at he + exact he.trans (congrFun (regularVectorCombination_evaluation k ι + (ρ (Multiplicative.ofAdd (-t))) f g) i) + let F : associatedSectionsSubmodule k ι ρ := ⟨f,hmem⟩ + have hx : associatedXChart k ι ρ F = f₀ := by + funext i + apply planeChartEvaluation_injective k 0 + funext x + have he := hev ⟨planeXSection k x, by + intro j + fin_cases j <;> simpa [planeXSection] using x.property _⟩ + have hx' : regularToPlaneTorus k ⟨planeXSection k x, by + intro j; fin_cases j <;> simpa [planeXSection] using x.property _⟩ = x := by + apply Subtype.ext + funext j + fin_cases j <;> simp [regularToPlaneTorus, planeXSection] + unfold associatedTorusValue at he + rw [hx'] at he + change regularVectorEvaluation k ι (planeXSection k x) f = + ρ (Multiplicative.ofAdd (-(0 / x.val 0))) + (fun j => planeChartEvaluation k 0 (f₀ j) x) at he + simp only [zero_div, neg_zero] at he + change regularVectorEvaluation k ι (planeXSection k x) f = + ρ 1 (fun j => planeChartEvaluation k 0 (f₀ j) x) at he + rw [map_one] at he + exact (congrFun (associatedXChart_evaluation k ι ρ F x) i).trans (congrFun he i) + refine ⟨F,hx,?_⟩ + funext i + apply planeChartEvaluation_injective k 1 + funext x + have he := associatedCharts_transition k ι ρ F x + rw [hx, ← hf x] at he + exact congrFun he i + +end + +universe u +variable (k : Type u) [Field k] +variable (ι : Type u) [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) + +noncomputable instance regularPlaneAlgebra : + Algebra (MvPolynomial (Fin 2) k) (regularSL2Functions k) := + (regularPlane k).toRingHom.toAlgebra + +instance regularPlaneScalarTower : + IsScalarTower k (MvPolynomial (Fin 2) k) (regularSL2Functions k) := + IsScalarTower.of_algHom (regularPlane k) + +lemma regularPlane_algebraMap (P : MvPolynomial (Fin 2) k) : + algebraMap (MvPolynomial (Fin 2) k) (regularSL2Functions k) P = regularPlane k P := rfl + +omit [Fintype ι] [DecidableEq ι] in +lemma regularVector_plane_smul (P : MvPolynomial (Fin 2) k) + (f : ι → regularSL2Functions k) (g : SL2 k) : + regularVectorEvaluation k ι g (P • f) = + MvPolynomial.eval (fun i => g i 0) P • regularVectorEvaluation k ι g f := by + funext i + change (P • f i).val g = _ + rw [Algebra.smul_def, regularPlane_algebraMap] + change (regularPlane k P).val g * (f i).val g = _ + rw [regularPlane_evaluation] + rfl + +omit [Fintype ι] [DecidableEq ι] in +lemma associatedSections_plane_smul_mem (P : MvPolynomial (Fin 2) k) + (f : ι → regularSL2Functions k) (hf : f ∈ associatedSectionsSubmodule k ι ρ) : + P • f ∈ associatedSectionsSubmodule k ι ρ := by + intro g t + rw [regularVector_plane_smul, regularVector_plane_smul, hf, map_smul] + simp only [firstColumn_unipotent_mul] + +noncomputable def associatedPolynomialSections : + Submodule (MvPolynomial (Fin 2) k) (ι → regularSL2Functions k) where + carrier := associatedSectionsSubmodule k ι ρ + zero_mem' := (associatedSectionsSubmodule k ι ρ).zero_mem + add_mem' := (associatedSectionsSubmodule k ι ρ).add_mem + smul_mem' := associatedSections_plane_smul_mem k ι ρ + +noncomputable instance associatedSectionsAddCommGroup : + AddCommGroup (associatedSectionsSubmodule k ι ρ) := + Submodule.addCommGroup (associatedSectionsSubmodule k ι ρ) + +noncomputable instance (priority := 2000) associatedSectionsPolynomialSMul : + SMul (MvPolynomial (Fin 2) k) (associatedSectionsSubmodule k ι ρ) := + (Submodule.module (associatedPolynomialSections k ι ρ)).toSMul + +noncomputable instance (priority := 2000) associatedSectionsPolynomialModule : + Module (MvPolynomial (Fin 2) k) (associatedSectionsSubmodule k ι ρ) := + Submodule.module (associatedPolynomialSections k ι ρ) + +instance associatedSectionsScalarTower : + IsScalarTower k (MvPolynomial (Fin 2) k) (associatedSectionsSubmodule k ι ρ) where + smul_assoc a P f := Subtype.ext (smul_assoc a P f.val) + +variable [Infinite k] +noncomputable def associatedXChartPolynomial : + (associatedSectionsSubmodule k ι ρ) →ₗ[MvPolynomial (Fin 2) k] + (ι → planeCoordinateChart k 0) where + toFun := associatedXChart k ι ρ + map_add' := (associatedXChart k ι ρ).map_add + map_smul' := by + intro P f + funext i + apply planeChartEvaluation_injective k 0 + funext x + have he := congrFun (associatedXChart_evaluation k ι ρ (P • f) x) i + change _ = _ at he + rw [show (P • f).val = P • f.val from rfl, regularVector_plane_smul] at he + rw [he] + change MvPolynomial.eval (fun j => (planeXSection k x) j 0) P * + regularVectorEvaluation k ι (planeXSection k x) f.val i = + planeChartEvaluation k 0 (P • associatedXChart k ι ρ f i) x + rw [Algebra.smul_def, map_mul, planeChartEvaluation_algebraMap] + change _ = planeTorusEvaluation k P x * + planeChartEvaluation k 0 (associatedXChart k ι ρ f i) x + rw [planeTorusEvaluation_apply, congrFun (associatedXChart_evaluation k ι ρ f x) i] + congr 2 + apply congrArg MvPolynomial.eval + funext j + fin_cases j <;> simp [planeXSection] + +end FiberFunctorProof + + + +open scoped TensorProduct +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialCovers.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialCovers.lean index 86d321103ba6b3df6b40645dec400b1c68d8c1a7..b5d853d92f086e8abf452ffc0e8ed9dd473e33ce 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialCovers.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialCovers.lean @@ -1,78 +1,78 @@ -import OAI.RepresentationTheory.RestrictedTilting.GoodKernel -import OAI.RepresentationTheory.RestrictedTilting.TensorWeights - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -universe u -variable (k : Type u) [Field k] [Infinite k] - -lemma costandard_zero_tilting : IsTilting k (costandard k 0) := - costandard_tilting_of_choose_ne_zero k 0 (by intro i; fin_cases i; norm_num) -lemma costandard_one_tilting : IsTilting k (costandard k 1) := - costandard_tilting_of_choose_ne_zero k 1 (by intro i; fin_cases i <;> norm_num) - -noncomputable def tensorPowerFrom (A : FDRep k (SL2 k)) : ℕ → FDRep k (SL2 k) - | 0 => A - | n+1 => tensorPowerFrom A n ⊗ costandard k 1 - -noncomputable def polynomialPowerMap (m : ℕ) : ∀ n, - tensorPowerFrom k (costandard k m) n ⟶ costandard k (m+n) - | 0 => 𝟙 _ - | n+1 => (tensorRight (costandard k 1)).map (polynomialPowerMap m n) ≫ - costandardMultiply k (m+n) 1 - -omit [Infinite k] in -lemma polynomialPowerMap_goodKernel (m n : ℕ) : - HasGoodKernel k (polynomialPowerMap k m n) := by - induction n with - | zero => exact HasGoodKernel.id k _ - | succ n ih => - exact (ih.tensor_right k _ (costandard_hasGoodFiltration k 1)).comp k - (costandardMultiply_goodKernel k (m+n) 1) - -lemma tensorPowerFrom_tilting {A : FDRep k (SL2 k)} (hA : IsTilting k A) (n : ℕ) : - IsTilting k (tensorPowerFrom k A n) := by - induction n with - | zero => exact hA - | succ n ih => exact ih.tensor k (costandard_one_tilting k) - -omit [Infinite k] in -lemma tensorPowerFrom_rational {A : FDRep k (SL2 k)} - (hA : IsRational k A.ρ) (n : ℕ) : IsRational k (tensorPowerFrom k A n).ρ := by - induction n with - | zero => exact hA - | succ n ih => - exact IsRational.tensor k (tensorPowerFrom k A n).ρ (costandard k 1).ρ ih - (costandard_rational k 1) - -lemma tensorPowerFrom_weights {A : FDRep k (SL2 k)} - (hA : IsRational k A.ρ) (a : ℕ) (ha : HasWeightsBetween A.ρ (-(a : ℤ)) a) (n : ℕ) : - HasWeightsBetween (tensorPowerFrom k A n).ρ (-((a+n : ℕ) : ℤ)) (a+n) := by - induction n with - | zero => - change HasWeightsBetween A.ρ (-((a+0 : ℕ) : ℤ)) (a+0) - simpa only [Nat.add_zero, add_zero] using ha - | succ n ih => - exact hasWeightsBetween_tensor (tensorPowerFrom k A n).ρ (costandard k 1).ρ - (tensorPowerFrom_rational k hA n) (costandard_rational k 1) (a+n) 1 ih - (fun m v hm hv => costandard_weight_bound k 1 m hm v hv) - - - -omit [Infinite k] in -lemma tensorPowerFrom_factor (m n : ℕ) : - Nonempty (tensorPowerFrom k (costandard k m) n ≅ - costandard k m ⊗ tensorPowerFrom k (costandard k 0) n) := by - induction n with - | zero => - have := costandardMultiply_isIso_of_zero k m 0 (Or.inr rfl) - exact ⟨(asIso (costandardMultiply k m 0)).symm⟩ - | succ n ih => - obtain ⟨e⟩ := ih - exact ⟨(tensorRight (costandard k 1)).mapIso e ≪≫ - α_ (costandard k m) (tensorPowerFrom k (costandard k 0) n) (costandard k 1)⟩ -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.GoodKernel +import OAI.RepresentationTheory.RestrictedTilting.TensorWeights + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +universe u +variable (k : Type u) [Field k] [Infinite k] + +lemma costandard_zero_tilting : IsTilting k (costandard k 0) := + costandard_tilting_of_choose_ne_zero k 0 (by intro i; fin_cases i; norm_num) +lemma costandard_one_tilting : IsTilting k (costandard k 1) := + costandard_tilting_of_choose_ne_zero k 1 (by intro i; fin_cases i <;> norm_num) + +noncomputable def tensorPowerFrom (A : FDRep k (SL2 k)) : ℕ → FDRep k (SL2 k) + | 0 => A + | n+1 => tensorPowerFrom A n ⊗ costandard k 1 + +noncomputable def polynomialPowerMap (m : ℕ) : ∀ n, + tensorPowerFrom k (costandard k m) n ⟶ costandard k (m+n) + | 0 => 𝟙 _ + | n+1 => (tensorRight (costandard k 1)).map (polynomialPowerMap m n) ≫ + costandardMultiply k (m+n) 1 + +omit [Infinite k] in +lemma polynomialPowerMap_goodKernel (m n : ℕ) : + HasGoodKernel k (polynomialPowerMap k m n) := by + induction n with + | zero => exact HasGoodKernel.id k _ + | succ n ih => + exact (ih.tensor_right k _ (costandard_hasGoodFiltration k 1)).comp k + (costandardMultiply_goodKernel k (m+n) 1) + +lemma tensorPowerFrom_tilting {A : FDRep k (SL2 k)} (hA : IsTilting k A) (n : ℕ) : + IsTilting k (tensorPowerFrom k A n) := by + induction n with + | zero => exact hA + | succ n ih => exact ih.tensor k (costandard_one_tilting k) + +omit [Infinite k] in +lemma tensorPowerFrom_rational {A : FDRep k (SL2 k)} + (hA : IsRational k A.ρ) (n : ℕ) : IsRational k (tensorPowerFrom k A n).ρ := by + induction n with + | zero => exact hA + | succ n ih => + exact IsRational.tensor k (tensorPowerFrom k A n).ρ (costandard k 1).ρ ih + (costandard_rational k 1) + +lemma tensorPowerFrom_weights {A : FDRep k (SL2 k)} + (hA : IsRational k A.ρ) (a : ℕ) (ha : HasWeightsBetween A.ρ (-(a : ℤ)) a) (n : ℕ) : + HasWeightsBetween (tensorPowerFrom k A n).ρ (-((a+n : ℕ) : ℤ)) (a+n) := by + induction n with + | zero => + change HasWeightsBetween A.ρ (-((a+0 : ℕ) : ℤ)) (a+0) + simpa only [Nat.add_zero, add_zero] using ha + | succ n ih => + exact hasWeightsBetween_tensor (tensorPowerFrom k A n).ρ (costandard k 1).ρ + (tensorPowerFrom_rational k hA n) (costandard_rational k 1) (a+n) 1 ih + (fun m v hm hv => costandard_weight_bound k 1 m hm v hv) + + + +omit [Infinite k] in +lemma tensorPowerFrom_factor (m n : ℕ) : + Nonempty (tensorPowerFrom k (costandard k m) n ≅ + costandard k m ⊗ tensorPowerFrom k (costandard k 0) n) := by + induction n with + | zero => + have := costandardMultiply_isIso_of_zero k m 0 (Or.inr rfl) + exact ⟨(asIso (costandardMultiply k m 0)).symm⟩ + | succ n ih => + obtain ⟨e⟩ := ih + exact ⟨(tensorRight (costandard k 1)).mapIso e ≪≫ + α_ (costandard k m) (tensorPowerFrom k (costandard k 0) n) (costandard k 1)⟩ +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialIntertwiner.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialIntertwiner.lean index 4bd003af0ffbcd6ce0e37443154695a254101b02..ea45b713cb6a0a4c3d1ad0c1a80fc94d3ef3add8 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialIntertwiner.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialIntertwiner.lean @@ -1,58 +1,58 @@ -import OAI.RepresentationTheory.RestrictedTilting.RationalMatrices -import OAI.RepresentationTheory.RestrictedTilting.LaurentPolynomialSeparation - -namespace OAI - -namespace FiberFunctorProof -open scoped BigOperators -section -variable {k K ι : Type*} [Field k] [Infinite k] [Field K] [Algebra k K] - [Fintype ι] [DecidableEq ι] - -omit [Infinite k] [Fintype ι] [DecidableEq ι] in -lemma polynomialMatrixEval_base (P : Matrix ι ι (Polynomial k)) (t : k) : - polynomialMatrixEval P (algebraMap k K t) = - (polynomialMatrixEval P t).map (algebraMap k K) := - (polynomialMatrixEval_map P (Algebra.ofId k K) t).symm - -omit [DecidableEq ι] in -lemma polynomial_intertwiner_extension (P B : Matrix ι ι (Polynomial k)) - (C : Matrix ι ι K) (z : K) - (h : ∀ t : k, C * polynomialMatrixEval B (algebraMap k K t) = - polynomialMatrixEval P (algebraMap k K t * z) * C) : - ∀ t : K, C * polynomialMatrixEval B t = polynomialMatrixEval P (t*z) * C := by - let CP : Matrix ι ι (Polynomial K) := C.map Polynomial.C - let BP := polynomialMatrixEval B (Polynomial.X : Polynomial K) - let PP := polynomialMatrixEval P (Polynomial.X * Polynomial.C z) - let ev (t : K) : Polynomial K →ₐ[k] K := (Polynomial.aeval t).restrictScalars k - have heC (t : K) : CP.map (ev t) = C := by - apply Matrix.ext - intro i j - exact Polynomial.aeval_C t (C i j) - have heB (t : K) : BP.map (ev t) = polynomialMatrixEval B t := by - rw [polynomialMatrixEval_map] - congr 1 - exact Polynomial.aeval_X t - have heP (t : K) : PP.map (ev t) = polynomialMatrixEval P (t*z) := by - rw [polynomialMatrixEval_map] - congr 1 - change Polynomial.aeval t (Polynomial.X * Polynomial.C z) = t*z - rw [map_mul, Polynomial.aeval_X, Polynomial.aeval_C] - rfl - have hid : CP * BP = PP * CP := by - apply Matrix.ext - intro i j - apply polynomial_eq_of_base_evals (k := k) - intro t - have hM : (CP * BP).map (ev (algebraMap k K t)) = - (PP*CP).map (ev (algebraMap k K t)) := by - rw [Matrix.map_mul, Matrix.map_mul, heC, heB, heP] - exact h t - exact congrArg (fun A : Matrix ι ι K => A i j) hM - intro t - have he := congrArg (fun A : Matrix ι ι (Polynomial K) => A.map (ev t)) hid - simpa only [Matrix.map_mul, heC, heB, heP] using he -end -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.RationalMatrices +import OAI.RepresentationTheory.RestrictedTilting.LaurentPolynomialSeparation + +namespace OAI + +namespace FiberFunctorProof +open scoped BigOperators +section +variable {k K ι : Type*} [Field k] [Infinite k] [Field K] [Algebra k K] + [Fintype ι] [DecidableEq ι] + +omit [Infinite k] [Fintype ι] [DecidableEq ι] in +lemma polynomialMatrixEval_base (P : Matrix ι ι (Polynomial k)) (t : k) : + polynomialMatrixEval P (algebraMap k K t) = + (polynomialMatrixEval P t).map (algebraMap k K) := + (polynomialMatrixEval_map P (Algebra.ofId k K) t).symm + +omit [DecidableEq ι] in +lemma polynomial_intertwiner_extension (P B : Matrix ι ι (Polynomial k)) + (C : Matrix ι ι K) (z : K) + (h : ∀ t : k, C * polynomialMatrixEval B (algebraMap k K t) = + polynomialMatrixEval P (algebraMap k K t * z) * C) : + ∀ t : K, C * polynomialMatrixEval B t = polynomialMatrixEval P (t*z) * C := by + let CP : Matrix ι ι (Polynomial K) := C.map Polynomial.C + let BP := polynomialMatrixEval B (Polynomial.X : Polynomial K) + let PP := polynomialMatrixEval P (Polynomial.X * Polynomial.C z) + let ev (t : K) : Polynomial K →ₐ[k] K := (Polynomial.aeval t).restrictScalars k + have heC (t : K) : CP.map (ev t) = C := by + apply Matrix.ext + intro i j + exact Polynomial.aeval_C t (C i j) + have heB (t : K) : BP.map (ev t) = polynomialMatrixEval B t := by + rw [polynomialMatrixEval_map] + congr 1 + exact Polynomial.aeval_X t + have heP (t : K) : PP.map (ev t) = polynomialMatrixEval P (t*z) := by + rw [polynomialMatrixEval_map] + congr 1 + change Polynomial.aeval t (Polynomial.X * Polynomial.C z) = t*z + rw [map_mul, Polynomial.aeval_X, Polynomial.aeval_C] + rfl + have hid : CP * BP = PP * CP := by + apply Matrix.ext + intro i j + apply polynomial_eq_of_base_evals (k := k) + intro t + have hM : (CP * BP).map (ev (algebraMap k K t)) = + (PP*CP).map (ev (algebraMap k K t)) := by + rw [Matrix.map_mul, Matrix.map_mul, heC, heB, heP] + exact h t + exact congrArg (fun A : Matrix ι ι K => A i j) hM + intro t + have he := congrArg (fun A : Matrix ι ι (Polynomial K) => A.map (ev t)) hid + simpa only [Matrix.map_mul, heC, heB, heP] using he +end +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialJets.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialJets.lean index cbd95c08d74bf587cc565c396af53cf533f38c00..12e93ad2b59ad0ec8f2d6c6f73750f302168d7ee 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialJets.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/PolynomialJets.lean @@ -1,109 +1,109 @@ -import OAI.RepresentationTheory.RestrictedTilting.JetTriviality - -namespace OAI - -namespace FiberFunctorProof -open scoped TensorProduct -universe u -variable {k : Type u} [Field k] -variable {T N : Type u} [AddCommGroup T] [Module k T] - [AddCommGroup N] [Module k N] - [Module (MvPolynomial (Fin 2) k) N] [IsScalarTower k (MvPolynomial (Fin 2) k) N] - -noncomputable def polynomialExtend (L : T →ₗ[k] N) : - (MvPolynomial (Fin 2) k) ⊗[k] T →ₗ[MvPolynomial (Fin 2) k] N := - TensorProduct.AlgebraTensorModule.lift - (LinearMap.toSpanSingleton (MvPolynomial (Fin 2) k) (T →ₗ[k] N) L) - -@[simp] lemma polynomialExtend_tmul (L : T →ₗ[k] N) - (P : MvPolynomial (Fin 2) k) (t : T) : - polynomialExtend L (P ⊗ₜ[k] t) = P • L t := rfl - -noncomputable def polynomialAugment : (MvPolynomial (Fin 2) k) ⊗[k] T →ₗ[k] T := - (TensorProduct.lid k T).toLinearMap ∘ₗ TensorProduct.map - ({ toFun := MvPolynomial.constantCoeff - map_add' := map_add _ - map_smul' := MvPolynomial.constantCoeff_smul } : MvPolynomial (Fin 2) k →ₗ[k] k) - LinearMap.id - -@[simp] lemma polynomialAugment_tmul (P : MvPolynomial (Fin 2) k) (t : T) : - polynomialAugment (P ⊗ₜ[k] t) = MvPolynomial.constantCoeff P • t := rfl - -lemma polynomialAugment_smul (P : MvPolynomial (Fin 2) k) - (z : (MvPolynomial (Fin 2) k) ⊗[k] T) : - polynomialAugment (P • z) = MvPolynomial.constantCoeff P • polynomialAugment z := by - induction z using TensorProduct.inductionOn with - | tmul Q t => rw [TensorProduct.smul_tmul', polynomialAugment_tmul]; simp [smul_eq_mul, mul_smul] - | add z w hz hw => simp [smul_add, hz, hw] - -lemma polynomialAugment_pairRelation - (z : (MvPolynomial (Fin 2) k) ⊗[k] T) - (hz : z ∈ pairRelation (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1)) : - polynomialAugment z = 0 := by - obtain ⟨a,b,rfl⟩ := (mem_pairRelation _ _ z).mp hz - simp [polynomialAugment_smul] - -lemma polynomial_origin_representative (z : (MvPolynomial (Fin 2) k) ⊗[k] T) : - z - (1 : MvPolynomial (Fin 2) k) ⊗ₜ[k] polynomialAugment z ∈ - pairRelation (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) := by - let Q := (pairRelation (M := (MvPolynomial (Fin 2) k) ⊗[k] T) - (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1)).restrictScalars k - suffices h : Q.mkQ z = Q.mkQ (1 ⊗ₜ[k] polynomialAugment z) by - exact (Submodule.Quotient.mk_eq_zero Q).mp (by change Q.mkQ (z - 1 ⊗ₜ[k] polynomialAugment z) = 0; rw [map_sub, h, sub_self]) - induction z using TensorProduct.inductionOn with - | tmul P t => - have hX : ∀ (i : Fin 2) (m : (MvPolynomial (Fin 2) k) ⊗[k] T), - (MvPolynomial.X i : MvPolynomial (Fin 2) k) • m ∈ Q := by - intro i m - fin_cases i - · exact x_smul_mem_pairRelation _ _ m - · exact y_smul_mem_pairRelation _ _ m - have hh := originQuotient_polynomial_smul Q hX P (1 ⊗ₜ[k] t) - rw [TensorProduct.smul_tmul', smul_eq_mul, mul_one] at hh - rw [polynomialAugment_tmul, TensorProduct.tmul_smul, map_smul] - exact hh - | add z w hz hw => simp [map_add, TensorProduct.tmul_add, hz, hw] - - - -theorem polynomialExtend_jet_bijective (q : N →ₗ[k] T) (L : T →ₗ[k] N) - (hq : ∀ n, q n = 0 ↔ n ∈ pairRelation (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1)) - (hL : q ∘ₗ L = LinearMap.id) - (hx : Function.Injective (fun n : N => (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n)) - (hy : ∀ v n : N, (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) • v = - (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n → - ∃ w, v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • w) (j : ℕ) : - Function.Bijective (jetMap (polynomialExtend L) (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) j) := by - have hqL : ∀ t, q (L t) = t := fun t => congrArg (fun f : T →ₗ[k] T => f t) hL - have hqX : ∀ i n, q ((MvPolynomial.X i : MvPolynomial (Fin 2) k) • n) = 0 := by - intro i n - apply (hq _).mpr - fin_cases i - · exact x_smul_mem_pairRelation _ _ n - · exact y_smul_mem_pairRelation _ _ n - have hqP : ∀ P n, q ((P : MvPolynomial (Fin 2) k) • n) = MvPolynomial.constantCoeff P • q n := by - intro P n - induction P using MvPolynomial.induction_on with - | C a => - rw [MvPolynomial.constantCoeff_C] - change q (algebraMap k (MvPolynomial (Fin 2) k) a • n) = a • q n - rw [algebraMap_smul, map_smul] - | add P Q hP hQ => simp only [add_smul, map_add, hP, hQ] - | mul_X P i _ => rw [mul_comm, mul_smul, hqX]; simp - have he : ∀ z, q (polynomialExtend L z) = polynomialAugment z := by - intro z - induction z using TensorProduct.inductionOn with - | tmul P t => simp [hqP, hqL] - | add z w hz hw => simp [hz, hw] - constructor - · apply jetMap_injective (polynomialExtend L) _ _ hx hy - intro z hz - have hzero : polynomialAugment z = 0 := (he z).symm.trans ((hq _).mpr hz) - simpa only [hzero, TensorProduct.tmul_zero, sub_zero] using polynomial_origin_representative z - · apply jetMap_surjective - intro n - refine ⟨1 ⊗ₜ[k] q n, (hq _).mp ?_⟩ - simp [hqL] -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.JetTriviality + +namespace OAI + +namespace FiberFunctorProof +open scoped TensorProduct +universe u +variable {k : Type u} [Field k] +variable {T N : Type u} [AddCommGroup T] [Module k T] + [AddCommGroup N] [Module k N] + [Module (MvPolynomial (Fin 2) k) N] [IsScalarTower k (MvPolynomial (Fin 2) k) N] + +noncomputable def polynomialExtend (L : T →ₗ[k] N) : + (MvPolynomial (Fin 2) k) ⊗[k] T →ₗ[MvPolynomial (Fin 2) k] N := + TensorProduct.AlgebraTensorModule.lift + (LinearMap.toSpanSingleton (MvPolynomial (Fin 2) k) (T →ₗ[k] N) L) + +@[simp] lemma polynomialExtend_tmul (L : T →ₗ[k] N) + (P : MvPolynomial (Fin 2) k) (t : T) : + polynomialExtend L (P ⊗ₜ[k] t) = P • L t := rfl + +noncomputable def polynomialAugment : (MvPolynomial (Fin 2) k) ⊗[k] T →ₗ[k] T := + (TensorProduct.lid k T).toLinearMap ∘ₗ TensorProduct.map + ({ toFun := MvPolynomial.constantCoeff + map_add' := map_add _ + map_smul' := MvPolynomial.constantCoeff_smul } : MvPolynomial (Fin 2) k →ₗ[k] k) + LinearMap.id + +@[simp] lemma polynomialAugment_tmul (P : MvPolynomial (Fin 2) k) (t : T) : + polynomialAugment (P ⊗ₜ[k] t) = MvPolynomial.constantCoeff P • t := rfl + +lemma polynomialAugment_smul (P : MvPolynomial (Fin 2) k) + (z : (MvPolynomial (Fin 2) k) ⊗[k] T) : + polynomialAugment (P • z) = MvPolynomial.constantCoeff P • polynomialAugment z := by + induction z using TensorProduct.inductionOn with + | tmul Q t => rw [TensorProduct.smul_tmul', polynomialAugment_tmul]; simp [smul_eq_mul, mul_smul] + | add z w hz hw => simp [smul_add, hz, hw] + +lemma polynomialAugment_pairRelation + (z : (MvPolynomial (Fin 2) k) ⊗[k] T) + (hz : z ∈ pairRelation (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1)) : + polynomialAugment z = 0 := by + obtain ⟨a,b,rfl⟩ := (mem_pairRelation _ _ z).mp hz + simp [polynomialAugment_smul] + +lemma polynomial_origin_representative (z : (MvPolynomial (Fin 2) k) ⊗[k] T) : + z - (1 : MvPolynomial (Fin 2) k) ⊗ₜ[k] polynomialAugment z ∈ + pairRelation (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) := by + let Q := (pairRelation (M := (MvPolynomial (Fin 2) k) ⊗[k] T) + (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1)).restrictScalars k + suffices h : Q.mkQ z = Q.mkQ (1 ⊗ₜ[k] polynomialAugment z) by + exact (Submodule.Quotient.mk_eq_zero Q).mp (by change Q.mkQ (z - 1 ⊗ₜ[k] polynomialAugment z) = 0; rw [map_sub, h, sub_self]) + induction z using TensorProduct.inductionOn with + | tmul P t => + have hX : ∀ (i : Fin 2) (m : (MvPolynomial (Fin 2) k) ⊗[k] T), + (MvPolynomial.X i : MvPolynomial (Fin 2) k) • m ∈ Q := by + intro i m + fin_cases i + · exact x_smul_mem_pairRelation _ _ m + · exact y_smul_mem_pairRelation _ _ m + have hh := originQuotient_polynomial_smul Q hX P (1 ⊗ₜ[k] t) + rw [TensorProduct.smul_tmul', smul_eq_mul, mul_one] at hh + rw [polynomialAugment_tmul, TensorProduct.tmul_smul, map_smul] + exact hh + | add z w hz hw => simp [map_add, TensorProduct.tmul_add, hz, hw] + + + +theorem polynomialExtend_jet_bijective (q : N →ₗ[k] T) (L : T →ₗ[k] N) + (hq : ∀ n, q n = 0 ↔ n ∈ pairRelation (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1)) + (hL : q ∘ₗ L = LinearMap.id) + (hx : Function.Injective (fun n : N => (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n)) + (hy : ∀ v n : N, (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) • v = + (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • n → + ∃ w, v = (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) • w) (j : ℕ) : + Function.Bijective (jetMap (polynomialExtend L) (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) (MvPolynomial.X 1) j) := by + have hqL : ∀ t, q (L t) = t := fun t => congrArg (fun f : T →ₗ[k] T => f t) hL + have hqX : ∀ i n, q ((MvPolynomial.X i : MvPolynomial (Fin 2) k) • n) = 0 := by + intro i n + apply (hq _).mpr + fin_cases i + · exact x_smul_mem_pairRelation _ _ n + · exact y_smul_mem_pairRelation _ _ n + have hqP : ∀ P n, q ((P : MvPolynomial (Fin 2) k) • n) = MvPolynomial.constantCoeff P • q n := by + intro P n + induction P using MvPolynomial.induction_on with + | C a => + rw [MvPolynomial.constantCoeff_C] + change q (algebraMap k (MvPolynomial (Fin 2) k) a • n) = a • q n + rw [algebraMap_smul, map_smul] + | add P Q hP hQ => simp only [add_smul, map_add, hP, hQ] + | mul_X P i _ => rw [mul_comm, mul_smul, hqX]; simp + have he : ∀ z, q (polynomialExtend L z) = polynomialAugment z := by + intro z + induction z using TensorProduct.inductionOn with + | tmul P t => simp [hqP, hqL] + | add z w hz hw => simp [hz, hw] + constructor + · apply jetMap_injective (polynomialExtend L) _ _ hx hy + intro z hz + have hzero : polynomialAugment z = 0 := (he z).symm.trans ((hq _).mpr hz) + simpa only [hzero, TensorProduct.tmul_zero, sub_zero] using polynomial_origin_representative z + · apply jetMap_surjective + intro n + refine ⟨1 ⊗ₜ[k] q n, (hq _).mp ?_⟩ + simp [hqL] +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/ProjectiveFactor.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/ProjectiveFactor.lean index 0d7fea08cde7c4b77f5e5d7744e71966bfa61eca..574a02c99b113ca5e3dfecfc18e5aba53941f0aa 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/ProjectiveFactor.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/ProjectiveFactor.lean @@ -1,46 +1,46 @@ -import Mathlib - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.Limits -open scoped ZeroObject - - -def FactorsThroughProjective {C : Type*} [Category* C] {X Y : C} (f : X ⟶ Y) : Prop := - ∃ P : C, Projective P ∧ ∃ a : X ⟶ P, ∃ b : P ⟶ Y, a ≫ b = f - -variable {k : Type*} [Field k] -variable {C : Type*} [Category* C] [Preadditive C] [Linear k C] -variable [HasFiniteBiproducts C] {X Y : C} - -lemma FactorsThroughProjective.zero : FactorsThroughProjective (0 : X ⟶ Y) := by - refine ⟨0, (isZero_zero C).projective, 0, 0, ?_⟩ - simp - -lemma FactorsThroughProjective.add {f g : X ⟶ Y} - (hf : FactorsThroughProjective f) (hg : FactorsThroughProjective g) : - FactorsThroughProjective (f+g) := by - obtain ⟨P,hP,a,b,rfl⟩ := hf - obtain ⟨Q,hQ,c,d,rfl⟩ := hg - let : HasBinaryBiproducts C := hasBinaryBiproducts_of_finite_biproducts C - let := hP - let := hQ - exact ⟨P ⊞ Q, inferInstance, biprod.lift a c, biprod.desc b d, by simp⟩ - -omit [HasFiniteBiproducts C] in -lemma FactorsThroughProjective.smul {f : X ⟶ Y} - (a : k) (hf : FactorsThroughProjective f) : FactorsThroughProjective (a • f) := by - obtain ⟨P,hP,b,c,rfl⟩ := hf - exact ⟨P,hP,a • b,c, by simp⟩ - - - -def projectiveFactorSubmodule (X Y : C) : Submodule k (X ⟶ Y) where - carrier := {f | FactorsThroughProjective f} - zero_mem' := FactorsThroughProjective.zero - add_mem' := FactorsThroughProjective.add - smul_mem' := fun a _ h => FactorsThroughProjective.smul a h -end FiberFunctorProof - -end OAI +import Mathlib + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.Limits +open scoped ZeroObject + + +def FactorsThroughProjective {C : Type*} [Category* C] {X Y : C} (f : X ⟶ Y) : Prop := + ∃ P : C, Projective P ∧ ∃ a : X ⟶ P, ∃ b : P ⟶ Y, a ≫ b = f + +variable {k : Type*} [Field k] +variable {C : Type*} [Category* C] [Preadditive C] [Linear k C] +variable [HasFiniteBiproducts C] {X Y : C} + +lemma FactorsThroughProjective.zero : FactorsThroughProjective (0 : X ⟶ Y) := by + refine ⟨0, (isZero_zero C).projective, 0, 0, ?_⟩ + simp + +lemma FactorsThroughProjective.add {f g : X ⟶ Y} + (hf : FactorsThroughProjective f) (hg : FactorsThroughProjective g) : + FactorsThroughProjective (f+g) := by + obtain ⟨P,hP,a,b,rfl⟩ := hf + obtain ⟨Q,hQ,c,d,rfl⟩ := hg + let : HasBinaryBiproducts C := hasBinaryBiproducts_of_finite_biproducts C + let := hP + let := hQ + exact ⟨P ⊞ Q, inferInstance, biprod.lift a c, biprod.desc b d, by simp⟩ + +omit [HasFiniteBiproducts C] in +lemma FactorsThroughProjective.smul {f : X ⟶ Y} + (a : k) (hf : FactorsThroughProjective f) : FactorsThroughProjective (a • f) := by + obtain ⟨P,hP,b,c,rfl⟩ := hf + exact ⟨P,hP,a • b,c, by simp⟩ + + + +def projectiveFactorSubmodule (X Y : C) : Submodule k (X ⟶ Y) where + carrier := {f | FactorsThroughProjective f} + zero_mem' := FactorsThroughProjective.zero + add_mem' := FactorsThroughProjective.add + smul_mem' := fun a _ h => FactorsThroughProjective.smul a h +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/ProjectiveRegular.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/ProjectiveRegular.lean index dd48b21abd91b6b38990893416236df0883473e2..0de554333f61b970bf1869baf2ccea1a28dda4fe 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/ProjectiveRegular.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/ProjectiveRegular.lean @@ -1,25 +1,25 @@ -import Mathlib - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory -universe u v -variable (k : Type u) [Field k] - - - -theorem rep_leftRegular_projective (G : Type v) [Group G] : - Projective (Rep.leftRegular k G) := by - let e := Representation.ofMulActionSelfAsModuleEquiv (k := k) (G := G) - let b := (Module.Basis.singleton (PUnit.{1}) (MonoidAlgebra k G)).map e.symm - exact (Rep.toModuleMonoidAlgebra (k := k) (G := G)).projective_of_map_projective - (P := Rep.leftRegular k G) (ModuleCat.projective_of_free b) - -theorem fdrep_leftRegular_projective (G : Type) [Group G] [Fintype G] : - Projective (FDRep.of (Representation.leftRegular k G)) := by - apply (forget₂ (FDRep k G) (Rep k G)).projective_of_map_projective - exact rep_leftRegular_projective k G -end FiberFunctorProof - -end OAI +import Mathlib + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory +universe u v +variable (k : Type u) [Field k] + + + +theorem rep_leftRegular_projective (G : Type v) [Group G] : + Projective (Rep.leftRegular k G) := by + let e := Representation.ofMulActionSelfAsModuleEquiv (k := k) (G := G) + let b := (Module.Basis.singleton (PUnit.{1}) (MonoidAlgebra k G)).map e.symm + exact (Rep.toModuleMonoidAlgebra (k := k) (G := G)).projective_of_map_projective + (P := Rep.leftRegular k G) (ModuleCat.projective_of_free b) + +theorem fdrep_leftRegular_projective (G : Type) [Group G] [Fintype G] : + Projective (FDRep.of (Representation.leftRegular k G)) := by + apply (forget₂ (FDRep k G) (Rep k G)).projective_of_map_projective + exact rep_leftRegular_projective k G +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/RationalHomWeights.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/RationalHomWeights.lean index d6d02e344a4364a5a03b8be9065f1b2b032b403b..62eb53fcbc2cfb77af6bb272fba20747a126abea 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/RationalHomWeights.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/RationalHomWeights.lean @@ -1,65 +1,65 @@ -import OAI.RepresentationTheory.RestrictedTilting.Basic - -namespace OAI - -namespace FiberFunctorProof -open scoped BigOperators -universe u -variable {k : Type u} [Field k] [Infinite k] -variable {V W : Type u} [AddCommGroup V] [Module k V] [Module.Finite k V] - [AddCommGroup W] [Module k W] [Module.Finite k W] - -omit [Infinite k] in -lemma IsRational.linHom (ρ : Representation k (SL2 k) V) - (σ : Representation k (SL2 k) W) (hρ : IsRational k ρ) (hσ : IsRational k σ) : - IsRational k (Representation.linHom ρ σ) := by - let e := Representation.Equiv.dualTensorHom ρ σ - exact IsRational.of_surjective k _ _ e.toLinearMap e.toLinearEquiv.surjective - (fun g x => congrArg (fun t => t x) (e.isIntertwining' g)) - (IsRational.tensor k _ _ (IsRational.dual k ρ hρ) hσ) - -omit [Infinite k] [Module.Finite k V] [Module.Finite k W] in -lemma linHom_weight_apply (ρ : Representation k (SL2 k) V) - (σ : Representation k (SL2 k) W) (n m : ℤ) (f : V →ₗ[k] W) (v : V) - (hf : ∀ a, (Representation.linHom ρ σ) (diagonalTorus k a) f = - integerCharacter k n a • f) - (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k m a • v) : - ∀ a, σ (diagonalTorus k a) (f v) = integerCharacter k (n+m) a • f v := by - intro a - have h := congrArg (fun q : V →ₗ[k] W => q (ρ (diagonalTorus k a) v)) (hf a) - simp only [Representation.linHom_apply, LinearMap.comp_apply] at h - rw [Representation.inv_self_apply] at h - have hh : integerCharacter k (n+m) a = - integerCharacter k n a * integerCharacter k m a := by - simp [integerCharacter, zpow_add] - simpa only [LinearMap.smul_apply, hv, map_smul, smul_smul, hh, mul_comm] using h - - -omit [Module.Finite k W] in -lemma hasWeightsBetween_linHom (ρ : Representation k (SL2 k) V) - (σ : Representation k (SL2 k) W) (hρ : IsRational k ρ) (a b : ℕ) - (hA : HasWeightsBetween ρ (-(a : ℤ)) a) - (hB : HasWeightsBetween σ (-(b : ℤ)) b) : - HasWeightsBetween (Representation.linHom ρ σ) (-(a+b : ℤ)) (a+b) := by - intro n f hn hf - have hvanish (m : ℤ) (v : V) - (hv : ∀ t, ρ (diagonalTorus k t) v = integerCharacter k m t • v) : f v = 0 := by - by_cases hz : v = 0 - · simp [hz] - have hm : -(a : ℤ) ≤ m ∧ m ≤ a := by - constructor <;> by_contra hh <;> apply hz - · exact hA m v (Or.inl (by omega)) hv - · exact hA m v (Or.inr (by omega)) hv - apply hB (n+m) (f v) (by omega) - exact linHom_weight_apply ρ σ n m f v hf hv - ext v - obtain ⟨c,hc⟩ := rational_torus_integerExpansions k ρ hρ v - have hs : v = ∑ n ∈ c.support, c n := by - simpa [Finsupp.sum, integerCharacter] using hc 1 - rw [hs, map_sum] - apply Finset.sum_eq_zero - intro m hm - exact hvanish m (c m) (integer_coefficient_eigen k ρ v c hc m) -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.Basic + +namespace OAI + +namespace FiberFunctorProof +open scoped BigOperators +universe u +variable {k : Type u} [Field k] [Infinite k] +variable {V W : Type u} [AddCommGroup V] [Module k V] [Module.Finite k V] + [AddCommGroup W] [Module k W] [Module.Finite k W] + +omit [Infinite k] in +lemma IsRational.linHom (ρ : Representation k (SL2 k) V) + (σ : Representation k (SL2 k) W) (hρ : IsRational k ρ) (hσ : IsRational k σ) : + IsRational k (Representation.linHom ρ σ) := by + let e := Representation.Equiv.dualTensorHom ρ σ + exact IsRational.of_surjective k _ _ e.toLinearMap e.toLinearEquiv.surjective + (fun g x => congrArg (fun t => t x) (e.isIntertwining' g)) + (IsRational.tensor k _ _ (IsRational.dual k ρ hρ) hσ) + +omit [Infinite k] [Module.Finite k V] [Module.Finite k W] in +lemma linHom_weight_apply (ρ : Representation k (SL2 k) V) + (σ : Representation k (SL2 k) W) (n m : ℤ) (f : V →ₗ[k] W) (v : V) + (hf : ∀ a, (Representation.linHom ρ σ) (diagonalTorus k a) f = + integerCharacter k n a • f) + (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k m a • v) : + ∀ a, σ (diagonalTorus k a) (f v) = integerCharacter k (n+m) a • f v := by + intro a + have h := congrArg (fun q : V →ₗ[k] W => q (ρ (diagonalTorus k a) v)) (hf a) + simp only [Representation.linHom_apply, LinearMap.comp_apply] at h + rw [Representation.inv_self_apply] at h + have hh : integerCharacter k (n+m) a = + integerCharacter k n a * integerCharacter k m a := by + simp [integerCharacter, zpow_add] + simpa only [LinearMap.smul_apply, hv, map_smul, smul_smul, hh, mul_comm] using h + + +omit [Module.Finite k W] in +lemma hasWeightsBetween_linHom (ρ : Representation k (SL2 k) V) + (σ : Representation k (SL2 k) W) (hρ : IsRational k ρ) (a b : ℕ) + (hA : HasWeightsBetween ρ (-(a : ℤ)) a) + (hB : HasWeightsBetween σ (-(b : ℤ)) b) : + HasWeightsBetween (Representation.linHom ρ σ) (-(a+b : ℤ)) (a+b) := by + intro n f hn hf + have hvanish (m : ℤ) (v : V) + (hv : ∀ t, ρ (diagonalTorus k t) v = integerCharacter k m t • v) : f v = 0 := by + by_cases hz : v = 0 + · simp [hz] + have hm : -(a : ℤ) ≤ m ∧ m ≤ a := by + constructor <;> by_contra hh <;> apply hz + · exact hA m v (Or.inl (by omega)) hv + · exact hA m v (Or.inr (by omega)) hv + apply hB (n+m) (f v) (by omega) + exact linHom_weight_apply ρ σ n m f v hf hv + ext v + obtain ⟨c,hc⟩ := rational_torus_integerExpansions k ρ hρ v + have hs : v = ∑ n ∈ c.support, c n := by + simpa [Finsupp.sum, integerCharacter] using hc 1 + rw [hs, map_sum] + apply Finset.sum_eq_zero + intro m hm + exact hvanish m (c m) (integer_coefficient_eigen k ρ v c hc m) +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/RationalMatrices.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/RationalMatrices.lean index d2b05f7f67511a6d5eafa6885bb5bf9a74005df3..4b3119cd4e20e103abb5d44273079f7c05995b5d 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/RationalMatrices.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/RationalMatrices.lean @@ -1,79 +1,79 @@ -import OAI.RepresentationTheory.RestrictedTilting.Basic - -namespace OAI - -namespace FiberFunctorProof -open scoped LaurentPolynomial BigOperators -universe u -variable (k : Type u) [Field k] -variable {ι : Type u} [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (SL2 k) (ι → k)) (hρ : IsRational k ρ) - -noncomputable def rationalCoefficient (i j : ι) : MvPolynomial (Fin 2 × Fin 2) k := - (hρ (Pi.single j 1) (LinearMap.proj i)).choose - -lemma eval_rationalCoefficient (g : SL2 k) (i j : ι) : - MvPolynomial.eval (fun ij => g ij.1 ij.2) (rationalCoefficient k ρ hρ i j) = - LinearMap.toMatrix' (ρ g) i j := by - exact ((hρ (Pi.single j 1) (LinearMap.proj i)).choose_spec g).symm - -noncomputable def unipotentPolynomialCoordinates (ij : Fin 2 × Fin 2) : Polynomial k := - if ij.1 = ij.2 then 1 else if ij = (0,1) then Polynomial.X else 0 - -noncomputable def torusLaurentCoordinates (ij : Fin 2 × Fin 2) : LaurentPolynomial k := - if ij = (0,0) then LaurentPolynomial.T 1 else - if ij = (1,1) then LaurentPolynomial.T (-1) else 0 - -noncomputable def rationalUnipotentMatrix : Matrix ι ι (Polynomial k) := fun i j => - MvPolynomial.eval₂ Polynomial.C (unipotentPolynomialCoordinates k) - (rationalCoefficient k ρ hρ i j) - -noncomputable def rationalTorusMatrix : Matrix ι ι (LaurentPolynomial k) := fun i j => - MvPolynomial.eval₂ LaurentPolynomial.C (torusLaurentCoordinates k) - (rationalCoefficient k ρ hρ i j) - -lemma eval_unipotentPolynomialCoordinates (t : k) (ij : Fin 2 × Fin 2) : - (unipotentPolynomialCoordinates k ij).eval t = unipotent k t ij.1 ij.2 := by - obtain ⟨i,j⟩ := ij - fin_cases i <;> fin_cases j <;> simp [unipotentPolynomialCoordinates, unipotent] - -lemma eval_torusLaurentCoordinates (a : kˣ) (ij : Fin 2 × Fin 2) : - LaurentPolynomial.eval₂ (RingHom.id k) a (torusLaurentCoordinates k ij) = - diagonalTorus k a ij.1 ij.2 := by - change _ = (!![(a : k), 0; 0, (↑a⁻¹ : k)] : Matrix (Fin 2) (Fin 2) k) ij.1 ij.2 - obtain ⟨i,j⟩ := ij - fin_cases i <;> fin_cases j <;> - simp [torusLaurentCoordinates, LaurentPolynomial.eval₂_T] - -lemma eval_rationalUnipotentMatrix (t : k) : - (rationalUnipotentMatrix k ρ hρ).map (Polynomial.evalRingHom t) = - LinearMap.toMatrix' (ρ (unipotent k t)) := by - ext i j - change Polynomial.eval t (MvPolynomial.eval₂ _ _ _) = _ - have hcomp : (Polynomial.evalRingHom t).comp - (MvPolynomial.eval₂Hom Polynomial.C (unipotentPolynomialCoordinates k)) = - MvPolynomial.eval (fun ij => unipotent k t ij.1 ij.2) := by - apply MvPolynomial.ringHom_ext - · intro c; simp - · intro ij; simpa using eval_unipotentPolynomialCoordinates k t ij - have he := congrArg (fun f : MvPolynomial (Fin 2 × Fin 2) k →+* k => - f (rationalCoefficient k ρ hρ i j)) hcomp - exact he.trans (eval_rationalCoefficient k ρ hρ _ i j) - -lemma eval_rationalTorusMatrix (a : kˣ) : - (rationalTorusMatrix k ρ hρ).map (LaurentPolynomial.eval₂ (RingHom.id k) a) = - LinearMap.toMatrix' (ρ (diagonalTorus k a)) := by - ext i j - change LaurentPolynomial.eval₂ (RingHom.id k) a (MvPolynomial.eval₂ _ _ _) = _ - have hcomp : (LaurentPolynomial.eval₂ (RingHom.id k) a).comp - (MvPolynomial.eval₂Hom LaurentPolynomial.C (torusLaurentCoordinates k)) = - MvPolynomial.eval (fun ij => diagonalTorus k a ij.1 ij.2) := by - apply MvPolynomial.ringHom_ext - · intro c; simp [LaurentPolynomial.eval₂_C] - · intro ij; simpa using eval_torusLaurentCoordinates k a ij - have he := congrArg (fun f : MvPolynomial (Fin 2 × Fin 2) k →+* k => - f (rationalCoefficient k ρ hρ i j)) hcomp - exact he.trans (eval_rationalCoefficient k ρ hρ _ i j) -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.Basic + +namespace OAI + +namespace FiberFunctorProof +open scoped LaurentPolynomial BigOperators +universe u +variable (k : Type u) [Field k] +variable {ι : Type u} [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (SL2 k) (ι → k)) (hρ : IsRational k ρ) + +noncomputable def rationalCoefficient (i j : ι) : MvPolynomial (Fin 2 × Fin 2) k := + (hρ (Pi.single j 1) (LinearMap.proj i)).choose + +lemma eval_rationalCoefficient (g : SL2 k) (i j : ι) : + MvPolynomial.eval (fun ij => g ij.1 ij.2) (rationalCoefficient k ρ hρ i j) = + LinearMap.toMatrix' (ρ g) i j := by + exact ((hρ (Pi.single j 1) (LinearMap.proj i)).choose_spec g).symm + +noncomputable def unipotentPolynomialCoordinates (ij : Fin 2 × Fin 2) : Polynomial k := + if ij.1 = ij.2 then 1 else if ij = (0,1) then Polynomial.X else 0 + +noncomputable def torusLaurentCoordinates (ij : Fin 2 × Fin 2) : LaurentPolynomial k := + if ij = (0,0) then LaurentPolynomial.T 1 else + if ij = (1,1) then LaurentPolynomial.T (-1) else 0 + +noncomputable def rationalUnipotentMatrix : Matrix ι ι (Polynomial k) := fun i j => + MvPolynomial.eval₂ Polynomial.C (unipotentPolynomialCoordinates k) + (rationalCoefficient k ρ hρ i j) + +noncomputable def rationalTorusMatrix : Matrix ι ι (LaurentPolynomial k) := fun i j => + MvPolynomial.eval₂ LaurentPolynomial.C (torusLaurentCoordinates k) + (rationalCoefficient k ρ hρ i j) + +lemma eval_unipotentPolynomialCoordinates (t : k) (ij : Fin 2 × Fin 2) : + (unipotentPolynomialCoordinates k ij).eval t = unipotent k t ij.1 ij.2 := by + obtain ⟨i,j⟩ := ij + fin_cases i <;> fin_cases j <;> simp [unipotentPolynomialCoordinates, unipotent] + +lemma eval_torusLaurentCoordinates (a : kˣ) (ij : Fin 2 × Fin 2) : + LaurentPolynomial.eval₂ (RingHom.id k) a (torusLaurentCoordinates k ij) = + diagonalTorus k a ij.1 ij.2 := by + change _ = (!![(a : k), 0; 0, (↑a⁻¹ : k)] : Matrix (Fin 2) (Fin 2) k) ij.1 ij.2 + obtain ⟨i,j⟩ := ij + fin_cases i <;> fin_cases j <;> + simp [torusLaurentCoordinates, LaurentPolynomial.eval₂_T] + +lemma eval_rationalUnipotentMatrix (t : k) : + (rationalUnipotentMatrix k ρ hρ).map (Polynomial.evalRingHom t) = + LinearMap.toMatrix' (ρ (unipotent k t)) := by + ext i j + change Polynomial.eval t (MvPolynomial.eval₂ _ _ _) = _ + have hcomp : (Polynomial.evalRingHom t).comp + (MvPolynomial.eval₂Hom Polynomial.C (unipotentPolynomialCoordinates k)) = + MvPolynomial.eval (fun ij => unipotent k t ij.1 ij.2) := by + apply MvPolynomial.ringHom_ext + · intro c; simp + · intro ij; simpa using eval_unipotentPolynomialCoordinates k t ij + have he := congrArg (fun f : MvPolynomial (Fin 2 × Fin 2) k →+* k => + f (rationalCoefficient k ρ hρ i j)) hcomp + exact he.trans (eval_rationalCoefficient k ρ hρ _ i j) + +lemma eval_rationalTorusMatrix (a : kˣ) : + (rationalTorusMatrix k ρ hρ).map (LaurentPolynomial.eval₂ (RingHom.id k) a) = + LinearMap.toMatrix' (ρ (diagonalTorus k a)) := by + ext i j + change LaurentPolynomial.eval₂ (RingHom.id k) a (MvPolynomial.eval₂ _ _ _) = _ + have hcomp : (LaurentPolynomial.eval₂ (RingHom.id k) a).comp + (MvPolynomial.eval₂Hom LaurentPolynomial.C (torusLaurentCoordinates k)) = + MvPolynomial.eval (fun ij => diagonalTorus k a ij.1 ij.2) := by + apply MvPolynomial.ringHom_ext + · intro c; simp [LaurentPolynomial.eval₂_C] + · intro ij; simpa using eval_torusLaurentCoordinates k a ij + have he := congrArg (fun f : MvPolynomial (Fin 2 × Fin 2) k →+* k => + f (rationalCoefficient k ρ hρ i j)) hcomp + exact he.trans (eval_rationalCoefficient k ρ hρ _ i j) +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/RegularActions.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/RegularActions.lean index 059259aec0281da44b10cf930c9bf90fa8261e74..ccbebc62246c8dd399e19e13046738af4686bdce 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/RegularActions.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/RegularActions.lean @@ -1,311 +1,311 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.DualSplitting - -namespace OAI - -/-! Polynomial coordinate representations and associated sections. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section -universe u -variable (k : Type u) [Field k] -open scoped Matrix Kronecker - -noncomputable def leftCoordinateMatrix : SL2 k →* Matrix (Fin 2 × Fin 2) (Fin 2 × Fin 2) k where - toFun g := (dualMatrix k g) ⊗ₖ (1 : Matrix (Fin 2) (Fin 2) k) - map_one' := by rw [map_one, Matrix.one_kronecker_one] - map_mul' g h := by rw [map_mul, ← Matrix.mul_kronecker_mul, one_mul] - -noncomputable def coordinatePolynomialRepresentation : - Representation k (SL2 k) (MvPolynomial (Fin 2 × Fin 2) k) where - toFun g := (linearChange (leftCoordinateMatrix k g)).toLinearMap - map_one' := by rw [map_one, linearChange_one]; rfl - map_mul' g h := by rw [map_mul, linearChange_mul]; rfl - -lemma coordinatePolynomial_rational : IsRational k (coordinatePolynomialRepresentation k) := by - intro v l - apply regular_linearChange_coeff k - (fun g : SL2 k => fun ij : Fin 2 × Fin 2 => g ij.1 ij.2) - (leftCoordinateMatrix k) _ v l - intro a b - refine ⟨inverseCoordinatePolynomial k (b.1,a.1) * - MvPolynomial.C ((1 : Matrix (Fin 2) (Fin 2) k) a.2 b.2), fun g => ?_⟩ - change (g⁻¹ : SL2 k) b.1 a.1 * (1 : Matrix (Fin 2) (Fin 2) k) a.2 b.2 = _ - rw [MvPolynomial.eval_mul, MvPolynomial.eval_C, eval_inverseCoordinatePolynomial] - -noncomputable def coordinateEvaluation : - MvPolynomial (Fin 2 × Fin 2) k →ₐ[k] (SL2 k → k) := - MvPolynomial.aeval (fun ij => fun g : SL2 k => g ij.1 ij.2) - -lemma coordinateEvaluation_apply (P : MvPolynomial (Fin 2 × Fin 2) k) (g : SL2 k) : - coordinateEvaluation k P g = MvPolynomial.eval (fun ij => g ij.1 ij.2) P := by - induction P using MvPolynomial.induction_on with - | C c => simp [coordinateEvaluation] - | add P Q hp hq => simp only [map_add, Pi.add_apply, hp, hq] - | mul_X P i hp => - simp only [map_mul, Pi.mul_apply, hp] - congr 1 - simp [coordinateEvaluation] - -lemma coordinatePolynomial_evaluation (g h : SL2 k) - (P : MvPolynomial (Fin 2 × Fin 2) k) : - coordinateEvaluation k (coordinatePolynomialRepresentation k g P) h = - coordinateEvaluation k P (g⁻¹ * h) := by - rw [coordinateEvaluation_apply, coordinateEvaluation_apply] - change MvPolynomial.eval _ (linearChange (leftCoordinateMatrix k g) P) = _ - rw [eval_linearChange] - apply congrArg (fun z => MvPolynomial.eval z P) - funext i - change (∑ j : Fin 2 × Fin 2, (g⁻¹ : SL2 k) i.1 j.1 * - (1 : Matrix (Fin 2) (Fin 2) k) j.2 i.2 * h j.1 j.2) = _ - simp [Fintype.sum_prod_type, Matrix.one_apply, Matrix.mul_apply] - - - -noncomputable def regularSL2Functions : Subalgebra k (SL2 k → k) := - (coordinateEvaluation k).range - -noncomputable def regularSL2Representation : - Representation k (SL2 k) (regularSL2Functions k) where - toFun g := - { toFun := fun f => ⟨fun h => f.val (g⁻¹ * h), by - obtain ⟨P,hP⟩ := f.property - refine ⟨coordinatePolynomialRepresentation k g P, ?_⟩ - ext h - change coordinateEvaluation k (coordinatePolynomialRepresentation k g P) h = _ - rw [coordinatePolynomial_evaluation] - exact congrArg (fun f : SL2 k → k => f (g⁻¹ * h)) hP⟩ - map_add' := by intro f f'; rfl - map_smul' := by intro a f; rfl } - map_one' := by ext f h; simp - map_mul' := by intro g h; ext f a; simp [mul_assoc] - -noncomputable def coordinateToRegular : - MvPolynomial (Fin 2 × Fin 2) k →ₗ[k] regularSL2Functions k := - (coordinateEvaluation k).rangeRestrict.toLinearMap - -lemma coordinateToRegular_surjective : Function.Surjective (coordinateToRegular k) := by - intro f - obtain ⟨P,hP⟩ := f.property - exact ⟨P, Subtype.ext hP⟩ - -lemma regularSL2_rational : IsRational k (regularSL2Representation k) := by - apply IsRational.of_surjective k (coordinatePolynomialRepresentation k) - (regularSL2Representation k) (coordinateToRegular k) (coordinateToRegular_surjective k) - _ (coordinatePolynomial_rational k) - intro g P - apply Subtype.ext - funext h - exact coordinatePolynomial_evaluation k g h P - - - -noncomputable def regularVectorRepresentation (ι : Type u) : - Representation k (SL2 k) (ι → regularSL2Functions k) where - toFun g := - { toFun := fun f i => regularSL2Representation k g (f i) - map_add' := by intro f f'; funext i; exact map_add (regularSL2Representation k g) _ _ - map_smul' := by intro a f; funext i; exact map_smul (regularSL2Representation k g) _ _ } - map_one' := by - apply LinearMap.ext - intro f - funext i - exact congrArg (fun a : Module.End k (regularSL2Functions k) => a (f i)) - (map_one (regularSL2Representation k)) - map_mul' := by - intro g h - apply LinearMap.ext - intro f - funext i - exact congrArg (fun a : Module.End k (regularSL2Functions k) => a (f i)) - (map_mul (regularSL2Representation k) g h) - -lemma regularVector_rational (ι : Type u) [Fintype ι] [DecidableEq ι] : - IsRational k (regularVectorRepresentation k ι) := by - intro v l - let ei (i : ι) : regularSL2Functions k →ₗ[k] (ι → regularSL2Functions k) := - LinearMap.single k (fun _ : ι => regularSL2Functions k) i - have hsum (w : ι → regularSL2Functions k) : ∑ i, ei i (w i) = w := by - ext i - simp [ei] - choose P hP using fun i => regularSL2_rational k (v i) (l.comp (ei i)) - refine ⟨∑ i, P i, fun g => ?_⟩ - rw [← hsum (regularVectorRepresentation k ι g v), map_sum, MvPolynomial.eval_sum] - apply Finset.sum_congr rfl - intro i _ - exact hP i g - -end - -universe u -variable (k : Type u) [Field k] -variable (ι : Type u) [Fintype ι] [DecidableEq ι] - -noncomputable def regularVectorEvaluation (g : SL2 k) : - (ι → regularSL2Functions k) →ₗ[k] (ι → k) where - toFun f i := (f i).val g - map_add' := by intro f h; rfl - map_smul' := by intro a f; rfl - -variable (ρ : Representation k (Multiplicative k) (ι → k)) - - - -noncomputable def associatedSectionsSubmodule : - Submodule k (ι → regularSL2Functions k) where - carrier := {f | ∀ (g : SL2 k) (t : k), - regularVectorEvaluation k ι (g * unipotent k t) f = - ρ (Multiplicative.ofAdd (-t)) (regularVectorEvaluation k ι g f)} - zero_mem' := by intro g t; simp - add_mem' := by - intro f h hf hh g t - rw [map_add, hf, hh, map_add, map_add] - smul_mem' := by - intro a f hf g t - rw [map_smul, hf, map_smul, map_smul] - -noncomputable def associatedSectionsSubrepresentation : - Subrepresentation (regularVectorRepresentation k ι) where - toSubmodule := associatedSectionsSubmodule k ι ρ - apply_mem_toSubmodule g f hf := by - intro h t - change regularVectorEvaluation k ι (g⁻¹ * (h * unipotent k t)) f = - ρ (Multiplicative.ofAdd (-t)) (regularVectorEvaluation k ι (g⁻¹ * h) f) - rw [← mul_assoc] - exact hf (g⁻¹ * h) t - -noncomputable def associatedSectionsRepresentation : - Representation k (SL2 k) (associatedSectionsSubmodule k ι ρ) := - (associatedSectionsSubrepresentation k ι ρ).toRepresentation - -lemma associatedSections_rational : IsRational k - (M := associatedSectionsSubmodule k ι ρ) (associatedSectionsRepresentation k ι ρ) := by - exact IsRational.of_injective k (M := associatedSectionsSubmodule k ι ρ) - (N := ι → regularSL2Functions k) (associatedSectionsRepresentation k ι ρ) - (regularVectorRepresentation k ι) (associatedSectionsSubmodule k ι ρ).subtype - (associatedSectionsSubmodule k ι ρ).injective_subtype (fun _ _ => rfl) - (regularVector_rational k ι) - -noncomputable def regularFirstColumn (i : Fin 2) : regularSL2Functions k := - coordinateToRegular k (MvPolynomial.X (i,0)) - -lemma regularFirstColumn_apply (i : Fin 2) (g : SL2 k) : - (regularFirstColumn k i).val g = g i 0 := by - change coordinateEvaluation k (MvPolynomial.X (i,0)) g = _ - rw [coordinateEvaluation_apply, MvPolynomial.eval_X] - -lemma firstColumn_unipotent_mul (g : SL2 k) (t : k) (i : Fin 2) : - (g * unipotent k t) i 0 = g i 0 := by - change (((g : Matrix (Fin 2) (Fin 2) k) * - (unipotent k t : Matrix (Fin 2) (Fin 2) k)) i 0) = _ - simp [Matrix.mul_apply, Fin.sum_univ_two, unipotent] - -noncomputable def regularVectorCoordinateMul (i : Fin 2) : - (ι → regularSL2Functions k) →ₗ[k] (ι → regularSL2Functions k) where - toFun f j := regularFirstColumn k i * f j - map_add' := by intro f h; funext j; exact mul_add _ _ _ - map_smul' := by intro a f; funext j; exact mul_smul_comm a (regularFirstColumn k i) (f j) - -omit [Fintype ι] [DecidableEq ι] in -lemma regularVectorCoordinateMul_evaluation (i : Fin 2) - (f : ι → regularSL2Functions k) (g : SL2 k) : - regularVectorEvaluation k ι g (regularVectorCoordinateMul k ι i f) = - g i 0 • regularVectorEvaluation k ι g f := by - funext j - change (regularFirstColumn k i).val g * (f j).val g = _ - rw [regularFirstColumn_apply] - rfl - -omit [Fintype ι] [DecidableEq ι] in -lemma associatedSections_coordinate_mul_mem (i : Fin 2) - (f : ι → regularSL2Functions k) (hf : f ∈ associatedSectionsSubmodule k ι ρ) : - regularVectorCoordinateMul k ι i f ∈ associatedSectionsSubmodule k ι ρ := by - intro g t - rw [regularVectorCoordinateMul_evaluation, regularVectorCoordinateMul_evaluation, - firstColumn_unipotent_mul, hf, map_smul] - -noncomputable def associatedCoordinateMul (i : Fin 2) : - (associatedSectionsSubmodule k ι ρ) →ₗ[k] (associatedSectionsSubmodule k ι ρ) := - (regularVectorCoordinateMul k ι i).restrict - (associatedSections_coordinate_mul_mem k ι ρ i) - -omit [Fintype ι] [DecidableEq ι] in - - -lemma associatedCoordinateMul_action (g : SL2 k) (i : Fin 2) - (f : associatedSectionsSubmodule k ι ρ) : - associatedSectionsRepresentation k ι ρ g (associatedCoordinateMul k ι ρ i f) = - ∑ j : Fin 2, (g⁻¹ : SL2 k) i j • - associatedCoordinateMul k ι ρ j (associatedSectionsRepresentation k ι ρ g f) := by - rw [Fin.sum_univ_two] - apply Subtype.ext - funext a - apply Subtype.ext - funext h - change (regularFirstColumn k i).val (g⁻¹ * h) * (f.val a).val (g⁻¹ * h) = - (g⁻¹ : SL2 k) i 0 * ((regularFirstColumn k 0).val h * (f.val a).val (g⁻¹ * h)) + - (g⁻¹ : SL2 k) i 1 * ((regularFirstColumn k 1).val h * (f.val a).val (g⁻¹ * h)) - rw [regularFirstColumn_apply, regularFirstColumn_apply, regularFirstColumn_apply] - change (((g⁻¹ : SL2 k) : Matrix (Fin 2) (Fin 2) k) * - (h : Matrix (Fin 2) (Fin 2) k)) i 0 * _ = _ - simp only [Matrix.mul_apply, Fin.sum_univ_two] - ring - - -noncomputable def associatedOriginRelations : Submodule k (associatedSectionsSubmodule k ι ρ) := - LinearMap.range (associatedCoordinateMul k ι ρ 0) ⊔ - LinearMap.range (associatedCoordinateMul k ι ρ 1) - -omit [Fintype ι] [DecidableEq ι] in -lemma associatedOriginRelations_stable (g : SL2 k) : - associatedOriginRelations k ι ρ ≤ - (associatedOriginRelations k ι ρ).comap (associatedSectionsRepresentation k ι ρ g) := by - have hcoord (i : Fin 2) (f : associatedSectionsSubmodule k ι ρ) : - associatedSectionsRepresentation k ι ρ g (associatedCoordinateMul k ι ρ i f) ∈ - associatedOriginRelations k ι ρ := by - rw [associatedCoordinateMul_action] - apply Submodule.sum_mem - intro j _ - apply Submodule.smul_mem - fin_cases j - · exact Submodule.mem_sup_left ⟨_,rfl⟩ - · exact Submodule.mem_sup_right ⟨_,rfl⟩ - apply sup_le - · rintro _ ⟨f,rfl⟩ - exact hcoord 0 f - · rintro _ ⟨f,rfl⟩ - exact hcoord 1 f - -noncomputable def quotientRationalModule {V : Type u} [AddCommGroup V] [Module k V] - (σ : Representation k (SL2 k) V) (P : Submodule k V) - (hP : ∀ g, P ≤ P.comap (σ g)) : Rep k (SL2 k) := - Rep.of (Representation.quotient σ P hP) - -omit [Fintype ι] [DecidableEq ι] in -lemma quotientRationalModule_rational {V : Type u} [AddCommGroup V] [Module k V] - (σ : Representation k (SL2 k) V) (P : Submodule k V) - (hP : ∀ g, P ≤ P.comap (σ g)) (hσ : IsRational k σ) : - IsRational k (quotientRationalModule k σ P hP).ρ := by - exact IsRational.of_surjective k (M := V) (N := V ⧸ P) - σ (Representation.quotient σ P hP) P.mkQ P.mkQ_surjective (fun _ _ => rfl) hσ - - -noncomputable def associatedOriginRep : Rep k (SL2 k) := - quotientRationalModule k (V := associatedSectionsSubmodule k ι ρ) - (associatedSectionsRepresentation k ι ρ) (associatedOriginRelations k ι ρ) - (associatedOriginRelations_stable k ι ρ) - - - -lemma associatedOrigin_rational : IsRational k (associatedOriginRep k ι ρ).ρ := by - exact quotientRationalModule_rational k _ _ _ (associatedSections_rational k ι ρ) - -end FiberFunctorProof - -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.DualSplitting + +namespace OAI + +/-! Polynomial coordinate representations and associated sections. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section +universe u +variable (k : Type u) [Field k] +open scoped Matrix Kronecker + +noncomputable def leftCoordinateMatrix : SL2 k →* Matrix (Fin 2 × Fin 2) (Fin 2 × Fin 2) k where + toFun g := (dualMatrix k g) ⊗ₖ (1 : Matrix (Fin 2) (Fin 2) k) + map_one' := by rw [map_one, Matrix.one_kronecker_one] + map_mul' g h := by rw [map_mul, ← Matrix.mul_kronecker_mul, one_mul] + +noncomputable def coordinatePolynomialRepresentation : + Representation k (SL2 k) (MvPolynomial (Fin 2 × Fin 2) k) where + toFun g := (linearChange (leftCoordinateMatrix k g)).toLinearMap + map_one' := by rw [map_one, linearChange_one]; rfl + map_mul' g h := by rw [map_mul, linearChange_mul]; rfl + +lemma coordinatePolynomial_rational : IsRational k (coordinatePolynomialRepresentation k) := by + intro v l + apply regular_linearChange_coeff k + (fun g : SL2 k => fun ij : Fin 2 × Fin 2 => g ij.1 ij.2) + (leftCoordinateMatrix k) _ v l + intro a b + refine ⟨inverseCoordinatePolynomial k (b.1,a.1) * + MvPolynomial.C ((1 : Matrix (Fin 2) (Fin 2) k) a.2 b.2), fun g => ?_⟩ + change (g⁻¹ : SL2 k) b.1 a.1 * (1 : Matrix (Fin 2) (Fin 2) k) a.2 b.2 = _ + rw [MvPolynomial.eval_mul, MvPolynomial.eval_C, eval_inverseCoordinatePolynomial] + +noncomputable def coordinateEvaluation : + MvPolynomial (Fin 2 × Fin 2) k →ₐ[k] (SL2 k → k) := + MvPolynomial.aeval (fun ij => fun g : SL2 k => g ij.1 ij.2) + +lemma coordinateEvaluation_apply (P : MvPolynomial (Fin 2 × Fin 2) k) (g : SL2 k) : + coordinateEvaluation k P g = MvPolynomial.eval (fun ij => g ij.1 ij.2) P := by + induction P using MvPolynomial.induction_on with + | C c => simp [coordinateEvaluation] + | add P Q hp hq => simp only [map_add, Pi.add_apply, hp, hq] + | mul_X P i hp => + simp only [map_mul, Pi.mul_apply, hp] + congr 1 + simp [coordinateEvaluation] + +lemma coordinatePolynomial_evaluation (g h : SL2 k) + (P : MvPolynomial (Fin 2 × Fin 2) k) : + coordinateEvaluation k (coordinatePolynomialRepresentation k g P) h = + coordinateEvaluation k P (g⁻¹ * h) := by + rw [coordinateEvaluation_apply, coordinateEvaluation_apply] + change MvPolynomial.eval _ (linearChange (leftCoordinateMatrix k g) P) = _ + rw [eval_linearChange] + apply congrArg (fun z => MvPolynomial.eval z P) + funext i + change (∑ j : Fin 2 × Fin 2, (g⁻¹ : SL2 k) i.1 j.1 * + (1 : Matrix (Fin 2) (Fin 2) k) j.2 i.2 * h j.1 j.2) = _ + simp [Fintype.sum_prod_type, Matrix.one_apply, Matrix.mul_apply] + + + +noncomputable def regularSL2Functions : Subalgebra k (SL2 k → k) := + (coordinateEvaluation k).range + +noncomputable def regularSL2Representation : + Representation k (SL2 k) (regularSL2Functions k) where + toFun g := + { toFun := fun f => ⟨fun h => f.val (g⁻¹ * h), by + obtain ⟨P,hP⟩ := f.property + refine ⟨coordinatePolynomialRepresentation k g P, ?_⟩ + ext h + change coordinateEvaluation k (coordinatePolynomialRepresentation k g P) h = _ + rw [coordinatePolynomial_evaluation] + exact congrArg (fun f : SL2 k → k => f (g⁻¹ * h)) hP⟩ + map_add' := by intro f f'; rfl + map_smul' := by intro a f; rfl } + map_one' := by ext f h; simp + map_mul' := by intro g h; ext f a; simp [mul_assoc] + +noncomputable def coordinateToRegular : + MvPolynomial (Fin 2 × Fin 2) k →ₗ[k] regularSL2Functions k := + (coordinateEvaluation k).rangeRestrict.toLinearMap + +lemma coordinateToRegular_surjective : Function.Surjective (coordinateToRegular k) := by + intro f + obtain ⟨P,hP⟩ := f.property + exact ⟨P, Subtype.ext hP⟩ + +lemma regularSL2_rational : IsRational k (regularSL2Representation k) := by + apply IsRational.of_surjective k (coordinatePolynomialRepresentation k) + (regularSL2Representation k) (coordinateToRegular k) (coordinateToRegular_surjective k) + _ (coordinatePolynomial_rational k) + intro g P + apply Subtype.ext + funext h + exact coordinatePolynomial_evaluation k g h P + + + +noncomputable def regularVectorRepresentation (ι : Type u) : + Representation k (SL2 k) (ι → regularSL2Functions k) where + toFun g := + { toFun := fun f i => regularSL2Representation k g (f i) + map_add' := by intro f f'; funext i; exact map_add (regularSL2Representation k g) _ _ + map_smul' := by intro a f; funext i; exact map_smul (regularSL2Representation k g) _ _ } + map_one' := by + apply LinearMap.ext + intro f + funext i + exact congrArg (fun a : Module.End k (regularSL2Functions k) => a (f i)) + (map_one (regularSL2Representation k)) + map_mul' := by + intro g h + apply LinearMap.ext + intro f + funext i + exact congrArg (fun a : Module.End k (regularSL2Functions k) => a (f i)) + (map_mul (regularSL2Representation k) g h) + +lemma regularVector_rational (ι : Type u) [Fintype ι] [DecidableEq ι] : + IsRational k (regularVectorRepresentation k ι) := by + intro v l + let ei (i : ι) : regularSL2Functions k →ₗ[k] (ι → regularSL2Functions k) := + LinearMap.single k (fun _ : ι => regularSL2Functions k) i + have hsum (w : ι → regularSL2Functions k) : ∑ i, ei i (w i) = w := by + ext i + simp [ei] + choose P hP using fun i => regularSL2_rational k (v i) (l.comp (ei i)) + refine ⟨∑ i, P i, fun g => ?_⟩ + rw [← hsum (regularVectorRepresentation k ι g v), map_sum, MvPolynomial.eval_sum] + apply Finset.sum_congr rfl + intro i _ + exact hP i g + +end + +universe u +variable (k : Type u) [Field k] +variable (ι : Type u) [Fintype ι] [DecidableEq ι] + +noncomputable def regularVectorEvaluation (g : SL2 k) : + (ι → regularSL2Functions k) →ₗ[k] (ι → k) where + toFun f i := (f i).val g + map_add' := by intro f h; rfl + map_smul' := by intro a f; rfl + +variable (ρ : Representation k (Multiplicative k) (ι → k)) + + + +noncomputable def associatedSectionsSubmodule : + Submodule k (ι → regularSL2Functions k) where + carrier := {f | ∀ (g : SL2 k) (t : k), + regularVectorEvaluation k ι (g * unipotent k t) f = + ρ (Multiplicative.ofAdd (-t)) (regularVectorEvaluation k ι g f)} + zero_mem' := by intro g t; simp + add_mem' := by + intro f h hf hh g t + rw [map_add, hf, hh, map_add, map_add] + smul_mem' := by + intro a f hf g t + rw [map_smul, hf, map_smul, map_smul] + +noncomputable def associatedSectionsSubrepresentation : + Subrepresentation (regularVectorRepresentation k ι) where + toSubmodule := associatedSectionsSubmodule k ι ρ + apply_mem_toSubmodule g f hf := by + intro h t + change regularVectorEvaluation k ι (g⁻¹ * (h * unipotent k t)) f = + ρ (Multiplicative.ofAdd (-t)) (regularVectorEvaluation k ι (g⁻¹ * h) f) + rw [← mul_assoc] + exact hf (g⁻¹ * h) t + +noncomputable def associatedSectionsRepresentation : + Representation k (SL2 k) (associatedSectionsSubmodule k ι ρ) := + (associatedSectionsSubrepresentation k ι ρ).toRepresentation + +lemma associatedSections_rational : IsRational k + (M := associatedSectionsSubmodule k ι ρ) (associatedSectionsRepresentation k ι ρ) := by + exact IsRational.of_injective k (M := associatedSectionsSubmodule k ι ρ) + (N := ι → regularSL2Functions k) (associatedSectionsRepresentation k ι ρ) + (regularVectorRepresentation k ι) (associatedSectionsSubmodule k ι ρ).subtype + (associatedSectionsSubmodule k ι ρ).injective_subtype (fun _ _ => rfl) + (regularVector_rational k ι) + +noncomputable def regularFirstColumn (i : Fin 2) : regularSL2Functions k := + coordinateToRegular k (MvPolynomial.X (i,0)) + +lemma regularFirstColumn_apply (i : Fin 2) (g : SL2 k) : + (regularFirstColumn k i).val g = g i 0 := by + change coordinateEvaluation k (MvPolynomial.X (i,0)) g = _ + rw [coordinateEvaluation_apply, MvPolynomial.eval_X] + +lemma firstColumn_unipotent_mul (g : SL2 k) (t : k) (i : Fin 2) : + (g * unipotent k t) i 0 = g i 0 := by + change (((g : Matrix (Fin 2) (Fin 2) k) * + (unipotent k t : Matrix (Fin 2) (Fin 2) k)) i 0) = _ + simp [Matrix.mul_apply, Fin.sum_univ_two, unipotent] + +noncomputable def regularVectorCoordinateMul (i : Fin 2) : + (ι → regularSL2Functions k) →ₗ[k] (ι → regularSL2Functions k) where + toFun f j := regularFirstColumn k i * f j + map_add' := by intro f h; funext j; exact mul_add _ _ _ + map_smul' := by intro a f; funext j; exact mul_smul_comm a (regularFirstColumn k i) (f j) + +omit [Fintype ι] [DecidableEq ι] in +lemma regularVectorCoordinateMul_evaluation (i : Fin 2) + (f : ι → regularSL2Functions k) (g : SL2 k) : + regularVectorEvaluation k ι g (regularVectorCoordinateMul k ι i f) = + g i 0 • regularVectorEvaluation k ι g f := by + funext j + change (regularFirstColumn k i).val g * (f j).val g = _ + rw [regularFirstColumn_apply] + rfl + +omit [Fintype ι] [DecidableEq ι] in +lemma associatedSections_coordinate_mul_mem (i : Fin 2) + (f : ι → regularSL2Functions k) (hf : f ∈ associatedSectionsSubmodule k ι ρ) : + regularVectorCoordinateMul k ι i f ∈ associatedSectionsSubmodule k ι ρ := by + intro g t + rw [regularVectorCoordinateMul_evaluation, regularVectorCoordinateMul_evaluation, + firstColumn_unipotent_mul, hf, map_smul] + +noncomputable def associatedCoordinateMul (i : Fin 2) : + (associatedSectionsSubmodule k ι ρ) →ₗ[k] (associatedSectionsSubmodule k ι ρ) := + (regularVectorCoordinateMul k ι i).restrict + (associatedSections_coordinate_mul_mem k ι ρ i) + +omit [Fintype ι] [DecidableEq ι] in + + +lemma associatedCoordinateMul_action (g : SL2 k) (i : Fin 2) + (f : associatedSectionsSubmodule k ι ρ) : + associatedSectionsRepresentation k ι ρ g (associatedCoordinateMul k ι ρ i f) = + ∑ j : Fin 2, (g⁻¹ : SL2 k) i j • + associatedCoordinateMul k ι ρ j (associatedSectionsRepresentation k ι ρ g f) := by + rw [Fin.sum_univ_two] + apply Subtype.ext + funext a + apply Subtype.ext + funext h + change (regularFirstColumn k i).val (g⁻¹ * h) * (f.val a).val (g⁻¹ * h) = + (g⁻¹ : SL2 k) i 0 * ((regularFirstColumn k 0).val h * (f.val a).val (g⁻¹ * h)) + + (g⁻¹ : SL2 k) i 1 * ((regularFirstColumn k 1).val h * (f.val a).val (g⁻¹ * h)) + rw [regularFirstColumn_apply, regularFirstColumn_apply, regularFirstColumn_apply] + change (((g⁻¹ : SL2 k) : Matrix (Fin 2) (Fin 2) k) * + (h : Matrix (Fin 2) (Fin 2) k)) i 0 * _ = _ + simp only [Matrix.mul_apply, Fin.sum_univ_two] + ring + + +noncomputable def associatedOriginRelations : Submodule k (associatedSectionsSubmodule k ι ρ) := + LinearMap.range (associatedCoordinateMul k ι ρ 0) ⊔ + LinearMap.range (associatedCoordinateMul k ι ρ 1) + +omit [Fintype ι] [DecidableEq ι] in +lemma associatedOriginRelations_stable (g : SL2 k) : + associatedOriginRelations k ι ρ ≤ + (associatedOriginRelations k ι ρ).comap (associatedSectionsRepresentation k ι ρ g) := by + have hcoord (i : Fin 2) (f : associatedSectionsSubmodule k ι ρ) : + associatedSectionsRepresentation k ι ρ g (associatedCoordinateMul k ι ρ i f) ∈ + associatedOriginRelations k ι ρ := by + rw [associatedCoordinateMul_action] + apply Submodule.sum_mem + intro j _ + apply Submodule.smul_mem + fin_cases j + · exact Submodule.mem_sup_left ⟨_,rfl⟩ + · exact Submodule.mem_sup_right ⟨_,rfl⟩ + apply sup_le + · rintro _ ⟨f,rfl⟩ + exact hcoord 0 f + · rintro _ ⟨f,rfl⟩ + exact hcoord 1 f + +noncomputable def quotientRationalModule {V : Type u} [AddCommGroup V] [Module k V] + (σ : Representation k (SL2 k) V) (P : Submodule k V) + (hP : ∀ g, P ≤ P.comap (σ g)) : Rep k (SL2 k) := + Rep.of (Representation.quotient σ P hP) + +omit [Fintype ι] [DecidableEq ι] in +lemma quotientRationalModule_rational {V : Type u} [AddCommGroup V] [Module k V] + (σ : Representation k (SL2 k) V) (P : Submodule k V) + (hP : ∀ g, P ≤ P.comap (σ g)) (hσ : IsRational k σ) : + IsRational k (quotientRationalModule k σ P hP).ρ := by + exact IsRational.of_surjective k (M := V) (N := V ⧸ P) + σ (Representation.quotient σ P hP) P.mkQ P.mkQ_surjective (fun _ _ => rfl) hσ + + +noncomputable def associatedOriginRep : Rep k (SL2 k) := + quotientRationalModule k (V := associatedSectionsSubmodule k ι ρ) + (associatedSectionsRepresentation k ι ρ) (associatedOriginRelations k ι ρ) + (associatedOriginRelations_stable k ι ρ) + + + +lemma associatedOrigin_rational : IsRational k (associatedOriginRep k ι ρ).ρ := by + exact quotientRationalModule_rational k _ _ _ (associatedSections_rational k ι ρ) + +end FiberFunctorProof + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/RegularSplitting.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/RegularSplitting.lean index 527ff9c6868979ced2efd1eb92dab91dfaafa303..508fbd89fd473bad4371ac5bb3d6fd7a6e8c7548 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/RegularSplitting.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/RegularSplitting.lean @@ -1,82 +1,82 @@ -import Mathlib - -namespace OAI - -namespace FiberFunctorProof -open Representation -universe u v -variable {k : Type u} [Field k] {G : Type v} [Group G] [Fintype G] -variable {V W : Type u} [AddCommGroup V] [Module k V] [AddCommGroup W] [Module k W] - -lemma intertwining_norm {ρ : Representation k G V} {σ : Representation k G W} - (f : ρ.IntertwiningMap σ) (v : V) : f (ρ.norm v) = σ.norm (f v) := by - simp only [Representation.norm, LinearMap.sum_apply, map_sum, f.isIntertwining] - -noncomputable def regularCoefficients : MonoidAlgebra k G ≃ₗ[k] (G → k) := - (MonoidAlgebra.coeffLinearEquiv k).trans (Finsupp.linearEquivFunOnFinite k k G) - -omit [Group G] in -@[simp] lemma regularCoefficients_apply (x : MonoidAlgebra k G) (g : G) : - regularCoefficients x g = x.coeff g := rfl - -omit [Group G] in -@[simp] lemma regularCoefficients_symm_coeff (v : G → k) (g : G) : - (regularCoefficients.symm v).coeff g = v g := by - exact congrFun (regularCoefficients.apply_symm_apply v) g - - - -noncomputable def regularCofree (ρ : Representation k G V) (φ : V →ₗ[k] k) : - ρ.IntertwiningMap (Representation.leftRegular k G) where - toLinearMap := regularCoefficients.symm.toLinearMap.comp - (LinearMap.pi fun g : G => φ.comp (ρ g⁻¹)) - isIntertwining' h := by - ext v g - simp [regularCoefficients_symm_coeff, Representation.coeff_ofMulAction, - mul_inv_rev, map_mul] - -@[simp] lemma regularCofree_coeff (ρ : Representation k G V) (φ : V →ₗ[k] k) - (v : V) (g : G) : (regularCofree ρ φ v).coeff g = φ (ρ g⁻¹ v) := by - exact regularCoefficients_symm_coeff _ g - - - -theorem regular_split_of_injective (ρ : Representation k G V) - (f : (Representation.leftRegular k G).IntertwiningMap ρ) - (hf : Function.Injective f) : - ∃ s : ρ.IntertwiningMap (Representation.leftRegular k G), - s.comp f = Representation.IntertwiningMap.id _ := by - obtain ⟨j,hj⟩ := f.toLinearMap.exists_leftInverse_of_injective - (LinearMap.ker_eq_bot.mpr hf) - have hji (x : MonoidAlgebra k G) : j (f x) = x := congr($(hj) x) - let φ : V →ₗ[k] k := (Finsupp.lapply 1).comp - ((MonoidAlgebra.coeffLinearEquiv k).toLinearMap.comp j) - refine ⟨regularCofree ρ φ, ?_⟩ - apply IntertwiningMap.ext - apply LinearMap.ext - intro x - apply MonoidAlgebra.ext - apply Finsupp.ext - intro g - change (regularCofree ρ φ (f x)).coeff g = x.coeff g - rw [regularCofree_coeff, ← f.isIntertwining] - change (j (f ((Representation.leftRegular k G) g⁻¹ x))).coeff 1 = x.coeff g - rw [hji] - simp [Representation.coeff_ofMulAction] - -lemma regular_norm_single_coeff (g : G) : - ((Representation.leftRegular k G).norm (MonoidAlgebra.single 1 1)).coeff g = 1 := by - classical - simp [Representation.norm] - - -theorem regular_invariant_eq (x : MonoidAlgebra k G) - (hx : ∀ g, (Representation.leftRegular k G) g x = x) : - x = x.coeff 1 • (Representation.leftRegular k G).norm (MonoidAlgebra.single 1 1) := by - ext g - have h := congrArg (fun a : MonoidAlgebra k G => a.coeff g) (hx g) - simp [Representation.coeff_ofMulAction] at h - simpa [regular_norm_single_coeff] using h.symm -end FiberFunctorProof - -end OAI +import Mathlib + +namespace OAI + +namespace FiberFunctorProof +open Representation +universe u v +variable {k : Type u} [Field k] {G : Type v} [Group G] [Fintype G] +variable {V W : Type u} [AddCommGroup V] [Module k V] [AddCommGroup W] [Module k W] + +lemma intertwining_norm {ρ : Representation k G V} {σ : Representation k G W} + (f : ρ.IntertwiningMap σ) (v : V) : f (ρ.norm v) = σ.norm (f v) := by + simp only [Representation.norm, LinearMap.sum_apply, map_sum, f.isIntertwining] + +noncomputable def regularCoefficients : MonoidAlgebra k G ≃ₗ[k] (G → k) := + (MonoidAlgebra.coeffLinearEquiv k).trans (Finsupp.linearEquivFunOnFinite k k G) + +omit [Group G] in +@[simp] lemma regularCoefficients_apply (x : MonoidAlgebra k G) (g : G) : + regularCoefficients x g = x.coeff g := rfl + +omit [Group G] in +@[simp] lemma regularCoefficients_symm_coeff (v : G → k) (g : G) : + (regularCoefficients.symm v).coeff g = v g := by + exact congrFun (regularCoefficients.apply_symm_apply v) g + + + +noncomputable def regularCofree (ρ : Representation k G V) (φ : V →ₗ[k] k) : + ρ.IntertwiningMap (Representation.leftRegular k G) where + toLinearMap := regularCoefficients.symm.toLinearMap.comp + (LinearMap.pi fun g : G => φ.comp (ρ g⁻¹)) + isIntertwining' h := by + ext v g + simp [regularCoefficients_symm_coeff, Representation.coeff_ofMulAction, + mul_inv_rev, map_mul] + +@[simp] lemma regularCofree_coeff (ρ : Representation k G V) (φ : V →ₗ[k] k) + (v : V) (g : G) : (regularCofree ρ φ v).coeff g = φ (ρ g⁻¹ v) := by + exact regularCoefficients_symm_coeff _ g + + + +theorem regular_split_of_injective (ρ : Representation k G V) + (f : (Representation.leftRegular k G).IntertwiningMap ρ) + (hf : Function.Injective f) : + ∃ s : ρ.IntertwiningMap (Representation.leftRegular k G), + s.comp f = Representation.IntertwiningMap.id _ := by + obtain ⟨j,hj⟩ := f.toLinearMap.exists_leftInverse_of_injective + (LinearMap.ker_eq_bot.mpr hf) + have hji (x : MonoidAlgebra k G) : j (f x) = x := congr($(hj) x) + let φ : V →ₗ[k] k := (Finsupp.lapply 1).comp + ((MonoidAlgebra.coeffLinearEquiv k).toLinearMap.comp j) + refine ⟨regularCofree ρ φ, ?_⟩ + apply IntertwiningMap.ext + apply LinearMap.ext + intro x + apply MonoidAlgebra.ext + apply Finsupp.ext + intro g + change (regularCofree ρ φ (f x)).coeff g = x.coeff g + rw [regularCofree_coeff, ← f.isIntertwining] + change (j (f ((Representation.leftRegular k G) g⁻¹ x))).coeff 1 = x.coeff g + rw [hji] + simp [Representation.coeff_ofMulAction] + +lemma regular_norm_single_coeff (g : G) : + ((Representation.leftRegular k G).norm (MonoidAlgebra.single 1 1)).coeff g = 1 := by + classical + simp [Representation.norm] + + +theorem regular_invariant_eq (x : MonoidAlgebra k G) + (hx : ∀ g, (Representation.leftRegular k G) g x = x) : + x = x.coeff 1 • (Representation.leftRegular k G).norm (MonoidAlgebra.single 1 1) := by + ext g + have h := congrArg (fun a : MonoidAlgebra k G => a.coeff g) (hx g) + simp [Representation.coeff_ofMulAction] at h + simpa [regular_norm_single_coeff] using h.symm +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/RegularTorus.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/RegularTorus.lean index c3a11de94288ce25cd12f3d566379a80e3acf4f7..d5961067b22d2634b1509ebc3bca9976783d2bc0 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/RegularTorus.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/RegularTorus.lean @@ -1,438 +1,438 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.RegularActions - -namespace OAI - -/-! Torus density, regular localization and coprime denominator gluing. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section -variable (k : Type*) [Field k] [Infinite k] - -abbrev planeTorusPoints := {x : Fin 2 → k // ∀ i, x i ≠ 0} - -noncomputable def planeTorusEvaluation : - MvPolynomial (Fin 2) k →ₐ[k] (planeTorusPoints k → k) := - MvPolynomial.aeval (fun i x => x.val i) - -omit [Infinite k] in -lemma planeTorusEvaluation_apply (P : MvPolynomial (Fin 2) k) (x : planeTorusPoints k) : - planeTorusEvaluation k P x = MvPolynomial.eval x.val P := by - induction P using MvPolynomial.induction_on with - | C c => simp [planeTorusEvaluation] - | add P Q hp hq => simp only [map_add, Pi.add_apply, hp, hq] - | mul_X P i hp => - simp only [map_mul, Pi.mul_apply, hp] - congr 1 - simp [planeTorusEvaluation] - -theorem planeTorusEvaluation_injective : Function.Injective (planeTorusEvaluation k) := by - intro P Q h - apply MvPolynomial.funext_set (fun _ : Fin 2 => ({0} : Set k)ᶜ) - (fun _ => (Set.finite_singleton (0 : k)).infinite_compl) - intro x hx - have hx' : ∀ i, x i ≠ 0 := by - intro i - simpa only [Set.mem_compl_iff, Set.mem_singleton_iff] using hx i (Set.mem_univ i) - exact (planeTorusEvaluation_apply k P ⟨x,hx'⟩).symm.trans - ((congrFun h ⟨x,hx'⟩).trans (planeTorusEvaluation_apply k Q ⟨x,hx'⟩)) - -omit [Infinite k] in -lemma planeTorusEvaluation_X_isUnit (i : Fin 2) : - IsUnit (planeTorusEvaluation k (MvPolynomial.X i)) := by - refine ⟨⟨fun x => x.val i, fun x => (x.val i)⁻¹, ?_, ?_⟩, ?_⟩ - · funext x; exact mul_inv_cancel₀ (x.property i) - · funext x; exact inv_mul_cancel₀ (x.property i) - · ext x; simp [planeTorusEvaluation] - -abbrev planeCoordinateChart (i : Fin 2) := - Localization.Away (MvPolynomial.X i : MvPolynomial (Fin 2) k) - -noncomputable def planeChartEvaluation (i : Fin 2) : - planeCoordinateChart k i →ₐ[k] (planeTorusPoints k → k) := - IsLocalization.Away.liftAlgHom (MvPolynomial.X i) (planeTorusEvaluation_X_isUnit k i) - -omit [Infinite k] in -lemma planeChartEvaluation_algebraMap (i : Fin 2) (P : MvPolynomial (Fin 2) k) : - planeChartEvaluation k i - (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i) P) = - planeTorusEvaluation k P := - IsLocalization.Away.lift_eq _ (planeTorusEvaluation_X_isUnit k i) _ - -theorem planeChartEvaluation_injective (i : Fin 2) : - Function.Injective (planeChartEvaluation k i) := by - apply (IsLocalization.injective_iff_map_algebraMap_eq - (R := MvPolynomial (Fin 2) k) (S := planeCoordinateChart k i) - (Submonoid.powers (MvPolynomial.X i)) (planeChartEvaluation k i).toRingHom).mpr - intro P Q - constructor - · exact congrArg (planeChartEvaluation k i) - · intro h - have h' : planeTorusEvaluation k P = planeTorusEvaluation k Q := by - simpa only [AlgHom.toRingHom_eq_coe, RingHom.coe_coe, - planeChartEvaluation_algebraMap] using h - exact congrArg (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i)) - (planeTorusEvaluation_injective k h') - -end - -section -universe u -variable (k : Type u) [Field k] - - -lemma regularSL2_polynomial_path (f : regularSL2Functions k) - (g : k → SL2 k) (A : Matrix (Fin 2) (Fin 2) (Polynomial k)) - (hA : ∀ t i j, (A i j).eval t = g t i j) : - ∃ P : Polynomial k, ∀ t, P.eval t = f.val (g t) := by - obtain ⟨Q,hQ⟩ := f.property - change coordinateEvaluation k Q = f.val at hQ - refine ⟨MvPolynomial.aeval (fun ij => A ij.1 ij.2) Q, ?_⟩ - intro t - rw [← congrFun hQ (g t), coordinateEvaluation_apply] - clear hQ - induction Q using MvPolynomial.induction_on with - | C c => simp - | add Q R hQ hR => simp only [map_add, Polynomial.eval_add, hQ, hR] - | mul_X Q i hQ => - simp only [map_mul, Polynomial.eval_mul, MvPolynomial.aeval_X, hA, - MvPolynomial.eval_X, hQ] - -noncomputable def regularLowerShear (t : k) : SL2 k := - ⟨!![1,0;t,1], by simp [Matrix.det_fin_two]⟩ - -lemma regularLowerShear_zero : regularLowerShear k 0 = 1 := by - apply Subtype.ext - ext i j - fin_cases i <;> fin_cases j <;> rfl - -lemma lowerShear_mul_entry (t : k) (g : SL2 k) (i j : Fin 2) : - (regularLowerShear k t * g) i j = - (!![g 0 0, g 0 1; t * g 0 0 + g 1 0, t * g 0 1 + g 1 1]) i j := by - change ((regularLowerShear k t : Matrix (Fin 2) (Fin 2) k) * - (g : Matrix (Fin 2) (Fin 2) k)) i j = _ - fin_cases i <;> fin_cases j <;> - simp [regularLowerShear, Matrix.mul_apply, Fin.sum_univ_two] - -lemma upperShear_mul_entry (t : k) (g : SL2 k) (i j : Fin 2) : - (unipotent k t * g) i j = - (!![g 0 0 + t * g 1 0, g 0 1 + t * g 1 1; g 1 0, g 1 1]) i j := by - change ((unipotent k t : Matrix (Fin 2) (Fin 2) k) * - (g : Matrix (Fin 2) (Fin 2) k)) i j = _ - fin_cases i <;> fin_cases j <;> - simp [unipotent, Matrix.mul_apply, Fin.sum_univ_two] - - - -theorem regularSL2_torus_dense [Infinite k] (f : regularSL2Functions k) - (hf : ∀ g : SL2 k, g 0 0 ≠ 0 → g 1 0 ≠ 0 → f.val g = 0) : f = 0 := by - have hfirst (g : SL2 k) (ha : g 0 0 ≠ 0) : f.val g = 0 := by - obtain ⟨P,hP⟩ := regularSL2_polynomial_path k f (fun t => regularLowerShear k t * g) - (!![Polynomial.C (g 0 0), Polynomial.C (g 0 1); - Polynomial.X * Polynomial.C (g 0 0) + Polynomial.C (g 1 0), - Polynomial.X * Polynomial.C (g 0 1) + Polynomial.C (g 1 1)]) (by - intro t i j - rw [lowerShear_mul_entry] - fin_cases i <;> fin_cases j <;> simp <;> ring) - have hzero : P = 0 := by - apply Polynomial.eq_zero_of_infinite_isRoot - apply ((Set.finite_singleton (-g 1 0 / g 0 0)).infinite_compl).mono - intro t ht - change P.eval t = 0 - rw [hP] - apply hf - · simpa [lowerShear_mul_entry] using ha - · have ht' : t ≠ -g 1 0 / g 0 0 := ht - simp only [lowerShear_mul_entry] - intro hz - exact ht' ((eq_div_iff ha).mpr (eq_neg_of_add_eq_zero_left hz)) - have h := hP 0 - rw [hzero, Polynomial.eval_zero, regularLowerShear_zero, one_mul] at h - exact h.symm - apply Subtype.ext - funext g - change f.val g = 0 - by_cases ha : g 0 0 = 0 - · have hc : g 1 0 ≠ 0 := by - intro hc - have hd := g.property - rw [Matrix.det_fin_two, ha, hc] at hd - norm_num at hd - obtain ⟨P,hP⟩ := regularSL2_polynomial_path k f (fun t => unipotent k t * g) - (!![Polynomial.C (g 0 0) + Polynomial.X * Polynomial.C (g 1 0), - Polynomial.C (g 0 1) + Polynomial.X * Polynomial.C (g 1 1); - Polynomial.C (g 1 0), Polynomial.C (g 1 1)]) (by - intro t i j - rw [upperShear_mul_entry] - fin_cases i <;> fin_cases j <;> simp <;> ring) - have hzero : P = 0 := by - apply Polynomial.eq_zero_of_infinite_isRoot - apply ((Set.finite_singleton (0 : k)).infinite_compl).mono - intro t ht - change P.eval t = 0 - rw [hP] - apply hfirst - simpa [upperShear_mul_entry, ha] using mul_ne_zero ht hc - have h := hP 0 - rw [hzero, Polynomial.eval_zero, unipotent_zero, one_mul] at h - exact h.symm - · exact hfirst g ha - - -noncomputable def regularEntry (i j : Fin 2) : regularSL2Functions k := - coordinateToRegular k (MvPolynomial.X (i,j)) - -lemma regularEntry_apply (i j : Fin 2) (g : SL2 k) : - (regularEntry k i j).val g = g i j := by - change coordinateEvaluation k (MvPolynomial.X (i,j)) g = _ - rw [coordinateEvaluation_apply, MvPolynomial.eval_X] - -lemma regularFirstColumn_eq_entry (i : Fin 2) : - regularFirstColumn k i = regularEntry k i 0 := rfl - -abbrev regularTorusPoints := {g : SL2 k // ∀ i, g i 0 ≠ 0} - -noncomputable def regularTorusRestriction : - regularSL2Functions k →ₐ[k] (regularTorusPoints k → k) where - toFun f g := f.val g.val - map_zero' := rfl - map_one' := rfl - map_add' _ _ := rfl - map_mul' _ _ := rfl - commutes' _ := rfl - -lemma regularTorusRestriction_injective [Infinite k] : - Function.Injective (regularTorusRestriction k) := by - intro f h he - apply sub_eq_zero.mp - apply regularSL2_torus_dense k - intro g ha hc - exact sub_eq_zero.mpr (congrFun he ⟨g, by intro i; fin_cases i; exact ha; exact hc⟩) - -noncomputable def regularPlane : - MvPolynomial (Fin 2) k →ₐ[k] regularSL2Functions k := - MvPolynomial.aeval (regularFirstColumn k) - -lemma regularPlane_evaluation (P : MvPolynomial (Fin 2) k) (g : SL2 k) : - (regularPlane k P).val g = MvPolynomial.eval (fun i => g i 0) P := by - induction P using MvPolynomial.induction_on with - | C c => simp [regularPlane] - | add P Q hP hQ => - simp only [map_add, Subalgebra.coe_add, Pi.add_apply, hP, hQ] - | mul_X P i hP => - rw [map_mul, MvPolynomial.eval_mul, MvPolynomial.eval_X] - simp only [Subalgebra.coe_mul, Pi.mul_apply] - rw [hP] - congr 1 - simpa only [regularPlane, MvPolynomial.aeval_X] using regularFirstColumn_apply k i g - -abbrev regularCoordinateLocalization (i : Fin 2) := - Localization.Away (regularFirstColumn k i) - -lemma regularTorusRestriction_coordinate_isUnit (i : Fin 2) : - IsUnit (regularTorusRestriction k (regularFirstColumn k i)) := by - refine ⟨⟨fun g => g.val i 0, fun g => (g.val i 0)⁻¹, ?_, ?_⟩, ?_⟩ - · funext g; exact mul_inv_cancel₀ (g.property i) - · funext g; exact inv_mul_cancel₀ (g.property i) - · funext g; exact (regularFirstColumn_apply k i g.val).symm - -noncomputable def regularLocalizationEvaluation (i : Fin 2) : - regularCoordinateLocalization k i →ₐ[k] (regularTorusPoints k → k) := - IsLocalization.Away.liftAlgHom (regularFirstColumn k i) - (regularTorusRestriction_coordinate_isUnit k i) - -lemma regularLocalizationEvaluation_algebraMap (i : Fin 2) (f : regularSL2Functions k) : - regularLocalizationEvaluation k i - (algebraMap (regularSL2Functions k) (regularCoordinateLocalization k i) f) = - regularTorusRestriction k f := - IsLocalization.Away.lift_eq _ (regularTorusRestriction_coordinate_isUnit k i) _ - -noncomputable def planeChartPullback (i : Fin 2) : - planeCoordinateChart k i →ₐ[k] regularCoordinateLocalization k i := - IsLocalization.Away.liftAlgHom (MvPolynomial.X i : MvPolynomial (Fin 2) k) - (f := (IsScalarTower.toAlgHom k (regularSL2Functions k) - (regularCoordinateLocalization k i)).comp (regularPlane k)) (by - change IsUnit (algebraMap (regularSL2Functions k) (regularCoordinateLocalization k i) - (regularPlane k (MvPolynomial.X i))) - simp only [regularPlane, MvPolynomial.aeval_X] - exact IsLocalization.Away.algebraMap_isUnit _) - -lemma planeChartPullback_algebraMap (i : Fin 2) (P : MvPolynomial (Fin 2) k) : - planeChartPullback k i - (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i) P) = - algebraMap (regularSL2Functions k) (regularCoordinateLocalization k i) (regularPlane k P) := by - unfold planeChartPullback - rw [IsLocalization.Away.liftAlgHom_apply, IsLocalization.Away.lift_eq] - rfl - -noncomputable def regularToPlaneTorus (g : regularTorusPoints k) : planeTorusPoints k := - ⟨fun i => g.val i 0, g.property⟩ - -lemma planeChartPullback_evaluation (i : Fin 2) (f : planeCoordinateChart k i) - (g : regularTorusPoints k) : - regularLocalizationEvaluation k i (planeChartPullback k i f) g = - planeChartEvaluation k i f (regularToPlaneTorus k g) := by - let ev : (planeTorusPoints k → k) →+* (regularTorusPoints k → k) := - { toFun := fun f g => f (regularToPlaneTorus k g) - map_zero' := rfl - map_one' := rfl - map_add' := fun _ _ => rfl - map_mul' := fun _ _ => rfl } - have h : (regularLocalizationEvaluation k i).toRingHom.comp - (planeChartPullback k i).toRingHom = ev.comp (planeChartEvaluation k i).toRingHom := by - apply IsLocalization.ringHom_ext (Submonoid.powers (MvPolynomial.X i : MvPolynomial (Fin 2) k)) - apply RingHom.ext - intro P - ext g - simp only [RingHom.comp_apply, AlgHom.toRingHom_eq_coe, RingHom.coe_coe, - planeChartPullback_algebraMap, regularLocalizationEvaluation_algebraMap, - planeChartEvaluation_algebraMap] - exact (regularPlane_evaluation k P g.val).trans - (planeTorusEvaluation_apply k P (regularToPlaneTorus k g)).symm - exact congrFun (RingHom.congr_fun h f) g - -noncomputable def regularCoordinateInverse (i : Fin 2) : regularCoordinateLocalization k i := - IsLocalization.Away.invSelf (S := regularCoordinateLocalization k i) (regularFirstColumn k i) - -lemma regularCoordinateInverse_evaluation (i : Fin 2) (g : regularTorusPoints k) : - regularLocalizationEvaluation k i (regularCoordinateInverse k i) g = (g.val i 0)⁻¹ := by - have hmul := IsLocalization.Away.mul_invSelf (S := regularCoordinateLocalization k i) - (regularFirstColumn k i) - have h := congrFun (congrArg (regularLocalizationEvaluation k i) hmul) g - simp only [map_mul, map_one, Pi.mul_apply, Pi.one_apply, - regularLocalizationEvaluation_algebraMap] at h - change (regularFirstColumn k i).val g.val * - regularLocalizationEvaluation k i (regularCoordinateInverse k i) g = 1 at h - rw [regularFirstColumn_apply] at h - exact mul_left_cancel₀ (g.property i) (h.trans (mul_inv_cancel₀ (g.property i)).symm) - - - -lemma regularLocalization_has_numerator (i : Fin 2) (f : regularCoordinateLocalization k i) : - ∃ (n : ℕ) (a : regularSL2Functions k), ∀ g : regularTorusPoints k, - (g.val i 0)^n * regularLocalizationEvaluation k i f g = a.val g.val := by - obtain ⟨n,a,ha⟩ := IsLocalization.Away.surj (regularFirstColumn k i) f - refine ⟨n,a,fun g => ?_⟩ - have h := congrFun (congrArg (regularLocalizationEvaluation k i) ha) g - simp only [map_mul, map_pow, regularLocalizationEvaluation_algebraMap, - Pi.mul_apply, Pi.pow_apply] at h - change _ * ((regularFirstColumn k i).val g.val)^n = a.val g.val at h - rwa [regularFirstColumn_apply, mul_comm] at h - -end - - - -lemma coprime_denominator_glue {R : Type*} [CommRing R] {a b : R} - (hab : IsCoprime a b) (n m : ℕ) (f g : R) - (hfg : b^m * f = a^n * g) : - ∃ h : R, a^n * h = f ∧ b^m * h = g := by - obtain ⟨c,d,hcd⟩ := (hab.pow : IsCoprime (a^n) (b^m)) - refine ⟨c*f+d*g, ?_, ?_⟩ - · calc - a^n * (c*f+d*g) = c*a^n*f + d*(a^n*g) := by ring - _ = c*a^n*f + d*(b^m*f) := by rw [hfg] - _ = (c*a^n+d*b^m)*f := by ring - _ = f := by rw [hcd, one_mul] - · calc - b^m * (c*f+d*g) = c*(b^m*f) + d*b^m*g := by ring - _ = c*(a^n*g) + d*b^m*g := by rw [hfg] - _ = (c*a^n+d*b^m)*g := by ring - _ = g := by rw [hcd, one_mul] - -universe u -variable (k : Type u) [Field k] [Infinite k] - -omit [Infinite k] in -lemma regularFirstColumns_coprime : - IsCoprime (regularFirstColumn k 0) (regularFirstColumn k 1) := by - refine ⟨regularEntry k 1 1, -regularEntry k 0 1, ?_⟩ - apply Subtype.ext - funext g - change (regularEntry k 1 1).val g * (regularFirstColumn k 0).val g + - -(regularEntry k 0 1).val g * (regularFirstColumn k 1).val g = 1 - rw [regularEntry_apply, regularEntry_apply, regularFirstColumn_apply, regularFirstColumn_apply] - have hd := g.property - rw [Matrix.det_fin_two] at hd - linear_combination hd - - - -theorem regularTorus_glue (F : regularTorusPoints k → k) - (f₀ : regularCoordinateLocalization k 0) (f₁ : regularCoordinateLocalization k 1) - (h₀ : regularLocalizationEvaluation k 0 f₀ = F) - (h₁ : regularLocalizationEvaluation k 1 f₁ = F) : - ∃ f : regularSL2Functions k, regularTorusRestriction k f = F := by - obtain ⟨n,a,ha⟩ := regularLocalization_has_numerator k 0 f₀ - obtain ⟨m,b,hb⟩ := regularLocalization_has_numerator k 1 f₁ - have hab : (regularFirstColumn k 1)^m * a = (regularFirstColumn k 0)^n * b := by - apply regularTorusRestriction_injective k - funext g - change ((regularFirstColumn k 1).val g.val)^m * a.val g.val = - ((regularFirstColumn k 0).val g.val)^n * b.val g.val - rw [regularFirstColumn_apply, regularFirstColumn_apply, ← ha g, ← hb g, h₀, h₁] - ring - obtain ⟨f,hf,-⟩ := coprime_denominator_glue (regularFirstColumns_coprime k) n m a b hab - refine ⟨f,funext fun g => ?_⟩ - apply mul_left_cancel₀ (pow_ne_zero n (g.property 0)) - have h := congrArg (fun a : regularSL2Functions k => a.val g.val) hf - change ((regularFirstColumn k 0).val g.val)^n * f.val g.val = a.val g.val at h - rw [regularFirstColumn_apply, ← ha g, h₀] at h - exact h - -omit [Infinite k] in -lemma subalgebra_polynomial_mem {Ω σ : Type*} (S : Subalgebra k (Ω → k)) - (x : σ → Ω → k) (hx : ∀ i, x i ∈ S) (P : MvPolynomial σ k) : - (fun g => MvPolynomial.eval (fun i => x i g) P) ∈ S := by - induction P using MvPolynomial.induction_on with - | C c => - convert S.algebraMap_mem c using 1 - ext g - simp - | add P Q hP hQ => - convert S.add_mem hP hQ using 1 - ext g - simp - | mul_X P i hP => - convert S.mul_mem hP (hx i) using 1 - ext g - simp - -omit [Infinite k] in -lemma regularSL2_pullback_mem (φ : SL2 k → SL2 k) - (A : Matrix (Fin 2) (Fin 2) (regularSL2Functions k)) - (hA : ∀ g i j, (A i j).val g = φ g i j) (f : regularSL2Functions k) : - (fun g => f.val (φ g)) ∈ regularSL2Functions k := by - obtain ⟨P,hP⟩ := f.property - have h := subalgebra_polynomial_mem k (regularSL2Functions k) - (fun ij : Fin 2 × Fin 2 => (A ij.1 ij.2).val) (fun ij => (A ij.1 ij.2).property) P - have he : (fun g => MvPolynomial.eval (fun ij => (A ij.1 ij.2).val g) P) = - (fun g => f.val (φ g)) := by - funext g - simp only [hA] - exact (coordinateEvaluation_apply k P (φ g)).symm.trans (congrFun hP (φ g)) - exact he ▸ h - -noncomputable def regularRightTranslation (h : SL2 k) (f : regularSL2Functions k) : - regularSL2Functions k := - ⟨fun g => f.val (g*h), regularSL2_pullback_mem k (fun g => g*h) - (fun i j => ∑ l : Fin 2, (h l j) • regularEntry k i l) (by - intro g i j - rw [Fin.sum_univ_two] - change h 0 j * (regularEntry k i 0).val g + h 1 j * (regularEntry k i 1).val g = - ((g : Matrix (Fin 2) (Fin 2) k) * (h : Matrix (Fin 2) (Fin 2) k)) i j - rw [regularEntry_apply, regularEntry_apply, Matrix.mul_apply, Fin.sum_univ_two] - ring) f⟩ - -omit [Infinite k] in -lemma regularRightTranslation_apply (h g : SL2 k) (f : regularSL2Functions k) : - (regularRightTranslation k h f).val g = f.val (g*h) := rfl - -end FiberFunctorProof -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.RegularActions + +namespace OAI + +/-! Torus density, regular localization and coprime denominator gluing. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section +variable (k : Type*) [Field k] [Infinite k] + +abbrev planeTorusPoints := {x : Fin 2 → k // ∀ i, x i ≠ 0} + +noncomputable def planeTorusEvaluation : + MvPolynomial (Fin 2) k →ₐ[k] (planeTorusPoints k → k) := + MvPolynomial.aeval (fun i x => x.val i) + +omit [Infinite k] in +lemma planeTorusEvaluation_apply (P : MvPolynomial (Fin 2) k) (x : planeTorusPoints k) : + planeTorusEvaluation k P x = MvPolynomial.eval x.val P := by + induction P using MvPolynomial.induction_on with + | C c => simp [planeTorusEvaluation] + | add P Q hp hq => simp only [map_add, Pi.add_apply, hp, hq] + | mul_X P i hp => + simp only [map_mul, Pi.mul_apply, hp] + congr 1 + simp [planeTorusEvaluation] + +theorem planeTorusEvaluation_injective : Function.Injective (planeTorusEvaluation k) := by + intro P Q h + apply MvPolynomial.funext_set (fun _ : Fin 2 => ({0} : Set k)ᶜ) + (fun _ => (Set.finite_singleton (0 : k)).infinite_compl) + intro x hx + have hx' : ∀ i, x i ≠ 0 := by + intro i + simpa only [Set.mem_compl_iff, Set.mem_singleton_iff] using hx i (Set.mem_univ i) + exact (planeTorusEvaluation_apply k P ⟨x,hx'⟩).symm.trans + ((congrFun h ⟨x,hx'⟩).trans (planeTorusEvaluation_apply k Q ⟨x,hx'⟩)) + +omit [Infinite k] in +lemma planeTorusEvaluation_X_isUnit (i : Fin 2) : + IsUnit (planeTorusEvaluation k (MvPolynomial.X i)) := by + refine ⟨⟨fun x => x.val i, fun x => (x.val i)⁻¹, ?_, ?_⟩, ?_⟩ + · funext x; exact mul_inv_cancel₀ (x.property i) + · funext x; exact inv_mul_cancel₀ (x.property i) + · ext x; simp [planeTorusEvaluation] + +abbrev planeCoordinateChart (i : Fin 2) := + Localization.Away (MvPolynomial.X i : MvPolynomial (Fin 2) k) + +noncomputable def planeChartEvaluation (i : Fin 2) : + planeCoordinateChart k i →ₐ[k] (planeTorusPoints k → k) := + IsLocalization.Away.liftAlgHom (MvPolynomial.X i) (planeTorusEvaluation_X_isUnit k i) + +omit [Infinite k] in +lemma planeChartEvaluation_algebraMap (i : Fin 2) (P : MvPolynomial (Fin 2) k) : + planeChartEvaluation k i + (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i) P) = + planeTorusEvaluation k P := + IsLocalization.Away.lift_eq _ (planeTorusEvaluation_X_isUnit k i) _ + +theorem planeChartEvaluation_injective (i : Fin 2) : + Function.Injective (planeChartEvaluation k i) := by + apply (IsLocalization.injective_iff_map_algebraMap_eq + (R := MvPolynomial (Fin 2) k) (S := planeCoordinateChart k i) + (Submonoid.powers (MvPolynomial.X i)) (planeChartEvaluation k i).toRingHom).mpr + intro P Q + constructor + · exact congrArg (planeChartEvaluation k i) + · intro h + have h' : planeTorusEvaluation k P = planeTorusEvaluation k Q := by + simpa only [AlgHom.toRingHom_eq_coe, RingHom.coe_coe, + planeChartEvaluation_algebraMap] using h + exact congrArg (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i)) + (planeTorusEvaluation_injective k h') + +end + +section +universe u +variable (k : Type u) [Field k] + + +lemma regularSL2_polynomial_path (f : regularSL2Functions k) + (g : k → SL2 k) (A : Matrix (Fin 2) (Fin 2) (Polynomial k)) + (hA : ∀ t i j, (A i j).eval t = g t i j) : + ∃ P : Polynomial k, ∀ t, P.eval t = f.val (g t) := by + obtain ⟨Q,hQ⟩ := f.property + change coordinateEvaluation k Q = f.val at hQ + refine ⟨MvPolynomial.aeval (fun ij => A ij.1 ij.2) Q, ?_⟩ + intro t + rw [← congrFun hQ (g t), coordinateEvaluation_apply] + clear hQ + induction Q using MvPolynomial.induction_on with + | C c => simp + | add Q R hQ hR => simp only [map_add, Polynomial.eval_add, hQ, hR] + | mul_X Q i hQ => + simp only [map_mul, Polynomial.eval_mul, MvPolynomial.aeval_X, hA, + MvPolynomial.eval_X, hQ] + +noncomputable def regularLowerShear (t : k) : SL2 k := + ⟨!![1,0;t,1], by simp [Matrix.det_fin_two]⟩ + +lemma regularLowerShear_zero : regularLowerShear k 0 = 1 := by + apply Subtype.ext + ext i j + fin_cases i <;> fin_cases j <;> rfl + +lemma lowerShear_mul_entry (t : k) (g : SL2 k) (i j : Fin 2) : + (regularLowerShear k t * g) i j = + (!![g 0 0, g 0 1; t * g 0 0 + g 1 0, t * g 0 1 + g 1 1]) i j := by + change ((regularLowerShear k t : Matrix (Fin 2) (Fin 2) k) * + (g : Matrix (Fin 2) (Fin 2) k)) i j = _ + fin_cases i <;> fin_cases j <;> + simp [regularLowerShear, Matrix.mul_apply, Fin.sum_univ_two] + +lemma upperShear_mul_entry (t : k) (g : SL2 k) (i j : Fin 2) : + (unipotent k t * g) i j = + (!![g 0 0 + t * g 1 0, g 0 1 + t * g 1 1; g 1 0, g 1 1]) i j := by + change ((unipotent k t : Matrix (Fin 2) (Fin 2) k) * + (g : Matrix (Fin 2) (Fin 2) k)) i j = _ + fin_cases i <;> fin_cases j <;> + simp [unipotent, Matrix.mul_apply, Fin.sum_univ_two] + + + +theorem regularSL2_torus_dense [Infinite k] (f : regularSL2Functions k) + (hf : ∀ g : SL2 k, g 0 0 ≠ 0 → g 1 0 ≠ 0 → f.val g = 0) : f = 0 := by + have hfirst (g : SL2 k) (ha : g 0 0 ≠ 0) : f.val g = 0 := by + obtain ⟨P,hP⟩ := regularSL2_polynomial_path k f (fun t => regularLowerShear k t * g) + (!![Polynomial.C (g 0 0), Polynomial.C (g 0 1); + Polynomial.X * Polynomial.C (g 0 0) + Polynomial.C (g 1 0), + Polynomial.X * Polynomial.C (g 0 1) + Polynomial.C (g 1 1)]) (by + intro t i j + rw [lowerShear_mul_entry] + fin_cases i <;> fin_cases j <;> simp <;> ring) + have hzero : P = 0 := by + apply Polynomial.eq_zero_of_infinite_isRoot + apply ((Set.finite_singleton (-g 1 0 / g 0 0)).infinite_compl).mono + intro t ht + change P.eval t = 0 + rw [hP] + apply hf + · simpa [lowerShear_mul_entry] using ha + · have ht' : t ≠ -g 1 0 / g 0 0 := ht + simp only [lowerShear_mul_entry] + intro hz + exact ht' ((eq_div_iff ha).mpr (eq_neg_of_add_eq_zero_left hz)) + have h := hP 0 + rw [hzero, Polynomial.eval_zero, regularLowerShear_zero, one_mul] at h + exact h.symm + apply Subtype.ext + funext g + change f.val g = 0 + by_cases ha : g 0 0 = 0 + · have hc : g 1 0 ≠ 0 := by + intro hc + have hd := g.property + rw [Matrix.det_fin_two, ha, hc] at hd + norm_num at hd + obtain ⟨P,hP⟩ := regularSL2_polynomial_path k f (fun t => unipotent k t * g) + (!![Polynomial.C (g 0 0) + Polynomial.X * Polynomial.C (g 1 0), + Polynomial.C (g 0 1) + Polynomial.X * Polynomial.C (g 1 1); + Polynomial.C (g 1 0), Polynomial.C (g 1 1)]) (by + intro t i j + rw [upperShear_mul_entry] + fin_cases i <;> fin_cases j <;> simp <;> ring) + have hzero : P = 0 := by + apply Polynomial.eq_zero_of_infinite_isRoot + apply ((Set.finite_singleton (0 : k)).infinite_compl).mono + intro t ht + change P.eval t = 0 + rw [hP] + apply hfirst + simpa [upperShear_mul_entry, ha] using mul_ne_zero ht hc + have h := hP 0 + rw [hzero, Polynomial.eval_zero, unipotent_zero, one_mul] at h + exact h.symm + · exact hfirst g ha + + +noncomputable def regularEntry (i j : Fin 2) : regularSL2Functions k := + coordinateToRegular k (MvPolynomial.X (i,j)) + +lemma regularEntry_apply (i j : Fin 2) (g : SL2 k) : + (regularEntry k i j).val g = g i j := by + change coordinateEvaluation k (MvPolynomial.X (i,j)) g = _ + rw [coordinateEvaluation_apply, MvPolynomial.eval_X] + +lemma regularFirstColumn_eq_entry (i : Fin 2) : + regularFirstColumn k i = regularEntry k i 0 := rfl + +abbrev regularTorusPoints := {g : SL2 k // ∀ i, g i 0 ≠ 0} + +noncomputable def regularTorusRestriction : + regularSL2Functions k →ₐ[k] (regularTorusPoints k → k) where + toFun f g := f.val g.val + map_zero' := rfl + map_one' := rfl + map_add' _ _ := rfl + map_mul' _ _ := rfl + commutes' _ := rfl + +lemma regularTorusRestriction_injective [Infinite k] : + Function.Injective (regularTorusRestriction k) := by + intro f h he + apply sub_eq_zero.mp + apply regularSL2_torus_dense k + intro g ha hc + exact sub_eq_zero.mpr (congrFun he ⟨g, by intro i; fin_cases i; exact ha; exact hc⟩) + +noncomputable def regularPlane : + MvPolynomial (Fin 2) k →ₐ[k] regularSL2Functions k := + MvPolynomial.aeval (regularFirstColumn k) + +lemma regularPlane_evaluation (P : MvPolynomial (Fin 2) k) (g : SL2 k) : + (regularPlane k P).val g = MvPolynomial.eval (fun i => g i 0) P := by + induction P using MvPolynomial.induction_on with + | C c => simp [regularPlane] + | add P Q hP hQ => + simp only [map_add, Subalgebra.coe_add, Pi.add_apply, hP, hQ] + | mul_X P i hP => + rw [map_mul, MvPolynomial.eval_mul, MvPolynomial.eval_X] + simp only [Subalgebra.coe_mul, Pi.mul_apply] + rw [hP] + congr 1 + simpa only [regularPlane, MvPolynomial.aeval_X] using regularFirstColumn_apply k i g + +abbrev regularCoordinateLocalization (i : Fin 2) := + Localization.Away (regularFirstColumn k i) + +lemma regularTorusRestriction_coordinate_isUnit (i : Fin 2) : + IsUnit (regularTorusRestriction k (regularFirstColumn k i)) := by + refine ⟨⟨fun g => g.val i 0, fun g => (g.val i 0)⁻¹, ?_, ?_⟩, ?_⟩ + · funext g; exact mul_inv_cancel₀ (g.property i) + · funext g; exact inv_mul_cancel₀ (g.property i) + · funext g; exact (regularFirstColumn_apply k i g.val).symm + +noncomputable def regularLocalizationEvaluation (i : Fin 2) : + regularCoordinateLocalization k i →ₐ[k] (regularTorusPoints k → k) := + IsLocalization.Away.liftAlgHom (regularFirstColumn k i) + (regularTorusRestriction_coordinate_isUnit k i) + +lemma regularLocalizationEvaluation_algebraMap (i : Fin 2) (f : regularSL2Functions k) : + regularLocalizationEvaluation k i + (algebraMap (regularSL2Functions k) (regularCoordinateLocalization k i) f) = + regularTorusRestriction k f := + IsLocalization.Away.lift_eq _ (regularTorusRestriction_coordinate_isUnit k i) _ + +noncomputable def planeChartPullback (i : Fin 2) : + planeCoordinateChart k i →ₐ[k] regularCoordinateLocalization k i := + IsLocalization.Away.liftAlgHom (MvPolynomial.X i : MvPolynomial (Fin 2) k) + (f := (IsScalarTower.toAlgHom k (regularSL2Functions k) + (regularCoordinateLocalization k i)).comp (regularPlane k)) (by + change IsUnit (algebraMap (regularSL2Functions k) (regularCoordinateLocalization k i) + (regularPlane k (MvPolynomial.X i))) + simp only [regularPlane, MvPolynomial.aeval_X] + exact IsLocalization.Away.algebraMap_isUnit _) + +lemma planeChartPullback_algebraMap (i : Fin 2) (P : MvPolynomial (Fin 2) k) : + planeChartPullback k i + (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k i) P) = + algebraMap (regularSL2Functions k) (regularCoordinateLocalization k i) (regularPlane k P) := by + unfold planeChartPullback + rw [IsLocalization.Away.liftAlgHom_apply, IsLocalization.Away.lift_eq] + rfl + +noncomputable def regularToPlaneTorus (g : regularTorusPoints k) : planeTorusPoints k := + ⟨fun i => g.val i 0, g.property⟩ + +lemma planeChartPullback_evaluation (i : Fin 2) (f : planeCoordinateChart k i) + (g : regularTorusPoints k) : + regularLocalizationEvaluation k i (planeChartPullback k i f) g = + planeChartEvaluation k i f (regularToPlaneTorus k g) := by + let ev : (planeTorusPoints k → k) →+* (regularTorusPoints k → k) := + { toFun := fun f g => f (regularToPlaneTorus k g) + map_zero' := rfl + map_one' := rfl + map_add' := fun _ _ => rfl + map_mul' := fun _ _ => rfl } + have h : (regularLocalizationEvaluation k i).toRingHom.comp + (planeChartPullback k i).toRingHom = ev.comp (planeChartEvaluation k i).toRingHom := by + apply IsLocalization.ringHom_ext (Submonoid.powers (MvPolynomial.X i : MvPolynomial (Fin 2) k)) + apply RingHom.ext + intro P + ext g + simp only [RingHom.comp_apply, AlgHom.toRingHom_eq_coe, RingHom.coe_coe, + planeChartPullback_algebraMap, regularLocalizationEvaluation_algebraMap, + planeChartEvaluation_algebraMap] + exact (regularPlane_evaluation k P g.val).trans + (planeTorusEvaluation_apply k P (regularToPlaneTorus k g)).symm + exact congrFun (RingHom.congr_fun h f) g + +noncomputable def regularCoordinateInverse (i : Fin 2) : regularCoordinateLocalization k i := + IsLocalization.Away.invSelf (S := regularCoordinateLocalization k i) (regularFirstColumn k i) + +lemma regularCoordinateInverse_evaluation (i : Fin 2) (g : regularTorusPoints k) : + regularLocalizationEvaluation k i (regularCoordinateInverse k i) g = (g.val i 0)⁻¹ := by + have hmul := IsLocalization.Away.mul_invSelf (S := regularCoordinateLocalization k i) + (regularFirstColumn k i) + have h := congrFun (congrArg (regularLocalizationEvaluation k i) hmul) g + simp only [map_mul, map_one, Pi.mul_apply, Pi.one_apply, + regularLocalizationEvaluation_algebraMap] at h + change (regularFirstColumn k i).val g.val * + regularLocalizationEvaluation k i (regularCoordinateInverse k i) g = 1 at h + rw [regularFirstColumn_apply] at h + exact mul_left_cancel₀ (g.property i) (h.trans (mul_inv_cancel₀ (g.property i)).symm) + + + +lemma regularLocalization_has_numerator (i : Fin 2) (f : regularCoordinateLocalization k i) : + ∃ (n : ℕ) (a : regularSL2Functions k), ∀ g : regularTorusPoints k, + (g.val i 0)^n * regularLocalizationEvaluation k i f g = a.val g.val := by + obtain ⟨n,a,ha⟩ := IsLocalization.Away.surj (regularFirstColumn k i) f + refine ⟨n,a,fun g => ?_⟩ + have h := congrFun (congrArg (regularLocalizationEvaluation k i) ha) g + simp only [map_mul, map_pow, regularLocalizationEvaluation_algebraMap, + Pi.mul_apply, Pi.pow_apply] at h + change _ * ((regularFirstColumn k i).val g.val)^n = a.val g.val at h + rwa [regularFirstColumn_apply, mul_comm] at h + +end + + + +lemma coprime_denominator_glue {R : Type*} [CommRing R] {a b : R} + (hab : IsCoprime a b) (n m : ℕ) (f g : R) + (hfg : b^m * f = a^n * g) : + ∃ h : R, a^n * h = f ∧ b^m * h = g := by + obtain ⟨c,d,hcd⟩ := (hab.pow : IsCoprime (a^n) (b^m)) + refine ⟨c*f+d*g, ?_, ?_⟩ + · calc + a^n * (c*f+d*g) = c*a^n*f + d*(a^n*g) := by ring + _ = c*a^n*f + d*(b^m*f) := by rw [hfg] + _ = (c*a^n+d*b^m)*f := by ring + _ = f := by rw [hcd, one_mul] + · calc + b^m * (c*f+d*g) = c*(b^m*f) + d*b^m*g := by ring + _ = c*(a^n*g) + d*b^m*g := by rw [hfg] + _ = (c*a^n+d*b^m)*g := by ring + _ = g := by rw [hcd, one_mul] + +universe u +variable (k : Type u) [Field k] [Infinite k] + +omit [Infinite k] in +lemma regularFirstColumns_coprime : + IsCoprime (regularFirstColumn k 0) (regularFirstColumn k 1) := by + refine ⟨regularEntry k 1 1, -regularEntry k 0 1, ?_⟩ + apply Subtype.ext + funext g + change (regularEntry k 1 1).val g * (regularFirstColumn k 0).val g + + -(regularEntry k 0 1).val g * (regularFirstColumn k 1).val g = 1 + rw [regularEntry_apply, regularEntry_apply, regularFirstColumn_apply, regularFirstColumn_apply] + have hd := g.property + rw [Matrix.det_fin_two] at hd + linear_combination hd + + + +theorem regularTorus_glue (F : regularTorusPoints k → k) + (f₀ : regularCoordinateLocalization k 0) (f₁ : regularCoordinateLocalization k 1) + (h₀ : regularLocalizationEvaluation k 0 f₀ = F) + (h₁ : regularLocalizationEvaluation k 1 f₁ = F) : + ∃ f : regularSL2Functions k, regularTorusRestriction k f = F := by + obtain ⟨n,a,ha⟩ := regularLocalization_has_numerator k 0 f₀ + obtain ⟨m,b,hb⟩ := regularLocalization_has_numerator k 1 f₁ + have hab : (regularFirstColumn k 1)^m * a = (regularFirstColumn k 0)^n * b := by + apply regularTorusRestriction_injective k + funext g + change ((regularFirstColumn k 1).val g.val)^m * a.val g.val = + ((regularFirstColumn k 0).val g.val)^n * b.val g.val + rw [regularFirstColumn_apply, regularFirstColumn_apply, ← ha g, ← hb g, h₀, h₁] + ring + obtain ⟨f,hf,-⟩ := coprime_denominator_glue (regularFirstColumns_coprime k) n m a b hab + refine ⟨f,funext fun g => ?_⟩ + apply mul_left_cancel₀ (pow_ne_zero n (g.property 0)) + have h := congrArg (fun a : regularSL2Functions k => a.val g.val) hf + change ((regularFirstColumn k 0).val g.val)^n * f.val g.val = a.val g.val at h + rw [regularFirstColumn_apply, ← ha g, h₀] at h + exact h + +omit [Infinite k] in +lemma subalgebra_polynomial_mem {Ω σ : Type*} (S : Subalgebra k (Ω → k)) + (x : σ → Ω → k) (hx : ∀ i, x i ∈ S) (P : MvPolynomial σ k) : + (fun g => MvPolynomial.eval (fun i => x i g) P) ∈ S := by + induction P using MvPolynomial.induction_on with + | C c => + convert S.algebraMap_mem c using 1 + ext g + simp + | add P Q hP hQ => + convert S.add_mem hP hQ using 1 + ext g + simp + | mul_X P i hP => + convert S.mul_mem hP (hx i) using 1 + ext g + simp + +omit [Infinite k] in +lemma regularSL2_pullback_mem (φ : SL2 k → SL2 k) + (A : Matrix (Fin 2) (Fin 2) (regularSL2Functions k)) + (hA : ∀ g i j, (A i j).val g = φ g i j) (f : regularSL2Functions k) : + (fun g => f.val (φ g)) ∈ regularSL2Functions k := by + obtain ⟨P,hP⟩ := f.property + have h := subalgebra_polynomial_mem k (regularSL2Functions k) + (fun ij : Fin 2 × Fin 2 => (A ij.1 ij.2).val) (fun ij => (A ij.1 ij.2).property) P + have he : (fun g => MvPolynomial.eval (fun ij => (A ij.1 ij.2).val g) P) = + (fun g => f.val (φ g)) := by + funext g + simp only [hA] + exact (coordinateEvaluation_apply k P (φ g)).symm.trans (congrFun hP (φ g)) + exact he ▸ h + +noncomputable def regularRightTranslation (h : SL2 k) (f : regularSL2Functions k) : + regularSL2Functions k := + ⟨fun g => f.val (g*h), regularSL2_pullback_mem k (fun g => g*h) + (fun i j => ∑ l : Fin 2, (h l j) • regularEntry k i l) (by + intro g i j + rw [Fin.sum_univ_two] + change h 0 j * (regularEntry k i 0).val g + h 1 j * (regularEntry k i 1).val g = + ((g : Matrix (Fin 2) (Fin 2) k) * (h : Matrix (Fin 2) (Fin 2) k)) i j + rw [regularEntry_apply, regularEntry_apply, Matrix.mul_apply, Fin.sum_univ_two] + ring) f⟩ + +omit [Infinite k] in +lemma regularRightTranslation_apply (h g : SL2 k) (f : regularSL2Functions k) : + (regularRightTranslation k h f).val g = f.val (g*h) := rfl + +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/RelativeTrace.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/RelativeTrace.lean index 8452652a6d7af97f08dfbe60bd59f89347b08c9b..0daadd699d645fd2ca0e5bfee2faeed34874809b 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/RelativeTrace.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/RelativeTrace.lean @@ -1,49 +1,49 @@ -import Mathlib - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory Representation -universe u v -variable {k : Type u} [Field k] {G : Type v} [Group G] [Fintype G] -variable {V W U : Type u} [AddCommGroup V] [Module k V] - [AddCommGroup W] [Module k W] [AddCommGroup U] [Module k U] - - -noncomputable def relativeTrace (ρ : Representation k G V) (σ : Representation k G W) : - (V →ₗ[k] W) →ₗ[k] (V →ₗ[k] W) := (Representation.linHom ρ σ).norm - -lemma relativeTrace_apply (ρ : Representation k G V) (σ : Representation k G W) - (t : V →ₗ[k] W) (v : V) : - relativeTrace ρ σ t v = ∑ g : G, σ g (t (ρ g⁻¹ v)) := by - simp [relativeTrace, Representation.norm, LinearMap.sum_apply] - -noncomputable def relativeTraceHom (ρ : Representation k G V) (σ : Representation k G W) - (t : V →ₗ[k] W) : ρ.IntertwiningMap σ where - toLinearMap := relativeTrace ρ σ t - isIntertwining' g := by - have h := (Representation.linHom ρ σ).self_norm_apply g t - have hh := congrArg (fun f : V →ₗ[k] W => f.comp (ρ g)) h - simpa only [Representation.linHom_apply, LinearMap.comp_assoc, - ← Module.End.mul_eq_comp, ← map_mul, inv_mul_cancel, map_one, Module.End.one_eq_id, LinearMap.comp_id, relativeTrace] - using hh.symm - -lemma relativeTrace_precomp (ρ : Representation k G V) (σ : Representation k G W) - (τ : Representation k G U) (a : ρ.IntertwiningMap σ) (t : W →ₗ[k] U) : - relativeTrace ρ τ (t.comp a.toLinearMap) = - (relativeTrace σ τ t).comp a.toLinearMap := by - ext v - simp only [relativeTrace_apply, LinearMap.comp_apply, IntertwiningMap.toLinearMap_apply, - a.isIntertwining] - -lemma relativeTrace_postcomp (ρ : Representation k G V) (σ : Representation k G W) - (τ : Representation k G U) (b : σ.IntertwiningMap τ) (t : V →ₗ[k] W) : - relativeTrace ρ τ (b.toLinearMap.comp t) = - b.toLinearMap.comp (relativeTrace ρ σ t) := by - ext v - simp only [relativeTrace_apply, LinearMap.comp_apply, IntertwiningMap.toLinearMap_apply, - map_sum, b.isIntertwining] - -end FiberFunctorProof - -end OAI +import Mathlib + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory Representation +universe u v +variable {k : Type u} [Field k] {G : Type v} [Group G] [Fintype G] +variable {V W U : Type u} [AddCommGroup V] [Module k V] + [AddCommGroup W] [Module k W] [AddCommGroup U] [Module k U] + + +noncomputable def relativeTrace (ρ : Representation k G V) (σ : Representation k G W) : + (V →ₗ[k] W) →ₗ[k] (V →ₗ[k] W) := (Representation.linHom ρ σ).norm + +lemma relativeTrace_apply (ρ : Representation k G V) (σ : Representation k G W) + (t : V →ₗ[k] W) (v : V) : + relativeTrace ρ σ t v = ∑ g : G, σ g (t (ρ g⁻¹ v)) := by + simp [relativeTrace, Representation.norm, LinearMap.sum_apply] + +noncomputable def relativeTraceHom (ρ : Representation k G V) (σ : Representation k G W) + (t : V →ₗ[k] W) : ρ.IntertwiningMap σ where + toLinearMap := relativeTrace ρ σ t + isIntertwining' g := by + have h := (Representation.linHom ρ σ).self_norm_apply g t + have hh := congrArg (fun f : V →ₗ[k] W => f.comp (ρ g)) h + simpa only [Representation.linHom_apply, LinearMap.comp_assoc, + ← Module.End.mul_eq_comp, ← map_mul, inv_mul_cancel, map_one, Module.End.one_eq_id, LinearMap.comp_id, relativeTrace] + using hh.symm + +lemma relativeTrace_precomp (ρ : Representation k G V) (σ : Representation k G W) + (τ : Representation k G U) (a : ρ.IntertwiningMap σ) (t : W →ₗ[k] U) : + relativeTrace ρ τ (t.comp a.toLinearMap) = + (relativeTrace σ τ t).comp a.toLinearMap := by + ext v + simp only [relativeTrace_apply, LinearMap.comp_apply, IntertwiningMap.toLinearMap_apply, + a.isIntertwining] + +lemma relativeTrace_postcomp (ρ : Representation k G V) (σ : Representation k G W) + (τ : Representation k G U) (b : σ.IntertwiningMap τ) (t : V →ₗ[k] W) : + relativeTrace ρ τ (b.toLinearMap.comp t) = + b.toLinearMap.comp (relativeTrace ρ σ t) := by + ext v + simp only [relativeTrace_apply, LinearMap.comp_apply, IntertwiningMap.toLinearMap_apply, + map_sum, b.isIntertwining] + +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/RepProducts.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/RepProducts.lean index 94395274df08469b7281450175690cfbb8db9c84..509b50a9827f6f196c3ce55824cbb38d1e3a6c1c 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/RepProducts.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/RepProducts.lean @@ -1,52 +1,52 @@ -import OAI.RepresentationTheory.RestrictedTilting.CompatibleJets - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -universe u -variable (k : Type u) [Field k] -variable {G : Type u} [Group G] - -noncomputable def repProduct (A B : FDRep k G) : FDRep k G := - FDRep.of (Representation.prod A.ρ B.ρ) - -noncomputable def repInl (A B : FDRep k G) : A ⟶ repProduct k A B := - fdrepHom k (LinearMap.inl k A B) (by - intro g v - change (A.ρ g v, (0 : B)) = (A.ρ g v, B.ρ g 0) - rw [map_zero]) -noncomputable def repInr (A B : FDRep k G) : B ⟶ repProduct k A B := - fdrepHom k (LinearMap.inr k A B) (by - intro g v - change ((0 : A), B.ρ g v) = (A.ρ g 0, B.ρ g v) - rw [map_zero]) -noncomputable def repFst (A B : FDRep k G) : repProduct k A B ⟶ A := - fdrepHom k (LinearMap.fst k A B) (by intros; rfl) -noncomputable def repSnd (A B : FDRep k G) : repProduct k A B ⟶ B := - fdrepHom k (LinearMap.snd k A B) (by intros; rfl) - -lemma repProduct_shortExact (A B : FDRep k G) : - (ShortComplex.mk (repInl k A B) (repSnd k A B) (by - apply fdrep_hom_ext k; intro x; rfl)).ShortExact := by - apply fdrep_shortExact k _ (by intro a b h; exact congrArg Prod.fst h) - (by intro b; exact ⟨(0,b), rfl⟩) - ext x - constructor - · rintro ⟨a,rfl⟩; rfl - · intro h - exact ⟨x.1, Prod.ext rfl h.symm⟩ - -lemma repProduct_decomposition (A B : FDRep k G) : - repFst k A B ≫ repInl k A B + repSnd k A B ≫ repInr k A B = 𝟙 _ := by - apply fdrep_hom_ext k - intro x - change (x.1, 0) + (0, x.2) = x - exact Prod.ext (add_zero _) (zero_add _) - -lemma IsTilting.product {A B : FDRep k (SL2 k)} (hA : IsTilting k A) - (hB : IsTilting k B) : IsTilting k (repProduct k A B) := - hA.extension k hB (hA.1.prod k hB.1) _ _ _ (repProduct_shortExact k A B) -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.CompatibleJets + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +universe u +variable (k : Type u) [Field k] +variable {G : Type u} [Group G] + +noncomputable def repProduct (A B : FDRep k G) : FDRep k G := + FDRep.of (Representation.prod A.ρ B.ρ) + +noncomputable def repInl (A B : FDRep k G) : A ⟶ repProduct k A B := + fdrepHom k (LinearMap.inl k A B) (by + intro g v + change (A.ρ g v, (0 : B)) = (A.ρ g v, B.ρ g 0) + rw [map_zero]) +noncomputable def repInr (A B : FDRep k G) : B ⟶ repProduct k A B := + fdrepHom k (LinearMap.inr k A B) (by + intro g v + change ((0 : A), B.ρ g v) = (A.ρ g 0, B.ρ g v) + rw [map_zero]) +noncomputable def repFst (A B : FDRep k G) : repProduct k A B ⟶ A := + fdrepHom k (LinearMap.fst k A B) (by intros; rfl) +noncomputable def repSnd (A B : FDRep k G) : repProduct k A B ⟶ B := + fdrepHom k (LinearMap.snd k A B) (by intros; rfl) + +lemma repProduct_shortExact (A B : FDRep k G) : + (ShortComplex.mk (repInl k A B) (repSnd k A B) (by + apply fdrep_hom_ext k; intro x; rfl)).ShortExact := by + apply fdrep_shortExact k _ (by intro a b h; exact congrArg Prod.fst h) + (by intro b; exact ⟨(0,b), rfl⟩) + ext x + constructor + · rintro ⟨a,rfl⟩; rfl + · intro h + exact ⟨x.1, Prod.ext rfl h.symm⟩ + +lemma repProduct_decomposition (A B : FDRep k G) : + repFst k A B ≫ repInl k A B + repSnd k A B ≫ repInr k A B = 𝟙 _ := by + apply fdrep_hom_ext k + intro x + change (x.1, 0) + (0, x.2) = x + exact Prod.ext (add_zero _) (zero_add _) + +lemma IsTilting.product {A B : FDRep k (SL2 k)} (hA : IsTilting k A) + (hB : IsTilting k B) : IsTilting k (repProduct k A B) := + hA.extension k hB (hA.1.prod k hB.1) _ _ _ (repProduct_shortExact k A B) +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/RepresentationMaps.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/RepresentationMaps.lean index fe61f852ee6de73c7f08985b01d6b9ceb498ca52..af3549b94ebdf75d6d43b2046c55826e0de16132 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/RepresentationMaps.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/RepresentationMaps.lean @@ -1,291 +1,291 @@ -import Mathlib - -namespace OAI - -/-! Kernels, ranges, quotients and factorization of finite-dimensional representations. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section -universe u -variable (k : Type u) [Field k] - - -def fdrepHom {G : Type u} [Monoid G] {A B : FDRep k G} - (f : A →ₗ[k] B) (hf : ∀ g x, f (A.ρ g x) = B.ρ g (f x)) : A ⟶ B where - hom := FGModuleCat.ofHom f - comm g := by - apply FGModuleCat.hom_ext - exact LinearMap.ext (hf g) - -noncomputable def fdrepForget (G : Type u) [Monoid G] : FDRep k G ⥤ ModuleCat k := - forget₂ (FDRep k G) (Rep k G) ⋙ forget₂ (Rep k G) (ModuleCat k) - -instance (G : Type u) [Monoid G] : (fdrepForget k G).Faithful := by - dsimp [fdrepForget] - infer_instance - -instance (G : Type u) [Monoid G] : PreservesFiniteLimits (fdrepForget k G) := by - dsimp [fdrepForget] - infer_instance - -instance (G : Type u) [Monoid G] : PreservesFiniteColimits (fdrepForget k G) := by - dsimp [fdrepForget] - infer_instance - -instance (G : Type u) [Monoid G] : (fdrepForget k G).Additive where - map_add := by intros; rfl - -lemma fdrep_shortExact {G : Type u} [Monoid G] (S : ShortComplex (FDRep k G)) - (hinj : Function.Injective S.f.hom.hom.hom) - (hsurj : Function.Surjective S.g.hom.hom.hom) - (heq : LinearMap.range S.f.hom.hom.hom = LinearMap.ker S.g.hom.hom.hom) : - S.ShortExact := by - let F := fdrepForget k G - have h : (S.map F).ShortExact := { - exact := ((S.map F).moduleCat_exact_iff_range_eq_ker).mpr heq - mono_f := (ModuleCat.mono_iff_injective _).mpr hinj - epi_g := (ModuleCat.epi_iff_surjective _).mpr hsurj } - exact { - exact := (S.exact_map_iff_of_faithful F).mp h.exact - mono_f := F.mono_of_mono_map h.mono_f - epi_g := F.epi_of_epi_map h.epi_g } - -end - -universe u -variable (k : Type u) [Field k] -variable {G : Type u} [Monoid G] - -abbrev fdrepLinear {A B : FDRep k G} (f : A ⟶ B) : A →ₗ[k] B := f.hom.hom.hom - -lemma fdrepLinear_comm {A B : FDRep k G} (f : A ⟶ B) (g : G) (x : A) : - fdrepLinear k f (A.ρ g x) = B.ρ g (fdrepLinear k f x) := by - exact LinearMap.congr_fun (congrArg (fun t => t.hom.hom) (f.comm g)) x - -lemma fdrep_injective {A B : FDRep k G} (f : A ⟶ B) [Mono f] : - Function.Injective (fdrepLinear k f) := - (ModuleCat.mono_iff_injective ((fdrepForget k G).map f)).mp (by infer_instance) - -lemma fdrep_surjective {A B : FDRep k G} (f : A ⟶ B) [Epi f] : - Function.Surjective (fdrepLinear k f) := - (ModuleCat.epi_iff_surjective ((fdrepForget k G).map f)).mp (by infer_instance) - -lemma fdrep_exact {S : ShortComplex (FDRep k G)} (h : S.Exact) : - LinearMap.range (fdrepLinear k S.f) = LinearMap.ker (fdrepLinear k S.g) := - ((S.map (fdrepForget k G)).moduleCat_exact_iff_range_eq_ker).mp (h.map (fdrepForget k G)) - - -def fdrepKernelSub {A B : FDRep k G} (f : A ⟶ B) : Subrepresentation A.ρ where - toSubmodule := LinearMap.ker (fdrepLinear k f) - apply_mem_toSubmodule g x hx := by - change fdrepLinear k f (A.ρ g x) = 0 - rw [fdrepLinear_comm, show fdrepLinear k f x = 0 from hx, map_zero] - -noncomputable def fdrepKernel {A B : FDRep k G} (f : A ⟶ B) : FDRep k G := - FDRep.of (fdrepKernelSub k f).toRepresentation - -noncomputable def fdrepKernelι {A B : FDRep k G} (f : A ⟶ B) : fdrepKernel k f ⟶ A := - fdrepHom k (LinearMap.ker (fdrepLinear k f)).subtype (by intros; rfl) - -noncomputable def fdrepKernelLift {A B C : FDRep k G} (f : A ⟶ B) (g : B ⟶ C) - (w : f ≫ g = 0) : A ⟶ fdrepKernel k g := - fdrepHom k ((fdrepLinear k f).codRestrict (LinearMap.ker (fdrepLinear k g)) (by - intro x - change fdrepLinear k g (fdrepLinear k f x) = 0 - exact LinearMap.congr_fun (congrArg (fdrepLinear k) w) x)) (by - intro a x - apply Subtype.ext - exact fdrepLinear_comm k f a x) - -lemma fdrepKernelLift_ι {A B C : FDRep k G} (f : A ⟶ B) (g : B ⟶ C) - (w : f ≫ g = 0) : fdrepKernelLift k f g w ≫ fdrepKernelι k g = f := rfl - - -noncomputable def linearFactor {A B C : Type u} [AddCommGroup A] [Module k A] - [AddCommGroup B] [Module k B] [AddCommGroup C] [Module k C] - (f : A →ₗ[k] B) (hf : Function.Injective f) (g : C →ₗ[k] B) - (hg : ∀ x, g x ∈ LinearMap.range f) : C →ₗ[k] A := - (LinearEquiv.ofInjective f hf).symm.toLinearMap.comp (g.codRestrict (LinearMap.range f) hg) - -lemma linearFactor_comp {A B C : Type u} [AddCommGroup A] [Module k A] - [AddCommGroup B] [Module k B] [AddCommGroup C] [Module k C] - (f : A →ₗ[k] B) (hf : Function.Injective f) (g : C →ₗ[k] B) - (hg : ∀ x, g x ∈ LinearMap.range f) (x : C) : - f (linearFactor k f hf g hg x) = g x := by - exact congrArg Subtype.val ((LinearEquiv.ofInjective f hf).apply_symm_apply - ⟨g x, hg x⟩) - -noncomputable def fdrepFactor {A B C : FDRep k G} (f : A ⟶ B) - (hf : Function.Injective (fdrepLinear k f)) (g : C ⟶ B) - (hg : ∀ x, fdrepLinear k g x ∈ LinearMap.range (fdrepLinear k f)) : C ⟶ A := - fdrepHom k (linearFactor k (fdrepLinear k f) hf (fdrepLinear k g) hg) (by - intro a x - apply hf - rw [linearFactor_comp, fdrepLinear_comm, fdrepLinear_comm, linearFactor_comp]) - -lemma fdrepFactor_comp {A B C : FDRep k G} (f : A ⟶ B) - (hf : Function.Injective (fdrepLinear k f)) (g : C ⟶ B) - (hg : ∀ x, fdrepLinear k g x ∈ LinearMap.range (fdrepLinear k f)) : - fdrepFactor k f hf g hg ≫ f = g := by - apply Action.hom_ext - apply FGModuleCat.hom_ext - exact LinearMap.ext (linearFactor_comp k (fdrepLinear k f) hf (fdrepLinear k g) hg) - - -lemma fdrep_splice {A B C D E : FDRep k G} - (f : A ⟶ B) (g : B ⟶ C) (w : f ≫ g = 0) - (hS : (ShortComplex.mk f g w).ShortExact) - (i : D ⟶ C) (j : C ⟶ E) (v : i ≫ j = 0) - (hT : (ShortComplex.mk i j v).ShortExact) : - ∃ (K : FDRep k G) (a : A ⟶ K) (b : K ⟶ D) (r : K ⟶ B) - (wab : a ≫ b = 0) (wr : r ≫ (g ≫ j) = 0), - (ShortComplex.mk a b wab).ShortExact ∧ - (ShortComplex.mk r (g ≫ j) wr).ShortExact := by - have := hS.mono_f - have := hS.epi_g - have := hT.mono_f - have := hT.epi_g - have hf := fdrep_injective k f - have hg := fdrep_surjective k g - have hi := fdrep_injective k i - have hj := fdrep_surjective k j - have hexS := fdrep_exact k hS.exact - have hexT := fdrep_exact k hT.exact - let K := fdrepKernel k (g ≫ j) - let r : K ⟶ B := fdrepKernelι k (g ≫ j) - have w' : f ≫ (g ≫ j) = 0 := by rw [← Category.assoc, w, zero_comp] - let a : A ⟶ K := fdrepKernelLift k f (g ≫ j) w' - have hrange (x : K) : fdrepLinear k (r ≫ g) x ∈ LinearMap.range (fdrepLinear k i) := by - rw [hexT] - exact x.property - let b : K ⟶ D := fdrepFactor k i hi (r ≫ g) hrange - have hb (x : K) : fdrepLinear k i (fdrepLinear k b x) = - fdrepLinear k g (fdrepLinear k r x) := - linearFactor_comp k _ hi _ hrange x - have ha (x : A) : fdrepLinear k r (fdrepLinear k a x) = fdrepLinear k f x := rfl - have hab : a ≫ b = 0 := by - apply Action.hom_ext - apply FGModuleCat.hom_ext - apply LinearMap.ext - intro x - apply hi - change fdrepLinear k i (fdrepLinear k b (fdrepLinear k a x)) = fdrepLinear k i 0 - rw [hb, ha, map_zero] - exact LinearMap.congr_fun (congrArg (fdrepLinear k) w) x - have hr : r ≫ (g ≫ j) = 0 := by - apply Action.hom_ext - apply FGModuleCat.hom_ext - exact LinearMap.ext (fun x => x.property) - refine ⟨K, a, b, r, hab, hr, fdrep_shortExact k _ ?_ ?_ ?_, - fdrep_shortExact k _ ?_ ?_ ?_⟩ - · intro x y hxy - apply hf - exact congrArg Subtype.val hxy - · intro d - obtain ⟨x, hx⟩ := hg (fdrepLinear k i d) - have hx' : fdrepLinear k (g ≫ j) x = 0 := by - change fdrepLinear k j (fdrepLinear k g x) = 0 - rw [hx] - exact LinearMap.congr_fun (congrArg (fdrepLinear k) v) d - let x' : K := ⟨x, hx'⟩ - refine ⟨x', hi ?_⟩ - rw [hb] - exact hx - · apply le_antisymm - · rw [LinearMap.range_le_ker_iff] - exact congrArg (fdrepLinear k) hab - · intro x hx - have hx' : fdrepLinear k r x ∈ LinearMap.ker (fdrepLinear k g) := by - change fdrepLinear k g (fdrepLinear k r x) = 0 - rw [← hb, show fdrepLinear k b x = 0 from hx, map_zero] - rw [← hexS] at hx' - obtain ⟨y, hy⟩ := hx' - refine ⟨y, ?_⟩ - apply Subtype.ext - exact hy - · exact Subtype.val_injective - · exact hj.comp hg - · apply le_antisymm - · rintro _ ⟨x, rfl⟩ - exact x.property - · intro x hx - exact ⟨⟨x, hx⟩, rfl⟩ - - -lemma fdrepDesc_range {A B C : FDRep k G} (f : A ⟶ B) - (g : A ⟶ C) (hker : LinearMap.ker (fdrepLinear k f) ≤ - LinearMap.ker (fdrepLinear k g)) (a b : A) - (h : fdrepLinear k f a = fdrepLinear k f b) : - fdrepLinear k g a = fdrepLinear k g b := by - have hz : a-b ∈ LinearMap.ker (fdrepLinear k f) := by - change fdrepLinear k f (a-b) = 0 - rw [map_sub, h, sub_self] - have := hker hz - change fdrepLinear k g (a-b) = 0 at this - simpa only [map_sub, sub_eq_zero] using this - - -noncomputable def fdrepDesc {A B C : FDRep k G} (f : A ⟶ B) - (hf : Function.Surjective (fdrepLinear k f)) (g : A ⟶ C) - (hker : LinearMap.ker (fdrepLinear k f) ≤ LinearMap.ker (fdrepLinear k g)) : B ⟶ C := - fdrepHom k (((LinearMap.ker (fdrepLinear k f)).liftQ (fdrepLinear k g) hker).comp - (LinearMap.quotKerEquivOfSurjective (fdrepLinear k f) hf).symm.toLinearMap) (by - intro a b - obtain ⟨x,rfl⟩ := hf b - have happ (x : A) : - (LinearMap.quotKerEquivOfSurjective (fdrepLinear k f) hf).symm - (fdrepLinear k f x) = (LinearMap.ker (fdrepLinear k f)).mkQ x := by - apply (LinearMap.quotKerEquivOfSurjective (fdrepLinear k f) hf).injective - simp - rw [← fdrepLinear_comm k f a x] - simp only [LinearMap.comp_apply, LinearEquiv.coe_coe, happ] - exact fdrepLinear_comm k g a x) - -lemma fdrepDesc_comp {A B C : FDRep k G} (f : A ⟶ B) - (hf : Function.Surjective (fdrepLinear k f)) (g : A ⟶ C) - (hker : LinearMap.ker (fdrepLinear k f) ≤ LinearMap.ker (fdrepLinear k g)) : - f ≫ fdrepDesc k f hf g hker = g := by - apply Action.hom_ext - apply FGModuleCat.hom_ext - apply LinearMap.ext - intro x - change (LinearMap.ker (fdrepLinear k f)).liftQ (fdrepLinear k g) hker - ((LinearMap.quotKerEquivOfSurjective (fdrepLinear k f) hf).symm (fdrepLinear k f x)) = _ - have happ : (LinearMap.quotKerEquivOfSurjective (fdrepLinear k f) hf).symm - (fdrepLinear k f x) = (LinearMap.ker (fdrepLinear k f)).mkQ x := by - apply (LinearMap.quotKerEquivOfSurjective (fdrepLinear k f) hf).injective - simp - rw [happ] - rfl - -def fdrepRangeSub {A B : FDRep k G} (f : A ⟶ B) : Subrepresentation B.ρ where - toSubmodule := LinearMap.range (fdrepLinear k f) - apply_mem_toSubmodule g x hx := by - obtain ⟨a,rfl⟩ := hx - exact ⟨A.ρ g a, fdrepLinear_comm k f g a⟩ - -noncomputable def fdrepQuotient {A B : FDRep k G} (f : A ⟶ B) : FDRep k G := - FDRep.of (Representation.quotient B.ρ (fdrepRangeSub k f).toSubmodule - (fdrepRangeSub k f).apply_mem_toSubmodule) - -noncomputable def fdrepQuotientπ {A B : FDRep k G} (f : A ⟶ B) : B ⟶ fdrepQuotient k f := - fdrepHom k (LinearMap.range (fdrepLinear k f)).mkQ (by - intros - rfl) - -lemma fdrepQuotientπ_surjective {A B : FDRep k G} (f : A ⟶ B) : - Function.Surjective (fdrepLinear k (fdrepQuotientπ k f)) := - (LinearMap.range (fdrepLinear k f)).mkQ_surjective - -lemma fdrepQuotientπ_eq_zero {A B : FDRep k G} (f : A ⟶ B) (x : B) : - fdrepLinear k (fdrepQuotientπ k f) x = 0 ↔ x ∈ LinearMap.range (fdrepLinear k f) := - Submodule.Quotient.mk_eq_zero _ - -end FiberFunctorProof -end - -end OAI +import Mathlib + +namespace OAI + +/-! Kernels, ranges, quotients and factorization of finite-dimensional representations. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section +universe u +variable (k : Type u) [Field k] + + +def fdrepHom {G : Type u} [Monoid G] {A B : FDRep k G} + (f : A →ₗ[k] B) (hf : ∀ g x, f (A.ρ g x) = B.ρ g (f x)) : A ⟶ B where + hom := FGModuleCat.ofHom f + comm g := by + apply FGModuleCat.hom_ext + exact LinearMap.ext (hf g) + +noncomputable def fdrepForget (G : Type u) [Monoid G] : FDRep k G ⥤ ModuleCat k := + forget₂ (FDRep k G) (Rep k G) ⋙ forget₂ (Rep k G) (ModuleCat k) + +instance (G : Type u) [Monoid G] : (fdrepForget k G).Faithful := by + dsimp [fdrepForget] + infer_instance + +instance (G : Type u) [Monoid G] : PreservesFiniteLimits (fdrepForget k G) := by + dsimp [fdrepForget] + infer_instance + +instance (G : Type u) [Monoid G] : PreservesFiniteColimits (fdrepForget k G) := by + dsimp [fdrepForget] + infer_instance + +instance (G : Type u) [Monoid G] : (fdrepForget k G).Additive where + map_add := by intros; rfl + +lemma fdrep_shortExact {G : Type u} [Monoid G] (S : ShortComplex (FDRep k G)) + (hinj : Function.Injective S.f.hom.hom.hom) + (hsurj : Function.Surjective S.g.hom.hom.hom) + (heq : LinearMap.range S.f.hom.hom.hom = LinearMap.ker S.g.hom.hom.hom) : + S.ShortExact := by + let F := fdrepForget k G + have h : (S.map F).ShortExact := { + exact := ((S.map F).moduleCat_exact_iff_range_eq_ker).mpr heq + mono_f := (ModuleCat.mono_iff_injective _).mpr hinj + epi_g := (ModuleCat.epi_iff_surjective _).mpr hsurj } + exact { + exact := (S.exact_map_iff_of_faithful F).mp h.exact + mono_f := F.mono_of_mono_map h.mono_f + epi_g := F.epi_of_epi_map h.epi_g } + +end + +universe u +variable (k : Type u) [Field k] +variable {G : Type u} [Monoid G] + +abbrev fdrepLinear {A B : FDRep k G} (f : A ⟶ B) : A →ₗ[k] B := f.hom.hom.hom + +lemma fdrepLinear_comm {A B : FDRep k G} (f : A ⟶ B) (g : G) (x : A) : + fdrepLinear k f (A.ρ g x) = B.ρ g (fdrepLinear k f x) := by + exact LinearMap.congr_fun (congrArg (fun t => t.hom.hom) (f.comm g)) x + +lemma fdrep_injective {A B : FDRep k G} (f : A ⟶ B) [Mono f] : + Function.Injective (fdrepLinear k f) := + (ModuleCat.mono_iff_injective ((fdrepForget k G).map f)).mp (by infer_instance) + +lemma fdrep_surjective {A B : FDRep k G} (f : A ⟶ B) [Epi f] : + Function.Surjective (fdrepLinear k f) := + (ModuleCat.epi_iff_surjective ((fdrepForget k G).map f)).mp (by infer_instance) + +lemma fdrep_exact {S : ShortComplex (FDRep k G)} (h : S.Exact) : + LinearMap.range (fdrepLinear k S.f) = LinearMap.ker (fdrepLinear k S.g) := + ((S.map (fdrepForget k G)).moduleCat_exact_iff_range_eq_ker).mp (h.map (fdrepForget k G)) + + +def fdrepKernelSub {A B : FDRep k G} (f : A ⟶ B) : Subrepresentation A.ρ where + toSubmodule := LinearMap.ker (fdrepLinear k f) + apply_mem_toSubmodule g x hx := by + change fdrepLinear k f (A.ρ g x) = 0 + rw [fdrepLinear_comm, show fdrepLinear k f x = 0 from hx, map_zero] + +noncomputable def fdrepKernel {A B : FDRep k G} (f : A ⟶ B) : FDRep k G := + FDRep.of (fdrepKernelSub k f).toRepresentation + +noncomputable def fdrepKernelι {A B : FDRep k G} (f : A ⟶ B) : fdrepKernel k f ⟶ A := + fdrepHom k (LinearMap.ker (fdrepLinear k f)).subtype (by intros; rfl) + +noncomputable def fdrepKernelLift {A B C : FDRep k G} (f : A ⟶ B) (g : B ⟶ C) + (w : f ≫ g = 0) : A ⟶ fdrepKernel k g := + fdrepHom k ((fdrepLinear k f).codRestrict (LinearMap.ker (fdrepLinear k g)) (by + intro x + change fdrepLinear k g (fdrepLinear k f x) = 0 + exact LinearMap.congr_fun (congrArg (fdrepLinear k) w) x)) (by + intro a x + apply Subtype.ext + exact fdrepLinear_comm k f a x) + +lemma fdrepKernelLift_ι {A B C : FDRep k G} (f : A ⟶ B) (g : B ⟶ C) + (w : f ≫ g = 0) : fdrepKernelLift k f g w ≫ fdrepKernelι k g = f := rfl + + +noncomputable def linearFactor {A B C : Type u} [AddCommGroup A] [Module k A] + [AddCommGroup B] [Module k B] [AddCommGroup C] [Module k C] + (f : A →ₗ[k] B) (hf : Function.Injective f) (g : C →ₗ[k] B) + (hg : ∀ x, g x ∈ LinearMap.range f) : C →ₗ[k] A := + (LinearEquiv.ofInjective f hf).symm.toLinearMap.comp (g.codRestrict (LinearMap.range f) hg) + +lemma linearFactor_comp {A B C : Type u} [AddCommGroup A] [Module k A] + [AddCommGroup B] [Module k B] [AddCommGroup C] [Module k C] + (f : A →ₗ[k] B) (hf : Function.Injective f) (g : C →ₗ[k] B) + (hg : ∀ x, g x ∈ LinearMap.range f) (x : C) : + f (linearFactor k f hf g hg x) = g x := by + exact congrArg Subtype.val ((LinearEquiv.ofInjective f hf).apply_symm_apply + ⟨g x, hg x⟩) + +noncomputable def fdrepFactor {A B C : FDRep k G} (f : A ⟶ B) + (hf : Function.Injective (fdrepLinear k f)) (g : C ⟶ B) + (hg : ∀ x, fdrepLinear k g x ∈ LinearMap.range (fdrepLinear k f)) : C ⟶ A := + fdrepHom k (linearFactor k (fdrepLinear k f) hf (fdrepLinear k g) hg) (by + intro a x + apply hf + rw [linearFactor_comp, fdrepLinear_comm, fdrepLinear_comm, linearFactor_comp]) + +lemma fdrepFactor_comp {A B C : FDRep k G} (f : A ⟶ B) + (hf : Function.Injective (fdrepLinear k f)) (g : C ⟶ B) + (hg : ∀ x, fdrepLinear k g x ∈ LinearMap.range (fdrepLinear k f)) : + fdrepFactor k f hf g hg ≫ f = g := by + apply Action.hom_ext + apply FGModuleCat.hom_ext + exact LinearMap.ext (linearFactor_comp k (fdrepLinear k f) hf (fdrepLinear k g) hg) + + +lemma fdrep_splice {A B C D E : FDRep k G} + (f : A ⟶ B) (g : B ⟶ C) (w : f ≫ g = 0) + (hS : (ShortComplex.mk f g w).ShortExact) + (i : D ⟶ C) (j : C ⟶ E) (v : i ≫ j = 0) + (hT : (ShortComplex.mk i j v).ShortExact) : + ∃ (K : FDRep k G) (a : A ⟶ K) (b : K ⟶ D) (r : K ⟶ B) + (wab : a ≫ b = 0) (wr : r ≫ (g ≫ j) = 0), + (ShortComplex.mk a b wab).ShortExact ∧ + (ShortComplex.mk r (g ≫ j) wr).ShortExact := by + have := hS.mono_f + have := hS.epi_g + have := hT.mono_f + have := hT.epi_g + have hf := fdrep_injective k f + have hg := fdrep_surjective k g + have hi := fdrep_injective k i + have hj := fdrep_surjective k j + have hexS := fdrep_exact k hS.exact + have hexT := fdrep_exact k hT.exact + let K := fdrepKernel k (g ≫ j) + let r : K ⟶ B := fdrepKernelι k (g ≫ j) + have w' : f ≫ (g ≫ j) = 0 := by rw [← Category.assoc, w, zero_comp] + let a : A ⟶ K := fdrepKernelLift k f (g ≫ j) w' + have hrange (x : K) : fdrepLinear k (r ≫ g) x ∈ LinearMap.range (fdrepLinear k i) := by + rw [hexT] + exact x.property + let b : K ⟶ D := fdrepFactor k i hi (r ≫ g) hrange + have hb (x : K) : fdrepLinear k i (fdrepLinear k b x) = + fdrepLinear k g (fdrepLinear k r x) := + linearFactor_comp k _ hi _ hrange x + have ha (x : A) : fdrepLinear k r (fdrepLinear k a x) = fdrepLinear k f x := rfl + have hab : a ≫ b = 0 := by + apply Action.hom_ext + apply FGModuleCat.hom_ext + apply LinearMap.ext + intro x + apply hi + change fdrepLinear k i (fdrepLinear k b (fdrepLinear k a x)) = fdrepLinear k i 0 + rw [hb, ha, map_zero] + exact LinearMap.congr_fun (congrArg (fdrepLinear k) w) x + have hr : r ≫ (g ≫ j) = 0 := by + apply Action.hom_ext + apply FGModuleCat.hom_ext + exact LinearMap.ext (fun x => x.property) + refine ⟨K, a, b, r, hab, hr, fdrep_shortExact k _ ?_ ?_ ?_, + fdrep_shortExact k _ ?_ ?_ ?_⟩ + · intro x y hxy + apply hf + exact congrArg Subtype.val hxy + · intro d + obtain ⟨x, hx⟩ := hg (fdrepLinear k i d) + have hx' : fdrepLinear k (g ≫ j) x = 0 := by + change fdrepLinear k j (fdrepLinear k g x) = 0 + rw [hx] + exact LinearMap.congr_fun (congrArg (fdrepLinear k) v) d + let x' : K := ⟨x, hx'⟩ + refine ⟨x', hi ?_⟩ + rw [hb] + exact hx + · apply le_antisymm + · rw [LinearMap.range_le_ker_iff] + exact congrArg (fdrepLinear k) hab + · intro x hx + have hx' : fdrepLinear k r x ∈ LinearMap.ker (fdrepLinear k g) := by + change fdrepLinear k g (fdrepLinear k r x) = 0 + rw [← hb, show fdrepLinear k b x = 0 from hx, map_zero] + rw [← hexS] at hx' + obtain ⟨y, hy⟩ := hx' + refine ⟨y, ?_⟩ + apply Subtype.ext + exact hy + · exact Subtype.val_injective + · exact hj.comp hg + · apply le_antisymm + · rintro _ ⟨x, rfl⟩ + exact x.property + · intro x hx + exact ⟨⟨x, hx⟩, rfl⟩ + + +lemma fdrepDesc_range {A B C : FDRep k G} (f : A ⟶ B) + (g : A ⟶ C) (hker : LinearMap.ker (fdrepLinear k f) ≤ + LinearMap.ker (fdrepLinear k g)) (a b : A) + (h : fdrepLinear k f a = fdrepLinear k f b) : + fdrepLinear k g a = fdrepLinear k g b := by + have hz : a-b ∈ LinearMap.ker (fdrepLinear k f) := by + change fdrepLinear k f (a-b) = 0 + rw [map_sub, h, sub_self] + have := hker hz + change fdrepLinear k g (a-b) = 0 at this + simpa only [map_sub, sub_eq_zero] using this + + +noncomputable def fdrepDesc {A B C : FDRep k G} (f : A ⟶ B) + (hf : Function.Surjective (fdrepLinear k f)) (g : A ⟶ C) + (hker : LinearMap.ker (fdrepLinear k f) ≤ LinearMap.ker (fdrepLinear k g)) : B ⟶ C := + fdrepHom k (((LinearMap.ker (fdrepLinear k f)).liftQ (fdrepLinear k g) hker).comp + (LinearMap.quotKerEquivOfSurjective (fdrepLinear k f) hf).symm.toLinearMap) (by + intro a b + obtain ⟨x,rfl⟩ := hf b + have happ (x : A) : + (LinearMap.quotKerEquivOfSurjective (fdrepLinear k f) hf).symm + (fdrepLinear k f x) = (LinearMap.ker (fdrepLinear k f)).mkQ x := by + apply (LinearMap.quotKerEquivOfSurjective (fdrepLinear k f) hf).injective + simp + rw [← fdrepLinear_comm k f a x] + simp only [LinearMap.comp_apply, LinearEquiv.coe_coe, happ] + exact fdrepLinear_comm k g a x) + +lemma fdrepDesc_comp {A B C : FDRep k G} (f : A ⟶ B) + (hf : Function.Surjective (fdrepLinear k f)) (g : A ⟶ C) + (hker : LinearMap.ker (fdrepLinear k f) ≤ LinearMap.ker (fdrepLinear k g)) : + f ≫ fdrepDesc k f hf g hker = g := by + apply Action.hom_ext + apply FGModuleCat.hom_ext + apply LinearMap.ext + intro x + change (LinearMap.ker (fdrepLinear k f)).liftQ (fdrepLinear k g) hker + ((LinearMap.quotKerEquivOfSurjective (fdrepLinear k f) hf).symm (fdrepLinear k f x)) = _ + have happ : (LinearMap.quotKerEquivOfSurjective (fdrepLinear k f) hf).symm + (fdrepLinear k f x) = (LinearMap.ker (fdrepLinear k f)).mkQ x := by + apply (LinearMap.quotKerEquivOfSurjective (fdrepLinear k f) hf).injective + simp + rw [happ] + rfl + +def fdrepRangeSub {A B : FDRep k G} (f : A ⟶ B) : Subrepresentation B.ρ where + toSubmodule := LinearMap.range (fdrepLinear k f) + apply_mem_toSubmodule g x hx := by + obtain ⟨a,rfl⟩ := hx + exact ⟨A.ρ g a, fdrepLinear_comm k f g a⟩ + +noncomputable def fdrepQuotient {A B : FDRep k G} (f : A ⟶ B) : FDRep k G := + FDRep.of (Representation.quotient B.ρ (fdrepRangeSub k f).toSubmodule + (fdrepRangeSub k f).apply_mem_toSubmodule) + +noncomputable def fdrepQuotientπ {A B : FDRep k G} (f : A ⟶ B) : B ⟶ fdrepQuotient k f := + fdrepHom k (LinearMap.range (fdrepLinear k f)).mkQ (by + intros + rfl) + +lemma fdrepQuotientπ_surjective {A B : FDRep k G} (f : A ⟶ B) : + Function.Surjective (fdrepLinear k (fdrepQuotientπ k f)) := + (LinearMap.range (fdrepLinear k f)).mkQ_surjective + +lemma fdrepQuotientπ_eq_zero {A B : FDRep k G} (f : A ⟶ B) (x : B) : + fdrepLinear k (fdrepQuotientπ k f) x = 0 ↔ x ∈ LinearMap.range (fdrepLinear k f) := + Submodule.Quotient.mk_eq_zero _ + +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/RestrictedLift.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/RestrictedLift.lean index e8e91d1770efac0dcf4cc9fe7dcbd7571159b978..b7d96e34a763815a58a624d3c645697b3f6098b2 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/RestrictedLift.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/RestrictedLift.lean @@ -1,144 +1,144 @@ -import Mathlib - -namespace OAI - - - -noncomputable section - -open scoped BigOperators -open Polynomial - -namespace FiberFunctorProof - -universe u v - -variable {k : Type u} [Field k] -variable (H : AddSubgroup k) [Fintype H] -variable {ι : Type v} [Fintype ι] [DecidableEq ι] - - -def liftEntry (ρ : Multiplicative H →* Matrix ι ι k) (i j : ι) : k[X] := by - classical - exact Lagrange.interpolate Finset.univ (fun h : H => (h : k)) - (fun h => ρ (Multiplicative.ofAdd h) i j) - - -def liftMatrix (ρ : Multiplicative H →* Matrix ι ι k) (t : k) : Matrix ι ι k := - fun i j => (liftEntry H ρ i j).eval t - -lemma liftEntry_degree (ρ : Multiplicative H →* Matrix ι ι k) (i j : ι) : - (liftEntry H ρ i j).degree < (Fintype.card H : WithBot ℕ) := by - classical - simpa only [liftEntry, Finset.card_univ] using Lagrange.degree_interpolate_lt - (s := Finset.univ) (v := fun h : H => (h : k)) - (fun h : H => ρ (Multiplicative.ofAdd h) i j) Subtype.val_injective.injOn - -@[simp] -lemma liftMatrix_at_subgroup (ρ : Multiplicative H →* Matrix ι ι k) (h : H) : - liftMatrix H ρ (h : k) = ρ (Multiplicative.ofAdd h) := by - classical - ext i j - exact Lagrange.eval_interpolate_at_node - (fun h : H => ρ (Multiplicative.ofAdd h) i j) - Subtype.val_injective.injOn (Finset.mem_univ h) - -lemma polynomial_degree_translate (f : k[X]) (t : k) : - (f.comp (X + C t)).degree = f.degree := by - rw [Polynomial.degree_comp (by simp), Polynomial.degree_X_add_C, mul_one] - -lemma polynomial_degree_mul_constant_le (f : k[X]) (a : k) : - (f * C a).degree ≤ f.degree := by - by_cases ha : a = 0 - · simp [ha] - · exact le_of_eq (Polynomial.degree_mul_C ha) - -lemma polynomial_degree_constant_mul_le (f : k[X]) (a : k) : - (C a * f).degree ≤ f.degree := by - simpa [mul_comm] using polynomial_degree_mul_constant_le f a - -lemma polynomial_degree_sum_lt {J : Type*} (s : Finset J) (f : J → k[X]) (b : ℕ) - (h : ∀ i ∈ s, (f i).degree < (b : WithBot ℕ)) : - (∑ i ∈ s, f i).degree < (b : WithBot ℕ) := by - rw [← Polynomial.mem_degreeLT] - exact Submodule.sum_mem _ fun i hi => Polynomial.mem_degreeLT.mpr (h i hi) - - -lemma liftMatrix_add_subgroup (ρ : Multiplicative H →* Matrix ι ι k) (t : k) (h : H) : - liftMatrix H ρ (t + (h : k)) = liftMatrix H ρ t * ρ (Multiplicative.ofAdd h) := by - classical - ext i j - have hp : (liftEntry H ρ i j).comp (X + C (h : k)) = - ∑ a : ι, liftEntry H ρ i a * C (ρ (Multiplicative.ofAdd h) a j) := by - refine Polynomial.eq_of_degrees_lt_of_eval_index_eq - (v := fun g : H => (g : k)) Finset.univ Subtype.val_injective.injOn ?_ ?_ ?_ - · simpa only [polynomial_degree_translate, Finset.card_univ] using liftEntry_degree H ρ i j - · exact polynomial_degree_sum_lt _ _ _ fun a _ => - lt_of_le_of_lt (polynomial_degree_mul_constant_le _ _) (by - simpa only [Finset.card_univ] using liftEntry_degree H ρ i a) - · intro g _ - simp only [Polynomial.eval_comp, Polynomial.eval_add, Polynomial.eval_X, - Polynomial.eval_C, Polynomial.eval_finsetSum, Polynomial.eval_mul] - change liftMatrix H ρ ((g : k) + (h : k)) i j = - (liftMatrix H ρ (g : k) * ρ (Multiplicative.ofAdd h)) i j - rw [← AddSubgroup.coe_add, liftMatrix_at_subgroup, liftMatrix_at_subgroup] - exact congrArg (fun M : Matrix ι ι k => M i j) (ρ.map_mul _ _) - have hp' := congrArg (Polynomial.eval t) hp - simpa only [Polynomial.eval_comp, Polynomial.eval_add, Polynomial.eval_X, - Polynomial.eval_C, Polynomial.eval_finsetSum, Polynomial.eval_mul, - liftMatrix, Matrix.mul_apply] using hp' - - -lemma liftMatrix_add (ρ : Multiplicative H →* Matrix ι ι k) (s t : k) : - liftMatrix H ρ (s + t) = liftMatrix H ρ s * liftMatrix H ρ t := by - classical - ext i j - have hp : (liftEntry H ρ i j).comp (X + C s) = - ∑ a : ι, C (liftMatrix H ρ s i a) * liftEntry H ρ a j := by - refine Polynomial.eq_of_degrees_lt_of_eval_index_eq - (v := fun g : H => (g : k)) Finset.univ Subtype.val_injective.injOn ?_ ?_ ?_ - · simpa only [polynomial_degree_translate, Finset.card_univ] using liftEntry_degree H ρ i j - · exact polynomial_degree_sum_lt _ _ _ fun a _ => - lt_of_le_of_lt (polynomial_degree_constant_mul_le _ _) (by - simpa only [Finset.card_univ] using liftEntry_degree H ρ a j) - · intro g _ - simp only [Polynomial.eval_comp, Polynomial.eval_add, Polynomial.eval_X, - Polynomial.eval_C, Polynomial.eval_finsetSum, Polynomial.eval_mul] - change liftMatrix H ρ ((g : k) + s) i j = - (liftMatrix H ρ s * liftMatrix H ρ (g : k)) i j - rw [add_comm, liftMatrix_add_subgroup, liftMatrix_at_subgroup] - have hp' := congrArg (Polynomial.eval t) hp - simpa only [Polynomial.eval_comp, Polynomial.eval_add, Polynomial.eval_X, - Polynomial.eval_C, Polynomial.eval_finsetSum, Polynomial.eval_mul, - liftMatrix, Matrix.mul_apply, add_comm t s] using hp' - -@[simp] -lemma liftMatrix_zero (ρ : Multiplicative H →* Matrix ι ι k) : - liftMatrix H ρ 0 = 1 := by - simpa using liftMatrix_at_subgroup H ρ (0 : H) - - -def extendedRepresentation (ρ : Multiplicative H →* Matrix ι ι k) : - Multiplicative k →* Matrix ι ι k where - toFun t := liftMatrix H ρ t.toAdd - map_one' := liftMatrix_zero H ρ - map_mul' s t := liftMatrix_add H ρ s.toAdd t.toAdd - - - -theorem finite_additive_representation_lift - (ρ : Multiplicative H →* Matrix ι ι k) : - ∃ σ : Multiplicative k →* Matrix ι ι k, - (∀ h : H, σ (Multiplicative.ofAdd (h : k)) = ρ (Multiplicative.ofAdd h)) ∧ - (∀ i j : ι, ∃ f : k[X], f.degree < (Fintype.card H : WithBot ℕ) ∧ - ∀ t : k, σ (Multiplicative.ofAdd t) i j = f.eval t) := by - refine ⟨extendedRepresentation H ρ, ?_, ?_⟩ - · exact liftMatrix_at_subgroup H ρ - · intro i j - exact ⟨liftEntry H ρ i j, liftEntry_degree H ρ i j, fun _ => rfl⟩ - -end FiberFunctorProof - -end - -end OAI +import Mathlib + +namespace OAI + + + +noncomputable section + +open scoped BigOperators +open Polynomial + +namespace FiberFunctorProof + +universe u v + +variable {k : Type u} [Field k] +variable (H : AddSubgroup k) [Fintype H] +variable {ι : Type v} [Fintype ι] [DecidableEq ι] + + +def liftEntry (ρ : Multiplicative H →* Matrix ι ι k) (i j : ι) : k[X] := by + classical + exact Lagrange.interpolate Finset.univ (fun h : H => (h : k)) + (fun h => ρ (Multiplicative.ofAdd h) i j) + + +def liftMatrix (ρ : Multiplicative H →* Matrix ι ι k) (t : k) : Matrix ι ι k := + fun i j => (liftEntry H ρ i j).eval t + +lemma liftEntry_degree (ρ : Multiplicative H →* Matrix ι ι k) (i j : ι) : + (liftEntry H ρ i j).degree < (Fintype.card H : WithBot ℕ) := by + classical + simpa only [liftEntry, Finset.card_univ] using Lagrange.degree_interpolate_lt + (s := Finset.univ) (v := fun h : H => (h : k)) + (fun h : H => ρ (Multiplicative.ofAdd h) i j) Subtype.val_injective.injOn + +@[simp] +lemma liftMatrix_at_subgroup (ρ : Multiplicative H →* Matrix ι ι k) (h : H) : + liftMatrix H ρ (h : k) = ρ (Multiplicative.ofAdd h) := by + classical + ext i j + exact Lagrange.eval_interpolate_at_node + (fun h : H => ρ (Multiplicative.ofAdd h) i j) + Subtype.val_injective.injOn (Finset.mem_univ h) + +lemma polynomial_degree_translate (f : k[X]) (t : k) : + (f.comp (X + C t)).degree = f.degree := by + rw [Polynomial.degree_comp (by simp), Polynomial.degree_X_add_C, mul_one] + +lemma polynomial_degree_mul_constant_le (f : k[X]) (a : k) : + (f * C a).degree ≤ f.degree := by + by_cases ha : a = 0 + · simp [ha] + · exact le_of_eq (Polynomial.degree_mul_C ha) + +lemma polynomial_degree_constant_mul_le (f : k[X]) (a : k) : + (C a * f).degree ≤ f.degree := by + simpa [mul_comm] using polynomial_degree_mul_constant_le f a + +lemma polynomial_degree_sum_lt {J : Type*} (s : Finset J) (f : J → k[X]) (b : ℕ) + (h : ∀ i ∈ s, (f i).degree < (b : WithBot ℕ)) : + (∑ i ∈ s, f i).degree < (b : WithBot ℕ) := by + rw [← Polynomial.mem_degreeLT] + exact Submodule.sum_mem _ fun i hi => Polynomial.mem_degreeLT.mpr (h i hi) + + +lemma liftMatrix_add_subgroup (ρ : Multiplicative H →* Matrix ι ι k) (t : k) (h : H) : + liftMatrix H ρ (t + (h : k)) = liftMatrix H ρ t * ρ (Multiplicative.ofAdd h) := by + classical + ext i j + have hp : (liftEntry H ρ i j).comp (X + C (h : k)) = + ∑ a : ι, liftEntry H ρ i a * C (ρ (Multiplicative.ofAdd h) a j) := by + refine Polynomial.eq_of_degrees_lt_of_eval_index_eq + (v := fun g : H => (g : k)) Finset.univ Subtype.val_injective.injOn ?_ ?_ ?_ + · simpa only [polynomial_degree_translate, Finset.card_univ] using liftEntry_degree H ρ i j + · exact polynomial_degree_sum_lt _ _ _ fun a _ => + lt_of_le_of_lt (polynomial_degree_mul_constant_le _ _) (by + simpa only [Finset.card_univ] using liftEntry_degree H ρ i a) + · intro g _ + simp only [Polynomial.eval_comp, Polynomial.eval_add, Polynomial.eval_X, + Polynomial.eval_C, Polynomial.eval_finsetSum, Polynomial.eval_mul] + change liftMatrix H ρ ((g : k) + (h : k)) i j = + (liftMatrix H ρ (g : k) * ρ (Multiplicative.ofAdd h)) i j + rw [← AddSubgroup.coe_add, liftMatrix_at_subgroup, liftMatrix_at_subgroup] + exact congrArg (fun M : Matrix ι ι k => M i j) (ρ.map_mul _ _) + have hp' := congrArg (Polynomial.eval t) hp + simpa only [Polynomial.eval_comp, Polynomial.eval_add, Polynomial.eval_X, + Polynomial.eval_C, Polynomial.eval_finsetSum, Polynomial.eval_mul, + liftMatrix, Matrix.mul_apply] using hp' + + +lemma liftMatrix_add (ρ : Multiplicative H →* Matrix ι ι k) (s t : k) : + liftMatrix H ρ (s + t) = liftMatrix H ρ s * liftMatrix H ρ t := by + classical + ext i j + have hp : (liftEntry H ρ i j).comp (X + C s) = + ∑ a : ι, C (liftMatrix H ρ s i a) * liftEntry H ρ a j := by + refine Polynomial.eq_of_degrees_lt_of_eval_index_eq + (v := fun g : H => (g : k)) Finset.univ Subtype.val_injective.injOn ?_ ?_ ?_ + · simpa only [polynomial_degree_translate, Finset.card_univ] using liftEntry_degree H ρ i j + · exact polynomial_degree_sum_lt _ _ _ fun a _ => + lt_of_le_of_lt (polynomial_degree_constant_mul_le _ _) (by + simpa only [Finset.card_univ] using liftEntry_degree H ρ a j) + · intro g _ + simp only [Polynomial.eval_comp, Polynomial.eval_add, Polynomial.eval_X, + Polynomial.eval_C, Polynomial.eval_finsetSum, Polynomial.eval_mul] + change liftMatrix H ρ ((g : k) + s) i j = + (liftMatrix H ρ s * liftMatrix H ρ (g : k)) i j + rw [add_comm, liftMatrix_add_subgroup, liftMatrix_at_subgroup] + have hp' := congrArg (Polynomial.eval t) hp + simpa only [Polynomial.eval_comp, Polynomial.eval_add, Polynomial.eval_X, + Polynomial.eval_C, Polynomial.eval_finsetSum, Polynomial.eval_mul, + liftMatrix, Matrix.mul_apply, add_comm t s] using hp' + +@[simp] +lemma liftMatrix_zero (ρ : Multiplicative H →* Matrix ι ι k) : + liftMatrix H ρ 0 = 1 := by + simpa using liftMatrix_at_subgroup H ρ (0 : H) + + +def extendedRepresentation (ρ : Multiplicative H →* Matrix ι ι k) : + Multiplicative k →* Matrix ι ι k where + toFun t := liftMatrix H ρ t.toAdd + map_one' := liftMatrix_zero H ρ + map_mul' s t := liftMatrix_add H ρ s.toAdd t.toAdd + + + +theorem finite_additive_representation_lift + (ρ : Multiplicative H →* Matrix ι ι k) : + ∃ σ : Multiplicative k →* Matrix ι ι k, + (∀ h : H, σ (Multiplicative.ofAdd (h : k)) = ρ (Multiplicative.ofAdd h)) ∧ + (∀ i j : ι, ∃ f : k[X], f.degree < (Fintype.card H : WithBot ℕ) ∧ + ∀ t : k, σ (Multiplicative.ofAdd t) i j = f.eval t) := by + refine ⟨extendedRepresentation H ρ, ?_, ?_⟩ + · exact liftMatrix_at_subgroup H ρ + · intro i j + exact ⟨liftEntry H ρ i j, liftEntry_degree H ρ i j, fun _ => rfl⟩ + +end FiberFunctorProof + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/RestrictedTarget.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/RestrictedTarget.lean index 44b0cbc46c15477de351bc07af1aebb482538213..fce745b3bfd145d9bff34b5cd40ef7b4fffa8643 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/RestrictedTarget.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/RestrictedTarget.lean @@ -1,167 +1,167 @@ -import Mathlib - -namespace OAI - - - -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof.RestrictedTarget - -universe u - -section PolynomialAction -variable {k : Type u} [CommRing k] {ι : Type*} [Fintype ι] - - -noncomputable def linearChange (A : Matrix ι ι k) : - MvPolynomial ι k →ₐ[k] MvPolynomial ι k := - MvPolynomial.aeval (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) - -@[simp] lemma linearChange_X (A : Matrix ι ι k) (i : ι) : - linearChange A (MvPolynomial.X i) = - ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j := by - simp [linearChange] - -@[simp] lemma linearChange_C (A : Matrix ι ι k) (x : k) : - linearChange A (MvPolynomial.C x) = MvPolynomial.C x := by - simp [linearChange] - -variable [DecidableEq ι] - -@[simp] lemma linearChange_one : linearChange (1 : Matrix ι ι k) = AlgHom.id k _ := by - ext i : 1 - simp [linearChange, Matrix.one_apply] - -omit [DecidableEq ι] in -lemma linearChange_mul (A B : Matrix ι ι k) : - linearChange (A * B) = (linearChange A).comp (linearChange B) := by - ext i : 1 - simp only [AlgHom.comp_apply, linearChange_X, map_sum, map_mul, linearChange_C, - Matrix.mul_apply, Finset.sum_mul, Finset.mul_sum] - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro j hj - apply Finset.sum_congr rfl - intro l hl - ring - -omit [DecidableEq ι] in -lemma linearChange_homogeneous (A : Matrix ι ι k) {f : MvPolynomial ι k} {n : ℕ} - (hf : f.IsHomogeneous n) : (linearChange A f).IsHomogeneous n := by - change (MvPolynomial.eval₂ MvPolynomial.C - (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) f).IsHomogeneous n - simpa only [one_mul] using - hf.eval₂ MvPolynomial.C - (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) - (fun x => MvPolynomial.isHomogeneous_C ι x) - (fun i => MvPolynomial.IsHomogeneous.sum _ _ _ - (fun j _ => (MvPolynomial.isHomogeneous_X k j).C_mul (A j i))) - -noncomputable def homogeneousRepresentation (n : ℕ) : - Representation k (Matrix ι ι k) (MvPolynomial.homogeneousSubmodule ι k n) where - toFun A := (linearChange A).toLinearMap.restrict (fun _ hf => linearChange_homogeneous A hf) - map_one' := by - ext f : 1 - apply Subtype.ext - change linearChange 1 f.val = f.val - rw [linearChange_one] - rfl - map_mul' A B := by - ext f : 1 - apply Subtype.ext - change linearChange (A * B) f.val = linearChange A (linearChange B f.val) - rw [linearChange_mul] - rfl - -end PolynomialAction - -section SL2 -variable (k : Type u) [Field k] - -abbrev SL2 := Matrix.SpecialLinearGroup (Fin 2) k - - -def IsRational {M : Type u} [AddCommGroup M] [Module k M] - (ρ : Representation k (SL2 k) M) : Prop := - ∀ (v : M) (l : M →ₗ[k] k), - ∃ P : MvPolynomial (Fin 2 × Fin 2) k, - ∀ g : SL2 k, l (ρ g v) = MvPolynomial.eval (fun ij => g ij.1 ij.2) P - - -noncomputable def dualMatrix : SL2 k →* Matrix (Fin 2) (Fin 2) k where - toFun g := ((g⁻¹ : SL2 k) : Matrix (Fin 2) (Fin 2) k).transpose - map_one' := by simp - map_mul' g h := by - simp [mul_inv_rev, Matrix.SpecialLinearGroup.coe_mul, Matrix.transpose_mul] - -instance homogeneous_finite (n : ℕ) : - Module.Finite k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) := - Module.Finite.of_fg (MvPolynomial.homogeneousSubmodule_fg (Fin 2) k n) - - -noncomputable def costandard (n : ℕ) : FDRep k (SL2 k) := - FDRep.of ((homogeneousRepresentation n).comp (dualMatrix k)) - - -inductive HasGoodFiltration : FDRep k (SL2 k) → Prop - | zero (V) (hV : IsZero V) : HasGoodFiltration V - | step {A B} (n : ℕ) (f : A ⟶ B) (g : B ⟶ costandard k n) - (w : f ≫ g = 0) (hS : (ShortComplex.mk f g w).ShortExact) - (hA : HasGoodFiltration A) : HasGoodFiltration B - - - -def IsTilting (V : FDRep k (SL2 k)) : Prop := - IsRational k V.ρ ∧ HasGoodFiltration k V ∧ HasGoodFiltration k Vᘁ - - -noncomputable def steinberg (p m : ℕ) : FDRep k (SL2 k) := - costandard k (p ^ m - 1) - - -def unipotent (t : k) : SL2 k := - ⟨!![1, t; 0, 1], by simp [Matrix.det_fin_two]⟩ - -lemma unipotent_zero : unipotent k 0 = 1 := by - apply Subtype.ext - ext i j - fin_cases i <;> fin_cases j <;> simp [unipotent] - -lemma unipotent_add (t s : k) : unipotent k (t + s) = unipotent k t * unipotent k s := by - apply Subtype.ext - change !![1, t + s; 0, 1] = !![1, t; 0, 1] * !![1, s; 0, 1] - ext i j - fin_cases i <;> fin_cases j <;> - simp [Matrix.mul_apply, Fin.sum_univ_two, add_comm] - - -def elementaryEmbedding (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : - Multiplicative (Fin r → ZMod p) →* SL2 k where - toFun a := unipotent k (l a.toAdd) - map_one' := by simp [unipotent_zero] - map_mul' a b := by simp [unipotent_add] - -noncomputable def restrictElementary (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : - FDRep k (SL2 k) ⥤ FDRep k (Multiplicative (Fin r → ZMod p)) := - Action.res (FGModuleCat k) (elementaryEmbedding k p r l) - -end SL2 -end FiberFunctorProof.RestrictedTarget - -namespace FiberFunctorProof.RestrictedTarget -open CategoryTheory CategoryTheory.MonoidalCategory -universe u - - -def RestrictedTiltingTheorem : Prop := - ∀ (k : Type u) [Field k] [IsAlgClosed k] (p : ℕ) [Fact p.Prime] [CharP k p] - (r : ℕ), 1 ≤ r → ∀ (l : (Fin r → ZMod p) →+ k), Function.Injective l → - ∀ (D : FDRep k (Multiplicative (Fin r → ZMod p))), - ∃ T : FDRep k (SL2 k), IsTilting k T ∧ - Nonempty (((restrictElementary k p r l).obj (steinberg k p (r-1)) ⊗ D) ≅ - (restrictElementary k p r l).obj T) -end FiberFunctorProof.RestrictedTarget - -end OAI +import Mathlib + +namespace OAI + + + +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof.RestrictedTarget + +universe u + +section PolynomialAction +variable {k : Type u} [CommRing k] {ι : Type*} [Fintype ι] + + +noncomputable def linearChange (A : Matrix ι ι k) : + MvPolynomial ι k →ₐ[k] MvPolynomial ι k := + MvPolynomial.aeval (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) + +@[simp] lemma linearChange_X (A : Matrix ι ι k) (i : ι) : + linearChange A (MvPolynomial.X i) = + ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j := by + simp [linearChange] + +@[simp] lemma linearChange_C (A : Matrix ι ι k) (x : k) : + linearChange A (MvPolynomial.C x) = MvPolynomial.C x := by + simp [linearChange] + +variable [DecidableEq ι] + +@[simp] lemma linearChange_one : linearChange (1 : Matrix ι ι k) = AlgHom.id k _ := by + ext i : 1 + simp [linearChange, Matrix.one_apply] + +omit [DecidableEq ι] in +lemma linearChange_mul (A B : Matrix ι ι k) : + linearChange (A * B) = (linearChange A).comp (linearChange B) := by + ext i : 1 + simp only [AlgHom.comp_apply, linearChange_X, map_sum, map_mul, linearChange_C, + Matrix.mul_apply, Finset.sum_mul, Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro j hj + apply Finset.sum_congr rfl + intro l hl + ring + +omit [DecidableEq ι] in +lemma linearChange_homogeneous (A : Matrix ι ι k) {f : MvPolynomial ι k} {n : ℕ} + (hf : f.IsHomogeneous n) : (linearChange A f).IsHomogeneous n := by + change (MvPolynomial.eval₂ MvPolynomial.C + (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) f).IsHomogeneous n + simpa only [one_mul] using + hf.eval₂ MvPolynomial.C + (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) + (fun x => MvPolynomial.isHomogeneous_C ι x) + (fun i => MvPolynomial.IsHomogeneous.sum _ _ _ + (fun j _ => (MvPolynomial.isHomogeneous_X k j).C_mul (A j i))) + +noncomputable def homogeneousRepresentation (n : ℕ) : + Representation k (Matrix ι ι k) (MvPolynomial.homogeneousSubmodule ι k n) where + toFun A := (linearChange A).toLinearMap.restrict (fun _ hf => linearChange_homogeneous A hf) + map_one' := by + ext f : 1 + apply Subtype.ext + change linearChange 1 f.val = f.val + rw [linearChange_one] + rfl + map_mul' A B := by + ext f : 1 + apply Subtype.ext + change linearChange (A * B) f.val = linearChange A (linearChange B f.val) + rw [linearChange_mul] + rfl + +end PolynomialAction + +section SL2 +variable (k : Type u) [Field k] + +abbrev SL2 := Matrix.SpecialLinearGroup (Fin 2) k + + +def IsRational {M : Type u} [AddCommGroup M] [Module k M] + (ρ : Representation k (SL2 k) M) : Prop := + ∀ (v : M) (l : M →ₗ[k] k), + ∃ P : MvPolynomial (Fin 2 × Fin 2) k, + ∀ g : SL2 k, l (ρ g v) = MvPolynomial.eval (fun ij => g ij.1 ij.2) P + + +noncomputable def dualMatrix : SL2 k →* Matrix (Fin 2) (Fin 2) k where + toFun g := ((g⁻¹ : SL2 k) : Matrix (Fin 2) (Fin 2) k).transpose + map_one' := by simp + map_mul' g h := by + simp [mul_inv_rev, Matrix.SpecialLinearGroup.coe_mul, Matrix.transpose_mul] + +instance homogeneous_finite (n : ℕ) : + Module.Finite k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) := + Module.Finite.of_fg (MvPolynomial.homogeneousSubmodule_fg (Fin 2) k n) + + +noncomputable def costandard (n : ℕ) : FDRep k (SL2 k) := + FDRep.of ((homogeneousRepresentation n).comp (dualMatrix k)) + + +inductive HasGoodFiltration : FDRep k (SL2 k) → Prop + | zero (V) (hV : IsZero V) : HasGoodFiltration V + | step {A B} (n : ℕ) (f : A ⟶ B) (g : B ⟶ costandard k n) + (w : f ≫ g = 0) (hS : (ShortComplex.mk f g w).ShortExact) + (hA : HasGoodFiltration A) : HasGoodFiltration B + + + +def IsTilting (V : FDRep k (SL2 k)) : Prop := + IsRational k V.ρ ∧ HasGoodFiltration k V ∧ HasGoodFiltration k Vᘁ + + +noncomputable def steinberg (p m : ℕ) : FDRep k (SL2 k) := + costandard k (p ^ m - 1) + + +def unipotent (t : k) : SL2 k := + ⟨!![1, t; 0, 1], by simp [Matrix.det_fin_two]⟩ + +lemma unipotent_zero : unipotent k 0 = 1 := by + apply Subtype.ext + ext i j + fin_cases i <;> fin_cases j <;> simp [unipotent] + +lemma unipotent_add (t s : k) : unipotent k (t + s) = unipotent k t * unipotent k s := by + apply Subtype.ext + change !![1, t + s; 0, 1] = !![1, t; 0, 1] * !![1, s; 0, 1] + ext i j + fin_cases i <;> fin_cases j <;> + simp [Matrix.mul_apply, Fin.sum_univ_two, add_comm] + + +def elementaryEmbedding (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : + Multiplicative (Fin r → ZMod p) →* SL2 k where + toFun a := unipotent k (l a.toAdd) + map_one' := by simp [unipotent_zero] + map_mul' a b := by simp [unipotent_add] + +noncomputable def restrictElementary (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : + FDRep k (SL2 k) ⥤ FDRep k (Multiplicative (Fin r → ZMod p)) := + Action.res (FGModuleCat k) (elementaryEmbedding k p r l) + +end SL2 +end FiberFunctorProof.RestrictedTarget + +namespace FiberFunctorProof.RestrictedTarget +open CategoryTheory CategoryTheory.MonoidalCategory +universe u + + +def RestrictedTiltingTheorem : Prop := + ∀ (k : Type u) [Field k] [IsAlgClosed k] (p : ℕ) [Fact p.Prime] [CharP k p] + (r : ℕ), 1 ≤ r → ∀ (l : (Fin r → ZMod p) →+ k), Function.Injective l → + ∀ (D : FDRep k (Multiplicative (Fin r → ZMod p))), + ∃ T : FDRep k (SL2 k), IsTilting k T ∧ + Nonempty (((restrictElementary k p r l).obj (steinberg k p (r-1)) ⊗ D) ≅ + (restrictElementary k p r l).obj T) +end FiberFunctorProof.RestrictedTarget + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/RestrictedTilting.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/RestrictedTilting.lean index 46f90615046efe3d95c24fc9a7578f555e0ada21..d998dd13f9d36a2d9a777f66b2ae14b0c14488c7 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/RestrictedTilting.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/RestrictedTilting.lean @@ -1,62 +1,62 @@ -import OAI.RepresentationTheory.RestrictedTilting.BoundedUnipotentTilting -import OAI.RepresentationTheory.RestrictedTilting.FiniteSubgroupLift -import OAI.RepresentationTheory.RestrictedTilting.TensorCoordinates - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory Matrix -open scoped TensorProduct Kronecker -universe u - - - -def RestrictedTiltingTheorem : Prop := - ∀ (k : Type u) [Field k] [IsAlgClosed k] (p : ℕ) [Fact p.Prime] [CharP k p] - (r : ℕ), 1 ≤ r → ∀ (l : (Fin r → ZMod p) →+ k), Function.Injective l → - ∀ (D : FDRep k (Multiplicative (Fin r → ZMod p))), - ∃ T : FDRep k (SL2 k), IsTilting k T ∧ - Nonempty (((restrictElementary k p r l).obj (steinberg k p (r-1)) ⊗ D) ≅ - (restrictElementary k p r l).obj T) - - - -theorem restricted_tilting : RestrictedTiltingTheorem.{u} := by - intro k _ _ p _ _ r hr l hl D - classical - let S := steinberg k p (r-1) - let β := ULift.{u} (Fin (Module.finrank k S)) - let ι := ULift.{u} (Fin (Module.finrank k D)) - let e : S ≃ₗ[k] (β → k) := ((Module.finBasis k S).reindex Equiv.ulift.symm).equivFun - let f : D ≃ₗ[k] (ι → k) := ((Module.finBasis k D).reindex Equiv.ulift.symm).equivFun - let σ := coordinateRepresentation k D.ρ f - obtain ⟨ρ,P,hP,hd,hρ⟩ := finite_subgroup_polynomial_lift k l hl σ - have hc : Fintype.card (Fin r → ZMod p) = p^r := by - simp only [Fintype.card_fun, Fintype.card_fin, ZMod.card] - rw [hc] at hd - have hp : 0 < p^r := Nat.pow_pos (Fact.out : p.Prime).pos - have hm : p^r-1 < p^((r-1)+1) := by - rw [Nat.sub_add_cancel hr] - omega - obtain ⟨T,hT,E,hE⟩ := bounded_unipotent_tilting_coordinates k p β ι ρ P hP (p^r-1) hd - (r-1) hm e - let C := tensorCoordinates k e f - let A := ((restrictElementary k p r l).obj S) ⊗ D - let B := (restrictElementary k p r l).obj T - let L : A ≃ₗ[k] B := C.trans E.symm - have hL : ∀ a, ∀ v : A, L (A.ρ a v) = B.ρ a (L v) := by - intro a v - apply E.injective - change E (E.symm (C (A.ρ a v))) = E (T.ρ (unipotent k (l a.toAdd)) (E.symm (C v))) - rw [E.apply_symm_apply, hE, E.apply_symm_apply] - have hC := tensorCoordinates_intertwines k - (S.ρ.comp (elementaryEmbedding k p r l)) D.ρ e f a v - change C (A.ρ a v) = _ at hC - rw [hC, hρ] - rfl - refine ⟨T,hT, ⟨Action.mkIso L.toFGModuleCatIso (fun a => ?_)⟩⟩ - apply FGModuleCat.hom_ext - exact LinearMap.ext (hL a) -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.BoundedUnipotentTilting +import OAI.RepresentationTheory.RestrictedTilting.FiniteSubgroupLift +import OAI.RepresentationTheory.RestrictedTilting.TensorCoordinates + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory Matrix +open scoped TensorProduct Kronecker +universe u + + + +def RestrictedTiltingTheorem : Prop := + ∀ (k : Type u) [Field k] [IsAlgClosed k] (p : ℕ) [Fact p.Prime] [CharP k p] + (r : ℕ), 1 ≤ r → ∀ (l : (Fin r → ZMod p) →+ k), Function.Injective l → + ∀ (D : FDRep k (Multiplicative (Fin r → ZMod p))), + ∃ T : FDRep k (SL2 k), IsTilting k T ∧ + Nonempty (((restrictElementary k p r l).obj (steinberg k p (r-1)) ⊗ D) ≅ + (restrictElementary k p r l).obj T) + + + +theorem restricted_tilting : RestrictedTiltingTheorem.{u} := by + intro k _ _ p _ _ r hr l hl D + classical + let S := steinberg k p (r-1) + let β := ULift.{u} (Fin (Module.finrank k S)) + let ι := ULift.{u} (Fin (Module.finrank k D)) + let e : S ≃ₗ[k] (β → k) := ((Module.finBasis k S).reindex Equiv.ulift.symm).equivFun + let f : D ≃ₗ[k] (ι → k) := ((Module.finBasis k D).reindex Equiv.ulift.symm).equivFun + let σ := coordinateRepresentation k D.ρ f + obtain ⟨ρ,P,hP,hd,hρ⟩ := finite_subgroup_polynomial_lift k l hl σ + have hc : Fintype.card (Fin r → ZMod p) = p^r := by + simp only [Fintype.card_fun, Fintype.card_fin, ZMod.card] + rw [hc] at hd + have hp : 0 < p^r := Nat.pow_pos (Fact.out : p.Prime).pos + have hm : p^r-1 < p^((r-1)+1) := by + rw [Nat.sub_add_cancel hr] + omega + obtain ⟨T,hT,E,hE⟩ := bounded_unipotent_tilting_coordinates k p β ι ρ P hP (p^r-1) hd + (r-1) hm e + let C := tensorCoordinates k e f + let A := ((restrictElementary k p r l).obj S) ⊗ D + let B := (restrictElementary k p r l).obj T + let L : A ≃ₗ[k] B := C.trans E.symm + have hL : ∀ a, ∀ v : A, L (A.ρ a v) = B.ρ a (L v) := by + intro a v + apply E.injective + change E (E.symm (C (A.ρ a v))) = E (T.ρ (unipotent k (l a.toAdd)) (E.symm (C v))) + rw [E.apply_symm_apply, hE, E.apply_symm_apply] + have hC := tensorCoordinates_intertwines k + (S.ρ.comp (elementaryEmbedding k p r l)) D.ρ e f a v + change C (A.ρ a v) = _ at hC + rw [hC, hρ] + rfl + refine ⟨T,hT, ⟨Action.mkIso L.toFGModuleCatIso (fun a => ?_)⟩⟩ + apply FGModuleCat.hom_ext + exact LinearMap.ext (hL a) +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/SL2Definitions.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/SL2Definitions.lean index db336a4d207547f81e6fa28d9824387ffe712eea..ec1b6a4185342ed9edaed4e0825b1cdabdb47250 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/SL2Definitions.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/SL2Definitions.lean @@ -1,159 +1,159 @@ -import Mathlib - -namespace OAI - -/-! Polynomial actions, rational SL₂ representations and tilting definitions. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof - -universe u - -section PolynomialAction -variable {k : Type u} [CommRing k] {ι : Type*} [Fintype ι] - - -noncomputable def linearChange (A : Matrix ι ι k) : - MvPolynomial ι k →ₐ[k] MvPolynomial ι k := - MvPolynomial.aeval (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) - -@[simp] lemma linearChange_X (A : Matrix ι ι k) (i : ι) : - linearChange A (MvPolynomial.X i) = - ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j := by - simp [linearChange] - -@[simp] lemma linearChange_C (A : Matrix ι ι k) (x : k) : - linearChange A (MvPolynomial.C x) = MvPolynomial.C x := by - simp [linearChange] - -variable [DecidableEq ι] - -@[simp] lemma linearChange_one : linearChange (1 : Matrix ι ι k) = AlgHom.id k _ := by - ext i : 1 - simp [linearChange, Matrix.one_apply] - -omit [DecidableEq ι] in -lemma linearChange_mul (A B : Matrix ι ι k) : - linearChange (A * B) = (linearChange A).comp (linearChange B) := by - ext i : 1 - simp only [AlgHom.comp_apply, linearChange_X, map_sum, map_mul, linearChange_C, - Matrix.mul_apply, Finset.sum_mul, Finset.mul_sum] - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro j hj - apply Finset.sum_congr rfl - intro l hl - ring - -omit [DecidableEq ι] in -lemma linearChange_homogeneous (A : Matrix ι ι k) {f : MvPolynomial ι k} {n : ℕ} - (hf : f.IsHomogeneous n) : (linearChange A f).IsHomogeneous n := by - change (MvPolynomial.eval₂ MvPolynomial.C - (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) f).IsHomogeneous n - simpa only [one_mul] using - hf.eval₂ MvPolynomial.C - (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) - (fun x => MvPolynomial.isHomogeneous_C ι x) - (fun i => MvPolynomial.IsHomogeneous.sum _ _ _ - (fun j _ => (MvPolynomial.isHomogeneous_X k j).C_mul (A j i))) - -noncomputable def homogeneousRepresentation (n : ℕ) : - Representation k (Matrix ι ι k) (MvPolynomial.homogeneousSubmodule ι k n) where - toFun A := (linearChange A).toLinearMap.restrict (fun _ hf => linearChange_homogeneous A hf) - map_one' := by - ext f : 1 - apply Subtype.ext - change linearChange 1 f.val = f.val - rw [linearChange_one] - rfl - map_mul' A B := by - ext f : 1 - apply Subtype.ext - change linearChange (A * B) f.val = linearChange A (linearChange B f.val) - rw [linearChange_mul] - rfl - -end PolynomialAction - -section SL2 -variable (k : Type u) [Field k] - -abbrev SL2 := Matrix.SpecialLinearGroup (Fin 2) k - - -def IsRational {M : Type u} [AddCommGroup M] [Module k M] - (ρ : Representation k (SL2 k) M) : Prop := - ∀ (v : M) (l : M →ₗ[k] k), - ∃ P : MvPolynomial (Fin 2 × Fin 2) k, - ∀ g : SL2 k, l (ρ g v) = MvPolynomial.eval (fun ij => g ij.1 ij.2) P - - -noncomputable def dualMatrix : SL2 k →* Matrix (Fin 2) (Fin 2) k where - toFun g := ((g⁻¹ : SL2 k) : Matrix (Fin 2) (Fin 2) k).transpose - map_one' := by simp - map_mul' g h := by - simp [mul_inv_rev, Matrix.SpecialLinearGroup.coe_mul, Matrix.transpose_mul] - -instance homogeneous_finite (n : ℕ) : - Module.Finite k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) := - Module.Finite.of_fg (MvPolynomial.homogeneousSubmodule_fg (Fin 2) k n) - - -noncomputable def costandard (n : ℕ) : FDRep k (SL2 k) := - FDRep.of ((homogeneousRepresentation n).comp (dualMatrix k)) - - -inductive HasGoodFiltration : FDRep k (SL2 k) → Prop - | zero (V) (hV : IsZero V) : HasGoodFiltration V - | step {A B} (n : ℕ) (f : A ⟶ B) (g : B ⟶ costandard k n) - (w : f ≫ g = 0) (hS : (ShortComplex.mk f g w).ShortExact) - (hA : HasGoodFiltration A) : HasGoodFiltration B - - - -def IsTilting (V : FDRep k (SL2 k)) : Prop := - IsRational k V.ρ ∧ HasGoodFiltration k V ∧ HasGoodFiltration k Vᘁ - - -noncomputable def steinberg (p m : ℕ) : FDRep k (SL2 k) := - costandard k (p ^ m - 1) - - -def unipotent (t : k) : SL2 k := - ⟨!![1, t; 0, 1], by simp [Matrix.det_fin_two]⟩ - -lemma unipotent_zero : unipotent k 0 = 1 := by - apply Subtype.ext - ext i j - fin_cases i <;> fin_cases j <;> simp [unipotent] - -lemma unipotent_add (t s : k) : unipotent k (t + s) = unipotent k t * unipotent k s := by - apply Subtype.ext - change !![1, t + s; 0, 1] = !![1, t; 0, 1] * !![1, s; 0, 1] - ext i j - fin_cases i <;> fin_cases j <;> - simp [Matrix.mul_apply, Fin.sum_univ_two, add_comm] - - -def elementaryEmbedding (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : - Multiplicative (Fin r → ZMod p) →* SL2 k where - toFun a := unipotent k (l a.toAdd) - map_one' := by simp [unipotent_zero] - map_mul' a b := by simp [unipotent_add] - -noncomputable def restrictElementary (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : - FDRep k (SL2 k) ⥤ FDRep k (Multiplicative (Fin r → ZMod p)) := - Action.res (FGModuleCat k) (elementaryEmbedding k p r l) - -end SL2 -end FiberFunctorProof - - - -open scoped BigOperators -end - -end OAI +import Mathlib + +namespace OAI + +/-! Polynomial actions, rational SL₂ representations and tilting definitions. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof + +universe u + +section PolynomialAction +variable {k : Type u} [CommRing k] {ι : Type*} [Fintype ι] + + +noncomputable def linearChange (A : Matrix ι ι k) : + MvPolynomial ι k →ₐ[k] MvPolynomial ι k := + MvPolynomial.aeval (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) + +@[simp] lemma linearChange_X (A : Matrix ι ι k) (i : ι) : + linearChange A (MvPolynomial.X i) = + ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j := by + simp [linearChange] + +@[simp] lemma linearChange_C (A : Matrix ι ι k) (x : k) : + linearChange A (MvPolynomial.C x) = MvPolynomial.C x := by + simp [linearChange] + +variable [DecidableEq ι] + +@[simp] lemma linearChange_one : linearChange (1 : Matrix ι ι k) = AlgHom.id k _ := by + ext i : 1 + simp [linearChange, Matrix.one_apply] + +omit [DecidableEq ι] in +lemma linearChange_mul (A B : Matrix ι ι k) : + linearChange (A * B) = (linearChange A).comp (linearChange B) := by + ext i : 1 + simp only [AlgHom.comp_apply, linearChange_X, map_sum, map_mul, linearChange_C, + Matrix.mul_apply, Finset.sum_mul, Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro j hj + apply Finset.sum_congr rfl + intro l hl + ring + +omit [DecidableEq ι] in +lemma linearChange_homogeneous (A : Matrix ι ι k) {f : MvPolynomial ι k} {n : ℕ} + (hf : f.IsHomogeneous n) : (linearChange A f).IsHomogeneous n := by + change (MvPolynomial.eval₂ MvPolynomial.C + (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) f).IsHomogeneous n + simpa only [one_mul] using + hf.eval₂ MvPolynomial.C + (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) + (fun x => MvPolynomial.isHomogeneous_C ι x) + (fun i => MvPolynomial.IsHomogeneous.sum _ _ _ + (fun j _ => (MvPolynomial.isHomogeneous_X k j).C_mul (A j i))) + +noncomputable def homogeneousRepresentation (n : ℕ) : + Representation k (Matrix ι ι k) (MvPolynomial.homogeneousSubmodule ι k n) where + toFun A := (linearChange A).toLinearMap.restrict (fun _ hf => linearChange_homogeneous A hf) + map_one' := by + ext f : 1 + apply Subtype.ext + change linearChange 1 f.val = f.val + rw [linearChange_one] + rfl + map_mul' A B := by + ext f : 1 + apply Subtype.ext + change linearChange (A * B) f.val = linearChange A (linearChange B f.val) + rw [linearChange_mul] + rfl + +end PolynomialAction + +section SL2 +variable (k : Type u) [Field k] + +abbrev SL2 := Matrix.SpecialLinearGroup (Fin 2) k + + +def IsRational {M : Type u} [AddCommGroup M] [Module k M] + (ρ : Representation k (SL2 k) M) : Prop := + ∀ (v : M) (l : M →ₗ[k] k), + ∃ P : MvPolynomial (Fin 2 × Fin 2) k, + ∀ g : SL2 k, l (ρ g v) = MvPolynomial.eval (fun ij => g ij.1 ij.2) P + + +noncomputable def dualMatrix : SL2 k →* Matrix (Fin 2) (Fin 2) k where + toFun g := ((g⁻¹ : SL2 k) : Matrix (Fin 2) (Fin 2) k).transpose + map_one' := by simp + map_mul' g h := by + simp [mul_inv_rev, Matrix.SpecialLinearGroup.coe_mul, Matrix.transpose_mul] + +instance homogeneous_finite (n : ℕ) : + Module.Finite k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) := + Module.Finite.of_fg (MvPolynomial.homogeneousSubmodule_fg (Fin 2) k n) + + +noncomputable def costandard (n : ℕ) : FDRep k (SL2 k) := + FDRep.of ((homogeneousRepresentation n).comp (dualMatrix k)) + + +inductive HasGoodFiltration : FDRep k (SL2 k) → Prop + | zero (V) (hV : IsZero V) : HasGoodFiltration V + | step {A B} (n : ℕ) (f : A ⟶ B) (g : B ⟶ costandard k n) + (w : f ≫ g = 0) (hS : (ShortComplex.mk f g w).ShortExact) + (hA : HasGoodFiltration A) : HasGoodFiltration B + + + +def IsTilting (V : FDRep k (SL2 k)) : Prop := + IsRational k V.ρ ∧ HasGoodFiltration k V ∧ HasGoodFiltration k Vᘁ + + +noncomputable def steinberg (p m : ℕ) : FDRep k (SL2 k) := + costandard k (p ^ m - 1) + + +def unipotent (t : k) : SL2 k := + ⟨!![1, t; 0, 1], by simp [Matrix.det_fin_two]⟩ + +lemma unipotent_zero : unipotent k 0 = 1 := by + apply Subtype.ext + ext i j + fin_cases i <;> fin_cases j <;> simp [unipotent] + +lemma unipotent_add (t s : k) : unipotent k (t + s) = unipotent k t * unipotent k s := by + apply Subtype.ext + change !![1, t + s; 0, 1] = !![1, t; 0, 1] * !![1, s; 0, 1] + ext i j + fin_cases i <;> fin_cases j <;> + simp [Matrix.mul_apply, Fin.sum_univ_two, add_comm] + + +def elementaryEmbedding (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : + Multiplicative (Fin r → ZMod p) →* SL2 k where + toFun a := unipotent k (l a.toAdd) + map_one' := by simp [unipotent_zero] + map_mul' a b := by simp [unipotent_add] + +noncomputable def restrictElementary (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : + FDRep k (SL2 k) ⥤ FDRep k (Multiplicative (Fin r → ZMod p)) := + Action.res (FGModuleCat k) (elementaryEmbedding k p r l) + +end SL2 +end FiberFunctorProof + + + +open scoped BigOperators +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/SimpleModules.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/SimpleModules.lean index 38f4677adf5b4783f9237d4d330f37075e3090ae..aa809c40c1877356ce84874396640807bf2647b3 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/SimpleModules.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/SimpleModules.lean @@ -1,479 +1,479 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.FrobeniusTensor - -namespace OAI - -/-! Costandard socles and the digit factorization of simple SL₂ modules. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section -universe u -variable (k : Type u) [Field k] [Infinite k] - -omit [Infinite k] in -lemma independent_sum_mem {ι T M : Type*} [AddCommGroup M] [Module k M] - (f : ι → T → k) (hf : LinearIndependent k f) (s : Finset ι) (c : ι → M) - (S : Submodule k M) (h : ∀ t, ∑ i ∈ s, f i t • c i ∈ S) : - ∀ i ∈ s, c i ∈ S := by - have hz : ∀ t, ∑ i ∈ s, f i t • S.mkQ (c i) = 0 := by - intro t - have hz : S.mkQ (∑ i ∈ s, f i t • c i) = 0 := - (Submodule.Quotient.mk_eq_zero S).mpr (h t) - simpa only [map_sum, map_smul] using hz - intro i hi - have hi' := function_sum_eq_zero f hf s (fun i => S.mkQ (c i)) hz i hi - exact (Submodule.Quotient.mk_eq_zero S).mp hi' - -lemma costandard_weight_component_mem (n : ℕ) (S : Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k))) - (v : MvPolynomial.homogeneousSubmodule (Fin 2) k n) (hv : v ∈ S) - (i : Fin (n+1)) : (binaryBasis k n).repr v i • binaryBasis k n i ∈ S := by - have hinj : Function.Injective (fun j : Fin (n+1) => integerCharacter k (2*(j:ℤ)-n)) := by - intro i j hij - have := integerCharacter_injective k hij - apply Fin.ext - omega - apply independent_sum_mem k - (fun j : Fin (n+1) => fun t : kˣ => integerCharacter k (2*(j:ℤ)-n) t) - ((linearIndependent_monoidHom kˣ k).comp _ hinj) Finset.univ - (fun j => (binaryBasis k n).repr v j • binaryBasis k n j) S.toSubmodule ?_ i - (Finset.mem_univ i) - intro t - let ρ : Representation k (SL2 k) (MvPolynomial.homogeneousSubmodule (Fin 2) k n) := - (homogeneousRepresentation n).comp (dualMatrix k) - have he : ρ (diagonalTorus k t) v = - ∑ j : Fin (n+1), integerCharacter k (2*(j:ℤ)-n) t • - ((binaryBasis k n).repr v j • binaryBasis k n j) := by - conv_lhs => rw [← (binaryBasis k n).sum_repr v, map_sum] - apply Finset.sum_congr rfl - intro j _ - rw [map_smul] - have hj : ρ (diagonalTorus k t) (binaryBasis k n j) = - integerCharacter k (2*(j:ℤ)-n) t • binaryBasis k n j := - costandard_basis_weight k n j t - rw [hj, smul_comm] - rw [← he] - exact S.apply_mem_toSubmodule (diagonalTorus k t) hv - -omit [Infinite k] in -lemma costandard_basis_upper_orbit (n : ℕ) (i : Fin (n+1)) (t : k) : - ((homogeneousRepresentation n).comp (dualMatrix k)) - (unipotent k t) (binaryBasis k n i) = - ∑ j : Fin (n-i.val+1), t^j.val • - (((-1 : k)^j.val * ((n-i.val).choose j.val : k)) • - binaryBasis k n ⟨i.val+j.val, by have := j.isLt; have := i.isLt; omega⟩) := by - apply Subtype.ext - change linearChange (dualMatrix k (unipotent k t)) (binaryBasis k n i).val = _ - rw [binaryBasis_apply] - have hx : linearChange (dualMatrix k (unipotent k t)) (MvPolynomial.X 0) = - (-MvPolynomial.C t * MvPolynomial.X 1 + MvPolynomial.X 0 : MvPolynomial (Fin 2) k) := by - simp [linearChange_X, dualMatrix, unipotent, Matrix.transpose_apply, Fin.sum_univ_two, add_comm] - have hy : linearChange (dualMatrix k (unipotent k t)) (MvPolynomial.X 1) = - (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) := by - simp [linearChange_X, dualMatrix, unipotent, Matrix.transpose_apply, Fin.sum_univ_two] - rw [map_mul, map_pow, map_pow, hx, hy, add_pow] - rw [← Fin.sum_univ_eq_sum_range, Finset.sum_mul] - simp only [Submodule.coe_sum, Submodule.coe_smul_of_tower, binaryBasis_apply, - MvPolynomial.smul_eq_C_mul] - apply Finset.sum_congr rfl - intro j _ - have he : n-(i.val+j.val) = n-i.val-j.val := by omega - rw [he] - have hneg : (-MvPolynomial.C t : MvPolynomial (Fin 2) k) = - MvPolynomial.C (-1 : k) * MvPolynomial.C t := by simp - rw [hneg] - simp only [map_mul, map_pow, map_neg, map_one, map_natCast, mul_pow] - rw [pow_add] - ring - -lemma costandardHighest_mem_of_basis_mem (n : ℕ) - (S : Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k))) (i : Fin (n+1)) - (hi : binaryBasis k n i ∈ S) : costandardHighest k n ∈ S := by - have h := independent_sum_mem k - (fun j : Fin (n-i.val+1) => fun t : k => t^j.val) - ((linearIndependent_powerFunctions k).comp Fin.val Fin.val_injective) Finset.univ - (fun j => ((-1 : k)^j.val * ((n-i.val).choose j.val : k)) • - binaryBasis k n ⟨i.val+j.val, by have := j.isLt; have := i.isLt; omega⟩) - S.toSubmodule (fun t => by - have h := S.apply_mem_toSubmodule (unipotent k t) hi - rw [costandard_basis_upper_orbit k n i t] at h - exact h) - (Fin.last (n-i.val)) (Finset.mem_univ _) - have he : i.val+(n-i.val) = n := by have := i.isLt; omega - have hind : (⟨i.val+(n-i.val), by omega⟩ : Fin (n+1)) = Fin.last n := Fin.ext he - simp only [Fin.val_last, Nat.choose_self,Nat.cast_one,mul_one,hind] at h - exact (Submodule.smul_mem_iff _ (pow_ne_zero _ (neg_ne_zero.mpr one_ne_zero))).mp h - - -lemma costandardHighest_mem_of_ne_bot (n : ℕ) - (S : Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k))) - (hS : S ≠ ⊥) : costandardHighest k n ∈ S := by - classical - have hS' : S.toSubmodule ≠ ⊥ := fun h => hS (Subrepresentation.ext h) - obtain ⟨v,hv,hv0⟩ := Submodule.exists_mem_ne_zero_of_ne_bot hS' - have hc : ∃ i, (binaryBasis k n).repr v i ≠ 0 := by - by_contra! hh - apply hv0 - apply (binaryBasis k n).repr.injective - ext i - simpa using hh i - obtain ⟨i,hi⟩ := hc - apply costandardHighest_mem_of_basis_mem k n S i - exact (Submodule.smul_mem_iff S.toSubmodule hi).mp - (costandard_weight_component_mem k n S v hv i) - -noncomputable def standardCostandardMap (n : ℕ) : - Representation.IntertwiningMap (standardRepresentation k n) - ((homogeneousRepresentation n).comp (dualMatrix k)) := - (exists_standard_costandard_map k n).choose.intertwiningMap_of_isIntertwiningMap _ _ - (exists_standard_costandard_map k n).choose_spec.1 - -lemma standardCostandardMap_basis (n : ℕ) (i : Fin (n+1)) : - standardCostandardMap k n (standardBasis k n i) = - ((-1:k)^i.val * (n.choose i : k)) • binaryBasis k n i.rev := - (exists_standard_costandard_map k n).choose_spec.2 i - -lemma standardCostandardMap_highest (n : ℕ) : - standardCostandardMap k n (standardHighest k n) = costandardHighest k n := by - change standardCostandardMap k n (standardBasis k n 0) = _ - rw [standardCostandardMap_basis] - simp only [Fin.val_zero,pow_zero,Nat.choose_zero_right,Nat.cast_one,mul_one,one_smul] - rfl - - - -noncomputable def costandardSocle (n : ℕ) : - Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k)) := - (standardCostandardMap k n).range - -lemma costandardHighest_mem_socle (n : ℕ) : - costandardHighest k n ∈ costandardSocle k n := - ⟨standardHighest k n, standardCostandardMap_highest k n⟩ - -lemma costandardSocle_le_of_highest_mem (n : ℕ) - (S : Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k))) - (hv : costandardHighest k n ∈ S) : costandardSocle k n ≤ S := by - intro v hv' - obtain ⟨x,rfl⟩ := hv' - have hc : ∀ i : Fin (n+1), - ((-1:k)^i.val * (n.choose i : k)) • binaryBasis k n i.rev ∈ S := by - intro i - apply independent_sum_mem k - (fun j : Fin (n+1) => fun t : k => t^j.val) - ((linearIndependent_powerFunctions k).comp Fin.val Fin.val_injective) Finset.univ - (fun j => ((-1:k)^j.val * (n.choose j : k)) • binaryBasis k n j.rev) - S.toSubmodule ?_ i (Finset.mem_univ _) - intro t - have ht := S.apply_mem_toSubmodule (lowerUnipotent k t) hv - change (costandard k n).ρ (lowerUnipotent k t) (costandardHighest k n) ∈ S at ht - rw [costandardHighest_lower_orbit] at ht - exact ht - rw [← (standardBasis k n).sum_repr x, map_sum] - apply S.toSubmodule.sum_mem - intro i _ - rw [map_smul] - change _ • standardCostandardMap k n (standardBasis k n i) ∈ S.toSubmodule - rw [standardCostandardMap_basis] - exact S.toSubmodule.smul_mem _ (hc i) - -lemma costandardSocle_le_of_ne_bot (n : ℕ) - (S : Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k))) - (hS : S ≠ ⊥) : costandardSocle k n ≤ S := - costandardSocle_le_of_highest_mem k n S (costandardHighest_mem_of_ne_bot k n S hS) - -lemma costandardSocle_ne_bot (n : ℕ) : costandardSocle k n ≠ ⊥ := by - intro h - have hv := costandardHighest_mem_socle k n - rw [h] at hv - exact (binaryBasis k n).ne_zero (Fin.last n) hv - -lemma binaryBasis_mem_costandardSocle (n : ℕ) (i : Fin (n+1)) - (hi : (n.choose i : k) ≠ 0) : binaryBasis k n i ∈ costandardSocle k n := by - have hc : (n.choose i.rev : k) = (n.choose i : k) := by - simpa only [Fin.val_rev,Nat.succ_sub_succ_eq_sub] using - congrArg (fun m : ℕ => (m : k)) (Nat.choose_symm (Nat.le_of_lt_succ i.isLt)) - let c : k := (-1:k)^i.rev.val * (n.choose i.rev : k) - have hc0 : c ≠ 0 := mul_ne_zero (pow_ne_zero _ (neg_ne_zero.mpr one_ne_zero)) (hc ▸ hi) - change binaryBasis k n i ∈ (standardCostandardMap k n).range - refine ⟨c⁻¹ • standardBasis k n i.rev, ?_⟩ - rw [map_smul] - change c⁻¹ • standardCostandardMap k n (standardBasis k n i.rev) = _ - rw [standardCostandardMap_basis, Fin.rev_rev, smul_smul, inv_mul_cancel₀ hc0, - one_smul] - -lemma costandardSocle_eq_top (n : ℕ) (hc : ∀ i : Fin (n+1), (n.choose i : k) ≠ 0) : - costandardSocle k n = ⊤ := by - apply Subrepresentation.ext - apply top_unique - rw [← (binaryBasis k n).span_eq] - exact Submodule.span_le.mpr (by - rintro _ ⟨i,rfl⟩ - exact binaryBasis_mem_costandardSocle k n i (hc i)) - - -noncomputable def simpleSL2 (n : ℕ) : FDRep k (SL2 k) := - FDRep.of (V := (costandardSocle k n).toSubmodule) (costandardSocle k n).toRepresentation - -lemma simpleSL2_rational (n : ℕ) : IsRational k (simpleSL2 k n).ρ := by - apply IsRational.of_injective k (simpleSL2 k n).ρ (costandard k n).ρ - (costandardSocle k n).toSubmodule.subtype Subtype.val_injective (by intros; rfl) - exact costandard_rational k n - -noncomputable def simpleCostandardι (n : ℕ) : simpleSL2 k n ⟶ costandard k n := - fdrepHom k (costandardSocle k n).toSubmodule.subtype (by intros; rfl) - -lemma simpleSL2_eq_costandard_of_choose (n : ℕ) - (hc : ∀ i : Fin (n+1), (n.choose i : k) ≠ 0) : - Nonempty (simpleSL2 k n ≅ costandard k n) := by - have hs : Function.Surjective (costandardSocle k n).toSubmodule.subtype := by - intro x - refine ⟨⟨x,?_⟩, rfl⟩ - rw [costandardSocle_eq_top k n hc] - trivial - have : IsIso (simpleCostandardι k n) := fdrepHom_isIso_of_bijective k _ - ⟨Subtype.val_injective,hs⟩ - exact ⟨asIso (simpleCostandardι k n)⟩ - -lemma simpleSL2_irreducible (n : ℕ) : Representation.IsIrreducible (simpleSL2 k n).ρ := by - let S := costandardSocle k n - have hw : (⟨costandardHighest k n,costandardHighest_mem_socle k n⟩ : S.toSubmodule) ≠ 0 := by - intro h - exact (binaryBasis k n).ne_zero (Fin.last n) (congrArg Subtype.val h) - let : Nontrivial (Subrepresentation S.toRepresentation) := - ⟨⟨⊥,⊤,by - intro h - have hz : (⟨costandardHighest k n,costandardHighest_mem_socle k n⟩ : S.toSubmodule) ∈ - (⊥ : Subrepresentation S.toRepresentation) := by rw [h]; trivial - exact hw hz⟩⟩ - change IsSimpleOrder (Subrepresentation S.toRepresentation) - apply IsSimpleOrder.of_forall_eq_top - intro T hT - let I : Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k)) := - { toSubmodule := T.toSubmodule.map S.toSubmodule.subtype - apply_mem_toSubmodule := by - intro g v hv - obtain ⟨x,hx,rfl⟩ := hv - exact ⟨S.toRepresentation g x,T.apply_mem_toSubmodule g hx,rfl⟩ } - have hI : I ≠ ⊥ := by - intro hI - apply hT - apply Subrepresentation.ext - apply le_antisymm ?_ bot_le - intro x hx - have hx' : x.val ∈ I := ⟨x,hx,rfl⟩ - rw [hI] at hx' - exact Subtype.ext hx' - have hle : S ≤ I := costandardSocle_le_of_ne_bot k n I hI - apply top_unique - intro x _ - have hx := hle x.property - obtain ⟨y,hy,he⟩ := hx - have he' : y = x := Subtype.ext he - exact he' ▸ hy -end - -section -open scoped TensorProduct -universe u -variable (k : Type u) [Field k] - -noncomputable def binaryDigitMultiply (p a b : ℕ) : - Binary k a ⊗[k] Binary k b →ₗ[k] Binary k (a+p*b) := - TensorProduct.lift - { toFun := fun f => - { toFun := fun g => ⟨f.val * MvPolynomial.expand p g.val, - f.property.mul (expand_homogeneous k p g.val g.property)⟩ - map_add' := by intro g h; apply Subtype.ext; simp [mul_add] - map_smul' := by intro c g; apply Subtype.ext; simp } - map_add' := by intro f g; ext h : 1; apply Subtype.ext; simp [add_mul] - map_smul' := by intro c f; ext g : 1; apply Subtype.ext; simp } - -lemma binaryDigitMultiply_basis (p a b : ℕ) (i : Fin (a+1)) (j : Fin (b+1)) : - binaryDigitMultiply k p a b (binaryBasis k a i ⊗ₜ[k] binaryBasis k b j) = - binaryBasis k (a+p*b) ⟨i.val+p*j.val, by - have := i.isLt; have := j.isLt; nlinarith⟩ := by - apply Subtype.ext - change (binaryBasis k a i).val * MvPolynomial.expand p (binaryBasis k b j).val = _ - simp only [binaryBasis_apply,map_mul,map_pow,MvPolynomial.expand_X,←pow_mul] - rw [mul_mul_mul_comm,←pow_add,←pow_add] - have he : a-i.val+p*(b-j.val) = a+p*b-(i.val+p*j.val) := by - rw [Nat.mul_sub_left_distrib] - have h₁ : i.val ≤ a := by omega - have h₂ : j.val ≤ b := by omega - have := Nat.mul_le_mul_left p h₂ - omega - rw [he] - -lemma digitIndex_injective (p a b : ℕ) (ha : a < p) : - Function.Injective (fun ij : Fin (a+1) × Fin (b+1) => ij.1.val+p*ij.2.val) := by - intro ⟨i,j⟩ ⟨i',j'⟩ h - have hi : i.val < p := by omega - have hi' : i'.val < p := by omega - have hm := congrArg (fun n => n % p) h - have hd := congrArg (fun n => n / p) h - have hp : 0 < p := by omega - simp only [Nat.add_mul_mod_self_left,Nat.mod_eq_of_lt hi,Nat.mod_eq_of_lt hi'] at hm - simp only [Nat.add_mul_div_left _ _ hp,Nat.div_eq_of_lt hi,Nat.div_eq_of_lt hi',zero_add] at hd - exact Prod.ext (Fin.ext hm) (Fin.ext hd) - -lemma binaryDigitMultiply_injective (p a b : ℕ) (ha : a < p) : - Function.Injective (binaryDigitMultiply k p a b) := by - let B := (binaryBasis k a).tensorProduct (binaryBasis k b) - apply LinearMap.injective_of_linearIndependent (R := k) - (f := binaryDigitMultiply k p a b) (v := B) B.span_eq - let idx : Fin (a+1) × Fin (b+1) → Fin (a+p*b+1) := - fun ij => ⟨ij.1.val+p*ij.2.val, by have := ij.1.isLt; have := ij.2.isLt; nlinarith⟩ - have hinj : Function.Injective idx := fun i j h => - digitIndex_injective p a b ha (congrArg Fin.val h) - have he : (binaryDigitMultiply k p a b) ∘ B = (binaryBasis k (a+p*b)) ∘ idx := by - funext ⟨i,j⟩ - simpa only [Function.comp_apply, B, idx, Module.Basis.tensorProduct_apply] using - binaryDigitMultiply_basis k p a b i j - rw [he] - exact (binaryBasis k (a+p*b)).linearIndependent.comp idx hinj - -variable (p : ℕ) [Fact p.Prime] [CharP k p] - -lemma choose_digit_cast (a b i j : ℕ) (ha : a < p) (hi : i < p) : - ((a+p*b).choose (i+p*j) : k) = (a.choose i : k) * (b.choose j : k) := by - have h := Choose.choose_modEq_choose_mod_mul_choose_div_nat - (p := p) (n := a+p*b) (k := i+p*j) - have hp := (Fact.out : p.Prime).pos - simp only [Nat.add_mul_mod_self_left,Nat.mod_eq_of_lt ha,Nat.mod_eq_of_lt hi, - Nat.add_mul_div_left _ _ hp,Nat.div_eq_of_lt ha,Nat.div_eq_of_lt hi,zero_add] at h - rw [← Nat.cast_mul] - exact (CharP.cast_eq_iff_mod_eq k p).mpr h - -lemma binaryDigitMultiply_intertwines (a b : ℕ) (g : SL2 k) - (z : Binary k a ⊗[k] Binary k b) : - binaryDigitMultiply k p a b - (Representation.tprod (costandard k a).ρ - ((costandard k b).ρ.comp (frobeniusSL2 k p)) g z) = - (costandard k (a+p*b)).ρ g (binaryDigitMultiply k p a b z) := by - change binaryDigitMultiply k p a b - (TensorProduct.map (homogeneousRepresentation a (dualMatrix k g)) - (homogeneousRepresentation b (dualMatrix k (frobeniusSL2 k p g))) z) = - homogeneousRepresentation (a+p*b) (dualMatrix k g) (binaryDigitMultiply k p a b z) - induction z using TensorProduct.inductionOn with - | add z w hz hw => simp only [map_add,hz,hw] - | tmul f h => - apply Subtype.ext - change linearChange (dualMatrix k g) f.val * - MvPolynomial.expand p (linearChange (dualMatrix k (frobeniusSL2 k p g)) h.val) = - linearChange (dualMatrix k g) (f.val * MvPolynomial.expand p h.val) - rw [map_mul,dualMatrix_frobeniusSL2,linearChange_expand] - -end - -open scoped TensorProduct -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (p : ℕ) [Fact p.Prime] [CharP k p] - -lemma binaryDigitMultiply_mem_socle (a b : ℕ) (ha : a < p) - (f : Binary k a) (g : (costandardSocle k b).toSubmodule) : - binaryDigitMultiply k p a b (f ⊗ₜ[k] g.val) ∈ costandardSocle k (a+p*b) := by - obtain ⟨x,hx⟩ := g.property - rw [← hx] - rw [← (binaryBasis k a).sum_repr f] - simp only [TensorProduct.sum_tmul,← TensorProduct.smul_tmul',map_sum,map_smul] - apply (costandardSocle k (a+p*b)).toSubmodule.sum_mem - intro i _ - apply (costandardSocle k (a+p*b)).toSubmodule.smul_mem - rw [← (standardBasis k b).sum_repr x] - simp only [map_sum,map_smul,TensorProduct.tmul_sum,TensorProduct.tmul_smul] - apply (costandardSocle k (a+p*b)).toSubmodule.sum_mem - intro j _ - apply (costandardSocle k (a+p*b)).toSubmodule.smul_mem - change binaryDigitMultiply k p a b - (binaryBasis k a i ⊗ₜ[k] standardCostandardMap k b (standardBasis k b j)) ∈ _ - rw [standardCostandardMap_basis,TensorProduct.tmul_smul,map_smul,binaryDigitMultiply_basis] - by_cases hj : (b.choose j : k) = 0 - · simp [hj] - · apply (costandardSocle k (a+p*b)).toSubmodule.smul_mem - apply binaryBasis_mem_costandardSocle - rw [choose_digit_cast k p a b i.val j.rev.val ha (by have := i.isLt; omega)] - apply mul_ne_zero (choose_cast_ne_zero_of_lt_char k p ha (Nat.le_of_lt_succ i.isLt)) - simpa only [Fin.val_rev,Nat.succ_sub_succ_eq_sub,Nat.choose_symm (Nat.le_of_lt_succ j.isLt)] using hj - -noncomputable def binarySocleDigitMultiply (a b : ℕ) : - Binary k a ⊗[k] (costandardSocle k b).toSubmodule →ₗ[k] Binary k (a+p*b) := - (binaryDigitMultiply k p a b).comp - ((costandardSocle k b).toSubmodule.subtype.lTensor (Binary k a)) - -omit [Fact p.Prime] [CharP k p] in -lemma binarySocleDigitMultiply_injective (a b : ℕ) (ha : a < p) : - Function.Injective (binarySocleDigitMultiply k p a b) := - (binaryDigitMultiply_injective k p a b ha).comp - (Module.Flat.lTensor_preserves_injective_linearMap - (costandardSocle k b).toSubmodule.subtype Subtype.val_injective) - -lemma binarySocleDigitMultiply_mem (a b : ℕ) (ha : a < p) - (z : Binary k a ⊗[k] (costandardSocle k b).toSubmodule) : - binarySocleDigitMultiply k p a b z ∈ costandardSocle k (a+p*b) := by - induction z using TensorProduct.inductionOn with - | add z w hz hw => - rw [map_add] - exact (costandardSocle k (a+p*b)).toSubmodule.add_mem hz hw - | tmul f g => exact binaryDigitMultiply_mem_socle k p a b ha f g - -lemma binarySocleDigitMultiply_intertwines (a b : ℕ) (g : SL2 k) - (z : Binary k a ⊗[k] (costandardSocle k b).toSubmodule) : - binarySocleDigitMultiply k p a b - (Representation.tprod ((homogeneousRepresentation a).comp (dualMatrix k)) - ((costandardSocle k b).toRepresentation.comp (frobeniusSL2 k p)) g z) = - ((homogeneousRepresentation (a+p*b)).comp (dualMatrix k)) g - (binarySocleDigitMultiply k p a b z) := by - induction z using TensorProduct.inductionOn with - | add z w hz hw => simp only [map_add,hz,hw] - | tmul f h => - exact binaryDigitMultiply_intertwines k p a b g (f ⊗ₜ[k] h.val) - -lemma binarySocleDigitMultiply_range (a b : ℕ) (ha : a < p) : - LinearMap.range (binarySocleDigitMultiply k p a b) = - (costandardSocle k (a+p*b)).toSubmodule := by - let f := (binarySocleDigitMultiply k p a b).intertwiningMap_of_isIntertwiningMap _ _ - (binarySocleDigitMultiply_intertwines k p a b) - apply le_antisymm - · rintro _ ⟨x,rfl⟩ - exact binarySocleDigitMultiply_mem k p a b ha x - · have h : costandardHighest k (a+p*b) ∈ f.range := by - refine ⟨costandardHighest k a ⊗ₜ[k] - ⟨costandardHighest k b,costandardHighest_mem_socle k b⟩, ?_⟩ - change binaryDigitMultiply k p a b - (binaryBasis k a (Fin.last a) ⊗ₜ[k] binaryBasis k b (Fin.last b)) = _ - rw [binaryDigitMultiply_basis] - rfl - exact costandardSocle_le_of_highest_mem k (a+p*b) f.range h - - - -noncomputable def simpleDigitIso (a b : ℕ) (ha : a < p) : - costandard k a ⊗ (Action.res (FGModuleCat k) (frobeniusSL2 k p)).obj (simpleSL2 k b) ≅ - simpleSL2 k (a+p*b) := by - let l := (binarySocleDigitMultiply k p a b).codRestrict - (costandardSocle k (a+p*b)).toSubmodule (binarySocleDigitMultiply_mem k p a b ha) - let f : costandard k a ⊗ - (Action.res (FGModuleCat k) (frobeniusSL2 k p)).obj (simpleSL2 k b) ⟶ - simpleSL2 k (a+p*b) := fdrepHom k l (by - intro g z - apply Subtype.ext - exact binarySocleDigitMultiply_intertwines k p a b g z) - have hinj : Function.Injective l := fun x y h => - binarySocleDigitMultiply_injective k p a b ha (congrArg Subtype.val h) - have hsurj : Function.Surjective l := by - intro x - have hx : x.val ∈ LinearMap.range (binarySocleDigitMultiply k p a b) := by - rw [binarySocleDigitMultiply_range k p a b ha] - exact x.property - obtain ⟨z,hz⟩ := hx - exact ⟨z,Subtype.ext hz⟩ - have : IsIso f := fdrepHom_isIso_of_bijective k f ⟨hinj,hsurj⟩ - exact asIso f -end FiberFunctorProof -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.FrobeniusTensor + +namespace OAI + +/-! Costandard socles and the digit factorization of simple SL₂ modules. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section +universe u +variable (k : Type u) [Field k] [Infinite k] + +omit [Infinite k] in +lemma independent_sum_mem {ι T M : Type*} [AddCommGroup M] [Module k M] + (f : ι → T → k) (hf : LinearIndependent k f) (s : Finset ι) (c : ι → M) + (S : Submodule k M) (h : ∀ t, ∑ i ∈ s, f i t • c i ∈ S) : + ∀ i ∈ s, c i ∈ S := by + have hz : ∀ t, ∑ i ∈ s, f i t • S.mkQ (c i) = 0 := by + intro t + have hz : S.mkQ (∑ i ∈ s, f i t • c i) = 0 := + (Submodule.Quotient.mk_eq_zero S).mpr (h t) + simpa only [map_sum, map_smul] using hz + intro i hi + have hi' := function_sum_eq_zero f hf s (fun i => S.mkQ (c i)) hz i hi + exact (Submodule.Quotient.mk_eq_zero S).mp hi' + +lemma costandard_weight_component_mem (n : ℕ) (S : Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k))) + (v : MvPolynomial.homogeneousSubmodule (Fin 2) k n) (hv : v ∈ S) + (i : Fin (n+1)) : (binaryBasis k n).repr v i • binaryBasis k n i ∈ S := by + have hinj : Function.Injective (fun j : Fin (n+1) => integerCharacter k (2*(j:ℤ)-n)) := by + intro i j hij + have := integerCharacter_injective k hij + apply Fin.ext + omega + apply independent_sum_mem k + (fun j : Fin (n+1) => fun t : kˣ => integerCharacter k (2*(j:ℤ)-n) t) + ((linearIndependent_monoidHom kˣ k).comp _ hinj) Finset.univ + (fun j => (binaryBasis k n).repr v j • binaryBasis k n j) S.toSubmodule ?_ i + (Finset.mem_univ i) + intro t + let ρ : Representation k (SL2 k) (MvPolynomial.homogeneousSubmodule (Fin 2) k n) := + (homogeneousRepresentation n).comp (dualMatrix k) + have he : ρ (diagonalTorus k t) v = + ∑ j : Fin (n+1), integerCharacter k (2*(j:ℤ)-n) t • + ((binaryBasis k n).repr v j • binaryBasis k n j) := by + conv_lhs => rw [← (binaryBasis k n).sum_repr v, map_sum] + apply Finset.sum_congr rfl + intro j _ + rw [map_smul] + have hj : ρ (diagonalTorus k t) (binaryBasis k n j) = + integerCharacter k (2*(j:ℤ)-n) t • binaryBasis k n j := + costandard_basis_weight k n j t + rw [hj, smul_comm] + rw [← he] + exact S.apply_mem_toSubmodule (diagonalTorus k t) hv + +omit [Infinite k] in +lemma costandard_basis_upper_orbit (n : ℕ) (i : Fin (n+1)) (t : k) : + ((homogeneousRepresentation n).comp (dualMatrix k)) + (unipotent k t) (binaryBasis k n i) = + ∑ j : Fin (n-i.val+1), t^j.val • + (((-1 : k)^j.val * ((n-i.val).choose j.val : k)) • + binaryBasis k n ⟨i.val+j.val, by have := j.isLt; have := i.isLt; omega⟩) := by + apply Subtype.ext + change linearChange (dualMatrix k (unipotent k t)) (binaryBasis k n i).val = _ + rw [binaryBasis_apply] + have hx : linearChange (dualMatrix k (unipotent k t)) (MvPolynomial.X 0) = + (-MvPolynomial.C t * MvPolynomial.X 1 + MvPolynomial.X 0 : MvPolynomial (Fin 2) k) := by + simp [linearChange_X, dualMatrix, unipotent, Matrix.transpose_apply, Fin.sum_univ_two, add_comm] + have hy : linearChange (dualMatrix k (unipotent k t)) (MvPolynomial.X 1) = + (MvPolynomial.X 1 : MvPolynomial (Fin 2) k) := by + simp [linearChange_X, dualMatrix, unipotent, Matrix.transpose_apply, Fin.sum_univ_two] + rw [map_mul, map_pow, map_pow, hx, hy, add_pow] + rw [← Fin.sum_univ_eq_sum_range, Finset.sum_mul] + simp only [Submodule.coe_sum, Submodule.coe_smul_of_tower, binaryBasis_apply, + MvPolynomial.smul_eq_C_mul] + apply Finset.sum_congr rfl + intro j _ + have he : n-(i.val+j.val) = n-i.val-j.val := by omega + rw [he] + have hneg : (-MvPolynomial.C t : MvPolynomial (Fin 2) k) = + MvPolynomial.C (-1 : k) * MvPolynomial.C t := by simp + rw [hneg] + simp only [map_mul, map_pow, map_neg, map_one, map_natCast, mul_pow] + rw [pow_add] + ring + +lemma costandardHighest_mem_of_basis_mem (n : ℕ) + (S : Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k))) (i : Fin (n+1)) + (hi : binaryBasis k n i ∈ S) : costandardHighest k n ∈ S := by + have h := independent_sum_mem k + (fun j : Fin (n-i.val+1) => fun t : k => t^j.val) + ((linearIndependent_powerFunctions k).comp Fin.val Fin.val_injective) Finset.univ + (fun j => ((-1 : k)^j.val * ((n-i.val).choose j.val : k)) • + binaryBasis k n ⟨i.val+j.val, by have := j.isLt; have := i.isLt; omega⟩) + S.toSubmodule (fun t => by + have h := S.apply_mem_toSubmodule (unipotent k t) hi + rw [costandard_basis_upper_orbit k n i t] at h + exact h) + (Fin.last (n-i.val)) (Finset.mem_univ _) + have he : i.val+(n-i.val) = n := by have := i.isLt; omega + have hind : (⟨i.val+(n-i.val), by omega⟩ : Fin (n+1)) = Fin.last n := Fin.ext he + simp only [Fin.val_last, Nat.choose_self,Nat.cast_one,mul_one,hind] at h + exact (Submodule.smul_mem_iff _ (pow_ne_zero _ (neg_ne_zero.mpr one_ne_zero))).mp h + + +lemma costandardHighest_mem_of_ne_bot (n : ℕ) + (S : Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k))) + (hS : S ≠ ⊥) : costandardHighest k n ∈ S := by + classical + have hS' : S.toSubmodule ≠ ⊥ := fun h => hS (Subrepresentation.ext h) + obtain ⟨v,hv,hv0⟩ := Submodule.exists_mem_ne_zero_of_ne_bot hS' + have hc : ∃ i, (binaryBasis k n).repr v i ≠ 0 := by + by_contra! hh + apply hv0 + apply (binaryBasis k n).repr.injective + ext i + simpa using hh i + obtain ⟨i,hi⟩ := hc + apply costandardHighest_mem_of_basis_mem k n S i + exact (Submodule.smul_mem_iff S.toSubmodule hi).mp + (costandard_weight_component_mem k n S v hv i) + +noncomputable def standardCostandardMap (n : ℕ) : + Representation.IntertwiningMap (standardRepresentation k n) + ((homogeneousRepresentation n).comp (dualMatrix k)) := + (exists_standard_costandard_map k n).choose.intertwiningMap_of_isIntertwiningMap _ _ + (exists_standard_costandard_map k n).choose_spec.1 + +lemma standardCostandardMap_basis (n : ℕ) (i : Fin (n+1)) : + standardCostandardMap k n (standardBasis k n i) = + ((-1:k)^i.val * (n.choose i : k)) • binaryBasis k n i.rev := + (exists_standard_costandard_map k n).choose_spec.2 i + +lemma standardCostandardMap_highest (n : ℕ) : + standardCostandardMap k n (standardHighest k n) = costandardHighest k n := by + change standardCostandardMap k n (standardBasis k n 0) = _ + rw [standardCostandardMap_basis] + simp only [Fin.val_zero,pow_zero,Nat.choose_zero_right,Nat.cast_one,mul_one,one_smul] + rfl + + + +noncomputable def costandardSocle (n : ℕ) : + Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k)) := + (standardCostandardMap k n).range + +lemma costandardHighest_mem_socle (n : ℕ) : + costandardHighest k n ∈ costandardSocle k n := + ⟨standardHighest k n, standardCostandardMap_highest k n⟩ + +lemma costandardSocle_le_of_highest_mem (n : ℕ) + (S : Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k))) + (hv : costandardHighest k n ∈ S) : costandardSocle k n ≤ S := by + intro v hv' + obtain ⟨x,rfl⟩ := hv' + have hc : ∀ i : Fin (n+1), + ((-1:k)^i.val * (n.choose i : k)) • binaryBasis k n i.rev ∈ S := by + intro i + apply independent_sum_mem k + (fun j : Fin (n+1) => fun t : k => t^j.val) + ((linearIndependent_powerFunctions k).comp Fin.val Fin.val_injective) Finset.univ + (fun j => ((-1:k)^j.val * (n.choose j : k)) • binaryBasis k n j.rev) + S.toSubmodule ?_ i (Finset.mem_univ _) + intro t + have ht := S.apply_mem_toSubmodule (lowerUnipotent k t) hv + change (costandard k n).ρ (lowerUnipotent k t) (costandardHighest k n) ∈ S at ht + rw [costandardHighest_lower_orbit] at ht + exact ht + rw [← (standardBasis k n).sum_repr x, map_sum] + apply S.toSubmodule.sum_mem + intro i _ + rw [map_smul] + change _ • standardCostandardMap k n (standardBasis k n i) ∈ S.toSubmodule + rw [standardCostandardMap_basis] + exact S.toSubmodule.smul_mem _ (hc i) + +lemma costandardSocle_le_of_ne_bot (n : ℕ) + (S : Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k))) + (hS : S ≠ ⊥) : costandardSocle k n ≤ S := + costandardSocle_le_of_highest_mem k n S (costandardHighest_mem_of_ne_bot k n S hS) + +lemma costandardSocle_ne_bot (n : ℕ) : costandardSocle k n ≠ ⊥ := by + intro h + have hv := costandardHighest_mem_socle k n + rw [h] at hv + exact (binaryBasis k n).ne_zero (Fin.last n) hv + +lemma binaryBasis_mem_costandardSocle (n : ℕ) (i : Fin (n+1)) + (hi : (n.choose i : k) ≠ 0) : binaryBasis k n i ∈ costandardSocle k n := by + have hc : (n.choose i.rev : k) = (n.choose i : k) := by + simpa only [Fin.val_rev,Nat.succ_sub_succ_eq_sub] using + congrArg (fun m : ℕ => (m : k)) (Nat.choose_symm (Nat.le_of_lt_succ i.isLt)) + let c : k := (-1:k)^i.rev.val * (n.choose i.rev : k) + have hc0 : c ≠ 0 := mul_ne_zero (pow_ne_zero _ (neg_ne_zero.mpr one_ne_zero)) (hc ▸ hi) + change binaryBasis k n i ∈ (standardCostandardMap k n).range + refine ⟨c⁻¹ • standardBasis k n i.rev, ?_⟩ + rw [map_smul] + change c⁻¹ • standardCostandardMap k n (standardBasis k n i.rev) = _ + rw [standardCostandardMap_basis, Fin.rev_rev, smul_smul, inv_mul_cancel₀ hc0, + one_smul] + +lemma costandardSocle_eq_top (n : ℕ) (hc : ∀ i : Fin (n+1), (n.choose i : k) ≠ 0) : + costandardSocle k n = ⊤ := by + apply Subrepresentation.ext + apply top_unique + rw [← (binaryBasis k n).span_eq] + exact Submodule.span_le.mpr (by + rintro _ ⟨i,rfl⟩ + exact binaryBasis_mem_costandardSocle k n i (hc i)) + + +noncomputable def simpleSL2 (n : ℕ) : FDRep k (SL2 k) := + FDRep.of (V := (costandardSocle k n).toSubmodule) (costandardSocle k n).toRepresentation + +lemma simpleSL2_rational (n : ℕ) : IsRational k (simpleSL2 k n).ρ := by + apply IsRational.of_injective k (simpleSL2 k n).ρ (costandard k n).ρ + (costandardSocle k n).toSubmodule.subtype Subtype.val_injective (by intros; rfl) + exact costandard_rational k n + +noncomputable def simpleCostandardι (n : ℕ) : simpleSL2 k n ⟶ costandard k n := + fdrepHom k (costandardSocle k n).toSubmodule.subtype (by intros; rfl) + +lemma simpleSL2_eq_costandard_of_choose (n : ℕ) + (hc : ∀ i : Fin (n+1), (n.choose i : k) ≠ 0) : + Nonempty (simpleSL2 k n ≅ costandard k n) := by + have hs : Function.Surjective (costandardSocle k n).toSubmodule.subtype := by + intro x + refine ⟨⟨x,?_⟩, rfl⟩ + rw [costandardSocle_eq_top k n hc] + trivial + have : IsIso (simpleCostandardι k n) := fdrepHom_isIso_of_bijective k _ + ⟨Subtype.val_injective,hs⟩ + exact ⟨asIso (simpleCostandardι k n)⟩ + +lemma simpleSL2_irreducible (n : ℕ) : Representation.IsIrreducible (simpleSL2 k n).ρ := by + let S := costandardSocle k n + have hw : (⟨costandardHighest k n,costandardHighest_mem_socle k n⟩ : S.toSubmodule) ≠ 0 := by + intro h + exact (binaryBasis k n).ne_zero (Fin.last n) (congrArg Subtype.val h) + let : Nontrivial (Subrepresentation S.toRepresentation) := + ⟨⟨⊥,⊤,by + intro h + have hz : (⟨costandardHighest k n,costandardHighest_mem_socle k n⟩ : S.toSubmodule) ∈ + (⊥ : Subrepresentation S.toRepresentation) := by rw [h]; trivial + exact hw hz⟩⟩ + change IsSimpleOrder (Subrepresentation S.toRepresentation) + apply IsSimpleOrder.of_forall_eq_top + intro T hT + let I : Subrepresentation ((homogeneousRepresentation n).comp (dualMatrix k)) := + { toSubmodule := T.toSubmodule.map S.toSubmodule.subtype + apply_mem_toSubmodule := by + intro g v hv + obtain ⟨x,hx,rfl⟩ := hv + exact ⟨S.toRepresentation g x,T.apply_mem_toSubmodule g hx,rfl⟩ } + have hI : I ≠ ⊥ := by + intro hI + apply hT + apply Subrepresentation.ext + apply le_antisymm ?_ bot_le + intro x hx + have hx' : x.val ∈ I := ⟨x,hx,rfl⟩ + rw [hI] at hx' + exact Subtype.ext hx' + have hle : S ≤ I := costandardSocle_le_of_ne_bot k n I hI + apply top_unique + intro x _ + have hx := hle x.property + obtain ⟨y,hy,he⟩ := hx + have he' : y = x := Subtype.ext he + exact he' ▸ hy +end + +section +open scoped TensorProduct +universe u +variable (k : Type u) [Field k] + +noncomputable def binaryDigitMultiply (p a b : ℕ) : + Binary k a ⊗[k] Binary k b →ₗ[k] Binary k (a+p*b) := + TensorProduct.lift + { toFun := fun f => + { toFun := fun g => ⟨f.val * MvPolynomial.expand p g.val, + f.property.mul (expand_homogeneous k p g.val g.property)⟩ + map_add' := by intro g h; apply Subtype.ext; simp [mul_add] + map_smul' := by intro c g; apply Subtype.ext; simp } + map_add' := by intro f g; ext h : 1; apply Subtype.ext; simp [add_mul] + map_smul' := by intro c f; ext g : 1; apply Subtype.ext; simp } + +lemma binaryDigitMultiply_basis (p a b : ℕ) (i : Fin (a+1)) (j : Fin (b+1)) : + binaryDigitMultiply k p a b (binaryBasis k a i ⊗ₜ[k] binaryBasis k b j) = + binaryBasis k (a+p*b) ⟨i.val+p*j.val, by + have := i.isLt; have := j.isLt; nlinarith⟩ := by + apply Subtype.ext + change (binaryBasis k a i).val * MvPolynomial.expand p (binaryBasis k b j).val = _ + simp only [binaryBasis_apply,map_mul,map_pow,MvPolynomial.expand_X,←pow_mul] + rw [mul_mul_mul_comm,←pow_add,←pow_add] + have he : a-i.val+p*(b-j.val) = a+p*b-(i.val+p*j.val) := by + rw [Nat.mul_sub_left_distrib] + have h₁ : i.val ≤ a := by omega + have h₂ : j.val ≤ b := by omega + have := Nat.mul_le_mul_left p h₂ + omega + rw [he] + +lemma digitIndex_injective (p a b : ℕ) (ha : a < p) : + Function.Injective (fun ij : Fin (a+1) × Fin (b+1) => ij.1.val+p*ij.2.val) := by + intro ⟨i,j⟩ ⟨i',j'⟩ h + have hi : i.val < p := by omega + have hi' : i'.val < p := by omega + have hm := congrArg (fun n => n % p) h + have hd := congrArg (fun n => n / p) h + have hp : 0 < p := by omega + simp only [Nat.add_mul_mod_self_left,Nat.mod_eq_of_lt hi,Nat.mod_eq_of_lt hi'] at hm + simp only [Nat.add_mul_div_left _ _ hp,Nat.div_eq_of_lt hi,Nat.div_eq_of_lt hi',zero_add] at hd + exact Prod.ext (Fin.ext hm) (Fin.ext hd) + +lemma binaryDigitMultiply_injective (p a b : ℕ) (ha : a < p) : + Function.Injective (binaryDigitMultiply k p a b) := by + let B := (binaryBasis k a).tensorProduct (binaryBasis k b) + apply LinearMap.injective_of_linearIndependent (R := k) + (f := binaryDigitMultiply k p a b) (v := B) B.span_eq + let idx : Fin (a+1) × Fin (b+1) → Fin (a+p*b+1) := + fun ij => ⟨ij.1.val+p*ij.2.val, by have := ij.1.isLt; have := ij.2.isLt; nlinarith⟩ + have hinj : Function.Injective idx := fun i j h => + digitIndex_injective p a b ha (congrArg Fin.val h) + have he : (binaryDigitMultiply k p a b) ∘ B = (binaryBasis k (a+p*b)) ∘ idx := by + funext ⟨i,j⟩ + simpa only [Function.comp_apply, B, idx, Module.Basis.tensorProduct_apply] using + binaryDigitMultiply_basis k p a b i j + rw [he] + exact (binaryBasis k (a+p*b)).linearIndependent.comp idx hinj + +variable (p : ℕ) [Fact p.Prime] [CharP k p] + +lemma choose_digit_cast (a b i j : ℕ) (ha : a < p) (hi : i < p) : + ((a+p*b).choose (i+p*j) : k) = (a.choose i : k) * (b.choose j : k) := by + have h := Choose.choose_modEq_choose_mod_mul_choose_div_nat + (p := p) (n := a+p*b) (k := i+p*j) + have hp := (Fact.out : p.Prime).pos + simp only [Nat.add_mul_mod_self_left,Nat.mod_eq_of_lt ha,Nat.mod_eq_of_lt hi, + Nat.add_mul_div_left _ _ hp,Nat.div_eq_of_lt ha,Nat.div_eq_of_lt hi,zero_add] at h + rw [← Nat.cast_mul] + exact (CharP.cast_eq_iff_mod_eq k p).mpr h + +lemma binaryDigitMultiply_intertwines (a b : ℕ) (g : SL2 k) + (z : Binary k a ⊗[k] Binary k b) : + binaryDigitMultiply k p a b + (Representation.tprod (costandard k a).ρ + ((costandard k b).ρ.comp (frobeniusSL2 k p)) g z) = + (costandard k (a+p*b)).ρ g (binaryDigitMultiply k p a b z) := by + change binaryDigitMultiply k p a b + (TensorProduct.map (homogeneousRepresentation a (dualMatrix k g)) + (homogeneousRepresentation b (dualMatrix k (frobeniusSL2 k p g))) z) = + homogeneousRepresentation (a+p*b) (dualMatrix k g) (binaryDigitMultiply k p a b z) + induction z using TensorProduct.inductionOn with + | add z w hz hw => simp only [map_add,hz,hw] + | tmul f h => + apply Subtype.ext + change linearChange (dualMatrix k g) f.val * + MvPolynomial.expand p (linearChange (dualMatrix k (frobeniusSL2 k p g)) h.val) = + linearChange (dualMatrix k g) (f.val * MvPolynomial.expand p h.val) + rw [map_mul,dualMatrix_frobeniusSL2,linearChange_expand] + +end + +open scoped TensorProduct +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (p : ℕ) [Fact p.Prime] [CharP k p] + +lemma binaryDigitMultiply_mem_socle (a b : ℕ) (ha : a < p) + (f : Binary k a) (g : (costandardSocle k b).toSubmodule) : + binaryDigitMultiply k p a b (f ⊗ₜ[k] g.val) ∈ costandardSocle k (a+p*b) := by + obtain ⟨x,hx⟩ := g.property + rw [← hx] + rw [← (binaryBasis k a).sum_repr f] + simp only [TensorProduct.sum_tmul,← TensorProduct.smul_tmul',map_sum,map_smul] + apply (costandardSocle k (a+p*b)).toSubmodule.sum_mem + intro i _ + apply (costandardSocle k (a+p*b)).toSubmodule.smul_mem + rw [← (standardBasis k b).sum_repr x] + simp only [map_sum,map_smul,TensorProduct.tmul_sum,TensorProduct.tmul_smul] + apply (costandardSocle k (a+p*b)).toSubmodule.sum_mem + intro j _ + apply (costandardSocle k (a+p*b)).toSubmodule.smul_mem + change binaryDigitMultiply k p a b + (binaryBasis k a i ⊗ₜ[k] standardCostandardMap k b (standardBasis k b j)) ∈ _ + rw [standardCostandardMap_basis,TensorProduct.tmul_smul,map_smul,binaryDigitMultiply_basis] + by_cases hj : (b.choose j : k) = 0 + · simp [hj] + · apply (costandardSocle k (a+p*b)).toSubmodule.smul_mem + apply binaryBasis_mem_costandardSocle + rw [choose_digit_cast k p a b i.val j.rev.val ha (by have := i.isLt; omega)] + apply mul_ne_zero (choose_cast_ne_zero_of_lt_char k p ha (Nat.le_of_lt_succ i.isLt)) + simpa only [Fin.val_rev,Nat.succ_sub_succ_eq_sub,Nat.choose_symm (Nat.le_of_lt_succ j.isLt)] using hj + +noncomputable def binarySocleDigitMultiply (a b : ℕ) : + Binary k a ⊗[k] (costandardSocle k b).toSubmodule →ₗ[k] Binary k (a+p*b) := + (binaryDigitMultiply k p a b).comp + ((costandardSocle k b).toSubmodule.subtype.lTensor (Binary k a)) + +omit [Fact p.Prime] [CharP k p] in +lemma binarySocleDigitMultiply_injective (a b : ℕ) (ha : a < p) : + Function.Injective (binarySocleDigitMultiply k p a b) := + (binaryDigitMultiply_injective k p a b ha).comp + (Module.Flat.lTensor_preserves_injective_linearMap + (costandardSocle k b).toSubmodule.subtype Subtype.val_injective) + +lemma binarySocleDigitMultiply_mem (a b : ℕ) (ha : a < p) + (z : Binary k a ⊗[k] (costandardSocle k b).toSubmodule) : + binarySocleDigitMultiply k p a b z ∈ costandardSocle k (a+p*b) := by + induction z using TensorProduct.inductionOn with + | add z w hz hw => + rw [map_add] + exact (costandardSocle k (a+p*b)).toSubmodule.add_mem hz hw + | tmul f g => exact binaryDigitMultiply_mem_socle k p a b ha f g + +lemma binarySocleDigitMultiply_intertwines (a b : ℕ) (g : SL2 k) + (z : Binary k a ⊗[k] (costandardSocle k b).toSubmodule) : + binarySocleDigitMultiply k p a b + (Representation.tprod ((homogeneousRepresentation a).comp (dualMatrix k)) + ((costandardSocle k b).toRepresentation.comp (frobeniusSL2 k p)) g z) = + ((homogeneousRepresentation (a+p*b)).comp (dualMatrix k)) g + (binarySocleDigitMultiply k p a b z) := by + induction z using TensorProduct.inductionOn with + | add z w hz hw => simp only [map_add,hz,hw] + | tmul f h => + exact binaryDigitMultiply_intertwines k p a b g (f ⊗ₜ[k] h.val) + +lemma binarySocleDigitMultiply_range (a b : ℕ) (ha : a < p) : + LinearMap.range (binarySocleDigitMultiply k p a b) = + (costandardSocle k (a+p*b)).toSubmodule := by + let f := (binarySocleDigitMultiply k p a b).intertwiningMap_of_isIntertwiningMap _ _ + (binarySocleDigitMultiply_intertwines k p a b) + apply le_antisymm + · rintro _ ⟨x,rfl⟩ + exact binarySocleDigitMultiply_mem k p a b ha x + · have h : costandardHighest k (a+p*b) ∈ f.range := by + refine ⟨costandardHighest k a ⊗ₜ[k] + ⟨costandardHighest k b,costandardHighest_mem_socle k b⟩, ?_⟩ + change binaryDigitMultiply k p a b + (binaryBasis k a (Fin.last a) ⊗ₜ[k] binaryBasis k b (Fin.last b)) = _ + rw [binaryDigitMultiply_basis] + rfl + exact costandardSocle_le_of_highest_mem k (a+p*b) f.range h + + + +noncomputable def simpleDigitIso (a b : ℕ) (ha : a < p) : + costandard k a ⊗ (Action.res (FGModuleCat k) (frobeniusSL2 k p)).obj (simpleSL2 k b) ≅ + simpleSL2 k (a+p*b) := by + let l := (binarySocleDigitMultiply k p a b).codRestrict + (costandardSocle k (a+p*b)).toSubmodule (binarySocleDigitMultiply_mem k p a b ha) + let f : costandard k a ⊗ + (Action.res (FGModuleCat k) (frobeniusSL2 k p)).obj (simpleSL2 k b) ⟶ + simpleSL2 k (a+p*b) := fdrepHom k l (by + intro g z + apply Subtype.ext + exact binarySocleDigitMultiply_intertwines k p a b g z) + have hinj : Function.Injective l := fun x y h => + binarySocleDigitMultiply_injective k p a b ha (congrArg Subtype.val h) + have hsurj : Function.Surjective l := by + intro x + have hx : x.val ∈ LinearMap.range (binarySocleDigitMultiply k p a b) := by + rw [binarySocleDigitMultiply_range k p a b ha] + exact x.property + obtain ⟨z,hz⟩ := hx + exact ⟨z,Subtype.ext hz⟩ + have : IsIso f := fdrepHom_isIso_of_bijective k f ⟨hinj,hsurj⟩ + exact asIso f +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/SmallGroupTrace.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/SmallGroupTrace.lean index eb2a3dba52433298f2a50011295ee8106c69f23c..9df25bc6da69f7e8237c7886dfe4e54de12ba101 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/SmallGroupTrace.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/SmallGroupTrace.lean @@ -1,196 +1,196 @@ -import OAI.RepresentationTheory.RestrictedTilting.RelativeTrace -import OAI.RepresentationTheory.RestrictedTilting.ProjectiveFactor -import OAI.RepresentationTheory.RestrictedTilting.ProjectiveRegular - -namespace OAI - -namespace FiberFunctorProof.SmallGroupTrace -open CategoryTheory Representation -universe u -variable {k : Type u} [Field k] {G : Type} [Group G] [Fintype G] -variable (I : Type u) - - - -noncomputable def freeNormRepresentative : - (I →₀ MonoidAlgebra k G) →ₗ[k] (I →₀ MonoidAlgebra k G) := - Finsupp.mapRange.linearMap - ((MonoidAlgebra.lsingle 1).comp - ((Finsupp.lapply 1).comp (MonoidAlgebra.coeffLinearEquiv k).toLinearMap)) - -omit [Fintype G] in -@[simp] lemma freeNormRepresentative_apply (x : I →₀ MonoidAlgebra k G) (i : I) : - freeNormRepresentative I x i = MonoidAlgebra.single 1 ((x i).coeff 1) := rfl - -omit [Fintype G] in -lemma free_action_apply (g : G) (x : I →₀ MonoidAlgebra k G) (i : I) : - Representation.free k G I g x i = Representation.leftRegular k G g (x i) := by - classical - have H : (Finsupp.lapply i).comp (Representation.free k G I g) = - (Representation.leftRegular k G g).comp (Finsupp.lapply i) := by - apply Finsupp.lhom_ext - intro j v - simp only [LinearMap.comp_apply, Representation.finsupp_single, Finsupp.lapply_apply] - by_cases h : j = i - · subst j; simp - · simp [Ne.symm h] - exact congr($(H) x) - -section -variable {k : Type u} [Field k] {G : Type} [Group G] [Fintype G] - - - -lemma free_relativeTrace (I : Type u) : - relativeTrace (Representation.free k G I) (Representation.free k G I) - (freeNormRepresentative I) = LinearMap.id := by - classical - apply LinearMap.ext - intro x - apply Finsupp.ext - intro i - apply MonoidAlgebra.ext - apply Finsupp.ext - intro g - simp only [relativeTrace_apply, Finsupp.finsetSum_apply, - free_action_apply, freeNormRepresentative_apply] - simp [Representation.coeff_ofMulAction] - - -noncomputable def finiteIntertwiner {V W : FDRep k G} (f : Representation.IntertwiningMap V.ρ W.ρ) : V ⟶ W := - (FDRep.forget₂HomLinearEquiv V W) (Rep.ofHom f) - -omit [Fintype G] in -@[simp] lemma finiteIntertwiner_hom {V W : FDRep k G} (f : Representation.IntertwiningMap V.ρ W.ρ) : - (finiteIntertwiner f).hom.hom.hom = f.toLinearMap := rfl - -omit [Fintype G] in -lemma finiteIntertwiner_epi {V W : FDRep k G} (f : Representation.IntertwiningMap V.ρ W.ρ) - (hf : Function.Surjective f) : Epi (finiteIntertwiner f) := by - let F := forget₂ (FDRep k G) (Rep k G) - have : Epi (F.map (finiteIntertwiner f)) := (Rep.epi_iff_surjective _).2 hf - exact F.epi_of_epi_map this - - - -lemma fdrep_free_projective (I : Type u) [Finite I] : - Projective (FDRep.of (Representation.free k G I)) := by - apply (forget₂ (FDRep k G) (Rep k G)).projective_of_map_projective - exact (Rep.toModuleMonoidAlgebra (k := k) (G := G)).projective_of_map_projective - (P := Rep.of (Representation.free k G I)) - (ModuleCat.projective_of_free (Representation.freeAsModuleBasis k G I)) - - -noncomputable def finiteFreeCover (V : FDRep k G) : - FDRep.of (Representation.free k G (ULift.{u} (Fin (Module.finrank k V)))) ⟶ V := - finiteIntertwiner (Representation.freeLift V.ρ - (fun i : ULift.{u} (Fin (Module.finrank k V)) => Module.finBasis k V i.down)) - -lemma finiteFreeCover_epi (V : FDRep k G) : Epi (finiteFreeCover V) := by - classical - apply finiteIntertwiner_epi - intro v - refine ⟨∑ i : Fin (Module.finrank k V), - Finsupp.single (ULift.up i) (MonoidAlgebra.single 1 ((Module.finBasis k V).repr v i)), ?_⟩ - change (Representation.freeLift V.ρ (fun i : ULift.{u} (Fin (Module.finrank k V)) => - Module.finBasis k V i.down)).toLinearMap _ = v - rw [map_sum] - simp only [IntertwiningMap.toLinearMap_apply, Representation.freeLift_single_single, - map_one, Module.End.one_apply] - exact (Module.finBasis k V).sum_repr v - -end - -section -variable {k : Type u} [Field k] {G : Type} [Group G] [Fintype G] -variable {V W : Type u} [AddCommGroup V] [Module k V] [AddCommGroup W] [Module k W] -variable {I : Type u} [Fintype I] - - -noncomputable def coordinateTraceLift (ρ : Representation k G V) - (b : Module.Basis I k W) (t : V →ₗ[k] W) : - V →ₗ[k] (I →₀ MonoidAlgebra k G) := - ∑ g : G, ∑ i : I, (Finsupp.lsingle i).comp - ((MonoidAlgebra.lsingle g).comp ((b.coord i).comp (t.comp (ρ g⁻¹)))) - -lemma coordinateTraceLift_apply (ρ : Representation k G V) - (b : Module.Basis I k W) (t : V →ₗ[k] W) (v : V) : - coordinateTraceLift ρ b t v = ∑ g : G, ∑ i : I, - Finsupp.single i (MonoidAlgebra.single g (b.repr (t (ρ g⁻¹ v)) i)) := by - simp [coordinateTraceLift, LinearMap.sum_apply] - -noncomputable def coordinateTraceHom (ρ : Representation k G V) - (b : Module.Basis I k W) (t : V →ₗ[k] W) : - ρ.IntertwiningMap (Representation.free k G I) where - toLinearMap := coordinateTraceLift ρ b t - isIntertwining' h := by - ext v : 1 - simp only [LinearMap.comp_apply, coordinateTraceLift_apply, map_sum, - Representation.free_single_single] - symm - apply Fintype.sum_equiv (Equiv.mulLeft h) - intro g - simp [mul_inv_rev, map_mul] - -lemma freeCover_traceLift (ρ : Representation k G V) (σ : Representation k G W) - (b : Module.Basis I k W) (t : V →ₗ[k] W) : - (Representation.freeLift σ b).toLinearMap.comp (coordinateTraceLift ρ b t) = - relativeTrace ρ σ t := by - ext v - simp only [LinearMap.comp_apply, coordinateTraceLift_apply, map_sum, - IntertwiningMap.toLinearMap_apply, Representation.freeLift_single_single, relativeTrace_apply] - apply Finset.sum_congr rfl - intro g hg - simp only [← map_smul] - rw [← map_sum, b.sum_repr] - - - -noncomputable def finiteTraceBasis (V : FDRep k G) : - Module.Basis (ULift.{u} (Fin (Module.finrank k V))) k V := - (Module.finBasis k V).reindex Equiv.ulift.symm - - -theorem relativeTrace_factors (V W : FDRep k G) (f : V ⟶ W) (t : V →ₗ[k] W) - (ht : relativeTrace V.ρ W.ρ t = f.hom.hom.hom) : FactorsThroughProjective f := by - let b := finiteTraceBasis W - let A := FDRep.of (Representation.free k G (ULift.{u} (Fin (Module.finrank k W)))) - refine ⟨A, fdrep_free_projective _, finiteIntertwiner (coordinateTraceHom V.ρ b t), - finiteIntertwiner (Representation.freeLift W.ρ b), ?_⟩ - apply Action.Hom.ext - apply InducedCategory.hom_ext - apply ModuleCat.hom_ext - exact (freeCover_traceLift V.ρ W.ρ b t).trans ht - - -def underlyingIntertwiner {V W : FDRep k G} (f : V ⟶ W) : - Representation.IntertwiningMap V.ρ W.ρ where - toLinearMap := f.hom.hom.hom - isIntertwining' g := congrArg (fun h : V.V ⟶ W.V => h.hom.hom) (f.comm g) - - -theorem relativeTrace_of_factors (V W : FDRep k G) (f : V ⟶ W) - (hf : FactorsThroughProjective f) : - ∃ t : V →ₗ[k] W, relativeTrace V.ρ W.ρ t = f.hom.hom.hom := by - obtain ⟨P,hP,a,b,rfl⟩ := hf - let e := finiteFreeCover P - let : Epi e := finiteFreeCover_epi P - obtain ⟨s,hs⟩ := hP.factors (𝟙 P) e - let a' := underlyingIntertwiner (a ≫ s) - let b' := underlyingIntertwiner (e ≫ b) - refine ⟨b'.toLinearMap.comp ((freeNormRepresentative _).comp a'.toLinearMap), ?_⟩ - rw [relativeTrace_postcomp, relativeTrace_precomp] - erw [free_relativeTrace] - change ((a ≫ s) ≫ (e ≫ b)).hom.hom.hom = (a ≫ b).hom.hom.hom - rw [Category.assoc, ← Category.assoc s, hs, Category.id_comp] - -theorem projective_factor_iff_relativeTrace (V W : FDRep k G) (f : V ⟶ W) : - FactorsThroughProjective f ↔ ∃ t : V →ₗ[k] W, - relativeTrace V.ρ W.ρ t = f.hom.hom.hom := - ⟨relativeTrace_of_factors V W f, fun ⟨t,ht⟩ => relativeTrace_factors V W f t ht⟩ - -end - -end FiberFunctorProof.SmallGroupTrace - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.RelativeTrace +import OAI.RepresentationTheory.RestrictedTilting.ProjectiveFactor +import OAI.RepresentationTheory.RestrictedTilting.ProjectiveRegular + +namespace OAI + +namespace FiberFunctorProof.SmallGroupTrace +open CategoryTheory Representation +universe u +variable {k : Type u} [Field k] {G : Type} [Group G] [Fintype G] +variable (I : Type u) + + + +noncomputable def freeNormRepresentative : + (I →₀ MonoidAlgebra k G) →ₗ[k] (I →₀ MonoidAlgebra k G) := + Finsupp.mapRange.linearMap + ((MonoidAlgebra.lsingle 1).comp + ((Finsupp.lapply 1).comp (MonoidAlgebra.coeffLinearEquiv k).toLinearMap)) + +omit [Fintype G] in +@[simp] lemma freeNormRepresentative_apply (x : I →₀ MonoidAlgebra k G) (i : I) : + freeNormRepresentative I x i = MonoidAlgebra.single 1 ((x i).coeff 1) := rfl + +omit [Fintype G] in +lemma free_action_apply (g : G) (x : I →₀ MonoidAlgebra k G) (i : I) : + Representation.free k G I g x i = Representation.leftRegular k G g (x i) := by + classical + have H : (Finsupp.lapply i).comp (Representation.free k G I g) = + (Representation.leftRegular k G g).comp (Finsupp.lapply i) := by + apply Finsupp.lhom_ext + intro j v + simp only [LinearMap.comp_apply, Representation.finsupp_single, Finsupp.lapply_apply] + by_cases h : j = i + · subst j; simp + · simp [Ne.symm h] + exact congr($(H) x) + +section +variable {k : Type u} [Field k] {G : Type} [Group G] [Fintype G] + + + +lemma free_relativeTrace (I : Type u) : + relativeTrace (Representation.free k G I) (Representation.free k G I) + (freeNormRepresentative I) = LinearMap.id := by + classical + apply LinearMap.ext + intro x + apply Finsupp.ext + intro i + apply MonoidAlgebra.ext + apply Finsupp.ext + intro g + simp only [relativeTrace_apply, Finsupp.finsetSum_apply, + free_action_apply, freeNormRepresentative_apply] + simp [Representation.coeff_ofMulAction] + + +noncomputable def finiteIntertwiner {V W : FDRep k G} (f : Representation.IntertwiningMap V.ρ W.ρ) : V ⟶ W := + (FDRep.forget₂HomLinearEquiv V W) (Rep.ofHom f) + +omit [Fintype G] in +@[simp] lemma finiteIntertwiner_hom {V W : FDRep k G} (f : Representation.IntertwiningMap V.ρ W.ρ) : + (finiteIntertwiner f).hom.hom.hom = f.toLinearMap := rfl + +omit [Fintype G] in +lemma finiteIntertwiner_epi {V W : FDRep k G} (f : Representation.IntertwiningMap V.ρ W.ρ) + (hf : Function.Surjective f) : Epi (finiteIntertwiner f) := by + let F := forget₂ (FDRep k G) (Rep k G) + have : Epi (F.map (finiteIntertwiner f)) := (Rep.epi_iff_surjective _).2 hf + exact F.epi_of_epi_map this + + + +lemma fdrep_free_projective (I : Type u) [Finite I] : + Projective (FDRep.of (Representation.free k G I)) := by + apply (forget₂ (FDRep k G) (Rep k G)).projective_of_map_projective + exact (Rep.toModuleMonoidAlgebra (k := k) (G := G)).projective_of_map_projective + (P := Rep.of (Representation.free k G I)) + (ModuleCat.projective_of_free (Representation.freeAsModuleBasis k G I)) + + +noncomputable def finiteFreeCover (V : FDRep k G) : + FDRep.of (Representation.free k G (ULift.{u} (Fin (Module.finrank k V)))) ⟶ V := + finiteIntertwiner (Representation.freeLift V.ρ + (fun i : ULift.{u} (Fin (Module.finrank k V)) => Module.finBasis k V i.down)) + +lemma finiteFreeCover_epi (V : FDRep k G) : Epi (finiteFreeCover V) := by + classical + apply finiteIntertwiner_epi + intro v + refine ⟨∑ i : Fin (Module.finrank k V), + Finsupp.single (ULift.up i) (MonoidAlgebra.single 1 ((Module.finBasis k V).repr v i)), ?_⟩ + change (Representation.freeLift V.ρ (fun i : ULift.{u} (Fin (Module.finrank k V)) => + Module.finBasis k V i.down)).toLinearMap _ = v + rw [map_sum] + simp only [IntertwiningMap.toLinearMap_apply, Representation.freeLift_single_single, + map_one, Module.End.one_apply] + exact (Module.finBasis k V).sum_repr v + +end + +section +variable {k : Type u} [Field k] {G : Type} [Group G] [Fintype G] +variable {V W : Type u} [AddCommGroup V] [Module k V] [AddCommGroup W] [Module k W] +variable {I : Type u} [Fintype I] + + +noncomputable def coordinateTraceLift (ρ : Representation k G V) + (b : Module.Basis I k W) (t : V →ₗ[k] W) : + V →ₗ[k] (I →₀ MonoidAlgebra k G) := + ∑ g : G, ∑ i : I, (Finsupp.lsingle i).comp + ((MonoidAlgebra.lsingle g).comp ((b.coord i).comp (t.comp (ρ g⁻¹)))) + +lemma coordinateTraceLift_apply (ρ : Representation k G V) + (b : Module.Basis I k W) (t : V →ₗ[k] W) (v : V) : + coordinateTraceLift ρ b t v = ∑ g : G, ∑ i : I, + Finsupp.single i (MonoidAlgebra.single g (b.repr (t (ρ g⁻¹ v)) i)) := by + simp [coordinateTraceLift, LinearMap.sum_apply] + +noncomputable def coordinateTraceHom (ρ : Representation k G V) + (b : Module.Basis I k W) (t : V →ₗ[k] W) : + ρ.IntertwiningMap (Representation.free k G I) where + toLinearMap := coordinateTraceLift ρ b t + isIntertwining' h := by + ext v : 1 + simp only [LinearMap.comp_apply, coordinateTraceLift_apply, map_sum, + Representation.free_single_single] + symm + apply Fintype.sum_equiv (Equiv.mulLeft h) + intro g + simp [mul_inv_rev, map_mul] + +lemma freeCover_traceLift (ρ : Representation k G V) (σ : Representation k G W) + (b : Module.Basis I k W) (t : V →ₗ[k] W) : + (Representation.freeLift σ b).toLinearMap.comp (coordinateTraceLift ρ b t) = + relativeTrace ρ σ t := by + ext v + simp only [LinearMap.comp_apply, coordinateTraceLift_apply, map_sum, + IntertwiningMap.toLinearMap_apply, Representation.freeLift_single_single, relativeTrace_apply] + apply Finset.sum_congr rfl + intro g hg + simp only [← map_smul] + rw [← map_sum, b.sum_repr] + + + +noncomputable def finiteTraceBasis (V : FDRep k G) : + Module.Basis (ULift.{u} (Fin (Module.finrank k V))) k V := + (Module.finBasis k V).reindex Equiv.ulift.symm + + +theorem relativeTrace_factors (V W : FDRep k G) (f : V ⟶ W) (t : V →ₗ[k] W) + (ht : relativeTrace V.ρ W.ρ t = f.hom.hom.hom) : FactorsThroughProjective f := by + let b := finiteTraceBasis W + let A := FDRep.of (Representation.free k G (ULift.{u} (Fin (Module.finrank k W)))) + refine ⟨A, fdrep_free_projective _, finiteIntertwiner (coordinateTraceHom V.ρ b t), + finiteIntertwiner (Representation.freeLift W.ρ b), ?_⟩ + apply Action.Hom.ext + apply InducedCategory.hom_ext + apply ModuleCat.hom_ext + exact (freeCover_traceLift V.ρ W.ρ b t).trans ht + + +def underlyingIntertwiner {V W : FDRep k G} (f : V ⟶ W) : + Representation.IntertwiningMap V.ρ W.ρ where + toLinearMap := f.hom.hom.hom + isIntertwining' g := congrArg (fun h : V.V ⟶ W.V => h.hom.hom) (f.comm g) + + +theorem relativeTrace_of_factors (V W : FDRep k G) (f : V ⟶ W) + (hf : FactorsThroughProjective f) : + ∃ t : V →ₗ[k] W, relativeTrace V.ρ W.ρ t = f.hom.hom.hom := by + obtain ⟨P,hP,a,b,rfl⟩ := hf + let e := finiteFreeCover P + let : Epi e := finiteFreeCover_epi P + obtain ⟨s,hs⟩ := hP.factors (𝟙 P) e + let a' := underlyingIntertwiner (a ≫ s) + let b' := underlyingIntertwiner (e ≫ b) + refine ⟨b'.toLinearMap.comp ((freeNormRepresentative _).comp a'.toLinearMap), ?_⟩ + rw [relativeTrace_postcomp, relativeTrace_precomp] + erw [free_relativeTrace] + change ((a ≫ s) ≫ (e ≫ b)).hom.hom.hom = (a ≫ b).hom.hom.hom + rw [Category.assoc, ← Category.assoc s, hs, Category.id_comp] + +theorem projective_factor_iff_relativeTrace (V W : FDRep k G) (f : V ⟶ W) : + FactorsThroughProjective f ↔ ∃ t : V →ₗ[k] W, + relativeTrace V.ρ W.ρ t = f.hom.hom.hom := + ⟨relativeTrace_of_factors V W f, fun ⟨t,ht⟩ => relativeTrace_factors V W f t ht⟩ + +end + +end FiberFunctorProof.SmallGroupTrace + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/SpecializeCompletion.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/SpecializeCompletion.lean index c9ca23690ddca4470a7847e1e8e6c99765e1aec8..d9a84214c01740da46e7c99bd5661d100237ab31 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/SpecializeCompletion.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/SpecializeCompletion.lean @@ -1,87 +1,87 @@ -import Mathlib - -namespace OAI - -namespace FiberFunctorProof -section -open scoped TensorProduct -section CompletionScalar -variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M] (I : Ideal R) -lemma completion_map_scalar (a : R) (v : AdicCompletion I M) : - AdicCompletion.map I (a • (LinearMap.id : M →ₗ[R] M)) v = - algebraMap R (AdicCompletion I R) a • v := by - ext n - simp only [AdicCompletion.map_val_apply] - change a • v.val n = _ - rw [algebraMap_smul] - rfl -end CompletionScalar - - - -variable {H L M F : Type*} [CommRing H] [Field L] [Algebra H L] - [AddCommGroup M] [Module H M] [AddCommGroup F] [Module H F] -variable (W : M →ₗ[H] F) (Z : F →ₗ[H] M) (a : H) - (hWZ : ∀ v, W (Z v) = a • v) (hZW : ∀ v, Z (W v) = a • v) - -include hWZ in -lemma baseChange_scalar_inverse_left (v : L ⊗[H] F) : - W.baseChange L (Z.baseChange L v) = algebraMap H L a • v := by - induction v using TensorProduct.inductionOn with - | add v w hv hw => simp only [map_add, smul_add, hv, hw] - | tmul l v => - simp only [LinearMap.baseChange_tmul, hWZ, TensorProduct.tmul_smul, - TensorProduct.smul_tmul', algebraMap_smul] - -include hZW in -lemma baseChange_scalar_inverse_right (v : L ⊗[H] M) : - Z.baseChange L (W.baseChange L v) = algebraMap H L a • v := - baseChange_scalar_inverse_left Z W a hZW v - -noncomputable def specializedScalarEquiv (ha : algebraMap H L a ≠ 0) : - (L ⊗[H] M) ≃ₗ[L] (L ⊗[H] F) := - LinearEquiv.ofLinearMap (W.baseChange L) ((algebraMap H L a)⁻¹ • Z.baseChange L) - (by - apply LinearMap.ext - intro v - change W.baseChange L ((algebraMap H L a)⁻¹ • Z.baseChange L v) = v - rw [map_smul, baseChange_scalar_inverse_left W Z a hWZ, inv_smul_smul₀ ha]) - (by - apply LinearMap.ext - intro v - change (algebraMap H L a)⁻¹ • Z.baseChange L (W.baseChange L v) = v - rw [baseChange_scalar_inverse_right W Z a hZW, inv_smul_smul₀ ha]) - -@[simp] lemma specializedScalarEquiv_tmul (ha : algebraMap H L a ≠ 0) (l : L) (m : M) : - specializedScalarEquiv W Z a hWZ hZW ha (l ⊗ₜ[H] m) = l ⊗ₜ[H] W m := - LinearMap.baseChange_tmul .. -end - -open scoped TensorProduct -variable {k H L T M : Type*} [CommRing k] [CommRing H] [Field L] - [Algebra k H] [Algebra H L] [Algebra k L] [IsScalarTower k H L] - [AddCommGroup T] [Module k T] [AddCommGroup M] [Module H M] -variable {ι : Type*} [Fintype ι] [DecidableEq ι] -variable (F : (H ⊗[k] T) ≃ₗ[H] M) (W : M →ₗ[H] (ι → H)) (Z : (ι → H) →ₗ[H] M) - (a : H) (hWZ : ∀ v, W (Z v) = a • v) (hZW : ∀ v, Z (W v) = a • v) - (ha : algebraMap H L a ≠ 0) - -noncomputable def fieldCoordinateTrivialization : (L ⊗[k] T) ≃ₗ[L] (ι → L) := - (TensorProduct.AlgebraTensorModule.cancelBaseChange k H L L T).symm ≪≫ₗ - (LinearEquiv.baseChange H L _ _ F) ≪≫ₗ - specializedScalarEquiv W Z a hWZ hZW ha ≪≫ₗ - TensorProduct.piRight H L L (fun _ : ι => H) ≪≫ₗ - LinearEquiv.piCongrRight (fun _ => TensorProduct.AlgebraTensorModule.rid H L L) - -lemma fieldCoordinateTrivialization_one (t : T) (i : ι) : - fieldCoordinateTrivialization F W Z a hWZ hZW ha (1 ⊗ₜ[k] t) i = - algebraMap H L (W (F (1 ⊗ₜ[k] t)) i) := by - simp only [fieldCoordinateTrivialization, LinearEquiv.trans_apply, - TensorProduct.AlgebraTensorModule.cancelBaseChange_symm_tmul, - LinearEquiv.baseChange_tmul, specializedScalarEquiv_tmul, - TensorProduct.piRight_apply, TensorProduct.piRightHom_tmul, LinearEquiv.piCongrRight_apply, - TensorProduct.AlgebraTensorModule.rid_tmul] - simp only [Algebra.smul_def, mul_one] -end FiberFunctorProof - -end OAI +import Mathlib + +namespace OAI + +namespace FiberFunctorProof +section +open scoped TensorProduct +section CompletionScalar +variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M] (I : Ideal R) +lemma completion_map_scalar (a : R) (v : AdicCompletion I M) : + AdicCompletion.map I (a • (LinearMap.id : M →ₗ[R] M)) v = + algebraMap R (AdicCompletion I R) a • v := by + ext n + simp only [AdicCompletion.map_val_apply] + change a • v.val n = _ + rw [algebraMap_smul] + rfl +end CompletionScalar + + + +variable {H L M F : Type*} [CommRing H] [Field L] [Algebra H L] + [AddCommGroup M] [Module H M] [AddCommGroup F] [Module H F] +variable (W : M →ₗ[H] F) (Z : F →ₗ[H] M) (a : H) + (hWZ : ∀ v, W (Z v) = a • v) (hZW : ∀ v, Z (W v) = a • v) + +include hWZ in +lemma baseChange_scalar_inverse_left (v : L ⊗[H] F) : + W.baseChange L (Z.baseChange L v) = algebraMap H L a • v := by + induction v using TensorProduct.inductionOn with + | add v w hv hw => simp only [map_add, smul_add, hv, hw] + | tmul l v => + simp only [LinearMap.baseChange_tmul, hWZ, TensorProduct.tmul_smul, + TensorProduct.smul_tmul', algebraMap_smul] + +include hZW in +lemma baseChange_scalar_inverse_right (v : L ⊗[H] M) : + Z.baseChange L (W.baseChange L v) = algebraMap H L a • v := + baseChange_scalar_inverse_left Z W a hZW v + +noncomputable def specializedScalarEquiv (ha : algebraMap H L a ≠ 0) : + (L ⊗[H] M) ≃ₗ[L] (L ⊗[H] F) := + LinearEquiv.ofLinearMap (W.baseChange L) ((algebraMap H L a)⁻¹ • Z.baseChange L) + (by + apply LinearMap.ext + intro v + change W.baseChange L ((algebraMap H L a)⁻¹ • Z.baseChange L v) = v + rw [map_smul, baseChange_scalar_inverse_left W Z a hWZ, inv_smul_smul₀ ha]) + (by + apply LinearMap.ext + intro v + change (algebraMap H L a)⁻¹ • Z.baseChange L (W.baseChange L v) = v + rw [baseChange_scalar_inverse_right W Z a hZW, inv_smul_smul₀ ha]) + +@[simp] lemma specializedScalarEquiv_tmul (ha : algebraMap H L a ≠ 0) (l : L) (m : M) : + specializedScalarEquiv W Z a hWZ hZW ha (l ⊗ₜ[H] m) = l ⊗ₜ[H] W m := + LinearMap.baseChange_tmul .. +end + +open scoped TensorProduct +variable {k H L T M : Type*} [CommRing k] [CommRing H] [Field L] + [Algebra k H] [Algebra H L] [Algebra k L] [IsScalarTower k H L] + [AddCommGroup T] [Module k T] [AddCommGroup M] [Module H M] +variable {ι : Type*} [Fintype ι] [DecidableEq ι] +variable (F : (H ⊗[k] T) ≃ₗ[H] M) (W : M →ₗ[H] (ι → H)) (Z : (ι → H) →ₗ[H] M) + (a : H) (hWZ : ∀ v, W (Z v) = a • v) (hZW : ∀ v, Z (W v) = a • v) + (ha : algebraMap H L a ≠ 0) + +noncomputable def fieldCoordinateTrivialization : (L ⊗[k] T) ≃ₗ[L] (ι → L) := + (TensorProduct.AlgebraTensorModule.cancelBaseChange k H L L T).symm ≪≫ₗ + (LinearEquiv.baseChange H L _ _ F) ≪≫ₗ + specializedScalarEquiv W Z a hWZ hZW ha ≪≫ₗ + TensorProduct.piRight H L L (fun _ : ι => H) ≪≫ₗ + LinearEquiv.piCongrRight (fun _ => TensorProduct.AlgebraTensorModule.rid H L L) + +lemma fieldCoordinateTrivialization_one (t : T) (i : ι) : + fieldCoordinateTrivialization F W Z a hWZ hZW ha (1 ⊗ₜ[k] t) i = + algebraMap H L (W (F (1 ⊗ₜ[k] t)) i) := by + simp only [fieldCoordinateTrivialization, LinearEquiv.trans_apply, + TensorProduct.AlgebraTensorModule.cancelBaseChange_symm_tmul, + LinearEquiv.baseChange_tmul, specializedScalarEquiv_tmul, + TensorProduct.piRight_apply, TensorProduct.piRightHom_tmul, LinearEquiv.piCongrRight_apply, + TensorProduct.AlgebraTensorModule.rid_tmul] + simp only [Algebra.smul_def, mul_one] +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/SplitRepresentation.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/SplitRepresentation.lean index bdca80f0e6e791c08b362bc9d7d0c9345ac2b4f6..12827194655bdac217af12a24c4a8710418a98dd 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/SplitRepresentation.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/SplitRepresentation.lean @@ -1,79 +1,79 @@ -import Mathlib - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory Representation -universe u -variable {k : Type u} [Field k] {G : Type u} [Group G] -variable {V W : Type u} [AddCommGroup V] [Module k V] [AddCommGroup W] [Module k W] -variable {ρ : Representation k G V} {σ : Representation k G W} - - -def kernelInclusion (s : ρ.IntertwiningMap σ) : s.ker.toRepresentation.IntertwiningMap ρ := - ⟨s.toLinearMap.ker.subtype, fun _ => rfl⟩ - - -def splitKernelProjection (f : σ.IntertwiningMap ρ) (s : ρ.IntertwiningMap σ) - (h : s.comp f = IntertwiningMap.id σ) : - ρ.IntertwiningMap s.ker.toRepresentation where - toLinearMap := (LinearMap.id - f.toLinearMap.comp s.toLinearMap).codRestrict _ (fun v => by - change s (v - f (s v)) = 0 - have hh : s (f (s v)) = s v := congr($(h) (s v)) - rw [map_sub,hh,sub_self]) - isIntertwining' g := by - apply LinearMap.ext - intro v - apply Subtype.ext - change ρ g v - f (s (ρ g v)) = ρ g (v - f (s v)) - rw [map_sub, s.isIntertwining, f.isIntertwining] - -@[simp] lemma splitKernelProjection_apply (f : σ.IntertwiningMap ρ) - (s : ρ.IntertwiningMap σ) (h : s.comp f = IntertwiningMap.id σ) (v : V) : - (splitKernelProjection f s h v : V) = v - f (s v) := rfl - -lemma splitKernelProjection_inclusion (f : σ.IntertwiningMap ρ) - (s : ρ.IntertwiningMap σ) (h : s.comp f = IntertwiningMap.id σ) : - (splitKernelProjection f s h).comp (kernelInclusion s) = - IntertwiningMap.id s.ker.toRepresentation := by - apply IntertwiningMap.ext - apply LinearMap.ext - intro v - apply Subtype.ext - change (v : V) - f (s v) = v - have hv : s v = 0 := v.property - simp [hv] - -lemma splitKernel_decompose (f : σ.IntertwiningMap ρ) - (s : ρ.IntertwiningMap σ) (h : s.comp f = IntertwiningMap.id σ) : - s.toLinearMap.ker.subtype.comp (splitKernelProjection f s h).toLinearMap + - f.toLinearMap.comp s.toLinearMap = LinearMap.id := by - ext v - change (v - f (s v)) + f (s v) = v - exact sub_add_cancel _ _ - -lemma projective_of_identity_sum {C : Type*} [Category* C] [Preadditive C] - {A P Q : C} (hP : Projective P) (hQ : Projective Q) - (a : A ⟶ P) (b : P ⟶ A) (c : A ⟶ Q) (d : Q ⟶ A) - (h : a ≫ b + c ≫ d = 𝟙 A) : Projective A := by - constructor - intro E X f e he - obtain ⟨i,hi⟩ := hP.factors (b ≫ f) e - obtain ⟨j,hj⟩ := hQ.factors (d ≫ f) e - refine ⟨a ≫ i + c ≫ j, ?_⟩ - simp only [Preadditive.add_comp, Category.assoc, hi, hj] - rw [← Category.assoc, ← Category.assoc, ← Preadditive.add_comp, h, Category.id_comp] - -lemma projective_of_split_kernel (f : σ.IntertwiningMap ρ) - (s : ρ.IntertwiningMap σ) (h : s.comp f = IntertwiningMap.id σ) - (hσ : Projective (Rep.of σ)) (hK : Projective (Rep.of s.ker.toRepresentation)) : - Projective (Rep.of ρ) := by - apply projective_of_identity_sum hK hσ - (Rep.ofHom (splitKernelProjection f s h)) (Rep.ofHom (kernelInclusion s)) - (Rep.ofHom s) (Rep.ofHom f) - apply Rep.hom_ext - apply IntertwiningMap.ext - exact splitKernel_decompose f s h -end FiberFunctorProof - -end OAI +import Mathlib + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory Representation +universe u +variable {k : Type u} [Field k] {G : Type u} [Group G] +variable {V W : Type u} [AddCommGroup V] [Module k V] [AddCommGroup W] [Module k W] +variable {ρ : Representation k G V} {σ : Representation k G W} + + +def kernelInclusion (s : ρ.IntertwiningMap σ) : s.ker.toRepresentation.IntertwiningMap ρ := + ⟨s.toLinearMap.ker.subtype, fun _ => rfl⟩ + + +def splitKernelProjection (f : σ.IntertwiningMap ρ) (s : ρ.IntertwiningMap σ) + (h : s.comp f = IntertwiningMap.id σ) : + ρ.IntertwiningMap s.ker.toRepresentation where + toLinearMap := (LinearMap.id - f.toLinearMap.comp s.toLinearMap).codRestrict _ (fun v => by + change s (v - f (s v)) = 0 + have hh : s (f (s v)) = s v := congr($(h) (s v)) + rw [map_sub,hh,sub_self]) + isIntertwining' g := by + apply LinearMap.ext + intro v + apply Subtype.ext + change ρ g v - f (s (ρ g v)) = ρ g (v - f (s v)) + rw [map_sub, s.isIntertwining, f.isIntertwining] + +@[simp] lemma splitKernelProjection_apply (f : σ.IntertwiningMap ρ) + (s : ρ.IntertwiningMap σ) (h : s.comp f = IntertwiningMap.id σ) (v : V) : + (splitKernelProjection f s h v : V) = v - f (s v) := rfl + +lemma splitKernelProjection_inclusion (f : σ.IntertwiningMap ρ) + (s : ρ.IntertwiningMap σ) (h : s.comp f = IntertwiningMap.id σ) : + (splitKernelProjection f s h).comp (kernelInclusion s) = + IntertwiningMap.id s.ker.toRepresentation := by + apply IntertwiningMap.ext + apply LinearMap.ext + intro v + apply Subtype.ext + change (v : V) - f (s v) = v + have hv : s v = 0 := v.property + simp [hv] + +lemma splitKernel_decompose (f : σ.IntertwiningMap ρ) + (s : ρ.IntertwiningMap σ) (h : s.comp f = IntertwiningMap.id σ) : + s.toLinearMap.ker.subtype.comp (splitKernelProjection f s h).toLinearMap + + f.toLinearMap.comp s.toLinearMap = LinearMap.id := by + ext v + change (v - f (s v)) + f (s v) = v + exact sub_add_cancel _ _ + +lemma projective_of_identity_sum {C : Type*} [Category* C] [Preadditive C] + {A P Q : C} (hP : Projective P) (hQ : Projective Q) + (a : A ⟶ P) (b : P ⟶ A) (c : A ⟶ Q) (d : Q ⟶ A) + (h : a ≫ b + c ≫ d = 𝟙 A) : Projective A := by + constructor + intro E X f e he + obtain ⟨i,hi⟩ := hP.factors (b ≫ f) e + obtain ⟨j,hj⟩ := hQ.factors (d ≫ f) e + refine ⟨a ≫ i + c ≫ j, ?_⟩ + simp only [Preadditive.add_comp, Category.assoc, hi, hj] + rw [← Category.assoc, ← Category.assoc, ← Preadditive.add_comp, h, Category.id_comp] + +lemma projective_of_split_kernel (f : σ.IntertwiningMap ρ) + (s : ρ.IntertwiningMap σ) (h : s.comp f = IntertwiningMap.id σ) + (hσ : Projective (Rep.of σ)) (hK : Projective (Rep.of s.ker.toRepresentation)) : + Projective (Rep.of ρ) := by + apply projective_of_identity_sum hK hσ + (Rep.ofHom (splitKernelProjection f s h)) (Rep.ofHom (kernelInclusion s)) + (Rep.ofHom s) (Rep.ofHom f) + apply Rep.hom_ext + apply IntertwiningMap.ext + exact splitKernel_decompose f s h +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/StableKernel.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/StableKernel.lean index 8254f355618716d8dd6f76c3d43be085f34eefca..45c52b620be59b18e6accdaa37030c9578b526ad 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/StableKernel.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/StableKernel.lean @@ -1,28 +1,28 @@ -import OAI.RepresentationTheory.RestrictedTilting.GeneratedStableKernel - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory -universe u - -def StableRestrictionKernelStatement : Prop := - ∀ (k : Type u) [Field k] [IsAlgClosed k] (p : ℕ) [Fact p.Prime] [CharP k p] - (r : ℕ), 1 ≤ r → ∀ (l : (Fin r → ZMod p) →+ k), Function.Injective l → - ∀ (A B : Tilting k) (f : A ⟶ B), - FactorsThroughProjective ((restrictElementary k p r l).map f.hom) ↔ - f ∈ steinbergIdeal k p r A B - - - -theorem stable_restriction_kernel : StableRestrictionKernelStatement.{u} := by - intro k _ _ p _ _ r hr l hl A B f - constructor - · intro hf - exact steinbergSpan_to_ideal k p r A B f.hom - (tilting_projective_factor_mem_steinbergSpan k p r l hl hr A.obj B.obj - A.property B.property f.hom hf) - · exact steinbergIdeal_restricts_projectively k p r l hl A B f -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.GeneratedStableKernel + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory +universe u + +def StableRestrictionKernelStatement : Prop := + ∀ (k : Type u) [Field k] [IsAlgClosed k] (p : ℕ) [Fact p.Prime] [CharP k p] + (r : ℕ), 1 ≤ r → ∀ (l : (Fin r → ZMod p) →+ k), Function.Injective l → + ∀ (A B : Tilting k) (f : A ⟶ B), + FactorsThroughProjective ((restrictElementary k p r l).map f.hom) ↔ + f ∈ steinbergIdeal k p r A B + + + +theorem stable_restriction_kernel : StableRestrictionKernelStatement.{u} := by + intro k _ _ p _ _ r hr l hl A B f + constructor + · intro hf + exact steinbergSpan_to_ideal k p r A B f.hom + (tilting_projective_factor_mem_steinbergSpan k p r l hl hr A.obj B.obj + A.property B.property f.hom hf) + · exact steinbergIdeal_restricts_projectively k p r l hl A B f +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/StableRestriction.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/StableRestriction.lean index 62c94772d98102a6b8fa1376bd4b41383aa4616e..e5de0b438919766e8978e3d25109df70f3c5c56e 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/StableRestriction.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/StableRestriction.lean @@ -1,67 +1,67 @@ -import OAI.RepresentationTheory.RestrictedTilting.SteinbergRegular -import OAI.RepresentationTheory.RestrictedTilting.ProjectiveRegular -import OAI.RepresentationTheory.RestrictedTilting.ProjectiveFactor -import OAI.RepresentationTheory.RestrictedTilting.TensorExactness - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -universe u - - -abbrev Tilting (k : Type u) [Field k] := - ObjectProperty.FullSubcategory (IsTilting k) - -abbrev tiltingInclusion (k : Type u) [Field k] : Tilting k ⥤ FDRep k (SL2 k) := - ObjectProperty.ι (IsTilting k) - - - -noncomputable def steinbergIdeal (k : Type u) [Field k] (p n : ℕ) (A B : Tilting k) : - Submodule k (A ⟶ B) := - Submodule.span k {f | ∃ X : Tilting k, - ∃ a : A.obj ⟶ steinberg k p n ⊗ X.obj, - ∃ b : steinberg k p n ⊗ X.obj ⟶ B.obj, f.hom = a ≫ b} - -variable (k : Type u) [Field k] (p r : ℕ) [Fact p.Prime] [CharP k p] -variable (l : (Fin r → ZMod p) →+ k) (hl : Function.Injective l) -include hl - - -theorem restricted_steinberg_projective : - Projective ((restrictElementary k p r l).obj (steinberg k p r)) := by - obtain ⟨e⟩ := steinberg_restriction_regular k p r l hl - exact Projective.of_iso e.symm (fdrep_leftRegular_projective k _) - - - -theorem steinbergIdeal_restricts_projectively (A B : Tilting k) (f : A ⟶ B) - (hf : f ∈ steinbergIdeal k p r A B) : - FactorsThroughProjective ((restrictElementary k p r l).map f.hom) := by - let R := restrictElementary k p r l - let : R.Additive := by dsimp [R, restrictElementary]; infer_instance - let : R.Linear k := by dsimp [R, restrictElementary]; infer_instance - let L : (A ⟶ B) →ₗ[k] (R.obj A.obj ⟶ R.obj B.obj) := - (R.mapLinearMap k).comp ((tiltingInclusion k).mapLinearMap k) - let : HasFiniteBiproducts (FDRep k (Multiplicative (Fin r → ZMod p))) := - HasFiniteBiproducts.of_hasFiniteProducts - let : RigidCategory (FDRep k (Multiplicative (Fin r → ZMod p))) := - BraidedCategory.rigidCategoryOfRightRigidCategory - let N := (projectiveFactorSubmodule (k := k) (R.obj A.obj) (R.obj B.obj)).comap L - have hspan : steinbergIdeal k p r A B ≤ N := by - apply Submodule.span_le.mpr - rintro g ⟨X,a,b,hg⟩ - change FactorsThroughProjective (R.map g.hom) - have hS : Projective (R.obj (steinberg k p r)) := - restricted_steinberg_projective k p r l hl - let := hS - have hT : Projective (R.obj (steinberg k p r ⊗ X.obj)) := by - change Projective (R.obj (steinberg k p r) ⊗ R.obj X.obj) - exact projective_tensor _ _ - refine ⟨_,hT,R.map a,R.map b,?_⟩ - rw [← R.map_comp, ← hg] - exact hspan hf -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.SteinbergRegular +import OAI.RepresentationTheory.RestrictedTilting.ProjectiveRegular +import OAI.RepresentationTheory.RestrictedTilting.ProjectiveFactor +import OAI.RepresentationTheory.RestrictedTilting.TensorExactness + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +universe u + + +abbrev Tilting (k : Type u) [Field k] := + ObjectProperty.FullSubcategory (IsTilting k) + +abbrev tiltingInclusion (k : Type u) [Field k] : Tilting k ⥤ FDRep k (SL2 k) := + ObjectProperty.ι (IsTilting k) + + + +noncomputable def steinbergIdeal (k : Type u) [Field k] (p n : ℕ) (A B : Tilting k) : + Submodule k (A ⟶ B) := + Submodule.span k {f | ∃ X : Tilting k, + ∃ a : A.obj ⟶ steinberg k p n ⊗ X.obj, + ∃ b : steinberg k p n ⊗ X.obj ⟶ B.obj, f.hom = a ≫ b} + +variable (k : Type u) [Field k] (p r : ℕ) [Fact p.Prime] [CharP k p] +variable (l : (Fin r → ZMod p) →+ k) (hl : Function.Injective l) +include hl + + +theorem restricted_steinberg_projective : + Projective ((restrictElementary k p r l).obj (steinberg k p r)) := by + obtain ⟨e⟩ := steinberg_restriction_regular k p r l hl + exact Projective.of_iso e.symm (fdrep_leftRegular_projective k _) + + + +theorem steinbergIdeal_restricts_projectively (A B : Tilting k) (f : A ⟶ B) + (hf : f ∈ steinbergIdeal k p r A B) : + FactorsThroughProjective ((restrictElementary k p r l).map f.hom) := by + let R := restrictElementary k p r l + let : R.Additive := by dsimp [R, restrictElementary]; infer_instance + let : R.Linear k := by dsimp [R, restrictElementary]; infer_instance + let L : (A ⟶ B) →ₗ[k] (R.obj A.obj ⟶ R.obj B.obj) := + (R.mapLinearMap k).comp ((tiltingInclusion k).mapLinearMap k) + let : HasFiniteBiproducts (FDRep k (Multiplicative (Fin r → ZMod p))) := + HasFiniteBiproducts.of_hasFiniteProducts + let : RigidCategory (FDRep k (Multiplicative (Fin r → ZMod p))) := + BraidedCategory.rigidCategoryOfRightRigidCategory + let N := (projectiveFactorSubmodule (k := k) (R.obj A.obj) (R.obj B.obj)).comap L + have hspan : steinbergIdeal k p r A B ≤ N := by + apply Submodule.span_le.mpr + rintro g ⟨X,a,b,hg⟩ + change FactorsThroughProjective (R.map g.hom) + have hS : Projective (R.obj (steinberg k p r)) := + restricted_steinberg_projective k p r l hl + let := hS + have hT : Projective (R.obj (steinberg k p r ⊗ X.obj)) := by + change Projective (R.obj (steinberg k p r) ⊗ R.obj X.obj) + exact projective_tensor _ _ + refine ⟨_,hT,R.map a,R.map b,?_⟩ + rw [← R.map_comp, ← hg] + exact hspan hf +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/StandardLifts.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/StandardLifts.lean index 238032e5ebda5362d3601b7620b138e4b42f92a0..b791886833a07699230f27734e79778cdffa240d 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/StandardLifts.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/StandardLifts.lean @@ -1,350 +1,350 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.WeightBounds - -namespace OAI - -/-! Highest coefficients, Bruhat intertwiners and standard module lifts. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof - -universe u -variable (k : Type u) [Field k] - - -noncomputable def standardRepresentation (n : ℕ) : - Representation k (SL2 k) - (Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n)) := - Representation.dual ((homogeneousRepresentation n).comp (dualMatrix k)) - -noncomputable def standardBasis (n : ℕ) := (binaryBasis k n).dualBasis - -noncomputable def standardHighest (n : ℕ) := standardBasis k n (0 : Fin (n + 1)) - -lemma eval_linearChange {ι : Type*} [Fintype ι] (A : Matrix ι ι k) - (z : ι → k) (f : MvPolynomial ι k) : - MvPolynomial.eval z (linearChange A f) = - MvPolynomial.eval (fun i => ∑ j, A j i * z j) f := by - induction f using MvPolynomial.induction_on with - | C c => simp - | add f g hf hg => simp only [map_add, hf, hg] - | mul_X f i hf => - simp only [map_mul, linearChange_X, MvPolynomial.eval_sum, - MvPolynomial.eval_C, MvPolynomial.eval_X, hf] - -lemma standardHighest_apply (n : ℕ) - (f : MvPolynomial.homogeneousSubmodule (Fin 2) k n) : - standardHighest k n f = MvPolynomial.eval ![1, 0] f.val := by - have heq : standardHighest k n = - (MvPolynomial.aeval (R := k) ![(1 : k), 0]).toLinearMap.comp - (MvPolynomial.homogeneousSubmodule (Fin 2) k n).subtype := by - apply (binaryBasis k n).ext - intro i - rw [show standardHighest k n = (binaryBasis k n).dualBasis 0 from rfl, - Module.Basis.dualBasis_apply_self] - change (if i = 0 then 1 else 0) = - MvPolynomial.eval ![1, 0] (binaryBasis k n i).val - rw [binaryBasis_apply] - simp only [MvPolynomial.eval_mul, MvPolynomial.eval_pow, MvPolynomial.eval_X, - Matrix.cons_val_zero, Matrix.cons_val_one, one_pow, one_mul] - by_cases hi : i = 0 - · subst i; simp - · have hi' : (i : ℕ) ≠ 0 := fun h => hi (Fin.ext h) - simp [hi, hi'] - change (standardHighest k n) f = _ - rw [heq] - rfl - -@[simp] lemma unipotent_inv (t : k) : (unipotent k t)⁻¹ = unipotent k (-t) := by - apply inv_eq_of_mul_eq_one_right - rw [← unipotent_add] - simp only [add_neg_cancel, unipotent_zero] - -lemma dualMatrix_inv (g : SL2 k) : dualMatrix k g⁻¹ = - (g : Matrix (Fin 2) (Fin 2) k).transpose := by - change ((g⁻¹)⁻¹ : SL2 k).val.transpose = _ - rw [inv_inv] - -lemma standardHighest_upper_fixed (n : ℕ) (t : k) : - standardRepresentation k n (unipotent k t) (standardHighest k n) = - standardHighest k n := by - ext f - change standardHighest k n ((homogeneousRepresentation n (dualMatrix k ((unipotent k t)⁻¹))) f) = _ - simp only [standardHighest_apply] - change MvPolynomial.eval ![1,0] - (linearChange (dualMatrix k ((unipotent k t)⁻¹)) f.val) = _ - rw [eval_linearChange, dualMatrix_inv] - have hrow : (fun i => ∑ j, (unipotent k t).val.transpose j i * ![(1 : k), 0] j) = - ![1, 0] := by - funext i - change (∑ j, (unipotent k t i j) * ![(1 : k), 0] j) = _ - fin_cases i <;> simp [unipotent, Fin.sum_univ_two] - rw [hrow] - -lemma standardHighest_lower_orbit (n : ℕ) (t : k) : - standardRepresentation k n (lowerUnipotent k t) (standardHighest k n) = - ∑ i : Fin (n + 1), t ^ (i : ℕ) • standardBasis k n i := by - apply (binaryBasis k n).ext - intro i - change standardHighest k n ((homogeneousRepresentation n (dualMatrix k ((lowerUnipotent k t)⁻¹))) - (binaryBasis k n i)) = _ - rw [standardHighest_apply] - change MvPolynomial.eval ![1,0] - (linearChange (dualMatrix k ((lowerUnipotent k t)⁻¹)) (binaryBasis k n i).val) = _ - rw [eval_linearChange] - have hrow : (fun i => ∑ j, dualMatrix k ((lowerUnipotent k t)⁻¹) j i * ![(1 : k), 0] j) = - ![1, t] := by - rw [dualMatrix_inv] - funext i - change (∑ j, (lowerUnipotent k t i j) * ![(1 : k), 0] j) = _ - fin_cases i <;> simp [lowerUnipotent, Fin.sum_univ_two] - rw [hrow, binaryBasis_apply] - simp only [MvPolynomial.eval_mul, MvPolynomial.eval_pow, MvPolynomial.eval_X, - Matrix.cons_val_zero, Matrix.cons_val_one, one_pow, one_mul, - standardBasis, LinearMap.sum_apply, LinearMap.smul_apply, - Module.Basis.dualBasis_apply_self, smul_eq_mul] - simp - -lemma standardBasis_weight (n : ℕ) (i : Fin (n + 1)) (a : kˣ) : - standardRepresentation k n (diagonalTorus k a) (standardBasis k n i) = - integerCharacter k ((n : ℤ) - 2 * i) a • standardBasis k n i := by - apply (binaryBasis k n).ext - intro j - change standardBasis k n i ((costandard k n).ρ ((diagonalTorus k a)⁻¹) - (binaryBasis k n j)) = _ - rw [← map_inv, costandard_basis_weight] - simp only [map_smul, LinearMap.smul_apply, smul_eq_mul, standardBasis, - Module.Basis.dualBasis_apply_self] - by_cases hji : j = i - · subst j - simp only [ite_true, mul_one] - change ((a⁻¹ ^ (2 * (i : ℤ) - n) : kˣ) : k) = - ((a ^ ((n : ℤ) - 2 * i) : kˣ) : k) - congr 1 - rw [inv_zpow, ← zpow_neg] - congr 1 - omega - · simp [hji] - -lemma standardHighest_weight (n : ℕ) (a : kˣ) : - standardRepresentation k n (diagonalTorus k a) (standardHighest k n) = - integerCharacter k n a • standardHighest k n := by - simpa only [standardHighest, Fin.val_zero, Nat.cast_zero, mul_zero, sub_zero] using - standardBasis_weight k n 0 a - - -lemma linearIndependent_powerFunctionsOn (S : Set k) (hS : S.Infinite) : - LinearIndependent k (fun (n : ℕ) (x : S) => (x : k) ^ n) := by - classical - apply linearIndependent_iff'.mpr - intro s a ha i hi - have hp : (∑ j ∈ s, Polynomial.monomial j (a j)) = (0 : Polynomial k) := by - apply Polynomial.eq_of_infinite_eval_eq - apply hS.mono - intro x hx - change Polynomial.eval x _ = Polynomial.eval x _ - have he := congrFun ha ⟨x, hx⟩ - simpa only [Polynomial.eval_finsetSum, Polynomial.eval_monomial, - Polynomial.eval_zero, Finset.sum_apply, Pi.smul_apply, Pi.zero_apply, - smul_eq_mul] using he - have hc := congrArg (fun p : Polynomial k => p.coeff i) hp - simpa [Polynomial.coeff_monomial, hi] using hc - - - -lemma upper_lower_bruhat (s t : k) (q : kˣ) (hq : (q : k) = 1 + s * t) : - unipotent k s * lowerUnipotent k t = - lowerUnipotent k (t / q) * diagonalTorus k q * unipotent k (s / q) := by - apply Subtype.ext - change !![1, s; 0, 1] * !![1, 0; t, 1] = - !![1, 0; t / q, 1] * !![(q : k), 0; 0, (↑q⁻¹ : k)] * !![1, s / q; 0, 1] - ext i j - fin_cases i <;> fin_cases j <;> - simp [Matrix.mul_apply, Fin.sum_univ_two, div_eq_mul_inv] - · exact hq.symm - · field_simp - · field_simp - linear_combination hq - -lemma lower_eq_transvection (t : k) : - lowerUnipotent k t = Matrix.SpecialLinearGroup.transvection (one_ne_zero : (1 : Fin 2) ≠ 0) t := by - apply Subtype.ext - ext i j - fin_cases i <;> fin_cases j <;> - simp [lowerUnipotent, Matrix.SpecialLinearGroup.transvection_coe] - -lemma upper_eq_transvection (t : k) : - unipotent k t = Matrix.SpecialLinearGroup.transvection (zero_ne_one : (0 : Fin 2) ≠ 1) t := by - apply Subtype.ext - ext i j - fin_cases i <;> fin_cases j <;> - simp [unipotent, Matrix.SpecialLinearGroup.transvection_coe] - - -lemma intertwiner_of_root_groups {M N : Type*} [AddCommGroup M] [Module k M] - [AddCommGroup N] [Module k N] - (ρ : Representation k (SL2 k) M) (σ : Representation k (SL2 k) N) - (f : M →ₗ[k] N) - (hu : ∀ t v, f (ρ (unipotent k t) v) = σ (unipotent k t) (f v)) - (hl : ∀ t v, f (ρ (lowerUnipotent k t) v) = σ (lowerUnipotent k t) (f v)) : - ∀ g v, f (ρ g v) = σ g (f v) := by - apply Matrix.SL2.transvection_induction - · intro i j hij t - fin_cases i <;> fin_cases j - · exact (hij rfl).elim - · simpa only [← upper_eq_transvection] using hu t - · simpa only [← lower_eq_transvection] using hl t - · exact (hij rfl).elim - · intro a b ha hb v - simp only [map_mul, Module.End.mul_apply, ha, hb] - - - - -lemma standard_lower_orbit_ext {M : Type*} [AddCommGroup M] [Module k M] - (n : ℕ) (S : Set k) (hS : S.Infinite) - (f g : Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) →ₗ[k] M) - (h : ∀ t ∈ S, f (standardRepresentation k n (lowerUnipotent k t) - (standardHighest k n)) = g (standardRepresentation k n (lowerUnipotent k t) - (standardHighest k n))) : f = g := by - classical - apply (standardBasis k n).ext - intro i - apply sub_eq_zero.mp - apply function_sum_eq_zero (fun (j : Fin (n+1)) (t : S) => (t : k) ^ (j : ℕ)) - ((linearIndependent_powerFunctionsOn k S hS).comp Fin.val Fin.val_injective) - Finset.univ (fun j => f (standardBasis k n j) - g (standardBasis k n j)) ?_ i - (Finset.mem_univ i) - intro t - have ht := h t t.property - rw [standardHighest_lower_orbit] at ht - simpa only [map_sum, map_smul, smul_sub, Finset.sum_sub_distrib, sub_eq_zero] using ht - -lemma finsupp_sum_fin_of_degree_bound {M : Type*} [AddCommGroup M] [Module k M] - (n : ℕ) (c : ℕ →₀ M) (hz : ∀ i, n < i → c i = 0) (t : k) : - c.sum (fun i x => t ^ i • x) = ∑ i : Fin (n + 1), t ^ (i : ℕ) • c i := by - classical - have hs : c.support ⊆ Finset.range (n + 1) := by - intro i hi - apply Finset.mem_range.mpr - by_contra hn - exact (Finsupp.mem_support_iff.mp hi) (hz i (by omega)) - rw [Finsupp.sum_of_support_subset c hs _ (fun i _ => smul_zero _)] - exact (Fin.sum_univ_eq_sum_range (fun i => t ^ i • c i) (n + 1)).symm - - - -noncomputable def highestCoefficientMap {M : Type*} [AddCommGroup M] [Module k M] - (n : ℕ) (c : ℕ →₀ M) : - Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) →ₗ[k] M := - (standardBasis k n).constr k (fun i => c i) - -lemma highestCoefficientMap_lower_orbit {M : Type*} [AddCommGroup M] [Module k M] - (ρ : Representation k (SL2 k) M) (n : ℕ) (v : M) (c : ℕ →₀ M) - (hc : ∀ t, ρ (lowerUnipotent k t) v = c.sum (fun i x => t ^ i • x)) - (hz : ∀ i, n < i → c i = 0) (t : k) : - highestCoefficientMap k n c (standardRepresentation k n (lowerUnipotent k t) - (standardHighest k n)) = ρ (lowerUnipotent k t) v := by - rw [standardHighest_lower_orbit, hc, finsupp_sum_fin_of_degree_bound k n c hz] - simp [highestCoefficientMap] - -lemma highestCoefficientMap_highest {M : Type*} [AddCommGroup M] [Module k M] - (ρ : Representation k (SL2 k) M) (n : ℕ) (v : M) (c : ℕ →₀ M) - (hc : ∀ t, ρ (lowerUnipotent k t) v = c.sum (fun i x => t ^ i • x)) - (hz : ∀ i, n < i → c i = 0) : - highestCoefficientMap k n c (standardHighest k n) = v := by - simpa only [lowerUnipotent_zero, map_one, Module.End.one_apply] using - highestCoefficientMap_lower_orbit k ρ n v c hc hz 0 - -lemma highestCoefficientMap_lower_intertwines [Infinite k] - {M : Type*} [AddCommGroup M] [Module k M] - (ρ : Representation k (SL2 k) M) (n : ℕ) (v : M) (c : ℕ →₀ M) - (hc : ∀ t, ρ (lowerUnipotent k t) v = c.sum (fun i x => t ^ i • x)) - (hz : ∀ i, n < i → c i = 0) (s : k) : - (highestCoefficientMap k n c).comp (standardRepresentation k n (lowerUnipotent k s)) = - (ρ (lowerUnipotent k s)).comp (highestCoefficientMap k n c) := by - apply standard_lower_orbit_ext k n Set.univ Set.infinite_univ - intro t ht - simp only [LinearMap.comp_apply] - rw [← Module.End.mul_apply, ← map_mul, ← lowerUnipotent_add, - highestCoefficientMap_lower_orbit k ρ n v c hc hz, - highestCoefficientMap_lower_orbit k ρ n v c hc hz, - lowerUnipotent_add, map_mul, Module.End.mul_apply] - - -lemma infinite_bruhat_parameters [Infinite k] (s : k) : - {t : k | 1 + s * t ≠ 0}.Infinite := by - by_cases hs : s = 0 - · simpa [hs] using (Set.infinite_univ (α := k)) - · have hf : {t : k | 1 + s * t = 0}.Finite := by - apply (Set.finite_singleton (-s⁻¹)).subset - intro t ht - apply Set.mem_singleton_iff.mpr - apply mul_left_cancel₀ hs - rw [mul_neg, mul_inv_cancel₀ hs] - change 1 + s * t = 0 at ht - linear_combination ht - exact hf.infinite_compl - -lemma upper_lower_on_highest {M : Type*} [AddCommGroup M] [Module k M] - (ρ : Representation k (SL2 k) M) (n : ℤ) (v : M) - (hu : ∀ t, ρ (unipotent k t) v = v) - (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) - (s t : k) (q : kˣ) (hq : (q : k) = 1 + s * t) : - ρ (unipotent k s) (ρ (lowerUnipotent k t) v) = - integerCharacter k n q • ρ (lowerUnipotent k (t / q)) v := by - rw [← Module.End.mul_apply, ← map_mul, upper_lower_bruhat k s t q hq] - simp only [map_mul, Module.End.mul_apply, hu, hv, map_smul] - -lemma highestCoefficientMap_upper_intertwines [Infinite k] - {M : Type*} [AddCommGroup M] [Module k M] - (ρ : Representation k (SL2 k) M) (n : ℕ) (v : M) - (hu : ∀ t, ρ (unipotent k t) v = v) - (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) - (c : ℕ →₀ M) - (hc : ∀ t, ρ (lowerUnipotent k t) v = c.sum (fun i x => t ^ i • x)) - (hz : ∀ i, n < i → c i = 0) (s : k) : - (highestCoefficientMap k n c).comp (standardRepresentation k n (unipotent k s)) = - (ρ (unipotent k s)).comp (highestCoefficientMap k n c) := by - apply standard_lower_orbit_ext k n {t : k | 1 + s * t ≠ 0} - (infinite_bruhat_parameters k s) - intro t ht - let q : kˣ := Units.mk0 (1 + s * t) ht - simp only [LinearMap.comp_apply] - rw [upper_lower_on_highest k (standardRepresentation k n) n (standardHighest k n) - (standardHighest_upper_fixed k n) (standardHighest_weight k n) s t q rfl, - map_smul, highestCoefficientMap_lower_orbit k ρ n v c hc hz, - highestCoefficientMap_lower_orbit k ρ n v c hc hz, - upper_lower_on_highest k ρ n v hu hv s t q rfl] - - - -theorem exists_standard_lift [Infinite k] {M : Type u} [AddCommGroup M] - [Module k M] [Module.Finite k M] - (ρ : Representation k (SL2 k) M) (hρ : IsRational k ρ) - (n : ℕ) (hbound : HasWeightsBetween ρ (-(n : ℤ)) n) - (v : M) (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) : - ∃ f : Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) →ₗ[k] M, - f (standardHighest k n) = v ∧ - ∀ g x, f (standardRepresentation k n g x) = ρ g (f x) := by - obtain ⟨c, hc⟩ := rational_lowerUnipotent_expansion k ρ hρ v - have hz := lowerUnipotent_degree_bound k ρ n hbound v hv c hc - have hu := highest_unipotent_fixed ρ hρ n v hv - (fun m w hm hw => hbound m w (Or.inr hm) hw) - refine ⟨highestCoefficientMap k n c, - highestCoefficientMap_highest k ρ n v c hc hz, ?_⟩ - apply intertwiner_of_root_groups k - · intro t x - exact congrArg (fun f => (f : _ →ₗ[k] M) x) - (highestCoefficientMap_upper_intertwines k ρ n v hu hv c hc hz t) - · intro t x - exact congrArg (fun f => (f : _ →ₗ[k] M) x) - (highestCoefficientMap_lower_intertwines k ρ n v c hc hz t) - -end FiberFunctorProof -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.WeightBounds + +namespace OAI + +/-! Highest coefficients, Bruhat intertwiners and standard module lifts. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof + +universe u +variable (k : Type u) [Field k] + + +noncomputable def standardRepresentation (n : ℕ) : + Representation k (SL2 k) + (Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n)) := + Representation.dual ((homogeneousRepresentation n).comp (dualMatrix k)) + +noncomputable def standardBasis (n : ℕ) := (binaryBasis k n).dualBasis + +noncomputable def standardHighest (n : ℕ) := standardBasis k n (0 : Fin (n + 1)) + +lemma eval_linearChange {ι : Type*} [Fintype ι] (A : Matrix ι ι k) + (z : ι → k) (f : MvPolynomial ι k) : + MvPolynomial.eval z (linearChange A f) = + MvPolynomial.eval (fun i => ∑ j, A j i * z j) f := by + induction f using MvPolynomial.induction_on with + | C c => simp + | add f g hf hg => simp only [map_add, hf, hg] + | mul_X f i hf => + simp only [map_mul, linearChange_X, MvPolynomial.eval_sum, + MvPolynomial.eval_C, MvPolynomial.eval_X, hf] + +lemma standardHighest_apply (n : ℕ) + (f : MvPolynomial.homogeneousSubmodule (Fin 2) k n) : + standardHighest k n f = MvPolynomial.eval ![1, 0] f.val := by + have heq : standardHighest k n = + (MvPolynomial.aeval (R := k) ![(1 : k), 0]).toLinearMap.comp + (MvPolynomial.homogeneousSubmodule (Fin 2) k n).subtype := by + apply (binaryBasis k n).ext + intro i + rw [show standardHighest k n = (binaryBasis k n).dualBasis 0 from rfl, + Module.Basis.dualBasis_apply_self] + change (if i = 0 then 1 else 0) = + MvPolynomial.eval ![1, 0] (binaryBasis k n i).val + rw [binaryBasis_apply] + simp only [MvPolynomial.eval_mul, MvPolynomial.eval_pow, MvPolynomial.eval_X, + Matrix.cons_val_zero, Matrix.cons_val_one, one_pow, one_mul] + by_cases hi : i = 0 + · subst i; simp + · have hi' : (i : ℕ) ≠ 0 := fun h => hi (Fin.ext h) + simp [hi, hi'] + change (standardHighest k n) f = _ + rw [heq] + rfl + +@[simp] lemma unipotent_inv (t : k) : (unipotent k t)⁻¹ = unipotent k (-t) := by + apply inv_eq_of_mul_eq_one_right + rw [← unipotent_add] + simp only [add_neg_cancel, unipotent_zero] + +lemma dualMatrix_inv (g : SL2 k) : dualMatrix k g⁻¹ = + (g : Matrix (Fin 2) (Fin 2) k).transpose := by + change ((g⁻¹)⁻¹ : SL2 k).val.transpose = _ + rw [inv_inv] + +lemma standardHighest_upper_fixed (n : ℕ) (t : k) : + standardRepresentation k n (unipotent k t) (standardHighest k n) = + standardHighest k n := by + ext f + change standardHighest k n ((homogeneousRepresentation n (dualMatrix k ((unipotent k t)⁻¹))) f) = _ + simp only [standardHighest_apply] + change MvPolynomial.eval ![1,0] + (linearChange (dualMatrix k ((unipotent k t)⁻¹)) f.val) = _ + rw [eval_linearChange, dualMatrix_inv] + have hrow : (fun i => ∑ j, (unipotent k t).val.transpose j i * ![(1 : k), 0] j) = + ![1, 0] := by + funext i + change (∑ j, (unipotent k t i j) * ![(1 : k), 0] j) = _ + fin_cases i <;> simp [unipotent, Fin.sum_univ_two] + rw [hrow] + +lemma standardHighest_lower_orbit (n : ℕ) (t : k) : + standardRepresentation k n (lowerUnipotent k t) (standardHighest k n) = + ∑ i : Fin (n + 1), t ^ (i : ℕ) • standardBasis k n i := by + apply (binaryBasis k n).ext + intro i + change standardHighest k n ((homogeneousRepresentation n (dualMatrix k ((lowerUnipotent k t)⁻¹))) + (binaryBasis k n i)) = _ + rw [standardHighest_apply] + change MvPolynomial.eval ![1,0] + (linearChange (dualMatrix k ((lowerUnipotent k t)⁻¹)) (binaryBasis k n i).val) = _ + rw [eval_linearChange] + have hrow : (fun i => ∑ j, dualMatrix k ((lowerUnipotent k t)⁻¹) j i * ![(1 : k), 0] j) = + ![1, t] := by + rw [dualMatrix_inv] + funext i + change (∑ j, (lowerUnipotent k t i j) * ![(1 : k), 0] j) = _ + fin_cases i <;> simp [lowerUnipotent, Fin.sum_univ_two] + rw [hrow, binaryBasis_apply] + simp only [MvPolynomial.eval_mul, MvPolynomial.eval_pow, MvPolynomial.eval_X, + Matrix.cons_val_zero, Matrix.cons_val_one, one_pow, one_mul, + standardBasis, LinearMap.sum_apply, LinearMap.smul_apply, + Module.Basis.dualBasis_apply_self, smul_eq_mul] + simp + +lemma standardBasis_weight (n : ℕ) (i : Fin (n + 1)) (a : kˣ) : + standardRepresentation k n (diagonalTorus k a) (standardBasis k n i) = + integerCharacter k ((n : ℤ) - 2 * i) a • standardBasis k n i := by + apply (binaryBasis k n).ext + intro j + change standardBasis k n i ((costandard k n).ρ ((diagonalTorus k a)⁻¹) + (binaryBasis k n j)) = _ + rw [← map_inv, costandard_basis_weight] + simp only [map_smul, LinearMap.smul_apply, smul_eq_mul, standardBasis, + Module.Basis.dualBasis_apply_self] + by_cases hji : j = i + · subst j + simp only [ite_true, mul_one] + change ((a⁻¹ ^ (2 * (i : ℤ) - n) : kˣ) : k) = + ((a ^ ((n : ℤ) - 2 * i) : kˣ) : k) + congr 1 + rw [inv_zpow, ← zpow_neg] + congr 1 + omega + · simp [hji] + +lemma standardHighest_weight (n : ℕ) (a : kˣ) : + standardRepresentation k n (diagonalTorus k a) (standardHighest k n) = + integerCharacter k n a • standardHighest k n := by + simpa only [standardHighest, Fin.val_zero, Nat.cast_zero, mul_zero, sub_zero] using + standardBasis_weight k n 0 a + + +lemma linearIndependent_powerFunctionsOn (S : Set k) (hS : S.Infinite) : + LinearIndependent k (fun (n : ℕ) (x : S) => (x : k) ^ n) := by + classical + apply linearIndependent_iff'.mpr + intro s a ha i hi + have hp : (∑ j ∈ s, Polynomial.monomial j (a j)) = (0 : Polynomial k) := by + apply Polynomial.eq_of_infinite_eval_eq + apply hS.mono + intro x hx + change Polynomial.eval x _ = Polynomial.eval x _ + have he := congrFun ha ⟨x, hx⟩ + simpa only [Polynomial.eval_finsetSum, Polynomial.eval_monomial, + Polynomial.eval_zero, Finset.sum_apply, Pi.smul_apply, Pi.zero_apply, + smul_eq_mul] using he + have hc := congrArg (fun p : Polynomial k => p.coeff i) hp + simpa [Polynomial.coeff_monomial, hi] using hc + + + +lemma upper_lower_bruhat (s t : k) (q : kˣ) (hq : (q : k) = 1 + s * t) : + unipotent k s * lowerUnipotent k t = + lowerUnipotent k (t / q) * diagonalTorus k q * unipotent k (s / q) := by + apply Subtype.ext + change !![1, s; 0, 1] * !![1, 0; t, 1] = + !![1, 0; t / q, 1] * !![(q : k), 0; 0, (↑q⁻¹ : k)] * !![1, s / q; 0, 1] + ext i j + fin_cases i <;> fin_cases j <;> + simp [Matrix.mul_apply, Fin.sum_univ_two, div_eq_mul_inv] + · exact hq.symm + · field_simp + · field_simp + linear_combination hq + +lemma lower_eq_transvection (t : k) : + lowerUnipotent k t = Matrix.SpecialLinearGroup.transvection (one_ne_zero : (1 : Fin 2) ≠ 0) t := by + apply Subtype.ext + ext i j + fin_cases i <;> fin_cases j <;> + simp [lowerUnipotent, Matrix.SpecialLinearGroup.transvection_coe] + +lemma upper_eq_transvection (t : k) : + unipotent k t = Matrix.SpecialLinearGroup.transvection (zero_ne_one : (0 : Fin 2) ≠ 1) t := by + apply Subtype.ext + ext i j + fin_cases i <;> fin_cases j <;> + simp [unipotent, Matrix.SpecialLinearGroup.transvection_coe] + + +lemma intertwiner_of_root_groups {M N : Type*} [AddCommGroup M] [Module k M] + [AddCommGroup N] [Module k N] + (ρ : Representation k (SL2 k) M) (σ : Representation k (SL2 k) N) + (f : M →ₗ[k] N) + (hu : ∀ t v, f (ρ (unipotent k t) v) = σ (unipotent k t) (f v)) + (hl : ∀ t v, f (ρ (lowerUnipotent k t) v) = σ (lowerUnipotent k t) (f v)) : + ∀ g v, f (ρ g v) = σ g (f v) := by + apply Matrix.SL2.transvection_induction + · intro i j hij t + fin_cases i <;> fin_cases j + · exact (hij rfl).elim + · simpa only [← upper_eq_transvection] using hu t + · simpa only [← lower_eq_transvection] using hl t + · exact (hij rfl).elim + · intro a b ha hb v + simp only [map_mul, Module.End.mul_apply, ha, hb] + + + + +lemma standard_lower_orbit_ext {M : Type*} [AddCommGroup M] [Module k M] + (n : ℕ) (S : Set k) (hS : S.Infinite) + (f g : Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) →ₗ[k] M) + (h : ∀ t ∈ S, f (standardRepresentation k n (lowerUnipotent k t) + (standardHighest k n)) = g (standardRepresentation k n (lowerUnipotent k t) + (standardHighest k n))) : f = g := by + classical + apply (standardBasis k n).ext + intro i + apply sub_eq_zero.mp + apply function_sum_eq_zero (fun (j : Fin (n+1)) (t : S) => (t : k) ^ (j : ℕ)) + ((linearIndependent_powerFunctionsOn k S hS).comp Fin.val Fin.val_injective) + Finset.univ (fun j => f (standardBasis k n j) - g (standardBasis k n j)) ?_ i + (Finset.mem_univ i) + intro t + have ht := h t t.property + rw [standardHighest_lower_orbit] at ht + simpa only [map_sum, map_smul, smul_sub, Finset.sum_sub_distrib, sub_eq_zero] using ht + +lemma finsupp_sum_fin_of_degree_bound {M : Type*} [AddCommGroup M] [Module k M] + (n : ℕ) (c : ℕ →₀ M) (hz : ∀ i, n < i → c i = 0) (t : k) : + c.sum (fun i x => t ^ i • x) = ∑ i : Fin (n + 1), t ^ (i : ℕ) • c i := by + classical + have hs : c.support ⊆ Finset.range (n + 1) := by + intro i hi + apply Finset.mem_range.mpr + by_contra hn + exact (Finsupp.mem_support_iff.mp hi) (hz i (by omega)) + rw [Finsupp.sum_of_support_subset c hs _ (fun i _ => smul_zero _)] + exact (Fin.sum_univ_eq_sum_range (fun i => t ^ i • c i) (n + 1)).symm + + + +noncomputable def highestCoefficientMap {M : Type*} [AddCommGroup M] [Module k M] + (n : ℕ) (c : ℕ →₀ M) : + Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) →ₗ[k] M := + (standardBasis k n).constr k (fun i => c i) + +lemma highestCoefficientMap_lower_orbit {M : Type*} [AddCommGroup M] [Module k M] + (ρ : Representation k (SL2 k) M) (n : ℕ) (v : M) (c : ℕ →₀ M) + (hc : ∀ t, ρ (lowerUnipotent k t) v = c.sum (fun i x => t ^ i • x)) + (hz : ∀ i, n < i → c i = 0) (t : k) : + highestCoefficientMap k n c (standardRepresentation k n (lowerUnipotent k t) + (standardHighest k n)) = ρ (lowerUnipotent k t) v := by + rw [standardHighest_lower_orbit, hc, finsupp_sum_fin_of_degree_bound k n c hz] + simp [highestCoefficientMap] + +lemma highestCoefficientMap_highest {M : Type*} [AddCommGroup M] [Module k M] + (ρ : Representation k (SL2 k) M) (n : ℕ) (v : M) (c : ℕ →₀ M) + (hc : ∀ t, ρ (lowerUnipotent k t) v = c.sum (fun i x => t ^ i • x)) + (hz : ∀ i, n < i → c i = 0) : + highestCoefficientMap k n c (standardHighest k n) = v := by + simpa only [lowerUnipotent_zero, map_one, Module.End.one_apply] using + highestCoefficientMap_lower_orbit k ρ n v c hc hz 0 + +lemma highestCoefficientMap_lower_intertwines [Infinite k] + {M : Type*} [AddCommGroup M] [Module k M] + (ρ : Representation k (SL2 k) M) (n : ℕ) (v : M) (c : ℕ →₀ M) + (hc : ∀ t, ρ (lowerUnipotent k t) v = c.sum (fun i x => t ^ i • x)) + (hz : ∀ i, n < i → c i = 0) (s : k) : + (highestCoefficientMap k n c).comp (standardRepresentation k n (lowerUnipotent k s)) = + (ρ (lowerUnipotent k s)).comp (highestCoefficientMap k n c) := by + apply standard_lower_orbit_ext k n Set.univ Set.infinite_univ + intro t ht + simp only [LinearMap.comp_apply] + rw [← Module.End.mul_apply, ← map_mul, ← lowerUnipotent_add, + highestCoefficientMap_lower_orbit k ρ n v c hc hz, + highestCoefficientMap_lower_orbit k ρ n v c hc hz, + lowerUnipotent_add, map_mul, Module.End.mul_apply] + + +lemma infinite_bruhat_parameters [Infinite k] (s : k) : + {t : k | 1 + s * t ≠ 0}.Infinite := by + by_cases hs : s = 0 + · simpa [hs] using (Set.infinite_univ (α := k)) + · have hf : {t : k | 1 + s * t = 0}.Finite := by + apply (Set.finite_singleton (-s⁻¹)).subset + intro t ht + apply Set.mem_singleton_iff.mpr + apply mul_left_cancel₀ hs + rw [mul_neg, mul_inv_cancel₀ hs] + change 1 + s * t = 0 at ht + linear_combination ht + exact hf.infinite_compl + +lemma upper_lower_on_highest {M : Type*} [AddCommGroup M] [Module k M] + (ρ : Representation k (SL2 k) M) (n : ℤ) (v : M) + (hu : ∀ t, ρ (unipotent k t) v = v) + (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) + (s t : k) (q : kˣ) (hq : (q : k) = 1 + s * t) : + ρ (unipotent k s) (ρ (lowerUnipotent k t) v) = + integerCharacter k n q • ρ (lowerUnipotent k (t / q)) v := by + rw [← Module.End.mul_apply, ← map_mul, upper_lower_bruhat k s t q hq] + simp only [map_mul, Module.End.mul_apply, hu, hv, map_smul] + +lemma highestCoefficientMap_upper_intertwines [Infinite k] + {M : Type*} [AddCommGroup M] [Module k M] + (ρ : Representation k (SL2 k) M) (n : ℕ) (v : M) + (hu : ∀ t, ρ (unipotent k t) v = v) + (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) + (c : ℕ →₀ M) + (hc : ∀ t, ρ (lowerUnipotent k t) v = c.sum (fun i x => t ^ i • x)) + (hz : ∀ i, n < i → c i = 0) (s : k) : + (highestCoefficientMap k n c).comp (standardRepresentation k n (unipotent k s)) = + (ρ (unipotent k s)).comp (highestCoefficientMap k n c) := by + apply standard_lower_orbit_ext k n {t : k | 1 + s * t ≠ 0} + (infinite_bruhat_parameters k s) + intro t ht + let q : kˣ := Units.mk0 (1 + s * t) ht + simp only [LinearMap.comp_apply] + rw [upper_lower_on_highest k (standardRepresentation k n) n (standardHighest k n) + (standardHighest_upper_fixed k n) (standardHighest_weight k n) s t q rfl, + map_smul, highestCoefficientMap_lower_orbit k ρ n v c hc hz, + highestCoefficientMap_lower_orbit k ρ n v c hc hz, + upper_lower_on_highest k ρ n v hu hv s t q rfl] + + + +theorem exists_standard_lift [Infinite k] {M : Type u} [AddCommGroup M] + [Module k M] [Module.Finite k M] + (ρ : Representation k (SL2 k) M) (hρ : IsRational k ρ) + (n : ℕ) (hbound : HasWeightsBetween ρ (-(n : ℤ)) n) + (v : M) (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) : + ∃ f : Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) →ₗ[k] M, + f (standardHighest k n) = v ∧ + ∀ g x, f (standardRepresentation k n g x) = ρ g (f x) := by + obtain ⟨c, hc⟩ := rational_lowerUnipotent_expansion k ρ hρ v + have hz := lowerUnipotent_degree_bound k ρ n hbound v hv c hc + have hu := highest_unipotent_fixed ρ hρ n v hv + (fun m w hm hw => hbound m w (Or.inr hm) hw) + refine ⟨highestCoefficientMap k n c, + highestCoefficientMap_highest k ρ n v c hc hz, ?_⟩ + apply intertwiner_of_root_groups k + · intro t x + exact congrArg (fun f => (f : _ →ₗ[k] M) x) + (highestCoefficientMap_upper_intertwines k ρ n v hu hv c hc hz t) + · intro t x + exact congrArg (fun f => (f : _ →ₗ[k] M) x) + (highestCoefficientMap_lower_intertwines k ρ n v c hc hz t) + +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/SteinbergDuality.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/SteinbergDuality.lean index c97d276632a8eefe4bfc376286991b8a2d16e1ac..acdd2fc30752b7127e86e8cfb283a31c722a7040 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/SteinbergDuality.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/SteinbergDuality.lean @@ -1,197 +1,197 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.ExtensionSplitting - -namespace OAI - -/-! Standard-costandard maps, binomial coefficients and Steinberg self-duality. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section -open CategoryTheory CategoryTheory.MonoidalCategory -universe u -variable (k : Type u) [Field k] - -noncomputable def costandardHighest (n : ℕ) : - MvPolynomial.homogeneousSubmodule (Fin 2) k n := binaryBasis k n (Fin.last n) - -lemma costandardHighest_weight (n : ℕ) (a : kˣ) : - (costandard k n).ρ (diagonalTorus k a) (costandardHighest k n) = - integerCharacter k n a • costandardHighest k n := by - have h := costandard_basis_weight k n (Fin.last n) a - have hn : (2 * (n : ℤ) - n) = n := by ring - simpa [costandardHighest, hn] using h - -lemma costandardHighest_lower_orbit (n : ℕ) (t : k) : - (costandard k n).ρ (lowerUnipotent k t) (costandardHighest k n) = - ∑ i : Fin (n + 1), t ^ (i : ℕ) • - (((-1 : k) ^ (i : ℕ) * (n.choose i : k)) • binaryBasis k n i.rev) := by - apply Subtype.ext - change linearChange (dualMatrix k (lowerUnipotent k t)) - (binaryBasis k n (Fin.last n)).val = _ - rw [binaryBasis_apply] - simp only [Fin.val_last, Nat.sub_self, pow_zero, one_mul, map_pow] - have he : linearChange (dualMatrix k (lowerUnipotent k t)) (MvPolynomial.X 1) = - (-MvPolynomial.C t * MvPolynomial.X 0 + MvPolynomial.X 1 : MvPolynomial (Fin 2) k) := by - simp [linearChange_X, dualMatrix, lowerUnipotent, - Matrix.transpose_apply, Fin.sum_univ_two] - rw [he, add_pow] - rw [← Fin.sum_univ_eq_sum_range] - simp only [Submodule.coe_sum, Submodule.coe_smul_of_tower, binaryBasis_apply, - MvPolynomial.smul_eq_C_mul, Fin.val_rev, Nat.succ_sub_succ_eq_sub] - apply Finset.sum_congr rfl - intro i _ - have hi : n - (n - (i : ℕ)) = i := by omega - rw [hi] - have hneg : (-MvPolynomial.C t : MvPolynomial (Fin 2) k) = - MvPolynomial.C (-1 : k) * MvPolynomial.C t := by simp - rw [hneg] - simp only [mul_pow, map_mul, map_pow, map_neg, map_one, map_natCast] - ring - -variable [Infinite k] - - - -theorem exists_standard_costandard_map (n : ℕ) : - ∃ f : Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) →ₗ[k] - MvPolynomial.homogeneousSubmodule (Fin 2) k n, - (∀ a x, f (standardRepresentation k n a x) = (costandard k n).ρ a (f x)) ∧ - ∀ i : Fin (n + 1), f (standardBasis k n i) = - ((-1 : k) ^ (i : ℕ) * (n.choose i : k)) • binaryBasis k n i.rev := by - obtain ⟨f,hfv,hf⟩ := exists_standard_lift k (costandard k n).ρ (costandard_rational k n) - n (fun m v hm hv => costandard_weight_bound k n m hm v hv) - (costandardHighest k n) (costandardHighest_weight k n) - change Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) →ₗ[k] - MvPolynomial.homogeneousSubmodule (Fin 2) k n at f - refine ⟨f,hf,?_⟩ - intro i - apply sub_eq_zero.mp - apply function_sum_eq_zero (fun (j : Fin (n+1)) (t : k) => t ^ (j : ℕ)) - ((linearIndependent_powerFunctions k).comp Fin.val Fin.val_injective) Finset.univ - (fun j => f (standardBasis k n j) - - ((-1 : k) ^ (j : ℕ) * (n.choose j : k)) • binaryBasis k n j.rev) ?_ i - (Finset.mem_univ i) - intro t - have ht := hf (lowerUnipotent k t) (standardHighest k n) - rw [hfv, costandardHighest_lower_orbit, standardHighest_lower_orbit] at ht - change f (∑ j : Fin (n+1), t ^ (j : ℕ) • standardBasis k n j) = - ∑ j : Fin (n+1), t ^ (j : ℕ) • - (((-1 : k) ^ (j : ℕ) * (n.choose j : k)) • binaryBasis k n j.rev) at ht - simpa only [Finset.mem_univ, forall_const, Finset.sum_const_zero, map_sum, map_smul, - smul_sub, Finset.sum_sub_distrib, Finset.sum_ite_irrel, ite_true, sub_eq_zero] using ht - - -theorem costandard_self_dual_of_choose_ne_zero (n : ℕ) - (hc : ∀ i : Fin (n + 1), (n.choose i : k) ≠ 0) : - Nonempty ((costandard k n)ᘁ ≅ costandard k n) := by - obtain ⟨f,hf,hfb⟩ := exists_standard_costandard_map k n - have hsurj : Function.Surjective f := by - apply LinearMap.range_eq_top.mp - have hr : Submodule.span k (Set.range (binaryBasis k n)) ≤ LinearMap.range f := by - apply Submodule.span_le.mpr - rintro _ ⟨i,rfl⟩ - let c : k := (-1 : k) ^ (i.rev : ℕ) * (n.choose i.rev : k) - have hc' : c ≠ 0 := mul_ne_zero (pow_ne_zero _ (neg_ne_zero.mpr one_ne_zero)) (hc i.rev) - refine ⟨c⁻¹ • standardBasis k n i.rev, ?_⟩ - rw [map_smul, hfb, Fin.rev_rev] - change c⁻¹ • (c • binaryBasis k n i) = _ - rw [inv_smul_smul₀ hc'] - rw [(binaryBasis k n).span_eq] at hr - exact top_le_iff.mp hr - have hinj : Function.Injective f := - (LinearMap.injective_iff_surjective_of_finrank_eq_finrank - (Subspace.dual_finrank_eq (K := k))).mpr hsurj - let f' : (costandard k n)ᘁ ⟶ costandard k n := fdrepHom k f (by - intro a x - rw [fdrep_dual_repr] - exact hf a x) - have : IsIso f' := fdrepHom_isIso_of_bijective k f' ⟨hinj,hsurj⟩ - exact ⟨asIso f'⟩ - - - -theorem costandard_tilting_of_choose_ne_zero (n : ℕ) - (hc : ∀ i : Fin (n + 1), (n.choose i : k) ≠ 0) : IsTilting k (costandard k n) := by - obtain ⟨e⟩ := costandard_self_dual_of_choose_ne_zero k n hc - exact ⟨costandard_rational k n, costandard_hasGoodFiltration k n, - (costandard_hasGoodFiltration k n).of_iso k e.symm⟩ - -end - -section -universe u -variable (k : Type u) [Field k] -variable (p : ℕ) [Fact p.Prime] [CharP k p] - -lemma choose_cast_ne_zero_of_lt_char {n i : ℕ} (hn : n < p) (hi : i ≤ n) : - (n.choose i : k) ≠ 0 := by - have hp := (Fact.out : p.Prime) - have hnf : (n.factorial : k) ≠ 0 := by - rw [Ne, CharP.cast_eq_zero_iff k p, hp.dvd_factorial] - exact not_le.mpr hn - intro h - have he := congrArg (fun a : ℕ => (a : k)) (Nat.choose_mul_factorial_mul_factorial hi) - simp only [Nat.cast_mul, h, zero_mul] at he - exact hnf he.symm - -lemma choose_prime_power_cast_eq_zero (m i : ℕ) (hi : 0 < i) (hi' : i < p ^ m) : - ((p ^ m).choose i : k) = 0 := by - have he : (Polynomial.X + 1 : Polynomial k) ^ p ^ m = Polynomial.X ^ p ^ m + 1 := by - simpa using add_pow_char_pow (Polynomial.X : Polynomial k) 1 p m - have h := congrArg (fun f : Polynomial k => f.coeff i) he - simpa [Polynomial.coeff_X_add_one_pow, Polynomial.coeff_one, ne_of_gt hi, ne_of_lt hi'] using h - - - -theorem choose_prime_power_sub_one_cast (m i : ℕ) (hi : i < p ^ m) : - ((p ^ m - 1).choose i : k) = (-1 : k) ^ i := by - have hq : 0 < p ^ m := pow_pos (Fact.out : p.Prime).pos m - induction i with - | zero => simp - | succ i ih => - have hi' : i < p ^ m := by omega - have hzero := choose_prime_power_cast_eq_zero k p m (i+1) (by omega) hi - have hpasc := congrArg (fun a : ℕ => (a : k)) - (Nat.choose_succ_succ' (p ^ m - 1) i) - rw [Nat.sub_add_cancel (by omega : 1 ≤ p ^ m), Nat.cast_add] at hpasc - rw [hzero, ih hi'] at hpasc - rw [pow_succ] - linear_combination -hpasc - -lemma choose_prime_power_sub_one_ne_zero (m : ℕ) (i : Fin (p ^ m - 1 + 1)) : - ((p ^ m - 1).choose i : k) ≠ 0 := by - rw [choose_prime_power_sub_one_cast k p m i (by - have hq : 0 < p ^ m := pow_pos (Fact.out : p.Prime).pos m - have := i.isLt - omega)] - exact pow_ne_zero _ (neg_ne_zero.mpr one_ne_zero) - -end - -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (p : ℕ) [Fact p.Prime] [CharP k p] - -theorem small_costandard_tilting (n : ℕ) (hn : n < p) : - IsTilting k (costandard k n) := - costandard_tilting_of_choose_ne_zero k n - (fun i => choose_cast_ne_zero_of_lt_char k p hn (by omega)) - - -theorem steinberg_tilting (m : ℕ) : IsTilting k (steinberg k p m) := - costandard_tilting_of_choose_ne_zero k (p ^ m - 1) - (choose_prime_power_sub_one_ne_zero k p m) - -theorem steinberg_self_dual (m : ℕ) : - Nonempty ((steinberg k p m)ᘁ ≅ steinberg k p m) := - costandard_self_dual_of_choose_ne_zero k (p ^ m - 1) - (choose_prime_power_sub_one_ne_zero k p m) - -end FiberFunctorProof -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.ExtensionSplitting + +namespace OAI + +/-! Standard-costandard maps, binomial coefficients and Steinberg self-duality. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section +open CategoryTheory CategoryTheory.MonoidalCategory +universe u +variable (k : Type u) [Field k] + +noncomputable def costandardHighest (n : ℕ) : + MvPolynomial.homogeneousSubmodule (Fin 2) k n := binaryBasis k n (Fin.last n) + +lemma costandardHighest_weight (n : ℕ) (a : kˣ) : + (costandard k n).ρ (diagonalTorus k a) (costandardHighest k n) = + integerCharacter k n a • costandardHighest k n := by + have h := costandard_basis_weight k n (Fin.last n) a + have hn : (2 * (n : ℤ) - n) = n := by ring + simpa [costandardHighest, hn] using h + +lemma costandardHighest_lower_orbit (n : ℕ) (t : k) : + (costandard k n).ρ (lowerUnipotent k t) (costandardHighest k n) = + ∑ i : Fin (n + 1), t ^ (i : ℕ) • + (((-1 : k) ^ (i : ℕ) * (n.choose i : k)) • binaryBasis k n i.rev) := by + apply Subtype.ext + change linearChange (dualMatrix k (lowerUnipotent k t)) + (binaryBasis k n (Fin.last n)).val = _ + rw [binaryBasis_apply] + simp only [Fin.val_last, Nat.sub_self, pow_zero, one_mul, map_pow] + have he : linearChange (dualMatrix k (lowerUnipotent k t)) (MvPolynomial.X 1) = + (-MvPolynomial.C t * MvPolynomial.X 0 + MvPolynomial.X 1 : MvPolynomial (Fin 2) k) := by + simp [linearChange_X, dualMatrix, lowerUnipotent, + Matrix.transpose_apply, Fin.sum_univ_two] + rw [he, add_pow] + rw [← Fin.sum_univ_eq_sum_range] + simp only [Submodule.coe_sum, Submodule.coe_smul_of_tower, binaryBasis_apply, + MvPolynomial.smul_eq_C_mul, Fin.val_rev, Nat.succ_sub_succ_eq_sub] + apply Finset.sum_congr rfl + intro i _ + have hi : n - (n - (i : ℕ)) = i := by omega + rw [hi] + have hneg : (-MvPolynomial.C t : MvPolynomial (Fin 2) k) = + MvPolynomial.C (-1 : k) * MvPolynomial.C t := by simp + rw [hneg] + simp only [mul_pow, map_mul, map_pow, map_neg, map_one, map_natCast] + ring + +variable [Infinite k] + + + +theorem exists_standard_costandard_map (n : ℕ) : + ∃ f : Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) →ₗ[k] + MvPolynomial.homogeneousSubmodule (Fin 2) k n, + (∀ a x, f (standardRepresentation k n a x) = (costandard k n).ρ a (f x)) ∧ + ∀ i : Fin (n + 1), f (standardBasis k n i) = + ((-1 : k) ^ (i : ℕ) * (n.choose i : k)) • binaryBasis k n i.rev := by + obtain ⟨f,hfv,hf⟩ := exists_standard_lift k (costandard k n).ρ (costandard_rational k n) + n (fun m v hm hv => costandard_weight_bound k n m hm v hv) + (costandardHighest k n) (costandardHighest_weight k n) + change Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) →ₗ[k] + MvPolynomial.homogeneousSubmodule (Fin 2) k n at f + refine ⟨f,hf,?_⟩ + intro i + apply sub_eq_zero.mp + apply function_sum_eq_zero (fun (j : Fin (n+1)) (t : k) => t ^ (j : ℕ)) + ((linearIndependent_powerFunctions k).comp Fin.val Fin.val_injective) Finset.univ + (fun j => f (standardBasis k n j) - + ((-1 : k) ^ (j : ℕ) * (n.choose j : k)) • binaryBasis k n j.rev) ?_ i + (Finset.mem_univ i) + intro t + have ht := hf (lowerUnipotent k t) (standardHighest k n) + rw [hfv, costandardHighest_lower_orbit, standardHighest_lower_orbit] at ht + change f (∑ j : Fin (n+1), t ^ (j : ℕ) • standardBasis k n j) = + ∑ j : Fin (n+1), t ^ (j : ℕ) • + (((-1 : k) ^ (j : ℕ) * (n.choose j : k)) • binaryBasis k n j.rev) at ht + simpa only [Finset.mem_univ, forall_const, Finset.sum_const_zero, map_sum, map_smul, + smul_sub, Finset.sum_sub_distrib, Finset.sum_ite_irrel, ite_true, sub_eq_zero] using ht + + +theorem costandard_self_dual_of_choose_ne_zero (n : ℕ) + (hc : ∀ i : Fin (n + 1), (n.choose i : k) ≠ 0) : + Nonempty ((costandard k n)ᘁ ≅ costandard k n) := by + obtain ⟨f,hf,hfb⟩ := exists_standard_costandard_map k n + have hsurj : Function.Surjective f := by + apply LinearMap.range_eq_top.mp + have hr : Submodule.span k (Set.range (binaryBasis k n)) ≤ LinearMap.range f := by + apply Submodule.span_le.mpr + rintro _ ⟨i,rfl⟩ + let c : k := (-1 : k) ^ (i.rev : ℕ) * (n.choose i.rev : k) + have hc' : c ≠ 0 := mul_ne_zero (pow_ne_zero _ (neg_ne_zero.mpr one_ne_zero)) (hc i.rev) + refine ⟨c⁻¹ • standardBasis k n i.rev, ?_⟩ + rw [map_smul, hfb, Fin.rev_rev] + change c⁻¹ • (c • binaryBasis k n i) = _ + rw [inv_smul_smul₀ hc'] + rw [(binaryBasis k n).span_eq] at hr + exact top_le_iff.mp hr + have hinj : Function.Injective f := + (LinearMap.injective_iff_surjective_of_finrank_eq_finrank + (Subspace.dual_finrank_eq (K := k))).mpr hsurj + let f' : (costandard k n)ᘁ ⟶ costandard k n := fdrepHom k f (by + intro a x + rw [fdrep_dual_repr] + exact hf a x) + have : IsIso f' := fdrepHom_isIso_of_bijective k f' ⟨hinj,hsurj⟩ + exact ⟨asIso f'⟩ + + + +theorem costandard_tilting_of_choose_ne_zero (n : ℕ) + (hc : ∀ i : Fin (n + 1), (n.choose i : k) ≠ 0) : IsTilting k (costandard k n) := by + obtain ⟨e⟩ := costandard_self_dual_of_choose_ne_zero k n hc + exact ⟨costandard_rational k n, costandard_hasGoodFiltration k n, + (costandard_hasGoodFiltration k n).of_iso k e.symm⟩ + +end + +section +universe u +variable (k : Type u) [Field k] +variable (p : ℕ) [Fact p.Prime] [CharP k p] + +lemma choose_cast_ne_zero_of_lt_char {n i : ℕ} (hn : n < p) (hi : i ≤ n) : + (n.choose i : k) ≠ 0 := by + have hp := (Fact.out : p.Prime) + have hnf : (n.factorial : k) ≠ 0 := by + rw [Ne, CharP.cast_eq_zero_iff k p, hp.dvd_factorial] + exact not_le.mpr hn + intro h + have he := congrArg (fun a : ℕ => (a : k)) (Nat.choose_mul_factorial_mul_factorial hi) + simp only [Nat.cast_mul, h, zero_mul] at he + exact hnf he.symm + +lemma choose_prime_power_cast_eq_zero (m i : ℕ) (hi : 0 < i) (hi' : i < p ^ m) : + ((p ^ m).choose i : k) = 0 := by + have he : (Polynomial.X + 1 : Polynomial k) ^ p ^ m = Polynomial.X ^ p ^ m + 1 := by + simpa using add_pow_char_pow (Polynomial.X : Polynomial k) 1 p m + have h := congrArg (fun f : Polynomial k => f.coeff i) he + simpa [Polynomial.coeff_X_add_one_pow, Polynomial.coeff_one, ne_of_gt hi, ne_of_lt hi'] using h + + + +theorem choose_prime_power_sub_one_cast (m i : ℕ) (hi : i < p ^ m) : + ((p ^ m - 1).choose i : k) = (-1 : k) ^ i := by + have hq : 0 < p ^ m := pow_pos (Fact.out : p.Prime).pos m + induction i with + | zero => simp + | succ i ih => + have hi' : i < p ^ m := by omega + have hzero := choose_prime_power_cast_eq_zero k p m (i+1) (by omega) hi + have hpasc := congrArg (fun a : ℕ => (a : k)) + (Nat.choose_succ_succ' (p ^ m - 1) i) + rw [Nat.sub_add_cancel (by omega : 1 ≤ p ^ m), Nat.cast_add] at hpasc + rw [hzero, ih hi'] at hpasc + rw [pow_succ] + linear_combination -hpasc + +lemma choose_prime_power_sub_one_ne_zero (m : ℕ) (i : Fin (p ^ m - 1 + 1)) : + ((p ^ m - 1).choose i : k) ≠ 0 := by + rw [choose_prime_power_sub_one_cast k p m i (by + have hq : 0 < p ^ m := pow_pos (Fact.out : p.Prime).pos m + have := i.isLt + omega)] + exact pow_ne_zero _ (neg_ne_zero.mpr one_ne_zero) + +end + +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (p : ℕ) [Fact p.Prime] [CharP k p] + +theorem small_costandard_tilting (n : ℕ) (hn : n < p) : + IsTilting k (costandard k n) := + costandard_tilting_of_choose_ne_zero k n + (fun i => choose_cast_ne_zero_of_lt_char k p hn (by omega)) + + +theorem steinberg_tilting (m : ℕ) : IsTilting k (steinberg k p m) := + costandard_tilting_of_choose_ne_zero k (p ^ m - 1) + (choose_prime_power_sub_one_ne_zero k p m) + +theorem steinberg_self_dual (m : ℕ) : + Nonempty ((steinberg k p m)ᘁ ≅ steinberg k p m) := + costandard_self_dual_of_choose_ne_zero k (p ^ m - 1) + (choose_prime_power_sub_one_ne_zero k p m) + +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/SteinbergRegular.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/SteinbergRegular.lean index 92a64340060ab9a9c837ebafdacffad0d0226272..ac3552bc0fa5fefb4166ff130291b2c2529f444c 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/SteinbergRegular.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/SteinbergRegular.lean @@ -1,146 +1,146 @@ -import OAI.RepresentationTheory.RestrictedTilting.Basic - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory -open scoped BigOperators -universe u v -variable (k : Type u) [Field k] - - -noncomputable def binaryEval (n : ℕ) (z : k) : - MvPolynomial.homogeneousSubmodule (Fin 2) k n →ₗ[k] k := - (MvPolynomial.aeval ![z,1]).toLinearMap.comp - (MvPolynomial.homogeneousSubmodule (Fin 2) k n).subtype - -lemma binaryEval_basis (n : ℕ) (z : k) (i : Fin (n+1)) : - binaryEval k n z (binaryBasis k n i) = z^(n-i.val) := by - simp [binaryEval, binaryBasis_apply] - - - -noncomputable def binaryHomogenize (n : ℕ) (P : Polynomial k) : - MvPolynomial.homogeneousSubmodule (Fin 2) k n := - ∑ i : Fin (n+1), P.coeff i.val • binaryBasis k n ⟨n-i.val, by omega⟩ - -lemma binaryEval_homogenize (n : ℕ) (P : Polynomial k) - (hP : P.natDegree ≤ n) (z : k) : - binaryEval k n z (binaryHomogenize k n P) = P.eval z := by - rw [binaryHomogenize, map_sum] - simp only [map_smul, binaryEval_basis, smul_eq_mul] - have hi (i : Fin (n+1)) : n-(n-i.val) = i.val := by omega - simp only [hi] - conv_rhs => rw [P.as_sum_range' (n+1) (by omega)] - simp only [Polynomial.eval_finsetSum, Polynomial.eval_monomial] - exact Fin.sum_univ_eq_sum_range (fun i => P.coeff i * z^i) (n+1) - -variable {E : Type v} [Fintype E] - -noncomputable def binarySubgroupEval (n : ℕ) (l : E → k) : - MvPolynomial.homogeneousSubmodule (Fin 2) k n →ₗ[k] (E → k) := - LinearMap.pi (fun a => binaryEval k n (l a)) - -lemma binarySubgroupEval_surjective (l : E → k) (hl : Function.Injective l) - [Nonempty E] : Function.Surjective (binarySubgroupEval k (Fintype.card E-1) l) := by - classical - intro f - let P := Lagrange.interpolate Finset.univ l f - have hp := Lagrange.degree_interpolate_lt (s := Finset.univ) (v := l) f hl.injOn - have hn : P.natDegree ≤ Fintype.card E-1 := by - by_cases h : P = 0 - · simp [h] - · have ht : P.natDegree < Fintype.card E := - (Polynomial.natDegree_lt_iff_degree_lt h).mpr (by simpa [P] using hp) - omega - refine ⟨binaryHomogenize k (Fintype.card E-1) P, ?_⟩ - funext a - change binaryEval k _ (l a) _ = _ - rw [binaryEval_homogenize k _ P hn] - exact Lagrange.eval_interpolate_at_node f hl.injOn (Finset.mem_univ a) - -noncomputable def binarySubgroupEquiv (l : E → k) (hl : Function.Injective l) - [Nonempty E] : - MvPolynomial.homogeneousSubmodule (Fin 2) k (Fintype.card E-1) ≃ₗ[k] (E → k) := - LinearEquiv.ofBijective (binarySubgroupEval k _ l) ⟨ - (LinearMap.injective_iff_surjective_of_finrank_eq_finrank (by - rw [binaryBasis_finrank, Module.finrank_pi] - exact Nat.sub_add_cancel Fintype.card_pos)).mpr (binarySubgroupEval_surjective k l hl), - binarySubgroupEval_surjective k l hl⟩ - -lemma binaryEval_unipotent (n : ℕ) (t z : k) - (v : MvPolynomial.homogeneousSubmodule (Fin 2) k n) : - binaryEval k n z ((costandard k n).ρ (unipotent k t) v) = - binaryEval k n (z-t) v := by - change MvPolynomial.aeval ![z,1] - (linearChange (dualMatrix k (unipotent k t)) v.val) = MvPolynomial.aeval ![z-t,1] v.val - have h : (MvPolynomial.aeval ![z,1]).comp (linearChange (dualMatrix k (unipotent k t))) = - (MvPolynomial.aeval ![z-t,1] : MvPolynomial (Fin 2) k →ₐ[k] k) := by - ext i - fin_cases i <;> - simp [linearChange_X, dualMatrix, unipotent, Matrix.transpose_apply, - Fin.sum_univ_two, sub_eq_add_neg, add_comm] - exact DFunLike.congr_fun h v.val - - -noncomputable def groupAlgebraCoefficients (G : Type v) [Fintype G] : - MonoidAlgebra k G ≃ₗ[k] (G → k) := - (MonoidAlgebra.coeffLinearEquiv k).trans (Finsupp.linearEquivFunOnFinite k k G) - -@[simp] lemma groupAlgebraCoefficients_apply (G : Type v) [Fintype G] - (x : MonoidAlgebra k G) (g : G) : groupAlgebraCoefficients k G x g = x.coeff g := rfl - - - -theorem steinberg_restriction_regular (p r : ℕ) [Fact p.Prime] [CharP k p] - (l : (Fin r → ZMod p) →+ k) (hl : Function.Injective l) : - Nonempty ((restrictElementary k p r l).obj (steinberg k p r) ≅ - FDRep.of (Representation.leftRegular k (Multiplicative (Fin r → ZMod p)))) := by - classical - let E := Multiplicative (Fin r → ZMod p) - let A := (restrictElementary k p r l).obj (steinberg k p r) - let B := FDRep.of (Representation.leftRegular k E) - have hc : Fintype.card E = p^r := by - simp [E, ZMod.card] - have hi : Function.Injective (fun a : E => l a.toAdd) := by - intro a b hab - exact congrArg Multiplicative.ofAdd (hl hab) - have hb := (binarySubgroupEquiv k (fun a : E => l a.toAdd) hi).bijective - change Function.Bijective (binarySubgroupEval k (Fintype.card E-1) - (fun a : E => l a.toAdd)) at hb - rw [hc] at hb - let e : A ≃ₗ[k] (E → k) := - LinearEquiv.ofBijective (binarySubgroupEval k (p^r-1) (fun a : E => l a.toAdd)) hb - let L : A ≃ₗ[k] B := e.trans (groupAlgebraCoefficients k E).symm - have hL (v : A) (b : E) : (L v).coeff b = binaryEval k (p^r-1) (l b.toAdd) v := by - change groupAlgebraCoefficients k E ((groupAlgebraCoefficients k E).symm (e v)) b = _ - rw [LinearEquiv.apply_symm_apply] - rfl - have heq (a : E) (v : A) : L (A.ρ a v) = B.ρ a (L v) := by - apply MonoidAlgebra.ext - ext b - rw [hL] - change binaryEval k (p^r-1) (l b.toAdd) - ((costandard k (p^r-1)).ρ (unipotent k (l a.toAdd)) v) = - ((Representation.leftRegular k E) a (L v)).coeff b - erw [binaryEval_unipotent k (p^r-1) (l a.toAdd) (l b.toAdd) v] - rw [Representation.coeff_ofMulAction, hL] - have hab : l (a⁻¹ • b).toAdd = l b.toAdd - l a.toAdd := by - change l (-a.toAdd + b.toAdd) = _ - simp [sub_eq_add_neg, add_comm] - rw [hab] - exact ⟨Action.mkIso L.toFGModuleCatIso (fun a => FGModuleCat.hom_ext (LinearMap.ext (heq a)))⟩ - - -def RegularSteinbergStatement : Prop := - ∀ (k : Type u) [Field k] [IsAlgClosed k] (p : ℕ) [Fact p.Prime] [CharP k p] - (r : ℕ), 1 ≤ r → ∀ (l : (Fin r → ZMod p) →+ k), Function.Injective l → - Nonempty ((restrictElementary k p r l).obj (steinberg k p r) ≅ - FDRep.of (Representation.leftRegular k (Multiplicative (Fin r → ZMod p)))) - -theorem regular_steinberg : RegularSteinbergStatement.{u} := by - intro k _ _ p _ _ r _ l hl - exact steinberg_restriction_regular k p r l hl -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.Basic + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory +open scoped BigOperators +universe u v +variable (k : Type u) [Field k] + + +noncomputable def binaryEval (n : ℕ) (z : k) : + MvPolynomial.homogeneousSubmodule (Fin 2) k n →ₗ[k] k := + (MvPolynomial.aeval ![z,1]).toLinearMap.comp + (MvPolynomial.homogeneousSubmodule (Fin 2) k n).subtype + +lemma binaryEval_basis (n : ℕ) (z : k) (i : Fin (n+1)) : + binaryEval k n z (binaryBasis k n i) = z^(n-i.val) := by + simp [binaryEval, binaryBasis_apply] + + + +noncomputable def binaryHomogenize (n : ℕ) (P : Polynomial k) : + MvPolynomial.homogeneousSubmodule (Fin 2) k n := + ∑ i : Fin (n+1), P.coeff i.val • binaryBasis k n ⟨n-i.val, by omega⟩ + +lemma binaryEval_homogenize (n : ℕ) (P : Polynomial k) + (hP : P.natDegree ≤ n) (z : k) : + binaryEval k n z (binaryHomogenize k n P) = P.eval z := by + rw [binaryHomogenize, map_sum] + simp only [map_smul, binaryEval_basis, smul_eq_mul] + have hi (i : Fin (n+1)) : n-(n-i.val) = i.val := by omega + simp only [hi] + conv_rhs => rw [P.as_sum_range' (n+1) (by omega)] + simp only [Polynomial.eval_finsetSum, Polynomial.eval_monomial] + exact Fin.sum_univ_eq_sum_range (fun i => P.coeff i * z^i) (n+1) + +variable {E : Type v} [Fintype E] + +noncomputable def binarySubgroupEval (n : ℕ) (l : E → k) : + MvPolynomial.homogeneousSubmodule (Fin 2) k n →ₗ[k] (E → k) := + LinearMap.pi (fun a => binaryEval k n (l a)) + +lemma binarySubgroupEval_surjective (l : E → k) (hl : Function.Injective l) + [Nonempty E] : Function.Surjective (binarySubgroupEval k (Fintype.card E-1) l) := by + classical + intro f + let P := Lagrange.interpolate Finset.univ l f + have hp := Lagrange.degree_interpolate_lt (s := Finset.univ) (v := l) f hl.injOn + have hn : P.natDegree ≤ Fintype.card E-1 := by + by_cases h : P = 0 + · simp [h] + · have ht : P.natDegree < Fintype.card E := + (Polynomial.natDegree_lt_iff_degree_lt h).mpr (by simpa [P] using hp) + omega + refine ⟨binaryHomogenize k (Fintype.card E-1) P, ?_⟩ + funext a + change binaryEval k _ (l a) _ = _ + rw [binaryEval_homogenize k _ P hn] + exact Lagrange.eval_interpolate_at_node f hl.injOn (Finset.mem_univ a) + +noncomputable def binarySubgroupEquiv (l : E → k) (hl : Function.Injective l) + [Nonempty E] : + MvPolynomial.homogeneousSubmodule (Fin 2) k (Fintype.card E-1) ≃ₗ[k] (E → k) := + LinearEquiv.ofBijective (binarySubgroupEval k _ l) ⟨ + (LinearMap.injective_iff_surjective_of_finrank_eq_finrank (by + rw [binaryBasis_finrank, Module.finrank_pi] + exact Nat.sub_add_cancel Fintype.card_pos)).mpr (binarySubgroupEval_surjective k l hl), + binarySubgroupEval_surjective k l hl⟩ + +lemma binaryEval_unipotent (n : ℕ) (t z : k) + (v : MvPolynomial.homogeneousSubmodule (Fin 2) k n) : + binaryEval k n z ((costandard k n).ρ (unipotent k t) v) = + binaryEval k n (z-t) v := by + change MvPolynomial.aeval ![z,1] + (linearChange (dualMatrix k (unipotent k t)) v.val) = MvPolynomial.aeval ![z-t,1] v.val + have h : (MvPolynomial.aeval ![z,1]).comp (linearChange (dualMatrix k (unipotent k t))) = + (MvPolynomial.aeval ![z-t,1] : MvPolynomial (Fin 2) k →ₐ[k] k) := by + ext i + fin_cases i <;> + simp [linearChange_X, dualMatrix, unipotent, Matrix.transpose_apply, + Fin.sum_univ_two, sub_eq_add_neg, add_comm] + exact DFunLike.congr_fun h v.val + + +noncomputable def groupAlgebraCoefficients (G : Type v) [Fintype G] : + MonoidAlgebra k G ≃ₗ[k] (G → k) := + (MonoidAlgebra.coeffLinearEquiv k).trans (Finsupp.linearEquivFunOnFinite k k G) + +@[simp] lemma groupAlgebraCoefficients_apply (G : Type v) [Fintype G] + (x : MonoidAlgebra k G) (g : G) : groupAlgebraCoefficients k G x g = x.coeff g := rfl + + + +theorem steinberg_restriction_regular (p r : ℕ) [Fact p.Prime] [CharP k p] + (l : (Fin r → ZMod p) →+ k) (hl : Function.Injective l) : + Nonempty ((restrictElementary k p r l).obj (steinberg k p r) ≅ + FDRep.of (Representation.leftRegular k (Multiplicative (Fin r → ZMod p)))) := by + classical + let E := Multiplicative (Fin r → ZMod p) + let A := (restrictElementary k p r l).obj (steinberg k p r) + let B := FDRep.of (Representation.leftRegular k E) + have hc : Fintype.card E = p^r := by + simp [E, ZMod.card] + have hi : Function.Injective (fun a : E => l a.toAdd) := by + intro a b hab + exact congrArg Multiplicative.ofAdd (hl hab) + have hb := (binarySubgroupEquiv k (fun a : E => l a.toAdd) hi).bijective + change Function.Bijective (binarySubgroupEval k (Fintype.card E-1) + (fun a : E => l a.toAdd)) at hb + rw [hc] at hb + let e : A ≃ₗ[k] (E → k) := + LinearEquiv.ofBijective (binarySubgroupEval k (p^r-1) (fun a : E => l a.toAdd)) hb + let L : A ≃ₗ[k] B := e.trans (groupAlgebraCoefficients k E).symm + have hL (v : A) (b : E) : (L v).coeff b = binaryEval k (p^r-1) (l b.toAdd) v := by + change groupAlgebraCoefficients k E ((groupAlgebraCoefficients k E).symm (e v)) b = _ + rw [LinearEquiv.apply_symm_apply] + rfl + have heq (a : E) (v : A) : L (A.ρ a v) = B.ρ a (L v) := by + apply MonoidAlgebra.ext + ext b + rw [hL] + change binaryEval k (p^r-1) (l b.toAdd) + ((costandard k (p^r-1)).ρ (unipotent k (l a.toAdd)) v) = + ((Representation.leftRegular k E) a (L v)).coeff b + erw [binaryEval_unipotent k (p^r-1) (l a.toAdd) (l b.toAdd) v] + rw [Representation.coeff_ofMulAction, hL] + have hab : l (a⁻¹ • b).toAdd = l b.toAdd - l a.toAdd := by + change l (-a.toAdd + b.toAdd) = _ + simp [sub_eq_add_neg, add_comm] + rw [hab] + exact ⟨Action.mkIso L.toFGModuleCatIso (fun a => FGModuleCat.hom_ext (LinearMap.ext (heq a)))⟩ + + +def RegularSteinbergStatement : Prop := + ∀ (k : Type u) [Field k] [IsAlgClosed k] (p : ℕ) [Fact p.Prime] [CharP k p] + (r : ℕ), 1 ≤ r → ∀ (l : (Fin r → ZMod p) →+ k), Function.Injective l → + Nonempty ((restrictElementary k p r l).obj (steinberg k p r) ≅ + FDRep.of (Representation.leftRegular k (Multiplicative (Fin r → ZMod p)))) + +theorem regular_steinberg : RegularSteinbergStatement.{u} := by + intro k _ _ p _ _ r _ l hl + exact steinberg_restriction_regular k p r l hl +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/SteinbergSpan.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/SteinbergSpan.lean index 296e0dbe5e5ea9975649b87aec40bf7f870d981e..45efff4789c51202aff1c74afe5be719e389ad31 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/SteinbergSpan.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/SteinbergSpan.lean @@ -1,79 +1,79 @@ -import OAI.RepresentationTheory.RestrictedTilting.StableRestriction -import OAI.RepresentationTheory.RestrictedTilting.RepProducts - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory -universe u -variable (k : Type u) [Field k] - - -noncomputable def steinbergSpan (p r : ℕ) (A B : FDRep k (SL2 k)) : - Submodule k (A ⟶ B) := - Submodule.span k {f | ∃ (X : FDRep k (SL2 k)), IsTilting k X ∧ - ∃ (a : A ⟶ steinberg k p r ⊗ X) (b : steinberg k p r ⊗ X ⟶ B), f = a ≫ b} - -variable (p r : ℕ) - -lemma steinbergSpan.precomp {A B C : FDRep k (SL2 k)} (a : A ⟶ B) (f : B ⟶ C) - (hf : f ∈ steinbergSpan k p r B C) : a ≫ f ∈ steinbergSpan k p r A C := by - induction hf using Submodule.span_induction with - | mem f hf => - obtain ⟨X,hX,b,c,rfl⟩ := hf - exact Submodule.subset_span ⟨X,hX,a ≫ b,c,by simp⟩ - | zero => simp - | add f g hf hg ihf ihg => simpa only [Preadditive.comp_add] using - (steinbergSpan k p r A C).add_mem ihf ihg - | smul c f hf ih => simpa only [Linear.comp_smul] using - (steinbergSpan k p r A C).smul_mem c ih - -lemma steinbergSpan.postcomp {A B C : FDRep k (SL2 k)} (f : A ⟶ B) (a : B ⟶ C) - (hf : f ∈ steinbergSpan k p r A B) : f ≫ a ∈ steinbergSpan k p r A C := by - induction hf using Submodule.span_induction with - | mem f hf => - obtain ⟨X,hX,b,c,rfl⟩ := hf - exact Submodule.subset_span ⟨X,hX,b,c ≫ a,by simp⟩ - | zero => simp - | add f g hf hg ihf ihg => simpa only [Preadditive.add_comp] using - (steinbergSpan k p r A C).add_mem ihf ihg - | smul c f hf ih => simpa only [Linear.smul_comp] using - (steinbergSpan k p r A C).smul_mem c ih - -lemma steinbergSpan_of_high_left (X : FDRep k (SL2 k)) (hX : IsTilting k X) - {B : FDRep k (SL2 k)} (f : steinberg k p r ⊗ X ⟶ B) : - f ∈ steinbergSpan k p r _ B := - Submodule.subset_span ⟨X,hX,𝟙 _,f, by simp⟩ - -lemma steinbergSpan_of_high_right (X : FDRep k (SL2 k)) (hX : IsTilting k X) - {A : FDRep k (SL2 k)} (f : A ⟶ steinberg k p r ⊗ X) : - f ∈ steinbergSpan k p r A _ := - Submodule.subset_span ⟨X,hX,f,𝟙 _, by simp⟩ - -lemma steinbergSpan_to_ideal (A B : Tilting k) (f : A.obj ⟶ B.obj) - (hf : f ∈ steinbergSpan k p r A.obj B.obj) : - ObjectProperty.homMk f ∈ steinbergIdeal k p r A B := by - induction hf using Submodule.span_induction with - | mem f hf => - obtain ⟨X,hX,a,b,hf⟩ := hf - exact Submodule.subset_span ⟨⟨X,hX⟩,a,b,hf⟩ - | zero => exact (steinbergIdeal k p r A B).zero_mem - | add f g hf hg ihf ihg => exact (steinbergIdeal k p r A B).add_mem ihf ihg - | smul c f hf ih => exact (steinbergIdeal k p r A B).smul_mem c ih - -end FiberFunctorProof - -namespace FiberFunctorProof.FactorsThroughProjective -open CategoryTheory -variable {C : Type*} [Category* C] {A B D : C} -lemma precomp (a : A ⟶ B) {f : B ⟶ D} (hf : FactorsThroughProjective f) : - FactorsThroughProjective (a ≫ f) := by - obtain ⟨P,hP,b,c,rfl⟩ := hf - exact ⟨P,hP,a ≫ b,c,by simp⟩ -lemma postcomp {f : A ⟶ B} (hf : FactorsThroughProjective f) (a : B ⟶ D) : - FactorsThroughProjective (f ≫ a) := by - obtain ⟨P,hP,b,c,rfl⟩ := hf - exact ⟨P,hP,b,c ≫ a,by simp⟩ -end FiberFunctorProof.FactorsThroughProjective - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.StableRestriction +import OAI.RepresentationTheory.RestrictedTilting.RepProducts + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory +universe u +variable (k : Type u) [Field k] + + +noncomputable def steinbergSpan (p r : ℕ) (A B : FDRep k (SL2 k)) : + Submodule k (A ⟶ B) := + Submodule.span k {f | ∃ (X : FDRep k (SL2 k)), IsTilting k X ∧ + ∃ (a : A ⟶ steinberg k p r ⊗ X) (b : steinberg k p r ⊗ X ⟶ B), f = a ≫ b} + +variable (p r : ℕ) + +lemma steinbergSpan.precomp {A B C : FDRep k (SL2 k)} (a : A ⟶ B) (f : B ⟶ C) + (hf : f ∈ steinbergSpan k p r B C) : a ≫ f ∈ steinbergSpan k p r A C := by + induction hf using Submodule.span_induction with + | mem f hf => + obtain ⟨X,hX,b,c,rfl⟩ := hf + exact Submodule.subset_span ⟨X,hX,a ≫ b,c,by simp⟩ + | zero => simp + | add f g hf hg ihf ihg => simpa only [Preadditive.comp_add] using + (steinbergSpan k p r A C).add_mem ihf ihg + | smul c f hf ih => simpa only [Linear.comp_smul] using + (steinbergSpan k p r A C).smul_mem c ih + +lemma steinbergSpan.postcomp {A B C : FDRep k (SL2 k)} (f : A ⟶ B) (a : B ⟶ C) + (hf : f ∈ steinbergSpan k p r A B) : f ≫ a ∈ steinbergSpan k p r A C := by + induction hf using Submodule.span_induction with + | mem f hf => + obtain ⟨X,hX,b,c,rfl⟩ := hf + exact Submodule.subset_span ⟨X,hX,b,c ≫ a,by simp⟩ + | zero => simp + | add f g hf hg ihf ihg => simpa only [Preadditive.add_comp] using + (steinbergSpan k p r A C).add_mem ihf ihg + | smul c f hf ih => simpa only [Linear.smul_comp] using + (steinbergSpan k p r A C).smul_mem c ih + +lemma steinbergSpan_of_high_left (X : FDRep k (SL2 k)) (hX : IsTilting k X) + {B : FDRep k (SL2 k)} (f : steinberg k p r ⊗ X ⟶ B) : + f ∈ steinbergSpan k p r _ B := + Submodule.subset_span ⟨X,hX,𝟙 _,f, by simp⟩ + +lemma steinbergSpan_of_high_right (X : FDRep k (SL2 k)) (hX : IsTilting k X) + {A : FDRep k (SL2 k)} (f : A ⟶ steinberg k p r ⊗ X) : + f ∈ steinbergSpan k p r A _ := + Submodule.subset_span ⟨X,hX,f,𝟙 _, by simp⟩ + +lemma steinbergSpan_to_ideal (A B : Tilting k) (f : A.obj ⟶ B.obj) + (hf : f ∈ steinbergSpan k p r A.obj B.obj) : + ObjectProperty.homMk f ∈ steinbergIdeal k p r A B := by + induction hf using Submodule.span_induction with + | mem f hf => + obtain ⟨X,hX,a,b,hf⟩ := hf + exact Submodule.subset_span ⟨⟨X,hX⟩,a,b,hf⟩ + | zero => exact (steinbergIdeal k p r A B).zero_mem + | add f g hf hg ihf ihg => exact (steinbergIdeal k p r A B).add_mem ihf ihg + | smul c f hf ih => exact (steinbergIdeal k p r A B).smul_mem c ih + +end FiberFunctorProof + +namespace FiberFunctorProof.FactorsThroughProjective +open CategoryTheory +variable {C : Type*} [Category* C] {A B D : C} +lemma precomp (a : A ⟶ B) {f : B ⟶ D} (hf : FactorsThroughProjective f) : + FactorsThroughProjective (a ≫ f) := by + obtain ⟨P,hP,b,c,rfl⟩ := hf + exact ⟨P,hP,a ≫ b,c,by simp⟩ +lemma postcomp {f : A ⟶ B} (hf : FactorsThroughProjective f) (a : B ⟶ D) : + FactorsThroughProjective (f ≫ a) := by + obtain ⟨P,hP,b,c,rfl⟩ := hf + exact ⟨P,hP,b,c ≫ a,by simp⟩ +end FiberFunctorProof.FactorsThroughProjective + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorAssociatedAction.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorAssociatedAction.lean index de5e31fc8d6c387586936a01cc06c332cf9074f1..b3f58056396d38a61ec8ec569254be5beb12fb13 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorAssociatedAction.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorAssociatedAction.lean @@ -1,65 +1,65 @@ -import OAI.RepresentationTheory.RestrictedTilting.TensorNumerator -import OAI.RepresentationTheory.RestrictedTilting.TensorPlaneTilting -import OAI.RepresentationTheory.RestrictedTilting.FormalAssociatedAction - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory -open scoped TensorProduct BigOperators Pointwise -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (β ι : Type u) [Fintype β] [DecidableEq β] [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) -variable (P : Matrix ι ι (Polynomial k)) -variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) -variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) -variable (τ : Representation k (SL2 k) (β → k)) -local notation "N" => associatedSectionsSubmodule k ι ρ -local notation "A" => MvPolynomial (Fin 2) k -local notation "I" => MvPolynomial.idealOfVars (Fin 2) k -local notation "σ" => matrixTensorRepresentation τ (associatedSectionsRepresentation k ι ρ) -local notation "hσ" => matrixTensor_planeCompatible k τ (associatedSectionsRepresentation k ι ρ) - (associatedSections_planeCompatible k ι ρ) -local notation "W" => tensorAssociatedNumerator k β ι ρ P hP d hd -variable [Module.Finite k ((β → associatedSectionsSubmodule k ι ρ) ⧸ - planeJetRelation (M := β → associatedSectionsSubmodule k ι ρ) k 1)] -local notation "T" => planeJetFD k σ hσ 1 - -noncomputable def formalTensorAssociatedCoordinates - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) (v : T) : - β × ι → planeCompletion k := completedCoordinates I W (formalPlaneSection k σ hσ s hs v) - -lemma formalTensorAssociatedCoordinates_unipotent - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (t : k) (v : T) (b : β) (i : ι) : - (PowerSeries.X : PowerSeries k)^(2*d) * formalLineMap k - (formalTensorAssociatedCoordinates k β ι ρ P hP d hd τ s hs ((planeJetFD k σ hσ 1).ρ (unipotent k t) v) (b,i)) = - ∑ c : β, ∑ j : ι, algebraMap k (PowerSeries k) (LinearMap.toMatrix' (τ (unipotent k t)) b c) * - clearedPolynomial (P i j) (algebraMap k (PowerSeries k) t) - ((PowerSeries.X : PowerSeries k)^2) d * formalLineMap k - (formalTensorAssociatedCoordinates k β ι ρ P hP d hd τ s hs v (c,j)) := by - let F : (β → N) →ₗ[A] A := (MvPolynomial.X 0 : A)^(2*d) • (LinearMap.proj (b,i)).comp W - let G : (β → N) →ₗ[A] A := ∑ c : β, ∑ j : ι, - (MvPolynomial.C (LinearMap.toMatrix' (τ (unipotent k t)) b c) * - clearedPolynomial (P i j) (MvPolynomial.C t) ((MvPolynomial.X 0 : A)^2) d) • - (LinearMap.proj (c,j)).comp W - have he : ∀ f : β → N, linePolynomial k (F (σ (unipotent k t) f)) = linePolynomial k (G f) := by - intro f - simpa only [F,G,LinearMap.smul_apply,LinearMap.sum_apply,LinearMap.comp_apply, - LinearMap.proj_apply,smul_eq_mul,map_mul,map_pow,map_sum, - show linePolynomial k (MvPolynomial.X 0) = Polynomial.X from by simp [linePolynomial], - show ∀ c : k, linePolynomial k (MvPolynomial.C c) = Polynomial.C c from by intro c; simp [linePolynomial], - linePolynomial_cleared] using tensorAssociatedNumerator_line_unipotent k β ι ρ P hP d hd τ t f b i - have h := formalPlaneSection_line_action k σ hσ s hs (unipotent k t) F G he v - simp only [F,G,completion_map_smul, LinearMap.sum_apply, completion_self_smul, map_mul, map_sum, - map_pow, formalLineMap_X, formalLineMap_cleared] at h - have hc (c : k) : formalLineMap k (algebraMap A (planeCompletion k) (MvPolynomial.C c)) = - algebraMap k (PowerSeries k) c := by - rw [MvPolynomial.C_eq_algebraMap, ← IsScalarTower.algebraMap_apply, AlgHom.commutes] - simpa only [formalTensorAssociatedCoordinates, completedCoordinates_apply, hc] using h -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.TensorNumerator +import OAI.RepresentationTheory.RestrictedTilting.TensorPlaneTilting +import OAI.RepresentationTheory.RestrictedTilting.FormalAssociatedAction + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory +open scoped TensorProduct BigOperators Pointwise +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (β ι : Type u) [Fintype β] [DecidableEq β] [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) +variable (P : Matrix ι ι (Polynomial k)) +variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) +variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) +variable (τ : Representation k (SL2 k) (β → k)) +local notation "N" => associatedSectionsSubmodule k ι ρ +local notation "A" => MvPolynomial (Fin 2) k +local notation "I" => MvPolynomial.idealOfVars (Fin 2) k +local notation "σ" => matrixTensorRepresentation τ (associatedSectionsRepresentation k ι ρ) +local notation "hσ" => matrixTensor_planeCompatible k τ (associatedSectionsRepresentation k ι ρ) + (associatedSections_planeCompatible k ι ρ) +local notation "W" => tensorAssociatedNumerator k β ι ρ P hP d hd +variable [Module.Finite k ((β → associatedSectionsSubmodule k ι ρ) ⧸ + planeJetRelation (M := β → associatedSectionsSubmodule k ι ρ) k 1)] +local notation "T" => planeJetFD k σ hσ 1 + +noncomputable def formalTensorAssociatedCoordinates + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) (v : T) : + β × ι → planeCompletion k := completedCoordinates I W (formalPlaneSection k σ hσ s hs v) + +lemma formalTensorAssociatedCoordinates_unipotent + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (t : k) (v : T) (b : β) (i : ι) : + (PowerSeries.X : PowerSeries k)^(2*d) * formalLineMap k + (formalTensorAssociatedCoordinates k β ι ρ P hP d hd τ s hs ((planeJetFD k σ hσ 1).ρ (unipotent k t) v) (b,i)) = + ∑ c : β, ∑ j : ι, algebraMap k (PowerSeries k) (LinearMap.toMatrix' (τ (unipotent k t)) b c) * + clearedPolynomial (P i j) (algebraMap k (PowerSeries k) t) + ((PowerSeries.X : PowerSeries k)^2) d * formalLineMap k + (formalTensorAssociatedCoordinates k β ι ρ P hP d hd τ s hs v (c,j)) := by + let F : (β → N) →ₗ[A] A := (MvPolynomial.X 0 : A)^(2*d) • (LinearMap.proj (b,i)).comp W + let G : (β → N) →ₗ[A] A := ∑ c : β, ∑ j : ι, + (MvPolynomial.C (LinearMap.toMatrix' (τ (unipotent k t)) b c) * + clearedPolynomial (P i j) (MvPolynomial.C t) ((MvPolynomial.X 0 : A)^2) d) • + (LinearMap.proj (c,j)).comp W + have he : ∀ f : β → N, linePolynomial k (F (σ (unipotent k t) f)) = linePolynomial k (G f) := by + intro f + simpa only [F,G,LinearMap.smul_apply,LinearMap.sum_apply,LinearMap.comp_apply, + LinearMap.proj_apply,smul_eq_mul,map_mul,map_pow,map_sum, + show linePolynomial k (MvPolynomial.X 0) = Polynomial.X from by simp [linePolynomial], + show ∀ c : k, linePolynomial k (MvPolynomial.C c) = Polynomial.C c from by intro c; simp [linePolynomial], + linePolynomial_cleared] using tensorAssociatedNumerator_line_unipotent k β ι ρ P hP d hd τ t f b i + have h := formalPlaneSection_line_action k σ hσ s hs (unipotent k t) F G he v + simp only [F,G,completion_map_smul, LinearMap.sum_apply, completion_self_smul, map_mul, map_sum, + map_pow, formalLineMap_X, formalLineMap_cleared] at h + have hc (c : k) : formalLineMap k (algebraMap A (planeCompletion k) (MvPolynomial.C c)) = + algebraMap k (PowerSeries k) c := by + rw [MvPolynomial.C_eq_algebraMap, ← IsScalarTower.algebraMap_apply, AlgHom.commutes] + simpa only [formalTensorAssociatedCoordinates, completedCoordinates_apply, hc] using h +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorAssociatedIso.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorAssociatedIso.lean index 2b1cfe0710c8fff5eb068cb9030b472584e1f2d5..ced9339f05257e8ce15ea6ea8738a9f0d4450bff 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorAssociatedIso.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorAssociatedIso.lean @@ -1,94 +1,94 @@ -import OAI.RepresentationTheory.RestrictedTilting.TensorAssociatedAction -import OAI.RepresentationTheory.RestrictedTilting.FormalAssociatedIso - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory Matrix -open scoped TensorProduct BigOperators Pointwise Kronecker -universe u -variable (k : Type u) [Field k] [Infinite k] -attribute [local instance 1100] HahnSeries.instAlgebra -variable (β ι : Type u) [Fintype β] [DecidableEq β] [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) -variable (P : Matrix ι ι (Polynomial k)) -variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) -variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) -variable (τ : Representation k (SL2 k) (β → k)) -local notation "N" => associatedSectionsSubmodule k ι ρ -local notation "A" => MvPolynomial (Fin 2) k -local notation "I" => MvPolynomial.idealOfVars (Fin 2) k -local notation "H" => planeCompletion k -local notation "K" => LaurentSeries k -local notation "σ" => matrixTensorRepresentation τ (associatedSectionsRepresentation k ι ρ) -local notation "hσ" => matrixTensor_planeCompatible k τ (associatedSectionsRepresentation k ι ρ) - (associatedSections_planeCompatible k ι ρ) -local notation "W" => tensorAssociatedNumerator k β ι ρ P hP d hd -local notation "Z" => tensorAssociatedDenominator k β ι ρ P hP d hd -local notation "hx" => pi_regular_x k (β := β) (And.left (associatedSections_regular k ι ρ P hP)) -local notation "hy" => pi_regular_y k (β := β) (And.right (associatedSections_regular k ι ρ P hP)) -variable [Module.Finite k ((β → associatedSectionsSubmodule k ι ρ) ⧸ - planeJetRelation (M := β → associatedSectionsSubmodule k ι ρ) k 1)] -local notation "T" => planeJetFD k σ hσ 1 - -noncomputable def tensorAssociatedFieldTrivialization - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) : (K ⊗[k] T) ≃ₗ[K] (β × ι → K) := by - letI : Algebra H K := (formalLineFieldMap k).toRingHom.toAlgebra - exact fieldCoordinateTrivialization (formalPlaneTrivialization k σ hσ s hs0 hs hx hy) - (completedCoordinates I W) (completedDenominator I Z) - (algebraMap A H ((MvPolynomial.X 0)^ (d+d))) - (completedCoordinates_denominator I W Z _ (tensorAssociatedNumerator_denominator k β ι ρ P hP d hd)) - (completedDenominator_coordinates I W Z _ (tensorAssociatedDenominator_numerator k β ι ρ P hP d hd)) - (by - change formalLineFieldMap k (algebraMap A H ((MvPolynomial.X 0)^(d+d))) ≠ 0 - rw [map_pow, map_pow] - exact pow_ne_zero _ (formalLineFieldMap_X_ne_zero k)) - -lemma tensorAssociatedFieldTrivialization_one - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (v : T) (i : β × ι) : - tensorAssociatedFieldTrivialization k β ι ρ P hP d hd τ s hs0 hs (1 ⊗ₜ[k] v) i = - HahnSeries.ofPowerSeries ℤ k - (formalLineMap k (formalTensorAssociatedCoordinates k β ι ρ P hP d hd τ s hs v i)) := by - let : Algebra H K := (formalLineFieldMap k).toRingHom.toAlgebra - dsimp only [tensorAssociatedFieldTrivialization] - rw [fieldCoordinateTrivialization_one, formalPlaneTrivialization_one_tmul] - rfl - -lemma tensorAssociatedFieldTrivialization_unipotent_one - (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) - (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) - (t : k) (v : T) : - tensorAssociatedFieldTrivialization k β ι ρ P hP d hd τ s hs0 hs - (1 ⊗ₜ[k] ((planeJetFD k σ hσ 1).ρ (unipotent k t) v)) = - ( (LinearMap.toMatrix' (τ (unipotent k t))).map (algebraMap k K) ⊗ₖ - polynomialMatrixEval P (algebraMap k K t / (formalLineParameter k)^2)) *ᵥ - tensorAssociatedFieldTrivialization k β ι ρ P hP d hd τ s hs0 hs (1 ⊗ₜ[k] v) := by - apply funext - rintro ⟨b,i⟩ - have he := congrArg (HahnSeries.ofPowerSeriesAlg ℤ k) - (formalTensorAssociatedCoordinates_unipotent k β ι ρ P hP d hd τ s hs t v b i) - simp only [map_mul, map_pow, map_sum] at he - have hc (j : ι) : (HahnSeries.ofPowerSeriesAlg ℤ k) - (clearedPolynomial (P i j) (algebraMap k (PowerSeries k) t) - ((PowerSeries.X : PowerSeries k)^2) d) = - (formalLineParameter k)^(2*d) * - Polynomial.aeval (algebraMap k K t / (formalLineParameter k)^2) (P i j) := by - have hc := clearedPolynomial_eval (HahnSeries.ofPowerSeriesAlg ℤ k) (P i j) - (algebraMap k (PowerSeries k) t) ((PowerSeries.X : PowerSeries k)^2) d (hd i j) - (by - rw [map_pow] - exact pow_ne_zero 2 (formalLineParameter_ne_zero k)) - simpa only [map_pow, AlgHom.commutes, ofPowerSeriesAlg_apply_eq, formalLineParameter, ← pow_mul, div_eq_mul_inv] using hc - simp only [hc, AlgHom.commutes] at he - simp only [mul_left_comm (algebraMap k K _) ((formalLineParameter k)^(2*d)), - mul_assoc, ← Finset.mul_sum] at he - apply mul_left_cancel₀ (pow_ne_zero (2*d) (formalLineParameter_ne_zero k)) - simpa only [tensorAssociatedFieldTrivialization_one, Matrix.mulVec, dotProduct, polynomialMatrixEval, - formalLineParameter, ofPowerSeriesAlg_apply_eq, Fintype.sum_prod_type, - Matrix.kronecker_apply, Matrix.map_apply, mul_assoc, ← Finset.mul_sum] using he -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.TensorAssociatedAction +import OAI.RepresentationTheory.RestrictedTilting.FormalAssociatedIso + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory Matrix +open scoped TensorProduct BigOperators Pointwise Kronecker +universe u +variable (k : Type u) [Field k] [Infinite k] +attribute [local instance 1100] HahnSeries.instAlgebra +variable (β ι : Type u) [Fintype β] [DecidableEq β] [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) +variable (P : Matrix ι ι (Polynomial k)) +variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) +variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) +variable (τ : Representation k (SL2 k) (β → k)) +local notation "N" => associatedSectionsSubmodule k ι ρ +local notation "A" => MvPolynomial (Fin 2) k +local notation "I" => MvPolynomial.idealOfVars (Fin 2) k +local notation "H" => planeCompletion k +local notation "K" => LaurentSeries k +local notation "σ" => matrixTensorRepresentation τ (associatedSectionsRepresentation k ι ρ) +local notation "hσ" => matrixTensor_planeCompatible k τ (associatedSectionsRepresentation k ι ρ) + (associatedSections_planeCompatible k ι ρ) +local notation "W" => tensorAssociatedNumerator k β ι ρ P hP d hd +local notation "Z" => tensorAssociatedDenominator k β ι ρ P hP d hd +local notation "hx" => pi_regular_x k (β := β) (And.left (associatedSections_regular k ι ρ P hP)) +local notation "hy" => pi_regular_y k (β := β) (And.right (associatedSections_regular k ι ρ P hP)) +variable [Module.Finite k ((β → associatedSectionsSubmodule k ι ρ) ⧸ + planeJetRelation (M := β → associatedSectionsSubmodule k ι ρ) k 1)] +local notation "T" => planeJetFD k σ hσ 1 + +noncomputable def tensorAssociatedFieldTrivialization + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) : (K ⊗[k] T) ≃ₗ[K] (β × ι → K) := by + letI : Algebra H K := (formalLineFieldMap k).toRingHom.toAlgebra + exact fieldCoordinateTrivialization (formalPlaneTrivialization k σ hσ s hs0 hs hx hy) + (completedCoordinates I W) (completedDenominator I Z) + (algebraMap A H ((MvPolynomial.X 0)^ (d+d))) + (completedCoordinates_denominator I W Z _ (tensorAssociatedNumerator_denominator k β ι ρ P hP d hd)) + (completedDenominator_coordinates I W Z _ (tensorAssociatedDenominator_numerator k β ι ρ P hP d hd)) + (by + change formalLineFieldMap k (algebraMap A H ((MvPolynomial.X 0)^(d+d))) ≠ 0 + rw [map_pow, map_pow] + exact pow_ne_zero _ (formalLineFieldMap_X_ne_zero k)) + +lemma tensorAssociatedFieldTrivialization_one + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (v : T) (i : β × ι) : + tensorAssociatedFieldTrivialization k β ι ρ P hP d hd τ s hs0 hs (1 ⊗ₜ[k] v) i = + HahnSeries.ofPowerSeries ℤ k + (formalLineMap k (formalTensorAssociatedCoordinates k β ι ρ P hP d hd τ s hs v i)) := by + let : Algebra H K := (formalLineFieldMap k).toRingHom.toAlgebra + dsimp only [tensorAssociatedFieldTrivialization] + rw [fieldCoordinateTrivialization_one, formalPlaneTrivialization_one_tmul] + rfl + +lemma tensorAssociatedFieldTrivialization_unipotent_one + (s : (j : ℕ) → T ⟶ planeJetFD k σ hσ (j+1)) (hs0 : s 0 = 𝟙 _) + (hs : ∀ j, s (j+1) ≫ planeJetTransitionHom k σ hσ (j+1) = s j) + (t : k) (v : T) : + tensorAssociatedFieldTrivialization k β ι ρ P hP d hd τ s hs0 hs + (1 ⊗ₜ[k] ((planeJetFD k σ hσ 1).ρ (unipotent k t) v)) = + ( (LinearMap.toMatrix' (τ (unipotent k t))).map (algebraMap k K) ⊗ₖ + polynomialMatrixEval P (algebraMap k K t / (formalLineParameter k)^2)) *ᵥ + tensorAssociatedFieldTrivialization k β ι ρ P hP d hd τ s hs0 hs (1 ⊗ₜ[k] v) := by + apply funext + rintro ⟨b,i⟩ + have he := congrArg (HahnSeries.ofPowerSeriesAlg ℤ k) + (formalTensorAssociatedCoordinates_unipotent k β ι ρ P hP d hd τ s hs t v b i) + simp only [map_mul, map_pow, map_sum] at he + have hc (j : ι) : (HahnSeries.ofPowerSeriesAlg ℤ k) + (clearedPolynomial (P i j) (algebraMap k (PowerSeries k) t) + ((PowerSeries.X : PowerSeries k)^2) d) = + (formalLineParameter k)^(2*d) * + Polynomial.aeval (algebraMap k K t / (formalLineParameter k)^2) (P i j) := by + have hc := clearedPolynomial_eval (HahnSeries.ofPowerSeriesAlg ℤ k) (P i j) + (algebraMap k (PowerSeries k) t) ((PowerSeries.X : PowerSeries k)^2) d (hd i j) + (by + rw [map_pow] + exact pow_ne_zero 2 (formalLineParameter_ne_zero k)) + simpa only [map_pow, AlgHom.commutes, ofPowerSeriesAlg_apply_eq, formalLineParameter, ← pow_mul, div_eq_mul_inv] using hc + simp only [hc, AlgHom.commutes] at he + simp only [mul_left_comm (algebraMap k K _) ((formalLineParameter k)^(2*d)), + mul_assoc, ← Finset.mul_sum] at he + apply mul_left_cancel₀ (pow_ne_zero (2*d) (formalLineParameter_ne_zero k)) + simpa only [tensorAssociatedFieldTrivialization_one, Matrix.mulVec, dotProduct, polynomialMatrixEval, + formalLineParameter, ofPowerSeriesAlg_apply_eq, Fintype.sum_prod_type, + Matrix.kronecker_apply, Matrix.map_apply, mul_assoc, ← Finset.mul_sum] using he +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorCoordinates.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorCoordinates.lean index 7f0e29595528a8aa8e03d1efd818a58457d0fe27..a1f42fe457d359aee8bacb1eb036e0c292dc390e 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorCoordinates.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorCoordinates.lean @@ -1,56 +1,56 @@ -import OAI.RepresentationTheory.RestrictedTilting.CoordinateTensor - -namespace OAI - -namespace FiberFunctorProof -open Matrix -open scoped TensorProduct BigOperators Kronecker -universe u v -variable (k : Type u) [Field k] -variable {β ι : Type u} [Fintype β] [DecidableEq β] [Fintype ι] [DecidableEq ι] - -noncomputable def uncurryLinearEquiv : (β → ι → k) ≃ₗ[k] (β × ι → k) where - toFun v bi := v bi.1 bi.2 - invFun v b i := v (b,i) - left_inv _ := rfl - right_inv _ := rfl - map_add' _ _ := rfl - map_smul' _ _ := rfl - -variable {V W : Type u} [AddCommGroup V] [Module k V] [AddCommGroup W] [Module k W] -noncomputable def tensorCoordinates (e : V ≃ₗ[k] (β → k)) (f : W ≃ₗ[k] (ι → k)) : - (V ⊗[k] W) ≃ₗ[k] (β × ι → k) := - (TensorProduct.congr e f).trans ((coordinateTensorEquiv k).trans (uncurryLinearEquiv k)) - -omit [Fintype ι] [DecidableEq ι] in -lemma tensorCoordinates_tmul (e : V ≃ₗ[k] (β → k)) (f : W ≃ₗ[k] (ι → k)) (v : V) (w : W) : - tensorCoordinates k e f (v ⊗ₜ[k] w) = fun bi => e v bi.1 * f w bi.2 := by - simp only [tensorCoordinates, LinearEquiv.trans_apply, TensorProduct.congr_tmul, - coordinateTensorEquiv_tmul] - rfl - -variable {G : Type v} [Monoid G] -lemma tensorCoordinates_intertwines (σ : Representation k G V) (ρ : Representation k G W) - (e : V ≃ₗ[k] (β → k)) (f : W ≃ₗ[k] (ι → k)) (g : G) (v : V ⊗[k] W) : - tensorCoordinates k e f ((σ.tprod ρ) g v) = - (LinearMap.toMatrix' (coordinateRepresentation k σ e g) ⊗ₖ - LinearMap.toMatrix' (coordinateRepresentation k ρ f g)) *ᵥ tensorCoordinates k e f v := by - induction v using TensorProduct.inductionOn with - | add v w hv hw => simp only [map_add, Matrix.mulVec_add, hv, hw] - | tmul v w => - rw [Representation.tprod_apply, TensorProduct.map_tmul, tensorCoordinates_tmul, - tensorCoordinates_tmul, coordinateRepresentation_equiv, coordinateRepresentation_equiv, - ← LinearMap.toMatrix'_mulVec (coordinateRepresentation k σ e g), - ← LinearMap.toMatrix'_mulVec (coordinateRepresentation k ρ f g)] - funext bi - simp only [Matrix.mulVec, dotProduct, Fintype.sum_prod_type, Matrix.kroneckerMap, - Finset.sum_mul, Finset.mul_sum, Matrix.of_apply] - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro b _ - apply Finset.sum_congr rfl - intro i _ - ring -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.CoordinateTensor + +namespace OAI + +namespace FiberFunctorProof +open Matrix +open scoped TensorProduct BigOperators Kronecker +universe u v +variable (k : Type u) [Field k] +variable {β ι : Type u} [Fintype β] [DecidableEq β] [Fintype ι] [DecidableEq ι] + +noncomputable def uncurryLinearEquiv : (β → ι → k) ≃ₗ[k] (β × ι → k) where + toFun v bi := v bi.1 bi.2 + invFun v b i := v (b,i) + left_inv _ := rfl + right_inv _ := rfl + map_add' _ _ := rfl + map_smul' _ _ := rfl + +variable {V W : Type u} [AddCommGroup V] [Module k V] [AddCommGroup W] [Module k W] +noncomputable def tensorCoordinates (e : V ≃ₗ[k] (β → k)) (f : W ≃ₗ[k] (ι → k)) : + (V ⊗[k] W) ≃ₗ[k] (β × ι → k) := + (TensorProduct.congr e f).trans ((coordinateTensorEquiv k).trans (uncurryLinearEquiv k)) + +omit [Fintype ι] [DecidableEq ι] in +lemma tensorCoordinates_tmul (e : V ≃ₗ[k] (β → k)) (f : W ≃ₗ[k] (ι → k)) (v : V) (w : W) : + tensorCoordinates k e f (v ⊗ₜ[k] w) = fun bi => e v bi.1 * f w bi.2 := by + simp only [tensorCoordinates, LinearEquiv.trans_apply, TensorProduct.congr_tmul, + coordinateTensorEquiv_tmul] + rfl + +variable {G : Type v} [Monoid G] +lemma tensorCoordinates_intertwines (σ : Representation k G V) (ρ : Representation k G W) + (e : V ≃ₗ[k] (β → k)) (f : W ≃ₗ[k] (ι → k)) (g : G) (v : V ⊗[k] W) : + tensorCoordinates k e f ((σ.tprod ρ) g v) = + (LinearMap.toMatrix' (coordinateRepresentation k σ e g) ⊗ₖ + LinearMap.toMatrix' (coordinateRepresentation k ρ f g)) *ᵥ tensorCoordinates k e f v := by + induction v using TensorProduct.inductionOn with + | add v w hv hw => simp only [map_add, Matrix.mulVec_add, hv, hw] + | tmul v w => + rw [Representation.tprod_apply, TensorProduct.map_tmul, tensorCoordinates_tmul, + tensorCoordinates_tmul, coordinateRepresentation_equiv, coordinateRepresentation_equiv, + ← LinearMap.toMatrix'_mulVec (coordinateRepresentation k σ e g), + ← LinearMap.toMatrix'_mulVec (coordinateRepresentation k ρ f g)] + funext bi + simp only [Matrix.mulVec, dotProduct, Fintype.sum_prod_type, Matrix.kroneckerMap, + Finset.sum_mul, Finset.mul_sum, Matrix.of_apply] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro i _ + ring +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorExactness.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorExactness.lean index 2fffc49dc0faf31e0be7be93bf8b4e86b41b354e..80ff0269f37ca748ee0d6caf29d93685bfb8d347 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorExactness.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorExactness.lean @@ -1,114 +1,114 @@ -import Mathlib - -namespace OAI - -open CategoryTheory CategoryTheory.Limits CategoryTheory.MonoidalCategory - -namespace FiberFunctorProof - -universe v₁ v₂ u₁ u₂ - -section Tensor -variable {C : Type u₁} [Category.{v₁} C] [MonoidalCategory C] [RigidCategory C] - -theorem tensorLeft_preservesFiniteLimits (X : C) : - PreservesFiniteLimits (tensorLeft X) := by - let : (tensorLeft X).IsRightAdjoint := (tensorLeftAdjunction X Xᘁ).isRightAdjoint - infer_instance - -theorem tensorLeft_preservesFiniteColimits (X : C) : - PreservesFiniteColimits (tensorLeft X) := by - let : (tensorLeft X).IsLeftAdjoint := (tensorLeftAdjunction (ᘁX) X).isLeftAdjoint - infer_instance - -theorem tensorRight_preservesFiniteLimits (X : C) : - PreservesFiniteLimits (tensorRight X) := by - let : (tensorRight X).IsRightAdjoint := (tensorRightAdjunction (ᘁX) X).isRightAdjoint - infer_instance - -theorem tensorRight_preservesFiniteColimits (X : C) : - PreservesFiniteColimits (tensorRight X) := by - let : (tensorRight X).IsLeftAdjoint := (tensorRightAdjunction X Xᘁ).isLeftAdjoint - infer_instance - -variable [Abelian C] [MonoidalPreadditive C] - -lemma coevaluation_ne_zero (X : C) (hX : ¬ IsZero X) : η_ X Xᘁ ≠ 0 := by - intro h - apply hX - apply (IsZero.iff_id_eq_zero _).2 - have he := ExactPairing.evaluation_coevaluation X Xᘁ - rw [h] at he - have hz : (λ_ X).hom ≫ (ρ_ X).inv = 0 := by simpa using he.symm - have hz' := congrArg (fun f => (λ_ X).inv ≫ f ≫ (ρ_ X).hom) hz - simpa using hz' - -lemma tensorRight_faithful (X : C) [Simple (𝟙_ C)] (hX : ¬ IsZero X) : - (tensorRight X).Faithful := by - let : Mono (η_ X Xᘁ) := mono_of_nonzero_from_simple (coevaluation_ne_zero X hX) - let : ∀ Y : C, Mono ((tensorRightAdjunction X Xᘁ).unit.app Y) := by - intro Y - let := tensorLeft_preservesFiniteLimits Y - change Mono ((ρ_ Y).inv ≫ Y ◁ η_ X Xᘁ ≫ (α_ Y X Xᘁ).inv ≫ (𝟙 (Y ⊗ X)) ▷ Xᘁ) - simp only [id_whiskerRight, Category.comp_id] - have : Mono (Y ◁ η_ X Xᘁ) := - inferInstanceAs (Mono ((tensorLeft Y).map (η_ X Xᘁ))) - infer_instance - exact (tensorRightAdjunction X Xᘁ).faithful_L_of_mono_unit_app - -lemma coevaluation_ne_zero_right (X : C) (hX : ¬ IsZero X) : η_ (ᘁX) X ≠ 0 := by - intro h - apply hX - apply (IsZero.iff_id_eq_zero _).2 - have he := ExactPairing.coevaluation_evaluation (ᘁX) X - rw [h] at he - have hz : (ρ_ X).hom ≫ (λ_ X).inv = 0 := by simpa using he.symm - have hz' := congrArg (fun f => (ρ_ X).inv ≫ f ≫ (λ_ X).hom) hz - simpa using hz' - -lemma tensorLeft_faithful (X : C) [Simple (𝟙_ C)] (hX : ¬ IsZero X) : - (tensorLeft X).Faithful := by - let : Mono (η_ (ᘁX) X) := mono_of_nonzero_from_simple (coevaluation_ne_zero_right X hX) - let : ∀ Y : C, Mono ((tensorLeftAdjunction (ᘁX) X).unit.app Y) := by - intro Y - let := tensorRight_preservesFiniteLimits Y - change Mono ((λ_ Y).inv ≫ η_ (ᘁX) X ▷ Y ≫ (α_ (ᘁX) X Y).hom ≫ (ᘁX) ◁ (𝟙 (X ⊗ Y))) - simp only [whiskerLeft_id, Category.comp_id] - have : Mono (η_ (ᘁX) X ▷ Y) := - inferInstanceAs (Mono ((tensorRight Y).map (η_ (ᘁX) X))) - infer_instance - exact (tensorLeftAdjunction (ᘁX) X).faithful_L_of_mono_unit_app - -omit [Abelian C] [MonoidalPreadditive C] in -lemma projective_tensor (P X : C) [Projective P] : Projective (P ⊗ X) := by - let := tensorRight_preservesFiniteColimits Xᘁ - exact (tensorRightAdjunction X Xᘁ).map_projective P inferInstance - -end Tensor - - -theorem exact_of_nonzero_projective - {C : Type u₁} [Category.{v₁} C] [Abelian C] - [MonoidalCategory C] [MonoidalPreadditive C] [RigidCategory C] - {D : Type u₂} [Category.{v₂} D] [Abelian D] - [MonoidalCategory D] [MonoidalPreadditive D] [RigidCategory D] - [Simple (𝟙_ D)] - (F : C ⥤ D) [F.Additive] [F.Monoidal] - (P : C) [Projective P] (hP : ¬ IsZero (F.obj P)) - (S : ShortComplex C) (hS : S.ShortExact) : - (S.map F).ShortExact := by - let := tensorLeft_preservesFiniteLimits P - let := tensorLeft_preservesFiniteColimits P - have ht : (S.map (tensorLeft P)).ShortExact := hS.map_of_exact (tensorLeft P) - let : Projective (S.map (tensorLeft P)).X₃ := projective_tensor P S.X₃ - have hs : ((S.map (tensorLeft P)).map F).ShortExact := - (ht.splittingOfProjective.map F).shortExact - have he : ((S.map F).map (tensorLeft (F.obj P))).ShortExact := - ShortComplex.shortExact_of_iso - (S.mapNatIso (Functor.Monoidal.commTensorLeft F P).symm) hs - let := tensorLeft_faithful (F.obj P) hP - exact CategoryTheory.ShortExact.reflects_shortExact_of_faithful _ he - -end FiberFunctorProof - -end OAI +import Mathlib + +namespace OAI + +open CategoryTheory CategoryTheory.Limits CategoryTheory.MonoidalCategory + +namespace FiberFunctorProof + +universe v₁ v₂ u₁ u₂ + +section Tensor +variable {C : Type u₁} [Category.{v₁} C] [MonoidalCategory C] [RigidCategory C] + +theorem tensorLeft_preservesFiniteLimits (X : C) : + PreservesFiniteLimits (tensorLeft X) := by + let : (tensorLeft X).IsRightAdjoint := (tensorLeftAdjunction X Xᘁ).isRightAdjoint + infer_instance + +theorem tensorLeft_preservesFiniteColimits (X : C) : + PreservesFiniteColimits (tensorLeft X) := by + let : (tensorLeft X).IsLeftAdjoint := (tensorLeftAdjunction (ᘁX) X).isLeftAdjoint + infer_instance + +theorem tensorRight_preservesFiniteLimits (X : C) : + PreservesFiniteLimits (tensorRight X) := by + let : (tensorRight X).IsRightAdjoint := (tensorRightAdjunction (ᘁX) X).isRightAdjoint + infer_instance + +theorem tensorRight_preservesFiniteColimits (X : C) : + PreservesFiniteColimits (tensorRight X) := by + let : (tensorRight X).IsLeftAdjoint := (tensorRightAdjunction X Xᘁ).isLeftAdjoint + infer_instance + +variable [Abelian C] [MonoidalPreadditive C] + +lemma coevaluation_ne_zero (X : C) (hX : ¬ IsZero X) : η_ X Xᘁ ≠ 0 := by + intro h + apply hX + apply (IsZero.iff_id_eq_zero _).2 + have he := ExactPairing.evaluation_coevaluation X Xᘁ + rw [h] at he + have hz : (λ_ X).hom ≫ (ρ_ X).inv = 0 := by simpa using he.symm + have hz' := congrArg (fun f => (λ_ X).inv ≫ f ≫ (ρ_ X).hom) hz + simpa using hz' + +lemma tensorRight_faithful (X : C) [Simple (𝟙_ C)] (hX : ¬ IsZero X) : + (tensorRight X).Faithful := by + let : Mono (η_ X Xᘁ) := mono_of_nonzero_from_simple (coevaluation_ne_zero X hX) + let : ∀ Y : C, Mono ((tensorRightAdjunction X Xᘁ).unit.app Y) := by + intro Y + let := tensorLeft_preservesFiniteLimits Y + change Mono ((ρ_ Y).inv ≫ Y ◁ η_ X Xᘁ ≫ (α_ Y X Xᘁ).inv ≫ (𝟙 (Y ⊗ X)) ▷ Xᘁ) + simp only [id_whiskerRight, Category.comp_id] + have : Mono (Y ◁ η_ X Xᘁ) := + inferInstanceAs (Mono ((tensorLeft Y).map (η_ X Xᘁ))) + infer_instance + exact (tensorRightAdjunction X Xᘁ).faithful_L_of_mono_unit_app + +lemma coevaluation_ne_zero_right (X : C) (hX : ¬ IsZero X) : η_ (ᘁX) X ≠ 0 := by + intro h + apply hX + apply (IsZero.iff_id_eq_zero _).2 + have he := ExactPairing.coevaluation_evaluation (ᘁX) X + rw [h] at he + have hz : (ρ_ X).hom ≫ (λ_ X).inv = 0 := by simpa using he.symm + have hz' := congrArg (fun f => (ρ_ X).inv ≫ f ≫ (λ_ X).hom) hz + simpa using hz' + +lemma tensorLeft_faithful (X : C) [Simple (𝟙_ C)] (hX : ¬ IsZero X) : + (tensorLeft X).Faithful := by + let : Mono (η_ (ᘁX) X) := mono_of_nonzero_from_simple (coevaluation_ne_zero_right X hX) + let : ∀ Y : C, Mono ((tensorLeftAdjunction (ᘁX) X).unit.app Y) := by + intro Y + let := tensorRight_preservesFiniteLimits Y + change Mono ((λ_ Y).inv ≫ η_ (ᘁX) X ▷ Y ≫ (α_ (ᘁX) X Y).hom ≫ (ᘁX) ◁ (𝟙 (X ⊗ Y))) + simp only [whiskerLeft_id, Category.comp_id] + have : Mono (η_ (ᘁX) X ▷ Y) := + inferInstanceAs (Mono ((tensorRight Y).map (η_ (ᘁX) X))) + infer_instance + exact (tensorLeftAdjunction (ᘁX) X).faithful_L_of_mono_unit_app + +omit [Abelian C] [MonoidalPreadditive C] in +lemma projective_tensor (P X : C) [Projective P] : Projective (P ⊗ X) := by + let := tensorRight_preservesFiniteColimits Xᘁ + exact (tensorRightAdjunction X Xᘁ).map_projective P inferInstance + +end Tensor + + +theorem exact_of_nonzero_projective + {C : Type u₁} [Category.{v₁} C] [Abelian C] + [MonoidalCategory C] [MonoidalPreadditive C] [RigidCategory C] + {D : Type u₂} [Category.{v₂} D] [Abelian D] + [MonoidalCategory D] [MonoidalPreadditive D] [RigidCategory D] + [Simple (𝟙_ D)] + (F : C ⥤ D) [F.Additive] [F.Monoidal] + (P : C) [Projective P] (hP : ¬ IsZero (F.obj P)) + (S : ShortComplex C) (hS : S.ShortExact) : + (S.map F).ShortExact := by + let := tensorLeft_preservesFiniteLimits P + let := tensorLeft_preservesFiniteColimits P + have ht : (S.map (tensorLeft P)).ShortExact := hS.map_of_exact (tensorLeft P) + let : Projective (S.map (tensorLeft P)).X₃ := projective_tensor P S.X₃ + have hs : ((S.map (tensorLeft P)).map F).ShortExact := + (ht.splittingOfProjective.map F).shortExact + have he : ((S.map F).map (tensorLeft (F.obj P))).ShortExact := + ShortComplex.shortExact_of_iso + (S.mapNatIso (Functor.Monoidal.commTensorLeft F P).symm) hs + let := tensorLeft_faithful (F.obj P) hP + exact CategoryTheory.ShortExact.reflects_shortExact_of_faithful _ he + +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorFormalComparison.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorFormalComparison.lean index 39f38d0868c4803e827561d019eeb59683ac227d..40795920a3b9574cf08ca1745742b654e138b4c8 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorFormalComparison.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorFormalComparison.lean @@ -1,68 +1,68 @@ -import OAI.RepresentationTheory.RestrictedTilting.LinearFormalComparison - -namespace OAI - -namespace FiberFunctorProof -open Matrix -open scoped TensorProduct Kronecker -universe u v -variable {k : Type u} [Field k] [Infinite k] -variable {K : Type v} [Field K] [Algebra k K] -variable {β ι : Type u} [Fintype β] [DecidableEq β] [Fintype ι] [DecidableEq ι] -variable {T : Type u} [AddCommGroup T] [Module k T] [Module.Finite k T] - -omit [Infinite k] [Fintype β] [DecidableEq β] [Fintype ι] [DecidableEq ι] in -lemma polynomialMatrixEval_kronecker (B : Matrix β β (Polynomial k)) - (P : Matrix ι ι (Polynomial k)) (t : K) : - polynomialMatrixEval (B ⊗ₖ P) t = polynomialMatrixEval B t ⊗ₖ polynomialMatrixEval P t := by - ext i j - exact map_mul (Polynomial.aeval t) _ _ - - - -theorem tensor_linear_formal_comparison - (σ : Representation k (SL2 k) T) (hσ : IsRational k σ) - (τ : Representation k (SL2 k) (β → k)) (hτ : IsRational k τ) - (P : Matrix ι ι (Polynomial k)) (x : K) (hx : x ≠ 0) - (F : (K ⊗[k] T) ≃ₗ[K] (β × ι → K)) - (hF : ∀ t : k, ∀ v : T, - F (1 ⊗ₜ[k] σ (unipotent k t) v) = - ((LinearMap.toMatrix' (τ (unipotent k t))).map (algebraMap k K) ⊗ₖ - polynomialMatrixEval P (algebraMap k K t / x^2)) *ᵥ F (1 ⊗ₜ[k] v)) : - ∃ E : T ≃ₗ[k] (β × ι → k), ∀ t : k, ∀ v : T, - E (σ (unipotent k t) v) = - (LinearMap.toMatrix' (τ (unipotent k t)) ⊗ₖ polynomialMatrixEval P t) *ᵥ E v := by - let xU : Kˣ := Units.mk0 x hx - let Q := torusMatrixAt τ hτ xU⁻¹ - let L : Matrix (β × ι) (β × ι) K := Q ⊗ₖ (1 : Matrix ι ι K) - have hL : L.det ≠ 0 := by - rw [Matrix.det_kronecker, Matrix.det_one, one_pow, mul_one] - exact pow_ne_zero _ (torusMatrixAt_det_ne_zero τ hτ xU⁻¹) - let E₀ := Matrix.toLinearEquiv (Pi.basisFun K (β × ι)) L (isUnit_iff_ne_zero.mpr hL) - have hE₀ (v : β × ι → K) : E₀ v = L *ᵥ v := by - rw [Matrix.toLinearEquiv_apply] - rfl - let B := rationalUnipotentMatrix k τ hτ - have hcorr (t : k) : L * ((LinearMap.toMatrix' (τ (unipotent k t))).map (algebraMap k K) ⊗ₖ - polynomialMatrixEval P (algebraMap k K t / x^2)) = - polynomialMatrixEval (B ⊗ₖ P) (algebraMap k K t / x^2) * L := by - rw [polynomialMatrixEval_kronecker] - change (Q ⊗ₖ (1 : Matrix ι ι K)) * _ = _ * (Q ⊗ₖ (1 : Matrix ι ι K)) - rw [← Matrix.mul_kronecker_mul, ← Matrix.mul_kronecker_mul, Matrix.one_mul, Matrix.mul_one] - have he := torusMatrixAt_unipotent τ hτ xU⁻¹ t - have hp : ((xU⁻¹ : Kˣ) : K)^2 * algebraMap k K t = algebraMap k K t / x^2 := by - change (x⁻¹)^2 * _ = _ - rw [inv_pow, div_eq_mul_inv, mul_comm] - rw [hp] at he - rw [he] - obtain ⟨E,hE⟩ := linear_formal_comparison σ hσ (B ⊗ₖ P) x hx (F.trans E₀) (by - intro t v - simp only [LinearEquiv.trans_apply, hE₀] - rw [hF, Matrix.mulVec_mulVec, hcorr, ← Matrix.mulVec_mulVec]) - refine ⟨E, fun t v => ?_⟩ - have hB : polynomialMatrixEval B t = LinearMap.toMatrix' (τ (unipotent k t)) := - eval_rationalUnipotentMatrix k τ hτ t - simpa only [polynomialMatrixEval_kronecker, hB] using hE t v -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.LinearFormalComparison + +namespace OAI + +namespace FiberFunctorProof +open Matrix +open scoped TensorProduct Kronecker +universe u v +variable {k : Type u} [Field k] [Infinite k] +variable {K : Type v} [Field K] [Algebra k K] +variable {β ι : Type u} [Fintype β] [DecidableEq β] [Fintype ι] [DecidableEq ι] +variable {T : Type u} [AddCommGroup T] [Module k T] [Module.Finite k T] + +omit [Infinite k] [Fintype β] [DecidableEq β] [Fintype ι] [DecidableEq ι] in +lemma polynomialMatrixEval_kronecker (B : Matrix β β (Polynomial k)) + (P : Matrix ι ι (Polynomial k)) (t : K) : + polynomialMatrixEval (B ⊗ₖ P) t = polynomialMatrixEval B t ⊗ₖ polynomialMatrixEval P t := by + ext i j + exact map_mul (Polynomial.aeval t) _ _ + + + +theorem tensor_linear_formal_comparison + (σ : Representation k (SL2 k) T) (hσ : IsRational k σ) + (τ : Representation k (SL2 k) (β → k)) (hτ : IsRational k τ) + (P : Matrix ι ι (Polynomial k)) (x : K) (hx : x ≠ 0) + (F : (K ⊗[k] T) ≃ₗ[K] (β × ι → K)) + (hF : ∀ t : k, ∀ v : T, + F (1 ⊗ₜ[k] σ (unipotent k t) v) = + ((LinearMap.toMatrix' (τ (unipotent k t))).map (algebraMap k K) ⊗ₖ + polynomialMatrixEval P (algebraMap k K t / x^2)) *ᵥ F (1 ⊗ₜ[k] v)) : + ∃ E : T ≃ₗ[k] (β × ι → k), ∀ t : k, ∀ v : T, + E (σ (unipotent k t) v) = + (LinearMap.toMatrix' (τ (unipotent k t)) ⊗ₖ polynomialMatrixEval P t) *ᵥ E v := by + let xU : Kˣ := Units.mk0 x hx + let Q := torusMatrixAt τ hτ xU⁻¹ + let L : Matrix (β × ι) (β × ι) K := Q ⊗ₖ (1 : Matrix ι ι K) + have hL : L.det ≠ 0 := by + rw [Matrix.det_kronecker, Matrix.det_one, one_pow, mul_one] + exact pow_ne_zero _ (torusMatrixAt_det_ne_zero τ hτ xU⁻¹) + let E₀ := Matrix.toLinearEquiv (Pi.basisFun K (β × ι)) L (isUnit_iff_ne_zero.mpr hL) + have hE₀ (v : β × ι → K) : E₀ v = L *ᵥ v := by + rw [Matrix.toLinearEquiv_apply] + rfl + let B := rationalUnipotentMatrix k τ hτ + have hcorr (t : k) : L * ((LinearMap.toMatrix' (τ (unipotent k t))).map (algebraMap k K) ⊗ₖ + polynomialMatrixEval P (algebraMap k K t / x^2)) = + polynomialMatrixEval (B ⊗ₖ P) (algebraMap k K t / x^2) * L := by + rw [polynomialMatrixEval_kronecker] + change (Q ⊗ₖ (1 : Matrix ι ι K)) * _ = _ * (Q ⊗ₖ (1 : Matrix ι ι K)) + rw [← Matrix.mul_kronecker_mul, ← Matrix.mul_kronecker_mul, Matrix.one_mul, Matrix.mul_one] + have he := torusMatrixAt_unipotent τ hτ xU⁻¹ t + have hp : ((xU⁻¹ : Kˣ) : K)^2 * algebraMap k K t = algebraMap k K t / x^2 := by + change (x⁻¹)^2 * _ = _ + rw [inv_pow, div_eq_mul_inv, mul_comm] + rw [hp] at he + rw [he] + obtain ⟨E,hE⟩ := linear_formal_comparison σ hσ (B ⊗ₖ P) x hx (F.trans E₀) (by + intro t v + simp only [LinearEquiv.trans_apply, hE₀] + rw [hF, Matrix.mulVec_mulVec, hcorr, ← Matrix.mulVec_mulVec]) + refine ⟨E, fun t v => ?_⟩ + have hB : polynomialMatrixEval B t = LinearMap.toMatrix' (τ (unipotent k t)) := + eval_rationalUnipotentMatrix k τ hτ t + simpa only [polynomialMatrixEval_kronecker, hB] using hE t v +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorLimits.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorLimits.lean index 82ea49ba4ec21b3cc1582eee52016d2a827486dd..8268512e18d61392f2b14ad670c5bc9997a0c845 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorLimits.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorLimits.lean @@ -1,119 +1,119 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.RepresentationMaps -import OAI.RepresentationTheory.RestrictedTilting.SL2Definitions - -namespace OAI - -/-! Exact tensor functors and rational tensor representations. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section -universe v₁ u₁ -variable {C : Type u₁} [Category.{v₁} C] [MonoidalCategory C] [RigidCategory C] - -theorem tensorLeft_preservesFiniteLimits (X : C) : - PreservesFiniteLimits (tensorLeft X) := by - let : (tensorLeft X).IsRightAdjoint := (tensorLeftAdjunction X Xᘁ).isRightAdjoint - infer_instance - -theorem tensorLeft_preservesFiniteColimits (X : C) : - PreservesFiniteColimits (tensorLeft X) := by - let : (tensorLeft X).IsLeftAdjoint := (tensorLeftAdjunction (ᘁX) X).isLeftAdjoint - infer_instance - -theorem tensorRight_preservesFiniteLimits (X : C) : - PreservesFiniteLimits (tensorRight X) := by - let : (tensorRight X).IsRightAdjoint := (tensorRightAdjunction (ᘁX) X).isRightAdjoint - infer_instance - -theorem tensorRight_preservesFiniteColimits (X : C) : - PreservesFiniteColimits (tensorRight X) := by - let : (tensorRight X).IsLeftAdjoint := (tensorRightAdjunction X Xᘁ).isLeftAdjoint - infer_instance - -end - -section -universe u -variable (k : Type u) [Field k] - -noncomputable instance fdrepRigid : RigidCategory (FDRep k (SL2 k)) := - BraidedCategory.rigidCategoryOfRightRigidCategory - - -lemma HasGoodFiltration.extension {A B C : FDRep k (SL2 k)} - (hA : HasGoodFiltration k A) (hC : HasGoodFiltration k C) - (f : A ⟶ B) (g : B ⟶ C) (w : f ≫ g = 0) - (hS : (ShortComplex.mk f g w).ShortExact) : HasGoodFiltration k B := by - induction hC generalizing A B with - | zero C hC => - have : IsIso f := hS.isIso_f_iff.mpr hC - cases hA with - | zero initial hInitial => - exact .zero B (hInitial.of_iso (asIso f).symm) - | @step prior initial degree inclusion quotient relation hSequence hPrior => - let equiv := asIso f - let inclusion' := inclusion ≫ equiv.hom - let quotient' := equiv.inv ≫ quotient - have relation' : inclusion' ≫ quotient' = 0 := by - simpa [inclusion', quotient'] using relation - have hSequence' : (ShortComplex.mk inclusion' quotient' relation').ShortExact := - ShortComplex.shortExact_of_iso - (ShortComplex.isoMk (Iso.refl prior) equiv (Iso.refl (costandard k degree)) - (by simp [inclusion']) (by simp [quotient'])) hSequence - exact .step degree inclusion' quotient' relation' hSequence' hPrior - | @step D C n i j v hT hD ih => - obtain ⟨K, a, b, r, wab, wr, hK, hB⟩ := fdrep_splice k f g w hS i j v hT - exact .step n r (g ≫ j) wr hB (ih hA a b wab hK) - -end - -section -universe u -variable (k : Type u) [Field k] -open TensorProduct - - -lemma IsRational.tensor {M N : Type u} [AddCommGroup M] [Module k M] - [AddCommGroup N] [Module k N] [Module.Finite k M] [Module.Finite k N] - (ρ : Representation k (SL2 k) M) (σ : Representation k (SL2 k) N) - (hρ : IsRational k ρ) (hσ : IsRational k σ) : - IsRational k (Representation.tprod ρ σ) := by - classical - let b := Module.finBasis k M - let c := Module.finBasis k N - intro v l - induction v using TensorProduct.inductionOn with - | add v w hv hw => - obtain ⟨P, hP⟩ := hv - obtain ⟨Q, hQ⟩ := hw - exact ⟨P + Q, by intro g; simp only [map_add, hP, hQ]⟩ - | tmul v w => - choose P hP using fun i => hρ v (b.coord i) - choose Q hQ using fun j => hσ w (c.coord j) - refine ⟨∑ j, ∑ i, MvPolynomial.C (l (b i ⊗ₜ[k] c j)) * P i * Q j, fun g => ?_⟩ - change l ((ρ g v) ⊗ₜ[k] (σ g w)) = _ - conv_lhs => rw [← b.sum_repr (ρ g v), ← c.sum_repr (σ g w)] - simp only [TensorProduct.sum_tmul, TensorProduct.tmul_sum, TensorProduct.smul_tmul, - TensorProduct.tmul_smul, map_sum, map_smul] - simp only [map_mul, MvPolynomial.eval_C, ← hP, ← hQ, Module.Basis.coord_apply, - Finset.smul_sum] - apply Finset.sum_congr rfl - intro i hi - apply Finset.sum_congr rfl - intro j hj - simp only [smul_eq_mul] - ring - -end - -universe u -abbrev Binary (k : Type u) [Field k] (n : ℕ) := MvPolynomial.homogeneousSubmodule (Fin 2) k n -end FiberFunctorProof -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.RepresentationMaps +import OAI.RepresentationTheory.RestrictedTilting.SL2Definitions + +namespace OAI + +/-! Exact tensor functors and rational tensor representations. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section +universe v₁ u₁ +variable {C : Type u₁} [Category.{v₁} C] [MonoidalCategory C] [RigidCategory C] + +theorem tensorLeft_preservesFiniteLimits (X : C) : + PreservesFiniteLimits (tensorLeft X) := by + let : (tensorLeft X).IsRightAdjoint := (tensorLeftAdjunction X Xᘁ).isRightAdjoint + infer_instance + +theorem tensorLeft_preservesFiniteColimits (X : C) : + PreservesFiniteColimits (tensorLeft X) := by + let : (tensorLeft X).IsLeftAdjoint := (tensorLeftAdjunction (ᘁX) X).isLeftAdjoint + infer_instance + +theorem tensorRight_preservesFiniteLimits (X : C) : + PreservesFiniteLimits (tensorRight X) := by + let : (tensorRight X).IsRightAdjoint := (tensorRightAdjunction (ᘁX) X).isRightAdjoint + infer_instance + +theorem tensorRight_preservesFiniteColimits (X : C) : + PreservesFiniteColimits (tensorRight X) := by + let : (tensorRight X).IsLeftAdjoint := (tensorRightAdjunction X Xᘁ).isLeftAdjoint + infer_instance + +end + +section +universe u +variable (k : Type u) [Field k] + +noncomputable instance fdrepRigid : RigidCategory (FDRep k (SL2 k)) := + BraidedCategory.rigidCategoryOfRightRigidCategory + + +lemma HasGoodFiltration.extension {A B C : FDRep k (SL2 k)} + (hA : HasGoodFiltration k A) (hC : HasGoodFiltration k C) + (f : A ⟶ B) (g : B ⟶ C) (w : f ≫ g = 0) + (hS : (ShortComplex.mk f g w).ShortExact) : HasGoodFiltration k B := by + induction hC generalizing A B with + | zero C hC => + have : IsIso f := hS.isIso_f_iff.mpr hC + cases hA with + | zero initial hInitial => + exact .zero B (hInitial.of_iso (asIso f).symm) + | @step prior initial degree inclusion quotient relation hSequence hPrior => + let equiv := asIso f + let inclusion' := inclusion ≫ equiv.hom + let quotient' := equiv.inv ≫ quotient + have relation' : inclusion' ≫ quotient' = 0 := by + simpa [inclusion', quotient'] using relation + have hSequence' : (ShortComplex.mk inclusion' quotient' relation').ShortExact := + ShortComplex.shortExact_of_iso + (ShortComplex.isoMk (Iso.refl prior) equiv (Iso.refl (costandard k degree)) + (by simp [inclusion']) (by simp [quotient'])) hSequence + exact .step degree inclusion' quotient' relation' hSequence' hPrior + | @step D C n i j v hT hD ih => + obtain ⟨K, a, b, r, wab, wr, hK, hB⟩ := fdrep_splice k f g w hS i j v hT + exact .step n r (g ≫ j) wr hB (ih hA a b wab hK) + +end + +section +universe u +variable (k : Type u) [Field k] +open TensorProduct + + +lemma IsRational.tensor {M N : Type u} [AddCommGroup M] [Module k M] + [AddCommGroup N] [Module k N] [Module.Finite k M] [Module.Finite k N] + (ρ : Representation k (SL2 k) M) (σ : Representation k (SL2 k) N) + (hρ : IsRational k ρ) (hσ : IsRational k σ) : + IsRational k (Representation.tprod ρ σ) := by + classical + let b := Module.finBasis k M + let c := Module.finBasis k N + intro v l + induction v using TensorProduct.inductionOn with + | add v w hv hw => + obtain ⟨P, hP⟩ := hv + obtain ⟨Q, hQ⟩ := hw + exact ⟨P + Q, by intro g; simp only [map_add, hP, hQ]⟩ + | tmul v w => + choose P hP using fun i => hρ v (b.coord i) + choose Q hQ using fun j => hσ w (c.coord j) + refine ⟨∑ j, ∑ i, MvPolynomial.C (l (b i ⊗ₜ[k] c j)) * P i * Q j, fun g => ?_⟩ + change l ((ρ g v) ⊗ₜ[k] (σ g w)) = _ + conv_lhs => rw [← b.sum_repr (ρ g v), ← c.sum_repr (σ g w)] + simp only [TensorProduct.sum_tmul, TensorProduct.tmul_sum, TensorProduct.smul_tmul, + TensorProduct.tmul_smul, map_sum, map_smul] + simp only [map_mul, MvPolynomial.eval_C, ← hP, ← hQ, Module.Basis.coord_apply, + Finset.smul_sum] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + simp only [smul_eq_mul] + ring + +end + +universe u +abbrev Binary (k : Type u) [Field k] (n : ℕ) := MvPolynomial.homogeneousSubmodule (Fin 2) k n +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorNumerator.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorNumerator.lean index 19edd09861c0eb94486f73b10e4dfd5a10327ab1..68c60a81bc77026cf5531d98e78d64c7f0dcf174 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorNumerator.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorNumerator.lean @@ -1,66 +1,66 @@ -import OAI.RepresentationTheory.RestrictedTilting.PlaneMatrixTensor -import OAI.RepresentationTheory.RestrictedTilting.NumeratorAction - -namespace OAI - -namespace FiberFunctorProof -open scoped BigOperators -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (β ι : Type u) [Fintype β] [DecidableEq β] [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) -variable (P : Matrix ι ι (Polynomial k)) -variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) -variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) -local notation "N" => associatedSectionsSubmodule k ι ρ -local notation "A" => MvPolynomial (Fin 2) k -local notation "W" => associatedNumeratorLinear k ι ρ P hP d hd -local notation "Z" => associatedDenominatorLinear k ι ρ P hP d hd - -noncomputable def tensorAssociatedNumerator : (β → N) →ₗ[A] (β × ι → A) := - LinearMap.pi fun bi => (LinearMap.proj bi.2).comp ((W).comp (LinearMap.proj bi.1)) -noncomputable def tensorAssociatedDenominator : (β × ι → A) →ₗ[A] (β → N) := - LinearMap.pi fun b => (Z).comp (LinearMap.pi fun i => LinearMap.proj (b,i)) - -omit [Fintype β] [DecidableEq β] in -lemma tensorAssociatedNumerator_apply (v : β → N) (b : β) (i : ι) : - tensorAssociatedNumerator k β ι ρ P hP d hd v (b,i) = W (v b) i := rfl -omit [Fintype β] [DecidableEq β] in -lemma tensorAssociatedDenominator_apply (v : β × ι → A) (b : β) : - tensorAssociatedDenominator k β ι ρ P hP d hd v b = Z (fun i => v (b,i)) := rfl - -omit [Fintype β] [DecidableEq β] in -lemma tensorAssociatedNumerator_denominator (v : β × ι → A) : - tensorAssociatedNumerator k β ι ρ P hP d hd - (tensorAssociatedDenominator k β ι ρ P hP d hd v) = (MvPolynomial.X 0 : A)^(d+d) • v := by - funext bi - exact congrFun (associatedNumerator_denominator k ι ρ P hP d hd (fun i => v (bi.1,i))) bi.2 -omit [Fintype β] [DecidableEq β] in -lemma tensorAssociatedDenominator_numerator (v : β → N) : - tensorAssociatedDenominator k β ι ρ P hP d hd - (tensorAssociatedNumerator k β ι ρ P hP d hd v) = (MvPolynomial.X 0 : A)^(d+d) • v := by - funext b - exact associatedDenominator_numerator k ι ρ P hP d hd (v b) - -variable (τ : Representation k (SL2 k) (β → k)) -lemma tensorAssociatedNumerator_line_unipotent (t : k) (v : β → N) (b : β) (i : ι) : - Polynomial.X^(2*d) * linePolynomial k - (tensorAssociatedNumerator k β ι ρ P hP d hd - (matrixTensorRepresentation τ (associatedSectionsRepresentation k ι ρ) (unipotent k t) v) (b,i)) = - ∑ c : β, ∑ j : ι, Polynomial.C (LinearMap.toMatrix' (τ (unipotent k t)) b c) * - clearedLineAction k (P i j) t d * - linePolynomial k (tensorAssociatedNumerator k β ι ρ P hP d hd v (c,j)) := by - simp only [tensorAssociatedNumerator_apply, matrixTensorRepresentation_apply, - map_sum, LinearMap.map_smul_of_tower, Finset.sum_apply, Pi.smul_apply, map_smul] - simp only [Algebra.smul_def, Polynomial.algebraMap_apply, Finset.mul_sum] - apply Finset.sum_congr rfl - intro c _ - rw [mul_left_comm, associatedNumerator_line_unipotent k ι ρ P hP d hd t (v c) i, - Finset.mul_sum] - apply Finset.sum_congr rfl - intro j _ - rw [mul_assoc] - rfl -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.PlaneMatrixTensor +import OAI.RepresentationTheory.RestrictedTilting.NumeratorAction + +namespace OAI + +namespace FiberFunctorProof +open scoped BigOperators +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (β ι : Type u) [Fintype β] [DecidableEq β] [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) +variable (P : Matrix ι ι (Polynomial k)) +variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) +variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) +local notation "N" => associatedSectionsSubmodule k ι ρ +local notation "A" => MvPolynomial (Fin 2) k +local notation "W" => associatedNumeratorLinear k ι ρ P hP d hd +local notation "Z" => associatedDenominatorLinear k ι ρ P hP d hd + +noncomputable def tensorAssociatedNumerator : (β → N) →ₗ[A] (β × ι → A) := + LinearMap.pi fun bi => (LinearMap.proj bi.2).comp ((W).comp (LinearMap.proj bi.1)) +noncomputable def tensorAssociatedDenominator : (β × ι → A) →ₗ[A] (β → N) := + LinearMap.pi fun b => (Z).comp (LinearMap.pi fun i => LinearMap.proj (b,i)) + +omit [Fintype β] [DecidableEq β] in +lemma tensorAssociatedNumerator_apply (v : β → N) (b : β) (i : ι) : + tensorAssociatedNumerator k β ι ρ P hP d hd v (b,i) = W (v b) i := rfl +omit [Fintype β] [DecidableEq β] in +lemma tensorAssociatedDenominator_apply (v : β × ι → A) (b : β) : + tensorAssociatedDenominator k β ι ρ P hP d hd v b = Z (fun i => v (b,i)) := rfl + +omit [Fintype β] [DecidableEq β] in +lemma tensorAssociatedNumerator_denominator (v : β × ι → A) : + tensorAssociatedNumerator k β ι ρ P hP d hd + (tensorAssociatedDenominator k β ι ρ P hP d hd v) = (MvPolynomial.X 0 : A)^(d+d) • v := by + funext bi + exact congrFun (associatedNumerator_denominator k ι ρ P hP d hd (fun i => v (bi.1,i))) bi.2 +omit [Fintype β] [DecidableEq β] in +lemma tensorAssociatedDenominator_numerator (v : β → N) : + tensorAssociatedDenominator k β ι ρ P hP d hd + (tensorAssociatedNumerator k β ι ρ P hP d hd v) = (MvPolynomial.X 0 : A)^(d+d) • v := by + funext b + exact associatedDenominator_numerator k ι ρ P hP d hd (v b) + +variable (τ : Representation k (SL2 k) (β → k)) +lemma tensorAssociatedNumerator_line_unipotent (t : k) (v : β → N) (b : β) (i : ι) : + Polynomial.X^(2*d) * linePolynomial k + (tensorAssociatedNumerator k β ι ρ P hP d hd + (matrixTensorRepresentation τ (associatedSectionsRepresentation k ι ρ) (unipotent k t) v) (b,i)) = + ∑ c : β, ∑ j : ι, Polynomial.C (LinearMap.toMatrix' (τ (unipotent k t)) b c) * + clearedLineAction k (P i j) t d * + linePolynomial k (tensorAssociatedNumerator k β ι ρ P hP d hd v (c,j)) := by + simp only [tensorAssociatedNumerator_apply, matrixTensorRepresentation_apply, + map_sum, LinearMap.map_smul_of_tower, Finset.sum_apply, Pi.smul_apply, map_smul] + simp only [Algebra.smul_def, Polynomial.algebraMap_apply, Finset.mul_sum] + apply Finset.sum_congr rfl + intro c _ + rw [mul_left_comm, associatedNumerator_line_unipotent k ι ρ P hP d hd t (v c) i, + Finset.mul_sum] + apply Finset.sum_congr rfl + intro j _ + rw [mul_assoc] + rfl +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorPlaneTilting.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorPlaneTilting.lean index 97b70e1fcf9a9f2ec59076f7d6cbd2cd83f863f7..8b380442bdcfa47ace55617f34ff57a040e3eb29 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorPlaneTilting.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorPlaneTilting.lean @@ -1,77 +1,77 @@ -import OAI.RepresentationTheory.RestrictedTilting.PiPlaneOrigin -import OAI.RepresentationTheory.RestrictedTilting.CoordinateTensor -import OAI.RepresentationTheory.RestrictedTilting.AssociatedPlaneJet - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory -open scoped TensorProduct -universe u -variable (k : Type u) [Field k] -variable {β : Type u} [Fintype β] [DecidableEq β] -variable {M : Type u} [AddCommGroup M] [Module k M] - [Module (MvPolynomial (Fin 2) k) M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] - [Module.Finite k (M ⧸ planeJetRelation (M := M) k 1)] -variable (τ : Representation k (SL2 k) (β → k)) (σ : Representation k (SL2 k) M) - (hσ : PlaneCompatible k σ) - -noncomputable def tensorPlaneOriginIso : - FDRep.of τ ⊗ planeJetFD k σ hσ 1 ≅ - @planeJetFD k _ (β → M) _ _ _ _ (piPlaneOrigin_finite (β := β) (M := M) k) - (matrixTensorRepresentation τ σ) (matrixTensor_planeCompatible k τ σ hσ) 1 := by - letI := piPlaneOrigin_finite (β := β) (M := M) k - let C := coordinateTensorEquiv (β := β) (M := M ⧸ planeJetRelation (M := M) k 1) k - let E := piPlaneOriginEquiv (β := β) (M := M) k - let f : FDRep.of τ ⊗ planeJetFD k σ hσ 1 ⟶ - planeJetFD k (matrixTensorRepresentation τ σ) (matrixTensor_planeCompatible k τ σ hσ) 1 := - fdrepHom k (C.trans E.symm).toLinearMap (by - intro g v - apply E.injective - change E (E.symm (C ((τ.tprod (planeJetRep k σ hσ 1)) g v))) = - E (planeJetRep k (matrixTensorRepresentation τ σ) (matrixTensor_planeCompatible k τ σ hσ) - 1 g (E.symm (C v))) - rw [E.apply_symm_apply, piPlaneOriginEquiv_intertwines, E.apply_symm_apply] - exact coordinateTensorEquiv_intertwines k τ (planeJetRep k σ hσ 1) g v) - letI : IsIso f := fdrepHom_isIso_of_bijective k f (C.trans E.symm).bijective - exact asIso f - -variable [Infinite k] -variable (ι : Type u) [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) -variable (P : Matrix ι ι (Polynomial k)) -variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) -variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) -local notation "N" => associatedSectionsSubmodule k ι ρ -local notation "σN" => associatedSectionsRepresentation k ι ρ -local notation "hN" => associatedSections_planeCompatible k ι ρ -variable [Module.Finite k ((associatedSectionsSubmodule k ι ρ) ⧸ - planeJetRelation (M := associatedSectionsSubmodule k ι ρ) k 1)] - -noncomputable def associatedOriginJetIso : - associatedOriginFD k ι ρ P hP d hd ≅ planeJetFD k σN hN 1 := by - let E : (associatedOriginRep k ι ρ).V ≃ₗ[k] N ⧸ planeJetRelation (M := N) k 1 := - Submodule.quotEquivOfEq _ _ (associated_planeJet_one k ι ρ).symm - let f : associatedOriginFD k ι ρ P hP d hd ⟶ planeJetFD k σN hN 1 := fdrepHom k E.toLinearMap (by - intro g v - obtain ⟨v,rfl⟩ := (associatedOriginRelations k ι ρ).mkQ_surjective v - rfl) - letI : IsIso f := fdrepHom_isIso_of_bijective k f E.bijective - exact asIso f - -variable (p : ℕ) [Fact p.Prime] [CharP k p] - -include hP hd in -lemma tensorAssociatedOrigin_tilting (m : ℕ) (hm : d < p^(m+1)) - (e : steinberg k p m ≃ₗ[k] (β → k)) : - IsTilting k (@planeJetFD k _ (β → N) _ _ _ _ (piPlaneOrigin_finite (β := β) (M := N) k) - (matrixTensorRepresentation (coordinateRepresentation k (steinberg k p m).ρ e) σN) - (matrixTensor_planeCompatible k _ σN hN) 1) := by - have h := associatedOrigin_tilting k p ι ρ P hP d hd m hm - exact h.of_iso k - ((MonoidalCategory.tensorIso (coordinateFDIso k (steinberg k p m) e) - (associatedOriginJetIso k ι ρ P hP d hd)) ≪≫ - tensorPlaneOriginIso k (coordinateRepresentation k (steinberg k p m).ρ e) σN hN) -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.PiPlaneOrigin +import OAI.RepresentationTheory.RestrictedTilting.CoordinateTensor +import OAI.RepresentationTheory.RestrictedTilting.AssociatedPlaneJet + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory +open scoped TensorProduct +universe u +variable (k : Type u) [Field k] +variable {β : Type u} [Fintype β] [DecidableEq β] +variable {M : Type u} [AddCommGroup M] [Module k M] + [Module (MvPolynomial (Fin 2) k) M] [IsScalarTower k (MvPolynomial (Fin 2) k) M] + [Module.Finite k (M ⧸ planeJetRelation (M := M) k 1)] +variable (τ : Representation k (SL2 k) (β → k)) (σ : Representation k (SL2 k) M) + (hσ : PlaneCompatible k σ) + +noncomputable def tensorPlaneOriginIso : + FDRep.of τ ⊗ planeJetFD k σ hσ 1 ≅ + @planeJetFD k _ (β → M) _ _ _ _ (piPlaneOrigin_finite (β := β) (M := M) k) + (matrixTensorRepresentation τ σ) (matrixTensor_planeCompatible k τ σ hσ) 1 := by + letI := piPlaneOrigin_finite (β := β) (M := M) k + let C := coordinateTensorEquiv (β := β) (M := M ⧸ planeJetRelation (M := M) k 1) k + let E := piPlaneOriginEquiv (β := β) (M := M) k + let f : FDRep.of τ ⊗ planeJetFD k σ hσ 1 ⟶ + planeJetFD k (matrixTensorRepresentation τ σ) (matrixTensor_planeCompatible k τ σ hσ) 1 := + fdrepHom k (C.trans E.symm).toLinearMap (by + intro g v + apply E.injective + change E (E.symm (C ((τ.tprod (planeJetRep k σ hσ 1)) g v))) = + E (planeJetRep k (matrixTensorRepresentation τ σ) (matrixTensor_planeCompatible k τ σ hσ) + 1 g (E.symm (C v))) + rw [E.apply_symm_apply, piPlaneOriginEquiv_intertwines, E.apply_symm_apply] + exact coordinateTensorEquiv_intertwines k τ (planeJetRep k σ hσ 1) g v) + letI : IsIso f := fdrepHom_isIso_of_bijective k f (C.trans E.symm).bijective + exact asIso f + +variable [Infinite k] +variable (ι : Type u) [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) +variable (P : Matrix ι ι (Polynomial k)) +variable (hP : ∀ t : k, polynomialMatrixEval P t = LinearMap.toMatrix' (ρ (Multiplicative.ofAdd t))) +variable (d : ℕ) (hd : ∀ i j, (P i j).natDegree ≤ d) +local notation "N" => associatedSectionsSubmodule k ι ρ +local notation "σN" => associatedSectionsRepresentation k ι ρ +local notation "hN" => associatedSections_planeCompatible k ι ρ +variable [Module.Finite k ((associatedSectionsSubmodule k ι ρ) ⧸ + planeJetRelation (M := associatedSectionsSubmodule k ι ρ) k 1)] + +noncomputable def associatedOriginJetIso : + associatedOriginFD k ι ρ P hP d hd ≅ planeJetFD k σN hN 1 := by + let E : (associatedOriginRep k ι ρ).V ≃ₗ[k] N ⧸ planeJetRelation (M := N) k 1 := + Submodule.quotEquivOfEq _ _ (associated_planeJet_one k ι ρ).symm + let f : associatedOriginFD k ι ρ P hP d hd ⟶ planeJetFD k σN hN 1 := fdrepHom k E.toLinearMap (by + intro g v + obtain ⟨v,rfl⟩ := (associatedOriginRelations k ι ρ).mkQ_surjective v + rfl) + letI : IsIso f := fdrepHom_isIso_of_bijective k f E.bijective + exact asIso f + +variable (p : ℕ) [Fact p.Prime] [CharP k p] + +include hP hd in +lemma tensorAssociatedOrigin_tilting (m : ℕ) (hm : d < p^(m+1)) + (e : steinberg k p m ≃ₗ[k] (β → k)) : + IsTilting k (@planeJetFD k _ (β → N) _ _ _ _ (piPlaneOrigin_finite (β := β) (M := N) k) + (matrixTensorRepresentation (coordinateRepresentation k (steinberg k p m).ρ e) σN) + (matrixTensor_planeCompatible k _ σN hN) 1) := by + have h := associatedOrigin_tilting k p ι ρ P hP d hd m hm + exact h.of_iso k + ((MonoidalCategory.tensorIso (coordinateFDIso k (steinberg k p m) e) + (associatedOriginJetIso k ι ρ P hP d hd)) ≪≫ + tensorPlaneOriginIso k (coordinateRepresentation k (steinberg k p m).ρ e) σN hN) +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorWeights.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorWeights.lean index 06a26033c69be33fd4a43f219ec2ac5da769a8f1..bdbccc5caf003ae86b81b392ea49c124e249048f 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TensorWeights.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TensorWeights.lean @@ -1,61 +1,61 @@ -import OAI.RepresentationTheory.RestrictedTilting.TorusWeightProjection - -namespace OAI - -namespace FiberFunctorProof -open scoped TensorProduct BigOperators -universe u -variable {k : Type u} [Field k] [Infinite k] -variable {V W : Type u} [AddCommGroup V] [Module k V] [Module.Finite k V] - [AddCommGroup W] [Module k W] [Module.Finite k W] - - -lemma hasWeightsBetween_tensor (ρ : Representation k (SL2 k) V) - (σ : Representation k (SL2 k) W) (hρ : IsRational k ρ) (hσ : IsRational k σ) - (a b : ℕ) (hA : HasWeightsBetween ρ (-(a : ℤ)) a) - (hB : HasWeightsBetween σ (-(b : ℤ)) b) : - HasWeightsBetween (Representation.tprod ρ σ) (-((a+b : ℕ) : ℤ)) (a+b) := by - let τ := Representation.tprod ρ σ - have hτ := IsRational.tensor k ρ σ hρ hσ - intro n z hn hz - have hzero (v : V) (w : W) : torusWeightProjection τ hτ n (v ⊗ₜ[k] w) = 0 := by - obtain ⟨c, hc⟩ := rational_torus_integerExpansions k ρ hρ v - obtain ⟨d, hd⟩ := rational_torus_integerExpansions k σ hσ w - have hv : v = ∑ i ∈ c.support, c i := by - simpa [Finsupp.sum, integerCharacter] using hc 1 - have hw : w = ∑ i ∈ d.support, d i := by - simpa [Finsupp.sum, integerCharacter] using hd 1 - rw [hv, hw, TensorProduct.sum_tmul] - simp only [TensorProduct.tmul_sum, map_sum] - apply Finset.sum_eq_zero - intro i hi - apply Finset.sum_eq_zero - intro j hj - have hci : c i ≠ 0 := Finsupp.mem_support_iff.mp hi - have hdj : d j ≠ 0 := Finsupp.mem_support_iff.mp hj - have hciw := integer_coefficient_eigen k ρ v c hc i - have hdjw := integer_coefficient_eigen k σ w d hd j - have hiB : -(a : ℤ) ≤ i ∧ i ≤ a := by - constructor <;> by_contra h <;> apply hci - · exact hA i (c i) (Or.inl (by omega)) hciw - · exact hA i (c i) (Or.inr (by omega)) hciw - have hjB : -(b : ℤ) ≤ j ∧ j ≤ b := by - constructor <;> by_contra h <;> apply hdj - · exact hB j (d j) (Or.inl (by omega)) hdjw - · exact hB j (d j) (Or.inr (by omega)) hdjw - have hij : ∀ t, τ (diagonalTorus k t) (c i ⊗ₜ[k] d j) = - integerCharacter k (i+j) t • (c i ⊗ₜ[k] d j) := by - intro t - simp only [τ, Representation.tprod_apply, TensorProduct.map_tmul, hciw, hdjw, - TensorProduct.smul_tmul', TensorProduct.tmul_smul, smul_smul] - congr 1 - simp [integerCharacter, zpow_add, mul_comm] - rw [torusWeightProjection_eigen τ hτ n (i+j) _ hij, ite_eq_right (by omega)] - have hp (z : V ⊗[k] W) : torusWeightProjection τ hτ n z = 0 := by - induction z using TensorProduct.inductionOn with - | tmul v w => exact hzero v w - | add x y hx hy => simp only [map_add, hx, hy, add_zero] - simpa only [torusWeightProjection_eigen τ hτ n n z hz, ite_true] using hp z -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.TorusWeightProjection + +namespace OAI + +namespace FiberFunctorProof +open scoped TensorProduct BigOperators +universe u +variable {k : Type u} [Field k] [Infinite k] +variable {V W : Type u} [AddCommGroup V] [Module k V] [Module.Finite k V] + [AddCommGroup W] [Module k W] [Module.Finite k W] + + +lemma hasWeightsBetween_tensor (ρ : Representation k (SL2 k) V) + (σ : Representation k (SL2 k) W) (hρ : IsRational k ρ) (hσ : IsRational k σ) + (a b : ℕ) (hA : HasWeightsBetween ρ (-(a : ℤ)) a) + (hB : HasWeightsBetween σ (-(b : ℤ)) b) : + HasWeightsBetween (Representation.tprod ρ σ) (-((a+b : ℕ) : ℤ)) (a+b) := by + let τ := Representation.tprod ρ σ + have hτ := IsRational.tensor k ρ σ hρ hσ + intro n z hn hz + have hzero (v : V) (w : W) : torusWeightProjection τ hτ n (v ⊗ₜ[k] w) = 0 := by + obtain ⟨c, hc⟩ := rational_torus_integerExpansions k ρ hρ v + obtain ⟨d, hd⟩ := rational_torus_integerExpansions k σ hσ w + have hv : v = ∑ i ∈ c.support, c i := by + simpa [Finsupp.sum, integerCharacter] using hc 1 + have hw : w = ∑ i ∈ d.support, d i := by + simpa [Finsupp.sum, integerCharacter] using hd 1 + rw [hv, hw, TensorProduct.sum_tmul] + simp only [TensorProduct.tmul_sum, map_sum] + apply Finset.sum_eq_zero + intro i hi + apply Finset.sum_eq_zero + intro j hj + have hci : c i ≠ 0 := Finsupp.mem_support_iff.mp hi + have hdj : d j ≠ 0 := Finsupp.mem_support_iff.mp hj + have hciw := integer_coefficient_eigen k ρ v c hc i + have hdjw := integer_coefficient_eigen k σ w d hd j + have hiB : -(a : ℤ) ≤ i ∧ i ≤ a := by + constructor <;> by_contra h <;> apply hci + · exact hA i (c i) (Or.inl (by omega)) hciw + · exact hA i (c i) (Or.inr (by omega)) hciw + have hjB : -(b : ℤ) ≤ j ∧ j ≤ b := by + constructor <;> by_contra h <;> apply hdj + · exact hB j (d j) (Or.inl (by omega)) hdjw + · exact hB j (d j) (Or.inr (by omega)) hdjw + have hij : ∀ t, τ (diagonalTorus k t) (c i ⊗ₜ[k] d j) = + integerCharacter k (i+j) t • (c i ⊗ₜ[k] d j) := by + intro t + simp only [τ, Representation.tprod_apply, TensorProduct.map_tmul, hciw, hdjw, + TensorProduct.smul_tmul', TensorProduct.tmul_smul, smul_smul] + congr 1 + simp [integerCharacter, zpow_add, mul_comm] + rw [torusWeightProjection_eigen τ hτ n (i+j) _ hij, ite_eq_right (by omega)] + have hp (z : V ⊗[k] W) : torusWeightProjection τ hτ n z = 0 := by + induction z using TensorProduct.inductionOn with + | tmul v w => exact hzero v w + | add x y hx hy => simp only [map_add, hx, hy, add_zero] + simpa only [torusWeightProjection_eigen τ hτ n n z hz, ite_true] using hp z +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/ThetaTarget.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/ThetaTarget.lean index c9bcb6d549ab42c61c95cd90771bb9670a53538e..fd938f078e51b2e50d6bdfc87c5fe38f93239f58 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/ThetaTarget.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/ThetaTarget.lean @@ -1,326 +1,326 @@ -import Mathlib - -namespace OAI - - - -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof.ThetaTarget -section - -universe u - -section PolynomialAction -variable {k : Type u} [CommRing k] {ι : Type*} [Fintype ι] - - -noncomputable def linearChange (A : Matrix ι ι k) : - MvPolynomial ι k →ₐ[k] MvPolynomial ι k := - MvPolynomial.aeval (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) - -@[simp] lemma linearChange_X (A : Matrix ι ι k) (i : ι) : - linearChange A (MvPolynomial.X i) = - ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j := by - simp [linearChange] - -@[simp] lemma linearChange_C (A : Matrix ι ι k) (x : k) : - linearChange A (MvPolynomial.C x) = MvPolynomial.C x := by - simp [linearChange] - -variable [DecidableEq ι] - -@[simp] lemma linearChange_one : linearChange (1 : Matrix ι ι k) = AlgHom.id k _ := by - ext i : 1 - simp [linearChange, Matrix.one_apply] - -omit [DecidableEq ι] in -lemma linearChange_mul (A B : Matrix ι ι k) : - linearChange (A * B) = (linearChange A).comp (linearChange B) := by - ext i : 1 - simp only [AlgHom.comp_apply, linearChange_X, map_sum, map_mul, linearChange_C, - Matrix.mul_apply, Finset.sum_mul, Finset.mul_sum] - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro j hj - apply Finset.sum_congr rfl - intro l hl - ring - -omit [DecidableEq ι] in -lemma linearChange_homogeneous (A : Matrix ι ι k) {f : MvPolynomial ι k} {n : ℕ} - (hf : f.IsHomogeneous n) : (linearChange A f).IsHomogeneous n := by - change (MvPolynomial.eval₂ MvPolynomial.C - (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) f).IsHomogeneous n - simpa only [one_mul] using - hf.eval₂ MvPolynomial.C - (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) - (fun x => MvPolynomial.isHomogeneous_C ι x) - (fun i => MvPolynomial.IsHomogeneous.sum _ _ _ - (fun j _ => (MvPolynomial.isHomogeneous_X k j).C_mul (A j i))) - -noncomputable def homogeneousRepresentation (n : ℕ) : - Representation k (Matrix ι ι k) (MvPolynomial.homogeneousSubmodule ι k n) where - toFun A := (linearChange A).toLinearMap.restrict (fun _ hf => linearChange_homogeneous A hf) - map_one' := by - ext f : 1 - apply Subtype.ext - change linearChange 1 f.val = f.val - rw [linearChange_one] - rfl - map_mul' A B := by - ext f : 1 - apply Subtype.ext - change linearChange (A * B) f.val = linearChange A (linearChange B f.val) - rw [linearChange_mul] - rfl - -end PolynomialAction - -variable (k : Type u) [Field k] - -abbrev SL2 := Matrix.SpecialLinearGroup (Fin 2) k - - -def IsRational {M : Type u} [AddCommGroup M] [Module k M] - (ρ : Representation k (SL2 k) M) : Prop := - ∀ (v : M) (l : M →ₗ[k] k), - ∃ P : MvPolynomial (Fin 2 × Fin 2) k, - ∀ g : SL2 k, l (ρ g v) = MvPolynomial.eval (fun ij => g ij.1 ij.2) P - - -noncomputable def dualMatrix : SL2 k →* Matrix (Fin 2) (Fin 2) k where - toFun g := ((g⁻¹ : SL2 k) : Matrix (Fin 2) (Fin 2) k).transpose - map_one' := by simp - map_mul' g h := by - simp [mul_inv_rev, Matrix.SpecialLinearGroup.coe_mul, Matrix.transpose_mul] - -instance homogeneous_finite (n : ℕ) : - Module.Finite k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) := - Module.Finite.of_fg (MvPolynomial.homogeneousSubmodule_fg (Fin 2) k n) - - -noncomputable def costandard (n : ℕ) : FDRep k (SL2 k) := - FDRep.of ((homogeneousRepresentation n).comp (dualMatrix k)) - - -inductive HasGoodFiltration : FDRep k (SL2 k) → Prop - | zero (V) (hV : IsZero V) : HasGoodFiltration V - | step {A B} (n : ℕ) (f : A ⟶ B) (g : B ⟶ costandard k n) - (w : f ≫ g = 0) (hS : (ShortComplex.mk f g w).ShortExact) - (hA : HasGoodFiltration A) : HasGoodFiltration B - - - -def IsTilting (V : FDRep k (SL2 k)) : Prop := - IsRational k V.ρ ∧ HasGoodFiltration k V ∧ HasGoodFiltration k Vᘁ - - -noncomputable def steinberg (p m : ℕ) : FDRep k (SL2 k) := - costandard k (p ^ m - 1) - - -def unipotent (t : k) : SL2 k := - ⟨!![1, t; 0, 1], by simp [Matrix.det_fin_two]⟩ - -lemma unipotent_zero : unipotent k 0 = 1 := by - apply Subtype.ext - ext i j - fin_cases i <;> fin_cases j <;> simp [unipotent] - -lemma unipotent_add (t s : k) : unipotent k (t + s) = unipotent k t * unipotent k s := by - apply Subtype.ext - change !![1, t + s; 0, 1] = !![1, t; 0, 1] * !![1, s; 0, 1] - ext i j - fin_cases i <;> fin_cases j <;> - simp [Matrix.mul_apply, Fin.sum_univ_two, add_comm] - - -def elementaryEmbedding (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : - Multiplicative (Fin r → ZMod p) →* SL2 k where - toFun a := unipotent k (l a.toAdd) - map_one' := by simp [unipotent_zero] - map_mul' a b := by simp [unipotent_add] - -noncomputable def restrictElementary (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : - FDRep k (SL2 k) ⥤ FDRep k (Multiplicative (Fin r → ZMod p)) := - Action.res (FGModuleCat k) (elementaryEmbedding k p r l) - -end - - - -section - -universe u - - -structure FiniteSymmetricTensorCategory (k : Type u) [Field k] where - Obj : Type (u + 1) - [category : Category.{u} Obj] - [abelian : Abelian Obj] - [linear : Linear k Obj] - [monoidal : MonoidalCategory Obj] - [monoidalPreadditive : MonoidalPreadditive Obj] - [monoidalLinear : MonoidalLinear k Obj] - [symmetric : SymmetricCategory Obj] - [rigid : RigidCategory Obj] - essentiallySmall : EssentiallySmall.{u} Obj - finiteHom : ∀ X Y : Obj, Module.Finite k (X ⟶ Y) - artinian : ∀ X : Obj, IsArtinianObject X - noetherian : ∀ X : Obj, IsNoetherianObject X - finiteSimple : ∃ (m : ℕ) (S : Fin m → Obj), - (∀ i, Simple (S i)) ∧ ∀ X : Obj, Simple X → ∃ i, Nonempty (S i ≅ X) - enoughProjectives : EnoughProjectives Obj - unitScalars : Function.Bijective (algebraMap k (End (𝟙_ Obj))) - tensorLeftExact : ∀ X : Obj, - PreservesFiniteLimits (tensorLeft X) ∧ PreservesFiniteColimits (tensorLeft X) - tensorRightExact : ∀ X : Obj, - PreservesFiniteLimits (tensorRight X) ∧ PreservesFiniteColimits (tensorRight X) - -attribute [instance] FiniteSymmetricTensorCategory.category - FiniteSymmetricTensorCategory.abelian FiniteSymmetricTensorCategory.linear - FiniteSymmetricTensorCategory.monoidal FiniteSymmetricTensorCategory.monoidalPreadditive - FiniteSymmetricTensorCategory.monoidalLinear FiniteSymmetricTensorCategory.symmetric - FiniteSymmetricTensorCategory.rigid - - -abbrev Tilting (k : Type u) [Field k] := - ObjectProperty.FullSubcategory (IsTilting k) - -abbrev tiltingInclusion (k : Type u) [Field k] : Tilting k ⥤ FDRep k (SL2 k) := - ObjectProperty.ι (IsTilting k) - - - -class TiltingTensorStructure (k : Type u) [Field k] where - [monoidal : MonoidalCategory (Tilting k)] - [monoidalPreadditive : MonoidalPreadditive (Tilting k)] - [monoidalLinear : MonoidalLinear k (Tilting k)] - [symmetric : SymmetricCategory (Tilting k)] - [rigid : RigidCategory (Tilting k)] - [inclusionBraided : (tiltingInclusion k).Braided] - -attribute [instance_reducible, instance] TiltingTensorStructure.monoidal - TiltingTensorStructure.symmetric TiltingTensorStructure.rigid - TiltingTensorStructure.inclusionBraided -attribute [instance] TiltingTensorStructure.monoidalPreadditive - TiltingTensorStructure.monoidalLinear - - - -noncomputable def steinbergIdeal (k : Type u) [Field k] (p n : ℕ) (A B : Tilting k) : - Submodule k (A ⟶ B) := - Submodule.span k {f | ∃ X : Tilting k, - ∃ a : A.obj ⟶ steinberg k p n ⊗ X.obj, - ∃ b : steinberg k p n ⊗ X.obj ⟶ B.obj, f.hom = a ≫ b} - - -structure TiltingFunctor (k : Type u) [Field k] [TiltingTensorStructure k] - (D : FiniteSymmetricTensorCategory k) where - toFunctor : Tilting k ⥤ D.Obj - [additive : toFunctor.Additive] - [linear : toFunctor.Linear k] - [braided : toFunctor.Braided] - -attribute [instance] TiltingFunctor.additive TiltingFunctor.linear TiltingFunctor.braided - - -structure ExactTensorFunctor {k : Type u} [Field k] - (C D : FiniteSymmetricTensorCategory k) where - toFunctor : C.Obj ⥤ D.Obj - [additive : toFunctor.Additive] - [linear : toFunctor.Linear k] - [braided : toFunctor.Braided] - exact : ∀ S : ShortComplex C.Obj, S.ShortExact → (S.map toFunctor).ShortExact - -attribute [instance] ExactTensorFunctor.additive ExactTensorFunctor.linear - ExactTensorFunctor.braided - - -structure FiberFunctor {k : Type u} [Field k] - (C D : FiniteSymmetricTensorCategory k) extends ExactTensorFunctor C D where - faithful : toFunctor.Faithful - - - -def MonoidallyIsomorphic {C D : Type*} [Category C] [Category D] - [MonoidalCategory C] [MonoidalCategory D] - (F G : C ⥤ D) [F.Monoidal] [G.Monoidal] : Prop := - ∃ e : F ≅ G, e.hom.IsMonoidal - - -def HasSteinbergKernel (k : Type u) [Field k] [TiltingTensorStructure k] - (p n : ℕ) {D : FiniteSymmetricTensorCategory k} (F : TiltingFunctor k D) : Prop := - ∀ (A B : Tilting k) (f : A ⟶ B), F.toFunctor.map f = 0 ↔ f ∈ steinbergIdeal k p n A B - - - -structure VerlindePresentation (k : Type u) [Field k] [TiltingTensorStructure k] - (p n : ℕ) (W : FiniteSymmetricTensorCategory k) where - sigma : TiltingFunctor k W - full : sigma.toFunctor.Full - kernel : HasSteinbergKernel k p n sigma - extend : ∀ (D : FiniteSymmetricTensorCategory k) (F : TiltingFunctor k D), - HasSteinbergKernel k p n F → ∃ H : ExactTensorFunctor W D, - MonoidallyIsomorphic (sigma.toFunctor ⋙ H.toFunctor) F.toFunctor - unique : ∀ (D : FiniteSymmetricTensorCategory k) (F G : ExactTensorFunctor W D), - MonoidallyIsomorphic (sigma.toFunctor ⋙ F.toFunctor) (sigma.toFunctor ⋙ G.toFunctor) → - MonoidallyIsomorphic F.toFunctor G.toFunctor - - - -def MainTheorem : Prop := - ∀ (k : Type u) [Field k] [IsAlgClosed k] - (p : ℕ) [Fact p.Prime] [CharP k p] (C : FiniteSymmetricTensorCategory k), - ∃ s : TiltingTensorStructure k, letI := s - ∃ n : ℕ, 1 ≤ n ∧ ∃ W : FiniteSymmetricTensorCategory k, - Nonempty (VerlindePresentation k p n W) ∧ Nonempty (FiberFunctor C W) - -end - - - -open CategoryTheory -universe u -noncomputable instance elementaryRestrictionMonoidal - (k : Type u) [Field k] (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : - (restrictElementary k p r l).Monoidal := - Functor.CoreMonoidal.toMonoidal { - εIso := Iso.refl _ - μIso := fun _ _ => Iso.refl _ - associativity := by - intro X Y Z - simp only [Iso.refl_hom] - erw [MonoidalCategory.id_whiskerRight, MonoidalCategory.whiskerLeft_id, - Category.id_comp, Category.id_comp] - left_unitality := by - intro X - simp only [Iso.refl_hom] - erw [MonoidalCategory.id_whiskerRight, Category.id_comp, Category.id_comp] - rfl - right_unitality := by - intro X - simp only [Iso.refl_hom] - erw [MonoidalCategory.whiskerLeft_id, Category.id_comp, Category.id_comp] - rfl } - - - -def HigherThetaConstruction : Prop := - ∀ (k : Type u) [Field k] [IsAlgClosed k] - (p : ℕ) [Fact p.Prime] [CharP k p] (r : ℕ), 1 ≤ r → - ∀ (l : (Fin r → ZMod p) →+ k), Function.Injective l → - ∃ s : TiltingTensorStructure k, letI := s - ∃ W : FiniteSymmetricTensorCategory k, - ∃ V : VerlindePresentation k p r W, - ∃ Θ : FDRep k (Multiplicative (Fin r → ZMod p)) ⥤ W.Obj, - ∃ _ : Θ.Additive, ∃ _ : Θ.Linear k, ∃ hΘ : Θ.Braided, - letI := hΘ - MonoidallyIsomorphic - (tiltingInclusion k ⋙ restrictElementary k p r l ⋙ Θ) - V.sigma.toFunctor -end FiberFunctorProof.ThetaTarget - -end OAI +import Mathlib + +namespace OAI + + + +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof.ThetaTarget +section + +universe u + +section PolynomialAction +variable {k : Type u} [CommRing k] {ι : Type*} [Fintype ι] + + +noncomputable def linearChange (A : Matrix ι ι k) : + MvPolynomial ι k →ₐ[k] MvPolynomial ι k := + MvPolynomial.aeval (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) + +@[simp] lemma linearChange_X (A : Matrix ι ι k) (i : ι) : + linearChange A (MvPolynomial.X i) = + ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j := by + simp [linearChange] + +@[simp] lemma linearChange_C (A : Matrix ι ι k) (x : k) : + linearChange A (MvPolynomial.C x) = MvPolynomial.C x := by + simp [linearChange] + +variable [DecidableEq ι] + +@[simp] lemma linearChange_one : linearChange (1 : Matrix ι ι k) = AlgHom.id k _ := by + ext i : 1 + simp [linearChange, Matrix.one_apply] + +omit [DecidableEq ι] in +lemma linearChange_mul (A B : Matrix ι ι k) : + linearChange (A * B) = (linearChange A).comp (linearChange B) := by + ext i : 1 + simp only [AlgHom.comp_apply, linearChange_X, map_sum, map_mul, linearChange_C, + Matrix.mul_apply, Finset.sum_mul, Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro j hj + apply Finset.sum_congr rfl + intro l hl + ring + +omit [DecidableEq ι] in +lemma linearChange_homogeneous (A : Matrix ι ι k) {f : MvPolynomial ι k} {n : ℕ} + (hf : f.IsHomogeneous n) : (linearChange A f).IsHomogeneous n := by + change (MvPolynomial.eval₂ MvPolynomial.C + (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) f).IsHomogeneous n + simpa only [one_mul] using + hf.eval₂ MvPolynomial.C + (fun i => ∑ j, MvPolynomial.C (A j i) * MvPolynomial.X j) + (fun x => MvPolynomial.isHomogeneous_C ι x) + (fun i => MvPolynomial.IsHomogeneous.sum _ _ _ + (fun j _ => (MvPolynomial.isHomogeneous_X k j).C_mul (A j i))) + +noncomputable def homogeneousRepresentation (n : ℕ) : + Representation k (Matrix ι ι k) (MvPolynomial.homogeneousSubmodule ι k n) where + toFun A := (linearChange A).toLinearMap.restrict (fun _ hf => linearChange_homogeneous A hf) + map_one' := by + ext f : 1 + apply Subtype.ext + change linearChange 1 f.val = f.val + rw [linearChange_one] + rfl + map_mul' A B := by + ext f : 1 + apply Subtype.ext + change linearChange (A * B) f.val = linearChange A (linearChange B f.val) + rw [linearChange_mul] + rfl + +end PolynomialAction + +variable (k : Type u) [Field k] + +abbrev SL2 := Matrix.SpecialLinearGroup (Fin 2) k + + +def IsRational {M : Type u} [AddCommGroup M] [Module k M] + (ρ : Representation k (SL2 k) M) : Prop := + ∀ (v : M) (l : M →ₗ[k] k), + ∃ P : MvPolynomial (Fin 2 × Fin 2) k, + ∀ g : SL2 k, l (ρ g v) = MvPolynomial.eval (fun ij => g ij.1 ij.2) P + + +noncomputable def dualMatrix : SL2 k →* Matrix (Fin 2) (Fin 2) k where + toFun g := ((g⁻¹ : SL2 k) : Matrix (Fin 2) (Fin 2) k).transpose + map_one' := by simp + map_mul' g h := by + simp [mul_inv_rev, Matrix.SpecialLinearGroup.coe_mul, Matrix.transpose_mul] + +instance homogeneous_finite (n : ℕ) : + Module.Finite k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) := + Module.Finite.of_fg (MvPolynomial.homogeneousSubmodule_fg (Fin 2) k n) + + +noncomputable def costandard (n : ℕ) : FDRep k (SL2 k) := + FDRep.of ((homogeneousRepresentation n).comp (dualMatrix k)) + + +inductive HasGoodFiltration : FDRep k (SL2 k) → Prop + | zero (V) (hV : IsZero V) : HasGoodFiltration V + | step {A B} (n : ℕ) (f : A ⟶ B) (g : B ⟶ costandard k n) + (w : f ≫ g = 0) (hS : (ShortComplex.mk f g w).ShortExact) + (hA : HasGoodFiltration A) : HasGoodFiltration B + + + +def IsTilting (V : FDRep k (SL2 k)) : Prop := + IsRational k V.ρ ∧ HasGoodFiltration k V ∧ HasGoodFiltration k Vᘁ + + +noncomputable def steinberg (p m : ℕ) : FDRep k (SL2 k) := + costandard k (p ^ m - 1) + + +def unipotent (t : k) : SL2 k := + ⟨!![1, t; 0, 1], by simp [Matrix.det_fin_two]⟩ + +lemma unipotent_zero : unipotent k 0 = 1 := by + apply Subtype.ext + ext i j + fin_cases i <;> fin_cases j <;> simp [unipotent] + +lemma unipotent_add (t s : k) : unipotent k (t + s) = unipotent k t * unipotent k s := by + apply Subtype.ext + change !![1, t + s; 0, 1] = !![1, t; 0, 1] * !![1, s; 0, 1] + ext i j + fin_cases i <;> fin_cases j <;> + simp [Matrix.mul_apply, Fin.sum_univ_two, add_comm] + + +def elementaryEmbedding (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : + Multiplicative (Fin r → ZMod p) →* SL2 k where + toFun a := unipotent k (l a.toAdd) + map_one' := by simp [unipotent_zero] + map_mul' a b := by simp [unipotent_add] + +noncomputable def restrictElementary (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : + FDRep k (SL2 k) ⥤ FDRep k (Multiplicative (Fin r → ZMod p)) := + Action.res (FGModuleCat k) (elementaryEmbedding k p r l) + +end + + + +section + +universe u + + +structure FiniteSymmetricTensorCategory (k : Type u) [Field k] where + Obj : Type (u + 1) + [category : Category.{u} Obj] + [abelian : Abelian Obj] + [linear : Linear k Obj] + [monoidal : MonoidalCategory Obj] + [monoidalPreadditive : MonoidalPreadditive Obj] + [monoidalLinear : MonoidalLinear k Obj] + [symmetric : SymmetricCategory Obj] + [rigid : RigidCategory Obj] + essentiallySmall : EssentiallySmall.{u} Obj + finiteHom : ∀ X Y : Obj, Module.Finite k (X ⟶ Y) + artinian : ∀ X : Obj, IsArtinianObject X + noetherian : ∀ X : Obj, IsNoetherianObject X + finiteSimple : ∃ (m : ℕ) (S : Fin m → Obj), + (∀ i, Simple (S i)) ∧ ∀ X : Obj, Simple X → ∃ i, Nonempty (S i ≅ X) + enoughProjectives : EnoughProjectives Obj + unitScalars : Function.Bijective (algebraMap k (End (𝟙_ Obj))) + tensorLeftExact : ∀ X : Obj, + PreservesFiniteLimits (tensorLeft X) ∧ PreservesFiniteColimits (tensorLeft X) + tensorRightExact : ∀ X : Obj, + PreservesFiniteLimits (tensorRight X) ∧ PreservesFiniteColimits (tensorRight X) + +attribute [instance] FiniteSymmetricTensorCategory.category + FiniteSymmetricTensorCategory.abelian FiniteSymmetricTensorCategory.linear + FiniteSymmetricTensorCategory.monoidal FiniteSymmetricTensorCategory.monoidalPreadditive + FiniteSymmetricTensorCategory.monoidalLinear FiniteSymmetricTensorCategory.symmetric + FiniteSymmetricTensorCategory.rigid + + +abbrev Tilting (k : Type u) [Field k] := + ObjectProperty.FullSubcategory (IsTilting k) + +abbrev tiltingInclusion (k : Type u) [Field k] : Tilting k ⥤ FDRep k (SL2 k) := + ObjectProperty.ι (IsTilting k) + + + +class TiltingTensorStructure (k : Type u) [Field k] where + [monoidal : MonoidalCategory (Tilting k)] + [monoidalPreadditive : MonoidalPreadditive (Tilting k)] + [monoidalLinear : MonoidalLinear k (Tilting k)] + [symmetric : SymmetricCategory (Tilting k)] + [rigid : RigidCategory (Tilting k)] + [inclusionBraided : (tiltingInclusion k).Braided] + +attribute [instance_reducible, instance] TiltingTensorStructure.monoidal + TiltingTensorStructure.symmetric TiltingTensorStructure.rigid + TiltingTensorStructure.inclusionBraided +attribute [instance] TiltingTensorStructure.monoidalPreadditive + TiltingTensorStructure.monoidalLinear + + + +noncomputable def steinbergIdeal (k : Type u) [Field k] (p n : ℕ) (A B : Tilting k) : + Submodule k (A ⟶ B) := + Submodule.span k {f | ∃ X : Tilting k, + ∃ a : A.obj ⟶ steinberg k p n ⊗ X.obj, + ∃ b : steinberg k p n ⊗ X.obj ⟶ B.obj, f.hom = a ≫ b} + + +structure TiltingFunctor (k : Type u) [Field k] [TiltingTensorStructure k] + (D : FiniteSymmetricTensorCategory k) where + toFunctor : Tilting k ⥤ D.Obj + [additive : toFunctor.Additive] + [linear : toFunctor.Linear k] + [braided : toFunctor.Braided] + +attribute [instance] TiltingFunctor.additive TiltingFunctor.linear TiltingFunctor.braided + + +structure ExactTensorFunctor {k : Type u} [Field k] + (C D : FiniteSymmetricTensorCategory k) where + toFunctor : C.Obj ⥤ D.Obj + [additive : toFunctor.Additive] + [linear : toFunctor.Linear k] + [braided : toFunctor.Braided] + exact : ∀ S : ShortComplex C.Obj, S.ShortExact → (S.map toFunctor).ShortExact + +attribute [instance] ExactTensorFunctor.additive ExactTensorFunctor.linear + ExactTensorFunctor.braided + + +structure FiberFunctor {k : Type u} [Field k] + (C D : FiniteSymmetricTensorCategory k) extends ExactTensorFunctor C D where + faithful : toFunctor.Faithful + + + +def MonoidallyIsomorphic {C D : Type*} [Category C] [Category D] + [MonoidalCategory C] [MonoidalCategory D] + (F G : C ⥤ D) [F.Monoidal] [G.Monoidal] : Prop := + ∃ e : F ≅ G, e.hom.IsMonoidal + + +def HasSteinbergKernel (k : Type u) [Field k] [TiltingTensorStructure k] + (p n : ℕ) {D : FiniteSymmetricTensorCategory k} (F : TiltingFunctor k D) : Prop := + ∀ (A B : Tilting k) (f : A ⟶ B), F.toFunctor.map f = 0 ↔ f ∈ steinbergIdeal k p n A B + + + +structure VerlindePresentation (k : Type u) [Field k] [TiltingTensorStructure k] + (p n : ℕ) (W : FiniteSymmetricTensorCategory k) where + sigma : TiltingFunctor k W + full : sigma.toFunctor.Full + kernel : HasSteinbergKernel k p n sigma + extend : ∀ (D : FiniteSymmetricTensorCategory k) (F : TiltingFunctor k D), + HasSteinbergKernel k p n F → ∃ H : ExactTensorFunctor W D, + MonoidallyIsomorphic (sigma.toFunctor ⋙ H.toFunctor) F.toFunctor + unique : ∀ (D : FiniteSymmetricTensorCategory k) (F G : ExactTensorFunctor W D), + MonoidallyIsomorphic (sigma.toFunctor ⋙ F.toFunctor) (sigma.toFunctor ⋙ G.toFunctor) → + MonoidallyIsomorphic F.toFunctor G.toFunctor + + + +def MainTheorem : Prop := + ∀ (k : Type u) [Field k] [IsAlgClosed k] + (p : ℕ) [Fact p.Prime] [CharP k p] (C : FiniteSymmetricTensorCategory k), + ∃ s : TiltingTensorStructure k, letI := s + ∃ n : ℕ, 1 ≤ n ∧ ∃ W : FiniteSymmetricTensorCategory k, + Nonempty (VerlindePresentation k p n W) ∧ Nonempty (FiberFunctor C W) + +end + + + +open CategoryTheory +universe u +noncomputable instance elementaryRestrictionMonoidal + (k : Type u) [Field k] (p r : ℕ) (l : (Fin r → ZMod p) →+ k) : + (restrictElementary k p r l).Monoidal := + Functor.CoreMonoidal.toMonoidal { + εIso := Iso.refl _ + μIso := fun _ _ => Iso.refl _ + associativity := by + intro X Y Z + simp only [Iso.refl_hom] + erw [MonoidalCategory.id_whiskerRight, MonoidalCategory.whiskerLeft_id, + Category.id_comp, Category.id_comp] + left_unitality := by + intro X + simp only [Iso.refl_hom] + erw [MonoidalCategory.id_whiskerRight, Category.id_comp, Category.id_comp] + rfl + right_unitality := by + intro X + simp only [Iso.refl_hom] + erw [MonoidalCategory.whiskerLeft_id, Category.id_comp, Category.id_comp] + rfl } + + + +def HigherThetaConstruction : Prop := + ∀ (k : Type u) [Field k] [IsAlgClosed k] + (p : ℕ) [Fact p.Prime] [CharP k p] (r : ℕ), 1 ≤ r → + ∀ (l : (Fin r → ZMod p) →+ k), Function.Injective l → + ∃ s : TiltingTensorStructure k, letI := s + ∃ W : FiniteSymmetricTensorCategory k, + ∃ V : VerlindePresentation k p r W, + ∃ Θ : FDRep k (Multiplicative (Fin r → ZMod p)) ⥤ W.Obj, + ∃ _ : Θ.Additive, ∃ _ : Θ.Linear k, ∃ hΘ : Θ.Braided, + letI := hΘ + MonoidallyIsomorphic + (tiltingInclusion k ⋙ restrictElementary k p r l ⋙ Θ) + V.sigma.toFunctor +end FiberFunctorProof.ThetaTarget + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TiltingBounds.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TiltingBounds.lean index f1153c5a30f44dc970965abf440a3ea56f207d22..db521e78bbda77e9d9f85f02b2da02cfb489cc1b 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TiltingBounds.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TiltingBounds.lean @@ -1,506 +1,506 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.SimpleModules -import OAI.RepresentationTheory.RestrictedTilting.BinarySequences - -namespace OAI - -/-! Highest weights, irreducible representations and bounded-weight tilting. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (p : ℕ) [Fact p.Prime] [CharP k p] - -noncomputable def steinbergStepIso (m : ℕ) : - costandard k (p-1) ⊗ (frobeniusTwist k p).obj (steinberg k p m) ≅ - steinberg k p (m+1) := by - have hp : 0 < p := (Fact.out : p.Prime).pos - have hm : 0 < p^m := pow_pos hp m - have he : p-1+p*(p^m-1) = p^(m+1)-1 := by - rw [pow_succ] - have hpM : 0 < p^m*p := mul_pos hm hp - nlinarith [Nat.sub_add_cancel hp, Nat.sub_add_cancel hm, Nat.sub_add_cancel hpM] - exact frobeniusCostandardIso k p (p^m-1) ≪≫ - eqToIso (congrArg (costandard k) he) - -omit [Infinite k] in -noncomputable def frobeniusTensorIso (A B : FDRep k (SL2 k)) : - (frobeniusTwist k p).obj (A ⊗ B) ≅ - (frobeniusTwist k p).obj A ⊗ (frobeniusTwist k p).obj B := Iso.refl _ - - - -theorem steinberg_tensor_simple_tilting (m h : ℕ) (hh : h < p^(m+1)) : - IsTilting k (steinberg k p m ⊗ simpleSL2 k h) := by - induction m generalizing h with - | zero => - have hh' : h < p := by simpa using hh - obtain ⟨e⟩ := simpleSL2_eq_costandard_of_choose k h - (fun i => choose_cast_ne_zero_of_lt_char k p hh' (Nat.le_of_lt_succ i.isLt)) - exact (steinberg_tilting k p 0).tensor k ((small_costandard_tilting k p h hh').of_iso k e.symm) - | succ m ih => - have hp : 0 < p := (Fact.out : p.Prime).pos - have ha : h%p < p := Nat.mod_lt _ hp - have hb : h/p < p^(m+1) := by - apply (Nat.div_lt_iff_lt_mul hp).mpr - simpa only [pow_succ] using hh - have ht := (ih (h/p) hb).steinberg_frobenius k p - have hS : IsTilting k (costandard k (h%p) ⊗ - (costandard k (p-1) ⊗ - ((frobeniusTwist k p).obj (steinberg k p m) ⊗ - (frobeniusTwist k p).obj (simpleSL2 k (h/p))))) := - (small_costandard_tilting k p (h%p) ha).tensor k - (ht.of_iso k (tensorIso (Iso.refl _) (frobeniusTensorIso k p _ _))) - let A := costandard k (h%p) - let B := costandard k (p-1) - let C := (frobeniusTwist k p).obj (steinberg k p m) - let D := (frobeniusTwist k p).obj (simpleSL2 k (h/p)) - let swap : (B ⊗ A) ⊗ (C ⊗ D) ≅ (B ⊗ C) ⊗ (A ⊗ D) := - { hom := tensorμ B A C D - inv := tensorδ B A C D - hom_inv_id := tensorμ_tensorδ B A C D - inv_hom_id := tensorδ_tensorμ B A C D } - let eL : A ⊗ D ≅ simpleSL2 k h := - simpleDigitIso k p (h%p) (h/p) ha ≪≫ - eqToIso (congrArg (simpleSL2 k) (Nat.mod_add_div h p)) - let e : A ⊗ (B ⊗ (C ⊗ D)) ≅ steinberg k p (m+1) ⊗ simpleSL2 k h := - (α_ A B (C ⊗ D)).symm ≪≫ tensorIso (β_ A B) (Iso.refl _) ≪≫ swap ≪≫ - tensorIso (steinbergStepIso k p m) eL - exact hS.of_iso k e -end - -section -universe u -variable (k : Type u) [Field k] -noncomputable def weylReflection : SL2 k := - ⟨!![0, -1; 1, 0], by simp [Matrix.det_fin_two]⟩ - -lemma diagonalTorus_weylReflection (a : kˣ) : - diagonalTorus k a * weylReflection k = weylReflection k * diagonalTorus k a⁻¹ := by - apply Subtype.ext - change !![(a : k),0;0,(↑a⁻¹ : k)] * !![0,-1;1,0] = - !![0,-1;1,0] * !![(↑a⁻¹ : k),0;0,(↑(a⁻¹)⁻¹ : k)] - ext i j - fin_cases i <;> fin_cases j <;> simp [Matrix.mul_apply, Fin.sum_univ_two] - -lemma reflected_weight {V : Type*} [AddCommGroup V] [Module k V] - (σ : Representation k (SL2 k) V) (n : ℤ) (v : V) - (hv : ∀ a : kˣ, σ (diagonalTorus k a) v = integerCharacter k n a • v) : - ∀ a : kˣ, σ (diagonalTorus k a) (σ (weylReflection k) v) = - integerCharacter k (-n) a • σ (weylReflection k) v := by - intro a - rw [← Module.End.mul_apply, ← map_mul, diagonalTorus_weylReflection, map_mul, - Module.End.mul_apply, hv, map_smul] - congr 1 - simp [integerCharacter, zpow_neg] - -lemma weights_between_of_upper {V : Type*} [AddCommGroup V] [Module k V] - (σ : Representation k (SL2 k) V) (d : ℤ) - (hσ : ∀ (n : ℤ), d < n → ∀ v : V, - (∀ a, σ (diagonalTorus k a) v = integerCharacter k n a • v) → v = 0) : - HasWeightsBetween σ (-d) d := by - intro n v hn hv - rcases hn with hn | hn - · have hz := hσ (-n) (by omega) (σ (weylReflection k) v) (reflected_weight k σ n v hv) - exact (σ.apply_bijective (weylReflection k)).1 (hz.trans (map_zero _).symm) - · exact hσ n hn v hv - -end - -section -universe u -variable (k : Type u) [Field k] [Infinite k] - -lemma integer_coefficient_eigen {M : Type u} [AddCommGroup M] [Module k M] - (ρ : Representation k (SL2 k) M) (v : M) (c : ℤ →₀ M) - (hc : ∀ a, ρ (diagonalTorus k a) v = c.sum (fun n x => integerCharacter k n a • x)) - (n : ℤ) (a : kˣ) : - ρ (diagonalTorus k a) (c n) = integerCharacter k n a • c n := by - let e : ℤ ↪ (kˣ →* k) := ⟨integerCharacter k, integerCharacter_injective k⟩ - have he : ∀ a, (ρ.comp (diagonalTorus k)) a v = - (c.embDomain e).sum (fun χ x => χ a • x) := by - intro a - rw [Finsupp.sum_embDomain] - exact hc a - have h := character_coefficient_eigen (ρ.comp (diagonalTorus k)) v - (c.embDomain e) he (e n) a - rw [Finsupp.embDomain_apply_self] at h - exact h - - - -lemma exists_highest_in_bound {M : Type u} [AddCommGroup M] [Module k M] - [Module.Finite k M] [Nontrivial M] (ρ : Representation k (SL2 k) M) - (hρ : IsRational k ρ) (d : ℕ) (hd : HasWeightsBetween ρ (-(d : ℤ)) d) : - ∃ n : ℕ, n ≤ d ∧ HasWeightsBetween ρ (-(n : ℤ)) n ∧ - ∃ v : M, v ≠ 0 ∧ ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v := by - classical - let S := (Finset.Icc (-(d : ℤ)) d).filter (fun n => - ∃ v : M, v ≠ 0 ∧ ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) - have hmem {n : ℤ} {v : M} (hv : v ≠ 0) - (hw : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) : n ∈ S := by - have hn : -(d : ℤ) ≤ n ∧ n ≤ d := by - constructor <;> by_contra h - · exact hv (hd n v (Or.inl (lt_of_not_ge h)) hw) - · exact hv (hd n v (Or.inr (lt_of_not_ge h)) hw) - exact Finset.mem_filter.mpr ⟨Finset.mem_Icc.mpr hn, v, hv, hw⟩ - have hS : S.Nonempty := by - obtain ⟨v,hv⟩ := exists_ne (0 : M) - obtain ⟨c,hc⟩ := rational_torus_integerExpansions k ρ hρ v - have hc0 : c ≠ 0 := by - intro h - have := hc 1 - simp only [h,Finsupp.sum_zero_index,map_one,Module.End.one_apply] at this - exact hv this - obtain ⟨n,hn⟩ := Finsupp.support_nonempty_iff.mpr hc0 - exact ⟨n,hmem (Finsupp.mem_support_iff.mp hn) (integer_coefficient_eigen k ρ v c hc n)⟩ - let m := S.max' hS - have hm : m ∈ S := Finset.max'_mem _ _ - obtain ⟨v,hv,hw⟩ := (Finset.mem_filter.mp hm).2 - have upper : ∀ l : ℤ, m < l → ∀ w : M, - (∀ a, ρ (diagonalTorus k a) w = integerCharacter k l a • w) → w = 0 := by - intro l hl w hw - by_contra h - exact (not_lt_of_ge (Finset.le_max' _ _ (hmem h hw))) hl - have hm0 : 0 ≤ m := by - by_contra hn - have hzero := upper (-m) (by omega) (ρ (weylReflection k) v) - (reflected_weight k ρ m v hw) - exact hv ((ρ.apply_bijective (weylReflection k)).1 (hzero.trans (map_zero _).symm)) - have he : (m.toNat : ℤ) = m := Int.toNat_of_nonneg hm0 - refine ⟨m.toNat, ?_, ?_, v,hv, ?_⟩ - · have := (Finset.mem_Icc.mp (Finset.mem_filter.mp hm).1).2 - omega - · rw [he] - exact weights_between_of_upper k ρ m upper - · simpa only [he] using hw - -omit [Infinite k] in -lemma exists_costandard_dual_embedding (A : FDRep k (SL2 k)) (n : ℕ) - (f : Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) →ₗ[k] A) - (hf : ∀ g v, f (standardRepresentation k n g v) = A.ρ g (f v)) - (hfs : Function.Surjective f) : - ∃ e : Module.Dual k A →ₗ[k] MvPolynomial.homogeneousSubmodule (Fin 2) k n, - Function.Injective e ∧ ∀ g l, e (Representation.dual A.ρ g l) = - ((homogeneousRepresentation n).comp (dualMatrix k)) g (e l) := by - let H := MvPolynomial.homogeneousSubmodule (Fin 2) k n - let e : Module.Dual k A →ₗ[k] H := - (Module.evalEquiv k H).symm.toLinearMap.comp f.dualMap - have hei : Function.Injective e := (Module.evalEquiv k H).symm.injective.comp - (LinearMap.dualMap_injective_of_surjective hfs) - have heq (l : Module.Dual k A) : Module.Dual.eval k H (e l) = f.dualMap l := - (Module.evalEquiv k H).apply_symm_apply _ - have heρ : ∀ g l, e (Representation.dual A.ρ g l) = - ((homogeneousRepresentation n).comp (dualMatrix k)) g (e l) := by - intro g l - apply (Module.evalEquiv k H).injective - change Module.Dual.eval k H (e (Representation.dual A.ρ g l)) = - Module.Dual.eval k H (((homogeneousRepresentation n).comp (dualMatrix k)) g (e l)) - rw [heq,eval_intertwines,heq] - exact dual_intertwines k (standardRepresentation k n) A.ρ f hf g l - exact ⟨e, hei, heρ⟩ - -lemma exists_socle_dual_embedding (A : FDRep k (SL2 k)) [Nontrivial A] (n : ℕ) - (e : Module.Dual k A →ₗ[k] MvPolynomial.homogeneousSubmodule (Fin 2) k n) - (hei : Function.Injective e) - (heρ : ∀ g l, e (Representation.dual A.ρ g l) = - ((homogeneousRepresentation n).comp (dualMatrix k)) g (e l)) : - ∃ s : (costandardSocle k n).toSubmodule →ₗ[k] Module.Dual k A, - Function.Injective s ∧ ∀ g x, s ((costandardSocle k n).toRepresentation g x) = - Representation.dual A.ρ g (s x) := by - let e' := e.intertwiningMap_of_isIntertwiningMap (Representation.dual A.ρ) - ((homogeneousRepresentation n).comp (dualMatrix k)) heρ - have her : e'.range ≠ ⊥ := by - intro h - obtain ⟨l,hl⟩ := exists_ne (0 : Module.Dual k A) - have hz : e l = 0 := by - have hm : e l ∈ e'.range := ⟨l,rfl⟩ - rw [h] at hm - exact hm - exact hl (hei (hz.trans (map_zero e).symm)) - have hle := costandardSocle_le_of_ne_bot k n e'.range her - let E := LinearEquiv.ofInjective e hei - let inc : (costandardSocle k n).toSubmodule →ₗ[k] LinearMap.range e := - Submodule.inclusion hle - let s : (costandardSocle k n).toSubmodule →ₗ[k] Module.Dual k A := - E.symm.toLinearMap.comp inc - have hs (x : (costandardSocle k n).toSubmodule) : e (s x) = x.val := by - have h := E.apply_symm_apply (inc x) - exact congrArg Subtype.val h - have hsi : Function.Injective s := E.symm.injective.comp (Submodule.inclusion_injective hle) - have hsρ : ∀ g x, s ((costandardSocle k n).toRepresentation g x) = - Representation.dual A.ρ g (s x) := by - intro g x - apply hei - rw [hs,heρ,hs] - rfl - exact ⟨s, hsi, hsρ⟩ - -omit [Infinite k] in -lemma dual_eval_surjective {V W : Type u} [AddCommGroup V] [Module k V] - [AddCommGroup W] [Module k W] [Module.Finite k W] - (s : V →ₗ[k] Module.Dual k W) (hs : Function.Injective s) : - Function.Surjective (s.dualMap.comp (Module.Dual.eval k W)) := - (LinearMap.dualMap_surjective_of_injective hs).comp (Module.evalEquiv k W).surjective - -lemma exists_simple_dual_surjection (A : FDRep k (SL2 k)) [Nontrivial A] (n : ℕ) - (e : Module.Dual k A →ₗ[k] MvPolynomial.homogeneousSubmodule (Fin 2) k n) - (hei : Function.Injective e) - (heρ : ∀ g l, e (Representation.dual A.ρ g l) = - ((homogeneousRepresentation n).comp (dualMatrix k)) g (e l)) : - ∃ r : A →ₗ[k] Module.Dual k (costandardSocle k n).toSubmodule, - Function.Surjective r ∧ ∀ g x, r (A.ρ g x) = - Representation.dual (costandardSocle k n).toRepresentation g (r x) := by - obtain ⟨s,hsi,hsρ⟩ := exists_socle_dual_embedding k A n e hei heρ - refine ⟨s.dualMap.comp (Module.Dual.eval k A), - dual_eval_surjective k (V := (costandardSocle k n).toSubmodule) (W := A) s hsi, ?_⟩ - intro g x - apply LinearMap.ext - intro y - change s y (A.ρ g x) = s ((costandardSocle k n).toRepresentation g⁻¹ y) x - rw [hsρ] - change s y (A.ρ g x) = s y (A.ρ (g⁻¹)⁻¹ x) - rw [inv_inv] - -lemma irreducible_iso_simple_dual (A : FDRep k (SL2 k)) - [Representation.IsIrreducible A.ρ] (n : ℕ) - (r : A →ₗ[k] Module.Dual k (costandardSocle k n).toSubmodule) - (hrs : Function.Surjective r) - (hrρ : ∀ g x, r (A.ρ g x) = - Representation.dual (costandardSocle k n).toRepresentation g (r x)) : - Nonempty (A ≅ (simpleSL2 k n)ᘁ) := by - let r' := r.intertwiningMap_of_isIntertwiningMap A.ρ - (Representation.dual (costandardSocle k n).toRepresentation) hrρ - let : Nontrivial (costandardSocle k n).toSubmodule := - Submodule.nontrivial_iff_ne_bot.mpr (by - intro hz - apply costandardSocle_ne_bot k n - apply Subrepresentation.ext - exact hz) - let : Module.Free k (costandardSocle k n).toSubmodule := Module.Free.of_divisionRing k (costandardSocle k n).toSubmodule - let : Nontrivial (Module.Dual k (costandardSocle k n).toSubmodule) := - (Module.nontrivial_dual_iff k).mpr inferInstance - have hri : Function.Injective r := by - rcases Representation.IsIrreducible.injective_or_eq_zero r' with h | h - · exact h - · obtain ⟨l,hl⟩ := exists_ne (0 : Module.Dual k (costandardSocle k n).toSubmodule) - obtain ⟨x,hx⟩ := hrs l - have hz : r x = 0 := congrArg (fun g => g x) h - exact (hl (hx.symm.trans hz)).elim - let q : A ⟶ (simpleSL2 k n)ᘁ := fdrepHom k r (by - intro g x - rw [fdrep_dual_repr] - exact hrρ g x) - have : IsIso q := fdrepHom_isIso_of_bijective k q ⟨hri,hrs⟩ - exact ⟨asIso q⟩ - - - -theorem irreducible_eq_simple_dual (A : FDRep k (SL2 k)) - (hA : IsRational k A.ρ) [Representation.IsIrreducible A.ρ] - (d : ℕ) (hd : HasWeightsBetween A.ρ (-(d : ℤ)) d) : - ∃ n : ℕ, n ≤ d ∧ Nonempty (A ≅ (simpleSL2 k n)ᘁ) := by - let : Nontrivial (Representation.asModule A.ρ) := - IsSimpleModule.nontrivial (MonoidAlgebra k (SL2 k)) (Representation.asModule A.ρ) - let : Nontrivial A := (Representation.asModuleEquiv A.ρ).symm.toEquiv.nontrivial - obtain ⟨n,hn,hb,v,hv,hw⟩ := exists_highest_in_bound k A.ρ hA d hd - obtain ⟨f,hfv,hf⟩ := exists_standard_lift k A.ρ hA n hb v hw - let f' := f.intertwiningMap_of_isIntertwiningMap (standardRepresentation k n) A.ρ hf - have hfs : Function.Surjective f := by - rcases Representation.IsIrreducible.surjective_or_eq_zero f' with h | h - · exact h - · have hz : f (standardHighest k n) = 0 := congrArg (fun g => g (standardHighest k n)) h - exact (hv (hfv.symm.trans hz)).elim - obtain ⟨e,hei,heρ⟩ := exists_costandard_dual_embedding k A n f hf hfs - obtain ⟨r,hrs,hrρ⟩ := exists_simple_dual_surjection k A n e hei heρ - exact ⟨n,hn,irreducible_iso_simple_dual k A n r hrs hrρ⟩ -end - -section -universe u -variable (k : Type u) [Field k] - -lemma hasWeightsBetween_of_injective {M N : Type u} [AddCommGroup M] [Module k M] - [AddCommGroup N] [Module k N] - (ρ : Representation k (SL2 k) M) (σ : Representation k (SL2 k) N) - (f : M →ₗ[k] N) (hf : Function.Injective f) - (he : ∀ g v, f (ρ g v) = σ g (f v)) (lo hi : ℤ) - (hσ : HasWeightsBetween σ lo hi) : HasWeightsBetween ρ lo hi := by - intro n v hn hv - apply hf - rw [map_zero] - apply hσ n (f v) hn - intro a - rw [← he,hv,map_smul] - -lemma hasWeightsBetween_of_surjective [Infinite k] - {M N : Type u} [AddCommGroup M] [Module k M] [Module.Finite k M] - [AddCommGroup N] [Module k N] - (ρ : Representation k (SL2 k) M) (σ : Representation k (SL2 k) N) - (hρ : IsRational k ρ) (f : M →ₗ[k] N) (hf : Function.Surjective f) - (he : ∀ g v, f (ρ g v) = σ g (f v)) (lo hi : ℤ) - (hb : HasWeightsBetween ρ lo hi) : HasWeightsBetween σ lo hi := by - intro n w hn hw - obtain ⟨v,hv,hvw⟩ := rational_weight_lift k ρ σ hρ f he hf (integerCharacter k n) w hw - rw [← hv,hb n v hn hvw,map_zero] - -lemma fdrep_isZero_of_subsingleton {G : Type u} [Monoid G] - (A : FDRep k G) [Subsingleton A] : IsZero A := by - apply (IsZero.iff_id_eq_zero _).mpr - apply fdrep_hom_ext k - intro x - exact Subsingleton.elim _ _ - -lemma IsTilting.of_subsingleton (A : FDRep k (SL2 k)) [Subsingleton A] - (hA : IsRational k A.ρ) : IsTilting k A := by - refine ⟨hA, .zero _ (fdrep_isZero_of_subsingleton k A), .zero _ ?_⟩ - let : Subsingleton (Aᘁ : FDRep k (SL2 k)) := by - change Subsingleton (Module.Dual k A) - infer_instance - exact fdrep_isZero_of_subsingleton k Aᘁ - -lemma IsTilting.extension {A B C : FDRep k (SL2 k)} - (hA : IsTilting k A) (hC : IsTilting k C) (hB : IsRational k B.ρ) - (f : A ⟶ B) (g : B ⟶ C) (w : f ≫ g = 0) - (hS : (ShortComplex.mk f g w).ShortExact) : IsTilting k B := by - refine ⟨hB,hA.2.1.extension k hC.2.1 f g w hS, ?_⟩ - exact hC.2.2.extension k hA.2.2 (fdrepDualMap k g) (fdrepDualMap k f) - (fdrepDualMap_zero_comp k f g w) (fdrep_dual_shortExact k f g w hS) - -end - -section -universe u -variable (k : Type u) [Field k] -variable {G : Type u} [Monoid G] - -lemma exists_proper_subrepresentation (A : FDRep k G) [Nontrivial A] - (h : ¬ Representation.IsIrreducible A.ρ) : - ∃ S : Subrepresentation A.ρ, S ≠ ⊥ ∧ S ≠ ⊤ := by - classical - let : Nontrivial (Subrepresentation A.ρ) := ⟨⟨⊥, ⊤, fun he => - bot_ne_top (congrArg Subrepresentation.toSubmodule he)⟩⟩ - by_contra hn - apply h - refine { eq_bot_or_eq_top := ?_ } - intro S - by_cases hs : S = ⊥ - · exact Or.inl hs - · exact Or.inr (by by_contra ht; exact hn ⟨S,hs,ht⟩) - - - -lemma fdrep_proper_shortExact (A : FDRep k G) (S : Subrepresentation A.ρ) - (hb : S ≠ ⊥) (ht : S ≠ ⊤) : - ∃ (L N : FDRep k G) (f : L ⟶ A) (g : A ⟶ N) (w : f ≫ g = 0), - (ShortComplex.mk f g w).ShortExact ∧ - Module.finrank k L < Module.finrank k A ∧ - Module.finrank k N < Module.finrank k A := by - let L := FDRep.of S.toRepresentation - let N := FDRep.of (Representation.quotient A.ρ S.toSubmodule S.apply_mem_toSubmodule) - let f : L ⟶ A := fdrepHom k S.toSubmodule.subtype (by intros; rfl) - let g : A ⟶ N := fdrepHom k S.toSubmodule.mkQ (by intros; rfl) - have w : f ≫ g = 0 := by - apply fdrep_hom_ext k - intro x - exact (Submodule.Quotient.mk_eq_zero _).mpr x.property - have hb' : S.toSubmodule ≠ ⊥ := fun h => hb (Subrepresentation.ext h) - have ht' : S.toSubmodule ≠ ⊤ := fun h => ht (Subrepresentation.ext h) - have hdim := S.toSubmodule.finrank_quotient_add_finrank - have hp : 0 < Module.finrank k S.toSubmodule := - Module.finrank_pos_iff.mpr (Submodule.nontrivial_iff_ne_bot.mpr hb') - refine ⟨L,N,f,g,w,fdrep_shortExact k _ Subtype.val_injective - S.toSubmodule.mkQ_surjective ?_, Submodule.finrank_lt ht', ?_⟩ - · change LinearMap.range S.toSubmodule.subtype = LinearMap.ker S.toSubmodule.mkQ - simp - · change Module.finrank k (A ⧸ S.toSubmodule) < Module.finrank k A - omega - - - -theorem fdrep_induction (P : FDRep k G → Prop) - (hz : ∀ A : FDRep k G, (Subsingleton A) → P A) - (hi : ∀ A, Representation.IsIrreducible A.ρ → P A) - (he : ∀ (A B C : FDRep k G) (f : A ⟶ B) (g : B ⟶ C) (w : f ≫ g = 0), - (ShortComplex.mk f g w).ShortExact → P A → P C → P B) (A : FDRep k G) : P A := by - classical - generalize hn : Module.finrank k A = n - induction n using Nat.strong_induction_on generalizing A with - | h n ih => - by_cases hzA : Subsingleton A - · exact hz A hzA - let : Nontrivial A := not_subsingleton_iff_nontrivial.mp hzA - by_cases hiA : Representation.IsIrreducible A.ρ - · exact hi A hiA - obtain ⟨S,hb,ht⟩ := exists_proper_subrepresentation k A hiA - obtain ⟨L,N,f,g,w,hS,hL,hN⟩ := fdrep_proper_shortExact k A S hb ht - apply he L A N f g w hS - · exact ih (Module.finrank k L) (hn ▸ hL) L rfl - · exact ih (Module.finrank k N) (hn ▸ hN) N rfl -end - -universe u -variable (k : Type u) [Field k] [Infinite k] -variable (p : ℕ) [Fact p.Prime] [CharP k p] - -lemma steinberg_tensor_simple_dual_tilting (m n : ℕ) (hn : n < p^(m+1)) : - IsTilting k (steinberg k p m ⊗ (simpleSL2 k n)ᘁ) := by - obtain ⟨eS⟩ := steinberg_self_dual k p m - let e : (steinberg k p m ⊗ simpleSL2 k n)ᘁ ≅ - steinberg k p m ⊗ (simpleSL2 k n)ᘁ := - rightDualTensorIso _ _ ≪≫ tensorIso (Iso.refl _) eS ≪≫ β_ _ _ - exact ((steinberg_tensor_simple_tilting k p m n hn).dual k).of_iso k e - -lemma steinberg_tensor_irreducible_tilting (m d : ℕ) (hd : d < p^(m+1)) - (A : FDRep k (SL2 k)) [Representation.IsIrreducible A.ρ] - (hA : IsRational k A.ρ) (hb : HasWeightsBetween A.ρ (-(d : ℤ)) d) : - IsTilting k (steinberg k p m ⊗ A) := by - obtain ⟨n,hn,⟨e⟩⟩ := irreducible_eq_simple_dual k A hA d hb - exact (steinberg_tensor_simple_dual_tilting k p m n (hn.trans_lt hd)).of_iso k - (tensorIso (Iso.refl _) e.symm) - - - -theorem bounded_weights_tilting (m d : ℕ) (hd : d < p^(m+1)) - (A : FDRep k (SL2 k)) (hA : IsRational k A.ρ) - (hb : HasWeightsBetween A.ρ (-(d : ℤ)) d) : - IsTilting k (steinberg k p m ⊗ A) := by - let P : FDRep k (SL2 k) → Prop := fun B => IsRational k B.ρ → - HasWeightsBetween B.ρ (-(d : ℤ)) d → IsTilting k (steinberg k p m ⊗ B) - apply fdrep_induction k P ?_ ?_ ?_ A hA hb - · intro B hB hr _ - let : Subsingleton B := hB - let : Subsingleton (steinberg k p m ⊗ B : FDRep k (SL2 k)) := by - change Subsingleton (TensorProduct k (steinberg k p m) B) - infer_instance - exact IsTilting.of_subsingleton k (steinberg k p m ⊗ B) - (IsRational.tensor k (steinberg k p m).ρ B.ρ (steinberg_tilting k p m).1 hr) - · intro B hi hr hw - let : Representation.IsIrreducible B.ρ := hi - exact steinberg_tensor_irreducible_tilting k p m d hd B hr hw - · intro L B N f g w hS hL hN hr hw - have := hS.mono_f - have := hS.epi_g - have hrL := IsRational.of_injective k L.ρ B.ρ (fdrepLinear k f) - (fdrep_injective k f) (fdrepLinear_comm k f) hr - have hrN := IsRational.of_surjective k B.ρ N.ρ (fdrepLinear k g) - (fdrep_surjective k g) (fdrepLinear_comm k g) hr - have hwL := hasWeightsBetween_of_injective k L.ρ B.ρ (fdrepLinear k f) - (fdrep_injective k f) (fdrepLinear_comm k f) _ _ hw - have hwN := hasWeightsBetween_of_surjective k B.ρ N.ρ hr (fdrepLinear k g) - (fdrep_surjective k g) (fdrepLinear_comm k g) _ _ hw - let F := tensorLeft (steinberg k p m) - let := tensorLeft_preservesFiniteLimits (steinberg k p m) - let := tensorLeft_preservesFiniteColimits (steinberg k p m) - have hT := hS.map_of_exact F - exact (hL hrL hwL).extension k (hN hrN hwN) - (IsRational.tensor k (steinberg k p m).ρ B.ρ (steinberg_tilting k p m).1 hr) _ _ _ hT -end FiberFunctorProof -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.SimpleModules +import OAI.RepresentationTheory.RestrictedTilting.BinarySequences + +namespace OAI + +/-! Highest weights, irreducible representations and bounded-weight tilting. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (p : ℕ) [Fact p.Prime] [CharP k p] + +noncomputable def steinbergStepIso (m : ℕ) : + costandard k (p-1) ⊗ (frobeniusTwist k p).obj (steinberg k p m) ≅ + steinberg k p (m+1) := by + have hp : 0 < p := (Fact.out : p.Prime).pos + have hm : 0 < p^m := pow_pos hp m + have he : p-1+p*(p^m-1) = p^(m+1)-1 := by + rw [pow_succ] + have hpM : 0 < p^m*p := mul_pos hm hp + nlinarith [Nat.sub_add_cancel hp, Nat.sub_add_cancel hm, Nat.sub_add_cancel hpM] + exact frobeniusCostandardIso k p (p^m-1) ≪≫ + eqToIso (congrArg (costandard k) he) + +omit [Infinite k] in +noncomputable def frobeniusTensorIso (A B : FDRep k (SL2 k)) : + (frobeniusTwist k p).obj (A ⊗ B) ≅ + (frobeniusTwist k p).obj A ⊗ (frobeniusTwist k p).obj B := Iso.refl _ + + + +theorem steinberg_tensor_simple_tilting (m h : ℕ) (hh : h < p^(m+1)) : + IsTilting k (steinberg k p m ⊗ simpleSL2 k h) := by + induction m generalizing h with + | zero => + have hh' : h < p := by simpa using hh + obtain ⟨e⟩ := simpleSL2_eq_costandard_of_choose k h + (fun i => choose_cast_ne_zero_of_lt_char k p hh' (Nat.le_of_lt_succ i.isLt)) + exact (steinberg_tilting k p 0).tensor k ((small_costandard_tilting k p h hh').of_iso k e.symm) + | succ m ih => + have hp : 0 < p := (Fact.out : p.Prime).pos + have ha : h%p < p := Nat.mod_lt _ hp + have hb : h/p < p^(m+1) := by + apply (Nat.div_lt_iff_lt_mul hp).mpr + simpa only [pow_succ] using hh + have ht := (ih (h/p) hb).steinberg_frobenius k p + have hS : IsTilting k (costandard k (h%p) ⊗ + (costandard k (p-1) ⊗ + ((frobeniusTwist k p).obj (steinberg k p m) ⊗ + (frobeniusTwist k p).obj (simpleSL2 k (h/p))))) := + (small_costandard_tilting k p (h%p) ha).tensor k + (ht.of_iso k (tensorIso (Iso.refl _) (frobeniusTensorIso k p _ _))) + let A := costandard k (h%p) + let B := costandard k (p-1) + let C := (frobeniusTwist k p).obj (steinberg k p m) + let D := (frobeniusTwist k p).obj (simpleSL2 k (h/p)) + let swap : (B ⊗ A) ⊗ (C ⊗ D) ≅ (B ⊗ C) ⊗ (A ⊗ D) := + { hom := tensorμ B A C D + inv := tensorδ B A C D + hom_inv_id := tensorμ_tensorδ B A C D + inv_hom_id := tensorδ_tensorμ B A C D } + let eL : A ⊗ D ≅ simpleSL2 k h := + simpleDigitIso k p (h%p) (h/p) ha ≪≫ + eqToIso (congrArg (simpleSL2 k) (Nat.mod_add_div h p)) + let e : A ⊗ (B ⊗ (C ⊗ D)) ≅ steinberg k p (m+1) ⊗ simpleSL2 k h := + (α_ A B (C ⊗ D)).symm ≪≫ tensorIso (β_ A B) (Iso.refl _) ≪≫ swap ≪≫ + tensorIso (steinbergStepIso k p m) eL + exact hS.of_iso k e +end + +section +universe u +variable (k : Type u) [Field k] +noncomputable def weylReflection : SL2 k := + ⟨!![0, -1; 1, 0], by simp [Matrix.det_fin_two]⟩ + +lemma diagonalTorus_weylReflection (a : kˣ) : + diagonalTorus k a * weylReflection k = weylReflection k * diagonalTorus k a⁻¹ := by + apply Subtype.ext + change !![(a : k),0;0,(↑a⁻¹ : k)] * !![0,-1;1,0] = + !![0,-1;1,0] * !![(↑a⁻¹ : k),0;0,(↑(a⁻¹)⁻¹ : k)] + ext i j + fin_cases i <;> fin_cases j <;> simp [Matrix.mul_apply, Fin.sum_univ_two] + +lemma reflected_weight {V : Type*} [AddCommGroup V] [Module k V] + (σ : Representation k (SL2 k) V) (n : ℤ) (v : V) + (hv : ∀ a : kˣ, σ (diagonalTorus k a) v = integerCharacter k n a • v) : + ∀ a : kˣ, σ (diagonalTorus k a) (σ (weylReflection k) v) = + integerCharacter k (-n) a • σ (weylReflection k) v := by + intro a + rw [← Module.End.mul_apply, ← map_mul, diagonalTorus_weylReflection, map_mul, + Module.End.mul_apply, hv, map_smul] + congr 1 + simp [integerCharacter, zpow_neg] + +lemma weights_between_of_upper {V : Type*} [AddCommGroup V] [Module k V] + (σ : Representation k (SL2 k) V) (d : ℤ) + (hσ : ∀ (n : ℤ), d < n → ∀ v : V, + (∀ a, σ (diagonalTorus k a) v = integerCharacter k n a • v) → v = 0) : + HasWeightsBetween σ (-d) d := by + intro n v hn hv + rcases hn with hn | hn + · have hz := hσ (-n) (by omega) (σ (weylReflection k) v) (reflected_weight k σ n v hv) + exact (σ.apply_bijective (weylReflection k)).1 (hz.trans (map_zero _).symm) + · exact hσ n hn v hv + +end + +section +universe u +variable (k : Type u) [Field k] [Infinite k] + +lemma integer_coefficient_eigen {M : Type u} [AddCommGroup M] [Module k M] + (ρ : Representation k (SL2 k) M) (v : M) (c : ℤ →₀ M) + (hc : ∀ a, ρ (diagonalTorus k a) v = c.sum (fun n x => integerCharacter k n a • x)) + (n : ℤ) (a : kˣ) : + ρ (diagonalTorus k a) (c n) = integerCharacter k n a • c n := by + let e : ℤ ↪ (kˣ →* k) := ⟨integerCharacter k, integerCharacter_injective k⟩ + have he : ∀ a, (ρ.comp (diagonalTorus k)) a v = + (c.embDomain e).sum (fun χ x => χ a • x) := by + intro a + rw [Finsupp.sum_embDomain] + exact hc a + have h := character_coefficient_eigen (ρ.comp (diagonalTorus k)) v + (c.embDomain e) he (e n) a + rw [Finsupp.embDomain_apply_self] at h + exact h + + + +lemma exists_highest_in_bound {M : Type u} [AddCommGroup M] [Module k M] + [Module.Finite k M] [Nontrivial M] (ρ : Representation k (SL2 k) M) + (hρ : IsRational k ρ) (d : ℕ) (hd : HasWeightsBetween ρ (-(d : ℤ)) d) : + ∃ n : ℕ, n ≤ d ∧ HasWeightsBetween ρ (-(n : ℤ)) n ∧ + ∃ v : M, v ≠ 0 ∧ ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v := by + classical + let S := (Finset.Icc (-(d : ℤ)) d).filter (fun n => + ∃ v : M, v ≠ 0 ∧ ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) + have hmem {n : ℤ} {v : M} (hv : v ≠ 0) + (hw : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) : n ∈ S := by + have hn : -(d : ℤ) ≤ n ∧ n ≤ d := by + constructor <;> by_contra h + · exact hv (hd n v (Or.inl (lt_of_not_ge h)) hw) + · exact hv (hd n v (Or.inr (lt_of_not_ge h)) hw) + exact Finset.mem_filter.mpr ⟨Finset.mem_Icc.mpr hn, v, hv, hw⟩ + have hS : S.Nonempty := by + obtain ⟨v,hv⟩ := exists_ne (0 : M) + obtain ⟨c,hc⟩ := rational_torus_integerExpansions k ρ hρ v + have hc0 : c ≠ 0 := by + intro h + have := hc 1 + simp only [h,Finsupp.sum_zero_index,map_one,Module.End.one_apply] at this + exact hv this + obtain ⟨n,hn⟩ := Finsupp.support_nonempty_iff.mpr hc0 + exact ⟨n,hmem (Finsupp.mem_support_iff.mp hn) (integer_coefficient_eigen k ρ v c hc n)⟩ + let m := S.max' hS + have hm : m ∈ S := Finset.max'_mem _ _ + obtain ⟨v,hv,hw⟩ := (Finset.mem_filter.mp hm).2 + have upper : ∀ l : ℤ, m < l → ∀ w : M, + (∀ a, ρ (diagonalTorus k a) w = integerCharacter k l a • w) → w = 0 := by + intro l hl w hw + by_contra h + exact (not_lt_of_ge (Finset.le_max' _ _ (hmem h hw))) hl + have hm0 : 0 ≤ m := by + by_contra hn + have hzero := upper (-m) (by omega) (ρ (weylReflection k) v) + (reflected_weight k ρ m v hw) + exact hv ((ρ.apply_bijective (weylReflection k)).1 (hzero.trans (map_zero _).symm)) + have he : (m.toNat : ℤ) = m := Int.toNat_of_nonneg hm0 + refine ⟨m.toNat, ?_, ?_, v,hv, ?_⟩ + · have := (Finset.mem_Icc.mp (Finset.mem_filter.mp hm).1).2 + omega + · rw [he] + exact weights_between_of_upper k ρ m upper + · simpa only [he] using hw + +omit [Infinite k] in +lemma exists_costandard_dual_embedding (A : FDRep k (SL2 k)) (n : ℕ) + (f : Module.Dual k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) →ₗ[k] A) + (hf : ∀ g v, f (standardRepresentation k n g v) = A.ρ g (f v)) + (hfs : Function.Surjective f) : + ∃ e : Module.Dual k A →ₗ[k] MvPolynomial.homogeneousSubmodule (Fin 2) k n, + Function.Injective e ∧ ∀ g l, e (Representation.dual A.ρ g l) = + ((homogeneousRepresentation n).comp (dualMatrix k)) g (e l) := by + let H := MvPolynomial.homogeneousSubmodule (Fin 2) k n + let e : Module.Dual k A →ₗ[k] H := + (Module.evalEquiv k H).symm.toLinearMap.comp f.dualMap + have hei : Function.Injective e := (Module.evalEquiv k H).symm.injective.comp + (LinearMap.dualMap_injective_of_surjective hfs) + have heq (l : Module.Dual k A) : Module.Dual.eval k H (e l) = f.dualMap l := + (Module.evalEquiv k H).apply_symm_apply _ + have heρ : ∀ g l, e (Representation.dual A.ρ g l) = + ((homogeneousRepresentation n).comp (dualMatrix k)) g (e l) := by + intro g l + apply (Module.evalEquiv k H).injective + change Module.Dual.eval k H (e (Representation.dual A.ρ g l)) = + Module.Dual.eval k H (((homogeneousRepresentation n).comp (dualMatrix k)) g (e l)) + rw [heq,eval_intertwines,heq] + exact dual_intertwines k (standardRepresentation k n) A.ρ f hf g l + exact ⟨e, hei, heρ⟩ + +lemma exists_socle_dual_embedding (A : FDRep k (SL2 k)) [Nontrivial A] (n : ℕ) + (e : Module.Dual k A →ₗ[k] MvPolynomial.homogeneousSubmodule (Fin 2) k n) + (hei : Function.Injective e) + (heρ : ∀ g l, e (Representation.dual A.ρ g l) = + ((homogeneousRepresentation n).comp (dualMatrix k)) g (e l)) : + ∃ s : (costandardSocle k n).toSubmodule →ₗ[k] Module.Dual k A, + Function.Injective s ∧ ∀ g x, s ((costandardSocle k n).toRepresentation g x) = + Representation.dual A.ρ g (s x) := by + let e' := e.intertwiningMap_of_isIntertwiningMap (Representation.dual A.ρ) + ((homogeneousRepresentation n).comp (dualMatrix k)) heρ + have her : e'.range ≠ ⊥ := by + intro h + obtain ⟨l,hl⟩ := exists_ne (0 : Module.Dual k A) + have hz : e l = 0 := by + have hm : e l ∈ e'.range := ⟨l,rfl⟩ + rw [h] at hm + exact hm + exact hl (hei (hz.trans (map_zero e).symm)) + have hle := costandardSocle_le_of_ne_bot k n e'.range her + let E := LinearEquiv.ofInjective e hei + let inc : (costandardSocle k n).toSubmodule →ₗ[k] LinearMap.range e := + Submodule.inclusion hle + let s : (costandardSocle k n).toSubmodule →ₗ[k] Module.Dual k A := + E.symm.toLinearMap.comp inc + have hs (x : (costandardSocle k n).toSubmodule) : e (s x) = x.val := by + have h := E.apply_symm_apply (inc x) + exact congrArg Subtype.val h + have hsi : Function.Injective s := E.symm.injective.comp (Submodule.inclusion_injective hle) + have hsρ : ∀ g x, s ((costandardSocle k n).toRepresentation g x) = + Representation.dual A.ρ g (s x) := by + intro g x + apply hei + rw [hs,heρ,hs] + rfl + exact ⟨s, hsi, hsρ⟩ + +omit [Infinite k] in +lemma dual_eval_surjective {V W : Type u} [AddCommGroup V] [Module k V] + [AddCommGroup W] [Module k W] [Module.Finite k W] + (s : V →ₗ[k] Module.Dual k W) (hs : Function.Injective s) : + Function.Surjective (s.dualMap.comp (Module.Dual.eval k W)) := + (LinearMap.dualMap_surjective_of_injective hs).comp (Module.evalEquiv k W).surjective + +lemma exists_simple_dual_surjection (A : FDRep k (SL2 k)) [Nontrivial A] (n : ℕ) + (e : Module.Dual k A →ₗ[k] MvPolynomial.homogeneousSubmodule (Fin 2) k n) + (hei : Function.Injective e) + (heρ : ∀ g l, e (Representation.dual A.ρ g l) = + ((homogeneousRepresentation n).comp (dualMatrix k)) g (e l)) : + ∃ r : A →ₗ[k] Module.Dual k (costandardSocle k n).toSubmodule, + Function.Surjective r ∧ ∀ g x, r (A.ρ g x) = + Representation.dual (costandardSocle k n).toRepresentation g (r x) := by + obtain ⟨s,hsi,hsρ⟩ := exists_socle_dual_embedding k A n e hei heρ + refine ⟨s.dualMap.comp (Module.Dual.eval k A), + dual_eval_surjective k (V := (costandardSocle k n).toSubmodule) (W := A) s hsi, ?_⟩ + intro g x + apply LinearMap.ext + intro y + change s y (A.ρ g x) = s ((costandardSocle k n).toRepresentation g⁻¹ y) x + rw [hsρ] + change s y (A.ρ g x) = s y (A.ρ (g⁻¹)⁻¹ x) + rw [inv_inv] + +lemma irreducible_iso_simple_dual (A : FDRep k (SL2 k)) + [Representation.IsIrreducible A.ρ] (n : ℕ) + (r : A →ₗ[k] Module.Dual k (costandardSocle k n).toSubmodule) + (hrs : Function.Surjective r) + (hrρ : ∀ g x, r (A.ρ g x) = + Representation.dual (costandardSocle k n).toRepresentation g (r x)) : + Nonempty (A ≅ (simpleSL2 k n)ᘁ) := by + let r' := r.intertwiningMap_of_isIntertwiningMap A.ρ + (Representation.dual (costandardSocle k n).toRepresentation) hrρ + let : Nontrivial (costandardSocle k n).toSubmodule := + Submodule.nontrivial_iff_ne_bot.mpr (by + intro hz + apply costandardSocle_ne_bot k n + apply Subrepresentation.ext + exact hz) + let : Module.Free k (costandardSocle k n).toSubmodule := Module.Free.of_divisionRing k (costandardSocle k n).toSubmodule + let : Nontrivial (Module.Dual k (costandardSocle k n).toSubmodule) := + (Module.nontrivial_dual_iff k).mpr inferInstance + have hri : Function.Injective r := by + rcases Representation.IsIrreducible.injective_or_eq_zero r' with h | h + · exact h + · obtain ⟨l,hl⟩ := exists_ne (0 : Module.Dual k (costandardSocle k n).toSubmodule) + obtain ⟨x,hx⟩ := hrs l + have hz : r x = 0 := congrArg (fun g => g x) h + exact (hl (hx.symm.trans hz)).elim + let q : A ⟶ (simpleSL2 k n)ᘁ := fdrepHom k r (by + intro g x + rw [fdrep_dual_repr] + exact hrρ g x) + have : IsIso q := fdrepHom_isIso_of_bijective k q ⟨hri,hrs⟩ + exact ⟨asIso q⟩ + + + +theorem irreducible_eq_simple_dual (A : FDRep k (SL2 k)) + (hA : IsRational k A.ρ) [Representation.IsIrreducible A.ρ] + (d : ℕ) (hd : HasWeightsBetween A.ρ (-(d : ℤ)) d) : + ∃ n : ℕ, n ≤ d ∧ Nonempty (A ≅ (simpleSL2 k n)ᘁ) := by + let : Nontrivial (Representation.asModule A.ρ) := + IsSimpleModule.nontrivial (MonoidAlgebra k (SL2 k)) (Representation.asModule A.ρ) + let : Nontrivial A := (Representation.asModuleEquiv A.ρ).symm.toEquiv.nontrivial + obtain ⟨n,hn,hb,v,hv,hw⟩ := exists_highest_in_bound k A.ρ hA d hd + obtain ⟨f,hfv,hf⟩ := exists_standard_lift k A.ρ hA n hb v hw + let f' := f.intertwiningMap_of_isIntertwiningMap (standardRepresentation k n) A.ρ hf + have hfs : Function.Surjective f := by + rcases Representation.IsIrreducible.surjective_or_eq_zero f' with h | h + · exact h + · have hz : f (standardHighest k n) = 0 := congrArg (fun g => g (standardHighest k n)) h + exact (hv (hfv.symm.trans hz)).elim + obtain ⟨e,hei,heρ⟩ := exists_costandard_dual_embedding k A n f hf hfs + obtain ⟨r,hrs,hrρ⟩ := exists_simple_dual_surjection k A n e hei heρ + exact ⟨n,hn,irreducible_iso_simple_dual k A n r hrs hrρ⟩ +end + +section +universe u +variable (k : Type u) [Field k] + +lemma hasWeightsBetween_of_injective {M N : Type u} [AddCommGroup M] [Module k M] + [AddCommGroup N] [Module k N] + (ρ : Representation k (SL2 k) M) (σ : Representation k (SL2 k) N) + (f : M →ₗ[k] N) (hf : Function.Injective f) + (he : ∀ g v, f (ρ g v) = σ g (f v)) (lo hi : ℤ) + (hσ : HasWeightsBetween σ lo hi) : HasWeightsBetween ρ lo hi := by + intro n v hn hv + apply hf + rw [map_zero] + apply hσ n (f v) hn + intro a + rw [← he,hv,map_smul] + +lemma hasWeightsBetween_of_surjective [Infinite k] + {M N : Type u} [AddCommGroup M] [Module k M] [Module.Finite k M] + [AddCommGroup N] [Module k N] + (ρ : Representation k (SL2 k) M) (σ : Representation k (SL2 k) N) + (hρ : IsRational k ρ) (f : M →ₗ[k] N) (hf : Function.Surjective f) + (he : ∀ g v, f (ρ g v) = σ g (f v)) (lo hi : ℤ) + (hb : HasWeightsBetween ρ lo hi) : HasWeightsBetween σ lo hi := by + intro n w hn hw + obtain ⟨v,hv,hvw⟩ := rational_weight_lift k ρ σ hρ f he hf (integerCharacter k n) w hw + rw [← hv,hb n v hn hvw,map_zero] + +lemma fdrep_isZero_of_subsingleton {G : Type u} [Monoid G] + (A : FDRep k G) [Subsingleton A] : IsZero A := by + apply (IsZero.iff_id_eq_zero _).mpr + apply fdrep_hom_ext k + intro x + exact Subsingleton.elim _ _ + +lemma IsTilting.of_subsingleton (A : FDRep k (SL2 k)) [Subsingleton A] + (hA : IsRational k A.ρ) : IsTilting k A := by + refine ⟨hA, .zero _ (fdrep_isZero_of_subsingleton k A), .zero _ ?_⟩ + let : Subsingleton (Aᘁ : FDRep k (SL2 k)) := by + change Subsingleton (Module.Dual k A) + infer_instance + exact fdrep_isZero_of_subsingleton k Aᘁ + +lemma IsTilting.extension {A B C : FDRep k (SL2 k)} + (hA : IsTilting k A) (hC : IsTilting k C) (hB : IsRational k B.ρ) + (f : A ⟶ B) (g : B ⟶ C) (w : f ≫ g = 0) + (hS : (ShortComplex.mk f g w).ShortExact) : IsTilting k B := by + refine ⟨hB,hA.2.1.extension k hC.2.1 f g w hS, ?_⟩ + exact hC.2.2.extension k hA.2.2 (fdrepDualMap k g) (fdrepDualMap k f) + (fdrepDualMap_zero_comp k f g w) (fdrep_dual_shortExact k f g w hS) + +end + +section +universe u +variable (k : Type u) [Field k] +variable {G : Type u} [Monoid G] + +lemma exists_proper_subrepresentation (A : FDRep k G) [Nontrivial A] + (h : ¬ Representation.IsIrreducible A.ρ) : + ∃ S : Subrepresentation A.ρ, S ≠ ⊥ ∧ S ≠ ⊤ := by + classical + let : Nontrivial (Subrepresentation A.ρ) := ⟨⟨⊥, ⊤, fun he => + bot_ne_top (congrArg Subrepresentation.toSubmodule he)⟩⟩ + by_contra hn + apply h + refine { eq_bot_or_eq_top := ?_ } + intro S + by_cases hs : S = ⊥ + · exact Or.inl hs + · exact Or.inr (by by_contra ht; exact hn ⟨S,hs,ht⟩) + + + +lemma fdrep_proper_shortExact (A : FDRep k G) (S : Subrepresentation A.ρ) + (hb : S ≠ ⊥) (ht : S ≠ ⊤) : + ∃ (L N : FDRep k G) (f : L ⟶ A) (g : A ⟶ N) (w : f ≫ g = 0), + (ShortComplex.mk f g w).ShortExact ∧ + Module.finrank k L < Module.finrank k A ∧ + Module.finrank k N < Module.finrank k A := by + let L := FDRep.of S.toRepresentation + let N := FDRep.of (Representation.quotient A.ρ S.toSubmodule S.apply_mem_toSubmodule) + let f : L ⟶ A := fdrepHom k S.toSubmodule.subtype (by intros; rfl) + let g : A ⟶ N := fdrepHom k S.toSubmodule.mkQ (by intros; rfl) + have w : f ≫ g = 0 := by + apply fdrep_hom_ext k + intro x + exact (Submodule.Quotient.mk_eq_zero _).mpr x.property + have hb' : S.toSubmodule ≠ ⊥ := fun h => hb (Subrepresentation.ext h) + have ht' : S.toSubmodule ≠ ⊤ := fun h => ht (Subrepresentation.ext h) + have hdim := S.toSubmodule.finrank_quotient_add_finrank + have hp : 0 < Module.finrank k S.toSubmodule := + Module.finrank_pos_iff.mpr (Submodule.nontrivial_iff_ne_bot.mpr hb') + refine ⟨L,N,f,g,w,fdrep_shortExact k _ Subtype.val_injective + S.toSubmodule.mkQ_surjective ?_, Submodule.finrank_lt ht', ?_⟩ + · change LinearMap.range S.toSubmodule.subtype = LinearMap.ker S.toSubmodule.mkQ + simp + · change Module.finrank k (A ⧸ S.toSubmodule) < Module.finrank k A + omega + + + +theorem fdrep_induction (P : FDRep k G → Prop) + (hz : ∀ A : FDRep k G, (Subsingleton A) → P A) + (hi : ∀ A, Representation.IsIrreducible A.ρ → P A) + (he : ∀ (A B C : FDRep k G) (f : A ⟶ B) (g : B ⟶ C) (w : f ≫ g = 0), + (ShortComplex.mk f g w).ShortExact → P A → P C → P B) (A : FDRep k G) : P A := by + classical + generalize hn : Module.finrank k A = n + induction n using Nat.strong_induction_on generalizing A with + | h n ih => + by_cases hzA : Subsingleton A + · exact hz A hzA + let : Nontrivial A := not_subsingleton_iff_nontrivial.mp hzA + by_cases hiA : Representation.IsIrreducible A.ρ + · exact hi A hiA + obtain ⟨S,hb,ht⟩ := exists_proper_subrepresentation k A hiA + obtain ⟨L,N,f,g,w,hS,hL,hN⟩ := fdrep_proper_shortExact k A S hb ht + apply he L A N f g w hS + · exact ih (Module.finrank k L) (hn ▸ hL) L rfl + · exact ih (Module.finrank k N) (hn ▸ hN) N rfl +end + +universe u +variable (k : Type u) [Field k] [Infinite k] +variable (p : ℕ) [Fact p.Prime] [CharP k p] + +lemma steinberg_tensor_simple_dual_tilting (m n : ℕ) (hn : n < p^(m+1)) : + IsTilting k (steinberg k p m ⊗ (simpleSL2 k n)ᘁ) := by + obtain ⟨eS⟩ := steinberg_self_dual k p m + let e : (steinberg k p m ⊗ simpleSL2 k n)ᘁ ≅ + steinberg k p m ⊗ (simpleSL2 k n)ᘁ := + rightDualTensorIso _ _ ≪≫ tensorIso (Iso.refl _) eS ≪≫ β_ _ _ + exact ((steinberg_tensor_simple_tilting k p m n hn).dual k).of_iso k e + +lemma steinberg_tensor_irreducible_tilting (m d : ℕ) (hd : d < p^(m+1)) + (A : FDRep k (SL2 k)) [Representation.IsIrreducible A.ρ] + (hA : IsRational k A.ρ) (hb : HasWeightsBetween A.ρ (-(d : ℤ)) d) : + IsTilting k (steinberg k p m ⊗ A) := by + obtain ⟨n,hn,⟨e⟩⟩ := irreducible_eq_simple_dual k A hA d hb + exact (steinberg_tensor_simple_dual_tilting k p m n (hn.trans_lt hd)).of_iso k + (tensorIso (Iso.refl _) e.symm) + + + +theorem bounded_weights_tilting (m d : ℕ) (hd : d < p^(m+1)) + (A : FDRep k (SL2 k)) (hA : IsRational k A.ρ) + (hb : HasWeightsBetween A.ρ (-(d : ℤ)) d) : + IsTilting k (steinberg k p m ⊗ A) := by + let P : FDRep k (SL2 k) → Prop := fun B => IsRational k B.ρ → + HasWeightsBetween B.ρ (-(d : ℤ)) d → IsTilting k (steinberg k p m ⊗ B) + apply fdrep_induction k P ?_ ?_ ?_ A hA hb + · intro B hB hr _ + let : Subsingleton B := hB + let : Subsingleton (steinberg k p m ⊗ B : FDRep k (SL2 k)) := by + change Subsingleton (TensorProduct k (steinberg k p m) B) + infer_instance + exact IsTilting.of_subsingleton k (steinberg k p m ⊗ B) + (IsRational.tensor k (steinberg k p m).ρ B.ρ (steinberg_tilting k p m).1 hr) + · intro B hi hr hw + let : Representation.IsIrreducible B.ρ := hi + exact steinberg_tensor_irreducible_tilting k p m d hd B hr hw + · intro L B N f g w hS hL hN hr hw + have := hS.mono_f + have := hS.epi_g + have hrL := IsRational.of_injective k L.ρ B.ρ (fdrepLinear k f) + (fdrep_injective k f) (fdrepLinear_comm k f) hr + have hrN := IsRational.of_surjective k B.ρ N.ρ (fdrepLinear k g) + (fdrep_surjective k g) (fdrepLinear_comm k g) hr + have hwL := hasWeightsBetween_of_injective k L.ρ B.ρ (fdrepLinear k f) + (fdrep_injective k f) (fdrepLinear_comm k f) _ _ hw + have hwN := hasWeightsBetween_of_surjective k B.ρ N.ρ hr (fdrepLinear k g) + (fdrep_surjective k g) (fdrepLinear_comm k g) _ _ hw + let F := tensorLeft (steinberg k p m) + let := tensorLeft_preservesFiniteLimits (steinberg k p m) + let := tensorLeft_preservesFiniteColimits (steinberg k p m) + have hT := hS.map_of_exact F + exact (hL hrL hwL).extension k (hN hrN hwN) + (IsRational.tensor k (steinberg k p m).ρ B.ρ (steinberg_tilting k p m).1 hr) _ _ _ hT +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TiltingCovers.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TiltingCovers.lean index c2d6b9f3f81cbfda5f887e8397c07d95551e9d58..722eadac6b2e390c0ae2f1a624d4c7d62ec9c403 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TiltingCovers.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TiltingCovers.lean @@ -1,96 +1,96 @@ -import OAI.RepresentationTheory.RestrictedTilting.PolynomialCovers -import OAI.RepresentationTheory.RestrictedTilting.GoodKernelExtension - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -universe u -variable (k : Type u) [Field k] - - - -inductive SteinbergGenerated (p r : ℕ) : FDRep k (SL2 k) → Prop - | low (A) (hA : IsTilting k A) (a : ℕ) (ha : a < p^r-1) - (hw : HasWeightsBetween A.ρ (-(a : ℤ)) a) : SteinbergGenerated p r A - | high (X) (hX : IsTilting k X) : SteinbergGenerated p r (steinberg k p r ⊗ X) - | of_iso {A B} (hA : SteinbergGenerated p r A) (e : A ≅ B) : SteinbergGenerated p r B - | prod {A B} (hA : SteinbergGenerated p r A) (hB : SteinbergGenerated p r B) : - SteinbergGenerated p r (repProduct k A B) - -variable [Infinite k] (p r : ℕ) [Fact p.Prime] [CharP k p] - -lemma SteinbergGenerated.tilting {A : FDRep k (SL2 k)} (h : SteinbergGenerated k p r A) : - IsTilting k A := by - induction h with - | low A hA a ha hw => exact hA - | high X hX => exact (steinberg_tilting k p r).tensor k hX - | of_iso hA e ih => exact ih.of_iso k e - | prod hA hB ihA ihB => exact ihA.product k ihB - - -omit [Fact p.Prime] [CharP k p] in -lemma costandard_generated_cover (n : ℕ) : - ∃ (P : FDRep k (SL2 k)) (g : P ⟶ costandard k n), - HasGoodKernel k g ∧ SteinbergGenerated k p r P := by - by_cases hn : n < p^r-1 - · let P := tensorPowerFrom k (costandard k 0) n - have hP : SteinbergGenerated k p r P := .low P - (tensorPowerFrom_tilting k (costandard_zero_tilting k) n) n hn (by - have h := tensorPowerFrom_weights k (costandard_rational k 0) 0 - (fun m v hm hv => costandard_weight_bound k 0 m hm v hv) n - simpa only [Nat.zero_add, Nat.cast_zero, zero_add] using h) - let e : costandard k (0+n) ≅ costandard k n := - eqToIso (congrArg (costandard k) (Nat.zero_add n)) - exact ⟨P,polynomialPowerMap k 0 n ≫ e.hom, - (polynomialPowerMap_goodKernel k 0 n).comp k (HasGoodKernel.of_isIso k e.hom),hP⟩ - · let m := p^r-1 - let t := n-m - let P := tensorPowerFrom k (costandard k m) t - let X := tensorPowerFrom k (costandard k 0) t - obtain ⟨e⟩ := tensorPowerFrom_factor k m t - have hX : IsTilting k X := tensorPowerFrom_tilting k (costandard_zero_tilting k) t - have hP : SteinbergGenerated k p r P := - (SteinbergGenerated.high X hX).of_iso e.symm - have hmt : m+t = n := Nat.add_sub_of_le (by dsimp [m]; omega) - let e' : costandard k (m+t) ≅ costandard k n := eqToIso (congrArg (costandard k) hmt) - exact ⟨P,polynomialPowerMap k m t ≫ e'.hom, - (polynomialPowerMap_goodKernel k m t).comp k (HasGoodKernel.of_isIso k e'.hom),hP⟩ - - - -lemma good_generated_cover (hr : 1 ≤ r) {A : FDRep k (SL2 k)} - (hA : HasGoodFiltration k A) (hR : IsRational k A.ρ) : - ∃ (P : FDRep k (SL2 k)) (g : P ⟶ A), - HasGoodKernel k g ∧ SteinbergGenerated k p r P := by - induction hA with - | zero A hz => - have hAZ : ∀ x : A, x = 0 := fun x => - congrArg (fun f => fdrepLinear k f x) (hz.eq_zero_of_src (𝟙 A)) - have : Subsingleton A := subsingleton_of_forall_eq 0 hAZ - have hq : 1 < p^r := Nat.one_lt_pow (by omega) (Fact.out : p.Prime).one_lt - refine ⟨A,𝟙 A,HasGoodKernel.id k A, - .low A (IsTilting.of_subsingleton k A hR) 0 (by omega) ?_⟩ - intro m v hm hv - exact hAZ v - | @step A B n f g w hS hA ih => - have := hS.mono_f - have hRA : IsRational k A.ρ := IsRational.of_injective k _ _ (fdrepLinear k f) - (fdrep_injective k f) (fdrepLinear_comm k f) hR - obtain ⟨P,a,ha,hP⟩ := ih hRA - obtain ⟨Q,q,hq,hQ⟩ := costandard_generated_cover k p r n - obtain ⟨s,hs⟩ := good_weyl_lift k f g w hS hR (hQ.tilting k p r) hA q - exact ⟨repProduct k P Q,extensionCoverMap k f a s, - extensionCoverMap_goodKernel k f g w hS a q ha hq s hs,.prod hP hQ⟩ - - - -theorem tilting_retract_generated (hr : 1 ≤ r) (A : FDRep k (SL2 k)) (hA : IsTilting k A) : - ∃ (P : FDRep k (SL2 k)) (g : P ⟶ A) (s : A ⟶ P), - s ≫ g = 𝟙 A ∧ SteinbergGenerated k p r P := by - obtain ⟨P,g,hg,hP⟩ := good_generated_cover k p r hr hA.2.1 hA.1 - obtain ⟨s,hs⟩ := hg.split k (hP.tilting k p r).1 hA - exact ⟨P,g,s,hs,hP⟩ -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.PolynomialCovers +import OAI.RepresentationTheory.RestrictedTilting.GoodKernelExtension + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +universe u +variable (k : Type u) [Field k] + + + +inductive SteinbergGenerated (p r : ℕ) : FDRep k (SL2 k) → Prop + | low (A) (hA : IsTilting k A) (a : ℕ) (ha : a < p^r-1) + (hw : HasWeightsBetween A.ρ (-(a : ℤ)) a) : SteinbergGenerated p r A + | high (X) (hX : IsTilting k X) : SteinbergGenerated p r (steinberg k p r ⊗ X) + | of_iso {A B} (hA : SteinbergGenerated p r A) (e : A ≅ B) : SteinbergGenerated p r B + | prod {A B} (hA : SteinbergGenerated p r A) (hB : SteinbergGenerated p r B) : + SteinbergGenerated p r (repProduct k A B) + +variable [Infinite k] (p r : ℕ) [Fact p.Prime] [CharP k p] + +lemma SteinbergGenerated.tilting {A : FDRep k (SL2 k)} (h : SteinbergGenerated k p r A) : + IsTilting k A := by + induction h with + | low A hA a ha hw => exact hA + | high X hX => exact (steinberg_tilting k p r).tensor k hX + | of_iso hA e ih => exact ih.of_iso k e + | prod hA hB ihA ihB => exact ihA.product k ihB + + +omit [Fact p.Prime] [CharP k p] in +lemma costandard_generated_cover (n : ℕ) : + ∃ (P : FDRep k (SL2 k)) (g : P ⟶ costandard k n), + HasGoodKernel k g ∧ SteinbergGenerated k p r P := by + by_cases hn : n < p^r-1 + · let P := tensorPowerFrom k (costandard k 0) n + have hP : SteinbergGenerated k p r P := .low P + (tensorPowerFrom_tilting k (costandard_zero_tilting k) n) n hn (by + have h := tensorPowerFrom_weights k (costandard_rational k 0) 0 + (fun m v hm hv => costandard_weight_bound k 0 m hm v hv) n + simpa only [Nat.zero_add, Nat.cast_zero, zero_add] using h) + let e : costandard k (0+n) ≅ costandard k n := + eqToIso (congrArg (costandard k) (Nat.zero_add n)) + exact ⟨P,polynomialPowerMap k 0 n ≫ e.hom, + (polynomialPowerMap_goodKernel k 0 n).comp k (HasGoodKernel.of_isIso k e.hom),hP⟩ + · let m := p^r-1 + let t := n-m + let P := tensorPowerFrom k (costandard k m) t + let X := tensorPowerFrom k (costandard k 0) t + obtain ⟨e⟩ := tensorPowerFrom_factor k m t + have hX : IsTilting k X := tensorPowerFrom_tilting k (costandard_zero_tilting k) t + have hP : SteinbergGenerated k p r P := + (SteinbergGenerated.high X hX).of_iso e.symm + have hmt : m+t = n := Nat.add_sub_of_le (by dsimp [m]; omega) + let e' : costandard k (m+t) ≅ costandard k n := eqToIso (congrArg (costandard k) hmt) + exact ⟨P,polynomialPowerMap k m t ≫ e'.hom, + (polynomialPowerMap_goodKernel k m t).comp k (HasGoodKernel.of_isIso k e'.hom),hP⟩ + + + +lemma good_generated_cover (hr : 1 ≤ r) {A : FDRep k (SL2 k)} + (hA : HasGoodFiltration k A) (hR : IsRational k A.ρ) : + ∃ (P : FDRep k (SL2 k)) (g : P ⟶ A), + HasGoodKernel k g ∧ SteinbergGenerated k p r P := by + induction hA with + | zero A hz => + have hAZ : ∀ x : A, x = 0 := fun x => + congrArg (fun f => fdrepLinear k f x) (hz.eq_zero_of_src (𝟙 A)) + have : Subsingleton A := subsingleton_of_forall_eq 0 hAZ + have hq : 1 < p^r := Nat.one_lt_pow (by omega) (Fact.out : p.Prime).one_lt + refine ⟨A,𝟙 A,HasGoodKernel.id k A, + .low A (IsTilting.of_subsingleton k A hR) 0 (by omega) ?_⟩ + intro m v hm hv + exact hAZ v + | @step A B n f g w hS hA ih => + have := hS.mono_f + have hRA : IsRational k A.ρ := IsRational.of_injective k _ _ (fdrepLinear k f) + (fdrep_injective k f) (fdrepLinear_comm k f) hR + obtain ⟨P,a,ha,hP⟩ := ih hRA + obtain ⟨Q,q,hq,hQ⟩ := costandard_generated_cover k p r n + obtain ⟨s,hs⟩ := good_weyl_lift k f g w hS hR (hQ.tilting k p r) hA q + exact ⟨repProduct k P Q,extensionCoverMap k f a s, + extensionCoverMap_goodKernel k f g w hS a q ha hq s hs,.prod hP hQ⟩ + + + +theorem tilting_retract_generated (hr : 1 ≤ r) (A : FDRep k (SL2 k)) (hA : IsTilting k A) : + ∃ (P : FDRep k (SL2 k)) (g : P ⟶ A) (s : A ⟶ P), + s ≫ g = 𝟙 A ∧ SteinbergGenerated k p r P := by + obtain ⟨P,g,hg,hP⟩ := good_generated_cover k p r hr hA.2.1 hA.1 + obtain ⟨s,hs⟩ := hg.split k (hP.tilting k p r).1 hA + exact ⟨P,g,s,hs,hP⟩ +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TorusExtension.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TorusExtension.lean index 2305b089fa67f69019676c17fcbcd94360e4d7c2..a09941d4c30e0578cc279ec5359dd513b1dd8b52 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TorusExtension.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TorusExtension.lean @@ -1,50 +1,50 @@ -import OAI.RepresentationTheory.RestrictedTilting.TorusRelations - -namespace OAI - -namespace FiberFunctorProof -open scoped LaurentPolynomial -universe u v -variable {k : Type u} [Field k] [Infinite k] -variable {K : Type v} [Field K] [Algebra k K] -variable {ι : Type u} [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (SL2 k) (ι → k)) (hρ : IsRational k ρ) - -noncomputable def laurentBaseEval (x : Kˣ) : LaurentPolynomial k →ₐ[k] K := - ⟨LaurentPolynomial.eval₂ (algebraMap k K) x, - fun c => LaurentPolynomial.eval₂_C _ _ c⟩ - -noncomputable def torusMatrixAt (x : Kˣ) : Matrix ι ι K := - (rationalTorusMatrix k ρ hρ).map (laurentBaseEval x) - -lemma torusMatrixAt_det_ne_zero (x : Kˣ) : (torusMatrixAt ρ hρ x).det ≠ 0 := by - let Qinv := ((rationalTorusMatrix k ρ hρ).map LaurentPolynomial.invert).map - (laurentBaseEval x) - have he : torusMatrixAt ρ hρ x * Qinv = 1 := by - rw [torusMatrixAt, ← Matrix.map_mul, rationalTorusMatrix_inverse, Matrix.map_one] - all_goals simp only [map_zero, map_one] - have hd := congrArg Matrix.det he - rw [Matrix.det_mul, Matrix.det_one] at hd - exact (mul_ne_zero_iff.mp (hd ▸ one_ne_zero)).1 - -lemma torusMatrixAt_unipotent (x : Kˣ) (t : k) : - torusMatrixAt ρ hρ x * (LinearMap.toMatrix' (ρ (unipotent k t))).map (algebraMap k K) = - polynomialMatrixEval (rationalUnipotentMatrix k ρ hρ) ((x : K)^2 * algebraMap k K t) * - torusMatrixAt ρ hρ x := by - have he := congrArg (fun A : Matrix ι ι (LaurentPolynomial k) => A.map (laurentBaseEval x)) - (rational_torus_unipotent_laurent k ρ hρ t) - have hc : ((LinearMap.toMatrix' (ρ (unipotent k t))).map LaurentPolynomial.C).map - (laurentBaseEval x) = (LinearMap.toMatrix' (ρ (unipotent k t))).map (algebraMap k K) := by - apply Matrix.ext - intro i j - exact LaurentPolynomial.eval₂_C _ _ _ - have hx : laurentBaseEval x ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t) = - (x : K)^2 * algebraMap k K t := by - change LaurentPolynomial.eval₂ (algebraMap k K) x - ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t) = _ - simp only [map_mul, LaurentPolynomial.eval₂_C, LaurentPolynomial.eval₂_T, zpow_ofNat, Units.val_pow_eq_pow_val] - simpa only [Matrix.map_mul, hc, polynomialMatrixEval_map, hx, torusMatrixAt] using he - -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.TorusRelations + +namespace OAI + +namespace FiberFunctorProof +open scoped LaurentPolynomial +universe u v +variable {k : Type u} [Field k] [Infinite k] +variable {K : Type v} [Field K] [Algebra k K] +variable {ι : Type u} [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (SL2 k) (ι → k)) (hρ : IsRational k ρ) + +noncomputable def laurentBaseEval (x : Kˣ) : LaurentPolynomial k →ₐ[k] K := + ⟨LaurentPolynomial.eval₂ (algebraMap k K) x, + fun c => LaurentPolynomial.eval₂_C _ _ c⟩ + +noncomputable def torusMatrixAt (x : Kˣ) : Matrix ι ι K := + (rationalTorusMatrix k ρ hρ).map (laurentBaseEval x) + +lemma torusMatrixAt_det_ne_zero (x : Kˣ) : (torusMatrixAt ρ hρ x).det ≠ 0 := by + let Qinv := ((rationalTorusMatrix k ρ hρ).map LaurentPolynomial.invert).map + (laurentBaseEval x) + have he : torusMatrixAt ρ hρ x * Qinv = 1 := by + rw [torusMatrixAt, ← Matrix.map_mul, rationalTorusMatrix_inverse, Matrix.map_one] + all_goals simp only [map_zero, map_one] + have hd := congrArg Matrix.det he + rw [Matrix.det_mul, Matrix.det_one] at hd + exact (mul_ne_zero_iff.mp (hd ▸ one_ne_zero)).1 + +lemma torusMatrixAt_unipotent (x : Kˣ) (t : k) : + torusMatrixAt ρ hρ x * (LinearMap.toMatrix' (ρ (unipotent k t))).map (algebraMap k K) = + polynomialMatrixEval (rationalUnipotentMatrix k ρ hρ) ((x : K)^2 * algebraMap k K t) * + torusMatrixAt ρ hρ x := by + have he := congrArg (fun A : Matrix ι ι (LaurentPolynomial k) => A.map (laurentBaseEval x)) + (rational_torus_unipotent_laurent k ρ hρ t) + have hc : ((LinearMap.toMatrix' (ρ (unipotent k t))).map LaurentPolynomial.C).map + (laurentBaseEval x) = (LinearMap.toMatrix' (ρ (unipotent k t))).map (algebraMap k K) := by + apply Matrix.ext + intro i j + exact LaurentPolynomial.eval₂_C _ _ _ + have hx : laurentBaseEval x ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t) = + (x : K)^2 * algebraMap k K t := by + change LaurentPolynomial.eval₂ (algebraMap k K) x + ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t) = _ + simp only [map_mul, LaurentPolynomial.eval₂_C, LaurentPolynomial.eval₂_T, zpow_ofNat, Units.val_pow_eq_pow_val] + simpa only [Matrix.map_mul, hc, polynomialMatrixEval_map, hx, torusMatrixAt] using he + +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TorusRelations.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TorusRelations.lean index e170b53db1c118b4b615c7f4c3cade40d4d54d5d..8453a012ee719e9521b7c5f62703591978c9e904 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TorusRelations.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TorusRelations.lean @@ -1,81 +1,81 @@ -import OAI.RepresentationTheory.RestrictedTilting.RationalMatrices -import OAI.RepresentationTheory.RestrictedTilting.LaurentPolynomialSeparation - -namespace OAI - -namespace FiberFunctorProof -open scoped LaurentPolynomial BigOperators -universe u -variable (k : Type u) [Field k] [Infinite k] -variable {ι : Type u} [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (SL2 k) (ι → k)) (hρ : IsRational k ρ) - -omit [Infinite k] in -lemma eval_laurent_invert (P : LaurentPolynomial k) (a : kˣ) : - LaurentPolynomial.eval₂ (RingHom.id k) a (LaurentPolynomial.invert P) = - LaurentPolynomial.eval₂ (RingHom.id k) a⁻¹ P := by - induction P using LaurentPolynomial.induction_on' with - | add P Q hP hQ => simp only [map_add, hP, hQ] - | C_mul_T n c => simp [zpow_neg] - -lemma rationalTorusMatrix_inverse : - rationalTorusMatrix k ρ hρ * (rationalTorusMatrix k ρ hρ).map LaurentPolynomial.invert = 1 := by - apply Matrix.ext - intro i j - apply laurent_eq_of_evals - intro a - have he : ((rationalTorusMatrix k ρ hρ).map LaurentPolynomial.invert).map - (LaurentPolynomial.eval₂ (RingHom.id k) a) = - (rationalTorusMatrix k ρ hρ).map (LaurentPolynomial.eval₂ (RingHom.id k) a⁻¹) := by - ext r s - exact eval_laurent_invert k _ a - have hM : (rationalTorusMatrix k ρ hρ * - (rationalTorusMatrix k ρ hρ).map LaurentPolynomial.invert).map - (LaurentPolynomial.eval₂ (RingHom.id k) a) = 1 := by - rw [Matrix.map_mul, he, eval_rationalTorusMatrix, eval_rationalTorusMatrix, - ← LinearMap.toMatrix'_mul, ← map_mul, ← map_mul, mul_inv_cancel, map_one] - simp only [map_one, LinearMap.toMatrix'_one] - have hh := congrArg (fun A : Matrix ι ι k => A i j) hM - simpa [Matrix.map_apply, Matrix.one_apply] using hh - -lemma rational_torus_unipotent_laurent (t : k) : - rationalTorusMatrix k ρ hρ * (LinearMap.toMatrix' (ρ (unipotent k t))).map LaurentPolynomial.C = - polynomialMatrixEval (rationalUnipotentMatrix k ρ hρ) - ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t) * - rationalTorusMatrix k ρ hρ := by - apply Matrix.ext - intro i j - apply laurent_eq_of_evals - intro a - let ev : LaurentPolynomial k →ₐ[k] k := - ⟨LaurentPolynomial.eval₂ (RingHom.id k) a, fun c => LaurentPolynomial.eval₂_C _ _ c⟩ - have he : ((LinearMap.toMatrix' (ρ (unipotent k t))).map LaurentPolynomial.C).map ev = - LinearMap.toMatrix' (ρ (unipotent k t)) := by - ext r s - exact LaurentPolynomial.eval₂_C _ _ _ - have hp : (polynomialMatrixEval (rationalUnipotentMatrix k ρ hρ) - ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t)).map ev = - LinearMap.toMatrix' (ρ (unipotent k ((a : k)^2*t))) := by - rw [polynomialMatrixEval_map] - have hev : ev ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t) = - (a : k)^2*t := by - change LaurentPolynomial.eval₂ (RingHom.id k) a - ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t) = _ - simp only [map_mul, LaurentPolynomial.eval₂_C, LaurentPolynomial.eval₂_T, - RingHom.id_apply, zpow_ofNat, Units.val_pow_eq_pow_val] - rw [hev] - exact eval_rationalUnipotentMatrix k ρ hρ _ - have hM : ((rationalTorusMatrix k ρ hρ) * - (LinearMap.toMatrix' (ρ (unipotent k t))).map LaurentPolynomial.C).map ev = - (polynomialMatrixEval (rationalUnipotentMatrix k ρ hρ) - ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t) * - rationalTorusMatrix k ρ hρ).map ev := by - rw [Matrix.map_mul, Matrix.map_mul, he, hp] - change (rationalTorusMatrix k ρ hρ).map (LaurentPolynomial.eval₂ (RingHom.id k) a) * _ = _ * - (rationalTorusMatrix k ρ hρ).map (LaurentPolynomial.eval₂ (RingHom.id k) a) - rw [eval_rationalTorusMatrix, ← LinearMap.toMatrix'_mul, ← LinearMap.toMatrix'_mul, - ← map_mul, ← map_mul, diagonal_unipotent] - exact congrArg (fun A : Matrix ι ι k => A i j) hM -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.RationalMatrices +import OAI.RepresentationTheory.RestrictedTilting.LaurentPolynomialSeparation + +namespace OAI + +namespace FiberFunctorProof +open scoped LaurentPolynomial BigOperators +universe u +variable (k : Type u) [Field k] [Infinite k] +variable {ι : Type u} [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (SL2 k) (ι → k)) (hρ : IsRational k ρ) + +omit [Infinite k] in +lemma eval_laurent_invert (P : LaurentPolynomial k) (a : kˣ) : + LaurentPolynomial.eval₂ (RingHom.id k) a (LaurentPolynomial.invert P) = + LaurentPolynomial.eval₂ (RingHom.id k) a⁻¹ P := by + induction P using LaurentPolynomial.induction_on' with + | add P Q hP hQ => simp only [map_add, hP, hQ] + | C_mul_T n c => simp [zpow_neg] + +lemma rationalTorusMatrix_inverse : + rationalTorusMatrix k ρ hρ * (rationalTorusMatrix k ρ hρ).map LaurentPolynomial.invert = 1 := by + apply Matrix.ext + intro i j + apply laurent_eq_of_evals + intro a + have he : ((rationalTorusMatrix k ρ hρ).map LaurentPolynomial.invert).map + (LaurentPolynomial.eval₂ (RingHom.id k) a) = + (rationalTorusMatrix k ρ hρ).map (LaurentPolynomial.eval₂ (RingHom.id k) a⁻¹) := by + ext r s + exact eval_laurent_invert k _ a + have hM : (rationalTorusMatrix k ρ hρ * + (rationalTorusMatrix k ρ hρ).map LaurentPolynomial.invert).map + (LaurentPolynomial.eval₂ (RingHom.id k) a) = 1 := by + rw [Matrix.map_mul, he, eval_rationalTorusMatrix, eval_rationalTorusMatrix, + ← LinearMap.toMatrix'_mul, ← map_mul, ← map_mul, mul_inv_cancel, map_one] + simp only [map_one, LinearMap.toMatrix'_one] + have hh := congrArg (fun A : Matrix ι ι k => A i j) hM + simpa [Matrix.map_apply, Matrix.one_apply] using hh + +lemma rational_torus_unipotent_laurent (t : k) : + rationalTorusMatrix k ρ hρ * (LinearMap.toMatrix' (ρ (unipotent k t))).map LaurentPolynomial.C = + polynomialMatrixEval (rationalUnipotentMatrix k ρ hρ) + ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t) * + rationalTorusMatrix k ρ hρ := by + apply Matrix.ext + intro i j + apply laurent_eq_of_evals + intro a + let ev : LaurentPolynomial k →ₐ[k] k := + ⟨LaurentPolynomial.eval₂ (RingHom.id k) a, fun c => LaurentPolynomial.eval₂_C _ _ c⟩ + have he : ((LinearMap.toMatrix' (ρ (unipotent k t))).map LaurentPolynomial.C).map ev = + LinearMap.toMatrix' (ρ (unipotent k t)) := by + ext r s + exact LaurentPolynomial.eval₂_C _ _ _ + have hp : (polynomialMatrixEval (rationalUnipotentMatrix k ρ hρ) + ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t)).map ev = + LinearMap.toMatrix' (ρ (unipotent k ((a : k)^2*t))) := by + rw [polynomialMatrixEval_map] + have hev : ev ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t) = + (a : k)^2*t := by + change LaurentPolynomial.eval₂ (RingHom.id k) a + ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t) = _ + simp only [map_mul, LaurentPolynomial.eval₂_C, LaurentPolynomial.eval₂_T, + RingHom.id_apply, zpow_ofNat, Units.val_pow_eq_pow_val] + rw [hev] + exact eval_rationalUnipotentMatrix k ρ hρ _ + have hM : ((rationalTorusMatrix k ρ hρ) * + (LinearMap.toMatrix' (ρ (unipotent k t))).map LaurentPolynomial.C).map ev = + (polynomialMatrixEval (rationalUnipotentMatrix k ρ hρ) + ((LaurentPolynomial.T 2 : LaurentPolynomial k) * LaurentPolynomial.C t) * + rationalTorusMatrix k ρ hρ).map ev := by + rw [Matrix.map_mul, Matrix.map_mul, he, hp] + change (rationalTorusMatrix k ρ hρ).map (LaurentPolynomial.eval₂ (RingHom.id k) a) * _ = _ * + (rationalTorusMatrix k ρ hρ).map (LaurentPolynomial.eval₂ (RingHom.id k) a) + rw [eval_rationalTorusMatrix, ← LinearMap.toMatrix'_mul, ← LinearMap.toMatrix'_mul, + ← map_mul, ← map_mul, diagonal_unipotent] + exact congrArg (fun A : Matrix ι ι k => A i j) hM +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TorusWeightProjection.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TorusWeightProjection.lean index 3c98b9f33a809d6ff7b978278ab01d63697be58b..0a841bacd0f733918e817122d1d4fcbad3cbe5e7 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TorusWeightProjection.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TorusWeightProjection.lean @@ -1,72 +1,72 @@ -import OAI.RepresentationTheory.RestrictedTilting.Basic - -namespace OAI - -namespace FiberFunctorProof -open scoped BigOperators -universe u -variable {k : Type u} [Field k] [Infinite k] -variable {V : Type u} [AddCommGroup V] [Module k V] [Module.Finite k V] - -noncomputable def torusExpansion (ρ : Representation k (SL2 k) V) - (hρ : IsRational k ρ) (v : V) : ℤ →₀ V := - Classical.choose (rational_torus_integerExpansions k ρ hρ v) - -omit [Infinite k] in -lemma torusExpansion_spec (ρ : Representation k (SL2 k) V) - (hρ : IsRational k ρ) (v : V) (a : kˣ) : - ρ (diagonalTorus k a) v = (torusExpansion ρ hρ v).sum - (fun n x => integerCharacter k n a • x) := - Classical.choose_spec (rational_torus_integerExpansions k ρ hρ v) a - -lemma torusExpansion_unique (ρ : Representation k (SL2 k) V) - (hρ : IsRational k ρ) (v : V) (c : ℤ →₀ V) - (hc : ∀ a, ρ (diagonalTorus k a) v = c.sum (fun n x => integerCharacter k n a • x)) : - torusExpansion ρ hρ v = c := by - apply function_finsupp_ext (fun n a => integerCharacter k n a) - ((linearIndependent_monoidHom kˣ k).comp _ (integerCharacter_injective k)) - intro a - rw [← torusExpansion_spec, hc] - - -noncomputable def torusWeightProjection (ρ : Representation k (SL2 k) V) - (hρ : IsRational k ρ) (n : ℤ) : V →ₗ[k] V where - toFun v := torusExpansion ρ hρ v n - map_add' v w := by - classical - have h := torusExpansion_unique ρ hρ (v+w) - (torusExpansion ρ hρ v + torusExpansion ρ hρ w) (fun a => by - rw [Finsupp.sum_add_index (fun _ _ => smul_zero _) (fun _ _ _ _ => smul_add _ _ _)] - rw [map_add, ← torusExpansion_spec, ← torusExpansion_spec]) - exact congrArg (fun c => c n) h - map_smul' t v := by - classical - have h := torusExpansion_unique ρ hρ (t • v) - (t • torusExpansion ρ hρ v) (fun a => by - rw [Finsupp.sum_smul_index' (fun _ => smul_zero _), map_smul, - torusExpansion_spec] - simp only [Finsupp.sum, Finset.smul_sum] - apply Finset.sum_congr rfl - intro i hi - exact smul_comm t (integerCharacter k i a) _) - exact congrArg (fun c => c n) h - -lemma torusWeightProjection_eigen (ρ : Representation k (SL2 k) V) - (hρ : IsRational k ρ) (n m : ℤ) (v : V) - (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k m a • v) : - torusWeightProjection ρ hρ n v = if m = n then v else 0 := by - classical - have h := torusExpansion_unique ρ hρ v (Finsupp.single m v) (fun a => by - simpa using hv a) - change torusExpansion ρ hρ v n = _ - rw [h, Finsupp.single_apply] - -lemma torusWeightProjection_zero_fixed (ρ : Representation k (SL2 k) V) - (hρ : IsRational k ρ) (v : V) - (hv : ∀ a, ρ (diagonalTorus k a) v = v) : - torusWeightProjection ρ hρ 0 v = v := by - rw [torusWeightProjection_eigen ρ hρ 0 0 v (by simpa [integerCharacter] using hv)] - simp -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.Basic + +namespace OAI + +namespace FiberFunctorProof +open scoped BigOperators +universe u +variable {k : Type u} [Field k] [Infinite k] +variable {V : Type u} [AddCommGroup V] [Module k V] [Module.Finite k V] + +noncomputable def torusExpansion (ρ : Representation k (SL2 k) V) + (hρ : IsRational k ρ) (v : V) : ℤ →₀ V := + Classical.choose (rational_torus_integerExpansions k ρ hρ v) + +omit [Infinite k] in +lemma torusExpansion_spec (ρ : Representation k (SL2 k) V) + (hρ : IsRational k ρ) (v : V) (a : kˣ) : + ρ (diagonalTorus k a) v = (torusExpansion ρ hρ v).sum + (fun n x => integerCharacter k n a • x) := + Classical.choose_spec (rational_torus_integerExpansions k ρ hρ v) a + +lemma torusExpansion_unique (ρ : Representation k (SL2 k) V) + (hρ : IsRational k ρ) (v : V) (c : ℤ →₀ V) + (hc : ∀ a, ρ (diagonalTorus k a) v = c.sum (fun n x => integerCharacter k n a • x)) : + torusExpansion ρ hρ v = c := by + apply function_finsupp_ext (fun n a => integerCharacter k n a) + ((linearIndependent_monoidHom kˣ k).comp _ (integerCharacter_injective k)) + intro a + rw [← torusExpansion_spec, hc] + + +noncomputable def torusWeightProjection (ρ : Representation k (SL2 k) V) + (hρ : IsRational k ρ) (n : ℤ) : V →ₗ[k] V where + toFun v := torusExpansion ρ hρ v n + map_add' v w := by + classical + have h := torusExpansion_unique ρ hρ (v+w) + (torusExpansion ρ hρ v + torusExpansion ρ hρ w) (fun a => by + rw [Finsupp.sum_add_index (fun _ _ => smul_zero _) (fun _ _ _ _ => smul_add _ _ _)] + rw [map_add, ← torusExpansion_spec, ← torusExpansion_spec]) + exact congrArg (fun c => c n) h + map_smul' t v := by + classical + have h := torusExpansion_unique ρ hρ (t • v) + (t • torusExpansion ρ hρ v) (fun a => by + rw [Finsupp.sum_smul_index' (fun _ => smul_zero _), map_smul, + torusExpansion_spec] + simp only [Finsupp.sum, Finset.smul_sum] + apply Finset.sum_congr rfl + intro i hi + exact smul_comm t (integerCharacter k i a) _) + exact congrArg (fun c => c n) h + +lemma torusWeightProjection_eigen (ρ : Representation k (SL2 k) V) + (hρ : IsRational k ρ) (n m : ℤ) (v : V) + (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k m a • v) : + torusWeightProjection ρ hρ n v = if m = n then v else 0 := by + classical + have h := torusExpansion_unique ρ hρ v (Finsupp.single m v) (fun a => by + simpa using hv a) + change torusExpansion ρ hρ v n = _ + rw [h, Finsupp.single_apply] + +lemma torusWeightProjection_zero_fixed (ρ : Representation k (SL2 k) V) + (hρ : IsRational k ρ) (v : V) + (hv : ∀ a, ρ (diagonalTorus k a) v = v) : + torusWeightProjection ρ hρ 0 v = v := by + rw [torusWeightProjection_eigen ρ hρ 0 0 v (by simpa [integerCharacter] using hv)] + simp +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/TraceFactor.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/TraceFactor.lean index 26f4b0e705bfa7313918702fc51f25a101c743d6..37312a13069ebfaa925b5d7adc93c3293b541931 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/TraceFactor.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/TraceFactor.lean @@ -1,96 +1,96 @@ -import OAI.RepresentationTheory.RestrictedTilting.FiniteFreeTrace - -namespace OAI - -namespace FiberFunctorProof -open CategoryTheory Representation -universe u -variable {k : Type u} [Field k] {G : Type u} [Group G] [Fintype G] -variable {V W : Type u} [AddCommGroup V] [Module k V] [AddCommGroup W] [Module k W] -variable {I : Type u} [Fintype I] - - -noncomputable def coordinateTraceLift (ρ : Representation k G V) - (b : Module.Basis I k W) (t : V →ₗ[k] W) : - V →ₗ[k] (I →₀ MonoidAlgebra k G) := - ∑ g : G, ∑ i : I, (Finsupp.lsingle i).comp - ((MonoidAlgebra.lsingle g).comp ((b.coord i).comp (t.comp (ρ g⁻¹)))) - -lemma coordinateTraceLift_apply (ρ : Representation k G V) - (b : Module.Basis I k W) (t : V →ₗ[k] W) (v : V) : - coordinateTraceLift ρ b t v = ∑ g : G, ∑ i : I, - Finsupp.single i (MonoidAlgebra.single g (b.repr (t (ρ g⁻¹ v)) i)) := by - simp [coordinateTraceLift, LinearMap.sum_apply] - -noncomputable def coordinateTraceHom (ρ : Representation k G V) - (b : Module.Basis I k W) (t : V →ₗ[k] W) : - ρ.IntertwiningMap (Representation.free k G I) where - toLinearMap := coordinateTraceLift ρ b t - isIntertwining' h := by - ext v : 1 - simp only [LinearMap.comp_apply, coordinateTraceLift_apply, map_sum, - Representation.free_single_single] - symm - apply Fintype.sum_equiv (Equiv.mulLeft h) - intro g - simp [mul_inv_rev, map_mul] - -lemma freeCover_traceLift (ρ : Representation k G V) (σ : Representation k G W) - (b : Module.Basis I k W) (t : V →ₗ[k] W) : - (Representation.freeLift σ b).toLinearMap.comp (coordinateTraceLift ρ b t) = - relativeTrace ρ σ t := by - ext v - simp only [LinearMap.comp_apply, coordinateTraceLift_apply, map_sum, - IntertwiningMap.toLinearMap_apply, Representation.freeLift_single_single, relativeTrace_apply] - apply Finset.sum_congr rfl - intro g hg - simp only [← map_smul] - rw [← map_sum, b.sum_repr] - - - -noncomputable def finiteTraceBasis (V : FDRep k G) : - Module.Basis (ULift.{u} (Fin (Module.finrank k V))) k V := - (Module.finBasis k V).reindex Equiv.ulift.symm - - -theorem relativeTrace_factors (V W : FDRep k G) (f : V ⟶ W) (t : V →ₗ[k] W) - (ht : relativeTrace V.ρ W.ρ t = f.hom.hom.hom) : FactorsThroughProjective f := by - let b := finiteTraceBasis W - let A := FDRep.of (Representation.free k G (ULift.{u} (Fin (Module.finrank k W)))) - refine ⟨A, fdrep_free_projective _, finiteIntertwiner (coordinateTraceHom V.ρ b t), - finiteIntertwiner (Representation.freeLift W.ρ b), ?_⟩ - apply Action.Hom.ext - apply InducedCategory.hom_ext - apply ModuleCat.hom_ext - exact (freeCover_traceLift V.ρ W.ρ b t).trans ht - - -def underlyingIntertwiner {V W : FDRep k G} (f : V ⟶ W) : - Representation.IntertwiningMap V.ρ W.ρ where - toLinearMap := f.hom.hom.hom - isIntertwining' g := congrArg (fun h : V.V ⟶ W.V => h.hom.hom) (f.comm g) - - -theorem relativeTrace_of_factors (V W : FDRep k G) (f : V ⟶ W) - (hf : FactorsThroughProjective f) : - ∃ t : V →ₗ[k] W, relativeTrace V.ρ W.ρ t = f.hom.hom.hom := by - obtain ⟨P,hP,a,b,rfl⟩ := hf - let e := finiteFreeCover P - let : Epi e := finiteFreeCover_epi P - obtain ⟨s,hs⟩ := hP.factors (𝟙 P) e - let a' := underlyingIntertwiner (a ≫ s) - let b' := underlyingIntertwiner (e ≫ b) - refine ⟨b'.toLinearMap.comp ((freeNormRepresentative _).comp a'.toLinearMap), ?_⟩ - rw [relativeTrace_postcomp, relativeTrace_precomp] - erw [free_relativeTrace] - change ((a ≫ s) ≫ (e ≫ b)).hom.hom.hom = (a ≫ b).hom.hom.hom - rw [Category.assoc, ← Category.assoc s, hs, Category.id_comp] - -theorem projective_factor_iff_relativeTrace (V W : FDRep k G) (f : V ⟶ W) : - FactorsThroughProjective f ↔ ∃ t : V →ₗ[k] W, - relativeTrace V.ρ W.ρ t = f.hom.hom.hom := - ⟨relativeTrace_of_factors V W f, fun ⟨t,ht⟩ => relativeTrace_factors V W f t ht⟩ -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.FiniteFreeTrace + +namespace OAI + +namespace FiberFunctorProof +open CategoryTheory Representation +universe u +variable {k : Type u} [Field k] {G : Type u} [Group G] [Fintype G] +variable {V W : Type u} [AddCommGroup V] [Module k V] [AddCommGroup W] [Module k W] +variable {I : Type u} [Fintype I] + + +noncomputable def coordinateTraceLift (ρ : Representation k G V) + (b : Module.Basis I k W) (t : V →ₗ[k] W) : + V →ₗ[k] (I →₀ MonoidAlgebra k G) := + ∑ g : G, ∑ i : I, (Finsupp.lsingle i).comp + ((MonoidAlgebra.lsingle g).comp ((b.coord i).comp (t.comp (ρ g⁻¹)))) + +lemma coordinateTraceLift_apply (ρ : Representation k G V) + (b : Module.Basis I k W) (t : V →ₗ[k] W) (v : V) : + coordinateTraceLift ρ b t v = ∑ g : G, ∑ i : I, + Finsupp.single i (MonoidAlgebra.single g (b.repr (t (ρ g⁻¹ v)) i)) := by + simp [coordinateTraceLift, LinearMap.sum_apply] + +noncomputable def coordinateTraceHom (ρ : Representation k G V) + (b : Module.Basis I k W) (t : V →ₗ[k] W) : + ρ.IntertwiningMap (Representation.free k G I) where + toLinearMap := coordinateTraceLift ρ b t + isIntertwining' h := by + ext v : 1 + simp only [LinearMap.comp_apply, coordinateTraceLift_apply, map_sum, + Representation.free_single_single] + symm + apply Fintype.sum_equiv (Equiv.mulLeft h) + intro g + simp [mul_inv_rev, map_mul] + +lemma freeCover_traceLift (ρ : Representation k G V) (σ : Representation k G W) + (b : Module.Basis I k W) (t : V →ₗ[k] W) : + (Representation.freeLift σ b).toLinearMap.comp (coordinateTraceLift ρ b t) = + relativeTrace ρ σ t := by + ext v + simp only [LinearMap.comp_apply, coordinateTraceLift_apply, map_sum, + IntertwiningMap.toLinearMap_apply, Representation.freeLift_single_single, relativeTrace_apply] + apply Finset.sum_congr rfl + intro g hg + simp only [← map_smul] + rw [← map_sum, b.sum_repr] + + + +noncomputable def finiteTraceBasis (V : FDRep k G) : + Module.Basis (ULift.{u} (Fin (Module.finrank k V))) k V := + (Module.finBasis k V).reindex Equiv.ulift.symm + + +theorem relativeTrace_factors (V W : FDRep k G) (f : V ⟶ W) (t : V →ₗ[k] W) + (ht : relativeTrace V.ρ W.ρ t = f.hom.hom.hom) : FactorsThroughProjective f := by + let b := finiteTraceBasis W + let A := FDRep.of (Representation.free k G (ULift.{u} (Fin (Module.finrank k W)))) + refine ⟨A, fdrep_free_projective _, finiteIntertwiner (coordinateTraceHom V.ρ b t), + finiteIntertwiner (Representation.freeLift W.ρ b), ?_⟩ + apply Action.Hom.ext + apply InducedCategory.hom_ext + apply ModuleCat.hom_ext + exact (freeCover_traceLift V.ρ W.ρ b t).trans ht + + +def underlyingIntertwiner {V W : FDRep k G} (f : V ⟶ W) : + Representation.IntertwiningMap V.ρ W.ρ where + toLinearMap := f.hom.hom.hom + isIntertwining' g := congrArg (fun h : V.V ⟶ W.V => h.hom.hom) (f.comm g) + + +theorem relativeTrace_of_factors (V W : FDRep k G) (f : V ⟶ W) + (hf : FactorsThroughProjective f) : + ∃ t : V →ₗ[k] W, relativeTrace V.ρ W.ρ t = f.hom.hom.hom := by + obtain ⟨P,hP,a,b,rfl⟩ := hf + let e := finiteFreeCover P + let : Epi e := finiteFreeCover_epi P + obtain ⟨s,hs⟩ := hP.factors (𝟙 P) e + let a' := underlyingIntertwiner (a ≫ s) + let b' := underlyingIntertwiner (e ≫ b) + refine ⟨b'.toLinearMap.comp ((freeNormRepresentative _).comp a'.toLinearMap), ?_⟩ + rw [relativeTrace_postcomp, relativeTrace_precomp] + erw [free_relativeTrace] + change ((a ≫ s) ≫ (e ≫ b)).hom.hom.hom = (a ≫ b).hom.hom.hom + rw [Category.assoc, ← Category.assoc s, hs, Category.id_comp] + +theorem projective_factor_iff_relativeTrace (V W : FDRep k G) (f : V ⟶ W) : + FactorsThroughProjective f ↔ ∃ t : V →ₗ[k] W, + relativeTrace V.ρ W.ρ t = f.hom.hom.hom := + ⟨relativeTrace_of_factors V W f, fun ⟨t,ht⟩ => relativeTrace_factors V W f t ht⟩ +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/UnitAnnihilator.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/UnitAnnihilator.lean index 15052840125323c1d1e8b3cb98e32144a00b2045..ba80e0832e993a73fa06b401a2e0af6416f82e11 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/UnitAnnihilator.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/UnitAnnihilator.lean @@ -1,124 +1,124 @@ -import OAI.RepresentationTheory.RestrictedTilting.TensorExactness - -namespace OAI - -open CategoryTheory CategoryTheory.Limits CategoryTheory.MonoidalCategory CategoryTheory.BraidedCategory -namespace FiberFunctorProof -universe v u -noncomputable section -variable {C : Type u} [Category.{v} C] [Abelian C] - [MonoidalCategory C] [MonoidalPreadditive C] [RigidCategory C] - - -omit [MonoidalPreadditive C] in -lemma cokernel_tensor_subunit_zero {U : C} (i : U ⟶ 𝟙_ C) [Mono i] : - IsZero (cokernel i ⊗ U) := by - let := tensorRight_preservesFiniteColimits U - let := tensorLeft_preservesFiniteLimits (cokernel i) - let q := cokernel.π i - have hq : Epi (q ▷ U) := inferInstanceAs (Epi ((tensorRight U).map q)) - have hi : Mono ((cokernel i) ◁ i) := - inferInstanceAs (Mono ((tensorLeft (cokernel i)).map i)) - have h : q ▷ U ≫ (cokernel i) ◁ i = 0 := by - calc - _ = (λ_ U).hom ≫ i ≫ q ≫ (ρ_ (cokernel i)).inv := by - rw [← whisker_exchange] - monoidal - _ = 0 := by simp [q] - have hz : (cokernel i) ◁ i = 0 := (cancel_epi (q ▷ U)).1 (by simpa using h) - exact IsZero.of_mono_eq_zero _ hz - - - -def unitTranspose {U : C} (i : U ⟶ 𝟙_ C) : 𝟙_ C ⟶ Uᘁ := - η_ U Uᘁ ≫ i ▷ Uᘁ ≫ (λ_ Uᘁ).hom - -omit [Abelian C] [MonoidalPreadditive C] in -lemma unitTranspose_homEquiv {U T X : C} (i : U ⟶ 𝟙_ C) (j : T ⟶ X) : - tensorRightHomEquiv T U Uᘁ X (T ◁ i ≫ (ρ_ T).hom ≫ j) = - j ≫ (ρ_ X).inv ≫ X ◁ unitTranspose i := by - calc - _ = (ρ_ T).inv ≫ T ◁ unitTranspose i ≫ j ▷ Uᘁ := by - dsimp [tensorRightHomEquiv, unitTranspose] - monoidal - _ = (ρ_ T).inv ≫ j ▷ (𝟙_ C) ≫ X ◁ unitTranspose i := by - rw [whisker_exchange] - _ = _ := by monoidal - - - -lemma unitTranspose_subobject_zero_iff {U T X : C} (i : U ⟶ 𝟙_ C) [Mono i] - (j : T ⟶ X) [Mono j] : - j ≫ (ρ_ X).inv ≫ X ◁ unitTranspose i = 0 ↔ IsZero (T ⊗ U) := by - let := tensorLeft_preservesFiniteLimits T - have : Mono (T ◁ i) := inferInstanceAs (Mono ((tensorLeft T).map i)) - have : Mono (T ◁ i ≫ (ρ_ T).hom ≫ j) := inferInstance - have hzero : tensorRightHomEquiv T U Uᘁ X (0 : T ⊗ U ⟶ X) = 0 := by - simp [tensorRightHomEquiv] - rw [← unitTranspose_homEquiv, ← hzero, Equiv.apply_eq_iff_eq] - constructor - · exact IsZero.of_mono_eq_zero _ - · intro h - exact h.eq_of_src _ _ - -variable [BraidedCategory C] - - - -lemma subunit_cokernel_section {U : C} (i : U ⟶ 𝟙_ C) [Mono i] : - ∃ s : cokernel i ⟶ 𝟙_ C, s ≫ cokernel.π i = 𝟙 (cokernel i) := by - let V := cokernel i - let q : 𝟙_ C ⟶ V := cokernel.π i - let d := unitTranspose i - let W := kernel d - let w : W ⟶ 𝟙_ C := kernel.ι d - have hw : IsZero (W ⊗ U) := (unitTranspose_subobject_zero_iff i w).1 (by - change w ≫ (ρ_ (𝟙_ C)).inv ≫ (𝟙_ C) ◁ d = 0 - calc - _ = w ≫ d ≫ (λ_ Uᘁ).inv := by monoidal - _ = 0 := by simp [w]) - have hV : V ◁ d = 0 := by - have h := (unitTranspose_subobject_zero_iff i (𝟙 V)).2 - (cokernel_tensor_subunit_zero i) - simpa [d] using (cancel_epi (ρ_ V).inv).1 (by simpa using h) - let := tensorLeft_preservesFiniteLimits V - let := tensorLeft_preservesFiniteColimits V - have hvw : Epi (V ◁ w) := - ((ShortComplex.kernelSequence_exact d).map (tensorLeft V)).epi_f hV - have hvwm : Mono (V ◁ w) := - inferInstanceAs (Mono ((tensorLeft V).map (kernel.ι d))) - have hvwi : IsIso (V ◁ w) := isIso_of_mono_of_epi _ - have hwi : IsIso (w ▷ V) := by - have he : w ▷ V = (β_ W V).hom ≫ V ◁ w ≫ (β_ (𝟙_ C) V).inv := by - rw [← braiding_naturality_left_assoc] - simp - rw [he] - infer_instance - let := tensorLeft_preservesFiniteLimits W - let := tensorLeft_preservesFiniteColimits W - have hwqm : Mono (W ◁ q) := - ((ShortComplex.cokernelSequence_exact i).map (tensorLeft W)).mono_g - (hw.eq_of_src _ _) - have hwqe : Epi (W ◁ q) := - inferInstanceAs (Epi ((tensorLeft W).map (cokernel.π i))) - have hwqi : IsIso (W ◁ q) := isIso_of_mono_of_epi _ - have hcomp : w ≫ q = (ρ_ W).inv ≫ W ◁ q ≫ w ▷ V ≫ (λ_ V).hom := by - rw [whisker_exchange_assoc] - monoidal - have : IsIso (w ≫ q) := by rw [hcomp]; infer_instance - refine ⟨inv (w ≫ q) ≫ w, ?_⟩ - change (inv (w ≫ q) ≫ w) ≫ q = _ - simp - rfl - - -lemma subunit_retraction {U : C} (i : U ⟶ 𝟙_ C) [Mono i] : - ∃ r : 𝟙_ C ⟶ U, i ≫ r = 𝟙 U := by - obtain ⟨s, hs⟩ := subunit_cokernel_section i - let e := ShortComplex.Splitting.ofExactOfSection (ShortComplex.cokernelSequence i) - (ShortComplex.cokernelSequence_exact i) s hs (show Mono i from inferInstance) - exact ⟨e.r, e.f_r⟩ -end -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.TensorExactness + +namespace OAI + +open CategoryTheory CategoryTheory.Limits CategoryTheory.MonoidalCategory CategoryTheory.BraidedCategory +namespace FiberFunctorProof +universe v u +noncomputable section +variable {C : Type u} [Category.{v} C] [Abelian C] + [MonoidalCategory C] [MonoidalPreadditive C] [RigidCategory C] + + +omit [MonoidalPreadditive C] in +lemma cokernel_tensor_subunit_zero {U : C} (i : U ⟶ 𝟙_ C) [Mono i] : + IsZero (cokernel i ⊗ U) := by + let := tensorRight_preservesFiniteColimits U + let := tensorLeft_preservesFiniteLimits (cokernel i) + let q := cokernel.π i + have hq : Epi (q ▷ U) := inferInstanceAs (Epi ((tensorRight U).map q)) + have hi : Mono ((cokernel i) ◁ i) := + inferInstanceAs (Mono ((tensorLeft (cokernel i)).map i)) + have h : q ▷ U ≫ (cokernel i) ◁ i = 0 := by + calc + _ = (λ_ U).hom ≫ i ≫ q ≫ (ρ_ (cokernel i)).inv := by + rw [← whisker_exchange] + monoidal + _ = 0 := by simp [q] + have hz : (cokernel i) ◁ i = 0 := (cancel_epi (q ▷ U)).1 (by simpa using h) + exact IsZero.of_mono_eq_zero _ hz + + + +def unitTranspose {U : C} (i : U ⟶ 𝟙_ C) : 𝟙_ C ⟶ Uᘁ := + η_ U Uᘁ ≫ i ▷ Uᘁ ≫ (λ_ Uᘁ).hom + +omit [Abelian C] [MonoidalPreadditive C] in +lemma unitTranspose_homEquiv {U T X : C} (i : U ⟶ 𝟙_ C) (j : T ⟶ X) : + tensorRightHomEquiv T U Uᘁ X (T ◁ i ≫ (ρ_ T).hom ≫ j) = + j ≫ (ρ_ X).inv ≫ X ◁ unitTranspose i := by + calc + _ = (ρ_ T).inv ≫ T ◁ unitTranspose i ≫ j ▷ Uᘁ := by + dsimp [tensorRightHomEquiv, unitTranspose] + monoidal + _ = (ρ_ T).inv ≫ j ▷ (𝟙_ C) ≫ X ◁ unitTranspose i := by + rw [whisker_exchange] + _ = _ := by monoidal + + + +lemma unitTranspose_subobject_zero_iff {U T X : C} (i : U ⟶ 𝟙_ C) [Mono i] + (j : T ⟶ X) [Mono j] : + j ≫ (ρ_ X).inv ≫ X ◁ unitTranspose i = 0 ↔ IsZero (T ⊗ U) := by + let := tensorLeft_preservesFiniteLimits T + have : Mono (T ◁ i) := inferInstanceAs (Mono ((tensorLeft T).map i)) + have : Mono (T ◁ i ≫ (ρ_ T).hom ≫ j) := inferInstance + have hzero : tensorRightHomEquiv T U Uᘁ X (0 : T ⊗ U ⟶ X) = 0 := by + simp [tensorRightHomEquiv] + rw [← unitTranspose_homEquiv, ← hzero, Equiv.apply_eq_iff_eq] + constructor + · exact IsZero.of_mono_eq_zero _ + · intro h + exact h.eq_of_src _ _ + +variable [BraidedCategory C] + + + +lemma subunit_cokernel_section {U : C} (i : U ⟶ 𝟙_ C) [Mono i] : + ∃ s : cokernel i ⟶ 𝟙_ C, s ≫ cokernel.π i = 𝟙 (cokernel i) := by + let V := cokernel i + let q : 𝟙_ C ⟶ V := cokernel.π i + let d := unitTranspose i + let W := kernel d + let w : W ⟶ 𝟙_ C := kernel.ι d + have hw : IsZero (W ⊗ U) := (unitTranspose_subobject_zero_iff i w).1 (by + change w ≫ (ρ_ (𝟙_ C)).inv ≫ (𝟙_ C) ◁ d = 0 + calc + _ = w ≫ d ≫ (λ_ Uᘁ).inv := by monoidal + _ = 0 := by simp [w]) + have hV : V ◁ d = 0 := by + have h := (unitTranspose_subobject_zero_iff i (𝟙 V)).2 + (cokernel_tensor_subunit_zero i) + simpa [d] using (cancel_epi (ρ_ V).inv).1 (by simpa using h) + let := tensorLeft_preservesFiniteLimits V + let := tensorLeft_preservesFiniteColimits V + have hvw : Epi (V ◁ w) := + ((ShortComplex.kernelSequence_exact d).map (tensorLeft V)).epi_f hV + have hvwm : Mono (V ◁ w) := + inferInstanceAs (Mono ((tensorLeft V).map (kernel.ι d))) + have hvwi : IsIso (V ◁ w) := isIso_of_mono_of_epi _ + have hwi : IsIso (w ▷ V) := by + have he : w ▷ V = (β_ W V).hom ≫ V ◁ w ≫ (β_ (𝟙_ C) V).inv := by + rw [← braiding_naturality_left_assoc] + simp + rw [he] + infer_instance + let := tensorLeft_preservesFiniteLimits W + let := tensorLeft_preservesFiniteColimits W + have hwqm : Mono (W ◁ q) := + ((ShortComplex.cokernelSequence_exact i).map (tensorLeft W)).mono_g + (hw.eq_of_src _ _) + have hwqe : Epi (W ◁ q) := + inferInstanceAs (Epi ((tensorLeft W).map (cokernel.π i))) + have hwqi : IsIso (W ◁ q) := isIso_of_mono_of_epi _ + have hcomp : w ≫ q = (ρ_ W).inv ≫ W ◁ q ≫ w ▷ V ≫ (λ_ V).hom := by + rw [whisker_exchange_assoc] + monoidal + have : IsIso (w ≫ q) := by rw [hcomp]; infer_instance + refine ⟨inv (w ≫ q) ≫ w, ?_⟩ + change (inv (w ≫ q) ≫ w) ≫ q = _ + simp + rfl + + +lemma subunit_retraction {U : C} (i : U ⟶ 𝟙_ C) [Mono i] : + ∃ r : 𝟙_ C ⟶ U, i ≫ r = 𝟙 U := by + obtain ⟨s, hs⟩ := subunit_cokernel_section i + let e := ShortComplex.Splitting.ofExactOfSection (ShortComplex.cokernelSequence i) + (ShortComplex.cokernelSequence_exact i) s hs (show Mono i from inferInstance) + exact ⟨e.r, e.f_r⟩ +end +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/UnitSimple.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/UnitSimple.lean index bb5096abf4d52f4b6c53bbe616ed9f3e26667db7..219be174c929b11b091c40dbe276e1a6e26736f2 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/UnitSimple.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/UnitSimple.lean @@ -1,53 +1,53 @@ -import OAI.RepresentationTheory.RestrictedTilting.UnitAnnihilator - -namespace OAI - -open CategoryTheory CategoryTheory.Limits CategoryTheory.MonoidalCategory -namespace FiberFunctorProof -universe v u w -noncomputable section - - - -theorem simple_unit_of_scalar_endomorphisms - (k : Type w) [Field k] (C : Type u) [Category.{v} C] [Abelian C] - [MonoidalCategory C] [SymmetricCategory C] [MonoidalPreadditive C] - [RigidCategory C] [Linear k C] [MonoidalLinear k C] - (h : Function.Bijective (algebraMap k (End (𝟙_ C)))) : Simple (𝟙_ C) := by - have hunit : (𝟙 (𝟙_ C)) ≠ (0 : End (𝟙_ C)) := by - intro hz - exact one_ne_zero (h.1 (by simpa using hz)) - refine ⟨fun {U} i _ => ?_⟩ - constructor - · intro hi hz - let := hi - apply hunit - have he := IsIso.inv_hom_id i - simpa [hz] using he.symm - · intro hi - obtain ⟨r, hr⟩ := subunit_retraction i - let e : End (𝟙_ C) := r ≫ i - have he : e * e = e := by - change (r ≫ i) ≫ r ≫ i = r ≫ i - simp only [Category.assoc, ← Category.assoc i, hr, Category.id_comp] - obtain ⟨a, ha⟩ := h.2 e - have haa : a * a = a := h.1 (by simpa only [map_mul, ha] using he) - have ha01 : a = 0 ∨ a = 1 := by - have : a * (a - 1) = 0 := by rw [mul_sub, haa, mul_one, sub_self] - rcases mul_eq_zero.mp this with hz | ho - · exact Or.inl hz - · exact Or.inr (sub_eq_zero.mp ho) - have hei : e = 𝟙 (𝟙_ C) := by - rcases ha01 with hz | ho - · have he0 : e = 0 := by simpa [hz] using ha.symm - exfalso - apply hi - calc - i = i ≫ e := by dsimp [e]; rw [← Category.assoc, hr, Category.id_comp] - _ = 0 := by rw [he0, comp_zero] - · simpa [ho] using ha.symm - exact ⟨⟨r, hr, hei⟩⟩ -end -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.UnitAnnihilator + +namespace OAI + +open CategoryTheory CategoryTheory.Limits CategoryTheory.MonoidalCategory +namespace FiberFunctorProof +universe v u w +noncomputable section + + + +theorem simple_unit_of_scalar_endomorphisms + (k : Type w) [Field k] (C : Type u) [Category.{v} C] [Abelian C] + [MonoidalCategory C] [SymmetricCategory C] [MonoidalPreadditive C] + [RigidCategory C] [Linear k C] [MonoidalLinear k C] + (h : Function.Bijective (algebraMap k (End (𝟙_ C)))) : Simple (𝟙_ C) := by + have hunit : (𝟙 (𝟙_ C)) ≠ (0 : End (𝟙_ C)) := by + intro hz + exact one_ne_zero (h.1 (by simpa using hz)) + refine ⟨fun {U} i _ => ?_⟩ + constructor + · intro hi hz + let := hi + apply hunit + have he := IsIso.inv_hom_id i + simpa [hz] using he.symm + · intro hi + obtain ⟨r, hr⟩ := subunit_retraction i + let e : End (𝟙_ C) := r ≫ i + have he : e * e = e := by + change (r ≫ i) ≫ r ≫ i = r ≫ i + simp only [Category.assoc, ← Category.assoc i, hr, Category.id_comp] + obtain ⟨a, ha⟩ := h.2 e + have haa : a * a = a := h.1 (by simpa only [map_mul, ha] using he) + have ha01 : a = 0 ∨ a = 1 := by + have : a * (a - 1) = 0 := by rw [mul_sub, haa, mul_one, sub_self] + rcases mul_eq_zero.mp this with hz | ho + · exact Or.inl hz + · exact Or.inr (sub_eq_zero.mp ho) + have hei : e = 𝟙 (𝟙_ C) := by + rcases ha01 with hz | ho + · have he0 : e = 0 := by simpa [hz] using ha.symm + exfalso + apply hi + calc + i = i ≫ e := by dsimp [e]; rw [← Category.assoc, hr, Category.id_comp] + _ = 0 := by rw [he0, comp_zero] + · simpa [ho] using ha.symm + exact ⟨⟨r, hr, hei⟩⟩ +end +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/WeightBounds.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/WeightBounds.lean index 363e39b1ff1b010a82d398121168e8d8efe33774..c85c49fa54efb4772b7152e89fe441d916daf946 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/WeightBounds.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/WeightBounds.lean @@ -1,347 +1,347 @@ -import Mathlib -import OAI.RepresentationTheory.RestrictedTilting.CharacterExpansions - -namespace OAI - -/-! Binary weight bases and upper and lower unipotent degree bounds. -/ - -noncomputable section -open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits -open scoped BigOperators - -namespace FiberFunctorProof -section - -universe u -variable (k : Type u) [Field k] - - - -noncomputable def binaryExponentEquiv (n : ℕ) : - {d : Fin 2 →₀ ℕ // Finsupp.degree d = n} ≃ Fin (n + 1) where - toFun d := ⟨d.val 1, by - have hd := d.property - rw [Finsupp.degree_eq_sum, Fin.sum_univ_two] at hd - omega⟩ - invFun i := ⟨Finsupp.single (0 : Fin 2) (n - (i : ℕ)) + Finsupp.single (1 : Fin 2) (i : ℕ), by - simp only [map_add, Finsupp.degree_single] - omega⟩ - left_inv d := by - apply Subtype.ext - have hd := d.property - rw [Finsupp.degree_eq_sum, Fin.sum_univ_two] at hd - ext i - fin_cases i <;> simp - omega - right_inv i := by - apply Fin.ext - simp - -noncomputable def homogeneousMonomialBasis (n : ℕ) : - Module.Basis {d : Fin 2 →₀ ℕ // Finsupp.degree d = n} k - (MvPolynomial.homogeneousSubmodule (Fin 2) k n) := - (MvPolynomial.basisRestrictSupport k {d : Fin 2 →₀ ℕ | Finsupp.degree d = n}).map - (LinearEquiv.ofEq _ _ (MvPolynomial.homogeneousSubmodule_eq_finsupp_supported - (Fin 2) k n).symm) - -noncomputable def binaryBasis (n : ℕ) : Module.Basis (Fin (n + 1)) k - (MvPolynomial.homogeneousSubmodule (Fin 2) k n) := - (homogeneousMonomialBasis k n).reindex (binaryExponentEquiv n) - -lemma homogeneousMonomialBasis_apply (n : ℕ) - (d : {d : Fin 2 →₀ ℕ // Finsupp.degree d = n}) : - ((homogeneousMonomialBasis k n d).val : MvPolynomial (Fin 2) k) = - MvPolynomial.monomial d.val 1 := by - change AddMonoidAlgebra.ofCoeff - (((Finsupp.supportedEquivFinsupp (R := k) - {d : Fin 2 →₀ ℕ | Finsupp.degree d = n}).symm (Finsupp.single d 1)).val) = _ - rw [Finsupp.supportedEquivFinsupp_symm_single] - rfl - -lemma binaryBasis_apply (n : ℕ) (i : Fin (n + 1)) : - (binaryBasis k n i).val = - (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) ^ (n - i) * MvPolynomial.X 1 ^ (i : ℕ) := by - rw [binaryBasis, Module.Basis.reindex_apply, homogeneousMonomialBasis_apply] - change MvPolynomial.monomial (Finsupp.single (0 : Fin 2) (n - (i : ℕ)) + Finsupp.single (1 : Fin 2) (i : ℕ)) 1 = _ - rw [← one_mul (1 : k), ← MvPolynomial.monomial_mul_monomial] - simp [MvPolynomial.X_pow_eq_monomial] - -lemma binaryBasis_finrank (n : ℕ) : - Module.finrank k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) = n + 1 := by - simpa using Module.finrank_eq_card_basis (binaryBasis k n) - - -lemma dualMatrix_diagonal (a : kˣ) : dualMatrix k (diagonalTorus k a) = - !![(↑a⁻¹ : k), 0; 0, (a : k)] := by - change (((diagonalTorus k a)⁻¹ : SL2 k) : Matrix (Fin 2) (Fin 2) k).transpose = _ - rw [← map_inv] - change (!![(↑a⁻¹ : k), 0; 0, (↑(a⁻¹)⁻¹ : k)] : Matrix (Fin 2) (Fin 2) k).transpose = _ - ext i j - fin_cases i <;> fin_cases j <;> simp - -lemma linearChange_diagonal_X0 (a : kˣ) : - linearChange (dualMatrix k (diagonalTorus k a)) (MvPolynomial.X 0) = - MvPolynomial.C (↑a⁻¹ : k) * MvPolynomial.X 0 := by - rw [dualMatrix_diagonal, linearChange_X] - simp [Fin.sum_univ_two] - -lemma linearChange_diagonal_X1 (a : kˣ) : - linearChange (dualMatrix k (diagonalTorus k a)) (MvPolynomial.X 1) = - MvPolynomial.C (a : k) * MvPolynomial.X 1 := by - rw [dualMatrix_diagonal, linearChange_X] - simp [Fin.sum_univ_two] - - -lemma costandard_basis_weight (n : ℕ) (i : Fin (n + 1)) (a : kˣ) : - (costandard k n).ρ (diagonalTorus k a) (binaryBasis k n i) = - integerCharacter k (2 * (i : ℤ) - n) a • binaryBasis k n i := by - apply Subtype.ext - change linearChange (dualMatrix k (diagonalTorus k a)) (binaryBasis k n i).val = _ - rw [binaryBasis_apply] - simp only [map_mul, map_pow, linearChange_diagonal_X0, linearChange_diagonal_X1, - Submodule.coe_smul_of_tower, binaryBasis_apply, MvPolynomial.smul_eq_C_mul] - have hscalar : (↑a⁻¹ : k) ^ (n - (i : ℕ)) * (a : k) ^ (i : ℕ) = - integerCharacter k (2 * (i : ℤ) - n) a := by - change ((a⁻¹ ^ (n - (i : ℕ)) * a ^ (i : ℕ) : kˣ) : k) = - ((a ^ (2 * (i : ℤ) - n) : kˣ) : k) - congr 1 - simp only [← zpow_natCast, inv_zpow, ← zpow_neg, ← zpow_add] - congr 1 - have hi := i.isLt - omega - calc - ((MvPolynomial.C (↑a⁻¹ : k) : MvPolynomial (Fin 2) k) * MvPolynomial.X 0) ^ (n - (i : ℕ)) * - (MvPolynomial.C (a : k) * MvPolynomial.X 1) ^ (i : ℕ) = - MvPolynomial.C ((↑a⁻¹ : k) ^ (n - (i : ℕ)) * (a : k) ^ (i : ℕ)) * - (MvPolynomial.X 0 ^ (n - (i : ℕ)) * MvPolynomial.X 1 ^ (i : ℕ)) := by - simp only [mul_pow, map_mul, map_pow] - ring - _ = _ := by rw [hscalar] - - -lemma eigenvector_eq_zero_of_basis {M : Type*} [AddCommGroup M] [Module k M] - {I : Type*} [Fintype I] (b : Module.Basis I k M) (w : I → ℤ) - (ρ : Representation k (SL2 k) M) - (hb : ∀ i a, ρ (diagonalTorus k a) (b i) = integerCharacter k (w i) a • b i) - [Infinite k] (n : ℤ) (hn : ∀ i, n ≠ w i) (v : M) - (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) : v = 0 := by - classical - apply b.repr.injective - ext i - simp only [map_zero, Finsupp.zero_apply] - by_contra hc - have heq : integerCharacter k n = integerCharacter k (w i) := by - ext a - have hcoord : (b.coord i).comp (ρ (diagonalTorus k a)) = - integerCharacter k (w i) a • b.coord i := by - apply b.ext - intro j - simp only [LinearMap.comp_apply, hb, map_smul, Module.Basis.coord_apply, - Module.Basis.repr_self, Finsupp.single_apply, LinearMap.smul_apply, smul_eq_mul] - split_ifs with hji - · subst j; rfl - · simp - have hv' := congrArg (b.coord i) (hv a) - rw [← LinearMap.comp_apply, hcoord] at hv' - simp only [LinearMap.smul_apply, Module.Basis.coord_apply, map_smul, smul_eq_mul] at hv' - exact (mul_right_cancel₀ hc hv').symm - exact hn i (integerCharacter_injective k heq) - - - -lemma costandard_weight_bound [Infinite k] (n : ℕ) (m : ℤ) - (hm : m < -(n : ℤ) ∨ (n : ℤ) < m) - (v : costandard k n) (hv : ∀ a, - (costandard k n).ρ (diagonalTorus k a) v = integerCharacter k m a • v) : v = 0 := by - apply eigenvector_eq_zero_of_basis k (binaryBasis k n) (fun i => 2 * (i : ℤ) - n) - (costandard k n).ρ (costandard_basis_weight k n) m ?_ v hv - intro i - have hi := i.isLt - rcases hm with hm | hm <;> omega - -end - -section - -universe u -variable {k : Type u} [Field k] - - -def HasWeightsBetween {M : Type*} [AddCommGroup M] [Module k M] - (ρ : Representation k (SL2 k) M) (lo hi : ℤ) : Prop := - ∀ (m : ℤ) (v : M), m < lo ∨ hi < m → - (∀ a, ρ (diagonalTorus k a) v = integerCharacter k m a • v) → v = 0 - -lemma hasWeightsBetween_extension {L M N : Type*} - [AddCommGroup L] [Module k L] [AddCommGroup M] [Module k M] - [AddCommGroup N] [Module k N] - (α : Representation k (SL2 k) L) (β : Representation k (SL2 k) M) - (γ : Representation k (SL2 k) N) (f : L →ₗ[k] M) (g : M →ₗ[k] N) - (hf : Function.Injective f) (he : LinearMap.ker g = LinearMap.range f) - (hfi : ∀ x a, f (α a x) = β a (f x)) - (hgi : ∀ x a, g (β a x) = γ a (g x)) - (lo hi : ℤ) (hα : HasWeightsBetween α lo hi) (hγ : HasWeightsBetween γ lo hi) : - HasWeightsBetween β lo hi := by - intro m v hm hv - have hgv : g v = 0 := hγ m (g v) hm (fun a => by - rw [← hgi, hv, map_smul]) - have hvf : v ∈ LinearMap.range f := he ▸ hgv - obtain ⟨v', hv'⟩ := hvf - have hv'0 : v' = 0 := hα m v' hm (fun a => by - apply hf - rw [hfi, hv', hv, map_smul, hv']) - simpa [hv'0] using hv'.symm - - -lemma highest_unipotent_fixed [Infinite k] {M : Type u} [AddCommGroup M] - [Module k M] [Module.Finite k M] (ρ : Representation k (SL2 k) M) - (hρ : IsRational k ρ) (n : ℤ) (v : M) - (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) - (hn : ∀ (m : ℤ) (w : M), n < m → - (∀ a, ρ (diagonalTorus k a) w = integerCharacter k m a • w) → w = 0) : - ∀ t, ρ (unipotent k t) v = v := by - classical - obtain ⟨c, hc⟩ := rational_unipotent_expansion k ρ hρ v - have hz (i : ℕ) (hi : i ≠ 0) : c i = 0 := - hn (n + 2 * i) (c i) (by omega) (unipotent_coefficient_weight k ρ v n hv c hc i) - have hc0 : c = Finsupp.single 0 (c 0) := by - ext i - by_cases hi : i = 0 - · subst i; simp - · simp [hi, hz i hi] - have hc' (t : k) : ρ (unipotent k t) v = c 0 := by - rw [hc t] - conv_lhs => rw [hc0] - rw [Finsupp.sum_single_index] - · simp only [pow_zero, one_smul] - · exact smul_zero _ - have hv0 : v = c 0 := by - simpa [unipotent_zero] using hc' 0 - intro t - exact (hc' t).trans hv0.symm - -end - -universe u -variable (k : Type u) [Field k] - - -def lowerUnipotent (t : k) : SL2 k := - ⟨!![1, 0; t, 1], by simp [Matrix.det_fin_two]⟩ - -@[simp] lemma lowerUnipotent_zero : lowerUnipotent k 0 = 1 := by - apply Subtype.ext - ext i j - fin_cases i <;> fin_cases j <;> simp [lowerUnipotent] - -lemma lowerUnipotent_add (s t : k) : - lowerUnipotent k (s + t) = lowerUnipotent k s * lowerUnipotent k t := by - apply Subtype.ext - change !![1, 0; s + t, 1] = !![1, 0; s, 1] * !![1, 0; t, 1] - ext i j - fin_cases i <;> fin_cases j <;> - simp [Matrix.mul_apply, Fin.sum_univ_two, add_comm] - -@[simp] lemma lowerUnipotent_inv (t : k) : - (lowerUnipotent k t)⁻¹ = lowerUnipotent k (-t) := by - apply inv_eq_of_mul_eq_one_right - rw [← lowerUnipotent_add] - simp - -lemma lowerUnipotent_coordinate_mem_powerAlgebra (i j : Fin 2) : - (fun t : k => lowerUnipotent k t i j) ∈ powerAlgebra k := by - fin_cases i <;> fin_cases j - · exact (powerAlgebra k).one_mem - · exact (powerAlgebra k).zero_mem - · change (fun t : k => t) ∈ powerAlgebra k - simpa only [pow_one] using power_mem_powerAlgebra k 1 - · exact (powerAlgebra k).one_mem - -lemma polynomial_on_lowerUnipotent_mem_powerAlgebra - (P : MvPolynomial (Fin 2 × Fin 2) k) : - (fun t : k => MvPolynomial.eval (fun ij => lowerUnipotent k t ij.1 ij.2) P) ∈ - powerAlgebra k := by - induction P using MvPolynomial.induction_on with - | C c => - simpa only [MvPolynomial.eval_C, Pi.algebraMap_def, Algebra.algebraMap_self, - RingHom.id_apply] using (powerAlgebra k).algebraMap_mem c - | add P Q hP hQ => - simpa only [MvPolynomial.eval_add, Pi.add_def] using (powerAlgebra k).add_mem hP hQ - | mul_X P ij hP => - simpa only [MvPolynomial.eval_mul, MvPolynomial.eval_X, Pi.mul_def] using - (powerAlgebra k).mul_mem hP (lowerUnipotent_coordinate_mem_powerAlgebra k ij.1 ij.2) - -lemma rational_lowerUnipotent_expansion {M : Type u} [AddCommGroup M] - [Module k M] [Module.Finite k M] (ρ : Representation k (SL2 k) M) - (hρ : IsRational k ρ) (v : M) : ∃ c : ℕ →₀ M, ∀ t : k, - ρ (lowerUnipotent k t) v = c.sum (fun n x => t ^ n • x) := by - apply vector_expansion_of_scalar_span - intro φ - obtain ⟨P, hP⟩ := hρ v φ - have heq : (fun t : k => φ (ρ (lowerUnipotent k t) v)) = - (fun t : k => MvPolynomial.eval (fun ij => lowerUnipotent k t ij.1 ij.2) P) := by - funext t - exact hP (lowerUnipotent k t) - rw [heq, ← powerAlgebra_toSubmodule] - exact polynomial_on_lowerUnipotent_mem_powerAlgebra k P - -lemma diagonal_lowerUnipotent (a : kˣ) (t : k) : - diagonalTorus k a * lowerUnipotent k t = - lowerUnipotent k ((↑a⁻¹ : k) ^ 2 * t) * diagonalTorus k a := by - apply Subtype.ext - change !![(a : k), 0; 0, (↑a⁻¹ : k)] * !![1, 0; t, 1] = - !![1, 0; (↑a⁻¹ : k) ^ 2 * t, 1] * !![(a : k), 0; 0, (↑a⁻¹ : k)] - ext i j - fin_cases i <;> fin_cases j <;> - simp [Matrix.mul_apply, Fin.sum_univ_two, pow_two, mul_comm, mul_left_comm] - -lemma lowerUnipotent_coefficient_weight [Infinite k] {M : Type u} - [AddCommGroup M] [Module k M] (ρ : Representation k (SL2 k) M) - (v : M) (n : ℤ) (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) - (c : ℕ →₀ M) (hc : ∀ t, ρ (lowerUnipotent k t) v = c.sum (fun i x => t ^ i • x)) : - ∀ i a, ρ (diagonalTorus k a) (c i) = integerCharacter k (n - 2 * i) a • c i := by - classical - intro i a - by_cases hi : i ∈ c.support - · apply sub_eq_zero.mp - apply function_sum_eq_zero (fun (j : ℕ) (t : k) => t ^ j) - (linearIndependent_powerFunctions k) c.support - (fun j => ρ (diagonalTorus k a) (c j) - integerCharacter k (n - 2 * j) a • c j) - ?_ i hi - intro t - calc - ∑ j ∈ c.support, t ^ j • - (ρ (diagonalTorus k a) (c j) - integerCharacter k (n - 2 * j) a • c j) = - ρ (diagonalTorus k a) (c.sum (fun j x => t ^ j • x)) - - integerCharacter k n a • c.sum (fun j x => ((↑a⁻¹ : k) ^ 2 * t) ^ j • x) := by - simp only [Finsupp.sum, map_sum, map_smul, smul_sub, Finset.sum_sub_distrib, - Finset.smul_sum, smul_smul] - congr 1 - apply Finset.sum_congr rfl - intro j hj - congr 1 - simp [integerCharacter, zpow_sub, zpow_mul, mul_pow, ← pow_mul, - mul_comm, mul_left_comm] - _ = 0 := by - rw [← hc, ← hc] - apply sub_eq_zero.mpr - have hh := congrArg (fun g => ρ g v) (diagonal_lowerUnipotent k a t) - simpa only [map_mul, Module.End.mul_apply, hv, map_smul] using hh - · rw [Finsupp.notMem_support_iff.mp hi, map_zero, smul_zero] - - - -lemma lowerUnipotent_degree_bound [Infinite k] {M : Type u} - [AddCommGroup M] [Module k M] (ρ : Representation k (SL2 k) M) - (n : ℕ) (hbound : HasWeightsBetween ρ (-(n : ℤ)) n) - (v : M) (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) - (c : ℕ →₀ M) (hc : ∀ t, ρ (lowerUnipotent k t) v = c.sum (fun i x => t ^ i • x)) : - ∀ i, n < i → c i = 0 := by - intro i hi - exact hbound ((n : ℤ) - 2 * i) (c i) (Or.inl (by omega)) - (lowerUnipotent_coefficient_weight k ρ v n hv c hc i) - -end FiberFunctorProof -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.RestrictedTilting.CharacterExpansions + +namespace OAI + +/-! Binary weight bases and upper and lower unipotent degree bounds. -/ + +noncomputable section +open CategoryTheory CategoryTheory.MonoidalCategory CategoryTheory.Limits +open scoped BigOperators + +namespace FiberFunctorProof +section + +universe u +variable (k : Type u) [Field k] + + + +noncomputable def binaryExponentEquiv (n : ℕ) : + {d : Fin 2 →₀ ℕ // Finsupp.degree d = n} ≃ Fin (n + 1) where + toFun d := ⟨d.val 1, by + have hd := d.property + rw [Finsupp.degree_eq_sum, Fin.sum_univ_two] at hd + omega⟩ + invFun i := ⟨Finsupp.single (0 : Fin 2) (n - (i : ℕ)) + Finsupp.single (1 : Fin 2) (i : ℕ), by + simp only [map_add, Finsupp.degree_single] + omega⟩ + left_inv d := by + apply Subtype.ext + have hd := d.property + rw [Finsupp.degree_eq_sum, Fin.sum_univ_two] at hd + ext i + fin_cases i <;> simp + omega + right_inv i := by + apply Fin.ext + simp + +noncomputable def homogeneousMonomialBasis (n : ℕ) : + Module.Basis {d : Fin 2 →₀ ℕ // Finsupp.degree d = n} k + (MvPolynomial.homogeneousSubmodule (Fin 2) k n) := + (MvPolynomial.basisRestrictSupport k {d : Fin 2 →₀ ℕ | Finsupp.degree d = n}).map + (LinearEquiv.ofEq _ _ (MvPolynomial.homogeneousSubmodule_eq_finsupp_supported + (Fin 2) k n).symm) + +noncomputable def binaryBasis (n : ℕ) : Module.Basis (Fin (n + 1)) k + (MvPolynomial.homogeneousSubmodule (Fin 2) k n) := + (homogeneousMonomialBasis k n).reindex (binaryExponentEquiv n) + +lemma homogeneousMonomialBasis_apply (n : ℕ) + (d : {d : Fin 2 →₀ ℕ // Finsupp.degree d = n}) : + ((homogeneousMonomialBasis k n d).val : MvPolynomial (Fin 2) k) = + MvPolynomial.monomial d.val 1 := by + change AddMonoidAlgebra.ofCoeff + (((Finsupp.supportedEquivFinsupp (R := k) + {d : Fin 2 →₀ ℕ | Finsupp.degree d = n}).symm (Finsupp.single d 1)).val) = _ + rw [Finsupp.supportedEquivFinsupp_symm_single] + rfl + +lemma binaryBasis_apply (n : ℕ) (i : Fin (n + 1)) : + (binaryBasis k n i).val = + (MvPolynomial.X 0 : MvPolynomial (Fin 2) k) ^ (n - i) * MvPolynomial.X 1 ^ (i : ℕ) := by + rw [binaryBasis, Module.Basis.reindex_apply, homogeneousMonomialBasis_apply] + change MvPolynomial.monomial (Finsupp.single (0 : Fin 2) (n - (i : ℕ)) + Finsupp.single (1 : Fin 2) (i : ℕ)) 1 = _ + rw [← one_mul (1 : k), ← MvPolynomial.monomial_mul_monomial] + simp [MvPolynomial.X_pow_eq_monomial] + +lemma binaryBasis_finrank (n : ℕ) : + Module.finrank k (MvPolynomial.homogeneousSubmodule (Fin 2) k n) = n + 1 := by + simpa using Module.finrank_eq_card_basis (binaryBasis k n) + + +lemma dualMatrix_diagonal (a : kˣ) : dualMatrix k (diagonalTorus k a) = + !![(↑a⁻¹ : k), 0; 0, (a : k)] := by + change (((diagonalTorus k a)⁻¹ : SL2 k) : Matrix (Fin 2) (Fin 2) k).transpose = _ + rw [← map_inv] + change (!![(↑a⁻¹ : k), 0; 0, (↑(a⁻¹)⁻¹ : k)] : Matrix (Fin 2) (Fin 2) k).transpose = _ + ext i j + fin_cases i <;> fin_cases j <;> simp + +lemma linearChange_diagonal_X0 (a : kˣ) : + linearChange (dualMatrix k (diagonalTorus k a)) (MvPolynomial.X 0) = + MvPolynomial.C (↑a⁻¹ : k) * MvPolynomial.X 0 := by + rw [dualMatrix_diagonal, linearChange_X] + simp [Fin.sum_univ_two] + +lemma linearChange_diagonal_X1 (a : kˣ) : + linearChange (dualMatrix k (diagonalTorus k a)) (MvPolynomial.X 1) = + MvPolynomial.C (a : k) * MvPolynomial.X 1 := by + rw [dualMatrix_diagonal, linearChange_X] + simp [Fin.sum_univ_two] + + +lemma costandard_basis_weight (n : ℕ) (i : Fin (n + 1)) (a : kˣ) : + (costandard k n).ρ (diagonalTorus k a) (binaryBasis k n i) = + integerCharacter k (2 * (i : ℤ) - n) a • binaryBasis k n i := by + apply Subtype.ext + change linearChange (dualMatrix k (diagonalTorus k a)) (binaryBasis k n i).val = _ + rw [binaryBasis_apply] + simp only [map_mul, map_pow, linearChange_diagonal_X0, linearChange_diagonal_X1, + Submodule.coe_smul_of_tower, binaryBasis_apply, MvPolynomial.smul_eq_C_mul] + have hscalar : (↑a⁻¹ : k) ^ (n - (i : ℕ)) * (a : k) ^ (i : ℕ) = + integerCharacter k (2 * (i : ℤ) - n) a := by + change ((a⁻¹ ^ (n - (i : ℕ)) * a ^ (i : ℕ) : kˣ) : k) = + ((a ^ (2 * (i : ℤ) - n) : kˣ) : k) + congr 1 + simp only [← zpow_natCast, inv_zpow, ← zpow_neg, ← zpow_add] + congr 1 + have hi := i.isLt + omega + calc + ((MvPolynomial.C (↑a⁻¹ : k) : MvPolynomial (Fin 2) k) * MvPolynomial.X 0) ^ (n - (i : ℕ)) * + (MvPolynomial.C (a : k) * MvPolynomial.X 1) ^ (i : ℕ) = + MvPolynomial.C ((↑a⁻¹ : k) ^ (n - (i : ℕ)) * (a : k) ^ (i : ℕ)) * + (MvPolynomial.X 0 ^ (n - (i : ℕ)) * MvPolynomial.X 1 ^ (i : ℕ)) := by + simp only [mul_pow, map_mul, map_pow] + ring + _ = _ := by rw [hscalar] + + +lemma eigenvector_eq_zero_of_basis {M : Type*} [AddCommGroup M] [Module k M] + {I : Type*} [Fintype I] (b : Module.Basis I k M) (w : I → ℤ) + (ρ : Representation k (SL2 k) M) + (hb : ∀ i a, ρ (diagonalTorus k a) (b i) = integerCharacter k (w i) a • b i) + [Infinite k] (n : ℤ) (hn : ∀ i, n ≠ w i) (v : M) + (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) : v = 0 := by + classical + apply b.repr.injective + ext i + simp only [map_zero, Finsupp.zero_apply] + by_contra hc + have heq : integerCharacter k n = integerCharacter k (w i) := by + ext a + have hcoord : (b.coord i).comp (ρ (diagonalTorus k a)) = + integerCharacter k (w i) a • b.coord i := by + apply b.ext + intro j + simp only [LinearMap.comp_apply, hb, map_smul, Module.Basis.coord_apply, + Module.Basis.repr_self, Finsupp.single_apply, LinearMap.smul_apply, smul_eq_mul] + split_ifs with hji + · subst j; rfl + · simp + have hv' := congrArg (b.coord i) (hv a) + rw [← LinearMap.comp_apply, hcoord] at hv' + simp only [LinearMap.smul_apply, Module.Basis.coord_apply, map_smul, smul_eq_mul] at hv' + exact (mul_right_cancel₀ hc hv').symm + exact hn i (integerCharacter_injective k heq) + + + +lemma costandard_weight_bound [Infinite k] (n : ℕ) (m : ℤ) + (hm : m < -(n : ℤ) ∨ (n : ℤ) < m) + (v : costandard k n) (hv : ∀ a, + (costandard k n).ρ (diagonalTorus k a) v = integerCharacter k m a • v) : v = 0 := by + apply eigenvector_eq_zero_of_basis k (binaryBasis k n) (fun i => 2 * (i : ℤ) - n) + (costandard k n).ρ (costandard_basis_weight k n) m ?_ v hv + intro i + have hi := i.isLt + rcases hm with hm | hm <;> omega + +end + +section + +universe u +variable {k : Type u} [Field k] + + +def HasWeightsBetween {M : Type*} [AddCommGroup M] [Module k M] + (ρ : Representation k (SL2 k) M) (lo hi : ℤ) : Prop := + ∀ (m : ℤ) (v : M), m < lo ∨ hi < m → + (∀ a, ρ (diagonalTorus k a) v = integerCharacter k m a • v) → v = 0 + +lemma hasWeightsBetween_extension {L M N : Type*} + [AddCommGroup L] [Module k L] [AddCommGroup M] [Module k M] + [AddCommGroup N] [Module k N] + (α : Representation k (SL2 k) L) (β : Representation k (SL2 k) M) + (γ : Representation k (SL2 k) N) (f : L →ₗ[k] M) (g : M →ₗ[k] N) + (hf : Function.Injective f) (he : LinearMap.ker g = LinearMap.range f) + (hfi : ∀ x a, f (α a x) = β a (f x)) + (hgi : ∀ x a, g (β a x) = γ a (g x)) + (lo hi : ℤ) (hα : HasWeightsBetween α lo hi) (hγ : HasWeightsBetween γ lo hi) : + HasWeightsBetween β lo hi := by + intro m v hm hv + have hgv : g v = 0 := hγ m (g v) hm (fun a => by + rw [← hgi, hv, map_smul]) + have hvf : v ∈ LinearMap.range f := he ▸ hgv + obtain ⟨v', hv'⟩ := hvf + have hv'0 : v' = 0 := hα m v' hm (fun a => by + apply hf + rw [hfi, hv', hv, map_smul, hv']) + simpa [hv'0] using hv'.symm + + +lemma highest_unipotent_fixed [Infinite k] {M : Type u} [AddCommGroup M] + [Module k M] [Module.Finite k M] (ρ : Representation k (SL2 k) M) + (hρ : IsRational k ρ) (n : ℤ) (v : M) + (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) + (hn : ∀ (m : ℤ) (w : M), n < m → + (∀ a, ρ (diagonalTorus k a) w = integerCharacter k m a • w) → w = 0) : + ∀ t, ρ (unipotent k t) v = v := by + classical + obtain ⟨c, hc⟩ := rational_unipotent_expansion k ρ hρ v + have hz (i : ℕ) (hi : i ≠ 0) : c i = 0 := + hn (n + 2 * i) (c i) (by omega) (unipotent_coefficient_weight k ρ v n hv c hc i) + have hc0 : c = Finsupp.single 0 (c 0) := by + ext i + by_cases hi : i = 0 + · subst i; simp + · simp [hi, hz i hi] + have hc' (t : k) : ρ (unipotent k t) v = c 0 := by + rw [hc t] + conv_lhs => rw [hc0] + rw [Finsupp.sum_single_index] + · simp only [pow_zero, one_smul] + · exact smul_zero _ + have hv0 : v = c 0 := by + simpa [unipotent_zero] using hc' 0 + intro t + exact (hc' t).trans hv0.symm + +end + +universe u +variable (k : Type u) [Field k] + + +def lowerUnipotent (t : k) : SL2 k := + ⟨!![1, 0; t, 1], by simp [Matrix.det_fin_two]⟩ + +@[simp] lemma lowerUnipotent_zero : lowerUnipotent k 0 = 1 := by + apply Subtype.ext + ext i j + fin_cases i <;> fin_cases j <;> simp [lowerUnipotent] + +lemma lowerUnipotent_add (s t : k) : + lowerUnipotent k (s + t) = lowerUnipotent k s * lowerUnipotent k t := by + apply Subtype.ext + change !![1, 0; s + t, 1] = !![1, 0; s, 1] * !![1, 0; t, 1] + ext i j + fin_cases i <;> fin_cases j <;> + simp [Matrix.mul_apply, Fin.sum_univ_two, add_comm] + +@[simp] lemma lowerUnipotent_inv (t : k) : + (lowerUnipotent k t)⁻¹ = lowerUnipotent k (-t) := by + apply inv_eq_of_mul_eq_one_right + rw [← lowerUnipotent_add] + simp + +lemma lowerUnipotent_coordinate_mem_powerAlgebra (i j : Fin 2) : + (fun t : k => lowerUnipotent k t i j) ∈ powerAlgebra k := by + fin_cases i <;> fin_cases j + · exact (powerAlgebra k).one_mem + · exact (powerAlgebra k).zero_mem + · change (fun t : k => t) ∈ powerAlgebra k + simpa only [pow_one] using power_mem_powerAlgebra k 1 + · exact (powerAlgebra k).one_mem + +lemma polynomial_on_lowerUnipotent_mem_powerAlgebra + (P : MvPolynomial (Fin 2 × Fin 2) k) : + (fun t : k => MvPolynomial.eval (fun ij => lowerUnipotent k t ij.1 ij.2) P) ∈ + powerAlgebra k := by + induction P using MvPolynomial.induction_on with + | C c => + simpa only [MvPolynomial.eval_C, Pi.algebraMap_def, Algebra.algebraMap_self, + RingHom.id_apply] using (powerAlgebra k).algebraMap_mem c + | add P Q hP hQ => + simpa only [MvPolynomial.eval_add, Pi.add_def] using (powerAlgebra k).add_mem hP hQ + | mul_X P ij hP => + simpa only [MvPolynomial.eval_mul, MvPolynomial.eval_X, Pi.mul_def] using + (powerAlgebra k).mul_mem hP (lowerUnipotent_coordinate_mem_powerAlgebra k ij.1 ij.2) + +lemma rational_lowerUnipotent_expansion {M : Type u} [AddCommGroup M] + [Module k M] [Module.Finite k M] (ρ : Representation k (SL2 k) M) + (hρ : IsRational k ρ) (v : M) : ∃ c : ℕ →₀ M, ∀ t : k, + ρ (lowerUnipotent k t) v = c.sum (fun n x => t ^ n • x) := by + apply vector_expansion_of_scalar_span + intro φ + obtain ⟨P, hP⟩ := hρ v φ + have heq : (fun t : k => φ (ρ (lowerUnipotent k t) v)) = + (fun t : k => MvPolynomial.eval (fun ij => lowerUnipotent k t ij.1 ij.2) P) := by + funext t + exact hP (lowerUnipotent k t) + rw [heq, ← powerAlgebra_toSubmodule] + exact polynomial_on_lowerUnipotent_mem_powerAlgebra k P + +lemma diagonal_lowerUnipotent (a : kˣ) (t : k) : + diagonalTorus k a * lowerUnipotent k t = + lowerUnipotent k ((↑a⁻¹ : k) ^ 2 * t) * diagonalTorus k a := by + apply Subtype.ext + change !![(a : k), 0; 0, (↑a⁻¹ : k)] * !![1, 0; t, 1] = + !![1, 0; (↑a⁻¹ : k) ^ 2 * t, 1] * !![(a : k), 0; 0, (↑a⁻¹ : k)] + ext i j + fin_cases i <;> fin_cases j <;> + simp [Matrix.mul_apply, Fin.sum_univ_two, pow_two, mul_comm, mul_left_comm] + +lemma lowerUnipotent_coefficient_weight [Infinite k] {M : Type u} + [AddCommGroup M] [Module k M] (ρ : Representation k (SL2 k) M) + (v : M) (n : ℤ) (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) + (c : ℕ →₀ M) (hc : ∀ t, ρ (lowerUnipotent k t) v = c.sum (fun i x => t ^ i • x)) : + ∀ i a, ρ (diagonalTorus k a) (c i) = integerCharacter k (n - 2 * i) a • c i := by + classical + intro i a + by_cases hi : i ∈ c.support + · apply sub_eq_zero.mp + apply function_sum_eq_zero (fun (j : ℕ) (t : k) => t ^ j) + (linearIndependent_powerFunctions k) c.support + (fun j => ρ (diagonalTorus k a) (c j) - integerCharacter k (n - 2 * j) a • c j) + ?_ i hi + intro t + calc + ∑ j ∈ c.support, t ^ j • + (ρ (diagonalTorus k a) (c j) - integerCharacter k (n - 2 * j) a • c j) = + ρ (diagonalTorus k a) (c.sum (fun j x => t ^ j • x)) - + integerCharacter k n a • c.sum (fun j x => ((↑a⁻¹ : k) ^ 2 * t) ^ j • x) := by + simp only [Finsupp.sum, map_sum, map_smul, smul_sub, Finset.sum_sub_distrib, + Finset.smul_sum, smul_smul] + congr 1 + apply Finset.sum_congr rfl + intro j hj + congr 1 + simp [integerCharacter, zpow_sub, zpow_mul, mul_pow, ← pow_mul, + mul_comm, mul_left_comm] + _ = 0 := by + rw [← hc, ← hc] + apply sub_eq_zero.mpr + have hh := congrArg (fun g => ρ g v) (diagonal_lowerUnipotent k a t) + simpa only [map_mul, Module.End.mul_apply, hv, map_smul] using hh + · rw [Finsupp.notMem_support_iff.mp hi, map_zero, smul_zero] + + + +lemma lowerUnipotent_degree_bound [Infinite k] {M : Type u} + [AddCommGroup M] [Module k M] (ρ : Representation k (SL2 k) M) + (n : ℕ) (hbound : HasWeightsBetween ρ (-(n : ℤ)) n) + (v : M) (hv : ∀ a, ρ (diagonalTorus k a) v = integerCharacter k n a • v) + (c : ℕ →₀ M) (hc : ∀ t, ρ (lowerUnipotent k t) v = c.sum (fun i x => t ^ i • x)) : + ∀ i, n < i → c i = 0 := by + intro i hi + exact hbound ((n : ℤ) - 2 * i) (c i) (Or.inl (by omega)) + (lowerUnipotent_coefficient_weight k ρ v n hv c hc i) + +end FiberFunctorProof +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RestrictedTilting/XChartLineEval.lean b/lean/OAI/RepresentationTheory/RestrictedTilting/XChartLineEval.lean index 31b4fdb03cb8efa1c5d854b9f0172c43a72a219c..1766caf12159a62a8df0f8a53244a87aca589115 100644 --- a/lean/OAI/RepresentationTheory/RestrictedTilting/XChartLineEval.lean +++ b/lean/OAI/RepresentationTheory/RestrictedTilting/XChartLineEval.lean @@ -1,87 +1,87 @@ -import OAI.RepresentationTheory.RestrictedTilting.Basic - -namespace OAI - -namespace FiberFunctorProof -universe u -variable (k : Type u) [Field k] - -noncomputable def planeLineEval (a : k) : MvPolynomial (Fin 2) k →ₐ[k] k := - MvPolynomial.aeval (fun i => if i = 0 then a else 0) - -lemma planeLineEval_X_isUnit (a : kˣ) : - IsUnit (planeLineEval k a (MvPolynomial.X 0)) := by - simp [planeLineEval] - -noncomputable def chartLineEval (a : kˣ) : planeCoordinateChart k 0 →ₐ[k] k := - IsLocalization.Away.liftAlgHom (MvPolynomial.X 0) (planeLineEval_X_isUnit k a) - -lemma chartLineEval_algebraMap (a : kˣ) (P : MvPolynomial (Fin 2) k) : - chartLineEval k a (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k 0) P) = - planeLineEval k a P := IsLocalization.Away.lift_eq _ (planeLineEval_X_isUnit k a) _ - -lemma chartLineEval_coordinate (a : kˣ) (i : Fin 2) : - chartLineEval k a (planeChartCoordinate k 0 i) = if i = 0 then (a : k) else 0 := by - rw [planeChartCoordinate, chartLineEval_algebraMap] - simp [planeLineEval] - -lemma chartLineEval_inverse (a : kˣ) : - chartLineEval k a (planeChartInverse k 0) = (a : k)⁻¹ := by - have hm : planeChartCoordinate k 0 0 * planeChartInverse k 0 = 1 := - IsLocalization.Away.mul_invSelf (S := planeCoordinateChart k 0) (MvPolynomial.X 0) - have h := congrArg (chartLineEval k a) hm - simp only [map_mul, map_one, chartLineEval_coordinate] at h - exact mul_left_cancel₀ a.ne_zero (h.trans (mul_inv_cancel₀ a.ne_zero).symm) - -lemma planeXPolynomialChart_line (a : kˣ) (P : MvPolynomial (Fin 2 × Fin 2) k) : - chartLineEval k a (planeXPolynomialChart k P) = coordinateEvaluation k P (diagonalTorus k a) := by - induction P using MvPolynomial.induction_on with - | C c => simp [planeXPolynomialChart, coordinateEvaluation] - | add P Q hp hq => simp only [map_add, Pi.add_apply, hp, hq] - | mul_X P i hp => - simp only [map_mul, Pi.mul_apply, hp] - congr 1 - rw [coordinateEvaluation_apply, MvPolynomial.eval_X] - rcases i with ⟨i,j⟩ - fin_cases i <;> fin_cases j <;> - simp [planeXPolynomialChart, diagonalTorus, chartLineEval_coordinate, chartLineEval_inverse] <;> rfl - -lemma regularXChartValue_line (a : kˣ) (f : regularSL2Functions k) : - chartLineEval k a (regularXChartValue k f) = f.val (diagonalTorus k a) := by - rw [regularXChartValue, planeXPolynomialChart_line] - exact congrFun f.property.choose_spec _ - -variable [Infinite k] -variable (ι : Type u) [Fintype ι] [DecidableEq ι] -variable (ρ : Representation k (Multiplicative k) (ι → k)) - -omit [Fintype ι] [DecidableEq ι] in -lemma associatedXChart_line (a : kˣ) (f : associatedSectionsSubmodule k ι ρ) : - (fun i => chartLineEval k a (associatedXChart k ι ρ f i)) = - regularVectorEvaluation k ι (diagonalTorus k a) f.val := by - funext i - exact regularXChartValue_line k a (f.val i) - -omit [Infinite k] in -lemma unipotent_inverse (t : k) : (unipotent k t)⁻¹ = unipotent k (-t) := by - apply inv_eq_of_mul_eq_one_right - rw [← unipotent_add, add_neg_cancel, unipotent_zero] - -omit [Infinite k] [Fintype ι] [DecidableEq ι] in -lemma associatedSections_line_unipotent (a : kˣ) (t : k) - (f : associatedSectionsSubmodule k ι ρ) : - regularVectorEvaluation k ι (diagonalTorus k a) - (associatedSectionsRepresentation k ι ρ (unipotent k t) f).val = - ρ (Multiplicative.ofAdd (t / (a : k)^2)) - (regularVectorEvaluation k ι (diagonalTorus k a) f.val) := by - change regularVectorEvaluation k ι ((unipotent k t)⁻¹ * diagonalTorus k a) f.val = _ - rw [unipotent_inverse] - have he := diagonal_unipotent k a (-t / (a : k)^2) - rw [mul_div_cancel₀ _ (pow_ne_zero 2 a.ne_zero)] at he - rw [← he, f.property] - congr 2 - rw [neg_div, neg_neg] - -end FiberFunctorProof - -end OAI +import OAI.RepresentationTheory.RestrictedTilting.Basic + +namespace OAI + +namespace FiberFunctorProof +universe u +variable (k : Type u) [Field k] + +noncomputable def planeLineEval (a : k) : MvPolynomial (Fin 2) k →ₐ[k] k := + MvPolynomial.aeval (fun i => if i = 0 then a else 0) + +lemma planeLineEval_X_isUnit (a : kˣ) : + IsUnit (planeLineEval k a (MvPolynomial.X 0)) := by + simp [planeLineEval] + +noncomputable def chartLineEval (a : kˣ) : planeCoordinateChart k 0 →ₐ[k] k := + IsLocalization.Away.liftAlgHom (MvPolynomial.X 0) (planeLineEval_X_isUnit k a) + +lemma chartLineEval_algebraMap (a : kˣ) (P : MvPolynomial (Fin 2) k) : + chartLineEval k a (algebraMap (MvPolynomial (Fin 2) k) (planeCoordinateChart k 0) P) = + planeLineEval k a P := IsLocalization.Away.lift_eq _ (planeLineEval_X_isUnit k a) _ + +lemma chartLineEval_coordinate (a : kˣ) (i : Fin 2) : + chartLineEval k a (planeChartCoordinate k 0 i) = if i = 0 then (a : k) else 0 := by + rw [planeChartCoordinate, chartLineEval_algebraMap] + simp [planeLineEval] + +lemma chartLineEval_inverse (a : kˣ) : + chartLineEval k a (planeChartInverse k 0) = (a : k)⁻¹ := by + have hm : planeChartCoordinate k 0 0 * planeChartInverse k 0 = 1 := + IsLocalization.Away.mul_invSelf (S := planeCoordinateChart k 0) (MvPolynomial.X 0) + have h := congrArg (chartLineEval k a) hm + simp only [map_mul, map_one, chartLineEval_coordinate] at h + exact mul_left_cancel₀ a.ne_zero (h.trans (mul_inv_cancel₀ a.ne_zero).symm) + +lemma planeXPolynomialChart_line (a : kˣ) (P : MvPolynomial (Fin 2 × Fin 2) k) : + chartLineEval k a (planeXPolynomialChart k P) = coordinateEvaluation k P (diagonalTorus k a) := by + induction P using MvPolynomial.induction_on with + | C c => simp [planeXPolynomialChart, coordinateEvaluation] + | add P Q hp hq => simp only [map_add, Pi.add_apply, hp, hq] + | mul_X P i hp => + simp only [map_mul, Pi.mul_apply, hp] + congr 1 + rw [coordinateEvaluation_apply, MvPolynomial.eval_X] + rcases i with ⟨i,j⟩ + fin_cases i <;> fin_cases j <;> + simp [planeXPolynomialChart, diagonalTorus, chartLineEval_coordinate, chartLineEval_inverse] <;> rfl + +lemma regularXChartValue_line (a : kˣ) (f : regularSL2Functions k) : + chartLineEval k a (regularXChartValue k f) = f.val (diagonalTorus k a) := by + rw [regularXChartValue, planeXPolynomialChart_line] + exact congrFun f.property.choose_spec _ + +variable [Infinite k] +variable (ι : Type u) [Fintype ι] [DecidableEq ι] +variable (ρ : Representation k (Multiplicative k) (ι → k)) + +omit [Fintype ι] [DecidableEq ι] in +lemma associatedXChart_line (a : kˣ) (f : associatedSectionsSubmodule k ι ρ) : + (fun i => chartLineEval k a (associatedXChart k ι ρ f i)) = + regularVectorEvaluation k ι (diagonalTorus k a) f.val := by + funext i + exact regularXChartValue_line k a (f.val i) + +omit [Infinite k] in +lemma unipotent_inverse (t : k) : (unipotent k t)⁻¹ = unipotent k (-t) := by + apply inv_eq_of_mul_eq_one_right + rw [← unipotent_add, add_neg_cancel, unipotent_zero] + +omit [Infinite k] [Fintype ι] [DecidableEq ι] in +lemma associatedSections_line_unipotent (a : kˣ) (t : k) + (f : associatedSectionsSubmodule k ι ρ) : + regularVectorEvaluation k ι (diagonalTorus k a) + (associatedSectionsRepresentation k ι ρ (unipotent k t) f).val = + ρ (Multiplicative.ofAdd (t / (a : k)^2)) + (regularVectorEvaluation k ι (diagonalTorus k a) f.val) := by + change regularVectorEvaluation k ι ((unipotent k t)⁻¹ * diagonalTorus k a) f.val = _ + rw [unipotent_inverse] + have he := diagonal_unipotent k a (-t / (a : k)^2) + rw [mul_div_cancel₀ _ (pow_ne_zero 2 a.ne_zero)] at he + rw [← he, f.property] + congr 2 + rw [neg_div, neg_neg] + +end FiberFunctorProof + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/Basic.lean b/lean/OAI/RepresentationTheory/RowColumn/Basic.lean index dd7ea7378091d69a6b0eeb101cae60f7fceae236..7291a5daee94d6a61711db8d3d0289aa02f8caf7 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/Basic.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/Basic.lean @@ -1,91 +1,91 @@ -import OAI.RepresentationTheory.YoungSymmetry.UnitaryModel - -namespace OAI - -noncomputable section - -open scoped BigOperators Classical - -namespace RowColumn -open CubeShuffle CubeShuffle.Specht CubeShuffle.UnitaryFinite - -/-- Permutations preserving each fibre of a given line map. -/ -def lineGroup {α β : Type*} (f : α → β) : Subgroup (Equiv.Perm α) where - carrier := {g | ∀ x, f (g x) = f x} - one_mem' := by intro x; rfl - mul_mem' := by - intro a b ha hb x - exact (ha (b x)).trans (hb x) - inv_mem' := by - intro a ha x - simpa using (ha (a⁻¹ x)).symm - -abbrev Board (m n : ℕ) := Fin m × Fin n -abbrev rowGroup {m n : ℕ} (Ω : Finset (Board m n)) := - lineGroup (fun x : Ω => x.1.1) -abbrev columnGroup {m n : ℕ} (Ω : Finset (Board m n)) := - lineGroup (fun x : Ω => x.1.2) - -/-- Zero-based form of the manuscript's (h,h)-hook. -/ -def InHook (a : YoungDiagram) (h : ℕ) : Prop := - ∀ c ∈ a.cells, c.1 < h ∨ c.2 < h - -section Copies -variable {G V W : Type*} [Group G] - [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] - [NormedAddCommGroup W] [InnerProductSpace ℂ W] [FiniteDimensional ℂ W] - -/-- An actual equivariant inclusion, not an unspecified overlap matrix. -/ -def Intertwines (ρ : Representation ℂ G V) (τ : Representation ℂ G W) - (I : V →ₗ[ℂ] W) : Prop := - ∀ g v, I (ρ g v) = τ g (I v) - -/-- All orthogonal multiplicity copies of one irreducible type. The completeness -condition quantifies over genuine intertwiners, i.e. it is exactly the isotypic -space condition. -/ -def CompleteCopies (ρ : Representation ℂ G V) (τ : Representation ℂ G W) - {u : ℕ} (I : Fin u → V →ₗᵢ[ℂ] W) : Prop := - (∀ i, Intertwines ρ τ (I i).toLinearMap) ∧ - (∀ i j, i ≠ j → ∀ v w, inner ℂ (I i v) (I j w) = 0) ∧ - ∀ J : V →ₗ[ℂ] W, Intertwines ρ τ J → - LinearMap.range J ≤ ⨆ i, LinearMap.range (I i).toLinearMap - -end Copies - -/-- The all-copy operator-overlap sum, with each squared operator norm. -/ -def allCopyOverlap {V W X : Type*} - [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] - [NormedAddCommGroup W] [InnerProductSpace ℂ W] [FiniteDimensional ℂ W] - [NormedAddCommGroup X] [InnerProductSpace ℂ X] [FiniteDimensional ℂ X] - {u v : ℕ} (I : Fin u → V →ₗᵢ[ℂ] X) (J : Fin v → W →ₗᵢ[ℂ] X) : ℝ := - ∑ i, ∑ j, ‖((I i).toContinuousLinearMap.adjoint).comp - (J j).toContinuousLinearMap‖ ^ 2 - -/-- Exact occupied-board main. Carriers are in orthonormal coordinates; arbitrary -unitary irreducibles of the two actual line groups are quantified over (equivalently, -the tuples of line partitions in the manuscript). Labelling `e` chooses the action -of the Specht module on the occupied cells and forces |a| = |Ω|. -/ -abbrev OccupiedOverlapEndpoint : Prop := - ∃ C : ℝ, 0 < C ∧ ∀ (m n : ℕ) (Ω : Finset (Board m n)) - (a : YoungDiagram) (e : Ω ≃ Cell a) (h : ℕ), - 1 ≤ h → h ≤ m * n → InHook a h → - ∀ (r c u v : ℕ) - (ρ : Representation ℂ (rowGroup Ω) (EuclideanSpace ℂ (Fin r))) - (τ : Representation ℂ (columnGroup Ω) (EuclideanSpace ℂ (Fin c))), - Representation.IsIrreducible ρ → Representation.IsIrreducible τ → - IsUnitary ρ → IsUnitary τ → - ∀ (I : Fin u → EuclideanSpace ℂ (Fin r) →ₗᵢ[ℂ] hilbertSpace a) - (J : Fin v → EuclideanSpace ℂ (Fin c) →ₗᵢ[ℂ] hilbertSpace a), - CompleteCopies (V := EuclideanSpace ℂ (Fin r)) (W := hilbertSpace a) ρ ((relabelledUnitary a e).comp (rowGroup Ω).subtype) I → - CompleteCopies (V := EuclideanSpace ℂ (Fin c)) (W := hilbertSpace a) τ ((relabelledUnitary a e).comp (columnGroup Ω).subtype) J → - allCopyOverlap (V := EuclideanSpace ℂ (Fin r)) (W := EuclideanSpace ℂ (Fin c)) - (X := hilbertSpace a) I J ≤ - Real.exp (C * (((m + n + 1 : ℕ) : ℝ) * (h : ℝ)^2 * - Real.log ((m * n : ℕ) + 2) + (m * n - Ω.card : ℕ))) * - min 1 ((r : ℝ) * c / Module.finrank ℂ (space a)) - -end RowColumn - -end - -end OAI +import OAI.RepresentationTheory.YoungSymmetry.UnitaryModel + +namespace OAI + +noncomputable section + +open scoped BigOperators Classical + +namespace RowColumn +open CubeShuffle CubeShuffle.Specht CubeShuffle.UnitaryFinite + +/-- Permutations preserving each fibre of a given line map. -/ +def lineGroup {α β : Type*} (f : α → β) : Subgroup (Equiv.Perm α) where + carrier := {g | ∀ x, f (g x) = f x} + one_mem' := by intro x; rfl + mul_mem' := by + intro a b ha hb x + exact (ha (b x)).trans (hb x) + inv_mem' := by + intro a ha x + simpa using (ha (a⁻¹ x)).symm + +abbrev Board (m n : ℕ) := Fin m × Fin n +abbrev rowGroup {m n : ℕ} (Ω : Finset (Board m n)) := + lineGroup (fun x : Ω => x.1.1) +abbrev columnGroup {m n : ℕ} (Ω : Finset (Board m n)) := + lineGroup (fun x : Ω => x.1.2) + +/-- Zero-based form of the manuscript's (h,h)-hook. -/ +def InHook (a : YoungDiagram) (h : ℕ) : Prop := + ∀ c ∈ a.cells, c.1 < h ∨ c.2 < h + +section Copies +variable {G V W : Type*} [Group G] + [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] + [NormedAddCommGroup W] [InnerProductSpace ℂ W] [FiniteDimensional ℂ W] + +/-- An actual equivariant inclusion, not an unspecified overlap matrix. -/ +def Intertwines (ρ : Representation ℂ G V) (τ : Representation ℂ G W) + (I : V →ₗ[ℂ] W) : Prop := + ∀ g v, I (ρ g v) = τ g (I v) + +/-- All orthogonal multiplicity copies of one irreducible type. The completeness +condition quantifies over genuine intertwiners, i.e. it is exactly the isotypic +space condition. -/ +def CompleteCopies (ρ : Representation ℂ G V) (τ : Representation ℂ G W) + {u : ℕ} (I : Fin u → V →ₗᵢ[ℂ] W) : Prop := + (∀ i, Intertwines ρ τ (I i).toLinearMap) ∧ + (∀ i j, i ≠ j → ∀ v w, inner ℂ (I i v) (I j w) = 0) ∧ + ∀ J : V →ₗ[ℂ] W, Intertwines ρ τ J → + LinearMap.range J ≤ ⨆ i, LinearMap.range (I i).toLinearMap + +end Copies + +/-- The all-copy operator-overlap sum, with each squared operator norm. -/ +def allCopyOverlap {V W X : Type*} + [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] + [NormedAddCommGroup W] [InnerProductSpace ℂ W] [FiniteDimensional ℂ W] + [NormedAddCommGroup X] [InnerProductSpace ℂ X] [FiniteDimensional ℂ X] + {u v : ℕ} (I : Fin u → V →ₗᵢ[ℂ] X) (J : Fin v → W →ₗᵢ[ℂ] X) : ℝ := + ∑ i, ∑ j, ‖((I i).toContinuousLinearMap.adjoint).comp + (J j).toContinuousLinearMap‖ ^ 2 + +/-- Exact occupied-board main. Carriers are in orthonormal coordinates; arbitrary +unitary irreducibles of the two actual line groups are quantified over (equivalently, +the tuples of line partitions in the manuscript). Labelling `e` chooses the action +of the Specht module on the occupied cells and forces |a| = |Ω|. -/ +abbrev OccupiedOverlapEndpoint : Prop := + ∃ C : ℝ, 0 < C ∧ ∀ (m n : ℕ) (Ω : Finset (Board m n)) + (a : YoungDiagram) (e : Ω ≃ Cell a) (h : ℕ), + 1 ≤ h → h ≤ m * n → InHook a h → + ∀ (r c u v : ℕ) + (ρ : Representation ℂ (rowGroup Ω) (EuclideanSpace ℂ (Fin r))) + (τ : Representation ℂ (columnGroup Ω) (EuclideanSpace ℂ (Fin c))), + Representation.IsIrreducible ρ → Representation.IsIrreducible τ → + IsUnitary ρ → IsUnitary τ → + ∀ (I : Fin u → EuclideanSpace ℂ (Fin r) →ₗᵢ[ℂ] hilbertSpace a) + (J : Fin v → EuclideanSpace ℂ (Fin c) →ₗᵢ[ℂ] hilbertSpace a), + CompleteCopies (V := EuclideanSpace ℂ (Fin r)) (W := hilbertSpace a) ρ ((relabelledUnitary a e).comp (rowGroup Ω).subtype) I → + CompleteCopies (V := EuclideanSpace ℂ (Fin c)) (W := hilbertSpace a) τ ((relabelledUnitary a e).comp (columnGroup Ω).subtype) J → + allCopyOverlap (V := EuclideanSpace ℂ (Fin r)) (W := EuclideanSpace ℂ (Fin c)) + (X := hilbertSpace a) I J ≤ + Real.exp (C * (((m + n + 1 : ℕ) : ℝ) * (h : ℝ)^2 * + Real.log ((m * n : ℕ) + 2) + (m * n - Ω.card : ℕ))) * + min 1 ((r : ℝ) * c / Module.finrank ℂ (space a)) + +end RowColumn + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/CopyOverlap.lean b/lean/OAI/RepresentationTheory/RowColumn/CopyOverlap.lean index 16eb3dfeb545ff638ed188152c4812b28be3fc63..0fd282a5d4e54733288b267dfd7916302a7968fb 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/CopyOverlap.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/CopyOverlap.lean @@ -1,293 +1,293 @@ -import OAI.RepresentationTheory.RowColumn.Multiplicity -import OAI.LinearAlgebra.MatrixState.HilbertSchmidt - -namespace OAI - -section -noncomputable section - -namespace RowColumn -open scoped BigOperators ComplexConjugate Classical - -section HilbertSchmidt -variable {V W : Type*} - [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] - [NormedAddCommGroup W] [InnerProductSpace ℂ W] [FiniteDimensional ℂ W] - -/-- Ordinary squared Hilbert--Schmidt norm on a possibly rectangular map. -/ -def hilbertSchmidtSq (B : V →L[ℂ] W) : ℝ := - (LinearMap.trace ℂ V (B.adjoint.comp B).toLinearMap).re - -lemma hilbertSchmidtSq_eq_sum (B : V →L[ℂ] W) - {ι : Type*} [Fintype ι] (b : OrthonormalBasis ι ℂ V) : - hilbertSchmidtSq B = ∑ i, ‖B (b i)‖ ^ 2 := by - rw [hilbertSchmidtSq, LinearMap.trace_eq_sum_inner _ b, Complex.re_sum] - apply Finset.sum_congr rfl - intro i _ - simpa using (B.apply_norm_sq_eq_inner_adjoint_right (b i)).symm - -lemma norm_sq_le_hilbertSchmidtSq (B : V →L[ℂ] W) : - ‖B‖ ^ 2 ≤ hilbertSchmidtSq B := by - let b := stdOrthonormalBasis ℂ V - have hn : 0 ≤ hilbertSchmidtSq B := by - rw [hilbertSchmidtSq_eq_sum B b] - exact Finset.sum_nonneg (fun _ _ => sq_nonneg _) - have hh : ‖B‖ ≤ Real.sqrt (hilbertSchmidtSq B) := by - apply B.opNorm_le_bound (Real.sqrt_nonneg _) - intro x - have ha : ‖B x‖ ≤ ∑ i, ‖inner ℂ (b i) x‖ * ‖B (b i)‖ := by - nth_rw 1 [← b.sum_repr' x] - rw [map_sum] - apply (norm_sum_le _ _).trans - simp only [map_smul, norm_smul] - exact le_rfl - have hb := Real.sum_mul_le_sqrt_mul_sqrt Finset.univ - (fun i => ‖inner ℂ (b i) x‖) (fun i => ‖B (b i)‖) - rw [b.sum_sq_norm_inner_right, Real.sqrt_sq (norm_nonneg x), - ← hilbertSchmidtSq_eq_sum B b, mul_comm] at hb - exact ha.trans hb - exact (pow_le_pow_left₀ (norm_nonneg _) hh 2).trans_eq (Real.sq_sqrt hn) - -end HilbertSchmidt - -section CopyTrace -variable {V W X : Type*} - [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] - [NormedAddCommGroup W] [InnerProductSpace ℂ W] [FiniteDimensional ℂ W] - [NormedAddCommGroup X] [InnerProductSpace ℂ X] [FiniteDimensional ℂ X] - {u v : ℕ} - -/-- Sum of the genuine range projections for the given isometric copies. -/ -def copyProjection (I : Fin u → V →ₗᵢ[ℂ] X) : X →L[ℂ] X := - ∑ i, (I i).toContinuousLinearMap.comp (I i).toContinuousLinearMap.adjoint - -lemma hilbertSchmidtSq_overlap (I : V →ₗᵢ[ℂ] X) (J : W →ₗᵢ[ℂ] X) : - hilbertSchmidtSq (I.toContinuousLinearMap.adjoint.comp J.toContinuousLinearMap) = - (LinearMap.trace ℂ X - ((I.toContinuousLinearMap.comp I.toContinuousLinearMap.adjoint).comp - (J.toContinuousLinearMap.comp J.toContinuousLinearMap.adjoint)).toLinearMap).re := by - unfold hilbertSchmidtSq - simp only [ContinuousLinearMap.adjoint_comp, ContinuousLinearMap.adjoint_adjoint, - ContinuousLinearMap.toLinearMap_comp] - congr 1 - rw [LinearMap.comp_assoc, LinearMap.comp_assoc] - rw [LinearMap.trace_comp_comm'] - simp only [LinearMap.comp_assoc] - -/-- The all-copy identity in weighted.tex:126–133, for the actual embeddings. -No overlap bound is an assumption. -/ -lemma allCopy_hilbertSchmidt_identity (I : Fin u → V →ₗᵢ[ℂ] X) - (J : Fin v → W →ₗᵢ[ℂ] X) : - ∑ i, ∑ j, hilbertSchmidtSq - ((I i).toContinuousLinearMap.adjoint.comp (J j).toContinuousLinearMap) = - (LinearMap.trace ℂ X ((copyProjection I).comp (copyProjection J)).toLinearMap).re := by - change _ = (LinearMap.trace ℂ X - ((∑ i, (I i).toContinuousLinearMap.comp (I i).toContinuousLinearMap.adjoint) * - (∑ j, (J j).toContinuousLinearMap.comp (J j).toContinuousLinearMap.adjoint)).toLinearMap).re - simp only [Finset.sum_mul, Finset.mul_sum, ContinuousLinearMap.toLinearMap_sum, - map_sum, Complex.re_sum] - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro j _ - apply Finset.sum_congr rfl - intro i _ - exact hilbertSchmidtSq_overlap (I i) (J j) - -lemma allCopyOverlap_le_trace (I : Fin u → V →ₗᵢ[ℂ] X) - (J : Fin v → W →ₗᵢ[ℂ] X) : - allCopyOverlap I J ≤ - (LinearMap.trace ℂ X ((copyProjection I).comp (copyProjection J)).toLinearMap).re := by - rw [← allCopy_hilbertSchmidt_identity I J] - apply Finset.sum_le_sum - intro i _ - apply Finset.sum_le_sum - intro j _ - exact norm_sq_le_hilbertSchmidtSq _ - -end CopyTrace -end RowColumn - -end -end - -section - -noncomputable section -open scoped BigOperators Classical ComplexOrder -namespace RowColumn -open CubeShuffle.UnitaryFinite -variable {V W X E G : Type*} - [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] - [NormedAddCommGroup W] [InnerProductSpace ℂ W] [FiniteDimensional ℂ W] - [NormedAddCommGroup X] [InnerProductSpace ℂ X] [FiniteDimensional ℂ X] - [NormedAddCommGroup E] [InnerProductSpace ℂ E] [FiniteDimensional ℂ E] - {u v : ℕ} - -lemma isometry_adjoint_apply (I : V →ₗᵢ[ℂ] X) (x : V) : - I.toContinuousLinearMap.adjoint (I x) = x := by - apply ext_inner_left ℂ - intro y - rw [ContinuousLinearMap.adjoint_inner_right] - exact I.inner_map_map y x - -lemma isometry_adjoint_comp (I : V →ₗᵢ[ℂ] X) : - I.toContinuousLinearMap.adjoint.comp I.toContinuousLinearMap = 1 := by - ext x - exact isometry_adjoint_apply I x - -lemma copyProjection_positive (I : Fin u → V →ₗᵢ[ℂ] X) : - (copyProjection I).IsPositive := by - apply ContinuousLinearMap.isPositive_sum - intro i _ - exact ContinuousLinearMap.isPositive_self_comp_adjoint _ - -lemma copyProjection_trace (I : Fin u → V →ₗᵢ[ℂ] X) : - LinearMap.trace ℂ X (copyProjection I).toLinearMap = (u * Module.finrank ℂ V : ℕ) := by - simp only [copyProjection, ContinuousLinearMap.toLinearMap_sum, map_sum, - ContinuousLinearMap.toLinearMap_comp] - have h (i : Fin u) : LinearMap.trace ℂ X - ((I i).toContinuousLinearMap.toLinearMap.comp (I i).toContinuousLinearMap.adjoint.toLinearMap) = - (Module.finrank ℂ V : ℂ) := by - rw [LinearMap.trace_comp_comm'] - change LinearMap.trace ℂ V ((I i).toContinuousLinearMap.adjoint.comp - (I i).toContinuousLinearMap).toLinearMap = _ - rw [isometry_adjoint_comp] - exact LinearMap.trace_id ℂ V - simp_rw [h] - simp [Nat.cast_mul] - -lemma copyProjection_intertwines [Group G] (ρ : Representation ℂ G V) (τ : Representation ℂ G X) - (hρ : IsUnitary ρ) (hτ : IsUnitary τ) (I : Fin u → V →ₗᵢ[ℂ] X) - (hI : ∀ i, Intertwines ρ τ (I i).toLinearMap) : - Intertwines τ τ (copyProjection I).toLinearMap := by - intro g x - simp only [copyProjection, ContinuousLinearMap.coe_coe, sum_apply, ContinuousLinearMap.comp_apply, map_sum] - apply Finset.sum_congr rfl - intro i _ - rw [show (I i).toContinuousLinearMap.adjoint (τ g x) = - ρ g ((I i).toContinuousLinearMap.adjoint x) from - adjoint_intertwines (I i).toLinearMap (hI i) hρ hτ g x] - exact hI i g _ - -lemma allCopyOverlap_comp_isometry (I : Fin u → V →ₗᵢ[ℂ] X) - (J : Fin v → W →ₗᵢ[ℂ] X) (K : X →ₗᵢ[ℂ] E) : - allCopyOverlap (fun i => K.comp (I i)) (fun j => K.comp (J j)) = allCopyOverlap I J := by - unfold allCopyOverlap - apply Finset.sum_congr rfl - intro i _ - apply Finset.sum_congr rfl - intro j _ - apply congrArg (fun T : W →L[ℂ] V => ‖T‖^2) - ext x - change (K.toContinuousLinearMap.comp (I i).toContinuousLinearMap).adjoint - (K (J j x)) = _ - rw [ContinuousLinearMap.adjoint_comp] - change (I i).toContinuousLinearMap.adjoint (K.toContinuousLinearMap.adjoint (K (J j x))) = _ - rw [isometry_adjoint_apply] - rfl - -lemma allCopyOverlap_le_count (I : Fin u → V →ₗᵢ[ℂ] X) - (J : Fin v → W →ₗᵢ[ℂ] X) : allCopyOverlap I J ≤ (u : ℝ) * v := by - unfold allCopyOverlap - have h (i : Fin u) (j : Fin v) : - ‖(I i).toContinuousLinearMap.adjoint.comp (J j).toContinuousLinearMap‖^2 ≤ 1 := by - have hn := ContinuousLinearMap.opNorm_comp_le (I i).toContinuousLinearMap.adjoint - (J j).toContinuousLinearMap - rw [ContinuousLinearMap.adjoint.norm_map] at hn - have hb := mul_le_mul (I i).norm_toContinuousLinearMap_le (J j).norm_toContinuousLinearMap_le - (norm_nonneg _) (by norm_num : (0:ℝ) ≤ 1) - have hz : ‖(I i).toContinuousLinearMap.adjoint.comp (J j).toContinuousLinearMap‖ ≤ 1 := - hn.trans (by simpa using hb) - nlinarith [norm_nonneg ((I i).toContinuousLinearMap.adjoint.comp (J j).toContinuousLinearMap)] - calc - _ ≤ ∑ _i : Fin u, ∑ _j : Fin v, (1 : ℝ) := - Finset.sum_le_sum fun i _ => Finset.sum_le_sum fun j _ => h i j - _ = _ := by simp - -end RowColumn - -end -end - - -section -noncomputable section -open scoped BigOperators Classical -namespace RowColumn -open CubeShuffle.UnitaryFinite -variable {G V E : Type*} [Group G] - [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] - [NormedAddCommGroup E] [InnerProductSpace ℂ E] [FiniteDimensional ℂ E] - (ρ : Representation ℂ G V) (τ : Representation ℂ G E) - (hρ : IsUnitary ρ) (hτ : IsUnitary τ) - -include hρ hτ -lemma isometric_adjoint_intertwines (f : Representation.IntertwiningMap ρ τ) (g : G) (x : E) : - LinearMap.adjoint f.toLinearMap (τ g x) = ρ g (LinearMap.adjoint f.toLinearMap x) := by - have hf : Intertwines ρ τ f.toLinearMap := by - intro g y - exact Representation.IntertwiningMap.isIntertwining ρ τ f g y - have hh := adjoint_intertwines f.toLinearMap hf hρ hτ g x - simpa only [LinearMap.adjoint_eq_toCLM_adjoint] using hh - -def gramIntertwiner (f : Representation.IntertwiningMap ρ τ) : Representation.IntertwiningMap ρ ρ where - toLinearMap := (LinearMap.adjoint f.toLinearMap).comp f.toLinearMap - isIntertwining' g := by - ext x - change (LinearMap.adjoint f.toLinearMap) (f (ρ g x)) = - ρ g ((LinearMap.adjoint f.toLinearMap) (f x)) - rw [Representation.IntertwiningMap.isIntertwining] - exact isometric_adjoint_intertwines ρ τ hρ hτ f g (f x) - -/-- Every actual nonzero algebraic embedding of irreducible unitary carriers -normalizes to an isometric intertwiner. No normalized embedding is assumed. -/ -theorem isometric_intertwiner_of_injective [Representation.IsIrreducible ρ] - (f : Representation.IntertwiningMap ρ τ) (hf : Function.Injective f) : - ∃ I : V →ₗᵢ[ℂ] E, ∀ g x, I (ρ g x)=τ g (I x) := by - let : Nontrivial V := by - let := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) ρ.asModule - exact ρ.asModuleEquiv.symm.toEquiv.nontrivial - obtain ⟨c,hc⟩ := - (Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed (ρ := ρ)).surjective - (gramIntertwiner ρ τ hρ hτ f) - have hgram : (LinearMap.adjoint f.toLinearMap).comp f.toLinearMap = c • LinearMap.id := by - change (gramIntertwiner ρ τ hρ hτ f).toLinearMap = _ - rw [← hc] - rfl - have hn (x : V) : ‖f x‖^2 = c.re * ‖x‖^2 := by - have hh := congrArg (fun T : V →ₗ[ℂ] V => inner ℂ x (T x)) hgram - simp only [LinearMap.comp_apply, LinearMap.adjoint_inner_right, LinearMap.smul_apply, - LinearMap.id_apply, inner_smul_right, inner_self_eq_norm_sq_to_K] at hh - change ‖f.toLinearMap x‖^2 = c.re * ‖x‖^2 - have he := congrArg Complex.re hh - simpa only [RCLike.ofReal_eq_complex_ofReal, ← Complex.ofReal_pow, Complex.mul_re, - Complex.ofReal_re, Complex.ofReal_im, zero_mul, sub_zero, mul_zero] using he - obtain ⟨x,hx⟩ := exists_ne (0 : V) - have hfx : f x ≠ 0 := by intro h; exact hx (hf (h.trans (map_zero f).symm)) - have hcpos : 0 < c.re := by - have hh := hn x - have hp : 0 < ‖f x‖^2 := sq_pos_of_ne_zero ((norm_ne_zero_iff).mpr hfx) - have hxnon : 0 ≤ ‖x‖^2 := sq_nonneg _ - nlinarith - let a : ℂ := (Real.sqrt c.re)⁻¹ - let F : V →ₗ[ℂ] E := a • f.toLinearMap - have ha : ‖a‖^2 * c.re = 1 := by - simp only [a, norm_inv, Complex.norm_real, Real.norm_eq_abs, - abs_of_nonneg (Real.sqrt_nonneg _)] - rw [inv_pow, Real.sq_sqrt hcpos.le, inv_mul_cancel₀ (ne_of_gt hcpos)] - have hnorm (y : V) : ‖F y‖ = ‖y‖ := by - change ‖a • f y‖=‖y‖ - rw [norm_smul] - have hh : (‖a‖*‖f y‖)^2=‖y‖^2 := by rw [mul_pow, hn, ← mul_assoc, ha, one_mul] - exact (sq_eq_sq₀ (mul_nonneg (norm_nonneg a) (norm_nonneg (f y))) (norm_nonneg y)).mp hh - let I : V →ₗᵢ[ℂ] E := { F with norm_map' := hnorm } - refine ⟨I,?_⟩ - intro g y - change a • f (ρ g y)=τ g (a • f y) - rw [Representation.IntertwiningMap.isIntertwining, map_smul] -end RowColumn - -end -end - -end OAI +import OAI.RepresentationTheory.RowColumn.Multiplicity +import OAI.LinearAlgebra.MatrixState.HilbertSchmidt + +namespace OAI + +section +noncomputable section + +namespace RowColumn +open scoped BigOperators ComplexConjugate Classical + +section HilbertSchmidt +variable {V W : Type*} + [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] + [NormedAddCommGroup W] [InnerProductSpace ℂ W] [FiniteDimensional ℂ W] + +/-- Ordinary squared Hilbert--Schmidt norm on a possibly rectangular map. -/ +def hilbertSchmidtSq (B : V →L[ℂ] W) : ℝ := + (LinearMap.trace ℂ V (B.adjoint.comp B).toLinearMap).re + +lemma hilbertSchmidtSq_eq_sum (B : V →L[ℂ] W) + {ι : Type*} [Fintype ι] (b : OrthonormalBasis ι ℂ V) : + hilbertSchmidtSq B = ∑ i, ‖B (b i)‖ ^ 2 := by + rw [hilbertSchmidtSq, LinearMap.trace_eq_sum_inner _ b, Complex.re_sum] + apply Finset.sum_congr rfl + intro i _ + simpa using (B.apply_norm_sq_eq_inner_adjoint_right (b i)).symm + +lemma norm_sq_le_hilbertSchmidtSq (B : V →L[ℂ] W) : + ‖B‖ ^ 2 ≤ hilbertSchmidtSq B := by + let b := stdOrthonormalBasis ℂ V + have hn : 0 ≤ hilbertSchmidtSq B := by + rw [hilbertSchmidtSq_eq_sum B b] + exact Finset.sum_nonneg (fun _ _ => sq_nonneg _) + have hh : ‖B‖ ≤ Real.sqrt (hilbertSchmidtSq B) := by + apply B.opNorm_le_bound (Real.sqrt_nonneg _) + intro x + have ha : ‖B x‖ ≤ ∑ i, ‖inner ℂ (b i) x‖ * ‖B (b i)‖ := by + nth_rw 1 [← b.sum_repr' x] + rw [map_sum] + apply (norm_sum_le _ _).trans + simp only [map_smul, norm_smul] + exact le_rfl + have hb := Real.sum_mul_le_sqrt_mul_sqrt Finset.univ + (fun i => ‖inner ℂ (b i) x‖) (fun i => ‖B (b i)‖) + rw [b.sum_sq_norm_inner_right, Real.sqrt_sq (norm_nonneg x), + ← hilbertSchmidtSq_eq_sum B b, mul_comm] at hb + exact ha.trans hb + exact (pow_le_pow_left₀ (norm_nonneg _) hh 2).trans_eq (Real.sq_sqrt hn) + +end HilbertSchmidt + +section CopyTrace +variable {V W X : Type*} + [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] + [NormedAddCommGroup W] [InnerProductSpace ℂ W] [FiniteDimensional ℂ W] + [NormedAddCommGroup X] [InnerProductSpace ℂ X] [FiniteDimensional ℂ X] + {u v : ℕ} + +/-- Sum of the genuine range projections for the given isometric copies. -/ +def copyProjection (I : Fin u → V →ₗᵢ[ℂ] X) : X →L[ℂ] X := + ∑ i, (I i).toContinuousLinearMap.comp (I i).toContinuousLinearMap.adjoint + +lemma hilbertSchmidtSq_overlap (I : V →ₗᵢ[ℂ] X) (J : W →ₗᵢ[ℂ] X) : + hilbertSchmidtSq (I.toContinuousLinearMap.adjoint.comp J.toContinuousLinearMap) = + (LinearMap.trace ℂ X + ((I.toContinuousLinearMap.comp I.toContinuousLinearMap.adjoint).comp + (J.toContinuousLinearMap.comp J.toContinuousLinearMap.adjoint)).toLinearMap).re := by + unfold hilbertSchmidtSq + simp only [ContinuousLinearMap.adjoint_comp, ContinuousLinearMap.adjoint_adjoint, + ContinuousLinearMap.toLinearMap_comp] + congr 1 + rw [LinearMap.comp_assoc, LinearMap.comp_assoc] + rw [LinearMap.trace_comp_comm'] + simp only [LinearMap.comp_assoc] + +/-- The all-copy identity in weighted.tex:126–133, for the actual embeddings. +No overlap bound is an assumption. -/ +lemma allCopy_hilbertSchmidt_identity (I : Fin u → V →ₗᵢ[ℂ] X) + (J : Fin v → W →ₗᵢ[ℂ] X) : + ∑ i, ∑ j, hilbertSchmidtSq + ((I i).toContinuousLinearMap.adjoint.comp (J j).toContinuousLinearMap) = + (LinearMap.trace ℂ X ((copyProjection I).comp (copyProjection J)).toLinearMap).re := by + change _ = (LinearMap.trace ℂ X + ((∑ i, (I i).toContinuousLinearMap.comp (I i).toContinuousLinearMap.adjoint) * + (∑ j, (J j).toContinuousLinearMap.comp (J j).toContinuousLinearMap.adjoint)).toLinearMap).re + simp only [Finset.sum_mul, Finset.mul_sum, ContinuousLinearMap.toLinearMap_sum, + map_sum, Complex.re_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro j _ + apply Finset.sum_congr rfl + intro i _ + exact hilbertSchmidtSq_overlap (I i) (J j) + +lemma allCopyOverlap_le_trace (I : Fin u → V →ₗᵢ[ℂ] X) + (J : Fin v → W →ₗᵢ[ℂ] X) : + allCopyOverlap I J ≤ + (LinearMap.trace ℂ X ((copyProjection I).comp (copyProjection J)).toLinearMap).re := by + rw [← allCopy_hilbertSchmidt_identity I J] + apply Finset.sum_le_sum + intro i _ + apply Finset.sum_le_sum + intro j _ + exact norm_sq_le_hilbertSchmidtSq _ + +end CopyTrace +end RowColumn + +end +end + +section + +noncomputable section +open scoped BigOperators Classical ComplexOrder +namespace RowColumn +open CubeShuffle.UnitaryFinite +variable {V W X E G : Type*} + [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] + [NormedAddCommGroup W] [InnerProductSpace ℂ W] [FiniteDimensional ℂ W] + [NormedAddCommGroup X] [InnerProductSpace ℂ X] [FiniteDimensional ℂ X] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] [FiniteDimensional ℂ E] + {u v : ℕ} + +lemma isometry_adjoint_apply (I : V →ₗᵢ[ℂ] X) (x : V) : + I.toContinuousLinearMap.adjoint (I x) = x := by + apply ext_inner_left ℂ + intro y + rw [ContinuousLinearMap.adjoint_inner_right] + exact I.inner_map_map y x + +lemma isometry_adjoint_comp (I : V →ₗᵢ[ℂ] X) : + I.toContinuousLinearMap.adjoint.comp I.toContinuousLinearMap = 1 := by + ext x + exact isometry_adjoint_apply I x + +lemma copyProjection_positive (I : Fin u → V →ₗᵢ[ℂ] X) : + (copyProjection I).IsPositive := by + apply ContinuousLinearMap.isPositive_sum + intro i _ + exact ContinuousLinearMap.isPositive_self_comp_adjoint _ + +lemma copyProjection_trace (I : Fin u → V →ₗᵢ[ℂ] X) : + LinearMap.trace ℂ X (copyProjection I).toLinearMap = (u * Module.finrank ℂ V : ℕ) := by + simp only [copyProjection, ContinuousLinearMap.toLinearMap_sum, map_sum, + ContinuousLinearMap.toLinearMap_comp] + have h (i : Fin u) : LinearMap.trace ℂ X + ((I i).toContinuousLinearMap.toLinearMap.comp (I i).toContinuousLinearMap.adjoint.toLinearMap) = + (Module.finrank ℂ V : ℂ) := by + rw [LinearMap.trace_comp_comm'] + change LinearMap.trace ℂ V ((I i).toContinuousLinearMap.adjoint.comp + (I i).toContinuousLinearMap).toLinearMap = _ + rw [isometry_adjoint_comp] + exact LinearMap.trace_id ℂ V + simp_rw [h] + simp [Nat.cast_mul] + +lemma copyProjection_intertwines [Group G] (ρ : Representation ℂ G V) (τ : Representation ℂ G X) + (hρ : IsUnitary ρ) (hτ : IsUnitary τ) (I : Fin u → V →ₗᵢ[ℂ] X) + (hI : ∀ i, Intertwines ρ τ (I i).toLinearMap) : + Intertwines τ τ (copyProjection I).toLinearMap := by + intro g x + simp only [copyProjection, ContinuousLinearMap.coe_coe, sum_apply, ContinuousLinearMap.comp_apply, map_sum] + apply Finset.sum_congr rfl + intro i _ + rw [show (I i).toContinuousLinearMap.adjoint (τ g x) = + ρ g ((I i).toContinuousLinearMap.adjoint x) from + adjoint_intertwines (I i).toLinearMap (hI i) hρ hτ g x] + exact hI i g _ + +lemma allCopyOverlap_comp_isometry (I : Fin u → V →ₗᵢ[ℂ] X) + (J : Fin v → W →ₗᵢ[ℂ] X) (K : X →ₗᵢ[ℂ] E) : + allCopyOverlap (fun i => K.comp (I i)) (fun j => K.comp (J j)) = allCopyOverlap I J := by + unfold allCopyOverlap + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + apply congrArg (fun T : W →L[ℂ] V => ‖T‖^2) + ext x + change (K.toContinuousLinearMap.comp (I i).toContinuousLinearMap).adjoint + (K (J j x)) = _ + rw [ContinuousLinearMap.adjoint_comp] + change (I i).toContinuousLinearMap.adjoint (K.toContinuousLinearMap.adjoint (K (J j x))) = _ + rw [isometry_adjoint_apply] + rfl + +lemma allCopyOverlap_le_count (I : Fin u → V →ₗᵢ[ℂ] X) + (J : Fin v → W →ₗᵢ[ℂ] X) : allCopyOverlap I J ≤ (u : ℝ) * v := by + unfold allCopyOverlap + have h (i : Fin u) (j : Fin v) : + ‖(I i).toContinuousLinearMap.adjoint.comp (J j).toContinuousLinearMap‖^2 ≤ 1 := by + have hn := ContinuousLinearMap.opNorm_comp_le (I i).toContinuousLinearMap.adjoint + (J j).toContinuousLinearMap + rw [ContinuousLinearMap.adjoint.norm_map] at hn + have hb := mul_le_mul (I i).norm_toContinuousLinearMap_le (J j).norm_toContinuousLinearMap_le + (norm_nonneg _) (by norm_num : (0:ℝ) ≤ 1) + have hz : ‖(I i).toContinuousLinearMap.adjoint.comp (J j).toContinuousLinearMap‖ ≤ 1 := + hn.trans (by simpa using hb) + nlinarith [norm_nonneg ((I i).toContinuousLinearMap.adjoint.comp (J j).toContinuousLinearMap)] + calc + _ ≤ ∑ _i : Fin u, ∑ _j : Fin v, (1 : ℝ) := + Finset.sum_le_sum fun i _ => Finset.sum_le_sum fun j _ => h i j + _ = _ := by simp + +end RowColumn + +end +end + + +section +noncomputable section +open scoped BigOperators Classical +namespace RowColumn +open CubeShuffle.UnitaryFinite +variable {G V E : Type*} [Group G] + [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] [FiniteDimensional ℂ E] + (ρ : Representation ℂ G V) (τ : Representation ℂ G E) + (hρ : IsUnitary ρ) (hτ : IsUnitary τ) + +include hρ hτ +lemma isometric_adjoint_intertwines (f : Representation.IntertwiningMap ρ τ) (g : G) (x : E) : + LinearMap.adjoint f.toLinearMap (τ g x) = ρ g (LinearMap.adjoint f.toLinearMap x) := by + have hf : Intertwines ρ τ f.toLinearMap := by + intro g y + exact Representation.IntertwiningMap.isIntertwining ρ τ f g y + have hh := adjoint_intertwines f.toLinearMap hf hρ hτ g x + simpa only [LinearMap.adjoint_eq_toCLM_adjoint] using hh + +def gramIntertwiner (f : Representation.IntertwiningMap ρ τ) : Representation.IntertwiningMap ρ ρ where + toLinearMap := (LinearMap.adjoint f.toLinearMap).comp f.toLinearMap + isIntertwining' g := by + ext x + change (LinearMap.adjoint f.toLinearMap) (f (ρ g x)) = + ρ g ((LinearMap.adjoint f.toLinearMap) (f x)) + rw [Representation.IntertwiningMap.isIntertwining] + exact isometric_adjoint_intertwines ρ τ hρ hτ f g (f x) + +/-- Every actual nonzero algebraic embedding of irreducible unitary carriers +normalizes to an isometric intertwiner. No normalized embedding is assumed. -/ +theorem isometric_intertwiner_of_injective [Representation.IsIrreducible ρ] + (f : Representation.IntertwiningMap ρ τ) (hf : Function.Injective f) : + ∃ I : V →ₗᵢ[ℂ] E, ∀ g x, I (ρ g x)=τ g (I x) := by + let : Nontrivial V := by + let := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) ρ.asModule + exact ρ.asModuleEquiv.symm.toEquiv.nontrivial + obtain ⟨c,hc⟩ := + (Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed (ρ := ρ)).surjective + (gramIntertwiner ρ τ hρ hτ f) + have hgram : (LinearMap.adjoint f.toLinearMap).comp f.toLinearMap = c • LinearMap.id := by + change (gramIntertwiner ρ τ hρ hτ f).toLinearMap = _ + rw [← hc] + rfl + have hn (x : V) : ‖f x‖^2 = c.re * ‖x‖^2 := by + have hh := congrArg (fun T : V →ₗ[ℂ] V => inner ℂ x (T x)) hgram + simp only [LinearMap.comp_apply, LinearMap.adjoint_inner_right, LinearMap.smul_apply, + LinearMap.id_apply, inner_smul_right, inner_self_eq_norm_sq_to_K] at hh + change ‖f.toLinearMap x‖^2 = c.re * ‖x‖^2 + have he := congrArg Complex.re hh + simpa only [RCLike.ofReal_eq_complex_ofReal, ← Complex.ofReal_pow, Complex.mul_re, + Complex.ofReal_re, Complex.ofReal_im, zero_mul, sub_zero, mul_zero] using he + obtain ⟨x,hx⟩ := exists_ne (0 : V) + have hfx : f x ≠ 0 := by intro h; exact hx (hf (h.trans (map_zero f).symm)) + have hcpos : 0 < c.re := by + have hh := hn x + have hp : 0 < ‖f x‖^2 := sq_pos_of_ne_zero ((norm_ne_zero_iff).mpr hfx) + have hxnon : 0 ≤ ‖x‖^2 := sq_nonneg _ + nlinarith + let a : ℂ := (Real.sqrt c.re)⁻¹ + let F : V →ₗ[ℂ] E := a • f.toLinearMap + have ha : ‖a‖^2 * c.re = 1 := by + simp only [a, norm_inv, Complex.norm_real, Real.norm_eq_abs, + abs_of_nonneg (Real.sqrt_nonneg _)] + rw [inv_pow, Real.sq_sqrt hcpos.le, inv_mul_cancel₀ (ne_of_gt hcpos)] + have hnorm (y : V) : ‖F y‖ = ‖y‖ := by + change ‖a • f y‖=‖y‖ + rw [norm_smul] + have hh : (‖a‖*‖f y‖)^2=‖y‖^2 := by rw [mul_pow, hn, ← mul_assoc, ha, one_mul] + exact (sq_eq_sq₀ (mul_nonneg (norm_nonneg a) (norm_nonneg (f y))) (norm_nonneg y)).mp hh + let I : V →ₗᵢ[ℂ] E := { F with norm_map' := hnorm } + refine ⟨I,?_⟩ + intro g y + change a • f (ρ g y)=τ g (a • f y) + rw [Representation.IntertwiningMap.isIntertwining, map_smul] +end RowColumn + +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/Dephasing.lean b/lean/OAI/RepresentationTheory/RowColumn/Dephasing.lean index cd2a6f51e1210cd49f57323d1c3949903ea7c527..639da87116bc80b60cae6f33dfbc3da54a76c55b 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/Dephasing.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/Dephasing.lean @@ -1,465 +1,465 @@ -import OAI.RepresentationTheory.RowColumn.LineStates -import OAI.LinearAlgebra.MatrixState.Postselection - -namespace OAI - -section - -namespace RowColumn.Signed -open scoped BigOperators Classical -open CubeShuffle.Specht - -variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - {odd : C → Prop} [DecidablePred odd] {k : ℕ} - -omit [Fintype C] [DecidableEq C] in -lemma actWord_swap_fixed (w : Words (S := S) odd k) (x y : S) (he : w.1 x = w.1 y) : - actWord (Equiv.swap x y) w = w := by - apply Subtype.ext - funext z - change w.1 ((Equiv.swap x y)⁻¹ z) = w.1 z - rw [Equiv.swap_inv] - by_cases hx : z = x - · subst z; simp [he] - by_cases hy : z = y - · subst z; simp [he] - · rw [Equiv.swap_apply_of_ne_of_ne hx hy] - -omit [Fintype C] [DecidableEq C] in -lemma oddPerm_swap_sign (w : Words (S := S) odd k) (x y : S) - (hxy : x ≠ y) (he : w.1 x = w.1 y) : - permSign (oddPerm (Equiv.swap x y) w) = if odd (w.1 x) then -1 else 1 := by - have hw := actWord_swap_fixed w x y he - split_ifs with ho - · rw [oddPerm_sign_of_stabilizes _ w hw] - · simp [permSign, Equiv.Perm.sign_swap hxy] - · intro z hz - apply Equiv.swap_apply_of_ne_of_ne - · intro h; subst z; exact hz ho - · intro h; subst z; exact hz (he ▸ ho) - · rw [oddPerm_of_odd_fixed _ w hw] - · simp [permSign] - · intro z hz - apply Equiv.swap_apply_of_ne_of_ne - · intro h; subst z; exact ho hz - · intro h; subst z; exact ho (he.symm ▸ hz) - -omit [Fintype C] in -/-- Repeated opposite-parity pair symbols force a commutant coefficient to -vanish. This is the finite-sign obstruction behind signed postselection. -/ -lemma commuting_coefficient_zero_of_pair_repeat - (T : Representation.IntertwiningMap (representation (S := S) (odd := odd) (k := k)) - (representation (S := S) (odd := odd) (k := k))) - (w v : Words (S := S) odd k) (x y : S) (hxy : x ≠ y) - (hw : w.1 x = w.1 y) (hv : v.1 x = v.1 y) - (hp : ¬ (odd (w.1 x) ↔ odd (v.1 x))) : T (wordVector v) w = 0 := by - let g := Equiv.swap x y - have he := congrArg (fun z : EuclideanSpace ℂ (Words (S := S) odd k) => z (actWord g w)) - (Representation.IntertwiningMap.isIntertwining _ _ T g (wordVector v)) - rw [signedMap_wordVector, map_smul, signedMap_transport_apply] at he - change permSign (oddPerm g v) * T (wordVector (actWord g v)) (actWord g w) = - permSign (oddPerm g w) * T (wordVector v) w at he - dsimp only [g] at he - rw [actWord_swap_fixed w x y hw, actWord_swap_fixed v x y hv, - oddPerm_swap_sign v x y hxy hv, oddPerm_swap_sign w x y hxy hw] at he - by_cases hwo : odd (w.1 x) <;> by_cases hvo : odd (v.1 x) - · exact (hp (iff_of_true hwo hvo)).elim - · simp only [ite_eq_left hwo, ite_eq_right hvo, one_mul, neg_mul, one_mul] at he - linear_combination (1/2 : ℂ) * he - · simp only [ite_eq_right hwo, ite_eq_left hvo, one_mul, neg_mul, one_mul] at he - linear_combination (-1/2 : ℂ) * he - · exact (hp (iff_of_false hwo hvo)).elim - -abbrev ParityMismatch (w v : Words (S := S) odd k) := - {x : S // ¬ (odd (w.1 x) ↔ odd (v.1 x))} - -omit [Fintype C] in -lemma mismatch_pair_injective - (T : Representation.IntertwiningMap (representation (S := S) (odd := odd) (k := k)) - (representation (S := S) (odd := odd) (k := k))) - (w v : Words (S := S) odd k) (hn : T (wordVector v) w ≠ 0) : - Function.Injective (fun x : ParityMismatch w v => (w.1 x.1, v.1 x.1)) := by - intro x y he - apply Subtype.ext - by_contra hxy - exact hn (commuting_coefficient_zero_of_pair_repeat T w v x.1 y.1 hxy - (congrArg Prod.fst he) (congrArg Prod.snd he) x.2) - -/-- Every nonzero coefficient changes parity in at most |C|² slots. For the -actual slot space C=Fin h ⊕ Fin h this is at most 4h², independent of s. -/ -lemma commuting_parity_bandwidth - (T : Representation.IntertwiningMap (representation (S := S) (odd := odd) (k := k)) - (representation (S := S) (odd := odd) (k := k))) - (w v : Words (S := S) odd k) (hn : T (wordVector v) w ≠ 0) : - Fintype.card (ParityMismatch w v) ≤ Fintype.card C ^ 2 := by - simpa only [Fintype.card_prod, pow_two] using - Fintype.card_le_of_injective _ (mismatch_pair_injective T w v hn) -end RowColumn.Signed - -noncomputable section -open scoped BigOperators Classical -namespace RowColumn - -variable {S : Type*} [Fintype S] [DecidableEq S] - -abbrev ShortSubsets (q : ℕ) := {t : Finset S // t.card ≤ q} - -def shortSubsetCode {q : ℕ} (t : ShortSubsets (S := S) q) (i : Fin q) : Option S := - if hi : i.1 < t.1.card then some ((t.1.equivFin).symm ⟨i.1, hi⟩).1 else none - -omit [Fintype S] [DecidableEq S] in -lemma shortSubsetCode_mem {q : ℕ} (t : ShortSubsets (S := S) q) (x : S) : - (∃ i, shortSubsetCode t i = some x) ↔ x ∈ t.1 := by - constructor - · rintro ⟨i, hi⟩ - unfold shortSubsetCode at hi - split_ifs at hi with hj - · have he := Option.some.inj hi - rw [← he] - exact ((t.1.equivFin).symm ⟨i.1, hj⟩).2 - · intro hx - let j := t.1.equivFin ⟨x, hx⟩ - refine ⟨⟨j.1, j.2.trans_le t.2⟩, ?_⟩ - simp only [shortSubsetCode, dite_eq_left j.2] - exact congrArg (fun z : t.1 => some z.1) (t.1.equivFin.symm_apply_apply ⟨x, hx⟩) - -omit [Fintype S] [DecidableEq S] in -lemma shortSubsetCode_injective {q : ℕ} : Function.Injective (shortSubsetCode (S := S) (q := q)) := by - intro t u he - apply Subtype.ext - apply Finset.ext - intro x - rw [← shortSubsetCode_mem t x, ← shortSubsetCode_mem u x, he] - -omit [DecidableEq S] in -lemma card_shortSubsets_le (q : ℕ) : - Fintype.card (ShortSubsets (S := S) q) ≤ (Fintype.card S + 1)^q := by - simpa only [Fintype.card_fun, Fintype.card_option, Fintype.card_fin] using - Fintype.card_le_of_injective _ (shortSubsetCode_injective (S := S) (q := q)) - -def parityDifference (b c : S → Bool) : Finset S := Finset.univ.filter (fun x => b x ≠ c x) - -def parityNear (q : ℕ) (b c : S → Bool) : Prop := (parityDifference b c).card ≤ q - -instance (q : ℕ) : DecidableRel (parityNear (S := S) q) := fun _ _ => inferInstanceAs (Decidable (_ ≤ _)) - -omit [DecidableEq S] in -lemma parityNear_symm (q : ℕ) : Std.Symm (parityNear (S := S) q) := by - constructor - intro b c hc - have he : parityDifference c b = parityDifference b c := by - ext x - simp only [parityDifference, Finset.mem_filter, Finset.mem_univ, true_and, ne_comm] - unfold parityNear at * - rwa [he] - -omit [DecidableEq S] in -lemma parityDifference_injective (b : S → Bool) : Function.Injective (parityDifference b) := by - intro c d he - funext x - have hh : (b x ≠ c x) ↔ (b x ≠ d x) := by - have ht := Finset.ext_iff.mp he x - simpa only [parityDifference, Finset.mem_filter, Finset.mem_univ, true_and] using ht - cases hbx : b x <;> cases hcx : c x <;> cases hdx : d x <;> simp_all - -lemma parityNear_count (q : ℕ) (b : S → Bool) : - (Finset.univ.filter (parityNear q b)).card ≤ (Fintype.card S + 1)^q := by - let f : {c : S → Bool // parityNear q b c} → ShortSubsets (S := S) q := - fun c => ⟨parityDifference b c.1, c.2⟩ - have hf : Function.Injective f := by - intro c d he - apply Subtype.ext - exact parityDifference_injective b (congrArg Subtype.val he) - have hh := (Fintype.card_le_of_injective f hf).trans (card_shortSubsets_le (S := S) q) - simpa only [Fintype.card_subtype] using hh - -end RowColumn -noncomputable section -open scoped BigOperators Classical -namespace RowColumn - -section PositiveBanded -variable {V B : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] - [Fintype B] [DecidableEq B] - -def energy (A : V →ₗ[ℂ] V) (x : V) : ℝ := (inner ℂ x (A x)).re - -lemma positive_cross_bound (A : V →ₗ[ℂ] V) (hA : A.IsPositive) (x y : V) : - 2 * (inner ℂ x (A y)).re ≤ energy A x + energy A y := by - have hp := hA.re_inner_nonneg_right (x-y) - have hs : (inner ℂ y (A x)).re = (inner ℂ x (A y)).re := by - rw [← hA.isSymmetric x y] - exact inner_re_symm (𝕜 := ℂ) _ _ - change 0 ≤ (inner ℂ (x-y) (A (x-y))).re at hp - simp only [map_sub, inner_sub_left, inner_sub_right, Complex.sub_re] at hp - rw [hs] at hp - dsimp only [energy] - linarith - -omit [DecidableEq B] in -/-- A positive block-banded matrix is dominated by its block diagonal times -the maximum number of nonzero block neighbours. This will be applied to -physical parity allocations, where signed symmetry supplies a polynomial bound. -/ -lemma positive_banded_sum (A : V →ₗ[ℂ] V) (hA : A.IsPositive) - (v : B → V) (R : B → B → Prop) [DecidableRel R] - (hRs : Std.Symm R) (D : ℕ) - (hD : ∀ i, (Finset.univ.filter (R i)).card ≤ D) - (hz : ∀ i j, ¬ R i j → inner ℂ (v i) (A (v j)) = 0) : - energy A (∑ i, v i) ≤ (D : ℝ) * ∑ i, energy A (v i) := by - have hn (i : B) : 0 ≤ energy A (v i) := hA.re_inner_nonneg_right _ - have he (i j : B) : 2 * (inner ℂ (v i) (A (v j))).re ≤ - if R i j then energy A (v i) + energy A (v j) else 0 := by - split_ifs with hr - · exact positive_cross_bound A hA _ _ - · rw [hz i j hr]; simp - have hs := Finset.sum_le_sum (fun i (_ : i ∈ Finset.univ) => - Finset.sum_le_sum (fun j (_ : j ∈ Finset.univ) => he i j)) - have hleft : (∑ i, ∑ j, 2 * (inner ℂ (v i) (A (v j))).re) = - 2 * energy A (∑ i, v i) := by - simp only [energy, map_sum, sum_inner, inner_sum, Complex.re_sum, Finset.mul_sum] - exact Finset.sum_comm - rw [hleft] at hs - have htrace : (∑ i, ∑ j, if R i j then energy A (v i) + energy A (v j) else 0) = - 2 * ∑ i, ((Finset.univ.filter (R i)).card : ℝ) * energy A (v i) := by - have hsplit (i j : B) : (if R i j then energy A (v i) + energy A (v j) else 0) = - (if R i j then energy A (v i) else 0) + (if R i j then energy A (v j) else 0) := by - split_ifs <;> simp - simp only [hsplit, Finset.sum_add_distrib] - have hswap : (∑ i, ∑ j, if R i j then energy A (v j) else 0) = - ∑ i, ∑ j, if R i j then energy A (v i) else 0 := by - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro i _ - apply Finset.sum_congr rfl - intro j _ - have hr : R j i ↔ R i j := ⟨fun h => hRs.symm _ _ h, fun h => hRs.symm _ _ h⟩ - simp only [hr] - rw [hswap] - have hcard (i : B) : (∑ j, if R i j then energy A (v i) else 0) = - ((Finset.univ.filter (R i)).card : ℝ) * energy A (v i) := by - rw [← Finset.sum_filter] - simp - simp only [hcard] - ring - rw [htrace] at hs - have hd : (∑ i, ((Finset.univ.filter (R i)).card : ℝ) * energy A (v i)) ≤ - (D : ℝ) * ∑ i, energy A (v i) := by - rw [Finset.mul_sum] - exact Finset.sum_le_sum (fun i _ => mul_le_mul_of_nonneg_right (by exact_mod_cast hD i) (hn i)) - linarith - -end PositiveBanded -end RowColumn -namespace RowColumn.Signed -open scoped BigOperators Classical -open CubeShuffle.Specht - -variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - {odd : C → Prop} [DecidablePred odd] {k : ℕ} - -def parityPattern (w : Words (S := S) odd k) : S → Bool := fun x => decide (odd (w.1 x)) - -def parityMask (b : S → Bool) (v : EuclideanSpace ℂ (Words (S := S) odd k)) : - EuclideanSpace ℂ (Words (S := S) odd k) := - WithLp.toLp 2 (fun w => if parityPattern w = b then v w else 0) - -omit [Fintype C] [DecidableEq C] in -lemma sum_parityMasks (v : EuclideanSpace ℂ (Words (S := S) odd k)) : - (∑ b : S → Bool, parityMask b v) = v := by - ext w - simp [WithLp.ofLp_sum, parityMask] - -lemma inner_wordVector (w : Words (S := S) odd k) - (x : EuclideanSpace ℂ (Words (S := S) odd k)) : inner ℂ (wordVector w) x = x w := by - simp [PiLp.inner_apply, wordVector, RCLike.inner_apply] - -lemma parityNear_of_coefficient_ne_zero - (T : Representation.IntertwiningMap (representation (S := S) (odd := odd) (k := k)) - (representation (S := S) (odd := odd) (k := k))) - (w v : Words (S := S) odd k) (hn : T (wordVector v) w ≠ 0) : - RowColumn.parityNear (Fintype.card C ^ 2) (parityPattern w) (parityPattern v) := by - have he : (RowColumn.parityDifference (parityPattern w) (parityPattern v)).card = - Fintype.card (ParityMismatch w v) := by - unfold RowColumn.parityDifference - rw [Fintype.card_subtype] - congr 2 - funext x - apply propext - simp [parityPattern] - change (RowColumn.parityDifference (parityPattern w) (parityPattern v)).card ≤ _ - rw [he] - exact commuting_parity_bandwidth T w v hn - -lemma parityMask_inner_zero - (T : Representation.IntertwiningMap (representation (S := S) (odd := odd) (k := k)) - (representation (S := S) (odd := odd) (k := k))) - (b c : S → Bool) - (hx : ¬ RowColumn.parityNear (Fintype.card C ^ 2) b c) - (x y : EuclideanSpace ℂ (Words (S := S) odd k)) : - inner ℂ (parityMask b x) (T (parityMask c y)) = 0 := by - rw [← sum_wordVectors (parityMask b x), ← sum_wordVectors (parityMask c y)] - simp only [map_sum, map_smul, sum_inner, inner_sum, inner_smul_left, inner_smul_right, - inner_wordVector] - apply Finset.sum_eq_zero - intro v _ - rw [Finset.mul_sum] - apply Finset.sum_eq_zero - intro w _ - change (parityMask c y) v * - ((starRingEnd ℂ) ((parityMask b x) w) * T (wordVector v) w) = 0 - by_cases hb : parityPattern w = b - · by_cases hc : parityPattern v = c - · have hz : T (wordVector v) w = 0 := by - by_contra hn - exact hx (by simpa only [hb, hc] using parityNear_of_coefficient_ne_zero T w v hn) - simp only [hz, mul_zero] - · simp [parityMask, hc] - · simp [parityMask, hb] - -/-- Exact signed dephasing inequality. No LR or highest-weight estimate: -positivity plus the swap-forced bandwidth yields polynomial cost in the -physical parity allocation, the hard structural step for local domination. -/ -theorem signed_parity_dephasing - (T : Representation.IntertwiningMap (representation (S := S) (odd := odd) (k := k)) - (representation (S := S) (odd := odd) (k := k))) - (hT : T.toLinearMap.IsPositive) - (x : EuclideanSpace ℂ (Words (S := S) odd k)) : - RowColumn.energy T.toLinearMap x ≤ - ((Fintype.card S + 1) ^ (Fintype.card C ^ 2) : ℕ) * - ∑ b : S → Bool, RowColumn.energy T.toLinearMap (parityMask b x) := by - have hh := RowColumn.positive_banded_sum T.toLinearMap hT - (fun b : S → Bool => parityMask b x) (RowColumn.parityNear (Fintype.card C ^ 2)) - (RowColumn.parityNear_symm _) ((Fintype.card S + 1) ^ (Fintype.card C ^ 2)) - (RowColumn.parityNear_count _) (fun b c h => parityMask_inner_zero T b c h x x) - simpa only [sum_parityMasks] using hh -end RowColumn.Signed - -namespace RowColumn.Signed -open scoped BigOperators Classical -open CubeShuffle.Specht -variable {S C L : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - [Fintype L] [DecidableEq L] {odd : C → Prop} [DecidablePred odd] {k : ℕ} - (line : S → L) - -omit [Fintype S] [Fintype L] [DecidableEq L] in -lemma swap_mem_lineGroup (x y : S) (hl : line x=line y) : - Equiv.swap x y ∈ RowColumn.lineGroup line := by - intro z - by_cases hx : z=x - · subst z; simp [hl] - by_cases hy : z=y - · subst z; simp [hl] - · rw [Equiv.swap_apply_of_ne_of_ne hx hy] - -omit [Fintype C] [Fintype L] [DecidableEq L] in -lemma line_coefficient_zero_of_pair_repeat - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) - (w v : Words (S := S) odd k) (x y : S) (hxy : x ≠ y) (hl : line x=line y) - (hw : w.1 x = w.1 y) (hv : v.1 x = v.1 y) - (hp : ¬ (odd (w.1 x) ↔ odd (v.1 x))) : T (wordVector v) w = 0 := by - have he := commuting_coefficient_relation line T - ⟨Equiv.swap x y,swap_mem_lineGroup line x y hl⟩ w v - change permSign (oddPerm (Equiv.swap x y) v) * - T (wordVector (actWord (Equiv.swap x y) v)) (actWord (Equiv.swap x y) w) = - permSign (oddPerm (Equiv.swap x y) w) * T (wordVector v) w at he - rw [actWord_swap_fixed w x y hw, actWord_swap_fixed v x y hv, - oddPerm_swap_sign v x y hxy hv, oddPerm_swap_sign w x y hxy hw] at he - by_cases hwo : odd (w.1 x) <;> by_cases hvo : odd (v.1 x) - · exact (hp (iff_of_true hwo hvo)).elim - · simp only [ite_eq_left hwo, ite_eq_right hvo, one_mul, neg_mul, one_mul] at he - linear_combination (1/2 : ℂ) * he - · simp only [ite_eq_right hwo, ite_eq_left hvo, one_mul, neg_mul, one_mul] at he - linear_combination (-1/2 : ℂ) * he - · exact (hp (iff_of_false hwo hvo)).elim - -omit [Fintype C] [Fintype L] [DecidableEq L] in -lemma line_mismatch_injective - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) - (w v : Words (S := S) odd k) (hn : T (wordVector v) w ≠ 0) : - Function.Injective (fun x : ParityMismatch w v => (line x.1, w.1 x.1, v.1 x.1)) := by - intro x y he - apply Subtype.ext - by_contra hxy - exact hn (line_coefficient_zero_of_pair_repeat line T w v x.1 y.1 hxy - (congrArg Prod.fst he) (congrArg (fun z => z.2.1) he) - (congrArg (fun z => z.2.2) he) x.2) - -omit [DecidableEq L] in -lemma line_parity_bandwidth - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) - (w v : Words (S := S) odd k) (hn : T (wordVector v) w ≠ 0) : - Fintype.card (ParityMismatch w v) ≤ Fintype.card L * Fintype.card C ^ 2 := by - simpa only [Fintype.card_prod, pow_two] using - Fintype.card_le_of_injective _ (line_mismatch_injective line T w v hn) - -omit [DecidableEq L] - -lemma line_parityNear_of_coefficient_ne_zero - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) - (w v : Words (S := S) odd k) (hn : T (wordVector v) w ≠ 0) : - RowColumn.parityNear (Fintype.card L * Fintype.card C ^ 2) (parityPattern w) (parityPattern v) := by - have he : (RowColumn.parityDifference (parityPattern w) (parityPattern v)).card = - Fintype.card (ParityMismatch w v) := by - unfold RowColumn.parityDifference - rw [Fintype.card_subtype] - congr 2 - funext x - apply propext - simp [parityPattern] - change (RowColumn.parityDifference (parityPattern w) (parityPattern v)).card ≤ _ - rw [he] - exact line_parity_bandwidth line T w v hn - -lemma line_parityMask_inner_zero - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) - (b c : S → Bool) - (hx : ¬ RowColumn.parityNear (Fintype.card L * Fintype.card C ^ 2) b c) - (x y : EuclideanSpace ℂ (Words (S := S) odd k)) : - inner ℂ (parityMask b x) (T (parityMask c y)) = 0 := by - rw [← sum_wordVectors (parityMask b x), ← sum_wordVectors (parityMask c y)] - simp only [map_sum, map_smul, sum_inner, inner_sum, inner_smul_left, inner_smul_right, - inner_wordVector] - apply Finset.sum_eq_zero - intro v _ - rw [Finset.mul_sum] - apply Finset.sum_eq_zero - intro w _ - change (parityMask c y) v * - ((starRingEnd ℂ) ((parityMask b x) w) * T (wordVector v) w) = 0 - by_cases hb : parityPattern w = b - · by_cases hc : parityPattern v = c - · have hz : T (wordVector v) w = 0 := by - by_contra hn - exact hx (by simpa only [hb, hc] using line_parityNear_of_coefficient_ne_zero line T w v hn) - simp only [hz, mul_zero] - · simp [parityMask, hc] - · simp [parityMask, hb] - -/-- Exact signed dephasing inequality. No LR or highest-weight estimate: -positivity plus the swap-forced bandwidth yields polynomial cost in the -physical parity allocation, the hard structural step for local domination. -/ -theorem line_signed_parity_dephasing - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) - (hT : T.toLinearMap.IsPositive) - (x : EuclideanSpace ℂ (Words (S := S) odd k)) : - RowColumn.energy T.toLinearMap x ≤ - ((Fintype.card S + 1) ^ (Fintype.card L * Fintype.card C ^ 2) : ℕ) * - ∑ b : S → Bool, RowColumn.energy T.toLinearMap (parityMask b x) := by - have hh := RowColumn.positive_banded_sum T.toLinearMap hT - (fun b : S → Bool => parityMask b x) (RowColumn.parityNear (Fintype.card L * Fintype.card C ^ 2)) - (RowColumn.parityNear_symm _) ((Fintype.card S + 1) ^ (Fintype.card L * Fintype.card C ^ 2)) - (RowColumn.parityNear_count _) (fun b c h => line_parityMask_inner_zero line T b c h x x) - simpa only [sum_parityMasks] using hh -end RowColumn.Signed - -end -end -end - -end OAI +import OAI.RepresentationTheory.RowColumn.LineStates +import OAI.LinearAlgebra.MatrixState.Postselection + +namespace OAI + +section + +namespace RowColumn.Signed +open scoped BigOperators Classical +open CubeShuffle.Specht + +variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + {odd : C → Prop} [DecidablePred odd] {k : ℕ} + +omit [Fintype C] [DecidableEq C] in +lemma actWord_swap_fixed (w : Words (S := S) odd k) (x y : S) (he : w.1 x = w.1 y) : + actWord (Equiv.swap x y) w = w := by + apply Subtype.ext + funext z + change w.1 ((Equiv.swap x y)⁻¹ z) = w.1 z + rw [Equiv.swap_inv] + by_cases hx : z = x + · subst z; simp [he] + by_cases hy : z = y + · subst z; simp [he] + · rw [Equiv.swap_apply_of_ne_of_ne hx hy] + +omit [Fintype C] [DecidableEq C] in +lemma oddPerm_swap_sign (w : Words (S := S) odd k) (x y : S) + (hxy : x ≠ y) (he : w.1 x = w.1 y) : + permSign (oddPerm (Equiv.swap x y) w) = if odd (w.1 x) then -1 else 1 := by + have hw := actWord_swap_fixed w x y he + split_ifs with ho + · rw [oddPerm_sign_of_stabilizes _ w hw] + · simp [permSign, Equiv.Perm.sign_swap hxy] + · intro z hz + apply Equiv.swap_apply_of_ne_of_ne + · intro h; subst z; exact hz ho + · intro h; subst z; exact hz (he ▸ ho) + · rw [oddPerm_of_odd_fixed _ w hw] + · simp [permSign] + · intro z hz + apply Equiv.swap_apply_of_ne_of_ne + · intro h; subst z; exact ho hz + · intro h; subst z; exact ho (he.symm ▸ hz) + +omit [Fintype C] in +/-- Repeated opposite-parity pair symbols force a commutant coefficient to +vanish. This is the finite-sign obstruction behind signed postselection. -/ +lemma commuting_coefficient_zero_of_pair_repeat + (T : Representation.IntertwiningMap (representation (S := S) (odd := odd) (k := k)) + (representation (S := S) (odd := odd) (k := k))) + (w v : Words (S := S) odd k) (x y : S) (hxy : x ≠ y) + (hw : w.1 x = w.1 y) (hv : v.1 x = v.1 y) + (hp : ¬ (odd (w.1 x) ↔ odd (v.1 x))) : T (wordVector v) w = 0 := by + let g := Equiv.swap x y + have he := congrArg (fun z : EuclideanSpace ℂ (Words (S := S) odd k) => z (actWord g w)) + (Representation.IntertwiningMap.isIntertwining _ _ T g (wordVector v)) + rw [signedMap_wordVector, map_smul, signedMap_transport_apply] at he + change permSign (oddPerm g v) * T (wordVector (actWord g v)) (actWord g w) = + permSign (oddPerm g w) * T (wordVector v) w at he + dsimp only [g] at he + rw [actWord_swap_fixed w x y hw, actWord_swap_fixed v x y hv, + oddPerm_swap_sign v x y hxy hv, oddPerm_swap_sign w x y hxy hw] at he + by_cases hwo : odd (w.1 x) <;> by_cases hvo : odd (v.1 x) + · exact (hp (iff_of_true hwo hvo)).elim + · simp only [ite_eq_left hwo, ite_eq_right hvo, one_mul, neg_mul, one_mul] at he + linear_combination (1/2 : ℂ) * he + · simp only [ite_eq_right hwo, ite_eq_left hvo, one_mul, neg_mul, one_mul] at he + linear_combination (-1/2 : ℂ) * he + · exact (hp (iff_of_false hwo hvo)).elim + +abbrev ParityMismatch (w v : Words (S := S) odd k) := + {x : S // ¬ (odd (w.1 x) ↔ odd (v.1 x))} + +omit [Fintype C] in +lemma mismatch_pair_injective + (T : Representation.IntertwiningMap (representation (S := S) (odd := odd) (k := k)) + (representation (S := S) (odd := odd) (k := k))) + (w v : Words (S := S) odd k) (hn : T (wordVector v) w ≠ 0) : + Function.Injective (fun x : ParityMismatch w v => (w.1 x.1, v.1 x.1)) := by + intro x y he + apply Subtype.ext + by_contra hxy + exact hn (commuting_coefficient_zero_of_pair_repeat T w v x.1 y.1 hxy + (congrArg Prod.fst he) (congrArg Prod.snd he) x.2) + +/-- Every nonzero coefficient changes parity in at most |C|² slots. For the +actual slot space C=Fin h ⊕ Fin h this is at most 4h², independent of s. -/ +lemma commuting_parity_bandwidth + (T : Representation.IntertwiningMap (representation (S := S) (odd := odd) (k := k)) + (representation (S := S) (odd := odd) (k := k))) + (w v : Words (S := S) odd k) (hn : T (wordVector v) w ≠ 0) : + Fintype.card (ParityMismatch w v) ≤ Fintype.card C ^ 2 := by + simpa only [Fintype.card_prod, pow_two] using + Fintype.card_le_of_injective _ (mismatch_pair_injective T w v hn) +end RowColumn.Signed + +noncomputable section +open scoped BigOperators Classical +namespace RowColumn + +variable {S : Type*} [Fintype S] [DecidableEq S] + +abbrev ShortSubsets (q : ℕ) := {t : Finset S // t.card ≤ q} + +def shortSubsetCode {q : ℕ} (t : ShortSubsets (S := S) q) (i : Fin q) : Option S := + if hi : i.1 < t.1.card then some ((t.1.equivFin).symm ⟨i.1, hi⟩).1 else none + +omit [Fintype S] [DecidableEq S] in +lemma shortSubsetCode_mem {q : ℕ} (t : ShortSubsets (S := S) q) (x : S) : + (∃ i, shortSubsetCode t i = some x) ↔ x ∈ t.1 := by + constructor + · rintro ⟨i, hi⟩ + unfold shortSubsetCode at hi + split_ifs at hi with hj + · have he := Option.some.inj hi + rw [← he] + exact ((t.1.equivFin).symm ⟨i.1, hj⟩).2 + · intro hx + let j := t.1.equivFin ⟨x, hx⟩ + refine ⟨⟨j.1, j.2.trans_le t.2⟩, ?_⟩ + simp only [shortSubsetCode, dite_eq_left j.2] + exact congrArg (fun z : t.1 => some z.1) (t.1.equivFin.symm_apply_apply ⟨x, hx⟩) + +omit [Fintype S] [DecidableEq S] in +lemma shortSubsetCode_injective {q : ℕ} : Function.Injective (shortSubsetCode (S := S) (q := q)) := by + intro t u he + apply Subtype.ext + apply Finset.ext + intro x + rw [← shortSubsetCode_mem t x, ← shortSubsetCode_mem u x, he] + +omit [DecidableEq S] in +lemma card_shortSubsets_le (q : ℕ) : + Fintype.card (ShortSubsets (S := S) q) ≤ (Fintype.card S + 1)^q := by + simpa only [Fintype.card_fun, Fintype.card_option, Fintype.card_fin] using + Fintype.card_le_of_injective _ (shortSubsetCode_injective (S := S) (q := q)) + +def parityDifference (b c : S → Bool) : Finset S := Finset.univ.filter (fun x => b x ≠ c x) + +def parityNear (q : ℕ) (b c : S → Bool) : Prop := (parityDifference b c).card ≤ q + +instance (q : ℕ) : DecidableRel (parityNear (S := S) q) := fun _ _ => inferInstanceAs (Decidable (_ ≤ _)) + +omit [DecidableEq S] in +lemma parityNear_symm (q : ℕ) : Std.Symm (parityNear (S := S) q) := by + constructor + intro b c hc + have he : parityDifference c b = parityDifference b c := by + ext x + simp only [parityDifference, Finset.mem_filter, Finset.mem_univ, true_and, ne_comm] + unfold parityNear at * + rwa [he] + +omit [DecidableEq S] in +lemma parityDifference_injective (b : S → Bool) : Function.Injective (parityDifference b) := by + intro c d he + funext x + have hh : (b x ≠ c x) ↔ (b x ≠ d x) := by + have ht := Finset.ext_iff.mp he x + simpa only [parityDifference, Finset.mem_filter, Finset.mem_univ, true_and] using ht + cases hbx : b x <;> cases hcx : c x <;> cases hdx : d x <;> simp_all + +lemma parityNear_count (q : ℕ) (b : S → Bool) : + (Finset.univ.filter (parityNear q b)).card ≤ (Fintype.card S + 1)^q := by + let f : {c : S → Bool // parityNear q b c} → ShortSubsets (S := S) q := + fun c => ⟨parityDifference b c.1, c.2⟩ + have hf : Function.Injective f := by + intro c d he + apply Subtype.ext + exact parityDifference_injective b (congrArg Subtype.val he) + have hh := (Fintype.card_le_of_injective f hf).trans (card_shortSubsets_le (S := S) q) + simpa only [Fintype.card_subtype] using hh + +end RowColumn +noncomputable section +open scoped BigOperators Classical +namespace RowColumn + +section PositiveBanded +variable {V B : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] + [Fintype B] [DecidableEq B] + +def energy (A : V →ₗ[ℂ] V) (x : V) : ℝ := (inner ℂ x (A x)).re + +lemma positive_cross_bound (A : V →ₗ[ℂ] V) (hA : A.IsPositive) (x y : V) : + 2 * (inner ℂ x (A y)).re ≤ energy A x + energy A y := by + have hp := hA.re_inner_nonneg_right (x-y) + have hs : (inner ℂ y (A x)).re = (inner ℂ x (A y)).re := by + rw [← hA.isSymmetric x y] + exact inner_re_symm (𝕜 := ℂ) _ _ + change 0 ≤ (inner ℂ (x-y) (A (x-y))).re at hp + simp only [map_sub, inner_sub_left, inner_sub_right, Complex.sub_re] at hp + rw [hs] at hp + dsimp only [energy] + linarith + +omit [DecidableEq B] in +/-- A positive block-banded matrix is dominated by its block diagonal times +the maximum number of nonzero block neighbours. This will be applied to +physical parity allocations, where signed symmetry supplies a polynomial bound. -/ +lemma positive_banded_sum (A : V →ₗ[ℂ] V) (hA : A.IsPositive) + (v : B → V) (R : B → B → Prop) [DecidableRel R] + (hRs : Std.Symm R) (D : ℕ) + (hD : ∀ i, (Finset.univ.filter (R i)).card ≤ D) + (hz : ∀ i j, ¬ R i j → inner ℂ (v i) (A (v j)) = 0) : + energy A (∑ i, v i) ≤ (D : ℝ) * ∑ i, energy A (v i) := by + have hn (i : B) : 0 ≤ energy A (v i) := hA.re_inner_nonneg_right _ + have he (i j : B) : 2 * (inner ℂ (v i) (A (v j))).re ≤ + if R i j then energy A (v i) + energy A (v j) else 0 := by + split_ifs with hr + · exact positive_cross_bound A hA _ _ + · rw [hz i j hr]; simp + have hs := Finset.sum_le_sum (fun i (_ : i ∈ Finset.univ) => + Finset.sum_le_sum (fun j (_ : j ∈ Finset.univ) => he i j)) + have hleft : (∑ i, ∑ j, 2 * (inner ℂ (v i) (A (v j))).re) = + 2 * energy A (∑ i, v i) := by + simp only [energy, map_sum, sum_inner, inner_sum, Complex.re_sum, Finset.mul_sum] + exact Finset.sum_comm + rw [hleft] at hs + have htrace : (∑ i, ∑ j, if R i j then energy A (v i) + energy A (v j) else 0) = + 2 * ∑ i, ((Finset.univ.filter (R i)).card : ℝ) * energy A (v i) := by + have hsplit (i j : B) : (if R i j then energy A (v i) + energy A (v j) else 0) = + (if R i j then energy A (v i) else 0) + (if R i j then energy A (v j) else 0) := by + split_ifs <;> simp + simp only [hsplit, Finset.sum_add_distrib] + have hswap : (∑ i, ∑ j, if R i j then energy A (v j) else 0) = + ∑ i, ∑ j, if R i j then energy A (v i) else 0 := by + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + have hr : R j i ↔ R i j := ⟨fun h => hRs.symm _ _ h, fun h => hRs.symm _ _ h⟩ + simp only [hr] + rw [hswap] + have hcard (i : B) : (∑ j, if R i j then energy A (v i) else 0) = + ((Finset.univ.filter (R i)).card : ℝ) * energy A (v i) := by + rw [← Finset.sum_filter] + simp + simp only [hcard] + ring + rw [htrace] at hs + have hd : (∑ i, ((Finset.univ.filter (R i)).card : ℝ) * energy A (v i)) ≤ + (D : ℝ) * ∑ i, energy A (v i) := by + rw [Finset.mul_sum] + exact Finset.sum_le_sum (fun i _ => mul_le_mul_of_nonneg_right (by exact_mod_cast hD i) (hn i)) + linarith + +end PositiveBanded +end RowColumn +namespace RowColumn.Signed +open scoped BigOperators Classical +open CubeShuffle.Specht + +variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + {odd : C → Prop} [DecidablePred odd] {k : ℕ} + +def parityPattern (w : Words (S := S) odd k) : S → Bool := fun x => decide (odd (w.1 x)) + +def parityMask (b : S → Bool) (v : EuclideanSpace ℂ (Words (S := S) odd k)) : + EuclideanSpace ℂ (Words (S := S) odd k) := + WithLp.toLp 2 (fun w => if parityPattern w = b then v w else 0) + +omit [Fintype C] [DecidableEq C] in +lemma sum_parityMasks (v : EuclideanSpace ℂ (Words (S := S) odd k)) : + (∑ b : S → Bool, parityMask b v) = v := by + ext w + simp [WithLp.ofLp_sum, parityMask] + +lemma inner_wordVector (w : Words (S := S) odd k) + (x : EuclideanSpace ℂ (Words (S := S) odd k)) : inner ℂ (wordVector w) x = x w := by + simp [PiLp.inner_apply, wordVector, RCLike.inner_apply] + +lemma parityNear_of_coefficient_ne_zero + (T : Representation.IntertwiningMap (representation (S := S) (odd := odd) (k := k)) + (representation (S := S) (odd := odd) (k := k))) + (w v : Words (S := S) odd k) (hn : T (wordVector v) w ≠ 0) : + RowColumn.parityNear (Fintype.card C ^ 2) (parityPattern w) (parityPattern v) := by + have he : (RowColumn.parityDifference (parityPattern w) (parityPattern v)).card = + Fintype.card (ParityMismatch w v) := by + unfold RowColumn.parityDifference + rw [Fintype.card_subtype] + congr 2 + funext x + apply propext + simp [parityPattern] + change (RowColumn.parityDifference (parityPattern w) (parityPattern v)).card ≤ _ + rw [he] + exact commuting_parity_bandwidth T w v hn + +lemma parityMask_inner_zero + (T : Representation.IntertwiningMap (representation (S := S) (odd := odd) (k := k)) + (representation (S := S) (odd := odd) (k := k))) + (b c : S → Bool) + (hx : ¬ RowColumn.parityNear (Fintype.card C ^ 2) b c) + (x y : EuclideanSpace ℂ (Words (S := S) odd k)) : + inner ℂ (parityMask b x) (T (parityMask c y)) = 0 := by + rw [← sum_wordVectors (parityMask b x), ← sum_wordVectors (parityMask c y)] + simp only [map_sum, map_smul, sum_inner, inner_sum, inner_smul_left, inner_smul_right, + inner_wordVector] + apply Finset.sum_eq_zero + intro v _ + rw [Finset.mul_sum] + apply Finset.sum_eq_zero + intro w _ + change (parityMask c y) v * + ((starRingEnd ℂ) ((parityMask b x) w) * T (wordVector v) w) = 0 + by_cases hb : parityPattern w = b + · by_cases hc : parityPattern v = c + · have hz : T (wordVector v) w = 0 := by + by_contra hn + exact hx (by simpa only [hb, hc] using parityNear_of_coefficient_ne_zero T w v hn) + simp only [hz, mul_zero] + · simp [parityMask, hc] + · simp [parityMask, hb] + +/-- Exact signed dephasing inequality. No LR or highest-weight estimate: +positivity plus the swap-forced bandwidth yields polynomial cost in the +physical parity allocation, the hard structural step for local domination. -/ +theorem signed_parity_dephasing + (T : Representation.IntertwiningMap (representation (S := S) (odd := odd) (k := k)) + (representation (S := S) (odd := odd) (k := k))) + (hT : T.toLinearMap.IsPositive) + (x : EuclideanSpace ℂ (Words (S := S) odd k)) : + RowColumn.energy T.toLinearMap x ≤ + ((Fintype.card S + 1) ^ (Fintype.card C ^ 2) : ℕ) * + ∑ b : S → Bool, RowColumn.energy T.toLinearMap (parityMask b x) := by + have hh := RowColumn.positive_banded_sum T.toLinearMap hT + (fun b : S → Bool => parityMask b x) (RowColumn.parityNear (Fintype.card C ^ 2)) + (RowColumn.parityNear_symm _) ((Fintype.card S + 1) ^ (Fintype.card C ^ 2)) + (RowColumn.parityNear_count _) (fun b c h => parityMask_inner_zero T b c h x x) + simpa only [sum_parityMasks] using hh +end RowColumn.Signed + +namespace RowColumn.Signed +open scoped BigOperators Classical +open CubeShuffle.Specht +variable {S C L : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + [Fintype L] [DecidableEq L] {odd : C → Prop} [DecidablePred odd] {k : ℕ} + (line : S → L) + +omit [Fintype S] [Fintype L] [DecidableEq L] in +lemma swap_mem_lineGroup (x y : S) (hl : line x=line y) : + Equiv.swap x y ∈ RowColumn.lineGroup line := by + intro z + by_cases hx : z=x + · subst z; simp [hl] + by_cases hy : z=y + · subst z; simp [hl] + · rw [Equiv.swap_apply_of_ne_of_ne hx hy] + +omit [Fintype C] [Fintype L] [DecidableEq L] in +lemma line_coefficient_zero_of_pair_repeat + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) + (w v : Words (S := S) odd k) (x y : S) (hxy : x ≠ y) (hl : line x=line y) + (hw : w.1 x = w.1 y) (hv : v.1 x = v.1 y) + (hp : ¬ (odd (w.1 x) ↔ odd (v.1 x))) : T (wordVector v) w = 0 := by + have he := commuting_coefficient_relation line T + ⟨Equiv.swap x y,swap_mem_lineGroup line x y hl⟩ w v + change permSign (oddPerm (Equiv.swap x y) v) * + T (wordVector (actWord (Equiv.swap x y) v)) (actWord (Equiv.swap x y) w) = + permSign (oddPerm (Equiv.swap x y) w) * T (wordVector v) w at he + rw [actWord_swap_fixed w x y hw, actWord_swap_fixed v x y hv, + oddPerm_swap_sign v x y hxy hv, oddPerm_swap_sign w x y hxy hw] at he + by_cases hwo : odd (w.1 x) <;> by_cases hvo : odd (v.1 x) + · exact (hp (iff_of_true hwo hvo)).elim + · simp only [ite_eq_left hwo, ite_eq_right hvo, one_mul, neg_mul, one_mul] at he + linear_combination (1/2 : ℂ) * he + · simp only [ite_eq_right hwo, ite_eq_left hvo, one_mul, neg_mul, one_mul] at he + linear_combination (-1/2 : ℂ) * he + · exact (hp (iff_of_false hwo hvo)).elim + +omit [Fintype C] [Fintype L] [DecidableEq L] in +lemma line_mismatch_injective + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) + (w v : Words (S := S) odd k) (hn : T (wordVector v) w ≠ 0) : + Function.Injective (fun x : ParityMismatch w v => (line x.1, w.1 x.1, v.1 x.1)) := by + intro x y he + apply Subtype.ext + by_contra hxy + exact hn (line_coefficient_zero_of_pair_repeat line T w v x.1 y.1 hxy + (congrArg Prod.fst he) (congrArg (fun z => z.2.1) he) + (congrArg (fun z => z.2.2) he) x.2) + +omit [DecidableEq L] in +lemma line_parity_bandwidth + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) + (w v : Words (S := S) odd k) (hn : T (wordVector v) w ≠ 0) : + Fintype.card (ParityMismatch w v) ≤ Fintype.card L * Fintype.card C ^ 2 := by + simpa only [Fintype.card_prod, pow_two] using + Fintype.card_le_of_injective _ (line_mismatch_injective line T w v hn) + +omit [DecidableEq L] + +lemma line_parityNear_of_coefficient_ne_zero + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) + (w v : Words (S := S) odd k) (hn : T (wordVector v) w ≠ 0) : + RowColumn.parityNear (Fintype.card L * Fintype.card C ^ 2) (parityPattern w) (parityPattern v) := by + have he : (RowColumn.parityDifference (parityPattern w) (parityPattern v)).card = + Fintype.card (ParityMismatch w v) := by + unfold RowColumn.parityDifference + rw [Fintype.card_subtype] + congr 2 + funext x + apply propext + simp [parityPattern] + change (RowColumn.parityDifference (parityPattern w) (parityPattern v)).card ≤ _ + rw [he] + exact line_parity_bandwidth line T w v hn + +lemma line_parityMask_inner_zero + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) + (b c : S → Bool) + (hx : ¬ RowColumn.parityNear (Fintype.card L * Fintype.card C ^ 2) b c) + (x y : EuclideanSpace ℂ (Words (S := S) odd k)) : + inner ℂ (parityMask b x) (T (parityMask c y)) = 0 := by + rw [← sum_wordVectors (parityMask b x), ← sum_wordVectors (parityMask c y)] + simp only [map_sum, map_smul, sum_inner, inner_sum, inner_smul_left, inner_smul_right, + inner_wordVector] + apply Finset.sum_eq_zero + intro v _ + rw [Finset.mul_sum] + apply Finset.sum_eq_zero + intro w _ + change (parityMask c y) v * + ((starRingEnd ℂ) ((parityMask b x) w) * T (wordVector v) w) = 0 + by_cases hb : parityPattern w = b + · by_cases hc : parityPattern v = c + · have hz : T (wordVector v) w = 0 := by + by_contra hn + exact hx (by simpa only [hb, hc] using line_parityNear_of_coefficient_ne_zero line T w v hn) + simp only [hz, mul_zero] + · simp [parityMask, hc] + · simp [parityMask, hb] + +/-- Exact signed dephasing inequality. No LR or highest-weight estimate: +positivity plus the swap-forced bandwidth yields polynomial cost in the +physical parity allocation, the hard structural step for local domination. -/ +theorem line_signed_parity_dephasing + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) + (hT : T.toLinearMap.IsPositive) + (x : EuclideanSpace ℂ (Words (S := S) odd k)) : + RowColumn.energy T.toLinearMap x ≤ + ((Fintype.card S + 1) ^ (Fintype.card L * Fintype.card C ^ 2) : ℕ) * + ∑ b : S → Bool, RowColumn.energy T.toLinearMap (parityMask b x) := by + have hh := RowColumn.positive_banded_sum T.toLinearMap hT + (fun b : S → Bool => parityMask b x) (RowColumn.parityNear (Fintype.card L * Fintype.card C ^ 2)) + (RowColumn.parityNear_symm _) ((Fintype.card S + 1) ^ (Fintype.card L * Fintype.card C ^ 2)) + (RowColumn.parityNear_count _) (fun b c h => line_parityMask_inner_zero line T b c h x x) + simpa only [sum_parityMasks] using hh +end RowColumn.Signed + +end +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/Entropy.lean b/lean/OAI/RepresentationTheory/RowColumn/Entropy.lean index 3c7d32d05960b85da51c51165eb42f42d6a69751..190ac33557537fa4ee6c18172a3a1466b67ec75a 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/Entropy.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/Entropy.lean @@ -1,190 +1,190 @@ -import Mathlib - -namespace OAI - -section -noncomputable section -open scoped BigOperators Classical -namespace RowColumn - -/-- The elementary Gibbs inequality in the exact finite form used for the -occupied-board product bound. No probability or overlap estimate is assumed. -/ -lemma weighted_log_le {ι : Type*} (s : Finset ι) (p z : ι → ℝ) - (hp : ∀ i ∈ s, 0 ≤ p i) (hz : ∀ i ∈ s, 0 < z i) : - ∑ i ∈ s, p i * Real.log (z i) ≤ ∑ i ∈ s, p i * (z i - 1) := by - exact Finset.sum_le_sum fun i hi => - mul_le_mul_of_nonneg_left (Real.log_le_sub_one_of_pos (hz i hi)) (hp i hi) - -/-- Entropy of a distribution on k symbols is at most log k, including -zero probabilities. This is the marginal-entropy step in both grid proofs. -/ -lemma entropy_le_log_card {ι : Type*} [Fintype ι] (p : ι → ℝ) - (hp : ∀ i, 0 ≤ p i) (hs : ∑ i, p i = 1) : - -∑ i, p i * Real.log (p i) ≤ Real.log (Fintype.card ι) := by - have hk : 0 < Fintype.card ι := by - by_contra h - have he : IsEmpty ι := Fintype.card_eq_zero_iff.mp (by omega) - have := hs - simp at this - have hkR : (0 : ℝ) < Fintype.card ι := by exact_mod_cast hk - have hb : ∀ i, -p i * Real.log (p i) - p i * Real.log (Fintype.card ι) ≤ - 1 / Fintype.card ι - p i := by - intro i - by_cases hpi : p i = 0 - · simp [hpi] - · have hpi' : 0 < p i := lt_of_le_of_ne (hp i) (Ne.symm hpi) - have hl := mul_le_mul_of_nonneg_left - (Real.log_le_sub_one_of_pos (one_div_pos.mpr (mul_pos hkR hpi'))) (hp i) - rw [Real.log_div (by norm_num) (mul_ne_zero (ne_of_gt hkR) hpi), - Real.log_one, Real.log_mul (ne_of_gt hkR) hpi] at hl - have he : p i * (1 / ((Fintype.card ι : ℝ) * p i) - 1) = - 1 / Fintype.card ι - p i := by field_simp - rw [he] at hl - nlinarith - have hsum := Finset.sum_le_sum (fun i (_ : i ∈ (Finset.univ : Finset ι)) => hb i) - simp only [neg_mul, Finset.sum_sub_distrib, ← Finset.sum_mul, Finset.sum_neg_distrib, - hs, one_mul] at hsum - have hc : ∑ _i : ι, 1 / (Fintype.card ι : ℝ) = 1 := by - simp [div_eq_mul_inv, ne_of_gt hkR] - rw [hc] at hsum - linarith - - -/-- Marginal of the uniform distribution on `ι` along an actual line map. -/ -def uniformMarginal {ι α : Type*} [Fintype ι] [DecidableEq α] (f : ι → α) (a : α) : ℝ := - ∑ i, if f i = a then (Fintype.card ι : ℝ)⁻¹ else 0 - -lemma uniformMarginal_nonneg {ι α : Type*} [Fintype ι] [DecidableEq α] - (f : ι → α) (a : α) : 0 ≤ uniformMarginal f a := by - apply Finset.sum_nonneg - intro i _ - split_ifs <;> positivity - -lemma sum_uniformMarginal_mul {ι α : Type*} [Fintype ι] [Fintype α] [DecidableEq α] - (f : ι → α) (g : α → ℝ) : - ∑ a, uniformMarginal f a * g a = (Fintype.card ι : ℝ)⁻¹ * ∑ i, g (f i) := by - simp only [uniformMarginal, Finset.sum_mul] - rw [Finset.sum_comm] - simp_rw [ite_mul, zero_mul] - simp [← Finset.mul_sum] - -lemma sum_uniformMarginal {ι α : Type*} [Fintype ι] [Fintype α] [DecidableEq α] - [Nonempty ι] (f : ι → α) : ∑ a, uniformMarginal f a = 1 := by - simpa using sum_uniformMarginal_mul f (fun _ => 1) - -lemma uniformMarginal_pos {ι α : Type*} [Fintype ι] [DecidableEq α] - [Nonempty ι] (f : ι → α) (i : ι) : 0 < uniformMarginal f (f i) := by - have h := Finset.single_le_sum - (f := fun j => if f j = f i then (Fintype.card ι : ℝ)⁻¹ else 0) - (fun j (_ : j ∈ Finset.univ) => by split_ifs <;> positivity) (Finset.mem_univ i) - simp only [ite_true] at h - exact lt_of_lt_of_le (by positivity) h - - -lemma sum_over_embedding_le {ι α : Type*} [Fintype ι] [Fintype α] - (e : ι ↪ α) (f : α → ℝ) (hf : ∀ a, 0 ≤ f a) : - ∑ i, f (e i) ≤ ∑ a, f a := by - rw [← Finset.sum_image (fun i _ j _ hij => e.injective hij)] - exact Finset.sum_le_sum_of_subset_of_nonneg (Finset.subset_univ _) - (fun a _ _ => hf a) - -/-- The exact exp(number of holes) product loss. The marginals are computed -from the actual occupied embedding, so arbitrary deletion patterns are covered. -This is the entropy/quarter-root normalization step of weighted.tex:143–150 -and coherent.tex:191–205. -/ -theorem occupied_product_of_mean_le {ι α β : Type*} - [Fintype ι] [Fintype α] [Fintype β] - [DecidableEq α] [DecidableEq β] - (e : ι ↪ α × β) (z : α → β → ℝ) (hz : ∀ a b, 0 ≤ z a b) - (hmean : ∑ a, ∑ b, - uniformMarginal (fun i => (e i).1) a * uniformMarginal (fun i => (e i).2) b * z a b ≤ 1) : - ∏ i, z (e i).1 (e i).2 ≤ - Real.exp ((Fintype.card α * Fintype.card β - Fintype.card ι : ℕ) : ℝ) := by - classical - by_cases hempty : IsEmpty ι - · let := hempty - simp only [Fintype.prod_empty] - exact Real.one_le_exp (Nat.cast_nonneg _) - have : Nonempty ι := not_isEmpty_iff.mp hempty - by_cases hz0 : ∃ i, z (e i).1 (e i).2 = 0 - · obtain ⟨i, hi⟩ := hz0 - rw [Finset.prod_eq_zero (Finset.mem_univ i) hi] - exact (Real.exp_pos _).le - have hzpos : ∀ i, 0 < z (e i).1 (e i).2 := by - intro i - exact lt_of_le_of_ne (hz _ _) (Ne.symm (fun h => hz0 ⟨i, h⟩)) - let p := uniformMarginal (fun i => (e i).1) - let q := uniformMarginal (fun i => (e i).2) - let s : ℝ := Fintype.card ι - have hs : 0 < s := by dsimp [s]; positivity - have hp : ∀ i, 0 < p (e i).1 := uniformMarginal_pos _ - have hq : ∀ i, 0 < q (e i).2 := uniformMarginal_pos _ - have hps : ∑ a, p a = 1 := sum_uniformMarginal _ - have hqs : ∑ b, q b = 1 := sum_uniformMarginal _ - have hpe := entropy_le_log_card p (uniformMarginal_nonneg _) hps - have hqe := entropy_le_log_card q (uniformMarginal_nonneg _) hqs - have hmean' : ∑ i, p (e i).1 * q (e i).2 * z (e i).1 (e i).2 ≤ 1 := by - apply (sum_over_embedding_le e (fun x => p x.1 * q x.2 * z x.1 x.2) ?_).trans - · simpa only [Fintype.sum_prod_type] using hmean - · intro x - exact mul_nonneg (mul_nonneg (uniformMarginal_nonneg _ _) (uniformMarginal_nonneg _ _)) (hz _ _) - have hlogs : ∑ i, Real.log (s * p (e i).1 * q (e i).2 * z (e i).1 (e i).2) ≤ 0 := by - calc - _ ≤ ∑ i, (s * (p (e i).1 * q (e i).2 * z (e i).1 (e i).2) - 1) := by - apply Finset.sum_le_sum - intro i _ - have hh := Real.log_le_sub_one_of_pos (mul_pos (mul_pos (mul_pos hs (hp i)) (hq i)) (hzpos i)) - simpa only [mul_assoc] using hh - _ = s * (∑ i, p (e i).1 * q (e i).2 * z (e i).1 (e i).2) - s := by - simp [Finset.sum_sub_distrib, ← Finset.mul_sum, s] - _ ≤ 0 := by nlinarith - have hlogexpand : ∑ i, Real.log (s * p (e i).1 * q (e i).2 * z (e i).1 (e i).2) = - s * Real.log s + (∑ i, Real.log (p (e i).1)) + (∑ i, Real.log (q (e i).2)) + - ∑ i, Real.log (z (e i).1 (e i).2) := by - simp_rw [Real.log_mul (ne_of_gt (mul_pos (mul_pos hs (hp _)) (hq _))) (ne_of_gt (hzpos _)), - Real.log_mul (ne_of_gt (mul_pos hs (hp _))) (ne_of_gt (hq _)), - Real.log_mul (ne_of_gt hs) (ne_of_gt (hp _))] - simp [Finset.sum_add_distrib, s] - rw [hlogexpand] at hlogs - have hplog : ∑ i, Real.log (p (e i).1) = s * ∑ a, p a * Real.log (p a) := by - have h := sum_uniformMarginal_mul (fun i => (e i).1) (fun a => Real.log (p a)) - change _ = s⁻¹ * _ at h - rw [h, ← mul_assoc, mul_inv_cancel₀ (ne_of_gt hs), one_mul] - have hqlog : ∑ i, Real.log (q (e i).2) = s * ∑ b, q b * Real.log (q b) := by - have h := sum_uniformMarginal_mul (fun i => (e i).2) (fun b => Real.log (q b)) - change _ = s⁻¹ * _ at h - rw [h, ← mul_assoc, mul_inv_cancel₀ (ne_of_gt hs), one_mul] - rw [hplog, hqlog] at hlogs - have hlogbound : ∑ i, Real.log (z (e i).1 (e i).2) ≤ - s * (Real.log (Fintype.card α) + Real.log (Fintype.card β) - Real.log s) := by - nlinarith [mul_le_mul_of_nonneg_left hpe hs.le, mul_le_mul_of_nonneg_left hqe hs.le] - have hm : (0 : ℝ) < Fintype.card α := by - have : Nonempty α := ⟨(e (Classical.choice inferInstance)).1⟩ - positivity - have hn : (0 : ℝ) < Fintype.card β := by - have : Nonempty β := ⟨(e (Classical.choice inferInstance)).2⟩ - positivity - have hfrac := Real.log_le_sub_one_of_pos (div_pos (mul_pos hm hn) hs) - rw [Real.log_div (ne_of_gt (mul_pos hm hn)) (ne_of_gt hs), - Real.log_mul (ne_of_gt hm) (ne_of_gt hn)] at hfrac - have hcancel : s * ((Fintype.card α : ℝ) * Fintype.card β / s - 1) = - (Fintype.card α : ℝ) * Fintype.card β - s := by field_simp - have hfinite : Fintype.card ι ≤ Fintype.card α * Fintype.card β := by - simpa using Fintype.card_le_of_injective e e.injective - have hfinal : ∑ i, Real.log (z (e i).1 (e i).2) ≤ - ((Fintype.card α * Fintype.card β - Fintype.card ι : ℕ) : ℝ) := by - rw [Nat.cast_sub hfinite, Nat.cast_mul] - have h := mul_le_mul_of_nonneg_left hfrac hs.le - rw [hcancel] at h - exact hlogbound.trans h - calc - _ = Real.exp (∑ i, Real.log (z (e i).1 (e i).2)) := by - rw [Real.exp_sum] - exact Finset.prod_congr rfl (fun i _ => (Real.exp_log (hzpos i)).symm) - _ ≤ _ := Real.exp_le_exp.mpr hfinal - -end RowColumn - -end -end - -end OAI +import Mathlib + +namespace OAI + +section +noncomputable section +open scoped BigOperators Classical +namespace RowColumn + +/-- The elementary Gibbs inequality in the exact finite form used for the +occupied-board product bound. No probability or overlap estimate is assumed. -/ +lemma weighted_log_le {ι : Type*} (s : Finset ι) (p z : ι → ℝ) + (hp : ∀ i ∈ s, 0 ≤ p i) (hz : ∀ i ∈ s, 0 < z i) : + ∑ i ∈ s, p i * Real.log (z i) ≤ ∑ i ∈ s, p i * (z i - 1) := by + exact Finset.sum_le_sum fun i hi => + mul_le_mul_of_nonneg_left (Real.log_le_sub_one_of_pos (hz i hi)) (hp i hi) + +/-- Entropy of a distribution on k symbols is at most log k, including +zero probabilities. This is the marginal-entropy step in both grid proofs. -/ +lemma entropy_le_log_card {ι : Type*} [Fintype ι] (p : ι → ℝ) + (hp : ∀ i, 0 ≤ p i) (hs : ∑ i, p i = 1) : + -∑ i, p i * Real.log (p i) ≤ Real.log (Fintype.card ι) := by + have hk : 0 < Fintype.card ι := by + by_contra h + have he : IsEmpty ι := Fintype.card_eq_zero_iff.mp (by omega) + have := hs + simp at this + have hkR : (0 : ℝ) < Fintype.card ι := by exact_mod_cast hk + have hb : ∀ i, -p i * Real.log (p i) - p i * Real.log (Fintype.card ι) ≤ + 1 / Fintype.card ι - p i := by + intro i + by_cases hpi : p i = 0 + · simp [hpi] + · have hpi' : 0 < p i := lt_of_le_of_ne (hp i) (Ne.symm hpi) + have hl := mul_le_mul_of_nonneg_left + (Real.log_le_sub_one_of_pos (one_div_pos.mpr (mul_pos hkR hpi'))) (hp i) + rw [Real.log_div (by norm_num) (mul_ne_zero (ne_of_gt hkR) hpi), + Real.log_one, Real.log_mul (ne_of_gt hkR) hpi] at hl + have he : p i * (1 / ((Fintype.card ι : ℝ) * p i) - 1) = + 1 / Fintype.card ι - p i := by field_simp + rw [he] at hl + nlinarith + have hsum := Finset.sum_le_sum (fun i (_ : i ∈ (Finset.univ : Finset ι)) => hb i) + simp only [neg_mul, Finset.sum_sub_distrib, ← Finset.sum_mul, Finset.sum_neg_distrib, + hs, one_mul] at hsum + have hc : ∑ _i : ι, 1 / (Fintype.card ι : ℝ) = 1 := by + simp [div_eq_mul_inv, ne_of_gt hkR] + rw [hc] at hsum + linarith + + +/-- Marginal of the uniform distribution on `ι` along an actual line map. -/ +def uniformMarginal {ι α : Type*} [Fintype ι] [DecidableEq α] (f : ι → α) (a : α) : ℝ := + ∑ i, if f i = a then (Fintype.card ι : ℝ)⁻¹ else 0 + +lemma uniformMarginal_nonneg {ι α : Type*} [Fintype ι] [DecidableEq α] + (f : ι → α) (a : α) : 0 ≤ uniformMarginal f a := by + apply Finset.sum_nonneg + intro i _ + split_ifs <;> positivity + +lemma sum_uniformMarginal_mul {ι α : Type*} [Fintype ι] [Fintype α] [DecidableEq α] + (f : ι → α) (g : α → ℝ) : + ∑ a, uniformMarginal f a * g a = (Fintype.card ι : ℝ)⁻¹ * ∑ i, g (f i) := by + simp only [uniformMarginal, Finset.sum_mul] + rw [Finset.sum_comm] + simp_rw [ite_mul, zero_mul] + simp [← Finset.mul_sum] + +lemma sum_uniformMarginal {ι α : Type*} [Fintype ι] [Fintype α] [DecidableEq α] + [Nonempty ι] (f : ι → α) : ∑ a, uniformMarginal f a = 1 := by + simpa using sum_uniformMarginal_mul f (fun _ => 1) + +lemma uniformMarginal_pos {ι α : Type*} [Fintype ι] [DecidableEq α] + [Nonempty ι] (f : ι → α) (i : ι) : 0 < uniformMarginal f (f i) := by + have h := Finset.single_le_sum + (f := fun j => if f j = f i then (Fintype.card ι : ℝ)⁻¹ else 0) + (fun j (_ : j ∈ Finset.univ) => by split_ifs <;> positivity) (Finset.mem_univ i) + simp only [ite_true] at h + exact lt_of_lt_of_le (by positivity) h + + +lemma sum_over_embedding_le {ι α : Type*} [Fintype ι] [Fintype α] + (e : ι ↪ α) (f : α → ℝ) (hf : ∀ a, 0 ≤ f a) : + ∑ i, f (e i) ≤ ∑ a, f a := by + rw [← Finset.sum_image (fun i _ j _ hij => e.injective hij)] + exact Finset.sum_le_sum_of_subset_of_nonneg (Finset.subset_univ _) + (fun a _ _ => hf a) + +/-- The exact exp(number of holes) product loss. The marginals are computed +from the actual occupied embedding, so arbitrary deletion patterns are covered. +This is the entropy/quarter-root normalization step of weighted.tex:143–150 +and coherent.tex:191–205. -/ +theorem occupied_product_of_mean_le {ι α β : Type*} + [Fintype ι] [Fintype α] [Fintype β] + [DecidableEq α] [DecidableEq β] + (e : ι ↪ α × β) (z : α → β → ℝ) (hz : ∀ a b, 0 ≤ z a b) + (hmean : ∑ a, ∑ b, + uniformMarginal (fun i => (e i).1) a * uniformMarginal (fun i => (e i).2) b * z a b ≤ 1) : + ∏ i, z (e i).1 (e i).2 ≤ + Real.exp ((Fintype.card α * Fintype.card β - Fintype.card ι : ℕ) : ℝ) := by + classical + by_cases hempty : IsEmpty ι + · let := hempty + simp only [Fintype.prod_empty] + exact Real.one_le_exp (Nat.cast_nonneg _) + have : Nonempty ι := not_isEmpty_iff.mp hempty + by_cases hz0 : ∃ i, z (e i).1 (e i).2 = 0 + · obtain ⟨i, hi⟩ := hz0 + rw [Finset.prod_eq_zero (Finset.mem_univ i) hi] + exact (Real.exp_pos _).le + have hzpos : ∀ i, 0 < z (e i).1 (e i).2 := by + intro i + exact lt_of_le_of_ne (hz _ _) (Ne.symm (fun h => hz0 ⟨i, h⟩)) + let p := uniformMarginal (fun i => (e i).1) + let q := uniformMarginal (fun i => (e i).2) + let s : ℝ := Fintype.card ι + have hs : 0 < s := by dsimp [s]; positivity + have hp : ∀ i, 0 < p (e i).1 := uniformMarginal_pos _ + have hq : ∀ i, 0 < q (e i).2 := uniformMarginal_pos _ + have hps : ∑ a, p a = 1 := sum_uniformMarginal _ + have hqs : ∑ b, q b = 1 := sum_uniformMarginal _ + have hpe := entropy_le_log_card p (uniformMarginal_nonneg _) hps + have hqe := entropy_le_log_card q (uniformMarginal_nonneg _) hqs + have hmean' : ∑ i, p (e i).1 * q (e i).2 * z (e i).1 (e i).2 ≤ 1 := by + apply (sum_over_embedding_le e (fun x => p x.1 * q x.2 * z x.1 x.2) ?_).trans + · simpa only [Fintype.sum_prod_type] using hmean + · intro x + exact mul_nonneg (mul_nonneg (uniformMarginal_nonneg _ _) (uniformMarginal_nonneg _ _)) (hz _ _) + have hlogs : ∑ i, Real.log (s * p (e i).1 * q (e i).2 * z (e i).1 (e i).2) ≤ 0 := by + calc + _ ≤ ∑ i, (s * (p (e i).1 * q (e i).2 * z (e i).1 (e i).2) - 1) := by + apply Finset.sum_le_sum + intro i _ + have hh := Real.log_le_sub_one_of_pos (mul_pos (mul_pos (mul_pos hs (hp i)) (hq i)) (hzpos i)) + simpa only [mul_assoc] using hh + _ = s * (∑ i, p (e i).1 * q (e i).2 * z (e i).1 (e i).2) - s := by + simp [Finset.sum_sub_distrib, ← Finset.mul_sum, s] + _ ≤ 0 := by nlinarith + have hlogexpand : ∑ i, Real.log (s * p (e i).1 * q (e i).2 * z (e i).1 (e i).2) = + s * Real.log s + (∑ i, Real.log (p (e i).1)) + (∑ i, Real.log (q (e i).2)) + + ∑ i, Real.log (z (e i).1 (e i).2) := by + simp_rw [Real.log_mul (ne_of_gt (mul_pos (mul_pos hs (hp _)) (hq _))) (ne_of_gt (hzpos _)), + Real.log_mul (ne_of_gt (mul_pos hs (hp _))) (ne_of_gt (hq _)), + Real.log_mul (ne_of_gt hs) (ne_of_gt (hp _))] + simp [Finset.sum_add_distrib, s] + rw [hlogexpand] at hlogs + have hplog : ∑ i, Real.log (p (e i).1) = s * ∑ a, p a * Real.log (p a) := by + have h := sum_uniformMarginal_mul (fun i => (e i).1) (fun a => Real.log (p a)) + change _ = s⁻¹ * _ at h + rw [h, ← mul_assoc, mul_inv_cancel₀ (ne_of_gt hs), one_mul] + have hqlog : ∑ i, Real.log (q (e i).2) = s * ∑ b, q b * Real.log (q b) := by + have h := sum_uniformMarginal_mul (fun i => (e i).2) (fun b => Real.log (q b)) + change _ = s⁻¹ * _ at h + rw [h, ← mul_assoc, mul_inv_cancel₀ (ne_of_gt hs), one_mul] + rw [hplog, hqlog] at hlogs + have hlogbound : ∑ i, Real.log (z (e i).1 (e i).2) ≤ + s * (Real.log (Fintype.card α) + Real.log (Fintype.card β) - Real.log s) := by + nlinarith [mul_le_mul_of_nonneg_left hpe hs.le, mul_le_mul_of_nonneg_left hqe hs.le] + have hm : (0 : ℝ) < Fintype.card α := by + have : Nonempty α := ⟨(e (Classical.choice inferInstance)).1⟩ + positivity + have hn : (0 : ℝ) < Fintype.card β := by + have : Nonempty β := ⟨(e (Classical.choice inferInstance)).2⟩ + positivity + have hfrac := Real.log_le_sub_one_of_pos (div_pos (mul_pos hm hn) hs) + rw [Real.log_div (ne_of_gt (mul_pos hm hn)) (ne_of_gt hs), + Real.log_mul (ne_of_gt hm) (ne_of_gt hn)] at hfrac + have hcancel : s * ((Fintype.card α : ℝ) * Fintype.card β / s - 1) = + (Fintype.card α : ℝ) * Fintype.card β - s := by field_simp + have hfinite : Fintype.card ι ≤ Fintype.card α * Fintype.card β := by + simpa using Fintype.card_le_of_injective e e.injective + have hfinal : ∑ i, Real.log (z (e i).1 (e i).2) ≤ + ((Fintype.card α * Fintype.card β - Fintype.card ι : ℕ) : ℝ) := by + rw [Nat.cast_sub hfinite, Nat.cast_mul] + have h := mul_le_mul_of_nonneg_left hfrac hs.le + rw [hcancel] at h + exact hlogbound.trans h + calc + _ = Real.exp (∑ i, Real.log (z (e i).1 (e i).2)) := by + rw [Real.exp_sum] + exact Finset.prod_congr rfl (fun i _ => (Real.exp_log (hzpos i)).symm) + _ ≤ _ := Real.exp_le_exp.mpr hfinal + +end RowColumn + +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/HookIsometry.lean b/lean/OAI/RepresentationTheory/RowColumn/HookIsometry.lean index 26f5f38364719ccf430314fdb07b0da6f80f8d1f..8f25dae3211c4108d9d179f535bf145a03396636 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/HookIsometry.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/HookIsometry.lean @@ -1,107 +1,107 @@ -import OAI.RepresentationTheory.RowColumn.CopyOverlap -import OAI.RepresentationTheory.RowColumn.Sectors - -namespace OAI - -section - -noncomputable section -open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder -namespace RowColumn -open CubeShuffle.Specht CubeShuffle.UnitaryFinite Signed MatrixState - - theorem exists_hook_isometry (a : YoungDiagram) (h : ℕ) (H : InHook a h) : - ∃ K : hilbertSpace a →ₗᵢ[ℂ] Sector (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H), - ∀ g x, K (unitaryRepresentation a g x) = HookModel.hookRepresentation a h H g (K x) := by - - let := unitaryRepresentation_irreducible a - - let f : Representation.IntertwiningMap (unitaryRepresentation a) (HookModel.hookRepresentation a h H) := - (HookModel.hookEmbedding a h H).comp (unitaryEquiv a).symm.toIntertwiningMap - - have hf : Function.Injective f := by - intro x y hxy - apply (spaceHilbertEquiv a).symm.injective - apply HookModel.hookEmbedding_injective a h H - exact hxy - - have hu : IsUnitary (V := Sector (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H)) (HookModel.hookRepresentation a h H) := - Signed.representation_unitary (S := Cell a) (odd := HookModel.IsOdd (h := h)) (k := HookModel.oddCount a h H) - - have hh := @isometric_intertwiner_of_injective - (Equiv.Perm (Cell a)) (hilbertSpace a) - (Sector (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H)) - inferInstance inferInstance inferInstance inferInstance inferInstance inferInstance inferInstance - (unitaryRepresentation a) (HookModel.hookRepresentation a h H) - (unitaryRepresentation_unitary a) hu (unitaryRepresentation_irreducible a) f hf - - exact hh - -section LineCopy -variable {S L V : Type*} [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] - [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] - {u : ℕ} (a : YoungDiagram) (e : S ≃ Cell a) (h : ℕ) (H : InHook a h) - (K : hilbertSpace a →ₗᵢ[ℂ] Sector (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H)) - (hK : ∀ g x, K (unitaryRepresentation a g x) = HookModel.hookRepresentation a h H g (K x)) - (line : S → L) (ρ : Representation ℂ (lineGroup line) V) (hρ : IsUnitary ρ) - (I : Fin u → V →ₗᵢ[ℂ] hilbertSpace a) - (hI : ∀ i, Intertwines (V := V) (W := hilbertSpace a) ρ ((relabelledUnitary a e).comp (lineGroup line).subtype) (I i).toLinearMap) - -include hK hρ hI in -omit [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] in -lemma hook_copy_projection_intertwines : - Intertwines (Signed.lineRepresentation (odd := HookModel.IsOdd (h := h)) - (k := HookModel.oddCount a h H) (line ∘ e.symm)) - (Signed.lineRepresentation (odd := HookModel.IsOdd (h := h)) - (k := HookModel.oddCount a h H) (line ∘ e.symm)) - (copyProjection (fun i => K.comp (I i))).toLinearMap := by - let τ := hookLineTarget line a e h H - have hKI : ∀ i, Intertwines ρ τ (K.comp (I i)).toLinearMap := by - intro i g x - change K (I i (ρ g x)) = HookModel.hookRepresentation a h H (e.permCongr g.1) (K (I i x)) - have hi : I i (ρ g x)=unitaryRepresentation a (e.permCongr g.1) (I i x) := hI i g x - rw [hi] - exact hK (e.permCongr g.1) _ - have hp := copyProjection_intertwines ρ τ hρ - (fun g => Signed.representation_unitary (e.permCongr g.1)) (fun i => K.comp (I i)) hKI - intro g x - have hh := hp ((lineGroupCongr e line).symm g) x - change copyProjection (fun i => K.comp (I i)) - (Signed.lineRepresentation (odd := HookModel.IsOdd (h := h)) (k := HookModel.oddCount a h H) - (line ∘ e.symm) ((lineGroupCongr e line) ((lineGroupCongr e line).symm g)) x) = - Signed.lineRepresentation (odd := HookModel.IsOdd (h := h)) (k := HookModel.oddCount a h H) - (line ∘ e.symm) ((lineGroupCongr e line) ((lineGroupCongr e line).symm g)) - (copyProjection (fun i => K.comp (I i)) x) at hh - rw [MulEquiv.apply_symm_apply] at hh - exact hh - -end LineCopy - -section Filter -variable {G V E X : Type*} [Group G] - [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] - [NormedAddCommGroup E] [InnerProductSpace ℂ E] [FiniteDimensional ℂ E] - [NormedAddCommGroup X] [InnerProductSpace ℂ X] [FiniteDimensional ℂ X] - -omit [FiniteDimensional ℂ X] in -lemma isotypic_filter_copy_projection (ρ : Representation ℂ G X) (τ : Representation ℂ G E) - (K : X →ₗᵢ[ℂ] E) (hK : ∀ g x, K (ρ g x)=τ g (K x)) - (Q : E →L[ℂ] E) (hQ : ∀ x ∈ Isotypic.carrier ρ τ, Q x=x) - {u : ℕ} (I : Fin u → V →ₗᵢ[ℂ] X) : - Q * copyProjection (fun i => K.comp (I i)) = copyProjection (fun i => K.comp (I i)) := by - let f : Representation.IntertwiningMap ρ τ := - { toLinearMap := K.toLinearMap - isIntertwining' g := by ext x; exact hK g x } - have hk (x : X) : Q (K x)=K x := hQ _ (Isotypic.mem_carrier ρ τ f x) - ext x - simp only [mul_apply_eq_comp, copyProjection, sum_apply, - map_sum, ContinuousLinearMap.comp_apply, LinearIsometry.coe_toContinuousLinearMap, - LinearIsometry.coe_comp, Function.comp_apply, hk] - -end Filter -end RowColumn - -end -end - -end OAI +import OAI.RepresentationTheory.RowColumn.CopyOverlap +import OAI.RepresentationTheory.RowColumn.Sectors + +namespace OAI + +section + +noncomputable section +open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder +namespace RowColumn +open CubeShuffle.Specht CubeShuffle.UnitaryFinite Signed MatrixState + + theorem exists_hook_isometry (a : YoungDiagram) (h : ℕ) (H : InHook a h) : + ∃ K : hilbertSpace a →ₗᵢ[ℂ] Sector (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H), + ∀ g x, K (unitaryRepresentation a g x) = HookModel.hookRepresentation a h H g (K x) := by + + let := unitaryRepresentation_irreducible a + + let f : Representation.IntertwiningMap (unitaryRepresentation a) (HookModel.hookRepresentation a h H) := + (HookModel.hookEmbedding a h H).comp (unitaryEquiv a).symm.toIntertwiningMap + + have hf : Function.Injective f := by + intro x y hxy + apply (spaceHilbertEquiv a).symm.injective + apply HookModel.hookEmbedding_injective a h H + exact hxy + + have hu : IsUnitary (V := Sector (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H)) (HookModel.hookRepresentation a h H) := + Signed.representation_unitary (S := Cell a) (odd := HookModel.IsOdd (h := h)) (k := HookModel.oddCount a h H) + + have hh := @isometric_intertwiner_of_injective + (Equiv.Perm (Cell a)) (hilbertSpace a) + (Sector (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H)) + inferInstance inferInstance inferInstance inferInstance inferInstance inferInstance inferInstance + (unitaryRepresentation a) (HookModel.hookRepresentation a h H) + (unitaryRepresentation_unitary a) hu (unitaryRepresentation_irreducible a) f hf + + exact hh + +section LineCopy +variable {S L V : Type*} [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] + [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] + {u : ℕ} (a : YoungDiagram) (e : S ≃ Cell a) (h : ℕ) (H : InHook a h) + (K : hilbertSpace a →ₗᵢ[ℂ] Sector (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H)) + (hK : ∀ g x, K (unitaryRepresentation a g x) = HookModel.hookRepresentation a h H g (K x)) + (line : S → L) (ρ : Representation ℂ (lineGroup line) V) (hρ : IsUnitary ρ) + (I : Fin u → V →ₗᵢ[ℂ] hilbertSpace a) + (hI : ∀ i, Intertwines (V := V) (W := hilbertSpace a) ρ ((relabelledUnitary a e).comp (lineGroup line).subtype) (I i).toLinearMap) + +include hK hρ hI in +omit [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] in +lemma hook_copy_projection_intertwines : + Intertwines (Signed.lineRepresentation (odd := HookModel.IsOdd (h := h)) + (k := HookModel.oddCount a h H) (line ∘ e.symm)) + (Signed.lineRepresentation (odd := HookModel.IsOdd (h := h)) + (k := HookModel.oddCount a h H) (line ∘ e.symm)) + (copyProjection (fun i => K.comp (I i))).toLinearMap := by + let τ := hookLineTarget line a e h H + have hKI : ∀ i, Intertwines ρ τ (K.comp (I i)).toLinearMap := by + intro i g x + change K (I i (ρ g x)) = HookModel.hookRepresentation a h H (e.permCongr g.1) (K (I i x)) + have hi : I i (ρ g x)=unitaryRepresentation a (e.permCongr g.1) (I i x) := hI i g x + rw [hi] + exact hK (e.permCongr g.1) _ + have hp := copyProjection_intertwines ρ τ hρ + (fun g => Signed.representation_unitary (e.permCongr g.1)) (fun i => K.comp (I i)) hKI + intro g x + have hh := hp ((lineGroupCongr e line).symm g) x + change copyProjection (fun i => K.comp (I i)) + (Signed.lineRepresentation (odd := HookModel.IsOdd (h := h)) (k := HookModel.oddCount a h H) + (line ∘ e.symm) ((lineGroupCongr e line) ((lineGroupCongr e line).symm g)) x) = + Signed.lineRepresentation (odd := HookModel.IsOdd (h := h)) (k := HookModel.oddCount a h H) + (line ∘ e.symm) ((lineGroupCongr e line) ((lineGroupCongr e line).symm g)) + (copyProjection (fun i => K.comp (I i)) x) at hh + rw [MulEquiv.apply_symm_apply] at hh + exact hh + +end LineCopy + +section Filter +variable {G V E X : Type*} [Group G] + [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] [FiniteDimensional ℂ E] + [NormedAddCommGroup X] [InnerProductSpace ℂ X] [FiniteDimensional ℂ X] + +omit [FiniteDimensional ℂ X] in +lemma isotypic_filter_copy_projection (ρ : Representation ℂ G X) (τ : Representation ℂ G E) + (K : X →ₗᵢ[ℂ] E) (hK : ∀ g x, K (ρ g x)=τ g (K x)) + (Q : E →L[ℂ] E) (hQ : ∀ x ∈ Isotypic.carrier ρ τ, Q x=x) + {u : ℕ} (I : Fin u → V →ₗᵢ[ℂ] X) : + Q * copyProjection (fun i => K.comp (I i)) = copyProjection (fun i => K.comp (I i)) := by + let f : Representation.IntertwiningMap ρ τ := + { toLinearMap := K.toLinearMap + isIntertwining' g := by ext x; exact hK g x } + have hk (x : X) : Q (K x)=K x := hQ _ (Isotypic.mem_carrier ρ τ f x) + ext x + simp only [mul_apply_eq_comp, copyProjection, sum_apply, + map_sum, ContinuousLinearMap.comp_apply, LinearIsometry.coe_toContinuousLinearMap, + LinearIsometry.coe_comp, Function.comp_apply, hk] + +end Filter +end RowColumn + +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/HookModel.lean b/lean/OAI/RepresentationTheory/RowColumn/HookModel.lean index b93a9705268dd33cfc06adbadc0e3c74b7046317..59b9f1b3233d724057ebba0329921864f84e1562 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/HookModel.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/HookModel.lean @@ -1,287 +1,287 @@ -import OAI.RepresentationTheory.RowColumn.SignedWords - -namespace OAI - -noncomputable section - -open scoped BigOperators Classical - -namespace RowColumn.HookModel -open scoped BigOperators Classical -open CubeShuffle.Specht RowColumn.Signed - -abbrev Color (h : ℕ) := Fin h ⊕ Fin h - -def IsOdd {h : ℕ} : Color h → Prop - | Sum.inl _ => False - | Sum.inr _ => True - -variable (μ : YoungDiagram) (h : ℕ) (H : RowColumn.InHook μ h) - -def template (x : Cell μ) : Color h := - if hx : row x < h then Sum.inl ⟨row x, hx⟩ - else Sum.inr ⟨col x, (H x.1 x.2).resolve_left hx⟩ - -lemma template_parity (x : Cell μ) : IsOdd (template μ h H x) ↔ h ≤ row x := by - unfold template - split_ifs <;> simp_all [IsOdd] - omega - -lemma template_row {x y : Cell μ} (he : template μ h H x = template μ h H y) - (hx : row x < h) : row x = row y := by - by_cases hy : row y < h - · simp only [template, dite_eq_left hx, dite_eq_left hy] at he - exact congrArg Fin.val (Sum.inl.inj he) - · simp only [template, dite_eq_left hx, dite_eq_right hy] at he - cases he - -lemma template_col {x y : Cell μ} (he : template μ h H x = template μ h H y) - (hx : h ≤ row x) : col x = col y := by - have hn : ¬ row x < h := by omega - by_cases hy : row y < h - · simp only [template, dite_eq_right hn, dite_eq_left hy] at he - cases he - · simp only [template, dite_eq_right hn, dite_eq_right hy] at he - exact congrArg Fin.val (Sum.inr.inj he) - -abbrev oddCount := Fintype.card {x : Cell μ // IsOdd (template μ h H x)} - -def templateWord : Words (S := Cell μ) (IsOdd (h := h)) (oddCount μ h H) := - ⟨template μ h H, rfl⟩ - -lemma row_preserved (r : CubeShuffle.Specht.rowGroup μ) (x : Cell μ) : row (r.1 x) = row x := - congrArg Fin.val (r.2 x) - -/-- The nonzero coefficient of the Young symmetrizer is protected from sign -cancellation: surviving row motions fix bottom cells, and column motions fix -all top cells. -/ -lemma template_rigidity (c : colGroup μ) (r : CubeShuffle.Specht.rowGroup μ) - (hw : actWord (c.1 * r.1) (templateWord μ h H) = templateWord μ h H) : - (∀ x : Cell μ, row x < h → c.1 x = x) ∧ - (∀ x : Cell μ, h ≤ row x → r.1 x = x) := by - have ht (x : Cell μ) : template μ h H (c.1 (r.1 x)) = template μ h H x := - word_stabilizer_eq _ _ hw x - constructor - · intro y hy - let x := r.1⁻¹ y - have hr : r.1 x = y := r.1.apply_symm_apply y - have hx : row x < h := by - have hh := row_preserved μ r x - rw [hr] at hh - omega - apply Subtype.ext - apply Prod.ext - · change row (c.1 y) = row y - have he := template_row μ h H (ht x).symm hx - have hh := row_preserved μ r x - rw [hr] at he hh - exact he.symm.trans hh.symm - · exact c.2 y - · intro x hx - apply Subtype.ext - apply Prod.ext - · exact row_preserved μ r x - · change col (r.1 x) = col x - have he := template_col μ h H (ht x).symm hx - exact (c.2 (r.1 x)).symm.trans he.symm - -lemma template_row_stabilized (r : CubeShuffle.Specht.rowGroup μ) - (hr : ∀ x : Cell μ, h ≤ row x → r.1 x = x) : - actWord r.1 (templateWord μ h H) = templateWord μ h H := by - apply Subtype.ext - funext x - change template μ h H (r.1⁻¹ x) = template μ h H x - have he : row (r.1⁻¹ x) = row x := row_preserved μ r⁻¹ x - by_cases hx : row x < h - · have hy : row (r.1⁻¹ x) < h := by omega - simp only [template, dite_eq_left hx, dite_eq_left hy] - exact congrArg Sum.inl (Fin.ext he) - · have hy : h ≤ row (r.1⁻¹ x) := by omega - have hh := hr (r.1⁻¹ x) hy - simpa using congrArg (template μ h H) hh.symm - -lemma template_young_sign (c : colGroup μ) (r : CubeShuffle.Specht.rowGroup μ) - (hw : actWord (c.1 * r.1) (templateWord μ h H) = templateWord μ h H) : - permSign c.1 * permSign (oddPerm (c.1 * r.1) (templateWord μ h H)) = 1 := by - obtain ⟨hc, hr⟩ := template_rigidity μ h H c r hw - have hrw := template_row_stabilized μ h H r hr - have hcw : actWord c.1 (templateWord μ h H) = templateWord μ h H := by - rwa [actWord_mul, hrw] at hw - have hro : oddPerm r.1 (templateWord μ h H) = 1 := by - apply oddPerm_of_odd_fixed _ _ hrw - intro x hx - exact hr x ((template_parity μ h H x).mp hx) - have hco : permSign (oddPerm c.1 (templateWord μ h H)) = permSign c.1 := by - apply oddPerm_sign_of_stabilizes _ _ hcw - intro x hx - apply hc x - have hh : ¬ h ≤ row x := fun he => hx ((template_parity μ h H x).mpr he) - omega - rw [oddPerm_mul, hrw, hro, mul_one, hco] - exact permSign_sq c.1 - -end RowColumn.HookModel - -namespace RowColumn -open CubeShuffle.Specht - -section YoungMap -variable {V : Type*} [AddCommGroup V] [Module ℂ V] - (μ : YoungDiagram) (ρ : Representation ℂ (Equiv.Perm (Cell μ)) V) (v : V) - -/-- The actual orbit sum giving the map out of the tabloid permutation module. -It is unnormalized, which is harmless for testing nonzero Young symmetrizers. -/ -def tabloidOrbitMap : (Tabloid μ → ℂ) →ₗ[ℂ] V where - toFun f := ∑ g : Equiv.Perm (Cell μ), f (tabloidAct g (baseTabloid μ)) • ρ g v - map_add' := by - intro f h - simp only [Pi.add_apply, add_smul, Finset.sum_add_distrib] - map_smul' := by - intro a f - simp only [Pi.smul_apply, smul_eq_mul, RingHom.id_apply, Finset.smul_sum, smul_smul] - -lemma tabloidOrbitMap_intertwines (g : Equiv.Perm (Cell μ)) (f : Tabloid μ → ℂ) : - tabloidOrbitMap μ ρ v (tabloidRep μ g f) = ρ g (tabloidOrbitMap μ ρ v f) := by - change (∑ h, f (tabloidAct g⁻¹ (tabloidAct h (baseTabloid μ))) • ρ h v) = - ρ g (∑ h, f (tabloidAct h (baseTabloid μ)) • ρ h v) - rw [map_sum] - simp only [map_smul] - apply Fintype.sum_equiv (Equiv.mulLeft g⁻¹) - intro h - simp only [Equiv.coe_mulLeft, tabloidAct_mul, Equiv.Perm.mul_apply, - map_mul, Module.End.mul_apply] - congr 1 - have hh : ρ g (ρ g⁻¹ (ρ h v)) = ρ h v := by - change (ρ g * ρ g⁻¹) (ρ h v) = _ - rw [← map_mul, mul_inv_cancel, map_one] - rfl - exact hh.symm - -lemma tabloidOrbitMap_delta_base : - tabloidOrbitMap μ ρ v (delta (baseTabloid μ)) = symmetrizer (CubeShuffle.Specht.rowGroup μ) ρ v := by - have hmem (g : Equiv.Perm (Cell μ)) : - tabloidAct g (baseTabloid μ) = baseTabloid μ ↔ g ∈ CubeShuffle.Specht.rowGroup μ := by - rw [← tabloid_stabilizer] - rfl - change (∑ g : Equiv.Perm (Cell μ), - (if tabloidAct g (baseTabloid μ) = baseTabloid μ then (1 : ℂ) else 0) • ρ g v) = _ - simp only [hmem, ite_smul, one_smul, zero_smul] - simp only [symmetrizer, LinearMap.sum_apply] - change _ = ∑ g : CubeShuffle.Specht.rowGroup μ, ρ g.1 v - rw [← Finset.sum_filter] - exact Finset.sum_subtype _ (by intro g; simp) (fun g => ρ g v) - -lemma tabloidOrbitMap_polytabloid : - tabloidOrbitMap μ ρ v (polytabloid μ) = - alternator (colGroup μ) ρ (symmetrizer (CubeShuffle.Specht.rowGroup μ) ρ v) := by - rw [polytabloid_formula, map_sum] - simp only [map_smul, alternator, LinearMap.sum_apply, LinearMap.smul_apply] - apply Finset.sum_congr rfl - intro c _ - rw [← tabloidRep_delta, tabloidOrbitMap_intertwines, tabloidOrbitMap_delta_base] - -/-- Restricting the orbit map to the already constructed, proved irreducible -Specht module. -/ -def youngIntertwiner : Representation.IntertwiningMap (CubeShuffle.Specht.representation μ) ρ where - toLinearMap := (tabloidOrbitMap μ ρ v).comp (space μ).subtype - isIntertwining' g := by - ext f - exact tabloidOrbitMap_intertwines μ ρ v g f.1 - -/-- A nonvanishing actual column-alternator/row-symmetrizer vector supplies an -embedding; no Littlewood--Richardson occurrence statement is assumed. -/ -theorem youngIntertwiner_injective - (hn : alternator (colGroup μ) ρ (symmetrizer (CubeShuffle.Specht.rowGroup μ) ρ v) ≠ 0) : - Function.Injective (youngIntertwiner μ ρ v) := by - let := representation_irreducible μ - rcases Representation.IsIrreducible.injective_or_eq_zero (youngIntertwiner μ ρ v) with hi | hz - · exact hi - · exfalso - apply hn - have he := congrArg (fun F : Representation.IntertwiningMap (CubeShuffle.Specht.representation μ) ρ => - F ⟨polytabloid μ, polytabloid_mem_space μ⟩) hz - change tabloidOrbitMap μ ρ v (polytabloid μ) = 0 at he - rwa [tabloidOrbitMap_polytabloid] at he - -end YoungMap -end RowColumn - -namespace RowColumn.HookModel -open scoped BigOperators Classical -open CubeShuffle.Specht RowColumn.Signed - -variable (μ : YoungDiagram) (h : ℕ) (H : RowColumn.InHook μ h) - -abbrev hookRepresentation := - Signed.representation (S := Cell μ) (odd := IsOdd (h := h)) (k := oddCount μ h H) - -def youngVector : EuclideanSpace ℂ (Words (S := Cell μ) (IsOdd (h := h)) (oddCount μ h H)) := - alternator (colGroup μ) (hookRepresentation μ h H) - (symmetrizer (CubeShuffle.Specht.rowGroup μ) (hookRepresentation μ h H) - (wordVector (templateWord μ h H))) - -lemma youngVector_coefficient : youngVector μ h H (templateWord μ h H) = - ∑ c : colGroup μ, ∑ r : CubeShuffle.Specht.rowGroup μ, - if actWord (c.1 * r.1) (templateWord μ h H) = templateWord μ h H then (1 : ℂ) else 0 := by - unfold youngVector - simp only [alternator, symmetrizer, LinearMap.sum_apply, - LinearMap.smul_apply, map_sum, Finset.sum_apply, - WithLp.ofLp_sum, WithLp.ofLp_smul, Finset.sum_apply, Pi.smul_apply, smul_eq_mul] - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro c _ - apply Finset.sum_congr rfl - intro r _ - change permSign c.1 * ((hookRepresentation μ h H c.1 * hookRepresentation μ h H r.1) - (wordVector (templateWord μ h H))) (templateWord μ h H) = _ - rw [← map_mul] - change permSign c.1 * Signed.representation (c.1 * r.1) - (wordVector (templateWord μ h H)) (templateWord μ h H) = _ - rw [wordVector_coefficient] - split_ifs with he - · exact template_young_sign μ h H c r he - · exact mul_zero _ - -lemma youngVector_nonzero : youngVector μ h H ≠ 0 := by - have he : (youngVector μ h H (templateWord μ h H)).re = - ∑ c : colGroup μ, ∑ r : CubeShuffle.Specht.rowGroup μ, - if actWord (c.1 * r.1) (templateWord μ h H) = templateWord μ h H then (1 : ℝ) else 0 := by - rw [youngVector_coefficient] - simp only [Complex.re_sum] - apply Finset.sum_congr rfl - intro c _ - apply Finset.sum_congr rfl - intro r _ - split_ifs <;> rfl - have hp : 0 < ∑ c : colGroup μ, ∑ r : CubeShuffle.Specht.rowGroup μ, - if actWord (c.1 * r.1) (templateWord μ h H) = templateWord μ h H then (1 : ℝ) else 0 := by - apply Finset.sum_pos' - · intro c _ - exact Finset.sum_nonneg (fun r _ => by split_ifs <;> norm_num) - · refine ⟨1, Finset.mem_univ _, ?_⟩ - apply Finset.sum_pos' - · intro r _ - split_ifs <;> norm_num - · refine ⟨1, Finset.mem_univ _, ?_⟩ - simp - intro hz - rw [hz] at he - change 0 = _ at he - linarith - -/-- Explicit signed-slot realization of every (h,h)-hook Specht module. -The target, action, and intertwiner are concrete; no LR/Schur-Weyl occurrence -axiom is used. This supplies the first necessary step of weighted.tex:88–93. -/ -def hookEmbedding : Representation.IntertwiningMap (CubeShuffle.Specht.representation μ) - (hookRepresentation μ h H) := - RowColumn.youngIntertwiner μ (hookRepresentation μ h H) (wordVector (templateWord μ h H)) - -theorem hookEmbedding_injective : Function.Injective (hookEmbedding μ h H) := - RowColumn.youngIntertwiner_injective μ (hookRepresentation μ h H) - (wordVector (templateWord μ h H)) (youngVector_nonzero μ h H) - -end RowColumn.HookModel - -end - -end OAI +import OAI.RepresentationTheory.RowColumn.SignedWords + +namespace OAI + +noncomputable section + +open scoped BigOperators Classical + +namespace RowColumn.HookModel +open scoped BigOperators Classical +open CubeShuffle.Specht RowColumn.Signed + +abbrev Color (h : ℕ) := Fin h ⊕ Fin h + +def IsOdd {h : ℕ} : Color h → Prop + | Sum.inl _ => False + | Sum.inr _ => True + +variable (μ : YoungDiagram) (h : ℕ) (H : RowColumn.InHook μ h) + +def template (x : Cell μ) : Color h := + if hx : row x < h then Sum.inl ⟨row x, hx⟩ + else Sum.inr ⟨col x, (H x.1 x.2).resolve_left hx⟩ + +lemma template_parity (x : Cell μ) : IsOdd (template μ h H x) ↔ h ≤ row x := by + unfold template + split_ifs <;> simp_all [IsOdd] + omega + +lemma template_row {x y : Cell μ} (he : template μ h H x = template μ h H y) + (hx : row x < h) : row x = row y := by + by_cases hy : row y < h + · simp only [template, dite_eq_left hx, dite_eq_left hy] at he + exact congrArg Fin.val (Sum.inl.inj he) + · simp only [template, dite_eq_left hx, dite_eq_right hy] at he + cases he + +lemma template_col {x y : Cell μ} (he : template μ h H x = template μ h H y) + (hx : h ≤ row x) : col x = col y := by + have hn : ¬ row x < h := by omega + by_cases hy : row y < h + · simp only [template, dite_eq_right hn, dite_eq_left hy] at he + cases he + · simp only [template, dite_eq_right hn, dite_eq_right hy] at he + exact congrArg Fin.val (Sum.inr.inj he) + +abbrev oddCount := Fintype.card {x : Cell μ // IsOdd (template μ h H x)} + +def templateWord : Words (S := Cell μ) (IsOdd (h := h)) (oddCount μ h H) := + ⟨template μ h H, rfl⟩ + +lemma row_preserved (r : CubeShuffle.Specht.rowGroup μ) (x : Cell μ) : row (r.1 x) = row x := + congrArg Fin.val (r.2 x) + +/-- The nonzero coefficient of the Young symmetrizer is protected from sign +cancellation: surviving row motions fix bottom cells, and column motions fix +all top cells. -/ +lemma template_rigidity (c : colGroup μ) (r : CubeShuffle.Specht.rowGroup μ) + (hw : actWord (c.1 * r.1) (templateWord μ h H) = templateWord μ h H) : + (∀ x : Cell μ, row x < h → c.1 x = x) ∧ + (∀ x : Cell μ, h ≤ row x → r.1 x = x) := by + have ht (x : Cell μ) : template μ h H (c.1 (r.1 x)) = template μ h H x := + word_stabilizer_eq _ _ hw x + constructor + · intro y hy + let x := r.1⁻¹ y + have hr : r.1 x = y := r.1.apply_symm_apply y + have hx : row x < h := by + have hh := row_preserved μ r x + rw [hr] at hh + omega + apply Subtype.ext + apply Prod.ext + · change row (c.1 y) = row y + have he := template_row μ h H (ht x).symm hx + have hh := row_preserved μ r x + rw [hr] at he hh + exact he.symm.trans hh.symm + · exact c.2 y + · intro x hx + apply Subtype.ext + apply Prod.ext + · exact row_preserved μ r x + · change col (r.1 x) = col x + have he := template_col μ h H (ht x).symm hx + exact (c.2 (r.1 x)).symm.trans he.symm + +lemma template_row_stabilized (r : CubeShuffle.Specht.rowGroup μ) + (hr : ∀ x : Cell μ, h ≤ row x → r.1 x = x) : + actWord r.1 (templateWord μ h H) = templateWord μ h H := by + apply Subtype.ext + funext x + change template μ h H (r.1⁻¹ x) = template μ h H x + have he : row (r.1⁻¹ x) = row x := row_preserved μ r⁻¹ x + by_cases hx : row x < h + · have hy : row (r.1⁻¹ x) < h := by omega + simp only [template, dite_eq_left hx, dite_eq_left hy] + exact congrArg Sum.inl (Fin.ext he) + · have hy : h ≤ row (r.1⁻¹ x) := by omega + have hh := hr (r.1⁻¹ x) hy + simpa using congrArg (template μ h H) hh.symm + +lemma template_young_sign (c : colGroup μ) (r : CubeShuffle.Specht.rowGroup μ) + (hw : actWord (c.1 * r.1) (templateWord μ h H) = templateWord μ h H) : + permSign c.1 * permSign (oddPerm (c.1 * r.1) (templateWord μ h H)) = 1 := by + obtain ⟨hc, hr⟩ := template_rigidity μ h H c r hw + have hrw := template_row_stabilized μ h H r hr + have hcw : actWord c.1 (templateWord μ h H) = templateWord μ h H := by + rwa [actWord_mul, hrw] at hw + have hro : oddPerm r.1 (templateWord μ h H) = 1 := by + apply oddPerm_of_odd_fixed _ _ hrw + intro x hx + exact hr x ((template_parity μ h H x).mp hx) + have hco : permSign (oddPerm c.1 (templateWord μ h H)) = permSign c.1 := by + apply oddPerm_sign_of_stabilizes _ _ hcw + intro x hx + apply hc x + have hh : ¬ h ≤ row x := fun he => hx ((template_parity μ h H x).mpr he) + omega + rw [oddPerm_mul, hrw, hro, mul_one, hco] + exact permSign_sq c.1 + +end RowColumn.HookModel + +namespace RowColumn +open CubeShuffle.Specht + +section YoungMap +variable {V : Type*} [AddCommGroup V] [Module ℂ V] + (μ : YoungDiagram) (ρ : Representation ℂ (Equiv.Perm (Cell μ)) V) (v : V) + +/-- The actual orbit sum giving the map out of the tabloid permutation module. +It is unnormalized, which is harmless for testing nonzero Young symmetrizers. -/ +def tabloidOrbitMap : (Tabloid μ → ℂ) →ₗ[ℂ] V where + toFun f := ∑ g : Equiv.Perm (Cell μ), f (tabloidAct g (baseTabloid μ)) • ρ g v + map_add' := by + intro f h + simp only [Pi.add_apply, add_smul, Finset.sum_add_distrib] + map_smul' := by + intro a f + simp only [Pi.smul_apply, smul_eq_mul, RingHom.id_apply, Finset.smul_sum, smul_smul] + +lemma tabloidOrbitMap_intertwines (g : Equiv.Perm (Cell μ)) (f : Tabloid μ → ℂ) : + tabloidOrbitMap μ ρ v (tabloidRep μ g f) = ρ g (tabloidOrbitMap μ ρ v f) := by + change (∑ h, f (tabloidAct g⁻¹ (tabloidAct h (baseTabloid μ))) • ρ h v) = + ρ g (∑ h, f (tabloidAct h (baseTabloid μ)) • ρ h v) + rw [map_sum] + simp only [map_smul] + apply Fintype.sum_equiv (Equiv.mulLeft g⁻¹) + intro h + simp only [Equiv.coe_mulLeft, tabloidAct_mul, Equiv.Perm.mul_apply, + map_mul, Module.End.mul_apply] + congr 1 + have hh : ρ g (ρ g⁻¹ (ρ h v)) = ρ h v := by + change (ρ g * ρ g⁻¹) (ρ h v) = _ + rw [← map_mul, mul_inv_cancel, map_one] + rfl + exact hh.symm + +lemma tabloidOrbitMap_delta_base : + tabloidOrbitMap μ ρ v (delta (baseTabloid μ)) = symmetrizer (CubeShuffle.Specht.rowGroup μ) ρ v := by + have hmem (g : Equiv.Perm (Cell μ)) : + tabloidAct g (baseTabloid μ) = baseTabloid μ ↔ g ∈ CubeShuffle.Specht.rowGroup μ := by + rw [← tabloid_stabilizer] + rfl + change (∑ g : Equiv.Perm (Cell μ), + (if tabloidAct g (baseTabloid μ) = baseTabloid μ then (1 : ℂ) else 0) • ρ g v) = _ + simp only [hmem, ite_smul, one_smul, zero_smul] + simp only [symmetrizer, LinearMap.sum_apply] + change _ = ∑ g : CubeShuffle.Specht.rowGroup μ, ρ g.1 v + rw [← Finset.sum_filter] + exact Finset.sum_subtype _ (by intro g; simp) (fun g => ρ g v) + +lemma tabloidOrbitMap_polytabloid : + tabloidOrbitMap μ ρ v (polytabloid μ) = + alternator (colGroup μ) ρ (symmetrizer (CubeShuffle.Specht.rowGroup μ) ρ v) := by + rw [polytabloid_formula, map_sum] + simp only [map_smul, alternator, LinearMap.sum_apply, LinearMap.smul_apply] + apply Finset.sum_congr rfl + intro c _ + rw [← tabloidRep_delta, tabloidOrbitMap_intertwines, tabloidOrbitMap_delta_base] + +/-- Restricting the orbit map to the already constructed, proved irreducible +Specht module. -/ +def youngIntertwiner : Representation.IntertwiningMap (CubeShuffle.Specht.representation μ) ρ where + toLinearMap := (tabloidOrbitMap μ ρ v).comp (space μ).subtype + isIntertwining' g := by + ext f + exact tabloidOrbitMap_intertwines μ ρ v g f.1 + +/-- A nonvanishing actual column-alternator/row-symmetrizer vector supplies an +embedding; no Littlewood--Richardson occurrence statement is assumed. -/ +theorem youngIntertwiner_injective + (hn : alternator (colGroup μ) ρ (symmetrizer (CubeShuffle.Specht.rowGroup μ) ρ v) ≠ 0) : + Function.Injective (youngIntertwiner μ ρ v) := by + let := representation_irreducible μ + rcases Representation.IsIrreducible.injective_or_eq_zero (youngIntertwiner μ ρ v) with hi | hz + · exact hi + · exfalso + apply hn + have he := congrArg (fun F : Representation.IntertwiningMap (CubeShuffle.Specht.representation μ) ρ => + F ⟨polytabloid μ, polytabloid_mem_space μ⟩) hz + change tabloidOrbitMap μ ρ v (polytabloid μ) = 0 at he + rwa [tabloidOrbitMap_polytabloid] at he + +end YoungMap +end RowColumn + +namespace RowColumn.HookModel +open scoped BigOperators Classical +open CubeShuffle.Specht RowColumn.Signed + +variable (μ : YoungDiagram) (h : ℕ) (H : RowColumn.InHook μ h) + +abbrev hookRepresentation := + Signed.representation (S := Cell μ) (odd := IsOdd (h := h)) (k := oddCount μ h H) + +def youngVector : EuclideanSpace ℂ (Words (S := Cell μ) (IsOdd (h := h)) (oddCount μ h H)) := + alternator (colGroup μ) (hookRepresentation μ h H) + (symmetrizer (CubeShuffle.Specht.rowGroup μ) (hookRepresentation μ h H) + (wordVector (templateWord μ h H))) + +lemma youngVector_coefficient : youngVector μ h H (templateWord μ h H) = + ∑ c : colGroup μ, ∑ r : CubeShuffle.Specht.rowGroup μ, + if actWord (c.1 * r.1) (templateWord μ h H) = templateWord μ h H then (1 : ℂ) else 0 := by + unfold youngVector + simp only [alternator, symmetrizer, LinearMap.sum_apply, + LinearMap.smul_apply, map_sum, Finset.sum_apply, + WithLp.ofLp_sum, WithLp.ofLp_smul, Finset.sum_apply, Pi.smul_apply, smul_eq_mul] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro c _ + apply Finset.sum_congr rfl + intro r _ + change permSign c.1 * ((hookRepresentation μ h H c.1 * hookRepresentation μ h H r.1) + (wordVector (templateWord μ h H))) (templateWord μ h H) = _ + rw [← map_mul] + change permSign c.1 * Signed.representation (c.1 * r.1) + (wordVector (templateWord μ h H)) (templateWord μ h H) = _ + rw [wordVector_coefficient] + split_ifs with he + · exact template_young_sign μ h H c r he + · exact mul_zero _ + +lemma youngVector_nonzero : youngVector μ h H ≠ 0 := by + have he : (youngVector μ h H (templateWord μ h H)).re = + ∑ c : colGroup μ, ∑ r : CubeShuffle.Specht.rowGroup μ, + if actWord (c.1 * r.1) (templateWord μ h H) = templateWord μ h H then (1 : ℝ) else 0 := by + rw [youngVector_coefficient] + simp only [Complex.re_sum] + apply Finset.sum_congr rfl + intro c _ + apply Finset.sum_congr rfl + intro r _ + split_ifs <;> rfl + have hp : 0 < ∑ c : colGroup μ, ∑ r : CubeShuffle.Specht.rowGroup μ, + if actWord (c.1 * r.1) (templateWord μ h H) = templateWord μ h H then (1 : ℝ) else 0 := by + apply Finset.sum_pos' + · intro c _ + exact Finset.sum_nonneg (fun r _ => by split_ifs <;> norm_num) + · refine ⟨1, Finset.mem_univ _, ?_⟩ + apply Finset.sum_pos' + · intro r _ + split_ifs <;> norm_num + · refine ⟨1, Finset.mem_univ _, ?_⟩ + simp + intro hz + rw [hz] at he + change 0 = _ at he + linarith + +/-- Explicit signed-slot realization of every (h,h)-hook Specht module. +The target, action, and intertwiner are concrete; no LR/Schur-Weyl occurrence +axiom is used. This supplies the first necessary step of weighted.tex:88–93. -/ +def hookEmbedding : Representation.IntertwiningMap (CubeShuffle.Specht.representation μ) + (hookRepresentation μ h H) := + RowColumn.youngIntertwiner μ (hookRepresentation μ h H) (wordVector (templateWord μ h H)) + +theorem hookEmbedding_injective : Function.Injective (hookEmbedding μ h H) := + RowColumn.youngIntertwiner_injective μ (hookRepresentation μ h H) + (wordVector (templateWord μ h H)) (youngVector_nonzero μ h H) + +end RowColumn.HookModel + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/LineStates.lean b/lean/OAI/RepresentationTheory/RowColumn/LineStates.lean index a148e4eb5ee1c28fb6fad04070547760c2a04c34..2b8a257b01eaca8d73a54f3ed46a1da8f5c9d5d7 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/LineStates.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/LineStates.lean @@ -1,384 +1,384 @@ -import OAI.RepresentationTheory.RowColumn.TensorFilter -import OAI.RepresentationTheory.RowColumn.HookIsometry - -namespace OAI - -section -noncomputable section -open scoped BigOperators Classical -namespace RowColumn.Postselection -open WordOrbits -variable {S L A : Type*} [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] - [Fintype A] [DecidableEq A] - -def allocationPerm (line b : S → L) (hb : counts b = counts line) : Equiv.Perm S := - (same_counts_permutation line b hb.symm).choose - -omit [DecidableEq S] [Fintype L] in -lemma allocationPerm_spec (line b : S → L) (hb : counts b = counts line) (i : S) : - b (allocationPerm line b hb i) = line i := - (same_counts_permutation line b hb.symm).choose_spec i - -omit [DecidableEq S] [Fintype A] in -lemma counts_precomp (w : S → A) (p : Equiv.Perm S) : counts (w ∘ p) = counts w := by - funext c - apply Fin.ext - exact Fintype.card_congr - { toFun := fun i => ⟨p i.1,i.2⟩ - invFun := fun i => ⟨p.symm i.1,by simpa using i.2⟩ - left_inv := by intro i; apply Subtype.ext; simp - right_inv := by intro i; apply Subtype.ext; simp } - -def symExtension (line : S → L) (v : (S → A) → ℂ) (w : S → L × A) : ℂ := - if hb : counts (fun i => (w i).1) = counts line then - v (fun i => (w (allocationPerm line _ hb i)).2) else 0 - -omit [Fintype A] [DecidableEq A] in -omit [DecidableEq S] in -lemma symExtension_on_line (line : S → L) (v : (S → A) → ℂ) - (hv : ∀ p : Equiv.Perm S, (∀ i, line (p i) = line i) → ∀ w, v (w ∘ p) = v w) - (w : S → A) : symExtension line v (fun i => (line i,w i)) = v w := by - simp only [symExtension] - exact hv (allocationPerm line line rfl) (allocationPerm_spec line line rfl) w - -omit [Fintype A] [DecidableEq A] in -omit [DecidableEq S] in -lemma symExtension_invariant (line : S → L) (v : (S → A) → ℂ) - (hv : ∀ p : Equiv.Perm S, (∀ i, line (p i) = line i) → ∀ w, v (w ∘ p) = v w) - (p : Equiv.Perm S) (w : S → L × A) : symExtension line v (w ∘ p) = symExtension line v w := by - have hc : counts (fun i => (w (p i)).1) = counts (fun i => (w i).1) := counts_precomp (fun i => (w i).1) p - by_cases hb : counts (fun i => (w i).1) = counts line - · have hb' : counts (fun i => (w (p i)).1) = counts line := hc.trans hb - simp only [symExtension, Function.comp_apply, dite_eq_left hb, dite_eq_left hb'] - let e := allocationPerm line (fun i => (w i).1) hb - let e' := allocationPerm line (fun i => (w (p i)).1) hb' - let q : Equiv.Perm S := e'.trans (p.trans e.symm) - have hq (i : S) : line (q i) = line i := by - rw [← allocationPerm_spec line (fun i => (w i).1) hb (q i)] - change (w (e (e.symm (p (e' i))))).1 = line i - rw [Equiv.apply_symm_apply] - exact allocationPerm_spec line (fun i => (w (p i)).1) hb' i - have hh := hv q hq (fun i => (w (e i)).2) - change v (fun i => (w (p (e' i))).2) = v (fun i => (w (e i)).2) - convert hh using 1 - congr 1 - ext i - simp only [q, Equiv.trans_apply, Function.comp_apply, Equiv.apply_symm_apply] - · have hb' : ¬ counts (fun i => (w (p i)).1) = counts line := fun hh => hb (hc.symm.trans hh) - simp only [symExtension, Function.comp_apply, dite_eq_right hb, dite_eq_right hb'] - -omit [Fintype A] in -omit [DecidableEq S] in -lemma symExtension_counts (line : S → L) (v : (S → A) → ℂ) - (hv : ∀ p : Equiv.Perm S, (∀ i, line (p i) = line i) → ∀ w, v (w ∘ p) = v w) - (w z : S → L × A) (he : counts w = counts z) : symExtension line v w = symExtension line v z := by - obtain ⟨p,hp⟩ := same_counts_permutation w z he - have hh : z ∘ p = w := funext hp - rw [← hh] - exact symExtension_invariant line v hv p z - -abbrev Allocations (line : S → L) := {b : S → L // counts b = counts line} - -def labelWordEquiv : (S → L × A) ≃ (S → L) × (S → A) where - toFun w := (fun i => (w i).1, fun i => (w i).2) - invFun w i := (w.1 i,w.2 i) - left_inv := by intro w; rfl - right_inv := by intro w; rfl - -def precompWordEquiv (p : Equiv.Perm S) : Equiv.Perm (S → A) where - toFun w := w ∘ p - invFun w := w ∘ p.symm - left_inv := by intro w; ext i; simp - right_inv := by intro w; ext i; simp - -omit [DecidableEq A] in -lemma symExtension_norm (line : S → L) (v : (S → A) → ℂ) : - (∑ w : S → L × A, Complex.normSq (symExtension line v w)) = - (Fintype.card (Allocations line) : ℝ) * ∑ w : S → A, Complex.normSq (v w) := by - rw [← (labelWordEquiv (S := S) (L := L) (A := A)).symm.sum_comp, - Fintype.sum_prod_type] - change (∑ b : S → L, ∑ w : S → A, Complex.normSq - (if hb : counts b=counts line then v (w ∘ allocationPerm line b hb) else 0)) = _ - have he (b : S → L) : (∑ w : S → A, Complex.normSq - (if hb : counts b=counts line then v (w ∘ allocationPerm line b hb) else 0)) = - if counts b=counts line then ∑ w : S → A, Complex.normSq (v w) else 0 := by - split_ifs with hb - · exact Equiv.sum_comp (precompWordEquiv (A := A) (allocationPerm line b hb)) (fun w => Complex.normSq (v w)) - · simp - simp_rw [he] - simp [Finset.sum_ite, Fintype.card_subtype, Allocations] - - -def labelTest (line : S → L) (x : (S → A) → ℂ) (w : S → L × A) : ℂ := - if (fun i => (w i).1)=line then x (fun i => (w i).2) else 0 - -omit [DecidableEq A] in -lemma labeled_pair (line : S → L) (x : (S → A) → ℂ) (f : (S → L × A) → ℂ) : - (∑ w, f w * labelTest line x w) = ∑ w : S → A, f (fun i => (line i,w i)) * x w := by - rw [← (labelWordEquiv (S := S) (L := L) (A := A)).symm.sum_comp, - Fintype.sum_prod_type] - change (∑ b : S → L, ∑ w : S → A, f (fun i => (b i,w i)) * - (if b=line then x w else 0)) = _ - simp only [mul_ite, mul_zero, Finset.sum_ite_irrel, Finset.sum_const_zero] - simp - -lemma allocation_probability (line : S → L) (r : L → ℝ) - (hr : ∀ l, 0 ≤ r l) (hs : ∑ l, r l ≤ 1) : - (Fintype.card (Allocations line) : ℝ) * (∏ i, r (line i)) ≤ 1 := by - have he (b : S → L) (hb : counts b=counts line) : - (∏ i, r (b i)) = ∏ i, r (line i) := by - rw [prod_by_counts, prod_by_counts, hb] - have hh : (∑ b : S → L, if counts b=counts line then ∏ i, r (line i) else 0) ≤ - ∑ b : S → L, ∏ i, r (b i) := by - apply Finset.sum_le_sum - intro b _ - split_ifs with hb - · exact le_of_eq (he b hb).symm - · exact Finset.prod_nonneg (fun _ _ => hr _) - have hl : (∑ b : S → L, if counts b=counts line then ∏ i, r (line i) else 0) = - (Fintype.card (Allocations line) : ℝ) * (∏ i, r (line i)) := by - simp [Finset.sum_ite, Fintype.card_subtype, Allocations] - rw [hl, ← Fintype.prod_sum] at hh - exact hh.trans (Finset.prod_le_one₀ (fun _ _ => Finset.sum_nonneg (fun l _ => hr l)) (fun _ _ => hs)) - -def lineMass (z : L × A → ℂ) (l : L) : ℝ := ∑ a, Complex.normSq (z (l,a)) -def normalizedLine (z : L × A → ℂ) (l : L) (a : A) : ℂ := - (Real.sqrt (lineMass z l) : ℂ)⁻¹ * z (l,a) - -omit [Fintype L] [DecidableEq L] [DecidableEq A] in -lemma lineMass_nonneg (z : L × A → ℂ) (l : L) : 0 ≤ lineMass z l := - Finset.sum_nonneg (fun _ _ => Complex.normSq_nonneg _) - -omit [Fintype L] [DecidableEq L] [DecidableEq A] in -lemma lineMass_zero (z : L × A → ℂ) (l : L) (h : lineMass z l=0) (a : A) : z (l,a)=0 := by - apply Complex.normSq_eq_zero.mp - have hh : Complex.normSq (z (l,a)) ≤ lineMass z l := - Finset.single_le_sum (fun b _ => Complex.normSq_nonneg (z (l,b))) (Finset.mem_univ a) - exact le_antisymm (h ▸ hh) (Complex.normSq_nonneg _) - -omit [Fintype L] [DecidableEq L] [DecidableEq A] in -lemma line_reconstruction (z : L × A → ℂ) (l : L) (a : A) : - z (l,a) = (Real.sqrt (lineMass z l) : ℂ) * normalizedLine z l a := by - by_cases hz : lineMass z l=0 - · simp [normalizedLine, hz, lineMass_zero z l hz a] - · have h : (Real.sqrt (lineMass z l) : ℂ) ≠ 0 := by - exact_mod_cast (Real.sqrt_ne_zero'.mpr (lt_of_le_of_ne (lineMass_nonneg z l) (Ne.symm hz))) - simp [normalizedLine, h] - -omit [Fintype L] [DecidableEq L] [DecidableEq A] in -lemma normalizedLine_norm (z : L × A → ℂ) (l : L) : - (∑ a, Complex.normSq (normalizedLine z l a)) ≤ 1 := by - by_cases hz : lineMass z l=0 - · simp [normalizedLine, hz] - · have hp : 0 < lineMass z l := lt_of_le_of_ne (lineMass_nonneg z l) (Ne.symm hz) - simp_rw [normalizedLine, map_mul, map_inv₀, Complex.normSq_ofReal, Real.mul_self_sqrt (le_of_lt hp)] - rw [← Finset.mul_sum] - change (lineMass z l)⁻¹ * lineMass z l ≤ 1 - rw [inv_mul_cancel₀ hz] - -omit [Fintype L] [DecidableEq L] [DecidableEq A] in -lemma labeled_tensor_pair (line : S → L) (z : L × A → ℂ) (x : (S → A) → ℂ) : - Complex.normSq (∑ w : S → A, tensorVector z (fun i => (line i,w i)) * x w) = - (∏ i, lineMass z (line i)) * - Complex.normSq (∑ w : S → A, (∏ i, normalizedLine z (line i) (w i)) * x w) := by - have he (w : S → A) : tensorVector z (fun i => (line i,w i)) = - (∏ i, (Real.sqrt (lineMass z (line i)) : ℂ)) * ∏ i, normalizedLine z (line i) (w i) := by - rw [← Finset.prod_mul_distrib] - exact Finset.prod_congr rfl (fun i _ => line_reconstruction z (line i) (w i)) - simp_rw [he, mul_assoc] - rw [← Finset.mul_sum, map_mul] - congr 1 - rw [map_prod] - apply Finset.prod_congr rfl - intro i _ - exact (Complex.normSq_ofReal _).trans (Real.mul_self_sqrt (lineMass_nonneg z (line i))) - - -omit [DecidableEq S] [Fintype A] [DecidableEq A] in -lemma symExtension_supported (line : S → L) (v : (S → A) → ℂ) - (good : A → Prop) [DecidablePred good] - (hv : ∀ w, ¬ (∀ i, good (w i)) → v w=0) - (w : S → L × A) (hw : ¬ ∀ i, good (w i).2) : symExtension line v w=0 := by - unfold symExtension - split_ifs with hb - · apply hv - intro h - apply hw - intro i - simpa using h ((allocationPerm line _ hb).symm i) - · rfl - -def lineAmplitude (line : S → L) (a₀ : S → A) (good : A → Prop) [DecidablePred good] - (q : Types (S := S) (A := L × A)) (θ : Phases (L × A) (Fintype.card S)) (l : L) (a : A) : ℂ := - normalizedLine (truncateAmplitude (fun c : L × A => good c.2) - (twistedAmplitude (typeRepresentative (fun i => (line i,a₀ i)) q) θ)) l a - -omit [DecidableEq S] in -omit [Fintype L] in -lemma lineAmplitude_norm (line : S → L) (a₀ : S → A) (good : A → Prop) [DecidablePred good] - (q : Types (S := S) (A := L × A)) (θ : Phases (L × A) (Fintype.card S)) (l : L) : - (∑ a, Complex.normSq (lineAmplitude line a₀ good q θ l a)) ≤ 1 := - normalizedLine_norm _ _ - -omit [DecidableEq S] [Fintype L] in -lemma lineAmplitude_support (line : S → L) (a₀ : S → A) (good : A → Prop) [DecidablePred good] - (q : Types (S := S) (A := L × A)) (θ : Phases (L × A) (Fintype.card S)) (l : L) (a : A) - (ha : ¬ good a) : lineAmplitude line a₀ good q θ l a=0 := by - simp [lineAmplitude, normalizedLine, truncateAmplitude, ha] - -/-- Independent fibre postselection, with the allocation factorial cancelled -by the exact multinomial probability rather than included in the overhead. -/ -theorem line_symmetric_postselection (line : S → L) (a₀ : S → A) (hn : 0 < Fintype.card S) - (good : A → Prop) [DecidablePred good] (v x : (S → A) → ℂ) - (hv : ∀ p : Equiv.Perm S, (∀ i, line (p i)=line i) → ∀ w, v (w ∘ p)=v w) - (hsupp : ∀ w, ¬ (∀ i, good (w i)) → v w=0) : - Complex.normSq (∑ w, v w*x w) ≤ - (∑ w, Complex.normSq (v w)) * - (((Fintype.card S+1)^(Fintype.card (L × A)) : ℕ) / - (Fintype.card (Phases (L × A) (Fintype.card S)) : ℝ) * - ∑ q : Types (S := S) (A := L × A), ∑ θ : Phases (L × A) (Fintype.card S), - Complex.normSq (∑ w : S → A, (∏ i, lineAmplitude line a₀ good q θ (line i) (w i)) * x w)) := by - let z (q : Types (S := S) (A := L × A)) (θ : Phases (L × A) (Fintype.card S)) := - truncateAmplitude (fun c : L × A => good c.2) - (twistedAmplitude (typeRepresentative (fun i => (line i,a₀ i)) q) θ) - let R (q : Types (S := S) (A := L × A)) (θ : Phases (L × A) (Fintype.card S)) := - Complex.normSq (∑ w : S → A, (∏ i, normalizedLine (z q θ) (line i) (w i)) * x w) - have hz (q : Types (S := S) (A := L × A)) (θ : Phases (L × A) (Fintype.card S)) : - (Fintype.card (Allocations line) : ℝ) * (∏ i, lineMass (z q θ) (line i)) ≤ 1 := by - apply allocation_probability line _ (lineMass_nonneg _) - rw [show (∑ l, lineMass (z q θ) l) = ∑ c : L × A, Complex.normSq (z q θ c) from - (Fintype.sum_prod_type (fun c : L × A => Complex.normSq (z q θ c))).symm] - exact truncated_twisted_subnormalized _ _ hn _ - have hh := supported_symmetric_postselection (fun i => (line i,a₀ i)) hn - (fun c : L × A => good c.2) (symExtension line v) (labelTest line x) - (symExtension_counts line v hv) (symExtension_supported line v good hsupp) - rw [labeled_pair] at hh - simp_rw [symExtension_on_line line v hv] at hh - rw [symExtension_norm] at hh - simp_rw [labeled_pair, labeled_tensor_pair] at hh - let c : ℝ := ((Fintype.card S+1)^(Fintype.card (L × A)) : ℕ) / - (Fintype.card (Phases (L × A) (Fintype.card S)) : ℝ) - change _ ≤ ((Fintype.card (Allocations line) : ℝ) * ∑ w, Complex.normSq (v w)) * - (c * ∑ q, ∑ θ, (∏ i, lineMass (z q θ) (line i)) * R q θ) at hh - change _ ≤ (∑ w, Complex.normSq (v w)) * (c * ∑ q, ∑ θ, R q θ) - apply hh.trans - rw [show ((Fintype.card (Allocations line) : ℝ) * ∑ w, Complex.normSq (v w)) * - (c * ∑ q, ∑ θ, (∏ i, lineMass (z q θ) (line i)) * R q θ) = - (∑ w, Complex.normSq (v w)) * (c * ((Fintype.card (Allocations line) : ℝ) * - ∑ q, ∑ θ, (∏ i, lineMass (z q θ) (line i)) * R q θ)) by ring] - apply mul_le_mul_of_nonneg_left _ (Finset.sum_nonneg (fun _ _ => Complex.normSq_nonneg _)) - apply mul_le_mul_of_nonneg_left _ (by positivity : 0 ≤ c) - simp_rw [Finset.mul_sum, ← mul_assoc] - exact Finset.sum_le_sum (fun q _ => Finset.sum_le_sum (fun θ _ => - (mul_le_mul_of_nonneg_right (hz q θ) (Complex.normSq_nonneg _)).trans_eq (one_mul _))) - -end RowColumn.Postselection - -end -end - - -section -noncomputable section -open scoped BigOperators Classical Matrix.Norms.L2Operator ComplexOrder MatrixOrder -namespace RowColumn.Postselection -open MatrixState WordOrbits -variable {S L C : Type*} [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] - [Fintype C] [DecidableEq C] - -def lineState (line : S → L) (a₀ : S → C × C) (odd : C → Prop) [DecidablePred odd] - (q : Types (S := S) (A := L × (C × C))) (θ : Phases (L × (C × C)) (Fintype.card S)) - (l : L) : Matrix C C ℂ := - gramState (lineAmplitude line a₀ (fun p : C × C => odd p.1 ↔ odd p.2) q θ l) - -omit [DecidableEq S] [Fintype L] in -lemma lineState_positive (line : S → L) (a₀ : S → C × C) (odd : C → Prop) [DecidablePred odd] - (q : Types (S := S) (A := L × (C × C))) (θ : Phases (L × (C × C)) (Fintype.card S)) (l : L) : - (lineState line a₀ odd q θ l).PosSemidef := gramState_posSemidef _ - -omit [DecidableEq S] in -omit [Fintype L] in -lemma lineState_trace (line : S → L) (a₀ : S → C × C) (odd : C → Prop) [DecidablePred odd] - (q : Types (S := S) (A := L × (C × C))) (θ : Phases (L × (C × C)) (Fintype.card S)) (l : L) : - (lineState line a₀ odd q θ l).trace.re ≤ 1 := by - rw [lineState, gramState_trace] - exact lineAmplitude_norm _ _ _ _ _ _ - -omit [DecidableEq S] [Fintype L] in -lemma lineState_even (line : S → L) (a₀ : S → C × C) (odd : C → Prop) [DecidablePred odd] - (q : Types (S := S) (A := L × (C × C))) (θ : Phases (L × (C × C)) (Fintype.card S)) - (l : L) (c d : C) (h : ¬ (odd c ↔ odd d)) : lineState line a₀ odd q θ l c d=0 := by - apply gramState_parity_supported odd _ _ c d h - exact fun c d h => lineAmplitude_support _ _ _ _ _ _ _ h - -lemma variable_purification_pair (z : S → C × C → ℂ) (x : (S → C) → ℂ) (v : S → C) : - (∑ a : S → C × C, (∏ i, z i (a i)) * purificationTest x v a) = - ∑ w : S → C, tensorMatrix (fun i => letterMatrix (z i)) w v * x w := by - exact purification_pair (tensorMatrix (fun i => letterMatrix (z i))) x v - -lemma variable_purification_quadratic (z : S → C × C → ℂ) (x : (S → C) → ℂ) : - (∑ v : S → C, Complex.normSq (∑ a : S → C × C, - (∏ i, z i (a i)) * purificationTest x v a)) = - quadratic (tensorMatrix (fun i => gramState (z i))) x := by - simp_rw [variable_purification_pair] - change factorQuadratic (tensorMatrix (fun i => letterMatrix (z i))) x = _ - rw [factorQuadratic_eq, tensorMatrix_star, tensorMatrix_mul] - rfl - -/-- Explicit local domination for independent row/column permutation fibres. -All mixture terms are genuine even positive identical-slot substates within -each fibre, irrespective of its size and the deletion layout. -/ -theorem positive_line_postselection (line : S → L) (a₀ : S → C × C) (hn : 0 < Fintype.card S) - (odd : C → Prop) [DecidablePred odd] (A : Matrix (S → C) (S → C) ℂ) - (hA : A.PosSemidef) - (hinv : ∀ (p : Equiv.Perm S), (∀ i, line (p i)=line i) → ∀ (w v : S → C), - A (w ∘ p) (v ∘ p)=A w v) - (hsupp : ∀ w v, ¬ (∀ i, odd (w i) ↔ odd (v i)) → A w v=0) - (x : (S → C) → ℂ) : - quadratic A x ≤ A.trace.re * - (((Fintype.card S+1)^(Fintype.card (L × (C × C))) : ℕ) / - (Fintype.card (Phases (L × (C × C)) (Fintype.card S)) : ℝ) * - ∑ q : Types (S := S) (A := L × (C × C)), - ∑ θ : Phases (L × (C × C)) (Fintype.card S), - quadratic (tensorMatrix (fun i : S => lineState line a₀ odd q θ (line i))) x) := by - let B : Matrix (S → C) (S → C) ℂ := CFC.sqrt A - have hi (p : Equiv.Perm S) (hp : ∀ i, line (p i)=line i) (w v : S → C) : - B (w ∘ p) (v ∘ p)=B w v := - sqrt_permutation_invariant A hA (reindexWord p) (hinv p hp) w v - have hz (w v : S → C) (hh : ¬ ∀ i, odd (w i) ↔ odd (v i)) : B w v=0 := by - apply sqrt_block_supported (fun u : S → C => fun i => odd (u i)) A hA - (fun u v he => hsupp u v (fun ht => he (funext fun i => propext (ht i)))) w v - intro he - exact hh (fun i => Iff.of_eq (congrFun he i)) - have hv (p : Equiv.Perm S) (hp : ∀ i, line (p i)=line i) (w : S → C × C) : - purificationVector B (w ∘ p)=purificationVector B w := - hi p hp (fun i => (w i).1) (fun i => (w i).2) - have hs (w : S → C × C) (hw : ¬ ∀ i, odd (w i).1 ↔ odd (w i).2) : purificationVector B w=0 := - hz _ _ hw - have hh (v : S → C) := line_symmetric_postselection line a₀ hn - (fun p : C × C => odd p.1 ↔ odd p.2) (purificationVector B) (purificationTest x v) hv hs - simp only [purification_pair B x, purification_normSq B] at hh - have hsum := Finset.sum_le_sum (fun v (_ : v ∈ Finset.univ) => hh v) - change factorQuadratic B x ≤ _ at hsum - have ht : purifierTrace B=A.trace.re := sqrt_trace A hA - rw [ht] at hsum - change factorQuadratic (CFC.sqrt A) x ≤ _ at hsum - rw [sqrt_factorQuadratic A hA] at hsum - apply hsum.trans_eq - simp only [Finset.mul_sum] - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro q _ - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro θ _ - rw [← Finset.mul_sum, ← Finset.mul_sum] - congr 2 - exact variable_purification_quadratic _ x - -end RowColumn.Postselection - -end -end - -end OAI +import OAI.RepresentationTheory.RowColumn.TensorFilter +import OAI.RepresentationTheory.RowColumn.HookIsometry + +namespace OAI + +section +noncomputable section +open scoped BigOperators Classical +namespace RowColumn.Postselection +open WordOrbits +variable {S L A : Type*} [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] + [Fintype A] [DecidableEq A] + +def allocationPerm (line b : S → L) (hb : counts b = counts line) : Equiv.Perm S := + (same_counts_permutation line b hb.symm).choose + +omit [DecidableEq S] [Fintype L] in +lemma allocationPerm_spec (line b : S → L) (hb : counts b = counts line) (i : S) : + b (allocationPerm line b hb i) = line i := + (same_counts_permutation line b hb.symm).choose_spec i + +omit [DecidableEq S] [Fintype A] in +lemma counts_precomp (w : S → A) (p : Equiv.Perm S) : counts (w ∘ p) = counts w := by + funext c + apply Fin.ext + exact Fintype.card_congr + { toFun := fun i => ⟨p i.1,i.2⟩ + invFun := fun i => ⟨p.symm i.1,by simpa using i.2⟩ + left_inv := by intro i; apply Subtype.ext; simp + right_inv := by intro i; apply Subtype.ext; simp } + +def symExtension (line : S → L) (v : (S → A) → ℂ) (w : S → L × A) : ℂ := + if hb : counts (fun i => (w i).1) = counts line then + v (fun i => (w (allocationPerm line _ hb i)).2) else 0 + +omit [Fintype A] [DecidableEq A] in +omit [DecidableEq S] in +lemma symExtension_on_line (line : S → L) (v : (S → A) → ℂ) + (hv : ∀ p : Equiv.Perm S, (∀ i, line (p i) = line i) → ∀ w, v (w ∘ p) = v w) + (w : S → A) : symExtension line v (fun i => (line i,w i)) = v w := by + simp only [symExtension] + exact hv (allocationPerm line line rfl) (allocationPerm_spec line line rfl) w + +omit [Fintype A] [DecidableEq A] in +omit [DecidableEq S] in +lemma symExtension_invariant (line : S → L) (v : (S → A) → ℂ) + (hv : ∀ p : Equiv.Perm S, (∀ i, line (p i) = line i) → ∀ w, v (w ∘ p) = v w) + (p : Equiv.Perm S) (w : S → L × A) : symExtension line v (w ∘ p) = symExtension line v w := by + have hc : counts (fun i => (w (p i)).1) = counts (fun i => (w i).1) := counts_precomp (fun i => (w i).1) p + by_cases hb : counts (fun i => (w i).1) = counts line + · have hb' : counts (fun i => (w (p i)).1) = counts line := hc.trans hb + simp only [symExtension, Function.comp_apply, dite_eq_left hb, dite_eq_left hb'] + let e := allocationPerm line (fun i => (w i).1) hb + let e' := allocationPerm line (fun i => (w (p i)).1) hb' + let q : Equiv.Perm S := e'.trans (p.trans e.symm) + have hq (i : S) : line (q i) = line i := by + rw [← allocationPerm_spec line (fun i => (w i).1) hb (q i)] + change (w (e (e.symm (p (e' i))))).1 = line i + rw [Equiv.apply_symm_apply] + exact allocationPerm_spec line (fun i => (w (p i)).1) hb' i + have hh := hv q hq (fun i => (w (e i)).2) + change v (fun i => (w (p (e' i))).2) = v (fun i => (w (e i)).2) + convert hh using 1 + congr 1 + ext i + simp only [q, Equiv.trans_apply, Function.comp_apply, Equiv.apply_symm_apply] + · have hb' : ¬ counts (fun i => (w (p i)).1) = counts line := fun hh => hb (hc.symm.trans hh) + simp only [symExtension, Function.comp_apply, dite_eq_right hb, dite_eq_right hb'] + +omit [Fintype A] in +omit [DecidableEq S] in +lemma symExtension_counts (line : S → L) (v : (S → A) → ℂ) + (hv : ∀ p : Equiv.Perm S, (∀ i, line (p i) = line i) → ∀ w, v (w ∘ p) = v w) + (w z : S → L × A) (he : counts w = counts z) : symExtension line v w = symExtension line v z := by + obtain ⟨p,hp⟩ := same_counts_permutation w z he + have hh : z ∘ p = w := funext hp + rw [← hh] + exact symExtension_invariant line v hv p z + +abbrev Allocations (line : S → L) := {b : S → L // counts b = counts line} + +def labelWordEquiv : (S → L × A) ≃ (S → L) × (S → A) where + toFun w := (fun i => (w i).1, fun i => (w i).2) + invFun w i := (w.1 i,w.2 i) + left_inv := by intro w; rfl + right_inv := by intro w; rfl + +def precompWordEquiv (p : Equiv.Perm S) : Equiv.Perm (S → A) where + toFun w := w ∘ p + invFun w := w ∘ p.symm + left_inv := by intro w; ext i; simp + right_inv := by intro w; ext i; simp + +omit [DecidableEq A] in +lemma symExtension_norm (line : S → L) (v : (S → A) → ℂ) : + (∑ w : S → L × A, Complex.normSq (symExtension line v w)) = + (Fintype.card (Allocations line) : ℝ) * ∑ w : S → A, Complex.normSq (v w) := by + rw [← (labelWordEquiv (S := S) (L := L) (A := A)).symm.sum_comp, + Fintype.sum_prod_type] + change (∑ b : S → L, ∑ w : S → A, Complex.normSq + (if hb : counts b=counts line then v (w ∘ allocationPerm line b hb) else 0)) = _ + have he (b : S → L) : (∑ w : S → A, Complex.normSq + (if hb : counts b=counts line then v (w ∘ allocationPerm line b hb) else 0)) = + if counts b=counts line then ∑ w : S → A, Complex.normSq (v w) else 0 := by + split_ifs with hb + · exact Equiv.sum_comp (precompWordEquiv (A := A) (allocationPerm line b hb)) (fun w => Complex.normSq (v w)) + · simp + simp_rw [he] + simp [Finset.sum_ite, Fintype.card_subtype, Allocations] + + +def labelTest (line : S → L) (x : (S → A) → ℂ) (w : S → L × A) : ℂ := + if (fun i => (w i).1)=line then x (fun i => (w i).2) else 0 + +omit [DecidableEq A] in +lemma labeled_pair (line : S → L) (x : (S → A) → ℂ) (f : (S → L × A) → ℂ) : + (∑ w, f w * labelTest line x w) = ∑ w : S → A, f (fun i => (line i,w i)) * x w := by + rw [← (labelWordEquiv (S := S) (L := L) (A := A)).symm.sum_comp, + Fintype.sum_prod_type] + change (∑ b : S → L, ∑ w : S → A, f (fun i => (b i,w i)) * + (if b=line then x w else 0)) = _ + simp only [mul_ite, mul_zero, Finset.sum_ite_irrel, Finset.sum_const_zero] + simp + +lemma allocation_probability (line : S → L) (r : L → ℝ) + (hr : ∀ l, 0 ≤ r l) (hs : ∑ l, r l ≤ 1) : + (Fintype.card (Allocations line) : ℝ) * (∏ i, r (line i)) ≤ 1 := by + have he (b : S → L) (hb : counts b=counts line) : + (∏ i, r (b i)) = ∏ i, r (line i) := by + rw [prod_by_counts, prod_by_counts, hb] + have hh : (∑ b : S → L, if counts b=counts line then ∏ i, r (line i) else 0) ≤ + ∑ b : S → L, ∏ i, r (b i) := by + apply Finset.sum_le_sum + intro b _ + split_ifs with hb + · exact le_of_eq (he b hb).symm + · exact Finset.prod_nonneg (fun _ _ => hr _) + have hl : (∑ b : S → L, if counts b=counts line then ∏ i, r (line i) else 0) = + (Fintype.card (Allocations line) : ℝ) * (∏ i, r (line i)) := by + simp [Finset.sum_ite, Fintype.card_subtype, Allocations] + rw [hl, ← Fintype.prod_sum] at hh + exact hh.trans (Finset.prod_le_one₀ (fun _ _ => Finset.sum_nonneg (fun l _ => hr l)) (fun _ _ => hs)) + +def lineMass (z : L × A → ℂ) (l : L) : ℝ := ∑ a, Complex.normSq (z (l,a)) +def normalizedLine (z : L × A → ℂ) (l : L) (a : A) : ℂ := + (Real.sqrt (lineMass z l) : ℂ)⁻¹ * z (l,a) + +omit [Fintype L] [DecidableEq L] [DecidableEq A] in +lemma lineMass_nonneg (z : L × A → ℂ) (l : L) : 0 ≤ lineMass z l := + Finset.sum_nonneg (fun _ _ => Complex.normSq_nonneg _) + +omit [Fintype L] [DecidableEq L] [DecidableEq A] in +lemma lineMass_zero (z : L × A → ℂ) (l : L) (h : lineMass z l=0) (a : A) : z (l,a)=0 := by + apply Complex.normSq_eq_zero.mp + have hh : Complex.normSq (z (l,a)) ≤ lineMass z l := + Finset.single_le_sum (fun b _ => Complex.normSq_nonneg (z (l,b))) (Finset.mem_univ a) + exact le_antisymm (h ▸ hh) (Complex.normSq_nonneg _) + +omit [Fintype L] [DecidableEq L] [DecidableEq A] in +lemma line_reconstruction (z : L × A → ℂ) (l : L) (a : A) : + z (l,a) = (Real.sqrt (lineMass z l) : ℂ) * normalizedLine z l a := by + by_cases hz : lineMass z l=0 + · simp [normalizedLine, hz, lineMass_zero z l hz a] + · have h : (Real.sqrt (lineMass z l) : ℂ) ≠ 0 := by + exact_mod_cast (Real.sqrt_ne_zero'.mpr (lt_of_le_of_ne (lineMass_nonneg z l) (Ne.symm hz))) + simp [normalizedLine, h] + +omit [Fintype L] [DecidableEq L] [DecidableEq A] in +lemma normalizedLine_norm (z : L × A → ℂ) (l : L) : + (∑ a, Complex.normSq (normalizedLine z l a)) ≤ 1 := by + by_cases hz : lineMass z l=0 + · simp [normalizedLine, hz] + · have hp : 0 < lineMass z l := lt_of_le_of_ne (lineMass_nonneg z l) (Ne.symm hz) + simp_rw [normalizedLine, map_mul, map_inv₀, Complex.normSq_ofReal, Real.mul_self_sqrt (le_of_lt hp)] + rw [← Finset.mul_sum] + change (lineMass z l)⁻¹ * lineMass z l ≤ 1 + rw [inv_mul_cancel₀ hz] + +omit [Fintype L] [DecidableEq L] [DecidableEq A] in +lemma labeled_tensor_pair (line : S → L) (z : L × A → ℂ) (x : (S → A) → ℂ) : + Complex.normSq (∑ w : S → A, tensorVector z (fun i => (line i,w i)) * x w) = + (∏ i, lineMass z (line i)) * + Complex.normSq (∑ w : S → A, (∏ i, normalizedLine z (line i) (w i)) * x w) := by + have he (w : S → A) : tensorVector z (fun i => (line i,w i)) = + (∏ i, (Real.sqrt (lineMass z (line i)) : ℂ)) * ∏ i, normalizedLine z (line i) (w i) := by + rw [← Finset.prod_mul_distrib] + exact Finset.prod_congr rfl (fun i _ => line_reconstruction z (line i) (w i)) + simp_rw [he, mul_assoc] + rw [← Finset.mul_sum, map_mul] + congr 1 + rw [map_prod] + apply Finset.prod_congr rfl + intro i _ + exact (Complex.normSq_ofReal _).trans (Real.mul_self_sqrt (lineMass_nonneg z (line i))) + + +omit [DecidableEq S] [Fintype A] [DecidableEq A] in +lemma symExtension_supported (line : S → L) (v : (S → A) → ℂ) + (good : A → Prop) [DecidablePred good] + (hv : ∀ w, ¬ (∀ i, good (w i)) → v w=0) + (w : S → L × A) (hw : ¬ ∀ i, good (w i).2) : symExtension line v w=0 := by + unfold symExtension + split_ifs with hb + · apply hv + intro h + apply hw + intro i + simpa using h ((allocationPerm line _ hb).symm i) + · rfl + +def lineAmplitude (line : S → L) (a₀ : S → A) (good : A → Prop) [DecidablePred good] + (q : Types (S := S) (A := L × A)) (θ : Phases (L × A) (Fintype.card S)) (l : L) (a : A) : ℂ := + normalizedLine (truncateAmplitude (fun c : L × A => good c.2) + (twistedAmplitude (typeRepresentative (fun i => (line i,a₀ i)) q) θ)) l a + +omit [DecidableEq S] in +omit [Fintype L] in +lemma lineAmplitude_norm (line : S → L) (a₀ : S → A) (good : A → Prop) [DecidablePred good] + (q : Types (S := S) (A := L × A)) (θ : Phases (L × A) (Fintype.card S)) (l : L) : + (∑ a, Complex.normSq (lineAmplitude line a₀ good q θ l a)) ≤ 1 := + normalizedLine_norm _ _ + +omit [DecidableEq S] [Fintype L] in +lemma lineAmplitude_support (line : S → L) (a₀ : S → A) (good : A → Prop) [DecidablePred good] + (q : Types (S := S) (A := L × A)) (θ : Phases (L × A) (Fintype.card S)) (l : L) (a : A) + (ha : ¬ good a) : lineAmplitude line a₀ good q θ l a=0 := by + simp [lineAmplitude, normalizedLine, truncateAmplitude, ha] + +/-- Independent fibre postselection, with the allocation factorial cancelled +by the exact multinomial probability rather than included in the overhead. -/ +theorem line_symmetric_postselection (line : S → L) (a₀ : S → A) (hn : 0 < Fintype.card S) + (good : A → Prop) [DecidablePred good] (v x : (S → A) → ℂ) + (hv : ∀ p : Equiv.Perm S, (∀ i, line (p i)=line i) → ∀ w, v (w ∘ p)=v w) + (hsupp : ∀ w, ¬ (∀ i, good (w i)) → v w=0) : + Complex.normSq (∑ w, v w*x w) ≤ + (∑ w, Complex.normSq (v w)) * + (((Fintype.card S+1)^(Fintype.card (L × A)) : ℕ) / + (Fintype.card (Phases (L × A) (Fintype.card S)) : ℝ) * + ∑ q : Types (S := S) (A := L × A), ∑ θ : Phases (L × A) (Fintype.card S), + Complex.normSq (∑ w : S → A, (∏ i, lineAmplitude line a₀ good q θ (line i) (w i)) * x w)) := by + let z (q : Types (S := S) (A := L × A)) (θ : Phases (L × A) (Fintype.card S)) := + truncateAmplitude (fun c : L × A => good c.2) + (twistedAmplitude (typeRepresentative (fun i => (line i,a₀ i)) q) θ) + let R (q : Types (S := S) (A := L × A)) (θ : Phases (L × A) (Fintype.card S)) := + Complex.normSq (∑ w : S → A, (∏ i, normalizedLine (z q θ) (line i) (w i)) * x w) + have hz (q : Types (S := S) (A := L × A)) (θ : Phases (L × A) (Fintype.card S)) : + (Fintype.card (Allocations line) : ℝ) * (∏ i, lineMass (z q θ) (line i)) ≤ 1 := by + apply allocation_probability line _ (lineMass_nonneg _) + rw [show (∑ l, lineMass (z q θ) l) = ∑ c : L × A, Complex.normSq (z q θ c) from + (Fintype.sum_prod_type (fun c : L × A => Complex.normSq (z q θ c))).symm] + exact truncated_twisted_subnormalized _ _ hn _ + have hh := supported_symmetric_postselection (fun i => (line i,a₀ i)) hn + (fun c : L × A => good c.2) (symExtension line v) (labelTest line x) + (symExtension_counts line v hv) (symExtension_supported line v good hsupp) + rw [labeled_pair] at hh + simp_rw [symExtension_on_line line v hv] at hh + rw [symExtension_norm] at hh + simp_rw [labeled_pair, labeled_tensor_pair] at hh + let c : ℝ := ((Fintype.card S+1)^(Fintype.card (L × A)) : ℕ) / + (Fintype.card (Phases (L × A) (Fintype.card S)) : ℝ) + change _ ≤ ((Fintype.card (Allocations line) : ℝ) * ∑ w, Complex.normSq (v w)) * + (c * ∑ q, ∑ θ, (∏ i, lineMass (z q θ) (line i)) * R q θ) at hh + change _ ≤ (∑ w, Complex.normSq (v w)) * (c * ∑ q, ∑ θ, R q θ) + apply hh.trans + rw [show ((Fintype.card (Allocations line) : ℝ) * ∑ w, Complex.normSq (v w)) * + (c * ∑ q, ∑ θ, (∏ i, lineMass (z q θ) (line i)) * R q θ) = + (∑ w, Complex.normSq (v w)) * (c * ((Fintype.card (Allocations line) : ℝ) * + ∑ q, ∑ θ, (∏ i, lineMass (z q θ) (line i)) * R q θ)) by ring] + apply mul_le_mul_of_nonneg_left _ (Finset.sum_nonneg (fun _ _ => Complex.normSq_nonneg _)) + apply mul_le_mul_of_nonneg_left _ (by positivity : 0 ≤ c) + simp_rw [Finset.mul_sum, ← mul_assoc] + exact Finset.sum_le_sum (fun q _ => Finset.sum_le_sum (fun θ _ => + (mul_le_mul_of_nonneg_right (hz q θ) (Complex.normSq_nonneg _)).trans_eq (one_mul _))) + +end RowColumn.Postselection + +end +end + + +section +noncomputable section +open scoped BigOperators Classical Matrix.Norms.L2Operator ComplexOrder MatrixOrder +namespace RowColumn.Postselection +open MatrixState WordOrbits +variable {S L C : Type*} [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] + [Fintype C] [DecidableEq C] + +def lineState (line : S → L) (a₀ : S → C × C) (odd : C → Prop) [DecidablePred odd] + (q : Types (S := S) (A := L × (C × C))) (θ : Phases (L × (C × C)) (Fintype.card S)) + (l : L) : Matrix C C ℂ := + gramState (lineAmplitude line a₀ (fun p : C × C => odd p.1 ↔ odd p.2) q θ l) + +omit [DecidableEq S] [Fintype L] in +lemma lineState_positive (line : S → L) (a₀ : S → C × C) (odd : C → Prop) [DecidablePred odd] + (q : Types (S := S) (A := L × (C × C))) (θ : Phases (L × (C × C)) (Fintype.card S)) (l : L) : + (lineState line a₀ odd q θ l).PosSemidef := gramState_posSemidef _ + +omit [DecidableEq S] in +omit [Fintype L] in +lemma lineState_trace (line : S → L) (a₀ : S → C × C) (odd : C → Prop) [DecidablePred odd] + (q : Types (S := S) (A := L × (C × C))) (θ : Phases (L × (C × C)) (Fintype.card S)) (l : L) : + (lineState line a₀ odd q θ l).trace.re ≤ 1 := by + rw [lineState, gramState_trace] + exact lineAmplitude_norm _ _ _ _ _ _ + +omit [DecidableEq S] [Fintype L] in +lemma lineState_even (line : S → L) (a₀ : S → C × C) (odd : C → Prop) [DecidablePred odd] + (q : Types (S := S) (A := L × (C × C))) (θ : Phases (L × (C × C)) (Fintype.card S)) + (l : L) (c d : C) (h : ¬ (odd c ↔ odd d)) : lineState line a₀ odd q θ l c d=0 := by + apply gramState_parity_supported odd _ _ c d h + exact fun c d h => lineAmplitude_support _ _ _ _ _ _ _ h + +lemma variable_purification_pair (z : S → C × C → ℂ) (x : (S → C) → ℂ) (v : S → C) : + (∑ a : S → C × C, (∏ i, z i (a i)) * purificationTest x v a) = + ∑ w : S → C, tensorMatrix (fun i => letterMatrix (z i)) w v * x w := by + exact purification_pair (tensorMatrix (fun i => letterMatrix (z i))) x v + +lemma variable_purification_quadratic (z : S → C × C → ℂ) (x : (S → C) → ℂ) : + (∑ v : S → C, Complex.normSq (∑ a : S → C × C, + (∏ i, z i (a i)) * purificationTest x v a)) = + quadratic (tensorMatrix (fun i => gramState (z i))) x := by + simp_rw [variable_purification_pair] + change factorQuadratic (tensorMatrix (fun i => letterMatrix (z i))) x = _ + rw [factorQuadratic_eq, tensorMatrix_star, tensorMatrix_mul] + rfl + +/-- Explicit local domination for independent row/column permutation fibres. +All mixture terms are genuine even positive identical-slot substates within +each fibre, irrespective of its size and the deletion layout. -/ +theorem positive_line_postselection (line : S → L) (a₀ : S → C × C) (hn : 0 < Fintype.card S) + (odd : C → Prop) [DecidablePred odd] (A : Matrix (S → C) (S → C) ℂ) + (hA : A.PosSemidef) + (hinv : ∀ (p : Equiv.Perm S), (∀ i, line (p i)=line i) → ∀ (w v : S → C), + A (w ∘ p) (v ∘ p)=A w v) + (hsupp : ∀ w v, ¬ (∀ i, odd (w i) ↔ odd (v i)) → A w v=0) + (x : (S → C) → ℂ) : + quadratic A x ≤ A.trace.re * + (((Fintype.card S+1)^(Fintype.card (L × (C × C))) : ℕ) / + (Fintype.card (Phases (L × (C × C)) (Fintype.card S)) : ℝ) * + ∑ q : Types (S := S) (A := L × (C × C)), + ∑ θ : Phases (L × (C × C)) (Fintype.card S), + quadratic (tensorMatrix (fun i : S => lineState line a₀ odd q θ (line i))) x) := by + let B : Matrix (S → C) (S → C) ℂ := CFC.sqrt A + have hi (p : Equiv.Perm S) (hp : ∀ i, line (p i)=line i) (w v : S → C) : + B (w ∘ p) (v ∘ p)=B w v := + sqrt_permutation_invariant A hA (reindexWord p) (hinv p hp) w v + have hz (w v : S → C) (hh : ¬ ∀ i, odd (w i) ↔ odd (v i)) : B w v=0 := by + apply sqrt_block_supported (fun u : S → C => fun i => odd (u i)) A hA + (fun u v he => hsupp u v (fun ht => he (funext fun i => propext (ht i)))) w v + intro he + exact hh (fun i => Iff.of_eq (congrFun he i)) + have hv (p : Equiv.Perm S) (hp : ∀ i, line (p i)=line i) (w : S → C × C) : + purificationVector B (w ∘ p)=purificationVector B w := + hi p hp (fun i => (w i).1) (fun i => (w i).2) + have hs (w : S → C × C) (hw : ¬ ∀ i, odd (w i).1 ↔ odd (w i).2) : purificationVector B w=0 := + hz _ _ hw + have hh (v : S → C) := line_symmetric_postselection line a₀ hn + (fun p : C × C => odd p.1 ↔ odd p.2) (purificationVector B) (purificationTest x v) hv hs + simp only [purification_pair B x, purification_normSq B] at hh + have hsum := Finset.sum_le_sum (fun v (_ : v ∈ Finset.univ) => hh v) + change factorQuadratic B x ≤ _ at hsum + have ht : purifierTrace B=A.trace.re := sqrt_trace A hA + rw [ht] at hsum + change factorQuadratic (CFC.sqrt A) x ≤ _ at hsum + rw [sqrt_factorQuadratic A hA] at hsum + apply hsum.trans_eq + simp only [Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro q _ + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro θ _ + rw [← Finset.mul_sum, ← Finset.mul_sum] + congr 2 + exact variable_purification_quadratic _ x + +end RowColumn.Postselection + +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/Multiplicity.lean b/lean/OAI/RepresentationTheory/RowColumn/Multiplicity.lean index 3a361d8df51c1d27452d5bb5888497b592d89498..7f046e73dda89a59a10e7ce9ec833e7f86ae5aa4 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/Multiplicity.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/Multiplicity.lean @@ -1,269 +1,269 @@ -import OAI.RepresentationTheory.RowColumn.HookModel - -namespace OAI - -noncomputable section - -open scoped BigOperators Classical - -namespace RowColumn - -section Retraction -variable {G V W : Type*} [Group G] [Fintype G] - [AddCommGroup V] [Module ℂ V] [AddCommGroup W] [Module ℂ W] - {ρ : Representation ℂ G V} {σ : Representation ℂ G W} - -def algebraicAverage (A : V →ₗ[ℂ] W) : Representation.IntertwiningMap ρ σ where - toLinearMap := ∑ g, (σ g).comp (A.comp (ρ g⁻¹)) - isIntertwining' h := by - ext v - simp only [LinearMap.comp_apply, LinearMap.sum_apply, map_sum] - apply Fintype.sum_equiv (Equiv.mulLeft h⁻¹) - intro g - simp only [Equiv.coe_mulLeft, mul_inv_rev, inv_inv, map_mul, Module.End.mul_apply] - have hh (w : W) : σ h (σ h⁻¹ w) = w := by - change (σ h * σ h⁻¹) w = w - rw [← map_mul, mul_inv_cancel, map_one] - rfl - rw [hh] - -/-- Averaging an algebraic left inverse produces a genuine equivariant retraction. -Used to transfer the signed-slot commutant bound to the hook Specht module. -/ -lemma intertwiner_has_retraction (L : Representation.IntertwiningMap ρ σ) - (hL : Function.Injective L) : - ∃ R : Representation.IntertwiningMap σ ρ, ∀ v, R (L v) = v := by - obtain ⟨A, hA⟩ := L.toLinearMap.exists_leftInverse_of_injective - (LinearMap.ker_eq_bot.mpr hL) - refine ⟨(Fintype.card G : ℂ)⁻¹ • algebraicAverage A, ?_⟩ - intro v - change (Fintype.card G : ℂ)⁻¹ • (∑ g, (ρ g).comp (A.comp (σ g⁻¹))) (L v) = v - simp only [LinearMap.sum_apply, LinearMap.comp_apply] - have ha (g : G) : ρ g (A (σ g⁻¹ (L v))) = v := by - rw [← Representation.IntertwiningMap.isIntertwining ρ σ L] - have he : A (L (ρ g⁻¹ v)) = ρ g⁻¹ v := - LinearMap.congr_fun hA (ρ g⁻¹ v) - rw [he] - change (ρ g * ρ g⁻¹) v = v - rw [← map_mul, mul_inv_cancel, map_one] - rfl - simp only [ha, Finset.sum_const, Finset.card_univ] - rw [← Nat.cast_smul_eq_nsmul ℂ, smul_smul, inv_mul_cancel₀, one_smul] - exact_mod_cast Fintype.card_ne_zero - -def extendCommutant (L : Representation.IntertwiningMap ρ σ) - (R : Representation.IntertwiningMap σ ρ) : - Representation.IntertwiningMap ρ ρ →ₗ[ℂ] Representation.IntertwiningMap σ σ where - toFun A := L.comp (A.comp R) - map_add' A B := by ext v; simp - map_smul' z A := by ext v; simp - -omit [Fintype G] in -lemma extendCommutant_injective (L : Representation.IntertwiningMap ρ σ) - (R : Representation.IntertwiningMap σ ρ) (hL : Function.Injective L) - (hR : ∀ v, R (L v) = v) : Function.Injective (extendCommutant L R) := by - intro A B h - apply Representation.IntertwiningMap.ext - ext v - change A v = B v - apply hL - have he := congrArg (fun T : Representation.IntertwiningMap σ σ => T (L v)) h - simpa only [extendCommutant, LinearMap.coe_mk, AddHom.coe_mk, - Representation.IntertwiningMap.comp_apply, hR] using he - -lemma commutant_finrank_le_of_embedding [FiniteDimensional ℂ W] - (L : Representation.IntertwiningMap ρ σ) (hL : Function.Injective L) : - Module.finrank ℂ (Representation.IntertwiningMap ρ ρ) ≤ - Module.finrank ℂ (Representation.IntertwiningMap σ σ) := by - obtain ⟨R, hR⟩ := intertwiner_has_retraction L hL - exact LinearMap.finrank_le_finrank_of_injective (f := extendCommutant L R) - (extendCommutant_injective L R hL hR) - -end Retraction -end RowColumn -namespace RowColumn -open scoped BigOperators Classical -open CubeShuffle.UnitaryFinite - -section CopyCount -variable {G V X : Type*} [Group G] - [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] - [NormedAddCommGroup X] [InnerProductSpace ℂ X] [FiniteDimensional ℂ X] - {ρ : Representation ℂ G V} {τ : Representation ℂ G X} - {u : ℕ} (I : Fin u → V →ₗᵢ[ℂ] X) - -lemma adjoint_intertwines (A : V →ₗ[ℂ] X) (hA : Intertwines ρ τ A) - (hρ : IsUnitary ρ) (hτ : IsUnitary τ) : - Intertwines τ ρ A.toContinuousLinearMap.adjoint.toLinearMap := by - intro g x - apply ext_inner_left ℂ - intro v - change inner ℂ v (A.toContinuousLinearMap.adjoint (τ g x)) = - inner ℂ v (ρ g (A.toContinuousLinearMap.adjoint x)) - rw [ContinuousLinearMap.adjoint_inner_right] - rw [← inv_inv g, unitary_inner_inv ρ hρ, ContinuousLinearMap.adjoint_inner_right] - change inner ℂ (A v) (τ (g⁻¹)⁻¹ x) = inner ℂ (A (ρ g⁻¹ v)) x - rw [hA, unitary_inner_inv τ hτ] - -def copyIdempotent (hI : ∀ i, Intertwines ρ τ (I i).toLinearMap) - (hρ : IsUnitary ρ) (hτ : IsUnitary τ) (i : Fin u) : - Representation.IntertwiningMap τ τ where - toLinearMap := (I i).toLinearMap.comp (I i).toContinuousLinearMap.adjoint.toLinearMap - isIntertwining' g := by - ext x - change I i ((I i).toContinuousLinearMap.adjoint (τ g x)) = - τ g (I i ((I i).toContinuousLinearMap.adjoint x)) - rw [show (I i).toContinuousLinearMap.adjoint (τ g x) = - ρ g ((I i).toContinuousLinearMap.adjoint x) from - adjoint_intertwines (I i).toLinearMap (hI i) hρ hτ g x] - exact hI i g _ - -lemma adjoint_copy_apply (ho : ∀ i j, i ≠ j → ∀ v w, inner ℂ (I i v) (I j w) = 0) - (i j : Fin u) (v : V) : - (I i).toContinuousLinearMap.adjoint (I j v) = if i = j then v else 0 := by - apply ext_inner_left ℂ - intro w - rw [ContinuousLinearMap.adjoint_inner_right] - by_cases he : i = j - · subst j - simp [LinearIsometry.inner_map_map] - · simp only [ite_eq_right he, inner_zero_right, LinearIsometry.coe_toContinuousLinearMap] - exact ho i j he w v - -lemma copyIdempotent_apply (hI : ∀ i, Intertwines ρ τ (I i).toLinearMap) - (hρ : IsUnitary ρ) (hτ : IsUnitary τ) - (ho : ∀ i j, i ≠ j → ∀ v w, inner ℂ (I i v) (I j w) = 0) - (i j : Fin u) (v : V) : - copyIdempotent I hI hρ hτ i (I j v) = if i = j then I j v else 0 := by - change I i ((I i).toContinuousLinearMap.adjoint (I j v)) = _ - rw [adjoint_copy_apply I ho] - split_ifs with he - · subst j; rfl - · exact map_zero _ - -/-- Orthogonal nonzero copies supply linearly independent elements of the -commutant by their actual range projections. -/ -lemma copyIdempotent_independent [Nontrivial V] - (hI : ∀ i, Intertwines ρ τ (I i).toLinearMap) - (hρ : IsUnitary ρ) (hτ : IsUnitary τ) - (ho : ∀ i j, i ≠ j → ∀ v w, inner ℂ (I i v) (I j w) = 0) : - LinearIndependent ℂ (copyIdempotent I hI hρ hτ) := by - obtain ⟨v, hv⟩ := exists_ne (0 : V) - rw [linearIndependent_iff'] - intro s z hz j hj - have he := congrArg (fun T : Representation.IntertwiningMap τ τ => T (I j v)) hz - simp only [Representation.IntertwiningMap.sum_apply, Representation.IntertwiningMap.smul_apply, - copyIdempotent_apply I hI hρ hτ ho] at he - have he' : ∑ i ∈ s, z i • (if i = j then I j v else 0) = 0 := he - simp only [smul_ite, smul_zero] at he' - simp only [Finset.sum_ite_eq', ite_eq_left hj] at he' - exact (smul_eq_zero.mp he').resolve_right (fun hz => hv ((I j).injective (hz.trans (map_zero _).symm))) - -lemma copy_count_le_commutant [Nontrivial V] - (hI : ∀ i, Intertwines ρ τ (I i).toLinearMap) - (hρ : IsUnitary ρ) (hτ : IsUnitary τ) - (ho : ∀ i j, i ≠ j → ∀ v w, inner ℂ (I i v) (I j w) = 0) : - u ≤ Module.finrank ℂ (Representation.IntertwiningMap τ τ) := by - simpa using (copyIdempotent_independent I hI hρ hτ ho).fintype_card_le_finrank -end CopyCount -end RowColumn -namespace RowColumn -open scoped BigOperators Classical -open CubeShuffle.Specht CubeShuffle.UnitaryFinite - -section Relabelling -variable {S T L : Type*} - -def lineGroupCongr (e : S ≃ T) (f : S → L) : - lineGroup f ≃* lineGroup (f ∘ e.symm) where - toFun g := ⟨e.permCongr g.1, by - intro x - simpa only [Function.comp_apply, Equiv.permCongr_apply, Equiv.symm_apply_apply] using g.2 (e.symm x)⟩ - invFun g := ⟨e.symm.permCongr g.1, by - intro x - simpa only [Function.comp_apply, Equiv.permCongr_apply, Equiv.symm_symm, - Equiv.symm_apply_apply] using g.2 (e x)⟩ - left_inv g := by apply Subtype.ext; exact e.permCongr.symm_apply_apply g.1 - right_inv g := by apply Subtype.ext; exact e.permCongr.apply_symm_apply g.1 - map_mul' g t := by apply Subtype.ext; exact e.permCongrHom.map_mul g.1 t.1 - -end Relabelling - -section Transfer -variable {G H V : Type*} [Group G] [Group H] [AddCommGroup V] [Module ℂ V] - -def commutantOfComp (ρ : Representation ℂ G V) (e : H ≃* G) : - Representation.IntertwiningMap (ρ.comp e.toMonoidHom) (ρ.comp e.toMonoidHom) →ₗ[ℂ] - Representation.IntertwiningMap ρ ρ where - toFun T := - { toLinearMap := T.toLinearMap - isIntertwining' g := by simpa using T.isIntertwining' (e.symm g) } - map_add' A B := rfl - map_smul' z A := rfl - -lemma commutantOfComp_injective (ρ : Representation ℂ G V) (e : H ≃* G) : - Function.Injective (commutantOfComp ρ e) := by - intro T U he - exact Representation.IntertwiningMap.ext - (congrArg (fun T : Representation.IntertwiningMap ρ ρ => T.toLinearMap) he) - -lemma commutant_comp_finrank_le [FiniteDimensional ℂ V] - (ρ : Representation ℂ G V) (e : H ≃* G) : - Module.finrank ℂ (Representation.IntertwiningMap (ρ.comp e.toMonoidHom) (ρ.comp e.toMonoidHom)) ≤ - Module.finrank ℂ (Representation.IntertwiningMap ρ ρ) := - LinearMap.finrank_le_finrank_of_injective (commutantOfComp_injective ρ e) -end Transfer - -section HookMultiplicity -variable {S L : Type*} [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] - (f : S → L) (a : YoungDiagram) (e : S ≃ Cell a) (h : ℕ) (H : InHook a h) - -abbrev hookLineTarget := - (Signed.lineRepresentation (odd := HookModel.IsOdd (h := h)) - (k := HookModel.oddCount a h H) (f ∘ e.symm)).comp (lineGroupCongr e f).toMonoidHom - -def hookLineEmbedding : Representation.IntertwiningMap - ((relabelledUnitary a e).comp (lineGroup f).subtype) (hookLineTarget f a e h H) where - toLinearMap := (HookModel.hookEmbedding a h H).toLinearMap.comp (spaceHilbertEquiv a).symm.toLinearMap - isIntertwining' g := by - apply LinearMap.ext - intro v - let T := (HookModel.hookEmbedding a h H).comp (unitaryEquiv a).symm.toIntertwiningMap - exact Representation.IntertwiningMap.isIntertwining _ _ T (e.permCongr g.1) v - -omit [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] in -lemma hookLineEmbedding_injective : Function.Injective (hookLineEmbedding f a e h H) := - (HookModel.hookEmbedding_injective a h H).comp (spaceHilbertEquiv a).symm.injective - -include H - -/-- Polynomial commutant estimate for the actual hook Specht representation -restricted to arbitrary fibres. This is the required first multiplicity bound -for both row and column restrictions in the occupied theorem. -/ -lemma hook_line_commutant_bound : - Module.finrank ℂ (Representation.IntertwiningMap - ((relabelledUnitary a e).comp (lineGroup f).subtype) - ((relabelledUnitary a e).comp (lineGroup f).subtype)) ≤ - (Fintype.card S + 1) ^ (4 * Fintype.card L * h ^ 2) := by - apply (commutant_finrank_le_of_embedding (hookLineEmbedding f a e h H) - (hookLineEmbedding_injective f a e h H)).trans - apply (commutant_comp_finrank_le _ (lineGroupCongr e f)).trans - have hc := Signed.commutant_dimension_bound (odd := HookModel.IsOdd (h := h)) - (k := HookModel.oddCount a h H) (f ∘ e.symm) - have hs : Fintype.card (Cell a) = Fintype.card S := (Fintype.card_congr e).symm - simpa only [hs, HookModel.Color, Fintype.card_sum, Fintype.card_fin, - show Fintype.card L * (h + h) ^ 2 = 4 * Fintype.card L * h ^ 2 by ring] using hc - -lemma hook_line_copy_count {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] - [FiniteDimensional ℂ V] [Nontrivial V] (ρ : Representation ℂ (lineGroup f) V) - (hρ : IsUnitary ρ) {u : ℕ} (I : Fin u → V →ₗᵢ[ℂ] hilbertSpace a) - (hI : CompleteCopies (V := V) (W := hilbertSpace a) ρ ((relabelledUnitary a e).comp (lineGroup f).subtype) I) : - u ≤ (Fintype.card S + 1) ^ (4 * Fintype.card L * h ^ 2) := - (copy_count_le_commutant (V := V) (X := hilbertSpace a) I hI.1 hρ (fun g => relabelledUnitary_unitary a e g.1) hI.2.1).trans - (hook_line_commutant_bound f a e h H) - -end HookMultiplicity -end RowColumn - -end - -end OAI +import OAI.RepresentationTheory.RowColumn.HookModel + +namespace OAI + +noncomputable section + +open scoped BigOperators Classical + +namespace RowColumn + +section Retraction +variable {G V W : Type*} [Group G] [Fintype G] + [AddCommGroup V] [Module ℂ V] [AddCommGroup W] [Module ℂ W] + {ρ : Representation ℂ G V} {σ : Representation ℂ G W} + +def algebraicAverage (A : V →ₗ[ℂ] W) : Representation.IntertwiningMap ρ σ where + toLinearMap := ∑ g, (σ g).comp (A.comp (ρ g⁻¹)) + isIntertwining' h := by + ext v + simp only [LinearMap.comp_apply, LinearMap.sum_apply, map_sum] + apply Fintype.sum_equiv (Equiv.mulLeft h⁻¹) + intro g + simp only [Equiv.coe_mulLeft, mul_inv_rev, inv_inv, map_mul, Module.End.mul_apply] + have hh (w : W) : σ h (σ h⁻¹ w) = w := by + change (σ h * σ h⁻¹) w = w + rw [← map_mul, mul_inv_cancel, map_one] + rfl + rw [hh] + +/-- Averaging an algebraic left inverse produces a genuine equivariant retraction. +Used to transfer the signed-slot commutant bound to the hook Specht module. -/ +lemma intertwiner_has_retraction (L : Representation.IntertwiningMap ρ σ) + (hL : Function.Injective L) : + ∃ R : Representation.IntertwiningMap σ ρ, ∀ v, R (L v) = v := by + obtain ⟨A, hA⟩ := L.toLinearMap.exists_leftInverse_of_injective + (LinearMap.ker_eq_bot.mpr hL) + refine ⟨(Fintype.card G : ℂ)⁻¹ • algebraicAverage A, ?_⟩ + intro v + change (Fintype.card G : ℂ)⁻¹ • (∑ g, (ρ g).comp (A.comp (σ g⁻¹))) (L v) = v + simp only [LinearMap.sum_apply, LinearMap.comp_apply] + have ha (g : G) : ρ g (A (σ g⁻¹ (L v))) = v := by + rw [← Representation.IntertwiningMap.isIntertwining ρ σ L] + have he : A (L (ρ g⁻¹ v)) = ρ g⁻¹ v := + LinearMap.congr_fun hA (ρ g⁻¹ v) + rw [he] + change (ρ g * ρ g⁻¹) v = v + rw [← map_mul, mul_inv_cancel, map_one] + rfl + simp only [ha, Finset.sum_const, Finset.card_univ] + rw [← Nat.cast_smul_eq_nsmul ℂ, smul_smul, inv_mul_cancel₀, one_smul] + exact_mod_cast Fintype.card_ne_zero + +def extendCommutant (L : Representation.IntertwiningMap ρ σ) + (R : Representation.IntertwiningMap σ ρ) : + Representation.IntertwiningMap ρ ρ →ₗ[ℂ] Representation.IntertwiningMap σ σ where + toFun A := L.comp (A.comp R) + map_add' A B := by ext v; simp + map_smul' z A := by ext v; simp + +omit [Fintype G] in +lemma extendCommutant_injective (L : Representation.IntertwiningMap ρ σ) + (R : Representation.IntertwiningMap σ ρ) (hL : Function.Injective L) + (hR : ∀ v, R (L v) = v) : Function.Injective (extendCommutant L R) := by + intro A B h + apply Representation.IntertwiningMap.ext + ext v + change A v = B v + apply hL + have he := congrArg (fun T : Representation.IntertwiningMap σ σ => T (L v)) h + simpa only [extendCommutant, LinearMap.coe_mk, AddHom.coe_mk, + Representation.IntertwiningMap.comp_apply, hR] using he + +lemma commutant_finrank_le_of_embedding [FiniteDimensional ℂ W] + (L : Representation.IntertwiningMap ρ σ) (hL : Function.Injective L) : + Module.finrank ℂ (Representation.IntertwiningMap ρ ρ) ≤ + Module.finrank ℂ (Representation.IntertwiningMap σ σ) := by + obtain ⟨R, hR⟩ := intertwiner_has_retraction L hL + exact LinearMap.finrank_le_finrank_of_injective (f := extendCommutant L R) + (extendCommutant_injective L R hL hR) + +end Retraction +end RowColumn +namespace RowColumn +open scoped BigOperators Classical +open CubeShuffle.UnitaryFinite + +section CopyCount +variable {G V X : Type*} [Group G] + [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] + [NormedAddCommGroup X] [InnerProductSpace ℂ X] [FiniteDimensional ℂ X] + {ρ : Representation ℂ G V} {τ : Representation ℂ G X} + {u : ℕ} (I : Fin u → V →ₗᵢ[ℂ] X) + +lemma adjoint_intertwines (A : V →ₗ[ℂ] X) (hA : Intertwines ρ τ A) + (hρ : IsUnitary ρ) (hτ : IsUnitary τ) : + Intertwines τ ρ A.toContinuousLinearMap.adjoint.toLinearMap := by + intro g x + apply ext_inner_left ℂ + intro v + change inner ℂ v (A.toContinuousLinearMap.adjoint (τ g x)) = + inner ℂ v (ρ g (A.toContinuousLinearMap.adjoint x)) + rw [ContinuousLinearMap.adjoint_inner_right] + rw [← inv_inv g, unitary_inner_inv ρ hρ, ContinuousLinearMap.adjoint_inner_right] + change inner ℂ (A v) (τ (g⁻¹)⁻¹ x) = inner ℂ (A (ρ g⁻¹ v)) x + rw [hA, unitary_inner_inv τ hτ] + +def copyIdempotent (hI : ∀ i, Intertwines ρ τ (I i).toLinearMap) + (hρ : IsUnitary ρ) (hτ : IsUnitary τ) (i : Fin u) : + Representation.IntertwiningMap τ τ where + toLinearMap := (I i).toLinearMap.comp (I i).toContinuousLinearMap.adjoint.toLinearMap + isIntertwining' g := by + ext x + change I i ((I i).toContinuousLinearMap.adjoint (τ g x)) = + τ g (I i ((I i).toContinuousLinearMap.adjoint x)) + rw [show (I i).toContinuousLinearMap.adjoint (τ g x) = + ρ g ((I i).toContinuousLinearMap.adjoint x) from + adjoint_intertwines (I i).toLinearMap (hI i) hρ hτ g x] + exact hI i g _ + +lemma adjoint_copy_apply (ho : ∀ i j, i ≠ j → ∀ v w, inner ℂ (I i v) (I j w) = 0) + (i j : Fin u) (v : V) : + (I i).toContinuousLinearMap.adjoint (I j v) = if i = j then v else 0 := by + apply ext_inner_left ℂ + intro w + rw [ContinuousLinearMap.adjoint_inner_right] + by_cases he : i = j + · subst j + simp [LinearIsometry.inner_map_map] + · simp only [ite_eq_right he, inner_zero_right, LinearIsometry.coe_toContinuousLinearMap] + exact ho i j he w v + +lemma copyIdempotent_apply (hI : ∀ i, Intertwines ρ τ (I i).toLinearMap) + (hρ : IsUnitary ρ) (hτ : IsUnitary τ) + (ho : ∀ i j, i ≠ j → ∀ v w, inner ℂ (I i v) (I j w) = 0) + (i j : Fin u) (v : V) : + copyIdempotent I hI hρ hτ i (I j v) = if i = j then I j v else 0 := by + change I i ((I i).toContinuousLinearMap.adjoint (I j v)) = _ + rw [adjoint_copy_apply I ho] + split_ifs with he + · subst j; rfl + · exact map_zero _ + +/-- Orthogonal nonzero copies supply linearly independent elements of the +commutant by their actual range projections. -/ +lemma copyIdempotent_independent [Nontrivial V] + (hI : ∀ i, Intertwines ρ τ (I i).toLinearMap) + (hρ : IsUnitary ρ) (hτ : IsUnitary τ) + (ho : ∀ i j, i ≠ j → ∀ v w, inner ℂ (I i v) (I j w) = 0) : + LinearIndependent ℂ (copyIdempotent I hI hρ hτ) := by + obtain ⟨v, hv⟩ := exists_ne (0 : V) + rw [linearIndependent_iff'] + intro s z hz j hj + have he := congrArg (fun T : Representation.IntertwiningMap τ τ => T (I j v)) hz + simp only [Representation.IntertwiningMap.sum_apply, Representation.IntertwiningMap.smul_apply, + copyIdempotent_apply I hI hρ hτ ho] at he + have he' : ∑ i ∈ s, z i • (if i = j then I j v else 0) = 0 := he + simp only [smul_ite, smul_zero] at he' + simp only [Finset.sum_ite_eq', ite_eq_left hj] at he' + exact (smul_eq_zero.mp he').resolve_right (fun hz => hv ((I j).injective (hz.trans (map_zero _).symm))) + +lemma copy_count_le_commutant [Nontrivial V] + (hI : ∀ i, Intertwines ρ τ (I i).toLinearMap) + (hρ : IsUnitary ρ) (hτ : IsUnitary τ) + (ho : ∀ i j, i ≠ j → ∀ v w, inner ℂ (I i v) (I j w) = 0) : + u ≤ Module.finrank ℂ (Representation.IntertwiningMap τ τ) := by + simpa using (copyIdempotent_independent I hI hρ hτ ho).fintype_card_le_finrank +end CopyCount +end RowColumn +namespace RowColumn +open scoped BigOperators Classical +open CubeShuffle.Specht CubeShuffle.UnitaryFinite + +section Relabelling +variable {S T L : Type*} + +def lineGroupCongr (e : S ≃ T) (f : S → L) : + lineGroup f ≃* lineGroup (f ∘ e.symm) where + toFun g := ⟨e.permCongr g.1, by + intro x + simpa only [Function.comp_apply, Equiv.permCongr_apply, Equiv.symm_apply_apply] using g.2 (e.symm x)⟩ + invFun g := ⟨e.symm.permCongr g.1, by + intro x + simpa only [Function.comp_apply, Equiv.permCongr_apply, Equiv.symm_symm, + Equiv.symm_apply_apply] using g.2 (e x)⟩ + left_inv g := by apply Subtype.ext; exact e.permCongr.symm_apply_apply g.1 + right_inv g := by apply Subtype.ext; exact e.permCongr.apply_symm_apply g.1 + map_mul' g t := by apply Subtype.ext; exact e.permCongrHom.map_mul g.1 t.1 + +end Relabelling + +section Transfer +variable {G H V : Type*} [Group G] [Group H] [AddCommGroup V] [Module ℂ V] + +def commutantOfComp (ρ : Representation ℂ G V) (e : H ≃* G) : + Representation.IntertwiningMap (ρ.comp e.toMonoidHom) (ρ.comp e.toMonoidHom) →ₗ[ℂ] + Representation.IntertwiningMap ρ ρ where + toFun T := + { toLinearMap := T.toLinearMap + isIntertwining' g := by simpa using T.isIntertwining' (e.symm g) } + map_add' A B := rfl + map_smul' z A := rfl + +lemma commutantOfComp_injective (ρ : Representation ℂ G V) (e : H ≃* G) : + Function.Injective (commutantOfComp ρ e) := by + intro T U he + exact Representation.IntertwiningMap.ext + (congrArg (fun T : Representation.IntertwiningMap ρ ρ => T.toLinearMap) he) + +lemma commutant_comp_finrank_le [FiniteDimensional ℂ V] + (ρ : Representation ℂ G V) (e : H ≃* G) : + Module.finrank ℂ (Representation.IntertwiningMap (ρ.comp e.toMonoidHom) (ρ.comp e.toMonoidHom)) ≤ + Module.finrank ℂ (Representation.IntertwiningMap ρ ρ) := + LinearMap.finrank_le_finrank_of_injective (commutantOfComp_injective ρ e) +end Transfer + +section HookMultiplicity +variable {S L : Type*} [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] + (f : S → L) (a : YoungDiagram) (e : S ≃ Cell a) (h : ℕ) (H : InHook a h) + +abbrev hookLineTarget := + (Signed.lineRepresentation (odd := HookModel.IsOdd (h := h)) + (k := HookModel.oddCount a h H) (f ∘ e.symm)).comp (lineGroupCongr e f).toMonoidHom + +def hookLineEmbedding : Representation.IntertwiningMap + ((relabelledUnitary a e).comp (lineGroup f).subtype) (hookLineTarget f a e h H) where + toLinearMap := (HookModel.hookEmbedding a h H).toLinearMap.comp (spaceHilbertEquiv a).symm.toLinearMap + isIntertwining' g := by + apply LinearMap.ext + intro v + let T := (HookModel.hookEmbedding a h H).comp (unitaryEquiv a).symm.toIntertwiningMap + exact Representation.IntertwiningMap.isIntertwining _ _ T (e.permCongr g.1) v + +omit [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] in +lemma hookLineEmbedding_injective : Function.Injective (hookLineEmbedding f a e h H) := + (HookModel.hookEmbedding_injective a h H).comp (spaceHilbertEquiv a).symm.injective + +include H + +/-- Polynomial commutant estimate for the actual hook Specht representation +restricted to arbitrary fibres. This is the required first multiplicity bound +for both row and column restrictions in the occupied theorem. -/ +lemma hook_line_commutant_bound : + Module.finrank ℂ (Representation.IntertwiningMap + ((relabelledUnitary a e).comp (lineGroup f).subtype) + ((relabelledUnitary a e).comp (lineGroup f).subtype)) ≤ + (Fintype.card S + 1) ^ (4 * Fintype.card L * h ^ 2) := by + apply (commutant_finrank_le_of_embedding (hookLineEmbedding f a e h H) + (hookLineEmbedding_injective f a e h H)).trans + apply (commutant_comp_finrank_le _ (lineGroupCongr e f)).trans + have hc := Signed.commutant_dimension_bound (odd := HookModel.IsOdd (h := h)) + (k := HookModel.oddCount a h H) (f ∘ e.symm) + have hs : Fintype.card (Cell a) = Fintype.card S := (Fintype.card_congr e).symm + simpa only [hs, HookModel.Color, Fintype.card_sum, Fintype.card_fin, + show Fintype.card L * (h + h) ^ 2 = 4 * Fintype.card L * h ^ 2 by ring] using hc + +lemma hook_line_copy_count {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] + [FiniteDimensional ℂ V] [Nontrivial V] (ρ : Representation ℂ (lineGroup f) V) + (hρ : IsUnitary ρ) {u : ℕ} (I : Fin u → V →ₗᵢ[ℂ] hilbertSpace a) + (hI : CompleteCopies (V := V) (W := hilbertSpace a) ρ ((relabelledUnitary a e).comp (lineGroup f).subtype) I) : + u ≤ (Fintype.card S + 1) ^ (4 * Fintype.card L * h ^ 2) := + (copy_count_le_commutant (V := V) (X := hilbertSpace a) I hI.1 hρ (fun g => relabelledUnitary_unitary a e g.1) hI.2.1).trans + (hook_line_commutant_bound f a e h H) + +end HookMultiplicity +end RowColumn + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/Occupied.lean b/lean/OAI/RepresentationTheory/RowColumn/Occupied.lean index 0f2c650f793ac7f1e342b02f7b10575765c1f023..7b41eed0aa70dbcf9031332a63e1b5114384bba0 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/Occupied.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/Occupied.lean @@ -1,277 +1,277 @@ -import OAI.RepresentationTheory.RowColumn.OverlapBound -import OAI.Probability.CubeShuffle.FourierBound - -namespace OAI - -section - -noncomputable section -open scoped BigOperators Classical -namespace RowColumn - -/-- Absorption of the exact polynomial loss into the absolute occupied-board -constant. This is used for both halves of the min. -/ -lemma occupied_numeric_absorb (m n h s : ℕ) (hh : 1 ≤ h) (hs : s ≤ m*n) : - 16 * ((s : ℝ)+1)^((16*(m+n)+8)*h^2) * Real.exp ((m*n-s : ℕ) : ℝ) ≤ - Real.exp (128 * (((m+n+1 : ℕ) : ℝ)*(h : ℝ)^2 * Real.log ((m*n : ℕ)+2) + - (m*n-s : ℕ))) := by - let N : ℝ := (m*n : ℕ)+2 - let E : ℕ := (16*(m+n)+8)*h^2 - have hN : 2 ≤ N := by dsimp [N]; have := (Nat.cast_nonneg (m*n) : (0 : ℝ) ≤ (m*n : ℕ)); linarith - have hNp : 0 < N := lt_of_lt_of_le (by norm_num) hN - have hb : 0 ≤ (s : ℝ)+1 := by positivity - have hbs : (s : ℝ)+1 ≤ N := by dsimp [N]; exact_mod_cast (by omega : s+1 ≤ m*n+2) - have h16 : (16 : ℝ) ≤ N^4 := by - calc 16 = (2 : ℝ)^4 := by norm_num - _ ≤ N^4 := pow_le_pow_left₀ (by norm_num) hN _ - have hp : 16 * ((s : ℝ)+1)^E ≤ N^(E+4) := by - calc _ ≤ N^4 * N^E := mul_le_mul h16 (pow_le_pow_left₀ hb hbs _) (by positivity) (by positivity) - _ = N^(E+4) := by rw [pow_add]; ring - have hh2 : (1 : ℝ) ≤ (h : ℝ)^2 := by exact_mod_cast (Nat.one_le_pow 2 h hh) - have he : ((E+4 : ℕ) : ℝ) ≤ 128*((m+n+1 : ℕ) : ℝ)*(h : ℝ)^2 := by - dsimp [E] - push_cast - nlinarith [sq_nonneg (h : ℝ), mul_nonneg (show 0 ≤ (m:ℝ)+(n:ℝ) by positivity) (sq_nonneg (h:ℝ))] - have hl : 0 ≤ Real.log N := Real.log_nonneg (by linarith) - have ht : (0 : ℝ) ≤ (m*n-s : ℕ) := Nat.cast_nonneg _ - have hexp : N^(E+4) = Real.exp (((E+4 : ℕ) : ℝ)*Real.log N) := by - rw [Real.exp_nat_mul, Real.exp_log hNp] - change 16 * ((s : ℝ)+1)^E * Real.exp ((m*n-s : ℕ) : ℝ) ≤ _ - calc - _ ≤ N^(E+4) * Real.exp ((m*n-s : ℕ) : ℝ) := mul_le_mul_of_nonneg_right hp (Real.exp_pos _).le - _ = Real.exp (((E+4 : ℕ) : ℝ)*Real.log N + (m*n-s : ℕ)) := by rw [hexp, Real.exp_add] - _ ≤ _ := by - apply Real.exp_le_exp.mpr - change ((E+4 : ℕ) : ℝ)*Real.log N + (m*n-s : ℕ) ≤ - 128 * (((m+n+1 : ℕ) : ℝ)*(h : ℝ)^2 * Real.log N + (m*n-s : ℕ)) - nlinarith [mul_le_mul_of_nonneg_right he hl] - -end RowColumn - -end -end - - -section - -noncomputable section -open scoped BigOperators Classical -namespace RowColumn - -lemma occupied_factor_bound (s m n h u v D : ℕ) (t : ℝ) - (hu : u ≤ (s+1)^(4*m*h^2)) (hv : v ≤ (s+1)^(4*n*h^2)) - (hD : D ≤ (s+1)^(4*h^2)) : - 16 * ((s+1 : ℕ) : ℝ)^(4*m*h^2*3) * ((s+1 : ℕ) : ℝ)^(4*n*h^2*3) * - (D : ℝ)^2 * Real.exp t * u * v ≤ - 16 * ((s : ℝ)+1)^((16*(m+n)+8)*h^2) * Real.exp t := by - have hu' : (u : ℝ) ≤ ((s : ℝ)+1)^(4*m*h^2) := by exact_mod_cast hu - have hv' : (v : ℝ) ≤ ((s : ℝ)+1)^(4*n*h^2) := by exact_mod_cast hv - have hD' : (D : ℝ) ≤ ((s : ℝ)+1)^(4*h^2) := by exact_mod_cast hD - calc - _ ≤ 16 * ((s : ℝ)+1)^(4*m*h^2*3) * ((s : ℝ)+1)^(4*n*h^2*3) * - (((s : ℝ)+1)^(4*h^2))^2 * Real.exp t * ((s : ℝ)+1)^(4*m*h^2) * - ((s : ℝ)+1)^(4*n*h^2) := by - push_cast - gcongr - _ = _ := by - rw [show (16*(m+n)+8)*h^2 = 4*m*h^2*3 + 4*n*h^2*3 + (4*h^2)*2 + 4*m*h^2 + 4*n*h^2 by ring] - simp only [pow_add, pow_mul] - ring - -lemma occupied_count_bound (s m n h u v : ℕ) (t : ℝ) (ht : 0 ≤ t) - (hu : u ≤ (s+1)^(4*m*h^2)) (hv : v ≤ (s+1)^(4*n*h^2)) : - (u : ℝ)*v ≤ 16 * ((s : ℝ)+1)^((16*(m+n)+8)*h^2) * Real.exp t := by - have huv : (u : ℝ)*v ≤ ((s : ℝ)+1)^(4*(m+n)*h^2) := by - have hu' : (u : ℝ) ≤ ((s : ℝ)+1)^(4*m*h^2) := by exact_mod_cast hu - have hv' : (v : ℝ) ≤ ((s : ℝ)+1)^(4*n*h^2) := by exact_mod_cast hv - calc _ ≤ ((s : ℝ)+1)^(4*m*h^2) * ((s : ℝ)+1)^(4*n*h^2) := - mul_le_mul hu' hv' (by positivity) (by positivity) - _ = _ := by rw [← pow_add]; congr 1; ring - have he : 4*(m+n)*h^2 ≤ (16*(m+n)+8)*h^2 := Nat.mul_le_mul_right _ (by omega) - have hb : 1 ≤ (s : ℝ)+1 := by have := Nat.cast_nonneg (α := ℝ) s; linarith - have hp := pow_le_pow_right₀ hb he - have hx : 1 ≤ Real.exp t := Real.one_le_exp_iff.mpr ht - have hbase : 0 ≤ ((s : ℝ)+1)^((16*(m+n)+8)*h^2) := by positivity - calc _ ≤ ((s : ℝ)+1)^((16*(m+n)+8)*h^2) := huv.trans hp - _ ≤ _ := by nlinarith [mul_le_mul_of_nonneg_left hx hbase] - -end RowColumn - -end -end - - -section - -noncomputable section -open scoped BigOperators Classical -namespace RowColumn -open CubeShuffle.Specht Signed MatrixState - -lemma irreducible_nontrivial {G V : Type*} [Group G] [AddCommGroup V] [Module ℂ V] - (ρ : Representation ℂ G V) [Representation.IsIrreducible ρ] : Nontrivial V := by - let := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) ρ.asModule - exact ρ.asModuleEquiv.symm.toEquiv.nontrivial - -lemma empty_hook_dimension_le (a : YoungDiagram) (h : ℕ) (H : InHook a h) - (ha : Fintype.card (Cell a)=0) : Module.finrank ℂ (space a) ≤ 1 := by - have hi := LinearMap.finrank_le_finrank_of_injective (HookModel.hookEmbedding_injective a h H) - change Module.finrank ℂ (space a) ≤ - Module.finrank ℂ (EuclideanSpace ℂ (Words (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H))) at hi - rw [finrank_euclideanSpace] at hi - calc _ ≤ Fintype.card (Words (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H)) := hi - _ ≤ Fintype.card (Cell a → HookModel.Color h) := Fintype.card_subtype_le _ - _ = 1 := by rw [Fintype.card_fun, ha, pow_zero] - -lemma hook_lineCost {S L : Type*} [Fintype S] [Fintype L] (h : ℕ) : - lineCost (S := S) (C := HookModel.Color h) (L := L) = - (Fintype.card S+1)^(4*Fintype.card L*h^2) := by - simp only [lineCost, HookModel.Color, Fintype.card_sum, Fintype.card_fin] - congr 1 - ring - -lemma hook_sectorAlgebra_bound {S : Type*} [Fintype S] [DecidableEq S] (h k : ℕ) : - Module.finrank ℂ (sectorAlgebra (S := S) (HookModel.IsOdd (h := h)) k) ≤ - (Fintype.card S+1)^(4*h^2) := by - have hh := sectorAlgebra_finrank (S := S) (HookModel.IsOdd (h := h)) k - simpa only [HookModel.Color, Fintype.card_sum, Fintype.card_fin, show (h+h)^2=4*h^2 by ring] using hh - -end RowColumn - -end -end - - -section - -noncomputable section -open scoped BigOperators Classical -namespace RowColumn -open CubeShuffle.Specht CubeShuffle.UnitaryFinite Signed MatrixState - -/-- The dimension-ratio half of the occupied main, now for the literal occupied -subset and all prescribed row and column embeddings. -/ -theorem occupied_dimension_ratio (m n : ℕ) (Ω : Finset (Board m n)) [Nonempty Ω] - (a : YoungDiagram) (e : Ω ≃ Cell a) (h : ℕ) (hh : 1 ≤ h) (H : InHook a h) - (r c u v : ℕ) - (ρ : Representation ℂ (rowGroup Ω) (EuclideanSpace ℂ (Fin r))) - (τ : Representation ℂ (columnGroup Ω) (EuclideanSpace ℂ (Fin c))) - (hρ : IsUnitary ρ) (hτ : IsUnitary τ) - (I : Fin u → EuclideanSpace ℂ (Fin r) →ₗᵢ[ℂ] hilbertSpace a) - (J : Fin v → EuclideanSpace ℂ (Fin c) →ₗᵢ[ℂ] hilbertSpace a) - (hI : ∀ i, Intertwines (V := EuclideanSpace ℂ (Fin r)) (W := hilbertSpace a) - ρ ((relabelledUnitary a e).comp (rowGroup Ω).subtype) (I i).toLinearMap) - (hJ : ∀ i, Intertwines (V := EuclideanSpace ℂ (Fin c)) (W := hilbertSpace a) - τ ((relabelledUnitary a e).comp (columnGroup Ω).subtype) (J i).toLinearMap) - (hu : u ≤ (Ω.card+1)^(4*m*h^2)) (hv : v ≤ (Ω.card+1)^(4*n*h^2)) : - allCopyOverlap (V := EuclideanSpace ℂ (Fin r)) (W := EuclideanSpace ℂ (Fin c)) - (X := hilbertSpace a) I J ≤ - (16 * ((Ω.card : ℝ)+1)^((16*(m+n)+8)*h^2) * Real.exp ((m*n-Ω.card : ℕ) : ℝ)) * - ((r : ℝ)*c / Module.finrank ℂ (space a)) := by - let board : Ω ↪ Fin m × Fin n := ⟨Subtype.val, Subtype.val_injective⟩ - let c₀ : HookModel.Color h := Sum.inl ⟨0, by omega⟩ - have ha := actual_copy_overlap_bound (V := EuclideanSpace ℂ (Fin r)) - (W := EuclideanSpace ℂ (Fin c)) board a e h H c₀ ρ τ hρ hτ I J hI hJ - have hc : Fintype.card (Cell a) = Ω.card := (Fintype.card_congr e).symm.trans (Fintype.card_coe Ω) - have hD := hook_sectorAlgebra_bound (S := Cell a) h (HookModel.oddCount a h H) - rw [hc] at hD - let D := Module.finrank ℂ (sectorAlgebra (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H)) - have hp := occupied_factor_bound Ω.card m n h u v D ((m*n-Ω.card : ℕ) : ℝ) hu hv hD - have hratio : 0 ≤ (r : ℝ)*c / (Module.finrank ℂ (space a) : ℝ) := by positivity - have hmul := mul_le_mul_of_nonneg_right hp hratio - simp only [hook_lineCost, hc, Fintype.card_fin, Fintype.card_coe, finrank_euclideanSpace, - Nat.cast_mul, Nat.cast_pow, ← pow_mul] at ha - apply ha.trans - convert hmul using 1; dsimp [D]; ring - -end RowColumn - -end -end - - -section - -noncomputable section -open scoped BigOperators Classical -namespace RowColumn -open CubeShuffle.Specht CubeShuffle.UnitaryFinite Signed MatrixState - -/-- `thm:occupied` (weighted.tex:76–84), including the empty occupied subset, -arbitrary deletion layout and every orthogonal multiplicity copy. The absolute -constant is 128; dimensions, unnormalized trace and operator norm are literal. -/ -theorem occupied_overlap_endpoint : OccupiedOverlapEndpoint := by - refine ⟨128, by norm_num, ?_⟩ - intro m n Ω a e h hh hN H r c u v ρ τ hirρ hirτ hρ hτ I J hI hJ - let : Representation.IsIrreducible ρ := hirρ - let : Representation.IsIrreducible τ := hirτ - let : Nontrivial (EuclideanSpace ℂ (Fin r)) := irreducible_nontrivial ρ - let : Nontrivial (EuclideanSpace ℂ (Fin c)) := irreducible_nontrivial τ - - have hu : u ≤ (Ω.card+1)^(4*m*h^2) := by - simpa only [Fintype.card_coe, Fintype.card_fin] using - hook_line_copy_count (V := EuclideanSpace ℂ (Fin r)) (fun x : Ω => x.1.1) a e h H ρ hρ I hI - have hv : v ≤ (Ω.card+1)^(4*n*h^2) := by - simpa only [Fintype.card_coe, Fintype.card_fin] using - hook_line_copy_count (V := EuclideanSpace ℂ (Fin c)) (fun x : Ω => x.1.2) a e h H τ hτ J hJ - - let loss : ℝ := 16 * ((Ω.card : ℝ)+1)^((16*(m+n)+8)*h^2) * Real.exp ((m*n-Ω.card : ℕ) : ℝ) - let ratio : ℝ := (r : ℝ)*c / Module.finrank ℂ (space a) - have hloss : 0 ≤ loss := by dsimp [loss]; positivity - have hratio : 0 ≤ ratio := by dsimp [ratio]; positivity - - have hplain : allCopyOverlap (V := EuclideanSpace ℂ (Fin r)) (W := EuclideanSpace ℂ (Fin c)) - (X := hilbertSpace a) I J ≤ loss := - (@allCopyOverlap_le_count (EuclideanSpace ℂ (Fin r)) (EuclideanSpace ℂ (Fin c)) - (hilbertSpace a) inferInstance inferInstance inferInstance - inferInstance inferInstance inferInstance inferInstance inferInstance inferInstance u v I J).trans - (occupied_count_bound Ω.card m n h u v ((m*n-Ω.card : ℕ) : ℝ) (Nat.cast_nonneg _) hu hv) - - have hdim : allCopyOverlap (V := EuclideanSpace ℂ (Fin r)) (W := EuclideanSpace ℂ (Fin c)) - (X := hilbertSpace a) I J ≤ loss * ratio := by - by_cases hΩ : Ω.Nonempty - · obtain ⟨x,hx⟩ := hΩ - let : Nonempty Ω := ⟨⟨x,hx⟩⟩ - exact occupied_dimension_ratio m n Ω a e h hh H r c u v ρ τ hρ hτ I J hI.1 hJ.1 hu hv - · have hempty : Ω=∅ := Finset.not_nonempty_iff_eq_empty.mp hΩ - have ha : Fintype.card (Cell a)=0 := by - rw [← Fintype.card_congr e, Fintype.card_coe, hempty, Finset.card_empty] - have hd : (Module.finrank ℂ (space a) : ℝ) ≤ 1 := by exact_mod_cast empty_hook_dimension_le a h H ha - have hdpos : (0 : ℝ) < Module.finrank ℂ (space a) := by exact_mod_cast dimension_pos a - have hr : (1 : ℝ) ≤ r := by - have hh : 0 < Module.finrank ℂ (EuclideanSpace ℂ (Fin r)) := Module.finrank_pos - simp only [finrank_euclideanSpace, Fintype.card_fin] at hh - exact_mod_cast hh - have hc : (1 : ℝ) ≤ c := by - have hh : 0 < Module.finrank ℂ (EuclideanSpace ℂ (Fin c)) := Module.finrank_pos - simp only [finrank_euclideanSpace, Fintype.card_fin] at hh - exact_mod_cast hh - have hrc : 1 ≤ ratio := by - dsimp [ratio] - apply (le_div_iff₀ hdpos).mpr - simp only [one_mul] - exact hd.trans (one_le_mul_of_one_le_of_one_le hr hc) - exact hplain.trans (by simpa using mul_le_mul_of_nonneg_left hrc hloss) - - have hmin : allCopyOverlap (V := EuclideanSpace ℂ (Fin r)) (W := EuclideanSpace ℂ (Fin c)) - (X := hilbertSpace a) I J ≤ loss * min 1 ratio := by - by_cases hx : ratio ≤ 1 - · rw [min_eq_right hx]; exact hdim - · rw [min_eq_left (le_of_not_ge hx), mul_one]; exact hplain - - have hs : Ω.card ≤ m*n := by - simpa only [Fintype.card_prod, Fintype.card_fin] using Finset.card_le_univ Ω - have hbound := occupied_numeric_absorb m n h Ω.card hh hs - - exact hmin.trans (mul_le_mul_of_nonneg_right hbound (le_min (by norm_num) hratio)) - -end RowColumn - -end -end - -/-- The occupied row-column overlap bound. -/ -theorem RowColumn.occupied_overlap : RowColumn.OccupiedOverlapEndpoint := - RowColumn.occupied_overlap_endpoint - -end OAI +import OAI.RepresentationTheory.RowColumn.OverlapBound +import OAI.Probability.CubeShuffle.FourierBound + +namespace OAI + +section + +noncomputable section +open scoped BigOperators Classical +namespace RowColumn + +/-- Absorption of the exact polynomial loss into the absolute occupied-board +constant. This is used for both halves of the min. -/ +lemma occupied_numeric_absorb (m n h s : ℕ) (hh : 1 ≤ h) (hs : s ≤ m*n) : + 16 * ((s : ℝ)+1)^((16*(m+n)+8)*h^2) * Real.exp ((m*n-s : ℕ) : ℝ) ≤ + Real.exp (128 * (((m+n+1 : ℕ) : ℝ)*(h : ℝ)^2 * Real.log ((m*n : ℕ)+2) + + (m*n-s : ℕ))) := by + let N : ℝ := (m*n : ℕ)+2 + let E : ℕ := (16*(m+n)+8)*h^2 + have hN : 2 ≤ N := by dsimp [N]; have := (Nat.cast_nonneg (m*n) : (0 : ℝ) ≤ (m*n : ℕ)); linarith + have hNp : 0 < N := lt_of_lt_of_le (by norm_num) hN + have hb : 0 ≤ (s : ℝ)+1 := by positivity + have hbs : (s : ℝ)+1 ≤ N := by dsimp [N]; exact_mod_cast (by omega : s+1 ≤ m*n+2) + have h16 : (16 : ℝ) ≤ N^4 := by + calc 16 = (2 : ℝ)^4 := by norm_num + _ ≤ N^4 := pow_le_pow_left₀ (by norm_num) hN _ + have hp : 16 * ((s : ℝ)+1)^E ≤ N^(E+4) := by + calc _ ≤ N^4 * N^E := mul_le_mul h16 (pow_le_pow_left₀ hb hbs _) (by positivity) (by positivity) + _ = N^(E+4) := by rw [pow_add]; ring + have hh2 : (1 : ℝ) ≤ (h : ℝ)^2 := by exact_mod_cast (Nat.one_le_pow 2 h hh) + have he : ((E+4 : ℕ) : ℝ) ≤ 128*((m+n+1 : ℕ) : ℝ)*(h : ℝ)^2 := by + dsimp [E] + push_cast + nlinarith [sq_nonneg (h : ℝ), mul_nonneg (show 0 ≤ (m:ℝ)+(n:ℝ) by positivity) (sq_nonneg (h:ℝ))] + have hl : 0 ≤ Real.log N := Real.log_nonneg (by linarith) + have ht : (0 : ℝ) ≤ (m*n-s : ℕ) := Nat.cast_nonneg _ + have hexp : N^(E+4) = Real.exp (((E+4 : ℕ) : ℝ)*Real.log N) := by + rw [Real.exp_nat_mul, Real.exp_log hNp] + change 16 * ((s : ℝ)+1)^E * Real.exp ((m*n-s : ℕ) : ℝ) ≤ _ + calc + _ ≤ N^(E+4) * Real.exp ((m*n-s : ℕ) : ℝ) := mul_le_mul_of_nonneg_right hp (Real.exp_pos _).le + _ = Real.exp (((E+4 : ℕ) : ℝ)*Real.log N + (m*n-s : ℕ)) := by rw [hexp, Real.exp_add] + _ ≤ _ := by + apply Real.exp_le_exp.mpr + change ((E+4 : ℕ) : ℝ)*Real.log N + (m*n-s : ℕ) ≤ + 128 * (((m+n+1 : ℕ) : ℝ)*(h : ℝ)^2 * Real.log N + (m*n-s : ℕ)) + nlinarith [mul_le_mul_of_nonneg_right he hl] + +end RowColumn + +end +end + + +section + +noncomputable section +open scoped BigOperators Classical +namespace RowColumn + +lemma occupied_factor_bound (s m n h u v D : ℕ) (t : ℝ) + (hu : u ≤ (s+1)^(4*m*h^2)) (hv : v ≤ (s+1)^(4*n*h^2)) + (hD : D ≤ (s+1)^(4*h^2)) : + 16 * ((s+1 : ℕ) : ℝ)^(4*m*h^2*3) * ((s+1 : ℕ) : ℝ)^(4*n*h^2*3) * + (D : ℝ)^2 * Real.exp t * u * v ≤ + 16 * ((s : ℝ)+1)^((16*(m+n)+8)*h^2) * Real.exp t := by + have hu' : (u : ℝ) ≤ ((s : ℝ)+1)^(4*m*h^2) := by exact_mod_cast hu + have hv' : (v : ℝ) ≤ ((s : ℝ)+1)^(4*n*h^2) := by exact_mod_cast hv + have hD' : (D : ℝ) ≤ ((s : ℝ)+1)^(4*h^2) := by exact_mod_cast hD + calc + _ ≤ 16 * ((s : ℝ)+1)^(4*m*h^2*3) * ((s : ℝ)+1)^(4*n*h^2*3) * + (((s : ℝ)+1)^(4*h^2))^2 * Real.exp t * ((s : ℝ)+1)^(4*m*h^2) * + ((s : ℝ)+1)^(4*n*h^2) := by + push_cast + gcongr + _ = _ := by + rw [show (16*(m+n)+8)*h^2 = 4*m*h^2*3 + 4*n*h^2*3 + (4*h^2)*2 + 4*m*h^2 + 4*n*h^2 by ring] + simp only [pow_add, pow_mul] + ring + +lemma occupied_count_bound (s m n h u v : ℕ) (t : ℝ) (ht : 0 ≤ t) + (hu : u ≤ (s+1)^(4*m*h^2)) (hv : v ≤ (s+1)^(4*n*h^2)) : + (u : ℝ)*v ≤ 16 * ((s : ℝ)+1)^((16*(m+n)+8)*h^2) * Real.exp t := by + have huv : (u : ℝ)*v ≤ ((s : ℝ)+1)^(4*(m+n)*h^2) := by + have hu' : (u : ℝ) ≤ ((s : ℝ)+1)^(4*m*h^2) := by exact_mod_cast hu + have hv' : (v : ℝ) ≤ ((s : ℝ)+1)^(4*n*h^2) := by exact_mod_cast hv + calc _ ≤ ((s : ℝ)+1)^(4*m*h^2) * ((s : ℝ)+1)^(4*n*h^2) := + mul_le_mul hu' hv' (by positivity) (by positivity) + _ = _ := by rw [← pow_add]; congr 1; ring + have he : 4*(m+n)*h^2 ≤ (16*(m+n)+8)*h^2 := Nat.mul_le_mul_right _ (by omega) + have hb : 1 ≤ (s : ℝ)+1 := by have := Nat.cast_nonneg (α := ℝ) s; linarith + have hp := pow_le_pow_right₀ hb he + have hx : 1 ≤ Real.exp t := Real.one_le_exp_iff.mpr ht + have hbase : 0 ≤ ((s : ℝ)+1)^((16*(m+n)+8)*h^2) := by positivity + calc _ ≤ ((s : ℝ)+1)^((16*(m+n)+8)*h^2) := huv.trans hp + _ ≤ _ := by nlinarith [mul_le_mul_of_nonneg_left hx hbase] + +end RowColumn + +end +end + + +section + +noncomputable section +open scoped BigOperators Classical +namespace RowColumn +open CubeShuffle.Specht Signed MatrixState + +lemma irreducible_nontrivial {G V : Type*} [Group G] [AddCommGroup V] [Module ℂ V] + (ρ : Representation ℂ G V) [Representation.IsIrreducible ρ] : Nontrivial V := by + let := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) ρ.asModule + exact ρ.asModuleEquiv.symm.toEquiv.nontrivial + +lemma empty_hook_dimension_le (a : YoungDiagram) (h : ℕ) (H : InHook a h) + (ha : Fintype.card (Cell a)=0) : Module.finrank ℂ (space a) ≤ 1 := by + have hi := LinearMap.finrank_le_finrank_of_injective (HookModel.hookEmbedding_injective a h H) + change Module.finrank ℂ (space a) ≤ + Module.finrank ℂ (EuclideanSpace ℂ (Words (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H))) at hi + rw [finrank_euclideanSpace] at hi + calc _ ≤ Fintype.card (Words (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H)) := hi + _ ≤ Fintype.card (Cell a → HookModel.Color h) := Fintype.card_subtype_le _ + _ = 1 := by rw [Fintype.card_fun, ha, pow_zero] + +lemma hook_lineCost {S L : Type*} [Fintype S] [Fintype L] (h : ℕ) : + lineCost (S := S) (C := HookModel.Color h) (L := L) = + (Fintype.card S+1)^(4*Fintype.card L*h^2) := by + simp only [lineCost, HookModel.Color, Fintype.card_sum, Fintype.card_fin] + congr 1 + ring + +lemma hook_sectorAlgebra_bound {S : Type*} [Fintype S] [DecidableEq S] (h k : ℕ) : + Module.finrank ℂ (sectorAlgebra (S := S) (HookModel.IsOdd (h := h)) k) ≤ + (Fintype.card S+1)^(4*h^2) := by + have hh := sectorAlgebra_finrank (S := S) (HookModel.IsOdd (h := h)) k + simpa only [HookModel.Color, Fintype.card_sum, Fintype.card_fin, show (h+h)^2=4*h^2 by ring] using hh + +end RowColumn + +end +end + + +section + +noncomputable section +open scoped BigOperators Classical +namespace RowColumn +open CubeShuffle.Specht CubeShuffle.UnitaryFinite Signed MatrixState + +/-- The dimension-ratio half of the occupied main, now for the literal occupied +subset and all prescribed row and column embeddings. -/ +theorem occupied_dimension_ratio (m n : ℕ) (Ω : Finset (Board m n)) [Nonempty Ω] + (a : YoungDiagram) (e : Ω ≃ Cell a) (h : ℕ) (hh : 1 ≤ h) (H : InHook a h) + (r c u v : ℕ) + (ρ : Representation ℂ (rowGroup Ω) (EuclideanSpace ℂ (Fin r))) + (τ : Representation ℂ (columnGroup Ω) (EuclideanSpace ℂ (Fin c))) + (hρ : IsUnitary ρ) (hτ : IsUnitary τ) + (I : Fin u → EuclideanSpace ℂ (Fin r) →ₗᵢ[ℂ] hilbertSpace a) + (J : Fin v → EuclideanSpace ℂ (Fin c) →ₗᵢ[ℂ] hilbertSpace a) + (hI : ∀ i, Intertwines (V := EuclideanSpace ℂ (Fin r)) (W := hilbertSpace a) + ρ ((relabelledUnitary a e).comp (rowGroup Ω).subtype) (I i).toLinearMap) + (hJ : ∀ i, Intertwines (V := EuclideanSpace ℂ (Fin c)) (W := hilbertSpace a) + τ ((relabelledUnitary a e).comp (columnGroup Ω).subtype) (J i).toLinearMap) + (hu : u ≤ (Ω.card+1)^(4*m*h^2)) (hv : v ≤ (Ω.card+1)^(4*n*h^2)) : + allCopyOverlap (V := EuclideanSpace ℂ (Fin r)) (W := EuclideanSpace ℂ (Fin c)) + (X := hilbertSpace a) I J ≤ + (16 * ((Ω.card : ℝ)+1)^((16*(m+n)+8)*h^2) * Real.exp ((m*n-Ω.card : ℕ) : ℝ)) * + ((r : ℝ)*c / Module.finrank ℂ (space a)) := by + let board : Ω ↪ Fin m × Fin n := ⟨Subtype.val, Subtype.val_injective⟩ + let c₀ : HookModel.Color h := Sum.inl ⟨0, by omega⟩ + have ha := actual_copy_overlap_bound (V := EuclideanSpace ℂ (Fin r)) + (W := EuclideanSpace ℂ (Fin c)) board a e h H c₀ ρ τ hρ hτ I J hI hJ + have hc : Fintype.card (Cell a) = Ω.card := (Fintype.card_congr e).symm.trans (Fintype.card_coe Ω) + have hD := hook_sectorAlgebra_bound (S := Cell a) h (HookModel.oddCount a h H) + rw [hc] at hD + let D := Module.finrank ℂ (sectorAlgebra (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H)) + have hp := occupied_factor_bound Ω.card m n h u v D ((m*n-Ω.card : ℕ) : ℝ) hu hv hD + have hratio : 0 ≤ (r : ℝ)*c / (Module.finrank ℂ (space a) : ℝ) := by positivity + have hmul := mul_le_mul_of_nonneg_right hp hratio + simp only [hook_lineCost, hc, Fintype.card_fin, Fintype.card_coe, finrank_euclideanSpace, + Nat.cast_mul, Nat.cast_pow, ← pow_mul] at ha + apply ha.trans + convert hmul using 1; dsimp [D]; ring + +end RowColumn + +end +end + + +section + +noncomputable section +open scoped BigOperators Classical +namespace RowColumn +open CubeShuffle.Specht CubeShuffle.UnitaryFinite Signed MatrixState + +/-- `thm:occupied` (weighted.tex:76–84), including the empty occupied subset, +arbitrary deletion layout and every orthogonal multiplicity copy. The absolute +constant is 128; dimensions, unnormalized trace and operator norm are literal. -/ +theorem occupied_overlap_endpoint : OccupiedOverlapEndpoint := by + refine ⟨128, by norm_num, ?_⟩ + intro m n Ω a e h hh hN H r c u v ρ τ hirρ hirτ hρ hτ I J hI hJ + let : Representation.IsIrreducible ρ := hirρ + let : Representation.IsIrreducible τ := hirτ + let : Nontrivial (EuclideanSpace ℂ (Fin r)) := irreducible_nontrivial ρ + let : Nontrivial (EuclideanSpace ℂ (Fin c)) := irreducible_nontrivial τ + + have hu : u ≤ (Ω.card+1)^(4*m*h^2) := by + simpa only [Fintype.card_coe, Fintype.card_fin] using + hook_line_copy_count (V := EuclideanSpace ℂ (Fin r)) (fun x : Ω => x.1.1) a e h H ρ hρ I hI + have hv : v ≤ (Ω.card+1)^(4*n*h^2) := by + simpa only [Fintype.card_coe, Fintype.card_fin] using + hook_line_copy_count (V := EuclideanSpace ℂ (Fin c)) (fun x : Ω => x.1.2) a e h H τ hτ J hJ + + let loss : ℝ := 16 * ((Ω.card : ℝ)+1)^((16*(m+n)+8)*h^2) * Real.exp ((m*n-Ω.card : ℕ) : ℝ) + let ratio : ℝ := (r : ℝ)*c / Module.finrank ℂ (space a) + have hloss : 0 ≤ loss := by dsimp [loss]; positivity + have hratio : 0 ≤ ratio := by dsimp [ratio]; positivity + + have hplain : allCopyOverlap (V := EuclideanSpace ℂ (Fin r)) (W := EuclideanSpace ℂ (Fin c)) + (X := hilbertSpace a) I J ≤ loss := + (@allCopyOverlap_le_count (EuclideanSpace ℂ (Fin r)) (EuclideanSpace ℂ (Fin c)) + (hilbertSpace a) inferInstance inferInstance inferInstance + inferInstance inferInstance inferInstance inferInstance inferInstance inferInstance u v I J).trans + (occupied_count_bound Ω.card m n h u v ((m*n-Ω.card : ℕ) : ℝ) (Nat.cast_nonneg _) hu hv) + + have hdim : allCopyOverlap (V := EuclideanSpace ℂ (Fin r)) (W := EuclideanSpace ℂ (Fin c)) + (X := hilbertSpace a) I J ≤ loss * ratio := by + by_cases hΩ : Ω.Nonempty + · obtain ⟨x,hx⟩ := hΩ + let : Nonempty Ω := ⟨⟨x,hx⟩⟩ + exact occupied_dimension_ratio m n Ω a e h hh H r c u v ρ τ hρ hτ I J hI.1 hJ.1 hu hv + · have hempty : Ω=∅ := Finset.not_nonempty_iff_eq_empty.mp hΩ + have ha : Fintype.card (Cell a)=0 := by + rw [← Fintype.card_congr e, Fintype.card_coe, hempty, Finset.card_empty] + have hd : (Module.finrank ℂ (space a) : ℝ) ≤ 1 := by exact_mod_cast empty_hook_dimension_le a h H ha + have hdpos : (0 : ℝ) < Module.finrank ℂ (space a) := by exact_mod_cast dimension_pos a + have hr : (1 : ℝ) ≤ r := by + have hh : 0 < Module.finrank ℂ (EuclideanSpace ℂ (Fin r)) := Module.finrank_pos + simp only [finrank_euclideanSpace, Fintype.card_fin] at hh + exact_mod_cast hh + have hc : (1 : ℝ) ≤ c := by + have hh : 0 < Module.finrank ℂ (EuclideanSpace ℂ (Fin c)) := Module.finrank_pos + simp only [finrank_euclideanSpace, Fintype.card_fin] at hh + exact_mod_cast hh + have hrc : 1 ≤ ratio := by + dsimp [ratio] + apply (le_div_iff₀ hdpos).mpr + simp only [one_mul] + exact hd.trans (one_le_mul_of_one_le_of_one_le hr hc) + exact hplain.trans (by simpa using mul_le_mul_of_nonneg_left hrc hloss) + + have hmin : allCopyOverlap (V := EuclideanSpace ℂ (Fin r)) (W := EuclideanSpace ℂ (Fin c)) + (X := hilbertSpace a) I J ≤ loss * min 1 ratio := by + by_cases hx : ratio ≤ 1 + · rw [min_eq_right hx]; exact hdim + · rw [min_eq_left (le_of_not_ge hx), mul_one]; exact hplain + + have hs : Ω.card ≤ m*n := by + simpa only [Fintype.card_prod, Fintype.card_fin] using Finset.card_le_univ Ω + have hbound := occupied_numeric_absorb m n h Ω.card hh hs + + exact hmin.trans (mul_le_mul_of_nonneg_right hbound (le_min (by norm_num) hratio)) + +end RowColumn + +end +end + +/-- The occupied row-column overlap bound. -/ +theorem RowColumn.occupied_overlap : RowColumn.OccupiedOverlapEndpoint := + RowColumn.occupied_overlap_endpoint + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/OverlapBound.lean b/lean/OAI/RepresentationTheory/RowColumn/OverlapBound.lean index f8dd648b6939e8088f14c1391382f9c6532ce2f5..4816c802f055824a26f65ee0884239e269ac62e0 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/OverlapBound.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/OverlapBound.lean @@ -1,371 +1,371 @@ -import OAI.RepresentationTheory.RowColumn.Postselection -import OAI.RepresentationTheory.RowColumn.CopyOverlap - -namespace OAI - -section - -noncomputable section -open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder -namespace RowColumn.Signed -open MatrixState -variable {S C L K : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - [Fintype L] [DecidableEq L] [Fintype K] [DecidableEq K] - {odd : C → Prop} [DecidablePred odd] {k : ℕ} - -omit [Fintype L] [DecidableEq L] in -lemma intertwinerMatrix_toCLM (l : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) l) - (lineRepresentation (odd := odd) (k := k) l)) : - Matrix.toEuclideanCLM (𝕜 := ℂ) (intertwinerMatrix l T) = T.toLinearMap.toContinuousLinearMap := - (Matrix.toEuclideanCLM (𝕜 := ℂ)).apply_symm_apply _ - -omit [Fintype L] [DecidableEq L] in -lemma intertwinerMatrix_trace (l : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) l) - (lineRepresentation (odd := odd) (k := k) l)) : - (intertwinerMatrix l T).trace = - LinearMap.trace ℂ (EuclideanSpace ℂ (Words (S := S) odd k)) T.toLinearMap := by - rw [← trace_toEuclideanCLM, intertwinerMatrix_toCLM] - rfl - -omit [Fintype L] [DecidableEq L] [Fintype K] [DecidableEq K] in -lemma intertwinerMatrix_product_trace (l : S → L) (r : S → K) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) l) - (lineRepresentation (odd := odd) (k := k) l)) - (U : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) r) - (lineRepresentation (odd := odd) (k := k) r)) : - (intertwinerMatrix l T * intertwinerMatrix r U).trace = - LinearMap.trace ℂ (EuclideanSpace ℂ (Words (S := S) odd k)) (T.toLinearMap.comp U.toLinearMap) := by - rw [← trace_toEuclideanCLM, map_mul, intertwinerMatrix_toCLM, intertwinerMatrix_toCLM] - rfl - -omit [Fintype L] [DecidableEq L] in -lemma intertwinerMatrix_filtered (l : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) l) - (lineRepresentation (odd := odd) (k := k) l)) - (q : sectorAlgebra (S := S) odd k) - (h : q.val * T.toLinearMap.toContinuousLinearMap=T.toLinearMap.toContinuousLinearMap) : - algebraMatrix (sectorAlgebra (S := S) odd k) q * intertwinerMatrix l T=intertwinerMatrix l T := by - apply (Matrix.toEuclideanCLM (𝕜 := ℂ)).injective - rw [map_mul] - change (Matrix.toEuclideanCLM (𝕜 := ℂ)) (algebraMatrix (sectorAlgebra (S := S) odd k) q) * - (Matrix.toEuclideanCLM (𝕜 := ℂ)) (intertwinerMatrix l T) = - (Matrix.toEuclideanCLM (𝕜 := ℂ)) (intertwinerMatrix l T) - rw [intertwinerMatrix_toCLM] - change (Matrix.toEuclideanCLM (𝕜 := ℂ)) ((Matrix.toEuclideanCLM (𝕜 := ℂ)).symm q.val) * _ = _ - rw [StarAlgEquiv.apply_symm_apply] - exact h - -end RowColumn.Signed - -end -end - - -section - -noncomputable section -open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder -namespace RowColumn.Signed -open MatrixState Postselection WordOrbits -variable {S C L : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - [Fintype L] [DecidableEq L] - -def lineCost : ℕ := (Fintype.card S+1)^(Fintype.card L*Fintype.card C^2) -abbrev MixtureIndex := Types (S := S) (A := L × (C × C)) × Phases (L × (C × C)) (Fintype.card S) - -omit [DecidableEq S] in -lemma phases_card : Fintype.card (Phases (L × (C × C)) (Fintype.card S)) = lineCost (S := S) (C := C) (L := L) := by - simp only [Phases, Fintype.card_fun, ZMod.card, Fintype.card_prod, lineCost, pow_two] -omit [DecidableEq S] in -lemma types_card : Fintype.card (Types (S := S) (A := L × (C × C))) = lineCost (S := S) (C := C) (L := L) := by - simp only [Types, CountIndex, Fintype.card_fun, Fintype.card_fin, Fintype.card_prod, lineCost, pow_two] -omit [DecidableEq S] in -lemma mixtureIndex_card : Fintype.card (MixtureIndex (S := S) (C := C) (L := L)) = lineCost (S := S) (C := C) (L := L)^2 := by - simp only [MixtureIndex, Fintype.card_prod, types_card, phases_card, pow_two] -omit [DecidableEq S] [DecidableEq C] [DecidableEq L] in -lemma lineCost_pos : 0 < lineCost (S := S) (C := C) (L := L) := pow_pos (Nat.succ_pos _) _ - -variable (odd : C → Prop) [DecidablePred odd] (k : ℕ) - -theorem signed_line_mixture (line : S → L) (a₀ : S → C × C) (hn : 0 < Fintype.card S) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) (hT : T.toLinearMap.IsPositive) : - intertwinerMatrix line T ≤ - ((lineCost (S := S) (C := C) (L := L) : ℝ) * (intertwinerMatrix line T).trace.re) • - ∑ z : MixtureIndex (S := S) (C := C) (L := L), - sectorTensor odd k (fun i => lineState line a₀ odd z.1 z.2 (line i)) := by - have hz : (lineCost (S := S) (C := C) (L := L) : ℝ) ≠ 0 := by exact_mod_cast (Nat.ne_of_gt (lineCost_pos (S := S) (C := C) (L := L))) - have hh := signed_line_postselection odd k line a₀ hn T hT - simp only [lineCost] at hz ⊢ - simpa only [Fintype.card_prod, ← pow_two, phases_card, lineCost, div_self hz, mul_one, - Fintype.sum_prod_type] using hh - -end RowColumn.Signed - -end -end - - -section - -noncomputable section -open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder -namespace RowColumn.MatrixState -variable {I U V : Type*} [Fintype I] [DecidableEq I] [Fintype U] [Fintype V] - -lemma filtered_trace_mono (A B A' B' Q : Matrix I I ℂ) - (hA : A.PosSemidef) (hB : B.PosSemidef) (hA' : A'.PosSemidef) - (hQ : Q.IsHermitian) (hQA : Q*A=A) (hQB : Q*B=B) - (hAA : A ≤ A') (hBB : B ≤ B') : - (A*B).trace.re ≤ (A'*Q*B'*Q).trace.re := by - have hAQ : A*Q=A := by - have hh := congrArg Matrix.conjTranspose hQA - simpa only [Matrix.conjTranspose_mul,hA.isHermitian.eq,hQ.eq] using hh - have hBQ : B*Q=B := by - have hh := congrArg Matrix.conjTranspose hQB - simpa only [Matrix.conjTranspose_mul,hB.isHermitian.eq,hQ.eq] using hh - have hp : (Q*A'*Q).PosSemidef := by - simpa only [hQ.eq] using hA'.conjTranspose_mul_mul_same Q - calc - _ ≤ (A'*B).trace.re := trace_mul_mono A A' B hAA hB - _ = (B*(Q*A'*Q)).trace.re := by - symm - simp only [← mul_assoc] - rw [hBQ, Matrix.trace_mul_cycle, hQB, Matrix.trace_mul_comm] - _ ≤ (B'*(Q*A'*Q)).trace.re := trace_mul_mono B B' _ hBB hp - _ = _ := by - calc - _ = ((B'*Q)*(A'*Q)).trace.re := by simp only [mul_assoc] - _ = ((A'*Q)*(B'*Q)).trace.re := congrArg Complex.re (Matrix.trace_mul_comm _ _) - _ = _ := by simp only [mul_assoc] - -lemma trace_filtered_smul_sum (a b : ℝ) (S : U → Matrix I I ℂ) (T : V → Matrix I I ℂ) - (Q : Matrix I I ℂ) : - ((a • ∑ i, S i)*Q*(b • ∑ j, T j)*Q).trace.re = - a*b*∑ i, ∑ j, (S i*Q*T j*Q).trace.re := by - simp only [smul_mul_assoc, mul_smul_comm, Finset.sum_mul, Finset.mul_sum, - Matrix.trace_smul, Matrix.trace_sum, Complex.re_sum, Complex.real_smul, - Complex.mul_re, Complex.ofReal_re, Complex.ofReal_im, zero_mul, sub_zero] - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro i _ - apply Finset.sum_congr rfl - intro j _ - ring - -lemma trace_mixture_bound (A B Q : Matrix I I ℂ) - (hA : A.PosSemidef) (hB : B.PosSemidef) (hQ : Q.IsHermitian) - (hQA : Q*A=A) (hQB : Q*B=B) - (S : U → Matrix I I ℂ) (T : V → Matrix I I ℂ) - (hS : ∀ i, (S i).PosSemidef) - (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) - (hAS : A ≤ a • ∑ i, S i) (hBT : B ≤ b • ∑ j, T j) - (z : ℝ) (hz : ∀ i j, (S i*Q*T j*Q).trace.re ≤ z) : - (A*B).trace.re ≤ a*b * ((Fintype.card U : ℝ)*Fintype.card V) * z := by - have hS' : (∑ i, S i).PosSemidef := Matrix.nonneg_iff_posSemidef.mp - (Finset.sum_nonneg fun i _ => (hS i).nonneg) - apply (filtered_trace_mono A B _ _ Q hA hB (hS'.smul ha) - hQ hQA hQB hAS hBT).trans - rw [trace_filtered_smul_sum] - have hh := Finset.sum_le_sum fun i (_ : i ∈ Finset.univ) => - Finset.sum_le_sum fun j (_ : j ∈ Finset.univ) => hz i j - have hh' := mul_le_mul_of_nonneg_left hh (mul_nonneg ha hb) - simpa only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, mul_assoc] using hh' - -end RowColumn.MatrixState - -end -end - - -section - -noncomputable section -open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder -namespace RowColumn.MatrixState -open Signed Postselection WordOrbits FiniteStarAlgebra -variable {S C L K : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - [Fintype L] [DecidableEq L] [Fintype K] [DecidableEq K] [Nonempty S] - -/-- Reconstruction of the occupied overlap for the actual signed row/column -commutants. The two trace factors retain every prescribed copy. -/ -theorem occupied_commutant_trace (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (e : S ↪ L × K) (a₀ : S → C × C) - (A : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) (fun i => (e i).1)) - (lineRepresentation (odd := odd) (k := k) (fun i => (e i).1))) - (B : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) (fun i => (e i).2)) - (lineRepresentation (odd := odd) (k := k) (fun i => (e i).2))) - (hA : A.toLinearMap.IsPositive) (hB : B.toLinearMap.IsPositive) - (q : sectorAlgebra (S := S) odd k) (hqs : star q=q) (hqq : q*q=q) (hqc : ∀ a, q*a=a*q) - (d : ℝ) (hd : 0 (e i).1) A = - intertwinerMatrix (fun i => (e i).1) A) - (hQB : algebraMatrix (sectorAlgebra (S := S) odd k) q * intertwinerMatrix (fun i => (e i).2) B = - intertwinerMatrix (fun i => (e i).2) B) : - (intertwinerMatrix (fun i => (e i).1) A * intertwinerMatrix (fun i => (e i).2) B).trace.re ≤ - 16 * (lineCost (S := S) (C := C) (L := L) : ℝ)^3 * - (lineCost (S := S) (C := C) (L := K) : ℝ)^3 * - (Module.finrank ℂ (sectorAlgebra (S := S) odd k) : ℝ)^2 * - Real.exp ((Fintype.card L * Fintype.card K - Fintype.card S : ℕ) : ℝ) * - (intertwinerMatrix (fun i => (e i).1) A).trace.re * - (intertwinerMatrix (fun i => (e i).2) B).trace.re / d := by - let l := fun i => (e i).1 - let r := fun i => (e i).2 - let M := fun z : MixtureIndex (S := S) (C := C) (L := L) => lineState l a₀ odd z.1 z.2 - let N := fun z : MixtureIndex (S := S) (C := C) (L := K) => lineState r a₀ odd z.1 z.2 - have hM z i : (M z i).PosSemidef := lineState_positive l a₀ odd z.1 z.2 i - have hN z i : (N z i).PosSemidef := lineState_positive r a₀ odd z.1 z.2 i - have heM z i : M z i ∈ evenAlgebra odd := lineState_even l a₀ odd z.1 z.2 i - have heN z i : N z i ∈ evenAlgebra odd := lineState_even r a₀ odd z.1 z.2 i - have htM z i : (M z i).trace.re ≤ 1 := lineState_trace l a₀ odd z.1 z.2 i - have htN z i : (N z i).trace.re ≤ 1 := lineState_trace r a₀ odd z.1 z.2 i - have hAp := intertwinerMatrix_positive l A hA - have hBp := intertwinerMatrix_positive r B hB - have hAS := signed_line_mixture odd k l a₀ Fintype.card_pos A hA - have hBN := signed_line_mixture odd k r a₀ Fintype.card_pos B hB - have hz z w := sector_filtered_trace_bound odd k e q hqs hqq hqc d hd hfilter - (M z) (N w) (hM z) (hN w) (heM z) (heN w) (htM z) (htN w) - have hh := trace_mixture_bound (intertwinerMatrix l A) (intertwinerMatrix r B) - (algebraMatrix (sectorAlgebra (S := S) odd k) q) hAp hBp (algebraMatrix_hermitian _ q hqs) - hQA hQB (fun z => sectorTensor odd k (fun i => M z (l i))) - (fun w => sectorTensor odd k (fun i => N w (r i))) - (fun z => sectorTensor_positive odd k _ (fun i => hM z (l i))) - ((lineCost (S := S) (C := C) (L := L) : ℝ) * (intertwinerMatrix l A).trace.re) - ((lineCost (S := S) (C := C) (L := K) : ℝ) * (intertwinerMatrix r B).trace.re) - (mul_nonneg (Nat.cast_nonneg _) hAp.trace_nonneg.1) - (mul_nonneg (Nat.cast_nonneg _) hBp.trace_nonneg.1) hAS hBN _ hz - apply hh.trans_eq - simp only [mixtureIndex_card, Nat.cast_pow] - ring - -end RowColumn.MatrixState - -end -end - - -section - -noncomputable section -open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder -namespace RowColumn -open CubeShuffle.Specht CubeShuffle.UnitaryFinite Signed MatrixState FiniteStarAlgebra - -variable {S L R V W : Type*} [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] - [Fintype R] [DecidableEq R] [Nonempty S] - [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] - [NormedAddCommGroup W] [InnerProductSpace ℂ W] [FiniteDimensional ℂ W] - -omit [DecidableEq S] in -/-- Actual hook-Specht all-copy overlap, with the concrete polynomial factors -before absorption into the one absolute constant. Orthogonality and completeness -are used later to bound the copy counts, not silently discarded from the main. -/ -theorem actual_copy_overlap_bound (board : S ↪ L × R) - (a : YoungDiagram) (e : S ≃ Cell a) (h : ℕ) (H : InHook a h) (c₀ : HookModel.Color h) - {u v : ℕ} - (ρ : Representation ℂ (lineGroup (fun i => (board i).1)) V) - (τ : Representation ℂ (lineGroup (fun i => (board i).2)) W) - (hρ : IsUnitary ρ) (hτ : IsUnitary τ) - (I : Fin u → V →ₗᵢ[ℂ] hilbertSpace a) (J : Fin v → W →ₗᵢ[ℂ] hilbertSpace a) - (hI : ∀ i, Intertwines (V := V) (W := hilbertSpace a) ρ - ((relabelledUnitary a e).comp (lineGroup (fun i => (board i).1)).subtype) (I i).toLinearMap) - (hJ : ∀ j, Intertwines (V := W) (W := hilbertSpace a) τ - ((relabelledUnitary a e).comp (lineGroup (fun i => (board i).2)).subtype) (J j).toLinearMap) : - allCopyOverlap (V := V) (W := W) (X := hilbertSpace a) I J ≤ - 16 * (lineCost (S := Cell a) (C := HookModel.Color h) (L := L) : ℝ)^3 * - (lineCost (S := Cell a) (C := HookModel.Color h) (L := R) : ℝ)^3 * - (Module.finrank ℂ (sectorAlgebra (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H)) : ℝ)^2 * - Real.exp ((Fintype.card L * Fintype.card R - Fintype.card S : ℕ) : ℝ) * - (u * Module.finrank ℂ V : ℕ) * (v * Module.finrank ℂ W : ℕ) / - Module.finrank ℂ (space a) := by - let : Nonempty (Cell a) := ⟨e (Classical.choice (inferInstance : Nonempty S))⟩ - let := unitaryRepresentation_irreducible a - obtain ⟨K,hK⟩ := exists_hook_isometry a h H - let odd := HookModel.IsOdd (h := h) - let k := HookModel.oddCount a h H - let eb : Cell a ↪ L × R := e.symm.toEmbedding.trans board - let KI := fun i => K.comp (I i) - let KJ := fun j => K.comp (J j) - have hr := hook_copy_projection_intertwines a e h H K hK (fun i => (board i).1) ρ hρ I hI - have hc := hook_copy_projection_intertwines a e h H K hK (fun i => (board i).2) τ hτ J hJ - let A : Representation.IntertwiningMap - (lineRepresentation (odd := odd) (k := k) (fun i => (eb i).1)) - (lineRepresentation (odd := odd) (k := k) (fun i => (eb i).1)) := - { toLinearMap := (copyProjection KI).toLinearMap - isIntertwining' g := by apply LinearMap.ext; intro x; exact hr g x } - let B : Representation.IntertwiningMap - (lineRepresentation (odd := odd) (k := k) (fun i => (eb i).2)) - (lineRepresentation (odd := odd) (k := k) (fun i => (eb i).2)) := - { toLinearMap := (copyProjection KJ).toLinearMap - isIntertwining' g := by apply LinearMap.ext; intro x; exact hc g x } - have hAp : A.toLinearMap.IsPositive := - (ContinuousLinearMap.isPositive_toLinearMap_iff _).mpr (copyProjection_positive KI) - have hBp : B.toLinearMap.IsPositive := - (ContinuousLinearMap.isPositive_toLinearMap_iff _).mpr (copyProjection_positive KJ) - - obtain ⟨q,hqs,hqq,hqc,hq,hfilter⟩ := exists_sector_isotypic_filter - (V := hilbertSpace a) odd k (unitaryRepresentation a) - - rw [finrank_hilbertSpace] at hfilter - have hd : (0 : ℝ) < Module.finrank ℂ (space a) := by - have hdim : 0 < Module.finrank ℂ (space a) := - Submodule.one_le_finrank_iff.mpr (space_ne_bot a) - exact_mod_cast hdim - - have filterCopies := isotypic_filter_copy_projection (G := Equiv.Perm (Cell a)) (V := V) - (E := Sector (S := Cell a) odd k) (X := hilbertSpace a) (unitaryRepresentation a) - (Signed.representation (S := Cell a) (odd := odd) (k := k)) K - have filterCopiesIntertwining := filterCopies hK - have filterCopiesOperator := filterCopiesIntertwining q.val - have filterCopiesCarrier := filterCopiesOperator hq (u := u) - have hKI := filterCopiesCarrier I - have hA : A.toLinearMap.toContinuousLinearMap = copyProjection KI := by - ext x - rfl - have hQA := intertwinerMatrix_filtered (fun i => (eb i).1) A q (by - rw [hA] - exact hKI) - - have filterColumnCopies := isotypic_filter_copy_projection (G := Equiv.Perm (Cell a)) (V := W) - (E := Sector (S := Cell a) odd k) (X := hilbertSpace a) (unitaryRepresentation a) - (Signed.representation (S := Cell a) (odd := odd) (k := k)) K - have filterColumnIntertwining := filterColumnCopies hK - have filterColumnOperator := filterColumnIntertwining q.val - have filterColumnCarrier := filterColumnOperator hq (u := v) - have hKJ := filterColumnCarrier J - have hB : B.toLinearMap.toContinuousLinearMap = copyProjection KJ := by - ext x - rfl - have hQB := intertwinerMatrix_filtered (fun i => (eb i).2) B q (by - rw [hB] - exact hKJ) - - - have hh := occupied_commutant_trace odd k eb (fun _ => (c₀,c₀)) A B hAp hBp - q hqs hqq hqc (Module.finrank ℂ (space a)) hd hfilter hQA hQB - - have hAt : (intertwinerMatrix (fun i => (eb i).1) A).trace = (u * Module.finrank ℂ V : ℕ) := by - rw [intertwinerMatrix_trace] - exact copyProjection_trace KI - have hBt : (intertwinerMatrix (fun i => (eb i).2) B).trace = (v * Module.finrank ℂ W : ℕ) := by - rw [intertwinerMatrix_trace] - exact copyProjection_trace KJ - rw [intertwinerMatrix_product_trace, hAt, hBt] at hh - have hcard : Fintype.card (Cell a)=Fintype.card S := (Fintype.card_congr e).symm - simp only [Complex.natCast_re, hcard] at hh - have hinv := allCopyOverlap_comp_isometry (V := V) (W := W) (X := hilbertSpace a) - (E := Sector (S := Cell a) odd k) I J K - calc _ = allCopyOverlap (V := V) (W := W) (X := Sector (S := Cell a) odd k) KI KJ := hinv.symm - _ ≤ _ := (allCopyOverlap_le_trace (V := V) (W := W) - (X := Sector (S := Cell a) odd k) KI KJ).trans hh - -end RowColumn - -end -end - -end OAI +import OAI.RepresentationTheory.RowColumn.Postselection +import OAI.RepresentationTheory.RowColumn.CopyOverlap + +namespace OAI + +section + +noncomputable section +open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder +namespace RowColumn.Signed +open MatrixState +variable {S C L K : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + [Fintype L] [DecidableEq L] [Fintype K] [DecidableEq K] + {odd : C → Prop} [DecidablePred odd] {k : ℕ} + +omit [Fintype L] [DecidableEq L] in +lemma intertwinerMatrix_toCLM (l : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) l) + (lineRepresentation (odd := odd) (k := k) l)) : + Matrix.toEuclideanCLM (𝕜 := ℂ) (intertwinerMatrix l T) = T.toLinearMap.toContinuousLinearMap := + (Matrix.toEuclideanCLM (𝕜 := ℂ)).apply_symm_apply _ + +omit [Fintype L] [DecidableEq L] in +lemma intertwinerMatrix_trace (l : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) l) + (lineRepresentation (odd := odd) (k := k) l)) : + (intertwinerMatrix l T).trace = + LinearMap.trace ℂ (EuclideanSpace ℂ (Words (S := S) odd k)) T.toLinearMap := by + rw [← trace_toEuclideanCLM, intertwinerMatrix_toCLM] + rfl + +omit [Fintype L] [DecidableEq L] [Fintype K] [DecidableEq K] in +lemma intertwinerMatrix_product_trace (l : S → L) (r : S → K) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) l) + (lineRepresentation (odd := odd) (k := k) l)) + (U : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) r) + (lineRepresentation (odd := odd) (k := k) r)) : + (intertwinerMatrix l T * intertwinerMatrix r U).trace = + LinearMap.trace ℂ (EuclideanSpace ℂ (Words (S := S) odd k)) (T.toLinearMap.comp U.toLinearMap) := by + rw [← trace_toEuclideanCLM, map_mul, intertwinerMatrix_toCLM, intertwinerMatrix_toCLM] + rfl + +omit [Fintype L] [DecidableEq L] in +lemma intertwinerMatrix_filtered (l : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) l) + (lineRepresentation (odd := odd) (k := k) l)) + (q : sectorAlgebra (S := S) odd k) + (h : q.val * T.toLinearMap.toContinuousLinearMap=T.toLinearMap.toContinuousLinearMap) : + algebraMatrix (sectorAlgebra (S := S) odd k) q * intertwinerMatrix l T=intertwinerMatrix l T := by + apply (Matrix.toEuclideanCLM (𝕜 := ℂ)).injective + rw [map_mul] + change (Matrix.toEuclideanCLM (𝕜 := ℂ)) (algebraMatrix (sectorAlgebra (S := S) odd k) q) * + (Matrix.toEuclideanCLM (𝕜 := ℂ)) (intertwinerMatrix l T) = + (Matrix.toEuclideanCLM (𝕜 := ℂ)) (intertwinerMatrix l T) + rw [intertwinerMatrix_toCLM] + change (Matrix.toEuclideanCLM (𝕜 := ℂ)) ((Matrix.toEuclideanCLM (𝕜 := ℂ)).symm q.val) * _ = _ + rw [StarAlgEquiv.apply_symm_apply] + exact h + +end RowColumn.Signed + +end +end + + +section + +noncomputable section +open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder +namespace RowColumn.Signed +open MatrixState Postselection WordOrbits +variable {S C L : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + [Fintype L] [DecidableEq L] + +def lineCost : ℕ := (Fintype.card S+1)^(Fintype.card L*Fintype.card C^2) +abbrev MixtureIndex := Types (S := S) (A := L × (C × C)) × Phases (L × (C × C)) (Fintype.card S) + +omit [DecidableEq S] in +lemma phases_card : Fintype.card (Phases (L × (C × C)) (Fintype.card S)) = lineCost (S := S) (C := C) (L := L) := by + simp only [Phases, Fintype.card_fun, ZMod.card, Fintype.card_prod, lineCost, pow_two] +omit [DecidableEq S] in +lemma types_card : Fintype.card (Types (S := S) (A := L × (C × C))) = lineCost (S := S) (C := C) (L := L) := by + simp only [Types, CountIndex, Fintype.card_fun, Fintype.card_fin, Fintype.card_prod, lineCost, pow_two] +omit [DecidableEq S] in +lemma mixtureIndex_card : Fintype.card (MixtureIndex (S := S) (C := C) (L := L)) = lineCost (S := S) (C := C) (L := L)^2 := by + simp only [MixtureIndex, Fintype.card_prod, types_card, phases_card, pow_two] +omit [DecidableEq S] [DecidableEq C] [DecidableEq L] in +lemma lineCost_pos : 0 < lineCost (S := S) (C := C) (L := L) := pow_pos (Nat.succ_pos _) _ + +variable (odd : C → Prop) [DecidablePred odd] (k : ℕ) + +theorem signed_line_mixture (line : S → L) (a₀ : S → C × C) (hn : 0 < Fintype.card S) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) (hT : T.toLinearMap.IsPositive) : + intertwinerMatrix line T ≤ + ((lineCost (S := S) (C := C) (L := L) : ℝ) * (intertwinerMatrix line T).trace.re) • + ∑ z : MixtureIndex (S := S) (C := C) (L := L), + sectorTensor odd k (fun i => lineState line a₀ odd z.1 z.2 (line i)) := by + have hz : (lineCost (S := S) (C := C) (L := L) : ℝ) ≠ 0 := by exact_mod_cast (Nat.ne_of_gt (lineCost_pos (S := S) (C := C) (L := L))) + have hh := signed_line_postselection odd k line a₀ hn T hT + simp only [lineCost] at hz ⊢ + simpa only [Fintype.card_prod, ← pow_two, phases_card, lineCost, div_self hz, mul_one, + Fintype.sum_prod_type] using hh + +end RowColumn.Signed + +end +end + + +section + +noncomputable section +open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder +namespace RowColumn.MatrixState +variable {I U V : Type*} [Fintype I] [DecidableEq I] [Fintype U] [Fintype V] + +lemma filtered_trace_mono (A B A' B' Q : Matrix I I ℂ) + (hA : A.PosSemidef) (hB : B.PosSemidef) (hA' : A'.PosSemidef) + (hQ : Q.IsHermitian) (hQA : Q*A=A) (hQB : Q*B=B) + (hAA : A ≤ A') (hBB : B ≤ B') : + (A*B).trace.re ≤ (A'*Q*B'*Q).trace.re := by + have hAQ : A*Q=A := by + have hh := congrArg Matrix.conjTranspose hQA + simpa only [Matrix.conjTranspose_mul,hA.isHermitian.eq,hQ.eq] using hh + have hBQ : B*Q=B := by + have hh := congrArg Matrix.conjTranspose hQB + simpa only [Matrix.conjTranspose_mul,hB.isHermitian.eq,hQ.eq] using hh + have hp : (Q*A'*Q).PosSemidef := by + simpa only [hQ.eq] using hA'.conjTranspose_mul_mul_same Q + calc + _ ≤ (A'*B).trace.re := trace_mul_mono A A' B hAA hB + _ = (B*(Q*A'*Q)).trace.re := by + symm + simp only [← mul_assoc] + rw [hBQ, Matrix.trace_mul_cycle, hQB, Matrix.trace_mul_comm] + _ ≤ (B'*(Q*A'*Q)).trace.re := trace_mul_mono B B' _ hBB hp + _ = _ := by + calc + _ = ((B'*Q)*(A'*Q)).trace.re := by simp only [mul_assoc] + _ = ((A'*Q)*(B'*Q)).trace.re := congrArg Complex.re (Matrix.trace_mul_comm _ _) + _ = _ := by simp only [mul_assoc] + +lemma trace_filtered_smul_sum (a b : ℝ) (S : U → Matrix I I ℂ) (T : V → Matrix I I ℂ) + (Q : Matrix I I ℂ) : + ((a • ∑ i, S i)*Q*(b • ∑ j, T j)*Q).trace.re = + a*b*∑ i, ∑ j, (S i*Q*T j*Q).trace.re := by + simp only [smul_mul_assoc, mul_smul_comm, Finset.sum_mul, Finset.mul_sum, + Matrix.trace_smul, Matrix.trace_sum, Complex.re_sum, Complex.real_smul, + Complex.mul_re, Complex.ofReal_re, Complex.ofReal_im, zero_mul, sub_zero] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + ring + +lemma trace_mixture_bound (A B Q : Matrix I I ℂ) + (hA : A.PosSemidef) (hB : B.PosSemidef) (hQ : Q.IsHermitian) + (hQA : Q*A=A) (hQB : Q*B=B) + (S : U → Matrix I I ℂ) (T : V → Matrix I I ℂ) + (hS : ∀ i, (S i).PosSemidef) + (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) + (hAS : A ≤ a • ∑ i, S i) (hBT : B ≤ b • ∑ j, T j) + (z : ℝ) (hz : ∀ i j, (S i*Q*T j*Q).trace.re ≤ z) : + (A*B).trace.re ≤ a*b * ((Fintype.card U : ℝ)*Fintype.card V) * z := by + have hS' : (∑ i, S i).PosSemidef := Matrix.nonneg_iff_posSemidef.mp + (Finset.sum_nonneg fun i _ => (hS i).nonneg) + apply (filtered_trace_mono A B _ _ Q hA hB (hS'.smul ha) + hQ hQA hQB hAS hBT).trans + rw [trace_filtered_smul_sum] + have hh := Finset.sum_le_sum fun i (_ : i ∈ Finset.univ) => + Finset.sum_le_sum fun j (_ : j ∈ Finset.univ) => hz i j + have hh' := mul_le_mul_of_nonneg_left hh (mul_nonneg ha hb) + simpa only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, mul_assoc] using hh' + +end RowColumn.MatrixState + +end +end + + +section + +noncomputable section +open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder +namespace RowColumn.MatrixState +open Signed Postselection WordOrbits FiniteStarAlgebra +variable {S C L K : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + [Fintype L] [DecidableEq L] [Fintype K] [DecidableEq K] [Nonempty S] + +/-- Reconstruction of the occupied overlap for the actual signed row/column +commutants. The two trace factors retain every prescribed copy. -/ +theorem occupied_commutant_trace (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (e : S ↪ L × K) (a₀ : S → C × C) + (A : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) (fun i => (e i).1)) + (lineRepresentation (odd := odd) (k := k) (fun i => (e i).1))) + (B : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) (fun i => (e i).2)) + (lineRepresentation (odd := odd) (k := k) (fun i => (e i).2))) + (hA : A.toLinearMap.IsPositive) (hB : B.toLinearMap.IsPositive) + (q : sectorAlgebra (S := S) odd k) (hqs : star q=q) (hqq : q*q=q) (hqc : ∀ a, q*a=a*q) + (d : ℝ) (hd : 0 (e i).1) A = + intertwinerMatrix (fun i => (e i).1) A) + (hQB : algebraMatrix (sectorAlgebra (S := S) odd k) q * intertwinerMatrix (fun i => (e i).2) B = + intertwinerMatrix (fun i => (e i).2) B) : + (intertwinerMatrix (fun i => (e i).1) A * intertwinerMatrix (fun i => (e i).2) B).trace.re ≤ + 16 * (lineCost (S := S) (C := C) (L := L) : ℝ)^3 * + (lineCost (S := S) (C := C) (L := K) : ℝ)^3 * + (Module.finrank ℂ (sectorAlgebra (S := S) odd k) : ℝ)^2 * + Real.exp ((Fintype.card L * Fintype.card K - Fintype.card S : ℕ) : ℝ) * + (intertwinerMatrix (fun i => (e i).1) A).trace.re * + (intertwinerMatrix (fun i => (e i).2) B).trace.re / d := by + let l := fun i => (e i).1 + let r := fun i => (e i).2 + let M := fun z : MixtureIndex (S := S) (C := C) (L := L) => lineState l a₀ odd z.1 z.2 + let N := fun z : MixtureIndex (S := S) (C := C) (L := K) => lineState r a₀ odd z.1 z.2 + have hM z i : (M z i).PosSemidef := lineState_positive l a₀ odd z.1 z.2 i + have hN z i : (N z i).PosSemidef := lineState_positive r a₀ odd z.1 z.2 i + have heM z i : M z i ∈ evenAlgebra odd := lineState_even l a₀ odd z.1 z.2 i + have heN z i : N z i ∈ evenAlgebra odd := lineState_even r a₀ odd z.1 z.2 i + have htM z i : (M z i).trace.re ≤ 1 := lineState_trace l a₀ odd z.1 z.2 i + have htN z i : (N z i).trace.re ≤ 1 := lineState_trace r a₀ odd z.1 z.2 i + have hAp := intertwinerMatrix_positive l A hA + have hBp := intertwinerMatrix_positive r B hB + have hAS := signed_line_mixture odd k l a₀ Fintype.card_pos A hA + have hBN := signed_line_mixture odd k r a₀ Fintype.card_pos B hB + have hz z w := sector_filtered_trace_bound odd k e q hqs hqq hqc d hd hfilter + (M z) (N w) (hM z) (hN w) (heM z) (heN w) (htM z) (htN w) + have hh := trace_mixture_bound (intertwinerMatrix l A) (intertwinerMatrix r B) + (algebraMatrix (sectorAlgebra (S := S) odd k) q) hAp hBp (algebraMatrix_hermitian _ q hqs) + hQA hQB (fun z => sectorTensor odd k (fun i => M z (l i))) + (fun w => sectorTensor odd k (fun i => N w (r i))) + (fun z => sectorTensor_positive odd k _ (fun i => hM z (l i))) + ((lineCost (S := S) (C := C) (L := L) : ℝ) * (intertwinerMatrix l A).trace.re) + ((lineCost (S := S) (C := C) (L := K) : ℝ) * (intertwinerMatrix r B).trace.re) + (mul_nonneg (Nat.cast_nonneg _) hAp.trace_nonneg.1) + (mul_nonneg (Nat.cast_nonneg _) hBp.trace_nonneg.1) hAS hBN _ hz + apply hh.trans_eq + simp only [mixtureIndex_card, Nat.cast_pow] + ring + +end RowColumn.MatrixState + +end +end + + +section + +noncomputable section +open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder +namespace RowColumn +open CubeShuffle.Specht CubeShuffle.UnitaryFinite Signed MatrixState FiniteStarAlgebra + +variable {S L R V W : Type*} [Fintype S] [DecidableEq S] [Fintype L] [DecidableEq L] + [Fintype R] [DecidableEq R] [Nonempty S] + [NormedAddCommGroup V] [InnerProductSpace ℂ V] [FiniteDimensional ℂ V] + [NormedAddCommGroup W] [InnerProductSpace ℂ W] [FiniteDimensional ℂ W] + +omit [DecidableEq S] in +/-- Actual hook-Specht all-copy overlap, with the concrete polynomial factors +before absorption into the one absolute constant. Orthogonality and completeness +are used later to bound the copy counts, not silently discarded from the main. -/ +theorem actual_copy_overlap_bound (board : S ↪ L × R) + (a : YoungDiagram) (e : S ≃ Cell a) (h : ℕ) (H : InHook a h) (c₀ : HookModel.Color h) + {u v : ℕ} + (ρ : Representation ℂ (lineGroup (fun i => (board i).1)) V) + (τ : Representation ℂ (lineGroup (fun i => (board i).2)) W) + (hρ : IsUnitary ρ) (hτ : IsUnitary τ) + (I : Fin u → V →ₗᵢ[ℂ] hilbertSpace a) (J : Fin v → W →ₗᵢ[ℂ] hilbertSpace a) + (hI : ∀ i, Intertwines (V := V) (W := hilbertSpace a) ρ + ((relabelledUnitary a e).comp (lineGroup (fun i => (board i).1)).subtype) (I i).toLinearMap) + (hJ : ∀ j, Intertwines (V := W) (W := hilbertSpace a) τ + ((relabelledUnitary a e).comp (lineGroup (fun i => (board i).2)).subtype) (J j).toLinearMap) : + allCopyOverlap (V := V) (W := W) (X := hilbertSpace a) I J ≤ + 16 * (lineCost (S := Cell a) (C := HookModel.Color h) (L := L) : ℝ)^3 * + (lineCost (S := Cell a) (C := HookModel.Color h) (L := R) : ℝ)^3 * + (Module.finrank ℂ (sectorAlgebra (S := Cell a) (HookModel.IsOdd (h := h)) (HookModel.oddCount a h H)) : ℝ)^2 * + Real.exp ((Fintype.card L * Fintype.card R - Fintype.card S : ℕ) : ℝ) * + (u * Module.finrank ℂ V : ℕ) * (v * Module.finrank ℂ W : ℕ) / + Module.finrank ℂ (space a) := by + let : Nonempty (Cell a) := ⟨e (Classical.choice (inferInstance : Nonempty S))⟩ + let := unitaryRepresentation_irreducible a + obtain ⟨K,hK⟩ := exists_hook_isometry a h H + let odd := HookModel.IsOdd (h := h) + let k := HookModel.oddCount a h H + let eb : Cell a ↪ L × R := e.symm.toEmbedding.trans board + let KI := fun i => K.comp (I i) + let KJ := fun j => K.comp (J j) + have hr := hook_copy_projection_intertwines a e h H K hK (fun i => (board i).1) ρ hρ I hI + have hc := hook_copy_projection_intertwines a e h H K hK (fun i => (board i).2) τ hτ J hJ + let A : Representation.IntertwiningMap + (lineRepresentation (odd := odd) (k := k) (fun i => (eb i).1)) + (lineRepresentation (odd := odd) (k := k) (fun i => (eb i).1)) := + { toLinearMap := (copyProjection KI).toLinearMap + isIntertwining' g := by apply LinearMap.ext; intro x; exact hr g x } + let B : Representation.IntertwiningMap + (lineRepresentation (odd := odd) (k := k) (fun i => (eb i).2)) + (lineRepresentation (odd := odd) (k := k) (fun i => (eb i).2)) := + { toLinearMap := (copyProjection KJ).toLinearMap + isIntertwining' g := by apply LinearMap.ext; intro x; exact hc g x } + have hAp : A.toLinearMap.IsPositive := + (ContinuousLinearMap.isPositive_toLinearMap_iff _).mpr (copyProjection_positive KI) + have hBp : B.toLinearMap.IsPositive := + (ContinuousLinearMap.isPositive_toLinearMap_iff _).mpr (copyProjection_positive KJ) + + obtain ⟨q,hqs,hqq,hqc,hq,hfilter⟩ := exists_sector_isotypic_filter + (V := hilbertSpace a) odd k (unitaryRepresentation a) + + rw [finrank_hilbertSpace] at hfilter + have hd : (0 : ℝ) < Module.finrank ℂ (space a) := by + have hdim : 0 < Module.finrank ℂ (space a) := + Submodule.one_le_finrank_iff.mpr (space_ne_bot a) + exact_mod_cast hdim + + have filterCopies := isotypic_filter_copy_projection (G := Equiv.Perm (Cell a)) (V := V) + (E := Sector (S := Cell a) odd k) (X := hilbertSpace a) (unitaryRepresentation a) + (Signed.representation (S := Cell a) (odd := odd) (k := k)) K + have filterCopiesIntertwining := filterCopies hK + have filterCopiesOperator := filterCopiesIntertwining q.val + have filterCopiesCarrier := filterCopiesOperator hq (u := u) + have hKI := filterCopiesCarrier I + have hA : A.toLinearMap.toContinuousLinearMap = copyProjection KI := by + ext x + rfl + have hQA := intertwinerMatrix_filtered (fun i => (eb i).1) A q (by + rw [hA] + exact hKI) + + have filterColumnCopies := isotypic_filter_copy_projection (G := Equiv.Perm (Cell a)) (V := W) + (E := Sector (S := Cell a) odd k) (X := hilbertSpace a) (unitaryRepresentation a) + (Signed.representation (S := Cell a) (odd := odd) (k := k)) K + have filterColumnIntertwining := filterColumnCopies hK + have filterColumnOperator := filterColumnIntertwining q.val + have filterColumnCarrier := filterColumnOperator hq (u := v) + have hKJ := filterColumnCarrier J + have hB : B.toLinearMap.toContinuousLinearMap = copyProjection KJ := by + ext x + rfl + have hQB := intertwinerMatrix_filtered (fun i => (eb i).2) B q (by + rw [hB] + exact hKJ) + + + have hh := occupied_commutant_trace odd k eb (fun _ => (c₀,c₀)) A B hAp hBp + q hqs hqq hqc (Module.finrank ℂ (space a)) hd hfilter hQA hQB + + have hAt : (intertwinerMatrix (fun i => (eb i).1) A).trace = (u * Module.finrank ℂ V : ℕ) := by + rw [intertwinerMatrix_trace] + exact copyProjection_trace KI + have hBt : (intertwinerMatrix (fun i => (eb i).2) B).trace = (v * Module.finrank ℂ W : ℕ) := by + rw [intertwinerMatrix_trace] + exact copyProjection_trace KJ + rw [intertwinerMatrix_product_trace, hAt, hBt] at hh + have hcard : Fintype.card (Cell a)=Fintype.card S := (Fintype.card_congr e).symm + simp only [Complex.natCast_re, hcard] at hh + have hinv := allCopyOverlap_comp_isometry (V := V) (W := W) (X := hilbertSpace a) + (E := Sector (S := Cell a) odd k) I J K + calc _ = allCopyOverlap (V := V) (W := W) (X := Sector (S := Cell a) odd k) KI KJ := hinv.symm + _ ≤ _ := (allCopyOverlap_le_trace (V := V) (W := W) + (X := Sector (S := Cell a) odd k) KI KJ).trans hh + +end RowColumn + +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/Postselection.lean b/lean/OAI/RepresentationTheory/RowColumn/Postselection.lean index 85c47d57439157408bf58e1ec02b527546eed27f..5c1d5b9fa77f052dcffc130bad46b2e6f452777c 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/Postselection.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/Postselection.lean @@ -1,410 +1,410 @@ -import OAI.RepresentationTheory.RowColumn.Dephasing -import OAI.RepresentationTheory.RowColumn.TensorFilter - -namespace OAI - -section -noncomputable section -open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder -namespace RowColumn.MatrixState -variable {I J B : Type*} [Fintype I] [Fintype J] [DecidableEq I] [DecidableEq J] - -/-- Rectangular coordinate inclusion for an actual injective index map. -/ -def indexInclusion (e : J ↪ I) : Matrix I J ℂ := fun i j => if i=e j then 1 else 0 - -omit [Fintype J] in -lemma indexInclusion_star_mul (e : J ↪ I) : (indexInclusion e).conjTranspose * indexInclusion e=1 := by - ext i j - simp only [Matrix.mul_apply,Matrix.conjTranspose_apply,indexInclusion,Matrix.one_apply] - simp only [apply_ite,star_one,star_zero] - rw [Finset.sum_eq_single (e i)] - · simp only [ite_true,one_mul,e.injective.eq_iff] - split_ifs <;> rfl - · intro b _ hb - simp [hb] - · simp - -def extendMatrix (e : J ↪ I) (A : Matrix J J ℂ) : Matrix I I ℂ := indexInclusion e * A * (indexInclusion e).conjTranspose - -omit [Fintype I] in -lemma indexInclusion_mul (e : J ↪ I) (A : Matrix J J ℂ) (i j : J) : - (indexInclusion e * A) (e i) j = A i j := by - simp [Matrix.mul_apply,indexInclusion,e.injective.eq_iff] - -omit [Fintype I] in -lemma extendMatrix_apply (e : J ↪ I) (A : Matrix J J ℂ) (i j : J) : - extendMatrix e A (e i) (e j)=A i j := by - simp only [extendMatrix,Matrix.mul_apply,Matrix.conjTranspose_apply,indexInclusion, - apply_ite,star_one,star_zero,e.injective.eq_iff] - simp - -omit [Fintype I] [DecidableEq J] in -lemma extendMatrix_eq_zero_left (e : J ↪ I) (A : Matrix J J ℂ) (i : I) (hi : i ∉ Set.range e) (j : I) : - extendMatrix e A i j=0 := by - have hh : ∀ k, i≠e k := by intro k he; exact hi ⟨k,he.symm⟩ - simp [extendMatrix,Matrix.mul_apply,indexInclusion,hh] - -omit [Fintype I] [DecidableEq J] in -lemma extendMatrix_eq_zero_right (e : J ↪ I) (A : Matrix J J ℂ) (i : I) (j : I) (hj : j ∉ Set.range e) : - extendMatrix e A i j=0 := by - have hh : ∀ k, j≠e k := by intro k he; exact hj ⟨k,he.symm⟩ - simp [extendMatrix,Matrix.mul_apply,indexInclusion,Matrix.conjTranspose_apply,hh] - -omit [DecidableEq J] in -lemma extendMatrix_positive (e : J ↪ I) (A : Matrix J J ℂ) (hA : A.PosSemidef) : - (extendMatrix e A).PosSemidef := hA.mul_mul_conjTranspose_same _ - -lemma extendMatrix_trace (e : J ↪ I) (A : Matrix J J ℂ) : - (extendMatrix e A).trace=A.trace := by - rw [extendMatrix,Matrix.trace_mul_cycle,indexInclusion_star_mul,one_mul] - -variable [Fintype B] [DecidableEq B] -def blockMask (b : I → B) (k : B) : Matrix I I ℂ := Matrix.diagonal (fun i => if b i=k then 1 else 0) -def pinchMatrix (b : I → B) (A : Matrix I I ℂ) : Matrix I I ℂ := ∑ k, blockMask b k * A * blockMask b k - -omit [Fintype I] [Fintype B] in -lemma blockMask_hermitian (b : I → B) (k : B) : (blockMask b k).IsHermitian := by - apply Matrix.isHermitian_diagonal_iff.mpr - intro i - split_ifs <;> simp - -lemma pinchMatrix_apply (b : I → B) (A : Matrix I I ℂ) (i j : I) : - pinchMatrix b A i j = if b i=b j then A i j else 0 := by - simp only [pinchMatrix,Matrix.sum_apply,blockMask,Matrix.diagonal_mul,Matrix.mul_diagonal] - rw [Finset.sum_eq_single (b i)] - · simp only [ite_true,one_mul] - by_cases h : b i=b j - · simp [h] - · simp [h,Ne.symm h] - · intro k _ hk - rw [ite_eq_right (Ne.symm hk),zero_mul,zero_mul] - · simp - -lemma pinchMatrix_positive (b : I → B) (A : Matrix I I ℂ) (hA : A.PosSemidef) : - (pinchMatrix b A).PosSemidef := by - apply Matrix.nonneg_iff_posSemidef.mp - apply Finset.sum_nonneg - intro k _ - have hh := hA.conjTranspose_mul_mul_same (blockMask b k) - rw [(blockMask_hermitian b k).eq] at hh - exact hh.nonneg - -lemma pinchMatrix_trace (b : I → B) (A : Matrix I I ℂ) : (pinchMatrix b A).trace=A.trace := by - unfold Matrix.trace Matrix.diag - simp_rw [pinchMatrix_apply,ite_true] - -lemma pinchMatrix_support (b : I → B) (A : Matrix I I ℂ) (i j : I) (h : b i ≠ b j) : - pinchMatrix b A i j=0 := by rw [pinchMatrix_apply,ite_eq_right h] -end RowColumn.MatrixState - -end -end - - -section - -noncomputable section -open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder -namespace RowColumn.MatrixState -variable {I J : Type*} [Fintype I] [DecidableEq I] [Fintype J] [DecidableEq J] - -lemma quadratic_eq_energy (A : Matrix I I ℂ) (x : I → ℂ) : - quadratic A x = RowColumn.energy (Matrix.toEuclideanLin A) (WithLp.toLp 2 (star x)) := by - unfold quadratic RowColumn.energy - apply congrArg Complex.re - simp only [PiLp.inner_apply, Matrix.toLpLin_apply, RCLike.inner_apply, - Pi.star_apply, starRingEnd_apply, star_star, Matrix.mulVec, dotProduct] - apply Finset.sum_congr rfl - intro i _ - rw [Finset.sum_mul] - apply Finset.sum_congr rfl - intro j _ - ring - -lemma posSemidef_of_quadratic (A : Matrix I I ℂ) (hA : A.IsHermitian) - (h : ∀ x, 0 ≤ quadratic A x) : A.PosSemidef := by - rw [← Matrix.isPositive_toEuclideanLin_iff] - refine ⟨Matrix.isSymmetric_toEuclideanLin_iff.mpr hA, fun x => ?_⟩ - have hh := h (star (WithLp.ofLp x)) - rw [quadratic_eq_energy] at hh - rw [inner_re_symm] - change 0 ≤ (inner ℂ x ((Matrix.toEuclideanLin A) x)).re - simpa only [star_star, WithLp.toLp_ofLp, RowColumn.energy] using hh - -omit [DecidableEq I] in -lemma quadratic_smul (t : ℝ) (A : Matrix I I ℂ) (x : I → ℂ) : - quadratic (t • A) x = t * quadratic A x := by - unfold quadratic - simp only [Matrix.smul_apply, Complex.real_smul, mul_assoc, ← Finset.mul_sum, - Complex.mul_re, Complex.ofReal_re, Complex.ofReal_im, zero_mul, sub_zero] - -omit [DecidableEq I] in -lemma quadratic_sub (A B : Matrix I I ℂ) (x : I → ℂ) : - quadratic (A-B) x = quadratic A x-quadratic B x := by - simp [quadratic, sub_mul, Finset.sum_sub_distrib] - -omit [DecidableEq I] in -lemma quadratic_sum {D : Type*} [Fintype D] (A : D → Matrix I I ℂ) (x : I → ℂ) : - quadratic (∑ d, A d) x = ∑ d, quadratic (A d) x := by - simp only [quadratic, Matrix.sum_apply, Finset.sum_mul, Complex.re_sum] - conv_lhs => arg 2; ext i; rw [Finset.sum_comm] - exact Finset.sum_comm - -lemma le_of_quadratic_le (A B : Matrix I I ℂ) (hA : A.IsHermitian) (hB : B.IsHermitian) - (h : ∀ x, quadratic A x ≤ quadratic B x) : A ≤ B := by - rw [← sub_nonneg, Matrix.nonneg_iff_posSemidef] - exact posSemidef_of_quadratic (B-A) (hB.sub hA) (fun x => by rw [quadratic_sub]; exact sub_nonneg.mpr (h x)) - -lemma quadratic_pinch {B : Type*} [Fintype B] [DecidableEq B] - (b : I → B) (A : Matrix I I ℂ) (x : I → ℂ) : - quadratic (pinchMatrix b A) x = ∑ z : B, quadratic A (fun i => if b i=z then x i else 0) := by - simp only [quadratic, pinchMatrix_apply, Complex.re_sum] - conv_rhs => rw [Finset.sum_comm]; arg 2; ext i; rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro i _ - apply Finset.sum_congr rfl - intro j _ - rw [Finset.sum_eq_single (b i)] - · by_cases h : b i=b j - · simp [h] - · simp [h, Ne.symm h] - · intro z _ hz - simp [Ne.symm hz] - · simp - -end RowColumn.MatrixState - -namespace RowColumn.Signed -open RowColumn.MatrixState CubeShuffle.Specht -variable {S C L : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - [Fintype L] [DecidableEq L] {odd : C → Prop} [DecidablePred odd] {k : ℕ} - -/-- Matrix in the actual orthonormal word basis, with no change of representation. -/ -def intertwinerMatrix (line : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) : - Matrix (Words (S := S) odd k) (Words (S := S) odd k) ℂ := - (Matrix.toEuclideanCLM (𝕜 := ℂ)).symm T.toLinearMap.toContinuousLinearMap - -omit [Fintype L] [DecidableEq L] in -lemma intertwinerMatrix_apply (line : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) (w v : Words (S := S) odd k) : - intertwinerMatrix line T w v=T (wordVector v) w := by - rw [← matrix_wordVector odd k (intertwinerMatrix line T) w v] - simp only [intertwinerMatrix, StarAlgEquiv.apply_symm_apply] - rfl - -omit [Fintype L] [DecidableEq L] in -lemma intertwinerMatrix_positive (line : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) (hT : T.toLinearMap.IsPositive) : - (intertwinerMatrix line T).PosSemidef := by - rw [← toEuclideanCLM_positive_iff] - rw [intertwinerMatrix, StarAlgEquiv.apply_symm_apply, - ← ContinuousLinearMap.isPositive_toLinearMap_iff] - exact hT - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma parityPattern_eq_iff (w v : Words (S := S) odd k) : - parityPattern w=parityPattern v ↔ ∀ i, odd (w.1 i) ↔ odd (v.1 i) := by - simp [parityPattern, funext_iff] - -omit [Fintype L] [DecidableEq L] in -lemma pinch_intertwiner_invariant (line : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) (g : lineGroup line) - (w v : Words (S := S) odd k) : - pinchMatrix parityPattern (intertwinerMatrix line T) (actWord g.1 w) (actWord g.1 v) = - pinchMatrix parityPattern (intertwinerMatrix line T) w v := by - have hp : parityPattern (actWord g.1 w)=parityPattern (actWord g.1 v) ↔ parityPattern w=parityPattern v := by - simp only [parityPattern_eq_iff, actWord_apply] - constructor - · intro h i; simpa using h (g.1 i) - · intro h i; exact h _ - simp only [pinchMatrix_apply, hp] - by_cases h : parityPattern w=parityPattern v - · simp only [h, ite_true, intertwinerMatrix_apply] - have hr := commuting_coefficient_relation line T g w v - rw [oddPerm_parity_congr g.1 w v (parityPattern_eq_iff w v |>.mp h)] at hr - have hs := congrArg (fun z => permSign (oddPerm g.1 v)*z) hr - simpa only [← mul_assoc, permSign_sq, one_mul] using hs - · simp only [h, ite_false] - -omit [DecidableEq L] in -lemma intertwiner_le_pinch (line : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) (hT : T.toLinearMap.IsPositive) : - intertwinerMatrix line T ≤ - (((Fintype.card S+1)^(Fintype.card L*Fintype.card C^2) : ℕ) : ℝ) • - pinchMatrix parityPattern (intertwinerMatrix line T) := by - have hM := intertwinerMatrix_positive line T hT - apply le_of_quadratic_le _ _ hM.isHermitian - ((pinchMatrix_positive parityPattern _ hM).smul (by positivity : (0 : ℝ) ≤ _)).isHermitian - intro x - rw [quadratic_smul, quadratic_pinch] - simp only [quadratic_eq_energy] - have he : Matrix.toEuclideanLin (intertwinerMatrix line T)=T.toLinearMap := by - exact congrArg ContinuousLinearMap.toLinearMap ((Matrix.toEuclideanCLM (𝕜 := ℂ)).apply_symm_apply T.toLinearMap.toContinuousLinearMap) - rw [he] - convert line_signed_parity_dephasing line T hT (WithLp.toLp 2 (star x)) using 1 - congr 1 - apply Finset.sum_congr rfl - intro b _ - congr 1 - ext w - simp only [parityMask, WithLp.ofLp_toLp, Pi.star_apply] - split_ifs <;> simp - -end RowColumn.Signed - -end -end - - -section - -noncomputable section -open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder -namespace RowColumn.MatrixState -variable {I J : Type*} [Fintype I] [DecidableEq I] [Fintype J] [DecidableEq J] - -omit [Fintype I] in -lemma extendMatrix_equiv (e : J ↪ I) (p : Equiv.Perm I) (q : Equiv.Perm J) - (he : ∀ j, p (e j)=e (q j)) (A : Matrix J J ℂ) - (hA : ∀ i j, A (q i) (q j)=A i j) (i j : I) : - extendMatrix e A (p i) (p j)=extendMatrix e A i j := by - have hh (x : I) (hx : x ∉ Set.range e) : p x ∉ Set.range e := by - rintro ⟨k,hk⟩ - apply hx - refine ⟨q.symm k, p.injective ?_⟩ - rw [he, Equiv.apply_symm_apply, hk] - by_cases hi : i ∈ Set.range e - · obtain ⟨i,rfl⟩ := hi - by_cases hj : j ∈ Set.range e - · obtain ⟨j,rfl⟩ := hj - rw [he, he, extendMatrix_apply, extendMatrix_apply, hA] - · rw [extendMatrix_eq_zero_right e A _ _ (hh j hj), extendMatrix_eq_zero_right e A _ _ hj] - · rw [extendMatrix_eq_zero_left e A _ (hh i hi), extendMatrix_eq_zero_left e A _ hi] - -omit [Fintype I] [DecidableEq I] [Fintype J] [DecidableEq J] in -lemma submatrix_mono (A B : Matrix I I ℂ) (h : A ≤ B) (e : J → I) : - A.submatrix e e ≤ B.submatrix e e := by - rw [← sub_nonneg, Matrix.nonneg_iff_posSemidef] at h ⊢ - exact h.submatrix e - -end RowColumn.MatrixState - -namespace RowColumn.Signed -open RowColumn.MatrixState RowColumn.Postselection RowColumn.WordOrbits -variable {S C L : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - [Fintype L] [DecidableEq L] (odd : C → Prop) [DecidablePred odd] (k : ℕ) - -def wordInclusion : Words (S := S) odd k ↪ (S → C) := ⟨Subtype.val, Subtype.val_injective⟩ - -def extendedPinch (line : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) : Matrix (S → C) (S → C) ℂ := - extendMatrix (wordInclusion odd k) (pinchMatrix parityPattern (intertwinerMatrix line T)) - -omit [Fintype L] [DecidableEq L] in -lemma extendedPinch_positive (line : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) (hT : T.toLinearMap.IsPositive) : - (extendedPinch odd k line T).PosSemidef := - extendMatrix_positive _ _ (pinchMatrix_positive _ _ (intertwinerMatrix_positive line T hT)) - -omit [Fintype L] [DecidableEq L] in -lemma extendedPinch_trace (line : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) : - (extendedPinch odd k line T).trace = (intertwinerMatrix line T).trace := by - rw [extendedPinch, extendMatrix_trace, pinchMatrix_trace] - -omit [Fintype L] [DecidableEq L] in -lemma extendedPinch_invariant (line : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) (p : Equiv.Perm S) - (hp : ∀ i, line (p i)=line i) (w v : S → C) : - extendedPinch odd k line T (w ∘ p) (v ∘ p)=extendedPinch odd k line T w v := by - let g : lineGroup line := ⟨p⁻¹, (lineGroup line).inv_mem hp⟩ - apply extendMatrix_equiv (wordInclusion odd k) (reindexWord p) (wordsEquiv g.1) - · intro j - ext i - change j.1 (p i) = j.1 ((p⁻¹)⁻¹ i) - rw [inv_inv] - · exact pinch_intertwiner_invariant line T g - -omit [Fintype L] [DecidableEq L] in -lemma extendedPinch_support (line : S → L) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) (w v : S → C) - (h : ¬ ∀ i, odd (w i) ↔ odd (v i)) : extendedPinch odd k line T w v=0 := by - by_cases hw : w ∈ Set.range (wordInclusion (S := S) odd k) - · obtain ⟨w,rfl⟩ := hw - by_cases hv : v ∈ Set.range (wordInclusion (S := S) odd k) - · obtain ⟨v,rfl⟩ := hv - rw [extendedPinch, extendMatrix_apply] - apply pinchMatrix_support - exact fun he => h ((parityPattern_eq_iff w v).mp he) - · exact extendMatrix_eq_zero_right _ _ _ _ hv - · exact extendMatrix_eq_zero_left _ _ _ hw _ - -/-- Finite positive even product-state majorant of the true signed line -commutant. Both parity bandwidth and the local-state normalization are retained. -/ -theorem signed_line_postselection (line : S → L) (a₀ : S → C × C) - (hn : 0 < Fintype.card S) - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) (hT : T.toLinearMap.IsPositive) : - intertwinerMatrix line T ≤ - ((((Fintype.card S+1)^(Fintype.card L*Fintype.card C^2) : ℕ) : ℝ) * - (intertwinerMatrix line T).trace.re * - (((Fintype.card S+1)^(Fintype.card (L × (C × C))) : ℕ) / - (Fintype.card (Phases (L × (C × C)) (Fintype.card S)) : ℝ))) • - (∑ q : Types (S := S) (A := L × (C × C)), - ∑ θ : Phases (L × (C × C)) (Fintype.card S), - sectorTensor odd k (fun i => lineState line a₀ odd q θ (line i))) := by - let A := extendedPinch odd k line T - let B := ∑ q : Types (S := S) (A := L × (C × C)), - ∑ θ : Phases (L × (C × C)) (Fintype.card S), - tensorMatrix (fun i : S => lineState line a₀ odd q θ (line i)) - let t : ℝ := (intertwinerMatrix line T).trace.re * - (((Fintype.card S+1)^(Fintype.card (L × (C × C))) : ℕ) / - (Fintype.card (Phases (L × (C × C)) (Fintype.card S)) : ℝ)) - have hA : A.PosSemidef := extendedPinch_positive odd k line T hT - have ht : 0 ≤ t := mul_nonneg (by - have hh := (intertwinerMatrix_positive line T hT).trace_nonneg - exact hh.1) (by positivity) - have hB : B.PosSemidef := by - apply Matrix.nonneg_iff_posSemidef.mp - apply Finset.sum_nonneg - intro q _ - apply Finset.sum_nonneg - intro θ _ - exact (tensorMatrix_posSemidef _ (fun i => lineState_positive line a₀ odd q θ (line i))).nonneg - have hab : A ≤ t • B := by - apply le_of_quadratic_le _ _ hA.isHermitian (hB.smul ht).isHermitian - intro x - simp only [quadratic_smul, B, quadratic_sum] - have hh := positive_line_postselection line a₀ hn odd A hA - (extendedPinch_invariant odd k line T) (extendedPinch_support odd k line T) x - simpa only [A, extendedPinch_trace, t, mul_assoc] using hh - have hsub := submatrix_mono A (t • B) hab (Subtype.val : Words (S := S) odd k → S → C) - have hleft : A.submatrix Subtype.val Subtype.val=pinchMatrix parityPattern (intertwinerMatrix line T) := by - ext w v - exact extendMatrix_apply (wordInclusion odd k) _ w v - rw [hleft] at hsub - have hs := smul_le_smul_of_nonneg_left hsub - (by positivity : (0 : ℝ) ≤ (((Fintype.card S+1)^(Fintype.card L*Fintype.card C^2) : ℕ) : ℝ)) - apply (intertwiner_le_pinch line T hT).trans - convert hs using 1 - ext w v - simp only [Matrix.smul_apply, Matrix.submatrix_apply, Matrix.sum_apply, B, t, - sectorTensor, smul_smul, mul_assoc] - -end RowColumn.Signed - -end -end - -end OAI +import OAI.RepresentationTheory.RowColumn.Dephasing +import OAI.RepresentationTheory.RowColumn.TensorFilter + +namespace OAI + +section +noncomputable section +open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder +namespace RowColumn.MatrixState +variable {I J B : Type*} [Fintype I] [Fintype J] [DecidableEq I] [DecidableEq J] + +/-- Rectangular coordinate inclusion for an actual injective index map. -/ +def indexInclusion (e : J ↪ I) : Matrix I J ℂ := fun i j => if i=e j then 1 else 0 + +omit [Fintype J] in +lemma indexInclusion_star_mul (e : J ↪ I) : (indexInclusion e).conjTranspose * indexInclusion e=1 := by + ext i j + simp only [Matrix.mul_apply,Matrix.conjTranspose_apply,indexInclusion,Matrix.one_apply] + simp only [apply_ite,star_one,star_zero] + rw [Finset.sum_eq_single (e i)] + · simp only [ite_true,one_mul,e.injective.eq_iff] + split_ifs <;> rfl + · intro b _ hb + simp [hb] + · simp + +def extendMatrix (e : J ↪ I) (A : Matrix J J ℂ) : Matrix I I ℂ := indexInclusion e * A * (indexInclusion e).conjTranspose + +omit [Fintype I] in +lemma indexInclusion_mul (e : J ↪ I) (A : Matrix J J ℂ) (i j : J) : + (indexInclusion e * A) (e i) j = A i j := by + simp [Matrix.mul_apply,indexInclusion,e.injective.eq_iff] + +omit [Fintype I] in +lemma extendMatrix_apply (e : J ↪ I) (A : Matrix J J ℂ) (i j : J) : + extendMatrix e A (e i) (e j)=A i j := by + simp only [extendMatrix,Matrix.mul_apply,Matrix.conjTranspose_apply,indexInclusion, + apply_ite,star_one,star_zero,e.injective.eq_iff] + simp + +omit [Fintype I] [DecidableEq J] in +lemma extendMatrix_eq_zero_left (e : J ↪ I) (A : Matrix J J ℂ) (i : I) (hi : i ∉ Set.range e) (j : I) : + extendMatrix e A i j=0 := by + have hh : ∀ k, i≠e k := by intro k he; exact hi ⟨k,he.symm⟩ + simp [extendMatrix,Matrix.mul_apply,indexInclusion,hh] + +omit [Fintype I] [DecidableEq J] in +lemma extendMatrix_eq_zero_right (e : J ↪ I) (A : Matrix J J ℂ) (i : I) (j : I) (hj : j ∉ Set.range e) : + extendMatrix e A i j=0 := by + have hh : ∀ k, j≠e k := by intro k he; exact hj ⟨k,he.symm⟩ + simp [extendMatrix,Matrix.mul_apply,indexInclusion,Matrix.conjTranspose_apply,hh] + +omit [DecidableEq J] in +lemma extendMatrix_positive (e : J ↪ I) (A : Matrix J J ℂ) (hA : A.PosSemidef) : + (extendMatrix e A).PosSemidef := hA.mul_mul_conjTranspose_same _ + +lemma extendMatrix_trace (e : J ↪ I) (A : Matrix J J ℂ) : + (extendMatrix e A).trace=A.trace := by + rw [extendMatrix,Matrix.trace_mul_cycle,indexInclusion_star_mul,one_mul] + +variable [Fintype B] [DecidableEq B] +def blockMask (b : I → B) (k : B) : Matrix I I ℂ := Matrix.diagonal (fun i => if b i=k then 1 else 0) +def pinchMatrix (b : I → B) (A : Matrix I I ℂ) : Matrix I I ℂ := ∑ k, blockMask b k * A * blockMask b k + +omit [Fintype I] [Fintype B] in +lemma blockMask_hermitian (b : I → B) (k : B) : (blockMask b k).IsHermitian := by + apply Matrix.isHermitian_diagonal_iff.mpr + intro i + split_ifs <;> simp + +lemma pinchMatrix_apply (b : I → B) (A : Matrix I I ℂ) (i j : I) : + pinchMatrix b A i j = if b i=b j then A i j else 0 := by + simp only [pinchMatrix,Matrix.sum_apply,blockMask,Matrix.diagonal_mul,Matrix.mul_diagonal] + rw [Finset.sum_eq_single (b i)] + · simp only [ite_true,one_mul] + by_cases h : b i=b j + · simp [h] + · simp [h,Ne.symm h] + · intro k _ hk + rw [ite_eq_right (Ne.symm hk),zero_mul,zero_mul] + · simp + +lemma pinchMatrix_positive (b : I → B) (A : Matrix I I ℂ) (hA : A.PosSemidef) : + (pinchMatrix b A).PosSemidef := by + apply Matrix.nonneg_iff_posSemidef.mp + apply Finset.sum_nonneg + intro k _ + have hh := hA.conjTranspose_mul_mul_same (blockMask b k) + rw [(blockMask_hermitian b k).eq] at hh + exact hh.nonneg + +lemma pinchMatrix_trace (b : I → B) (A : Matrix I I ℂ) : (pinchMatrix b A).trace=A.trace := by + unfold Matrix.trace Matrix.diag + simp_rw [pinchMatrix_apply,ite_true] + +lemma pinchMatrix_support (b : I → B) (A : Matrix I I ℂ) (i j : I) (h : b i ≠ b j) : + pinchMatrix b A i j=0 := by rw [pinchMatrix_apply,ite_eq_right h] +end RowColumn.MatrixState + +end +end + + +section + +noncomputable section +open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder +namespace RowColumn.MatrixState +variable {I J : Type*} [Fintype I] [DecidableEq I] [Fintype J] [DecidableEq J] + +lemma quadratic_eq_energy (A : Matrix I I ℂ) (x : I → ℂ) : + quadratic A x = RowColumn.energy (Matrix.toEuclideanLin A) (WithLp.toLp 2 (star x)) := by + unfold quadratic RowColumn.energy + apply congrArg Complex.re + simp only [PiLp.inner_apply, Matrix.toLpLin_apply, RCLike.inner_apply, + Pi.star_apply, starRingEnd_apply, star_star, Matrix.mulVec, dotProduct] + apply Finset.sum_congr rfl + intro i _ + rw [Finset.sum_mul] + apply Finset.sum_congr rfl + intro j _ + ring + +lemma posSemidef_of_quadratic (A : Matrix I I ℂ) (hA : A.IsHermitian) + (h : ∀ x, 0 ≤ quadratic A x) : A.PosSemidef := by + rw [← Matrix.isPositive_toEuclideanLin_iff] + refine ⟨Matrix.isSymmetric_toEuclideanLin_iff.mpr hA, fun x => ?_⟩ + have hh := h (star (WithLp.ofLp x)) + rw [quadratic_eq_energy] at hh + rw [inner_re_symm] + change 0 ≤ (inner ℂ x ((Matrix.toEuclideanLin A) x)).re + simpa only [star_star, WithLp.toLp_ofLp, RowColumn.energy] using hh + +omit [DecidableEq I] in +lemma quadratic_smul (t : ℝ) (A : Matrix I I ℂ) (x : I → ℂ) : + quadratic (t • A) x = t * quadratic A x := by + unfold quadratic + simp only [Matrix.smul_apply, Complex.real_smul, mul_assoc, ← Finset.mul_sum, + Complex.mul_re, Complex.ofReal_re, Complex.ofReal_im, zero_mul, sub_zero] + +omit [DecidableEq I] in +lemma quadratic_sub (A B : Matrix I I ℂ) (x : I → ℂ) : + quadratic (A-B) x = quadratic A x-quadratic B x := by + simp [quadratic, sub_mul, Finset.sum_sub_distrib] + +omit [DecidableEq I] in +lemma quadratic_sum {D : Type*} [Fintype D] (A : D → Matrix I I ℂ) (x : I → ℂ) : + quadratic (∑ d, A d) x = ∑ d, quadratic (A d) x := by + simp only [quadratic, Matrix.sum_apply, Finset.sum_mul, Complex.re_sum] + conv_lhs => arg 2; ext i; rw [Finset.sum_comm] + exact Finset.sum_comm + +lemma le_of_quadratic_le (A B : Matrix I I ℂ) (hA : A.IsHermitian) (hB : B.IsHermitian) + (h : ∀ x, quadratic A x ≤ quadratic B x) : A ≤ B := by + rw [← sub_nonneg, Matrix.nonneg_iff_posSemidef] + exact posSemidef_of_quadratic (B-A) (hB.sub hA) (fun x => by rw [quadratic_sub]; exact sub_nonneg.mpr (h x)) + +lemma quadratic_pinch {B : Type*} [Fintype B] [DecidableEq B] + (b : I → B) (A : Matrix I I ℂ) (x : I → ℂ) : + quadratic (pinchMatrix b A) x = ∑ z : B, quadratic A (fun i => if b i=z then x i else 0) := by + simp only [quadratic, pinchMatrix_apply, Complex.re_sum] + conv_rhs => rw [Finset.sum_comm]; arg 2; ext i; rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + rw [Finset.sum_eq_single (b i)] + · by_cases h : b i=b j + · simp [h] + · simp [h, Ne.symm h] + · intro z _ hz + simp [Ne.symm hz] + · simp + +end RowColumn.MatrixState + +namespace RowColumn.Signed +open RowColumn.MatrixState CubeShuffle.Specht +variable {S C L : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + [Fintype L] [DecidableEq L] {odd : C → Prop} [DecidablePred odd] {k : ℕ} + +/-- Matrix in the actual orthonormal word basis, with no change of representation. -/ +def intertwinerMatrix (line : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) : + Matrix (Words (S := S) odd k) (Words (S := S) odd k) ℂ := + (Matrix.toEuclideanCLM (𝕜 := ℂ)).symm T.toLinearMap.toContinuousLinearMap + +omit [Fintype L] [DecidableEq L] in +lemma intertwinerMatrix_apply (line : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) (w v : Words (S := S) odd k) : + intertwinerMatrix line T w v=T (wordVector v) w := by + rw [← matrix_wordVector odd k (intertwinerMatrix line T) w v] + simp only [intertwinerMatrix, StarAlgEquiv.apply_symm_apply] + rfl + +omit [Fintype L] [DecidableEq L] in +lemma intertwinerMatrix_positive (line : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) (hT : T.toLinearMap.IsPositive) : + (intertwinerMatrix line T).PosSemidef := by + rw [← toEuclideanCLM_positive_iff] + rw [intertwinerMatrix, StarAlgEquiv.apply_symm_apply, + ← ContinuousLinearMap.isPositive_toLinearMap_iff] + exact hT + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma parityPattern_eq_iff (w v : Words (S := S) odd k) : + parityPattern w=parityPattern v ↔ ∀ i, odd (w.1 i) ↔ odd (v.1 i) := by + simp [parityPattern, funext_iff] + +omit [Fintype L] [DecidableEq L] in +lemma pinch_intertwiner_invariant (line : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) (g : lineGroup line) + (w v : Words (S := S) odd k) : + pinchMatrix parityPattern (intertwinerMatrix line T) (actWord g.1 w) (actWord g.1 v) = + pinchMatrix parityPattern (intertwinerMatrix line T) w v := by + have hp : parityPattern (actWord g.1 w)=parityPattern (actWord g.1 v) ↔ parityPattern w=parityPattern v := by + simp only [parityPattern_eq_iff, actWord_apply] + constructor + · intro h i; simpa using h (g.1 i) + · intro h i; exact h _ + simp only [pinchMatrix_apply, hp] + by_cases h : parityPattern w=parityPattern v + · simp only [h, ite_true, intertwinerMatrix_apply] + have hr := commuting_coefficient_relation line T g w v + rw [oddPerm_parity_congr g.1 w v (parityPattern_eq_iff w v |>.mp h)] at hr + have hs := congrArg (fun z => permSign (oddPerm g.1 v)*z) hr + simpa only [← mul_assoc, permSign_sq, one_mul] using hs + · simp only [h, ite_false] + +omit [DecidableEq L] in +lemma intertwiner_le_pinch (line : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) (hT : T.toLinearMap.IsPositive) : + intertwinerMatrix line T ≤ + (((Fintype.card S+1)^(Fintype.card L*Fintype.card C^2) : ℕ) : ℝ) • + pinchMatrix parityPattern (intertwinerMatrix line T) := by + have hM := intertwinerMatrix_positive line T hT + apply le_of_quadratic_le _ _ hM.isHermitian + ((pinchMatrix_positive parityPattern _ hM).smul (by positivity : (0 : ℝ) ≤ _)).isHermitian + intro x + rw [quadratic_smul, quadratic_pinch] + simp only [quadratic_eq_energy] + have he : Matrix.toEuclideanLin (intertwinerMatrix line T)=T.toLinearMap := by + exact congrArg ContinuousLinearMap.toLinearMap ((Matrix.toEuclideanCLM (𝕜 := ℂ)).apply_symm_apply T.toLinearMap.toContinuousLinearMap) + rw [he] + convert line_signed_parity_dephasing line T hT (WithLp.toLp 2 (star x)) using 1 + congr 1 + apply Finset.sum_congr rfl + intro b _ + congr 1 + ext w + simp only [parityMask, WithLp.ofLp_toLp, Pi.star_apply] + split_ifs <;> simp + +end RowColumn.Signed + +end +end + + +section + +noncomputable section +open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder +namespace RowColumn.MatrixState +variable {I J : Type*} [Fintype I] [DecidableEq I] [Fintype J] [DecidableEq J] + +omit [Fintype I] in +lemma extendMatrix_equiv (e : J ↪ I) (p : Equiv.Perm I) (q : Equiv.Perm J) + (he : ∀ j, p (e j)=e (q j)) (A : Matrix J J ℂ) + (hA : ∀ i j, A (q i) (q j)=A i j) (i j : I) : + extendMatrix e A (p i) (p j)=extendMatrix e A i j := by + have hh (x : I) (hx : x ∉ Set.range e) : p x ∉ Set.range e := by + rintro ⟨k,hk⟩ + apply hx + refine ⟨q.symm k, p.injective ?_⟩ + rw [he, Equiv.apply_symm_apply, hk] + by_cases hi : i ∈ Set.range e + · obtain ⟨i,rfl⟩ := hi + by_cases hj : j ∈ Set.range e + · obtain ⟨j,rfl⟩ := hj + rw [he, he, extendMatrix_apply, extendMatrix_apply, hA] + · rw [extendMatrix_eq_zero_right e A _ _ (hh j hj), extendMatrix_eq_zero_right e A _ _ hj] + · rw [extendMatrix_eq_zero_left e A _ (hh i hi), extendMatrix_eq_zero_left e A _ hi] + +omit [Fintype I] [DecidableEq I] [Fintype J] [DecidableEq J] in +lemma submatrix_mono (A B : Matrix I I ℂ) (h : A ≤ B) (e : J → I) : + A.submatrix e e ≤ B.submatrix e e := by + rw [← sub_nonneg, Matrix.nonneg_iff_posSemidef] at h ⊢ + exact h.submatrix e + +end RowColumn.MatrixState + +namespace RowColumn.Signed +open RowColumn.MatrixState RowColumn.Postselection RowColumn.WordOrbits +variable {S C L : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + [Fintype L] [DecidableEq L] (odd : C → Prop) [DecidablePred odd] (k : ℕ) + +def wordInclusion : Words (S := S) odd k ↪ (S → C) := ⟨Subtype.val, Subtype.val_injective⟩ + +def extendedPinch (line : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) : Matrix (S → C) (S → C) ℂ := + extendMatrix (wordInclusion odd k) (pinchMatrix parityPattern (intertwinerMatrix line T)) + +omit [Fintype L] [DecidableEq L] in +lemma extendedPinch_positive (line : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) (hT : T.toLinearMap.IsPositive) : + (extendedPinch odd k line T).PosSemidef := + extendMatrix_positive _ _ (pinchMatrix_positive _ _ (intertwinerMatrix_positive line T hT)) + +omit [Fintype L] [DecidableEq L] in +lemma extendedPinch_trace (line : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) : + (extendedPinch odd k line T).trace = (intertwinerMatrix line T).trace := by + rw [extendedPinch, extendMatrix_trace, pinchMatrix_trace] + +omit [Fintype L] [DecidableEq L] in +lemma extendedPinch_invariant (line : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) (p : Equiv.Perm S) + (hp : ∀ i, line (p i)=line i) (w v : S → C) : + extendedPinch odd k line T (w ∘ p) (v ∘ p)=extendedPinch odd k line T w v := by + let g : lineGroup line := ⟨p⁻¹, (lineGroup line).inv_mem hp⟩ + apply extendMatrix_equiv (wordInclusion odd k) (reindexWord p) (wordsEquiv g.1) + · intro j + ext i + change j.1 (p i) = j.1 ((p⁻¹)⁻¹ i) + rw [inv_inv] + · exact pinch_intertwiner_invariant line T g + +omit [Fintype L] [DecidableEq L] in +lemma extendedPinch_support (line : S → L) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) (w v : S → C) + (h : ¬ ∀ i, odd (w i) ↔ odd (v i)) : extendedPinch odd k line T w v=0 := by + by_cases hw : w ∈ Set.range (wordInclusion (S := S) odd k) + · obtain ⟨w,rfl⟩ := hw + by_cases hv : v ∈ Set.range (wordInclusion (S := S) odd k) + · obtain ⟨v,rfl⟩ := hv + rw [extendedPinch, extendMatrix_apply] + apply pinchMatrix_support + exact fun he => h ((parityPattern_eq_iff w v).mp he) + · exact extendMatrix_eq_zero_right _ _ _ _ hv + · exact extendMatrix_eq_zero_left _ _ _ hw _ + +/-- Finite positive even product-state majorant of the true signed line +commutant. Both parity bandwidth and the local-state normalization are retained. -/ +theorem signed_line_postselection (line : S → L) (a₀ : S → C × C) + (hn : 0 < Fintype.card S) + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) (hT : T.toLinearMap.IsPositive) : + intertwinerMatrix line T ≤ + ((((Fintype.card S+1)^(Fintype.card L*Fintype.card C^2) : ℕ) : ℝ) * + (intertwinerMatrix line T).trace.re * + (((Fintype.card S+1)^(Fintype.card (L × (C × C))) : ℕ) / + (Fintype.card (Phases (L × (C × C)) (Fintype.card S)) : ℝ))) • + (∑ q : Types (S := S) (A := L × (C × C)), + ∑ θ : Phases (L × (C × C)) (Fintype.card S), + sectorTensor odd k (fun i => lineState line a₀ odd q θ (line i))) := by + let A := extendedPinch odd k line T + let B := ∑ q : Types (S := S) (A := L × (C × C)), + ∑ θ : Phases (L × (C × C)) (Fintype.card S), + tensorMatrix (fun i : S => lineState line a₀ odd q θ (line i)) + let t : ℝ := (intertwinerMatrix line T).trace.re * + (((Fintype.card S+1)^(Fintype.card (L × (C × C))) : ℕ) / + (Fintype.card (Phases (L × (C × C)) (Fintype.card S)) : ℝ)) + have hA : A.PosSemidef := extendedPinch_positive odd k line T hT + have ht : 0 ≤ t := mul_nonneg (by + have hh := (intertwinerMatrix_positive line T hT).trace_nonneg + exact hh.1) (by positivity) + have hB : B.PosSemidef := by + apply Matrix.nonneg_iff_posSemidef.mp + apply Finset.sum_nonneg + intro q _ + apply Finset.sum_nonneg + intro θ _ + exact (tensorMatrix_posSemidef _ (fun i => lineState_positive line a₀ odd q θ (line i))).nonneg + have hab : A ≤ t • B := by + apply le_of_quadratic_le _ _ hA.isHermitian (hB.smul ht).isHermitian + intro x + simp only [quadratic_smul, B, quadratic_sum] + have hh := positive_line_postselection line a₀ hn odd A hA + (extendedPinch_invariant odd k line T) (extendedPinch_support odd k line T) x + simpa only [A, extendedPinch_trace, t, mul_assoc] using hh + have hsub := submatrix_mono A (t • B) hab (Subtype.val : Words (S := S) odd k → S → C) + have hleft : A.submatrix Subtype.val Subtype.val=pinchMatrix parityPattern (intertwinerMatrix line T) := by + ext w v + exact extendMatrix_apply (wordInclusion odd k) _ w v + rw [hleft] at hsub + have hs := smul_le_smul_of_nonneg_left hsub + (by positivity : (0 : ℝ) ≤ (((Fintype.card S+1)^(Fintype.card L*Fintype.card C^2) : ℕ) : ℝ)) + apply (intertwiner_le_pinch line T hT).trans + convert hs using 1 + ext w v + simp only [Matrix.smul_apply, Matrix.submatrix_apply, Matrix.sum_apply, B, t, + sectorTensor, smul_smul, mul_assoc] + +end RowColumn.Signed + +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/Sectors.lean b/lean/OAI/RepresentationTheory/RowColumn/Sectors.lean index 8a02978001d4d76ee52cd6e64972bc48f7b74842..b9016b4ef2c2a4a9ccadc20a3961dd3324f5b647 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/Sectors.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/Sectors.lean @@ -1,562 +1,562 @@ -import OAI.LinearAlgebra.MatrixState.Postselection -import OAI.RepresentationTheory.FiniteUnitary.Reconstruction -import OAI.RepresentationTheory.RowColumn.SignedWords - -namespace OAI - -section - -noncomputable section -open scoped BigOperators Classical Matrix.Norms.L2Operator MatrixOrder -namespace RowColumn.MatrixState -variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - -def evenAlgebra (odd : C → Prop) : StarSubalgebra ℂ (Matrix C C ℂ) where - carrier := {M | ∀ c d, ¬(odd c ↔ odd d) → M c d=0} - zero_mem' := by intro c d h; rfl - add_mem' := by intro M N hM hN c d h; change M c d + N c d=0; simp only [hM c d h,hN c d h,add_zero] - mul_mem' := by - intro M N hM hN c d h - change (∑ e, M c e * N e d)=0 - apply Finset.sum_eq_zero - intro e _ - change M c e * N e d=0 - by_cases he : odd c ↔ odd e - · rw [hN e d (fun hd => h (he.trans hd)), mul_zero] - · rw [hM c e he, zero_mul] - one_mem' := by - intro c d h - exact Matrix.one_apply_ne (fun he => h (he ▸ Iff.rfl)) - algebraMap_mem' := by - intro z c d h - have hcd : c≠d := fun he => h (he ▸ Iff.rfl) - simp [Algebra.algebraMap_eq_smul_one, hcd] - star_mem' := by - intro M hM c d h - change star (M d c)=0 - rw [hM d c (fun hh => h hh.symm), star_zero] - -lemma evenAlgebra_mem (odd : C → Prop) (M : Matrix C C ℂ) : - M ∈ evenAlgebra odd ↔ ∀ c d, ¬(odd c ↔ odd d) → M c d=0 := Iff.rfl - -omit [DecidableEq S] in -lemma tensorMatrix_even_support (odd : C → Prop) (M : S → Matrix C C ℂ) - (hM : ∀ i, M i ∈ evenAlgebra odd) (w v : S → C) - (h : ¬ ∀ i, odd (w i) ↔ odd (v i)) : tensorMatrix M w v=0 := by - obtain ⟨i,hi⟩ := not_forall.mp h - exact Finset.prod_eq_zero (Finset.mem_univ i) (hM i (w i) (v i) hi) - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma oddCount_eq (odd : C → Prop) [DecidablePred odd] (w v : S → C) - (h : ∀ i, odd (w i) ↔ odd (v i)) : - Fintype.card {i : S // odd (w i)} = Fintype.card {i : S // odd (v i)} := by - exact Fintype.card_congr (Equiv.subtypeEquivRight h) - -def sectorTensor (odd : C → Prop) [DecidablePred odd] (k : ℕ) (M : S → Matrix C C ℂ) : - Matrix (Signed.Words (S := S) odd k) (Signed.Words (S := S) odd k) ℂ := - (tensorMatrix M).submatrix Subtype.val Subtype.val - -lemma sectorTensor_mul (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M N : S → Matrix C C ℂ) (hM : ∀ i, M i ∈ evenAlgebra odd) : - sectorTensor odd k (fun i => M i * N i) = sectorTensor odd k M * sectorTensor odd k N := by - ext w v - change tensorMatrix (fun i => M i*N i) w.1 v.1 = _ - rw [← tensorMatrix_mul] - change (∑ z : S → C, tensorMatrix M w.1 z * tensorMatrix N z v.1) = - ∑ z : Signed.Words (S := S) odd k, tensorMatrix M w.1 z.1 * tensorMatrix N z.1 v.1 - have hz : (∑ z : {z : S → C // ¬ Fintype.card {i : S // odd (z i)}=k}, - tensorMatrix M w.1 z.1 * tensorMatrix N z.1 v.1)=0 := by - apply Finset.sum_eq_zero - intro z _ - rw [tensorMatrix_even_support odd M hM w.1 z.1, zero_mul] - intro hh - exact z.2 ((oddCount_eq odd w.1 z.1 hh).symm.trans w.2) - have he := Fintype.sum_subtype_add_sum_subtype - (fun z : S → C => Fintype.card {i : S // odd (z i)}=k) - (fun z : S → C => tensorMatrix M w.1 z * tensorMatrix N z v.1) - rw [hz, add_zero] at he - exact he.symm - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma sectorTensor_star (odd : C → Prop) [DecidablePred odd] (k : ℕ) (M : S → Matrix C C ℂ) : - sectorTensor odd k (fun i => star (M i)) = star (sectorTensor odd k M) := by - unfold sectorTensor - change (tensorMatrix (fun i => (M i).conjTranspose)).submatrix Subtype.val Subtype.val = _ - rw [← tensorMatrix_star] - rfl - -omit [DecidableEq S] [Fintype C] in -lemma sectorTensor_one (odd : C → Prop) [DecidablePred odd] (k : ℕ) : - sectorTensor odd k (fun _ : S => (1 : Matrix C C ℂ))=1 := by - rw [sectorTensor, tensorMatrix_one] - exact Matrix.submatrix_one Subtype.val Subtype.val_injective - -def sectorPowerHom (odd : C → Prop) [DecidablePred odd] (k : ℕ) : - evenAlgebra odd →⋆* Matrix (Signed.Words (S := S) odd k) (Signed.Words (S := S) odd k) ℂ where - toFun M := sectorTensor odd k (fun _ : S => M.val) - map_one' := sectorTensor_one odd k - map_mul' M _ := sectorTensor_mul odd k _ _ (fun _ => M.property) - map_star' _ := sectorTensor_star odd k _ - -end RowColumn.MatrixState - -noncomputable section -namespace RowColumn.Signed -open scoped Classical -variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - {odd : C → Prop} [DecidablePred odd] {k : ℕ} - -omit [DecidableEq S] in -lemma frame_pred_congr (p q : S → Prop) [dp : DecidablePred p] [dq : DecidablePred q] - (hp : Fintype.card {x : S // p x} = k) - (hq : Fintype.card {x : S // q x} = k) - (he : p = q) (x : S) (hx : p x) (hy : q x) : - Fintype.equivFinOfCardEq hp ⟨x,hx⟩ = Fintype.equivFinOfCardEq hq ⟨x,hy⟩ := by - subst q - have hd : dq = dp := Subsingleton.elim _ _ - subst dq - rfl - -omit [Fintype C] [DecidableEq C] in -omit [DecidableEq S] in -lemma oddFrame_parity_congr (w v : Words (S := S) odd k) - (hp : ∀ x, odd (w.1 x) ↔ odd (v.1 x)) (x : S) - (hx : odd (w.1 x)) (hv : odd (v.1 x)) : - oddFrame w ⟨x,hx⟩ = oddFrame v ⟨x,hv⟩ := by - exact frame_pred_congr _ _ w.2 v.2 (funext fun x => propext (hp x)) x hx hv - -omit [Fintype C] [DecidableEq C] [DecidableEq S] in -lemma oddPerm_parity_congr (g : Equiv.Perm S) (w v : Words (S := S) odd k) - (hp : ∀ x, odd (w.1 x) ↔ odd (v.1 x)) : oddPerm g w = oddPerm g v := by - apply Equiv.ext - intro i - have he : ((oddFrame w).symm i).val = ((oddFrame v).symm i).val := by - have hh := oddFrame_parity_congr w v hp ((oddFrame w).symm i).val - ((oddFrame w).symm i).property ((hp _).mp ((oddFrame w).symm i).property) - rw [Equiv.apply_symm_apply] at hh - have ht := congrArg (fun z => ((oddFrame v).symm z).val) hh - simpa using ht.symm - have ha : ∀ x, odd ((actWord g w).1 x) ↔ odd ((actWord g v).1 x) := fun x => hp _ - change oddFrame (actWord g w) ⟨g ((oddFrame w).symm i).val, _⟩ = - oddFrame (actWord g v) ⟨g ((oddFrame v).symm i).val, _⟩ - have hw : odd ((actWord g w).1 (g ((oddFrame w).symm i).val)) := by - simpa using ((oddFrame w).symm i).property - calc - _ = oddFrame (actWord g v) ⟨g ((oddFrame w).symm i).val, (ha _).mp hw⟩ := - oddFrame_parity_congr _ _ ha _ _ _ - _ = _ := congrArg (oddFrame (actWord g v)) (Subtype.ext (congrArg g he)) -end RowColumn.Signed - -noncomputable section -namespace RowColumn.FiniteStarAlgebra -variable {R A G : Type*} [CommSemiring R] [StarRing R] [Ring A] [Algebra R A] - [StarRing A] [StarModule R A] [Group G] - -def unitarySpan (u : G →* unitary A) : StarSubalgebra R A where - __ := Algebra.adjoin R (Set.range fun g : G => (u g : A)) - star_mem' := by - intro a ha - induction ha using Algebra.adjoin_induction with - | mem a ha => - obtain ⟨g,rfl⟩ := ha - apply Algebra.subset_adjoin - refine ⟨g⁻¹,?_⟩ - change (u g⁻¹ : A) = star (u g : A) - rw [map_inv] - rfl - | algebraMap r => rw [← algebraMap_star_comm]; exact (Algebra.adjoin R _).algebraMap_mem _ - | add a b ha hb iha ihb => rw [star_add]; exact (Algebra.adjoin R _).add_mem iha ihb - | mul a b ha hb iha ihb => rw [star_mul]; exact (Algebra.adjoin R _).mul_mem ihb iha - -lemma unitarySpan_eq_span (u : G →* unitary A) : - (unitarySpan (R := R) u).toSubmodule = Submodule.span R (Set.range fun g : G => (u g : A)) := by - apply Algebra.adjoin_eq_span_of_subset - intro a ha - have hh : a ∈ Set.range (fun g : G => (u g : A)) := by - induction ha using Submonoid.closure_induction with - | mem a ha => exact ha - | one => exact ⟨1,by simp⟩ - | mul a b ha hb iha ihb => - obtain ⟨g,rfl⟩ := iha - obtain ⟨h,rfl⟩ := ihb - exact ⟨g*h,by simp⟩ - exact Submodule.subset_span hh - -lemma unitarySpan_mem (u : G →* unitary A) (g : G) : (u g : A) ∈ unitarySpan (R := R) u := - Algebra.subset_adjoin ⟨g,rfl⟩ - -def unitarySpanHom (u : G →* unitary A) : G →* unitary (unitarySpan (R := R) u) where - toFun g := ⟨⟨(u g : A),unitarySpan_mem u g⟩,by - constructor <;> apply Subtype.ext - · exact (u g).property.1 - · exact (u g).property.2⟩ - map_one' := by apply Subtype.ext; apply Subtype.ext; change (u 1 : A)=1; simp - map_mul' g h := by apply Subtype.ext; apply Subtype.ext; change (u (g*h) : A)=(u g : A)*(u h : A); simp - -lemma unitarySpanHom_spans (u : G →* unitary A) : - Submodule.span R (Set.range fun g : G => (unitarySpanHom (R := R) u g : unitarySpan (R := R) u))=⊤ := by - apply Submodule.map_injective_of_injective (Submodule.subtype_injective (unitarySpan (R := R) u).toSubmodule) - rw [Submodule.map_span, ← Set.range_comp] - change Submodule.span R (Set.range fun g : G => (u g : A)) = - Submodule.map (unitarySpan (R := R) u).toSubmodule.subtype ⊤ - rw [Submodule.map_top, Submodule.range_subtype] - exact (unitarySpan_eq_span u).symm - -end RowColumn.FiniteStarAlgebra - -noncomputable section -open scoped BigOperators Classical Matrix.Norms.L2Operator -open ComplexConjugate -namespace RowColumn.MatrixState - -def discreteContinuousHom (J : Type*) [TopologicalSpace J] [DiscreteTopology J] : - (J → ℂ) →⋆ₐ[ℂ] C(J,ℂ) where - toFun f := ⟨f,continuous_of_discreteTopology⟩ - map_zero' := rfl - map_one' := rfl - map_add' _ _ := rfl - map_mul' _ _ := rfl - commutes' _ := rfl - map_star' _ := rfl - -def precompFunctionHom {J K : Type*} (f : J → K) : (K → ℂ) →⋆ₐ[ℂ] (J → ℂ) where - toFun g := g ∘ f - map_zero' := rfl - map_one' := rfl - map_add' _ _ := rfl - map_mul' _ _ := rfl - commutes' _ := rfl - map_star' _ := rfl - -lemma sum_single_function {J : Type*} [Fintype J] [DecidableEq J] (z : J → ℂ) : - (∑ i : J, z i • (Pi.single i 1 : J → ℂ)) = z := by - ext j - simp [Pi.single_apply] - -lemma function_unitary {J : Type*} (z : J → ℂ) (hz : ∀ i, ‖z i‖=1) : z ∈ unitary (J → ℂ) := by - constructor <;> ext i - · change conj (z i)*z i=1 - rw [Complex.conj_mul', hz i] - norm_num - · change z i*conj (z i)=1 - rw [Complex.mul_conj', hz i] - norm_num - -/-- A genuine finite spectral phase family inside the prescribed closed -star algebra. In the application this is the even one-slot matrix algebra. -/ -theorem exists_spectral_phase_family {C : Type*} [Fintype C] [DecidableEq C] - (M : Matrix C C ℂ) (hM : M.IsHermitian) - (K : StarSubalgebra ℂ (Matrix C C ℂ)) (hK : IsClosed (K : Set (Matrix C C ℂ))) - (hMK : M ∈ K) : - ∃ (d : ℕ) (P : Fin d → Matrix C C ℂ) (z : Fin d → ℂ), - (∑ i, z i • P i) = M ∧ (∀ i, P i ∈ K) ∧ - ∀ θ : Fin d → ℂ, (∀ i, ‖θ i‖=1) → (∑ i, θ i • P i) ∈ unitary (Matrix C C ℂ) := by - have hfin : (spectrum ℂ M).Finite := by - rw [hM.spectrum_eq_image_range] - exact (Set.finite_range hM.eigenvalues).image _ - let J := spectrum ℂ M - let : Fintype J := hfin.fintype - let : DiscreteTopology J := inferInstance - let e : J ≃ Fin (Fintype.card J) := Fintype.equivFin J - let ψ := (cfcHom hM.isSelfAdjoint.isStarNormal (R := ℂ)).comp - ((discreteContinuousHom J).comp (precompFunctionHom e)) - let P (i : Fin (Fintype.card J)) : Matrix C C ℂ := ψ (Pi.single i 1) - let z (i : Fin (Fintype.card J)) : ℂ := (e.symm i).val - have hsum (f : Fin (Fintype.card J) → ℂ) : ∑ i, f i • P i = ψ f := by - simp only [P, ← map_smul, ← map_sum, sum_single_function] - refine ⟨Fintype.card J,P,z,?_,?_,?_⟩ - · rw [hsum] - have he : ((discreteContinuousHom J).comp (precompFunctionHom e)) z = - (ContinuousMap.id ℂ).restrict (spectrum ℂ M) := by - ext j - exact congrArg Subtype.val (e.symm_apply_apply j) - change cfcHom hM.isSelfAdjoint.isStarNormal (((discreteContinuousHom J).comp (precompFunctionHom e)) z) = M - rw [he] - exact cfcHom_id _ - · intro i - apply StarAlgebra.elemental.le_of_mem hK hMK - exact cfcHom_mem_elemental hM.isSelfAdjoint.isStarNormal _ - · intro θ hθ - rw [hsum] - exact Unitary.map_mem ψ (function_unitary θ hθ) - -end RowColumn.MatrixState - -noncomputable section -open scoped BigOperators Classical -namespace RowColumn.MatrixState -open WordOrbits Postselection -variable {S C J : Type*} [Fintype S] [DecidableEq S] - [Fintype C] [DecidableEq C] [Fintype J] [DecidableEq J] - -omit [Fintype C] [DecidableEq C] [DecidableEq J] in -lemma tensorMatrix_linear_combination (P : J → Matrix C C ℂ) (z : J → ℂ) : - tensorMatrix (fun _ : S => ∑ j, z j • P j) = - ∑ w : S → J, (∏ i, z (w i)) • tensorMatrix (fun i => P (w i)) := by - ext a b - simp only [tensorMatrix, Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul] - rw [Fintype.prod_sum] - apply Finset.sum_congr rfl - intro w _ - exact Finset.prod_mul_distrib - -def typeTensor (P : J → Matrix C C ℂ) (q : Types (S := S) (A := J)) : - Matrix (S → C) (S → C) ℂ := - ∑ w : {w : S → J // counts w = q}, tensorMatrix (fun i => P (w.1 i)) - -omit [Fintype C] [DecidableEq C] in -lemma tensorMatrix_by_type (P : J → Matrix C C ℂ) (z : J → ℂ) : - tensorMatrix (fun _ : S => ∑ j, z j • P j) = - ∑ q : Types (S := S) (A := J), typeAmplitude z q • typeTensor P q := by - rw [tensorMatrix_linear_combination] - simp_rw [prod_by_counts _ z] - change (∑ w : S → J, typeAmplitude z (counts w) • tensorMatrix (fun i => P (w i))) = _ - rw [← Fintype.sum_fiberwise counts (fun w : S → J => - typeAmplitude z (counts w) • tensorMatrix (fun i => P (w i)))] - apply Finset.sum_congr rfl - intro q _ - simp only [show ∀ w : {w : S → J // counts w = q}, counts w.1=q from fun w => w.2] - exact (Finset.smul_sum).symm - -def phaseMatrix (P : J → Matrix C C ℂ) (θ : Phases J (Fintype.card S)) : Matrix C C ℂ := - ∑ j, ZMod.stdAddChar (θ j) • P j - -omit [Fintype C] [DecidableEq C] in -lemma tensorMatrix_phase (P : J → Matrix C C ℂ) (θ : Phases J (Fintype.card S)) : - tensorMatrix (fun _ : S => phaseMatrix P θ) = - ∑ q : Types (S := S) (A := J), countCharacter q θ • typeTensor P q := by - rw [phaseMatrix, tensorMatrix_by_type] - apply Finset.sum_congr rfl - intro q _ - congr 1 - exact (countCharacter_eq_prod q θ).symm - -omit [Fintype C] [DecidableEq C] in -lemma typeTensor_fourier (P : J → Matrix C C ℂ) (q : Types (S := S) (A := J)) : - (∑ θ : Phases J (Fintype.card S), star (countCharacter q θ) • - tensorMatrix (fun _ : S => phaseMatrix P θ)) = - (Fintype.card (Phases J (Fintype.card S)) : ℂ) • typeTensor P q := by - simp_rw [tensorMatrix_phase, Finset.smul_sum, smul_smul] - rw [Finset.sum_comm] - simp_rw [← Finset.sum_smul] - have he (r : Types (S := S) (A := J)) : - (∑ θ : Phases J (Fintype.card S), star (countCharacter q θ) * countCharacter r θ) = - if r=q then (Fintype.card (Phases J (Fintype.card S)) : ℂ) else 0 := by - simpa only [starRingEnd_apply, mul_comm] using character_orthogonality r q - simp_rw [he] - simp - -omit [Fintype C] [DecidableEq C] in -/-- Every identical tensor of a linear combination of a finite family lies -in the span of its finite phase tensors. Applied to an even spectral family, -all the spanning tensors are genuine global even unitaries. -/ -theorem tensorMatrix_mem_phase_span (P : J → Matrix C C ℂ) (z : J → ℂ) : - tensorMatrix (fun _ : S => ∑ j, z j • P j) ∈ - Submodule.span ℂ (Set.range fun θ : Phases J (Fintype.card S) => - tensorMatrix (fun _ : S => phaseMatrix P θ)) := by - let K := Submodule.span ℂ (Set.range fun θ : Phases J (Fintype.card S) => - tensorMatrix (fun _ : S => phaseMatrix P θ)) - have hm (q : Types (S := S) (A := J)) : typeTensor P q ∈ K := by - have hcard : (Fintype.card (Phases J (Fintype.card S)) : ℂ) ≠ 0 := by - exact_mod_cast Fintype.card_ne_zero - rw [← one_smul ℂ (typeTensor P q), ← inv_mul_cancel₀ hcard, mul_smul, - ← typeTensor_fourier P q] - apply K.smul_mem - apply K.sum_mem - intro θ _ - exact K.smul_mem _ (Submodule.subset_span ⟨θ,rfl⟩) - rw [tensorMatrix_by_type] - exact K.sum_mem (fun q _ => K.smul_mem _ (hm q)) - -end RowColumn.MatrixState - -namespace RowColumn.MatrixState -open Signed WordOrbits Postselection FiniteStarAlgebra -open scoped BigOperators Classical Matrix.Norms.L2Operator MatrixOrder -variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - (odd : C → Prop) [DecidablePred odd] (k : ℕ) - -abbrev Sector := EuclideanSpace ℂ (Words (S := S) odd k) - -def sectorUnitary : unitary (evenAlgebra odd) →* unitary (Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) := - ((Unitary.map (StarMonoidHom.ofClass (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)))).comp - (Unitary.map (sectorPowerHom (S := S) odd k))).toMonoidHom - -def sectorAlgebra : StarSubalgebra ℂ (Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) := - unitarySpan (sectorUnitary (S := S) odd k) - -lemma sectorUnitary_apply (U : unitary (evenAlgebra odd)) : - (sectorUnitary (S := S) odd k U : Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) = - (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)) (sectorTensor odd k (fun _ : S => U.val.val)) := rfl - -def tensorRestriction : Matrix (S → C) (S → C) ℂ →ₗ[ℂ] - (Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) := - (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)).toAlgEquiv.toLinearMap.comp - ({ toFun M := M.submatrix Subtype.val Subtype.val - map_add' _ _ := rfl - map_smul' _ _ := by ext w v; rfl } : - Matrix (S → C) (S → C) ℂ →ₗ[ℂ] Matrix (Words (S := S) odd k) (Words (S := S) odd k) ℂ) - -lemma tensorRestriction_apply (M : S → Matrix C C ℂ) : - tensorRestriction (S := S) odd k (tensorMatrix M) = (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)) (sectorTensor odd k M) := rfl - -/-- Identical even positive tensors really belong to the finite algebra of -actual global even unitary tensors. This is a proved phase-Fourier identity, -not a commutant-duality assumption. -/ -theorem sectorTensor_mem_algebra (M : Matrix C C ℂ) (hM : M.IsHermitian) (heven : M ∈ evenAlgebra odd) : - (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)) (sectorTensor odd k (fun _ : S => M)) ∈ sectorAlgebra (S := S) odd k := by - have hclosed : IsClosed (evenAlgebra odd : Set (Matrix C C ℂ)) := - (evenAlgebra odd).toSubalgebra.toSubmodule.closed_of_finiteDimensional - obtain ⟨d,P,z,he,hP,hU⟩ := exists_spectral_phase_family M hM (evenAlgebra odd) hclosed heven - let F := tensorRestriction (S := S) odd k - have ha (θ : Phases (Fin d) (Fintype.card S)) : F (tensorMatrix (fun _ : S => phaseMatrix (S := S) P θ)) ∈ sectorAlgebra (S := S) odd k := by - have hphase : phaseMatrix (S := S) P θ ∈ evenAlgebra odd := - (evenAlgebra odd).sum_mem (fun i _ => (evenAlgebra odd).smul_mem (hP i) _) - have hunit : phaseMatrix (S := S) P θ ∈ unitary (Matrix C C ℂ) := - hU _ (fun i => AddChar.norm_apply _ _) - let U : unitary (evenAlgebra odd) := ⟨⟨phaseMatrix (S := S) P θ,hphase⟩,by - constructor <;> apply Subtype.ext - · exact hunit.1 - · exact hunit.2⟩ - exact unitarySpan_mem (R := ℂ) (sectorUnitary (S := S) odd k) U - have hs : Submodule.span ℂ (Set.range fun θ : Phases (Fin d) (Fintype.card S) => - tensorMatrix (fun _ : S => phaseMatrix (S := S) P θ)) ≤ - (sectorAlgebra (S := S) odd k).toSubmodule.comap F := by - apply Submodule.span_le.mpr - rintro _ ⟨θ,rfl⟩ - exact ha θ - have hh := hs (tensorMatrix_mem_phase_span (S := S) P z) - rw [he] at hh - exact hh - -end RowColumn.MatrixState - -namespace RowColumn.MatrixState -open Signed WordOrbits Postselection FiniteStarAlgebra -open scoped BigOperators Classical Matrix.Norms.L2Operator MatrixOrder -variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - (odd : C → Prop) [DecidablePred odd] (k : ℕ) - -abbrev GlobalTypes := Types (S := S) (A := C × C) - -def sectorTypeMatrix (q : GlobalTypes (S := S) (C := C)) : - Matrix (Words (S := S) odd k) (Words (S := S) odd k) ℂ := - fun w v => if counts (fun i => (w.1 i,v.1 i))=q then 1 else 0 - -omit [DecidableEq S] in -lemma sectorTensor_type_expansion (M : Matrix C C ℂ) : - sectorTensor odd k (fun _ : S => M) = - ∑ q : GlobalTypes (S := S) (C := C), - typeAmplitude (fun c : C × C => M c.1 c.2) q • sectorTypeMatrix odd k q := by - ext w v - simp only [Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, sectorTypeMatrix] - simp only [mul_ite, mul_one, mul_zero, Finset.sum_ite_eq, Finset.mem_univ, ite_true] - exact prod_by_counts (fun i => (w.1 i,v.1 i)) (fun c : C × C => M c.1 c.2) - -lemma sectorAlgebra_le_type_span : (sectorAlgebra (S := S) odd k).toSubmodule ≤ - Submodule.span ℂ (Set.range fun q : GlobalTypes (S := S) (C := C) => - (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)) (sectorTypeMatrix odd k q)) := by - rw [sectorAlgebra, unitarySpan_eq_span] - apply Submodule.span_le.mpr - rintro _ ⟨U,rfl⟩ - dsimp only - rw [sectorUnitary_apply, sectorTensor_type_expansion] - simp only [map_sum, map_smul] - apply Submodule.sum_mem - intro q _ - exact Submodule.smul_mem _ _ (Submodule.subset_span ⟨q,rfl⟩) - -/-- Polynomial Fourier algebra dimension, counted by joint word types. -No representation-theoretic carrier-dimension estimate is assumed. -/ -theorem sectorAlgebra_finrank : Module.finrank ℂ (sectorAlgebra (S := S) odd k) ≤ - (Fintype.card S+1)^(Fintype.card C^2) := by - have hh := Submodule.finrank_mono (sectorAlgebra_le_type_span (S := S) odd k) - have hc := finrank_range_le_card (R := ℂ) (fun q : GlobalTypes (S := S) (C := C) => - (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)) (sectorTypeMatrix odd k q)) - exact hh.trans (by simpa only [Set.finrank, GlobalTypes, Types, CountIndex, Fintype.card_fun, - Fintype.card_fin, Fintype.card_prod, pow_two] using hc) - -end RowColumn.MatrixState - -end -end -end -end -end -end - -section -noncomputable section -open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator -namespace RowColumn.MatrixState -open Signed FiniteStarAlgebra -variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - (odd : C → Prop) [DecidablePred odd] (k : ℕ) - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma sectorTensor_transport (M : Matrix C C ℂ) (g : Equiv.Perm S) (w v : Words (S := S) odd k) : - sectorTensor odd k (fun _ : S => M) (actWord g w) (actWord g v) = - sectorTensor odd k (fun _ : S => M) w v := by - change (∏ i, M (w.1 (g⁻¹ i)) (v.1 (g⁻¹ i))) = ∏ i, M (w.1 i) (v.1 i) - exact Equiv.prod_comp g.symm (fun i => M (w.1 i) (v.1 i)) - -lemma matrix_wordVector (M : Matrix (Words (S := S) odd k) (Words (S := S) odd k) ℂ) - (w v : Words (S := S) odd k) : - Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ) M (wordVector v) w = M w v := by - change (∑ z, M w z * (if z=v then 1 else 0)) = M w v - simp - -lemma tensor_commutes_signed (M : Matrix C C ℂ) (heven : M ∈ evenAlgebra odd) - (g : Equiv.Perm S) (x : Sector (S := S) odd k) : - Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ) - (sectorTensor odd k (fun _ : S => M)) (representation g x) = - representation g (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ) - (sectorTensor odd k (fun _ : S => M)) x) := by - let T := Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ) - (sectorTensor odd k (fun _ : S => M)) - have hv (v : Words (S := S) odd k) : T (representation g (wordVector v)) = representation g (T (wordVector v)) := by - ext z - obtain ⟨w,rfl⟩ := (wordsEquiv g).surjective z - change T (representation g (wordVector v)) (actWord g w) = representation g (T (wordVector v)) (actWord g w) - rw [signedMap_wordVector, map_smul, signedMap_transport_apply] - change CubeShuffle.Specht.permSign (oddPerm g v) * T (wordVector (actWord g v)) (actWord g w) = - CubeShuffle.Specht.permSign (oddPerm g w) * T (wordVector v) w - dsimp only [T] - rw [matrix_wordVector, matrix_wordVector, sectorTensor_transport] - by_cases hp : ∀ i, odd (w.1 i) ↔ odd (v.1 i) - · rw [oddPerm_parity_congr g w v hp] - · have hz : sectorTensor odd k (fun _ : S => M) w v=0 := - tensorMatrix_even_support odd _ (fun _ => heven) w.1 v.1 hp - rw [hz, mul_zero, mul_zero] - change T (representation g x) = representation g (T x) - rw [← sum_wordVectors x] - simp only [map_sum, map_smul, hv] - -/-- The polynomial-dimensional tensor algebra commutes with the genuine -signed permutation representation, with no commutant-duality assumption. -/ -theorem sectorAlgebra_commutes (a : sectorAlgebra (S := S) odd k) - (g : Equiv.Perm S) (x : Sector (S := S) odd k) : - (a : Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) (representation g x) = representation g ((a : Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) x) := by - have ha := a.property - change (a : Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) ∈ - (unitarySpan (R := ℂ) (sectorUnitary (S := S) odd k)).toSubmodule at ha - rw [unitarySpan_eq_span] at ha - suffices hh : ∀ b ∈ Submodule.span ℂ - (Set.range fun U => ((sectorUnitary (S := S) odd k U).val : Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k)), - b (representation g x) = representation g (b x) from hh _ ha - intro b hb - induction hb using Submodule.span_induction with - | mem b hb => - obtain ⟨U,rfl⟩ := hb - dsimp only - rw [sectorUnitary_apply] - exact tensor_commutes_signed odd k U.val.val U.val.property g x - | zero => simp - | add b c hb hc ihb ihc => simp only [add_apply, map_add, ihb, ihc] - | smul z b hb ih => simp only [smul_apply, map_smul, ih] -end RowColumn.MatrixState - -end -end - -end OAI +import OAI.LinearAlgebra.MatrixState.Postselection +import OAI.RepresentationTheory.FiniteUnitary.Reconstruction +import OAI.RepresentationTheory.RowColumn.SignedWords + +namespace OAI + +section + +noncomputable section +open scoped BigOperators Classical Matrix.Norms.L2Operator MatrixOrder +namespace RowColumn.MatrixState +variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + +def evenAlgebra (odd : C → Prop) : StarSubalgebra ℂ (Matrix C C ℂ) where + carrier := {M | ∀ c d, ¬(odd c ↔ odd d) → M c d=0} + zero_mem' := by intro c d h; rfl + add_mem' := by intro M N hM hN c d h; change M c d + N c d=0; simp only [hM c d h,hN c d h,add_zero] + mul_mem' := by + intro M N hM hN c d h + change (∑ e, M c e * N e d)=0 + apply Finset.sum_eq_zero + intro e _ + change M c e * N e d=0 + by_cases he : odd c ↔ odd e + · rw [hN e d (fun hd => h (he.trans hd)), mul_zero] + · rw [hM c e he, zero_mul] + one_mem' := by + intro c d h + exact Matrix.one_apply_ne (fun he => h (he ▸ Iff.rfl)) + algebraMap_mem' := by + intro z c d h + have hcd : c≠d := fun he => h (he ▸ Iff.rfl) + simp [Algebra.algebraMap_eq_smul_one, hcd] + star_mem' := by + intro M hM c d h + change star (M d c)=0 + rw [hM d c (fun hh => h hh.symm), star_zero] + +lemma evenAlgebra_mem (odd : C → Prop) (M : Matrix C C ℂ) : + M ∈ evenAlgebra odd ↔ ∀ c d, ¬(odd c ↔ odd d) → M c d=0 := Iff.rfl + +omit [DecidableEq S] in +lemma tensorMatrix_even_support (odd : C → Prop) (M : S → Matrix C C ℂ) + (hM : ∀ i, M i ∈ evenAlgebra odd) (w v : S → C) + (h : ¬ ∀ i, odd (w i) ↔ odd (v i)) : tensorMatrix M w v=0 := by + obtain ⟨i,hi⟩ := not_forall.mp h + exact Finset.prod_eq_zero (Finset.mem_univ i) (hM i (w i) (v i) hi) + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma oddCount_eq (odd : C → Prop) [DecidablePred odd] (w v : S → C) + (h : ∀ i, odd (w i) ↔ odd (v i)) : + Fintype.card {i : S // odd (w i)} = Fintype.card {i : S // odd (v i)} := by + exact Fintype.card_congr (Equiv.subtypeEquivRight h) + +def sectorTensor (odd : C → Prop) [DecidablePred odd] (k : ℕ) (M : S → Matrix C C ℂ) : + Matrix (Signed.Words (S := S) odd k) (Signed.Words (S := S) odd k) ℂ := + (tensorMatrix M).submatrix Subtype.val Subtype.val + +lemma sectorTensor_mul (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M N : S → Matrix C C ℂ) (hM : ∀ i, M i ∈ evenAlgebra odd) : + sectorTensor odd k (fun i => M i * N i) = sectorTensor odd k M * sectorTensor odd k N := by + ext w v + change tensorMatrix (fun i => M i*N i) w.1 v.1 = _ + rw [← tensorMatrix_mul] + change (∑ z : S → C, tensorMatrix M w.1 z * tensorMatrix N z v.1) = + ∑ z : Signed.Words (S := S) odd k, tensorMatrix M w.1 z.1 * tensorMatrix N z.1 v.1 + have hz : (∑ z : {z : S → C // ¬ Fintype.card {i : S // odd (z i)}=k}, + tensorMatrix M w.1 z.1 * tensorMatrix N z.1 v.1)=0 := by + apply Finset.sum_eq_zero + intro z _ + rw [tensorMatrix_even_support odd M hM w.1 z.1, zero_mul] + intro hh + exact z.2 ((oddCount_eq odd w.1 z.1 hh).symm.trans w.2) + have he := Fintype.sum_subtype_add_sum_subtype + (fun z : S → C => Fintype.card {i : S // odd (z i)}=k) + (fun z : S → C => tensorMatrix M w.1 z * tensorMatrix N z v.1) + rw [hz, add_zero] at he + exact he.symm + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma sectorTensor_star (odd : C → Prop) [DecidablePred odd] (k : ℕ) (M : S → Matrix C C ℂ) : + sectorTensor odd k (fun i => star (M i)) = star (sectorTensor odd k M) := by + unfold sectorTensor + change (tensorMatrix (fun i => (M i).conjTranspose)).submatrix Subtype.val Subtype.val = _ + rw [← tensorMatrix_star] + rfl + +omit [DecidableEq S] [Fintype C] in +lemma sectorTensor_one (odd : C → Prop) [DecidablePred odd] (k : ℕ) : + sectorTensor odd k (fun _ : S => (1 : Matrix C C ℂ))=1 := by + rw [sectorTensor, tensorMatrix_one] + exact Matrix.submatrix_one Subtype.val Subtype.val_injective + +def sectorPowerHom (odd : C → Prop) [DecidablePred odd] (k : ℕ) : + evenAlgebra odd →⋆* Matrix (Signed.Words (S := S) odd k) (Signed.Words (S := S) odd k) ℂ where + toFun M := sectorTensor odd k (fun _ : S => M.val) + map_one' := sectorTensor_one odd k + map_mul' M _ := sectorTensor_mul odd k _ _ (fun _ => M.property) + map_star' _ := sectorTensor_star odd k _ + +end RowColumn.MatrixState + +noncomputable section +namespace RowColumn.Signed +open scoped Classical +variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + {odd : C → Prop} [DecidablePred odd] {k : ℕ} + +omit [DecidableEq S] in +lemma frame_pred_congr (p q : S → Prop) [dp : DecidablePred p] [dq : DecidablePred q] + (hp : Fintype.card {x : S // p x} = k) + (hq : Fintype.card {x : S // q x} = k) + (he : p = q) (x : S) (hx : p x) (hy : q x) : + Fintype.equivFinOfCardEq hp ⟨x,hx⟩ = Fintype.equivFinOfCardEq hq ⟨x,hy⟩ := by + subst q + have hd : dq = dp := Subsingleton.elim _ _ + subst dq + rfl + +omit [Fintype C] [DecidableEq C] in +omit [DecidableEq S] in +lemma oddFrame_parity_congr (w v : Words (S := S) odd k) + (hp : ∀ x, odd (w.1 x) ↔ odd (v.1 x)) (x : S) + (hx : odd (w.1 x)) (hv : odd (v.1 x)) : + oddFrame w ⟨x,hx⟩ = oddFrame v ⟨x,hv⟩ := by + exact frame_pred_congr _ _ w.2 v.2 (funext fun x => propext (hp x)) x hx hv + +omit [Fintype C] [DecidableEq C] [DecidableEq S] in +lemma oddPerm_parity_congr (g : Equiv.Perm S) (w v : Words (S := S) odd k) + (hp : ∀ x, odd (w.1 x) ↔ odd (v.1 x)) : oddPerm g w = oddPerm g v := by + apply Equiv.ext + intro i + have he : ((oddFrame w).symm i).val = ((oddFrame v).symm i).val := by + have hh := oddFrame_parity_congr w v hp ((oddFrame w).symm i).val + ((oddFrame w).symm i).property ((hp _).mp ((oddFrame w).symm i).property) + rw [Equiv.apply_symm_apply] at hh + have ht := congrArg (fun z => ((oddFrame v).symm z).val) hh + simpa using ht.symm + have ha : ∀ x, odd ((actWord g w).1 x) ↔ odd ((actWord g v).1 x) := fun x => hp _ + change oddFrame (actWord g w) ⟨g ((oddFrame w).symm i).val, _⟩ = + oddFrame (actWord g v) ⟨g ((oddFrame v).symm i).val, _⟩ + have hw : odd ((actWord g w).1 (g ((oddFrame w).symm i).val)) := by + simpa using ((oddFrame w).symm i).property + calc + _ = oddFrame (actWord g v) ⟨g ((oddFrame w).symm i).val, (ha _).mp hw⟩ := + oddFrame_parity_congr _ _ ha _ _ _ + _ = _ := congrArg (oddFrame (actWord g v)) (Subtype.ext (congrArg g he)) +end RowColumn.Signed + +noncomputable section +namespace RowColumn.FiniteStarAlgebra +variable {R A G : Type*} [CommSemiring R] [StarRing R] [Ring A] [Algebra R A] + [StarRing A] [StarModule R A] [Group G] + +def unitarySpan (u : G →* unitary A) : StarSubalgebra R A where + __ := Algebra.adjoin R (Set.range fun g : G => (u g : A)) + star_mem' := by + intro a ha + induction ha using Algebra.adjoin_induction with + | mem a ha => + obtain ⟨g,rfl⟩ := ha + apply Algebra.subset_adjoin + refine ⟨g⁻¹,?_⟩ + change (u g⁻¹ : A) = star (u g : A) + rw [map_inv] + rfl + | algebraMap r => rw [← algebraMap_star_comm]; exact (Algebra.adjoin R _).algebraMap_mem _ + | add a b ha hb iha ihb => rw [star_add]; exact (Algebra.adjoin R _).add_mem iha ihb + | mul a b ha hb iha ihb => rw [star_mul]; exact (Algebra.adjoin R _).mul_mem ihb iha + +lemma unitarySpan_eq_span (u : G →* unitary A) : + (unitarySpan (R := R) u).toSubmodule = Submodule.span R (Set.range fun g : G => (u g : A)) := by + apply Algebra.adjoin_eq_span_of_subset + intro a ha + have hh : a ∈ Set.range (fun g : G => (u g : A)) := by + induction ha using Submonoid.closure_induction with + | mem a ha => exact ha + | one => exact ⟨1,by simp⟩ + | mul a b ha hb iha ihb => + obtain ⟨g,rfl⟩ := iha + obtain ⟨h,rfl⟩ := ihb + exact ⟨g*h,by simp⟩ + exact Submodule.subset_span hh + +lemma unitarySpan_mem (u : G →* unitary A) (g : G) : (u g : A) ∈ unitarySpan (R := R) u := + Algebra.subset_adjoin ⟨g,rfl⟩ + +def unitarySpanHom (u : G →* unitary A) : G →* unitary (unitarySpan (R := R) u) where + toFun g := ⟨⟨(u g : A),unitarySpan_mem u g⟩,by + constructor <;> apply Subtype.ext + · exact (u g).property.1 + · exact (u g).property.2⟩ + map_one' := by apply Subtype.ext; apply Subtype.ext; change (u 1 : A)=1; simp + map_mul' g h := by apply Subtype.ext; apply Subtype.ext; change (u (g*h) : A)=(u g : A)*(u h : A); simp + +lemma unitarySpanHom_spans (u : G →* unitary A) : + Submodule.span R (Set.range fun g : G => (unitarySpanHom (R := R) u g : unitarySpan (R := R) u))=⊤ := by + apply Submodule.map_injective_of_injective (Submodule.subtype_injective (unitarySpan (R := R) u).toSubmodule) + rw [Submodule.map_span, ← Set.range_comp] + change Submodule.span R (Set.range fun g : G => (u g : A)) = + Submodule.map (unitarySpan (R := R) u).toSubmodule.subtype ⊤ + rw [Submodule.map_top, Submodule.range_subtype] + exact (unitarySpan_eq_span u).symm + +end RowColumn.FiniteStarAlgebra + +noncomputable section +open scoped BigOperators Classical Matrix.Norms.L2Operator +open ComplexConjugate +namespace RowColumn.MatrixState + +def discreteContinuousHom (J : Type*) [TopologicalSpace J] [DiscreteTopology J] : + (J → ℂ) →⋆ₐ[ℂ] C(J,ℂ) where + toFun f := ⟨f,continuous_of_discreteTopology⟩ + map_zero' := rfl + map_one' := rfl + map_add' _ _ := rfl + map_mul' _ _ := rfl + commutes' _ := rfl + map_star' _ := rfl + +def precompFunctionHom {J K : Type*} (f : J → K) : (K → ℂ) →⋆ₐ[ℂ] (J → ℂ) where + toFun g := g ∘ f + map_zero' := rfl + map_one' := rfl + map_add' _ _ := rfl + map_mul' _ _ := rfl + commutes' _ := rfl + map_star' _ := rfl + +lemma sum_single_function {J : Type*} [Fintype J] [DecidableEq J] (z : J → ℂ) : + (∑ i : J, z i • (Pi.single i 1 : J → ℂ)) = z := by + ext j + simp [Pi.single_apply] + +lemma function_unitary {J : Type*} (z : J → ℂ) (hz : ∀ i, ‖z i‖=1) : z ∈ unitary (J → ℂ) := by + constructor <;> ext i + · change conj (z i)*z i=1 + rw [Complex.conj_mul', hz i] + norm_num + · change z i*conj (z i)=1 + rw [Complex.mul_conj', hz i] + norm_num + +/-- A genuine finite spectral phase family inside the prescribed closed +star algebra. In the application this is the even one-slot matrix algebra. -/ +theorem exists_spectral_phase_family {C : Type*} [Fintype C] [DecidableEq C] + (M : Matrix C C ℂ) (hM : M.IsHermitian) + (K : StarSubalgebra ℂ (Matrix C C ℂ)) (hK : IsClosed (K : Set (Matrix C C ℂ))) + (hMK : M ∈ K) : + ∃ (d : ℕ) (P : Fin d → Matrix C C ℂ) (z : Fin d → ℂ), + (∑ i, z i • P i) = M ∧ (∀ i, P i ∈ K) ∧ + ∀ θ : Fin d → ℂ, (∀ i, ‖θ i‖=1) → (∑ i, θ i • P i) ∈ unitary (Matrix C C ℂ) := by + have hfin : (spectrum ℂ M).Finite := by + rw [hM.spectrum_eq_image_range] + exact (Set.finite_range hM.eigenvalues).image _ + let J := spectrum ℂ M + let : Fintype J := hfin.fintype + let : DiscreteTopology J := inferInstance + let e : J ≃ Fin (Fintype.card J) := Fintype.equivFin J + let ψ := (cfcHom hM.isSelfAdjoint.isStarNormal (R := ℂ)).comp + ((discreteContinuousHom J).comp (precompFunctionHom e)) + let P (i : Fin (Fintype.card J)) : Matrix C C ℂ := ψ (Pi.single i 1) + let z (i : Fin (Fintype.card J)) : ℂ := (e.symm i).val + have hsum (f : Fin (Fintype.card J) → ℂ) : ∑ i, f i • P i = ψ f := by + simp only [P, ← map_smul, ← map_sum, sum_single_function] + refine ⟨Fintype.card J,P,z,?_,?_,?_⟩ + · rw [hsum] + have he : ((discreteContinuousHom J).comp (precompFunctionHom e)) z = + (ContinuousMap.id ℂ).restrict (spectrum ℂ M) := by + ext j + exact congrArg Subtype.val (e.symm_apply_apply j) + change cfcHom hM.isSelfAdjoint.isStarNormal (((discreteContinuousHom J).comp (precompFunctionHom e)) z) = M + rw [he] + exact cfcHom_id _ + · intro i + apply StarAlgebra.elemental.le_of_mem hK hMK + exact cfcHom_mem_elemental hM.isSelfAdjoint.isStarNormal _ + · intro θ hθ + rw [hsum] + exact Unitary.map_mem ψ (function_unitary θ hθ) + +end RowColumn.MatrixState + +noncomputable section +open scoped BigOperators Classical +namespace RowColumn.MatrixState +open WordOrbits Postselection +variable {S C J : Type*} [Fintype S] [DecidableEq S] + [Fintype C] [DecidableEq C] [Fintype J] [DecidableEq J] + +omit [Fintype C] [DecidableEq C] [DecidableEq J] in +lemma tensorMatrix_linear_combination (P : J → Matrix C C ℂ) (z : J → ℂ) : + tensorMatrix (fun _ : S => ∑ j, z j • P j) = + ∑ w : S → J, (∏ i, z (w i)) • tensorMatrix (fun i => P (w i)) := by + ext a b + simp only [tensorMatrix, Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul] + rw [Fintype.prod_sum] + apply Finset.sum_congr rfl + intro w _ + exact Finset.prod_mul_distrib + +def typeTensor (P : J → Matrix C C ℂ) (q : Types (S := S) (A := J)) : + Matrix (S → C) (S → C) ℂ := + ∑ w : {w : S → J // counts w = q}, tensorMatrix (fun i => P (w.1 i)) + +omit [Fintype C] [DecidableEq C] in +lemma tensorMatrix_by_type (P : J → Matrix C C ℂ) (z : J → ℂ) : + tensorMatrix (fun _ : S => ∑ j, z j • P j) = + ∑ q : Types (S := S) (A := J), typeAmplitude z q • typeTensor P q := by + rw [tensorMatrix_linear_combination] + simp_rw [prod_by_counts _ z] + change (∑ w : S → J, typeAmplitude z (counts w) • tensorMatrix (fun i => P (w i))) = _ + rw [← Fintype.sum_fiberwise counts (fun w : S → J => + typeAmplitude z (counts w) • tensorMatrix (fun i => P (w i)))] + apply Finset.sum_congr rfl + intro q _ + simp only [show ∀ w : {w : S → J // counts w = q}, counts w.1=q from fun w => w.2] + exact (Finset.smul_sum).symm + +def phaseMatrix (P : J → Matrix C C ℂ) (θ : Phases J (Fintype.card S)) : Matrix C C ℂ := + ∑ j, ZMod.stdAddChar (θ j) • P j + +omit [Fintype C] [DecidableEq C] in +lemma tensorMatrix_phase (P : J → Matrix C C ℂ) (θ : Phases J (Fintype.card S)) : + tensorMatrix (fun _ : S => phaseMatrix P θ) = + ∑ q : Types (S := S) (A := J), countCharacter q θ • typeTensor P q := by + rw [phaseMatrix, tensorMatrix_by_type] + apply Finset.sum_congr rfl + intro q _ + congr 1 + exact (countCharacter_eq_prod q θ).symm + +omit [Fintype C] [DecidableEq C] in +lemma typeTensor_fourier (P : J → Matrix C C ℂ) (q : Types (S := S) (A := J)) : + (∑ θ : Phases J (Fintype.card S), star (countCharacter q θ) • + tensorMatrix (fun _ : S => phaseMatrix P θ)) = + (Fintype.card (Phases J (Fintype.card S)) : ℂ) • typeTensor P q := by + simp_rw [tensorMatrix_phase, Finset.smul_sum, smul_smul] + rw [Finset.sum_comm] + simp_rw [← Finset.sum_smul] + have he (r : Types (S := S) (A := J)) : + (∑ θ : Phases J (Fintype.card S), star (countCharacter q θ) * countCharacter r θ) = + if r=q then (Fintype.card (Phases J (Fintype.card S)) : ℂ) else 0 := by + simpa only [starRingEnd_apply, mul_comm] using character_orthogonality r q + simp_rw [he] + simp + +omit [Fintype C] [DecidableEq C] in +/-- Every identical tensor of a linear combination of a finite family lies +in the span of its finite phase tensors. Applied to an even spectral family, +all the spanning tensors are genuine global even unitaries. -/ +theorem tensorMatrix_mem_phase_span (P : J → Matrix C C ℂ) (z : J → ℂ) : + tensorMatrix (fun _ : S => ∑ j, z j • P j) ∈ + Submodule.span ℂ (Set.range fun θ : Phases J (Fintype.card S) => + tensorMatrix (fun _ : S => phaseMatrix P θ)) := by + let K := Submodule.span ℂ (Set.range fun θ : Phases J (Fintype.card S) => + tensorMatrix (fun _ : S => phaseMatrix P θ)) + have hm (q : Types (S := S) (A := J)) : typeTensor P q ∈ K := by + have hcard : (Fintype.card (Phases J (Fintype.card S)) : ℂ) ≠ 0 := by + exact_mod_cast Fintype.card_ne_zero + rw [← one_smul ℂ (typeTensor P q), ← inv_mul_cancel₀ hcard, mul_smul, + ← typeTensor_fourier P q] + apply K.smul_mem + apply K.sum_mem + intro θ _ + exact K.smul_mem _ (Submodule.subset_span ⟨θ,rfl⟩) + rw [tensorMatrix_by_type] + exact K.sum_mem (fun q _ => K.smul_mem _ (hm q)) + +end RowColumn.MatrixState + +namespace RowColumn.MatrixState +open Signed WordOrbits Postselection FiniteStarAlgebra +open scoped BigOperators Classical Matrix.Norms.L2Operator MatrixOrder +variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + (odd : C → Prop) [DecidablePred odd] (k : ℕ) + +abbrev Sector := EuclideanSpace ℂ (Words (S := S) odd k) + +def sectorUnitary : unitary (evenAlgebra odd) →* unitary (Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) := + ((Unitary.map (StarMonoidHom.ofClass (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)))).comp + (Unitary.map (sectorPowerHom (S := S) odd k))).toMonoidHom + +def sectorAlgebra : StarSubalgebra ℂ (Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) := + unitarySpan (sectorUnitary (S := S) odd k) + +lemma sectorUnitary_apply (U : unitary (evenAlgebra odd)) : + (sectorUnitary (S := S) odd k U : Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) = + (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)) (sectorTensor odd k (fun _ : S => U.val.val)) := rfl + +def tensorRestriction : Matrix (S → C) (S → C) ℂ →ₗ[ℂ] + (Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) := + (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)).toAlgEquiv.toLinearMap.comp + ({ toFun M := M.submatrix Subtype.val Subtype.val + map_add' _ _ := rfl + map_smul' _ _ := by ext w v; rfl } : + Matrix (S → C) (S → C) ℂ →ₗ[ℂ] Matrix (Words (S := S) odd k) (Words (S := S) odd k) ℂ) + +lemma tensorRestriction_apply (M : S → Matrix C C ℂ) : + tensorRestriction (S := S) odd k (tensorMatrix M) = (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)) (sectorTensor odd k M) := rfl + +/-- Identical even positive tensors really belong to the finite algebra of +actual global even unitary tensors. This is a proved phase-Fourier identity, +not a commutant-duality assumption. -/ +theorem sectorTensor_mem_algebra (M : Matrix C C ℂ) (hM : M.IsHermitian) (heven : M ∈ evenAlgebra odd) : + (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)) (sectorTensor odd k (fun _ : S => M)) ∈ sectorAlgebra (S := S) odd k := by + have hclosed : IsClosed (evenAlgebra odd : Set (Matrix C C ℂ)) := + (evenAlgebra odd).toSubalgebra.toSubmodule.closed_of_finiteDimensional + obtain ⟨d,P,z,he,hP,hU⟩ := exists_spectral_phase_family M hM (evenAlgebra odd) hclosed heven + let F := tensorRestriction (S := S) odd k + have ha (θ : Phases (Fin d) (Fintype.card S)) : F (tensorMatrix (fun _ : S => phaseMatrix (S := S) P θ)) ∈ sectorAlgebra (S := S) odd k := by + have hphase : phaseMatrix (S := S) P θ ∈ evenAlgebra odd := + (evenAlgebra odd).sum_mem (fun i _ => (evenAlgebra odd).smul_mem (hP i) _) + have hunit : phaseMatrix (S := S) P θ ∈ unitary (Matrix C C ℂ) := + hU _ (fun i => AddChar.norm_apply _ _) + let U : unitary (evenAlgebra odd) := ⟨⟨phaseMatrix (S := S) P θ,hphase⟩,by + constructor <;> apply Subtype.ext + · exact hunit.1 + · exact hunit.2⟩ + exact unitarySpan_mem (R := ℂ) (sectorUnitary (S := S) odd k) U + have hs : Submodule.span ℂ (Set.range fun θ : Phases (Fin d) (Fintype.card S) => + tensorMatrix (fun _ : S => phaseMatrix (S := S) P θ)) ≤ + (sectorAlgebra (S := S) odd k).toSubmodule.comap F := by + apply Submodule.span_le.mpr + rintro _ ⟨θ,rfl⟩ + exact ha θ + have hh := hs (tensorMatrix_mem_phase_span (S := S) P z) + rw [he] at hh + exact hh + +end RowColumn.MatrixState + +namespace RowColumn.MatrixState +open Signed WordOrbits Postselection FiniteStarAlgebra +open scoped BigOperators Classical Matrix.Norms.L2Operator MatrixOrder +variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + (odd : C → Prop) [DecidablePred odd] (k : ℕ) + +abbrev GlobalTypes := Types (S := S) (A := C × C) + +def sectorTypeMatrix (q : GlobalTypes (S := S) (C := C)) : + Matrix (Words (S := S) odd k) (Words (S := S) odd k) ℂ := + fun w v => if counts (fun i => (w.1 i,v.1 i))=q then 1 else 0 + +omit [DecidableEq S] in +lemma sectorTensor_type_expansion (M : Matrix C C ℂ) : + sectorTensor odd k (fun _ : S => M) = + ∑ q : GlobalTypes (S := S) (C := C), + typeAmplitude (fun c : C × C => M c.1 c.2) q • sectorTypeMatrix odd k q := by + ext w v + simp only [Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, sectorTypeMatrix] + simp only [mul_ite, mul_one, mul_zero, Finset.sum_ite_eq, Finset.mem_univ, ite_true] + exact prod_by_counts (fun i => (w.1 i,v.1 i)) (fun c : C × C => M c.1 c.2) + +lemma sectorAlgebra_le_type_span : (sectorAlgebra (S := S) odd k).toSubmodule ≤ + Submodule.span ℂ (Set.range fun q : GlobalTypes (S := S) (C := C) => + (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)) (sectorTypeMatrix odd k q)) := by + rw [sectorAlgebra, unitarySpan_eq_span] + apply Submodule.span_le.mpr + rintro _ ⟨U,rfl⟩ + dsimp only + rw [sectorUnitary_apply, sectorTensor_type_expansion] + simp only [map_sum, map_smul] + apply Submodule.sum_mem + intro q _ + exact Submodule.smul_mem _ _ (Submodule.subset_span ⟨q,rfl⟩) + +/-- Polynomial Fourier algebra dimension, counted by joint word types. +No representation-theoretic carrier-dimension estimate is assumed. -/ +theorem sectorAlgebra_finrank : Module.finrank ℂ (sectorAlgebra (S := S) odd k) ≤ + (Fintype.card S+1)^(Fintype.card C^2) := by + have hh := Submodule.finrank_mono (sectorAlgebra_le_type_span (S := S) odd k) + have hc := finrank_range_le_card (R := ℂ) (fun q : GlobalTypes (S := S) (C := C) => + (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ)) (sectorTypeMatrix odd k q)) + exact hh.trans (by simpa only [Set.finrank, GlobalTypes, Types, CountIndex, Fintype.card_fun, + Fintype.card_fin, Fintype.card_prod, pow_two] using hc) + +end RowColumn.MatrixState + +end +end +end +end +end +end + +section +noncomputable section +open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator +namespace RowColumn.MatrixState +open Signed FiniteStarAlgebra +variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + (odd : C → Prop) [DecidablePred odd] (k : ℕ) + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma sectorTensor_transport (M : Matrix C C ℂ) (g : Equiv.Perm S) (w v : Words (S := S) odd k) : + sectorTensor odd k (fun _ : S => M) (actWord g w) (actWord g v) = + sectorTensor odd k (fun _ : S => M) w v := by + change (∏ i, M (w.1 (g⁻¹ i)) (v.1 (g⁻¹ i))) = ∏ i, M (w.1 i) (v.1 i) + exact Equiv.prod_comp g.symm (fun i => M (w.1 i) (v.1 i)) + +lemma matrix_wordVector (M : Matrix (Words (S := S) odd k) (Words (S := S) odd k) ℂ) + (w v : Words (S := S) odd k) : + Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ) M (wordVector v) w = M w v := by + change (∑ z, M w z * (if z=v then 1 else 0)) = M w v + simp + +lemma tensor_commutes_signed (M : Matrix C C ℂ) (heven : M ∈ evenAlgebra odd) + (g : Equiv.Perm S) (x : Sector (S := S) odd k) : + Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ) + (sectorTensor odd k (fun _ : S => M)) (representation g x) = + representation g (Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ) + (sectorTensor odd k (fun _ : S => M)) x) := by + let T := Matrix.toEuclideanCLM (n := Words (S := S) odd k) (𝕜 := ℂ) + (sectorTensor odd k (fun _ : S => M)) + have hv (v : Words (S := S) odd k) : T (representation g (wordVector v)) = representation g (T (wordVector v)) := by + ext z + obtain ⟨w,rfl⟩ := (wordsEquiv g).surjective z + change T (representation g (wordVector v)) (actWord g w) = representation g (T (wordVector v)) (actWord g w) + rw [signedMap_wordVector, map_smul, signedMap_transport_apply] + change CubeShuffle.Specht.permSign (oddPerm g v) * T (wordVector (actWord g v)) (actWord g w) = + CubeShuffle.Specht.permSign (oddPerm g w) * T (wordVector v) w + dsimp only [T] + rw [matrix_wordVector, matrix_wordVector, sectorTensor_transport] + by_cases hp : ∀ i, odd (w.1 i) ↔ odd (v.1 i) + · rw [oddPerm_parity_congr g w v hp] + · have hz : sectorTensor odd k (fun _ : S => M) w v=0 := + tensorMatrix_even_support odd _ (fun _ => heven) w.1 v.1 hp + rw [hz, mul_zero, mul_zero] + change T (representation g x) = representation g (T x) + rw [← sum_wordVectors x] + simp only [map_sum, map_smul, hv] + +/-- The polynomial-dimensional tensor algebra commutes with the genuine +signed permutation representation, with no commutant-duality assumption. -/ +theorem sectorAlgebra_commutes (a : sectorAlgebra (S := S) odd k) + (g : Equiv.Perm S) (x : Sector (S := S) odd k) : + (a : Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) (representation g x) = representation g ((a : Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) x) := by + have ha := a.property + change (a : Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k) ∈ + (unitarySpan (R := ℂ) (sectorUnitary (S := S) odd k)).toSubmodule at ha + rw [unitarySpan_eq_span] at ha + suffices hh : ∀ b ∈ Submodule.span ℂ + (Set.range fun U => ((sectorUnitary (S := S) odd k U).val : Sector (S := S) odd k →L[ℂ] Sector (S := S) odd k)), + b (representation g x) = representation g (b x) from hh _ ha + intro b hb + induction hb using Submodule.span_induction with + | mem b hb => + obtain ⟨U,rfl⟩ := hb + dsimp only + rw [sectorUnitary_apply] + exact tensor_commutes_signed odd k U.val.val U.val.property g x + | zero => simp + | add b c hb hc ihb ihc => simp only [add_apply, map_add, ihb, ihc] + | smul z b hb ih => simp only [smul_apply, map_smul, ih] +end RowColumn.MatrixState + +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/SignedWords.lean b/lean/OAI/RepresentationTheory/RowColumn/SignedWords.lean index 2d9929a5d635d9b6358e036a4eaa5e3f6c93e6a7..049d61206bb6f2af9452f7fc422e8cc239b63c03 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/SignedWords.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/SignedWords.lean @@ -1,425 +1,425 @@ -import OAI.RepresentationTheory.RowColumn.Basic - -namespace OAI - -noncomputable section - -open scoped BigOperators Classical - -namespace RowColumn.Signed -open CubeShuffle.Specht - -variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] -variable (odd : C → Prop) [DecidablePred odd] - -/-- Words with exactly k odd entries. This is the k-parity sector of the -literal signed slot space, not a formal unknown representation. -/ -abbrev Words (k : ℕ) := {w : S → C // Fintype.card {x : S // odd (w x)} = k} - - -variable {odd} {k : ℕ} - -/-- Odd slots of a word, genuinely a subset of the board slots. -/ -abbrev OddSlots (w : Words (S := S) odd k) := {x : S // odd (w.1 x)} - -def relabelOddEquiv (g : Equiv.Perm S) (w : S → C) : - {x : S // odd (w x)} ≃ {x : S // odd (w (g⁻¹ x))} where - toFun x := ⟨g x.1, by simpa using x.2⟩ - invFun x := ⟨g⁻¹ x.1, x.2⟩ - left_inv := by intro x; ext; simp - right_inv := by intro x; ext; simp - -def actWord (g : Equiv.Perm S) (w : Words (S := S) odd k) : Words (S := S) odd k := - ⟨fun x => w.1 (g⁻¹ x), (Fintype.card_congr (relabelOddEquiv g w.1)).symm.trans w.2⟩ - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -@[simp] lemma actWord_apply (g : Equiv.Perm S) (w : Words (S := S) odd k) (x : S) : - (actWord g w).1 x = w.1 (g⁻¹ x) := rfl - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -@[simp] lemma actWord_one (w : Words (S := S) odd k) : actWord 1 w = w := by - apply Subtype.ext - funext x - rfl - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma actWord_mul (g h : Equiv.Perm S) (w : Words (S := S) odd k) : - actWord (g * h) w = actWord g (actWord h w) := by - apply Subtype.ext - funext x - simp [actWord, mul_inv_rev] - -/-- Canonical frames choose the odd-slot orientation. Different choices conjugate -by a diagonal sign; the signed action is exactly reordering the odd slots. -/ -def oddFrame (w : Words (S := S) odd k) : OddSlots w ≃ Fin k := - Fintype.equivFinOfCardEq w.2 - -def oddPerm (g : Equiv.Perm S) (w : Words (S := S) odd k) : Equiv.Perm (Fin k) := - (oddFrame w).symm |>.trans ((relabelOddEquiv g w.1).trans (oddFrame (actWord g w))) - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma oddFrame_congr {w v : Words (S := S) odd k} (he : w = v) - (x : S) (hx : odd (w.1 x)) (hv : odd (v.1 x)) : - oddFrame w ⟨x, hx⟩ = oddFrame v ⟨x, hv⟩ := by - subst v - rfl - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -@[simp] lemma oddPerm_one (w : Words (S := S) odd k) : oddPerm 1 w = 1 := by - apply Equiv.ext - intro i - change oddFrame (actWord 1 w) ⟨(oddFrame w).symm i, _⟩ = i - have h := oddFrame_congr (actWord_one w) ((oddFrame w).symm i).1 - (show odd ((actWord 1 w).1 ((oddFrame w).symm i)) from ((oddFrame w).symm i).2) - ((oddFrame w).symm i).2 - exact h.trans ((oddFrame w).apply_symm_apply i) - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma oddPerm_mul (g h : Equiv.Perm S) (w : Words (S := S) odd k) : - oddPerm (g * h) w = oddPerm g (actWord h w) * oddPerm h w := by - apply Equiv.ext - intro i - change oddFrame (actWord (g * h) w) - ((relabelOddEquiv (g * h) w.1) ((oddFrame w).symm i)) = - oddFrame (actWord g (actWord h w)) - ((relabelOddEquiv g (actWord h w).1) - ((oddFrame (actWord h w)).symm - (oddFrame (actWord h w) ((relabelOddEquiv h w.1) ((oddFrame w).symm i))))) - erw [Equiv.symm_apply_apply] - exact oddFrame_congr (actWord_mul g h w) _ _ _ - -def wordsEquiv (g : Equiv.Perm S) : Equiv.Perm (Words (S := S) odd k) where - toFun := actWord g - invFun := actWord g⁻¹ - left_inv := by intro w; rw [← actWord_mul, inv_mul_cancel, actWord_one] - right_inv := by intro w; rw [← actWord_mul, mul_inv_cancel, actWord_one] - -/-- Signed slot action in the orthonormal word basis. It reorders the odd -subsequence, and does not introduce a sign for even slots. -/ -def signedMap (g : Equiv.Perm S) : - EuclideanSpace ℂ (Words (S := S) odd k) →ₗ[ℂ] EuclideanSpace ℂ (Words (S := S) odd k) where - toFun v := WithLp.toLp 2 (fun w => permSign (oddPerm g⁻¹ w) * v (actWord g⁻¹ w)) - map_add' := by intro v z; ext w; simp [mul_add] - map_smul' := by intro a v; ext w; simp [mul_left_comm] - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -@[simp] lemma signedMap_apply (g : Equiv.Perm S) - (v : EuclideanSpace ℂ (Words (S := S) odd k)) (w : Words (S := S) odd k) : - signedMap g v w = permSign (oddPerm g⁻¹ w) * v (actWord g⁻¹ w) := rfl - -/-- The signs genuinely compose; no group-action relation is assumed. -/ -def representation : Representation ℂ (Equiv.Perm S) (EuclideanSpace ℂ (Words (S := S) odd k)) where - toFun := signedMap - map_one' := by ext v w; simp - map_mul' g h := by - ext v w - simp only [signedMap_apply, Module.End.mul_apply, mul_inv_rev, oddPerm_mul, - permSign_mul, actWord_mul, mul_assoc] - ring - -omit [DecidableEq C] in -lemma representation_unitary : CubeShuffle.UnitaryFinite.IsUnitary - (representation (S := S) (odd := odd) (k := k)) := by - intro g v z - rw [PiLp.inner_apply, PiLp.inner_apply] - change (∑ w, inner ℂ (permSign (oddPerm g⁻¹ w) * v (actWord g⁻¹ w)) - (permSign (oddPerm g⁻¹ w) * z (actWord g⁻¹ w))) = _ - have hh (w : Words (S := S) odd k) : - inner ℂ (permSign (oddPerm g⁻¹ w) * v (actWord g⁻¹ w)) - (permSign (oddPerm g⁻¹ w) * z (actWord g⁻¹ w)) = - inner ℂ (v (actWord g⁻¹ w)) (z (actWord g⁻¹ w)) := by - simp only [RCLike.inner_apply, map_mul, conj_permSign] - rw [show permSign (oddPerm g⁻¹ w) * z (actWord g⁻¹ w) * - (permSign (oddPerm g⁻¹ w) * (starRingEnd ℂ) (v (actWord g⁻¹ w))) = - (permSign (oddPerm g⁻¹ w) * permSign (oddPerm g⁻¹ w)) * - (z (actWord g⁻¹ w) * (starRingEnd ℂ) (v (actWord g⁻¹ w))) by ring, - permSign_sq, one_mul] - simp_rw [hh] - exact Equiv.sum_comp (wordsEquiv g⁻¹) (fun w => inner ℂ (v w) (z w)) - -end RowColumn.Signed - -namespace RowColumn.Signed -open scoped BigOperators Classical -open CubeShuffle.Specht - -variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - {odd : C → Prop} [DecidablePred odd] {k : ℕ} - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma word_stabilizer_eq (g : Equiv.Perm S) (w : Words (S := S) odd k) - (hw : actWord g w = w) (x : S) : w.1 (g x) = w.1 x := by - have he := congrArg (fun z : Words (S := S) odd k => z.1 (g x)) hw - simpa using he.symm - -omit [Fintype C] [DecidableEq C] in -lemma oddPerm_sign_of_stabilizes (g : Equiv.Perm S) (w : Words (S := S) odd k) - (hw : actWord g w = w) (hfix : ∀ x, ¬ odd (w.1 x) → g x = x) : - permSign (oddPerm g w) = permSign g := by - have hs : ∀ x, odd (w.1 (g x)) ↔ odd (w.1 x) := fun x => by - rw [word_stabilizer_eq g w hw x] - have he := Equiv.Perm.sign_eq_sign_of_equiv (g.subtypePerm hs) - (oddPerm g w) (oddFrame w) (by - intro x - change oddFrame w ⟨g x.1, _⟩ = - oddFrame (actWord g w) - ((relabelOddEquiv g w.1) ((oddFrame w).symm (oddFrame w x))) - erw [Equiv.symm_apply_apply] - exact (oddFrame_congr hw (g x.1) _ _).symm) - have hf : ∀ x, g x ≠ x → odd (w.1 x) := by - intro x hn - by_contra h - exact hn (hfix x h) - rw [Equiv.Perm.sign_subtypePerm g hs hf] at he - exact congrArg (fun z : ℤˣ => ((z : ℤ) : ℂ)) he.symm - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma oddPerm_of_odd_fixed (g : Equiv.Perm S) (w : Words (S := S) odd k) - (hw : actWord g w = w) (hfix : ∀ x, odd (w.1 x) → g x = x) : - oddPerm g w = 1 := by - apply Equiv.ext - intro i - let x := (oddFrame w).symm i - change oddFrame (actWord g w) ⟨g x.1, _⟩ = i - have he := oddFrame_congr hw (g x.1) - (show odd ((actWord g w).1 (g x.1)) by simpa using x.2) - (by rw [hfix x.1 x.2]; exact x.2) - refine he.trans ?_ - have hh : (⟨g x.1, by rw [hfix x.1 x.2]; exact x.2⟩ : OddSlots w) = x := - Subtype.ext (hfix x.1 x.2) - rw [hh] - exact (oddFrame w).apply_symm_apply i - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma actWord_inv_eq_iff (g : Equiv.Perm S) (w : Words (S := S) odd k) : - actWord g⁻¹ w = w ↔ actWord g w = w := by - constructor - · intro he - have hh := congrArg (actWord g) he - rw [← actWord_mul, mul_inv_cancel, actWord_one] at hh - exact hh.symm - · intro he - have hh := congrArg (actWord g⁻¹) he - rw [← actWord_mul, inv_mul_cancel, actWord_one] at hh - exact hh.symm - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma oddPerm_inv_stabilizer (g : Equiv.Perm S) (w : Words (S := S) odd k) - (hw : actWord g w = w) : oddPerm g⁻¹ w = (oddPerm g w)⁻¹ := by - have hh := oddPerm_mul g⁻¹ g w - rw [inv_mul_cancel, oddPerm_one, hw] at hh - exact eq_inv_of_mul_eq_one_left hh.symm - -def wordVector (w : Words (S := S) odd k) : EuclideanSpace ℂ (Words (S := S) odd k) := - WithLp.toLp 2 (fun z => if z = w then 1 else 0) - -omit [DecidableEq S] [Fintype C] in -lemma wordVector_coefficient (g : Equiv.Perm S) (w : Words (S := S) odd k) : - Signed.representation g (wordVector w) w = - if actWord g w = w then permSign (oddPerm g w) else 0 := by - change permSign (oddPerm g⁻¹ w) * (if actWord g⁻¹ w = w then (1 : ℂ) else 0) = _ - simp only [actWord_inv_eq_iff] - split_ifs with he - · rw [oddPerm_inv_stabilizer g w he, permSign_inv, mul_one] - · exact mul_zero _ - -end RowColumn.Signed - -namespace RowColumn.Signed -open CubeShuffle.Specht -open scoped BigOperators Classical - -variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - {odd : C → Prop} [DecidablePred odd] {k : ℕ} - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma oddPerm_inv (g : Equiv.Perm S) (w : Words (S := S) odd k) : - oddPerm g⁻¹ (actWord g w) = (oddPerm g w)⁻¹ := by - have hh := oddPerm_mul g⁻¹ g w - rw [inv_mul_cancel, oddPerm_one] at hh - exact eq_inv_of_mul_eq_one_left hh.symm - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma signedMap_transport_apply (g : Equiv.Perm S) - (x : EuclideanSpace ℂ (Words (S := S) odd k)) (w : Words (S := S) odd k) : - representation g x (actWord g w) = permSign (oddPerm g w) * x w := by - change permSign (oddPerm g⁻¹ (actWord g w)) * x (actWord g⁻¹ (actWord g w)) = _ - rw [oddPerm_inv, permSign_inv, ← actWord_mul, inv_mul_cancel, actWord_one] - -omit [DecidableEq S] [Fintype C] in -lemma signedMap_wordVector (g : Equiv.Perm S) (w : Words (S := S) odd k) : - representation g (wordVector w) = permSign (oddPerm g w) • wordVector (actWord g w) := by - ext z - obtain ⟨v, rfl⟩ := (wordsEquiv g).surjective z - change representation g (wordVector w) (actWord g v) = _ - rw [signedMap_transport_apply] - change permSign (oddPerm g v) * (if v = w then (1 : ℂ) else 0) = - permSign (oddPerm g w) * (if actWord g v = actWord g w then (1 : ℂ) else 0) - have he : actWord g v = actWord g w ↔ v = w := (wordsEquiv g).apply_eq_iff_eq - simp only [he] - by_cases hv : v = w - · subst v; rfl - · simp [hv] - -lemma permSign_ne_zero (g : Equiv.Perm S) : permSign g ≠ 0 := by - intro he - have H := permSign_sq g - rw [he, zero_mul] at H - exact zero_ne_one H - -lemma sum_wordVectors (x : EuclideanSpace ℂ (Words (S := S) odd k)) : - (∑ w, x w • wordVector w) = x := by - ext z - simp [WithLp.ofLp_sum, wordVector, WithLp.ofLp_smul] - -variable {L : Type*} [Fintype L] [DecidableEq L] (line : S → L) - -abbrev lineRepresentation := - (representation (S := S) (odd := odd) (k := k)).comp (RowColumn.lineGroup line).subtype - -omit [Fintype L] [DecidableEq L] [DecidableEq S] [Fintype C] in -lemma commuting_coefficient_relation - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) - (g : RowColumn.lineGroup line) (w v : Words (S := S) odd k) : - permSign (oddPerm g.1 v) * T (wordVector (actWord g.1 v)) (actWord g.1 w) = - permSign (oddPerm g.1 w) * T (wordVector v) w := by - have he := congrArg (fun x : EuclideanSpace ℂ (Words (S := S) odd k) => x (actWord g.1 w)) - (Representation.IntertwiningMap.isIntertwining _ _ T g (wordVector v)) - change T (representation g.1 (wordVector v)) (actWord g.1 w) = - representation g.1 (T (wordVector v)) (actWord g.1 w) at he - rw [signedMap_wordVector, map_smul, signedMap_transport_apply] at he - exact he - -end RowColumn.Signed - -namespace RowColumn.WordOrbits - -variable {S A : Type*} [Fintype S] [Fintype A] [DecidableEq A] - -/-- A complete invariant of the simultaneous permutation orbit of finitely -many words: the counts of their joint symbols. -/ -def counts (f : S → A) : A → Fin (Fintype.card S + 1) := fun a => - ⟨Fintype.card {x : S // f x = a}, - Nat.lt_succ_of_le (Fintype.card_subtype_le (fun x => f x = a))⟩ - -omit [Fintype A] in -lemma same_counts_permutation (f g : S → A) (he : counts f = counts g) : - ∃ p : Equiv.Perm S, ∀ x, g (p x) = f x := by - have hc (a : A) : Fintype.card {x : S // f x = a} = Fintype.card {x : S // g x = a} := - congrArg (fun z : A → Fin (Fintype.card S + 1) => (z a).1) he - let e (a : A) : {x : S // f x = a} ≃ {x : S // g x = a} := Fintype.equivOfCardEq (hc a) - let p : Equiv.Perm S := (Equiv.sigmaFiberEquiv f).symm |>.trans - ((Equiv.sigmaCongrRight e).trans (Equiv.sigmaFiberEquiv g)) - refine ⟨p, ?_⟩ - intro x - change g ((e (f x) ⟨x, rfl⟩).1) = f x - exact (e (f x) ⟨x, rfl⟩).2 - -/-- The label can record a row or a column. Joint counts then give a -word transporter inside the actual line subgroup, not an abstract action. -/ -lemma line_pair_transporter {L C : Type*} [Fintype L] [Fintype C] - [DecidableEq L] [DecidableEq C] - (line : S → L) (w v w' v' : S → C) - (he : counts (fun x => (line x, w x, v x)) = counts (fun x => (line x, w' x, v' x))) : - ∃ p : Equiv.Perm S, (∀ x, line (p x) = line x) ∧ - (∀ x, w' (p x) = w x) ∧ (∀ x, v' (p x) = v x) := by - obtain ⟨p, hp⟩ := same_counts_permutation _ _ he - refine ⟨p, (fun x => congrArg Prod.fst (hp x)), ?_⟩ - exact ⟨(fun x => congrArg (fun z => z.2.1) (hp x)), - (fun x => congrArg (fun z => z.2.2) (hp x))⟩ - -end RowColumn.WordOrbits - -namespace RowColumn.Signed -open CubeShuffle.Specht -open scoped BigOperators Classical - -variable {S C L : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - [Fintype L] [DecidableEq L] {odd : C → Prop} [DecidablePred odd] {k : ℕ} - (line : S → L) - -abbrev PairCountIndex := (L × C × C) → Fin (Fintype.card S + 1) - -def pairCounts (wv : Words (S := S) odd k × Words (S := S) odd k) : - PairCountIndex (S := S) (C := C) (L := L) := - RowColumn.WordOrbits.counts (fun x => (line x, wv.1.1 x, wv.2.1 x)) - -/-- Record one matrix coefficient per joint-symbol contingency table. Zero -coefficients in these representatives force every coefficient to be zero. -/ -def commutantData : - Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line) →ₗ[ℂ] - (PairCountIndex (S := S) (C := C) (L := L) → ℂ) where - toFun T a := if ha : ∃ wv, pairCounts (odd := odd) (k := k) line wv = a then - T (wordVector (Classical.choose ha).2) (Classical.choose ha).1 else 0 - map_add' T U := by - funext a - dsimp only [Pi.add_apply] - split_ifs <;> simp - map_smul' z T := by - funext a - dsimp only [Pi.smul_apply, RingHom.id_apply] - split_ifs <;> simp - -lemma commutantData_zero - (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) - (hz : commutantData line T = 0) : T = 0 := by - have hT (v : Words (S := S) odd k) : T (wordVector v) = 0 := by - ext w - let a := pairCounts line (w, v) - have ha : ∃ wv, pairCounts (odd := odd) (k := k) line wv = a := ⟨(w, v), rfl⟩ - let p := Classical.choose ha - have hp : pairCounts line p = a := Classical.choose_spec ha - have hrep : T (wordVector p.2) p.1 = 0 := by - have hh := congrArg (fun z : PairCountIndex (S := S) (C := C) (L := L) → ℂ => z a) hz - simpa only [commutantData, LinearMap.coe_mk, AddHom.coe_mk, dite_eq_left ha, Pi.zero_apply] - using hh - obtain ⟨g, hl, hw, hv⟩ := RowColumn.WordOrbits.line_pair_transporter line - w.1 v.1 p.1.1 p.2.1 hp.symm - have hgw : actWord g w = p.1 := by - apply Subtype.ext - funext x - have hh := hw (g⁻¹ x) - simpa using hh.symm - have hgv : actWord g v = p.2 := by - apply Subtype.ext - funext x - have hh := hv (g⁻¹ x) - simpa using hh.symm - have hre := commuting_coefficient_relation line T ⟨g, hl⟩ w v - rw [hgw, hgv, hrep, mul_zero] at hre - exact (mul_eq_zero.mp hre.symm).resolve_left (permSign_ne_zero _) - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - change T x = 0 - rw [← sum_wordVectors x, map_sum] - simp only [map_smul, hT, smul_zero, Finset.sum_const_zero] - -lemma commutantData_injective : Function.Injective - (commutantData (odd := odd) (k := k) line) := by - intro T U he - apply sub_eq_zero.mp - apply commutantData_zero line - rw [map_sub, he, sub_self] - -/-- Polynomial local multiplicity infrastructure, proved directly from -simultaneous signed-word orbits. This avoids assuming any LR-count estimate. -For the occupied board C has 2h colors, giving exponent 4*|lines|*h². -/ -theorem commutant_dimension_bound : - Module.finrank ℂ - (Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) - (lineRepresentation (odd := odd) (k := k) line)) ≤ - (Fintype.card S + 1) ^ (Fintype.card L * Fintype.card C ^ 2) := by - have hf := LinearMap.finrank_le_finrank_of_injective - (f := commutantData (odd := odd) (k := k) line) (commutantData_injective line) - simpa only [Module.finrank_fintype_fun_eq_card, PairCountIndex, Fintype.card_fun, - Fintype.card_fin, Fintype.card_prod, pow_two] using hf - -end RowColumn.Signed - -end - -end OAI +import OAI.RepresentationTheory.RowColumn.Basic + +namespace OAI + +noncomputable section + +open scoped BigOperators Classical + +namespace RowColumn.Signed +open CubeShuffle.Specht + +variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] +variable (odd : C → Prop) [DecidablePred odd] + +/-- Words with exactly k odd entries. This is the k-parity sector of the +literal signed slot space, not a formal unknown representation. -/ +abbrev Words (k : ℕ) := {w : S → C // Fintype.card {x : S // odd (w x)} = k} + + +variable {odd} {k : ℕ} + +/-- Odd slots of a word, genuinely a subset of the board slots. -/ +abbrev OddSlots (w : Words (S := S) odd k) := {x : S // odd (w.1 x)} + +def relabelOddEquiv (g : Equiv.Perm S) (w : S → C) : + {x : S // odd (w x)} ≃ {x : S // odd (w (g⁻¹ x))} where + toFun x := ⟨g x.1, by simpa using x.2⟩ + invFun x := ⟨g⁻¹ x.1, x.2⟩ + left_inv := by intro x; ext; simp + right_inv := by intro x; ext; simp + +def actWord (g : Equiv.Perm S) (w : Words (S := S) odd k) : Words (S := S) odd k := + ⟨fun x => w.1 (g⁻¹ x), (Fintype.card_congr (relabelOddEquiv g w.1)).symm.trans w.2⟩ + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +@[simp] lemma actWord_apply (g : Equiv.Perm S) (w : Words (S := S) odd k) (x : S) : + (actWord g w).1 x = w.1 (g⁻¹ x) := rfl + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +@[simp] lemma actWord_one (w : Words (S := S) odd k) : actWord 1 w = w := by + apply Subtype.ext + funext x + rfl + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma actWord_mul (g h : Equiv.Perm S) (w : Words (S := S) odd k) : + actWord (g * h) w = actWord g (actWord h w) := by + apply Subtype.ext + funext x + simp [actWord, mul_inv_rev] + +/-- Canonical frames choose the odd-slot orientation. Different choices conjugate +by a diagonal sign; the signed action is exactly reordering the odd slots. -/ +def oddFrame (w : Words (S := S) odd k) : OddSlots w ≃ Fin k := + Fintype.equivFinOfCardEq w.2 + +def oddPerm (g : Equiv.Perm S) (w : Words (S := S) odd k) : Equiv.Perm (Fin k) := + (oddFrame w).symm |>.trans ((relabelOddEquiv g w.1).trans (oddFrame (actWord g w))) + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma oddFrame_congr {w v : Words (S := S) odd k} (he : w = v) + (x : S) (hx : odd (w.1 x)) (hv : odd (v.1 x)) : + oddFrame w ⟨x, hx⟩ = oddFrame v ⟨x, hv⟩ := by + subst v + rfl + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +@[simp] lemma oddPerm_one (w : Words (S := S) odd k) : oddPerm 1 w = 1 := by + apply Equiv.ext + intro i + change oddFrame (actWord 1 w) ⟨(oddFrame w).symm i, _⟩ = i + have h := oddFrame_congr (actWord_one w) ((oddFrame w).symm i).1 + (show odd ((actWord 1 w).1 ((oddFrame w).symm i)) from ((oddFrame w).symm i).2) + ((oddFrame w).symm i).2 + exact h.trans ((oddFrame w).apply_symm_apply i) + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma oddPerm_mul (g h : Equiv.Perm S) (w : Words (S := S) odd k) : + oddPerm (g * h) w = oddPerm g (actWord h w) * oddPerm h w := by + apply Equiv.ext + intro i + change oddFrame (actWord (g * h) w) + ((relabelOddEquiv (g * h) w.1) ((oddFrame w).symm i)) = + oddFrame (actWord g (actWord h w)) + ((relabelOddEquiv g (actWord h w).1) + ((oddFrame (actWord h w)).symm + (oddFrame (actWord h w) ((relabelOddEquiv h w.1) ((oddFrame w).symm i))))) + erw [Equiv.symm_apply_apply] + exact oddFrame_congr (actWord_mul g h w) _ _ _ + +def wordsEquiv (g : Equiv.Perm S) : Equiv.Perm (Words (S := S) odd k) where + toFun := actWord g + invFun := actWord g⁻¹ + left_inv := by intro w; rw [← actWord_mul, inv_mul_cancel, actWord_one] + right_inv := by intro w; rw [← actWord_mul, mul_inv_cancel, actWord_one] + +/-- Signed slot action in the orthonormal word basis. It reorders the odd +subsequence, and does not introduce a sign for even slots. -/ +def signedMap (g : Equiv.Perm S) : + EuclideanSpace ℂ (Words (S := S) odd k) →ₗ[ℂ] EuclideanSpace ℂ (Words (S := S) odd k) where + toFun v := WithLp.toLp 2 (fun w => permSign (oddPerm g⁻¹ w) * v (actWord g⁻¹ w)) + map_add' := by intro v z; ext w; simp [mul_add] + map_smul' := by intro a v; ext w; simp [mul_left_comm] + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +@[simp] lemma signedMap_apply (g : Equiv.Perm S) + (v : EuclideanSpace ℂ (Words (S := S) odd k)) (w : Words (S := S) odd k) : + signedMap g v w = permSign (oddPerm g⁻¹ w) * v (actWord g⁻¹ w) := rfl + +/-- The signs genuinely compose; no group-action relation is assumed. -/ +def representation : Representation ℂ (Equiv.Perm S) (EuclideanSpace ℂ (Words (S := S) odd k)) where + toFun := signedMap + map_one' := by ext v w; simp + map_mul' g h := by + ext v w + simp only [signedMap_apply, Module.End.mul_apply, mul_inv_rev, oddPerm_mul, + permSign_mul, actWord_mul, mul_assoc] + ring + +omit [DecidableEq C] in +lemma representation_unitary : CubeShuffle.UnitaryFinite.IsUnitary + (representation (S := S) (odd := odd) (k := k)) := by + intro g v z + rw [PiLp.inner_apply, PiLp.inner_apply] + change (∑ w, inner ℂ (permSign (oddPerm g⁻¹ w) * v (actWord g⁻¹ w)) + (permSign (oddPerm g⁻¹ w) * z (actWord g⁻¹ w))) = _ + have hh (w : Words (S := S) odd k) : + inner ℂ (permSign (oddPerm g⁻¹ w) * v (actWord g⁻¹ w)) + (permSign (oddPerm g⁻¹ w) * z (actWord g⁻¹ w)) = + inner ℂ (v (actWord g⁻¹ w)) (z (actWord g⁻¹ w)) := by + simp only [RCLike.inner_apply, map_mul, conj_permSign] + rw [show permSign (oddPerm g⁻¹ w) * z (actWord g⁻¹ w) * + (permSign (oddPerm g⁻¹ w) * (starRingEnd ℂ) (v (actWord g⁻¹ w))) = + (permSign (oddPerm g⁻¹ w) * permSign (oddPerm g⁻¹ w)) * + (z (actWord g⁻¹ w) * (starRingEnd ℂ) (v (actWord g⁻¹ w))) by ring, + permSign_sq, one_mul] + simp_rw [hh] + exact Equiv.sum_comp (wordsEquiv g⁻¹) (fun w => inner ℂ (v w) (z w)) + +end RowColumn.Signed + +namespace RowColumn.Signed +open scoped BigOperators Classical +open CubeShuffle.Specht + +variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + {odd : C → Prop} [DecidablePred odd] {k : ℕ} + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma word_stabilizer_eq (g : Equiv.Perm S) (w : Words (S := S) odd k) + (hw : actWord g w = w) (x : S) : w.1 (g x) = w.1 x := by + have he := congrArg (fun z : Words (S := S) odd k => z.1 (g x)) hw + simpa using he.symm + +omit [Fintype C] [DecidableEq C] in +lemma oddPerm_sign_of_stabilizes (g : Equiv.Perm S) (w : Words (S := S) odd k) + (hw : actWord g w = w) (hfix : ∀ x, ¬ odd (w.1 x) → g x = x) : + permSign (oddPerm g w) = permSign g := by + have hs : ∀ x, odd (w.1 (g x)) ↔ odd (w.1 x) := fun x => by + rw [word_stabilizer_eq g w hw x] + have he := Equiv.Perm.sign_eq_sign_of_equiv (g.subtypePerm hs) + (oddPerm g w) (oddFrame w) (by + intro x + change oddFrame w ⟨g x.1, _⟩ = + oddFrame (actWord g w) + ((relabelOddEquiv g w.1) ((oddFrame w).symm (oddFrame w x))) + erw [Equiv.symm_apply_apply] + exact (oddFrame_congr hw (g x.1) _ _).symm) + have hf : ∀ x, g x ≠ x → odd (w.1 x) := by + intro x hn + by_contra h + exact hn (hfix x h) + rw [Equiv.Perm.sign_subtypePerm g hs hf] at he + exact congrArg (fun z : ℤˣ => ((z : ℤ) : ℂ)) he.symm + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma oddPerm_of_odd_fixed (g : Equiv.Perm S) (w : Words (S := S) odd k) + (hw : actWord g w = w) (hfix : ∀ x, odd (w.1 x) → g x = x) : + oddPerm g w = 1 := by + apply Equiv.ext + intro i + let x := (oddFrame w).symm i + change oddFrame (actWord g w) ⟨g x.1, _⟩ = i + have he := oddFrame_congr hw (g x.1) + (show odd ((actWord g w).1 (g x.1)) by simpa using x.2) + (by rw [hfix x.1 x.2]; exact x.2) + refine he.trans ?_ + have hh : (⟨g x.1, by rw [hfix x.1 x.2]; exact x.2⟩ : OddSlots w) = x := + Subtype.ext (hfix x.1 x.2) + rw [hh] + exact (oddFrame w).apply_symm_apply i + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma actWord_inv_eq_iff (g : Equiv.Perm S) (w : Words (S := S) odd k) : + actWord g⁻¹ w = w ↔ actWord g w = w := by + constructor + · intro he + have hh := congrArg (actWord g) he + rw [← actWord_mul, mul_inv_cancel, actWord_one] at hh + exact hh.symm + · intro he + have hh := congrArg (actWord g⁻¹) he + rw [← actWord_mul, inv_mul_cancel, actWord_one] at hh + exact hh.symm + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma oddPerm_inv_stabilizer (g : Equiv.Perm S) (w : Words (S := S) odd k) + (hw : actWord g w = w) : oddPerm g⁻¹ w = (oddPerm g w)⁻¹ := by + have hh := oddPerm_mul g⁻¹ g w + rw [inv_mul_cancel, oddPerm_one, hw] at hh + exact eq_inv_of_mul_eq_one_left hh.symm + +def wordVector (w : Words (S := S) odd k) : EuclideanSpace ℂ (Words (S := S) odd k) := + WithLp.toLp 2 (fun z => if z = w then 1 else 0) + +omit [DecidableEq S] [Fintype C] in +lemma wordVector_coefficient (g : Equiv.Perm S) (w : Words (S := S) odd k) : + Signed.representation g (wordVector w) w = + if actWord g w = w then permSign (oddPerm g w) else 0 := by + change permSign (oddPerm g⁻¹ w) * (if actWord g⁻¹ w = w then (1 : ℂ) else 0) = _ + simp only [actWord_inv_eq_iff] + split_ifs with he + · rw [oddPerm_inv_stabilizer g w he, permSign_inv, mul_one] + · exact mul_zero _ + +end RowColumn.Signed + +namespace RowColumn.Signed +open CubeShuffle.Specht +open scoped BigOperators Classical + +variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + {odd : C → Prop} [DecidablePred odd] {k : ℕ} + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma oddPerm_inv (g : Equiv.Perm S) (w : Words (S := S) odd k) : + oddPerm g⁻¹ (actWord g w) = (oddPerm g w)⁻¹ := by + have hh := oddPerm_mul g⁻¹ g w + rw [inv_mul_cancel, oddPerm_one] at hh + exact eq_inv_of_mul_eq_one_left hh.symm + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma signedMap_transport_apply (g : Equiv.Perm S) + (x : EuclideanSpace ℂ (Words (S := S) odd k)) (w : Words (S := S) odd k) : + representation g x (actWord g w) = permSign (oddPerm g w) * x w := by + change permSign (oddPerm g⁻¹ (actWord g w)) * x (actWord g⁻¹ (actWord g w)) = _ + rw [oddPerm_inv, permSign_inv, ← actWord_mul, inv_mul_cancel, actWord_one] + +omit [DecidableEq S] [Fintype C] in +lemma signedMap_wordVector (g : Equiv.Perm S) (w : Words (S := S) odd k) : + representation g (wordVector w) = permSign (oddPerm g w) • wordVector (actWord g w) := by + ext z + obtain ⟨v, rfl⟩ := (wordsEquiv g).surjective z + change representation g (wordVector w) (actWord g v) = _ + rw [signedMap_transport_apply] + change permSign (oddPerm g v) * (if v = w then (1 : ℂ) else 0) = + permSign (oddPerm g w) * (if actWord g v = actWord g w then (1 : ℂ) else 0) + have he : actWord g v = actWord g w ↔ v = w := (wordsEquiv g).apply_eq_iff_eq + simp only [he] + by_cases hv : v = w + · subst v; rfl + · simp [hv] + +lemma permSign_ne_zero (g : Equiv.Perm S) : permSign g ≠ 0 := by + intro he + have H := permSign_sq g + rw [he, zero_mul] at H + exact zero_ne_one H + +lemma sum_wordVectors (x : EuclideanSpace ℂ (Words (S := S) odd k)) : + (∑ w, x w • wordVector w) = x := by + ext z + simp [WithLp.ofLp_sum, wordVector, WithLp.ofLp_smul] + +variable {L : Type*} [Fintype L] [DecidableEq L] (line : S → L) + +abbrev lineRepresentation := + (representation (S := S) (odd := odd) (k := k)).comp (RowColumn.lineGroup line).subtype + +omit [Fintype L] [DecidableEq L] [DecidableEq S] [Fintype C] in +lemma commuting_coefficient_relation + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) + (g : RowColumn.lineGroup line) (w v : Words (S := S) odd k) : + permSign (oddPerm g.1 v) * T (wordVector (actWord g.1 v)) (actWord g.1 w) = + permSign (oddPerm g.1 w) * T (wordVector v) w := by + have he := congrArg (fun x : EuclideanSpace ℂ (Words (S := S) odd k) => x (actWord g.1 w)) + (Representation.IntertwiningMap.isIntertwining _ _ T g (wordVector v)) + change T (representation g.1 (wordVector v)) (actWord g.1 w) = + representation g.1 (T (wordVector v)) (actWord g.1 w) at he + rw [signedMap_wordVector, map_smul, signedMap_transport_apply] at he + exact he + +end RowColumn.Signed + +namespace RowColumn.WordOrbits + +variable {S A : Type*} [Fintype S] [Fintype A] [DecidableEq A] + +/-- A complete invariant of the simultaneous permutation orbit of finitely +many words: the counts of their joint symbols. -/ +def counts (f : S → A) : A → Fin (Fintype.card S + 1) := fun a => + ⟨Fintype.card {x : S // f x = a}, + Nat.lt_succ_of_le (Fintype.card_subtype_le (fun x => f x = a))⟩ + +omit [Fintype A] in +lemma same_counts_permutation (f g : S → A) (he : counts f = counts g) : + ∃ p : Equiv.Perm S, ∀ x, g (p x) = f x := by + have hc (a : A) : Fintype.card {x : S // f x = a} = Fintype.card {x : S // g x = a} := + congrArg (fun z : A → Fin (Fintype.card S + 1) => (z a).1) he + let e (a : A) : {x : S // f x = a} ≃ {x : S // g x = a} := Fintype.equivOfCardEq (hc a) + let p : Equiv.Perm S := (Equiv.sigmaFiberEquiv f).symm |>.trans + ((Equiv.sigmaCongrRight e).trans (Equiv.sigmaFiberEquiv g)) + refine ⟨p, ?_⟩ + intro x + change g ((e (f x) ⟨x, rfl⟩).1) = f x + exact (e (f x) ⟨x, rfl⟩).2 + +/-- The label can record a row or a column. Joint counts then give a +word transporter inside the actual line subgroup, not an abstract action. -/ +lemma line_pair_transporter {L C : Type*} [Fintype L] [Fintype C] + [DecidableEq L] [DecidableEq C] + (line : S → L) (w v w' v' : S → C) + (he : counts (fun x => (line x, w x, v x)) = counts (fun x => (line x, w' x, v' x))) : + ∃ p : Equiv.Perm S, (∀ x, line (p x) = line x) ∧ + (∀ x, w' (p x) = w x) ∧ (∀ x, v' (p x) = v x) := by + obtain ⟨p, hp⟩ := same_counts_permutation _ _ he + refine ⟨p, (fun x => congrArg Prod.fst (hp x)), ?_⟩ + exact ⟨(fun x => congrArg (fun z => z.2.1) (hp x)), + (fun x => congrArg (fun z => z.2.2) (hp x))⟩ + +end RowColumn.WordOrbits + +namespace RowColumn.Signed +open CubeShuffle.Specht +open scoped BigOperators Classical + +variable {S C L : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + [Fintype L] [DecidableEq L] {odd : C → Prop} [DecidablePred odd] {k : ℕ} + (line : S → L) + +abbrev PairCountIndex := (L × C × C) → Fin (Fintype.card S + 1) + +def pairCounts (wv : Words (S := S) odd k × Words (S := S) odd k) : + PairCountIndex (S := S) (C := C) (L := L) := + RowColumn.WordOrbits.counts (fun x => (line x, wv.1.1 x, wv.2.1 x)) + +/-- Record one matrix coefficient per joint-symbol contingency table. Zero +coefficients in these representatives force every coefficient to be zero. -/ +def commutantData : + Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line) →ₗ[ℂ] + (PairCountIndex (S := S) (C := C) (L := L) → ℂ) where + toFun T a := if ha : ∃ wv, pairCounts (odd := odd) (k := k) line wv = a then + T (wordVector (Classical.choose ha).2) (Classical.choose ha).1 else 0 + map_add' T U := by + funext a + dsimp only [Pi.add_apply] + split_ifs <;> simp + map_smul' z T := by + funext a + dsimp only [Pi.smul_apply, RingHom.id_apply] + split_ifs <;> simp + +lemma commutantData_zero + (T : Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) + (hz : commutantData line T = 0) : T = 0 := by + have hT (v : Words (S := S) odd k) : T (wordVector v) = 0 := by + ext w + let a := pairCounts line (w, v) + have ha : ∃ wv, pairCounts (odd := odd) (k := k) line wv = a := ⟨(w, v), rfl⟩ + let p := Classical.choose ha + have hp : pairCounts line p = a := Classical.choose_spec ha + have hrep : T (wordVector p.2) p.1 = 0 := by + have hh := congrArg (fun z : PairCountIndex (S := S) (C := C) (L := L) → ℂ => z a) hz + simpa only [commutantData, LinearMap.coe_mk, AddHom.coe_mk, dite_eq_left ha, Pi.zero_apply] + using hh + obtain ⟨g, hl, hw, hv⟩ := RowColumn.WordOrbits.line_pair_transporter line + w.1 v.1 p.1.1 p.2.1 hp.symm + have hgw : actWord g w = p.1 := by + apply Subtype.ext + funext x + have hh := hw (g⁻¹ x) + simpa using hh.symm + have hgv : actWord g v = p.2 := by + apply Subtype.ext + funext x + have hh := hv (g⁻¹ x) + simpa using hh.symm + have hre := commuting_coefficient_relation line T ⟨g, hl⟩ w v + rw [hgw, hgv, hrep, mul_zero] at hre + exact (mul_eq_zero.mp hre.symm).resolve_left (permSign_ne_zero _) + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + change T x = 0 + rw [← sum_wordVectors x, map_sum] + simp only [map_smul, hT, smul_zero, Finset.sum_const_zero] + +lemma commutantData_injective : Function.Injective + (commutantData (odd := odd) (k := k) line) := by + intro T U he + apply sub_eq_zero.mp + apply commutantData_zero line + rw [map_sub, he, sub_self] + +/-- Polynomial local multiplicity infrastructure, proved directly from +simultaneous signed-word orbits. This avoids assuming any LR-count estimate. +For the occupied board C has 2h colors, giving exponent 4*|lines|*h². -/ +theorem commutant_dimension_bound : + Module.finrank ℂ + (Representation.IntertwiningMap (lineRepresentation (odd := odd) (k := k) line) + (lineRepresentation (odd := odd) (k := k) line)) ≤ + (Fintype.card S + 1) ^ (Fintype.card L * Fintype.card C ^ 2) := by + have hf := LinearMap.finrank_le_finrank_of_injective + (f := commutantData (odd := odd) (k := k) line) (commutantData_injective line) + simpa only [Module.finrank_fintype_fun_eq_card, PairCountIndex, Fintype.card_fun, + Fintype.card_fin, Fintype.card_prod, pow_two] using hf + +end RowColumn.Signed + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/RowColumn/TensorFilter.lean b/lean/OAI/RepresentationTheory/RowColumn/TensorFilter.lean index b8e3c0d3e52854ad43049f6cda51eb4484bd3b53..2b15b2bd96e30a497c7282c6a55fb25cc7575f98 100644 --- a/lean/OAI/RepresentationTheory/RowColumn/TensorFilter.lean +++ b/lean/OAI/RepresentationTheory/RowColumn/TensorFilter.lean @@ -1,429 +1,429 @@ -import OAI.RepresentationTheory.RowColumn.Sectors -import OAI.LinearAlgebra.MatrixState.Whitening -import OAI.RepresentationTheory.RowColumn.Entropy - -namespace OAI - -section - -noncomputable section -open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder -namespace RowColumn.MatrixState -open FiniteStarAlgebra Signed -variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - -omit [DecidableEq C] in -lemma hsVector_tensor_norm_sq (M : S → Matrix C C ℂ) : - ‖hsVector (tensorMatrix M)‖^2 = ∏ i, ‖hsVector (M i)‖^2 := by - rw [hsVector_norm_sq, tensorMatrix_star, tensorMatrix_mul, tensorMatrix_trace] - simp_rw [← hsVector_inner, inner_self_eq_norm_sq_to_K] - change (∏ i, ((‖hsVector (M i)‖ : ℝ) : ℂ)^2).re = _ - simp only [← Complex.ofReal_pow, ← Complex.ofReal_prod, Complex.ofReal_re] - -omit [DecidableEq S] [Fintype C] [DecidableEq C] in -lemma sectorTensor_hermitian (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M : S → Matrix C C ℂ) (hM : ∀ i, (M i).IsHermitian) : - (sectorTensor odd k M).IsHermitian := by - change star (sectorTensor odd k M) = sectorTensor odd k M - rw [← sectorTensor_star] - congr 1 - funext i - exact hM i - -lemma sectorTensor_positive (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M : S → Matrix C C ℂ) (hM : ∀ i, (M i).PosSemidef) : - (sectorTensor odd k M).PosSemidef := - (tensorMatrix_posSemidef M hM).submatrix _ - -lemma sectorTensor_root_square (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M : S → Matrix C C ℂ) (hM : ∀ i, (M i).PosSemidef) - (he : ∀ i, M i ∈ evenAlgebra odd) : - sectorTensor odd k (fun i => CFC.sqrt (M i)) ^ 2 = sectorTensor odd k M := by - rw [pow_two, ← sectorTensor_mul odd k _ _ (fun i => sqrt_even odd (M i) (hM i) (he i))] - congr 1 - funext i - exact CFC.sqrt_mul_sqrt_self _ (hM i).nonneg - -/-- The restriction is taken only after factoring the positive weighted -Hilbert--Schmidt norm. In particular no diagonal of a nonpositive product is -compared to the full trace. -/ -lemma sector_unitary_sandwich_bound (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M N : S → Matrix C C ℂ) (U : Matrix C C ℂ) - (hM : ∀ i, (M i).PosSemidef) (hN : ∀ i, (N i).PosSemidef) - (heM : ∀ i, M i ∈ evenAlgebra odd) (_ : ∀ i, N i ∈ evenAlgebra odd) - (heU : U ∈ evenAlgebra odd) : - ‖hsVector (sectorTensor odd k (fun i => CFC.sqrt (M i)) * - sectorTensor odd k (fun _ : S => U) * - sectorTensor odd k (fun i => CFC.sqrt (N i)))‖^2 ≤ - ∏ i, (M i * U * N i * U.conjTranspose).trace.re := by - rw [← sectorTensor_mul odd k _ _ (fun i => sqrt_even odd (M i) (hM i) (heM i))] - rw [← sectorTensor_mul odd k _ _ (fun i => (evenAlgebra odd).mul_mem - (sqrt_even odd (M i) (hM i) (heM i)) heU)] - let e : Words (S := S) odd k ↪ (S → C) := ⟨Subtype.val, Subtype.val_injective⟩ - have hb := hsVector_submatrix_norm_sq_le e e - (tensorMatrix (fun i => CFC.sqrt (M i) * U * CFC.sqrt (N i))) - change ‖hsVector (sectorTensor odd k _)‖^2 ≤ _ at hb - rw [hsVector_tensor_norm_sq] at hb - convert hb using 1 - apply Finset.prod_congr rfl - intro i _ - rw [hsVector_sandwich_sq _ _ U - (Matrix.nonneg_iff_posSemidef.mp (CFC.sqrt_nonneg (M i))).isHermitian - (Matrix.nonneg_iff_posSemidef.mp (CFC.sqrt_nonneg (N i))).isHermitian] - rw [CFC.sq_sqrt (M i) (hM i).nonneg, CFC.sq_sqrt (N i) (hN i).nonneg] - -/-- Use the intrinsic spectral order on the closed finite C*-algebra. Its -physical Hilbert--Schmidt structure and existing operator norm are unchanged. -/ -lemma algebra_reconstruction_hilbert_bound - {E H G : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] - [FiniteDimensional ℂ E] [NormedAddCommGroup H] [InnerProductSpace ℂ H] [Group G] - (A : StarSubalgebra ℂ (E →L[ℂ] E)) (u : G →* unitary A) - (hspan : Submodule.span ℂ (Set.range fun g : G => (u g : A)) = ⊤) - (B : A) (F : A →ₗ[ℂ] H) (R : ℝ) (hR : 0 ≤ R) - (hU : ∀ g, ‖F (u g : A)‖ ≤ R) : - ‖F B‖ ≤ 4 * (Module.finrank ℂ A : ℝ) * ‖B‖ * R := by - let : PartialOrder A := CStarAlgebra.spectralOrder A - let : StarOrderedRing A := CStarAlgebra.spectralOrderedRing A - exact UnitaryFrame.reconstruction_hilbert_bound (physicalTrace A) (algebraCore A) - (core_inner_trace A) u hspan B F R hR hU - -/-- Matrix form of an actual algebra element, with the unchanged physical -coordinate basis on the signed tensor sector. -/ -def algebraMatrix {I : Type*} [Fintype I] [DecidableEq I] - (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) : - A →ₗ[ℂ] Matrix I I ℂ := - (Matrix.toEuclideanCLM (𝕜 := ℂ)).symm.toAlgEquiv.toLinearMap.comp A.subtype.toLinearMap - -def sandwichMap {I : Type*} [Fintype I] [DecidableEq I] - (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) - (M N : Matrix I I ℂ) : A →ₗ[ℂ] EuclideanSpace ℂ (I × I) := - hsVector.comp ((LinearMap.mulRight ℂ N).comp ((LinearMap.mulLeft ℂ M).comp (algebraMatrix A))) - -lemma sandwichMap_apply {I : Type*} [Fintype I] [DecidableEq I] - (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) - (M N : Matrix I I ℂ) (a : A) : - sandwichMap A M N a = hsVector (M * algebraMatrix A a * N) := rfl - -lemma sector_unitary_matrix (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (U : unitary (evenAlgebra odd)) : - algebraMatrix (sectorAlgebra (S := S) odd k) - (unitarySpanHom (R := ℂ) (sectorUnitary (S := S) odd k) U).val = sectorTensor odd k (fun _ : S => U.val.val) := by - exact (Matrix.toEuclideanCLM (𝕜 := ℂ)).symm_apply_apply _ - -/-- Weighted reconstruction in the actual signed sector, with the exact -occupied-board entropy loss and singular quarter-root normalization. -/ -theorem whitened_reconstruction_bound {L K : Type*} [Fintype L] [Fintype K] - [DecidableEq L] [DecidableEq K] [Nonempty S] - (odd : C → Prop) [DecidablePred odd] (k : ℕ) (e : S ↪ L × K) - (M : L → Matrix C C ℂ) (N : K → Matrix C C ℂ) - (hM : ∀ i, (M i).PosSemidef) (hN : ∀ j, (N j).PosSemidef) - (heM : ∀ i, M i ∈ evenAlgebra odd) (heN : ∀ j, N j ∈ evenAlgebra odd) - (hMt : ∀ i, (M i).trace.re ≤ 1) (hNt : ∀ j, (N j).trace.re ≤ 1) - (B : sectorAlgebra (S := S) odd k) : - let p := uniformMarginal (fun i => (e i).1) - let q := uniformMarginal (fun i => (e i).2) - let M' := fun i => whitenState (stateMean p M) (M i) - let N' := fun j => whitenState (stateMean q N) (N j) - ‖hsVector (sectorTensor odd k (fun i => CFC.sqrt (M' (e i).1)) * - algebraMatrix (sectorAlgebra (S := S) odd k) B * - sectorTensor odd k (fun i => CFC.sqrt (N' (e i).2)))‖^2 ≤ - 16 * (Module.finrank ℂ (sectorAlgebra (S := S) odd k) : ℝ)^2 * ‖B‖^2 * - Real.exp ((Fintype.card L * Fintype.card K - Fintype.card S : ℕ) : ℝ) := by - dsimp only - let p := uniformMarginal (fun i => (e i).1) - let q := uniformMarginal (fun i => (e i).2) - let M' := fun i => whitenState (stateMean p M) (M i) - let N' := fun j => whitenState (stateMean q N) (N j) - let A := sectorAlgebra (S := S) odd k - let R := Real.exp ((Fintype.card L * Fintype.card K - Fintype.card S : ℕ) : ℝ) - let F := sandwichMap A (sectorTensor odd k (fun i => CFC.sqrt (M' (e i).1))) - (sectorTensor odd k (fun i => CFC.sqrt (N' (e i).2))) - have hp := uniformMarginal_nonneg (fun i => (e i).1) - have hq := uniformMarginal_nonneg (fun i => (e i).2) - have hMp : ∀ i, (M' i).PosSemidef := fun i => whitenState_positive _ _ (hM i) - have hNp : ∀ j, (N' j).PosSemidef := fun j => whitenState_positive _ _ (hN j) - have hMe : ∀ i, M' i ∈ evenAlgebra odd := fun i => - whitenState_even odd _ _ (stateMean_positive p M hp hM) (stateMean_even odd p M heM) (heM i) - have hNe : ∀ j, N' j ∈ evenAlgebra odd := fun j => - whitenState_even odd _ _ (stateMean_positive q N hq hN) (stateMean_even odd q N heN) (heN j) - have hu (U : unitary (evenAlgebra odd)) : - ‖F (unitarySpanHom (R := ℂ) (sectorUnitary (S := S) odd k) U).val‖ ≤ Real.sqrt R := by - apply Real.le_sqrt_of_sq_le - change ‖hsVector (sectorTensor odd k (fun i => CFC.sqrt (M' (e i).1)) * - algebraMatrix (sectorAlgebra (S := S) odd k) - (unitarySpanHom (R := ℂ) (sectorUnitary (S := S) odd k) U).val * - sectorTensor odd k (fun i => CFC.sqrt (N' (e i).2)))‖^2 ≤ R - rw [sector_unitary_matrix] - apply (sector_unitary_sandwich_bound odd k (fun i => M' (e i).1) (fun i => N' (e i).2) - U.val.val (fun i => hMp _) (fun i => hNp _) (fun i => hMe _) (fun i => hNe _) - U.val.property).trans - apply occupied_product_of_mean_le e (fun i j => (M' i * U.val.val * N' j * U.val.val.conjTranspose).trace.re) - · exact fun i j => local_overlap_nonneg _ _ _ (hMp i) (hNp j) - · exact weighted_whitened_mean_le_one p q M N hp hq (sum_uniformMarginal _) - (sum_uniformMarginal _) hM hN hMt hNt U.val.val - ⟨congrArg Subtype.val U.property.1, congrArg Subtype.val U.property.2⟩ - have hh := algebra_reconstruction_hilbert_bound A - (unitarySpanHom (R := ℂ) (sectorUnitary (S := S) odd k)) - (unitarySpanHom_spans (R := ℂ) (sectorUnitary (S := S) odd k)) B F - (Real.sqrt R) (Real.sqrt_nonneg _) hu - have hs := pow_le_pow_left₀ (norm_nonneg (F B)) hh 2 - change ‖F B‖^2 ≤ _ - calc - _ ≤ (4 * (Module.finrank ℂ A : ℝ) * ‖B‖ * Real.sqrt R)^2 := hs - _ = _ := by - dsimp only [A, R] - simp only [mul_pow, Real.sq_sqrt (le_of_lt (Real.exp_pos _))] - ring - -lemma filtered_trace_identity {I : Type*} [Fintype I] [DecidableEq I] - (A B R T F G Q : Matrix I I ℂ) - (hR : R.IsHermitian) (hT : T.IsHermitian) - (hF : F.IsHermitian) (hG : G.IsHermitian) (hQ : Q.IsHermitian) - (hA : F * R^2 * F = A) (hB : G * T^2 * G = B) : - (A * Q * B * Q).trace.re = ‖hsVector (R * (F * Q * G) * T)‖^2 := by - rw [hsVector_sandwich_sq R T _ hR hT] - simp only [Matrix.conjTranspose_mul, hF.eq, hG.eq, hQ.eq] - rw [← hA, ← hB] - apply congrArg Complex.re - calc - _ = (F * (R^2 * F * Q * G * T^2 * G * Q)).trace := by simp only [mul_assoc] - _ = ((R^2 * F * Q * G * T^2 * G * Q) * F).trace := Matrix.trace_mul_comm _ _ - _ = _ := by simp only [mul_assoc] - -end RowColumn.MatrixState - -end -end - - -section - -noncomputable section -open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder -namespace RowColumn.MatrixState -open FiniteStarAlgebra Signed -variable {I : Type*} [Fintype I] [DecidableEq I] - -lemma algebraMatrix_mul (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) - (a b : A) : algebraMatrix A (a*b) = algebraMatrix A a * algebraMatrix A b := - (Matrix.toEuclideanCLM (𝕜 := ℂ)).symm.map_mul a.val b.val -lemma algebraMatrix_star (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) - (a : A) : algebraMatrix A (star a) = star (algebraMatrix A a) := - (Matrix.toEuclideanCLM (n := I) (𝕜 := ℂ)).symm.map_star' a.val -lemma algebraMatrix_hermitian (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) - (a : A) (ha : star a=a) : (algebraMatrix A a).IsHermitian := by - change star (algebraMatrix A a)=_ - rw [← algebraMatrix_star, ha] -lemma algebraMatrix_trace (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) - (a : A) : (algebraMatrix A a).trace = physicalTrace A a := by - rw [← trace_toEuclideanCLM] - change LinearMap.trace ℂ (EuclideanSpace ℂ I) - ((Matrix.toEuclideanCLM (𝕜 := ℂ)) ((Matrix.toEuclideanCLM (𝕜 := ℂ)).symm a.val)).toLinearMap = _ - rw [(Matrix.toEuclideanCLM (𝕜 := ℂ)).apply_symm_apply] - rfl - -variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] - -lemma tensorMatrix_trace_re (M : S → Matrix C C ℂ) (hM : ∀ i, (M i).PosSemidef) : - (tensorMatrix M).trace.re = ∏ i, (M i).trace.re := by - have hs (i : S) : (CFC.sqrt (M i)).conjTranspose * CFC.sqrt (M i) = M i := by - rw [(Matrix.nonneg_iff_posSemidef.mp (CFC.sqrt_nonneg (M i))).isHermitian.eq] - exact CFC.sqrt_mul_sqrt_self _ (hM i).nonneg - have ht := hsVector_tensor_norm_sq (fun i => CFC.sqrt (M i)) - simp only [hsVector_norm_sq, tensorMatrix_star, tensorMatrix_mul, hs] at ht - exact ht - -lemma sectorTensor_trace_le (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M : S → Matrix C C ℂ) (hM : ∀ i, (M i).PosSemidef) : - (sectorTensor odd k M).trace.re ≤ (tensorMatrix M).trace.re := by - let e : Words (S := S) odd k ↪ (S → C) := ⟨Subtype.val, Subtype.val_injective⟩ - have hh := finite_sum_embedding_le e (fun w => (tensorMatrix M w w).re) - (fun w => ((tensorMatrix_posSemidef M hM).diag_nonneg (i := w)).1) - simpa only [sectorTensor, Matrix.trace, Matrix.diag, Complex.re_sum, Matrix.submatrix_apply, e, Function.Embedding.coeFn_mk] using hh - -lemma sectorTensor_substate_trace (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M : S → Matrix C C ℂ) (hM : ∀ i, (M i).PosSemidef) - (htr : ∀ i, (M i).trace.re ≤ 1) : (sectorTensor odd k M).trace.re ≤ 1 := by - apply (sectorTensor_trace_le odd k M hM).trans - rw [tensorMatrix_trace_re M hM] - exact Finset.prod_le_one₀ (fun i _ => (hM i).trace_nonneg.1) (fun i _ => htr i) - -def positiveTensor (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M : Matrix C C ℂ) (hM : M.PosSemidef) (he : M ∈ evenAlgebra odd) : - sectorAlgebra (S := S) odd k := - ⟨Matrix.toEuclideanCLM (𝕜 := ℂ) (sectorTensor odd k (fun _ : S => M)), - sectorTensor_mem_algebra odd k M hM.isHermitian he⟩ - -lemma positiveTensor_matrix (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M : Matrix C C ℂ) (hM : M.PosSemidef) (he : M ∈ evenAlgebra odd) : - algebraMatrix (sectorAlgebra (S := S) odd k) (positiveTensor odd k M hM he) = - sectorTensor odd k (fun _ : S => M) := - (Matrix.toEuclideanCLM (𝕜 := ℂ)).symm_apply_apply _ - -lemma positiveTensor_isPositive (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M : Matrix C C ℂ) (hM : M.PosSemidef) (he : M ∈ evenAlgebra odd) : - (positiveTensor (S := S) odd k M hM he).val.IsPositive := - (toEuclideanCLM_positive_iff _).mpr (sectorTensor_positive odd k _ (fun _ : S => hM)) - -lemma positiveTensor_selfAdjoint (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M : Matrix C C ℂ) (hM : M.PosSemidef) (he : M ∈ evenAlgebra odd) : - IsSelfAdjoint (positiveTensor (S := S) odd k M hM he) := by - apply Subtype.ext - exact (positiveTensor_isPositive odd k M hM he).isSelfAdjoint - -lemma positiveTensor_trace_le_one (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M : Matrix C C ℂ) (hM : M.PosSemidef) (he : M ∈ evenAlgebra odd) (htr : M.trace.re ≤ 1) : - (physicalTrace (sectorAlgebra (S := S) odd k) (positiveTensor odd k M hM he)).re ≤ 1 := by - rw [← algebraMatrix_trace, positiveTensor_matrix] - exact sectorTensor_substate_trace odd k _ (fun _ : S => hM) (fun _ => htr) - -lemma positiveTensor_quarter_four (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (M : Matrix C C ℂ) (hM : M.PosSemidef) (he : M ∈ evenAlgebra odd) : - positiveTensor (S := S) odd k (quarterRoot M) (quarter_positive M) (quarter_even odd M hM he) ^ 4 = - positiveTensor odd k M hM he := by - apply Subtype.ext - change (Matrix.toEuclideanCLM (𝕜 := ℂ) (sectorTensor odd k (fun _ : S => quarterRoot M)))^4 = _ - rw [← map_pow] - have hh := (sectorPowerHom (S := S) odd k).map_pow - (⟨quarterRoot M, quarter_even odd M hM he⟩ : evenAlgebra odd) 4 - change sectorTensor odd k (fun _ : S => quarterRoot M ^ 4) = - (sectorTensor odd k (fun _ : S => quarterRoot M)) ^ 4 at hh - rw [← hh, quarter_four M hM] - rfl - -/-- The actual irreducible-dimension filter acts on fourth powers of both -mean-state tensors. Its quarter-root sandwich has squared norm at most 1/d. -/ -theorem quarter_tensor_filter_bound (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (q : sectorAlgebra (S := S) odd k) (hqs : star q=q) (hqq : q*q=q) - (hqc : ∀ a, q*a=a*q) (d : ℝ) (hd : 0 whitenState A (M i) - sectorTensor odd k (fun _ : S => quarterRoot A) * - sectorTensor odd k (fun x => CFC.sqrt (M' (line x))) ^ 2 * - sectorTensor odd k (fun _ : S => quarterRoot A) = - sectorTensor odd k (fun x => M (line x)) := by - dsimp only - let p := uniformMarginal line - let A := stateMean p M - let M' := fun i => whitenState A (M i) - have hp := uniformMarginal_nonneg line - have hA := stateMean_positive p M hp hM - have heA := stateMean_even odd p M heM - have hMp : ∀ i, (M' i).PosSemidef := fun i => whitenState_positive A (M i) (hM i) - have hMe : ∀ i, M' i ∈ evenAlgebra odd := fun i => whitenState_even odd A (M i) hA heA (heM i) - change sectorTensor odd k (fun _ : S => quarterRoot A) * - sectorTensor odd k (fun x => CFC.sqrt (M' (line x))) ^ 2 * - sectorTensor odd k (fun _ : S => quarterRoot A) = _ - rw [sectorTensor_root_square odd k _ (fun x => hMp _) (fun x => hMe _)] - rw [← sectorTensor_mul odd k _ _ (fun _ => quarter_even odd A hA heA)] - rw [← sectorTensor_mul odd k _ _ (fun x => (evenAlgebra odd).mul_mem - (quarter_even odd A hA heA) (hMe _))] - congr 1 - funext x - exact unwhitenState p M hp hM (line x) (uniformMarginal_pos line x) - -/-- The quantitative global bridge: two arbitrary admissible fibre-product -substates, on the actual signed sector and the actual central isotypic filter. -No invertibility, sector-surrogate, or postselection bound is assumed. -/ -theorem sector_filtered_trace_bound {L K : Type*} [Fintype L] [Fintype K] - [DecidableEq L] [DecidableEq K] [Nonempty S] - (odd : C → Prop) [DecidablePred odd] (k : ℕ) (e : S ↪ L × K) - (q : sectorAlgebra (S := S) odd k) (hqs : star q=q) (hqq : q*q=q) - (hqc : ∀ a, q*a=a*q) (d : ℝ) (hd : 0 M (e x).1) * algebraMatrix (sectorAlgebra (S := S) odd k) q * - sectorTensor odd k (fun x => N (e x).2) * algebraMatrix (sectorAlgebra (S := S) odd k) q).trace.re ≤ - 16 * (Module.finrank ℂ (sectorAlgebra (S := S) odd k) : ℝ)^2 * - Real.exp ((Fintype.card L * Fintype.card K - Fintype.card S : ℕ) : ℝ) / d := by - let p := uniformMarginal (fun x => (e x).1) - let r := uniformMarginal (fun x => (e x).2) - let A := stateMean p M - let B := stateMean r N - let M' := fun i => whitenState A (M i) - let N' := fun j => whitenState B (N j) - have hp := uniformMarginal_nonneg (fun x => (e x).1) - have hr := uniformMarginal_nonneg (fun x => (e x).2) - have hA := stateMean_positive p M hp hM - have hB := stateMean_positive r N hr hN - have heA := stateMean_even odd p M heM - have heB := stateMean_even odd r N heN - let F := positiveTensor (S := S) odd k (quarterRoot A) (quarter_positive A) (quarter_even odd A hA heA) - let G := positiveTensor (S := S) odd k (quarterRoot B) (quarter_positive B) (quarter_even odd B hB heB) - have hnorm : ‖F*q*G‖^2 ≤ 1/d := quarter_tensor_filter_bound odd k q hqs hqq hqc d hd hfilter - A B hA hB heA heB (stateMean_trace_le_one p M hp (sum_uniformMarginal _) hMt) - (stateMean_trace_le_one r N hr (sum_uniformMarginal _) hNt) - have hrec := whitened_reconstruction_bound odd k e M N hM hN heM heN hMt hNt (F*q*G) - change ‖hsVector (sectorTensor odd k (fun x => CFC.sqrt (M' (e x).1)) * - algebraMatrix (sectorAlgebra (S := S) odd k) (F*q*G) * - sectorTensor odd k (fun x => CFC.sqrt (N' (e x).2)))‖^2 ≤ _ at hrec - simp only [algebraMatrix_mul, F, G, positiveTensor_matrix] at hrec - have hi := filtered_trace_identity - (sectorTensor odd k (fun x => M (e x).1)) (sectorTensor odd k (fun x => N (e x).2)) - (sectorTensor odd k (fun x => CFC.sqrt (M' (e x).1))) - (sectorTensor odd k (fun x => CFC.sqrt (N' (e x).2))) - (sectorTensor odd k (fun _ : S => quarterRoot A)) - (sectorTensor odd k (fun _ : S => quarterRoot B)) - (algebraMatrix (sectorAlgebra (S := S) odd k) q) - (sectorTensor_hermitian odd k _ (fun x => (Matrix.nonneg_iff_posSemidef.mp (CFC.sqrt_nonneg _)).isHermitian)) - (sectorTensor_hermitian odd k _ (fun x => (Matrix.nonneg_iff_posSemidef.mp (CFC.sqrt_nonneg _)).isHermitian)) - (sectorTensor_hermitian odd k _ (fun _ => (quarter_positive A).isHermitian)) - (sectorTensor_hermitian odd k _ (fun _ => (quarter_positive B).isHermitian)) - (algebraMatrix_hermitian _ q hqs) - (sector_unwhiten_identity odd k (fun x => (e x).1) M hM heM) - (sector_unwhiten_identity odd k (fun x => (e x).2) N hN heN) - rw [hi] - apply hrec.trans - have hh := mul_le_mul_of_nonneg_right - (mul_le_mul_of_nonneg_left hnorm - (by positivity : 0 ≤ 16 * (Module.finrank ℂ (sectorAlgebra (S := S) odd k) : ℝ)^2)) - (le_of_lt (Real.exp_pos ((Fintype.card L * Fintype.card K - Fintype.card S : ℕ) : ℝ))) - convert hh using 1; ring - -/-- The filter used above exists in the concrete tensor algebra, for every -actual irreducible that occurs. The identity condition on its isotypic carrier -will be applied to the explicit isometric hook embedding. -/ -theorem exists_sector_isotypic_filter {V : Type*} [AddCommGroup V] - [Module ℂ V] [FiniteDimensional ℂ V] - (odd : C → Prop) [DecidablePred odd] (k : ℕ) - (ρ : Representation ℂ (Equiv.Perm S) V) [Representation.IsIrreducible ρ] : - ∃ q : sectorAlgebra (S := S) odd k, star q=q ∧ q*q=q ∧ (∀ a, q*a=a*q) ∧ - (∀ x ∈ Isotypic.carrier ρ (Signed.representation (S := S) (odd := odd) (k := k)), q.val x=x) ∧ - ∀ a : sectorAlgebra (S := S) odd k, a.val.IsPositive → - ‖q*a‖ ≤ (physicalTrace (sectorAlgebra (S := S) odd k) a).re / Module.finrank ℂ V := - exists_isotypic_filter ρ (Signed.representation (S := S) (odd := odd) (k := k)) - (Signed.representation_unitary (S := S) (odd := odd) (k := k)) (sectorAlgebra (S := S) odd k) - (sectorAlgebra_commutes odd k) - -end RowColumn.MatrixState - -end -end - -end OAI +import OAI.RepresentationTheory.RowColumn.Sectors +import OAI.LinearAlgebra.MatrixState.Whitening +import OAI.RepresentationTheory.RowColumn.Entropy + +namespace OAI + +section + +noncomputable section +open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder +namespace RowColumn.MatrixState +open FiniteStarAlgebra Signed +variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + +omit [DecidableEq C] in +lemma hsVector_tensor_norm_sq (M : S → Matrix C C ℂ) : + ‖hsVector (tensorMatrix M)‖^2 = ∏ i, ‖hsVector (M i)‖^2 := by + rw [hsVector_norm_sq, tensorMatrix_star, tensorMatrix_mul, tensorMatrix_trace] + simp_rw [← hsVector_inner, inner_self_eq_norm_sq_to_K] + change (∏ i, ((‖hsVector (M i)‖ : ℝ) : ℂ)^2).re = _ + simp only [← Complex.ofReal_pow, ← Complex.ofReal_prod, Complex.ofReal_re] + +omit [DecidableEq S] [Fintype C] [DecidableEq C] in +lemma sectorTensor_hermitian (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M : S → Matrix C C ℂ) (hM : ∀ i, (M i).IsHermitian) : + (sectorTensor odd k M).IsHermitian := by + change star (sectorTensor odd k M) = sectorTensor odd k M + rw [← sectorTensor_star] + congr 1 + funext i + exact hM i + +lemma sectorTensor_positive (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M : S → Matrix C C ℂ) (hM : ∀ i, (M i).PosSemidef) : + (sectorTensor odd k M).PosSemidef := + (tensorMatrix_posSemidef M hM).submatrix _ + +lemma sectorTensor_root_square (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M : S → Matrix C C ℂ) (hM : ∀ i, (M i).PosSemidef) + (he : ∀ i, M i ∈ evenAlgebra odd) : + sectorTensor odd k (fun i => CFC.sqrt (M i)) ^ 2 = sectorTensor odd k M := by + rw [pow_two, ← sectorTensor_mul odd k _ _ (fun i => sqrt_even odd (M i) (hM i) (he i))] + congr 1 + funext i + exact CFC.sqrt_mul_sqrt_self _ (hM i).nonneg + +/-- The restriction is taken only after factoring the positive weighted +Hilbert--Schmidt norm. In particular no diagonal of a nonpositive product is +compared to the full trace. -/ +lemma sector_unitary_sandwich_bound (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M N : S → Matrix C C ℂ) (U : Matrix C C ℂ) + (hM : ∀ i, (M i).PosSemidef) (hN : ∀ i, (N i).PosSemidef) + (heM : ∀ i, M i ∈ evenAlgebra odd) (_ : ∀ i, N i ∈ evenAlgebra odd) + (heU : U ∈ evenAlgebra odd) : + ‖hsVector (sectorTensor odd k (fun i => CFC.sqrt (M i)) * + sectorTensor odd k (fun _ : S => U) * + sectorTensor odd k (fun i => CFC.sqrt (N i)))‖^2 ≤ + ∏ i, (M i * U * N i * U.conjTranspose).trace.re := by + rw [← sectorTensor_mul odd k _ _ (fun i => sqrt_even odd (M i) (hM i) (heM i))] + rw [← sectorTensor_mul odd k _ _ (fun i => (evenAlgebra odd).mul_mem + (sqrt_even odd (M i) (hM i) (heM i)) heU)] + let e : Words (S := S) odd k ↪ (S → C) := ⟨Subtype.val, Subtype.val_injective⟩ + have hb := hsVector_submatrix_norm_sq_le e e + (tensorMatrix (fun i => CFC.sqrt (M i) * U * CFC.sqrt (N i))) + change ‖hsVector (sectorTensor odd k _)‖^2 ≤ _ at hb + rw [hsVector_tensor_norm_sq] at hb + convert hb using 1 + apply Finset.prod_congr rfl + intro i _ + rw [hsVector_sandwich_sq _ _ U + (Matrix.nonneg_iff_posSemidef.mp (CFC.sqrt_nonneg (M i))).isHermitian + (Matrix.nonneg_iff_posSemidef.mp (CFC.sqrt_nonneg (N i))).isHermitian] + rw [CFC.sq_sqrt (M i) (hM i).nonneg, CFC.sq_sqrt (N i) (hN i).nonneg] + +/-- Use the intrinsic spectral order on the closed finite C*-algebra. Its +physical Hilbert--Schmidt structure and existing operator norm are unchanged. -/ +lemma algebra_reconstruction_hilbert_bound + {E H G : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] + [FiniteDimensional ℂ E] [NormedAddCommGroup H] [InnerProductSpace ℂ H] [Group G] + (A : StarSubalgebra ℂ (E →L[ℂ] E)) (u : G →* unitary A) + (hspan : Submodule.span ℂ (Set.range fun g : G => (u g : A)) = ⊤) + (B : A) (F : A →ₗ[ℂ] H) (R : ℝ) (hR : 0 ≤ R) + (hU : ∀ g, ‖F (u g : A)‖ ≤ R) : + ‖F B‖ ≤ 4 * (Module.finrank ℂ A : ℝ) * ‖B‖ * R := by + let : PartialOrder A := CStarAlgebra.spectralOrder A + let : StarOrderedRing A := CStarAlgebra.spectralOrderedRing A + exact UnitaryFrame.reconstruction_hilbert_bound (physicalTrace A) (algebraCore A) + (core_inner_trace A) u hspan B F R hR hU + +/-- Matrix form of an actual algebra element, with the unchanged physical +coordinate basis on the signed tensor sector. -/ +def algebraMatrix {I : Type*} [Fintype I] [DecidableEq I] + (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) : + A →ₗ[ℂ] Matrix I I ℂ := + (Matrix.toEuclideanCLM (𝕜 := ℂ)).symm.toAlgEquiv.toLinearMap.comp A.subtype.toLinearMap + +def sandwichMap {I : Type*} [Fintype I] [DecidableEq I] + (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) + (M N : Matrix I I ℂ) : A →ₗ[ℂ] EuclideanSpace ℂ (I × I) := + hsVector.comp ((LinearMap.mulRight ℂ N).comp ((LinearMap.mulLeft ℂ M).comp (algebraMatrix A))) + +lemma sandwichMap_apply {I : Type*} [Fintype I] [DecidableEq I] + (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) + (M N : Matrix I I ℂ) (a : A) : + sandwichMap A M N a = hsVector (M * algebraMatrix A a * N) := rfl + +lemma sector_unitary_matrix (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (U : unitary (evenAlgebra odd)) : + algebraMatrix (sectorAlgebra (S := S) odd k) + (unitarySpanHom (R := ℂ) (sectorUnitary (S := S) odd k) U).val = sectorTensor odd k (fun _ : S => U.val.val) := by + exact (Matrix.toEuclideanCLM (𝕜 := ℂ)).symm_apply_apply _ + +/-- Weighted reconstruction in the actual signed sector, with the exact +occupied-board entropy loss and singular quarter-root normalization. -/ +theorem whitened_reconstruction_bound {L K : Type*} [Fintype L] [Fintype K] + [DecidableEq L] [DecidableEq K] [Nonempty S] + (odd : C → Prop) [DecidablePred odd] (k : ℕ) (e : S ↪ L × K) + (M : L → Matrix C C ℂ) (N : K → Matrix C C ℂ) + (hM : ∀ i, (M i).PosSemidef) (hN : ∀ j, (N j).PosSemidef) + (heM : ∀ i, M i ∈ evenAlgebra odd) (heN : ∀ j, N j ∈ evenAlgebra odd) + (hMt : ∀ i, (M i).trace.re ≤ 1) (hNt : ∀ j, (N j).trace.re ≤ 1) + (B : sectorAlgebra (S := S) odd k) : + let p := uniformMarginal (fun i => (e i).1) + let q := uniformMarginal (fun i => (e i).2) + let M' := fun i => whitenState (stateMean p M) (M i) + let N' := fun j => whitenState (stateMean q N) (N j) + ‖hsVector (sectorTensor odd k (fun i => CFC.sqrt (M' (e i).1)) * + algebraMatrix (sectorAlgebra (S := S) odd k) B * + sectorTensor odd k (fun i => CFC.sqrt (N' (e i).2)))‖^2 ≤ + 16 * (Module.finrank ℂ (sectorAlgebra (S := S) odd k) : ℝ)^2 * ‖B‖^2 * + Real.exp ((Fintype.card L * Fintype.card K - Fintype.card S : ℕ) : ℝ) := by + dsimp only + let p := uniformMarginal (fun i => (e i).1) + let q := uniformMarginal (fun i => (e i).2) + let M' := fun i => whitenState (stateMean p M) (M i) + let N' := fun j => whitenState (stateMean q N) (N j) + let A := sectorAlgebra (S := S) odd k + let R := Real.exp ((Fintype.card L * Fintype.card K - Fintype.card S : ℕ) : ℝ) + let F := sandwichMap A (sectorTensor odd k (fun i => CFC.sqrt (M' (e i).1))) + (sectorTensor odd k (fun i => CFC.sqrt (N' (e i).2))) + have hp := uniformMarginal_nonneg (fun i => (e i).1) + have hq := uniformMarginal_nonneg (fun i => (e i).2) + have hMp : ∀ i, (M' i).PosSemidef := fun i => whitenState_positive _ _ (hM i) + have hNp : ∀ j, (N' j).PosSemidef := fun j => whitenState_positive _ _ (hN j) + have hMe : ∀ i, M' i ∈ evenAlgebra odd := fun i => + whitenState_even odd _ _ (stateMean_positive p M hp hM) (stateMean_even odd p M heM) (heM i) + have hNe : ∀ j, N' j ∈ evenAlgebra odd := fun j => + whitenState_even odd _ _ (stateMean_positive q N hq hN) (stateMean_even odd q N heN) (heN j) + have hu (U : unitary (evenAlgebra odd)) : + ‖F (unitarySpanHom (R := ℂ) (sectorUnitary (S := S) odd k) U).val‖ ≤ Real.sqrt R := by + apply Real.le_sqrt_of_sq_le + change ‖hsVector (sectorTensor odd k (fun i => CFC.sqrt (M' (e i).1)) * + algebraMatrix (sectorAlgebra (S := S) odd k) + (unitarySpanHom (R := ℂ) (sectorUnitary (S := S) odd k) U).val * + sectorTensor odd k (fun i => CFC.sqrt (N' (e i).2)))‖^2 ≤ R + rw [sector_unitary_matrix] + apply (sector_unitary_sandwich_bound odd k (fun i => M' (e i).1) (fun i => N' (e i).2) + U.val.val (fun i => hMp _) (fun i => hNp _) (fun i => hMe _) (fun i => hNe _) + U.val.property).trans + apply occupied_product_of_mean_le e (fun i j => (M' i * U.val.val * N' j * U.val.val.conjTranspose).trace.re) + · exact fun i j => local_overlap_nonneg _ _ _ (hMp i) (hNp j) + · exact weighted_whitened_mean_le_one p q M N hp hq (sum_uniformMarginal _) + (sum_uniformMarginal _) hM hN hMt hNt U.val.val + ⟨congrArg Subtype.val U.property.1, congrArg Subtype.val U.property.2⟩ + have hh := algebra_reconstruction_hilbert_bound A + (unitarySpanHom (R := ℂ) (sectorUnitary (S := S) odd k)) + (unitarySpanHom_spans (R := ℂ) (sectorUnitary (S := S) odd k)) B F + (Real.sqrt R) (Real.sqrt_nonneg _) hu + have hs := pow_le_pow_left₀ (norm_nonneg (F B)) hh 2 + change ‖F B‖^2 ≤ _ + calc + _ ≤ (4 * (Module.finrank ℂ A : ℝ) * ‖B‖ * Real.sqrt R)^2 := hs + _ = _ := by + dsimp only [A, R] + simp only [mul_pow, Real.sq_sqrt (le_of_lt (Real.exp_pos _))] + ring + +lemma filtered_trace_identity {I : Type*} [Fintype I] [DecidableEq I] + (A B R T F G Q : Matrix I I ℂ) + (hR : R.IsHermitian) (hT : T.IsHermitian) + (hF : F.IsHermitian) (hG : G.IsHermitian) (hQ : Q.IsHermitian) + (hA : F * R^2 * F = A) (hB : G * T^2 * G = B) : + (A * Q * B * Q).trace.re = ‖hsVector (R * (F * Q * G) * T)‖^2 := by + rw [hsVector_sandwich_sq R T _ hR hT] + simp only [Matrix.conjTranspose_mul, hF.eq, hG.eq, hQ.eq] + rw [← hA, ← hB] + apply congrArg Complex.re + calc + _ = (F * (R^2 * F * Q * G * T^2 * G * Q)).trace := by simp only [mul_assoc] + _ = ((R^2 * F * Q * G * T^2 * G * Q) * F).trace := Matrix.trace_mul_comm _ _ + _ = _ := by simp only [mul_assoc] + +end RowColumn.MatrixState + +end +end + + +section + +noncomputable section +open scoped BigOperators Classical MatrixOrder Matrix.Norms.L2Operator ComplexOrder +namespace RowColumn.MatrixState +open FiniteStarAlgebra Signed +variable {I : Type*} [Fintype I] [DecidableEq I] + +lemma algebraMatrix_mul (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) + (a b : A) : algebraMatrix A (a*b) = algebraMatrix A a * algebraMatrix A b := + (Matrix.toEuclideanCLM (𝕜 := ℂ)).symm.map_mul a.val b.val +lemma algebraMatrix_star (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) + (a : A) : algebraMatrix A (star a) = star (algebraMatrix A a) := + (Matrix.toEuclideanCLM (n := I) (𝕜 := ℂ)).symm.map_star' a.val +lemma algebraMatrix_hermitian (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) + (a : A) (ha : star a=a) : (algebraMatrix A a).IsHermitian := by + change star (algebraMatrix A a)=_ + rw [← algebraMatrix_star, ha] +lemma algebraMatrix_trace (A : StarSubalgebra ℂ (EuclideanSpace ℂ I →L[ℂ] EuclideanSpace ℂ I)) + (a : A) : (algebraMatrix A a).trace = physicalTrace A a := by + rw [← trace_toEuclideanCLM] + change LinearMap.trace ℂ (EuclideanSpace ℂ I) + ((Matrix.toEuclideanCLM (𝕜 := ℂ)) ((Matrix.toEuclideanCLM (𝕜 := ℂ)).symm a.val)).toLinearMap = _ + rw [(Matrix.toEuclideanCLM (𝕜 := ℂ)).apply_symm_apply] + rfl + +variable {S C : Type*} [Fintype S] [DecidableEq S] [Fintype C] [DecidableEq C] + +lemma tensorMatrix_trace_re (M : S → Matrix C C ℂ) (hM : ∀ i, (M i).PosSemidef) : + (tensorMatrix M).trace.re = ∏ i, (M i).trace.re := by + have hs (i : S) : (CFC.sqrt (M i)).conjTranspose * CFC.sqrt (M i) = M i := by + rw [(Matrix.nonneg_iff_posSemidef.mp (CFC.sqrt_nonneg (M i))).isHermitian.eq] + exact CFC.sqrt_mul_sqrt_self _ (hM i).nonneg + have ht := hsVector_tensor_norm_sq (fun i => CFC.sqrt (M i)) + simp only [hsVector_norm_sq, tensorMatrix_star, tensorMatrix_mul, hs] at ht + exact ht + +lemma sectorTensor_trace_le (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M : S → Matrix C C ℂ) (hM : ∀ i, (M i).PosSemidef) : + (sectorTensor odd k M).trace.re ≤ (tensorMatrix M).trace.re := by + let e : Words (S := S) odd k ↪ (S → C) := ⟨Subtype.val, Subtype.val_injective⟩ + have hh := finite_sum_embedding_le e (fun w => (tensorMatrix M w w).re) + (fun w => ((tensorMatrix_posSemidef M hM).diag_nonneg (i := w)).1) + simpa only [sectorTensor, Matrix.trace, Matrix.diag, Complex.re_sum, Matrix.submatrix_apply, e, Function.Embedding.coeFn_mk] using hh + +lemma sectorTensor_substate_trace (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M : S → Matrix C C ℂ) (hM : ∀ i, (M i).PosSemidef) + (htr : ∀ i, (M i).trace.re ≤ 1) : (sectorTensor odd k M).trace.re ≤ 1 := by + apply (sectorTensor_trace_le odd k M hM).trans + rw [tensorMatrix_trace_re M hM] + exact Finset.prod_le_one₀ (fun i _ => (hM i).trace_nonneg.1) (fun i _ => htr i) + +def positiveTensor (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M : Matrix C C ℂ) (hM : M.PosSemidef) (he : M ∈ evenAlgebra odd) : + sectorAlgebra (S := S) odd k := + ⟨Matrix.toEuclideanCLM (𝕜 := ℂ) (sectorTensor odd k (fun _ : S => M)), + sectorTensor_mem_algebra odd k M hM.isHermitian he⟩ + +lemma positiveTensor_matrix (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M : Matrix C C ℂ) (hM : M.PosSemidef) (he : M ∈ evenAlgebra odd) : + algebraMatrix (sectorAlgebra (S := S) odd k) (positiveTensor odd k M hM he) = + sectorTensor odd k (fun _ : S => M) := + (Matrix.toEuclideanCLM (𝕜 := ℂ)).symm_apply_apply _ + +lemma positiveTensor_isPositive (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M : Matrix C C ℂ) (hM : M.PosSemidef) (he : M ∈ evenAlgebra odd) : + (positiveTensor (S := S) odd k M hM he).val.IsPositive := + (toEuclideanCLM_positive_iff _).mpr (sectorTensor_positive odd k _ (fun _ : S => hM)) + +lemma positiveTensor_selfAdjoint (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M : Matrix C C ℂ) (hM : M.PosSemidef) (he : M ∈ evenAlgebra odd) : + IsSelfAdjoint (positiveTensor (S := S) odd k M hM he) := by + apply Subtype.ext + exact (positiveTensor_isPositive odd k M hM he).isSelfAdjoint + +lemma positiveTensor_trace_le_one (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M : Matrix C C ℂ) (hM : M.PosSemidef) (he : M ∈ evenAlgebra odd) (htr : M.trace.re ≤ 1) : + (physicalTrace (sectorAlgebra (S := S) odd k) (positiveTensor odd k M hM he)).re ≤ 1 := by + rw [← algebraMatrix_trace, positiveTensor_matrix] + exact sectorTensor_substate_trace odd k _ (fun _ : S => hM) (fun _ => htr) + +lemma positiveTensor_quarter_four (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (M : Matrix C C ℂ) (hM : M.PosSemidef) (he : M ∈ evenAlgebra odd) : + positiveTensor (S := S) odd k (quarterRoot M) (quarter_positive M) (quarter_even odd M hM he) ^ 4 = + positiveTensor odd k M hM he := by + apply Subtype.ext + change (Matrix.toEuclideanCLM (𝕜 := ℂ) (sectorTensor odd k (fun _ : S => quarterRoot M)))^4 = _ + rw [← map_pow] + have hh := (sectorPowerHom (S := S) odd k).map_pow + (⟨quarterRoot M, quarter_even odd M hM he⟩ : evenAlgebra odd) 4 + change sectorTensor odd k (fun _ : S => quarterRoot M ^ 4) = + (sectorTensor odd k (fun _ : S => quarterRoot M)) ^ 4 at hh + rw [← hh, quarter_four M hM] + rfl + +/-- The actual irreducible-dimension filter acts on fourth powers of both +mean-state tensors. Its quarter-root sandwich has squared norm at most 1/d. -/ +theorem quarter_tensor_filter_bound (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (q : sectorAlgebra (S := S) odd k) (hqs : star q=q) (hqq : q*q=q) + (hqc : ∀ a, q*a=a*q) (d : ℝ) (hd : 0 whitenState A (M i) + sectorTensor odd k (fun _ : S => quarterRoot A) * + sectorTensor odd k (fun x => CFC.sqrt (M' (line x))) ^ 2 * + sectorTensor odd k (fun _ : S => quarterRoot A) = + sectorTensor odd k (fun x => M (line x)) := by + dsimp only + let p := uniformMarginal line + let A := stateMean p M + let M' := fun i => whitenState A (M i) + have hp := uniformMarginal_nonneg line + have hA := stateMean_positive p M hp hM + have heA := stateMean_even odd p M heM + have hMp : ∀ i, (M' i).PosSemidef := fun i => whitenState_positive A (M i) (hM i) + have hMe : ∀ i, M' i ∈ evenAlgebra odd := fun i => whitenState_even odd A (M i) hA heA (heM i) + change sectorTensor odd k (fun _ : S => quarterRoot A) * + sectorTensor odd k (fun x => CFC.sqrt (M' (line x))) ^ 2 * + sectorTensor odd k (fun _ : S => quarterRoot A) = _ + rw [sectorTensor_root_square odd k _ (fun x => hMp _) (fun x => hMe _)] + rw [← sectorTensor_mul odd k _ _ (fun _ => quarter_even odd A hA heA)] + rw [← sectorTensor_mul odd k _ _ (fun x => (evenAlgebra odd).mul_mem + (quarter_even odd A hA heA) (hMe _))] + congr 1 + funext x + exact unwhitenState p M hp hM (line x) (uniformMarginal_pos line x) + +/-- The quantitative global bridge: two arbitrary admissible fibre-product +substates, on the actual signed sector and the actual central isotypic filter. +No invertibility, sector-surrogate, or postselection bound is assumed. -/ +theorem sector_filtered_trace_bound {L K : Type*} [Fintype L] [Fintype K] + [DecidableEq L] [DecidableEq K] [Nonempty S] + (odd : C → Prop) [DecidablePred odd] (k : ℕ) (e : S ↪ L × K) + (q : sectorAlgebra (S := S) odd k) (hqs : star q=q) (hqq : q*q=q) + (hqc : ∀ a, q*a=a*q) (d : ℝ) (hd : 0 M (e x).1) * algebraMatrix (sectorAlgebra (S := S) odd k) q * + sectorTensor odd k (fun x => N (e x).2) * algebraMatrix (sectorAlgebra (S := S) odd k) q).trace.re ≤ + 16 * (Module.finrank ℂ (sectorAlgebra (S := S) odd k) : ℝ)^2 * + Real.exp ((Fintype.card L * Fintype.card K - Fintype.card S : ℕ) : ℝ) / d := by + let p := uniformMarginal (fun x => (e x).1) + let r := uniformMarginal (fun x => (e x).2) + let A := stateMean p M + let B := stateMean r N + let M' := fun i => whitenState A (M i) + let N' := fun j => whitenState B (N j) + have hp := uniformMarginal_nonneg (fun x => (e x).1) + have hr := uniformMarginal_nonneg (fun x => (e x).2) + have hA := stateMean_positive p M hp hM + have hB := stateMean_positive r N hr hN + have heA := stateMean_even odd p M heM + have heB := stateMean_even odd r N heN + let F := positiveTensor (S := S) odd k (quarterRoot A) (quarter_positive A) (quarter_even odd A hA heA) + let G := positiveTensor (S := S) odd k (quarterRoot B) (quarter_positive B) (quarter_even odd B hB heB) + have hnorm : ‖F*q*G‖^2 ≤ 1/d := quarter_tensor_filter_bound odd k q hqs hqq hqc d hd hfilter + A B hA hB heA heB (stateMean_trace_le_one p M hp (sum_uniformMarginal _) hMt) + (stateMean_trace_le_one r N hr (sum_uniformMarginal _) hNt) + have hrec := whitened_reconstruction_bound odd k e M N hM hN heM heN hMt hNt (F*q*G) + change ‖hsVector (sectorTensor odd k (fun x => CFC.sqrt (M' (e x).1)) * + algebraMatrix (sectorAlgebra (S := S) odd k) (F*q*G) * + sectorTensor odd k (fun x => CFC.sqrt (N' (e x).2)))‖^2 ≤ _ at hrec + simp only [algebraMatrix_mul, F, G, positiveTensor_matrix] at hrec + have hi := filtered_trace_identity + (sectorTensor odd k (fun x => M (e x).1)) (sectorTensor odd k (fun x => N (e x).2)) + (sectorTensor odd k (fun x => CFC.sqrt (M' (e x).1))) + (sectorTensor odd k (fun x => CFC.sqrt (N' (e x).2))) + (sectorTensor odd k (fun _ : S => quarterRoot A)) + (sectorTensor odd k (fun _ : S => quarterRoot B)) + (algebraMatrix (sectorAlgebra (S := S) odd k) q) + (sectorTensor_hermitian odd k _ (fun x => (Matrix.nonneg_iff_posSemidef.mp (CFC.sqrt_nonneg _)).isHermitian)) + (sectorTensor_hermitian odd k _ (fun x => (Matrix.nonneg_iff_posSemidef.mp (CFC.sqrt_nonneg _)).isHermitian)) + (sectorTensor_hermitian odd k _ (fun _ => (quarter_positive A).isHermitian)) + (sectorTensor_hermitian odd k _ (fun _ => (quarter_positive B).isHermitian)) + (algebraMatrix_hermitian _ q hqs) + (sector_unwhiten_identity odd k (fun x => (e x).1) M hM heM) + (sector_unwhiten_identity odd k (fun x => (e x).2) N hN heN) + rw [hi] + apply hrec.trans + have hh := mul_le_mul_of_nonneg_right + (mul_le_mul_of_nonneg_left hnorm + (by positivity : 0 ≤ 16 * (Module.finrank ℂ (sectorAlgebra (S := S) odd k) : ℝ)^2)) + (le_of_lt (Real.exp_pos ((Fintype.card L * Fintype.card K - Fintype.card S : ℕ) : ℝ))) + convert hh using 1; ring + +/-- The filter used above exists in the concrete tensor algebra, for every +actual irreducible that occurs. The identity condition on its isotypic carrier +will be applied to the explicit isometric hook embedding. -/ +theorem exists_sector_isotypic_filter {V : Type*} [AddCommGroup V] + [Module ℂ V] [FiniteDimensional ℂ V] + (odd : C → Prop) [DecidablePred odd] (k : ℕ) + (ρ : Representation ℂ (Equiv.Perm S) V) [Representation.IsIrreducible ρ] : + ∃ q : sectorAlgebra (S := S) odd k, star q=q ∧ q*q=q ∧ (∀ a, q*a=a*q) ∧ + (∀ x ∈ Isotypic.carrier ρ (Signed.representation (S := S) (odd := odd) (k := k)), q.val x=x) ∧ + ∀ a : sectorAlgebra (S := S) odd k, a.val.IsPositive → + ‖q*a‖ ≤ (physicalTrace (sectorAlgebra (S := S) odd k) a).re / Module.finrank ℂ V := + exists_isotypic_filter ρ (Signed.representation (S := S) (odd := odd) (k := k)) + (Signed.representation_unitary (S := S) (odd := odd) (k := k)) (sectorAlgebra (S := S) odd k) + (sectorAlgebra_commutes odd k) + +end RowColumn.MatrixState + +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/BandFactorization.lean b/lean/OAI/RepresentationTheory/Saxl/BandFactorization.lean index 21bdde4c15fa00bdedcd558401c7c2e5ddc689af..675998f8a6c9a058cbd7cf4613b4d8bcd36d88fa 100644 --- a/lean/OAI/RepresentationTheory/Saxl/BandFactorization.lean +++ b/lean/OAI/RepresentationTheory/Saxl/BandFactorization.lean @@ -1,232 +1,232 @@ -import OAI.RepresentationTheory.Saxl.PositionSplit - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl - -def highPositionsEquiv (h s : ℕ) : - {i : Fin (staircase (h+s)).card // stairHigh h s i} ≃ Fin (staircase h).card where - toFun i := (stairTableau h).symm ⟨(stairTableau (h+s) i.val).val, mem_staircase.mpr i.property⟩ - invFun j := ⟨(stairTableau (h+s)).symm ⟨(stairTableau h j).val, by - apply mem_staircase.mpr - have := mem_staircase.mp (stairTableau h j).property - omega⟩, by - change ((stairTableau (h+s)) ((stairTableau (h+s)).symm _)).val.1 + - ((stairTableau (h+s)) ((stairTableau (h+s)).symm _)).val.2 < h - simp only [Equiv.apply_symm_apply] - exact mem_staircase.mp (stairTableau h j).property⟩ - left_inv i := by apply Subtype.ext; simp - right_inv i := by simp - -abbrev bandSize (h s : ℕ) := Nat.card {i : Fin (staircase (h+s)).card // ¬stairHigh h s i} - -def cutPositions (h s : ℕ) : - Fin (staircase (h+s)).card ≃ Fin (staircase h).card ⊕ Fin (bandSize h s) := by - classical - exact (Equiv.sumCompl (stairHigh h s)).symm.trans - (Equiv.sumCongr (highPositionsEquiv h s) (Fintype.equivFinOfCardEq (show Fintype.card {i : Fin (staircase (h+s)).card // ¬stairHigh h s i} = bandSize h s from Fintype.card_eq_nat_card))) - -lemma cutPositions_high (h s : ℕ) (i : Fin (staircase (h+s)).card) : - (cutPositions h s i).isLeft = true ↔ stairHigh h s i := by - classical - by_cases hi : stairHigh h s i <;> simp [cutPositions, Equiv.sumCompl, Equiv.sumCongr, hi] - -lemma cutPositions_left (h s : ℕ) (i : Fin (staircase h).card) : - (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i))).val = (stairTableau h i).val := by - classical - simp [cutPositions, Equiv.sumCompl, highPositionsEquiv] - -lemma bandSize_add (h s : ℕ) : (staircase h).card + bandSize h s = (staircase (h+s)).card := by - have hh := Fintype.card_congr (cutPositions h s) - simpa using hh.symm - -def bandTableau (h s : ℕ) (j : Fin (bandSize h s)) : (staircase (h+s)).cells := - stairTableau (h+s) ((cutPositions h s).symm (Sum.inr j)) - -def bandRowGroup (h s : ℕ) := fiberGroup (fun j => (bandTableau h s j).val.1) -def bandColumnGroup (h s : ℕ) := fiberGroup (fun j => (bandTableau h s j).val.2) - -def highLetter (h s : ℕ) : Fin ((staircase h).colLen 0) → Fin ((staircase (h+s)).colLen 0) := - fun a => ⟨a.val+s, by have := a.isLt; simp only [staircase_colLen, Nat.sub_zero] at *; omega⟩ - -def letterLift {n d e : ℕ} (f : Fin d → Fin e) : - Representation.IntertwiningMap (wordRep n d) (wordRep n e) := - wordMap (fun a b => if f a = b then 1 else 0) - -lemma letterLift_single {n d e : ℕ} (f : Fin d → Fin e) (a : Fin n → Fin d) : - letterLift f (Pi.single a 1) = Pi.single (f ∘ a) (1:ℂ) := by - classical - ext b - rw [letterLift, wordMap_single, Pi.single_apply] - by_cases he : b = f ∘ a - · subst b; simp - · rw [ite_eq_right he] - have hn : ∃ i, f (a i) ≠ b i := by - by_contra hh - push Not at hh - exact he (funext (fun i => (hh i).symm)) - obtain ⟨i,hi⟩ := hn - exact Finset.prod_eq_zero (Finset.mem_univ i) (ite_eq_right hi) - -lemma letterLift_altWord {n d e : ℕ} (f : Fin d → Fin e) - (G : Subgroup (Equiv.Perm (Fin n))) (a : Fin n → Fin d) : - letterLift f (altWord G a) = altWord G (f ∘ a) := by - classical - unfold altWord - rw [map_sum] - apply Finset.sum_congr rfl - intro g hg - rw [map_smul, Representation.IntertwiningMap.isIntertwining, letterLift_single] - -def bandRowWord (h s : ℕ) : WordSpace (bandSize h s) ((staircase (h+s)).colLen 0) := - altWord (bandRowGroup h s) (rightWord (cutPositions h s) - (rowWord (stairRowTableau (h+s)) ∘ (rotateRowPositions h s : Equiv.Perm _))) - -def bandColumnWord (h s : ℕ) : WordSpace (bandSize h s) ((staircase (h+s)).colLen 0) := - altWord (bandColumnGroup h s) (rightWord (cutPositions h s) - (rowWord (stairTableau (h+s)) ∘ (rotateColumnPositions h s : Equiv.Perm _))) - -lemma row_cut_group (h s : ℕ) : - columnGroup (stairRowTableau (h+s)) ⊓ sectorGroup (stairHigh h s) = - fiberGroup (fun i => (stairTableau (h+s) i).val.1) ⊓ - sectorGroup (fun i => (cutPositions h s i).isLeft = true) := by - congr 1 - congr 1; funext i; exact propext (cutPositions_high h s i).symm - -lemma column_cut_group (h s : ℕ) : - columnGroup (stairTableau (h+s)) ⊓ sectorGroup (stairHigh h s) = - fiberGroup (fun i => (stairTableau (h+s) i).val.2) ⊓ - sectorGroup (fun i => (cutPositions h s i).isLeft = true) := by - congr 1 - congr 1; funext i; exact propext (cutPositions_high h s i).symm - -lemma highRow_word (h s : ℕ) : - leftWord (cutPositions h s) (rowWord (stairRowTableau (h+s)) ∘ (rotateRowPositions h s : Equiv.Perm _)) = - highLetter h s ∘ rowWord (stairRowTableau h) := by - funext i - apply Fin.ext - have hi : (stairTableau h i).val.1 + (stairTableau h i).val.2 < h := - mem_staircase.mp (stairTableau h i).property - have he := cutPositions_left h s i - simp only [leftWord, Function.comp_apply, rowWord, stairRowTableau, rotateRowPositions, - Equiv.trans_apply, Equiv.apply_symm_apply, staircaseSwap, highLetter] - change (rotateRow h s (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i)))).val.2 = _ - change (if _ then _ else _) = (stairTableau h i).val.2+s - rw [he] - rw [ite_eq_left (by omega)] - -lemma highColumn_word (h s : ℕ) : - leftWord (cutPositions h s) (rowWord (stairTableau (h+s)) ∘ (rotateColumnPositions h s : Equiv.Perm _)) = - highLetter h s ∘ rowWord (stairTableau h) := by - funext i - apply Fin.ext - have hi : (stairTableau h i).val.1 + (stairTableau h i).val.2 < h := - mem_staircase.mp (stairTableau h i).property - have he := cutPositions_left h s i - simp only [leftWord, Function.comp_apply, rowWord, rotateColumnPositions, - Equiv.trans_apply, Equiv.apply_symm_apply, highLetter] - change (rotateColumn h s (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i)))).val.1 = _ - change (if (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i))).val.1 < - h - (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i))).val.2 then - (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i))).val.1+s else - (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i))).val.1 - - (h - (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i))).val.2)) = _ - simp only [he] - rw [ite_eq_left (by omega)] - -/- The first-layer exact band factorization, including the high-letter shift. -/ -theorem cutRowWord_factor (h s : ℕ) : cutRowWord h s = - positionProduct (cutPositions h s) - (letterLift (highLetter h s) (polytabloid (stairRowTableau h))) (bandRowWord h s) := by - unfold cutRowWord - rw [row_cut_group, altWord_fiber_split] - congr 1 - rw [highRow_word, polytabloid_eq_altWord, letterLift_altWord] - congr 1 - change fiberGroup _ = fiberGroup (fun i => (stairTableau h i).val.1) - congr 1 - funext i - exact congrArg Prod.fst (cutPositions_left h s i) - -/- The second-layer exact band factorization. -/ -theorem cutColumnWord_factor (h s : ℕ) : cutColumnWord h s = - positionProduct (cutPositions h s) - (letterLift (highLetter h s) (polytabloid (stairTableau h))) (bandColumnWord h s) := by - unfold cutColumnWord - rw [column_cut_group, altWord_fiber_split] - congr 1 - rw [highColumn_word, polytabloid_eq_altWord, letterLift_altWord] - congr 1 - change fiberGroup _ = fiberGroup (fun i => (stairTableau h i).val.2) - congr 1 - funext i - exact congrArg Prod.snd (cutPositions_left h s i) - - - -lemma bandTableau_bounds (h s : ℕ) (j : Fin (bandSize h s)) : - h ≤ (bandTableau h s j).val.1 + (bandTableau h s j).val.2 ∧ - (bandTableau h s j).val.1 + (bandTableau h s j).val.2 < h+s := by - refine ⟨?_,mem_staircase.mp (bandTableau h s j).property⟩ - have hh := cutPositions_high h s ((cutPositions h s).symm (Sum.inr j)) - simp only [Equiv.apply_symm_apply, Sum.isLeft_inr, Bool.false_eq_true, false_iff] at hh - change ¬ (bandTableau h s j).val.1 + (bandTableau h s j).val.2 < h at hh - omega - -def bandCellsEquiv (h s : ℕ) : Fin (bandSize h s) ≃ - {c : ℕ × ℕ // h ≤ c.1+c.2 ∧ c.1+c.2 < h+s} := - Equiv.ofBijective (fun j => ⟨(bandTableau h s j).val,bandTableau_bounds h s j⟩) (by - constructor - · intro i j hij - have hh : bandTableau h s i = bandTableau h s j := Subtype.ext (congrArg (fun c : {c : ℕ × ℕ // h ≤ c.1+c.2 ∧ c.1+c.2 < h+s} => c.val) hij) - exact Sum.inr.inj ((cutPositions h s).symm.injective ((stairTableau (h+s)).injective hh)) - · intro c - let x : (staircase (h+s)).cells := ⟨c.val,mem_staircase.mpr c.property.2⟩ - let i := (stairTableau (h+s)).symm x - have hi : ¬ stairHigh h s i := by - change ¬ (stairTableau (h+s) ((stairTableau (h+s)).symm x)).val.1 + - (stairTableau (h+s) ((stairTableau (h+s)).symm x)).val.2 < h - simp only [Equiv.apply_symm_apply] - exact Nat.not_lt.mpr c.property.1 - have he := cutPositions_high h s i - cases hp : cutPositions h s i with - | inl j => simp only [hp, Sum.isLeft_inl, true_iff] at he; exact False.elim (hi he) - | inr j => - refine ⟨j, ?_⟩ - apply Subtype.ext - have hj : (cutPositions h s).symm (Sum.inr j) = i := by rw [← hp,Equiv.symm_apply_apply] - change (stairTableau (h+s) ((cutPositions h s).symm (Sum.inr j))).val = c.val - rw [hj] - exact congrArg Subtype.val ((stairTableau (h+s)).apply_symm_apply x)) - -def pathCellsEquiv (h : ℕ) : Fin (2*(h+1)+1) ≃ - {c : ℕ × ℕ // h ≤ c.1+c.2 ∧ c.1+c.2 < h+2} where - toFun k := ⟨(h+1-(k.val+1)/2,k.val/2), by have := k.isLt; omega⟩ - invFun c := ⟨h+1-c.val.1+c.val.2, by have := c.property; omega⟩ - left_inv k := by apply Fin.ext; dsimp; have := k.isLt; omega - right_inv c := by - apply Subtype.ext - apply Prod.ext <;> dsimp <;> have := c.property <;> omega - -/- The exact path order, starting at the bottom row singleton and ending -at the rightmost column singleton. -/ -def bandPathEquiv (h : ℕ) : Fin (2*(h+1)+1) ≃ Fin (bandSize h 2) := - (pathCellsEquiv h).trans (bandCellsEquiv h 2).symm - -lemma bandPath_coordinates (h : ℕ) (k : Fin (2*(h+1)+1)) : - (bandTableau h 2 (bandPathEquiv h k)).val = (h+1-(k.val+1)/2,k.val/2) := by - have hh := (bandCellsEquiv h 2).apply_symm_apply (pathCellsEquiv h k) - exact congrArg Subtype.val hh - -lemma bandPath_card (h : ℕ) : bandSize h 2 = 2*(h+1)+1 := by - simpa only [Fintype.card_fin] using (Fintype.card_congr (bandPathEquiv h)).symm - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.PositionSplit + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl + +def highPositionsEquiv (h s : ℕ) : + {i : Fin (staircase (h+s)).card // stairHigh h s i} ≃ Fin (staircase h).card where + toFun i := (stairTableau h).symm ⟨(stairTableau (h+s) i.val).val, mem_staircase.mpr i.property⟩ + invFun j := ⟨(stairTableau (h+s)).symm ⟨(stairTableau h j).val, by + apply mem_staircase.mpr + have := mem_staircase.mp (stairTableau h j).property + omega⟩, by + change ((stairTableau (h+s)) ((stairTableau (h+s)).symm _)).val.1 + + ((stairTableau (h+s)) ((stairTableau (h+s)).symm _)).val.2 < h + simp only [Equiv.apply_symm_apply] + exact mem_staircase.mp (stairTableau h j).property⟩ + left_inv i := by apply Subtype.ext; simp + right_inv i := by simp + +abbrev bandSize (h s : ℕ) := Nat.card {i : Fin (staircase (h+s)).card // ¬stairHigh h s i} + +def cutPositions (h s : ℕ) : + Fin (staircase (h+s)).card ≃ Fin (staircase h).card ⊕ Fin (bandSize h s) := by + classical + exact (Equiv.sumCompl (stairHigh h s)).symm.trans + (Equiv.sumCongr (highPositionsEquiv h s) (Fintype.equivFinOfCardEq (show Fintype.card {i : Fin (staircase (h+s)).card // ¬stairHigh h s i} = bandSize h s from Fintype.card_eq_nat_card))) + +lemma cutPositions_high (h s : ℕ) (i : Fin (staircase (h+s)).card) : + (cutPositions h s i).isLeft = true ↔ stairHigh h s i := by + classical + by_cases hi : stairHigh h s i <;> simp [cutPositions, Equiv.sumCompl, Equiv.sumCongr, hi] + +lemma cutPositions_left (h s : ℕ) (i : Fin (staircase h).card) : + (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i))).val = (stairTableau h i).val := by + classical + simp [cutPositions, Equiv.sumCompl, highPositionsEquiv] + +lemma bandSize_add (h s : ℕ) : (staircase h).card + bandSize h s = (staircase (h+s)).card := by + have hh := Fintype.card_congr (cutPositions h s) + simpa using hh.symm + +def bandTableau (h s : ℕ) (j : Fin (bandSize h s)) : (staircase (h+s)).cells := + stairTableau (h+s) ((cutPositions h s).symm (Sum.inr j)) + +def bandRowGroup (h s : ℕ) := fiberGroup (fun j => (bandTableau h s j).val.1) +def bandColumnGroup (h s : ℕ) := fiberGroup (fun j => (bandTableau h s j).val.2) + +def highLetter (h s : ℕ) : Fin ((staircase h).colLen 0) → Fin ((staircase (h+s)).colLen 0) := + fun a => ⟨a.val+s, by have := a.isLt; simp only [staircase_colLen, Nat.sub_zero] at *; omega⟩ + +def letterLift {n d e : ℕ} (f : Fin d → Fin e) : + Representation.IntertwiningMap (wordRep n d) (wordRep n e) := + wordMap (fun a b => if f a = b then 1 else 0) + +lemma letterLift_single {n d e : ℕ} (f : Fin d → Fin e) (a : Fin n → Fin d) : + letterLift f (Pi.single a 1) = Pi.single (f ∘ a) (1:ℂ) := by + classical + ext b + rw [letterLift, wordMap_single, Pi.single_apply] + by_cases he : b = f ∘ a + · subst b; simp + · rw [ite_eq_right he] + have hn : ∃ i, f (a i) ≠ b i := by + by_contra hh + push Not at hh + exact he (funext (fun i => (hh i).symm)) + obtain ⟨i,hi⟩ := hn + exact Finset.prod_eq_zero (Finset.mem_univ i) (ite_eq_right hi) + +lemma letterLift_altWord {n d e : ℕ} (f : Fin d → Fin e) + (G : Subgroup (Equiv.Perm (Fin n))) (a : Fin n → Fin d) : + letterLift f (altWord G a) = altWord G (f ∘ a) := by + classical + unfold altWord + rw [map_sum] + apply Finset.sum_congr rfl + intro g hg + rw [map_smul, Representation.IntertwiningMap.isIntertwining, letterLift_single] + +def bandRowWord (h s : ℕ) : WordSpace (bandSize h s) ((staircase (h+s)).colLen 0) := + altWord (bandRowGroup h s) (rightWord (cutPositions h s) + (rowWord (stairRowTableau (h+s)) ∘ (rotateRowPositions h s : Equiv.Perm _))) + +def bandColumnWord (h s : ℕ) : WordSpace (bandSize h s) ((staircase (h+s)).colLen 0) := + altWord (bandColumnGroup h s) (rightWord (cutPositions h s) + (rowWord (stairTableau (h+s)) ∘ (rotateColumnPositions h s : Equiv.Perm _))) + +lemma row_cut_group (h s : ℕ) : + columnGroup (stairRowTableau (h+s)) ⊓ sectorGroup (stairHigh h s) = + fiberGroup (fun i => (stairTableau (h+s) i).val.1) ⊓ + sectorGroup (fun i => (cutPositions h s i).isLeft = true) := by + congr 1 + congr 1; funext i; exact propext (cutPositions_high h s i).symm + +lemma column_cut_group (h s : ℕ) : + columnGroup (stairTableau (h+s)) ⊓ sectorGroup (stairHigh h s) = + fiberGroup (fun i => (stairTableau (h+s) i).val.2) ⊓ + sectorGroup (fun i => (cutPositions h s i).isLeft = true) := by + congr 1 + congr 1; funext i; exact propext (cutPositions_high h s i).symm + +lemma highRow_word (h s : ℕ) : + leftWord (cutPositions h s) (rowWord (stairRowTableau (h+s)) ∘ (rotateRowPositions h s : Equiv.Perm _)) = + highLetter h s ∘ rowWord (stairRowTableau h) := by + funext i + apply Fin.ext + have hi : (stairTableau h i).val.1 + (stairTableau h i).val.2 < h := + mem_staircase.mp (stairTableau h i).property + have he := cutPositions_left h s i + simp only [leftWord, Function.comp_apply, rowWord, stairRowTableau, rotateRowPositions, + Equiv.trans_apply, Equiv.apply_symm_apply, staircaseSwap, highLetter] + change (rotateRow h s (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i)))).val.2 = _ + change (if _ then _ else _) = (stairTableau h i).val.2+s + rw [he] + rw [ite_eq_left (by omega)] + +lemma highColumn_word (h s : ℕ) : + leftWord (cutPositions h s) (rowWord (stairTableau (h+s)) ∘ (rotateColumnPositions h s : Equiv.Perm _)) = + highLetter h s ∘ rowWord (stairTableau h) := by + funext i + apply Fin.ext + have hi : (stairTableau h i).val.1 + (stairTableau h i).val.2 < h := + mem_staircase.mp (stairTableau h i).property + have he := cutPositions_left h s i + simp only [leftWord, Function.comp_apply, rowWord, rotateColumnPositions, + Equiv.trans_apply, Equiv.apply_symm_apply, highLetter] + change (rotateColumn h s (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i)))).val.1 = _ + change (if (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i))).val.1 < + h - (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i))).val.2 then + (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i))).val.1+s else + (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i))).val.1 - + (h - (stairTableau (h+s) ((cutPositions h s).symm (Sum.inl i))).val.2)) = _ + simp only [he] + rw [ite_eq_left (by omega)] + +/- The first-layer exact band factorization, including the high-letter shift. -/ +theorem cutRowWord_factor (h s : ℕ) : cutRowWord h s = + positionProduct (cutPositions h s) + (letterLift (highLetter h s) (polytabloid (stairRowTableau h))) (bandRowWord h s) := by + unfold cutRowWord + rw [row_cut_group, altWord_fiber_split] + congr 1 + rw [highRow_word, polytabloid_eq_altWord, letterLift_altWord] + congr 1 + change fiberGroup _ = fiberGroup (fun i => (stairTableau h i).val.1) + congr 1 + funext i + exact congrArg Prod.fst (cutPositions_left h s i) + +/- The second-layer exact band factorization. -/ +theorem cutColumnWord_factor (h s : ℕ) : cutColumnWord h s = + positionProduct (cutPositions h s) + (letterLift (highLetter h s) (polytabloid (stairTableau h))) (bandColumnWord h s) := by + unfold cutColumnWord + rw [column_cut_group, altWord_fiber_split] + congr 1 + rw [highColumn_word, polytabloid_eq_altWord, letterLift_altWord] + congr 1 + change fiberGroup _ = fiberGroup (fun i => (stairTableau h i).val.2) + congr 1 + funext i + exact congrArg Prod.snd (cutPositions_left h s i) + + + +lemma bandTableau_bounds (h s : ℕ) (j : Fin (bandSize h s)) : + h ≤ (bandTableau h s j).val.1 + (bandTableau h s j).val.2 ∧ + (bandTableau h s j).val.1 + (bandTableau h s j).val.2 < h+s := by + refine ⟨?_,mem_staircase.mp (bandTableau h s j).property⟩ + have hh := cutPositions_high h s ((cutPositions h s).symm (Sum.inr j)) + simp only [Equiv.apply_symm_apply, Sum.isLeft_inr, Bool.false_eq_true, false_iff] at hh + change ¬ (bandTableau h s j).val.1 + (bandTableau h s j).val.2 < h at hh + omega + +def bandCellsEquiv (h s : ℕ) : Fin (bandSize h s) ≃ + {c : ℕ × ℕ // h ≤ c.1+c.2 ∧ c.1+c.2 < h+s} := + Equiv.ofBijective (fun j => ⟨(bandTableau h s j).val,bandTableau_bounds h s j⟩) (by + constructor + · intro i j hij + have hh : bandTableau h s i = bandTableau h s j := Subtype.ext (congrArg (fun c : {c : ℕ × ℕ // h ≤ c.1+c.2 ∧ c.1+c.2 < h+s} => c.val) hij) + exact Sum.inr.inj ((cutPositions h s).symm.injective ((stairTableau (h+s)).injective hh)) + · intro c + let x : (staircase (h+s)).cells := ⟨c.val,mem_staircase.mpr c.property.2⟩ + let i := (stairTableau (h+s)).symm x + have hi : ¬ stairHigh h s i := by + change ¬ (stairTableau (h+s) ((stairTableau (h+s)).symm x)).val.1 + + (stairTableau (h+s) ((stairTableau (h+s)).symm x)).val.2 < h + simp only [Equiv.apply_symm_apply] + exact Nat.not_lt.mpr c.property.1 + have he := cutPositions_high h s i + cases hp : cutPositions h s i with + | inl j => simp only [hp, Sum.isLeft_inl, true_iff] at he; exact False.elim (hi he) + | inr j => + refine ⟨j, ?_⟩ + apply Subtype.ext + have hj : (cutPositions h s).symm (Sum.inr j) = i := by rw [← hp,Equiv.symm_apply_apply] + change (stairTableau (h+s) ((cutPositions h s).symm (Sum.inr j))).val = c.val + rw [hj] + exact congrArg Subtype.val ((stairTableau (h+s)).apply_symm_apply x)) + +def pathCellsEquiv (h : ℕ) : Fin (2*(h+1)+1) ≃ + {c : ℕ × ℕ // h ≤ c.1+c.2 ∧ c.1+c.2 < h+2} where + toFun k := ⟨(h+1-(k.val+1)/2,k.val/2), by have := k.isLt; omega⟩ + invFun c := ⟨h+1-c.val.1+c.val.2, by have := c.property; omega⟩ + left_inv k := by apply Fin.ext; dsimp; have := k.isLt; omega + right_inv c := by + apply Subtype.ext + apply Prod.ext <;> dsimp <;> have := c.property <;> omega + +/- The exact path order, starting at the bottom row singleton and ending +at the rightmost column singleton. -/ +def bandPathEquiv (h : ℕ) : Fin (2*(h+1)+1) ≃ Fin (bandSize h 2) := + (pathCellsEquiv h).trans (bandCellsEquiv h 2).symm + +lemma bandPath_coordinates (h : ℕ) (k : Fin (2*(h+1)+1)) : + (bandTableau h 2 (bandPathEquiv h k)).val = (h+1-(k.val+1)/2,k.val/2) := by + have hh := (bandCellsEquiv h 2).apply_symm_apply (pathCellsEquiv h k) + exact congrArg Subtype.val hh + +lemma bandPath_card (h : ℕ) : bandSize h 2 = 2*(h+1)+1 := by + simpa only [Fintype.card_fin] using (Fintype.card_congr (bandPathEquiv h)).symm + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/BandGlue.lean b/lean/OAI/RepresentationTheory/Saxl/BandGlue.lean index 9b29add41152d117d025f1f33c9f83bc6d4abcd4..fe9deb262ddac4caf270c9e6f8bf7e3c1464fffb 100644 --- a/lean/OAI/RepresentationTheory/Saxl/BandGlue.lean +++ b/lean/OAI/RepresentationTheory/Saxl/BandGlue.lean @@ -1,218 +1,218 @@ -import OAI.RepresentationTheory.Saxl.BandOrbit - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uX - -namespace Saxl - -/- Apply a band intertwiner to every scalar high-coordinate of a colored -strip orbit map. This is the concrete tensor product of the two maps. -/ -def bandGlue {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] - (e : Fin n ≃ Fin a ⊕ Fin b) - (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) - (L : WordSpace b k →ₗ[ℂ] WordSpace b d) : X →ₗ[ℂ] WordSpace n d where - toFun x w := L (fun cb => T x cb (leftWord e w)) (rightWord e w) - map_add' x y := by - ext w - simp only [map_add, Pi.add_apply] - change L ((fun cb => T x cb (leftWord e w)) + (fun cb => T y cb (leftWord e w))) (rightWord e w) = _ - rw [map_add] - rfl - map_smul' c x := by - ext w - simp only [map_smul, Pi.smul_apply, RingHom.id_apply] - change L (c • (fun cb => T x cb (leftWord e w))) (rightWord e w) = _ - rw [map_smul] - rfl - -lemma bandGlue_sum {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] - (e : Fin n ≃ Fin a ⊕ Fin b) - (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) - (L : WordSpace b k →ₗ[ℂ] WordSpace b d) (x : X) : - bandGlue e T L x = ∑ c : Fin b → Fin k, positionProduct e (T x c) (L (Pi.single c 1)) := by - classical - ext w - change L (fun cb => T x cb (leftWord e w)) (rightWord e w) = _ - have he : (fun cb => T x cb (leftWord e w)) = - ∑ c : Fin b → Fin k, T x c (leftWord e w) • (Pi.single c (1:ℂ) : WordSpace b k) := by - ext c - simp [Pi.single_apply] - rw [he, map_sum] - simp only [Finset.sum_apply, map_smul, Pi.smul_apply, smul_eq_mul, positionProduct] - -lemma bandGlue_equivariant {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] - (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) - (hT : ∀ h q x w, T (ρ (sumPerm e h q) x) w = wordRep a d h (T x (w ∘ q))) - (L : Representation.IntertwiningMap (wordRep b k) (wordRep b d)) - (h : Equiv.Perm (Fin a)) (q : Equiv.Perm (Fin b)) (x : X) : - bandGlue e T L.toLinearMap (ρ (sumPerm e h q) x) = - wordRep n d (sumPerm e h q) (bandGlue e T L.toLinearMap x) := by - ext w - change L (fun cb => T (ρ (sumPerm e h q) x) cb (leftWord e w)) (rightWord e w) = _ - simp only [hT] - have he : (fun cb => (wordRep a d h (T x (cb ∘ q))) (leftWord e w)) = - wordRep b k q (fun cb => T x cb ((leftWord e w) ∘ h)) := rfl - rw [he] - have hL : L (wordRep b k q (fun cb => T x cb ((leftWord e w) ∘ h))) = - wordRep b d q (L (fun cb => T x cb ((leftWord e w) ∘ h))) := - LinearMap.congr_fun (L.isIntertwining' q) _ - rw [hL] - change L (fun cb => T x cb ((leftWord e w) ∘ h)) ((rightWord e w) ∘ q) = - L (fun cb => T x cb (leftWord e (w ∘ sumPerm e h q))) (rightWord e (w ∘ sumPerm e h q)) - have hl : leftWord e (w ∘ sumPerm e h q) = (leftWord e w) ∘ h := by - funext i - simp [leftWord,sumPerm_left] - have hr : rightWord e (w ∘ sumPerm e h q) = (rightWord e w) ∘ q := by - funext i - simp [rightWord,sumPerm_right] - rw [hl,hr] - -lemma bandGlue_mem {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] - (e : Fin n ≃ Fin a ⊕ Fin b) (v : WordSpace a d) (u : WordSpace b d) - (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) - (hT : ∀ x c, T x c ∈ cyclic (wordRep a d) v) - (L : WordSpace b k →ₗ[ℂ] WordSpace b d) - (hL : ∀ y, L y ∈ cyclic (wordRep b d) u) (x : X) : - bandGlue e T L x ∈ cyclic (wordRep n d) (positionProduct e v u) := by - rw [bandGlue_sum] - apply Submodule.sum_mem - intro c hc - exact product_mem_cyclic e v u _ _ (hT x c) (hL _) - -/- A module containing every band Specht type of the relevant height detects -any nonzero high-valued colored-band vector. No multiplicity hypothesis is needed. -/ -theorem bandGlue_exists {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] - (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (v : WordSpace a d) (u : WordSpace b d) - (hband : ∀ (μ : YoungDiagram) (t : Tableau b μ), μ.colLen 0 ≤ k → - ∃ f : Representation.IntertwiningMap (spechtRep t) (cyclic (wordRep b d) u).toRepresentation, f ≠ 0) - (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) (hT0 : T ≠ 0) - (hT : ∀ h q x w, T (ρ (sumPerm e h q) x) w = wordRep a d h (T x (w ∘ q))) - (hTm : ∀ x c, T x c ∈ cyclic (wordRep a d) v) : - ∃ f : X →ₗ[ℂ] WordSpace n d, f ≠ 0 ∧ - (∀ h q x, f (ρ (sumPerm e h q) x) = wordRep n d (sumPerm e h q) (f x)) ∧ - (∀ x, f x ∈ cyclic (wordRep n d) (positionProduct e v u)) := by - classical - obtain ⟨x,c,w,hxc⟩ : ∃ x c w, T x c w ≠ 0 := by - by_contra hh - push Not at hh - apply hT0 - ext x c w - exact hh x c w - have hv : (fun cb => T x cb w) ≠ (0 : WordSpace b k) := by - intro hz - exact hxc (congrFun hz c) - obtain ⟨L,hL⟩ := word_support_separates (cyclic (wordRep b d) u).toRepresentation hband _ hv - let L' := (subrepInclusion (cyclic (wordRep b d) u)).comp L - have hL' : L' (fun cb => T x cb w) ≠ 0 := by - intro hz - apply hL - exact Subtype.ext hz - obtain ⟨z,hz⟩ : ∃ z, L' (fun cb => T x cb w) z ≠ 0 := by - by_contra hh - push Not at hh - exact hL' (funext hh) - refine ⟨bandGlue e T L'.toLinearMap, ?_, bandGlue_equivariant e ρ T hT L', ?_⟩ - · intro he - apply hz - have hh := congrArg (fun f : X →ₗ[ℂ] WordSpace n d => f x (joinPositions e w z)) he - change L' (fun cb => T x cb (leftWord e (joinPositions e w z))) (rightWord e (joinPositions e w z)) = 0 at hh - simpa only [leftWord_join, rightWord_join] using hh - · exact bandGlue_mem e v u T hTm L'.toLinearMap (fun y => (L y).property) - - -def coordinateSub (n d : ℕ) (P : (Fin n → Fin d) → Prop) : Submodule ℂ (WordSpace n d) where - carrier := {x | ∀ w, ¬ P w → x w = 0} - zero_mem' := by intro w hw; rfl - add_mem' := by intro x y hx hy w hw; change x w+y w=0; rw [hx w hw,hy w hw,add_zero] - smul_mem' := by intro c x hx w hw; change c*x w=0; rw [hx w hw,mul_zero] - -lemma positionProduct_sector {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (A : Fin d → Prop) (x : WordSpace a d) (y : WordSpace b d) - (hx : x ∈ alphabetSub a d A) (hy : y ∈ alphabetSub b d (fun z => ¬A z)) : - positionProduct e x y ∈ coordinateSub n d (wordSector (fun i => (e i).isLeft = true) A) := by - intro w hw - by_contra hn - apply hw - have hxy : x (leftWord e w) ≠ 0 ∧ y (rightWord e w) ≠ 0 := mul_ne_zero_iff.mp hn - intro i - obtain ⟨j,rfl⟩ := e.symm.surjective i - cases j with - | inl j => - simpa only [Equiv.apply_symm_apply, Sum.isLeft_inl, iff_true,leftWord] using - (alphabetSub_iff A x).mp hx _ hxy.1 j - | inr j => - simpa only [Equiv.apply_symm_apply, Sum.isLeft_inr, Bool.false_eq_true, iff_false,rightWord] using - (alphabetSub_iff (fun z => ¬A z) y).mp hy _ hxy.2 j - -lemma bandGlue_sector {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] - (e : Fin n ≃ Fin a ⊕ Fin b) (A : Fin d → Prop) - (v : WordSpace a d) (u : WordSpace b d) - (hv : v ∈ alphabetSub a d A) (hu : u ∈ alphabetSub b d (fun z => ¬A z)) - (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) - (hT : ∀ x c, T x c ∈ cyclic (wordRep a d) v) - (L : WordSpace b k →ₗ[ℂ] WordSpace b d) - (hL : ∀ y, L y ∈ cyclic (wordRep b d) u) (x : X) : - bandGlue e T L x ∈ coordinateSub n d (wordSector (fun i => (e i).isLeft = true) A) := by - rw [bandGlue_sum] - apply Submodule.sum_mem - intro c hc - apply positionProduct_sector - · exact cyclic_alphabet A v hv _ (hT x c) - · exact cyclic_alphabet (fun z => ¬A z) u hu _ (hL _) - -theorem bandGlue_sector_exists {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] - (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (v : WordSpace a d) (u : WordSpace b d) - (A : Fin d → Prop) (hvA : v ∈ alphabetSub a d A) - (huA : u ∈ alphabetSub b d (fun z => ¬A z)) - (hband : ∀ (μ : YoungDiagram) (t : Tableau b μ), μ.colLen 0 ≤ k → - ∃ f : Representation.IntertwiningMap (spechtRep t) (cyclic (wordRep b d) u).toRepresentation, f ≠ 0) - (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) (hT0 : T ≠ 0) - (hT : ∀ h q x w, T (ρ (sumPerm e h q) x) w = wordRep a d h (T x (w ∘ q))) - (hTm : ∀ x c, T x c ∈ cyclic (wordRep a d) v) : - ∃ f : X →ₗ[ℂ] WordSpace n d, f ≠ 0 ∧ - (∀ h q x, f (ρ (sumPerm e h q) x) = wordRep n d (sumPerm e h q) (f x)) ∧ - (∀ x, f x ∈ cyclic (wordRep n d) (positionProduct e v u)) ∧ - (∀ x, f x ∈ coordinateSub n d (wordSector (fun i => (e i).isLeft = true) A)) := by - classical - obtain ⟨x,c,w,hxc⟩ : ∃ x c w, T x c w ≠ 0 := by - by_contra hh - push Not at hh - apply hT0 - ext x c w - exact hh x c w - have hv : (fun cb => T x cb w) ≠ (0 : WordSpace b k) := by - intro hz - exact hxc (congrFun hz c) - obtain ⟨L,hL⟩ := word_support_separates (cyclic (wordRep b d) u).toRepresentation hband _ hv - let L' := (subrepInclusion (cyclic (wordRep b d) u)).comp L - have hL' : L' (fun cb => T x cb w) ≠ 0 := by - intro hz - apply hL - exact Subtype.ext hz - obtain ⟨z,hz⟩ : ∃ z, L' (fun cb => T x cb w) z ≠ 0 := by - by_contra hh - push Not at hh - exact hL' (funext hh) - refine ⟨bandGlue e T L'.toLinearMap, ?_, bandGlue_equivariant e ρ T hT L', ?_, ?_⟩ - · intro he - apply hz - have hh := congrArg (fun f : X →ₗ[ℂ] WordSpace n d => f x (joinPositions e w z)) he - change L' (fun cb => T x cb (leftWord e (joinPositions e w z))) (rightWord e (joinPositions e w z)) = 0 at hh - simpa only [leftWord_join, rightWord_join] using hh - · exact bandGlue_mem e v u T hTm L'.toLinearMap (fun y => (L y).property) - - · exact bandGlue_sector e A v u hvA huA T hTm L'.toLinearMap (fun y => (L y).property) - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.BandOrbit + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uX + +namespace Saxl + +/- Apply a band intertwiner to every scalar high-coordinate of a colored +strip orbit map. This is the concrete tensor product of the two maps. -/ +def bandGlue {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] + (e : Fin n ≃ Fin a ⊕ Fin b) + (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) + (L : WordSpace b k →ₗ[ℂ] WordSpace b d) : X →ₗ[ℂ] WordSpace n d where + toFun x w := L (fun cb => T x cb (leftWord e w)) (rightWord e w) + map_add' x y := by + ext w + simp only [map_add, Pi.add_apply] + change L ((fun cb => T x cb (leftWord e w)) + (fun cb => T y cb (leftWord e w))) (rightWord e w) = _ + rw [map_add] + rfl + map_smul' c x := by + ext w + simp only [map_smul, Pi.smul_apply, RingHom.id_apply] + change L (c • (fun cb => T x cb (leftWord e w))) (rightWord e w) = _ + rw [map_smul] + rfl + +lemma bandGlue_sum {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] + (e : Fin n ≃ Fin a ⊕ Fin b) + (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) + (L : WordSpace b k →ₗ[ℂ] WordSpace b d) (x : X) : + bandGlue e T L x = ∑ c : Fin b → Fin k, positionProduct e (T x c) (L (Pi.single c 1)) := by + classical + ext w + change L (fun cb => T x cb (leftWord e w)) (rightWord e w) = _ + have he : (fun cb => T x cb (leftWord e w)) = + ∑ c : Fin b → Fin k, T x c (leftWord e w) • (Pi.single c (1:ℂ) : WordSpace b k) := by + ext c + simp [Pi.single_apply] + rw [he, map_sum] + simp only [Finset.sum_apply, map_smul, Pi.smul_apply, smul_eq_mul, positionProduct] + +lemma bandGlue_equivariant {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] + (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) + (hT : ∀ h q x w, T (ρ (sumPerm e h q) x) w = wordRep a d h (T x (w ∘ q))) + (L : Representation.IntertwiningMap (wordRep b k) (wordRep b d)) + (h : Equiv.Perm (Fin a)) (q : Equiv.Perm (Fin b)) (x : X) : + bandGlue e T L.toLinearMap (ρ (sumPerm e h q) x) = + wordRep n d (sumPerm e h q) (bandGlue e T L.toLinearMap x) := by + ext w + change L (fun cb => T (ρ (sumPerm e h q) x) cb (leftWord e w)) (rightWord e w) = _ + simp only [hT] + have he : (fun cb => (wordRep a d h (T x (cb ∘ q))) (leftWord e w)) = + wordRep b k q (fun cb => T x cb ((leftWord e w) ∘ h)) := rfl + rw [he] + have hL : L (wordRep b k q (fun cb => T x cb ((leftWord e w) ∘ h))) = + wordRep b d q (L (fun cb => T x cb ((leftWord e w) ∘ h))) := + LinearMap.congr_fun (L.isIntertwining' q) _ + rw [hL] + change L (fun cb => T x cb ((leftWord e w) ∘ h)) ((rightWord e w) ∘ q) = + L (fun cb => T x cb (leftWord e (w ∘ sumPerm e h q))) (rightWord e (w ∘ sumPerm e h q)) + have hl : leftWord e (w ∘ sumPerm e h q) = (leftWord e w) ∘ h := by + funext i + simp [leftWord,sumPerm_left] + have hr : rightWord e (w ∘ sumPerm e h q) = (rightWord e w) ∘ q := by + funext i + simp [rightWord,sumPerm_right] + rw [hl,hr] + +lemma bandGlue_mem {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] + (e : Fin n ≃ Fin a ⊕ Fin b) (v : WordSpace a d) (u : WordSpace b d) + (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) + (hT : ∀ x c, T x c ∈ cyclic (wordRep a d) v) + (L : WordSpace b k →ₗ[ℂ] WordSpace b d) + (hL : ∀ y, L y ∈ cyclic (wordRep b d) u) (x : X) : + bandGlue e T L x ∈ cyclic (wordRep n d) (positionProduct e v u) := by + rw [bandGlue_sum] + apply Submodule.sum_mem + intro c hc + exact product_mem_cyclic e v u _ _ (hT x c) (hL _) + +/- A module containing every band Specht type of the relevant height detects +any nonzero high-valued colored-band vector. No multiplicity hypothesis is needed. -/ +theorem bandGlue_exists {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] + (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (v : WordSpace a d) (u : WordSpace b d) + (hband : ∀ (μ : YoungDiagram) (t : Tableau b μ), μ.colLen 0 ≤ k → + ∃ f : Representation.IntertwiningMap (spechtRep t) (cyclic (wordRep b d) u).toRepresentation, f ≠ 0) + (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) (hT0 : T ≠ 0) + (hT : ∀ h q x w, T (ρ (sumPerm e h q) x) w = wordRep a d h (T x (w ∘ q))) + (hTm : ∀ x c, T x c ∈ cyclic (wordRep a d) v) : + ∃ f : X →ₗ[ℂ] WordSpace n d, f ≠ 0 ∧ + (∀ h q x, f (ρ (sumPerm e h q) x) = wordRep n d (sumPerm e h q) (f x)) ∧ + (∀ x, f x ∈ cyclic (wordRep n d) (positionProduct e v u)) := by + classical + obtain ⟨x,c,w,hxc⟩ : ∃ x c w, T x c w ≠ 0 := by + by_contra hh + push Not at hh + apply hT0 + ext x c w + exact hh x c w + have hv : (fun cb => T x cb w) ≠ (0 : WordSpace b k) := by + intro hz + exact hxc (congrFun hz c) + obtain ⟨L,hL⟩ := word_support_separates (cyclic (wordRep b d) u).toRepresentation hband _ hv + let L' := (subrepInclusion (cyclic (wordRep b d) u)).comp L + have hL' : L' (fun cb => T x cb w) ≠ 0 := by + intro hz + apply hL + exact Subtype.ext hz + obtain ⟨z,hz⟩ : ∃ z, L' (fun cb => T x cb w) z ≠ 0 := by + by_contra hh + push Not at hh + exact hL' (funext hh) + refine ⟨bandGlue e T L'.toLinearMap, ?_, bandGlue_equivariant e ρ T hT L', ?_⟩ + · intro he + apply hz + have hh := congrArg (fun f : X →ₗ[ℂ] WordSpace n d => f x (joinPositions e w z)) he + change L' (fun cb => T x cb (leftWord e (joinPositions e w z))) (rightWord e (joinPositions e w z)) = 0 at hh + simpa only [leftWord_join, rightWord_join] using hh + · exact bandGlue_mem e v u T hTm L'.toLinearMap (fun y => (L y).property) + + +def coordinateSub (n d : ℕ) (P : (Fin n → Fin d) → Prop) : Submodule ℂ (WordSpace n d) where + carrier := {x | ∀ w, ¬ P w → x w = 0} + zero_mem' := by intro w hw; rfl + add_mem' := by intro x y hx hy w hw; change x w+y w=0; rw [hx w hw,hy w hw,add_zero] + smul_mem' := by intro c x hx w hw; change c*x w=0; rw [hx w hw,mul_zero] + +lemma positionProduct_sector {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (A : Fin d → Prop) (x : WordSpace a d) (y : WordSpace b d) + (hx : x ∈ alphabetSub a d A) (hy : y ∈ alphabetSub b d (fun z => ¬A z)) : + positionProduct e x y ∈ coordinateSub n d (wordSector (fun i => (e i).isLeft = true) A) := by + intro w hw + by_contra hn + apply hw + have hxy : x (leftWord e w) ≠ 0 ∧ y (rightWord e w) ≠ 0 := mul_ne_zero_iff.mp hn + intro i + obtain ⟨j,rfl⟩ := e.symm.surjective i + cases j with + | inl j => + simpa only [Equiv.apply_symm_apply, Sum.isLeft_inl, iff_true,leftWord] using + (alphabetSub_iff A x).mp hx _ hxy.1 j + | inr j => + simpa only [Equiv.apply_symm_apply, Sum.isLeft_inr, Bool.false_eq_true, iff_false,rightWord] using + (alphabetSub_iff (fun z => ¬A z) y).mp hy _ hxy.2 j + +lemma bandGlue_sector {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] + (e : Fin n ≃ Fin a ⊕ Fin b) (A : Fin d → Prop) + (v : WordSpace a d) (u : WordSpace b d) + (hv : v ∈ alphabetSub a d A) (hu : u ∈ alphabetSub b d (fun z => ¬A z)) + (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) + (hT : ∀ x c, T x c ∈ cyclic (wordRep a d) v) + (L : WordSpace b k →ₗ[ℂ] WordSpace b d) + (hL : ∀ y, L y ∈ cyclic (wordRep b d) u) (x : X) : + bandGlue e T L x ∈ coordinateSub n d (wordSector (fun i => (e i).isLeft = true) A) := by + rw [bandGlue_sum] + apply Submodule.sum_mem + intro c hc + apply positionProduct_sector + · exact cyclic_alphabet A v hv _ (hT x c) + · exact cyclic_alphabet (fun z => ¬A z) u hu _ (hL _) + +theorem bandGlue_sector_exists {n a b k d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] + (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (v : WordSpace a d) (u : WordSpace b d) + (A : Fin d → Prop) (hvA : v ∈ alphabetSub a d A) + (huA : u ∈ alphabetSub b d (fun z => ¬A z)) + (hband : ∀ (μ : YoungDiagram) (t : Tableau b μ), μ.colLen 0 ≤ k → + ∃ f : Representation.IntertwiningMap (spechtRep t) (cyclic (wordRep b d) u).toRepresentation, f ≠ 0) + (T : X →ₗ[ℂ] ((Fin b → Fin k) → WordSpace a d)) (hT0 : T ≠ 0) + (hT : ∀ h q x w, T (ρ (sumPerm e h q) x) w = wordRep a d h (T x (w ∘ q))) + (hTm : ∀ x c, T x c ∈ cyclic (wordRep a d) v) : + ∃ f : X →ₗ[ℂ] WordSpace n d, f ≠ 0 ∧ + (∀ h q x, f (ρ (sumPerm e h q) x) = wordRep n d (sumPerm e h q) (f x)) ∧ + (∀ x, f x ∈ cyclic (wordRep n d) (positionProduct e v u)) ∧ + (∀ x, f x ∈ coordinateSub n d (wordSector (fun i => (e i).isLeft = true) A)) := by + classical + obtain ⟨x,c,w,hxc⟩ : ∃ x c w, T x c w ≠ 0 := by + by_contra hh + push Not at hh + apply hT0 + ext x c w + exact hh x c w + have hv : (fun cb => T x cb w) ≠ (0 : WordSpace b k) := by + intro hz + exact hxc (congrFun hz c) + obtain ⟨L,hL⟩ := word_support_separates (cyclic (wordRep b d) u).toRepresentation hband _ hv + let L' := (subrepInclusion (cyclic (wordRep b d) u)).comp L + have hL' : L' (fun cb => T x cb w) ≠ 0 := by + intro hz + apply hL + exact Subtype.ext hz + obtain ⟨z,hz⟩ : ∃ z, L' (fun cb => T x cb w) z ≠ 0 := by + by_contra hh + push Not at hh + exact hL' (funext hh) + refine ⟨bandGlue e T L'.toLinearMap, ?_, bandGlue_equivariant e ρ T hT L', ?_, ?_⟩ + · intro he + apply hz + have hh := congrArg (fun f : X →ₗ[ℂ] WordSpace n d => f x (joinPositions e w z)) he + change L' (fun cb => T x cb (leftWord e (joinPositions e w z))) (rightWord e (joinPositions e w z)) = 0 at hh + simpa only [leftWord_join, rightWord_join] using hh + · exact bandGlue_mem e v u T hTm L'.toLinearMap (fun y => (L y).property) + + · exact bandGlue_sector e A v u hvA huA T hTm L'.toLinearMap (fun y => (L y).property) + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/BandMatrices.lean b/lean/OAI/RepresentationTheory/Saxl/BandMatrices.lean index 03f75fff9cbae17745e81b020ba3d5baa213e4a8..038d2728613288407235bae91239560ff8861b6a 100644 --- a/lean/OAI/RepresentationTheory/Saxl/BandMatrices.lean +++ b/lean/OAI/RepresentationTheory/Saxl/BandMatrices.lean @@ -1,313 +1,313 @@ -import OAI.RepresentationTheory.Saxl.PathAlternation - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uA - -namespace Saxl.Band -abbrev Mat := Matrix (Fin 2) (Fin 2) ℂ - -def basis (i : ℕ) : Mat := - match i with - | 0 => 1 - | 1 => !![1, 0; 0, -1] - | 2 => !![0, 1; 1, 0] - | _ => !![0, 1; -1, 0] - -def D (q : ℕ) (X : Mat) : Mat := if q % 2 = 0 then X.adjugate else X - -def segment (r p : ℕ) : Mat := - ∑ π : Equiv.Perm (Fin r), - ((((Equiv.Perm.sign π) : ℤ) : ℂ)) • - (List.ofFn (fun j : Fin r => D (p + j.val) (basis (π j).val))).prod - -/- Consecutive segments with the original global position parities. -/ -def blocks : ℕ → List ℕ → Mat - | _, [] => 1 - | p, r :: rs => segment r p * blocks (p + r) rs - -/- Enumeration of the finite symmetric group for the four small matrix calculations. -/ -lemma sum_perm_succ {A : Type uA} [AddCommMonoid A] (n : ℕ) - (f : Equiv.Perm (Fin (n + 1)) → A) : - (∑ π, f π) = ∑ i : Fin (n + 1), ∑ σ : Equiv.Perm (Fin n), - f (Equiv.Perm.decomposeFin.symm (i, σ)) := by - calc - (∑ π, f π) = ∑ x : Fin (n + 1) × Equiv.Perm (Fin n), - f (Equiv.Perm.decomposeFin.symm x) := - Fintype.sum_equiv Equiv.Perm.decomposeFin _ _ (by intro π; simp) - _ = _ := Fintype.sum_prod_type _ - -lemma decompose_apply_two {n : ℕ} (e : Equiv.Perm (Fin (n + 2))) (p : Fin (n + 3)) : - Equiv.Perm.decomposeFin.symm (p, e) 2 = Equiv.swap 0 p (e 1).succ := by - change Equiv.Perm.decomposeFin.symm (p, e) (1 : Fin (n + 2)).succ = _ - exact Equiv.Perm.decomposeFin_symm_apply_succ e p 1 - -lemma decompose_apply_three {n : ℕ} (e : Equiv.Perm (Fin (n + 3))) (p : Fin (n + 4)) : - Equiv.Perm.decomposeFin.symm (p, e) 3 = Equiv.swap 0 p (e 2).succ := by - change Equiv.Perm.decomposeFin.symm (p, e) (2 : Fin (n + 3)).succ = _ - exact Equiv.Perm.decomposeFin_symm_apply_succ e p 2 - -lemma segment_one_even : segment 1 0 = 1 := by - simp [segment, List.ofFn_succ, basis, D] - -lemma segment_one_odd : segment 1 1 = 1 := by - simp [segment, List.ofFn_succ, basis, D] - -lemma segment_two_even : segment 2 0 = (2 : ℂ) • basis 1 := by - unfold segment - simp only [sum_perm_succ, Fin.sum_univ_succ, Fintype.sum_unique, - List.ofFn_succ, List.ofFn_zero, List.prod_cons, List.prod_nil] - norm_num only [Equiv.Perm.decomposeFin.symm_sign, - Equiv.Perm.decomposeFin_symm_apply_zero, - Equiv.Perm.decomposeFin_symm_apply_one, decompose_apply_two, decompose_apply_three, - Equiv.Perm.decomposeFin_symm_of_one, Equiv.swap_self, Equiv.swap_apply_def, - Equiv.Perm.sign_one, Equiv.Perm.sign_swap, Equiv.Perm.one_apply, - Fin.ext_iff, Fin.isValue, Fin.reduceFinMk, Fin.succ_mk, Fin.val_mk, Fin.zero_eta, - Fin.succ_zero_eq_one] - ext i j - fin_cases i <;> fin_cases j <;> - norm_num [D, basis, decompose_apply_two, decompose_apply_three, Fin.ext_iff, - Equiv.Perm.decomposeFin.symm_sign, - Equiv.Perm.decomposeFin_symm_apply_succ, Equiv.swap_apply_def, - Matrix.adjugate_fin_two, Matrix.mul_apply, Fin.sum_univ_two] - -lemma segment_two_odd : segment 2 1 = (-2 : ℂ) • basis 1 := by - unfold segment - simp only [sum_perm_succ, Fin.sum_univ_succ, Fintype.sum_unique, - List.ofFn_succ, List.ofFn_zero, List.prod_cons, List.prod_nil] - norm_num only [Equiv.Perm.decomposeFin.symm_sign, - Equiv.Perm.decomposeFin_symm_apply_zero, - Equiv.Perm.decomposeFin_symm_apply_one, decompose_apply_two, decompose_apply_three, - Equiv.Perm.decomposeFin_symm_of_one, Equiv.swap_self, Equiv.swap_apply_def, - Equiv.Perm.sign_one, Equiv.Perm.sign_swap, Equiv.Perm.one_apply, - Fin.ext_iff, Fin.isValue, Fin.reduceFinMk, Fin.succ_mk, Fin.val_mk, Fin.zero_eta, - Fin.succ_zero_eq_one] - ext i j - fin_cases i <;> fin_cases j <;> - norm_num [D, basis, decompose_apply_two, decompose_apply_three, Fin.ext_iff, - Equiv.Perm.decomposeFin.symm_sign, - Equiv.Perm.decomposeFin_symm_apply_succ, Equiv.swap_apply_def, - Matrix.adjugate_fin_two, Matrix.mul_apply, Fin.sum_univ_two] - -lemma segment_three_even : segment 3 0 = (-6 : ℂ) • basis 3 := by - unfold segment - simp only [sum_perm_succ, Fin.sum_univ_succ, Fintype.sum_unique, - List.ofFn_succ, List.ofFn_zero, List.prod_cons, List.prod_nil] - norm_num only [Equiv.Perm.decomposeFin.symm_sign, - Equiv.Perm.decomposeFin_symm_apply_zero, - Equiv.Perm.decomposeFin_symm_apply_one, decompose_apply_two, decompose_apply_three, - Equiv.Perm.decomposeFin_symm_of_one, Equiv.swap_self, Equiv.swap_apply_def, - Equiv.Perm.sign_one, Equiv.Perm.sign_swap, Equiv.Perm.one_apply, - Fin.ext_iff, Fin.isValue, Fin.reduceFinMk, Fin.succ_mk, Fin.val_mk, Fin.zero_eta, - Fin.succ_zero_eq_one] - ext i j - fin_cases i <;> fin_cases j <;> - norm_num [D, basis, decompose_apply_two, decompose_apply_three, Fin.ext_iff, - Equiv.Perm.decomposeFin.symm_sign, - Equiv.Perm.decomposeFin_symm_apply_succ, Equiv.swap_apply_def, - Matrix.adjugate_fin_two, Matrix.mul_apply, Fin.sum_univ_two] - -lemma segment_three_odd : segment 3 1 = (-6 : ℂ) • basis 3 := by - unfold segment - simp only [sum_perm_succ, Fin.sum_univ_succ, Fintype.sum_unique, - List.ofFn_succ, List.ofFn_zero, List.prod_cons, List.prod_nil] - norm_num only [Equiv.Perm.decomposeFin.symm_sign, - Equiv.Perm.decomposeFin_symm_apply_zero, - Equiv.Perm.decomposeFin_symm_apply_one, decompose_apply_two, decompose_apply_three, - Equiv.Perm.decomposeFin_symm_of_one, Equiv.swap_self, Equiv.swap_apply_def, - Equiv.Perm.sign_one, Equiv.Perm.sign_swap, Equiv.Perm.one_apply, - Fin.ext_iff, Fin.isValue, Fin.reduceFinMk, Fin.succ_mk, Fin.val_mk, Fin.zero_eta, - Fin.succ_zero_eq_one] - ext i j - fin_cases i <;> fin_cases j <;> - norm_num [D, basis, decompose_apply_two, decompose_apply_three, Fin.ext_iff, - Equiv.Perm.decomposeFin.symm_sign, - Equiv.Perm.decomposeFin_symm_apply_succ, Equiv.swap_apply_def, - Matrix.adjugate_fin_two, Matrix.mul_apply, Fin.sum_univ_two] - -lemma segment_four_even : segment 4 0 = (24 : ℂ) • basis 0 := by - unfold segment - simp only [sum_perm_succ, Fin.sum_univ_succ, Fintype.sum_unique, - List.ofFn_succ, List.ofFn_zero, List.prod_cons, List.prod_nil] - norm_num only [Equiv.Perm.decomposeFin.symm_sign, - Equiv.Perm.decomposeFin_symm_apply_zero, - Equiv.Perm.decomposeFin_symm_apply_one, decompose_apply_two, decompose_apply_three, - Equiv.Perm.decomposeFin_symm_of_one, Equiv.swap_self, Equiv.swap_apply_def, - Equiv.Perm.sign_one, Equiv.Perm.sign_swap, Equiv.Perm.one_apply, - Fin.ext_iff, Fin.isValue, Fin.reduceFinMk, Fin.succ_mk, Fin.val_mk, Fin.zero_eta, - Fin.succ_zero_eq_one] - ext i j - fin_cases i <;> fin_cases j <;> - norm_num [D, basis, decompose_apply_two, decompose_apply_three, Fin.ext_iff, - Equiv.Perm.decomposeFin.symm_sign, - Equiv.Perm.decomposeFin_symm_apply_succ, Equiv.swap_apply_def, - Matrix.adjugate_fin_two, Matrix.mul_apply, Fin.sum_univ_two] - -lemma segment_four_odd : segment 4 1 = (-24 : ℂ) • basis 0 := by - unfold segment - simp only [sum_perm_succ, Fin.sum_univ_succ, Fintype.sum_unique, - List.ofFn_succ, List.ofFn_zero, List.prod_cons, List.prod_nil] - norm_num only [Equiv.Perm.decomposeFin.symm_sign, - Equiv.Perm.decomposeFin_symm_apply_zero, - Equiv.Perm.decomposeFin_symm_apply_one, decompose_apply_two, decompose_apply_three, - Equiv.Perm.decomposeFin_symm_of_one, Equiv.swap_self, Equiv.swap_apply_def, - Equiv.Perm.sign_one, Equiv.Perm.sign_swap, Equiv.Perm.one_apply, - Fin.ext_iff, Fin.isValue, Fin.reduceFinMk, Fin.succ_mk, Fin.val_mk, Fin.zero_eta, - Fin.succ_zero_eq_one] - ext i j - fin_cases i <;> fin_cases j <;> - norm_num [D, basis, decompose_apply_two, decompose_apply_three, Fin.ext_iff, - Equiv.Perm.decomposeFin.symm_sign, - Equiv.Perm.decomposeFin_symm_apply_succ, Equiv.swap_apply_def, - Matrix.adjugate_fin_two, Matrix.mul_apply, Fin.sum_univ_two] - -/- Only the original global parity matters. -/ -lemma segment_mod (r p : ℕ) : segment r p = segment r (p % 2) := by - simp [segment, D, Nat.add_mod] - -def ScaledBasis (X : Mat) : Prop := - ∃ c : ℂ, c ≠ 0 ∧ ∃ i : Fin 4, X = c • basis i.val - -lemma scaledBasis_smul (c : ℂ) (hc : c ≠ 0) (i : Fin 4) : - ScaledBasis (c • basis i.val) := ⟨c, hc, i, rfl⟩ - -lemma scaledBasis_one : ScaledBasis 1 := by - exact ⟨1, one_ne_zero, 0, by simp [basis]⟩ - -lemma basis_mul (i j : Fin 4) : ScaledBasis (basis i.val * basis j.val) := by - fin_cases i <;> fin_cases j - · refine ⟨1, by norm_num, 0, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨1, by norm_num, 1, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨1, by norm_num, 2, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨1, by norm_num, 3, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨1, by norm_num, 1, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨1, by norm_num, 0, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨1, by norm_num, 3, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨1, by norm_num, 2, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨1, by norm_num, 2, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨-1, by norm_num, 3, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨1, by norm_num, 0, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨-1, by norm_num, 1, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨1, by norm_num, 3, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨-1, by norm_num, 2, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨1, by norm_num, 1, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - · refine ⟨-1, by norm_num, 0, ?_⟩ - ext a b - fin_cases a <;> fin_cases b <;> - norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] - -lemma ScaledBasis.mul {X Y : Mat} (hX : ScaledBasis X) (hY : ScaledBasis Y) : - ScaledBasis (X * Y) := by - obtain ⟨c, hc, i, rfl⟩ := hX - obtain ⟨d, hd, j, rfl⟩ := hY - obtain ⟨e, he, k, hk⟩ := basis_mul i j - refine ⟨c * d * e, mul_ne_zero (mul_ne_zero hc hd) he, k, ?_⟩ - rw [smul_mul_smul_comm, hk, smul_smul] - -lemma segment_scaled (r p : ℕ) (hr : 1 ≤ r ∧ r ≤ 4) : ScaledBasis (segment r p) := by - rw [segment_mod] - have hp := Nat.mod_two_eq_zero_or_one p - obtain ⟨hr1, hr4⟩ := hr - interval_cases r <;> rcases hp with hp | hp <;> rw [hp] - all_goals simp only [segment_one_even, segment_one_odd, - segment_two_even, segment_two_odd, segment_three_even, segment_three_odd, - segment_four_even, segment_four_odd] - all_goals first - | exact scaledBasis_one - | exact scaledBasis_smul _ (by norm_num) 0 - | exact scaledBasis_smul _ (by norm_num) 1 - | exact scaledBasis_smul _ (by norm_num) 3 - -lemma blocks_scaled (rs : List ℕ) (hrs : ∀ r ∈ rs, 1 ≤ r ∧ r ≤ 4) (p : ℕ) : - ScaledBasis (blocks p rs) := by - induction rs generalizing p with - | nil => exact scaledBasis_one - | cons r rs ih => - exact (segment_scaled r p (hrs r (by simp))).mul - (ih (fun a ha => hrs a (by simp [ha])) (p + r)) - -def Q : Mat := !![1, 1; 1, 2] -def Qinv : Mat := !![2, -1; -1, 1] - -lemma Q_mul_Qinv : Q * Qinv = 1 := by - ext i j - fin_cases i <;> fin_cases j <;> - norm_num [Q, Qinv, Matrix.mul_apply, Fin.sum_univ_two] - -lemma Qinv_mul_Q : Qinv * Q = 1 := by - ext i j - fin_cases i <;> fin_cases j <;> - norm_num [Q, Qinv, Matrix.mul_apply, Fin.sum_univ_two] - -lemma Q_isUnit : IsUnit Q := ⟨⟨Q, Qinv, Q_mul_Qinv, Qinv_mul_Q⟩, rfl⟩ - -lemma Q_inverse : Q⁻¹ = Qinv := by - exact Matrix.inv_eq_left_inv Qinv_mul_Q - -lemma Q_basis_ne_zero (i : Fin 4) : (Q * basis i.val * Q⁻¹) 0 0 ≠ 0 := by - rw [Q_inverse] - fin_cases i <;> norm_num [Q, Qinv, basis, Matrix.mul_apply, Fin.sum_univ_two] - -/- Endpoint noncancellation for arbitrary consecutive columns of lengths at most four. -/ -theorem band_nonzero_pairing (rs : List ℕ) - (hrs : ∀ r ∈ rs, 1 ≤ r ∧ r ≤ 4) : - ∃ Q : Mat, IsUnit Q ∧ (Q * blocks 1 rs * Q⁻¹) 0 0 ≠ 0 := by - obtain ⟨c, hc, i, hi⟩ := blocks_scaled rs hrs 1 - refine ⟨Q, Q_isUnit, ?_⟩ - rw [hi, Matrix.mul_smul, Matrix.smul_mul] - exact mul_ne_zero hc (Q_basis_ne_zero i) - -end Saxl.Band - -end - -end OAI +import OAI.RepresentationTheory.Saxl.PathAlternation + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uA + +namespace Saxl.Band +abbrev Mat := Matrix (Fin 2) (Fin 2) ℂ + +def basis (i : ℕ) : Mat := + match i with + | 0 => 1 + | 1 => !![1, 0; 0, -1] + | 2 => !![0, 1; 1, 0] + | _ => !![0, 1; -1, 0] + +def D (q : ℕ) (X : Mat) : Mat := if q % 2 = 0 then X.adjugate else X + +def segment (r p : ℕ) : Mat := + ∑ π : Equiv.Perm (Fin r), + ((((Equiv.Perm.sign π) : ℤ) : ℂ)) • + (List.ofFn (fun j : Fin r => D (p + j.val) (basis (π j).val))).prod + +/- Consecutive segments with the original global position parities. -/ +def blocks : ℕ → List ℕ → Mat + | _, [] => 1 + | p, r :: rs => segment r p * blocks (p + r) rs + +/- Enumeration of the finite symmetric group for the four small matrix calculations. -/ +lemma sum_perm_succ {A : Type uA} [AddCommMonoid A] (n : ℕ) + (f : Equiv.Perm (Fin (n + 1)) → A) : + (∑ π, f π) = ∑ i : Fin (n + 1), ∑ σ : Equiv.Perm (Fin n), + f (Equiv.Perm.decomposeFin.symm (i, σ)) := by + calc + (∑ π, f π) = ∑ x : Fin (n + 1) × Equiv.Perm (Fin n), + f (Equiv.Perm.decomposeFin.symm x) := + Fintype.sum_equiv Equiv.Perm.decomposeFin _ _ (by intro π; simp) + _ = _ := Fintype.sum_prod_type _ + +lemma decompose_apply_two {n : ℕ} (e : Equiv.Perm (Fin (n + 2))) (p : Fin (n + 3)) : + Equiv.Perm.decomposeFin.symm (p, e) 2 = Equiv.swap 0 p (e 1).succ := by + change Equiv.Perm.decomposeFin.symm (p, e) (1 : Fin (n + 2)).succ = _ + exact Equiv.Perm.decomposeFin_symm_apply_succ e p 1 + +lemma decompose_apply_three {n : ℕ} (e : Equiv.Perm (Fin (n + 3))) (p : Fin (n + 4)) : + Equiv.Perm.decomposeFin.symm (p, e) 3 = Equiv.swap 0 p (e 2).succ := by + change Equiv.Perm.decomposeFin.symm (p, e) (2 : Fin (n + 3)).succ = _ + exact Equiv.Perm.decomposeFin_symm_apply_succ e p 2 + +lemma segment_one_even : segment 1 0 = 1 := by + simp [segment, List.ofFn_succ, basis, D] + +lemma segment_one_odd : segment 1 1 = 1 := by + simp [segment, List.ofFn_succ, basis, D] + +lemma segment_two_even : segment 2 0 = (2 : ℂ) • basis 1 := by + unfold segment + simp only [sum_perm_succ, Fin.sum_univ_succ, Fintype.sum_unique, + List.ofFn_succ, List.ofFn_zero, List.prod_cons, List.prod_nil] + norm_num only [Equiv.Perm.decomposeFin.symm_sign, + Equiv.Perm.decomposeFin_symm_apply_zero, + Equiv.Perm.decomposeFin_symm_apply_one, decompose_apply_two, decompose_apply_three, + Equiv.Perm.decomposeFin_symm_of_one, Equiv.swap_self, Equiv.swap_apply_def, + Equiv.Perm.sign_one, Equiv.Perm.sign_swap, Equiv.Perm.one_apply, + Fin.ext_iff, Fin.isValue, Fin.reduceFinMk, Fin.succ_mk, Fin.val_mk, Fin.zero_eta, + Fin.succ_zero_eq_one] + ext i j + fin_cases i <;> fin_cases j <;> + norm_num [D, basis, decompose_apply_two, decompose_apply_three, Fin.ext_iff, + Equiv.Perm.decomposeFin.symm_sign, + Equiv.Perm.decomposeFin_symm_apply_succ, Equiv.swap_apply_def, + Matrix.adjugate_fin_two, Matrix.mul_apply, Fin.sum_univ_two] + +lemma segment_two_odd : segment 2 1 = (-2 : ℂ) • basis 1 := by + unfold segment + simp only [sum_perm_succ, Fin.sum_univ_succ, Fintype.sum_unique, + List.ofFn_succ, List.ofFn_zero, List.prod_cons, List.prod_nil] + norm_num only [Equiv.Perm.decomposeFin.symm_sign, + Equiv.Perm.decomposeFin_symm_apply_zero, + Equiv.Perm.decomposeFin_symm_apply_one, decompose_apply_two, decompose_apply_three, + Equiv.Perm.decomposeFin_symm_of_one, Equiv.swap_self, Equiv.swap_apply_def, + Equiv.Perm.sign_one, Equiv.Perm.sign_swap, Equiv.Perm.one_apply, + Fin.ext_iff, Fin.isValue, Fin.reduceFinMk, Fin.succ_mk, Fin.val_mk, Fin.zero_eta, + Fin.succ_zero_eq_one] + ext i j + fin_cases i <;> fin_cases j <;> + norm_num [D, basis, decompose_apply_two, decompose_apply_three, Fin.ext_iff, + Equiv.Perm.decomposeFin.symm_sign, + Equiv.Perm.decomposeFin_symm_apply_succ, Equiv.swap_apply_def, + Matrix.adjugate_fin_two, Matrix.mul_apply, Fin.sum_univ_two] + +lemma segment_three_even : segment 3 0 = (-6 : ℂ) • basis 3 := by + unfold segment + simp only [sum_perm_succ, Fin.sum_univ_succ, Fintype.sum_unique, + List.ofFn_succ, List.ofFn_zero, List.prod_cons, List.prod_nil] + norm_num only [Equiv.Perm.decomposeFin.symm_sign, + Equiv.Perm.decomposeFin_symm_apply_zero, + Equiv.Perm.decomposeFin_symm_apply_one, decompose_apply_two, decompose_apply_three, + Equiv.Perm.decomposeFin_symm_of_one, Equiv.swap_self, Equiv.swap_apply_def, + Equiv.Perm.sign_one, Equiv.Perm.sign_swap, Equiv.Perm.one_apply, + Fin.ext_iff, Fin.isValue, Fin.reduceFinMk, Fin.succ_mk, Fin.val_mk, Fin.zero_eta, + Fin.succ_zero_eq_one] + ext i j + fin_cases i <;> fin_cases j <;> + norm_num [D, basis, decompose_apply_two, decompose_apply_three, Fin.ext_iff, + Equiv.Perm.decomposeFin.symm_sign, + Equiv.Perm.decomposeFin_symm_apply_succ, Equiv.swap_apply_def, + Matrix.adjugate_fin_two, Matrix.mul_apply, Fin.sum_univ_two] + +lemma segment_three_odd : segment 3 1 = (-6 : ℂ) • basis 3 := by + unfold segment + simp only [sum_perm_succ, Fin.sum_univ_succ, Fintype.sum_unique, + List.ofFn_succ, List.ofFn_zero, List.prod_cons, List.prod_nil] + norm_num only [Equiv.Perm.decomposeFin.symm_sign, + Equiv.Perm.decomposeFin_symm_apply_zero, + Equiv.Perm.decomposeFin_symm_apply_one, decompose_apply_two, decompose_apply_three, + Equiv.Perm.decomposeFin_symm_of_one, Equiv.swap_self, Equiv.swap_apply_def, + Equiv.Perm.sign_one, Equiv.Perm.sign_swap, Equiv.Perm.one_apply, + Fin.ext_iff, Fin.isValue, Fin.reduceFinMk, Fin.succ_mk, Fin.val_mk, Fin.zero_eta, + Fin.succ_zero_eq_one] + ext i j + fin_cases i <;> fin_cases j <;> + norm_num [D, basis, decompose_apply_two, decompose_apply_three, Fin.ext_iff, + Equiv.Perm.decomposeFin.symm_sign, + Equiv.Perm.decomposeFin_symm_apply_succ, Equiv.swap_apply_def, + Matrix.adjugate_fin_two, Matrix.mul_apply, Fin.sum_univ_two] + +lemma segment_four_even : segment 4 0 = (24 : ℂ) • basis 0 := by + unfold segment + simp only [sum_perm_succ, Fin.sum_univ_succ, Fintype.sum_unique, + List.ofFn_succ, List.ofFn_zero, List.prod_cons, List.prod_nil] + norm_num only [Equiv.Perm.decomposeFin.symm_sign, + Equiv.Perm.decomposeFin_symm_apply_zero, + Equiv.Perm.decomposeFin_symm_apply_one, decompose_apply_two, decompose_apply_three, + Equiv.Perm.decomposeFin_symm_of_one, Equiv.swap_self, Equiv.swap_apply_def, + Equiv.Perm.sign_one, Equiv.Perm.sign_swap, Equiv.Perm.one_apply, + Fin.ext_iff, Fin.isValue, Fin.reduceFinMk, Fin.succ_mk, Fin.val_mk, Fin.zero_eta, + Fin.succ_zero_eq_one] + ext i j + fin_cases i <;> fin_cases j <;> + norm_num [D, basis, decompose_apply_two, decompose_apply_three, Fin.ext_iff, + Equiv.Perm.decomposeFin.symm_sign, + Equiv.Perm.decomposeFin_symm_apply_succ, Equiv.swap_apply_def, + Matrix.adjugate_fin_two, Matrix.mul_apply, Fin.sum_univ_two] + +lemma segment_four_odd : segment 4 1 = (-24 : ℂ) • basis 0 := by + unfold segment + simp only [sum_perm_succ, Fin.sum_univ_succ, Fintype.sum_unique, + List.ofFn_succ, List.ofFn_zero, List.prod_cons, List.prod_nil] + norm_num only [Equiv.Perm.decomposeFin.symm_sign, + Equiv.Perm.decomposeFin_symm_apply_zero, + Equiv.Perm.decomposeFin_symm_apply_one, decompose_apply_two, decompose_apply_three, + Equiv.Perm.decomposeFin_symm_of_one, Equiv.swap_self, Equiv.swap_apply_def, + Equiv.Perm.sign_one, Equiv.Perm.sign_swap, Equiv.Perm.one_apply, + Fin.ext_iff, Fin.isValue, Fin.reduceFinMk, Fin.succ_mk, Fin.val_mk, Fin.zero_eta, + Fin.succ_zero_eq_one] + ext i j + fin_cases i <;> fin_cases j <;> + norm_num [D, basis, decompose_apply_two, decompose_apply_three, Fin.ext_iff, + Equiv.Perm.decomposeFin.symm_sign, + Equiv.Perm.decomposeFin_symm_apply_succ, Equiv.swap_apply_def, + Matrix.adjugate_fin_two, Matrix.mul_apply, Fin.sum_univ_two] + +/- Only the original global parity matters. -/ +lemma segment_mod (r p : ℕ) : segment r p = segment r (p % 2) := by + simp [segment, D, Nat.add_mod] + +def ScaledBasis (X : Mat) : Prop := + ∃ c : ℂ, c ≠ 0 ∧ ∃ i : Fin 4, X = c • basis i.val + +lemma scaledBasis_smul (c : ℂ) (hc : c ≠ 0) (i : Fin 4) : + ScaledBasis (c • basis i.val) := ⟨c, hc, i, rfl⟩ + +lemma scaledBasis_one : ScaledBasis 1 := by + exact ⟨1, one_ne_zero, 0, by simp [basis]⟩ + +lemma basis_mul (i j : Fin 4) : ScaledBasis (basis i.val * basis j.val) := by + fin_cases i <;> fin_cases j + · refine ⟨1, by norm_num, 0, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨1, by norm_num, 1, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨1, by norm_num, 2, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨1, by norm_num, 3, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨1, by norm_num, 1, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨1, by norm_num, 0, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨1, by norm_num, 3, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨1, by norm_num, 2, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨1, by norm_num, 2, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨-1, by norm_num, 3, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨1, by norm_num, 0, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨-1, by norm_num, 1, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨1, by norm_num, 3, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨-1, by norm_num, 2, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨1, by norm_num, 1, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + · refine ⟨-1, by norm_num, 0, ?_⟩ + ext a b + fin_cases a <;> fin_cases b <;> + norm_num [basis, Matrix.mul_apply, Fin.sum_univ_two] + +lemma ScaledBasis.mul {X Y : Mat} (hX : ScaledBasis X) (hY : ScaledBasis Y) : + ScaledBasis (X * Y) := by + obtain ⟨c, hc, i, rfl⟩ := hX + obtain ⟨d, hd, j, rfl⟩ := hY + obtain ⟨e, he, k, hk⟩ := basis_mul i j + refine ⟨c * d * e, mul_ne_zero (mul_ne_zero hc hd) he, k, ?_⟩ + rw [smul_mul_smul_comm, hk, smul_smul] + +lemma segment_scaled (r p : ℕ) (hr : 1 ≤ r ∧ r ≤ 4) : ScaledBasis (segment r p) := by + rw [segment_mod] + have hp := Nat.mod_two_eq_zero_or_one p + obtain ⟨hr1, hr4⟩ := hr + interval_cases r <;> rcases hp with hp | hp <;> rw [hp] + all_goals simp only [segment_one_even, segment_one_odd, + segment_two_even, segment_two_odd, segment_three_even, segment_three_odd, + segment_four_even, segment_four_odd] + all_goals first + | exact scaledBasis_one + | exact scaledBasis_smul _ (by norm_num) 0 + | exact scaledBasis_smul _ (by norm_num) 1 + | exact scaledBasis_smul _ (by norm_num) 3 + +lemma blocks_scaled (rs : List ℕ) (hrs : ∀ r ∈ rs, 1 ≤ r ∧ r ≤ 4) (p : ℕ) : + ScaledBasis (blocks p rs) := by + induction rs generalizing p with + | nil => exact scaledBasis_one + | cons r rs ih => + exact (segment_scaled r p (hrs r (by simp))).mul + (ih (fun a ha => hrs a (by simp [ha])) (p + r)) + +def Q : Mat := !![1, 1; 1, 2] +def Qinv : Mat := !![2, -1; -1, 1] + +lemma Q_mul_Qinv : Q * Qinv = 1 := by + ext i j + fin_cases i <;> fin_cases j <;> + norm_num [Q, Qinv, Matrix.mul_apply, Fin.sum_univ_two] + +lemma Qinv_mul_Q : Qinv * Q = 1 := by + ext i j + fin_cases i <;> fin_cases j <;> + norm_num [Q, Qinv, Matrix.mul_apply, Fin.sum_univ_two] + +lemma Q_isUnit : IsUnit Q := ⟨⟨Q, Qinv, Q_mul_Qinv, Qinv_mul_Q⟩, rfl⟩ + +lemma Q_inverse : Q⁻¹ = Qinv := by + exact Matrix.inv_eq_left_inv Qinv_mul_Q + +lemma Q_basis_ne_zero (i : Fin 4) : (Q * basis i.val * Q⁻¹) 0 0 ≠ 0 := by + rw [Q_inverse] + fin_cases i <;> norm_num [Q, Qinv, basis, Matrix.mul_apply, Fin.sum_univ_two] + +/- Endpoint noncancellation for arbitrary consecutive columns of lengths at most four. -/ +theorem band_nonzero_pairing (rs : List ℕ) + (hrs : ∀ r ∈ rs, 1 ≤ r ∧ r ≤ 4) : + ∃ Q : Mat, IsUnit Q ∧ (Q * blocks 1 rs * Q⁻¹) 0 0 ≠ 0 := by + obtain ⟨c, hc, i, hi⟩ := blocks_scaled rs hrs 1 + refine ⟨Q, Q_isUnit, ?_⟩ + rw [hi, Matrix.mul_smul, Matrix.smul_mul] + exact mul_ne_zero hc (Q_basis_ne_zero i) + +end Saxl.Band + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/BandOrbit.lean b/lean/OAI/RepresentationTheory/Saxl/BandOrbit.lean index ac9f4fa0d7c59956441ecd8d0e953781dd47e867..672705108e083e680f24fc168c4f0d1a3a68ef7c 100644 --- a/lean/OAI/RepresentationTheory/Saxl/BandOrbit.lean +++ b/lean/OAI/RepresentationTheory/Saxl/BandOrbit.lean @@ -1,125 +1,125 @@ -import OAI.RepresentationTheory.Saxl.PositionTensor - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uX uY - -namespace Saxl - -@[simp] lemma sumPerm_mul {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g g' : Equiv.Perm (Fin a)) (h h' : Equiv.Perm (Fin b)) : - sumPerm e (g*g') (h*h') = sumPerm e g h * sumPerm e g' h' := by - apply Equiv.ext - intro i - obtain ⟨j,rfl⟩ := e.symm.surjective i - cases j <;> simp only [sumPerm_left, sumPerm_right, Equiv.Perm.mul_apply] - -@[simp] lemma sumPerm_one {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : - sumPerm e 1 1 = 1 := by - apply Equiv.ext - intro i - obtain ⟨j,rfl⟩ := e.symm.surjective i - cases j <;> simp only [sumPerm_left,sumPerm_right,Equiv.Perm.one_apply] - -lemma sumPerm_inv {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) : - sumPerm e g⁻¹ h⁻¹ = (sumPerm e g h)⁻¹ := by - symm - apply inv_eq_of_mul_eq_one_left - rw [← sumPerm_mul, inv_mul_cancel, inv_mul_cancel, sumPerm_one] - -def bandOrbitMap {n a b k : ℕ} {X : Type uX} {Y : Type uY} - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (c : Fin b → Fin k) (F : X →ₗ[ℂ] Y) : - X →ₗ[ℂ] ((Fin b → Fin k) → Y) where - toFun x w := ∑ g : Equiv.Perm (Fin b), - ((Pi.single (c ∘ (g⁻¹ : Equiv.Perm (Fin b))) (1:ℂ) : WordSpace b k) w) • F (ρ (sumPerm e 1 g⁻¹) x) - map_add' x y := by ext w; simp only [map_add,smul_add,Finset.sum_add_distrib,Pi.add_apply] - map_smul' c x := by - ext w - simp only [map_smul,Pi.smul_apply,Finset.smul_sum] - apply Finset.sum_congr rfl - intro g hg - exact smul_comm _ _ _ - -lemma bandOrbitMap_base {n a b k : ℕ} {X : Type uX} {Y : Type uY} - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (c : Fin b → Fin k) (F : X →ₗ[ℂ] Y) - (hF : ∀ g : Equiv.Perm (Fin b), c ∘ g = c → ∀ x, F (ρ (sumPerm e 1 g) x) = F x) - (x : X) : bandOrbitMap e ρ c F x c = - ((Finset.univ.filter (fun g : Equiv.Perm (Fin b) => c ∘ (g⁻¹ : Equiv.Perm (Fin b)) = c)).card : ℂ) • F x := by - classical - change (∑ g : Equiv.Perm (Fin b), _) = _ - have hh (g : Equiv.Perm (Fin b)) : - ((Pi.single (c ∘ (g⁻¹ : Equiv.Perm (Fin b))) (1:ℂ) : WordSpace b k) c) • F (ρ (sumPerm e 1 g⁻¹) x) = - if c ∘ (g⁻¹ : Equiv.Perm (Fin b)) = c then F x else 0 := by - by_cases h : c ∘ (g⁻¹ : Equiv.Perm (Fin b)) = c - · rw [ite_eq_left h, h, Pi.single_eq_same, one_smul, hF g⁻¹ h] - · rw [ite_eq_right h, Pi.single_eq_of_ne (Ne.symm h), zero_smul] - simp only [hh] - simp [Finset.sum_ite,Nat.cast_smul_eq_nsmul] - -lemma bandOrbitMap_nonzero {n a b k : ℕ} {X : Type uX} {Y : Type uY} - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (c : Fin b → Fin k) (F : X →ₗ[ℂ] Y) (hF0 : F ≠ 0) - (hF : ∀ g : Equiv.Perm (Fin b), c ∘ g = c → ∀ x, F (ρ (sumPerm e 1 g) x) = F x) : - bandOrbitMap e ρ c F ≠ 0 := by - classical - intro hz - apply hF0 - ext x - have hh := bandOrbitMap_base e ρ c F hF x - rw [hz] at hh - change 0 = _ at hh - have hc : ((Finset.univ.filter (fun g : Equiv.Perm (Fin b) => - c ∘ (g⁻¹ : Equiv.Perm (Fin b)) = c)).card : ℂ) ≠ 0 := by - apply Nat.cast_ne_zero.mpr - exact Finset.card_ne_zero.mpr ⟨1,Finset.mem_filter.mpr ⟨Finset.mem_univ _, rfl⟩⟩ - exact (smul_eq_zero.mp hh.symm).resolve_left hc - -lemma bandOrbitMap_equivariant {n a b k : ℕ} {X : Type uX} {Y : Type uY} - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (τ : Representation ℂ (Equiv.Perm (Fin a)) Y) - (c : Fin b → Fin k) (F : X →ₗ[ℂ] Y) - (hF : ∀ h : Equiv.Perm (Fin a), ∀ x, F (ρ (sumPerm e h 1) x) = τ h (F x)) - (h : Equiv.Perm (Fin a)) (q : Equiv.Perm (Fin b)) (x : X) (w : Fin b → Fin k) : - bandOrbitMap e ρ c F (ρ (sumPerm e h q) x) w = - τ h (bandOrbitMap e ρ c F x (w ∘ q)) := by - classical - change (∑ g : Equiv.Perm (Fin b), _) = τ h (∑ g : Equiv.Perm (Fin b), _) - rw [map_sum] - apply (Equiv.sum_comp (Equiv.mulLeft q) _).symm.trans - apply Finset.sum_congr rfl - intro g hg - have he : sumPerm e 1 (q*g)⁻¹ * sumPerm e h q = sumPerm e h 1 * sumPerm e 1 g⁻¹ := by - rw [← sumPerm_mul, ← sumPerm_mul] - simp only [one_mul,mul_one,mul_inv_rev,mul_assoc,inv_mul_cancel,mul_one] - change _ • F (ρ (sumPerm e 1 (q*g)⁻¹) (ρ (sumPerm e h q) x)) = _ - rw [← Module.End.mul_apply, ← map_mul, he, map_mul, Module.End.mul_apply, hF, map_smul] - congr 1 - simp only [Pi.single_apply] - congr 1 - apply propext - constructor - · intro hh - funext i - have hi := congrFun hh (q i) - simpa using hi - · intro hh - funext i - have hi := congrFun hh (q⁻¹ i) - simpa using hi - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.PositionTensor + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uX uY + +namespace Saxl + +@[simp] lemma sumPerm_mul {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g g' : Equiv.Perm (Fin a)) (h h' : Equiv.Perm (Fin b)) : + sumPerm e (g*g') (h*h') = sumPerm e g h * sumPerm e g' h' := by + apply Equiv.ext + intro i + obtain ⟨j,rfl⟩ := e.symm.surjective i + cases j <;> simp only [sumPerm_left, sumPerm_right, Equiv.Perm.mul_apply] + +@[simp] lemma sumPerm_one {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : + sumPerm e 1 1 = 1 := by + apply Equiv.ext + intro i + obtain ⟨j,rfl⟩ := e.symm.surjective i + cases j <;> simp only [sumPerm_left,sumPerm_right,Equiv.Perm.one_apply] + +lemma sumPerm_inv {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) : + sumPerm e g⁻¹ h⁻¹ = (sumPerm e g h)⁻¹ := by + symm + apply inv_eq_of_mul_eq_one_left + rw [← sumPerm_mul, inv_mul_cancel, inv_mul_cancel, sumPerm_one] + +def bandOrbitMap {n a b k : ℕ} {X : Type uX} {Y : Type uY} + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (c : Fin b → Fin k) (F : X →ₗ[ℂ] Y) : + X →ₗ[ℂ] ((Fin b → Fin k) → Y) where + toFun x w := ∑ g : Equiv.Perm (Fin b), + ((Pi.single (c ∘ (g⁻¹ : Equiv.Perm (Fin b))) (1:ℂ) : WordSpace b k) w) • F (ρ (sumPerm e 1 g⁻¹) x) + map_add' x y := by ext w; simp only [map_add,smul_add,Finset.sum_add_distrib,Pi.add_apply] + map_smul' c x := by + ext w + simp only [map_smul,Pi.smul_apply,Finset.smul_sum] + apply Finset.sum_congr rfl + intro g hg + exact smul_comm _ _ _ + +lemma bandOrbitMap_base {n a b k : ℕ} {X : Type uX} {Y : Type uY} + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (c : Fin b → Fin k) (F : X →ₗ[ℂ] Y) + (hF : ∀ g : Equiv.Perm (Fin b), c ∘ g = c → ∀ x, F (ρ (sumPerm e 1 g) x) = F x) + (x : X) : bandOrbitMap e ρ c F x c = + ((Finset.univ.filter (fun g : Equiv.Perm (Fin b) => c ∘ (g⁻¹ : Equiv.Perm (Fin b)) = c)).card : ℂ) • F x := by + classical + change (∑ g : Equiv.Perm (Fin b), _) = _ + have hh (g : Equiv.Perm (Fin b)) : + ((Pi.single (c ∘ (g⁻¹ : Equiv.Perm (Fin b))) (1:ℂ) : WordSpace b k) c) • F (ρ (sumPerm e 1 g⁻¹) x) = + if c ∘ (g⁻¹ : Equiv.Perm (Fin b)) = c then F x else 0 := by + by_cases h : c ∘ (g⁻¹ : Equiv.Perm (Fin b)) = c + · rw [ite_eq_left h, h, Pi.single_eq_same, one_smul, hF g⁻¹ h] + · rw [ite_eq_right h, Pi.single_eq_of_ne (Ne.symm h), zero_smul] + simp only [hh] + simp [Finset.sum_ite,Nat.cast_smul_eq_nsmul] + +lemma bandOrbitMap_nonzero {n a b k : ℕ} {X : Type uX} {Y : Type uY} + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (c : Fin b → Fin k) (F : X →ₗ[ℂ] Y) (hF0 : F ≠ 0) + (hF : ∀ g : Equiv.Perm (Fin b), c ∘ g = c → ∀ x, F (ρ (sumPerm e 1 g) x) = F x) : + bandOrbitMap e ρ c F ≠ 0 := by + classical + intro hz + apply hF0 + ext x + have hh := bandOrbitMap_base e ρ c F hF x + rw [hz] at hh + change 0 = _ at hh + have hc : ((Finset.univ.filter (fun g : Equiv.Perm (Fin b) => + c ∘ (g⁻¹ : Equiv.Perm (Fin b)) = c)).card : ℂ) ≠ 0 := by + apply Nat.cast_ne_zero.mpr + exact Finset.card_ne_zero.mpr ⟨1,Finset.mem_filter.mpr ⟨Finset.mem_univ _, rfl⟩⟩ + exact (smul_eq_zero.mp hh.symm).resolve_left hc + +lemma bandOrbitMap_equivariant {n a b k : ℕ} {X : Type uX} {Y : Type uY} + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + (e : Fin n ≃ Fin a ⊕ Fin b) (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (τ : Representation ℂ (Equiv.Perm (Fin a)) Y) + (c : Fin b → Fin k) (F : X →ₗ[ℂ] Y) + (hF : ∀ h : Equiv.Perm (Fin a), ∀ x, F (ρ (sumPerm e h 1) x) = τ h (F x)) + (h : Equiv.Perm (Fin a)) (q : Equiv.Perm (Fin b)) (x : X) (w : Fin b → Fin k) : + bandOrbitMap e ρ c F (ρ (sumPerm e h q) x) w = + τ h (bandOrbitMap e ρ c F x (w ∘ q)) := by + classical + change (∑ g : Equiv.Perm (Fin b), _) = τ h (∑ g : Equiv.Perm (Fin b), _) + rw [map_sum] + apply (Equiv.sum_comp (Equiv.mulLeft q) _).symm.trans + apply Finset.sum_congr rfl + intro g hg + have he : sumPerm e 1 (q*g)⁻¹ * sumPerm e h q = sumPerm e h 1 * sumPerm e 1 g⁻¹ := by + rw [← sumPerm_mul, ← sumPerm_mul] + simp only [one_mul,mul_one,mul_inv_rev,mul_assoc,inv_mul_cancel,mul_one] + change _ • F (ρ (sumPerm e 1 (q*g)⁻¹) (ρ (sumPerm e h q) x)) = _ + rw [← Module.End.mul_apply, ← map_mul, he, map_mul, Module.End.mul_apply, hF, map_smul] + congr 1 + simp only [Pi.single_apply] + congr 1 + apply propext + constructor + · intro hh + funext i + have hi := congrFun hh (q i) + simpa using hi + · intro hh + funext i + have hi := congrFun hh (q⁻¹ i) + simpa using hi + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/BandPairing.lean b/lean/OAI/RepresentationTheory/Saxl/BandPairing.lean index 321d9013022c4162973c918fc2443fcedf9af59d..ba6db427b20c33e816dc86b59421c8f99acfa97f 100644 --- a/lean/OAI/RepresentationTheory/Saxl/BandPairing.lean +++ b/lean/OAI/RepresentationTheory/Saxl/BandPairing.lean @@ -1,172 +1,172 @@ -import OAI.RepresentationTheory.Saxl.ColumnContraction - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl.Band - -def conjugation : Mat →ₗ[ℂ] Mat where - toFun X := Q * X * Qinv - map_add' X Y := by simp [Matrix.mul_add, Matrix.add_mul] - map_smul' c X := by simp - -lemma conjugation_one : conjugation 1 = 1 := by - change Q * 1 * Qinv = 1 - rw [mul_one, Q_mul_Qinv] - -lemma conjugation_mul (X Y : Mat) : conjugation (X * Y) = conjugation X * conjugation Y := by - change Q * (X * Y) * Qinv = (Q * X * Qinv) * (Q * Y * Qinv) - simp only [mul_assoc, ← mul_assoc Qinv Q, Qinv_mul_Q, one_mul] - -lemma conjugation_D (q : ℕ) (X : Mat) : D q (conjugation X) = conjugation (D q X) := by - by_cases h : q % 2 = 0 - · ext i j - fin_cases i <;> fin_cases j <;> - simp [D, h, conjugation, Q, Qinv, Matrix.adjugate_fin_two, Matrix.mul_apply, - Matrix.vecMul, dotProduct, Fin.sum_univ_two] <;> ring - · simp [D, h] - -lemma conjugation_prod (l : List Mat) : (l.map conjugation).prod = conjugation l.prod := by - induction l with - | nil => simp [conjugation_one] - | cons a l ih => simp [ih, conjugation_mul] - -lemma segments_conjugation (rs : List ℕ) (p : ℕ) : - Columns.segments p rs (fun i => conjugation (basis i)) = conjugation (blocks p rs) := by - induction rs generalizing p with - | nil => exact conjugation_one.symm - | cons r rs ih => - simp only [Columns.segments, blocks, ih, conjugation_mul] - congr 1 - unfold segment - rw [map_sum] - apply Finset.sum_congr rfl - intro π hπ - rw [map_smul] - congr 1 - simp_rw [conjugation_D] - have he := conjugation_prod (List.ofFn fun j : Fin r => D (p + j.val) (basis (π j).val)) - rw [List.map_ofFn] at he - exact he - -lemma conjugation_blocks_ne_zero (rs : List ℕ) - (hrs : ∀ r ∈ rs, 1 ≤ r ∧ r ≤ 4) : conjugation (blocks 1 rs) 0 0 ≠ 0 := by - obtain ⟨c, hc, i, hi⟩ := blocks_scaled rs hrs 1 - rw [hi, map_smul] - apply mul_ne_zero hc - simpa only [conjugation, LinearMap.coe_mk, AddHom.coe_mk, Q_inverse] using Q_basis_ne_zero i - -end Saxl.Band -namespace Saxl.Path - -def chainFunctional (n p : ℕ) : WordSpace n 4 →ₗ[ℂ] Mat where - toFun x := ∑ w : Fin n → Fin 4, x w • chainML n p (fun i => entry (w i)) - map_add' x y := by simp [add_smul, Finset.sum_add_distrib] - map_smul' c x := by simp [smul_smul, Finset.smul_sum] - -lemma chainFunctional_pure (n p : ℕ) (X : Fin n → Mat) : - chainFunctional n p (pureWord X) = chainML n p X := (chain_expand n p X).symm - -lemma chainFunctional_column (μ : YoungDiagram) (p : ℕ) (N : ℕ → Mat) : - chainFunctional μ.transpose.rowLens.sum p - (wordMap (fun (i : Fin (μ.colLen 0)) (a : Fin 4) => - N i.val (parts a).1 (parts a).2) (polytabloid (Columns.columnTableau μ))) = - Columns.segments p μ.transpose.rowLens N := by - rw [Columns.mapped_columnTableau, map_sum] - simp_rw [map_smul, chainFunctional_pure] - exact Columns.sum_chain μ.transpose.rowLens p N - -lemma chainFunctional_endpoint (r : ℕ) (x : WordSpace (2*r+1) 4) : - chainFunctional (2*r+1) 1 x 0 0 = (-1 : ℂ)^r * dotProduct x (bandWord r) := by - change (∑ w : Fin (2*r+1) → Fin 4, - x w • chainML (2*r+1) 1 (fun i => entry (w i))) 0 0 = _ - simp only [Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, chain_entries_endpoint] - simp [dotProduct, Finset.mul_sum, mul_left_comm] - - -lemma fourRow_column_lengths (μ : YoungDiagram) (hμ : μ.colLen 0 ≤ 4) : - ∀ r ∈ μ.transpose.rowLens, 1 ≤ r ∧ r ≤ 4 := by - intro r hr - refine ⟨μ.transpose.pos_of_mem_rowLens r hr, ?_⟩ - obtain ⟨j, hj, he⟩ := List.mem_iff_getElem.mp hr - rw [← he, YoungDiagram.get_rowLens, YoungDiagram.rowLen_transpose] - exact (μ.colLen_anti 0 j (Nat.zero_le _)).trans hμ - -lemma fourRow_tableau_noncancellation (n : ℕ) (μ : YoungDiagram) - (hn : μ.transpose.rowLens.sum = n) (hμ : μ.colLen 0 ≤ 4) : - ∃ s : Tableau n μ, chainFunctional n 1 - (wordMap (fun (i : Fin (μ.colLen 0)) (a : Fin 4) => - Band.conjugation (Band.basis i.val) (parts a).1 (parts a).2) (polytabloid s)) 0 0 ≠ 0 := by - subst n - refine ⟨Columns.columnTableau μ, ?_⟩ - rw [chainFunctional_column μ 1 (fun i => Band.conjugation (Band.basis i)), - Band.segments_conjugation] - exact Band.conjugation_blocks_ne_zero _ (fourRow_column_lengths μ hμ) - -/- The actual complex Specht modules with at most four rows occur in the -specified two-layer alternating path cyclic module. -/ -theorem fourRow_support (r : ℕ) (_hr : 2 ≤ r) (μ : YoungDiagram) - (t : Tableau (2*r+1) μ) (hμ : μ.colLen 0 ≤ 4) : - ∃ f : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep (2*r+1) 4) (bandWord r)).toRepresentation, f ≠ 0 := by - have hn : μ.transpose.rowLens.sum = 2*r+1 := by - simpa only [Fintype.card_fin] using - Fintype.card_congr ((Columns.columnTableau μ).trans t.symm) - obtain ⟨s, hs⟩ := fourRow_tableau_noncancellation (2*r+1) μ hn hμ - let L : Fin (μ.colLen 0) → Fin 4 → ℂ := fun i a => - Band.conjugation (Band.basis i.val) (parts a).1 (parts a).2 - apply hom_to_cyclic_of_pair L (spechtSub t) - ⟨polytabloid s, polytabloid_mem_all t s⟩ (bandWord r) (bandWord_real r) - intro h - rw [chainFunctional_endpoint] at hs - exact hs (by change (-1 : ℂ)^r * dotProduct (wordMap L (polytabloid s)) (bandWord r) = 0 - rw [h, mul_zero]) - -end Saxl.Path - -namespace Saxl.PathLayer - -lemma J_flip (a b : Fin 2) : J a b = - J b a := by - fin_cases a <;> fin_cases b <;> norm_num [J] - -lemma rowAlt_rev_formula (r : ℕ) (w : Fin (2*r+1) → Fin 2) : - rowAlt r (w ∘ Fin.rev) = (if w (Fin.last (2*r)) = 0 then 1 else 0) * - ((-1 : ℂ)^r * ∏ i : Fin r, J (w ⟨2*i.val,by omega⟩) (w ⟨2*i.val+1,by omega⟩)) := by - rw [rowAlt_formula] - have hzero : (0 : Fin (2*r+1)).rev = Fin.last (2*r) := by apply Fin.ext; simp - simp only [Function.comp_apply, hzero] - congr 1 - calc - (∏ i : Fin r, J (w (⟨2*i.val+1,by omega⟩ : Fin (2*r+1)).rev) - (w (⟨2*i.val+2,by omega⟩ : Fin (2*r+1)).rev)) = - ∏ i : Fin r, (-1 : ℂ) * J (w ⟨2*i.val,by omega⟩) (w ⟨2*i.val+1,by omega⟩) := by - apply Fintype.prod_equiv Fin.revPerm - intro i - have h₁ : (⟨2*i.val+1,by omega⟩ : Fin (2*r+1)).rev = ⟨2*i.rev.val+1,by omega⟩ := by - apply Fin.ext; simp only [Fin.val_rev]; have := i.isLt; omega - have h₂ : (⟨2*i.val+2,by omega⟩ : Fin (2*r+1)).rev = ⟨2*i.rev.val,by omega⟩ := by - apply Fin.ext; simp only [Fin.val_rev]; have := i.isLt; omega - rw [h₁,h₂,J_flip] - simp - _ = _ := by rw [Finset.prod_mul_distrib]; simp - -theorem paired_rowAlt (r : ℕ) (w : Fin (2*r+1) → Saxl.Path.Letter) : - rowAlt r (fun i => (Saxl.Path.parts (w i)).1) * - rowAlt r ((fun i => (Saxl.Path.parts (w i)).2) ∘ Fin.rev) = - (-1 : ℂ)^r * Saxl.Path.bandWord r w := by - rw [rowAlt_formula,rowAlt_rev_formula] - unfold Saxl.Path.bandWord - rw [Finset.prod_mul_distrib] - change _ = (-1:ℂ)^r * (_ * _ * - ((∏ i : Fin r, J (Saxl.Path.parts (w ⟨2*i.val,by omega⟩)).2 (Saxl.Path.parts (w ⟨2*i.val+1,by omega⟩)).2) * - (∏ i : Fin r, J (Saxl.Path.parts (w ⟨2*i.val+1,by omega⟩)).1 (Saxl.Path.parts (w ⟨2*i.val+2,by omega⟩)).1))) - ring - -end Saxl.PathLayer - -end - -end OAI +import OAI.RepresentationTheory.Saxl.ColumnContraction + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl.Band + +def conjugation : Mat →ₗ[ℂ] Mat where + toFun X := Q * X * Qinv + map_add' X Y := by simp [Matrix.mul_add, Matrix.add_mul] + map_smul' c X := by simp + +lemma conjugation_one : conjugation 1 = 1 := by + change Q * 1 * Qinv = 1 + rw [mul_one, Q_mul_Qinv] + +lemma conjugation_mul (X Y : Mat) : conjugation (X * Y) = conjugation X * conjugation Y := by + change Q * (X * Y) * Qinv = (Q * X * Qinv) * (Q * Y * Qinv) + simp only [mul_assoc, ← mul_assoc Qinv Q, Qinv_mul_Q, one_mul] + +lemma conjugation_D (q : ℕ) (X : Mat) : D q (conjugation X) = conjugation (D q X) := by + by_cases h : q % 2 = 0 + · ext i j + fin_cases i <;> fin_cases j <;> + simp [D, h, conjugation, Q, Qinv, Matrix.adjugate_fin_two, Matrix.mul_apply, + Matrix.vecMul, dotProduct, Fin.sum_univ_two] <;> ring + · simp [D, h] + +lemma conjugation_prod (l : List Mat) : (l.map conjugation).prod = conjugation l.prod := by + induction l with + | nil => simp [conjugation_one] + | cons a l ih => simp [ih, conjugation_mul] + +lemma segments_conjugation (rs : List ℕ) (p : ℕ) : + Columns.segments p rs (fun i => conjugation (basis i)) = conjugation (blocks p rs) := by + induction rs generalizing p with + | nil => exact conjugation_one.symm + | cons r rs ih => + simp only [Columns.segments, blocks, ih, conjugation_mul] + congr 1 + unfold segment + rw [map_sum] + apply Finset.sum_congr rfl + intro π hπ + rw [map_smul] + congr 1 + simp_rw [conjugation_D] + have he := conjugation_prod (List.ofFn fun j : Fin r => D (p + j.val) (basis (π j).val)) + rw [List.map_ofFn] at he + exact he + +lemma conjugation_blocks_ne_zero (rs : List ℕ) + (hrs : ∀ r ∈ rs, 1 ≤ r ∧ r ≤ 4) : conjugation (blocks 1 rs) 0 0 ≠ 0 := by + obtain ⟨c, hc, i, hi⟩ := blocks_scaled rs hrs 1 + rw [hi, map_smul] + apply mul_ne_zero hc + simpa only [conjugation, LinearMap.coe_mk, AddHom.coe_mk, Q_inverse] using Q_basis_ne_zero i + +end Saxl.Band +namespace Saxl.Path + +def chainFunctional (n p : ℕ) : WordSpace n 4 →ₗ[ℂ] Mat where + toFun x := ∑ w : Fin n → Fin 4, x w • chainML n p (fun i => entry (w i)) + map_add' x y := by simp [add_smul, Finset.sum_add_distrib] + map_smul' c x := by simp [smul_smul, Finset.smul_sum] + +lemma chainFunctional_pure (n p : ℕ) (X : Fin n → Mat) : + chainFunctional n p (pureWord X) = chainML n p X := (chain_expand n p X).symm + +lemma chainFunctional_column (μ : YoungDiagram) (p : ℕ) (N : ℕ → Mat) : + chainFunctional μ.transpose.rowLens.sum p + (wordMap (fun (i : Fin (μ.colLen 0)) (a : Fin 4) => + N i.val (parts a).1 (parts a).2) (polytabloid (Columns.columnTableau μ))) = + Columns.segments p μ.transpose.rowLens N := by + rw [Columns.mapped_columnTableau, map_sum] + simp_rw [map_smul, chainFunctional_pure] + exact Columns.sum_chain μ.transpose.rowLens p N + +lemma chainFunctional_endpoint (r : ℕ) (x : WordSpace (2*r+1) 4) : + chainFunctional (2*r+1) 1 x 0 0 = (-1 : ℂ)^r * dotProduct x (bandWord r) := by + change (∑ w : Fin (2*r+1) → Fin 4, + x w • chainML (2*r+1) 1 (fun i => entry (w i))) 0 0 = _ + simp only [Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, chain_entries_endpoint] + simp [dotProduct, Finset.mul_sum, mul_left_comm] + + +lemma fourRow_column_lengths (μ : YoungDiagram) (hμ : μ.colLen 0 ≤ 4) : + ∀ r ∈ μ.transpose.rowLens, 1 ≤ r ∧ r ≤ 4 := by + intro r hr + refine ⟨μ.transpose.pos_of_mem_rowLens r hr, ?_⟩ + obtain ⟨j, hj, he⟩ := List.mem_iff_getElem.mp hr + rw [← he, YoungDiagram.get_rowLens, YoungDiagram.rowLen_transpose] + exact (μ.colLen_anti 0 j (Nat.zero_le _)).trans hμ + +lemma fourRow_tableau_noncancellation (n : ℕ) (μ : YoungDiagram) + (hn : μ.transpose.rowLens.sum = n) (hμ : μ.colLen 0 ≤ 4) : + ∃ s : Tableau n μ, chainFunctional n 1 + (wordMap (fun (i : Fin (μ.colLen 0)) (a : Fin 4) => + Band.conjugation (Band.basis i.val) (parts a).1 (parts a).2) (polytabloid s)) 0 0 ≠ 0 := by + subst n + refine ⟨Columns.columnTableau μ, ?_⟩ + rw [chainFunctional_column μ 1 (fun i => Band.conjugation (Band.basis i)), + Band.segments_conjugation] + exact Band.conjugation_blocks_ne_zero _ (fourRow_column_lengths μ hμ) + +/- The actual complex Specht modules with at most four rows occur in the +specified two-layer alternating path cyclic module. -/ +theorem fourRow_support (r : ℕ) (_hr : 2 ≤ r) (μ : YoungDiagram) + (t : Tableau (2*r+1) μ) (hμ : μ.colLen 0 ≤ 4) : + ∃ f : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep (2*r+1) 4) (bandWord r)).toRepresentation, f ≠ 0 := by + have hn : μ.transpose.rowLens.sum = 2*r+1 := by + simpa only [Fintype.card_fin] using + Fintype.card_congr ((Columns.columnTableau μ).trans t.symm) + obtain ⟨s, hs⟩ := fourRow_tableau_noncancellation (2*r+1) μ hn hμ + let L : Fin (μ.colLen 0) → Fin 4 → ℂ := fun i a => + Band.conjugation (Band.basis i.val) (parts a).1 (parts a).2 + apply hom_to_cyclic_of_pair L (spechtSub t) + ⟨polytabloid s, polytabloid_mem_all t s⟩ (bandWord r) (bandWord_real r) + intro h + rw [chainFunctional_endpoint] at hs + exact hs (by change (-1 : ℂ)^r * dotProduct (wordMap L (polytabloid s)) (bandWord r) = 0 + rw [h, mul_zero]) + +end Saxl.Path + +namespace Saxl.PathLayer + +lemma J_flip (a b : Fin 2) : J a b = - J b a := by + fin_cases a <;> fin_cases b <;> norm_num [J] + +lemma rowAlt_rev_formula (r : ℕ) (w : Fin (2*r+1) → Fin 2) : + rowAlt r (w ∘ Fin.rev) = (if w (Fin.last (2*r)) = 0 then 1 else 0) * + ((-1 : ℂ)^r * ∏ i : Fin r, J (w ⟨2*i.val,by omega⟩) (w ⟨2*i.val+1,by omega⟩)) := by + rw [rowAlt_formula] + have hzero : (0 : Fin (2*r+1)).rev = Fin.last (2*r) := by apply Fin.ext; simp + simp only [Function.comp_apply, hzero] + congr 1 + calc + (∏ i : Fin r, J (w (⟨2*i.val+1,by omega⟩ : Fin (2*r+1)).rev) + (w (⟨2*i.val+2,by omega⟩ : Fin (2*r+1)).rev)) = + ∏ i : Fin r, (-1 : ℂ) * J (w ⟨2*i.val,by omega⟩) (w ⟨2*i.val+1,by omega⟩) := by + apply Fintype.prod_equiv Fin.revPerm + intro i + have h₁ : (⟨2*i.val+1,by omega⟩ : Fin (2*r+1)).rev = ⟨2*i.rev.val+1,by omega⟩ := by + apply Fin.ext; simp only [Fin.val_rev]; have := i.isLt; omega + have h₂ : (⟨2*i.val+2,by omega⟩ : Fin (2*r+1)).rev = ⟨2*i.rev.val,by omega⟩ := by + apply Fin.ext; simp only [Fin.val_rev]; have := i.isLt; omega + rw [h₁,h₂,J_flip] + simp + _ = _ := by rw [Finset.prod_mul_distrib]; simp + +theorem paired_rowAlt (r : ℕ) (w : Fin (2*r+1) → Saxl.Path.Letter) : + rowAlt r (fun i => (Saxl.Path.parts (w i)).1) * + rowAlt r ((fun i => (Saxl.Path.parts (w i)).2) ∘ Fin.rev) = + (-1 : ℂ)^r * Saxl.Path.bandWord r w := by + rw [rowAlt_formula,rowAlt_rev_formula] + unfold Saxl.Path.bandWord + rw [Finset.prod_mul_distrib] + change _ = (-1:ℂ)^r * (_ * _ * + ((∏ i : Fin r, J (Saxl.Path.parts (w ⟨2*i.val,by omega⟩)).2 (Saxl.Path.parts (w ⟨2*i.val+1,by omega⟩)).2) * + (∏ i : Fin r, J (Saxl.Path.parts (w ⟨2*i.val+1,by omega⟩)).1 (Saxl.Path.parts (w ⟨2*i.val+2,by omega⟩)).1))) + ring + +end Saxl.PathLayer + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/BandSupport.lean b/lean/OAI/RepresentationTheory/Saxl/BandSupport.lean index 30c04e312dd1ddcfe293c8d702e88df351c08170..044a239c9ad4c8fcac5df1df42ea46a3c87e7eef 100644 --- a/lean/OAI/RepresentationTheory/Saxl/BandSupport.lean +++ b/lean/OAI/RepresentationTheory/Saxl/BandSupport.lean @@ -1,336 +1,336 @@ -import OAI.RepresentationTheory.Saxl.CyclicSector - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl - -def stairBandWord (h s : ℕ) : WordSpace (bandSize h s) - ((staircase (h+s)).colLen 0 * (staircase (h+s)).colLen 0) := - wordTensor _ _ _ (bandRowWord h s ⊗ₜ[ℂ] bandColumnWord h s) - -def lowPairLetter (h : ℕ) (x : Fin 4) : - Fin ((staircase (h+2)).colLen 0 * (staircase (h+2)).colLen 0) := - finProdFinEquiv (lowLetter h (Path.parts x).1, lowLetter h (Path.parts x).2) - -lemma bandColumn_path_eval' (h : ℕ) (w : Fin (2*(h+1)+1) → Fin 2) : - bandColumnWord h 2 ((lowLetter h ∘ w) ∘ (bandPathEquiv h).symm) = - PathLayer.rowAlt (h+1) (w ∘ Fin.rev) := by - have he : (lowLetter h ∘ (w ∘ Fin.rev)) ∘ (bandColumnPathEquiv h).symm = - (lowLetter h ∘ w) ∘ (bandPathEquiv h).symm := by - funext i - simp [bandColumnPathEquiv, Function.comp_def, Fin.revPerm] - rw [← he, bandColumn_path_eval] - -lemma stairBandWord_path_eval (h : ℕ) (w : Fin (2*(h+1)+1) → Fin 4) : - restrictLetters (lowPairLetter h) (stairBandWord h 2) (w ∘ (bandPathEquiv h).symm) = - (-1 : ℂ)^(h+1) * Path.bandWord (h+1) w := by - change wordTensor _ _ _ (bandRowWord h 2 ⊗ₜ[ℂ] bandColumnWord h 2) - (lowPairLetter h ∘ (w ∘ (bandPathEquiv h).symm)) = _ - rw [wordTensor_tmul] - have hl : splitLeft (lowPairLetter h ∘ (w ∘ (bandPathEquiv h).symm)) = - (lowLetter h ∘ (fun i => (Path.parts (w i)).1)) ∘ (bandPathEquiv h).symm := by - funext i; simp [splitLeft, lowPairLetter] - have hr : splitRight (lowPairLetter h ∘ (w ∘ (bandPathEquiv h).symm)) = - (lowLetter h ∘ (fun i => (Path.parts (w i)).2)) ∘ (bandPathEquiv h).symm := by - funext i; simp [splitRight, lowPairLetter] - rw [hl,hr,bandRow_path_eval,bandColumn_path_eval'] - exact PathLayer.paired_rowAlt _ w - -/- Every Specht shape with at most four rows occurs in the cyclic module -generated by the prescribed two-band vector. -/ -theorem twoBand_support (h : ℕ) (hh : 1 ≤ h) (μ : YoungDiagram) - (t : Tableau (bandSize h 2) μ) (hμ : μ.colLen 0 ≤ 4) : - ∃ f : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep _ _) (stairBandWord h 2)).toRepresentation, f ≠ 0 := by - have he : restrictLetters (lowPairLetter h) (stairBandWord h 2) = - (-1 : ℂ)^(h+1) • (fun w => Path.bandWord (h+1) (w ∘ bandPathEquiv h)) := by - funext w - have hw : (w ∘ bandPathEquiv h) ∘ (bandPathEquiv h).symm = w := by funext i; simp - simpa only [hw,Pi.smul_apply,smul_eq_mul] using stairBandWord_path_eval h (w ∘ bandPathEquiv h) - have hs := support_relabel (bandPathEquiv h) (Path.bandWord (h+1)) - (fun ν s hν => Path.fourRow_support (h+1) (by omega) ν s hν) μ t hμ - have hc : cyclic (wordRep (bandSize h 2) 4) (restrictLetters (lowPairLetter h) (stairBandWord h 2)) = - cyclic (wordRep (bandSize h 2) 4) (fun w => Path.bandWord (h+1) (w ∘ bandPathEquiv h)) := by - rw [he,cyclic_smul_eq _ _ _ (pow_ne_zero _ (by norm_num))] - rw [← hc] at hs - obtain ⟨f,hf⟩ := hs - exact cyclic_projection_support (restrictLetters (lowPairLetter h)) (stairBandWord h 2) f hf - -end Saxl - -namespace Saxl - -/- Coordinate subrepresentation using only letters with property A. -/ -def alphabetSub (n d : ℕ) (A : Fin d → Prop) : Subrepresentation (wordRep n d) where - toSubmodule := - { carrier := {x | ∀ w, (∃ i, ¬ A (w i)) → x w = 0} - zero_mem' := by intro w hw; rfl - add_mem' := by intro x y hx hy w hw; change x w+y w=0; rw [hx w hw,hy w hw,add_zero] - smul_mem' := by intro c x hx w hw; change c*x w=0; rw [hx w hw,mul_zero] } - apply_mem_toSubmodule g := by - intro x hx w hw - obtain ⟨i,hi⟩ := hw - apply hx (w ∘ g) - exact ⟨g⁻¹ i, by simpa using hi⟩ - -lemma alphabetSub_iff {n d : ℕ} (A : Fin d → Prop) (x : WordSpace n d) : - x ∈ alphabetSub n d A ↔ ∀ w, x w ≠ 0 → ∀ i, A (w i) := by - change (∀ w, (∃ i, ¬ A (w i)) → x w = 0) ↔ _ - constructor - · intro h w hw i - by_contra hn - exact hw (h w ⟨i,hn⟩) - · intro h w hw - by_contra hn - obtain ⟨i,hi⟩ := hw - exact hi (h w hn i) - -lemma cyclic_alphabet {n d : ℕ} (A : Fin d → Prop) (v : WordSpace n d) - (hv : v ∈ alphabetSub n d A) (x : WordSpace n d) (hx : x ∈ cyclic (wordRep n d) v) : - x ∈ alphabetSub n d A := (cyclic_le _ _ _).mpr hv hx - -lemma single_mem_alphabet {n d : ℕ} (A : Fin d → Prop) (a : Fin n → Fin d) (ha : ∀ i, A (a i)) : - (Pi.single a (1:ℂ) : WordSpace n d) ∈ alphabetSub n d A := by - classical - intro w hw - apply Pi.single_eq_of_ne - intro he - subst w - obtain ⟨i,hi⟩ := hw - exact hi (ha i) - -lemma altWord_mem_alphabet {n d : ℕ} (A : Fin d → Prop) - (G : Subgroup (Equiv.Perm (Fin n))) (a : Fin n → Fin d) (ha : ∀ i, A (a i)) : - altWord G a ∈ alphabetSub n d A := by - classical - unfold altWord - apply Submodule.sum_mem - intro g hg - apply Submodule.smul_mem - exact (alphabetSub n d A).apply_mem_toSubmodule g.val (single_mem_alphabet A a ha) - -lemma letterLift_mem_alphabet {n d D : ℕ} (A : Fin D → Prop) - (φ : Fin d → Fin D) (hφ : ∀ i, A (φ i)) (x : WordSpace n d) : - letterLift φ x ∈ alphabetSub n D A := by - classical - intro w hw - obtain ⟨i,hi⟩ := hw - change (∑ a, x a * ∏ j, (if φ (a j) = w j then (1:ℂ) else 0)) = 0 - apply Finset.sum_eq_zero - intro a ha - apply mul_eq_zero_of_right - apply Finset.prod_eq_zero (Finset.mem_univ i) - exact ite_eq_right (fun hh : φ (a i) = w i => hi (hh ▸ hφ (a i))) - -lemma letterLift_eval {n d D : ℕ} (φ : Fin d → Fin D) (hφ : Function.Injective φ) - (x : WordSpace n d) (w : Fin n → Fin d) : letterLift φ x (φ ∘ w) = x w := by - classical - change (∑ a, x a * ∏ i, (if φ (a i) = φ (w i) then (1:ℂ) else 0)) = x w - rw [Finset.sum_eq_single w] - · simp - · intro a ha haw - apply mul_eq_zero_of_right - obtain ⟨i,hi⟩ : ∃ i, a i ≠ w i := by by_contra hh; push Not at hh; exact haw (funext hh) - apply Finset.prod_eq_zero (Finset.mem_univ i) - exact ite_eq_right (fun hh => hi (hφ hh)) - · simp - -lemma letterLift_injective {n d D : ℕ} (φ : Fin d → Fin D) (hφ : Function.Injective φ) : - Function.Injective (letterLift (n := n) φ) := by - intro x y hxy - funext w - have hh := congrFun hxy (φ ∘ w) - simpa only [letterLift_eval φ hφ] using hh - -def pairLift {n d D : ℕ} (φ : Fin d → Fin D) : - Representation.IntertwiningMap (wordRep n (d*d)) (wordRep n (D*D)) := - (wordTensorIntertwiner _ _ _).comp (((letterLift φ).tensor (letterLift φ)).comp - ((wordTensorIntertwiner n d d).ofBijective (wordTensor n d d).bijective).symm.toIntertwiningMap) - -lemma pairLift_wordTensor {n d D : ℕ} (φ : Fin d → Fin D) (x y : WordSpace n d) : - pairLift φ (wordTensor n d d (x ⊗ₜ[ℂ] y)) = - wordTensor n D D (letterLift φ x ⊗ₜ[ℂ] letterLift φ y) := by - let E := (wordTensorIntertwiner n d d).ofBijective (wordTensor n d d).bijective - change wordTensor n D D (((letterLift φ).tensor (letterLift φ)) (E.symm (E (x ⊗ₜ[ℂ] y)))) = _ - rw [E.symm_apply_apply] - rfl - -lemma pairLift_injective {n d D : ℕ} (φ : Fin d → Fin D) (hφ : Function.Injective φ) : - Function.Injective (pairLift (n := n) φ) := by - apply (wordTensor n D D).injective.comp - apply (TensorProduct.map_injective_of_flat_flat _ _ (letterLift_injective φ hφ) (letterLift_injective φ hφ)).comp - exact ((wordTensorIntertwiner n d d).ofBijective (wordTensor n d d).bijective).symm.injective - -lemma pairWord_mem_alphabetLeft {n d : ℕ} (A : Fin d → Prop) - (x y : WordSpace n d) (hx : x ∈ alphabetSub n d A) : - wordTensor n d d (x ⊗ₜ[ℂ] y) ∈ - alphabetSub n (d*d) (fun a => A (finProdFinEquiv.symm a).1) := by - apply (alphabetSub_iff _ _).mpr - intro w hw i - rw [wordTensor_tmul] at hw - exact (alphabetSub_iff A x).mp hx (splitLeft w) ((mul_ne_zero_iff.mp hw).1) i - - - -def shiftedStairWord (h s : ℕ) := pairLift (highLetter h s) (staircaseWord h) - -lemma highLetter_injective (h s : ℕ) : Function.Injective (highLetter h s) := by - intro a b hab - apply Fin.ext - have := congrArg Fin.val hab - dsimp [highLetter] at this - omega - -lemma shiftedStairWord_support (h s : ℕ) (μ : YoungDiagram) (t : Tableau (staircase h).card μ) - (f : Representation.IntertwiningMap (spechtRep t) (staircaseCyclic h).toRepresentation) - (hf : f ≠ 0) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep _ _) (shiftedStairWord h s)).toRepresentation, F ≠ 0 := by - let F := (cyclicMap (pairLift (highLetter h s)) (staircaseWord h)).comp f - refine ⟨F, ?_⟩ - intro hz - apply hf - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - apply Subtype.ext - apply pairLift_injective (highLetter h s) (highLetter_injective h s) - have hh := congrArg (fun l => (l x).val) hz - exact hh.trans (map_zero _).symm - -lemma shiftedStairWord_alphabet (h s : ℕ) : - shiftedStairWord h s ∈ alphabetSub _ _ (fun a => s ≤ ((finProdFinEquiv.symm a).1).val) := by - unfold shiftedStairWord staircaseWord - rw [pairLift_wordTensor] - apply pairWord_mem_alphabetLeft (fun a => s ≤ a.val) - apply letterLift_mem_alphabet - intro i - dsimp [highLetter] - omega - -lemma bandRowWord_alphabet (h s : ℕ) : - bandRowWord h s ∈ alphabetSub _ _ (fun a => ¬s ≤ a.val) := by - apply altWord_mem_alphabet - intro j - have hb := (bandTableau_bounds h s j).1 - have hr := rotateRow_high h s (bandTableau h s j) - have hh : ¬ s ≤ (rotateRow h s (bandTableau h s j)).val.2 := - fun hh => (Nat.not_lt.mpr hb) (hr.mp hh) - simpa [rightWord,rowWord,stairRowTableau,rotateRowPositions,bandTableau,staircaseSwap] using hh - -lemma stairBandWord_alphabet (h s : ℕ) : - stairBandWord h s ∈ alphabetSub _ _ (fun a => ¬ s ≤ ((finProdFinEquiv.symm a).1).val) := by - apply pairWord_mem_alphabetLeft (fun a => ¬s ≤ a.val) - exact bandRowWord_alphabet h s - -/- The actual same-high image factors as the smaller Specht tensor cyclic -vector and the exact retained band vector on independent position blocks. -/ -theorem staircase_cut_factor (h s : ℕ) : - sameHighProjection _ _ _ s (staircaseWord (h+s)) = - positionProduct (cutPositions h s) (shiftedStairWord h s) (stairBandWord h s) := by - rw [staircase_cut_layers,cutRowWord_factor,cutColumnWord_factor] - unfold shiftedStairWord staircaseWord - rw [pairLift_wordTensor] - ext w - simp only [wordTensor_tmul, stairBandWord, positionProduct] - exact mul_mul_mul_comm _ _ _ _ - - - -lemma bandColumnWord_alphabet (h s : ℕ) : - bandColumnWord h s ∈ alphabetSub _ _ (fun a => ¬s ≤ a.val) := by - apply altWord_mem_alphabet - intro j - have hb := (bandTableau_bounds h s j).1 - have hr := rotateColumn_high h s (bandTableau h s j) - have hh : ¬ s ≤ (rotateColumn h s (bandTableau h s j)).val.1 := - fun hh => (Nat.not_lt.mpr hb) (hr.mp hh) - simpa [rightWord,rowWord,rotateColumnPositions,bandTableau] using hh - -lemma alphabet_small_invariant {n d : ℕ} (A : Fin d → Prop) - (hA : ∀ a b, A a → A b → a = b) (x : WordSpace n d) - (hx : x ∈ alphabetSub n d A) (g : Equiv.Perm (Fin n)) : wordRep n d g x = x := by - ext w - change x (w ∘ g) = x w - have he : (∀ i, A (w i)) → w ∘ g = w := by - intro h - funext i - exact hA _ _ (h (g i)) (h i) - by_cases h : ∀ i, A (w i) - · rw [he h] - · have hz : x w = 0 := by - by_contra hn - exact h ((alphabetSub_iff A x).mp hx w hn) - rw [hz] - by_contra hn - have hh := (alphabetSub_iff A x).mp hx (w ∘ g) hn - apply h - intro i - simpa using hh (g⁻¹ i) - -lemma oneBand_invariant (h : ℕ) (g : Equiv.Perm (Fin (bandSize h 1))) : - wordRep _ _ g (stairBandWord h 1) = stairBandWord h 1 := by - have ha (a b : Fin ((staircase (h+1)).colLen 0)) (ha : ¬1 ≤ a.val) (hb : ¬1 ≤ b.val) : a = b := by - apply Fin.ext; omega - have hr := alphabet_small_invariant (fun a => ¬1 ≤ a.val) ha _ (bandRowWord_alphabet h 1) g - have hc := alphabet_small_invariant (fun a => ¬1 ≤ a.val) ha _ (bandColumnWord_alphabet h 1) g - ext w - change stairBandWord h 1 (w ∘ g) = stairBandWord h 1 w - simp only [stairBandWord,wordTensor_tmul] - exact congrArg₂ (fun x y : ℂ => x*y) (congrFun hr (splitLeft w)) (congrFun hc (splitRight w)) - -lemma stairBandWord_ne_zero (h s : ℕ) : stairBandWord h s ≠ 0 := by - intro hz - apply staircase_projected_ne_zero h s - rw [staircase_cut_factor,hz] - ext w - change _ * 0 = 0 - exact mul_zero _ - -lemma oneRow_support_invariant {n d : ℕ} (μ : YoungDiagram) (t : Tableau n μ) - (hμ : μ.colLen 0 ≤ 1) (u : WordSpace n d) (hu : u ≠ 0) - (he : ∀ g, wordRep n d g u = u) : - ∃ f : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n d) u).toRepresentation, f ≠ 0 := by - have hw (g : Equiv.Perm (Fin n)) : rowWord t ∘ g = rowWord t := by - funext i - apply Fin.ext - have h₁ := (rowWord t (g i)).isLt - have h₂ := (rowWord t i).isLt - omega - let F : Specht t →ₗ[ℂ] (cyclic (wordRep n d) u).toSubmodule := - { toFun := fun x => ⟨x.val (rowWord t) • u, Submodule.smul_mem _ _ (mem_cyclic _ _)⟩ - map_add' := by intro x y; apply Subtype.ext; exact add_smul _ _ _ - map_smul' := by intro c x; apply Subtype.ext; exact mul_smul _ _ _ } - let f : Representation.IntertwiningMap (spechtRep t) (cyclic (wordRep n d) u).toRepresentation := - { toLinearMap := F - isIntertwining' := by - intro g - apply LinearMap.ext - intro x - apply Subtype.ext - change x.val (rowWord t ∘ g) • u = wordRep n d g (x.val (rowWord t) • u) - rw [hw,map_smul,he] } - refine ⟨f, ?_⟩ - intro hz - have hh := congrArg (fun f => (f ⟨polytabloid t,mem_cyclic _ _⟩).val) hz - change polytabloid t (rowWord t) • u = 0 at hh - rw [polytabloid_rowWord,one_smul] at hh - exact hu hh - -/- The width-one band is the genuine trivial constituent required by Pieri. -/ -theorem oneBand_support (h : ℕ) (μ : YoungDiagram) (t : Tableau (bandSize h 1) μ) - (hμ : μ.colLen 0 ≤ 1) : - ∃ f : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep _ _) (stairBandWord h 1)).toRepresentation, f ≠ 0 := - oneRow_support_invariant μ t hμ _ (stairBandWord_ne_zero h 1) (oneBand_invariant h) - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.CyclicSector + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl + +def stairBandWord (h s : ℕ) : WordSpace (bandSize h s) + ((staircase (h+s)).colLen 0 * (staircase (h+s)).colLen 0) := + wordTensor _ _ _ (bandRowWord h s ⊗ₜ[ℂ] bandColumnWord h s) + +def lowPairLetter (h : ℕ) (x : Fin 4) : + Fin ((staircase (h+2)).colLen 0 * (staircase (h+2)).colLen 0) := + finProdFinEquiv (lowLetter h (Path.parts x).1, lowLetter h (Path.parts x).2) + +lemma bandColumn_path_eval' (h : ℕ) (w : Fin (2*(h+1)+1) → Fin 2) : + bandColumnWord h 2 ((lowLetter h ∘ w) ∘ (bandPathEquiv h).symm) = + PathLayer.rowAlt (h+1) (w ∘ Fin.rev) := by + have he : (lowLetter h ∘ (w ∘ Fin.rev)) ∘ (bandColumnPathEquiv h).symm = + (lowLetter h ∘ w) ∘ (bandPathEquiv h).symm := by + funext i + simp [bandColumnPathEquiv, Function.comp_def, Fin.revPerm] + rw [← he, bandColumn_path_eval] + +lemma stairBandWord_path_eval (h : ℕ) (w : Fin (2*(h+1)+1) → Fin 4) : + restrictLetters (lowPairLetter h) (stairBandWord h 2) (w ∘ (bandPathEquiv h).symm) = + (-1 : ℂ)^(h+1) * Path.bandWord (h+1) w := by + change wordTensor _ _ _ (bandRowWord h 2 ⊗ₜ[ℂ] bandColumnWord h 2) + (lowPairLetter h ∘ (w ∘ (bandPathEquiv h).symm)) = _ + rw [wordTensor_tmul] + have hl : splitLeft (lowPairLetter h ∘ (w ∘ (bandPathEquiv h).symm)) = + (lowLetter h ∘ (fun i => (Path.parts (w i)).1)) ∘ (bandPathEquiv h).symm := by + funext i; simp [splitLeft, lowPairLetter] + have hr : splitRight (lowPairLetter h ∘ (w ∘ (bandPathEquiv h).symm)) = + (lowLetter h ∘ (fun i => (Path.parts (w i)).2)) ∘ (bandPathEquiv h).symm := by + funext i; simp [splitRight, lowPairLetter] + rw [hl,hr,bandRow_path_eval,bandColumn_path_eval'] + exact PathLayer.paired_rowAlt _ w + +/- Every Specht shape with at most four rows occurs in the cyclic module +generated by the prescribed two-band vector. -/ +theorem twoBand_support (h : ℕ) (hh : 1 ≤ h) (μ : YoungDiagram) + (t : Tableau (bandSize h 2) μ) (hμ : μ.colLen 0 ≤ 4) : + ∃ f : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep _ _) (stairBandWord h 2)).toRepresentation, f ≠ 0 := by + have he : restrictLetters (lowPairLetter h) (stairBandWord h 2) = + (-1 : ℂ)^(h+1) • (fun w => Path.bandWord (h+1) (w ∘ bandPathEquiv h)) := by + funext w + have hw : (w ∘ bandPathEquiv h) ∘ (bandPathEquiv h).symm = w := by funext i; simp + simpa only [hw,Pi.smul_apply,smul_eq_mul] using stairBandWord_path_eval h (w ∘ bandPathEquiv h) + have hs := support_relabel (bandPathEquiv h) (Path.bandWord (h+1)) + (fun ν s hν => Path.fourRow_support (h+1) (by omega) ν s hν) μ t hμ + have hc : cyclic (wordRep (bandSize h 2) 4) (restrictLetters (lowPairLetter h) (stairBandWord h 2)) = + cyclic (wordRep (bandSize h 2) 4) (fun w => Path.bandWord (h+1) (w ∘ bandPathEquiv h)) := by + rw [he,cyclic_smul_eq _ _ _ (pow_ne_zero _ (by norm_num))] + rw [← hc] at hs + obtain ⟨f,hf⟩ := hs + exact cyclic_projection_support (restrictLetters (lowPairLetter h)) (stairBandWord h 2) f hf + +end Saxl + +namespace Saxl + +/- Coordinate subrepresentation using only letters with property A. -/ +def alphabetSub (n d : ℕ) (A : Fin d → Prop) : Subrepresentation (wordRep n d) where + toSubmodule := + { carrier := {x | ∀ w, (∃ i, ¬ A (w i)) → x w = 0} + zero_mem' := by intro w hw; rfl + add_mem' := by intro x y hx hy w hw; change x w+y w=0; rw [hx w hw,hy w hw,add_zero] + smul_mem' := by intro c x hx w hw; change c*x w=0; rw [hx w hw,mul_zero] } + apply_mem_toSubmodule g := by + intro x hx w hw + obtain ⟨i,hi⟩ := hw + apply hx (w ∘ g) + exact ⟨g⁻¹ i, by simpa using hi⟩ + +lemma alphabetSub_iff {n d : ℕ} (A : Fin d → Prop) (x : WordSpace n d) : + x ∈ alphabetSub n d A ↔ ∀ w, x w ≠ 0 → ∀ i, A (w i) := by + change (∀ w, (∃ i, ¬ A (w i)) → x w = 0) ↔ _ + constructor + · intro h w hw i + by_contra hn + exact hw (h w ⟨i,hn⟩) + · intro h w hw + by_contra hn + obtain ⟨i,hi⟩ := hw + exact hi (h w hn i) + +lemma cyclic_alphabet {n d : ℕ} (A : Fin d → Prop) (v : WordSpace n d) + (hv : v ∈ alphabetSub n d A) (x : WordSpace n d) (hx : x ∈ cyclic (wordRep n d) v) : + x ∈ alphabetSub n d A := (cyclic_le _ _ _).mpr hv hx + +lemma single_mem_alphabet {n d : ℕ} (A : Fin d → Prop) (a : Fin n → Fin d) (ha : ∀ i, A (a i)) : + (Pi.single a (1:ℂ) : WordSpace n d) ∈ alphabetSub n d A := by + classical + intro w hw + apply Pi.single_eq_of_ne + intro he + subst w + obtain ⟨i,hi⟩ := hw + exact hi (ha i) + +lemma altWord_mem_alphabet {n d : ℕ} (A : Fin d → Prop) + (G : Subgroup (Equiv.Perm (Fin n))) (a : Fin n → Fin d) (ha : ∀ i, A (a i)) : + altWord G a ∈ alphabetSub n d A := by + classical + unfold altWord + apply Submodule.sum_mem + intro g hg + apply Submodule.smul_mem + exact (alphabetSub n d A).apply_mem_toSubmodule g.val (single_mem_alphabet A a ha) + +lemma letterLift_mem_alphabet {n d D : ℕ} (A : Fin D → Prop) + (φ : Fin d → Fin D) (hφ : ∀ i, A (φ i)) (x : WordSpace n d) : + letterLift φ x ∈ alphabetSub n D A := by + classical + intro w hw + obtain ⟨i,hi⟩ := hw + change (∑ a, x a * ∏ j, (if φ (a j) = w j then (1:ℂ) else 0)) = 0 + apply Finset.sum_eq_zero + intro a ha + apply mul_eq_zero_of_right + apply Finset.prod_eq_zero (Finset.mem_univ i) + exact ite_eq_right (fun hh : φ (a i) = w i => hi (hh ▸ hφ (a i))) + +lemma letterLift_eval {n d D : ℕ} (φ : Fin d → Fin D) (hφ : Function.Injective φ) + (x : WordSpace n d) (w : Fin n → Fin d) : letterLift φ x (φ ∘ w) = x w := by + classical + change (∑ a, x a * ∏ i, (if φ (a i) = φ (w i) then (1:ℂ) else 0)) = x w + rw [Finset.sum_eq_single w] + · simp + · intro a ha haw + apply mul_eq_zero_of_right + obtain ⟨i,hi⟩ : ∃ i, a i ≠ w i := by by_contra hh; push Not at hh; exact haw (funext hh) + apply Finset.prod_eq_zero (Finset.mem_univ i) + exact ite_eq_right (fun hh => hi (hφ hh)) + · simp + +lemma letterLift_injective {n d D : ℕ} (φ : Fin d → Fin D) (hφ : Function.Injective φ) : + Function.Injective (letterLift (n := n) φ) := by + intro x y hxy + funext w + have hh := congrFun hxy (φ ∘ w) + simpa only [letterLift_eval φ hφ] using hh + +def pairLift {n d D : ℕ} (φ : Fin d → Fin D) : + Representation.IntertwiningMap (wordRep n (d*d)) (wordRep n (D*D)) := + (wordTensorIntertwiner _ _ _).comp (((letterLift φ).tensor (letterLift φ)).comp + ((wordTensorIntertwiner n d d).ofBijective (wordTensor n d d).bijective).symm.toIntertwiningMap) + +lemma pairLift_wordTensor {n d D : ℕ} (φ : Fin d → Fin D) (x y : WordSpace n d) : + pairLift φ (wordTensor n d d (x ⊗ₜ[ℂ] y)) = + wordTensor n D D (letterLift φ x ⊗ₜ[ℂ] letterLift φ y) := by + let E := (wordTensorIntertwiner n d d).ofBijective (wordTensor n d d).bijective + change wordTensor n D D (((letterLift φ).tensor (letterLift φ)) (E.symm (E (x ⊗ₜ[ℂ] y)))) = _ + rw [E.symm_apply_apply] + rfl + +lemma pairLift_injective {n d D : ℕ} (φ : Fin d → Fin D) (hφ : Function.Injective φ) : + Function.Injective (pairLift (n := n) φ) := by + apply (wordTensor n D D).injective.comp + apply (TensorProduct.map_injective_of_flat_flat _ _ (letterLift_injective φ hφ) (letterLift_injective φ hφ)).comp + exact ((wordTensorIntertwiner n d d).ofBijective (wordTensor n d d).bijective).symm.injective + +lemma pairWord_mem_alphabetLeft {n d : ℕ} (A : Fin d → Prop) + (x y : WordSpace n d) (hx : x ∈ alphabetSub n d A) : + wordTensor n d d (x ⊗ₜ[ℂ] y) ∈ + alphabetSub n (d*d) (fun a => A (finProdFinEquiv.symm a).1) := by + apply (alphabetSub_iff _ _).mpr + intro w hw i + rw [wordTensor_tmul] at hw + exact (alphabetSub_iff A x).mp hx (splitLeft w) ((mul_ne_zero_iff.mp hw).1) i + + + +def shiftedStairWord (h s : ℕ) := pairLift (highLetter h s) (staircaseWord h) + +lemma highLetter_injective (h s : ℕ) : Function.Injective (highLetter h s) := by + intro a b hab + apply Fin.ext + have := congrArg Fin.val hab + dsimp [highLetter] at this + omega + +lemma shiftedStairWord_support (h s : ℕ) (μ : YoungDiagram) (t : Tableau (staircase h).card μ) + (f : Representation.IntertwiningMap (spechtRep t) (staircaseCyclic h).toRepresentation) + (hf : f ≠ 0) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep _ _) (shiftedStairWord h s)).toRepresentation, F ≠ 0 := by + let F := (cyclicMap (pairLift (highLetter h s)) (staircaseWord h)).comp f + refine ⟨F, ?_⟩ + intro hz + apply hf + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + apply Subtype.ext + apply pairLift_injective (highLetter h s) (highLetter_injective h s) + have hh := congrArg (fun l => (l x).val) hz + exact hh.trans (map_zero _).symm + +lemma shiftedStairWord_alphabet (h s : ℕ) : + shiftedStairWord h s ∈ alphabetSub _ _ (fun a => s ≤ ((finProdFinEquiv.symm a).1).val) := by + unfold shiftedStairWord staircaseWord + rw [pairLift_wordTensor] + apply pairWord_mem_alphabetLeft (fun a => s ≤ a.val) + apply letterLift_mem_alphabet + intro i + dsimp [highLetter] + omega + +lemma bandRowWord_alphabet (h s : ℕ) : + bandRowWord h s ∈ alphabetSub _ _ (fun a => ¬s ≤ a.val) := by + apply altWord_mem_alphabet + intro j + have hb := (bandTableau_bounds h s j).1 + have hr := rotateRow_high h s (bandTableau h s j) + have hh : ¬ s ≤ (rotateRow h s (bandTableau h s j)).val.2 := + fun hh => (Nat.not_lt.mpr hb) (hr.mp hh) + simpa [rightWord,rowWord,stairRowTableau,rotateRowPositions,bandTableau,staircaseSwap] using hh + +lemma stairBandWord_alphabet (h s : ℕ) : + stairBandWord h s ∈ alphabetSub _ _ (fun a => ¬ s ≤ ((finProdFinEquiv.symm a).1).val) := by + apply pairWord_mem_alphabetLeft (fun a => ¬s ≤ a.val) + exact bandRowWord_alphabet h s + +/- The actual same-high image factors as the smaller Specht tensor cyclic +vector and the exact retained band vector on independent position blocks. -/ +theorem staircase_cut_factor (h s : ℕ) : + sameHighProjection _ _ _ s (staircaseWord (h+s)) = + positionProduct (cutPositions h s) (shiftedStairWord h s) (stairBandWord h s) := by + rw [staircase_cut_layers,cutRowWord_factor,cutColumnWord_factor] + unfold shiftedStairWord staircaseWord + rw [pairLift_wordTensor] + ext w + simp only [wordTensor_tmul, stairBandWord, positionProduct] + exact mul_mul_mul_comm _ _ _ _ + + + +lemma bandColumnWord_alphabet (h s : ℕ) : + bandColumnWord h s ∈ alphabetSub _ _ (fun a => ¬s ≤ a.val) := by + apply altWord_mem_alphabet + intro j + have hb := (bandTableau_bounds h s j).1 + have hr := rotateColumn_high h s (bandTableau h s j) + have hh : ¬ s ≤ (rotateColumn h s (bandTableau h s j)).val.1 := + fun hh => (Nat.not_lt.mpr hb) (hr.mp hh) + simpa [rightWord,rowWord,rotateColumnPositions,bandTableau] using hh + +lemma alphabet_small_invariant {n d : ℕ} (A : Fin d → Prop) + (hA : ∀ a b, A a → A b → a = b) (x : WordSpace n d) + (hx : x ∈ alphabetSub n d A) (g : Equiv.Perm (Fin n)) : wordRep n d g x = x := by + ext w + change x (w ∘ g) = x w + have he : (∀ i, A (w i)) → w ∘ g = w := by + intro h + funext i + exact hA _ _ (h (g i)) (h i) + by_cases h : ∀ i, A (w i) + · rw [he h] + · have hz : x w = 0 := by + by_contra hn + exact h ((alphabetSub_iff A x).mp hx w hn) + rw [hz] + by_contra hn + have hh := (alphabetSub_iff A x).mp hx (w ∘ g) hn + apply h + intro i + simpa using hh (g⁻¹ i) + +lemma oneBand_invariant (h : ℕ) (g : Equiv.Perm (Fin (bandSize h 1))) : + wordRep _ _ g (stairBandWord h 1) = stairBandWord h 1 := by + have ha (a b : Fin ((staircase (h+1)).colLen 0)) (ha : ¬1 ≤ a.val) (hb : ¬1 ≤ b.val) : a = b := by + apply Fin.ext; omega + have hr := alphabet_small_invariant (fun a => ¬1 ≤ a.val) ha _ (bandRowWord_alphabet h 1) g + have hc := alphabet_small_invariant (fun a => ¬1 ≤ a.val) ha _ (bandColumnWord_alphabet h 1) g + ext w + change stairBandWord h 1 (w ∘ g) = stairBandWord h 1 w + simp only [stairBandWord,wordTensor_tmul] + exact congrArg₂ (fun x y : ℂ => x*y) (congrFun hr (splitLeft w)) (congrFun hc (splitRight w)) + +lemma stairBandWord_ne_zero (h s : ℕ) : stairBandWord h s ≠ 0 := by + intro hz + apply staircase_projected_ne_zero h s + rw [staircase_cut_factor,hz] + ext w + change _ * 0 = 0 + exact mul_zero _ + +lemma oneRow_support_invariant {n d : ℕ} (μ : YoungDiagram) (t : Tableau n μ) + (hμ : μ.colLen 0 ≤ 1) (u : WordSpace n d) (hu : u ≠ 0) + (he : ∀ g, wordRep n d g u = u) : + ∃ f : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n d) u).toRepresentation, f ≠ 0 := by + have hw (g : Equiv.Perm (Fin n)) : rowWord t ∘ g = rowWord t := by + funext i + apply Fin.ext + have h₁ := (rowWord t (g i)).isLt + have h₂ := (rowWord t i).isLt + omega + let F : Specht t →ₗ[ℂ] (cyclic (wordRep n d) u).toSubmodule := + { toFun := fun x => ⟨x.val (rowWord t) • u, Submodule.smul_mem _ _ (mem_cyclic _ _)⟩ + map_add' := by intro x y; apply Subtype.ext; exact add_smul _ _ _ + map_smul' := by intro c x; apply Subtype.ext; exact mul_smul _ _ _ } + let f : Representation.IntertwiningMap (spechtRep t) (cyclic (wordRep n d) u).toRepresentation := + { toLinearMap := F + isIntertwining' := by + intro g + apply LinearMap.ext + intro x + apply Subtype.ext + change x.val (rowWord t ∘ g) • u = wordRep n d g (x.val (rowWord t) • u) + rw [hw,map_smul,he] } + refine ⟨f, ?_⟩ + intro hz + have hh := congrArg (fun f => (f ⟨polytabloid t,mem_cyclic _ _⟩).val) hz + change polytabloid t (rowWord t) • u = 0 at hh + rw [polytabloid_rowWord,one_smul] at hh + exact hu hh + +/- The width-one band is the genuine trivial constituent required by Pieri. -/ +theorem oneBand_support (h : ℕ) (μ : YoungDiagram) (t : Tableau (bandSize h 1) μ) + (hμ : μ.colLen 0 ≤ 1) : + ∃ f : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep _ _) (stairBandWord h 1)).toRepresentation, f ≠ 0 := + oneRow_support_invariant μ t hμ _ (stairBandWord_ne_zero h 1) (oneBand_invariant h) + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/Basic.lean b/lean/OAI/RepresentationTheory/Saxl/Basic.lean index 45426aae979369d91d4a0ba4aee10605802a2877..1eaddacb7d2372ff3ac17bf4b6daaccbf88096d2 100644 --- a/lean/OAI/RepresentationTheory/Saxl/Basic.lean +++ b/lean/OAI/RepresentationTheory/Saxl/Basic.lean @@ -1,107 +1,107 @@ -import OAI.RepresentationTheory.Saxl.Model - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uG uV uW - -namespace Saxl - -/- The genuine finite-dimensional Hom criterion; no simplicity hypothesis. -/ -theorem intertwining_finrank_pos_iff {G : Type uG} {V : Type uV} {W : Type uW} [Group G] - [AddCommGroup V] [AddCommGroup W] [Module ℂ V] [Module ℂ W] - [Module.Finite ℂ V] [Module.Finite ℂ W] - (ρ : Representation ℂ G V) (σ : Representation ℂ G W) : - 0 < Module.finrank ℂ (Representation.IntertwiningMap ρ σ) ↔ - ∃ f : Representation.IntertwiningMap ρ σ, f ≠ 0 := - Module.finrank_pos_iff_exists_ne_zero (R := ℂ) (M := Representation.IntertwiningMap ρ σ) - -theorem kronecker_pos_iff {n : ℕ} {α β μ : YoungDiagram} - (a : Tableau n α) (b : Tableau n β) (t : Tableau n μ) : - 0 < kronecker a b t ↔ - ∃ f : Representation.IntertwiningMap (spechtRep t) - ((spechtRep a).tprod (spechtRep b)), f ≠ 0 := by - exact @intertwining_finrank_pos_iff (Equiv.Perm (Fin n)) (Specht t) - (Specht a ⊗[ℂ] Specht b) _ _ _ _ _ _ _ - (spechtRep t) ((spechtRep a).tprod (spechtRep b)) - -/- Column permutations cannot also fix the row word unless they are identity. -/ -theorem column_perm_rowWord {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (g : columnGroup t) (hg : rowWord t ∘ (g : Equiv.Perm (Fin n)) = rowWord t) : - g = 1 := by - apply Subtype.ext - apply Equiv.ext - intro i - apply t.injective - apply Subtype.ext - apply Prod.ext - · exact congrArg Fin.val (congrFun hg i) - · exact g.property i - -/- The coefficient of the canonical row word in its polytabloid is one. -/ -theorem polytabloid_rowWord {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - polytabloid t (rowWord t) = 1 := by - classical - unfold polytabloid - simp only [Finset.sum_apply, Pi.smul_apply, wordRep, MonoidHom.coe_mk, - OneHom.coe_mk, LinearMap.coe_mk, AddHom.coe_mk, Pi.single_apply] - rw [Finset.sum_eq_single (1 : columnGroup t)] - · simp - · intro b hb hb1 - have hn : rowWord t ∘ (b : Equiv.Perm (Fin n)) ≠ rowWord t := - fun h => hb1 (column_perm_rowWord t b h) - simp [hn] - · simp - - -@[simp] theorem mem_staircase {m i j : ℕ} : - (i, j) ∈ staircase m ↔ i + j < m := by - change (i, j) ∈ ((Finset.range m) ×ˢ (Finset.range m)).filter - (fun x => x.1 + x.2 < m) ↔ _ - simp only [Finset.mem_filter, Finset.mem_product, Finset.mem_range] - omega - -theorem staircase_cells_succ (m : ℕ) : - (staircase (m + 1)).cells = (staircase m).cells ∪ Finset.HasAntidiagonal.antidiagonal m := by - ext x - rcases x with ⟨i, j⟩ - simp only [YoungDiagram.mem_cells, mem_staircase, Finset.mem_union, - Finset.HasAntidiagonal.mem_antidiagonal] - omega - -theorem staircase_card_succ (m : ℕ) : - (staircase (m + 1)).card = (staircase m).card + (m + 1) := by - change (staircase (m + 1)).cells.card = _ - rw [staircase_cells_succ, Finset.card_union_of_disjoint] - · rw [Finset.Nat.card_antidiagonal] - · apply Finset.disjoint_left.mpr - intro x hx hy - rcases x with ⟨i, j⟩ - simp only [YoungDiagram.mem_cells, mem_staircase] at hx - simp only [Finset.HasAntidiagonal.mem_antidiagonal] at hy - omega - -@[simp] theorem staircase_card_zero : (staircase 0).card = 0 := by - simp [staircase, YoungDiagram.card] - -theorem staircase_card_double (m : ℕ) : - (staircase m).card * 2 = m * (m + 1) := by - induction m with - | zero => simp - | succ m ih => - rw [staircase_card_succ] - nlinarith - -/- The staircase has triangular cardinality. -/ -theorem staircase_card (m : ℕ) : (staircase m).card = m * (m + 1) / 2 := by - rw [← staircase_card_double] - simp - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.Model + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uG uV uW + +namespace Saxl + +/- The genuine finite-dimensional Hom criterion; no simplicity hypothesis. -/ +theorem intertwining_finrank_pos_iff {G : Type uG} {V : Type uV} {W : Type uW} [Group G] + [AddCommGroup V] [AddCommGroup W] [Module ℂ V] [Module ℂ W] + [Module.Finite ℂ V] [Module.Finite ℂ W] + (ρ : Representation ℂ G V) (σ : Representation ℂ G W) : + 0 < Module.finrank ℂ (Representation.IntertwiningMap ρ σ) ↔ + ∃ f : Representation.IntertwiningMap ρ σ, f ≠ 0 := + Module.finrank_pos_iff_exists_ne_zero (R := ℂ) (M := Representation.IntertwiningMap ρ σ) + +theorem kronecker_pos_iff {n : ℕ} {α β μ : YoungDiagram} + (a : Tableau n α) (b : Tableau n β) (t : Tableau n μ) : + 0 < kronecker a b t ↔ + ∃ f : Representation.IntertwiningMap (spechtRep t) + ((spechtRep a).tprod (spechtRep b)), f ≠ 0 := by + exact @intertwining_finrank_pos_iff (Equiv.Perm (Fin n)) (Specht t) + (Specht a ⊗[ℂ] Specht b) _ _ _ _ _ _ _ + (spechtRep t) ((spechtRep a).tprod (spechtRep b)) + +/- Column permutations cannot also fix the row word unless they are identity. -/ +theorem column_perm_rowWord {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (g : columnGroup t) (hg : rowWord t ∘ (g : Equiv.Perm (Fin n)) = rowWord t) : + g = 1 := by + apply Subtype.ext + apply Equiv.ext + intro i + apply t.injective + apply Subtype.ext + apply Prod.ext + · exact congrArg Fin.val (congrFun hg i) + · exact g.property i + +/- The coefficient of the canonical row word in its polytabloid is one. -/ +theorem polytabloid_rowWord {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + polytabloid t (rowWord t) = 1 := by + classical + unfold polytabloid + simp only [Finset.sum_apply, Pi.smul_apply, wordRep, MonoidHom.coe_mk, + OneHom.coe_mk, LinearMap.coe_mk, AddHom.coe_mk, Pi.single_apply] + rw [Finset.sum_eq_single (1 : columnGroup t)] + · simp + · intro b hb hb1 + have hn : rowWord t ∘ (b : Equiv.Perm (Fin n)) ≠ rowWord t := + fun h => hb1 (column_perm_rowWord t b h) + simp [hn] + · simp + + +@[simp] theorem mem_staircase {m i j : ℕ} : + (i, j) ∈ staircase m ↔ i + j < m := by + change (i, j) ∈ ((Finset.range m) ×ˢ (Finset.range m)).filter + (fun x => x.1 + x.2 < m) ↔ _ + simp only [Finset.mem_filter, Finset.mem_product, Finset.mem_range] + omega + +theorem staircase_cells_succ (m : ℕ) : + (staircase (m + 1)).cells = (staircase m).cells ∪ Finset.HasAntidiagonal.antidiagonal m := by + ext x + rcases x with ⟨i, j⟩ + simp only [YoungDiagram.mem_cells, mem_staircase, Finset.mem_union, + Finset.HasAntidiagonal.mem_antidiagonal] + omega + +theorem staircase_card_succ (m : ℕ) : + (staircase (m + 1)).card = (staircase m).card + (m + 1) := by + change (staircase (m + 1)).cells.card = _ + rw [staircase_cells_succ, Finset.card_union_of_disjoint] + · rw [Finset.Nat.card_antidiagonal] + · apply Finset.disjoint_left.mpr + intro x hx hy + rcases x with ⟨i, j⟩ + simp only [YoungDiagram.mem_cells, mem_staircase] at hx + simp only [Finset.HasAntidiagonal.mem_antidiagonal] at hy + omega + +@[simp] theorem staircase_card_zero : (staircase 0).card = 0 := by + simp [staircase, YoungDiagram.card] + +theorem staircase_card_double (m : ℕ) : + (staircase m).card * 2 = m * (m + 1) := by + induction m with + | zero => simp + | succ m ih => + rw [staircase_card_succ] + nlinarith + +/- The staircase has triangular cardinality. -/ +theorem staircase_card (m : ℕ) : (staircase m).card = m * (m + 1) / 2 := by + rw [← staircase_card_double] + simp + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/ColumnContraction.lean b/lean/OAI/RepresentationTheory/Saxl/ColumnContraction.lean index 6aa848971b5f7179e41d61a65820a2b037a81237..b8769742f136dd3c9c0e12d776a0c2fb6c883e20 100644 --- a/lean/OAI/RepresentationTheory/Saxl/ColumnContraction.lean +++ b/lean/OAI/RepresentationTheory/Saxl/ColumnContraction.lean @@ -1,310 +1,310 @@ -import OAI.RepresentationTheory.Saxl.PathContraction - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl.Columns -/- A concrete ordered disjoint union of consecutive columns. -/ -@[reducible] def Cells : List ℕ → Type - | [] => Empty - | r :: rs => Fin r ⊕ Cells rs - -instance cellsFintype : (rs : List ℕ) → Fintype (Cells rs) - | [] => inferInstanceAs (Fintype Empty) - | r :: rs => @instFintypeSum (Fin r) (Cells rs) inferInstance (cellsFintype rs) - -instance cellsDecEq : (rs : List ℕ) → DecidableEq (Cells rs) - | [] => inferInstanceAs (DecidableEq Empty) - | r :: rs => @instDecidableEqSum (Fin r) (Cells rs) inferInstance (cellsDecEq rs) - -def row : {rs : List ℕ} → Cells rs → ℕ - | _ :: _, .inl i => i.val - | _ :: _, .inr c => row c - -def col : {rs : List ℕ} → Cells rs → ℕ - | _ :: _, .inl _ => 0 - | _ :: _, .inr c => col c + 1 - -def enumerate : (rs : List ℕ) → Fin rs.sum ≃ Cells rs - | [] => (Equiv.equivOfIsEmpty (Fin 0) Empty) - | r :: rs => finSumFinEquiv.symm.trans ((Equiv.refl (Fin r)).sumCongr (enumerate rs)) - -@[simp] lemma enumerate_left (r : ℕ) (rs : List ℕ) (i : Fin r) : - enumerate (r :: rs) (Fin.castAdd rs.sum i) = Sum.inl i := by - exact congrArg ((Equiv.refl (Fin r)).sumCongr (enumerate rs)) - (finSumFinEquiv_symm_apply_castAdd i) - -@[simp] lemma enumerate_right (r : ℕ) (rs : List ℕ) (i : Fin rs.sum) : - enumerate (r :: rs) (Fin.natAdd r i) = Sum.inr (enumerate rs i) := by - exact congrArg ((Equiv.refl (Fin r)).sumCongr (enumerate rs)) - (finSumFinEquiv_symm_apply_natAdd i) - -@[reducible] def Perms : List ℕ → Type - | [] => Unit - | r :: rs => Equiv.Perm (Fin r) × Perms rs - -instance permsFintype : (rs : List ℕ) → Fintype (Perms rs) - | [] => inferInstanceAs (Fintype Unit) - | r :: rs => @instFintypeProd (Equiv.Perm (Fin r)) (Perms rs) inferInstance (permsFintype rs) - -def perm : {rs : List ℕ} → Perms rs → Equiv.Perm (Cells rs) - | [], _ => Equiv.refl _ - | _ :: _, (π, σ) => Equiv.sumCongr π (perm σ) - -def sg : {rs : List ℕ} → Perms rs → ℂ - | [], _ => 1 - | _ :: _, (π, σ) => (((Equiv.Perm.sign π : ℤ) : ℂ)) * sg σ - -lemma sign_perm {rs : List ℕ} (π : Perms rs) : - (((Equiv.Perm.sign (perm π) : ℤ) : ℂ)) = sg π := by - induction rs with - | nil => simp [perm, sg] - | cons r rs ih => - obtain ⟨π, σ⟩ := π - have hh := congrArg (fun u : ℤˣ => ((u : ℤ) : ℂ)) - (Equiv.Perm.sign_sumCongr π (perm σ)) - exact hh.trans (by simp only [Units.val_mul, Int.cast_mul, ih]; rfl) - -lemma perm_col {rs : List ℕ} (π : Perms rs) (c : Cells rs) : col (perm π c) = col c := by - induction rs with - | nil => exact isEmptyElim c - | cons r rs ih => - obtain ⟨π, σ⟩ := π - cases c with - | inl i => rfl - | inr c => exact congrArg (· + 1) (ih σ c) - -lemma coords_injective (rs : List ℕ) : - Function.Injective (fun c : Cells rs => (row c, col c)) := by - induction rs with - | nil => exact Function.injective_of_subsingleton _ - | cons r rs ih => - intro a b h - cases a with - | inl a => - cases b with - | inl b => exact congrArg Sum.inl (Fin.ext (congrArg Prod.fst h)) - | inr b => have := congrArg Prod.snd h; simp [col] at this - | inr a => - cases b with - | inl b => have := congrArg Prod.snd h; simp [col] at this - | inr b => - apply congrArg Sum.inr - apply ih - dsimp only [row, col] at h - have hr := congrArg Prod.fst h - have hc := congrArg Prod.snd h - exact Prod.ext hr (Nat.add_right_cancel hc) - -lemma coords_range (rs : List ℕ) (i j : ℕ) : - (∃ c : Cells rs, row c = i ∧ col c = j) ↔ ∃ h : j < rs.length, i < rs[j] := by - induction rs generalizing j with - | nil => simp [Cells] - | cons r rs ih => - cases j with - | zero => - constructor - · rintro ⟨c, hr, hc⟩ - cases c with - | inl a => exact ⟨by simp, by simpa [row] using hr ▸ a.isLt⟩ - | inr a => simp [col] at hc - · rintro ⟨h, hi⟩ - exact ⟨Sum.inl ⟨i, hi⟩, rfl, rfl⟩ - | succ j => - constructor - · rintro ⟨c, hr, hc⟩ - cases c with - | inl a => simp [col] at hc - | inr a => - have hj : col a = j := Nat.add_right_cancel hc - obtain ⟨hj, hi⟩ := (ih j).mp ⟨a, hr, hj⟩ - exact ⟨Nat.succ_lt_succ hj, hi⟩ - · rintro ⟨h, hi⟩ - obtain ⟨a, ha, hc⟩ := (ih j).mpr ⟨Nat.lt_of_succ_lt_succ h, hi⟩ - exact ⟨Sum.inr a, ha, congrArg (· + 1) hc⟩ - -/- The matrix product indexed by the actual consecutive position order. -/ -def chain (rs : List ℕ) (p : ℕ) (N : ℕ → Band.Mat) (π : Perms rs) : Band.Mat := - (List.ofFn fun q : Fin rs.sum => Band.D (p + q.val) (N (row (perm π (enumerate rs q))))).prod - -lemma chain_cons (r : ℕ) (rs : List ℕ) (p : ℕ) (N : ℕ → Band.Mat) - (π : Equiv.Perm (Fin r)) (σ : Perms rs) : - chain (r :: rs) p N (π, σ) = - (List.ofFn fun j : Fin r => Band.D (p + j.val) (N (π j).val)).prod * - chain rs (p + r) N σ := by - unfold chain - erw [List.ofFn_add, List.prod_append] - congr 2 - · apply congrArg List.ofFn - funext j - change Band.D (p + j.val) (N (row (@perm (r :: rs) (π, σ) (enumerate (r :: rs) (Fin.castAdd rs.sum j))))) = _ - rw [enumerate_left] - rfl - · apply congrArg List.ofFn - funext j - change Band.D (p + (r + j.val)) (N (row (@perm (r :: rs) (π, σ) (enumerate (r :: rs) (Fin.natAdd r j))))) = _ - erw [enumerate_right r rs (show Fin rs.sum from j)] - simp only [perm, Equiv.sumCongr_apply, Sum.map_inr, row, Nat.add_assoc] - -/- Ordered product of independent alternating column segments. -/ -def segments : ℕ → List ℕ → (ℕ → Band.Mat) → Band.Mat - | _, [], _ => 1 - | p, r :: rs, N => - (∑ π : Equiv.Perm (Fin r), (((Equiv.Perm.sign π : ℤ) : ℂ)) • - (List.ofFn fun i : Fin r => Band.D (p + i.val) (N (π i).val)).prod) * - segments (p+r) rs N - -/- Factorization over independent column permutations, without commuting factors. -/ -lemma sum_chain (rs : List ℕ) (p : ℕ) (N : ℕ → Band.Mat) : - (∑ π : Perms rs, sg π • chain rs p N π) = segments p rs N := by - induction rs generalizing p with - | nil => simp [Perms, chain, sg, segments] - | cons r rs ih => - simp only [Perms, Fintype.sum_prod_type, sg, chain_cons, segments] - simp_rw [← smul_mul_smul_comm, ← Finset.mul_sum, ← Finset.sum_mul, ih] - -lemma perm_injective (rs : List ℕ) : Function.Injective (@perm rs) := by - induction rs with - | nil => exact Function.injective_of_subsingleton _ - | cons r rs ih => - rintro ⟨π, σ⟩ ⟨π', σ'⟩ h - apply Prod.ext - · apply Equiv.ext - intro i - exact Sum.inl.inj (Equiv.congr_fun h (Sum.inl i)) - · apply ih - apply Equiv.ext - intro c - exact Sum.inr.inj (Equiv.congr_fun h (Sum.inr c)) - -lemma perm_surjective (rs : List ℕ) (g : Equiv.Perm (Cells rs)) - (hg : ∀ c, col (g c) = col c) : ∃ π : Perms rs, perm π = g := by - induction rs with - | nil => exact ⟨(), Subsingleton.elim _ _⟩ - | cons r rs ih => - have hm : Set.MapsTo g (Set.range Sum.inl) (Set.range Sum.inl) := by - rintro c ⟨i, rfl⟩ - have hh := hg (Sum.inl i) - cases h : g (Sum.inl i) with - | inl j => exact ⟨j, rfl⟩ - | inr c => simp [h, col] at hh - obtain ⟨⟨π, σ⟩, he⟩ := Equiv.Perm.mem_sumCongrHom_range_of_perm_mapsTo_inl hm - have hs : ∀ c : Cells rs, col (σ c) = col c := by - intro c - have hh := hg (Sum.inr c) - rw [← he] at hh - exact Nat.add_right_cancel hh - obtain ⟨τ, hτ⟩ := ih σ hs - exact ⟨(π, τ), by simp only [perm, hτ]; exact he⟩ - -/- The column-recursive coordinates enumerate the actual Ferrers cells. -/ -def toYoung (μ : YoungDiagram) : Cells μ.transpose.rowLens ≃ μ.cells := by - let f : Cells μ.transpose.rowLens → μ.cells := fun c => - ⟨(row c, col c), by - obtain ⟨hj, hi⟩ := (coords_range μ.transpose.rowLens (row c) (col c)).mp ⟨c, rfl, rfl⟩ - simpa only [YoungDiagram.mem_cells, YoungDiagram.mem_iff_lt_colLen, - YoungDiagram.get_rowLens, YoungDiagram.rowLen_transpose] using hi⟩ - exact Equiv.ofBijective f ⟨fun _ _ h => coords_injective _ (congrArg Subtype.val h), by - intro c - have hmem : c.val.1 < μ.colLen c.val.2 := YoungDiagram.mem_iff_lt_colLen.mp c.property - have hj : c.val.2 < μ.rowLen 0 := YoungDiagram.mem_iff_lt_rowLen.mp - (μ.up_left_mem (Nat.zero_le _) le_rfl c.property) - have hj' : c.val.2 < μ.transpose.rowLens.length := by simpa using hj - obtain ⟨a, ha, hb⟩ := (coords_range μ.transpose.rowLens c.val.1 c.val.2).mpr - ⟨hj', by simpa using hmem⟩ - exact ⟨a, Subtype.ext (Prod.ext ha hb)⟩⟩ - -@[simp] lemma toYoung_val (μ : YoungDiagram) (c : Cells μ.transpose.rowLens) : - (toYoung μ c).val = (row c, col c) := rfl - -lemma row_lt (μ : YoungDiagram) (c : Cells μ.transpose.rowLens) : row c < μ.colLen 0 := - YoungDiagram.mem_iff_lt_colLen.mp - (μ.up_left_mem le_rfl (Nat.zero_le _) (toYoung μ c).property) - - -def columnTableau (μ : YoungDiagram) : Tableau μ.transpose.rowLens.sum μ := - (enumerate μ.transpose.rowLens).trans (toYoung μ) - -@[simp] lemma columnTableau_val (μ : YoungDiagram) (i : Fin μ.transpose.rowLens.sum) : - (columnTableau μ i).val = (row (enumerate μ.transpose.rowLens i), - col (enumerate μ.transpose.rowLens i)) := rfl - -def columnPerm (μ : YoungDiagram) (π : Perms μ.transpose.rowLens) : - columnGroup (columnTableau μ) := - ⟨(enumerate μ.transpose.rowLens).symm.permCongr (perm π), by - intro i - simp only [columnTableau_val, Equiv.permCongr_apply, Equiv.symm_symm, - Equiv.apply_symm_apply] - exact perm_col π _⟩ - -lemma columnPerm_bijective (μ : YoungDiagram) : Function.Bijective (columnPerm μ) := by - constructor - · intro π σ h - apply perm_injective μ.transpose.rowLens - apply (enumerate μ.transpose.rowLens).symm.permCongr.injective - exact congrArg Subtype.val h - · intro g - let e := enumerate μ.transpose.rowLens - obtain ⟨π, hπ⟩ := perm_surjective μ.transpose.rowLens (e.permCongr g.val) (by - intro c - have hh := g.property (e.symm c) - simpa only [columnTableau_val, Equiv.permCongr_apply, e, Equiv.apply_symm_apply] using hh) - refine ⟨π, ?_⟩ - apply Subtype.ext - change e.symm.permCongr (perm π) = g.val - rw [hπ] - apply Equiv.ext - intro i - simp [Equiv.permCongr_apply] - -def columnEquiv (μ : YoungDiagram) : Perms μ.transpose.rowLens ≃ columnGroup (columnTableau μ) := - Equiv.ofBijective (columnPerm μ) (columnPerm_bijective μ) - -lemma columnPerm_sign (μ : YoungDiagram) (π : Perms μ.transpose.rowLens) : - signC (columnPerm μ π).val = sg π := by - change (((Equiv.Perm.sign ((enumerate μ.transpose.rowLens).symm.permCongr (perm π)) : ℤ) : ℂ)) = sg π - rw [Equiv.Perm.sign_permCongr] - exact sign_perm π - -lemma mapped_columnTableau (μ : YoungDiagram) (N : ℕ → Band.Mat) : - wordMap (fun (i : Fin (μ.colLen 0)) (a : Fin 4) => - N i.val (Path.parts a).1 (Path.parts a).2) (polytabloid (columnTableau μ)) = - ∑ π : Perms μ.transpose.rowLens, sg π • Path.pureWord - (fun q => N (row (perm π (enumerate μ.transpose.rowLens q)))) := by - classical - let := Fintype.ofFinite (columnGroup (columnTableau μ)) - unfold polytabloid - rw [map_sum] - let e : Perms μ.transpose.rowLens ≃ columnGroup (columnTableau μ) := - (columnEquiv μ).trans (Equiv.inv _) - symm - apply Fintype.sum_equiv e - intro π - rw [map_smul, wordRep_single] - have hs : signC (e π).val = sg π := by - change signC (columnPerm μ π).val⁻¹ = sg π - rw [signC_inv, columnPerm_sign] - change sg π • _ = signC (e π).val • _ - rw [hs] - congr 1 - funext w - rw [wordMap_single] - unfold Path.pureWord - apply Finset.prod_congr rfl - intro q hq - have hr : row (perm π (enumerate μ.transpose.rowLens q)) = - ((columnTableau μ) ((e π).val⁻¹ q)).val.1 := by - change _ = ((columnTableau μ) (((columnPerm μ π).val⁻¹)⁻¹ q)).val.1 - rw [inv_inv, columnTableau_val] - dsimp only [columnPerm, Equiv.permCongr_apply] - rw [Equiv.apply_symm_apply, Equiv.symm_symm] - exact congrArg (fun j => N j (Path.parts (w q)).1 (Path.parts (w q)).2) hr - -end Saxl.Columns - -end - -end OAI +import OAI.RepresentationTheory.Saxl.PathContraction + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl.Columns +/- A concrete ordered disjoint union of consecutive columns. -/ +@[reducible] def Cells : List ℕ → Type + | [] => Empty + | r :: rs => Fin r ⊕ Cells rs + +instance cellsFintype : (rs : List ℕ) → Fintype (Cells rs) + | [] => inferInstanceAs (Fintype Empty) + | r :: rs => @instFintypeSum (Fin r) (Cells rs) inferInstance (cellsFintype rs) + +instance cellsDecEq : (rs : List ℕ) → DecidableEq (Cells rs) + | [] => inferInstanceAs (DecidableEq Empty) + | r :: rs => @instDecidableEqSum (Fin r) (Cells rs) inferInstance (cellsDecEq rs) + +def row : {rs : List ℕ} → Cells rs → ℕ + | _ :: _, .inl i => i.val + | _ :: _, .inr c => row c + +def col : {rs : List ℕ} → Cells rs → ℕ + | _ :: _, .inl _ => 0 + | _ :: _, .inr c => col c + 1 + +def enumerate : (rs : List ℕ) → Fin rs.sum ≃ Cells rs + | [] => (Equiv.equivOfIsEmpty (Fin 0) Empty) + | r :: rs => finSumFinEquiv.symm.trans ((Equiv.refl (Fin r)).sumCongr (enumerate rs)) + +@[simp] lemma enumerate_left (r : ℕ) (rs : List ℕ) (i : Fin r) : + enumerate (r :: rs) (Fin.castAdd rs.sum i) = Sum.inl i := by + exact congrArg ((Equiv.refl (Fin r)).sumCongr (enumerate rs)) + (finSumFinEquiv_symm_apply_castAdd i) + +@[simp] lemma enumerate_right (r : ℕ) (rs : List ℕ) (i : Fin rs.sum) : + enumerate (r :: rs) (Fin.natAdd r i) = Sum.inr (enumerate rs i) := by + exact congrArg ((Equiv.refl (Fin r)).sumCongr (enumerate rs)) + (finSumFinEquiv_symm_apply_natAdd i) + +@[reducible] def Perms : List ℕ → Type + | [] => Unit + | r :: rs => Equiv.Perm (Fin r) × Perms rs + +instance permsFintype : (rs : List ℕ) → Fintype (Perms rs) + | [] => inferInstanceAs (Fintype Unit) + | r :: rs => @instFintypeProd (Equiv.Perm (Fin r)) (Perms rs) inferInstance (permsFintype rs) + +def perm : {rs : List ℕ} → Perms rs → Equiv.Perm (Cells rs) + | [], _ => Equiv.refl _ + | _ :: _, (π, σ) => Equiv.sumCongr π (perm σ) + +def sg : {rs : List ℕ} → Perms rs → ℂ + | [], _ => 1 + | _ :: _, (π, σ) => (((Equiv.Perm.sign π : ℤ) : ℂ)) * sg σ + +lemma sign_perm {rs : List ℕ} (π : Perms rs) : + (((Equiv.Perm.sign (perm π) : ℤ) : ℂ)) = sg π := by + induction rs with + | nil => simp [perm, sg] + | cons r rs ih => + obtain ⟨π, σ⟩ := π + have hh := congrArg (fun u : ℤˣ => ((u : ℤ) : ℂ)) + (Equiv.Perm.sign_sumCongr π (perm σ)) + exact hh.trans (by simp only [Units.val_mul, Int.cast_mul, ih]; rfl) + +lemma perm_col {rs : List ℕ} (π : Perms rs) (c : Cells rs) : col (perm π c) = col c := by + induction rs with + | nil => exact isEmptyElim c + | cons r rs ih => + obtain ⟨π, σ⟩ := π + cases c with + | inl i => rfl + | inr c => exact congrArg (· + 1) (ih σ c) + +lemma coords_injective (rs : List ℕ) : + Function.Injective (fun c : Cells rs => (row c, col c)) := by + induction rs with + | nil => exact Function.injective_of_subsingleton _ + | cons r rs ih => + intro a b h + cases a with + | inl a => + cases b with + | inl b => exact congrArg Sum.inl (Fin.ext (congrArg Prod.fst h)) + | inr b => have := congrArg Prod.snd h; simp [col] at this + | inr a => + cases b with + | inl b => have := congrArg Prod.snd h; simp [col] at this + | inr b => + apply congrArg Sum.inr + apply ih + dsimp only [row, col] at h + have hr := congrArg Prod.fst h + have hc := congrArg Prod.snd h + exact Prod.ext hr (Nat.add_right_cancel hc) + +lemma coords_range (rs : List ℕ) (i j : ℕ) : + (∃ c : Cells rs, row c = i ∧ col c = j) ↔ ∃ h : j < rs.length, i < rs[j] := by + induction rs generalizing j with + | nil => simp [Cells] + | cons r rs ih => + cases j with + | zero => + constructor + · rintro ⟨c, hr, hc⟩ + cases c with + | inl a => exact ⟨by simp, by simpa [row] using hr ▸ a.isLt⟩ + | inr a => simp [col] at hc + · rintro ⟨h, hi⟩ + exact ⟨Sum.inl ⟨i, hi⟩, rfl, rfl⟩ + | succ j => + constructor + · rintro ⟨c, hr, hc⟩ + cases c with + | inl a => simp [col] at hc + | inr a => + have hj : col a = j := Nat.add_right_cancel hc + obtain ⟨hj, hi⟩ := (ih j).mp ⟨a, hr, hj⟩ + exact ⟨Nat.succ_lt_succ hj, hi⟩ + · rintro ⟨h, hi⟩ + obtain ⟨a, ha, hc⟩ := (ih j).mpr ⟨Nat.lt_of_succ_lt_succ h, hi⟩ + exact ⟨Sum.inr a, ha, congrArg (· + 1) hc⟩ + +/- The matrix product indexed by the actual consecutive position order. -/ +def chain (rs : List ℕ) (p : ℕ) (N : ℕ → Band.Mat) (π : Perms rs) : Band.Mat := + (List.ofFn fun q : Fin rs.sum => Band.D (p + q.val) (N (row (perm π (enumerate rs q))))).prod + +lemma chain_cons (r : ℕ) (rs : List ℕ) (p : ℕ) (N : ℕ → Band.Mat) + (π : Equiv.Perm (Fin r)) (σ : Perms rs) : + chain (r :: rs) p N (π, σ) = + (List.ofFn fun j : Fin r => Band.D (p + j.val) (N (π j).val)).prod * + chain rs (p + r) N σ := by + unfold chain + erw [List.ofFn_add, List.prod_append] + congr 2 + · apply congrArg List.ofFn + funext j + change Band.D (p + j.val) (N (row (@perm (r :: rs) (π, σ) (enumerate (r :: rs) (Fin.castAdd rs.sum j))))) = _ + rw [enumerate_left] + rfl + · apply congrArg List.ofFn + funext j + change Band.D (p + (r + j.val)) (N (row (@perm (r :: rs) (π, σ) (enumerate (r :: rs) (Fin.natAdd r j))))) = _ + erw [enumerate_right r rs (show Fin rs.sum from j)] + simp only [perm, Equiv.sumCongr_apply, Sum.map_inr, row, Nat.add_assoc] + +/- Ordered product of independent alternating column segments. -/ +def segments : ℕ → List ℕ → (ℕ → Band.Mat) → Band.Mat + | _, [], _ => 1 + | p, r :: rs, N => + (∑ π : Equiv.Perm (Fin r), (((Equiv.Perm.sign π : ℤ) : ℂ)) • + (List.ofFn fun i : Fin r => Band.D (p + i.val) (N (π i).val)).prod) * + segments (p+r) rs N + +/- Factorization over independent column permutations, without commuting factors. -/ +lemma sum_chain (rs : List ℕ) (p : ℕ) (N : ℕ → Band.Mat) : + (∑ π : Perms rs, sg π • chain rs p N π) = segments p rs N := by + induction rs generalizing p with + | nil => simp [Perms, chain, sg, segments] + | cons r rs ih => + simp only [Perms, Fintype.sum_prod_type, sg, chain_cons, segments] + simp_rw [← smul_mul_smul_comm, ← Finset.mul_sum, ← Finset.sum_mul, ih] + +lemma perm_injective (rs : List ℕ) : Function.Injective (@perm rs) := by + induction rs with + | nil => exact Function.injective_of_subsingleton _ + | cons r rs ih => + rintro ⟨π, σ⟩ ⟨π', σ'⟩ h + apply Prod.ext + · apply Equiv.ext + intro i + exact Sum.inl.inj (Equiv.congr_fun h (Sum.inl i)) + · apply ih + apply Equiv.ext + intro c + exact Sum.inr.inj (Equiv.congr_fun h (Sum.inr c)) + +lemma perm_surjective (rs : List ℕ) (g : Equiv.Perm (Cells rs)) + (hg : ∀ c, col (g c) = col c) : ∃ π : Perms rs, perm π = g := by + induction rs with + | nil => exact ⟨(), Subsingleton.elim _ _⟩ + | cons r rs ih => + have hm : Set.MapsTo g (Set.range Sum.inl) (Set.range Sum.inl) := by + rintro c ⟨i, rfl⟩ + have hh := hg (Sum.inl i) + cases h : g (Sum.inl i) with + | inl j => exact ⟨j, rfl⟩ + | inr c => simp [h, col] at hh + obtain ⟨⟨π, σ⟩, he⟩ := Equiv.Perm.mem_sumCongrHom_range_of_perm_mapsTo_inl hm + have hs : ∀ c : Cells rs, col (σ c) = col c := by + intro c + have hh := hg (Sum.inr c) + rw [← he] at hh + exact Nat.add_right_cancel hh + obtain ⟨τ, hτ⟩ := ih σ hs + exact ⟨(π, τ), by simp only [perm, hτ]; exact he⟩ + +/- The column-recursive coordinates enumerate the actual Ferrers cells. -/ +def toYoung (μ : YoungDiagram) : Cells μ.transpose.rowLens ≃ μ.cells := by + let f : Cells μ.transpose.rowLens → μ.cells := fun c => + ⟨(row c, col c), by + obtain ⟨hj, hi⟩ := (coords_range μ.transpose.rowLens (row c) (col c)).mp ⟨c, rfl, rfl⟩ + simpa only [YoungDiagram.mem_cells, YoungDiagram.mem_iff_lt_colLen, + YoungDiagram.get_rowLens, YoungDiagram.rowLen_transpose] using hi⟩ + exact Equiv.ofBijective f ⟨fun _ _ h => coords_injective _ (congrArg Subtype.val h), by + intro c + have hmem : c.val.1 < μ.colLen c.val.2 := YoungDiagram.mem_iff_lt_colLen.mp c.property + have hj : c.val.2 < μ.rowLen 0 := YoungDiagram.mem_iff_lt_rowLen.mp + (μ.up_left_mem (Nat.zero_le _) le_rfl c.property) + have hj' : c.val.2 < μ.transpose.rowLens.length := by simpa using hj + obtain ⟨a, ha, hb⟩ := (coords_range μ.transpose.rowLens c.val.1 c.val.2).mpr + ⟨hj', by simpa using hmem⟩ + exact ⟨a, Subtype.ext (Prod.ext ha hb)⟩⟩ + +@[simp] lemma toYoung_val (μ : YoungDiagram) (c : Cells μ.transpose.rowLens) : + (toYoung μ c).val = (row c, col c) := rfl + +lemma row_lt (μ : YoungDiagram) (c : Cells μ.transpose.rowLens) : row c < μ.colLen 0 := + YoungDiagram.mem_iff_lt_colLen.mp + (μ.up_left_mem le_rfl (Nat.zero_le _) (toYoung μ c).property) + + +def columnTableau (μ : YoungDiagram) : Tableau μ.transpose.rowLens.sum μ := + (enumerate μ.transpose.rowLens).trans (toYoung μ) + +@[simp] lemma columnTableau_val (μ : YoungDiagram) (i : Fin μ.transpose.rowLens.sum) : + (columnTableau μ i).val = (row (enumerate μ.transpose.rowLens i), + col (enumerate μ.transpose.rowLens i)) := rfl + +def columnPerm (μ : YoungDiagram) (π : Perms μ.transpose.rowLens) : + columnGroup (columnTableau μ) := + ⟨(enumerate μ.transpose.rowLens).symm.permCongr (perm π), by + intro i + simp only [columnTableau_val, Equiv.permCongr_apply, Equiv.symm_symm, + Equiv.apply_symm_apply] + exact perm_col π _⟩ + +lemma columnPerm_bijective (μ : YoungDiagram) : Function.Bijective (columnPerm μ) := by + constructor + · intro π σ h + apply perm_injective μ.transpose.rowLens + apply (enumerate μ.transpose.rowLens).symm.permCongr.injective + exact congrArg Subtype.val h + · intro g + let e := enumerate μ.transpose.rowLens + obtain ⟨π, hπ⟩ := perm_surjective μ.transpose.rowLens (e.permCongr g.val) (by + intro c + have hh := g.property (e.symm c) + simpa only [columnTableau_val, Equiv.permCongr_apply, e, Equiv.apply_symm_apply] using hh) + refine ⟨π, ?_⟩ + apply Subtype.ext + change e.symm.permCongr (perm π) = g.val + rw [hπ] + apply Equiv.ext + intro i + simp [Equiv.permCongr_apply] + +def columnEquiv (μ : YoungDiagram) : Perms μ.transpose.rowLens ≃ columnGroup (columnTableau μ) := + Equiv.ofBijective (columnPerm μ) (columnPerm_bijective μ) + +lemma columnPerm_sign (μ : YoungDiagram) (π : Perms μ.transpose.rowLens) : + signC (columnPerm μ π).val = sg π := by + change (((Equiv.Perm.sign ((enumerate μ.transpose.rowLens).symm.permCongr (perm π)) : ℤ) : ℂ)) = sg π + rw [Equiv.Perm.sign_permCongr] + exact sign_perm π + +lemma mapped_columnTableau (μ : YoungDiagram) (N : ℕ → Band.Mat) : + wordMap (fun (i : Fin (μ.colLen 0)) (a : Fin 4) => + N i.val (Path.parts a).1 (Path.parts a).2) (polytabloid (columnTableau μ)) = + ∑ π : Perms μ.transpose.rowLens, sg π • Path.pureWord + (fun q => N (row (perm π (enumerate μ.transpose.rowLens q)))) := by + classical + let := Fintype.ofFinite (columnGroup (columnTableau μ)) + unfold polytabloid + rw [map_sum] + let e : Perms μ.transpose.rowLens ≃ columnGroup (columnTableau μ) := + (columnEquiv μ).trans (Equiv.inv _) + symm + apply Fintype.sum_equiv e + intro π + rw [map_smul, wordRep_single] + have hs : signC (e π).val = sg π := by + change signC (columnPerm μ π).val⁻¹ = sg π + rw [signC_inv, columnPerm_sign] + change sg π • _ = signC (e π).val • _ + rw [hs] + congr 1 + funext w + rw [wordMap_single] + unfold Path.pureWord + apply Finset.prod_congr rfl + intro q hq + have hr : row (perm π (enumerate μ.transpose.rowLens q)) = + ((columnTableau μ) ((e π).val⁻¹ q)).val.1 := by + change _ = ((columnTableau μ) (((columnPerm μ π).val⁻¹)⁻¹ q)).val.1 + rw [inv_inv, columnTableau_val] + dsimp only [columnPerm, Equiv.permCongr_apply] + rw [Equiv.apply_symm_apply, Equiv.symm_symm] + exact congrArg (fun j => N j (Path.parts (w q)).1 (Path.parts (w q)).2) hr + +end Saxl.Columns + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/CoordinateSector.lean b/lean/OAI/RepresentationTheory/Saxl/CoordinateSector.lean index 9e5578b0f74acfb955b306e99c8ebabea0a1429b..bce1188e5e1d63b68c52f008e01847af129c3e4f 100644 --- a/lean/OAI/RepresentationTheory/Saxl/CoordinateSector.lean +++ b/lean/OAI/RepresentationTheory/Saxl/CoordinateSector.lean @@ -1,209 +1,209 @@ -import OAI.RepresentationTheory.Saxl.HighProjection - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl -/- Coordinate projection; equivariance is asserted only for preserved predicates. -/ -def coordinateProjection {n d : ℕ} (P : (Fin n → Fin d) → Prop) : - Module.End ℂ (WordSpace n d) := by - classical - exact { - toFun := fun x a => if P a then x a else 0 - map_add' := by intros; funext a; by_cases h : P a <;> simp [h] - map_smul' := by intros; funext a; by_cases h : P a <;> simp [h] } - -@[simp] lemma coordinateProjection_apply {n d : ℕ} (P : (Fin n → Fin d) → Prop) - (x : WordSpace n d) (a : Fin n → Fin d) [Decidable (P a)] : - coordinateProjection P x a = if P a then x a else 0 := by - classical - by_cases h : P a <;> simp [coordinateProjection, h] - -lemma coordinateProjection_single {n d : ℕ} (P : (Fin n → Fin d) → Prop) - (a : Fin n → Fin d) [Decidable (P a)] : - coordinateProjection P (Pi.single a 1) = if P a then Pi.single a 1 else 0 := by - classical - ext b - by_cases he : b = a - · subst b; by_cases h : P a <;> simp [h] - · by_cases h : P a <;> simp [he, h] - -/- Permutations preserving a position sector. -/ -def sectorGroup {n : ℕ} (D : Fin n → Prop) : Subgroup (Equiv.Perm (Fin n)) where - carrier := {g | ∀ i, D (g i) ↔ D i} - one_mem' _ := Iff.rfl - mul_mem' hg hh i := (hg _).trans (hh i) - inv_mem' := by - intro g hg i - simpa using (hg (g⁻¹ i)).symm - -/- The genuine unnormalized signed block alternation. -/ -def altWord {n d : ℕ} (G : Subgroup (Equiv.Perm (Fin n))) (a : Fin n → Fin d) : - WordSpace n d := by - classical - letI := Fintype.ofFinite G - exact ∑ g : G, signC (g : Equiv.Perm (Fin n)) • - wordRep n d (g : Equiv.Perm (Fin n)) (Pi.single a 1) - -lemma altWord_move {n d : ℕ} (G : Subgroup (Equiv.Perm (Fin n))) - (a : Fin n → Fin d) (r : G) : - altWord G (a ∘ (r : Equiv.Perm (Fin n))) = - signC (r : Equiv.Perm (Fin n)) • altWord G a := by - classical - let := Fintype.ofFinite G - have he : Pi.single (a ∘ (r : Equiv.Perm (Fin n))) (1 : ℂ) = - wordRep n d (r⁻¹ : G) (Pi.single a 1) := by - rw [wordRep_single] - rfl - unfold altWord - rw [he] - simp only [← Module.End.mul_apply, ← map_mul, Subgroup.coe_inv, Finset.smul_sum] - apply (Equiv.sum_comp (Equiv.mulRight r) _).symm.trans - apply Finset.sum_congr rfl - intro g hg - change signC ((g*r : G) : Equiv.Perm (Fin n)) • - wordRep n d (((g*r : G) : Equiv.Perm (Fin n)) * (r : Equiv.Perm (Fin n))⁻¹) (Pi.single a 1) = _ - simp only [Subgroup.coe_mul, map_mul, mul_inv_cancel_right, smul_smul] - rw [mul_comm (signC (g : Equiv.Perm (Fin n)))] - -/- Keeping a prescribed coloring restricts the alternating group to its -sector stabilizer. This is the finite coset calculation behind block-factorization. -/ -theorem altWord_sector {n d : ℕ} (G : Subgroup (Equiv.Perm (Fin n))) - (a : Fin n → Fin d) (Q : Fin d → Prop) (D : Fin n → Prop) - (ha : ∀ i, Q (a i) ↔ D i) : - coordinateProjection (fun b => ∀ i, Q (b i) ↔ D i) (altWord G a) = - altWord (G ⊓ sectorGroup D) a := by - classical - let := Fintype.ofFinite G - let := Fintype.ofFinite ↥(G ⊓ sectorGroup D) - have hh (g : G) : - (∀ i, Q ((a ∘ ((g : Equiv.Perm (Fin n))⁻¹ : Equiv.Perm (Fin n))) i) ↔ D i) ↔ - (g : Equiv.Perm (Fin n)) ∈ sectorGroup D := by - constructor - · intro h i - have h' := (ha _).symm.trans (h ((g : Equiv.Perm (Fin n)) i)) - simpa using h'.symm - · intro h i - exact (ha _).trans (by simpa using (h (((g : Equiv.Perm (Fin n))⁻¹) i)).symm) - unfold altWord - simp only [map_sum, map_smul, wordRep_single, coordinateProjection_single, hh, smul_ite, smul_zero] - let e : {g : G // (g : Equiv.Perm (Fin n)) ∈ sectorGroup D} ≃ ↥(G ⊓ sectorGroup D) := { - toFun := fun g => ⟨g.val.val, g.val.property, g.property⟩ - invFun := fun g => ⟨⟨g.val, g.property.1⟩, g.property.2⟩ - left_inv := fun _ => rfl - right_inv := fun _ => rfl } - rw [← Finset.sum_filter] - rw [← Finset.sum_attach] - apply Fintype.sum_equiv ?_ _ _ ?_ - · exact (Equiv.subtypeEquivRight (fun g => by simp)).trans e - · intro g - rfl - -end Saxl - -namespace Saxl -/- The prescribed high sector in the actual staircase enumeration. -/ -def stairHigh (h s : ℕ) (i : Fin (staircase (h+s)).card) : Prop := - (stairTableau (h+s) i).val.1 + (stairTableau (h+s) i).val.2 < h - -lemma staircase_projected_sector (h s : ℕ) : - sameHighProjection _ _ _ s (staircaseWord (h+s)) = - coordinateProjection (fun w => (∀ i, s ≤ (splitLeft w i).val ↔ stairHigh h s i) ∧ - (∀ i, s ≤ (splitRight w i).val ↔ stairHigh h s i)) (staircaseWord (h+s)) := by - classical - ext w - by_cases he : ∀ i, s ≤ (splitLeft w i).val ↔ s ≤ (splitRight w i).val - · by_cases hw : sameHighProjection _ _ _ s (staircaseWord (h+s)) w = 0 - · have hw' : staircaseWord (h+s) w = 0 := by simpa [sameHighProjection, he] using hw - simp [hw, hw'] - · have hD := staircase_projected_high_positions h s w hw - have hD' : ∀ i, s ≤ (splitRight w i).val ↔ stairHigh h s i := - fun i => (he i).symm.trans (hD i) - simp [sameHighProjection, he, hD', stairHigh] - · have hn : ¬ ((∀ i, s ≤ (splitLeft w i).val ↔ stairHigh h s i) ∧ - (∀ i, s ≤ (splitRight w i).val ↔ stairHigh h s i)) := by - rintro ⟨h₁,h₂⟩ - exact he (fun i => (h₁ i).trans (h₂ i).symm) - simp [sameHighProjection, he, hn] - -lemma coordinateProjection_tensor {n d e : ℕ} - (P : (Fin n → Fin d) → Prop) (Q : (Fin n → Fin e) → Prop) - (x : WordSpace n d) (y : WordSpace n e) : - coordinateProjection (fun w => P (splitLeft w) ∧ Q (splitRight w)) - (wordTensor n d e (x ⊗ₜ[ℂ] y)) = - wordTensor n d e (coordinateProjection P x ⊗ₜ[ℂ] coordinateProjection Q y) := by - classical - ext w - by_cases hp : P (splitLeft w) <;> by_cases hq : Q (splitRight w) <;> - simp [hp,hq] - -lemma altWord_sector_rotated {n d : ℕ} (G : Subgroup (Equiv.Perm (Fin n))) - (a : Fin n → Fin d) (Q : Fin d → Prop) (D : Fin n → Prop) (r : G) - (ha : ∀ i, Q ((a ∘ (r : Equiv.Perm (Fin n))) i) ↔ D i) : - coordinateProjection (fun b => ∀ i, Q (b i) ↔ D i) (altWord G a) = - signC (r : Equiv.Perm (Fin n)) • altWord (G ⊓ sectorGroup D) (a ∘ (r : Equiv.Perm (Fin n))) := by - have hh := altWord_sector G (a ∘ (r : Equiv.Perm (Fin n))) Q D ha - rw [altWord_move, map_smul] at hh - rw [← hh, smul_smul, signC_mul_self, one_smul] - -lemma polytabloid_eq_altWord {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - polytabloid t = altWord (columnGroup t) (rowWord t) := rfl - -/- The cut's two layers, with their exact retained row and column permutations. -/ -def cutRowWord (h s : ℕ) := - altWord (columnGroup (stairRowTableau (h+s)) ⊓ sectorGroup (stairHigh h s)) - (rowWord (stairRowTableau (h+s)) ∘ (rotateRowPositions h s : Equiv.Perm _)) - -def cutColumnWord (h s : ℕ) := - altWord (columnGroup (stairTableau (h+s)) ⊓ sectorGroup (stairHigh h s)) - (rowWord (stairTableau (h+s)) ∘ (rotateColumnPositions h s : Equiv.Perm _)) - -lemma rotatePositions_sign (h s : ℕ) : - signC (rotateColumnPositions h s : Equiv.Perm (Fin (staircase (h+s)).card)) = - signC (rotateRowPositions h s : Equiv.Perm (Fin (staircase (h+s)).card)) := by - let q : Equiv.Perm (Fin (staircase (h+s)).card) := - ((stairTableau (h+s)).trans (staircaseSwap (h+s))).trans (stairTableau (h+s)).symm - have he : (rotateColumnPositions h s : Equiv.Perm (Fin (staircase (h+s)).card)) = - q * (rotateRowPositions h s : Equiv.Perm (Fin (staircase (h+s)).card)) * q := by - ext i - simp [q, rotateColumnPositions, rotateRowPositions, rotateColumn] - rw [he, map_mul, map_mul] - calc - signC q * signC (rotateRowPositions h s : Equiv.Perm (Fin (staircase (h+s)).card)) * signC q = - signC (rotateRowPositions h s : Equiv.Perm (Fin (staircase (h+s)).card)) * (signC q * signC q) := by ring - _ = _ := by rw [signC_mul_self, mul_one] - -/- Exact sign cancellation in the two retained layers. -/ -theorem staircase_cut_layers (h s : ℕ) : - sameHighProjection _ _ _ s (staircaseWord (h+s)) = - wordTensor _ _ _ (cutRowWord h s ⊗ₜ[ℂ] cutColumnWord h s) := by - rw [staircase_projected_sector, staircaseWord] - rw [coordinateProjection_tensor - (fun a : Fin (staircase (h+s)).card → Fin ((staircase (h+s)).colLen 0) => - ∀ i, s ≤ (a i).val ↔ stairHigh h s i) - (fun a : Fin (staircase (h+s)).card → Fin ((staircase (h+s)).colLen 0) => - ∀ i, s ≤ (a i).val ↔ stairHigh h s i)] - have hr := altWord_sector_rotated (columnGroup (stairRowTableau (h+s))) - (rowWord (stairRowTableau (h+s))) (fun a => s ≤ a.val) (stairHigh h s) - (rotateRowPositions h s) (by - intro i - simpa [rowWord, stairRowTableau, rotateRowPositions, stairHigh, staircaseSwap] using - rotateRow_high h s (stairTableau (h+s) i)) - have hc := altWord_sector_rotated (columnGroup (stairTableau (h+s))) - (rowWord (stairTableau (h+s))) (fun a => s ≤ a.val) (stairHigh h s) - (rotateColumnPositions h s) (by - intro i - simpa [rowWord, rotateColumnPositions, stairHigh] using - rotateColumn_high h s (stairTableau (h+s) i)) - rw [polytabloid_eq_altWord, polytabloid_eq_altWord, hr, hc] - rw [TensorProduct.smul_tmul_smul, rotatePositions_sign, signC_mul_self, one_smul] - rfl - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.HighProjection + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl +/- Coordinate projection; equivariance is asserted only for preserved predicates. -/ +def coordinateProjection {n d : ℕ} (P : (Fin n → Fin d) → Prop) : + Module.End ℂ (WordSpace n d) := by + classical + exact { + toFun := fun x a => if P a then x a else 0 + map_add' := by intros; funext a; by_cases h : P a <;> simp [h] + map_smul' := by intros; funext a; by_cases h : P a <;> simp [h] } + +@[simp] lemma coordinateProjection_apply {n d : ℕ} (P : (Fin n → Fin d) → Prop) + (x : WordSpace n d) (a : Fin n → Fin d) [Decidable (P a)] : + coordinateProjection P x a = if P a then x a else 0 := by + classical + by_cases h : P a <;> simp [coordinateProjection, h] + +lemma coordinateProjection_single {n d : ℕ} (P : (Fin n → Fin d) → Prop) + (a : Fin n → Fin d) [Decidable (P a)] : + coordinateProjection P (Pi.single a 1) = if P a then Pi.single a 1 else 0 := by + classical + ext b + by_cases he : b = a + · subst b; by_cases h : P a <;> simp [h] + · by_cases h : P a <;> simp [he, h] + +/- Permutations preserving a position sector. -/ +def sectorGroup {n : ℕ} (D : Fin n → Prop) : Subgroup (Equiv.Perm (Fin n)) where + carrier := {g | ∀ i, D (g i) ↔ D i} + one_mem' _ := Iff.rfl + mul_mem' hg hh i := (hg _).trans (hh i) + inv_mem' := by + intro g hg i + simpa using (hg (g⁻¹ i)).symm + +/- The genuine unnormalized signed block alternation. -/ +def altWord {n d : ℕ} (G : Subgroup (Equiv.Perm (Fin n))) (a : Fin n → Fin d) : + WordSpace n d := by + classical + letI := Fintype.ofFinite G + exact ∑ g : G, signC (g : Equiv.Perm (Fin n)) • + wordRep n d (g : Equiv.Perm (Fin n)) (Pi.single a 1) + +lemma altWord_move {n d : ℕ} (G : Subgroup (Equiv.Perm (Fin n))) + (a : Fin n → Fin d) (r : G) : + altWord G (a ∘ (r : Equiv.Perm (Fin n))) = + signC (r : Equiv.Perm (Fin n)) • altWord G a := by + classical + let := Fintype.ofFinite G + have he : Pi.single (a ∘ (r : Equiv.Perm (Fin n))) (1 : ℂ) = + wordRep n d (r⁻¹ : G) (Pi.single a 1) := by + rw [wordRep_single] + rfl + unfold altWord + rw [he] + simp only [← Module.End.mul_apply, ← map_mul, Subgroup.coe_inv, Finset.smul_sum] + apply (Equiv.sum_comp (Equiv.mulRight r) _).symm.trans + apply Finset.sum_congr rfl + intro g hg + change signC ((g*r : G) : Equiv.Perm (Fin n)) • + wordRep n d (((g*r : G) : Equiv.Perm (Fin n)) * (r : Equiv.Perm (Fin n))⁻¹) (Pi.single a 1) = _ + simp only [Subgroup.coe_mul, map_mul, mul_inv_cancel_right, smul_smul] + rw [mul_comm (signC (g : Equiv.Perm (Fin n)))] + +/- Keeping a prescribed coloring restricts the alternating group to its +sector stabilizer. This is the finite coset calculation behind block-factorization. -/ +theorem altWord_sector {n d : ℕ} (G : Subgroup (Equiv.Perm (Fin n))) + (a : Fin n → Fin d) (Q : Fin d → Prop) (D : Fin n → Prop) + (ha : ∀ i, Q (a i) ↔ D i) : + coordinateProjection (fun b => ∀ i, Q (b i) ↔ D i) (altWord G a) = + altWord (G ⊓ sectorGroup D) a := by + classical + let := Fintype.ofFinite G + let := Fintype.ofFinite ↥(G ⊓ sectorGroup D) + have hh (g : G) : + (∀ i, Q ((a ∘ ((g : Equiv.Perm (Fin n))⁻¹ : Equiv.Perm (Fin n))) i) ↔ D i) ↔ + (g : Equiv.Perm (Fin n)) ∈ sectorGroup D := by + constructor + · intro h i + have h' := (ha _).symm.trans (h ((g : Equiv.Perm (Fin n)) i)) + simpa using h'.symm + · intro h i + exact (ha _).trans (by simpa using (h (((g : Equiv.Perm (Fin n))⁻¹) i)).symm) + unfold altWord + simp only [map_sum, map_smul, wordRep_single, coordinateProjection_single, hh, smul_ite, smul_zero] + let e : {g : G // (g : Equiv.Perm (Fin n)) ∈ sectorGroup D} ≃ ↥(G ⊓ sectorGroup D) := { + toFun := fun g => ⟨g.val.val, g.val.property, g.property⟩ + invFun := fun g => ⟨⟨g.val, g.property.1⟩, g.property.2⟩ + left_inv := fun _ => rfl + right_inv := fun _ => rfl } + rw [← Finset.sum_filter] + rw [← Finset.sum_attach] + apply Fintype.sum_equiv ?_ _ _ ?_ + · exact (Equiv.subtypeEquivRight (fun g => by simp)).trans e + · intro g + rfl + +end Saxl + +namespace Saxl +/- The prescribed high sector in the actual staircase enumeration. -/ +def stairHigh (h s : ℕ) (i : Fin (staircase (h+s)).card) : Prop := + (stairTableau (h+s) i).val.1 + (stairTableau (h+s) i).val.2 < h + +lemma staircase_projected_sector (h s : ℕ) : + sameHighProjection _ _ _ s (staircaseWord (h+s)) = + coordinateProjection (fun w => (∀ i, s ≤ (splitLeft w i).val ↔ stairHigh h s i) ∧ + (∀ i, s ≤ (splitRight w i).val ↔ stairHigh h s i)) (staircaseWord (h+s)) := by + classical + ext w + by_cases he : ∀ i, s ≤ (splitLeft w i).val ↔ s ≤ (splitRight w i).val + · by_cases hw : sameHighProjection _ _ _ s (staircaseWord (h+s)) w = 0 + · have hw' : staircaseWord (h+s) w = 0 := by simpa [sameHighProjection, he] using hw + simp [hw, hw'] + · have hD := staircase_projected_high_positions h s w hw + have hD' : ∀ i, s ≤ (splitRight w i).val ↔ stairHigh h s i := + fun i => (he i).symm.trans (hD i) + simp [sameHighProjection, he, hD', stairHigh] + · have hn : ¬ ((∀ i, s ≤ (splitLeft w i).val ↔ stairHigh h s i) ∧ + (∀ i, s ≤ (splitRight w i).val ↔ stairHigh h s i)) := by + rintro ⟨h₁,h₂⟩ + exact he (fun i => (h₁ i).trans (h₂ i).symm) + simp [sameHighProjection, he, hn] + +lemma coordinateProjection_tensor {n d e : ℕ} + (P : (Fin n → Fin d) → Prop) (Q : (Fin n → Fin e) → Prop) + (x : WordSpace n d) (y : WordSpace n e) : + coordinateProjection (fun w => P (splitLeft w) ∧ Q (splitRight w)) + (wordTensor n d e (x ⊗ₜ[ℂ] y)) = + wordTensor n d e (coordinateProjection P x ⊗ₜ[ℂ] coordinateProjection Q y) := by + classical + ext w + by_cases hp : P (splitLeft w) <;> by_cases hq : Q (splitRight w) <;> + simp [hp,hq] + +lemma altWord_sector_rotated {n d : ℕ} (G : Subgroup (Equiv.Perm (Fin n))) + (a : Fin n → Fin d) (Q : Fin d → Prop) (D : Fin n → Prop) (r : G) + (ha : ∀ i, Q ((a ∘ (r : Equiv.Perm (Fin n))) i) ↔ D i) : + coordinateProjection (fun b => ∀ i, Q (b i) ↔ D i) (altWord G a) = + signC (r : Equiv.Perm (Fin n)) • altWord (G ⊓ sectorGroup D) (a ∘ (r : Equiv.Perm (Fin n))) := by + have hh := altWord_sector G (a ∘ (r : Equiv.Perm (Fin n))) Q D ha + rw [altWord_move, map_smul] at hh + rw [← hh, smul_smul, signC_mul_self, one_smul] + +lemma polytabloid_eq_altWord {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + polytabloid t = altWord (columnGroup t) (rowWord t) := rfl + +/- The cut's two layers, with their exact retained row and column permutations. -/ +def cutRowWord (h s : ℕ) := + altWord (columnGroup (stairRowTableau (h+s)) ⊓ sectorGroup (stairHigh h s)) + (rowWord (stairRowTableau (h+s)) ∘ (rotateRowPositions h s : Equiv.Perm _)) + +def cutColumnWord (h s : ℕ) := + altWord (columnGroup (stairTableau (h+s)) ⊓ sectorGroup (stairHigh h s)) + (rowWord (stairTableau (h+s)) ∘ (rotateColumnPositions h s : Equiv.Perm _)) + +lemma rotatePositions_sign (h s : ℕ) : + signC (rotateColumnPositions h s : Equiv.Perm (Fin (staircase (h+s)).card)) = + signC (rotateRowPositions h s : Equiv.Perm (Fin (staircase (h+s)).card)) := by + let q : Equiv.Perm (Fin (staircase (h+s)).card) := + ((stairTableau (h+s)).trans (staircaseSwap (h+s))).trans (stairTableau (h+s)).symm + have he : (rotateColumnPositions h s : Equiv.Perm (Fin (staircase (h+s)).card)) = + q * (rotateRowPositions h s : Equiv.Perm (Fin (staircase (h+s)).card)) * q := by + ext i + simp [q, rotateColumnPositions, rotateRowPositions, rotateColumn] + rw [he, map_mul, map_mul] + calc + signC q * signC (rotateRowPositions h s : Equiv.Perm (Fin (staircase (h+s)).card)) * signC q = + signC (rotateRowPositions h s : Equiv.Perm (Fin (staircase (h+s)).card)) * (signC q * signC q) := by ring + _ = _ := by rw [signC_mul_self, mul_one] + +/- Exact sign cancellation in the two retained layers. -/ +theorem staircase_cut_layers (h s : ℕ) : + sameHighProjection _ _ _ s (staircaseWord (h+s)) = + wordTensor _ _ _ (cutRowWord h s ⊗ₜ[ℂ] cutColumnWord h s) := by + rw [staircase_projected_sector, staircaseWord] + rw [coordinateProjection_tensor + (fun a : Fin (staircase (h+s)).card → Fin ((staircase (h+s)).colLen 0) => + ∀ i, s ≤ (a i).val ↔ stairHigh h s i) + (fun a : Fin (staircase (h+s)).card → Fin ((staircase (h+s)).colLen 0) => + ∀ i, s ≤ (a i).val ↔ stairHigh h s i)] + have hr := altWord_sector_rotated (columnGroup (stairRowTableau (h+s))) + (rowWord (stairRowTableau (h+s))) (fun a => s ≤ a.val) (stairHigh h s) + (rotateRowPositions h s) (by + intro i + simpa [rowWord, stairRowTableau, rotateRowPositions, stairHigh, staircaseSwap] using + rotateRow_high h s (stairTableau (h+s) i)) + have hc := altWord_sector_rotated (columnGroup (stairTableau (h+s))) + (rowWord (stairTableau (h+s))) (fun a => s ≤ a.val) (stairHigh h s) + (rotateColumnPositions h s) (by + intro i + simpa [rowWord, rotateColumnPositions, stairHigh] using + rotateColumn_high h s (stairTableau (h+s) i)) + rw [polytabloid_eq_altWord, polytabloid_eq_altWord, hr, hc] + rw [TensorProduct.smul_tmul_smul, rotatePositions_sign, signC_mul_self, one_smul] + rfl + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/CyclicSector.lean b/lean/OAI/RepresentationTheory/Saxl/CyclicSector.lean index 77fe7668c1e8cf86b705c22e47f059665606a13e..e6cd3ae422ebc362df7c04e99c73f6ae712b842c 100644 --- a/lean/OAI/RepresentationTheory/Saxl/CyclicSector.lean +++ b/lean/OAI/RepresentationTheory/Saxl/CyclicSector.lean @@ -1,279 +1,279 @@ -import OAI.RepresentationTheory.Saxl.BandPairing - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uG uX uY uZ uV - -namespace Saxl - -/- Explicit finite-group induction on a linear map. -/ -def averagedMap {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [Fintype G] - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - (ρ : Representation ℂ G X) (σ : Representation ℂ G Y) (f : X →ₗ[ℂ] Y) : - Representation.IntertwiningMap ρ σ where - toLinearMap := ∑ g : G, (σ g).comp (f.comp (ρ g⁻¹)) - isIntertwining' h := by - apply LinearMap.ext - intro x - simp only [LinearMap.comp_apply, LinearMap.sum_apply] - rw [map_sum] - apply (Equiv.sum_comp (Equiv.mulLeft h) _).symm.trans - apply Finset.sum_congr rfl - intro g hg - change σ (h*g) (f (ρ (h*g)⁻¹ (ρ h x))) = σ h (σ g (f (ρ g⁻¹ x))) - simp only [mul_inv_rev, map_mul, Module.End.mul_apply] - have he : ρ h⁻¹ (ρ h x) = x := by - rw [← Module.End.mul_apply, ← map_mul, inv_mul_cancel, map_one] - rfl - rw [he] - -lemma averagedMap_apply {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [Fintype G] - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - (ρ : Representation ℂ G X) (σ : Representation ℂ G Y) (f : X →ₗ[ℂ] Y) (x : X) : - averagedMap ρ σ f x = ∑ g : G, σ g (f (ρ g⁻¹ x)) := by - simp only [averagedMap, Representation.IntertwiningMap.coe_mk, LinearMap.sum_apply, - LinearMap.comp_apply] - -/- Coordinate-sector induction, in precisely the nonzero-Hom form used in -the staircase induction. The projector kills translates outside the stabilizer. -/ -theorem sector_average_nonzero {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [Fintype G] - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - (ρ : Representation ℂ G X) (σ : Representation ℂ G Y) - (H : Subgroup G) (f : X →ₗ[ℂ] Y) (hf : f ≠ 0) - (he : ∀ g ∈ H, ∀ x, f (ρ g x) = σ g (f x)) - (P : Y →ₗ[ℂ] Y) (hP : ∀ x, P (f x) = f x) - (hkill : ∀ g ∉ H, ∀ x, P (σ g (f x)) = 0) : - averagedMap ρ σ f ≠ 0 := by - classical - have hproj (x : X) : P (averagedMap ρ σ f x) = - ((Finset.univ.filter (fun g : G => g ∈ H)).card : ℂ) • f x := by - rw [averagedMap_apply, map_sum] - have hh (g : G) : P (σ g (f (ρ g⁻¹ x))) = if g ∈ H then f x else 0 := by - by_cases hg : g ∈ H - · rw [ite_eq_left hg, ← he g hg, ← Module.End.mul_apply, ← map_mul, - mul_inv_cancel, map_one] - exact hP x - · rw [ite_eq_right hg] - exact hkill g hg _ - simp only [hh] - simp [Finset.sum_ite, Nat.cast_smul_eq_nsmul] - have hc : ((Finset.univ.filter (fun g : G => g ∈ H)).card : ℂ) ≠ 0 := by - apply Nat.cast_ne_zero.mpr - exact ne_of_gt (Finset.card_pos.mpr ⟨1, by simp⟩) - intro hz - apply hf - ext x - have heq := hproj x - rw [hz] at heq - change P 0 = _ at heq - rw [map_zero] at heq - exact (smul_eq_zero.mp heq.symm).resolve_left hc - -open scoped MonoidAlgebra - -theorem intertwining_lift_surjective {G : Type uG} {X : Type uX} {Y : Type uY} {Z : Type uZ} - [Group G] [Finite G] [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] [AddCommGroup Z] [Module ℂ Z] - {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} - {τ : Representation ℂ G Z} - (F : Representation.IntertwiningMap ρ σ) (hF : Function.Surjective F) - (f : Representation.IntertwiningMap τ σ) : - ∃ h : Representation.IntertwiningMap τ ρ, F.comp h = f := by - let EF := Representation.IntertwiningMap.equivLinearMapAsModule ρ σ - let EH := Representation.IntertwiningMap.equivLinearMapAsModule τ ρ - let Ef := Representation.IntertwiningMap.equivLinearMapAsModule τ σ - obtain ⟨h, hh⟩ := IsSemisimpleModule.lifting_property (EF F) hF (Ef f) - refine ⟨EH.symm h, ?_⟩ - ext z - exact LinearMap.congr_fun hh z - -end Saxl - -namespace Saxl - -def wordSector {n d : ℕ} (D : Fin n → Prop) (A : Fin d → Prop) - (w : Fin n → Fin d) : Prop := ∀ i, A (w i) ↔ D i - -/- Concrete sector averaging produces a constituent of the full cyclic -module from an equivariant map on its coordinate sector. -/ -theorem sector_support_transfer {n d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (D : Fin n → Prop) (A : Fin d → Prop) (z : WordSpace n d) - (f : X →ₗ[ℂ] WordSpace n d) (hf : f ≠ 0) - (he : ∀ g ∈ sectorGroup D, ∀ x, f (ρ g x) = wordRep n d g (f x)) - (hm : ∀ x, f x ∈ cyclic (wordRep n d) z) - (hs : ∀ x w, f x w ≠ 0 → wordSector D A w) : - ∃ F : Representation.IntertwiningMap ρ (cyclic (wordRep n d) z).toRepresentation, - F ≠ 0 := by - classical - let P := coordinateProjection (wordSector D A) - have hP (x) : P (f x) = f x := by - ext w - change (if wordSector D A w then f x w else 0) = _ - split_ifs with h - · rfl - · exact (not_ne_iff.mp (fun hh => h (hs x w hh))).symm - have hk (g : Equiv.Perm (Fin n)) (hg : g ∉ sectorGroup D) (x) : - P (wordRep n d g (f x)) = 0 := by - ext w - change (if wordSector D A w then f x (w ∘ g) else 0) = 0 - split_ifs with hw - · by_contra hn - have hh := hs x (w ∘ g) hn - apply hg - intro i - exact (hw (g i)).symm.trans (hh i) - · rfl - let F := averagedMap ρ (wordRep n d) f - have hF : F ≠ 0 := sector_average_nonzero ρ (wordRep n d) (sectorGroup D) f hf he P hP hk - have hmem (x) : F x ∈ cyclic (wordRep n d) z := by - rw [show F x = _ from averagedMap_apply ρ (wordRep n d) f x] - apply Submodule.sum_mem - intro g hg - exact (cyclic (wordRep n d) z).apply_mem_toSubmodule g (hm _) - let G : Representation.IntertwiningMap ρ (cyclic (wordRep n d) z).toRepresentation := - { toLinearMap := F.toLinearMap.codRestrict _ hmem - isIntertwining' := by - intro g - apply LinearMap.ext - intro x - apply Subtype.ext - exact LinearMap.congr_fun (F.isIntertwining' g) x } - refine ⟨G, ?_⟩ - intro hz - apply hF - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - exact congrArg Subtype.val (congrArg (fun l => l x) hz) - -lemma intertwiner_cyclic_mem {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} - (F : Representation.IntertwiningMap ρ σ) (v : X) (x : X) (hx : x ∈ cyclic ρ v) : - F x ∈ cyclic σ (F v) := by - change x ∈ Submodule.span ℂ _ at hx - induction hx using Submodule.span_induction with - | mem x hx => - obtain ⟨g,rfl⟩ := hx - change F (ρ g v) ∈ _ - have hF : F (ρ g v) = σ g (F v) := LinearMap.congr_fun (F.isIntertwining' g) v - rw [hF] - exact (cyclic σ (F v)).apply_mem_toSubmodule g (mem_cyclic _ _) - | zero => rw [map_zero]; exact Submodule.zero_mem _ - | add x y hx hy ihx ihy => rw [map_add]; exact Submodule.add_mem _ ihx ihy - | smul c x hx ih => rw [map_smul]; exact Submodule.smul_mem _ c ih - -def cyclicMap {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} - (F : Representation.IntertwiningMap ρ σ) (v : X) : - Representation.IntertwiningMap (cyclic ρ v).toRepresentation (cyclic σ (F v)).toRepresentation where - toLinearMap := (F.toLinearMap.comp (cyclic ρ v).toSubmodule.subtype).codRestrict _ - (fun x => intertwiner_cyclic_mem F v x.val x.property) - isIntertwining' g := by - apply LinearMap.ext - intro x - apply Subtype.ext - exact LinearMap.congr_fun (F.isIntertwining' g) x.val - -lemma cyclicMap_surjective {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} - (F : Representation.IntertwiningMap ρ σ) (v : X) : Function.Surjective (cyclicMap F v) := by - intro y - have hy := y.property - change y.val ∈ Submodule.span ℂ _ at hy - suffices ∃ x : (cyclic ρ v).toSubmodule, (cyclicMap F v x).val = y.val by - obtain ⟨x,hx⟩ := this - exact ⟨x,Subtype.ext hx⟩ - generalize hz : y.val = z at hy ⊢ - clear y hz - induction hy using Submodule.span_induction with - | mem z hz => - obtain ⟨g,rfl⟩ := hz - refine ⟨(cyclic ρ v).toRepresentation g ⟨v,mem_cyclic _ _⟩, ?_⟩ - change F (ρ g v) = σ g (F v) - exact LinearMap.congr_fun (F.isIntertwining' g) v - | zero => exact ⟨0,map_zero F⟩ - | add x y hx hy ihx ihy => - obtain ⟨u,hu⟩ := ihx - obtain ⟨w,hw⟩ := ihy - refine ⟨u+w, ?_⟩ - change F (u.val+w.val) = _ - rw [map_add,show F u.val = x from hu,show F w.val = y from hw] - | smul c x hx ih => - obtain ⟨u,hu⟩ := ih - refine ⟨c • u, ?_⟩ - change F (c • u.val) = _ - rw [map_smul,show F u.val = x from hu] - -/- A genuine equivariant projection of a cyclic generator transfers every -nonzero constituent map back to the original cyclic module by Maschke. -/ -theorem cyclic_projection_support {G : Type uG} {X : Type uX} {Y : Type uY} {Z : Type uZ} [Group G] [Finite G] - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - [AddCommGroup Z] [Module ℂ Z] - {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} {τ : Representation ℂ G Z} - (F : Representation.IntertwiningMap ρ σ) (v : X) - (f : Representation.IntertwiningMap τ (cyclic σ (F v)).toRepresentation) (hf : f ≠ 0) : - ∃ g : Representation.IntertwiningMap τ (cyclic ρ v).toRepresentation, g ≠ 0 := by - obtain ⟨g,hg⟩ := intertwining_lift_surjective (cyclicMap F v) (cyclicMap_surjective F v) f - refine ⟨g, ?_⟩ - intro hz - apply hf - rw [← hg,hz] - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - exact map_zero (cyclicMap F v) - - - -lemma cyclic_smul_eq {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] - (ρ : Representation ℂ G V) (v : V) (c : ℂ) (hc : c ≠ 0) : - cyclic ρ (c • v) = cyclic ρ v := by - apply le_antisymm - · apply (cyclic_le _ _ _).mpr - exact Submodule.smul_mem _ _ (mem_cyclic ρ v) - · apply (cyclic_le _ _ _).mpr - have hh := Submodule.smul_mem (cyclic ρ (c • v)).toSubmodule c⁻¹ (mem_cyclic ρ (c • v)) - change v ∈ (cyclic ρ (c • v)).toSubmodule - simpa only [smul_smul, inv_mul_cancel₀ hc, one_smul] using hh - -lemma cyclic_action_eq {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] - (ρ : Representation ℂ G V) (v : V) (g : G) : cyclic ρ (ρ g v) = cyclic ρ v := by - apply le_antisymm - · exact (cyclic_le _ _ _).mpr ((cyclic ρ v).apply_mem_toSubmodule g (mem_cyclic ρ v)) - · apply (cyclic_le _ _ _).mpr - have hh := (cyclic ρ (ρ g v)).apply_mem_toSubmodule g⁻¹ (mem_cyclic ρ (ρ g v)) - rw [← Module.End.mul_apply, ← map_mul, inv_mul_cancel, map_one] at hh - exact hh - -lemma support_relabel {n m d k : ℕ} (e : Fin n ≃ Fin m) (v : WordSpace n d) - (hv : ∀ (μ : YoungDiagram) (t : Tableau n μ), μ.colLen 0 ≤ k → - ∃ f : Representation.IntertwiningMap (spechtRep t) (cyclic (wordRep n d) v).toRepresentation, f ≠ 0) : - ∀ (μ : YoungDiagram) (t : Tableau m μ), μ.colLen 0 ≤ k → - ∃ f : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep m d) (fun w => v (w ∘ e))).toRepresentation, f ≠ 0 := by - have hnm : n = m := by simpa only [Fintype.card_fin] using Fintype.card_congr e - subst m - intro μ t hμ - change ∃ f : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n d) (wordRep n d e v)).toRepresentation, f ≠ 0 - rw [cyclic_action_eq] - exact hv μ t hμ - -def restrictLetters {n d D : ℕ} (φ : Fin d → Fin D) : - Representation.IntertwiningMap (wordRep n D) (wordRep n d) where - toLinearMap := - { toFun := fun x w => x (φ ∘ w) - map_add' := by intros; rfl - map_smul' := by intros; rfl } - isIntertwining' g := by ext x w; rfl - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.BandPairing + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uG uX uY uZ uV + +namespace Saxl + +/- Explicit finite-group induction on a linear map. -/ +def averagedMap {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [Fintype G] + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + (ρ : Representation ℂ G X) (σ : Representation ℂ G Y) (f : X →ₗ[ℂ] Y) : + Representation.IntertwiningMap ρ σ where + toLinearMap := ∑ g : G, (σ g).comp (f.comp (ρ g⁻¹)) + isIntertwining' h := by + apply LinearMap.ext + intro x + simp only [LinearMap.comp_apply, LinearMap.sum_apply] + rw [map_sum] + apply (Equiv.sum_comp (Equiv.mulLeft h) _).symm.trans + apply Finset.sum_congr rfl + intro g hg + change σ (h*g) (f (ρ (h*g)⁻¹ (ρ h x))) = σ h (σ g (f (ρ g⁻¹ x))) + simp only [mul_inv_rev, map_mul, Module.End.mul_apply] + have he : ρ h⁻¹ (ρ h x) = x := by + rw [← Module.End.mul_apply, ← map_mul, inv_mul_cancel, map_one] + rfl + rw [he] + +lemma averagedMap_apply {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [Fintype G] + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + (ρ : Representation ℂ G X) (σ : Representation ℂ G Y) (f : X →ₗ[ℂ] Y) (x : X) : + averagedMap ρ σ f x = ∑ g : G, σ g (f (ρ g⁻¹ x)) := by + simp only [averagedMap, Representation.IntertwiningMap.coe_mk, LinearMap.sum_apply, + LinearMap.comp_apply] + +/- Coordinate-sector induction, in precisely the nonzero-Hom form used in +the staircase induction. The projector kills translates outside the stabilizer. -/ +theorem sector_average_nonzero {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [Fintype G] + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + (ρ : Representation ℂ G X) (σ : Representation ℂ G Y) + (H : Subgroup G) (f : X →ₗ[ℂ] Y) (hf : f ≠ 0) + (he : ∀ g ∈ H, ∀ x, f (ρ g x) = σ g (f x)) + (P : Y →ₗ[ℂ] Y) (hP : ∀ x, P (f x) = f x) + (hkill : ∀ g ∉ H, ∀ x, P (σ g (f x)) = 0) : + averagedMap ρ σ f ≠ 0 := by + classical + have hproj (x : X) : P (averagedMap ρ σ f x) = + ((Finset.univ.filter (fun g : G => g ∈ H)).card : ℂ) • f x := by + rw [averagedMap_apply, map_sum] + have hh (g : G) : P (σ g (f (ρ g⁻¹ x))) = if g ∈ H then f x else 0 := by + by_cases hg : g ∈ H + · rw [ite_eq_left hg, ← he g hg, ← Module.End.mul_apply, ← map_mul, + mul_inv_cancel, map_one] + exact hP x + · rw [ite_eq_right hg] + exact hkill g hg _ + simp only [hh] + simp [Finset.sum_ite, Nat.cast_smul_eq_nsmul] + have hc : ((Finset.univ.filter (fun g : G => g ∈ H)).card : ℂ) ≠ 0 := by + apply Nat.cast_ne_zero.mpr + exact ne_of_gt (Finset.card_pos.mpr ⟨1, by simp⟩) + intro hz + apply hf + ext x + have heq := hproj x + rw [hz] at heq + change P 0 = _ at heq + rw [map_zero] at heq + exact (smul_eq_zero.mp heq.symm).resolve_left hc + +open scoped MonoidAlgebra + +theorem intertwining_lift_surjective {G : Type uG} {X : Type uX} {Y : Type uY} {Z : Type uZ} + [Group G] [Finite G] [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] [AddCommGroup Z] [Module ℂ Z] + {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} + {τ : Representation ℂ G Z} + (F : Representation.IntertwiningMap ρ σ) (hF : Function.Surjective F) + (f : Representation.IntertwiningMap τ σ) : + ∃ h : Representation.IntertwiningMap τ ρ, F.comp h = f := by + let EF := Representation.IntertwiningMap.equivLinearMapAsModule ρ σ + let EH := Representation.IntertwiningMap.equivLinearMapAsModule τ ρ + let Ef := Representation.IntertwiningMap.equivLinearMapAsModule τ σ + obtain ⟨h, hh⟩ := IsSemisimpleModule.lifting_property (EF F) hF (Ef f) + refine ⟨EH.symm h, ?_⟩ + ext z + exact LinearMap.congr_fun hh z + +end Saxl + +namespace Saxl + +def wordSector {n d : ℕ} (D : Fin n → Prop) (A : Fin d → Prop) + (w : Fin n → Fin d) : Prop := ∀ i, A (w i) ↔ D i + +/- Concrete sector averaging produces a constituent of the full cyclic +module from an equivariant map on its coordinate sector. -/ +theorem sector_support_transfer {n d : ℕ} {X : Type uX} [AddCommGroup X] [Module ℂ X] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (D : Fin n → Prop) (A : Fin d → Prop) (z : WordSpace n d) + (f : X →ₗ[ℂ] WordSpace n d) (hf : f ≠ 0) + (he : ∀ g ∈ sectorGroup D, ∀ x, f (ρ g x) = wordRep n d g (f x)) + (hm : ∀ x, f x ∈ cyclic (wordRep n d) z) + (hs : ∀ x w, f x w ≠ 0 → wordSector D A w) : + ∃ F : Representation.IntertwiningMap ρ (cyclic (wordRep n d) z).toRepresentation, + F ≠ 0 := by + classical + let P := coordinateProjection (wordSector D A) + have hP (x) : P (f x) = f x := by + ext w + change (if wordSector D A w then f x w else 0) = _ + split_ifs with h + · rfl + · exact (not_ne_iff.mp (fun hh => h (hs x w hh))).symm + have hk (g : Equiv.Perm (Fin n)) (hg : g ∉ sectorGroup D) (x) : + P (wordRep n d g (f x)) = 0 := by + ext w + change (if wordSector D A w then f x (w ∘ g) else 0) = 0 + split_ifs with hw + · by_contra hn + have hh := hs x (w ∘ g) hn + apply hg + intro i + exact (hw (g i)).symm.trans (hh i) + · rfl + let F := averagedMap ρ (wordRep n d) f + have hF : F ≠ 0 := sector_average_nonzero ρ (wordRep n d) (sectorGroup D) f hf he P hP hk + have hmem (x) : F x ∈ cyclic (wordRep n d) z := by + rw [show F x = _ from averagedMap_apply ρ (wordRep n d) f x] + apply Submodule.sum_mem + intro g hg + exact (cyclic (wordRep n d) z).apply_mem_toSubmodule g (hm _) + let G : Representation.IntertwiningMap ρ (cyclic (wordRep n d) z).toRepresentation := + { toLinearMap := F.toLinearMap.codRestrict _ hmem + isIntertwining' := by + intro g + apply LinearMap.ext + intro x + apply Subtype.ext + exact LinearMap.congr_fun (F.isIntertwining' g) x } + refine ⟨G, ?_⟩ + intro hz + apply hF + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + exact congrArg Subtype.val (congrArg (fun l => l x) hz) + +lemma intertwiner_cyclic_mem {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} + (F : Representation.IntertwiningMap ρ σ) (v : X) (x : X) (hx : x ∈ cyclic ρ v) : + F x ∈ cyclic σ (F v) := by + change x ∈ Submodule.span ℂ _ at hx + induction hx using Submodule.span_induction with + | mem x hx => + obtain ⟨g,rfl⟩ := hx + change F (ρ g v) ∈ _ + have hF : F (ρ g v) = σ g (F v) := LinearMap.congr_fun (F.isIntertwining' g) v + rw [hF] + exact (cyclic σ (F v)).apply_mem_toSubmodule g (mem_cyclic _ _) + | zero => rw [map_zero]; exact Submodule.zero_mem _ + | add x y hx hy ihx ihy => rw [map_add]; exact Submodule.add_mem _ ihx ihy + | smul c x hx ih => rw [map_smul]; exact Submodule.smul_mem _ c ih + +def cyclicMap {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} + (F : Representation.IntertwiningMap ρ σ) (v : X) : + Representation.IntertwiningMap (cyclic ρ v).toRepresentation (cyclic σ (F v)).toRepresentation where + toLinearMap := (F.toLinearMap.comp (cyclic ρ v).toSubmodule.subtype).codRestrict _ + (fun x => intertwiner_cyclic_mem F v x.val x.property) + isIntertwining' g := by + apply LinearMap.ext + intro x + apply Subtype.ext + exact LinearMap.congr_fun (F.isIntertwining' g) x.val + +lemma cyclicMap_surjective {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} + (F : Representation.IntertwiningMap ρ σ) (v : X) : Function.Surjective (cyclicMap F v) := by + intro y + have hy := y.property + change y.val ∈ Submodule.span ℂ _ at hy + suffices ∃ x : (cyclic ρ v).toSubmodule, (cyclicMap F v x).val = y.val by + obtain ⟨x,hx⟩ := this + exact ⟨x,Subtype.ext hx⟩ + generalize hz : y.val = z at hy ⊢ + clear y hz + induction hy using Submodule.span_induction with + | mem z hz => + obtain ⟨g,rfl⟩ := hz + refine ⟨(cyclic ρ v).toRepresentation g ⟨v,mem_cyclic _ _⟩, ?_⟩ + change F (ρ g v) = σ g (F v) + exact LinearMap.congr_fun (F.isIntertwining' g) v + | zero => exact ⟨0,map_zero F⟩ + | add x y hx hy ihx ihy => + obtain ⟨u,hu⟩ := ihx + obtain ⟨w,hw⟩ := ihy + refine ⟨u+w, ?_⟩ + change F (u.val+w.val) = _ + rw [map_add,show F u.val = x from hu,show F w.val = y from hw] + | smul c x hx ih => + obtain ⟨u,hu⟩ := ih + refine ⟨c • u, ?_⟩ + change F (c • u.val) = _ + rw [map_smul,show F u.val = x from hu] + +/- A genuine equivariant projection of a cyclic generator transfers every +nonzero constituent map back to the original cyclic module by Maschke. -/ +theorem cyclic_projection_support {G : Type uG} {X : Type uX} {Y : Type uY} {Z : Type uZ} [Group G] [Finite G] + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + [AddCommGroup Z] [Module ℂ Z] + {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} {τ : Representation ℂ G Z} + (F : Representation.IntertwiningMap ρ σ) (v : X) + (f : Representation.IntertwiningMap τ (cyclic σ (F v)).toRepresentation) (hf : f ≠ 0) : + ∃ g : Representation.IntertwiningMap τ (cyclic ρ v).toRepresentation, g ≠ 0 := by + obtain ⟨g,hg⟩ := intertwining_lift_surjective (cyclicMap F v) (cyclicMap_surjective F v) f + refine ⟨g, ?_⟩ + intro hz + apply hf + rw [← hg,hz] + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + exact map_zero (cyclicMap F v) + + + +lemma cyclic_smul_eq {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] + (ρ : Representation ℂ G V) (v : V) (c : ℂ) (hc : c ≠ 0) : + cyclic ρ (c • v) = cyclic ρ v := by + apply le_antisymm + · apply (cyclic_le _ _ _).mpr + exact Submodule.smul_mem _ _ (mem_cyclic ρ v) + · apply (cyclic_le _ _ _).mpr + have hh := Submodule.smul_mem (cyclic ρ (c • v)).toSubmodule c⁻¹ (mem_cyclic ρ (c • v)) + change v ∈ (cyclic ρ (c • v)).toSubmodule + simpa only [smul_smul, inv_mul_cancel₀ hc, one_smul] using hh + +lemma cyclic_action_eq {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] + (ρ : Representation ℂ G V) (v : V) (g : G) : cyclic ρ (ρ g v) = cyclic ρ v := by + apply le_antisymm + · exact (cyclic_le _ _ _).mpr ((cyclic ρ v).apply_mem_toSubmodule g (mem_cyclic ρ v)) + · apply (cyclic_le _ _ _).mpr + have hh := (cyclic ρ (ρ g v)).apply_mem_toSubmodule g⁻¹ (mem_cyclic ρ (ρ g v)) + rw [← Module.End.mul_apply, ← map_mul, inv_mul_cancel, map_one] at hh + exact hh + +lemma support_relabel {n m d k : ℕ} (e : Fin n ≃ Fin m) (v : WordSpace n d) + (hv : ∀ (μ : YoungDiagram) (t : Tableau n μ), μ.colLen 0 ≤ k → + ∃ f : Representation.IntertwiningMap (spechtRep t) (cyclic (wordRep n d) v).toRepresentation, f ≠ 0) : + ∀ (μ : YoungDiagram) (t : Tableau m μ), μ.colLen 0 ≤ k → + ∃ f : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep m d) (fun w => v (w ∘ e))).toRepresentation, f ≠ 0 := by + have hnm : n = m := by simpa only [Fintype.card_fin] using Fintype.card_congr e + subst m + intro μ t hμ + change ∃ f : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n d) (wordRep n d e v)).toRepresentation, f ≠ 0 + rw [cyclic_action_eq] + exact hv μ t hμ + +def restrictLetters {n d D : ℕ} (φ : Fin d → Fin D) : + Representation.IntertwiningMap (wordRep n D) (wordRep n d) where + toLinearMap := + { toFun := fun x w => x (φ ∘ w) + map_add' := by intros; rfl + map_smul' := by intros; rfl } + isIntertwining' g := by ext x w; rfl + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/CyclicTensor.lean b/lean/OAI/RepresentationTheory/Saxl/CyclicTensor.lean index 1b7daf442a36bc50571c155cfe51b26ae13ee35e..033ac7763de0644ee028bde63e0fba856dda079e 100644 --- a/lean/OAI/RepresentationTheory/Saxl/CyclicTensor.lean +++ b/lean/OAI/RepresentationTheory/Saxl/CyclicTensor.lean @@ -1,165 +1,165 @@ -import OAI.RepresentationTheory.Saxl.YoungRule - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uG uX uY - -namespace Saxl - -def equivOfSubrepEq {G : Type uG} {X : Type uX} [Group G] [AddCommGroup X] [Module ℂ X] - {ρ : Representation ℂ G X} (S T : Subrepresentation ρ) (h : S = T) : - Representation.Equiv S.toRepresentation T.toRepresentation := by - subst T - exact Representation.Equiv.refl _ - -/- Positive Young rule as a concrete orbit map (including reordered contents). -/ -theorem young_orbit_map {n : ℕ} (θ τ : YoungDiagram) (t : Tableau n τ) - (hc : τ.card = θ.card) (hd : Dominates τ θ) - (w : Fin n → Fin (θ.colLen 0)) (e : Equiv.Perm (Fin (θ.colLen 0))) - (hw : ∀ j, (Finset.univ.filter (fun i => w i = e j)).card = θ.rowLen j) : - ∃ F : Representation.IntertwiningMap (wordRep n (θ.colLen 0)) (spechtRep t), - F (Pi.single w 1) ≠ 0 := by - classical - have hn : τ.card = n := by - have hh := Fintype.card_congr t - simpa using hh.symm - subst n - obtain ⟨a,l,hl,hac,hle⟩ := young_invariant_functional θ τ hc hd - obtain ⟨y,hy,hye⟩ := vector_of_invariant_functional (shapeTableau τ) a l hl hle - let a' := e ∘ a - have ha' : ∀ g : Equiv.Perm (Fin τ.card), a' ∘ g = a' → - spechtRep (shapeTableau τ) g y = y := by - intro g hg - apply hye g - funext i - exact e.injective (congrFun hg i) - let F := orbitAverage (spechtRep (shapeTableau τ)) a' y - have hF : F (Pi.single a' 1) ≠ 0 := by - rw [show F (Pi.single a' 1) = _ from orbitAverage_base _ a' y ha'] - apply smul_ne_zero _ hy - apply Nat.cast_ne_zero.mpr - exact Finset.card_ne_zero.mpr ⟨1, by simp⟩ - have hcnt (j : Fin (θ.colLen 0)) : - (Finset.univ.filter (fun i => w i = j)).card = - (Finset.univ.filter (fun i => a' i = j)).card := by - have haeq : Finset.univ.filter (fun i => a' i = j) = - Finset.univ.filter (fun i => a i = e.symm j) := by - ext i - simp only [Finset.mem_filter, Finset.mem_univ, true_and] - exact e.eq_symm_apply.symm - rw [haeq, hac] - simpa only [Equiv.apply_symm_apply] using hw (e.symm j) - obtain ⟨g,hg⟩ := perm_of_equal_content w a' hcnt - have hwF : F (Pi.single w 1) ≠ 0 := by - have hw' : Pi.single w (1:ℂ) = wordRep τ.card (θ.colLen 0) g⁻¹ (Pi.single a' 1) := by - rw [wordRep_single, inv_inv, hg] - rw [hw', F.isIntertwining] - intro hz - apply hF - have hh := congrArg (spechtRep (shapeTableau τ) g) hz - rw [map_zero, ← Module.End.mul_apply, ← map_mul, mul_inv_cancel, map_one] at hh - exact hh - let E := equivOfSubrepEq (spechtSub (shapeTableau τ)) (spechtSub t) - (spechtSub_tableau_independent _ _) - refine ⟨E.toIntertwiningMap.comp F, ?_⟩ - intro hz - exact hwF (E.injective (hz.trans (map_zero _).symm)) - - - -def intertwiningRangeEquiv {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} - (f : Representation.IntertwiningMap ρ σ) (hf : Function.Injective f) : - ρ.Equiv f.range.toRepresentation where - toLinearEquiv := LinearEquiv.ofInjective f.toLinearMap hf - isIntertwining' g := by - apply LinearMap.ext - intro x - apply Subtype.ext - exact LinearMap.congr_fun (f.isIntertwining' g) x - -def staircaseCyclicInclusion (m : ℕ) : - Representation.IntertwiningMap (staircaseCyclic m).toRepresentation - ((staircaseTensorMap m).range.toRepresentation) where - toLinearMap := Submodule.inclusion (staircaseCyclic_le_tensorRange m) - isIntertwining' _ := rfl - -def intertwiningLiftSubrep {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} - (f : Representation.IntertwiningMap ρ σ) (hf : Function.Injective f) - (S : Subrepresentation σ) (hS : S ≤ f.range) : - Representation.IntertwiningMap S.toRepresentation ρ := by - let e : ρ.Equiv f.range.toRepresentation := intertwiningRangeEquiv f hf - let i : Representation.IntertwiningMap S.toRepresentation f.range.toRepresentation := - { toLinearMap := Submodule.inclusion hS, isIntertwining' := fun _ => rfl } - exact e.symm.toIntertwiningMap.comp i - -lemma intertwiningLiftSubrep_injective {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} - (f : Representation.IntertwiningMap ρ σ) (hf : Function.Injective f) - (S : Subrepresentation σ) (hS : S ≤ f.range) : - Function.Injective (intertwiningLiftSubrep f hf S hS) := by - intro x y h - apply Subtype.ext - have hh := (intertwiningRangeEquiv f hf).symm.injective h - exact congrArg (fun z : f.range => (z : Y)) hh - -attribute [irreducible] intertwiningLiftSubrep - -/- The genuine cyclic module is embedded in the actual staircase Specht square. -/ -def staircaseToTensor (m : ℕ) : - Representation.IntertwiningMap (staircaseCyclic m).toRepresentation - ((spechtRep (stairTableau m)).tprod (spechtRep (stairTableau m))) := - @intertwiningLiftSubrep (Equiv.Perm (Fin (staircase m).card)) - (Specht (stairTableau m) ⊗[ℂ] Specht (stairTableau m)) - (WordSpace (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) - _ _ _ _ _ - ((spechtRep (stairTableau m)).tprod (spechtRep (stairTableau m))) - (wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) - (staircaseTensorMap m) (staircaseTensorMap_injective m) - (staircaseCyclic m) (staircaseCyclic_le_tensorRange m) - -attribute [irreducible] staircaseToTensor - -lemma staircaseToTensor_injective (m : ℕ) : Function.Injective (staircaseToTensor m) := by - unfold staircaseToTensor - exact @intertwiningLiftSubrep_injective (Equiv.Perm (Fin (staircase m).card)) - (Specht (stairTableau m) ⊗[ℂ] Specht (stairTableau m)) - (WordSpace (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) - _ _ _ _ _ - ((spechtRep (stairTableau m)).tprod (spechtRep (stairTableau m))) - (wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) - (staircaseTensorMap m) (staircaseTensorMap_injective m) - (staircaseCyclic m) (staircaseCyclic_le_tensorRange m) - -/- Every Specht type occurs in the specified staircase cyclic module. -/ -def CyclicSaxlConjecture : Prop := - ∀ m, 1 ≤ m → ∀ (μ : YoungDiagram) (hμ : μ.card = (staircase m).card), - ∃ f : Representation.IntertwiningMap (spechtRep (canonicalTableau μ hμ)) - (staircaseCyclic m).toRepresentation, f ≠ 0 - -/- A proof of cyclic support proves the original Kronecker-multiplicity target. -/ -theorem saxl_of_cyclic_support (h : CyclicSaxlConjecture) : SaxlConjecture := by - intro m hm μ hμ - apply (kronecker_pos_iff _ _ _).mpr - obtain ⟨f, hf⟩ := h m hm μ hμ - refine ⟨(staircaseToTensor m).comp f, ?_⟩ - intro he - apply hf - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - apply staircaseToTensor_injective m - exact (congrArg (fun F : Representation.IntertwiningMap (spechtRep (canonicalTableau μ hμ)) - ((spechtRep (stairTableau m)).tprod (spechtRep (stairTableau m))) => F x) he).trans - (map_zero _).symm - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.YoungRule + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uG uX uY + +namespace Saxl + +def equivOfSubrepEq {G : Type uG} {X : Type uX} [Group G] [AddCommGroup X] [Module ℂ X] + {ρ : Representation ℂ G X} (S T : Subrepresentation ρ) (h : S = T) : + Representation.Equiv S.toRepresentation T.toRepresentation := by + subst T + exact Representation.Equiv.refl _ + +/- Positive Young rule as a concrete orbit map (including reordered contents). -/ +theorem young_orbit_map {n : ℕ} (θ τ : YoungDiagram) (t : Tableau n τ) + (hc : τ.card = θ.card) (hd : Dominates τ θ) + (w : Fin n → Fin (θ.colLen 0)) (e : Equiv.Perm (Fin (θ.colLen 0))) + (hw : ∀ j, (Finset.univ.filter (fun i => w i = e j)).card = θ.rowLen j) : + ∃ F : Representation.IntertwiningMap (wordRep n (θ.colLen 0)) (spechtRep t), + F (Pi.single w 1) ≠ 0 := by + classical + have hn : τ.card = n := by + have hh := Fintype.card_congr t + simpa using hh.symm + subst n + obtain ⟨a,l,hl,hac,hle⟩ := young_invariant_functional θ τ hc hd + obtain ⟨y,hy,hye⟩ := vector_of_invariant_functional (shapeTableau τ) a l hl hle + let a' := e ∘ a + have ha' : ∀ g : Equiv.Perm (Fin τ.card), a' ∘ g = a' → + spechtRep (shapeTableau τ) g y = y := by + intro g hg + apply hye g + funext i + exact e.injective (congrFun hg i) + let F := orbitAverage (spechtRep (shapeTableau τ)) a' y + have hF : F (Pi.single a' 1) ≠ 0 := by + rw [show F (Pi.single a' 1) = _ from orbitAverage_base _ a' y ha'] + apply smul_ne_zero _ hy + apply Nat.cast_ne_zero.mpr + exact Finset.card_ne_zero.mpr ⟨1, by simp⟩ + have hcnt (j : Fin (θ.colLen 0)) : + (Finset.univ.filter (fun i => w i = j)).card = + (Finset.univ.filter (fun i => a' i = j)).card := by + have haeq : Finset.univ.filter (fun i => a' i = j) = + Finset.univ.filter (fun i => a i = e.symm j) := by + ext i + simp only [Finset.mem_filter, Finset.mem_univ, true_and] + exact e.eq_symm_apply.symm + rw [haeq, hac] + simpa only [Equiv.apply_symm_apply] using hw (e.symm j) + obtain ⟨g,hg⟩ := perm_of_equal_content w a' hcnt + have hwF : F (Pi.single w 1) ≠ 0 := by + have hw' : Pi.single w (1:ℂ) = wordRep τ.card (θ.colLen 0) g⁻¹ (Pi.single a' 1) := by + rw [wordRep_single, inv_inv, hg] + rw [hw', F.isIntertwining] + intro hz + apply hF + have hh := congrArg (spechtRep (shapeTableau τ) g) hz + rw [map_zero, ← Module.End.mul_apply, ← map_mul, mul_inv_cancel, map_one] at hh + exact hh + let E := equivOfSubrepEq (spechtSub (shapeTableau τ)) (spechtSub t) + (spechtSub_tableau_independent _ _) + refine ⟨E.toIntertwiningMap.comp F, ?_⟩ + intro hz + exact hwF (E.injective (hz.trans (map_zero _).symm)) + + + +def intertwiningRangeEquiv {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} + (f : Representation.IntertwiningMap ρ σ) (hf : Function.Injective f) : + ρ.Equiv f.range.toRepresentation where + toLinearEquiv := LinearEquiv.ofInjective f.toLinearMap hf + isIntertwining' g := by + apply LinearMap.ext + intro x + apply Subtype.ext + exact LinearMap.congr_fun (f.isIntertwining' g) x + +def staircaseCyclicInclusion (m : ℕ) : + Representation.IntertwiningMap (staircaseCyclic m).toRepresentation + ((staircaseTensorMap m).range.toRepresentation) where + toLinearMap := Submodule.inclusion (staircaseCyclic_le_tensorRange m) + isIntertwining' _ := rfl + +def intertwiningLiftSubrep {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} + (f : Representation.IntertwiningMap ρ σ) (hf : Function.Injective f) + (S : Subrepresentation σ) (hS : S ≤ f.range) : + Representation.IntertwiningMap S.toRepresentation ρ := by + let e : ρ.Equiv f.range.toRepresentation := intertwiningRangeEquiv f hf + let i : Representation.IntertwiningMap S.toRepresentation f.range.toRepresentation := + { toLinearMap := Submodule.inclusion hS, isIntertwining' := fun _ => rfl } + exact e.symm.toIntertwiningMap.comp i + +lemma intertwiningLiftSubrep_injective {G : Type uG} {X : Type uX} {Y : Type uY} [Group G] [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} + (f : Representation.IntertwiningMap ρ σ) (hf : Function.Injective f) + (S : Subrepresentation σ) (hS : S ≤ f.range) : + Function.Injective (intertwiningLiftSubrep f hf S hS) := by + intro x y h + apply Subtype.ext + have hh := (intertwiningRangeEquiv f hf).symm.injective h + exact congrArg (fun z : f.range => (z : Y)) hh + +attribute [irreducible] intertwiningLiftSubrep + +/- The genuine cyclic module is embedded in the actual staircase Specht square. -/ +def staircaseToTensor (m : ℕ) : + Representation.IntertwiningMap (staircaseCyclic m).toRepresentation + ((spechtRep (stairTableau m)).tprod (spechtRep (stairTableau m))) := + @intertwiningLiftSubrep (Equiv.Perm (Fin (staircase m).card)) + (Specht (stairTableau m) ⊗[ℂ] Specht (stairTableau m)) + (WordSpace (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) + _ _ _ _ _ + ((spechtRep (stairTableau m)).tprod (spechtRep (stairTableau m))) + (wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) + (staircaseTensorMap m) (staircaseTensorMap_injective m) + (staircaseCyclic m) (staircaseCyclic_le_tensorRange m) + +attribute [irreducible] staircaseToTensor + +lemma staircaseToTensor_injective (m : ℕ) : Function.Injective (staircaseToTensor m) := by + unfold staircaseToTensor + exact @intertwiningLiftSubrep_injective (Equiv.Perm (Fin (staircase m).card)) + (Specht (stairTableau m) ⊗[ℂ] Specht (stairTableau m)) + (WordSpace (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) + _ _ _ _ _ + ((spechtRep (stairTableau m)).tprod (spechtRep (stairTableau m))) + (wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) + (staircaseTensorMap m) (staircaseTensorMap_injective m) + (staircaseCyclic m) (staircaseCyclic_le_tensorRange m) + +/- Every Specht type occurs in the specified staircase cyclic module. -/ +def CyclicSaxlConjecture : Prop := + ∀ m, 1 ≤ m → ∀ (μ : YoungDiagram) (hμ : μ.card = (staircase m).card), + ∃ f : Representation.IntertwiningMap (spechtRep (canonicalTableau μ hμ)) + (staircaseCyclic m).toRepresentation, f ≠ 0 + +/- A proof of cyclic support proves the original Kronecker-multiplicity target. -/ +theorem saxl_of_cyclic_support (h : CyclicSaxlConjecture) : SaxlConjecture := by + intro m hm μ hμ + apply (kronecker_pos_iff _ _ _).mpr + obtain ⟨f, hf⟩ := h m hm μ hμ + refine ⟨(staircaseToTensor m).comp f, ?_⟩ + intro he + apply hf + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + apply staircaseToTensor_injective m + exact (congrArg (fun F : Representation.IntertwiningMap (spechtRep (canonicalTableau μ hμ)) + ((spechtRep (stairTableau m)).tprod (spechtRep (stairTableau m))) => F x) he).trans + (map_zero _).symm + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/DominatedQuotient.lean b/lean/OAI/RepresentationTheory/Saxl/DominatedQuotient.lean index e078e303437e7ccf62bcea0e50b49bfaf3d86d14..2975652113cf93d0210f57b5a1c1d5a29381df76 100644 --- a/lean/OAI/RepresentationTheory/Saxl/DominatedQuotient.lean +++ b/lean/OAI/RepresentationTheory/Saxl/DominatedQuotient.lean @@ -1,125 +1,125 @@ -import OAI.RepresentationTheory.Saxl.StaircaseSign - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl - -lemma subrepProject_subtype {n d : ℕ} (S : Subrepresentation (wordRep n d)) - (hS : ∀ x ∈ S.toSubmodule, star x ∈ S.toSubmodule) (x : S) : - subrepProject S hS x.val = x := by - change (subrepSelfDual S hS).symm (subrepSelfDual S hS x) = x - exact (subrepSelfDual S hS).symm_apply_apply x - -def wordTensorEquiv (n d e : ℕ) : - ((wordRep n d).tprod (wordRep n e)).Equiv (wordRep n (d*e)) where - toLinearEquiv := wordTensor n d e - isIntertwining' g := by - apply LinearMap.ext - intro z - exact wordTensor_equivariant g z - -def ambientSignMap (m : ℕ) - (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) : - Representation.IntertwiningMap (wordRep (staircase m).card ((staircase m).colLen 0)) - (signTwist (wordRep (staircase m).card ((staircase m).colLen 0))) := - (signTwistMap (spechtInclusion (stairRowTableau m))).comp - (φ.toIntertwiningMap.comp (subrepProject (spechtSub (stairTableau m)) - (fun _ hx => cyclic_star _ (polytabloid_real _) hx))) - -lemma ambientSignMap_subtype (m : ℕ) - (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) - (x : Specht (stairTableau m)) : ambientSignMap m φ x.val = (φ x).val := by - change (φ (subrepProject (spechtSub (stairTableau m)) _ x.val)).val = _ - exact congrArg (fun y : Specht (stairTableau m) => (φ y).val) - (subrepProject_subtype (spechtSub (stairTableau m)) _ x) - -def pairAntiMap (m : ℕ) - (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) : - Representation.IntertwiningMap - (signTwist (wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0))) - (wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) := - (wordTensorEquiv _ _ _).toIntertwiningMap.comp - ((tensorAnti (wordRep _ _) (ambientSignMap m φ)).comp - (signTwistMap (wordTensorEquiv _ _ _).symm.toIntertwiningMap)) - -lemma pairAntiMap_tensor (m : ℕ) - (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) - (x y : WordSpace (staircase m).card ((staircase m).colLen 0)) : - pairAntiMap m φ (wordTensor _ _ _ (x ⊗ₜ[ℂ] y)) = - wordTensor _ _ _ (x ⊗ₜ[ℂ] ambientSignMap m φ y) := by - change wordTensor _ _ _ (TensorProduct.map LinearMap.id (ambientSignMap m φ).toLinearMap - ((wordTensor _ _ _).symm (wordTensor _ _ _ (x ⊗ₜ[ℂ] y)))) = _ - rw [LinearEquiv.symm_apply_apply, TensorProduct.map_tmul, LinearMap.id_apply] - rfl - -lemma signed_average_staircase (m : ℕ) : - letI := Fintype.ofFinite (columnGroup (stairRowTableau m)) - ∑ g : columnGroup (stairRowTableau m), signC g.val • - wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0) g.val (staircaseWord m) = - wordTensor _ _ _ (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] (rowAverage m).val) := by - classical - let := Fintype.ofFinite (columnGroup (stairRowTableau m)) - change _ = wordTensor _ _ _ (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] - (∑ g : columnGroup (stairRowTableau m), - spechtRep (stairTableau m) g.val ⟨polytabloid (stairTableau m), mem_cyclic _ _⟩).val) - rw [Submodule.coe_sum, TensorProduct.tmul_sum, map_sum] - apply Finset.sum_congr rfl - intro g hg - change signC g.val • wordRep _ _ g.val (wordTensor _ _ _ - (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] polytabloid (stairTableau m))) = _ - rw [← wordTensor_equivariant] - change signC g.val • wordTensor _ _ _ - (wordRep _ _ g.val (polytabloid (stairRowTableau m)) ⊗ₜ[ℂ] - wordRep _ _ g.val (polytabloid (stairTableau m))) = _ - rw [polytabloid_alternating _ g, TensorProduct.smul_tmul, TensorProduct.tmul_smul, map_smul, - smul_smul, signC_mul_self, one_smul] - rfl - -def dominatedQuotient (m : ℕ) - (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) : - Representation.IntertwiningMap (signTwist (staircaseCyclic m).toRepresentation) - (wordRep (staircase m).card ((staircase m).colLen 0)) := - (orbitProjection (repeatedTarget m)).comp ((pairSumMap _ _ _).comp - ((pairAntiMap m φ).comp (signTwistMap - { toLinearMap := (staircaseCyclic m).toSubmodule.subtype - isIntertwining' := fun _ => rfl }))) - -/- The exact staircase permutation generator occurs in the image of the -sign-twisted cyclic staircase module, with no Young-rule input. -/ -theorem repeatedTarget_in_quotient (m : ℕ) - (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) : - Pi.single (repeatedTarget m) (1:ℂ) ∈ (dominatedQuotient m φ).range := by - classical - let := Fintype.ofFinite (columnGroup (stairRowTableau m)) - obtain ⟨c,hc,hφ⟩ := signEquiv_rowAverage m φ - let x : (staircaseCyclic m).toSubmodule := ∑ g : columnGroup (stairRowTableau m), signC g.val • - (staircaseCyclic m).toRepresentation g.val ⟨staircaseWord m, mem_cyclic _ _⟩ - have hx : x.val = wordTensor _ _ _ (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] (rowAverage m).val) := by - change (∑ g : columnGroup (stairRowTableau m), signC g.val • - (staircaseCyclic m).toRepresentation g.val ⟨staircaseWord m, mem_cyclic _ _⟩).val = _ - simp only [Submodule.coe_sum, Submodule.coe_smul_of_tower] - exact signed_average_staircase m - let q : ℂ := (Nat.card (columnGroup (stairRowTableau m)) : ℂ) * signC (rowReversal m).val - have hq : q ≠ 0 := by - apply mul_ne_zero (Nat.cast_ne_zero.mpr (Nat.card_pos (α := columnGroup (stairRowTableau m))).ne') - intro hz - have hh := signC_mul_self (rowReversal m).val - rw [hz, zero_mul] at hh - exact zero_ne_one hh - have hF : dominatedQuotient m φ x = (c*q) • Pi.single (repeatedTarget m) (1:ℂ) := by - change orbitProjection (repeatedTarget m) (pairSumMap _ _ _ (pairAntiMap m φ x.val)) = _ - rw [hx, pairAntiMap_tensor, ambientSignMap_subtype, hφ, - TensorProduct.tmul_smul, map_smul, map_smul, map_smul, staircase_repeated_projection, smul_smul] - have hm : (c*q) • Pi.single (repeatedTarget m) (1:ℂ) ∈ (dominatedQuotient m φ).range := - ⟨x,hF⟩ - exact (Submodule.smul_mem_iff _ (mul_ne_zero hc hq)).mp hm - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.StaircaseSign + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl + +lemma subrepProject_subtype {n d : ℕ} (S : Subrepresentation (wordRep n d)) + (hS : ∀ x ∈ S.toSubmodule, star x ∈ S.toSubmodule) (x : S) : + subrepProject S hS x.val = x := by + change (subrepSelfDual S hS).symm (subrepSelfDual S hS x) = x + exact (subrepSelfDual S hS).symm_apply_apply x + +def wordTensorEquiv (n d e : ℕ) : + ((wordRep n d).tprod (wordRep n e)).Equiv (wordRep n (d*e)) where + toLinearEquiv := wordTensor n d e + isIntertwining' g := by + apply LinearMap.ext + intro z + exact wordTensor_equivariant g z + +def ambientSignMap (m : ℕ) + (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) : + Representation.IntertwiningMap (wordRep (staircase m).card ((staircase m).colLen 0)) + (signTwist (wordRep (staircase m).card ((staircase m).colLen 0))) := + (signTwistMap (spechtInclusion (stairRowTableau m))).comp + (φ.toIntertwiningMap.comp (subrepProject (spechtSub (stairTableau m)) + (fun _ hx => cyclic_star _ (polytabloid_real _) hx))) + +lemma ambientSignMap_subtype (m : ℕ) + (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) + (x : Specht (stairTableau m)) : ambientSignMap m φ x.val = (φ x).val := by + change (φ (subrepProject (spechtSub (stairTableau m)) _ x.val)).val = _ + exact congrArg (fun y : Specht (stairTableau m) => (φ y).val) + (subrepProject_subtype (spechtSub (stairTableau m)) _ x) + +def pairAntiMap (m : ℕ) + (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) : + Representation.IntertwiningMap + (signTwist (wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0))) + (wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) := + (wordTensorEquiv _ _ _).toIntertwiningMap.comp + ((tensorAnti (wordRep _ _) (ambientSignMap m φ)).comp + (signTwistMap (wordTensorEquiv _ _ _).symm.toIntertwiningMap)) + +lemma pairAntiMap_tensor (m : ℕ) + (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) + (x y : WordSpace (staircase m).card ((staircase m).colLen 0)) : + pairAntiMap m φ (wordTensor _ _ _ (x ⊗ₜ[ℂ] y)) = + wordTensor _ _ _ (x ⊗ₜ[ℂ] ambientSignMap m φ y) := by + change wordTensor _ _ _ (TensorProduct.map LinearMap.id (ambientSignMap m φ).toLinearMap + ((wordTensor _ _ _).symm (wordTensor _ _ _ (x ⊗ₜ[ℂ] y)))) = _ + rw [LinearEquiv.symm_apply_apply, TensorProduct.map_tmul, LinearMap.id_apply] + rfl + +lemma signed_average_staircase (m : ℕ) : + letI := Fintype.ofFinite (columnGroup (stairRowTableau m)) + ∑ g : columnGroup (stairRowTableau m), signC g.val • + wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0) g.val (staircaseWord m) = + wordTensor _ _ _ (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] (rowAverage m).val) := by + classical + let := Fintype.ofFinite (columnGroup (stairRowTableau m)) + change _ = wordTensor _ _ _ (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] + (∑ g : columnGroup (stairRowTableau m), + spechtRep (stairTableau m) g.val ⟨polytabloid (stairTableau m), mem_cyclic _ _⟩).val) + rw [Submodule.coe_sum, TensorProduct.tmul_sum, map_sum] + apply Finset.sum_congr rfl + intro g hg + change signC g.val • wordRep _ _ g.val (wordTensor _ _ _ + (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] polytabloid (stairTableau m))) = _ + rw [← wordTensor_equivariant] + change signC g.val • wordTensor _ _ _ + (wordRep _ _ g.val (polytabloid (stairRowTableau m)) ⊗ₜ[ℂ] + wordRep _ _ g.val (polytabloid (stairTableau m))) = _ + rw [polytabloid_alternating _ g, TensorProduct.smul_tmul, TensorProduct.tmul_smul, map_smul, + smul_smul, signC_mul_self, one_smul] + rfl + +def dominatedQuotient (m : ℕ) + (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) : + Representation.IntertwiningMap (signTwist (staircaseCyclic m).toRepresentation) + (wordRep (staircase m).card ((staircase m).colLen 0)) := + (orbitProjection (repeatedTarget m)).comp ((pairSumMap _ _ _).comp + ((pairAntiMap m φ).comp (signTwistMap + { toLinearMap := (staircaseCyclic m).toSubmodule.subtype + isIntertwining' := fun _ => rfl }))) + +/- The exact staircase permutation generator occurs in the image of the +sign-twisted cyclic staircase module, with no Young-rule input. -/ +theorem repeatedTarget_in_quotient (m : ℕ) + (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) : + Pi.single (repeatedTarget m) (1:ℂ) ∈ (dominatedQuotient m φ).range := by + classical + let := Fintype.ofFinite (columnGroup (stairRowTableau m)) + obtain ⟨c,hc,hφ⟩ := signEquiv_rowAverage m φ + let x : (staircaseCyclic m).toSubmodule := ∑ g : columnGroup (stairRowTableau m), signC g.val • + (staircaseCyclic m).toRepresentation g.val ⟨staircaseWord m, mem_cyclic _ _⟩ + have hx : x.val = wordTensor _ _ _ (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] (rowAverage m).val) := by + change (∑ g : columnGroup (stairRowTableau m), signC g.val • + (staircaseCyclic m).toRepresentation g.val ⟨staircaseWord m, mem_cyclic _ _⟩).val = _ + simp only [Submodule.coe_sum, Submodule.coe_smul_of_tower] + exact signed_average_staircase m + let q : ℂ := (Nat.card (columnGroup (stairRowTableau m)) : ℂ) * signC (rowReversal m).val + have hq : q ≠ 0 := by + apply mul_ne_zero (Nat.cast_ne_zero.mpr (Nat.card_pos (α := columnGroup (stairRowTableau m))).ne') + intro hz + have hh := signC_mul_self (rowReversal m).val + rw [hz, zero_mul] at hh + exact zero_ne_one hh + have hF : dominatedQuotient m φ x = (c*q) • Pi.single (repeatedTarget m) (1:ℂ) := by + change orbitProjection (repeatedTarget m) (pairSumMap _ _ _ (pairAntiMap m φ x.val)) = _ + rw [hx, pairAntiMap_tensor, ambientSignMap_subtype, hφ, + TensorProduct.tmul_smul, map_smul, map_smul, map_smul, staircase_repeated_projection, smul_smul] + have hm : (c*q) • Pi.single (repeatedTarget m) (1:ℂ) ∈ (dominatedQuotient m φ).range := + ⟨x,hF⟩ + exact (Submodule.smul_mem_iff _ (mul_ne_zero hc hq)).mp hm + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/DominatedSupport.lean b/lean/OAI/RepresentationTheory/Saxl/DominatedSupport.lean index e2338cdb9892d09fd9a0d421d67e09ff30379c17..033b43fd7288b298ec9010ed7ce350f8b1e859f9 100644 --- a/lean/OAI/RepresentationTheory/Saxl/DominatedSupport.lean +++ b/lean/OAI/RepresentationTheory/Saxl/DominatedSupport.lean @@ -1,214 +1,214 @@ -import OAI.RepresentationTheory.Saxl.DominatedQuotient - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uX uY - -namespace Saxl - -lemma transpose_card (μ : YoungDiagram) : μ.transpose.card = μ.card := by - change ((Equiv.prodComm ℕ ℕ).finsetCongr μ.cells).card = μ.cells.card - simp only [Equiv.finsetCongr_apply, Finset.card_map] - -def colTruncate (μ : YoungDiagram) (k : ℕ) := (rowTruncate μ.transpose k).transpose - -lemma colTruncate_rowLen (μ : YoungDiagram) (k i : ℕ) : - (colTruncate μ k).rowLen i = min k (μ.rowLen i) := by - have hh : ∀ j, j < (colTruncate μ k).rowLen i ↔ j < min k (μ.rowLen i) := by - intro j - rw [← YoungDiagram.mem_iff_lt_rowLen] - change (i,j) ∈ (rowTruncate μ.transpose k).transpose ↔ _ - rw [YoungDiagram.mem_transpose] - change (j,i) ∈ rowTruncate μ.transpose k ↔ _ - rw [mem_rowTruncate, YoungDiagram.mem_transpose] - simp only [Prod.swap_prod_mk, YoungDiagram.mem_iff_lt_rowLen, lt_min_iff] - omega - have h₁ := hh ((colTruncate μ k).rowLen i) - have h₂ := hh (min k (μ.rowLen i)) - omega - -lemma colTruncate_height (μ : YoungDiagram) (k : ℕ) : - (colTruncate μ k).colLen 0 ≤ μ.colLen 0 := by - by_contra h - have hm : (μ.colLen 0,0) ∈ colTruncate μ k := YoungDiagram.mem_iff_lt_colLen.mpr (by omega) - have hr := YoungDiagram.mem_iff_lt_rowLen.mp hm - rw [colTruncate_rowLen, rowLen_zero_of_height_le μ le_rfl] at hr - simp at hr - -lemma sum_range_if_lt (f : ℕ → ℕ) {r H : ℕ} (hr : r ≤ H) : - (∑ i ∈ Finset.range H, if i < r then f i else 0) = ∑ i ∈ Finset.range r, f i := by - classical - rw [← Finset.sum_filter] - congr 1 - ext i - simp only [Finset.mem_filter, Finset.mem_range] - omega - -lemma corner_inequality (μ : YoungDiagram) (k r : ℕ) : - rowPrefix μ.transpose k + rowPrefix μ r ≤ μ.card + r*k := by - let H := max (μ.colLen 0) r - have hh : μ.colLen 0 ≤ H := Nat.le_max_left _ _ - have hr : r ≤ H := Nat.le_max_right _ _ - have hm : rowPrefix μ.transpose k = ∑ i ∈ Finset.range H, min k (μ.rowLen i) := by - rw [← rowTruncate_card, ← transpose_card (rowTruncate μ.transpose k)] - change (colTruncate μ k).card = _ - rw [← rowPrefix_eq_card _ ((colTruncate_height μ k).trans hh)] - exact Finset.sum_congr rfl (fun i _ => colTruncate_rowLen μ k i) - rw [hm, ← rowPrefix_eq_card μ hh] - change _ + (∑ i ∈ Finset.range r, μ.rowLen i) ≤ (∑ i ∈ Finset.range H, μ.rowLen i) + r*k - have hconst : (∑ i ∈ Finset.range r, k) = r*k := by simp - rw [← hconst, ← sum_range_if_lt μ.rowLen hr, ← sum_range_if_lt (fun _ => k) hr, - ← Finset.sum_add_distrib, ← Finset.sum_add_distrib] - apply Finset.sum_le_sum - intro i hi - split_ifs <;> omega - -lemma corner_equality (μ : YoungDiagram) (k : ℕ) : - rowPrefix μ.transpose k + rowPrefix μ (μ.colLen k) = μ.card + μ.colLen k*k := by - let r := μ.colLen k - let H := μ.colLen 0 - have hr : r ≤ H := μ.colLen_anti 0 k (Nat.zero_le _) - have hm : rowPrefix μ.transpose k = ∑ i ∈ Finset.range H, min k (μ.rowLen i) := by - rw [← rowTruncate_card, ← transpose_card (rowTruncate μ.transpose k)] - change (colTruncate μ k).card = _ - rw [← rowPrefix_eq_card _ (colTruncate_height μ k)] - exact Finset.sum_congr rfl (fun i _ => colTruncate_rowLen μ k i) - change rowPrefix μ.transpose k + rowPrefix μ r = μ.card + r*k - rw [hm, ← rowPrefix_eq_card μ (le_refl H)] - change _ + (∑ i ∈ Finset.range r, μ.rowLen i) = (∑ i ∈ Finset.range H, μ.rowLen i) + r*k - have hconst : (∑ i ∈ Finset.range r, k) = r*k := by simp - rw [← hconst, ← sum_range_if_lt μ.rowLen hr, ← sum_range_if_lt (fun _ => k) hr, - ← Finset.sum_add_distrib, ← Finset.sum_add_distrib] - apply Finset.sum_congr rfl - intro i hi - have he : i < r ↔ k < μ.rowLen i := by - exact YoungDiagram.mem_iff_lt_colLen.symm.trans YoungDiagram.mem_iff_lt_rowLen - split_ifs with h - · have hh := he.mp h - omega - · have hh := not_congr he |>.mp h - omega - -/- Ordinary conjugation reverses dominance, including empty diagrams. -/ -theorem dominates_transpose {μ ν : YoungDiagram} (hc : μ.card = ν.card) - (h : Dominates μ ν) : Dominates ν.transpose μ.transpose := by - intro k - have h₁ := corner_inequality μ k (ν.colLen k) - have h₂ := corner_equality ν k - have h₃ := h (ν.colLen k) - omega - -open scoped MonoidAlgebra - -end Saxl - -namespace Saxl - -lemma rowWord_content {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (j : Fin (μ.colLen 0)) : - (Finset.univ.filter (fun i => rowWord t i = j)).card = μ.rowLen j := by - classical - let e : {i // rowWord t i = j} ≃ Fin (μ.rowLen j) := - { toFun := fun i => ⟨(t i.val).val.2, by - have hh := YoungDiagram.mem_iff_lt_rowLen.mp (t i.val).property - have hj := congrArg Fin.val i.property - change (t i.val).val.1 = j.val at hj - simpa only [hj] using hh⟩ - invFun := fun k => ⟨t.symm ⟨(j.val,k.val), YoungDiagram.mem_iff_lt_rowLen.mpr k.isLt⟩, - by apply Fin.ext; change (t (t.symm _)).val.1 = _; simp only [Equiv.apply_symm_apply]⟩ - left_inv := by - intro i - apply Subtype.ext - apply t.injective - simp only [Equiv.apply_symm_apply] - apply Subtype.ext - apply Prod.ext - · exact (congrArg Fin.val i.property).symm - · rfl - right_inv := by intro k; apply Fin.ext; simp only [Equiv.apply_symm_apply] } - simpa only [Fintype.card_subtype, Fintype.card_fin] using Fintype.card_congr e - -@[simp] lemma staircase_transpose (m : ℕ) : (staircase m).transpose = staircase m := by - apply YoungDiagram.ext - apply Finset.ext - intro x - rcases x with ⟨i,j⟩ - simp only [YoungDiagram.mem_cells, YoungDiagram.mem_transpose, Prod.swap_prod_mk, mem_staircase] - omega - -def signCancelMap {n : ℕ} {X : Type uX} {Y : Type uY} [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] - {ρ : Representation ℂ (Equiv.Perm (Fin n)) X} {σ : Representation ℂ (Equiv.Perm (Fin n)) Y} - (f : Representation.IntertwiningMap (signTwist ρ) σ) : - Representation.IntertwiningMap ρ (signTwist σ) where - toLinearMap := f.toLinearMap - isIntertwining' g := by - ext x - change f (ρ g x) = signC g • σ g (f x) - have hh := LinearMap.congr_fun (f.isIntertwining' g) x - change f (signC g • ρ g x) = σ g (f x) at hh - have he := congrArg (fun y => signC g • y) hh - rw [map_smul, smul_smul, signC_mul_self, one_smul] at he - exact he - -theorem dominated_support (m : ℕ) (_hm : 1 ≤ m) (μ : YoungDiagram) - (t : Tableau (staircase m).card μ) (hμ : Dominates (staircase m) μ) : - ∃ f : Representation.IntertwiningMap (spechtRep t) - (staircaseCyclic m).toRepresentation, f ≠ 0 := by - classical - have hc : μ.card = (staircase m).card := by - simpa only [Fintype.card_fin, Fintype.card_coe] using (Fintype.card_congr t).symm - have ht : μ.transpose.card = (staircase m).card := by rw [transpose_card, hc] - have hd : Dominates μ.transpose (staircase m) := by - simpa only [staircase_transpose] using dominates_transpose hc.symm hμ - have hw (j : Fin ((staircase m).colLen 0)) : - (Finset.univ.filter (fun i => repeatedTarget m i = Fin.rev j)).card = (staircase m).rowLen j := by - simpa only [repeatedTarget, Fin.rev_inj] using rowWord_content (stairTableau m) j - obtain ⟨F,hF⟩ := young_orbit_map (staircase m) μ.transpose (transposeTableau t) - ht hd (repeatedTarget m) Fin.revPerm hw - obtain ⟨φ⟩ := staircase_sign_equiv m - let Q := F.comp (dominatedQuotient m φ) - have hQ : Q ≠ 0 := by - obtain ⟨x,hx⟩ := repeatedTarget_in_quotient m φ - intro hz - apply hF - have hh := congrArg (fun l => l x) hz - change F (dominatedQuotient m φ x) = 0 at hh - change dominatedQuotient m φ x = Pi.single (repeatedTarget m) 1 at hx - rwa [hx] at hh - obtain ⟨E⟩ := specht_sign_transpose t - let R := E.symm.toIntertwiningMap.comp (signCancelMap Q) - have hR : R ≠ 0 := by - intro hz - apply hQ - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - have hh := congrArg (fun l => l x) hz - change E.symm (Q x) = 0 at hh - exact E.symm.injective (hh.trans (map_zero _).symm) - let := specht_irreducible t - have hRs : Function.Surjective R := - (Representation.IsIrreducible.surjective_or_eq_zero R).resolve_right hR - obtain ⟨f,hf⟩ := intertwining_lift_surjective R hRs (Representation.IntertwiningMap.id (spechtRep t)) - refine ⟨f, ?_⟩ - intro hz - have hzero : (Representation.IntertwiningMap.id (spechtRep t)) = 0 := by - rw [← hf, hz] - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - exact map_zero R - have he := congrArg (fun l : Representation.IntertwiningMap (spechtRep t) (spechtRep t) => - l ⟨polytabloid t, mem_cyclic _ _⟩) hzero - exact polytabloid_ne_zero t (congrArg Subtype.val he) - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.DominatedQuotient + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uX uY + +namespace Saxl + +lemma transpose_card (μ : YoungDiagram) : μ.transpose.card = μ.card := by + change ((Equiv.prodComm ℕ ℕ).finsetCongr μ.cells).card = μ.cells.card + simp only [Equiv.finsetCongr_apply, Finset.card_map] + +def colTruncate (μ : YoungDiagram) (k : ℕ) := (rowTruncate μ.transpose k).transpose + +lemma colTruncate_rowLen (μ : YoungDiagram) (k i : ℕ) : + (colTruncate μ k).rowLen i = min k (μ.rowLen i) := by + have hh : ∀ j, j < (colTruncate μ k).rowLen i ↔ j < min k (μ.rowLen i) := by + intro j + rw [← YoungDiagram.mem_iff_lt_rowLen] + change (i,j) ∈ (rowTruncate μ.transpose k).transpose ↔ _ + rw [YoungDiagram.mem_transpose] + change (j,i) ∈ rowTruncate μ.transpose k ↔ _ + rw [mem_rowTruncate, YoungDiagram.mem_transpose] + simp only [Prod.swap_prod_mk, YoungDiagram.mem_iff_lt_rowLen, lt_min_iff] + omega + have h₁ := hh ((colTruncate μ k).rowLen i) + have h₂ := hh (min k (μ.rowLen i)) + omega + +lemma colTruncate_height (μ : YoungDiagram) (k : ℕ) : + (colTruncate μ k).colLen 0 ≤ μ.colLen 0 := by + by_contra h + have hm : (μ.colLen 0,0) ∈ colTruncate μ k := YoungDiagram.mem_iff_lt_colLen.mpr (by omega) + have hr := YoungDiagram.mem_iff_lt_rowLen.mp hm + rw [colTruncate_rowLen, rowLen_zero_of_height_le μ le_rfl] at hr + simp at hr + +lemma sum_range_if_lt (f : ℕ → ℕ) {r H : ℕ} (hr : r ≤ H) : + (∑ i ∈ Finset.range H, if i < r then f i else 0) = ∑ i ∈ Finset.range r, f i := by + classical + rw [← Finset.sum_filter] + congr 1 + ext i + simp only [Finset.mem_filter, Finset.mem_range] + omega + +lemma corner_inequality (μ : YoungDiagram) (k r : ℕ) : + rowPrefix μ.transpose k + rowPrefix μ r ≤ μ.card + r*k := by + let H := max (μ.colLen 0) r + have hh : μ.colLen 0 ≤ H := Nat.le_max_left _ _ + have hr : r ≤ H := Nat.le_max_right _ _ + have hm : rowPrefix μ.transpose k = ∑ i ∈ Finset.range H, min k (μ.rowLen i) := by + rw [← rowTruncate_card, ← transpose_card (rowTruncate μ.transpose k)] + change (colTruncate μ k).card = _ + rw [← rowPrefix_eq_card _ ((colTruncate_height μ k).trans hh)] + exact Finset.sum_congr rfl (fun i _ => colTruncate_rowLen μ k i) + rw [hm, ← rowPrefix_eq_card μ hh] + change _ + (∑ i ∈ Finset.range r, μ.rowLen i) ≤ (∑ i ∈ Finset.range H, μ.rowLen i) + r*k + have hconst : (∑ i ∈ Finset.range r, k) = r*k := by simp + rw [← hconst, ← sum_range_if_lt μ.rowLen hr, ← sum_range_if_lt (fun _ => k) hr, + ← Finset.sum_add_distrib, ← Finset.sum_add_distrib] + apply Finset.sum_le_sum + intro i hi + split_ifs <;> omega + +lemma corner_equality (μ : YoungDiagram) (k : ℕ) : + rowPrefix μ.transpose k + rowPrefix μ (μ.colLen k) = μ.card + μ.colLen k*k := by + let r := μ.colLen k + let H := μ.colLen 0 + have hr : r ≤ H := μ.colLen_anti 0 k (Nat.zero_le _) + have hm : rowPrefix μ.transpose k = ∑ i ∈ Finset.range H, min k (μ.rowLen i) := by + rw [← rowTruncate_card, ← transpose_card (rowTruncate μ.transpose k)] + change (colTruncate μ k).card = _ + rw [← rowPrefix_eq_card _ (colTruncate_height μ k)] + exact Finset.sum_congr rfl (fun i _ => colTruncate_rowLen μ k i) + change rowPrefix μ.transpose k + rowPrefix μ r = μ.card + r*k + rw [hm, ← rowPrefix_eq_card μ (le_refl H)] + change _ + (∑ i ∈ Finset.range r, μ.rowLen i) = (∑ i ∈ Finset.range H, μ.rowLen i) + r*k + have hconst : (∑ i ∈ Finset.range r, k) = r*k := by simp + rw [← hconst, ← sum_range_if_lt μ.rowLen hr, ← sum_range_if_lt (fun _ => k) hr, + ← Finset.sum_add_distrib, ← Finset.sum_add_distrib] + apply Finset.sum_congr rfl + intro i hi + have he : i < r ↔ k < μ.rowLen i := by + exact YoungDiagram.mem_iff_lt_colLen.symm.trans YoungDiagram.mem_iff_lt_rowLen + split_ifs with h + · have hh := he.mp h + omega + · have hh := not_congr he |>.mp h + omega + +/- Ordinary conjugation reverses dominance, including empty diagrams. -/ +theorem dominates_transpose {μ ν : YoungDiagram} (hc : μ.card = ν.card) + (h : Dominates μ ν) : Dominates ν.transpose μ.transpose := by + intro k + have h₁ := corner_inequality μ k (ν.colLen k) + have h₂ := corner_equality ν k + have h₃ := h (ν.colLen k) + omega + +open scoped MonoidAlgebra + +end Saxl + +namespace Saxl + +lemma rowWord_content {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (j : Fin (μ.colLen 0)) : + (Finset.univ.filter (fun i => rowWord t i = j)).card = μ.rowLen j := by + classical + let e : {i // rowWord t i = j} ≃ Fin (μ.rowLen j) := + { toFun := fun i => ⟨(t i.val).val.2, by + have hh := YoungDiagram.mem_iff_lt_rowLen.mp (t i.val).property + have hj := congrArg Fin.val i.property + change (t i.val).val.1 = j.val at hj + simpa only [hj] using hh⟩ + invFun := fun k => ⟨t.symm ⟨(j.val,k.val), YoungDiagram.mem_iff_lt_rowLen.mpr k.isLt⟩, + by apply Fin.ext; change (t (t.symm _)).val.1 = _; simp only [Equiv.apply_symm_apply]⟩ + left_inv := by + intro i + apply Subtype.ext + apply t.injective + simp only [Equiv.apply_symm_apply] + apply Subtype.ext + apply Prod.ext + · exact (congrArg Fin.val i.property).symm + · rfl + right_inv := by intro k; apply Fin.ext; simp only [Equiv.apply_symm_apply] } + simpa only [Fintype.card_subtype, Fintype.card_fin] using Fintype.card_congr e + +@[simp] lemma staircase_transpose (m : ℕ) : (staircase m).transpose = staircase m := by + apply YoungDiagram.ext + apply Finset.ext + intro x + rcases x with ⟨i,j⟩ + simp only [YoungDiagram.mem_cells, YoungDiagram.mem_transpose, Prod.swap_prod_mk, mem_staircase] + omega + +def signCancelMap {n : ℕ} {X : Type uX} {Y : Type uY} [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] + {ρ : Representation ℂ (Equiv.Perm (Fin n)) X} {σ : Representation ℂ (Equiv.Perm (Fin n)) Y} + (f : Representation.IntertwiningMap (signTwist ρ) σ) : + Representation.IntertwiningMap ρ (signTwist σ) where + toLinearMap := f.toLinearMap + isIntertwining' g := by + ext x + change f (ρ g x) = signC g • σ g (f x) + have hh := LinearMap.congr_fun (f.isIntertwining' g) x + change f (signC g • ρ g x) = σ g (f x) at hh + have he := congrArg (fun y => signC g • y) hh + rw [map_smul, smul_smul, signC_mul_self, one_smul] at he + exact he + +theorem dominated_support (m : ℕ) (_hm : 1 ≤ m) (μ : YoungDiagram) + (t : Tableau (staircase m).card μ) (hμ : Dominates (staircase m) μ) : + ∃ f : Representation.IntertwiningMap (spechtRep t) + (staircaseCyclic m).toRepresentation, f ≠ 0 := by + classical + have hc : μ.card = (staircase m).card := by + simpa only [Fintype.card_fin, Fintype.card_coe] using (Fintype.card_congr t).symm + have ht : μ.transpose.card = (staircase m).card := by rw [transpose_card, hc] + have hd : Dominates μ.transpose (staircase m) := by + simpa only [staircase_transpose] using dominates_transpose hc.symm hμ + have hw (j : Fin ((staircase m).colLen 0)) : + (Finset.univ.filter (fun i => repeatedTarget m i = Fin.rev j)).card = (staircase m).rowLen j := by + simpa only [repeatedTarget, Fin.rev_inj] using rowWord_content (stairTableau m) j + obtain ⟨F,hF⟩ := young_orbit_map (staircase m) μ.transpose (transposeTableau t) + ht hd (repeatedTarget m) Fin.revPerm hw + obtain ⟨φ⟩ := staircase_sign_equiv m + let Q := F.comp (dominatedQuotient m φ) + have hQ : Q ≠ 0 := by + obtain ⟨x,hx⟩ := repeatedTarget_in_quotient m φ + intro hz + apply hF + have hh := congrArg (fun l => l x) hz + change F (dominatedQuotient m φ x) = 0 at hh + change dominatedQuotient m φ x = Pi.single (repeatedTarget m) 1 at hx + rwa [hx] at hh + obtain ⟨E⟩ := specht_sign_transpose t + let R := E.symm.toIntertwiningMap.comp (signCancelMap Q) + have hR : R ≠ 0 := by + intro hz + apply hQ + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + have hh := congrArg (fun l => l x) hz + change E.symm (Q x) = 0 at hh + exact E.symm.injective (hh.trans (map_zero _).symm) + let := specht_irreducible t + have hRs : Function.Surjective R := + (Representation.IsIrreducible.surjective_or_eq_zero R).resolve_right hR + obtain ⟨f,hf⟩ := intertwining_lift_surjective R hRs (Representation.IntertwiningMap.id (spechtRep t)) + refine ⟨f, ?_⟩ + intro hz + have hzero : (Representation.IntertwiningMap.id (spechtRep t)) = 0 := by + rw [← hf, hz] + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + exact map_zero R + have he := congrArg (fun l : Representation.IntertwiningMap (spechtRep t) (spechtRep t) => + l ⟨polytabloid t, mem_cyclic _ _⟩) hzero + exact polytabloid_ne_zero t (congrArg Subtype.val he) + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/HighProjection.lean b/lean/OAI/RepresentationTheory/Saxl/HighProjection.lean index 917cda305308761f08897533ea7eb38512893e04..e6a2be0d14a1a09a6d61650d348e4a3f4161165a 100644 --- a/lean/OAI/RepresentationTheory/Saxl/HighProjection.lean +++ b/lean/OAI/RepresentationTheory/Saxl/HighProjection.lean @@ -1,292 +1,292 @@ -import OAI.RepresentationTheory.Saxl.StaircaseTensor - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl -/- Translate the high part of each row to the smaller staircase. -/ -def highRowEquiv (h s : ℕ) : - {x : (staircase (h+s)).cells // s ≤ x.val.2} ≃ (staircase h).cells where - toFun x := ⟨(x.val.val.1, x.val.val.2 - s), by - have hx : x.val.val.1 + x.val.val.2 < h+s := mem_staircase.mp x.val.property - exact mem_staircase.mpr (by have := x.property; omega)⟩ - invFun x := ⟨⟨(x.val.1, x.val.2+s), by - have hx : x.val.1 + x.val.2 < h := mem_staircase.mp x.property - exact mem_staircase.mpr (by omega)⟩, by dsimp; omega⟩ - left_inv x := by - apply Subtype.ext - apply Subtype.ext - dsimp - have := x.property - ext <;> omega - right_inv x := by apply Subtype.ext; simp - -def highColEquiv (h s : ℕ) : - {x : (staircase (h+s)).cells // s ≤ x.val.1} ≃ (staircase h).cells where - toFun x := ⟨(x.val.val.1 - s, x.val.val.2), by - have hx : x.val.val.1 + x.val.val.2 < h+s := mem_staircase.mp x.val.property - exact mem_staircase.mpr (by have := x.property; omega)⟩ - invFun x := ⟨⟨(x.val.1+s, x.val.2), by - have hx : x.val.1 + x.val.2 < h := mem_staircase.mp x.property - exact mem_staircase.mpr (by omega)⟩, by dsimp; omega⟩ - left_inv x := by - apply Subtype.ext - apply Subtype.ext - dsimp - have := x.property - ext <;> omega - right_inv x := by apply Subtype.ext; simp - -theorem high_positions_rigidity (h s : ℕ) - (g k : Equiv.Perm (staircase (h+s)).cells) - (hg : ∀ x, (g x).val.1 = x.val.1) - (hk : ∀ x, (k x).val.2 = x.val.2) - (hc : ∀ x, s ≤ (g x).val.2 ↔ s ≤ (k x).val.1) : - ∀ x, s ≤ (g x).val.2 ↔ x.val.1 + x.val.2 < h := by - classical - let A : Finset (staircase (h+s)).cells := Finset.univ.filter (fun x => s ≤ (g x).val.2) - let B : Finset (staircase (h+s)).cells := Finset.univ.filter (fun x => x.val.1 + x.val.2 < h) - let eR : A ≃ (staircase h).cells := - (Equiv.subtypeEquiv g (by intro x; simp only [A, Finset.mem_filter, Finset.mem_univ, true_and])).trans - (highRowEquiv h s) - let eC : A ≃ (staircase h).cells := - (Equiv.subtypeEquiv k (by intro x; simp only [A, Finset.mem_filter, Finset.mem_univ, true_and]; exact hc x)).trans - (highColEquiv h s) - let eB : B ≃ (staircase h).cells := - { toFun := fun x => ⟨x.val.val, mem_staircase.mpr (by simpa [B] using x.property)⟩ - invFun := fun x => ⟨⟨x.val, mem_staircase.mpr (by - have hx := mem_staircase.mp x.property; omega)⟩, by simp [B, mem_staircase.mp x.property]⟩ - left_inv := fun _ => rfl - right_inv := fun _ => rfl } - have hcard : A.card = B.card := by - have he := Fintype.card_congr (eR.trans eB.symm) - simpa using he - have hrow : ∑ x ∈ A, (x.val.1 : ℤ) = ∑ x ∈ B, (x.val.1 : ℤ) := by - rw [← Finset.sum_coe_sort A, ← Finset.sum_coe_sort B] - have hR := Equiv.sum_comp eR (fun x => (x.val.1 : ℤ)) - have hB := Equiv.sum_comp eB (fun x => (x.val.1 : ℤ)) - simpa [eR, eB, highRowEquiv, hg] using hR.trans hB.symm - have hcol : ∑ x ∈ A, (x.val.2 : ℤ) = ∑ x ∈ B, (x.val.2 : ℤ) := by - rw [← Finset.sum_coe_sort A, ← Finset.sum_coe_sort B] - have hC := Equiv.sum_comp eC (fun x => (x.val.2 : ℤ)) - have hB := Equiv.sum_comp eB (fun x => (x.val.2 : ℤ)) - simpa [eC, eB, highColEquiv, hk] using hC.trans hB.symm - let w := fun x : (staircase (h+s)).cells => - 2 * (h : ℤ) - 1 - 2 * (x.val.1 : ℤ) - 2 * (x.val.2 : ℤ) - have he : ∑ x ∈ A, w x = ∑ x ∈ B, w x := by - simp only [w, Finset.sum_sub_distrib, ← Finset.mul_sum, Finset.sum_const, nsmul_eq_mul] - rw [hcard, hrow, hcol] - have hab := finset_eq_of_signed_sum A B w - (fun x hx => by - have hh : x.val.1 + x.val.2 < h := by simpa [B] using hx - dsimp [w] - omega) - (fun x hx => by - have hh : ¬x.val.1 + x.val.2 < h := by simpa [B] using hx - dsimp [w] - omega) he - intro x - have := Finset.ext_iff.mp hab x - simpa [A, B] using this - - -lemma polytabloid_support {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (a : Fin n → Fin (μ.colLen 0)) (ha : polytabloid t a ≠ 0) : - ∃ g : columnGroup t, a = rowWord t ∘ (g : Equiv.Perm (Fin n)) := by - classical - have hex : ∃ g : columnGroup t, a ∘ (g : Equiv.Perm (Fin n)) = rowWord t := by - by_contra! hh - apply ha - unfold polytabloid - simp only [Finset.sum_apply, Pi.smul_apply, wordRep, MonoidHom.coe_mk, - OneHom.coe_mk, LinearMap.coe_mk, AddHom.coe_mk, Pi.single_apply] - simp [hh] - obtain ⟨g, hg⟩ := hex - refine ⟨g⁻¹, ?_⟩ - funext i - have he := congrFun hg ((g : Equiv.Perm (Fin n))⁻¹ i) - simpa using he - -/- Local same-high projection in the ordinary pair-letter coordinate space. -/ -def sameHighProjection (n d e s : ℕ) : - Representation.IntertwiningMap (wordRep n (d*e)) (wordRep n (d*e)) where - toFun z w := if (∀ i, s ≤ (splitLeft w i).val ↔ s ≤ (splitRight w i).val) then z w else 0 - map_add' z y := by ext w; dsimp; split_ifs <;> simp - map_smul' c z := by ext w; dsimp; split_ifs <;> simp - isIntertwining' g := by - apply LinearMap.ext - intro z - funext w - change (if (∀ i, s ≤ (splitLeft w i).val ↔ s ≤ (splitRight w i).val) then z (w ∘ g) else 0) = - (if (∀ i, s ≤ (splitLeft (w ∘ g) i).val ↔ s ≤ (splitRight (w ∘ g) i).val) then z (w ∘ g) else 0) - congr 1 - apply propext - exact (g.forall_congr_right).symm - -theorem staircase_projected_high_positions (h s : ℕ) - (w : Fin (staircase (h+s)).card → Fin ((staircase (h+s)).colLen 0 * (staircase (h+s)).colLen 0)) - (hw : sameHighProjection _ _ _ s (staircaseWord (h+s)) w ≠ 0) : - ∀ i, s ≤ (splitLeft w i).val ↔ - ((stairTableau (h+s) i).val.1 + (stairTableau (h+s) i).val.2 < h) := by - classical - have heq : ∀ i, s ≤ (splitLeft w i).val ↔ s ≤ (splitRight w i).val := by - by_contra hh - apply hw - simp [sameHighProjection, hh] - have hww : staircaseWord (h+s) w ≠ 0 := by - simpa [sameHighProjection, heq] using hw - have hp : polytabloid (stairRowTableau (h+s)) (splitLeft w) * - polytabloid (stairTableau (h+s)) (splitRight w) ≠ 0 := by - simpa only [staircaseWord, wordTensor_tmul] using hww - obtain ⟨g, hg⟩ := polytabloid_support (stairRowTableau (h+s)) _ (mul_ne_zero_iff.mp hp).1 - obtain ⟨k, hk⟩ := polytabloid_support (stairTableau (h+s)) _ (mul_ne_zero_iff.mp hp).2 - let t := stairTableau (h+s) - let gc : Equiv.Perm (staircase (h+s)).cells := (t.symm.trans (g : Equiv.Perm _)).trans t - let kc : Equiv.Perm (staircase (h+s)).cells := (t.symm.trans (k : Equiv.Perm _)).trans t - have hgc : ∀ x, (gc x).val.1 = x.val.1 := by - intro x - have hh := g.property (t.symm x) - change (t ((g : Equiv.Perm _) (t.symm x))).val.1 = (t (t.symm x)).val.1 at hh - simpa [gc] using hh - have hkc : ∀ x, (kc x).val.2 = x.val.2 := by - intro x - have hh := k.property (t.symm x) - change (t ((k : Equiv.Perm _) (t.symm x))).val.2 = (t (t.symm x)).val.2 at hh - simpa [kc] using hh - have hcommon : ∀ x, s ≤ (gc x).val.2 ↔ s ≤ (kc x).val.1 := by - intro x - have hh := heq (t.symm x) - rw [hg, hk] at hh - exact hh - have hr := high_positions_rigidity h s gc kc hgc hkc hcommon - intro i - have hh := hr (t i) - rw [hg] - simpa [gc, t, rowWord, stairRowTableau, staircaseSwap] using hh - - -lemma columnAlt_left {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (h : columnGroup t) : - wordRep n d (h : Equiv.Perm (Fin n)) * columnAlt (d := d) t = - signC (h : Equiv.Perm (Fin n)) • columnAlt t := by - classical - let := Fintype.ofFinite (columnGroup t) - unfold columnAlt - simp only [Finset.mul_sum, mul_smul_comm, Finset.smul_sum] - symm - apply (Equiv.sum_comp (Equiv.mulLeft h) _).symm.trans - apply Finset.sum_congr rfl - intro g hg - change signC (h : Equiv.Perm (Fin n)) • - signC ((h * g : columnGroup t) : Equiv.Perm (Fin n)) • - wordRep n d ((h * g : columnGroup t) : Equiv.Perm (Fin n)) = _ - simp only [Subgroup.coe_mul, map_mul, smul_smul] - rw [← mul_assoc, signC_mul_self, one_mul] - -lemma polytabloid_alternating {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (h : columnGroup t) : wordRep n (μ.colLen 0) (h : Equiv.Perm (Fin n)) - (polytabloid t) = signC (h : Equiv.Perm (Fin n)) • polytabloid t := by - rw [← columnAlt_row] - exact congrArg (fun L : Module.End ℂ (WordSpace n (μ.colLen 0)) => - L (Pi.single (rowWord t) 1)) (columnAlt_left t h) - -/- Move low row letters to the band and high row letters to B_h. -/ -def rotateRowCell (h s : ℕ) (x : (staircase (h+s)).cells) : (staircase (h+s)).cells := - ⟨(x.val.1, if x.val.2 < h - x.val.1 then x.val.2+s else x.val.2-(h-x.val.1)), by - have hx : x.val.1 + x.val.2 < h+s := mem_staircase.mp x.property - apply mem_staircase.mpr - split_ifs <;> omega⟩ - -lemma rotateRowCell_injective (h s : ℕ) : Function.Injective (rotateRowCell h s) := by - intro x y he - have hi0 := congrArg (fun z : (staircase (h+s)).cells => z.val.1) he - have hi : x.val.1 = y.val.1 := hi0 - have hj := congrArg (fun z : (staircase (h+s)).cells => z.val.2) he - have hx : x.val.1 + x.val.2 < h+s := mem_staircase.mp x.property - have hy : y.val.1 + y.val.2 < h+s := mem_staircase.mp y.property - dsimp [rotateRowCell] at hj - apply Subtype.ext - apply Prod.ext hi - split_ifs at hj <;> omega - -def rotateRow (h s : ℕ) : Equiv.Perm (staircase (h+s)).cells := - Equiv.ofBijective (rotateRowCell h s) (⟨rotateRowCell_injective h s, Finite.surjective_of_injective (rotateRowCell_injective h s)⟩) - -lemma rotateRow_high (h s : ℕ) (x : (staircase (h+s)).cells) : - s ≤ (rotateRow h s x).val.2 ↔ x.val.1 + x.val.2 < h := by - have hx : x.val.1 + x.val.2 < h+s := mem_staircase.mp x.property - change s ≤ (if x.val.2 < h - x.val.1 then x.val.2+s else x.val.2-(h-x.val.1)) ↔ _ - split_ifs <;> omega - -def rotateColumn (h s : ℕ) : Equiv.Perm (staircase (h+s)).cells := - ((staircaseSwap (h+s)).trans (rotateRow h s)).trans (staircaseSwap (h+s)) - -lemma rotateColumn_high (h s : ℕ) (x : (staircase (h+s)).cells) : - s ≤ (rotateColumn h s x).val.1 ↔ x.val.1 + x.val.2 < h := by - have hh := rotateRow_high h s (staircaseSwap (h+s) x) - change s ≤ (rotateRow h s (staircaseSwap (h+s) x)).val.2 ↔ _ - simpa [staircaseSwap, Nat.add_comm] using hh - -def rotateRowPositions (h s : ℕ) : columnGroup (stairRowTableau (h+s)) := - ⟨((stairTableau (h+s)).trans (rotateRow h s)).trans (stairTableau (h+s)).symm, by - intro i - change (stairTableau (h+s) ((stairTableau (h+s)).symm (rotateRow h s (stairTableau (h+s) i)))).val.1 = _ - simp only [Equiv.apply_symm_apply] - rfl⟩ - -def rotateColumnPositions (h s : ℕ) : columnGroup (stairTableau (h+s)) := - ⟨((stairTableau (h+s)).trans (rotateColumn h s)).trans (stairTableau (h+s)).symm, by - intro i - change (stairTableau (h+s) ((stairTableau (h+s)).symm (rotateColumn h s (stairTableau (h+s) i)))).val.2 = _ - simp only [Equiv.apply_symm_apply] - rfl⟩ - -lemma polytabloid_column_coeff {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (g : columnGroup t) : - polytabloid t (rowWord t ∘ (g : Equiv.Perm (Fin n))) = signC (g : Equiv.Perm (Fin n)) := by - have hh := congrFun (polytabloid_alternating t g) (rowWord t) - change polytabloid t (rowWord t ∘ (g : Equiv.Perm (Fin n))) = - signC (g : Equiv.Perm (Fin n)) * polytabloid t (rowWord t) at hh - simpa [polytabloid_rowWord] using hh - -/- The projected generator is genuinely nonzero for every band width, -without assuming a tensor factorization. -/ -theorem staircase_projected_ne_zero (h s : ℕ) : - sameHighProjection _ _ _ s (staircaseWord (h+s)) ≠ 0 := by - classical - let a := rowWord (stairRowTableau (h+s)) ∘ (rotateRowPositions h s : Equiv.Perm _) - let b := rowWord (stairTableau (h+s)) ∘ (rotateColumnPositions h s : Equiv.Perm _) - let w := mergeWords a b - have ha (i) : s ≤ (a i).val ↔ (stairTableau (h+s) i).val.1 + (stairTableau (h+s) i).val.2 < h := by - have hh := rotateRow_high h s (stairTableau (h+s) i) - simpa [a, rowWord, stairRowTableau, rotateRowPositions, staircaseSwap] using hh - have hb (i) : s ≤ (b i).val ↔ (stairTableau (h+s) i).val.1 + (stairTableau (h+s) i).val.2 < h := by - have hh := rotateColumn_high h s (stairTableau (h+s) i) - simpa [b, rowWord, rotateColumnPositions] using hh - have hp : ∀ i, s ≤ (splitLeft w i).val ↔ s ≤ (splitRight w i).val := by - intro i - simp only [w, splitLeft_merge, splitRight_merge] - exact (ha i).trans (hb i).symm - intro hz - have he := congrFun hz w - change sameHighProjection _ _ _ s (staircaseWord (h+s)) w = 0 at he - simp only [sameHighProjection, Representation.IntertwiningMap.coe_mk, LinearMap.coe_mk, - AddHom.coe_mk, staircaseWord, wordTensor_tmul, w, splitLeft_merge, splitRight_merge, - a, b, polytabloid_column_coeff] at he - have hn (g : Equiv.Perm (Fin (staircase (h+s)).card)) : signC g ≠ 0 := by - intro hz - have hh := signC_mul_self g - rw [hz, zero_mul] at hh - exact zero_ne_one hh - have hpab : ∀ i, s ≤ (a i).val ↔ s ≤ (b i).val := fun i => (ha i).trans (hb i).symm - rw [ite_eq_left hpab] at he - exact mul_ne_zero (hn _) (hn _) he - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.StaircaseTensor + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl +/- Translate the high part of each row to the smaller staircase. -/ +def highRowEquiv (h s : ℕ) : + {x : (staircase (h+s)).cells // s ≤ x.val.2} ≃ (staircase h).cells where + toFun x := ⟨(x.val.val.1, x.val.val.2 - s), by + have hx : x.val.val.1 + x.val.val.2 < h+s := mem_staircase.mp x.val.property + exact mem_staircase.mpr (by have := x.property; omega)⟩ + invFun x := ⟨⟨(x.val.1, x.val.2+s), by + have hx : x.val.1 + x.val.2 < h := mem_staircase.mp x.property + exact mem_staircase.mpr (by omega)⟩, by dsimp; omega⟩ + left_inv x := by + apply Subtype.ext + apply Subtype.ext + dsimp + have := x.property + ext <;> omega + right_inv x := by apply Subtype.ext; simp + +def highColEquiv (h s : ℕ) : + {x : (staircase (h+s)).cells // s ≤ x.val.1} ≃ (staircase h).cells where + toFun x := ⟨(x.val.val.1 - s, x.val.val.2), by + have hx : x.val.val.1 + x.val.val.2 < h+s := mem_staircase.mp x.val.property + exact mem_staircase.mpr (by have := x.property; omega)⟩ + invFun x := ⟨⟨(x.val.1+s, x.val.2), by + have hx : x.val.1 + x.val.2 < h := mem_staircase.mp x.property + exact mem_staircase.mpr (by omega)⟩, by dsimp; omega⟩ + left_inv x := by + apply Subtype.ext + apply Subtype.ext + dsimp + have := x.property + ext <;> omega + right_inv x := by apply Subtype.ext; simp + +theorem high_positions_rigidity (h s : ℕ) + (g k : Equiv.Perm (staircase (h+s)).cells) + (hg : ∀ x, (g x).val.1 = x.val.1) + (hk : ∀ x, (k x).val.2 = x.val.2) + (hc : ∀ x, s ≤ (g x).val.2 ↔ s ≤ (k x).val.1) : + ∀ x, s ≤ (g x).val.2 ↔ x.val.1 + x.val.2 < h := by + classical + let A : Finset (staircase (h+s)).cells := Finset.univ.filter (fun x => s ≤ (g x).val.2) + let B : Finset (staircase (h+s)).cells := Finset.univ.filter (fun x => x.val.1 + x.val.2 < h) + let eR : A ≃ (staircase h).cells := + (Equiv.subtypeEquiv g (by intro x; simp only [A, Finset.mem_filter, Finset.mem_univ, true_and])).trans + (highRowEquiv h s) + let eC : A ≃ (staircase h).cells := + (Equiv.subtypeEquiv k (by intro x; simp only [A, Finset.mem_filter, Finset.mem_univ, true_and]; exact hc x)).trans + (highColEquiv h s) + let eB : B ≃ (staircase h).cells := + { toFun := fun x => ⟨x.val.val, mem_staircase.mpr (by simpa [B] using x.property)⟩ + invFun := fun x => ⟨⟨x.val, mem_staircase.mpr (by + have hx := mem_staircase.mp x.property; omega)⟩, by simp [B, mem_staircase.mp x.property]⟩ + left_inv := fun _ => rfl + right_inv := fun _ => rfl } + have hcard : A.card = B.card := by + have he := Fintype.card_congr (eR.trans eB.symm) + simpa using he + have hrow : ∑ x ∈ A, (x.val.1 : ℤ) = ∑ x ∈ B, (x.val.1 : ℤ) := by + rw [← Finset.sum_coe_sort A, ← Finset.sum_coe_sort B] + have hR := Equiv.sum_comp eR (fun x => (x.val.1 : ℤ)) + have hB := Equiv.sum_comp eB (fun x => (x.val.1 : ℤ)) + simpa [eR, eB, highRowEquiv, hg] using hR.trans hB.symm + have hcol : ∑ x ∈ A, (x.val.2 : ℤ) = ∑ x ∈ B, (x.val.2 : ℤ) := by + rw [← Finset.sum_coe_sort A, ← Finset.sum_coe_sort B] + have hC := Equiv.sum_comp eC (fun x => (x.val.2 : ℤ)) + have hB := Equiv.sum_comp eB (fun x => (x.val.2 : ℤ)) + simpa [eC, eB, highColEquiv, hk] using hC.trans hB.symm + let w := fun x : (staircase (h+s)).cells => + 2 * (h : ℤ) - 1 - 2 * (x.val.1 : ℤ) - 2 * (x.val.2 : ℤ) + have he : ∑ x ∈ A, w x = ∑ x ∈ B, w x := by + simp only [w, Finset.sum_sub_distrib, ← Finset.mul_sum, Finset.sum_const, nsmul_eq_mul] + rw [hcard, hrow, hcol] + have hab := finset_eq_of_signed_sum A B w + (fun x hx => by + have hh : x.val.1 + x.val.2 < h := by simpa [B] using hx + dsimp [w] + omega) + (fun x hx => by + have hh : ¬x.val.1 + x.val.2 < h := by simpa [B] using hx + dsimp [w] + omega) he + intro x + have := Finset.ext_iff.mp hab x + simpa [A, B] using this + + +lemma polytabloid_support {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (a : Fin n → Fin (μ.colLen 0)) (ha : polytabloid t a ≠ 0) : + ∃ g : columnGroup t, a = rowWord t ∘ (g : Equiv.Perm (Fin n)) := by + classical + have hex : ∃ g : columnGroup t, a ∘ (g : Equiv.Perm (Fin n)) = rowWord t := by + by_contra! hh + apply ha + unfold polytabloid + simp only [Finset.sum_apply, Pi.smul_apply, wordRep, MonoidHom.coe_mk, + OneHom.coe_mk, LinearMap.coe_mk, AddHom.coe_mk, Pi.single_apply] + simp [hh] + obtain ⟨g, hg⟩ := hex + refine ⟨g⁻¹, ?_⟩ + funext i + have he := congrFun hg ((g : Equiv.Perm (Fin n))⁻¹ i) + simpa using he + +/- Local same-high projection in the ordinary pair-letter coordinate space. -/ +def sameHighProjection (n d e s : ℕ) : + Representation.IntertwiningMap (wordRep n (d*e)) (wordRep n (d*e)) where + toFun z w := if (∀ i, s ≤ (splitLeft w i).val ↔ s ≤ (splitRight w i).val) then z w else 0 + map_add' z y := by ext w; dsimp; split_ifs <;> simp + map_smul' c z := by ext w; dsimp; split_ifs <;> simp + isIntertwining' g := by + apply LinearMap.ext + intro z + funext w + change (if (∀ i, s ≤ (splitLeft w i).val ↔ s ≤ (splitRight w i).val) then z (w ∘ g) else 0) = + (if (∀ i, s ≤ (splitLeft (w ∘ g) i).val ↔ s ≤ (splitRight (w ∘ g) i).val) then z (w ∘ g) else 0) + congr 1 + apply propext + exact (g.forall_congr_right).symm + +theorem staircase_projected_high_positions (h s : ℕ) + (w : Fin (staircase (h+s)).card → Fin ((staircase (h+s)).colLen 0 * (staircase (h+s)).colLen 0)) + (hw : sameHighProjection _ _ _ s (staircaseWord (h+s)) w ≠ 0) : + ∀ i, s ≤ (splitLeft w i).val ↔ + ((stairTableau (h+s) i).val.1 + (stairTableau (h+s) i).val.2 < h) := by + classical + have heq : ∀ i, s ≤ (splitLeft w i).val ↔ s ≤ (splitRight w i).val := by + by_contra hh + apply hw + simp [sameHighProjection, hh] + have hww : staircaseWord (h+s) w ≠ 0 := by + simpa [sameHighProjection, heq] using hw + have hp : polytabloid (stairRowTableau (h+s)) (splitLeft w) * + polytabloid (stairTableau (h+s)) (splitRight w) ≠ 0 := by + simpa only [staircaseWord, wordTensor_tmul] using hww + obtain ⟨g, hg⟩ := polytabloid_support (stairRowTableau (h+s)) _ (mul_ne_zero_iff.mp hp).1 + obtain ⟨k, hk⟩ := polytabloid_support (stairTableau (h+s)) _ (mul_ne_zero_iff.mp hp).2 + let t := stairTableau (h+s) + let gc : Equiv.Perm (staircase (h+s)).cells := (t.symm.trans (g : Equiv.Perm _)).trans t + let kc : Equiv.Perm (staircase (h+s)).cells := (t.symm.trans (k : Equiv.Perm _)).trans t + have hgc : ∀ x, (gc x).val.1 = x.val.1 := by + intro x + have hh := g.property (t.symm x) + change (t ((g : Equiv.Perm _) (t.symm x))).val.1 = (t (t.symm x)).val.1 at hh + simpa [gc] using hh + have hkc : ∀ x, (kc x).val.2 = x.val.2 := by + intro x + have hh := k.property (t.symm x) + change (t ((k : Equiv.Perm _) (t.symm x))).val.2 = (t (t.symm x)).val.2 at hh + simpa [kc] using hh + have hcommon : ∀ x, s ≤ (gc x).val.2 ↔ s ≤ (kc x).val.1 := by + intro x + have hh := heq (t.symm x) + rw [hg, hk] at hh + exact hh + have hr := high_positions_rigidity h s gc kc hgc hkc hcommon + intro i + have hh := hr (t i) + rw [hg] + simpa [gc, t, rowWord, stairRowTableau, staircaseSwap] using hh + + +lemma columnAlt_left {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (h : columnGroup t) : + wordRep n d (h : Equiv.Perm (Fin n)) * columnAlt (d := d) t = + signC (h : Equiv.Perm (Fin n)) • columnAlt t := by + classical + let := Fintype.ofFinite (columnGroup t) + unfold columnAlt + simp only [Finset.mul_sum, mul_smul_comm, Finset.smul_sum] + symm + apply (Equiv.sum_comp (Equiv.mulLeft h) _).symm.trans + apply Finset.sum_congr rfl + intro g hg + change signC (h : Equiv.Perm (Fin n)) • + signC ((h * g : columnGroup t) : Equiv.Perm (Fin n)) • + wordRep n d ((h * g : columnGroup t) : Equiv.Perm (Fin n)) = _ + simp only [Subgroup.coe_mul, map_mul, smul_smul] + rw [← mul_assoc, signC_mul_self, one_mul] + +lemma polytabloid_alternating {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (h : columnGroup t) : wordRep n (μ.colLen 0) (h : Equiv.Perm (Fin n)) + (polytabloid t) = signC (h : Equiv.Perm (Fin n)) • polytabloid t := by + rw [← columnAlt_row] + exact congrArg (fun L : Module.End ℂ (WordSpace n (μ.colLen 0)) => + L (Pi.single (rowWord t) 1)) (columnAlt_left t h) + +/- Move low row letters to the band and high row letters to B_h. -/ +def rotateRowCell (h s : ℕ) (x : (staircase (h+s)).cells) : (staircase (h+s)).cells := + ⟨(x.val.1, if x.val.2 < h - x.val.1 then x.val.2+s else x.val.2-(h-x.val.1)), by + have hx : x.val.1 + x.val.2 < h+s := mem_staircase.mp x.property + apply mem_staircase.mpr + split_ifs <;> omega⟩ + +lemma rotateRowCell_injective (h s : ℕ) : Function.Injective (rotateRowCell h s) := by + intro x y he + have hi0 := congrArg (fun z : (staircase (h+s)).cells => z.val.1) he + have hi : x.val.1 = y.val.1 := hi0 + have hj := congrArg (fun z : (staircase (h+s)).cells => z.val.2) he + have hx : x.val.1 + x.val.2 < h+s := mem_staircase.mp x.property + have hy : y.val.1 + y.val.2 < h+s := mem_staircase.mp y.property + dsimp [rotateRowCell] at hj + apply Subtype.ext + apply Prod.ext hi + split_ifs at hj <;> omega + +def rotateRow (h s : ℕ) : Equiv.Perm (staircase (h+s)).cells := + Equiv.ofBijective (rotateRowCell h s) (⟨rotateRowCell_injective h s, Finite.surjective_of_injective (rotateRowCell_injective h s)⟩) + +lemma rotateRow_high (h s : ℕ) (x : (staircase (h+s)).cells) : + s ≤ (rotateRow h s x).val.2 ↔ x.val.1 + x.val.2 < h := by + have hx : x.val.1 + x.val.2 < h+s := mem_staircase.mp x.property + change s ≤ (if x.val.2 < h - x.val.1 then x.val.2+s else x.val.2-(h-x.val.1)) ↔ _ + split_ifs <;> omega + +def rotateColumn (h s : ℕ) : Equiv.Perm (staircase (h+s)).cells := + ((staircaseSwap (h+s)).trans (rotateRow h s)).trans (staircaseSwap (h+s)) + +lemma rotateColumn_high (h s : ℕ) (x : (staircase (h+s)).cells) : + s ≤ (rotateColumn h s x).val.1 ↔ x.val.1 + x.val.2 < h := by + have hh := rotateRow_high h s (staircaseSwap (h+s) x) + change s ≤ (rotateRow h s (staircaseSwap (h+s) x)).val.2 ↔ _ + simpa [staircaseSwap, Nat.add_comm] using hh + +def rotateRowPositions (h s : ℕ) : columnGroup (stairRowTableau (h+s)) := + ⟨((stairTableau (h+s)).trans (rotateRow h s)).trans (stairTableau (h+s)).symm, by + intro i + change (stairTableau (h+s) ((stairTableau (h+s)).symm (rotateRow h s (stairTableau (h+s) i)))).val.1 = _ + simp only [Equiv.apply_symm_apply] + rfl⟩ + +def rotateColumnPositions (h s : ℕ) : columnGroup (stairTableau (h+s)) := + ⟨((stairTableau (h+s)).trans (rotateColumn h s)).trans (stairTableau (h+s)).symm, by + intro i + change (stairTableau (h+s) ((stairTableau (h+s)).symm (rotateColumn h s (stairTableau (h+s) i)))).val.2 = _ + simp only [Equiv.apply_symm_apply] + rfl⟩ + +lemma polytabloid_column_coeff {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (g : columnGroup t) : + polytabloid t (rowWord t ∘ (g : Equiv.Perm (Fin n))) = signC (g : Equiv.Perm (Fin n)) := by + have hh := congrFun (polytabloid_alternating t g) (rowWord t) + change polytabloid t (rowWord t ∘ (g : Equiv.Perm (Fin n))) = + signC (g : Equiv.Perm (Fin n)) * polytabloid t (rowWord t) at hh + simpa [polytabloid_rowWord] using hh + +/- The projected generator is genuinely nonzero for every band width, +without assuming a tensor factorization. -/ +theorem staircase_projected_ne_zero (h s : ℕ) : + sameHighProjection _ _ _ s (staircaseWord (h+s)) ≠ 0 := by + classical + let a := rowWord (stairRowTableau (h+s)) ∘ (rotateRowPositions h s : Equiv.Perm _) + let b := rowWord (stairTableau (h+s)) ∘ (rotateColumnPositions h s : Equiv.Perm _) + let w := mergeWords a b + have ha (i) : s ≤ (a i).val ↔ (stairTableau (h+s) i).val.1 + (stairTableau (h+s) i).val.2 < h := by + have hh := rotateRow_high h s (stairTableau (h+s) i) + simpa [a, rowWord, stairRowTableau, rotateRowPositions, staircaseSwap] using hh + have hb (i) : s ≤ (b i).val ↔ (stairTableau (h+s) i).val.1 + (stairTableau (h+s) i).val.2 < h := by + have hh := rotateColumn_high h s (stairTableau (h+s) i) + simpa [b, rowWord, rotateColumnPositions] using hh + have hp : ∀ i, s ≤ (splitLeft w i).val ↔ s ≤ (splitRight w i).val := by + intro i + simp only [w, splitLeft_merge, splitRight_merge] + exact (ha i).trans (hb i).symm + intro hz + have he := congrFun hz w + change sameHighProjection _ _ _ s (staircaseWord (h+s)) w = 0 at he + simp only [sameHighProjection, Representation.IntertwiningMap.coe_mk, LinearMap.coe_mk, + AddHom.coe_mk, staircaseWord, wordTensor_tmul, w, splitLeft_merge, splitRight_merge, + a, b, polytabloid_column_coeff] at he + have hn (g : Equiv.Perm (Fin (staircase (h+s)).card)) : signC g ≠ 0 := by + intro hz + have hh := signC_mul_self g + rw [hz, zero_mul] at hh + exact zero_ne_one hh + have hpab : ∀ i, s ≤ (a i).val ↔ s ≤ (b i).val := fun i => (ha i).trans (hb i).symm + rw [ite_eq_left hpab] at he + exact mul_ne_zero (hn _) (hn _) he + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/HorizontalRemoval.lean b/lean/OAI/RepresentationTheory/Saxl/HorizontalRemoval.lean index 605bf9258e17c2be5058ab7f6405ebc3062a1d7c..6bd69a6de351a04a5b0f3b14b7a129250622115a 100644 --- a/lean/OAI/RepresentationTheory/Saxl/HorizontalRemoval.lean +++ b/lean/OAI/RepresentationTheory/Saxl/HorizontalRemoval.lean @@ -1,214 +1,214 @@ -import OAI.RepresentationTheory.Saxl.StripSupport - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl -def rowPrefix (μ : YoungDiagram) (k : ℕ) : ℕ := ∑ i ∈ Finset.range k, μ.rowLen i - -def Dominates (μ ν : YoungDiagram) : Prop := ∀ k, rowPrefix ν k ≤ rowPrefix μ k - -lemma rowLen_zero_of_height_le (μ : YoungDiagram) {i : ℕ} (hi : μ.colLen 0 ≤ i) : - μ.rowLen i = 0 := by - apply Nat.eq_zero_of_not_pos - intro h - have hm := YoungDiagram.mem_iff_lt_rowLen.mpr h - have hh := YoungDiagram.mem_iff_lt_colLen.mp hm - omega - -lemma rowPrefix_eq_card (μ : YoungDiagram) {k : ℕ} (hk : μ.colLen 0 ≤ k) : - rowPrefix μ k = μ.card := by - have he : μ.card = ∑ i : Fin (μ.colLen 0), μ.rowLen i := by - have hh := Fintype.card_congr (rowCellEquiv μ) - simpa using hh - rw [he, Fin.sum_univ_eq_sum_range] - symm - apply Finset.sum_subset (Finset.range_mono hk) - intro i hik hin - exact rowLen_zero_of_height_le μ (by simpa using hin) - -/- Tallest-column bottom deletion, expressed by interlacing rows. -/ -def stripRow (μ : YoungDiagram) (t i : ℕ) := μ.rowLen i - t + min t (μ.rowLen (i+1)) - -lemma stripRow_bounds (μ : YoungDiagram) (t i : ℕ) : - μ.rowLen (i+1) ≤ stripRow μ t i ∧ stripRow μ t i ≤ μ.rowLen i := by - have h := μ.rowLen_anti i (i+1) (by omega) - dsimp [stripRow] - omega - -lemma stripRow_antitone (μ : YoungDiagram) (t : ℕ) : Antitone (stripRow μ t) := by - intro i j hij - exact Nat.add_le_add (Nat.sub_le_sub_right (μ.rowLen_anti i j hij) t) - (min_le_min_left t (μ.rowLen_anti (i+1) (j+1) (by omega))) - -def stripRemove (μ : YoungDiagram) (t : ℕ) : YoungDiagram where - cells := μ.cells.filter (fun x => x.2 < stripRow μ t x.1) - isLowerSet := by - intro x y hxy hy - simp only [Finset.mem_coe, Finset.mem_filter] at hy ⊢ - exact ⟨μ.up_left_mem hxy.1 hxy.2 hy.1, - lt_of_le_of_lt hxy.2 (lt_of_lt_of_le hy.2 (stripRow_antitone μ t hxy.1))⟩ - -@[simp] lemma mem_stripRemove {μ : YoungDiagram} {t i j : ℕ} : - (i,j) ∈ stripRemove μ t ↔ j < stripRow μ t i := by - change (i,j) ∈ μ.cells.filter _ ↔ _ - simp only [Finset.mem_filter, YoungDiagram.mem_cells] - exact ⟨And.right, fun h => ⟨YoungDiagram.mem_iff_lt_rowLen.mpr - (lt_of_lt_of_le h (stripRow_bounds μ t i).2), h⟩⟩ - -@[simp] lemma stripRemove_rowLen (μ : YoungDiagram) (t i : ℕ) : - (stripRemove μ t).rowLen i = stripRow μ t i := by - have hh : ∀ j, j < (stripRemove μ t).rowLen i ↔ j < stripRow μ t i := by - intro j - rw [← YoungDiagram.mem_iff_lt_rowLen, mem_stripRemove] - have h₁ := hh ((stripRemove μ t).rowLen i) - have h₂ := hh (stripRow μ t i) - omega - -lemma stripRemove_le (μ : YoungDiagram) (t : ℕ) : stripRemove μ t ≤ μ := by - intro x hx - exact (Finset.mem_filter.mp hx).1 - -lemma stripRemove_horizontal (μ : YoungDiagram) (t : ℕ) : HorizontalStrip (stripRemove μ t) μ := by - refine ⟨stripRemove_le μ t, ?_⟩ - intro x hx hxn y hy hyn hcol - have hhx := YoungDiagram.mem_iff_lt_rowLen.mp hx - have hhy := YoungDiagram.mem_iff_lt_rowLen.mp hy - have hnx : stripRow μ t x.1 ≤ x.2 := le_of_not_gt (fun h => hxn (mem_stripRemove.mpr h)) - have hny : stripRow μ t y.1 ≤ y.2 := le_of_not_gt (fun h => hyn (mem_stripRemove.mpr h)) - have hr : x.1 = y.1 := by - rcases lt_trichotomy x.1 y.1 with hr | hr | hr - · have hh := μ.rowLen_anti (x.1+1) y.1 (by omega) - have hb := (stripRow_bounds μ t x.1).1 - omega - · exact hr - · have hh := μ.rowLen_anti (y.1+1) x.1 (by omega) - have hb := (stripRow_bounds μ t y.1).1 - omega - exact Prod.ext hr hcol - -lemma stripRemove_prefix (μ : YoungDiagram) (t k : ℕ) : - rowPrefix (stripRemove μ t) k + min t (μ.rowLen 0) = - rowPrefix μ k + min t (μ.rowLen k) := by - induction k with - | zero => simp [rowPrefix] - | succ k ih => - have hr : (stripRemove μ t).rowLen k + min t (μ.rowLen k) = - μ.rowLen k + min t (μ.rowLen (k+1)) := by - rw [stripRemove_rowLen] - dsimp [stripRow] - omega - simp only [rowPrefix, Finset.sum_range_succ] at ih ⊢ - omega - -lemma stripRemove_card (μ : YoungDiagram) (t : ℕ) : - (stripRemove μ t).card + min t (μ.rowLen 0) = μ.card := by - have hh := stripRemove_prefix μ t (μ.colLen 0) - rw [rowPrefix_eq_card μ le_rfl, rowLen_zero_of_height_le μ le_rfl, min_zero, add_zero] at hh - have ht : (stripRemove μ t).colLen 0 ≤ μ.colLen 0 := by - by_contra h - have hm : (μ.colLen 0, 0) ∈ stripRemove μ t := YoungDiagram.mem_iff_lt_colLen.mpr (by omega) - have hh := YoungDiagram.mem_iff_lt_colLen.mp (stripRemove_le μ t hm) - omega - rwa [rowPrefix_eq_card _ ht] at hh - -lemma stripRemove_full (μ : YoungDiagram) (i : ℕ) : - (stripRemove μ (μ.rowLen 0)).rowLen i = μ.rowLen (i+1) := by - rw [stripRemove_rowLen] - have hi := μ.rowLen_anti 0 i (Nat.zero_le _) - have hs := μ.rowLen_anti 0 (i+1) (Nat.zero_le _) - dsimp [stripRow] - omega - - -lemma rowPrefix_succ (μ : YoungDiagram) (k : ℕ) : - rowPrefix μ (k+1) = rowPrefix μ k + μ.rowLen k := by - simp [rowPrefix, Finset.sum_range_succ] - -lemma rowPrefix_le_card (μ : YoungDiagram) (k : ℕ) : rowPrefix μ k ≤ μ.card := by - rw [← rowPrefix_eq_card μ (Nat.le_max_left _ k)] - exact Finset.sum_le_sum_of_subset (Finset.range_mono (Nat.le_max_right _ _)) - -lemma rowPrefix_mono (μ : YoungDiagram) {k l : ℕ} (h : k ≤ l) : - rowPrefix μ k ≤ rowPrefix μ l := - Finset.sum_le_sum_of_subset (Finset.range_mono h) - -def rowTruncate (μ : YoungDiagram) (k : ℕ) : YoungDiagram where - cells := μ.cells.filter (fun x => x.1 < k) - isLowerSet := by - intro x y hxy hy - simp only [Finset.mem_coe, Finset.mem_filter] at hy ⊢ - exact ⟨μ.up_left_mem hxy.1 hxy.2 hy.1, lt_of_le_of_lt hxy.1 hy.2⟩ - -@[simp] lemma mem_rowTruncate {μ : YoungDiagram} {k i j : ℕ} : - (i,j) ∈ rowTruncate μ k ↔ (i,j) ∈ μ ∧ i < k := by - change (i,j) ∈ μ.cells.filter (fun x => x.1 < k) ↔ (i,j) ∈ μ.cells ∧ i < k - exact Finset.mem_filter - -lemma rowTruncate_rowLen (μ : YoungDiagram) (k i : ℕ) : - (rowTruncate μ k).rowLen i = if i < k then μ.rowLen i else 0 := by - have hh : ∀ j, j < (rowTruncate μ k).rowLen i ↔ j < if i < k then μ.rowLen i else 0 := by - intro j - rw [← YoungDiagram.mem_iff_lt_rowLen, mem_rowTruncate, YoungDiagram.mem_iff_lt_rowLen] - split_ifs <;> simp_all - have h₁ := hh ((rowTruncate μ k).rowLen i) - have h₂ := hh (if i < k then μ.rowLen i else 0) - omega - -lemma rowTruncate_height (μ : YoungDiagram) (k : ℕ) : (rowTruncate μ k).colLen 0 ≤ k := by - by_contra h - have hm : (k,0) ∈ rowTruncate μ k := YoungDiagram.mem_iff_lt_colLen.mpr (by omega) - exact Nat.lt_irrefl k (mem_rowTruncate.mp hm).2 - -lemma rowTruncate_prefix (μ : YoungDiagram) (k q : ℕ) (hq : q ≤ k) : - rowPrefix (rowTruncate μ k) q = rowPrefix μ q := by - apply Finset.sum_congr rfl - intro i hi - rw [rowTruncate_rowLen, ite_eq_left (lt_of_lt_of_le (Finset.mem_range.mp hi) hq)] - -lemma rowTruncate_card (μ : YoungDiagram) (k : ℕ) : - (rowTruncate μ k).card = rowPrefix μ k := by - rw [← rowPrefix_eq_card _ (rowTruncate_height μ k), rowTruncate_prefix _ _ _ le_rfl] - -lemma dominates_stripRemove_last (θ τ : YoungDiagram) (k : ℕ) - (hh : θ.colLen 0 ≤ k+1) (hc : τ.card = θ.card) (hd : Dominates τ θ) : - (stripRemove τ (θ.rowLen k)).card = (rowTruncate θ k).card ∧ - Dominates (stripRemove τ (θ.rowLen k)) (rowTruncate θ k) := by - have hw : θ.rowLen k ≤ τ.rowLen 0 := by - have hh := hd 1 - simp only [rowPrefix, Finset.sum_range_one] at hh - exact (θ.rowLen_anti 0 k (Nat.zero_le _)).trans hh - have hθ : (rowTruncate θ k).card + θ.rowLen k = θ.card := by - rw [rowTruncate_card, ← rowPrefix_succ, rowPrefix_eq_card θ hh] - have hτ : (stripRemove τ (θ.rowLen k)).card + θ.rowLen k = τ.card := by - simpa only [min_eq_left hw] using stripRemove_card τ (θ.rowLen k) - have hcard : (stripRemove τ (θ.rowLen k)).card = (rowTruncate θ k).card := by omega - refine ⟨hcard, ?_⟩ - have hsmall (q : ℕ) (hq : q ≤ k) : rowPrefix θ q ≤ rowPrefix (stripRemove τ (θ.rowLen k)) q := by - have he := stripRemove_prefix τ (θ.rowLen k) q - rw [min_eq_left hw] at he - by_cases hr : θ.rowLen k ≤ τ.rowLen q - · rw [min_eq_left hr] at he - have hh := hd q - omega - · rw [min_eq_right (by omega : τ.rowLen q ≤ θ.rowLen k)] at he - have hsq := hd (q+1) - rw [rowPrefix_succ, rowPrefix_succ] at hsq - have ht := θ.rowLen_anti q k hq - omega - intro q - by_cases hq : q ≤ k - · rw [rowTruncate_prefix _ _ _ hq] - exact hsmall q hq - · have hle := rowPrefix_le_card (rowTruncate θ k) q - rw [rowTruncate_card] at hle - exact hle.trans ((hsmall k le_rfl).trans (rowPrefix_mono _ (by omega))) - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.StripSupport + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl +def rowPrefix (μ : YoungDiagram) (k : ℕ) : ℕ := ∑ i ∈ Finset.range k, μ.rowLen i + +def Dominates (μ ν : YoungDiagram) : Prop := ∀ k, rowPrefix ν k ≤ rowPrefix μ k + +lemma rowLen_zero_of_height_le (μ : YoungDiagram) {i : ℕ} (hi : μ.colLen 0 ≤ i) : + μ.rowLen i = 0 := by + apply Nat.eq_zero_of_not_pos + intro h + have hm := YoungDiagram.mem_iff_lt_rowLen.mpr h + have hh := YoungDiagram.mem_iff_lt_colLen.mp hm + omega + +lemma rowPrefix_eq_card (μ : YoungDiagram) {k : ℕ} (hk : μ.colLen 0 ≤ k) : + rowPrefix μ k = μ.card := by + have he : μ.card = ∑ i : Fin (μ.colLen 0), μ.rowLen i := by + have hh := Fintype.card_congr (rowCellEquiv μ) + simpa using hh + rw [he, Fin.sum_univ_eq_sum_range] + symm + apply Finset.sum_subset (Finset.range_mono hk) + intro i hik hin + exact rowLen_zero_of_height_le μ (by simpa using hin) + +/- Tallest-column bottom deletion, expressed by interlacing rows. -/ +def stripRow (μ : YoungDiagram) (t i : ℕ) := μ.rowLen i - t + min t (μ.rowLen (i+1)) + +lemma stripRow_bounds (μ : YoungDiagram) (t i : ℕ) : + μ.rowLen (i+1) ≤ stripRow μ t i ∧ stripRow μ t i ≤ μ.rowLen i := by + have h := μ.rowLen_anti i (i+1) (by omega) + dsimp [stripRow] + omega + +lemma stripRow_antitone (μ : YoungDiagram) (t : ℕ) : Antitone (stripRow μ t) := by + intro i j hij + exact Nat.add_le_add (Nat.sub_le_sub_right (μ.rowLen_anti i j hij) t) + (min_le_min_left t (μ.rowLen_anti (i+1) (j+1) (by omega))) + +def stripRemove (μ : YoungDiagram) (t : ℕ) : YoungDiagram where + cells := μ.cells.filter (fun x => x.2 < stripRow μ t x.1) + isLowerSet := by + intro x y hxy hy + simp only [Finset.mem_coe, Finset.mem_filter] at hy ⊢ + exact ⟨μ.up_left_mem hxy.1 hxy.2 hy.1, + lt_of_le_of_lt hxy.2 (lt_of_lt_of_le hy.2 (stripRow_antitone μ t hxy.1))⟩ + +@[simp] lemma mem_stripRemove {μ : YoungDiagram} {t i j : ℕ} : + (i,j) ∈ stripRemove μ t ↔ j < stripRow μ t i := by + change (i,j) ∈ μ.cells.filter _ ↔ _ + simp only [Finset.mem_filter, YoungDiagram.mem_cells] + exact ⟨And.right, fun h => ⟨YoungDiagram.mem_iff_lt_rowLen.mpr + (lt_of_lt_of_le h (stripRow_bounds μ t i).2), h⟩⟩ + +@[simp] lemma stripRemove_rowLen (μ : YoungDiagram) (t i : ℕ) : + (stripRemove μ t).rowLen i = stripRow μ t i := by + have hh : ∀ j, j < (stripRemove μ t).rowLen i ↔ j < stripRow μ t i := by + intro j + rw [← YoungDiagram.mem_iff_lt_rowLen, mem_stripRemove] + have h₁ := hh ((stripRemove μ t).rowLen i) + have h₂ := hh (stripRow μ t i) + omega + +lemma stripRemove_le (μ : YoungDiagram) (t : ℕ) : stripRemove μ t ≤ μ := by + intro x hx + exact (Finset.mem_filter.mp hx).1 + +lemma stripRemove_horizontal (μ : YoungDiagram) (t : ℕ) : HorizontalStrip (stripRemove μ t) μ := by + refine ⟨stripRemove_le μ t, ?_⟩ + intro x hx hxn y hy hyn hcol + have hhx := YoungDiagram.mem_iff_lt_rowLen.mp hx + have hhy := YoungDiagram.mem_iff_lt_rowLen.mp hy + have hnx : stripRow μ t x.1 ≤ x.2 := le_of_not_gt (fun h => hxn (mem_stripRemove.mpr h)) + have hny : stripRow μ t y.1 ≤ y.2 := le_of_not_gt (fun h => hyn (mem_stripRemove.mpr h)) + have hr : x.1 = y.1 := by + rcases lt_trichotomy x.1 y.1 with hr | hr | hr + · have hh := μ.rowLen_anti (x.1+1) y.1 (by omega) + have hb := (stripRow_bounds μ t x.1).1 + omega + · exact hr + · have hh := μ.rowLen_anti (y.1+1) x.1 (by omega) + have hb := (stripRow_bounds μ t y.1).1 + omega + exact Prod.ext hr hcol + +lemma stripRemove_prefix (μ : YoungDiagram) (t k : ℕ) : + rowPrefix (stripRemove μ t) k + min t (μ.rowLen 0) = + rowPrefix μ k + min t (μ.rowLen k) := by + induction k with + | zero => simp [rowPrefix] + | succ k ih => + have hr : (stripRemove μ t).rowLen k + min t (μ.rowLen k) = + μ.rowLen k + min t (μ.rowLen (k+1)) := by + rw [stripRemove_rowLen] + dsimp [stripRow] + omega + simp only [rowPrefix, Finset.sum_range_succ] at ih ⊢ + omega + +lemma stripRemove_card (μ : YoungDiagram) (t : ℕ) : + (stripRemove μ t).card + min t (μ.rowLen 0) = μ.card := by + have hh := stripRemove_prefix μ t (μ.colLen 0) + rw [rowPrefix_eq_card μ le_rfl, rowLen_zero_of_height_le μ le_rfl, min_zero, add_zero] at hh + have ht : (stripRemove μ t).colLen 0 ≤ μ.colLen 0 := by + by_contra h + have hm : (μ.colLen 0, 0) ∈ stripRemove μ t := YoungDiagram.mem_iff_lt_colLen.mpr (by omega) + have hh := YoungDiagram.mem_iff_lt_colLen.mp (stripRemove_le μ t hm) + omega + rwa [rowPrefix_eq_card _ ht] at hh + +lemma stripRemove_full (μ : YoungDiagram) (i : ℕ) : + (stripRemove μ (μ.rowLen 0)).rowLen i = μ.rowLen (i+1) := by + rw [stripRemove_rowLen] + have hi := μ.rowLen_anti 0 i (Nat.zero_le _) + have hs := μ.rowLen_anti 0 (i+1) (Nat.zero_le _) + dsimp [stripRow] + omega + + +lemma rowPrefix_succ (μ : YoungDiagram) (k : ℕ) : + rowPrefix μ (k+1) = rowPrefix μ k + μ.rowLen k := by + simp [rowPrefix, Finset.sum_range_succ] + +lemma rowPrefix_le_card (μ : YoungDiagram) (k : ℕ) : rowPrefix μ k ≤ μ.card := by + rw [← rowPrefix_eq_card μ (Nat.le_max_left _ k)] + exact Finset.sum_le_sum_of_subset (Finset.range_mono (Nat.le_max_right _ _)) + +lemma rowPrefix_mono (μ : YoungDiagram) {k l : ℕ} (h : k ≤ l) : + rowPrefix μ k ≤ rowPrefix μ l := + Finset.sum_le_sum_of_subset (Finset.range_mono h) + +def rowTruncate (μ : YoungDiagram) (k : ℕ) : YoungDiagram where + cells := μ.cells.filter (fun x => x.1 < k) + isLowerSet := by + intro x y hxy hy + simp only [Finset.mem_coe, Finset.mem_filter] at hy ⊢ + exact ⟨μ.up_left_mem hxy.1 hxy.2 hy.1, lt_of_le_of_lt hxy.1 hy.2⟩ + +@[simp] lemma mem_rowTruncate {μ : YoungDiagram} {k i j : ℕ} : + (i,j) ∈ rowTruncate μ k ↔ (i,j) ∈ μ ∧ i < k := by + change (i,j) ∈ μ.cells.filter (fun x => x.1 < k) ↔ (i,j) ∈ μ.cells ∧ i < k + exact Finset.mem_filter + +lemma rowTruncate_rowLen (μ : YoungDiagram) (k i : ℕ) : + (rowTruncate μ k).rowLen i = if i < k then μ.rowLen i else 0 := by + have hh : ∀ j, j < (rowTruncate μ k).rowLen i ↔ j < if i < k then μ.rowLen i else 0 := by + intro j + rw [← YoungDiagram.mem_iff_lt_rowLen, mem_rowTruncate, YoungDiagram.mem_iff_lt_rowLen] + split_ifs <;> simp_all + have h₁ := hh ((rowTruncate μ k).rowLen i) + have h₂ := hh (if i < k then μ.rowLen i else 0) + omega + +lemma rowTruncate_height (μ : YoungDiagram) (k : ℕ) : (rowTruncate μ k).colLen 0 ≤ k := by + by_contra h + have hm : (k,0) ∈ rowTruncate μ k := YoungDiagram.mem_iff_lt_colLen.mpr (by omega) + exact Nat.lt_irrefl k (mem_rowTruncate.mp hm).2 + +lemma rowTruncate_prefix (μ : YoungDiagram) (k q : ℕ) (hq : q ≤ k) : + rowPrefix (rowTruncate μ k) q = rowPrefix μ q := by + apply Finset.sum_congr rfl + intro i hi + rw [rowTruncate_rowLen, ite_eq_left (lt_of_lt_of_le (Finset.mem_range.mp hi) hq)] + +lemma rowTruncate_card (μ : YoungDiagram) (k : ℕ) : + (rowTruncate μ k).card = rowPrefix μ k := by + rw [← rowPrefix_eq_card _ (rowTruncate_height μ k), rowTruncate_prefix _ _ _ le_rfl] + +lemma dominates_stripRemove_last (θ τ : YoungDiagram) (k : ℕ) + (hh : θ.colLen 0 ≤ k+1) (hc : τ.card = θ.card) (hd : Dominates τ θ) : + (stripRemove τ (θ.rowLen k)).card = (rowTruncate θ k).card ∧ + Dominates (stripRemove τ (θ.rowLen k)) (rowTruncate θ k) := by + have hw : θ.rowLen k ≤ τ.rowLen 0 := by + have hh := hd 1 + simp only [rowPrefix, Finset.sum_range_one] at hh + exact (θ.rowLen_anti 0 k (Nat.zero_le _)).trans hh + have hθ : (rowTruncate θ k).card + θ.rowLen k = θ.card := by + rw [rowTruncate_card, ← rowPrefix_succ, rowPrefix_eq_card θ hh] + have hτ : (stripRemove τ (θ.rowLen k)).card + θ.rowLen k = τ.card := by + simpa only [min_eq_left hw] using stripRemove_card τ (θ.rowLen k) + have hcard : (stripRemove τ (θ.rowLen k)).card = (rowTruncate θ k).card := by omega + refine ⟨hcard, ?_⟩ + have hsmall (q : ℕ) (hq : q ≤ k) : rowPrefix θ q ≤ rowPrefix (stripRemove τ (θ.rowLen k)) q := by + have he := stripRemove_prefix τ (θ.rowLen k) q + rw [min_eq_left hw] at he + by_cases hr : θ.rowLen k ≤ τ.rowLen q + · rw [min_eq_left hr] at he + have hh := hd q + omega + · rw [min_eq_right (by omega : τ.rowLen q ≤ θ.rowLen k)] at he + have hsq := hd (q+1) + rw [rowPrefix_succ, rowPrefix_succ] at hsq + have ht := θ.rowLen_anti q k hq + omega + intro q + by_cases hq : q ≤ k + · rw [rowTruncate_prefix _ _ _ hq] + exact hsmall q hq + · have hle := rowPrefix_le_card (rowTruncate θ k) q + rw [rowTruncate_card] at hle + exact hle.trans ((hsmall k le_rfl).trans (rowPrefix_mono _ (by omega))) + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/Main.lean b/lean/OAI/RepresentationTheory/Saxl/Main.lean index e56f8228fc841e9eb4b0a69f1d7d0c7ae27258be..4bbc2f71b96cb4d920f3e5094856ca899dd3419a 100644 --- a/lean/OAI/RepresentationTheory/Saxl/Main.lean +++ b/lean/OAI/RepresentationTheory/Saxl/Main.lean @@ -1,128 +1,128 @@ -import OAI.RepresentationTheory.Saxl.StripReduction - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uV - -namespace Saxl - -lemma SizedStripChain.of_horizontal {ν μ : YoungDiagram} (hs : HorizontalStrip ν μ) : - SizedStripChain [μ.card-ν.card] ν μ := by - have hc : ν.card ≤ μ.card := Finset.card_le_card hs.1 - exact SizedStripChain.snoc (SizedStripChain.nil ν) hs (Nat.add_sub_of_le hc) - -lemma StripChain.sized {q ν μ} (hs : StripChain q ν μ) : - ∃ bs : List ℕ, bs.length = q ∧ SizedStripChain bs ν μ := by - induction hs with - | nil μ => exact ⟨[],rfl,SizedStripChain.nil μ⟩ - | @snoc q ν η μ hs hh hn ih => - obtain ⟨bs,hbs,hS⟩ := ih - have hc : η.card ≤ μ.card := Finset.card_le_card hh.1 - exact ⟨bs++[μ.card-η.card], by simp [hbs], SizedStripChain.snoc hS hh (Nat.add_sub_of_le hc)⟩ - -/- Lift the factor support through the exact same-high quotient. -/ -theorem band_cut_support (h s m : ℕ) (he : h+s=m) - (ν μ : YoungDiagram) (hν : ν.card = (staircase h).card) - (t : Tableau (staircase m).card μ) (bs : List ℕ) (hs : SizedStripChain bs ν μ) - (fh : Representation.IntertwiningMap (spechtRep (canonicalTableau ν hν)) - (staircaseCyclic h).toRepresentation) (hfh : fh ≠ 0) - (hband : ∀ (η : YoungDiagram) (r : Tableau (bandSize h s) η), η.colLen 0 ≤ bs.length → - ∃ F : Representation.IntertwiningMap (spechtRep r) - (cyclic (wordRep _ _) (stairBandWord h s)).toRepresentation, F ≠ 0) : - ∃ F : Representation.IntertwiningMap (spechtRep t) (staircaseCyclic m).toRepresentation, F ≠ 0 := by - subst m - obtain ⟨f,hf⟩ := shiftedStairWord_support h s ν (canonicalTableau ν hν) fh hfh - have H := strip_product_support hs (canonicalTableau ν hν) t (cutPositions h s) - (shiftedStairWord h s) (stairBandWord h s) - (fun a => s ≤ ((finProdFinEquiv.symm a).1).val) - (shiftedStairWord_alphabet h s) (stairBandWord_alphabet h s) f hf hband - rw [← staircase_cut_factor] at H - obtain ⟨F,hF⟩ := H - exact cyclic_projection_support (sameHighProjection _ _ _ s) (staircaseWord (h+s)) F hF - -lemma staircase_one_dominates (μ : YoungDiagram) (hμ : μ.card = (staircase 1).card) : - Dominates (staircase 1) μ := by - intro k - by_cases hk : k=0 - · subst k; simp [rowPrefix] - · have hh : (staircase 1).colLen 0 ≤ k := by simp only [staircase_colLen]; omega - rw [rowPrefix_eq_card _ hh,← hμ] - exact rowPrefix_le_card μ k - -/- Strong induction, including m=1 and every -partition of the exact triangular size. -/ -theorem full_cyclic_support (m : ℕ) (hm : 1 ≤ m) (μ : YoungDiagram) - (t : Tableau (staircase m).card μ) : - ∃ F : Representation.IntertwiningMap (spechtRep t) (staircaseCyclic m).toRepresentation, F ≠ 0 := by - induction m using Nat.strong_induction_on generalizing μ with - | h m ih => - have hμ : μ.card = (staircase m).card := by - simpa only [Fintype.card_fin,Fintype.card_coe] using (Fintype.card_congr t).symm - by_cases hd : Dominates (staircase m) μ - · exact dominated_support m hm μ t hd - have hm2 : 2 ≤ m := by - by_contra hn - have he : m=1 := by omega - subst m - exact hd (staircase_one_dominates μ hμ) - rcases strip_reduction m hm2 μ hμ hd with ⟨ν,hν,hs⟩ | ⟨hm5,q,hq,ν,hν,hs⟩ - · obtain ⟨f,hf⟩ := ih (m-1) (by omega) (by omega) ν (canonicalTableau ν hν) - exact band_cut_support (m-1) 1 m (by omega) ν μ hν t [μ.card-ν.card] - (SizedStripChain.of_horizontal hs) f hf (fun η r hη => oneBand_support (m-1) η r hη) - · obtain ⟨f,hf⟩ := ih (m-2) (by omega) (by omega) ν (canonicalTableau ν hν) - obtain ⟨bs,hbs,hS⟩ := hs.sized - exact band_cut_support (m-2) 2 m (by omega) ν μ hν t bs hS f hf - (fun η r hη => twoBand_support (m-2) (by omega) η r (by omega)) - -/- The strengthened cyclic form of Saxl’s conjecture. -/ -theorem cyclic_saxl_conjecture : CyclicSaxlConjecture := by - intro m hm μ hμ - exact full_cyclic_support m hm μ (canonicalTableau μ hμ) - -/- Every complex staircase tensor square contains -all Specht irreducibles of its symmetric group. -/ -theorem saxl_conjecture : SaxlConjecture := saxl_of_cyclic_support cyclic_saxl_conjecture - - - -theorem cyclic_saxl : CyclicSaxlConjecture := cyclic_saxl_conjecture - -/- Specht classification implies that every finite-dimensional irreducible -complex representation embeds in the staircase tensor square. -/ -theorem saxl_contains_every_irreducible (m : ℕ) (hm : 1 ≤ m) - {V : Type uV} [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin (staircase m).card)) V) - [Representation.IsIrreducible ρ] : - ∃ F : Representation.IntertwiningMap ρ - ((spechtRep (stairTableau m)).tprod (spechtRep (stairTableau m))), - Function.Injective F := by - obtain ⟨p,⟨e⟩⟩ := irreducible_equiv_specht ρ - obtain ⟨f,hf⟩ := full_cyclic_support m hm (partitionDiagram p) (partitionTableau p) - let := specht_irreducible (partitionTableau p) - have hi := (Representation.IsIrreducible.injective_or_eq_zero f).resolve_right hf - exact ⟨((staircaseToTensor m).comp f).comp e.toIntertwiningMap, - (staircaseToTensor_injective m).comp (hi.comp e.injective)⟩ - -/- The positive-multiplicity conclusion with the literal -triangular degree, rather than the definitionally convenient cell count. -/ -theorem saxl_kronecker_pos (m : ℕ) (hm : 1 ≤ m) (μ : YoungDiagram) - (hμ : μ.card = m * (m + 1) / 2) : - 0 < kronecker (canonicalTableau (staircase m) (staircase_card m)) - (canonicalTableau (staircase m) (staircase_card m)) (canonicalTableau μ hμ) := by - have H : ∀ (n : ℕ) (hn : (staircase m).card = n) (hnu : μ.card = n), - 0 < kronecker (canonicalTableau (staircase m) hn) - (canonicalTableau (staircase m) hn) (canonicalTableau μ hnu) := by - intro n hn hnu - subst n - exact saxl_conjecture m hm μ hnu - exact H _ (staircase_card m) hμ - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.StripReduction + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uV + +namespace Saxl + +lemma SizedStripChain.of_horizontal {ν μ : YoungDiagram} (hs : HorizontalStrip ν μ) : + SizedStripChain [μ.card-ν.card] ν μ := by + have hc : ν.card ≤ μ.card := Finset.card_le_card hs.1 + exact SizedStripChain.snoc (SizedStripChain.nil ν) hs (Nat.add_sub_of_le hc) + +lemma StripChain.sized {q ν μ} (hs : StripChain q ν μ) : + ∃ bs : List ℕ, bs.length = q ∧ SizedStripChain bs ν μ := by + induction hs with + | nil μ => exact ⟨[],rfl,SizedStripChain.nil μ⟩ + | @snoc q ν η μ hs hh hn ih => + obtain ⟨bs,hbs,hS⟩ := ih + have hc : η.card ≤ μ.card := Finset.card_le_card hh.1 + exact ⟨bs++[μ.card-η.card], by simp [hbs], SizedStripChain.snoc hS hh (Nat.add_sub_of_le hc)⟩ + +/- Lift the factor support through the exact same-high quotient. -/ +theorem band_cut_support (h s m : ℕ) (he : h+s=m) + (ν μ : YoungDiagram) (hν : ν.card = (staircase h).card) + (t : Tableau (staircase m).card μ) (bs : List ℕ) (hs : SizedStripChain bs ν μ) + (fh : Representation.IntertwiningMap (spechtRep (canonicalTableau ν hν)) + (staircaseCyclic h).toRepresentation) (hfh : fh ≠ 0) + (hband : ∀ (η : YoungDiagram) (r : Tableau (bandSize h s) η), η.colLen 0 ≤ bs.length → + ∃ F : Representation.IntertwiningMap (spechtRep r) + (cyclic (wordRep _ _) (stairBandWord h s)).toRepresentation, F ≠ 0) : + ∃ F : Representation.IntertwiningMap (spechtRep t) (staircaseCyclic m).toRepresentation, F ≠ 0 := by + subst m + obtain ⟨f,hf⟩ := shiftedStairWord_support h s ν (canonicalTableau ν hν) fh hfh + have H := strip_product_support hs (canonicalTableau ν hν) t (cutPositions h s) + (shiftedStairWord h s) (stairBandWord h s) + (fun a => s ≤ ((finProdFinEquiv.symm a).1).val) + (shiftedStairWord_alphabet h s) (stairBandWord_alphabet h s) f hf hband + rw [← staircase_cut_factor] at H + obtain ⟨F,hF⟩ := H + exact cyclic_projection_support (sameHighProjection _ _ _ s) (staircaseWord (h+s)) F hF + +lemma staircase_one_dominates (μ : YoungDiagram) (hμ : μ.card = (staircase 1).card) : + Dominates (staircase 1) μ := by + intro k + by_cases hk : k=0 + · subst k; simp [rowPrefix] + · have hh : (staircase 1).colLen 0 ≤ k := by simp only [staircase_colLen]; omega + rw [rowPrefix_eq_card _ hh,← hμ] + exact rowPrefix_le_card μ k + +/- Strong induction, including m=1 and every +partition of the exact triangular size. -/ +theorem full_cyclic_support (m : ℕ) (hm : 1 ≤ m) (μ : YoungDiagram) + (t : Tableau (staircase m).card μ) : + ∃ F : Representation.IntertwiningMap (spechtRep t) (staircaseCyclic m).toRepresentation, F ≠ 0 := by + induction m using Nat.strong_induction_on generalizing μ with + | h m ih => + have hμ : μ.card = (staircase m).card := by + simpa only [Fintype.card_fin,Fintype.card_coe] using (Fintype.card_congr t).symm + by_cases hd : Dominates (staircase m) μ + · exact dominated_support m hm μ t hd + have hm2 : 2 ≤ m := by + by_contra hn + have he : m=1 := by omega + subst m + exact hd (staircase_one_dominates μ hμ) + rcases strip_reduction m hm2 μ hμ hd with ⟨ν,hν,hs⟩ | ⟨hm5,q,hq,ν,hν,hs⟩ + · obtain ⟨f,hf⟩ := ih (m-1) (by omega) (by omega) ν (canonicalTableau ν hν) + exact band_cut_support (m-1) 1 m (by omega) ν μ hν t [μ.card-ν.card] + (SizedStripChain.of_horizontal hs) f hf (fun η r hη => oneBand_support (m-1) η r hη) + · obtain ⟨f,hf⟩ := ih (m-2) (by omega) (by omega) ν (canonicalTableau ν hν) + obtain ⟨bs,hbs,hS⟩ := hs.sized + exact band_cut_support (m-2) 2 m (by omega) ν μ hν t bs hS f hf + (fun η r hη => twoBand_support (m-2) (by omega) η r (by omega)) + +/- The strengthened cyclic form of Saxl’s conjecture. -/ +theorem cyclic_saxl_conjecture : CyclicSaxlConjecture := by + intro m hm μ hμ + exact full_cyclic_support m hm μ (canonicalTableau μ hμ) + +/- Every complex staircase tensor square contains +all Specht irreducibles of its symmetric group. -/ +theorem saxl_conjecture : SaxlConjecture := saxl_of_cyclic_support cyclic_saxl_conjecture + + + +theorem cyclic_saxl : CyclicSaxlConjecture := cyclic_saxl_conjecture + +/- Specht classification implies that every finite-dimensional irreducible +complex representation embeds in the staircase tensor square. -/ +theorem saxl_contains_every_irreducible (m : ℕ) (hm : 1 ≤ m) + {V : Type uV} [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin (staircase m).card)) V) + [Representation.IsIrreducible ρ] : + ∃ F : Representation.IntertwiningMap ρ + ((spechtRep (stairTableau m)).tprod (spechtRep (stairTableau m))), + Function.Injective F := by + obtain ⟨p,⟨e⟩⟩ := irreducible_equiv_specht ρ + obtain ⟨f,hf⟩ := full_cyclic_support m hm (partitionDiagram p) (partitionTableau p) + let := specht_irreducible (partitionTableau p) + have hi := (Representation.IsIrreducible.injective_or_eq_zero f).resolve_right hf + exact ⟨((staircaseToTensor m).comp f).comp e.toIntertwiningMap, + (staircaseToTensor_injective m).comp (hi.comp e.injective)⟩ + +/- The positive-multiplicity conclusion with the literal +triangular degree, rather than the definitionally convenient cell count. -/ +theorem saxl_kronecker_pos (m : ℕ) (hm : 1 ≤ m) (μ : YoungDiagram) + (hμ : μ.card = m * (m + 1) / 2) : + 0 < kronecker (canonicalTableau (staircase m) (staircase_card m)) + (canonicalTableau (staircase m) (staircase_card m)) (canonicalTableau μ hμ) := by + have H : ∀ (n : ℕ) (hn : (staircase m).card = n) (hnu : μ.card = n), + 0 < kronecker (canonicalTableau (staircase m) hn) + (canonicalTableau (staircase m) hn) (canonicalTableau μ hnu) := by + intro n hn hnu + subst n + exact saxl_conjecture m hm μ hnu + exact H _ (staircase_card m) hμ + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/Model.lean b/lean/OAI/RepresentationTheory/Saxl/Model.lean index bcca1b184bb3bb69a6ffcd46f11415a546e730fe..c38e0ae8efdb2006c9cae6553e9c6b92a8f35442 100644 --- a/lean/OAI/RepresentationTheory/Saxl/Model.lean +++ b/lean/OAI/RepresentationTheory/Saxl/Model.lean @@ -1,116 +1,116 @@ -import Mathlib - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uG uV - -namespace Saxl - -/- Coefficients of position tensors on an alphabet of size `d`. -/ -abbrev WordSpace (n d : ℕ) := (Fin n → Fin d) → ℂ - -/- The position action satisfies `g e_a = e_(a ∘ g⁻¹)`. -/ -def wordRep (n d : ℕ) : Representation ℂ (Equiv.Perm (Fin n)) (WordSpace n d) where - toFun g := - { toFun := fun f a => f (a ∘ g) - map_add' := by intros; rfl - map_smul' := by intros; rfl } - map_one' := by ext f a; rfl - map_mul' g h := by ext f a; rfl - -/- The cyclic subrepresentation generated by an actual vector. -/ -def cyclic {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] - (ρ : Representation ℂ G V) (v : V) : Subrepresentation ρ where - toSubmodule := Submodule.span ℂ (Set.range fun g : G => ρ g v) - apply_mem_toSubmodule g := by - intro x hx - induction hx using Submodule.span_induction with - | mem x hx => - obtain ⟨h, rfl⟩ := hx - apply Submodule.subset_span - exact ⟨g * h, by simp only [map_mul, Module.End.mul_apply]⟩ - | zero => simp - | add x y hx hy ihx ihy => - simpa only [map_add] using Submodule.add_mem _ ihx ihy - | smul a x hx ih => - simpa only [map_smul] using Submodule.smul_mem _ a ih - -/- A tableau is an enumeration of all cells by the position set. -/ -abbrev Tableau (n : ℕ) (μ : YoungDiagram) := Fin n ≃ μ.cells - -/- One fixed tableau; changing its enumeration gives an isomorphic Specht module. -/ -def canonicalTableau {n : ℕ} (μ : YoungDiagram) (hn : μ.card = n) : Tableau n μ := - (Fintype.equivFinOfCardEq (by simpa using hn)).symm - -/- The row word corresponding to the tabloid of a tableau. -/ -def rowWord {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : Fin n → Fin (μ.colLen 0) := - fun i => ⟨(t i).val.1, YoungDiagram.mem_iff_lt_colLen.mp - (μ.up_left_mem le_rfl (Nat.zero_le _) (t i).property)⟩ - -/- The column permutations of a tableau. -/ -def columnGroup {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - Subgroup (Equiv.Perm (Fin n)) where - carrier := {g | ∀ i, (t (g i)).val.2 = (t i).val.2} - one_mem' := by intro i; rfl - mul_mem' := by - intro g h hg hh i - exact (hg (h i)).trans (hh i) - inv_mem' := by - intro g hg i - have h := hg (g⁻¹ i) - simpa using h.symm - -/- The standard column-antisymmetrized row tabloid, with complex coefficients. -/ -def polytabloid {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - WordSpace n (μ.colLen 0) := by - classical - letI := Fintype.ofFinite (columnGroup t) - exact ∑ g : columnGroup t, - (((Equiv.Perm.sign (g : Equiv.Perm (Fin n))) : ℤ) : ℂ) • - wordRep n (μ.colLen 0) (g : Equiv.Perm (Fin n)) (Pi.single (rowWord t) 1) - -/- The Specht module, defined as the orbit span of a polytabloid in the -row-tabloid permutation module, realized inside the word space. -/ -def spechtSub {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) := - cyclic (wordRep n (μ.colLen 0)) (polytabloid t) - -abbrev Specht {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) := - (spechtSub t).toSubmodule - -/- The genuine symmetric-group representation on the complex Specht module. -/ -def spechtRep {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - Representation ℂ (Equiv.Perm (Fin n)) (Specht t) := - (spechtSub t).toRepresentation - -/- Kronecker multiplicity is the complex dimension of Hom, with the -diagonal symmetric-group action on the tensor product. -/ -def kronecker {n : ℕ} {α β μ : YoungDiagram} - (a : Tableau n α) (b : Tableau n β) (t : Tableau n μ) : ℕ := - Module.finrank ℂ (Representation.IntertwiningMap (spechtRep t) - ((spechtRep a).tprod (spechtRep b))) - - -def staircase (m : ℕ) : YoungDiagram where - cells := ((Finset.range m) ×ˢ (Finset.range m)).filter (fun x => x.1 + x.2 < m) - isLowerSet := by - intro x y hxy hy - simp only [Finset.mem_coe, Finset.mem_filter, Finset.mem_product, - Finset.mem_range] at hy ⊢ - exact ⟨⟨lt_of_le_of_lt hxy.1 hy.1.1, lt_of_le_of_lt hxy.2 hy.1.2⟩, - lt_of_le_of_lt (Nat.add_le_add hxy.1 hxy.2) hy.2⟩ - - -def SaxlConjecture : Prop := - ∀ (m : ℕ), 1 ≤ m → ∀ (μ : YoungDiagram) (hμ : μ.card = (staircase m).card), - 0 < kronecker (canonicalTableau (staircase m) rfl) - (canonicalTableau (staircase m) rfl) (canonicalTableau μ hμ) - -end Saxl - -end - -end OAI +import Mathlib + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uG uV + +namespace Saxl + +/- Coefficients of position tensors on an alphabet of size `d`. -/ +abbrev WordSpace (n d : ℕ) := (Fin n → Fin d) → ℂ + +/- The position action satisfies `g e_a = e_(a ∘ g⁻¹)`. -/ +def wordRep (n d : ℕ) : Representation ℂ (Equiv.Perm (Fin n)) (WordSpace n d) where + toFun g := + { toFun := fun f a => f (a ∘ g) + map_add' := by intros; rfl + map_smul' := by intros; rfl } + map_one' := by ext f a; rfl + map_mul' g h := by ext f a; rfl + +/- The cyclic subrepresentation generated by an actual vector. -/ +def cyclic {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] + (ρ : Representation ℂ G V) (v : V) : Subrepresentation ρ where + toSubmodule := Submodule.span ℂ (Set.range fun g : G => ρ g v) + apply_mem_toSubmodule g := by + intro x hx + induction hx using Submodule.span_induction with + | mem x hx => + obtain ⟨h, rfl⟩ := hx + apply Submodule.subset_span + exact ⟨g * h, by simp only [map_mul, Module.End.mul_apply]⟩ + | zero => simp + | add x y hx hy ihx ihy => + simpa only [map_add] using Submodule.add_mem _ ihx ihy + | smul a x hx ih => + simpa only [map_smul] using Submodule.smul_mem _ a ih + +/- A tableau is an enumeration of all cells by the position set. -/ +abbrev Tableau (n : ℕ) (μ : YoungDiagram) := Fin n ≃ μ.cells + +/- One fixed tableau; changing its enumeration gives an isomorphic Specht module. -/ +def canonicalTableau {n : ℕ} (μ : YoungDiagram) (hn : μ.card = n) : Tableau n μ := + (Fintype.equivFinOfCardEq (by simpa using hn)).symm + +/- The row word corresponding to the tabloid of a tableau. -/ +def rowWord {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : Fin n → Fin (μ.colLen 0) := + fun i => ⟨(t i).val.1, YoungDiagram.mem_iff_lt_colLen.mp + (μ.up_left_mem le_rfl (Nat.zero_le _) (t i).property)⟩ + +/- The column permutations of a tableau. -/ +def columnGroup {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + Subgroup (Equiv.Perm (Fin n)) where + carrier := {g | ∀ i, (t (g i)).val.2 = (t i).val.2} + one_mem' := by intro i; rfl + mul_mem' := by + intro g h hg hh i + exact (hg (h i)).trans (hh i) + inv_mem' := by + intro g hg i + have h := hg (g⁻¹ i) + simpa using h.symm + +/- The standard column-antisymmetrized row tabloid, with complex coefficients. -/ +def polytabloid {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + WordSpace n (μ.colLen 0) := by + classical + letI := Fintype.ofFinite (columnGroup t) + exact ∑ g : columnGroup t, + (((Equiv.Perm.sign (g : Equiv.Perm (Fin n))) : ℤ) : ℂ) • + wordRep n (μ.colLen 0) (g : Equiv.Perm (Fin n)) (Pi.single (rowWord t) 1) + +/- The Specht module, defined as the orbit span of a polytabloid in the +row-tabloid permutation module, realized inside the word space. -/ +def spechtSub {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) := + cyclic (wordRep n (μ.colLen 0)) (polytabloid t) + +abbrev Specht {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) := + (spechtSub t).toSubmodule + +/- The genuine symmetric-group representation on the complex Specht module. -/ +def spechtRep {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + Representation ℂ (Equiv.Perm (Fin n)) (Specht t) := + (spechtSub t).toRepresentation + +/- Kronecker multiplicity is the complex dimension of Hom, with the +diagonal symmetric-group action on the tensor product. -/ +def kronecker {n : ℕ} {α β μ : YoungDiagram} + (a : Tableau n α) (b : Tableau n β) (t : Tableau n μ) : ℕ := + Module.finrank ℂ (Representation.IntertwiningMap (spechtRep t) + ((spechtRep a).tprod (spechtRep b))) + + +def staircase (m : ℕ) : YoungDiagram where + cells := ((Finset.range m) ×ˢ (Finset.range m)).filter (fun x => x.1 + x.2 < m) + isLowerSet := by + intro x y hxy hy + simp only [Finset.mem_coe, Finset.mem_filter, Finset.mem_product, + Finset.mem_range] at hy ⊢ + exact ⟨⟨lt_of_le_of_lt hxy.1 hy.1.1, lt_of_le_of_lt hxy.2 hy.1.2⟩, + lt_of_le_of_lt (Nat.add_le_add hxy.1 hxy.2) hy.2⟩ + + +def SaxlConjecture : Prop := + ∀ (m : ℕ), 1 ≤ m → ∀ (μ : YoungDiagram) (hμ : μ.card = (staircase m).card), + 0 < kronecker (canonicalTableau (staircase m) rfl) + (canonicalTableau (staircase m) rfl) (canonicalTableau μ hμ) + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/PathAlternation.lean b/lean/OAI/RepresentationTheory/Saxl/PathAlternation.lean index b7ba965ca4c8cd3bdf41f69ee026ff06ee288520..af710eb78637a09b6eef0b5ca5e594ea4df88afa 100644 --- a/lean/OAI/RepresentationTheory/Saxl/PathAlternation.lean +++ b/lean/OAI/RepresentationTheory/Saxl/PathAlternation.lean @@ -1,300 +1,300 @@ -import OAI.RepresentationTheory.Saxl.BandFactorization - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uAlpha - -namespace Saxl.PathLayer - -def tag {r : ℕ} (i : Fin (2*r+1)) : ℕ := (i.val+1)/2 - -def base {r : ℕ} (i : Fin (2*r+1)) : Fin 2 := if i.val=0 then 0 else ⟨(i.val+1)%2, Nat.mod_lt _ (by omega)⟩ - -def rowAlt (r : ℕ) : Saxl.WordSpace (2*r+1) 2 := - Saxl.altWord (Saxl.fiberGroup (@tag r)) (@base r) - -def appendPair (r : ℕ) : Fin (2*(r+1)+1) ≃ Fin (2*r+1) ⊕ Fin 2 := - (finCongr (by omega : 2*(r+1)+1 = (2*r+1)+2)).trans finSumFinEquiv.symm - -@[simp] lemma appendPair_left (r : ℕ) (i : Fin (2*r+1)) : - ((appendPair r).symm (Sum.inl i)).val = i.val := rfl -@[simp] lemma appendPair_right (r : ℕ) (i : Fin 2) : - ((appendPair r).symm (Sum.inr i)).val = 2*r+1+i.val := rfl - -lemma tag_left (r : ℕ) (i : Fin (2*r+1)) : - tag ((appendPair r).symm (Sum.inl i)) = tag i := rfl -lemma tag_right (r : ℕ) (i : Fin 2) : - tag ((appendPair r).symm (Sum.inr i)) = r+1 := by - unfold tag - rw [appendPair_right] - omega - -lemma tag_side (r : ℕ) (i : Fin (2*(r+1)+1)) : - (appendPair r i).isLeft = true ↔ tag i < r+1 := by - obtain ⟨j,rfl⟩ := (appendPair r).symm.surjective i - cases j with - | inl j => simp only [Equiv.apply_symm_apply, Sum.isLeft_inl, true_iff, tag_left]; unfold tag; omega - | inr j => simp only [Equiv.apply_symm_apply, Sum.isLeft_inr, Bool.false_eq_true, tag_right, lt_self_iff_false] - -lemma rowGroup_sector (r : ℕ) : - Saxl.fiberGroup (@tag (r+1)) = Saxl.fiberGroup (@tag (r+1)) ⊓ - Saxl.sectorGroup (fun i => (appendPair r i).isLeft = true) := by - apply le_antisymm - · intro g hg - refine ⟨hg, ?_⟩ - intro i - change (appendPair r (g i)).isLeft = true ↔ (appendPair r i).isLeft = true - rw [tag_side,tag_side] - change ∀ i, tag (g i) = tag i at hg - rw [hg] - · exact inf_le_left - -lemma rowAlt_step (r : ℕ) : - rowAlt (r+1) = Saxl.positionProduct (appendPair r) (rowAlt r) - (Saxl.altWord (⊤ : Subgroup (Equiv.Perm (Fin 2))) (fun i => i)) := by - unfold rowAlt - rw [rowGroup_sector, Saxl.altWord_fiber_split] - have hl : Saxl.fiberGroup (fun i => tag ((appendPair r).symm (Sum.inl i))) = - Saxl.fiberGroup (@tag r) := rfl - have hr : Saxl.fiberGroup (fun i => tag ((appendPair r).symm (Sum.inr i))) = ⊤ := by - apply Subgroup.ext - intro g - change (∀ i, tag ((appendPair r).symm (Sum.inr (g i))) = tag ((appendPair r).symm (Sum.inr i))) ↔ True - simp only [tag_right, implies_true] - rw [hl,hr] - congr 2 - funext i - apply Fin.ext - change (base ((appendPair r).symm (Sum.inr i))).val = i.val - have hn : ((appendPair r).symm (Sum.inr i)).val ≠ 0 := by rw [appendPair_right]; omega - unfold base - rw [ite_eq_right hn] - change (2*r+1+i.val+1)%2 = i.val - omega - -def J : Matrix (Fin 2) (Fin 2) ℂ := !![0,1;-1,0] - -lemma pair_alt (w : Fin 2 → Fin 2) : - Saxl.altWord (⊤ : Subgroup (Equiv.Perm (Fin 2))) (fun i => i) w = J (w 0) (w 1) := by - classical - let := Fintype.ofFinite (⊤ : Subgroup (Equiv.Perm (Fin 2))) - unfold Saxl.altWord - rw [Finset.sum_apply] - change (∑ g : (⊤ : Subgroup (Equiv.Perm (Fin 2))), Saxl.signC (g : Equiv.Perm (Fin 2)) * - ((Pi.single (fun i : Fin 2 => i) (1:ℂ) : Saxl.WordSpace 2 2) (w ∘ (g : Equiv.Perm (Fin 2))))) = _ - calc - _ = ∑ g : Equiv.Perm (Fin 2), Saxl.signC g * - ((Pi.single (fun i : Fin 2 => i) (1:ℂ) : Saxl.WordSpace 2 2) (w ∘ g)) := - Fintype.sum_equiv (Subgroup.topEquiv (G := Equiv.Perm (Fin 2))).toEquiv _ _ (by intro g; rfl) - _ = _ := by - have hu : (Finset.univ : Finset (Equiv.Perm (Fin 2))) = {1,Equiv.swap 0 1} := by decide - rw [hu] - have hne : (1 : Equiv.Perm (Fin 2)) ≠ Equiv.swap 0 1 := by decide - simp only [Finset.sum_insert (Finset.notMem_singleton.mpr hne), Finset.sum_singleton] - have hw : w = ![w 0,w 1] := by ext i; fin_cases i <;> rfl - rw [hw] - generalize h0 : w 0 = a - generalize h1 : w 1 = b - fin_cases a <;> fin_cases b <;> - norm_num [Saxl.wordRep,Saxl.signC_def,Pi.single_apply,funext_iff,Fin.forall_fin_two,J] - -lemma rowAlt_zero (w : Fin 1 → Fin 2) : - rowAlt 0 w = if w 0 = 0 then 1 else 0 := by - classical - change Saxl.altWord (Saxl.fiberGroup (@tag 0)) (@base 0) w = _ - let := Fintype.ofFinite (Saxl.fiberGroup (@tag 0)) - unfold Saxl.altWord - have hu : (Finset.univ : Finset (Saxl.fiberGroup (@tag 0))) = {1} := by - ext g - simp only [Finset.mem_univ, Finset.mem_singleton, true_iff] - apply Subtype.ext - apply Equiv.ext - intro i - apply Fin.ext - have := ((g : Equiv.Perm (Fin (2*0+1))) i).isLt - have := i.isLt - omega - rw [hu,Finset.sum_singleton] - simp only [OneMemClass.coe_one, map_one, one_smul] - change (Pi.single (@base 0) (1:ℂ) : Saxl.WordSpace 1 2) w = _ - rw [Pi.single_apply] - congr 1 - apply propext - constructor - · intro h; have := congrFun h 0; simpa [base] using this - · intro h; funext i; have hi : i=0 := Subsingleton.elim _ _; subst i; simpa [base] using h - -lemma rowAlt_formula (r : ℕ) (w : Fin (2*r+1) → Fin 2) : - rowAlt r w = (if w 0 = 0 then 1 else 0) * - ∏ i : Fin r, J (w ⟨2*i.val+1,by omega⟩) (w ⟨2*i.val+2,by omega⟩) := by - induction r with - | zero => simpa using rowAlt_zero w - | succ r ih => - rw [rowAlt_step] - change rowAlt r (Saxl.leftWord (appendPair r) w) * - Saxl.altWord ⊤ (fun i : Fin 2 => i) (Saxl.rightWord (appendPair r) w) = _ - rw [ih, pair_alt, Fin.prod_univ_castSucc] - exact mul_assoc _ _ _ - -end Saxl.PathLayer - -namespace Saxl - -def fiberRelabel {n m : ℕ} {α : Type uAlpha} (e : Fin n ≃ Fin m) (c : Fin m → α) : - fiberGroup (c ∘ e) ≃ fiberGroup c where - toFun g := ⟨e.permCongr g.val, by - intro i - obtain ⟨j,rfl⟩ := e.surjective i - change c (e (g.val (e.symm (e j)))) = c (e j) - rw [Equiv.symm_apply_apply] - exact g.property j⟩ - invFun g := ⟨e.symm.permCongr g.val, by - intro i - change c (e (e.symm (g.val (e i)))) = c (e i) - rw [Equiv.apply_symm_apply] - exact g.property (e i)⟩ - left_inv g := by apply Subtype.ext; ext i; simp [Equiv.permCongr] - right_inv g := by apply Subtype.ext; ext i; simp [Equiv.permCongr] - -lemma altWord_fiber_relabel {n m d : ℕ} {α : Type uAlpha} - (e : Fin n ≃ Fin m) (c : Fin m → α) (a : Fin m → Fin d) (w : Fin n → Fin d) : - altWord (fiberGroup c) a (w ∘ e.symm) = - altWord (fiberGroup (c ∘ e)) (a ∘ e) w := by - classical - let := Fintype.ofFinite (fiberGroup c) - let := Fintype.ofFinite (fiberGroup (c ∘ e)) - unfold altWord - simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul] - symm - apply Fintype.sum_equiv (fiberRelabel e c) - intro g - have hs : signC ((fiberRelabel e c g).val) = signC g.val := by - change signC (e.permCongr g.val) = _ - simp only [signC_def, Equiv.Perm.sign_permCongr] - rw [hs] - congr 1 - change (Pi.single (a ∘ e) (1:ℂ) : WordSpace n d) (w ∘ g.val) = - (Pi.single a (1:ℂ) : WordSpace m d) ((w ∘ e.symm) ∘ (e.permCongr g.val)) - simp only [Pi.single_apply] - congr 1 - apply propext - constructor - · intro h - funext i - obtain ⟨j,rfl⟩ := e.surjective i - simpa [Equiv.permCongr] using congrFun h j - · intro h - funext i - simpa [Equiv.permCongr] using congrFun h (e i) - -lemma altWord_letter_eval {n d D : ℕ} (φ : Fin d → Fin D) (hφ : Function.Injective φ) - (G : Subgroup (Equiv.Perm (Fin n))) (a w : Fin n → Fin d) : - altWord G (φ ∘ a) (φ ∘ w) = altWord G a w := by - classical - unfold altWord - simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul] - apply Finset.sum_congr rfl - intro g hg - congr 1 - change (Pi.single (φ ∘ a) (1:ℂ) : WordSpace n D) ((φ ∘ w) ∘ g.val) = - (Pi.single a (1:ℂ) : WordSpace n d) (w ∘ g.val) - simp only [Pi.single_apply] - congr 1 - apply propext - constructor - · intro h; funext i; exact hφ (congrFun h i) - · intro h; funext i; exact congrArg φ (congrFun h i) - - - -def lowLetter (h : ℕ) : Fin 2 → Fin ((staircase (h+2)).colLen 0) := - fun i => ⟨i.val, by rw [staircase_colLen]; have := i.isLt; omega⟩ - -lemma lowLetter_injective (h : ℕ) : Function.Injective (lowLetter h) := by - intro i j hij - exact Fin.ext (congrArg (fun x : Fin ((staircase (h+2)).colLen 0) => x.val) hij) - -def bandColumnPathEquiv (h : ℕ) : Fin (2*(h+1)+1) ≃ Fin (bandSize h 2) := - Fin.revPerm.trans (bandPathEquiv h) - -lemma bandColumnPath_coordinates (h : ℕ) (k : Fin (2*(h+1)+1)) : - (bandTableau h 2 (bandColumnPathEquiv h k)).val = (k.val/2,h+1-(k.val+1)/2) := by - change (bandTableau h 2 (bandPathEquiv h k.rev)).val = _ - rw [bandPath_coordinates] - apply Prod.ext <;> simp only [Fin.val_rev] <;> have := k.isLt <;> omega - -lemma bandRow_path_group (h : ℕ) : - fiberGroup ((fun j => (bandTableau h 2 j).val.1) ∘ bandPathEquiv h) = - fiberGroup (@PathLayer.tag (h+1)) := by - apply Subgroup.ext - intro g - change (∀ i, _ = _) ↔ (∀ i, _ = _) - simp only [Function.comp_apply, bandPath_coordinates, PathLayer.tag] - constructor <;> intro hg i <;> have hh := hg i <;> - have := i.isLt <;> have := (g i).isLt <;> omega - -lemma bandColumn_path_group (h : ℕ) : - fiberGroup ((fun j => (bandTableau h 2 j).val.2) ∘ bandColumnPathEquiv h) = - fiberGroup (@PathLayer.tag (h+1)) := by - apply Subgroup.ext - intro g - change (∀ i, _ = _) ↔ (∀ i, _ = _) - simp only [Function.comp_apply, bandColumnPath_coordinates, PathLayer.tag] - constructor <;> intro hg i <;> have hh := hg i <;> - have := i.isLt <;> have := (g i).isLt <;> omega - -lemma bandRow_path_base (h : ℕ) : - (rightWord (cutPositions h 2) - (rowWord (stairRowTableau (h+2)) ∘ (rotateRowPositions h 2 : Equiv.Perm _))) ∘ bandPathEquiv h = - lowLetter h ∘ (@PathLayer.base (h+1)) := by - funext k - apply Fin.ext - simp only [Function.comp_apply, rightWord, rowWord, stairRowTableau, rotateRowPositions, - Equiv.trans_apply, Equiv.apply_symm_apply, staircaseSwap] - change (rotateRow h 2 (bandTableau h 2 (bandPathEquiv h k))).val.2 = _ - change (if (bandTableau h 2 (bandPathEquiv h k)).val.2 < h-(bandTableau h 2 (bandPathEquiv h k)).val.1 then - (bandTableau h 2 (bandPathEquiv h k)).val.2+2 else - (bandTableau h 2 (bandPathEquiv h k)).val.2-(h-(bandTableau h 2 (bandPathEquiv h k)).val.1)) = _ - rw [bandPath_coordinates] - simp only [lowLetter, PathLayer.base] - split_ifs <;> have := k.isLt <;> simp only [Fin.val_zero] <;> omega - -lemma bandColumn_path_base (h : ℕ) : - (rightWord (cutPositions h 2) - (rowWord (stairTableau (h+2)) ∘ (rotateColumnPositions h 2 : Equiv.Perm _))) ∘ bandColumnPathEquiv h = - lowLetter h ∘ (@PathLayer.base (h+1)) := by - funext k - apply Fin.ext - simp only [Function.comp_apply, rightWord, rowWord, rotateColumnPositions, - Equiv.trans_apply, Equiv.apply_symm_apply] - change (rotateColumn h 2 (bandTableau h 2 (bandColumnPathEquiv h k))).val.1 = _ - change (if (bandTableau h 2 (bandColumnPathEquiv h k)).val.1 < h-(bandTableau h 2 (bandColumnPathEquiv h k)).val.2 then - (bandTableau h 2 (bandColumnPathEquiv h k)).val.1+2 else - (bandTableau h 2 (bandColumnPathEquiv h k)).val.1-(h-(bandTableau h 2 (bandColumnPathEquiv h k)).val.2)) = _ - rw [bandColumnPath_coordinates] - simp only [lowLetter, PathLayer.base] - split_ifs <;> have := k.isLt <;> simp only [Fin.val_zero] <;> omega - -lemma bandRow_path_eval (h : ℕ) (w : Fin (2*(h+1)+1) → Fin 2) : - bandRowWord h 2 ((lowLetter h ∘ w) ∘ (bandPathEquiv h).symm) = PathLayer.rowAlt (h+1) w := by - unfold bandRowWord bandRowGroup - rw [altWord_fiber_relabel, bandRow_path_group, bandRow_path_base, - altWord_letter_eval _ (lowLetter_injective h)] - rfl - -lemma bandColumn_path_eval (h : ℕ) (w : Fin (2*(h+1)+1) → Fin 2) : - bandColumnWord h 2 ((lowLetter h ∘ w) ∘ (bandColumnPathEquiv h).symm) = PathLayer.rowAlt (h+1) w := by - unfold bandColumnWord bandColumnGroup - rw [altWord_fiber_relabel, bandColumn_path_group, bandColumn_path_base, - altWord_letter_eval _ (lowLetter_injective h)] - rfl - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.BandFactorization + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uAlpha + +namespace Saxl.PathLayer + +def tag {r : ℕ} (i : Fin (2*r+1)) : ℕ := (i.val+1)/2 + +def base {r : ℕ} (i : Fin (2*r+1)) : Fin 2 := if i.val=0 then 0 else ⟨(i.val+1)%2, Nat.mod_lt _ (by omega)⟩ + +def rowAlt (r : ℕ) : Saxl.WordSpace (2*r+1) 2 := + Saxl.altWord (Saxl.fiberGroup (@tag r)) (@base r) + +def appendPair (r : ℕ) : Fin (2*(r+1)+1) ≃ Fin (2*r+1) ⊕ Fin 2 := + (finCongr (by omega : 2*(r+1)+1 = (2*r+1)+2)).trans finSumFinEquiv.symm + +@[simp] lemma appendPair_left (r : ℕ) (i : Fin (2*r+1)) : + ((appendPair r).symm (Sum.inl i)).val = i.val := rfl +@[simp] lemma appendPair_right (r : ℕ) (i : Fin 2) : + ((appendPair r).symm (Sum.inr i)).val = 2*r+1+i.val := rfl + +lemma tag_left (r : ℕ) (i : Fin (2*r+1)) : + tag ((appendPair r).symm (Sum.inl i)) = tag i := rfl +lemma tag_right (r : ℕ) (i : Fin 2) : + tag ((appendPair r).symm (Sum.inr i)) = r+1 := by + unfold tag + rw [appendPair_right] + omega + +lemma tag_side (r : ℕ) (i : Fin (2*(r+1)+1)) : + (appendPair r i).isLeft = true ↔ tag i < r+1 := by + obtain ⟨j,rfl⟩ := (appendPair r).symm.surjective i + cases j with + | inl j => simp only [Equiv.apply_symm_apply, Sum.isLeft_inl, true_iff, tag_left]; unfold tag; omega + | inr j => simp only [Equiv.apply_symm_apply, Sum.isLeft_inr, Bool.false_eq_true, tag_right, lt_self_iff_false] + +lemma rowGroup_sector (r : ℕ) : + Saxl.fiberGroup (@tag (r+1)) = Saxl.fiberGroup (@tag (r+1)) ⊓ + Saxl.sectorGroup (fun i => (appendPair r i).isLeft = true) := by + apply le_antisymm + · intro g hg + refine ⟨hg, ?_⟩ + intro i + change (appendPair r (g i)).isLeft = true ↔ (appendPair r i).isLeft = true + rw [tag_side,tag_side] + change ∀ i, tag (g i) = tag i at hg + rw [hg] + · exact inf_le_left + +lemma rowAlt_step (r : ℕ) : + rowAlt (r+1) = Saxl.positionProduct (appendPair r) (rowAlt r) + (Saxl.altWord (⊤ : Subgroup (Equiv.Perm (Fin 2))) (fun i => i)) := by + unfold rowAlt + rw [rowGroup_sector, Saxl.altWord_fiber_split] + have hl : Saxl.fiberGroup (fun i => tag ((appendPair r).symm (Sum.inl i))) = + Saxl.fiberGroup (@tag r) := rfl + have hr : Saxl.fiberGroup (fun i => tag ((appendPair r).symm (Sum.inr i))) = ⊤ := by + apply Subgroup.ext + intro g + change (∀ i, tag ((appendPair r).symm (Sum.inr (g i))) = tag ((appendPair r).symm (Sum.inr i))) ↔ True + simp only [tag_right, implies_true] + rw [hl,hr] + congr 2 + funext i + apply Fin.ext + change (base ((appendPair r).symm (Sum.inr i))).val = i.val + have hn : ((appendPair r).symm (Sum.inr i)).val ≠ 0 := by rw [appendPair_right]; omega + unfold base + rw [ite_eq_right hn] + change (2*r+1+i.val+1)%2 = i.val + omega + +def J : Matrix (Fin 2) (Fin 2) ℂ := !![0,1;-1,0] + +lemma pair_alt (w : Fin 2 → Fin 2) : + Saxl.altWord (⊤ : Subgroup (Equiv.Perm (Fin 2))) (fun i => i) w = J (w 0) (w 1) := by + classical + let := Fintype.ofFinite (⊤ : Subgroup (Equiv.Perm (Fin 2))) + unfold Saxl.altWord + rw [Finset.sum_apply] + change (∑ g : (⊤ : Subgroup (Equiv.Perm (Fin 2))), Saxl.signC (g : Equiv.Perm (Fin 2)) * + ((Pi.single (fun i : Fin 2 => i) (1:ℂ) : Saxl.WordSpace 2 2) (w ∘ (g : Equiv.Perm (Fin 2))))) = _ + calc + _ = ∑ g : Equiv.Perm (Fin 2), Saxl.signC g * + ((Pi.single (fun i : Fin 2 => i) (1:ℂ) : Saxl.WordSpace 2 2) (w ∘ g)) := + Fintype.sum_equiv (Subgroup.topEquiv (G := Equiv.Perm (Fin 2))).toEquiv _ _ (by intro g; rfl) + _ = _ := by + have hu : (Finset.univ : Finset (Equiv.Perm (Fin 2))) = {1,Equiv.swap 0 1} := by decide + rw [hu] + have hne : (1 : Equiv.Perm (Fin 2)) ≠ Equiv.swap 0 1 := by decide + simp only [Finset.sum_insert (Finset.notMem_singleton.mpr hne), Finset.sum_singleton] + have hw : w = ![w 0,w 1] := by ext i; fin_cases i <;> rfl + rw [hw] + generalize h0 : w 0 = a + generalize h1 : w 1 = b + fin_cases a <;> fin_cases b <;> + norm_num [Saxl.wordRep,Saxl.signC_def,Pi.single_apply,funext_iff,Fin.forall_fin_two,J] + +lemma rowAlt_zero (w : Fin 1 → Fin 2) : + rowAlt 0 w = if w 0 = 0 then 1 else 0 := by + classical + change Saxl.altWord (Saxl.fiberGroup (@tag 0)) (@base 0) w = _ + let := Fintype.ofFinite (Saxl.fiberGroup (@tag 0)) + unfold Saxl.altWord + have hu : (Finset.univ : Finset (Saxl.fiberGroup (@tag 0))) = {1} := by + ext g + simp only [Finset.mem_univ, Finset.mem_singleton, true_iff] + apply Subtype.ext + apply Equiv.ext + intro i + apply Fin.ext + have := ((g : Equiv.Perm (Fin (2*0+1))) i).isLt + have := i.isLt + omega + rw [hu,Finset.sum_singleton] + simp only [OneMemClass.coe_one, map_one, one_smul] + change (Pi.single (@base 0) (1:ℂ) : Saxl.WordSpace 1 2) w = _ + rw [Pi.single_apply] + congr 1 + apply propext + constructor + · intro h; have := congrFun h 0; simpa [base] using this + · intro h; funext i; have hi : i=0 := Subsingleton.elim _ _; subst i; simpa [base] using h + +lemma rowAlt_formula (r : ℕ) (w : Fin (2*r+1) → Fin 2) : + rowAlt r w = (if w 0 = 0 then 1 else 0) * + ∏ i : Fin r, J (w ⟨2*i.val+1,by omega⟩) (w ⟨2*i.val+2,by omega⟩) := by + induction r with + | zero => simpa using rowAlt_zero w + | succ r ih => + rw [rowAlt_step] + change rowAlt r (Saxl.leftWord (appendPair r) w) * + Saxl.altWord ⊤ (fun i : Fin 2 => i) (Saxl.rightWord (appendPair r) w) = _ + rw [ih, pair_alt, Fin.prod_univ_castSucc] + exact mul_assoc _ _ _ + +end Saxl.PathLayer + +namespace Saxl + +def fiberRelabel {n m : ℕ} {α : Type uAlpha} (e : Fin n ≃ Fin m) (c : Fin m → α) : + fiberGroup (c ∘ e) ≃ fiberGroup c where + toFun g := ⟨e.permCongr g.val, by + intro i + obtain ⟨j,rfl⟩ := e.surjective i + change c (e (g.val (e.symm (e j)))) = c (e j) + rw [Equiv.symm_apply_apply] + exact g.property j⟩ + invFun g := ⟨e.symm.permCongr g.val, by + intro i + change c (e (e.symm (g.val (e i)))) = c (e i) + rw [Equiv.apply_symm_apply] + exact g.property (e i)⟩ + left_inv g := by apply Subtype.ext; ext i; simp [Equiv.permCongr] + right_inv g := by apply Subtype.ext; ext i; simp [Equiv.permCongr] + +lemma altWord_fiber_relabel {n m d : ℕ} {α : Type uAlpha} + (e : Fin n ≃ Fin m) (c : Fin m → α) (a : Fin m → Fin d) (w : Fin n → Fin d) : + altWord (fiberGroup c) a (w ∘ e.symm) = + altWord (fiberGroup (c ∘ e)) (a ∘ e) w := by + classical + let := Fintype.ofFinite (fiberGroup c) + let := Fintype.ofFinite (fiberGroup (c ∘ e)) + unfold altWord + simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul] + symm + apply Fintype.sum_equiv (fiberRelabel e c) + intro g + have hs : signC ((fiberRelabel e c g).val) = signC g.val := by + change signC (e.permCongr g.val) = _ + simp only [signC_def, Equiv.Perm.sign_permCongr] + rw [hs] + congr 1 + change (Pi.single (a ∘ e) (1:ℂ) : WordSpace n d) (w ∘ g.val) = + (Pi.single a (1:ℂ) : WordSpace m d) ((w ∘ e.symm) ∘ (e.permCongr g.val)) + simp only [Pi.single_apply] + congr 1 + apply propext + constructor + · intro h + funext i + obtain ⟨j,rfl⟩ := e.surjective i + simpa [Equiv.permCongr] using congrFun h j + · intro h + funext i + simpa [Equiv.permCongr] using congrFun h (e i) + +lemma altWord_letter_eval {n d D : ℕ} (φ : Fin d → Fin D) (hφ : Function.Injective φ) + (G : Subgroup (Equiv.Perm (Fin n))) (a w : Fin n → Fin d) : + altWord G (φ ∘ a) (φ ∘ w) = altWord G a w := by + classical + unfold altWord + simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul] + apply Finset.sum_congr rfl + intro g hg + congr 1 + change (Pi.single (φ ∘ a) (1:ℂ) : WordSpace n D) ((φ ∘ w) ∘ g.val) = + (Pi.single a (1:ℂ) : WordSpace n d) (w ∘ g.val) + simp only [Pi.single_apply] + congr 1 + apply propext + constructor + · intro h; funext i; exact hφ (congrFun h i) + · intro h; funext i; exact congrArg φ (congrFun h i) + + + +def lowLetter (h : ℕ) : Fin 2 → Fin ((staircase (h+2)).colLen 0) := + fun i => ⟨i.val, by rw [staircase_colLen]; have := i.isLt; omega⟩ + +lemma lowLetter_injective (h : ℕ) : Function.Injective (lowLetter h) := by + intro i j hij + exact Fin.ext (congrArg (fun x : Fin ((staircase (h+2)).colLen 0) => x.val) hij) + +def bandColumnPathEquiv (h : ℕ) : Fin (2*(h+1)+1) ≃ Fin (bandSize h 2) := + Fin.revPerm.trans (bandPathEquiv h) + +lemma bandColumnPath_coordinates (h : ℕ) (k : Fin (2*(h+1)+1)) : + (bandTableau h 2 (bandColumnPathEquiv h k)).val = (k.val/2,h+1-(k.val+1)/2) := by + change (bandTableau h 2 (bandPathEquiv h k.rev)).val = _ + rw [bandPath_coordinates] + apply Prod.ext <;> simp only [Fin.val_rev] <;> have := k.isLt <;> omega + +lemma bandRow_path_group (h : ℕ) : + fiberGroup ((fun j => (bandTableau h 2 j).val.1) ∘ bandPathEquiv h) = + fiberGroup (@PathLayer.tag (h+1)) := by + apply Subgroup.ext + intro g + change (∀ i, _ = _) ↔ (∀ i, _ = _) + simp only [Function.comp_apply, bandPath_coordinates, PathLayer.tag] + constructor <;> intro hg i <;> have hh := hg i <;> + have := i.isLt <;> have := (g i).isLt <;> omega + +lemma bandColumn_path_group (h : ℕ) : + fiberGroup ((fun j => (bandTableau h 2 j).val.2) ∘ bandColumnPathEquiv h) = + fiberGroup (@PathLayer.tag (h+1)) := by + apply Subgroup.ext + intro g + change (∀ i, _ = _) ↔ (∀ i, _ = _) + simp only [Function.comp_apply, bandColumnPath_coordinates, PathLayer.tag] + constructor <;> intro hg i <;> have hh := hg i <;> + have := i.isLt <;> have := (g i).isLt <;> omega + +lemma bandRow_path_base (h : ℕ) : + (rightWord (cutPositions h 2) + (rowWord (stairRowTableau (h+2)) ∘ (rotateRowPositions h 2 : Equiv.Perm _))) ∘ bandPathEquiv h = + lowLetter h ∘ (@PathLayer.base (h+1)) := by + funext k + apply Fin.ext + simp only [Function.comp_apply, rightWord, rowWord, stairRowTableau, rotateRowPositions, + Equiv.trans_apply, Equiv.apply_symm_apply, staircaseSwap] + change (rotateRow h 2 (bandTableau h 2 (bandPathEquiv h k))).val.2 = _ + change (if (bandTableau h 2 (bandPathEquiv h k)).val.2 < h-(bandTableau h 2 (bandPathEquiv h k)).val.1 then + (bandTableau h 2 (bandPathEquiv h k)).val.2+2 else + (bandTableau h 2 (bandPathEquiv h k)).val.2-(h-(bandTableau h 2 (bandPathEquiv h k)).val.1)) = _ + rw [bandPath_coordinates] + simp only [lowLetter, PathLayer.base] + split_ifs <;> have := k.isLt <;> simp only [Fin.val_zero] <;> omega + +lemma bandColumn_path_base (h : ℕ) : + (rightWord (cutPositions h 2) + (rowWord (stairTableau (h+2)) ∘ (rotateColumnPositions h 2 : Equiv.Perm _))) ∘ bandColumnPathEquiv h = + lowLetter h ∘ (@PathLayer.base (h+1)) := by + funext k + apply Fin.ext + simp only [Function.comp_apply, rightWord, rowWord, rotateColumnPositions, + Equiv.trans_apply, Equiv.apply_symm_apply] + change (rotateColumn h 2 (bandTableau h 2 (bandColumnPathEquiv h k))).val.1 = _ + change (if (bandTableau h 2 (bandColumnPathEquiv h k)).val.1 < h-(bandTableau h 2 (bandColumnPathEquiv h k)).val.2 then + (bandTableau h 2 (bandColumnPathEquiv h k)).val.1+2 else + (bandTableau h 2 (bandColumnPathEquiv h k)).val.1-(h-(bandTableau h 2 (bandColumnPathEquiv h k)).val.2)) = _ + rw [bandColumnPath_coordinates] + simp only [lowLetter, PathLayer.base] + split_ifs <;> have := k.isLt <;> simp only [Fin.val_zero] <;> omega + +lemma bandRow_path_eval (h : ℕ) (w : Fin (2*(h+1)+1) → Fin 2) : + bandRowWord h 2 ((lowLetter h ∘ w) ∘ (bandPathEquiv h).symm) = PathLayer.rowAlt (h+1) w := by + unfold bandRowWord bandRowGroup + rw [altWord_fiber_relabel, bandRow_path_group, bandRow_path_base, + altWord_letter_eval _ (lowLetter_injective h)] + rfl + +lemma bandColumn_path_eval (h : ℕ) (w : Fin (2*(h+1)+1) → Fin 2) : + bandColumnWord h 2 ((lowLetter h ∘ w) ∘ (bandColumnPathEquiv h).symm) = PathLayer.rowAlt (h+1) w := by + unfold bandColumnWord bandColumnGroup + rw [altWord_fiber_relabel, bandColumn_path_group, bandColumn_path_base, + altWord_letter_eval _ (lowLetter_injective h)] + rfl + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/PathContraction.lean b/lean/OAI/RepresentationTheory/Saxl/PathContraction.lean index 3cd295c775387effc432dd815d1023d694b4b428..37614309595165595aef0b5052ffc6b2f73dc233 100644 --- a/lean/OAI/RepresentationTheory/Saxl/PathContraction.lean +++ b/lean/OAI/RepresentationTheory/Saxl/PathContraction.lean @@ -1,174 +1,174 @@ -import OAI.RepresentationTheory.Saxl.BandMatrices - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl.Path -abbrev Mat := Matrix (Fin 2) (Fin 2) ℂ -abbrev Letter := Fin 4 - -def parts (x : Letter) : Fin 2 × Fin 2 := finProdFinEquiv.symm x -def J : Mat := !![0, 1; -1, 0] - -def leftPos {r : ℕ} (i : Fin r) : Fin (2 * r + 1) := ⟨2 * i.val, by omega⟩ -def midPos {r : ℕ} (i : Fin r) : Fin (2 * r + 1) := ⟨2 * i.val + 1, by omega⟩ -def rightPos {r : ℕ} (i : Fin r) : Fin (2 * r + 1) := ⟨2 * i.val + 2, by omega⟩ - -/- EXACT coefficients of the path-ordered alternating band: the two endpoint -singletons carry letter 0, and row/column pairs have coefficients J. Here r=m-1. -/ -def bandWord (r : ℕ) (w : Fin (2 * r + 1) → Letter) : ℂ := - (if (parts (w 0)).1 = 0 then 1 else 0) * - (if (parts (w (Fin.last (2 * r)))).2 = 0 then 1 else 0) * - ∏ i : Fin r, J (parts (w (leftPos i))).2 (parts (w (midPos i))).2 * - J (parts (w (midPos i))).1 (parts (w (rightPos i))).1 - -/- Ordinary pure position tensor pairing, with no conjugation. -/ -def pureWord {n : ℕ} (X : Fin n → Mat) (w : Fin n → Letter) : ℂ := - ∏ i, X i (parts (w i)).1 (parts (w i)).2 - -def entry (a : Letter) : Mat := Matrix.single (parts a).1 (parts a).2 1 - -def DL (q : ℕ) : Mat →ₗ[ℂ] Mat where - toFun := Band.D q - map_add' X Y := by - by_cases h : q % 2 = 0 - · ext i j; fin_cases i <;> fin_cases j <;> - simp [Band.D, h, Matrix.adjugate_fin_two, add_comm] - · simp [Band.D, h] - map_smul' c X := by - by_cases h : q % 2 = 0 - · ext i j; fin_cases i <;> fin_cases j <;> - simp [Band.D, h, Matrix.adjugate_fin_two] - · simp [Band.D, h] - -def chainML (n p : ℕ) : MultilinearMap ℂ (fun _ : Fin n => Mat) Mat := - (MultilinearMap.mkPiAlgebraFin ℂ n Mat).compLinearMap (fun i => DL (p + i.val)) - -lemma chainML_apply (n p : ℕ) (X : Fin n → Mat) : - chainML n p X = (List.ofFn fun i => Band.D (p + i.val) (X i)).prod := rfl - -lemma entry_sum (X : Mat) : - (∑ a : Letter, X (parts a).1 (parts a).2 • entry a) = X := by - ext i j - fin_cases i <;> fin_cases j <;> - norm_num [Fin.sum_univ_succ, parts, entry, Matrix.single, finProdFinEquiv, Fin.divNat, Fin.modNat, Fin.ext_iff] - -lemma chain_expand (n p : ℕ) (X : Fin n → Mat) : - chainML n p X = ∑ w : Fin n → Letter, pureWord X w • - chainML n p (fun i => entry (w i)) := by - calc - chainML n p X = chainML n p (fun i => ∑ a : Letter, - X i (parts a).1 (parts a).2 • entry a) := by - congr 1; funext i; exact (entry_sum (X i)).symm - _ = _ := ?_ - rw [MultilinearMap.map_sum] - apply Finset.sum_congr rfl - intro w hw - rw [MultilinearMap.map_smul_univ] - rfl - -lemma adj_entry (a : Letter) (i j : Fin 2) : - (entry a).adjugate i j = -(J i (parts a).2 * J (parts a).1 j) := by - fin_cases a <;> fin_cases i <;> fin_cases j <;> - norm_num [entry, parts, J, Matrix.single, Matrix.adjugate_fin_two, finProdFinEquiv, Fin.divNat, Fin.modNat, Fin.ext_iff] - -lemma D_shift (q : ℕ) (X : Mat) : Band.D (q + 2) X = Band.D q X := by - simp [Band.D] - -lemma chain_step (r : ℕ) (w : Fin (2 * (r+1) + 1) → Letter) : - chainML (2 * (r+1) + 1) 1 (fun i => entry (w i)) = - entry (w 0) * (entry (w 1)).adjugate * - chainML (2 * r + 1) 1 (fun i => entry (w i.succ.succ)) := by - rw [chainML_apply, List.ofFn_succ, List.prod_cons, List.ofFn_succ, - List.prod_cons, chainML_apply] - simp only [Fin.val_zero, Fin.val_succ, add_zero] - rw [show Band.D 1 = id from by funext X; simp [Band.D], - show Band.D 2 = Matrix.adjugate from by funext X; simp [Band.D]] - simp only [id_eq] - rw [mul_assoc] - apply congrArg (fun A : Mat => entry (w 0) * ((entry (w 1)).adjugate * A)) - apply congrArg List.prod - apply congrArg List.ofFn - funext i - rw [show 1 + (i.val + 1 + 1) = (1 + i.val) + 2 by omega, D_shift] - -lemma pair_product_step (r : ℕ) (w : Fin (2 * (r+1) + 1) → Letter) : - (∏ i : Fin (r+1), J (parts (w (leftPos i))).2 (parts (w (midPos i))).2 * - J (parts (w (midPos i))).1 (parts (w (rightPos i))).1) = - (J (parts (w 0)).2 (parts (w 1)).2 * J (parts (w 1)).1 (parts (w 2)).1) * - ∏ i : Fin r, J (parts (w (leftPos i).succ.succ)).2 - (parts (w (midPos i).succ.succ)).2 * - J (parts (w (midPos i).succ.succ)).1 (parts (w (rightPos i).succ.succ)).1 := by - rw [Fin.prod_univ_succ] - rfl - -lemma chain_entries (r : ℕ) (w : Fin (2*r+1) → Letter) : - chainML (2*r+1) 1 (fun i => entry (w i)) = - ((-1 : ℂ)^r * ∏ i : Fin r, - J (parts (w (leftPos i))).2 (parts (w (midPos i))).2 * - J (parts (w (midPos i))).1 (parts (w (rightPos i))).1) • - Matrix.single (parts (w 0)).1 (parts (w (Fin.last (2*r)))).2 1 := by - induction r with - | zero => simp [chainML_apply, List.ofFn_succ, Band.D, entry] - | succ r ih => - rw [chain_step, ih, Matrix.mul_smul, pair_product_step] - rw [show (0 : Fin (2*r+1)).succ.succ = 2 from Fin.ext rfl] - change _ = _ • Matrix.single _ (parts (w (Fin.last (2*r)).succ.succ)).2 1 - unfold entry at * - rw [Matrix.single_mul_mul_single, one_mul, mul_one] - rw [show (Matrix.single (parts (w 1)).1 (parts (w 1)).2 (1 : ℂ)).adjugate - (parts (w 0)).2 (parts (w 2)).1 = - -(J (parts (w 0)).2 (parts (w 1)).2 * J (parts (w 1)).1 (parts (w 2)).1) - from adj_entry (w 1) _ _] - rw [show ∀ (c : ℂ) (i j : Fin 2), Matrix.single i j c = c • Matrix.single i j 1 - from fun c i j => by ext a b; simp [Matrix.single, smul_eq_mul]] - rw [smul_smul] - congr 1 - rw [pow_succ] - ring - -lemma chain_entries_endpoint (r : ℕ) (w : Fin (2*r+1) → Letter) : - chainML (2*r+1) 1 (fun i => entry (w i)) 0 0 = - (-1 : ℂ)^r * bandWord r w := by - rw [chain_entries] - by_cases h₁ : (parts (w 0)).1 = 0 <;> - by_cases h₂ : (parts (w (Fin.last (2*r)))).2 = 0 <;> - simp [bandWord, Matrix.single, h₁, h₂] - -theorem path_contraction (r : ℕ) (X : Fin (2*r+1) → Mat) : - dotProduct (bandWord r) (pureWord X) = - (-1 : ℂ)^r * (List.ofFn fun q => Band.D (1+q.val) (X q)).prod 0 0 := by - have h := congrArg (fun A : Mat => A 0 0) (chain_expand (2*r+1) 1 X) - change chainML (2*r+1) 1 X 0 0 = - (∑ w : Fin (2*r+1) → Letter, - pureWord X w • chainML (2*r+1) 1 (fun i => entry (w i))) 0 0 at h - simp only [Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, - chain_entries_endpoint] at h - rw [← chainML_apply, h, Finset.mul_sum] - unfold dotProduct - apply Finset.sum_congr rfl - intro w hw - have hs : (-1 : ℂ)^r * (-1 : ℂ)^r = 1 := by - rw [← mul_pow]; norm_num - calc - bandWord r w * pureWord X w = - ((-1 : ℂ)^r * (-1 : ℂ)^r) * (bandWord r w * pureWord X w) := by rw [hs, one_mul] - _ = _ := by ring - -lemma J_real (i j : Fin 2) : star (J i j) = J i j := by - fin_cases i <;> fin_cases j <;> simp [J] - -lemma bandWord_real (r : ℕ) : star (bandWord r) = bandWord r := by - funext w - change star (bandWord r w) = bandWord r w - by_cases h₁ : (parts (w 0)).1 = 0 <;> - by_cases h₂ : (parts (w (Fin.last (2*r)))).2 = 0 <;> - simp [bandWord, h₁, h₂, star_mul, star_prod, J_real, mul_comm] -end Saxl.Path - -end - -end OAI +import OAI.RepresentationTheory.Saxl.BandMatrices + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl.Path +abbrev Mat := Matrix (Fin 2) (Fin 2) ℂ +abbrev Letter := Fin 4 + +def parts (x : Letter) : Fin 2 × Fin 2 := finProdFinEquiv.symm x +def J : Mat := !![0, 1; -1, 0] + +def leftPos {r : ℕ} (i : Fin r) : Fin (2 * r + 1) := ⟨2 * i.val, by omega⟩ +def midPos {r : ℕ} (i : Fin r) : Fin (2 * r + 1) := ⟨2 * i.val + 1, by omega⟩ +def rightPos {r : ℕ} (i : Fin r) : Fin (2 * r + 1) := ⟨2 * i.val + 2, by omega⟩ + +/- EXACT coefficients of the path-ordered alternating band: the two endpoint +singletons carry letter 0, and row/column pairs have coefficients J. Here r=m-1. -/ +def bandWord (r : ℕ) (w : Fin (2 * r + 1) → Letter) : ℂ := + (if (parts (w 0)).1 = 0 then 1 else 0) * + (if (parts (w (Fin.last (2 * r)))).2 = 0 then 1 else 0) * + ∏ i : Fin r, J (parts (w (leftPos i))).2 (parts (w (midPos i))).2 * + J (parts (w (midPos i))).1 (parts (w (rightPos i))).1 + +/- Ordinary pure position tensor pairing, with no conjugation. -/ +def pureWord {n : ℕ} (X : Fin n → Mat) (w : Fin n → Letter) : ℂ := + ∏ i, X i (parts (w i)).1 (parts (w i)).2 + +def entry (a : Letter) : Mat := Matrix.single (parts a).1 (parts a).2 1 + +def DL (q : ℕ) : Mat →ₗ[ℂ] Mat where + toFun := Band.D q + map_add' X Y := by + by_cases h : q % 2 = 0 + · ext i j; fin_cases i <;> fin_cases j <;> + simp [Band.D, h, Matrix.adjugate_fin_two, add_comm] + · simp [Band.D, h] + map_smul' c X := by + by_cases h : q % 2 = 0 + · ext i j; fin_cases i <;> fin_cases j <;> + simp [Band.D, h, Matrix.adjugate_fin_two] + · simp [Band.D, h] + +def chainML (n p : ℕ) : MultilinearMap ℂ (fun _ : Fin n => Mat) Mat := + (MultilinearMap.mkPiAlgebraFin ℂ n Mat).compLinearMap (fun i => DL (p + i.val)) + +lemma chainML_apply (n p : ℕ) (X : Fin n → Mat) : + chainML n p X = (List.ofFn fun i => Band.D (p + i.val) (X i)).prod := rfl + +lemma entry_sum (X : Mat) : + (∑ a : Letter, X (parts a).1 (parts a).2 • entry a) = X := by + ext i j + fin_cases i <;> fin_cases j <;> + norm_num [Fin.sum_univ_succ, parts, entry, Matrix.single, finProdFinEquiv, Fin.divNat, Fin.modNat, Fin.ext_iff] + +lemma chain_expand (n p : ℕ) (X : Fin n → Mat) : + chainML n p X = ∑ w : Fin n → Letter, pureWord X w • + chainML n p (fun i => entry (w i)) := by + calc + chainML n p X = chainML n p (fun i => ∑ a : Letter, + X i (parts a).1 (parts a).2 • entry a) := by + congr 1; funext i; exact (entry_sum (X i)).symm + _ = _ := ?_ + rw [MultilinearMap.map_sum] + apply Finset.sum_congr rfl + intro w hw + rw [MultilinearMap.map_smul_univ] + rfl + +lemma adj_entry (a : Letter) (i j : Fin 2) : + (entry a).adjugate i j = -(J i (parts a).2 * J (parts a).1 j) := by + fin_cases a <;> fin_cases i <;> fin_cases j <;> + norm_num [entry, parts, J, Matrix.single, Matrix.adjugate_fin_two, finProdFinEquiv, Fin.divNat, Fin.modNat, Fin.ext_iff] + +lemma D_shift (q : ℕ) (X : Mat) : Band.D (q + 2) X = Band.D q X := by + simp [Band.D] + +lemma chain_step (r : ℕ) (w : Fin (2 * (r+1) + 1) → Letter) : + chainML (2 * (r+1) + 1) 1 (fun i => entry (w i)) = + entry (w 0) * (entry (w 1)).adjugate * + chainML (2 * r + 1) 1 (fun i => entry (w i.succ.succ)) := by + rw [chainML_apply, List.ofFn_succ, List.prod_cons, List.ofFn_succ, + List.prod_cons, chainML_apply] + simp only [Fin.val_zero, Fin.val_succ, add_zero] + rw [show Band.D 1 = id from by funext X; simp [Band.D], + show Band.D 2 = Matrix.adjugate from by funext X; simp [Band.D]] + simp only [id_eq] + rw [mul_assoc] + apply congrArg (fun A : Mat => entry (w 0) * ((entry (w 1)).adjugate * A)) + apply congrArg List.prod + apply congrArg List.ofFn + funext i + rw [show 1 + (i.val + 1 + 1) = (1 + i.val) + 2 by omega, D_shift] + +lemma pair_product_step (r : ℕ) (w : Fin (2 * (r+1) + 1) → Letter) : + (∏ i : Fin (r+1), J (parts (w (leftPos i))).2 (parts (w (midPos i))).2 * + J (parts (w (midPos i))).1 (parts (w (rightPos i))).1) = + (J (parts (w 0)).2 (parts (w 1)).2 * J (parts (w 1)).1 (parts (w 2)).1) * + ∏ i : Fin r, J (parts (w (leftPos i).succ.succ)).2 + (parts (w (midPos i).succ.succ)).2 * + J (parts (w (midPos i).succ.succ)).1 (parts (w (rightPos i).succ.succ)).1 := by + rw [Fin.prod_univ_succ] + rfl + +lemma chain_entries (r : ℕ) (w : Fin (2*r+1) → Letter) : + chainML (2*r+1) 1 (fun i => entry (w i)) = + ((-1 : ℂ)^r * ∏ i : Fin r, + J (parts (w (leftPos i))).2 (parts (w (midPos i))).2 * + J (parts (w (midPos i))).1 (parts (w (rightPos i))).1) • + Matrix.single (parts (w 0)).1 (parts (w (Fin.last (2*r)))).2 1 := by + induction r with + | zero => simp [chainML_apply, List.ofFn_succ, Band.D, entry] + | succ r ih => + rw [chain_step, ih, Matrix.mul_smul, pair_product_step] + rw [show (0 : Fin (2*r+1)).succ.succ = 2 from Fin.ext rfl] + change _ = _ • Matrix.single _ (parts (w (Fin.last (2*r)).succ.succ)).2 1 + unfold entry at * + rw [Matrix.single_mul_mul_single, one_mul, mul_one] + rw [show (Matrix.single (parts (w 1)).1 (parts (w 1)).2 (1 : ℂ)).adjugate + (parts (w 0)).2 (parts (w 2)).1 = + -(J (parts (w 0)).2 (parts (w 1)).2 * J (parts (w 1)).1 (parts (w 2)).1) + from adj_entry (w 1) _ _] + rw [show ∀ (c : ℂ) (i j : Fin 2), Matrix.single i j c = c • Matrix.single i j 1 + from fun c i j => by ext a b; simp [Matrix.single, smul_eq_mul]] + rw [smul_smul] + congr 1 + rw [pow_succ] + ring + +lemma chain_entries_endpoint (r : ℕ) (w : Fin (2*r+1) → Letter) : + chainML (2*r+1) 1 (fun i => entry (w i)) 0 0 = + (-1 : ℂ)^r * bandWord r w := by + rw [chain_entries] + by_cases h₁ : (parts (w 0)).1 = 0 <;> + by_cases h₂ : (parts (w (Fin.last (2*r)))).2 = 0 <;> + simp [bandWord, Matrix.single, h₁, h₂] + +theorem path_contraction (r : ℕ) (X : Fin (2*r+1) → Mat) : + dotProduct (bandWord r) (pureWord X) = + (-1 : ℂ)^r * (List.ofFn fun q => Band.D (1+q.val) (X q)).prod 0 0 := by + have h := congrArg (fun A : Mat => A 0 0) (chain_expand (2*r+1) 1 X) + change chainML (2*r+1) 1 X 0 0 = + (∑ w : Fin (2*r+1) → Letter, + pureWord X w • chainML (2*r+1) 1 (fun i => entry (w i))) 0 0 at h + simp only [Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, + chain_entries_endpoint] at h + rw [← chainML_apply, h, Finset.mul_sum] + unfold dotProduct + apply Finset.sum_congr rfl + intro w hw + have hs : (-1 : ℂ)^r * (-1 : ℂ)^r = 1 := by + rw [← mul_pow]; norm_num + calc + bandWord r w * pureWord X w = + ((-1 : ℂ)^r * (-1 : ℂ)^r) * (bandWord r w * pureWord X w) := by rw [hs, one_mul] + _ = _ := by ring + +lemma J_real (i j : Fin 2) : star (J i j) = J i j := by + fin_cases i <;> fin_cases j <;> simp [J] + +lemma bandWord_real (r : ℕ) : star (bandWord r) = bandWord r := by + funext w + change star (bandWord r w) = bandWord r w + by_cases h₁ : (parts (w 0)).1 = 0 <;> + by_cases h₂ : (parts (w (Fin.last (2*r)))).2 = 0 <;> + simp [bandWord, h₁, h₂, star_mul, star_prod, J_real, mul_comm] +end Saxl.Path + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/PieriRestriction.lean b/lean/OAI/RepresentationTheory/Saxl/PieriRestriction.lean index 9ee668d9d703b371f1999c14c77365e7fc44edab..81714bb17ec0986123da039f64a22b48a76a44a2 100644 --- a/lean/OAI/RepresentationTheory/Saxl/PieriRestriction.lean +++ b/lean/OAI/RepresentationTheory/Saxl/PieriRestriction.lean @@ -1,228 +1,228 @@ -import OAI.RepresentationTheory.Saxl.SignEquivalence - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl -/- A horizontal strip removes at most one cell in each column. -/ -def HorizontalStrip (ν μ : YoungDiagram) : Prop := - ν ≤ μ ∧ ∀ x ∈ μ, x ∉ ν → ∀ y ∈ μ, y ∉ ν → x.2 = y.2 → x = y - -/- Position embedding induced by inclusion of the actual Young diagrams. -/ -def tableauInclusion {a n : ℕ} {ν μ : YoungDiagram} (s : Tableau a ν) (t : Tableau n μ) - (h : ν ≤ μ) : Fin a ↪ Fin n where - toFun i := t.symm ⟨(s i).val, h (s i).property⟩ - inj' := by - intro i j hij - apply s.injective - apply Subtype.ext - simpa using congrArg (fun k => (t k).val) hij - -lemma colLen_mono {ν μ : YoungDiagram} (h : ν ≤ μ) (j : ℕ) : - ν.colLen j ≤ μ.colLen j := by - by_contra hn - have hm : (μ.colLen j, j) ∈ ν := YoungDiagram.mem_iff_lt_colLen.mpr (lt_of_not_ge hn) - exact (lt_irrefl _) (YoungDiagram.mem_iff_lt_colLen.mp (h hm)) - -def rowLetterInclusion {ν μ : YoungDiagram} (h : ν ≤ μ) : Fin (ν.colLen 0) ↪ Fin (μ.colLen 0) := - Fin.castLEEmb (colLen_mono h 0) - -/- Restrict letters on a specified position set, and sum over all other letters. -This is precisely contraction with the all-ones functional at deleted positions. -/ -def wordRestrict {a n d e : ℕ} (i : Fin a ↪ Fin n) (j : Fin d ↪ Fin e) : - WordSpace n e →ₗ[ℂ] WordSpace a d where - toFun x b := ∑ c : Fin n → Fin e, if c ∘ i = j ∘ b then x c else 0 - map_add' x y := by - ext b - change (∑ c, if c ∘ i = j ∘ b then x c + y c else 0) = - (∑ c, if c ∘ i = j ∘ b then x c else 0) + (∑ c, if c ∘ i = j ∘ b then y c else 0) - rw [← Finset.sum_add_distrib] - apply Finset.sum_congr rfl - intro c hc - split <;> simp_all - map_smul' r x := by - ext b - change (∑ c, if c ∘ i = j ∘ b then r * x c else 0) = - r * ∑ c, if c ∘ i = j ∘ b then x c else 0 - rw [Finset.mul_sum] - apply Finset.sum_congr rfl - intro c hc - split <;> simp_all - -lemma wordRestrict_single {a n d e : ℕ} (i : Fin a ↪ Fin n) (j : Fin d ↪ Fin e) - (c : Fin n → Fin e) (b : Fin a → Fin d) : - wordRestrict i j (Pi.single c 1) b = if c ∘ i = j ∘ b then 1 else 0 := by - classical - change (∑ z : Fin n → Fin e, if z ∘ i = j ∘ b then (Pi.single c (1 : ℂ) : WordSpace n e) z else 0) = _ - rw [Finset.sum_eq_single c] - · simp - · intro z hz hzc - simp [hzc] - · simp - -lemma wordRestrict_equivariant {a n d e : ℕ} (i : Fin a ↪ Fin n) (j : Fin d ↪ Fin e) - (g : Equiv.Perm (Fin n)) (h : Equiv.Perm (Fin a)) (hi : ∀ k, g (i k) = i (h k)) - (x : WordSpace n e) : - wordRestrict i j (wordRep n e g x) = wordRep a d h (wordRestrict i j x) := by - classical - ext b - change (∑ c : Fin n → Fin e, if c ∘ i = j ∘ b then x (c ∘ g) else 0) = - ∑ c : Fin n → Fin e, if c ∘ i = j ∘ (b ∘ h) then x c else 0 - apply Eq.trans ?_ (Equiv.sum_comp (wordPerm n e g) - (fun c => if c ∘ i = j ∘ (b ∘ h) then x c else 0)) - apply Finset.sum_congr rfl - intro c hc - change (if c ∘ i = j ∘ b then x (c ∘ g) else 0) = - if (c ∘ g) ∘ i = j ∘ (b ∘ h) then x (c ∘ g) else 0 - congr 1 - apply propext - constructor - · intro hh - funext k - simpa only [Function.comp_apply, hi] using congrFun hh (h k) - · intro hh - funext k - have he := congrFun hh (h⁻¹ k) - simpa [Function.comp_apply, hi] using he - - -@[simp] lemma tableauInclusion_cell {a n : ℕ} {ν μ : YoungDiagram} - (s : Tableau a ν) (t : Tableau n μ) (h : ν ≤ μ) (k : Fin a) : - (t (tableauInclusion s t h k)).val = (s k).val := by - change (t (t.symm ⟨(s k).val, h (s k).property⟩)).val = _ - simp - -lemma column_fixed_of_strip {a n : ℕ} {ν μ : YoungDiagram} - (s : Tableau a ν) (t : Tableau n μ) (hs : HorizontalStrip ν μ) - (g : columnGroup t) (hg : ∀ i, (g : Equiv.Perm (Fin n)) (tableauInclusion s t hs.1 i) = - tableauInclusion s t hs.1 i) : g = 1 := by - have hin (k : Fin n) (hk : (t k).val ∈ ν) : (g : Equiv.Perm (Fin n)) k = k := by - let i := s.symm ⟨(t k).val, hk⟩ - have he : tableauInclusion s t hs.1 i = k := by - apply t.injective - apply Subtype.ext - rw [tableauInclusion_cell] - simp [i] - simpa only [he] using hg i - apply Subtype.ext - apply Equiv.ext - intro k - by_cases hk : (t k).val ∈ ν - · exact hin k hk - · have ho : (t ((g : Equiv.Perm (Fin n)) k)).val ∉ ν := by - intro hh - have he := hin ((g : Equiv.Perm (Fin n)) k) hh - have he' := (g : Equiv.Perm (Fin n)).injective he - exact hk (he' ▸ hh) - apply t.injective - apply Subtype.ext - exact hs.2 _ (t _).property ho _ (t _).property hk (g.property k) - -lemma strip_contraction_coefficient {a n : ℕ} {ν μ : YoungDiagram} - (s : Tableau a ν) (t : Tableau n μ) (hs : HorizontalStrip ν μ) : - wordRestrict (tableauInclusion s t hs.1) (rowLetterInclusion hs.1) - (polytabloid t) (rowWord s) = 1 := by - classical - let i := tableauInclusion s t hs.1 - let j := rowLetterInclusion hs.1 - have he (g : columnGroup t) : - (rowWord t ∘ ((g : Equiv.Perm (Fin n))⁻¹ : Equiv.Perm (Fin n))) ∘ i = j ∘ rowWord s ↔ g = 1 := by - constructor - · intro hh - have hf : ∀ k, ((g : Equiv.Perm (Fin n))⁻¹) (i k) = i k := by - intro k - apply t.injective - apply Subtype.ext - apply Prod.ext - · have hh' := congrArg Fin.val (congrFun hh k) - simpa [rowWord, j, rowLetterInclusion, i] using hh' - · exact (g⁻¹).property (i k) - have hh' : (g⁻¹ : columnGroup t) = 1 := column_fixed_of_strip s t hs (g⁻¹) hf - simpa using congrArg Inv.inv hh' - · rintro rfl - funext k - apply Fin.ext - exact congrArg Prod.fst (tableauInclusion_cell s t hs.1 k) - let := Fintype.ofFinite (columnGroup t) - change wordRestrict i j (∑ g : columnGroup t, - signC (g : Equiv.Perm (Fin n)) • wordRep n (μ.colLen 0) - (g : Equiv.Perm (Fin n)) (Pi.single (rowWord t) 1)) (rowWord s) = _ - simp only [map_sum, map_smul, Finset.sum_apply, Pi.smul_apply, smul_eq_mul, - wordRep_single, wordRestrict_single, he] - simp - -lemma column_viaEmbedding {a n : ℕ} {ν μ : YoungDiagram} - (s : Tableau a ν) (t : Tableau n μ) (h : ν ≤ μ) (g : columnGroup s) : - (g : Equiv.Perm (Fin a)).viaEmbedding (tableauInclusion s t h) ∈ columnGroup t := by - intro k - by_cases hk : k ∈ Set.range (tableauInclusion s t h) - · obtain ⟨l, rfl⟩ := hk - rw [Equiv.Perm.viaEmbedding_apply] - simpa only [tableauInclusion_cell] using g.property l - · rw [Equiv.Perm.viaEmbedding_apply_of_notMem _ _ _ hk] - -lemma signC_viaEmbedding {a n : ℕ} (i : Fin a ↪ Fin n) (g : Equiv.Perm (Fin a)) : - signC (g.viaEmbedding i) = signC g := by - classical - simp [signC_def, Equiv.Perm.viaEmbedding, Equiv.Perm.sign_extendDomain] - -lemma strip_contraction_pair {a n : ℕ} {ν μ : YoungDiagram} - (s : Tableau a ν) (t : Tableau n μ) (hs : HorizontalStrip ν μ) : - dotProduct (wordRestrict (tableauInclusion s t hs.1) (rowLetterInclusion hs.1) - (polytabloid t)) (polytabloid s) ≠ 0 := by - classical - let i := tableauInclusion s t hs.1 - let j := rowLetterInclusion hs.1 - let x := wordRestrict i j (polytabloid t) - have hx (g : columnGroup s) : wordRep a (ν.colLen 0) (g : Equiv.Perm (Fin a)) x = - signC (g : Equiv.Perm (Fin a)) • x := by - rw [← wordRestrict_equivariant i j ((g : Equiv.Perm (Fin a)).viaEmbedding i) - (g : Equiv.Perm (Fin a)) (Equiv.Perm.viaEmbedding_apply _ _) (polytabloid t)] - rw [polytabloid_alternating t ⟨_, column_viaEmbedding s t hs.1 g⟩] - rw [map_smul, signC_viaEmbedding] - rw [← columnAlt_coefficient] - let := Fintype.ofFinite (columnGroup s) - have he : columnAlt s x = (Fintype.card (columnGroup s) : ℂ) • x := by - change (∑ g : columnGroup s, signC (g : Equiv.Perm (Fin a)) • - wordRep a (ν.colLen 0) (g : Equiv.Perm (Fin a))) x = _ - simp only [LinearMap.sum_apply, LinearMap.smul_apply, hx, smul_smul, - signC_mul_self, one_smul, Finset.sum_const, Finset.card_univ, Nat.cast_smul_eq_nsmul] - change columnAlt s x (rowWord s) ≠ 0 - rw [he] - change (Fintype.card (columnGroup s) : ℂ) * - wordRestrict (tableauInclusion s t hs.1) (rowLetterInclusion hs.1) (polytabloid t) (rowWord s) ≠ 0 - rw [strip_contraction_coefficient s t hs, mul_one] - exact Nat.cast_ne_zero.mpr Fintype.card_ne_zero - -/- Positive horizontal-strip Pieri map, equivariant for the full Young subgroup. -/ -theorem pieri_strip_restriction {a n : ℕ} {ν μ : YoungDiagram} - (s : Tableau a ν) (t : Tableau n μ) (hs : HorizontalStrip ν μ) : - ∃ F : Specht t →ₗ[ℂ] Specht s, F ≠ 0 ∧ - ∀ (g : Equiv.Perm (Fin n)) (h : Equiv.Perm (Fin a)), - (∀ k, g (tableauInclusion s t hs.1 k) = tableauInclusion s t hs.1 (h k)) → - ∀ x, F (spechtRep t g x) = spechtRep s h (F x) := by - let pr := subrepProject (spechtSub s) (fun _ hx => cyclic_star _ (polytabloid_real s) hx) - let T := wordRestrict (tableauInclusion s t hs.1) (rowLetterInclusion hs.1) - let F := pr.toLinearMap.comp (T.comp (spechtSub t).toSubmodule.subtype) - refine ⟨F, ?_, ?_⟩ - · intro hF - have hp := subrepProject_pair (spechtSub s) - (fun _ hx => cyclic_star _ (polytabloid_real s) hx) - (T (polytabloid t)) ⟨polytabloid s, mem_cyclic _ _⟩ - have he : pr (T (polytabloid t)) = 0 := by - exact congrArg (fun L : Specht t →ₗ[ℂ] Specht s => L ⟨polytabloid t, mem_cyclic _ _⟩) hF - rw [he] at hp - exact strip_contraction_pair s t hs (hp.symm.trans (zero_dotProduct _)) - · intro g h hh x - change pr (T (wordRep n (μ.colLen 0) g x.val)) = spechtRep s h (pr (T x.val)) - rw [wordRestrict_equivariant _ _ g h hh x.val] - exact LinearMap.congr_fun (pr.isIntertwining' h) (T x.val) - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.SignEquivalence + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl +/- A horizontal strip removes at most one cell in each column. -/ +def HorizontalStrip (ν μ : YoungDiagram) : Prop := + ν ≤ μ ∧ ∀ x ∈ μ, x ∉ ν → ∀ y ∈ μ, y ∉ ν → x.2 = y.2 → x = y + +/- Position embedding induced by inclusion of the actual Young diagrams. -/ +def tableauInclusion {a n : ℕ} {ν μ : YoungDiagram} (s : Tableau a ν) (t : Tableau n μ) + (h : ν ≤ μ) : Fin a ↪ Fin n where + toFun i := t.symm ⟨(s i).val, h (s i).property⟩ + inj' := by + intro i j hij + apply s.injective + apply Subtype.ext + simpa using congrArg (fun k => (t k).val) hij + +lemma colLen_mono {ν μ : YoungDiagram} (h : ν ≤ μ) (j : ℕ) : + ν.colLen j ≤ μ.colLen j := by + by_contra hn + have hm : (μ.colLen j, j) ∈ ν := YoungDiagram.mem_iff_lt_colLen.mpr (lt_of_not_ge hn) + exact (lt_irrefl _) (YoungDiagram.mem_iff_lt_colLen.mp (h hm)) + +def rowLetterInclusion {ν μ : YoungDiagram} (h : ν ≤ μ) : Fin (ν.colLen 0) ↪ Fin (μ.colLen 0) := + Fin.castLEEmb (colLen_mono h 0) + +/- Restrict letters on a specified position set, and sum over all other letters. +This is precisely contraction with the all-ones functional at deleted positions. -/ +def wordRestrict {a n d e : ℕ} (i : Fin a ↪ Fin n) (j : Fin d ↪ Fin e) : + WordSpace n e →ₗ[ℂ] WordSpace a d where + toFun x b := ∑ c : Fin n → Fin e, if c ∘ i = j ∘ b then x c else 0 + map_add' x y := by + ext b + change (∑ c, if c ∘ i = j ∘ b then x c + y c else 0) = + (∑ c, if c ∘ i = j ∘ b then x c else 0) + (∑ c, if c ∘ i = j ∘ b then y c else 0) + rw [← Finset.sum_add_distrib] + apply Finset.sum_congr rfl + intro c hc + split <;> simp_all + map_smul' r x := by + ext b + change (∑ c, if c ∘ i = j ∘ b then r * x c else 0) = + r * ∑ c, if c ∘ i = j ∘ b then x c else 0 + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro c hc + split <;> simp_all + +lemma wordRestrict_single {a n d e : ℕ} (i : Fin a ↪ Fin n) (j : Fin d ↪ Fin e) + (c : Fin n → Fin e) (b : Fin a → Fin d) : + wordRestrict i j (Pi.single c 1) b = if c ∘ i = j ∘ b then 1 else 0 := by + classical + change (∑ z : Fin n → Fin e, if z ∘ i = j ∘ b then (Pi.single c (1 : ℂ) : WordSpace n e) z else 0) = _ + rw [Finset.sum_eq_single c] + · simp + · intro z hz hzc + simp [hzc] + · simp + +lemma wordRestrict_equivariant {a n d e : ℕ} (i : Fin a ↪ Fin n) (j : Fin d ↪ Fin e) + (g : Equiv.Perm (Fin n)) (h : Equiv.Perm (Fin a)) (hi : ∀ k, g (i k) = i (h k)) + (x : WordSpace n e) : + wordRestrict i j (wordRep n e g x) = wordRep a d h (wordRestrict i j x) := by + classical + ext b + change (∑ c : Fin n → Fin e, if c ∘ i = j ∘ b then x (c ∘ g) else 0) = + ∑ c : Fin n → Fin e, if c ∘ i = j ∘ (b ∘ h) then x c else 0 + apply Eq.trans ?_ (Equiv.sum_comp (wordPerm n e g) + (fun c => if c ∘ i = j ∘ (b ∘ h) then x c else 0)) + apply Finset.sum_congr rfl + intro c hc + change (if c ∘ i = j ∘ b then x (c ∘ g) else 0) = + if (c ∘ g) ∘ i = j ∘ (b ∘ h) then x (c ∘ g) else 0 + congr 1 + apply propext + constructor + · intro hh + funext k + simpa only [Function.comp_apply, hi] using congrFun hh (h k) + · intro hh + funext k + have he := congrFun hh (h⁻¹ k) + simpa [Function.comp_apply, hi] using he + + +@[simp] lemma tableauInclusion_cell {a n : ℕ} {ν μ : YoungDiagram} + (s : Tableau a ν) (t : Tableau n μ) (h : ν ≤ μ) (k : Fin a) : + (t (tableauInclusion s t h k)).val = (s k).val := by + change (t (t.symm ⟨(s k).val, h (s k).property⟩)).val = _ + simp + +lemma column_fixed_of_strip {a n : ℕ} {ν μ : YoungDiagram} + (s : Tableau a ν) (t : Tableau n μ) (hs : HorizontalStrip ν μ) + (g : columnGroup t) (hg : ∀ i, (g : Equiv.Perm (Fin n)) (tableauInclusion s t hs.1 i) = + tableauInclusion s t hs.1 i) : g = 1 := by + have hin (k : Fin n) (hk : (t k).val ∈ ν) : (g : Equiv.Perm (Fin n)) k = k := by + let i := s.symm ⟨(t k).val, hk⟩ + have he : tableauInclusion s t hs.1 i = k := by + apply t.injective + apply Subtype.ext + rw [tableauInclusion_cell] + simp [i] + simpa only [he] using hg i + apply Subtype.ext + apply Equiv.ext + intro k + by_cases hk : (t k).val ∈ ν + · exact hin k hk + · have ho : (t ((g : Equiv.Perm (Fin n)) k)).val ∉ ν := by + intro hh + have he := hin ((g : Equiv.Perm (Fin n)) k) hh + have he' := (g : Equiv.Perm (Fin n)).injective he + exact hk (he' ▸ hh) + apply t.injective + apply Subtype.ext + exact hs.2 _ (t _).property ho _ (t _).property hk (g.property k) + +lemma strip_contraction_coefficient {a n : ℕ} {ν μ : YoungDiagram} + (s : Tableau a ν) (t : Tableau n μ) (hs : HorizontalStrip ν μ) : + wordRestrict (tableauInclusion s t hs.1) (rowLetterInclusion hs.1) + (polytabloid t) (rowWord s) = 1 := by + classical + let i := tableauInclusion s t hs.1 + let j := rowLetterInclusion hs.1 + have he (g : columnGroup t) : + (rowWord t ∘ ((g : Equiv.Perm (Fin n))⁻¹ : Equiv.Perm (Fin n))) ∘ i = j ∘ rowWord s ↔ g = 1 := by + constructor + · intro hh + have hf : ∀ k, ((g : Equiv.Perm (Fin n))⁻¹) (i k) = i k := by + intro k + apply t.injective + apply Subtype.ext + apply Prod.ext + · have hh' := congrArg Fin.val (congrFun hh k) + simpa [rowWord, j, rowLetterInclusion, i] using hh' + · exact (g⁻¹).property (i k) + have hh' : (g⁻¹ : columnGroup t) = 1 := column_fixed_of_strip s t hs (g⁻¹) hf + simpa using congrArg Inv.inv hh' + · rintro rfl + funext k + apply Fin.ext + exact congrArg Prod.fst (tableauInclusion_cell s t hs.1 k) + let := Fintype.ofFinite (columnGroup t) + change wordRestrict i j (∑ g : columnGroup t, + signC (g : Equiv.Perm (Fin n)) • wordRep n (μ.colLen 0) + (g : Equiv.Perm (Fin n)) (Pi.single (rowWord t) 1)) (rowWord s) = _ + simp only [map_sum, map_smul, Finset.sum_apply, Pi.smul_apply, smul_eq_mul, + wordRep_single, wordRestrict_single, he] + simp + +lemma column_viaEmbedding {a n : ℕ} {ν μ : YoungDiagram} + (s : Tableau a ν) (t : Tableau n μ) (h : ν ≤ μ) (g : columnGroup s) : + (g : Equiv.Perm (Fin a)).viaEmbedding (tableauInclusion s t h) ∈ columnGroup t := by + intro k + by_cases hk : k ∈ Set.range (tableauInclusion s t h) + · obtain ⟨l, rfl⟩ := hk + rw [Equiv.Perm.viaEmbedding_apply] + simpa only [tableauInclusion_cell] using g.property l + · rw [Equiv.Perm.viaEmbedding_apply_of_notMem _ _ _ hk] + +lemma signC_viaEmbedding {a n : ℕ} (i : Fin a ↪ Fin n) (g : Equiv.Perm (Fin a)) : + signC (g.viaEmbedding i) = signC g := by + classical + simp [signC_def, Equiv.Perm.viaEmbedding, Equiv.Perm.sign_extendDomain] + +lemma strip_contraction_pair {a n : ℕ} {ν μ : YoungDiagram} + (s : Tableau a ν) (t : Tableau n μ) (hs : HorizontalStrip ν μ) : + dotProduct (wordRestrict (tableauInclusion s t hs.1) (rowLetterInclusion hs.1) + (polytabloid t)) (polytabloid s) ≠ 0 := by + classical + let i := tableauInclusion s t hs.1 + let j := rowLetterInclusion hs.1 + let x := wordRestrict i j (polytabloid t) + have hx (g : columnGroup s) : wordRep a (ν.colLen 0) (g : Equiv.Perm (Fin a)) x = + signC (g : Equiv.Perm (Fin a)) • x := by + rw [← wordRestrict_equivariant i j ((g : Equiv.Perm (Fin a)).viaEmbedding i) + (g : Equiv.Perm (Fin a)) (Equiv.Perm.viaEmbedding_apply _ _) (polytabloid t)] + rw [polytabloid_alternating t ⟨_, column_viaEmbedding s t hs.1 g⟩] + rw [map_smul, signC_viaEmbedding] + rw [← columnAlt_coefficient] + let := Fintype.ofFinite (columnGroup s) + have he : columnAlt s x = (Fintype.card (columnGroup s) : ℂ) • x := by + change (∑ g : columnGroup s, signC (g : Equiv.Perm (Fin a)) • + wordRep a (ν.colLen 0) (g : Equiv.Perm (Fin a))) x = _ + simp only [LinearMap.sum_apply, LinearMap.smul_apply, hx, smul_smul, + signC_mul_self, one_smul, Finset.sum_const, Finset.card_univ, Nat.cast_smul_eq_nsmul] + change columnAlt s x (rowWord s) ≠ 0 + rw [he] + change (Fintype.card (columnGroup s) : ℂ) * + wordRestrict (tableauInclusion s t hs.1) (rowLetterInclusion hs.1) (polytabloid t) (rowWord s) ≠ 0 + rw [strip_contraction_coefficient s t hs, mul_one] + exact Nat.cast_ne_zero.mpr Fintype.card_ne_zero + +/- Positive horizontal-strip Pieri map, equivariant for the full Young subgroup. -/ +theorem pieri_strip_restriction {a n : ℕ} {ν μ : YoungDiagram} + (s : Tableau a ν) (t : Tableau n μ) (hs : HorizontalStrip ν μ) : + ∃ F : Specht t →ₗ[ℂ] Specht s, F ≠ 0 ∧ + ∀ (g : Equiv.Perm (Fin n)) (h : Equiv.Perm (Fin a)), + (∀ k, g (tableauInclusion s t hs.1 k) = tableauInclusion s t hs.1 (h k)) → + ∀ x, F (spechtRep t g x) = spechtRep s h (F x) := by + let pr := subrepProject (spechtSub s) (fun _ hx => cyclic_star _ (polytabloid_real s) hx) + let T := wordRestrict (tableauInclusion s t hs.1) (rowLetterInclusion hs.1) + let F := pr.toLinearMap.comp (T.comp (spechtSub t).toSubmodule.subtype) + refine ⟨F, ?_, ?_⟩ + · intro hF + have hp := subrepProject_pair (spechtSub s) + (fun _ hx => cyclic_star _ (polytabloid_real s) hx) + (T (polytabloid t)) ⟨polytabloid s, mem_cyclic _ _⟩ + have he : pr (T (polytabloid t)) = 0 := by + exact congrArg (fun L : Specht t →ₗ[ℂ] Specht s => L ⟨polytabloid t, mem_cyclic _ _⟩) hF + rw [he] at hp + exact strip_contraction_pair s t hs (hp.symm.trans (zero_dotProduct _)) + · intro g h hh x + change pr (T (wordRep n (μ.colLen 0) g x.val)) = spechtRep s h (pr (T x.val)) + rw [wordRestrict_equivariant _ _ g h hh x.val] + exact LinearMap.congr_fun (pr.isIntertwining' h) (T x.val) + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/Polytabloid.lean b/lean/OAI/RepresentationTheory/Saxl/Polytabloid.lean index efd801afa64aa7f2102402fce8d67733683280fa..046274ac7aee6e92b0b2f97f027360098770ca5a 100644 --- a/lean/OAI/RepresentationTheory/Saxl/Polytabloid.lean +++ b/lean/OAI/RepresentationTheory/Saxl/Polytabloid.lean @@ -1,231 +1,231 @@ -import OAI.RepresentationTheory.Saxl.Basic - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uX - -namespace Saxl - -/- A finite set is the unique maximizer of its strictly signed separator. -Used below for the Ferrers equality case in the Specht submodule theorem. -/ -lemma finset_eq_of_signed_sum {X : Type uX} [DecidableEq X] - (A B : Finset X) (w : X → ℤ) - (hp : ∀ x ∈ B, 0 < w x) (hn : ∀ x ∉ B, w x < 0) - (he : ∑ x ∈ A, w x = ∑ x ∈ B, w x) : A = B := by - classical - let f := fun x => if x ∈ A then w x else 0 - let g := fun x => if x ∈ B then w x else 0 - have hle : ∀ x ∈ A ∪ B, f x ≤ g x := by - intro x hx - dsimp [f, g] - split_ifs with ha hb hb - · rfl - · exact (hn x hb).le - · exact (hp x hb).le - · rfl - have hs : ∑ x ∈ A ∪ B, f x = ∑ x ∈ A ∪ B, g x := by - simpa [f, g, ← Finset.sum_filter] using he - have hh := (Finset.sum_eq_sum_iff_of_le hle).mp hs - ext x - by_cases ha : x ∈ A <;> by_cases hb : x ∈ B - · simp [ha, hb] - · have hx := hh x (Finset.mem_union_left B ha) - have hneg := hn x hb - simp [f, g, ha, hb] at hx - omega - · have hx := hh x (Finset.mem_union_right A hb) - have hpos := hp x hb - simp [f, g, ha, hb] at hx - omega - · simp [ha, hb] - -/- A column-injective rearrangement of the canonical row word has precisely -Ferrers support. This is the equality-of-margins argument, without using -unproved Specht or Young-rule inputs. -/ -lemma ferrers_rearrangement {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (g : Equiv.Perm (Fin n)) - (hinj : Function.Injective (fun i => ((t (g i)).val.1, (t i).val.2))) : - ∀ i, ((t (g i)).val.1, (t i).val.2) ∈ μ := by - classical - let f : Fin n → ℕ × ℕ := fun i => ((t (g i)).val.1, (t i).val.2) - let w : ℕ × ℕ → ℤ := fun c => 2 * (μ.rowLen c.1 : ℤ) - 2 * c.2 - 1 - have ht : Function.Injective (fun i : Fin n => (t i).val) := - Subtype.val_injective.comp t.injective - have himage : Finset.univ.image (fun i : Fin n => (t i).val) = μ.cells := by - ext x - simp only [Finset.mem_image, Finset.mem_univ, true_and] - constructor - · rintro ⟨i, rfl⟩ - exact (t i).property - · intro hx - exact ⟨t.symm ⟨x, hx⟩, by simp⟩ - have he : ∑ x ∈ Finset.univ.image f, w x = ∑ x ∈ μ.cells, w x := by - rw [← himage, Finset.sum_image (fun _ _ _ _ h => hinj h), - Finset.sum_image (fun _ _ _ _ h => ht h)] - simp only [w, Finset.sum_sub_distrib, ← Finset.mul_sum] - rw [Equiv.sum_comp g (fun i => (μ.rowLen (t i).val.1 : ℤ))] - have heq := finset_eq_of_signed_sum (Finset.univ.image f) μ.cells w - (fun c hc => by - have h := YoungDiagram.mem_iff_lt_rowLen.mp hc - dsimp [w] - omega) - (fun c hc => by - have h : μ.rowLen c.1 ≤ c.2 := - le_of_not_gt (fun h => hc (YoungDiagram.mem_iff_lt_rowLen.mpr h)) - dsimp [w] - omega) he - intro i - exact (le_of_eq heq) (Finset.mem_image.mpr ⟨i, Finset.mem_univ _, rfl⟩) - -/- The complex-valued sign character. -/ -def signC {n : ℕ} : Equiv.Perm (Fin n) →* ℂ := - ((Int.castRingHom ℂ).toMonoidHom.comp (Units.coeHom ℤ)).comp Equiv.Perm.sign - -@[simp] lemma signC_def {n : ℕ} (g : Equiv.Perm (Fin n)) : - signC g = (((Equiv.Perm.sign g) : ℤ) : ℂ) := rfl - -@[simp] lemma signC_inv {n : ℕ} (g : Equiv.Perm (Fin n)) : signC g⁻¹ = signC g := by - simp [signC_def, Equiv.Perm.sign_inv] - -@[simp] lemma signC_mul_self {n : ℕ} (g : Equiv.Perm (Fin n)) : signC g * signC g = 1 := by - calc signC g * signC g = signC (g⁻¹ * g) := by rw [map_mul, signC_inv] - _ = 1 := by rw [inv_mul_cancel, map_one] - -lemma wordRep_single {n d : ℕ} (g : Equiv.Perm (Fin n)) (a : Fin n → Fin d) : - wordRep n d g (Pi.single a 1) = Pi.single (a ∘ (g⁻¹ : Equiv.Perm (Fin n))) (1 : ℂ) := by - classical - ext b - change (Pi.single a (1 : ℂ) : WordSpace n d) (b ∘ g) = _ - simp only [Pi.single_apply] - congr 1 - apply propext - constructor - · intro h - funext i - have hh := congrFun h (g⁻¹ i) - simpa using hh - · intro h - funext i - have hh := congrFun h (g i) - simpa using hh - -/- Actual column antisymmetrizer on the word-coordinate module. -/ -def columnAlt {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - Module.End ℂ (WordSpace n d) := by - classical - letI := Fintype.ofFinite (columnGroup t) - exact ∑ g : columnGroup t, - signC (g : Equiv.Perm (Fin n)) • wordRep n d (g : Equiv.Perm (Fin n)) - -lemma columnAlt_mul {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (h : columnGroup t) : - columnAlt (d := d) t * wordRep n d (h : Equiv.Perm (Fin n)) = - signC (h : Equiv.Perm (Fin n)) • columnAlt t := by - classical - let := Fintype.ofFinite (columnGroup t) - unfold columnAlt - simp only [Finset.sum_mul, smul_mul_assoc, Finset.smul_sum] - symm - apply (Equiv.sum_comp (Equiv.mulRight h) _).symm.trans - apply Finset.sum_congr rfl - intro g hg - change signC (h : Equiv.Perm (Fin n)) • - signC ((g * h : columnGroup t) : Equiv.Perm (Fin n)) • - wordRep n d ((g * h : columnGroup t) : Equiv.Perm (Fin n)) = _ - simp only [Subgroup.coe_mul, map_mul, smul_smul] - congr 1 - calc signC (h : Equiv.Perm (Fin n)) * - (signC (g : Equiv.Perm (Fin n)) * signC (h : Equiv.Perm (Fin n))) = - signC (g : Equiv.Perm (Fin n)) * - (signC (h : Equiv.Perm (Fin n)) * signC (h : Equiv.Perm (Fin n))) := by ring - _ = signC (g : Equiv.Perm (Fin n)) := by rw [signC_mul_self, mul_one] - -lemma columnAlt_row {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - columnAlt t (Pi.single (rowWord t) 1) = polytabloid t := by - simp [columnAlt, polytabloid, LinearMap.sum_apply] - -/- Construction of the witnessing column rearrangement. -/ -lemma column_rearrangement {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (g : Equiv.Perm (Fin n)) - (hinj : Function.Injective (fun i => ((t (g i)).val.1, (t i).val.2))) : - ∃ h : columnGroup t, rowWord t ∘ g = rowWord t ∘ (h : Equiv.Perm (Fin n)) := by - classical - let f : Fin n → Fin n := fun i => - t.symm ⟨((t (g i)).val.1, (t i).val.2), ferrers_rearrangement t g hinj i⟩ - have hf : Function.Injective f := by - intro i j hij - apply hinj - have hh := congrArg (fun k => (t k).val) hij - simpa [f] using hh - let h : Equiv.Perm (Fin n) := Equiv.ofBijective f ⟨hf, Finite.surjective_of_injective hf⟩ - have hcol : h ∈ columnGroup t := by - intro i - change (t (f i)).val.2 = _ - simp [f] - refine ⟨⟨h, hcol⟩, ?_⟩ - funext i - apply Fin.ext - change (t (g i)).val.1 = (t (f i)).val.1 - simp [f] - -lemma columnAlt_collision {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (a : Fin n → Fin d) (i j : Fin n) (hij : i ≠ j) - (hc : (t i).val.2 = (t j).val.2) (ha : a i = a j) : - columnAlt t (Pi.single a (1 : ℂ)) = 0 := by - classical - let h : columnGroup t := ⟨Equiv.swap i j, fun k => Equiv.apply_swap_eq_self (v := fun l => (t l).val.2) hc k⟩ - have hs : signC (h : Equiv.Perm (Fin n)) = -1 := by - simp [h, signC_def, Equiv.Perm.sign_swap hij] - have hf : wordRep n d (h : Equiv.Perm (Fin n)) (Pi.single a 1) = Pi.single a 1 := by - rw [wordRep_single] - congr 1 - funext k - exact Equiv.apply_swap_eq_self ha k - have hh := congrArg (fun f : Module.End ℂ (WordSpace n d) => f (Pi.single a 1)) - (columnAlt_mul (d := d) t h) - simp only [Module.End.mul_apply, hf, LinearMap.smul_apply, hs, neg_one_smul] at hh - ext b - exact CharZero.eq_neg_self_iff.mp (congrFun hh b) - -lemma columnAlt_column {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (h : columnGroup t) : - columnAlt t (Pi.single (rowWord t ∘ (h : Equiv.Perm (Fin n))) 1) = - signC (h : Equiv.Perm (Fin n)) • polytabloid t := by - classical - have he : wordRep n (μ.colLen 0) ((h⁻¹ : columnGroup t) : Equiv.Perm (Fin n)) - (Pi.single (rowWord t) 1) = - Pi.single (rowWord t ∘ (h : Equiv.Perm (Fin n))) 1 := by - rw [wordRep_single] - simp only [Subgroup.coe_inv, inv_inv] - rw [← he, ← Module.End.mul_apply, columnAlt_mul, LinearMap.smul_apply, - columnAlt_row, Subgroup.coe_inv, signC_inv] - -lemma columnAlt_single {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (g : Equiv.Perm (Fin n)) : - columnAlt t (Pi.single (rowWord t ∘ g) 1) ∈ - Submodule.span ℂ {polytabloid t} := by - classical - by_cases hi : Function.Injective (fun i : Fin n => ((t (g i)).val.1, (t i).val.2)) - · obtain ⟨h, hh⟩ := column_rearrangement t g hi - rw [hh, columnAlt_column] - exact Submodule.smul_mem _ _ (Submodule.subset_span (Set.mem_singleton _)) - · simp only [Function.Injective] at hi - push Not at hi - obtain ⟨i, j, hc, hij⟩ := hi - have ha : (rowWord t ∘ g) i = (rowWord t ∘ g) j := by - apply Fin.ext - have hh := congrArg Prod.fst hc - exact hh - have hcol := congrArg Prod.snd hc - rw [columnAlt_collision t _ i j hij hcol ha] - exact Submodule.zero_mem _ - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.Basic + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uX + +namespace Saxl + +/- A finite set is the unique maximizer of its strictly signed separator. +Used below for the Ferrers equality case in the Specht submodule theorem. -/ +lemma finset_eq_of_signed_sum {X : Type uX} [DecidableEq X] + (A B : Finset X) (w : X → ℤ) + (hp : ∀ x ∈ B, 0 < w x) (hn : ∀ x ∉ B, w x < 0) + (he : ∑ x ∈ A, w x = ∑ x ∈ B, w x) : A = B := by + classical + let f := fun x => if x ∈ A then w x else 0 + let g := fun x => if x ∈ B then w x else 0 + have hle : ∀ x ∈ A ∪ B, f x ≤ g x := by + intro x hx + dsimp [f, g] + split_ifs with ha hb hb + · rfl + · exact (hn x hb).le + · exact (hp x hb).le + · rfl + have hs : ∑ x ∈ A ∪ B, f x = ∑ x ∈ A ∪ B, g x := by + simpa [f, g, ← Finset.sum_filter] using he + have hh := (Finset.sum_eq_sum_iff_of_le hle).mp hs + ext x + by_cases ha : x ∈ A <;> by_cases hb : x ∈ B + · simp [ha, hb] + · have hx := hh x (Finset.mem_union_left B ha) + have hneg := hn x hb + simp [f, g, ha, hb] at hx + omega + · have hx := hh x (Finset.mem_union_right A hb) + have hpos := hp x hb + simp [f, g, ha, hb] at hx + omega + · simp [ha, hb] + +/- A column-injective rearrangement of the canonical row word has precisely +Ferrers support. This is the equality-of-margins argument, without using +unproved Specht or Young-rule inputs. -/ +lemma ferrers_rearrangement {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (g : Equiv.Perm (Fin n)) + (hinj : Function.Injective (fun i => ((t (g i)).val.1, (t i).val.2))) : + ∀ i, ((t (g i)).val.1, (t i).val.2) ∈ μ := by + classical + let f : Fin n → ℕ × ℕ := fun i => ((t (g i)).val.1, (t i).val.2) + let w : ℕ × ℕ → ℤ := fun c => 2 * (μ.rowLen c.1 : ℤ) - 2 * c.2 - 1 + have ht : Function.Injective (fun i : Fin n => (t i).val) := + Subtype.val_injective.comp t.injective + have himage : Finset.univ.image (fun i : Fin n => (t i).val) = μ.cells := by + ext x + simp only [Finset.mem_image, Finset.mem_univ, true_and] + constructor + · rintro ⟨i, rfl⟩ + exact (t i).property + · intro hx + exact ⟨t.symm ⟨x, hx⟩, by simp⟩ + have he : ∑ x ∈ Finset.univ.image f, w x = ∑ x ∈ μ.cells, w x := by + rw [← himage, Finset.sum_image (fun _ _ _ _ h => hinj h), + Finset.sum_image (fun _ _ _ _ h => ht h)] + simp only [w, Finset.sum_sub_distrib, ← Finset.mul_sum] + rw [Equiv.sum_comp g (fun i => (μ.rowLen (t i).val.1 : ℤ))] + have heq := finset_eq_of_signed_sum (Finset.univ.image f) μ.cells w + (fun c hc => by + have h := YoungDiagram.mem_iff_lt_rowLen.mp hc + dsimp [w] + omega) + (fun c hc => by + have h : μ.rowLen c.1 ≤ c.2 := + le_of_not_gt (fun h => hc (YoungDiagram.mem_iff_lt_rowLen.mpr h)) + dsimp [w] + omega) he + intro i + exact (le_of_eq heq) (Finset.mem_image.mpr ⟨i, Finset.mem_univ _, rfl⟩) + +/- The complex-valued sign character. -/ +def signC {n : ℕ} : Equiv.Perm (Fin n) →* ℂ := + ((Int.castRingHom ℂ).toMonoidHom.comp (Units.coeHom ℤ)).comp Equiv.Perm.sign + +@[simp] lemma signC_def {n : ℕ} (g : Equiv.Perm (Fin n)) : + signC g = (((Equiv.Perm.sign g) : ℤ) : ℂ) := rfl + +@[simp] lemma signC_inv {n : ℕ} (g : Equiv.Perm (Fin n)) : signC g⁻¹ = signC g := by + simp [signC_def, Equiv.Perm.sign_inv] + +@[simp] lemma signC_mul_self {n : ℕ} (g : Equiv.Perm (Fin n)) : signC g * signC g = 1 := by + calc signC g * signC g = signC (g⁻¹ * g) := by rw [map_mul, signC_inv] + _ = 1 := by rw [inv_mul_cancel, map_one] + +lemma wordRep_single {n d : ℕ} (g : Equiv.Perm (Fin n)) (a : Fin n → Fin d) : + wordRep n d g (Pi.single a 1) = Pi.single (a ∘ (g⁻¹ : Equiv.Perm (Fin n))) (1 : ℂ) := by + classical + ext b + change (Pi.single a (1 : ℂ) : WordSpace n d) (b ∘ g) = _ + simp only [Pi.single_apply] + congr 1 + apply propext + constructor + · intro h + funext i + have hh := congrFun h (g⁻¹ i) + simpa using hh + · intro h + funext i + have hh := congrFun h (g i) + simpa using hh + +/- Actual column antisymmetrizer on the word-coordinate module. -/ +def columnAlt {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + Module.End ℂ (WordSpace n d) := by + classical + letI := Fintype.ofFinite (columnGroup t) + exact ∑ g : columnGroup t, + signC (g : Equiv.Perm (Fin n)) • wordRep n d (g : Equiv.Perm (Fin n)) + +lemma columnAlt_mul {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (h : columnGroup t) : + columnAlt (d := d) t * wordRep n d (h : Equiv.Perm (Fin n)) = + signC (h : Equiv.Perm (Fin n)) • columnAlt t := by + classical + let := Fintype.ofFinite (columnGroup t) + unfold columnAlt + simp only [Finset.sum_mul, smul_mul_assoc, Finset.smul_sum] + symm + apply (Equiv.sum_comp (Equiv.mulRight h) _).symm.trans + apply Finset.sum_congr rfl + intro g hg + change signC (h : Equiv.Perm (Fin n)) • + signC ((g * h : columnGroup t) : Equiv.Perm (Fin n)) • + wordRep n d ((g * h : columnGroup t) : Equiv.Perm (Fin n)) = _ + simp only [Subgroup.coe_mul, map_mul, smul_smul] + congr 1 + calc signC (h : Equiv.Perm (Fin n)) * + (signC (g : Equiv.Perm (Fin n)) * signC (h : Equiv.Perm (Fin n))) = + signC (g : Equiv.Perm (Fin n)) * + (signC (h : Equiv.Perm (Fin n)) * signC (h : Equiv.Perm (Fin n))) := by ring + _ = signC (g : Equiv.Perm (Fin n)) := by rw [signC_mul_self, mul_one] + +lemma columnAlt_row {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + columnAlt t (Pi.single (rowWord t) 1) = polytabloid t := by + simp [columnAlt, polytabloid, LinearMap.sum_apply] + +/- Construction of the witnessing column rearrangement. -/ +lemma column_rearrangement {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (g : Equiv.Perm (Fin n)) + (hinj : Function.Injective (fun i => ((t (g i)).val.1, (t i).val.2))) : + ∃ h : columnGroup t, rowWord t ∘ g = rowWord t ∘ (h : Equiv.Perm (Fin n)) := by + classical + let f : Fin n → Fin n := fun i => + t.symm ⟨((t (g i)).val.1, (t i).val.2), ferrers_rearrangement t g hinj i⟩ + have hf : Function.Injective f := by + intro i j hij + apply hinj + have hh := congrArg (fun k => (t k).val) hij + simpa [f] using hh + let h : Equiv.Perm (Fin n) := Equiv.ofBijective f ⟨hf, Finite.surjective_of_injective hf⟩ + have hcol : h ∈ columnGroup t := by + intro i + change (t (f i)).val.2 = _ + simp [f] + refine ⟨⟨h, hcol⟩, ?_⟩ + funext i + apply Fin.ext + change (t (g i)).val.1 = (t (f i)).val.1 + simp [f] + +lemma columnAlt_collision {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (a : Fin n → Fin d) (i j : Fin n) (hij : i ≠ j) + (hc : (t i).val.2 = (t j).val.2) (ha : a i = a j) : + columnAlt t (Pi.single a (1 : ℂ)) = 0 := by + classical + let h : columnGroup t := ⟨Equiv.swap i j, fun k => Equiv.apply_swap_eq_self (v := fun l => (t l).val.2) hc k⟩ + have hs : signC (h : Equiv.Perm (Fin n)) = -1 := by + simp [h, signC_def, Equiv.Perm.sign_swap hij] + have hf : wordRep n d (h : Equiv.Perm (Fin n)) (Pi.single a 1) = Pi.single a 1 := by + rw [wordRep_single] + congr 1 + funext k + exact Equiv.apply_swap_eq_self ha k + have hh := congrArg (fun f : Module.End ℂ (WordSpace n d) => f (Pi.single a 1)) + (columnAlt_mul (d := d) t h) + simp only [Module.End.mul_apply, hf, LinearMap.smul_apply, hs, neg_one_smul] at hh + ext b + exact CharZero.eq_neg_self_iff.mp (congrFun hh b) + +lemma columnAlt_column {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (h : columnGroup t) : + columnAlt t (Pi.single (rowWord t ∘ (h : Equiv.Perm (Fin n))) 1) = + signC (h : Equiv.Perm (Fin n)) • polytabloid t := by + classical + have he : wordRep n (μ.colLen 0) ((h⁻¹ : columnGroup t) : Equiv.Perm (Fin n)) + (Pi.single (rowWord t) 1) = + Pi.single (rowWord t ∘ (h : Equiv.Perm (Fin n))) 1 := by + rw [wordRep_single] + simp only [Subgroup.coe_inv, inv_inv] + rw [← he, ← Module.End.mul_apply, columnAlt_mul, LinearMap.smul_apply, + columnAlt_row, Subgroup.coe_inv, signC_inv] + +lemma columnAlt_single {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (g : Equiv.Perm (Fin n)) : + columnAlt t (Pi.single (rowWord t ∘ g) 1) ∈ + Submodule.span ℂ {polytabloid t} := by + classical + by_cases hi : Function.Injective (fun i : Fin n => ((t (g i)).val.1, (t i).val.2)) + · obtain ⟨h, hh⟩ := column_rearrangement t g hi + rw [hh, columnAlt_column] + exact Submodule.smul_mem _ _ (Submodule.subset_span (Set.mem_singleton _)) + · simp only [Function.Injective] at hi + push Not at hi + obtain ⟨i, j, hc, hij⟩ := hi + have ha : (rowWord t ∘ g) i = (rowWord t ∘ g) j := by + apply Fin.ext + have hh := congrArg Prod.fst hc + exact hh + have hcol := congrArg Prod.snd hc + rw [columnAlt_collision t _ i j hij hcol ha] + exact Submodule.zero_mem _ + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/PositionSplit.lean b/lean/OAI/RepresentationTheory/Saxl/PositionSplit.lean index 1524f4671af45513bdd637c8cc8763bfaf04134d..3a73c035928aa248468a078f3b26ac60194ac293 100644 --- a/lean/OAI/RepresentationTheory/Saxl/PositionSplit.lean +++ b/lean/OAI/RepresentationTheory/Saxl/PositionSplit.lean @@ -1,250 +1,250 @@ -import OAI.RepresentationTheory.Saxl.CoordinateSector - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uAlpha - -namespace Saxl -/- The genuine product position permutation under a disjoint-set enumeration. -/ -def sumPerm {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) : Equiv.Perm (Fin n) := - e.symm.permCongr (Equiv.sumCongr g h) - -lemma signC_sumPerm {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) : - signC (sumPerm e g h) = signC g * signC h := by - simp [signC_def, sumPerm, Equiv.Perm.sign_permCongr, Equiv.Perm.sign_sumCongr] - -@[simp] lemma sumPerm_left {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) (i : Fin a) : - sumPerm e g h (e.symm (Sum.inl i)) = e.symm (Sum.inl (g i)) := by - simp [sumPerm, Equiv.permCongr_apply] - -@[simp] lemma sumPerm_right {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) (i : Fin b) : - sumPerm e g h (e.symm (Sum.inr i)) = e.symm (Sum.inr (h i)) := by - simp [sumPerm, Equiv.permCongr_apply] - -def leftWord {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) (w : Fin n → Fin d) : Fin a → Fin d := - fun i => w (e.symm (Sum.inl i)) - -def rightWord {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) (w : Fin n → Fin d) : Fin b → Fin d := - fun i => w (e.symm (Sum.inr i)) - -lemma word_eq_iff_parts {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (w v : Fin n → Fin d) : w = v ↔ leftWord e w = leftWord e v ∧ rightWord e w = rightWord e v := by - constructor - · rintro rfl; exact ⟨rfl,rfl⟩ - · rintro ⟨h₁,h₂⟩ - funext i - obtain ⟨k, rfl⟩ := e.symm.surjective i - cases k with - | inl k => exact congrFun h₁ k - | inr k => exact congrFun h₂ k - -def positionProduct {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (x : WordSpace a d) (y : WordSpace b d) : WordSpace n d := - fun w => x (leftWord e w) * y (rightWord e w) - -lemma single_positionProduct {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (w : Fin n → Fin d) : - (Pi.single w (1:ℂ) : WordSpace n d) = - positionProduct e (Pi.single (leftWord e w) 1) (Pi.single (rightWord e w) 1) := by - classical - ext v - simp only [positionProduct, Pi.single_apply] - simp only [word_eq_iff_parts e] - split_ifs <;> simp_all - -lemma altWord_split_term {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (w v : Fin n → Fin d) (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) : - (signC (sumPerm e g h) • wordRep n d (sumPerm e g h) (Pi.single w 1)) v = - (signC g • wordRep a d g (Pi.single (leftWord e w) 1)) (leftWord e v) * - (signC h • wordRep b d h (Pi.single (rightWord e w) 1)) (rightWord e v) := by - rw [single_positionProduct e w] - change signC (sumPerm e g h) * - ((Pi.single (leftWord e w) (1:ℂ) : WordSpace a d) (leftWord e (v ∘ sumPerm e g h)) * - (Pi.single (rightWord e w) (1:ℂ) : WordSpace b d) (rightWord e (v ∘ sumPerm e g h))) = _ - have h₁ : leftWord e (v ∘ sumPerm e g h) = leftWord e v ∘ g := by - ext i; simp [leftWord] - have h₂ : rightWord e (v ∘ sumPerm e g h) = rightWord e v ∘ h := by - ext i; simp [rightWord] - rw [h₁,h₂,signC_sumPerm] - change _ = (signC g * (Pi.single (leftWord e w) (1:ℂ) : WordSpace a d) (leftWord e v ∘ g)) * - (signC h * (Pi.single (rightWord e w) (1:ℂ) : WordSpace b d) (rightWord e v ∘ h)) - ring - -/- Independent block permutations factor with exactly the product sign. -/ -theorem altWord_split {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (G : Subgroup (Equiv.Perm (Fin n))) (G₁ : Subgroup (Equiv.Perm (Fin a))) - (G₂ : Subgroup (Equiv.Perm (Fin b))) (E : G ≃ G₁ × G₂) - (hE : ∀ g : G, (g : Equiv.Perm (Fin n)) = - sumPerm e ((E g).1 : Equiv.Perm (Fin a)) ((E g).2 : Equiv.Perm (Fin b))) - (w : Fin n → Fin d) : - altWord G w = positionProduct e (altWord G₁ (leftWord e w)) (altWord G₂ (rightWord e w)) := by - classical - let := Fintype.ofFinite G - let := Fintype.ofFinite G₁ - let := Fintype.ofFinite G₂ - ext v - unfold altWord - simp only [Finset.sum_apply, positionProduct, Finset.sum_mul, Finset.mul_sum] - rw [Finset.sum_comm] - calc - _ = ∑ p : G₁ × G₂, - (signC (p.1 : Equiv.Perm (Fin a)) • wordRep a d p.1 (Pi.single (leftWord e w) 1)) (leftWord e v) * - (signC (p.2 : Equiv.Perm (Fin b)) • wordRep b d p.2 (Pi.single (rightWord e w) 1)) (rightWord e v) := by - apply Fintype.sum_equiv E - intro g - rw [hE g] - exact altWord_split_term e w v _ _ - _ = _ := Fintype.sum_prod_type _ - - - -def fiberGroup {n : ℕ} {α : Type uAlpha} (f : Fin n → α) : Subgroup (Equiv.Perm (Fin n)) where - carrier := {g | ∀ i, f (g i) = f i} - one_mem' _ := rfl - mul_mem' hg hh i := (hg _).trans (hh i) - inv_mem' := by - intro g hg i - simpa using (hg (g⁻¹ i)).symm - -def leftPositions {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : - Fin a ≃ {i : Fin n // (e i).isLeft = true} where - toFun i := ⟨e.symm (Sum.inl i), by simp⟩ - invFun i := (e i.val).getLeft i.property - left_inv i := by simp - right_inv i := by - apply Subtype.ext - apply e.injective - simp only [Equiv.apply_symm_apply] - exact Sum.inl_getLeft _ _ - -def rightPositions {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : - Fin b ≃ {i : Fin n // ¬(e i).isLeft = true} where - toFun i := ⟨e.symm (Sum.inr i), by simp⟩ - invFun i := (e i.val).getRight (by - have hi := i.property - cases h : e i.val <;> simp_all) - left_inv i := by simp - right_inv i := by - apply Subtype.ext - apply e.injective - simp only [Equiv.apply_symm_apply] - exact Sum.inr_getRight _ _ - -def leftRestriction {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g : sectorGroup (fun i => (e i).isLeft = true)) : Equiv.Perm (Fin a) := - (leftPositions e).symm.permCongr ((g : Equiv.Perm (Fin n)).subtypePerm g.property) - -def rightRestriction {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g : sectorGroup (fun i => (e i).isLeft = true)) : Equiv.Perm (Fin b) := - (rightPositions e).symm.permCongr ((g : Equiv.Perm (Fin n)).subtypePerm (fun i => not_congr (g.property i))) - -lemma leftRestriction_apply {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g : sectorGroup (fun i => (e i).isLeft = true)) (i : Fin a) : - e.symm (Sum.inl (leftRestriction e g i)) = g.val (e.symm (Sum.inl i)) := by - apply e.injective - simp only [Equiv.apply_symm_apply] - exact Sum.inl_getLeft _ _ - -lemma rightRestriction_apply {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g : sectorGroup (fun i => (e i).isLeft = true)) (i : Fin b) : - e.symm (Sum.inr (rightRestriction e g i)) = g.val (e.symm (Sum.inr i)) := by - apply e.injective - simp only [Equiv.apply_symm_apply] - exact Sum.inr_getRight _ _ - -lemma sumPerm_restrictions {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g : sectorGroup (fun i => (e i).isLeft = true)) : - sumPerm e (leftRestriction e g) (rightRestriction e g) = g.val := by - apply Equiv.ext - intro i - obtain ⟨j,rfl⟩ := e.symm.surjective i - cases j with - | inl j => simpa using leftRestriction_apply e g j - | inr j => simpa using rightRestriction_apply e g j - -lemma sumPerm_injective {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : - Function.Injective (fun p : Equiv.Perm (Fin a) × Equiv.Perm (Fin b) => sumPerm e p.1 p.2) := by - intro p q hpq - apply Prod.ext - · apply Equiv.ext - intro i - have h := congrArg (fun g : Equiv.Perm (Fin n) => e (g (e.symm (Sum.inl i)))) hpq - simpa using h - · apply Equiv.ext - intro i - have h := congrArg (fun g : Equiv.Perm (Fin n) => e (g (e.symm (Sum.inr i)))) hpq - simpa using h - -def fiberSplit {n a b : ℕ} {α : Type uAlpha} (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin n → α) : - (fiberGroup (fun i => f (e.symm (Sum.inl i)))) × (fiberGroup (fun i => f (e.symm (Sum.inr i)))) ≃ - ↥(fiberGroup f ⊓ sectorGroup (fun i => (e i).isLeft = true)) := by - let F : (fiberGroup (fun i => f (e.symm (Sum.inl i)))) × - (fiberGroup (fun i => f (e.symm (Sum.inr i)))) → - ↥(fiberGroup f ⊓ sectorGroup (fun i => (e i).isLeft = true)) := fun p => - ⟨sumPerm e p.1.val p.2.val, by - constructor - · intro i - obtain ⟨j,rfl⟩ := e.symm.surjective i - cases j with - | inl j => simpa using p.1.property j - | inr j => simpa using p.2.property j - · intro i - obtain ⟨j,rfl⟩ := e.symm.surjective i - cases j <;> simp⟩ - apply Equiv.ofBijective F - constructor - · intro p q hpq - have hh : sumPerm e p.1.val p.2.val = sumPerm e q.1.val q.2.val := congrArg Subtype.val hpq - have h := @sumPerm_injective n a b e (p.1.val,p.2.val) (q.1.val,q.2.val) hh - exact Prod.ext (Subtype.ext (congrArg Prod.fst h)) (Subtype.ext (congrArg Prod.snd h)) - · intro g - let g' : sectorGroup (fun i => (e i).isLeft = true) := ⟨g.val,g.property.2⟩ - refine ⟨(⟨leftRestriction e g', ?_⟩, ⟨rightRestriction e g', ?_⟩), ?_⟩ - · intro i - dsimp only - rw [leftRestriction_apply] - exact g.property.1 _ - · intro i - dsimp only - rw [rightRestriction_apply] - exact g.property.1 _ - · exact Subtype.ext (sumPerm_restrictions e g') - -lemma fiberSplit_apply {n a b : ℕ} {α : Type uAlpha} (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin n → α) - (p : (fiberGroup (fun i => f (e.symm (Sum.inl i)))) × (fiberGroup (fun i => f (e.symm (Sum.inr i))))) : - (fiberSplit e f p).val = sumPerm e p.1.val p.2.val := rfl - -/- Exact independent-block factorization for arbitrary row/column labels. -/ -theorem altWord_fiber_split {n a b d : ℕ} {α : Type uAlpha} (e : Fin n ≃ Fin a ⊕ Fin b) - (f : Fin n → α) (w : Fin n → Fin d) : - altWord (fiberGroup f ⊓ sectorGroup (fun i => (e i).isLeft = true)) w = - positionProduct e - (altWord (fiberGroup (fun i => f (e.symm (Sum.inl i)))) (leftWord e w)) - (altWord (fiberGroup (fun i => f (e.symm (Sum.inr i)))) (rightWord e w)) := by - apply altWord_split e _ _ _ (fiberSplit e f).symm - intro g - exact (congrArg Subtype.val ((fiberSplit e f).apply_symm_apply g)).symm - - -@[simp] lemma staircase_colLen (m j : ℕ) : (staircase m).colLen j = m-j := by - have hh : ∀ i, i < (staircase m).colLen j ↔ i < m-j := by - intro i - rw [← YoungDiagram.mem_iff_lt_colLen, mem_staircase] - omega - have h₁ := hh ((staircase m).colLen j) - have h₂ := hh (m-j) - omega - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.CoordinateSector + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uAlpha + +namespace Saxl +/- The genuine product position permutation under a disjoint-set enumeration. -/ +def sumPerm {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) : Equiv.Perm (Fin n) := + e.symm.permCongr (Equiv.sumCongr g h) + +lemma signC_sumPerm {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) : + signC (sumPerm e g h) = signC g * signC h := by + simp [signC_def, sumPerm, Equiv.Perm.sign_permCongr, Equiv.Perm.sign_sumCongr] + +@[simp] lemma sumPerm_left {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) (i : Fin a) : + sumPerm e g h (e.symm (Sum.inl i)) = e.symm (Sum.inl (g i)) := by + simp [sumPerm, Equiv.permCongr_apply] + +@[simp] lemma sumPerm_right {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) (i : Fin b) : + sumPerm e g h (e.symm (Sum.inr i)) = e.symm (Sum.inr (h i)) := by + simp [sumPerm, Equiv.permCongr_apply] + +def leftWord {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) (w : Fin n → Fin d) : Fin a → Fin d := + fun i => w (e.symm (Sum.inl i)) + +def rightWord {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) (w : Fin n → Fin d) : Fin b → Fin d := + fun i => w (e.symm (Sum.inr i)) + +lemma word_eq_iff_parts {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (w v : Fin n → Fin d) : w = v ↔ leftWord e w = leftWord e v ∧ rightWord e w = rightWord e v := by + constructor + · rintro rfl; exact ⟨rfl,rfl⟩ + · rintro ⟨h₁,h₂⟩ + funext i + obtain ⟨k, rfl⟩ := e.symm.surjective i + cases k with + | inl k => exact congrFun h₁ k + | inr k => exact congrFun h₂ k + +def positionProduct {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (x : WordSpace a d) (y : WordSpace b d) : WordSpace n d := + fun w => x (leftWord e w) * y (rightWord e w) + +lemma single_positionProduct {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (w : Fin n → Fin d) : + (Pi.single w (1:ℂ) : WordSpace n d) = + positionProduct e (Pi.single (leftWord e w) 1) (Pi.single (rightWord e w) 1) := by + classical + ext v + simp only [positionProduct, Pi.single_apply] + simp only [word_eq_iff_parts e] + split_ifs <;> simp_all + +lemma altWord_split_term {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (w v : Fin n → Fin d) (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) : + (signC (sumPerm e g h) • wordRep n d (sumPerm e g h) (Pi.single w 1)) v = + (signC g • wordRep a d g (Pi.single (leftWord e w) 1)) (leftWord e v) * + (signC h • wordRep b d h (Pi.single (rightWord e w) 1)) (rightWord e v) := by + rw [single_positionProduct e w] + change signC (sumPerm e g h) * + ((Pi.single (leftWord e w) (1:ℂ) : WordSpace a d) (leftWord e (v ∘ sumPerm e g h)) * + (Pi.single (rightWord e w) (1:ℂ) : WordSpace b d) (rightWord e (v ∘ sumPerm e g h))) = _ + have h₁ : leftWord e (v ∘ sumPerm e g h) = leftWord e v ∘ g := by + ext i; simp [leftWord] + have h₂ : rightWord e (v ∘ sumPerm e g h) = rightWord e v ∘ h := by + ext i; simp [rightWord] + rw [h₁,h₂,signC_sumPerm] + change _ = (signC g * (Pi.single (leftWord e w) (1:ℂ) : WordSpace a d) (leftWord e v ∘ g)) * + (signC h * (Pi.single (rightWord e w) (1:ℂ) : WordSpace b d) (rightWord e v ∘ h)) + ring + +/- Independent block permutations factor with exactly the product sign. -/ +theorem altWord_split {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (G : Subgroup (Equiv.Perm (Fin n))) (G₁ : Subgroup (Equiv.Perm (Fin a))) + (G₂ : Subgroup (Equiv.Perm (Fin b))) (E : G ≃ G₁ × G₂) + (hE : ∀ g : G, (g : Equiv.Perm (Fin n)) = + sumPerm e ((E g).1 : Equiv.Perm (Fin a)) ((E g).2 : Equiv.Perm (Fin b))) + (w : Fin n → Fin d) : + altWord G w = positionProduct e (altWord G₁ (leftWord e w)) (altWord G₂ (rightWord e w)) := by + classical + let := Fintype.ofFinite G + let := Fintype.ofFinite G₁ + let := Fintype.ofFinite G₂ + ext v + unfold altWord + simp only [Finset.sum_apply, positionProduct, Finset.sum_mul, Finset.mul_sum] + rw [Finset.sum_comm] + calc + _ = ∑ p : G₁ × G₂, + (signC (p.1 : Equiv.Perm (Fin a)) • wordRep a d p.1 (Pi.single (leftWord e w) 1)) (leftWord e v) * + (signC (p.2 : Equiv.Perm (Fin b)) • wordRep b d p.2 (Pi.single (rightWord e w) 1)) (rightWord e v) := by + apply Fintype.sum_equiv E + intro g + rw [hE g] + exact altWord_split_term e w v _ _ + _ = _ := Fintype.sum_prod_type _ + + + +def fiberGroup {n : ℕ} {α : Type uAlpha} (f : Fin n → α) : Subgroup (Equiv.Perm (Fin n)) where + carrier := {g | ∀ i, f (g i) = f i} + one_mem' _ := rfl + mul_mem' hg hh i := (hg _).trans (hh i) + inv_mem' := by + intro g hg i + simpa using (hg (g⁻¹ i)).symm + +def leftPositions {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : + Fin a ≃ {i : Fin n // (e i).isLeft = true} where + toFun i := ⟨e.symm (Sum.inl i), by simp⟩ + invFun i := (e i.val).getLeft i.property + left_inv i := by simp + right_inv i := by + apply Subtype.ext + apply e.injective + simp only [Equiv.apply_symm_apply] + exact Sum.inl_getLeft _ _ + +def rightPositions {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : + Fin b ≃ {i : Fin n // ¬(e i).isLeft = true} where + toFun i := ⟨e.symm (Sum.inr i), by simp⟩ + invFun i := (e i.val).getRight (by + have hi := i.property + cases h : e i.val <;> simp_all) + left_inv i := by simp + right_inv i := by + apply Subtype.ext + apply e.injective + simp only [Equiv.apply_symm_apply] + exact Sum.inr_getRight _ _ + +def leftRestriction {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g : sectorGroup (fun i => (e i).isLeft = true)) : Equiv.Perm (Fin a) := + (leftPositions e).symm.permCongr ((g : Equiv.Perm (Fin n)).subtypePerm g.property) + +def rightRestriction {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g : sectorGroup (fun i => (e i).isLeft = true)) : Equiv.Perm (Fin b) := + (rightPositions e).symm.permCongr ((g : Equiv.Perm (Fin n)).subtypePerm (fun i => not_congr (g.property i))) + +lemma leftRestriction_apply {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g : sectorGroup (fun i => (e i).isLeft = true)) (i : Fin a) : + e.symm (Sum.inl (leftRestriction e g i)) = g.val (e.symm (Sum.inl i)) := by + apply e.injective + simp only [Equiv.apply_symm_apply] + exact Sum.inl_getLeft _ _ + +lemma rightRestriction_apply {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g : sectorGroup (fun i => (e i).isLeft = true)) (i : Fin b) : + e.symm (Sum.inr (rightRestriction e g i)) = g.val (e.symm (Sum.inr i)) := by + apply e.injective + simp only [Equiv.apply_symm_apply] + exact Sum.inr_getRight _ _ + +lemma sumPerm_restrictions {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g : sectorGroup (fun i => (e i).isLeft = true)) : + sumPerm e (leftRestriction e g) (rightRestriction e g) = g.val := by + apply Equiv.ext + intro i + obtain ⟨j,rfl⟩ := e.symm.surjective i + cases j with + | inl j => simpa using leftRestriction_apply e g j + | inr j => simpa using rightRestriction_apply e g j + +lemma sumPerm_injective {n a b : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : + Function.Injective (fun p : Equiv.Perm (Fin a) × Equiv.Perm (Fin b) => sumPerm e p.1 p.2) := by + intro p q hpq + apply Prod.ext + · apply Equiv.ext + intro i + have h := congrArg (fun g : Equiv.Perm (Fin n) => e (g (e.symm (Sum.inl i)))) hpq + simpa using h + · apply Equiv.ext + intro i + have h := congrArg (fun g : Equiv.Perm (Fin n) => e (g (e.symm (Sum.inr i)))) hpq + simpa using h + +def fiberSplit {n a b : ℕ} {α : Type uAlpha} (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin n → α) : + (fiberGroup (fun i => f (e.symm (Sum.inl i)))) × (fiberGroup (fun i => f (e.symm (Sum.inr i)))) ≃ + ↥(fiberGroup f ⊓ sectorGroup (fun i => (e i).isLeft = true)) := by + let F : (fiberGroup (fun i => f (e.symm (Sum.inl i)))) × + (fiberGroup (fun i => f (e.symm (Sum.inr i)))) → + ↥(fiberGroup f ⊓ sectorGroup (fun i => (e i).isLeft = true)) := fun p => + ⟨sumPerm e p.1.val p.2.val, by + constructor + · intro i + obtain ⟨j,rfl⟩ := e.symm.surjective i + cases j with + | inl j => simpa using p.1.property j + | inr j => simpa using p.2.property j + · intro i + obtain ⟨j,rfl⟩ := e.symm.surjective i + cases j <;> simp⟩ + apply Equiv.ofBijective F + constructor + · intro p q hpq + have hh : sumPerm e p.1.val p.2.val = sumPerm e q.1.val q.2.val := congrArg Subtype.val hpq + have h := @sumPerm_injective n a b e (p.1.val,p.2.val) (q.1.val,q.2.val) hh + exact Prod.ext (Subtype.ext (congrArg Prod.fst h)) (Subtype.ext (congrArg Prod.snd h)) + · intro g + let g' : sectorGroup (fun i => (e i).isLeft = true) := ⟨g.val,g.property.2⟩ + refine ⟨(⟨leftRestriction e g', ?_⟩, ⟨rightRestriction e g', ?_⟩), ?_⟩ + · intro i + dsimp only + rw [leftRestriction_apply] + exact g.property.1 _ + · intro i + dsimp only + rw [rightRestriction_apply] + exact g.property.1 _ + · exact Subtype.ext (sumPerm_restrictions e g') + +lemma fiberSplit_apply {n a b : ℕ} {α : Type uAlpha} (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin n → α) + (p : (fiberGroup (fun i => f (e.symm (Sum.inl i)))) × (fiberGroup (fun i => f (e.symm (Sum.inr i))))) : + (fiberSplit e f p).val = sumPerm e p.1.val p.2.val := rfl + +/- Exact independent-block factorization for arbitrary row/column labels. -/ +theorem altWord_fiber_split {n a b d : ℕ} {α : Type uAlpha} (e : Fin n ≃ Fin a ⊕ Fin b) + (f : Fin n → α) (w : Fin n → Fin d) : + altWord (fiberGroup f ⊓ sectorGroup (fun i => (e i).isLeft = true)) w = + positionProduct e + (altWord (fiberGroup (fun i => f (e.symm (Sum.inl i)))) (leftWord e w)) + (altWord (fiberGroup (fun i => f (e.symm (Sum.inr i)))) (rightWord e w)) := by + apply altWord_split e _ _ _ (fiberSplit e f).symm + intro g + exact (congrArg Subtype.val ((fiberSplit e f).apply_symm_apply g)).symm + + +@[simp] lemma staircase_colLen (m j : ℕ) : (staircase m).colLen j = m-j := by + have hh : ∀ i, i < (staircase m).colLen j ↔ i < m-j := by + intro i + rw [← YoungDiagram.mem_iff_lt_colLen, mem_staircase] + omega + have h₁ := hh ((staircase m).colLen j) + have h₂ := hh (m-j) + omega + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/PositionTensor.lean b/lean/OAI/RepresentationTheory/Saxl/PositionTensor.lean index f663d8844dd61d86b0ea36d20a028b73ce299cf5..d84f2ed99deb15b3f904391802130a97c3473980 100644 --- a/lean/OAI/RepresentationTheory/Saxl/PositionTensor.lean +++ b/lean/OAI/RepresentationTheory/Saxl/PositionTensor.lean @@ -1,127 +1,127 @@ -import OAI.RepresentationTheory.Saxl.SupportSeparation - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl - -/- Concatenation of words on independent position blocks. -/ -def joinPositions {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (x : Fin a → Fin d) (y : Fin b → Fin d) : Fin n → Fin d := - fun i => Sum.elim x y (e i) - -@[simp] lemma leftWord_join {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (x : Fin a → Fin d) (y : Fin b → Fin d) : leftWord e (joinPositions e x y) = x := by - funext i - simp [leftWord, joinPositions] - -@[simp] lemma rightWord_join {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (x : Fin a → Fin d) (y : Fin b → Fin d) : rightWord e (joinPositions e x y) = y := by - funext i - simp [rightWord, joinPositions] - -@[simp] lemma joinPositions_parts {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (w : Fin n → Fin d) : joinPositions e (leftWord e w) (rightWord e w) = w := by - funext i - obtain ⟨j,rfl⟩ := e.symm.surjective i - cases j <;> simp [joinPositions,leftWord,rightWord] - -def positionUncurry {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : - ((Fin b → Fin d) → WordSpace a d) ≃ₗ[ℂ] WordSpace n d where - toFun f w := f (rightWord e w) (leftWord e w) - invFun z y x := z (joinPositions e x y) - left_inv f := by ext y x; simp - right_inv z := by ext w; simp - map_add' _ _ := rfl - map_smul' _ _ := rfl - -def positionTensor {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : - WordSpace a d ⊗[ℂ] WordSpace b d ≃ₗ[ℂ] WordSpace n d := - TensorProduct.piScalarRight ℂ ℂ (WordSpace a d) (Fin b → Fin d) ≪≫ₗ positionUncurry e - -@[simp] lemma positionTensor_tmul {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (x : WordSpace a d) (y : WordSpace b d) : - positionTensor e (x ⊗ₜ[ℂ] y) = positionProduct e x y := by - funext w - change y (rightWord e w) * x (leftWord e w) = _ - exact mul_comm _ _ - -lemma positionProduct_equivariant {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) - (x : WordSpace a d) (y : WordSpace b d) : - wordRep n d (sumPerm e g h) (positionProduct e x y) = - positionProduct e (wordRep a d g x) (wordRep b d h y) := by - funext w - change x (leftWord e (w ∘ sumPerm e g h)) * y (rightWord e (w ∘ sumPerm e g h)) = _ - have hl : leftWord e (w ∘ sumPerm e g h) = leftWord e w ∘ g := by - funext i - simp [leftWord] - have hr : rightWord e (w ∘ sumPerm e g h) = rightWord e w ∘ h := by - funext i - simp [rightWord] - rw [hl,hr] - rfl - -lemma positionTensor_equivariant {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) - (z : WordSpace a d ⊗[ℂ] WordSpace b d) : - positionTensor e (TensorProduct.map (wordRep a d g) (wordRep b d h) z) = - wordRep n d (sumPerm e g h) (positionTensor e z) := by - induction z using TensorProduct.inductionOn with - | add x y hx hy => simp only [map_add,hx,hy] - | tmul x y => rw [TensorProduct.map_tmul, positionTensor_tmul, positionTensor_tmul, positionProduct_equivariant] - -lemma product_mem_cyclic {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (v : WordSpace a d) (u : WordSpace b d) - (x : WordSpace a d) (y : WordSpace b d) - (hx : x ∈ cyclic (wordRep a d) v) (hy : y ∈ cyclic (wordRep b d) u) : - positionProduct e x y ∈ cyclic (wordRep n d) (positionProduct e v u) := by - let S := cyclic (wordRep n d) (positionProduct e v u) - change x ∈ Submodule.span ℂ _ at hx - change y ∈ Submodule.span ℂ _ at hy - induction hx using Submodule.span_induction with - | mem x hx => - obtain ⟨g,rfl⟩ := hx - induction hy using Submodule.span_induction with - | mem y hy => - obtain ⟨h,rfl⟩ := hy - rw [← positionProduct_equivariant] - exact S.apply_mem_toSubmodule (sumPerm e g h) (mem_cyclic _ _) - | zero => - have hz : positionProduct e (wordRep a d g v) 0 = 0 := by ext; simp [positionProduct] - rw [hz] - exact S.toSubmodule.zero_mem - | add y z hy hz ihy ihz => - have he : positionProduct e (wordRep a d g v) (y+z) = - positionProduct e (wordRep a d g v) y + positionProduct e (wordRep a d g v) z := by - ext; simp [positionProduct,mul_add] - rw [he] - exact S.toSubmodule.add_mem ihy ihz - | smul c y hy ih => - have he : positionProduct e (wordRep a d g v) (c • y) = - c • positionProduct e (wordRep a d g v) y := by ext; simp [positionProduct,mul_left_comm] - rw [he] - exact S.toSubmodule.smul_mem c ih - | zero => - have hz : positionProduct e 0 y = 0 := by ext; simp [positionProduct] - rw [hz] - exact S.toSubmodule.zero_mem - | add x z hx hz ihx ihz => - have he : positionProduct e (x+z) y = positionProduct e x y + positionProduct e z y := by - ext; simp [positionProduct,add_mul] - rw [he] - exact S.toSubmodule.add_mem ihx ihz - | smul c x hx ih => - have he : positionProduct e (c • x) y = c • positionProduct e x y := by - ext; simp [positionProduct,mul_assoc] - rw [he] - exact S.toSubmodule.smul_mem c ih - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.SupportSeparation + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl + +/- Concatenation of words on independent position blocks. -/ +def joinPositions {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (x : Fin a → Fin d) (y : Fin b → Fin d) : Fin n → Fin d := + fun i => Sum.elim x y (e i) + +@[simp] lemma leftWord_join {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (x : Fin a → Fin d) (y : Fin b → Fin d) : leftWord e (joinPositions e x y) = x := by + funext i + simp [leftWord, joinPositions] + +@[simp] lemma rightWord_join {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (x : Fin a → Fin d) (y : Fin b → Fin d) : rightWord e (joinPositions e x y) = y := by + funext i + simp [rightWord, joinPositions] + +@[simp] lemma joinPositions_parts {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (w : Fin n → Fin d) : joinPositions e (leftWord e w) (rightWord e w) = w := by + funext i + obtain ⟨j,rfl⟩ := e.symm.surjective i + cases j <;> simp [joinPositions,leftWord,rightWord] + +def positionUncurry {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : + ((Fin b → Fin d) → WordSpace a d) ≃ₗ[ℂ] WordSpace n d where + toFun f w := f (rightWord e w) (leftWord e w) + invFun z y x := z (joinPositions e x y) + left_inv f := by ext y x; simp + right_inv z := by ext w; simp + map_add' _ _ := rfl + map_smul' _ _ := rfl + +def positionTensor {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : + WordSpace a d ⊗[ℂ] WordSpace b d ≃ₗ[ℂ] WordSpace n d := + TensorProduct.piScalarRight ℂ ℂ (WordSpace a d) (Fin b → Fin d) ≪≫ₗ positionUncurry e + +@[simp] lemma positionTensor_tmul {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (x : WordSpace a d) (y : WordSpace b d) : + positionTensor e (x ⊗ₜ[ℂ] y) = positionProduct e x y := by + funext w + change y (rightWord e w) * x (leftWord e w) = _ + exact mul_comm _ _ + +lemma positionProduct_equivariant {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) + (x : WordSpace a d) (y : WordSpace b d) : + wordRep n d (sumPerm e g h) (positionProduct e x y) = + positionProduct e (wordRep a d g x) (wordRep b d h y) := by + funext w + change x (leftWord e (w ∘ sumPerm e g h)) * y (rightWord e (w ∘ sumPerm e g h)) = _ + have hl : leftWord e (w ∘ sumPerm e g h) = leftWord e w ∘ g := by + funext i + simp [leftWord] + have hr : rightWord e (w ∘ sumPerm e g h) = rightWord e w ∘ h := by + funext i + simp [rightWord] + rw [hl,hr] + rfl + +lemma positionTensor_equivariant {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (g : Equiv.Perm (Fin a)) (h : Equiv.Perm (Fin b)) + (z : WordSpace a d ⊗[ℂ] WordSpace b d) : + positionTensor e (TensorProduct.map (wordRep a d g) (wordRep b d h) z) = + wordRep n d (sumPerm e g h) (positionTensor e z) := by + induction z using TensorProduct.inductionOn with + | add x y hx hy => simp only [map_add,hx,hy] + | tmul x y => rw [TensorProduct.map_tmul, positionTensor_tmul, positionTensor_tmul, positionProduct_equivariant] + +lemma product_mem_cyclic {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (v : WordSpace a d) (u : WordSpace b d) + (x : WordSpace a d) (y : WordSpace b d) + (hx : x ∈ cyclic (wordRep a d) v) (hy : y ∈ cyclic (wordRep b d) u) : + positionProduct e x y ∈ cyclic (wordRep n d) (positionProduct e v u) := by + let S := cyclic (wordRep n d) (positionProduct e v u) + change x ∈ Submodule.span ℂ _ at hx + change y ∈ Submodule.span ℂ _ at hy + induction hx using Submodule.span_induction with + | mem x hx => + obtain ⟨g,rfl⟩ := hx + induction hy using Submodule.span_induction with + | mem y hy => + obtain ⟨h,rfl⟩ := hy + rw [← positionProduct_equivariant] + exact S.apply_mem_toSubmodule (sumPerm e g h) (mem_cyclic _ _) + | zero => + have hz : positionProduct e (wordRep a d g v) 0 = 0 := by ext; simp [positionProduct] + rw [hz] + exact S.toSubmodule.zero_mem + | add y z hy hz ihy ihz => + have he : positionProduct e (wordRep a d g v) (y+z) = + positionProduct e (wordRep a d g v) y + positionProduct e (wordRep a d g v) z := by + ext; simp [positionProduct,mul_add] + rw [he] + exact S.toSubmodule.add_mem ihy ihz + | smul c y hy ih => + have he : positionProduct e (wordRep a d g v) (c • y) = + c • positionProduct e (wordRep a d g v) y := by ext; simp [positionProduct,mul_left_comm] + rw [he] + exact S.toSubmodule.smul_mem c ih + | zero => + have hz : positionProduct e 0 y = 0 := by ext; simp [positionProduct] + rw [hz] + exact S.toSubmodule.zero_mem + | add x z hx hz ihx ihz => + have he : positionProduct e (x+z) y = positionProduct e x y + positionProduct e z y := by + ext; simp [positionProduct,add_mul] + rw [he] + exact S.toSubmodule.add_mem ihx ihz + | smul c x hx ih => + have he : positionProduct e (c • x) y = c • positionProduct e x y := by + ext; simp [positionProduct,mul_assoc] + rw [he] + exact S.toSubmodule.smul_mem c ih + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/RepeatedProjection.lean b/lean/OAI/RepresentationTheory/Saxl/RepeatedProjection.lean index 395598801d567ed1e4a81517a4f677f8682da9a1..61a6204f79bb002f7816ecf61d2d25eb74a8feb0 100644 --- a/lean/OAI/RepresentationTheory/Saxl/RepeatedProjection.lean +++ b/lean/OAI/RepresentationTheory/Saxl/RepeatedProjection.lean @@ -1,235 +1,235 @@ -import OAI.RepresentationTheory.Saxl.CyclicTensor - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uX - -namespace Saxl - -lemma weighted_perm_sum {X : Type uX} [Fintype X] (t a : X → ℝ) - (g : Equiv.Perm X) (hg : ∀ i, t (g i) = t i) : - ∑ i, t i * a (g i) = ∑ i, t i * a i := by - simpa only [hg] using Equiv.sum_comp g (fun i => t i * a i) - -/- The strict square-moment equality used in the dominance projection. -The labels may be real; the application uses actual nonnegative integer letters. -/ -theorem pair_sum_rigidity {X : Type uX} [Fintype X] - (a t c : X → ℝ) (ω g h k : Equiv.Perm X) - (hω : ∀ i, t (ω i) = t i) (hcomp : ∀ i, a i + a (ω i) = t i) - (hg : ∀ i, t (g i) = t i) (hh : ∀ i, t (h i) = t i) - (hc : ∀ i, c i = a (g i) + a (h i)) (hk : ∀ i, c i = t (k i)) : c = t := by - have hbase : 2 * (∑ i, t i * a i) = ∑ i, t i ^ 2 := by - have he := weighted_perm_sum t a ω hω - have hs : (∑ i, t i * a i) + (∑ i, t i * a (ω i)) = ∑ i, t i ^ 2 := by - rw [← Finset.sum_add_distrib] - apply Finset.sum_congr rfl - intro i hi - rw [← mul_add, hcomp i, pow_two] - linarith - have hcross : ∑ i, t i * c i = ∑ i, t i ^ 2 := by - simp_rw [hc, mul_add] - rw [Finset.sum_add_distrib, weighted_perm_sum t a g hg, weighted_perm_sum t a h hh] - linarith - have hsquare : ∑ i, c i ^ 2 = ∑ i, t i ^ 2 := by - simp only [hk] - exact Equiv.sum_comp k (fun i => t i ^ 2) - have hsum : ∑ i, (c i - t i) ^ 2 = 0 := by - calc - (∑ i, (c i - t i) ^ 2) = (∑ i, c i ^ 2) - 2 * (∑ i, t i * c i) + - (∑ i, t i ^ 2) := by - simp only [Finset.mul_sum, ← Finset.sum_sub_distrib, ← Finset.sum_add_distrib] - apply Finset.sum_congr rfl - intro i hi - ring - _ = 0 := by rw [hsquare, hcross]; ring - funext i - have hz : (c i - t i) ^ 2 = 0 := - (Finset.sum_eq_zero_iff_of_nonneg (fun j _ => sq_nonneg (c j-t j))).mp hsum i - (Finset.mem_univ i) - exact sub_eq_zero.mp (sq_eq_zero_iff.mp hz) - -end Saxl - -namespace Saxl -/- Coordinate projection; equivariance is asserted only for preserved predicates. -/ - -def wordOrbit {n d : ℕ} (t : Fin n → Fin d) (c : Fin n → Fin d) : Prop := - ∃ g : Equiv.Perm (Fin n), c = t ∘ g - -lemma wordOrbit_perm {n d : ℕ} (t c : Fin n → Fin d) (g : Equiv.Perm (Fin n)) : - wordOrbit t (c ∘ g) ↔ wordOrbit t c := by - constructor - · rintro ⟨h, hh⟩ - refine ⟨h*g⁻¹, ?_⟩ - funext i - have he := congrFun hh (g⁻¹ i) - simpa using he - · rintro ⟨h, rfl⟩ - exact ⟨h*g, rfl⟩ - -def orbitProjection {n d : ℕ} (t : Fin n → Fin d) : - Representation.IntertwiningMap (wordRep n d) (wordRep n d) where - toLinearMap := coordinateProjection (wordOrbit t) - isIntertwining' g := by - classical - apply LinearMap.ext - intro x - ext c - change (if wordOrbit t c then x (c ∘ g) else 0) = - (if wordOrbit t (c ∘ g) then x (c ∘ g) else 0) - rw [wordOrbit_perm] - -def pairSumMap (n d e : ℕ) : - Representation.IntertwiningMap (wordRep n (d*d)) (wordRep n e) := - wordMap (fun a c => if (finProdFinEquiv.symm a).1.val + - (finProdFinEquiv.symm a).2.val = c.val then 1 else 0) - -lemma wordTensor_single {n d e : ℕ} (a : Fin n → Fin d) (b : Fin n → Fin e) : - wordTensor n d e (Pi.single a 1 ⊗ₜ[ℂ] Pi.single b 1) = Pi.single (mergeWords a b) 1 := by - classical - ext c - rw [wordTensor_tmul] - by_cases h : c = mergeWords a b - · subst c; simp - · have hh : splitLeft c ≠ a ∨ splitRight c ≠ b := by - by_contra hn - push Not at hn - exact h (by rw [← merge_split c, hn.1, hn.2]) - rcases hh with hl | hr - · simp [Pi.single_apply, h, hl] - · simp [Pi.single_apply, h, hr] - -lemma pairSumMap_single {n d e : ℕ} (a b : Fin n → Fin d) (c : Fin n → Fin e) : - pairSumMap n d e (Pi.single (mergeWords a b) 1) c = - if ∀ i, (a i).val + (b i).val = (c i).val then 1 else 0 := by - classical - rw [pairSumMap, wordMap_single] - simp only [mergeWords, Equiv.symm_apply_apply] - by_cases h : ∀ i, (a i).val + (b i).val = (c i).val - · simp [h] - · rw [ite_eq_right h] - push Not at h - obtain ⟨i, hi⟩ := h - exact Finset.prod_eq_zero (Finset.mem_univ i) (ite_eq_right hi) - -lemma altWord_inverse_sum {n d : ℕ} (H : Subgroup (Equiv.Perm (Fin n))) - (a : Fin n → Fin d) : - letI := Fintype.ofFinite H - altWord H a = ∑ g : H, signC (g : Equiv.Perm (Fin n)) • Pi.single (a ∘ (g : Equiv.Perm (Fin n))) 1 := by - classical - let := Fintype.ofFinite H - unfold altWord - simp_rw [wordRep_single] - apply Eq.trans ?_ (Equiv.sum_comp (Equiv.inv H) _) - apply Finset.sum_congr rfl - intro g hg - congr 1 - exact (signC_inv g.val).symm - - -lemma paired_relation_iff {n d e : ℕ} (H : Subgroup (Equiv.Perm (Fin n))) - (a : Fin n → Fin d) (t : Fin n → Fin e) (ω : H) - (ht : ∀ g : H, ∀ i, t (g.val i) = t i) - (ha : Function.Injective (fun i => (t i, a i))) - (hω : ∀ i, (a i).val + (a (ω.val i)).val = (t i).val) (g h : H) : - (∀ i, (a (g.val i)).val + (a (h.val i)).val = (t i).val) ↔ h = ω*g := by - constructor - · intro hh - apply Subtype.ext - apply Equiv.ext - intro i - apply ha - apply Prod.ext - · exact (ht h i).trans ((ht ω (g.val i)).trans (ht g i)).symm - · apply Fin.ext - have he := hω (g.val i) - rw [ht g i] at he - exact Nat.add_left_cancel ((hh i).trans he.symm) - · rintro rfl i - have he := hω (g.val i) - rw [ht g i] at he - exact he - -lemma paired_term_projection {n d e : ℕ} (H : Subgroup (Equiv.Perm (Fin n))) - (a : Fin n → Fin d) (t : Fin n → Fin e) (ω : H) - (ht : ∀ g : H, ∀ i, t (g.val i) = t i) - (ha : Function.Injective (fun i => (t i, a i))) - (hω : ∀ i, (a i).val + (a (ω.val i)).val = (t i).val) (g h : H) : - orbitProjection t (pairSumMap n d e (Pi.single - (mergeWords (a ∘ g.val) (a ∘ h.val)) 1)) = - if h = ω*g then Pi.single t 1 else 0 := by - classical - ext c - change (if wordOrbit t c then pairSumMap n d e (Pi.single - (mergeWords (a ∘ g.val) (a ∘ h.val)) 1) c else 0) = _ - rw [pairSumMap_single] - simp only [Function.comp_apply] - by_cases he : h = ω*g - · rw [ite_eq_left he] - have hr := (paired_relation_iff H a t ω ht ha hω g h).mpr he - by_cases hc : c = t - · subst c - rw [ite_eq_left ⟨1, rfl⟩, ite_eq_left hr] - simp - · rw [Pi.single_eq_of_ne hc] - have hn : ¬ ∀ i, (a (g.val i)).val + (a (h.val i)).val = (c i).val := by - intro hh - apply hc - funext i - exact Fin.ext ((hh i).symm.trans (hr i)) - simp only [hn, ite_false, ite_self] - · rw [ite_eq_right he] - change (if wordOrbit t c then _ else _) = (0:ℂ) - by_cases ho : wordOrbit t c - · rw [ite_eq_left ho] - apply ite_eq_right - intro hh - obtain ⟨k,hk⟩ := ho - have heq : (fun i => ((c i).val : ℝ)) = fun i => ((t i).val : ℝ) := by - apply pair_sum_rigidity (fun i => ((a i).val : ℝ)) (fun i => ((t i).val : ℝ)) - (fun i => ((c i).val : ℝ)) ω.val g.val h.val k - · intro i; rw [ht ω i] - · intro i; exact_mod_cast hω i - · intro i; rw [ht g i] - · intro i; rw [ht h i] - · intro i; exact_mod_cast (hh i).symm - · intro i; rw [hk]; rfl - have hct : c = t := by - funext i - apply Fin.ext - exact_mod_cast congrFun heq i - rw [hct] at hh - exact he ((paired_relation_iff H a t ω ht ha hω g h).mp hh) - · rw [ite_eq_right ho] - -theorem repeated_alt_projection {n d e : ℕ} (H : Subgroup (Equiv.Perm (Fin n))) - (a : Fin n → Fin d) (t : Fin n → Fin e) (ω : H) - (ht : ∀ g : H, ∀ i, t (g.val i) = t i) - (ha : Function.Injective (fun i => (t i, a i))) - (hω : ∀ i, (a i).val + (a (ω.val i)).val = (t i).val) : - orbitProjection t (pairSumMap n d e (wordTensor n d d - (altWord H a ⊗ₜ[ℂ] altWord H a))) = - ((Nat.card H : ℂ) * signC ω.val) • Pi.single t 1 := by - classical - let := Fintype.ofFinite H - rw [altWord_inverse_sum, TensorProduct.sum_tmul] - simp only [TensorProduct.tmul_sum, map_sum, TensorProduct.smul_tmul_smul, map_smul, - wordTensor_single, paired_term_projection H a t ω ht ha hω] - simp only [smul_ite, smul_zero, Finset.sum_ite_eq', Finset.mem_univ, ite_true] - have hs (g : H) : signC g.val * signC (ω*g).val = signC ω.val := by - simp only [Subgroup.coe_mul, map_mul] - calc - signC g.val * (signC ω.val * signC g.val) = signC ω.val * (signC g.val * signC g.val) := by ring - _ = signC ω.val := by rw [signC_mul_self, mul_one] - simp only [hs, Finset.sum_const, Finset.card_univ] - rw [← Nat.cast_smul_eq_nsmul ℂ, smul_smul, Fintype.card_eq_nat_card] - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.CyclicTensor + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uX + +namespace Saxl + +lemma weighted_perm_sum {X : Type uX} [Fintype X] (t a : X → ℝ) + (g : Equiv.Perm X) (hg : ∀ i, t (g i) = t i) : + ∑ i, t i * a (g i) = ∑ i, t i * a i := by + simpa only [hg] using Equiv.sum_comp g (fun i => t i * a i) + +/- The strict square-moment equality used in the dominance projection. +The labels may be real; the application uses actual nonnegative integer letters. -/ +theorem pair_sum_rigidity {X : Type uX} [Fintype X] + (a t c : X → ℝ) (ω g h k : Equiv.Perm X) + (hω : ∀ i, t (ω i) = t i) (hcomp : ∀ i, a i + a (ω i) = t i) + (hg : ∀ i, t (g i) = t i) (hh : ∀ i, t (h i) = t i) + (hc : ∀ i, c i = a (g i) + a (h i)) (hk : ∀ i, c i = t (k i)) : c = t := by + have hbase : 2 * (∑ i, t i * a i) = ∑ i, t i ^ 2 := by + have he := weighted_perm_sum t a ω hω + have hs : (∑ i, t i * a i) + (∑ i, t i * a (ω i)) = ∑ i, t i ^ 2 := by + rw [← Finset.sum_add_distrib] + apply Finset.sum_congr rfl + intro i hi + rw [← mul_add, hcomp i, pow_two] + linarith + have hcross : ∑ i, t i * c i = ∑ i, t i ^ 2 := by + simp_rw [hc, mul_add] + rw [Finset.sum_add_distrib, weighted_perm_sum t a g hg, weighted_perm_sum t a h hh] + linarith + have hsquare : ∑ i, c i ^ 2 = ∑ i, t i ^ 2 := by + simp only [hk] + exact Equiv.sum_comp k (fun i => t i ^ 2) + have hsum : ∑ i, (c i - t i) ^ 2 = 0 := by + calc + (∑ i, (c i - t i) ^ 2) = (∑ i, c i ^ 2) - 2 * (∑ i, t i * c i) + + (∑ i, t i ^ 2) := by + simp only [Finset.mul_sum, ← Finset.sum_sub_distrib, ← Finset.sum_add_distrib] + apply Finset.sum_congr rfl + intro i hi + ring + _ = 0 := by rw [hsquare, hcross]; ring + funext i + have hz : (c i - t i) ^ 2 = 0 := + (Finset.sum_eq_zero_iff_of_nonneg (fun j _ => sq_nonneg (c j-t j))).mp hsum i + (Finset.mem_univ i) + exact sub_eq_zero.mp (sq_eq_zero_iff.mp hz) + +end Saxl + +namespace Saxl +/- Coordinate projection; equivariance is asserted only for preserved predicates. -/ + +def wordOrbit {n d : ℕ} (t : Fin n → Fin d) (c : Fin n → Fin d) : Prop := + ∃ g : Equiv.Perm (Fin n), c = t ∘ g + +lemma wordOrbit_perm {n d : ℕ} (t c : Fin n → Fin d) (g : Equiv.Perm (Fin n)) : + wordOrbit t (c ∘ g) ↔ wordOrbit t c := by + constructor + · rintro ⟨h, hh⟩ + refine ⟨h*g⁻¹, ?_⟩ + funext i + have he := congrFun hh (g⁻¹ i) + simpa using he + · rintro ⟨h, rfl⟩ + exact ⟨h*g, rfl⟩ + +def orbitProjection {n d : ℕ} (t : Fin n → Fin d) : + Representation.IntertwiningMap (wordRep n d) (wordRep n d) where + toLinearMap := coordinateProjection (wordOrbit t) + isIntertwining' g := by + classical + apply LinearMap.ext + intro x + ext c + change (if wordOrbit t c then x (c ∘ g) else 0) = + (if wordOrbit t (c ∘ g) then x (c ∘ g) else 0) + rw [wordOrbit_perm] + +def pairSumMap (n d e : ℕ) : + Representation.IntertwiningMap (wordRep n (d*d)) (wordRep n e) := + wordMap (fun a c => if (finProdFinEquiv.symm a).1.val + + (finProdFinEquiv.symm a).2.val = c.val then 1 else 0) + +lemma wordTensor_single {n d e : ℕ} (a : Fin n → Fin d) (b : Fin n → Fin e) : + wordTensor n d e (Pi.single a 1 ⊗ₜ[ℂ] Pi.single b 1) = Pi.single (mergeWords a b) 1 := by + classical + ext c + rw [wordTensor_tmul] + by_cases h : c = mergeWords a b + · subst c; simp + · have hh : splitLeft c ≠ a ∨ splitRight c ≠ b := by + by_contra hn + push Not at hn + exact h (by rw [← merge_split c, hn.1, hn.2]) + rcases hh with hl | hr + · simp [Pi.single_apply, h, hl] + · simp [Pi.single_apply, h, hr] + +lemma pairSumMap_single {n d e : ℕ} (a b : Fin n → Fin d) (c : Fin n → Fin e) : + pairSumMap n d e (Pi.single (mergeWords a b) 1) c = + if ∀ i, (a i).val + (b i).val = (c i).val then 1 else 0 := by + classical + rw [pairSumMap, wordMap_single] + simp only [mergeWords, Equiv.symm_apply_apply] + by_cases h : ∀ i, (a i).val + (b i).val = (c i).val + · simp [h] + · rw [ite_eq_right h] + push Not at h + obtain ⟨i, hi⟩ := h + exact Finset.prod_eq_zero (Finset.mem_univ i) (ite_eq_right hi) + +lemma altWord_inverse_sum {n d : ℕ} (H : Subgroup (Equiv.Perm (Fin n))) + (a : Fin n → Fin d) : + letI := Fintype.ofFinite H + altWord H a = ∑ g : H, signC (g : Equiv.Perm (Fin n)) • Pi.single (a ∘ (g : Equiv.Perm (Fin n))) 1 := by + classical + let := Fintype.ofFinite H + unfold altWord + simp_rw [wordRep_single] + apply Eq.trans ?_ (Equiv.sum_comp (Equiv.inv H) _) + apply Finset.sum_congr rfl + intro g hg + congr 1 + exact (signC_inv g.val).symm + + +lemma paired_relation_iff {n d e : ℕ} (H : Subgroup (Equiv.Perm (Fin n))) + (a : Fin n → Fin d) (t : Fin n → Fin e) (ω : H) + (ht : ∀ g : H, ∀ i, t (g.val i) = t i) + (ha : Function.Injective (fun i => (t i, a i))) + (hω : ∀ i, (a i).val + (a (ω.val i)).val = (t i).val) (g h : H) : + (∀ i, (a (g.val i)).val + (a (h.val i)).val = (t i).val) ↔ h = ω*g := by + constructor + · intro hh + apply Subtype.ext + apply Equiv.ext + intro i + apply ha + apply Prod.ext + · exact (ht h i).trans ((ht ω (g.val i)).trans (ht g i)).symm + · apply Fin.ext + have he := hω (g.val i) + rw [ht g i] at he + exact Nat.add_left_cancel ((hh i).trans he.symm) + · rintro rfl i + have he := hω (g.val i) + rw [ht g i] at he + exact he + +lemma paired_term_projection {n d e : ℕ} (H : Subgroup (Equiv.Perm (Fin n))) + (a : Fin n → Fin d) (t : Fin n → Fin e) (ω : H) + (ht : ∀ g : H, ∀ i, t (g.val i) = t i) + (ha : Function.Injective (fun i => (t i, a i))) + (hω : ∀ i, (a i).val + (a (ω.val i)).val = (t i).val) (g h : H) : + orbitProjection t (pairSumMap n d e (Pi.single + (mergeWords (a ∘ g.val) (a ∘ h.val)) 1)) = + if h = ω*g then Pi.single t 1 else 0 := by + classical + ext c + change (if wordOrbit t c then pairSumMap n d e (Pi.single + (mergeWords (a ∘ g.val) (a ∘ h.val)) 1) c else 0) = _ + rw [pairSumMap_single] + simp only [Function.comp_apply] + by_cases he : h = ω*g + · rw [ite_eq_left he] + have hr := (paired_relation_iff H a t ω ht ha hω g h).mpr he + by_cases hc : c = t + · subst c + rw [ite_eq_left ⟨1, rfl⟩, ite_eq_left hr] + simp + · rw [Pi.single_eq_of_ne hc] + have hn : ¬ ∀ i, (a (g.val i)).val + (a (h.val i)).val = (c i).val := by + intro hh + apply hc + funext i + exact Fin.ext ((hh i).symm.trans (hr i)) + simp only [hn, ite_false, ite_self] + · rw [ite_eq_right he] + change (if wordOrbit t c then _ else _) = (0:ℂ) + by_cases ho : wordOrbit t c + · rw [ite_eq_left ho] + apply ite_eq_right + intro hh + obtain ⟨k,hk⟩ := ho + have heq : (fun i => ((c i).val : ℝ)) = fun i => ((t i).val : ℝ) := by + apply pair_sum_rigidity (fun i => ((a i).val : ℝ)) (fun i => ((t i).val : ℝ)) + (fun i => ((c i).val : ℝ)) ω.val g.val h.val k + · intro i; rw [ht ω i] + · intro i; exact_mod_cast hω i + · intro i; rw [ht g i] + · intro i; rw [ht h i] + · intro i; exact_mod_cast (hh i).symm + · intro i; rw [hk]; rfl + have hct : c = t := by + funext i + apply Fin.ext + exact_mod_cast congrFun heq i + rw [hct] at hh + exact he ((paired_relation_iff H a t ω ht ha hω g h).mp hh) + · rw [ite_eq_right ho] + +theorem repeated_alt_projection {n d e : ℕ} (H : Subgroup (Equiv.Perm (Fin n))) + (a : Fin n → Fin d) (t : Fin n → Fin e) (ω : H) + (ht : ∀ g : H, ∀ i, t (g.val i) = t i) + (ha : Function.Injective (fun i => (t i, a i))) + (hω : ∀ i, (a i).val + (a (ω.val i)).val = (t i).val) : + orbitProjection t (pairSumMap n d e (wordTensor n d d + (altWord H a ⊗ₜ[ℂ] altWord H a))) = + ((Nat.card H : ℂ) * signC ω.val) • Pi.single t 1 := by + classical + let := Fintype.ofFinite H + rw [altWord_inverse_sum, TensorProduct.sum_tmul] + simp only [TensorProduct.tmul_sum, map_sum, TensorProduct.smul_tmul_smul, map_smul, + wordTensor_single, paired_term_projection H a t ω ht ha hω] + simp only [smul_ite, smul_zero, Finset.sum_ite_eq', Finset.mem_univ, ite_true] + have hs (g : H) : signC g.val * signC (ω*g).val = signC ω.val := by + simp only [Subgroup.coe_mul, map_mul] + calc + signC g.val * (signC ω.val * signC g.val) = signC ω.val * (signC g.val * signC g.val) := by ring + _ = signC ω.val := by rw [signC_mul_self, mul_one] + simp only [hs, Finset.sum_const, Finset.card_univ] + rw [← Nat.cast_smul_eq_nsmul ℂ, smul_smul, Fintype.card_eq_nat_card] + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/ShapeRigidity.lean b/lean/OAI/RepresentationTheory/Saxl/ShapeRigidity.lean index 803de5905b496207c7aa8cb403c57cffc6d73ff5..fed68482a671bfb456556c422a922445b80f4617 100644 --- a/lean/OAI/RepresentationTheory/Saxl/ShapeRigidity.lean +++ b/lean/OAI/RepresentationTheory/Saxl/ShapeRigidity.lean @@ -1,223 +1,223 @@ -import OAI.RepresentationTheory.Saxl.BandSupport - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uX uV uW - -namespace Saxl - -lemma tableau_image {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - Finset.univ.image (fun i : Fin n => (t i).val) = μ.cells := by - classical - ext x - simp only [Finset.mem_image, Finset.mem_univ, true_and] - constructor - · rintro ⟨i, rfl⟩; exact (t i).property - · intro hx; exact ⟨t.symm ⟨x, hx⟩, by simp⟩ - -lemma tableau_sum {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) (f : ℕ × ℕ → ℤ) : - ∑ i, f (t i).val = ∑ c ∈ μ.cells, f c := by - classical - conv_rhs => rw [← tableau_image t] - rw [Finset.sum_image] - intro i hi j hj h - exact t.injective (Subtype.val_injective h) - -/- Zero-based row-index statistic of a partition. -/ -def rowMoment (μ : YoungDiagram) : ℤ := ∑ c ∈ μ.cells, (c.1 : ℤ) - -lemma finset_signed_sum_le {X : Type uX} [DecidableEq X] - (A B : Finset X) (w : X → ℤ) - (hp : ∀ x ∈ B, 0 ≤ w x) (hn : ∀ x ∉ B, w x ≤ 0) : - ∑ x ∈ A, w x ≤ ∑ x ∈ B, w x := by - classical - have hle : ∀ x ∈ A ∪ B, - (if x ∈ A then w x else 0) ≤ (if x ∈ B then w x else 0) := by - intro x hx - split_ifs with ha hb hb - · rfl - · exact hn x hb - · exact hp x hb - · rfl - simpa [← Finset.sum_filter] using Finset.sum_le_sum hle - -lemma mixed_moment_le {n : ℕ} {μ ν : YoungDiagram} - (t : Tableau n μ) (u : Tableau n ν) (g : Equiv.Perm (Fin n)) - (hi : Function.Injective (fun i => ((u (g i)).val.1, (t i).val.2))) : - rowMoment μ ≤ rowMoment ν := by - classical - let f : Fin n → ℕ × ℕ := fun i => ((u (g i)).val.1, (t i).val.2) - let w : ℕ × ℕ → ℤ := fun c => 2 * (μ.colLen c.2 : ℤ) - 2 * c.1 - 1 - have h := finset_signed_sum_le (Finset.univ.image f) μ.cells w - (fun c hc => by have hh := YoungDiagram.mem_iff_lt_colLen.mp hc; dsimp [w]; omega) - (fun c hc => by - have hh : μ.colLen c.2 ≤ c.1 := - le_of_not_gt (fun h => hc (YoungDiagram.mem_iff_lt_colLen.mpr h)) - dsimp [w]; omega) - rw [Finset.sum_image (fun _ _ _ _ h => hi h), ← tableau_sum t w] at h - simp only [w, Finset.sum_sub_distrib, ← Finset.mul_sum] at h - rw [Equiv.sum_comp g (fun i => ((u i).val.1 : ℤ))] at h - have ht := tableau_sum t (fun c => (c.1 : ℤ)) - have hu := tableau_sum u (fun c => (c.1 : ℤ)) - change _ = rowMoment μ at ht - change _ = rowMoment ν at hu - omega - -lemma mixed_support_eq {n : ℕ} {μ ν : YoungDiagram} - (t : Tableau n μ) (u : Tableau n ν) (g : Equiv.Perm (Fin n)) - (hi : Function.Injective (fun i => ((u (g i)).val.1, (t i).val.2))) - (hm : rowMoment μ = rowMoment ν) : - Finset.univ.image (fun i => ((u (g i)).val.1, (t i).val.2)) = μ.cells := by - classical - let f : Fin n → ℕ × ℕ := fun i => ((u (g i)).val.1, (t i).val.2) - let w : ℕ × ℕ → ℤ := fun c => 2 * (μ.colLen c.2 : ℤ) - 2 * c.1 - 1 - apply finset_eq_of_signed_sum _ _ w - (fun c hc => by have hh := YoungDiagram.mem_iff_lt_colLen.mp hc; dsimp [w]; omega) - (fun c hc => by - have hh : μ.colLen c.2 ≤ c.1 := - le_of_not_gt (fun h => hc (YoungDiagram.mem_iff_lt_colLen.mpr h)) - dsimp [w]; omega) - rw [Finset.sum_image (fun _ _ _ _ h => hi h), ← tableau_sum t w] - simp only [w, Finset.sum_sub_distrib, ← Finset.mul_sum] - rw [Equiv.sum_comp g (fun i => ((u i).val.1 : ℤ))] - have ht := tableau_sum t (fun c => (c.1 : ℤ)) - have hu := tableau_sum u (fun c => (c.1 : ℤ)) - change _ = rowMoment μ at ht - change _ = rowMoment ν at hu - rw [ht, hu, hm] - -lemma rowLen_eq_count {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) (r : ℕ) : - μ.rowLen r = (Finset.univ.filter (fun i => (t i).val.1 = r)).card := by - classical - rw [YoungDiagram.rowLen_eq_card] - have hf : μ.row r = (Finset.univ.filter (fun i => (t i).val.1 = r)).image - (fun i => (t i).val) := by - unfold YoungDiagram.row - conv_lhs => rw [← tableau_image t] - rw [Finset.filter_image] - rw [hf, Finset.card_image_iff.mpr] - intro i hi j hj h - exact t.injective (Subtype.val_injective h) - -lemma shapes_eq_of_mixed {n : ℕ} {μ ν : YoungDiagram} - (t : Tableau n μ) (u : Tableau n ν) (g : Equiv.Perm (Fin n)) - (hi : Function.Injective (fun i => ((u (g i)).val.1, (t i).val.2))) - (hm : rowMoment μ = rowMoment ν) : μ = ν := by - classical - have hs := mixed_support_eq t u g hi hm - have hrow : ∀ r, μ.rowLen r = ν.rowLen r := by - intro r - rw [YoungDiagram.rowLen_eq_card, YoungDiagram.row, ← hs, - Finset.filter_image, Finset.card_image_iff.mpr (fun i _ j _ h => hi h), - rowLen_eq_count u r] - apply Finset.card_equiv g - intro i - simp - apply YoungDiagram.ext - ext c - rcases c with ⟨r, s⟩ - change (r, s) ∈ μ ↔ (r, s) ∈ ν - simp only [YoungDiagram.mem_iff_lt_rowLen, hrow] - -lemma columnAlt_polytabloid_ne_zero {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - columnAlt t (polytabloid t) ≠ 0 := by - intro hz - have h := congrFun hz (rowWord t) - rw [columnAlt_coefficient] at h - change dotProduct (polytabloid t) (polytabloid t) = 0 at h - conv at h => lhs; rhs; rw [← polytabloid_real t] - let : PartialOrder ℂ := RCLike.toPartialOrder - let : StarOrderedRing ℂ := RCLike.toStarOrderedRing - exact polytabloid_ne_zero t (dotProduct_self_star_eq_zero.mp h) - -lemma mixed_injective_of_columnAlt_ne_zero {n : ℕ} {μ ν : YoungDiagram} - (t : Tableau n μ) (u : Tableau n ν) - {x : WordSpace n (ν.colLen 0)} (hx : x ∈ tabloidSub u) - (hz : columnAlt t x ≠ 0) : - ∃ g : Equiv.Perm (Fin n), - Function.Injective (fun i => ((u (g i)).val.1, (t i).val.2)) := by - classical - by_contra h - push Not at h - have hall : ∀ g : Equiv.Perm (Fin n), - columnAlt t (wordRep n (ν.colLen 0) g (Pi.single (rowWord u) 1)) = 0 := by - intro g - have hh := h g⁻¹ - simp only [Function.Injective] at hh - push Not at hh - obtain ⟨i, j, he, hij⟩ := hh - rw [wordRep_single] - exact columnAlt_collision t _ i j hij (Prod.mk.inj he).2 - (Fin.ext (Prod.mk.inj he).1) - apply hz - clear hz - induction hx using Submodule.span_induction with - | mem y hy => obtain ⟨g, rfl⟩ := hy; exact hall g - | zero => exact map_zero _ - | add y z hy hz ihy ihz => rw [map_add, ihy, ihz, add_zero] - | smul c y hy ih => rw [map_smul, ih, smul_zero] - -/- The column operator on any genuine representation of the same group. -/ -def columnOperator {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - {V : Type uV} [AddCommGroup V] [Module ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) : Module.End ℂ V := by - classical - letI := Fintype.ofFinite (columnGroup t) - exact ∑ g : columnGroup t, signC (g : Equiv.Perm (Fin n)) • ρ g - -lemma columnOperator_intertwining {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - {V : Type uV} {W : Type uW} [AddCommGroup V] [Module ℂ V] [AddCommGroup W] [Module ℂ W] - {ρ : Representation ℂ (Equiv.Perm (Fin n)) V} - {σ : Representation ℂ (Equiv.Perm (Fin n)) W} - (f : Representation.IntertwiningMap ρ σ) (x : V) : - f (columnOperator t ρ x) = columnOperator t σ (f x) := by - classical - simp only [columnOperator, LinearMap.sum_apply, LinearMap.smul_apply, - map_sum, map_smul, Representation.IntertwiningMap.isIntertwining] - -lemma columnOperator_subtype {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (S : Subrepresentation (wordRep n d)) (x : S.toSubmodule) : - (columnOperator t S.toRepresentation x).val = columnAlt t x.val := by - let inc : Representation.IntertwiningMap S.toRepresentation (wordRep n d) := - { toLinearMap := S.toSubmodule.subtype - isIntertwining' := fun g => rfl } - exact columnOperator_intertwining t inc x - -lemma mixed_injective_of_equiv {n : ℕ} {μ ν : YoungDiagram} - (t : Tableau n μ) (u : Tableau n ν) - (e : Representation.Equiv (spechtRep t) (spechtRep u)) : - ∃ g : Equiv.Perm (Fin n), - Function.Injective (fun i => ((u (g i)).val.1, (t i).val.2)) := by - let p : Specht t := ⟨polytabloid t, mem_cyclic _ _⟩ - apply mixed_injective_of_columnAlt_ne_zero t u - (spechtSub_le_tabloidSub u (e p).property) - intro hz - have he := columnOperator_intertwining t e.toIntertwiningMap p - have hy : columnOperator t (spechtRep u) (e p) = 0 := by - apply Subtype.ext - exact (columnOperator_subtype t (spechtSub u) (e p)).trans hz - change e (columnOperator t (spechtRep t) p) = columnOperator t (spechtRep u) (e p) at he - rw [hy] at he - have ht : columnOperator t (spechtRep t) p = 0 := e.injective (he.trans (map_zero e).symm) - have hh := congrArg Subtype.val ht - exact columnAlt_polytabloid_ne_zero t - ((columnOperator_subtype t (spechtSub t) p).symm.trans hh) - -/- Distinct genuine complex Specht shapes are inequivalent. -/ -theorem specht_shape_rigidity {n : ℕ} {μ ν : YoungDiagram} - (t : Tableau n μ) (u : Tableau n ν) - (e : Representation.Equiv (spechtRep t) (spechtRep u)) : μ = ν := by - obtain ⟨g, hg⟩ := mixed_injective_of_equiv t u e - obtain ⟨h, hh⟩ := mixed_injective_of_equiv u t e.symm - exact shapes_eq_of_mixed t u g hg - (le_antisymm (mixed_moment_le t u g hg) (mixed_moment_le u t h hh)) - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.BandSupport + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uX uV uW + +namespace Saxl + +lemma tableau_image {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + Finset.univ.image (fun i : Fin n => (t i).val) = μ.cells := by + classical + ext x + simp only [Finset.mem_image, Finset.mem_univ, true_and] + constructor + · rintro ⟨i, rfl⟩; exact (t i).property + · intro hx; exact ⟨t.symm ⟨x, hx⟩, by simp⟩ + +lemma tableau_sum {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) (f : ℕ × ℕ → ℤ) : + ∑ i, f (t i).val = ∑ c ∈ μ.cells, f c := by + classical + conv_rhs => rw [← tableau_image t] + rw [Finset.sum_image] + intro i hi j hj h + exact t.injective (Subtype.val_injective h) + +/- Zero-based row-index statistic of a partition. -/ +def rowMoment (μ : YoungDiagram) : ℤ := ∑ c ∈ μ.cells, (c.1 : ℤ) + +lemma finset_signed_sum_le {X : Type uX} [DecidableEq X] + (A B : Finset X) (w : X → ℤ) + (hp : ∀ x ∈ B, 0 ≤ w x) (hn : ∀ x ∉ B, w x ≤ 0) : + ∑ x ∈ A, w x ≤ ∑ x ∈ B, w x := by + classical + have hle : ∀ x ∈ A ∪ B, + (if x ∈ A then w x else 0) ≤ (if x ∈ B then w x else 0) := by + intro x hx + split_ifs with ha hb hb + · rfl + · exact hn x hb + · exact hp x hb + · rfl + simpa [← Finset.sum_filter] using Finset.sum_le_sum hle + +lemma mixed_moment_le {n : ℕ} {μ ν : YoungDiagram} + (t : Tableau n μ) (u : Tableau n ν) (g : Equiv.Perm (Fin n)) + (hi : Function.Injective (fun i => ((u (g i)).val.1, (t i).val.2))) : + rowMoment μ ≤ rowMoment ν := by + classical + let f : Fin n → ℕ × ℕ := fun i => ((u (g i)).val.1, (t i).val.2) + let w : ℕ × ℕ → ℤ := fun c => 2 * (μ.colLen c.2 : ℤ) - 2 * c.1 - 1 + have h := finset_signed_sum_le (Finset.univ.image f) μ.cells w + (fun c hc => by have hh := YoungDiagram.mem_iff_lt_colLen.mp hc; dsimp [w]; omega) + (fun c hc => by + have hh : μ.colLen c.2 ≤ c.1 := + le_of_not_gt (fun h => hc (YoungDiagram.mem_iff_lt_colLen.mpr h)) + dsimp [w]; omega) + rw [Finset.sum_image (fun _ _ _ _ h => hi h), ← tableau_sum t w] at h + simp only [w, Finset.sum_sub_distrib, ← Finset.mul_sum] at h + rw [Equiv.sum_comp g (fun i => ((u i).val.1 : ℤ))] at h + have ht := tableau_sum t (fun c => (c.1 : ℤ)) + have hu := tableau_sum u (fun c => (c.1 : ℤ)) + change _ = rowMoment μ at ht + change _ = rowMoment ν at hu + omega + +lemma mixed_support_eq {n : ℕ} {μ ν : YoungDiagram} + (t : Tableau n μ) (u : Tableau n ν) (g : Equiv.Perm (Fin n)) + (hi : Function.Injective (fun i => ((u (g i)).val.1, (t i).val.2))) + (hm : rowMoment μ = rowMoment ν) : + Finset.univ.image (fun i => ((u (g i)).val.1, (t i).val.2)) = μ.cells := by + classical + let f : Fin n → ℕ × ℕ := fun i => ((u (g i)).val.1, (t i).val.2) + let w : ℕ × ℕ → ℤ := fun c => 2 * (μ.colLen c.2 : ℤ) - 2 * c.1 - 1 + apply finset_eq_of_signed_sum _ _ w + (fun c hc => by have hh := YoungDiagram.mem_iff_lt_colLen.mp hc; dsimp [w]; omega) + (fun c hc => by + have hh : μ.colLen c.2 ≤ c.1 := + le_of_not_gt (fun h => hc (YoungDiagram.mem_iff_lt_colLen.mpr h)) + dsimp [w]; omega) + rw [Finset.sum_image (fun _ _ _ _ h => hi h), ← tableau_sum t w] + simp only [w, Finset.sum_sub_distrib, ← Finset.mul_sum] + rw [Equiv.sum_comp g (fun i => ((u i).val.1 : ℤ))] + have ht := tableau_sum t (fun c => (c.1 : ℤ)) + have hu := tableau_sum u (fun c => (c.1 : ℤ)) + change _ = rowMoment μ at ht + change _ = rowMoment ν at hu + rw [ht, hu, hm] + +lemma rowLen_eq_count {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) (r : ℕ) : + μ.rowLen r = (Finset.univ.filter (fun i => (t i).val.1 = r)).card := by + classical + rw [YoungDiagram.rowLen_eq_card] + have hf : μ.row r = (Finset.univ.filter (fun i => (t i).val.1 = r)).image + (fun i => (t i).val) := by + unfold YoungDiagram.row + conv_lhs => rw [← tableau_image t] + rw [Finset.filter_image] + rw [hf, Finset.card_image_iff.mpr] + intro i hi j hj h + exact t.injective (Subtype.val_injective h) + +lemma shapes_eq_of_mixed {n : ℕ} {μ ν : YoungDiagram} + (t : Tableau n μ) (u : Tableau n ν) (g : Equiv.Perm (Fin n)) + (hi : Function.Injective (fun i => ((u (g i)).val.1, (t i).val.2))) + (hm : rowMoment μ = rowMoment ν) : μ = ν := by + classical + have hs := mixed_support_eq t u g hi hm + have hrow : ∀ r, μ.rowLen r = ν.rowLen r := by + intro r + rw [YoungDiagram.rowLen_eq_card, YoungDiagram.row, ← hs, + Finset.filter_image, Finset.card_image_iff.mpr (fun i _ j _ h => hi h), + rowLen_eq_count u r] + apply Finset.card_equiv g + intro i + simp + apply YoungDiagram.ext + ext c + rcases c with ⟨r, s⟩ + change (r, s) ∈ μ ↔ (r, s) ∈ ν + simp only [YoungDiagram.mem_iff_lt_rowLen, hrow] + +lemma columnAlt_polytabloid_ne_zero {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + columnAlt t (polytabloid t) ≠ 0 := by + intro hz + have h := congrFun hz (rowWord t) + rw [columnAlt_coefficient] at h + change dotProduct (polytabloid t) (polytabloid t) = 0 at h + conv at h => lhs; rhs; rw [← polytabloid_real t] + let : PartialOrder ℂ := RCLike.toPartialOrder + let : StarOrderedRing ℂ := RCLike.toStarOrderedRing + exact polytabloid_ne_zero t (dotProduct_self_star_eq_zero.mp h) + +lemma mixed_injective_of_columnAlt_ne_zero {n : ℕ} {μ ν : YoungDiagram} + (t : Tableau n μ) (u : Tableau n ν) + {x : WordSpace n (ν.colLen 0)} (hx : x ∈ tabloidSub u) + (hz : columnAlt t x ≠ 0) : + ∃ g : Equiv.Perm (Fin n), + Function.Injective (fun i => ((u (g i)).val.1, (t i).val.2)) := by + classical + by_contra h + push Not at h + have hall : ∀ g : Equiv.Perm (Fin n), + columnAlt t (wordRep n (ν.colLen 0) g (Pi.single (rowWord u) 1)) = 0 := by + intro g + have hh := h g⁻¹ + simp only [Function.Injective] at hh + push Not at hh + obtain ⟨i, j, he, hij⟩ := hh + rw [wordRep_single] + exact columnAlt_collision t _ i j hij (Prod.mk.inj he).2 + (Fin.ext (Prod.mk.inj he).1) + apply hz + clear hz + induction hx using Submodule.span_induction with + | mem y hy => obtain ⟨g, rfl⟩ := hy; exact hall g + | zero => exact map_zero _ + | add y z hy hz ihy ihz => rw [map_add, ihy, ihz, add_zero] + | smul c y hy ih => rw [map_smul, ih, smul_zero] + +/- The column operator on any genuine representation of the same group. -/ +def columnOperator {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + {V : Type uV} [AddCommGroup V] [Module ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) : Module.End ℂ V := by + classical + letI := Fintype.ofFinite (columnGroup t) + exact ∑ g : columnGroup t, signC (g : Equiv.Perm (Fin n)) • ρ g + +lemma columnOperator_intertwining {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + {V : Type uV} {W : Type uW} [AddCommGroup V] [Module ℂ V] [AddCommGroup W] [Module ℂ W] + {ρ : Representation ℂ (Equiv.Perm (Fin n)) V} + {σ : Representation ℂ (Equiv.Perm (Fin n)) W} + (f : Representation.IntertwiningMap ρ σ) (x : V) : + f (columnOperator t ρ x) = columnOperator t σ (f x) := by + classical + simp only [columnOperator, LinearMap.sum_apply, LinearMap.smul_apply, + map_sum, map_smul, Representation.IntertwiningMap.isIntertwining] + +lemma columnOperator_subtype {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (S : Subrepresentation (wordRep n d)) (x : S.toSubmodule) : + (columnOperator t S.toRepresentation x).val = columnAlt t x.val := by + let inc : Representation.IntertwiningMap S.toRepresentation (wordRep n d) := + { toLinearMap := S.toSubmodule.subtype + isIntertwining' := fun g => rfl } + exact columnOperator_intertwining t inc x + +lemma mixed_injective_of_equiv {n : ℕ} {μ ν : YoungDiagram} + (t : Tableau n μ) (u : Tableau n ν) + (e : Representation.Equiv (spechtRep t) (spechtRep u)) : + ∃ g : Equiv.Perm (Fin n), + Function.Injective (fun i => ((u (g i)).val.1, (t i).val.2)) := by + let p : Specht t := ⟨polytabloid t, mem_cyclic _ _⟩ + apply mixed_injective_of_columnAlt_ne_zero t u + (spechtSub_le_tabloidSub u (e p).property) + intro hz + have he := columnOperator_intertwining t e.toIntertwiningMap p + have hy : columnOperator t (spechtRep u) (e p) = 0 := by + apply Subtype.ext + exact (columnOperator_subtype t (spechtSub u) (e p)).trans hz + change e (columnOperator t (spechtRep t) p) = columnOperator t (spechtRep u) (e p) at he + rw [hy] at he + have ht : columnOperator t (spechtRep t) p = 0 := e.injective (he.trans (map_zero e).symm) + have hh := congrArg Subtype.val ht + exact columnAlt_polytabloid_ne_zero t + ((columnOperator_subtype t (spechtSub t) p).symm.trans hh) + +/- Distinct genuine complex Specht shapes are inequivalent. -/ +theorem specht_shape_rigidity {n : ℕ} {μ ν : YoungDiagram} + (t : Tableau n μ) (u : Tableau n ν) + (e : Representation.Equiv (spechtRep t) (spechtRep u)) : μ = ν := by + obtain ⟨g, hg⟩ := mixed_injective_of_equiv t u e + obtain ⟨h, hh⟩ := mixed_injective_of_equiv u t e.symm + exact shapes_eq_of_mixed t u g hg + (le_antisymm (mixed_moment_le t u g hg) (mixed_moment_le u t h hh)) + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/SignEquivalence.lean b/lean/OAI/RepresentationTheory/Saxl/SignEquivalence.lean index b4ee6468589d3c29c01acc0da8d64f503877970b..abff57a1bed508a0eafee726913ebb16a18a15a1 100644 --- a/lean/OAI/RepresentationTheory/Saxl/SignEquivalence.lean +++ b/lean/OAI/RepresentationTheory/Saxl/SignEquivalence.lean @@ -1,155 +1,155 @@ -import OAI.RepresentationTheory.Saxl.BandGlue - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uV - -namespace Saxl - -def transposeTableau {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - Tableau n μ.transpose := t.trans - { toFun := fun c => ⟨c.val.swap, YoungDiagram.mem_transpose.mpr (by simp)⟩ - invFun := fun c => ⟨c.val.swap, YoungDiagram.mem_transpose.mp c.property⟩ - left_inv := by intro c; apply Subtype.ext; exact Prod.swap_swap _ - right_inv := by intro c; apply Subtype.ext; exact Prod.swap_swap _ } - -/- Twisting by the actual sign character, on the same complex vector space. -/ -def signTwist {n : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) : - Representation ℂ (Equiv.Perm (Fin n)) V where - toFun g := signC g • ρ g - map_one' := by simp - map_mul' g h := by ext x; simp [map_mul, smul_smul, mul_comm] - -lemma signTwist_irreducible {n : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) [Representation.IsIrreducible ρ] : - Representation.IsIrreducible (signTwist ρ) := by - let cv : Subrepresentation (signTwist ρ) ≃o Subrepresentation ρ := - { toFun := fun S => - { toSubmodule := S.toSubmodule - apply_mem_toSubmodule := by - intro g x hx - have h := S.toSubmodule.smul_mem (signC g) (S.apply_mem_toSubmodule g hx) - change signC g • (signC g • (ρ g x)) ∈ S.toSubmodule at h - simpa only [smul_smul, signC_mul_self, one_smul] using h } - invFun := fun S => - { toSubmodule := S.toSubmodule - apply_mem_toSubmodule := by - intro g x hx - exact S.toSubmodule.smul_mem (signC g) (S.apply_mem_toSubmodule g hx) } - left_inv := by intro S; rfl - right_inv := by intro S; rfl - map_rel_iff' := by intros; rfl } - exact cv.isSimpleOrder_iff.mpr inferInstance - -def orbitAverage {n d : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) (a : Fin n → Fin d) (y : V) : - Representation.IntertwiningMap (wordRep n d) ρ where - toFun x := ∑ g : Equiv.Perm (Fin n), x (a ∘ (g⁻¹ : Equiv.Perm (Fin n))) • ρ g y - map_add' x z := by simp [add_smul, Finset.sum_add_distrib] - map_smul' c x := by simp [smul_smul, Finset.smul_sum] - isIntertwining' h := by - apply LinearMap.ext - intro x - change (∑ g : Equiv.Perm (Fin n), x ((a ∘ (g⁻¹ : Equiv.Perm (Fin n))) ∘ h) • ρ g y) = - ρ h (∑ g : Equiv.Perm (Fin n), x (a ∘ (g⁻¹ : Equiv.Perm (Fin n))) • ρ g y) - simp only [map_sum, map_smul] - apply (Equiv.sum_comp (Equiv.mulLeft h) _).symm.trans - apply Finset.sum_congr rfl - intro g hg - change x ((a ∘ ((h * g)⁻¹ : Equiv.Perm (Fin n))) ∘ h) • ρ (h * g) y = - x (a ∘ (g⁻¹ : Equiv.Perm (Fin n))) • ρ h (ρ g y) - simp only [mul_inv_rev, map_mul, Module.End.mul_apply] - congr 2 - funext i - simp - -lemma orbitAverage_base {n d : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) (a : Fin n → Fin d) (y : V) - (hy : ∀ g : Equiv.Perm (Fin n), a ∘ g = a → ρ g y = y) : - orbitAverage ρ a y (Pi.single a 1) = - ((Finset.univ.filter (fun g : Equiv.Perm (Fin n) => a ∘ g = a)).card : ℂ) • y := by - classical - change (∑ g : Equiv.Perm (Fin n), (Pi.single a (1 : ℂ) : WordSpace n d) (a ∘ (g⁻¹ : Equiv.Perm (Fin n))) • ρ g y) = _ - have hi (g : Equiv.Perm (Fin n)) : a ∘ (g⁻¹ : Equiv.Perm (Fin n)) = a ↔ a ∘ g = a := by - constructor <;> intro hh <;> funext i - · have he := congrFun hh (g i); simpa using he.symm - · have he := congrFun hh (g⁻¹ i); simpa using he.symm - simp only [Pi.single_apply, hi] - simp only [ite_smul, one_smul, zero_smul, Finset.sum_ite, Finset.sum_const_zero, add_zero] - rw [Finset.sum_congr rfl (fun g hg => hy g (Finset.mem_filter.mp hg).2)] - simp [Nat.cast_smul_eq_nsmul] - -end Saxl - -namespace Saxl -/- Sign-conjugacy proved using the column-antisymmetrized row tabloids. -/ -theorem specht_sign_transpose {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - Nonempty ((spechtRep t).Equiv (signTwist (spechtRep (transposeTableau t)))) := by - classical - let tt := transposeTableau t - let y : Specht tt := ⟨polytabloid tt, mem_cyclic _ _⟩ - let R := signTwist (spechtRep tt) - let F := orbitAverage R (rowWord t) y - let c : ℂ := ((Finset.univ.filter - (fun g : Equiv.Perm (Fin n) => rowWord t ∘ g = rowWord t)).card : ℂ) - have hy : ∀ g : Equiv.Perm (Fin n), rowWord t ∘ g = rowWord t → R g y = y := by - intro g hg - have hc : g ∈ columnGroup tt := by - intro i - exact congrArg Fin.val (congrFun hg i) - apply Subtype.ext - change signC g • wordRep n (μ.transpose.colLen 0) g (polytabloid tt) = polytabloid tt - rw [polytabloid_alternating tt ⟨g, hc⟩, smul_smul, signC_mul_self, one_smul] - have hF : F (Pi.single (rowWord t) 1) = c • y := orbitAverage_base R _ y hy - have hc0 : c ≠ 0 := by - apply Nat.cast_ne_zero.mpr - apply Finset.card_ne_zero.mpr - refine ⟨1, Finset.mem_filter.mpr ⟨Finset.mem_univ _, ?_⟩⟩ - rfl - have hm (g : columnGroup t) : - (F (wordRep n (μ.colLen 0) (g : Equiv.Perm (Fin n)) - (Pi.single (rowWord t) 1))).val (rowWord tt) = signC (g : Equiv.Perm (Fin n)) * c := by - rw [F.isIntertwining, hF] - change signC (g : Equiv.Perm (Fin n)) * (c * - polytabloid tt (rowWord tt ∘ (g : Equiv.Perm (Fin n)))) = _ - have he : rowWord tt ∘ (g : Equiv.Perm (Fin n)) = rowWord tt := by - funext i - apply Fin.ext - exact g.property i - rw [he, polytabloid_rowWord, mul_one] - let inc : Representation.IntertwiningMap (spechtRep t) (wordRep n (μ.colLen 0)) := - { toLinearMap := (spechtSub t).toSubmodule.subtype - isIntertwining' := fun _ => rfl } - let f := F.comp inc - have hf : f ≠ 0 := by - intro hz - have he : (F (polytabloid t)).val (rowWord tt) = 0 := by - have he := congrArg (fun l : Representation.IntertwiningMap (spechtRep t) R => - (l ⟨polytabloid t, mem_cyclic _ _⟩).val (rowWord tt)) hz - exact he - let := Fintype.ofFinite (columnGroup t) - have hp : (F (polytabloid t)).val (rowWord tt) = - (Fintype.card (columnGroup t) : ℂ) * c := by - change (F (∑ g : columnGroup t, signC (g : Equiv.Perm (Fin n)) • - wordRep n (μ.colLen 0) (g : Equiv.Perm (Fin n)) (Pi.single (rowWord t) 1))).val _ = _ - simp only [map_sum, map_smul, Submodule.coe_sum, Submodule.coe_smul, - Finset.sum_apply, Pi.smul_apply, smul_eq_mul, hm] - simp only [← mul_assoc, signC_mul_self, one_mul, Finset.sum_const, - Finset.card_univ, nsmul_eq_mul] - have hn : (Fintype.card (columnGroup t) : ℂ) ≠ 0 := by - exact Nat.cast_ne_zero.mpr Fintype.card_ne_zero - exact (mul_ne_zero hn hc0) (hp.symm.trans he) - let := specht_irreducible t - let := specht_irreducible tt - let := signTwist_irreducible (spechtRep tt) - exact ⟨f.ofBijective ((Representation.IsIrreducible.bijective_or_eq_zero f).resolve_right hf)⟩ -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.BandGlue + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uV + +namespace Saxl + +def transposeTableau {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + Tableau n μ.transpose := t.trans + { toFun := fun c => ⟨c.val.swap, YoungDiagram.mem_transpose.mpr (by simp)⟩ + invFun := fun c => ⟨c.val.swap, YoungDiagram.mem_transpose.mp c.property⟩ + left_inv := by intro c; apply Subtype.ext; exact Prod.swap_swap _ + right_inv := by intro c; apply Subtype.ext; exact Prod.swap_swap _ } + +/- Twisting by the actual sign character, on the same complex vector space. -/ +def signTwist {n : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) : + Representation ℂ (Equiv.Perm (Fin n)) V where + toFun g := signC g • ρ g + map_one' := by simp + map_mul' g h := by ext x; simp [map_mul, smul_smul, mul_comm] + +lemma signTwist_irreducible {n : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) [Representation.IsIrreducible ρ] : + Representation.IsIrreducible (signTwist ρ) := by + let cv : Subrepresentation (signTwist ρ) ≃o Subrepresentation ρ := + { toFun := fun S => + { toSubmodule := S.toSubmodule + apply_mem_toSubmodule := by + intro g x hx + have h := S.toSubmodule.smul_mem (signC g) (S.apply_mem_toSubmodule g hx) + change signC g • (signC g • (ρ g x)) ∈ S.toSubmodule at h + simpa only [smul_smul, signC_mul_self, one_smul] using h } + invFun := fun S => + { toSubmodule := S.toSubmodule + apply_mem_toSubmodule := by + intro g x hx + exact S.toSubmodule.smul_mem (signC g) (S.apply_mem_toSubmodule g hx) } + left_inv := by intro S; rfl + right_inv := by intro S; rfl + map_rel_iff' := by intros; rfl } + exact cv.isSimpleOrder_iff.mpr inferInstance + +def orbitAverage {n d : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) (a : Fin n → Fin d) (y : V) : + Representation.IntertwiningMap (wordRep n d) ρ where + toFun x := ∑ g : Equiv.Perm (Fin n), x (a ∘ (g⁻¹ : Equiv.Perm (Fin n))) • ρ g y + map_add' x z := by simp [add_smul, Finset.sum_add_distrib] + map_smul' c x := by simp [smul_smul, Finset.smul_sum] + isIntertwining' h := by + apply LinearMap.ext + intro x + change (∑ g : Equiv.Perm (Fin n), x ((a ∘ (g⁻¹ : Equiv.Perm (Fin n))) ∘ h) • ρ g y) = + ρ h (∑ g : Equiv.Perm (Fin n), x (a ∘ (g⁻¹ : Equiv.Perm (Fin n))) • ρ g y) + simp only [map_sum, map_smul] + apply (Equiv.sum_comp (Equiv.mulLeft h) _).symm.trans + apply Finset.sum_congr rfl + intro g hg + change x ((a ∘ ((h * g)⁻¹ : Equiv.Perm (Fin n))) ∘ h) • ρ (h * g) y = + x (a ∘ (g⁻¹ : Equiv.Perm (Fin n))) • ρ h (ρ g y) + simp only [mul_inv_rev, map_mul, Module.End.mul_apply] + congr 2 + funext i + simp + +lemma orbitAverage_base {n d : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) (a : Fin n → Fin d) (y : V) + (hy : ∀ g : Equiv.Perm (Fin n), a ∘ g = a → ρ g y = y) : + orbitAverage ρ a y (Pi.single a 1) = + ((Finset.univ.filter (fun g : Equiv.Perm (Fin n) => a ∘ g = a)).card : ℂ) • y := by + classical + change (∑ g : Equiv.Perm (Fin n), (Pi.single a (1 : ℂ) : WordSpace n d) (a ∘ (g⁻¹ : Equiv.Perm (Fin n))) • ρ g y) = _ + have hi (g : Equiv.Perm (Fin n)) : a ∘ (g⁻¹ : Equiv.Perm (Fin n)) = a ↔ a ∘ g = a := by + constructor <;> intro hh <;> funext i + · have he := congrFun hh (g i); simpa using he.symm + · have he := congrFun hh (g⁻¹ i); simpa using he.symm + simp only [Pi.single_apply, hi] + simp only [ite_smul, one_smul, zero_smul, Finset.sum_ite, Finset.sum_const_zero, add_zero] + rw [Finset.sum_congr rfl (fun g hg => hy g (Finset.mem_filter.mp hg).2)] + simp [Nat.cast_smul_eq_nsmul] + +end Saxl + +namespace Saxl +/- Sign-conjugacy proved using the column-antisymmetrized row tabloids. -/ +theorem specht_sign_transpose {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + Nonempty ((spechtRep t).Equiv (signTwist (spechtRep (transposeTableau t)))) := by + classical + let tt := transposeTableau t + let y : Specht tt := ⟨polytabloid tt, mem_cyclic _ _⟩ + let R := signTwist (spechtRep tt) + let F := orbitAverage R (rowWord t) y + let c : ℂ := ((Finset.univ.filter + (fun g : Equiv.Perm (Fin n) => rowWord t ∘ g = rowWord t)).card : ℂ) + have hy : ∀ g : Equiv.Perm (Fin n), rowWord t ∘ g = rowWord t → R g y = y := by + intro g hg + have hc : g ∈ columnGroup tt := by + intro i + exact congrArg Fin.val (congrFun hg i) + apply Subtype.ext + change signC g • wordRep n (μ.transpose.colLen 0) g (polytabloid tt) = polytabloid tt + rw [polytabloid_alternating tt ⟨g, hc⟩, smul_smul, signC_mul_self, one_smul] + have hF : F (Pi.single (rowWord t) 1) = c • y := orbitAverage_base R _ y hy + have hc0 : c ≠ 0 := by + apply Nat.cast_ne_zero.mpr + apply Finset.card_ne_zero.mpr + refine ⟨1, Finset.mem_filter.mpr ⟨Finset.mem_univ _, ?_⟩⟩ + rfl + have hm (g : columnGroup t) : + (F (wordRep n (μ.colLen 0) (g : Equiv.Perm (Fin n)) + (Pi.single (rowWord t) 1))).val (rowWord tt) = signC (g : Equiv.Perm (Fin n)) * c := by + rw [F.isIntertwining, hF] + change signC (g : Equiv.Perm (Fin n)) * (c * + polytabloid tt (rowWord tt ∘ (g : Equiv.Perm (Fin n)))) = _ + have he : rowWord tt ∘ (g : Equiv.Perm (Fin n)) = rowWord tt := by + funext i + apply Fin.ext + exact g.property i + rw [he, polytabloid_rowWord, mul_one] + let inc : Representation.IntertwiningMap (spechtRep t) (wordRep n (μ.colLen 0)) := + { toLinearMap := (spechtSub t).toSubmodule.subtype + isIntertwining' := fun _ => rfl } + let f := F.comp inc + have hf : f ≠ 0 := by + intro hz + have he : (F (polytabloid t)).val (rowWord tt) = 0 := by + have he := congrArg (fun l : Representation.IntertwiningMap (spechtRep t) R => + (l ⟨polytabloid t, mem_cyclic _ _⟩).val (rowWord tt)) hz + exact he + let := Fintype.ofFinite (columnGroup t) + have hp : (F (polytabloid t)).val (rowWord tt) = + (Fintype.card (columnGroup t) : ℂ) * c := by + change (F (∑ g : columnGroup t, signC (g : Equiv.Perm (Fin n)) • + wordRep n (μ.colLen 0) (g : Equiv.Perm (Fin n)) (Pi.single (rowWord t) 1))).val _ = _ + simp only [map_sum, map_smul, Submodule.coe_sum, Submodule.coe_smul, + Finset.sum_apply, Pi.smul_apply, smul_eq_mul, hm] + simp only [← mul_assoc, signC_mul_self, one_mul, Finset.sum_const, + Finset.card_univ, nsmul_eq_mul] + have hn : (Fintype.card (columnGroup t) : ℂ) ≠ 0 := by + exact Nat.cast_ne_zero.mpr Fintype.card_ne_zero + exact (mul_ne_zero hn hc0) (hp.symm.trans he) + let := specht_irreducible t + let := specht_irreducible tt + let := signTwist_irreducible (spechtRep tt) + exact ⟨f.ofBijective ((Representation.IsIrreducible.bijective_or_eq_zero f).resolve_right hf)⟩ +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/SizedStrips.lean b/lean/OAI/RepresentationTheory/Saxl/SizedStrips.lean index b0c3483403f7c2853c912b95a9b291b690046c97..71607aac525dc084d68f8de6c59fb4a95a1c3e23 100644 --- a/lean/OAI/RepresentationTheory/Saxl/SizedStrips.lean +++ b/lean/OAI/RepresentationTheory/Saxl/SizedStrips.lean @@ -1,212 +1,212 @@ -import OAI.RepresentationTheory.Saxl.StripExtension - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl - -inductive SizedStripChain : List ℕ → YoungDiagram → YoungDiagram → Prop - | nil (μ) : SizedStripChain [] μ μ - | snoc {bs ν η μ b} : SizedStripChain bs ν η → HorizontalStrip η μ → - η.card + b = μ.card → SizedStripChain (bs ++ [b]) ν μ - -lemma SizedStripChain.le {bs ν μ} (hs : SizedStripChain bs ν μ) : ν ≤ μ := by - induction hs with - | nil => exact le_rfl - | snoc hs hh hc ih => exact ih.trans hh.1 - -abbrev shapeTableau (μ : YoungDiagram) : Tableau μ.card μ := canonicalTableau μ rfl - -lemma tableauInclusion_self {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) (k : Fin n) : - tableauInclusion t t le_rfl k = k := by - change t.symm (t k) = k - exact t.symm_apply_apply k - -/- Iterated positive Pieri, with an explicit coloring of the added strips. -The map is surjective and equivariant for all permutations preserving each -strip, not just for the smaller symmetric group. -/ -theorem stripChain_restriction {bs ν μ} (hs : SizedStripChain bs ν μ) : - ∃ (c : Fin μ.card → ℕ) (F : Specht (shapeTableau μ) →ₗ[ℂ] Specht (shapeTableau ν)), - Function.Surjective F ∧ - (∀ i, c i ≤ bs.length) ∧ - (∀ i, c i = 0 ↔ i ∈ Set.range (tableauInclusion (shapeTableau ν) (shapeTableau μ) hs.le)) ∧ - (∀ j (hj : j < bs.length), (Finset.univ.filter (fun i => c i = j+1)).card = bs[j]) ∧ - (∀ (g : Equiv.Perm (Fin μ.card)) (h : Equiv.Perm (Fin ν.card)), - (∀ i, c (g i) = c i) → - (∀ k, g (tableauInclusion (shapeTableau ν) (shapeTableau μ) hs.le k) = - tableauInclusion (shapeTableau ν) (shapeTableau μ) hs.le (h k)) → - ∀ x, F (spechtRep (shapeTableau μ) g x) = spechtRep (shapeTableau ν) h (F x)) := by - classical - induction hs with - | nil ν => - refine ⟨fun _ => 0, LinearMap.id, Function.surjective_id, by simp, ?_, ?_, ?_⟩ - · intro i - constructor - · intro _; exact ⟨i,tableauInclusion_self _ i⟩ - · intro _; rfl - · intro j hj; simp at hj - · intro g h hc he x - have hh : g = h := by - apply Equiv.ext - intro k - simpa only [tableauInclusion_self] using he k - subst h - rfl - | @snoc bs ν η μ b hs hh hcard ih => - obtain ⟨c,F,hF,hc,hzero,hcount,he⟩ := ih - obtain ⟨P,hP,hPe⟩ := pieri_strip_surjective (shapeTableau η) (shapeTableau μ) hh - let i := tableauInclusion (shapeTableau η) (shapeTableau μ) hh.1 - let c' := extendColor i c (bs.length+1) - refine ⟨c', F.comp P, hF.comp hP, ?_, ?_, ?_, ?_⟩ - · intro k - simpa only [List.length_append, List.length_singleton] using extendColor_le i c bs.length hc k - · intro k - constructor - · intro hk - change extendColor i c (bs.length+1) k = 0 at hk - have hr : k ∈ Set.range i := (extendColor_mem i c bs.length hc k).mp (by omega) - obtain ⟨l,rfl⟩ := hr - have hl : c l = 0 := (extendColor_apply i c _ l).symm.trans hk - obtain ⟨j,hj⟩ := (hzero l).mp hl - refine ⟨j, ?_⟩ - rw [← tableauInclusion_trans (shapeTableau ν) (shapeTableau η) (shapeTableau μ) hs.le hh.1] - exact congrArg i hj - · rintro ⟨j,rfl⟩ - rw [← tableauInclusion_trans (shapeTableau ν) (shapeTableau η) (shapeTableau μ) hs.le hh.1] - change extendColor i c _ (i _) = 0 - rw [extendColor_apply] - exact (hzero _).mpr ⟨j,rfl⟩ - · intro j hj - have hjle : j ≤ bs.length := by - simp only [List.length_append, List.length_singleton] at hj - omega - rcases lt_or_eq_of_le hjle with hjlt | rfl - · change (Finset.univ.filter (fun x => extendColor i c (bs.length+1) x = j+1)).card = _ - rw [extendColor_count_old i c (bs.length+1) (j+1) (by omega), hcount j hjlt, - List.getElem_append_left hjlt] - · change (Finset.univ.filter (fun x => extendColor i c (bs.length+1) x = bs.length+1)).card = _ - rw [extendColor_count_new i c bs.length hc] - simp only [List.getElem_append_right le_rfl, Nat.sub_self, List.getElem_singleton] - omega - · intro g h hg hgi x - have hgmem : ∀ k, g k ∈ Set.range i ↔ k ∈ Set.range i := by - intro k - rw [← extendColor_mem i c bs.length hc, ← extendColor_mem i c bs.length hc] - exact (congrArg (fun c => c ≤ bs.length) (hg k)).to_iff - let k := restrictPerm i g hgmem - have hik (l) : i (k l) = g (i l) := restrictPerm_apply i g hgmem l - have hkcolor (l) : c (k l) = c l := by - rw [← extendColor_apply i c (bs.length+1) (k l), hik, ← extendColor_apply i c (bs.length+1) l] - exact hg (i l) - have hkbase (l) : k (tableauInclusion (shapeTableau ν) (shapeTableau η) hs.le l) = - tableauInclusion (shapeTableau ν) (shapeTableau η) hs.le (h l) := by - apply i.injective - rw [hik] - change g (tableauInclusion (shapeTableau η) (shapeTableau μ) hh.1 _) = - tableauInclusion (shapeTableau η) (shapeTableau μ) hh.1 _ - rw [tableauInclusion_trans, tableauInclusion_trans] - exact hgi l - change F (P (spechtRep (shapeTableau μ) g x)) = _ - rw [hPe g k (fun l => (hik l).symm), he k h hkcolor hkbase] - rfl - - - -theorem stripChain_restriction_any {bs ν μ} (hs : SizedStripChain bs ν μ) - {a n : ℕ} (s : Tableau a ν) (t : Tableau n μ) : - ∃ (c : Fin n → ℕ) (F : Specht t →ₗ[ℂ] Specht s), - Function.Surjective F ∧ - (∀ i, c i ≤ bs.length) ∧ - (∀ i, c i = 0 ↔ i ∈ Set.range (tableauInclusion s t hs.le)) ∧ - (∀ j (hj : j < bs.length), (Finset.univ.filter (fun i => c i = j+1)).card = bs[j]) ∧ - (∀ (g : Equiv.Perm (Fin n)) (h : Equiv.Perm (Fin a)), - (∀ i, c (g i) = c i) → - (∀ k, g (tableauInclusion s t hs.le k) = - tableauInclusion s t hs.le (h k)) → - ∀ x, F (spechtRep t g x) = spechtRep s h (F x)) := by - classical - induction hs generalizing a n with - | nil ν => - obtain ⟨F,hF,hFe⟩ := pieri_strip_surjective s t - (show HorizontalStrip ν ν from ⟨le_rfl, by intros x hx hn; exact False.elim (hn hx)⟩) - refine ⟨fun _ => 0, F, hF, by simp, ?_, ?_, ?_⟩ - · intro i - constructor - · intro _ - refine ⟨s.symm (t i), ?_⟩ - change t.symm ⟨(s (s.symm (t i))).val, _⟩ = i - simp only [Equiv.apply_symm_apply] - exact t.symm_apply_apply i - · intro _; rfl - · intro j hj; simp at hj - · intro g h hc he x - exact hFe g h he x - | @snoc bs ν η μ b hs hh hcard ih => - obtain ⟨c,F,hF,hc,hzero,hcount,he⟩ := ih s (shapeTableau η) - obtain ⟨P,hP,hPe⟩ := pieri_strip_surjective (shapeTableau η) t hh - let i := tableauInclusion (shapeTableau η) t hh.1 - let c' := extendColor i c (bs.length+1) - refine ⟨c', F.comp P, hF.comp hP, ?_, ?_, ?_, ?_⟩ - · intro k - simpa only [List.length_append, List.length_singleton] using extendColor_le i c bs.length hc k - · intro k - constructor - · intro hk - change extendColor i c (bs.length+1) k = 0 at hk - have hr : k ∈ Set.range i := (extendColor_mem i c bs.length hc k).mp (by omega) - obtain ⟨l,rfl⟩ := hr - have hl : c l = 0 := (extendColor_apply i c _ l).symm.trans hk - obtain ⟨j,hj⟩ := (hzero l).mp hl - refine ⟨j, ?_⟩ - rw [← tableauInclusion_trans s (shapeTableau η) t hs.le hh.1] - exact congrArg i hj - · rintro ⟨j,rfl⟩ - rw [← tableauInclusion_trans s (shapeTableau η) t hs.le hh.1] - change extendColor i c _ (i _) = 0 - rw [extendColor_apply] - exact (hzero _).mpr ⟨j,rfl⟩ - · intro j hj - have hjle : j ≤ bs.length := by - simp only [List.length_append, List.length_singleton] at hj - omega - rcases lt_or_eq_of_le hjle with hjlt | rfl - · change (Finset.univ.filter (fun x => extendColor i c (bs.length+1) x = j+1)).card = _ - rw [extendColor_count_old i c (bs.length+1) (j+1) (by omega), hcount j hjlt, - List.getElem_append_left hjlt] - · change (Finset.univ.filter (fun x => extendColor i c (bs.length+1) x = bs.length+1)).card = _ - rw [extendColor_count_new i c bs.length hc] - simp only [List.getElem_append_right le_rfl, Nat.sub_self, List.getElem_singleton] - have ht : n = μ.card := by - have := Fintype.card_congr t - simpa only [Fintype.card_fin, Fintype.card_coe] using this - omega - · intro g h hg hgi x - have hgmem : ∀ k, g k ∈ Set.range i ↔ k ∈ Set.range i := by - intro k - rw [← extendColor_mem i c bs.length hc, ← extendColor_mem i c bs.length hc] - exact (congrArg (fun c => c ≤ bs.length) (hg k)).to_iff - let k := restrictPerm i g hgmem - have hik (l) : i (k l) = g (i l) := restrictPerm_apply i g hgmem l - have hkcolor (l) : c (k l) = c l := by - rw [← extendColor_apply i c (bs.length+1) (k l), hik, ← extendColor_apply i c (bs.length+1) l] - exact hg (i l) - have hkbase (l) : k (tableauInclusion s (shapeTableau η) hs.le l) = - tableauInclusion s (shapeTableau η) hs.le (h l) := by - apply i.injective - rw [hik] - change g (tableauInclusion (shapeTableau η) t hh.1 _) = - tableauInclusion (shapeTableau η) t hh.1 _ - rw [tableauInclusion_trans, tableauInclusion_trans] - exact hgi l - change F (P (spechtRep t g x)) = _ - rw [hPe g k (fun l => (hik l).symm), he k h hkcolor hkbase] - rfl - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.StripExtension + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl + +inductive SizedStripChain : List ℕ → YoungDiagram → YoungDiagram → Prop + | nil (μ) : SizedStripChain [] μ μ + | snoc {bs ν η μ b} : SizedStripChain bs ν η → HorizontalStrip η μ → + η.card + b = μ.card → SizedStripChain (bs ++ [b]) ν μ + +lemma SizedStripChain.le {bs ν μ} (hs : SizedStripChain bs ν μ) : ν ≤ μ := by + induction hs with + | nil => exact le_rfl + | snoc hs hh hc ih => exact ih.trans hh.1 + +abbrev shapeTableau (μ : YoungDiagram) : Tableau μ.card μ := canonicalTableau μ rfl + +lemma tableauInclusion_self {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) (k : Fin n) : + tableauInclusion t t le_rfl k = k := by + change t.symm (t k) = k + exact t.symm_apply_apply k + +/- Iterated positive Pieri, with an explicit coloring of the added strips. +The map is surjective and equivariant for all permutations preserving each +strip, not just for the smaller symmetric group. -/ +theorem stripChain_restriction {bs ν μ} (hs : SizedStripChain bs ν μ) : + ∃ (c : Fin μ.card → ℕ) (F : Specht (shapeTableau μ) →ₗ[ℂ] Specht (shapeTableau ν)), + Function.Surjective F ∧ + (∀ i, c i ≤ bs.length) ∧ + (∀ i, c i = 0 ↔ i ∈ Set.range (tableauInclusion (shapeTableau ν) (shapeTableau μ) hs.le)) ∧ + (∀ j (hj : j < bs.length), (Finset.univ.filter (fun i => c i = j+1)).card = bs[j]) ∧ + (∀ (g : Equiv.Perm (Fin μ.card)) (h : Equiv.Perm (Fin ν.card)), + (∀ i, c (g i) = c i) → + (∀ k, g (tableauInclusion (shapeTableau ν) (shapeTableau μ) hs.le k) = + tableauInclusion (shapeTableau ν) (shapeTableau μ) hs.le (h k)) → + ∀ x, F (spechtRep (shapeTableau μ) g x) = spechtRep (shapeTableau ν) h (F x)) := by + classical + induction hs with + | nil ν => + refine ⟨fun _ => 0, LinearMap.id, Function.surjective_id, by simp, ?_, ?_, ?_⟩ + · intro i + constructor + · intro _; exact ⟨i,tableauInclusion_self _ i⟩ + · intro _; rfl + · intro j hj; simp at hj + · intro g h hc he x + have hh : g = h := by + apply Equiv.ext + intro k + simpa only [tableauInclusion_self] using he k + subst h + rfl + | @snoc bs ν η μ b hs hh hcard ih => + obtain ⟨c,F,hF,hc,hzero,hcount,he⟩ := ih + obtain ⟨P,hP,hPe⟩ := pieri_strip_surjective (shapeTableau η) (shapeTableau μ) hh + let i := tableauInclusion (shapeTableau η) (shapeTableau μ) hh.1 + let c' := extendColor i c (bs.length+1) + refine ⟨c', F.comp P, hF.comp hP, ?_, ?_, ?_, ?_⟩ + · intro k + simpa only [List.length_append, List.length_singleton] using extendColor_le i c bs.length hc k + · intro k + constructor + · intro hk + change extendColor i c (bs.length+1) k = 0 at hk + have hr : k ∈ Set.range i := (extendColor_mem i c bs.length hc k).mp (by omega) + obtain ⟨l,rfl⟩ := hr + have hl : c l = 0 := (extendColor_apply i c _ l).symm.trans hk + obtain ⟨j,hj⟩ := (hzero l).mp hl + refine ⟨j, ?_⟩ + rw [← tableauInclusion_trans (shapeTableau ν) (shapeTableau η) (shapeTableau μ) hs.le hh.1] + exact congrArg i hj + · rintro ⟨j,rfl⟩ + rw [← tableauInclusion_trans (shapeTableau ν) (shapeTableau η) (shapeTableau μ) hs.le hh.1] + change extendColor i c _ (i _) = 0 + rw [extendColor_apply] + exact (hzero _).mpr ⟨j,rfl⟩ + · intro j hj + have hjle : j ≤ bs.length := by + simp only [List.length_append, List.length_singleton] at hj + omega + rcases lt_or_eq_of_le hjle with hjlt | rfl + · change (Finset.univ.filter (fun x => extendColor i c (bs.length+1) x = j+1)).card = _ + rw [extendColor_count_old i c (bs.length+1) (j+1) (by omega), hcount j hjlt, + List.getElem_append_left hjlt] + · change (Finset.univ.filter (fun x => extendColor i c (bs.length+1) x = bs.length+1)).card = _ + rw [extendColor_count_new i c bs.length hc] + simp only [List.getElem_append_right le_rfl, Nat.sub_self, List.getElem_singleton] + omega + · intro g h hg hgi x + have hgmem : ∀ k, g k ∈ Set.range i ↔ k ∈ Set.range i := by + intro k + rw [← extendColor_mem i c bs.length hc, ← extendColor_mem i c bs.length hc] + exact (congrArg (fun c => c ≤ bs.length) (hg k)).to_iff + let k := restrictPerm i g hgmem + have hik (l) : i (k l) = g (i l) := restrictPerm_apply i g hgmem l + have hkcolor (l) : c (k l) = c l := by + rw [← extendColor_apply i c (bs.length+1) (k l), hik, ← extendColor_apply i c (bs.length+1) l] + exact hg (i l) + have hkbase (l) : k (tableauInclusion (shapeTableau ν) (shapeTableau η) hs.le l) = + tableauInclusion (shapeTableau ν) (shapeTableau η) hs.le (h l) := by + apply i.injective + rw [hik] + change g (tableauInclusion (shapeTableau η) (shapeTableau μ) hh.1 _) = + tableauInclusion (shapeTableau η) (shapeTableau μ) hh.1 _ + rw [tableauInclusion_trans, tableauInclusion_trans] + exact hgi l + change F (P (spechtRep (shapeTableau μ) g x)) = _ + rw [hPe g k (fun l => (hik l).symm), he k h hkcolor hkbase] + rfl + + + +theorem stripChain_restriction_any {bs ν μ} (hs : SizedStripChain bs ν μ) + {a n : ℕ} (s : Tableau a ν) (t : Tableau n μ) : + ∃ (c : Fin n → ℕ) (F : Specht t →ₗ[ℂ] Specht s), + Function.Surjective F ∧ + (∀ i, c i ≤ bs.length) ∧ + (∀ i, c i = 0 ↔ i ∈ Set.range (tableauInclusion s t hs.le)) ∧ + (∀ j (hj : j < bs.length), (Finset.univ.filter (fun i => c i = j+1)).card = bs[j]) ∧ + (∀ (g : Equiv.Perm (Fin n)) (h : Equiv.Perm (Fin a)), + (∀ i, c (g i) = c i) → + (∀ k, g (tableauInclusion s t hs.le k) = + tableauInclusion s t hs.le (h k)) → + ∀ x, F (spechtRep t g x) = spechtRep s h (F x)) := by + classical + induction hs generalizing a n with + | nil ν => + obtain ⟨F,hF,hFe⟩ := pieri_strip_surjective s t + (show HorizontalStrip ν ν from ⟨le_rfl, by intros x hx hn; exact False.elim (hn hx)⟩) + refine ⟨fun _ => 0, F, hF, by simp, ?_, ?_, ?_⟩ + · intro i + constructor + · intro _ + refine ⟨s.symm (t i), ?_⟩ + change t.symm ⟨(s (s.symm (t i))).val, _⟩ = i + simp only [Equiv.apply_symm_apply] + exact t.symm_apply_apply i + · intro _; rfl + · intro j hj; simp at hj + · intro g h hc he x + exact hFe g h he x + | @snoc bs ν η μ b hs hh hcard ih => + obtain ⟨c,F,hF,hc,hzero,hcount,he⟩ := ih s (shapeTableau η) + obtain ⟨P,hP,hPe⟩ := pieri_strip_surjective (shapeTableau η) t hh + let i := tableauInclusion (shapeTableau η) t hh.1 + let c' := extendColor i c (bs.length+1) + refine ⟨c', F.comp P, hF.comp hP, ?_, ?_, ?_, ?_⟩ + · intro k + simpa only [List.length_append, List.length_singleton] using extendColor_le i c bs.length hc k + · intro k + constructor + · intro hk + change extendColor i c (bs.length+1) k = 0 at hk + have hr : k ∈ Set.range i := (extendColor_mem i c bs.length hc k).mp (by omega) + obtain ⟨l,rfl⟩ := hr + have hl : c l = 0 := (extendColor_apply i c _ l).symm.trans hk + obtain ⟨j,hj⟩ := (hzero l).mp hl + refine ⟨j, ?_⟩ + rw [← tableauInclusion_trans s (shapeTableau η) t hs.le hh.1] + exact congrArg i hj + · rintro ⟨j,rfl⟩ + rw [← tableauInclusion_trans s (shapeTableau η) t hs.le hh.1] + change extendColor i c _ (i _) = 0 + rw [extendColor_apply] + exact (hzero _).mpr ⟨j,rfl⟩ + · intro j hj + have hjle : j ≤ bs.length := by + simp only [List.length_append, List.length_singleton] at hj + omega + rcases lt_or_eq_of_le hjle with hjlt | rfl + · change (Finset.univ.filter (fun x => extendColor i c (bs.length+1) x = j+1)).card = _ + rw [extendColor_count_old i c (bs.length+1) (j+1) (by omega), hcount j hjlt, + List.getElem_append_left hjlt] + · change (Finset.univ.filter (fun x => extendColor i c (bs.length+1) x = bs.length+1)).card = _ + rw [extendColor_count_new i c bs.length hc] + simp only [List.getElem_append_right le_rfl, Nat.sub_self, List.getElem_singleton] + have ht : n = μ.card := by + have := Fintype.card_congr t + simpa only [Fintype.card_fin, Fintype.card_coe] using this + omega + · intro g h hg hgi x + have hgmem : ∀ k, g k ∈ Set.range i ↔ k ∈ Set.range i := by + intro k + rw [← extendColor_mem i c bs.length hc, ← extendColor_mem i c bs.length hc] + exact (congrArg (fun c => c ≤ bs.length) (hg k)).to_iff + let k := restrictPerm i g hgmem + have hik (l) : i (k l) = g (i l) := restrictPerm_apply i g hgmem l + have hkcolor (l) : c (k l) = c l := by + rw [← extendColor_apply i c (bs.length+1) (k l), hik, ← extendColor_apply i c (bs.length+1) l] + exact hg (i l) + have hkbase (l) : k (tableauInclusion s (shapeTableau η) hs.le l) = + tableauInclusion s (shapeTableau η) hs.le (h l) := by + apply i.injective + rw [hik] + change g (tableauInclusion (shapeTableau η) t hh.1 _) = + tableauInclusion (shapeTableau η) t hh.1 _ + rw [tableauInclusion_trans, tableauInclusion_trans] + exact hgi l + change F (P (spechtRep t g x)) = _ + rw [hPe g k (fun l => (hik l).symm), he k h hkcolor hkbase] + rfl + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/SpechtClassification.lean b/lean/OAI/RepresentationTheory/Saxl/SpechtClassification.lean index f0cb4296a0176bb6650158aa0fb70a97913a126d..856b3cd20de7a4bd33eb08095643fbe7e6d18008 100644 --- a/lean/OAI/RepresentationTheory/Saxl/SpechtClassification.lean +++ b/lean/OAI/RepresentationTheory/Saxl/SpechtClassification.lean @@ -1,252 +1,252 @@ -import OAI.RepresentationTheory.Saxl.ShapeRigidity - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uV uG - -namespace Saxl - -/- Rows enumerate exactly the actual cells, including the empty diagram. -/ -def rowCellEquiv (μ : YoungDiagram) : μ.cells ≃ (i : Fin (μ.colLen 0)) × Fin (μ.rowLen i) where - toFun c := ⟨⟨c.val.1, YoungDiagram.mem_iff_lt_colLen.mp - (μ.up_left_mem le_rfl (Nat.zero_le _) c.property)⟩, - ⟨c.val.2, YoungDiagram.mem_iff_lt_rowLen.mp c.property⟩⟩ - invFun c := ⟨(c.1.val, c.2.val), YoungDiagram.mem_iff_lt_rowLen.mpr c.2.isLt⟩ - left_inv c := Subtype.ext rfl - right_inv c := by rcases c with ⟨⟨i, hi⟩, ⟨j, hj⟩⟩; rfl - -lemma card_eq_sum_rowLens (μ : YoungDiagram) : μ.card = μ.rowLens.sum := by - classical - have h := Fintype.card_congr (rowCellEquiv μ) - simp only [Fintype.card_coe, Fintype.card_sigma, Fintype.card_fin] at h - change μ.card = ∑ x : Fin (μ.colLen 0), μ.rowLen x at h - rw [h, YoungDiagram.rowLens] - rw [← List.sum_toFinset _ List.nodup_range] - have he : (List.range (μ.colLen 0)).toFinset = Finset.range (μ.colLen 0) := by - ext i; simp - rw [he] - exact Fin.sum_univ_eq_sum_range μ.rowLen (μ.colLen 0) - -/- Conversion from Mathlib's partition type to its Young diagram. -/ -def partitionDiagram {n : ℕ} (p : Nat.Partition n) : YoungDiagram := - YoungDiagram.ofRowLens (p.parts.sort (· ≥ ·)) (Multiset.pairwise_sort _ _).sortedGE - -lemma partitionDiagram_rowLens {n : ℕ} (p : Nat.Partition n) : - (partitionDiagram p).rowLens = p.parts.sort (· ≥ ·) := by - apply YoungDiagram.rowLens_ofRowLens_eq_self - intro a ha - exact p.parts_pos (by simpa only [← Multiset.mem_coe, Multiset.sort_eq] using ha) - -lemma partitionDiagram_card {n : ℕ} (p : Nat.Partition n) : (partitionDiagram p).card = n := by - rw [card_eq_sum_rowLens, partitionDiagram_rowLens, ← Multiset.sum_coe, - Multiset.sort_eq, p.parts_sum] - -lemma partitionDiagram_injective {n : ℕ} : - Function.Injective (partitionDiagram (n := n)) := by - intro p q h - apply Nat.Partition.ext - have he := congrArg (fun μ => (μ.rowLens : Multiset ℕ)) h - simpa only [partitionDiagram_rowLens, Multiset.sort_eq] using he - -def partitionTableau {n : ℕ} (p : Nat.Partition n) : Tableau n (partitionDiagram p) := - canonicalTableau _ (partitionDiagram_card p) - -/- Cycle-type partition, with only the definitional `card (Fin n)=n` transport. -/ -def permPartition {n : ℕ} (g : Equiv.Perm (Fin n)) : Nat.Partition n := - ⟨g.partition.parts, g.partition.parts_pos, g.partition.parts_sum.trans (Fintype.card_fin n)⟩ - -lemma isConj_of_permPartition_eq {n : ℕ} {g h : Equiv.Perm (Fin n)} - (hh : permPartition g = permPartition h) : IsConj g h := by - apply Equiv.Perm.partition_eq_of_isConj.mpr - have hp := congrArg (fun p : Nat.Partition n => p.parts) hh - exact Nat.Partition.ext hp - -/- Class functions on the symmetric group, indexed by cycle type. -/ -def classFunctions (n : ℕ) : Submodule ℂ (Equiv.Perm (Fin n) → ℂ) where - carrier := {f | ∀ g h, permPartition g = permPartition h → f g = f h} - zero_mem' := by - change ∀ g h, permPartition g = permPartition h → (0 : Equiv.Perm (Fin n) → ℂ) g = 0 - intro g h hh; rfl - add_mem' := by intro f h hf hh g k hk; simp only [Pi.add_apply, hf g k hk, hh g k hk] - smul_mem' := by intro c f hf g k hk; simp only [Pi.smul_apply, hf g k hk] - -/- Select one representative where a cycle partition is realized; unused -coordinates are zero. This gives an injection even without surjectivity of -cycle-type realization. -/ -def classEvaluation (n : ℕ) : (classFunctions n) →ₗ[ℂ] (Nat.Partition n → ℂ) where - toFun f p := if h : ∃ g : Equiv.Perm (Fin n), permPartition g = p then f.val h.choose else 0 - map_add' f h := by - ext p - simp only [Pi.add_apply, Submodule.coe_add] - split_ifs <;> simp - map_smul' c f := by - ext p - simp only [Pi.smul_apply, Submodule.coe_smul, RingHom.id_apply] - split_ifs <;> simp - -lemma classEvaluation_injective (n : ℕ) : Function.Injective (classEvaluation n) := by - intro f h he - apply Subtype.ext - funext g - have hh := congrFun he (permPartition g) - have hex : ∃ k : Equiv.Perm (Fin n), permPartition k = permPartition g := ⟨g, rfl⟩ - change (if hc : ∃ k : Equiv.Perm (Fin n), permPartition k = permPartition g then - f.val hc.choose else 0) = (if hc : ∃ k : Equiv.Perm (Fin n), permPartition k = permPartition g then - h.val hc.choose else 0) at hh - rw [dite_eq_left hex, dite_eq_left hex] at hh - exact (f.property _ _ hex.choose_spec).symm.trans (hh.trans (h.property _ _ hex.choose_spec)) - -lemma classFunctions_finrank_le (n : ℕ) : - Module.finrank ℂ (classFunctions n) ≤ Fintype.card (Nat.Partition n) := by - have h := LinearMap.finrank_le_finrank_of_injective (classEvaluation_injective n) - simpa using h - -lemma char_mem_classFunctions {n : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] - [Module.Finite ℂ V] (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) : - ρ.character ∈ classFunctions n := by - intro g h he - obtain ⟨k, rfl⟩ := isConj_iff.mp (isConj_of_permPartition_eq he) - exact (Representation.char_conj ρ g k).symm - -/- Character of the actual Specht module as an actual class function. -/ -def spechtCharacter {n : ℕ} (p : Nat.Partition n) : classFunctions n := - ⟨(spechtRep (partitionTableau p)).character, char_mem_classFunctions _⟩ - -/- Bilinear character scalar product used by the finite-group orthogonality theorem. -/ -def charFunctional {G : Type uG} [Group G] [Fintype G] (y : G → ℂ) : (G → ℂ) →ₗ[ℂ] ℂ where - toFun x := (Nat.card G : ℂ)⁻¹ * ∑ g, x g * y g⁻¹ - map_add' x z := by simp [Finset.sum_add_distrib, add_mul, mul_add] - map_smul' c x := by simp [Finset.mul_sum, mul_assoc, mul_left_comm] - -lemma complex_card_ne_zero (G : Type uG) [Group G] [Fintype G] : (Nat.card G : ℂ) ≠ 0 := by - exact_mod_cast Nat.card_pos.ne' - -lemma spechtCharacter_orthonormal {n : ℕ} (p q : Nat.Partition n) : - charFunctional (spechtCharacter q).val (spechtCharacter p).val = if p = q then 1 else 0 := by - classical - let : Invertible (Nat.card (Equiv.Perm (Fin n)) : ℂ) := - invertibleOfNonzero (complex_card_ne_zero _) - let := specht_irreducible (partitionTableau p) - let := specht_irreducible (partitionTableau q) - have h := Representation.char_orthonormal (spechtRep (partitionTableau p)) - (spechtRep (partitionTableau q)) - change _ = _ at h - have he : Nonempty ((spechtRep (partitionTableau q)).Equiv - (spechtRep (partitionTableau p))) ↔ p = q := by - constructor - · rintro ⟨e⟩ - exact (partitionDiagram_injective - (specht_shape_rigidity (partitionTableau q) (partitionTableau p) e)).symm - · rintro rfl - exact ⟨Representation.Equiv.refl _⟩ - simpa only [he, charFunctional, spechtCharacter, LinearMap.coe_mk, AddHom.coe_mk] using h - -lemma spechtCharacter_linearIndependent (n : ℕ) : - LinearIndependent ℂ (spechtCharacter (n := n)) := by - classical - rw [Fintype.linearIndependent_iff] - intro c hc p - have h := congrArg (fun f : classFunctions n => charFunctional (spechtCharacter p).val f.val) hc - change charFunctional (spechtCharacter p).val - ((classFunctions n).subtype (∑ i, c i • spechtCharacter i)) = - charFunctional (spechtCharacter p).val ((classFunctions n).subtype 0) at h - simp only [map_sum, map_smul, map_zero] at h - change (∑ i, c i * charFunctional (spechtCharacter p).val (spechtCharacter i).val) = 0 at h - simp_rw [spechtCharacter_orthonormal] at h - simpa using h - -lemma spechtCharacter_span (n : ℕ) : - Submodule.span ℂ (Set.range (spechtCharacter (n := n))) = ⊤ := by - apply (spechtCharacter_linearIndependent n).span_eq_top_of_card_eq_finrank' - exact le_antisymm (spechtCharacter_linearIndependent n).fintype_card_le_finrank - (classFunctions_finrank_le n) - - - -theorem irreducible_equiv_specht {n : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] - [Module.Finite ℂ V] (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) - [Representation.IsIrreducible ρ] : - ∃ p : Nat.Partition n, Nonempty (ρ.Equiv (spechtRep (partitionTableau p))) := by - classical - let : Invertible (Nat.card (Equiv.Perm (Fin n)) : ℂ) := - invertibleOfNonzero (complex_card_ne_zero _) - by_contra h - push Not at h - let f : (classFunctions n) →ₗ[ℂ] ℂ := - (charFunctional ρ.character).comp (classFunctions n).subtype - have hf : ∀ p : Nat.Partition n, f (spechtCharacter p) = 0 := by - intro p - let := specht_irreducible (partitionTableau p) - have hp := Representation.char_orthonormal (spechtRep (partitionTableau p)) ρ - rw [ite_eq_right (fun he => (h p).false he.some)] at hp - exact hp - have hk : Submodule.span ℂ (Set.range (spechtCharacter (n := n))) ≤ LinearMap.ker f := by - rw [Submodule.span_le] - rintro _ ⟨p, rfl⟩ - exact hf p - rw [spechtCharacter_span] at hk - have hz := hk (show (⟨ρ.character, char_mem_classFunctions ρ⟩ : classFunctions n) ∈ ⊤ from trivial) - change charFunctional ρ.character ρ.character = 0 at hz - have hone := Representation.char_orthonormal ρ ρ - rw [ite_eq_left ⟨Representation.Equiv.refl ρ⟩] at hone - exact one_ne_zero (hone.symm.trans hz) - - - -lemma columnAlt_eq_zero_of_rows {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (hd : d < μ.colLen 0) : columnAlt (d := d) t = 0 := by - classical - have hz : ∀ a : Fin n → Fin d, columnAlt t (Pi.single a (1 : ℂ)) = 0 := by - intro a - let j : Fin (μ.colLen 0) → Fin n := fun i => t.symm - ⟨(i.val, 0), YoungDiagram.mem_iff_lt_colLen.mpr i.isLt⟩ - have hnot : ¬ Function.Injective (a ∘ j) := by - intro hi - have hh := Fintype.card_le_of_injective _ hi - simp only [Fintype.card_fin] at hh - omega - simp only [Function.Injective] at hnot - push Not at hnot - obtain ⟨i, k, ha, hik⟩ := hnot - have hj : j i ≠ j k := by - intro he - apply hik - apply Fin.ext - have hh := congrArg (fun l => (t l).val.1) he - simpa [j] using hh - exact columnAlt_collision t a (j i) (j k) hj (by simp [j]) ha - apply LinearMap.ext - intro x - have he : x = ∑ a, x a • Pi.single a (1 : ℂ) := by - ext b - simp [Pi.single_apply] - rw [he, map_sum] - simp only [map_smul, hz, smul_zero, Finset.sum_const_zero, LinearMap.zero_apply] - -/- A Specht constituent of a `d`-letter position representation has at most -`d` rows, proved by the genuine first-column antisymmetrizer. -/ -theorem specht_rows_of_hom {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (f : Representation.IntertwiningMap (spechtRep t) (wordRep n d)) (hf : f ≠ 0) : - μ.colLen 0 ≤ d := by - classical - let := specht_irreducible t - have hi := (Representation.IsIrreducible.injective_or_eq_zero f).resolve_right hf - by_contra h - have hd : d < μ.colLen 0 := lt_of_not_ge h - let p : Specht t := ⟨polytabloid t, mem_cyclic _ _⟩ - have he := columnOperator_intertwining t f p - change f (columnOperator t (spechtRep t) p) = columnAlt t (f p) at he - rw [columnAlt_eq_zero_of_rows t hd, LinearMap.zero_apply] at he - have hz : columnOperator t (spechtRep t) p = 0 := hi (he.trans (map_zero f).symm) - exact columnAlt_polytabloid_ne_zero t - ((columnOperator_subtype t (spechtSub t) p).symm.trans (congrArg Subtype.val hz)) - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.ShapeRigidity + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uV uG + +namespace Saxl + +/- Rows enumerate exactly the actual cells, including the empty diagram. -/ +def rowCellEquiv (μ : YoungDiagram) : μ.cells ≃ (i : Fin (μ.colLen 0)) × Fin (μ.rowLen i) where + toFun c := ⟨⟨c.val.1, YoungDiagram.mem_iff_lt_colLen.mp + (μ.up_left_mem le_rfl (Nat.zero_le _) c.property)⟩, + ⟨c.val.2, YoungDiagram.mem_iff_lt_rowLen.mp c.property⟩⟩ + invFun c := ⟨(c.1.val, c.2.val), YoungDiagram.mem_iff_lt_rowLen.mpr c.2.isLt⟩ + left_inv c := Subtype.ext rfl + right_inv c := by rcases c with ⟨⟨i, hi⟩, ⟨j, hj⟩⟩; rfl + +lemma card_eq_sum_rowLens (μ : YoungDiagram) : μ.card = μ.rowLens.sum := by + classical + have h := Fintype.card_congr (rowCellEquiv μ) + simp only [Fintype.card_coe, Fintype.card_sigma, Fintype.card_fin] at h + change μ.card = ∑ x : Fin (μ.colLen 0), μ.rowLen x at h + rw [h, YoungDiagram.rowLens] + rw [← List.sum_toFinset _ List.nodup_range] + have he : (List.range (μ.colLen 0)).toFinset = Finset.range (μ.colLen 0) := by + ext i; simp + rw [he] + exact Fin.sum_univ_eq_sum_range μ.rowLen (μ.colLen 0) + +/- Conversion from Mathlib's partition type to its Young diagram. -/ +def partitionDiagram {n : ℕ} (p : Nat.Partition n) : YoungDiagram := + YoungDiagram.ofRowLens (p.parts.sort (· ≥ ·)) (Multiset.pairwise_sort _ _).sortedGE + +lemma partitionDiagram_rowLens {n : ℕ} (p : Nat.Partition n) : + (partitionDiagram p).rowLens = p.parts.sort (· ≥ ·) := by + apply YoungDiagram.rowLens_ofRowLens_eq_self + intro a ha + exact p.parts_pos (by simpa only [← Multiset.mem_coe, Multiset.sort_eq] using ha) + +lemma partitionDiagram_card {n : ℕ} (p : Nat.Partition n) : (partitionDiagram p).card = n := by + rw [card_eq_sum_rowLens, partitionDiagram_rowLens, ← Multiset.sum_coe, + Multiset.sort_eq, p.parts_sum] + +lemma partitionDiagram_injective {n : ℕ} : + Function.Injective (partitionDiagram (n := n)) := by + intro p q h + apply Nat.Partition.ext + have he := congrArg (fun μ => (μ.rowLens : Multiset ℕ)) h + simpa only [partitionDiagram_rowLens, Multiset.sort_eq] using he + +def partitionTableau {n : ℕ} (p : Nat.Partition n) : Tableau n (partitionDiagram p) := + canonicalTableau _ (partitionDiagram_card p) + +/- Cycle-type partition, with only the definitional `card (Fin n)=n` transport. -/ +def permPartition {n : ℕ} (g : Equiv.Perm (Fin n)) : Nat.Partition n := + ⟨g.partition.parts, g.partition.parts_pos, g.partition.parts_sum.trans (Fintype.card_fin n)⟩ + +lemma isConj_of_permPartition_eq {n : ℕ} {g h : Equiv.Perm (Fin n)} + (hh : permPartition g = permPartition h) : IsConj g h := by + apply Equiv.Perm.partition_eq_of_isConj.mpr + have hp := congrArg (fun p : Nat.Partition n => p.parts) hh + exact Nat.Partition.ext hp + +/- Class functions on the symmetric group, indexed by cycle type. -/ +def classFunctions (n : ℕ) : Submodule ℂ (Equiv.Perm (Fin n) → ℂ) where + carrier := {f | ∀ g h, permPartition g = permPartition h → f g = f h} + zero_mem' := by + change ∀ g h, permPartition g = permPartition h → (0 : Equiv.Perm (Fin n) → ℂ) g = 0 + intro g h hh; rfl + add_mem' := by intro f h hf hh g k hk; simp only [Pi.add_apply, hf g k hk, hh g k hk] + smul_mem' := by intro c f hf g k hk; simp only [Pi.smul_apply, hf g k hk] + +/- Select one representative where a cycle partition is realized; unused +coordinates are zero. This gives an injection even without surjectivity of +cycle-type realization. -/ +def classEvaluation (n : ℕ) : (classFunctions n) →ₗ[ℂ] (Nat.Partition n → ℂ) where + toFun f p := if h : ∃ g : Equiv.Perm (Fin n), permPartition g = p then f.val h.choose else 0 + map_add' f h := by + ext p + simp only [Pi.add_apply, Submodule.coe_add] + split_ifs <;> simp + map_smul' c f := by + ext p + simp only [Pi.smul_apply, Submodule.coe_smul, RingHom.id_apply] + split_ifs <;> simp + +lemma classEvaluation_injective (n : ℕ) : Function.Injective (classEvaluation n) := by + intro f h he + apply Subtype.ext + funext g + have hh := congrFun he (permPartition g) + have hex : ∃ k : Equiv.Perm (Fin n), permPartition k = permPartition g := ⟨g, rfl⟩ + change (if hc : ∃ k : Equiv.Perm (Fin n), permPartition k = permPartition g then + f.val hc.choose else 0) = (if hc : ∃ k : Equiv.Perm (Fin n), permPartition k = permPartition g then + h.val hc.choose else 0) at hh + rw [dite_eq_left hex, dite_eq_left hex] at hh + exact (f.property _ _ hex.choose_spec).symm.trans (hh.trans (h.property _ _ hex.choose_spec)) + +lemma classFunctions_finrank_le (n : ℕ) : + Module.finrank ℂ (classFunctions n) ≤ Fintype.card (Nat.Partition n) := by + have h := LinearMap.finrank_le_finrank_of_injective (classEvaluation_injective n) + simpa using h + +lemma char_mem_classFunctions {n : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] + [Module.Finite ℂ V] (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) : + ρ.character ∈ classFunctions n := by + intro g h he + obtain ⟨k, rfl⟩ := isConj_iff.mp (isConj_of_permPartition_eq he) + exact (Representation.char_conj ρ g k).symm + +/- Character of the actual Specht module as an actual class function. -/ +def spechtCharacter {n : ℕ} (p : Nat.Partition n) : classFunctions n := + ⟨(spechtRep (partitionTableau p)).character, char_mem_classFunctions _⟩ + +/- Bilinear character scalar product used by the finite-group orthogonality theorem. -/ +def charFunctional {G : Type uG} [Group G] [Fintype G] (y : G → ℂ) : (G → ℂ) →ₗ[ℂ] ℂ where + toFun x := (Nat.card G : ℂ)⁻¹ * ∑ g, x g * y g⁻¹ + map_add' x z := by simp [Finset.sum_add_distrib, add_mul, mul_add] + map_smul' c x := by simp [Finset.mul_sum, mul_assoc, mul_left_comm] + +lemma complex_card_ne_zero (G : Type uG) [Group G] [Fintype G] : (Nat.card G : ℂ) ≠ 0 := by + exact_mod_cast Nat.card_pos.ne' + +lemma spechtCharacter_orthonormal {n : ℕ} (p q : Nat.Partition n) : + charFunctional (spechtCharacter q).val (spechtCharacter p).val = if p = q then 1 else 0 := by + classical + let : Invertible (Nat.card (Equiv.Perm (Fin n)) : ℂ) := + invertibleOfNonzero (complex_card_ne_zero _) + let := specht_irreducible (partitionTableau p) + let := specht_irreducible (partitionTableau q) + have h := Representation.char_orthonormal (spechtRep (partitionTableau p)) + (spechtRep (partitionTableau q)) + change _ = _ at h + have he : Nonempty ((spechtRep (partitionTableau q)).Equiv + (spechtRep (partitionTableau p))) ↔ p = q := by + constructor + · rintro ⟨e⟩ + exact (partitionDiagram_injective + (specht_shape_rigidity (partitionTableau q) (partitionTableau p) e)).symm + · rintro rfl + exact ⟨Representation.Equiv.refl _⟩ + simpa only [he, charFunctional, spechtCharacter, LinearMap.coe_mk, AddHom.coe_mk] using h + +lemma spechtCharacter_linearIndependent (n : ℕ) : + LinearIndependent ℂ (spechtCharacter (n := n)) := by + classical + rw [Fintype.linearIndependent_iff] + intro c hc p + have h := congrArg (fun f : classFunctions n => charFunctional (spechtCharacter p).val f.val) hc + change charFunctional (spechtCharacter p).val + ((classFunctions n).subtype (∑ i, c i • spechtCharacter i)) = + charFunctional (spechtCharacter p).val ((classFunctions n).subtype 0) at h + simp only [map_sum, map_smul, map_zero] at h + change (∑ i, c i * charFunctional (spechtCharacter p).val (spechtCharacter i).val) = 0 at h + simp_rw [spechtCharacter_orthonormal] at h + simpa using h + +lemma spechtCharacter_span (n : ℕ) : + Submodule.span ℂ (Set.range (spechtCharacter (n := n))) = ⊤ := by + apply (spechtCharacter_linearIndependent n).span_eq_top_of_card_eq_finrank' + exact le_antisymm (spechtCharacter_linearIndependent n).fintype_card_le_finrank + (classFunctions_finrank_le n) + + + +theorem irreducible_equiv_specht {n : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] + [Module.Finite ℂ V] (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) + [Representation.IsIrreducible ρ] : + ∃ p : Nat.Partition n, Nonempty (ρ.Equiv (spechtRep (partitionTableau p))) := by + classical + let : Invertible (Nat.card (Equiv.Perm (Fin n)) : ℂ) := + invertibleOfNonzero (complex_card_ne_zero _) + by_contra h + push Not at h + let f : (classFunctions n) →ₗ[ℂ] ℂ := + (charFunctional ρ.character).comp (classFunctions n).subtype + have hf : ∀ p : Nat.Partition n, f (spechtCharacter p) = 0 := by + intro p + let := specht_irreducible (partitionTableau p) + have hp := Representation.char_orthonormal (spechtRep (partitionTableau p)) ρ + rw [ite_eq_right (fun he => (h p).false he.some)] at hp + exact hp + have hk : Submodule.span ℂ (Set.range (spechtCharacter (n := n))) ≤ LinearMap.ker f := by + rw [Submodule.span_le] + rintro _ ⟨p, rfl⟩ + exact hf p + rw [spechtCharacter_span] at hk + have hz := hk (show (⟨ρ.character, char_mem_classFunctions ρ⟩ : classFunctions n) ∈ ⊤ from trivial) + change charFunctional ρ.character ρ.character = 0 at hz + have hone := Representation.char_orthonormal ρ ρ + rw [ite_eq_left ⟨Representation.Equiv.refl ρ⟩] at hone + exact one_ne_zero (hone.symm.trans hz) + + + +lemma columnAlt_eq_zero_of_rows {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (hd : d < μ.colLen 0) : columnAlt (d := d) t = 0 := by + classical + have hz : ∀ a : Fin n → Fin d, columnAlt t (Pi.single a (1 : ℂ)) = 0 := by + intro a + let j : Fin (μ.colLen 0) → Fin n := fun i => t.symm + ⟨(i.val, 0), YoungDiagram.mem_iff_lt_colLen.mpr i.isLt⟩ + have hnot : ¬ Function.Injective (a ∘ j) := by + intro hi + have hh := Fintype.card_le_of_injective _ hi + simp only [Fintype.card_fin] at hh + omega + simp only [Function.Injective] at hnot + push Not at hnot + obtain ⟨i, k, ha, hik⟩ := hnot + have hj : j i ≠ j k := by + intro he + apply hik + apply Fin.ext + have hh := congrArg (fun l => (t l).val.1) he + simpa [j] using hh + exact columnAlt_collision t a (j i) (j k) hj (by simp [j]) ha + apply LinearMap.ext + intro x + have he : x = ∑ a, x a • Pi.single a (1 : ℂ) := by + ext b + simp [Pi.single_apply] + rw [he, map_sum] + simp only [map_smul, hz, smul_zero, Finset.sum_const_zero, LinearMap.zero_apply] + +/- A Specht constituent of a `d`-letter position representation has at most +`d` rows, proved by the genuine first-column antisymmetrizer. -/ +theorem specht_rows_of_hom {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (f : Representation.IntertwiningMap (spechtRep t) (wordRep n d)) (hf : f ≠ 0) : + μ.colLen 0 ≤ d := by + classical + let := specht_irreducible t + have hi := (Representation.IsIrreducible.injective_or_eq_zero f).resolve_right hf + by_contra h + have hd : d < μ.colLen 0 := lt_of_not_ge h + let p : Specht t := ⟨polytabloid t, mem_cyclic _ _⟩ + have he := columnOperator_intertwining t f p + change f (columnOperator t (spechtRep t) p) = columnAlt t (f p) at he + rw [columnAlt_eq_zero_of_rows t hd, LinearMap.zero_apply] at he + have hz : columnOperator t (spechtRep t) p = 0 := hi (he.trans (map_zero f).symm) + exact columnAlt_polytabloid_ne_zero t + ((columnOperator_subtype t (spechtSub t) p).symm.trans (congrArg Subtype.val hz)) + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/SpechtDuality.lean b/lean/OAI/RepresentationTheory/Saxl/SpechtDuality.lean index 895bf9abab42ee139d700b5c89da103cb5362f56..54c3af8724268c24bf010d6b5ab4c1925de387ca 100644 --- a/lean/OAI/RepresentationTheory/Saxl/SpechtDuality.lean +++ b/lean/OAI/RepresentationTheory/Saxl/SpechtDuality.lean @@ -1,145 +1,145 @@ -import OAI.RepresentationTheory.Saxl.SpechtSubmodule - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl - -/- The ordinary bilinear coordinate pairing restricted to any invariant word subspace. -/ -def subrepPairMap {n d : ℕ} (S : Subrepresentation (wordRep n d)) : - Representation.IntertwiningMap S.toRepresentation S.toRepresentation.dual where - toLinearMap := - { toFun := fun x => - { toFun := fun y => dotProduct x.val y.val - map_add' := by intro y z; exact dotProduct_add _ _ _ - map_smul' := by intro a y; exact dotProduct_smul a _ _ } - map_add' := by intro x y; ext z; exact add_dotProduct _ _ _ - map_smul' := by intro a x; ext z; exact smul_dotProduct a _ _ } - isIntertwining' g := by - ext x y - exact wordPair_move g x.val y.val - -lemma subrepPairMap_injective {n d : ℕ} (S : Subrepresentation (wordRep n d)) - (hS : ∀ x ∈ S.toSubmodule, star x ∈ S.toSubmodule) : - Function.Injective (subrepPairMap S) := by - classical - apply (subrepPairMap S).toLinearMap.ker_eq_bot.mp - apply (Submodule.eq_bot_iff _).mpr - intro x hx - have hh : subrepPairMap S x = 0 := hx - have hz : dotProduct x.val (star x.val) = 0 := - congrArg (fun f : Module.Dual ℂ S.toSubmodule => f ⟨star x.val, hS x.val x.property⟩) hh - let : PartialOrder ℂ := RCLike.toPartialOrder - let : StarOrderedRing ℂ := RCLike.toStarOrderedRing - exact Subtype.ext (dotProduct_self_star_eq_zero.mp hz) - -/- Complex conjugation-stable invariant word subspaces are canonically self-dual -via bilinear evaluation, yielding equivariant projections. -/ -def subrepSelfDual {n d : ℕ} (S : Subrepresentation (wordRep n d)) - (hS : ∀ x ∈ S.toSubmodule, star x ∈ S.toSubmodule) : - Representation.Equiv S.toRepresentation S.toRepresentation.dual := - (subrepPairMap S).ofBijective - ⟨subrepPairMap_injective S hS, - (LinearMap.injective_iff_surjective_of_finrank_eq_finrank - (Subspace.dual_finrank_eq (K := ℂ) (V := S.toSubmodule)).symm).mp (subrepPairMap_injective S hS)⟩ - -/- Actual self-duality of every complex Specht representation. -/ -def spechtSelfDual {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - Representation.Equiv (spechtRep t) (spechtRep t).dual := - subrepSelfDual (spechtSub t) (fun _ hx => cyclic_star _ (polytabloid_real t) hx) - -/- Restriction of the ambient bilinear coordinate pairing to an invariant subspace. -/ -def subrepPairFromAmbient {n d : ℕ} (S : Subrepresentation (wordRep n d)) : - Representation.IntertwiningMap (wordRep n d) S.toRepresentation.dual where - toLinearMap := - { toFun := fun x => - { toFun := fun y => dotProduct x y.val - map_add' := by intro y z; exact dotProduct_add _ _ _ - map_smul' := by intro a y; exact dotProduct_smul a _ _ } - map_add' := by intro x y; ext z; exact add_dotProduct _ _ _ - map_smul' := by intro a x; ext z; exact smul_dotProduct a _ _ } - isIntertwining' g := by - apply LinearMap.ext - intro x - apply LinearMap.ext - intro y - exact wordPair_move g x y.val - -/- The genuine equivariant orthogonal-coordinate projection. -/ -def subrepProject {n d : ℕ} (S : Subrepresentation (wordRep n d)) - (hS : ∀ x ∈ S.toSubmodule, star x ∈ S.toSubmodule) : - Representation.IntertwiningMap (wordRep n d) S.toRepresentation := - (subrepSelfDual S hS).symm.toIntertwiningMap.comp (subrepPairFromAmbient S) - -lemma subrepProject_pair {n d : ℕ} (S : Subrepresentation (wordRep n d)) - (hS : ∀ x ∈ S.toSubmodule, star x ∈ S.toSubmodule) - (x : WordSpace n d) (y : S.toSubmodule) : - dotProduct (subrepProject S hS x).val y.val = dotProduct x y.val := by - have hh := (subrepSelfDual S hS).apply_symm_apply (subrepPairFromAmbient S x) - exact congrArg (fun f : Module.Dual ℂ S.toSubmodule => f y) hh - -/- A tensor power of a single letter-linear map, in ordinary word coordinates. -/ -def wordMap {n d e : ℕ} (L : Fin d → Fin e → ℂ) : - Representation.IntertwiningMap (wordRep n d) (wordRep n e) where - toLinearMap := - { toFun := fun x b => ∑ a, x a * ∏ i, L (a i) (b i) - map_add' := by - intro x y - ext b - simp only [Pi.add_apply, add_mul, Finset.sum_add_distrib] - map_smul' := by - intro c x - ext b - simp only [Pi.smul_apply, smul_eq_mul, Finset.mul_sum, mul_assoc, - RingHom.id_apply] } - isIntertwining' g := by - apply LinearMap.ext - intro x - funext b - change (∑ a, x (a ∘ g) * ∏ i, L (a i) (b i)) = - ∑ a, x a * ∏ i, L (a i) (b (g i)) - apply Eq.trans ?_ (Equiv.sum_comp (wordPerm n d g) - (fun a => x a * ∏ i, L (a i) (b (g i)))) - apply Finset.sum_congr rfl - intro a ha - dsimp [wordPerm] - congr 1 - exact (Equiv.prod_comp g (fun i => L (a i) (b i))).symm - -@[simp] lemma wordMap_single {n d e : ℕ} (L : Fin d → Fin e → ℂ) - (a : Fin n → Fin d) (b : Fin n → Fin e) : - wordMap L (Pi.single a 1) b = ∏ i, L (a i) (b i) := by - classical - simp [wordMap, Pi.single_apply] - -/- A nonzero contraction with a real cyclic vector gives an actual nonzero -intertwiner into its cyclic representation. -/ -theorem hom_to_cyclic_of_pair {n d e : ℕ} (L : Fin d → Fin e → ℂ) - (S : Subrepresentation (wordRep n d)) (x : S.toSubmodule) - (u : WordSpace n e) (hu : star u = u) - (h : dotProduct (wordMap L x.val) u ≠ 0) : - ∃ f : Representation.IntertwiningMap S.toRepresentation - (cyclic (wordRep n e) u).toRepresentation, f ≠ 0 := by - let inc : Representation.IntertwiningMap S.toRepresentation (wordRep n d) := - { toLinearMap := S.toSubmodule.subtype - isIntertwining' := fun g => rfl } - let f := (subrepProject (cyclic (wordRep n e) u) - (fun _ hx => cyclic_star u hu hx)).comp ((wordMap L).comp inc) - refine ⟨f, ?_⟩ - intro hf - have hp := subrepProject_pair (cyclic (wordRep n e) u) - (fun _ hx => cyclic_star u hu hx) (wordMap L x.val) ⟨u, mem_cyclic _ _⟩ - have he : f x = 0 := by rw [hf]; rfl - change (subrepProject (cyclic (wordRep n e) u) - (fun _ hx => cyclic_star u hu hx)) (wordMap L x.val) = 0 at he - rw [he] at hp - exact h (hp.symm.trans (zero_dotProduct _)) - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.SpechtSubmodule + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl + +/- The ordinary bilinear coordinate pairing restricted to any invariant word subspace. -/ +def subrepPairMap {n d : ℕ} (S : Subrepresentation (wordRep n d)) : + Representation.IntertwiningMap S.toRepresentation S.toRepresentation.dual where + toLinearMap := + { toFun := fun x => + { toFun := fun y => dotProduct x.val y.val + map_add' := by intro y z; exact dotProduct_add _ _ _ + map_smul' := by intro a y; exact dotProduct_smul a _ _ } + map_add' := by intro x y; ext z; exact add_dotProduct _ _ _ + map_smul' := by intro a x; ext z; exact smul_dotProduct a _ _ } + isIntertwining' g := by + ext x y + exact wordPair_move g x.val y.val + +lemma subrepPairMap_injective {n d : ℕ} (S : Subrepresentation (wordRep n d)) + (hS : ∀ x ∈ S.toSubmodule, star x ∈ S.toSubmodule) : + Function.Injective (subrepPairMap S) := by + classical + apply (subrepPairMap S).toLinearMap.ker_eq_bot.mp + apply (Submodule.eq_bot_iff _).mpr + intro x hx + have hh : subrepPairMap S x = 0 := hx + have hz : dotProduct x.val (star x.val) = 0 := + congrArg (fun f : Module.Dual ℂ S.toSubmodule => f ⟨star x.val, hS x.val x.property⟩) hh + let : PartialOrder ℂ := RCLike.toPartialOrder + let : StarOrderedRing ℂ := RCLike.toStarOrderedRing + exact Subtype.ext (dotProduct_self_star_eq_zero.mp hz) + +/- Complex conjugation-stable invariant word subspaces are canonically self-dual +via bilinear evaluation, yielding equivariant projections. -/ +def subrepSelfDual {n d : ℕ} (S : Subrepresentation (wordRep n d)) + (hS : ∀ x ∈ S.toSubmodule, star x ∈ S.toSubmodule) : + Representation.Equiv S.toRepresentation S.toRepresentation.dual := + (subrepPairMap S).ofBijective + ⟨subrepPairMap_injective S hS, + (LinearMap.injective_iff_surjective_of_finrank_eq_finrank + (Subspace.dual_finrank_eq (K := ℂ) (V := S.toSubmodule)).symm).mp (subrepPairMap_injective S hS)⟩ + +/- Actual self-duality of every complex Specht representation. -/ +def spechtSelfDual {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + Representation.Equiv (spechtRep t) (spechtRep t).dual := + subrepSelfDual (spechtSub t) (fun _ hx => cyclic_star _ (polytabloid_real t) hx) + +/- Restriction of the ambient bilinear coordinate pairing to an invariant subspace. -/ +def subrepPairFromAmbient {n d : ℕ} (S : Subrepresentation (wordRep n d)) : + Representation.IntertwiningMap (wordRep n d) S.toRepresentation.dual where + toLinearMap := + { toFun := fun x => + { toFun := fun y => dotProduct x y.val + map_add' := by intro y z; exact dotProduct_add _ _ _ + map_smul' := by intro a y; exact dotProduct_smul a _ _ } + map_add' := by intro x y; ext z; exact add_dotProduct _ _ _ + map_smul' := by intro a x; ext z; exact smul_dotProduct a _ _ } + isIntertwining' g := by + apply LinearMap.ext + intro x + apply LinearMap.ext + intro y + exact wordPair_move g x y.val + +/- The genuine equivariant orthogonal-coordinate projection. -/ +def subrepProject {n d : ℕ} (S : Subrepresentation (wordRep n d)) + (hS : ∀ x ∈ S.toSubmodule, star x ∈ S.toSubmodule) : + Representation.IntertwiningMap (wordRep n d) S.toRepresentation := + (subrepSelfDual S hS).symm.toIntertwiningMap.comp (subrepPairFromAmbient S) + +lemma subrepProject_pair {n d : ℕ} (S : Subrepresentation (wordRep n d)) + (hS : ∀ x ∈ S.toSubmodule, star x ∈ S.toSubmodule) + (x : WordSpace n d) (y : S.toSubmodule) : + dotProduct (subrepProject S hS x).val y.val = dotProduct x y.val := by + have hh := (subrepSelfDual S hS).apply_symm_apply (subrepPairFromAmbient S x) + exact congrArg (fun f : Module.Dual ℂ S.toSubmodule => f y) hh + +/- A tensor power of a single letter-linear map, in ordinary word coordinates. -/ +def wordMap {n d e : ℕ} (L : Fin d → Fin e → ℂ) : + Representation.IntertwiningMap (wordRep n d) (wordRep n e) where + toLinearMap := + { toFun := fun x b => ∑ a, x a * ∏ i, L (a i) (b i) + map_add' := by + intro x y + ext b + simp only [Pi.add_apply, add_mul, Finset.sum_add_distrib] + map_smul' := by + intro c x + ext b + simp only [Pi.smul_apply, smul_eq_mul, Finset.mul_sum, mul_assoc, + RingHom.id_apply] } + isIntertwining' g := by + apply LinearMap.ext + intro x + funext b + change (∑ a, x (a ∘ g) * ∏ i, L (a i) (b i)) = + ∑ a, x a * ∏ i, L (a i) (b (g i)) + apply Eq.trans ?_ (Equiv.sum_comp (wordPerm n d g) + (fun a => x a * ∏ i, L (a i) (b (g i)))) + apply Finset.sum_congr rfl + intro a ha + dsimp [wordPerm] + congr 1 + exact (Equiv.prod_comp g (fun i => L (a i) (b i))).symm + +@[simp] lemma wordMap_single {n d e : ℕ} (L : Fin d → Fin e → ℂ) + (a : Fin n → Fin d) (b : Fin n → Fin e) : + wordMap L (Pi.single a 1) b = ∏ i, L (a i) (b i) := by + classical + simp [wordMap, Pi.single_apply] + +/- A nonzero contraction with a real cyclic vector gives an actual nonzero +intertwiner into its cyclic representation. -/ +theorem hom_to_cyclic_of_pair {n d e : ℕ} (L : Fin d → Fin e → ℂ) + (S : Subrepresentation (wordRep n d)) (x : S.toSubmodule) + (u : WordSpace n e) (hu : star u = u) + (h : dotProduct (wordMap L x.val) u ≠ 0) : + ∃ f : Representation.IntertwiningMap S.toRepresentation + (cyclic (wordRep n e) u).toRepresentation, f ≠ 0 := by + let inc : Representation.IntertwiningMap S.toRepresentation (wordRep n d) := + { toLinearMap := S.toSubmodule.subtype + isIntertwining' := fun g => rfl } + let f := (subrepProject (cyclic (wordRep n e) u) + (fun _ hx => cyclic_star u hu hx)).comp ((wordMap L).comp inc) + refine ⟨f, ?_⟩ + intro hf + have hp := subrepProject_pair (cyclic (wordRep n e) u) + (fun _ hx => cyclic_star u hu hx) (wordMap L x.val) ⟨u, mem_cyclic _ _⟩ + have he : f x = 0 := by rw [hf]; rfl + change (subrepProject (cyclic (wordRep n e) u) + (fun _ hx => cyclic_star u hu hx)) (wordMap L x.val) = 0 at he + rw [he] at hp + exact h (hp.symm.trans (zero_dotProduct _)) + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/SpechtSubmodule.lean b/lean/OAI/RepresentationTheory/Saxl/SpechtSubmodule.lean index 282c7c8b402078e38e491ac05a0af95d335608c5..095960265592a054bddadf8ed13c1b58ab09ce4d 100644 --- a/lean/OAI/RepresentationTheory/Saxl/SpechtSubmodule.lean +++ b/lean/OAI/RepresentationTheory/Saxl/SpechtSubmodule.lean @@ -1,232 +1,232 @@ -import OAI.RepresentationTheory.Saxl.Polytabloid - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uG uV - -namespace Saxl - -lemma mem_cyclic {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] - (ρ : Representation ℂ G V) (v : V) : v ∈ cyclic ρ v := by - change v ∈ Submodule.span ℂ _ - apply Submodule.subset_span - exact ⟨1, by simp⟩ - -lemma cyclic_le {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] - (ρ : Representation ℂ G V) (v : V) (P : Subrepresentation ρ) : - cyclic ρ v ≤ P ↔ v ∈ P := by - constructor - · intro h - exact h (mem_cyclic ρ v) - · intro hv - change Submodule.span ℂ _ ≤ P.toSubmodule - rw [Submodule.span_le] - rintro _ ⟨g, rfl⟩ - exact P.apply_mem_toSubmodule g hv - -/- The actual row-tabloid permutation module, embedded in the word space. -/ -def tabloidSub {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) := - cyclic (wordRep n (μ.colLen 0)) (Pi.single (rowWord t) 1) - -lemma columnAlt_mem {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (P : Subrepresentation (wordRep n d)) {x : WordSpace n d} (hx : x ∈ P) : - columnAlt t x ∈ P := by - classical - unfold columnAlt - simp only [LinearMap.sum_apply, LinearMap.smul_apply] - exact Submodule.sum_mem _ (fun g _ => - Submodule.smul_mem _ _ (P.apply_mem_toSubmodule (g : Equiv.Perm (Fin n)) hx)) - -lemma spechtSub_le_tabloidSub {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - spechtSub t ≤ tabloidSub t := by - apply (cyclic_le _ _ _).mpr - rw [← columnAlt_row] - exact columnAlt_mem t (tabloidSub t) (mem_cyclic _ _) - -/- The Ferrers shape forces the column antisymmetrizer to have rank one -on the row-tabloid module. -/ -lemma columnAlt_tabloid {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - {x : WordSpace n (μ.colLen 0)} (hx : x ∈ tabloidSub t) : - columnAlt t x ∈ Submodule.span ℂ {polytabloid t} := by - classical - induction hx using Submodule.span_induction with - | mem x hx => - obtain ⟨g, rfl⟩ := hx - dsimp only - rw [wordRep_single] - exact columnAlt_single t g⁻¹ - | zero => simpa only [map_zero] using (Submodule.zero_mem (Submodule.span ℂ {polytabloid t})) - | add x y hx hy ihx ihy => - simpa only [map_add] using Submodule.add_mem _ ihx ihy - | smul c x hx ih => - simpa only [map_smul] using Submodule.smul_mem _ c ih - -@[simp] lemma wordRep_star {n d : ℕ} (g : Equiv.Perm (Fin n)) (x : WordSpace n d) : - star (wordRep n d g x) = wordRep n d g (star x) := rfl - -lemma polytabloid_real {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - star (polytabloid t) = polytabloid t := by - classical - unfold polytabloid - rw [star_sum] - apply Finset.sum_congr rfl - intro g hg - rw [star_smul, wordRep_star] - simp only [star_intCast] - congr 2 - ext a - simp [Pi.single_apply] - -lemma cyclic_star {n d : ℕ} (v : WordSpace n d) (hv : star v = v) - {x : WordSpace n d} (hx : x ∈ cyclic (wordRep n d) v) : - star x ∈ cyclic (wordRep n d) v := by - change star x ∈ (cyclic (wordRep n d) v).toSubmodule - induction hx using Submodule.span_induction with - | mem x hx => - obtain ⟨g, rfl⟩ := hx - dsimp only - rw [wordRep_star, hv] - exact (cyclic (wordRep n d) v).apply_mem_toSubmodule g (mem_cyclic _ _) - | zero => simpa only [star_zero] using (Submodule.zero_mem (cyclic (wordRep n d) v).toSubmodule) - | add x y hx hy ihx ihy => - simpa only [star_add] using Submodule.add_mem _ ihx ihy - | smul c x hx ih => - simpa only [star_smul] using Submodule.smul_mem _ (star c) ih - -/- On words, precomposition by a position permutation is a bijection. -/ -def wordPerm (n d : ℕ) (g : Equiv.Perm (Fin n)) : Equiv.Perm (Fin n → Fin d) where - toFun a := a ∘ g - invFun a := a ∘ (g⁻¹ : Equiv.Perm (Fin n)) - left_inv a := by ext i; simp - right_inv a := by ext i; simp - -lemma wordPair_move {n d : ℕ} (g : Equiv.Perm (Fin n)) (x y : WordSpace n d) : - dotProduct (wordRep n d g x) y = dotProduct x (wordRep n d g⁻¹ y) := by - have hh := Equiv.sum_comp (wordPerm n d g) - (fun a => x a * y (a ∘ (g⁻¹ : Equiv.Perm (Fin n)))) - simpa [dotProduct, wordPerm, wordRep, Function.comp_assoc] using hh - -lemma columnAlt_pair {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (x y : WordSpace n d) : - dotProduct (columnAlt t x) y = dotProduct x (columnAlt t y) := by - classical - let := Fintype.ofFinite (columnGroup t) - unfold columnAlt - simp only [LinearMap.sum_apply, LinearMap.smul_apply, sum_dotProduct, - dotProduct_sum, smul_dotProduct, dotProduct_smul, wordPair_move] - apply (Equiv.sum_comp (Equiv.inv (columnGroup t)) _).symm.trans - apply Finset.sum_congr rfl - intro g hg - simp only [Equiv.inv_apply, Subgroup.coe_inv, signC_inv, inv_inv] - -lemma columnAlt_coefficient {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (x : WordSpace n (μ.colLen 0)) : - columnAlt t x (rowWord t) = dotProduct x (polytabloid t) := by - classical - rw [← dotProduct_single_one (columnAlt t x), columnAlt_pair, columnAlt_row] - -lemma polytabloid_ne_zero {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - polytabloid t ≠ 0 := by - intro h - have hh := congrFun h (rowWord t) - rw [polytabloid_rowWord] at hh - exact one_ne_zero hh - -lemma specht_detect {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - {x : WordSpace n (μ.colLen 0)} (hx : x ∈ spechtSub t) (hx0 : x ≠ 0) : - ∃ g : Equiv.Perm (Fin n), dotProduct (wordRep n (μ.colLen 0) g x) (polytabloid t) ≠ 0 := by - classical - by_contra h - push Not at h - have hy : ∀ y ∈ (spechtSub t).toSubmodule, dotProduct x y = 0 := by - intro y hy - induction hy using Submodule.span_induction with - | mem y hy => - obtain ⟨g, rfl⟩ := hy - have hh := wordPair_move g⁻¹ x (polytabloid t) - rw [inv_inv] at hh - exact hh.symm.trans (h g⁻¹) - | zero => exact dotProduct_zero _ - | add y z hy hz ihy ihz => rw [dotProduct_add, ihy, ihz, add_zero] - | smul c y hy ih => rw [dotProduct_smul, ih, smul_zero] - have hs : star x ∈ (spechtSub t).toSubmodule := - cyclic_star (polytabloid t) (polytabloid_real t) hx - let : PartialOrder ℂ := RCLike.toPartialOrder - let : StarOrderedRing ℂ := RCLike.toStarOrderedRing - exact hx0 (dotProduct_self_star_eq_zero.mp (hy (star x) hs)) - -/- Every nonzero vector in the genuine complex Specht cyclic subspace -again generates that whole subspace. -/ -theorem specht_cyclic_of_ne_zero {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - {x : WordSpace n (μ.colLen 0)} (hx : x ∈ spechtSub t) (hx0 : x ≠ 0) : - cyclic (wordRep n (μ.colLen 0)) x = spechtSub t := by - classical - apply le_antisymm ((cyclic_le _ _ _).mpr hx) - apply (cyclic_le _ _ _).mpr - obtain ⟨g, hg⟩ := specht_detect t hx hx0 - have he : wordRep n (μ.colLen 0) g x ∈ spechtSub t := - (spechtSub t).apply_mem_toSubmodule g hx - obtain ⟨c, hc⟩ := Submodule.mem_span_singleton.mp - (columnAlt_tabloid t (spechtSub_le_tabloidSub t he)) - have hc0 : c ≠ 0 := by - intro h0 - rw [h0, zero_smul] at hc - apply hg - rw [← columnAlt_coefficient, ← hc] - rfl - have hh := columnAlt_mem t (cyclic (wordRep n (μ.colLen 0)) x) - ((cyclic (wordRep n (μ.colLen 0)) x).apply_mem_toSubmodule g (mem_cyclic _ _)) - rw [← hc] at hh - exact (Submodule.smul_mem_iff _ hc0).mp hh - -/- Inclusion of a subrepresentation of a subrepresentation into the ambient space. -/ -def subrepAmbient {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] - {ρ : Representation ℂ G V} (U : Subrepresentation ρ) - (S : Subrepresentation U.toRepresentation) : Subrepresentation ρ where - toSubmodule := S.toSubmodule.map U.toSubmodule.subtype - apply_mem_toSubmodule g x hx := by - obtain ⟨y, hy, rfl⟩ := hx - exact ⟨U.toRepresentation g y, S.apply_mem_toSubmodule g hy, rfl⟩ - -/- The complex polytabloid module is irreducible. -/ -theorem specht_irreducible {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - Representation.IsIrreducible (spechtRep t) := by - classical - have hb : (⊥ : Subrepresentation (spechtRep t)) ≠ ⊤ := by - intro h - have hp : (⟨polytabloid t, mem_cyclic _ _⟩ : Specht t) ∈ - (⊥ : Subrepresentation (spechtRep t)).toSubmodule := by - rw [h] - trivial - have he : (⟨polytabloid t, mem_cyclic _ _⟩ : Specht t) = 0 := - (Submodule.mem_bot ℂ).mp hp - exact polytabloid_ne_zero t (congrArg Subtype.val he) - let : Nontrivial (Subrepresentation (spechtRep t)) := ⟨⟨⊥, ⊤, hb⟩⟩ - apply IsSimpleOrder.of_forall_eq_top - intro S hS - have hn : S.toSubmodule ≠ ⊥ := by - intro h - exact hS (Subrepresentation.toSubmodule_injective h) - obtain ⟨x, hx, hx0⟩ := (Submodule.ne_bot_iff S.toSubmodule).mp hn - have hv : (x : WordSpace n (μ.colLen 0)) ≠ 0 := by - intro h - exact hx0 (Subtype.ext h) - have hl : cyclic (wordRep n (μ.colLen 0)) x.val ≤ subrepAmbient (spechtSub t) S := - (cyclic_le _ _ _).mpr ⟨x, hx, rfl⟩ - rw [specht_cyclic_of_ne_zero t x.property hv] at hl - apply le_antisymm le_top - intro y hy - have hm := hl y.property - obtain ⟨z, hz, he⟩ := hm - have he' : z = y := Subtype.ext he - exact he' ▸ hz - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.Polytabloid + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uG uV + +namespace Saxl + +lemma mem_cyclic {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] + (ρ : Representation ℂ G V) (v : V) : v ∈ cyclic ρ v := by + change v ∈ Submodule.span ℂ _ + apply Submodule.subset_span + exact ⟨1, by simp⟩ + +lemma cyclic_le {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] + (ρ : Representation ℂ G V) (v : V) (P : Subrepresentation ρ) : + cyclic ρ v ≤ P ↔ v ∈ P := by + constructor + · intro h + exact h (mem_cyclic ρ v) + · intro hv + change Submodule.span ℂ _ ≤ P.toSubmodule + rw [Submodule.span_le] + rintro _ ⟨g, rfl⟩ + exact P.apply_mem_toSubmodule g hv + +/- The actual row-tabloid permutation module, embedded in the word space. -/ +def tabloidSub {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) := + cyclic (wordRep n (μ.colLen 0)) (Pi.single (rowWord t) 1) + +lemma columnAlt_mem {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (P : Subrepresentation (wordRep n d)) {x : WordSpace n d} (hx : x ∈ P) : + columnAlt t x ∈ P := by + classical + unfold columnAlt + simp only [LinearMap.sum_apply, LinearMap.smul_apply] + exact Submodule.sum_mem _ (fun g _ => + Submodule.smul_mem _ _ (P.apply_mem_toSubmodule (g : Equiv.Perm (Fin n)) hx)) + +lemma spechtSub_le_tabloidSub {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + spechtSub t ≤ tabloidSub t := by + apply (cyclic_le _ _ _).mpr + rw [← columnAlt_row] + exact columnAlt_mem t (tabloidSub t) (mem_cyclic _ _) + +/- The Ferrers shape forces the column antisymmetrizer to have rank one +on the row-tabloid module. -/ +lemma columnAlt_tabloid {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + {x : WordSpace n (μ.colLen 0)} (hx : x ∈ tabloidSub t) : + columnAlt t x ∈ Submodule.span ℂ {polytabloid t} := by + classical + induction hx using Submodule.span_induction with + | mem x hx => + obtain ⟨g, rfl⟩ := hx + dsimp only + rw [wordRep_single] + exact columnAlt_single t g⁻¹ + | zero => simpa only [map_zero] using (Submodule.zero_mem (Submodule.span ℂ {polytabloid t})) + | add x y hx hy ihx ihy => + simpa only [map_add] using Submodule.add_mem _ ihx ihy + | smul c x hx ih => + simpa only [map_smul] using Submodule.smul_mem _ c ih + +@[simp] lemma wordRep_star {n d : ℕ} (g : Equiv.Perm (Fin n)) (x : WordSpace n d) : + star (wordRep n d g x) = wordRep n d g (star x) := rfl + +lemma polytabloid_real {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + star (polytabloid t) = polytabloid t := by + classical + unfold polytabloid + rw [star_sum] + apply Finset.sum_congr rfl + intro g hg + rw [star_smul, wordRep_star] + simp only [star_intCast] + congr 2 + ext a + simp [Pi.single_apply] + +lemma cyclic_star {n d : ℕ} (v : WordSpace n d) (hv : star v = v) + {x : WordSpace n d} (hx : x ∈ cyclic (wordRep n d) v) : + star x ∈ cyclic (wordRep n d) v := by + change star x ∈ (cyclic (wordRep n d) v).toSubmodule + induction hx using Submodule.span_induction with + | mem x hx => + obtain ⟨g, rfl⟩ := hx + dsimp only + rw [wordRep_star, hv] + exact (cyclic (wordRep n d) v).apply_mem_toSubmodule g (mem_cyclic _ _) + | zero => simpa only [star_zero] using (Submodule.zero_mem (cyclic (wordRep n d) v).toSubmodule) + | add x y hx hy ihx ihy => + simpa only [star_add] using Submodule.add_mem _ ihx ihy + | smul c x hx ih => + simpa only [star_smul] using Submodule.smul_mem _ (star c) ih + +/- On words, precomposition by a position permutation is a bijection. -/ +def wordPerm (n d : ℕ) (g : Equiv.Perm (Fin n)) : Equiv.Perm (Fin n → Fin d) where + toFun a := a ∘ g + invFun a := a ∘ (g⁻¹ : Equiv.Perm (Fin n)) + left_inv a := by ext i; simp + right_inv a := by ext i; simp + +lemma wordPair_move {n d : ℕ} (g : Equiv.Perm (Fin n)) (x y : WordSpace n d) : + dotProduct (wordRep n d g x) y = dotProduct x (wordRep n d g⁻¹ y) := by + have hh := Equiv.sum_comp (wordPerm n d g) + (fun a => x a * y (a ∘ (g⁻¹ : Equiv.Perm (Fin n)))) + simpa [dotProduct, wordPerm, wordRep, Function.comp_assoc] using hh + +lemma columnAlt_pair {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (x y : WordSpace n d) : + dotProduct (columnAlt t x) y = dotProduct x (columnAlt t y) := by + classical + let := Fintype.ofFinite (columnGroup t) + unfold columnAlt + simp only [LinearMap.sum_apply, LinearMap.smul_apply, sum_dotProduct, + dotProduct_sum, smul_dotProduct, dotProduct_smul, wordPair_move] + apply (Equiv.sum_comp (Equiv.inv (columnGroup t)) _).symm.trans + apply Finset.sum_congr rfl + intro g hg + simp only [Equiv.inv_apply, Subgroup.coe_inv, signC_inv, inv_inv] + +lemma columnAlt_coefficient {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (x : WordSpace n (μ.colLen 0)) : + columnAlt t x (rowWord t) = dotProduct x (polytabloid t) := by + classical + rw [← dotProduct_single_one (columnAlt t x), columnAlt_pair, columnAlt_row] + +lemma polytabloid_ne_zero {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + polytabloid t ≠ 0 := by + intro h + have hh := congrFun h (rowWord t) + rw [polytabloid_rowWord] at hh + exact one_ne_zero hh + +lemma specht_detect {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + {x : WordSpace n (μ.colLen 0)} (hx : x ∈ spechtSub t) (hx0 : x ≠ 0) : + ∃ g : Equiv.Perm (Fin n), dotProduct (wordRep n (μ.colLen 0) g x) (polytabloid t) ≠ 0 := by + classical + by_contra h + push Not at h + have hy : ∀ y ∈ (spechtSub t).toSubmodule, dotProduct x y = 0 := by + intro y hy + induction hy using Submodule.span_induction with + | mem y hy => + obtain ⟨g, rfl⟩ := hy + have hh := wordPair_move g⁻¹ x (polytabloid t) + rw [inv_inv] at hh + exact hh.symm.trans (h g⁻¹) + | zero => exact dotProduct_zero _ + | add y z hy hz ihy ihz => rw [dotProduct_add, ihy, ihz, add_zero] + | smul c y hy ih => rw [dotProduct_smul, ih, smul_zero] + have hs : star x ∈ (spechtSub t).toSubmodule := + cyclic_star (polytabloid t) (polytabloid_real t) hx + let : PartialOrder ℂ := RCLike.toPartialOrder + let : StarOrderedRing ℂ := RCLike.toStarOrderedRing + exact hx0 (dotProduct_self_star_eq_zero.mp (hy (star x) hs)) + +/- Every nonzero vector in the genuine complex Specht cyclic subspace +again generates that whole subspace. -/ +theorem specht_cyclic_of_ne_zero {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + {x : WordSpace n (μ.colLen 0)} (hx : x ∈ spechtSub t) (hx0 : x ≠ 0) : + cyclic (wordRep n (μ.colLen 0)) x = spechtSub t := by + classical + apply le_antisymm ((cyclic_le _ _ _).mpr hx) + apply (cyclic_le _ _ _).mpr + obtain ⟨g, hg⟩ := specht_detect t hx hx0 + have he : wordRep n (μ.colLen 0) g x ∈ spechtSub t := + (spechtSub t).apply_mem_toSubmodule g hx + obtain ⟨c, hc⟩ := Submodule.mem_span_singleton.mp + (columnAlt_tabloid t (spechtSub_le_tabloidSub t he)) + have hc0 : c ≠ 0 := by + intro h0 + rw [h0, zero_smul] at hc + apply hg + rw [← columnAlt_coefficient, ← hc] + rfl + have hh := columnAlt_mem t (cyclic (wordRep n (μ.colLen 0)) x) + ((cyclic (wordRep n (μ.colLen 0)) x).apply_mem_toSubmodule g (mem_cyclic _ _)) + rw [← hc] at hh + exact (Submodule.smul_mem_iff _ hc0).mp hh + +/- Inclusion of a subrepresentation of a subrepresentation into the ambient space. -/ +def subrepAmbient {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] + {ρ : Representation ℂ G V} (U : Subrepresentation ρ) + (S : Subrepresentation U.toRepresentation) : Subrepresentation ρ where + toSubmodule := S.toSubmodule.map U.toSubmodule.subtype + apply_mem_toSubmodule g x hx := by + obtain ⟨y, hy, rfl⟩ := hx + exact ⟨U.toRepresentation g y, S.apply_mem_toSubmodule g hy, rfl⟩ + +/- The complex polytabloid module is irreducible. -/ +theorem specht_irreducible {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + Representation.IsIrreducible (spechtRep t) := by + classical + have hb : (⊥ : Subrepresentation (spechtRep t)) ≠ ⊤ := by + intro h + have hp : (⟨polytabloid t, mem_cyclic _ _⟩ : Specht t) ∈ + (⊥ : Subrepresentation (spechtRep t)).toSubmodule := by + rw [h] + trivial + have he : (⟨polytabloid t, mem_cyclic _ _⟩ : Specht t) = 0 := + (Submodule.mem_bot ℂ).mp hp + exact polytabloid_ne_zero t (congrArg Subtype.val he) + let : Nontrivial (Subrepresentation (spechtRep t)) := ⟨⟨⊥, ⊤, hb⟩⟩ + apply IsSimpleOrder.of_forall_eq_top + intro S hS + have hn : S.toSubmodule ≠ ⊥ := by + intro h + exact hS (Subrepresentation.toSubmodule_injective h) + obtain ⟨x, hx, hx0⟩ := (Submodule.ne_bot_iff S.toSubmodule).mp hn + have hv : (x : WordSpace n (μ.colLen 0)) ≠ 0 := by + intro h + exact hx0 (Subtype.ext h) + have hl : cyclic (wordRep n (μ.colLen 0)) x.val ≤ subrepAmbient (spechtSub t) S := + (cyclic_le _ _ _).mpr ⟨x, hx, rfl⟩ + rw [specht_cyclic_of_ne_zero t x.property hv] at hl + apply le_antisymm le_top + intro y hy + have hm := hl y.property + obtain ⟨z, hz, he⟩ := hm + have he' : z = y := Subtype.ext he + exact he' ▸ hz + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/StaircaseSign.lean b/lean/OAI/RepresentationTheory/Saxl/StaircaseSign.lean index a4db547b23c2a3216caa17caac9bf60c69f852b6..ffae7a10a68e8ad44c3aa8c90a5790c504b18b1e 100644 --- a/lean/OAI/RepresentationTheory/Saxl/StaircaseSign.lean +++ b/lean/OAI/RepresentationTheory/Saxl/StaircaseSign.lean @@ -1,264 +1,264 @@ -import OAI.RepresentationTheory.Saxl.RepeatedProjection - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uX uY uZ - -namespace Saxl - -def rowReversalCell (m : ℕ) (x : (staircase m).cells) : (staircase m).cells := - ⟨(x.val.1, m-1-x.val.1-x.val.2), by - have hx : x.val.1 + x.val.2 < m := mem_staircase.mp x.property - apply mem_staircase.mpr - omega⟩ - -lemma rowReversalCell_involutive (m : ℕ) : Function.Involutive (rowReversalCell m) := by - intro x - have hx : x.val.1 + x.val.2 < m := mem_staircase.mp x.property - apply Subtype.ext - apply Prod.ext - · rfl - · change m-1-x.val.1-(m-1-x.val.1-x.val.2) = x.val.2 - omega - -def rowReversalEquiv (m : ℕ) : Equiv.Perm (staircase m).cells := - ⟨rowReversalCell m, rowReversalCell m, rowReversalCell_involutive m, rowReversalCell_involutive m⟩ - -def rowReversal (m : ℕ) : columnGroup (stairRowTableau m) := - ⟨((stairTableau m).trans (rowReversalEquiv m)).trans (stairTableau m).symm, by - intro i - change (stairTableau m ((stairTableau m).symm (rowReversalEquiv m (stairTableau m i)))).val.1 = _ - simp only [Equiv.apply_symm_apply] - rfl⟩ - -def repeatedTarget (m : ℕ) : Fin (staircase m).card → Fin ((staircase m).colLen 0) := - fun i => Fin.rev (rowWord (stairTableau m) i) - -lemma repeatedTarget_fixed (m : ℕ) (g : columnGroup (stairRowTableau m)) (i) : - repeatedTarget m (g.val i) = repeatedTarget m i := by - apply congrArg Fin.rev - apply Fin.ext - exact g.property i - -lemma repeated_letters_injective (m : ℕ) : - Function.Injective (fun i => (repeatedTarget m i, rowWord (stairRowTableau m) i)) := by - intro i j he - apply (stairTableau m).injective - apply Subtype.ext - apply Prod.ext - · have hh : Fin.rev (rowWord (stairTableau m) i) = Fin.rev (rowWord (stairTableau m) j) := - congrArg Prod.fst he - exact congrArg Fin.val (Fin.rev_injective hh) - · exact congrArg Fin.val (congrArg Prod.snd he) - -lemma repeated_complement (m : ℕ) (i) : - (rowWord (stairRowTableau m) i).val + - (rowWord (stairRowTableau m) ((rowReversal m).val i)).val = - (repeatedTarget m i).val := by - have hi : (stairTableau m i).val.1 + (stairTableau m i).val.2 < m := - mem_staircase.mp (stairTableau m i).property - simp only [rowWord, stairRowTableau, rowReversal, Equiv.trans_apply, - Equiv.apply_symm_apply, repeatedTarget, Fin.val_rev, staircase_colLen, Nat.sub_zero] - change (stairTableau m i).val.2 + (m-1-(stairTableau m i).val.1-(stairTableau m i).val.2) = - m-((stairTableau m i).val.1+1) - omega - -theorem staircase_repeated_projection (m : ℕ) : - orbitProjection (repeatedTarget m) - (pairSumMap (staircase m).card ((staircase m).colLen 0) ((staircase m).colLen 0) - (wordTensor _ _ _ (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] polytabloid (stairRowTableau m)))) = - ((Nat.card (columnGroup (stairRowTableau m)) : ℂ) * signC (rowReversal m).val) • - Pi.single (repeatedTarget m) 1 := by - exact repeated_alt_projection (columnGroup (stairRowTableau m)) - (rowWord (stairRowTableau m)) (repeatedTarget m) (rowReversal m) - (repeatedTarget_fixed m) (repeated_letters_injective m) (repeated_complement m) - -lemma staircase_repeated_projection_nonzero (m : ℕ) : - orbitProjection (repeatedTarget m) - (pairSumMap (staircase m).card ((staircase m).colLen 0) ((staircase m).colLen 0) - (wordTensor _ _ _ (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] polytabloid (stairRowTableau m)))) ≠ 0 := by - rw [staircase_repeated_projection] - apply smul_ne_zero - · apply mul_ne_zero - · exact Nat.cast_ne_zero.mpr (Nat.card_pos (α := columnGroup (stairRowTableau m))).ne' - · intro hh - have he := signC_mul_self (rowReversal m).val - rw [hh, zero_mul] at he - exact zero_ne_one he - · intro hz - have he := congrFun hz (repeatedTarget m) - simp at he - - -theorem staircase_sign_equiv (m : ℕ) : - Nonempty ((spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) := by - classical - let t := stairTableau m - let tt := stairRowTableau m - let y : Specht tt := ⟨polytabloid tt, mem_cyclic _ _⟩ - let R := signTwist (spechtRep tt) - let F := orbitAverage R (rowWord t) y - let c : ℂ := ((Finset.univ.filter - (fun g : Equiv.Perm (Fin (staircase m).card) => rowWord t ∘ g = rowWord t)).card : ℂ) - have hy : ∀ g : Equiv.Perm (Fin (staircase m).card), rowWord t ∘ g = rowWord t → R g y = y := by - intro g hg - have hc : g ∈ columnGroup tt := by - intro i - exact congrArg Fin.val (congrFun hg i) - apply Subtype.ext - change signC g • wordRep (staircase m).card ((staircase m).colLen 0) g (polytabloid tt) = polytabloid tt - rw [polytabloid_alternating tt ⟨g, hc⟩, smul_smul, signC_mul_self, one_smul] - have hF : F (Pi.single (rowWord t) 1) = c • y := orbitAverage_base R _ y hy - have hc0 : c ≠ 0 := by - apply Nat.cast_ne_zero.mpr - apply Finset.card_ne_zero.mpr - refine ⟨1, Finset.mem_filter.mpr ⟨Finset.mem_univ _, ?_⟩⟩ - rfl - have hm (g : columnGroup t) : - (F (wordRep (staircase m).card ((staircase m).colLen 0) (g : Equiv.Perm (Fin (staircase m).card)) - (Pi.single (rowWord t) 1))).val (rowWord tt) = signC (g : Equiv.Perm (Fin (staircase m).card)) * c := by - rw [F.isIntertwining, hF] - change signC (g : Equiv.Perm (Fin (staircase m).card)) * (c * - polytabloid tt (rowWord tt ∘ (g : Equiv.Perm (Fin (staircase m).card)))) = _ - have he : rowWord tt ∘ (g : Equiv.Perm (Fin (staircase m).card)) = rowWord tt := by - funext i - apply Fin.ext - exact g.property i - rw [he, polytabloid_rowWord, mul_one] - let inc : Representation.IntertwiningMap (spechtRep t) (wordRep (staircase m).card ((staircase m).colLen 0)) := - { toLinearMap := (spechtSub t).toSubmodule.subtype - isIntertwining' := fun _ => rfl } - let f := F.comp inc - have hf : f ≠ 0 := by - intro hz - have he : (F (polytabloid t)).val (rowWord tt) = 0 := by - have he := congrArg (fun l : Representation.IntertwiningMap (spechtRep t) R => - (l ⟨polytabloid t, mem_cyclic _ _⟩).val (rowWord tt)) hz - exact he - let := Fintype.ofFinite (columnGroup t) - have hp : (F (polytabloid t)).val (rowWord tt) = - (Fintype.card (columnGroup t) : ℂ) * c := by - change (F (∑ g : columnGroup t, signC (g : Equiv.Perm (Fin (staircase m).card)) • - wordRep (staircase m).card ((staircase m).colLen 0) (g : Equiv.Perm (Fin (staircase m).card)) (Pi.single (rowWord t) 1))).val _ = _ - simp only [map_sum, map_smul, Submodule.coe_sum, Submodule.coe_smul, - Finset.sum_apply, Pi.smul_apply, smul_eq_mul, hm] - simp only [← mul_assoc, signC_mul_self, one_mul, Finset.sum_const, - Finset.card_univ, nsmul_eq_mul] - have hn : (Fintype.card (columnGroup t) : ℂ) ≠ 0 := by - exact Nat.cast_ne_zero.mpr Fintype.card_ne_zero - exact (mul_ne_zero hn hc0) (hp.symm.trans he) - let := specht_irreducible t - let := specht_irreducible tt - let := signTwist_irreducible (spechtRep tt) - exact ⟨f.ofBijective ((Representation.IsIrreducible.bijective_or_eq_zero f).resolve_right hf)⟩ - -lemma alternating_specht_line {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (y : Specht t) (hy : ∀ g : columnGroup t, - spechtRep t g.val y = signC g.val • y) : - ∃ c : ℂ, y.val = c • polytabloid t := by - classical - let := Fintype.ofFinite (columnGroup t) - have he : columnAlt t y.val = (Fintype.card (columnGroup t) : ℂ) • y.val := by - change (∑ g : columnGroup t, signC g.val • wordRep n (μ.colLen 0) g.val) y.val = _ - simp only [LinearMap.sum_apply, LinearMap.smul_apply] - have hh (g : columnGroup t) : wordRep n (μ.colLen 0) g.val y.val = signC g.val • y.val := - congrArg Subtype.val (hy g) - simp only [hh, smul_smul, signC_mul_self, one_smul, Finset.sum_const, - Finset.card_univ, Nat.cast_smul_eq_nsmul] - have hm := columnAlt_tabloid t (spechtSub_le_tabloidSub t y.property) - rw [he] at hm - have hc : (Fintype.card (columnGroup t) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - have hx : y.val ∈ Submodule.span ℂ {polytabloid t} := - (Submodule.smul_mem_iff _ hc).mp hm - obtain ⟨c,hc⟩ := Submodule.mem_span_singleton.mp hx - exact ⟨c,hc.symm⟩ - -def rowAverage (m : ℕ) : Specht (stairTableau m) := by - classical - letI := Fintype.ofFinite (columnGroup (stairRowTableau m)) - exact ∑ g : columnGroup (stairRowTableau m), - spechtRep (stairTableau m) g.val ⟨polytabloid (stairTableau m), mem_cyclic _ _⟩ - -lemma rowAverage_nonzero (m : ℕ) : rowAverage m ≠ 0 := by - classical - let := Fintype.ofFinite (columnGroup (stairRowTableau m)) - intro he - have hh := congrArg (fun y : Specht (stairTableau m) => y.val (rowWord (stairTableau m))) he - have hg (g : columnGroup (stairRowTableau m)) : - rowWord (stairTableau m) ∘ g.val = rowWord (stairTableau m) := by - funext i - apply Fin.ext - exact g.property i - simp only [rowAverage, Submodule.coe_sum, Finset.sum_apply] at hh - change (∑ g : columnGroup (stairRowTableau m), - polytabloid (stairTableau m) (rowWord (stairTableau m) ∘ g.val)) = 0 at hh - simp only [hg, polytabloid_rowWord, Finset.sum_const, Finset.card_univ, nsmul_eq_mul, mul_one] at hh - exact Nat.cast_ne_zero.mpr Fintype.card_ne_zero hh - -lemma rowAverage_fixed (m : ℕ) (g : columnGroup (stairRowTableau m)) : - spechtRep (stairTableau m) g.val (rowAverage m) = rowAverage m := by - classical - let := Fintype.ofFinite (columnGroup (stairRowTableau m)) - unfold rowAverage - rw [map_sum] - simp only [← Module.End.mul_apply, ← map_mul] - exact Equiv.sum_comp (Equiv.mulLeft g) (fun h : columnGroup (stairRowTableau m) => - spechtRep (stairTableau m) h.val ⟨polytabloid (stairTableau m), mem_cyclic _ _⟩) - -lemma signEquiv_rowAverage (m : ℕ) - (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) : - ∃ c : ℂ, c ≠ 0 ∧ (φ (rowAverage m)).val = c • polytabloid (stairRowTableau m) := by - have ha (g : columnGroup (stairRowTableau m)) : - spechtRep (stairRowTableau m) g.val (φ (rowAverage m)) = signC g.val • φ (rowAverage m) := by - have he := LinearMap.congr_fun (φ.isIntertwining' g.val) (rowAverage m) - change φ (spechtRep (stairTableau m) g.val (rowAverage m)) = - signC g.val • spechtRep (stairRowTableau m) g.val (φ (rowAverage m)) at he - rw [rowAverage_fixed] at he - have hh := congrArg (fun x => signC g.val • x) he - simpa only [smul_smul, signC_mul_self, one_smul] using hh.symm - obtain ⟨c,hc⟩ := alternating_specht_line (stairRowTableau m) (φ (rowAverage m)) ha - refine ⟨c, ?_, hc⟩ - intro hz - rw [hz, zero_smul] at hc - apply rowAverage_nonzero m - apply φ.injective - exact (Subtype.ext hc).trans (map_zero φ).symm - -def signTwistMap {n : ℕ} {X : Type uX} {Y : Type uY} [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] - {ρ : Representation ℂ (Equiv.Perm (Fin n)) X} {σ : Representation ℂ (Equiv.Perm (Fin n)) Y} - (f : Representation.IntertwiningMap ρ σ) : - Representation.IntertwiningMap (signTwist ρ) (signTwist σ) where - toLinearMap := f.toLinearMap - isIntertwining' g := by - ext x - change f (signC g • ρ g x) = signC g • σ g (f x) - rw [map_smul, f.isIntertwining] - -/- A sign intertwiner in the second factor twists the diagonal product. -/ -def tensorAnti {n : ℕ} {X : Type uX} {Y : Type uY} {Z : Type uZ} [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] [AddCommGroup Z] [Module ℂ Z] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - {σ : Representation ℂ (Equiv.Perm (Fin n)) Y} {τ : Representation ℂ (Equiv.Perm (Fin n)) Z} - (f : Representation.IntertwiningMap σ (signTwist τ)) : - Representation.IntertwiningMap (signTwist (ρ.tprod σ)) (ρ.tprod τ) where - toLinearMap := TensorProduct.map LinearMap.id f.toLinearMap - isIntertwining' g := by - ext x y - change TensorProduct.map LinearMap.id f.toLinearMap - (signC g • (ρ g x ⊗ₜ[ℂ] σ g y)) = ρ g x ⊗ₜ[ℂ] τ g (f y) - rw [map_smul, TensorProduct.map_tmul] - change signC g • (ρ g x ⊗ₜ[ℂ] f (σ g y)) = _ - rw [f.isIntertwining] - change signC g • (ρ g x ⊗ₜ[ℂ] (signC g • τ g (f y))) = _ - rw [TensorProduct.tmul_smul, smul_smul, signC_mul_self, one_smul] - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.RepeatedProjection + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uX uY uZ + +namespace Saxl + +def rowReversalCell (m : ℕ) (x : (staircase m).cells) : (staircase m).cells := + ⟨(x.val.1, m-1-x.val.1-x.val.2), by + have hx : x.val.1 + x.val.2 < m := mem_staircase.mp x.property + apply mem_staircase.mpr + omega⟩ + +lemma rowReversalCell_involutive (m : ℕ) : Function.Involutive (rowReversalCell m) := by + intro x + have hx : x.val.1 + x.val.2 < m := mem_staircase.mp x.property + apply Subtype.ext + apply Prod.ext + · rfl + · change m-1-x.val.1-(m-1-x.val.1-x.val.2) = x.val.2 + omega + +def rowReversalEquiv (m : ℕ) : Equiv.Perm (staircase m).cells := + ⟨rowReversalCell m, rowReversalCell m, rowReversalCell_involutive m, rowReversalCell_involutive m⟩ + +def rowReversal (m : ℕ) : columnGroup (stairRowTableau m) := + ⟨((stairTableau m).trans (rowReversalEquiv m)).trans (stairTableau m).symm, by + intro i + change (stairTableau m ((stairTableau m).symm (rowReversalEquiv m (stairTableau m i)))).val.1 = _ + simp only [Equiv.apply_symm_apply] + rfl⟩ + +def repeatedTarget (m : ℕ) : Fin (staircase m).card → Fin ((staircase m).colLen 0) := + fun i => Fin.rev (rowWord (stairTableau m) i) + +lemma repeatedTarget_fixed (m : ℕ) (g : columnGroup (stairRowTableau m)) (i) : + repeatedTarget m (g.val i) = repeatedTarget m i := by + apply congrArg Fin.rev + apply Fin.ext + exact g.property i + +lemma repeated_letters_injective (m : ℕ) : + Function.Injective (fun i => (repeatedTarget m i, rowWord (stairRowTableau m) i)) := by + intro i j he + apply (stairTableau m).injective + apply Subtype.ext + apply Prod.ext + · have hh : Fin.rev (rowWord (stairTableau m) i) = Fin.rev (rowWord (stairTableau m) j) := + congrArg Prod.fst he + exact congrArg Fin.val (Fin.rev_injective hh) + · exact congrArg Fin.val (congrArg Prod.snd he) + +lemma repeated_complement (m : ℕ) (i) : + (rowWord (stairRowTableau m) i).val + + (rowWord (stairRowTableau m) ((rowReversal m).val i)).val = + (repeatedTarget m i).val := by + have hi : (stairTableau m i).val.1 + (stairTableau m i).val.2 < m := + mem_staircase.mp (stairTableau m i).property + simp only [rowWord, stairRowTableau, rowReversal, Equiv.trans_apply, + Equiv.apply_symm_apply, repeatedTarget, Fin.val_rev, staircase_colLen, Nat.sub_zero] + change (stairTableau m i).val.2 + (m-1-(stairTableau m i).val.1-(stairTableau m i).val.2) = + m-((stairTableau m i).val.1+1) + omega + +theorem staircase_repeated_projection (m : ℕ) : + orbitProjection (repeatedTarget m) + (pairSumMap (staircase m).card ((staircase m).colLen 0) ((staircase m).colLen 0) + (wordTensor _ _ _ (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] polytabloid (stairRowTableau m)))) = + ((Nat.card (columnGroup (stairRowTableau m)) : ℂ) * signC (rowReversal m).val) • + Pi.single (repeatedTarget m) 1 := by + exact repeated_alt_projection (columnGroup (stairRowTableau m)) + (rowWord (stairRowTableau m)) (repeatedTarget m) (rowReversal m) + (repeatedTarget_fixed m) (repeated_letters_injective m) (repeated_complement m) + +lemma staircase_repeated_projection_nonzero (m : ℕ) : + orbitProjection (repeatedTarget m) + (pairSumMap (staircase m).card ((staircase m).colLen 0) ((staircase m).colLen 0) + (wordTensor _ _ _ (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] polytabloid (stairRowTableau m)))) ≠ 0 := by + rw [staircase_repeated_projection] + apply smul_ne_zero + · apply mul_ne_zero + · exact Nat.cast_ne_zero.mpr (Nat.card_pos (α := columnGroup (stairRowTableau m))).ne' + · intro hh + have he := signC_mul_self (rowReversal m).val + rw [hh, zero_mul] at he + exact zero_ne_one he + · intro hz + have he := congrFun hz (repeatedTarget m) + simp at he + + +theorem staircase_sign_equiv (m : ℕ) : + Nonempty ((spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) := by + classical + let t := stairTableau m + let tt := stairRowTableau m + let y : Specht tt := ⟨polytabloid tt, mem_cyclic _ _⟩ + let R := signTwist (spechtRep tt) + let F := orbitAverage R (rowWord t) y + let c : ℂ := ((Finset.univ.filter + (fun g : Equiv.Perm (Fin (staircase m).card) => rowWord t ∘ g = rowWord t)).card : ℂ) + have hy : ∀ g : Equiv.Perm (Fin (staircase m).card), rowWord t ∘ g = rowWord t → R g y = y := by + intro g hg + have hc : g ∈ columnGroup tt := by + intro i + exact congrArg Fin.val (congrFun hg i) + apply Subtype.ext + change signC g • wordRep (staircase m).card ((staircase m).colLen 0) g (polytabloid tt) = polytabloid tt + rw [polytabloid_alternating tt ⟨g, hc⟩, smul_smul, signC_mul_self, one_smul] + have hF : F (Pi.single (rowWord t) 1) = c • y := orbitAverage_base R _ y hy + have hc0 : c ≠ 0 := by + apply Nat.cast_ne_zero.mpr + apply Finset.card_ne_zero.mpr + refine ⟨1, Finset.mem_filter.mpr ⟨Finset.mem_univ _, ?_⟩⟩ + rfl + have hm (g : columnGroup t) : + (F (wordRep (staircase m).card ((staircase m).colLen 0) (g : Equiv.Perm (Fin (staircase m).card)) + (Pi.single (rowWord t) 1))).val (rowWord tt) = signC (g : Equiv.Perm (Fin (staircase m).card)) * c := by + rw [F.isIntertwining, hF] + change signC (g : Equiv.Perm (Fin (staircase m).card)) * (c * + polytabloid tt (rowWord tt ∘ (g : Equiv.Perm (Fin (staircase m).card)))) = _ + have he : rowWord tt ∘ (g : Equiv.Perm (Fin (staircase m).card)) = rowWord tt := by + funext i + apply Fin.ext + exact g.property i + rw [he, polytabloid_rowWord, mul_one] + let inc : Representation.IntertwiningMap (spechtRep t) (wordRep (staircase m).card ((staircase m).colLen 0)) := + { toLinearMap := (spechtSub t).toSubmodule.subtype + isIntertwining' := fun _ => rfl } + let f := F.comp inc + have hf : f ≠ 0 := by + intro hz + have he : (F (polytabloid t)).val (rowWord tt) = 0 := by + have he := congrArg (fun l : Representation.IntertwiningMap (spechtRep t) R => + (l ⟨polytabloid t, mem_cyclic _ _⟩).val (rowWord tt)) hz + exact he + let := Fintype.ofFinite (columnGroup t) + have hp : (F (polytabloid t)).val (rowWord tt) = + (Fintype.card (columnGroup t) : ℂ) * c := by + change (F (∑ g : columnGroup t, signC (g : Equiv.Perm (Fin (staircase m).card)) • + wordRep (staircase m).card ((staircase m).colLen 0) (g : Equiv.Perm (Fin (staircase m).card)) (Pi.single (rowWord t) 1))).val _ = _ + simp only [map_sum, map_smul, Submodule.coe_sum, Submodule.coe_smul, + Finset.sum_apply, Pi.smul_apply, smul_eq_mul, hm] + simp only [← mul_assoc, signC_mul_self, one_mul, Finset.sum_const, + Finset.card_univ, nsmul_eq_mul] + have hn : (Fintype.card (columnGroup t) : ℂ) ≠ 0 := by + exact Nat.cast_ne_zero.mpr Fintype.card_ne_zero + exact (mul_ne_zero hn hc0) (hp.symm.trans he) + let := specht_irreducible t + let := specht_irreducible tt + let := signTwist_irreducible (spechtRep tt) + exact ⟨f.ofBijective ((Representation.IsIrreducible.bijective_or_eq_zero f).resolve_right hf)⟩ + +lemma alternating_specht_line {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (y : Specht t) (hy : ∀ g : columnGroup t, + spechtRep t g.val y = signC g.val • y) : + ∃ c : ℂ, y.val = c • polytabloid t := by + classical + let := Fintype.ofFinite (columnGroup t) + have he : columnAlt t y.val = (Fintype.card (columnGroup t) : ℂ) • y.val := by + change (∑ g : columnGroup t, signC g.val • wordRep n (μ.colLen 0) g.val) y.val = _ + simp only [LinearMap.sum_apply, LinearMap.smul_apply] + have hh (g : columnGroup t) : wordRep n (μ.colLen 0) g.val y.val = signC g.val • y.val := + congrArg Subtype.val (hy g) + simp only [hh, smul_smul, signC_mul_self, one_smul, Finset.sum_const, + Finset.card_univ, Nat.cast_smul_eq_nsmul] + have hm := columnAlt_tabloid t (spechtSub_le_tabloidSub t y.property) + rw [he] at hm + have hc : (Fintype.card (columnGroup t) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + have hx : y.val ∈ Submodule.span ℂ {polytabloid t} := + (Submodule.smul_mem_iff _ hc).mp hm + obtain ⟨c,hc⟩ := Submodule.mem_span_singleton.mp hx + exact ⟨c,hc.symm⟩ + +def rowAverage (m : ℕ) : Specht (stairTableau m) := by + classical + letI := Fintype.ofFinite (columnGroup (stairRowTableau m)) + exact ∑ g : columnGroup (stairRowTableau m), + spechtRep (stairTableau m) g.val ⟨polytabloid (stairTableau m), mem_cyclic _ _⟩ + +lemma rowAverage_nonzero (m : ℕ) : rowAverage m ≠ 0 := by + classical + let := Fintype.ofFinite (columnGroup (stairRowTableau m)) + intro he + have hh := congrArg (fun y : Specht (stairTableau m) => y.val (rowWord (stairTableau m))) he + have hg (g : columnGroup (stairRowTableau m)) : + rowWord (stairTableau m) ∘ g.val = rowWord (stairTableau m) := by + funext i + apply Fin.ext + exact g.property i + simp only [rowAverage, Submodule.coe_sum, Finset.sum_apply] at hh + change (∑ g : columnGroup (stairRowTableau m), + polytabloid (stairTableau m) (rowWord (stairTableau m) ∘ g.val)) = 0 at hh + simp only [hg, polytabloid_rowWord, Finset.sum_const, Finset.card_univ, nsmul_eq_mul, mul_one] at hh + exact Nat.cast_ne_zero.mpr Fintype.card_ne_zero hh + +lemma rowAverage_fixed (m : ℕ) (g : columnGroup (stairRowTableau m)) : + spechtRep (stairTableau m) g.val (rowAverage m) = rowAverage m := by + classical + let := Fintype.ofFinite (columnGroup (stairRowTableau m)) + unfold rowAverage + rw [map_sum] + simp only [← Module.End.mul_apply, ← map_mul] + exact Equiv.sum_comp (Equiv.mulLeft g) (fun h : columnGroup (stairRowTableau m) => + spechtRep (stairTableau m) h.val ⟨polytabloid (stairTableau m), mem_cyclic _ _⟩) + +lemma signEquiv_rowAverage (m : ℕ) + (φ : (spechtRep (stairTableau m)).Equiv (signTwist (spechtRep (stairRowTableau m)))) : + ∃ c : ℂ, c ≠ 0 ∧ (φ (rowAverage m)).val = c • polytabloid (stairRowTableau m) := by + have ha (g : columnGroup (stairRowTableau m)) : + spechtRep (stairRowTableau m) g.val (φ (rowAverage m)) = signC g.val • φ (rowAverage m) := by + have he := LinearMap.congr_fun (φ.isIntertwining' g.val) (rowAverage m) + change φ (spechtRep (stairTableau m) g.val (rowAverage m)) = + signC g.val • spechtRep (stairRowTableau m) g.val (φ (rowAverage m)) at he + rw [rowAverage_fixed] at he + have hh := congrArg (fun x => signC g.val • x) he + simpa only [smul_smul, signC_mul_self, one_smul] using hh.symm + obtain ⟨c,hc⟩ := alternating_specht_line (stairRowTableau m) (φ (rowAverage m)) ha + refine ⟨c, ?_, hc⟩ + intro hz + rw [hz, zero_smul] at hc + apply rowAverage_nonzero m + apply φ.injective + exact (Subtype.ext hc).trans (map_zero φ).symm + +def signTwistMap {n : ℕ} {X : Type uX} {Y : Type uY} [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] + {ρ : Representation ℂ (Equiv.Perm (Fin n)) X} {σ : Representation ℂ (Equiv.Perm (Fin n)) Y} + (f : Representation.IntertwiningMap ρ σ) : + Representation.IntertwiningMap (signTwist ρ) (signTwist σ) where + toLinearMap := f.toLinearMap + isIntertwining' g := by + ext x + change f (signC g • ρ g x) = signC g • σ g (f x) + rw [map_smul, f.isIntertwining] + +/- A sign intertwiner in the second factor twists the diagonal product. -/ +def tensorAnti {n : ℕ} {X : Type uX} {Y : Type uY} {Z : Type uZ} [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] [AddCommGroup Z] [Module ℂ Z] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + {σ : Representation ℂ (Equiv.Perm (Fin n)) Y} {τ : Representation ℂ (Equiv.Perm (Fin n)) Z} + (f : Representation.IntertwiningMap σ (signTwist τ)) : + Representation.IntertwiningMap (signTwist (ρ.tprod σ)) (ρ.tprod τ) where + toLinearMap := TensorProduct.map LinearMap.id f.toLinearMap + isIntertwining' g := by + ext x y + change TensorProduct.map LinearMap.id f.toLinearMap + (signC g • (ρ g x ⊗ₜ[ℂ] σ g y)) = ρ g x ⊗ₜ[ℂ] τ g (f y) + rw [map_smul, TensorProduct.map_tmul] + change signC g • (ρ g x ⊗ₜ[ℂ] f (σ g y)) = _ + rw [f.isIntertwining] + change signC g • (ρ g x ⊗ₜ[ℂ] (signC g • τ g (f y))) = _ + rw [TensorProduct.tmul_smul, smul_smul, signC_mul_self, one_smul] + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/StaircaseTensor.lean b/lean/OAI/RepresentationTheory/Saxl/StaircaseTensor.lean index 2a7c5428ef208d5c962c053ead27729665ebd0ac..60d3961e6bf183f70d25425ae0ca1af4d209ba6b 100644 --- a/lean/OAI/RepresentationTheory/Saxl/StaircaseTensor.lean +++ b/lean/OAI/RepresentationTheory/Saxl/StaircaseTensor.lean @@ -1,128 +1,128 @@ -import OAI.RepresentationTheory.Saxl.TableauTransport - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl -def splitLeft {n d e : ℕ} (w : Fin n → Fin (d*e)) : Fin n → Fin d := - fun i => (finProdFinEquiv.symm (w i)).1 - -def splitRight {n d e : ℕ} (w : Fin n → Fin (d*e)) : Fin n → Fin e := - fun i => (finProdFinEquiv.symm (w i)).2 - -def mergeWords {n d e : ℕ} (a : Fin n → Fin d) (b : Fin n → Fin e) : Fin n → Fin (d*e) := - fun i => finProdFinEquiv (a i, b i) - -@[simp] lemma splitLeft_merge {n d e : ℕ} (a : Fin n → Fin d) (b : Fin n → Fin e) : - splitLeft (mergeWords a b) = a := by ext i; simp [splitLeft, mergeWords] -@[simp] lemma splitRight_merge {n d e : ℕ} (a : Fin n → Fin d) (b : Fin n → Fin e) : - splitRight (mergeWords a b) = b := by ext i; simp [splitRight, mergeWords] -@[simp] lemma merge_split {n d e : ℕ} (w : Fin n → Fin (d*e)) : - mergeWords (splitLeft w) (splitRight w) = w := by - funext i - exact finProdFinEquiv.apply_symm_apply (w i) - -def wordUncurry (n d e : ℕ) : - ((Fin n → Fin e) → WordSpace n d) ≃ₗ[ℂ] WordSpace n (d*e) where - toFun f w := f (splitRight w) (splitLeft w) - invFun z b a := z (mergeWords a b) - left_inv f := by ext b a; simp - right_inv z := by ext w; simp - map_add' _ _ := rfl - map_smul' _ _ := rfl - -/- Tensor regrouping by positions. -/ -def wordTensor (n d e : ℕ) : - WordSpace n d ⊗[ℂ] WordSpace n e ≃ₗ[ℂ] WordSpace n (d*e) := - TensorProduct.piScalarRight ℂ ℂ (WordSpace n d) (Fin n → Fin e) ≪≫ₗ wordUncurry n d e - -@[simp] lemma wordTensor_tmul {n d e : ℕ} (x : WordSpace n d) (y : WordSpace n e) - (w : Fin n → Fin (d*e)) : - wordTensor n d e (x ⊗ₜ[ℂ] y) w = x (splitLeft w) * y (splitRight w) := by - change y (splitRight w) • x (splitLeft w) = _ - exact mul_comm _ _ - -lemma wordTensor_equivariant {n d e : ℕ} (g : Equiv.Perm (Fin n)) - (z : WordSpace n d ⊗[ℂ] WordSpace n e) : - wordTensor n d e (((wordRep n d).tprod (wordRep n e)) g z) = - wordRep n (d*e) g (wordTensor n d e z) := by - induction z using TensorProduct.inductionOn with - | add x y hx hy => simp only [map_add, hx, hy] - | tmul x y => - ext w - change wordTensor n d e (wordRep n d g x ⊗ₜ[ℂ] wordRep n e g y) w = _ - change wordTensor n d e (wordRep n d g x ⊗ₜ[ℂ] wordRep n e g y) w = - wordTensor n d e (x ⊗ₜ[ℂ] y) (w ∘ g) - simp only [wordTensor_tmul] - rfl - -def wordTensorIntertwiner (n d e : ℕ) : - Representation.IntertwiningMap ((wordRep n d).tprod (wordRep n e)) (wordRep n (d*e)) where - toLinearMap := (wordTensor n d e).toLinearMap - isIntertwining' g := by - apply LinearMap.ext - intro z - exact wordTensor_equivariant g z - -end Saxl - -namespace Saxl - -/- Transposition is an honest permutation of the self-conjugate staircase. -/ -def staircaseSwap (m : ℕ) : (staircase m).cells ≃ (staircase m).cells where - toFun x := ⟨(x.val.2, x.val.1), by - have h : x.val.1 + x.val.2 < m := mem_staircase.mp x.property - exact mem_staircase.mpr (by omega)⟩ - invFun x := ⟨(x.val.2, x.val.1), by - have h : x.val.1 + x.val.2 < m := mem_staircase.mp x.property - exact mem_staircase.mpr (by omega)⟩ - left_inv _ := rfl - right_inv _ := rfl - -abbrev stairTableau (m : ℕ) : Tableau (staircase m).card (staircase m) := - canonicalTableau (staircase m) rfl - -def stairRowTableau (m : ℕ) : Tableau (staircase m).card (staircase m) := - (stairTableau m).trans (staircaseSwap m) - -def staircaseWord (m : ℕ) : WordSpace (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0) := - wordTensor _ _ _ (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] polytabloid (stairTableau m)) - -def staircaseCyclic (m : ℕ) : Subrepresentation - (wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) := - cyclic (wordRep _ _) (staircaseWord m) - -def spechtInclusion {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - Representation.IntertwiningMap (spechtRep t) (wordRep n (μ.colLen 0)) where - toLinearMap := (spechtSub t).toSubmodule.subtype - isIntertwining' _ := rfl - -def staircaseTensorMap (m : ℕ) : - Representation.IntertwiningMap ((spechtRep (stairTableau m)).tprod (spechtRep (stairTableau m))) - (wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) := - (wordTensorIntertwiner _ _ _).comp - ((spechtInclusion (stairTableau m)).tensor (spechtInclusion (stairTableau m))) - -lemma staircaseTensorMap_injective (m : ℕ) : Function.Injective (staircaseTensorMap m) := by - apply (wordTensor _ _ _).injective.comp - exact TensorProduct.map_injective_of_flat_flat _ _ - (spechtSub (stairTableau m)).toSubmodule.subtype_injective - (spechtSub (stairTableau m)).toSubmodule.subtype_injective - -lemma staircaseCyclic_le_tensorRange (m : ℕ) : - staircaseCyclic m ≤ (staircaseTensorMap m).range := by - apply (cyclic_le _ _ _).mpr - refine ⟨(⟨polytabloid (stairRowTableau m), polytabloid_mem_all _ _⟩ : Specht (stairTableau m)) ⊗ₜ[ℂ] - (⟨polytabloid (stairTableau m), mem_cyclic _ _⟩ : Specht (stairTableau m)), ?_⟩ - rfl - -attribute [irreducible] staircaseTensorMap - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.TableauTransport + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl +def splitLeft {n d e : ℕ} (w : Fin n → Fin (d*e)) : Fin n → Fin d := + fun i => (finProdFinEquiv.symm (w i)).1 + +def splitRight {n d e : ℕ} (w : Fin n → Fin (d*e)) : Fin n → Fin e := + fun i => (finProdFinEquiv.symm (w i)).2 + +def mergeWords {n d e : ℕ} (a : Fin n → Fin d) (b : Fin n → Fin e) : Fin n → Fin (d*e) := + fun i => finProdFinEquiv (a i, b i) + +@[simp] lemma splitLeft_merge {n d e : ℕ} (a : Fin n → Fin d) (b : Fin n → Fin e) : + splitLeft (mergeWords a b) = a := by ext i; simp [splitLeft, mergeWords] +@[simp] lemma splitRight_merge {n d e : ℕ} (a : Fin n → Fin d) (b : Fin n → Fin e) : + splitRight (mergeWords a b) = b := by ext i; simp [splitRight, mergeWords] +@[simp] lemma merge_split {n d e : ℕ} (w : Fin n → Fin (d*e)) : + mergeWords (splitLeft w) (splitRight w) = w := by + funext i + exact finProdFinEquiv.apply_symm_apply (w i) + +def wordUncurry (n d e : ℕ) : + ((Fin n → Fin e) → WordSpace n d) ≃ₗ[ℂ] WordSpace n (d*e) where + toFun f w := f (splitRight w) (splitLeft w) + invFun z b a := z (mergeWords a b) + left_inv f := by ext b a; simp + right_inv z := by ext w; simp + map_add' _ _ := rfl + map_smul' _ _ := rfl + +/- Tensor regrouping by positions. -/ +def wordTensor (n d e : ℕ) : + WordSpace n d ⊗[ℂ] WordSpace n e ≃ₗ[ℂ] WordSpace n (d*e) := + TensorProduct.piScalarRight ℂ ℂ (WordSpace n d) (Fin n → Fin e) ≪≫ₗ wordUncurry n d e + +@[simp] lemma wordTensor_tmul {n d e : ℕ} (x : WordSpace n d) (y : WordSpace n e) + (w : Fin n → Fin (d*e)) : + wordTensor n d e (x ⊗ₜ[ℂ] y) w = x (splitLeft w) * y (splitRight w) := by + change y (splitRight w) • x (splitLeft w) = _ + exact mul_comm _ _ + +lemma wordTensor_equivariant {n d e : ℕ} (g : Equiv.Perm (Fin n)) + (z : WordSpace n d ⊗[ℂ] WordSpace n e) : + wordTensor n d e (((wordRep n d).tprod (wordRep n e)) g z) = + wordRep n (d*e) g (wordTensor n d e z) := by + induction z using TensorProduct.inductionOn with + | add x y hx hy => simp only [map_add, hx, hy] + | tmul x y => + ext w + change wordTensor n d e (wordRep n d g x ⊗ₜ[ℂ] wordRep n e g y) w = _ + change wordTensor n d e (wordRep n d g x ⊗ₜ[ℂ] wordRep n e g y) w = + wordTensor n d e (x ⊗ₜ[ℂ] y) (w ∘ g) + simp only [wordTensor_tmul] + rfl + +def wordTensorIntertwiner (n d e : ℕ) : + Representation.IntertwiningMap ((wordRep n d).tprod (wordRep n e)) (wordRep n (d*e)) where + toLinearMap := (wordTensor n d e).toLinearMap + isIntertwining' g := by + apply LinearMap.ext + intro z + exact wordTensor_equivariant g z + +end Saxl + +namespace Saxl + +/- Transposition is an honest permutation of the self-conjugate staircase. -/ +def staircaseSwap (m : ℕ) : (staircase m).cells ≃ (staircase m).cells where + toFun x := ⟨(x.val.2, x.val.1), by + have h : x.val.1 + x.val.2 < m := mem_staircase.mp x.property + exact mem_staircase.mpr (by omega)⟩ + invFun x := ⟨(x.val.2, x.val.1), by + have h : x.val.1 + x.val.2 < m := mem_staircase.mp x.property + exact mem_staircase.mpr (by omega)⟩ + left_inv _ := rfl + right_inv _ := rfl + +abbrev stairTableau (m : ℕ) : Tableau (staircase m).card (staircase m) := + canonicalTableau (staircase m) rfl + +def stairRowTableau (m : ℕ) : Tableau (staircase m).card (staircase m) := + (stairTableau m).trans (staircaseSwap m) + +def staircaseWord (m : ℕ) : WordSpace (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0) := + wordTensor _ _ _ (polytabloid (stairRowTableau m) ⊗ₜ[ℂ] polytabloid (stairTableau m)) + +def staircaseCyclic (m : ℕ) : Subrepresentation + (wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) := + cyclic (wordRep _ _) (staircaseWord m) + +def spechtInclusion {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + Representation.IntertwiningMap (spechtRep t) (wordRep n (μ.colLen 0)) where + toLinearMap := (spechtSub t).toSubmodule.subtype + isIntertwining' _ := rfl + +def staircaseTensorMap (m : ℕ) : + Representation.IntertwiningMap ((spechtRep (stairTableau m)).tprod (spechtRep (stairTableau m))) + (wordRep (staircase m).card ((staircase m).colLen 0 * (staircase m).colLen 0)) := + (wordTensorIntertwiner _ _ _).comp + ((spechtInclusion (stairTableau m)).tensor (spechtInclusion (stairTableau m))) + +lemma staircaseTensorMap_injective (m : ℕ) : Function.Injective (staircaseTensorMap m) := by + apply (wordTensor _ _ _).injective.comp + exact TensorProduct.map_injective_of_flat_flat _ _ + (spechtSub (stairTableau m)).toSubmodule.subtype_injective + (spechtSub (stairTableau m)).toSubmodule.subtype_injective + +lemma staircaseCyclic_le_tensorRange (m : ℕ) : + staircaseCyclic m ≤ (staircaseTensorMap m).range := by + apply (cyclic_le _ _ _).mpr + refine ⟨(⟨polytabloid (stairRowTableau m), polytabloid_mem_all _ _⟩ : Specht (stairTableau m)) ⊗ₜ[ℂ] + (⟨polytabloid (stairTableau m), mem_cyclic _ _⟩ : Specht (stairTableau m)), ?_⟩ + rfl + +attribute [irreducible] staircaseTensorMap + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/StripExtension.lean b/lean/OAI/RepresentationTheory/Saxl/StripExtension.lean index 4ab701afb8cafd1677d31d6659effe9168b2e5aa..7f70f15ea1b3a8560b76de8631d8ec79f3797fdd 100644 --- a/lean/OAI/RepresentationTheory/Saxl/StripExtension.lean +++ b/lean/OAI/RepresentationTheory/Saxl/StripExtension.lean @@ -1,122 +1,122 @@ -import OAI.RepresentationTheory.Saxl.PieriRestriction - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl - -lemma pieri_strip_surjective {a n : ℕ} {ν μ : YoungDiagram} - (s : Tableau a ν) (t : Tableau n μ) (hs : HorizontalStrip ν μ) : - ∃ F : Specht t →ₗ[ℂ] Specht s, Function.Surjective F ∧ - ∀ (g : Equiv.Perm (Fin n)) (h : Equiv.Perm (Fin a)), - (∀ k, g (tableauInclusion s t hs.1 k) = tableauInclusion s t hs.1 (h k)) → - ∀ x, F (spechtRep t g x) = spechtRep s h (F x) := by - obtain ⟨F,hF,he⟩ := pieri_strip_restriction s t hs - let E : Representation.IntertwiningMap - ((spechtRep t).comp (Equiv.Perm.viaEmbeddingHom (tableauInclusion s t hs.1))) - (spechtRep s) := - { toLinearMap := F - isIntertwining' := by - intro h - apply LinearMap.ext - intro x - exact he _ h (fun k => Equiv.Perm.viaEmbedding_apply _ _ k) x } - have hE : E ≠ 0 := by - intro hz - exact hF (congrArg Representation.IntertwiningMap.toLinearMap hz) - have := specht_irreducible s - exact ⟨F, (Representation.IsIrreducible.surjective_or_eq_zero E).resolve_right hE, he⟩ - -def restrictPerm {a n : ℕ} (i : Fin a ↪ Fin n) (g : Equiv.Perm (Fin n)) - (hg : ∀ x, g x ∈ Set.range i ↔ x ∈ Set.range i) : Equiv.Perm (Fin a) := - (Equiv.ofInjective i i.injective).trans ((g.subtypePerm hg).trans - (Equiv.ofInjective i i.injective).symm) - -lemma restrictPerm_apply {a n : ℕ} (i : Fin a ↪ Fin n) (g : Equiv.Perm (Fin n)) - (hg : ∀ x, g x ∈ Set.range i ↔ x ∈ Set.range i) (k : Fin a) : - i (restrictPerm i g hg k) = g (i k) := by - change ((Equiv.ofInjective i i.injective) - ((Equiv.ofInjective i i.injective).symm _)).val = _ - rw [Equiv.apply_symm_apply] - rfl - -lemma tableauInclusion_trans {a b n : ℕ} {ν η μ : YoungDiagram} - (s : Tableau a ν) (u : Tableau b η) (t : Tableau n μ) - (h₁ : ν ≤ η) (h₂ : η ≤ μ) (k : Fin a) : - tableauInclusion u t h₂ (tableauInclusion s u h₁ k) = - tableauInclusion s t (h₁.trans h₂) k := by - change t.symm ⟨(u (u.symm ⟨(s k).val, _⟩)).val, _⟩ = t.symm ⟨(s k).val, _⟩ - simp only [Equiv.apply_symm_apply] - -def extendColor {a n : ℕ} (i : Fin a ↪ Fin n) (c : Fin a → ℕ) (q : ℕ) : Fin n → ℕ := - fun x => if h : x ∈ Set.range i then c ((Equiv.ofInjective i i.injective).symm ⟨x,h⟩) else q - -lemma extendColor_apply {a n : ℕ} (i : Fin a ↪ Fin n) (c : Fin a → ℕ) (q : ℕ) - (x : Fin a) : extendColor i c q (i x) = c x := by - classical - unfold extendColor - rw [dite_eq_left ⟨x,rfl⟩] - congr 1 - exact (Equiv.ofInjective i i.injective).symm_apply_apply x - -lemma extendColor_mem {a n : ℕ} (i : Fin a ↪ Fin n) (c : Fin a → ℕ) (q : ℕ) - (hc : ∀ x, c x ≤ q) (x : Fin n) : - extendColor i c (q+1) x ≤ q ↔ x ∈ Set.range i := by - classical - unfold extendColor - split_ifs with h - · exact iff_of_true (hc _) h - · simp [h] - -lemma extendColor_le {a n : ℕ} (i : Fin a ↪ Fin n) (c : Fin a → ℕ) (q : ℕ) - (hc : ∀ x, c x ≤ q) (x : Fin n) : extendColor i c (q+1) x ≤ q+1 := by - classical - unfold extendColor - split_ifs - · exact (hc _).trans (Nat.le_succ q) - · exact le_rfl - -lemma extendColor_count_old {a n : ℕ} (i : Fin a ↪ Fin n) (c : Fin a → ℕ) (q j : ℕ) - (hj : j ≠ q) : - (Finset.univ.filter (fun x => extendColor i c q x = j)).card = - (Finset.univ.filter (fun x => c x = j)).card := by - classical - symm - apply Finset.card_bij (fun x _ => i x) - · intro x hx - simpa only [Finset.mem_filter, Finset.mem_univ, true_and, extendColor_apply] using hx - · intro x hx y hy hxy - exact i.injective hxy - · intro y hy - have hyj := (Finset.mem_filter.mp hy).2 - have hym : y ∈ Set.range i := by - by_contra hn - simp only [extendColor, dite_eq_right hn] at hyj - exact hj hyj.symm - obtain ⟨x,rfl⟩ := hym - refine ⟨x, ?_, rfl⟩ - simpa only [Finset.mem_filter, Finset.mem_univ, true_and, extendColor_apply] using hyj - -lemma extendColor_count_new {a n : ℕ} (i : Fin a ↪ Fin n) (c : Fin a → ℕ) (q : ℕ) - (hc : ∀ x, c x ≤ q) : - (Finset.univ.filter (fun x => extendColor i c (q+1) x = q+1)).card = n-a := by - classical - have he : Finset.univ.filter (fun x => extendColor i c (q+1) x = q+1) = - Finset.univ \ Finset.univ.map i := by - ext x - simp only [Finset.mem_filter, Finset.mem_univ, true_and, Finset.mem_sdiff, Finset.mem_map] - change extendColor i c (q+1) x = q+1 ↔ ¬ x ∈ Set.range i - rw [← extendColor_mem i c q hc x] - have hl := extendColor_le i c q hc x - omega - rw [he, Finset.card_sdiff_of_subset (Finset.subset_univ _), Finset.card_univ, Fintype.card_fin, - Finset.card_map, Finset.card_univ, Fintype.card_fin] - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.PieriRestriction + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl + +lemma pieri_strip_surjective {a n : ℕ} {ν μ : YoungDiagram} + (s : Tableau a ν) (t : Tableau n μ) (hs : HorizontalStrip ν μ) : + ∃ F : Specht t →ₗ[ℂ] Specht s, Function.Surjective F ∧ + ∀ (g : Equiv.Perm (Fin n)) (h : Equiv.Perm (Fin a)), + (∀ k, g (tableauInclusion s t hs.1 k) = tableauInclusion s t hs.1 (h k)) → + ∀ x, F (spechtRep t g x) = spechtRep s h (F x) := by + obtain ⟨F,hF,he⟩ := pieri_strip_restriction s t hs + let E : Representation.IntertwiningMap + ((spechtRep t).comp (Equiv.Perm.viaEmbeddingHom (tableauInclusion s t hs.1))) + (spechtRep s) := + { toLinearMap := F + isIntertwining' := by + intro h + apply LinearMap.ext + intro x + exact he _ h (fun k => Equiv.Perm.viaEmbedding_apply _ _ k) x } + have hE : E ≠ 0 := by + intro hz + exact hF (congrArg Representation.IntertwiningMap.toLinearMap hz) + have := specht_irreducible s + exact ⟨F, (Representation.IsIrreducible.surjective_or_eq_zero E).resolve_right hE, he⟩ + +def restrictPerm {a n : ℕ} (i : Fin a ↪ Fin n) (g : Equiv.Perm (Fin n)) + (hg : ∀ x, g x ∈ Set.range i ↔ x ∈ Set.range i) : Equiv.Perm (Fin a) := + (Equiv.ofInjective i i.injective).trans ((g.subtypePerm hg).trans + (Equiv.ofInjective i i.injective).symm) + +lemma restrictPerm_apply {a n : ℕ} (i : Fin a ↪ Fin n) (g : Equiv.Perm (Fin n)) + (hg : ∀ x, g x ∈ Set.range i ↔ x ∈ Set.range i) (k : Fin a) : + i (restrictPerm i g hg k) = g (i k) := by + change ((Equiv.ofInjective i i.injective) + ((Equiv.ofInjective i i.injective).symm _)).val = _ + rw [Equiv.apply_symm_apply] + rfl + +lemma tableauInclusion_trans {a b n : ℕ} {ν η μ : YoungDiagram} + (s : Tableau a ν) (u : Tableau b η) (t : Tableau n μ) + (h₁ : ν ≤ η) (h₂ : η ≤ μ) (k : Fin a) : + tableauInclusion u t h₂ (tableauInclusion s u h₁ k) = + tableauInclusion s t (h₁.trans h₂) k := by + change t.symm ⟨(u (u.symm ⟨(s k).val, _⟩)).val, _⟩ = t.symm ⟨(s k).val, _⟩ + simp only [Equiv.apply_symm_apply] + +def extendColor {a n : ℕ} (i : Fin a ↪ Fin n) (c : Fin a → ℕ) (q : ℕ) : Fin n → ℕ := + fun x => if h : x ∈ Set.range i then c ((Equiv.ofInjective i i.injective).symm ⟨x,h⟩) else q + +lemma extendColor_apply {a n : ℕ} (i : Fin a ↪ Fin n) (c : Fin a → ℕ) (q : ℕ) + (x : Fin a) : extendColor i c q (i x) = c x := by + classical + unfold extendColor + rw [dite_eq_left ⟨x,rfl⟩] + congr 1 + exact (Equiv.ofInjective i i.injective).symm_apply_apply x + +lemma extendColor_mem {a n : ℕ} (i : Fin a ↪ Fin n) (c : Fin a → ℕ) (q : ℕ) + (hc : ∀ x, c x ≤ q) (x : Fin n) : + extendColor i c (q+1) x ≤ q ↔ x ∈ Set.range i := by + classical + unfold extendColor + split_ifs with h + · exact iff_of_true (hc _) h + · simp [h] + +lemma extendColor_le {a n : ℕ} (i : Fin a ↪ Fin n) (c : Fin a → ℕ) (q : ℕ) + (hc : ∀ x, c x ≤ q) (x : Fin n) : extendColor i c (q+1) x ≤ q+1 := by + classical + unfold extendColor + split_ifs + · exact (hc _).trans (Nat.le_succ q) + · exact le_rfl + +lemma extendColor_count_old {a n : ℕ} (i : Fin a ↪ Fin n) (c : Fin a → ℕ) (q j : ℕ) + (hj : j ≠ q) : + (Finset.univ.filter (fun x => extendColor i c q x = j)).card = + (Finset.univ.filter (fun x => c x = j)).card := by + classical + symm + apply Finset.card_bij (fun x _ => i x) + · intro x hx + simpa only [Finset.mem_filter, Finset.mem_univ, true_and, extendColor_apply] using hx + · intro x hx y hy hxy + exact i.injective hxy + · intro y hy + have hyj := (Finset.mem_filter.mp hy).2 + have hym : y ∈ Set.range i := by + by_contra hn + simp only [extendColor, dite_eq_right hn] at hyj + exact hj hyj.symm + obtain ⟨x,rfl⟩ := hym + refine ⟨x, ?_, rfl⟩ + simpa only [Finset.mem_filter, Finset.mem_univ, true_and, extendColor_apply] using hyj + +lemma extendColor_count_new {a n : ℕ} (i : Fin a ↪ Fin n) (c : Fin a → ℕ) (q : ℕ) + (hc : ∀ x, c x ≤ q) : + (Finset.univ.filter (fun x => extendColor i c (q+1) x = q+1)).card = n-a := by + classical + have he : Finset.univ.filter (fun x => extendColor i c (q+1) x = q+1) = + Finset.univ \ Finset.univ.map i := by + ext x + simp only [Finset.mem_filter, Finset.mem_univ, true_and, Finset.mem_sdiff, Finset.mem_map] + change extendColor i c (q+1) x = q+1 ↔ ¬ x ∈ Set.range i + rw [← extendColor_mem i c q hc x] + have hl := extendColor_le i c q hc x + omega + rw [he, Finset.card_sdiff_of_subset (Finset.subset_univ _), Finset.card_univ, Fintype.card_fin, + Finset.card_map, Finset.card_univ, Fintype.card_fin] + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/StripReduction.lean b/lean/OAI/RepresentationTheory/Saxl/StripReduction.lean index 3133b67d8d94ebd1fb35446b6355cf733e9ea965..87d2e8b8cce2024db91a3af24459c50e71584a83 100644 --- a/lean/OAI/RepresentationTheory/Saxl/StripReduction.lean +++ b/lean/OAI/RepresentationTheory/Saxl/StripReduction.lean @@ -1,167 +1,167 @@ -import OAI.RepresentationTheory.Saxl.DominatedSupport - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl -inductive StripChain : ℕ → YoungDiagram → YoungDiagram → Prop - | nil (μ) : StripChain 0 μ μ - | snoc {q ν η μ} : StripChain q ν η → HorizontalStrip η μ → η ≠ μ → StripChain (q+1) ν μ - - -lemma stripRemove_full_prefix (μ : YoungDiagram) (q : ℕ) : - rowPrefix (stripRemove μ (μ.rowLen 0)) q + μ.rowLen 0 = rowPrefix μ (q+1) := by - have hh := stripRemove_prefix μ (μ.rowLen 0) q - rw [min_self, min_eq_right (μ.rowLen_anti 0 q (Nat.zero_le _))] at hh - exact hh.trans (rowPrefix_succ μ q).symm - -/- Sweeps remove any prescribed number within the first q-row capacity. -/ -theorem stripChain_of_capacity (q t : ℕ) (μ : YoungDiagram) - (ht : t ≤ rowPrefix μ q) : - ∃ k ≤ q, ∃ ν, ν.card + t = μ.card ∧ StripChain k ν μ := by - induction q generalizing t μ with - | zero => - have hz : t = 0 := by simpa [rowPrefix] using ht - exact ⟨0, le_rfl, μ, by omega, StripChain.nil μ⟩ - | succ q ih => - by_cases hz : t = 0 - · exact ⟨0, Nat.zero_le _, μ, by omega, StripChain.nil μ⟩ - by_cases hb : t ≤ μ.rowLen 0 - · let ν := stripRemove μ t - have hc : ν.card + t = μ.card := by - simpa only [ν, min_eq_left hb] using stripRemove_card μ t - have hn : ν ≠ μ := by intro he; rw [he] at hc; omega - exact ⟨1, by omega, ν, hc, - StripChain.snoc (StripChain.nil ν) (stripRemove_horizontal μ t) hn⟩ - · let η := stripRemove μ (μ.rowLen 0) - have hp : rowPrefix η q + μ.rowLen 0 = rowPrefix μ (q+1) := - stripRemove_full_prefix μ q - have hcap : t - μ.rowLen 0 ≤ rowPrefix η q := by omega - obtain ⟨k, hk, ν, hc, hchain⟩ := ih (t-μ.rowLen 0) η hcap - have hec : η.card + μ.rowLen 0 = μ.card := by - simpa only [η, min_self] using stripRemove_card μ (μ.rowLen 0) - have hpos : 0 < μ.rowLen 0 := by - by_contra h - have hz0 : μ.rowLen 0 = 0 := by omega - have hp0 : rowPrefix μ (q+1) = 0 := by - apply Finset.sum_eq_zero - intro i hi - have hh := μ.rowLen_anti 0 i (Nat.zero_le _) - omega - omega - have hn : η ≠ μ := by intro he; rw [he] at hec; omega - refine ⟨k+1, by omega, ν, ?_, StripChain.snoc hchain (stripRemove_horizontal μ _) hn⟩ - omega - -lemma rowPrefix_mean (μ : YoungDiagram) {q k : ℕ} (hqk : q ≤ k) : - q * rowPrefix μ k ≤ k * rowPrefix μ q := by - have hlow : q * μ.rowLen q ≤ rowPrefix μ q := by - calc - q * μ.rowLen q = ∑ i ∈ Finset.range q, μ.rowLen q := by simp - _ ≤ rowPrefix μ q := Finset.sum_le_sum (fun i hi => - μ.rowLen_anti i q (Nat.le_of_lt (Finset.mem_range.mp hi))) - have he : rowPrefix μ k = rowPrefix μ q + - ∑ i ∈ Finset.range (k-q), μ.rowLen (q+i) := by - simp only [rowPrefix] - rw [← Finset.sum_range_add] - congr 2 - omega - have htail : (∑ i ∈ Finset.range (k-q), μ.rowLen (q+i)) ≤ (k-q)*μ.rowLen q := by - calc - _ ≤ ∑ i ∈ Finset.range (k-q), μ.rowLen q := - Finset.sum_le_sum (fun i hi => μ.rowLen_anti q (q+i) (by omega)) - _ = _ := by simp - have hm := Nat.mul_le_mul_left (k-q) hlow - have hs := Nat.mul_le_mul_left q htail - rw [he] - have hsum : q + (k-q) = k := by omega - nlinarith - -@[simp] lemma staircase_rowLen (m i : ℕ) : (staircase m).rowLen i = m-i := by - have hh : ∀ j, j < (staircase m).rowLen i ↔ j < m-i := by - intro j - rw [← YoungDiagram.mem_iff_lt_rowLen, mem_staircase] - omega - have h₁ := hh ((staircase m).rowLen i) - have h₂ := hh (m-i) - omega - -lemma staircase_prefix_double (m k : ℕ) (hk : k ≤ m) : - 2 * rowPrefix (staircase m) k = k * (2*m+1-k) := by - induction k with - | zero => simp [rowPrefix] - | succ k ih => - rw [rowPrefix_succ, staircase_rowLen] - have hi := ih (by omega) - have hs : k + (m-k) = m := by omega - have ht : k + (2*m+1-k) = 2*m+1 := by omega - have ht' : (k+1) + (2*m+1-(k+1)) = 2*m+1 := by omega - nlinarith - -/- The exact capacity alternative used by the main induction. -/ -lemma strip_reduction_capacity (m : ℕ) (hm : 2 ≤ m) (μ : YoungDiagram) - (hμ : μ.card = (staircase m).card) (hdom : ¬ Dominates (staircase m) μ) - (hfirst : μ.rowLen 0 < m) : 5 ≤ m ∧ 2*m-1 ≤ rowPrefix μ 4 := by - obtain ⟨k, hk⟩ : ∃ k, rowPrefix (staircase m) k < rowPrefix μ k := by - simpa only [Dominates, not_forall, not_le] using hdom - have hkm : k < m := by - by_contra hh - have hc : (staircase m).colLen 0 ≤ k := by simp; omega - rw [rowPrefix_eq_card _ hc] at hk - have hle := rowPrefix_le_card μ k - omega - have hbound : rowPrefix μ k ≤ k * (m-1) := by - calc - _ ≤ ∑ i ∈ Finset.range k, (m-1) := by - apply Finset.sum_le_sum - intro i hi - have hh := μ.rowLen_anti 0 i (Nat.zero_le _) - omega - _ = _ := by simp - have hstair := staircase_prefix_double m k (by omega) - have hk4 : 4 ≤ k := by - have hm1 : m = (m-1)+1 := by omega - by_contra hh - interval_cases k <;> omega - have hmean := rowPrefix_mean μ hk4 - have hpos : 0 < k := by omega - have hsum : k + (2*m+1-k) = 2*m+1 := by omega - constructor - · omega - · have ha : 4*(2*m+1-k) < 2*rowPrefix μ 4 := by - nlinarith - have hb : 2*m-1 ≤ 2*(2*m+1-k) := by omega - omega - -theorem strip_reduction (m : ℕ) (hm : 2 ≤ m) (μ : YoungDiagram) - (hμ : μ.card = (staircase m).card) (hdom : ¬ Dominates (staircase m) μ) : - (∃ ν, ν.card = (staircase (m-1)).card ∧ HorizontalStrip ν μ) ∨ - (5 ≤ m ∧ ∃ q ≤ 4, ∃ ν, ν.card = (staircase (m-2)).card ∧ StripChain q ν μ) := by - by_cases hfirst : m ≤ μ.rowLen 0 - · left - let ν := stripRemove μ m - have hc : ν.card + m = μ.card := by - simpa only [ν, min_eq_left hfirst] using stripRemove_card μ m - have hs : (staircase m).card = (staircase (m-1)).card + m := by - have hh := staircase_card_succ (m-1) - have he : m-1+1 = m := by omega - simpa only [he] using hh - exact ⟨ν, by omega, stripRemove_horizontal μ m⟩ - · right - obtain ⟨hm5, hcap⟩ := strip_reduction_capacity m hm μ hμ hdom (by omega) - obtain ⟨q, hq, ν, hc, hs⟩ := stripChain_of_capacity 4 (2*m-1) μ hcap - refine ⟨hm5, q, hq, ν, ?_, hs⟩ - have hc₁ := staircase_card_double m - have hc₂ := staircase_card_double (m-2) - have hh : m = (m-2)+2 := by omega - have ht : 2*m-1+1 = 2*m := by omega - nlinarith - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.DominatedSupport + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl +inductive StripChain : ℕ → YoungDiagram → YoungDiagram → Prop + | nil (μ) : StripChain 0 μ μ + | snoc {q ν η μ} : StripChain q ν η → HorizontalStrip η μ → η ≠ μ → StripChain (q+1) ν μ + + +lemma stripRemove_full_prefix (μ : YoungDiagram) (q : ℕ) : + rowPrefix (stripRemove μ (μ.rowLen 0)) q + μ.rowLen 0 = rowPrefix μ (q+1) := by + have hh := stripRemove_prefix μ (μ.rowLen 0) q + rw [min_self, min_eq_right (μ.rowLen_anti 0 q (Nat.zero_le _))] at hh + exact hh.trans (rowPrefix_succ μ q).symm + +/- Sweeps remove any prescribed number within the first q-row capacity. -/ +theorem stripChain_of_capacity (q t : ℕ) (μ : YoungDiagram) + (ht : t ≤ rowPrefix μ q) : + ∃ k ≤ q, ∃ ν, ν.card + t = μ.card ∧ StripChain k ν μ := by + induction q generalizing t μ with + | zero => + have hz : t = 0 := by simpa [rowPrefix] using ht + exact ⟨0, le_rfl, μ, by omega, StripChain.nil μ⟩ + | succ q ih => + by_cases hz : t = 0 + · exact ⟨0, Nat.zero_le _, μ, by omega, StripChain.nil μ⟩ + by_cases hb : t ≤ μ.rowLen 0 + · let ν := stripRemove μ t + have hc : ν.card + t = μ.card := by + simpa only [ν, min_eq_left hb] using stripRemove_card μ t + have hn : ν ≠ μ := by intro he; rw [he] at hc; omega + exact ⟨1, by omega, ν, hc, + StripChain.snoc (StripChain.nil ν) (stripRemove_horizontal μ t) hn⟩ + · let η := stripRemove μ (μ.rowLen 0) + have hp : rowPrefix η q + μ.rowLen 0 = rowPrefix μ (q+1) := + stripRemove_full_prefix μ q + have hcap : t - μ.rowLen 0 ≤ rowPrefix η q := by omega + obtain ⟨k, hk, ν, hc, hchain⟩ := ih (t-μ.rowLen 0) η hcap + have hec : η.card + μ.rowLen 0 = μ.card := by + simpa only [η, min_self] using stripRemove_card μ (μ.rowLen 0) + have hpos : 0 < μ.rowLen 0 := by + by_contra h + have hz0 : μ.rowLen 0 = 0 := by omega + have hp0 : rowPrefix μ (q+1) = 0 := by + apply Finset.sum_eq_zero + intro i hi + have hh := μ.rowLen_anti 0 i (Nat.zero_le _) + omega + omega + have hn : η ≠ μ := by intro he; rw [he] at hec; omega + refine ⟨k+1, by omega, ν, ?_, StripChain.snoc hchain (stripRemove_horizontal μ _) hn⟩ + omega + +lemma rowPrefix_mean (μ : YoungDiagram) {q k : ℕ} (hqk : q ≤ k) : + q * rowPrefix μ k ≤ k * rowPrefix μ q := by + have hlow : q * μ.rowLen q ≤ rowPrefix μ q := by + calc + q * μ.rowLen q = ∑ i ∈ Finset.range q, μ.rowLen q := by simp + _ ≤ rowPrefix μ q := Finset.sum_le_sum (fun i hi => + μ.rowLen_anti i q (Nat.le_of_lt (Finset.mem_range.mp hi))) + have he : rowPrefix μ k = rowPrefix μ q + + ∑ i ∈ Finset.range (k-q), μ.rowLen (q+i) := by + simp only [rowPrefix] + rw [← Finset.sum_range_add] + congr 2 + omega + have htail : (∑ i ∈ Finset.range (k-q), μ.rowLen (q+i)) ≤ (k-q)*μ.rowLen q := by + calc + _ ≤ ∑ i ∈ Finset.range (k-q), μ.rowLen q := + Finset.sum_le_sum (fun i hi => μ.rowLen_anti q (q+i) (by omega)) + _ = _ := by simp + have hm := Nat.mul_le_mul_left (k-q) hlow + have hs := Nat.mul_le_mul_left q htail + rw [he] + have hsum : q + (k-q) = k := by omega + nlinarith + +@[simp] lemma staircase_rowLen (m i : ℕ) : (staircase m).rowLen i = m-i := by + have hh : ∀ j, j < (staircase m).rowLen i ↔ j < m-i := by + intro j + rw [← YoungDiagram.mem_iff_lt_rowLen, mem_staircase] + omega + have h₁ := hh ((staircase m).rowLen i) + have h₂ := hh (m-i) + omega + +lemma staircase_prefix_double (m k : ℕ) (hk : k ≤ m) : + 2 * rowPrefix (staircase m) k = k * (2*m+1-k) := by + induction k with + | zero => simp [rowPrefix] + | succ k ih => + rw [rowPrefix_succ, staircase_rowLen] + have hi := ih (by omega) + have hs : k + (m-k) = m := by omega + have ht : k + (2*m+1-k) = 2*m+1 := by omega + have ht' : (k+1) + (2*m+1-(k+1)) = 2*m+1 := by omega + nlinarith + +/- The exact capacity alternative used by the main induction. -/ +lemma strip_reduction_capacity (m : ℕ) (hm : 2 ≤ m) (μ : YoungDiagram) + (hμ : μ.card = (staircase m).card) (hdom : ¬ Dominates (staircase m) μ) + (hfirst : μ.rowLen 0 < m) : 5 ≤ m ∧ 2*m-1 ≤ rowPrefix μ 4 := by + obtain ⟨k, hk⟩ : ∃ k, rowPrefix (staircase m) k < rowPrefix μ k := by + simpa only [Dominates, not_forall, not_le] using hdom + have hkm : k < m := by + by_contra hh + have hc : (staircase m).colLen 0 ≤ k := by simp; omega + rw [rowPrefix_eq_card _ hc] at hk + have hle := rowPrefix_le_card μ k + omega + have hbound : rowPrefix μ k ≤ k * (m-1) := by + calc + _ ≤ ∑ i ∈ Finset.range k, (m-1) := by + apply Finset.sum_le_sum + intro i hi + have hh := μ.rowLen_anti 0 i (Nat.zero_le _) + omega + _ = _ := by simp + have hstair := staircase_prefix_double m k (by omega) + have hk4 : 4 ≤ k := by + have hm1 : m = (m-1)+1 := by omega + by_contra hh + interval_cases k <;> omega + have hmean := rowPrefix_mean μ hk4 + have hpos : 0 < k := by omega + have hsum : k + (2*m+1-k) = 2*m+1 := by omega + constructor + · omega + · have ha : 4*(2*m+1-k) < 2*rowPrefix μ 4 := by + nlinarith + have hb : 2*m-1 ≤ 2*(2*m+1-k) := by omega + omega + +theorem strip_reduction (m : ℕ) (hm : 2 ≤ m) (μ : YoungDiagram) + (hμ : μ.card = (staircase m).card) (hdom : ¬ Dominates (staircase m) μ) : + (∃ ν, ν.card = (staircase (m-1)).card ∧ HorizontalStrip ν μ) ∨ + (5 ≤ m ∧ ∃ q ≤ 4, ∃ ν, ν.card = (staircase (m-2)).card ∧ StripChain q ν μ) := by + by_cases hfirst : m ≤ μ.rowLen 0 + · left + let ν := stripRemove μ m + have hc : ν.card + m = μ.card := by + simpa only [ν, min_eq_left hfirst] using stripRemove_card μ m + have hs : (staircase m).card = (staircase (m-1)).card + m := by + have hh := staircase_card_succ (m-1) + have he : m-1+1 = m := by omega + simpa only [he] using hh + exact ⟨ν, by omega, stripRemove_horizontal μ m⟩ + · right + obtain ⟨hm5, hcap⟩ := strip_reduction_capacity m hm μ hμ hdom (by omega) + obtain ⟨q, hq, ν, hc, hs⟩ := stripChain_of_capacity 4 (2*m-1) μ hcap + refine ⟨hm5, q, hq, ν, ?_, hs⟩ + have hc₁ := staircase_card_double m + have hc₂ := staircase_card_double (m-2) + have hh : m = (m-2)+2 := by omega + have ht : 2*m-1+1 = 2*m := by omega + nlinarith + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/StripSupport.lean b/lean/OAI/RepresentationTheory/Saxl/StripSupport.lean index f268cd64d6f665a327ad9295964266bc86a5d528..34aa6bb7dd8937356bf2428ee77de8dd3094f132 100644 --- a/lean/OAI/RepresentationTheory/Saxl/StripSupport.lean +++ b/lean/OAI/RepresentationTheory/Saxl/StripSupport.lean @@ -1,135 +1,135 @@ -import OAI.RepresentationTheory.Saxl.SizedStrips - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl - -/- Place the smaller tableau on any chosen block, with the remaining strip -colors on its complement. No transitivity or induction rule is assumed. -/ -theorem placed_strip_restriction {n a b : ℕ} {ν μ : YoungDiagram} {bs : List ℕ} - (hs : SizedStripChain bs ν μ) (s : Tableau a ν) (t : Tableau n μ) - (e : Fin n ≃ Fin a ⊕ Fin b) : - ∃ (c : Fin b → Fin bs.length) (F : Specht t →ₗ[ℂ] Specht s), Function.Surjective F ∧ - ∀ (h : Equiv.Perm (Fin a)) (q : Equiv.Perm (Fin b)), c ∘ q = c → - ∀ x, F (spechtRep t (sumPerm e h q) x) = spechtRep s h (F x) := by - classical - obtain ⟨c,F,hF,hcb,hcz,hcount,hFe⟩ := stripChain_restriction_any hs s t - let i := tableauInclusion s t hs.le - let l : Fin a → Fin n := fun j => e.symm (Sum.inl j) - obtain ⟨p,hp⟩ := Equiv.Perm.exists_extending_pair l i - (fun x y h => Sum.inl.inj (e.symm.injective h)) i.injective - have hcL (j : Fin a) : c (p (e.symm (Sum.inl j))) = 0 := by - rw [show p (e.symm (Sum.inl j)) = i j from hp j] - exact (hcz _).mpr ⟨j,rfl⟩ - have hcRpos (j : Fin b) : 0 < c (p (e.symm (Sum.inr j))) := by - by_contra hn - have hz : c (p (e.symm (Sum.inr j))) = 0 := by omega - obtain ⟨k,hk⟩ := (hcz _).mp hz - have hh : e.symm (Sum.inl k) = e.symm (Sum.inr j) := p.injective ((hp k).trans hk) - have := e.symm.injective hh - cases this - let cb : Fin b → Fin bs.length := fun j => ⟨c (p (e.symm (Sum.inr j)))-1, by - have := hcRpos j - have := hcb (p (e.symm (Sum.inr j))) - omega⟩ - have hcR (j : Fin b) : c (p (e.symm (Sum.inr j))) = (cb j).val+1 := by - have := hcRpos j - change _ = (c (p (e.symm (Sum.inr j)))-1)+1 - omega - let F' := F.comp (spechtRep t p) - have hP : Function.Surjective (spechtRep t p) := by - intro x - refine ⟨spechtRep t p⁻¹ x, ?_⟩ - rw [← Module.End.mul_apply, ← map_mul, mul_inv_cancel, map_one] - rfl - refine ⟨cb,F',hF.comp hP, ?_⟩ - intro h q hq x - let g := p * sumPerm e h q * p⁻¹ - have hgL (j : Fin a) : g (p (e.symm (Sum.inl j))) = p (e.symm (Sum.inl (h j))) := by - simp [g] - have hgR (j : Fin b) : g (p (e.symm (Sum.inr j))) = p (e.symm (Sum.inr (q j))) := by - simp [g] - have hgc (j : Fin n) : c (g j) = c j := by - obtain ⟨z,rfl⟩ := p.surjective j - obtain ⟨z,rfl⟩ := e.symm.surjective z - cases z with - | inl j => rw [hgL,hcL,hcL] - | inr j => - rw [hgR,hcR,hcR] - exact congrArg (fun x : Fin bs.length => x.val+1) (congrFun hq j) - have hgi (j : Fin a) : g (i j) = i (h j) := by rw [← hp j,← hp (h j)]; exact hgL j - change F (spechtRep t p (spechtRep t (sumPerm e h q) x)) = spechtRep s h (F (spechtRep t p x)) - have hmul : p * sumPerm e h q = g * p := by simp [g,mul_assoc] - rw [← Module.End.mul_apply, ← map_mul, hmul, map_mul, Module.End.mul_apply] - exact hFe g h hgc hgi _ - -end Saxl - -namespace Saxl - -/- Required support transfer from a genuine iterated horizontal-strip -restriction and genuine independent high/band cyclic factors. -/ -theorem strip_product_support {n a b d : ℕ} {ν μ : YoungDiagram} {bs : List ℕ} - (hs : SizedStripChain bs ν μ) (s : Tableau a ν) (t : Tableau n μ) - (e : Fin n ≃ Fin a ⊕ Fin b) (v : WordSpace a d) (u : WordSpace b d) - (A : Fin d → Prop) (hv : v ∈ alphabetSub a d A) - (hu : u ∈ alphabetSub b d (fun z => ¬A z)) - (f : Representation.IntertwiningMap (spechtRep s) (cyclic (wordRep a d) v).toRepresentation) - (hf : f ≠ 0) - (hband : ∀ (η : YoungDiagram) (r : Tableau b η), η.colLen 0 ≤ bs.length → - ∃ F : Representation.IntertwiningMap (spechtRep r) (cyclic (wordRep b d) u).toRepresentation, F ≠ 0) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n d) (positionProduct e v u)).toRepresentation, F ≠ 0 := by - classical - obtain ⟨c,F,hF,hFe⟩ := placed_strip_restriction hs s t e - let G := (subrepInclusion (cyclic (wordRep a d) v)).comp f - let F₀ : Specht t →ₗ[ℂ] WordSpace a d := G.toLinearMap.comp F - have hF₀ : F₀ ≠ 0 := by - intro hz - apply hf - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro y - obtain ⟨x,rfl⟩ := hF y - apply Subtype.ext - exact LinearMap.congr_fun hz x - have hFb (q : Equiv.Perm (Fin b)) (hq : c ∘ q = c) (x : Specht t) : - F₀ (spechtRep t (sumPerm e 1 q) x) = F₀ x := by - change G (F (spechtRep t (sumPerm e 1 q) x)) = G (F x) - rw [hFe 1 q hq, map_one] - rfl - have hFa (h : Equiv.Perm (Fin a)) (x : Specht t) : - F₀ (spechtRep t (sumPerm e h 1) x) = wordRep a d h (F₀ x) := by - change G (F (spechtRep t (sumPerm e h 1) x)) = wordRep a d h (G (F x)) - rw [hFe h 1 rfl] - exact LinearMap.congr_fun (G.isIntertwining' h) (F x) - let T := bandOrbitMap e (spechtRep t) c F₀ - have hTm (x : Specht t) (w : Fin b → Fin bs.length) : T x w ∈ cyclic (wordRep a d) v := by - change (∑ g : Equiv.Perm (Fin b), _) ∈ (cyclic (wordRep a d) v).toSubmodule - apply Submodule.sum_mem - intro g hg - apply Submodule.smul_mem - exact (f (F (spechtRep t (sumPerm e 1 g⁻¹) x))).property - obtain ⟨L,hL,hLe,hLm,hLs⟩ := bandGlue_sector_exists e (spechtRep t) v u A hv hu hband T - (bandOrbitMap_nonzero e (spechtRep t) c F₀ hF₀ hFb) - (bandOrbitMap_equivariant e (spechtRep t) (wordRep a d) c F₀ hFa) hTm - apply sector_support_transfer (spechtRep t) (fun i => (e i).isLeft = true) A - (positionProduct e v u) L hL _ hLm - · intro x w hw - by_contra hn - exact hw (hLs x w hn) - · intro g hg x - let g' : sectorGroup (fun i => (e i).isLeft = true) := ⟨g,hg⟩ - have heq : sumPerm e (leftRestriction e g') (rightRestriction e g') = g := sumPerm_restrictions e g' - rw [← heq] - exact hLe _ _ x - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.SizedStrips + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl + +/- Place the smaller tableau on any chosen block, with the remaining strip +colors on its complement. No transitivity or induction rule is assumed. -/ +theorem placed_strip_restriction {n a b : ℕ} {ν μ : YoungDiagram} {bs : List ℕ} + (hs : SizedStripChain bs ν μ) (s : Tableau a ν) (t : Tableau n μ) + (e : Fin n ≃ Fin a ⊕ Fin b) : + ∃ (c : Fin b → Fin bs.length) (F : Specht t →ₗ[ℂ] Specht s), Function.Surjective F ∧ + ∀ (h : Equiv.Perm (Fin a)) (q : Equiv.Perm (Fin b)), c ∘ q = c → + ∀ x, F (spechtRep t (sumPerm e h q) x) = spechtRep s h (F x) := by + classical + obtain ⟨c,F,hF,hcb,hcz,hcount,hFe⟩ := stripChain_restriction_any hs s t + let i := tableauInclusion s t hs.le + let l : Fin a → Fin n := fun j => e.symm (Sum.inl j) + obtain ⟨p,hp⟩ := Equiv.Perm.exists_extending_pair l i + (fun x y h => Sum.inl.inj (e.symm.injective h)) i.injective + have hcL (j : Fin a) : c (p (e.symm (Sum.inl j))) = 0 := by + rw [show p (e.symm (Sum.inl j)) = i j from hp j] + exact (hcz _).mpr ⟨j,rfl⟩ + have hcRpos (j : Fin b) : 0 < c (p (e.symm (Sum.inr j))) := by + by_contra hn + have hz : c (p (e.symm (Sum.inr j))) = 0 := by omega + obtain ⟨k,hk⟩ := (hcz _).mp hz + have hh : e.symm (Sum.inl k) = e.symm (Sum.inr j) := p.injective ((hp k).trans hk) + have := e.symm.injective hh + cases this + let cb : Fin b → Fin bs.length := fun j => ⟨c (p (e.symm (Sum.inr j)))-1, by + have := hcRpos j + have := hcb (p (e.symm (Sum.inr j))) + omega⟩ + have hcR (j : Fin b) : c (p (e.symm (Sum.inr j))) = (cb j).val+1 := by + have := hcRpos j + change _ = (c (p (e.symm (Sum.inr j)))-1)+1 + omega + let F' := F.comp (spechtRep t p) + have hP : Function.Surjective (spechtRep t p) := by + intro x + refine ⟨spechtRep t p⁻¹ x, ?_⟩ + rw [← Module.End.mul_apply, ← map_mul, mul_inv_cancel, map_one] + rfl + refine ⟨cb,F',hF.comp hP, ?_⟩ + intro h q hq x + let g := p * sumPerm e h q * p⁻¹ + have hgL (j : Fin a) : g (p (e.symm (Sum.inl j))) = p (e.symm (Sum.inl (h j))) := by + simp [g] + have hgR (j : Fin b) : g (p (e.symm (Sum.inr j))) = p (e.symm (Sum.inr (q j))) := by + simp [g] + have hgc (j : Fin n) : c (g j) = c j := by + obtain ⟨z,rfl⟩ := p.surjective j + obtain ⟨z,rfl⟩ := e.symm.surjective z + cases z with + | inl j => rw [hgL,hcL,hcL] + | inr j => + rw [hgR,hcR,hcR] + exact congrArg (fun x : Fin bs.length => x.val+1) (congrFun hq j) + have hgi (j : Fin a) : g (i j) = i (h j) := by rw [← hp j,← hp (h j)]; exact hgL j + change F (spechtRep t p (spechtRep t (sumPerm e h q) x)) = spechtRep s h (F (spechtRep t p x)) + have hmul : p * sumPerm e h q = g * p := by simp [g,mul_assoc] + rw [← Module.End.mul_apply, ← map_mul, hmul, map_mul, Module.End.mul_apply] + exact hFe g h hgc hgi _ + +end Saxl + +namespace Saxl + +/- Required support transfer from a genuine iterated horizontal-strip +restriction and genuine independent high/band cyclic factors. -/ +theorem strip_product_support {n a b d : ℕ} {ν μ : YoungDiagram} {bs : List ℕ} + (hs : SizedStripChain bs ν μ) (s : Tableau a ν) (t : Tableau n μ) + (e : Fin n ≃ Fin a ⊕ Fin b) (v : WordSpace a d) (u : WordSpace b d) + (A : Fin d → Prop) (hv : v ∈ alphabetSub a d A) + (hu : u ∈ alphabetSub b d (fun z => ¬A z)) + (f : Representation.IntertwiningMap (spechtRep s) (cyclic (wordRep a d) v).toRepresentation) + (hf : f ≠ 0) + (hband : ∀ (η : YoungDiagram) (r : Tableau b η), η.colLen 0 ≤ bs.length → + ∃ F : Representation.IntertwiningMap (spechtRep r) (cyclic (wordRep b d) u).toRepresentation, F ≠ 0) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n d) (positionProduct e v u)).toRepresentation, F ≠ 0 := by + classical + obtain ⟨c,F,hF,hFe⟩ := placed_strip_restriction hs s t e + let G := (subrepInclusion (cyclic (wordRep a d) v)).comp f + let F₀ : Specht t →ₗ[ℂ] WordSpace a d := G.toLinearMap.comp F + have hF₀ : F₀ ≠ 0 := by + intro hz + apply hf + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro y + obtain ⟨x,rfl⟩ := hF y + apply Subtype.ext + exact LinearMap.congr_fun hz x + have hFb (q : Equiv.Perm (Fin b)) (hq : c ∘ q = c) (x : Specht t) : + F₀ (spechtRep t (sumPerm e 1 q) x) = F₀ x := by + change G (F (spechtRep t (sumPerm e 1 q) x)) = G (F x) + rw [hFe 1 q hq, map_one] + rfl + have hFa (h : Equiv.Perm (Fin a)) (x : Specht t) : + F₀ (spechtRep t (sumPerm e h 1) x) = wordRep a d h (F₀ x) := by + change G (F (spechtRep t (sumPerm e h 1) x)) = wordRep a d h (G (F x)) + rw [hFe h 1 rfl] + exact LinearMap.congr_fun (G.isIntertwining' h) (F x) + let T := bandOrbitMap e (spechtRep t) c F₀ + have hTm (x : Specht t) (w : Fin b → Fin bs.length) : T x w ∈ cyclic (wordRep a d) v := by + change (∑ g : Equiv.Perm (Fin b), _) ∈ (cyclic (wordRep a d) v).toSubmodule + apply Submodule.sum_mem + intro g hg + apply Submodule.smul_mem + exact (f (F (spechtRep t (sumPerm e 1 g⁻¹) x))).property + obtain ⟨L,hL,hLe,hLm,hLs⟩ := bandGlue_sector_exists e (spechtRep t) v u A hv hu hband T + (bandOrbitMap_nonzero e (spechtRep t) c F₀ hF₀ hFb) + (bandOrbitMap_equivariant e (spechtRep t) (wordRep a d) c F₀ hFa) hTm + apply sector_support_transfer (spechtRep t) (fun i => (e i).isLeft = true) A + (positionProduct e v u) L hL _ hLm + · intro x w hw + by_contra hn + exact hw (hLs x w hn) + · intro g hg x + let g' : sectorGroup (fun i => (e i).isLeft = true) := ⟨g,hg⟩ + have heq : sumPerm e (leftRestriction e g') (rightRestriction e g') = g := sumPerm_restrictions e g' + rw [← heq] + exact hLe _ _ x + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/SupportSeparation.lean b/lean/OAI/RepresentationTheory/Saxl/SupportSeparation.lean index d638bc66ba4d24cefcb432b1cb39b1431b912fa8..7722dd50081513b2c5184ff383856bd0f1f3c4ca 100644 --- a/lean/OAI/RepresentationTheory/Saxl/SupportSeparation.lean +++ b/lean/OAI/RepresentationTheory/Saxl/SupportSeparation.lean @@ -1,162 +1,162 @@ -import OAI.RepresentationTheory.Saxl.SpechtClassification - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -universe uR uX uY uG uV - -namespace Saxl -open scoped MonoidAlgebra - -/- In a semisimple module, support containment is equivalent to separation -by homomorphisms (multiplicities are immaterial for the band step). -/ -theorem hom_separates_of_simple_support {R : Type uR} {X : Type uX} {Y : Type uY} [Ring R] - [AddCommGroup X] [Module R X] [AddCommGroup Y] [Module R Y] - [IsSemisimpleModule R X] - (h : ∀ S : Submodule R X, IsSimpleModule R S → - ∃ f : S →ₗ[R] Y, f ≠ 0) (x : X) (hx : x ≠ 0) : - ∃ f : X →ₗ[R] Y, f x ≠ 0 := by - classical - let K : Submodule R X := ⨅ f : X →ₗ[R] Y, LinearMap.ker f - have hK : K = ⊥ := by - rcases IsSemisimpleModule.eq_bot_or_exists_simple_le K with hk | ⟨S, hS, hs⟩ - · exact hk - obtain ⟨f, hf⟩ := h S hs - obtain ⟨F, hF⟩ := IsSemisimpleModule.extension_property S.subtype S.subtype_injective f - exfalso - apply hf - ext s - have hm : s.val ∈ K := hS s.property - have he : F s.val = 0 := ((Submodule.mem_iInf _).mp hm F) - change f s = 0 - exact (LinearMap.congr_fun hF s).symm.trans he - by_contra hf - push Not at hf - apply hx - have hm : x ∈ K := (Submodule.mem_iInf _).mpr (fun f => hf f) - simpa only [hK, Submodule.mem_bot] using hm - -end Saxl - -namespace Saxl -open scoped MonoidAlgebra - -/- The invariant-subspace and group-algebra subtype constructions agree. -/ -def subrepModuleEquiv {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] - {ρ : Representation ℂ G V} (S : Subrepresentation ρ) : - S.toRepresentation.asModule ≃ₗ[ℂ[G]] S.asSubmodule where - toFun x := ⟨x.val, x.property⟩ - invFun x := ⟨x.val, x.property⟩ - left_inv _ := rfl - right_inv _ := rfl - map_add' _ _ := rfl - map_smul' a x := by - change (⟨(a • x).val, _⟩ : S.asSubmodule) = a • ⟨x.val, x.property⟩ - apply Subtype.ext - change (a • x).val = ρ.asModuleEquiv (a • ρ.asModuleEquiv.symm x.val) - induction a using MonoidAlgebra.induction_linear with - | zero => simp only [zero_smul, map_zero]; rfl - | add a b ha hb => - simp only [add_smul, map_add] - change (a • x).val + (b • x).val = _ - rw [ha, hb] - | single g c => - rw [Representation.single_smul, Representation.single_smul] - rfl - -lemma subrep_irreducible_of_simple {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] - {ρ : Representation ℂ G V} (S : Submodule ℂ[G] ρ.asModule) - [IsSimpleModule ℂ[G] S] : - Representation.IsIrreducible (Subrepresentation.ofSubmodule' S).toRepresentation := by - apply (Representation.irreducible_iff_isSimpleModule_asModule _).mpr - let e : (Subrepresentation.ofSubmodule' S).toRepresentation.asModule ≃ₗ[ℂ[G]] S := - subrepModuleEquiv (Subrepresentation.ofSubmodule' S) - exact IsSimpleModule.congr e - -end Saxl - -namespace Saxl -open scoped MonoidAlgebra - -theorem intertwining_separates_of_simple_support {G : Type uG} {X : Type uX} {Y : Type uY} - [Group G] [Finite G] [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] - (ρ : Representation ℂ G X) (σ : Representation ℂ G Y) - (h : ∀ S : Subrepresentation ρ, Representation.IsIrreducible S.toRepresentation → - ∃ f : Representation.IntertwiningMap S.toRepresentation σ, f ≠ 0) - (x : X) (hx : x ≠ 0) : - ∃ f : Representation.IntertwiningMap ρ σ, f x ≠ 0 := by - classical - have hs (S : Submodule ℂ[G] ρ.asModule) (hS : IsSimpleModule ℂ[G] S) : - ∃ f : S →ₗ[ℂ[G]] σ.asModule, f ≠ 0 := by - let P := Subrepresentation.ofSubmodule' S - let := hS - obtain ⟨f, hf⟩ := h P (subrep_irreducible_of_simple S) - let F := Representation.IntertwiningMap.equivLinearMapAsModule _ _ f - let E : P.toRepresentation.asModule ≃ₗ[ℂ[G]] S := subrepModuleEquiv P - refine ⟨F.comp E.symm.toLinearMap, ?_⟩ - intro hz - apply hf - apply (Representation.IntertwiningMap.equivLinearMapAsModule _ _).injective - ext v - have he := LinearMap.congr_fun hz (E v) - change F v = 0 - simpa only [LinearMap.comp_apply, LinearEquiv.coe_coe, - E.symm_apply_apply, LinearMap.zero_apply] using he - obtain ⟨f, hf⟩ := hom_separates_of_simple_support hs (ρ.asModuleEquiv.symm x) - (fun he => hx (ρ.asModuleEquiv.symm.injective (he.trans (map_zero _).symm))) - exact ⟨(Representation.IntertwiningMap.equivLinearMapAsModule _ _).symm f, hf⟩ - -end Saxl - -namespace Saxl -open scoped MonoidAlgebra - -end Saxl - -namespace Saxl - -def subrepInclusion {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] - {ρ : Representation ℂ G V} (S : Subrepresentation ρ) : - Representation.IntertwiningMap S.toRepresentation ρ where - toLinearMap := S.toSubmodule.subtype - isIntertwining' _ := rfl - -/- All constituents needed from a d-letter permutation module are detected -by a module containing each Specht type of height at most d. -/ -theorem word_support_separates {n d : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] - (σ : Representation ℂ (Equiv.Perm (Fin n)) V) - (h : ∀ (μ : YoungDiagram) (t : Tableau n μ), μ.colLen 0 ≤ d → - ∃ f : Representation.IntertwiningMap (spechtRep t) σ, f ≠ 0) - (x : WordSpace n d) (hx : x ≠ 0) : - ∃ f : Representation.IntertwiningMap (wordRep n d) σ, f x ≠ 0 := by - apply intertwining_separates_of_simple_support (wordRep n d) σ ?_ x hx - intro S hS - let := hS - obtain ⟨p, ⟨e⟩⟩ := irreducible_equiv_specht S.toRepresentation - let t := partitionTableau p - let i : Representation.IntertwiningMap (spechtRep t) (wordRep n d) := - (subrepInclusion S).comp e.symm.toIntertwiningMap - have hi : i ≠ 0 := by - intro he - have hz := congrArg (fun F : Representation.IntertwiningMap (spechtRep t) (wordRep n d) => - F ⟨polytabloid t, mem_cyclic _ _⟩) he - have h0 : e.symm ⟨polytabloid t, mem_cyclic _ _⟩ = 0 := Subtype.ext hz - have h1 := e.symm.injective (h0.trans (map_zero _).symm) - exact polytabloid_ne_zero t (congrArg Subtype.val h1) - obtain ⟨f, hf⟩ := h _ t (specht_rows_of_hom t i hi) - refine ⟨f.comp e.toIntertwiningMap, ?_⟩ - intro he - apply hf - ext y - obtain ⟨z, rfl⟩ := e.surjective y - exact congrArg (fun F : Representation.IntertwiningMap S.toRepresentation σ => F z) he - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.SpechtClassification + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +universe uR uX uY uG uV + +namespace Saxl +open scoped MonoidAlgebra + +/- In a semisimple module, support containment is equivalent to separation +by homomorphisms (multiplicities are immaterial for the band step). -/ +theorem hom_separates_of_simple_support {R : Type uR} {X : Type uX} {Y : Type uY} [Ring R] + [AddCommGroup X] [Module R X] [AddCommGroup Y] [Module R Y] + [IsSemisimpleModule R X] + (h : ∀ S : Submodule R X, IsSimpleModule R S → + ∃ f : S →ₗ[R] Y, f ≠ 0) (x : X) (hx : x ≠ 0) : + ∃ f : X →ₗ[R] Y, f x ≠ 0 := by + classical + let K : Submodule R X := ⨅ f : X →ₗ[R] Y, LinearMap.ker f + have hK : K = ⊥ := by + rcases IsSemisimpleModule.eq_bot_or_exists_simple_le K with hk | ⟨S, hS, hs⟩ + · exact hk + obtain ⟨f, hf⟩ := h S hs + obtain ⟨F, hF⟩ := IsSemisimpleModule.extension_property S.subtype S.subtype_injective f + exfalso + apply hf + ext s + have hm : s.val ∈ K := hS s.property + have he : F s.val = 0 := ((Submodule.mem_iInf _).mp hm F) + change f s = 0 + exact (LinearMap.congr_fun hF s).symm.trans he + by_contra hf + push Not at hf + apply hx + have hm : x ∈ K := (Submodule.mem_iInf _).mpr (fun f => hf f) + simpa only [hK, Submodule.mem_bot] using hm + +end Saxl + +namespace Saxl +open scoped MonoidAlgebra + +/- The invariant-subspace and group-algebra subtype constructions agree. -/ +def subrepModuleEquiv {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] + {ρ : Representation ℂ G V} (S : Subrepresentation ρ) : + S.toRepresentation.asModule ≃ₗ[ℂ[G]] S.asSubmodule where + toFun x := ⟨x.val, x.property⟩ + invFun x := ⟨x.val, x.property⟩ + left_inv _ := rfl + right_inv _ := rfl + map_add' _ _ := rfl + map_smul' a x := by + change (⟨(a • x).val, _⟩ : S.asSubmodule) = a • ⟨x.val, x.property⟩ + apply Subtype.ext + change (a • x).val = ρ.asModuleEquiv (a • ρ.asModuleEquiv.symm x.val) + induction a using MonoidAlgebra.induction_linear with + | zero => simp only [zero_smul, map_zero]; rfl + | add a b ha hb => + simp only [add_smul, map_add] + change (a • x).val + (b • x).val = _ + rw [ha, hb] + | single g c => + rw [Representation.single_smul, Representation.single_smul] + rfl + +lemma subrep_irreducible_of_simple {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] + {ρ : Representation ℂ G V} (S : Submodule ℂ[G] ρ.asModule) + [IsSimpleModule ℂ[G] S] : + Representation.IsIrreducible (Subrepresentation.ofSubmodule' S).toRepresentation := by + apply (Representation.irreducible_iff_isSimpleModule_asModule _).mpr + let e : (Subrepresentation.ofSubmodule' S).toRepresentation.asModule ≃ₗ[ℂ[G]] S := + subrepModuleEquiv (Subrepresentation.ofSubmodule' S) + exact IsSimpleModule.congr e + +end Saxl + +namespace Saxl +open scoped MonoidAlgebra + +theorem intertwining_separates_of_simple_support {G : Type uG} {X : Type uX} {Y : Type uY} + [Group G] [Finite G] [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] + (ρ : Representation ℂ G X) (σ : Representation ℂ G Y) + (h : ∀ S : Subrepresentation ρ, Representation.IsIrreducible S.toRepresentation → + ∃ f : Representation.IntertwiningMap S.toRepresentation σ, f ≠ 0) + (x : X) (hx : x ≠ 0) : + ∃ f : Representation.IntertwiningMap ρ σ, f x ≠ 0 := by + classical + have hs (S : Submodule ℂ[G] ρ.asModule) (hS : IsSimpleModule ℂ[G] S) : + ∃ f : S →ₗ[ℂ[G]] σ.asModule, f ≠ 0 := by + let P := Subrepresentation.ofSubmodule' S + let := hS + obtain ⟨f, hf⟩ := h P (subrep_irreducible_of_simple S) + let F := Representation.IntertwiningMap.equivLinearMapAsModule _ _ f + let E : P.toRepresentation.asModule ≃ₗ[ℂ[G]] S := subrepModuleEquiv P + refine ⟨F.comp E.symm.toLinearMap, ?_⟩ + intro hz + apply hf + apply (Representation.IntertwiningMap.equivLinearMapAsModule _ _).injective + ext v + have he := LinearMap.congr_fun hz (E v) + change F v = 0 + simpa only [LinearMap.comp_apply, LinearEquiv.coe_coe, + E.symm_apply_apply, LinearMap.zero_apply] using he + obtain ⟨f, hf⟩ := hom_separates_of_simple_support hs (ρ.asModuleEquiv.symm x) + (fun he => hx (ρ.asModuleEquiv.symm.injective (he.trans (map_zero _).symm))) + exact ⟨(Representation.IntertwiningMap.equivLinearMapAsModule _ _).symm f, hf⟩ + +end Saxl + +namespace Saxl +open scoped MonoidAlgebra + +end Saxl + +namespace Saxl + +def subrepInclusion {G : Type uG} {V : Type uV} [Group G] [AddCommGroup V] [Module ℂ V] + {ρ : Representation ℂ G V} (S : Subrepresentation ρ) : + Representation.IntertwiningMap S.toRepresentation ρ where + toLinearMap := S.toSubmodule.subtype + isIntertwining' _ := rfl + +/- All constituents needed from a d-letter permutation module are detected +by a module containing each Specht type of height at most d. -/ +theorem word_support_separates {n d : ℕ} {V : Type uV} [AddCommGroup V] [Module ℂ V] + (σ : Representation ℂ (Equiv.Perm (Fin n)) V) + (h : ∀ (μ : YoungDiagram) (t : Tableau n μ), μ.colLen 0 ≤ d → + ∃ f : Representation.IntertwiningMap (spechtRep t) σ, f ≠ 0) + (x : WordSpace n d) (hx : x ≠ 0) : + ∃ f : Representation.IntertwiningMap (wordRep n d) σ, f x ≠ 0 := by + apply intertwining_separates_of_simple_support (wordRep n d) σ ?_ x hx + intro S hS + let := hS + obtain ⟨p, ⟨e⟩⟩ := irreducible_equiv_specht S.toRepresentation + let t := partitionTableau p + let i : Representation.IntertwiningMap (spechtRep t) (wordRep n d) := + (subrepInclusion S).comp e.symm.toIntertwiningMap + have hi : i ≠ 0 := by + intro he + have hz := congrArg (fun F : Representation.IntertwiningMap (spechtRep t) (wordRep n d) => + F ⟨polytabloid t, mem_cyclic _ _⟩) he + have h0 : e.symm ⟨polytabloid t, mem_cyclic _ _⟩ = 0 := Subtype.ext hz + have h1 := e.symm.injective (h0.trans (map_zero _).symm) + exact polytabloid_ne_zero t (congrArg Subtype.val h1) + obtain ⟨f, hf⟩ := h _ t (specht_rows_of_hom t i hi) + refine ⟨f.comp e.toIntertwiningMap, ?_⟩ + intro he + apply hf + ext y + obtain ⟨z, rfl⟩ := e.surjective y + exact congrArg (fun F : Representation.IntertwiningMap S.toRepresentation σ => F z) he + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/TableauTransport.lean b/lean/OAI/RepresentationTheory/Saxl/TableauTransport.lean index 1dee7c52c0b7d2883f94203ff34eb6fa6df48b24..a3df4e36264b03486bf1d9ae838c61dd01d6eb06 100644 --- a/lean/OAI/RepresentationTheory/Saxl/TableauTransport.lean +++ b/lean/OAI/RepresentationTheory/Saxl/TableauTransport.lean @@ -1,82 +1,82 @@ -import OAI.RepresentationTheory.Saxl.SpechtDuality - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl -/- A change of tableau enumeration only applies a position permutation. -/ -def tableauMove {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) : Equiv.Perm (Fin n) := - s.trans t.symm - -@[simp] lemma tableauMove_apply {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) (i : Fin n) : - t (tableauMove s t i) = s i := by simp [tableauMove] - -@[simp] lemma tableauMove_inv_apply {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) (i : Fin n) : - s ((tableauMove s t)⁻¹ i) = t i := by simp [tableauMove, Equiv.Perm.inv_def] - -def columnMove {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) : - columnGroup s ≃ columnGroup t where - toFun h := ⟨tableauMove s t * h.val * (tableauMove s t)⁻¹, by - intro i - simp only [Equiv.Perm.mul_apply, tableauMove_apply] - rw [h.property, tableauMove_inv_apply]⟩ - invFun h := ⟨(tableauMove s t)⁻¹ * h.val * tableauMove s t, by - intro i - simp only [Equiv.Perm.mul_apply, tableauMove_inv_apply] - rw [h.property, tableauMove_apply]⟩ - left_inv h := by apply Subtype.ext; simp [mul_assoc] - right_inv h := by apply Subtype.ext; simp [mul_assoc] - -lemma rowWord_move {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) : - rowWord t = rowWord s ∘ ((tableauMove s t)⁻¹ : Equiv.Perm (Fin n)) := by - funext i - apply Fin.ext - exact congrArg (fun c : μ.cells => c.val.1) (tableauMove_inv_apply s t i).symm - -lemma polytabloid_move {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) : - polytabloid t = wordRep n (μ.colLen 0) (tableauMove s t) (polytabloid s) := by - classical - let := Fintype.ofFinite (columnGroup s) - let := Fintype.ofFinite (columnGroup t) - unfold polytabloid - rw [map_sum] - refine (Fintype.sum_equiv (columnMove s t).symm _ _ ?_) - intro h - let g := tableauMove s t - change signC (h : Equiv.Perm (Fin n)) • wordRep n (μ.colLen 0) h.val (Pi.single (rowWord t) 1) = - wordRep n (μ.colLen 0) g - (signC ((columnMove s t).symm h).val • - wordRep n (μ.colLen 0) ((columnMove s t).symm h).val (Pi.single (rowWord s) 1)) - have hs : signC ((columnMove s t).symm h).val = signC h.val := by - change signC (g⁻¹ * h.val * g) = signC h.val - rw [map_mul, map_mul, signC_inv] - calc signC g * signC h.val * signC g = signC h.val * (signC g * signC g) := by ring - _ = signC h.val := by rw [signC_mul_self, mul_one] - rw [map_smul, hs] - congr 1 - rw [← Module.End.mul_apply, ← map_mul] - change wordRep n (μ.colLen 0) h.val (Pi.single (rowWord t) 1) = - wordRep n (μ.colLen 0) (g * (g⁻¹ * h.val * g)) (Pi.single (rowWord s) 1) - have he : g * (g⁻¹ * h.val * g) = h.val * g := by group - have hv : wordRep n (μ.colLen 0) g (Pi.single (rowWord s) 1) = Pi.single (rowWord t) 1 := by - rw [wordRep_single, rowWord_move s t] - rw [he, map_mul, Module.End.mul_apply, hv] - -lemma polytabloid_mem_all {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) : - polytabloid t ∈ spechtSub s := by - rw [polytabloid_move s t] - exact (spechtSub s).apply_mem_toSubmodule _ (mem_cyclic _ _) - -lemma spechtSub_tableau_independent {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) : - spechtSub s = spechtSub t := by - apply le_antisymm - · exact (cyclic_le _ _ _).mpr (polytabloid_mem_all t s) - · exact (cyclic_le _ _ _).mpr (polytabloid_mem_all s t) -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.SpechtDuality + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl +/- A change of tableau enumeration only applies a position permutation. -/ +def tableauMove {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) : Equiv.Perm (Fin n) := + s.trans t.symm + +@[simp] lemma tableauMove_apply {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) (i : Fin n) : + t (tableauMove s t i) = s i := by simp [tableauMove] + +@[simp] lemma tableauMove_inv_apply {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) (i : Fin n) : + s ((tableauMove s t)⁻¹ i) = t i := by simp [tableauMove, Equiv.Perm.inv_def] + +def columnMove {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) : + columnGroup s ≃ columnGroup t where + toFun h := ⟨tableauMove s t * h.val * (tableauMove s t)⁻¹, by + intro i + simp only [Equiv.Perm.mul_apply, tableauMove_apply] + rw [h.property, tableauMove_inv_apply]⟩ + invFun h := ⟨(tableauMove s t)⁻¹ * h.val * tableauMove s t, by + intro i + simp only [Equiv.Perm.mul_apply, tableauMove_inv_apply] + rw [h.property, tableauMove_apply]⟩ + left_inv h := by apply Subtype.ext; simp [mul_assoc] + right_inv h := by apply Subtype.ext; simp [mul_assoc] + +lemma rowWord_move {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) : + rowWord t = rowWord s ∘ ((tableauMove s t)⁻¹ : Equiv.Perm (Fin n)) := by + funext i + apply Fin.ext + exact congrArg (fun c : μ.cells => c.val.1) (tableauMove_inv_apply s t i).symm + +lemma polytabloid_move {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) : + polytabloid t = wordRep n (μ.colLen 0) (tableauMove s t) (polytabloid s) := by + classical + let := Fintype.ofFinite (columnGroup s) + let := Fintype.ofFinite (columnGroup t) + unfold polytabloid + rw [map_sum] + refine (Fintype.sum_equiv (columnMove s t).symm _ _ ?_) + intro h + let g := tableauMove s t + change signC (h : Equiv.Perm (Fin n)) • wordRep n (μ.colLen 0) h.val (Pi.single (rowWord t) 1) = + wordRep n (μ.colLen 0) g + (signC ((columnMove s t).symm h).val • + wordRep n (μ.colLen 0) ((columnMove s t).symm h).val (Pi.single (rowWord s) 1)) + have hs : signC ((columnMove s t).symm h).val = signC h.val := by + change signC (g⁻¹ * h.val * g) = signC h.val + rw [map_mul, map_mul, signC_inv] + calc signC g * signC h.val * signC g = signC h.val * (signC g * signC g) := by ring + _ = signC h.val := by rw [signC_mul_self, mul_one] + rw [map_smul, hs] + congr 1 + rw [← Module.End.mul_apply, ← map_mul] + change wordRep n (μ.colLen 0) h.val (Pi.single (rowWord t) 1) = + wordRep n (μ.colLen 0) (g * (g⁻¹ * h.val * g)) (Pi.single (rowWord s) 1) + have he : g * (g⁻¹ * h.val * g) = h.val * g := by group + have hv : wordRep n (μ.colLen 0) g (Pi.single (rowWord s) 1) = Pi.single (rowWord t) 1 := by + rw [wordRep_single, rowWord_move s t] + rw [he, map_mul, Module.End.mul_apply, hv] + +lemma polytabloid_mem_all {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) : + polytabloid t ∈ spechtSub s := by + rw [polytabloid_move s t] + exact (spechtSub s).apply_mem_toSubmodule _ (mem_cyclic _ _) + +lemma spechtSub_tableau_independent {n : ℕ} {μ : YoungDiagram} (s t : Tableau n μ) : + spechtSub s = spechtSub t := by + apply le_antisymm + · exact (cyclic_le _ _ _).mpr (polytabloid_mem_all t s) + · exact (cyclic_le _ _ _).mpr (polytabloid_mem_all s t) +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Saxl/YoungRule.lean b/lean/OAI/RepresentationTheory/Saxl/YoungRule.lean index 40b91784795ef617dbe6a7741cf2c11b31f3e52b..a152d5b35afcad55e20c65d1bc83d4c47b674eeb 100644 --- a/lean/OAI/RepresentationTheory/Saxl/YoungRule.lean +++ b/lean/OAI/RepresentationTheory/Saxl/YoungRule.lean @@ -1,179 +1,179 @@ -import OAI.RepresentationTheory.Saxl.HorizontalRemoval - -namespace OAI - -noncomputable section - -open scoped TensorProduct - -namespace Saxl - -/- Horizontal-strip chains recording the exact ordered strip sizes. -/ -def rowWeights (θ : YoungDiagram) : ℕ → List ℕ - | 0 => [] - | k+1 => rowWeights θ k ++ [θ.rowLen k] - -lemma rowWeights_congr (θ τ : YoungDiagram) (k : ℕ) - (he : ∀ i < k, θ.rowLen i = τ.rowLen i) : rowWeights θ k = rowWeights τ k := by - induction k with - | zero => rfl - | succ k ih => - rw [rowWeights, rowWeights, ih (fun i hi => he i (by omega)), he k (by omega)] - -lemma card_zero_iff_bot (μ : YoungDiagram) : μ.card = 0 ↔ μ = ⊥ := by - change μ.cells.card = 0 ↔ _ - rw [Finset.card_eq_zero] - constructor - · intro h; exact YoungDiagram.ext h - · intro h; subst μ; rfl - -/- The actual constructive sufficiency step in Young's rule. No tableau, -Pieri, or representation hypothesis is assumed by this combinatorial theorem. -/ -theorem sizedStripChain_of_dominates (θ τ : YoungDiagram) (k : ℕ) - (hh : θ.colLen 0 ≤ k) (hc : τ.card = θ.card) (hd : Dominates τ θ) : - SizedStripChain (rowWeights θ k) ⊥ τ := by - induction k generalizing θ τ with - | zero => - have hcθ : θ.card = 0 := by - have he := rowPrefix_eq_card θ hh - simpa [rowPrefix] using he.symm - have ht : τ = ⊥ := (card_zero_iff_bot τ).mp (hc.trans hcθ) - subst τ - exact SizedStripChain.nil ⊥ - | succ k ih => - obtain ⟨hcν,hdν⟩ := dominates_stripRemove_last θ τ k hh hc hd - have hs := ih (rowTruncate θ k) (stripRemove τ (θ.rowLen k)) - (rowTruncate_height θ k) hcν hdν - have he : rowWeights (rowTruncate θ k) k = rowWeights θ k := by - apply rowWeights_congr - intro i hi - rw [rowTruncate_rowLen, ite_eq_left hi] - rw [he] at hs - apply SizedStripChain.snoc hs (stripRemove_horizontal τ (θ.rowLen k)) - have hw : θ.rowLen k ≤ τ.rowLen 0 := by - have hp := hd 1 - simp only [rowPrefix, Finset.sum_range_one] at hp - exact (θ.rowLen_anti 0 k (Nat.zero_le _)).trans hp - simpa only [min_eq_left hw] using stripRemove_card τ (θ.rowLen k) - - - -lemma rowWeights_length (θ : YoungDiagram) (k : ℕ) : (rowWeights θ k).length = k := by - induction k with - | zero => rfl - | succ k ih => simp only [rowWeights, List.length_append, List.length_singleton, ih] - -lemma rowWeights_getElem (θ : YoungDiagram) (k j : ℕ) (hj : j < k) : - (rowWeights θ k)[j]'(by rw [rowWeights_length]; exact hj) = θ.rowLen j := by - induction k with - | zero => omega - | succ k ih => - change (rowWeights θ k ++ [θ.rowLen k])[j]'(by simpa only [List.length_append, List.length_singleton, rowWeights_length] using hj) = θ.rowLen j - by_cases h : j < k - · rw [List.getElem_append_left (by rwa [rowWeights_length]), ih h] - · have he : j = k := by omega - subst j - rw [List.getElem_append_right (by rw [rowWeights_length])] - simp only [rowWeights_length, Nat.sub_self, List.getElem_singleton] - -lemma perm_of_equal_content {n d : ℕ} (a b : Fin n → Fin d) - (h : ∀ j, (Finset.univ.filter (fun i => a i = j)).card = - (Finset.univ.filter (fun i => b i = j)).card) : - ∃ g : Equiv.Perm (Fin n), b ∘ g = a := by - classical - let e (j) : {i // a i = j} ≃ {i // b i = j} := - Fintype.equivOfCardEq (by simpa only [Fintype.card_subtype] using h j) - let g := (Equiv.sigmaFiberEquiv a).symm.trans - ((Equiv.sigmaCongrRight e).trans (Equiv.sigmaFiberEquiv b)) - refine ⟨g, ?_⟩ - funext i - exact (e (a i) ⟨i,rfl⟩).property - -lemma vector_of_invariant_functional {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (a : Fin n → Fin d) (l : Module.Dual ℂ (Specht t)) (hl : l ≠ 0) - (he : ∀ g : Equiv.Perm (Fin n), a ∘ g = a → ∀ x, l (spechtRep t g x) = l x) : - ∃ y : Specht t, y ≠ 0 ∧ ∀ g : Equiv.Perm (Fin n), a ∘ g = a → spechtRep t g y = y := by - let e := spechtSelfDual t - refine ⟨e.symm l, ?_, ?_⟩ - · intro hz - exact hl (e.symm.injective (hz.trans (map_zero _).symm)) - · intro g hg - have hi : a ∘ (g⁻¹ : Equiv.Perm (Fin n)) = a := by - funext i - have hh := congrFun hg (g⁻¹ i) - simpa using hh.symm - have hdual : (spechtRep t).dual g l = l := by - apply LinearMap.ext - intro x - exact he g⁻¹ hi x - have hh := LinearMap.congr_fun (e.symm.isIntertwining' g) l - change e.symm ((spechtRep t).dual g l) = spechtRep t g (e.symm l) at hh - rw [hdual] at hh - exact hh.symm - -/- Young's sufficiency in the exact form needed for the repeated-row quotient: -a dominant Specht has a nonzero invariant functional for a word of the -prescribed content. -/ -theorem young_invariant_functional (θ τ : YoungDiagram) - (hc : τ.card = θ.card) (hd : Dominates τ θ) : - ∃ (a : Fin τ.card → Fin (θ.colLen 0)) (l : Module.Dual ℂ (Specht (shapeTableau τ))), - l ≠ 0 ∧ - (∀ j, (Finset.univ.filter (fun i => a i = j)).card = θ.rowLen j) ∧ - (∀ g : Equiv.Perm (Fin τ.card), a ∘ g = a → - ∀ x, l (spechtRep (shapeTableau τ) g x) = l x) := by - classical - let bs := rowWeights θ (θ.colLen 0) - have hs := sizedStripChain_of_dominates θ τ (θ.colLen 0) le_rfl hc hd - obtain ⟨c,F,hF,hcB,hzero,hcount,he⟩ := stripChain_restriction hs - have hpos (i) : 0 < c i := by - have hz := hzero i - have hn : ¬ i ∈ Set.range (tableauInclusion (shapeTableau ⊥) (shapeTableau τ) hs.le) := by - rintro ⟨j,hj⟩ - exact Fin.elim0 j - have hc0 : c i ≠ 0 := fun h => hn (hz.mp h) - omega - have hbound (i) : c i ≤ θ.colLen 0 := by simpa only [rowWeights_length] using hcB i - let a : Fin τ.card → Fin (θ.colLen 0) := fun i => ⟨c i-1, by have hh := hpos i; have ht := hbound i; omega⟩ - let v : Specht (shapeTableau ⊥) := ⟨polytabloid (shapeTableau ⊥), mem_cyclic _ _⟩ - let l₀ := spechtSelfDual (shapeTableau ⊥) v - have hl₀ : l₀ ≠ 0 := by - intro hz - have hh := (spechtSelfDual (shapeTableau ⊥)).injective (hz.trans (map_zero _).symm) - exact polytabloid_ne_zero _ (congrArg Subtype.val hh) - let l := l₀.comp F - have hl : l ≠ 0 := by - intro hz - apply hl₀ - apply LinearMap.ext - intro y - obtain ⟨x,rfl⟩ := hF y - exact LinearMap.congr_fun hz x - refine ⟨a,l,hl,?_,?_⟩ - · intro j - have hj : j.val < (rowWeights θ (θ.colLen 0)).length := by rw [rowWeights_length]; exact j.isLt - rw [← rowWeights_getElem θ (θ.colLen 0) j.val j.isLt, ← hcount j.val hj] - congr 1 - ext i - simp only [Finset.mem_filter, Finset.mem_univ, true_and] - change (⟨c i-1, _⟩ : Fin (θ.colLen 0)) = j ↔ c i = j.val+1 - rw [Fin.ext_iff] - change c i-1 = j.val ↔ c i = j.val+1 - have hh := hpos i - omega - · intro g hg x - have hcol (i) : c (g i) = c i := by - have hh := congrArg Fin.val (congrFun hg i) - change c (g i)-1 = c i-1 at hh - have hp := hpos i - have hpg := hpos (g i) - omega - have hh := he g 1 hcol (fun k => Fin.elim0 k) x - change l₀ (F (spechtRep (shapeTableau τ) g x)) = l₀ (F x) - rw [hh, map_one] - rfl - -end Saxl - -end - -end OAI +import OAI.RepresentationTheory.Saxl.HorizontalRemoval + +namespace OAI + +noncomputable section + +open scoped TensorProduct + +namespace Saxl + +/- Horizontal-strip chains recording the exact ordered strip sizes. -/ +def rowWeights (θ : YoungDiagram) : ℕ → List ℕ + | 0 => [] + | k+1 => rowWeights θ k ++ [θ.rowLen k] + +lemma rowWeights_congr (θ τ : YoungDiagram) (k : ℕ) + (he : ∀ i < k, θ.rowLen i = τ.rowLen i) : rowWeights θ k = rowWeights τ k := by + induction k with + | zero => rfl + | succ k ih => + rw [rowWeights, rowWeights, ih (fun i hi => he i (by omega)), he k (by omega)] + +lemma card_zero_iff_bot (μ : YoungDiagram) : μ.card = 0 ↔ μ = ⊥ := by + change μ.cells.card = 0 ↔ _ + rw [Finset.card_eq_zero] + constructor + · intro h; exact YoungDiagram.ext h + · intro h; subst μ; rfl + +/- The actual constructive sufficiency step in Young's rule. No tableau, +Pieri, or representation hypothesis is assumed by this combinatorial theorem. -/ +theorem sizedStripChain_of_dominates (θ τ : YoungDiagram) (k : ℕ) + (hh : θ.colLen 0 ≤ k) (hc : τ.card = θ.card) (hd : Dominates τ θ) : + SizedStripChain (rowWeights θ k) ⊥ τ := by + induction k generalizing θ τ with + | zero => + have hcθ : θ.card = 0 := by + have he := rowPrefix_eq_card θ hh + simpa [rowPrefix] using he.symm + have ht : τ = ⊥ := (card_zero_iff_bot τ).mp (hc.trans hcθ) + subst τ + exact SizedStripChain.nil ⊥ + | succ k ih => + obtain ⟨hcν,hdν⟩ := dominates_stripRemove_last θ τ k hh hc hd + have hs := ih (rowTruncate θ k) (stripRemove τ (θ.rowLen k)) + (rowTruncate_height θ k) hcν hdν + have he : rowWeights (rowTruncate θ k) k = rowWeights θ k := by + apply rowWeights_congr + intro i hi + rw [rowTruncate_rowLen, ite_eq_left hi] + rw [he] at hs + apply SizedStripChain.snoc hs (stripRemove_horizontal τ (θ.rowLen k)) + have hw : θ.rowLen k ≤ τ.rowLen 0 := by + have hp := hd 1 + simp only [rowPrefix, Finset.sum_range_one] at hp + exact (θ.rowLen_anti 0 k (Nat.zero_le _)).trans hp + simpa only [min_eq_left hw] using stripRemove_card τ (θ.rowLen k) + + + +lemma rowWeights_length (θ : YoungDiagram) (k : ℕ) : (rowWeights θ k).length = k := by + induction k with + | zero => rfl + | succ k ih => simp only [rowWeights, List.length_append, List.length_singleton, ih] + +lemma rowWeights_getElem (θ : YoungDiagram) (k j : ℕ) (hj : j < k) : + (rowWeights θ k)[j]'(by rw [rowWeights_length]; exact hj) = θ.rowLen j := by + induction k with + | zero => omega + | succ k ih => + change (rowWeights θ k ++ [θ.rowLen k])[j]'(by simpa only [List.length_append, List.length_singleton, rowWeights_length] using hj) = θ.rowLen j + by_cases h : j < k + · rw [List.getElem_append_left (by rwa [rowWeights_length]), ih h] + · have he : j = k := by omega + subst j + rw [List.getElem_append_right (by rw [rowWeights_length])] + simp only [rowWeights_length, Nat.sub_self, List.getElem_singleton] + +lemma perm_of_equal_content {n d : ℕ} (a b : Fin n → Fin d) + (h : ∀ j, (Finset.univ.filter (fun i => a i = j)).card = + (Finset.univ.filter (fun i => b i = j)).card) : + ∃ g : Equiv.Perm (Fin n), b ∘ g = a := by + classical + let e (j) : {i // a i = j} ≃ {i // b i = j} := + Fintype.equivOfCardEq (by simpa only [Fintype.card_subtype] using h j) + let g := (Equiv.sigmaFiberEquiv a).symm.trans + ((Equiv.sigmaCongrRight e).trans (Equiv.sigmaFiberEquiv b)) + refine ⟨g, ?_⟩ + funext i + exact (e (a i) ⟨i,rfl⟩).property + +lemma vector_of_invariant_functional {n d : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (a : Fin n → Fin d) (l : Module.Dual ℂ (Specht t)) (hl : l ≠ 0) + (he : ∀ g : Equiv.Perm (Fin n), a ∘ g = a → ∀ x, l (spechtRep t g x) = l x) : + ∃ y : Specht t, y ≠ 0 ∧ ∀ g : Equiv.Perm (Fin n), a ∘ g = a → spechtRep t g y = y := by + let e := spechtSelfDual t + refine ⟨e.symm l, ?_, ?_⟩ + · intro hz + exact hl (e.symm.injective (hz.trans (map_zero _).symm)) + · intro g hg + have hi : a ∘ (g⁻¹ : Equiv.Perm (Fin n)) = a := by + funext i + have hh := congrFun hg (g⁻¹ i) + simpa using hh.symm + have hdual : (spechtRep t).dual g l = l := by + apply LinearMap.ext + intro x + exact he g⁻¹ hi x + have hh := LinearMap.congr_fun (e.symm.isIntertwining' g) l + change e.symm ((spechtRep t).dual g l) = spechtRep t g (e.symm l) at hh + rw [hdual] at hh + exact hh.symm + +/- Young's sufficiency in the exact form needed for the repeated-row quotient: +a dominant Specht has a nonzero invariant functional for a word of the +prescribed content. -/ +theorem young_invariant_functional (θ τ : YoungDiagram) + (hc : τ.card = θ.card) (hd : Dominates τ θ) : + ∃ (a : Fin τ.card → Fin (θ.colLen 0)) (l : Module.Dual ℂ (Specht (shapeTableau τ))), + l ≠ 0 ∧ + (∀ j, (Finset.univ.filter (fun i => a i = j)).card = θ.rowLen j) ∧ + (∀ g : Equiv.Perm (Fin τ.card), a ∘ g = a → + ∀ x, l (spechtRep (shapeTableau τ) g x) = l x) := by + classical + let bs := rowWeights θ (θ.colLen 0) + have hs := sizedStripChain_of_dominates θ τ (θ.colLen 0) le_rfl hc hd + obtain ⟨c,F,hF,hcB,hzero,hcount,he⟩ := stripChain_restriction hs + have hpos (i) : 0 < c i := by + have hz := hzero i + have hn : ¬ i ∈ Set.range (tableauInclusion (shapeTableau ⊥) (shapeTableau τ) hs.le) := by + rintro ⟨j,hj⟩ + exact Fin.elim0 j + have hc0 : c i ≠ 0 := fun h => hn (hz.mp h) + omega + have hbound (i) : c i ≤ θ.colLen 0 := by simpa only [rowWeights_length] using hcB i + let a : Fin τ.card → Fin (θ.colLen 0) := fun i => ⟨c i-1, by have hh := hpos i; have ht := hbound i; omega⟩ + let v : Specht (shapeTableau ⊥) := ⟨polytabloid (shapeTableau ⊥), mem_cyclic _ _⟩ + let l₀ := spechtSelfDual (shapeTableau ⊥) v + have hl₀ : l₀ ≠ 0 := by + intro hz + have hh := (spechtSelfDual (shapeTableau ⊥)).injective (hz.trans (map_zero _).symm) + exact polytabloid_ne_zero _ (congrArg Subtype.val hh) + let l := l₀.comp F + have hl : l ≠ 0 := by + intro hz + apply hl₀ + apply LinearMap.ext + intro y + obtain ⟨x,rfl⟩ := hF y + exact LinearMap.congr_fun hz x + refine ⟨a,l,hl,?_,?_⟩ + · intro j + have hj : j.val < (rowWeights θ (θ.colLen 0)).length := by rw [rowWeights_length]; exact j.isLt + rw [← rowWeights_getElem θ (θ.colLen 0) j.val j.isLt, ← hcount j.val hj] + congr 1 + ext i + simp only [Finset.mem_filter, Finset.mem_univ, true_and] + change (⟨c i-1, _⟩ : Fin (θ.colLen 0)) = j ↔ c i = j.val+1 + rw [Fin.ext_iff] + change c i-1 = j.val ↔ c i = j.val+1 + have hh := hpos i + omega + · intro g hg x + have hcol (i) : c (g i) = c i := by + have hh := congrArg Fin.val (congrFun hg i) + change c (g i)-1 = c i-1 at hh + have hp := hpos i + have hpg := hpos (g i) + omega + have hh := he g 1 hcol (fun k => Fin.elim0 k) x + change l₀ (F (spechtRep (shapeTableau τ) g x)) = l₀ (F x) + rw [hh, map_one] + rfl + +end Saxl + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/SignedTensor/Basic.lean b/lean/OAI/RepresentationTheory/SignedTensor/Basic.lean index 9ece14bfd9aa6f34739290fa0e0a0e9cff4ac0fd..6bc8c8bdd195e7fb5cae2ff040446b8398269069 100644 --- a/lean/OAI/RepresentationTheory/SignedTensor/Basic.lean +++ b/lean/OAI/RepresentationTheory/SignedTensor/Basic.lean @@ -1,688 +1,688 @@ -import Mathlib -import OAI.RepresentationTheory.Unitary.Basic - -namespace OAI - -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable - -namespace CoordinateSweeps - -namespace SignedTensor - -/- p even basis symbols followed by p odd ones, exactly E⊕O in05. -/ -abbrev Letter (p : ℕ) := Fin (2*p) -abbrev Word (p l : ℕ) := Fin l → Letter p - -def odd {p : ℕ} (a : Letter p) : Prop := p ≤ a.val - -/- The sign from reordering the odd factors, with positions ordered as in -ordinary tensor words. There is no choice of orientation hidden here. -/ -def koszulExponent {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) : ℕ := - ((Equiv.Perm.finPairsLT l).filter (fun ij => - odd (w ij.1) ∧ odd (w ij.2) ∧ σ ij.1 < σ ij.2)).card - -def phase {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) : ℂ := - (-1)^koszulExponent σ w - -/- The underlying ordinary slot permutation; gh applies h first. -/ -def wordPerm {p l : ℕ} (σ : Equiv.Perm (Fin l)) : Equiv.Perm (Word p l) where - toFun w i := w (σ⁻¹ i) - invFun w i := w (σ i) - left_inv w := by funext i; simp - right_inv w := by funext i; simp - -/- Matrix of the exact parity-signed action in the tensor word basis. -/ -def matrix {p l : ℕ} (σ : Equiv.Perm (Fin l)) : Matrix (Word p l) (Word p l) ℂ := - fun u w => if u=wordPerm σ w then phase σ w else 0 - -lemma phase_star_mul {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) : - star (phase σ w)*phase σ w=1 := by - simp only [phase,star_pow,star_neg,star_one] - rw [← mul_pow] - simp - -lemma phase_prod {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) : - phase σ w = ∏ ij ∈ Equiv.Perm.finPairsLT l, - (if odd (w ij.1) ∧ odd (w ij.2) ∧ σ ij.1 < σ ij.2 then (-1 : ℂ) else 1) := by - rw [Finset.prod_ite] - simp [phase,koszulExponent] - -lemma wordPerm_mul {p l : ℕ} (σ τ : Equiv.Perm (Fin l)) : - wordPerm (p := p) (σ*τ) = wordPerm σ * wordPerm τ := by - ext w i - simp [wordPerm] - -/- The exact Koszul cocycle, proved from pair inversions, not an action axiom. -/ -theorem phase_mul {p l : ℕ} (σ τ : Equiv.Perm (Fin l)) (w : Word p l) : - phase (σ*τ) w = phase σ (wordPerm τ w) * phase τ w := by - rw [phase_prod,phase_prod,phase_prod] - have hreindex : - (∏ ij ∈ Equiv.Perm.finPairsLT l, - (if odd (wordPerm τ w ij.1) ∧ odd (wordPerm τ w ij.2) ∧ σ ij.1 < σ ij.2 - then (-1 : ℂ) else 1)) = - ∏ ij ∈ Equiv.Perm.finPairsLT l, - (if odd (wordPerm τ w (Equiv.Perm.signBijAux τ ij).1) ∧ - odd (wordPerm τ w (Equiv.Perm.signBijAux τ ij).2) ∧ - σ (Equiv.Perm.signBijAux τ ij).1 < σ (Equiv.Perm.signBijAux τ ij).2 - then (-1 : ℂ) else 1) := by - symm - exact Finset.prod_nbij (Equiv.Perm.signBijAux τ) - Equiv.Perm.signBijAux_mem Equiv.Perm.signBijAux_injOn - Equiv.Perm.signBijAux_surj (fun _ _ => rfl) - rw [hreindex,← Finset.prod_mul_distrib] - apply Finset.prod_congr rfl - rintro ⟨i,j⟩ hij - have hji : j < i := Equiv.Perm.mem_finPairsLT.mp hij - have hne : τ j ≠ τ i := τ.injective.ne hji.ne - have hneσ : σ (τ j) ≠ σ (τ i) := σ.injective.ne hne - by_cases hi : odd (w i) - · by_cases hj : odd (w j) - · by_cases ht : τ j < τ i - · simp [Equiv.Perm.signBijAux,wordPerm,Equiv.Perm.mul_apply,ht,hi,hj,ht.not_gt] - · have ht' : τ i < τ j := lt_of_le_of_ne (le_of_not_gt ht) hne.symm - by_cases hs : σ (τ i) < σ (τ j) - · simp [Equiv.Perm.signBijAux,wordPerm,Equiv.Perm.mul_apply,ht,ht',hi,hj,hs,hs.not_gt] - · have hs' : σ (τ j) < σ (τ i) := lt_of_le_of_ne (le_of_not_gt hs) hneσ - simp [Equiv.Perm.signBijAux,wordPerm,Equiv.Perm.mul_apply,ht,ht',hi,hj,hs,hs'] - · by_cases ht : τ j < τ i <;> - simp [Equiv.Perm.signBijAux,wordPerm,Equiv.Perm.mul_apply,ht,hi,hj] - · by_cases ht : τ j < τ i <;> - simp [Equiv.Perm.signBijAux,wordPerm,Equiv.Perm.mul_apply,ht,hi] - -/- Unitarity follows directly, without assuming the Schur-Weyl -or Pieri decomposition. -/ -theorem matrix_unitary {p l : ℕ} (σ : Equiv.Perm (Fin l)) : - (matrix (p := p) σ).conjTranspose * matrix σ=1 := by - ext u w - simp only [Matrix.mul_apply,Matrix.conjTranspose_apply,matrix] - rw [Finset.sum_eq_single (wordPerm σ u)] - · by_cases hu : u=w - · subst w - simp only [ite_true,Matrix.one_apply_eq,phase_star_mul] - · have hne : wordPerm σ u ≠ wordPerm σ w := - fun hh => hu ((wordPerm σ).injective hh) - simp [hne,hu] - · intro v hv hne - simp [hne] - · simp - -lemma phase_one {p l : ℕ} (w : Word p l) : phase (1 : Equiv.Perm (Fin l)) w=1 := by - rw [phase_prod] - apply Finset.prod_eq_one - intro ij hij - have hji := Equiv.Perm.mem_finPairsLT.mp hij - simp [Equiv.Perm.one_apply,hji.not_gt] - -theorem matrix_one (p l : ℕ) : matrix (p := p) (1 : Equiv.Perm (Fin l))=1 := by - ext u w - simp [matrix,wordPerm,phase_one,Matrix.one_apply] - -theorem matrix_mul {p l : ℕ} (σ τ : Equiv.Perm (Fin l)) : - matrix (p := p) (σ*τ)=matrix σ * matrix τ := by - ext u w - simp only [Matrix.mul_apply,matrix] - rw [Finset.sum_eq_single (wordPerm τ w)] - · simp only [ite_true,wordPerm_mul,Equiv.Perm.mul_apply,phase_mul] - split_ifs <;> simp - · intro v hv hne - simp [hne] - · simp - -/- Exact signed tensor representation of the symmetric group. -/ -def action (p l : ℕ) : Equiv.Perm (Fin l) →* Matrix (Word p l) (Word p l) ℂ where - toFun := matrix - map_one' := matrix_one p l - map_mul' := matrix_mul - -/- Ordinary (not graded) tensor power of a one-site density, as in05. -/ -def densityPower {p : ℕ} (l : ℕ) (r : Matrix (Letter p) (Letter p) ℂ) : - Matrix (Word p l) (Word p l) ℂ := fun u w => ∏ i, r (u i) (w i) - -lemma densityPower_mul {p : ℕ} (l : ℕ) (a b : Matrix (Letter p) (Letter p) ℂ) : - densityPower l (a*b)=densityPower l a * densityPower l b := by - ext u w - simp only [densityPower,Matrix.mul_apply] - rw [Fintype.prod_sum] - apply Finset.sum_congr rfl - intro v hv - exact Finset.prod_mul_distrib - -lemma densityPower_star {p : ℕ} (l : ℕ) (r : Matrix (Letter p) (Letter p) ℂ) : - densityPower l r.conjTranspose=(densityPower l r).conjTranspose := by - ext u w - simp [densityPower,Matrix.conjTranspose_apply] - -lemma densityPower_trace {p : ℕ} (l : ℕ) (r : Matrix (Letter p) (Letter p) ℂ) : - Matrix.trace (densityPower l r)=(Matrix.trace r)^l := by - change (∑ w : Word p l, ∏ i, r (w i) (w i))=(∑ i, r i i)^l - exact (Fintype.sum_pow (fun i : Letter p => r i i) l).symm - -open scoped MatrixOrder in -lemma densityPower_posSemidef {p : ℕ} (l : ℕ) (r : Matrix (Letter p) (Letter p) ℂ) - (hr : r.PosSemidef) : (densityPower l r).PosSemidef := by - obtain ⟨b,rfl⟩ := CStarAlgebra.nonneg_iff_eq_star_mul_self.mp hr.nonneg - rw [densityPower_mul,Matrix.star_eq_conjTranspose,densityPower_star] - exact Matrix.posSemidef_conjTranspose_mul_self _ - -/- Even means positive trace-one and block diagonal for E,O, exactly as in05. -/ -def EvenDensity (p : ℕ) := {r : Matrix (Letter p) (Letter p) ℂ // - r.PosSemidef ∧ Matrix.trace r=1 ∧ - ∀ i j, (odd i ↔ ¬ odd j) → r i j=0} - -instance (p : ℕ) : MeasurableSpace (EvenDensity p) := - MeasurableSpace.comap Subtype.val (borel (Matrix (Letter p) (Letter p) ℂ)) - -lemma phase_eq_of_parity {p l : ℕ} (σ : Equiv.Perm (Fin l)) - (u w : Word p l) (h : ∀ i, odd (u i) ↔ odd (w i)) : phase σ u=phase σ w := by - simp only [phase,koszulExponent] - congr 2 - apply Finset.filter_congr - intro ij hij - rw [h ij.1,h ij.2] - -lemma densityPower_parity_of_ne_zero {p l : ℕ} (r : EvenDensity p) - {u w : Word p l} (h : densityPower l r.val u w ≠ 0) : - ∀ i, odd (u i) ↔ odd (w i) := by - intro i - have he : r.val (u i) (w i) ≠ 0 := - (Finset.prod_ne_zero_iff.mp h) i (Finset.mem_univ _) - by_contra hn - apply he - apply r.property.2.2 - tauto - -lemma densityPower_permute {p l : ℕ} (σ : Equiv.Perm (Fin l)) - (r : Matrix (Letter p) (Letter p) ℂ) (u w : Word p l) : - densityPower l r (wordPerm σ u) (wordPerm σ w)=densityPower l r u w := by - simp only [densityPower,wordPerm,Equiv.coe_fn_mk] - exact Equiv.prod_comp σ⁻¹ (fun i => r (u i) (w i)) - -/- Even densities commute with the signed action; omission of evenness here -would be false. This is also the block-reordering claim at the end of05. -/ -theorem densityPower_commute {p l : ℕ} (r : EvenDensity p) - (σ : Equiv.Perm (Fin l)) : - matrix σ * densityPower l r.val=densityPower l r.val * matrix σ := by - ext u w - simp only [Matrix.mul_apply,matrix] - rw [Finset.sum_eq_single ((wordPerm σ).symm u), - Finset.sum_eq_single (wordPerm σ w)] - · simp only [(wordPerm σ).apply_symm_apply,ite_true] - have hd : densityPower l r.val u (wordPerm σ w)= - densityPower l r.val ((wordPerm σ).symm u) w := by - simpa using densityPower_permute σ r.val ((wordPerm σ).symm u) w - rw [hd] - by_cases hn : densityPower l r.val ((wordPerm σ).symm u) w=0 - · simp [hn] - · rw [phase_eq_of_parity σ _ _ (densityPower_parity_of_ne_zero r hn),mul_comm] - · intro v hv hne - simp [hne] - · simp - · intro v hv hne - have hh : u ≠ wordPerm σ v := by - intro he - apply hne - exact (Equiv.eq_symm_apply _).mpr he.symm - simp [hh] - · simp - -lemma evenDensityPower_trace {p : ℕ} (l : ℕ) (r : EvenDensity p) : - Matrix.trace (densityPower l r.val)=1 := by - rw [densityPower_trace,r.property.2.1,one_pow] - -/- The standard central character formula for the isotypic projection. Its -projection properties require the signed action laws (not assumed here). -/ -def isotypic {p l : ℕ} (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - Matrix (Word p l) (Word p l) ℂ := - ((ρ.dimension : ℂ)/(Fintype.card (Equiv.Perm (Fin l)) : ℂ)) • - ∑ σ, Matrix.trace (ρ.matrix σ⁻¹) • matrix σ - -/- Exact signed-density domination05 eq13, expressed for every irreducible -(including absent ones whose projection is zero). The mixture is a genuine -probability measure on the source's even density matrices, not an unproved -positive operator supplied as a hypothesis. -/ -def Domination : Prop := - ∃ C : ℝ, 0 < C ∧ ∀ s p : ℕ, 1 ≤ p → p ≤ s → ∀ l : ℕ, l ≤ s → - ∀ ρ : UnitaryIrrep (Equiv.Perm (Fin l)), - ∃ μ : MeasureTheory.Measure (EvenDensity p), MeasureTheory.IsProbabilityMeasure μ ∧ - (Complex.ofReal (Real.exp (Real.log ρ.dimension+C*p^2*Real.log (s+1))) • - (∫ r : EvenDensity p, densityPower l r.val ∂μ) - isotypic (p := p) ρ).PosSemidef - -end SignedTensor -end CoordinateSweeps - -/- A direct counting approach to the polynomial multiplicity bound in05, -without replacing Schur-Weyl or the density inequality by an axiom. -The signed tensor commutant is determined by pair-word histograms. -/ -namespace CoordinateSweeps.SignedTensor - -lemma phase_ne_zero {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) : phase σ w ≠ 0 := by - intro h - have hh := phase_star_mul σ w - simp [h] at hh - -lemma mul_signed_entry {p l : ℕ} (A : Matrix (Word p l) (Word p l) ℂ) - (σ : Equiv.Perm (Fin l)) (u w : Word p l) : - (A*matrix (p := p) σ) u w=A u (wordPerm σ w)*phase σ w := by - simp only [Matrix.mul_apply,matrix] - rw [Finset.sum_eq_single (wordPerm σ w)] - · simp - · intro v hv hne; simp [hne] - · simp - -lemma signed_mul_entry {p l : ℕ} (A : Matrix (Word p l) (Word p l) ℂ) - (σ : Equiv.Perm (Fin l)) (u w : Word p l) : - (matrix (p := p) σ*A) (wordPerm σ u) w=phase σ u*A u w := by - simp only [Matrix.mul_apply,matrix] - rw [Finset.sum_eq_single u] - · simp - · intro v hv hne - have hne' : wordPerm σ u ≠ wordPerm σ v := - fun hh => hne (((wordPerm σ).injective hh).symm) - simp [hne'] - · simp - -/- The actual signed-action commutant as a linear subspace of matrices. -/ -def commutant (p l : ℕ) : Submodule ℂ (Matrix (Word p l) (Word p l) ℂ) where - carrier := {A | ∀ σ : Equiv.Perm (Fin l), A*matrix σ=matrix σ*A} - zero_mem' := by simp - add_mem' hA hB := by intro σ; simp only [add_mul,mul_add,hA σ,hB σ] - smul_mem' c A hA := by intro σ; simp only [smul_mul_assoc,mul_smul_comm,hA σ] - -lemma commutant_zero_transport {p l : ℕ} (A : commutant p l) - (σ : Equiv.Perm (Fin l)) {u w : Word p l} (h : A.val u w=0) : - A.val (wordPerm σ u) (wordPerm σ w)=0 := by - have hh := congrArg (fun B : Matrix (Word p l) (Word p l) ℂ => B (wordPerm σ u) w) - (A.property σ) - rw [mul_signed_entry,signed_mul_entry,h,mul_zero] at hh - exact (mul_eq_zero.mp hh).resolve_right (phase_ne_zero σ w) - -abbrev Profile (p l : ℕ) := (Letter p × Letter p) → Fin (l+1) - -def profile {p l : ℕ} (u w : Word p l) : Profile p l := fun a => - ⟨(Finset.univ.filter (fun i => (u i,w i)=a)).card, - Nat.lt_succ_iff.mpr (by - simpa using Finset.card_filter_le (Finset.univ : Finset (Fin l)) - (fun i => (u i,w i)=a))⟩ - -lemma profile_fiber_card {p l : ℕ} (u w : Word p l) (a : Letter p × Letter p) : - Fintype.card {i : Fin l // (u i,w i)=a}=(profile u w a).val := by - simp [profile,Fintype.card_subtype] - -/- Two word pairs have the same histogram exactly when a position permutation -carries one to the other. This supplies the finite orbit-counting parameter. -/ -lemma profile_eq_exists_perm {p l : ℕ} {u w u' w' : Word p l} - (hh : profile u w=profile u' w') : - ∃ σ : Equiv.Perm (Fin l), wordPerm σ u=u' ∧ wordPerm σ w=w' := by - have hc (a : Letter p × Letter p) : Fintype.card {i : Fin l // (u i,w i)=a}= - Fintype.card {i : Fin l // (u' i,w' i)=a} := by - rw [profile_fiber_card,profile_fiber_card,hh] - let e (a : Letter p × Letter p) : {i : Fin l // (u i,w i)=a} ≃ - {i : Fin l // (u' i,w' i)=a} := Fintype.equivOfCardEq (hc a) - let σ : Equiv.Perm (Fin l) := Equiv.ofFiberEquiv e - have he (i : Fin l) : (u' (σ i),w' (σ i))=(u i,w i) := Equiv.ofFiberEquiv_map e i - refine ⟨σ,?_,?_⟩ - · funext i - have hi := congrArg Prod.fst (he (σ⁻¹ i)) - simpa [wordPerm] using hi.symm - · funext i - have hi := congrArg Prod.snd (he (σ⁻¹ i)) - simpa [wordPerm] using hi.symm - -abbrev OccurringProfile (p l : ℕ) := - {q : Profile p l // q ∈ Set.range (fun uw : Word p l × Word p l => profile uw.1 uw.2)} - -def profileRep {p l : ℕ} (q : OccurringProfile p l) : Word p l × Word p l := - Classical.choose q.property - -lemma profileRep_spec {p l : ℕ} (q : OccurringProfile p l) : - profile (profileRep q).1 (profileRep q).2=q.val := Classical.choose_spec q.property - -def commutantEval (p l : ℕ) : commutant p l →ₗ[ℂ] (OccurringProfile p l → ℂ) where - toFun A q := A.val (profileRep q).1 (profileRep q).2 - map_add' _ _ := rfl - map_smul' _ _ := rfl - -lemma commutantEval_injective (p l : ℕ) : Function.Injective (commutantEval p l) := by - apply (LinearMap.ker_eq_bot).mp - apply LinearMap.ker_eq_bot'.mpr - intro A hA - apply Subtype.ext - ext u w - let q : OccurringProfile p l := ⟨profile u w,Set.mem_range_self (u,w)⟩ - have he : A.val (profileRep q).1 (profileRep q).2=0 := congrFun hA q - have hp : profile (profileRep q).1 (profileRep q).2=profile u w := profileRep_spec q - obtain ⟨σ,hσu,hσw⟩ := profile_eq_exists_perm hp - have hh := commutant_zero_transport A σ he - simpa [hσu,hσw] using hh - -/- Polynomial signed-commutant bound of exactly the O(p² log(s+1)) scale -required by the main induction. No classification of partitions is used. -/ -theorem commutant_finrank_le (p l : ℕ) : - Module.finrank ℂ (commutant p l) ≤ (l+1)^((2*p)*(2*p)) := by - have h := LinearMap.finrank_le_finrank_of_injective (commutantEval_injective p l) - have hc : Fintype.card (OccurringProfile p l) ≤ Fintype.card (Profile p l) := - Fintype.card_subtype_le _ - have he : Fintype.card (Profile p l)=(l+1)^((2*p)*(2*p)) := by - simp [Profile,Letter] - simpa [he] using h.trans (by simpa using hc) - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor - -lemma matrix_inv {p l : ℕ} (σ : Equiv.Perm (Fin l)) : - matrix (p := p) σ⁻¹=(matrix (p := p) σ).conjTranspose := by - calc - matrix σ⁻¹=1*matrix (p := p) σ⁻¹ := (one_mul _).symm - _ = ((matrix σ).conjTranspose*matrix σ)*matrix (p := p) σ⁻¹ := by rw [matrix_unitary] - _ = (matrix (p := p) σ).conjTranspose := by - rw [mul_assoc,← matrix_mul,mul_inv_cancel,matrix_one,mul_one] - -abbrev tensorRepresentation (p l : ℕ) := UnitaryIrrep.matrixRepresentation (action p l) - -/- An actual intertwining endomorphism has its coefficient matrix in the -signed commutant. This is not an assumed decomposition of the tensor action. -/ -def endomorphismMatrix (p l : ℕ) : - (tensorRepresentation p l).IntertwiningMap (tensorRepresentation p l) →ₗ[ℂ] - commutant p l where - toFun F := ⟨LinearMap.toMatrixAlgEquiv' F.toLinearMap,by - intro σ - apply Matrix.toLinAlgEquiv'.injective - simp only [map_mul,Matrix.toLinAlgEquiv'_toMatrixAlgEquiv'] - exact F.isIntertwining' σ⟩ - map_add' F H := by - apply Subtype.ext - exact map_add LinearMap.toMatrixAlgEquiv' _ _ - map_smul' c F := by - apply Subtype.ext - exact map_smul LinearMap.toMatrixAlgEquiv'.toLinearMap c _ - -lemma endomorphismMatrix_injective (p l : ℕ) : - Function.Injective (endomorphismMatrix p l) := by - intro F H hh - apply Representation.IntertwiningMap.ext - exact LinearMap.toMatrixAlgEquiv'.injective (congrArg Subtype.val hh) - -theorem tensor_endomorphisms_finrank_le (p l : ℕ) : - Module.finrank ℂ ((tensorRepresentation p l).IntertwiningMap (tensorRepresentation p l)) ≤ - (l+1)^((2*p)*(2*p)) := - (LinearMap.finrank_le_finrank_of_injective (endomorphismMatrix_injective p l)).trans - (commutant_finrank_le p l) - -/- The polynomial multiplicity clause of05 signed density lemma, proved -without Young diagrams. Multiplicity is the actual space of equivariant embeddings. -/ -theorem multiplicity_le (p l : ℕ) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (tensorRepresentation p l)) ≤ - (l+1)^((2*p)*(2*p)) := by - have hh := ρ.multiplicity_sq_le_commutant (action p l) - (fun σ => matrix_inv σ |>.symm) - have hm : Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (tensorRepresentation p l)) ≤ - (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (tensorRepresentation p l)))^2 := by - exact Nat.le_self_pow (by omega) _ - exact hm.trans (hh.trans (tensor_endomorphisms_finrank_le p l)) - -lemma isotypic_eq_projector {p l : ℕ} (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - isotypic (p := p) ρ=ρ.projector (action p l) := by - simp only [isotypic,UnitaryIrrep.projector,UnitaryIrrep.coefficient,Finset.smul_sum,mul_smul] - rfl - -theorem isotypic_posSemidef {p l : ℕ} (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - (isotypic (p := p) ρ).PosSemidef := by - rw [isotypic_eq_projector] - exact ρ.projector_posSemidef (action p l) (fun σ => (matrix_inv σ).symm) - -theorem isotypic_trace {p l : ℕ} (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - Matrix.trace (isotypic (p := p) ρ)=(ρ.dimension : ℂ)* - Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (tensorRepresentation p l)) := by - rw [isotypic_eq_projector] - simp only [UnitaryIrrep.projector,Matrix.trace_sum,Matrix.trace_smul, - UnitaryIrrep.coefficient,smul_eq_mul] - calc - _ = ((ρ.dimension : ℂ)/(Fintype.card (Equiv.Perm (Fin l)) : ℂ)) * - ∑ σ, Matrix.trace (action p l σ)*Matrix.trace (ρ.matrix σ⁻¹) := by - rw [Finset.mul_sum] - apply Finset.sum_congr rfl - intro σ hσ - ring - _ = _ := by - rw [ρ.character_sum_multiplicity (action p l)] - have hN : (Fintype.card (Equiv.Perm (Fin l)) : ℂ) ≠ 0 := - Nat.cast_ne_zero.mpr Fintype.card_ne_zero - field_simp - -end CoordinateSweeps.SignedTensor - -/- Mismatched symbols in a purification -obey a Pauli exclusion rule. This is derived from the literal Koszul action. -/ -namespace CoordinateSweeps.SignedTensor - -lemma swap01_inversion_iff (n : ℕ) (i j : Fin (n+2)) : - (j < i ∧ Equiv.swap (0 : Fin (n+2)) 1 i < Equiv.swap 0 1 j) ↔ - i = 1 ∧ j = 0 := by - simp only [Equiv.swap_apply_def] - split_ifs <;> simp_all - omega - -lemma phase_swap01 {p n : ℕ} (w : Word p (n+2)) : - phase (Equiv.swap (0 : Fin (n+2)) 1) w = - if odd (w 1) ∧ odd (w 0) then (-1 : ℂ) else 1 := by - have he : ((Equiv.Perm.finPairsLT (n+2)).filter (fun ij => - odd (w ij.1) ∧ odd (w ij.2) ∧ - Equiv.swap (0 : Fin (n+2)) 1 ij.1 < Equiv.swap 0 1 ij.2)) = - if odd (w 1) ∧ odd (w 0) then {⟨1,0⟩} else ∅ := by - ext ⟨i,j⟩ - simp only [Finset.mem_filter, Equiv.Perm.mem_finPairsLT] - have hi := swap01_inversion_iff n i j - split_ifs with hw - · simp only [Finset.mem_singleton, Sigma.mk.inj_iff, heq_eq_eq] - constructor - · rintro ⟨hji,hiw,hjw,hs⟩ - exact hi.mp ⟨hji,hs⟩ - · rintro ⟨rfl,rfl⟩ - exact ⟨by simp, hw.1, hw.2, by simp⟩ - · simp only [Finset.notMem_empty, iff_false] - rintro ⟨hji,hiw,hjw,hs⟩ - obtain ⟨rfl,rfl⟩ := hi.mp ⟨hji,hs⟩ - exact hw ⟨hiw,hjw⟩ - unfold phase koszulExponent - rw [he] - split_ifs <;> simp - -lemma wordPerm_swap01_of_equal {p n : ℕ} (w : Word p (n+2)) (hw : w 0 = w 1) : - wordPerm (Equiv.swap (0 : Fin (n+2)) 1) w = w := by - ext i - simp only [wordPerm, Equiv.coe_fn_mk, Equiv.swap_inv, Equiv.swap_apply_def] - split_ifs <;> simp_all - -/- Two repeated, parity-mismatched pair symbols force a zero entry in every -commuting matrix, hence in the canonical purification of an isotypic projector. -/ -theorem commutant_entry_zero_adjacent_mismatch {p n : ℕ} (A : commutant p (n+2)) - (u w : Word p (n+2)) (hu : u 0 = u 1) (hw : w 0 = w 1) - (hm : odd (u 0) ↔ ¬ odd (w 0)) : A.val u w = 0 := by - let σ := Equiv.swap (0 : Fin (n+2)) 1 - have h := congrArg (fun B : Matrix (Word p (n+2)) (Word p (n+2)) ℂ => - B (wordPerm σ u) w) (A.property σ) - rw [mul_signed_entry, signed_mul_entry, - wordPerm_swap01_of_equal u hu, wordPerm_swap01_of_equal w hw] at h - dsimp [σ] at h - rw [phase_swap01, phase_swap01, ← hu, ← hw] at h - by_cases ho : odd (u 0) - · have hw' : ¬ odd (w 0) := hm.mp ho - simp only [ho, hw', and_self, ↓reduceIte, mul_one, neg_one_mul] at h - linear_combination (1/2 : ℂ)*h - · have hw' : odd (w 0) := Classical.byContradiction (fun hh => ho (hm.mpr hh)) - simp only [ho, hw', and_self, ↓reduceIte, one_mul, mul_neg_one] at h - linear_combination (-1/2 : ℂ)*h - -/- An explicit two-point transporter, avoiding any unproved transitivity -principle or choice of ordering of the other positions. -/ -lemma exists_perm_pair {X : Type*} [DecidableEq X] (a b c d : X) - (hab : a ≠ b) (hcd : c ≠ d) : - ∃ g : Equiv.Perm X, g a = c ∧ g b = d := by - let s := Equiv.swap a c - have hs : s b ≠ c := by - intro h - have he : s a = c := by simp [s] - exact hab (s.injective (he.trans h.symm)) - refine ⟨Equiv.swap (s b) d * s, ?_, ?_⟩ - · simp only [Equiv.Perm.mul_apply] - have he : s a = c := by simp [s] - rw [he, Equiv.swap_apply_of_ne_of_ne hs.symm hcd] - · simp - -/- All repeated parity-mismatched pair symbols are impossible, at arbitrary -positions. Distinct mismatched symbols will therefore account for every -exceptional slot in the postselection argument. -/ -theorem commutant_entry_zero_repeated_mismatch {p l : ℕ} (A : commutant p l) - (u w : Word p l) (i j : Fin l) (hij : i ≠ j) (hu : u i = u j) (hw : w i = w j) - (hm : odd (u i) ↔ ¬ odd (w i)) : A.val u w = 0 := by - have hl : 2 ≤ l := by - have hn : i.val ≠ j.val := fun h => hij (Fin.ext h) - have hi := i.isLt - have hj := j.isLt - omega - obtain ⟨n, rfl⟩ : ∃ n, l = n+2 := ⟨l-2, by omega⟩ - obtain ⟨g,hi,hj⟩ := exists_perm_pair i j (0 : Fin (n+2)) 1 hij (by simp) - let u' := wordPerm g u - let w' := wordPerm g w - have hue (x : Fin (n+2)) : u' (g x) = u x := by simp [u',wordPerm] - have hwe (x : Fin (n+2)) : w' (g x) = w x := by simp [w',wordPerm] - have hui : u' 0 = u i := hi ▸ hue i - have huj : u' 1 = u j := hj ▸ hue j - have hwi : w' 0 = w i := hi ▸ hwe i - have hwj : w' 1 = w j := hj ▸ hwe j - have hz : A.val u' w' = 0 := by - apply commutant_entry_zero_adjacent_mismatch A u' w' - · exact hui.trans (hu.trans huj.symm) - · exact hwi.trans (hw.trans hwj.symm) - · simpa [hui,hwi] using hm - have hz' := commutant_zero_transport A g⁻¹ hz - simpa [u',w',wordPerm] using hz' -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -/- Exceptional slots of a vectorized commuting matrix. -/ -def mismatchSlots {p l : ℕ} (u w : Word p l) : Finset (Fin l) := - Finset.univ.filter (fun i => odd (u i) ↔ ¬ odd (w i)) - -/- The exclusion bound needed for even-density postselection. The coarse -constant four rather than two is harmless in the source's absolute Cp² error. -/ -theorem mismatchSlots_card_le {p l : ℕ} (A : commutant p l) - (u w : Word p l) (hne : A.val u w ≠ 0) : - (mismatchSlots u w).card ≤ (2*p)*(2*p) := by - classical - let f : {i // i ∈ mismatchSlots u w} → Letter p × Letter p := fun i => (u i.val,w i.val) - have hf : Function.Injective f := by - intro i j he - apply Subtype.ext - by_contra hij - apply hne - exact commutant_entry_zero_repeated_mismatch A u w i.val j.val hij - (congrArg Prod.fst he) (congrArg Prod.snd he) (Finset.mem_filter.mp i.property).2 - have hc := Fintype.card_le_of_injective f hf - simpa only [Fintype.card_coe, Fintype.card_prod, Fintype.card_fin] using hc -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -/- The actual Koszul regrouping phase from (V⊗V̄)^⊗l to -V^⊗l⊗V̄^⊗l. It will cancel, not be dropped, under partial trace. -/ -def regroupPhase {p l : ℕ} (u w : Word p l) : ℂ := - ∏ ij ∈ Equiv.Perm.finPairsLT l, - if odd (u ij.1) ∧ odd (w ij.2) then (-1 : ℂ) else 1 - -lemma phase_square {p l : ℕ} (σ : Equiv.Perm (Fin l)) (u : Word p l) : - phase σ u * phase σ u = 1 := by - simpa only [phase,star_pow,star_neg,star_one] using phase_star_mul σ u - -lemma regroupPhase_square {p l : ℕ} (u w : Word p l) : - regroupPhase u w * regroupPhase u w = 1 := by - unfold regroupPhase - rw [← Finset.prod_mul_distrib] - apply Finset.prod_eq_one - intro ij _ - split_ifs <;> norm_num - -lemma regroupPhase_star {p l : ℕ} (u w : Word p l) : - star (regroupPhase u w) = regroupPhase u w := by - unfold regroupPhase - rw [star_prod] - apply Finset.prod_congr rfl - intro ij _ - split_ifs <;> simp - -/- Permutations of the matched slots have no residual super-sign after -literal Koszul regrouping; the positions of mismatched symbols are fixed. -/ -theorem regroupPhase_permute {p l : ℕ} (σ : Equiv.Perm (Fin l)) (u w : Word p l) - (hfix : ∀ i, (odd (u i) ↔ ¬ odd (w i)) → σ i = i) : - regroupPhase (wordPerm σ u) (wordPerm σ w) * phase σ u * phase σ w = - regroupPhase u w := by - unfold regroupPhase - rw [phase_prod,phase_prod] - have hreindex : - (∏ ij ∈ Equiv.Perm.finPairsLT l, - (if odd (wordPerm σ u ij.1) ∧ odd (wordPerm σ w ij.2) then (-1 : ℂ) else 1)) = - ∏ ij ∈ Equiv.Perm.finPairsLT l, - (if odd (wordPerm σ u (Equiv.Perm.signBijAux σ ij).1) ∧ - odd (wordPerm σ w (Equiv.Perm.signBijAux σ ij).2) then (-1 : ℂ) else 1) := by - symm - exact Finset.prod_nbij (Equiv.Perm.signBijAux σ) - Equiv.Perm.signBijAux_mem Equiv.Perm.signBijAux_injOn - Equiv.Perm.signBijAux_surj (fun _ _ => rfl) - rw [hreindex,← Finset.prod_mul_distrib,← Finset.prod_mul_distrib] - apply Finset.prod_congr rfl - rintro ⟨i,j⟩ hij - have hji : j < i := Equiv.Perm.mem_finPairsLT.mp hij - have hne : σ j ≠ σ i := σ.injective.ne hji.ne - by_cases ht : σ j < σ i - · simp [Equiv.Perm.signBijAux,wordPerm,ht,ht.not_gt] - · have ht' : σ i < σ j := lt_of_le_of_ne (le_of_not_gt ht) hne.symm - have hm : ¬ ((odd (u i) ↔ ¬ odd (w i)) ∧ (odd (u j) ↔ ¬ odd (w j))) := by - rintro ⟨hi,hj⟩ - have hi' := hfix i hi - have hj' := hfix j hj - rw [hi',hj'] at ht' - exact hji.not_gt ht' - by_cases hui : odd (u i) <;> by_cases huj : odd (u j) <;> - by_cases hwi : odd (w i) <;> by_cases hwj : odd (w j) <;> - simp [Equiv.Perm.signBijAux,wordPerm,ht,ht',hui,huj,hwi,hwj] at hm ⊢ - -lemma commutant_transport {p l : ℕ} (A : commutant p l) (σ : Equiv.Perm (Fin l)) - (u w : Word p l) : - A.val (wordPerm σ u) (wordPerm σ w) = phase σ u * phase σ w * A.val u w := by - have hh := congrArg (fun B : Matrix (Word p l) (Word p l) ℂ => B (wordPerm σ u) w) - (A.property σ) - rw [mul_signed_entry,signed_mul_entry] at hh - calc - _ = (A.val (wordPerm σ u) (wordPerm σ w) * phase σ w) * phase σ w := by - rw [mul_assoc,phase_square,mul_one] - _ = (phase σ u * A.val u w) * phase σ w := by rw [hh] - _ = _ := by ring - -/- Rephased purification components are ordinary symmetric on the free, -matched-pair slots, a proved conclusion from the signed commutant relation. -/ -theorem regrouped_commutant_invariant {p l : ℕ} (A : commutant p l) - (σ : Equiv.Perm (Fin l)) (u w : Word p l) - (hfix : ∀ i, (odd (u i) ↔ ¬ odd (w i)) → σ i = i) : - regroupPhase (wordPerm σ u) (wordPerm σ w) * - A.val (wordPerm σ u) (wordPerm σ w) = regroupPhase u w * A.val u w := by - rw [commutant_transport] - calc - _ = (regroupPhase (wordPerm σ u) (wordPerm σ w) * phase σ u * phase σ w) * A.val u w := by ring - _ = _ := by rw [regroupPhase_permute σ u w hfix] - -/- Equal local parities in the system copies give equal regrouping signs. -This is what justifies cancellation under the actual auxiliary partial trace. -/ -lemma regroupPhase_of_same_parity {p l : ℕ} (u u' w : Word p l) - (h : ∀ i, odd (u i) ↔ odd (u' i)) : regroupPhase u w = regroupPhase u' w := by - unfold regroupPhase - apply Finset.prod_congr rfl - intro ij _ - rw [h ij.1] -end CoordinateSweeps.SignedTensor - -end -open scoped Matrix.Norms.L2Operator - -end OAI +import Mathlib +import OAI.RepresentationTheory.Unitary.Basic + +namespace OAI + +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable + +namespace CoordinateSweeps + +namespace SignedTensor + +/- p even basis symbols followed by p odd ones, exactly E⊕O in05. -/ +abbrev Letter (p : ℕ) := Fin (2*p) +abbrev Word (p l : ℕ) := Fin l → Letter p + +def odd {p : ℕ} (a : Letter p) : Prop := p ≤ a.val + +/- The sign from reordering the odd factors, with positions ordered as in +ordinary tensor words. There is no choice of orientation hidden here. -/ +def koszulExponent {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) : ℕ := + ((Equiv.Perm.finPairsLT l).filter (fun ij => + odd (w ij.1) ∧ odd (w ij.2) ∧ σ ij.1 < σ ij.2)).card + +def phase {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) : ℂ := + (-1)^koszulExponent σ w + +/- The underlying ordinary slot permutation; gh applies h first. -/ +def wordPerm {p l : ℕ} (σ : Equiv.Perm (Fin l)) : Equiv.Perm (Word p l) where + toFun w i := w (σ⁻¹ i) + invFun w i := w (σ i) + left_inv w := by funext i; simp + right_inv w := by funext i; simp + +/- Matrix of the exact parity-signed action in the tensor word basis. -/ +def matrix {p l : ℕ} (σ : Equiv.Perm (Fin l)) : Matrix (Word p l) (Word p l) ℂ := + fun u w => if u=wordPerm σ w then phase σ w else 0 + +lemma phase_star_mul {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) : + star (phase σ w)*phase σ w=1 := by + simp only [phase,star_pow,star_neg,star_one] + rw [← mul_pow] + simp + +lemma phase_prod {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) : + phase σ w = ∏ ij ∈ Equiv.Perm.finPairsLT l, + (if odd (w ij.1) ∧ odd (w ij.2) ∧ σ ij.1 < σ ij.2 then (-1 : ℂ) else 1) := by + rw [Finset.prod_ite] + simp [phase,koszulExponent] + +lemma wordPerm_mul {p l : ℕ} (σ τ : Equiv.Perm (Fin l)) : + wordPerm (p := p) (σ*τ) = wordPerm σ * wordPerm τ := by + ext w i + simp [wordPerm] + +/- The exact Koszul cocycle, proved from pair inversions, not an action axiom. -/ +theorem phase_mul {p l : ℕ} (σ τ : Equiv.Perm (Fin l)) (w : Word p l) : + phase (σ*τ) w = phase σ (wordPerm τ w) * phase τ w := by + rw [phase_prod,phase_prod,phase_prod] + have hreindex : + (∏ ij ∈ Equiv.Perm.finPairsLT l, + (if odd (wordPerm τ w ij.1) ∧ odd (wordPerm τ w ij.2) ∧ σ ij.1 < σ ij.2 + then (-1 : ℂ) else 1)) = + ∏ ij ∈ Equiv.Perm.finPairsLT l, + (if odd (wordPerm τ w (Equiv.Perm.signBijAux τ ij).1) ∧ + odd (wordPerm τ w (Equiv.Perm.signBijAux τ ij).2) ∧ + σ (Equiv.Perm.signBijAux τ ij).1 < σ (Equiv.Perm.signBijAux τ ij).2 + then (-1 : ℂ) else 1) := by + symm + exact Finset.prod_nbij (Equiv.Perm.signBijAux τ) + Equiv.Perm.signBijAux_mem Equiv.Perm.signBijAux_injOn + Equiv.Perm.signBijAux_surj (fun _ _ => rfl) + rw [hreindex,← Finset.prod_mul_distrib] + apply Finset.prod_congr rfl + rintro ⟨i,j⟩ hij + have hji : j < i := Equiv.Perm.mem_finPairsLT.mp hij + have hne : τ j ≠ τ i := τ.injective.ne hji.ne + have hneσ : σ (τ j) ≠ σ (τ i) := σ.injective.ne hne + by_cases hi : odd (w i) + · by_cases hj : odd (w j) + · by_cases ht : τ j < τ i + · simp [Equiv.Perm.signBijAux,wordPerm,Equiv.Perm.mul_apply,ht,hi,hj,ht.not_gt] + · have ht' : τ i < τ j := lt_of_le_of_ne (le_of_not_gt ht) hne.symm + by_cases hs : σ (τ i) < σ (τ j) + · simp [Equiv.Perm.signBijAux,wordPerm,Equiv.Perm.mul_apply,ht,ht',hi,hj,hs,hs.not_gt] + · have hs' : σ (τ j) < σ (τ i) := lt_of_le_of_ne (le_of_not_gt hs) hneσ + simp [Equiv.Perm.signBijAux,wordPerm,Equiv.Perm.mul_apply,ht,ht',hi,hj,hs,hs'] + · by_cases ht : τ j < τ i <;> + simp [Equiv.Perm.signBijAux,wordPerm,Equiv.Perm.mul_apply,ht,hi,hj] + · by_cases ht : τ j < τ i <;> + simp [Equiv.Perm.signBijAux,wordPerm,Equiv.Perm.mul_apply,ht,hi] + +/- Unitarity follows directly, without assuming the Schur-Weyl +or Pieri decomposition. -/ +theorem matrix_unitary {p l : ℕ} (σ : Equiv.Perm (Fin l)) : + (matrix (p := p) σ).conjTranspose * matrix σ=1 := by + ext u w + simp only [Matrix.mul_apply,Matrix.conjTranspose_apply,matrix] + rw [Finset.sum_eq_single (wordPerm σ u)] + · by_cases hu : u=w + · subst w + simp only [ite_true,Matrix.one_apply_eq,phase_star_mul] + · have hne : wordPerm σ u ≠ wordPerm σ w := + fun hh => hu ((wordPerm σ).injective hh) + simp [hne,hu] + · intro v hv hne + simp [hne] + · simp + +lemma phase_one {p l : ℕ} (w : Word p l) : phase (1 : Equiv.Perm (Fin l)) w=1 := by + rw [phase_prod] + apply Finset.prod_eq_one + intro ij hij + have hji := Equiv.Perm.mem_finPairsLT.mp hij + simp [Equiv.Perm.one_apply,hji.not_gt] + +theorem matrix_one (p l : ℕ) : matrix (p := p) (1 : Equiv.Perm (Fin l))=1 := by + ext u w + simp [matrix,wordPerm,phase_one,Matrix.one_apply] + +theorem matrix_mul {p l : ℕ} (σ τ : Equiv.Perm (Fin l)) : + matrix (p := p) (σ*τ)=matrix σ * matrix τ := by + ext u w + simp only [Matrix.mul_apply,matrix] + rw [Finset.sum_eq_single (wordPerm τ w)] + · simp only [ite_true,wordPerm_mul,Equiv.Perm.mul_apply,phase_mul] + split_ifs <;> simp + · intro v hv hne + simp [hne] + · simp + +/- Exact signed tensor representation of the symmetric group. -/ +def action (p l : ℕ) : Equiv.Perm (Fin l) →* Matrix (Word p l) (Word p l) ℂ where + toFun := matrix + map_one' := matrix_one p l + map_mul' := matrix_mul + +/- Ordinary (not graded) tensor power of a one-site density, as in05. -/ +def densityPower {p : ℕ} (l : ℕ) (r : Matrix (Letter p) (Letter p) ℂ) : + Matrix (Word p l) (Word p l) ℂ := fun u w => ∏ i, r (u i) (w i) + +lemma densityPower_mul {p : ℕ} (l : ℕ) (a b : Matrix (Letter p) (Letter p) ℂ) : + densityPower l (a*b)=densityPower l a * densityPower l b := by + ext u w + simp only [densityPower,Matrix.mul_apply] + rw [Fintype.prod_sum] + apply Finset.sum_congr rfl + intro v hv + exact Finset.prod_mul_distrib + +lemma densityPower_star {p : ℕ} (l : ℕ) (r : Matrix (Letter p) (Letter p) ℂ) : + densityPower l r.conjTranspose=(densityPower l r).conjTranspose := by + ext u w + simp [densityPower,Matrix.conjTranspose_apply] + +lemma densityPower_trace {p : ℕ} (l : ℕ) (r : Matrix (Letter p) (Letter p) ℂ) : + Matrix.trace (densityPower l r)=(Matrix.trace r)^l := by + change (∑ w : Word p l, ∏ i, r (w i) (w i))=(∑ i, r i i)^l + exact (Fintype.sum_pow (fun i : Letter p => r i i) l).symm + +open scoped MatrixOrder in +lemma densityPower_posSemidef {p : ℕ} (l : ℕ) (r : Matrix (Letter p) (Letter p) ℂ) + (hr : r.PosSemidef) : (densityPower l r).PosSemidef := by + obtain ⟨b,rfl⟩ := CStarAlgebra.nonneg_iff_eq_star_mul_self.mp hr.nonneg + rw [densityPower_mul,Matrix.star_eq_conjTranspose,densityPower_star] + exact Matrix.posSemidef_conjTranspose_mul_self _ + +/- Even means positive trace-one and block diagonal for E,O, exactly as in05. -/ +def EvenDensity (p : ℕ) := {r : Matrix (Letter p) (Letter p) ℂ // + r.PosSemidef ∧ Matrix.trace r=1 ∧ + ∀ i j, (odd i ↔ ¬ odd j) → r i j=0} + +instance (p : ℕ) : MeasurableSpace (EvenDensity p) := + MeasurableSpace.comap Subtype.val (borel (Matrix (Letter p) (Letter p) ℂ)) + +lemma phase_eq_of_parity {p l : ℕ} (σ : Equiv.Perm (Fin l)) + (u w : Word p l) (h : ∀ i, odd (u i) ↔ odd (w i)) : phase σ u=phase σ w := by + simp only [phase,koszulExponent] + congr 2 + apply Finset.filter_congr + intro ij hij + rw [h ij.1,h ij.2] + +lemma densityPower_parity_of_ne_zero {p l : ℕ} (r : EvenDensity p) + {u w : Word p l} (h : densityPower l r.val u w ≠ 0) : + ∀ i, odd (u i) ↔ odd (w i) := by + intro i + have he : r.val (u i) (w i) ≠ 0 := + (Finset.prod_ne_zero_iff.mp h) i (Finset.mem_univ _) + by_contra hn + apply he + apply r.property.2.2 + tauto + +lemma densityPower_permute {p l : ℕ} (σ : Equiv.Perm (Fin l)) + (r : Matrix (Letter p) (Letter p) ℂ) (u w : Word p l) : + densityPower l r (wordPerm σ u) (wordPerm σ w)=densityPower l r u w := by + simp only [densityPower,wordPerm,Equiv.coe_fn_mk] + exact Equiv.prod_comp σ⁻¹ (fun i => r (u i) (w i)) + +/- Even densities commute with the signed action; omission of evenness here +would be false. This is also the block-reordering claim at the end of05. -/ +theorem densityPower_commute {p l : ℕ} (r : EvenDensity p) + (σ : Equiv.Perm (Fin l)) : + matrix σ * densityPower l r.val=densityPower l r.val * matrix σ := by + ext u w + simp only [Matrix.mul_apply,matrix] + rw [Finset.sum_eq_single ((wordPerm σ).symm u), + Finset.sum_eq_single (wordPerm σ w)] + · simp only [(wordPerm σ).apply_symm_apply,ite_true] + have hd : densityPower l r.val u (wordPerm σ w)= + densityPower l r.val ((wordPerm σ).symm u) w := by + simpa using densityPower_permute σ r.val ((wordPerm σ).symm u) w + rw [hd] + by_cases hn : densityPower l r.val ((wordPerm σ).symm u) w=0 + · simp [hn] + · rw [phase_eq_of_parity σ _ _ (densityPower_parity_of_ne_zero r hn),mul_comm] + · intro v hv hne + simp [hne] + · simp + · intro v hv hne + have hh : u ≠ wordPerm σ v := by + intro he + apply hne + exact (Equiv.eq_symm_apply _).mpr he.symm + simp [hh] + · simp + +lemma evenDensityPower_trace {p : ℕ} (l : ℕ) (r : EvenDensity p) : + Matrix.trace (densityPower l r.val)=1 := by + rw [densityPower_trace,r.property.2.1,one_pow] + +/- The standard central character formula for the isotypic projection. Its +projection properties require the signed action laws (not assumed here). -/ +def isotypic {p l : ℕ} (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + Matrix (Word p l) (Word p l) ℂ := + ((ρ.dimension : ℂ)/(Fintype.card (Equiv.Perm (Fin l)) : ℂ)) • + ∑ σ, Matrix.trace (ρ.matrix σ⁻¹) • matrix σ + +/- Exact signed-density domination05 eq13, expressed for every irreducible +(including absent ones whose projection is zero). The mixture is a genuine +probability measure on the source's even density matrices, not an unproved +positive operator supplied as a hypothesis. -/ +def Domination : Prop := + ∃ C : ℝ, 0 < C ∧ ∀ s p : ℕ, 1 ≤ p → p ≤ s → ∀ l : ℕ, l ≤ s → + ∀ ρ : UnitaryIrrep (Equiv.Perm (Fin l)), + ∃ μ : MeasureTheory.Measure (EvenDensity p), MeasureTheory.IsProbabilityMeasure μ ∧ + (Complex.ofReal (Real.exp (Real.log ρ.dimension+C*p^2*Real.log (s+1))) • + (∫ r : EvenDensity p, densityPower l r.val ∂μ) - isotypic (p := p) ρ).PosSemidef + +end SignedTensor +end CoordinateSweeps + +/- A direct counting approach to the polynomial multiplicity bound in05, +without replacing Schur-Weyl or the density inequality by an axiom. +The signed tensor commutant is determined by pair-word histograms. -/ +namespace CoordinateSweeps.SignedTensor + +lemma phase_ne_zero {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) : phase σ w ≠ 0 := by + intro h + have hh := phase_star_mul σ w + simp [h] at hh + +lemma mul_signed_entry {p l : ℕ} (A : Matrix (Word p l) (Word p l) ℂ) + (σ : Equiv.Perm (Fin l)) (u w : Word p l) : + (A*matrix (p := p) σ) u w=A u (wordPerm σ w)*phase σ w := by + simp only [Matrix.mul_apply,matrix] + rw [Finset.sum_eq_single (wordPerm σ w)] + · simp + · intro v hv hne; simp [hne] + · simp + +lemma signed_mul_entry {p l : ℕ} (A : Matrix (Word p l) (Word p l) ℂ) + (σ : Equiv.Perm (Fin l)) (u w : Word p l) : + (matrix (p := p) σ*A) (wordPerm σ u) w=phase σ u*A u w := by + simp only [Matrix.mul_apply,matrix] + rw [Finset.sum_eq_single u] + · simp + · intro v hv hne + have hne' : wordPerm σ u ≠ wordPerm σ v := + fun hh => hne (((wordPerm σ).injective hh).symm) + simp [hne'] + · simp + +/- The actual signed-action commutant as a linear subspace of matrices. -/ +def commutant (p l : ℕ) : Submodule ℂ (Matrix (Word p l) (Word p l) ℂ) where + carrier := {A | ∀ σ : Equiv.Perm (Fin l), A*matrix σ=matrix σ*A} + zero_mem' := by simp + add_mem' hA hB := by intro σ; simp only [add_mul,mul_add,hA σ,hB σ] + smul_mem' c A hA := by intro σ; simp only [smul_mul_assoc,mul_smul_comm,hA σ] + +lemma commutant_zero_transport {p l : ℕ} (A : commutant p l) + (σ : Equiv.Perm (Fin l)) {u w : Word p l} (h : A.val u w=0) : + A.val (wordPerm σ u) (wordPerm σ w)=0 := by + have hh := congrArg (fun B : Matrix (Word p l) (Word p l) ℂ => B (wordPerm σ u) w) + (A.property σ) + rw [mul_signed_entry,signed_mul_entry,h,mul_zero] at hh + exact (mul_eq_zero.mp hh).resolve_right (phase_ne_zero σ w) + +abbrev Profile (p l : ℕ) := (Letter p × Letter p) → Fin (l+1) + +def profile {p l : ℕ} (u w : Word p l) : Profile p l := fun a => + ⟨(Finset.univ.filter (fun i => (u i,w i)=a)).card, + Nat.lt_succ_iff.mpr (by + simpa using Finset.card_filter_le (Finset.univ : Finset (Fin l)) + (fun i => (u i,w i)=a))⟩ + +lemma profile_fiber_card {p l : ℕ} (u w : Word p l) (a : Letter p × Letter p) : + Fintype.card {i : Fin l // (u i,w i)=a}=(profile u w a).val := by + simp [profile,Fintype.card_subtype] + +/- Two word pairs have the same histogram exactly when a position permutation +carries one to the other. This supplies the finite orbit-counting parameter. -/ +lemma profile_eq_exists_perm {p l : ℕ} {u w u' w' : Word p l} + (hh : profile u w=profile u' w') : + ∃ σ : Equiv.Perm (Fin l), wordPerm σ u=u' ∧ wordPerm σ w=w' := by + have hc (a : Letter p × Letter p) : Fintype.card {i : Fin l // (u i,w i)=a}= + Fintype.card {i : Fin l // (u' i,w' i)=a} := by + rw [profile_fiber_card,profile_fiber_card,hh] + let e (a : Letter p × Letter p) : {i : Fin l // (u i,w i)=a} ≃ + {i : Fin l // (u' i,w' i)=a} := Fintype.equivOfCardEq (hc a) + let σ : Equiv.Perm (Fin l) := Equiv.ofFiberEquiv e + have he (i : Fin l) : (u' (σ i),w' (σ i))=(u i,w i) := Equiv.ofFiberEquiv_map e i + refine ⟨σ,?_,?_⟩ + · funext i + have hi := congrArg Prod.fst (he (σ⁻¹ i)) + simpa [wordPerm] using hi.symm + · funext i + have hi := congrArg Prod.snd (he (σ⁻¹ i)) + simpa [wordPerm] using hi.symm + +abbrev OccurringProfile (p l : ℕ) := + {q : Profile p l // q ∈ Set.range (fun uw : Word p l × Word p l => profile uw.1 uw.2)} + +def profileRep {p l : ℕ} (q : OccurringProfile p l) : Word p l × Word p l := + Classical.choose q.property + +lemma profileRep_spec {p l : ℕ} (q : OccurringProfile p l) : + profile (profileRep q).1 (profileRep q).2=q.val := Classical.choose_spec q.property + +def commutantEval (p l : ℕ) : commutant p l →ₗ[ℂ] (OccurringProfile p l → ℂ) where + toFun A q := A.val (profileRep q).1 (profileRep q).2 + map_add' _ _ := rfl + map_smul' _ _ := rfl + +lemma commutantEval_injective (p l : ℕ) : Function.Injective (commutantEval p l) := by + apply (LinearMap.ker_eq_bot).mp + apply LinearMap.ker_eq_bot'.mpr + intro A hA + apply Subtype.ext + ext u w + let q : OccurringProfile p l := ⟨profile u w,Set.mem_range_self (u,w)⟩ + have he : A.val (profileRep q).1 (profileRep q).2=0 := congrFun hA q + have hp : profile (profileRep q).1 (profileRep q).2=profile u w := profileRep_spec q + obtain ⟨σ,hσu,hσw⟩ := profile_eq_exists_perm hp + have hh := commutant_zero_transport A σ he + simpa [hσu,hσw] using hh + +/- Polynomial signed-commutant bound of exactly the O(p² log(s+1)) scale +required by the main induction. No classification of partitions is used. -/ +theorem commutant_finrank_le (p l : ℕ) : + Module.finrank ℂ (commutant p l) ≤ (l+1)^((2*p)*(2*p)) := by + have h := LinearMap.finrank_le_finrank_of_injective (commutantEval_injective p l) + have hc : Fintype.card (OccurringProfile p l) ≤ Fintype.card (Profile p l) := + Fintype.card_subtype_le _ + have he : Fintype.card (Profile p l)=(l+1)^((2*p)*(2*p)) := by + simp [Profile,Letter] + simpa [he] using h.trans (by simpa using hc) + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor + +lemma matrix_inv {p l : ℕ} (σ : Equiv.Perm (Fin l)) : + matrix (p := p) σ⁻¹=(matrix (p := p) σ).conjTranspose := by + calc + matrix σ⁻¹=1*matrix (p := p) σ⁻¹ := (one_mul _).symm + _ = ((matrix σ).conjTranspose*matrix σ)*matrix (p := p) σ⁻¹ := by rw [matrix_unitary] + _ = (matrix (p := p) σ).conjTranspose := by + rw [mul_assoc,← matrix_mul,mul_inv_cancel,matrix_one,mul_one] + +abbrev tensorRepresentation (p l : ℕ) := UnitaryIrrep.matrixRepresentation (action p l) + +/- An actual intertwining endomorphism has its coefficient matrix in the +signed commutant. This is not an assumed decomposition of the tensor action. -/ +def endomorphismMatrix (p l : ℕ) : + (tensorRepresentation p l).IntertwiningMap (tensorRepresentation p l) →ₗ[ℂ] + commutant p l where + toFun F := ⟨LinearMap.toMatrixAlgEquiv' F.toLinearMap,by + intro σ + apply Matrix.toLinAlgEquiv'.injective + simp only [map_mul,Matrix.toLinAlgEquiv'_toMatrixAlgEquiv'] + exact F.isIntertwining' σ⟩ + map_add' F H := by + apply Subtype.ext + exact map_add LinearMap.toMatrixAlgEquiv' _ _ + map_smul' c F := by + apply Subtype.ext + exact map_smul LinearMap.toMatrixAlgEquiv'.toLinearMap c _ + +lemma endomorphismMatrix_injective (p l : ℕ) : + Function.Injective (endomorphismMatrix p l) := by + intro F H hh + apply Representation.IntertwiningMap.ext + exact LinearMap.toMatrixAlgEquiv'.injective (congrArg Subtype.val hh) + +theorem tensor_endomorphisms_finrank_le (p l : ℕ) : + Module.finrank ℂ ((tensorRepresentation p l).IntertwiningMap (tensorRepresentation p l)) ≤ + (l+1)^((2*p)*(2*p)) := + (LinearMap.finrank_le_finrank_of_injective (endomorphismMatrix_injective p l)).trans + (commutant_finrank_le p l) + +/- The polynomial multiplicity clause of05 signed density lemma, proved +without Young diagrams. Multiplicity is the actual space of equivariant embeddings. -/ +theorem multiplicity_le (p l : ℕ) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (tensorRepresentation p l)) ≤ + (l+1)^((2*p)*(2*p)) := by + have hh := ρ.multiplicity_sq_le_commutant (action p l) + (fun σ => matrix_inv σ |>.symm) + have hm : Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (tensorRepresentation p l)) ≤ + (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (tensorRepresentation p l)))^2 := by + exact Nat.le_self_pow (by omega) _ + exact hm.trans (hh.trans (tensor_endomorphisms_finrank_le p l)) + +lemma isotypic_eq_projector {p l : ℕ} (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + isotypic (p := p) ρ=ρ.projector (action p l) := by + simp only [isotypic,UnitaryIrrep.projector,UnitaryIrrep.coefficient,Finset.smul_sum,mul_smul] + rfl + +theorem isotypic_posSemidef {p l : ℕ} (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + (isotypic (p := p) ρ).PosSemidef := by + rw [isotypic_eq_projector] + exact ρ.projector_posSemidef (action p l) (fun σ => (matrix_inv σ).symm) + +theorem isotypic_trace {p l : ℕ} (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + Matrix.trace (isotypic (p := p) ρ)=(ρ.dimension : ℂ)* + Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (tensorRepresentation p l)) := by + rw [isotypic_eq_projector] + simp only [UnitaryIrrep.projector,Matrix.trace_sum,Matrix.trace_smul, + UnitaryIrrep.coefficient,smul_eq_mul] + calc + _ = ((ρ.dimension : ℂ)/(Fintype.card (Equiv.Perm (Fin l)) : ℂ)) * + ∑ σ, Matrix.trace (action p l σ)*Matrix.trace (ρ.matrix σ⁻¹) := by + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro σ hσ + ring + _ = _ := by + rw [ρ.character_sum_multiplicity (action p l)] + have hN : (Fintype.card (Equiv.Perm (Fin l)) : ℂ) ≠ 0 := + Nat.cast_ne_zero.mpr Fintype.card_ne_zero + field_simp + +end CoordinateSweeps.SignedTensor + +/- Mismatched symbols in a purification +obey a Pauli exclusion rule. This is derived from the literal Koszul action. -/ +namespace CoordinateSweeps.SignedTensor + +lemma swap01_inversion_iff (n : ℕ) (i j : Fin (n+2)) : + (j < i ∧ Equiv.swap (0 : Fin (n+2)) 1 i < Equiv.swap 0 1 j) ↔ + i = 1 ∧ j = 0 := by + simp only [Equiv.swap_apply_def] + split_ifs <;> simp_all + omega + +lemma phase_swap01 {p n : ℕ} (w : Word p (n+2)) : + phase (Equiv.swap (0 : Fin (n+2)) 1) w = + if odd (w 1) ∧ odd (w 0) then (-1 : ℂ) else 1 := by + have he : ((Equiv.Perm.finPairsLT (n+2)).filter (fun ij => + odd (w ij.1) ∧ odd (w ij.2) ∧ + Equiv.swap (0 : Fin (n+2)) 1 ij.1 < Equiv.swap 0 1 ij.2)) = + if odd (w 1) ∧ odd (w 0) then {⟨1,0⟩} else ∅ := by + ext ⟨i,j⟩ + simp only [Finset.mem_filter, Equiv.Perm.mem_finPairsLT] + have hi := swap01_inversion_iff n i j + split_ifs with hw + · simp only [Finset.mem_singleton, Sigma.mk.inj_iff, heq_eq_eq] + constructor + · rintro ⟨hji,hiw,hjw,hs⟩ + exact hi.mp ⟨hji,hs⟩ + · rintro ⟨rfl,rfl⟩ + exact ⟨by simp, hw.1, hw.2, by simp⟩ + · simp only [Finset.notMem_empty, iff_false] + rintro ⟨hji,hiw,hjw,hs⟩ + obtain ⟨rfl,rfl⟩ := hi.mp ⟨hji,hs⟩ + exact hw ⟨hiw,hjw⟩ + unfold phase koszulExponent + rw [he] + split_ifs <;> simp + +lemma wordPerm_swap01_of_equal {p n : ℕ} (w : Word p (n+2)) (hw : w 0 = w 1) : + wordPerm (Equiv.swap (0 : Fin (n+2)) 1) w = w := by + ext i + simp only [wordPerm, Equiv.coe_fn_mk, Equiv.swap_inv, Equiv.swap_apply_def] + split_ifs <;> simp_all + +/- Two repeated, parity-mismatched pair symbols force a zero entry in every +commuting matrix, hence in the canonical purification of an isotypic projector. -/ +theorem commutant_entry_zero_adjacent_mismatch {p n : ℕ} (A : commutant p (n+2)) + (u w : Word p (n+2)) (hu : u 0 = u 1) (hw : w 0 = w 1) + (hm : odd (u 0) ↔ ¬ odd (w 0)) : A.val u w = 0 := by + let σ := Equiv.swap (0 : Fin (n+2)) 1 + have h := congrArg (fun B : Matrix (Word p (n+2)) (Word p (n+2)) ℂ => + B (wordPerm σ u) w) (A.property σ) + rw [mul_signed_entry, signed_mul_entry, + wordPerm_swap01_of_equal u hu, wordPerm_swap01_of_equal w hw] at h + dsimp [σ] at h + rw [phase_swap01, phase_swap01, ← hu, ← hw] at h + by_cases ho : odd (u 0) + · have hw' : ¬ odd (w 0) := hm.mp ho + simp only [ho, hw', and_self, ↓reduceIte, mul_one, neg_one_mul] at h + linear_combination (1/2 : ℂ)*h + · have hw' : odd (w 0) := Classical.byContradiction (fun hh => ho (hm.mpr hh)) + simp only [ho, hw', and_self, ↓reduceIte, one_mul, mul_neg_one] at h + linear_combination (-1/2 : ℂ)*h + +/- An explicit two-point transporter, avoiding any unproved transitivity +principle or choice of ordering of the other positions. -/ +lemma exists_perm_pair {X : Type*} [DecidableEq X] (a b c d : X) + (hab : a ≠ b) (hcd : c ≠ d) : + ∃ g : Equiv.Perm X, g a = c ∧ g b = d := by + let s := Equiv.swap a c + have hs : s b ≠ c := by + intro h + have he : s a = c := by simp [s] + exact hab (s.injective (he.trans h.symm)) + refine ⟨Equiv.swap (s b) d * s, ?_, ?_⟩ + · simp only [Equiv.Perm.mul_apply] + have he : s a = c := by simp [s] + rw [he, Equiv.swap_apply_of_ne_of_ne hs.symm hcd] + · simp + +/- All repeated parity-mismatched pair symbols are impossible, at arbitrary +positions. Distinct mismatched symbols will therefore account for every +exceptional slot in the postselection argument. -/ +theorem commutant_entry_zero_repeated_mismatch {p l : ℕ} (A : commutant p l) + (u w : Word p l) (i j : Fin l) (hij : i ≠ j) (hu : u i = u j) (hw : w i = w j) + (hm : odd (u i) ↔ ¬ odd (w i)) : A.val u w = 0 := by + have hl : 2 ≤ l := by + have hn : i.val ≠ j.val := fun h => hij (Fin.ext h) + have hi := i.isLt + have hj := j.isLt + omega + obtain ⟨n, rfl⟩ : ∃ n, l = n+2 := ⟨l-2, by omega⟩ + obtain ⟨g,hi,hj⟩ := exists_perm_pair i j (0 : Fin (n+2)) 1 hij (by simp) + let u' := wordPerm g u + let w' := wordPerm g w + have hue (x : Fin (n+2)) : u' (g x) = u x := by simp [u',wordPerm] + have hwe (x : Fin (n+2)) : w' (g x) = w x := by simp [w',wordPerm] + have hui : u' 0 = u i := hi ▸ hue i + have huj : u' 1 = u j := hj ▸ hue j + have hwi : w' 0 = w i := hi ▸ hwe i + have hwj : w' 1 = w j := hj ▸ hwe j + have hz : A.val u' w' = 0 := by + apply commutant_entry_zero_adjacent_mismatch A u' w' + · exact hui.trans (hu.trans huj.symm) + · exact hwi.trans (hw.trans hwj.symm) + · simpa [hui,hwi] using hm + have hz' := commutant_zero_transport A g⁻¹ hz + simpa [u',w',wordPerm] using hz' +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +/- Exceptional slots of a vectorized commuting matrix. -/ +def mismatchSlots {p l : ℕ} (u w : Word p l) : Finset (Fin l) := + Finset.univ.filter (fun i => odd (u i) ↔ ¬ odd (w i)) + +/- The exclusion bound needed for even-density postselection. The coarse +constant four rather than two is harmless in the source's absolute Cp² error. -/ +theorem mismatchSlots_card_le {p l : ℕ} (A : commutant p l) + (u w : Word p l) (hne : A.val u w ≠ 0) : + (mismatchSlots u w).card ≤ (2*p)*(2*p) := by + classical + let f : {i // i ∈ mismatchSlots u w} → Letter p × Letter p := fun i => (u i.val,w i.val) + have hf : Function.Injective f := by + intro i j he + apply Subtype.ext + by_contra hij + apply hne + exact commutant_entry_zero_repeated_mismatch A u w i.val j.val hij + (congrArg Prod.fst he) (congrArg Prod.snd he) (Finset.mem_filter.mp i.property).2 + have hc := Fintype.card_le_of_injective f hf + simpa only [Fintype.card_coe, Fintype.card_prod, Fintype.card_fin] using hc +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +/- The actual Koszul regrouping phase from (V⊗V̄)^⊗l to +V^⊗l⊗V̄^⊗l. It will cancel, not be dropped, under partial trace. -/ +def regroupPhase {p l : ℕ} (u w : Word p l) : ℂ := + ∏ ij ∈ Equiv.Perm.finPairsLT l, + if odd (u ij.1) ∧ odd (w ij.2) then (-1 : ℂ) else 1 + +lemma phase_square {p l : ℕ} (σ : Equiv.Perm (Fin l)) (u : Word p l) : + phase σ u * phase σ u = 1 := by + simpa only [phase,star_pow,star_neg,star_one] using phase_star_mul σ u + +lemma regroupPhase_square {p l : ℕ} (u w : Word p l) : + regroupPhase u w * regroupPhase u w = 1 := by + unfold regroupPhase + rw [← Finset.prod_mul_distrib] + apply Finset.prod_eq_one + intro ij _ + split_ifs <;> norm_num + +lemma regroupPhase_star {p l : ℕ} (u w : Word p l) : + star (regroupPhase u w) = regroupPhase u w := by + unfold regroupPhase + rw [star_prod] + apply Finset.prod_congr rfl + intro ij _ + split_ifs <;> simp + +/- Permutations of the matched slots have no residual super-sign after +literal Koszul regrouping; the positions of mismatched symbols are fixed. -/ +theorem regroupPhase_permute {p l : ℕ} (σ : Equiv.Perm (Fin l)) (u w : Word p l) + (hfix : ∀ i, (odd (u i) ↔ ¬ odd (w i)) → σ i = i) : + regroupPhase (wordPerm σ u) (wordPerm σ w) * phase σ u * phase σ w = + regroupPhase u w := by + unfold regroupPhase + rw [phase_prod,phase_prod] + have hreindex : + (∏ ij ∈ Equiv.Perm.finPairsLT l, + (if odd (wordPerm σ u ij.1) ∧ odd (wordPerm σ w ij.2) then (-1 : ℂ) else 1)) = + ∏ ij ∈ Equiv.Perm.finPairsLT l, + (if odd (wordPerm σ u (Equiv.Perm.signBijAux σ ij).1) ∧ + odd (wordPerm σ w (Equiv.Perm.signBijAux σ ij).2) then (-1 : ℂ) else 1) := by + symm + exact Finset.prod_nbij (Equiv.Perm.signBijAux σ) + Equiv.Perm.signBijAux_mem Equiv.Perm.signBijAux_injOn + Equiv.Perm.signBijAux_surj (fun _ _ => rfl) + rw [hreindex,← Finset.prod_mul_distrib,← Finset.prod_mul_distrib] + apply Finset.prod_congr rfl + rintro ⟨i,j⟩ hij + have hji : j < i := Equiv.Perm.mem_finPairsLT.mp hij + have hne : σ j ≠ σ i := σ.injective.ne hji.ne + by_cases ht : σ j < σ i + · simp [Equiv.Perm.signBijAux,wordPerm,ht,ht.not_gt] + · have ht' : σ i < σ j := lt_of_le_of_ne (le_of_not_gt ht) hne.symm + have hm : ¬ ((odd (u i) ↔ ¬ odd (w i)) ∧ (odd (u j) ↔ ¬ odd (w j))) := by + rintro ⟨hi,hj⟩ + have hi' := hfix i hi + have hj' := hfix j hj + rw [hi',hj'] at ht' + exact hji.not_gt ht' + by_cases hui : odd (u i) <;> by_cases huj : odd (u j) <;> + by_cases hwi : odd (w i) <;> by_cases hwj : odd (w j) <;> + simp [Equiv.Perm.signBijAux,wordPerm,ht,ht',hui,huj,hwi,hwj] at hm ⊢ + +lemma commutant_transport {p l : ℕ} (A : commutant p l) (σ : Equiv.Perm (Fin l)) + (u w : Word p l) : + A.val (wordPerm σ u) (wordPerm σ w) = phase σ u * phase σ w * A.val u w := by + have hh := congrArg (fun B : Matrix (Word p l) (Word p l) ℂ => B (wordPerm σ u) w) + (A.property σ) + rw [mul_signed_entry,signed_mul_entry] at hh + calc + _ = (A.val (wordPerm σ u) (wordPerm σ w) * phase σ w) * phase σ w := by + rw [mul_assoc,phase_square,mul_one] + _ = (phase σ u * A.val u w) * phase σ w := by rw [hh] + _ = _ := by ring + +/- Rephased purification components are ordinary symmetric on the free, +matched-pair slots, a proved conclusion from the signed commutant relation. -/ +theorem regrouped_commutant_invariant {p l : ℕ} (A : commutant p l) + (σ : Equiv.Perm (Fin l)) (u w : Word p l) + (hfix : ∀ i, (odd (u i) ↔ ¬ odd (w i)) → σ i = i) : + regroupPhase (wordPerm σ u) (wordPerm σ w) * + A.val (wordPerm σ u) (wordPerm σ w) = regroupPhase u w * A.val u w := by + rw [commutant_transport] + calc + _ = (regroupPhase (wordPerm σ u) (wordPerm σ w) * phase σ u * phase σ w) * A.val u w := by ring + _ = _ := by rw [regroupPhase_permute σ u w hfix] + +/- Equal local parities in the system copies give equal regrouping signs. +This is what justifies cancellation under the actual auxiliary partial trace. -/ +lemma regroupPhase_of_same_parity {p l : ℕ} (u u' w : Word p l) + (h : ∀ i, odd (u i) ↔ odd (u' i)) : regroupPhase u w = regroupPhase u' w := by + unfold regroupPhase + apply Finset.prod_congr rfl + intro ij _ + rw [h ij.1] +end CoordinateSweeps.SignedTensor + +end +open scoped Matrix.Norms.L2Operator + +end OAI diff --git a/lean/OAI/RepresentationTheory/SignedTensor/Blocks.lean b/lean/OAI/RepresentationTheory/SignedTensor/Blocks.lean index 843801ff1a11ea4a968493ff6df45282297bee0d..b14d1daf19e8b6d9e9edb16fd516a6ae57969a19 100644 --- a/lean/OAI/RepresentationTheory/SignedTensor/Blocks.lean +++ b/lean/OAI/RepresentationTheory/SignedTensor/Blocks.lean @@ -1,966 +1,966 @@ -import Mathlib -import OAI.RepresentationTheory.SignedTensor.Domination - -namespace OAI - -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ComplexConjugate Matrix.Norms.L2Operator -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ComplexOrder MatrixOrder -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ENNReal -open MeasureTheory - -namespace CoordinateSweeps.SignedTensor -variable {B : Type} [Fintype B] [DecidableEq B] - -/- Tensorization of finite density domination, preserving -finite probability normalization and the exact product of local dimensions. -/ -theorem finite_block_density_domination (s p : ℕ) (hp : 0 < p) (hps : p ≤ s) - (l : B → ℕ) (hl : ∀ i, l i ≤ s) (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (l i)))) : - ∃ (K : Type) (_ : Fintype K) (_ : Nonempty K) (r : K → B → EvenDensity p), - (((∏ i, ((ρ i).dimension : ℂ))*((s+1 : ℕ) : ℂ)^(Fintype.card B*(41*p^2))) • - ((Fintype.card K : ℂ)⁻¹ • ∑ x, DependentTensor.tensor (fun i => densityPower (l i) (r x i).val))- - DependentTensor.tensor (fun i => isotypic (p := p) (ρ i))).PosSemidef := by - choose K fK nK r hr using fun i => finite_density_domination s p (l i) hp hps (hl i) (ρ i) - let : ∀ i, Fintype (K i) := fK - let : ∀ i, Nonempty (K i) := nK - refine ⟨(∀ i, K i),inferInstance,inferInstance,fun x i => r i (x i),?_⟩ - have hh := DependentTensor.tensor_mono - (fun i => isotypic (p := p) (ρ i)) - (fun i => (((ρ i).dimension : ℂ)*((s+1 : ℕ) : ℂ)^(41*p^2)) • - ((Fintype.card (K i) : ℂ)⁻¹ • ∑ x, densityPower (l i) (r i x).val)) - (fun i => isotypic_posSemidef (ρ i)) hr - rw [DependentTensor.tensor_smul] at hh - have hm : DependentTensor.tensor (fun i => (Fintype.card (K i) : ℂ)⁻¹ • - ∑ x, densityPower (l i) (r i x).val) = - (Fintype.card (∀ i, K i) : ℂ)⁻¹ • ∑ x : ∀ i, K i, - DependentTensor.tensor (fun i => densityPower (l i) (r i (x i)).val) := by - simp only [Finset.smul_sum] - rw [DependentTensor.tensor_mixture] - rw [Fintype.card_pi,Nat.cast_prod,Finset.prod_inv_distrib] - have hc : (∏ i, ((ρ i).dimension : ℂ)*((s+1 : ℕ) : ℂ)^(41*p^2)) = - (∏ i, ((ρ i).dimension : ℂ))*((s+1 : ℕ) : ℂ)^(Fintype.card B*(41*p^2)) := by - rw [Finset.prod_mul_distrib,Finset.prod_const,Finset.card_univ,← pow_mul,mul_comm (41*p^2)] - rwa [hm,hc] at hh - -end CoordinateSweeps.SignedTensor - -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder - -noncomputable section -open scoped BigOperators -attribute [local instance] Classical.propDecidable -namespace CoordinateSweeps.OrderedBlocks -variable {r : ℕ} (n : Fin r → ℕ) - -def offset (i : Fin r) : ℕ := ∑ j ∈ Finset.Iio i, n j - -lemma offset_next_le (i j : Fin r) (hij : i < j) : offset n i+n i ≤ offset n j := by - have he : Finset.Iic i=insert i (Finset.Iio i) := by ext x; simp [le_iff_lt_or_eq,or_comm] - have hh : ∑ k ∈ Finset.Iic i, n k ≤ ∑ k ∈ Finset.Iio j, n k := - Finset.sum_le_sum_of_subset (fun k hk => Finset.mem_Iio.mpr (lt_of_le_of_lt (Finset.mem_Iic.mp hk) hij)) - rw [he,Finset.sum_insert (by simp)] at hh - simpa only [offset,add_comm] using hh - -lemma offset_next_le_total (i : Fin r) : offset n i+n i ≤ ∑ j, n j := by - have he : Finset.Iic i=insert i (Finset.Iio i) := by ext x; simp [le_iff_lt_or_eq,or_comm] - have hh : ∑ k ∈ Finset.Iic i, n k ≤ ∑ k, n k := Finset.sum_le_sum_of_subset (Finset.subset_univ _) - rw [he,Finset.sum_insert (by simp)] at hh - simpa only [offset,add_comm] using hh - -def encode (x : (i : Fin r) × Fin (n i)) : Fin (∑ i, n i) := - ⟨offset n x.1+x.2,lt_of_lt_of_le (Nat.add_lt_add_left x.2.isLt _) (offset_next_le_total n x.1)⟩ - -lemma encode_lt_of_block {i j : Fin r} (hij : i < j) (a : Fin (n i)) (b : Fin (n j)) : - encode n ⟨i,a⟩ < encode n ⟨j,b⟩ := by - change offset n i+a.val < offset n j+b.val - have hh := offset_next_le n i j hij - have ha := a.isLt - omega - -lemma encode_lt_same {i : Fin r} (a b : Fin (n i)) : - encode n ⟨i,a⟩ < encode n ⟨i,b⟩ ↔ a < b := by - change offset n i+a.val < offset n i+b.val ↔ a.val < b.val - omega - -lemma encode_injective : Function.Injective (encode n) := by - rintro ⟨i,a⟩ ⟨j,b⟩ h - have hi : i=j := by - rcases lt_trichotomy i j with hij | hij | hij - · exact False.elim ((ne_of_lt (encode_lt_of_block n hij a b)) h) - · exact hij - · exact False.elim ((ne_of_lt (encode_lt_of_block n hij b a)) h.symm) - subst j - have hab : a=b := Fin.ext (by have hh := congrArg Fin.val h; dsimp [encode] at hh; omega) - subst b - rfl - -/- Explicit contiguous coordinate chart, including zero-length blocks. -/ -def positions : ((i : Fin r) × Fin (n i)) ≃ Fin (∑ i, n i) := - Equiv.ofBijective (encode n) ((Fintype.bijective_iff_injective_and_card _).mpr - ⟨encode_injective n,by simp [Fintype.card_sigma]⟩) - -lemma positions_apply (x : (i : Fin r) × Fin (n i)) : positions n x=encode n x := rfl - -lemma positions_lt_of_block {i j : Fin r} (hij : i < j) (a : Fin (n i)) (b : Fin (n j)) : - positions n ⟨i,a⟩ < positions n ⟨j,b⟩ := encode_lt_of_block n hij a b - -lemma positions_lt_same {i : Fin r} (a b : Fin (n i)) : - positions n ⟨i,a⟩ < positions n ⟨i,b⟩ ↔ a < b := encode_lt_same n a b - -def perm (σ : ∀ i, Equiv.Perm (Fin (n i))) : Equiv.Perm (Fin (∑ i, n i)) := - (positions n).permCongr (Equiv.sigmaCongrRight σ) - -@[simp] lemma perm_apply (σ : ∀ i, Equiv.Perm (Fin (n i))) (i : Fin r) (j : Fin (n i)) : - perm n σ (positions n ⟨i,j⟩)=positions n ⟨i,σ i j⟩ := by - simp [perm,Equiv.permCongr_apply] - -lemma perm_inv (σ : ∀ i, Equiv.Perm (Fin (n i))) : - (perm n σ)⁻¹=perm n (fun i => (σ i)⁻¹) := by - apply Equiv.ext - intro x - obtain ⟨⟨i,j⟩,rfl⟩ := (positions n).surjective x - apply (perm n σ).injective - simp - -def permHom : (∀ i, Equiv.Perm (Fin (n i))) →* Equiv.Perm (Fin (∑ i, n i)) where - toFun := perm n - map_one' := by - apply Equiv.ext; intro x - obtain ⟨⟨i,j⟩,rfl⟩ := (positions n).surjective x - simp - map_mul' σ τ := by - apply Equiv.ext; intro x - obtain ⟨⟨i,j⟩,rfl⟩ := (positions n).surjective x - simp - -end CoordinateSweeps.OrderedBlocks - -namespace CoordinateSweeps.SignedTensor - -lemma phase_double_prod {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) : - phase σ w=∏ i : Fin l, ∏ j : Fin l, - if j < i ∧ odd (w i) ∧ odd (w j) ∧ σ i < σ j then (-1 : ℂ) else 1 := by - have he : Equiv.Perm.finPairsLT l=(Finset.univ : Finset ((i : Fin l) × Fin l)).filter (fun x => x.2 < x.1) := by - ext x - simp only [Equiv.Perm.mem_finPairsLT,Finset.mem_filter,Finset.mem_univ,true_and] - rw [phase_prod,he,Finset.prod_filter,Fintype.prod_sigma] - apply Finset.prod_congr rfl - intro i hi - apply Finset.prod_congr rfl - intro j hj - split_ifs <;> simp_all - -def blockPerm {m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) : - Equiv.Perm (Fin (m+n)) := finSumFinEquiv.permCongr (Equiv.Perm.sumCongr σ τ) - -@[simp] lemma blockPerm_left {m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) (i : Fin m) : - blockPerm σ τ (Fin.castAdd n i)=Fin.castAdd n (σ i) := by - simp [blockPerm,Equiv.permCongr_apply] - -@[simp] lemma blockPerm_right {m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) (i : Fin n) : - blockPerm σ τ (Fin.natAdd m i)=Fin.natAdd m (τ i) := by - simp [blockPerm,Equiv.permCongr_apply] - -lemma blockPerm_inv {m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) : - (blockPerm σ τ)⁻¹=blockPerm σ⁻¹ τ⁻¹ := by - apply Equiv.ext - intro i - apply (blockPerm σ τ).injective - induction i using Fin.addCases <;> simp - -lemma phase_blockPerm {p m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) - (w : Word p (m+n)) : - phase (blockPerm σ τ) w=phase σ (fun i => w (Fin.castAdd n i))* - phase τ (fun i => w (Fin.natAdd m i)) := by - have hlr (i : Fin m) (j : Fin n) : ¬ Fin.natAdd m j w (Fin.castAdd n i),fun i => w (Fin.natAdd m i)) - invFun w := Fin.addCases w.1 w.2 - left_inv w := by funext i; induction i using Fin.addCases <;> simp - right_inv w := by ext <;> simp - -lemma splitWord_wordPerm {p m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) - (w : Word p (m+n)) : - splitWord p m n (wordPerm (blockPerm σ τ) w)= - (wordPerm σ (splitWord p m n w).1,wordPerm τ (splitWord p m n w).2) := by - ext i <;> simp [splitWord,wordPerm,blockPerm_inv] - -def blockMatrix {p m n : ℕ} (A : Matrix (Word p m) (Word p m) ℂ) - (B : Matrix (Word p n) (Word p n) ℂ) : Matrix (Word p (m+n)) (Word p (m+n)) ℂ := - fun u w => A (splitWord p m n u).1 (splitWord p m n w).1 * - B (splitWord p m n u).2 (splitWord p m n w).2 - -/- Exact block multiplicativity of the signed permutation action. -/ -theorem matrix_blockPerm {p m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) : - matrix (p := p) (blockPerm σ τ)=blockMatrix (matrix σ) (matrix τ) := by - ext u w - have he : u=wordPerm (blockPerm σ τ) w ↔ - (splitWord p m n u).1=wordPerm σ (splitWord p m n w).1 ∧ - (splitWord p m n u).2=wordPerm τ (splitWord p m n w).2 := by - rw [← (splitWord p m n).injective.eq_iff,splitWord_wordPerm,Prod.mk.injEq] - simp only [matrix,blockMatrix,he,phase_blockPerm] - split_ifs <;> simp_all [splitWord] - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open OrderedBlocks -variable {p r : ℕ} (n : Fin r → ℕ) - -lemma prod_positions (f : Fin (∑ i, n i) → ℂ) : - ∏ x, f x=∏ i, ∏ j : Fin (n i), f (positions n ⟨i,j⟩) := by - rw [← Equiv.prod_comp (positions n) f,Fintype.prod_sigma] - -lemma phase_grouped (σ : ∀ i, Equiv.Perm (Fin (n i))) (w : Word p (∑ i, n i)) : - phase (perm n σ) w=∏ i, phase (σ i) (fun j => w (positions n ⟨i,j⟩)) := by - rw [phase_double_prod,prod_positions n] - apply Finset.prod_congr rfl - intro i hi - rw [phase_double_prod] - apply Finset.prod_congr rfl - intro a ha - rw [prod_positions n,Finset.prod_eq_single i] - · apply Finset.prod_congr rfl - intro b hb - simp only [perm_apply,positions_lt_same] - · intro j hj hji - apply Finset.prod_eq_one - intro b hb - rcases lt_or_gt_of_ne hji with hlt | hgt - · have hn : ¬ positions n ⟨i,σ i a⟩ < positions n ⟨j,σ j b⟩ := - not_lt_of_ge (positions_lt_of_block n hlt _ _).le - simp [hn] - · have hn : ¬ positions n ⟨j,b⟩ < positions n ⟨i,a⟩ := - not_lt_of_ge (positions_lt_of_block n hgt _ _).le - simp [hn] - · simp - -def groupWord (p : ℕ) : Word p (∑ i, n i) ≃ (∀ i, Word p (n i)) where - toFun w i j := w (positions n ⟨i,j⟩) - invFun w x := w ((positions n).symm x).1 ((positions n).symm x).2 - left_inv w := by funext x; simp - right_inv w := by - funext i j - change (fun x : (i : Fin r) × Fin (n i) => w x.1 x.2) ((positions n).symm (positions n ⟨i,j⟩)) = _ - rw [Equiv.symm_apply_apply] - -lemma groupWord_wordPerm (σ : ∀ i, Equiv.Perm (Fin (n i))) (w : Word p (∑ i, n i)) : - groupWord n p (wordPerm (perm n σ) w)=fun i => wordPerm (σ i) (groupWord n p w i) := by - funext i j - simp [groupWord,wordPerm,perm_inv] - -/- Genuine product-subgroup action, with no suppressed Koszul signs. -/ -theorem matrix_grouped (σ : ∀ i, Equiv.Perm (Fin (n i))) : - matrix (p := p) (perm n σ)= - Matrix.reindex (groupWord n p).symm (groupWord n p).symm - (DependentTensor.tensor (fun i => matrix (σ i))) := by - ext u w - have he : u=wordPerm (perm n σ) w ↔ - ∀ i, groupWord n p u i=wordPerm (σ i) (groupWord n p w i) := by - rw [← (groupWord n p).injective.eq_iff,groupWord_wordPerm] - exact funext_iff - change (if u=wordPerm (perm n σ) w then phase (perm n σ) w else 0)= - ∏ i, if groupWord n p u i=wordPerm (σ i) (groupWord n p w i) - then phase (σ i) (groupWord n p w i) else 0 - simp only [he] - by_cases h : ∀ i, groupWord n p u i=wordPerm (σ i) (groupWord n p w i) - · rw [ite_eq_left h,phase_grouped] - simp only [h,ite_true] - rfl - · rw [ite_eq_right h] - obtain ⟨i,hi⟩ := not_forall.mp h - symm - apply Finset.prod_eq_zero (Finset.mem_univ i) - simp [hi] - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open OrderedBlocks UnitaryIrrep -variable {p r : ℕ} (n : Fin r → ℕ) - -/- The subgroup operator is an actual group-algebra average on the full set -of slots, not an operator posited to factor. -/ -def groupedAverage {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] - (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) : - Matrix (Word p (∑ i, n i)) (Word p (∑ i, n i)) ℂ := - averageMatrix (action p (∑ i, n i)) (fun ω : ∀ i, Ω i => ∏ i, w i (ω i)) - (fun ω => perm n (fun i => g i (ω i))) - -lemma groupedAverage_factor {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] - (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) : - groupedAverage (p := p) n w g= - Matrix.reindex (groupWord n p).symm (groupWord n p).symm - (DependentTensor.tensor (fun i => averageMatrix (action p (n i)) (w i) (g i))) := by - ext u v - simp only [groupedAverage,averageMatrix,Matrix.reindex_apply,Matrix.submatrix_apply, - Equiv.symm_symm,DependentTensor.tensor,Matrix.sum_apply,Matrix.smul_apply,smul_eq_mul] - change (∑ ω : ∀ i, Ω i, (∏ i, w i (ω i))* - matrix (perm n (fun i => g i (ω i))) u v)= - ∏ i, ∑ ω : Ω i, w i ω*matrix (g i ω) (groupWord n p u i) (groupWord n p v i) - have he (σ : ∀ i, Equiv.Perm (Fin (n i))) : - matrix (perm n σ) u v=∏ i, matrix (σ i) (groupWord n p u i) (groupWord n p v i) := by - have hh := congrArg (fun A : Matrix (Word p (∑ i, n i)) (Word p (∑ i, n i)) ℂ => A u v) - (matrix_grouped (p := p) n σ) - exact hh - simp only [he] - rw [Fintype.prod_sum] - apply Finset.sum_congr rfl - intro ω hω - exact (Finset.prod_mul_distrib : - (∏ i, w i (ω i)*matrix (g i (ω i)) (groupWord n p u i) (groupWord n p v i))=_).symm - -def groupedProjector (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : - Matrix (Word p (∑ i, n i)) (Word p (∑ i, n i)) ℂ := - groupedAverage n (fun i => (ρ i).coefficient) (fun _ => id) - -lemma groupedProjector_factor (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : - groupedProjector (p := p) n ρ= - Matrix.reindex (groupWord n p).symm (groupWord n p).symm - (DependentTensor.tensor (fun i => (ρ i).projector (action p (n i)))) := by - exact groupedAverage_factor n _ _ - -lemma matrix_trace_reindex {X Y : Type*} [Fintype X] [Fintype Y] (e : X ≃ Y) - (A : Matrix X X ℂ) : Matrix.trace (Matrix.reindex e e A)=Matrix.trace A := by - exact Equiv.sum_comp e.symm (fun i => A i i) - -lemma reindex_moment {X Y : Type*} [Fintype X] [Fintype Y] [DecidableEq X] [DecidableEq Y] - (e : X ≃ Y) (A : Matrix X X ℂ) (q : ℕ) : - Matrix.trace ((((Matrix.reindexAlgEquiv ℂ ℂ e A).conjTranspose)*(Matrix.reindexAlgEquiv ℂ ℂ e A))^q)= - Matrix.trace ((A.conjTranspose*A)^q) := by - have hs : (Matrix.reindexAlgEquiv ℂ ℂ e A).conjTranspose= - Matrix.reindexAlgEquiv ℂ ℂ e A.conjTranspose := by ext i j; rfl - rw [hs,← map_mul,← map_pow] - exact matrix_trace_reindex e _ - -/- Exact isotypic child moment factorization, including the true Hom -multiplicities and all zero-length blocks. -/ -theorem grouped_projected_moment {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) - (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) - {q : ℕ} (hq : q ≠ 0) : - Matrix.trace (((groupedProjector (p := p) n ρ*groupedAverage n w g).conjTranspose* - (groupedProjector n ρ*groupedAverage n w g))^q)= - ∏ i, (Module.finrank ℂ ((ρ i).asRepresentation.IntertwiningMap - (matrixRepresentation (action p (n i)))) : ℂ)* - Matrix.trace (((averageMatrix (ρ i).matrix (w i) (g i)).conjTranspose* - averageMatrix (ρ i).matrix (w i) (g i))^q) := by - rw [groupedProjector_factor,groupedAverage_factor] - let e := (groupWord n p).symm - change Matrix.trace (((Matrix.reindexAlgEquiv ℂ ℂ e _*Matrix.reindexAlgEquiv ℂ ℂ e _).conjTranspose* - (Matrix.reindexAlgEquiv ℂ ℂ e _*Matrix.reindexAlgEquiv ℂ ℂ e _))^q)=_ - rw [← map_mul,reindex_moment,← DependentTensor.tensor_mul,DependentTensor.tensor_moment] - apply Finset.prod_congr rfl - intro i hi - exact (ρ i).projected_operator_moment _ (fun σ => (matrix_inv σ).symm) (w i) (g i) hq - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -variable {p : ℕ} - -def IsEven (A : Matrix (Letter p) (Letter p) ℂ) : Prop := - ∀ i j, (odd i ↔ ¬ odd j) → A i j=0 - -def grading (p : ℕ) : Matrix (Letter p) (Letter p) ℂ := - Matrix.diagonal (fun i => if odd i then 1 else 0) - -lemma isEven_iff_commute (A : Matrix (Letter p) (Letter p) ℂ) : - IsEven A ↔ Commute A (grading p) := by - constructor - · intro h - show A*grading p=grading p*A - ext i j - simp only [grading,Matrix.mul_diagonal,Matrix.diagonal_mul] - by_cases hi : odd i - · by_cases hj : odd j - · simp [hi,hj] - · simp [hi,hj,h i j (by tauto)] - · by_cases hj : odd j - · simp [hi,hj,h i j (by tauto)] - · simp [hi,hj] - · intro h i j hij - have hh := congrArg (fun M : Matrix (Letter p) (Letter p) ℂ => M i j) h.eq - simp only [grading,Matrix.mul_diagonal,Matrix.diagonal_mul] at hh - by_cases hi : odd i - · have hj : ¬ odd j := hij.mp hi - simpa [hi,hj] using hh.symm - · have hj : odd j := by tauto - simpa [hi,hj] using hh - -lemma isEven_add {A B : Matrix (Letter p) (Letter p) ℂ} (hA : IsEven A) (hB : IsEven B) : - IsEven (A+B) := by intro i j hij; simp only [Matrix.add_apply,hA i j hij,hB i j hij,add_zero] - -lemma isEven_smul (c : ℂ) {A : Matrix (Letter p) (Letter p) ℂ} (hA : IsEven A) : - IsEven (c • A) := by intro i j hij; simp only [Matrix.smul_apply,smul_eq_mul,hA i j hij,mul_zero] - -lemma isEven_sum {I : Type*} [Fintype I] (A : I → Matrix (Letter p) (Letter p) ℂ) - (hA : ∀ i, IsEven (A i)) : IsEven (∑ i, A i) := by - intro i j hij - simp only [Matrix.sum_apply] - exact Finset.sum_eq_zero (fun a _ => hA a i j hij) - -lemma isEven_one : IsEven (1 : Matrix (Letter p) (Letter p) ℂ) := by - intro i j hij - apply Matrix.one_apply_ne - intro he - subst j - tauto - -lemma densityPower_commute_of_even {l : ℕ} (r : Matrix (Letter p) (Letter p) ℂ) - (hr : IsEven r) (σ : Equiv.Perm (Fin l)) : - matrix σ*densityPower l r=densityPower l r*matrix σ := by - have hpar {u w : Word p l} (h : densityPower l r u w ≠ 0) : - ∀ i, odd (u i) ↔ odd (w i) := by - intro i - have he : r (u i) (w i) ≠ 0 := (Finset.prod_ne_zero_iff.mp h) i (Finset.mem_univ _) - by_contra hn - exact he (hr _ _ (by tauto)) - ext u w - simp only [Matrix.mul_apply,matrix] - rw [Finset.sum_eq_single ((wordPerm σ).symm u),Finset.sum_eq_single (wordPerm σ w)] - · simp only [(wordPerm σ).apply_symm_apply,ite_true] - have hd : densityPower l r u (wordPerm σ w)=densityPower l r ((wordPerm σ).symm u) w := by - simpa using densityPower_permute σ r ((wordPerm σ).symm u) w - rw [hd] - by_cases hn : densityPower l r ((wordPerm σ).symm u) w=0 - · simp [hn] - · rw [phase_eq_of_parity σ _ _ (hpar hn),mul_comm] - · intro v hv hne; simp [hne] - · simp - · intro v hv hne - have hh : u ≠ wordPerm σ v := by - intro he - exact hne ((Equiv.eq_symm_apply _).mpr he.symm) - simp [hh] - · simp - -lemma densityPower_commute_lift {l : ℕ} (r : Matrix (Letter p) (Letter p) ℂ) - (hr : IsEven r) (x : MonoidAlgebra ℂ (Equiv.Perm (Fin l))) : - (MonoidAlgebra.lift ℂ _ _ (action p l) x)*densityPower l r = - densityPower l r*(MonoidAlgebra.lift ℂ _ _ (action p l) x) := by - induction x using MonoidAlgebra.induction_on with - | of g => simpa [action] using densityPower_commute_of_even r hr g - | add x y hx hy => simp only [map_add,add_mul,mul_add,hx,hy] - | smul c x hx => simp only [map_smul,smul_mul_assoc,mul_smul_comm,hx] - -/- Constructed even whitening of the regularized empirical row density. -/ -theorem exists_even_whitening {R : Type*} [Fintype R] [Nonempty R] - (r : R → EvenDensity p) {ε : ℝ} (hε : 0 < ε) : - let B := (Fintype.card R : ℂ)⁻¹ • ∑ i, (r i).val + (ε : ℂ) • (1 : Matrix (Letter p) (Letter p) ℂ) - ∃ A : Matrix (Letter p) (Letter p) ℂ, A.PosSemidef ∧ IsEven A ∧ A*B*A=1 ∧ - ((Fintype.card R : ℂ) • (1 : Matrix (Letter p) (Letter p) ℂ)- - ∑ i, A*(r i).val*A).PosSemidef := by - dsimp only - let B := (Fintype.card R : ℂ)⁻¹ • ∑ i, (r i).val + (ε : ℂ) • (1 : Matrix (Letter p) (Letter p) ℂ) - have hBp : B.PosDef := TensorBoard.average_regularization_posDef (fun i => (r i).val) - (fun i => (r i).property.1) hε - have hBe : IsEven B := isEven_add (isEven_smul _ (isEven_sum _ (fun i => (r i).property.2.2))) - (isEven_smul _ isEven_one) - obtain ⟨A,hA,hABA,hcomm⟩ := TensorBoard.exists_whitening B hBp - refine ⟨A,hA,(isEven_iff_commute A).mpr (hcomm _ ((isEven_iff_commute B).mp hBe)),hABA,?_⟩ - apply TensorBoard.whitening_sum_bound _ B A hA.isHermitian hABA - dsimp [B] - convert (Matrix.PosSemidef.one (n := Letter p) (R := ℂ)).smul hε.le using 1 - module - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -variable {p l : ℕ} - -/- Even inhomogeneous site tensors transform by the *signed* permutation -matrix with no residual phase. This is what permits regrouping deleted rows -and columns without identifying the two Koszul charts by an unsigned map. -/ -lemma tensor_covariance (A : Fin l → Matrix (Letter p) (Letter p) ℂ) - (hA : ∀ i, IsEven (A i)) (σ : Equiv.Perm (Fin l)) : - matrix σ*TensorBoard.tensor A= - TensorBoard.tensor (fun i => A (σ⁻¹ i))*matrix σ := by - have hpar {u w : Word p l} (h : TensorBoard.tensor A u w ≠ 0) : - ∀ i, odd (u i) ↔ odd (w i) := by - intro i - have he : A i (u i) (w i) ≠ 0 := (Finset.prod_ne_zero_iff.mp h) i (Finset.mem_univ _) - by_contra hn - exact he (hA i _ _ (by tauto)) - ext u w - simp only [Matrix.mul_apply,matrix] - rw [Finset.sum_eq_single ((wordPerm σ).symm u),Finset.sum_eq_single (wordPerm σ w)] - · simp only [(wordPerm σ).apply_symm_apply,ite_true] - have hd : TensorBoard.tensor (fun i => A (σ⁻¹ i)) u (wordPerm σ w)= - TensorBoard.tensor A ((wordPerm σ).symm u) w := by - change (∏ i, A (σ⁻¹ i) (u i) (w (σ⁻¹ i)))=∏ i, A i (u (σ i)) (w i) - simpa using (Equiv.prod_comp σ (fun i => A (σ⁻¹ i) (u i) (w (σ⁻¹ i)))).symm - rw [hd] - by_cases hn : TensorBoard.tensor A ((wordPerm σ).symm u) w=0 - · simp [hn] - · rw [phase_eq_of_parity σ _ _ (hpar hn),mul_comm] - · intro v hv hne; simp [hne] - · simp - · intro v hv hne - have hh : u ≠ wordPerm σ v := by - intro he - exact hne ((Equiv.eq_symm_apply _).mpr he.symm) - simp [hh] - · simp - -lemma tensor_signed_conjugate (A : Fin l → Matrix (Letter p) (Letter p) ℂ) - (hA : ∀ i, IsEven (A i)) (σ : Equiv.Perm (Fin l)) : - matrix σ*TensorBoard.tensor A*(matrix σ).conjTranspose= - TensorBoard.tensor (fun i => A (σ⁻¹ i)) := by - rw [tensor_covariance A hA σ,mul_assoc,← matrix_inv,← matrix_mul,mul_inv_cancel,matrix_one,mul_one] - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open OrderedBlocks -variable {p r : ℕ} (n : Fin r → ℕ) - -def groupedSite (a : Fin r → EvenDensity p) (k : Fin (∑ i, n i)) : EvenDensity p := - a ((positions n).symm k).1 - -lemma grouped_densityPower (a : Fin r → EvenDensity p) : - (DependentTensor.tensor (fun i => densityPower (n i) (a i).val)).submatrix - (groupWord n p) (groupWord n p)=TensorBoard.tensor (fun k => (groupedSite n a k).val) := by - ext u v - change (∏ i, ∏ j : Fin (n i), (a i).val (u (positions n ⟨i,j⟩)) (v (positions n ⟨i,j⟩)))= - ∏ k, (a ((positions n).symm k).1).val (u k) (v k) - rw [prod_positions] - apply Finset.prod_congr rfl - intro i _ - apply Finset.prod_congr rfl - intro j _ - rw [Equiv.symm_apply_apply] - -/- Literal contiguous-block projectors are dominated by independent finite -mixtures of even site densities, with all local dimension factors. -/ -theorem finite_grouped_density_domination (s : ℕ) (hp : 0 < p) (hps : p ≤ s) - (hn : ∀ i, n i ≤ s) (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : - ∃ (K : Type) (_ : Fintype K) (_ : Nonempty K) (a : K → Fin r → EvenDensity p), - (((∏ i, ((ρ i).dimension : ℂ))*((s+1 : ℕ) : ℂ)^(r*(41*p^2))) • - ((Fintype.card K : ℂ)⁻¹ • ∑ x, - TensorBoard.tensor (fun k => (groupedSite n (a x) k).val))- - groupedProjector (p := p) n ρ).PosSemidef := by - obtain ⟨K,hK,nK,a,ha⟩ := finite_block_density_domination s p hp hps n hn ρ - let := hK - let := nK - refine ⟨K,hK,nK,a,?_⟩ - have hh := ha.submatrix (groupWord n p) - have hm : (∑ x, DependentTensor.tensor (fun i => densityPower (n i) (a x i).val)).submatrix - (groupWord n p) (groupWord n p)=∑ x, TensorBoard.tensor (fun k => (groupedSite n (a x) k).val) := by - ext u v - simp only [Matrix.submatrix_apply,Matrix.sum_apply] - apply Finset.sum_congr rfl - intro x _ - exact congrArg (fun M => M u v) (grouped_densityPower n (a x)) - simp only [Fintype.card_fin,Matrix.submatrix_sub,Matrix.submatrix_smul, - Pi.sub_apply,Pi.smul_apply,hm] at hh - have he : (DependentTensor.tensor (fun i => isotypic (p := p) (ρ i))).submatrix - (groupWord n p) (groupWord n p)=groupedProjector (p := p) n ρ := by - simp only [groupedProjector_factor,isotypic_eq_projector] - rfl - rwa [he] at hh - -/- The same domination after an arbitrary *signed* change of slot chart. -/ -theorem finite_regrouped_density_domination (s : ℕ) (hp : 0 < p) (hps : p ≤ s) - (hn : ∀ i, n i ≤ s) (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) - (σ : Equiv.Perm (Fin (∑ i, n i))) : - ∃ (K : Type) (_ : Fintype K) (_ : Nonempty K) (a : K → Fin r → EvenDensity p), - (((∏ i, ((ρ i).dimension : ℂ))*((s+1 : ℕ) : ℂ)^(r*(41*p^2))) • - ((Fintype.card K : ℂ)⁻¹ • ∑ x, - TensorBoard.tensor (fun k => (groupedSite n (a x) (σ⁻¹ k)).val))- - matrix σ*groupedProjector (p := p) n ρ*(matrix σ).conjTranspose).PosSemidef := by - obtain ⟨K,hK,nK,a,ha⟩ := finite_grouped_density_domination n s hp hps hn ρ - let := hK - let := nK - refine ⟨K,hK,nK,a,?_⟩ - have hh := ha.mul_mul_conjTranspose_same (matrix σ) - simp only [mul_sub,sub_mul,Matrix.mul_smul,Matrix.smul_mul,Matrix.mul_sum,Matrix.sum_mul] at hh - have ht (x : K) : matrix σ*TensorBoard.tensor (fun k => (groupedSite n (a x) k).val)*(matrix σ).conjTranspose= - TensorBoard.tensor (fun k => (groupedSite n (a x) (σ⁻¹ k)).val) := - tensor_signed_conjugate _ (fun k => (groupedSite n (a x) k).property.2.2) σ - simpa only [ht] using hh - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -variable {p r : ℕ} (n : Fin r → ℕ) - -lemma groupedProjector_posSemidef (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : - (groupedProjector (p := p) n ρ).PosSemidef := by - rw [groupedProjector_factor] - exact (DependentTensor.tensor_posSemidef _ (fun i => (ρ i).projector_posSemidef _ - (fun σ => (matrix_inv σ).symm))).submatrix _ - -lemma groupedProjector_idempotent (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : - groupedProjector (p := p) n ρ*groupedProjector n ρ=groupedProjector n ρ := by - rw [groupedProjector_factor] - change Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _* - Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _=Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _ - rw [← map_mul,← DependentTensor.tensor_mul] - simp only [UnitaryIrrep.projector_idempotent] - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open OrderedBlocks UnitaryIrrep -variable {p r l : ℕ} (n : Fin r → ℕ) - -def lengthMatrix {a b : ℕ} (h : a=b) (M : Matrix (Word p a) (Word p a) ℂ) : - Matrix (Word p b) (Word p b) ℂ := h ▸ M - -def ambientProjector (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : Matrix (Word p l) (Word p l) ℂ := - matrix σ*lengthMatrix h (groupedProjector n ρ)*(matrix σ).conjTranspose - -def ambientProjectorAlgebra (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : MonoidAlgebra ℂ (Equiv.Perm (Fin l)) := - averageAlgebra (fun ω : ∀ i, Equiv.Perm (Fin (n i)) => ∏ i, (ρ i).coefficient (ω i)) - (fun ω => σ*(Equiv.permCongr (finCongr h) (perm n ω))*σ⁻¹) - -lemma ambientProjectorAlgebra_lift (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : - MonoidAlgebra.lift ℂ _ _ (action p l) (ambientProjectorAlgebra n h σ ρ)= - ambientProjector (p := p) n h σ ρ := by - subst l - simp only [ambientProjectorAlgebra,lift_averageAlgebra,averageMatrix,ambientProjector, - lengthMatrix,groupedProjector,groupedAverage,Matrix.mul_sum,Matrix.sum_mul,Matrix.mul_smul,Matrix.smul_mul] - apply Finset.sum_congr rfl - intro ω _ - congr 1 - change matrix (σ*(Equiv.permCongr (finCongr rfl) (perm n ω))*σ⁻¹)=_ - simp only [finCongr_refl,matrix_mul,matrix_inv] - rfl - -lemma ambientProjector_posSemidef (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : - (ambientProjector (p := p) n h σ ρ).PosSemidef := by - subst l - exact (groupedProjector_posSemidef n ρ).mul_mul_conjTranspose_same (matrix σ) - -lemma ambientProjector_idempotent (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : - ambientProjector (p := p) n h σ ρ*ambientProjector n h σ ρ=ambientProjector n h σ ρ := by - subst l - unfold ambientProjector lengthMatrix - calc - _ = matrix σ*(groupedProjector n ρ*((matrix σ).conjTranspose*matrix σ)*groupedProjector n ρ)* - (matrix (p := p) σ).conjTranspose := by noncomm_ring - _ = _ := by rw [matrix_unitary,mul_one,groupedProjector_idempotent] - -/- Actual ambient projectors, not hypothesized density mixtures. -/ -theorem finite_ambient_density_domination (s : ℕ) (hp : 0 < p) (hps : p ≤ s) - (hn : ∀ i, n i ≤ s) (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) - (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) : - ∃ (K : Type) (_ : Fintype K) (_ : Nonempty K) (a : K → Fin r → EvenDensity p), - (((∏ i, ((ρ i).dimension : ℂ))*((s+1 : ℕ) : ℂ)^(r*(41*p^2))) • - ((Fintype.card K : ℂ)⁻¹ • ∑ x, - TensorBoard.tensor (fun k => (groupedSite n (a x) ((finCongr h).symm (σ⁻¹ k))).val))- - ambientProjector (p := p) n h σ ρ).PosSemidef := by - subst l - simpa [ambientProjector,lengthMatrix] using - finite_regrouped_density_domination n s hp hps hn ρ σ - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open OrderedBlocks UnitaryIrrep -variable {p r l : ℕ} (n : Fin r → ℕ) - -def ambientAverage (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) - {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] - (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) : - Matrix (Word p l) (Word p l) ℂ := - averageMatrix (action p l) (fun ω : ∀ i, Ω i => ∏ i, w i (ω i)) - (fun ω => σ*Equiv.permCongr (finCongr h) (perm n (fun i => g i (ω i)))*σ⁻¹) - -lemma ambientAverage_factor (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) - {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] - (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) : - ambientAverage (p := p) n h σ w g= - matrix σ*lengthMatrix h (groupedAverage n w g)*(matrix σ).conjTranspose := by - subst l - simp only [ambientAverage,averageMatrix,groupedAverage,lengthMatrix, - Matrix.mul_sum,Matrix.sum_mul,Matrix.mul_smul,Matrix.smul_mul] - apply Finset.sum_congr rfl - intro ω _ - congr 1 - change matrix (σ*Equiv.permCongr (finCongr rfl) (perm n (fun i => g i (ω i)))*σ⁻¹)=_ - simp only [finCongr_refl,matrix_mul,matrix_inv] - rfl - -lemma matrix_unitary_reverse (σ : Equiv.Perm (Fin l)) : - matrix (p := p) σ*(matrix σ).conjTranspose=1 := by - rw [← matrix_inv,← matrix_mul,mul_inv_cancel,matrix_one] - -lemma conjugate_mul {X : Type*} [Fintype X] [DecidableEq X] - (U A B : Matrix X X ℂ) (hU : U.conjTranspose*U=1) : - (U*A*U.conjTranspose)*(U*B*U.conjTranspose)=U*(A*B)*U.conjTranspose := by - calc - _ = U*A*(U.conjTranspose*U)*B*U.conjTranspose := by noncomm_ring - _ = _ := by rw [hU,mul_one]; noncomm_ring - -lemma conjugate_pow {X : Type*} [Fintype X] [DecidableEq X] - (U A : Matrix X X ℂ) (hU : U.conjTranspose*U=1) (hU' : U*U.conjTranspose=1) (q : ℕ) : - (U*A*U.conjTranspose)^q=U*A^q*U.conjTranspose := by - induction q with - | zero => simpa using hU'.symm - | succ q ih => rw [pow_succ,ih,conjugate_mul U _ _ hU,pow_succ] - -lemma conjugate_moment {X : Type*} [Fintype X] [DecidableEq X] - (U A : Matrix X X ℂ) (hU : U.conjTranspose*U=1) (hU' : U*U.conjTranspose=1) (q : ℕ) : - Matrix.trace (((U*A*U.conjTranspose).conjTranspose*(U*A*U.conjTranspose))^q)= - Matrix.trace ((A.conjTranspose*A)^q) := by - have hs : (U*A*U.conjTranspose).conjTranspose=U*A.conjTranspose*U.conjTranspose := by - simp only [Matrix.conjTranspose_mul,Matrix.conjTranspose_conjTranspose] - noncomm_ring - rw [hs,conjugate_mul U _ _ hU,conjugate_pow U _ hU hU'] - rw [Matrix.trace_mul_cycle,hU,one_mul] - -/- The child moment formula survives the literal slot chart, with actual Hom multiplicities. -/ -theorem ambient_projected_moment (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) - {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) - (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) - {q : ℕ} (hq : q ≠ 0) : - Matrix.trace (((ambientProjector (p := p) n h σ ρ*ambientAverage n h σ w g).conjTranspose* - (ambientProjector n h σ ρ*ambientAverage n h σ w g))^q)= - ∏ i, (Module.finrank ℂ ((ρ i).asRepresentation.IntertwiningMap - (matrixRepresentation (action p (n i)))) : ℂ)* - Matrix.trace (((averageMatrix (ρ i).matrix (w i) (g i)).conjTranspose* - averageMatrix (ρ i).matrix (w i) (g i))^q) := by - subst l - rw [ambientAverage_factor] - unfold ambientProjector lengthMatrix - rw [conjugate_mul _ _ _ (matrix_unitary σ),conjugate_moment _ _ - (matrix_unitary σ) (matrix_unitary_reverse σ)] - exact grouped_projected_moment n ρ w g hq - -end CoordinateSweeps.SignedTensor - -/-! -All definitions are finite and use ordinary probability and trace normalizations. --/ - -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable - -noncomputable section -attribute [local instance] Classical.propDecidable -namespace CoordinateSweeps.FiberBlocks -open OrderedBlocks -variable {L : Type*} [Fintype L] {r : ℕ} (f : L → Fin r) - -def size (i : Fin r) : ℕ := Fintype.card {x : L // f x=i} -def cards (i : Fin r) : Fin (size f i) ≃ {x : L // f x=i} := (Fintype.equivFin _).symm - -/- Contiguous finite label fibers give a genuine ordered slot chart. -/ -def slots : Fin (∑ i, size f i) ≃ L := - (positions (size f)).symm.trans - ((Equiv.sigmaCongrRight (cards f)).trans (Equiv.sigmaFiberEquiv f)) - -lemma total : ∑ i, size f i=Fintype.card L := by - simpa only [Fintype.card_fin] using Fintype.card_congr (slots f) - -lemma label_slots (k : Fin (∑ i, size f i)) : - f (slots f k)=((positions (size f)).symm k).1 := by - exact (cards f ((positions (size f)).symm k).1 ((positions (size f)).symm k).2).property - -/- The same chart with the literal cardinal as ambient length. -/ -def chart : Fin (Fintype.card L) ≃ L := - (finCongr (total f).symm).trans (slots f) - -/- Permutation changing the contiguous fiber chart to any given ambient chart. -/ -def regroup (e : Fin (Fintype.card L) ≃ L) : Equiv.Perm (Fin (Fintype.card L)) := - (chart f).trans e.symm - -lemma label_regroup (e : Fin (Fintype.card L) ≃ L) (k : Fin (Fintype.card L)) : - ((positions (size f)).symm ((finCongr (total f)).symm ((regroup f e)⁻¹ k))).1=f (e k) := by - have he : slots f ((finCongr (total f)).symm ((regroup f e)⁻¹ k))=e k := by - change chart f ((regroup f e).symm k)=e k - simp [regroup] - rw [← label_slots f,he] - -end CoordinateSweeps.FiberBlocks - -namespace CoordinateSweeps.FiberBlocks -open OrderedBlocks -variable {L : Type*} [Fintype L] {r : ℕ} (f : L → Fin r) - -lemma slots_positions (i : Fin r) (j : Fin (size f i)) : - slots f (positions (size f) ⟨i,j⟩)=(cards f i j).val := by - simp [slots] - -/- Independent permutations of the actual fibers, on the literal ambient set. -/ -def action : (∀ i, Equiv.Perm (Fin (size f i))) →* Equiv.Perm L := - (slots f).permCongrHom.toMonoidHom.comp (permHom (size f)) - -lemma action_apply (σ : ∀ i, Equiv.Perm (Fin (size f i))) (i : Fin r) (j : Fin (size f i)) : - action f σ (cards f i j).val=(cards f i (σ i j)).val := by - rw [← slots_positions f i j,← slots_positions f i (σ i j)] - change slots f (perm (size f) σ ((slots f).symm (slots f (positions (size f) ⟨i,j⟩))))=_ - rw [Equiv.symm_apply_apply,perm_apply] - -lemma ambient_action (e : Fin (Fintype.card L) ≃ L) - (σ : ∀ i, Equiv.Perm (Fin (size f i))) : - Equiv.permCongr e.symm (action f σ)= - regroup f e*Equiv.permCongr (finCongr (total f)) (perm (size f) σ)*(regroup f e)⁻¹ := by - apply Equiv.ext - intro x - change e.symm (slots f (perm (size f) σ ((slots f).symm (e x))))=_ - simp only [Equiv.Perm.mul_apply,Equiv.permCongr_apply,regroup,chart, - Equiv.trans_apply,Equiv.symm_trans_apply,Equiv.Perm.coe_inv] - simp - -/- A label-preserving permutation has genuine induced local permutations. -/ -def restrict (σ : Equiv.Perm L) (hσ : ∀ x, f (σ x)=f x) (i : Fin r) : Equiv.Perm (Fin (size f i)) := - Equiv.permCongr (cards f i).symm (Equiv.subtypeEquiv σ (by - intro x - change f x=i ↔ f (σ x)=i - rw [hσ x])) - -lemma restrict_apply (σ : Equiv.Perm L) (hσ : ∀ x, f (σ x)=f x) - (i : Fin r) (j : Fin (size f i)) : - (cards f i (restrict f σ hσ i j)).val=σ (cards f i j).val := by - simp [restrict,Equiv.permCongr_apply] - -lemma action_restrict (σ : Equiv.Perm L) (hσ : ∀ x, f (σ x)=f x) : - action f (restrict f σ hσ)=σ := by - apply Equiv.ext - intro x - let i := f x - let j := (cards f i).symm ⟨x,rfl⟩ - have hx : (cards f i j).val=x := congrArg Subtype.val ((cards f i).apply_symm_apply ⟨x,rfl⟩) - rw [← hx,action_apply,restrict_apply] - -end CoordinateSweeps.FiberBlocks -namespace CoordinateSweeps.SignedTensor -open UnitaryIrrep -variable {p r l : ℕ} (n : Fin r → ℕ) -lemma groupedProjector_commute_average {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) - (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) : - groupedProjector (p := p) n ρ*groupedAverage n w g=groupedAverage n w g*groupedProjector n ρ := by - rw [groupedProjector_factor,groupedAverage_factor] - change Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _* - Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _= - Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _* - Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _ - rw [← map_mul,← map_mul,← DependentTensor.tensor_mul,← DependentTensor.tensor_mul] - congr 1 - apply congrArg DependentTensor.tensor - funext i - simp only [averageMatrix,Matrix.mul_sum,Matrix.sum_mul,Matrix.mul_smul,Matrix.smul_mul] - apply Finset.sum_congr rfl - intro ω _ - exact congrArg (fun A => w i ω • A) ((ρ i).projector_commute (action p (n i)) (g i ω)).symm - -lemma ambientProjector_commute_average (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) - {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) - (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) : - ambientProjector (p := p) n h σ ρ*ambientAverage n h σ w g= - ambientAverage n h σ w g*ambientProjector n h σ ρ := by - subst l - rw [ambientAverage_factor] - unfold ambientProjector lengthMatrix - rw [conjugate_mul _ _ _ (matrix_unitary σ),conjugate_mul _ _ _ (matrix_unitary σ)] - rw [groupedProjector_commute_average] -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open UnitaryIrrep -variable {p r : ℕ} (n : Fin r → ℕ) -lemma child_product_bound (s : ℕ) (hn : ∀ i, n i ≤ s) - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) (T E : Fin r → ℝ) - (hT : ∀ i, 0 ≤ T i) (hE : ∀ i, T i ≤ Real.exp (E i)) : - (∏ i, (Module.finrank ℂ ((ρ i).asRepresentation.IntertwiningMap - (matrixRepresentation (action p (n i)))) : ℝ)*T i) ≤ - ((s+1 : ℕ) : ℝ)^(r*((2*p)*(2*p)))*Real.exp (∑ i, E i) := by - rw [Finset.prod_mul_distrib] - have hm : (∏ i, (Module.finrank ℂ ((ρ i).asRepresentation.IntertwiningMap - (matrixRepresentation (action p (n i)))) : ℝ)) ≤ ((s+1 : ℕ) : ℝ)^(r*((2*p)*(2*p))) := by - calc - _ ≤ ∏ _ : Fin r, ((s+1 : ℕ) : ℝ)^((2*p)*(2*p)) := Finset.prod_le_prod₀ - (fun _ _ => Nat.cast_nonneg _) (fun i _ => by - exact_mod_cast (multiplicity_le p (n i) (ρ i)).trans - (Nat.pow_le_pow_left (Nat.add_le_add_right (hn i) 1) _)) - _ = _ := by rw [Finset.prod_const,Finset.card_univ,Fintype.card_fin,← pow_mul,Nat.mul_comm] - have ht : (∏ i, T i) ≤ Real.exp (∑ i, E i) := by - rw [Real.exp_sum] - exact Finset.prod_le_prod₀ (fun i _ => hT i) (fun i _ => hE i) - exact mul_le_mul hm ht (Finset.prod_nonneg (fun i _ => hT i)) (by positivity) -end CoordinateSweeps.SignedTensor -namespace CoordinateSweeps.SignedTensor -variable {p r : ℕ} {L : Type*} [Fintype L] (f : L → Fin r) - -def fiberProjector (e : Fin (Fintype.card L) ≃ L) - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) := - ambientProjector (p := p) (FiberBlocks.size f) (FiberBlocks.total f) (FiberBlocks.regroup f e) ρ - -def fiberProjectorAlgebra (e : Fin (Fintype.card L) ≃ L) - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) := - ambientProjectorAlgebra (FiberBlocks.size f) (FiberBlocks.total f) (FiberBlocks.regroup f e) ρ - -lemma fiberProjectorAlgebra_lift (e : Fin (Fintype.card L) ≃ L) - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) : - MonoidAlgebra.lift ℂ _ _ (action p (Fintype.card L)) (fiberProjectorAlgebra f e ρ)= - fiberProjector (p := p) f e ρ := ambientProjectorAlgebra_lift _ _ _ _ - -lemma fiberProjector_posSemidef (e : Fin (Fintype.card L) ≃ L) - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) : - (fiberProjector (p := p) f e ρ).PosSemidef := ambientProjector_posSemidef _ _ _ _ - -lemma fiberProjector_idempotent (e : Fin (Fintype.card L) ≃ L) - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) : - fiberProjector (p := p) f e ρ*fiberProjector f e ρ=fiberProjector f e ρ := - ambientProjector_idempotent _ _ _ _ - -/- Exact regrouping connects local isotypic products to the literal site labels. -/ -theorem finite_fiber_density_domination (e : Fin (Fintype.card L) ≃ L) - (s : ℕ) (hp : 0 < p) (hps : p ≤ s) (hn : ∀ i, FiberBlocks.size f i ≤ s) - (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) : - ∃ (K : Type) (_ : Fintype K) (_ : Nonempty K) (a : K → Fin r → EvenDensity p), - (((∏ i, ((ρ i).dimension : ℂ))*((s+1 : ℕ) : ℂ)^(r*(41*p^2))) • - ((Fintype.card K : ℂ)⁻¹ • ∑ x, - TensorBoard.tensor (fun k => (a x (f (e k))).val))-fiberProjector (p := p) f e ρ).PosSemidef := by - obtain ⟨K,hK,nK,a,ha⟩ := finite_ambient_density_domination (FiberBlocks.size f) s hp hps hn ρ - (FiberBlocks.total f) (FiberBlocks.regroup f e) - let := hK - let := nK - refine ⟨K,hK,nK,a,?_⟩ - simpa only [groupedSite,FiberBlocks.label_regroup,fiberProjector] using ha - -end CoordinateSweeps.SignedTensor -end -end -end -end -end -end -end -end -open scoped Matrix.Norms.L2Operator - -end OAI +import Mathlib +import OAI.RepresentationTheory.SignedTensor.Domination + +namespace OAI + +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ComplexConjugate Matrix.Norms.L2Operator +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ComplexOrder MatrixOrder +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ENNReal +open MeasureTheory + +namespace CoordinateSweeps.SignedTensor +variable {B : Type} [Fintype B] [DecidableEq B] + +/- Tensorization of finite density domination, preserving +finite probability normalization and the exact product of local dimensions. -/ +theorem finite_block_density_domination (s p : ℕ) (hp : 0 < p) (hps : p ≤ s) + (l : B → ℕ) (hl : ∀ i, l i ≤ s) (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (l i)))) : + ∃ (K : Type) (_ : Fintype K) (_ : Nonempty K) (r : K → B → EvenDensity p), + (((∏ i, ((ρ i).dimension : ℂ))*((s+1 : ℕ) : ℂ)^(Fintype.card B*(41*p^2))) • + ((Fintype.card K : ℂ)⁻¹ • ∑ x, DependentTensor.tensor (fun i => densityPower (l i) (r x i).val))- + DependentTensor.tensor (fun i => isotypic (p := p) (ρ i))).PosSemidef := by + choose K fK nK r hr using fun i => finite_density_domination s p (l i) hp hps (hl i) (ρ i) + let : ∀ i, Fintype (K i) := fK + let : ∀ i, Nonempty (K i) := nK + refine ⟨(∀ i, K i),inferInstance,inferInstance,fun x i => r i (x i),?_⟩ + have hh := DependentTensor.tensor_mono + (fun i => isotypic (p := p) (ρ i)) + (fun i => (((ρ i).dimension : ℂ)*((s+1 : ℕ) : ℂ)^(41*p^2)) • + ((Fintype.card (K i) : ℂ)⁻¹ • ∑ x, densityPower (l i) (r i x).val)) + (fun i => isotypic_posSemidef (ρ i)) hr + rw [DependentTensor.tensor_smul] at hh + have hm : DependentTensor.tensor (fun i => (Fintype.card (K i) : ℂ)⁻¹ • + ∑ x, densityPower (l i) (r i x).val) = + (Fintype.card (∀ i, K i) : ℂ)⁻¹ • ∑ x : ∀ i, K i, + DependentTensor.tensor (fun i => densityPower (l i) (r i (x i)).val) := by + simp only [Finset.smul_sum] + rw [DependentTensor.tensor_mixture] + rw [Fintype.card_pi,Nat.cast_prod,Finset.prod_inv_distrib] + have hc : (∏ i, ((ρ i).dimension : ℂ)*((s+1 : ℕ) : ℂ)^(41*p^2)) = + (∏ i, ((ρ i).dimension : ℂ))*((s+1 : ℕ) : ℂ)^(Fintype.card B*(41*p^2)) := by + rw [Finset.prod_mul_distrib,Finset.prod_const,Finset.card_univ,← pow_mul,mul_comm (41*p^2)] + rwa [hm,hc] at hh + +end CoordinateSweeps.SignedTensor + +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder + +noncomputable section +open scoped BigOperators +attribute [local instance] Classical.propDecidable +namespace CoordinateSweeps.OrderedBlocks +variable {r : ℕ} (n : Fin r → ℕ) + +def offset (i : Fin r) : ℕ := ∑ j ∈ Finset.Iio i, n j + +lemma offset_next_le (i j : Fin r) (hij : i < j) : offset n i+n i ≤ offset n j := by + have he : Finset.Iic i=insert i (Finset.Iio i) := by ext x; simp [le_iff_lt_or_eq,or_comm] + have hh : ∑ k ∈ Finset.Iic i, n k ≤ ∑ k ∈ Finset.Iio j, n k := + Finset.sum_le_sum_of_subset (fun k hk => Finset.mem_Iio.mpr (lt_of_le_of_lt (Finset.mem_Iic.mp hk) hij)) + rw [he,Finset.sum_insert (by simp)] at hh + simpa only [offset,add_comm] using hh + +lemma offset_next_le_total (i : Fin r) : offset n i+n i ≤ ∑ j, n j := by + have he : Finset.Iic i=insert i (Finset.Iio i) := by ext x; simp [le_iff_lt_or_eq,or_comm] + have hh : ∑ k ∈ Finset.Iic i, n k ≤ ∑ k, n k := Finset.sum_le_sum_of_subset (Finset.subset_univ _) + rw [he,Finset.sum_insert (by simp)] at hh + simpa only [offset,add_comm] using hh + +def encode (x : (i : Fin r) × Fin (n i)) : Fin (∑ i, n i) := + ⟨offset n x.1+x.2,lt_of_lt_of_le (Nat.add_lt_add_left x.2.isLt _) (offset_next_le_total n x.1)⟩ + +lemma encode_lt_of_block {i j : Fin r} (hij : i < j) (a : Fin (n i)) (b : Fin (n j)) : + encode n ⟨i,a⟩ < encode n ⟨j,b⟩ := by + change offset n i+a.val < offset n j+b.val + have hh := offset_next_le n i j hij + have ha := a.isLt + omega + +lemma encode_lt_same {i : Fin r} (a b : Fin (n i)) : + encode n ⟨i,a⟩ < encode n ⟨i,b⟩ ↔ a < b := by + change offset n i+a.val < offset n i+b.val ↔ a.val < b.val + omega + +lemma encode_injective : Function.Injective (encode n) := by + rintro ⟨i,a⟩ ⟨j,b⟩ h + have hi : i=j := by + rcases lt_trichotomy i j with hij | hij | hij + · exact False.elim ((ne_of_lt (encode_lt_of_block n hij a b)) h) + · exact hij + · exact False.elim ((ne_of_lt (encode_lt_of_block n hij b a)) h.symm) + subst j + have hab : a=b := Fin.ext (by have hh := congrArg Fin.val h; dsimp [encode] at hh; omega) + subst b + rfl + +/- Explicit contiguous coordinate chart, including zero-length blocks. -/ +def positions : ((i : Fin r) × Fin (n i)) ≃ Fin (∑ i, n i) := + Equiv.ofBijective (encode n) ((Fintype.bijective_iff_injective_and_card _).mpr + ⟨encode_injective n,by simp [Fintype.card_sigma]⟩) + +lemma positions_apply (x : (i : Fin r) × Fin (n i)) : positions n x=encode n x := rfl + +lemma positions_lt_of_block {i j : Fin r} (hij : i < j) (a : Fin (n i)) (b : Fin (n j)) : + positions n ⟨i,a⟩ < positions n ⟨j,b⟩ := encode_lt_of_block n hij a b + +lemma positions_lt_same {i : Fin r} (a b : Fin (n i)) : + positions n ⟨i,a⟩ < positions n ⟨i,b⟩ ↔ a < b := encode_lt_same n a b + +def perm (σ : ∀ i, Equiv.Perm (Fin (n i))) : Equiv.Perm (Fin (∑ i, n i)) := + (positions n).permCongr (Equiv.sigmaCongrRight σ) + +@[simp] lemma perm_apply (σ : ∀ i, Equiv.Perm (Fin (n i))) (i : Fin r) (j : Fin (n i)) : + perm n σ (positions n ⟨i,j⟩)=positions n ⟨i,σ i j⟩ := by + simp [perm,Equiv.permCongr_apply] + +lemma perm_inv (σ : ∀ i, Equiv.Perm (Fin (n i))) : + (perm n σ)⁻¹=perm n (fun i => (σ i)⁻¹) := by + apply Equiv.ext + intro x + obtain ⟨⟨i,j⟩,rfl⟩ := (positions n).surjective x + apply (perm n σ).injective + simp + +def permHom : (∀ i, Equiv.Perm (Fin (n i))) →* Equiv.Perm (Fin (∑ i, n i)) where + toFun := perm n + map_one' := by + apply Equiv.ext; intro x + obtain ⟨⟨i,j⟩,rfl⟩ := (positions n).surjective x + simp + map_mul' σ τ := by + apply Equiv.ext; intro x + obtain ⟨⟨i,j⟩,rfl⟩ := (positions n).surjective x + simp + +end CoordinateSweeps.OrderedBlocks + +namespace CoordinateSweeps.SignedTensor + +lemma phase_double_prod {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) : + phase σ w=∏ i : Fin l, ∏ j : Fin l, + if j < i ∧ odd (w i) ∧ odd (w j) ∧ σ i < σ j then (-1 : ℂ) else 1 := by + have he : Equiv.Perm.finPairsLT l=(Finset.univ : Finset ((i : Fin l) × Fin l)).filter (fun x => x.2 < x.1) := by + ext x + simp only [Equiv.Perm.mem_finPairsLT,Finset.mem_filter,Finset.mem_univ,true_and] + rw [phase_prod,he,Finset.prod_filter,Fintype.prod_sigma] + apply Finset.prod_congr rfl + intro i hi + apply Finset.prod_congr rfl + intro j hj + split_ifs <;> simp_all + +def blockPerm {m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) : + Equiv.Perm (Fin (m+n)) := finSumFinEquiv.permCongr (Equiv.Perm.sumCongr σ τ) + +@[simp] lemma blockPerm_left {m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) (i : Fin m) : + blockPerm σ τ (Fin.castAdd n i)=Fin.castAdd n (σ i) := by + simp [blockPerm,Equiv.permCongr_apply] + +@[simp] lemma blockPerm_right {m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) (i : Fin n) : + blockPerm σ τ (Fin.natAdd m i)=Fin.natAdd m (τ i) := by + simp [blockPerm,Equiv.permCongr_apply] + +lemma blockPerm_inv {m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) : + (blockPerm σ τ)⁻¹=blockPerm σ⁻¹ τ⁻¹ := by + apply Equiv.ext + intro i + apply (blockPerm σ τ).injective + induction i using Fin.addCases <;> simp + +lemma phase_blockPerm {p m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) + (w : Word p (m+n)) : + phase (blockPerm σ τ) w=phase σ (fun i => w (Fin.castAdd n i))* + phase τ (fun i => w (Fin.natAdd m i)) := by + have hlr (i : Fin m) (j : Fin n) : ¬ Fin.natAdd m j w (Fin.castAdd n i),fun i => w (Fin.natAdd m i)) + invFun w := Fin.addCases w.1 w.2 + left_inv w := by funext i; induction i using Fin.addCases <;> simp + right_inv w := by ext <;> simp + +lemma splitWord_wordPerm {p m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) + (w : Word p (m+n)) : + splitWord p m n (wordPerm (blockPerm σ τ) w)= + (wordPerm σ (splitWord p m n w).1,wordPerm τ (splitWord p m n w).2) := by + ext i <;> simp [splitWord,wordPerm,blockPerm_inv] + +def blockMatrix {p m n : ℕ} (A : Matrix (Word p m) (Word p m) ℂ) + (B : Matrix (Word p n) (Word p n) ℂ) : Matrix (Word p (m+n)) (Word p (m+n)) ℂ := + fun u w => A (splitWord p m n u).1 (splitWord p m n w).1 * + B (splitWord p m n u).2 (splitWord p m n w).2 + +/- Exact block multiplicativity of the signed permutation action. -/ +theorem matrix_blockPerm {p m n : ℕ} (σ : Equiv.Perm (Fin m)) (τ : Equiv.Perm (Fin n)) : + matrix (p := p) (blockPerm σ τ)=blockMatrix (matrix σ) (matrix τ) := by + ext u w + have he : u=wordPerm (blockPerm σ τ) w ↔ + (splitWord p m n u).1=wordPerm σ (splitWord p m n w).1 ∧ + (splitWord p m n u).2=wordPerm τ (splitWord p m n w).2 := by + rw [← (splitWord p m n).injective.eq_iff,splitWord_wordPerm,Prod.mk.injEq] + simp only [matrix,blockMatrix,he,phase_blockPerm] + split_ifs <;> simp_all [splitWord] + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open OrderedBlocks +variable {p r : ℕ} (n : Fin r → ℕ) + +lemma prod_positions (f : Fin (∑ i, n i) → ℂ) : + ∏ x, f x=∏ i, ∏ j : Fin (n i), f (positions n ⟨i,j⟩) := by + rw [← Equiv.prod_comp (positions n) f,Fintype.prod_sigma] + +lemma phase_grouped (σ : ∀ i, Equiv.Perm (Fin (n i))) (w : Word p (∑ i, n i)) : + phase (perm n σ) w=∏ i, phase (σ i) (fun j => w (positions n ⟨i,j⟩)) := by + rw [phase_double_prod,prod_positions n] + apply Finset.prod_congr rfl + intro i hi + rw [phase_double_prod] + apply Finset.prod_congr rfl + intro a ha + rw [prod_positions n,Finset.prod_eq_single i] + · apply Finset.prod_congr rfl + intro b hb + simp only [perm_apply,positions_lt_same] + · intro j hj hji + apply Finset.prod_eq_one + intro b hb + rcases lt_or_gt_of_ne hji with hlt | hgt + · have hn : ¬ positions n ⟨i,σ i a⟩ < positions n ⟨j,σ j b⟩ := + not_lt_of_ge (positions_lt_of_block n hlt _ _).le + simp [hn] + · have hn : ¬ positions n ⟨j,b⟩ < positions n ⟨i,a⟩ := + not_lt_of_ge (positions_lt_of_block n hgt _ _).le + simp [hn] + · simp + +def groupWord (p : ℕ) : Word p (∑ i, n i) ≃ (∀ i, Word p (n i)) where + toFun w i j := w (positions n ⟨i,j⟩) + invFun w x := w ((positions n).symm x).1 ((positions n).symm x).2 + left_inv w := by funext x; simp + right_inv w := by + funext i j + change (fun x : (i : Fin r) × Fin (n i) => w x.1 x.2) ((positions n).symm (positions n ⟨i,j⟩)) = _ + rw [Equiv.symm_apply_apply] + +lemma groupWord_wordPerm (σ : ∀ i, Equiv.Perm (Fin (n i))) (w : Word p (∑ i, n i)) : + groupWord n p (wordPerm (perm n σ) w)=fun i => wordPerm (σ i) (groupWord n p w i) := by + funext i j + simp [groupWord,wordPerm,perm_inv] + +/- Genuine product-subgroup action, with no suppressed Koszul signs. -/ +theorem matrix_grouped (σ : ∀ i, Equiv.Perm (Fin (n i))) : + matrix (p := p) (perm n σ)= + Matrix.reindex (groupWord n p).symm (groupWord n p).symm + (DependentTensor.tensor (fun i => matrix (σ i))) := by + ext u w + have he : u=wordPerm (perm n σ) w ↔ + ∀ i, groupWord n p u i=wordPerm (σ i) (groupWord n p w i) := by + rw [← (groupWord n p).injective.eq_iff,groupWord_wordPerm] + exact funext_iff + change (if u=wordPerm (perm n σ) w then phase (perm n σ) w else 0)= + ∏ i, if groupWord n p u i=wordPerm (σ i) (groupWord n p w i) + then phase (σ i) (groupWord n p w i) else 0 + simp only [he] + by_cases h : ∀ i, groupWord n p u i=wordPerm (σ i) (groupWord n p w i) + · rw [ite_eq_left h,phase_grouped] + simp only [h,ite_true] + rfl + · rw [ite_eq_right h] + obtain ⟨i,hi⟩ := not_forall.mp h + symm + apply Finset.prod_eq_zero (Finset.mem_univ i) + simp [hi] + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open OrderedBlocks UnitaryIrrep +variable {p r : ℕ} (n : Fin r → ℕ) + +/- The subgroup operator is an actual group-algebra average on the full set +of slots, not an operator posited to factor. -/ +def groupedAverage {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] + (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) : + Matrix (Word p (∑ i, n i)) (Word p (∑ i, n i)) ℂ := + averageMatrix (action p (∑ i, n i)) (fun ω : ∀ i, Ω i => ∏ i, w i (ω i)) + (fun ω => perm n (fun i => g i (ω i))) + +lemma groupedAverage_factor {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] + (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) : + groupedAverage (p := p) n w g= + Matrix.reindex (groupWord n p).symm (groupWord n p).symm + (DependentTensor.tensor (fun i => averageMatrix (action p (n i)) (w i) (g i))) := by + ext u v + simp only [groupedAverage,averageMatrix,Matrix.reindex_apply,Matrix.submatrix_apply, + Equiv.symm_symm,DependentTensor.tensor,Matrix.sum_apply,Matrix.smul_apply,smul_eq_mul] + change (∑ ω : ∀ i, Ω i, (∏ i, w i (ω i))* + matrix (perm n (fun i => g i (ω i))) u v)= + ∏ i, ∑ ω : Ω i, w i ω*matrix (g i ω) (groupWord n p u i) (groupWord n p v i) + have he (σ : ∀ i, Equiv.Perm (Fin (n i))) : + matrix (perm n σ) u v=∏ i, matrix (σ i) (groupWord n p u i) (groupWord n p v i) := by + have hh := congrArg (fun A : Matrix (Word p (∑ i, n i)) (Word p (∑ i, n i)) ℂ => A u v) + (matrix_grouped (p := p) n σ) + exact hh + simp only [he] + rw [Fintype.prod_sum] + apply Finset.sum_congr rfl + intro ω hω + exact (Finset.prod_mul_distrib : + (∏ i, w i (ω i)*matrix (g i (ω i)) (groupWord n p u i) (groupWord n p v i))=_).symm + +def groupedProjector (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : + Matrix (Word p (∑ i, n i)) (Word p (∑ i, n i)) ℂ := + groupedAverage n (fun i => (ρ i).coefficient) (fun _ => id) + +lemma groupedProjector_factor (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : + groupedProjector (p := p) n ρ= + Matrix.reindex (groupWord n p).symm (groupWord n p).symm + (DependentTensor.tensor (fun i => (ρ i).projector (action p (n i)))) := by + exact groupedAverage_factor n _ _ + +lemma matrix_trace_reindex {X Y : Type*} [Fintype X] [Fintype Y] (e : X ≃ Y) + (A : Matrix X X ℂ) : Matrix.trace (Matrix.reindex e e A)=Matrix.trace A := by + exact Equiv.sum_comp e.symm (fun i => A i i) + +lemma reindex_moment {X Y : Type*} [Fintype X] [Fintype Y] [DecidableEq X] [DecidableEq Y] + (e : X ≃ Y) (A : Matrix X X ℂ) (q : ℕ) : + Matrix.trace ((((Matrix.reindexAlgEquiv ℂ ℂ e A).conjTranspose)*(Matrix.reindexAlgEquiv ℂ ℂ e A))^q)= + Matrix.trace ((A.conjTranspose*A)^q) := by + have hs : (Matrix.reindexAlgEquiv ℂ ℂ e A).conjTranspose= + Matrix.reindexAlgEquiv ℂ ℂ e A.conjTranspose := by ext i j; rfl + rw [hs,← map_mul,← map_pow] + exact matrix_trace_reindex e _ + +/- Exact isotypic child moment factorization, including the true Hom +multiplicities and all zero-length blocks. -/ +theorem grouped_projected_moment {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) + (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) + {q : ℕ} (hq : q ≠ 0) : + Matrix.trace (((groupedProjector (p := p) n ρ*groupedAverage n w g).conjTranspose* + (groupedProjector n ρ*groupedAverage n w g))^q)= + ∏ i, (Module.finrank ℂ ((ρ i).asRepresentation.IntertwiningMap + (matrixRepresentation (action p (n i)))) : ℂ)* + Matrix.trace (((averageMatrix (ρ i).matrix (w i) (g i)).conjTranspose* + averageMatrix (ρ i).matrix (w i) (g i))^q) := by + rw [groupedProjector_factor,groupedAverage_factor] + let e := (groupWord n p).symm + change Matrix.trace (((Matrix.reindexAlgEquiv ℂ ℂ e _*Matrix.reindexAlgEquiv ℂ ℂ e _).conjTranspose* + (Matrix.reindexAlgEquiv ℂ ℂ e _*Matrix.reindexAlgEquiv ℂ ℂ e _))^q)=_ + rw [← map_mul,reindex_moment,← DependentTensor.tensor_mul,DependentTensor.tensor_moment] + apply Finset.prod_congr rfl + intro i hi + exact (ρ i).projected_operator_moment _ (fun σ => (matrix_inv σ).symm) (w i) (g i) hq + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +variable {p : ℕ} + +def IsEven (A : Matrix (Letter p) (Letter p) ℂ) : Prop := + ∀ i j, (odd i ↔ ¬ odd j) → A i j=0 + +def grading (p : ℕ) : Matrix (Letter p) (Letter p) ℂ := + Matrix.diagonal (fun i => if odd i then 1 else 0) + +lemma isEven_iff_commute (A : Matrix (Letter p) (Letter p) ℂ) : + IsEven A ↔ Commute A (grading p) := by + constructor + · intro h + show A*grading p=grading p*A + ext i j + simp only [grading,Matrix.mul_diagonal,Matrix.diagonal_mul] + by_cases hi : odd i + · by_cases hj : odd j + · simp [hi,hj] + · simp [hi,hj,h i j (by tauto)] + · by_cases hj : odd j + · simp [hi,hj,h i j (by tauto)] + · simp [hi,hj] + · intro h i j hij + have hh := congrArg (fun M : Matrix (Letter p) (Letter p) ℂ => M i j) h.eq + simp only [grading,Matrix.mul_diagonal,Matrix.diagonal_mul] at hh + by_cases hi : odd i + · have hj : ¬ odd j := hij.mp hi + simpa [hi,hj] using hh.symm + · have hj : odd j := by tauto + simpa [hi,hj] using hh + +lemma isEven_add {A B : Matrix (Letter p) (Letter p) ℂ} (hA : IsEven A) (hB : IsEven B) : + IsEven (A+B) := by intro i j hij; simp only [Matrix.add_apply,hA i j hij,hB i j hij,add_zero] + +lemma isEven_smul (c : ℂ) {A : Matrix (Letter p) (Letter p) ℂ} (hA : IsEven A) : + IsEven (c • A) := by intro i j hij; simp only [Matrix.smul_apply,smul_eq_mul,hA i j hij,mul_zero] + +lemma isEven_sum {I : Type*} [Fintype I] (A : I → Matrix (Letter p) (Letter p) ℂ) + (hA : ∀ i, IsEven (A i)) : IsEven (∑ i, A i) := by + intro i j hij + simp only [Matrix.sum_apply] + exact Finset.sum_eq_zero (fun a _ => hA a i j hij) + +lemma isEven_one : IsEven (1 : Matrix (Letter p) (Letter p) ℂ) := by + intro i j hij + apply Matrix.one_apply_ne + intro he + subst j + tauto + +lemma densityPower_commute_of_even {l : ℕ} (r : Matrix (Letter p) (Letter p) ℂ) + (hr : IsEven r) (σ : Equiv.Perm (Fin l)) : + matrix σ*densityPower l r=densityPower l r*matrix σ := by + have hpar {u w : Word p l} (h : densityPower l r u w ≠ 0) : + ∀ i, odd (u i) ↔ odd (w i) := by + intro i + have he : r (u i) (w i) ≠ 0 := (Finset.prod_ne_zero_iff.mp h) i (Finset.mem_univ _) + by_contra hn + exact he (hr _ _ (by tauto)) + ext u w + simp only [Matrix.mul_apply,matrix] + rw [Finset.sum_eq_single ((wordPerm σ).symm u),Finset.sum_eq_single (wordPerm σ w)] + · simp only [(wordPerm σ).apply_symm_apply,ite_true] + have hd : densityPower l r u (wordPerm σ w)=densityPower l r ((wordPerm σ).symm u) w := by + simpa using densityPower_permute σ r ((wordPerm σ).symm u) w + rw [hd] + by_cases hn : densityPower l r ((wordPerm σ).symm u) w=0 + · simp [hn] + · rw [phase_eq_of_parity σ _ _ (hpar hn),mul_comm] + · intro v hv hne; simp [hne] + · simp + · intro v hv hne + have hh : u ≠ wordPerm σ v := by + intro he + exact hne ((Equiv.eq_symm_apply _).mpr he.symm) + simp [hh] + · simp + +lemma densityPower_commute_lift {l : ℕ} (r : Matrix (Letter p) (Letter p) ℂ) + (hr : IsEven r) (x : MonoidAlgebra ℂ (Equiv.Perm (Fin l))) : + (MonoidAlgebra.lift ℂ _ _ (action p l) x)*densityPower l r = + densityPower l r*(MonoidAlgebra.lift ℂ _ _ (action p l) x) := by + induction x using MonoidAlgebra.induction_on with + | of g => simpa [action] using densityPower_commute_of_even r hr g + | add x y hx hy => simp only [map_add,add_mul,mul_add,hx,hy] + | smul c x hx => simp only [map_smul,smul_mul_assoc,mul_smul_comm,hx] + +/- Constructed even whitening of the regularized empirical row density. -/ +theorem exists_even_whitening {R : Type*} [Fintype R] [Nonempty R] + (r : R → EvenDensity p) {ε : ℝ} (hε : 0 < ε) : + let B := (Fintype.card R : ℂ)⁻¹ • ∑ i, (r i).val + (ε : ℂ) • (1 : Matrix (Letter p) (Letter p) ℂ) + ∃ A : Matrix (Letter p) (Letter p) ℂ, A.PosSemidef ∧ IsEven A ∧ A*B*A=1 ∧ + ((Fintype.card R : ℂ) • (1 : Matrix (Letter p) (Letter p) ℂ)- + ∑ i, A*(r i).val*A).PosSemidef := by + dsimp only + let B := (Fintype.card R : ℂ)⁻¹ • ∑ i, (r i).val + (ε : ℂ) • (1 : Matrix (Letter p) (Letter p) ℂ) + have hBp : B.PosDef := TensorBoard.average_regularization_posDef (fun i => (r i).val) + (fun i => (r i).property.1) hε + have hBe : IsEven B := isEven_add (isEven_smul _ (isEven_sum _ (fun i => (r i).property.2.2))) + (isEven_smul _ isEven_one) + obtain ⟨A,hA,hABA,hcomm⟩ := TensorBoard.exists_whitening B hBp + refine ⟨A,hA,(isEven_iff_commute A).mpr (hcomm _ ((isEven_iff_commute B).mp hBe)),hABA,?_⟩ + apply TensorBoard.whitening_sum_bound _ B A hA.isHermitian hABA + dsimp [B] + convert (Matrix.PosSemidef.one (n := Letter p) (R := ℂ)).smul hε.le using 1 + module + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +variable {p l : ℕ} + +/- Even inhomogeneous site tensors transform by the *signed* permutation +matrix with no residual phase. This is what permits regrouping deleted rows +and columns without identifying the two Koszul charts by an unsigned map. -/ +lemma tensor_covariance (A : Fin l → Matrix (Letter p) (Letter p) ℂ) + (hA : ∀ i, IsEven (A i)) (σ : Equiv.Perm (Fin l)) : + matrix σ*TensorBoard.tensor A= + TensorBoard.tensor (fun i => A (σ⁻¹ i))*matrix σ := by + have hpar {u w : Word p l} (h : TensorBoard.tensor A u w ≠ 0) : + ∀ i, odd (u i) ↔ odd (w i) := by + intro i + have he : A i (u i) (w i) ≠ 0 := (Finset.prod_ne_zero_iff.mp h) i (Finset.mem_univ _) + by_contra hn + exact he (hA i _ _ (by tauto)) + ext u w + simp only [Matrix.mul_apply,matrix] + rw [Finset.sum_eq_single ((wordPerm σ).symm u),Finset.sum_eq_single (wordPerm σ w)] + · simp only [(wordPerm σ).apply_symm_apply,ite_true] + have hd : TensorBoard.tensor (fun i => A (σ⁻¹ i)) u (wordPerm σ w)= + TensorBoard.tensor A ((wordPerm σ).symm u) w := by + change (∏ i, A (σ⁻¹ i) (u i) (w (σ⁻¹ i)))=∏ i, A i (u (σ i)) (w i) + simpa using (Equiv.prod_comp σ (fun i => A (σ⁻¹ i) (u i) (w (σ⁻¹ i)))).symm + rw [hd] + by_cases hn : TensorBoard.tensor A ((wordPerm σ).symm u) w=0 + · simp [hn] + · rw [phase_eq_of_parity σ _ _ (hpar hn),mul_comm] + · intro v hv hne; simp [hne] + · simp + · intro v hv hne + have hh : u ≠ wordPerm σ v := by + intro he + exact hne ((Equiv.eq_symm_apply _).mpr he.symm) + simp [hh] + · simp + +lemma tensor_signed_conjugate (A : Fin l → Matrix (Letter p) (Letter p) ℂ) + (hA : ∀ i, IsEven (A i)) (σ : Equiv.Perm (Fin l)) : + matrix σ*TensorBoard.tensor A*(matrix σ).conjTranspose= + TensorBoard.tensor (fun i => A (σ⁻¹ i)) := by + rw [tensor_covariance A hA σ,mul_assoc,← matrix_inv,← matrix_mul,mul_inv_cancel,matrix_one,mul_one] + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open OrderedBlocks +variable {p r : ℕ} (n : Fin r → ℕ) + +def groupedSite (a : Fin r → EvenDensity p) (k : Fin (∑ i, n i)) : EvenDensity p := + a ((positions n).symm k).1 + +lemma grouped_densityPower (a : Fin r → EvenDensity p) : + (DependentTensor.tensor (fun i => densityPower (n i) (a i).val)).submatrix + (groupWord n p) (groupWord n p)=TensorBoard.tensor (fun k => (groupedSite n a k).val) := by + ext u v + change (∏ i, ∏ j : Fin (n i), (a i).val (u (positions n ⟨i,j⟩)) (v (positions n ⟨i,j⟩)))= + ∏ k, (a ((positions n).symm k).1).val (u k) (v k) + rw [prod_positions] + apply Finset.prod_congr rfl + intro i _ + apply Finset.prod_congr rfl + intro j _ + rw [Equiv.symm_apply_apply] + +/- Literal contiguous-block projectors are dominated by independent finite +mixtures of even site densities, with all local dimension factors. -/ +theorem finite_grouped_density_domination (s : ℕ) (hp : 0 < p) (hps : p ≤ s) + (hn : ∀ i, n i ≤ s) (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : + ∃ (K : Type) (_ : Fintype K) (_ : Nonempty K) (a : K → Fin r → EvenDensity p), + (((∏ i, ((ρ i).dimension : ℂ))*((s+1 : ℕ) : ℂ)^(r*(41*p^2))) • + ((Fintype.card K : ℂ)⁻¹ • ∑ x, + TensorBoard.tensor (fun k => (groupedSite n (a x) k).val))- + groupedProjector (p := p) n ρ).PosSemidef := by + obtain ⟨K,hK,nK,a,ha⟩ := finite_block_density_domination s p hp hps n hn ρ + let := hK + let := nK + refine ⟨K,hK,nK,a,?_⟩ + have hh := ha.submatrix (groupWord n p) + have hm : (∑ x, DependentTensor.tensor (fun i => densityPower (n i) (a x i).val)).submatrix + (groupWord n p) (groupWord n p)=∑ x, TensorBoard.tensor (fun k => (groupedSite n (a x) k).val) := by + ext u v + simp only [Matrix.submatrix_apply,Matrix.sum_apply] + apply Finset.sum_congr rfl + intro x _ + exact congrArg (fun M => M u v) (grouped_densityPower n (a x)) + simp only [Fintype.card_fin,Matrix.submatrix_sub,Matrix.submatrix_smul, + Pi.sub_apply,Pi.smul_apply,hm] at hh + have he : (DependentTensor.tensor (fun i => isotypic (p := p) (ρ i))).submatrix + (groupWord n p) (groupWord n p)=groupedProjector (p := p) n ρ := by + simp only [groupedProjector_factor,isotypic_eq_projector] + rfl + rwa [he] at hh + +/- The same domination after an arbitrary *signed* change of slot chart. -/ +theorem finite_regrouped_density_domination (s : ℕ) (hp : 0 < p) (hps : p ≤ s) + (hn : ∀ i, n i ≤ s) (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) + (σ : Equiv.Perm (Fin (∑ i, n i))) : + ∃ (K : Type) (_ : Fintype K) (_ : Nonempty K) (a : K → Fin r → EvenDensity p), + (((∏ i, ((ρ i).dimension : ℂ))*((s+1 : ℕ) : ℂ)^(r*(41*p^2))) • + ((Fintype.card K : ℂ)⁻¹ • ∑ x, + TensorBoard.tensor (fun k => (groupedSite n (a x) (σ⁻¹ k)).val))- + matrix σ*groupedProjector (p := p) n ρ*(matrix σ).conjTranspose).PosSemidef := by + obtain ⟨K,hK,nK,a,ha⟩ := finite_grouped_density_domination n s hp hps hn ρ + let := hK + let := nK + refine ⟨K,hK,nK,a,?_⟩ + have hh := ha.mul_mul_conjTranspose_same (matrix σ) + simp only [mul_sub,sub_mul,Matrix.mul_smul,Matrix.smul_mul,Matrix.mul_sum,Matrix.sum_mul] at hh + have ht (x : K) : matrix σ*TensorBoard.tensor (fun k => (groupedSite n (a x) k).val)*(matrix σ).conjTranspose= + TensorBoard.tensor (fun k => (groupedSite n (a x) (σ⁻¹ k)).val) := + tensor_signed_conjugate _ (fun k => (groupedSite n (a x) k).property.2.2) σ + simpa only [ht] using hh + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +variable {p r : ℕ} (n : Fin r → ℕ) + +lemma groupedProjector_posSemidef (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : + (groupedProjector (p := p) n ρ).PosSemidef := by + rw [groupedProjector_factor] + exact (DependentTensor.tensor_posSemidef _ (fun i => (ρ i).projector_posSemidef _ + (fun σ => (matrix_inv σ).symm))).submatrix _ + +lemma groupedProjector_idempotent (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : + groupedProjector (p := p) n ρ*groupedProjector n ρ=groupedProjector n ρ := by + rw [groupedProjector_factor] + change Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _* + Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _=Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _ + rw [← map_mul,← DependentTensor.tensor_mul] + simp only [UnitaryIrrep.projector_idempotent] + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open OrderedBlocks UnitaryIrrep +variable {p r l : ℕ} (n : Fin r → ℕ) + +def lengthMatrix {a b : ℕ} (h : a=b) (M : Matrix (Word p a) (Word p a) ℂ) : + Matrix (Word p b) (Word p b) ℂ := h ▸ M + +def ambientProjector (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : Matrix (Word p l) (Word p l) ℂ := + matrix σ*lengthMatrix h (groupedProjector n ρ)*(matrix σ).conjTranspose + +def ambientProjectorAlgebra (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : MonoidAlgebra ℂ (Equiv.Perm (Fin l)) := + averageAlgebra (fun ω : ∀ i, Equiv.Perm (Fin (n i)) => ∏ i, (ρ i).coefficient (ω i)) + (fun ω => σ*(Equiv.permCongr (finCongr h) (perm n ω))*σ⁻¹) + +lemma ambientProjectorAlgebra_lift (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : + MonoidAlgebra.lift ℂ _ _ (action p l) (ambientProjectorAlgebra n h σ ρ)= + ambientProjector (p := p) n h σ ρ := by + subst l + simp only [ambientProjectorAlgebra,lift_averageAlgebra,averageMatrix,ambientProjector, + lengthMatrix,groupedProjector,groupedAverage,Matrix.mul_sum,Matrix.sum_mul,Matrix.mul_smul,Matrix.smul_mul] + apply Finset.sum_congr rfl + intro ω _ + congr 1 + change matrix (σ*(Equiv.permCongr (finCongr rfl) (perm n ω))*σ⁻¹)=_ + simp only [finCongr_refl,matrix_mul,matrix_inv] + rfl + +lemma ambientProjector_posSemidef (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : + (ambientProjector (p := p) n h σ ρ).PosSemidef := by + subst l + exact (groupedProjector_posSemidef n ρ).mul_mul_conjTranspose_same (matrix σ) + +lemma ambientProjector_idempotent (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) : + ambientProjector (p := p) n h σ ρ*ambientProjector n h σ ρ=ambientProjector n h σ ρ := by + subst l + unfold ambientProjector lengthMatrix + calc + _ = matrix σ*(groupedProjector n ρ*((matrix σ).conjTranspose*matrix σ)*groupedProjector n ρ)* + (matrix (p := p) σ).conjTranspose := by noncomm_ring + _ = _ := by rw [matrix_unitary,mul_one,groupedProjector_idempotent] + +/- Actual ambient projectors, not hypothesized density mixtures. -/ +theorem finite_ambient_density_domination (s : ℕ) (hp : 0 < p) (hps : p ≤ s) + (hn : ∀ i, n i ≤ s) (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) + (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) : + ∃ (K : Type) (_ : Fintype K) (_ : Nonempty K) (a : K → Fin r → EvenDensity p), + (((∏ i, ((ρ i).dimension : ℂ))*((s+1 : ℕ) : ℂ)^(r*(41*p^2))) • + ((Fintype.card K : ℂ)⁻¹ • ∑ x, + TensorBoard.tensor (fun k => (groupedSite n (a x) ((finCongr h).symm (σ⁻¹ k))).val))- + ambientProjector (p := p) n h σ ρ).PosSemidef := by + subst l + simpa [ambientProjector,lengthMatrix] using + finite_regrouped_density_domination n s hp hps hn ρ σ + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open OrderedBlocks UnitaryIrrep +variable {p r l : ℕ} (n : Fin r → ℕ) + +def ambientAverage (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) + {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] + (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) : + Matrix (Word p l) (Word p l) ℂ := + averageMatrix (action p l) (fun ω : ∀ i, Ω i => ∏ i, w i (ω i)) + (fun ω => σ*Equiv.permCongr (finCongr h) (perm n (fun i => g i (ω i)))*σ⁻¹) + +lemma ambientAverage_factor (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) + {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] + (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) : + ambientAverage (p := p) n h σ w g= + matrix σ*lengthMatrix h (groupedAverage n w g)*(matrix σ).conjTranspose := by + subst l + simp only [ambientAverage,averageMatrix,groupedAverage,lengthMatrix, + Matrix.mul_sum,Matrix.sum_mul,Matrix.mul_smul,Matrix.smul_mul] + apply Finset.sum_congr rfl + intro ω _ + congr 1 + change matrix (σ*Equiv.permCongr (finCongr rfl) (perm n (fun i => g i (ω i)))*σ⁻¹)=_ + simp only [finCongr_refl,matrix_mul,matrix_inv] + rfl + +lemma matrix_unitary_reverse (σ : Equiv.Perm (Fin l)) : + matrix (p := p) σ*(matrix σ).conjTranspose=1 := by + rw [← matrix_inv,← matrix_mul,mul_inv_cancel,matrix_one] + +lemma conjugate_mul {X : Type*} [Fintype X] [DecidableEq X] + (U A B : Matrix X X ℂ) (hU : U.conjTranspose*U=1) : + (U*A*U.conjTranspose)*(U*B*U.conjTranspose)=U*(A*B)*U.conjTranspose := by + calc + _ = U*A*(U.conjTranspose*U)*B*U.conjTranspose := by noncomm_ring + _ = _ := by rw [hU,mul_one]; noncomm_ring + +lemma conjugate_pow {X : Type*} [Fintype X] [DecidableEq X] + (U A : Matrix X X ℂ) (hU : U.conjTranspose*U=1) (hU' : U*U.conjTranspose=1) (q : ℕ) : + (U*A*U.conjTranspose)^q=U*A^q*U.conjTranspose := by + induction q with + | zero => simpa using hU'.symm + | succ q ih => rw [pow_succ,ih,conjugate_mul U _ _ hU,pow_succ] + +lemma conjugate_moment {X : Type*} [Fintype X] [DecidableEq X] + (U A : Matrix X X ℂ) (hU : U.conjTranspose*U=1) (hU' : U*U.conjTranspose=1) (q : ℕ) : + Matrix.trace (((U*A*U.conjTranspose).conjTranspose*(U*A*U.conjTranspose))^q)= + Matrix.trace ((A.conjTranspose*A)^q) := by + have hs : (U*A*U.conjTranspose).conjTranspose=U*A.conjTranspose*U.conjTranspose := by + simp only [Matrix.conjTranspose_mul,Matrix.conjTranspose_conjTranspose] + noncomm_ring + rw [hs,conjugate_mul U _ _ hU,conjugate_pow U _ hU hU'] + rw [Matrix.trace_mul_cycle,hU,one_mul] + +/- The child moment formula survives the literal slot chart, with actual Hom multiplicities. -/ +theorem ambient_projected_moment (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) + {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) + (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) + {q : ℕ} (hq : q ≠ 0) : + Matrix.trace (((ambientProjector (p := p) n h σ ρ*ambientAverage n h σ w g).conjTranspose* + (ambientProjector n h σ ρ*ambientAverage n h σ w g))^q)= + ∏ i, (Module.finrank ℂ ((ρ i).asRepresentation.IntertwiningMap + (matrixRepresentation (action p (n i)))) : ℂ)* + Matrix.trace (((averageMatrix (ρ i).matrix (w i) (g i)).conjTranspose* + averageMatrix (ρ i).matrix (w i) (g i))^q) := by + subst l + rw [ambientAverage_factor] + unfold ambientProjector lengthMatrix + rw [conjugate_mul _ _ _ (matrix_unitary σ),conjugate_moment _ _ + (matrix_unitary σ) (matrix_unitary_reverse σ)] + exact grouped_projected_moment n ρ w g hq + +end CoordinateSweeps.SignedTensor + +/-! +All definitions are finite and use ordinary probability and trace normalizations. +-/ + +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable + +noncomputable section +attribute [local instance] Classical.propDecidable +namespace CoordinateSweeps.FiberBlocks +open OrderedBlocks +variable {L : Type*} [Fintype L] {r : ℕ} (f : L → Fin r) + +def size (i : Fin r) : ℕ := Fintype.card {x : L // f x=i} +def cards (i : Fin r) : Fin (size f i) ≃ {x : L // f x=i} := (Fintype.equivFin _).symm + +/- Contiguous finite label fibers give a genuine ordered slot chart. -/ +def slots : Fin (∑ i, size f i) ≃ L := + (positions (size f)).symm.trans + ((Equiv.sigmaCongrRight (cards f)).trans (Equiv.sigmaFiberEquiv f)) + +lemma total : ∑ i, size f i=Fintype.card L := by + simpa only [Fintype.card_fin] using Fintype.card_congr (slots f) + +lemma label_slots (k : Fin (∑ i, size f i)) : + f (slots f k)=((positions (size f)).symm k).1 := by + exact (cards f ((positions (size f)).symm k).1 ((positions (size f)).symm k).2).property + +/- The same chart with the literal cardinal as ambient length. -/ +def chart : Fin (Fintype.card L) ≃ L := + (finCongr (total f).symm).trans (slots f) + +/- Permutation changing the contiguous fiber chart to any given ambient chart. -/ +def regroup (e : Fin (Fintype.card L) ≃ L) : Equiv.Perm (Fin (Fintype.card L)) := + (chart f).trans e.symm + +lemma label_regroup (e : Fin (Fintype.card L) ≃ L) (k : Fin (Fintype.card L)) : + ((positions (size f)).symm ((finCongr (total f)).symm ((regroup f e)⁻¹ k))).1=f (e k) := by + have he : slots f ((finCongr (total f)).symm ((regroup f e)⁻¹ k))=e k := by + change chart f ((regroup f e).symm k)=e k + simp [regroup] + rw [← label_slots f,he] + +end CoordinateSweeps.FiberBlocks + +namespace CoordinateSweeps.FiberBlocks +open OrderedBlocks +variable {L : Type*} [Fintype L] {r : ℕ} (f : L → Fin r) + +lemma slots_positions (i : Fin r) (j : Fin (size f i)) : + slots f (positions (size f) ⟨i,j⟩)=(cards f i j).val := by + simp [slots] + +/- Independent permutations of the actual fibers, on the literal ambient set. -/ +def action : (∀ i, Equiv.Perm (Fin (size f i))) →* Equiv.Perm L := + (slots f).permCongrHom.toMonoidHom.comp (permHom (size f)) + +lemma action_apply (σ : ∀ i, Equiv.Perm (Fin (size f i))) (i : Fin r) (j : Fin (size f i)) : + action f σ (cards f i j).val=(cards f i (σ i j)).val := by + rw [← slots_positions f i j,← slots_positions f i (σ i j)] + change slots f (perm (size f) σ ((slots f).symm (slots f (positions (size f) ⟨i,j⟩))))=_ + rw [Equiv.symm_apply_apply,perm_apply] + +lemma ambient_action (e : Fin (Fintype.card L) ≃ L) + (σ : ∀ i, Equiv.Perm (Fin (size f i))) : + Equiv.permCongr e.symm (action f σ)= + regroup f e*Equiv.permCongr (finCongr (total f)) (perm (size f) σ)*(regroup f e)⁻¹ := by + apply Equiv.ext + intro x + change e.symm (slots f (perm (size f) σ ((slots f).symm (e x))))=_ + simp only [Equiv.Perm.mul_apply,Equiv.permCongr_apply,regroup,chart, + Equiv.trans_apply,Equiv.symm_trans_apply,Equiv.Perm.coe_inv] + simp + +/- A label-preserving permutation has genuine induced local permutations. -/ +def restrict (σ : Equiv.Perm L) (hσ : ∀ x, f (σ x)=f x) (i : Fin r) : Equiv.Perm (Fin (size f i)) := + Equiv.permCongr (cards f i).symm (Equiv.subtypeEquiv σ (by + intro x + change f x=i ↔ f (σ x)=i + rw [hσ x])) + +lemma restrict_apply (σ : Equiv.Perm L) (hσ : ∀ x, f (σ x)=f x) + (i : Fin r) (j : Fin (size f i)) : + (cards f i (restrict f σ hσ i j)).val=σ (cards f i j).val := by + simp [restrict,Equiv.permCongr_apply] + +lemma action_restrict (σ : Equiv.Perm L) (hσ : ∀ x, f (σ x)=f x) : + action f (restrict f σ hσ)=σ := by + apply Equiv.ext + intro x + let i := f x + let j := (cards f i).symm ⟨x,rfl⟩ + have hx : (cards f i j).val=x := congrArg Subtype.val ((cards f i).apply_symm_apply ⟨x,rfl⟩) + rw [← hx,action_apply,restrict_apply] + +end CoordinateSweeps.FiberBlocks +namespace CoordinateSweeps.SignedTensor +open UnitaryIrrep +variable {p r l : ℕ} (n : Fin r → ℕ) +lemma groupedProjector_commute_average {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) + (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) : + groupedProjector (p := p) n ρ*groupedAverage n w g=groupedAverage n w g*groupedProjector n ρ := by + rw [groupedProjector_factor,groupedAverage_factor] + change Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _* + Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _= + Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _* + Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm _ + rw [← map_mul,← map_mul,← DependentTensor.tensor_mul,← DependentTensor.tensor_mul] + congr 1 + apply congrArg DependentTensor.tensor + funext i + simp only [averageMatrix,Matrix.mul_sum,Matrix.sum_mul,Matrix.mul_smul,Matrix.smul_mul] + apply Finset.sum_congr rfl + intro ω _ + exact congrArg (fun A => w i ω • A) ((ρ i).projector_commute (action p (n i)) (g i ω)).symm + +lemma ambientProjector_commute_average (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) + {Ω : Fin r → Type*} [∀ i, Fintype (Ω i)] + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) + (w : ∀ i, Ω i → ℂ) (g : ∀ i, Ω i → Equiv.Perm (Fin (n i))) : + ambientProjector (p := p) n h σ ρ*ambientAverage n h σ w g= + ambientAverage n h σ w g*ambientProjector n h σ ρ := by + subst l + rw [ambientAverage_factor] + unfold ambientProjector lengthMatrix + rw [conjugate_mul _ _ _ (matrix_unitary σ),conjugate_mul _ _ _ (matrix_unitary σ)] + rw [groupedProjector_commute_average] +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open UnitaryIrrep +variable {p r : ℕ} (n : Fin r → ℕ) +lemma child_product_bound (s : ℕ) (hn : ∀ i, n i ≤ s) + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (n i)))) (T E : Fin r → ℝ) + (hT : ∀ i, 0 ≤ T i) (hE : ∀ i, T i ≤ Real.exp (E i)) : + (∏ i, (Module.finrank ℂ ((ρ i).asRepresentation.IntertwiningMap + (matrixRepresentation (action p (n i)))) : ℝ)*T i) ≤ + ((s+1 : ℕ) : ℝ)^(r*((2*p)*(2*p)))*Real.exp (∑ i, E i) := by + rw [Finset.prod_mul_distrib] + have hm : (∏ i, (Module.finrank ℂ ((ρ i).asRepresentation.IntertwiningMap + (matrixRepresentation (action p (n i)))) : ℝ)) ≤ ((s+1 : ℕ) : ℝ)^(r*((2*p)*(2*p))) := by + calc + _ ≤ ∏ _ : Fin r, ((s+1 : ℕ) : ℝ)^((2*p)*(2*p)) := Finset.prod_le_prod₀ + (fun _ _ => Nat.cast_nonneg _) (fun i _ => by + exact_mod_cast (multiplicity_le p (n i) (ρ i)).trans + (Nat.pow_le_pow_left (Nat.add_le_add_right (hn i) 1) _)) + _ = _ := by rw [Finset.prod_const,Finset.card_univ,Fintype.card_fin,← pow_mul,Nat.mul_comm] + have ht : (∏ i, T i) ≤ Real.exp (∑ i, E i) := by + rw [Real.exp_sum] + exact Finset.prod_le_prod₀ (fun i _ => hT i) (fun i _ => hE i) + exact mul_le_mul hm ht (Finset.prod_nonneg (fun i _ => hT i)) (by positivity) +end CoordinateSweeps.SignedTensor +namespace CoordinateSweeps.SignedTensor +variable {p r : ℕ} {L : Type*} [Fintype L] (f : L → Fin r) + +def fiberProjector (e : Fin (Fintype.card L) ≃ L) + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) := + ambientProjector (p := p) (FiberBlocks.size f) (FiberBlocks.total f) (FiberBlocks.regroup f e) ρ + +def fiberProjectorAlgebra (e : Fin (Fintype.card L) ≃ L) + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) := + ambientProjectorAlgebra (FiberBlocks.size f) (FiberBlocks.total f) (FiberBlocks.regroup f e) ρ + +lemma fiberProjectorAlgebra_lift (e : Fin (Fintype.card L) ≃ L) + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) : + MonoidAlgebra.lift ℂ _ _ (action p (Fintype.card L)) (fiberProjectorAlgebra f e ρ)= + fiberProjector (p := p) f e ρ := ambientProjectorAlgebra_lift _ _ _ _ + +lemma fiberProjector_posSemidef (e : Fin (Fintype.card L) ≃ L) + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) : + (fiberProjector (p := p) f e ρ).PosSemidef := ambientProjector_posSemidef _ _ _ _ + +lemma fiberProjector_idempotent (e : Fin (Fintype.card L) ≃ L) + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) : + fiberProjector (p := p) f e ρ*fiberProjector f e ρ=fiberProjector f e ρ := + ambientProjector_idempotent _ _ _ _ + +/- Exact regrouping connects local isotypic products to the literal site labels. -/ +theorem finite_fiber_density_domination (e : Fin (Fintype.card L) ≃ L) + (s : ℕ) (hp : 0 < p) (hps : p ≤ s) (hn : ∀ i, FiberBlocks.size f i ≤ s) + (ρ : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) : + ∃ (K : Type) (_ : Fintype K) (_ : Nonempty K) (a : K → Fin r → EvenDensity p), + (((∏ i, ((ρ i).dimension : ℂ))*((s+1 : ℕ) : ℂ)^(r*(41*p^2))) • + ((Fintype.card K : ℂ)⁻¹ • ∑ x, + TensorBoard.tensor (fun k => (a x (f (e k))).val))-fiberProjector (p := p) f e ρ).PosSemidef := by + obtain ⟨K,hK,nK,a,ha⟩ := finite_ambient_density_domination (FiberBlocks.size f) s hp hps hn ρ + (FiberBlocks.total f) (FiberBlocks.regroup f e) + let := hK + let := nK + refine ⟨K,hK,nK,a,?_⟩ + simpa only [groupedSite,FiberBlocks.label_regroup,fiberProjector] using ha + +end CoordinateSweeps.SignedTensor +end +end +end +end +end +end +end +end +open scoped Matrix.Norms.L2Operator + +end OAI diff --git a/lean/OAI/RepresentationTheory/SignedTensor/Domination.lean b/lean/OAI/RepresentationTheory/SignedTensor/Domination.lean index c2c6578238496aef7419f712eadaa049fa3fce3e..4fd0e04767eab32b7021cb48eab6ae3e9689ee3b 100644 --- a/lean/OAI/RepresentationTheory/SignedTensor/Domination.lean +++ b/lean/OAI/RepresentationTheory/SignedTensor/Domination.lean @@ -1,1195 +1,1195 @@ -import Mathlib -import OAI.RepresentationTheory.SignedTensor.Basic -import OAI.RepresentationTheory.Tensor.Postselection -import OAI.Analysis.Matrix.TensorMoment - -namespace OAI - -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ComplexConjugate Matrix.Norms.L2Operator -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ComplexOrder MatrixOrder -attribute [local instance] Classical.propDecidable - -namespace CoordinateSweeps.SignedTensor -open PositiveTensor - -/- Partial-trace invariance of the actual regrouping signs on each fixed -exception sector. No assumption of complex conditional probabilities occurs. -/ -theorem partialTrace_regroup {p l : ℕ} (E : Finset (Fin l)) - (v : Word p l × Word p l → ℂ) - (hv : ∀ u w, v (u,w) ≠ 0 → ∀ i, - (odd (u i) ↔ ¬ odd (w i)) ↔ i ∈ E) : - partialTrace (PositiveTensor.outer (fun uw => regroupPhase uw.1 uw.2 * v uw)) = - partialTrace (PositiveTensor.outer v) := by - ext u u' - apply Finset.sum_congr rfl - intro w _ - change (regroupPhase u w * v (u,w)) * star (regroupPhase u' w * v (u',w)) = - v (u,w)*star (v (u',w)) - by_cases hu : v (u,w) = 0 - · simp [hu] - by_cases hu' : v (u',w) = 0 - · simp [hu'] - have he : regroupPhase u w = regroupPhase u' w := by - apply regroupPhase_of_same_parity - intro i - have hi := hv u w hu i - have hi' := hv u' w hu' i - tauto - rw [star_mul,regroupPhase_star,he] - calc - _ = (regroupPhase u' w * regroupPhase u' w) * (v (u,w)*star (v (u',w))) := by ring - _ = _ := by rw [regroupPhase_square,one_mul] - -abbrev Pair (p : ℕ) := Letter p × Letter p -abbrev MatchedPair (p : ℕ) := {a : Pair p // odd a.1 ↔ odd a.2} - -/- Valid pinned exceptional data. Injectivity is essential: it is supplied -by the proved repeated-mismatch cancellation, not imposed on the kernel. -/ -structure ExceptionPattern (p l : ℕ) where - sites : Finset (Fin l) - pair : sites → Pair p - mismatch : ∀ i, odd (pair i).1 ↔ ¬ odd (pair i).2 - injective : Function.Injective pair - deriving Fintype - -/- Every nonzero commuting matrix entry has literal valid exceptional data. -/ -def entryPattern {p l : ℕ} (A : commutant p l) (u w : Word p l) (h : A.val u w ≠ 0) : - ExceptionPattern p l where - sites := mismatchSlots u w - pair i := (u i.val,w i.val) - mismatch i := (Finset.mem_filter.mp i.property).2 - injective := by - intro i j he - apply Subtype.ext - by_contra hij - exact h (commutant_entry_zero_repeated_mismatch A u w i.val j.val hij - (congrArg Prod.fst he) (congrArg Prod.snd he) (Finset.mem_filter.mp i.property).2) - -namespace ExceptionPattern -variable {p l : ℕ} - -def encode (F : ExceptionPattern p l) (a : Pair p) : Option (Fin l) := - if h : ∃ i : F.sites, F.pair i = a then some (Classical.choose h).val else none - -lemma encode_eq_some (F : ExceptionPattern p l) (a : Pair p) (i : Fin l) : - F.encode a = some i ↔ ∃ hi : i ∈ F.sites, F.pair ⟨i,hi⟩ = a := by - unfold encode - split_ifs with h - · constructor - · intro he - have hi := Option.some.inj he - subst i - exact ⟨(Classical.choose h).property, Classical.choose_spec h⟩ - · rintro ⟨hi,he⟩ - have hh : Classical.choose h = ⟨i,hi⟩ := F.injective ((Classical.choose_spec h).trans he.symm) - rw [hh] - · constructor - · intro he; cases he - · rintro ⟨hi,he⟩ - exact (h ⟨⟨i,hi⟩,he⟩).elim - -lemma mem_sites_iff (F : ExceptionPattern p l) (i : Fin l) : - i ∈ F.sites ↔ ∃ a, F.encode a = some i := by - constructor - · intro hi - exact ⟨F.pair ⟨i,hi⟩,(F.encode_eq_some _ i).mpr ⟨hi,rfl⟩⟩ - · rintro ⟨a,ha⟩ - exact ((F.encode_eq_some a i).mp ha).choose - -lemma encode_injective : Function.Injective (encode (p := p) (l := l)) := by - intro F G he - have hs : F.sites = G.sites := by - ext i - rw [F.mem_sites_iff,G.mem_sites_iff] - simp only [he] - cases F with | mk E f hf hfi => - cases G with | mk E' g hg hgi => - dsimp at hs - subst E' - have hp : f = g := by - funext i - have hh : (ExceptionPattern.mk E f hf hfi).encode (f i) = some i.val := - ((ExceptionPattern.mk E f hf hfi).encode_eq_some _ _).mpr ⟨i.property,rfl⟩ - rw [congrFun he (f i)] at hh - obtain ⟨hi,hv⟩ := ((ExceptionPattern.mk E g hg hgi).encode_eq_some _ _).mp hh - exact hv.symm - subst g - rfl - -lemma card_le : Fintype.card (ExceptionPattern p l) ≤ (l+1)^((2*p)*(2*p)) := by - have hc := Fintype.card_le_of_injective (encode (p := p) (l := l)) encode_injective - simpa only [Fintype.card_fun,Fintype.card_option,Fintype.card_fin, - Fintype.card_prod] using hc - -lemma sites_card_le (F : ExceptionPattern p l) : F.sites.card ≤ (2*p)*(2*p) := by - have hc := Fintype.card_le_of_injective F.pair F.injective - simpa only [Fintype.card_coe,Fintype.card_prod,Fintype.card_fin] using hc - -/- Slots not occupied by a pinned exceptional symbol. -/ -abbrev Free (F : ExceptionPattern p l) := {i : Fin l // i ∉ F.sites} -abbrev FreeWord (F : ExceptionPattern p l) := F.Free → MatchedPair p - -def fillPair (F : ExceptionPattern p l) (x : F.FreeWord) (i : Fin l) : Pair p := - if hi : i ∈ F.sites then F.pair ⟨i,hi⟩ else (x ⟨i,hi⟩).val - -def fill (F : ExceptionPattern p l) (x : F.FreeWord) : Word p l × Word p l := - (fun i => (F.fillPair x i).1, fun i => (F.fillPair x i).2) - -lemma fillPair_at_pin (F : ExceptionPattern p l) (x : F.FreeWord) (i : F.sites) : - F.fillPair x i.val = F.pair i := by simp [fillPair,i.property] - -lemma fillPair_at_free (F : ExceptionPattern p l) (x : F.FreeWord) (i : F.Free) : - F.fillPair x i.val = (x i).val := by simp [fillPair,i.property] - -lemma fill_mismatch_iff (F : ExceptionPattern p l) (x : F.FreeWord) (i : Fin l) : - (odd ((F.fill x).1 i) ↔ ¬ odd ((F.fill x).2 i)) ↔ i ∈ F.sites := by - change (odd (F.fillPair x i).1 ↔ ¬ odd (F.fillPair x i).2) ↔ _ - by_cases hi : i ∈ F.sites - · rw [show F.fillPair x i = F.pair ⟨i,hi⟩ from F.fillPair_at_pin x ⟨i,hi⟩] - exact iff_of_true (F.mismatch ⟨i,hi⟩) hi - · rw [show F.fillPair x i = (x ⟨i,hi⟩).val from F.fillPair_at_free x ⟨i,hi⟩] - have hm := (x ⟨i,hi⟩).property - tauto - -lemma fill_injective (F : ExceptionPattern p l) : Function.Injective F.fill := by - intro x y he - funext i - apply Subtype.ext - have hh : F.fillPair x i.val = F.fillPair y i.val := - Prod.ext (congrFun (congrArg Prod.fst he) i.val) (congrFun (congrArg Prod.snd he) i.val) - simpa only [F.fillPair_at_free] using hh - -lemma fill_disjoint {F G : ExceptionPattern p l} (x : F.FreeWord) (y : G.FreeWord) - (he : F.fill x = G.fill y) : F = G := by - have hs : F.sites = G.sites := by - ext i - rw [← F.fill_mismatch_iff x i,← G.fill_mismatch_iff y i,he] - cases F with | mk E f hf hfi => - cases G with | mk E' g hg hgi => - dsimp at hs - subst E' - have hp : f = g := by - funext i - have hh : (ExceptionPattern.mk E f hf hfi).fillPair x i.val = - (ExceptionPattern.mk E g hg hgi).fillPair y i.val := - Prod.ext (congrFun (congrArg Prod.fst he) i.val) (congrFun (congrArg Prod.snd he) i.val) - simpa only [fillPair_at_pin] using hh - subst g - rfl - -lemma entry_in_range (A : commutant p l) (u w : Word p l) (h : A.val u w ≠ 0) : - ∃ x : (entryPattern A u w h).FreeWord, (entryPattern A u w h).fill x = (u,w) := by - let F := entryPattern A u w h - let x : F.FreeWord := fun i => ⟨(u i.val,w i.val),by - have hi : i.val ∉ mismatchSlots u w := i.property - have hm : ¬ (odd (u i.val) ↔ ¬ odd (w i.val)) := by - simpa only [mismatchSlots,Finset.mem_filter,Finset.mem_univ,true_and] using hi - tauto⟩ - refine ⟨x,?_⟩ - have he (i : Fin l) : F.fillPair x i = (u i,w i) := by - unfold fillPair - split_ifs <;> rfl - exact Prod.ext (funext fun i => congrArg Prod.fst (he i)) - (funext fun i => congrArg Prod.snd (he i)) - -/- Extend a permutation of the free slots by the identity on the exceptions. -/ -def extendPerm (F : ExceptionPattern p l) (σ : Equiv.Perm F.Free) : Equiv.Perm (Fin l) := - Equiv.Perm.ofSubtype σ - -lemma extendPerm_pin (F : ExceptionPattern p l) (σ : Equiv.Perm F.Free) (i : F.sites) : - F.extendPerm σ i.val = i.val := by - simp [extendPerm,Equiv.Perm.ofSubtype_apply_of_not_mem,i.property] - -lemma extendPerm_free (F : ExceptionPattern p l) (σ : Equiv.Perm F.Free) (i : F.Free) : - F.extendPerm σ i.val = (σ i).val := by - exact Equiv.Perm.ofSubtype_apply_of_mem σ i.property - -lemma fill_transport (F : ExceptionPattern p l) (σ : Equiv.Perm F.Free) (x : F.FreeWord) : - F.fill (fun i => x (σ⁻¹ i)) = - (wordPerm (F.extendPerm σ) (F.fill x).1, wordPerm (F.extendPerm σ) (F.fill x).2) := by - have hinv : (F.extendPerm σ)⁻¹ = F.extendPerm σ⁻¹ := by - simp only [extendPerm,map_inv] - have he (i : Fin l) : F.fillPair (fun i => x (σ⁻¹ i)) i = - F.fillPair x ((F.extendPerm σ)⁻¹ i) := by - rw [hinv] - by_cases hi : i ∈ F.sites - · rw [show F.extendPerm σ⁻¹ i = i from F.extendPerm_pin σ⁻¹ ⟨i,hi⟩] - simp [fillPair,hi] - · rw [show F.extendPerm σ⁻¹ i = (σ⁻¹ ⟨i,hi⟩).val from F.extendPerm_free σ⁻¹ ⟨i,hi⟩] - rw [show F.fillPair (fun i => x (σ⁻¹ i)) i = (x (σ⁻¹ ⟨i,hi⟩)).val from - F.fillPair_at_free (fun i => x (σ⁻¹ i)) ⟨i,hi⟩,F.fillPair_at_free] - exact Prod.ext (funext fun i => congrArg Prod.fst (he i)) - (funext fun i => congrArg Prod.snd (he i)) - -def purified (F : ExceptionPattern p l) (A : commutant p l) (x : F.FreeWord) : ℂ := - regroupPhase (F.fill x).1 (F.fill x).2 * A.val (F.fill x).1 (F.fill x).2 - -lemma purified_invariant (F : ExceptionPattern p l) (A : commutant p l) - (σ : Equiv.Perm F.Free) (x : F.FreeWord) : - F.purified A (fun i => x (σ⁻¹ i)) = F.purified A x := by - unfold purified - rw [F.fill_transport] - apply regrouped_commutant_invariant - intro i hi - exact F.extendPerm_pin σ ⟨i,(F.fill_mismatch_iff x i).mp hi⟩ - -end ExceptionPattern -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor.ExceptionPattern -open PositiveTensor -variable {p l : ℕ} - -def embedding (F : ExceptionPattern p l) : F.FreeWord ↪ (Word p l × Word p l) := - ⟨F.fill,F.fill_injective⟩ - -def component (F : ExceptionPattern p l) (A : commutant p l) (uw : Word p l × Word p l) : ℂ := - if uw ∈ Set.range F.fill then A.val uw.1 uw.2 else 0 - -lemma component_image (F : ExceptionPattern p l) (A : commutant p l) (x : F.FreeWord) : - F.component A (F.fill x) = A.val (F.fill x).1 (F.fill x).2 := by - simp [component] - -lemma component_inclusion (F : ExceptionPattern p l) (A : commutant p l) : - F.component A = (inclusion F.embedding).mulVec (fun x => A.val (F.fill x).1 (F.fill x).2) := by - funext q - by_cases hq : q ∈ Set.range F.fill - · obtain ⟨x,rfl⟩ := hq - have hh := inclusion_mulVec_image F.embedding (fun x => A.val (F.fill x).1 (F.fill x).2) x - change (inclusion F.embedding).mulVec (fun x => A.val (F.fill x).1 (F.fill x).2) (F.fill x) = _ at hh - exact (F.component_image A x).trans hh.symm - · rw [show F.component A q = 0 from ite_eq_right hq] - exact (inclusion_mulVec_notin F.embedding _ q hq).symm - -lemma purified_inclusion (F : ExceptionPattern p l) (A : commutant p l) : - (inclusion F.embedding).mulVec (F.purified A) = - fun q => regroupPhase q.1 q.2 * F.component A q := by - funext q - by_cases hq : q ∈ Set.range F.fill - · obtain ⟨x,rfl⟩ := hq - have hh := inclusion_mulVec_image F.embedding (F.purified A) x - change (inclusion F.embedding).mulVec (F.purified A) (F.fill x) = _ at hh - rw [hh,F.component_image] - rfl - · rw [inclusion_mulVec_notin F.embedding _ q hq] - simp [component,hq] - -lemma component_partialTrace (F : ExceptionPattern p l) (A : commutant p l) : - partialTrace (PositiveTensor.outer ((inclusion F.embedding).mulVec (F.purified A))) = - partialTrace (PositiveTensor.outer (F.component A)) := by - rw [F.purified_inclusion] - apply partialTrace_regroup F.sites - intro u w h i - have hq : (u,w) ∈ Set.range F.fill := by - by_contra hn - exact h (ite_eq_right hn) - obtain ⟨x,hx⟩ := hq - have he := F.fill_mismatch_iff x i - simpa only [hx] using he - -lemma component_sum (A : commutant p l) : - ∑ F : ExceptionPattern p l, F.component A = fun q => A.val q.1 q.2 := by - funext q - rw [Finset.sum_apply] - by_cases hq : A.val q.1 q.2 = 0 - · simp [component,hq] - · let F := entryPattern A q.1 q.2 hq - obtain ⟨x,hx⟩ := entry_in_range A q.1 q.2 hq - have hmem : q ∈ Set.range F.fill := ⟨x,hx⟩ - rw [Finset.sum_eq_single F] - · exact ite_eq_left hmem - · intro G _ hG - apply ite_eq_right - rintro ⟨y,hy⟩ - exact hG (fill_disjoint y x (hy.trans hx.symm)) - · simp - -lemma component_square_sum (A : commutant p l) (q : Word p l × Word p l) : - ∑ F : ExceptionPattern p l, F.component A q * star (F.component A q) = - A.val q.1 q.2 * star (A.val q.1 q.2) := by - by_cases hq : A.val q.1 q.2 = 0 - · simp [component,hq] - · let F := entryPattern A q.1 q.2 hq - obtain ⟨x,hx⟩ := entry_in_range A q.1 q.2 hq - have hmem : q ∈ Set.range F.fill := ⟨x,hx⟩ - rw [Finset.sum_eq_single F] - · simp [component,hmem] - · intro G _ hG - have hn : q ∉ Set.range G.fill := by - rintro ⟨y,hy⟩ - exact hG (fill_disjoint y x (hy.trans hx.symm)) - simp [component,hn] - · simp - -lemma purified_trace (F : ExceptionPattern p l) (A : commutant p l) : - Matrix.trace (OrdinaryTensor.outer (F.purified A)) = - Matrix.trace (PositiveTensor.outer (F.component A)) := by - rw [show OrdinaryTensor.outer (F.purified A) = Matrix.vecMulVec (F.purified A) (star (F.purified A)) from rfl, - ← inclusion_trace_outer F.embedding,F.purified_inclusion] - apply Finset.sum_congr rfl - intro q _ - change (regroupPhase q.1 q.2 * F.component A q) * - star (regroupPhase q.1 q.2 * F.component A q) = F.component A q * star (F.component A q) - rw [star_mul,regroupPhase_star] - calc - _ = (regroupPhase q.1 q.2 * regroupPhase q.1 q.2) * (F.component A q * star (F.component A q)) := by ring - _ = _ := by rw [regroupPhase_square,one_mul] - -lemma sum_purified_trace (A : commutant p l) : - ∑ F : ExceptionPattern p l, Matrix.trace (OrdinaryTensor.outer (F.purified A)) = - Matrix.trace (A.val*A.val.conjTranspose) := by - simp_rw [purified_trace] - simp only [PositiveTensor.outer,Matrix.trace,Matrix.diag_apply,Matrix.vecMulVec_apply,Pi.star_apply] - rw [Finset.sum_comm] - simp_rw [component_square_sum] - simp only [Fintype.sum_prod_type,Matrix.mul_apply,Matrix.conjTranspose_apply] -end CoordinateSweeps.SignedTensor.ExceptionPattern - -namespace CoordinateSweeps.SignedTensor.ExceptionPattern -open PositiveTensor -variable {p l : ℕ} -lemma free_card (F : ExceptionPattern p l) : Fintype.card F.Free = l-F.sites.card := by - simp only [Free,Fintype.card_subtype_compl,Fintype.card_coe,Fintype.card_fin] -lemma free_card_pos (F : ExceptionPattern p l) (hl : (2*p)*(2*p) < l) : 0 < Fintype.card F.Free := by - rw [F.free_card] - exact Nat.sub_pos_of_lt (lt_of_le_of_lt F.sites_card_le hl) -lemma free_card_le (F : ExceptionPattern p l) : Fintype.card F.Free ≤ l := by - rw [F.free_card] - exact Nat.sub_le _ _ - -lemma matchedPair_nonempty (hp : 0 < p) : Nonempty (MatchedPair p) := - ⟨⟨(⟨0,by omega⟩,⟨0,by omega⟩),Iff.rfl⟩⟩ - -/- Exact domination of a pinned component by a finite product mixture on its -free slots, after the proved sign cancellation in the genuine partial trace. -/ -theorem component_postselection (F : ExceptionPattern p l) (hp : 0 < p) - (hl : (2*p)*(2*p) < l) (A : commutant p l) : - ((Matrix.trace (OrdinaryTensor.outer (F.purified A)) * - ((Fintype.card F.Free+1 : ℕ) : ℂ)^(2*Fintype.card (MatchedPair p))) • - partialTrace (inclusion F.embedding * (OrdinaryTensor.finiteMixture (I := F.Free) (A := MatchedPair p)) * (inclusion F.embedding).conjTranspose) - - partialTrace (PositiveTensor.outer (F.component A))).PosSemidef := by - let : Nonempty (MatchedPair p) := matchedPair_nonempty hp - have h := OrdinaryTensor.invariant_vector_postselection (I := F.Free) (A := MatchedPair p) (F.free_card_pos hl) - (F.purified A) (F.purified_invariant A) - have hc := h.mul_mul_conjTranspose_same (inclusion F.embedding) - rw [Matrix.mul_sub,Matrix.sub_mul,Matrix.mul_smul,Matrix.smul_mul] at hc - have ho : inclusion F.embedding * OrdinaryTensor.outer (F.purified A) * (inclusion F.embedding).conjTranspose = - PositiveTensor.outer ((inclusion F.embedding).mulVec (F.purified A)) := - mul_outer_mul_star _ _ - rw [ho] at hc - have hp := partialTrace_posSemidef _ hc - simpa only [partialTrace_sub,partialTrace_smul,F.component_partialTrace A] using hp -end CoordinateSweeps.SignedTensor.ExceptionPattern - -namespace CoordinateSweeps.SignedTensor - -def pairAmplitude {p : ℕ} (z : MatchedPair p → ℂ) : Matrix (Letter p) (Letter p) ℂ := - fun a b => if h : odd a ↔ odd b then z ⟨(a,b),h⟩ else 0 - -lemma pairAmplitude_unit_trace {p : ℕ} (z : MatchedPair p → ℂ) - (hz : ∑ a, z a * star (z a) = 1) : - Matrix.trace (pairAmplitude z * (pairAmplitude z).conjTranspose) = 1 := by - have hs := Fintype.sum_of_injective - (Subtype.val : MatchedPair p → Pair p) Subtype.val_injective - (fun a => z a * star (z a)) - (fun a : Pair p => pairAmplitude z a.1 a.2 * star (pairAmplitude z a.1 a.2)) - (by - intro a ha - have hn : ¬ (odd a.1 ↔ odd a.2) := by - intro h - exact ha ⟨⟨a,h⟩,rfl⟩ - simp [pairAmplitude,hn]) - (by intro a; simp [pairAmplitude,a.property]) - rw [hz] at hs - simpa only [Matrix.trace,Matrix.diag_apply,Matrix.mul_apply,Matrix.conjTranspose_apply, - Fintype.sum_prod_type] using hs.symm - -lemma pairAmplitude_even {p : ℕ} (z : MatchedPair p → ℂ) (a b : Letter p) - (hab : odd a ↔ ¬ odd b) : - (pairAmplitude z * (pairAmplitude z).conjTranspose) a b = 0 := by - rw [Matrix.mul_apply] - apply Finset.sum_eq_zero - intro c _ - by_cases hac : odd a ↔ odd c - · have hbc : ¬ (odd b ↔ odd c) := by tauto - simp [Matrix.conjTranspose_apply,pairAmplitude,hbc] - · simp [Matrix.conjTranspose_apply,pairAmplitude,hac] - -/- The real even one-site density obtained by the literal auxiliary partial -trace of a unit matched-pair vector. -/ -def pairDensity {p : ℕ} (z : MatchedPair p → ℂ) (hz : ∑ a, z a * star (z a) = 1) : EvenDensity p := - ⟨pairAmplitude z * (pairAmplitude z).conjTranspose, - Matrix.posSemidef_self_mul_conjTranspose _, pairAmplitude_unit_trace z hz, - pairAmplitude_even z⟩ -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -variable {p : ℕ} - -def basisDensity (a : Letter p) : Matrix (Letter p) (Letter p) ℂ := - Matrix.diagonal (fun b => if b=a then 1 else 0) - -lemma basisDensity_posSemidef (a : Letter p) : (basisDensity a).PosSemidef := by - apply Matrix.PosSemidef.diagonal - intro b - change (0 : ℂ) ≤ if b=a then _ else _ - split_ifs <;> norm_num - -lemma basisDensity_le_one (a : Letter p) : (1-basisDensity a).PosSemidef := by - have he : (1-basisDensity a) = Matrix.diagonal (fun b => if b=a then (0 : ℂ) else 1) := by - ext i j - by_cases hij : i=j - · subst j - by_cases hi : i=a <;> simp [basisDensity,Matrix.diagonal,hi] - · simp [basisDensity,Matrix.diagonal,hij] - - rw [he] - apply Matrix.PosSemidef.diagonal - intro b - change (0 : ℂ) ≤ if b=a then _ else _ - split_ifs <;> norm_num - -lemma basisDensity_trace (a : Letter p) : Matrix.trace (basisDensity a) = 1 := by - simp [basisDensity,Matrix.trace_diagonal] - -def pinAmplitude (a : Pair p) : Matrix (Letter p) (Letter p) ℂ := - fun i j => if (i,j)=a then 1 else 0 - -lemma pinAmplitude_density (a : Pair p) : pinAmplitude a * (pinAmplitude a).conjTranspose = basisDensity a.1 := by - ext i j - simp only [Matrix.mul_apply,Matrix.conjTranspose_apply,pinAmplitude] - rw [Finset.sum_eq_single a.2] - · by_cases hi : i=a.1 <;> by_cases hj : j=a.1 <;> - simp [Prod.ext_iff,hi,hj,basisDensity,Matrix.diagonal,eq_comm] - · intro k _ hk - simp [Prod.ext_iff,hk] - · simp - -def keep (s : ℕ) : ℝ := s/(s+1) -def noise (s p : ℕ) : ℝ := 1/((s+1)*(2*p)) - -lemma keep_nonneg (s : ℕ) : 0 ≤ keep s := div_nonneg (Nat.cast_nonneg _) (by positivity) -lemma noise_nonneg (s p : ℕ) : 0 ≤ noise s p := by unfold noise; positivity -lemma keep_add_noise (s p : ℕ) (hp : 0 < p) : keep s + noise s p*(2*p) = 1 := by - have hp' : (p : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr hp.ne' - have hs : (s : ℝ)+1 ≠ 0 := by positivity - unfold keep noise - field_simp - -def depolarized (s : ℕ) (r : EvenDensity p) : Matrix (Letter p) (Letter p) ℂ := - (keep s : ℂ) • r.val + (noise s p : ℂ) • 1 - -lemma depolarized_posSemidef (s : ℕ) (r : EvenDensity p) : (depolarized s r).PosSemidef := by - exact (r.property.1.smul (by exact_mod_cast keep_nonneg s)).add - (Matrix.PosSemidef.one.smul (by exact_mod_cast noise_nonneg s p)) - -lemma depolarized_trace (s : ℕ) (hp : 0 < p) (r : EvenDensity p) : Matrix.trace (depolarized s r) = 1 := by - rw [depolarized,Matrix.trace_add,Matrix.trace_smul,Matrix.trace_smul,r.property.2.1] - simp only [Matrix.trace_one,Fintype.card_fin,smul_eq_mul,mul_one] - exact_mod_cast keep_add_noise s p hp - -lemma depolarized_even (s : ℕ) (r : EvenDensity p) (i j : Letter p) - (hij : odd i ↔ ¬ odd j) : depolarized s r i j = 0 := by - have hne : i ≠ j := by intro h; subst j; tauto - simp [depolarized,Matrix.smul_apply,r.property.2.2 i j hij,hne] - -def depolarizedDensity (s : ℕ) (hp : 0 < p) (r : EvenDensity p) : EvenDensity p := - ⟨depolarized s r,depolarized_posSemidef s r,depolarized_trace s hp r,depolarized_even s r⟩ - -lemma depolarized_free (s : ℕ) (r : EvenDensity p) : - (depolarized s r - (keep s : ℂ) • r.val).PosSemidef := by - simpa only [depolarized,add_sub_cancel_left] using - (Matrix.PosSemidef.one (n := Letter p) (R := ℂ)).smul (by exact_mod_cast noise_nonneg s p) - -lemma depolarized_pin (s : ℕ) (r : EvenDensity p) (a : Letter p) : - (depolarized s r - (noise s p : ℂ) • basisDensity a).PosSemidef := by - have ht : (0 : ℂ) ≤ (keep s : ℂ) := by exact_mod_cast keep_nonneg s - have hu : (0 : ℂ) ≤ (noise s p : ℂ) := by exact_mod_cast noise_nonneg s p - have h := (r.property.1.smul ht).add ((basisDensity_le_one a).smul hu) - simpa only [depolarized,smul_sub,add_sub_assoc] using h -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open PositiveTensor -variable {p l : ℕ} - -def pinnedDensity (E : Finset (Fin l)) (a : E → Letter p) (r : EvenDensity p) : - Matrix (Word p l) (Word p l) ℂ := - productMatrix (fun i => if hi : i ∈ E then basisDensity (a ⟨i,hi⟩) else r.val) - -lemma pinnedDensity_posSemidef (E : Finset (Fin l)) (a : E → Letter p) (r : EvenDensity p) : - (pinnedDensity E a r).PosSemidef := by - apply productMatrix_posSemidef - intro i - split_ifs with hi - · exact basisDensity_posSemidef _ - · exact r.property.1 - -lemma keep_pow_lower (s n : ℕ) (hn : n ≤ s) : 1 ≤ (s+1 : ℝ) * (keep s)^n := by - have hs : (0 : ℝ) < s+1 := by positivity - have hi : (s+1 : ℝ)⁻¹ ≤ 1 := (inv_le_one₀ hs).mpr (by linarith [Nat.cast_nonneg (α := ℝ) s]) - have hb := one_add_mul_le_pow (a := -((s+1 : ℝ)⁻¹)) (by linarith : -2 ≤ -((s+1 : ℝ)⁻¹)) n - have he : (1 - (s+1 : ℝ)⁻¹) = keep s := by unfold keep; field_simp; ring - calc - 1 ≤ (s+1 : ℝ)-n := by - have hn' : (n : ℝ) ≤ s := by exact_mod_cast hn - linarith - _ = (s+1 : ℝ)*(1+n * (-((s+1 : ℝ)⁻¹))) := by field_simp; ring - _ ≤ (s+1 : ℝ)*(1+(-((s+1 : ℝ)⁻¹)))^n := mul_le_mul_of_nonneg_left hb hs.le - _ = _ := by rw [show 1+(-((s+1 : ℝ)⁻¹)) = keep s from he] - -lemma pin_coefficient_le (s p k : ℕ) (hp : 0 < p) (hps : p ≤ s) - (hk : k ≤ (2*p)*(2*p)) : - (s+1 : ℝ) * ((s+1 : ℝ)*(2*p))^k ≤ (s+1 : ℝ)^(13*p^2) := by - have hs : (1 : ℝ) ≤ s+1 := by linarith [Nat.cast_nonneg (α := ℝ) s] - have hp' : (p : ℝ) ≤ s := by exact_mod_cast hps - have ha : (2*p : ℝ) ≤ (s+1 : ℝ)^2 := by nlinarith [sq_nonneg (s : ℝ)] - have hbase : (s+1 : ℝ)*(2*p) ≤ (s+1 : ℝ)^3 := by - nlinarith [mul_le_mul_of_nonneg_left ha (by positivity : (0 : ℝ) ≤ s+1)] - have hexp : 3*k+1 ≤ 13*p^2 := by - have hp1 : 1 ≤ p*p := by nlinarith - nlinarith [hk] - calc - _ ≤ (s+1 : ℝ) * ((s+1 : ℝ)^3)^k := - mul_le_mul_of_nonneg_left (pow_le_pow_left₀ (by positivity) hbase k) (by positivity) - _ = (s+1 : ℝ)^(3*k+1) := by rw [← pow_mul,pow_succ]; ring - _ ≤ _ := pow_le_pow_right₀ hs hexp - -/- Each pinned ordinary product density is dominated by a tensor power of a -single even density, with only polynomial cost per actual exception. -/ -theorem pinned_absorption (s : ℕ) (hp : 0 < p) (hls : l ≤ s) - (E : Finset (Fin l)) (a : E → Letter p) (r : EvenDensity p) : - (((s+1 : ℝ) * ((s+1 : ℝ)*(2*p))^E.card : ℝ) : ℂ) • - densityPower l (depolarized s r) - pinnedDensity E a r |>.PosSemidef := by - let c : Fin l → ℂ := fun i => if i ∈ E then (noise s p : ℂ) else (keep s : ℂ) - let f : Fin l → Matrix (Letter p) (Letter p) ℂ := - fun i => if hi : i ∈ E then basisDensity (a ⟨i,hi⟩) else r.val - have hlocal (i : Fin l) : (c i • f i).PosSemidef := by - by_cases hi : i ∈ E - · simpa only [c,f,ite_eq_left hi,dite_eq_left hi] using - (basisDensity_posSemidef (a ⟨i,hi⟩)).smul (show (0 : ℂ) ≤ (noise s p : ℂ) by exact_mod_cast noise_nonneg s p) - · simpa only [c,f,ite_eq_right hi,dite_eq_right hi] using - r.property.1.smul (show (0 : ℂ) ≤ (keep s : ℂ) by exact_mod_cast keep_nonneg s) - have hdiff (i : Fin l) : (depolarized s r - c i • f i).PosSemidef := by - by_cases hi : i ∈ E - · simpa only [c,f,ite_eq_left hi,dite_eq_left hi] using depolarized_pin s r (a ⟨i,hi⟩) - · simpa only [c,f,ite_eq_right hi,dite_eq_right hi] using depolarized_free s r - have h := productMatrix_mono (fun i => c i • f i) (fun _ => depolarized s r) hlocal hdiff - rw [productMatrix_smul] at h - have hc : (∏ i, c i) = ((keep s)^(l-E.card) * (noise s p)^E.card : ℝ) := by - have hE : Finset.univ.filter (fun i : Fin l => i ∈ E) = E := by ext i; simp - have hC : Finset.univ.filter (fun i : Fin l => i ∉ E) = Eᶜ := by ext i; simp - simp only [c,Finset.prod_ite,hE,hC,Finset.prod_const,Finset.card_compl,Fintype.card_fin] - push_cast - ring - rw [hc] at h - let C : ℝ := (s+1 : ℝ) * ((s+1 : ℝ)*(2*p))^E.card - have hC : (0 : ℝ) ≤ C := by dsimp [C]; positivity - have hu : ((s+1 : ℝ)*(2*p))*noise s p = 1 := by - have hp' : (p : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr hp.ne' - unfold noise - field_simp - have hCW : 1 ≤ C*((keep s)^(l-E.card)*(noise s p)^E.card) := by - calc - _ ≤ (s+1 : ℝ)*(keep s)^(l-E.card) := keep_pow_lower s _ (le_trans (Nat.sub_le _ _) hls) - _ = _ := by - dsimp [C] - calc - _ = ((s+1 : ℝ)*(keep s)^(l-E.card))*((((s+1 : ℝ)*(2*p))*noise s p)^E.card) := by rw [hu,one_pow,mul_one] - _ = _ := by rw [mul_pow]; ring - have hh := h.smul (show (0 : ℂ) ≤ (C : ℂ) by exact_mod_cast hC) - have hz := (pinnedDensity_posSemidef E a r).smul - (show (0 : ℂ) ≤ ((C*((keep s)^(l-E.card)*(noise s p)^E.card)-1 : ℝ) : ℂ) by exact_mod_cast sub_nonneg.mpr hCW) - have ht := hh.add hz - change ((C : ℂ) • (densityPower l (depolarized s r) - - (((keep s)^(l-E.card)*(noise s p)^E.card : ℝ) : ℂ) • pinnedDensity E a r) + - ((C*((keep s)^(l-E.card)*(noise s p)^E.card)-1 : ℝ) : ℂ) • pinnedDensity E a r).PosSemidef at ht - change ((C : ℂ) • densityPower l (depolarized s r) - pinnedDensity E a r).PosSemidef - convert ht using 1 - simp only [smul_sub,smul_smul,Complex.ofReal_sub,Complex.ofReal_mul,Complex.ofReal_one, - sub_smul,one_smul] - module -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open PositiveTensor -variable {p l : ℕ} -theorem pinned_absorption_uniform (s : ℕ) (hp : 0 < p) (hps : p ≤ s) (hls : l ≤ s) - (E : Finset (Fin l)) (hE : E.card ≤ (2*p)*(2*p)) (a : E → Letter p) (r : EvenDensity p) : - ((((s+1 : ℝ)^(13*p^2)) : ℂ) • densityPower l (depolarized s r) - pinnedDensity E a r).PosSemidef := by - have h := pinned_absorption s hp hls E a r - have hle := pin_coefficient_le s p E.card hp hps hE - have hr : (densityPower l (depolarized s r)).PosSemidef := - productMatrix_posSemidef (fun _ : Fin l => depolarized s r) (fun _ => depolarized_posSemidef s r) - have hh := (hr.smul (show (0 : ℂ) ≤ (((s+1 : ℝ)^(13*p^2) - - (s+1 : ℝ)*((s+1 : ℝ)*(2*p))^E.card : ℝ) : ℂ) by exact_mod_cast sub_nonneg.mpr hle)).add h - convert hh using 1 - push_cast - module -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor.ExceptionPattern -open PositiveTensor -variable {p l : ℕ} - -def siteAmplitude (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) (i : Fin l) : - Matrix (Letter p) (Letter p) ℂ := - if hi : i ∈ F.sites then pinAmplitude (F.pair ⟨i,hi⟩) else pairAmplitude z - -def pairProduct (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) - (q : Word p l × Word p l) : ℂ := ∏ i, F.siteAmplitude z i (q.1 i) (q.2 i) - -lemma siteAmplitude_pin (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) (x : F.FreeWord) (i : F.sites) : - F.siteAmplitude z i.val ((F.fill x).1 i.val) ((F.fill x).2 i.val) = 1 := by - change F.siteAmplitude z i.val (F.fillPair x i.val).1 (F.fillPair x i.val).2 = 1 - rw [F.fillPair_at_pin] - simp [siteAmplitude,i.property,pinAmplitude] - -lemma siteAmplitude_free (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) (x : F.FreeWord) (i : F.Free) : - F.siteAmplitude z i.val ((F.fill x).1 i.val) ((F.fill x).2 i.val) = z (x i) := by - change F.siteAmplitude z i.val (F.fillPair x i.val).1 (F.fillPair x i.val).2 = z (x i) - rw [F.fillPair_at_free] - simp [siteAmplitude,i.property,pairAmplitude,(x i).property] - -lemma pairProduct_fill (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) (x : F.FreeWord) : - F.pairProduct z (F.fill x) = OrdinaryTensor.tensorVector z x := by - unfold pairProduct - rw [← Fintype.prod_subtype_mul_prod_subtype (fun i => i ∈ F.sites)] - simp only [F.siteAmplitude_pin,F.siteAmplitude_free,Finset.prod_const_one,one_mul] - rfl - -lemma pairProduct_nonzero (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) - (q : Word p l × Word p l) (hq : F.pairProduct z q ≠ 0) : q ∈ Set.range F.fill := by - have hi (i : Fin l) : F.siteAmplitude z i (q.1 i) (q.2 i) ≠ 0 := - (Finset.prod_ne_zero_iff.mp hq) i (Finset.mem_univ i) - have hp (i : F.sites) : (q.1 i.val,q.2 i.val) = F.pair i := by - by_contra hn - exact hi i.val (by simp [siteAmplitude,i.property,pinAmplitude,hn]) - have hf (i : F.Free) : odd (q.1 i.val) ↔ odd (q.2 i.val) := by - by_contra hn - exact hi i.val (by simp [siteAmplitude,i.property,pairAmplitude,hn]) - let x : F.FreeWord := fun i => ⟨(q.1 i.val,q.2 i.val),hf i⟩ - have he (i : Fin l) : F.fillPair x i = (q.1 i,q.2 i) := by - by_cases hi : i ∈ F.sites - · exact (F.fillPair_at_pin x ⟨i,hi⟩).trans (hp ⟨i,hi⟩).symm - · exact F.fillPair_at_free x ⟨i,hi⟩ - exact ⟨x,Prod.ext (funext fun i => congrArg Prod.fst (he i)) (funext fun i => congrArg Prod.snd (he i))⟩ - -lemma pairProduct_inclusion (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) : - (inclusion F.embedding).mulVec (OrdinaryTensor.tensorVector z) = F.pairProduct z := by - funext q - by_cases hq : q ∈ Set.range F.fill - · obtain ⟨x,rfl⟩ := hq - have hh := inclusion_mulVec_image F.embedding (OrdinaryTensor.tensorVector z) x - change (inclusion F.embedding).mulVec (OrdinaryTensor.tensorVector z) (F.fill x) = _ at hh - exact hh.trans (F.pairProduct_fill z x).symm - · rw [inclusion_mulVec_notin F.embedding _ q hq] - exact (not_ne_iff.mp (fun hh => hq (F.pairProduct_nonzero z q hh))).symm - -/- Partial tracing a filled product vector yields pinned basis densities at -the true exceptions and the same even density at every remaining slot. -/ -lemma filled_product_partialTrace (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) - (hz : ∑ a, z a * star (z a) = 1) : - partialTrace (PositiveTensor.outer ((inclusion F.embedding).mulVec (OrdinaryTensor.tensorVector z))) = - pinnedDensity F.sites (fun i => (F.pair i).1) (pairDensity z hz) := by - rw [F.pairProduct_inclusion] - have he : partialTrace (PositiveTensor.outer (F.pairProduct z)) = - productMatrix (fun i => F.siteAmplitude z i * (F.siteAmplitude z i).conjTranspose) := by - ext u v - simpa only [partialTrace,PositiveTensor.outer,Matrix.vecMulVec_apply,Pi.star_apply,pairProduct] using - pair_product_partialTrace (F.siteAmplitude z) u v - rw [he] - congr 1 - funext i - by_cases hi : i ∈ F.sites - · simp only [siteAmplitude,hi,dite_eq_left,pinAmplitude_density] - · simp [siteAmplitude,hi,pairDensity] -end CoordinateSweeps.SignedTensor.ExceptionPattern - -namespace CoordinateSweeps.SignedTensor.ExceptionPattern -open PositiveTensor -variable {p l : ℕ} - -lemma purified_trace_le (F : ExceptionPattern p l) (A : commutant p l) : - Matrix.trace (OrdinaryTensor.outer (F.purified A)) ≤ Matrix.trace (A.val*A.val.conjTranspose) := by - rw [← sum_purified_trace A] - exact Finset.single_le_sum (fun G _ => OrdinaryTensor.outer_trace_nonneg (G.purified A)) (Finset.mem_univ F) - -abbrev Data (F : ExceptionPattern p l) := - OrdinaryTensor.Histogram F.Free (MatchedPair p) × OrdinaryTensor.PhaseSpace F.Free (MatchedPair p) - -def dataDensity (F : ExceptionPattern p l) (hn : 0 < Fintype.card F.Free) (d : F.Data) : EvenDensity p := - pairDensity (OrdinaryTensor.empiricalVector d.1 d.2) (OrdinaryTensor.empiricalVector_unit hn d.1 d.2) - -def dataPoint (F : ExceptionPattern p l) (s : ℕ) (hp : 0 < p) - (hn : 0 < Fintype.card F.Free) (d : F.Data) : EvenDensity p := - depolarizedDensity s hp (F.dataDensity hn d) - -def rawPinned (F : ExceptionPattern p l) (hn : 0 < Fintype.card F.Free) : - Matrix (Word p l) (Word p l) ℂ := - ∑ d : F.Data, pinnedDensity F.sites (fun i => (F.pair i).1) (F.dataDensity hn d) - -def rawDensity (F : ExceptionPattern p l) (s : ℕ) (hp : 0 < p) (hn : 0 < Fintype.card F.Free) : - Matrix (Word p l) (Word p l) ℂ := - ∑ d : F.Data, densityPower l (F.dataPoint s hp hn d).val - -lemma rawPinned_posSemidef (F : ExceptionPattern p l) (hn : 0 < Fintype.card F.Free) : - (F.rawPinned hn).PosSemidef := by - exact Matrix.posSemidef_sum _ (fun d _ => pinnedDensity_posSemidef _ _ _) -lemma rawDensity_posSemidef (F : ExceptionPattern p l) (s : ℕ) (hp : 0 < p) (hn : 0 < Fintype.card F.Free) : - (F.rawDensity s hp hn).PosSemidef := by - exact Matrix.posSemidef_sum _ (fun d _ => densityPower_posSemidef _ _ (F.dataPoint s hp hn d).property.1) - -lemma rawMixture_partialTrace (F : ExceptionPattern p l) (hn : 0 < Fintype.card F.Free) : - partialTrace (inclusion F.embedding * - (OrdinaryTensor.rawMixture (I := F.Free) (A := MatchedPair p)) * (inclusion F.embedding).conjTranspose) = - F.rawPinned hn := by - unfold OrdinaryTensor.rawMixture rawPinned - rw [Fintype.sum_prod_type] - simp only [Matrix.mul_sum,Matrix.sum_mul,partialTrace_sum] - apply Finset.sum_congr rfl - intro h _ - apply Finset.sum_congr rfl - intro t _ - have he := congrArg (partialTrace (J := Word p l) (K := Word p l)) - (mul_outer_mul_star (inclusion F.embedding) - (OrdinaryTensor.tensorVector (OrdinaryTensor.empiricalVector h t))) - exact he.trans (F.filled_product_partialTrace _ (OrdinaryTensor.empiricalVector_unit hn h t)) - -lemma rawPinned_domination (F : ExceptionPattern p l) (hp : 0 < p) (hn : 0 < Fintype.card F.Free) : - (F.rawPinned hn - partialTrace (inclusion F.embedding * - (OrdinaryTensor.finiteMixture (I := F.Free) (A := MatchedPair p)) * (inclusion F.embedding).conjTranspose)).PosSemidef := by - let : Nonempty (MatchedPair p) := matchedPair_nonempty hp - have h := (OrdinaryTensor.rawMixture_domination (I := F.Free) (A := MatchedPair p)).mul_mul_conjTranspose_same (inclusion F.embedding) - rw [Matrix.mul_sub,Matrix.sub_mul] at h - have hh := partialTrace_posSemidef _ h - simpa only [partialTrace_sub,F.rawMixture_partialTrace hn] using hh - -lemma rawPinned_absorption (F : ExceptionPattern p l) (s : ℕ) (hp : 0 < p) - (hps : p ≤ s) (hls : l ≤ s) (hn : 0 < Fintype.card F.Free) : - ((((s+1 : ℝ)^(13*p^2)) : ℂ) • F.rawDensity s hp hn - F.rawPinned hn).PosSemidef := by - have hh := Matrix.posSemidef_sum Finset.univ (fun d _ => - pinned_absorption_uniform s hp hps hls F.sites F.sites_card_le - (fun i => (F.pair i).1) (F.dataDensity hn d)) - simpa only [Finset.sum_sub_distrib,← Finset.smul_sum,rawPinned,rawDensity,dataPoint,depolarizedDensity] using hh -end CoordinateSweeps.SignedTensor.ExceptionPattern - -namespace CoordinateSweeps.SignedTensor -open PositiveTensor -variable {p l : ℕ} - -lemma matchedPair_card_le (p : ℕ) : Fintype.card (MatchedPair p) ≤ (2*p)*(2*p) := by - simpa only [Pair,Fintype.card_prod,Letter,Fintype.card_fin] using - (Fintype.card_subtype_le (fun a : Pair p => odd a.1 ↔ odd a.2)) - -namespace ExceptionPattern - -def empty (p l : ℕ) : ExceptionPattern p l where - sites := ∅ - pair i := False.elim (Finset.notMem_empty i.val i.property) - mismatch i := False.elim (Finset.notMem_empty i.val i.property) - injective i := False.elim (Finset.notMem_empty i.val i.property) - -instance : Nonempty (ExceptionPattern p l) := ⟨empty p l⟩ - -lemma data_card_le (F : ExceptionPattern p l) : Fintype.card F.Data ≤ (l+1)^(8*p^2) := by - have hh := OrdinaryTensor.histogram_card_le (I := F.Free) (A := MatchedPair p) - have ht : Fintype.card (OrdinaryTensor.PhaseSpace F.Free (MatchedPair p)) = - (Fintype.card F.Free+1)^Fintype.card (MatchedPair p) := by - simp [OrdinaryTensor.PhaseSpace] - rw [Fintype.card_prod,ht] - calc - _ ≤ (Fintype.card F.Free+1)^(2*Fintype.card (MatchedPair p)) := by - rw [two_mul (Fintype.card (MatchedPair p)),pow_add] - exact Nat.mul_le_mul_right _ hh - _ ≤ (l+1)^(2*Fintype.card (MatchedPair p)) := - Nat.pow_le_pow_left (Nat.add_le_add_right F.free_card_le 1) _ - _ ≤ _ := Nat.pow_le_pow_right (by omega) (by nlinarith [matchedPair_card_le p]) - -lemma free_power_le (F : ExceptionPattern p l) (s : ℕ) (hls : l ≤ s) : - (Fintype.card F.Free+1 : ℕ)^(2*Fintype.card (MatchedPair p)) ≤ (s+1)^(8*p^2) := by - calc - _ ≤ (s+1)^(2*Fintype.card (MatchedPair p)) := - Nat.pow_le_pow_left (Nat.add_le_add_right (F.free_card_le.trans hls) 1) _ - _ ≤ _ := Nat.pow_le_pow_right (by omega) (by nlinarith [matchedPair_card_le p]) - -lemma component_uniform_domination (F : ExceptionPattern p l) (s : ℕ) (hp : 0 < p) - (hps : p ≤ s) (hls : l ≤ s) (hl : (2*p)*(2*p) < l) (A : commutant p l) : - ((Matrix.trace (A.val*A.val.conjTranspose) * ((s+1 : ℕ) : ℂ)^(21*p^2)) • - F.rawDensity s hp (F.free_card_pos hl) - partialTrace (PositiveTensor.outer (F.component A))).PosSemidef := by - let hn := F.free_card_pos hl - let M := partialTrace (inclusion F.embedding * - (OrdinaryTensor.finiteMixture (I := F.Free) (A := MatchedPair p)) * (inclusion F.embedding).conjTranspose) - have hM : M.PosSemidef := partialTrace_posSemidef _ - (OrdinaryTensor.finiteMixture_posSemidef.mul_mul_conjTranspose_same _) - have ht : (0 : ℂ) ≤ Matrix.trace (A.val*A.val.conjTranspose) := - (Matrix.posSemidef_self_mul_conjTranspose A.val).trace_nonneg - have ha : (0 : ℂ) ≤ Matrix.trace (A.val*A.val.conjTranspose) * ((s+1 : ℕ) : ℂ)^(8*p^2) := - mul_nonneg ht (by positivity) - have hc : Matrix.trace (OrdinaryTensor.outer (F.purified A)) * - ((Fintype.card F.Free+1 : ℕ) : ℂ)^(2*Fintype.card (MatchedPair p)) ≤ - Matrix.trace (A.val*A.val.conjTranspose) * ((s+1 : ℕ) : ℂ)^(8*p^2) := by - exact mul_le_mul (F.purified_trace_le A) (by exact_mod_cast F.free_power_le s hls) - (by positivity) ht - have h₁ := domination_pad _ M _ _ hM hc (F.component_postselection hp hl A) - have h₂ := domination_trans _ M (F.rawPinned hn) _ 1 ha h₁ (by - simpa only [one_smul] using F.rawPinned_domination hp hn) - rw [mul_one] at h₂ - have h₃ := domination_trans _ (F.rawPinned hn) (F.rawDensity s hp hn) _ - (((s+1 : ℝ)^(13*p^2)) : ℂ) ha h₂ (F.rawPinned_absorption s hp hps hls hn) - convert h₃ using 1 - push_cast - rw [mul_assoc,← pow_add] - congr 2; ring -end ExceptionPattern - -abbrev DensityProfile (p l : ℕ) := Σ F : ExceptionPattern p l, F.Data - -lemma densityProfile_card_le (p l : ℕ) : Fintype.card (DensityProfile p l) ≤ (l+1)^(12*p^2) := by - rw [Fintype.card_sigma] - calc - _ ≤ ∑ _F : ExceptionPattern p l, (l+1)^(8*p^2) := - Finset.sum_le_sum (fun F _ => F.data_card_le) - _ = Fintype.card (ExceptionPattern p l) * (l+1)^(8*p^2) := by simp - _ ≤ (l+1)^((2*p)*(2*p)) * (l+1)^(8*p^2) := - Nat.mul_le_mul_right _ (ExceptionPattern.card_le (p := p) (l := l)) - _ = _ := by rw [← pow_add]; congr 1; ring - -lemma densityProfile_nonempty (hp : 0 < p) : Nonempty (DensityProfile p l) := by - let : Nonempty (MatchedPair p) := ExceptionPattern.matchedPair_nonempty hp - let F := ExceptionPattern.empty p l - exact ⟨⟨F,Classical.choice inferInstance⟩⟩ - -def profilePoint (s p l : ℕ) (hp : 0 < p) (hl : (2*p)*(2*p) < l) - (d : DensityProfile p l) : EvenDensity p := d.1.dataPoint s hp (d.1.free_card_pos hl) d.2 - -def rawProfileDensity (s p l : ℕ) (hp : 0 < p) (hl : (2*p)*(2*p) < l) : - Matrix (Word p l) (Word p l) ℂ := - ∑ d : DensityProfile p l, densityPower l (profilePoint s p l hp hl d).val - -lemma rawProfileDensity_eq (s p l : ℕ) (hp : 0 < p) (hl : (2*p)*(2*p) < l) : - rawProfileDensity s p l hp hl = ∑ F : ExceptionPattern p l, F.rawDensity s hp (F.free_card_pos hl) := by - exact Fintype.sum_sigma _ - -lemma rawProfileDensity_posSemidef (s p l : ℕ) (hp : 0 < p) (hl : (2*p)*(2*p) < l) : - (rawProfileDensity s p l hp hl).PosSemidef := by - exact Matrix.posSemidef_sum _ (fun d _ => densityPower_posSemidef _ _ (profilePoint s p l hp hl d).property.1) - -/- Finite postselection for the literal signed action commutant. -/ -theorem commutant_covariance_domination (s p l : ℕ) (hp : 0 < p) (hps : p ≤ s) - (hls : l ≤ s) (hl : (2*p)*(2*p) < l) (A : commutant p l) : - ((Matrix.trace (A.val*A.val.conjTranspose) * ((s+1 : ℕ) : ℂ)^(25*p^2)) • - rawProfileDensity s p l hp hl - A.val*A.val.conjTranspose).PosSemidef := by - have hc := partialTrace_posSemidef _ (outer_sum_domination (fun F : ExceptionPattern p l => F.component A)) - rw [ExceptionPattern.component_sum,partialTrace_sub,partialTrace_smul,partialTrace_sum, - partialTrace_outer_matrix] at hc - have hsum := Matrix.posSemidef_sum Finset.univ (fun (F : ExceptionPattern p l) _ => - F.component_uniform_domination s hp hps hls hl A) - rw [Finset.sum_sub_distrib,← Finset.smul_sum,← rawProfileDensity_eq s p l hp hl] at hsum - have h := domination_trans _ _ _ (Fintype.card (ExceptionPattern p l) : ℂ) _ (by positivity) hc hsum - have hcard : Fintype.card (ExceptionPattern p l) ≤ (s+1)^(4*p^2) := by - calc - _ ≤ (l+1)^((2*p)*(2*p)) := ExceptionPattern.card_le (p := p) (l := l) - _ ≤ (s+1)^((2*p)*(2*p)) := Nat.pow_le_pow_left (Nat.add_le_add_right hls 1) _ - _ = _ := by congr 1; ring - apply domination_pad _ _ _ _ (rawProfileDensity_posSemidef s p l hp hl) _ h - calc - _ ≤ ((s+1 : ℕ) : ℂ)^(4*p^2) * - (Matrix.trace (A.val*A.val.conjTranspose) * ((s+1 : ℕ) : ℂ)^(21*p^2)) := - mul_le_mul_of_nonneg_right (by exact_mod_cast hcard) - (mul_nonneg (Matrix.posSemidef_self_mul_conjTranspose _).trace_nonneg (by positivity)) - _ = _ := by rw [mul_left_comm,← pow_add]; congr 2; ring -end CoordinateSweeps.SignedTensor - -noncomputable section -open scoped BigOperators ENNReal -open MeasureTheory - -namespace CoordinateSweeps.FiniteAtomic -variable {I X V : Type*} [Fintype I] [Nonempty I] [MeasurableSpace X] - [MeasurableSingletonClass X] [NormedAddCommGroup V] [NormedSpace ℝ V] [CompleteSpace V] - -def uniform (x : I → X) : Measure X := - (Fintype.card I : ℝ≥0∞)⁻¹ • ∑ i, Measure.dirac (x i) - -instance uniform_probability (x : I → X) : IsProbabilityMeasure (uniform x) := by - constructor - simp [uniform, Measure.finsetSum_apply, ENNReal.inv_mul_cancel, - Fintype.card_ne_zero] - -omit [Nonempty I] in -lemma uniform_integral (x : I → X) (f : X → V) : - (∫ z, f z ∂uniform x) = (Fintype.card I : ℝ)⁻¹ • ∑ i, f (x i) := by - unfold uniform - rw [integral_smul_measure,integral_finsetSum_measure] - · simp [integral_dirac] - · intro i _ - exact integrable_dirac enorm_lt_top -end CoordinateSweeps.FiniteAtomic - -namespace CoordinateSweeps.SignedTensor -open PositiveTensor MeasureTheory - -instance (p : ℕ) : MeasurableSingletonClass (EvenDensity p) := by - let : MeasurableSpace (Matrix (Letter p) (Letter p) ℂ) := borel _ - let : BorelSpace (Matrix (Letter p) (Letter p) ℂ) := ⟨rfl⟩ - change MeasurableSingletonClass {r : Matrix (Letter p) (Letter p) ℂ // _} - infer_instance - -lemma isotypic_mem_commutant {p l : ℕ} (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - isotypic (p := p) ρ ∈ commutant p l := by - intro σ - rw [isotypic_eq_projector] - exact (ρ.projector_commute (action p l) σ).symm - -lemma isotypic_self_mul {p l : ℕ} (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - isotypic (p := p) ρ * (isotypic (p := p) ρ).conjTranspose = isotypic (p := p) ρ := by - rw [(isotypic_posSemidef ρ).isHermitian.eq,isotypic_eq_projector,ρ.projector_idempotent] - -lemma isotypic_trace_le (s p l : ℕ) (hls : l ≤ s) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - Matrix.trace (isotypic (p := p) ρ) ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2) := by - rw [isotypic_trace] - apply mul_le_mul_of_nonneg_left _ (by positivity) - have hh := (multiplicity_le p l ρ).trans (Nat.pow_le_pow_left (Nat.add_le_add_right hls 1) _) - have he : (2*p)*(2*p) = 4*p^2 := by ring - rw [he] at hh - exact_mod_cast hh - -/- The large-slot case, as an actual probability mixture of even densities. -/ -theorem density_domination_large (s p l : ℕ) (hp : 0 < p) (hps : p ≤ s) (hls : l ≤ s) - (hl : (2*p)*(2*p) < l) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - ∃ μ : Measure (EvenDensity p), IsProbabilityMeasure μ ∧ - (((ρ.dimension : ℂ) * ((s+1 : ℕ) : ℂ)^(41*p^2)) • - (∫ r : EvenDensity p, densityPower l r.val ∂μ) - isotypic (p := p) ρ).PosSemidef := by - let : Nonempty (DensityProfile p l) := densityProfile_nonempty hp - let x := profilePoint s p l hp hl - let μ := FiniteAtomic.uniform x - refine ⟨μ,inferInstance,?_⟩ - have hint : (∫ r : EvenDensity p, densityPower l r.val ∂μ) = - (Fintype.card (DensityProfile p l) : ℂ)⁻¹ • rawProfileDensity s p l hp hl := by - rw [FiniteAtomic.uniform_integral] - change (Fintype.card (DensityProfile p l) : ℝ)⁻¹ • rawProfileDensity s p l hp hl = _ - ext u v - simp [Complex.real_smul] - rw [hint] - let A : commutant p l := ⟨isotypic ρ,isotypic_mem_commutant ρ⟩ - have h := commutant_covariance_domination s p l hp hps hls hl A - change ((_ * _) • _ - isotypic ρ * (isotypic ρ).conjTranspose).PosSemidef at h - simp only [A,isotypic_self_mul] at h - have hcard : Fintype.card (DensityProfile p l) ≤ (s+1)^(12*p^2) := - (densityProfile_card_le p l).trans (Nat.pow_le_pow_left (Nat.add_le_add_right hls 1) _) - have hc0 : (Fintype.card (DensityProfile p l) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - have hbig : ((s+1 : ℕ) : ℂ)^(12*p^2) * (Fintype.card (DensityProfile p l) : ℂ)⁻¹ ≥ 1 := by - have hi : (0 : ℂ) ≤ (Fintype.card (DensityProfile p l) : ℂ)⁻¹ := by positivity - have hh := mul_le_mul_of_nonneg_right (show (Fintype.card (DensityProfile p l) : ℂ) ≤ - ((s+1 : ℕ) : ℂ)^(12*p^2) by exact_mod_cast hcard) hi - simpa only [mul_inv_cancel₀ hc0] using hh - rw [smul_smul] - apply domination_pad _ _ _ _ (rawProfileDensity_posSemidef s p l hp hl) _ h - calc - _ ≤ ((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2)) * ((s+1 : ℕ) : ℂ)^(25*p^2) := - mul_le_mul_of_nonneg_right (isotypic_trace_le s p l hls ρ) (by positivity) - _ = (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(29*p^2) := by - rw [mul_assoc,← pow_add]; congr 2; ring - _ ≤ ((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(29*p^2)) * - (((s+1 : ℕ) : ℂ)^(12*p^2) * (Fintype.card (DensityProfile p l) : ℂ)⁻¹) := by - have hh := mul_le_mul_of_nonneg_left hbig - (show (0 : ℂ) ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(29*p^2) by positivity) - simpa only [mul_one] using hh - _ = _ := by - rw [← mul_assoc,mul_assoc (ρ.dimension : ℂ),← pow_add] - congr 3; ring - -def uniformDensity (p : ℕ) (hp : 0 < p) : EvenDensity p := - ⟨((2*p : ℕ) : ℂ)⁻¹ • 1, Matrix.PosSemidef.one.smul (by positivity), by - rw [Matrix.trace_smul,Matrix.trace_one] - have hc : ((2*p : ℕ) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr (by omega) - simpa only [Letter,Fintype.card_fin,smul_eq_mul] using inv_mul_cancel₀ hc, - by - intro i j hij - have hne : i ≠ j := by intro he; subst j; tauto - simp [hne]⟩ - -lemma densityPower_one (p l : ℕ) : densityPower l (1 : Matrix (Letter p) (Letter p) ℂ) = 1 := by - ext u v - by_cases huv : u=v - · subst v - simp [densityPower] - · have hi : ∃ i, u i ≠ v i := Function.ne_iff.mp huv - obtain ⟨i,hi⟩ := hi - simp only [densityPower,Matrix.one_apply,ite_eq_right huv] - exact Finset.prod_eq_zero (Finset.mem_univ i) (ite_eq_right hi) - -lemma densityPower_smul {p : ℕ} (l : ℕ) (c : ℂ) (r : Matrix (Letter p) (Letter p) ℂ) : - densityPower l (c • r) = c^l • densityPower l r := by - ext u v - simp [densityPower,Finset.prod_mul_distrib] - -lemma uniformDensity_power (p l : ℕ) (hp : 0 < p) : - densityPower l (uniformDensity p hp).val = (((2*p : ℕ) : ℂ)^l)⁻¹ • 1 := by - change densityPower l ((((2*p : ℕ) : ℂ)⁻¹) • 1) = _ - rw [densityPower_smul,densityPower_one,inv_pow] - -lemma small_power_le (s p l : ℕ) (hps : p ≤ s) (hl : l ≤ (2*p)*(2*p)) : - (2*p)^l ≤ (s+1)^(8*p^2) := by - have hb : 2*p ≤ (s+1)^2 := by nlinarith - calc - _ ≤ ((s+1)^2)^l := Nat.pow_le_pow_left hb l - _ = (s+1)^(2*l) := by rw [pow_mul] - _ ≤ _ := Nat.pow_le_pow_right (by omega) (by nlinarith) - -/- Small slot counts, including zero, require no exceptional-sector chart. -/ -theorem density_domination_small (s p l : ℕ) (hp : 0 < p) (hps : p ≤ s) (hls : l ≤ s) - (hl : l ≤ (2*p)*(2*p)) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - ∃ μ : Measure (EvenDensity p), IsProbabilityMeasure μ ∧ - (((ρ.dimension : ℂ) * ((s+1 : ℕ) : ℂ)^(12*p^2)) • - (∫ r : EvenDensity p, densityPower l r.val ∂μ) - isotypic (p := p) ρ).PosSemidef := by - refine ⟨Measure.dirac (uniformDensity p hp),inferInstance,?_⟩ - rw [integral_dirac,uniformDensity_power,smul_smul] - have hP := trace_domination (isotypic (p := p) ρ) (isotypic_posSemidef ρ) - apply domination_pad _ 1 _ _ Matrix.PosSemidef.one _ hP - have hc0 : (((2*p : ℕ) : ℂ)^l) ≠ 0 := pow_ne_zero _ (Nat.cast_ne_zero.mpr (by omega)) - have hi : (0 : ℂ) ≤ (((2*p : ℕ) : ℂ)^l)⁻¹ := by positivity - have hh := mul_le_mul_of_nonneg_right (show (((2*p : ℕ) : ℂ)^l) ≤ - ((s+1 : ℕ) : ℂ)^(8*p^2) by exact_mod_cast small_power_le s p l hps hl) hi - rw [mul_inv_cancel₀ hc0] at hh - calc - _ ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2) := isotypic_trace_le s p l hls ρ - _ ≤ ((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2)) * - (((s+1 : ℕ) : ℂ)^(8*p^2)*(((2*p : ℕ) : ℂ)^l)⁻¹) := by - simpa only [mul_one] using mul_le_mul_of_nonneg_left hh - (show (0 : ℂ) ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2) by positivity) - _ = _ := by rw [← mul_assoc,mul_assoc (ρ.dimension : ℂ),← pow_add]; congr 3; ring - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open PositiveTensor MeasureTheory - -lemma domination_coefficient (D s p : ℕ) (hD : 0 < D) : - (Complex.ofReal (Real.exp (Real.log D+41*p^2*Real.log (s+1)))) = - (D : ℂ)*((s+1 : ℕ) : ℂ)^(41*p^2) := by - have hD' : (0 : ℝ) < D := by exact_mod_cast hD - have hs : (0 : ℝ) < s+1 := by positivity - rw [Real.exp_add,Real.exp_log hD'] - have he : (41 : ℝ)*p^2*Real.log (s+1) = ((41*p^2 : ℕ) : ℝ)*Real.log (s+1) := by push_cast; ring - rw [he,Real.exp_nat_mul,Real.exp_log hs] - push_cast - rfl - -/- Source05 equation13, with a concrete absolute constant. The measure is -constructed from finite empirical phase mixtures, not an added hypothesis. -/ -theorem signed_density_domination : Domination := by - refine ⟨41,by norm_num,?_⟩ - intro s p hp hps l hls ρ - have hp0 : 0 < p := by omega - rw [domination_coefficient ρ.dimension s p ρ.positive] - by_cases hl : (2*p)*(2*p) < l - · exact density_domination_large s p l hp0 hps hls hl ρ - · obtain ⟨μ,hμ,h⟩ := density_domination_small s p l hp0 hps hls (by omega) ρ - refine ⟨μ,hμ,?_⟩ - have hM : (∫ r : EvenDensity p, densityPower l r.val ∂μ).PosSemidef := by - -- Positivity of the integral follows from the explicitly proved lower - -- bound by a PSD projection; no measurability of arbitrary kernels is needed. - have ha : 0 < (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(12*p^2) := by - exact_mod_cast mul_pos (show (0 : ℝ) < ρ.dimension by exact_mod_cast ρ.positive) - (pow_pos (show (0 : ℝ) < s+1 by positivity) _) - have hh := h.add (isotypic_posSemidef ρ) - rw [sub_add_cancel] at hh - have hc : (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(12*p^2) ≠ 0 := ne_of_gt ha - have hh' := hh.smul (le_of_lt (inv_pos.mpr ha)) - rwa [smul_smul,inv_mul_cancel₀ hc,one_smul] at hh' - apply domination_pad _ _ _ _ hM _ h - apply mul_le_mul_of_nonneg_left _ (by positivity) - have he : 12*p^2 ≤ 41*p^2 := by omega - exact_mod_cast Nat.pow_le_pow_right (show 0 < s+1 by omega) he - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open PositiveTensor - -lemma finite_profile_domination (s p l : ℕ) (hp : 0 < p) (hps : p ≤ s) (hls : l ≤ s) - (hl : (2*p)*(2*p) < l) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - (((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(41*p^2)) • - ((Fintype.card (DensityProfile p l) : ℂ)⁻¹ • rawProfileDensity s p l hp hl) - - isotypic (p := p) ρ).PosSemidef := by - let : Nonempty (DensityProfile p l) := densityProfile_nonempty hp - let A : commutant p l := ⟨isotypic ρ,isotypic_mem_commutant ρ⟩ - have h := commutant_covariance_domination s p l hp hps hls hl A - change ((_ * _) • _ - isotypic ρ * (isotypic ρ).conjTranspose).PosSemidef at h - simp only [A,isotypic_self_mul] at h - have hcard : Fintype.card (DensityProfile p l) ≤ (s+1)^(12*p^2) := - (densityProfile_card_le p l).trans (Nat.pow_le_pow_left (Nat.add_le_add_right hls 1) _) - have hc0 : (Fintype.card (DensityProfile p l) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - have hbig : ((s+1 : ℕ) : ℂ)^(12*p^2) * (Fintype.card (DensityProfile p l) : ℂ)⁻¹ ≥ 1 := by - have hi : (0 : ℂ) ≤ (Fintype.card (DensityProfile p l) : ℂ)⁻¹ := by positivity - have hh := mul_le_mul_of_nonneg_right (show (Fintype.card (DensityProfile p l) : ℂ) ≤ - ((s+1 : ℕ) : ℂ)^(12*p^2) by exact_mod_cast hcard) hi - simpa only [mul_inv_cancel₀ hc0] using hh - rw [smul_smul] - apply domination_pad _ _ _ _ (rawProfileDensity_posSemidef s p l hp hl) _ h - calc - _ ≤ ((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2)) * ((s+1 : ℕ) : ℂ)^(25*p^2) := - mul_le_mul_of_nonneg_right (isotypic_trace_le s p l hls ρ) (by positivity) - _ = (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(29*p^2) := by - rw [mul_assoc,← pow_add]; congr 2; ring - _ ≤ ((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(29*p^2)) * - (((s+1 : ℕ) : ℂ)^(12*p^2) * (Fintype.card (DensityProfile p l) : ℂ)⁻¹) := by - have hh := mul_le_mul_of_nonneg_left hbig - (show (0 : ℂ) ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(29*p^2) by positivity) - simpa only [mul_one] using hh - _ = _ := by - rw [← mul_assoc,mul_assoc (ρ.dimension : ℂ),← pow_add] - congr 3; ring - -lemma finite_uniform_domination (s p l : ℕ) (hp : 0 < p) (hps : p ≤ s) (hls : l ≤ s) - (hl : l ≤ (2*p)*(2*p)) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - (((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(12*p^2)) • - densityPower l (uniformDensity p hp).val-isotypic (p := p) ρ).PosSemidef := by - rw [uniformDensity_power,smul_smul] - have hP := trace_domination (isotypic (p := p) ρ) (isotypic_posSemidef ρ) - apply domination_pad _ 1 _ _ Matrix.PosSemidef.one _ hP - have hc0 : (((2*p : ℕ) : ℂ)^l) ≠ 0 := pow_ne_zero _ (Nat.cast_ne_zero.mpr (by omega)) - have hi : (0 : ℂ) ≤ (((2*p : ℕ) : ℂ)^l)⁻¹ := by positivity - have hh := mul_le_mul_of_nonneg_right (show (((2*p : ℕ) : ℂ)^l) ≤ - ((s+1 : ℕ) : ℂ)^(8*p^2) by exact_mod_cast small_power_le s p l hps hl) hi - rw [mul_inv_cancel₀ hc0] at hh - calc - _ ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2) := isotypic_trace_le s p l hls ρ - _ ≤ ((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2)) * - (((s+1 : ℕ) : ℂ)^(8*p^2)*(((2*p : ℕ) : ℂ)^l)⁻¹) := by - simpa only [mul_one] using mul_le_mul_of_nonneg_left hh - (show (0 : ℂ) ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2) by positivity) - _ = _ := by rw [← mul_assoc,mul_assoc (ρ.dimension : ℂ),← pow_add]; congr 3; ring - -/- Finite (not a hypothetical measure) version of source05:eq13. -/ -theorem finite_density_domination (s p l : ℕ) (hp : 0 < p) (hps : p ≤ s) (hls : l ≤ s) - (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - ∃ (I : Type) (_ : Fintype I) (_ : Nonempty I) (r : I → EvenDensity p), - (((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(41*p^2)) • - ((Fintype.card I : ℂ)⁻¹ • ∑ i, densityPower l (r i).val)-isotypic (p := p) ρ).PosSemidef := by - by_cases hl : (2*p)*(2*p) uniformDensity p hp,?_⟩ - simp only [Fintype.card_punit,Nat.cast_one,inv_one,Finset.univ_unique,Finset.sum_singleton,one_smul] - apply domination_pad _ _ _ _ (densityPower_posSemidef _ _ (uniformDensity p hp).property.1) _ - (finite_uniform_domination s p l hp hps hls (by omega) ρ) - apply mul_le_mul_of_nonneg_left _ (by positivity) - exact_mod_cast Nat.pow_le_pow_right (show 0 < s+1 by omega) (show 12*p^2≤41*p^2 by omega) -end CoordinateSweeps.SignedTensor - -end -end -end -end -open scoped Matrix.Norms.L2Operator - -end OAI +import Mathlib +import OAI.RepresentationTheory.SignedTensor.Basic +import OAI.RepresentationTheory.Tensor.Postselection +import OAI.Analysis.Matrix.TensorMoment + +namespace OAI + +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ComplexConjugate Matrix.Norms.L2Operator +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ComplexOrder MatrixOrder +attribute [local instance] Classical.propDecidable + +namespace CoordinateSweeps.SignedTensor +open PositiveTensor + +/- Partial-trace invariance of the actual regrouping signs on each fixed +exception sector. No assumption of complex conditional probabilities occurs. -/ +theorem partialTrace_regroup {p l : ℕ} (E : Finset (Fin l)) + (v : Word p l × Word p l → ℂ) + (hv : ∀ u w, v (u,w) ≠ 0 → ∀ i, + (odd (u i) ↔ ¬ odd (w i)) ↔ i ∈ E) : + partialTrace (PositiveTensor.outer (fun uw => regroupPhase uw.1 uw.2 * v uw)) = + partialTrace (PositiveTensor.outer v) := by + ext u u' + apply Finset.sum_congr rfl + intro w _ + change (regroupPhase u w * v (u,w)) * star (regroupPhase u' w * v (u',w)) = + v (u,w)*star (v (u',w)) + by_cases hu : v (u,w) = 0 + · simp [hu] + by_cases hu' : v (u',w) = 0 + · simp [hu'] + have he : regroupPhase u w = regroupPhase u' w := by + apply regroupPhase_of_same_parity + intro i + have hi := hv u w hu i + have hi' := hv u' w hu' i + tauto + rw [star_mul,regroupPhase_star,he] + calc + _ = (regroupPhase u' w * regroupPhase u' w) * (v (u,w)*star (v (u',w))) := by ring + _ = _ := by rw [regroupPhase_square,one_mul] + +abbrev Pair (p : ℕ) := Letter p × Letter p +abbrev MatchedPair (p : ℕ) := {a : Pair p // odd a.1 ↔ odd a.2} + +/- Valid pinned exceptional data. Injectivity is essential: it is supplied +by the proved repeated-mismatch cancellation, not imposed on the kernel. -/ +structure ExceptionPattern (p l : ℕ) where + sites : Finset (Fin l) + pair : sites → Pair p + mismatch : ∀ i, odd (pair i).1 ↔ ¬ odd (pair i).2 + injective : Function.Injective pair + deriving Fintype + +/- Every nonzero commuting matrix entry has literal valid exceptional data. -/ +def entryPattern {p l : ℕ} (A : commutant p l) (u w : Word p l) (h : A.val u w ≠ 0) : + ExceptionPattern p l where + sites := mismatchSlots u w + pair i := (u i.val,w i.val) + mismatch i := (Finset.mem_filter.mp i.property).2 + injective := by + intro i j he + apply Subtype.ext + by_contra hij + exact h (commutant_entry_zero_repeated_mismatch A u w i.val j.val hij + (congrArg Prod.fst he) (congrArg Prod.snd he) (Finset.mem_filter.mp i.property).2) + +namespace ExceptionPattern +variable {p l : ℕ} + +def encode (F : ExceptionPattern p l) (a : Pair p) : Option (Fin l) := + if h : ∃ i : F.sites, F.pair i = a then some (Classical.choose h).val else none + +lemma encode_eq_some (F : ExceptionPattern p l) (a : Pair p) (i : Fin l) : + F.encode a = some i ↔ ∃ hi : i ∈ F.sites, F.pair ⟨i,hi⟩ = a := by + unfold encode + split_ifs with h + · constructor + · intro he + have hi := Option.some.inj he + subst i + exact ⟨(Classical.choose h).property, Classical.choose_spec h⟩ + · rintro ⟨hi,he⟩ + have hh : Classical.choose h = ⟨i,hi⟩ := F.injective ((Classical.choose_spec h).trans he.symm) + rw [hh] + · constructor + · intro he; cases he + · rintro ⟨hi,he⟩ + exact (h ⟨⟨i,hi⟩,he⟩).elim + +lemma mem_sites_iff (F : ExceptionPattern p l) (i : Fin l) : + i ∈ F.sites ↔ ∃ a, F.encode a = some i := by + constructor + · intro hi + exact ⟨F.pair ⟨i,hi⟩,(F.encode_eq_some _ i).mpr ⟨hi,rfl⟩⟩ + · rintro ⟨a,ha⟩ + exact ((F.encode_eq_some a i).mp ha).choose + +lemma encode_injective : Function.Injective (encode (p := p) (l := l)) := by + intro F G he + have hs : F.sites = G.sites := by + ext i + rw [F.mem_sites_iff,G.mem_sites_iff] + simp only [he] + cases F with | mk E f hf hfi => + cases G with | mk E' g hg hgi => + dsimp at hs + subst E' + have hp : f = g := by + funext i + have hh : (ExceptionPattern.mk E f hf hfi).encode (f i) = some i.val := + ((ExceptionPattern.mk E f hf hfi).encode_eq_some _ _).mpr ⟨i.property,rfl⟩ + rw [congrFun he (f i)] at hh + obtain ⟨hi,hv⟩ := ((ExceptionPattern.mk E g hg hgi).encode_eq_some _ _).mp hh + exact hv.symm + subst g + rfl + +lemma card_le : Fintype.card (ExceptionPattern p l) ≤ (l+1)^((2*p)*(2*p)) := by + have hc := Fintype.card_le_of_injective (encode (p := p) (l := l)) encode_injective + simpa only [Fintype.card_fun,Fintype.card_option,Fintype.card_fin, + Fintype.card_prod] using hc + +lemma sites_card_le (F : ExceptionPattern p l) : F.sites.card ≤ (2*p)*(2*p) := by + have hc := Fintype.card_le_of_injective F.pair F.injective + simpa only [Fintype.card_coe,Fintype.card_prod,Fintype.card_fin] using hc + +/- Slots not occupied by a pinned exceptional symbol. -/ +abbrev Free (F : ExceptionPattern p l) := {i : Fin l // i ∉ F.sites} +abbrev FreeWord (F : ExceptionPattern p l) := F.Free → MatchedPair p + +def fillPair (F : ExceptionPattern p l) (x : F.FreeWord) (i : Fin l) : Pair p := + if hi : i ∈ F.sites then F.pair ⟨i,hi⟩ else (x ⟨i,hi⟩).val + +def fill (F : ExceptionPattern p l) (x : F.FreeWord) : Word p l × Word p l := + (fun i => (F.fillPair x i).1, fun i => (F.fillPair x i).2) + +lemma fillPair_at_pin (F : ExceptionPattern p l) (x : F.FreeWord) (i : F.sites) : + F.fillPair x i.val = F.pair i := by simp [fillPair,i.property] + +lemma fillPair_at_free (F : ExceptionPattern p l) (x : F.FreeWord) (i : F.Free) : + F.fillPair x i.val = (x i).val := by simp [fillPair,i.property] + +lemma fill_mismatch_iff (F : ExceptionPattern p l) (x : F.FreeWord) (i : Fin l) : + (odd ((F.fill x).1 i) ↔ ¬ odd ((F.fill x).2 i)) ↔ i ∈ F.sites := by + change (odd (F.fillPair x i).1 ↔ ¬ odd (F.fillPair x i).2) ↔ _ + by_cases hi : i ∈ F.sites + · rw [show F.fillPair x i = F.pair ⟨i,hi⟩ from F.fillPair_at_pin x ⟨i,hi⟩] + exact iff_of_true (F.mismatch ⟨i,hi⟩) hi + · rw [show F.fillPair x i = (x ⟨i,hi⟩).val from F.fillPair_at_free x ⟨i,hi⟩] + have hm := (x ⟨i,hi⟩).property + tauto + +lemma fill_injective (F : ExceptionPattern p l) : Function.Injective F.fill := by + intro x y he + funext i + apply Subtype.ext + have hh : F.fillPair x i.val = F.fillPair y i.val := + Prod.ext (congrFun (congrArg Prod.fst he) i.val) (congrFun (congrArg Prod.snd he) i.val) + simpa only [F.fillPair_at_free] using hh + +lemma fill_disjoint {F G : ExceptionPattern p l} (x : F.FreeWord) (y : G.FreeWord) + (he : F.fill x = G.fill y) : F = G := by + have hs : F.sites = G.sites := by + ext i + rw [← F.fill_mismatch_iff x i,← G.fill_mismatch_iff y i,he] + cases F with | mk E f hf hfi => + cases G with | mk E' g hg hgi => + dsimp at hs + subst E' + have hp : f = g := by + funext i + have hh : (ExceptionPattern.mk E f hf hfi).fillPair x i.val = + (ExceptionPattern.mk E g hg hgi).fillPair y i.val := + Prod.ext (congrFun (congrArg Prod.fst he) i.val) (congrFun (congrArg Prod.snd he) i.val) + simpa only [fillPair_at_pin] using hh + subst g + rfl + +lemma entry_in_range (A : commutant p l) (u w : Word p l) (h : A.val u w ≠ 0) : + ∃ x : (entryPattern A u w h).FreeWord, (entryPattern A u w h).fill x = (u,w) := by + let F := entryPattern A u w h + let x : F.FreeWord := fun i => ⟨(u i.val,w i.val),by + have hi : i.val ∉ mismatchSlots u w := i.property + have hm : ¬ (odd (u i.val) ↔ ¬ odd (w i.val)) := by + simpa only [mismatchSlots,Finset.mem_filter,Finset.mem_univ,true_and] using hi + tauto⟩ + refine ⟨x,?_⟩ + have he (i : Fin l) : F.fillPair x i = (u i,w i) := by + unfold fillPair + split_ifs <;> rfl + exact Prod.ext (funext fun i => congrArg Prod.fst (he i)) + (funext fun i => congrArg Prod.snd (he i)) + +/- Extend a permutation of the free slots by the identity on the exceptions. -/ +def extendPerm (F : ExceptionPattern p l) (σ : Equiv.Perm F.Free) : Equiv.Perm (Fin l) := + Equiv.Perm.ofSubtype σ + +lemma extendPerm_pin (F : ExceptionPattern p l) (σ : Equiv.Perm F.Free) (i : F.sites) : + F.extendPerm σ i.val = i.val := by + simp [extendPerm,Equiv.Perm.ofSubtype_apply_of_not_mem,i.property] + +lemma extendPerm_free (F : ExceptionPattern p l) (σ : Equiv.Perm F.Free) (i : F.Free) : + F.extendPerm σ i.val = (σ i).val := by + exact Equiv.Perm.ofSubtype_apply_of_mem σ i.property + +lemma fill_transport (F : ExceptionPattern p l) (σ : Equiv.Perm F.Free) (x : F.FreeWord) : + F.fill (fun i => x (σ⁻¹ i)) = + (wordPerm (F.extendPerm σ) (F.fill x).1, wordPerm (F.extendPerm σ) (F.fill x).2) := by + have hinv : (F.extendPerm σ)⁻¹ = F.extendPerm σ⁻¹ := by + simp only [extendPerm,map_inv] + have he (i : Fin l) : F.fillPair (fun i => x (σ⁻¹ i)) i = + F.fillPair x ((F.extendPerm σ)⁻¹ i) := by + rw [hinv] + by_cases hi : i ∈ F.sites + · rw [show F.extendPerm σ⁻¹ i = i from F.extendPerm_pin σ⁻¹ ⟨i,hi⟩] + simp [fillPair,hi] + · rw [show F.extendPerm σ⁻¹ i = (σ⁻¹ ⟨i,hi⟩).val from F.extendPerm_free σ⁻¹ ⟨i,hi⟩] + rw [show F.fillPair (fun i => x (σ⁻¹ i)) i = (x (σ⁻¹ ⟨i,hi⟩)).val from + F.fillPair_at_free (fun i => x (σ⁻¹ i)) ⟨i,hi⟩,F.fillPair_at_free] + exact Prod.ext (funext fun i => congrArg Prod.fst (he i)) + (funext fun i => congrArg Prod.snd (he i)) + +def purified (F : ExceptionPattern p l) (A : commutant p l) (x : F.FreeWord) : ℂ := + regroupPhase (F.fill x).1 (F.fill x).2 * A.val (F.fill x).1 (F.fill x).2 + +lemma purified_invariant (F : ExceptionPattern p l) (A : commutant p l) + (σ : Equiv.Perm F.Free) (x : F.FreeWord) : + F.purified A (fun i => x (σ⁻¹ i)) = F.purified A x := by + unfold purified + rw [F.fill_transport] + apply regrouped_commutant_invariant + intro i hi + exact F.extendPerm_pin σ ⟨i,(F.fill_mismatch_iff x i).mp hi⟩ + +end ExceptionPattern +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor.ExceptionPattern +open PositiveTensor +variable {p l : ℕ} + +def embedding (F : ExceptionPattern p l) : F.FreeWord ↪ (Word p l × Word p l) := + ⟨F.fill,F.fill_injective⟩ + +def component (F : ExceptionPattern p l) (A : commutant p l) (uw : Word p l × Word p l) : ℂ := + if uw ∈ Set.range F.fill then A.val uw.1 uw.2 else 0 + +lemma component_image (F : ExceptionPattern p l) (A : commutant p l) (x : F.FreeWord) : + F.component A (F.fill x) = A.val (F.fill x).1 (F.fill x).2 := by + simp [component] + +lemma component_inclusion (F : ExceptionPattern p l) (A : commutant p l) : + F.component A = (inclusion F.embedding).mulVec (fun x => A.val (F.fill x).1 (F.fill x).2) := by + funext q + by_cases hq : q ∈ Set.range F.fill + · obtain ⟨x,rfl⟩ := hq + have hh := inclusion_mulVec_image F.embedding (fun x => A.val (F.fill x).1 (F.fill x).2) x + change (inclusion F.embedding).mulVec (fun x => A.val (F.fill x).1 (F.fill x).2) (F.fill x) = _ at hh + exact (F.component_image A x).trans hh.symm + · rw [show F.component A q = 0 from ite_eq_right hq] + exact (inclusion_mulVec_notin F.embedding _ q hq).symm + +lemma purified_inclusion (F : ExceptionPattern p l) (A : commutant p l) : + (inclusion F.embedding).mulVec (F.purified A) = + fun q => regroupPhase q.1 q.2 * F.component A q := by + funext q + by_cases hq : q ∈ Set.range F.fill + · obtain ⟨x,rfl⟩ := hq + have hh := inclusion_mulVec_image F.embedding (F.purified A) x + change (inclusion F.embedding).mulVec (F.purified A) (F.fill x) = _ at hh + rw [hh,F.component_image] + rfl + · rw [inclusion_mulVec_notin F.embedding _ q hq] + simp [component,hq] + +lemma component_partialTrace (F : ExceptionPattern p l) (A : commutant p l) : + partialTrace (PositiveTensor.outer ((inclusion F.embedding).mulVec (F.purified A))) = + partialTrace (PositiveTensor.outer (F.component A)) := by + rw [F.purified_inclusion] + apply partialTrace_regroup F.sites + intro u w h i + have hq : (u,w) ∈ Set.range F.fill := by + by_contra hn + exact h (ite_eq_right hn) + obtain ⟨x,hx⟩ := hq + have he := F.fill_mismatch_iff x i + simpa only [hx] using he + +lemma component_sum (A : commutant p l) : + ∑ F : ExceptionPattern p l, F.component A = fun q => A.val q.1 q.2 := by + funext q + rw [Finset.sum_apply] + by_cases hq : A.val q.1 q.2 = 0 + · simp [component,hq] + · let F := entryPattern A q.1 q.2 hq + obtain ⟨x,hx⟩ := entry_in_range A q.1 q.2 hq + have hmem : q ∈ Set.range F.fill := ⟨x,hx⟩ + rw [Finset.sum_eq_single F] + · exact ite_eq_left hmem + · intro G _ hG + apply ite_eq_right + rintro ⟨y,hy⟩ + exact hG (fill_disjoint y x (hy.trans hx.symm)) + · simp + +lemma component_square_sum (A : commutant p l) (q : Word p l × Word p l) : + ∑ F : ExceptionPattern p l, F.component A q * star (F.component A q) = + A.val q.1 q.2 * star (A.val q.1 q.2) := by + by_cases hq : A.val q.1 q.2 = 0 + · simp [component,hq] + · let F := entryPattern A q.1 q.2 hq + obtain ⟨x,hx⟩ := entry_in_range A q.1 q.2 hq + have hmem : q ∈ Set.range F.fill := ⟨x,hx⟩ + rw [Finset.sum_eq_single F] + · simp [component,hmem] + · intro G _ hG + have hn : q ∉ Set.range G.fill := by + rintro ⟨y,hy⟩ + exact hG (fill_disjoint y x (hy.trans hx.symm)) + simp [component,hn] + · simp + +lemma purified_trace (F : ExceptionPattern p l) (A : commutant p l) : + Matrix.trace (OrdinaryTensor.outer (F.purified A)) = + Matrix.trace (PositiveTensor.outer (F.component A)) := by + rw [show OrdinaryTensor.outer (F.purified A) = Matrix.vecMulVec (F.purified A) (star (F.purified A)) from rfl, + ← inclusion_trace_outer F.embedding,F.purified_inclusion] + apply Finset.sum_congr rfl + intro q _ + change (regroupPhase q.1 q.2 * F.component A q) * + star (regroupPhase q.1 q.2 * F.component A q) = F.component A q * star (F.component A q) + rw [star_mul,regroupPhase_star] + calc + _ = (regroupPhase q.1 q.2 * regroupPhase q.1 q.2) * (F.component A q * star (F.component A q)) := by ring + _ = _ := by rw [regroupPhase_square,one_mul] + +lemma sum_purified_trace (A : commutant p l) : + ∑ F : ExceptionPattern p l, Matrix.trace (OrdinaryTensor.outer (F.purified A)) = + Matrix.trace (A.val*A.val.conjTranspose) := by + simp_rw [purified_trace] + simp only [PositiveTensor.outer,Matrix.trace,Matrix.diag_apply,Matrix.vecMulVec_apply,Pi.star_apply] + rw [Finset.sum_comm] + simp_rw [component_square_sum] + simp only [Fintype.sum_prod_type,Matrix.mul_apply,Matrix.conjTranspose_apply] +end CoordinateSweeps.SignedTensor.ExceptionPattern + +namespace CoordinateSweeps.SignedTensor.ExceptionPattern +open PositiveTensor +variable {p l : ℕ} +lemma free_card (F : ExceptionPattern p l) : Fintype.card F.Free = l-F.sites.card := by + simp only [Free,Fintype.card_subtype_compl,Fintype.card_coe,Fintype.card_fin] +lemma free_card_pos (F : ExceptionPattern p l) (hl : (2*p)*(2*p) < l) : 0 < Fintype.card F.Free := by + rw [F.free_card] + exact Nat.sub_pos_of_lt (lt_of_le_of_lt F.sites_card_le hl) +lemma free_card_le (F : ExceptionPattern p l) : Fintype.card F.Free ≤ l := by + rw [F.free_card] + exact Nat.sub_le _ _ + +lemma matchedPair_nonempty (hp : 0 < p) : Nonempty (MatchedPair p) := + ⟨⟨(⟨0,by omega⟩,⟨0,by omega⟩),Iff.rfl⟩⟩ + +/- Exact domination of a pinned component by a finite product mixture on its +free slots, after the proved sign cancellation in the genuine partial trace. -/ +theorem component_postselection (F : ExceptionPattern p l) (hp : 0 < p) + (hl : (2*p)*(2*p) < l) (A : commutant p l) : + ((Matrix.trace (OrdinaryTensor.outer (F.purified A)) * + ((Fintype.card F.Free+1 : ℕ) : ℂ)^(2*Fintype.card (MatchedPair p))) • + partialTrace (inclusion F.embedding * (OrdinaryTensor.finiteMixture (I := F.Free) (A := MatchedPair p)) * (inclusion F.embedding).conjTranspose) - + partialTrace (PositiveTensor.outer (F.component A))).PosSemidef := by + let : Nonempty (MatchedPair p) := matchedPair_nonempty hp + have h := OrdinaryTensor.invariant_vector_postselection (I := F.Free) (A := MatchedPair p) (F.free_card_pos hl) + (F.purified A) (F.purified_invariant A) + have hc := h.mul_mul_conjTranspose_same (inclusion F.embedding) + rw [Matrix.mul_sub,Matrix.sub_mul,Matrix.mul_smul,Matrix.smul_mul] at hc + have ho : inclusion F.embedding * OrdinaryTensor.outer (F.purified A) * (inclusion F.embedding).conjTranspose = + PositiveTensor.outer ((inclusion F.embedding).mulVec (F.purified A)) := + mul_outer_mul_star _ _ + rw [ho] at hc + have hp := partialTrace_posSemidef _ hc + simpa only [partialTrace_sub,partialTrace_smul,F.component_partialTrace A] using hp +end CoordinateSweeps.SignedTensor.ExceptionPattern + +namespace CoordinateSweeps.SignedTensor + +def pairAmplitude {p : ℕ} (z : MatchedPair p → ℂ) : Matrix (Letter p) (Letter p) ℂ := + fun a b => if h : odd a ↔ odd b then z ⟨(a,b),h⟩ else 0 + +lemma pairAmplitude_unit_trace {p : ℕ} (z : MatchedPair p → ℂ) + (hz : ∑ a, z a * star (z a) = 1) : + Matrix.trace (pairAmplitude z * (pairAmplitude z).conjTranspose) = 1 := by + have hs := Fintype.sum_of_injective + (Subtype.val : MatchedPair p → Pair p) Subtype.val_injective + (fun a => z a * star (z a)) + (fun a : Pair p => pairAmplitude z a.1 a.2 * star (pairAmplitude z a.1 a.2)) + (by + intro a ha + have hn : ¬ (odd a.1 ↔ odd a.2) := by + intro h + exact ha ⟨⟨a,h⟩,rfl⟩ + simp [pairAmplitude,hn]) + (by intro a; simp [pairAmplitude,a.property]) + rw [hz] at hs + simpa only [Matrix.trace,Matrix.diag_apply,Matrix.mul_apply,Matrix.conjTranspose_apply, + Fintype.sum_prod_type] using hs.symm + +lemma pairAmplitude_even {p : ℕ} (z : MatchedPair p → ℂ) (a b : Letter p) + (hab : odd a ↔ ¬ odd b) : + (pairAmplitude z * (pairAmplitude z).conjTranspose) a b = 0 := by + rw [Matrix.mul_apply] + apply Finset.sum_eq_zero + intro c _ + by_cases hac : odd a ↔ odd c + · have hbc : ¬ (odd b ↔ odd c) := by tauto + simp [Matrix.conjTranspose_apply,pairAmplitude,hbc] + · simp [Matrix.conjTranspose_apply,pairAmplitude,hac] + +/- The real even one-site density obtained by the literal auxiliary partial +trace of a unit matched-pair vector. -/ +def pairDensity {p : ℕ} (z : MatchedPair p → ℂ) (hz : ∑ a, z a * star (z a) = 1) : EvenDensity p := + ⟨pairAmplitude z * (pairAmplitude z).conjTranspose, + Matrix.posSemidef_self_mul_conjTranspose _, pairAmplitude_unit_trace z hz, + pairAmplitude_even z⟩ +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +variable {p : ℕ} + +def basisDensity (a : Letter p) : Matrix (Letter p) (Letter p) ℂ := + Matrix.diagonal (fun b => if b=a then 1 else 0) + +lemma basisDensity_posSemidef (a : Letter p) : (basisDensity a).PosSemidef := by + apply Matrix.PosSemidef.diagonal + intro b + change (0 : ℂ) ≤ if b=a then _ else _ + split_ifs <;> norm_num + +lemma basisDensity_le_one (a : Letter p) : (1-basisDensity a).PosSemidef := by + have he : (1-basisDensity a) = Matrix.diagonal (fun b => if b=a then (0 : ℂ) else 1) := by + ext i j + by_cases hij : i=j + · subst j + by_cases hi : i=a <;> simp [basisDensity,Matrix.diagonal,hi] + · simp [basisDensity,Matrix.diagonal,hij] + + rw [he] + apply Matrix.PosSemidef.diagonal + intro b + change (0 : ℂ) ≤ if b=a then _ else _ + split_ifs <;> norm_num + +lemma basisDensity_trace (a : Letter p) : Matrix.trace (basisDensity a) = 1 := by + simp [basisDensity,Matrix.trace_diagonal] + +def pinAmplitude (a : Pair p) : Matrix (Letter p) (Letter p) ℂ := + fun i j => if (i,j)=a then 1 else 0 + +lemma pinAmplitude_density (a : Pair p) : pinAmplitude a * (pinAmplitude a).conjTranspose = basisDensity a.1 := by + ext i j + simp only [Matrix.mul_apply,Matrix.conjTranspose_apply,pinAmplitude] + rw [Finset.sum_eq_single a.2] + · by_cases hi : i=a.1 <;> by_cases hj : j=a.1 <;> + simp [Prod.ext_iff,hi,hj,basisDensity,Matrix.diagonal,eq_comm] + · intro k _ hk + simp [Prod.ext_iff,hk] + · simp + +def keep (s : ℕ) : ℝ := s/(s+1) +def noise (s p : ℕ) : ℝ := 1/((s+1)*(2*p)) + +lemma keep_nonneg (s : ℕ) : 0 ≤ keep s := div_nonneg (Nat.cast_nonneg _) (by positivity) +lemma noise_nonneg (s p : ℕ) : 0 ≤ noise s p := by unfold noise; positivity +lemma keep_add_noise (s p : ℕ) (hp : 0 < p) : keep s + noise s p*(2*p) = 1 := by + have hp' : (p : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr hp.ne' + have hs : (s : ℝ)+1 ≠ 0 := by positivity + unfold keep noise + field_simp + +def depolarized (s : ℕ) (r : EvenDensity p) : Matrix (Letter p) (Letter p) ℂ := + (keep s : ℂ) • r.val + (noise s p : ℂ) • 1 + +lemma depolarized_posSemidef (s : ℕ) (r : EvenDensity p) : (depolarized s r).PosSemidef := by + exact (r.property.1.smul (by exact_mod_cast keep_nonneg s)).add + (Matrix.PosSemidef.one.smul (by exact_mod_cast noise_nonneg s p)) + +lemma depolarized_trace (s : ℕ) (hp : 0 < p) (r : EvenDensity p) : Matrix.trace (depolarized s r) = 1 := by + rw [depolarized,Matrix.trace_add,Matrix.trace_smul,Matrix.trace_smul,r.property.2.1] + simp only [Matrix.trace_one,Fintype.card_fin,smul_eq_mul,mul_one] + exact_mod_cast keep_add_noise s p hp + +lemma depolarized_even (s : ℕ) (r : EvenDensity p) (i j : Letter p) + (hij : odd i ↔ ¬ odd j) : depolarized s r i j = 0 := by + have hne : i ≠ j := by intro h; subst j; tauto + simp [depolarized,Matrix.smul_apply,r.property.2.2 i j hij,hne] + +def depolarizedDensity (s : ℕ) (hp : 0 < p) (r : EvenDensity p) : EvenDensity p := + ⟨depolarized s r,depolarized_posSemidef s r,depolarized_trace s hp r,depolarized_even s r⟩ + +lemma depolarized_free (s : ℕ) (r : EvenDensity p) : + (depolarized s r - (keep s : ℂ) • r.val).PosSemidef := by + simpa only [depolarized,add_sub_cancel_left] using + (Matrix.PosSemidef.one (n := Letter p) (R := ℂ)).smul (by exact_mod_cast noise_nonneg s p) + +lemma depolarized_pin (s : ℕ) (r : EvenDensity p) (a : Letter p) : + (depolarized s r - (noise s p : ℂ) • basisDensity a).PosSemidef := by + have ht : (0 : ℂ) ≤ (keep s : ℂ) := by exact_mod_cast keep_nonneg s + have hu : (0 : ℂ) ≤ (noise s p : ℂ) := by exact_mod_cast noise_nonneg s p + have h := (r.property.1.smul ht).add ((basisDensity_le_one a).smul hu) + simpa only [depolarized,smul_sub,add_sub_assoc] using h +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open PositiveTensor +variable {p l : ℕ} + +def pinnedDensity (E : Finset (Fin l)) (a : E → Letter p) (r : EvenDensity p) : + Matrix (Word p l) (Word p l) ℂ := + productMatrix (fun i => if hi : i ∈ E then basisDensity (a ⟨i,hi⟩) else r.val) + +lemma pinnedDensity_posSemidef (E : Finset (Fin l)) (a : E → Letter p) (r : EvenDensity p) : + (pinnedDensity E a r).PosSemidef := by + apply productMatrix_posSemidef + intro i + split_ifs with hi + · exact basisDensity_posSemidef _ + · exact r.property.1 + +lemma keep_pow_lower (s n : ℕ) (hn : n ≤ s) : 1 ≤ (s+1 : ℝ) * (keep s)^n := by + have hs : (0 : ℝ) < s+1 := by positivity + have hi : (s+1 : ℝ)⁻¹ ≤ 1 := (inv_le_one₀ hs).mpr (by linarith [Nat.cast_nonneg (α := ℝ) s]) + have hb := one_add_mul_le_pow (a := -((s+1 : ℝ)⁻¹)) (by linarith : -2 ≤ -((s+1 : ℝ)⁻¹)) n + have he : (1 - (s+1 : ℝ)⁻¹) = keep s := by unfold keep; field_simp; ring + calc + 1 ≤ (s+1 : ℝ)-n := by + have hn' : (n : ℝ) ≤ s := by exact_mod_cast hn + linarith + _ = (s+1 : ℝ)*(1+n * (-((s+1 : ℝ)⁻¹))) := by field_simp; ring + _ ≤ (s+1 : ℝ)*(1+(-((s+1 : ℝ)⁻¹)))^n := mul_le_mul_of_nonneg_left hb hs.le + _ = _ := by rw [show 1+(-((s+1 : ℝ)⁻¹)) = keep s from he] + +lemma pin_coefficient_le (s p k : ℕ) (hp : 0 < p) (hps : p ≤ s) + (hk : k ≤ (2*p)*(2*p)) : + (s+1 : ℝ) * ((s+1 : ℝ)*(2*p))^k ≤ (s+1 : ℝ)^(13*p^2) := by + have hs : (1 : ℝ) ≤ s+1 := by linarith [Nat.cast_nonneg (α := ℝ) s] + have hp' : (p : ℝ) ≤ s := by exact_mod_cast hps + have ha : (2*p : ℝ) ≤ (s+1 : ℝ)^2 := by nlinarith [sq_nonneg (s : ℝ)] + have hbase : (s+1 : ℝ)*(2*p) ≤ (s+1 : ℝ)^3 := by + nlinarith [mul_le_mul_of_nonneg_left ha (by positivity : (0 : ℝ) ≤ s+1)] + have hexp : 3*k+1 ≤ 13*p^2 := by + have hp1 : 1 ≤ p*p := by nlinarith + nlinarith [hk] + calc + _ ≤ (s+1 : ℝ) * ((s+1 : ℝ)^3)^k := + mul_le_mul_of_nonneg_left (pow_le_pow_left₀ (by positivity) hbase k) (by positivity) + _ = (s+1 : ℝ)^(3*k+1) := by rw [← pow_mul,pow_succ]; ring + _ ≤ _ := pow_le_pow_right₀ hs hexp + +/- Each pinned ordinary product density is dominated by a tensor power of a +single even density, with only polynomial cost per actual exception. -/ +theorem pinned_absorption (s : ℕ) (hp : 0 < p) (hls : l ≤ s) + (E : Finset (Fin l)) (a : E → Letter p) (r : EvenDensity p) : + (((s+1 : ℝ) * ((s+1 : ℝ)*(2*p))^E.card : ℝ) : ℂ) • + densityPower l (depolarized s r) - pinnedDensity E a r |>.PosSemidef := by + let c : Fin l → ℂ := fun i => if i ∈ E then (noise s p : ℂ) else (keep s : ℂ) + let f : Fin l → Matrix (Letter p) (Letter p) ℂ := + fun i => if hi : i ∈ E then basisDensity (a ⟨i,hi⟩) else r.val + have hlocal (i : Fin l) : (c i • f i).PosSemidef := by + by_cases hi : i ∈ E + · simpa only [c,f,ite_eq_left hi,dite_eq_left hi] using + (basisDensity_posSemidef (a ⟨i,hi⟩)).smul (show (0 : ℂ) ≤ (noise s p : ℂ) by exact_mod_cast noise_nonneg s p) + · simpa only [c,f,ite_eq_right hi,dite_eq_right hi] using + r.property.1.smul (show (0 : ℂ) ≤ (keep s : ℂ) by exact_mod_cast keep_nonneg s) + have hdiff (i : Fin l) : (depolarized s r - c i • f i).PosSemidef := by + by_cases hi : i ∈ E + · simpa only [c,f,ite_eq_left hi,dite_eq_left hi] using depolarized_pin s r (a ⟨i,hi⟩) + · simpa only [c,f,ite_eq_right hi,dite_eq_right hi] using depolarized_free s r + have h := productMatrix_mono (fun i => c i • f i) (fun _ => depolarized s r) hlocal hdiff + rw [productMatrix_smul] at h + have hc : (∏ i, c i) = ((keep s)^(l-E.card) * (noise s p)^E.card : ℝ) := by + have hE : Finset.univ.filter (fun i : Fin l => i ∈ E) = E := by ext i; simp + have hC : Finset.univ.filter (fun i : Fin l => i ∉ E) = Eᶜ := by ext i; simp + simp only [c,Finset.prod_ite,hE,hC,Finset.prod_const,Finset.card_compl,Fintype.card_fin] + push_cast + ring + rw [hc] at h + let C : ℝ := (s+1 : ℝ) * ((s+1 : ℝ)*(2*p))^E.card + have hC : (0 : ℝ) ≤ C := by dsimp [C]; positivity + have hu : ((s+1 : ℝ)*(2*p))*noise s p = 1 := by + have hp' : (p : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr hp.ne' + unfold noise + field_simp + have hCW : 1 ≤ C*((keep s)^(l-E.card)*(noise s p)^E.card) := by + calc + _ ≤ (s+1 : ℝ)*(keep s)^(l-E.card) := keep_pow_lower s _ (le_trans (Nat.sub_le _ _) hls) + _ = _ := by + dsimp [C] + calc + _ = ((s+1 : ℝ)*(keep s)^(l-E.card))*((((s+1 : ℝ)*(2*p))*noise s p)^E.card) := by rw [hu,one_pow,mul_one] + _ = _ := by rw [mul_pow]; ring + have hh := h.smul (show (0 : ℂ) ≤ (C : ℂ) by exact_mod_cast hC) + have hz := (pinnedDensity_posSemidef E a r).smul + (show (0 : ℂ) ≤ ((C*((keep s)^(l-E.card)*(noise s p)^E.card)-1 : ℝ) : ℂ) by exact_mod_cast sub_nonneg.mpr hCW) + have ht := hh.add hz + change ((C : ℂ) • (densityPower l (depolarized s r) - + (((keep s)^(l-E.card)*(noise s p)^E.card : ℝ) : ℂ) • pinnedDensity E a r) + + ((C*((keep s)^(l-E.card)*(noise s p)^E.card)-1 : ℝ) : ℂ) • pinnedDensity E a r).PosSemidef at ht + change ((C : ℂ) • densityPower l (depolarized s r) - pinnedDensity E a r).PosSemidef + convert ht using 1 + simp only [smul_sub,smul_smul,Complex.ofReal_sub,Complex.ofReal_mul,Complex.ofReal_one, + sub_smul,one_smul] + module +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open PositiveTensor +variable {p l : ℕ} +theorem pinned_absorption_uniform (s : ℕ) (hp : 0 < p) (hps : p ≤ s) (hls : l ≤ s) + (E : Finset (Fin l)) (hE : E.card ≤ (2*p)*(2*p)) (a : E → Letter p) (r : EvenDensity p) : + ((((s+1 : ℝ)^(13*p^2)) : ℂ) • densityPower l (depolarized s r) - pinnedDensity E a r).PosSemidef := by + have h := pinned_absorption s hp hls E a r + have hle := pin_coefficient_le s p E.card hp hps hE + have hr : (densityPower l (depolarized s r)).PosSemidef := + productMatrix_posSemidef (fun _ : Fin l => depolarized s r) (fun _ => depolarized_posSemidef s r) + have hh := (hr.smul (show (0 : ℂ) ≤ (((s+1 : ℝ)^(13*p^2) - + (s+1 : ℝ)*((s+1 : ℝ)*(2*p))^E.card : ℝ) : ℂ) by exact_mod_cast sub_nonneg.mpr hle)).add h + convert hh using 1 + push_cast + module +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor.ExceptionPattern +open PositiveTensor +variable {p l : ℕ} + +def siteAmplitude (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) (i : Fin l) : + Matrix (Letter p) (Letter p) ℂ := + if hi : i ∈ F.sites then pinAmplitude (F.pair ⟨i,hi⟩) else pairAmplitude z + +def pairProduct (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) + (q : Word p l × Word p l) : ℂ := ∏ i, F.siteAmplitude z i (q.1 i) (q.2 i) + +lemma siteAmplitude_pin (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) (x : F.FreeWord) (i : F.sites) : + F.siteAmplitude z i.val ((F.fill x).1 i.val) ((F.fill x).2 i.val) = 1 := by + change F.siteAmplitude z i.val (F.fillPair x i.val).1 (F.fillPair x i.val).2 = 1 + rw [F.fillPair_at_pin] + simp [siteAmplitude,i.property,pinAmplitude] + +lemma siteAmplitude_free (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) (x : F.FreeWord) (i : F.Free) : + F.siteAmplitude z i.val ((F.fill x).1 i.val) ((F.fill x).2 i.val) = z (x i) := by + change F.siteAmplitude z i.val (F.fillPair x i.val).1 (F.fillPair x i.val).2 = z (x i) + rw [F.fillPair_at_free] + simp [siteAmplitude,i.property,pairAmplitude,(x i).property] + +lemma pairProduct_fill (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) (x : F.FreeWord) : + F.pairProduct z (F.fill x) = OrdinaryTensor.tensorVector z x := by + unfold pairProduct + rw [← Fintype.prod_subtype_mul_prod_subtype (fun i => i ∈ F.sites)] + simp only [F.siteAmplitude_pin,F.siteAmplitude_free,Finset.prod_const_one,one_mul] + rfl + +lemma pairProduct_nonzero (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) + (q : Word p l × Word p l) (hq : F.pairProduct z q ≠ 0) : q ∈ Set.range F.fill := by + have hi (i : Fin l) : F.siteAmplitude z i (q.1 i) (q.2 i) ≠ 0 := + (Finset.prod_ne_zero_iff.mp hq) i (Finset.mem_univ i) + have hp (i : F.sites) : (q.1 i.val,q.2 i.val) = F.pair i := by + by_contra hn + exact hi i.val (by simp [siteAmplitude,i.property,pinAmplitude,hn]) + have hf (i : F.Free) : odd (q.1 i.val) ↔ odd (q.2 i.val) := by + by_contra hn + exact hi i.val (by simp [siteAmplitude,i.property,pairAmplitude,hn]) + let x : F.FreeWord := fun i => ⟨(q.1 i.val,q.2 i.val),hf i⟩ + have he (i : Fin l) : F.fillPair x i = (q.1 i,q.2 i) := by + by_cases hi : i ∈ F.sites + · exact (F.fillPair_at_pin x ⟨i,hi⟩).trans (hp ⟨i,hi⟩).symm + · exact F.fillPair_at_free x ⟨i,hi⟩ + exact ⟨x,Prod.ext (funext fun i => congrArg Prod.fst (he i)) (funext fun i => congrArg Prod.snd (he i))⟩ + +lemma pairProduct_inclusion (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) : + (inclusion F.embedding).mulVec (OrdinaryTensor.tensorVector z) = F.pairProduct z := by + funext q + by_cases hq : q ∈ Set.range F.fill + · obtain ⟨x,rfl⟩ := hq + have hh := inclusion_mulVec_image F.embedding (OrdinaryTensor.tensorVector z) x + change (inclusion F.embedding).mulVec (OrdinaryTensor.tensorVector z) (F.fill x) = _ at hh + exact hh.trans (F.pairProduct_fill z x).symm + · rw [inclusion_mulVec_notin F.embedding _ q hq] + exact (not_ne_iff.mp (fun hh => hq (F.pairProduct_nonzero z q hh))).symm + +/- Partial tracing a filled product vector yields pinned basis densities at +the true exceptions and the same even density at every remaining slot. -/ +lemma filled_product_partialTrace (F : ExceptionPattern p l) (z : MatchedPair p → ℂ) + (hz : ∑ a, z a * star (z a) = 1) : + partialTrace (PositiveTensor.outer ((inclusion F.embedding).mulVec (OrdinaryTensor.tensorVector z))) = + pinnedDensity F.sites (fun i => (F.pair i).1) (pairDensity z hz) := by + rw [F.pairProduct_inclusion] + have he : partialTrace (PositiveTensor.outer (F.pairProduct z)) = + productMatrix (fun i => F.siteAmplitude z i * (F.siteAmplitude z i).conjTranspose) := by + ext u v + simpa only [partialTrace,PositiveTensor.outer,Matrix.vecMulVec_apply,Pi.star_apply,pairProduct] using + pair_product_partialTrace (F.siteAmplitude z) u v + rw [he] + congr 1 + funext i + by_cases hi : i ∈ F.sites + · simp only [siteAmplitude,hi,dite_eq_left,pinAmplitude_density] + · simp [siteAmplitude,hi,pairDensity] +end CoordinateSweeps.SignedTensor.ExceptionPattern + +namespace CoordinateSweeps.SignedTensor.ExceptionPattern +open PositiveTensor +variable {p l : ℕ} + +lemma purified_trace_le (F : ExceptionPattern p l) (A : commutant p l) : + Matrix.trace (OrdinaryTensor.outer (F.purified A)) ≤ Matrix.trace (A.val*A.val.conjTranspose) := by + rw [← sum_purified_trace A] + exact Finset.single_le_sum (fun G _ => OrdinaryTensor.outer_trace_nonneg (G.purified A)) (Finset.mem_univ F) + +abbrev Data (F : ExceptionPattern p l) := + OrdinaryTensor.Histogram F.Free (MatchedPair p) × OrdinaryTensor.PhaseSpace F.Free (MatchedPair p) + +def dataDensity (F : ExceptionPattern p l) (hn : 0 < Fintype.card F.Free) (d : F.Data) : EvenDensity p := + pairDensity (OrdinaryTensor.empiricalVector d.1 d.2) (OrdinaryTensor.empiricalVector_unit hn d.1 d.2) + +def dataPoint (F : ExceptionPattern p l) (s : ℕ) (hp : 0 < p) + (hn : 0 < Fintype.card F.Free) (d : F.Data) : EvenDensity p := + depolarizedDensity s hp (F.dataDensity hn d) + +def rawPinned (F : ExceptionPattern p l) (hn : 0 < Fintype.card F.Free) : + Matrix (Word p l) (Word p l) ℂ := + ∑ d : F.Data, pinnedDensity F.sites (fun i => (F.pair i).1) (F.dataDensity hn d) + +def rawDensity (F : ExceptionPattern p l) (s : ℕ) (hp : 0 < p) (hn : 0 < Fintype.card F.Free) : + Matrix (Word p l) (Word p l) ℂ := + ∑ d : F.Data, densityPower l (F.dataPoint s hp hn d).val + +lemma rawPinned_posSemidef (F : ExceptionPattern p l) (hn : 0 < Fintype.card F.Free) : + (F.rawPinned hn).PosSemidef := by + exact Matrix.posSemidef_sum _ (fun d _ => pinnedDensity_posSemidef _ _ _) +lemma rawDensity_posSemidef (F : ExceptionPattern p l) (s : ℕ) (hp : 0 < p) (hn : 0 < Fintype.card F.Free) : + (F.rawDensity s hp hn).PosSemidef := by + exact Matrix.posSemidef_sum _ (fun d _ => densityPower_posSemidef _ _ (F.dataPoint s hp hn d).property.1) + +lemma rawMixture_partialTrace (F : ExceptionPattern p l) (hn : 0 < Fintype.card F.Free) : + partialTrace (inclusion F.embedding * + (OrdinaryTensor.rawMixture (I := F.Free) (A := MatchedPair p)) * (inclusion F.embedding).conjTranspose) = + F.rawPinned hn := by + unfold OrdinaryTensor.rawMixture rawPinned + rw [Fintype.sum_prod_type] + simp only [Matrix.mul_sum,Matrix.sum_mul,partialTrace_sum] + apply Finset.sum_congr rfl + intro h _ + apply Finset.sum_congr rfl + intro t _ + have he := congrArg (partialTrace (J := Word p l) (K := Word p l)) + (mul_outer_mul_star (inclusion F.embedding) + (OrdinaryTensor.tensorVector (OrdinaryTensor.empiricalVector h t))) + exact he.trans (F.filled_product_partialTrace _ (OrdinaryTensor.empiricalVector_unit hn h t)) + +lemma rawPinned_domination (F : ExceptionPattern p l) (hp : 0 < p) (hn : 0 < Fintype.card F.Free) : + (F.rawPinned hn - partialTrace (inclusion F.embedding * + (OrdinaryTensor.finiteMixture (I := F.Free) (A := MatchedPair p)) * (inclusion F.embedding).conjTranspose)).PosSemidef := by + let : Nonempty (MatchedPair p) := matchedPair_nonempty hp + have h := (OrdinaryTensor.rawMixture_domination (I := F.Free) (A := MatchedPair p)).mul_mul_conjTranspose_same (inclusion F.embedding) + rw [Matrix.mul_sub,Matrix.sub_mul] at h + have hh := partialTrace_posSemidef _ h + simpa only [partialTrace_sub,F.rawMixture_partialTrace hn] using hh + +lemma rawPinned_absorption (F : ExceptionPattern p l) (s : ℕ) (hp : 0 < p) + (hps : p ≤ s) (hls : l ≤ s) (hn : 0 < Fintype.card F.Free) : + ((((s+1 : ℝ)^(13*p^2)) : ℂ) • F.rawDensity s hp hn - F.rawPinned hn).PosSemidef := by + have hh := Matrix.posSemidef_sum Finset.univ (fun d _ => + pinned_absorption_uniform s hp hps hls F.sites F.sites_card_le + (fun i => (F.pair i).1) (F.dataDensity hn d)) + simpa only [Finset.sum_sub_distrib,← Finset.smul_sum,rawPinned,rawDensity,dataPoint,depolarizedDensity] using hh +end CoordinateSweeps.SignedTensor.ExceptionPattern + +namespace CoordinateSweeps.SignedTensor +open PositiveTensor +variable {p l : ℕ} + +lemma matchedPair_card_le (p : ℕ) : Fintype.card (MatchedPair p) ≤ (2*p)*(2*p) := by + simpa only [Pair,Fintype.card_prod,Letter,Fintype.card_fin] using + (Fintype.card_subtype_le (fun a : Pair p => odd a.1 ↔ odd a.2)) + +namespace ExceptionPattern + +def empty (p l : ℕ) : ExceptionPattern p l where + sites := ∅ + pair i := False.elim (Finset.notMem_empty i.val i.property) + mismatch i := False.elim (Finset.notMem_empty i.val i.property) + injective i := False.elim (Finset.notMem_empty i.val i.property) + +instance : Nonempty (ExceptionPattern p l) := ⟨empty p l⟩ + +lemma data_card_le (F : ExceptionPattern p l) : Fintype.card F.Data ≤ (l+1)^(8*p^2) := by + have hh := OrdinaryTensor.histogram_card_le (I := F.Free) (A := MatchedPair p) + have ht : Fintype.card (OrdinaryTensor.PhaseSpace F.Free (MatchedPair p)) = + (Fintype.card F.Free+1)^Fintype.card (MatchedPair p) := by + simp [OrdinaryTensor.PhaseSpace] + rw [Fintype.card_prod,ht] + calc + _ ≤ (Fintype.card F.Free+1)^(2*Fintype.card (MatchedPair p)) := by + rw [two_mul (Fintype.card (MatchedPair p)),pow_add] + exact Nat.mul_le_mul_right _ hh + _ ≤ (l+1)^(2*Fintype.card (MatchedPair p)) := + Nat.pow_le_pow_left (Nat.add_le_add_right F.free_card_le 1) _ + _ ≤ _ := Nat.pow_le_pow_right (by omega) (by nlinarith [matchedPair_card_le p]) + +lemma free_power_le (F : ExceptionPattern p l) (s : ℕ) (hls : l ≤ s) : + (Fintype.card F.Free+1 : ℕ)^(2*Fintype.card (MatchedPair p)) ≤ (s+1)^(8*p^2) := by + calc + _ ≤ (s+1)^(2*Fintype.card (MatchedPair p)) := + Nat.pow_le_pow_left (Nat.add_le_add_right (F.free_card_le.trans hls) 1) _ + _ ≤ _ := Nat.pow_le_pow_right (by omega) (by nlinarith [matchedPair_card_le p]) + +lemma component_uniform_domination (F : ExceptionPattern p l) (s : ℕ) (hp : 0 < p) + (hps : p ≤ s) (hls : l ≤ s) (hl : (2*p)*(2*p) < l) (A : commutant p l) : + ((Matrix.trace (A.val*A.val.conjTranspose) * ((s+1 : ℕ) : ℂ)^(21*p^2)) • + F.rawDensity s hp (F.free_card_pos hl) - partialTrace (PositiveTensor.outer (F.component A))).PosSemidef := by + let hn := F.free_card_pos hl + let M := partialTrace (inclusion F.embedding * + (OrdinaryTensor.finiteMixture (I := F.Free) (A := MatchedPair p)) * (inclusion F.embedding).conjTranspose) + have hM : M.PosSemidef := partialTrace_posSemidef _ + (OrdinaryTensor.finiteMixture_posSemidef.mul_mul_conjTranspose_same _) + have ht : (0 : ℂ) ≤ Matrix.trace (A.val*A.val.conjTranspose) := + (Matrix.posSemidef_self_mul_conjTranspose A.val).trace_nonneg + have ha : (0 : ℂ) ≤ Matrix.trace (A.val*A.val.conjTranspose) * ((s+1 : ℕ) : ℂ)^(8*p^2) := + mul_nonneg ht (by positivity) + have hc : Matrix.trace (OrdinaryTensor.outer (F.purified A)) * + ((Fintype.card F.Free+1 : ℕ) : ℂ)^(2*Fintype.card (MatchedPair p)) ≤ + Matrix.trace (A.val*A.val.conjTranspose) * ((s+1 : ℕ) : ℂ)^(8*p^2) := by + exact mul_le_mul (F.purified_trace_le A) (by exact_mod_cast F.free_power_le s hls) + (by positivity) ht + have h₁ := domination_pad _ M _ _ hM hc (F.component_postselection hp hl A) + have h₂ := domination_trans _ M (F.rawPinned hn) _ 1 ha h₁ (by + simpa only [one_smul] using F.rawPinned_domination hp hn) + rw [mul_one] at h₂ + have h₃ := domination_trans _ (F.rawPinned hn) (F.rawDensity s hp hn) _ + (((s+1 : ℝ)^(13*p^2)) : ℂ) ha h₂ (F.rawPinned_absorption s hp hps hls hn) + convert h₃ using 1 + push_cast + rw [mul_assoc,← pow_add] + congr 2; ring +end ExceptionPattern + +abbrev DensityProfile (p l : ℕ) := Σ F : ExceptionPattern p l, F.Data + +lemma densityProfile_card_le (p l : ℕ) : Fintype.card (DensityProfile p l) ≤ (l+1)^(12*p^2) := by + rw [Fintype.card_sigma] + calc + _ ≤ ∑ _F : ExceptionPattern p l, (l+1)^(8*p^2) := + Finset.sum_le_sum (fun F _ => F.data_card_le) + _ = Fintype.card (ExceptionPattern p l) * (l+1)^(8*p^2) := by simp + _ ≤ (l+1)^((2*p)*(2*p)) * (l+1)^(8*p^2) := + Nat.mul_le_mul_right _ (ExceptionPattern.card_le (p := p) (l := l)) + _ = _ := by rw [← pow_add]; congr 1; ring + +lemma densityProfile_nonempty (hp : 0 < p) : Nonempty (DensityProfile p l) := by + let : Nonempty (MatchedPair p) := ExceptionPattern.matchedPair_nonempty hp + let F := ExceptionPattern.empty p l + exact ⟨⟨F,Classical.choice inferInstance⟩⟩ + +def profilePoint (s p l : ℕ) (hp : 0 < p) (hl : (2*p)*(2*p) < l) + (d : DensityProfile p l) : EvenDensity p := d.1.dataPoint s hp (d.1.free_card_pos hl) d.2 + +def rawProfileDensity (s p l : ℕ) (hp : 0 < p) (hl : (2*p)*(2*p) < l) : + Matrix (Word p l) (Word p l) ℂ := + ∑ d : DensityProfile p l, densityPower l (profilePoint s p l hp hl d).val + +lemma rawProfileDensity_eq (s p l : ℕ) (hp : 0 < p) (hl : (2*p)*(2*p) < l) : + rawProfileDensity s p l hp hl = ∑ F : ExceptionPattern p l, F.rawDensity s hp (F.free_card_pos hl) := by + exact Fintype.sum_sigma _ + +lemma rawProfileDensity_posSemidef (s p l : ℕ) (hp : 0 < p) (hl : (2*p)*(2*p) < l) : + (rawProfileDensity s p l hp hl).PosSemidef := by + exact Matrix.posSemidef_sum _ (fun d _ => densityPower_posSemidef _ _ (profilePoint s p l hp hl d).property.1) + +/- Finite postselection for the literal signed action commutant. -/ +theorem commutant_covariance_domination (s p l : ℕ) (hp : 0 < p) (hps : p ≤ s) + (hls : l ≤ s) (hl : (2*p)*(2*p) < l) (A : commutant p l) : + ((Matrix.trace (A.val*A.val.conjTranspose) * ((s+1 : ℕ) : ℂ)^(25*p^2)) • + rawProfileDensity s p l hp hl - A.val*A.val.conjTranspose).PosSemidef := by + have hc := partialTrace_posSemidef _ (outer_sum_domination (fun F : ExceptionPattern p l => F.component A)) + rw [ExceptionPattern.component_sum,partialTrace_sub,partialTrace_smul,partialTrace_sum, + partialTrace_outer_matrix] at hc + have hsum := Matrix.posSemidef_sum Finset.univ (fun (F : ExceptionPattern p l) _ => + F.component_uniform_domination s hp hps hls hl A) + rw [Finset.sum_sub_distrib,← Finset.smul_sum,← rawProfileDensity_eq s p l hp hl] at hsum + have h := domination_trans _ _ _ (Fintype.card (ExceptionPattern p l) : ℂ) _ (by positivity) hc hsum + have hcard : Fintype.card (ExceptionPattern p l) ≤ (s+1)^(4*p^2) := by + calc + _ ≤ (l+1)^((2*p)*(2*p)) := ExceptionPattern.card_le (p := p) (l := l) + _ ≤ (s+1)^((2*p)*(2*p)) := Nat.pow_le_pow_left (Nat.add_le_add_right hls 1) _ + _ = _ := by congr 1; ring + apply domination_pad _ _ _ _ (rawProfileDensity_posSemidef s p l hp hl) _ h + calc + _ ≤ ((s+1 : ℕ) : ℂ)^(4*p^2) * + (Matrix.trace (A.val*A.val.conjTranspose) * ((s+1 : ℕ) : ℂ)^(21*p^2)) := + mul_le_mul_of_nonneg_right (by exact_mod_cast hcard) + (mul_nonneg (Matrix.posSemidef_self_mul_conjTranspose _).trace_nonneg (by positivity)) + _ = _ := by rw [mul_left_comm,← pow_add]; congr 2; ring +end CoordinateSweeps.SignedTensor + +noncomputable section +open scoped BigOperators ENNReal +open MeasureTheory + +namespace CoordinateSweeps.FiniteAtomic +variable {I X V : Type*} [Fintype I] [Nonempty I] [MeasurableSpace X] + [MeasurableSingletonClass X] [NormedAddCommGroup V] [NormedSpace ℝ V] [CompleteSpace V] + +def uniform (x : I → X) : Measure X := + (Fintype.card I : ℝ≥0∞)⁻¹ • ∑ i, Measure.dirac (x i) + +instance uniform_probability (x : I → X) : IsProbabilityMeasure (uniform x) := by + constructor + simp [uniform, Measure.finsetSum_apply, ENNReal.inv_mul_cancel, + Fintype.card_ne_zero] + +omit [Nonempty I] in +lemma uniform_integral (x : I → X) (f : X → V) : + (∫ z, f z ∂uniform x) = (Fintype.card I : ℝ)⁻¹ • ∑ i, f (x i) := by + unfold uniform + rw [integral_smul_measure,integral_finsetSum_measure] + · simp [integral_dirac] + · intro i _ + exact integrable_dirac enorm_lt_top +end CoordinateSweeps.FiniteAtomic + +namespace CoordinateSweeps.SignedTensor +open PositiveTensor MeasureTheory + +instance (p : ℕ) : MeasurableSingletonClass (EvenDensity p) := by + let : MeasurableSpace (Matrix (Letter p) (Letter p) ℂ) := borel _ + let : BorelSpace (Matrix (Letter p) (Letter p) ℂ) := ⟨rfl⟩ + change MeasurableSingletonClass {r : Matrix (Letter p) (Letter p) ℂ // _} + infer_instance + +lemma isotypic_mem_commutant {p l : ℕ} (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + isotypic (p := p) ρ ∈ commutant p l := by + intro σ + rw [isotypic_eq_projector] + exact (ρ.projector_commute (action p l) σ).symm + +lemma isotypic_self_mul {p l : ℕ} (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + isotypic (p := p) ρ * (isotypic (p := p) ρ).conjTranspose = isotypic (p := p) ρ := by + rw [(isotypic_posSemidef ρ).isHermitian.eq,isotypic_eq_projector,ρ.projector_idempotent] + +lemma isotypic_trace_le (s p l : ℕ) (hls : l ≤ s) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + Matrix.trace (isotypic (p := p) ρ) ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2) := by + rw [isotypic_trace] + apply mul_le_mul_of_nonneg_left _ (by positivity) + have hh := (multiplicity_le p l ρ).trans (Nat.pow_le_pow_left (Nat.add_le_add_right hls 1) _) + have he : (2*p)*(2*p) = 4*p^2 := by ring + rw [he] at hh + exact_mod_cast hh + +/- The large-slot case, as an actual probability mixture of even densities. -/ +theorem density_domination_large (s p l : ℕ) (hp : 0 < p) (hps : p ≤ s) (hls : l ≤ s) + (hl : (2*p)*(2*p) < l) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + ∃ μ : Measure (EvenDensity p), IsProbabilityMeasure μ ∧ + (((ρ.dimension : ℂ) * ((s+1 : ℕ) : ℂ)^(41*p^2)) • + (∫ r : EvenDensity p, densityPower l r.val ∂μ) - isotypic (p := p) ρ).PosSemidef := by + let : Nonempty (DensityProfile p l) := densityProfile_nonempty hp + let x := profilePoint s p l hp hl + let μ := FiniteAtomic.uniform x + refine ⟨μ,inferInstance,?_⟩ + have hint : (∫ r : EvenDensity p, densityPower l r.val ∂μ) = + (Fintype.card (DensityProfile p l) : ℂ)⁻¹ • rawProfileDensity s p l hp hl := by + rw [FiniteAtomic.uniform_integral] + change (Fintype.card (DensityProfile p l) : ℝ)⁻¹ • rawProfileDensity s p l hp hl = _ + ext u v + simp [Complex.real_smul] + rw [hint] + let A : commutant p l := ⟨isotypic ρ,isotypic_mem_commutant ρ⟩ + have h := commutant_covariance_domination s p l hp hps hls hl A + change ((_ * _) • _ - isotypic ρ * (isotypic ρ).conjTranspose).PosSemidef at h + simp only [A,isotypic_self_mul] at h + have hcard : Fintype.card (DensityProfile p l) ≤ (s+1)^(12*p^2) := + (densityProfile_card_le p l).trans (Nat.pow_le_pow_left (Nat.add_le_add_right hls 1) _) + have hc0 : (Fintype.card (DensityProfile p l) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + have hbig : ((s+1 : ℕ) : ℂ)^(12*p^2) * (Fintype.card (DensityProfile p l) : ℂ)⁻¹ ≥ 1 := by + have hi : (0 : ℂ) ≤ (Fintype.card (DensityProfile p l) : ℂ)⁻¹ := by positivity + have hh := mul_le_mul_of_nonneg_right (show (Fintype.card (DensityProfile p l) : ℂ) ≤ + ((s+1 : ℕ) : ℂ)^(12*p^2) by exact_mod_cast hcard) hi + simpa only [mul_inv_cancel₀ hc0] using hh + rw [smul_smul] + apply domination_pad _ _ _ _ (rawProfileDensity_posSemidef s p l hp hl) _ h + calc + _ ≤ ((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2)) * ((s+1 : ℕ) : ℂ)^(25*p^2) := + mul_le_mul_of_nonneg_right (isotypic_trace_le s p l hls ρ) (by positivity) + _ = (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(29*p^2) := by + rw [mul_assoc,← pow_add]; congr 2; ring + _ ≤ ((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(29*p^2)) * + (((s+1 : ℕ) : ℂ)^(12*p^2) * (Fintype.card (DensityProfile p l) : ℂ)⁻¹) := by + have hh := mul_le_mul_of_nonneg_left hbig + (show (0 : ℂ) ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(29*p^2) by positivity) + simpa only [mul_one] using hh + _ = _ := by + rw [← mul_assoc,mul_assoc (ρ.dimension : ℂ),← pow_add] + congr 3; ring + +def uniformDensity (p : ℕ) (hp : 0 < p) : EvenDensity p := + ⟨((2*p : ℕ) : ℂ)⁻¹ • 1, Matrix.PosSemidef.one.smul (by positivity), by + rw [Matrix.trace_smul,Matrix.trace_one] + have hc : ((2*p : ℕ) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr (by omega) + simpa only [Letter,Fintype.card_fin,smul_eq_mul] using inv_mul_cancel₀ hc, + by + intro i j hij + have hne : i ≠ j := by intro he; subst j; tauto + simp [hne]⟩ + +lemma densityPower_one (p l : ℕ) : densityPower l (1 : Matrix (Letter p) (Letter p) ℂ) = 1 := by + ext u v + by_cases huv : u=v + · subst v + simp [densityPower] + · have hi : ∃ i, u i ≠ v i := Function.ne_iff.mp huv + obtain ⟨i,hi⟩ := hi + simp only [densityPower,Matrix.one_apply,ite_eq_right huv] + exact Finset.prod_eq_zero (Finset.mem_univ i) (ite_eq_right hi) + +lemma densityPower_smul {p : ℕ} (l : ℕ) (c : ℂ) (r : Matrix (Letter p) (Letter p) ℂ) : + densityPower l (c • r) = c^l • densityPower l r := by + ext u v + simp [densityPower,Finset.prod_mul_distrib] + +lemma uniformDensity_power (p l : ℕ) (hp : 0 < p) : + densityPower l (uniformDensity p hp).val = (((2*p : ℕ) : ℂ)^l)⁻¹ • 1 := by + change densityPower l ((((2*p : ℕ) : ℂ)⁻¹) • 1) = _ + rw [densityPower_smul,densityPower_one,inv_pow] + +lemma small_power_le (s p l : ℕ) (hps : p ≤ s) (hl : l ≤ (2*p)*(2*p)) : + (2*p)^l ≤ (s+1)^(8*p^2) := by + have hb : 2*p ≤ (s+1)^2 := by nlinarith + calc + _ ≤ ((s+1)^2)^l := Nat.pow_le_pow_left hb l + _ = (s+1)^(2*l) := by rw [pow_mul] + _ ≤ _ := Nat.pow_le_pow_right (by omega) (by nlinarith) + +/- Small slot counts, including zero, require no exceptional-sector chart. -/ +theorem density_domination_small (s p l : ℕ) (hp : 0 < p) (hps : p ≤ s) (hls : l ≤ s) + (hl : l ≤ (2*p)*(2*p)) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + ∃ μ : Measure (EvenDensity p), IsProbabilityMeasure μ ∧ + (((ρ.dimension : ℂ) * ((s+1 : ℕ) : ℂ)^(12*p^2)) • + (∫ r : EvenDensity p, densityPower l r.val ∂μ) - isotypic (p := p) ρ).PosSemidef := by + refine ⟨Measure.dirac (uniformDensity p hp),inferInstance,?_⟩ + rw [integral_dirac,uniformDensity_power,smul_smul] + have hP := trace_domination (isotypic (p := p) ρ) (isotypic_posSemidef ρ) + apply domination_pad _ 1 _ _ Matrix.PosSemidef.one _ hP + have hc0 : (((2*p : ℕ) : ℂ)^l) ≠ 0 := pow_ne_zero _ (Nat.cast_ne_zero.mpr (by omega)) + have hi : (0 : ℂ) ≤ (((2*p : ℕ) : ℂ)^l)⁻¹ := by positivity + have hh := mul_le_mul_of_nonneg_right (show (((2*p : ℕ) : ℂ)^l) ≤ + ((s+1 : ℕ) : ℂ)^(8*p^2) by exact_mod_cast small_power_le s p l hps hl) hi + rw [mul_inv_cancel₀ hc0] at hh + calc + _ ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2) := isotypic_trace_le s p l hls ρ + _ ≤ ((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2)) * + (((s+1 : ℕ) : ℂ)^(8*p^2)*(((2*p : ℕ) : ℂ)^l)⁻¹) := by + simpa only [mul_one] using mul_le_mul_of_nonneg_left hh + (show (0 : ℂ) ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2) by positivity) + _ = _ := by rw [← mul_assoc,mul_assoc (ρ.dimension : ℂ),← pow_add]; congr 3; ring + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open PositiveTensor MeasureTheory + +lemma domination_coefficient (D s p : ℕ) (hD : 0 < D) : + (Complex.ofReal (Real.exp (Real.log D+41*p^2*Real.log (s+1)))) = + (D : ℂ)*((s+1 : ℕ) : ℂ)^(41*p^2) := by + have hD' : (0 : ℝ) < D := by exact_mod_cast hD + have hs : (0 : ℝ) < s+1 := by positivity + rw [Real.exp_add,Real.exp_log hD'] + have he : (41 : ℝ)*p^2*Real.log (s+1) = ((41*p^2 : ℕ) : ℝ)*Real.log (s+1) := by push_cast; ring + rw [he,Real.exp_nat_mul,Real.exp_log hs] + push_cast + rfl + +/- Source05 equation13, with a concrete absolute constant. The measure is +constructed from finite empirical phase mixtures, not an added hypothesis. -/ +theorem signed_density_domination : Domination := by + refine ⟨41,by norm_num,?_⟩ + intro s p hp hps l hls ρ + have hp0 : 0 < p := by omega + rw [domination_coefficient ρ.dimension s p ρ.positive] + by_cases hl : (2*p)*(2*p) < l + · exact density_domination_large s p l hp0 hps hls hl ρ + · obtain ⟨μ,hμ,h⟩ := density_domination_small s p l hp0 hps hls (by omega) ρ + refine ⟨μ,hμ,?_⟩ + have hM : (∫ r : EvenDensity p, densityPower l r.val ∂μ).PosSemidef := by + -- Positivity of the integral follows from the explicitly proved lower + -- bound by a PSD projection; no measurability of arbitrary kernels is needed. + have ha : 0 < (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(12*p^2) := by + exact_mod_cast mul_pos (show (0 : ℝ) < ρ.dimension by exact_mod_cast ρ.positive) + (pow_pos (show (0 : ℝ) < s+1 by positivity) _) + have hh := h.add (isotypic_posSemidef ρ) + rw [sub_add_cancel] at hh + have hc : (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(12*p^2) ≠ 0 := ne_of_gt ha + have hh' := hh.smul (le_of_lt (inv_pos.mpr ha)) + rwa [smul_smul,inv_mul_cancel₀ hc,one_smul] at hh' + apply domination_pad _ _ _ _ hM _ h + apply mul_le_mul_of_nonneg_left _ (by positivity) + have he : 12*p^2 ≤ 41*p^2 := by omega + exact_mod_cast Nat.pow_le_pow_right (show 0 < s+1 by omega) he + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open PositiveTensor + +lemma finite_profile_domination (s p l : ℕ) (hp : 0 < p) (hps : p ≤ s) (hls : l ≤ s) + (hl : (2*p)*(2*p) < l) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + (((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(41*p^2)) • + ((Fintype.card (DensityProfile p l) : ℂ)⁻¹ • rawProfileDensity s p l hp hl) - + isotypic (p := p) ρ).PosSemidef := by + let : Nonempty (DensityProfile p l) := densityProfile_nonempty hp + let A : commutant p l := ⟨isotypic ρ,isotypic_mem_commutant ρ⟩ + have h := commutant_covariance_domination s p l hp hps hls hl A + change ((_ * _) • _ - isotypic ρ * (isotypic ρ).conjTranspose).PosSemidef at h + simp only [A,isotypic_self_mul] at h + have hcard : Fintype.card (DensityProfile p l) ≤ (s+1)^(12*p^2) := + (densityProfile_card_le p l).trans (Nat.pow_le_pow_left (Nat.add_le_add_right hls 1) _) + have hc0 : (Fintype.card (DensityProfile p l) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + have hbig : ((s+1 : ℕ) : ℂ)^(12*p^2) * (Fintype.card (DensityProfile p l) : ℂ)⁻¹ ≥ 1 := by + have hi : (0 : ℂ) ≤ (Fintype.card (DensityProfile p l) : ℂ)⁻¹ := by positivity + have hh := mul_le_mul_of_nonneg_right (show (Fintype.card (DensityProfile p l) : ℂ) ≤ + ((s+1 : ℕ) : ℂ)^(12*p^2) by exact_mod_cast hcard) hi + simpa only [mul_inv_cancel₀ hc0] using hh + rw [smul_smul] + apply domination_pad _ _ _ _ (rawProfileDensity_posSemidef s p l hp hl) _ h + calc + _ ≤ ((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2)) * ((s+1 : ℕ) : ℂ)^(25*p^2) := + mul_le_mul_of_nonneg_right (isotypic_trace_le s p l hls ρ) (by positivity) + _ = (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(29*p^2) := by + rw [mul_assoc,← pow_add]; congr 2; ring + _ ≤ ((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(29*p^2)) * + (((s+1 : ℕ) : ℂ)^(12*p^2) * (Fintype.card (DensityProfile p l) : ℂ)⁻¹) := by + have hh := mul_le_mul_of_nonneg_left hbig + (show (0 : ℂ) ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(29*p^2) by positivity) + simpa only [mul_one] using hh + _ = _ := by + rw [← mul_assoc,mul_assoc (ρ.dimension : ℂ),← pow_add] + congr 3; ring + +lemma finite_uniform_domination (s p l : ℕ) (hp : 0 < p) (hps : p ≤ s) (hls : l ≤ s) + (hl : l ≤ (2*p)*(2*p)) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + (((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(12*p^2)) • + densityPower l (uniformDensity p hp).val-isotypic (p := p) ρ).PosSemidef := by + rw [uniformDensity_power,smul_smul] + have hP := trace_domination (isotypic (p := p) ρ) (isotypic_posSemidef ρ) + apply domination_pad _ 1 _ _ Matrix.PosSemidef.one _ hP + have hc0 : (((2*p : ℕ) : ℂ)^l) ≠ 0 := pow_ne_zero _ (Nat.cast_ne_zero.mpr (by omega)) + have hi : (0 : ℂ) ≤ (((2*p : ℕ) : ℂ)^l)⁻¹ := by positivity + have hh := mul_le_mul_of_nonneg_right (show (((2*p : ℕ) : ℂ)^l) ≤ + ((s+1 : ℕ) : ℂ)^(8*p^2) by exact_mod_cast small_power_le s p l hps hl) hi + rw [mul_inv_cancel₀ hc0] at hh + calc + _ ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2) := isotypic_trace_le s p l hls ρ + _ ≤ ((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2)) * + (((s+1 : ℕ) : ℂ)^(8*p^2)*(((2*p : ℕ) : ℂ)^l)⁻¹) := by + simpa only [mul_one] using mul_le_mul_of_nonneg_left hh + (show (0 : ℂ) ≤ (ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(4*p^2) by positivity) + _ = _ := by rw [← mul_assoc,mul_assoc (ρ.dimension : ℂ),← pow_add]; congr 3; ring + +/- Finite (not a hypothetical measure) version of source05:eq13. -/ +theorem finite_density_domination (s p l : ℕ) (hp : 0 < p) (hps : p ≤ s) (hls : l ≤ s) + (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + ∃ (I : Type) (_ : Fintype I) (_ : Nonempty I) (r : I → EvenDensity p), + (((ρ.dimension : ℂ)*((s+1 : ℕ) : ℂ)^(41*p^2)) • + ((Fintype.card I : ℂ)⁻¹ • ∑ i, densityPower l (r i).val)-isotypic (p := p) ρ).PosSemidef := by + by_cases hl : (2*p)*(2*p) uniformDensity p hp,?_⟩ + simp only [Fintype.card_punit,Nat.cast_one,inv_one,Finset.univ_unique,Finset.sum_singleton,one_smul] + apply domination_pad _ _ _ _ (densityPower_posSemidef _ _ (uniformDensity p hp).property.1) _ + (finite_uniform_domination s p l hp hps hls (by omega) ρ) + apply mul_le_mul_of_nonneg_left _ (by positivity) + exact_mod_cast Nat.pow_le_pow_right (show 0 < s+1 by omega) (show 12*p^2≤41*p^2 by omega) +end CoordinateSweeps.SignedTensor + +end +end +end +end +open scoped Matrix.Norms.L2Operator + +end OAI diff --git a/lean/OAI/RepresentationTheory/SignedTensor/Overlap.lean b/lean/OAI/RepresentationTheory/SignedTensor/Overlap.lean index 860a143065268698d8c6ecfa38855e76cf738b22..2fe025268c52b4baa63145c60a9db26abe04332d 100644 --- a/lean/OAI/RepresentationTheory/SignedTensor/Overlap.lean +++ b/lean/OAI/RepresentationTheory/SignedTensor/Overlap.lean @@ -1,454 +1,454 @@ -import Mathlib -import OAI.RepresentationTheory.SignedTensor.Blocks -import OAI.RepresentationTheory.Unitary.Spectral - -namespace OAI - -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ComplexConjugate Matrix.Norms.L2Operator -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ComplexOrder MatrixOrder -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ENNReal -open MeasureTheory -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -noncomputable section -open scoped BigOperators -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable -noncomputable section -attribute [local instance] Classical.propDecidable -namespace CoordinateSweeps.TensorBoard -variable {R C J : Type*} [Fintype R] [DecidableEq R] [Nonempty R] - [Fintype C] [DecidableEq C] [Fintype J] [DecidableEq J] - -omit [Nonempty R] in -lemma board_trace_le_reindexed {l : ℕ} (F : Finset (R × C)) (e : Fin l ≃ F) - (r : R → Matrix J J ℂ) (v : C → Matrix J J ℂ) - (hr : ∀ i, (r i).PosSemidef) (hv : ∀ j, (v j).PosSemidef) - (ht : ∀ j, Matrix.trace (v j)=1) (A : Matrix J J ℂ) (hA : A.IsHermitian) - (hw : ((Fintype.card R : ℂ) • (1 : Matrix J J ℂ)-∑ i, A*r i*A).PosSemidef) : - (Matrix.trace (tensor (fun _ : Fin l => A)*tensor (fun x => r (e x).val.1)* - tensor (fun _ : Fin l => A)*tensor (fun x => v (e x).val.2))).re ≤ - Real.exp (Fintype.card R*Fintype.card C-F.card) := by - have hh := board_trace_le F r v hr hv ht A hA hw - rw [← tensor_mul,tensor_trace] at hh - rw [← tensor_mul,← tensor_mul,← tensor_mul,tensor_trace] - have he := Equiv.prod_comp e (fun x : F => Matrix.trace (A*r x.val.1*A*v x.val.2)) - simpa only [he] using hh - -end CoordinateSweeps.TensorBoard - -namespace CoordinateSweeps.UnitaryIrrep -variable {Γ n : Type*} [Group Γ] [Fintype Γ] [Fintype n] [DecidableEq n] -lemma projector_commute_lift (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - (x : MonoidAlgebra ℂ Γ) : - ρ.projector τ*MonoidAlgebra.lift ℂ _ _ τ x=MonoidAlgebra.lift ℂ _ _ τ x*ρ.projector τ := by - induction x using MonoidAlgebra.induction_on with - | of g => simpa using (ρ.projector_commute τ g).symm - | add x y hx hy => simp only [map_add,add_mul,mul_add,hx,hy] - | smul c x hx => simp only [map_smul,smul_mul_assoc,mul_smul_comm,hx] -end CoordinateSweeps.UnitaryIrrep - -namespace CoordinateSweeps.SignedTensor - -lemma densityPower_commute_projector {p l : ℕ} (r : Matrix (Letter p) (Letter p) ℂ) - (hr : IsEven r) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : - densityPower l r*ρ.projector (action p l)=ρ.projector (action p l)*densityPower l r := by - simp only [UnitaryIrrep.projector,Matrix.mul_sum,Matrix.sum_mul,Matrix.mul_smul,Matrix.smul_mul] - apply Finset.sum_congr rfl - intro σ hσ - exact congrArg (fun A => ρ.coefficient σ • A) (densityPower_commute_of_even r hr σ).symm - -lemma even_average_trace {R : Type*} [Fintype R] [Nonempty R] {p : ℕ} - (r : R → EvenDensity p) (ε : ℝ) : - Matrix.trace ((Fintype.card R : ℂ)⁻¹ • (∑ i, (r i).val)+ - (ε : ℂ) • (1 : Matrix (Letter p) (Letter p) ℂ)) = 1+ε*(2*p) := by - rw [Matrix.trace_add,Matrix.trace_smul,Matrix.trace_sum,Matrix.trace_smul,Matrix.trace_one] - simp only [(r _).property.2.1,Finset.sum_const,Finset.card_univ,nsmul_eq_mul,mul_one, - smul_eq_mul,Fintype.card_fin] - have hc : (Fintype.card R : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - rw [inv_mul_cancel₀ hc] - push_cast - rfl - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open TensorBoard Overlap -variable {R C I J : Type*} [Fintype R] [DecidableEq R] [Nonempty R] - [Fintype C] [DecidableEq C] [Fintype I] [Fintype J] - -abbrev groupOperator {p l : ℕ} (x : MonoidAlgebra ℂ (Equiv.Perm (Fin l))) : - Matrix (Word p l) (Word p l) ℂ := MonoidAlgebra.lift ℂ _ _ (action p l) x - -def rowProduct {p l : ℕ} {F : Finset (R × C)} (e : Fin l ≃ F) (r : R → EvenDensity p) : - Matrix (Word p l) (Word p l) ℂ := TensorBoard.tensor (fun x => (r (e x).val.1).val) - -def columnProduct {p l : ℕ} {F : Finset (R × C)} (e : Fin l ≃ F) (r : C → EvenDensity p) : - Matrix (Word p l) (Word p l) ℂ := TensorBoard.tensor (fun x => (r (e x).val.2).val) - -/- Literal deleted-board overlap with actual signed tensor action. The two -mixture dominations will be obtained by tensoring the local density theorem; -the whitening and the full-group dimension loss are constructed here. -/ -theorem board_overlap_regularized {p l : ℕ} (hp : 0 < p) - (F : Finset (R × C)) (e : Fin l ≃ F) - (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) - (PR : Matrix (Word p l) (Word p l) ℂ) (xC : MonoidAlgebra ℂ (Equiv.Perm (Fin l))) - (hPR : PR.IsHermitian) (hPR2 : PR*PR=PR) - (hPC : (groupOperator (p := p) xC).IsHermitian) - (hPC2 : groupOperator (p := p) xC*groupOperator (p := p) xC=groupOperator (p := p) xC) - (u : I → ℝ) (v : J → ℝ) (hu : ∀ i, 0 ≤ u i) (hv : ∀ j, 0 ≤ v j) - (hsu : ∑ i, u i=1) (hsv : ∑ j, v j=1) - (r : I → R → EvenDensity p) (c : J → C → EvenDensity p) - (cr cc : ℝ) (hcr : 0 ≤ cr) (hcc : 0 ≤ cc) - (hrow : ((cr : ℂ) • (∑ i, (u i : ℂ) • rowProduct e (r i))-PR).PosSemidef) - (hcol : ((cc : ℂ) • (∑ j, (v j : ℂ) • columnProduct e (c j))-groupOperator xC).PosSemidef) - {ε : ℝ} (hε : 0 < ε) : - (ρ.dimension : ℝ)*‖groupOperator (p := p) xC*ρ.projector (action p l)*PR‖^2 ≤ - cr*cc*(1+ε*(2*p : ℕ))^l*Real.exp (Fintype.card R*Fintype.card C-F.card) := by - let : NeZero (2*p) := ⟨by omega⟩ - let τ := action p l - let PC := groupOperator (p := p) xC - let B (i : I) : Matrix (Letter p) (Letter p) ℂ := - (Fintype.card R : ℂ)⁻¹ • (∑ k, (r i k).val)+(ε : ℂ) • 1 - choose A hA hAe hABA hAw using fun i => exists_even_whitening (r i) hε - have hb (i : I) : (B i).PosSemidef := - (average_regularization_posDef (fun k => (r i k).val) (fun k => (r i k).property.1) hε).posSemidef - have he (i : I) : IsEven (B i) := isEven_add - (isEven_smul _ (isEven_sum _ (fun k => (r i k).property.2.2))) (isEven_smul _ isEven_one) - have htau (g : Equiv.Perm (Fin l)) : (τ g).conjTranspose=τ g⁻¹ := (matrix_inv g).symm - have hpq : ρ.projector τ*PC=PC*ρ.projector τ := ρ.projector_commute_lift τ xC - have htt : 0 ≤ (1+ε*(2*p : ℕ))^l := pow_nonneg (by positivity) _ - have hwhite (i : I) : - (((1+ε*(2*p : ℕ))^l : ℝ) : ℂ) • (densityPower l (A i)*PC*densityPower l (A i)) - - (ρ.dimension : ℂ) • (PC*ρ.projector τ) |>.PosSemidef := by - have hWA : (densityPower l (A i)).IsHermitian := (densityPower_posSemidef l (A i) (hA i)).isHermitian - have hWABA : densityPower l (A i)*densityPower l (B i)*densityPower l (A i)=1 := by - rw [← densityPower_mul,← densityPower_mul,hABA i,densityPower_one] - have hh := Overlap.whitened_projector_domination ρ τ htau - (densityPower l (B i)) (densityPower l (A i)) PC (densityPower_posSemidef l (B i) (hb i)) - (fun g => densityPower_commute_of_even (B i) (he i) g) hWA hWABA - (densityPower_commute_projector (A i) (hAe i) ρ) - (densityPower_commute_lift (A i) (hAe i) xC).symm hPC hPC2 hpq - have ht : Matrix.trace (densityPower l (B i))=(((1+ε*(2*p : ℕ))^l : ℝ) : ℂ) := by - rw [densityPower_trace,even_average_trace] - push_cast - rfl - rwa [ht] at hh - apply Overlap.finite_mixture_overlap PR PC (ρ.projector τ) hPR hPR2 hPC hPC2 - (ρ.projector_hermitian τ htau) (ρ.projector_idempotent τ) hpq u v hu hv hsu hsv - (fun i => rowProduct e (r i)) (fun j => columnProduct e (c j)) (fun i => densityPower l (A i)) - (fun i => TensorBoard.tensor_posSemidef _ (fun x => (r i (e x).val.1).property.1)) - (fun i => (densityPower_posSemidef l (A i) (hA i)).isHermitian) - cr cc ρ.dimension ((1+ε*(2*p : ℕ))^l) _ hcr hcc (Nat.cast_nonneg _) htt hrow hcol hwhite - intro i j - exact board_trace_le_reindexed F e (fun k => (r i k).val) (fun k => (c j k).val) - (fun k => (r i k).property.1) (fun k => (c j k).property.1) (fun k => (c j k).property.2.1) - (A i) (hA i).isHermitian (hAw i) - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open TensorBoard Overlap -variable {R C I J : Type*} [Fintype R] [DecidableEq R] [Nonempty R] - [Fintype C] [DecidableEq C] [Fintype I] [Fintype J] - -theorem board_overlap {p l : ℕ} (hp : 0 < p) - (F : Finset (R × C)) (e : Fin l ≃ F) - (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) - (PR : Matrix (Word p l) (Word p l) ℂ) (xC : MonoidAlgebra ℂ (Equiv.Perm (Fin l))) - (hPR : PR.IsHermitian) (hPR2 : PR*PR=PR) - (hPC : (groupOperator (p := p) xC).IsHermitian) - (hPC2 : groupOperator (p := p) xC*groupOperator (p := p) xC=groupOperator (p := p) xC) - (u : I → ℝ) (v : J → ℝ) (hu : ∀ i, 0 ≤ u i) (hv : ∀ j, 0 ≤ v j) - (hsu : ∑ i, u i=1) (hsv : ∑ j, v j=1) - (r : I → R → EvenDensity p) (c : J → C → EvenDensity p) - (cr cc : ℝ) (hcr : 0 ≤ cr) (hcc : 0 ≤ cc) - (hrow : ((cr : ℂ) • (∑ i, (u i : ℂ) • rowProduct e (r i))-PR).PosSemidef) - (hcol : ((cc : ℂ) • (∑ j, (v j : ℂ) • columnProduct e (c j))-groupOperator xC).PosSemidef) - : - (ρ.dimension : ℝ)*‖groupOperator (p := p) xC*ρ.projector (action p l)*PR‖^2 ≤ - cr*cc*Real.exp (Fintype.card R*Fintype.card C-F.card) := by - let f (ε : ℝ) := cr*cc*(1+ε*(2*p : ℕ))^l*Real.exp (Fintype.card R*Fintype.card C-F.card) - have hf : Continuous f := by fun_prop - have hh : ∀ᶠ ε : ℝ in nhdsWithin 0 (Set.Ioi 0), - (ρ.dimension : ℝ)*‖groupOperator (p := p) xC*ρ.projector (action p l)*PR‖^2 ≤ f ε := by - filter_upwards [self_mem_nhdsWithin] with ε hε - exact board_overlap_regularized hp F e ρ PR xC hPR hPR2 hPC hPC2 - u v hu hv hsu hsv r c cr cc hcr hcc hrow hcol hε - have hh' := ge_of_tendsto (hf.continuousAt.tendsto.mono_left - (nhdsWithin_le_nhds : nhdsWithin (0 : ℝ) (Set.Ioi 0) ≤ nhds 0)) hh - simpa [f] using hh' - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open TensorBoard -variable {p r c : ℕ} [NeZero r] - -/- Source 06:eq19 for literal row and column subgroup projectors on an -arbitrary board with holes. The mixtures and signed regroupings are constructed. -/ -theorem actual_board_overlap (F : Finset (Fin r × Fin c)) - (e : Fin (Fintype.card F) ≃ F) (s : ℕ) (hp : 0 < p) (hps : p ≤ s) - (hnR : ∀ i, FiberBlocks.size (fun x : F => x.val.1) i ≤ s) - (hnC : ∀ j, FiberBlocks.size (fun x : F => x.val.2) j ≤ s) - (ρR : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size (fun x : F => x.val.1) i)))) - (ρC : ∀ j, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size (fun x : F => x.val.2) j)))) - (ρ : UnitaryIrrep (Equiv.Perm (Fin (Fintype.card F)))) : - (ρ.dimension : ℝ)*‖fiberProjector (p := p) (fun x : F => x.val.2) e ρC* - ρ.projector (action p (Fintype.card F))*fiberProjector (fun x : F => x.val.1) e ρR‖^2 ≤ - ((∏ i, ((ρR i).dimension : ℝ))*(s+1 : ℕ)^(r*(41*p^2)))* - ((∏ j, ((ρC j).dimension : ℝ))*(s+1 : ℕ)^(c*(41*p^2)))* - Real.exp (r*c-F.card) := by - obtain ⟨I,hI,nI,a,ha⟩ := finite_fiber_density_domination (fun x : F => x.val.1) e s hp hps hnR ρR - obtain ⟨J,hJ,nJ,b,hb⟩ := finite_fiber_density_domination (fun x : F => x.val.2) e s hp hps hnC ρC - let := hI - let := hJ - let := nI - let := nJ - have hI0 : (Fintype.card I : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - have hJ0 : (Fintype.card J : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - have hu : ∑ _ : I, (Fintype.card I : ℝ)⁻¹=1 := by - rw [Finset.sum_const,Finset.card_univ,nsmul_eq_mul,mul_inv_cancel₀ hI0] - have hv : ∑ _ : J, (Fintype.card J : ℝ)⁻¹=1 := by - rw [Finset.sum_const,Finset.card_univ,nsmul_eq_mul,mul_inv_cancel₀ hJ0] - have hr := fiberProjector_posSemidef (p := p) (fun x : F => x.val.1) e ρR - have hc := fiberProjector_posSemidef (p := p) (fun x : F => x.val.2) e ρC - have hr2 := fiberProjector_idempotent (p := p) (fun x : F => x.val.1) e ρR - have hc2 := fiberProjector_idempotent (p := p) (fun x : F => x.val.2) e ρC - let xC := fiberProjectorAlgebra (fun x : F => x.val.2) e ρC - have hx : groupOperator (p := p) xC=fiberProjector (p := p) (fun x : F => x.val.2) e ρC := - fiberProjectorAlgebra_lift _ _ _ - have hrow : (((∏ i, ((ρR i).dimension : ℝ))*(s+1 : ℕ)^(r*(41*p^2)) : ℝ) : ℂ) • - (∑ i : I, (((Fintype.card I : ℝ)⁻¹ : ℝ) : ℂ) • rowProduct e (a i))- - fiberProjector (p := p) (fun x : F => x.val.1) e ρR |>.PosSemidef := by - simpa only [Complex.ofReal_mul,Complex.ofReal_prod,Complex.ofReal_natCast,Complex.ofReal_pow, - Complex.ofReal_inv,← Finset.smul_sum,rowProduct] using ha - have hcol : (((∏ j, ((ρC j).dimension : ℝ))*(s+1 : ℕ)^(c*(41*p^2)) : ℝ) : ℂ) • - (∑ j : J, (((Fintype.card J : ℝ)⁻¹ : ℝ) : ℂ) • columnProduct e (b j))- - groupOperator (p := p) xC |>.PosSemidef := by - rw [hx] - simpa only [Complex.ofReal_mul,Complex.ofReal_prod,Complex.ofReal_natCast,Complex.ofReal_pow, - Complex.ofReal_inv,← Finset.smul_sum,columnProduct] using hb - have hh := board_overlap hp F e ρ _ xC hr.isHermitian hr2 (hx ▸ hc.isHermitian) - (by rw [hx]; exact hc2) (fun _ : I => (Fintype.card I : ℝ)⁻¹) - (fun _ : J => (Fintype.card J : ℝ)⁻¹) (fun _ => by positivity) (fun _ => by positivity) - hu hv a b ((∏ i, ((ρR i).dimension : ℝ))*(s+1 : ℕ)^(r*(41*p^2))) - ((∏ j, ((ρC j).dimension : ℝ))*(s+1 : ℕ)^(c*(41*p^2))) (by positivity) (by positivity) hrow hcol - simpa only [hx,Fintype.card_fin] using hh - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.TensorBoard -variable {R C J : Type*} [Fintype R] [DecidableEq R] [Nonempty R] - [Fintype C] [DecidableEq C] [Fintype J] [DecidableEq J] -omit [Nonempty R] in -lemma board_trace_le_labels {l : ℕ} (e : Fin l → R × C) (he : Function.Injective e) - (r : R → Matrix J J ℂ) (v : C → Matrix J J ℂ) - (hr : ∀ i, (r i).PosSemidef) (hv : ∀ j, (v j).PosSemidef) - (ht : ∀ j, Matrix.trace (v j)=1) (A : Matrix J J ℂ) (hA : A.IsHermitian) - (hw : ((Fintype.card R : ℂ) • (1 : Matrix J J ℂ)-∑ i, A*r i*A).PosSemidef) : - (Matrix.trace (tensor (fun _ : Fin l => A)*tensor (fun x => r (e x).1)* - tensor (fun _ : Fin l => A)*tensor (fun x => v (e x).2))).re ≤ - Real.exp (Fintype.card R*Fintype.card C-l) := by - let F : Finset (R × C) := Finset.univ.image e - let E : Fin l ≃ F := Equiv.ofBijective (fun x => ⟨e x,by simp [F]⟩) (by - constructor - · intro x y h; exact he (congrArg Subtype.val h) - · intro y - obtain ⟨x,_,hx⟩ := Finset.mem_image.mp y.property - exact ⟨x,Subtype.ext hx⟩) - have hc : F.card=l := by - dsimp [F] - rw [Finset.card_image_of_injective _ he,Finset.card_univ,Fintype.card_fin] - have hh := board_trace_le_reindexed F E r v hr hv ht A hA hw - have hE (x : Fin l) : (E x).val=e x := rfl - simpa only [hE,hc] using hh -end CoordinateSweeps.TensorBoard - -namespace CoordinateSweeps.SignedTensor -open TensorBoard -variable {R C I J : Type*} [Fintype R] [DecidableEq R] [Nonempty R] - [Fintype C] [DecidableEq C] [Fintype I] [Fintype J] - -def labelRowProduct {p l : ℕ} (e : Fin l → R × C) (r : R → EvenDensity p) : - Matrix (Word p l) (Word p l) ℂ := TensorBoard.tensor (fun x => (r (e x).1).val) - -def labelColumnProduct {p l : ℕ} (e : Fin l → R × C) (r : C → EvenDensity p) : - Matrix (Word p l) (Word p l) ℂ := TensorBoard.tensor (fun x => (r (e x).2).val) - -/- Literal deleted-board overlap with actual signed tensor action. The two -mixture dominations will be obtained by tensoring the local density theorem; -the whitening and the full-group dimension loss are constructed here. -/ -theorem label_board_overlap_regularized {p l : ℕ} (hp : 0 < p) - (e : Fin l → R × C) (hinj : Function.Injective e) - (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) - (PR : Matrix (Word p l) (Word p l) ℂ) (xC : MonoidAlgebra ℂ (Equiv.Perm (Fin l))) - (hPR : PR.IsHermitian) (hPR2 : PR*PR=PR) - (hPC : (groupOperator (p := p) xC).IsHermitian) - (hPC2 : groupOperator (p := p) xC*groupOperator (p := p) xC=groupOperator (p := p) xC) - (u : I → ℝ) (v : J → ℝ) (hu : ∀ i, 0 ≤ u i) (hv : ∀ j, 0 ≤ v j) - (hsu : ∑ i, u i=1) (hsv : ∑ j, v j=1) - (r : I → R → EvenDensity p) (c : J → C → EvenDensity p) - (cr cc : ℝ) (hcr : 0 ≤ cr) (hcc : 0 ≤ cc) - (hrow : ((cr : ℂ) • (∑ i, (u i : ℂ) • labelRowProduct e (r i))-PR).PosSemidef) - (hcol : ((cc : ℂ) • (∑ j, (v j : ℂ) • labelColumnProduct e (c j))-groupOperator xC).PosSemidef) - {ε : ℝ} (hε : 0 < ε) : - (ρ.dimension : ℝ)*‖groupOperator (p := p) xC*ρ.projector (action p l)*PR‖^2 ≤ - cr*cc*(1+ε*(2*p : ℕ))^l*Real.exp (Fintype.card R*Fintype.card C-l) := by - let : NeZero (2*p) := ⟨by omega⟩ - let τ := action p l - let PC := groupOperator (p := p) xC - let B (i : I) : Matrix (Letter p) (Letter p) ℂ := - (Fintype.card R : ℂ)⁻¹ • (∑ k, (r i k).val)+(ε : ℂ) • 1 - choose A hA hAe hABA hAw using fun i => exists_even_whitening (r i) hε - have hb (i : I) : (B i).PosSemidef := - (average_regularization_posDef (fun k => (r i k).val) (fun k => (r i k).property.1) hε).posSemidef - have he (i : I) : IsEven (B i) := isEven_add - (isEven_smul _ (isEven_sum _ (fun k => (r i k).property.2.2))) (isEven_smul _ isEven_one) - have htau (g : Equiv.Perm (Fin l)) : (τ g).conjTranspose=τ g⁻¹ := (matrix_inv g).symm - have hpq : ρ.projector τ*PC=PC*ρ.projector τ := ρ.projector_commute_lift τ xC - have htt : 0 ≤ (1+ε*(2*p : ℕ))^l := pow_nonneg (by positivity) _ - have hwhite (i : I) : - (((1+ε*(2*p : ℕ))^l : ℝ) : ℂ) • (densityPower l (A i)*PC*densityPower l (A i)) - - (ρ.dimension : ℂ) • (PC*ρ.projector τ) |>.PosSemidef := by - have hWA : (densityPower l (A i)).IsHermitian := (densityPower_posSemidef l (A i) (hA i)).isHermitian - have hWABA : densityPower l (A i)*densityPower l (B i)*densityPower l (A i)=1 := by - rw [← densityPower_mul,← densityPower_mul,hABA i,densityPower_one] - have hh := Overlap.whitened_projector_domination ρ τ htau - (densityPower l (B i)) (densityPower l (A i)) PC (densityPower_posSemidef l (B i) (hb i)) - (fun g => densityPower_commute_of_even (B i) (he i) g) hWA hWABA - (densityPower_commute_projector (A i) (hAe i) ρ) - (densityPower_commute_lift (A i) (hAe i) xC).symm hPC hPC2 hpq - have ht : Matrix.trace (densityPower l (B i))=(((1+ε*(2*p : ℕ))^l : ℝ) : ℂ) := by - rw [densityPower_trace,even_average_trace] - push_cast - rfl - rwa [ht] at hh - apply Overlap.finite_mixture_overlap PR PC (ρ.projector τ) hPR hPR2 hPC hPC2 - (ρ.projector_hermitian τ htau) (ρ.projector_idempotent τ) hpq u v hu hv hsu hsv - (fun i => labelRowProduct e (r i)) (fun j => labelColumnProduct e (c j)) (fun i => densityPower l (A i)) - (fun i => TensorBoard.tensor_posSemidef _ (fun x => (r i (e x).1).property.1)) - (fun i => (densityPower_posSemidef l (A i) (hA i)).isHermitian) - cr cc ρ.dimension ((1+ε*(2*p : ℕ))^l) _ hcr hcc (Nat.cast_nonneg _) htt hrow hcol hwhite - intro i j - exact board_trace_le_labels e hinj (fun k => (r i k).val) (fun k => (c j k).val) - (fun k => (r i k).property.1) (fun k => (c j k).property.1) (fun k => (c j k).property.2.1) - (A i) (hA i).isHermitian (hAw i) - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open TensorBoard Overlap -variable {R C I J : Type*} [Fintype R] [DecidableEq R] [Nonempty R] - [Fintype C] [DecidableEq C] [Fintype I] [Fintype J] - -theorem label_board_overlap {p l : ℕ} (hp : 0 < p) - (e : Fin l → R × C) (hinj : Function.Injective e) - (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) - (PR : Matrix (Word p l) (Word p l) ℂ) (xC : MonoidAlgebra ℂ (Equiv.Perm (Fin l))) - (hPR : PR.IsHermitian) (hPR2 : PR*PR=PR) - (hPC : (groupOperator (p := p) xC).IsHermitian) - (hPC2 : groupOperator (p := p) xC*groupOperator (p := p) xC=groupOperator (p := p) xC) - (u : I → ℝ) (v : J → ℝ) (hu : ∀ i, 0 ≤ u i) (hv : ∀ j, 0 ≤ v j) - (hsu : ∑ i, u i=1) (hsv : ∑ j, v j=1) - (r : I → R → EvenDensity p) (c : J → C → EvenDensity p) - (cr cc : ℝ) (hcr : 0 ≤ cr) (hcc : 0 ≤ cc) - (hrow : ((cr : ℂ) • (∑ i, (u i : ℂ) • labelRowProduct e (r i))-PR).PosSemidef) - (hcol : ((cc : ℂ) • (∑ j, (v j : ℂ) • labelColumnProduct e (c j))-groupOperator xC).PosSemidef) - : - (ρ.dimension : ℝ)*‖groupOperator (p := p) xC*ρ.projector (action p l)*PR‖^2 ≤ - cr*cc*Real.exp (Fintype.card R*Fintype.card C-l) := by - let f (ε : ℝ) := cr*cc*(1+ε*(2*p : ℕ))^l*Real.exp (Fintype.card R*Fintype.card C-l) - have hf : Continuous f := by fun_prop - have hh : ∀ᶠ ε : ℝ in nhdsWithin 0 (Set.Ioi 0), - (ρ.dimension : ℝ)*‖groupOperator (p := p) xC*ρ.projector (action p l)*PR‖^2 ≤ f ε := by - filter_upwards [self_mem_nhdsWithin] with ε hε - exact label_board_overlap_regularized hp e hinj ρ PR xC hPR hPR2 hPC hPC2 - u v hu hv hsu hsv r c cr cc hcr hcc hrow hcol hε - have hh' := ge_of_tendsto (hf.continuousAt.tendsto.mono_left - (nhdsWithin_le_nhds : nhdsWithin (0 : ℝ) (Set.Ioi 0) ≤ nhds 0)) hh - simpa [f] using hh' - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open TensorBoard -variable {p r c : ℕ} [NeZero r] - {L : Type*} [Fintype L] [DecidableEq L] - -/- Source 06:eq19 for literal row and column subgroup projectors on an -arbitrary board with holes. The mixtures and signed regroupings are constructed. -/ -omit [DecidableEq L] in -theorem actual_label_overlap (f : L → Fin r) (g : L → Fin c) - (hinj : Function.Injective (fun x => (f x,g x))) - (e : Fin (Fintype.card L) ≃ L) (s : ℕ) (hp : 0 < p) (hps : p ≤ s) - (hnR : ∀ i, FiberBlocks.size f i ≤ s) - (hnC : ∀ j, FiberBlocks.size g j ≤ s) - (ρR : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) - (ρC : ∀ j, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size g j)))) - (ρ : UnitaryIrrep (Equiv.Perm (Fin (Fintype.card L)))) : - (ρ.dimension : ℝ)*‖fiberProjector (p := p) g e ρC* - ρ.projector (action p (Fintype.card L))*fiberProjector f e ρR‖^2 ≤ - ((∏ i, ((ρR i).dimension : ℝ))*(s+1 : ℕ)^(r*(41*p^2)))* - ((∏ j, ((ρC j).dimension : ℝ))*(s+1 : ℕ)^(c*(41*p^2)))* - Real.exp (r*c-Fintype.card L) := by - obtain ⟨I,hI,nI,a,ha⟩ := finite_fiber_density_domination f e s hp hps hnR ρR - obtain ⟨J,hJ,nJ,b,hb⟩ := finite_fiber_density_domination g e s hp hps hnC ρC - let := hI - let := hJ - let := nI - let := nJ - have hI0 : (Fintype.card I : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - have hJ0 : (Fintype.card J : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - have hu : ∑ _ : I, (Fintype.card I : ℝ)⁻¹=1 := by - rw [Finset.sum_const,Finset.card_univ,nsmul_eq_mul,mul_inv_cancel₀ hI0] - have hv : ∑ _ : J, (Fintype.card J : ℝ)⁻¹=1 := by - rw [Finset.sum_const,Finset.card_univ,nsmul_eq_mul,mul_inv_cancel₀ hJ0] - have hr := fiberProjector_posSemidef (p := p) f e ρR - have hc := fiberProjector_posSemidef (p := p) g e ρC - have hr2 := fiberProjector_idempotent (p := p) f e ρR - have hc2 := fiberProjector_idempotent (p := p) g e ρC - let xC := fiberProjectorAlgebra g e ρC - have hx : groupOperator (p := p) xC=fiberProjector (p := p) g e ρC := - fiberProjectorAlgebra_lift _ _ _ - have hrow : (((∏ i, ((ρR i).dimension : ℝ))*(s+1 : ℕ)^(r*(41*p^2)) : ℝ) : ℂ) • - (∑ i : I, (((Fintype.card I : ℝ)⁻¹ : ℝ) : ℂ) • labelRowProduct (fun x => (f (e x),g (e x))) (a i))- - fiberProjector (p := p) f e ρR |>.PosSemidef := by - simpa only [Complex.ofReal_mul,Complex.ofReal_prod,Complex.ofReal_natCast,Complex.ofReal_pow, - Complex.ofReal_inv,← Finset.smul_sum,labelRowProduct] using ha - have hcol : (((∏ j, ((ρC j).dimension : ℝ))*(s+1 : ℕ)^(c*(41*p^2)) : ℝ) : ℂ) • - (∑ j : J, (((Fintype.card J : ℝ)⁻¹ : ℝ) : ℂ) • labelColumnProduct (fun x => (f (e x),g (e x))) (b j))- - groupOperator (p := p) xC |>.PosSemidef := by - rw [hx] - simpa only [Complex.ofReal_mul,Complex.ofReal_prod,Complex.ofReal_natCast,Complex.ofReal_pow, - Complex.ofReal_inv,← Finset.smul_sum,labelColumnProduct] using hb - have hh := label_board_overlap hp (fun x => (f (e x),g (e x))) (hinj.comp e.injective) ρ _ xC hr.isHermitian hr2 (hx ▸ hc.isHermitian) - (by rw [hx]; exact hc2) (fun _ : I => (Fintype.card I : ℝ)⁻¹) - (fun _ : J => (Fintype.card J : ℝ)⁻¹) (fun _ => by positivity) (fun _ => by positivity) - hu hv a b ((∏ i, ((ρR i).dimension : ℝ))*(s+1 : ℕ)^(r*(41*p^2))) - ((∏ j, ((ρC j).dimension : ℝ))*(s+1 : ℕ)^(c*(41*p^2))) (by positivity) (by positivity) hrow hcol - simpa only [hx,Fintype.card_fin] using hh - -end CoordinateSweeps.SignedTensor - -end -end -end -end -end -end -end -end -open scoped Matrix.Norms.L2Operator - -end OAI +import Mathlib +import OAI.RepresentationTheory.SignedTensor.Blocks +import OAI.RepresentationTheory.Unitary.Spectral + +namespace OAI + +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ComplexConjugate Matrix.Norms.L2Operator +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ComplexOrder MatrixOrder +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ENNReal +open MeasureTheory +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +noncomputable section +open scoped BigOperators +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable +noncomputable section +attribute [local instance] Classical.propDecidable +namespace CoordinateSweeps.TensorBoard +variable {R C J : Type*} [Fintype R] [DecidableEq R] [Nonempty R] + [Fintype C] [DecidableEq C] [Fintype J] [DecidableEq J] + +omit [Nonempty R] in +lemma board_trace_le_reindexed {l : ℕ} (F : Finset (R × C)) (e : Fin l ≃ F) + (r : R → Matrix J J ℂ) (v : C → Matrix J J ℂ) + (hr : ∀ i, (r i).PosSemidef) (hv : ∀ j, (v j).PosSemidef) + (ht : ∀ j, Matrix.trace (v j)=1) (A : Matrix J J ℂ) (hA : A.IsHermitian) + (hw : ((Fintype.card R : ℂ) • (1 : Matrix J J ℂ)-∑ i, A*r i*A).PosSemidef) : + (Matrix.trace (tensor (fun _ : Fin l => A)*tensor (fun x => r (e x).val.1)* + tensor (fun _ : Fin l => A)*tensor (fun x => v (e x).val.2))).re ≤ + Real.exp (Fintype.card R*Fintype.card C-F.card) := by + have hh := board_trace_le F r v hr hv ht A hA hw + rw [← tensor_mul,tensor_trace] at hh + rw [← tensor_mul,← tensor_mul,← tensor_mul,tensor_trace] + have he := Equiv.prod_comp e (fun x : F => Matrix.trace (A*r x.val.1*A*v x.val.2)) + simpa only [he] using hh + +end CoordinateSweeps.TensorBoard + +namespace CoordinateSweeps.UnitaryIrrep +variable {Γ n : Type*} [Group Γ] [Fintype Γ] [Fintype n] [DecidableEq n] +lemma projector_commute_lift (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + (x : MonoidAlgebra ℂ Γ) : + ρ.projector τ*MonoidAlgebra.lift ℂ _ _ τ x=MonoidAlgebra.lift ℂ _ _ τ x*ρ.projector τ := by + induction x using MonoidAlgebra.induction_on with + | of g => simpa using (ρ.projector_commute τ g).symm + | add x y hx hy => simp only [map_add,add_mul,mul_add,hx,hy] + | smul c x hx => simp only [map_smul,smul_mul_assoc,mul_smul_comm,hx] +end CoordinateSweeps.UnitaryIrrep + +namespace CoordinateSweeps.SignedTensor + +lemma densityPower_commute_projector {p l : ℕ} (r : Matrix (Letter p) (Letter p) ℂ) + (hr : IsEven r) (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) : + densityPower l r*ρ.projector (action p l)=ρ.projector (action p l)*densityPower l r := by + simp only [UnitaryIrrep.projector,Matrix.mul_sum,Matrix.sum_mul,Matrix.mul_smul,Matrix.smul_mul] + apply Finset.sum_congr rfl + intro σ hσ + exact congrArg (fun A => ρ.coefficient σ • A) (densityPower_commute_of_even r hr σ).symm + +lemma even_average_trace {R : Type*} [Fintype R] [Nonempty R] {p : ℕ} + (r : R → EvenDensity p) (ε : ℝ) : + Matrix.trace ((Fintype.card R : ℂ)⁻¹ • (∑ i, (r i).val)+ + (ε : ℂ) • (1 : Matrix (Letter p) (Letter p) ℂ)) = 1+ε*(2*p) := by + rw [Matrix.trace_add,Matrix.trace_smul,Matrix.trace_sum,Matrix.trace_smul,Matrix.trace_one] + simp only [(r _).property.2.1,Finset.sum_const,Finset.card_univ,nsmul_eq_mul,mul_one, + smul_eq_mul,Fintype.card_fin] + have hc : (Fintype.card R : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + rw [inv_mul_cancel₀ hc] + push_cast + rfl + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open TensorBoard Overlap +variable {R C I J : Type*} [Fintype R] [DecidableEq R] [Nonempty R] + [Fintype C] [DecidableEq C] [Fintype I] [Fintype J] + +abbrev groupOperator {p l : ℕ} (x : MonoidAlgebra ℂ (Equiv.Perm (Fin l))) : + Matrix (Word p l) (Word p l) ℂ := MonoidAlgebra.lift ℂ _ _ (action p l) x + +def rowProduct {p l : ℕ} {F : Finset (R × C)} (e : Fin l ≃ F) (r : R → EvenDensity p) : + Matrix (Word p l) (Word p l) ℂ := TensorBoard.tensor (fun x => (r (e x).val.1).val) + +def columnProduct {p l : ℕ} {F : Finset (R × C)} (e : Fin l ≃ F) (r : C → EvenDensity p) : + Matrix (Word p l) (Word p l) ℂ := TensorBoard.tensor (fun x => (r (e x).val.2).val) + +/- Literal deleted-board overlap with actual signed tensor action. The two +mixture dominations will be obtained by tensoring the local density theorem; +the whitening and the full-group dimension loss are constructed here. -/ +theorem board_overlap_regularized {p l : ℕ} (hp : 0 < p) + (F : Finset (R × C)) (e : Fin l ≃ F) + (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) + (PR : Matrix (Word p l) (Word p l) ℂ) (xC : MonoidAlgebra ℂ (Equiv.Perm (Fin l))) + (hPR : PR.IsHermitian) (hPR2 : PR*PR=PR) + (hPC : (groupOperator (p := p) xC).IsHermitian) + (hPC2 : groupOperator (p := p) xC*groupOperator (p := p) xC=groupOperator (p := p) xC) + (u : I → ℝ) (v : J → ℝ) (hu : ∀ i, 0 ≤ u i) (hv : ∀ j, 0 ≤ v j) + (hsu : ∑ i, u i=1) (hsv : ∑ j, v j=1) + (r : I → R → EvenDensity p) (c : J → C → EvenDensity p) + (cr cc : ℝ) (hcr : 0 ≤ cr) (hcc : 0 ≤ cc) + (hrow : ((cr : ℂ) • (∑ i, (u i : ℂ) • rowProduct e (r i))-PR).PosSemidef) + (hcol : ((cc : ℂ) • (∑ j, (v j : ℂ) • columnProduct e (c j))-groupOperator xC).PosSemidef) + {ε : ℝ} (hε : 0 < ε) : + (ρ.dimension : ℝ)*‖groupOperator (p := p) xC*ρ.projector (action p l)*PR‖^2 ≤ + cr*cc*(1+ε*(2*p : ℕ))^l*Real.exp (Fintype.card R*Fintype.card C-F.card) := by + let : NeZero (2*p) := ⟨by omega⟩ + let τ := action p l + let PC := groupOperator (p := p) xC + let B (i : I) : Matrix (Letter p) (Letter p) ℂ := + (Fintype.card R : ℂ)⁻¹ • (∑ k, (r i k).val)+(ε : ℂ) • 1 + choose A hA hAe hABA hAw using fun i => exists_even_whitening (r i) hε + have hb (i : I) : (B i).PosSemidef := + (average_regularization_posDef (fun k => (r i k).val) (fun k => (r i k).property.1) hε).posSemidef + have he (i : I) : IsEven (B i) := isEven_add + (isEven_smul _ (isEven_sum _ (fun k => (r i k).property.2.2))) (isEven_smul _ isEven_one) + have htau (g : Equiv.Perm (Fin l)) : (τ g).conjTranspose=τ g⁻¹ := (matrix_inv g).symm + have hpq : ρ.projector τ*PC=PC*ρ.projector τ := ρ.projector_commute_lift τ xC + have htt : 0 ≤ (1+ε*(2*p : ℕ))^l := pow_nonneg (by positivity) _ + have hwhite (i : I) : + (((1+ε*(2*p : ℕ))^l : ℝ) : ℂ) • (densityPower l (A i)*PC*densityPower l (A i)) - + (ρ.dimension : ℂ) • (PC*ρ.projector τ) |>.PosSemidef := by + have hWA : (densityPower l (A i)).IsHermitian := (densityPower_posSemidef l (A i) (hA i)).isHermitian + have hWABA : densityPower l (A i)*densityPower l (B i)*densityPower l (A i)=1 := by + rw [← densityPower_mul,← densityPower_mul,hABA i,densityPower_one] + have hh := Overlap.whitened_projector_domination ρ τ htau + (densityPower l (B i)) (densityPower l (A i)) PC (densityPower_posSemidef l (B i) (hb i)) + (fun g => densityPower_commute_of_even (B i) (he i) g) hWA hWABA + (densityPower_commute_projector (A i) (hAe i) ρ) + (densityPower_commute_lift (A i) (hAe i) xC).symm hPC hPC2 hpq + have ht : Matrix.trace (densityPower l (B i))=(((1+ε*(2*p : ℕ))^l : ℝ) : ℂ) := by + rw [densityPower_trace,even_average_trace] + push_cast + rfl + rwa [ht] at hh + apply Overlap.finite_mixture_overlap PR PC (ρ.projector τ) hPR hPR2 hPC hPC2 + (ρ.projector_hermitian τ htau) (ρ.projector_idempotent τ) hpq u v hu hv hsu hsv + (fun i => rowProduct e (r i)) (fun j => columnProduct e (c j)) (fun i => densityPower l (A i)) + (fun i => TensorBoard.tensor_posSemidef _ (fun x => (r i (e x).val.1).property.1)) + (fun i => (densityPower_posSemidef l (A i) (hA i)).isHermitian) + cr cc ρ.dimension ((1+ε*(2*p : ℕ))^l) _ hcr hcc (Nat.cast_nonneg _) htt hrow hcol hwhite + intro i j + exact board_trace_le_reindexed F e (fun k => (r i k).val) (fun k => (c j k).val) + (fun k => (r i k).property.1) (fun k => (c j k).property.1) (fun k => (c j k).property.2.1) + (A i) (hA i).isHermitian (hAw i) + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open TensorBoard Overlap +variable {R C I J : Type*} [Fintype R] [DecidableEq R] [Nonempty R] + [Fintype C] [DecidableEq C] [Fintype I] [Fintype J] + +theorem board_overlap {p l : ℕ} (hp : 0 < p) + (F : Finset (R × C)) (e : Fin l ≃ F) + (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) + (PR : Matrix (Word p l) (Word p l) ℂ) (xC : MonoidAlgebra ℂ (Equiv.Perm (Fin l))) + (hPR : PR.IsHermitian) (hPR2 : PR*PR=PR) + (hPC : (groupOperator (p := p) xC).IsHermitian) + (hPC2 : groupOperator (p := p) xC*groupOperator (p := p) xC=groupOperator (p := p) xC) + (u : I → ℝ) (v : J → ℝ) (hu : ∀ i, 0 ≤ u i) (hv : ∀ j, 0 ≤ v j) + (hsu : ∑ i, u i=1) (hsv : ∑ j, v j=1) + (r : I → R → EvenDensity p) (c : J → C → EvenDensity p) + (cr cc : ℝ) (hcr : 0 ≤ cr) (hcc : 0 ≤ cc) + (hrow : ((cr : ℂ) • (∑ i, (u i : ℂ) • rowProduct e (r i))-PR).PosSemidef) + (hcol : ((cc : ℂ) • (∑ j, (v j : ℂ) • columnProduct e (c j))-groupOperator xC).PosSemidef) + : + (ρ.dimension : ℝ)*‖groupOperator (p := p) xC*ρ.projector (action p l)*PR‖^2 ≤ + cr*cc*Real.exp (Fintype.card R*Fintype.card C-F.card) := by + let f (ε : ℝ) := cr*cc*(1+ε*(2*p : ℕ))^l*Real.exp (Fintype.card R*Fintype.card C-F.card) + have hf : Continuous f := by fun_prop + have hh : ∀ᶠ ε : ℝ in nhdsWithin 0 (Set.Ioi 0), + (ρ.dimension : ℝ)*‖groupOperator (p := p) xC*ρ.projector (action p l)*PR‖^2 ≤ f ε := by + filter_upwards [self_mem_nhdsWithin] with ε hε + exact board_overlap_regularized hp F e ρ PR xC hPR hPR2 hPC hPC2 + u v hu hv hsu hsv r c cr cc hcr hcc hrow hcol hε + have hh' := ge_of_tendsto (hf.continuousAt.tendsto.mono_left + (nhdsWithin_le_nhds : nhdsWithin (0 : ℝ) (Set.Ioi 0) ≤ nhds 0)) hh + simpa [f] using hh' + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open TensorBoard +variable {p r c : ℕ} [NeZero r] + +/- Source 06:eq19 for literal row and column subgroup projectors on an +arbitrary board with holes. The mixtures and signed regroupings are constructed. -/ +theorem actual_board_overlap (F : Finset (Fin r × Fin c)) + (e : Fin (Fintype.card F) ≃ F) (s : ℕ) (hp : 0 < p) (hps : p ≤ s) + (hnR : ∀ i, FiberBlocks.size (fun x : F => x.val.1) i ≤ s) + (hnC : ∀ j, FiberBlocks.size (fun x : F => x.val.2) j ≤ s) + (ρR : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size (fun x : F => x.val.1) i)))) + (ρC : ∀ j, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size (fun x : F => x.val.2) j)))) + (ρ : UnitaryIrrep (Equiv.Perm (Fin (Fintype.card F)))) : + (ρ.dimension : ℝ)*‖fiberProjector (p := p) (fun x : F => x.val.2) e ρC* + ρ.projector (action p (Fintype.card F))*fiberProjector (fun x : F => x.val.1) e ρR‖^2 ≤ + ((∏ i, ((ρR i).dimension : ℝ))*(s+1 : ℕ)^(r*(41*p^2)))* + ((∏ j, ((ρC j).dimension : ℝ))*(s+1 : ℕ)^(c*(41*p^2)))* + Real.exp (r*c-F.card) := by + obtain ⟨I,hI,nI,a,ha⟩ := finite_fiber_density_domination (fun x : F => x.val.1) e s hp hps hnR ρR + obtain ⟨J,hJ,nJ,b,hb⟩ := finite_fiber_density_domination (fun x : F => x.val.2) e s hp hps hnC ρC + let := hI + let := hJ + let := nI + let := nJ + have hI0 : (Fintype.card I : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + have hJ0 : (Fintype.card J : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + have hu : ∑ _ : I, (Fintype.card I : ℝ)⁻¹=1 := by + rw [Finset.sum_const,Finset.card_univ,nsmul_eq_mul,mul_inv_cancel₀ hI0] + have hv : ∑ _ : J, (Fintype.card J : ℝ)⁻¹=1 := by + rw [Finset.sum_const,Finset.card_univ,nsmul_eq_mul,mul_inv_cancel₀ hJ0] + have hr := fiberProjector_posSemidef (p := p) (fun x : F => x.val.1) e ρR + have hc := fiberProjector_posSemidef (p := p) (fun x : F => x.val.2) e ρC + have hr2 := fiberProjector_idempotent (p := p) (fun x : F => x.val.1) e ρR + have hc2 := fiberProjector_idempotent (p := p) (fun x : F => x.val.2) e ρC + let xC := fiberProjectorAlgebra (fun x : F => x.val.2) e ρC + have hx : groupOperator (p := p) xC=fiberProjector (p := p) (fun x : F => x.val.2) e ρC := + fiberProjectorAlgebra_lift _ _ _ + have hrow : (((∏ i, ((ρR i).dimension : ℝ))*(s+1 : ℕ)^(r*(41*p^2)) : ℝ) : ℂ) • + (∑ i : I, (((Fintype.card I : ℝ)⁻¹ : ℝ) : ℂ) • rowProduct e (a i))- + fiberProjector (p := p) (fun x : F => x.val.1) e ρR |>.PosSemidef := by + simpa only [Complex.ofReal_mul,Complex.ofReal_prod,Complex.ofReal_natCast,Complex.ofReal_pow, + Complex.ofReal_inv,← Finset.smul_sum,rowProduct] using ha + have hcol : (((∏ j, ((ρC j).dimension : ℝ))*(s+1 : ℕ)^(c*(41*p^2)) : ℝ) : ℂ) • + (∑ j : J, (((Fintype.card J : ℝ)⁻¹ : ℝ) : ℂ) • columnProduct e (b j))- + groupOperator (p := p) xC |>.PosSemidef := by + rw [hx] + simpa only [Complex.ofReal_mul,Complex.ofReal_prod,Complex.ofReal_natCast,Complex.ofReal_pow, + Complex.ofReal_inv,← Finset.smul_sum,columnProduct] using hb + have hh := board_overlap hp F e ρ _ xC hr.isHermitian hr2 (hx ▸ hc.isHermitian) + (by rw [hx]; exact hc2) (fun _ : I => (Fintype.card I : ℝ)⁻¹) + (fun _ : J => (Fintype.card J : ℝ)⁻¹) (fun _ => by positivity) (fun _ => by positivity) + hu hv a b ((∏ i, ((ρR i).dimension : ℝ))*(s+1 : ℕ)^(r*(41*p^2))) + ((∏ j, ((ρC j).dimension : ℝ))*(s+1 : ℕ)^(c*(41*p^2))) (by positivity) (by positivity) hrow hcol + simpa only [hx,Fintype.card_fin] using hh + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.TensorBoard +variable {R C J : Type*} [Fintype R] [DecidableEq R] [Nonempty R] + [Fintype C] [DecidableEq C] [Fintype J] [DecidableEq J] +omit [Nonempty R] in +lemma board_trace_le_labels {l : ℕ} (e : Fin l → R × C) (he : Function.Injective e) + (r : R → Matrix J J ℂ) (v : C → Matrix J J ℂ) + (hr : ∀ i, (r i).PosSemidef) (hv : ∀ j, (v j).PosSemidef) + (ht : ∀ j, Matrix.trace (v j)=1) (A : Matrix J J ℂ) (hA : A.IsHermitian) + (hw : ((Fintype.card R : ℂ) • (1 : Matrix J J ℂ)-∑ i, A*r i*A).PosSemidef) : + (Matrix.trace (tensor (fun _ : Fin l => A)*tensor (fun x => r (e x).1)* + tensor (fun _ : Fin l => A)*tensor (fun x => v (e x).2))).re ≤ + Real.exp (Fintype.card R*Fintype.card C-l) := by + let F : Finset (R × C) := Finset.univ.image e + let E : Fin l ≃ F := Equiv.ofBijective (fun x => ⟨e x,by simp [F]⟩) (by + constructor + · intro x y h; exact he (congrArg Subtype.val h) + · intro y + obtain ⟨x,_,hx⟩ := Finset.mem_image.mp y.property + exact ⟨x,Subtype.ext hx⟩) + have hc : F.card=l := by + dsimp [F] + rw [Finset.card_image_of_injective _ he,Finset.card_univ,Fintype.card_fin] + have hh := board_trace_le_reindexed F E r v hr hv ht A hA hw + have hE (x : Fin l) : (E x).val=e x := rfl + simpa only [hE,hc] using hh +end CoordinateSweeps.TensorBoard + +namespace CoordinateSweeps.SignedTensor +open TensorBoard +variable {R C I J : Type*} [Fintype R] [DecidableEq R] [Nonempty R] + [Fintype C] [DecidableEq C] [Fintype I] [Fintype J] + +def labelRowProduct {p l : ℕ} (e : Fin l → R × C) (r : R → EvenDensity p) : + Matrix (Word p l) (Word p l) ℂ := TensorBoard.tensor (fun x => (r (e x).1).val) + +def labelColumnProduct {p l : ℕ} (e : Fin l → R × C) (r : C → EvenDensity p) : + Matrix (Word p l) (Word p l) ℂ := TensorBoard.tensor (fun x => (r (e x).2).val) + +/- Literal deleted-board overlap with actual signed tensor action. The two +mixture dominations will be obtained by tensoring the local density theorem; +the whitening and the full-group dimension loss are constructed here. -/ +theorem label_board_overlap_regularized {p l : ℕ} (hp : 0 < p) + (e : Fin l → R × C) (hinj : Function.Injective e) + (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) + (PR : Matrix (Word p l) (Word p l) ℂ) (xC : MonoidAlgebra ℂ (Equiv.Perm (Fin l))) + (hPR : PR.IsHermitian) (hPR2 : PR*PR=PR) + (hPC : (groupOperator (p := p) xC).IsHermitian) + (hPC2 : groupOperator (p := p) xC*groupOperator (p := p) xC=groupOperator (p := p) xC) + (u : I → ℝ) (v : J → ℝ) (hu : ∀ i, 0 ≤ u i) (hv : ∀ j, 0 ≤ v j) + (hsu : ∑ i, u i=1) (hsv : ∑ j, v j=1) + (r : I → R → EvenDensity p) (c : J → C → EvenDensity p) + (cr cc : ℝ) (hcr : 0 ≤ cr) (hcc : 0 ≤ cc) + (hrow : ((cr : ℂ) • (∑ i, (u i : ℂ) • labelRowProduct e (r i))-PR).PosSemidef) + (hcol : ((cc : ℂ) • (∑ j, (v j : ℂ) • labelColumnProduct e (c j))-groupOperator xC).PosSemidef) + {ε : ℝ} (hε : 0 < ε) : + (ρ.dimension : ℝ)*‖groupOperator (p := p) xC*ρ.projector (action p l)*PR‖^2 ≤ + cr*cc*(1+ε*(2*p : ℕ))^l*Real.exp (Fintype.card R*Fintype.card C-l) := by + let : NeZero (2*p) := ⟨by omega⟩ + let τ := action p l + let PC := groupOperator (p := p) xC + let B (i : I) : Matrix (Letter p) (Letter p) ℂ := + (Fintype.card R : ℂ)⁻¹ • (∑ k, (r i k).val)+(ε : ℂ) • 1 + choose A hA hAe hABA hAw using fun i => exists_even_whitening (r i) hε + have hb (i : I) : (B i).PosSemidef := + (average_regularization_posDef (fun k => (r i k).val) (fun k => (r i k).property.1) hε).posSemidef + have he (i : I) : IsEven (B i) := isEven_add + (isEven_smul _ (isEven_sum _ (fun k => (r i k).property.2.2))) (isEven_smul _ isEven_one) + have htau (g : Equiv.Perm (Fin l)) : (τ g).conjTranspose=τ g⁻¹ := (matrix_inv g).symm + have hpq : ρ.projector τ*PC=PC*ρ.projector τ := ρ.projector_commute_lift τ xC + have htt : 0 ≤ (1+ε*(2*p : ℕ))^l := pow_nonneg (by positivity) _ + have hwhite (i : I) : + (((1+ε*(2*p : ℕ))^l : ℝ) : ℂ) • (densityPower l (A i)*PC*densityPower l (A i)) - + (ρ.dimension : ℂ) • (PC*ρ.projector τ) |>.PosSemidef := by + have hWA : (densityPower l (A i)).IsHermitian := (densityPower_posSemidef l (A i) (hA i)).isHermitian + have hWABA : densityPower l (A i)*densityPower l (B i)*densityPower l (A i)=1 := by + rw [← densityPower_mul,← densityPower_mul,hABA i,densityPower_one] + have hh := Overlap.whitened_projector_domination ρ τ htau + (densityPower l (B i)) (densityPower l (A i)) PC (densityPower_posSemidef l (B i) (hb i)) + (fun g => densityPower_commute_of_even (B i) (he i) g) hWA hWABA + (densityPower_commute_projector (A i) (hAe i) ρ) + (densityPower_commute_lift (A i) (hAe i) xC).symm hPC hPC2 hpq + have ht : Matrix.trace (densityPower l (B i))=(((1+ε*(2*p : ℕ))^l : ℝ) : ℂ) := by + rw [densityPower_trace,even_average_trace] + push_cast + rfl + rwa [ht] at hh + apply Overlap.finite_mixture_overlap PR PC (ρ.projector τ) hPR hPR2 hPC hPC2 + (ρ.projector_hermitian τ htau) (ρ.projector_idempotent τ) hpq u v hu hv hsu hsv + (fun i => labelRowProduct e (r i)) (fun j => labelColumnProduct e (c j)) (fun i => densityPower l (A i)) + (fun i => TensorBoard.tensor_posSemidef _ (fun x => (r i (e x).1).property.1)) + (fun i => (densityPower_posSemidef l (A i) (hA i)).isHermitian) + cr cc ρ.dimension ((1+ε*(2*p : ℕ))^l) _ hcr hcc (Nat.cast_nonneg _) htt hrow hcol hwhite + intro i j + exact board_trace_le_labels e hinj (fun k => (r i k).val) (fun k => (c j k).val) + (fun k => (r i k).property.1) (fun k => (c j k).property.1) (fun k => (c j k).property.2.1) + (A i) (hA i).isHermitian (hAw i) + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open TensorBoard Overlap +variable {R C I J : Type*} [Fintype R] [DecidableEq R] [Nonempty R] + [Fintype C] [DecidableEq C] [Fintype I] [Fintype J] + +theorem label_board_overlap {p l : ℕ} (hp : 0 < p) + (e : Fin l → R × C) (hinj : Function.Injective e) + (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) + (PR : Matrix (Word p l) (Word p l) ℂ) (xC : MonoidAlgebra ℂ (Equiv.Perm (Fin l))) + (hPR : PR.IsHermitian) (hPR2 : PR*PR=PR) + (hPC : (groupOperator (p := p) xC).IsHermitian) + (hPC2 : groupOperator (p := p) xC*groupOperator (p := p) xC=groupOperator (p := p) xC) + (u : I → ℝ) (v : J → ℝ) (hu : ∀ i, 0 ≤ u i) (hv : ∀ j, 0 ≤ v j) + (hsu : ∑ i, u i=1) (hsv : ∑ j, v j=1) + (r : I → R → EvenDensity p) (c : J → C → EvenDensity p) + (cr cc : ℝ) (hcr : 0 ≤ cr) (hcc : 0 ≤ cc) + (hrow : ((cr : ℂ) • (∑ i, (u i : ℂ) • labelRowProduct e (r i))-PR).PosSemidef) + (hcol : ((cc : ℂ) • (∑ j, (v j : ℂ) • labelColumnProduct e (c j))-groupOperator xC).PosSemidef) + : + (ρ.dimension : ℝ)*‖groupOperator (p := p) xC*ρ.projector (action p l)*PR‖^2 ≤ + cr*cc*Real.exp (Fintype.card R*Fintype.card C-l) := by + let f (ε : ℝ) := cr*cc*(1+ε*(2*p : ℕ))^l*Real.exp (Fintype.card R*Fintype.card C-l) + have hf : Continuous f := by fun_prop + have hh : ∀ᶠ ε : ℝ in nhdsWithin 0 (Set.Ioi 0), + (ρ.dimension : ℝ)*‖groupOperator (p := p) xC*ρ.projector (action p l)*PR‖^2 ≤ f ε := by + filter_upwards [self_mem_nhdsWithin] with ε hε + exact label_board_overlap_regularized hp e hinj ρ PR xC hPR hPR2 hPC hPC2 + u v hu hv hsu hsv r c cr cc hcr hcc hrow hcol hε + have hh' := ge_of_tendsto (hf.continuousAt.tendsto.mono_left + (nhdsWithin_le_nhds : nhdsWithin (0 : ℝ) (Set.Ioi 0) ≤ nhds 0)) hh + simpa [f] using hh' + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open TensorBoard +variable {p r c : ℕ} [NeZero r] + {L : Type*} [Fintype L] [DecidableEq L] + +/- Source 06:eq19 for literal row and column subgroup projectors on an +arbitrary board with holes. The mixtures and signed regroupings are constructed. -/ +omit [DecidableEq L] in +theorem actual_label_overlap (f : L → Fin r) (g : L → Fin c) + (hinj : Function.Injective (fun x => (f x,g x))) + (e : Fin (Fintype.card L) ≃ L) (s : ℕ) (hp : 0 < p) (hps : p ≤ s) + (hnR : ∀ i, FiberBlocks.size f i ≤ s) + (hnC : ∀ j, FiberBlocks.size g j ≤ s) + (ρR : ∀ i, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size f i)))) + (ρC : ∀ j, UnitaryIrrep (Equiv.Perm (Fin (FiberBlocks.size g j)))) + (ρ : UnitaryIrrep (Equiv.Perm (Fin (Fintype.card L)))) : + (ρ.dimension : ℝ)*‖fiberProjector (p := p) g e ρC* + ρ.projector (action p (Fintype.card L))*fiberProjector f e ρR‖^2 ≤ + ((∏ i, ((ρR i).dimension : ℝ))*(s+1 : ℕ)^(r*(41*p^2)))* + ((∏ j, ((ρC j).dimension : ℝ))*(s+1 : ℕ)^(c*(41*p^2)))* + Real.exp (r*c-Fintype.card L) := by + obtain ⟨I,hI,nI,a,ha⟩ := finite_fiber_density_domination f e s hp hps hnR ρR + obtain ⟨J,hJ,nJ,b,hb⟩ := finite_fiber_density_domination g e s hp hps hnC ρC + let := hI + let := hJ + let := nI + let := nJ + have hI0 : (Fintype.card I : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + have hJ0 : (Fintype.card J : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + have hu : ∑ _ : I, (Fintype.card I : ℝ)⁻¹=1 := by + rw [Finset.sum_const,Finset.card_univ,nsmul_eq_mul,mul_inv_cancel₀ hI0] + have hv : ∑ _ : J, (Fintype.card J : ℝ)⁻¹=1 := by + rw [Finset.sum_const,Finset.card_univ,nsmul_eq_mul,mul_inv_cancel₀ hJ0] + have hr := fiberProjector_posSemidef (p := p) f e ρR + have hc := fiberProjector_posSemidef (p := p) g e ρC + have hr2 := fiberProjector_idempotent (p := p) f e ρR + have hc2 := fiberProjector_idempotent (p := p) g e ρC + let xC := fiberProjectorAlgebra g e ρC + have hx : groupOperator (p := p) xC=fiberProjector (p := p) g e ρC := + fiberProjectorAlgebra_lift _ _ _ + have hrow : (((∏ i, ((ρR i).dimension : ℝ))*(s+1 : ℕ)^(r*(41*p^2)) : ℝ) : ℂ) • + (∑ i : I, (((Fintype.card I : ℝ)⁻¹ : ℝ) : ℂ) • labelRowProduct (fun x => (f (e x),g (e x))) (a i))- + fiberProjector (p := p) f e ρR |>.PosSemidef := by + simpa only [Complex.ofReal_mul,Complex.ofReal_prod,Complex.ofReal_natCast,Complex.ofReal_pow, + Complex.ofReal_inv,← Finset.smul_sum,labelRowProduct] using ha + have hcol : (((∏ j, ((ρC j).dimension : ℝ))*(s+1 : ℕ)^(c*(41*p^2)) : ℝ) : ℂ) • + (∑ j : J, (((Fintype.card J : ℝ)⁻¹ : ℝ) : ℂ) • labelColumnProduct (fun x => (f (e x),g (e x))) (b j))- + groupOperator (p := p) xC |>.PosSemidef := by + rw [hx] + simpa only [Complex.ofReal_mul,Complex.ofReal_prod,Complex.ofReal_natCast,Complex.ofReal_pow, + Complex.ofReal_inv,← Finset.smul_sum,labelColumnProduct] using hb + have hh := label_board_overlap hp (fun x => (f (e x),g (e x))) (hinj.comp e.injective) ρ _ xC hr.isHermitian hr2 (hx ▸ hc.isHermitian) + (by rw [hx]; exact hc2) (fun _ : I => (Fintype.card I : ℝ)⁻¹) + (fun _ : J => (Fintype.card J : ℝ)⁻¹) (fun _ => by positivity) (fun _ => by positivity) + hu hv a b ((∏ i, ((ρR i).dimension : ℝ))*(s+1 : ℕ)^(r*(41*p^2))) + ((∏ j, ((ρC j).dimension : ℝ))*(s+1 : ℕ)^(c*(41*p^2))) (by positivity) (by positivity) hrow hcol + simpa only [hx,Fintype.card_fin] using hh + +end CoordinateSweeps.SignedTensor + +end +end +end +end +end +end +end +end +open scoped Matrix.Norms.L2Operator + +end OAI diff --git a/lean/OAI/RepresentationTheory/SignedTensor/Resolution.lean b/lean/OAI/RepresentationTheory/SignedTensor/Resolution.lean index 175b5b6eb30c4ae7d88b5652edcb22370712fda7..82f306cd9a5e602bd82a50706a5f78cb927f8633 100644 --- a/lean/OAI/RepresentationTheory/SignedTensor/Resolution.lean +++ b/lean/OAI/RepresentationTheory/SignedTensor/Resolution.lean @@ -1,575 +1,575 @@ -import Mathlib -import OAI.RepresentationTheory.SignedTensor.Overlap -import OAI.Analysis.Matrix.Holder -import OAI.RepresentationTheory.Young.Classification - -namespace OAI - -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ComplexConjugate Matrix.Norms.L2Operator -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ComplexOrder MatrixOrder -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ENNReal -open MeasureTheory -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -noncomputable section -open scoped BigOperators -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable -noncomputable section -attribute [local instance] Classical.propDecidable -noncomputable section -open Set Complex -open scoped BigOperators Topology -open scoped Matrix.Norms.L2Operator -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -namespace CoordinateSweeps.SignedTensor - -def ActiveType (p l : ℕ) := - { a : Nat.Partition (Fintype.card (Fin l)) // (YoungCorner.partitionUnitary (Fin l) a).projector (action p l) ≠ 0 } - -instance (p l : ℕ) : Fintype (ActiveType p l) := by - unfold ActiveType - infer_instance - -instance (p l : ℕ) : DecidableEq (ActiveType p l) := Classical.decEq _ - -def activeIrrep {p l : ℕ} (a : ActiveType p l) : UnitaryIrrep (Equiv.Perm (Fin l)) := - YoungCorner.partitionUnitary (Fin l) a.val - -def activeProjector {p l : ℕ} (a : ActiveType p l) : commutant p l := - ⟨(activeIrrep a).projector (action p l),fun σ => - ((activeIrrep a).projector_commute (action p l) σ).symm⟩ - -lemma activeProjector_nonzero {p l : ℕ} (a : ActiveType p l) : - (activeProjector a).val ≠ 0 := a.property - -lemma active_inequivalent {p l : ℕ} (a b : ActiveType p l) (hab : a ≠ b) : - ¬Nonempty (Representation.Equiv (activeIrrep a).asRepresentation (activeIrrep b).asRepresentation) := by - apply YoungCorner.partitionUnitary_inequivalent - intro h - apply hab - apply Subtype.ext - simpa using h - -lemma activeProjector_mul {p l : ℕ} (a b : ActiveType p l) : - (activeProjector a).val*(activeProjector b).val= - if a=b then (activeProjector a).val else 0 := by - split_ifs with h - · subst b; exact (activeIrrep a).projector_idempotent _ - · exact (activeIrrep a).projector_orthogonal (activeIrrep b) - (active_inequivalent b a (Ne.symm h)) _ - -lemma activeProjector_independent (p l : ℕ) : - LinearIndependent ℂ (activeProjector (p := p) (l := l)) := by - apply linearIndependent_iff'.mpr - intro t c hc a ha - have hh := congrArg (fun A : commutant p l => (activeProjector a).val*A.val) hc - have hv : ∑ b ∈ t, c b • ((activeProjector a).val*(activeProjector b).val)=0 := by - simpa only [Submodule.coe_sum,Submodule.coe_smul,ZeroMemClass.coe_zero, - Matrix.mul_sum,Matrix.mul_smul,mul_zero] using hh - simp only [activeProjector_mul,smul_ite,smul_zero] at hv - have he : c a • (activeProjector a).val=0 := by simpa [ha] using hv - exact (smul_eq_zero.mp he).resolve_right (activeProjector_nonzero a) - -/- Number of actually occurring local types is polynomial even without a -hook-support classification; this is exactly the term-count scale in06:eq20. -/ -theorem active_card_le (p l : ℕ) : - Fintype.card (ActiveType p l) ≤ (l+1)^((2*p)*(2*p)) := - (activeProjector_independent p l).fintype_card_le_finrank.trans (commutant_finrank_le p l) - -/- Omitting zero type projections preserves the actual identity resolution. -/ -theorem active_resolution (p l : ℕ) : - ∑ a : ActiveType p l, (activeProjector a).val=1 := by - let f (a : Nat.Partition (Fintype.card (Fin l))) := - (YoungCorner.partitionUnitary (Fin l) a).projector (action p l) - have he : ∑ a : ActiveType p l, (activeProjector a).val=∑ a : Nat.Partition (Fintype.card (Fin l)), f a := by - change (∑ a : {a : Nat.Partition (Fintype.card (Fin l)) // f a ≠ 0}, f a.val)=∑ a, f a - rw [← Finset.sum_subtype (Finset.univ.filter (fun a => f a ≠ 0)) (by simp),Finset.sum_filter] - apply Finset.sum_congr rfl - intro a ha - split_ifs with h - · rfl - · exact (not_ne_iff.mp h).symm - rw [he] - have hh := YoungCorner.partition_matrix_resolution (Fin l) (action p l) - simpa [f] using hh - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -variable {p r : ℕ} (n : Fin r → ℕ) -abbrev BlockType (p : ℕ) := ∀ i, ActiveType p (n i) - -abbrev blockProjector (α : BlockType n p) := groupedProjector (p := p) n (fun i => activeIrrep (α i)) - -/- Actual polynomial-size identity resolution of each product subgroup. -/ -lemma block_resolution : ∑ α : BlockType n p, blockProjector n α=1 := by - simp only [blockProjector,groupedProjector_factor] - change (∑ α : BlockType n p, Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm - (DependentTensor.tensor (fun i => (activeIrrep (α i)).projector (action p (n i)))))=1 - rw [← map_sum] - rw [← DependentTensor.tensor_sum (fun i (a : ActiveType p (n i)) => (activeIrrep a).projector (action p (n i)))] - have hh (i : Fin r) : ∑ a : ActiveType p (n i), (activeIrrep a).projector (action p (n i))=1 := - active_resolution p (n i) - simp only [hh,DependentTensor.tensor_one,map_one] - -lemma block_card_le (s : ℕ) (hn : ∀ i, n i ≤ s) : - Fintype.card (BlockType n p) ≤ (s+1)^(r*((2*p)*(2*p))) := by - rw [Fintype.card_pi] - calc - _ ≤ ∏ i : Fin r, (s+1)^((2*p)*(2*p)) := Finset.prod_le_prod (fun i hi => - (active_card_le p (n i)).trans (Nat.pow_le_pow_left (Nat.succ_le_succ (hn i)) _)) - _ = _ := by rw [Finset.prod_const,Finset.card_univ,Fintype.card_fin,← pow_mul,Nat.mul_comm] - -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -open UnitaryIrrep FiberBlocks -variable {p r l : ℕ} (n : Fin r → ℕ) -lemma ambient_block_resolution (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) : - (∑ α : BlockType n p, ambientProjector (p := p) n h σ (fun i => activeIrrep (α i)))=1 := by - subst l - unfold ambientProjector lengthMatrix - rw [← Matrix.sum_mul,← Matrix.mul_sum,block_resolution,mul_one,matrix_unitary_reverse] - -variable {L : Type*} [Fintype L] -lemma fiber_block_resolution (f : L → Fin r) (e : Fin (Fintype.card L) ≃ L) : - (∑ α : BlockType (size f) p, fiberProjector (p := p) f e (fun i => activeIrrep (α i)))=1 := - ambient_block_resolution _ _ _ - -def blockEntropy {n : Fin r → ℕ} (α : BlockType n p) : ℝ := - ∑ i, Real.log (activeIrrep (α i)).dimension - -lemma exp_blockEntropy {n : Fin r → ℕ} (α : BlockType n p) : - Real.exp (blockEntropy α)=∏ i, ((activeIrrep (α i)).dimension : ℝ) := by - rw [blockEntropy,Real.exp_sum] - apply Finset.prod_congr rfl - intro i _ - exact Real.exp_log (Nat.cast_pos.mpr (activeIrrep (α i)).positive) - -lemma nat_pow_eq_exp (s t : ℕ) : ((s+1 : ℕ) : ℝ)^t=Real.exp ((t : ℝ)*Real.log (s+1 : ℕ)) := by - rw [mul_comm,Real.exp_mul,Real.exp_log (by positivity),Real.rpow_natCast] - -lemma block_card_real_le (f : L → Fin r) (s : ℕ) (hn : ∀ i, size f i ≤ s) : - (Fintype.card (BlockType (size f) p) : ℝ) ≤ - Real.exp ((r*((2*p)*(2*p)) : ℕ)*Real.log (s+1 : ℕ)) := by - rw [← nat_pow_eq_exp] - exact_mod_cast block_card_le (size f) s hn - -lemma actual_label_overlap_exp {c : ℕ} [NeZero r] - (f : L → Fin r) (g : L → Fin c) (hinj : Function.Injective (fun x => (f x,g x))) - (e : Fin (Fintype.card L) ≃ L) (s : ℕ) (hp : 0 < p) (hps : p ≤ s) - (hnR : ∀ i, size f i ≤ s) (hnC : ∀ j, size g j ≤ s) - (α : BlockType (size f) p) (β : BlockType (size g) p) - (ρ : UnitaryIrrep (Equiv.Perm (Fin (Fintype.card L)))) : - ‖fiberProjector g e (fun j => activeIrrep (β j))*ρ.projector (action p (Fintype.card L))* - fiberProjector f e (fun i => activeIrrep (α i))‖^2 ≤ - Real.exp (blockEntropy α+blockEntropy β-Real.log ρ.dimension+ - ((r : ℝ)*c-Fintype.card L)+((r+c)*(41*p^2) : ℕ)*Real.log (s+1 : ℕ)) := by - have hh := actual_label_overlap f g hinj e s hp hps hnR hnC - (fun i => activeIrrep (α i)) (fun j => activeIrrep (β j)) ρ - have hD : 0 < (ρ.dimension : ℝ) := Nat.cast_pos.mpr ρ.positive - apply (mul_le_mul_iff_right₀ hD).mp - apply hh.trans_eq - rw [← exp_blockEntropy α,← exp_blockEntropy β,nat_pow_eq_exp,nat_pow_eq_exp] - nth_rw 1 [← Real.exp_log hD] - simp only [← Real.exp_add] - congr 1 - push_cast - ring - -lemma actual_label_overlap_contract {c : ℕ} (f : L → Fin r) (g : L → Fin c) - (e : Fin (Fintype.card L) ≃ L) (hp : 0 < p) - (α : BlockType (size f) p) (β : BlockType (size g) p) - (ρ : UnitaryIrrep (Equiv.Perm (Fin (Fintype.card L)))) : - ‖fiberProjector g e (fun j => activeIrrep (β j))*ρ.projector (action p (Fintype.card L))* - fiberProjector f e (fun i => activeIrrep (α i))‖ ≤ 1 := by - let : NeZero (2*p) := ⟨by omega⟩ - have hR := TraceHolder.projector_norm_le _ (fiberProjector_posSemidef f e _).isHermitian - (fiberProjector_idempotent (p := p) f e (fun i => activeIrrep (α i))) - have hC := TraceHolder.projector_norm_le _ (fiberProjector_posSemidef g e _).isHermitian - (fiberProjector_idempotent (p := p) g e (fun i => activeIrrep (β i))) - have hP := TraceHolder.projector_norm_le _ (ρ.projector_posSemidef _ (fun σ => (matrix_inv σ).symm)).isHermitian - (ρ.projector_idempotent (action p (Fintype.card L))) - calc - _ ≤ (‖fiberProjector g e (fun j => activeIrrep (β j))‖*‖ρ.projector (action p (Fintype.card L))‖)* - ‖fiberProjector f e (fun i => activeIrrep (α i))‖ := by - exact (Matrix.l2_opNorm_mul _ _).trans - (mul_le_mul_of_nonneg_right (Matrix.l2_opNorm_mul _ _) (norm_nonneg _)) - _ ≤ (1*1)*1 := mul_le_mul (mul_le_mul hC hP (norm_nonneg _) (by positivity)) hR - (norm_nonneg _) (by positivity) - _ = 1 := by norm_num - -/- The actual two-product-subgroup inequality. Its only analytic inputs are -child moments; the resolution, polynomial number of types and board overlap -are all constructed above. This is the row/column step of the main induction. -/ -theorem labeled_projected_moment_bound {c : ℕ} [NeZero r] - (f : L → Fin r) (g : L → Fin c) (hinj : Function.Injective (fun x => (f x,g x))) - (e : Fin (Fintype.card L) ≃ L) (s : ℕ) (hp : 0 < p) (hps : p ≤ s) - (hnR : ∀ i, size f i ≤ s) (hnC : ∀ j, size g j ≤ s) - (ρ : UnitaryIrrep (Equiv.Perm (Fin (Fintype.card L)))) (q : ℕ) (hq : 0 < q) - (c₀ ER EC : ℝ) (hc : 0 ≤ c₀) (hcq : c₀ ≤ q) - (X Y : Matrix (Word p (Fintype.card L)) (Word p (Fintype.card L)) ℂ) - (hR : ∀ α : BlockType (size f) p, - (Matrix.trace (((fiberProjector f e (fun i => activeIrrep (α i))*X).conjTranspose* - (fiberProjector f e (fun i => activeIrrep (α i))*X))^q)).re ≤ Real.exp (-c₀*blockEntropy α+ER)) - (hC : ∀ β : BlockType (size g) p, - (Matrix.trace (((Y*fiberProjector g e (fun j => activeIrrep (β j))).conjTranspose* - (Y*fiberProjector g e (fun j => activeIrrep (β j))))^q)).re ≤ Real.exp (-c₀*blockEntropy β+EC)) : - (Matrix.trace (((Y*ρ.projector (action p (Fintype.card L))*X).conjTranspose* - (Y*ρ.projector (action p (Fintype.card L))*X))^q)).re ≤ - Real.exp (-c₀*Real.log ρ.dimension+ER+EC+c₀*((r : ℝ)*c-Fintype.card L)+ - ((2*q : ℕ)*((r+c)*((2*p)*(2*p)) : ℕ)+c₀*((r+c)*(41*p^2) : ℕ))*Real.log (s+1 : ℕ)) := by - let : NeZero (2*p) := ⟨by omega⟩ - have hh := TraceHolder.row_column_moment q hq - (fun α : BlockType (size f) p => fiberProjector f e (fun i => activeIrrep (α i))) - (fun β : BlockType (size g) p => fiberProjector g e (fun j => activeIrrep (β j))) - (fiber_block_resolution f e) (fiber_block_resolution g e) - (fun α => fiberProjector_idempotent f e _) (fun β => fiberProjector_idempotent g e _) - (ρ.projector (action p (Fintype.card L))) X Y blockEntropy blockEntropy (Real.log ρ.dimension) - (ER+EC) (((r : ℝ)*c-Fintype.card L)+((r+c)*(41*p^2) : ℕ)*Real.log (s+1 : ℕ)) c₀ hc hcq - (fun α β => (mul_le_mul (hR α) (hC β) - (by exact (Complex.nonneg_iff.mp (Matrix.posSemidef_conjTranspose_mul_self _ |>.pow q |>.trace_nonneg)).1) - (Real.exp_pos _).le).trans_eq (by rw [← Real.exp_add]; congr 1; ring)) - (fun α β => by simpa only [add_assoc] using actual_label_overlap_exp f g hinj e s hp hps hnR hnC α β ρ) - (fun α β => actual_label_overlap_contract f g e hp α β ρ) - apply hh.trans - have hcard := mul_le_mul (block_card_real_le (p := p) f s hnR) (block_card_real_le (p := p) g s hnC) - (Nat.cast_nonneg _) (Real.exp_pos _).le - rw [← Real.exp_add] at hcard - have hpow := pow_le_pow_left₀ (by positivity : 0 ≤ - (Fintype.card (BlockType (size f) p) : ℝ)*(Fintype.card (BlockType (size g) p) : ℝ)) hcard (2*q) - rw [← Real.exp_nat_mul] at hpow - rw [Nat.cast_mul] - apply (mul_le_mul_of_nonneg_right hpow (Real.exp_pos _).le).trans_eq - rw [← Real.exp_add] - congr 1 - push_cast - ring -end CoordinateSweeps.SignedTensor - -namespace CoordinateSweeps.SignedTensor -lemma phase_eq_of_same_parity {p l : ℕ} (σ : Equiv.Perm (Fin l)) (u w : Word p l) - (h : ∀ i, odd (u i) ↔ odd (w i)) : phase σ u=phase σ w := by - rw [phase_prod,phase_prod] - apply Finset.prod_congr rfl - intro ij hij - simp only [h] - -lemma wordPerm_same_parity {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) - (h : ∀ i, odd (w (σ i)) ↔ odd (w i)) : - ∀ i, odd (wordPerm σ w i) ↔ odd (w i) := by - intro i - simpa [wordPerm] using (h (σ⁻¹ i)).symm - -lemma phase_conj_of_parity_stable {p l : ℕ} (σ g : Equiv.Perm (Fin l)) (w : Word p l) - (h : ∀ i, odd (w (σ i)) ↔ odd (w i)) : - phase (g*σ*g⁻¹) (wordPerm g w)=phase σ w := by - have he : (g*σ*g⁻¹)*g=g*σ := by simp [mul_assoc] - have hh := phase_mul (g*σ*g⁻¹) g w - rw [he,phase_mul,phase_eq_of_same_parity g _ w (wordPerm_same_parity σ w h)] at hh - apply mul_right_cancel₀ (phase_ne_zero g w) - rw [← hh,mul_comm] - -lemma phase_of_fix_odd {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) - (h : ∀ i, odd (w i) → σ i=i) : phase σ w=1 := by - rw [phase_prod] - apply Finset.prod_eq_one - intro ij hij - have hj := Equiv.Perm.mem_finPairsLT.mp hij - split_ifs with hh - · rw [h _ hh.1,h _ hh.2.1] at hh - exact False.elim (hj.not_gt hh.2.2) - · rfl - -lemma phase_swap_odd {p l : ℕ} (w : Word p l) (i j : Fin l) (hij : i ≠ j) - (hi : odd (w i)) (hj : odd (w j)) : phase (Equiv.swap i j) w = -1 := by - have hl : 2 ≤ l := by - have hn : i.val ≠ j.val := fun h => hij (Fin.ext h) - have hi := i.isLt - have hj := j.isLt - omega - obtain ⟨n,rfl⟩ : ∃ n, l=n+2 := ⟨l-2,by omega⟩ - obtain ⟨g,hgi,hgj⟩ := exists_perm_pair i j (0 : Fin (n+2)) 1 hij (by simp) - have hp : ∀ x, odd (w (Equiv.swap i j x)) ↔ odd (w x) := by - intro x - simp only [Equiv.swap_apply_def] - split_ifs <;> simp_all - have he : g*Equiv.swap i j*g⁻¹=Equiv.swap (0 : Fin (n+2)) 1 := by - rw [Equiv.mul_swap_eq_swap_mul,mul_assoc,mul_inv_cancel,mul_one,hgi,hgj] - have hh:=phase_conj_of_parity_stable (Equiv.swap i j) g w hp - rw [he,phase_swap01] at hh - have h0 : wordPerm g w 0=w i := by rw [← hgi]; simp [wordPerm] - have h1 : wordPerm g w 1=w j := by rw [← hgj]; simp [wordPerm] - simpa [h0,h1,hi,hj] using hh.symm - -lemma phase_ofSubtype {p l : ℕ} (w : Word p l) - (σ : Equiv.Perm {i : Fin l // odd (w i)}) : - phase (Equiv.Perm.ofSubtype σ) w = YoungCorner.signScalar σ := by - induction σ using Equiv.Perm.swap_induction_on with - | one => simp [phase_one] - | swap_mul σ i j hij ih => - rw [map_mul,phase_mul,Equiv.Perm.ofSubtype_swap_eq] - have hp := wordPerm_same_parity (Equiv.Perm.ofSubtype σ) w - (Equiv.Perm.ofSubtype_apply_mem_iff_mem σ) - rw [phase_eq_of_same_parity _ _ w hp, - phase_swap_odd w i j (fun he => hij (Subtype.ext he)) i.property j.property, - ih,map_mul,YoungCorner.signScalar_swap i j hij] - -lemma phase_of_fix_even {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) - (h : ∀ i, ¬ odd (w i) → σ i=i) : phase σ w=YoungCorner.signScalar σ := by - have hp : ∀ i, odd (w (σ i)) ↔ odd (w i) := by - intro i - by_cases hi : odd (w i) - · have hs : odd (w (σ i)) := by - by_contra hn - have hh := h (σ i) hn - have he := σ.injective hh - rw [he] at hn - exact hn hi - simp [hi,hs] - · rw [h i hi] - let υ := Equiv.Perm.subtypePerm (p := fun i => odd (w i)) σ hp - have he : Equiv.Perm.ofSubtype υ=σ := Equiv.Perm.ofSubtype_subtypePerm (p := fun i => odd (w i)) hp (by - intro i hi - exact Classical.byContradiction (fun hn => hi (h i hn))) - rw [← he,phase_ofSubtype] - simp [YoungCorner.signScalar,Equiv.Perm.sign_ofSubtype] - -end CoordinateSweeps.SignedTensor -namespace CoordinateSweeps.YoungCorner -variable {μ : YoungDiagram} {p : ℕ} - -def Hook (μ : YoungDiagram) (p : ℕ) : Prop := ∀ x : Boxes μ, x.val.1

simp_all - omega - -lemma hookLetter_row_eq (h : Hook μ p) (x y : Boxes μ) - (hx : x.val.1 simp_all - omega - -lemma hookLetter_col_eq (h : Hook μ p) (x y : Boxes μ) - (hx : p≤x.val.1) (he : hookLetter h x=hookLetter h y) : x.val.2=y.val.2 := by - have he' := congrArg Fin.val he - simp only [hookLetter] at he' - split_ifs at he' <;> simp_all <;> omega - -/- The geometric reason all diagonal Young-corner coefficients have positive -sign on the actual even-row/odd-column hook word. -/ -lemma hook_corner_fixed {X : Type*} (t : X ≃ Boxes μ) (h : Hook μ p) - (r : colorStabilizer (rowColor t)) (c : colorStabilizer (colColor t)) - (hw : ∀ x, hookLetter h (t ((r : Equiv.Perm X) (c.val x)))=hookLetter h (t x)) : - (∀ x, (t x).val.1

hookLetter h (t x))= - signScalar (c : Equiv.Perm (Fin l)) := by - obtain ⟨hc,hr⟩ := hook_corner_fixed t h r c hw - let w : SignedTensor.Word p l := fun x => hookLetter h (t x) - have hce : ∀ i, ¬ SignedTensor.odd (w i) → (c : Equiv.Perm (Fin l)) i=i := by - intro i hi - exact hc i (by simpa only [w,hookLetter_odd,not_le] using hi) - have hcp : ∀ i, SignedTensor.odd (w (c.val i)) ↔ SignedTensor.odd (w i) := by - intro i - by_cases hi : SignedTensor.odd (w i) - · have hh : SignedTensor.odd (w (c.val i)) := by - by_contra hn - have he := c.val.injective (hce (c.val i) hn) - rw [he] at hn - exact hn hi - simp [hi,hh] - · rw [hce i hi] - rw [SignedTensor.phase_mul,SignedTensor.phase_eq_of_same_parity _ _ w - (SignedTensor.wordPerm_same_parity c.val w hcp),SignedTensor.phase_of_fix_odd _ w] - · rw [one_mul,SignedTensor.phase_of_fix_even c.val w hce] - · intro i hi - exact hr i ((hookLetter_odd h (t i)).mp hi) - -end CoordinateSweeps.YoungCorner - -namespace CoordinateSweeps.YoungCorner -variable {μ : YoungDiagram} {p l : ℕ} - -lemma signScalar_square {X : Type*} [Fintype X] [DecidableEq X] (c : Equiv.Perm X) : - signScalar c * signScalar c=1 := by - rcases Int.units_eq_one_or (Equiv.Perm.sign c) with h|h <;> simp [signScalar,h] - -lemma hook_contribution (t : Fin l ≃ Boxes μ) (h : Hook μ p) - (r : colorStabilizer (rowColor t)) (c : colorStabilizer (colColor t)) : - let w : SignedTensor.Word p l := fun x => hookLetter h (t x) - signScalar c.val * SignedTensor.matrix (r.val*c.val) w w = - if w=SignedTensor.wordPerm (r.val*c.val) w then 1 else 0 := by - dsimp only - rw [SignedTensor.matrix] - split_ifs with he - · have hw : ∀ x, hookLetter h (t (r.val (c.val x)))=hookLetter h (t x) := by - intro x - have hh := congrFun he ((r.val*c.val) x) - simpa [SignedTensor.wordPerm,Equiv.Perm.mul_apply] using hh - rw [hook_corner_phase t h r c hw,signScalar_square] - · simp - -lemma hook_corner_matrix_ne (t : Fin l ≃ Boxes μ) (h : Hook μ p) : - fixedSum (rowColor t) (SignedTensor.action p l) * - alternatingSum (colColor t) (SignedTensor.action p l) ≠ 0 := by - let w : SignedTensor.Word p l := fun x => hookLetter h (t x) - have he : (fixedSum (rowColor t) (SignedTensor.action p l) * - alternatingSum (colColor t) (SignedTensor.action p l)) w w = - ∑ r : colorStabilizer (rowColor t), ∑ c : colorStabilizer (colColor t), - if w=SignedTensor.wordPerm (r.val*c.val) w then (1 : ℂ) else 0 := by - rw [fixedSum,alternatingSum,Finset.sum_mul] - simp only [Finset.mul_sum,mul_smul_comm,← map_mul,Matrix.sum_apply,Matrix.smul_apply,smul_eq_mul] - apply Finset.sum_congr rfl - intro r hr - apply Finset.sum_congr rfl - intro c hc - exact hook_contribution t h r c - have hpos : 0 < ((fixedSum (rowColor t) (SignedTensor.action p l) * - alternatingSum (colColor t) (SignedTensor.action p l)) w w).re := by - rw [he] - simp only [Complex.re_sum,apply_ite,Complex.one_re,Complex.zero_re] - apply Finset.sum_pos' - · intro r hr - apply Finset.sum_nonneg - intro c hc - split_ifs <;> norm_num - · refine ⟨1,Finset.mem_univ _,?_⟩ - apply Finset.sum_pos' - · intro c hc - split_ifs <;> norm_num - · refine ⟨1,Finset.mem_univ _,?_⟩ - simp [SignedTensor.wordPerm] - intro hz - rw [hz] at hpos - simp at hpos - -/- The literal signed action, as a linear representation. -/ -def signedRep (p l : ℕ) : Representation ℂ (Equiv.Perm (Fin l)) (SignedTensor.Word p l → ℂ) := - Matrix.toLinAlgEquiv'.toMonoidHom.comp (SignedTensor.action p l) - -lemma signedRep_hasShape (t : Fin l ≃ Boxes μ) (h : Hook μ p) : - hasShape μ t (signedRep p l) := by - have he : fixedSum (rowColor t) (signedRep p l) * alternatingSum (colColor t) (signedRep p l) = - Matrix.toLinAlgEquiv' (fixedSum (rowColor t) (SignedTensor.action p l) * - alternatingSum (colColor t) (SignedTensor.action p l)) := by - simp [fixedSum,alternatingSum,signedRep,map_sum,map_mul] - intro hz - rw [he] at hz - exact hook_corner_matrix_ne t h (Matrix.toLinAlgEquiv'.injective (hz.trans (map_zero _).symm)) - -lemma detecting_shape_constituent {X V : Type*} [Fintype X] [DecidableEq X] - [AddCommGroup V] [Module ℂ V] [FiniteDimensional ℂ V] - (τ : Representation ℂ (Equiv.Perm X) V) (t : X ≃ Boxes μ) (h : hasShape μ t τ) : - ∃ S : Subrepresentation τ, S.toRepresentation.IsIrreducible ∧ hasShape μ t S.toRepresentation := by - obtain ⟨S,hS,v,hv⟩ := RepDetection.exists_irreducible_detecting τ - (fixedSum (rowColor t) τ*alternatingSum (colColor t) τ) h - refine ⟨S,hS,?_⟩ - intro hh - apply hv - have hz := congrArg (fun A : Module.End ℂ S.toSubmodule => (A v : V)) hh - simp only [Module.End.mul_apply,fixedSum_subrepresentation,alternatingSum_subrepresentation] at hz - exact hz - -/- Source05 hook occurrence, derived for actual irreps in the exact Koszul -representation. No Pieri/Schur--Weyl or hook classification is assumed. -/ -theorem hook_occurs {V : Type} [AddCommGroup V] [Module ℂ V] [FiniteDimensional ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin l)) V) [ρ.IsIrreducible] - (t : Fin l ≃ Boxes μ) (hρ : hasShape μ t ρ) (h : Hook μ p) : - ∃ S : Subrepresentation (signedRep p l), - Nonempty (Representation.Equiv ρ S.toRepresentation) := by - obtain ⟨S,hS,hSh⟩ := detecting_shape_constituent (signedRep p l) t (signedRep_hasShape t h) - let := hS - exact ⟨S,equiv_of_same_shape ρ S.toRepresentation μ t t hρ hSh⟩ - -end CoordinateSweeps.YoungCorner - -namespace CoordinateSweeps.YoungCorner -open UnitaryIrrep SignedTensor -lemma hook_multiplicity_pos {p l : ℕ} {μ : YoungDiagram} - (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) (t : Fin l ≃ Boxes μ) - (hρ : hasShape μ t ρ.asRepresentation) (hhook : Hook μ p) : - 0 < Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation (action p l))) := by - obtain ⟨S,⟨e⟩⟩ := hook_occurs ρ.asRepresentation t hρ hhook - let inc : S.toRepresentation.IntertwiningMap (signedRep p l) := - ⟨S.toSubmodule.subtype,fun _ => rfl⟩ - let f := inc.comp e.toIntertwiningMap - have hf : f ≠ 0 := by - intro hz - have hzero : ∀ v : Fin ρ.dimension → ℂ, v=0 := by - intro v - apply e.toLinearEquiv.injective - apply Subtype.val_injective - have hh := congrArg (fun g : ρ.asRepresentation.IntertwiningMap (signedRep p l) => g v) hz - change ((e.toLinearEquiv v : S.toSubmodule) : SignedTensor.Word p l → ℂ)=0 at hh - rw [map_zero] - exact hh - have : Nonempty (Fin ρ.dimension) := Fin.pos_iff_nonempty.mp ρ.positive - exact one_ne_zero (congrFun (hzero (fun _ => 1)) (Classical.arbitrary (Fin ρ.dimension))) - let : Nontrivial (ρ.asRepresentation.IntertwiningMap (signedRep p l)) := nontrivial_of_ne f 0 hf - change 0 < Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (signedRep p l)) - exact Module.finrank_pos -end CoordinateSweeps.YoungCorner -end -end -end -end -end -end -end -end -end -end -open scoped Matrix.Norms.L2Operator - -end OAI +import Mathlib +import OAI.RepresentationTheory.SignedTensor.Overlap +import OAI.Analysis.Matrix.Holder +import OAI.RepresentationTheory.Young.Classification + +namespace OAI + +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ComplexConjugate Matrix.Norms.L2Operator +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ComplexOrder MatrixOrder +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ENNReal +open MeasureTheory +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +noncomputable section +open scoped BigOperators +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable +noncomputable section +attribute [local instance] Classical.propDecidable +noncomputable section +open Set Complex +open scoped BigOperators Topology +open scoped Matrix.Norms.L2Operator +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +namespace CoordinateSweeps.SignedTensor + +def ActiveType (p l : ℕ) := + { a : Nat.Partition (Fintype.card (Fin l)) // (YoungCorner.partitionUnitary (Fin l) a).projector (action p l) ≠ 0 } + +instance (p l : ℕ) : Fintype (ActiveType p l) := by + unfold ActiveType + infer_instance + +instance (p l : ℕ) : DecidableEq (ActiveType p l) := Classical.decEq _ + +def activeIrrep {p l : ℕ} (a : ActiveType p l) : UnitaryIrrep (Equiv.Perm (Fin l)) := + YoungCorner.partitionUnitary (Fin l) a.val + +def activeProjector {p l : ℕ} (a : ActiveType p l) : commutant p l := + ⟨(activeIrrep a).projector (action p l),fun σ => + ((activeIrrep a).projector_commute (action p l) σ).symm⟩ + +lemma activeProjector_nonzero {p l : ℕ} (a : ActiveType p l) : + (activeProjector a).val ≠ 0 := a.property + +lemma active_inequivalent {p l : ℕ} (a b : ActiveType p l) (hab : a ≠ b) : + ¬Nonempty (Representation.Equiv (activeIrrep a).asRepresentation (activeIrrep b).asRepresentation) := by + apply YoungCorner.partitionUnitary_inequivalent + intro h + apply hab + apply Subtype.ext + simpa using h + +lemma activeProjector_mul {p l : ℕ} (a b : ActiveType p l) : + (activeProjector a).val*(activeProjector b).val= + if a=b then (activeProjector a).val else 0 := by + split_ifs with h + · subst b; exact (activeIrrep a).projector_idempotent _ + · exact (activeIrrep a).projector_orthogonal (activeIrrep b) + (active_inequivalent b a (Ne.symm h)) _ + +lemma activeProjector_independent (p l : ℕ) : + LinearIndependent ℂ (activeProjector (p := p) (l := l)) := by + apply linearIndependent_iff'.mpr + intro t c hc a ha + have hh := congrArg (fun A : commutant p l => (activeProjector a).val*A.val) hc + have hv : ∑ b ∈ t, c b • ((activeProjector a).val*(activeProjector b).val)=0 := by + simpa only [Submodule.coe_sum,Submodule.coe_smul,ZeroMemClass.coe_zero, + Matrix.mul_sum,Matrix.mul_smul,mul_zero] using hh + simp only [activeProjector_mul,smul_ite,smul_zero] at hv + have he : c a • (activeProjector a).val=0 := by simpa [ha] using hv + exact (smul_eq_zero.mp he).resolve_right (activeProjector_nonzero a) + +/- Number of actually occurring local types is polynomial even without a +hook-support classification; this is exactly the term-count scale in06:eq20. -/ +theorem active_card_le (p l : ℕ) : + Fintype.card (ActiveType p l) ≤ (l+1)^((2*p)*(2*p)) := + (activeProjector_independent p l).fintype_card_le_finrank.trans (commutant_finrank_le p l) + +/- Omitting zero type projections preserves the actual identity resolution. -/ +theorem active_resolution (p l : ℕ) : + ∑ a : ActiveType p l, (activeProjector a).val=1 := by + let f (a : Nat.Partition (Fintype.card (Fin l))) := + (YoungCorner.partitionUnitary (Fin l) a).projector (action p l) + have he : ∑ a : ActiveType p l, (activeProjector a).val=∑ a : Nat.Partition (Fintype.card (Fin l)), f a := by + change (∑ a : {a : Nat.Partition (Fintype.card (Fin l)) // f a ≠ 0}, f a.val)=∑ a, f a + rw [← Finset.sum_subtype (Finset.univ.filter (fun a => f a ≠ 0)) (by simp),Finset.sum_filter] + apply Finset.sum_congr rfl + intro a ha + split_ifs with h + · rfl + · exact (not_ne_iff.mp h).symm + rw [he] + have hh := YoungCorner.partition_matrix_resolution (Fin l) (action p l) + simpa [f] using hh + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +variable {p r : ℕ} (n : Fin r → ℕ) +abbrev BlockType (p : ℕ) := ∀ i, ActiveType p (n i) + +abbrev blockProjector (α : BlockType n p) := groupedProjector (p := p) n (fun i => activeIrrep (α i)) + +/- Actual polynomial-size identity resolution of each product subgroup. -/ +lemma block_resolution : ∑ α : BlockType n p, blockProjector n α=1 := by + simp only [blockProjector,groupedProjector_factor] + change (∑ α : BlockType n p, Matrix.reindexAlgEquiv ℂ ℂ (groupWord n p).symm + (DependentTensor.tensor (fun i => (activeIrrep (α i)).projector (action p (n i)))))=1 + rw [← map_sum] + rw [← DependentTensor.tensor_sum (fun i (a : ActiveType p (n i)) => (activeIrrep a).projector (action p (n i)))] + have hh (i : Fin r) : ∑ a : ActiveType p (n i), (activeIrrep a).projector (action p (n i))=1 := + active_resolution p (n i) + simp only [hh,DependentTensor.tensor_one,map_one] + +lemma block_card_le (s : ℕ) (hn : ∀ i, n i ≤ s) : + Fintype.card (BlockType n p) ≤ (s+1)^(r*((2*p)*(2*p))) := by + rw [Fintype.card_pi] + calc + _ ≤ ∏ i : Fin r, (s+1)^((2*p)*(2*p)) := Finset.prod_le_prod (fun i hi => + (active_card_le p (n i)).trans (Nat.pow_le_pow_left (Nat.succ_le_succ (hn i)) _)) + _ = _ := by rw [Finset.prod_const,Finset.card_univ,Fintype.card_fin,← pow_mul,Nat.mul_comm] + +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +open UnitaryIrrep FiberBlocks +variable {p r l : ℕ} (n : Fin r → ℕ) +lemma ambient_block_resolution (h : (∑ i, n i)=l) (σ : Equiv.Perm (Fin l)) : + (∑ α : BlockType n p, ambientProjector (p := p) n h σ (fun i => activeIrrep (α i)))=1 := by + subst l + unfold ambientProjector lengthMatrix + rw [← Matrix.sum_mul,← Matrix.mul_sum,block_resolution,mul_one,matrix_unitary_reverse] + +variable {L : Type*} [Fintype L] +lemma fiber_block_resolution (f : L → Fin r) (e : Fin (Fintype.card L) ≃ L) : + (∑ α : BlockType (size f) p, fiberProjector (p := p) f e (fun i => activeIrrep (α i)))=1 := + ambient_block_resolution _ _ _ + +def blockEntropy {n : Fin r → ℕ} (α : BlockType n p) : ℝ := + ∑ i, Real.log (activeIrrep (α i)).dimension + +lemma exp_blockEntropy {n : Fin r → ℕ} (α : BlockType n p) : + Real.exp (blockEntropy α)=∏ i, ((activeIrrep (α i)).dimension : ℝ) := by + rw [blockEntropy,Real.exp_sum] + apply Finset.prod_congr rfl + intro i _ + exact Real.exp_log (Nat.cast_pos.mpr (activeIrrep (α i)).positive) + +lemma nat_pow_eq_exp (s t : ℕ) : ((s+1 : ℕ) : ℝ)^t=Real.exp ((t : ℝ)*Real.log (s+1 : ℕ)) := by + rw [mul_comm,Real.exp_mul,Real.exp_log (by positivity),Real.rpow_natCast] + +lemma block_card_real_le (f : L → Fin r) (s : ℕ) (hn : ∀ i, size f i ≤ s) : + (Fintype.card (BlockType (size f) p) : ℝ) ≤ + Real.exp ((r*((2*p)*(2*p)) : ℕ)*Real.log (s+1 : ℕ)) := by + rw [← nat_pow_eq_exp] + exact_mod_cast block_card_le (size f) s hn + +lemma actual_label_overlap_exp {c : ℕ} [NeZero r] + (f : L → Fin r) (g : L → Fin c) (hinj : Function.Injective (fun x => (f x,g x))) + (e : Fin (Fintype.card L) ≃ L) (s : ℕ) (hp : 0 < p) (hps : p ≤ s) + (hnR : ∀ i, size f i ≤ s) (hnC : ∀ j, size g j ≤ s) + (α : BlockType (size f) p) (β : BlockType (size g) p) + (ρ : UnitaryIrrep (Equiv.Perm (Fin (Fintype.card L)))) : + ‖fiberProjector g e (fun j => activeIrrep (β j))*ρ.projector (action p (Fintype.card L))* + fiberProjector f e (fun i => activeIrrep (α i))‖^2 ≤ + Real.exp (blockEntropy α+blockEntropy β-Real.log ρ.dimension+ + ((r : ℝ)*c-Fintype.card L)+((r+c)*(41*p^2) : ℕ)*Real.log (s+1 : ℕ)) := by + have hh := actual_label_overlap f g hinj e s hp hps hnR hnC + (fun i => activeIrrep (α i)) (fun j => activeIrrep (β j)) ρ + have hD : 0 < (ρ.dimension : ℝ) := Nat.cast_pos.mpr ρ.positive + apply (mul_le_mul_iff_right₀ hD).mp + apply hh.trans_eq + rw [← exp_blockEntropy α,← exp_blockEntropy β,nat_pow_eq_exp,nat_pow_eq_exp] + nth_rw 1 [← Real.exp_log hD] + simp only [← Real.exp_add] + congr 1 + push_cast + ring + +lemma actual_label_overlap_contract {c : ℕ} (f : L → Fin r) (g : L → Fin c) + (e : Fin (Fintype.card L) ≃ L) (hp : 0 < p) + (α : BlockType (size f) p) (β : BlockType (size g) p) + (ρ : UnitaryIrrep (Equiv.Perm (Fin (Fintype.card L)))) : + ‖fiberProjector g e (fun j => activeIrrep (β j))*ρ.projector (action p (Fintype.card L))* + fiberProjector f e (fun i => activeIrrep (α i))‖ ≤ 1 := by + let : NeZero (2*p) := ⟨by omega⟩ + have hR := TraceHolder.projector_norm_le _ (fiberProjector_posSemidef f e _).isHermitian + (fiberProjector_idempotent (p := p) f e (fun i => activeIrrep (α i))) + have hC := TraceHolder.projector_norm_le _ (fiberProjector_posSemidef g e _).isHermitian + (fiberProjector_idempotent (p := p) g e (fun i => activeIrrep (β i))) + have hP := TraceHolder.projector_norm_le _ (ρ.projector_posSemidef _ (fun σ => (matrix_inv σ).symm)).isHermitian + (ρ.projector_idempotent (action p (Fintype.card L))) + calc + _ ≤ (‖fiberProjector g e (fun j => activeIrrep (β j))‖*‖ρ.projector (action p (Fintype.card L))‖)* + ‖fiberProjector f e (fun i => activeIrrep (α i))‖ := by + exact (Matrix.l2_opNorm_mul _ _).trans + (mul_le_mul_of_nonneg_right (Matrix.l2_opNorm_mul _ _) (norm_nonneg _)) + _ ≤ (1*1)*1 := mul_le_mul (mul_le_mul hC hP (norm_nonneg _) (by positivity)) hR + (norm_nonneg _) (by positivity) + _ = 1 := by norm_num + +/- The actual two-product-subgroup inequality. Its only analytic inputs are +child moments; the resolution, polynomial number of types and board overlap +are all constructed above. This is the row/column step of the main induction. -/ +theorem labeled_projected_moment_bound {c : ℕ} [NeZero r] + (f : L → Fin r) (g : L → Fin c) (hinj : Function.Injective (fun x => (f x,g x))) + (e : Fin (Fintype.card L) ≃ L) (s : ℕ) (hp : 0 < p) (hps : p ≤ s) + (hnR : ∀ i, size f i ≤ s) (hnC : ∀ j, size g j ≤ s) + (ρ : UnitaryIrrep (Equiv.Perm (Fin (Fintype.card L)))) (q : ℕ) (hq : 0 < q) + (c₀ ER EC : ℝ) (hc : 0 ≤ c₀) (hcq : c₀ ≤ q) + (X Y : Matrix (Word p (Fintype.card L)) (Word p (Fintype.card L)) ℂ) + (hR : ∀ α : BlockType (size f) p, + (Matrix.trace (((fiberProjector f e (fun i => activeIrrep (α i))*X).conjTranspose* + (fiberProjector f e (fun i => activeIrrep (α i))*X))^q)).re ≤ Real.exp (-c₀*blockEntropy α+ER)) + (hC : ∀ β : BlockType (size g) p, + (Matrix.trace (((Y*fiberProjector g e (fun j => activeIrrep (β j))).conjTranspose* + (Y*fiberProjector g e (fun j => activeIrrep (β j))))^q)).re ≤ Real.exp (-c₀*blockEntropy β+EC)) : + (Matrix.trace (((Y*ρ.projector (action p (Fintype.card L))*X).conjTranspose* + (Y*ρ.projector (action p (Fintype.card L))*X))^q)).re ≤ + Real.exp (-c₀*Real.log ρ.dimension+ER+EC+c₀*((r : ℝ)*c-Fintype.card L)+ + ((2*q : ℕ)*((r+c)*((2*p)*(2*p)) : ℕ)+c₀*((r+c)*(41*p^2) : ℕ))*Real.log (s+1 : ℕ)) := by + let : NeZero (2*p) := ⟨by omega⟩ + have hh := TraceHolder.row_column_moment q hq + (fun α : BlockType (size f) p => fiberProjector f e (fun i => activeIrrep (α i))) + (fun β : BlockType (size g) p => fiberProjector g e (fun j => activeIrrep (β j))) + (fiber_block_resolution f e) (fiber_block_resolution g e) + (fun α => fiberProjector_idempotent f e _) (fun β => fiberProjector_idempotent g e _) + (ρ.projector (action p (Fintype.card L))) X Y blockEntropy blockEntropy (Real.log ρ.dimension) + (ER+EC) (((r : ℝ)*c-Fintype.card L)+((r+c)*(41*p^2) : ℕ)*Real.log (s+1 : ℕ)) c₀ hc hcq + (fun α β => (mul_le_mul (hR α) (hC β) + (by exact (Complex.nonneg_iff.mp (Matrix.posSemidef_conjTranspose_mul_self _ |>.pow q |>.trace_nonneg)).1) + (Real.exp_pos _).le).trans_eq (by rw [← Real.exp_add]; congr 1; ring)) + (fun α β => by simpa only [add_assoc] using actual_label_overlap_exp f g hinj e s hp hps hnR hnC α β ρ) + (fun α β => actual_label_overlap_contract f g e hp α β ρ) + apply hh.trans + have hcard := mul_le_mul (block_card_real_le (p := p) f s hnR) (block_card_real_le (p := p) g s hnC) + (Nat.cast_nonneg _) (Real.exp_pos _).le + rw [← Real.exp_add] at hcard + have hpow := pow_le_pow_left₀ (by positivity : 0 ≤ + (Fintype.card (BlockType (size f) p) : ℝ)*(Fintype.card (BlockType (size g) p) : ℝ)) hcard (2*q) + rw [← Real.exp_nat_mul] at hpow + rw [Nat.cast_mul] + apply (mul_le_mul_of_nonneg_right hpow (Real.exp_pos _).le).trans_eq + rw [← Real.exp_add] + congr 1 + push_cast + ring +end CoordinateSweeps.SignedTensor + +namespace CoordinateSweeps.SignedTensor +lemma phase_eq_of_same_parity {p l : ℕ} (σ : Equiv.Perm (Fin l)) (u w : Word p l) + (h : ∀ i, odd (u i) ↔ odd (w i)) : phase σ u=phase σ w := by + rw [phase_prod,phase_prod] + apply Finset.prod_congr rfl + intro ij hij + simp only [h] + +lemma wordPerm_same_parity {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) + (h : ∀ i, odd (w (σ i)) ↔ odd (w i)) : + ∀ i, odd (wordPerm σ w i) ↔ odd (w i) := by + intro i + simpa [wordPerm] using (h (σ⁻¹ i)).symm + +lemma phase_conj_of_parity_stable {p l : ℕ} (σ g : Equiv.Perm (Fin l)) (w : Word p l) + (h : ∀ i, odd (w (σ i)) ↔ odd (w i)) : + phase (g*σ*g⁻¹) (wordPerm g w)=phase σ w := by + have he : (g*σ*g⁻¹)*g=g*σ := by simp [mul_assoc] + have hh := phase_mul (g*σ*g⁻¹) g w + rw [he,phase_mul,phase_eq_of_same_parity g _ w (wordPerm_same_parity σ w h)] at hh + apply mul_right_cancel₀ (phase_ne_zero g w) + rw [← hh,mul_comm] + +lemma phase_of_fix_odd {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) + (h : ∀ i, odd (w i) → σ i=i) : phase σ w=1 := by + rw [phase_prod] + apply Finset.prod_eq_one + intro ij hij + have hj := Equiv.Perm.mem_finPairsLT.mp hij + split_ifs with hh + · rw [h _ hh.1,h _ hh.2.1] at hh + exact False.elim (hj.not_gt hh.2.2) + · rfl + +lemma phase_swap_odd {p l : ℕ} (w : Word p l) (i j : Fin l) (hij : i ≠ j) + (hi : odd (w i)) (hj : odd (w j)) : phase (Equiv.swap i j) w = -1 := by + have hl : 2 ≤ l := by + have hn : i.val ≠ j.val := fun h => hij (Fin.ext h) + have hi := i.isLt + have hj := j.isLt + omega + obtain ⟨n,rfl⟩ : ∃ n, l=n+2 := ⟨l-2,by omega⟩ + obtain ⟨g,hgi,hgj⟩ := exists_perm_pair i j (0 : Fin (n+2)) 1 hij (by simp) + have hp : ∀ x, odd (w (Equiv.swap i j x)) ↔ odd (w x) := by + intro x + simp only [Equiv.swap_apply_def] + split_ifs <;> simp_all + have he : g*Equiv.swap i j*g⁻¹=Equiv.swap (0 : Fin (n+2)) 1 := by + rw [Equiv.mul_swap_eq_swap_mul,mul_assoc,mul_inv_cancel,mul_one,hgi,hgj] + have hh:=phase_conj_of_parity_stable (Equiv.swap i j) g w hp + rw [he,phase_swap01] at hh + have h0 : wordPerm g w 0=w i := by rw [← hgi]; simp [wordPerm] + have h1 : wordPerm g w 1=w j := by rw [← hgj]; simp [wordPerm] + simpa [h0,h1,hi,hj] using hh.symm + +lemma phase_ofSubtype {p l : ℕ} (w : Word p l) + (σ : Equiv.Perm {i : Fin l // odd (w i)}) : + phase (Equiv.Perm.ofSubtype σ) w = YoungCorner.signScalar σ := by + induction σ using Equiv.Perm.swap_induction_on with + | one => simp [phase_one] + | swap_mul σ i j hij ih => + rw [map_mul,phase_mul,Equiv.Perm.ofSubtype_swap_eq] + have hp := wordPerm_same_parity (Equiv.Perm.ofSubtype σ) w + (Equiv.Perm.ofSubtype_apply_mem_iff_mem σ) + rw [phase_eq_of_same_parity _ _ w hp, + phase_swap_odd w i j (fun he => hij (Subtype.ext he)) i.property j.property, + ih,map_mul,YoungCorner.signScalar_swap i j hij] + +lemma phase_of_fix_even {p l : ℕ} (σ : Equiv.Perm (Fin l)) (w : Word p l) + (h : ∀ i, ¬ odd (w i) → σ i=i) : phase σ w=YoungCorner.signScalar σ := by + have hp : ∀ i, odd (w (σ i)) ↔ odd (w i) := by + intro i + by_cases hi : odd (w i) + · have hs : odd (w (σ i)) := by + by_contra hn + have hh := h (σ i) hn + have he := σ.injective hh + rw [he] at hn + exact hn hi + simp [hi,hs] + · rw [h i hi] + let υ := Equiv.Perm.subtypePerm (p := fun i => odd (w i)) σ hp + have he : Equiv.Perm.ofSubtype υ=σ := Equiv.Perm.ofSubtype_subtypePerm (p := fun i => odd (w i)) hp (by + intro i hi + exact Classical.byContradiction (fun hn => hi (h i hn))) + rw [← he,phase_ofSubtype] + simp [YoungCorner.signScalar,Equiv.Perm.sign_ofSubtype] + +end CoordinateSweeps.SignedTensor +namespace CoordinateSweeps.YoungCorner +variable {μ : YoungDiagram} {p : ℕ} + +def Hook (μ : YoungDiagram) (p : ℕ) : Prop := ∀ x : Boxes μ, x.val.1

simp_all + omega + +lemma hookLetter_row_eq (h : Hook μ p) (x y : Boxes μ) + (hx : x.val.1 simp_all + omega + +lemma hookLetter_col_eq (h : Hook μ p) (x y : Boxes μ) + (hx : p≤x.val.1) (he : hookLetter h x=hookLetter h y) : x.val.2=y.val.2 := by + have he' := congrArg Fin.val he + simp only [hookLetter] at he' + split_ifs at he' <;> simp_all <;> omega + +/- The geometric reason all diagonal Young-corner coefficients have positive +sign on the actual even-row/odd-column hook word. -/ +lemma hook_corner_fixed {X : Type*} (t : X ≃ Boxes μ) (h : Hook μ p) + (r : colorStabilizer (rowColor t)) (c : colorStabilizer (colColor t)) + (hw : ∀ x, hookLetter h (t ((r : Equiv.Perm X) (c.val x)))=hookLetter h (t x)) : + (∀ x, (t x).val.1

hookLetter h (t x))= + signScalar (c : Equiv.Perm (Fin l)) := by + obtain ⟨hc,hr⟩ := hook_corner_fixed t h r c hw + let w : SignedTensor.Word p l := fun x => hookLetter h (t x) + have hce : ∀ i, ¬ SignedTensor.odd (w i) → (c : Equiv.Perm (Fin l)) i=i := by + intro i hi + exact hc i (by simpa only [w,hookLetter_odd,not_le] using hi) + have hcp : ∀ i, SignedTensor.odd (w (c.val i)) ↔ SignedTensor.odd (w i) := by + intro i + by_cases hi : SignedTensor.odd (w i) + · have hh : SignedTensor.odd (w (c.val i)) := by + by_contra hn + have he := c.val.injective (hce (c.val i) hn) + rw [he] at hn + exact hn hi + simp [hi,hh] + · rw [hce i hi] + rw [SignedTensor.phase_mul,SignedTensor.phase_eq_of_same_parity _ _ w + (SignedTensor.wordPerm_same_parity c.val w hcp),SignedTensor.phase_of_fix_odd _ w] + · rw [one_mul,SignedTensor.phase_of_fix_even c.val w hce] + · intro i hi + exact hr i ((hookLetter_odd h (t i)).mp hi) + +end CoordinateSweeps.YoungCorner + +namespace CoordinateSweeps.YoungCorner +variable {μ : YoungDiagram} {p l : ℕ} + +lemma signScalar_square {X : Type*} [Fintype X] [DecidableEq X] (c : Equiv.Perm X) : + signScalar c * signScalar c=1 := by + rcases Int.units_eq_one_or (Equiv.Perm.sign c) with h|h <;> simp [signScalar,h] + +lemma hook_contribution (t : Fin l ≃ Boxes μ) (h : Hook μ p) + (r : colorStabilizer (rowColor t)) (c : colorStabilizer (colColor t)) : + let w : SignedTensor.Word p l := fun x => hookLetter h (t x) + signScalar c.val * SignedTensor.matrix (r.val*c.val) w w = + if w=SignedTensor.wordPerm (r.val*c.val) w then 1 else 0 := by + dsimp only + rw [SignedTensor.matrix] + split_ifs with he + · have hw : ∀ x, hookLetter h (t (r.val (c.val x)))=hookLetter h (t x) := by + intro x + have hh := congrFun he ((r.val*c.val) x) + simpa [SignedTensor.wordPerm,Equiv.Perm.mul_apply] using hh + rw [hook_corner_phase t h r c hw,signScalar_square] + · simp + +lemma hook_corner_matrix_ne (t : Fin l ≃ Boxes μ) (h : Hook μ p) : + fixedSum (rowColor t) (SignedTensor.action p l) * + alternatingSum (colColor t) (SignedTensor.action p l) ≠ 0 := by + let w : SignedTensor.Word p l := fun x => hookLetter h (t x) + have he : (fixedSum (rowColor t) (SignedTensor.action p l) * + alternatingSum (colColor t) (SignedTensor.action p l)) w w = + ∑ r : colorStabilizer (rowColor t), ∑ c : colorStabilizer (colColor t), + if w=SignedTensor.wordPerm (r.val*c.val) w then (1 : ℂ) else 0 := by + rw [fixedSum,alternatingSum,Finset.sum_mul] + simp only [Finset.mul_sum,mul_smul_comm,← map_mul,Matrix.sum_apply,Matrix.smul_apply,smul_eq_mul] + apply Finset.sum_congr rfl + intro r hr + apply Finset.sum_congr rfl + intro c hc + exact hook_contribution t h r c + have hpos : 0 < ((fixedSum (rowColor t) (SignedTensor.action p l) * + alternatingSum (colColor t) (SignedTensor.action p l)) w w).re := by + rw [he] + simp only [Complex.re_sum,apply_ite,Complex.one_re,Complex.zero_re] + apply Finset.sum_pos' + · intro r hr + apply Finset.sum_nonneg + intro c hc + split_ifs <;> norm_num + · refine ⟨1,Finset.mem_univ _,?_⟩ + apply Finset.sum_pos' + · intro c hc + split_ifs <;> norm_num + · refine ⟨1,Finset.mem_univ _,?_⟩ + simp [SignedTensor.wordPerm] + intro hz + rw [hz] at hpos + simp at hpos + +/- The literal signed action, as a linear representation. -/ +def signedRep (p l : ℕ) : Representation ℂ (Equiv.Perm (Fin l)) (SignedTensor.Word p l → ℂ) := + Matrix.toLinAlgEquiv'.toMonoidHom.comp (SignedTensor.action p l) + +lemma signedRep_hasShape (t : Fin l ≃ Boxes μ) (h : Hook μ p) : + hasShape μ t (signedRep p l) := by + have he : fixedSum (rowColor t) (signedRep p l) * alternatingSum (colColor t) (signedRep p l) = + Matrix.toLinAlgEquiv' (fixedSum (rowColor t) (SignedTensor.action p l) * + alternatingSum (colColor t) (SignedTensor.action p l)) := by + simp [fixedSum,alternatingSum,signedRep,map_sum,map_mul] + intro hz + rw [he] at hz + exact hook_corner_matrix_ne t h (Matrix.toLinAlgEquiv'.injective (hz.trans (map_zero _).symm)) + +lemma detecting_shape_constituent {X V : Type*} [Fintype X] [DecidableEq X] + [AddCommGroup V] [Module ℂ V] [FiniteDimensional ℂ V] + (τ : Representation ℂ (Equiv.Perm X) V) (t : X ≃ Boxes μ) (h : hasShape μ t τ) : + ∃ S : Subrepresentation τ, S.toRepresentation.IsIrreducible ∧ hasShape μ t S.toRepresentation := by + obtain ⟨S,hS,v,hv⟩ := RepDetection.exists_irreducible_detecting τ + (fixedSum (rowColor t) τ*alternatingSum (colColor t) τ) h + refine ⟨S,hS,?_⟩ + intro hh + apply hv + have hz := congrArg (fun A : Module.End ℂ S.toSubmodule => (A v : V)) hh + simp only [Module.End.mul_apply,fixedSum_subrepresentation,alternatingSum_subrepresentation] at hz + exact hz + +/- Source05 hook occurrence, derived for actual irreps in the exact Koszul +representation. No Pieri/Schur--Weyl or hook classification is assumed. -/ +theorem hook_occurs {V : Type} [AddCommGroup V] [Module ℂ V] [FiniteDimensional ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin l)) V) [ρ.IsIrreducible] + (t : Fin l ≃ Boxes μ) (hρ : hasShape μ t ρ) (h : Hook μ p) : + ∃ S : Subrepresentation (signedRep p l), + Nonempty (Representation.Equiv ρ S.toRepresentation) := by + obtain ⟨S,hS,hSh⟩ := detecting_shape_constituent (signedRep p l) t (signedRep_hasShape t h) + let := hS + exact ⟨S,equiv_of_same_shape ρ S.toRepresentation μ t t hρ hSh⟩ + +end CoordinateSweeps.YoungCorner + +namespace CoordinateSweeps.YoungCorner +open UnitaryIrrep SignedTensor +lemma hook_multiplicity_pos {p l : ℕ} {μ : YoungDiagram} + (ρ : UnitaryIrrep (Equiv.Perm (Fin l))) (t : Fin l ≃ Boxes μ) + (hρ : hasShape μ t ρ.asRepresentation) (hhook : Hook μ p) : + 0 < Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation (action p l))) := by + obtain ⟨S,⟨e⟩⟩ := hook_occurs ρ.asRepresentation t hρ hhook + let inc : S.toRepresentation.IntertwiningMap (signedRep p l) := + ⟨S.toSubmodule.subtype,fun _ => rfl⟩ + let f := inc.comp e.toIntertwiningMap + have hf : f ≠ 0 := by + intro hz + have hzero : ∀ v : Fin ρ.dimension → ℂ, v=0 := by + intro v + apply e.toLinearEquiv.injective + apply Subtype.val_injective + have hh := congrArg (fun g : ρ.asRepresentation.IntertwiningMap (signedRep p l) => g v) hz + change ((e.toLinearEquiv v : S.toSubmodule) : SignedTensor.Word p l → ℂ)=0 at hh + rw [map_zero] + exact hh + have : Nonempty (Fin ρ.dimension) := Fin.pos_iff_nonempty.mp ρ.positive + exact one_ne_zero (congrFun (hzero (fun _ => 1)) (Classical.arbitrary (Fin ρ.dimension))) + let : Nontrivial (ρ.asRepresentation.IntertwiningMap (signedRep p l)) := nontrivial_of_ne f 0 hf + change 0 < Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (signedRep p l)) + exact Module.finrank_pos +end CoordinateSweeps.YoungCorner +end +end +end +end +end +end +end +end +end +end +open scoped Matrix.Norms.L2Operator + +end OAI diff --git a/lean/OAI/RepresentationTheory/SpinAngle/Compression.lean b/lean/OAI/RepresentationTheory/SpinAngle/Compression.lean index 39cbefaebd246d548a14c22f1fee3d50798ecdd9..572a78e4f233da4293e2c586522429d619b009fc 100644 --- a/lean/OAI/RepresentationTheory/SpinAngle/Compression.lean +++ b/lean/OAI/RepresentationTheory/SpinAngle/Compression.lean @@ -1,204 +1,204 @@ -import OAI.RepresentationTheory.SpinAngle.Core - -namespace OAI - -noncomputable section -open scoped BigOperators ComplexConjugate InnerProductSpace -open scoped BigOperators ComplexConjugate InnerProductSpace Matrix -open scoped Matrix ComplexOrder -open scoped TensorProduct InnerProductSpace BigOperators -open scoped BigOperators ComplexConjugate -open scoped InnerProductSpace -open scoped TensorProduct InnerProductSpace ComplexOrder -open scoped BigOperators -open scoped InnerProductSpace ComplexOrder BigOperators -open scoped InnerProductSpace BigOperators ComplexOrder -open scoped BigOperators -open scoped BigOperators -open MeasureTheory TopologicalSpace Set -open scoped BigOperators -open scoped BigOperators -open Set -open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder -open scoped BigOperators -open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder - - - - - - - - -noncomputable section -open scoped BigOperators -namespace SpinAngle.Analytic - -variable {A : Type*} [contextInstance35_21 : CStarAlgebra A] [contextInstance35_38 : PartialOrder A] [contextInstance35_55 : StarOrderedRing A] - [contextInstance36_2 : NonnegSpectrumClass ℝ A] - -lemma norm_mul_projection_sq - {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] - [NonnegSpectrumClass ℝ A] (a p : A) (hp : IsStarProjection p) : - ‖a * p‖ ^ 2 = ‖a * p * star a‖ := by - rw [sq, ← CStarRing.norm_self_mul_star, star_mul, hp.isSelfAdjoint.star_eq] - congr 1 - calc - a * p * (p * star a) = a * (p * p) * star a := by simp only [mul_assoc] - _ = a * p * star a := by rw [hp.isIdempotentElem.eq] - -lemma norm_projection_mul_sq - {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] - [NonnegSpectrumClass ℝ A] (p a : A) (hp : IsStarProjection p) : - ‖p * a‖ ^ 2 = ‖star a * p * a‖ := by - rw [sq, ← CStarRing.norm_star_mul_self, star_mul, hp.isSelfAdjoint.star_eq] - congr 1 - calc - star a * p * (p * a) = star a * (p * p) * a := by simp only [mul_assoc] - _ = star a * p * a := by rw [hp.isIdempotentElem.eq] - - - -lemma norm_mul_projection_sq_le_sum {ι : Type*} [Fintype ι] - (a p : A) (hp : IsStarProjection p) (w : ι → ℝ) (r : ι → A) - (hw : ∀ i, 0 ≤ w i) (hdom : p ≤ ∑ i, w i • (r i * star (r i))) : - ‖a * p‖ ^ 2 ≤ ∑ i, w i * ‖a * r i‖ ^ 2 := by - rw [norm_mul_projection_sq a p hp] - have hcomp := star_right_conjugate_le_conjugate hdom a - have hpos : 0 ≤ a * p * star a := - star_right_conjugate_nonneg hp.nonneg a - calc - ‖a * p * star a‖ ≤ ‖a * (∑ i, w i • (r i * star (r i))) * star a‖ := - CStarAlgebra.norm_le_norm_of_le_of_nonneg hcomp hpos - _ = ‖∑ i, w i • ((a * r i) * star (a * r i))‖ := by - congr 1 - simp only [Finset.mul_sum, Finset.sum_mul, mul_smul_comm, smul_mul_assoc, - star_mul, mul_assoc] - _ ≤ ∑ i, ‖w i • ((a * r i) * star (a * r i))‖ := norm_sum_le _ _ - _ = ∑ i, w i * ‖a * r i‖ ^ 2 := by - apply Finset.sum_congr rfl - intro i _ - rw [norm_smul, Real.norm_of_nonneg (hw i), CStarRing.norm_self_mul_star, sq] - -lemma norm_projection_mul_sq_le_sum {ι : Type*} [Fintype ι] - (p a : A) (hp : IsStarProjection p) (w : ι → ℝ) (r : ι → A) - (hw : ∀ i, 0 ≤ w i) (hdom : p ≤ ∑ i, w i • (star (r i) * r i)) : - ‖p * a‖ ^ 2 ≤ ∑ i, w i * ‖r i * a‖ ^ 2 := by - have h := norm_mul_projection_sq_le_sum (star a) p hp w (fun i => star (r i)) hw - (by simpa using hdom) - have hab : ‖star a * p‖ = ‖p * a‖ := by - calc - ‖star a * p‖ = ‖star (p * a)‖ := by rw [star_mul, hp.isSelfAdjoint.star_eq] - _ = ‖p * a‖ := norm_star _ - have hr (i : ι) : ‖star a * star (r i)‖ = ‖r i * a‖ := by - rw [← star_mul, norm_star] - simpa only [hab, hr] using h - - - - -lemma support_inverse_factorization - {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] - [NonnegSpectrumClass ℝ A] (r v t q k p : A) - (hvt : v * t = q) (hrq : r * q = r) - (htk : Commute t k) (htp : Commute t p) : - r * k * p = (r * v * k) * (p * t) := by - calc - r * k * p = (r * q) * k * p := by rw [hrq] - _ = (r * (v * t)) * k * p := by rw [hvt] - _ = (r * v * k) * (p * t) := by - simp only [mul_assoc] - rw [← mul_assoc t k, htk.eq, mul_assoc k, htp.eq] - - -lemma norm_support_inverse_le (r v t q k p : A) - (hvt : v * t = q) (hrq : r * q = r) - (htk : Commute t k) (htp : Commute t p) : - ‖r * k * p‖ ^ 2 ≤ ‖r * v * k‖ ^ 2 * ‖p * t‖ ^ 2 := by - rw [support_inverse_factorization r v t q k p hvt hrq htk htp] - calc - ‖(r * v * k) * (p * t)‖ ^ 2 ≤ (‖r * v * k‖ * ‖p * t‖) ^ 2 := by - exact pow_le_pow_left₀ (norm_nonneg _) (norm_mul_le _ _) 2 - _ = _ := mul_pow _ _ _ - - - -lemma norm_projection_sqrt_sq (p t : A) (hp : IsStarProjection p) - (ht : IsSelfAdjoint t) (htp : Commute t p) : - ‖p * t‖ ^ 2 = ‖(t * t) * p‖ := by - rw [norm_projection_mul_sq p t hp, ht.star_eq] - congr 1 - calc - t * p * t = t * (p * t) := mul_assoc _ _ _ - _ = t * (t * p) := by rw [htp.eq] - _ = t * t * p := (mul_assoc _ _ _).symm - -lemma norm_three_projections_sq_le_one - {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] - [NonnegSpectrumClass ℝ A] (h k p : A) - (hh : IsStarProjection h) (hk : IsStarProjection k) (hp : IsStarProjection p) : - ‖h * k * p‖ ^ 2 ≤ 1 := by - have hn : ‖h * k * p‖ ≤ 1 := calc - _ ≤ (‖h‖ * ‖k‖) * ‖p‖ := (norm_mul_le _ _).trans <| - mul_le_mul_of_nonneg_right (norm_mul_le _ _) (norm_nonneg _) - _ ≤ (1 * 1) * 1 := mul_le_mul - (mul_le_mul hh.norm_le hk.norm_le (norm_nonneg _) zero_le_one) - hp.norm_le (norm_nonneg _) (by norm_num) - _ = 1 := by norm_num - calc - _ ≤ (1 : ℝ) ^ 2 := pow_le_pow_left₀ (norm_nonneg _) hn 2 - _ = 1 := by norm_num - - - - - - - -theorem three_projection_angle_of_density_mixtures - {ι κ : Type*} [Fintype ι] [Fintype κ] - (h k p : A) (hh : IsStarProjection h) (hk : IsStarProjection k) - (hp : IsStarProjection p) - (w : ι → ℝ) (z : κ → ℝ) (hw : ∀ i, 0 ≤ w i) (hz : ∀ j, 0 ≤ z j) - (r v t q : ι → A) (s : κ → A) - (hH : h ≤ ∑ i, w i • (star (r i) * r i)) - (hK : k ≤ ∑ j, z j • (s j * star (s j))) - (hvt : ∀ i, v i * t i = q i) (hrq : ∀ i, r i * q i = r i) - (htk : ∀ i, Commute (t i) k) (htp : ∀ i, Commute (t i) p) - (g phi : ℝ) (hg : 0 ≤ g) (hphi : 0 ≤ phi) - (hglobal : ∀ i, ‖p * t i‖ ^ 2 ≤ g) - (hcell : ∀ i j, ‖r i * v i * s j‖ ^ 2 ≤ phi) : - ‖h * k * p‖ ^ 2 ≤ min 1 ((∑ i, w i) * (∑ j, z j) * g * phi) := by - apply le_min (norm_three_projections_sq_le_one h k p hh hk hp) - have hs (i : ι) : ‖r i * v i * k‖ ^ 2 ≤ (∑ j, z j) * phi := by - calc - _ ≤ ∑ j, z j * ‖r i * v i * s j‖ ^ 2 := - norm_mul_projection_sq_le_sum (r i * v i) k hk z s hz hK - _ ≤ ∑ j, z j * phi := Finset.sum_le_sum fun j _ => - mul_le_mul_of_nonneg_left (hcell i j) (hz j) - _ = _ := (Finset.sum_mul _ _ _).symm - have hb (i : ι) : ‖r i * k * p‖ ^ 2 ≤ ((∑ j, z j) * phi) * g := calc - _ ≤ ‖r i * v i * k‖ ^ 2 * ‖p * t i‖ ^ 2 := - norm_support_inverse_le (r i) (v i) (t i) (q i) k p - (hvt i) (hrq i) (htk i) (htp i) - _ ≤ ((∑ j, z j) * phi) * g := by - by_cases hzero : ‖p * t i‖ ^ 2 = 0 - · rw [hzero, mul_zero] - exact mul_nonneg (mul_nonneg (Finset.sum_nonneg fun j _ => hz j) hphi) hg - · exact mul_le_mul (hs i) (hglobal i) (sq_nonneg _) - (mul_nonneg (Finset.sum_nonneg fun j _ => hz j) hphi) - calc - ‖h * k * p‖ ^ 2 = ‖h * (k * p)‖ ^ 2 := by rw [mul_assoc] - _ ≤ ∑ i, w i * ‖r i * (k * p)‖ ^ 2 := - norm_projection_mul_sq_le_sum h (k * p) hh w r hw hH - _ = ∑ i, w i * ‖r i * k * p‖ ^ 2 := by simp only [mul_assoc] - _ ≤ ∑ i, w i * (((∑ j, z j) * phi) * g) := - Finset.sum_le_sum fun i _ => mul_le_mul_of_nonneg_left (hb i) (hw i) - _ = (∑ i, w i) * (∑ j, z j) * g * phi := by rw [← Finset.sum_mul]; ring - -end SpinAngle.Analytic - -end -end - -end OAI +import OAI.RepresentationTheory.SpinAngle.Core + +namespace OAI + +noncomputable section +open scoped BigOperators ComplexConjugate InnerProductSpace +open scoped BigOperators ComplexConjugate InnerProductSpace Matrix +open scoped Matrix ComplexOrder +open scoped TensorProduct InnerProductSpace BigOperators +open scoped BigOperators ComplexConjugate +open scoped InnerProductSpace +open scoped TensorProduct InnerProductSpace ComplexOrder +open scoped BigOperators +open scoped InnerProductSpace ComplexOrder BigOperators +open scoped InnerProductSpace BigOperators ComplexOrder +open scoped BigOperators +open scoped BigOperators +open MeasureTheory TopologicalSpace Set +open scoped BigOperators +open scoped BigOperators +open Set +open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder +open scoped BigOperators +open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder + + + + + + + + +noncomputable section +open scoped BigOperators +namespace SpinAngle.Analytic + +variable {A : Type*} [contextInstance35_21 : CStarAlgebra A] [contextInstance35_38 : PartialOrder A] [contextInstance35_55 : StarOrderedRing A] + [contextInstance36_2 : NonnegSpectrumClass ℝ A] + +lemma norm_mul_projection_sq + {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NonnegSpectrumClass ℝ A] (a p : A) (hp : IsStarProjection p) : + ‖a * p‖ ^ 2 = ‖a * p * star a‖ := by + rw [sq, ← CStarRing.norm_self_mul_star, star_mul, hp.isSelfAdjoint.star_eq] + congr 1 + calc + a * p * (p * star a) = a * (p * p) * star a := by simp only [mul_assoc] + _ = a * p * star a := by rw [hp.isIdempotentElem.eq] + +lemma norm_projection_mul_sq + {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NonnegSpectrumClass ℝ A] (p a : A) (hp : IsStarProjection p) : + ‖p * a‖ ^ 2 = ‖star a * p * a‖ := by + rw [sq, ← CStarRing.norm_star_mul_self, star_mul, hp.isSelfAdjoint.star_eq] + congr 1 + calc + star a * p * (p * a) = star a * (p * p) * a := by simp only [mul_assoc] + _ = star a * p * a := by rw [hp.isIdempotentElem.eq] + + + +lemma norm_mul_projection_sq_le_sum {ι : Type*} [Fintype ι] + (a p : A) (hp : IsStarProjection p) (w : ι → ℝ) (r : ι → A) + (hw : ∀ i, 0 ≤ w i) (hdom : p ≤ ∑ i, w i • (r i * star (r i))) : + ‖a * p‖ ^ 2 ≤ ∑ i, w i * ‖a * r i‖ ^ 2 := by + rw [norm_mul_projection_sq a p hp] + have hcomp := star_right_conjugate_le_conjugate hdom a + have hpos : 0 ≤ a * p * star a := + star_right_conjugate_nonneg hp.nonneg a + calc + ‖a * p * star a‖ ≤ ‖a * (∑ i, w i • (r i * star (r i))) * star a‖ := + CStarAlgebra.norm_le_norm_of_le_of_nonneg hcomp hpos + _ = ‖∑ i, w i • ((a * r i) * star (a * r i))‖ := by + congr 1 + simp only [Finset.mul_sum, Finset.sum_mul, mul_smul_comm, smul_mul_assoc, + star_mul, mul_assoc] + _ ≤ ∑ i, ‖w i • ((a * r i) * star (a * r i))‖ := norm_sum_le _ _ + _ = ∑ i, w i * ‖a * r i‖ ^ 2 := by + apply Finset.sum_congr rfl + intro i _ + rw [norm_smul, Real.norm_of_nonneg (hw i), CStarRing.norm_self_mul_star, sq] + +lemma norm_projection_mul_sq_le_sum {ι : Type*} [Fintype ι] + (p a : A) (hp : IsStarProjection p) (w : ι → ℝ) (r : ι → A) + (hw : ∀ i, 0 ≤ w i) (hdom : p ≤ ∑ i, w i • (star (r i) * r i)) : + ‖p * a‖ ^ 2 ≤ ∑ i, w i * ‖r i * a‖ ^ 2 := by + have h := norm_mul_projection_sq_le_sum (star a) p hp w (fun i => star (r i)) hw + (by simpa using hdom) + have hab : ‖star a * p‖ = ‖p * a‖ := by + calc + ‖star a * p‖ = ‖star (p * a)‖ := by rw [star_mul, hp.isSelfAdjoint.star_eq] + _ = ‖p * a‖ := norm_star _ + have hr (i : ι) : ‖star a * star (r i)‖ = ‖r i * a‖ := by + rw [← star_mul, norm_star] + simpa only [hab, hr] using h + + + + +lemma support_inverse_factorization + {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NonnegSpectrumClass ℝ A] (r v t q k p : A) + (hvt : v * t = q) (hrq : r * q = r) + (htk : Commute t k) (htp : Commute t p) : + r * k * p = (r * v * k) * (p * t) := by + calc + r * k * p = (r * q) * k * p := by rw [hrq] + _ = (r * (v * t)) * k * p := by rw [hvt] + _ = (r * v * k) * (p * t) := by + simp only [mul_assoc] + rw [← mul_assoc t k, htk.eq, mul_assoc k, htp.eq] + + +lemma norm_support_inverse_le (r v t q k p : A) + (hvt : v * t = q) (hrq : r * q = r) + (htk : Commute t k) (htp : Commute t p) : + ‖r * k * p‖ ^ 2 ≤ ‖r * v * k‖ ^ 2 * ‖p * t‖ ^ 2 := by + rw [support_inverse_factorization r v t q k p hvt hrq htk htp] + calc + ‖(r * v * k) * (p * t)‖ ^ 2 ≤ (‖r * v * k‖ * ‖p * t‖) ^ 2 := by + exact pow_le_pow_left₀ (norm_nonneg _) (norm_mul_le _ _) 2 + _ = _ := mul_pow _ _ _ + + + +lemma norm_projection_sqrt_sq (p t : A) (hp : IsStarProjection p) + (ht : IsSelfAdjoint t) (htp : Commute t p) : + ‖p * t‖ ^ 2 = ‖(t * t) * p‖ := by + rw [norm_projection_mul_sq p t hp, ht.star_eq] + congr 1 + calc + t * p * t = t * (p * t) := mul_assoc _ _ _ + _ = t * (t * p) := by rw [htp.eq] + _ = t * t * p := (mul_assoc _ _ _).symm + +lemma norm_three_projections_sq_le_one + {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NonnegSpectrumClass ℝ A] (h k p : A) + (hh : IsStarProjection h) (hk : IsStarProjection k) (hp : IsStarProjection p) : + ‖h * k * p‖ ^ 2 ≤ 1 := by + have hn : ‖h * k * p‖ ≤ 1 := calc + _ ≤ (‖h‖ * ‖k‖) * ‖p‖ := (norm_mul_le _ _).trans <| + mul_le_mul_of_nonneg_right (norm_mul_le _ _) (norm_nonneg _) + _ ≤ (1 * 1) * 1 := mul_le_mul + (mul_le_mul hh.norm_le hk.norm_le (norm_nonneg _) zero_le_one) + hp.norm_le (norm_nonneg _) (by norm_num) + _ = 1 := by norm_num + calc + _ ≤ (1 : ℝ) ^ 2 := pow_le_pow_left₀ (norm_nonneg _) hn 2 + _ = 1 := by norm_num + + + + + + + +theorem three_projection_angle_of_density_mixtures + {ι κ : Type*} [Fintype ι] [Fintype κ] + (h k p : A) (hh : IsStarProjection h) (hk : IsStarProjection k) + (hp : IsStarProjection p) + (w : ι → ℝ) (z : κ → ℝ) (hw : ∀ i, 0 ≤ w i) (hz : ∀ j, 0 ≤ z j) + (r v t q : ι → A) (s : κ → A) + (hH : h ≤ ∑ i, w i • (star (r i) * r i)) + (hK : k ≤ ∑ j, z j • (s j * star (s j))) + (hvt : ∀ i, v i * t i = q i) (hrq : ∀ i, r i * q i = r i) + (htk : ∀ i, Commute (t i) k) (htp : ∀ i, Commute (t i) p) + (g phi : ℝ) (hg : 0 ≤ g) (hphi : 0 ≤ phi) + (hglobal : ∀ i, ‖p * t i‖ ^ 2 ≤ g) + (hcell : ∀ i j, ‖r i * v i * s j‖ ^ 2 ≤ phi) : + ‖h * k * p‖ ^ 2 ≤ min 1 ((∑ i, w i) * (∑ j, z j) * g * phi) := by + apply le_min (norm_three_projections_sq_le_one h k p hh hk hp) + have hs (i : ι) : ‖r i * v i * k‖ ^ 2 ≤ (∑ j, z j) * phi := by + calc + _ ≤ ∑ j, z j * ‖r i * v i * s j‖ ^ 2 := + norm_mul_projection_sq_le_sum (r i * v i) k hk z s hz hK + _ ≤ ∑ j, z j * phi := Finset.sum_le_sum fun j _ => + mul_le_mul_of_nonneg_left (hcell i j) (hz j) + _ = _ := (Finset.sum_mul _ _ _).symm + have hb (i : ι) : ‖r i * k * p‖ ^ 2 ≤ ((∑ j, z j) * phi) * g := calc + _ ≤ ‖r i * v i * k‖ ^ 2 * ‖p * t i‖ ^ 2 := + norm_support_inverse_le (r i) (v i) (t i) (q i) k p + (hvt i) (hrq i) (htk i) (htp i) + _ ≤ ((∑ j, z j) * phi) * g := by + by_cases hzero : ‖p * t i‖ ^ 2 = 0 + · rw [hzero, mul_zero] + exact mul_nonneg (mul_nonneg (Finset.sum_nonneg fun j _ => hz j) hphi) hg + · exact mul_le_mul (hs i) (hglobal i) (sq_nonneg _) + (mul_nonneg (Finset.sum_nonneg fun j _ => hz j) hphi) + calc + ‖h * k * p‖ ^ 2 = ‖h * (k * p)‖ ^ 2 := by rw [mul_assoc] + _ ≤ ∑ i, w i * ‖r i * (k * p)‖ ^ 2 := + norm_projection_mul_sq_le_sum h (k * p) hh w r hw hH + _ = ∑ i, w i * ‖r i * k * p‖ ^ 2 := by simp only [mul_assoc] + _ ≤ ∑ i, w i * (((∑ j, z j) * phi) * g) := + Finset.sum_le_sum fun i _ => mul_le_mul_of_nonneg_left (hb i) (hw i) + _ = (∑ i, w i) * (∑ j, z j) * g * phi := by rw [← Finset.sum_mul]; ring + +end SpinAngle.Analytic + +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/SpinAngle/Core.lean b/lean/OAI/RepresentationTheory/SpinAngle/Core.lean index 67d5e4e472a3db0f93aea2c76ce84b262bf82a78..e2ba21d01769a770fdfab2de547c17e0f1dc08dc 100644 --- a/lean/OAI/RepresentationTheory/SpinAngle/Core.lean +++ b/lean/OAI/RepresentationTheory/SpinAngle/Core.lean @@ -1,4813 +1,4813 @@ -import Mathlib - -namespace OAI - - - -noncomputable section -open scoped BigOperators ComplexConjugate InnerProductSpace - -namespace SpinAngle.Specht - -variable {G : Type*} [contextInstance10_21 : Group G] -variable {E : Type*} [contextInstance11_21 : NormedAddCommGroup E] [contextInstance11_44 : InnerProductSpace ℂ E] - - -def cyclic (ρ : Representation ℂ G E) (e : E) : Subrepresentation ρ where - toSubmodule := Submodule.span ℂ (Set.range fun g => ρ g e) - apply_mem_toSubmodule g := by - intro v hv - induction hv using Submodule.span_induction with - | mem v hv => - obtain ⟨h, rfl⟩ := hv - exact Submodule.subset_span ⟨g * h, by simp⟩ - | zero => simp - | add x y hx hy ihx ihy => - simpa using (Submodule.span ℂ (Set.range fun h => ρ h e)).add_mem ihx ihy - | smul a x hx ih => - simpa using (Submodule.span ℂ (Set.range fun h => ρ h e)).smul_mem a ih - -lemma self_mem_cyclic (ρ : Representation ℂ G E) (e : E) : e ∈ cyclic ρ e := by - exact Submodule.subset_span ⟨1, by simp⟩ - - -variable [contextInstance32_9 : FiniteDimensional ℂ E] - -lemma starProjection_rep (ρ : Representation ℂ G E) - (hunit : ∀ g x y, ⟪ρ g x, ρ g y⟫_ℂ = ⟪x, y⟫_ℂ) - (U : Subrepresentation ρ) (g : G) (v : E) : - U.toSubmodule.starProjection (ρ g v) = ρ g (U.toSubmodule.starProjection v) := by - apply U.toSubmodule.eq_starProjection_of_mem_of_inner_eq_zero - · exact U.apply_mem_toSubmodule g (U.toSubmodule.starProjection_apply_mem v) - · intro w hw - have hw' := U.apply_mem_toSubmodule g⁻¹ hw - have he : ρ g (ρ g⁻¹ w) = w := by - rw [← Module.End.mul_apply, ← map_mul, mul_inv_cancel, map_one, Module.End.one_apply] - rw [← map_sub] - conv_lhs => rhs; rw [← he] - rw [hunit] - exact U.toSubmodule.starProjection_inner_eq_zero v _ hw' - - - - -theorem simple_eigen_submodule_alternative (ρ : Representation ℂ G E) (e : E) - (hunit : ∀ g x y, ⟪ρ g x, ρ g y⟫_ℂ = ⟪x, y⟫_ℂ) - (g₀ : G) (c : ℂ) (heig : ρ g₀ e = c • e) - (hsimple : ∀ v : E, ρ g₀ v = c • v → v ∈ Submodule.span ℂ {e}) - (U : Subrepresentation ρ) : - cyclic ρ e ≤ U ∨ ∀ u ∈ U, ∀ v ∈ cyclic ρ e, ⟪v, u⟫_ℂ = 0 := by - classical - by_cases he : e ∈ U - · left - exact Submodule.span_le.mpr (by rintro _ ⟨g, rfl⟩; exact U.apply_mem_toSubmodule g he) - · right - have hp : U.toSubmodule.starProjection e = 0 := by - have hpeig : ρ g₀ (U.toSubmodule.starProjection e) = - c • U.toSubmodule.starProjection e := by - rw [← starProjection_rep ρ hunit U g₀ e, heig, map_smul] - obtain ⟨a, ha⟩ := Submodule.mem_span_singleton.mp (hsimple _ hpeig) - by_cases ha0 : a = 0 - · simpa [ha0] using ha.symm - · apply False.elim - apply he - have hm := U.toSubmodule.starProjection_apply_mem e - rw [← ha] at hm - have hh := U.toSubmodule.smul_mem a⁻¹ hm - change e ∈ U.toSubmodule - simpa [smul_smul, ha0] using hh - have heorth (u : E) (hu : u ∈ U) : ⟪e, u⟫_ℂ = 0 := by - have hh := U.toSubmodule.starProjection_inner_eq_zero e u hu - simpa [hp] using hh - intro u hu v hv - have horth (g : G) : ⟪ρ g e, u⟫_ℂ = 0 := by - have hgu : ρ g⁻¹ u ∈ U := U.apply_mem_toSubmodule g⁻¹ hu - have hi := hunit g e (ρ g⁻¹ u) - simpa only [← Module.End.mul_apply, ← map_mul, mul_inv_cancel, map_one, - Module.End.one_apply] using hi.trans (heorth _ hgu) - induction hv using Submodule.span_induction with - | mem v hv => obtain ⟨g, rfl⟩ := hv; exact horth g - | zero => simp - | add x y hx hy ihx ihy => simp [ihx, ihy] - | smul a x hx ih => simp [ih] - -theorem cyclic_irreducible_of_simple_eigen (ρ : Representation ℂ G E) (e : E) (he : e ≠ 0) - (hunit : ∀ g x y, ⟪ρ g x, ρ g y⟫_ℂ = ⟪x, y⟫_ℂ) - (g₀ : G) (c : ℂ) (heig : ρ g₀ e = c • e) - (hsimple : ∀ v : E, ρ g₀ v = c • v → v ∈ Submodule.span ℂ {e}) : - Representation.IsIrreducible (cyclic ρ e).toRepresentation := by - let S := cyclic ρ e - let eS : S.toSubmodule := ⟨e, self_mem_cyclic ρ e⟩ - have heS : eS ≠ 0 := by intro hh; apply he; exact congrArg Subtype.val hh - have htb : (⊤ : Subrepresentation S.toRepresentation) ≠ ⊥ := by - intro hh - have hel : eS ∈ (⊤ : Subrepresentation S.toRepresentation) := by trivial - rw [hh] at hel - exact heS hel - let : Nontrivial (Subrepresentation S.toRepresentation) := ⟨⟨⊤, ⊥, htb⟩⟩ - refine ⟨fun U => ?_⟩ - let U' : Subrepresentation ρ := { - toSubmodule := U.toSubmodule.map S.toSubmodule.subtype - apply_mem_toSubmodule := by - intro g v hv - obtain ⟨u, hu, rfl⟩ := hv - exact ⟨S.toRepresentation g u, U.apply_mem_toSubmodule g hu, rfl⟩ } - rcases simple_eigen_submodule_alternative ρ e hunit g₀ c heig hsimple U' with h | h - · right - apply top_unique - intro u _ - obtain ⟨v, hv, heq⟩ := h u.property - have hvu : v = u := Subtype.ext heq - exact hvu ▸ hv - · left - apply bot_unique - intro u hu - have hum : (u : E) ∈ U' := ⟨u, hu, rfl⟩ - have hh := h _ hum _ u.property - have hz : (u : E) = 0 := inner_self_eq_zero.mp hh - exact Subtype.ext hz -end SpinAngle.Specht - - - - -noncomputable section -open scoped BigOperators ComplexConjugate InnerProductSpace Matrix -namespace SpinAngle.TensorRep -variable {ι n : Type*} [contextInstance135_23 : Fintype ι] [contextInstance135_35 : DecidableEq ι] [contextInstance135_51 : Fintype n] [contextInstance135_63 : DecidableEq n] - - -def tensor (a : ι → Matrix n n ℂ) : Matrix (ι → n) (ι → n) ℂ := - fun x y => ∏ i, a i (x i) (y i) - -lemma tensor_star - {ι : Type*} {n : Type*} - [contextInstance135_23 : Fintype ι] - [DecidableEq ι] - [Fintype n] - [DecidableEq n] (a : ι → Matrix n n ℂ) : - tensor (fun i => star (a i)) = star (tensor a) := by - ext x y - simp [tensor, Matrix.star_apply] - -lemma tensor_mul - {ι : Type*} {n : Type*} - [contextInstance135_23 : Fintype ι] - [contextInstance135_35 : DecidableEq ι] - [contextInstance135_51 : Fintype n] - [DecidableEq n] (a b : ι → Matrix n n ℂ) : - tensor (fun i => a i * b i) = tensor a * tensor b := by - ext x y - simp only [tensor, Matrix.mul_apply, ← Finset.prod_mul_distrib] - symm - simpa using (Finset.sum_prod_piFinset (ι := ι) Finset.univ - (fun i j => a i (x i) j * b i j (y i))) - -lemma tensor_one - {ι : Type*} {n : Type*} - [contextInstance135_23 : Fintype ι] - [DecidableEq ι] - [Fintype n] - [contextInstance135_63 : DecidableEq n] : tensor (fun _ : ι => (1 : Matrix n n ℂ)) = 1 := by - ext x y - classical - by_cases h : x = y - · subst y - simp [tensor] - · obtain ⟨i, hi⟩ := Function.ne_iff.mp h - simp only [tensor, Matrix.one_apply, ite_eq_right h] - apply Finset.prod_eq_zero (Finset.mem_univ i) - simp [hi] - -lemma tensor_diagonal - {ι : Type*} {n : Type*} - [contextInstance135_23 : Fintype ι] - [DecidableEq ι] - [Fintype n] - [contextInstance135_63 : DecidableEq n] (a : ι → n → ℂ) : - tensor (fun i => Matrix.diagonal (a i)) = Matrix.diagonal (fun x => ∏ i, a i (x i)) := by - ext x y - classical - by_cases h : x = y - · subst y - simp [tensor] - · obtain ⟨i, hi⟩ := Function.ne_iff.mp h - simp only [tensor, Matrix.diagonal_apply, ite_eq_right h] - apply Finset.prod_eq_zero (Finset.mem_univ i) - simp [hi] - -lemma toEuclideanLin_mul - {ι : Type*} {n : Type*} - [Fintype ι] - [DecidableEq ι] - [contextInstance135_51 : Fintype n] - [contextInstance135_63 : DecidableEq n] (a b : Matrix n n ℂ) : - Matrix.toEuclideanLin (a * b) = - Matrix.toEuclideanLin a * Matrix.toEuclideanLin b := by - ext v x - change ((a * b) *ᵥ (WithLp.ofLp v)) x = (a *ᵥ (b *ᵥ (WithLp.ofLp v))) x - rw [Matrix.mulVec_mulVec] - -lemma toEuclideanLin_one - {ι : Type*} {n : Type*} - [Fintype ι] - [DecidableEq ι] - [contextInstance135_51 : Fintype n] - [contextInstance135_63 : DecidableEq n] : Matrix.toEuclideanLin (1 : Matrix n n ℂ) = 1 := by - ext v x - change ((1 : Matrix n n ℂ) *ᵥ (WithLp.ofLp v)) x = v x - simp - - -def action : Matrix n n ℂ →* Module.End ℂ (EuclideanSpace ℂ (ι → n)) where - toFun a := Matrix.toEuclideanLin (tensor (fun _ : ι => a)) - map_one' := by rw [tensor_one, toEuclideanLin_one (ι := ι)] - map_mul' a b := by rw [tensor_mul, toEuclideanLin_mul (ι := ι)] - - - -def rep : Representation ℂ (Matrix.unitaryGroup n ℂ) (EuclideanSpace ℂ (ι → n)) := - action.comp (Matrix.unitaryGroup n ℂ).subtype - -lemma tensor_mem_unitary (a : ι → Matrix.unitaryGroup n ℂ) : - tensor (fun i => (a i : Matrix n n ℂ)) ∈ Matrix.unitaryGroup (ι → n) ℂ := by - rw [Matrix.mem_unitaryGroup_iff', ← tensor_star, ← tensor_mul] - convert tensor_one (ι := ι) (n := n) using 1 - congr 1 - funext i - exact (a i).property.1 - -lemma toEuclideanLin_unitary (a : Matrix n n ℂ) (ha : a ∈ Matrix.unitaryGroup n ℂ) - (v w : EuclideanSpace ℂ n) : - ⟪Matrix.toEuclideanLin a v, Matrix.toEuclideanLin a w⟫_ℂ = ⟪v, w⟫_ℂ := by - rw [← LinearMap.adjoint_inner_right] - rw [← Matrix.toEuclideanLin_conjTranspose_eq_adjoint] - change ⟪v, (Matrix.toEuclideanLin (star a) * Matrix.toEuclideanLin a) w⟫_ℂ = _ - rw [← toEuclideanLin_mul (ι := n), ha.1, toEuclideanLin_one (ι := n)] - rfl - -lemma rep_unitary (g : Matrix.unitaryGroup n ℂ) - (v w : EuclideanSpace ℂ (ι → n)) : ⟪rep g v, rep g w⟫_ℂ = ⟪v, w⟫_ℂ := - toEuclideanLin_unitary _ (tensor_mem_unitary (fun _ : ι => g)) v w - - -lemma tensor_reindex - {ι : Type*} {n : Type*} - [contextInstance135_23 : Fintype ι] - [DecidableEq ι] - [Fintype n] - [DecidableEq n] (a : Matrix n n ℂ) (σ : Equiv.Perm ι) (x y : ι → n) : - tensor (fun _ : ι => a) (x ∘ σ) (y ∘ σ) = tensor (fun _ : ι => a) x y := by - exact Equiv.prod_comp σ (fun i => a (x i) (y i)) - - -lemma action_diagonal (a : n → ℂ) (v : EuclideanSpace ℂ (ι → n)) (x : ι → n) : - action (Matrix.diagonal a) v x = (∏ i, a (x i)) * v x := by - change (Matrix.toEuclideanLin (tensor (fun _ : ι => Matrix.diagonal a)) v) x = _ - rw [tensor_diagonal] - change (Matrix.diagonal (fun x : ι → n => ∏ i, a (x i)) *ᵥ WithLp.ofLp v) x = _ - exact Matrix.mulVec_diagonal _ _ _ - -end SpinAngle.TensorRep - -namespace SpinAngle.Specht -open scoped Classical -variable {G : Type*} [contextInstance243_21 : Group G] -namespace PermutationSpace -open scoped Classical - -variable {X : Type*} [contextInstance247_21 : Fintype X] [contextInstance247_33 : MulAction G X] - - -def rep : Representation ℂ G (EuclideanSpace ℂ X) where - toFun g := { - toFun v := WithLp.toLp 2 (fun x => v (g⁻¹ • x)) - map_add' := by intro v w; rfl - map_smul' := by intro a v; rfl } - map_one' := by ext v x; simp - map_mul' := by - intro g h - ext v x - change v ((g * h)⁻¹ • x) = v (h⁻¹ • g⁻¹ • x) - simp [mul_smul] - -omit [Fintype X] in -@[simp] lemma rep_apply (g : G) (v : EuclideanSpace ℂ X) (x : X) : - rep g v x = v (g⁻¹ • x) := rfl - -lemma rep_unitary (g : G) (v w : EuclideanSpace ℂ X) : - ⟪rep g v, rep g w⟫_ℂ = ⟪v, w⟫_ℂ := by - simp only [PiLp.inner_apply, rep_apply] - exact Equiv.sum_comp (MulAction.toPerm g⁻¹) (fun x => inner ℂ (v x) (w x)) - -omit [Fintype X] in -lemma rep_single (g : G) (x : X) : - rep g (EuclideanSpace.single x (1 : ℂ)) = EuclideanSpace.single (g • x) (1 : ℂ) := by - classical - ext y - simp only [rep_apply, PiLp.single_apply, inv_smul_eq_iff] - -variable {H : Type*} [contextInstance278_21 : Group H] [contextInstance278_31 : Fintype H] - - - -def alternator (ι : H →* G) (χ : H →* ℂ) : Module.End ℂ (EuclideanSpace ℂ X) := - ∑ h, χ h • rep (ι h) - -omit [Fintype X] in -lemma alternator_apply (ι : H →* G) (χ : H →* ℂ) (v : EuclideanSpace ℂ X) : - alternator ι χ v = ∑ h, χ h • rep (ι h) v := by - simp [alternator, LinearMap.sum_apply] - -omit [Fintype X] in -lemma alternator_stable (ι : H →* G) (χ : H →* ℂ) - (U : Subrepresentation (rep : Representation ℂ G (EuclideanSpace ℂ X))) - (v : EuclideanSpace ℂ X) (hv : v ∈ U) : alternator ι χ v ∈ U := by - rw [alternator_apply] - exact U.toSubmodule.sum_mem fun h _ => U.toSubmodule.smul_mem _ (U.apply_mem_toSubmodule _ hv) - -omit [Fintype X] in -lemma alternator_translate (ι : H →* G) (χ : H →* ℂ) (a : H) - (v : EuclideanSpace ℂ X) : - alternator ι χ (rep (ι a) v) = χ a⁻¹ • alternator ι χ v := by - rw [alternator_apply, alternator_apply, Finset.smul_sum] - have he := Equiv.sum_comp (Equiv.mulRight a) - (fun h => χ a⁻¹ • (χ h • (rep (ι h) v : EuclideanSpace ℂ X))) - rw [← he] - apply Finset.sum_congr rfl - intro h _ - simp only [Equiv.coe_mulRight, smul_smul, map_mul] - rw [show χ a⁻¹ * (χ h * χ a) = χ h by - calc - _ = χ h * (χ a⁻¹ * χ a) := by ring - _ = χ h := by rw [← map_mul, inv_mul_cancel, map_one, mul_one]] - simp only [Module.End.mul_apply] - -omit [Fintype X] in -lemma alternator_single_zero (ι : H →* G) (χ : H →* ℂ) - (x : X) (a : H) (ha : ι a • x = x) (hs : χ a = -1) : - alternator ι χ (EuclideanSpace.single x (1 : ℂ)) = 0 := by - have hh := alternator_translate ι χ a (EuclideanSpace.single x (1 : ℂ)) - rw [rep_single, ha, map_inv, hs, inv_neg, inv_one, neg_smul, one_smul] at hh - have hz := congrArg (fun z => z + alternator ι χ (EuclideanSpace.single x (1 : ℂ))) hh - have ht : (2 : ℂ) • alternator ι χ (EuclideanSpace.single x (1 : ℂ)) = 0 := by - simpa [two_smul] using hz - exact (smul_eq_zero.mp ht).resolve_left (by norm_num) - -omit [Fintype X] in -lemma alternator_coeff (ι : H →* G) (χ : H →* ℂ) (v : EuclideanSpace ℂ X) (x : X) : - alternator ι χ v x = ∑ h, χ h * v ((ι h)⁻¹ • x) := by - simp [alternator_apply, WithLp.ofLp_sum, Finset.sum_apply] - -omit [Fintype X] in -lemma polytabloid_base [DecidableEq X] (ι : H →* G) (χ : H →* ℂ) (b : X) - (hfree : ∀ h : H, ι h • b = b → h = 1) : - alternator ι χ (EuclideanSpace.single b (1 : ℂ)) b = 1 := by - classical - rw [alternator_coeff, Finset.sum_eq_single 1] - · simp - · intro h _ hh - have hn : (ι h)⁻¹ • b ≠ b := by - intro he - have hi : h⁻¹ = 1 := hfree h⁻¹ (by simpa using he) - exact hh (inv_eq_one.mp hi) - simp [hn] - · simp - -lemma polytabloid_inner (ι : H →* G) (χ : H →* ℂ) (b : X) - (hreal : ∀ h, conj (χ h) = χ h) (hinv : ∀ h, χ h⁻¹ = χ h) - (v : EuclideanSpace ℂ X) : - ⟪alternator ι χ (EuclideanSpace.single b (1 : ℂ)), v⟫_ℂ = alternator ι χ v b := by - classical - rw [alternator_apply, sum_inner, alternator_coeff] - simp only [inner_smul_left, rep_single, EuclideanSpace.inner_single_left, map_one, - one_mul, hreal] - have hh := Equiv.sum_comp (Equiv.inv H) (fun h => χ h * v ((ι h)⁻¹ • b)) - simpa only [Equiv.inv_apply, map_inv, inv_inv, hinv] using hh - - - -theorem alternator_rank_one (ι : H →* G) (χ : H →* ℂ) (b : X) - (hreal : ∀ h, conj (χ h) = χ h) (hinv : ∀ h, χ h⁻¹ = χ h) - (hfree : ∀ h : H, ι h • b = b → h = 1) - (halt : ∀ x : X, (∃ a : H, ι a • x = x ∧ χ a = -1) ∨ - ∃ a : H, x = ι a • b) (v : EuclideanSpace ℂ X) : - alternator ι χ v = - ⟪alternator ι χ (EuclideanSpace.single b (1 : ℂ)), v⟫_ℂ • - alternator ι χ (EuclideanSpace.single b (1 : ℂ)) := by - classical - let e := alternator ι χ (EuclideanSpace.single b (1 : ℂ)) - have hs (x : X) : alternator ι χ (EuclideanSpace.single x (1 : ℂ)) ∈ Submodule.span ℂ {e} := by - rcases halt x with ⟨a, ha, hχ⟩ | ⟨a, rfl⟩ - · rw [alternator_single_zero ι χ x a ha hχ] - exact Submodule.zero_mem _ - · rw [← rep_single, alternator_translate] - exact Submodule.smul_mem _ _ (Submodule.subset_span (Set.mem_singleton e)) - have hv : alternator ι χ v ∈ Submodule.span ℂ {e} := by - have hexp := (EuclideanSpace.basisFun X ℂ).sum_repr v - simp only [EuclideanSpace.basisFun_repr, EuclideanSpace.basisFun_apply] at hexp - rw [← hexp, map_sum] - exact Submodule.sum_mem _ fun x _ => by - rw [map_smul] - exact Submodule.smul_mem _ _ (hs x) - obtain ⟨a, ha⟩ := Submodule.mem_span_singleton.mp hv - have heb : e b = 1 := polytabloid_base ι χ b hfree - have hab : a = alternator ι χ v b := by - have hh := congrArg (fun z : EuclideanSpace ℂ X => z b) ha - simpa only [PiLp.smul_apply, smul_eq_mul, heb, mul_one] using hh - rw [← ha, hab, polytabloid_inner ι χ b hreal hinv] - -end PermutationSpace -variable {α : Type*} [contextInstance389_21 : Fintype α] - -def complexSign : Equiv.Perm α →* ℂ where - toFun g := ((Equiv.Perm.sign g : ℤˣ) : ℤ) - map_one' := by simp - map_mul' := by intro g h; simp - -@[simp] lemma complexSign_conj (g : Equiv.Perm α) : conj (complexSign g) = complexSign g := by - simp [complexSign] - -@[simp] lemma complexSign_inv (g : Equiv.Perm α) : complexSign g⁻¹ = complexSign g := by - simp [complexSign] - -@[simp] lemma complexSign_swap (x y : α) (h : x ≠ y) : complexSign (Equiv.swap x y) = -1 := by - simp [complexSign, Equiv.Perm.sign_swap h] - - -end SpinAngle.Specht - -namespace SpinAngle.Young - -abbrev Cells (D : YoungDiagram) := {p : ℕ × ℕ // p ∈ D.cells} - -lemma fin_le_strictMono {n : ℕ} (f : Fin n → ℕ) (hf : StrictMono f) (i : Fin n) : - i.val ≤ f i := by - have aux : ∀ k (hk : k < n), k ≤ f ⟨k, hk⟩ := by - intro k - induction k with - | zero => intro hk; exact Nat.zero_le _ - | succ k ih => - intro hk - have hk' : k < n := by omega - have hl := hf (show (⟨k, hk'⟩ : Fin n) < ⟨k + 1, hk⟩ from by simp) - have hi := ih hk' - omega - exact aux i.val i.isLt - -lemma card_column (D : YoungDiagram) (j : ℕ) : - (Finset.univ.filter fun x : Cells D => x.val.2 = j).card = D.colLen j := by - classical - let e : {x : Cells D // x.val.2 = j} ≃ Fin (D.colLen j) := { - toFun := fun x => ⟨x.val.val.1, YoungDiagram.mem_iff_lt_colLen.mp (by - have hx : (x.val.val.1, x.val.val.2) ∈ D := x.val.property - simpa only [x.property] using hx)⟩ - invFun := fun i => ⟨⟨(i, j), YoungDiagram.mem_iff_lt_colLen.mpr i.isLt⟩, rfl⟩ - left_inv := by intro x; apply Subtype.ext; apply Subtype.ext; exact Prod.ext rfl x.property.symm - right_inv := by intro i; rfl } - rw [← Fintype.card_subtype] - exact (Fintype.card_congr e).trans (Fintype.card_fin _) - -lemma card_row_subtype (D : YoungDiagram) (i : ℕ) : - Fintype.card {x : Cells D // x.val.1 = i} = D.rowLen i := by - let e : {x : Cells D // x.val.1 = i} ≃ Fin (D.rowLen i) := { - toFun := fun x => ⟨x.val.val.2, YoungDiagram.mem_iff_lt_rowLen.mp (by - have hx : (x.val.val.1, x.val.val.2) ∈ D := x.val.property - simpa only [x.property] using hx)⟩ - invFun := fun j => ⟨⟨(i, j), YoungDiagram.mem_iff_lt_rowLen.mpr j.isLt⟩, rfl⟩ - left_inv := by intro x; apply Subtype.ext; apply Subtype.ext; exact Prod.ext x.property.symm rfl - right_inv := by intro j; rfl } - exact (Fintype.card_congr e).trans (Fintype.card_fin _) - -lemma eq_of_rowPreserving (D E : YoungDiagram) (e : Cells D ≃ Cells E) - (he : ∀ x, (e x).val.1 = x.val.1) : D = E := by - have hr (i : ℕ) : D.rowLen i = E.rowLen i := by - rw [← card_row_subtype D i, ← card_row_subtype E i] - exact Fintype.card_congr (e.subtypeEquiv (fun x => by rw [he])) - apply YoungDiagram.ext - ext p - obtain ⟨i, j⟩ := p - change (i, j) ∈ D ↔ (i, j) ∈ E - simp only [YoungDiagram.mem_iff_lt_rowLen, hr] - - - - -theorem column_sort_le (D : YoungDiagram) (r : Cells D → ℕ) - (hinj : ∀ x y : Cells D, x.val.2 = y.val.2 → r x = r y → x = y) - : - ∃ σ : Equiv.Perm (Cells D), (∀ x, (σ x).val.2 = x.val.2) ∧ - ∀ x, x.val.1 ≤ r (σ x) := by - classical - let S (j : ℕ) : Finset ℕ := (Finset.univ.filter fun x : Cells D => x.val.2 = j).image r - have hc (j : ℕ) : (S j).card = D.colLen j := by - change ((Finset.univ.filter fun x : Cells D => x.val.2 = j).image r).card = _ - rw [Finset.card_image_iff.mpr (show Set.InjOn r ↑(Finset.univ.filter fun x : Cells D => x.val.2 = j) from by - intro x hx y hy hxy - exact hinj x y ((Finset.mem_filter.mp hx).2.trans (Finset.mem_filter.mp hy).2.symm) hxy)] - exact card_column D j - let F (j : ℕ) := (S j).orderEmbOfFin (hc j) - have hpre (x : Cells D) : ∃ y : Cells D, y.val.2 = x.val.2 ∧ - r y = F x.val.2 ⟨x.val.1, YoungDiagram.mem_iff_lt_colLen.mp x.property⟩ := by - have hm := (S x.val.2).orderEmbOfFin_mem (hc _) ⟨x.val.1, YoungDiagram.mem_iff_lt_colLen.mp x.property⟩ - obtain ⟨y, hy, he⟩ := Finset.mem_image.mp hm - exact ⟨y, (Finset.mem_filter.mp hy).2, he⟩ - choose f hcol hr using hpre - have hf : Function.Injective f := by - intro x y he - have hj : x.val.2 = y.val.2 := (hcol x).symm.trans ((congrArg (fun z : Cells D => z.val.2) he).trans (hcol y)) - have hi : x.val.1 = y.val.1 := by - have hval : F x.val.2 ⟨x.val.1, YoungDiagram.mem_iff_lt_colLen.mp x.property⟩ = - F y.val.2 ⟨y.val.1, YoungDiagram.mem_iff_lt_colLen.mp y.property⟩ := by - rw [← hr x, ← hr y, he] - have hy : y.val.1 < D.colLen x.val.2 := by rw [hj]; exact YoungDiagram.mem_iff_lt_colLen.mp y.property - have hid : F y.val.2 ⟨y.val.1, YoungDiagram.mem_iff_lt_colLen.mp y.property⟩ = F x.val.2 ⟨y.val.1, hy⟩ := by - have aux (j k i : ℕ) (hk : j = k) (hi : i < D.colLen j) (hi' : i < D.colLen k) : - F j ⟨i, hi⟩ = F k ⟨i, hi'⟩ := by subst k; rfl - exact aux _ _ _ hj.symm _ _ - rw [hid] at hval - exact congrArg Fin.val ((F x.val.2).injective hval) - exact Subtype.ext (Prod.ext hi hj) - let σ : Equiv.Perm (Cells D) := Equiv.ofBijective f ⟨hf, Finite.surjective_of_injective hf⟩ - refine ⟨σ, hcol, ?_⟩ - have hle (x : Cells D) : x.val.1 ≤ r (σ x) := by - change x.val.1 ≤ r (f x) - rw [hr] - exact fin_le_strictMono _ (F x.val.2).strictMono ⟨x.val.1, YoungDiagram.mem_iff_lt_colLen.mp x.property⟩ - exact hle - -lemma rowRankSum_le (D : YoungDiagram) (r : Cells D → ℕ) - (hinj : ∀ x y : Cells D, x.val.2 = y.val.2 → r x = r y → x = y) : - ∑ x : Cells D, x.val.1 ≤ ∑ x : Cells D, r x := by - obtain ⟨σ, -, hσ⟩ := column_sort_le D r hinj - rw [← Equiv.sum_comp σ r] - exact Finset.sum_le_sum fun x _ => hσ x - -theorem column_sort (D : YoungDiagram) (r : Cells D → ℕ) - (hinj : ∀ x y : Cells D, x.val.2 = y.val.2 → r x = r y → x = y) - (hsum : ∑ x : Cells D, r x = ∑ x : Cells D, x.val.1) : - ∃ σ : Equiv.Perm (Cells D), (∀ x, (σ x).val.2 = x.val.2) ∧ - ∀ x, r (σ x) = x.val.1 := by - obtain ⟨σ, hc, hle⟩ := column_sort_le D r hinj - refine ⟨σ, hc, ?_⟩ - have heq : ∑ x : Cells D, x.val.1 = ∑ x : Cells D, r (σ x) := by - rw [Equiv.sum_comp σ r, hsum] - have hh := (Finset.sum_eq_sum_iff_of_le (s := Finset.univ) (fun x _ => hle x)).mp heq - intro x - exact (hh x (Finset.mem_univ x)).symm - -end SpinAngle.Young - -namespace SpinAngle.PolynomialCarrier -open scoped Classical Matrix -open SpinAngle.Specht SpinAngle.Young -variable {ι n : Type*} [contextInstance532_23 : Fintype ι] [contextInstance532_35 : DecidableEq ι] [contextInstance532_51 : Fintype n] [contextInstance532_63 : DecidableEq n] - - -instance coloringAction : MulAction (Equiv.Perm ι) (ι → n) where - smul g x := x ∘ g.symm - one_smul _ := rfl - mul_smul _ _ _ := rfl - -lemma site_apply - {ι : Type*} {n : Type*} - [Fintype ι] - [DecidableEq ι] - [Fintype n] - [DecidableEq n] (g : Equiv.Perm ι) (v : EuclideanSpace ℂ (ι → n)) (x : ι → n) : - PermutationSpace.rep g v x = v (x ∘ g) := rfl - -def reindex (g : Equiv.Perm ι) : (ι → n) ≃ (ι → n) where - toFun x := x ∘ g - invFun x := x ∘ g.symm - left_inv x := by funext i; simp - right_inv x := by funext i; simp - -lemma action_site_commute (a : Matrix n n ℂ) (g : Equiv.Perm ι) - (v : EuclideanSpace ℂ (ι → n)) : - TensorRep.action a (PermutationSpace.rep g v) = - PermutationSpace.rep g (TensorRep.action a v) := by - ext x - change (∑ y, TensorRep.tensor (fun _ : ι => a) x y * v (y ∘ g)) = - ∑ y, TensorRep.tensor (fun _ : ι => a) (x ∘ g) y * v y - rw [← Equiv.sum_comp (reindex (n := n) g) - (fun y => TensorRep.tensor (fun _ : ι => a) (x ∘ g) y * v y)] - apply Finset.sum_congr rfl - intro y _ - change _ = TensorRep.tensor (fun _ : ι => a) (x ∘ g) (y ∘ g) * v (y ∘ g) - rw [TensorRep.tensor_reindex] - - -def columnGroup (D : YoungDiagram) : Subgroup (Equiv.Perm (Cells D)) where - carrier := {g | ∀ x, (g x).val.2 = x.val.2} - one_mem' := fun _ => rfl - mul_mem' := by intro g h hg hh x; exact (hg (h x)).trans (hh x) - inv_mem' := by - intro g hg x - simpa using (hg (g⁻¹ x)).symm - -variable (D : YoungDiagram) (q : ℕ) -abbrev TensorSpace := EuclideanSpace ℂ (Cells D → Fin q) - - - -def alternating : Subrepresentation (TensorRep.rep (ι := Cells D) (n := Fin q)) where - toSubmodule := { - carrier := {v | ∀ g : columnGroup D, - PermutationSpace.rep (g : Equiv.Perm (Cells D)) v = complexSign g.val • v} - zero_mem' := by intro g; simp - add_mem' := by intro x y hx hy g; simp [map_add, hx g, hy g, smul_add] - smul_mem' := by intro c x hx g; simp [map_smul, hx g, smul_comm c] } - apply_mem_toSubmodule a := by - intro v hv g - change PermutationSpace.rep g.val (TensorRep.action (a : Matrix (Fin q) (Fin q) ℂ) v) = _ - rw [← action_site_commute, hv g, map_smul] - rfl - -variable (hq : D.colLen 0 ≤ q) - -def rowColor : Cells D → Fin q := fun x => ⟨x.val.1, by - have hm := D.up_left_mem le_rfl (Nat.zero_le x.val.2) x.property - have hl := YoungDiagram.mem_iff_lt_colLen.mp hm - exact lt_of_lt_of_le hl hq⟩ - -def highest : TensorSpace D q := by - classical - exact PermutationSpace.alternator (columnGroup D).subtype - (complexSign.comp (columnGroup D).subtype) - (EuclideanSpace.single (rowColor D q hq) (1 : ℂ)) - -lemma rowColor_column_free - {ι : Type*} - [Fintype ι] - [DecidableEq ι] - (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) (g : columnGroup D) - (hg : g.val • rowColor D q hq = rowColor D q hq) : g = 1 := by - apply Subtype.ext - apply Equiv.Perm.ext - intro x - apply Subtype.ext - apply Prod.ext - · have hh := congrFun hg (g.val x) - have hh' := congrArg Fin.val hh - change (g.val x).val.1 = x.val.1 - change ((g.val x |> g.val.symm)).val.1 = (g.val x).val.1 at hh' - simp only [Equiv.symm_apply_apply] at hh' - exact hh'.symm - · exact g.property x - -lemma highest_base : highest D q hq (rowColor D q hq) = 1 := by - classical - unfold highest - exact PermutationSpace.polytabloid_base (columnGroup D).subtype - (complexSign.comp (columnGroup D).subtype) (rowColor D q hq) - (rowColor_column_free (ι := Cells D) D q hq) - -lemma highest_ne_zero : highest D q hq ≠ 0 := by - intro he - have hh := congrArg (fun v : TensorSpace D q => v (rowColor D q hq)) he - simp [highest_base] at hh - -end SpinAngle.PolynomialCarrier - -namespace SpinAngle.Specht.PermutationSpace -open scoped Classical -variable {G H X : Type*} [contextInstance635_25 : Group G] [contextInstance635_35 : Group H] [contextInstance635_45 : Fintype H] [contextInstance635_57 : Fintype X] [contextInstance635_69 : MulAction G X] -lemma rep_alternator - {G : Type*} {H : Type*} {X : Type*} - [contextInstance635_25 : Group G] - [contextInstance635_35 : Group H] - [contextInstance635_45 : Fintype H] - [Fintype X] - [contextInstance635_69 : MulAction G X] (ι : H →* G) (χ : H →* ℂ) (a : H) - (v : EuclideanSpace ℂ X) : - rep (ι a) (alternator ι χ v) = χ a⁻¹ • alternator ι χ v := by - rw [alternator_apply, map_sum, Finset.smul_sum] - have he := Equiv.sum_comp (Equiv.mulLeft a) - (fun h => χ a⁻¹ • (χ h • (rep (ι h) v : EuclideanSpace ℂ X))) - rw [← he] - apply Finset.sum_congr rfl - intro h _ - simp only [Equiv.coe_mulLeft, smul_smul, map_mul, map_smul] - rw [show χ a⁻¹ * (χ a * χ h) = χ h by - rw [← mul_assoc, ← map_mul, inv_mul_cancel, map_one, one_mul]] - rfl -end SpinAngle.Specht.PermutationSpace - -namespace SpinAngle.PolynomialCarrier -open scoped Classical Matrix -open SpinAngle.Specht SpinAngle.Young -variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) - -lemma highest_mem : highest D q hq ∈ alternating D q := by - classical - intro g - change PermutationSpace.rep g.val (PermutationSpace.alternator _ _ _) = _ - have hh := PermutationSpace.rep_alternator (columnGroup D).subtype - (complexSign.comp (columnGroup D).subtype) g (EuclideanSpace.single (rowColor D q hq) (1 : ℂ)) - change PermutationSpace.rep g.val (highest D q hq) = complexSign (g.val⁻¹) • highest D q hq at hh - rw [complexSign_inv] at hh - exact hh - - -lemma alternating_collision (v : TensorSpace D q) (hv : v ∈ alternating D q) - (x : Cells D → Fin q) (i j : Cells D) (hij : i ≠ j) - (hc : i.val.2 = j.val.2) (hx : x i = x j) : v x = 0 := by - classical - let : DecidableEq (Cells D) := Classical.decEq _ - let g : columnGroup D := ⟨Equiv.swap i j, by - intro k - by_cases hki : k = i - · subst k; simp [hc] - by_cases hkj : k = j - · subst k; simp [hc] - rw [Equiv.swap_apply_of_ne_of_ne hki hkj]⟩ - have hperm : x ∘ (g : Equiv.Perm (Cells D)) = x := by - funext k - change x (Equiv.swap i j k) = x k - by_cases hki : k = i - · subst k; simp [hx] - by_cases hkj : k = j - · subst k; simp [hx] - rw [Equiv.swap_apply_of_ne_of_ne hki hkj] - have hh := congrArg (fun w : TensorSpace D q => w x) (hv g) - simp only [site_apply, hperm, PiLp.smul_apply, smul_eq_mul] at hh - have hg : complexSign g.val = -1 := by - simpa only [g] using complexSign_swap i j hij - rw [hg, neg_one_mul] at hh - linear_combination (1/2 : ℂ) * hh - -lemma alternating_injective (v : TensorSpace D q) (hv : v ∈ alternating D q) - (x : Cells D → Fin q) (hx : v x ≠ 0) : - ∀ i j : Cells D, i.val.2 = j.val.2 → (x i).val = (x j).val → i = j := by - intro i j hc he - by_contra hij - exact hx (alternating_collision D q v hv x i j hij hc (Fin.ext he)) - - - -lemma alternating_minimal_weight (v : TensorSpace D q) (hv : v ∈ alternating D q) - (x : Cells D → Fin q) (hw : ∑ i, (x i).val = ∑ i : Cells D, i.val.1) : - v x = v (rowColor D q hq) * highest D q hq x := by - by_cases hx : v x = 0 - · by_cases he : highest D q hq x = 0 - · rw [hx, he, mul_zero] - · obtain ⟨σ, hc, hr⟩ := column_sort D (fun i => (x i).val) - (alternating_injective D q (highest D q hq) (highest_mem D q hq) x he) hw - let g : columnGroup D := ⟨σ, hc⟩ - have hcolor : x ∘ σ = rowColor D q hq := by funext i; exact Fin.ext (hr i) - have hh := congrArg (fun w : TensorSpace D q => w x) (hv g) - simp only [site_apply, PiLp.smul_apply, smul_eq_mul] at hh - change v (x ∘ σ) = complexSign σ * v x at hh - rw [hcolor, hx, mul_zero] at hh - rw [hx, hh, zero_mul] - · obtain ⟨σ, hc, hr⟩ := column_sort D (fun i => (x i).val) - (alternating_injective D q v hv x hx) hw - let g : columnGroup D := ⟨σ, hc⟩ - have hcolor : x ∘ σ = rowColor D q hq := by funext i; exact Fin.ext (hr i) - have hh := congrArg (fun w : TensorSpace D q => w x) (hv g) - have he := congrArg (fun w : TensorSpace D q => w x) (highest_mem D q hq g) - simp only [site_apply, PiLp.smul_apply, smul_eq_mul] at hh he - change v (x ∘ σ) = complexSign σ * v x at hh - change highest D q hq (x ∘ σ) = complexSign σ * highest D q hq x at he - rw [hcolor] at hh he - rw [highest_base] at he - rw [hh] - calc - v x = v x * 1 := (mul_one _).symm - _ = v x * (complexSign σ * highest D q hq x) := by rw [← he] - _ = complexSign σ * v x * highest D q hq x := by ring - -end SpinAngle.PolynomialCarrier - -namespace SpinAngle.PolynomialCarrier -open scoped Classical Matrix -open SpinAngle.Specht SpinAngle.Young -variable {ι : Type*} [contextInstance741_21 : Fintype ι] [contextInstance741_33 : DecidableEq ι] {q : ℕ} - -lemma diagonal_single (a : Fin q → ℂ) (b : ι → Fin q) : - TensorRep.action (Matrix.diagonal a) (EuclideanSpace.single b (1 : ℂ)) = - (∏ i, a (b i)) • EuclideanSpace.single b (1 : ℂ) := by - ext x - rw [TensorRep.action_diagonal] - simp only [PiLp.smul_apply, smul_eq_mul, PiLp.single_apply] - by_cases h : x = b - · subst x; rfl - · simp [h] - -lemma diagonal_unitary {z : ℂ} (hz : star z * z = 1) : - Matrix.diagonal (fun i : Fin q => z ^ i.val) ∈ Matrix.unitaryGroup (Fin q) ℂ := by - have hd : star (Matrix.diagonal (fun i : Fin q => z ^ i.val)) = - Matrix.diagonal (fun i : Fin q => star (z ^ i.val)) := by - ext i j - by_cases h : i = j - · subst j; simp [Matrix.star_apply] - · simp [Matrix.star_apply, h, Ne.symm h] - rw [Matrix.mem_unitaryGroup_iff', hd, Matrix.diagonal_mul_diagonal] - simp only [star_pow, ← mul_pow, hz, one_pow] - exact Matrix.diagonal_one - -variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) - -def weightOrder : ℕ := Fintype.card (Cells D) * q + 1 - -def weightRoot : ℂ := Complex.exp (2 * Real.pi * Complex.I / weightOrder D q) - -lemma weightRoot_primitive : IsPrimitiveRoot (weightRoot D q) (weightOrder D q) := - Complex.isPrimitiveRoot_exp _ (by unfold weightOrder; omega) - -lemma weightRoot_unitary : star (weightRoot D q) * weightRoot D q = 1 := by - have hn := Complex.norm_eq_one_of_pow_eq_one - (weightRoot_primitive D q).pow_eq_one (show weightOrder D q ≠ 0 by unfold weightOrder; omega) - rw [mul_comm, Complex.star_def, Complex.mul_conj, Complex.normSq_eq_norm_sq, hn] - norm_num - -def weightElement : Matrix.unitaryGroup (Fin q) ℂ := - ⟨Matrix.diagonal (fun i => weightRoot D q ^ i.val), diagonal_unitary (weightRoot_unitary D q)⟩ - -lemma weight_sum_lt (x : Cells D → Fin q) : ∑ i, (x i).val < weightOrder D q := by - have hh : (∑ i, (x i).val) ≤ ∑ _i : Cells D, q := - Finset.sum_le_sum fun i _ => (x i).isLt.le - simp only [Finset.sum_const, Finset.card_univ, smul_eq_mul] at hh - unfold weightOrder - omega - -lemma weight_action (v : TensorSpace D q) (x : Cells D → Fin q) : - TensorRep.rep (weightElement D q) v x = weightRoot D q ^ (∑ i, (x i).val) * v x := by - change TensorRep.action (Matrix.diagonal (fun i : Fin q => weightRoot D q ^ i.val)) v x = _ - rw [TensorRep.action_diagonal, Finset.prod_pow_eq_pow_sum] - -lemma highest_diagonal (a : Fin q → ℂ) : - TensorRep.action (Matrix.diagonal a) (highest D q hq) = - (∏ i, a (rowColor D q hq i)) • highest D q hq := by - unfold highest - rw [PermutationSpace.alternator_apply, map_sum, Finset.smul_sum] - apply Finset.sum_congr rfl - intro g _ - rw [map_smul, action_site_commute, diagonal_single, map_smul] - exact smul_comm _ _ _ - -lemma highest_weight_eigen : - TensorRep.rep (weightElement D q) (highest D q hq) = - weightRoot D q ^ (∑ i : Cells D, i.val.1) • highest D q hq := by - change TensorRep.action (Matrix.diagonal _) _ = _ - rw [highest_diagonal] - congr 1 - exact Finset.prod_pow_eq_pow_sum _ _ _ - -include hq in -lemma weight_eigen_support (v : TensorSpace D q) - (hv : TensorRep.rep (weightElement D q) v = - weightRoot D q ^ (∑ i : Cells D, i.val.1) • v) - (x : Cells D → Fin q) (hx : v x ≠ 0) : - ∑ i, (x i).val = ∑ i : Cells D, i.val.1 := by - have hh := congrArg (fun w : TensorSpace D q => w x) hv - rw [weight_action] at hh - simp only [PiLp.smul_apply, smul_eq_mul] at hh - have hp := mul_right_cancel₀ hx hh - apply (weightRoot_primitive D q).pow_inj (weight_sum_lt D q x) _ hp - exact weight_sum_lt D q (rowColor D q hq) - - -theorem weight_eigenspace_one_dimensional (v : TensorSpace D q) - (hv : v ∈ alternating D q) - (heig : TensorRep.rep (weightElement D q) v = - weightRoot D q ^ (∑ i : Cells D, i.val.1) • v) : - v = v (rowColor D q hq) • highest D q hq := by - ext x - change v x = v (rowColor D q hq) * highest D q hq x - by_cases hw : ∑ i, (x i).val = ∑ i : Cells D, i.val.1 - · exact alternating_minimal_weight D q hq v hv x hw - · have hv0 : v x = 0 := by - by_contra hn - exact hw (weight_eigen_support D q hq v heig x hn) - have he0 : highest D q hq x = 0 := by - by_contra hn - exact hw (weight_eigen_support D q hq _ (highest_weight_eigen D q hq) x hn) - rw [hv0, he0, mul_zero] - - - -def ordinary : Subrepresentation (alternating D q).toRepresentation := - cyclic (alternating D q).toRepresentation - (⟨highest D q hq, highest_mem D q hq⟩ : (alternating D q).toSubmodule) - -theorem ordinary_irreducible : Representation.IsIrreducible (ordinary D q hq).toRepresentation := by - refine cyclic_irreducible_of_simple_eigen _ _ ?_ ?_ (weightElement D q) - (weightRoot D q ^ (∑ i : Cells D, i.val.1)) ?_ ?_ - · intro he - exact highest_ne_zero D q hq (congrArg Subtype.val he) - · intro g x y - exact TensorRep.rep_unitary g (x : TensorSpace D q) (y : TensorSpace D q) - · exact Subtype.ext (highest_weight_eigen D q hq) - · intro v hv - apply Submodule.mem_span_singleton.mpr - refine ⟨v.val (rowColor D q hq), ?_⟩ - apply Subtype.ext - exact (weight_eigenspace_one_dimensional D q hq v.val v.property (congrArg Subtype.val hv)).symm - -end SpinAngle.PolynomialCarrier - -namespace SpinAngle.TensorRep -open scoped Classical -variable {ι κ n : Type*} [contextInstance868_25 : Fintype ι] [contextInstance868_37 : DecidableEq ι] [contextInstance868_53 : Fintype κ] [contextInstance868_65 : DecidableEq κ] - [contextInstance869_2 : Fintype n] [contextInstance869_14 : DecidableEq n] - -lemma diagonal_unitary_of_star_mul (a : n → ℂ) (ha : ∀ i, star (a i) * a i = 1) : - Matrix.diagonal a ∈ Matrix.unitaryGroup n ℂ := by - have hd : star (Matrix.diagonal a) = Matrix.diagonal (fun i => star (a i)) := by - ext i j - by_cases h : i = j - · subst j; simp [Matrix.star_apply] - · simp [Matrix.star_apply, h, Ne.symm h] - rw [Matrix.mem_unitaryGroup_iff', hd, Matrix.diagonal_mul_diagonal] - simp only [ha] - exact Matrix.diagonal_one - -lemma diagonal_single [DecidableEq (ι → n)] (a : n → ℂ) (b : ι → n) : - action (Matrix.diagonal a) (EuclideanSpace.single b (1 : ℂ)) = - (∏ i, a (b i)) • EuclideanSpace.single b (1 : ℂ) := by - ext x - rw [action_diagonal] - simp only [PiLp.smul_apply, smul_eq_mul, PiLp.single_apply] - by_cases h : x = b - · subst x; rfl - · simp [h] - -def content (x : ι → n) (j : n) : ℕ := (Finset.univ.filter fun i => x i = j).card - -lemma product_content - {ι : Type*} {n : Type*} - [contextInstance868_25 : Fintype ι] - [DecidableEq ι] - [contextInstance869_2 : Fintype n] - [contextInstance869_14 : DecidableEq n] (a : n → ℂ) (x : ι → n) : - ∏ i, a (x i) = ∏ j, a j ^ content x j := by - rw [← Finset.prod_fiberwise' Finset.univ x a] - simp only [Finset.prod_const, content] - -lemma phase_product - {ι : Type*} {n : Type*} - [contextInstance868_25 : Fintype ι] - [DecidableEq ι] - [Fintype n] - [contextInstance869_14 : DecidableEq n] (z : ℂ) (j : n) (x : ι → n) : - ∏ i, (if x i = j then z else 1) = z ^ content x j := by - rw [← Finset.prod_filter] - simp [content] - -lemma content_le_card - {ι : Type*} {n : Type*} - [contextInstance868_25 : Fintype ι] - [DecidableEq ι] - [Fintype n] - [contextInstance869_14 : DecidableEq n] (x : ι → n) (j : n) : content x j ≤ Fintype.card ι := - (Finset.card_filter_le _ _).trans_eq (Finset.card_univ) - - - -lemma intertwiner_content_zero - (L : EuclideanSpace ℂ (ι → n) →ₗ[ℂ] EuclideanSpace ℂ (κ → n)) - (hL : ∀ (g : Matrix.unitaryGroup n ℂ) v, L (rep g v) = rep g (L v)) - (x : ι → n) (y : κ → n) (j : n) (hxy : content x j ≠ content y j) : - L (EuclideanSpace.single x (1 : ℂ)) y = 0 := by - let N := Fintype.card ι + Fintype.card κ + 1 - let z : ℂ := Complex.exp (2 * Real.pi * Complex.I / N) - have hz : IsPrimitiveRoot z N := Complex.isPrimitiveRoot_exp _ (by dsimp [N]; omega) - have hzn : ‖z‖ = 1 := Complex.norm_eq_one_of_pow_eq_one hz.pow_eq_one (by dsimp [N]; omega) - have hzu : star z * z = 1 := by - rw [mul_comm, Complex.star_def, Complex.mul_conj, Complex.normSq_eq_norm_sq, hzn] - norm_num - let g : Matrix.unitaryGroup n ℂ := ⟨Matrix.diagonal (fun k => if k = j then z else 1), - diagonal_unitary_of_star_mul _ (fun k => by split_ifs; exact hzu; simp)⟩ - have hh := congrArg (fun v : EuclideanSpace ℂ (κ → n) => v y) - (hL g (EuclideanSpace.single x (1 : ℂ))) - change L (action (Matrix.diagonal _) _) y = action (Matrix.diagonal _) _ y at hh - rw [diagonal_single, map_smul, action_diagonal] at hh - simp only [PiLp.smul_apply, smul_eq_mul, phase_product] at hh - by_contra hn - apply hxy - exact hz.pow_inj (by have := content_le_card x j; dsimp [N]; omega) - (by have := content_le_card y j; dsimp [N]; omega) (mul_right_cancel₀ hn hh) - - - -lemma intertwiner_diagonal - (L : EuclideanSpace ℂ (ι → n) →ₗ[ℂ] EuclideanSpace ℂ (κ → n)) - (hL : ∀ (g : Matrix.unitaryGroup n ℂ) v, L (rep g v) = rep g (L v)) - (a : n → ℂ) (v : EuclideanSpace ℂ (ι → n)) : - L (action (Matrix.diagonal a) v) = action (Matrix.diagonal a) (L v) := by - have hsingle (x : ι → n) : - L (action (Matrix.diagonal a) (EuclideanSpace.single x (1 : ℂ))) = - action (Matrix.diagonal a) (L (EuclideanSpace.single x (1 : ℂ))) := by - ext y - rw [diagonal_single, map_smul, action_diagonal] - simp only [PiLp.smul_apply, smul_eq_mul] - by_cases he : ∀ j, content x j = content y j - · rw [product_content a x, product_content a y] - congr 1 - exact Finset.prod_congr rfl fun j _ => congrArg (fun k => a j ^ k) (he j) - · push Not at he - obtain ⟨j, hj⟩ := he - rw [intertwiner_content_zero L hL x y j hj, mul_zero, mul_zero] - have hexp := (EuclideanSpace.basisFun (ι → n) ℂ).sum_repr v - simp only [EuclideanSpace.basisFun_repr, EuclideanSpace.basisFun_apply] at hexp - rw [← hexp, map_sum, map_sum, map_sum, map_sum] - apply Finset.sum_congr rfl - intro x _ - rw [map_smul, map_smul, map_smul, map_smul, hsingle] - - - -lemma intertwiner_hermitian - (L : EuclideanSpace ℂ (ι → n) →ₗ[ℂ] EuclideanSpace ℂ (κ → n)) - (hL : ∀ (g : Matrix.unitaryGroup n ℂ) v, L (rep g v) = rep g (L v)) - (a : Matrix n n ℂ) (ha : a.IsHermitian) (v : EuclideanSpace ℂ (ι → n)) : - L (action a v) = action a (L v) := by - rw [ha.spectral_theorem] - simp only [Unitary.conjStarAlgAut_apply, map_mul, Module.End.mul_apply] - change L (rep ha.eigenvectorUnitary (action (Matrix.diagonal _) (rep (star ha.eigenvectorUnitary) v))) = _ - rw [hL, intertwiner_diagonal L hL, hL] - rfl - -end SpinAngle.TensorRep - -namespace SpinAngle.TensorRep -open SpinAngle.Specht -variable {ι n : Type*} [contextInstance980_23 : Fintype ι] [contextInstance980_35 : DecidableEq ι] [contextInstance980_51 : Fintype n] [contextInstance980_63 : DecidableEq n] - - - -lemma apply_mem_hermitian (U : Subrepresentation (rep (ι := ι) (n := n))) - (a : Matrix n n ℂ) (ha : a.IsHermitian) - (v : EuclideanSpace ℂ (ι → n)) (hv : v ∈ U) : action a v ∈ U := by - let L : EuclideanSpace ℂ (ι → n) →ₗ[ℂ] EuclideanSpace ℂ (ι → n) := - U.toSubmodule.starProjection.toLinearMap - have hu : ∀ (g : Matrix.unitaryGroup n ℂ) (x y : EuclideanSpace ℂ (ι → n)), - ⟪rep g x, rep g y⟫_ℂ = ⟪x, y⟫_ℂ := rep_unitary - have hL : ∀ (g : Matrix.unitaryGroup n ℂ) (w : EuclideanSpace ℂ (ι → n)), - L (rep g w) = rep g (L w) := by - intro g w - exact starProjection_rep (rep (ι := ι) (n := n)) hu U g w - have hlv : L v = v := U.toSubmodule.starProjection_eq_self_iff.mpr hv - have hh := intertwiner_hermitian L hL a ha v - rw [hlv] at hh - rw [← hh] - exact U.toSubmodule.starProjection_apply_mem _ - -end SpinAngle.TensorRep - -namespace SpinAngle.PolynomialCarrier -open scoped Classical Matrix -open SpinAngle.Specht SpinAngle.Young -variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) - - -def highestMonomial (t : Fin q → ℝ) : ℝ := ∏ i : Cells D, t (rowColor D q hq i) - -lemma highestMonomial_nonneg (t : Fin q → ℝ) (ht : ∀ j, 0 ≤ t j) : - 0 ≤ highestMonomial D q hq t := Finset.prod_nonneg fun _ _ => ht _ - - - -lemma monomial_le_highest (t : Fin q → ℝ) (ht : ∀ j, 0 ≤ t j) (hanti : Antitone t) - (x : Cells D → Fin q) - (hinj : ∀ i j : Cells D, i.val.2 = j.val.2 → (x i).val = (x j).val → i = j) : - (∏ i, t (x i)) ≤ highestMonomial D q hq t := by - obtain ⟨σ, -, hσ⟩ := column_sort_le D (fun i => (x i).val) hinj - rw [← Equiv.prod_comp σ (fun i => t (x i))] - apply Finset.prod_le_prod₀ (fun _ _ => ht _) - intro i _ - exact hanti (show rowColor D q hq i ≤ x (σ i) from hσ i) - - - -theorem diagonal_norm_bound (t : Fin q → ℝ) (ht : ∀ j, 0 ≤ t j) (hanti : Antitone t) - (v : TensorSpace D q) (hv : v ∈ alternating D q) : - ‖TensorRep.action (Matrix.diagonal (fun j => (t j : ℂ))) v‖ ≤ - highestMonomial D q hq t * ‖v‖ := by - have hb := highestMonomial_nonneg D q hq t ht - apply (sq_le_sq₀ (norm_nonneg _) (mul_nonneg hb (norm_nonneg _))).mp - rw [mul_pow, EuclideanSpace.norm_sq_eq, EuclideanSpace.norm_sq_eq, Finset.mul_sum] - apply Finset.sum_le_sum - intro x _ - rw [TensorRep.action_diagonal, norm_mul, norm_prod, mul_pow] - simp only [Complex.norm_real, Real.norm_eq_abs, abs_of_nonneg (ht _)] - by_cases hz : v x = 0 - · simp [hz] - · apply mul_le_mul_of_nonneg_right _ (sq_nonneg _) - exact pow_le_pow_left₀ (Finset.prod_nonneg fun _ _ => ht _) - (monomial_le_highest D q hq t ht hanti x (alternating_injective D q v hv x hz)) 2 - -end SpinAngle.PolynomialCarrier - - - - - -noncomputable section -open scoped Matrix ComplexOrder -namespace SpinAngle.SortedSpectrum -variable {q : ℕ} (A : Matrix (Fin q) (Fin q) ℂ) (hA : A.IsHermitian) - -def values : Fin q → ℝ := - (Matrix.isSymmetric_toEuclideanLin_iff.mpr hA).eigenvalues (by simp) - -def basis : OrthonormalBasis (Fin q) ℂ (EuclideanSpace ℂ (Fin q)) := - (Matrix.isSymmetric_toEuclideanLin_iff.mpr hA).eigenvectorBasis (by simp) - -def changeBasis : Matrix.unitaryGroup (Fin q) ℂ := - ⟨(EuclideanSpace.basisFun (Fin q) ℂ).toBasis.toMatrix (basis A hA).toBasis, - (EuclideanSpace.basisFun (Fin q) ℂ).toMatrix_orthonormalBasis_mem_unitary (basis A hA)⟩ - -@[simp] lemma changeBasis_apply (i j : Fin q) : changeBasis A hA i j = basis A hA j i := rfl - -lemma values_antitone : Antitone (values A hA) := - LinearMap.IsSymmetric.eigenvalues_antitone _ _ - -lemma eigenvector (i : Fin q) : - Matrix.toEuclideanLin A (basis A hA i) = (values A hA i : ℂ) • basis A hA i := - LinearMap.IsSymmetric.apply_eigenvectorBasis _ _ _ - -lemma spectral_theorem : A = (changeBasis A hA : Matrix _ _ ℂ) * - Matrix.diagonal (fun i => (values A hA i : ℂ)) * star (changeBasis A hA : Matrix _ _ ℂ) := by - have he : A * (changeBasis A hA : Matrix _ _ ℂ) = - (changeBasis A hA : Matrix _ _ ℂ) * Matrix.diagonal (fun i => (values A hA i : ℂ)) := by - ext i j - rw [Matrix.mul_diagonal] - simpa only [Matrix.mul_apply, changeBasis_apply, - Matrix.toLpLin_apply, Matrix.mulVec, dotProduct, PiLp.smul_apply, smul_eq_mul, - mul_comm] using congrArg (fun v : EuclideanSpace ℂ (Fin q) => v i) (eigenvector A hA j) - have hh := congrArg (fun B : Matrix (Fin q) (Fin q) ℂ => B * star (changeBasis A hA : Matrix _ _ ℂ)) he - simpa only [Matrix.mul_assoc, (changeBasis A hA).property.2, Matrix.mul_one] using hh - -lemma values_nonneg (hpos : A.PosSemidef) (i : Fin q) : 0 ≤ values A hA i := by - have hp := (Matrix.isPositive_toEuclideanLin_iff.mpr hpos).inner_nonneg_left (basis A hA i) - rw [eigenvector, inner_smul_left, (basis A hA).inner_eq_one i] at hp - have hp' : (0 : ℂ) ≤ (values A hA i : ℂ) := by simpa only [Complex.conj_ofReal, mul_one] using hp - exact RCLike.ofReal_nonneg.mp hp' - -lemma trace_eq_sum : Matrix.trace A = ∑ i, (values A hA i : ℂ) := by - conv_lhs => rw [spectral_theorem A hA] - rw [Matrix.trace_mul_cycle, (changeBasis A hA).property.1, - Matrix.one_mul, Matrix.trace_diagonal] - -end SpinAngle.SortedSpectrum - -namespace SpinAngle.PolynomialCarrier -open scoped Classical Matrix InnerProductSpace -open SpinAngle.Specht SpinAngle.Young Module -variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) - -abbrev Carrier : Type := (ordinary D q hq).toSubmodule - -instance carrierInner : InnerProductSpace ℂ (Carrier D q hq) := - @Submodule.innerProductSpace ℂ (alternating D q).toSubmodule _ _ inferInstance - (ordinary D q hq).toSubmodule - - -def inclusion : Carrier D q hq →ₗᵢ[ℂ] TensorSpace D q := - (alternating D q).toSubmodule.subtypeₗᵢ.comp (ordinary D q hq).toSubmodule.subtypeₗᵢ - -@[simp] lemma inclusion_apply (v : Carrier D q hq) : inclusion D q hq v = v.val.val := rfl - -lemma inclusion_equivariant (g : Matrix.unitaryGroup (Fin q) ℂ) (v : Carrier D q hq) : - inclusion D q hq ((ordinary D q hq).toRepresentation g v) = - TensorRep.rep g (inclusion D q hq v) := rfl - -def image : Subrepresentation (TensorRep.rep (ι := Cells D) (n := Fin q)) where - toSubmodule := LinearMap.range (inclusion D q hq).toLinearMap - apply_mem_toSubmodule := by - rintro g v ⟨x,rfl⟩ - exact ⟨(ordinary D q hq).toRepresentation g x,rfl⟩ - -lemma inclusion_image (v : Carrier D q hq) : inclusion D q hq v ∈ image D q hq := ⟨v,rfl⟩ - - -def hermitianAction (a : Matrix (Fin q) (Fin q) ℂ) (ha : a.IsHermitian) : - Carrier D q hq →ₗ[ℂ] Carrier D q hq := - (LinearEquiv.ofInjective (inclusion D q hq).toLinearMap (inclusion D q hq).injective).symm.toLinearMap.comp - ((TensorRep.action a).comp (inclusion D q hq).toLinearMap |>.codRestrict - (image D q hq).toSubmodule (fun v => TensorRep.apply_mem_hermitian _ a ha _ (inclusion_image D q hq v))) - -@[simp] lemma inclusion_hermitianAction (a : Matrix (Fin q) (Fin q) ℂ) (ha : a.IsHermitian) - (v : Carrier D q hq) : - inclusion D q hq (hermitianAction D q hq a ha v) = TensorRep.action a (inclusion D q hq v) := by - exact congrArg Subtype.val ((LinearEquiv.ofInjective (inclusion D q hq).toLinearMap - (inclusion D q hq).injective).apply_symm_apply _) - -lemma tensor_hermitian (a : Matrix (Fin q) (Fin q) ℂ) (ha : a.IsHermitian) : - (TensorRep.tensor (fun _ : Cells D => a)).IsHermitian := by - change star (TensorRep.tensor (fun _ : Cells D => a)) = _ - rw [← TensorRep.tensor_star] - congr 1 - funext i - exact ha - -lemma hermitianAction_symmetric (a : Matrix (Fin q) (Fin q) ℂ) (ha : a.IsHermitian) : - LinearMap.IsSymmetric (𝕜 := ℂ) (E := Carrier D q hq) (hermitianAction D q hq a ha) := by - intro x y - rw [← (inclusion D q hq).inner_map_map, ← (inclusion D q hq).inner_map_map x, - inclusion_hermitianAction, inclusion_hermitianAction] - exact (Matrix.isSymmetric_toEuclideanLin_iff.mpr (tensor_hermitian D q a ha)) x.val.val y.val.val - -lemma ordinary_rep_unitary (g : Matrix.unitaryGroup (Fin q) ℂ) (v w : Carrier D q hq) : - ⟪(ordinary D q hq).toRepresentation g v, (ordinary D q hq).toRepresentation g w⟫_ℂ = ⟪v,w⟫_ℂ := - TensorRep.rep_unitary g v.val.val w.val.val - -lemma raw_norm_unitary (g : Matrix.unitaryGroup (Fin q) ℂ) (v : TensorSpace D q) : - ‖TensorRep.rep g v‖ = ‖v‖ := - (TensorRep.rep g).isometryOfInner (TensorRep.rep_unitary g) |>.norm_map v - - -theorem hermitianAction_norm_bound (a : Matrix (Fin q) (Fin q) ℂ) (ha : a.PosSemidef) - (v : Carrier D q hq) : - ‖hermitianAction D q hq a ha.isHermitian v‖ ≤ - highestMonomial D q hq (SortedSpectrum.values a ha.isHermitian) * ‖v‖ := by - rw [← (inclusion D q hq).norm_map (hermitianAction D q hq a ha.isHermitian v), - inclusion_hermitianAction, ← (inclusion D q hq).norm_map v] - let u := SortedSpectrum.changeBasis a ha.isHermitian - let t := SortedSpectrum.values a ha.isHermitian - have he := SortedSpectrum.spectral_theorem a ha.isHermitian - have hin : TensorRep.rep u⁻¹ (inclusion D q hq v) ∈ alternating D q := - (alternating D q).apply_mem_toSubmodule u⁻¹ v.val.property - have hb := diagonal_norm_bound D q hq t (SortedSpectrum.values_nonneg a ha.isHermitian ha) - (SortedSpectrum.values_antitone a ha.isHermitian) _ hin - change a = (u : Matrix _ _ ℂ) * Matrix.diagonal (fun i => (t i : ℂ)) * (↑(u⁻¹) : Matrix _ _ ℂ) at he - conv_lhs => rw [he] - simp only [map_mul, Module.End.mul_apply] - change ‖TensorRep.rep u (TensorRep.action (Matrix.diagonal _) (TensorRep.rep u⁻¹ _))‖ ≤ _ - rw [raw_norm_unitary] - simpa only [raw_norm_unitary] using hb - -end SpinAngle.PolynomialCarrier - - - - -noncomputable section -open scoped TensorProduct InnerProductSpace BigOperators -namespace SpinAngle.ExternalTensor -open Module -variable {E F : Type*} [contextInstance1195_23 : NormedAddCommGroup E] [contextInstance1195_46 : InnerProductSpace ℂ E] - [contextInstance1196_2 : NormedAddCommGroup F] [contextInstance1196_25 : InnerProductSpace ℂ F] - [contextInstance1197_2 : FiniteDimensional ℂ E] [contextInstance1197_26 : FiniteDimensional ℂ F] -variable {G H : Type*} [contextInstance1198_23 : Group G] [contextInstance1198_33 : Group H] - -def rep (ρ : Representation ℂ G E) (σ : Representation ℂ H F) : - Representation ℂ (G × H) (E ⊗[ℂ] F) := - Representation.tprod (ρ.comp (MonoidHom.fst G H)) (σ.comp (MonoidHom.snd G H)) - -@[simp] lemma rep_tmul - {E : Type*} {F : Type*} - [contextInstance1195_23 : NormedAddCommGroup E] - [contextInstance1195_46 : InnerProductSpace ℂ E] - [contextInstance1196_2 : NormedAddCommGroup F] - [contextInstance1196_25 : InnerProductSpace ℂ F] - [FiniteDimensional ℂ E] - [FiniteDimensional ℂ F] - {G : Type*} {H : Type*} - [contextInstance1198_23 : Group G] - [contextInstance1198_33 : Group H] (ρ : Representation ℂ G E) (σ : Representation ℂ H F) - (g : G × H) (x : E) (y : F) : - rep ρ σ g (x ⊗ₜ[ℂ] y) = ρ g.1 x ⊗ₜ σ g.2 y := rfl - -def rightSlice (β : Module.Dual ℂ F) : E ⊗[ℂ] F →ₗ[ℂ] E := - (TensorProduct.rid ℂ E).toLinearMap.comp (TensorProduct.map LinearMap.id β) - -def leftSlice (α : Module.Dual ℂ E) : E ⊗[ℂ] F →ₗ[ℂ] F := - (TensorProduct.lid ℂ F).toLinearMap.comp (TensorProduct.map α LinearMap.id) - -@[simp] lemma rightSlice_tmul - {E : Type*} {F : Type*} - [contextInstance1195_23 : NormedAddCommGroup E] - [contextInstance1195_46 : InnerProductSpace ℂ E] - [contextInstance1196_2 : NormedAddCommGroup F] - [contextInstance1196_25 : InnerProductSpace ℂ F] - [FiniteDimensional ℂ E] - [FiniteDimensional ℂ F] (β : Module.Dual ℂ F) (x : E) (y : F) : - rightSlice β (x ⊗ₜ[ℂ] y) = β y • x := rfl -@[simp] lemma leftSlice_tmul - {E : Type*} {F : Type*} - [contextInstance1195_23 : NormedAddCommGroup E] - [contextInstance1195_46 : InnerProductSpace ℂ E] - [contextInstance1196_2 : NormedAddCommGroup F] - [contextInstance1196_25 : InnerProductSpace ℂ F] - [FiniteDimensional ℂ E] - [FiniteDimensional ℂ F] (α : Module.Dual ℂ E) (x : E) (y : F) : - leftSlice α (x ⊗ₜ[ℂ] y) = α x • y := rfl - -lemma slice_commute - {E : Type*} {F : Type*} - [contextInstance1195_23 : NormedAddCommGroup E] - [contextInstance1195_46 : InnerProductSpace ℂ E] - [contextInstance1196_2 : NormedAddCommGroup F] - [contextInstance1196_25 : InnerProductSpace ℂ F] - [FiniteDimensional ℂ E] - [FiniteDimensional ℂ F] (α : Module.Dual ℂ E) (β : Module.Dual ℂ F) (v : E ⊗[ℂ] F) : - α (rightSlice β v) = β (leftSlice α v) := by - induction v using TensorProduct.inductionOn with - | tmul x y => simp [mul_comm] - | add x y hx hy => simp [hx, hy] - -lemma slice_map_left - {E : Type*} {F : Type*} - [contextInstance1195_23 : NormedAddCommGroup E] - [contextInstance1195_46 : InnerProductSpace ℂ E] - [contextInstance1196_2 : NormedAddCommGroup F] - [contextInstance1196_25 : InnerProductSpace ℂ F] - [FiniteDimensional ℂ E] - [FiniteDimensional ℂ F] (β : Module.Dual ℂ F) (A : E →ₗ[ℂ] E) (v : E ⊗[ℂ] F) : - rightSlice β (TensorProduct.map A LinearMap.id v) = A (rightSlice β v) := by - induction v using TensorProduct.inductionOn with - | tmul x y => simp - | add x y hx hy => simp [hx, hy] - -lemma eq_sum_slices - {E : Type*} {F : Type*} - [contextInstance1195_23 : NormedAddCommGroup E] - [contextInstance1195_46 : InnerProductSpace ℂ E] - [contextInstance1196_2 : NormedAddCommGroup F] - [contextInstance1196_25 : InnerProductSpace ℂ F] - [FiniteDimensional ℂ E] - [FiniteDimensional ℂ F] {ι : Type*} [Fintype ι] (b : Basis ι ℂ F) (v : E ⊗[ℂ] F) : - v = ∑ i, rightSlice (b.coord i) v ⊗ₜ[ℂ] b i := by - induction v using TensorProduct.inductionOn with - | tmul x y => - simp only [rightSlice_tmul, TensorProduct.smul_tmul, - ← TensorProduct.tmul_sum, Basis.coord_apply, Basis.sum_repr] - | add x y hx hy => simp only [map_add, TensorProduct.add_tmul, Finset.sum_add_distrib, ← hx, ← hy] - -lemma rightSlice_ext {v w : E ⊗[ℂ] F} - (h : ∀ β : Module.Dual ℂ F, rightSlice β v = rightSlice β w) : v = w := by - classical - let b := Module.finBasis ℂ F - rw [eq_sum_slices b v, eq_sum_slices b w] - exact Finset.sum_congr rfl fun i _ => congrArg (fun x : E => x ⊗ₜ[ℂ] b i) (h _) - -lemma scalar_of_commute (ρ : Representation ℂ G E) [ρ.IsIrreducible] - (A : E →ₗ[ℂ] E) (hA : ∀ g x, A (ρ g x) = ρ g (A x)) : - ∃ z : ℂ, A = z • LinearMap.id := by - let f := A.intertwiningMap_of_isIntertwiningMap ρ ρ hA - obtain ⟨z, hz⟩ := - (Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed (ρ := ρ)).surjective f - refine ⟨z, ?_⟩ - ext x - exact (congrArg (fun L : ρ.IntertwiningMap ρ => L x) hz).symm - - -lemma left_commutant (ρ : Representation ℂ G E) [ρ.IsIrreducible] - (d : E ⊗[ℂ] F →ₗ[ℂ] E ⊗[ℂ] F) - (hd : ∀ g v, d (TensorProduct.map (ρ g) LinearMap.id v) = - TensorProduct.map (ρ g) LinearMap.id (d v)) : - ∃ B : F →ₗ[ℂ] F, d = TensorProduct.map LinearMap.id B := by - classical - let : Nontrivial E := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) ρ.asModule - obtain ⟨x₀, hx₀⟩ := exists_ne (0 : E) - obtain ⟨α, hα⟩ := Module.Projective.exists_dual_eq_one ℂ hx₀ - let B : F →ₗ[ℂ] F := (leftSlice α).comp (d.comp (TensorProduct.mk ℂ E F x₀)) - refine ⟨B, ?_⟩ - ext x y - change d (x ⊗ₜ[ℂ] y) = TensorProduct.map LinearMap.id B (x ⊗ₜ[ℂ] y) - apply rightSlice_ext - intro β - let A : E →ₗ[ℂ] E := (rightSlice β).comp (d.comp ((TensorProduct.mk ℂ E F).flip y)) - have hA (g : G) (v : E) : A (ρ g v) = ρ g (A v) := by - change rightSlice β (d (ρ g v ⊗ₜ[ℂ] y)) = ρ g (rightSlice β (d (v ⊗ₜ[ℂ] y))) - rw [← slice_map_left, ← hd] - rfl - obtain ⟨z,hz⟩ := scalar_of_commute ρ A hA - have hzv (v : E) : rightSlice β (d (v ⊗ₜ[ℂ] y)) = z • v := - congrArg (fun f : E →ₗ[ℂ] E => f v) hz - have hzB : β (B y) = z := by - change β (leftSlice α (d (x₀ ⊗ₜ[ℂ] y))) = z - rw [← slice_commute, hzv, map_smul, hα, smul_eq_mul, mul_one] - change rightSlice β (d (x ⊗ₜ[ℂ] y)) = β (B y) • x - rw [hzv, hzB] - -lemma commutant_scalar (ρ : Representation ℂ G E) (σ : Representation ℂ H F) - [ρ.IsIrreducible] [σ.IsIrreducible] - (d : (rep ρ σ).IntertwiningMap (rep ρ σ)) : - ∃ z : ℂ, d.toLinearMap = z • LinearMap.id := by - obtain ⟨B,hB⟩ := left_commutant ρ d.toLinearMap (by - intro g v - simpa [rep, Representation.tprod_apply, Module.End.one_eq_id] using Representation.IntertwiningMap.isIntertwining _ _ d (g,1) v) - have hσ (h : H) (y : F) : B (σ h y) = σ h (B y) := by - let : Nontrivial E := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) ρ.asModule - obtain ⟨x,hx⟩ := exists_ne (0 : E) - obtain ⟨α,hα⟩ := Module.Projective.exists_dual_eq_one ℂ hx - have hh := Representation.IntertwiningMap.isIntertwining _ _ d (1,h) (x ⊗ₜ[ℂ] y) - change d.toLinearMap (rep ρ σ (1,h) (x ⊗ₜ y)) = - rep ρ σ (1,h) (d.toLinearMap (x ⊗ₜ y)) at hh - rw [hB] at hh - simp only [rep_tmul, map_one, Module.End.one_apply, TensorProduct.map_tmul, - LinearMap.id_apply] at hh - have := congrArg (leftSlice α) hh - simpa [hα] using this - obtain ⟨z,hz⟩ := scalar_of_commute σ B hσ - refine ⟨z, ?_⟩ - rw [hB, hz] - ext x y - simp - -lemma unitary - {E : Type*} {F : Type*} - [contextInstance1195_23 : NormedAddCommGroup E] - [contextInstance1195_46 : InnerProductSpace ℂ E] - [contextInstance1196_2 : NormedAddCommGroup F] - [contextInstance1196_25 : InnerProductSpace ℂ F] - [FiniteDimensional ℂ E] - [FiniteDimensional ℂ F] - {G : Type*} {H : Type*} - [contextInstance1198_23 : Group G] - [contextInstance1198_33 : Group H] (ρ : Representation ℂ G E) (σ : Representation ℂ H F) - (hρ : ∀ g x y, ⟪ρ g x, ρ g y⟫_ℂ = ⟪x,y⟫_ℂ) - (hσ : ∀ h x y, ⟪σ h x, σ h y⟫_ℂ = ⟪x,y⟫_ℂ) - (g : G × H) (v w : E ⊗[ℂ] F) : - ⟪rep ρ σ g v, rep ρ σ g w⟫_ℂ = ⟪v,w⟫_ℂ := by - let a : E →ₗᵢ[ℂ] E := (ρ g.1).isometryOfInner (hρ g.1) - let b : F →ₗᵢ[ℂ] F := (σ g.2).isometryOfInner (hσ g.2) - exact TensorProduct.inner_map_map a b v w - -lemma projection_commute (τ : Representation ℂ G E) - (hτ : ∀ g x y, ⟪τ g x, τ g y⟫_ℂ = ⟪x,y⟫_ℂ) - (U : Subrepresentation τ) (g : G) (v : E) : - U.toSubmodule.starProjection (τ g v) = τ g (U.toSubmodule.starProjection v) := by - apply U.toSubmodule.eq_starProjection_of_mem_of_inner_eq_zero - · exact U.apply_mem_toSubmodule g (U.toSubmodule.starProjection_apply_mem v) - · intro w hw - have hw' := U.apply_mem_toSubmodule g⁻¹ hw - have he : τ g (τ g⁻¹ w) = w := by - rw [← Module.End.mul_apply, ← map_mul, mul_inv_cancel, map_one, Module.End.one_apply] - rw [← map_sub] - conv_lhs => rhs; rw [← he] - rw [hτ] - exact U.toSubmodule.starProjection_inner_eq_zero v _ hw' - - - -theorem irreducible (ρ : Representation ℂ G E) (σ : Representation ℂ H F) - [ρ.IsIrreducible] [σ.IsIrreducible] - (hρ : ∀ g x y, ⟪ρ g x, ρ g y⟫_ℂ = ⟪x,y⟫_ℂ) - (hσ : ∀ h x y, ⟪σ h x, σ h y⟫_ℂ = ⟪x,y⟫_ℂ) : - (rep ρ σ).IsIrreducible := by - let : Nontrivial E := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) ρ.asModule - let : Nontrivial F := IsSimpleModule.nontrivial (MonoidAlgebra ℂ H) σ.asModule - obtain ⟨x,hx⟩ := exists_ne (0 : E) - obtain ⟨y,hy⟩ := exists_ne (0 : F) - have hxy : x ⊗ₜ[ℂ] y ≠ 0 := by - intro h - have := congrArg norm h - simp only [TensorProduct.norm_tmul, norm_zero] at this - exact (mul_ne_zero (norm_ne_zero_iff.mpr hx) (norm_ne_zero_iff.mpr hy)) this - have htb : (⊤ : Subrepresentation (rep ρ σ)) ≠ ⊥ := by - intro h - have hh : x ⊗ₜ[ℂ] y ∈ (⊤ : Subrepresentation (rep ρ σ)) := by trivial - rw [h] at hh - exact hxy hh - let : Nontrivial (Subrepresentation (rep ρ σ)) := ⟨⟨⊤,⊥,htb⟩⟩ - refine ⟨fun U => ?_⟩ - let d : (rep ρ σ).IntertwiningMap (rep ρ σ) := - U.toSubmodule.starProjection.toLinearMap.intertwiningMap_of_isIntertwiningMap _ _ - (projection_commute _ (unitary ρ σ hρ hσ) U) - obtain ⟨z,hz⟩ := commutant_scalar ρ σ d - have hproj (v : E ⊗[ℂ] F) : U.toSubmodule.starProjection v = z • v := - congrArg (fun f : E ⊗[ℂ] F →ₗ[ℂ] E ⊗[ℂ] F => f v) hz - by_cases hz0 : z = 0 - · left - apply bot_unique - intro v hv - change v = 0 - have hh := hproj v - rw [U.toSubmodule.starProjection_eq_self_iff.mpr hv, hz0, zero_smul] at hh - exact hh - · right - apply top_unique - intro v _ - have hv := U.toSubmodule.starProjection_apply_mem (z⁻¹ • v) - rw [hproj, smul_smul, mul_inv_cancel₀ hz0, one_smul] at hv - exact hv - -end SpinAngle.ExternalTensor - - - - - - -noncomputable section -open scoped BigOperators ComplexConjugate -namespace SpinAngle.TorusNaturality -open Module -variable {n X Y E F : Type*} [contextInstance1400_29 : Fintype n] [contextInstance1400_41 : Fintype X] [contextInstance1400_53 : Fintype Y] - [contextInstance1401_2 : AddCommGroup E] [contextInstance1401_19 : Module ℂ E] [contextInstance1401_32 : AddCommGroup F] [contextInstance1401_49 : Module ℂ F] -variable (b : Basis X ℂ E) (c : Basis Y ℂ F) - (w : X → n → ℕ) (v : Y → n → ℕ) - (D : (n → ℂ) → E →ₗ[ℂ] E) (D' : (n → ℂ) → F →ₗ[ℂ] F) - (hb : ∀ a x, D a (b x) = (∏ j, a j ^ w x j) • b x) - (hc : ∀ a y, D' a (c y) = (∏ j, a j ^ v y j) • c y) - -include hc in -lemma repr_diagonal (a : n → ℂ) (f : F) (y : Y) : - c.repr (D' a f) y = (∏ j, a j ^ v y j) * c.repr f y := by - classical - calc - c.repr (D' a f) y = c.repr (D' a (∑ k, c.repr f k • c k)) y := by rw [c.sum_repr] - _ = _ := by - simp only [map_sum, map_smul, hc, - Basis.repr_self] - simp [Finset.sum_apply, Finsupp.single_apply, mul_comm] - -lemma coefficient_zero - {n : Type*} {X : Type*} {Y : Type*} {E : Type*} {F : Type*} - [contextInstance1400_29 : Fintype n] - [Fintype X] - [contextInstance1400_53 : Fintype Y] - [contextInstance1401_2 : AddCommGroup E] - [contextInstance1401_19 : Module ℂ E] - [contextInstance1401_32 : AddCommGroup F] - [contextInstance1401_49 : Module ℂ F] - (b : Basis X ℂ E) (c : Basis Y ℂ F) - (w : X → n → ℕ) (v : Y → n → ℕ) - (D : (n → ℂ) → E →ₗ[ℂ] E) (D' : (n → ℂ) → F →ₗ[ℂ] F) - (hb : ∀ a x, D a (b x) = (∏ j, a j ^ w x j) • b x) - (hc : ∀ a y, D' a (c y) = (∏ j, a j ^ v y j) • c y) (L : E →ₗ[ℂ] F) - (hL : ∀ a : n → ℂ, (∀ j, star (a j) * a j = 1) → ∀ x, L (D a x) = D' a (L x)) - (x : X) (y : Y) (j : n) (hxy : w x j ≠ v y j) : - c.repr (L (b x)) y = 0 := by - classical - let N := w x j + v y j + 1 - let z : ℂ := Complex.exp (2 * Real.pi * Complex.I / N) - have hN : N ≠ 0 := by dsimp [N]; omega - have hz : IsPrimitiveRoot z N := Complex.isPrimitiveRoot_exp _ hN - have hzn : ‖z‖ = 1 := Complex.norm_eq_one_of_pow_eq_one hz.pow_eq_one hN - have hzu : star z * z = 1 := by - rw [mul_comm, Complex.star_def, Complex.mul_conj, Complex.normSq_eq_norm_sq, hzn] - norm_num - let a : n → ℂ := fun k => if k = j then z else 1 - have ha : ∀ k, star (a k) * a k = 1 := by - intro k - dsimp [a] - split_ifs - · exact hzu - · simp - have hh := congrArg (fun f => c.repr f y) (hL a ha (b x)) - rw [hb, map_smul, map_smul, Finsupp.smul_apply, smul_eq_mul, - repr_diagonal c v D' hc] at hh - have hprod (u : n → ℕ) : (∏ k, a k ^ u k) = z ^ u j := by - simp [a] - rw [hprod, hprod] at hh - by_contra hn - exact hxy (hz.pow_inj (by dsimp [N]; omega) (by dsimp [N]; omega) - (mul_right_cancel₀ hn hh)) - -include b c w v hb hc in - - -theorem diagonal (L : E →ₗ[ℂ] F) - (hL : ∀ a : n → ℂ, (∀ j, star (a j) * a j = 1) → ∀ x, L (D a x) = D' a (L x)) - (a : n → ℂ) : L.comp (D a) = (D' a).comp L := by - classical - apply b.ext - intro x - apply c.repr.injective - ext y - simp only [LinearMap.comp_apply, hb, map_smul, Finsupp.smul_apply, smul_eq_mul, - repr_diagonal c v D' hc] - by_cases hw : w x = v y - · rw [hw] - · obtain ⟨j,hj⟩ := Function.ne_iff.mp hw - rw [coefficient_zero b c w v D D' hb hc L hL x y j hj] - simp - -end SpinAngle.TorusNaturality - - -namespace SpinAngle.SignedTensor -open scoped Classical Matrix TensorProduct InnerProductSpace -open Module -variable {q : ℕ} -abbrev Spin (q : ℕ) := Fin q × Bool -abbrev Mat (q : ℕ) := Matrix (Fin q) (Fin q) ℂ -abbrev Group (q : ℕ) := Matrix.unitaryGroup (Fin q) ℂ × Matrix.unitaryGroup (Fin q) ℂ - -def block : (Mat q × Mat q) →* Matrix (Spin q) (Spin q) ℂ where - toFun a := Matrix.blockDiagonal (fun b : Bool => cond b a.2 a.1) - map_one' := by - convert (Matrix.blockDiagonal_one (m := Fin q) (o := Bool) (α := ℂ)) using 1 - congr 1 - funext b - cases b <;> rfl - map_mul' a b := by - rw [← Matrix.blockDiagonal_mul] - congr 1 - funext c - cases c <;> rfl - -lemma block_star (a : Mat q × Mat q) : block (star a) = star (block a) := by - change Matrix.blockDiagonal (fun b : Bool => cond b (star a.2) (star a.1)) = (Matrix.blockDiagonal (fun b : Bool => cond b a.2 a.1))ᴴ - rw [Matrix.blockDiagonal_conjTranspose] - congr 1 - funext b - cases b <;> rfl - -def blockGroup : Group q →* Matrix.unitaryGroup (Spin q) ℂ where - toFun g := ⟨block (g.1.val,g.2.val), by - rw [Matrix.mem_unitaryGroup_iff', ← block_star, ← map_mul] - have he : star (g.1.val,g.2.val) * (g.1.val,g.2.val) = 1 := - Prod.ext g.1.property.1 g.2.property.1 - rw [he, map_one]⟩ - map_one' := by - apply Subtype.ext - change block (1 : Mat q × Mat q) = 1 - exact block.map_one - map_mul' g h := by - apply Subtype.ext - change block ((g.1.val,g.2.val) * (h.1.val,h.2.val)) = - block (g.1.val,g.2.val) * block (h.1.val,h.2.val) - exact block.map_mul _ _ - -variable {ι κ τ : Type*} [contextInstance1517_25 : Fintype ι] [contextInstance1517_37 : DecidableEq ι] [contextInstance1517_53 : Fintype κ] [contextInstance1517_65 : DecidableEq κ] - [contextInstance1518_2 : Fintype τ] [contextInstance1518_14 : DecidableEq τ] - -abbrev Raw := EuclideanSpace ℂ (τ → Spin q) -abbrev PairRaw := EuclideanSpace ℂ (ι → Fin q) ⊗[ℂ] EuclideanSpace ℂ (κ → Fin q) - -def rep : Representation ℂ (Group q) (Raw (q := q) (τ := τ)) := - (TensorRep.rep (ι := τ)).comp blockGroup - -def pairRep : Representation ℂ (Group q) (PairRaw (q := q) (ι := ι) (κ := κ)) := - ExternalTensor.rep TensorRep.rep TensorRep.rep - -def pairAction : (Mat q × Mat q) →* Module.End ℂ (PairRaw (q := q) (ι := ι) (κ := κ)) where - toFun a := TensorProduct.map (TensorRep.action a.1) (TensorRep.action a.2) - map_one' := by - ext x y - change TensorProduct.map _ _ (x ⊗ₜ[ℂ] y) = x ⊗ₜ[ℂ] y - simp only [Prod.fst_one, Prod.snd_one, map_one, TensorProduct.map_tmul, - Module.End.one_apply] - map_mul' a b := by - ext x y - change TensorProduct.map _ _ (x ⊗ₜ[ℂ] y) = - TensorProduct.map _ _ (TensorProduct.map _ _ (x ⊗ₜ[ℂ] y)) - simp only [Prod.fst_mul, Prod.snd_mul, map_mul, TensorProduct.map_tmul, - Module.End.mul_apply] - -@[simp] lemma pairAction_tmul (a : Mat q × Mat q) - (x : EuclideanSpace ℂ (ι → Fin q)) (y : EuclideanSpace ℂ (κ → Fin q)) : - pairAction a (x ⊗ₜ[ℂ] y) = TensorRep.action a.1 x ⊗ₜ TensorRep.action a.2 y := rfl - -lemma pairRep_eq (g : Group q) : pairRep (ι := ι) (κ := κ) g = pairAction (g.1.val,g.2.val) := rfl - -lemma rep_unitary (g : Group q) (v w : Raw (q := q) (τ := τ)) : - ⟪rep g v,rep g w⟫_ℂ = ⟪v,w⟫_ℂ := TensorRep.rep_unitary (blockGroup g) v w - -lemma pairRep_unitary (g : Group q) (v w : PairRaw (q := q) (ι := ι) (κ := κ)) : - ⟪pairRep g v,pairRep g w⟫_ℂ = ⟪v,w⟫_ℂ := - ExternalTensor.unitary (TensorRep.rep (ι := ι) (n := Fin q)) (TensorRep.rep (ι := κ) (n := Fin q)) - TensorRep.rep_unitary TensorRep.rep_unitary g v w - -def pairBasis : OrthonormalBasis ((ι → Fin q) × (κ → Fin q)) ℂ (PairRaw (q := q) (ι := ι) (κ := κ)) := - (EuclideanSpace.basisFun _ ℂ).tensorProduct (EuclideanSpace.basisFun _ ℂ) - -def pairContent (x : (ι → Fin q) × (κ → Fin q)) (j : Spin q) : ℕ := - cond j.2 (TensorRep.content x.2 j.1) (TensorRep.content x.1 j.1) - -def diagPair (a : Spin q → ℂ) : Mat q × Mat q := - (Matrix.diagonal (fun j => a (j,false)), Matrix.diagonal (fun j => a (j,true))) - -lemma block_diagPair (a : Spin q → ℂ) : block (diagPair a) = Matrix.diagonal a := by - change Matrix.blockDiagonal (fun b : Bool => cond b (Matrix.diagonal (fun j => a (j,true))) (Matrix.diagonal (fun j => a (j,false)))) = Matrix.diagonal a - convert Matrix.blockDiagonal_diagonal (fun (b : Bool) (j : Fin q) => a (j,b)) using 1 - congr 1 - funext b - cases b <;> rfl - -lemma pairBasis_diagonal (a : Spin q → ℂ) (x : (ι → Fin q) × (κ → Fin q)) : - pairAction (diagPair a) (pairBasis x) = - (∏ j, a j ^ pairContent x j) • pairBasis x := by - simp only [pairBasis, OrthonormalBasis.tensorProduct_apply', EuclideanSpace.basisFun_apply, - pairAction_tmul, diagPair, TensorRep.diagonal_single, TensorProduct.smul_tmul, - TensorProduct.tmul_smul, smul_smul] - congr 1 - rw [Fintype.prod_prod_type] - simp only [pairContent, Fintype.prod_bool, Bool.cond_false, Bool.cond_true] - rw [Finset.prod_mul_distrib, TensorRep.product_content (fun j : Fin q => a (j,true)) x.2, - TensorRep.product_content (fun j : Fin q => a (j,false)) x.1] - - - -theorem intertwiner_diagonal - (L : PairRaw (q := q) (ι := ι) (κ := κ) →ₗ[ℂ] Raw (q := q) (τ := τ)) - (hL : ∀ g : Group q, ∀ v, L (pairRep g v) = rep g (L v)) - (a : Spin q → ℂ) (v : PairRaw (q := q) (ι := ι) (κ := κ)) : - L (pairAction (diagPair a) v) = TensorRep.action (Matrix.diagonal a) (L v) := by - have hh := TorusNaturality.diagonal (pairBasis (q := q) (ι := ι) (κ := κ)).toBasis - (EuclideanSpace.basisFun (τ → Spin q) ℂ).toBasis pairContent TensorRep.content - (fun a => pairAction (diagPair a)) (fun a => TensorRep.action (Matrix.diagonal a)) - pairBasis_diagonal (fun a x => by - simpa only [OrthonormalBasis.coe_toBasis, EuclideanSpace.basisFun_apply, TensorRep.product_content] using - (TensorRep.diagonal_single a x)) L (fun a ha v => by - let g : Group q := - (⟨(diagPair a).1, TensorRep.diagonal_unitary_of_star_mul _ (fun j => ha (j,false))⟩, - ⟨(diagPair a).2, TensorRep.diagonal_unitary_of_star_mul _ (fun j => ha (j,true))⟩) - have hh := hL g v - change L (pairAction (diagPair a) v) = TensorRep.action (block (diagPair a)) (L v) at hh - rwa [block_diagPair] at hh) a - exact congrArg (fun f : _ →ₗ[ℂ] _ => f v) hh - -lemma pair_spectral (a : Mat q × Mat q) (ha : a.1.IsHermitian) (hb : a.2.IsHermitian) : - ∃ (g : Group q) (d : Spin q → ℂ), - a = (g.1.val,g.2.val) * diagPair d * (g.1⁻¹.val,g.2⁻¹.val) := by - refine ⟨(ha.eigenvectorUnitary,hb.eigenvectorUnitary), - (fun j => cond j.2 (hb.eigenvalues j.1 : ℂ) (ha.eigenvalues j.1 : ℂ)), ?_⟩ - apply Prod.ext - · exact ha.spectral_theorem - · exact hb.spectral_theorem - - - -theorem intertwiner_hermitian - (L : PairRaw (q := q) (ι := ι) (κ := κ) →ₗ[ℂ] Raw (q := q) (τ := τ)) - (hL : ∀ g : Group q, ∀ v, L (pairRep g v) = rep g (L v)) - (a : Mat q × Mat q) (ha : a.1.IsHermitian) (hb : a.2.IsHermitian) - (v : PairRaw (q := q) (ι := ι) (κ := κ)) : - L (pairAction a v) = TensorRep.action (block a) (L v) := by - obtain ⟨g,d,he⟩ := pair_spectral a ha hb - rw [he] - simp only [map_mul, Module.End.mul_apply, block_diagPair] - change L (pairRep g (pairAction (diagPair d) (pairRep g⁻¹ v))) = - rep g (TensorRep.action (Matrix.diagonal d) (rep g⁻¹ (L v))) - rw [hL, intertwiner_diagonal L hL, hL] - -end SpinAngle.SignedTensor - - - - - - -noncomputable section -open scoped InnerProductSpace -namespace SpinAngle.UnitaryNaturality -variable {G : Type*} [contextInstance1640_21 : Group G] -variable {E F : Type*} [contextInstance1641_23 : NormedAddCommGroup E] [contextInstance1641_46 : InnerProductSpace ℂ E] - [contextInstance1642_2 : NormedAddCommGroup F] [contextInstance1642_25 : InnerProductSpace ℂ F] - [contextInstance1643_2 : FiniteDimensional ℂ E] [contextInstance1643_26 : FiniteDimensional ℂ F] -variable (ρ : Representation ℂ G E) (σ : Representation ℂ G F) - (hρ : ∀ g x y, ⟪ρ g x,ρ g y⟫_ℂ = ⟪x,y⟫_ℂ) - (hσ : ∀ g x y, ⟪σ g x,σ g y⟫_ℂ = ⟪x,y⟫_ℂ) - -lemma inner_move - {G : Type*} - [contextInstance1640_21 : Group G] - {E : Type*} - [contextInstance1641_23 : NormedAddCommGroup E] - [contextInstance1641_46 : InnerProductSpace ℂ E] - [FiniteDimensional ℂ E] - (ρ : Representation ℂ G E) - (hρ : ∀ g x y, ⟪ρ g x,ρ g y⟫_ℂ = ⟪x,y⟫_ℂ) (g : G) (x y : E) : ⟪x,ρ g y⟫_ℂ = ⟪ρ g⁻¹ x,y⟫_ℂ := by - have h := hρ g (ρ g⁻¹ x) y - simpa only [← Module.End.mul_apply, ← map_mul, mul_inv_cancel, map_one, - Module.End.one_apply] using h - -include hρ hσ in -lemma adjoint_intertwines (L : E →ₗ[ℂ] F) - (hL : ∀ g x, L (ρ g x) = σ g (L x)) (g : G) (y : F) : - LinearMap.adjoint L (σ g y) = ρ g (LinearMap.adjoint L y) := by - apply ext_inner_left ℂ - intro x - rw [LinearMap.adjoint_inner_right, inner_move σ hσ, ← hL, - ← LinearMap.adjoint_inner_right, ← inner_move ρ hρ] - -lemma adjoint_isometry (L : E →ₗᵢ[ℂ] F) (x : E) : - LinearMap.adjoint L.toLinearMap (L x) = x := by - apply ext_inner_left ℂ - intro y - rw [LinearMap.adjoint_inner_right] - exact L.inner_map_map y x - -end SpinAngle.UnitaryNaturality - -namespace SpinAngle.SignedCarrier -open scoped Classical TensorProduct InnerProductSpace -open SpinAngle.Young SpinAngle.Specht PolynomialCarrier Module SignedTensor -variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) - -abbrev Carrier := PolynomialCarrier.Carrier a q ha ⊗[ℂ] PolynomialCarrier.Carrier b q hb - -instance carrierNormed : NormedAddCommGroup (Carrier a b q ha hb) := - TensorProduct.instNormedAddCommGroup (𝕜 := ℂ) - (E := PolynomialCarrier.Carrier a q ha) (F := PolynomialCarrier.Carrier b q hb) - -instance carrierInner : InnerProductSpace ℂ (Carrier a b q ha hb) := - TensorProduct.instInnerProductSpace (𝕜 := ℂ) - (E := PolynomialCarrier.Carrier a q ha) (F := PolynomialCarrier.Carrier b q hb) - -instance carrierFinite : FiniteDimensional ℂ (Carrier a b q ha hb) := - inferInstanceAs (FiniteDimensional ℂ (PolynomialCarrier.Carrier a q ha ⊗[ℂ] PolynomialCarrier.Carrier b q hb)) - -abbrev rep : Representation ℂ (Group q) (Carrier a b q ha hb) := - ExternalTensor.rep (E := PolynomialCarrier.Carrier a q ha) - (F := PolynomialCarrier.Carrier b q hb) - (ordinary a q ha).toRepresentation (ordinary b q hb).toRepresentation - -instance irreducible : (rep a b q ha hb).IsIrreducible := by - let := ordinary_irreducible a q ha - let := ordinary_irreducible b q hb - exact ExternalTensor.irreducible _ _ (ordinary_rep_unitary a q ha) (ordinary_rep_unitary b q hb) - -def inclusion : Carrier a b q ha hb →ₗᵢ[ℂ] - PairRaw (q := q) (ι := Cells a) (κ := Cells b) := - TensorProduct.mapIsometry (E := PolynomialCarrier.Carrier a q ha) (F := PolynomialCarrier.Carrier b q hb) - (PolynomialCarrier.inclusion a q ha) (PolynomialCarrier.inclusion b q hb) - -lemma inclusion_equivariant (g : Group q) (v : Carrier a b q ha hb) : - inclusion a b q ha hb (rep a b q ha hb g v) = - pairRep g (inclusion a b q ha hb v) := by - induction v using TensorProduct.inductionOn with - | tmul x y => rfl - | add x y hx hy => simp [hx,hy] - -lemma rep_unitary (g : Group q) (v w : Carrier a b q ha hb) : - ⟪rep a b q ha hb g v,rep a b q ha hb g w⟫_ℂ = ⟪v,w⟫_ℂ := by - rw [← (inclusion a b q ha hb).inner_map_map, - ← (inclusion a b q ha hb).inner_map_map v w, - inclusion_equivariant, inclusion_equivariant] - exact SignedTensor.pairRep_unitary g _ _ - -def hermitianAction (A : Mat q × Mat q) (hA : A.1.IsHermitian) (hB : A.2.IsHermitian) : - Carrier a b q ha hb →ₗ[ℂ] Carrier a b q ha hb := - TensorProduct.map (PolynomialCarrier.hermitianAction a q ha A.1 hA) - (PolynomialCarrier.hermitianAction b q hb A.2 hB) - -lemma inclusion_hermitianAction (A : Mat q × Mat q) (hA : A.1.IsHermitian) (hB : A.2.IsHermitian) - (v : Carrier a b q ha hb) : - inclusion a b q ha hb (hermitianAction a b q ha hb A hA hB v) = - pairAction A (inclusion a b q ha hb v) := by - induction v using TensorProduct.inductionOn with - | tmul x y => - simp only [inclusion, hermitianAction, TensorProduct.mapIsometry_apply, - TensorProduct.map_tmul, pairAction_tmul] - change PolynomialCarrier.inclusion a q ha (PolynomialCarrier.hermitianAction a q ha A.1 hA x) ⊗ₜ[ℂ] - PolynomialCarrier.inclusion b q hb (PolynomialCarrier.hermitianAction b q hb A.2 hB y) = _ - rw [PolynomialCarrier.inclusion_hermitianAction, PolynomialCarrier.inclusion_hermitianAction] - rfl - | add x y hx hy => simp [hx,hy] - -variable {τ : Type*} [contextInstance1741_21 : Fintype τ] [contextInstance1741_33 : DecidableEq τ] - - - -theorem intertwiner_hermitian - (L : (rep a b q ha hb).IntertwiningMap (SignedTensor.rep (q := q) (τ := τ))) - (A : Mat q × Mat q) (hA : A.1.IsHermitian) (hB : A.2.IsHermitian) - (v : Carrier a b q ha hb) : - L (hermitianAction a b q ha hb A hA hB v) = TensorRep.action (block A) (L v) := by - let J := inclusion a b q ha hb - let L' := L.toLinearMap.comp (LinearMap.adjoint J.toLinearMap) - have hequiv (g : Group q) (x : PairRaw (q := q) (ι := Cells a) (κ := Cells b)) : - L' (pairRep g x) = SignedTensor.rep g (L' x) := by - dsimp [L'] - rw [UnitaryNaturality.adjoint_intertwines (rep a b q ha hb) pairRep - (rep_unitary a b q ha hb) SignedTensor.pairRep_unitary J.toLinearMap - (inclusion_equivariant a b q ha hb), L.isIntertwining] - have h := SignedTensor.intertwiner_hermitian L' hequiv A hA hB (J v) - have hj (x : Carrier a b q ha hb) : L' (J x) = L x := by - dsimp [L'] - rw [UnitaryNaturality.adjoint_isometry] - rw [← inclusion_hermitianAction a b q ha hb A hA hB v, hj, hj] at h - exact h - -end SpinAngle.SignedCarrier - - - -namespace SpinAngle.TensorRep -variable {ι n : Type*} [contextInstance1770_23 : Fintype ι] [contextInstance1770_35 : DecidableEq ι] [contextInstance1770_51 : Fintype n] [contextInstance1770_63 : DecidableEq n] - -lemma continuous_action (v : EuclideanSpace ℂ (ι → n)) : - Continuous (fun A : Matrix n n ℂ => action A v) := by - change Continuous (fun A : Matrix n n ℂ => - WithLp.toLp 2 (fun x : ι → n => ∑ y, (∏ i, A (x i) (y i)) * v y)) - apply (PiLp.continuous_toLp 2 (fun _ : ι → n => ℂ)).comp - fun_prop - -lemma continuous_rep : Continuous (fun g : Matrix.unitaryGroup n ℂ => - (rep (ι := ι) g).toContinuousLinearMap) := by - apply continuous_clm_apply.mpr - intro v - exact (continuous_action v).comp continuous_subtype_val -end SpinAngle.TensorRep - -namespace SpinAngle.PolynomialCarrier -open SpinAngle.Young SpinAngle.Specht -variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) -lemma continuous_rep : Continuous (fun g : Matrix.unitaryGroup (Fin q) ℂ => - ((ordinary D q hq).toRepresentation g).toContinuousLinearMap) := by - let : InnerProductSpace ℂ (ordinary D q hq).toSubmodule := carrierInner D q hq - apply (continuous_clm_apply (𝕜 := ℂ) (E := Carrier D q hq) (F := Carrier D q hq)).mpr - intro v - apply (inclusion D q hq).comp_continuous_iff.mp - change Continuous (fun g : Matrix.unitaryGroup (Fin q) ℂ => - TensorRep.rep g (inclusion D q hq v)) - exact continuous_clm_apply.mp (TensorRep.continuous_rep (ι := Cells D) (n := Fin q)) _ -end SpinAngle.PolynomialCarrier - -namespace SpinAngle.ExternalTensor -open scoped TensorProduct -variable {G H : Type*} [contextInstance1802_23 : Group G] [contextInstance1802_33 : Group H] [contextInstance1802_43 : TopologicalSpace G] [contextInstance1802_64 : TopologicalSpace H] -variable {E F : Type*} [contextInstance1803_23 : NormedAddCommGroup E] [contextInstance1803_46 : InnerProductSpace ℂ E] - [contextInstance1804_2 : NormedAddCommGroup F] [contextInstance1804_25 : InnerProductSpace ℂ F] - [contextInstance1805_2 : FiniteDimensional ℂ E] [contextInstance1805_26 : FiniteDimensional ℂ F] -lemma continuous_rep (ρ : Representation ℂ G E) (σ : Representation ℂ H F) - (hρ : Continuous (fun g => (ρ g).toContinuousLinearMap)) - (hσ : Continuous (fun h => (σ h).toContinuousLinearMap)) : - Continuous (fun g : G × H => (rep ρ σ g).toContinuousLinearMap) := by - apply continuous_clm_apply.mpr - intro v - induction v using TensorProduct.inductionOn with - | tmul x y => - change Continuous (fun g : G × H => ρ g.1 x ⊗ₜ[ℂ] σ g.2 y) - exact TensorProduct.continuous_tmul.comp - (((continuous_clm_apply.mp hρ x).comp continuous_fst).prodMk - ((continuous_clm_apply.mp hσ y).comp continuous_snd)) - | add x y hx hy => - have hh : Continuous (fun g : G × H => (rep ρ σ g).toContinuousLinearMap x + - (rep ρ σ g).toContinuousLinearMap y) := hx.add hy - convert hh using 1 - funext g - exact map_add _ x y -end SpinAngle.ExternalTensor - -namespace SpinAngle.SignedTensor -variable {q : ℕ} {τ : Type*} [contextInstance1828_29 : Fintype τ] [contextInstance1828_41 : DecidableEq τ] -lemma continuous_block : Continuous (block (q := q)) := by - apply continuous_pi - intro i - apply continuous_pi - intro j - change Continuous (fun A : Mat q × Mat q => if i.2 = j.2 then (cond i.2 A.2 A.1) i.1 j.1 else 0) - split_ifs - · cases i.2 <;> simp only [Bool.cond_false, Bool.cond_true] <;> fun_prop - · fun_prop - -lemma continuous_blockGroup : Continuous (blockGroup (q := q)) := by - apply Continuous.subtype_mk - exact continuous_block.comp ((continuous_subtype_val.comp continuous_fst).prodMk - (continuous_subtype_val.comp continuous_snd)) - -lemma continuous_rep : Continuous (fun g : Group q => (rep (τ := τ) g).toContinuousLinearMap) := - TensorRep.continuous_rep.comp continuous_blockGroup -end SpinAngle.SignedTensor - -namespace SpinAngle.SignedCarrier -open SpinAngle.Young SpinAngle.Specht SignedTensor -variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) -lemma continuous_rep : Continuous (fun g : Group q => (rep a b q ha hb g).toContinuousLinearMap) := - ExternalTensor.continuous_rep _ _ (PolynomialCarrier.continuous_rep a q ha) - (PolynomialCarrier.continuous_rep b q hb) -end SpinAngle.SignedCarrier - - -namespace SpinAngle.TensorRep -open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder -variable {ι n : Type*} [contextInstance1859_23 : Fintype ι] [contextInstance1859_35 : DecidableEq ι] [contextInstance1859_51 : Fintype n] [contextInstance1859_63 : DecidableEq n] -lemma tensor_posSemidef (a : ι → Matrix n n ℂ) (ha : ∀ i, (a i).PosSemidef) : - (tensor a).PosSemidef := by - let r : ι → Matrix n n ℂ := fun i => CFC.sqrt (a i) - have he : tensor a = star (tensor r) * tensor r := by - rw [← tensor_star, ← tensor_mul] - congr 1 - funext i - dsimp [r] - rw [(IsSelfAdjoint.of_nonneg (CFC.sqrt_nonneg (a i))).star_eq, - CFC.sqrt_mul_sqrt_self (a i) (ha i).nonneg] - rw [he] - exact Matrix.posSemidef_conjTranspose_mul_self _ - -lemma action_positive (a : Matrix n n ℂ) (ha : a.PosSemidef) : - LinearMap.IsPositive (𝕜 := ℂ) (E := EuclideanSpace ℂ (ι → n)) (action a) := - Matrix.isPositive_toEuclideanLin_iff.mpr (tensor_posSemidef (fun _ : ι => a) (fun _ => ha)) -end SpinAngle.TensorRep - -namespace SpinAngle.PolynomialCarrier -open scoped Classical InnerProductSpace -open SpinAngle.Young SpinAngle.Specht -variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) - -lemma hermitianAction_positive (a : Matrix (Fin q) (Fin q) ℂ) (ha : a.PosSemidef) : - LinearMap.IsPositive (𝕜 := ℂ) (E := Carrier D q hq) (hermitianAction D q hq a ha.isHermitian) := by - refine ⟨hermitianAction_symmetric D q hq a ha.isHermitian, ?_⟩ - intro x - rw [← (inclusion D q hq).inner_map_map, inclusion_hermitianAction] - exact (TensorRep.action_positive a ha).2 (inclusion D q hq x) - -def highestVector : Carrier D q hq := - ⟨⟨highest D q hq,highest_mem D q hq⟩, self_mem_cyclic _ _⟩ - -lemma highestVector_ne_zero : highestVector D q hq ≠ 0 := by - intro h - have he := congrArg (inclusion D q hq) h - exact highest_ne_zero D q hq (by simpa [highestVector] using he) - -lemma inclusion_linear_hermitianAction (A : Matrix (Fin q) (Fin q) ℂ) (hA : A.IsHermitian) - (v : Carrier D q hq) : - (inclusion D q hq).toLinearMap (hermitianAction D q hq A hA v) = - TensorRep.action A ((inclusion D q hq).toLinearMap v) := - inclusion_hermitianAction D q hq A hA v - -lemma highestVector_diagonal (t : Fin q → ℝ) : - hermitianAction D q hq (Matrix.diagonal (fun i => (t i : ℂ))) - (Matrix.isHermitian_diagonal_iff.mpr (fun i => by simp [IsSelfAdjoint])) (highestVector D q hq) = - (highestMonomial D q hq t : ℂ) • highestVector D q hq := by - have hinj : Function.Injective (inclusion D q hq).toLinearMap := by - intro x y h - exact Subtype.ext (Subtype.ext h) - apply hinj - rw [inclusion_linear_hermitianAction, map_smul] - change TensorRep.action (Matrix.diagonal (fun i => (t i : ℂ))) (highest D q hq) = - (highestMonomial D q hq t : ℂ) • highest D q hq - rw [highest_diagonal] - congr 1 - exact (map_prod Complex.ofRealHom _ _).symm - -lemma card_rowColor (j : Fin q) : - (Finset.univ.filter fun i : Cells D => rowColor D q hq i = j).card = D.rowLen j := by - rw [← Fintype.card_subtype] - calc - Fintype.card {i : Cells D // rowColor D q hq i = j} = Fintype.card {i : Cells D // i.val.1 = j.val} := - Fintype.card_congr (Equiv.subtypeEquivRight (fun i => Fin.ext_iff)) - _ = D.rowLen j := card_row_subtype D j - -lemma highestMonomial_eq_rowLen (t : Fin q → ℝ) : - highestMonomial D q hq t = ∏ j : Fin q, t j ^ D.rowLen j := by - unfold highestMonomial - rw [← Finset.prod_fiberwise' Finset.univ (rowColor D q hq) t] - simp only [Finset.prod_const, card_rowColor] - -include hq in -lemma sum_rowLen_eq_card : ∑ j : Fin q, D.rowLen j = Fintype.card (Cells D) := by - have h := Finset.sum_fiberwise Finset.univ (rowColor D q hq) (fun _ : Cells D => (1 : ℕ)) - simp only [Finset.sum_const, nsmul_eq_mul, mul_one, card_rowColor, Finset.card_univ] at h - exact_mod_cast h - -end SpinAngle.PolynomialCarrier - - - - -noncomputable section -open scoped TensorProduct InnerProductSpace ComplexOrder -namespace SpinAngle.TensorPositive -variable {E F : Type*} [contextInstance1947_23 : NormedAddCommGroup E] [contextInstance1947_46 : InnerProductSpace ℂ E] - [contextInstance1948_2 : NormedAddCommGroup F] [contextInstance1948_25 : InnerProductSpace ℂ F] - [contextInstance1949_2 : FiniteDimensional ℂ E] [contextInstance1949_26 : FiniteDimensional ℂ F] - -lemma mapL_nonneg (A : E →L[ℂ] E) (B : F →L[ℂ] F) (hA : 0 ≤ A) (hB : 0 ≤ B) : - 0 ≤ TensorProduct.mapL A B := by - let a := CFC.sqrt A - let b := CFC.sqrt B - have ha : star a = a := (IsSelfAdjoint.of_nonneg (CFC.sqrt_nonneg A)).star_eq - have hb : star b = b := (IsSelfAdjoint.of_nonneg (CFC.sqrt_nonneg B)).star_eq - have hstar : star (TensorProduct.mapL a b) = TensorProduct.mapL a b := by - change ContinuousLinearMap.adjoint (TensorProduct.mapL a b) = _ - rw [TensorProduct.adjoint_mapL] - change TensorProduct.mapL (star a) (star b) = _ - rw [ha,hb] - have he : star (TensorProduct.mapL a b) * TensorProduct.mapL a b = TensorProduct.mapL A B := by - rw [hstar, ← TensorProduct.mapL_mul] - dsimp [a,b] - rw [CFC.sqrt_mul_sqrt_self A hA, CFC.sqrt_mul_sqrt_self B hB] - rw [← he] - exact star_mul_self_nonneg _ - -lemma map_positive (A : E →ₗ[ℂ] E) (B : F →ₗ[ℂ] F) (hA : A.IsPositive) (hB : B.IsPositive) : - (TensorProduct.map A B).IsPositive := by - have ha : 0 ≤ A.toContinuousLinearMap := - (ContinuousLinearMap.nonneg_iff_isPositive).mpr hA - have hb : 0 ≤ B.toContinuousLinearMap := - (ContinuousLinearMap.nonneg_iff_isPositive).mpr hB - have h := (ContinuousLinearMap.nonneg_iff_isPositive).mp (mapL_nonneg _ _ ha hb) - change ((TensorProduct.mapL A.toContinuousLinearMap B.toContinuousLinearMap).toLinearMap).IsPositive at h - simpa only [TensorProduct.toLinearMap_mapL, LinearMap.coe_toContinuousLinearMap] using h - -lemma map_norm_bound (A : E →ₗ[ℂ] E) (B : F →ₗ[ℂ] F) - (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) - (hA : ∀ x, ‖A x‖ ≤ a * ‖x‖) (hB : ∀ y, ‖B y‖ ≤ b * ‖y‖) - (v : E ⊗[ℂ] F) : ‖TensorProduct.map A B v‖ ≤ (a*b)*‖v‖ := by - have ha' : ‖A.toContinuousLinearMap‖ ≤ a := - ContinuousLinearMap.opNorm_le_bound _ ha hA - have hb' : ‖B.toContinuousLinearMap‖ ≤ b := - ContinuousLinearMap.opNorm_le_bound _ hb hB - calc - ‖TensorProduct.map A B v‖ ≤ ‖TensorProduct.mapL A.toContinuousLinearMap B.toContinuousLinearMap‖ * ‖v‖ := - by simpa only [TensorProduct.mapL_apply, LinearMap.coe_toContinuousLinearMap] using - (ContinuousLinearMap.le_opNorm (TensorProduct.mapL A.toContinuousLinearMap B.toContinuousLinearMap) v) - _ ≤ (a*b)*‖v‖ := mul_le_mul_of_nonneg_right - ((TensorProduct.norm_mapL_le _ _).trans (mul_le_mul ha' hb' (norm_nonneg _) ha)) (norm_nonneg _) -end SpinAngle.TensorPositive - - - - -noncomputable section -open scoped BigOperators -namespace SpinAngle.EntropyMonomial -variable {ι : Type*} [contextInstance2001_21 : Fintype ι] - -def entropy (n : ι → ℕ) : ℝ := - (∑ i, n i : ℕ) * Real.log (∑ i, n i : ℕ) - ∑ i, (n i : ℝ) * Real.log (n i) - -lemma sum_log_ratio (n : ι → ℕ) (p : ℕ) (hp : 0 < p) (hn : ∑ i, n i = p) : - ∑ i, (n i : ℝ) * Real.log ((n i : ℝ) / p) = -entropy n := by - have hp0 : (p : ℝ) ≠ 0 := by exact_mod_cast hp.ne' - have he (i : ι) : (n i : ℝ) * Real.log ((n i : ℝ) / p) = - (n i : ℝ) * Real.log (n i) - (n i : ℝ) * Real.log p := by - by_cases hi : n i = 0 - · simp [hi] - · rw [Real.log_div (by exact_mod_cast hi) hp0, mul_sub] - simp only [he, Finset.sum_sub_distrib, ← Finset.sum_mul] - have hn' : ∑ i, (n i : ℝ) = p := by exact_mod_cast hn - rw [hn'] - simp only [entropy, hn] - ring - -lemma power_le_exponential (k p : ℕ) (hp : 0 < p) (t : ℝ) (ht : 0 ≤ t) : - t ^ k ≤ Real.exp ((k : ℝ) * Real.log ((k : ℝ) / p) + p * t - k) := by - by_cases hk : k = 0 - · subst k - simpa using (Real.one_le_exp_iff.mpr (mul_nonneg (Nat.cast_nonneg p) ht)) - by_cases ht0 : t = 0 - · simp only [ht0, zero_pow hk] - exact (Real.exp_pos _).le - have hk' : 0 < (k : ℝ) := by exact_mod_cast Nat.pos_of_ne_zero hk - have hp' : 0 < (p : ℝ) := by exact_mod_cast hp - have ht' : 0 < t := lt_of_le_of_ne ht (Ne.symm ht0) - have hr : 0 < (k : ℝ) / p := div_pos hk' hp' - have hlog := Real.log_le_sub_one_of_pos (div_pos ht' hr) - rw [Real.log_div ht0 hr.ne'] at hlog - have hmul := mul_le_mul_of_nonneg_left hlog hk'.le - have hc : (k : ℝ) * (t / ((k : ℝ) / p) - 1) = p * t - k := by - field_simp - - rw [hc] at hmul - calc - t ^ k = Real.exp ((k : ℝ) * Real.log t) := by - rw [Real.exp_nat_mul, Real.exp_log ht'] - _ ≤ _ := Real.exp_le_exp.mpr (by nlinarith) - - - -theorem prod_pow_le (n : ι → ℕ) (t : ι → ℝ) (ht : ∀ i, 0 ≤ t i) - (hsum : ∑ i, t i ≤ 1) : - ∏ i, t i ^ n i ≤ Real.exp (-entropy n) := by - classical - let p : ℕ := ∑ i, n i - by_cases hp : p = 0 - · have hn : ∀ i, n i = 0 := by - intro i - have hle := Finset.single_le_sum (fun j (_ : j ∈ Finset.univ) => Nat.zero_le (n j)) (Finset.mem_univ i) - change n i ≤ p at hle - omega - simp [entropy, hn] - have hp' : 0 < p := Nat.pos_of_ne_zero hp - calc - ∏ i, t i ^ n i ≤ ∏ i, Real.exp ((n i : ℝ) * Real.log ((n i : ℝ) / p) + p * t i - n i) := - Finset.prod_le_prod₀ (fun i _ => pow_nonneg (ht i) _) (fun i _ => power_le_exponential _ p hp' _ (ht i)) - _ = Real.exp (∑ i, ((n i : ℝ) * Real.log ((n i : ℝ) / p) + p * t i - n i)) := - (Real.exp_sum _ _).symm - _ ≤ Real.exp (-entropy n) := by - apply Real.exp_le_exp.mpr - simp only [Finset.sum_sub_distrib, Finset.sum_add_distrib, ← Finset.mul_sum] - rw [sum_log_ratio n p hp' rfl] - have hn : ∑ i, (n i : ℝ) = p := by simp [p] - rw [hn] - have h := mul_le_mul_of_nonneg_left hsum (Nat.cast_nonneg p : (0 : ℝ) ≤ p) - nlinarith - -lemma optimal_prod (n : ι → ℕ) (p : ℕ) (hp : 0 < p) (hn : ∑ i, n i = p) : - ∏ i, ((n i : ℝ) / p) ^ n i = Real.exp (-entropy n) := by - rw [← sum_log_ratio n p hp hn, Real.exp_sum] - apply Finset.prod_congr rfl - intro i _ - by_cases hi : n i = 0 - · simp [hi] - have hpos : 0 < (n i : ℝ) / p := div_pos (by exact_mod_cast Nat.pos_of_ne_zero hi) (by exact_mod_cast hp) - rw [Real.exp_nat_mul, Real.exp_log hpos] - -end SpinAngle.EntropyMonomial - - - -noncomputable section -open scoped InnerProductSpace ComplexOrder BigOperators -namespace SpinAngle.PositiveTrace -variable {E : Type*} [contextInstance2090_21 : NormedAddCommGroup E] [contextInstance2090_44 : InnerProductSpace ℂ E] - [contextInstance2091_2 : FiniteDimensional ℂ E] - -lemma eigenvalues_nonneg (A : E →ₗ[ℂ] E) (hA : A.IsPositive) - (i : Fin (Module.finrank ℂ E)) : 0 ≤ hA.isSymmetric.eigenvalues rfl i := by - have h := hA.inner_nonneg_right (hA.isSymmetric.eigenvectorBasis rfl i) - rw [hA.isSymmetric.apply_eigenvectorBasis rfl i, inner_smul_right, - (hA.isSymmetric.eigenvectorBasis rfl).inner_eq_one] at h - simpa only [mul_one, RCLike.ofReal_nonneg] using h - - -theorem eigenvalue_le_trace (A : E →ₗ[ℂ] E) (hA : A.IsPositive) - (v : E) (hv : v ≠ 0) (t : ℝ) (he : A v = (t : ℂ) • v) : - t ≤ (LinearMap.trace ℂ E A).re := by - classical - let b := hA.isSymmetric.eigenvectorBasis rfl - have hcoord : ∃ i, b.repr v i ≠ 0 := by - by_contra! hh - apply hv - apply b.repr.injective - ext i - simpa using hh i - obtain ⟨i,hi⟩ := hcoord - have h := congrArg (fun x : E => b.repr x i) he - rw [hA.isSymmetric.eigenvectorBasis_apply_self_apply, map_smul, PiLp.smul_apply, - smul_eq_mul] at h - have ht : hA.isSymmetric.eigenvalues rfl i = t := by - exact Complex.ofReal_injective (mul_right_cancel₀ hi h) - change t ≤ RCLike.re (LinearMap.trace ℂ E A) - rw [hA.isSymmetric.re_trace_eq_sum_eigenvalues rfl, ← ht] - exact Finset.single_le_sum (fun j _ => eigenvalues_nonneg A hA j) (Finset.mem_univ i) - -end SpinAngle.PositiveTrace - - - - - -noncomputable section -open scoped InnerProductSpace BigOperators ComplexOrder -namespace SpinAngle.Isotypic -variable {G : Type*} [contextInstance2131_21 : Group G] -variable {E F : Type*} [contextInstance2132_23 : NormedAddCommGroup E] [contextInstance2132_46 : InnerProductSpace ℂ E] - [contextInstance2133_2 : NormedAddCommGroup F] [contextInstance2133_25 : InnerProductSpace ℂ F] - [contextInstance2134_2 : FiniteDimensional ℂ E] [contextInstance2134_26 : FiniteDimensional ℂ F] -variable (ρ : Representation ℂ G E) (σ : Representation ℂ G F) - -def space : Subrepresentation σ where - toSubmodule := Submodule.span ℂ (Set.range fun z : ρ.IntertwiningMap σ × E => z.1 z.2) - apply_mem_toSubmodule := by - intro g v hv - induction hv using Submodule.span_induction with - | mem v hv => - obtain ⟨⟨f,x⟩,rfl⟩ := hv - apply Submodule.subset_span - refine ⟨⟨f,ρ g x⟩, ?_⟩ - exact Representation.IntertwiningMap.isIntertwining ρ σ f g x - | zero => simp - | add x y hx hy ihx ihy => simpa only [map_add] using Submodule.add_mem _ ihx ihy - | smul a x hx ih => simpa only [map_smul] using Submodule.smul_mem _ a ih - -def projection : F →L[ℂ] F := (space ρ σ).toSubmodule.starProjection - -lemma projection_mem - {G : Type*} - [contextInstance2131_21 : Group G] - {E : Type*} {F : Type*} - [contextInstance2132_23 : NormedAddCommGroup E] - [contextInstance2132_46 : InnerProductSpace ℂ E] - [contextInstance2133_2 : NormedAddCommGroup F] - [contextInstance2133_25 : InnerProductSpace ℂ F] - [FiniteDimensional ℂ E] - [contextInstance2134_26 : FiniteDimensional ℂ F] - (ρ : Representation ℂ G E) (σ : Representation ℂ G F) (v : F) : projection ρ σ v ∈ space ρ σ := - (space ρ σ).toSubmodule.starProjection_apply_mem v - -lemma projection_norm_apply_le - {G : Type*} - [contextInstance2131_21 : Group G] - {E : Type*} {F : Type*} - [contextInstance2132_23 : NormedAddCommGroup E] - [contextInstance2132_46 : InnerProductSpace ℂ E] - [contextInstance2133_2 : NormedAddCommGroup F] - [contextInstance2133_25 : InnerProductSpace ℂ F] - [FiniteDimensional ℂ E] - [contextInstance2134_26 : FiniteDimensional ℂ F] - (ρ : Representation ℂ G E) (σ : Representation ℂ G F) (v : F) : ‖projection ρ σ v‖ ≤ ‖v‖ := - (space ρ σ).toSubmodule.norm_starProjection_apply_le v - -lemma map_mem - {G : Type*} - [contextInstance2131_21 : Group G] - {E : Type*} {F : Type*} - [contextInstance2132_23 : NormedAddCommGroup E] - [contextInstance2132_46 : InnerProductSpace ℂ E] - [contextInstance2133_2 : NormedAddCommGroup F] - [contextInstance2133_25 : InnerProductSpace ℂ F] - [FiniteDimensional ℂ E] - [FiniteDimensional ℂ F] - (ρ : Representation ℂ G E) (σ : Representation ℂ G F) (f : ρ.IntertwiningMap σ) (x : E) : f x ∈ space ρ σ := - Submodule.subset_span ⟨⟨f,x⟩,rfl⟩ - -lemma endomorphism_mem (d : σ.IntertwiningMap σ) (v : F) (hv : v ∈ space ρ σ) : - d v ∈ space ρ σ := by - induction hv using Submodule.span_induction with - | mem v hv => - obtain ⟨⟨f,x⟩,rfl⟩ := hv - exact map_mem ρ σ (d.comp f) x - | zero => simp only [map_zero]; exact (space ρ σ).toSubmodule.zero_mem - | add x y hx hy ihx ihy => rw [map_add]; exact (space ρ σ).toSubmodule.add_mem ihx ihy - | smul a x hx ih => rw [map_smul]; exact (space ρ σ).toSubmodule.smul_mem a ih - -lemma natural_mem (a : E →ₗ[ℂ] E) (A : F →ₗ[ℂ] F) - (h : ∀ f : ρ.IntertwiningMap σ, ∀ x, A (f x) = f (a x)) - (v : F) (hv : v ∈ space ρ σ) : A v ∈ space ρ σ := by - induction hv using Submodule.span_induction with - | mem v hv => - obtain ⟨⟨f,x⟩,rfl⟩ := hv - rw [h] - exact map_mem ρ σ f _ - | zero => simp only [map_zero]; exact (space ρ σ).toSubmodule.zero_mem - | add x y hx hy ihx ihy => rw [map_add]; exact (space ρ σ).toSubmodule.add_mem ihx ihy - | smul z x hx ih => rw [map_smul]; exact (space ρ σ).toSubmodule.smul_mem z ih - -lemma scalar_on_space - {G : Type*} - [contextInstance2131_21 : Group G] - {E : Type*} {F : Type*} - [contextInstance2132_23 : NormedAddCommGroup E] - [contextInstance2132_46 : InnerProductSpace ℂ E] - [contextInstance2133_2 : NormedAddCommGroup F] - [contextInstance2133_25 : InnerProductSpace ℂ F] - [FiniteDimensional ℂ E] - [FiniteDimensional ℂ F] - (ρ : Representation ℂ G E) (σ : Representation ℂ G F) (A : F →ₗ[ℂ] F) (c : ℂ) - (h : ∀ f : ρ.IntertwiningMap σ, ∀ x, A (f x) = c • f x) - (v : F) (hv : v ∈ space ρ σ) : A v = c • v := by - induction hv using Submodule.span_induction with - | mem v hv => obtain ⟨⟨f,x⟩,rfl⟩ := hv; exact h f x - | zero => simp - | add x y hx hy ihx ihy => simp [ihx, ihy, smul_add] - | smul z x hx ih => simp [ih, smul_comm c z] - -lemma exists_nonzero_adjoint (v : F) (hv : v ∈ space ρ σ) (hv0 : v ≠ 0) : - ∃ f : ρ.IntertwiningMap σ, LinearMap.adjoint f.toLinearMap v ≠ 0 := by - by_contra! hn - have horth (w : F) (hw : w ∈ space ρ σ) : ⟪w,v⟫_ℂ = 0 := by - induction hw using Submodule.span_induction with - | mem w hw => - obtain ⟨⟨f,x⟩,rfl⟩ := hw - change ⟪f.toLinearMap x,v⟫_ℂ = 0 - rw [← LinearMap.adjoint_inner_right, hn] - simp - | zero => simp - | add x y hx hy ihx ihy => simp [ihx, ihy] - | smul z x hx ih => simp [ih] - exact hv0 (inner_self_eq_zero.mp (horth v hv)) - -lemma transfer_eigenvalue_bound (a : E →ₗ[ℂ] E) (A : F →ₗ[ℂ] F) - (ha : a.IsSymmetric) (hA : A.IsSymmetric) - (hnat : ∀ f : ρ.IntertwiningMap σ, ∀ x, A (f x) = f (a x)) - (c : ℝ) (hc : ∀ x, ‖a x‖ ≤ c * ‖x‖) - (v : F) (hv : v ∈ space ρ σ) (hv0 : v ≠ 0) - (t : ℂ) (ht : A v = t • v) : ‖t‖ ≤ c := by - obtain ⟨f,hf⟩ := exists_nonzero_adjoint ρ σ v hv hv0 - have he : A.comp f.toLinearMap = f.toLinearMap.comp a := by ext x; exact hnat f x - have hadj := congrArg LinearMap.adjoint he - rw [LinearMap.adjoint_comp, LinearMap.adjoint_comp, ha.adjoint_eq, hA.adjoint_eq] at hadj - have hev : a (LinearMap.adjoint f.toLinearMap v) = t • LinearMap.adjoint f.toLinearMap v := by - have hh := congrArg (fun L : F →ₗ[ℂ] E => L v) hadj - simpa only [LinearMap.comp_apply, ht, map_smul] using hh.symm - have hh := hc (LinearMap.adjoint f.toLinearMap v) - rw [hev, norm_smul] at hh - exact (mul_le_mul_iff_left₀ (norm_pos_iff.mpr hf)).mp hh - - - -theorem norm_bound (a : E →ₗ[ℂ] E) (A : F →ₗ[ℂ] F) - (ha : a.IsSymmetric) (hA : A.IsSymmetric) - (hnat : ∀ f : ρ.IntertwiningMap σ, ∀ x, A (f x) = f (a x)) - (c : ℝ) (hc0 : 0 ≤ c) (hc : ∀ x, ‖a x‖ ≤ c * ‖x‖) - (v : F) (hv : v ∈ space ρ σ) : ‖A v‖ ≤ c * ‖v‖ := by - classical - let S := (space ρ σ).toSubmodule - have hinv : ∀ w ∈ S, A w ∈ S := natural_mem ρ σ a A hnat - let B : S →ₗ[ℂ] S := A.restrict hinv - have hB : B.IsSymmetric := hA.restrict_invariant hinv - let b := hB.eigenvectorBasis rfl - have hb (i : Fin (Module.finrank ℂ S)) : ‖(hB.eigenvalues rfl i : ℂ)‖ ≤ c := by - apply transfer_eigenvalue_bound ρ σ a A ha hA hnat c hc (b i).val (b i).property - · intro hh - have hn := b.orthonormal.ne_zero i - exact hn (Subtype.ext hh) - · exact congrArg Subtype.val (hB.apply_eigenvectorBasis rfl i) - let w : S := ⟨v,hv⟩ - change ‖B w‖ ≤ c * ‖w‖ - apply (sq_le_sq₀ (norm_nonneg _) (mul_nonneg hc0 (norm_nonneg _))).mp - rw [← b.repr.norm_map (B w), ← b.repr.norm_map w, mul_pow, - EuclideanSpace.norm_sq_eq, EuclideanSpace.norm_sq_eq, Finset.mul_sum] - apply Finset.sum_le_sum - intro i _ - rw [hB.eigenvectorBasis_apply_self_apply, norm_mul, mul_pow] - exact mul_le_mul_of_nonneg_right (pow_le_pow_left₀ (norm_nonneg _) (hb i) 2) (sq_nonneg _) - -lemma projection_commute_of_invariant - {G : Type*} - [Group G] - {F : Type*} - [contextInstance2133_2 : NormedAddCommGroup F] - [contextInstance2133_25 : InnerProductSpace ℂ F] - [contextInstance2134_26 : FiniteDimensional ℂ F] (S : Submodule ℂ F) (A : F →ₗ[ℂ] F) - (hA : A.IsSymmetric) (hinv : ∀ v ∈ S, A v ∈ S) (v : F) : - S.starProjection (A v) = A (S.starProjection v) := by - apply S.eq_starProjection_of_mem_of_inner_eq_zero - · exact hinv _ (S.starProjection_apply_mem v) - · intro w hw - rw [← map_sub, hA] - exact S.starProjection_inner_eq_zero v _ (hinv _ hw) - -lemma projection_commute_endomorphism (d : σ.IntertwiningMap σ) - (hd : d.toLinearMap.IsSymmetric) (v : F) : - projection ρ σ (d v) = d (projection ρ σ v) := - projection_commute_of_invariant (G := G) _ d.toLinearMap hd (endomorphism_mem ρ σ d) v - -lemma projection_commute_natural (a : E →ₗ[ℂ] E) (A : F →ₗ[ℂ] F) - (hA : A.IsSymmetric) - (h : ∀ f : ρ.IntertwiningMap σ, ∀ x, A (f x) = f (a x)) (v : F) : - projection ρ σ (A v) = A (projection ρ σ v) := - projection_commute_of_invariant (G := G) _ A hA (natural_mem ρ σ a A h) v - -end SpinAngle.Isotypic - -namespace SpinAngle.SignedTensor -open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder -variable {q : ℕ} - -def IsEvenDensity (A : Mat q × Mat q) : Prop := - A.1.PosSemidef ∧ A.2.PosSemidef ∧ Matrix.trace A.1 + Matrix.trace A.2 = 1 - -lemma block_posSemidef (A : Mat q × Mat q) (hA : A.1.PosSemidef) (hB : A.2.PosSemidef) : - (block A).PosSemidef := by - let R : Mat q × Mat q := (CFC.sqrt A.1, CFC.sqrt A.2) - have he : block A = star (block R) * block R := by - rw [← block_star, ← map_mul] - congr 1 - apply Prod.ext - · change A.1 = star (CFC.sqrt A.1) * CFC.sqrt A.1 - rw [(IsSelfAdjoint.of_nonneg (CFC.sqrt_nonneg A.1)).star_eq, - CFC.sqrt_mul_sqrt_self A.1 hA.nonneg] - · change A.2 = star (CFC.sqrt A.2) * CFC.sqrt A.2 - rw [(IsSelfAdjoint.of_nonneg (CFC.sqrt_nonneg A.2)).star_eq, - CFC.sqrt_mul_sqrt_self A.2 hB.nonneg] - rw [he] - exact Matrix.posSemidef_conjTranspose_mul_self _ -end SpinAngle.SignedTensor - -namespace SpinAngle.SignedCarrier -open scoped Classical TensorProduct BigOperators InnerProductSpace -open SpinAngle.Young SpinAngle.Specht SignedTensor -variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) - -lemma hermitianAction_positive (A : Mat q × Mat q) (hA : A.1.PosSemidef) (hB : A.2.PosSemidef) : - LinearMap.IsPositive (𝕜 := ℂ) (E := Carrier a b q ha hb) - (hermitianAction a b q ha hb A hA.isHermitian hB.isHermitian) := - TensorPositive.map_positive (E := PolynomialCarrier.Carrier a q ha) - (F := PolynomialCarrier.Carrier b q hb) _ _ - (PolynomialCarrier.hermitianAction_positive a q ha A.1 hA) - (PolynomialCarrier.hermitianAction_positive b q hb A.2 hB) - -lemma hermitianAction_norm_bound (A : Mat q × Mat q) (hA : A.1.PosSemidef) (hB : A.2.PosSemidef) - (v : Carrier a b q ha hb) : - ‖hermitianAction a b q ha hb A hA.isHermitian hB.isHermitian v‖ ≤ - (PolynomialCarrier.highestMonomial a q ha (SortedSpectrum.values A.1 hA.isHermitian) * - PolynomialCarrier.highestMonomial b q hb (SortedSpectrum.values A.2 hB.isHermitian)) * ‖v‖ := by - apply TensorPositive.map_norm_bound (E := PolynomialCarrier.Carrier a q ha) - (F := PolynomialCarrier.Carrier b q hb) - · exact Finset.prod_nonneg (fun i _ => SortedSpectrum.values_nonneg A.1 hA.isHermitian hA _) - · exact Finset.prod_nonneg (fun i _ => SortedSpectrum.values_nonneg A.2 hB.isHermitian hB _) - · exact PolynomialCarrier.hermitianAction_norm_bound a q ha A.1 hA - · exact PolynomialCarrier.hermitianAction_norm_bound b q hb A.2 hB - -def parts : Fin q ⊕ Fin q → ℕ := Sum.elim (fun i => a.rowLen i) (fun i => b.rowLen i) -def entropy : ℝ := EntropyMonomial.entropy (parts a b q) -def dimension : ℕ := Module.finrank ℂ (Carrier a b q ha hb) - -include ha hb in -lemma sum_parts : ∑ i, parts a b q i = Fintype.card (Cells a) + Fintype.card (Cells b) := by - rw [Fintype.sum_sum_type] - change (∑ i : Fin q, a.rowLen i) + (∑ i : Fin q, b.rowLen i) = _ - rw [PolynomialCarrier.sum_rowLen_eq_card a q ha, PolynomialCarrier.sum_rowLen_eq_card b q hb] - -include ha hb in -lemma entropy_eq_source : entropy a b q = - (Fintype.card (Cells a) + Fintype.card (Cells b) : ℕ) * - Real.log (Fintype.card (Cells a) + Fintype.card (Cells b) : ℕ) - - (∑ i : Fin q, (a.rowLen i : ℝ) * Real.log (a.rowLen i)) - - (∑ i : Fin q, (b.rowLen i : ℝ) * Real.log (b.rowLen i)) := by - unfold entropy EntropyMonomial.entropy - rw [sum_parts a b q ha hb, Fintype.sum_sum_type] - simp only [parts, Sum.elim_inl, Sum.elim_inr] - ring - -lemma hermitianAction_density_bound (A : Mat q × Mat q) (hA : IsEvenDensity A) - (v : Carrier a b q ha hb) : - ‖hermitianAction a b q ha hb A hA.1.isHermitian hA.2.1.isHermitian v‖ ≤ - Real.exp (-entropy a b q) * ‖v‖ := by - apply (hermitianAction_norm_bound a b q ha hb A hA.1 hA.2.1 v).trans - apply mul_le_mul_of_nonneg_right _ (norm_nonneg _) - rw [PolynomialCarrier.highestMonomial_eq_rowLen, PolynomialCarrier.highestMonomial_eq_rowLen] - let t : Fin q ⊕ Fin q → ℝ := Sum.elim - (SortedSpectrum.values A.1 hA.1.isHermitian) (SortedSpectrum.values A.2 hA.2.1.isHermitian) - have ht (i) : 0 ≤ t i := by - cases i with - | inl i => exact SortedSpectrum.values_nonneg A.1 hA.1.isHermitian hA.1 i - | inr i => exact SortedSpectrum.values_nonneg A.2 hA.2.1.isHermitian hA.2.1 i - have hs : ∑ i, t i = 1 := by - rw [Fintype.sum_sum_type] - have he1 := SortedSpectrum.trace_eq_sum A.1 hA.1.isHermitian - have he2 := SortedSpectrum.trace_eq_sum A.2 hA.2.1.isHermitian - have h : (∑ i, (SortedSpectrum.values A.1 hA.1.isHermitian i : ℂ)) + - (∑ i, (SortedSpectrum.values A.2 hA.2.1.isHermitian i : ℂ)) = 1 := - (congrArg₂ (· + ·) he1.symm he2.symm).trans hA.2.2 - have hh := congrArg Complex.re h - simpa only [t, Sum.elim_inl, Sum.elim_inr, Complex.add_re, Complex.re_sum, Complex.ofReal_re, Complex.one_re] using hh - have h := EntropyMonomial.prod_pow_le (parts a b q) t ht hs.le - simpa only [Fintype.prod_sum_type, parts, t, entropy, Sum.elim_inl, Sum.elim_inr] using h - -end SpinAngle.SignedCarrier - -namespace SpinAngle.EntropyMonomial -open scoped BigOperators -variable {ι : Type*} [contextInstance2379_21 : Fintype ι] [contextInstance2379_33 : Nonempty ι] - -lemma exists_optimal (n : ι → ℕ) : ∃ t : ι → ℝ, - (∀ i, 0 ≤ t i) ∧ (∑ i, t i = 1) ∧ (∏ i, t i ^ n i = Real.exp (-entropy n)) := by - classical - let p := ∑ i, n i - by_cases hp : p = 0 - · have hn : ∀ i, n i = 0 := by - intro i - have h := Finset.single_le_sum (fun j (_ : j ∈ Finset.univ) => Nat.zero_le (n j)) (Finset.mem_univ i) - change n i ≤ p at h - omega - let i₀ := Classical.choice (inferInstance : Nonempty ι) - refine ⟨fun i => if i = i₀ then 1 else 0, ?_, ?_, ?_⟩ - · intro i; dsimp only; split_ifs <;> norm_num - · simp - · simp [hn, entropy] - · refine ⟨fun i => (n i : ℝ) / p, fun i => div_nonneg (Nat.cast_nonneg _) (Nat.cast_nonneg _), ?_, ?_⟩ - · rw [← Finset.sum_div] - have he : ∑ i, (n i : ℝ) = p := by simp [p] - rw [he, div_self (by exact_mod_cast hp)] - · exact optimal_prod n p (Nat.pos_of_ne_zero hp) rfl -end SpinAngle.EntropyMonomial - -namespace SpinAngle.SignedCarrier -open scoped Classical TensorProduct BigOperators InnerProductSpace ComplexOrder -open SpinAngle.Young SpinAngle.Specht SignedTensor -variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) -variable {τ : Type*} [contextInstance2407_21 : Fintype τ] [contextInstance2407_33 : DecidableEq τ] - -abbrev typeProjection : Raw (q := q) (τ := τ) →L[ℂ] Raw (q := q) (τ := τ) := - Isotypic.projection (rep a b q ha hb) SignedTensor.rep - -lemma density_on_space (A : Mat q × Mat q) (hA : IsEvenDensity A) - (v : Raw (q := q) (τ := τ)) - (hv : v ∈ Isotypic.space (rep a b q ha hb) (SignedTensor.rep (q := q) (τ := τ))) : - ‖TensorRep.action (block A) v‖ ≤ Real.exp (-entropy a b q) * ‖v‖ := by - exact Isotypic.norm_bound (E := Carrier a b q ha hb) (F := Raw (q := q) (τ := τ)) - (rep a b q ha hb) (SignedTensor.rep (q := q) (τ := τ)) - (hermitianAction a b q ha hb A hA.1.isHermitian hA.2.1.isHermitian) - (TensorRep.action (block A)) - (hermitianAction_positive a b q ha hb A hA.1 hA.2.1).isSymmetric - (TensorRep.action_positive (block A) (block_posSemidef A hA.1 hA.2.1)).isSymmetric - (fun L x => (intertwiner_hermitian a b q ha hb L A hA.1.isHermitian hA.2.1.isHermitian x).symm) - (Real.exp (-entropy a b q)) (Real.exp_pos _).le - (hermitianAction_density_bound a b q ha hb A hA) v hv - -lemma projected_density_bound (A : Mat q × Mat q) (hA : IsEvenDensity A) - (v : Raw (q := q) (τ := τ)) : - ‖TensorRep.action (block A) (typeProjection a b q ha hb v)‖ ≤ - Real.exp (-entropy a b q) * ‖v‖ := by - exact (density_on_space a b q ha hb A hA _ - (Isotypic.projection_mem (rep a b q ha hb) (SignedTensor.rep (q := q) (τ := τ)) v)).trans - (mul_le_mul_of_nonneg_left - (Isotypic.projection_norm_apply_le (rep a b q ha hb) (SignedTensor.rep (q := q) (τ := τ)) v) - (Real.exp_pos _).le) - - -theorem global_density_upper (A : Mat q × Mat q) (hA : IsEvenDensity A) : - ‖LinearMap.toContinuousLinearMap (TensorRep.action (ι := τ) (block A)) * - typeProjection (τ := τ) a b q ha hb‖ ≤ Real.exp (-entropy a b q) := by - apply ContinuousLinearMap.opNorm_le_bound _ (Real.exp_pos _).le - intro v - exact projected_density_bound a b q ha hb A hA v - -def highestVector : Carrier a b q ha hb := - PolynomialCarrier.highestVector a q ha ⊗ₜ[ℂ] PolynomialCarrier.highestVector b q hb - -lemma highestVector_ne_zero : highestVector a b q ha hb ≠ 0 := by - intro h - have hn := congrArg norm h - rw [highestVector, TensorProduct.norm_tmul (E := PolynomialCarrier.Carrier a q ha) - (F := PolynomialCarrier.Carrier b q hb), norm_zero] at hn - exact (mul_ne_zero (norm_ne_zero_iff.mpr (PolynomialCarrier.highestVector_ne_zero a q ha)) - (norm_ne_zero_iff.mpr (PolynomialCarrier.highestVector_ne_zero b q hb))) hn - -lemma highestVector_diagonal (t : Fin q ⊕ Fin q → ℝ) : - hermitianAction a b q ha hb - (Matrix.diagonal (fun i => (t (.inl i) : ℂ)), Matrix.diagonal (fun i => (t (.inr i) : ℂ))) - (Matrix.isHermitian_diagonal_iff.mpr (fun i => by simp [IsSelfAdjoint])) - (Matrix.isHermitian_diagonal_iff.mpr (fun i => by simp [IsSelfAdjoint])) - (highestVector a b q ha hb) = - ((∏ i, t i ^ parts a b q i : ℝ) : ℂ) • highestVector a b q ha hb := by - rw [hermitianAction, highestVector, TensorProduct.map_tmul, - PolynomialCarrier.highestVector_diagonal, PolynomialCarrier.highestVector_diagonal, - TensorProduct.smul_tmul_smul, PolynomialCarrier.highestMonomial_eq_rowLen, - PolynomialCarrier.highestMonomial_eq_rowLen] - congr 1 - rw [Fintype.prod_sum_type, Complex.ofReal_mul] - rfl - - -lemma exists_density_trace_lower [Nonempty (Fin q)] : ∃ (A : Mat q × Mat q) (hA : IsEvenDensity A), - Real.exp (-entropy a b q) ≤ - (LinearMap.trace ℂ (Carrier a b q ha hb) - (hermitianAction a b q ha hb A hA.1.isHermitian hA.2.1.isHermitian)).re := by - obtain ⟨t,ht,hs,he⟩ := EntropyMonomial.exists_optimal (parts a b q) - let A : Mat q × Mat q := - (Matrix.diagonal (fun i => (t (.inl i) : ℂ)), Matrix.diagonal (fun i => (t (.inr i) : ℂ))) - have hA : IsEvenDensity A := by - refine ⟨Matrix.PosSemidef.diagonal (fun i => by simpa using ht (.inl i)), - Matrix.PosSemidef.diagonal (fun i => by simpa using ht (.inr i)), ?_⟩ - simp only [A, Matrix.trace_diagonal] - have hh := congrArg Complex.ofReal hs - simpa only [Fintype.sum_sum_type, Complex.ofReal_add, Complex.ofReal_sum, Complex.ofReal_one] using hh - refine ⟨A,hA,?_⟩ - apply PositiveTrace.eigenvalue_le_trace _ (hermitianAction_positive a b q ha hb A hA.1 hA.2.1) - (highestVector a b q ha hb) (highestVector_ne_zero a b q ha hb) - have h := highestVector_diagonal a b q ha hb t - rw [he] at h - exact h -end SpinAngle.SignedCarrier - - -noncomputable section -open scoped BigOperators -namespace SpinAngle.DenseLU - -abbrev Mat (n : ℕ) := Matrix (Fin n) (Fin n) ℂ - -def border {n : ℕ} (a : ℂ) (b c : Fin n → ℂ) (D : Mat n) : Mat (n+1) := - fun i => Fin.cases (Fin.cases a b) (fun i => Fin.cases (c i) (D i)) i - -@[simp] lemma border_zero_zero {n : ℕ} (a : ℂ) (b c : Fin n → ℂ) (D : Mat n) : - border a b c D 0 0 = a := rfl -@[simp] lemma border_zero_succ {n : ℕ} (a : ℂ) (b c : Fin n → ℂ) (D : Mat n) (j : Fin n) : - border a b c D 0 j.succ = b j := rfl -@[simp] lemma border_succ_zero {n : ℕ} (a : ℂ) (b c : Fin n → ℂ) (D : Mat n) (i : Fin n) : - border a b c D i.succ 0 = c i := rfl -@[simp] lemma border_succ_succ {n : ℕ} (a : ℂ) (b c : Fin n → ℂ) (D : Mat n) (i j : Fin n) : - border a b c D i.succ j.succ = D i j := rfl - -lemma border_eq {n : ℕ} (A : Mat (n+1)) : - border (A 0 0) (fun j => A 0 j.succ) (fun i => A i.succ 0) - (fun i j => A i.succ j.succ) = A := by - ext i j - refine Fin.cases ?_ (fun i => ?_) i <;> refine Fin.cases ?_ (fun j => ?_) j <;> rfl - -lemma continuous_border {X : Type*} [TopologicalSpace X] {n : ℕ} - {a : X → ℂ} {b c : X → Fin n → ℂ} {D : X → Mat n} - (ha : Continuous a) (hb : Continuous b) (hc : Continuous c) (hD : Continuous D) : - Continuous (fun x => border (a x) (b x) (c x) (D x)) := by - apply continuous_pi - intro i - apply continuous_pi - intro j - refine Fin.cases ?_ (fun i => ?_) i <;> refine Fin.cases ?_ (fun j => ?_) j - · exact ha - · exact (continuous_apply j).comp hb - · exact (continuous_apply i).comp hc - · exact (continuous_apply j).comp ((continuous_apply i).comp hD) - - -lemma border_factor {n : ℕ} (a : ℂ) (ha : a ≠ 0) (b c : Fin n → ℂ) (L U : Mat n) : - border 1 0 (fun i => c i / a) L * border a b 0 U = - border a b c (L * U + (Matrix.of fun i j => c i / a * b j)) := by - ext i j - refine Fin.cases ?_ (fun i => ?_) i <;> refine Fin.cases ?_ (fun j => ?_) j - · simp [Matrix.mul_apply, Fin.sum_univ_succ] - · simp [Matrix.mul_apply, Fin.sum_univ_succ] - · simp [Matrix.mul_apply, Fin.sum_univ_succ, ha] - · simp [Matrix.mul_apply, Fin.sum_univ_succ, add_comm] - -def LowerUnipotent {n : ℕ} (L : Mat n) : Prop := - L.IsLowerTriangular ∧ ∀ i, L i i = 1 - -lemma lower_border {n : ℕ} (c : Fin n → ℂ) (L : Mat n) (hL : LowerUnipotent L) : - LowerUnipotent (border 1 0 c L) := by - constructor - · intro i j hij - change i < j at hij - induction i using Fin.cases <;> induction j using Fin.cases - · simp at hij - · rfl - · simp at hij - · exact hL.1 (by simpa using hij) - · intro i - refine Fin.cases ?_ (fun i => ?_) i - · rfl - · exact hL.2 i - -lemma upper_border {n : ℕ} (a : ℂ) (b : Fin n → ℂ) (U : Mat n) (hU : U.IsUpperTriangular) : - (border a b 0 U).IsUpperTriangular := by - intro i j hij - induction i using Fin.cases <;> induction j using Fin.cases - · simp at hij - · simp at hij - · rfl - · exact hU (by simpa using hij) - -def bigCell (n : ℕ) : Set (Mat n) := - {A | ∃ L U, LowerUnipotent L ∧ U.IsUpperTriangular ∧ A = L * U} - -lemma border_mem_bigCell {n : ℕ} (a : ℂ) (ha : a ≠ 0) (b c : Fin n → ℂ) (S : Mat n) - (hS : S ∈ bigCell n) : - border a b c (S + (Matrix.of fun i j => c i / a * b j)) ∈ bigCell (n+1) := by - obtain ⟨L,U,hL,hU,rfl⟩ := hS - exact ⟨border 1 0 (fun i => c i / a) L, border a b 0 U, - lower_border _ _ hL, upper_border _ _ _ hU, (border_factor a ha b c L U).symm⟩ - - - -theorem dense_bigCell (n : ℕ) : Dense (bigCell n) := by - induction n with - | zero => - intro A - apply subset_closure - refine ⟨1,1,?_,?_,?_⟩ - · refine ⟨?_,?_⟩ <;> intro i <;> exact Fin.elim0 i - · intro i; exact Fin.elim0 i - · exact Subsingleton.elim _ _ - | succ n ih => - have hpivot (a : ℂ) (ha : a ≠ 0) (b c : Fin n → ℂ) (D : Mat n) : - border a b c D ∈ closure (bigCell (n+1)) := by - let X : Mat n := fun i j => c i / a * b j - have hf : Continuous (fun S : Mat n => border a b c (S + X)) := - continuous_border continuous_const continuous_const continuous_const - (continuous_id.add continuous_const) - have hh := map_mem_closure hf (ih (D-X)) - (fun S hS => border_mem_bigCell a ha b c S hS) - change border a b c (D - X + X) ∈ closure (bigCell (n+1)) at hh - simpa only [sub_add_cancel] using hh - intro A - let b : Fin n → ℂ := fun j => A 0 j.succ - let c : Fin n → ℂ := fun i => A i.succ 0 - let D : Mat n := fun i j => A i.succ j.succ - have hf : Continuous (fun a : ℂ => border a b c D) := - continuous_border continuous_id continuous_const continuous_const continuous_const - have hh := map_mem_closure hf ((dense_compl_singleton (0 : ℂ)) (A 0 0)) - (fun a ha => hpivot a (by simpa using ha) b c D) - simpa only [closure_closure, b, c, D, border_eq] using hh - -end SpinAngle.DenseLU - -namespace SpinAngle.PolynomialCarrier -open scoped Classical Matrix -open SpinAngle.Specht SpinAngle.Young -variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) - -lemma action_mem_alternating (A : Matrix (Fin q) (Fin q) ℂ) - (v : TensorSpace D q) (hv : v ∈ alternating D q) : - TensorRep.action A v ∈ alternating D q := by - intro g - rw [← action_site_commute, hv g, map_smul] - -lemma upper_weight_support (U : Matrix (Fin q) (Fin q) ℂ) (hU : U.IsUpperTriangular) - (x : Cells D → Fin q) (hx : TensorRep.action U (highest D q hq) x ≠ 0) : - ∑ i, (x i).val = ∑ i : Cells D, i.val.1 := by - have hl := rowRankSum_le D (fun i => (x i).val) - (alternating_injective D q _ (action_mem_alternating D q U _ (highest_mem D q hq)) x hx) - apply le_antisymm _ hl - change (∑ y, (∏ i, U (x i) (y i)) * highest D q hq y) ≠ 0 at hx - obtain ⟨y, -, hy⟩ := Finset.exists_ne_zero_of_sum_ne_zero hx - have hyv : highest D q hq y ≠ 0 := (mul_ne_zero_iff.mp hy).2 - have hp : ∀ i, x i ≤ y i := by - intro i - by_contra hi - have hz : U (x i) (y i) = 0 := hU (lt_of_not_ge hi) - exact (mul_ne_zero_iff.mp hy).1 (Finset.prod_eq_zero (Finset.mem_univ i) hz) - rw [← weight_eigen_support D q hq _ (highest_weight_eigen D q hq) y hyv] - exact Finset.sum_le_sum fun i _ => hp i - - - -lemma upper_highest (U : Matrix (Fin q) (Fin q) ℂ) (hU : U.IsUpperTriangular) : - TensorRep.action U (highest D q hq) = - (TensorRep.action U (highest D q hq) (rowColor D q hq)) • highest D q hq := by - ext x - change _ = _ * highest D q hq x - by_cases hw : ∑ i, (x i).val = ∑ i : Cells D, i.val.1 - · exact alternating_minimal_weight D q hq _ - (action_mem_alternating D q U _ (highest_mem D q hq)) x hw - · have hv0 : TensorRep.action U (highest D q hq) x = 0 := by - by_contra hn - exact hw (upper_weight_support D q hq U hU x hn) - have he0 : highest D q hq x = 0 := by - by_contra hn - exact hw (weight_eigen_support D q hq _ (highest_weight_eigen D q hq) x hn) - rw [hv0, he0, mul_zero] - -lemma continuous_action_highest : - Continuous (fun A : Matrix (Fin q) (Fin q) ℂ => TensorRep.action A (highest D q hq)) := by - change Continuous (fun A : Matrix (Fin q) (Fin q) ℂ => - WithLp.toLp 2 (fun x : Cells D → Fin q => ∑ y, (∏ i, A (x i) (y i)) * highest D q hq y)) - apply (PiLp.continuous_toLp 2 (fun _ : Cells D → Fin q => ℂ)).comp - fun_prop - - - -lemma action_highest_mem_of_lower (S : Submodule ℂ (TensorSpace D q)) - (hS : ∀ L : Matrix (Fin q) (Fin q) ℂ, DenseLU.LowerUnipotent L → - TensorRep.action L (highest D q hq) ∈ S) - (A : Matrix (Fin q) (Fin q) ℂ) : TensorRep.action A (highest D q hq) ∈ S := by - have hsub : DenseLU.bigCell q ⊆ - (fun B : Matrix (Fin q) (Fin q) ℂ => TensorRep.action B (highest D q hq)) ⁻¹' - (S : Set (TensorSpace D q)) := by - intro B hB - obtain ⟨L,U,hL,hU,rfl⟩ := hB - change TensorRep.action (L * U) (highest D q hq) ∈ S - rw [map_mul, Module.End.mul_apply, upper_highest D q hq U hU, map_smul] - exact S.smul_mem _ (hS L hL) - exact closure_minimal hsub - (S.closed_of_finiteDimensional.preimage (continuous_action_highest D q hq)) - (DenseLU.dense_bigCell q A) - -end SpinAngle.PolynomialCarrier -noncomputable section -open scoped BigOperators -namespace SpinAngle.PolyDimension -open MvPolynomial Module -variable (σ : Type*) [contextInstance2689_21 : Fintype σ] [contextInstance2689_33 : DecidableEq σ] (p : ℕ) - - -def boundedExponentEquiv : {f : σ →₀ ℕ // ∀ i, f i ≤ p} ≃ (σ → Fin (p+1)) where - toFun f i := ⟨f.val i, Nat.lt_succ_of_le (f.property i)⟩ - invFun f := ⟨Finsupp.equivFunOnFinite.symm (fun i => (f i).val), by - intro i; exact Nat.le_of_lt_succ (f i).isLt⟩ - left_inv f := by apply Subtype.ext; ext i; rfl - right_inv f := by funext i; apply Fin.ext; rfl - - -theorem finrank_restrictDegree : - Module.finrank ℂ (restrictDegree σ ℂ p) = (p+1) ^ Fintype.card σ := by - let s : Set (σ →₀ ℕ) := {f | ∀ i, f i ≤ p} - let : Fintype s := Fintype.ofEquiv (σ → Fin (p+1)) (boundedExponentEquiv σ p).symm - change Module.finrank ℂ (restrictSupport ℂ s) = _ - rw [Module.finrank_eq_card_basis (basisRestrictSupport ℂ s)] - calc - Fintype.card s = Fintype.card (σ → Fin (p+1)) := Fintype.card_congr (boundedExponentEquiv σ p) - _ = _ := by simp - -abbrev LowerIndex (q : ℕ) := (i : Fin q) × Fin i.val - -lemma card_lowerIndex (q : ℕ) : Fintype.card (LowerIndex q) = q * (q-1) / 2 := by - simp only [LowerIndex, Fintype.card_sigma, Fintype.card_fin] - rw [Fin.sum_univ_eq_sum_range (fun i : ℕ => i) q, Finset.sum_range_id] - -lemma twice_card_lowerIndex (q : ℕ) : 2 * Fintype.card (LowerIndex q) = q * (q-1) := by - simp only [LowerIndex, Fintype.card_sigma, Fintype.card_fin] - rw [Fin.sum_univ_eq_sum_range (fun i : ℕ => i) q, mul_comm, Finset.sum_range_id_mul_two] - -variable {q : ℕ} -def lowerEntry (i j : Fin q) : MvPolynomial (LowerIndex q) ℂ := - if h : j < i then X ⟨i, ⟨j.val, h⟩⟩ else if i = j then 1 else 0 - -lemma lowerEntry_degree (i j : Fin q) : (lowerEntry i j).totalDegree ≤ 1 := by - unfold lowerEntry - split_ifs <;> simp - -lemma totalDegree_sum_le - (σ : Type*) - [Fintype σ] - [DecidableEq σ] - (p : ℕ) {ι : Type*} (s : Finset ι) (f : ι → MvPolynomial σ ℂ) - (hf : ∀ i ∈ s, (f i).totalDegree ≤ p) : (∑ i ∈ s, f i).totalDegree ≤ p := - (MvPolynomial.totalDegree_finsetSum s f).trans (Finset.sup_le hf) - -end SpinAngle.PolyDimension - -namespace SpinAngle.PolyDimension -open MvPolynomial Module -variable {σ X : Type*} [contextInstance2737_23 : Fintype σ] [contextInstance2737_35 : DecidableEq σ] [contextInstance2737_51 : Fintype X] (p : ℕ) - - - - -def valueTranspose (P : X → restrictDegree σ ℂ p) : - Module.Dual ℂ (restrictDegree σ ℂ p) →ₗ[ℂ] EuclideanSpace ℂ X where - toFun φ := WithLp.toLp 2 (fun x => φ (P x)) - map_add' φ ψ := by ext x; rfl - map_smul' c φ := by ext x; rfl - -lemma value_mem_range - {σ : Type*} {X : Type*} - [Fintype σ] - [DecidableEq σ] - [Fintype X] - (p : ℕ) (P : X → restrictDegree σ ℂ p) (a : σ → ℂ) : - WithLp.toLp 2 (fun x => MvPolynomial.aeval a (P x).val) ∈ - LinearMap.range (valueTranspose p P) := by - refine ⟨(MvPolynomial.aeval a).toLinearMap.comp (restrictDegree σ ℂ p).subtype, ?_⟩ - rfl - -lemma finrank_value_range - {σ : Type*} {X : Type*} - [contextInstance2737_23 : Fintype σ] - [contextInstance2737_35 : DecidableEq σ] - [Fintype X] - (p : ℕ) (P : X → restrictDegree σ ℂ p) : - Module.finrank ℂ (LinearMap.range (valueTranspose p P)) ≤ (p+1)^Fintype.card σ := by - have hh := (valueTranspose p P).finrank_range_le - rw [Subspace.dual_finrank_eq, finrank_restrictDegree] at hh - exact hh - -end SpinAngle.PolyDimension - -namespace SpinAngle.PolynomialCarrier -open scoped Classical Matrix -open SpinAngle.Specht SpinAngle.Young PolyDimension MvPolynomial -variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) - - -def lowerCoordinate (x : Cells D → Fin q) : MvPolynomial (LowerIndex q) ℂ := - ∑ y : Cells D → Fin q, (∏ i : Cells D, lowerEntry (x i) (y i)) * C (highest D q hq y) - -lemma lowerCoordinate_degree (x : Cells D → Fin q) : - (lowerCoordinate D q hq x).totalDegree ≤ Fintype.card (Cells D) := by - apply PolyDimension.totalDegree_sum_le - intro y _ - apply (MvPolynomial.totalDegree_mul _ _).trans - rw [MvPolynomial.totalDegree_C, add_zero] - apply (MvPolynomial.totalDegree_finsetProd _ _).trans - exact (Finset.sum_le_sum fun i _ => lowerEntry_degree (x i) (y i)).trans_eq (by simp) - -def lowerCoordinateBounded (x : Cells D → Fin q) : - restrictDegree (LowerIndex q) ℂ (Fintype.card (Cells D)) := - ⟨lowerCoordinate D q hq x, - restrictTotalDegree_le_restrictDegree _ _ _ - ((mem_restrictTotalDegree _ _ _).mpr (lowerCoordinate_degree D q hq x))⟩ - -def lowerParameters (L : Matrix (Fin q) (Fin q) ℂ) (z : LowerIndex q) : ℂ := - L z.1 ⟨z.2.val, z.2.isLt.trans z.1.isLt⟩ - -lemma eval_lowerEntry (L : Matrix (Fin q) (Fin q) ℂ) (hL : DenseLU.LowerUnipotent L) - (i j : Fin q) : aeval (lowerParameters q L) (lowerEntry i j) = L i j := by - unfold lowerEntry - split_ifs with hlt heq - · simp [aeval_X, lowerParameters] - · subst j; simp [hL.2 i] - · have hij : i < j := lt_of_le_of_ne (le_of_not_gt hlt) heq - rw [map_zero, hL.1 hij] - -lemma eval_lowerCoordinate (L : Matrix (Fin q) (Fin q) ℂ) (hL : DenseLU.LowerUnipotent L) - (x : Cells D → Fin q) : - aeval (lowerParameters q L) (lowerCoordinate D q hq x) = - TensorRep.action L (highest D q hq) x := by - simp only [lowerCoordinate, map_sum, map_mul, map_prod, eval_lowerEntry q L hL] - change (∑ y : Cells D → Fin q, (∏ i, L (x i) (y i)) * - aeval (lowerParameters q L) (C (highest D q hq y))) = - ∑ y : Cells D → Fin q, (∏ i, L (x i) (y i)) * highest D q hq y - apply Finset.sum_congr rfl - intro y _ - simp - - - -theorem ordinary_finrank_le : - Module.finrank ℂ (ordinary D q hq).toSubmodule ≤ - (Fintype.card (Cells D)+1) ^ (q*(q-1)/2) := by - let P := lowerCoordinateBounded D q hq - let S := LinearMap.range (PolyDimension.valueTranspose (Fintype.card (Cells D)) P) - have hL (L : Matrix (Fin q) (Fin q) ℂ) (hL : DenseLU.LowerUnipotent L) : - TensorRep.action L (highest D q hq) ∈ S := by - have hh := PolyDimension.value_mem_range (Fintype.card (Cells D)) P (lowerParameters q L) - have he : WithLp.toLp 2 (fun x => aeval (lowerParameters q L) (P x).val) = - TensorRep.action L (highest D q hq) := by - ext x; exact eval_lowerCoordinate D q hq L hL x - rw [he] at hh - exact hh - let inc : (ordinary D q hq).toSubmodule →ₗ[ℂ] TensorSpace D q := - (alternating D q).toSubmodule.subtype.comp (ordinary D q hq).toSubmodule.subtype - have hcarrier (v : (alternating D q).toSubmodule) - (hv : v ∈ (ordinary D q hq).toSubmodule) : (v : TensorSpace D q) ∈ S := by - change v ∈ Submodule.span ℂ (Set.range fun g => - (alternating D q).toRepresentation g - (⟨highest D q hq, highest_mem D q hq⟩ : (alternating D q).toSubmodule)) at hv - induction hv using Submodule.span_induction with - | mem v hv => - obtain ⟨g,rfl⟩ := hv - exact action_highest_mem_of_lower D q hq S hL g.val - | zero => exact S.zero_mem - | add x y hx hy ihx ihy => exact S.add_mem ihx ihy - | smul a x hx ih => exact S.smul_mem a ih - have hinc (v : (ordinary D q hq).toSubmodule) : inc v ∈ S := hcarrier v.val v.property - let f : (ordinary D q hq).toSubmodule →ₗ[ℂ] S := LinearMap.codRestrict S inc hinc - have hf : Function.Injective f := by - intro x y he - apply Subtype.ext - apply Subtype.ext - exact congrArg (fun v : S => v.val) he - have hh := LinearMap.finrank_le_finrank_of_injective hf - exact hh.trans (by - simpa only [PolyDimension.card_lowerIndex] using - PolyDimension.finrank_value_range (Fintype.card (Cells D)) P) - -end SpinAngle.PolynomialCarrier - - -noncomputable section -open MeasureTheory TopologicalSpace Set -open scoped BigOperators -namespace SpinAngle.CompactTwirl - -variable {G : Type*} [contextInstance2861_21 : Group G] [contextInstance2861_31 : TopologicalSpace G] [contextInstance2861_52 : IsTopologicalGroup G] - [contextInstance2862_2 : CompactSpace G] [contextInstance2862_19 : MeasurableSpace G] [contextInstance2862_39 : BorelSpace G] - -def compactHaar : Measure G := - Measure.haarMeasure (⟨⟨Set.univ, isCompact_univ⟩, by simp⟩ : PositiveCompacts G) - -instance : IsProbabilityMeasure (compactHaar (G := G)) where - measure_univ := Measure.haarMeasure_self - -instance : (compactHaar (G := G)).IsMulLeftInvariant := - inferInstanceAs (Measure.IsMulLeftInvariant (Measure.haarMeasure _)) - -lemma continuous_integrable {A : Type*} [NormedAddCommGroup A] (f : G → A) - (hf : Continuous f) : Integrable f (compactHaar (G := G)) := - hf.integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace f) - -variable {A : Type*} [contextInstance2877_21 : NormedRing A] [contextInstance2877_36 : NormedAlgebra ℝ A] [contextInstance2877_56 : CompleteSpace A] - - -def conjugate (ρ : G →* A) (a : A) (g : G) : A := ρ g * a * ρ g⁻¹ - -def twirl (ρ : G →* A) (a : A) : A := ∫ g, conjugate ρ a g ∂compactHaar - -lemma continuous_conjugate - {G : Type*} - [contextInstance2861_21 : Group G] - [contextInstance2861_31 : TopologicalSpace G] - [contextInstance2861_52 : IsTopologicalGroup G] - [CompactSpace G] - [MeasurableSpace G] - [BorelSpace G] - {A : Type*} - [contextInstance2877_21 : NormedRing A] - [NormedAlgebra ℝ A] - [CompleteSpace A] (ρ : G →* A) (hρ : Continuous ρ) (a : A) : - Continuous (conjugate ρ a) := - (hρ.mul continuous_const).mul (hρ.comp continuous_inv) - -lemma integrable_conjugate (ρ : G →* A) (hρ : Continuous ρ) (a : A) : - Integrable (conjugate ρ a) compactHaar := - continuous_integrable _ (continuous_conjugate ρ hρ a) - -lemma conjugate_mul - {G : Type*} - [contextInstance2861_21 : Group G] - [TopologicalSpace G] - [IsTopologicalGroup G] - [CompactSpace G] - [MeasurableSpace G] - [BorelSpace G] - {A : Type*} - [contextInstance2877_21 : NormedRing A] - [NormedAlgebra ℝ A] - [CompleteSpace A] (ρ : G →* A) (a : A) (g h : G) : - conjugate ρ a (g * h) = ρ g * conjugate ρ a h * ρ g⁻¹ := by - simp only [conjugate, mul_inv_rev, map_mul, mul_assoc] - - -lemma twirl_commute (ρ : G →* A) (hρ : Continuous ρ) (a : A) (g : G) : - Commute (ρ g) (twirl ρ a) := by - have hi := integrable_conjugate ρ hρ a - have hinv : (ρ g⁻¹) * ρ g = 1 := by rw [← map_mul, inv_mul_cancel, map_one] - have he : ρ g * twirl ρ a * ρ g⁻¹ = twirl ρ a := by - rw [twirl, ← integral_const_mul_of_integrable hi] - rw [← integral_mul_const_of_integrable (hi.const_mul _)] - simp_rw [← conjugate_mul] - exact integral_mul_left_eq_self _ g - have hc := congrArg (fun x : A => x * ρ g) he - simpa only [Commute, SemiconjBy, mul_assoc, hinv, mul_one] using hc - -lemma twirl_trace (τ : A →L[ℝ] ℂ) (hτ : ∀ x y : A, τ (x * y) = τ (y * x)) - (ρ : G →* A) (hρ : Continuous ρ) (a : A) : τ (twirl ρ a) = τ a := by - rw [twirl, ← τ.integral_comp_comm (integrable_conjugate ρ hρ a)] - have he (g : G) : τ (conjugate ρ a g) = τ a := by - rw [conjugate, hτ, ← mul_assoc, ← map_mul, inv_mul_cancel, map_one, one_mul] - simp [he, integral_const, measureReal_def] - -section Positivity -variable [contextInstance2919_9 : PartialOrder A] [contextInstance2919_26 : IsOrderedAddMonoid A] [contextInstance2919_49 : StarRing A] [contextInstance2919_62 : StarOrderedRing A] - [contextInstance2920_2 : ClosedIciTopology A] [contextInstance2920_24 : IsOrderedModule ℝ A] - -lemma twirl_nonneg - {G : Type*} - [contextInstance2861_21 : Group G] - [contextInstance2861_31 : TopologicalSpace G] - [contextInstance2861_52 : IsTopologicalGroup G] - [contextInstance2862_2 : CompactSpace G] - [contextInstance2862_19 : MeasurableSpace G] - [contextInstance2862_39 : BorelSpace G] - {A : Type*} - [contextInstance2877_21 : NormedRing A] - [contextInstance2877_36 : NormedAlgebra ℝ A] - [CompleteSpace A] - [contextInstance2919_9 : PartialOrder A] - [contextInstance2919_26 : IsOrderedAddMonoid A] - [contextInstance2919_49 : StarRing A] - [contextInstance2919_62 : StarOrderedRing A] - [contextInstance2920_2 : ClosedIciTopology A] - [contextInstance2920_24 : IsOrderedModule ℝ A] (ρ : G →* A) (a : A) - (hρ : ∀ g, ρ g⁻¹ = star (ρ g)) (ha : 0 ≤ a) : 0 ≤ twirl ρ a := by - apply integral_nonneg - intro g - dsimp [conjugate] - rw [hρ] - exact star_right_conjugate_nonneg ha _ -end Positivity - -end SpinAngle.CompactTwirl - -namespace SpinAngle -open scoped Matrix.Norms.L2Operator - - -lemma unitaryGroup_compactSpace (n : Type*) [Fintype n] [DecidableEq n] [Nonempty n] : - CompactSpace (Matrix.unitaryGroup n ℂ) := by - apply isCompact_iff_compactSpace.mp - apply (isCompact_closedBall (0 : Matrix n n ℂ) 1).of_isClosed_subset isClosed_unitary - intro a ha - rw [Metric.mem_closedBall, dist_zero_right] - exact (CStarRing.norm_coe_unitary (⟨a, ha⟩ : unitary (Matrix n n ℂ))).le - -end SpinAngle - -namespace SpinAngle.CompactTwirl -variable {G : Type*} [contextInstance2949_21 : Group G] [contextInstance2949_31 : TopologicalSpace G] [contextInstance2949_52 : IsTopologicalGroup G] - [contextInstance2950_2 : CompactSpace G] [contextInstance2950_19 : MeasurableSpace G] [contextInstance2950_39 : BorelSpace G] -variable {E : Type*} [contextInstance2951_21 : NormedAddCommGroup E] [contextInstance2951_44 : InnerProductSpace ℂ E] - [contextInstance2952_2 : FiniteDimensional ℂ E] - - -def continuousAction (ρ : Representation ℂ G E) : G →* (E →L[ℂ] E) := - (Module.End.toContinuousLinearMap (𝕜 := ℂ) E).toMonoidHom.comp ρ - -@[simp] lemma continuousAction_apply - {G : Type*} - [contextInstance2949_21 : Group G] - [TopologicalSpace G] - [IsTopologicalGroup G] - [CompactSpace G] - [MeasurableSpace G] - [BorelSpace G] - {E : Type*} - [contextInstance2951_21 : NormedAddCommGroup E] - [contextInstance2951_44 : InnerProductSpace ℂ E] - [contextInstance2952_2 : FiniteDimensional ℂ E] (ρ : Representation ℂ G E) (g : G) (v : E) : - continuousAction ρ g v = ρ g v := rfl - -def operatorTrace : (E →L[ℂ] E) →L[ℂ] ℂ := - ((LinearMap.trace ℂ E).comp - (Module.End.toContinuousLinearMap (𝕜 := ℂ) E).symm.toLinearMap).toContinuousLinearMap - -@[simp] lemma operatorTrace_apply - {G : Type*} - [Group G] - [TopologicalSpace G] - [IsTopologicalGroup G] - [CompactSpace G] - [MeasurableSpace G] - [BorelSpace G] - {E : Type*} - [contextInstance2951_21 : NormedAddCommGroup E] - [contextInstance2951_44 : InnerProductSpace ℂ E] - [contextInstance2952_2 : FiniteDimensional ℂ E] (a : E →L[ℂ] E) : - operatorTrace a = LinearMap.trace ℂ E a.toLinearMap := rfl - -lemma operatorTrace_mul_comm - {G : Type*} - [Group G] - [TopologicalSpace G] - [IsTopologicalGroup G] - [CompactSpace G] - [MeasurableSpace G] - [BorelSpace G] - {E : Type*} - [contextInstance2951_21 : NormedAddCommGroup E] - [contextInstance2951_44 : InnerProductSpace ℂ E] - [FiniteDimensional ℂ E] (a b : E →L[ℂ] E) : - operatorTrace (a * b) = operatorTrace (b * a) := - LinearMap.trace_mul_comm ℂ a.toLinearMap b.toLinearMap - - - -theorem twirl_irreducible (ρ : Representation ℂ G E) [ρ.IsIrreducible] - (hρ : Continuous (continuousAction ρ)) (a : E →L[ℂ] E) : - twirl (continuousAction ρ) a = - (operatorTrace a / (Module.finrank ℂ E : ℂ)) • (1 : E →L[ℂ] E) := by - let t := twirl (continuousAction ρ) a - let f : ρ.IntertwiningMap ρ := - t.toLinearMap.intertwiningMap_of_isIntertwiningMap ρ ρ (by - intro g v - have h := twirl_commute (continuousAction ρ) hρ a g - exact (congrArg (fun L : E →L[ℂ] E => L v) h.eq).symm) - obtain ⟨z, hz⟩ := - (Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed (ρ := ρ)).surjective f - have ht : t = z • (1 : E →L[ℂ] E) := by - ext v - exact (congrArg (fun L : ρ.IntertwiningMap ρ => L v) hz).symm - have htr : operatorTrace t = operatorTrace a := - twirl_trace (operatorTrace.restrictScalars ℝ) (operatorTrace_mul_comm (G := G)) - (continuousAction ρ) hρ a - let : Nontrivial E := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) ρ.asModule - have hn : (Module.finrank ℂ E : ℂ) ≠ 0 := by - exact_mod_cast Module.finrank_pos.ne' - have hz' : z = operatorTrace a / (Module.finrank ℂ E : ℂ) := by - apply (eq_div_iff hn).mpr - rw [ht, map_smul] at htr - simpa [operatorTrace_apply (G := G), LinearMap.trace_one] using htr - simpa only [hz'] using ht - -end SpinAngle.CompactTwirl - - - -namespace SpinAngle.CompactTwirl -open scoped InnerProductSpace ComplexOrder -variable {G : Type*} [contextInstance3008_21 : Group G] [contextInstance3008_31 : TopologicalSpace G] [contextInstance3008_52 : IsTopologicalGroup G] - [contextInstance3009_2 : CompactSpace G] [contextInstance3009_19 : MeasurableSpace G] [contextInstance3009_39 : BorelSpace G] -variable {E F : Type*} [contextInstance3010_23 : NormedAddCommGroup E] [contextInstance3010_46 : InnerProductSpace ℂ E] - [contextInstance3011_2 : NormedAddCommGroup F] [contextInstance3011_25 : InnerProductSpace ℂ F] - [contextInstance3012_2 : FiniteDimensional ℂ E] [contextInstance3012_26 : FiniteDimensional ℂ F] - -lemma twirl_natural (ρ : Representation ℂ G E) (σ : Representation ℂ G F) - (hρ : Continuous (continuousAction ρ)) (hσ : Continuous (continuousAction σ)) - (a : E →L[ℂ] E) (A : F →L[ℂ] F) (L : ρ.IntertwiningMap σ) - (hnat : ∀ x, A (L x) = L (a x)) (x : E) : - twirl (continuousAction σ) A (L x) = L (twirl (continuousAction ρ) a x) := by - have hi := integrable_conjugate (continuousAction ρ) hρ a - have hI := integrable_conjugate (continuousAction σ) hσ A - rw [twirl, ContinuousLinearMap.integral_apply hI, twirl, ContinuousLinearMap.integral_apply hi] - change _ = L.toLinearMap.toContinuousLinearMap (∫ g, conjugate (continuousAction ρ) a g x ∂compactHaar) - rw [← ContinuousLinearMap.integral_comp_comm _ (hi.apply_continuousLinearMap x)] - apply integral_congr_ae - filter_upwards [] with g - change σ g (A (σ g⁻¹ (L x))) = L (ρ g (a (ρ g⁻¹ x))) - rw [← L.isIntertwining, hnat, L.isIntertwining] - -lemma continuousAction_inverse_star - {G : Type*} - [contextInstance3008_21 : Group G] - [TopologicalSpace G] - [IsTopologicalGroup G] - [CompactSpace G] - [MeasurableSpace G] - [BorelSpace G] - {E : Type*} - [contextInstance3010_23 : NormedAddCommGroup E] - [contextInstance3010_46 : InnerProductSpace ℂ E] - [contextInstance3012_2 : FiniteDimensional ℂ E] (ρ : Representation ℂ G E) - (hρ : ∀ g x y, ⟪ρ g x,ρ g y⟫_ℂ = ⟪x,y⟫_ℂ) (g : G) : - continuousAction ρ g⁻¹ = star (continuousAction ρ g) := by - ext x - apply ext_inner_left ℂ - intro y - change ⟪y,ρ g⁻¹ x⟫_ℂ = ⟪y,(continuousAction ρ g).adjoint x⟫_ℂ - rw [ContinuousLinearMap.adjoint_inner_right] - simpa only [inv_inv, continuousAction_apply] using (UnitaryNaturality.inner_move ρ hρ g⁻¹ y x) - -end SpinAngle.CompactTwirl - -namespace SpinAngle.ProjectionOrder -variable {A : Type*} [contextInstance3043_21 : CStarAlgebra A] [contextInstance3043_38 : PartialOrder A] [contextInstance3043_55 : StarOrderedRing A] - [contextInstance3044_2 : NonnegSpectrumClass ℝ A] - -lemma scalar_projection_le (T P : A) (hT : 0 ≤ T) (hP : IsStarProjection P) - (c : ℝ) (he : T * P = c • P) : c • P ≤ T := by - have hstar := congrArg star he - have hpT : P * T = c • P := by - simpa only [star_mul, hP.isSelfAdjoint.star_eq, (IsSelfAdjoint.of_nonneg hT).star_eq, - star_smul, star_trivial] using hstar - have hc : Commute (1-P) T := by - dsimp [Commute,SemiconjBy] - rw [sub_mul,mul_sub,one_mul,mul_one,hpT,he] - have hn := hc.mul_nonneg (sub_nonneg.mpr hP.le_one) hT - rw [sub_mul,one_mul,hpT] at hn - exact sub_nonneg.mp hn -end SpinAngle.ProjectionOrder - -namespace SpinAngle.CompactTwirl -open scoped InnerProductSpace ComplexOrder -variable {G : Type*} [contextInstance3062_21 : Group G] [contextInstance3062_31 : TopologicalSpace G] [contextInstance3062_52 : IsTopologicalGroup G] - [contextInstance3063_2 : CompactSpace G] [contextInstance3063_19 : MeasurableSpace G] [contextInstance3063_39 : BorelSpace G] -variable {E F : Type*} [contextInstance3064_23 : NormedAddCommGroup E] [contextInstance3064_46 : InnerProductSpace ℂ E] - [contextInstance3065_2 : NormedAddCommGroup F] [contextInstance3065_25 : InnerProductSpace ℂ F] - [contextInstance3066_2 : FiniteDimensional ℂ E] [contextInstance3066_26 : FiniteDimensional ℂ F] - -lemma isotypic_twirl_scalar (ρ : Representation ℂ G E) [ρ.IsIrreducible] - (σ : Representation ℂ G F) - (hρ : Continuous (continuousAction ρ)) (hσ : Continuous (continuousAction σ)) - (a : E →L[ℂ] E) (A : F →L[ℂ] F) - (hnat : ∀ L : ρ.IntertwiningMap σ, ∀ x, A (L x) = L (a x)) : - twirl (continuousAction σ) A * Isotypic.projection ρ σ = - (operatorTrace a / (Module.finrank ℂ E : ℂ)) • Isotypic.projection ρ σ := by - ext v - apply Isotypic.scalar_on_space ρ σ - (twirl (continuousAction σ) A).toLinearMap - (operatorTrace a / (Module.finrank ℂ E : ℂ)) - · intro L x - change twirl (continuousAction σ) A (L x) = _ - rw [twirl_natural ρ σ hρ hσ a A L (hnat L), twirl_irreducible ρ hρ a] - simp only [smul_apply, one_apply_eq_self, map_smul] - · exact (Isotypic.space ρ σ).toSubmodule.starProjection_apply_mem v - - -lemma isotypic_twirl_lower (ρ : Representation ℂ G E) [ρ.IsIrreducible] - (σ : Representation ℂ G F) - (hρ : Continuous (continuousAction ρ)) (hσ : Continuous (continuousAction σ)) - (hσunit : ∀ g x y, ⟪σ g x,σ g y⟫_ℂ = ⟪x,y⟫_ℂ) - (a : E →L[ℂ] E) (A : F →L[ℂ] F) (ha : 0 ≤ a) (hA : 0 ≤ A) - (hnat : ∀ L : ρ.IntertwiningMap σ, ∀ x, A (L x) = L (a x)) : - ((operatorTrace a).re / (Module.finrank ℂ E : ℝ)) • Isotypic.projection ρ σ ≤ - twirl (continuousAction σ) A := by - apply ProjectionOrder.scalar_projection_le _ _ - (twirl_nonneg _ A (continuousAction_inverse_star σ hσunit) hA) - (isStarProjection_starProjection (U := (Isotypic.space ρ σ).toSubmodule)) - have ht : operatorTrace a = ((operatorTrace a).re : ℂ) := - Complex.eq_re_of_ofReal_le (LinearMap.IsPositive.trace_nonneg - ((ContinuousLinearMap.nonneg_iff_isPositive).mp ha)) - have h := isotypic_twirl_scalar ρ σ hρ hσ a A hnat - rw [ht] at h - convert h using 1 <;> simp only [Isotypic.projection, - RCLike.real_smul_eq_coe_smul (K := ℂ)] - congr 1 - change (((operatorTrace a).re / (Module.finrank ℂ E : ℝ) : ℝ) : ℂ) = _ - simp only [Complex.ofReal_div, Complex.ofReal_natCast] - -end SpinAngle.CompactTwirl - - - - - - -noncomputable section -open scoped BigOperators -open Set -namespace SpinAngle.CompactMixture -variable {E : Type*} [contextInstance3119_21 : NormedAddCommGroup E] [contextInstance3119_44 : NormedSpace ℝ E] [contextInstance3119_62 : FiniteDimensional ℝ E] - -lemma convexHull_compact {s : Set E} (hs : IsCompact s) : IsCompact (convexHull ℝ s) := by - classical - let : CompactSpace s := isCompact_iff_compactSpace.mp hs - let C (k : ℕ) := (Convexity.StdSimplex ℝ (Fin k)) × (Fin k → s) - let f (k : ℕ) (v : C k) : E := ∑ i, v.1.weights i • (v.2 i).val - have hf (k : ℕ) : Continuous (f k) := by - change Continuous (fun v : (Convexity.StdSimplex ℝ (Fin k)) × (Fin k → s) => - ∑ i, v.1.weights i • (v.2 i).val) - apply continuous_finsetSum - intro i hi - exact ((Convexity.StdSimplex.continuous_weights_apply ℝ i).comp continuous_fst).smul - (continuous_subtype_val.comp ((continuous_apply i).comp continuous_snd)) - have hc : IsCompact (⋃ k : Fin (Module.finrank ℝ E + 2), Set.range (f k.val)) := - isCompact_iUnion (fun k => isCompact_range (hf k.val)) - convert hc using 1 - ext x - constructor - · intro hx - let t := Caratheodory.minCardFinsetOfMemConvexHull hx - have ht : (t : Set E) ⊆ s := Caratheodory.minCardFinsetOfMemConvexHull_subseteq hx - have hm : x ∈ convexHull ℝ (t : Set E) := Caratheodory.mem_minCardFinsetOfMemConvexHull hx - have hi : AffineIndependent ℝ ((↑) : t → E) := - Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull hx - have hn : Fintype.card t ≤ Module.finrank ℝ E + 1 := - hi.card_le_finrank_succ.trans (Nat.add_le_add_right (Submodule.finrank_le _) 1) - let k : Fin (Module.finrank ℝ E + 2) := ⟨Fintype.card t, by omega⟩ - let e := (Fintype.equivFin t).symm - obtain ⟨w,hw,hws,hxw⟩ := Finset.mem_convexHull'.mp hm - let z : Fin k.val → s := fun i => ⟨(e i).val, ht (e i).property⟩ - have hsum : ∑ i : Fin k.val, w (e i).val = 1 := by - rw [show (∑ i : Fin k.val, w (e i).val) = ∑ j : t, w j.val from - e.sum_comp (fun j : t => w j.val)] - simpa only [Finset.sum_coe_sort] using hws - let v : C k.val := (⟨Finsupp.equivFunOnFinite.symm (fun i => w (e i).val), - fun i => by simpa using hw _ (e i).property, - by simpa [Finsupp.sum_fintype] using hsum⟩, z) - apply Set.mem_iUnion.mpr - refine ⟨k,v,?_⟩ - simp only [f, v, z, Finsupp.coe_equivFunOnFinite_symm] - rw [show (∑ i : Fin k.val, w (e i).val • (e i).val) = ∑ j : t, w j.val • j.val from - e.sum_comp (fun j : t => w j.val • j.val)] - exact (Finset.sum_coe_sort t (fun j : E => w j • j)).trans hxw - · intro hx - obtain ⟨k,v,rfl⟩ := Set.mem_iUnion.mp hx - exact mem_convexHull_of_exists_fintype (fun i => v.1.weights i) (fun i => (v.2 i).val) - v.1.weights_nonneg v.1.total_of_fintype (fun i => (v.2 i).property) rfl -end SpinAngle.CompactMixture - -namespace SpinAngle.CompactTwirl -variable {G : Type*} [contextInstance3168_21 : Group G] [contextInstance3168_31 : TopologicalSpace G] [contextInstance3168_52 : IsTopologicalGroup G] - [contextInstance3169_2 : CompactSpace G] [contextInstance3169_19 : MeasurableSpace G] [contextInstance3169_39 : BorelSpace G] -variable {E : Type*} [contextInstance3170_21 : NormedAddCommGroup E] [contextInstance3170_44 : InnerProductSpace ℂ E] - [contextInstance3171_2 : FiniteDimensional ℂ E] - - - -lemma twirl_finite_mixture (ρ : Representation ℂ G E) - (hρ : Continuous (continuousAction ρ)) (a : E →L[ℂ] E) : - ∃ (ι : Type) (_ : Fintype ι) (w : ι → ℝ) (g : ι → G), - (∀ i, 0 ≤ w i) ∧ (∑ i, w i = 1) ∧ - twirl (continuousAction ρ) a = ∑ i, w i • conjugate (continuousAction ρ) a (g i) := by - let f := conjugate (continuousAction ρ) a - have hf : Continuous f := continuous_conjugate _ hρ a - have hc : IsCompact (Set.range f) := isCompact_range hf - have hm : twirl (continuousAction ρ) a ∈ convexHull ℝ (Set.range f) := - (convex_convexHull ℝ _).integral_mem (CompactMixture.convexHull_compact hc).isClosed - (Filter.Eventually.of_forall fun g => subset_convexHull ℝ _ (Set.mem_range_self g)) - (integrable_conjugate _ hρ a) - obtain ⟨ι,hι,w,z,hw,hs,hz,he⟩ := mem_convexHull_iff_exists_fintype.mp hm - let := hι - choose g hg using hz - refine ⟨ι,hι,w,g,hw,hs,?_⟩ - rw [← he] - apply Finset.sum_congr rfl - intro i _ - rw [← hg i] -end SpinAngle.CompactTwirl - -namespace SpinAngle.SignedCarrier -open scoped Classical TensorProduct BigOperators InnerProductSpace ComplexOrder Matrix.Norms.L2Operator MatrixOrder -open SpinAngle.Young SpinAngle.Specht SignedTensor -variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) - -lemma dimension_eq : dimension a b q ha hb = - Module.finrank ℂ (PolynomialCarrier.Carrier a q ha) * - Module.finrank ℂ (PolynomialCarrier.Carrier b q hb) := - Module.finrank_tensorProduct - -lemma dimension_pos : 0 < dimension a b q ha hb := by - have : Nontrivial (Carrier a b q ha hb) := IsSimpleModule.nontrivial (MonoidAlgebra ℂ (Group q)) - (rep a b q ha hb).asModule - exact Module.finrank_pos - - -theorem dimension_le : dimension a b q ha hb ≤ - (Fintype.card (Cells a) + Fintype.card (Cells b) + 1) ^ (q * (q-1)) := by - rw [dimension_eq] - let p := Fintype.card (Cells a) + Fintype.card (Cells b) + 1 - have hA : Module.finrank ℂ (PolynomialCarrier.Carrier a q ha) ≤ p ^ (q*(q-1)/2) := - (PolynomialCarrier.ordinary_finrank_le a q ha).trans (Nat.pow_le_pow_left (by dsimp [p]; omega) _) - have hB : Module.finrank ℂ (PolynomialCarrier.Carrier b q hb) ≤ p ^ (q*(q-1)/2) := - (PolynomialCarrier.ordinary_finrank_le b q hb).trans (Nat.pow_le_pow_left (by dsimp [p]; omega) _) - apply (Nat.mul_le_mul hA hB).trans - rw [← pow_add] - have he : q*(q-1)/2 + q*(q-1)/2 = q*(q-1) := by - have hh := PolyDimension.twice_card_lowerIndex q - rw [PolyDimension.card_lowerIndex] at hh - omega - rw [he] - -end SpinAngle.SignedCarrier - -namespace SpinAngle.SignedTensor -open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder -variable {q : ℕ} - -def conjugateDensity (g : Group q) (A : Mat q × Mat q) : Mat q × Mat q := - (g.1.val * A.1 * star g.1.val, g.2.val * A.2 * star g.2.val) - -lemma conjugateDensity_isEvenDensity (g : Group q) (A : Mat q × Mat q) (hA : IsEvenDensity A) : - IsEvenDensity (conjugateDensity g A) := by - refine ⟨?_, ?_, ?_⟩ - · exact Matrix.nonneg_iff_posSemidef.mp (star_right_conjugate_nonneg hA.1.nonneg g.1.val) - · exact Matrix.nonneg_iff_posSemidef.mp (star_right_conjugate_nonneg hA.2.1.nonneg g.2.val) - · change (g.1.val * A.1 * star g.1.val).trace + (g.2.val * A.2 * star g.2.val).trace = 1 - rw [Matrix.trace_mul_cycle, g.1.property.1, one_mul, - Matrix.trace_mul_cycle, g.2.property.1, one_mul] - exact hA.2.2 - -lemma block_conjugateDensity (g : Group q) (A : Mat q × Mat q) : - block (conjugateDensity g A) = (blockGroup g).val * block A * (blockGroup g⁻¹).val := by - change block (((g.1.val,g.2.val) * A) * star (g.1.val,g.2.val)) = _ - rw [map_mul, map_mul, block_star, map_inv] - rfl - -variable {τ : Type*} [contextInstance3254_21 : Fintype τ] [contextInstance3254_33 : DecidableEq τ] -lemma tensor_conjugateDensity (g : Group q) (A : Mat q × Mat q) : - LinearMap.toContinuousLinearMap (TensorRep.action (ι := τ) (block (conjugateDensity g A))) = - CompactTwirl.conjugate (CompactTwirl.continuousAction (rep (τ := τ))) - (LinearMap.toContinuousLinearMap (TensorRep.action (block A))) g := by - apply ContinuousLinearMap.ext - intro v - change TensorRep.action (block (conjugateDensity g A)) v = - TensorRep.action (blockGroup g).val (TensorRep.action (block A) - (TensorRep.action (blockGroup g⁻¹).val v)) - rw [block_conjugateDensity, map_mul, map_mul] - rfl -end SpinAngle.SignedTensor - -namespace SpinAngle.SignedTensor -open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder -variable {q : ℕ} -instance groupMeasurableSpace : MeasurableSpace (Group q) := borel _ -instance groupBorelSpace : BorelSpace (Group q) := ⟨rfl⟩ -variable [contextInstance3273_9 : Nonempty (Fin q)] -instance groupCompactSpace : CompactSpace (Group q) := by - let := unitaryGroup_compactSpace (Fin q) - infer_instance -end SpinAngle.SignedTensor - -namespace SpinAngle.SignedCarrier -open scoped Classical TensorProduct BigOperators InnerProductSpace ComplexOrder Matrix.Norms.L2Operator MatrixOrder -open SpinAngle.Young SpinAngle.Specht SignedTensor CompactTwirl -variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) -variable {τ : Type*} [contextInstance3283_21 : Fintype τ] [contextInstance3283_33 : DecidableEq τ] - -lemma projection_isStarProjection : IsStarProjection (typeProjection (τ := τ) a b q ha hb) := - isStarProjection_starProjection - -variable [contextInstance3288_9 : Nonempty (Fin q)] -lemma twirl_lower (A : Mat q × Mat q) (hA : IsEvenDensity A) : - ((LinearMap.trace ℂ (Carrier a b q ha hb) - (hermitianAction a b q ha hb A hA.1.isHermitian hA.2.1.isHermitian)).re / - (dimension a b q ha hb : ℝ)) • typeProjection (τ := τ) a b q ha hb ≤ - twirl (continuousAction (SignedTensor.rep (q := q) (τ := τ))) - (LinearMap.toContinuousLinearMap (TensorRep.action (block A))) := by - exact isotypic_twirl_lower (E := Carrier a b q ha hb) (F := Raw (q := q) (τ := τ)) - (rep a b q ha hb) SignedTensor.rep - (continuous_rep a b q ha hb) SignedTensor.continuous_rep SignedTensor.rep_unitary - (LinearMap.toContinuousLinearMap (hermitianAction a b q ha hb A hA.1.isHermitian hA.2.1.isHermitian)) - (LinearMap.toContinuousLinearMap (TensorRep.action (block A))) - ((ContinuousLinearMap.nonneg_iff_isPositive).mpr - (hermitianAction_positive a b q ha hb A hA.1 hA.2.1)) - ((ContinuousLinearMap.nonneg_iff_isPositive).mpr - (TensorRep.action_positive (block A) (block_posSemidef A hA.1 hA.2.1))) - (fun L x => (intertwiner_hermitian a b q ha hb L A hA.1.isHermitian hA.2.1.isHermitian x).symm) -end SpinAngle.SignedCarrier - -noncomputable section -namespace SpinAngle.ProjectionOrder -variable {A : Type*} [contextInstance3309_21 : CStarAlgebra A] [contextInstance3309_38 : PartialOrder A] [contextInstance3309_55 : StarOrderedRing A] - -lemma rescale_trace_lower (P B : A) (hP : 0 ≤ P) (F t d : ℝ) (hd : 0 < d) - (ht : Real.exp (-F) ≤ t) (h : (t / d) • P ≤ B) : - P ≤ (Real.exp F * d) • B := by - have hbase : (Real.exp (-F) / d) • P ≤ B := - (smul_le_smul_of_nonneg_right (div_le_div_of_nonneg_right ht hd.le) hP).trans h - have hs := smul_le_smul_of_nonneg_left hbase (mul_pos (Real.exp_pos F) hd).le - have he : (Real.exp F * d) * (Real.exp (-F) / d) = 1 := by - rw [← mul_div_assoc, mul_right_comm, mul_div_cancel_right₀ _ hd.ne', ← Real.exp_add] - simp - simpa only [smul_smul, he, one_smul] using hs -end SpinAngle.ProjectionOrder - -namespace SpinAngle.MatrixBridge -open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder -variable {n : Type*} [contextInstance3325_21 : Fintype n] [contextInstance3325_33 : DecidableEq n] -lemma inverse_mono (a b : EuclideanSpace ℂ n →L[ℂ] EuclideanSpace ℂ n) (h : a ≤ b) : - (Matrix.toEuclideanCLM (n := n) (𝕜 := ℂ)).symm a ≤ (Matrix.toEuclideanCLM (n := n) (𝕜 := ℂ)).symm b := by - apply sub_nonneg.mp - rw [← map_sub] - exact map_nonneg (Matrix.toEuclideanCLM (n := n) (𝕜 := ℂ)).symm (sub_nonneg.mpr h) -end SpinAngle.MatrixBridge - -namespace SpinAngle.SignedCarrier -open scoped Classical TensorProduct BigOperators InnerProductSpace ComplexOrder Matrix.Norms.L2Operator MatrixOrder -open SpinAngle.Young SpinAngle.Specht SignedTensor CompactTwirl -variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) -variable {τ : Type*} [contextInstance3337_21 : Fintype τ] [contextInstance3337_33 : DecidableEq τ] [contextInstance3337_49 : Nonempty (Fin q)] - - - -theorem exists_density_mixture : - ∃ (ι : Type) (_ : Fintype ι) (w : ι → ℝ) (R : ι → Mat q × Mat q), - (∀ i, 0 ≤ w i) ∧ (∑ i, w i = 1) ∧ (∀ i, IsEvenDensity (R i)) ∧ - typeProjection (τ := τ) a b q ha hb ≤ - (Real.exp (entropy a b q) * (dimension a b q ha hb : ℝ)) • - ∑ i, w i • LinearMap.toContinuousLinearMap (TensorRep.action (block (R i))) := by - obtain ⟨A,hA,htr⟩ := exists_density_trace_lower a b q ha hb - obtain ⟨ι,hι,w,g,hw,hs,he⟩ := twirl_finite_mixture - (SignedTensor.rep (q := q) (τ := τ)) SignedTensor.continuous_rep - (LinearMap.toContinuousLinearMap (TensorRep.action (block A))) - let := hι - refine ⟨ι,hι,w,fun i => conjugateDensity (g i) A,hw,hs, - fun i => conjugateDensity_isEvenDensity (g i) A hA,?_⟩ - have hh := twirl_lower (τ := τ) a b q ha hb A hA - have hbound := ProjectionOrder.rescale_trace_lower _ _ - (projection_isStarProjection (τ := τ) a b q ha hb).nonneg (entropy a b q) - _ (dimension a b q ha hb : ℝ) (by exact_mod_cast dimension_pos a b q ha hb) htr hh - rw [he] at hbound - simpa only [tensor_conjugateDensity] using hbound -end SpinAngle.SignedCarrier - -namespace SpinAngle.MatrixBridge -open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder -variable {n : Type*} [contextInstance3364_21 : Fintype n] [contextInstance3364_33 : DecidableEq n] -local notation "Φ" => (Matrix.toEuclideanCLM (n := n) (𝕜 := ℂ)) -lemma inverse_real_smul (r : ℝ) (a : EuclideanSpace ℂ n →L[ℂ] EuclideanSpace ℂ n) : - (Φ).symm (r • a) = r • (Φ).symm a := by - change (Φ).symm ((r : ℂ) • a) = (r : ℂ) • (Φ).symm a - exact map_smul (Φ).symm _ _ - -lemma forward_real_smul (r : ℝ) (a : Matrix n n ℂ) : - Φ (r • a) = r • Φ a := by - change Φ ((r : ℂ) • a) = (r : ℂ) • Φ a - exact map_smul Φ _ _ - -lemma forward_norm (a : Matrix n n ℂ) : ‖Φ a‖ = ‖a‖ := rfl - -lemma inverse_norm (a : EuclideanSpace ℂ n →L[ℂ] EuclideanSpace ℂ n) : - ‖(Φ).symm a‖ = ‖a‖ := by - rw [← forward_norm, (Φ).apply_symm_apply] - -lemma inverse_toContinuous (a : Matrix n n ℂ) : - (Φ).symm (LinearMap.toContinuousLinearMap (Matrix.toEuclideanLin a)) = a := by - exact (Φ).symm_apply_apply a -end SpinAngle.MatrixBridge - - -namespace SpinAngle.SignedCarrier -open scoped Classical TensorProduct BigOperators InnerProductSpace ComplexOrder Matrix.Norms.L2Operator MatrixOrder -open SpinAngle.Young SpinAngle.Specht SignedTensor -variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) -variable {τ : Type*} [contextInstance3392_21 : Fintype τ] [contextInstance3392_33 : DecidableEq τ] - -def matrixProjection : Matrix (τ → Spin q) (τ → Spin q) ℂ := - (Matrix.toEuclideanCLM (n := τ → Spin q) (𝕜 := ℂ)).symm (typeProjection a b q ha hb) - -lemma matrixProjection_isStarProjection : IsStarProjection (matrixProjection (τ := τ) a b q ha hb) := by - have hp := projection_isStarProjection (τ := τ) a b q ha hb - constructor - · change matrixProjection a b q ha hb * matrixProjection a b q ha hb = _ - unfold matrixProjection - rw [← map_mul, hp.isIdempotentElem.eq] - · change star (matrixProjection a b q ha hb) = _ - unfold matrixProjection - have hs := (Matrix.toEuclideanCLM (n := τ → Spin q) (𝕜 := ℂ)).symm.map_star' - (typeProjection a b q ha hb) - exact hs.symm.trans (congrArg (Matrix.toEuclideanCLM (n := τ → Spin q) (𝕜 := ℂ)).symm hp.isSelfAdjoint.star_eq) - -lemma inverse_action (A : Matrix (Spin q) (Spin q) ℂ) : - (Matrix.toEuclideanCLM (n := τ → Spin q) (𝕜 := ℂ)).symm - (LinearMap.toContinuousLinearMap (TensorRep.action A)) = TensorRep.tensor (fun _ : τ => A) := - MatrixBridge.inverse_toContinuous _ - -lemma matrix_density_upper (A : Mat q × Mat q) (hA : IsEvenDensity A) : - ‖TensorRep.tensor (fun _ : τ => block A) * matrixProjection a b q ha hb‖ ≤ - Real.exp (-entropy a b q) := by - have h := global_density_upper (τ := τ) a b q ha hb A hA - rw [← MatrixBridge.inverse_norm] at h - simpa only [map_mul, inverse_action, matrixProjection] using h - -lemma density_projection_commute (A : Mat q × Mat q) (hA : IsEvenDensity A) : - Commute (LinearMap.toContinuousLinearMap (TensorRep.action (ι := τ) (block A))) - (typeProjection a b q ha hb) := by - change _ * _ = _ * _ - apply ContinuousLinearMap.ext - intro v - exact (Isotypic.projection_commute_natural (E := Carrier a b q ha hb) (F := Raw (q := q) (τ := τ)) - (rep a b q ha hb) SignedTensor.rep - (hermitianAction a b q ha hb A hA.1.isHermitian hA.2.1.isHermitian) - (TensorRep.action (block A)) - (TensorRep.action_positive (block A) (block_posSemidef A hA.1 hA.2.1)).isSymmetric - (fun L x => (intertwiner_hermitian a b q ha hb L A hA.1.isHermitian hA.2.1.isHermitian x).symm) - v).symm - -lemma matrix_density_commute (A : Mat q × Mat q) (hA : IsEvenDensity A) : - Commute (TensorRep.tensor (fun _ : τ => block A)) (matrixProjection a b q ha hb) := by - have h := (density_projection_commute (τ := τ) a b q ha hb A hA).map - (Matrix.toEuclideanCLM (n := τ → Spin q) (𝕜 := ℂ)).symm - simpa only [inverse_action, matrixProjection] using h - -variable [contextInstance3441_9 : Nonempty (Fin q)] - - -theorem exists_matrix_density_mixture : - ∃ (ι : Type) (_ : Fintype ι) (w : ι → ℝ) (R : ι → Mat q × Mat q), - (∀ i, 0 ≤ w i) ∧ (∑ i, w i = 1) ∧ (∀ i, IsEvenDensity (R i)) ∧ - matrixProjection (τ := τ) a b q ha hb ≤ - (Real.exp (entropy a b q) * (dimension a b q ha hb : ℝ)) • - ∑ i, w i • TensorRep.tensor (fun _ : τ => block (R i)) := by - obtain ⟨ι,hι,w,R,hw,hs,hR,hdom⟩ := exists_density_mixture (τ := τ) a b q ha hb - let := hι - refine ⟨ι,hι,w,R,hw,hs,hR,?_⟩ - have h := MatrixBridge.inverse_mono _ _ hdom - simpa only [MatrixBridge.inverse_real_smul, map_sum, inverse_action, matrixProjection] using h -end SpinAngle.SignedCarrier - -namespace SpinAngle.SignedTensor -open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder -variable {q : ℕ} -lemma block_add (A B : Mat q × Mat q) : block (A+B) = block A + block B := by - ext i j - rcases i with ⟨i,bi⟩; rcases j with ⟨j,bj⟩ - cases bi <;> cases bj <;> simp [block, Matrix.blockDiagonal_apply] - -lemma block_real_smul (r : ℝ) (A : Mat q × Mat q) : block (r • A) = r • block A := by - ext i j - rcases i with ⟨i,bi⟩; rcases j with ⟨j,bj⟩ - cases bi <;> cases bj <;> simp [block, Matrix.blockDiagonal_apply] - -lemma block_zero : block (0 : Mat q × Mat q) = 0 := by - ext i j - rcases i with ⟨i,bi⟩; rcases j with ⟨j,bj⟩ - cases bi <;> cases bj <;> simp [block, Matrix.blockDiagonal_apply] - -lemma block_sum {ι : Type*} (s : Finset ι) (A : ι → Mat q × Mat q) : - block (∑ i ∈ s, A i) = ∑ i ∈ s, block (A i) := by - classical - induction s using Finset.induction_on with - | empty => simp [block_zero] - | insert i s hi ih => simp only [Finset.sum_insert hi, block_add, ih] - -lemma block_trace (A : Mat q × Mat q) : (block A).trace = A.1.trace + A.2.trace := by - change (Matrix.blockDiagonal (fun b : Bool => cond b A.2 A.1)).trace = _ - rw [Matrix.trace_blockDiagonal] - simp [add_comm] - -variable {J : Type*} [contextInstance3487_21 : Fintype J] - -def evenAverage (A : J → Mat q × Mat q) : Mat q × Mat q := - (Fintype.card J : ℝ)⁻¹ • ∑ j, A j - -lemma evenAverage_isEvenDensity [Nonempty J] (A : J → Mat q × Mat q) - (hA : ∀ j, IsEvenDensity (A j)) : IsEvenDensity (evenAverage A) := by - have hpos : 0 < (Fintype.card J : ℝ) := by exact_mod_cast Fintype.card_pos - have he (A : Mat q × Mat q) : A.1.trace + A.2.trace = (block A).trace := (block_trace A).symm - refine ⟨?_,?_,?_⟩ - · apply Matrix.nonneg_iff_posSemidef.mp - simp only [evenAverage, Prod.smul_fst, Prod.fst_sum] - exact smul_nonneg (inv_nonneg.mpr hpos.le) (Finset.sum_nonneg fun j _ => (hA j).1.nonneg) - · apply Matrix.nonneg_iff_posSemidef.mp - simp only [evenAverage, Prod.smul_snd, Prod.snd_sum] - exact smul_nonneg (inv_nonneg.mpr hpos.le) (Finset.sum_nonneg fun j _ => (hA j).2.1.nonneg) - · rw [he] - unfold evenAverage - rw [block_real_smul, block_sum, Matrix.trace_smul, Matrix.trace_sum] - simp only [block_trace, (hA _).2.2, Finset.sum_const, Finset.card_univ, nsmul_eq_mul, mul_one] - rw [RCLike.real_smul_eq_coe_smul (K := ℂ), smul_eq_mul] - norm_cast - exact inv_mul_cancel₀ (by exact_mod_cast hpos.ne') -end SpinAngle.SignedTensor - - - - - - -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder - -namespace SpinAngle.MatrixAnalysis -variable {n : Type*} [contextInstance3521_21 : Fintype n] [contextInstance3521_33 : DecidableEq n] -abbrev Mat (n : Type*) := Matrix n n ℂ - - -def root (a : Mat n) : Mat n := cfc Real.sqrt a - -def invRoot (a : Mat n) : Mat n := cfc (fun x : ℝ => (Real.sqrt x)⁻¹) a - -def support (a : Mat n) : Mat n := cfc (fun x : ℝ => if x = 0 then 0 else 1) a - -lemma root_selfAdjoint (a : Mat n) : IsSelfAdjoint (root a) := - cfc_predicate _ _ -lemma root_nonneg (a : Mat n) : 0 ≤ root a := - cfc_nonneg fun _ _ => Real.sqrt_nonneg _ -lemma invRoot_selfAdjoint (a : Mat n) : IsSelfAdjoint (invRoot a) := - cfc_predicate _ _ -lemma invRoot_nonneg (a : Mat n) : 0 ≤ invRoot a := - cfc_nonneg fun _ _ => inv_nonneg.mpr (Real.sqrt_nonneg _) -lemma support_selfAdjoint (a : Mat n) : IsSelfAdjoint (support a) := - cfc_predicate _ _ - -lemma root_mul_self (a : Mat n) (ha : 0 ≤ a) : root a * root a = a := by - rw [root, ← cfc_mul _ _ _ (Matrix.finite_real_spectrum (A := a) |>.continuousOn _) - (Matrix.finite_real_spectrum (A := a) |>.continuousOn _)] - calc - _ = cfc (fun x : ℝ => x) a := by - apply cfc_congr - intro x hx - exact Real.mul_self_sqrt (spectrum_nonneg_of_nonneg ha hx) - _ = a := cfc_id' ℝ (ha := .of_nonneg ha) - -lemma invRoot_mul_root (a : Mat n) (ha : 0 ≤ a) : - invRoot a * root a = support a := by - rw [invRoot, root, ← cfc_mul _ _ _ (Matrix.finite_real_spectrum (A := a) |>.continuousOn _) - (Matrix.finite_real_spectrum (A := a) |>.continuousOn _)] - apply cfc_congr - intro x hx - by_cases hx0 : x = 0 - · simp [hx0] - · have hs : Real.sqrt x ≠ 0 := ne_of_gt (Real.sqrt_pos.mpr - (lt_of_le_of_ne (spectrum_nonneg_of_nonneg ha hx) (Ne.symm hx0))) - simp [hx0, hs] - -lemma support_isStarProjection (a : Mat n) : IsStarProjection (support a) := by - refine ⟨?_, support_selfAdjoint a⟩ - change support a * support a = support a - rw [support, ← cfc_mul _ _ _ (Matrix.finite_real_spectrum (A := a) |>.continuousOn _) - (Matrix.finite_real_spectrum (A := a) |>.continuousOn _)] - apply cfc_congr - intro x _ - dsimp only - split_ifs <;> norm_num - -lemma mul_support (a : Mat n) (ha : 0 ≤ a) : a * support a = a := by - conv_lhs => lhs; rw [← cfc_id' ℝ (a := a)] - rw [support, ← cfc_mul _ _ _ (Matrix.finite_real_spectrum (A := a) |>.continuousOn _) - (Matrix.finite_real_spectrum (A := a) |>.continuousOn _)] - calc - _ = cfc (fun x : ℝ => x) a := by - apply cfc_congr - intro x _ - by_cases hx : x = 0 <;> simp [hx] - _ = a := cfc_id' ℝ (ha := .of_nonneg ha) - -lemma root_mul_support (a : Mat n) : root a * support a = root a := by - rw [root, support, ← cfc_mul _ _ _ (Matrix.finite_real_spectrum (A := a) |>.continuousOn _) - (Matrix.finite_real_spectrum (A := a) |>.continuousOn _)] - apply cfc_congr - intro x _ - by_cases hx : x = 0 <;> simp [hx] - -lemma root_commute {a b : Mat n} (h : Commute a b) : Commute (root a) b := - h.cfc_real _ -lemma invRoot_commute {a b : Mat n} (h : Commute a b) : Commute (invRoot a) b := - h.cfc_real _ -lemma support_commute {a b : Mat n} (h : Commute a b) : Commute (support a) b := - h.cfc_real _ - - - -lemma norm_le_re_trace (a : Mat n) (ha : 0 ≤ a) : ‖a‖ ≤ (Matrix.trace a).re := by - have hA := Matrix.nonneg_iff_posSemidef.mp ha - rw [hA.isHermitian.trace_eq_sum_eigenvalues, Complex.re_sum] - conv_lhs => rw [hA.isHermitian.spectral_theorem] - simp only [Unitary.conjStarAlgAut_apply, ← Unitary.coe_star, - CStarRing.norm_mul_coe_unitary, CStarRing.norm_coe_unitary_mul, - Matrix.l2_opNorm_diagonal] - apply (pi_norm_le_iff_of_nonneg (by - exact Finset.sum_nonneg fun i _ => hA.eigenvalues_nonneg i)).mpr - intro i - simp only [Function.comp_apply, RCLike.norm_ofReal, - abs_of_nonneg (hA.eigenvalues_nonneg i)] - exact Finset.single_le_sum (fun j _ => hA.eigenvalues_nonneg j) (Finset.mem_univ i) - -lemma norm_sq_le_re_trace_star_mul_self (a : Mat n) : - ‖a‖ ^ 2 ≤ (Matrix.trace (star a * a)).re := by - rw [sq, ← CStarRing.norm_star_mul_self] - exact norm_le_re_trace _ (star_mul_self_nonneg _) - - - -lemma root_mul_support_of_le_smul (a b : Mat n) (ha : 0 ≤ a) (hb : 0 ≤ b) - (c : ℝ) (hba : b ≤ c • a) : root b * support a = root b := by - let e := 1 - support a - have he : IsStarProjection e := (support_isStarProjection a).one_sub - have hae : a * e = 0 := by - dsimp [e] - rw [mul_sub, mul_one, mul_support a ha, sub_self] - have hupper : star e * b * e ≤ 0 := by - have hc := star_left_conjugate_le_conjugate hba e - simpa only [mul_smul_comm, smul_mul_assoc, mul_assoc, hae, mul_zero, smul_zero] using hc - have hzero : star e * b * e = 0 := - le_antisymm hupper (star_left_conjugate_nonneg hb e) - have hrootzero : star (root b * e) * (root b * e) = 0 := by - rw [star_mul, (root_selfAdjoint b).star_eq] - calc - (star e * root b) * (root b * e) = star e * (root b * root b) * e := by - simp only [mul_assoc] - _ = 0 := by rw [root_mul_self b hb, hzero] - have h := (CStarRing.star_mul_self_eq_zero_iff _).mp hrootzero - dsimp [e] at h - rw [mul_sub, mul_one] at h - exact (sub_eq_zero.mp h).symm - -lemma invRoot_mul_self_mul_invRoot (a : Mat n) (ha : 0 ≤ a) : - invRoot a * a * invRoot a = support a := by - have hc : Commute (invRoot a) a := invRoot_commute (Commute.refl a) - have hr : Commute (root a) (invRoot a) := root_commute hc.symm - calc - invRoot a * a * invRoot a = invRoot a * (root a * root a) * invRoot a := - congrArg (fun x => invRoot a * x * invRoot a) (root_mul_self a ha).symm - _ = (invRoot a * root a) * (root a * invRoot a) := by simp only [mul_assoc] - _ = support a * support a := by rw [hr.eq, invRoot_mul_root a ha] - _ = support a := (support_isStarProjection a).isIdempotentElem.eq - -lemma cell_trace_identity (a b c : Mat n) (ha : 0 ≤ a) (hc : 0 ≤ c) : - (star (root a * invRoot b * root c) * (root a * invRoot b * root c)).trace = - (invRoot b * a * invRoot b * c).trace := by - have he : star (root a * invRoot b * root c) * (root a * invRoot b * root c) = - root c * (invRoot b * a * invRoot b) * root c := by - simp only [star_mul, (root_selfAdjoint a).star_eq, - (root_selfAdjoint c).star_eq, (invRoot_selfAdjoint b).star_eq] - calc - root c * (invRoot b * root a) * (root a * invRoot b * root c) = - root c * (invRoot b * (root a * root a) * invRoot b) * root c := by - simp only [mul_assoc] - _ = _ := by rw [root_mul_self a ha] - rw [he, Matrix.trace_mul_comm (root c * (invRoot b * a * invRoot b)) (root c)] - rw [← mul_assoc, root_mul_self c hc, Matrix.trace_mul_comm c] - -lemma cell_trace_nonneg (a b c : Mat n) (ha : 0 ≤ a) (hc : 0 ≤ c) : - 0 ≤ (invRoot b * a * invRoot b * c).trace := by - rw [← cell_trace_identity a b c ha hc] - exact (Matrix.nonneg_iff_posSemidef.mp (star_mul_self_nonneg _)).trace_nonneg - - -lemma re_trace_nonneg - {n : Type*} - [contextInstance3521_21 : Fintype n] - [DecidableEq n] (a : Mat n) (ha : 0 ≤ a) : 0 ≤ a.trace.re := - (Complex.nonneg_iff.mp ((Matrix.nonneg_iff_posSemidef.mp ha).trace_nonneg)).1 - -lemma re_trace_mono {a b : Mat n} (hab : a ≤ b) : a.trace.re ≤ b.trace.re := by - have h := re_trace_nonneg (b - a) (sub_nonneg.mpr hab) - simpa only [Matrix.trace_sub, Complex.sub_re, sub_nonneg] using h - - - -lemma re_trace_projection_mul_le (q b : Mat n) (hq : IsStarProjection q) (hb : 0 ≤ b) : - (q * b).trace.re ≤ b.trace.re := by - have h := re_trace_mono (star_left_conjugate_le_conjugate hq.le_one (root b)) - rw [mul_one, (root_selfAdjoint b).star_eq, root_mul_self b hb] at h - rw [Matrix.trace_mul_comm (root b * q) (root b), ← mul_assoc, - root_mul_self b hb, Matrix.trace_mul_comm b q] at h - exact h - - -lemma cell_norm_sq_le_trace (a b c : Mat n) (ha : 0 ≤ a) (hc : 0 ≤ c) : - ‖root a * invRoot b * root c‖ ^ 2 ≤ - (invRoot b * a * invRoot b * c).trace.re := by - have h := norm_sq_le_re_trace_star_mul_self (root a * invRoot b * root c) - rw [cell_trace_identity a b c ha hc] at h - exact h - -end SpinAngle.MatrixAnalysis - -namespace SpinAngle.TensorMatrix -open SpinAngle.MatrixAnalysis -variable {ι n : Type*} [contextInstance3707_23 : Fintype ι] [contextInstance3707_35 : DecidableEq ι] [contextInstance3707_51 : Fintype n] [contextInstance3707_63 : DecidableEq n] - - -def tensor (a : ι → Mat n) : Mat (ι → n) := fun x y => ∏ i, a i (x i) (y i) - -lemma tensor_star - {ι : Type*} {n : Type*} - [contextInstance3707_23 : Fintype ι] - [DecidableEq ι] - [Fintype n] - [DecidableEq n] (a : ι → Mat n) : - tensor (fun i => star (a i)) = star (tensor a) := by - ext x y - simp [tensor, Matrix.star_apply] - -lemma tensor_mul - {ι : Type*} {n : Type*} - [contextInstance3707_23 : Fintype ι] - [contextInstance3707_35 : DecidableEq ι] - [contextInstance3707_51 : Fintype n] - [DecidableEq n] (a b : ι → Mat n) : - tensor (fun i => a i * b i) = tensor a * tensor b := by - ext x y - simp only [tensor, Matrix.mul_apply, ← Finset.prod_mul_distrib] - symm - simpa using (Finset.sum_prod_piFinset (ι := ι) Finset.univ - (fun i j => a i (x i) j * b i j (y i))) - -lemma tensor_one - {ι : Type*} {n : Type*} - [contextInstance3707_23 : Fintype ι] - [DecidableEq ι] - [Fintype n] - [contextInstance3707_63 : DecidableEq n] : tensor (fun _ : ι => (1 : Mat n)) = 1 := by - ext x y - classical - by_cases h : x = y - · subst y - simp [tensor] - · have hxy : ∃ i, x i ≠ y i := Function.ne_iff.mp h - obtain ⟨i, hi⟩ := hxy - simp only [tensor, Matrix.one_apply, ite_eq_right h] - apply Finset.prod_eq_zero (Finset.mem_univ i) - simp [hi] - -lemma tensor_trace - {ι : Type*} {n : Type*} - [contextInstance3707_23 : Fintype ι] - [contextInstance3707_35 : DecidableEq ι] - [contextInstance3707_51 : Fintype n] - [DecidableEq n] (a : ι → Mat n) : - (tensor a).trace = ∏ i, (a i).trace := by - simp only [Matrix.trace, Matrix.diag, tensor] - simpa using (Finset.sum_prod_piFinset (ι := ι) Finset.univ - (fun i j => a i j j)) - -lemma tensor_nonneg (a : ι → Mat n) (ha : ∀ i, 0 ≤ a i) : - 0 ≤ tensor a := by - have hr : tensor a = star (tensor (fun i => root (a i))) * tensor (fun i => root (a i)) := by - rw [← tensor_star, ← tensor_mul] - congr 1 - funext i - rw [(root_selfAdjoint (a i)).star_eq, root_mul_self _ (ha i)] - rw [hr] - exact star_mul_self_nonneg _ - -lemma tensor_selfAdjoint (a : ι → Mat n) (ha : ∀ i, IsSelfAdjoint (a i)) : - IsSelfAdjoint (tensor a) := by - change star (tensor a) = tensor a - rw [← tensor_star] - congr 1 - funext i - exact (ha i).star_eq - -lemma tensor_norm_sq_le_trace_product (a : ι → Mat n) : - ‖tensor a‖ ^ 2 ≤ (∏ i, (star (a i) * a i).trace).re := by - have h := norm_sq_le_re_trace_star_mul_self (tensor a) - rw [← tensor_star, ← tensor_mul, tensor_trace] at h - exact h - -lemma tensor_norm_sq_le_re_trace_product (a : ι → Mat n) : - ‖tensor a‖ ^ 2 ≤ ∏ i, (star (a i) * a i).trace.re := by - have hreal (i : ι) : (star (a i) * a i).trace = ((star (a i) * a i).trace.re : ℂ) := - Complex.eq_re_of_ofReal_le (r := 0) - (by exact (Matrix.nonneg_iff_posSemidef.mp (star_mul_self_nonneg _)).trace_nonneg) - calc - _ ≤ (∏ i, (star (a i) * a i).trace).re := tensor_norm_sq_le_trace_product a - _ = (∏ i, ((star (a i) * a i).trace.re : ℂ)).re := - congrArg Complex.re (Finset.prod_congr rfl fun i _ => hreal i) - _ = _ := by rw [← Complex.ofReal_prod, Complex.ofReal_re] - -lemma tensor_cell_norm_sq_le_product (a b c : ι → Mat n) - (ha : ∀ i, 0 ≤ a i) (hc : ∀ i, 0 ≤ c i) : - ‖tensor (fun i => root (a i) * invRoot (b i) * root (c i))‖ ^ 2 ≤ - ∏ i, (invRoot (b i) * a i * invRoot (b i) * c i).trace.re := by - have h := tensor_norm_sq_le_re_trace_product (fun i => root (a i) * invRoot (b i) * root (c i)) - simpa only [cell_trace_identity _ _ _ (ha _) (hc _)] using h - -end SpinAngle.TensorMatrix - - - - -noncomputable section -open scoped BigOperators -namespace SpinAngle - -def missingCellFactor (m b : ℕ) : ℝ := - if b < m then ((m : ℝ) / (m - b : ℕ)) ^ (m - b) else 1 - -def missingCellProductFactor {ι : Type*} [Fintype ι] (m : ℕ) (b : ι → ℕ) : ℝ := - ∏ i, missingCellFactor m (b i) - -lemma missingCellFactor_nonneg (m b : ℕ) : 0 ≤ missingCellFactor m b := by - unfold missingCellFactor - split_ifs <;> positivity - -lemma missingCellFactor_le_exp (m b : ℕ) (hb : b ≤ m) : - missingCellFactor m b ≤ Real.exp b := by - unfold missingCellFactor - split_ifs with h - · have hk : 0 < m - b := Nat.sub_pos_of_lt h - have hkR : (0 : ℝ) < (m - b : ℕ) := by exact_mod_cast hk - have hmR : 0 < (m : ℝ) := by exact_mod_cast (lt_of_le_of_lt (Nat.zero_le b) h) - have hratio : 0 < (m : ℝ) / (m - b : ℕ) := div_pos hmR hkR - apply (Real.log_le_iff_le_exp (pow_pos hratio _)).mp - rw [Real.log_pow] - calc - (m - b : ℕ) * Real.log ((m : ℝ) / (m - b : ℕ)) - ≤ (m - b : ℕ) * ((m : ℝ) / (m - b : ℕ) - 1) := - mul_le_mul_of_nonneg_left (Real.log_le_sub_one_of_pos hratio) hkR.le - _ = (b : ℝ) := by - rw [mul_sub, mul_div_cancel₀ _ hkR.ne', mul_one, Nat.cast_sub hb] - ring - · exact Real.one_le_exp (Nat.cast_nonneg b) - -theorem missingCellProduct {ι : Type*} [Fintype ι] - (m : ℕ) (b : ι → ℕ) (hb : ∀ i, b i ≤ m) : - missingCellProductFactor m b ≤ Real.exp (∑ i, (b i : ℝ)) := by - unfold missingCellProductFactor - calc - ∏ i, missingCellFactor m (b i) ≤ ∏ i, Real.exp (b i : ℝ) := - Finset.prod_le_prod₀ (fun i _ => missingCellFactor_nonneg m (b i)) - (fun i _ => missingCellFactor_le_exp m (b i) (hb i)) - _ = Real.exp (∑ i, (b i : ℝ)) := (Real.exp_sum _ _).symm - -end SpinAngle - -namespace SpinAngle -open scoped BigOperators -variable {ι : Type*} [contextInstance3841_21 : Fintype ι] [contextInstance3841_33 : DecidableEq ι] - - -lemma retained_product_le - {ι : Type*} - [contextInstance3841_21 : Fintype ι] - [DecidableEq ι] (t : Finset ι) (z : ι → ℝ) - (hz : ∀ i, 0 ≤ z i) (hs : ∑ i, z i ≤ Fintype.card ι) : - ∏ i ∈ t, z i ≤ ((Fintype.card ι : ℝ) / t.card) ^ t.card := by - by_cases ht : t.Nonempty - · have hkR : 0 < (t.card : ℝ) := by exact_mod_cast ht.card_pos - have hmR : 0 < (Fintype.card ι : ℝ) := - hkR.trans_le (by exact_mod_cast Finset.card_le_univ t) - let c : ℝ := Fintype.card ι / t.card - have hc : 0 < c := div_pos hmR hkR - have hsum : ∑ i ∈ t, z i ≤ Fintype.card ι := - (Finset.sum_le_sum_of_subset_of_nonneg (Finset.subset_univ _) (by - intro i _ _; exact hz i)).trans hs - have hnorm : ∑ i ∈ t, z i / c ≤ t.card := by - rw [← Finset.sum_div] - apply (div_le_iff₀ hc).mpr - dsimp [c] - rwa [mul_div_cancel₀ _ hkR.ne'] - have hn : ∏ i ∈ t, z i / c ≤ 1 := calc - _ ≤ ∏ i ∈ t, Real.exp (z i / c - 1) := - Finset.prod_le_prod₀ (fun i _ => div_nonneg (hz i) hc.le) fun i _ => by - have h := Real.add_one_le_exp (z i / c - 1) - linarith - _ = Real.exp (∑ i ∈ t, (z i / c - 1)) := (Real.exp_sum _ _).symm - _ ≤ Real.exp 0 := by - apply Real.exp_le_exp.mpr - rw [Finset.sum_sub_distrib] - simpa using sub_nonpos.mpr hnorm - _ = 1 := Real.exp_zero - rw [Finset.prod_div_distrib, Finset.prod_const] at hn - exact (div_le_one (pow_pos hc _)).mp hn - · have he : t = ∅ := Finset.not_nonempty_iff_eq_empty.mp ht - simp [he] - -variable {R C : Type*} [contextInstance3877_23 : Fintype R] [contextInstance3877_35 : DecidableEq R] [contextInstance3877_51 : Fintype C] [contextInstance3877_63 : DecidableEq C] - - -def occupiedRow (W : Finset (R × C)) (i : R) : Finset C := - Finset.univ.filter (fun j => (i, j) ∈ W) - -def missingInRow (W : Finset (R × C)) (i : R) : ℕ := - Fintype.card C - (occupiedRow W i).card - -lemma occupiedRow_card_le - {R : Type*} {C : Type*} - [Fintype R] - [contextInstance3877_35 : DecidableEq R] - [contextInstance3877_51 : Fintype C] - [contextInstance3877_63 : DecidableEq C] (W : Finset (R × C)) (i : R) : - (occupiedRow W i).card ≤ Fintype.card C := Finset.card_le_univ _ - -lemma missingInRow_le - {R : Type*} {C : Type*} - [Fintype R] - [contextInstance3877_35 : DecidableEq R] - [contextInstance3877_51 : Fintype C] - [contextInstance3877_63 : DecidableEq C] (W : Finset (R × C)) (i : R) : - missingInRow W i ≤ Fintype.card C := Nat.sub_le _ _ - -lemma retained_factor_eq_missingCellFactor (W : Finset (R × C)) (i : R) : - ((Fintype.card C : ℝ) / (occupiedRow W i).card) ^ (occupiedRow W i).card = - missingCellFactor (Fintype.card C) (missingInRow W i) := by - have hc := occupiedRow_card_le W i - unfold missingInRow missingCellFactor - rw [Nat.sub_sub_self hc] - split_ifs with h - · rfl - · have hk : (occupiedRow W i).card = 0 := by omega - simp [hk] - -lemma prod_occupiedRow - {ι : Type*} - [Fintype ι] - [DecidableEq ι] - {R : Type*} {C : Type*} - [contextInstance3877_23 : Fintype R] - [contextInstance3877_35 : DecidableEq R] - [contextInstance3877_51 : Fintype C] - [contextInstance3877_63 : DecidableEq C] (W : Finset (R × C)) (z : R → C → ℝ) : - (∏ i, ∏ j ∈ occupiedRow W i, z i j) = ∏ x ∈ W, z x.1 x.2 := by - simp only [occupiedRow, Finset.prod_filter] - rw [← Finset.prod_product (f := fun x : R × C => if x ∈ W then z x.1 x.2 else 1)] - simp only [Finset.univ_product_univ, ← Finset.prod_filter] - congr 1 - ext x - simp - - -lemma board_product_le (W : Finset (R × C)) (z : R → C → ℝ) - (hz : ∀ i j, 0 ≤ z i j) (hs : ∀ i, ∑ j, z i j ≤ Fintype.card C) : - (∏ x ∈ W, z x.1 x.2) ≤ - missingCellProductFactor (Fintype.card C) (missingInRow W) := by - rw [← prod_occupiedRow (ι := R) W z] - unfold missingCellProductFactor - apply Finset.prod_le_prod₀ - · intro i _ - exact Finset.prod_nonneg fun j _ => hz i j - · intro i _ - rw [← retained_factor_eq_missingCellFactor] - exact retained_product_le (occupiedRow W i) (z i) (hz i) (hs i) - -end SpinAngle - -namespace SpinAngle.MatrixAnalysis -variable {n C : Type*} [contextInstance3931_23 : Fintype n] [contextInstance3931_35 : DecidableEq n] [contextInstance3931_51 : Fintype C] [contextInstance3931_63 : DecidableEq C] - - -structure Density (n : Type*) [Fintype n] [DecidableEq n] where - matrix : Mat n - nonneg : 0 ≤ matrix - trace_eq_one : matrix.trace = 1 - -instance : Coe (Density n) (Mat n) := ⟨Density.matrix⟩ - -def average (r : C → Density n) : Mat n := - (Fintype.card C : ℝ)⁻¹ • ∑ j, (r j).matrix - -lemma average_nonneg - {n : Type*} {C : Type*} - [contextInstance3931_23 : Fintype n] - [contextInstance3931_35 : DecidableEq n] - [contextInstance3931_51 : Fintype C] - [DecidableEq C] (r : C → Density n) : 0 ≤ average r := - smul_nonneg (inv_nonneg.mpr (Nat.cast_nonneg _)) (Finset.sum_nonneg fun j _ => (r j).nonneg) - -lemma sum_eq_smul_average - {n : Type*} {C : Type*} - [contextInstance3931_23 : Fintype n] - [contextInstance3931_35 : DecidableEq n] - [contextInstance3931_51 : Fintype C] - [DecidableEq C] [Nonempty C] (r : C → Density n) : - (∑ j, (r j).matrix) = (Fintype.card C : ℝ) • average r := by - unfold average - rw [smul_smul, mul_inv_cancel₀ (by exact_mod_cast Fintype.card_ne_zero (α := C)), one_smul] - -lemma le_smul_average [Nonempty C] (r : C → Density n) (j : C) : - (r j).matrix ≤ (Fintype.card C : ℝ) • average r := by - rw [← sum_eq_smul_average] - exact Finset.single_le_sum (fun k _ => (r k).nonneg) (Finset.mem_univ j) - -lemma support_cell_trace_sum [Nonempty C] (r : C → Density n) (s : Density n) : - ∑ j, (invRoot (average r) * (r j).matrix * invRoot (average r) * s.matrix).trace.re ≤ - Fintype.card C := by - have he : (∑ j, invRoot (average r) * (r j).matrix * invRoot (average r) * s.matrix) = - (Fintype.card C : ℝ) • (support (average r) * s.matrix) := by - rw [← Finset.sum_mul, ← Finset.sum_mul, ← Finset.mul_sum, - sum_eq_smul_average r, mul_smul_comm, smul_mul_assoc, smul_mul_assoc, - invRoot_mul_self_mul_invRoot _ (average_nonneg r)] - have ht := congrArg (fun a : Mat n => a.trace.re) he - simp only [Matrix.trace_sum, Complex.re_sum, Matrix.trace_smul, Complex.smul_re, smul_eq_mul] at ht - rw [ht] - have h := re_trace_projection_mul_le (support (average r)) s.matrix - (support_isStarProjection _) s.nonneg - rw [s.trace_eq_one, Complex.one_re] at h - simpa using mul_le_mul_of_nonneg_left h (Nat.cast_nonneg (Fintype.card C)) - -end SpinAngle.MatrixAnalysis - -namespace SpinAngle -open MatrixAnalysis TensorMatrix -variable {n R C : Type*} [contextInstance3979_25 : Fintype n] [contextInstance3979_37 : DecidableEq n] - [contextInstance3980_2 : Fintype R] [contextInstance3980_14 : DecidableEq R] [contextInstance3980_30 : Fintype C] [contextInstance3980_42 : DecidableEq C] [contextInstance3980_58 : Nonempty C] - - - -theorem normalized_board_bound (W : Finset (R × C)) - (r : C → Density n) (s : R → Density n) : - ‖tensor (fun w : W => root (r w.val.2).matrix * - invRoot (average r) * root (s w.val.1).matrix)‖ ^ 2 ≤ - missingCellProductFactor (Fintype.card C) (missingInRow W) := by - let z : R → C → ℝ := fun i j => - (invRoot (average r) * (r j).matrix * invRoot (average r) * (s i).matrix).trace.re - have hz : ∀ i j, 0 ≤ z i j := fun i j => - (Complex.nonneg_iff.mp (cell_trace_nonneg _ _ _ (r j).nonneg (s i).nonneg)).1 - have hs : ∀ i, ∑ j, z i j ≤ Fintype.card C := fun i => support_cell_trace_sum r (s i) - calc - _ ≤ ∏ w : W, z w.val.1 w.val.2 := - tensor_cell_norm_sq_le_product _ _ _ (fun w => (r w.val.2).nonneg) - (fun w => (s w.val.1).nonneg) - _ = ∏ w ∈ W, z w.1 w.2 := - (Finset.prod_subtype W (by intro w; rfl) (fun w => z w.1 w.2)).symm - _ ≤ _ := board_product_le W z hz hs - -end SpinAngle - - - - - - -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder -namespace SpinAngle.DependentTensor -variable {ι : Type*} [contextInstance4012_21 : Fintype ι] [contextInstance4012_33 : DecidableEq ι] -variable {ν : ι → Type*} [contextInstance4013_25 : ∀ i, Fintype (ν i)] [contextInstance4013_46 : ∀ i, DecidableEq (ν i)] - -abbrev Mat (n : Type*) := Matrix n n ℂ - -def tensor (A : ∀ i, Mat (ν i)) : Mat (∀ i, ν i) := fun x y => ∏ i, A i (x i) (y i) - -lemma tensor_star - {ι : Type*} - [contextInstance4012_21 : Fintype ι] - [DecidableEq ι] - {ν : ι → Type*} - [∀ i, Fintype (ν i)] - [∀ i, DecidableEq (ν i)] (A : ∀ i, Mat (ν i)) : tensor (fun i => star (A i)) = star (tensor A) := by - ext x y - simp [tensor, Matrix.star_apply] - -lemma tensor_mul - {ι : Type*} - [contextInstance4012_21 : Fintype ι] - [contextInstance4012_33 : DecidableEq ι] - {ν : ι → Type*} - [contextInstance4013_25 : ∀ i, Fintype (ν i)] - [∀ i, DecidableEq (ν i)] (A B : ∀ i, Mat (ν i)) : tensor (fun i => A i * B i) = tensor A * tensor B := by - ext x y - simp only [tensor, Matrix.mul_apply, ← Finset.prod_mul_distrib] - exact (Fintype.prod_sum (fun i (j : ν i) => A i (x i) j * B i j (y i))) - -lemma tensor_one - {ι : Type*} - [contextInstance4012_21 : Fintype ι] - [DecidableEq ι] - {ν : ι → Type*} - [∀ i, Fintype (ν i)] - [contextInstance4013_46 : ∀ i, DecidableEq (ν i)] : tensor (fun i : ι => (1 : Mat (ν i))) = 1 := by - ext x y - classical - by_cases h : x = y - · subst y; simp [tensor] - · obtain ⟨i,hi⟩ := Function.ne_iff.mp h - simp only [tensor, Matrix.one_apply, ite_eq_right h] - apply Finset.prod_eq_zero (Finset.mem_univ i) - simp [hi] - -lemma tensor_nonneg (A : ∀ i, Mat (ν i)) (hA : ∀ i, 0 ≤ A i) : 0 ≤ tensor A := by - have he : tensor A = star (tensor (fun i => CFC.sqrt (A i))) * tensor (fun i => CFC.sqrt (A i)) := by - rw [← tensor_star, ← tensor_mul] - congr 1 - funext i - rw [(IsSelfAdjoint.of_nonneg (CFC.sqrt_nonneg (A i))).star_eq, - CFC.sqrt_mul_sqrt_self (A i) (hA i)] - rw [he] - exact star_mul_self_nonneg _ - -lemma tensor_projection (P : ∀ i, Mat (ν i)) (hP : ∀ i, IsStarProjection (P i)) : - IsStarProjection (tensor P) := by - constructor - · change tensor P * tensor P = tensor P - rw [← tensor_mul] - congr 1 - funext i - exact (hP i).isIdempotentElem.eq - · change star (tensor P) = tensor P - rw [← tensor_star] - congr 1 - funext i - exact (hP i).isSelfAdjoint.star_eq - -lemma tensor_sum - {ι : Type*} - [contextInstance4012_21 : Fintype ι] - [contextInstance4012_33 : DecidableEq ι] - {ν : ι → Type*} - [∀ i, Fintype (ν i)] - [∀ i, DecidableEq (ν i)] {κ : ι → Type*} [∀ i, Fintype (κ i)] - (A : ∀ i, κ i → Mat (ν i)) : - tensor (fun i => ∑ k, A i k) = ∑ f : ∀ i, κ i, tensor (fun i => A i (f i)) := by - ext x y - simp only [tensor, Matrix.sum_apply] - exact (Fintype.prod_sum (fun i (k : κ i) => A i k (x i) (y i))) - -lemma tensor_smul - {ι : Type*} - [contextInstance4012_21 : Fintype ι] - [DecidableEq ι] - {ν : ι → Type*} - [∀ i, Fintype (ν i)] - [∀ i, DecidableEq (ν i)] (w : ι → ℝ) (A : ∀ i, Mat (ν i)) : - tensor (fun i => w i • A i) = (∏ i, w i) • tensor A := by - ext x y - simp only [tensor, Matrix.smul_apply, RCLike.real_smul_eq_coe_smul (K := ℂ), smul_eq_mul, - Finset.prod_mul_distrib] - change (∏ i, (w i : ℂ)) * _ = ((∏ i, w i : ℝ) : ℂ) * _ - rw [Complex.ofReal_prod] - -lemma tensor_sum_smul {κ : ι → Type*} [∀ i, Fintype (κ i)] - (w : ∀ i, κ i → ℝ) (A : ∀ i, κ i → Mat (ν i)) : - tensor (fun i => ∑ k, w i k • A i k) = - ∑ f : ∀ i, κ i, (∏ i, w i (f i)) • tensor (fun i => A i (f i)) := by - rw [tensor_sum] - simp only [tensor_smul] - -lemma tensor_mono (A B : ∀ i, Mat (ν i)) (hA : ∀ i, 0 ≤ A i) (hAB : ∀ i, A i ≤ B i) : - tensor A ≤ tensor B := by - let M (i : ι) (b : Bool) : Mat (ν i) := if b then B i - A i else A i - have he (i : ι) : (∑ b : Bool, M i b) = B i := by - simp [M] - have hm (i : ι) (b : Bool) : 0 ≤ M i b := by - cases b - · exact hA i - · exact sub_nonneg.mpr (hAB i) - rw [show B = (fun i => ∑ b : Bool, M i b) by funext i; exact (he i).symm, tensor_sum] - have h := Finset.single_le_sum (s := (Finset.univ : Finset (ι → Bool))) - (f := fun f => tensor (fun i => M i (f i))) - (fun f _ => tensor_nonneg _ (fun i => hm i (f i))) (Finset.mem_univ (fun _ => false)) - exact h -end SpinAngle.DependentTensor - -namespace SpinAngle.BlockTensor -open DependentTensor -variable {τ J n : Type*} [contextInstance4107_25 : Fintype τ] [contextInstance4107_37 : DecidableEq τ] [contextInstance4107_53 : Fintype J] [contextInstance4107_65 : DecidableEq J] - [contextInstance4108_2 : Fintype n] [contextInstance4108_14 : DecidableEq n] -variable (f : τ → J) - -abbrev Fiber (j : J) := {i : τ // f i = j} - -def splitEquiv : (τ → n) ≃ (∀ j : J, Fiber f j → n) where - toFun x j i := x i.val - invFun y i := y (f i) ⟨i,rfl⟩ - left_inv x := rfl - right_inv y := by - funext j i - rcases i with ⟨i,hi⟩ - subst j - rfl - - -def tensor (A : ∀ j, Mat (Fiber f j → n)) : Mat (τ → n) := - fun x y => DependentTensor.tensor A (splitEquiv f x) (splitEquiv f y) - -lemma tensor_mul (A B : ∀ j, Mat (Fiber f j → n)) : - tensor f (fun j => A j * B j) = tensor f A * tensor f B := by - change (DependentTensor.tensor (fun j => A j * B j)).submatrix (splitEquiv f) (splitEquiv f) = _ - rw [DependentTensor.tensor_mul] - exact (Matrix.submatrix_mul_equiv _ _ (splitEquiv f) (splitEquiv f) (splitEquiv f)).symm - -lemma tensor_star - {τ : Type*} {J : Type*} {n : Type*} - [Fintype τ] - [DecidableEq τ] - [contextInstance4107_53 : Fintype J] - [DecidableEq J] - [Fintype n] - [DecidableEq n] - (f : τ → J) (A : ∀ j, Mat (Fiber f j → n)) : - tensor f (fun j => star (A j)) = star (tensor f A) := by - ext x y - simp [tensor, DependentTensor.tensor, Matrix.star_apply] - -lemma tensor_one : tensor f (fun j => (1 : Mat (Fiber f j → n))) = 1 := by - ext x y - change DependentTensor.tensor (fun j => (1 : Mat (Fiber f j → n))) _ _ = _ - rw [DependentTensor.tensor_one] - simp only [Matrix.one_apply, Equiv.apply_eq_iff_eq] - -lemma tensor_nonneg (A : ∀ j, Mat (Fiber f j → n)) (hA : ∀ j, 0 ≤ A j) : 0 ≤ tensor f A := by - exact (Matrix.nonneg_iff_posSemidef.mp (DependentTensor.tensor_nonneg A hA)).submatrix (splitEquiv f) |>.nonneg - -lemma tensor_mono (A B : ∀ j, Mat (Fiber f j → n)) (hA : ∀ j, 0 ≤ A j) (hAB : ∀ j, A j ≤ B j) : - tensor f A ≤ tensor f B := by - have he := DependentTensor.tensor_mono A B hA hAB - have hn := (Matrix.nonneg_iff_posSemidef.mp (sub_nonneg.mpr he)).submatrix (splitEquiv f) |>.nonneg - exact sub_nonneg.mp hn - -lemma tensor_projection (P : ∀ j, Mat (Fiber f j → n)) (hP : ∀ j, IsStarProjection (P j)) : - IsStarProjection (tensor f P) := by - constructor - · change tensor f P * tensor f P = tensor f P - rw [← tensor_mul] - congr 1 - funext j - exact (hP j).isIdempotentElem.eq - · change star (tensor f P) = tensor f P - rw [← tensor_star] - congr 1 - funext j - exact (hP j).isSelfAdjoint.star_eq - -lemma tensor_sum_smul {κ : J → Type*} [∀ j, Fintype (κ j)] - (w : ∀ j, κ j → ℝ) (A : ∀ j, κ j → Mat (Fiber f j → n)) : - tensor f (fun j => ∑ k, w j k • A j k) = - ∑ k : ∀ j, κ j, (∏ j, w j (k j)) • tensor f (fun j => A j (k j)) := by - ext x y - change DependentTensor.tensor (fun j => ∑ k, w j k • A j k) _ _ = _ - rw [DependentTensor.tensor_sum_smul] - simp only [Matrix.sum_apply, Matrix.smul_apply, tensor] -end SpinAngle.BlockTensor - -namespace SpinAngle.BlockTensor -open DependentTensor -variable {τ J n : Type*} [contextInstance4180_25 : Fintype τ] [contextInstance4180_37 : DecidableEq τ] [contextInstance4180_53 : Fintype J] [contextInstance4180_65 : DecidableEq J] - [contextInstance4181_2 : Fintype n] [contextInstance4181_14 : DecidableEq n] -variable (f : τ → J) - -lemma prod_fibers - {τ : Type*} {J : Type*} - [contextInstance4180_25 : Fintype τ] - [DecidableEq τ] - [contextInstance4180_53 : Fintype J] - [contextInstance4180_65 : DecidableEq J] - (f : τ → J) {M : Type*} [CommMonoid M] (a : τ → M) : - (∏ j : J, ∏ i : Fiber f j, a i.val) = ∏ i, a i := by - calc - _ = ∏ z : Sigma (Fiber f), a z.2.val := - (Fintype.prod_sigma (fun z : Sigma (Fiber f) => a z.2.val)).symm - _ = _ := (Equiv.sigmaFiberEquiv f).prod_comp a - - -lemma tensor_cells - {τ : Type*} {J : Type*} {n : Type*} - [contextInstance4180_25 : Fintype τ] - [contextInstance4180_37 : DecidableEq τ] - [contextInstance4180_53 : Fintype J] - [contextInstance4180_65 : DecidableEq J] - [Fintype n] - [DecidableEq n] - (f : τ → J) (A : τ → Mat n) : - tensor f (fun j => DependentTensor.tensor (fun i : Fiber f j => A i.val)) = - DependentTensor.tensor A := by - ext x y - change (∏ j, ∏ i : Fiber f j, A i.val (x i.val) (y i.val)) = _ - exact prod_fibers f (fun i => A i (x i) (y i)) - -lemma tensor_commute (A B : ∀ j, Mat (Fiber f j → n)) - (h : ∀ j, Commute (A j) (B j)) : Commute (tensor f A) (tensor f B) := by - change tensor f A * tensor f B = tensor f B * tensor f A - rw [← tensor_mul, ← tensor_mul] - congr 1 - funext j - exact (h j).eq -end SpinAngle.BlockTensor - - -namespace SpinAngle.TensorMatrix -open MatrixAnalysis -open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder -variable {ι n : Type*} [contextInstance4214_23 : Fintype ι] [contextInstance4214_35 : DecidableEq ι] [contextInstance4214_51 : Fintype n] [contextInstance4214_63 : DecidableEq n] - -lemma tensor_root_square (A : ι → Mat n) (hA : ∀ i, 0 ≤ A i) : - tensor (fun i => root (A i)) * tensor (fun i => root (A i)) = tensor A := by - rw [← tensor_mul] - congr 1 - funext i - exact root_mul_self _ (hA i) - -lemma tensor_root (A : ι → Mat n) (hA : ∀ i, 0 ≤ A i) : - tensor (fun i => root (A i)) = root (tensor A) := by - apply (CFC.mul_self_eq_mul_self_iff _ _ - (tensor_nonneg _ (fun i => root_nonneg (A i))) (root_nonneg _)).mp - rw [tensor_root_square A hA, root_mul_self _ (tensor_nonneg A hA)] - -lemma tensor_invRoot_mul_root (A : ι → Mat n) (hA : ∀ i, 0 ≤ A i) : - tensor (fun i => invRoot (A i)) * tensor (fun i => root (A i)) = - tensor (fun i => support (A i)) := by - rw [← tensor_mul] - congr 1 - funext i - exact invRoot_mul_root _ (hA i) - -lemma tensor_root_mul_support_of_le_smul (A B : ι → Mat n) - (hA : ∀ i, 0 ≤ A i) (hB : ∀ i, 0 ≤ B i) - (c : ℝ) (hAB : ∀ i, A i ≤ c • B i) : - tensor (fun i => root (A i)) * tensor (fun i => support (B i)) = - tensor (fun i => root (A i)) := by - rw [← tensor_mul] - congr 1 - funext i - exact root_mul_support_of_le_smul _ _ (hB i) (hA i) c (hAB i) -end SpinAngle.TensorMatrix - -namespace SpinAngle -open scoped BigOperators -variable {R C : Type*} [contextInstance4250_23 : Fintype R] [contextInstance4250_35 : DecidableEq R] [contextInstance4250_51 : Fintype C] [contextInstance4250_63 : DecidableEq C] - -lemma sum_occupiedRow_card (W : Finset (R × C)) : - ∑ i, (occupiedRow W i).card = W.card := by - have he (i : R) : (occupiedRow W i).card = ∑ j : C, if (i,j) ∈ W then 1 else 0 := by - simp only [occupiedRow, Finset.card_eq_sum_ones, Finset.sum_filter] - simp only [he] - rw [← Finset.sum_product (f := fun x : R × C => if x ∈ W then (1 : ℕ) else 0)] - simp only [Finset.univ_product_univ, ← Finset.sum_filter] - have he : (Finset.univ.filter fun x : R × C => x ∈ W) = W := by ext x; simp - rw [he] - simp - -lemma sum_missingInRow (W : Finset (R × C)) : - ∑ i, missingInRow W i = Fintype.card R * Fintype.card C - W.card := by - have he : (∑ i, missingInRow W i) + W.card = Fintype.card R * Fintype.card C := by - rw [← sum_occupiedRow_card W, ← Finset.sum_add_distrib] - have hi (i : R) : missingInRow W i + (occupiedRow W i).card = Fintype.card C := - Nat.sub_add_cancel (occupiedRow_card_le W i) - simp [hi] - omega - -lemma boardPhi_nonneg (W : Finset (R × C)) : - 0 ≤ missingCellProductFactor (Fintype.card C) (missingInRow W) := - Finset.prod_nonneg fun rowIndex _ => missingCellFactor_nonneg _ (missingInRow W rowIndex) - -lemma boardPhi_le_exp_holes (W : Finset (R × C)) : - missingCellProductFactor (Fintype.card C) (missingInRow W) ≤ - Real.exp (Fintype.card R * Fintype.card C - W.card : ℕ) := by - have h := missingCellProduct (Fintype.card C) (missingInRow W) (missingInRow_le W) - have hs : (∑ i, (missingInRow W i : ℝ)) = - (Fintype.card R * Fintype.card C - W.card : ℕ) := by - exact_mod_cast sum_missingInRow W - rwa [hs] at h -end SpinAngle - - -namespace SpinAngle -open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder -open SpinAngle.Young - - - -structure TypeLabel (q : ℕ) where - even : YoungDiagram - odd : YoungDiagram - even_height : even.colLen 0 ≤ q - odd_height : odd.colLen 0 ≤ q - -namespace TypeLabel -variable {q : ℕ} -def size (D : TypeLabel q) : ℕ := Fintype.card (Cells D.even) + Fintype.card (Cells D.odd) -def entropy (D : TypeLabel q) : ℝ := SignedCarrier.entropy D.even D.odd q -def dimension (D : TypeLabel q) : ℕ := SignedCarrier.dimension D.even D.odd q D.even_height D.odd_height - -def projection (D : TypeLabel q) (τ : Type*) [Fintype τ] [DecidableEq τ] : - Matrix (τ → SignedTensor.Spin q) (τ → SignedTensor.Spin q) ℂ := - SignedCarrier.matrixProjection D.even D.odd q D.even_height D.odd_height - -lemma projection_isStarProjection (D : TypeLabel q) (τ : Type*) [Fintype τ] [DecidableEq τ] : - IsStarProjection (D.projection τ) := - SignedCarrier.matrixProjection_isStarProjection D.even D.odd q D.even_height D.odd_height - -lemma dimension_pos (D : TypeLabel q) : 0 < D.dimension := - SignedCarrier.dimension_pos D.even D.odd q D.even_height D.odd_height - -lemma dimension_le (D : TypeLabel q) : D.dimension ≤ (D.size + 1) ^ (q*(q-1)) := - SignedCarrier.dimension_le D.even D.odd q D.even_height D.odd_height - -lemma entropy_eq_zero_of_size_zero (D : TypeLabel q) (hD : D.size = 0) : D.entropy = 0 := by - have hs : ∑ i, SignedCarrier.parts D.even D.odd q i = 0 := - (SignedCarrier.sum_parts D.even D.odd q D.even_height D.odd_height).trans hD - have hi : ∀ i, SignedCarrier.parts D.even D.odd q i = 0 := by - intro i - have h := Finset.single_le_sum (s := Finset.univ) - (fun j _ => Nat.zero_le (SignedCarrier.parts D.even D.odd q j)) (Finset.mem_univ i) - rw [hs] at h - exact Nat.eq_zero_of_le_zero h - simp [entropy, SignedCarrier.entropy, EntropyMonomial.entropy, hi] -end TypeLabel - -abbrev EvenDensity (q : ℕ) := {A : SignedTensor.Mat q × SignedTensor.Mat q // SignedTensor.IsEvenDensity A} -namespace EvenDensity -variable {q : ℕ} -def matrix (A : EvenDensity q) : Matrix (SignedTensor.Spin q) (SignedTensor.Spin q) ℂ := - SignedTensor.block A.val -lemma nonneg (A : EvenDensity q) : 0 ≤ A.matrix := - (SignedTensor.block_posSemidef A.val A.property.1 A.property.2.1).nonneg -lemma trace_eq_one (A : EvenDensity q) : A.matrix.trace = 1 := by - rw [matrix, SignedTensor.block_trace] - exact A.property.2.2 - -def toDensity (A : EvenDensity q) : MatrixAnalysis.Density (SignedTensor.Spin q) := - ⟨A.matrix,A.nonneg,A.trace_eq_one⟩ - -variable {J : Type*} [contextInstance4345_21 : Fintype J] [contextInstance4345_33 : Nonempty J] -def mean (A : J → EvenDensity q) : EvenDensity q := - ⟨SignedTensor.evenAverage (fun j => (A j).val), - SignedTensor.evenAverage_isEvenDensity _ (fun j => (A j).property)⟩ -lemma mean_matrix (A : J → EvenDensity q) [DecidableEq J] : - (mean A).matrix = MatrixAnalysis.average (fun j => (A j).toDensity) := by - unfold mean matrix SignedTensor.evenAverage - rw [SignedTensor.block_real_smul, SignedTensor.block_sum] - rfl -end EvenDensity - -namespace TypeLabel -variable {q : ℕ} -variable {τ : Type*} [contextInstance4358_21 : Fintype τ] [contextInstance4358_33 : DecidableEq τ] -lemma density_upper (D : TypeLabel q) (A : EvenDensity q) : - ‖TensorMatrix.tensor (fun _ : τ => A.matrix) * D.projection τ‖ ≤ Real.exp (-D.entropy) := - SignedCarrier.matrix_density_upper D.even D.odd q D.even_height D.odd_height A.val A.property - -lemma density_commute (D : TypeLabel q) (A : EvenDensity q) : - Commute (TensorMatrix.tensor (fun _ : τ => A.matrix)) (D.projection τ) := - SignedCarrier.matrix_density_commute D.even D.odd q D.even_height D.odd_height A.val A.property - -variable [contextInstance4367_9 : Nonempty (Fin q)] -lemma density_mixture (D : TypeLabel q) : - ∃ (ι : Type) (_ : Fintype ι) (w : ι → ℝ) (R : ι → EvenDensity q), - (∀ i, 0 ≤ w i) ∧ (∑ i, w i = 1) ∧ - D.projection τ ≤ (Real.exp D.entropy * (D.dimension : ℝ)) • - ∑ i, w i • TensorMatrix.tensor (fun _ : τ => (R i).matrix) := by - obtain ⟨ι,hι,w,R,hw,hs,hR,hdom⟩ := SignedCarrier.exists_matrix_density_mixture - (τ := τ) D.even D.odd q D.even_height D.odd_height - let := hι - exact ⟨ι,hι,w,fun i => ⟨R i,hR i⟩,hw,hs,hdom⟩ -end TypeLabel - -namespace TypeBlocks -universe u -open MatrixAnalysis -variable {q : ℕ} -variable {τ : Type*} {J : Type u} [contextInstance4383_34 : Fintype τ] [contextInstance4383_46 : DecidableEq τ] [contextInstance4383_62 : Fintype J] [contextInstance4383_74 : DecidableEq J] - -abbrev Fiber (f : τ → J) (j : J) := BlockTensor.Fiber f j - -def projection (f : τ → J) (D : J → TypeLabel q) : Mat (τ → SignedTensor.Spin q) := - BlockTensor.tensor f (fun j => (D j).projection (Fiber f j)) - -def entropy (D : J → TypeLabel q) : ℝ := ∑ j, (D j).entropy -def dimension (D : J → TypeLabel q) : ℕ := ∏ j, (D j).dimension - -lemma projection_isStarProjection (f : τ → J) (D : J → TypeLabel q) : - IsStarProjection (projection f D) := - BlockTensor.tensor_projection f _ (fun j => (D j).projection_isStarProjection _) - -lemma density_commute (f : τ → J) (D : J → TypeLabel q) (A : EvenDensity q) : - Commute (TensorMatrix.tensor (fun _ : τ => A.matrix)) (projection f D) := by - have h := BlockTensor.tensor_commute f - (fun j => TensorMatrix.tensor (fun _ : Fiber f j => A.matrix)) - (fun j => (D j).projection (Fiber f j)) (fun j => (D j).density_commute A) - have he : BlockTensor.tensor f (fun j => TensorMatrix.tensor (fun _ : Fiber f j => A.matrix)) = - TensorMatrix.tensor (fun _ : τ => A.matrix) := by - ext x y - change (∏ j : J, ∏ t : Fiber f j, A.matrix (x t.val) (y t.val)) = - ∏ t : τ, A.matrix (x t) (y t) - exact BlockTensor.prod_fibers f (fun t => A.matrix (x t) (y t)) - rwa [he] at h - -variable [contextInstance4410_9 : Nonempty (Fin q)] - - -theorem density_mixture (f : τ → J) (D : J → TypeLabel q) : - ∃ (ι : Type u) (_ : Fintype ι) (w : ι → ℝ) (R : ι → J → EvenDensity q), - (∀ i, 0 ≤ w i) ∧ (∑ i, w i = Real.exp (entropy D) * (dimension D : ℝ)) ∧ - projection f D ≤ ∑ i, w i • TensorMatrix.tensor (fun t : τ => (R i (f t)).matrix) := by - classical - choose κ hκ w R hw hs hdom using (fun j : J => (D j).density_mixture (τ := Fiber f j)) - let : ∀ j, Fintype (κ j) := hκ - let c (j : J) : ℝ := Real.exp (D j).entropy * (D j).dimension - let z (j : J) (i : κ j) : ℝ := c j * w j i - have hz (j : J) (i : κ j) : 0 ≤ z j i := - mul_nonneg (mul_nonneg (Real.exp_pos _).le (Nat.cast_nonneg _)) (hw j i) - have hsum (j : J) : ∑ i, z j i = c j := by - simp only [z, ← Finset.mul_sum, hs, mul_one] - have hlocal (j : J) : (D j).projection (Fiber f j) ≤ - ∑ i, z j i • TensorMatrix.tensor (fun _ : Fiber f j => (R j i).matrix) := by - simpa only [z, c, Finset.smul_sum, smul_smul] using hdom j - refine ⟨(∀ j, κ j), inferInstance, (fun i => ∏ j, z j (i j)), - (fun i j => R j (i j)), (fun i => Finset.prod_nonneg fun j _ => hz j (i j)), ?_, ?_⟩ - · rw [← Fintype.prod_sum] - simp only [hsum, c, Finset.prod_mul_distrib] - rw [← Real.exp_sum] - simp only [entropy, dimension, Nat.cast_prod] - · have h := BlockTensor.tensor_mono f _ _ - (fun j => ((D j).projection_isStarProjection (Fiber f j)).nonneg) hlocal - rw [BlockTensor.tensor_sum_smul] at h - have he (i : ∀ j, κ j) : BlockTensor.tensor f - (fun j => TensorMatrix.tensor (fun _ : Fiber f j => (R j (i j)).matrix)) = - TensorMatrix.tensor (fun t : τ => (R (f t) (i (f t))).matrix) := by - ext x y - change (∏ j : J, ∏ t : Fiber f j, (R j (i j)).matrix (x t.val) (y t.val)) = - ∏ t : τ, (R (f t) (i (f t))).matrix (x t) (y t) - calc - _ = ∏ j : J, ∏ t : Fiber f j, (R (f t.val) (i (f t.val))).matrix (x t.val) (y t.val) := by - apply Finset.prod_congr rfl - intro j hj - apply Finset.prod_congr rfl - intro t ht - rw [t.property] - _ = _ := BlockTensor.prod_fibers f (fun t => (R (f t) (i (f t))).matrix (x t) (y t)) - simpa only [he, projection] using h -end TypeBlocks -end SpinAngle - -end -end -end -end -end -end -end -end -end -end -end -end -end -end -end -end -end -end - -end OAI +import Mathlib + +namespace OAI + + + +noncomputable section +open scoped BigOperators ComplexConjugate InnerProductSpace + +namespace SpinAngle.Specht + +variable {G : Type*} [contextInstance10_21 : Group G] +variable {E : Type*} [contextInstance11_21 : NormedAddCommGroup E] [contextInstance11_44 : InnerProductSpace ℂ E] + + +def cyclic (ρ : Representation ℂ G E) (e : E) : Subrepresentation ρ where + toSubmodule := Submodule.span ℂ (Set.range fun g => ρ g e) + apply_mem_toSubmodule g := by + intro v hv + induction hv using Submodule.span_induction with + | mem v hv => + obtain ⟨h, rfl⟩ := hv + exact Submodule.subset_span ⟨g * h, by simp⟩ + | zero => simp + | add x y hx hy ihx ihy => + simpa using (Submodule.span ℂ (Set.range fun h => ρ h e)).add_mem ihx ihy + | smul a x hx ih => + simpa using (Submodule.span ℂ (Set.range fun h => ρ h e)).smul_mem a ih + +lemma self_mem_cyclic (ρ : Representation ℂ G E) (e : E) : e ∈ cyclic ρ e := by + exact Submodule.subset_span ⟨1, by simp⟩ + + +variable [contextInstance32_9 : FiniteDimensional ℂ E] + +lemma starProjection_rep (ρ : Representation ℂ G E) + (hunit : ∀ g x y, ⟪ρ g x, ρ g y⟫_ℂ = ⟪x, y⟫_ℂ) + (U : Subrepresentation ρ) (g : G) (v : E) : + U.toSubmodule.starProjection (ρ g v) = ρ g (U.toSubmodule.starProjection v) := by + apply U.toSubmodule.eq_starProjection_of_mem_of_inner_eq_zero + · exact U.apply_mem_toSubmodule g (U.toSubmodule.starProjection_apply_mem v) + · intro w hw + have hw' := U.apply_mem_toSubmodule g⁻¹ hw + have he : ρ g (ρ g⁻¹ w) = w := by + rw [← Module.End.mul_apply, ← map_mul, mul_inv_cancel, map_one, Module.End.one_apply] + rw [← map_sub] + conv_lhs => rhs; rw [← he] + rw [hunit] + exact U.toSubmodule.starProjection_inner_eq_zero v _ hw' + + + + +theorem simple_eigen_submodule_alternative (ρ : Representation ℂ G E) (e : E) + (hunit : ∀ g x y, ⟪ρ g x, ρ g y⟫_ℂ = ⟪x, y⟫_ℂ) + (g₀ : G) (c : ℂ) (heig : ρ g₀ e = c • e) + (hsimple : ∀ v : E, ρ g₀ v = c • v → v ∈ Submodule.span ℂ {e}) + (U : Subrepresentation ρ) : + cyclic ρ e ≤ U ∨ ∀ u ∈ U, ∀ v ∈ cyclic ρ e, ⟪v, u⟫_ℂ = 0 := by + classical + by_cases he : e ∈ U + · left + exact Submodule.span_le.mpr (by rintro _ ⟨g, rfl⟩; exact U.apply_mem_toSubmodule g he) + · right + have hp : U.toSubmodule.starProjection e = 0 := by + have hpeig : ρ g₀ (U.toSubmodule.starProjection e) = + c • U.toSubmodule.starProjection e := by + rw [← starProjection_rep ρ hunit U g₀ e, heig, map_smul] + obtain ⟨a, ha⟩ := Submodule.mem_span_singleton.mp (hsimple _ hpeig) + by_cases ha0 : a = 0 + · simpa [ha0] using ha.symm + · apply False.elim + apply he + have hm := U.toSubmodule.starProjection_apply_mem e + rw [← ha] at hm + have hh := U.toSubmodule.smul_mem a⁻¹ hm + change e ∈ U.toSubmodule + simpa [smul_smul, ha0] using hh + have heorth (u : E) (hu : u ∈ U) : ⟪e, u⟫_ℂ = 0 := by + have hh := U.toSubmodule.starProjection_inner_eq_zero e u hu + simpa [hp] using hh + intro u hu v hv + have horth (g : G) : ⟪ρ g e, u⟫_ℂ = 0 := by + have hgu : ρ g⁻¹ u ∈ U := U.apply_mem_toSubmodule g⁻¹ hu + have hi := hunit g e (ρ g⁻¹ u) + simpa only [← Module.End.mul_apply, ← map_mul, mul_inv_cancel, map_one, + Module.End.one_apply] using hi.trans (heorth _ hgu) + induction hv using Submodule.span_induction with + | mem v hv => obtain ⟨g, rfl⟩ := hv; exact horth g + | zero => simp + | add x y hx hy ihx ihy => simp [ihx, ihy] + | smul a x hx ih => simp [ih] + +theorem cyclic_irreducible_of_simple_eigen (ρ : Representation ℂ G E) (e : E) (he : e ≠ 0) + (hunit : ∀ g x y, ⟪ρ g x, ρ g y⟫_ℂ = ⟪x, y⟫_ℂ) + (g₀ : G) (c : ℂ) (heig : ρ g₀ e = c • e) + (hsimple : ∀ v : E, ρ g₀ v = c • v → v ∈ Submodule.span ℂ {e}) : + Representation.IsIrreducible (cyclic ρ e).toRepresentation := by + let S := cyclic ρ e + let eS : S.toSubmodule := ⟨e, self_mem_cyclic ρ e⟩ + have heS : eS ≠ 0 := by intro hh; apply he; exact congrArg Subtype.val hh + have htb : (⊤ : Subrepresentation S.toRepresentation) ≠ ⊥ := by + intro hh + have hel : eS ∈ (⊤ : Subrepresentation S.toRepresentation) := by trivial + rw [hh] at hel + exact heS hel + let : Nontrivial (Subrepresentation S.toRepresentation) := ⟨⟨⊤, ⊥, htb⟩⟩ + refine ⟨fun U => ?_⟩ + let U' : Subrepresentation ρ := { + toSubmodule := U.toSubmodule.map S.toSubmodule.subtype + apply_mem_toSubmodule := by + intro g v hv + obtain ⟨u, hu, rfl⟩ := hv + exact ⟨S.toRepresentation g u, U.apply_mem_toSubmodule g hu, rfl⟩ } + rcases simple_eigen_submodule_alternative ρ e hunit g₀ c heig hsimple U' with h | h + · right + apply top_unique + intro u _ + obtain ⟨v, hv, heq⟩ := h u.property + have hvu : v = u := Subtype.ext heq + exact hvu ▸ hv + · left + apply bot_unique + intro u hu + have hum : (u : E) ∈ U' := ⟨u, hu, rfl⟩ + have hh := h _ hum _ u.property + have hz : (u : E) = 0 := inner_self_eq_zero.mp hh + exact Subtype.ext hz +end SpinAngle.Specht + + + + +noncomputable section +open scoped BigOperators ComplexConjugate InnerProductSpace Matrix +namespace SpinAngle.TensorRep +variable {ι n : Type*} [contextInstance135_23 : Fintype ι] [contextInstance135_35 : DecidableEq ι] [contextInstance135_51 : Fintype n] [contextInstance135_63 : DecidableEq n] + + +def tensor (a : ι → Matrix n n ℂ) : Matrix (ι → n) (ι → n) ℂ := + fun x y => ∏ i, a i (x i) (y i) + +lemma tensor_star + {ι : Type*} {n : Type*} + [contextInstance135_23 : Fintype ι] + [DecidableEq ι] + [Fintype n] + [DecidableEq n] (a : ι → Matrix n n ℂ) : + tensor (fun i => star (a i)) = star (tensor a) := by + ext x y + simp [tensor, Matrix.star_apply] + +lemma tensor_mul + {ι : Type*} {n : Type*} + [contextInstance135_23 : Fintype ι] + [contextInstance135_35 : DecidableEq ι] + [contextInstance135_51 : Fintype n] + [DecidableEq n] (a b : ι → Matrix n n ℂ) : + tensor (fun i => a i * b i) = tensor a * tensor b := by + ext x y + simp only [tensor, Matrix.mul_apply, ← Finset.prod_mul_distrib] + symm + simpa using (Finset.sum_prod_piFinset (ι := ι) Finset.univ + (fun i j => a i (x i) j * b i j (y i))) + +lemma tensor_one + {ι : Type*} {n : Type*} + [contextInstance135_23 : Fintype ι] + [DecidableEq ι] + [Fintype n] + [contextInstance135_63 : DecidableEq n] : tensor (fun _ : ι => (1 : Matrix n n ℂ)) = 1 := by + ext x y + classical + by_cases h : x = y + · subst y + simp [tensor] + · obtain ⟨i, hi⟩ := Function.ne_iff.mp h + simp only [tensor, Matrix.one_apply, ite_eq_right h] + apply Finset.prod_eq_zero (Finset.mem_univ i) + simp [hi] + +lemma tensor_diagonal + {ι : Type*} {n : Type*} + [contextInstance135_23 : Fintype ι] + [DecidableEq ι] + [Fintype n] + [contextInstance135_63 : DecidableEq n] (a : ι → n → ℂ) : + tensor (fun i => Matrix.diagonal (a i)) = Matrix.diagonal (fun x => ∏ i, a i (x i)) := by + ext x y + classical + by_cases h : x = y + · subst y + simp [tensor] + · obtain ⟨i, hi⟩ := Function.ne_iff.mp h + simp only [tensor, Matrix.diagonal_apply, ite_eq_right h] + apply Finset.prod_eq_zero (Finset.mem_univ i) + simp [hi] + +lemma toEuclideanLin_mul + {ι : Type*} {n : Type*} + [Fintype ι] + [DecidableEq ι] + [contextInstance135_51 : Fintype n] + [contextInstance135_63 : DecidableEq n] (a b : Matrix n n ℂ) : + Matrix.toEuclideanLin (a * b) = + Matrix.toEuclideanLin a * Matrix.toEuclideanLin b := by + ext v x + change ((a * b) *ᵥ (WithLp.ofLp v)) x = (a *ᵥ (b *ᵥ (WithLp.ofLp v))) x + rw [Matrix.mulVec_mulVec] + +lemma toEuclideanLin_one + {ι : Type*} {n : Type*} + [Fintype ι] + [DecidableEq ι] + [contextInstance135_51 : Fintype n] + [contextInstance135_63 : DecidableEq n] : Matrix.toEuclideanLin (1 : Matrix n n ℂ) = 1 := by + ext v x + change ((1 : Matrix n n ℂ) *ᵥ (WithLp.ofLp v)) x = v x + simp + + +def action : Matrix n n ℂ →* Module.End ℂ (EuclideanSpace ℂ (ι → n)) where + toFun a := Matrix.toEuclideanLin (tensor (fun _ : ι => a)) + map_one' := by rw [tensor_one, toEuclideanLin_one (ι := ι)] + map_mul' a b := by rw [tensor_mul, toEuclideanLin_mul (ι := ι)] + + + +def rep : Representation ℂ (Matrix.unitaryGroup n ℂ) (EuclideanSpace ℂ (ι → n)) := + action.comp (Matrix.unitaryGroup n ℂ).subtype + +lemma tensor_mem_unitary (a : ι → Matrix.unitaryGroup n ℂ) : + tensor (fun i => (a i : Matrix n n ℂ)) ∈ Matrix.unitaryGroup (ι → n) ℂ := by + rw [Matrix.mem_unitaryGroup_iff', ← tensor_star, ← tensor_mul] + convert tensor_one (ι := ι) (n := n) using 1 + congr 1 + funext i + exact (a i).property.1 + +lemma toEuclideanLin_unitary (a : Matrix n n ℂ) (ha : a ∈ Matrix.unitaryGroup n ℂ) + (v w : EuclideanSpace ℂ n) : + ⟪Matrix.toEuclideanLin a v, Matrix.toEuclideanLin a w⟫_ℂ = ⟪v, w⟫_ℂ := by + rw [← LinearMap.adjoint_inner_right] + rw [← Matrix.toEuclideanLin_conjTranspose_eq_adjoint] + change ⟪v, (Matrix.toEuclideanLin (star a) * Matrix.toEuclideanLin a) w⟫_ℂ = _ + rw [← toEuclideanLin_mul (ι := n), ha.1, toEuclideanLin_one (ι := n)] + rfl + +lemma rep_unitary (g : Matrix.unitaryGroup n ℂ) + (v w : EuclideanSpace ℂ (ι → n)) : ⟪rep g v, rep g w⟫_ℂ = ⟪v, w⟫_ℂ := + toEuclideanLin_unitary _ (tensor_mem_unitary (fun _ : ι => g)) v w + + +lemma tensor_reindex + {ι : Type*} {n : Type*} + [contextInstance135_23 : Fintype ι] + [DecidableEq ι] + [Fintype n] + [DecidableEq n] (a : Matrix n n ℂ) (σ : Equiv.Perm ι) (x y : ι → n) : + tensor (fun _ : ι => a) (x ∘ σ) (y ∘ σ) = tensor (fun _ : ι => a) x y := by + exact Equiv.prod_comp σ (fun i => a (x i) (y i)) + + +lemma action_diagonal (a : n → ℂ) (v : EuclideanSpace ℂ (ι → n)) (x : ι → n) : + action (Matrix.diagonal a) v x = (∏ i, a (x i)) * v x := by + change (Matrix.toEuclideanLin (tensor (fun _ : ι => Matrix.diagonal a)) v) x = _ + rw [tensor_diagonal] + change (Matrix.diagonal (fun x : ι → n => ∏ i, a (x i)) *ᵥ WithLp.ofLp v) x = _ + exact Matrix.mulVec_diagonal _ _ _ + +end SpinAngle.TensorRep + +namespace SpinAngle.Specht +open scoped Classical +variable {G : Type*} [contextInstance243_21 : Group G] +namespace PermutationSpace +open scoped Classical + +variable {X : Type*} [contextInstance247_21 : Fintype X] [contextInstance247_33 : MulAction G X] + + +def rep : Representation ℂ G (EuclideanSpace ℂ X) where + toFun g := { + toFun v := WithLp.toLp 2 (fun x => v (g⁻¹ • x)) + map_add' := by intro v w; rfl + map_smul' := by intro a v; rfl } + map_one' := by ext v x; simp + map_mul' := by + intro g h + ext v x + change v ((g * h)⁻¹ • x) = v (h⁻¹ • g⁻¹ • x) + simp [mul_smul] + +omit [Fintype X] in +@[simp] lemma rep_apply (g : G) (v : EuclideanSpace ℂ X) (x : X) : + rep g v x = v (g⁻¹ • x) := rfl + +lemma rep_unitary (g : G) (v w : EuclideanSpace ℂ X) : + ⟪rep g v, rep g w⟫_ℂ = ⟪v, w⟫_ℂ := by + simp only [PiLp.inner_apply, rep_apply] + exact Equiv.sum_comp (MulAction.toPerm g⁻¹) (fun x => inner ℂ (v x) (w x)) + +omit [Fintype X] in +lemma rep_single (g : G) (x : X) : + rep g (EuclideanSpace.single x (1 : ℂ)) = EuclideanSpace.single (g • x) (1 : ℂ) := by + classical + ext y + simp only [rep_apply, PiLp.single_apply, inv_smul_eq_iff] + +variable {H : Type*} [contextInstance278_21 : Group H] [contextInstance278_31 : Fintype H] + + + +def alternator (ι : H →* G) (χ : H →* ℂ) : Module.End ℂ (EuclideanSpace ℂ X) := + ∑ h, χ h • rep (ι h) + +omit [Fintype X] in +lemma alternator_apply (ι : H →* G) (χ : H →* ℂ) (v : EuclideanSpace ℂ X) : + alternator ι χ v = ∑ h, χ h • rep (ι h) v := by + simp [alternator, LinearMap.sum_apply] + +omit [Fintype X] in +lemma alternator_stable (ι : H →* G) (χ : H →* ℂ) + (U : Subrepresentation (rep : Representation ℂ G (EuclideanSpace ℂ X))) + (v : EuclideanSpace ℂ X) (hv : v ∈ U) : alternator ι χ v ∈ U := by + rw [alternator_apply] + exact U.toSubmodule.sum_mem fun h _ => U.toSubmodule.smul_mem _ (U.apply_mem_toSubmodule _ hv) + +omit [Fintype X] in +lemma alternator_translate (ι : H →* G) (χ : H →* ℂ) (a : H) + (v : EuclideanSpace ℂ X) : + alternator ι χ (rep (ι a) v) = χ a⁻¹ • alternator ι χ v := by + rw [alternator_apply, alternator_apply, Finset.smul_sum] + have he := Equiv.sum_comp (Equiv.mulRight a) + (fun h => χ a⁻¹ • (χ h • (rep (ι h) v : EuclideanSpace ℂ X))) + rw [← he] + apply Finset.sum_congr rfl + intro h _ + simp only [Equiv.coe_mulRight, smul_smul, map_mul] + rw [show χ a⁻¹ * (χ h * χ a) = χ h by + calc + _ = χ h * (χ a⁻¹ * χ a) := by ring + _ = χ h := by rw [← map_mul, inv_mul_cancel, map_one, mul_one]] + simp only [Module.End.mul_apply] + +omit [Fintype X] in +lemma alternator_single_zero (ι : H →* G) (χ : H →* ℂ) + (x : X) (a : H) (ha : ι a • x = x) (hs : χ a = -1) : + alternator ι χ (EuclideanSpace.single x (1 : ℂ)) = 0 := by + have hh := alternator_translate ι χ a (EuclideanSpace.single x (1 : ℂ)) + rw [rep_single, ha, map_inv, hs, inv_neg, inv_one, neg_smul, one_smul] at hh + have hz := congrArg (fun z => z + alternator ι χ (EuclideanSpace.single x (1 : ℂ))) hh + have ht : (2 : ℂ) • alternator ι χ (EuclideanSpace.single x (1 : ℂ)) = 0 := by + simpa [two_smul] using hz + exact (smul_eq_zero.mp ht).resolve_left (by norm_num) + +omit [Fintype X] in +lemma alternator_coeff (ι : H →* G) (χ : H →* ℂ) (v : EuclideanSpace ℂ X) (x : X) : + alternator ι χ v x = ∑ h, χ h * v ((ι h)⁻¹ • x) := by + simp [alternator_apply, WithLp.ofLp_sum, Finset.sum_apply] + +omit [Fintype X] in +lemma polytabloid_base [DecidableEq X] (ι : H →* G) (χ : H →* ℂ) (b : X) + (hfree : ∀ h : H, ι h • b = b → h = 1) : + alternator ι χ (EuclideanSpace.single b (1 : ℂ)) b = 1 := by + classical + rw [alternator_coeff, Finset.sum_eq_single 1] + · simp + · intro h _ hh + have hn : (ι h)⁻¹ • b ≠ b := by + intro he + have hi : h⁻¹ = 1 := hfree h⁻¹ (by simpa using he) + exact hh (inv_eq_one.mp hi) + simp [hn] + · simp + +lemma polytabloid_inner (ι : H →* G) (χ : H →* ℂ) (b : X) + (hreal : ∀ h, conj (χ h) = χ h) (hinv : ∀ h, χ h⁻¹ = χ h) + (v : EuclideanSpace ℂ X) : + ⟪alternator ι χ (EuclideanSpace.single b (1 : ℂ)), v⟫_ℂ = alternator ι χ v b := by + classical + rw [alternator_apply, sum_inner, alternator_coeff] + simp only [inner_smul_left, rep_single, EuclideanSpace.inner_single_left, map_one, + one_mul, hreal] + have hh := Equiv.sum_comp (Equiv.inv H) (fun h => χ h * v ((ι h)⁻¹ • b)) + simpa only [Equiv.inv_apply, map_inv, inv_inv, hinv] using hh + + + +theorem alternator_rank_one (ι : H →* G) (χ : H →* ℂ) (b : X) + (hreal : ∀ h, conj (χ h) = χ h) (hinv : ∀ h, χ h⁻¹ = χ h) + (hfree : ∀ h : H, ι h • b = b → h = 1) + (halt : ∀ x : X, (∃ a : H, ι a • x = x ∧ χ a = -1) ∨ + ∃ a : H, x = ι a • b) (v : EuclideanSpace ℂ X) : + alternator ι χ v = + ⟪alternator ι χ (EuclideanSpace.single b (1 : ℂ)), v⟫_ℂ • + alternator ι χ (EuclideanSpace.single b (1 : ℂ)) := by + classical + let e := alternator ι χ (EuclideanSpace.single b (1 : ℂ)) + have hs (x : X) : alternator ι χ (EuclideanSpace.single x (1 : ℂ)) ∈ Submodule.span ℂ {e} := by + rcases halt x with ⟨a, ha, hχ⟩ | ⟨a, rfl⟩ + · rw [alternator_single_zero ι χ x a ha hχ] + exact Submodule.zero_mem _ + · rw [← rep_single, alternator_translate] + exact Submodule.smul_mem _ _ (Submodule.subset_span (Set.mem_singleton e)) + have hv : alternator ι χ v ∈ Submodule.span ℂ {e} := by + have hexp := (EuclideanSpace.basisFun X ℂ).sum_repr v + simp only [EuclideanSpace.basisFun_repr, EuclideanSpace.basisFun_apply] at hexp + rw [← hexp, map_sum] + exact Submodule.sum_mem _ fun x _ => by + rw [map_smul] + exact Submodule.smul_mem _ _ (hs x) + obtain ⟨a, ha⟩ := Submodule.mem_span_singleton.mp hv + have heb : e b = 1 := polytabloid_base ι χ b hfree + have hab : a = alternator ι χ v b := by + have hh := congrArg (fun z : EuclideanSpace ℂ X => z b) ha + simpa only [PiLp.smul_apply, smul_eq_mul, heb, mul_one] using hh + rw [← ha, hab, polytabloid_inner ι χ b hreal hinv] + +end PermutationSpace +variable {α : Type*} [contextInstance389_21 : Fintype α] + +def complexSign : Equiv.Perm α →* ℂ where + toFun g := ((Equiv.Perm.sign g : ℤˣ) : ℤ) + map_one' := by simp + map_mul' := by intro g h; simp + +@[simp] lemma complexSign_conj (g : Equiv.Perm α) : conj (complexSign g) = complexSign g := by + simp [complexSign] + +@[simp] lemma complexSign_inv (g : Equiv.Perm α) : complexSign g⁻¹ = complexSign g := by + simp [complexSign] + +@[simp] lemma complexSign_swap (x y : α) (h : x ≠ y) : complexSign (Equiv.swap x y) = -1 := by + simp [complexSign, Equiv.Perm.sign_swap h] + + +end SpinAngle.Specht + +namespace SpinAngle.Young + +abbrev Cells (D : YoungDiagram) := {p : ℕ × ℕ // p ∈ D.cells} + +lemma fin_le_strictMono {n : ℕ} (f : Fin n → ℕ) (hf : StrictMono f) (i : Fin n) : + i.val ≤ f i := by + have aux : ∀ k (hk : k < n), k ≤ f ⟨k, hk⟩ := by + intro k + induction k with + | zero => intro hk; exact Nat.zero_le _ + | succ k ih => + intro hk + have hk' : k < n := by omega + have hl := hf (show (⟨k, hk'⟩ : Fin n) < ⟨k + 1, hk⟩ from by simp) + have hi := ih hk' + omega + exact aux i.val i.isLt + +lemma card_column (D : YoungDiagram) (j : ℕ) : + (Finset.univ.filter fun x : Cells D => x.val.2 = j).card = D.colLen j := by + classical + let e : {x : Cells D // x.val.2 = j} ≃ Fin (D.colLen j) := { + toFun := fun x => ⟨x.val.val.1, YoungDiagram.mem_iff_lt_colLen.mp (by + have hx : (x.val.val.1, x.val.val.2) ∈ D := x.val.property + simpa only [x.property] using hx)⟩ + invFun := fun i => ⟨⟨(i, j), YoungDiagram.mem_iff_lt_colLen.mpr i.isLt⟩, rfl⟩ + left_inv := by intro x; apply Subtype.ext; apply Subtype.ext; exact Prod.ext rfl x.property.symm + right_inv := by intro i; rfl } + rw [← Fintype.card_subtype] + exact (Fintype.card_congr e).trans (Fintype.card_fin _) + +lemma card_row_subtype (D : YoungDiagram) (i : ℕ) : + Fintype.card {x : Cells D // x.val.1 = i} = D.rowLen i := by + let e : {x : Cells D // x.val.1 = i} ≃ Fin (D.rowLen i) := { + toFun := fun x => ⟨x.val.val.2, YoungDiagram.mem_iff_lt_rowLen.mp (by + have hx : (x.val.val.1, x.val.val.2) ∈ D := x.val.property + simpa only [x.property] using hx)⟩ + invFun := fun j => ⟨⟨(i, j), YoungDiagram.mem_iff_lt_rowLen.mpr j.isLt⟩, rfl⟩ + left_inv := by intro x; apply Subtype.ext; apply Subtype.ext; exact Prod.ext x.property.symm rfl + right_inv := by intro j; rfl } + exact (Fintype.card_congr e).trans (Fintype.card_fin _) + +lemma eq_of_rowPreserving (D E : YoungDiagram) (e : Cells D ≃ Cells E) + (he : ∀ x, (e x).val.1 = x.val.1) : D = E := by + have hr (i : ℕ) : D.rowLen i = E.rowLen i := by + rw [← card_row_subtype D i, ← card_row_subtype E i] + exact Fintype.card_congr (e.subtypeEquiv (fun x => by rw [he])) + apply YoungDiagram.ext + ext p + obtain ⟨i, j⟩ := p + change (i, j) ∈ D ↔ (i, j) ∈ E + simp only [YoungDiagram.mem_iff_lt_rowLen, hr] + + + + +theorem column_sort_le (D : YoungDiagram) (r : Cells D → ℕ) + (hinj : ∀ x y : Cells D, x.val.2 = y.val.2 → r x = r y → x = y) + : + ∃ σ : Equiv.Perm (Cells D), (∀ x, (σ x).val.2 = x.val.2) ∧ + ∀ x, x.val.1 ≤ r (σ x) := by + classical + let S (j : ℕ) : Finset ℕ := (Finset.univ.filter fun x : Cells D => x.val.2 = j).image r + have hc (j : ℕ) : (S j).card = D.colLen j := by + change ((Finset.univ.filter fun x : Cells D => x.val.2 = j).image r).card = _ + rw [Finset.card_image_iff.mpr (show Set.InjOn r ↑(Finset.univ.filter fun x : Cells D => x.val.2 = j) from by + intro x hx y hy hxy + exact hinj x y ((Finset.mem_filter.mp hx).2.trans (Finset.mem_filter.mp hy).2.symm) hxy)] + exact card_column D j + let F (j : ℕ) := (S j).orderEmbOfFin (hc j) + have hpre (x : Cells D) : ∃ y : Cells D, y.val.2 = x.val.2 ∧ + r y = F x.val.2 ⟨x.val.1, YoungDiagram.mem_iff_lt_colLen.mp x.property⟩ := by + have hm := (S x.val.2).orderEmbOfFin_mem (hc _) ⟨x.val.1, YoungDiagram.mem_iff_lt_colLen.mp x.property⟩ + obtain ⟨y, hy, he⟩ := Finset.mem_image.mp hm + exact ⟨y, (Finset.mem_filter.mp hy).2, he⟩ + choose f hcol hr using hpre + have hf : Function.Injective f := by + intro x y he + have hj : x.val.2 = y.val.2 := (hcol x).symm.trans ((congrArg (fun z : Cells D => z.val.2) he).trans (hcol y)) + have hi : x.val.1 = y.val.1 := by + have hval : F x.val.2 ⟨x.val.1, YoungDiagram.mem_iff_lt_colLen.mp x.property⟩ = + F y.val.2 ⟨y.val.1, YoungDiagram.mem_iff_lt_colLen.mp y.property⟩ := by + rw [← hr x, ← hr y, he] + have hy : y.val.1 < D.colLen x.val.2 := by rw [hj]; exact YoungDiagram.mem_iff_lt_colLen.mp y.property + have hid : F y.val.2 ⟨y.val.1, YoungDiagram.mem_iff_lt_colLen.mp y.property⟩ = F x.val.2 ⟨y.val.1, hy⟩ := by + have aux (j k i : ℕ) (hk : j = k) (hi : i < D.colLen j) (hi' : i < D.colLen k) : + F j ⟨i, hi⟩ = F k ⟨i, hi'⟩ := by subst k; rfl + exact aux _ _ _ hj.symm _ _ + rw [hid] at hval + exact congrArg Fin.val ((F x.val.2).injective hval) + exact Subtype.ext (Prod.ext hi hj) + let σ : Equiv.Perm (Cells D) := Equiv.ofBijective f ⟨hf, Finite.surjective_of_injective hf⟩ + refine ⟨σ, hcol, ?_⟩ + have hle (x : Cells D) : x.val.1 ≤ r (σ x) := by + change x.val.1 ≤ r (f x) + rw [hr] + exact fin_le_strictMono _ (F x.val.2).strictMono ⟨x.val.1, YoungDiagram.mem_iff_lt_colLen.mp x.property⟩ + exact hle + +lemma rowRankSum_le (D : YoungDiagram) (r : Cells D → ℕ) + (hinj : ∀ x y : Cells D, x.val.2 = y.val.2 → r x = r y → x = y) : + ∑ x : Cells D, x.val.1 ≤ ∑ x : Cells D, r x := by + obtain ⟨σ, -, hσ⟩ := column_sort_le D r hinj + rw [← Equiv.sum_comp σ r] + exact Finset.sum_le_sum fun x _ => hσ x + +theorem column_sort (D : YoungDiagram) (r : Cells D → ℕ) + (hinj : ∀ x y : Cells D, x.val.2 = y.val.2 → r x = r y → x = y) + (hsum : ∑ x : Cells D, r x = ∑ x : Cells D, x.val.1) : + ∃ σ : Equiv.Perm (Cells D), (∀ x, (σ x).val.2 = x.val.2) ∧ + ∀ x, r (σ x) = x.val.1 := by + obtain ⟨σ, hc, hle⟩ := column_sort_le D r hinj + refine ⟨σ, hc, ?_⟩ + have heq : ∑ x : Cells D, x.val.1 = ∑ x : Cells D, r (σ x) := by + rw [Equiv.sum_comp σ r, hsum] + have hh := (Finset.sum_eq_sum_iff_of_le (s := Finset.univ) (fun x _ => hle x)).mp heq + intro x + exact (hh x (Finset.mem_univ x)).symm + +end SpinAngle.Young + +namespace SpinAngle.PolynomialCarrier +open scoped Classical Matrix +open SpinAngle.Specht SpinAngle.Young +variable {ι n : Type*} [contextInstance532_23 : Fintype ι] [contextInstance532_35 : DecidableEq ι] [contextInstance532_51 : Fintype n] [contextInstance532_63 : DecidableEq n] + + +instance coloringAction : MulAction (Equiv.Perm ι) (ι → n) where + smul g x := x ∘ g.symm + one_smul _ := rfl + mul_smul _ _ _ := rfl + +lemma site_apply + {ι : Type*} {n : Type*} + [Fintype ι] + [DecidableEq ι] + [Fintype n] + [DecidableEq n] (g : Equiv.Perm ι) (v : EuclideanSpace ℂ (ι → n)) (x : ι → n) : + PermutationSpace.rep g v x = v (x ∘ g) := rfl + +def reindex (g : Equiv.Perm ι) : (ι → n) ≃ (ι → n) where + toFun x := x ∘ g + invFun x := x ∘ g.symm + left_inv x := by funext i; simp + right_inv x := by funext i; simp + +lemma action_site_commute (a : Matrix n n ℂ) (g : Equiv.Perm ι) + (v : EuclideanSpace ℂ (ι → n)) : + TensorRep.action a (PermutationSpace.rep g v) = + PermutationSpace.rep g (TensorRep.action a v) := by + ext x + change (∑ y, TensorRep.tensor (fun _ : ι => a) x y * v (y ∘ g)) = + ∑ y, TensorRep.tensor (fun _ : ι => a) (x ∘ g) y * v y + rw [← Equiv.sum_comp (reindex (n := n) g) + (fun y => TensorRep.tensor (fun _ : ι => a) (x ∘ g) y * v y)] + apply Finset.sum_congr rfl + intro y _ + change _ = TensorRep.tensor (fun _ : ι => a) (x ∘ g) (y ∘ g) * v (y ∘ g) + rw [TensorRep.tensor_reindex] + + +def columnGroup (D : YoungDiagram) : Subgroup (Equiv.Perm (Cells D)) where + carrier := {g | ∀ x, (g x).val.2 = x.val.2} + one_mem' := fun _ => rfl + mul_mem' := by intro g h hg hh x; exact (hg (h x)).trans (hh x) + inv_mem' := by + intro g hg x + simpa using (hg (g⁻¹ x)).symm + +variable (D : YoungDiagram) (q : ℕ) +abbrev TensorSpace := EuclideanSpace ℂ (Cells D → Fin q) + + + +def alternating : Subrepresentation (TensorRep.rep (ι := Cells D) (n := Fin q)) where + toSubmodule := { + carrier := {v | ∀ g : columnGroup D, + PermutationSpace.rep (g : Equiv.Perm (Cells D)) v = complexSign g.val • v} + zero_mem' := by intro g; simp + add_mem' := by intro x y hx hy g; simp [map_add, hx g, hy g, smul_add] + smul_mem' := by intro c x hx g; simp [map_smul, hx g, smul_comm c] } + apply_mem_toSubmodule a := by + intro v hv g + change PermutationSpace.rep g.val (TensorRep.action (a : Matrix (Fin q) (Fin q) ℂ) v) = _ + rw [← action_site_commute, hv g, map_smul] + rfl + +variable (hq : D.colLen 0 ≤ q) + +def rowColor : Cells D → Fin q := fun x => ⟨x.val.1, by + have hm := D.up_left_mem le_rfl (Nat.zero_le x.val.2) x.property + have hl := YoungDiagram.mem_iff_lt_colLen.mp hm + exact lt_of_lt_of_le hl hq⟩ + +def highest : TensorSpace D q := by + classical + exact PermutationSpace.alternator (columnGroup D).subtype + (complexSign.comp (columnGroup D).subtype) + (EuclideanSpace.single (rowColor D q hq) (1 : ℂ)) + +lemma rowColor_column_free + {ι : Type*} + [Fintype ι] + [DecidableEq ι] + (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) (g : columnGroup D) + (hg : g.val • rowColor D q hq = rowColor D q hq) : g = 1 := by + apply Subtype.ext + apply Equiv.Perm.ext + intro x + apply Subtype.ext + apply Prod.ext + · have hh := congrFun hg (g.val x) + have hh' := congrArg Fin.val hh + change (g.val x).val.1 = x.val.1 + change ((g.val x |> g.val.symm)).val.1 = (g.val x).val.1 at hh' + simp only [Equiv.symm_apply_apply] at hh' + exact hh'.symm + · exact g.property x + +lemma highest_base : highest D q hq (rowColor D q hq) = 1 := by + classical + unfold highest + exact PermutationSpace.polytabloid_base (columnGroup D).subtype + (complexSign.comp (columnGroup D).subtype) (rowColor D q hq) + (rowColor_column_free (ι := Cells D) D q hq) + +lemma highest_ne_zero : highest D q hq ≠ 0 := by + intro he + have hh := congrArg (fun v : TensorSpace D q => v (rowColor D q hq)) he + simp [highest_base] at hh + +end SpinAngle.PolynomialCarrier + +namespace SpinAngle.Specht.PermutationSpace +open scoped Classical +variable {G H X : Type*} [contextInstance635_25 : Group G] [contextInstance635_35 : Group H] [contextInstance635_45 : Fintype H] [contextInstance635_57 : Fintype X] [contextInstance635_69 : MulAction G X] +lemma rep_alternator + {G : Type*} {H : Type*} {X : Type*} + [contextInstance635_25 : Group G] + [contextInstance635_35 : Group H] + [contextInstance635_45 : Fintype H] + [Fintype X] + [contextInstance635_69 : MulAction G X] (ι : H →* G) (χ : H →* ℂ) (a : H) + (v : EuclideanSpace ℂ X) : + rep (ι a) (alternator ι χ v) = χ a⁻¹ • alternator ι χ v := by + rw [alternator_apply, map_sum, Finset.smul_sum] + have he := Equiv.sum_comp (Equiv.mulLeft a) + (fun h => χ a⁻¹ • (χ h • (rep (ι h) v : EuclideanSpace ℂ X))) + rw [← he] + apply Finset.sum_congr rfl + intro h _ + simp only [Equiv.coe_mulLeft, smul_smul, map_mul, map_smul] + rw [show χ a⁻¹ * (χ a * χ h) = χ h by + rw [← mul_assoc, ← map_mul, inv_mul_cancel, map_one, one_mul]] + rfl +end SpinAngle.Specht.PermutationSpace + +namespace SpinAngle.PolynomialCarrier +open scoped Classical Matrix +open SpinAngle.Specht SpinAngle.Young +variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) + +lemma highest_mem : highest D q hq ∈ alternating D q := by + classical + intro g + change PermutationSpace.rep g.val (PermutationSpace.alternator _ _ _) = _ + have hh := PermutationSpace.rep_alternator (columnGroup D).subtype + (complexSign.comp (columnGroup D).subtype) g (EuclideanSpace.single (rowColor D q hq) (1 : ℂ)) + change PermutationSpace.rep g.val (highest D q hq) = complexSign (g.val⁻¹) • highest D q hq at hh + rw [complexSign_inv] at hh + exact hh + + +lemma alternating_collision (v : TensorSpace D q) (hv : v ∈ alternating D q) + (x : Cells D → Fin q) (i j : Cells D) (hij : i ≠ j) + (hc : i.val.2 = j.val.2) (hx : x i = x j) : v x = 0 := by + classical + let : DecidableEq (Cells D) := Classical.decEq _ + let g : columnGroup D := ⟨Equiv.swap i j, by + intro k + by_cases hki : k = i + · subst k; simp [hc] + by_cases hkj : k = j + · subst k; simp [hc] + rw [Equiv.swap_apply_of_ne_of_ne hki hkj]⟩ + have hperm : x ∘ (g : Equiv.Perm (Cells D)) = x := by + funext k + change x (Equiv.swap i j k) = x k + by_cases hki : k = i + · subst k; simp [hx] + by_cases hkj : k = j + · subst k; simp [hx] + rw [Equiv.swap_apply_of_ne_of_ne hki hkj] + have hh := congrArg (fun w : TensorSpace D q => w x) (hv g) + simp only [site_apply, hperm, PiLp.smul_apply, smul_eq_mul] at hh + have hg : complexSign g.val = -1 := by + simpa only [g] using complexSign_swap i j hij + rw [hg, neg_one_mul] at hh + linear_combination (1/2 : ℂ) * hh + +lemma alternating_injective (v : TensorSpace D q) (hv : v ∈ alternating D q) + (x : Cells D → Fin q) (hx : v x ≠ 0) : + ∀ i j : Cells D, i.val.2 = j.val.2 → (x i).val = (x j).val → i = j := by + intro i j hc he + by_contra hij + exact hx (alternating_collision D q v hv x i j hij hc (Fin.ext he)) + + + +lemma alternating_minimal_weight (v : TensorSpace D q) (hv : v ∈ alternating D q) + (x : Cells D → Fin q) (hw : ∑ i, (x i).val = ∑ i : Cells D, i.val.1) : + v x = v (rowColor D q hq) * highest D q hq x := by + by_cases hx : v x = 0 + · by_cases he : highest D q hq x = 0 + · rw [hx, he, mul_zero] + · obtain ⟨σ, hc, hr⟩ := column_sort D (fun i => (x i).val) + (alternating_injective D q (highest D q hq) (highest_mem D q hq) x he) hw + let g : columnGroup D := ⟨σ, hc⟩ + have hcolor : x ∘ σ = rowColor D q hq := by funext i; exact Fin.ext (hr i) + have hh := congrArg (fun w : TensorSpace D q => w x) (hv g) + simp only [site_apply, PiLp.smul_apply, smul_eq_mul] at hh + change v (x ∘ σ) = complexSign σ * v x at hh + rw [hcolor, hx, mul_zero] at hh + rw [hx, hh, zero_mul] + · obtain ⟨σ, hc, hr⟩ := column_sort D (fun i => (x i).val) + (alternating_injective D q v hv x hx) hw + let g : columnGroup D := ⟨σ, hc⟩ + have hcolor : x ∘ σ = rowColor D q hq := by funext i; exact Fin.ext (hr i) + have hh := congrArg (fun w : TensorSpace D q => w x) (hv g) + have he := congrArg (fun w : TensorSpace D q => w x) (highest_mem D q hq g) + simp only [site_apply, PiLp.smul_apply, smul_eq_mul] at hh he + change v (x ∘ σ) = complexSign σ * v x at hh + change highest D q hq (x ∘ σ) = complexSign σ * highest D q hq x at he + rw [hcolor] at hh he + rw [highest_base] at he + rw [hh] + calc + v x = v x * 1 := (mul_one _).symm + _ = v x * (complexSign σ * highest D q hq x) := by rw [← he] + _ = complexSign σ * v x * highest D q hq x := by ring + +end SpinAngle.PolynomialCarrier + +namespace SpinAngle.PolynomialCarrier +open scoped Classical Matrix +open SpinAngle.Specht SpinAngle.Young +variable {ι : Type*} [contextInstance741_21 : Fintype ι] [contextInstance741_33 : DecidableEq ι] {q : ℕ} + +lemma diagonal_single (a : Fin q → ℂ) (b : ι → Fin q) : + TensorRep.action (Matrix.diagonal a) (EuclideanSpace.single b (1 : ℂ)) = + (∏ i, a (b i)) • EuclideanSpace.single b (1 : ℂ) := by + ext x + rw [TensorRep.action_diagonal] + simp only [PiLp.smul_apply, smul_eq_mul, PiLp.single_apply] + by_cases h : x = b + · subst x; rfl + · simp [h] + +lemma diagonal_unitary {z : ℂ} (hz : star z * z = 1) : + Matrix.diagonal (fun i : Fin q => z ^ i.val) ∈ Matrix.unitaryGroup (Fin q) ℂ := by + have hd : star (Matrix.diagonal (fun i : Fin q => z ^ i.val)) = + Matrix.diagonal (fun i : Fin q => star (z ^ i.val)) := by + ext i j + by_cases h : i = j + · subst j; simp [Matrix.star_apply] + · simp [Matrix.star_apply, h, Ne.symm h] + rw [Matrix.mem_unitaryGroup_iff', hd, Matrix.diagonal_mul_diagonal] + simp only [star_pow, ← mul_pow, hz, one_pow] + exact Matrix.diagonal_one + +variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) + +def weightOrder : ℕ := Fintype.card (Cells D) * q + 1 + +def weightRoot : ℂ := Complex.exp (2 * Real.pi * Complex.I / weightOrder D q) + +lemma weightRoot_primitive : IsPrimitiveRoot (weightRoot D q) (weightOrder D q) := + Complex.isPrimitiveRoot_exp _ (by unfold weightOrder; omega) + +lemma weightRoot_unitary : star (weightRoot D q) * weightRoot D q = 1 := by + have hn := Complex.norm_eq_one_of_pow_eq_one + (weightRoot_primitive D q).pow_eq_one (show weightOrder D q ≠ 0 by unfold weightOrder; omega) + rw [mul_comm, Complex.star_def, Complex.mul_conj, Complex.normSq_eq_norm_sq, hn] + norm_num + +def weightElement : Matrix.unitaryGroup (Fin q) ℂ := + ⟨Matrix.diagonal (fun i => weightRoot D q ^ i.val), diagonal_unitary (weightRoot_unitary D q)⟩ + +lemma weight_sum_lt (x : Cells D → Fin q) : ∑ i, (x i).val < weightOrder D q := by + have hh : (∑ i, (x i).val) ≤ ∑ _i : Cells D, q := + Finset.sum_le_sum fun i _ => (x i).isLt.le + simp only [Finset.sum_const, Finset.card_univ, smul_eq_mul] at hh + unfold weightOrder + omega + +lemma weight_action (v : TensorSpace D q) (x : Cells D → Fin q) : + TensorRep.rep (weightElement D q) v x = weightRoot D q ^ (∑ i, (x i).val) * v x := by + change TensorRep.action (Matrix.diagonal (fun i : Fin q => weightRoot D q ^ i.val)) v x = _ + rw [TensorRep.action_diagonal, Finset.prod_pow_eq_pow_sum] + +lemma highest_diagonal (a : Fin q → ℂ) : + TensorRep.action (Matrix.diagonal a) (highest D q hq) = + (∏ i, a (rowColor D q hq i)) • highest D q hq := by + unfold highest + rw [PermutationSpace.alternator_apply, map_sum, Finset.smul_sum] + apply Finset.sum_congr rfl + intro g _ + rw [map_smul, action_site_commute, diagonal_single, map_smul] + exact smul_comm _ _ _ + +lemma highest_weight_eigen : + TensorRep.rep (weightElement D q) (highest D q hq) = + weightRoot D q ^ (∑ i : Cells D, i.val.1) • highest D q hq := by + change TensorRep.action (Matrix.diagonal _) _ = _ + rw [highest_diagonal] + congr 1 + exact Finset.prod_pow_eq_pow_sum _ _ _ + +include hq in +lemma weight_eigen_support (v : TensorSpace D q) + (hv : TensorRep.rep (weightElement D q) v = + weightRoot D q ^ (∑ i : Cells D, i.val.1) • v) + (x : Cells D → Fin q) (hx : v x ≠ 0) : + ∑ i, (x i).val = ∑ i : Cells D, i.val.1 := by + have hh := congrArg (fun w : TensorSpace D q => w x) hv + rw [weight_action] at hh + simp only [PiLp.smul_apply, smul_eq_mul] at hh + have hp := mul_right_cancel₀ hx hh + apply (weightRoot_primitive D q).pow_inj (weight_sum_lt D q x) _ hp + exact weight_sum_lt D q (rowColor D q hq) + + +theorem weight_eigenspace_one_dimensional (v : TensorSpace D q) + (hv : v ∈ alternating D q) + (heig : TensorRep.rep (weightElement D q) v = + weightRoot D q ^ (∑ i : Cells D, i.val.1) • v) : + v = v (rowColor D q hq) • highest D q hq := by + ext x + change v x = v (rowColor D q hq) * highest D q hq x + by_cases hw : ∑ i, (x i).val = ∑ i : Cells D, i.val.1 + · exact alternating_minimal_weight D q hq v hv x hw + · have hv0 : v x = 0 := by + by_contra hn + exact hw (weight_eigen_support D q hq v heig x hn) + have he0 : highest D q hq x = 0 := by + by_contra hn + exact hw (weight_eigen_support D q hq _ (highest_weight_eigen D q hq) x hn) + rw [hv0, he0, mul_zero] + + + +def ordinary : Subrepresentation (alternating D q).toRepresentation := + cyclic (alternating D q).toRepresentation + (⟨highest D q hq, highest_mem D q hq⟩ : (alternating D q).toSubmodule) + +theorem ordinary_irreducible : Representation.IsIrreducible (ordinary D q hq).toRepresentation := by + refine cyclic_irreducible_of_simple_eigen _ _ ?_ ?_ (weightElement D q) + (weightRoot D q ^ (∑ i : Cells D, i.val.1)) ?_ ?_ + · intro he + exact highest_ne_zero D q hq (congrArg Subtype.val he) + · intro g x y + exact TensorRep.rep_unitary g (x : TensorSpace D q) (y : TensorSpace D q) + · exact Subtype.ext (highest_weight_eigen D q hq) + · intro v hv + apply Submodule.mem_span_singleton.mpr + refine ⟨v.val (rowColor D q hq), ?_⟩ + apply Subtype.ext + exact (weight_eigenspace_one_dimensional D q hq v.val v.property (congrArg Subtype.val hv)).symm + +end SpinAngle.PolynomialCarrier + +namespace SpinAngle.TensorRep +open scoped Classical +variable {ι κ n : Type*} [contextInstance868_25 : Fintype ι] [contextInstance868_37 : DecidableEq ι] [contextInstance868_53 : Fintype κ] [contextInstance868_65 : DecidableEq κ] + [contextInstance869_2 : Fintype n] [contextInstance869_14 : DecidableEq n] + +lemma diagonal_unitary_of_star_mul (a : n → ℂ) (ha : ∀ i, star (a i) * a i = 1) : + Matrix.diagonal a ∈ Matrix.unitaryGroup n ℂ := by + have hd : star (Matrix.diagonal a) = Matrix.diagonal (fun i => star (a i)) := by + ext i j + by_cases h : i = j + · subst j; simp [Matrix.star_apply] + · simp [Matrix.star_apply, h, Ne.symm h] + rw [Matrix.mem_unitaryGroup_iff', hd, Matrix.diagonal_mul_diagonal] + simp only [ha] + exact Matrix.diagonal_one + +lemma diagonal_single [DecidableEq (ι → n)] (a : n → ℂ) (b : ι → n) : + action (Matrix.diagonal a) (EuclideanSpace.single b (1 : ℂ)) = + (∏ i, a (b i)) • EuclideanSpace.single b (1 : ℂ) := by + ext x + rw [action_diagonal] + simp only [PiLp.smul_apply, smul_eq_mul, PiLp.single_apply] + by_cases h : x = b + · subst x; rfl + · simp [h] + +def content (x : ι → n) (j : n) : ℕ := (Finset.univ.filter fun i => x i = j).card + +lemma product_content + {ι : Type*} {n : Type*} + [contextInstance868_25 : Fintype ι] + [DecidableEq ι] + [contextInstance869_2 : Fintype n] + [contextInstance869_14 : DecidableEq n] (a : n → ℂ) (x : ι → n) : + ∏ i, a (x i) = ∏ j, a j ^ content x j := by + rw [← Finset.prod_fiberwise' Finset.univ x a] + simp only [Finset.prod_const, content] + +lemma phase_product + {ι : Type*} {n : Type*} + [contextInstance868_25 : Fintype ι] + [DecidableEq ι] + [Fintype n] + [contextInstance869_14 : DecidableEq n] (z : ℂ) (j : n) (x : ι → n) : + ∏ i, (if x i = j then z else 1) = z ^ content x j := by + rw [← Finset.prod_filter] + simp [content] + +lemma content_le_card + {ι : Type*} {n : Type*} + [contextInstance868_25 : Fintype ι] + [DecidableEq ι] + [Fintype n] + [contextInstance869_14 : DecidableEq n] (x : ι → n) (j : n) : content x j ≤ Fintype.card ι := + (Finset.card_filter_le _ _).trans_eq (Finset.card_univ) + + + +lemma intertwiner_content_zero + (L : EuclideanSpace ℂ (ι → n) →ₗ[ℂ] EuclideanSpace ℂ (κ → n)) + (hL : ∀ (g : Matrix.unitaryGroup n ℂ) v, L (rep g v) = rep g (L v)) + (x : ι → n) (y : κ → n) (j : n) (hxy : content x j ≠ content y j) : + L (EuclideanSpace.single x (1 : ℂ)) y = 0 := by + let N := Fintype.card ι + Fintype.card κ + 1 + let z : ℂ := Complex.exp (2 * Real.pi * Complex.I / N) + have hz : IsPrimitiveRoot z N := Complex.isPrimitiveRoot_exp _ (by dsimp [N]; omega) + have hzn : ‖z‖ = 1 := Complex.norm_eq_one_of_pow_eq_one hz.pow_eq_one (by dsimp [N]; omega) + have hzu : star z * z = 1 := by + rw [mul_comm, Complex.star_def, Complex.mul_conj, Complex.normSq_eq_norm_sq, hzn] + norm_num + let g : Matrix.unitaryGroup n ℂ := ⟨Matrix.diagonal (fun k => if k = j then z else 1), + diagonal_unitary_of_star_mul _ (fun k => by split_ifs; exact hzu; simp)⟩ + have hh := congrArg (fun v : EuclideanSpace ℂ (κ → n) => v y) + (hL g (EuclideanSpace.single x (1 : ℂ))) + change L (action (Matrix.diagonal _) _) y = action (Matrix.diagonal _) _ y at hh + rw [diagonal_single, map_smul, action_diagonal] at hh + simp only [PiLp.smul_apply, smul_eq_mul, phase_product] at hh + by_contra hn + apply hxy + exact hz.pow_inj (by have := content_le_card x j; dsimp [N]; omega) + (by have := content_le_card y j; dsimp [N]; omega) (mul_right_cancel₀ hn hh) + + + +lemma intertwiner_diagonal + (L : EuclideanSpace ℂ (ι → n) →ₗ[ℂ] EuclideanSpace ℂ (κ → n)) + (hL : ∀ (g : Matrix.unitaryGroup n ℂ) v, L (rep g v) = rep g (L v)) + (a : n → ℂ) (v : EuclideanSpace ℂ (ι → n)) : + L (action (Matrix.diagonal a) v) = action (Matrix.diagonal a) (L v) := by + have hsingle (x : ι → n) : + L (action (Matrix.diagonal a) (EuclideanSpace.single x (1 : ℂ))) = + action (Matrix.diagonal a) (L (EuclideanSpace.single x (1 : ℂ))) := by + ext y + rw [diagonal_single, map_smul, action_diagonal] + simp only [PiLp.smul_apply, smul_eq_mul] + by_cases he : ∀ j, content x j = content y j + · rw [product_content a x, product_content a y] + congr 1 + exact Finset.prod_congr rfl fun j _ => congrArg (fun k => a j ^ k) (he j) + · push Not at he + obtain ⟨j, hj⟩ := he + rw [intertwiner_content_zero L hL x y j hj, mul_zero, mul_zero] + have hexp := (EuclideanSpace.basisFun (ι → n) ℂ).sum_repr v + simp only [EuclideanSpace.basisFun_repr, EuclideanSpace.basisFun_apply] at hexp + rw [← hexp, map_sum, map_sum, map_sum, map_sum] + apply Finset.sum_congr rfl + intro x _ + rw [map_smul, map_smul, map_smul, map_smul, hsingle] + + + +lemma intertwiner_hermitian + (L : EuclideanSpace ℂ (ι → n) →ₗ[ℂ] EuclideanSpace ℂ (κ → n)) + (hL : ∀ (g : Matrix.unitaryGroup n ℂ) v, L (rep g v) = rep g (L v)) + (a : Matrix n n ℂ) (ha : a.IsHermitian) (v : EuclideanSpace ℂ (ι → n)) : + L (action a v) = action a (L v) := by + rw [ha.spectral_theorem] + simp only [Unitary.conjStarAlgAut_apply, map_mul, Module.End.mul_apply] + change L (rep ha.eigenvectorUnitary (action (Matrix.diagonal _) (rep (star ha.eigenvectorUnitary) v))) = _ + rw [hL, intertwiner_diagonal L hL, hL] + rfl + +end SpinAngle.TensorRep + +namespace SpinAngle.TensorRep +open SpinAngle.Specht +variable {ι n : Type*} [contextInstance980_23 : Fintype ι] [contextInstance980_35 : DecidableEq ι] [contextInstance980_51 : Fintype n] [contextInstance980_63 : DecidableEq n] + + + +lemma apply_mem_hermitian (U : Subrepresentation (rep (ι := ι) (n := n))) + (a : Matrix n n ℂ) (ha : a.IsHermitian) + (v : EuclideanSpace ℂ (ι → n)) (hv : v ∈ U) : action a v ∈ U := by + let L : EuclideanSpace ℂ (ι → n) →ₗ[ℂ] EuclideanSpace ℂ (ι → n) := + U.toSubmodule.starProjection.toLinearMap + have hu : ∀ (g : Matrix.unitaryGroup n ℂ) (x y : EuclideanSpace ℂ (ι → n)), + ⟪rep g x, rep g y⟫_ℂ = ⟪x, y⟫_ℂ := rep_unitary + have hL : ∀ (g : Matrix.unitaryGroup n ℂ) (w : EuclideanSpace ℂ (ι → n)), + L (rep g w) = rep g (L w) := by + intro g w + exact starProjection_rep (rep (ι := ι) (n := n)) hu U g w + have hlv : L v = v := U.toSubmodule.starProjection_eq_self_iff.mpr hv + have hh := intertwiner_hermitian L hL a ha v + rw [hlv] at hh + rw [← hh] + exact U.toSubmodule.starProjection_apply_mem _ + +end SpinAngle.TensorRep + +namespace SpinAngle.PolynomialCarrier +open scoped Classical Matrix +open SpinAngle.Specht SpinAngle.Young +variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) + + +def highestMonomial (t : Fin q → ℝ) : ℝ := ∏ i : Cells D, t (rowColor D q hq i) + +lemma highestMonomial_nonneg (t : Fin q → ℝ) (ht : ∀ j, 0 ≤ t j) : + 0 ≤ highestMonomial D q hq t := Finset.prod_nonneg fun _ _ => ht _ + + + +lemma monomial_le_highest (t : Fin q → ℝ) (ht : ∀ j, 0 ≤ t j) (hanti : Antitone t) + (x : Cells D → Fin q) + (hinj : ∀ i j : Cells D, i.val.2 = j.val.2 → (x i).val = (x j).val → i = j) : + (∏ i, t (x i)) ≤ highestMonomial D q hq t := by + obtain ⟨σ, -, hσ⟩ := column_sort_le D (fun i => (x i).val) hinj + rw [← Equiv.prod_comp σ (fun i => t (x i))] + apply Finset.prod_le_prod₀ (fun _ _ => ht _) + intro i _ + exact hanti (show rowColor D q hq i ≤ x (σ i) from hσ i) + + + +theorem diagonal_norm_bound (t : Fin q → ℝ) (ht : ∀ j, 0 ≤ t j) (hanti : Antitone t) + (v : TensorSpace D q) (hv : v ∈ alternating D q) : + ‖TensorRep.action (Matrix.diagonal (fun j => (t j : ℂ))) v‖ ≤ + highestMonomial D q hq t * ‖v‖ := by + have hb := highestMonomial_nonneg D q hq t ht + apply (sq_le_sq₀ (norm_nonneg _) (mul_nonneg hb (norm_nonneg _))).mp + rw [mul_pow, EuclideanSpace.norm_sq_eq, EuclideanSpace.norm_sq_eq, Finset.mul_sum] + apply Finset.sum_le_sum + intro x _ + rw [TensorRep.action_diagonal, norm_mul, norm_prod, mul_pow] + simp only [Complex.norm_real, Real.norm_eq_abs, abs_of_nonneg (ht _)] + by_cases hz : v x = 0 + · simp [hz] + · apply mul_le_mul_of_nonneg_right _ (sq_nonneg _) + exact pow_le_pow_left₀ (Finset.prod_nonneg fun _ _ => ht _) + (monomial_le_highest D q hq t ht hanti x (alternating_injective D q v hv x hz)) 2 + +end SpinAngle.PolynomialCarrier + + + + + +noncomputable section +open scoped Matrix ComplexOrder +namespace SpinAngle.SortedSpectrum +variable {q : ℕ} (A : Matrix (Fin q) (Fin q) ℂ) (hA : A.IsHermitian) + +def values : Fin q → ℝ := + (Matrix.isSymmetric_toEuclideanLin_iff.mpr hA).eigenvalues (by simp) + +def basis : OrthonormalBasis (Fin q) ℂ (EuclideanSpace ℂ (Fin q)) := + (Matrix.isSymmetric_toEuclideanLin_iff.mpr hA).eigenvectorBasis (by simp) + +def changeBasis : Matrix.unitaryGroup (Fin q) ℂ := + ⟨(EuclideanSpace.basisFun (Fin q) ℂ).toBasis.toMatrix (basis A hA).toBasis, + (EuclideanSpace.basisFun (Fin q) ℂ).toMatrix_orthonormalBasis_mem_unitary (basis A hA)⟩ + +@[simp] lemma changeBasis_apply (i j : Fin q) : changeBasis A hA i j = basis A hA j i := rfl + +lemma values_antitone : Antitone (values A hA) := + LinearMap.IsSymmetric.eigenvalues_antitone _ _ + +lemma eigenvector (i : Fin q) : + Matrix.toEuclideanLin A (basis A hA i) = (values A hA i : ℂ) • basis A hA i := + LinearMap.IsSymmetric.apply_eigenvectorBasis _ _ _ + +lemma spectral_theorem : A = (changeBasis A hA : Matrix _ _ ℂ) * + Matrix.diagonal (fun i => (values A hA i : ℂ)) * star (changeBasis A hA : Matrix _ _ ℂ) := by + have he : A * (changeBasis A hA : Matrix _ _ ℂ) = + (changeBasis A hA : Matrix _ _ ℂ) * Matrix.diagonal (fun i => (values A hA i : ℂ)) := by + ext i j + rw [Matrix.mul_diagonal] + simpa only [Matrix.mul_apply, changeBasis_apply, + Matrix.toLpLin_apply, Matrix.mulVec, dotProduct, PiLp.smul_apply, smul_eq_mul, + mul_comm] using congrArg (fun v : EuclideanSpace ℂ (Fin q) => v i) (eigenvector A hA j) + have hh := congrArg (fun B : Matrix (Fin q) (Fin q) ℂ => B * star (changeBasis A hA : Matrix _ _ ℂ)) he + simpa only [Matrix.mul_assoc, (changeBasis A hA).property.2, Matrix.mul_one] using hh + +lemma values_nonneg (hpos : A.PosSemidef) (i : Fin q) : 0 ≤ values A hA i := by + have hp := (Matrix.isPositive_toEuclideanLin_iff.mpr hpos).inner_nonneg_left (basis A hA i) + rw [eigenvector, inner_smul_left, (basis A hA).inner_eq_one i] at hp + have hp' : (0 : ℂ) ≤ (values A hA i : ℂ) := by simpa only [Complex.conj_ofReal, mul_one] using hp + exact RCLike.ofReal_nonneg.mp hp' + +lemma trace_eq_sum : Matrix.trace A = ∑ i, (values A hA i : ℂ) := by + conv_lhs => rw [spectral_theorem A hA] + rw [Matrix.trace_mul_cycle, (changeBasis A hA).property.1, + Matrix.one_mul, Matrix.trace_diagonal] + +end SpinAngle.SortedSpectrum + +namespace SpinAngle.PolynomialCarrier +open scoped Classical Matrix InnerProductSpace +open SpinAngle.Specht SpinAngle.Young Module +variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) + +abbrev Carrier : Type := (ordinary D q hq).toSubmodule + +instance carrierInner : InnerProductSpace ℂ (Carrier D q hq) := + @Submodule.innerProductSpace ℂ (alternating D q).toSubmodule _ _ inferInstance + (ordinary D q hq).toSubmodule + + +def inclusion : Carrier D q hq →ₗᵢ[ℂ] TensorSpace D q := + (alternating D q).toSubmodule.subtypeₗᵢ.comp (ordinary D q hq).toSubmodule.subtypeₗᵢ + +@[simp] lemma inclusion_apply (v : Carrier D q hq) : inclusion D q hq v = v.val.val := rfl + +lemma inclusion_equivariant (g : Matrix.unitaryGroup (Fin q) ℂ) (v : Carrier D q hq) : + inclusion D q hq ((ordinary D q hq).toRepresentation g v) = + TensorRep.rep g (inclusion D q hq v) := rfl + +def image : Subrepresentation (TensorRep.rep (ι := Cells D) (n := Fin q)) where + toSubmodule := LinearMap.range (inclusion D q hq).toLinearMap + apply_mem_toSubmodule := by + rintro g v ⟨x,rfl⟩ + exact ⟨(ordinary D q hq).toRepresentation g x,rfl⟩ + +lemma inclusion_image (v : Carrier D q hq) : inclusion D q hq v ∈ image D q hq := ⟨v,rfl⟩ + + +def hermitianAction (a : Matrix (Fin q) (Fin q) ℂ) (ha : a.IsHermitian) : + Carrier D q hq →ₗ[ℂ] Carrier D q hq := + (LinearEquiv.ofInjective (inclusion D q hq).toLinearMap (inclusion D q hq).injective).symm.toLinearMap.comp + ((TensorRep.action a).comp (inclusion D q hq).toLinearMap |>.codRestrict + (image D q hq).toSubmodule (fun v => TensorRep.apply_mem_hermitian _ a ha _ (inclusion_image D q hq v))) + +@[simp] lemma inclusion_hermitianAction (a : Matrix (Fin q) (Fin q) ℂ) (ha : a.IsHermitian) + (v : Carrier D q hq) : + inclusion D q hq (hermitianAction D q hq a ha v) = TensorRep.action a (inclusion D q hq v) := by + exact congrArg Subtype.val ((LinearEquiv.ofInjective (inclusion D q hq).toLinearMap + (inclusion D q hq).injective).apply_symm_apply _) + +lemma tensor_hermitian (a : Matrix (Fin q) (Fin q) ℂ) (ha : a.IsHermitian) : + (TensorRep.tensor (fun _ : Cells D => a)).IsHermitian := by + change star (TensorRep.tensor (fun _ : Cells D => a)) = _ + rw [← TensorRep.tensor_star] + congr 1 + funext i + exact ha + +lemma hermitianAction_symmetric (a : Matrix (Fin q) (Fin q) ℂ) (ha : a.IsHermitian) : + LinearMap.IsSymmetric (𝕜 := ℂ) (E := Carrier D q hq) (hermitianAction D q hq a ha) := by + intro x y + rw [← (inclusion D q hq).inner_map_map, ← (inclusion D q hq).inner_map_map x, + inclusion_hermitianAction, inclusion_hermitianAction] + exact (Matrix.isSymmetric_toEuclideanLin_iff.mpr (tensor_hermitian D q a ha)) x.val.val y.val.val + +lemma ordinary_rep_unitary (g : Matrix.unitaryGroup (Fin q) ℂ) (v w : Carrier D q hq) : + ⟪(ordinary D q hq).toRepresentation g v, (ordinary D q hq).toRepresentation g w⟫_ℂ = ⟪v,w⟫_ℂ := + TensorRep.rep_unitary g v.val.val w.val.val + +lemma raw_norm_unitary (g : Matrix.unitaryGroup (Fin q) ℂ) (v : TensorSpace D q) : + ‖TensorRep.rep g v‖ = ‖v‖ := + (TensorRep.rep g).isometryOfInner (TensorRep.rep_unitary g) |>.norm_map v + + +theorem hermitianAction_norm_bound (a : Matrix (Fin q) (Fin q) ℂ) (ha : a.PosSemidef) + (v : Carrier D q hq) : + ‖hermitianAction D q hq a ha.isHermitian v‖ ≤ + highestMonomial D q hq (SortedSpectrum.values a ha.isHermitian) * ‖v‖ := by + rw [← (inclusion D q hq).norm_map (hermitianAction D q hq a ha.isHermitian v), + inclusion_hermitianAction, ← (inclusion D q hq).norm_map v] + let u := SortedSpectrum.changeBasis a ha.isHermitian + let t := SortedSpectrum.values a ha.isHermitian + have he := SortedSpectrum.spectral_theorem a ha.isHermitian + have hin : TensorRep.rep u⁻¹ (inclusion D q hq v) ∈ alternating D q := + (alternating D q).apply_mem_toSubmodule u⁻¹ v.val.property + have hb := diagonal_norm_bound D q hq t (SortedSpectrum.values_nonneg a ha.isHermitian ha) + (SortedSpectrum.values_antitone a ha.isHermitian) _ hin + change a = (u : Matrix _ _ ℂ) * Matrix.diagonal (fun i => (t i : ℂ)) * (↑(u⁻¹) : Matrix _ _ ℂ) at he + conv_lhs => rw [he] + simp only [map_mul, Module.End.mul_apply] + change ‖TensorRep.rep u (TensorRep.action (Matrix.diagonal _) (TensorRep.rep u⁻¹ _))‖ ≤ _ + rw [raw_norm_unitary] + simpa only [raw_norm_unitary] using hb + +end SpinAngle.PolynomialCarrier + + + + +noncomputable section +open scoped TensorProduct InnerProductSpace BigOperators +namespace SpinAngle.ExternalTensor +open Module +variable {E F : Type*} [contextInstance1195_23 : NormedAddCommGroup E] [contextInstance1195_46 : InnerProductSpace ℂ E] + [contextInstance1196_2 : NormedAddCommGroup F] [contextInstance1196_25 : InnerProductSpace ℂ F] + [contextInstance1197_2 : FiniteDimensional ℂ E] [contextInstance1197_26 : FiniteDimensional ℂ F] +variable {G H : Type*} [contextInstance1198_23 : Group G] [contextInstance1198_33 : Group H] + +def rep (ρ : Representation ℂ G E) (σ : Representation ℂ H F) : + Representation ℂ (G × H) (E ⊗[ℂ] F) := + Representation.tprod (ρ.comp (MonoidHom.fst G H)) (σ.comp (MonoidHom.snd G H)) + +@[simp] lemma rep_tmul + {E : Type*} {F : Type*} + [contextInstance1195_23 : NormedAddCommGroup E] + [contextInstance1195_46 : InnerProductSpace ℂ E] + [contextInstance1196_2 : NormedAddCommGroup F] + [contextInstance1196_25 : InnerProductSpace ℂ F] + [FiniteDimensional ℂ E] + [FiniteDimensional ℂ F] + {G : Type*} {H : Type*} + [contextInstance1198_23 : Group G] + [contextInstance1198_33 : Group H] (ρ : Representation ℂ G E) (σ : Representation ℂ H F) + (g : G × H) (x : E) (y : F) : + rep ρ σ g (x ⊗ₜ[ℂ] y) = ρ g.1 x ⊗ₜ σ g.2 y := rfl + +def rightSlice (β : Module.Dual ℂ F) : E ⊗[ℂ] F →ₗ[ℂ] E := + (TensorProduct.rid ℂ E).toLinearMap.comp (TensorProduct.map LinearMap.id β) + +def leftSlice (α : Module.Dual ℂ E) : E ⊗[ℂ] F →ₗ[ℂ] F := + (TensorProduct.lid ℂ F).toLinearMap.comp (TensorProduct.map α LinearMap.id) + +@[simp] lemma rightSlice_tmul + {E : Type*} {F : Type*} + [contextInstance1195_23 : NormedAddCommGroup E] + [contextInstance1195_46 : InnerProductSpace ℂ E] + [contextInstance1196_2 : NormedAddCommGroup F] + [contextInstance1196_25 : InnerProductSpace ℂ F] + [FiniteDimensional ℂ E] + [FiniteDimensional ℂ F] (β : Module.Dual ℂ F) (x : E) (y : F) : + rightSlice β (x ⊗ₜ[ℂ] y) = β y • x := rfl +@[simp] lemma leftSlice_tmul + {E : Type*} {F : Type*} + [contextInstance1195_23 : NormedAddCommGroup E] + [contextInstance1195_46 : InnerProductSpace ℂ E] + [contextInstance1196_2 : NormedAddCommGroup F] + [contextInstance1196_25 : InnerProductSpace ℂ F] + [FiniteDimensional ℂ E] + [FiniteDimensional ℂ F] (α : Module.Dual ℂ E) (x : E) (y : F) : + leftSlice α (x ⊗ₜ[ℂ] y) = α x • y := rfl + +lemma slice_commute + {E : Type*} {F : Type*} + [contextInstance1195_23 : NormedAddCommGroup E] + [contextInstance1195_46 : InnerProductSpace ℂ E] + [contextInstance1196_2 : NormedAddCommGroup F] + [contextInstance1196_25 : InnerProductSpace ℂ F] + [FiniteDimensional ℂ E] + [FiniteDimensional ℂ F] (α : Module.Dual ℂ E) (β : Module.Dual ℂ F) (v : E ⊗[ℂ] F) : + α (rightSlice β v) = β (leftSlice α v) := by + induction v using TensorProduct.inductionOn with + | tmul x y => simp [mul_comm] + | add x y hx hy => simp [hx, hy] + +lemma slice_map_left + {E : Type*} {F : Type*} + [contextInstance1195_23 : NormedAddCommGroup E] + [contextInstance1195_46 : InnerProductSpace ℂ E] + [contextInstance1196_2 : NormedAddCommGroup F] + [contextInstance1196_25 : InnerProductSpace ℂ F] + [FiniteDimensional ℂ E] + [FiniteDimensional ℂ F] (β : Module.Dual ℂ F) (A : E →ₗ[ℂ] E) (v : E ⊗[ℂ] F) : + rightSlice β (TensorProduct.map A LinearMap.id v) = A (rightSlice β v) := by + induction v using TensorProduct.inductionOn with + | tmul x y => simp + | add x y hx hy => simp [hx, hy] + +lemma eq_sum_slices + {E : Type*} {F : Type*} + [contextInstance1195_23 : NormedAddCommGroup E] + [contextInstance1195_46 : InnerProductSpace ℂ E] + [contextInstance1196_2 : NormedAddCommGroup F] + [contextInstance1196_25 : InnerProductSpace ℂ F] + [FiniteDimensional ℂ E] + [FiniteDimensional ℂ F] {ι : Type*} [Fintype ι] (b : Basis ι ℂ F) (v : E ⊗[ℂ] F) : + v = ∑ i, rightSlice (b.coord i) v ⊗ₜ[ℂ] b i := by + induction v using TensorProduct.inductionOn with + | tmul x y => + simp only [rightSlice_tmul, TensorProduct.smul_tmul, + ← TensorProduct.tmul_sum, Basis.coord_apply, Basis.sum_repr] + | add x y hx hy => simp only [map_add, TensorProduct.add_tmul, Finset.sum_add_distrib, ← hx, ← hy] + +lemma rightSlice_ext {v w : E ⊗[ℂ] F} + (h : ∀ β : Module.Dual ℂ F, rightSlice β v = rightSlice β w) : v = w := by + classical + let b := Module.finBasis ℂ F + rw [eq_sum_slices b v, eq_sum_slices b w] + exact Finset.sum_congr rfl fun i _ => congrArg (fun x : E => x ⊗ₜ[ℂ] b i) (h _) + +lemma scalar_of_commute (ρ : Representation ℂ G E) [ρ.IsIrreducible] + (A : E →ₗ[ℂ] E) (hA : ∀ g x, A (ρ g x) = ρ g (A x)) : + ∃ z : ℂ, A = z • LinearMap.id := by + let f := A.intertwiningMap_of_isIntertwiningMap ρ ρ hA + obtain ⟨z, hz⟩ := + (Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed (ρ := ρ)).surjective f + refine ⟨z, ?_⟩ + ext x + exact (congrArg (fun L : ρ.IntertwiningMap ρ => L x) hz).symm + + +lemma left_commutant (ρ : Representation ℂ G E) [ρ.IsIrreducible] + (d : E ⊗[ℂ] F →ₗ[ℂ] E ⊗[ℂ] F) + (hd : ∀ g v, d (TensorProduct.map (ρ g) LinearMap.id v) = + TensorProduct.map (ρ g) LinearMap.id (d v)) : + ∃ B : F →ₗ[ℂ] F, d = TensorProduct.map LinearMap.id B := by + classical + let : Nontrivial E := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) ρ.asModule + obtain ⟨x₀, hx₀⟩ := exists_ne (0 : E) + obtain ⟨α, hα⟩ := Module.Projective.exists_dual_eq_one ℂ hx₀ + let B : F →ₗ[ℂ] F := (leftSlice α).comp (d.comp (TensorProduct.mk ℂ E F x₀)) + refine ⟨B, ?_⟩ + ext x y + change d (x ⊗ₜ[ℂ] y) = TensorProduct.map LinearMap.id B (x ⊗ₜ[ℂ] y) + apply rightSlice_ext + intro β + let A : E →ₗ[ℂ] E := (rightSlice β).comp (d.comp ((TensorProduct.mk ℂ E F).flip y)) + have hA (g : G) (v : E) : A (ρ g v) = ρ g (A v) := by + change rightSlice β (d (ρ g v ⊗ₜ[ℂ] y)) = ρ g (rightSlice β (d (v ⊗ₜ[ℂ] y))) + rw [← slice_map_left, ← hd] + rfl + obtain ⟨z,hz⟩ := scalar_of_commute ρ A hA + have hzv (v : E) : rightSlice β (d (v ⊗ₜ[ℂ] y)) = z • v := + congrArg (fun f : E →ₗ[ℂ] E => f v) hz + have hzB : β (B y) = z := by + change β (leftSlice α (d (x₀ ⊗ₜ[ℂ] y))) = z + rw [← slice_commute, hzv, map_smul, hα, smul_eq_mul, mul_one] + change rightSlice β (d (x ⊗ₜ[ℂ] y)) = β (B y) • x + rw [hzv, hzB] + +lemma commutant_scalar (ρ : Representation ℂ G E) (σ : Representation ℂ H F) + [ρ.IsIrreducible] [σ.IsIrreducible] + (d : (rep ρ σ).IntertwiningMap (rep ρ σ)) : + ∃ z : ℂ, d.toLinearMap = z • LinearMap.id := by + obtain ⟨B,hB⟩ := left_commutant ρ d.toLinearMap (by + intro g v + simpa [rep, Representation.tprod_apply, Module.End.one_eq_id] using Representation.IntertwiningMap.isIntertwining _ _ d (g,1) v) + have hσ (h : H) (y : F) : B (σ h y) = σ h (B y) := by + let : Nontrivial E := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) ρ.asModule + obtain ⟨x,hx⟩ := exists_ne (0 : E) + obtain ⟨α,hα⟩ := Module.Projective.exists_dual_eq_one ℂ hx + have hh := Representation.IntertwiningMap.isIntertwining _ _ d (1,h) (x ⊗ₜ[ℂ] y) + change d.toLinearMap (rep ρ σ (1,h) (x ⊗ₜ y)) = + rep ρ σ (1,h) (d.toLinearMap (x ⊗ₜ y)) at hh + rw [hB] at hh + simp only [rep_tmul, map_one, Module.End.one_apply, TensorProduct.map_tmul, + LinearMap.id_apply] at hh + have := congrArg (leftSlice α) hh + simpa [hα] using this + obtain ⟨z,hz⟩ := scalar_of_commute σ B hσ + refine ⟨z, ?_⟩ + rw [hB, hz] + ext x y + simp + +lemma unitary + {E : Type*} {F : Type*} + [contextInstance1195_23 : NormedAddCommGroup E] + [contextInstance1195_46 : InnerProductSpace ℂ E] + [contextInstance1196_2 : NormedAddCommGroup F] + [contextInstance1196_25 : InnerProductSpace ℂ F] + [FiniteDimensional ℂ E] + [FiniteDimensional ℂ F] + {G : Type*} {H : Type*} + [contextInstance1198_23 : Group G] + [contextInstance1198_33 : Group H] (ρ : Representation ℂ G E) (σ : Representation ℂ H F) + (hρ : ∀ g x y, ⟪ρ g x, ρ g y⟫_ℂ = ⟪x,y⟫_ℂ) + (hσ : ∀ h x y, ⟪σ h x, σ h y⟫_ℂ = ⟪x,y⟫_ℂ) + (g : G × H) (v w : E ⊗[ℂ] F) : + ⟪rep ρ σ g v, rep ρ σ g w⟫_ℂ = ⟪v,w⟫_ℂ := by + let a : E →ₗᵢ[ℂ] E := (ρ g.1).isometryOfInner (hρ g.1) + let b : F →ₗᵢ[ℂ] F := (σ g.2).isometryOfInner (hσ g.2) + exact TensorProduct.inner_map_map a b v w + +lemma projection_commute (τ : Representation ℂ G E) + (hτ : ∀ g x y, ⟪τ g x, τ g y⟫_ℂ = ⟪x,y⟫_ℂ) + (U : Subrepresentation τ) (g : G) (v : E) : + U.toSubmodule.starProjection (τ g v) = τ g (U.toSubmodule.starProjection v) := by + apply U.toSubmodule.eq_starProjection_of_mem_of_inner_eq_zero + · exact U.apply_mem_toSubmodule g (U.toSubmodule.starProjection_apply_mem v) + · intro w hw + have hw' := U.apply_mem_toSubmodule g⁻¹ hw + have he : τ g (τ g⁻¹ w) = w := by + rw [← Module.End.mul_apply, ← map_mul, mul_inv_cancel, map_one, Module.End.one_apply] + rw [← map_sub] + conv_lhs => rhs; rw [← he] + rw [hτ] + exact U.toSubmodule.starProjection_inner_eq_zero v _ hw' + + + +theorem irreducible (ρ : Representation ℂ G E) (σ : Representation ℂ H F) + [ρ.IsIrreducible] [σ.IsIrreducible] + (hρ : ∀ g x y, ⟪ρ g x, ρ g y⟫_ℂ = ⟪x,y⟫_ℂ) + (hσ : ∀ h x y, ⟪σ h x, σ h y⟫_ℂ = ⟪x,y⟫_ℂ) : + (rep ρ σ).IsIrreducible := by + let : Nontrivial E := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) ρ.asModule + let : Nontrivial F := IsSimpleModule.nontrivial (MonoidAlgebra ℂ H) σ.asModule + obtain ⟨x,hx⟩ := exists_ne (0 : E) + obtain ⟨y,hy⟩ := exists_ne (0 : F) + have hxy : x ⊗ₜ[ℂ] y ≠ 0 := by + intro h + have := congrArg norm h + simp only [TensorProduct.norm_tmul, norm_zero] at this + exact (mul_ne_zero (norm_ne_zero_iff.mpr hx) (norm_ne_zero_iff.mpr hy)) this + have htb : (⊤ : Subrepresentation (rep ρ σ)) ≠ ⊥ := by + intro h + have hh : x ⊗ₜ[ℂ] y ∈ (⊤ : Subrepresentation (rep ρ σ)) := by trivial + rw [h] at hh + exact hxy hh + let : Nontrivial (Subrepresentation (rep ρ σ)) := ⟨⟨⊤,⊥,htb⟩⟩ + refine ⟨fun U => ?_⟩ + let d : (rep ρ σ).IntertwiningMap (rep ρ σ) := + U.toSubmodule.starProjection.toLinearMap.intertwiningMap_of_isIntertwiningMap _ _ + (projection_commute _ (unitary ρ σ hρ hσ) U) + obtain ⟨z,hz⟩ := commutant_scalar ρ σ d + have hproj (v : E ⊗[ℂ] F) : U.toSubmodule.starProjection v = z • v := + congrArg (fun f : E ⊗[ℂ] F →ₗ[ℂ] E ⊗[ℂ] F => f v) hz + by_cases hz0 : z = 0 + · left + apply bot_unique + intro v hv + change v = 0 + have hh := hproj v + rw [U.toSubmodule.starProjection_eq_self_iff.mpr hv, hz0, zero_smul] at hh + exact hh + · right + apply top_unique + intro v _ + have hv := U.toSubmodule.starProjection_apply_mem (z⁻¹ • v) + rw [hproj, smul_smul, mul_inv_cancel₀ hz0, one_smul] at hv + exact hv + +end SpinAngle.ExternalTensor + + + + + + +noncomputable section +open scoped BigOperators ComplexConjugate +namespace SpinAngle.TorusNaturality +open Module +variable {n X Y E F : Type*} [contextInstance1400_29 : Fintype n] [contextInstance1400_41 : Fintype X] [contextInstance1400_53 : Fintype Y] + [contextInstance1401_2 : AddCommGroup E] [contextInstance1401_19 : Module ℂ E] [contextInstance1401_32 : AddCommGroup F] [contextInstance1401_49 : Module ℂ F] +variable (b : Basis X ℂ E) (c : Basis Y ℂ F) + (w : X → n → ℕ) (v : Y → n → ℕ) + (D : (n → ℂ) → E →ₗ[ℂ] E) (D' : (n → ℂ) → F →ₗ[ℂ] F) + (hb : ∀ a x, D a (b x) = (∏ j, a j ^ w x j) • b x) + (hc : ∀ a y, D' a (c y) = (∏ j, a j ^ v y j) • c y) + +include hc in +lemma repr_diagonal (a : n → ℂ) (f : F) (y : Y) : + c.repr (D' a f) y = (∏ j, a j ^ v y j) * c.repr f y := by + classical + calc + c.repr (D' a f) y = c.repr (D' a (∑ k, c.repr f k • c k)) y := by rw [c.sum_repr] + _ = _ := by + simp only [map_sum, map_smul, hc, + Basis.repr_self] + simp [Finset.sum_apply, Finsupp.single_apply, mul_comm] + +lemma coefficient_zero + {n : Type*} {X : Type*} {Y : Type*} {E : Type*} {F : Type*} + [contextInstance1400_29 : Fintype n] + [Fintype X] + [contextInstance1400_53 : Fintype Y] + [contextInstance1401_2 : AddCommGroup E] + [contextInstance1401_19 : Module ℂ E] + [contextInstance1401_32 : AddCommGroup F] + [contextInstance1401_49 : Module ℂ F] + (b : Basis X ℂ E) (c : Basis Y ℂ F) + (w : X → n → ℕ) (v : Y → n → ℕ) + (D : (n → ℂ) → E →ₗ[ℂ] E) (D' : (n → ℂ) → F →ₗ[ℂ] F) + (hb : ∀ a x, D a (b x) = (∏ j, a j ^ w x j) • b x) + (hc : ∀ a y, D' a (c y) = (∏ j, a j ^ v y j) • c y) (L : E →ₗ[ℂ] F) + (hL : ∀ a : n → ℂ, (∀ j, star (a j) * a j = 1) → ∀ x, L (D a x) = D' a (L x)) + (x : X) (y : Y) (j : n) (hxy : w x j ≠ v y j) : + c.repr (L (b x)) y = 0 := by + classical + let N := w x j + v y j + 1 + let z : ℂ := Complex.exp (2 * Real.pi * Complex.I / N) + have hN : N ≠ 0 := by dsimp [N]; omega + have hz : IsPrimitiveRoot z N := Complex.isPrimitiveRoot_exp _ hN + have hzn : ‖z‖ = 1 := Complex.norm_eq_one_of_pow_eq_one hz.pow_eq_one hN + have hzu : star z * z = 1 := by + rw [mul_comm, Complex.star_def, Complex.mul_conj, Complex.normSq_eq_norm_sq, hzn] + norm_num + let a : n → ℂ := fun k => if k = j then z else 1 + have ha : ∀ k, star (a k) * a k = 1 := by + intro k + dsimp [a] + split_ifs + · exact hzu + · simp + have hh := congrArg (fun f => c.repr f y) (hL a ha (b x)) + rw [hb, map_smul, map_smul, Finsupp.smul_apply, smul_eq_mul, + repr_diagonal c v D' hc] at hh + have hprod (u : n → ℕ) : (∏ k, a k ^ u k) = z ^ u j := by + simp [a] + rw [hprod, hprod] at hh + by_contra hn + exact hxy (hz.pow_inj (by dsimp [N]; omega) (by dsimp [N]; omega) + (mul_right_cancel₀ hn hh)) + +include b c w v hb hc in + + +theorem diagonal (L : E →ₗ[ℂ] F) + (hL : ∀ a : n → ℂ, (∀ j, star (a j) * a j = 1) → ∀ x, L (D a x) = D' a (L x)) + (a : n → ℂ) : L.comp (D a) = (D' a).comp L := by + classical + apply b.ext + intro x + apply c.repr.injective + ext y + simp only [LinearMap.comp_apply, hb, map_smul, Finsupp.smul_apply, smul_eq_mul, + repr_diagonal c v D' hc] + by_cases hw : w x = v y + · rw [hw] + · obtain ⟨j,hj⟩ := Function.ne_iff.mp hw + rw [coefficient_zero b c w v D D' hb hc L hL x y j hj] + simp + +end SpinAngle.TorusNaturality + + +namespace SpinAngle.SignedTensor +open scoped Classical Matrix TensorProduct InnerProductSpace +open Module +variable {q : ℕ} +abbrev Spin (q : ℕ) := Fin q × Bool +abbrev Mat (q : ℕ) := Matrix (Fin q) (Fin q) ℂ +abbrev Group (q : ℕ) := Matrix.unitaryGroup (Fin q) ℂ × Matrix.unitaryGroup (Fin q) ℂ + +def block : (Mat q × Mat q) →* Matrix (Spin q) (Spin q) ℂ where + toFun a := Matrix.blockDiagonal (fun b : Bool => cond b a.2 a.1) + map_one' := by + convert (Matrix.blockDiagonal_one (m := Fin q) (o := Bool) (α := ℂ)) using 1 + congr 1 + funext b + cases b <;> rfl + map_mul' a b := by + rw [← Matrix.blockDiagonal_mul] + congr 1 + funext c + cases c <;> rfl + +lemma block_star (a : Mat q × Mat q) : block (star a) = star (block a) := by + change Matrix.blockDiagonal (fun b : Bool => cond b (star a.2) (star a.1)) = (Matrix.blockDiagonal (fun b : Bool => cond b a.2 a.1))ᴴ + rw [Matrix.blockDiagonal_conjTranspose] + congr 1 + funext b + cases b <;> rfl + +def blockGroup : Group q →* Matrix.unitaryGroup (Spin q) ℂ where + toFun g := ⟨block (g.1.val,g.2.val), by + rw [Matrix.mem_unitaryGroup_iff', ← block_star, ← map_mul] + have he : star (g.1.val,g.2.val) * (g.1.val,g.2.val) = 1 := + Prod.ext g.1.property.1 g.2.property.1 + rw [he, map_one]⟩ + map_one' := by + apply Subtype.ext + change block (1 : Mat q × Mat q) = 1 + exact block.map_one + map_mul' g h := by + apply Subtype.ext + change block ((g.1.val,g.2.val) * (h.1.val,h.2.val)) = + block (g.1.val,g.2.val) * block (h.1.val,h.2.val) + exact block.map_mul _ _ + +variable {ι κ τ : Type*} [contextInstance1517_25 : Fintype ι] [contextInstance1517_37 : DecidableEq ι] [contextInstance1517_53 : Fintype κ] [contextInstance1517_65 : DecidableEq κ] + [contextInstance1518_2 : Fintype τ] [contextInstance1518_14 : DecidableEq τ] + +abbrev Raw := EuclideanSpace ℂ (τ → Spin q) +abbrev PairRaw := EuclideanSpace ℂ (ι → Fin q) ⊗[ℂ] EuclideanSpace ℂ (κ → Fin q) + +def rep : Representation ℂ (Group q) (Raw (q := q) (τ := τ)) := + (TensorRep.rep (ι := τ)).comp blockGroup + +def pairRep : Representation ℂ (Group q) (PairRaw (q := q) (ι := ι) (κ := κ)) := + ExternalTensor.rep TensorRep.rep TensorRep.rep + +def pairAction : (Mat q × Mat q) →* Module.End ℂ (PairRaw (q := q) (ι := ι) (κ := κ)) where + toFun a := TensorProduct.map (TensorRep.action a.1) (TensorRep.action a.2) + map_one' := by + ext x y + change TensorProduct.map _ _ (x ⊗ₜ[ℂ] y) = x ⊗ₜ[ℂ] y + simp only [Prod.fst_one, Prod.snd_one, map_one, TensorProduct.map_tmul, + Module.End.one_apply] + map_mul' a b := by + ext x y + change TensorProduct.map _ _ (x ⊗ₜ[ℂ] y) = + TensorProduct.map _ _ (TensorProduct.map _ _ (x ⊗ₜ[ℂ] y)) + simp only [Prod.fst_mul, Prod.snd_mul, map_mul, TensorProduct.map_tmul, + Module.End.mul_apply] + +@[simp] lemma pairAction_tmul (a : Mat q × Mat q) + (x : EuclideanSpace ℂ (ι → Fin q)) (y : EuclideanSpace ℂ (κ → Fin q)) : + pairAction a (x ⊗ₜ[ℂ] y) = TensorRep.action a.1 x ⊗ₜ TensorRep.action a.2 y := rfl + +lemma pairRep_eq (g : Group q) : pairRep (ι := ι) (κ := κ) g = pairAction (g.1.val,g.2.val) := rfl + +lemma rep_unitary (g : Group q) (v w : Raw (q := q) (τ := τ)) : + ⟪rep g v,rep g w⟫_ℂ = ⟪v,w⟫_ℂ := TensorRep.rep_unitary (blockGroup g) v w + +lemma pairRep_unitary (g : Group q) (v w : PairRaw (q := q) (ι := ι) (κ := κ)) : + ⟪pairRep g v,pairRep g w⟫_ℂ = ⟪v,w⟫_ℂ := + ExternalTensor.unitary (TensorRep.rep (ι := ι) (n := Fin q)) (TensorRep.rep (ι := κ) (n := Fin q)) + TensorRep.rep_unitary TensorRep.rep_unitary g v w + +def pairBasis : OrthonormalBasis ((ι → Fin q) × (κ → Fin q)) ℂ (PairRaw (q := q) (ι := ι) (κ := κ)) := + (EuclideanSpace.basisFun _ ℂ).tensorProduct (EuclideanSpace.basisFun _ ℂ) + +def pairContent (x : (ι → Fin q) × (κ → Fin q)) (j : Spin q) : ℕ := + cond j.2 (TensorRep.content x.2 j.1) (TensorRep.content x.1 j.1) + +def diagPair (a : Spin q → ℂ) : Mat q × Mat q := + (Matrix.diagonal (fun j => a (j,false)), Matrix.diagonal (fun j => a (j,true))) + +lemma block_diagPair (a : Spin q → ℂ) : block (diagPair a) = Matrix.diagonal a := by + change Matrix.blockDiagonal (fun b : Bool => cond b (Matrix.diagonal (fun j => a (j,true))) (Matrix.diagonal (fun j => a (j,false)))) = Matrix.diagonal a + convert Matrix.blockDiagonal_diagonal (fun (b : Bool) (j : Fin q) => a (j,b)) using 1 + congr 1 + funext b + cases b <;> rfl + +lemma pairBasis_diagonal (a : Spin q → ℂ) (x : (ι → Fin q) × (κ → Fin q)) : + pairAction (diagPair a) (pairBasis x) = + (∏ j, a j ^ pairContent x j) • pairBasis x := by + simp only [pairBasis, OrthonormalBasis.tensorProduct_apply', EuclideanSpace.basisFun_apply, + pairAction_tmul, diagPair, TensorRep.diagonal_single, TensorProduct.smul_tmul, + TensorProduct.tmul_smul, smul_smul] + congr 1 + rw [Fintype.prod_prod_type] + simp only [pairContent, Fintype.prod_bool, Bool.cond_false, Bool.cond_true] + rw [Finset.prod_mul_distrib, TensorRep.product_content (fun j : Fin q => a (j,true)) x.2, + TensorRep.product_content (fun j : Fin q => a (j,false)) x.1] + + + +theorem intertwiner_diagonal + (L : PairRaw (q := q) (ι := ι) (κ := κ) →ₗ[ℂ] Raw (q := q) (τ := τ)) + (hL : ∀ g : Group q, ∀ v, L (pairRep g v) = rep g (L v)) + (a : Spin q → ℂ) (v : PairRaw (q := q) (ι := ι) (κ := κ)) : + L (pairAction (diagPair a) v) = TensorRep.action (Matrix.diagonal a) (L v) := by + have hh := TorusNaturality.diagonal (pairBasis (q := q) (ι := ι) (κ := κ)).toBasis + (EuclideanSpace.basisFun (τ → Spin q) ℂ).toBasis pairContent TensorRep.content + (fun a => pairAction (diagPair a)) (fun a => TensorRep.action (Matrix.diagonal a)) + pairBasis_diagonal (fun a x => by + simpa only [OrthonormalBasis.coe_toBasis, EuclideanSpace.basisFun_apply, TensorRep.product_content] using + (TensorRep.diagonal_single a x)) L (fun a ha v => by + let g : Group q := + (⟨(diagPair a).1, TensorRep.diagonal_unitary_of_star_mul _ (fun j => ha (j,false))⟩, + ⟨(diagPair a).2, TensorRep.diagonal_unitary_of_star_mul _ (fun j => ha (j,true))⟩) + have hh := hL g v + change L (pairAction (diagPair a) v) = TensorRep.action (block (diagPair a)) (L v) at hh + rwa [block_diagPair] at hh) a + exact congrArg (fun f : _ →ₗ[ℂ] _ => f v) hh + +lemma pair_spectral (a : Mat q × Mat q) (ha : a.1.IsHermitian) (hb : a.2.IsHermitian) : + ∃ (g : Group q) (d : Spin q → ℂ), + a = (g.1.val,g.2.val) * diagPair d * (g.1⁻¹.val,g.2⁻¹.val) := by + refine ⟨(ha.eigenvectorUnitary,hb.eigenvectorUnitary), + (fun j => cond j.2 (hb.eigenvalues j.1 : ℂ) (ha.eigenvalues j.1 : ℂ)), ?_⟩ + apply Prod.ext + · exact ha.spectral_theorem + · exact hb.spectral_theorem + + + +theorem intertwiner_hermitian + (L : PairRaw (q := q) (ι := ι) (κ := κ) →ₗ[ℂ] Raw (q := q) (τ := τ)) + (hL : ∀ g : Group q, ∀ v, L (pairRep g v) = rep g (L v)) + (a : Mat q × Mat q) (ha : a.1.IsHermitian) (hb : a.2.IsHermitian) + (v : PairRaw (q := q) (ι := ι) (κ := κ)) : + L (pairAction a v) = TensorRep.action (block a) (L v) := by + obtain ⟨g,d,he⟩ := pair_spectral a ha hb + rw [he] + simp only [map_mul, Module.End.mul_apply, block_diagPair] + change L (pairRep g (pairAction (diagPair d) (pairRep g⁻¹ v))) = + rep g (TensorRep.action (Matrix.diagonal d) (rep g⁻¹ (L v))) + rw [hL, intertwiner_diagonal L hL, hL] + +end SpinAngle.SignedTensor + + + + + + +noncomputable section +open scoped InnerProductSpace +namespace SpinAngle.UnitaryNaturality +variable {G : Type*} [contextInstance1640_21 : Group G] +variable {E F : Type*} [contextInstance1641_23 : NormedAddCommGroup E] [contextInstance1641_46 : InnerProductSpace ℂ E] + [contextInstance1642_2 : NormedAddCommGroup F] [contextInstance1642_25 : InnerProductSpace ℂ F] + [contextInstance1643_2 : FiniteDimensional ℂ E] [contextInstance1643_26 : FiniteDimensional ℂ F] +variable (ρ : Representation ℂ G E) (σ : Representation ℂ G F) + (hρ : ∀ g x y, ⟪ρ g x,ρ g y⟫_ℂ = ⟪x,y⟫_ℂ) + (hσ : ∀ g x y, ⟪σ g x,σ g y⟫_ℂ = ⟪x,y⟫_ℂ) + +lemma inner_move + {G : Type*} + [contextInstance1640_21 : Group G] + {E : Type*} + [contextInstance1641_23 : NormedAddCommGroup E] + [contextInstance1641_46 : InnerProductSpace ℂ E] + [FiniteDimensional ℂ E] + (ρ : Representation ℂ G E) + (hρ : ∀ g x y, ⟪ρ g x,ρ g y⟫_ℂ = ⟪x,y⟫_ℂ) (g : G) (x y : E) : ⟪x,ρ g y⟫_ℂ = ⟪ρ g⁻¹ x,y⟫_ℂ := by + have h := hρ g (ρ g⁻¹ x) y + simpa only [← Module.End.mul_apply, ← map_mul, mul_inv_cancel, map_one, + Module.End.one_apply] using h + +include hρ hσ in +lemma adjoint_intertwines (L : E →ₗ[ℂ] F) + (hL : ∀ g x, L (ρ g x) = σ g (L x)) (g : G) (y : F) : + LinearMap.adjoint L (σ g y) = ρ g (LinearMap.adjoint L y) := by + apply ext_inner_left ℂ + intro x + rw [LinearMap.adjoint_inner_right, inner_move σ hσ, ← hL, + ← LinearMap.adjoint_inner_right, ← inner_move ρ hρ] + +lemma adjoint_isometry (L : E →ₗᵢ[ℂ] F) (x : E) : + LinearMap.adjoint L.toLinearMap (L x) = x := by + apply ext_inner_left ℂ + intro y + rw [LinearMap.adjoint_inner_right] + exact L.inner_map_map y x + +end SpinAngle.UnitaryNaturality + +namespace SpinAngle.SignedCarrier +open scoped Classical TensorProduct InnerProductSpace +open SpinAngle.Young SpinAngle.Specht PolynomialCarrier Module SignedTensor +variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) + +abbrev Carrier := PolynomialCarrier.Carrier a q ha ⊗[ℂ] PolynomialCarrier.Carrier b q hb + +instance carrierNormed : NormedAddCommGroup (Carrier a b q ha hb) := + TensorProduct.instNormedAddCommGroup (𝕜 := ℂ) + (E := PolynomialCarrier.Carrier a q ha) (F := PolynomialCarrier.Carrier b q hb) + +instance carrierInner : InnerProductSpace ℂ (Carrier a b q ha hb) := + TensorProduct.instInnerProductSpace (𝕜 := ℂ) + (E := PolynomialCarrier.Carrier a q ha) (F := PolynomialCarrier.Carrier b q hb) + +instance carrierFinite : FiniteDimensional ℂ (Carrier a b q ha hb) := + inferInstanceAs (FiniteDimensional ℂ (PolynomialCarrier.Carrier a q ha ⊗[ℂ] PolynomialCarrier.Carrier b q hb)) + +abbrev rep : Representation ℂ (Group q) (Carrier a b q ha hb) := + ExternalTensor.rep (E := PolynomialCarrier.Carrier a q ha) + (F := PolynomialCarrier.Carrier b q hb) + (ordinary a q ha).toRepresentation (ordinary b q hb).toRepresentation + +instance irreducible : (rep a b q ha hb).IsIrreducible := by + let := ordinary_irreducible a q ha + let := ordinary_irreducible b q hb + exact ExternalTensor.irreducible _ _ (ordinary_rep_unitary a q ha) (ordinary_rep_unitary b q hb) + +def inclusion : Carrier a b q ha hb →ₗᵢ[ℂ] + PairRaw (q := q) (ι := Cells a) (κ := Cells b) := + TensorProduct.mapIsometry (E := PolynomialCarrier.Carrier a q ha) (F := PolynomialCarrier.Carrier b q hb) + (PolynomialCarrier.inclusion a q ha) (PolynomialCarrier.inclusion b q hb) + +lemma inclusion_equivariant (g : Group q) (v : Carrier a b q ha hb) : + inclusion a b q ha hb (rep a b q ha hb g v) = + pairRep g (inclusion a b q ha hb v) := by + induction v using TensorProduct.inductionOn with + | tmul x y => rfl + | add x y hx hy => simp [hx,hy] + +lemma rep_unitary (g : Group q) (v w : Carrier a b q ha hb) : + ⟪rep a b q ha hb g v,rep a b q ha hb g w⟫_ℂ = ⟪v,w⟫_ℂ := by + rw [← (inclusion a b q ha hb).inner_map_map, + ← (inclusion a b q ha hb).inner_map_map v w, + inclusion_equivariant, inclusion_equivariant] + exact SignedTensor.pairRep_unitary g _ _ + +def hermitianAction (A : Mat q × Mat q) (hA : A.1.IsHermitian) (hB : A.2.IsHermitian) : + Carrier a b q ha hb →ₗ[ℂ] Carrier a b q ha hb := + TensorProduct.map (PolynomialCarrier.hermitianAction a q ha A.1 hA) + (PolynomialCarrier.hermitianAction b q hb A.2 hB) + +lemma inclusion_hermitianAction (A : Mat q × Mat q) (hA : A.1.IsHermitian) (hB : A.2.IsHermitian) + (v : Carrier a b q ha hb) : + inclusion a b q ha hb (hermitianAction a b q ha hb A hA hB v) = + pairAction A (inclusion a b q ha hb v) := by + induction v using TensorProduct.inductionOn with + | tmul x y => + simp only [inclusion, hermitianAction, TensorProduct.mapIsometry_apply, + TensorProduct.map_tmul, pairAction_tmul] + change PolynomialCarrier.inclusion a q ha (PolynomialCarrier.hermitianAction a q ha A.1 hA x) ⊗ₜ[ℂ] + PolynomialCarrier.inclusion b q hb (PolynomialCarrier.hermitianAction b q hb A.2 hB y) = _ + rw [PolynomialCarrier.inclusion_hermitianAction, PolynomialCarrier.inclusion_hermitianAction] + rfl + | add x y hx hy => simp [hx,hy] + +variable {τ : Type*} [contextInstance1741_21 : Fintype τ] [contextInstance1741_33 : DecidableEq τ] + + + +theorem intertwiner_hermitian + (L : (rep a b q ha hb).IntertwiningMap (SignedTensor.rep (q := q) (τ := τ))) + (A : Mat q × Mat q) (hA : A.1.IsHermitian) (hB : A.2.IsHermitian) + (v : Carrier a b q ha hb) : + L (hermitianAction a b q ha hb A hA hB v) = TensorRep.action (block A) (L v) := by + let J := inclusion a b q ha hb + let L' := L.toLinearMap.comp (LinearMap.adjoint J.toLinearMap) + have hequiv (g : Group q) (x : PairRaw (q := q) (ι := Cells a) (κ := Cells b)) : + L' (pairRep g x) = SignedTensor.rep g (L' x) := by + dsimp [L'] + rw [UnitaryNaturality.adjoint_intertwines (rep a b q ha hb) pairRep + (rep_unitary a b q ha hb) SignedTensor.pairRep_unitary J.toLinearMap + (inclusion_equivariant a b q ha hb), L.isIntertwining] + have h := SignedTensor.intertwiner_hermitian L' hequiv A hA hB (J v) + have hj (x : Carrier a b q ha hb) : L' (J x) = L x := by + dsimp [L'] + rw [UnitaryNaturality.adjoint_isometry] + rw [← inclusion_hermitianAction a b q ha hb A hA hB v, hj, hj] at h + exact h + +end SpinAngle.SignedCarrier + + + +namespace SpinAngle.TensorRep +variable {ι n : Type*} [contextInstance1770_23 : Fintype ι] [contextInstance1770_35 : DecidableEq ι] [contextInstance1770_51 : Fintype n] [contextInstance1770_63 : DecidableEq n] + +lemma continuous_action (v : EuclideanSpace ℂ (ι → n)) : + Continuous (fun A : Matrix n n ℂ => action A v) := by + change Continuous (fun A : Matrix n n ℂ => + WithLp.toLp 2 (fun x : ι → n => ∑ y, (∏ i, A (x i) (y i)) * v y)) + apply (PiLp.continuous_toLp 2 (fun _ : ι → n => ℂ)).comp + fun_prop + +lemma continuous_rep : Continuous (fun g : Matrix.unitaryGroup n ℂ => + (rep (ι := ι) g).toContinuousLinearMap) := by + apply continuous_clm_apply.mpr + intro v + exact (continuous_action v).comp continuous_subtype_val +end SpinAngle.TensorRep + +namespace SpinAngle.PolynomialCarrier +open SpinAngle.Young SpinAngle.Specht +variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) +lemma continuous_rep : Continuous (fun g : Matrix.unitaryGroup (Fin q) ℂ => + ((ordinary D q hq).toRepresentation g).toContinuousLinearMap) := by + let : InnerProductSpace ℂ (ordinary D q hq).toSubmodule := carrierInner D q hq + apply (continuous_clm_apply (𝕜 := ℂ) (E := Carrier D q hq) (F := Carrier D q hq)).mpr + intro v + apply (inclusion D q hq).comp_continuous_iff.mp + change Continuous (fun g : Matrix.unitaryGroup (Fin q) ℂ => + TensorRep.rep g (inclusion D q hq v)) + exact continuous_clm_apply.mp (TensorRep.continuous_rep (ι := Cells D) (n := Fin q)) _ +end SpinAngle.PolynomialCarrier + +namespace SpinAngle.ExternalTensor +open scoped TensorProduct +variable {G H : Type*} [contextInstance1802_23 : Group G] [contextInstance1802_33 : Group H] [contextInstance1802_43 : TopologicalSpace G] [contextInstance1802_64 : TopologicalSpace H] +variable {E F : Type*} [contextInstance1803_23 : NormedAddCommGroup E] [contextInstance1803_46 : InnerProductSpace ℂ E] + [contextInstance1804_2 : NormedAddCommGroup F] [contextInstance1804_25 : InnerProductSpace ℂ F] + [contextInstance1805_2 : FiniteDimensional ℂ E] [contextInstance1805_26 : FiniteDimensional ℂ F] +lemma continuous_rep (ρ : Representation ℂ G E) (σ : Representation ℂ H F) + (hρ : Continuous (fun g => (ρ g).toContinuousLinearMap)) + (hσ : Continuous (fun h => (σ h).toContinuousLinearMap)) : + Continuous (fun g : G × H => (rep ρ σ g).toContinuousLinearMap) := by + apply continuous_clm_apply.mpr + intro v + induction v using TensorProduct.inductionOn with + | tmul x y => + change Continuous (fun g : G × H => ρ g.1 x ⊗ₜ[ℂ] σ g.2 y) + exact TensorProduct.continuous_tmul.comp + (((continuous_clm_apply.mp hρ x).comp continuous_fst).prodMk + ((continuous_clm_apply.mp hσ y).comp continuous_snd)) + | add x y hx hy => + have hh : Continuous (fun g : G × H => (rep ρ σ g).toContinuousLinearMap x + + (rep ρ σ g).toContinuousLinearMap y) := hx.add hy + convert hh using 1 + funext g + exact map_add _ x y +end SpinAngle.ExternalTensor + +namespace SpinAngle.SignedTensor +variable {q : ℕ} {τ : Type*} [contextInstance1828_29 : Fintype τ] [contextInstance1828_41 : DecidableEq τ] +lemma continuous_block : Continuous (block (q := q)) := by + apply continuous_pi + intro i + apply continuous_pi + intro j + change Continuous (fun A : Mat q × Mat q => if i.2 = j.2 then (cond i.2 A.2 A.1) i.1 j.1 else 0) + split_ifs + · cases i.2 <;> simp only [Bool.cond_false, Bool.cond_true] <;> fun_prop + · fun_prop + +lemma continuous_blockGroup : Continuous (blockGroup (q := q)) := by + apply Continuous.subtype_mk + exact continuous_block.comp ((continuous_subtype_val.comp continuous_fst).prodMk + (continuous_subtype_val.comp continuous_snd)) + +lemma continuous_rep : Continuous (fun g : Group q => (rep (τ := τ) g).toContinuousLinearMap) := + TensorRep.continuous_rep.comp continuous_blockGroup +end SpinAngle.SignedTensor + +namespace SpinAngle.SignedCarrier +open SpinAngle.Young SpinAngle.Specht SignedTensor +variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) +lemma continuous_rep : Continuous (fun g : Group q => (rep a b q ha hb g).toContinuousLinearMap) := + ExternalTensor.continuous_rep _ _ (PolynomialCarrier.continuous_rep a q ha) + (PolynomialCarrier.continuous_rep b q hb) +end SpinAngle.SignedCarrier + + +namespace SpinAngle.TensorRep +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {ι n : Type*} [contextInstance1859_23 : Fintype ι] [contextInstance1859_35 : DecidableEq ι] [contextInstance1859_51 : Fintype n] [contextInstance1859_63 : DecidableEq n] +lemma tensor_posSemidef (a : ι → Matrix n n ℂ) (ha : ∀ i, (a i).PosSemidef) : + (tensor a).PosSemidef := by + let r : ι → Matrix n n ℂ := fun i => CFC.sqrt (a i) + have he : tensor a = star (tensor r) * tensor r := by + rw [← tensor_star, ← tensor_mul] + congr 1 + funext i + dsimp [r] + rw [(IsSelfAdjoint.of_nonneg (CFC.sqrt_nonneg (a i))).star_eq, + CFC.sqrt_mul_sqrt_self (a i) (ha i).nonneg] + rw [he] + exact Matrix.posSemidef_conjTranspose_mul_self _ + +lemma action_positive (a : Matrix n n ℂ) (ha : a.PosSemidef) : + LinearMap.IsPositive (𝕜 := ℂ) (E := EuclideanSpace ℂ (ι → n)) (action a) := + Matrix.isPositive_toEuclideanLin_iff.mpr (tensor_posSemidef (fun _ : ι => a) (fun _ => ha)) +end SpinAngle.TensorRep + +namespace SpinAngle.PolynomialCarrier +open scoped Classical InnerProductSpace +open SpinAngle.Young SpinAngle.Specht +variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) + +lemma hermitianAction_positive (a : Matrix (Fin q) (Fin q) ℂ) (ha : a.PosSemidef) : + LinearMap.IsPositive (𝕜 := ℂ) (E := Carrier D q hq) (hermitianAction D q hq a ha.isHermitian) := by + refine ⟨hermitianAction_symmetric D q hq a ha.isHermitian, ?_⟩ + intro x + rw [← (inclusion D q hq).inner_map_map, inclusion_hermitianAction] + exact (TensorRep.action_positive a ha).2 (inclusion D q hq x) + +def highestVector : Carrier D q hq := + ⟨⟨highest D q hq,highest_mem D q hq⟩, self_mem_cyclic _ _⟩ + +lemma highestVector_ne_zero : highestVector D q hq ≠ 0 := by + intro h + have he := congrArg (inclusion D q hq) h + exact highest_ne_zero D q hq (by simpa [highestVector] using he) + +lemma inclusion_linear_hermitianAction (A : Matrix (Fin q) (Fin q) ℂ) (hA : A.IsHermitian) + (v : Carrier D q hq) : + (inclusion D q hq).toLinearMap (hermitianAction D q hq A hA v) = + TensorRep.action A ((inclusion D q hq).toLinearMap v) := + inclusion_hermitianAction D q hq A hA v + +lemma highestVector_diagonal (t : Fin q → ℝ) : + hermitianAction D q hq (Matrix.diagonal (fun i => (t i : ℂ))) + (Matrix.isHermitian_diagonal_iff.mpr (fun i => by simp [IsSelfAdjoint])) (highestVector D q hq) = + (highestMonomial D q hq t : ℂ) • highestVector D q hq := by + have hinj : Function.Injective (inclusion D q hq).toLinearMap := by + intro x y h + exact Subtype.ext (Subtype.ext h) + apply hinj + rw [inclusion_linear_hermitianAction, map_smul] + change TensorRep.action (Matrix.diagonal (fun i => (t i : ℂ))) (highest D q hq) = + (highestMonomial D q hq t : ℂ) • highest D q hq + rw [highest_diagonal] + congr 1 + exact (map_prod Complex.ofRealHom _ _).symm + +lemma card_rowColor (j : Fin q) : + (Finset.univ.filter fun i : Cells D => rowColor D q hq i = j).card = D.rowLen j := by + rw [← Fintype.card_subtype] + calc + Fintype.card {i : Cells D // rowColor D q hq i = j} = Fintype.card {i : Cells D // i.val.1 = j.val} := + Fintype.card_congr (Equiv.subtypeEquivRight (fun i => Fin.ext_iff)) + _ = D.rowLen j := card_row_subtype D j + +lemma highestMonomial_eq_rowLen (t : Fin q → ℝ) : + highestMonomial D q hq t = ∏ j : Fin q, t j ^ D.rowLen j := by + unfold highestMonomial + rw [← Finset.prod_fiberwise' Finset.univ (rowColor D q hq) t] + simp only [Finset.prod_const, card_rowColor] + +include hq in +lemma sum_rowLen_eq_card : ∑ j : Fin q, D.rowLen j = Fintype.card (Cells D) := by + have h := Finset.sum_fiberwise Finset.univ (rowColor D q hq) (fun _ : Cells D => (1 : ℕ)) + simp only [Finset.sum_const, nsmul_eq_mul, mul_one, card_rowColor, Finset.card_univ] at h + exact_mod_cast h + +end SpinAngle.PolynomialCarrier + + + + +noncomputable section +open scoped TensorProduct InnerProductSpace ComplexOrder +namespace SpinAngle.TensorPositive +variable {E F : Type*} [contextInstance1947_23 : NormedAddCommGroup E] [contextInstance1947_46 : InnerProductSpace ℂ E] + [contextInstance1948_2 : NormedAddCommGroup F] [contextInstance1948_25 : InnerProductSpace ℂ F] + [contextInstance1949_2 : FiniteDimensional ℂ E] [contextInstance1949_26 : FiniteDimensional ℂ F] + +lemma mapL_nonneg (A : E →L[ℂ] E) (B : F →L[ℂ] F) (hA : 0 ≤ A) (hB : 0 ≤ B) : + 0 ≤ TensorProduct.mapL A B := by + let a := CFC.sqrt A + let b := CFC.sqrt B + have ha : star a = a := (IsSelfAdjoint.of_nonneg (CFC.sqrt_nonneg A)).star_eq + have hb : star b = b := (IsSelfAdjoint.of_nonneg (CFC.sqrt_nonneg B)).star_eq + have hstar : star (TensorProduct.mapL a b) = TensorProduct.mapL a b := by + change ContinuousLinearMap.adjoint (TensorProduct.mapL a b) = _ + rw [TensorProduct.adjoint_mapL] + change TensorProduct.mapL (star a) (star b) = _ + rw [ha,hb] + have he : star (TensorProduct.mapL a b) * TensorProduct.mapL a b = TensorProduct.mapL A B := by + rw [hstar, ← TensorProduct.mapL_mul] + dsimp [a,b] + rw [CFC.sqrt_mul_sqrt_self A hA, CFC.sqrt_mul_sqrt_self B hB] + rw [← he] + exact star_mul_self_nonneg _ + +lemma map_positive (A : E →ₗ[ℂ] E) (B : F →ₗ[ℂ] F) (hA : A.IsPositive) (hB : B.IsPositive) : + (TensorProduct.map A B).IsPositive := by + have ha : 0 ≤ A.toContinuousLinearMap := + (ContinuousLinearMap.nonneg_iff_isPositive).mpr hA + have hb : 0 ≤ B.toContinuousLinearMap := + (ContinuousLinearMap.nonneg_iff_isPositive).mpr hB + have h := (ContinuousLinearMap.nonneg_iff_isPositive).mp (mapL_nonneg _ _ ha hb) + change ((TensorProduct.mapL A.toContinuousLinearMap B.toContinuousLinearMap).toLinearMap).IsPositive at h + simpa only [TensorProduct.toLinearMap_mapL, LinearMap.coe_toContinuousLinearMap] using h + +lemma map_norm_bound (A : E →ₗ[ℂ] E) (B : F →ₗ[ℂ] F) + (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) + (hA : ∀ x, ‖A x‖ ≤ a * ‖x‖) (hB : ∀ y, ‖B y‖ ≤ b * ‖y‖) + (v : E ⊗[ℂ] F) : ‖TensorProduct.map A B v‖ ≤ (a*b)*‖v‖ := by + have ha' : ‖A.toContinuousLinearMap‖ ≤ a := + ContinuousLinearMap.opNorm_le_bound _ ha hA + have hb' : ‖B.toContinuousLinearMap‖ ≤ b := + ContinuousLinearMap.opNorm_le_bound _ hb hB + calc + ‖TensorProduct.map A B v‖ ≤ ‖TensorProduct.mapL A.toContinuousLinearMap B.toContinuousLinearMap‖ * ‖v‖ := + by simpa only [TensorProduct.mapL_apply, LinearMap.coe_toContinuousLinearMap] using + (ContinuousLinearMap.le_opNorm (TensorProduct.mapL A.toContinuousLinearMap B.toContinuousLinearMap) v) + _ ≤ (a*b)*‖v‖ := mul_le_mul_of_nonneg_right + ((TensorProduct.norm_mapL_le _ _).trans (mul_le_mul ha' hb' (norm_nonneg _) ha)) (norm_nonneg _) +end SpinAngle.TensorPositive + + + + +noncomputable section +open scoped BigOperators +namespace SpinAngle.EntropyMonomial +variable {ι : Type*} [contextInstance2001_21 : Fintype ι] + +def entropy (n : ι → ℕ) : ℝ := + (∑ i, n i : ℕ) * Real.log (∑ i, n i : ℕ) - ∑ i, (n i : ℝ) * Real.log (n i) + +lemma sum_log_ratio (n : ι → ℕ) (p : ℕ) (hp : 0 < p) (hn : ∑ i, n i = p) : + ∑ i, (n i : ℝ) * Real.log ((n i : ℝ) / p) = -entropy n := by + have hp0 : (p : ℝ) ≠ 0 := by exact_mod_cast hp.ne' + have he (i : ι) : (n i : ℝ) * Real.log ((n i : ℝ) / p) = + (n i : ℝ) * Real.log (n i) - (n i : ℝ) * Real.log p := by + by_cases hi : n i = 0 + · simp [hi] + · rw [Real.log_div (by exact_mod_cast hi) hp0, mul_sub] + simp only [he, Finset.sum_sub_distrib, ← Finset.sum_mul] + have hn' : ∑ i, (n i : ℝ) = p := by exact_mod_cast hn + rw [hn'] + simp only [entropy, hn] + ring + +lemma power_le_exponential (k p : ℕ) (hp : 0 < p) (t : ℝ) (ht : 0 ≤ t) : + t ^ k ≤ Real.exp ((k : ℝ) * Real.log ((k : ℝ) / p) + p * t - k) := by + by_cases hk : k = 0 + · subst k + simpa using (Real.one_le_exp_iff.mpr (mul_nonneg (Nat.cast_nonneg p) ht)) + by_cases ht0 : t = 0 + · simp only [ht0, zero_pow hk] + exact (Real.exp_pos _).le + have hk' : 0 < (k : ℝ) := by exact_mod_cast Nat.pos_of_ne_zero hk + have hp' : 0 < (p : ℝ) := by exact_mod_cast hp + have ht' : 0 < t := lt_of_le_of_ne ht (Ne.symm ht0) + have hr : 0 < (k : ℝ) / p := div_pos hk' hp' + have hlog := Real.log_le_sub_one_of_pos (div_pos ht' hr) + rw [Real.log_div ht0 hr.ne'] at hlog + have hmul := mul_le_mul_of_nonneg_left hlog hk'.le + have hc : (k : ℝ) * (t / ((k : ℝ) / p) - 1) = p * t - k := by + field_simp + + rw [hc] at hmul + calc + t ^ k = Real.exp ((k : ℝ) * Real.log t) := by + rw [Real.exp_nat_mul, Real.exp_log ht'] + _ ≤ _ := Real.exp_le_exp.mpr (by nlinarith) + + + +theorem prod_pow_le (n : ι → ℕ) (t : ι → ℝ) (ht : ∀ i, 0 ≤ t i) + (hsum : ∑ i, t i ≤ 1) : + ∏ i, t i ^ n i ≤ Real.exp (-entropy n) := by + classical + let p : ℕ := ∑ i, n i + by_cases hp : p = 0 + · have hn : ∀ i, n i = 0 := by + intro i + have hle := Finset.single_le_sum (fun j (_ : j ∈ Finset.univ) => Nat.zero_le (n j)) (Finset.mem_univ i) + change n i ≤ p at hle + omega + simp [entropy, hn] + have hp' : 0 < p := Nat.pos_of_ne_zero hp + calc + ∏ i, t i ^ n i ≤ ∏ i, Real.exp ((n i : ℝ) * Real.log ((n i : ℝ) / p) + p * t i - n i) := + Finset.prod_le_prod₀ (fun i _ => pow_nonneg (ht i) _) (fun i _ => power_le_exponential _ p hp' _ (ht i)) + _ = Real.exp (∑ i, ((n i : ℝ) * Real.log ((n i : ℝ) / p) + p * t i - n i)) := + (Real.exp_sum _ _).symm + _ ≤ Real.exp (-entropy n) := by + apply Real.exp_le_exp.mpr + simp only [Finset.sum_sub_distrib, Finset.sum_add_distrib, ← Finset.mul_sum] + rw [sum_log_ratio n p hp' rfl] + have hn : ∑ i, (n i : ℝ) = p := by simp [p] + rw [hn] + have h := mul_le_mul_of_nonneg_left hsum (Nat.cast_nonneg p : (0 : ℝ) ≤ p) + nlinarith + +lemma optimal_prod (n : ι → ℕ) (p : ℕ) (hp : 0 < p) (hn : ∑ i, n i = p) : + ∏ i, ((n i : ℝ) / p) ^ n i = Real.exp (-entropy n) := by + rw [← sum_log_ratio n p hp hn, Real.exp_sum] + apply Finset.prod_congr rfl + intro i _ + by_cases hi : n i = 0 + · simp [hi] + have hpos : 0 < (n i : ℝ) / p := div_pos (by exact_mod_cast Nat.pos_of_ne_zero hi) (by exact_mod_cast hp) + rw [Real.exp_nat_mul, Real.exp_log hpos] + +end SpinAngle.EntropyMonomial + + + +noncomputable section +open scoped InnerProductSpace ComplexOrder BigOperators +namespace SpinAngle.PositiveTrace +variable {E : Type*} [contextInstance2090_21 : NormedAddCommGroup E] [contextInstance2090_44 : InnerProductSpace ℂ E] + [contextInstance2091_2 : FiniteDimensional ℂ E] + +lemma eigenvalues_nonneg (A : E →ₗ[ℂ] E) (hA : A.IsPositive) + (i : Fin (Module.finrank ℂ E)) : 0 ≤ hA.isSymmetric.eigenvalues rfl i := by + have h := hA.inner_nonneg_right (hA.isSymmetric.eigenvectorBasis rfl i) + rw [hA.isSymmetric.apply_eigenvectorBasis rfl i, inner_smul_right, + (hA.isSymmetric.eigenvectorBasis rfl).inner_eq_one] at h + simpa only [mul_one, RCLike.ofReal_nonneg] using h + + +theorem eigenvalue_le_trace (A : E →ₗ[ℂ] E) (hA : A.IsPositive) + (v : E) (hv : v ≠ 0) (t : ℝ) (he : A v = (t : ℂ) • v) : + t ≤ (LinearMap.trace ℂ E A).re := by + classical + let b := hA.isSymmetric.eigenvectorBasis rfl + have hcoord : ∃ i, b.repr v i ≠ 0 := by + by_contra! hh + apply hv + apply b.repr.injective + ext i + simpa using hh i + obtain ⟨i,hi⟩ := hcoord + have h := congrArg (fun x : E => b.repr x i) he + rw [hA.isSymmetric.eigenvectorBasis_apply_self_apply, map_smul, PiLp.smul_apply, + smul_eq_mul] at h + have ht : hA.isSymmetric.eigenvalues rfl i = t := by + exact Complex.ofReal_injective (mul_right_cancel₀ hi h) + change t ≤ RCLike.re (LinearMap.trace ℂ E A) + rw [hA.isSymmetric.re_trace_eq_sum_eigenvalues rfl, ← ht] + exact Finset.single_le_sum (fun j _ => eigenvalues_nonneg A hA j) (Finset.mem_univ i) + +end SpinAngle.PositiveTrace + + + + + +noncomputable section +open scoped InnerProductSpace BigOperators ComplexOrder +namespace SpinAngle.Isotypic +variable {G : Type*} [contextInstance2131_21 : Group G] +variable {E F : Type*} [contextInstance2132_23 : NormedAddCommGroup E] [contextInstance2132_46 : InnerProductSpace ℂ E] + [contextInstance2133_2 : NormedAddCommGroup F] [contextInstance2133_25 : InnerProductSpace ℂ F] + [contextInstance2134_2 : FiniteDimensional ℂ E] [contextInstance2134_26 : FiniteDimensional ℂ F] +variable (ρ : Representation ℂ G E) (σ : Representation ℂ G F) + +def space : Subrepresentation σ where + toSubmodule := Submodule.span ℂ (Set.range fun z : ρ.IntertwiningMap σ × E => z.1 z.2) + apply_mem_toSubmodule := by + intro g v hv + induction hv using Submodule.span_induction with + | mem v hv => + obtain ⟨⟨f,x⟩,rfl⟩ := hv + apply Submodule.subset_span + refine ⟨⟨f,ρ g x⟩, ?_⟩ + exact Representation.IntertwiningMap.isIntertwining ρ σ f g x + | zero => simp + | add x y hx hy ihx ihy => simpa only [map_add] using Submodule.add_mem _ ihx ihy + | smul a x hx ih => simpa only [map_smul] using Submodule.smul_mem _ a ih + +def projection : F →L[ℂ] F := (space ρ σ).toSubmodule.starProjection + +lemma projection_mem + {G : Type*} + [contextInstance2131_21 : Group G] + {E : Type*} {F : Type*} + [contextInstance2132_23 : NormedAddCommGroup E] + [contextInstance2132_46 : InnerProductSpace ℂ E] + [contextInstance2133_2 : NormedAddCommGroup F] + [contextInstance2133_25 : InnerProductSpace ℂ F] + [FiniteDimensional ℂ E] + [contextInstance2134_26 : FiniteDimensional ℂ F] + (ρ : Representation ℂ G E) (σ : Representation ℂ G F) (v : F) : projection ρ σ v ∈ space ρ σ := + (space ρ σ).toSubmodule.starProjection_apply_mem v + +lemma projection_norm_apply_le + {G : Type*} + [contextInstance2131_21 : Group G] + {E : Type*} {F : Type*} + [contextInstance2132_23 : NormedAddCommGroup E] + [contextInstance2132_46 : InnerProductSpace ℂ E] + [contextInstance2133_2 : NormedAddCommGroup F] + [contextInstance2133_25 : InnerProductSpace ℂ F] + [FiniteDimensional ℂ E] + [contextInstance2134_26 : FiniteDimensional ℂ F] + (ρ : Representation ℂ G E) (σ : Representation ℂ G F) (v : F) : ‖projection ρ σ v‖ ≤ ‖v‖ := + (space ρ σ).toSubmodule.norm_starProjection_apply_le v + +lemma map_mem + {G : Type*} + [contextInstance2131_21 : Group G] + {E : Type*} {F : Type*} + [contextInstance2132_23 : NormedAddCommGroup E] + [contextInstance2132_46 : InnerProductSpace ℂ E] + [contextInstance2133_2 : NormedAddCommGroup F] + [contextInstance2133_25 : InnerProductSpace ℂ F] + [FiniteDimensional ℂ E] + [FiniteDimensional ℂ F] + (ρ : Representation ℂ G E) (σ : Representation ℂ G F) (f : ρ.IntertwiningMap σ) (x : E) : f x ∈ space ρ σ := + Submodule.subset_span ⟨⟨f,x⟩,rfl⟩ + +lemma endomorphism_mem (d : σ.IntertwiningMap σ) (v : F) (hv : v ∈ space ρ σ) : + d v ∈ space ρ σ := by + induction hv using Submodule.span_induction with + | mem v hv => + obtain ⟨⟨f,x⟩,rfl⟩ := hv + exact map_mem ρ σ (d.comp f) x + | zero => simp only [map_zero]; exact (space ρ σ).toSubmodule.zero_mem + | add x y hx hy ihx ihy => rw [map_add]; exact (space ρ σ).toSubmodule.add_mem ihx ihy + | smul a x hx ih => rw [map_smul]; exact (space ρ σ).toSubmodule.smul_mem a ih + +lemma natural_mem (a : E →ₗ[ℂ] E) (A : F →ₗ[ℂ] F) + (h : ∀ f : ρ.IntertwiningMap σ, ∀ x, A (f x) = f (a x)) + (v : F) (hv : v ∈ space ρ σ) : A v ∈ space ρ σ := by + induction hv using Submodule.span_induction with + | mem v hv => + obtain ⟨⟨f,x⟩,rfl⟩ := hv + rw [h] + exact map_mem ρ σ f _ + | zero => simp only [map_zero]; exact (space ρ σ).toSubmodule.zero_mem + | add x y hx hy ihx ihy => rw [map_add]; exact (space ρ σ).toSubmodule.add_mem ihx ihy + | smul z x hx ih => rw [map_smul]; exact (space ρ σ).toSubmodule.smul_mem z ih + +lemma scalar_on_space + {G : Type*} + [contextInstance2131_21 : Group G] + {E : Type*} {F : Type*} + [contextInstance2132_23 : NormedAddCommGroup E] + [contextInstance2132_46 : InnerProductSpace ℂ E] + [contextInstance2133_2 : NormedAddCommGroup F] + [contextInstance2133_25 : InnerProductSpace ℂ F] + [FiniteDimensional ℂ E] + [FiniteDimensional ℂ F] + (ρ : Representation ℂ G E) (σ : Representation ℂ G F) (A : F →ₗ[ℂ] F) (c : ℂ) + (h : ∀ f : ρ.IntertwiningMap σ, ∀ x, A (f x) = c • f x) + (v : F) (hv : v ∈ space ρ σ) : A v = c • v := by + induction hv using Submodule.span_induction with + | mem v hv => obtain ⟨⟨f,x⟩,rfl⟩ := hv; exact h f x + | zero => simp + | add x y hx hy ihx ihy => simp [ihx, ihy, smul_add] + | smul z x hx ih => simp [ih, smul_comm c z] + +lemma exists_nonzero_adjoint (v : F) (hv : v ∈ space ρ σ) (hv0 : v ≠ 0) : + ∃ f : ρ.IntertwiningMap σ, LinearMap.adjoint f.toLinearMap v ≠ 0 := by + by_contra! hn + have horth (w : F) (hw : w ∈ space ρ σ) : ⟪w,v⟫_ℂ = 0 := by + induction hw using Submodule.span_induction with + | mem w hw => + obtain ⟨⟨f,x⟩,rfl⟩ := hw + change ⟪f.toLinearMap x,v⟫_ℂ = 0 + rw [← LinearMap.adjoint_inner_right, hn] + simp + | zero => simp + | add x y hx hy ihx ihy => simp [ihx, ihy] + | smul z x hx ih => simp [ih] + exact hv0 (inner_self_eq_zero.mp (horth v hv)) + +lemma transfer_eigenvalue_bound (a : E →ₗ[ℂ] E) (A : F →ₗ[ℂ] F) + (ha : a.IsSymmetric) (hA : A.IsSymmetric) + (hnat : ∀ f : ρ.IntertwiningMap σ, ∀ x, A (f x) = f (a x)) + (c : ℝ) (hc : ∀ x, ‖a x‖ ≤ c * ‖x‖) + (v : F) (hv : v ∈ space ρ σ) (hv0 : v ≠ 0) + (t : ℂ) (ht : A v = t • v) : ‖t‖ ≤ c := by + obtain ⟨f,hf⟩ := exists_nonzero_adjoint ρ σ v hv hv0 + have he : A.comp f.toLinearMap = f.toLinearMap.comp a := by ext x; exact hnat f x + have hadj := congrArg LinearMap.adjoint he + rw [LinearMap.adjoint_comp, LinearMap.adjoint_comp, ha.adjoint_eq, hA.adjoint_eq] at hadj + have hev : a (LinearMap.adjoint f.toLinearMap v) = t • LinearMap.adjoint f.toLinearMap v := by + have hh := congrArg (fun L : F →ₗ[ℂ] E => L v) hadj + simpa only [LinearMap.comp_apply, ht, map_smul] using hh.symm + have hh := hc (LinearMap.adjoint f.toLinearMap v) + rw [hev, norm_smul] at hh + exact (mul_le_mul_iff_left₀ (norm_pos_iff.mpr hf)).mp hh + + + +theorem norm_bound (a : E →ₗ[ℂ] E) (A : F →ₗ[ℂ] F) + (ha : a.IsSymmetric) (hA : A.IsSymmetric) + (hnat : ∀ f : ρ.IntertwiningMap σ, ∀ x, A (f x) = f (a x)) + (c : ℝ) (hc0 : 0 ≤ c) (hc : ∀ x, ‖a x‖ ≤ c * ‖x‖) + (v : F) (hv : v ∈ space ρ σ) : ‖A v‖ ≤ c * ‖v‖ := by + classical + let S := (space ρ σ).toSubmodule + have hinv : ∀ w ∈ S, A w ∈ S := natural_mem ρ σ a A hnat + let B : S →ₗ[ℂ] S := A.restrict hinv + have hB : B.IsSymmetric := hA.restrict_invariant hinv + let b := hB.eigenvectorBasis rfl + have hb (i : Fin (Module.finrank ℂ S)) : ‖(hB.eigenvalues rfl i : ℂ)‖ ≤ c := by + apply transfer_eigenvalue_bound ρ σ a A ha hA hnat c hc (b i).val (b i).property + · intro hh + have hn := b.orthonormal.ne_zero i + exact hn (Subtype.ext hh) + · exact congrArg Subtype.val (hB.apply_eigenvectorBasis rfl i) + let w : S := ⟨v,hv⟩ + change ‖B w‖ ≤ c * ‖w‖ + apply (sq_le_sq₀ (norm_nonneg _) (mul_nonneg hc0 (norm_nonneg _))).mp + rw [← b.repr.norm_map (B w), ← b.repr.norm_map w, mul_pow, + EuclideanSpace.norm_sq_eq, EuclideanSpace.norm_sq_eq, Finset.mul_sum] + apply Finset.sum_le_sum + intro i _ + rw [hB.eigenvectorBasis_apply_self_apply, norm_mul, mul_pow] + exact mul_le_mul_of_nonneg_right (pow_le_pow_left₀ (norm_nonneg _) (hb i) 2) (sq_nonneg _) + +lemma projection_commute_of_invariant + {G : Type*} + [Group G] + {F : Type*} + [contextInstance2133_2 : NormedAddCommGroup F] + [contextInstance2133_25 : InnerProductSpace ℂ F] + [contextInstance2134_26 : FiniteDimensional ℂ F] (S : Submodule ℂ F) (A : F →ₗ[ℂ] F) + (hA : A.IsSymmetric) (hinv : ∀ v ∈ S, A v ∈ S) (v : F) : + S.starProjection (A v) = A (S.starProjection v) := by + apply S.eq_starProjection_of_mem_of_inner_eq_zero + · exact hinv _ (S.starProjection_apply_mem v) + · intro w hw + rw [← map_sub, hA] + exact S.starProjection_inner_eq_zero v _ (hinv _ hw) + +lemma projection_commute_endomorphism (d : σ.IntertwiningMap σ) + (hd : d.toLinearMap.IsSymmetric) (v : F) : + projection ρ σ (d v) = d (projection ρ σ v) := + projection_commute_of_invariant (G := G) _ d.toLinearMap hd (endomorphism_mem ρ σ d) v + +lemma projection_commute_natural (a : E →ₗ[ℂ] E) (A : F →ₗ[ℂ] F) + (hA : A.IsSymmetric) + (h : ∀ f : ρ.IntertwiningMap σ, ∀ x, A (f x) = f (a x)) (v : F) : + projection ρ σ (A v) = A (projection ρ σ v) := + projection_commute_of_invariant (G := G) _ A hA (natural_mem ρ σ a A h) v + +end SpinAngle.Isotypic + +namespace SpinAngle.SignedTensor +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {q : ℕ} + +def IsEvenDensity (A : Mat q × Mat q) : Prop := + A.1.PosSemidef ∧ A.2.PosSemidef ∧ Matrix.trace A.1 + Matrix.trace A.2 = 1 + +lemma block_posSemidef (A : Mat q × Mat q) (hA : A.1.PosSemidef) (hB : A.2.PosSemidef) : + (block A).PosSemidef := by + let R : Mat q × Mat q := (CFC.sqrt A.1, CFC.sqrt A.2) + have he : block A = star (block R) * block R := by + rw [← block_star, ← map_mul] + congr 1 + apply Prod.ext + · change A.1 = star (CFC.sqrt A.1) * CFC.sqrt A.1 + rw [(IsSelfAdjoint.of_nonneg (CFC.sqrt_nonneg A.1)).star_eq, + CFC.sqrt_mul_sqrt_self A.1 hA.nonneg] + · change A.2 = star (CFC.sqrt A.2) * CFC.sqrt A.2 + rw [(IsSelfAdjoint.of_nonneg (CFC.sqrt_nonneg A.2)).star_eq, + CFC.sqrt_mul_sqrt_self A.2 hB.nonneg] + rw [he] + exact Matrix.posSemidef_conjTranspose_mul_self _ +end SpinAngle.SignedTensor + +namespace SpinAngle.SignedCarrier +open scoped Classical TensorProduct BigOperators InnerProductSpace +open SpinAngle.Young SpinAngle.Specht SignedTensor +variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) + +lemma hermitianAction_positive (A : Mat q × Mat q) (hA : A.1.PosSemidef) (hB : A.2.PosSemidef) : + LinearMap.IsPositive (𝕜 := ℂ) (E := Carrier a b q ha hb) + (hermitianAction a b q ha hb A hA.isHermitian hB.isHermitian) := + TensorPositive.map_positive (E := PolynomialCarrier.Carrier a q ha) + (F := PolynomialCarrier.Carrier b q hb) _ _ + (PolynomialCarrier.hermitianAction_positive a q ha A.1 hA) + (PolynomialCarrier.hermitianAction_positive b q hb A.2 hB) + +lemma hermitianAction_norm_bound (A : Mat q × Mat q) (hA : A.1.PosSemidef) (hB : A.2.PosSemidef) + (v : Carrier a b q ha hb) : + ‖hermitianAction a b q ha hb A hA.isHermitian hB.isHermitian v‖ ≤ + (PolynomialCarrier.highestMonomial a q ha (SortedSpectrum.values A.1 hA.isHermitian) * + PolynomialCarrier.highestMonomial b q hb (SortedSpectrum.values A.2 hB.isHermitian)) * ‖v‖ := by + apply TensorPositive.map_norm_bound (E := PolynomialCarrier.Carrier a q ha) + (F := PolynomialCarrier.Carrier b q hb) + · exact Finset.prod_nonneg (fun i _ => SortedSpectrum.values_nonneg A.1 hA.isHermitian hA _) + · exact Finset.prod_nonneg (fun i _ => SortedSpectrum.values_nonneg A.2 hB.isHermitian hB _) + · exact PolynomialCarrier.hermitianAction_norm_bound a q ha A.1 hA + · exact PolynomialCarrier.hermitianAction_norm_bound b q hb A.2 hB + +def parts : Fin q ⊕ Fin q → ℕ := Sum.elim (fun i => a.rowLen i) (fun i => b.rowLen i) +def entropy : ℝ := EntropyMonomial.entropy (parts a b q) +def dimension : ℕ := Module.finrank ℂ (Carrier a b q ha hb) + +include ha hb in +lemma sum_parts : ∑ i, parts a b q i = Fintype.card (Cells a) + Fintype.card (Cells b) := by + rw [Fintype.sum_sum_type] + change (∑ i : Fin q, a.rowLen i) + (∑ i : Fin q, b.rowLen i) = _ + rw [PolynomialCarrier.sum_rowLen_eq_card a q ha, PolynomialCarrier.sum_rowLen_eq_card b q hb] + +include ha hb in +lemma entropy_eq_source : entropy a b q = + (Fintype.card (Cells a) + Fintype.card (Cells b) : ℕ) * + Real.log (Fintype.card (Cells a) + Fintype.card (Cells b) : ℕ) - + (∑ i : Fin q, (a.rowLen i : ℝ) * Real.log (a.rowLen i)) - + (∑ i : Fin q, (b.rowLen i : ℝ) * Real.log (b.rowLen i)) := by + unfold entropy EntropyMonomial.entropy + rw [sum_parts a b q ha hb, Fintype.sum_sum_type] + simp only [parts, Sum.elim_inl, Sum.elim_inr] + ring + +lemma hermitianAction_density_bound (A : Mat q × Mat q) (hA : IsEvenDensity A) + (v : Carrier a b q ha hb) : + ‖hermitianAction a b q ha hb A hA.1.isHermitian hA.2.1.isHermitian v‖ ≤ + Real.exp (-entropy a b q) * ‖v‖ := by + apply (hermitianAction_norm_bound a b q ha hb A hA.1 hA.2.1 v).trans + apply mul_le_mul_of_nonneg_right _ (norm_nonneg _) + rw [PolynomialCarrier.highestMonomial_eq_rowLen, PolynomialCarrier.highestMonomial_eq_rowLen] + let t : Fin q ⊕ Fin q → ℝ := Sum.elim + (SortedSpectrum.values A.1 hA.1.isHermitian) (SortedSpectrum.values A.2 hA.2.1.isHermitian) + have ht (i) : 0 ≤ t i := by + cases i with + | inl i => exact SortedSpectrum.values_nonneg A.1 hA.1.isHermitian hA.1 i + | inr i => exact SortedSpectrum.values_nonneg A.2 hA.2.1.isHermitian hA.2.1 i + have hs : ∑ i, t i = 1 := by + rw [Fintype.sum_sum_type] + have he1 := SortedSpectrum.trace_eq_sum A.1 hA.1.isHermitian + have he2 := SortedSpectrum.trace_eq_sum A.2 hA.2.1.isHermitian + have h : (∑ i, (SortedSpectrum.values A.1 hA.1.isHermitian i : ℂ)) + + (∑ i, (SortedSpectrum.values A.2 hA.2.1.isHermitian i : ℂ)) = 1 := + (congrArg₂ (· + ·) he1.symm he2.symm).trans hA.2.2 + have hh := congrArg Complex.re h + simpa only [t, Sum.elim_inl, Sum.elim_inr, Complex.add_re, Complex.re_sum, Complex.ofReal_re, Complex.one_re] using hh + have h := EntropyMonomial.prod_pow_le (parts a b q) t ht hs.le + simpa only [Fintype.prod_sum_type, parts, t, entropy, Sum.elim_inl, Sum.elim_inr] using h + +end SpinAngle.SignedCarrier + +namespace SpinAngle.EntropyMonomial +open scoped BigOperators +variable {ι : Type*} [contextInstance2379_21 : Fintype ι] [contextInstance2379_33 : Nonempty ι] + +lemma exists_optimal (n : ι → ℕ) : ∃ t : ι → ℝ, + (∀ i, 0 ≤ t i) ∧ (∑ i, t i = 1) ∧ (∏ i, t i ^ n i = Real.exp (-entropy n)) := by + classical + let p := ∑ i, n i + by_cases hp : p = 0 + · have hn : ∀ i, n i = 0 := by + intro i + have h := Finset.single_le_sum (fun j (_ : j ∈ Finset.univ) => Nat.zero_le (n j)) (Finset.mem_univ i) + change n i ≤ p at h + omega + let i₀ := Classical.choice (inferInstance : Nonempty ι) + refine ⟨fun i => if i = i₀ then 1 else 0, ?_, ?_, ?_⟩ + · intro i; dsimp only; split_ifs <;> norm_num + · simp + · simp [hn, entropy] + · refine ⟨fun i => (n i : ℝ) / p, fun i => div_nonneg (Nat.cast_nonneg _) (Nat.cast_nonneg _), ?_, ?_⟩ + · rw [← Finset.sum_div] + have he : ∑ i, (n i : ℝ) = p := by simp [p] + rw [he, div_self (by exact_mod_cast hp)] + · exact optimal_prod n p (Nat.pos_of_ne_zero hp) rfl +end SpinAngle.EntropyMonomial + +namespace SpinAngle.SignedCarrier +open scoped Classical TensorProduct BigOperators InnerProductSpace ComplexOrder +open SpinAngle.Young SpinAngle.Specht SignedTensor +variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) +variable {τ : Type*} [contextInstance2407_21 : Fintype τ] [contextInstance2407_33 : DecidableEq τ] + +abbrev typeProjection : Raw (q := q) (τ := τ) →L[ℂ] Raw (q := q) (τ := τ) := + Isotypic.projection (rep a b q ha hb) SignedTensor.rep + +lemma density_on_space (A : Mat q × Mat q) (hA : IsEvenDensity A) + (v : Raw (q := q) (τ := τ)) + (hv : v ∈ Isotypic.space (rep a b q ha hb) (SignedTensor.rep (q := q) (τ := τ))) : + ‖TensorRep.action (block A) v‖ ≤ Real.exp (-entropy a b q) * ‖v‖ := by + exact Isotypic.norm_bound (E := Carrier a b q ha hb) (F := Raw (q := q) (τ := τ)) + (rep a b q ha hb) (SignedTensor.rep (q := q) (τ := τ)) + (hermitianAction a b q ha hb A hA.1.isHermitian hA.2.1.isHermitian) + (TensorRep.action (block A)) + (hermitianAction_positive a b q ha hb A hA.1 hA.2.1).isSymmetric + (TensorRep.action_positive (block A) (block_posSemidef A hA.1 hA.2.1)).isSymmetric + (fun L x => (intertwiner_hermitian a b q ha hb L A hA.1.isHermitian hA.2.1.isHermitian x).symm) + (Real.exp (-entropy a b q)) (Real.exp_pos _).le + (hermitianAction_density_bound a b q ha hb A hA) v hv + +lemma projected_density_bound (A : Mat q × Mat q) (hA : IsEvenDensity A) + (v : Raw (q := q) (τ := τ)) : + ‖TensorRep.action (block A) (typeProjection a b q ha hb v)‖ ≤ + Real.exp (-entropy a b q) * ‖v‖ := by + exact (density_on_space a b q ha hb A hA _ + (Isotypic.projection_mem (rep a b q ha hb) (SignedTensor.rep (q := q) (τ := τ)) v)).trans + (mul_le_mul_of_nonneg_left + (Isotypic.projection_norm_apply_le (rep a b q ha hb) (SignedTensor.rep (q := q) (τ := τ)) v) + (Real.exp_pos _).le) + + +theorem global_density_upper (A : Mat q × Mat q) (hA : IsEvenDensity A) : + ‖LinearMap.toContinuousLinearMap (TensorRep.action (ι := τ) (block A)) * + typeProjection (τ := τ) a b q ha hb‖ ≤ Real.exp (-entropy a b q) := by + apply ContinuousLinearMap.opNorm_le_bound _ (Real.exp_pos _).le + intro v + exact projected_density_bound a b q ha hb A hA v + +def highestVector : Carrier a b q ha hb := + PolynomialCarrier.highestVector a q ha ⊗ₜ[ℂ] PolynomialCarrier.highestVector b q hb + +lemma highestVector_ne_zero : highestVector a b q ha hb ≠ 0 := by + intro h + have hn := congrArg norm h + rw [highestVector, TensorProduct.norm_tmul (E := PolynomialCarrier.Carrier a q ha) + (F := PolynomialCarrier.Carrier b q hb), norm_zero] at hn + exact (mul_ne_zero (norm_ne_zero_iff.mpr (PolynomialCarrier.highestVector_ne_zero a q ha)) + (norm_ne_zero_iff.mpr (PolynomialCarrier.highestVector_ne_zero b q hb))) hn + +lemma highestVector_diagonal (t : Fin q ⊕ Fin q → ℝ) : + hermitianAction a b q ha hb + (Matrix.diagonal (fun i => (t (.inl i) : ℂ)), Matrix.diagonal (fun i => (t (.inr i) : ℂ))) + (Matrix.isHermitian_diagonal_iff.mpr (fun i => by simp [IsSelfAdjoint])) + (Matrix.isHermitian_diagonal_iff.mpr (fun i => by simp [IsSelfAdjoint])) + (highestVector a b q ha hb) = + ((∏ i, t i ^ parts a b q i : ℝ) : ℂ) • highestVector a b q ha hb := by + rw [hermitianAction, highestVector, TensorProduct.map_tmul, + PolynomialCarrier.highestVector_diagonal, PolynomialCarrier.highestVector_diagonal, + TensorProduct.smul_tmul_smul, PolynomialCarrier.highestMonomial_eq_rowLen, + PolynomialCarrier.highestMonomial_eq_rowLen] + congr 1 + rw [Fintype.prod_sum_type, Complex.ofReal_mul] + rfl + + +lemma exists_density_trace_lower [Nonempty (Fin q)] : ∃ (A : Mat q × Mat q) (hA : IsEvenDensity A), + Real.exp (-entropy a b q) ≤ + (LinearMap.trace ℂ (Carrier a b q ha hb) + (hermitianAction a b q ha hb A hA.1.isHermitian hA.2.1.isHermitian)).re := by + obtain ⟨t,ht,hs,he⟩ := EntropyMonomial.exists_optimal (parts a b q) + let A : Mat q × Mat q := + (Matrix.diagonal (fun i => (t (.inl i) : ℂ)), Matrix.diagonal (fun i => (t (.inr i) : ℂ))) + have hA : IsEvenDensity A := by + refine ⟨Matrix.PosSemidef.diagonal (fun i => by simpa using ht (.inl i)), + Matrix.PosSemidef.diagonal (fun i => by simpa using ht (.inr i)), ?_⟩ + simp only [A, Matrix.trace_diagonal] + have hh := congrArg Complex.ofReal hs + simpa only [Fintype.sum_sum_type, Complex.ofReal_add, Complex.ofReal_sum, Complex.ofReal_one] using hh + refine ⟨A,hA,?_⟩ + apply PositiveTrace.eigenvalue_le_trace _ (hermitianAction_positive a b q ha hb A hA.1 hA.2.1) + (highestVector a b q ha hb) (highestVector_ne_zero a b q ha hb) + have h := highestVector_diagonal a b q ha hb t + rw [he] at h + exact h +end SpinAngle.SignedCarrier + + +noncomputable section +open scoped BigOperators +namespace SpinAngle.DenseLU + +abbrev Mat (n : ℕ) := Matrix (Fin n) (Fin n) ℂ + +def border {n : ℕ} (a : ℂ) (b c : Fin n → ℂ) (D : Mat n) : Mat (n+1) := + fun i => Fin.cases (Fin.cases a b) (fun i => Fin.cases (c i) (D i)) i + +@[simp] lemma border_zero_zero {n : ℕ} (a : ℂ) (b c : Fin n → ℂ) (D : Mat n) : + border a b c D 0 0 = a := rfl +@[simp] lemma border_zero_succ {n : ℕ} (a : ℂ) (b c : Fin n → ℂ) (D : Mat n) (j : Fin n) : + border a b c D 0 j.succ = b j := rfl +@[simp] lemma border_succ_zero {n : ℕ} (a : ℂ) (b c : Fin n → ℂ) (D : Mat n) (i : Fin n) : + border a b c D i.succ 0 = c i := rfl +@[simp] lemma border_succ_succ {n : ℕ} (a : ℂ) (b c : Fin n → ℂ) (D : Mat n) (i j : Fin n) : + border a b c D i.succ j.succ = D i j := rfl + +lemma border_eq {n : ℕ} (A : Mat (n+1)) : + border (A 0 0) (fun j => A 0 j.succ) (fun i => A i.succ 0) + (fun i j => A i.succ j.succ) = A := by + ext i j + refine Fin.cases ?_ (fun i => ?_) i <;> refine Fin.cases ?_ (fun j => ?_) j <;> rfl + +lemma continuous_border {X : Type*} [TopologicalSpace X] {n : ℕ} + {a : X → ℂ} {b c : X → Fin n → ℂ} {D : X → Mat n} + (ha : Continuous a) (hb : Continuous b) (hc : Continuous c) (hD : Continuous D) : + Continuous (fun x => border (a x) (b x) (c x) (D x)) := by + apply continuous_pi + intro i + apply continuous_pi + intro j + refine Fin.cases ?_ (fun i => ?_) i <;> refine Fin.cases ?_ (fun j => ?_) j + · exact ha + · exact (continuous_apply j).comp hb + · exact (continuous_apply i).comp hc + · exact (continuous_apply j).comp ((continuous_apply i).comp hD) + + +lemma border_factor {n : ℕ} (a : ℂ) (ha : a ≠ 0) (b c : Fin n → ℂ) (L U : Mat n) : + border 1 0 (fun i => c i / a) L * border a b 0 U = + border a b c (L * U + (Matrix.of fun i j => c i / a * b j)) := by + ext i j + refine Fin.cases ?_ (fun i => ?_) i <;> refine Fin.cases ?_ (fun j => ?_) j + · simp [Matrix.mul_apply, Fin.sum_univ_succ] + · simp [Matrix.mul_apply, Fin.sum_univ_succ] + · simp [Matrix.mul_apply, Fin.sum_univ_succ, ha] + · simp [Matrix.mul_apply, Fin.sum_univ_succ, add_comm] + +def LowerUnipotent {n : ℕ} (L : Mat n) : Prop := + L.IsLowerTriangular ∧ ∀ i, L i i = 1 + +lemma lower_border {n : ℕ} (c : Fin n → ℂ) (L : Mat n) (hL : LowerUnipotent L) : + LowerUnipotent (border 1 0 c L) := by + constructor + · intro i j hij + change i < j at hij + induction i using Fin.cases <;> induction j using Fin.cases + · simp at hij + · rfl + · simp at hij + · exact hL.1 (by simpa using hij) + · intro i + refine Fin.cases ?_ (fun i => ?_) i + · rfl + · exact hL.2 i + +lemma upper_border {n : ℕ} (a : ℂ) (b : Fin n → ℂ) (U : Mat n) (hU : U.IsUpperTriangular) : + (border a b 0 U).IsUpperTriangular := by + intro i j hij + induction i using Fin.cases <;> induction j using Fin.cases + · simp at hij + · simp at hij + · rfl + · exact hU (by simpa using hij) + +def bigCell (n : ℕ) : Set (Mat n) := + {A | ∃ L U, LowerUnipotent L ∧ U.IsUpperTriangular ∧ A = L * U} + +lemma border_mem_bigCell {n : ℕ} (a : ℂ) (ha : a ≠ 0) (b c : Fin n → ℂ) (S : Mat n) + (hS : S ∈ bigCell n) : + border a b c (S + (Matrix.of fun i j => c i / a * b j)) ∈ bigCell (n+1) := by + obtain ⟨L,U,hL,hU,rfl⟩ := hS + exact ⟨border 1 0 (fun i => c i / a) L, border a b 0 U, + lower_border _ _ hL, upper_border _ _ _ hU, (border_factor a ha b c L U).symm⟩ + + + +theorem dense_bigCell (n : ℕ) : Dense (bigCell n) := by + induction n with + | zero => + intro A + apply subset_closure + refine ⟨1,1,?_,?_,?_⟩ + · refine ⟨?_,?_⟩ <;> intro i <;> exact Fin.elim0 i + · intro i; exact Fin.elim0 i + · exact Subsingleton.elim _ _ + | succ n ih => + have hpivot (a : ℂ) (ha : a ≠ 0) (b c : Fin n → ℂ) (D : Mat n) : + border a b c D ∈ closure (bigCell (n+1)) := by + let X : Mat n := fun i j => c i / a * b j + have hf : Continuous (fun S : Mat n => border a b c (S + X)) := + continuous_border continuous_const continuous_const continuous_const + (continuous_id.add continuous_const) + have hh := map_mem_closure hf (ih (D-X)) + (fun S hS => border_mem_bigCell a ha b c S hS) + change border a b c (D - X + X) ∈ closure (bigCell (n+1)) at hh + simpa only [sub_add_cancel] using hh + intro A + let b : Fin n → ℂ := fun j => A 0 j.succ + let c : Fin n → ℂ := fun i => A i.succ 0 + let D : Mat n := fun i j => A i.succ j.succ + have hf : Continuous (fun a : ℂ => border a b c D) := + continuous_border continuous_id continuous_const continuous_const continuous_const + have hh := map_mem_closure hf ((dense_compl_singleton (0 : ℂ)) (A 0 0)) + (fun a ha => hpivot a (by simpa using ha) b c D) + simpa only [closure_closure, b, c, D, border_eq] using hh + +end SpinAngle.DenseLU + +namespace SpinAngle.PolynomialCarrier +open scoped Classical Matrix +open SpinAngle.Specht SpinAngle.Young +variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) + +lemma action_mem_alternating (A : Matrix (Fin q) (Fin q) ℂ) + (v : TensorSpace D q) (hv : v ∈ alternating D q) : + TensorRep.action A v ∈ alternating D q := by + intro g + rw [← action_site_commute, hv g, map_smul] + +lemma upper_weight_support (U : Matrix (Fin q) (Fin q) ℂ) (hU : U.IsUpperTriangular) + (x : Cells D → Fin q) (hx : TensorRep.action U (highest D q hq) x ≠ 0) : + ∑ i, (x i).val = ∑ i : Cells D, i.val.1 := by + have hl := rowRankSum_le D (fun i => (x i).val) + (alternating_injective D q _ (action_mem_alternating D q U _ (highest_mem D q hq)) x hx) + apply le_antisymm _ hl + change (∑ y, (∏ i, U (x i) (y i)) * highest D q hq y) ≠ 0 at hx + obtain ⟨y, -, hy⟩ := Finset.exists_ne_zero_of_sum_ne_zero hx + have hyv : highest D q hq y ≠ 0 := (mul_ne_zero_iff.mp hy).2 + have hp : ∀ i, x i ≤ y i := by + intro i + by_contra hi + have hz : U (x i) (y i) = 0 := hU (lt_of_not_ge hi) + exact (mul_ne_zero_iff.mp hy).1 (Finset.prod_eq_zero (Finset.mem_univ i) hz) + rw [← weight_eigen_support D q hq _ (highest_weight_eigen D q hq) y hyv] + exact Finset.sum_le_sum fun i _ => hp i + + + +lemma upper_highest (U : Matrix (Fin q) (Fin q) ℂ) (hU : U.IsUpperTriangular) : + TensorRep.action U (highest D q hq) = + (TensorRep.action U (highest D q hq) (rowColor D q hq)) • highest D q hq := by + ext x + change _ = _ * highest D q hq x + by_cases hw : ∑ i, (x i).val = ∑ i : Cells D, i.val.1 + · exact alternating_minimal_weight D q hq _ + (action_mem_alternating D q U _ (highest_mem D q hq)) x hw + · have hv0 : TensorRep.action U (highest D q hq) x = 0 := by + by_contra hn + exact hw (upper_weight_support D q hq U hU x hn) + have he0 : highest D q hq x = 0 := by + by_contra hn + exact hw (weight_eigen_support D q hq _ (highest_weight_eigen D q hq) x hn) + rw [hv0, he0, mul_zero] + +lemma continuous_action_highest : + Continuous (fun A : Matrix (Fin q) (Fin q) ℂ => TensorRep.action A (highest D q hq)) := by + change Continuous (fun A : Matrix (Fin q) (Fin q) ℂ => + WithLp.toLp 2 (fun x : Cells D → Fin q => ∑ y, (∏ i, A (x i) (y i)) * highest D q hq y)) + apply (PiLp.continuous_toLp 2 (fun _ : Cells D → Fin q => ℂ)).comp + fun_prop + + + +lemma action_highest_mem_of_lower (S : Submodule ℂ (TensorSpace D q)) + (hS : ∀ L : Matrix (Fin q) (Fin q) ℂ, DenseLU.LowerUnipotent L → + TensorRep.action L (highest D q hq) ∈ S) + (A : Matrix (Fin q) (Fin q) ℂ) : TensorRep.action A (highest D q hq) ∈ S := by + have hsub : DenseLU.bigCell q ⊆ + (fun B : Matrix (Fin q) (Fin q) ℂ => TensorRep.action B (highest D q hq)) ⁻¹' + (S : Set (TensorSpace D q)) := by + intro B hB + obtain ⟨L,U,hL,hU,rfl⟩ := hB + change TensorRep.action (L * U) (highest D q hq) ∈ S + rw [map_mul, Module.End.mul_apply, upper_highest D q hq U hU, map_smul] + exact S.smul_mem _ (hS L hL) + exact closure_minimal hsub + (S.closed_of_finiteDimensional.preimage (continuous_action_highest D q hq)) + (DenseLU.dense_bigCell q A) + +end SpinAngle.PolynomialCarrier +noncomputable section +open scoped BigOperators +namespace SpinAngle.PolyDimension +open MvPolynomial Module +variable (σ : Type*) [contextInstance2689_21 : Fintype σ] [contextInstance2689_33 : DecidableEq σ] (p : ℕ) + + +def boundedExponentEquiv : {f : σ →₀ ℕ // ∀ i, f i ≤ p} ≃ (σ → Fin (p+1)) where + toFun f i := ⟨f.val i, Nat.lt_succ_of_le (f.property i)⟩ + invFun f := ⟨Finsupp.equivFunOnFinite.symm (fun i => (f i).val), by + intro i; exact Nat.le_of_lt_succ (f i).isLt⟩ + left_inv f := by apply Subtype.ext; ext i; rfl + right_inv f := by funext i; apply Fin.ext; rfl + + +theorem finrank_restrictDegree : + Module.finrank ℂ (restrictDegree σ ℂ p) = (p+1) ^ Fintype.card σ := by + let s : Set (σ →₀ ℕ) := {f | ∀ i, f i ≤ p} + let : Fintype s := Fintype.ofEquiv (σ → Fin (p+1)) (boundedExponentEquiv σ p).symm + change Module.finrank ℂ (restrictSupport ℂ s) = _ + rw [Module.finrank_eq_card_basis (basisRestrictSupport ℂ s)] + calc + Fintype.card s = Fintype.card (σ → Fin (p+1)) := Fintype.card_congr (boundedExponentEquiv σ p) + _ = _ := by simp + +abbrev LowerIndex (q : ℕ) := (i : Fin q) × Fin i.val + +lemma card_lowerIndex (q : ℕ) : Fintype.card (LowerIndex q) = q * (q-1) / 2 := by + simp only [LowerIndex, Fintype.card_sigma, Fintype.card_fin] + rw [Fin.sum_univ_eq_sum_range (fun i : ℕ => i) q, Finset.sum_range_id] + +lemma twice_card_lowerIndex (q : ℕ) : 2 * Fintype.card (LowerIndex q) = q * (q-1) := by + simp only [LowerIndex, Fintype.card_sigma, Fintype.card_fin] + rw [Fin.sum_univ_eq_sum_range (fun i : ℕ => i) q, mul_comm, Finset.sum_range_id_mul_two] + +variable {q : ℕ} +def lowerEntry (i j : Fin q) : MvPolynomial (LowerIndex q) ℂ := + if h : j < i then X ⟨i, ⟨j.val, h⟩⟩ else if i = j then 1 else 0 + +lemma lowerEntry_degree (i j : Fin q) : (lowerEntry i j).totalDegree ≤ 1 := by + unfold lowerEntry + split_ifs <;> simp + +lemma totalDegree_sum_le + (σ : Type*) + [Fintype σ] + [DecidableEq σ] + (p : ℕ) {ι : Type*} (s : Finset ι) (f : ι → MvPolynomial σ ℂ) + (hf : ∀ i ∈ s, (f i).totalDegree ≤ p) : (∑ i ∈ s, f i).totalDegree ≤ p := + (MvPolynomial.totalDegree_finsetSum s f).trans (Finset.sup_le hf) + +end SpinAngle.PolyDimension + +namespace SpinAngle.PolyDimension +open MvPolynomial Module +variable {σ X : Type*} [contextInstance2737_23 : Fintype σ] [contextInstance2737_35 : DecidableEq σ] [contextInstance2737_51 : Fintype X] (p : ℕ) + + + + +def valueTranspose (P : X → restrictDegree σ ℂ p) : + Module.Dual ℂ (restrictDegree σ ℂ p) →ₗ[ℂ] EuclideanSpace ℂ X where + toFun φ := WithLp.toLp 2 (fun x => φ (P x)) + map_add' φ ψ := by ext x; rfl + map_smul' c φ := by ext x; rfl + +lemma value_mem_range + {σ : Type*} {X : Type*} + [Fintype σ] + [DecidableEq σ] + [Fintype X] + (p : ℕ) (P : X → restrictDegree σ ℂ p) (a : σ → ℂ) : + WithLp.toLp 2 (fun x => MvPolynomial.aeval a (P x).val) ∈ + LinearMap.range (valueTranspose p P) := by + refine ⟨(MvPolynomial.aeval a).toLinearMap.comp (restrictDegree σ ℂ p).subtype, ?_⟩ + rfl + +lemma finrank_value_range + {σ : Type*} {X : Type*} + [contextInstance2737_23 : Fintype σ] + [contextInstance2737_35 : DecidableEq σ] + [Fintype X] + (p : ℕ) (P : X → restrictDegree σ ℂ p) : + Module.finrank ℂ (LinearMap.range (valueTranspose p P)) ≤ (p+1)^Fintype.card σ := by + have hh := (valueTranspose p P).finrank_range_le + rw [Subspace.dual_finrank_eq, finrank_restrictDegree] at hh + exact hh + +end SpinAngle.PolyDimension + +namespace SpinAngle.PolynomialCarrier +open scoped Classical Matrix +open SpinAngle.Specht SpinAngle.Young PolyDimension MvPolynomial +variable (D : YoungDiagram) (q : ℕ) (hq : D.colLen 0 ≤ q) + + +def lowerCoordinate (x : Cells D → Fin q) : MvPolynomial (LowerIndex q) ℂ := + ∑ y : Cells D → Fin q, (∏ i : Cells D, lowerEntry (x i) (y i)) * C (highest D q hq y) + +lemma lowerCoordinate_degree (x : Cells D → Fin q) : + (lowerCoordinate D q hq x).totalDegree ≤ Fintype.card (Cells D) := by + apply PolyDimension.totalDegree_sum_le + intro y _ + apply (MvPolynomial.totalDegree_mul _ _).trans + rw [MvPolynomial.totalDegree_C, add_zero] + apply (MvPolynomial.totalDegree_finsetProd _ _).trans + exact (Finset.sum_le_sum fun i _ => lowerEntry_degree (x i) (y i)).trans_eq (by simp) + +def lowerCoordinateBounded (x : Cells D → Fin q) : + restrictDegree (LowerIndex q) ℂ (Fintype.card (Cells D)) := + ⟨lowerCoordinate D q hq x, + restrictTotalDegree_le_restrictDegree _ _ _ + ((mem_restrictTotalDegree _ _ _).mpr (lowerCoordinate_degree D q hq x))⟩ + +def lowerParameters (L : Matrix (Fin q) (Fin q) ℂ) (z : LowerIndex q) : ℂ := + L z.1 ⟨z.2.val, z.2.isLt.trans z.1.isLt⟩ + +lemma eval_lowerEntry (L : Matrix (Fin q) (Fin q) ℂ) (hL : DenseLU.LowerUnipotent L) + (i j : Fin q) : aeval (lowerParameters q L) (lowerEntry i j) = L i j := by + unfold lowerEntry + split_ifs with hlt heq + · simp [aeval_X, lowerParameters] + · subst j; simp [hL.2 i] + · have hij : i < j := lt_of_le_of_ne (le_of_not_gt hlt) heq + rw [map_zero, hL.1 hij] + +lemma eval_lowerCoordinate (L : Matrix (Fin q) (Fin q) ℂ) (hL : DenseLU.LowerUnipotent L) + (x : Cells D → Fin q) : + aeval (lowerParameters q L) (lowerCoordinate D q hq x) = + TensorRep.action L (highest D q hq) x := by + simp only [lowerCoordinate, map_sum, map_mul, map_prod, eval_lowerEntry q L hL] + change (∑ y : Cells D → Fin q, (∏ i, L (x i) (y i)) * + aeval (lowerParameters q L) (C (highest D q hq y))) = + ∑ y : Cells D → Fin q, (∏ i, L (x i) (y i)) * highest D q hq y + apply Finset.sum_congr rfl + intro y _ + simp + + + +theorem ordinary_finrank_le : + Module.finrank ℂ (ordinary D q hq).toSubmodule ≤ + (Fintype.card (Cells D)+1) ^ (q*(q-1)/2) := by + let P := lowerCoordinateBounded D q hq + let S := LinearMap.range (PolyDimension.valueTranspose (Fintype.card (Cells D)) P) + have hL (L : Matrix (Fin q) (Fin q) ℂ) (hL : DenseLU.LowerUnipotent L) : + TensorRep.action L (highest D q hq) ∈ S := by + have hh := PolyDimension.value_mem_range (Fintype.card (Cells D)) P (lowerParameters q L) + have he : WithLp.toLp 2 (fun x => aeval (lowerParameters q L) (P x).val) = + TensorRep.action L (highest D q hq) := by + ext x; exact eval_lowerCoordinate D q hq L hL x + rw [he] at hh + exact hh + let inc : (ordinary D q hq).toSubmodule →ₗ[ℂ] TensorSpace D q := + (alternating D q).toSubmodule.subtype.comp (ordinary D q hq).toSubmodule.subtype + have hcarrier (v : (alternating D q).toSubmodule) + (hv : v ∈ (ordinary D q hq).toSubmodule) : (v : TensorSpace D q) ∈ S := by + change v ∈ Submodule.span ℂ (Set.range fun g => + (alternating D q).toRepresentation g + (⟨highest D q hq, highest_mem D q hq⟩ : (alternating D q).toSubmodule)) at hv + induction hv using Submodule.span_induction with + | mem v hv => + obtain ⟨g,rfl⟩ := hv + exact action_highest_mem_of_lower D q hq S hL g.val + | zero => exact S.zero_mem + | add x y hx hy ihx ihy => exact S.add_mem ihx ihy + | smul a x hx ih => exact S.smul_mem a ih + have hinc (v : (ordinary D q hq).toSubmodule) : inc v ∈ S := hcarrier v.val v.property + let f : (ordinary D q hq).toSubmodule →ₗ[ℂ] S := LinearMap.codRestrict S inc hinc + have hf : Function.Injective f := by + intro x y he + apply Subtype.ext + apply Subtype.ext + exact congrArg (fun v : S => v.val) he + have hh := LinearMap.finrank_le_finrank_of_injective hf + exact hh.trans (by + simpa only [PolyDimension.card_lowerIndex] using + PolyDimension.finrank_value_range (Fintype.card (Cells D)) P) + +end SpinAngle.PolynomialCarrier + + +noncomputable section +open MeasureTheory TopologicalSpace Set +open scoped BigOperators +namespace SpinAngle.CompactTwirl + +variable {G : Type*} [contextInstance2861_21 : Group G] [contextInstance2861_31 : TopologicalSpace G] [contextInstance2861_52 : IsTopologicalGroup G] + [contextInstance2862_2 : CompactSpace G] [contextInstance2862_19 : MeasurableSpace G] [contextInstance2862_39 : BorelSpace G] + +def compactHaar : Measure G := + Measure.haarMeasure (⟨⟨Set.univ, isCompact_univ⟩, by simp⟩ : PositiveCompacts G) + +instance : IsProbabilityMeasure (compactHaar (G := G)) where + measure_univ := Measure.haarMeasure_self + +instance : (compactHaar (G := G)).IsMulLeftInvariant := + inferInstanceAs (Measure.IsMulLeftInvariant (Measure.haarMeasure _)) + +lemma continuous_integrable {A : Type*} [NormedAddCommGroup A] (f : G → A) + (hf : Continuous f) : Integrable f (compactHaar (G := G)) := + hf.integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace f) + +variable {A : Type*} [contextInstance2877_21 : NormedRing A] [contextInstance2877_36 : NormedAlgebra ℝ A] [contextInstance2877_56 : CompleteSpace A] + + +def conjugate (ρ : G →* A) (a : A) (g : G) : A := ρ g * a * ρ g⁻¹ + +def twirl (ρ : G →* A) (a : A) : A := ∫ g, conjugate ρ a g ∂compactHaar + +lemma continuous_conjugate + {G : Type*} + [contextInstance2861_21 : Group G] + [contextInstance2861_31 : TopologicalSpace G] + [contextInstance2861_52 : IsTopologicalGroup G] + [CompactSpace G] + [MeasurableSpace G] + [BorelSpace G] + {A : Type*} + [contextInstance2877_21 : NormedRing A] + [NormedAlgebra ℝ A] + [CompleteSpace A] (ρ : G →* A) (hρ : Continuous ρ) (a : A) : + Continuous (conjugate ρ a) := + (hρ.mul continuous_const).mul (hρ.comp continuous_inv) + +lemma integrable_conjugate (ρ : G →* A) (hρ : Continuous ρ) (a : A) : + Integrable (conjugate ρ a) compactHaar := + continuous_integrable _ (continuous_conjugate ρ hρ a) + +lemma conjugate_mul + {G : Type*} + [contextInstance2861_21 : Group G] + [TopologicalSpace G] + [IsTopologicalGroup G] + [CompactSpace G] + [MeasurableSpace G] + [BorelSpace G] + {A : Type*} + [contextInstance2877_21 : NormedRing A] + [NormedAlgebra ℝ A] + [CompleteSpace A] (ρ : G →* A) (a : A) (g h : G) : + conjugate ρ a (g * h) = ρ g * conjugate ρ a h * ρ g⁻¹ := by + simp only [conjugate, mul_inv_rev, map_mul, mul_assoc] + + +lemma twirl_commute (ρ : G →* A) (hρ : Continuous ρ) (a : A) (g : G) : + Commute (ρ g) (twirl ρ a) := by + have hi := integrable_conjugate ρ hρ a + have hinv : (ρ g⁻¹) * ρ g = 1 := by rw [← map_mul, inv_mul_cancel, map_one] + have he : ρ g * twirl ρ a * ρ g⁻¹ = twirl ρ a := by + rw [twirl, ← integral_const_mul_of_integrable hi] + rw [← integral_mul_const_of_integrable (hi.const_mul _)] + simp_rw [← conjugate_mul] + exact integral_mul_left_eq_self _ g + have hc := congrArg (fun x : A => x * ρ g) he + simpa only [Commute, SemiconjBy, mul_assoc, hinv, mul_one] using hc + +lemma twirl_trace (τ : A →L[ℝ] ℂ) (hτ : ∀ x y : A, τ (x * y) = τ (y * x)) + (ρ : G →* A) (hρ : Continuous ρ) (a : A) : τ (twirl ρ a) = τ a := by + rw [twirl, ← τ.integral_comp_comm (integrable_conjugate ρ hρ a)] + have he (g : G) : τ (conjugate ρ a g) = τ a := by + rw [conjugate, hτ, ← mul_assoc, ← map_mul, inv_mul_cancel, map_one, one_mul] + simp [he, integral_const, measureReal_def] + +section Positivity +variable [contextInstance2919_9 : PartialOrder A] [contextInstance2919_26 : IsOrderedAddMonoid A] [contextInstance2919_49 : StarRing A] [contextInstance2919_62 : StarOrderedRing A] + [contextInstance2920_2 : ClosedIciTopology A] [contextInstance2920_24 : IsOrderedModule ℝ A] + +lemma twirl_nonneg + {G : Type*} + [contextInstance2861_21 : Group G] + [contextInstance2861_31 : TopologicalSpace G] + [contextInstance2861_52 : IsTopologicalGroup G] + [contextInstance2862_2 : CompactSpace G] + [contextInstance2862_19 : MeasurableSpace G] + [contextInstance2862_39 : BorelSpace G] + {A : Type*} + [contextInstance2877_21 : NormedRing A] + [contextInstance2877_36 : NormedAlgebra ℝ A] + [CompleteSpace A] + [contextInstance2919_9 : PartialOrder A] + [contextInstance2919_26 : IsOrderedAddMonoid A] + [contextInstance2919_49 : StarRing A] + [contextInstance2919_62 : StarOrderedRing A] + [contextInstance2920_2 : ClosedIciTopology A] + [contextInstance2920_24 : IsOrderedModule ℝ A] (ρ : G →* A) (a : A) + (hρ : ∀ g, ρ g⁻¹ = star (ρ g)) (ha : 0 ≤ a) : 0 ≤ twirl ρ a := by + apply integral_nonneg + intro g + dsimp [conjugate] + rw [hρ] + exact star_right_conjugate_nonneg ha _ +end Positivity + +end SpinAngle.CompactTwirl + +namespace SpinAngle +open scoped Matrix.Norms.L2Operator + + +lemma unitaryGroup_compactSpace (n : Type*) [Fintype n] [DecidableEq n] [Nonempty n] : + CompactSpace (Matrix.unitaryGroup n ℂ) := by + apply isCompact_iff_compactSpace.mp + apply (isCompact_closedBall (0 : Matrix n n ℂ) 1).of_isClosed_subset isClosed_unitary + intro a ha + rw [Metric.mem_closedBall, dist_zero_right] + exact (CStarRing.norm_coe_unitary (⟨a, ha⟩ : unitary (Matrix n n ℂ))).le + +end SpinAngle + +namespace SpinAngle.CompactTwirl +variable {G : Type*} [contextInstance2949_21 : Group G] [contextInstance2949_31 : TopologicalSpace G] [contextInstance2949_52 : IsTopologicalGroup G] + [contextInstance2950_2 : CompactSpace G] [contextInstance2950_19 : MeasurableSpace G] [contextInstance2950_39 : BorelSpace G] +variable {E : Type*} [contextInstance2951_21 : NormedAddCommGroup E] [contextInstance2951_44 : InnerProductSpace ℂ E] + [contextInstance2952_2 : FiniteDimensional ℂ E] + + +def continuousAction (ρ : Representation ℂ G E) : G →* (E →L[ℂ] E) := + (Module.End.toContinuousLinearMap (𝕜 := ℂ) E).toMonoidHom.comp ρ + +@[simp] lemma continuousAction_apply + {G : Type*} + [contextInstance2949_21 : Group G] + [TopologicalSpace G] + [IsTopologicalGroup G] + [CompactSpace G] + [MeasurableSpace G] + [BorelSpace G] + {E : Type*} + [contextInstance2951_21 : NormedAddCommGroup E] + [contextInstance2951_44 : InnerProductSpace ℂ E] + [contextInstance2952_2 : FiniteDimensional ℂ E] (ρ : Representation ℂ G E) (g : G) (v : E) : + continuousAction ρ g v = ρ g v := rfl + +def operatorTrace : (E →L[ℂ] E) →L[ℂ] ℂ := + ((LinearMap.trace ℂ E).comp + (Module.End.toContinuousLinearMap (𝕜 := ℂ) E).symm.toLinearMap).toContinuousLinearMap + +@[simp] lemma operatorTrace_apply + {G : Type*} + [Group G] + [TopologicalSpace G] + [IsTopologicalGroup G] + [CompactSpace G] + [MeasurableSpace G] + [BorelSpace G] + {E : Type*} + [contextInstance2951_21 : NormedAddCommGroup E] + [contextInstance2951_44 : InnerProductSpace ℂ E] + [contextInstance2952_2 : FiniteDimensional ℂ E] (a : E →L[ℂ] E) : + operatorTrace a = LinearMap.trace ℂ E a.toLinearMap := rfl + +lemma operatorTrace_mul_comm + {G : Type*} + [Group G] + [TopologicalSpace G] + [IsTopologicalGroup G] + [CompactSpace G] + [MeasurableSpace G] + [BorelSpace G] + {E : Type*} + [contextInstance2951_21 : NormedAddCommGroup E] + [contextInstance2951_44 : InnerProductSpace ℂ E] + [FiniteDimensional ℂ E] (a b : E →L[ℂ] E) : + operatorTrace (a * b) = operatorTrace (b * a) := + LinearMap.trace_mul_comm ℂ a.toLinearMap b.toLinearMap + + + +theorem twirl_irreducible (ρ : Representation ℂ G E) [ρ.IsIrreducible] + (hρ : Continuous (continuousAction ρ)) (a : E →L[ℂ] E) : + twirl (continuousAction ρ) a = + (operatorTrace a / (Module.finrank ℂ E : ℂ)) • (1 : E →L[ℂ] E) := by + let t := twirl (continuousAction ρ) a + let f : ρ.IntertwiningMap ρ := + t.toLinearMap.intertwiningMap_of_isIntertwiningMap ρ ρ (by + intro g v + have h := twirl_commute (continuousAction ρ) hρ a g + exact (congrArg (fun L : E →L[ℂ] E => L v) h.eq).symm) + obtain ⟨z, hz⟩ := + (Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed (ρ := ρ)).surjective f + have ht : t = z • (1 : E →L[ℂ] E) := by + ext v + exact (congrArg (fun L : ρ.IntertwiningMap ρ => L v) hz).symm + have htr : operatorTrace t = operatorTrace a := + twirl_trace (operatorTrace.restrictScalars ℝ) (operatorTrace_mul_comm (G := G)) + (continuousAction ρ) hρ a + let : Nontrivial E := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) ρ.asModule + have hn : (Module.finrank ℂ E : ℂ) ≠ 0 := by + exact_mod_cast Module.finrank_pos.ne' + have hz' : z = operatorTrace a / (Module.finrank ℂ E : ℂ) := by + apply (eq_div_iff hn).mpr + rw [ht, map_smul] at htr + simpa [operatorTrace_apply (G := G), LinearMap.trace_one] using htr + simpa only [hz'] using ht + +end SpinAngle.CompactTwirl + + + +namespace SpinAngle.CompactTwirl +open scoped InnerProductSpace ComplexOrder +variable {G : Type*} [contextInstance3008_21 : Group G] [contextInstance3008_31 : TopologicalSpace G] [contextInstance3008_52 : IsTopologicalGroup G] + [contextInstance3009_2 : CompactSpace G] [contextInstance3009_19 : MeasurableSpace G] [contextInstance3009_39 : BorelSpace G] +variable {E F : Type*} [contextInstance3010_23 : NormedAddCommGroup E] [contextInstance3010_46 : InnerProductSpace ℂ E] + [contextInstance3011_2 : NormedAddCommGroup F] [contextInstance3011_25 : InnerProductSpace ℂ F] + [contextInstance3012_2 : FiniteDimensional ℂ E] [contextInstance3012_26 : FiniteDimensional ℂ F] + +lemma twirl_natural (ρ : Representation ℂ G E) (σ : Representation ℂ G F) + (hρ : Continuous (continuousAction ρ)) (hσ : Continuous (continuousAction σ)) + (a : E →L[ℂ] E) (A : F →L[ℂ] F) (L : ρ.IntertwiningMap σ) + (hnat : ∀ x, A (L x) = L (a x)) (x : E) : + twirl (continuousAction σ) A (L x) = L (twirl (continuousAction ρ) a x) := by + have hi := integrable_conjugate (continuousAction ρ) hρ a + have hI := integrable_conjugate (continuousAction σ) hσ A + rw [twirl, ContinuousLinearMap.integral_apply hI, twirl, ContinuousLinearMap.integral_apply hi] + change _ = L.toLinearMap.toContinuousLinearMap (∫ g, conjugate (continuousAction ρ) a g x ∂compactHaar) + rw [← ContinuousLinearMap.integral_comp_comm _ (hi.apply_continuousLinearMap x)] + apply integral_congr_ae + filter_upwards [] with g + change σ g (A (σ g⁻¹ (L x))) = L (ρ g (a (ρ g⁻¹ x))) + rw [← L.isIntertwining, hnat, L.isIntertwining] + +lemma continuousAction_inverse_star + {G : Type*} + [contextInstance3008_21 : Group G] + [TopologicalSpace G] + [IsTopologicalGroup G] + [CompactSpace G] + [MeasurableSpace G] + [BorelSpace G] + {E : Type*} + [contextInstance3010_23 : NormedAddCommGroup E] + [contextInstance3010_46 : InnerProductSpace ℂ E] + [contextInstance3012_2 : FiniteDimensional ℂ E] (ρ : Representation ℂ G E) + (hρ : ∀ g x y, ⟪ρ g x,ρ g y⟫_ℂ = ⟪x,y⟫_ℂ) (g : G) : + continuousAction ρ g⁻¹ = star (continuousAction ρ g) := by + ext x + apply ext_inner_left ℂ + intro y + change ⟪y,ρ g⁻¹ x⟫_ℂ = ⟪y,(continuousAction ρ g).adjoint x⟫_ℂ + rw [ContinuousLinearMap.adjoint_inner_right] + simpa only [inv_inv, continuousAction_apply] using (UnitaryNaturality.inner_move ρ hρ g⁻¹ y x) + +end SpinAngle.CompactTwirl + +namespace SpinAngle.ProjectionOrder +variable {A : Type*} [contextInstance3043_21 : CStarAlgebra A] [contextInstance3043_38 : PartialOrder A] [contextInstance3043_55 : StarOrderedRing A] + [contextInstance3044_2 : NonnegSpectrumClass ℝ A] + +lemma scalar_projection_le (T P : A) (hT : 0 ≤ T) (hP : IsStarProjection P) + (c : ℝ) (he : T * P = c • P) : c • P ≤ T := by + have hstar := congrArg star he + have hpT : P * T = c • P := by + simpa only [star_mul, hP.isSelfAdjoint.star_eq, (IsSelfAdjoint.of_nonneg hT).star_eq, + star_smul, star_trivial] using hstar + have hc : Commute (1-P) T := by + dsimp [Commute,SemiconjBy] + rw [sub_mul,mul_sub,one_mul,mul_one,hpT,he] + have hn := hc.mul_nonneg (sub_nonneg.mpr hP.le_one) hT + rw [sub_mul,one_mul,hpT] at hn + exact sub_nonneg.mp hn +end SpinAngle.ProjectionOrder + +namespace SpinAngle.CompactTwirl +open scoped InnerProductSpace ComplexOrder +variable {G : Type*} [contextInstance3062_21 : Group G] [contextInstance3062_31 : TopologicalSpace G] [contextInstance3062_52 : IsTopologicalGroup G] + [contextInstance3063_2 : CompactSpace G] [contextInstance3063_19 : MeasurableSpace G] [contextInstance3063_39 : BorelSpace G] +variable {E F : Type*} [contextInstance3064_23 : NormedAddCommGroup E] [contextInstance3064_46 : InnerProductSpace ℂ E] + [contextInstance3065_2 : NormedAddCommGroup F] [contextInstance3065_25 : InnerProductSpace ℂ F] + [contextInstance3066_2 : FiniteDimensional ℂ E] [contextInstance3066_26 : FiniteDimensional ℂ F] + +lemma isotypic_twirl_scalar (ρ : Representation ℂ G E) [ρ.IsIrreducible] + (σ : Representation ℂ G F) + (hρ : Continuous (continuousAction ρ)) (hσ : Continuous (continuousAction σ)) + (a : E →L[ℂ] E) (A : F →L[ℂ] F) + (hnat : ∀ L : ρ.IntertwiningMap σ, ∀ x, A (L x) = L (a x)) : + twirl (continuousAction σ) A * Isotypic.projection ρ σ = + (operatorTrace a / (Module.finrank ℂ E : ℂ)) • Isotypic.projection ρ σ := by + ext v + apply Isotypic.scalar_on_space ρ σ + (twirl (continuousAction σ) A).toLinearMap + (operatorTrace a / (Module.finrank ℂ E : ℂ)) + · intro L x + change twirl (continuousAction σ) A (L x) = _ + rw [twirl_natural ρ σ hρ hσ a A L (hnat L), twirl_irreducible ρ hρ a] + simp only [smul_apply, one_apply_eq_self, map_smul] + · exact (Isotypic.space ρ σ).toSubmodule.starProjection_apply_mem v + + +lemma isotypic_twirl_lower (ρ : Representation ℂ G E) [ρ.IsIrreducible] + (σ : Representation ℂ G F) + (hρ : Continuous (continuousAction ρ)) (hσ : Continuous (continuousAction σ)) + (hσunit : ∀ g x y, ⟪σ g x,σ g y⟫_ℂ = ⟪x,y⟫_ℂ) + (a : E →L[ℂ] E) (A : F →L[ℂ] F) (ha : 0 ≤ a) (hA : 0 ≤ A) + (hnat : ∀ L : ρ.IntertwiningMap σ, ∀ x, A (L x) = L (a x)) : + ((operatorTrace a).re / (Module.finrank ℂ E : ℝ)) • Isotypic.projection ρ σ ≤ + twirl (continuousAction σ) A := by + apply ProjectionOrder.scalar_projection_le _ _ + (twirl_nonneg _ A (continuousAction_inverse_star σ hσunit) hA) + (isStarProjection_starProjection (U := (Isotypic.space ρ σ).toSubmodule)) + have ht : operatorTrace a = ((operatorTrace a).re : ℂ) := + Complex.eq_re_of_ofReal_le (LinearMap.IsPositive.trace_nonneg + ((ContinuousLinearMap.nonneg_iff_isPositive).mp ha)) + have h := isotypic_twirl_scalar ρ σ hρ hσ a A hnat + rw [ht] at h + convert h using 1 <;> simp only [Isotypic.projection, + RCLike.real_smul_eq_coe_smul (K := ℂ)] + congr 1 + change (((operatorTrace a).re / (Module.finrank ℂ E : ℝ) : ℝ) : ℂ) = _ + simp only [Complex.ofReal_div, Complex.ofReal_natCast] + +end SpinAngle.CompactTwirl + + + + + + +noncomputable section +open scoped BigOperators +open Set +namespace SpinAngle.CompactMixture +variable {E : Type*} [contextInstance3119_21 : NormedAddCommGroup E] [contextInstance3119_44 : NormedSpace ℝ E] [contextInstance3119_62 : FiniteDimensional ℝ E] + +lemma convexHull_compact {s : Set E} (hs : IsCompact s) : IsCompact (convexHull ℝ s) := by + classical + let : CompactSpace s := isCompact_iff_compactSpace.mp hs + let C (k : ℕ) := (Convexity.StdSimplex ℝ (Fin k)) × (Fin k → s) + let f (k : ℕ) (v : C k) : E := ∑ i, v.1.weights i • (v.2 i).val + have hf (k : ℕ) : Continuous (f k) := by + change Continuous (fun v : (Convexity.StdSimplex ℝ (Fin k)) × (Fin k → s) => + ∑ i, v.1.weights i • (v.2 i).val) + apply continuous_finsetSum + intro i hi + exact ((Convexity.StdSimplex.continuous_weights_apply ℝ i).comp continuous_fst).smul + (continuous_subtype_val.comp ((continuous_apply i).comp continuous_snd)) + have hc : IsCompact (⋃ k : Fin (Module.finrank ℝ E + 2), Set.range (f k.val)) := + isCompact_iUnion (fun k => isCompact_range (hf k.val)) + convert hc using 1 + ext x + constructor + · intro hx + let t := Caratheodory.minCardFinsetOfMemConvexHull hx + have ht : (t : Set E) ⊆ s := Caratheodory.minCardFinsetOfMemConvexHull_subseteq hx + have hm : x ∈ convexHull ℝ (t : Set E) := Caratheodory.mem_minCardFinsetOfMemConvexHull hx + have hi : AffineIndependent ℝ ((↑) : t → E) := + Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull hx + have hn : Fintype.card t ≤ Module.finrank ℝ E + 1 := + hi.card_le_finrank_succ.trans (Nat.add_le_add_right (Submodule.finrank_le _) 1) + let k : Fin (Module.finrank ℝ E + 2) := ⟨Fintype.card t, by omega⟩ + let e := (Fintype.equivFin t).symm + obtain ⟨w,hw,hws,hxw⟩ := Finset.mem_convexHull'.mp hm + let z : Fin k.val → s := fun i => ⟨(e i).val, ht (e i).property⟩ + have hsum : ∑ i : Fin k.val, w (e i).val = 1 := by + rw [show (∑ i : Fin k.val, w (e i).val) = ∑ j : t, w j.val from + e.sum_comp (fun j : t => w j.val)] + simpa only [Finset.sum_coe_sort] using hws + let v : C k.val := (⟨Finsupp.equivFunOnFinite.symm (fun i => w (e i).val), + fun i => by simpa using hw _ (e i).property, + by simpa [Finsupp.sum_fintype] using hsum⟩, z) + apply Set.mem_iUnion.mpr + refine ⟨k,v,?_⟩ + simp only [f, v, z, Finsupp.coe_equivFunOnFinite_symm] + rw [show (∑ i : Fin k.val, w (e i).val • (e i).val) = ∑ j : t, w j.val • j.val from + e.sum_comp (fun j : t => w j.val • j.val)] + exact (Finset.sum_coe_sort t (fun j : E => w j • j)).trans hxw + · intro hx + obtain ⟨k,v,rfl⟩ := Set.mem_iUnion.mp hx + exact mem_convexHull_of_exists_fintype (fun i => v.1.weights i) (fun i => (v.2 i).val) + v.1.weights_nonneg v.1.total_of_fintype (fun i => (v.2 i).property) rfl +end SpinAngle.CompactMixture + +namespace SpinAngle.CompactTwirl +variable {G : Type*} [contextInstance3168_21 : Group G] [contextInstance3168_31 : TopologicalSpace G] [contextInstance3168_52 : IsTopologicalGroup G] + [contextInstance3169_2 : CompactSpace G] [contextInstance3169_19 : MeasurableSpace G] [contextInstance3169_39 : BorelSpace G] +variable {E : Type*} [contextInstance3170_21 : NormedAddCommGroup E] [contextInstance3170_44 : InnerProductSpace ℂ E] + [contextInstance3171_2 : FiniteDimensional ℂ E] + + + +lemma twirl_finite_mixture (ρ : Representation ℂ G E) + (hρ : Continuous (continuousAction ρ)) (a : E →L[ℂ] E) : + ∃ (ι : Type) (_ : Fintype ι) (w : ι → ℝ) (g : ι → G), + (∀ i, 0 ≤ w i) ∧ (∑ i, w i = 1) ∧ + twirl (continuousAction ρ) a = ∑ i, w i • conjugate (continuousAction ρ) a (g i) := by + let f := conjugate (continuousAction ρ) a + have hf : Continuous f := continuous_conjugate _ hρ a + have hc : IsCompact (Set.range f) := isCompact_range hf + have hm : twirl (continuousAction ρ) a ∈ convexHull ℝ (Set.range f) := + (convex_convexHull ℝ _).integral_mem (CompactMixture.convexHull_compact hc).isClosed + (Filter.Eventually.of_forall fun g => subset_convexHull ℝ _ (Set.mem_range_self g)) + (integrable_conjugate _ hρ a) + obtain ⟨ι,hι,w,z,hw,hs,hz,he⟩ := mem_convexHull_iff_exists_fintype.mp hm + let := hι + choose g hg using hz + refine ⟨ι,hι,w,g,hw,hs,?_⟩ + rw [← he] + apply Finset.sum_congr rfl + intro i _ + rw [← hg i] +end SpinAngle.CompactTwirl + +namespace SpinAngle.SignedCarrier +open scoped Classical TensorProduct BigOperators InnerProductSpace ComplexOrder Matrix.Norms.L2Operator MatrixOrder +open SpinAngle.Young SpinAngle.Specht SignedTensor +variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) + +lemma dimension_eq : dimension a b q ha hb = + Module.finrank ℂ (PolynomialCarrier.Carrier a q ha) * + Module.finrank ℂ (PolynomialCarrier.Carrier b q hb) := + Module.finrank_tensorProduct + +lemma dimension_pos : 0 < dimension a b q ha hb := by + have : Nontrivial (Carrier a b q ha hb) := IsSimpleModule.nontrivial (MonoidAlgebra ℂ (Group q)) + (rep a b q ha hb).asModule + exact Module.finrank_pos + + +theorem dimension_le : dimension a b q ha hb ≤ + (Fintype.card (Cells a) + Fintype.card (Cells b) + 1) ^ (q * (q-1)) := by + rw [dimension_eq] + let p := Fintype.card (Cells a) + Fintype.card (Cells b) + 1 + have hA : Module.finrank ℂ (PolynomialCarrier.Carrier a q ha) ≤ p ^ (q*(q-1)/2) := + (PolynomialCarrier.ordinary_finrank_le a q ha).trans (Nat.pow_le_pow_left (by dsimp [p]; omega) _) + have hB : Module.finrank ℂ (PolynomialCarrier.Carrier b q hb) ≤ p ^ (q*(q-1)/2) := + (PolynomialCarrier.ordinary_finrank_le b q hb).trans (Nat.pow_le_pow_left (by dsimp [p]; omega) _) + apply (Nat.mul_le_mul hA hB).trans + rw [← pow_add] + have he : q*(q-1)/2 + q*(q-1)/2 = q*(q-1) := by + have hh := PolyDimension.twice_card_lowerIndex q + rw [PolyDimension.card_lowerIndex] at hh + omega + rw [he] + +end SpinAngle.SignedCarrier + +namespace SpinAngle.SignedTensor +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {q : ℕ} + +def conjugateDensity (g : Group q) (A : Mat q × Mat q) : Mat q × Mat q := + (g.1.val * A.1 * star g.1.val, g.2.val * A.2 * star g.2.val) + +lemma conjugateDensity_isEvenDensity (g : Group q) (A : Mat q × Mat q) (hA : IsEvenDensity A) : + IsEvenDensity (conjugateDensity g A) := by + refine ⟨?_, ?_, ?_⟩ + · exact Matrix.nonneg_iff_posSemidef.mp (star_right_conjugate_nonneg hA.1.nonneg g.1.val) + · exact Matrix.nonneg_iff_posSemidef.mp (star_right_conjugate_nonneg hA.2.1.nonneg g.2.val) + · change (g.1.val * A.1 * star g.1.val).trace + (g.2.val * A.2 * star g.2.val).trace = 1 + rw [Matrix.trace_mul_cycle, g.1.property.1, one_mul, + Matrix.trace_mul_cycle, g.2.property.1, one_mul] + exact hA.2.2 + +lemma block_conjugateDensity (g : Group q) (A : Mat q × Mat q) : + block (conjugateDensity g A) = (blockGroup g).val * block A * (blockGroup g⁻¹).val := by + change block (((g.1.val,g.2.val) * A) * star (g.1.val,g.2.val)) = _ + rw [map_mul, map_mul, block_star, map_inv] + rfl + +variable {τ : Type*} [contextInstance3254_21 : Fintype τ] [contextInstance3254_33 : DecidableEq τ] +lemma tensor_conjugateDensity (g : Group q) (A : Mat q × Mat q) : + LinearMap.toContinuousLinearMap (TensorRep.action (ι := τ) (block (conjugateDensity g A))) = + CompactTwirl.conjugate (CompactTwirl.continuousAction (rep (τ := τ))) + (LinearMap.toContinuousLinearMap (TensorRep.action (block A))) g := by + apply ContinuousLinearMap.ext + intro v + change TensorRep.action (block (conjugateDensity g A)) v = + TensorRep.action (blockGroup g).val (TensorRep.action (block A) + (TensorRep.action (blockGroup g⁻¹).val v)) + rw [block_conjugateDensity, map_mul, map_mul] + rfl +end SpinAngle.SignedTensor + +namespace SpinAngle.SignedTensor +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {q : ℕ} +instance groupMeasurableSpace : MeasurableSpace (Group q) := borel _ +instance groupBorelSpace : BorelSpace (Group q) := ⟨rfl⟩ +variable [contextInstance3273_9 : Nonempty (Fin q)] +instance groupCompactSpace : CompactSpace (Group q) := by + let := unitaryGroup_compactSpace (Fin q) + infer_instance +end SpinAngle.SignedTensor + +namespace SpinAngle.SignedCarrier +open scoped Classical TensorProduct BigOperators InnerProductSpace ComplexOrder Matrix.Norms.L2Operator MatrixOrder +open SpinAngle.Young SpinAngle.Specht SignedTensor CompactTwirl +variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) +variable {τ : Type*} [contextInstance3283_21 : Fintype τ] [contextInstance3283_33 : DecidableEq τ] + +lemma projection_isStarProjection : IsStarProjection (typeProjection (τ := τ) a b q ha hb) := + isStarProjection_starProjection + +variable [contextInstance3288_9 : Nonempty (Fin q)] +lemma twirl_lower (A : Mat q × Mat q) (hA : IsEvenDensity A) : + ((LinearMap.trace ℂ (Carrier a b q ha hb) + (hermitianAction a b q ha hb A hA.1.isHermitian hA.2.1.isHermitian)).re / + (dimension a b q ha hb : ℝ)) • typeProjection (τ := τ) a b q ha hb ≤ + twirl (continuousAction (SignedTensor.rep (q := q) (τ := τ))) + (LinearMap.toContinuousLinearMap (TensorRep.action (block A))) := by + exact isotypic_twirl_lower (E := Carrier a b q ha hb) (F := Raw (q := q) (τ := τ)) + (rep a b q ha hb) SignedTensor.rep + (continuous_rep a b q ha hb) SignedTensor.continuous_rep SignedTensor.rep_unitary + (LinearMap.toContinuousLinearMap (hermitianAction a b q ha hb A hA.1.isHermitian hA.2.1.isHermitian)) + (LinearMap.toContinuousLinearMap (TensorRep.action (block A))) + ((ContinuousLinearMap.nonneg_iff_isPositive).mpr + (hermitianAction_positive a b q ha hb A hA.1 hA.2.1)) + ((ContinuousLinearMap.nonneg_iff_isPositive).mpr + (TensorRep.action_positive (block A) (block_posSemidef A hA.1 hA.2.1))) + (fun L x => (intertwiner_hermitian a b q ha hb L A hA.1.isHermitian hA.2.1.isHermitian x).symm) +end SpinAngle.SignedCarrier + +noncomputable section +namespace SpinAngle.ProjectionOrder +variable {A : Type*} [contextInstance3309_21 : CStarAlgebra A] [contextInstance3309_38 : PartialOrder A] [contextInstance3309_55 : StarOrderedRing A] + +lemma rescale_trace_lower (P B : A) (hP : 0 ≤ P) (F t d : ℝ) (hd : 0 < d) + (ht : Real.exp (-F) ≤ t) (h : (t / d) • P ≤ B) : + P ≤ (Real.exp F * d) • B := by + have hbase : (Real.exp (-F) / d) • P ≤ B := + (smul_le_smul_of_nonneg_right (div_le_div_of_nonneg_right ht hd.le) hP).trans h + have hs := smul_le_smul_of_nonneg_left hbase (mul_pos (Real.exp_pos F) hd).le + have he : (Real.exp F * d) * (Real.exp (-F) / d) = 1 := by + rw [← mul_div_assoc, mul_right_comm, mul_div_cancel_right₀ _ hd.ne', ← Real.exp_add] + simp + simpa only [smul_smul, he, one_smul] using hs +end SpinAngle.ProjectionOrder + +namespace SpinAngle.MatrixBridge +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {n : Type*} [contextInstance3325_21 : Fintype n] [contextInstance3325_33 : DecidableEq n] +lemma inverse_mono (a b : EuclideanSpace ℂ n →L[ℂ] EuclideanSpace ℂ n) (h : a ≤ b) : + (Matrix.toEuclideanCLM (n := n) (𝕜 := ℂ)).symm a ≤ (Matrix.toEuclideanCLM (n := n) (𝕜 := ℂ)).symm b := by + apply sub_nonneg.mp + rw [← map_sub] + exact map_nonneg (Matrix.toEuclideanCLM (n := n) (𝕜 := ℂ)).symm (sub_nonneg.mpr h) +end SpinAngle.MatrixBridge + +namespace SpinAngle.SignedCarrier +open scoped Classical TensorProduct BigOperators InnerProductSpace ComplexOrder Matrix.Norms.L2Operator MatrixOrder +open SpinAngle.Young SpinAngle.Specht SignedTensor CompactTwirl +variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) +variable {τ : Type*} [contextInstance3337_21 : Fintype τ] [contextInstance3337_33 : DecidableEq τ] [contextInstance3337_49 : Nonempty (Fin q)] + + + +theorem exists_density_mixture : + ∃ (ι : Type) (_ : Fintype ι) (w : ι → ℝ) (R : ι → Mat q × Mat q), + (∀ i, 0 ≤ w i) ∧ (∑ i, w i = 1) ∧ (∀ i, IsEvenDensity (R i)) ∧ + typeProjection (τ := τ) a b q ha hb ≤ + (Real.exp (entropy a b q) * (dimension a b q ha hb : ℝ)) • + ∑ i, w i • LinearMap.toContinuousLinearMap (TensorRep.action (block (R i))) := by + obtain ⟨A,hA,htr⟩ := exists_density_trace_lower a b q ha hb + obtain ⟨ι,hι,w,g,hw,hs,he⟩ := twirl_finite_mixture + (SignedTensor.rep (q := q) (τ := τ)) SignedTensor.continuous_rep + (LinearMap.toContinuousLinearMap (TensorRep.action (block A))) + let := hι + refine ⟨ι,hι,w,fun i => conjugateDensity (g i) A,hw,hs, + fun i => conjugateDensity_isEvenDensity (g i) A hA,?_⟩ + have hh := twirl_lower (τ := τ) a b q ha hb A hA + have hbound := ProjectionOrder.rescale_trace_lower _ _ + (projection_isStarProjection (τ := τ) a b q ha hb).nonneg (entropy a b q) + _ (dimension a b q ha hb : ℝ) (by exact_mod_cast dimension_pos a b q ha hb) htr hh + rw [he] at hbound + simpa only [tensor_conjugateDensity] using hbound +end SpinAngle.SignedCarrier + +namespace SpinAngle.MatrixBridge +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {n : Type*} [contextInstance3364_21 : Fintype n] [contextInstance3364_33 : DecidableEq n] +local notation "Φ" => (Matrix.toEuclideanCLM (n := n) (𝕜 := ℂ)) +lemma inverse_real_smul (r : ℝ) (a : EuclideanSpace ℂ n →L[ℂ] EuclideanSpace ℂ n) : + (Φ).symm (r • a) = r • (Φ).symm a := by + change (Φ).symm ((r : ℂ) • a) = (r : ℂ) • (Φ).symm a + exact map_smul (Φ).symm _ _ + +lemma forward_real_smul (r : ℝ) (a : Matrix n n ℂ) : + Φ (r • a) = r • Φ a := by + change Φ ((r : ℂ) • a) = (r : ℂ) • Φ a + exact map_smul Φ _ _ + +lemma forward_norm (a : Matrix n n ℂ) : ‖Φ a‖ = ‖a‖ := rfl + +lemma inverse_norm (a : EuclideanSpace ℂ n →L[ℂ] EuclideanSpace ℂ n) : + ‖(Φ).symm a‖ = ‖a‖ := by + rw [← forward_norm, (Φ).apply_symm_apply] + +lemma inverse_toContinuous (a : Matrix n n ℂ) : + (Φ).symm (LinearMap.toContinuousLinearMap (Matrix.toEuclideanLin a)) = a := by + exact (Φ).symm_apply_apply a +end SpinAngle.MatrixBridge + + +namespace SpinAngle.SignedCarrier +open scoped Classical TensorProduct BigOperators InnerProductSpace ComplexOrder Matrix.Norms.L2Operator MatrixOrder +open SpinAngle.Young SpinAngle.Specht SignedTensor +variable (a b : YoungDiagram) (q : ℕ) (ha : a.colLen 0 ≤ q) (hb : b.colLen 0 ≤ q) +variable {τ : Type*} [contextInstance3392_21 : Fintype τ] [contextInstance3392_33 : DecidableEq τ] + +def matrixProjection : Matrix (τ → Spin q) (τ → Spin q) ℂ := + (Matrix.toEuclideanCLM (n := τ → Spin q) (𝕜 := ℂ)).symm (typeProjection a b q ha hb) + +lemma matrixProjection_isStarProjection : IsStarProjection (matrixProjection (τ := τ) a b q ha hb) := by + have hp := projection_isStarProjection (τ := τ) a b q ha hb + constructor + · change matrixProjection a b q ha hb * matrixProjection a b q ha hb = _ + unfold matrixProjection + rw [← map_mul, hp.isIdempotentElem.eq] + · change star (matrixProjection a b q ha hb) = _ + unfold matrixProjection + have hs := (Matrix.toEuclideanCLM (n := τ → Spin q) (𝕜 := ℂ)).symm.map_star' + (typeProjection a b q ha hb) + exact hs.symm.trans (congrArg (Matrix.toEuclideanCLM (n := τ → Spin q) (𝕜 := ℂ)).symm hp.isSelfAdjoint.star_eq) + +lemma inverse_action (A : Matrix (Spin q) (Spin q) ℂ) : + (Matrix.toEuclideanCLM (n := τ → Spin q) (𝕜 := ℂ)).symm + (LinearMap.toContinuousLinearMap (TensorRep.action A)) = TensorRep.tensor (fun _ : τ => A) := + MatrixBridge.inverse_toContinuous _ + +lemma matrix_density_upper (A : Mat q × Mat q) (hA : IsEvenDensity A) : + ‖TensorRep.tensor (fun _ : τ => block A) * matrixProjection a b q ha hb‖ ≤ + Real.exp (-entropy a b q) := by + have h := global_density_upper (τ := τ) a b q ha hb A hA + rw [← MatrixBridge.inverse_norm] at h + simpa only [map_mul, inverse_action, matrixProjection] using h + +lemma density_projection_commute (A : Mat q × Mat q) (hA : IsEvenDensity A) : + Commute (LinearMap.toContinuousLinearMap (TensorRep.action (ι := τ) (block A))) + (typeProjection a b q ha hb) := by + change _ * _ = _ * _ + apply ContinuousLinearMap.ext + intro v + exact (Isotypic.projection_commute_natural (E := Carrier a b q ha hb) (F := Raw (q := q) (τ := τ)) + (rep a b q ha hb) SignedTensor.rep + (hermitianAction a b q ha hb A hA.1.isHermitian hA.2.1.isHermitian) + (TensorRep.action (block A)) + (TensorRep.action_positive (block A) (block_posSemidef A hA.1 hA.2.1)).isSymmetric + (fun L x => (intertwiner_hermitian a b q ha hb L A hA.1.isHermitian hA.2.1.isHermitian x).symm) + v).symm + +lemma matrix_density_commute (A : Mat q × Mat q) (hA : IsEvenDensity A) : + Commute (TensorRep.tensor (fun _ : τ => block A)) (matrixProjection a b q ha hb) := by + have h := (density_projection_commute (τ := τ) a b q ha hb A hA).map + (Matrix.toEuclideanCLM (n := τ → Spin q) (𝕜 := ℂ)).symm + simpa only [inverse_action, matrixProjection] using h + +variable [contextInstance3441_9 : Nonempty (Fin q)] + + +theorem exists_matrix_density_mixture : + ∃ (ι : Type) (_ : Fintype ι) (w : ι → ℝ) (R : ι → Mat q × Mat q), + (∀ i, 0 ≤ w i) ∧ (∑ i, w i = 1) ∧ (∀ i, IsEvenDensity (R i)) ∧ + matrixProjection (τ := τ) a b q ha hb ≤ + (Real.exp (entropy a b q) * (dimension a b q ha hb : ℝ)) • + ∑ i, w i • TensorRep.tensor (fun _ : τ => block (R i)) := by + obtain ⟨ι,hι,w,R,hw,hs,hR,hdom⟩ := exists_density_mixture (τ := τ) a b q ha hb + let := hι + refine ⟨ι,hι,w,R,hw,hs,hR,?_⟩ + have h := MatrixBridge.inverse_mono _ _ hdom + simpa only [MatrixBridge.inverse_real_smul, map_sum, inverse_action, matrixProjection] using h +end SpinAngle.SignedCarrier + +namespace SpinAngle.SignedTensor +open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {q : ℕ} +lemma block_add (A B : Mat q × Mat q) : block (A+B) = block A + block B := by + ext i j + rcases i with ⟨i,bi⟩; rcases j with ⟨j,bj⟩ + cases bi <;> cases bj <;> simp [block, Matrix.blockDiagonal_apply] + +lemma block_real_smul (r : ℝ) (A : Mat q × Mat q) : block (r • A) = r • block A := by + ext i j + rcases i with ⟨i,bi⟩; rcases j with ⟨j,bj⟩ + cases bi <;> cases bj <;> simp [block, Matrix.blockDiagonal_apply] + +lemma block_zero : block (0 : Mat q × Mat q) = 0 := by + ext i j + rcases i with ⟨i,bi⟩; rcases j with ⟨j,bj⟩ + cases bi <;> cases bj <;> simp [block, Matrix.blockDiagonal_apply] + +lemma block_sum {ι : Type*} (s : Finset ι) (A : ι → Mat q × Mat q) : + block (∑ i ∈ s, A i) = ∑ i ∈ s, block (A i) := by + classical + induction s using Finset.induction_on with + | empty => simp [block_zero] + | insert i s hi ih => simp only [Finset.sum_insert hi, block_add, ih] + +lemma block_trace (A : Mat q × Mat q) : (block A).trace = A.1.trace + A.2.trace := by + change (Matrix.blockDiagonal (fun b : Bool => cond b A.2 A.1)).trace = _ + rw [Matrix.trace_blockDiagonal] + simp [add_comm] + +variable {J : Type*} [contextInstance3487_21 : Fintype J] + +def evenAverage (A : J → Mat q × Mat q) : Mat q × Mat q := + (Fintype.card J : ℝ)⁻¹ • ∑ j, A j + +lemma evenAverage_isEvenDensity [Nonempty J] (A : J → Mat q × Mat q) + (hA : ∀ j, IsEvenDensity (A j)) : IsEvenDensity (evenAverage A) := by + have hpos : 0 < (Fintype.card J : ℝ) := by exact_mod_cast Fintype.card_pos + have he (A : Mat q × Mat q) : A.1.trace + A.2.trace = (block A).trace := (block_trace A).symm + refine ⟨?_,?_,?_⟩ + · apply Matrix.nonneg_iff_posSemidef.mp + simp only [evenAverage, Prod.smul_fst, Prod.fst_sum] + exact smul_nonneg (inv_nonneg.mpr hpos.le) (Finset.sum_nonneg fun j _ => (hA j).1.nonneg) + · apply Matrix.nonneg_iff_posSemidef.mp + simp only [evenAverage, Prod.smul_snd, Prod.snd_sum] + exact smul_nonneg (inv_nonneg.mpr hpos.le) (Finset.sum_nonneg fun j _ => (hA j).2.1.nonneg) + · rw [he] + unfold evenAverage + rw [block_real_smul, block_sum, Matrix.trace_smul, Matrix.trace_sum] + simp only [block_trace, (hA _).2.2, Finset.sum_const, Finset.card_univ, nsmul_eq_mul, mul_one] + rw [RCLike.real_smul_eq_coe_smul (K := ℂ), smul_eq_mul] + norm_cast + exact inv_mul_cancel₀ (by exact_mod_cast hpos.ne') +end SpinAngle.SignedTensor + + + + + + +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder + +namespace SpinAngle.MatrixAnalysis +variable {n : Type*} [contextInstance3521_21 : Fintype n] [contextInstance3521_33 : DecidableEq n] +abbrev Mat (n : Type*) := Matrix n n ℂ + + +def root (a : Mat n) : Mat n := cfc Real.sqrt a + +def invRoot (a : Mat n) : Mat n := cfc (fun x : ℝ => (Real.sqrt x)⁻¹) a + +def support (a : Mat n) : Mat n := cfc (fun x : ℝ => if x = 0 then 0 else 1) a + +lemma root_selfAdjoint (a : Mat n) : IsSelfAdjoint (root a) := + cfc_predicate _ _ +lemma root_nonneg (a : Mat n) : 0 ≤ root a := + cfc_nonneg fun _ _ => Real.sqrt_nonneg _ +lemma invRoot_selfAdjoint (a : Mat n) : IsSelfAdjoint (invRoot a) := + cfc_predicate _ _ +lemma invRoot_nonneg (a : Mat n) : 0 ≤ invRoot a := + cfc_nonneg fun _ _ => inv_nonneg.mpr (Real.sqrt_nonneg _) +lemma support_selfAdjoint (a : Mat n) : IsSelfAdjoint (support a) := + cfc_predicate _ _ + +lemma root_mul_self (a : Mat n) (ha : 0 ≤ a) : root a * root a = a := by + rw [root, ← cfc_mul _ _ _ (Matrix.finite_real_spectrum (A := a) |>.continuousOn _) + (Matrix.finite_real_spectrum (A := a) |>.continuousOn _)] + calc + _ = cfc (fun x : ℝ => x) a := by + apply cfc_congr + intro x hx + exact Real.mul_self_sqrt (spectrum_nonneg_of_nonneg ha hx) + _ = a := cfc_id' ℝ (ha := .of_nonneg ha) + +lemma invRoot_mul_root (a : Mat n) (ha : 0 ≤ a) : + invRoot a * root a = support a := by + rw [invRoot, root, ← cfc_mul _ _ _ (Matrix.finite_real_spectrum (A := a) |>.continuousOn _) + (Matrix.finite_real_spectrum (A := a) |>.continuousOn _)] + apply cfc_congr + intro x hx + by_cases hx0 : x = 0 + · simp [hx0] + · have hs : Real.sqrt x ≠ 0 := ne_of_gt (Real.sqrt_pos.mpr + (lt_of_le_of_ne (spectrum_nonneg_of_nonneg ha hx) (Ne.symm hx0))) + simp [hx0, hs] + +lemma support_isStarProjection (a : Mat n) : IsStarProjection (support a) := by + refine ⟨?_, support_selfAdjoint a⟩ + change support a * support a = support a + rw [support, ← cfc_mul _ _ _ (Matrix.finite_real_spectrum (A := a) |>.continuousOn _) + (Matrix.finite_real_spectrum (A := a) |>.continuousOn _)] + apply cfc_congr + intro x _ + dsimp only + split_ifs <;> norm_num + +lemma mul_support (a : Mat n) (ha : 0 ≤ a) : a * support a = a := by + conv_lhs => lhs; rw [← cfc_id' ℝ (a := a)] + rw [support, ← cfc_mul _ _ _ (Matrix.finite_real_spectrum (A := a) |>.continuousOn _) + (Matrix.finite_real_spectrum (A := a) |>.continuousOn _)] + calc + _ = cfc (fun x : ℝ => x) a := by + apply cfc_congr + intro x _ + by_cases hx : x = 0 <;> simp [hx] + _ = a := cfc_id' ℝ (ha := .of_nonneg ha) + +lemma root_mul_support (a : Mat n) : root a * support a = root a := by + rw [root, support, ← cfc_mul _ _ _ (Matrix.finite_real_spectrum (A := a) |>.continuousOn _) + (Matrix.finite_real_spectrum (A := a) |>.continuousOn _)] + apply cfc_congr + intro x _ + by_cases hx : x = 0 <;> simp [hx] + +lemma root_commute {a b : Mat n} (h : Commute a b) : Commute (root a) b := + h.cfc_real _ +lemma invRoot_commute {a b : Mat n} (h : Commute a b) : Commute (invRoot a) b := + h.cfc_real _ +lemma support_commute {a b : Mat n} (h : Commute a b) : Commute (support a) b := + h.cfc_real _ + + + +lemma norm_le_re_trace (a : Mat n) (ha : 0 ≤ a) : ‖a‖ ≤ (Matrix.trace a).re := by + have hA := Matrix.nonneg_iff_posSemidef.mp ha + rw [hA.isHermitian.trace_eq_sum_eigenvalues, Complex.re_sum] + conv_lhs => rw [hA.isHermitian.spectral_theorem] + simp only [Unitary.conjStarAlgAut_apply, ← Unitary.coe_star, + CStarRing.norm_mul_coe_unitary, CStarRing.norm_coe_unitary_mul, + Matrix.l2_opNorm_diagonal] + apply (pi_norm_le_iff_of_nonneg (by + exact Finset.sum_nonneg fun i _ => hA.eigenvalues_nonneg i)).mpr + intro i + simp only [Function.comp_apply, RCLike.norm_ofReal, + abs_of_nonneg (hA.eigenvalues_nonneg i)] + exact Finset.single_le_sum (fun j _ => hA.eigenvalues_nonneg j) (Finset.mem_univ i) + +lemma norm_sq_le_re_trace_star_mul_self (a : Mat n) : + ‖a‖ ^ 2 ≤ (Matrix.trace (star a * a)).re := by + rw [sq, ← CStarRing.norm_star_mul_self] + exact norm_le_re_trace _ (star_mul_self_nonneg _) + + + +lemma root_mul_support_of_le_smul (a b : Mat n) (ha : 0 ≤ a) (hb : 0 ≤ b) + (c : ℝ) (hba : b ≤ c • a) : root b * support a = root b := by + let e := 1 - support a + have he : IsStarProjection e := (support_isStarProjection a).one_sub + have hae : a * e = 0 := by + dsimp [e] + rw [mul_sub, mul_one, mul_support a ha, sub_self] + have hupper : star e * b * e ≤ 0 := by + have hc := star_left_conjugate_le_conjugate hba e + simpa only [mul_smul_comm, smul_mul_assoc, mul_assoc, hae, mul_zero, smul_zero] using hc + have hzero : star e * b * e = 0 := + le_antisymm hupper (star_left_conjugate_nonneg hb e) + have hrootzero : star (root b * e) * (root b * e) = 0 := by + rw [star_mul, (root_selfAdjoint b).star_eq] + calc + (star e * root b) * (root b * e) = star e * (root b * root b) * e := by + simp only [mul_assoc] + _ = 0 := by rw [root_mul_self b hb, hzero] + have h := (CStarRing.star_mul_self_eq_zero_iff _).mp hrootzero + dsimp [e] at h + rw [mul_sub, mul_one] at h + exact (sub_eq_zero.mp h).symm + +lemma invRoot_mul_self_mul_invRoot (a : Mat n) (ha : 0 ≤ a) : + invRoot a * a * invRoot a = support a := by + have hc : Commute (invRoot a) a := invRoot_commute (Commute.refl a) + have hr : Commute (root a) (invRoot a) := root_commute hc.symm + calc + invRoot a * a * invRoot a = invRoot a * (root a * root a) * invRoot a := + congrArg (fun x => invRoot a * x * invRoot a) (root_mul_self a ha).symm + _ = (invRoot a * root a) * (root a * invRoot a) := by simp only [mul_assoc] + _ = support a * support a := by rw [hr.eq, invRoot_mul_root a ha] + _ = support a := (support_isStarProjection a).isIdempotentElem.eq + +lemma cell_trace_identity (a b c : Mat n) (ha : 0 ≤ a) (hc : 0 ≤ c) : + (star (root a * invRoot b * root c) * (root a * invRoot b * root c)).trace = + (invRoot b * a * invRoot b * c).trace := by + have he : star (root a * invRoot b * root c) * (root a * invRoot b * root c) = + root c * (invRoot b * a * invRoot b) * root c := by + simp only [star_mul, (root_selfAdjoint a).star_eq, + (root_selfAdjoint c).star_eq, (invRoot_selfAdjoint b).star_eq] + calc + root c * (invRoot b * root a) * (root a * invRoot b * root c) = + root c * (invRoot b * (root a * root a) * invRoot b) * root c := by + simp only [mul_assoc] + _ = _ := by rw [root_mul_self a ha] + rw [he, Matrix.trace_mul_comm (root c * (invRoot b * a * invRoot b)) (root c)] + rw [← mul_assoc, root_mul_self c hc, Matrix.trace_mul_comm c] + +lemma cell_trace_nonneg (a b c : Mat n) (ha : 0 ≤ a) (hc : 0 ≤ c) : + 0 ≤ (invRoot b * a * invRoot b * c).trace := by + rw [← cell_trace_identity a b c ha hc] + exact (Matrix.nonneg_iff_posSemidef.mp (star_mul_self_nonneg _)).trace_nonneg + + +lemma re_trace_nonneg + {n : Type*} + [contextInstance3521_21 : Fintype n] + [DecidableEq n] (a : Mat n) (ha : 0 ≤ a) : 0 ≤ a.trace.re := + (Complex.nonneg_iff.mp ((Matrix.nonneg_iff_posSemidef.mp ha).trace_nonneg)).1 + +lemma re_trace_mono {a b : Mat n} (hab : a ≤ b) : a.trace.re ≤ b.trace.re := by + have h := re_trace_nonneg (b - a) (sub_nonneg.mpr hab) + simpa only [Matrix.trace_sub, Complex.sub_re, sub_nonneg] using h + + + +lemma re_trace_projection_mul_le (q b : Mat n) (hq : IsStarProjection q) (hb : 0 ≤ b) : + (q * b).trace.re ≤ b.trace.re := by + have h := re_trace_mono (star_left_conjugate_le_conjugate hq.le_one (root b)) + rw [mul_one, (root_selfAdjoint b).star_eq, root_mul_self b hb] at h + rw [Matrix.trace_mul_comm (root b * q) (root b), ← mul_assoc, + root_mul_self b hb, Matrix.trace_mul_comm b q] at h + exact h + + +lemma cell_norm_sq_le_trace (a b c : Mat n) (ha : 0 ≤ a) (hc : 0 ≤ c) : + ‖root a * invRoot b * root c‖ ^ 2 ≤ + (invRoot b * a * invRoot b * c).trace.re := by + have h := norm_sq_le_re_trace_star_mul_self (root a * invRoot b * root c) + rw [cell_trace_identity a b c ha hc] at h + exact h + +end SpinAngle.MatrixAnalysis + +namespace SpinAngle.TensorMatrix +open SpinAngle.MatrixAnalysis +variable {ι n : Type*} [contextInstance3707_23 : Fintype ι] [contextInstance3707_35 : DecidableEq ι] [contextInstance3707_51 : Fintype n] [contextInstance3707_63 : DecidableEq n] + + +def tensor (a : ι → Mat n) : Mat (ι → n) := fun x y => ∏ i, a i (x i) (y i) + +lemma tensor_star + {ι : Type*} {n : Type*} + [contextInstance3707_23 : Fintype ι] + [DecidableEq ι] + [Fintype n] + [DecidableEq n] (a : ι → Mat n) : + tensor (fun i => star (a i)) = star (tensor a) := by + ext x y + simp [tensor, Matrix.star_apply] + +lemma tensor_mul + {ι : Type*} {n : Type*} + [contextInstance3707_23 : Fintype ι] + [contextInstance3707_35 : DecidableEq ι] + [contextInstance3707_51 : Fintype n] + [DecidableEq n] (a b : ι → Mat n) : + tensor (fun i => a i * b i) = tensor a * tensor b := by + ext x y + simp only [tensor, Matrix.mul_apply, ← Finset.prod_mul_distrib] + symm + simpa using (Finset.sum_prod_piFinset (ι := ι) Finset.univ + (fun i j => a i (x i) j * b i j (y i))) + +lemma tensor_one + {ι : Type*} {n : Type*} + [contextInstance3707_23 : Fintype ι] + [DecidableEq ι] + [Fintype n] + [contextInstance3707_63 : DecidableEq n] : tensor (fun _ : ι => (1 : Mat n)) = 1 := by + ext x y + classical + by_cases h : x = y + · subst y + simp [tensor] + · have hxy : ∃ i, x i ≠ y i := Function.ne_iff.mp h + obtain ⟨i, hi⟩ := hxy + simp only [tensor, Matrix.one_apply, ite_eq_right h] + apply Finset.prod_eq_zero (Finset.mem_univ i) + simp [hi] + +lemma tensor_trace + {ι : Type*} {n : Type*} + [contextInstance3707_23 : Fintype ι] + [contextInstance3707_35 : DecidableEq ι] + [contextInstance3707_51 : Fintype n] + [DecidableEq n] (a : ι → Mat n) : + (tensor a).trace = ∏ i, (a i).trace := by + simp only [Matrix.trace, Matrix.diag, tensor] + simpa using (Finset.sum_prod_piFinset (ι := ι) Finset.univ + (fun i j => a i j j)) + +lemma tensor_nonneg (a : ι → Mat n) (ha : ∀ i, 0 ≤ a i) : + 0 ≤ tensor a := by + have hr : tensor a = star (tensor (fun i => root (a i))) * tensor (fun i => root (a i)) := by + rw [← tensor_star, ← tensor_mul] + congr 1 + funext i + rw [(root_selfAdjoint (a i)).star_eq, root_mul_self _ (ha i)] + rw [hr] + exact star_mul_self_nonneg _ + +lemma tensor_selfAdjoint (a : ι → Mat n) (ha : ∀ i, IsSelfAdjoint (a i)) : + IsSelfAdjoint (tensor a) := by + change star (tensor a) = tensor a + rw [← tensor_star] + congr 1 + funext i + exact (ha i).star_eq + +lemma tensor_norm_sq_le_trace_product (a : ι → Mat n) : + ‖tensor a‖ ^ 2 ≤ (∏ i, (star (a i) * a i).trace).re := by + have h := norm_sq_le_re_trace_star_mul_self (tensor a) + rw [← tensor_star, ← tensor_mul, tensor_trace] at h + exact h + +lemma tensor_norm_sq_le_re_trace_product (a : ι → Mat n) : + ‖tensor a‖ ^ 2 ≤ ∏ i, (star (a i) * a i).trace.re := by + have hreal (i : ι) : (star (a i) * a i).trace = ((star (a i) * a i).trace.re : ℂ) := + Complex.eq_re_of_ofReal_le (r := 0) + (by exact (Matrix.nonneg_iff_posSemidef.mp (star_mul_self_nonneg _)).trace_nonneg) + calc + _ ≤ (∏ i, (star (a i) * a i).trace).re := tensor_norm_sq_le_trace_product a + _ = (∏ i, ((star (a i) * a i).trace.re : ℂ)).re := + congrArg Complex.re (Finset.prod_congr rfl fun i _ => hreal i) + _ = _ := by rw [← Complex.ofReal_prod, Complex.ofReal_re] + +lemma tensor_cell_norm_sq_le_product (a b c : ι → Mat n) + (ha : ∀ i, 0 ≤ a i) (hc : ∀ i, 0 ≤ c i) : + ‖tensor (fun i => root (a i) * invRoot (b i) * root (c i))‖ ^ 2 ≤ + ∏ i, (invRoot (b i) * a i * invRoot (b i) * c i).trace.re := by + have h := tensor_norm_sq_le_re_trace_product (fun i => root (a i) * invRoot (b i) * root (c i)) + simpa only [cell_trace_identity _ _ _ (ha _) (hc _)] using h + +end SpinAngle.TensorMatrix + + + + +noncomputable section +open scoped BigOperators +namespace SpinAngle + +def missingCellFactor (m b : ℕ) : ℝ := + if b < m then ((m : ℝ) / (m - b : ℕ)) ^ (m - b) else 1 + +def missingCellProductFactor {ι : Type*} [Fintype ι] (m : ℕ) (b : ι → ℕ) : ℝ := + ∏ i, missingCellFactor m (b i) + +lemma missingCellFactor_nonneg (m b : ℕ) : 0 ≤ missingCellFactor m b := by + unfold missingCellFactor + split_ifs <;> positivity + +lemma missingCellFactor_le_exp (m b : ℕ) (hb : b ≤ m) : + missingCellFactor m b ≤ Real.exp b := by + unfold missingCellFactor + split_ifs with h + · have hk : 0 < m - b := Nat.sub_pos_of_lt h + have hkR : (0 : ℝ) < (m - b : ℕ) := by exact_mod_cast hk + have hmR : 0 < (m : ℝ) := by exact_mod_cast (lt_of_le_of_lt (Nat.zero_le b) h) + have hratio : 0 < (m : ℝ) / (m - b : ℕ) := div_pos hmR hkR + apply (Real.log_le_iff_le_exp (pow_pos hratio _)).mp + rw [Real.log_pow] + calc + (m - b : ℕ) * Real.log ((m : ℝ) / (m - b : ℕ)) + ≤ (m - b : ℕ) * ((m : ℝ) / (m - b : ℕ) - 1) := + mul_le_mul_of_nonneg_left (Real.log_le_sub_one_of_pos hratio) hkR.le + _ = (b : ℝ) := by + rw [mul_sub, mul_div_cancel₀ _ hkR.ne', mul_one, Nat.cast_sub hb] + ring + · exact Real.one_le_exp (Nat.cast_nonneg b) + +theorem missingCellProduct {ι : Type*} [Fintype ι] + (m : ℕ) (b : ι → ℕ) (hb : ∀ i, b i ≤ m) : + missingCellProductFactor m b ≤ Real.exp (∑ i, (b i : ℝ)) := by + unfold missingCellProductFactor + calc + ∏ i, missingCellFactor m (b i) ≤ ∏ i, Real.exp (b i : ℝ) := + Finset.prod_le_prod₀ (fun i _ => missingCellFactor_nonneg m (b i)) + (fun i _ => missingCellFactor_le_exp m (b i) (hb i)) + _ = Real.exp (∑ i, (b i : ℝ)) := (Real.exp_sum _ _).symm + +end SpinAngle + +namespace SpinAngle +open scoped BigOperators +variable {ι : Type*} [contextInstance3841_21 : Fintype ι] [contextInstance3841_33 : DecidableEq ι] + + +lemma retained_product_le + {ι : Type*} + [contextInstance3841_21 : Fintype ι] + [DecidableEq ι] (t : Finset ι) (z : ι → ℝ) + (hz : ∀ i, 0 ≤ z i) (hs : ∑ i, z i ≤ Fintype.card ι) : + ∏ i ∈ t, z i ≤ ((Fintype.card ι : ℝ) / t.card) ^ t.card := by + by_cases ht : t.Nonempty + · have hkR : 0 < (t.card : ℝ) := by exact_mod_cast ht.card_pos + have hmR : 0 < (Fintype.card ι : ℝ) := + hkR.trans_le (by exact_mod_cast Finset.card_le_univ t) + let c : ℝ := Fintype.card ι / t.card + have hc : 0 < c := div_pos hmR hkR + have hsum : ∑ i ∈ t, z i ≤ Fintype.card ι := + (Finset.sum_le_sum_of_subset_of_nonneg (Finset.subset_univ _) (by + intro i _ _; exact hz i)).trans hs + have hnorm : ∑ i ∈ t, z i / c ≤ t.card := by + rw [← Finset.sum_div] + apply (div_le_iff₀ hc).mpr + dsimp [c] + rwa [mul_div_cancel₀ _ hkR.ne'] + have hn : ∏ i ∈ t, z i / c ≤ 1 := calc + _ ≤ ∏ i ∈ t, Real.exp (z i / c - 1) := + Finset.prod_le_prod₀ (fun i _ => div_nonneg (hz i) hc.le) fun i _ => by + have h := Real.add_one_le_exp (z i / c - 1) + linarith + _ = Real.exp (∑ i ∈ t, (z i / c - 1)) := (Real.exp_sum _ _).symm + _ ≤ Real.exp 0 := by + apply Real.exp_le_exp.mpr + rw [Finset.sum_sub_distrib] + simpa using sub_nonpos.mpr hnorm + _ = 1 := Real.exp_zero + rw [Finset.prod_div_distrib, Finset.prod_const] at hn + exact (div_le_one (pow_pos hc _)).mp hn + · have he : t = ∅ := Finset.not_nonempty_iff_eq_empty.mp ht + simp [he] + +variable {R C : Type*} [contextInstance3877_23 : Fintype R] [contextInstance3877_35 : DecidableEq R] [contextInstance3877_51 : Fintype C] [contextInstance3877_63 : DecidableEq C] + + +def occupiedRow (W : Finset (R × C)) (i : R) : Finset C := + Finset.univ.filter (fun j => (i, j) ∈ W) + +def missingInRow (W : Finset (R × C)) (i : R) : ℕ := + Fintype.card C - (occupiedRow W i).card + +lemma occupiedRow_card_le + {R : Type*} {C : Type*} + [Fintype R] + [contextInstance3877_35 : DecidableEq R] + [contextInstance3877_51 : Fintype C] + [contextInstance3877_63 : DecidableEq C] (W : Finset (R × C)) (i : R) : + (occupiedRow W i).card ≤ Fintype.card C := Finset.card_le_univ _ + +lemma missingInRow_le + {R : Type*} {C : Type*} + [Fintype R] + [contextInstance3877_35 : DecidableEq R] + [contextInstance3877_51 : Fintype C] + [contextInstance3877_63 : DecidableEq C] (W : Finset (R × C)) (i : R) : + missingInRow W i ≤ Fintype.card C := Nat.sub_le _ _ + +lemma retained_factor_eq_missingCellFactor (W : Finset (R × C)) (i : R) : + ((Fintype.card C : ℝ) / (occupiedRow W i).card) ^ (occupiedRow W i).card = + missingCellFactor (Fintype.card C) (missingInRow W i) := by + have hc := occupiedRow_card_le W i + unfold missingInRow missingCellFactor + rw [Nat.sub_sub_self hc] + split_ifs with h + · rfl + · have hk : (occupiedRow W i).card = 0 := by omega + simp [hk] + +lemma prod_occupiedRow + {ι : Type*} + [Fintype ι] + [DecidableEq ι] + {R : Type*} {C : Type*} + [contextInstance3877_23 : Fintype R] + [contextInstance3877_35 : DecidableEq R] + [contextInstance3877_51 : Fintype C] + [contextInstance3877_63 : DecidableEq C] (W : Finset (R × C)) (z : R → C → ℝ) : + (∏ i, ∏ j ∈ occupiedRow W i, z i j) = ∏ x ∈ W, z x.1 x.2 := by + simp only [occupiedRow, Finset.prod_filter] + rw [← Finset.prod_product (f := fun x : R × C => if x ∈ W then z x.1 x.2 else 1)] + simp only [Finset.univ_product_univ, ← Finset.prod_filter] + congr 1 + ext x + simp + + +lemma board_product_le (W : Finset (R × C)) (z : R → C → ℝ) + (hz : ∀ i j, 0 ≤ z i j) (hs : ∀ i, ∑ j, z i j ≤ Fintype.card C) : + (∏ x ∈ W, z x.1 x.2) ≤ + missingCellProductFactor (Fintype.card C) (missingInRow W) := by + rw [← prod_occupiedRow (ι := R) W z] + unfold missingCellProductFactor + apply Finset.prod_le_prod₀ + · intro i _ + exact Finset.prod_nonneg fun j _ => hz i j + · intro i _ + rw [← retained_factor_eq_missingCellFactor] + exact retained_product_le (occupiedRow W i) (z i) (hz i) (hs i) + +end SpinAngle + +namespace SpinAngle.MatrixAnalysis +variable {n C : Type*} [contextInstance3931_23 : Fintype n] [contextInstance3931_35 : DecidableEq n] [contextInstance3931_51 : Fintype C] [contextInstance3931_63 : DecidableEq C] + + +structure Density (n : Type*) [Fintype n] [DecidableEq n] where + matrix : Mat n + nonneg : 0 ≤ matrix + trace_eq_one : matrix.trace = 1 + +instance : Coe (Density n) (Mat n) := ⟨Density.matrix⟩ + +def average (r : C → Density n) : Mat n := + (Fintype.card C : ℝ)⁻¹ • ∑ j, (r j).matrix + +lemma average_nonneg + {n : Type*} {C : Type*} + [contextInstance3931_23 : Fintype n] + [contextInstance3931_35 : DecidableEq n] + [contextInstance3931_51 : Fintype C] + [DecidableEq C] (r : C → Density n) : 0 ≤ average r := + smul_nonneg (inv_nonneg.mpr (Nat.cast_nonneg _)) (Finset.sum_nonneg fun j _ => (r j).nonneg) + +lemma sum_eq_smul_average + {n : Type*} {C : Type*} + [contextInstance3931_23 : Fintype n] + [contextInstance3931_35 : DecidableEq n] + [contextInstance3931_51 : Fintype C] + [DecidableEq C] [Nonempty C] (r : C → Density n) : + (∑ j, (r j).matrix) = (Fintype.card C : ℝ) • average r := by + unfold average + rw [smul_smul, mul_inv_cancel₀ (by exact_mod_cast Fintype.card_ne_zero (α := C)), one_smul] + +lemma le_smul_average [Nonempty C] (r : C → Density n) (j : C) : + (r j).matrix ≤ (Fintype.card C : ℝ) • average r := by + rw [← sum_eq_smul_average] + exact Finset.single_le_sum (fun k _ => (r k).nonneg) (Finset.mem_univ j) + +lemma support_cell_trace_sum [Nonempty C] (r : C → Density n) (s : Density n) : + ∑ j, (invRoot (average r) * (r j).matrix * invRoot (average r) * s.matrix).trace.re ≤ + Fintype.card C := by + have he : (∑ j, invRoot (average r) * (r j).matrix * invRoot (average r) * s.matrix) = + (Fintype.card C : ℝ) • (support (average r) * s.matrix) := by + rw [← Finset.sum_mul, ← Finset.sum_mul, ← Finset.mul_sum, + sum_eq_smul_average r, mul_smul_comm, smul_mul_assoc, smul_mul_assoc, + invRoot_mul_self_mul_invRoot _ (average_nonneg r)] + have ht := congrArg (fun a : Mat n => a.trace.re) he + simp only [Matrix.trace_sum, Complex.re_sum, Matrix.trace_smul, Complex.smul_re, smul_eq_mul] at ht + rw [ht] + have h := re_trace_projection_mul_le (support (average r)) s.matrix + (support_isStarProjection _) s.nonneg + rw [s.trace_eq_one, Complex.one_re] at h + simpa using mul_le_mul_of_nonneg_left h (Nat.cast_nonneg (Fintype.card C)) + +end SpinAngle.MatrixAnalysis + +namespace SpinAngle +open MatrixAnalysis TensorMatrix +variable {n R C : Type*} [contextInstance3979_25 : Fintype n] [contextInstance3979_37 : DecidableEq n] + [contextInstance3980_2 : Fintype R] [contextInstance3980_14 : DecidableEq R] [contextInstance3980_30 : Fintype C] [contextInstance3980_42 : DecidableEq C] [contextInstance3980_58 : Nonempty C] + + + +theorem normalized_board_bound (W : Finset (R × C)) + (r : C → Density n) (s : R → Density n) : + ‖tensor (fun w : W => root (r w.val.2).matrix * + invRoot (average r) * root (s w.val.1).matrix)‖ ^ 2 ≤ + missingCellProductFactor (Fintype.card C) (missingInRow W) := by + let z : R → C → ℝ := fun i j => + (invRoot (average r) * (r j).matrix * invRoot (average r) * (s i).matrix).trace.re + have hz : ∀ i j, 0 ≤ z i j := fun i j => + (Complex.nonneg_iff.mp (cell_trace_nonneg _ _ _ (r j).nonneg (s i).nonneg)).1 + have hs : ∀ i, ∑ j, z i j ≤ Fintype.card C := fun i => support_cell_trace_sum r (s i) + calc + _ ≤ ∏ w : W, z w.val.1 w.val.2 := + tensor_cell_norm_sq_le_product _ _ _ (fun w => (r w.val.2).nonneg) + (fun w => (s w.val.1).nonneg) + _ = ∏ w ∈ W, z w.1 w.2 := + (Finset.prod_subtype W (by intro w; rfl) (fun w => z w.1 w.2)).symm + _ ≤ _ := board_product_le W z hz hs + +end SpinAngle + + + + + + +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder +namespace SpinAngle.DependentTensor +variable {ι : Type*} [contextInstance4012_21 : Fintype ι] [contextInstance4012_33 : DecidableEq ι] +variable {ν : ι → Type*} [contextInstance4013_25 : ∀ i, Fintype (ν i)] [contextInstance4013_46 : ∀ i, DecidableEq (ν i)] + +abbrev Mat (n : Type*) := Matrix n n ℂ + +def tensor (A : ∀ i, Mat (ν i)) : Mat (∀ i, ν i) := fun x y => ∏ i, A i (x i) (y i) + +lemma tensor_star + {ι : Type*} + [contextInstance4012_21 : Fintype ι] + [DecidableEq ι] + {ν : ι → Type*} + [∀ i, Fintype (ν i)] + [∀ i, DecidableEq (ν i)] (A : ∀ i, Mat (ν i)) : tensor (fun i => star (A i)) = star (tensor A) := by + ext x y + simp [tensor, Matrix.star_apply] + +lemma tensor_mul + {ι : Type*} + [contextInstance4012_21 : Fintype ι] + [contextInstance4012_33 : DecidableEq ι] + {ν : ι → Type*} + [contextInstance4013_25 : ∀ i, Fintype (ν i)] + [∀ i, DecidableEq (ν i)] (A B : ∀ i, Mat (ν i)) : tensor (fun i => A i * B i) = tensor A * tensor B := by + ext x y + simp only [tensor, Matrix.mul_apply, ← Finset.prod_mul_distrib] + exact (Fintype.prod_sum (fun i (j : ν i) => A i (x i) j * B i j (y i))) + +lemma tensor_one + {ι : Type*} + [contextInstance4012_21 : Fintype ι] + [DecidableEq ι] + {ν : ι → Type*} + [∀ i, Fintype (ν i)] + [contextInstance4013_46 : ∀ i, DecidableEq (ν i)] : tensor (fun i : ι => (1 : Mat (ν i))) = 1 := by + ext x y + classical + by_cases h : x = y + · subst y; simp [tensor] + · obtain ⟨i,hi⟩ := Function.ne_iff.mp h + simp only [tensor, Matrix.one_apply, ite_eq_right h] + apply Finset.prod_eq_zero (Finset.mem_univ i) + simp [hi] + +lemma tensor_nonneg (A : ∀ i, Mat (ν i)) (hA : ∀ i, 0 ≤ A i) : 0 ≤ tensor A := by + have he : tensor A = star (tensor (fun i => CFC.sqrt (A i))) * tensor (fun i => CFC.sqrt (A i)) := by + rw [← tensor_star, ← tensor_mul] + congr 1 + funext i + rw [(IsSelfAdjoint.of_nonneg (CFC.sqrt_nonneg (A i))).star_eq, + CFC.sqrt_mul_sqrt_self (A i) (hA i)] + rw [he] + exact star_mul_self_nonneg _ + +lemma tensor_projection (P : ∀ i, Mat (ν i)) (hP : ∀ i, IsStarProjection (P i)) : + IsStarProjection (tensor P) := by + constructor + · change tensor P * tensor P = tensor P + rw [← tensor_mul] + congr 1 + funext i + exact (hP i).isIdempotentElem.eq + · change star (tensor P) = tensor P + rw [← tensor_star] + congr 1 + funext i + exact (hP i).isSelfAdjoint.star_eq + +lemma tensor_sum + {ι : Type*} + [contextInstance4012_21 : Fintype ι] + [contextInstance4012_33 : DecidableEq ι] + {ν : ι → Type*} + [∀ i, Fintype (ν i)] + [∀ i, DecidableEq (ν i)] {κ : ι → Type*} [∀ i, Fintype (κ i)] + (A : ∀ i, κ i → Mat (ν i)) : + tensor (fun i => ∑ k, A i k) = ∑ f : ∀ i, κ i, tensor (fun i => A i (f i)) := by + ext x y + simp only [tensor, Matrix.sum_apply] + exact (Fintype.prod_sum (fun i (k : κ i) => A i k (x i) (y i))) + +lemma tensor_smul + {ι : Type*} + [contextInstance4012_21 : Fintype ι] + [DecidableEq ι] + {ν : ι → Type*} + [∀ i, Fintype (ν i)] + [∀ i, DecidableEq (ν i)] (w : ι → ℝ) (A : ∀ i, Mat (ν i)) : + tensor (fun i => w i • A i) = (∏ i, w i) • tensor A := by + ext x y + simp only [tensor, Matrix.smul_apply, RCLike.real_smul_eq_coe_smul (K := ℂ), smul_eq_mul, + Finset.prod_mul_distrib] + change (∏ i, (w i : ℂ)) * _ = ((∏ i, w i : ℝ) : ℂ) * _ + rw [Complex.ofReal_prod] + +lemma tensor_sum_smul {κ : ι → Type*} [∀ i, Fintype (κ i)] + (w : ∀ i, κ i → ℝ) (A : ∀ i, κ i → Mat (ν i)) : + tensor (fun i => ∑ k, w i k • A i k) = + ∑ f : ∀ i, κ i, (∏ i, w i (f i)) • tensor (fun i => A i (f i)) := by + rw [tensor_sum] + simp only [tensor_smul] + +lemma tensor_mono (A B : ∀ i, Mat (ν i)) (hA : ∀ i, 0 ≤ A i) (hAB : ∀ i, A i ≤ B i) : + tensor A ≤ tensor B := by + let M (i : ι) (b : Bool) : Mat (ν i) := if b then B i - A i else A i + have he (i : ι) : (∑ b : Bool, M i b) = B i := by + simp [M] + have hm (i : ι) (b : Bool) : 0 ≤ M i b := by + cases b + · exact hA i + · exact sub_nonneg.mpr (hAB i) + rw [show B = (fun i => ∑ b : Bool, M i b) by funext i; exact (he i).symm, tensor_sum] + have h := Finset.single_le_sum (s := (Finset.univ : Finset (ι → Bool))) + (f := fun f => tensor (fun i => M i (f i))) + (fun f _ => tensor_nonneg _ (fun i => hm i (f i))) (Finset.mem_univ (fun _ => false)) + exact h +end SpinAngle.DependentTensor + +namespace SpinAngle.BlockTensor +open DependentTensor +variable {τ J n : Type*} [contextInstance4107_25 : Fintype τ] [contextInstance4107_37 : DecidableEq τ] [contextInstance4107_53 : Fintype J] [contextInstance4107_65 : DecidableEq J] + [contextInstance4108_2 : Fintype n] [contextInstance4108_14 : DecidableEq n] +variable (f : τ → J) + +abbrev Fiber (j : J) := {i : τ // f i = j} + +def splitEquiv : (τ → n) ≃ (∀ j : J, Fiber f j → n) where + toFun x j i := x i.val + invFun y i := y (f i) ⟨i,rfl⟩ + left_inv x := rfl + right_inv y := by + funext j i + rcases i with ⟨i,hi⟩ + subst j + rfl + + +def tensor (A : ∀ j, Mat (Fiber f j → n)) : Mat (τ → n) := + fun x y => DependentTensor.tensor A (splitEquiv f x) (splitEquiv f y) + +lemma tensor_mul (A B : ∀ j, Mat (Fiber f j → n)) : + tensor f (fun j => A j * B j) = tensor f A * tensor f B := by + change (DependentTensor.tensor (fun j => A j * B j)).submatrix (splitEquiv f) (splitEquiv f) = _ + rw [DependentTensor.tensor_mul] + exact (Matrix.submatrix_mul_equiv _ _ (splitEquiv f) (splitEquiv f) (splitEquiv f)).symm + +lemma tensor_star + {τ : Type*} {J : Type*} {n : Type*} + [Fintype τ] + [DecidableEq τ] + [contextInstance4107_53 : Fintype J] + [DecidableEq J] + [Fintype n] + [DecidableEq n] + (f : τ → J) (A : ∀ j, Mat (Fiber f j → n)) : + tensor f (fun j => star (A j)) = star (tensor f A) := by + ext x y + simp [tensor, DependentTensor.tensor, Matrix.star_apply] + +lemma tensor_one : tensor f (fun j => (1 : Mat (Fiber f j → n))) = 1 := by + ext x y + change DependentTensor.tensor (fun j => (1 : Mat (Fiber f j → n))) _ _ = _ + rw [DependentTensor.tensor_one] + simp only [Matrix.one_apply, Equiv.apply_eq_iff_eq] + +lemma tensor_nonneg (A : ∀ j, Mat (Fiber f j → n)) (hA : ∀ j, 0 ≤ A j) : 0 ≤ tensor f A := by + exact (Matrix.nonneg_iff_posSemidef.mp (DependentTensor.tensor_nonneg A hA)).submatrix (splitEquiv f) |>.nonneg + +lemma tensor_mono (A B : ∀ j, Mat (Fiber f j → n)) (hA : ∀ j, 0 ≤ A j) (hAB : ∀ j, A j ≤ B j) : + tensor f A ≤ tensor f B := by + have he := DependentTensor.tensor_mono A B hA hAB + have hn := (Matrix.nonneg_iff_posSemidef.mp (sub_nonneg.mpr he)).submatrix (splitEquiv f) |>.nonneg + exact sub_nonneg.mp hn + +lemma tensor_projection (P : ∀ j, Mat (Fiber f j → n)) (hP : ∀ j, IsStarProjection (P j)) : + IsStarProjection (tensor f P) := by + constructor + · change tensor f P * tensor f P = tensor f P + rw [← tensor_mul] + congr 1 + funext j + exact (hP j).isIdempotentElem.eq + · change star (tensor f P) = tensor f P + rw [← tensor_star] + congr 1 + funext j + exact (hP j).isSelfAdjoint.star_eq + +lemma tensor_sum_smul {κ : J → Type*} [∀ j, Fintype (κ j)] + (w : ∀ j, κ j → ℝ) (A : ∀ j, κ j → Mat (Fiber f j → n)) : + tensor f (fun j => ∑ k, w j k • A j k) = + ∑ k : ∀ j, κ j, (∏ j, w j (k j)) • tensor f (fun j => A j (k j)) := by + ext x y + change DependentTensor.tensor (fun j => ∑ k, w j k • A j k) _ _ = _ + rw [DependentTensor.tensor_sum_smul] + simp only [Matrix.sum_apply, Matrix.smul_apply, tensor] +end SpinAngle.BlockTensor + +namespace SpinAngle.BlockTensor +open DependentTensor +variable {τ J n : Type*} [contextInstance4180_25 : Fintype τ] [contextInstance4180_37 : DecidableEq τ] [contextInstance4180_53 : Fintype J] [contextInstance4180_65 : DecidableEq J] + [contextInstance4181_2 : Fintype n] [contextInstance4181_14 : DecidableEq n] +variable (f : τ → J) + +lemma prod_fibers + {τ : Type*} {J : Type*} + [contextInstance4180_25 : Fintype τ] + [DecidableEq τ] + [contextInstance4180_53 : Fintype J] + [contextInstance4180_65 : DecidableEq J] + (f : τ → J) {M : Type*} [CommMonoid M] (a : τ → M) : + (∏ j : J, ∏ i : Fiber f j, a i.val) = ∏ i, a i := by + calc + _ = ∏ z : Sigma (Fiber f), a z.2.val := + (Fintype.prod_sigma (fun z : Sigma (Fiber f) => a z.2.val)).symm + _ = _ := (Equiv.sigmaFiberEquiv f).prod_comp a + + +lemma tensor_cells + {τ : Type*} {J : Type*} {n : Type*} + [contextInstance4180_25 : Fintype τ] + [contextInstance4180_37 : DecidableEq τ] + [contextInstance4180_53 : Fintype J] + [contextInstance4180_65 : DecidableEq J] + [Fintype n] + [DecidableEq n] + (f : τ → J) (A : τ → Mat n) : + tensor f (fun j => DependentTensor.tensor (fun i : Fiber f j => A i.val)) = + DependentTensor.tensor A := by + ext x y + change (∏ j, ∏ i : Fiber f j, A i.val (x i.val) (y i.val)) = _ + exact prod_fibers f (fun i => A i (x i) (y i)) + +lemma tensor_commute (A B : ∀ j, Mat (Fiber f j → n)) + (h : ∀ j, Commute (A j) (B j)) : Commute (tensor f A) (tensor f B) := by + change tensor f A * tensor f B = tensor f B * tensor f A + rw [← tensor_mul, ← tensor_mul] + congr 1 + funext j + exact (h j).eq +end SpinAngle.BlockTensor + + +namespace SpinAngle.TensorMatrix +open MatrixAnalysis +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {ι n : Type*} [contextInstance4214_23 : Fintype ι] [contextInstance4214_35 : DecidableEq ι] [contextInstance4214_51 : Fintype n] [contextInstance4214_63 : DecidableEq n] + +lemma tensor_root_square (A : ι → Mat n) (hA : ∀ i, 0 ≤ A i) : + tensor (fun i => root (A i)) * tensor (fun i => root (A i)) = tensor A := by + rw [← tensor_mul] + congr 1 + funext i + exact root_mul_self _ (hA i) + +lemma tensor_root (A : ι → Mat n) (hA : ∀ i, 0 ≤ A i) : + tensor (fun i => root (A i)) = root (tensor A) := by + apply (CFC.mul_self_eq_mul_self_iff _ _ + (tensor_nonneg _ (fun i => root_nonneg (A i))) (root_nonneg _)).mp + rw [tensor_root_square A hA, root_mul_self _ (tensor_nonneg A hA)] + +lemma tensor_invRoot_mul_root (A : ι → Mat n) (hA : ∀ i, 0 ≤ A i) : + tensor (fun i => invRoot (A i)) * tensor (fun i => root (A i)) = + tensor (fun i => support (A i)) := by + rw [← tensor_mul] + congr 1 + funext i + exact invRoot_mul_root _ (hA i) + +lemma tensor_root_mul_support_of_le_smul (A B : ι → Mat n) + (hA : ∀ i, 0 ≤ A i) (hB : ∀ i, 0 ≤ B i) + (c : ℝ) (hAB : ∀ i, A i ≤ c • B i) : + tensor (fun i => root (A i)) * tensor (fun i => support (B i)) = + tensor (fun i => root (A i)) := by + rw [← tensor_mul] + congr 1 + funext i + exact root_mul_support_of_le_smul _ _ (hB i) (hA i) c (hAB i) +end SpinAngle.TensorMatrix + +namespace SpinAngle +open scoped BigOperators +variable {R C : Type*} [contextInstance4250_23 : Fintype R] [contextInstance4250_35 : DecidableEq R] [contextInstance4250_51 : Fintype C] [contextInstance4250_63 : DecidableEq C] + +lemma sum_occupiedRow_card (W : Finset (R × C)) : + ∑ i, (occupiedRow W i).card = W.card := by + have he (i : R) : (occupiedRow W i).card = ∑ j : C, if (i,j) ∈ W then 1 else 0 := by + simp only [occupiedRow, Finset.card_eq_sum_ones, Finset.sum_filter] + simp only [he] + rw [← Finset.sum_product (f := fun x : R × C => if x ∈ W then (1 : ℕ) else 0)] + simp only [Finset.univ_product_univ, ← Finset.sum_filter] + have he : (Finset.univ.filter fun x : R × C => x ∈ W) = W := by ext x; simp + rw [he] + simp + +lemma sum_missingInRow (W : Finset (R × C)) : + ∑ i, missingInRow W i = Fintype.card R * Fintype.card C - W.card := by + have he : (∑ i, missingInRow W i) + W.card = Fintype.card R * Fintype.card C := by + rw [← sum_occupiedRow_card W, ← Finset.sum_add_distrib] + have hi (i : R) : missingInRow W i + (occupiedRow W i).card = Fintype.card C := + Nat.sub_add_cancel (occupiedRow_card_le W i) + simp [hi] + omega + +lemma boardPhi_nonneg (W : Finset (R × C)) : + 0 ≤ missingCellProductFactor (Fintype.card C) (missingInRow W) := + Finset.prod_nonneg fun rowIndex _ => missingCellFactor_nonneg _ (missingInRow W rowIndex) + +lemma boardPhi_le_exp_holes (W : Finset (R × C)) : + missingCellProductFactor (Fintype.card C) (missingInRow W) ≤ + Real.exp (Fintype.card R * Fintype.card C - W.card : ℕ) := by + have h := missingCellProduct (Fintype.card C) (missingInRow W) (missingInRow_le W) + have hs : (∑ i, (missingInRow W i : ℝ)) = + (Fintype.card R * Fintype.card C - W.card : ℕ) := by + exact_mod_cast sum_missingInRow W + rwa [hs] at h +end SpinAngle + + +namespace SpinAngle +open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder +open SpinAngle.Young + + + +structure TypeLabel (q : ℕ) where + even : YoungDiagram + odd : YoungDiagram + even_height : even.colLen 0 ≤ q + odd_height : odd.colLen 0 ≤ q + +namespace TypeLabel +variable {q : ℕ} +def size (D : TypeLabel q) : ℕ := Fintype.card (Cells D.even) + Fintype.card (Cells D.odd) +def entropy (D : TypeLabel q) : ℝ := SignedCarrier.entropy D.even D.odd q +def dimension (D : TypeLabel q) : ℕ := SignedCarrier.dimension D.even D.odd q D.even_height D.odd_height + +def projection (D : TypeLabel q) (τ : Type*) [Fintype τ] [DecidableEq τ] : + Matrix (τ → SignedTensor.Spin q) (τ → SignedTensor.Spin q) ℂ := + SignedCarrier.matrixProjection D.even D.odd q D.even_height D.odd_height + +lemma projection_isStarProjection (D : TypeLabel q) (τ : Type*) [Fintype τ] [DecidableEq τ] : + IsStarProjection (D.projection τ) := + SignedCarrier.matrixProjection_isStarProjection D.even D.odd q D.even_height D.odd_height + +lemma dimension_pos (D : TypeLabel q) : 0 < D.dimension := + SignedCarrier.dimension_pos D.even D.odd q D.even_height D.odd_height + +lemma dimension_le (D : TypeLabel q) : D.dimension ≤ (D.size + 1) ^ (q*(q-1)) := + SignedCarrier.dimension_le D.even D.odd q D.even_height D.odd_height + +lemma entropy_eq_zero_of_size_zero (D : TypeLabel q) (hD : D.size = 0) : D.entropy = 0 := by + have hs : ∑ i, SignedCarrier.parts D.even D.odd q i = 0 := + (SignedCarrier.sum_parts D.even D.odd q D.even_height D.odd_height).trans hD + have hi : ∀ i, SignedCarrier.parts D.even D.odd q i = 0 := by + intro i + have h := Finset.single_le_sum (s := Finset.univ) + (fun j _ => Nat.zero_le (SignedCarrier.parts D.even D.odd q j)) (Finset.mem_univ i) + rw [hs] at h + exact Nat.eq_zero_of_le_zero h + simp [entropy, SignedCarrier.entropy, EntropyMonomial.entropy, hi] +end TypeLabel + +abbrev EvenDensity (q : ℕ) := {A : SignedTensor.Mat q × SignedTensor.Mat q // SignedTensor.IsEvenDensity A} +namespace EvenDensity +variable {q : ℕ} +def matrix (A : EvenDensity q) : Matrix (SignedTensor.Spin q) (SignedTensor.Spin q) ℂ := + SignedTensor.block A.val +lemma nonneg (A : EvenDensity q) : 0 ≤ A.matrix := + (SignedTensor.block_posSemidef A.val A.property.1 A.property.2.1).nonneg +lemma trace_eq_one (A : EvenDensity q) : A.matrix.trace = 1 := by + rw [matrix, SignedTensor.block_trace] + exact A.property.2.2 + +def toDensity (A : EvenDensity q) : MatrixAnalysis.Density (SignedTensor.Spin q) := + ⟨A.matrix,A.nonneg,A.trace_eq_one⟩ + +variable {J : Type*} [contextInstance4345_21 : Fintype J] [contextInstance4345_33 : Nonempty J] +def mean (A : J → EvenDensity q) : EvenDensity q := + ⟨SignedTensor.evenAverage (fun j => (A j).val), + SignedTensor.evenAverage_isEvenDensity _ (fun j => (A j).property)⟩ +lemma mean_matrix (A : J → EvenDensity q) [DecidableEq J] : + (mean A).matrix = MatrixAnalysis.average (fun j => (A j).toDensity) := by + unfold mean matrix SignedTensor.evenAverage + rw [SignedTensor.block_real_smul, SignedTensor.block_sum] + rfl +end EvenDensity + +namespace TypeLabel +variable {q : ℕ} +variable {τ : Type*} [contextInstance4358_21 : Fintype τ] [contextInstance4358_33 : DecidableEq τ] +lemma density_upper (D : TypeLabel q) (A : EvenDensity q) : + ‖TensorMatrix.tensor (fun _ : τ => A.matrix) * D.projection τ‖ ≤ Real.exp (-D.entropy) := + SignedCarrier.matrix_density_upper D.even D.odd q D.even_height D.odd_height A.val A.property + +lemma density_commute (D : TypeLabel q) (A : EvenDensity q) : + Commute (TensorMatrix.tensor (fun _ : τ => A.matrix)) (D.projection τ) := + SignedCarrier.matrix_density_commute D.even D.odd q D.even_height D.odd_height A.val A.property + +variable [contextInstance4367_9 : Nonempty (Fin q)] +lemma density_mixture (D : TypeLabel q) : + ∃ (ι : Type) (_ : Fintype ι) (w : ι → ℝ) (R : ι → EvenDensity q), + (∀ i, 0 ≤ w i) ∧ (∑ i, w i = 1) ∧ + D.projection τ ≤ (Real.exp D.entropy * (D.dimension : ℝ)) • + ∑ i, w i • TensorMatrix.tensor (fun _ : τ => (R i).matrix) := by + obtain ⟨ι,hι,w,R,hw,hs,hR,hdom⟩ := SignedCarrier.exists_matrix_density_mixture + (τ := τ) D.even D.odd q D.even_height D.odd_height + let := hι + exact ⟨ι,hι,w,fun i => ⟨R i,hR i⟩,hw,hs,hdom⟩ +end TypeLabel + +namespace TypeBlocks +universe u +open MatrixAnalysis +variable {q : ℕ} +variable {τ : Type*} {J : Type u} [contextInstance4383_34 : Fintype τ] [contextInstance4383_46 : DecidableEq τ] [contextInstance4383_62 : Fintype J] [contextInstance4383_74 : DecidableEq J] + +abbrev Fiber (f : τ → J) (j : J) := BlockTensor.Fiber f j + +def projection (f : τ → J) (D : J → TypeLabel q) : Mat (τ → SignedTensor.Spin q) := + BlockTensor.tensor f (fun j => (D j).projection (Fiber f j)) + +def entropy (D : J → TypeLabel q) : ℝ := ∑ j, (D j).entropy +def dimension (D : J → TypeLabel q) : ℕ := ∏ j, (D j).dimension + +lemma projection_isStarProjection (f : τ → J) (D : J → TypeLabel q) : + IsStarProjection (projection f D) := + BlockTensor.tensor_projection f _ (fun j => (D j).projection_isStarProjection _) + +lemma density_commute (f : τ → J) (D : J → TypeLabel q) (A : EvenDensity q) : + Commute (TensorMatrix.tensor (fun _ : τ => A.matrix)) (projection f D) := by + have h := BlockTensor.tensor_commute f + (fun j => TensorMatrix.tensor (fun _ : Fiber f j => A.matrix)) + (fun j => (D j).projection (Fiber f j)) (fun j => (D j).density_commute A) + have he : BlockTensor.tensor f (fun j => TensorMatrix.tensor (fun _ : Fiber f j => A.matrix)) = + TensorMatrix.tensor (fun _ : τ => A.matrix) := by + ext x y + change (∏ j : J, ∏ t : Fiber f j, A.matrix (x t.val) (y t.val)) = + ∏ t : τ, A.matrix (x t) (y t) + exact BlockTensor.prod_fibers f (fun t => A.matrix (x t) (y t)) + rwa [he] at h + +variable [contextInstance4410_9 : Nonempty (Fin q)] + + +theorem density_mixture (f : τ → J) (D : J → TypeLabel q) : + ∃ (ι : Type u) (_ : Fintype ι) (w : ι → ℝ) (R : ι → J → EvenDensity q), + (∀ i, 0 ≤ w i) ∧ (∑ i, w i = Real.exp (entropy D) * (dimension D : ℝ)) ∧ + projection f D ≤ ∑ i, w i • TensorMatrix.tensor (fun t : τ => (R i (f t)).matrix) := by + classical + choose κ hκ w R hw hs hdom using (fun j : J => (D j).density_mixture (τ := Fiber f j)) + let : ∀ j, Fintype (κ j) := hκ + let c (j : J) : ℝ := Real.exp (D j).entropy * (D j).dimension + let z (j : J) (i : κ j) : ℝ := c j * w j i + have hz (j : J) (i : κ j) : 0 ≤ z j i := + mul_nonneg (mul_nonneg (Real.exp_pos _).le (Nat.cast_nonneg _)) (hw j i) + have hsum (j : J) : ∑ i, z j i = c j := by + simp only [z, ← Finset.mul_sum, hs, mul_one] + have hlocal (j : J) : (D j).projection (Fiber f j) ≤ + ∑ i, z j i • TensorMatrix.tensor (fun _ : Fiber f j => (R j i).matrix) := by + simpa only [z, c, Finset.smul_sum, smul_smul] using hdom j + refine ⟨(∀ j, κ j), inferInstance, (fun i => ∏ j, z j (i j)), + (fun i j => R j (i j)), (fun i => Finset.prod_nonneg fun j _ => hz j (i j)), ?_, ?_⟩ + · rw [← Fintype.prod_sum] + simp only [hsum, c, Finset.prod_mul_distrib] + rw [← Real.exp_sum] + simp only [entropy, dimension, Nat.cast_prod] + · have h := BlockTensor.tensor_mono f _ _ + (fun j => ((D j).projection_isStarProjection (Fiber f j)).nonneg) hlocal + rw [BlockTensor.tensor_sum_smul] at h + have he (i : ∀ j, κ j) : BlockTensor.tensor f + (fun j => TensorMatrix.tensor (fun _ : Fiber f j => (R j (i j)).matrix)) = + TensorMatrix.tensor (fun t : τ => (R (f t) (i (f t))).matrix) := by + ext x y + change (∏ j : J, ∏ t : Fiber f j, (R j (i j)).matrix (x t.val) (y t.val)) = + ∏ t : τ, (R (f t) (i (f t))).matrix (x t) (y t) + calc + _ = ∏ j : J, ∏ t : Fiber f j, (R (f t.val) (i (f t.val))).matrix (x t.val) (y t.val) := by + apply Finset.prod_congr rfl + intro j hj + apply Finset.prod_congr rfl + intro t ht + rw [t.property] + _ = _ := BlockTensor.prod_fibers f (fun t => (R (f t) (i (f t))).matrix (x t) (y t)) + simpa only [he, projection] using h +end TypeBlocks +end SpinAngle + +end +end +end +end +end +end +end +end +end +end +end +end +end +end +end +end +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/SpinAngle/TypeAngle.lean b/lean/OAI/RepresentationTheory/SpinAngle/TypeAngle.lean index 741c13236b182f9a358b12581311c47db3a44aae..96c70bd77693aa5e833c255c65ca75ea01b2724a 100644 --- a/lean/OAI/RepresentationTheory/SpinAngle/TypeAngle.lean +++ b/lean/OAI/RepresentationTheory/SpinAngle/TypeAngle.lean @@ -1,242 +1,242 @@ -import OAI.RepresentationTheory.SpinAngle.Compression - -namespace OAI - -noncomputable section -open scoped BigOperators ComplexConjugate InnerProductSpace -open scoped BigOperators ComplexConjugate InnerProductSpace Matrix -open scoped Matrix ComplexOrder -open scoped TensorProduct InnerProductSpace BigOperators -open scoped BigOperators ComplexConjugate -open scoped InnerProductSpace -open scoped TensorProduct InnerProductSpace ComplexOrder -open scoped BigOperators -open scoped InnerProductSpace ComplexOrder BigOperators -open scoped InnerProductSpace BigOperators ComplexOrder -open scoped BigOperators -open scoped BigOperators -open MeasureTheory TopologicalSpace Set -open scoped BigOperators -open scoped BigOperators -open Set -open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder -open scoped BigOperators -open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder -open scoped BigOperators - - - -namespace SpinAngle.TypeAngle -open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder -open MatrixAnalysis TensorMatrix -variable {q : ℕ} [contextInstance30_17 : Nonempty (Fin q)] -variable {R C : Type*} [contextInstance31_23 : Fintype R] [contextInstance31_35 : DecidableEq R] [contextInstance31_51 : Fintype C] [contextInstance31_63 : DecidableEq C] - -def row (W : Finset (R × C)) (w : W) : R := w.val.1 -def column (W : Finset (R × C)) (w : W) : C := w.val.2 - -def phi (W : Finset (R × C)) : ℝ := - missingCellProductFactor (Fintype.card C) (missingInRow W) - -def columnRoot (W : Finset (R × C)) (A : C → EvenDensity q) := - tensor (fun x : W => root (A x.val.2).matrix) -def meanRoot [Nonempty C] (W : Finset (R × C)) (A : C → EvenDensity q) := - tensor (fun _ : W => root (EvenDensity.mean A).matrix) -def meanInvRoot [Nonempty C] (W : Finset (R × C)) (A : C → EvenDensity q) := - tensor (fun _ : W => invRoot (EvenDensity.mean A).matrix) -def meanSupport [Nonempty C] (W : Finset (R × C)) (A : C → EvenDensity q) := - tensor (fun _ : W => support (EvenDensity.mean A).matrix) -def rowRoot (W : Finset (R × C)) (B : R → EvenDensity q) := - tensor (fun x : W => root (B x.val.1).matrix) - -lemma columnRoot_support - {q : ℕ} [Nonempty (Fin q)] {R : Type*} {C : Type*} - [Fintype R] [DecidableEq R] [Fintype C] [DecidableEq C] [Nonempty C] (W : Finset (R × C)) (A : C → EvenDensity q) : - columnRoot W A * meanSupport W A = columnRoot W A := by - apply tensor_root_mul_support_of_le_smul - (fun x : W => (A x.val.2).matrix) (fun _ : W => (EvenDensity.mean A).matrix) - (fun x => (A x.val.2).nonneg) (fun _ => (EvenDensity.mean A).nonneg) (Fintype.card C) - intro x - rw [EvenDensity.mean_matrix] - exact le_smul_average (fun j => (A j).toDensity) x.val.2 - -lemma meanRoot_eq - {q : ℕ} [Nonempty (Fin q)] {R : Type*} {C : Type*} - [Fintype R] [DecidableEq R] [Fintype C] [DecidableEq C] [Nonempty C] (W : Finset (R × C)) (A : C → EvenDensity q) : - meanRoot W A = root (tensor (fun _ : W => (EvenDensity.mean A).matrix)) := - tensor_root _ (fun _ => (EvenDensity.mean A).nonneg) - -lemma meanRoot_commute_global [Nonempty C] (W : Finset (R × C)) - (D : TypeLabel q) (A : C → EvenDensity q) : - Commute (meanRoot W A) (D.projection W) := by - rw [meanRoot_eq] - exact root_commute (D.density_commute (EvenDensity.mean A)) - -lemma meanRoot_commute_rows [Nonempty C] (W : Finset (R × C)) - (K : R → TypeLabel q) (A : C → EvenDensity q) : - Commute (meanRoot W A) (TypeBlocks.projection (row W) K) := by - rw [meanRoot_eq] - exact root_commute (TypeBlocks.density_commute (row W) K (EvenDensity.mean A)) - -lemma global_norm [Nonempty C] (W : Finset (R × C)) (D : TypeLabel q) - (A : C → EvenDensity q) : - ‖D.projection W * meanRoot W A‖ ^ 2 ≤ Real.exp (-D.entropy) := by - have hs : IsSelfAdjoint (meanRoot W A) := - tensor_selfAdjoint _ (fun _ => root_selfAdjoint _) - rw [Analytic.norm_projection_sqrt_sq _ _ (D.projection_isStarProjection W) - hs (meanRoot_commute_global W D A)] - change ‖(tensor (fun _ : W => root (EvenDensity.mean A).matrix) * - tensor (fun _ : W => root (EvenDensity.mean A).matrix)) * D.projection W‖ ≤ _ - rw [tensor_root_square _ (fun _ => (EvenDensity.mean A).nonneg)] - exact D.density_upper (EvenDensity.mean A) - -lemma cell_norm - {q : ℕ} [Nonempty (Fin q)] {R : Type*} {C : Type*} - [Fintype R] [DecidableEq R] [Fintype C] [DecidableEq C] [Nonempty C] (W : Finset (R × C)) - (A : C → EvenDensity q) (B : R → EvenDensity q) : - ‖columnRoot W A * meanInvRoot W A * rowRoot W B‖ ^ 2 ≤ phi W := by - unfold columnRoot meanInvRoot rowRoot - rw [← tensor_mul, ← tensor_mul, EvenDensity.mean_matrix] - exact normalized_board_bound W (fun c => (A c).toDensity) (fun r => (B r).toDensity) - - - - -theorem nonempty_columns [Nonempty C] (W : Finset (R × C)) - (D : TypeLabel q) (H : C → TypeLabel q) (K : R → TypeLabel q) : - ‖TypeBlocks.projection (column W) H * TypeBlocks.projection (row W) K * D.projection W‖ ^ 2 ≤ - min 1 (Real.exp (TypeBlocks.entropy H + TypeBlocks.entropy K - D.entropy) * - (TypeBlocks.dimension H : ℝ) * (TypeBlocks.dimension K : ℝ) * phi W) := by - classical - obtain ⟨ι,hι,w,A,hw,hsw,hH⟩ := TypeBlocks.density_mixture (column W) H - obtain ⟨κ,hκ,z,B,hz,hsz,hK⟩ := TypeBlocks.density_mixture (row W) K - let := hι - let := hκ - let M (i : ι) : EvenDensity q := EvenDensity.mean (A i) - let r (i : ι) := columnRoot W (A i) - let v (i : ι) := meanInvRoot W (A i) - let t (i : ι) := meanRoot W (A i) - let Q (i : ι) := meanSupport W (A i) - let s (j : κ) := rowRoot W (B j) - let P := D.projection W - let PH := TypeBlocks.projection (column W) H - let PK := TypeBlocks.projection (row W) K - have hp : IsStarProjection P := D.projection_isStarProjection W - have hh : IsStarProjection PH := TypeBlocks.projection_isStarProjection _ _ - have hk : IsStarProjection PK := TypeBlocks.projection_isStarProjection _ _ - have hrstar (i : ι) : star (r i) = r i := - (tensor_selfAdjoint _ (fun _ => root_selfAdjoint _)).star_eq - have hsstar (j : κ) : star (s j) = s j := - (tensor_selfAdjoint _ (fun _ => root_selfAdjoint _)).star_eq - have htstar (i : ι) : IsSelfAdjoint (t i) := - tensor_selfAdjoint _ (fun _ => root_selfAdjoint _) - have hr (i : ι) : star (r i) * r i = tensor (fun x : W => (A i x.val.2).matrix) := by - rw [hrstar] - exact tensor_root_square _ (fun x => (A i x.val.2).nonneg) - have hss (j : κ) : s j * star (s j) = tensor (fun x : W => (B j x.val.1).matrix) := by - rw [hsstar] - exact tensor_root_square _ (fun x => (B j x.val.1).nonneg) - have hdomH : PH ≤ ∑ i, w i • (star (r i) * r i) := by - simpa only [hr, PH, column] using hH - have hdomK : PK ≤ ∑ j, z j • (s j * star (s j)) := by - simpa only [hss, PK, row] using hK - have hvt (i : ι) : v i * t i = Q i := - tensor_invRoot_mul_root _ (fun _ => (M i).nonneg) - have hrQ (i : ι) : r i * Q i = r i := columnRoot_support W (A i) - have htk (i : ι) : Commute (t i) PK := meanRoot_commute_rows W K (A i) - have htp (i : ι) : Commute (t i) P := meanRoot_commute_global W D (A i) - have hglobal (i : ι) : ‖P * t i‖ ^ 2 ≤ Real.exp (-D.entropy) := global_norm W D (A i) - have hcell (i : ι) (j : κ) : ‖r i * v i * s j‖ ^ 2 ≤ phi W := cell_norm W (A i) (B j) - have h := Analytic.three_projection_angle_of_density_mixtures PH PK P hh hk hp w z hw hz - r v t Q s hdomH hdomK hvt hrQ htk htp (Real.exp (-D.entropy)) (phi W) - (Real.exp_pos _).le (boardPhi_nonneg W) hglobal hcell - rw [hsw,hsz] at h - convert h using 2 - rw [sub_eq_add_neg, Real.exp_add, Real.exp_add] - ring -end SpinAngle.TypeAngle - -namespace SpinAngle.TypeBlocks -open scoped BigOperators -variable {q : ℕ} -variable {τ J : Type*} [contextInstance157_23 : Fintype τ] [contextInstance157_35 : DecidableEq τ] [contextInstance157_51 : Fintype J] [contextInstance157_63 : DecidableEq J] - -lemma dimension_pos {q : ℕ} {J : Type*} [Fintype J] [DecidableEq J] (D : J → TypeLabel q) : 0 < dimension D := - Finset.prod_pos fun j _ => (D j).dimension_pos - -lemma dimension_le {q : ℕ} {τ : Type*} {J : Type*} - [Fintype τ] [DecidableEq τ] [Fintype J] [DecidableEq J] (f : τ → J) (D : J → TypeLabel q) - (hsize : ∀ j, (D j).size = Fintype.card (Fiber f j)) : - dimension D ≤ (Fintype.card τ + 1) ^ (Fintype.card J * (q*(q-1))) := by - have h (j : J) : (D j).dimension ≤ (Fintype.card τ + 1) ^ (q*(q-1)) := by - apply (D j).dimension_le.trans - apply Nat.pow_le_pow_left - rw [hsize] - exact Nat.add_le_add_right (Fintype.card_subtype_le _) 1 - calc - dimension D ≤ ∏ _j : J, (Fintype.card τ + 1) ^ (q*(q-1)) := - Finset.prod_le_prod₀ (fun j _ => Nat.zero_le _) (fun j _ => h j) - _ = _ := by rw [Finset.prod_const, Finset.card_univ, ← pow_mul]; congr 1; exact Nat.mul_comm _ _ -end SpinAngle.TypeBlocks - -namespace SpinAngle.TypeAngle -open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder -variable {q : ℕ} [contextInstance179_17 : Nonempty (Fin q)] -variable {R C : Type*} [contextInstance180_23 : Fintype R] [contextInstance180_35 : DecidableEq R] [contextInstance180_51 : Fintype C] [contextInstance180_63 : DecidableEq C] - - - -theorem one_sided_type_angle (W : Finset (R × C)) - (D : TypeLabel q) (H : C → TypeLabel q) (K : R → TypeLabel q) - (hD : D.size = W.card) - (hH : ∀ j, (H j).size = Fintype.card (TypeBlocks.Fiber (column W) j)) - (hK : ∀ i, (K i).size = Fintype.card (TypeBlocks.Fiber (row W) i)) : - (‖TypeBlocks.projection (column W) H * TypeBlocks.projection (row W) K * D.projection W‖ ^ 2 ≤ - min 1 (Real.exp (TypeBlocks.entropy H + TypeBlocks.entropy K - D.entropy) * - (TypeBlocks.dimension H : ℝ) * (TypeBlocks.dimension K : ℝ) * phi W)) ∧ - (min 1 (Real.exp (TypeBlocks.entropy H + TypeBlocks.entropy K - D.entropy) * - (TypeBlocks.dimension H : ℝ) * (TypeBlocks.dimension K : ℝ) * phi W) ≤ - min 1 (Real.exp (TypeBlocks.entropy H + TypeBlocks.entropy K - D.entropy + - (Fintype.card R * Fintype.card C - W.card : ℕ)) * - (TypeBlocks.dimension H : ℝ) * (TypeBlocks.dimension K : ℝ))) ∧ - TypeBlocks.dimension H * TypeBlocks.dimension K ≤ - (W.card + 1) ^ ((Fintype.card R + Fintype.card C) * q * (q-1)) := by - classical - have hangle : ‖TypeBlocks.projection (column W) H * TypeBlocks.projection (row W) K * D.projection W‖ ^ 2 ≤ - min 1 (Real.exp (TypeBlocks.entropy H + TypeBlocks.entropy K - D.entropy) * - (TypeBlocks.dimension H : ℝ) * (TypeBlocks.dimension K : ℝ) * phi W) := by - cases isEmpty_or_nonempty C with - | inr h => exact nonempty_columns W D H K - | inl h => - have hW : W = ∅ := Finset.eq_empty_of_isEmpty W - have hd : D.entropy = 0 := D.entropy_eq_zero_of_size_zero (by simpa [hW] using hD) - have hksize (i : R) : (K i).size = 0 := by simpa [hW] using hK i - have hkentropy : TypeBlocks.entropy K = 0 := by - simp only [TypeBlocks.entropy, fun i => (K i).entropy_eq_zero_of_size_zero (hksize i), Finset.sum_const_zero] - have hphi : phi W = 1 := by simp [phi, missingCellProductFactor, missingCellFactor] - have hdim : 1 ≤ (TypeBlocks.dimension K : ℝ) := by - exact_mod_cast TypeBlocks.dimension_pos K - have hnorm := Analytic.norm_three_projections_sq_le_one - (TypeBlocks.projection (column W) H) (TypeBlocks.projection (row W) K) (D.projection W) - (TypeBlocks.projection_isStarProjection _ _) (TypeBlocks.projection_isStarProjection _ _) - (D.projection_isStarProjection W) - have hhent : TypeBlocks.entropy H = 0 := by simp [TypeBlocks.entropy] - have hhdim : TypeBlocks.dimension H = 1 := by simp [TypeBlocks.dimension] - simpa only [hhent, hhdim, Nat.cast_one, hd, hkentropy, hphi, add_zero, - sub_zero, Real.exp_zero, one_mul, mul_one, min_eq_left hdim] using hnorm - refine ⟨hangle, ?_, ?_⟩ - · apply min_le_min_left - have h := mul_le_mul_of_nonneg_left (boardPhi_le_exp_holes W) - (mul_nonneg (mul_nonneg (Real.exp_pos (TypeBlocks.entropy H + TypeBlocks.entropy K - D.entropy)).le (Nat.cast_nonneg (TypeBlocks.dimension H))) - (Nat.cast_nonneg (TypeBlocks.dimension K))) - convert h using 1 <;> simp only [phi, Real.exp_add] ; ring - · have h := Nat.mul_le_mul (TypeBlocks.dimension_le (column W) H hH) - (TypeBlocks.dimension_le (row W) K hK) - rw [← pow_add] at h - simpa only [Fintype.card_coe, show Fintype.card C * (q * (q-1)) + Fintype.card R * (q * (q-1)) = - (Fintype.card R + Fintype.card C) * q * (q-1) by ring] using h -end SpinAngle.TypeAngle - -end - -end OAI +import OAI.RepresentationTheory.SpinAngle.Compression + +namespace OAI + +noncomputable section +open scoped BigOperators ComplexConjugate InnerProductSpace +open scoped BigOperators ComplexConjugate InnerProductSpace Matrix +open scoped Matrix ComplexOrder +open scoped TensorProduct InnerProductSpace BigOperators +open scoped BigOperators ComplexConjugate +open scoped InnerProductSpace +open scoped TensorProduct InnerProductSpace ComplexOrder +open scoped BigOperators +open scoped InnerProductSpace ComplexOrder BigOperators +open scoped InnerProductSpace BigOperators ComplexOrder +open scoped BigOperators +open scoped BigOperators +open MeasureTheory TopologicalSpace Set +open scoped BigOperators +open scoped BigOperators +open Set +open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder +open scoped BigOperators +open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder +open scoped BigOperators + + + +namespace SpinAngle.TypeAngle +open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder +open MatrixAnalysis TensorMatrix +variable {q : ℕ} [contextInstance30_17 : Nonempty (Fin q)] +variable {R C : Type*} [contextInstance31_23 : Fintype R] [contextInstance31_35 : DecidableEq R] [contextInstance31_51 : Fintype C] [contextInstance31_63 : DecidableEq C] + +def row (W : Finset (R × C)) (w : W) : R := w.val.1 +def column (W : Finset (R × C)) (w : W) : C := w.val.2 + +def phi (W : Finset (R × C)) : ℝ := + missingCellProductFactor (Fintype.card C) (missingInRow W) + +def columnRoot (W : Finset (R × C)) (A : C → EvenDensity q) := + tensor (fun x : W => root (A x.val.2).matrix) +def meanRoot [Nonempty C] (W : Finset (R × C)) (A : C → EvenDensity q) := + tensor (fun _ : W => root (EvenDensity.mean A).matrix) +def meanInvRoot [Nonempty C] (W : Finset (R × C)) (A : C → EvenDensity q) := + tensor (fun _ : W => invRoot (EvenDensity.mean A).matrix) +def meanSupport [Nonempty C] (W : Finset (R × C)) (A : C → EvenDensity q) := + tensor (fun _ : W => support (EvenDensity.mean A).matrix) +def rowRoot (W : Finset (R × C)) (B : R → EvenDensity q) := + tensor (fun x : W => root (B x.val.1).matrix) + +lemma columnRoot_support + {q : ℕ} [Nonempty (Fin q)] {R : Type*} {C : Type*} + [Fintype R] [DecidableEq R] [Fintype C] [DecidableEq C] [Nonempty C] (W : Finset (R × C)) (A : C → EvenDensity q) : + columnRoot W A * meanSupport W A = columnRoot W A := by + apply tensor_root_mul_support_of_le_smul + (fun x : W => (A x.val.2).matrix) (fun _ : W => (EvenDensity.mean A).matrix) + (fun x => (A x.val.2).nonneg) (fun _ => (EvenDensity.mean A).nonneg) (Fintype.card C) + intro x + rw [EvenDensity.mean_matrix] + exact le_smul_average (fun j => (A j).toDensity) x.val.2 + +lemma meanRoot_eq + {q : ℕ} [Nonempty (Fin q)] {R : Type*} {C : Type*} + [Fintype R] [DecidableEq R] [Fintype C] [DecidableEq C] [Nonempty C] (W : Finset (R × C)) (A : C → EvenDensity q) : + meanRoot W A = root (tensor (fun _ : W => (EvenDensity.mean A).matrix)) := + tensor_root _ (fun _ => (EvenDensity.mean A).nonneg) + +lemma meanRoot_commute_global [Nonempty C] (W : Finset (R × C)) + (D : TypeLabel q) (A : C → EvenDensity q) : + Commute (meanRoot W A) (D.projection W) := by + rw [meanRoot_eq] + exact root_commute (D.density_commute (EvenDensity.mean A)) + +lemma meanRoot_commute_rows [Nonempty C] (W : Finset (R × C)) + (K : R → TypeLabel q) (A : C → EvenDensity q) : + Commute (meanRoot W A) (TypeBlocks.projection (row W) K) := by + rw [meanRoot_eq] + exact root_commute (TypeBlocks.density_commute (row W) K (EvenDensity.mean A)) + +lemma global_norm [Nonempty C] (W : Finset (R × C)) (D : TypeLabel q) + (A : C → EvenDensity q) : + ‖D.projection W * meanRoot W A‖ ^ 2 ≤ Real.exp (-D.entropy) := by + have hs : IsSelfAdjoint (meanRoot W A) := + tensor_selfAdjoint _ (fun _ => root_selfAdjoint _) + rw [Analytic.norm_projection_sqrt_sq _ _ (D.projection_isStarProjection W) + hs (meanRoot_commute_global W D A)] + change ‖(tensor (fun _ : W => root (EvenDensity.mean A).matrix) * + tensor (fun _ : W => root (EvenDensity.mean A).matrix)) * D.projection W‖ ≤ _ + rw [tensor_root_square _ (fun _ => (EvenDensity.mean A).nonneg)] + exact D.density_upper (EvenDensity.mean A) + +lemma cell_norm + {q : ℕ} [Nonempty (Fin q)] {R : Type*} {C : Type*} + [Fintype R] [DecidableEq R] [Fintype C] [DecidableEq C] [Nonempty C] (W : Finset (R × C)) + (A : C → EvenDensity q) (B : R → EvenDensity q) : + ‖columnRoot W A * meanInvRoot W A * rowRoot W B‖ ^ 2 ≤ phi W := by + unfold columnRoot meanInvRoot rowRoot + rw [← tensor_mul, ← tensor_mul, EvenDensity.mean_matrix] + exact normalized_board_bound W (fun c => (A c).toDensity) (fun r => (B r).toDensity) + + + + +theorem nonempty_columns [Nonempty C] (W : Finset (R × C)) + (D : TypeLabel q) (H : C → TypeLabel q) (K : R → TypeLabel q) : + ‖TypeBlocks.projection (column W) H * TypeBlocks.projection (row W) K * D.projection W‖ ^ 2 ≤ + min 1 (Real.exp (TypeBlocks.entropy H + TypeBlocks.entropy K - D.entropy) * + (TypeBlocks.dimension H : ℝ) * (TypeBlocks.dimension K : ℝ) * phi W) := by + classical + obtain ⟨ι,hι,w,A,hw,hsw,hH⟩ := TypeBlocks.density_mixture (column W) H + obtain ⟨κ,hκ,z,B,hz,hsz,hK⟩ := TypeBlocks.density_mixture (row W) K + let := hι + let := hκ + let M (i : ι) : EvenDensity q := EvenDensity.mean (A i) + let r (i : ι) := columnRoot W (A i) + let v (i : ι) := meanInvRoot W (A i) + let t (i : ι) := meanRoot W (A i) + let Q (i : ι) := meanSupport W (A i) + let s (j : κ) := rowRoot W (B j) + let P := D.projection W + let PH := TypeBlocks.projection (column W) H + let PK := TypeBlocks.projection (row W) K + have hp : IsStarProjection P := D.projection_isStarProjection W + have hh : IsStarProjection PH := TypeBlocks.projection_isStarProjection _ _ + have hk : IsStarProjection PK := TypeBlocks.projection_isStarProjection _ _ + have hrstar (i : ι) : star (r i) = r i := + (tensor_selfAdjoint _ (fun _ => root_selfAdjoint _)).star_eq + have hsstar (j : κ) : star (s j) = s j := + (tensor_selfAdjoint _ (fun _ => root_selfAdjoint _)).star_eq + have htstar (i : ι) : IsSelfAdjoint (t i) := + tensor_selfAdjoint _ (fun _ => root_selfAdjoint _) + have hr (i : ι) : star (r i) * r i = tensor (fun x : W => (A i x.val.2).matrix) := by + rw [hrstar] + exact tensor_root_square _ (fun x => (A i x.val.2).nonneg) + have hss (j : κ) : s j * star (s j) = tensor (fun x : W => (B j x.val.1).matrix) := by + rw [hsstar] + exact tensor_root_square _ (fun x => (B j x.val.1).nonneg) + have hdomH : PH ≤ ∑ i, w i • (star (r i) * r i) := by + simpa only [hr, PH, column] using hH + have hdomK : PK ≤ ∑ j, z j • (s j * star (s j)) := by + simpa only [hss, PK, row] using hK + have hvt (i : ι) : v i * t i = Q i := + tensor_invRoot_mul_root _ (fun _ => (M i).nonneg) + have hrQ (i : ι) : r i * Q i = r i := columnRoot_support W (A i) + have htk (i : ι) : Commute (t i) PK := meanRoot_commute_rows W K (A i) + have htp (i : ι) : Commute (t i) P := meanRoot_commute_global W D (A i) + have hglobal (i : ι) : ‖P * t i‖ ^ 2 ≤ Real.exp (-D.entropy) := global_norm W D (A i) + have hcell (i : ι) (j : κ) : ‖r i * v i * s j‖ ^ 2 ≤ phi W := cell_norm W (A i) (B j) + have h := Analytic.three_projection_angle_of_density_mixtures PH PK P hh hk hp w z hw hz + r v t Q s hdomH hdomK hvt hrQ htk htp (Real.exp (-D.entropy)) (phi W) + (Real.exp_pos _).le (boardPhi_nonneg W) hglobal hcell + rw [hsw,hsz] at h + convert h using 2 + rw [sub_eq_add_neg, Real.exp_add, Real.exp_add] + ring +end SpinAngle.TypeAngle + +namespace SpinAngle.TypeBlocks +open scoped BigOperators +variable {q : ℕ} +variable {τ J : Type*} [contextInstance157_23 : Fintype τ] [contextInstance157_35 : DecidableEq τ] [contextInstance157_51 : Fintype J] [contextInstance157_63 : DecidableEq J] + +lemma dimension_pos {q : ℕ} {J : Type*} [Fintype J] [DecidableEq J] (D : J → TypeLabel q) : 0 < dimension D := + Finset.prod_pos fun j _ => (D j).dimension_pos + +lemma dimension_le {q : ℕ} {τ : Type*} {J : Type*} + [Fintype τ] [DecidableEq τ] [Fintype J] [DecidableEq J] (f : τ → J) (D : J → TypeLabel q) + (hsize : ∀ j, (D j).size = Fintype.card (Fiber f j)) : + dimension D ≤ (Fintype.card τ + 1) ^ (Fintype.card J * (q*(q-1))) := by + have h (j : J) : (D j).dimension ≤ (Fintype.card τ + 1) ^ (q*(q-1)) := by + apply (D j).dimension_le.trans + apply Nat.pow_le_pow_left + rw [hsize] + exact Nat.add_le_add_right (Fintype.card_subtype_le _) 1 + calc + dimension D ≤ ∏ _j : J, (Fintype.card τ + 1) ^ (q*(q-1)) := + Finset.prod_le_prod₀ (fun j _ => Nat.zero_le _) (fun j _ => h j) + _ = _ := by rw [Finset.prod_const, Finset.card_univ, ← pow_mul]; congr 1; exact Nat.mul_comm _ _ +end SpinAngle.TypeBlocks + +namespace SpinAngle.TypeAngle +open scoped BigOperators Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {q : ℕ} [contextInstance179_17 : Nonempty (Fin q)] +variable {R C : Type*} [contextInstance180_23 : Fintype R] [contextInstance180_35 : DecidableEq R] [contextInstance180_51 : Fintype C] [contextInstance180_63 : DecidableEq C] + + + +theorem one_sided_type_angle (W : Finset (R × C)) + (D : TypeLabel q) (H : C → TypeLabel q) (K : R → TypeLabel q) + (hD : D.size = W.card) + (hH : ∀ j, (H j).size = Fintype.card (TypeBlocks.Fiber (column W) j)) + (hK : ∀ i, (K i).size = Fintype.card (TypeBlocks.Fiber (row W) i)) : + (‖TypeBlocks.projection (column W) H * TypeBlocks.projection (row W) K * D.projection W‖ ^ 2 ≤ + min 1 (Real.exp (TypeBlocks.entropy H + TypeBlocks.entropy K - D.entropy) * + (TypeBlocks.dimension H : ℝ) * (TypeBlocks.dimension K : ℝ) * phi W)) ∧ + (min 1 (Real.exp (TypeBlocks.entropy H + TypeBlocks.entropy K - D.entropy) * + (TypeBlocks.dimension H : ℝ) * (TypeBlocks.dimension K : ℝ) * phi W) ≤ + min 1 (Real.exp (TypeBlocks.entropy H + TypeBlocks.entropy K - D.entropy + + (Fintype.card R * Fintype.card C - W.card : ℕ)) * + (TypeBlocks.dimension H : ℝ) * (TypeBlocks.dimension K : ℝ))) ∧ + TypeBlocks.dimension H * TypeBlocks.dimension K ≤ + (W.card + 1) ^ ((Fintype.card R + Fintype.card C) * q * (q-1)) := by + classical + have hangle : ‖TypeBlocks.projection (column W) H * TypeBlocks.projection (row W) K * D.projection W‖ ^ 2 ≤ + min 1 (Real.exp (TypeBlocks.entropy H + TypeBlocks.entropy K - D.entropy) * + (TypeBlocks.dimension H : ℝ) * (TypeBlocks.dimension K : ℝ) * phi W) := by + cases isEmpty_or_nonempty C with + | inr h => exact nonempty_columns W D H K + | inl h => + have hW : W = ∅ := Finset.eq_empty_of_isEmpty W + have hd : D.entropy = 0 := D.entropy_eq_zero_of_size_zero (by simpa [hW] using hD) + have hksize (i : R) : (K i).size = 0 := by simpa [hW] using hK i + have hkentropy : TypeBlocks.entropy K = 0 := by + simp only [TypeBlocks.entropy, fun i => (K i).entropy_eq_zero_of_size_zero (hksize i), Finset.sum_const_zero] + have hphi : phi W = 1 := by simp [phi, missingCellProductFactor, missingCellFactor] + have hdim : 1 ≤ (TypeBlocks.dimension K : ℝ) := by + exact_mod_cast TypeBlocks.dimension_pos K + have hnorm := Analytic.norm_three_projections_sq_le_one + (TypeBlocks.projection (column W) H) (TypeBlocks.projection (row W) K) (D.projection W) + (TypeBlocks.projection_isStarProjection _ _) (TypeBlocks.projection_isStarProjection _ _) + (D.projection_isStarProjection W) + have hhent : TypeBlocks.entropy H = 0 := by simp [TypeBlocks.entropy] + have hhdim : TypeBlocks.dimension H = 1 := by simp [TypeBlocks.dimension] + simpa only [hhent, hhdim, Nat.cast_one, hd, hkentropy, hphi, add_zero, + sub_zero, Real.exp_zero, one_mul, mul_one, min_eq_left hdim] using hnorm + refine ⟨hangle, ?_, ?_⟩ + · apply min_le_min_left + have h := mul_le_mul_of_nonneg_left (boardPhi_le_exp_holes W) + (mul_nonneg (mul_nonneg (Real.exp_pos (TypeBlocks.entropy H + TypeBlocks.entropy K - D.entropy)).le (Nat.cast_nonneg (TypeBlocks.dimension H))) + (Nat.cast_nonneg (TypeBlocks.dimension K))) + convert h using 1 <;> simp only [phi, Real.exp_add] ; ring + · have h := Nat.mul_le_mul (TypeBlocks.dimension_le (column W) H hH) + (TypeBlocks.dimension_le (row W) K hK) + rw [← pow_add] at h + simpa only [Fintype.card_coe, show Fintype.card C * (q * (q-1)) + Fintype.card R * (q * (q-1)) = + (Fintype.card R + Fintype.card C) * q * (q-1) by ring] using h +end SpinAngle.TypeAngle + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Tensor/Postselection.lean b/lean/OAI/RepresentationTheory/Tensor/Postselection.lean index 1e684f4a30e282844c552fee53cc6a967961bab4..a902e0cfb5d21c51b35dbf569b671712a1c6ca52 100644 --- a/lean/OAI/RepresentationTheory/Tensor/Postselection.lean +++ b/lean/OAI/RepresentationTheory/Tensor/Postselection.lean @@ -1,781 +1,781 @@ -import Mathlib -import OAI.Analysis.Matrix.TensorMoment - -namespace OAI - -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ComplexConjugate Matrix.Norms.L2Operator -attribute [local instance] Classical.propDecidable - -namespace CoordinateSweeps.OrdinaryTensor -variable {I A : Type*} [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] - -/- Occupancies of single alphabet symbols in an ordinary tensor word. -/ -def count (w : I → A) (a : A) : ℕ := Fintype.card {i : I // w i = a} - -/- Ordinary tensor permutation, with the manuscript's product convention. -/ -def permute (σ : Equiv.Perm I) : Equiv.Perm (I → A) where - toFun w i := w (σ⁻¹ i) - invFun w i := w (σ i) - left_inv w := by ext i; simp - right_inv w := by ext i; simp - -omit [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] in -lemma permute_mul (σ τ : Equiv.Perm I) : - permute (A := A) (σ*τ) = permute σ * permute τ := by - ext w i; simp [permute] - -omit [Fintype A] [DecidableEq I] in -lemma count_le (w : I → A) (a : A) : count w a ≤ Fintype.card I := Fintype.card_subtype_le _ - -omit [DecidableEq I] in -lemma sum_count (w : I → A) : ∑ a, count w a = Fintype.card I := by - classical - simpa only [count, Fintype.card_sigma] using Fintype.card_congr (Equiv.sigmaFiberEquiv w) - -omit [Fintype A] [DecidableEq I] in -lemma counts_eq_exists_perm {u w : I → A} (h : count u = count w) : - ∃ σ : Equiv.Perm I, permute σ u = w := by - let e (a : A) : {i : I // u i = a} ≃ {i : I // w i = a} := - Fintype.equivOfCardEq (congrFun h a) - let σ : Equiv.Perm I := Equiv.ofFiberEquiv e - refine ⟨σ, ?_⟩ - ext i - have hi : w (σ (σ⁻¹ i)) = u (σ⁻¹ i) := Equiv.ofFiberEquiv_map e (σ⁻¹ i) - change u (σ⁻¹ i) = w i - simpa using hi.symm - -/- Word-preserving permutations and independent permutations of its fibers -are literally equivalent finite sets. This yields the factorial frame moments. -/ -def fiberPermEquiv (w : I → A) : - {σ : Equiv.Perm I // ∀ i, w (σ i) = w i} ≃ (∀ a : A, Equiv.Perm {i : I // w i = a}) where - toFun σ a := σ.val.subtypePerm (fun i => by rw [σ.property i]) - invFun τ := ⟨Equiv.ofFiberEquiv τ, Equiv.ofFiberEquiv_map τ⟩ - left_inv σ := by - apply Subtype.ext - ext i - rfl - right_inv τ := by - funext a - apply Equiv.ext - rintro ⟨i,hi⟩ - apply Subtype.ext - subst a - rfl - -lemma card_wordStabilizer (w : I → A) : - Fintype.card {σ : Equiv.Perm I // ∀ i, w (σ i) = w i} = - ∏ a : A, (count w a).factorial := by - rw [Fintype.card_congr (fiberPermEquiv w), Fintype.card_pi] - simp only [Fintype.card_perm, count] - -/- A transporter fiber is a coset of the literal word stabilizer. -/ -def transporterEquiv (u w : I → A) (σ : Equiv.Perm I) (hσ : permute σ u = w) : - {g : Equiv.Perm I // permute g u = w} ≃ - {g : Equiv.Perm I // ∀ i, u (g i) = u i} where - toFun g := ⟨σ⁻¹*g.val, by - intro i - have hg : u (g.val⁻¹ (g.val i)) = w (g.val i) := congrFun g.property (g.val i) - have hs : u (σ⁻¹ (g.val i)) = w (g.val i) := congrFun hσ (g.val i) - simpa using hs.trans hg.symm⟩ - invFun g := ⟨σ*g.val, by - ext i - change u (g.val⁻¹ (σ⁻¹ i)) = w i - have hg := g.property (g.val⁻¹ (σ⁻¹ i)) - have hs : u (σ⁻¹ i) = w i := congrFun hσ i - have hh : u (g.val⁻¹ (σ⁻¹ i)) = u (σ⁻¹ i) := by simpa using hg.symm - exact hh.trans hs⟩ - left_inv g := Subtype.ext (by simp) - right_inv g := Subtype.ext (by simp) - -omit [Fintype A] [DecidableEq I] in -lemma permute_count (σ : Equiv.Perm I) (w : I → A) : count (permute σ w) = count w := by - ext a - apply Fintype.card_congr - exact - { toFun := fun i => ⟨σ⁻¹ i.val, i.property⟩ - invFun := fun i => ⟨σ i.val, by simpa [permute] using i.property⟩ - left_inv := fun i => Subtype.ext (by simp) - right_inv := fun i => Subtype.ext (by simp) } - -lemma card_transporter (u w : I → A) : - Fintype.card {g : Equiv.Perm I // permute g u = w} = - if count u = count w then ∏ a, (count u a).factorial else 0 := by - split_ifs with h - · obtain ⟨σ,hσ⟩ := counts_eq_exists_perm h - rw [Fintype.card_congr (transporterEquiv u w σ hσ), card_wordStabilizer] - · have : IsEmpty {g : Equiv.Perm I // permute g u = w} := - ⟨fun g => h (by rw [← g.property, permute_count])⟩ - exact Fintype.card_eq_zero - -/- The finite moment matrix which will be realized by actual radial Gamma -variables and root phases rather than an assumed de Finetti density. -/ -def momentFrame : Matrix (I → A) (I → A) ℂ := fun u w => - if count u = count w then (∏ a, ((count u a).factorial : ℂ)) else 0 - -lemma momentFrame_eq_perm_sum : - (momentFrame (I := I) (A := A)) = - ∑ σ : Equiv.Perm I, (fun u w => if permute σ w = u then (1 : ℂ) else 0 : Matrix _ _ ℂ) := by - apply Matrix.ext - intro u w - simp only [momentFrame, Finset.sum_apply] - rw [← Finset.sum_filter] - simp only [Finset.sum_const, nsmul_eq_mul, mul_one, ← Fintype.card_subtype, - card_transporter] - split_ifs with h hw <;> simp_all [eq_comm, Nat.cast_prod] -end CoordinateSweeps.OrdinaryTensor - -namespace CoordinateSweeps.OrdinaryTensor - -/- A factorial ratio is bounded by the largest factor; used to avoid -any assumed entropy/Stirling estimate in the empirical postselection measure. -/ -lemma factorial_step_upper (t k : ℕ) : (t+k).factorial ≤ t.factorial * (t+k)^k := by - induction k with - | zero => simp - | succ k ih => - calc - (t+(k+1)).factorial = (t+k+1)*(t+k).factorial := by rw [← Nat.add_assoc, Nat.factorial_succ] - _ ≤ (t+k+1)*(t.factorial*(t+k)^k) := Nat.mul_le_mul_left _ ih - _ ≤ (t+k+1)*(t.factorial*(t+k+1)^k) := - Nat.mul_le_mul_left _ (Nat.mul_le_mul_left _ (Nat.pow_le_pow_left (by omega) _)) - _ = t.factorial*(t+(k+1))^(k+1) := by rw [pow_succ]; ring - -/- For any integral Poisson mean n, n is a mode. This elementary exact -inequality is the only numerical ingredient for the finite tensor mixture. -/ -lemma factorial_mode (n t : ℕ) : n^t * n.factorial ≤ n^n * t.factorial := by - rcases le_total t n with h | h - · have hu : n.factorial ≤ t.factorial*n^(n-t) := by - simpa only [Nat.add_sub_of_le h] using factorial_step_upper t (n-t) - calc - _ ≤ n^t * (t.factorial*n^(n-t)) := Nat.mul_le_mul_left _ hu - _ = n^n*t.factorial := by rw [mul_left_comm, ← pow_add, Nat.add_sub_of_le h]; ring - · have hl := Nat.factorial_mul_pow_sub_le_factorial h - calc - n^t*n.factorial = n^n*(n.factorial*n^(t-n)) := by - rw [mul_left_comm, ← pow_add, Nat.add_sub_of_le h]; ring - _ ≤ n^n*t.factorial := Nat.mul_le_mul_left _ hl - -variable {I A : Type*} [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] - -omit [DecidableEq I] in -lemma prod_word_eq_counts {R : Type*} [CommMonoid R] (r : A → R) (w : I → A) : - (∏ i, r (w i)) = ∏ a, r a ^ count w a := by - rw [← Finset.prod_fiberwise' Finset.univ w r] - simp only [Finset.prod_const, ← Fintype.card_subtype, count] - -/- Exact sigma decomposition of a word orbit and its transporter fibers. -/ -def orbitFiberEquiv (u : I → A) : - (Σ w : {w : I → A // count w = count u}, {σ : Equiv.Perm I // permute σ u = w.val}) ≃ - Equiv.Perm I where - toFun x := x.2.val - invFun σ := ⟨⟨permute σ u, permute_count σ u⟩,⟨σ,rfl⟩⟩ - left_inv := by - rintro ⟨⟨w,hw⟩,⟨σ,hσ⟩⟩ - change permute σ u = w at hσ - subst w - rfl - right_inv σ := rfl - -lemma orbit_card_mul_factorials (u : I → A) : - Fintype.card {w : I → A // count w = count u} * (∏ a, (count u a).factorial) = - (Fintype.card I).factorial := by - have he := Fintype.card_congr (orbitFiberEquiv u) - rw [Fintype.card_sigma, Fintype.card_perm] at he - calc - _ = ∑ _w : {w : I → A // count w = count u}, (∏ a, (count u a).factorial) := by - simp only [Finset.sum_const, Finset.card_univ, smul_eq_mul] - _ = ∑ w : {w : I → A // count w = count u}, - Fintype.card {σ : Equiv.Perm I // permute σ u = w.val} := by - apply Finset.sum_congr rfl - intro w _ - rw [card_transporter, ite_eq_left w.property.symm] - _ = _ := he - -/- Histogram space is an actual finite set of attained occupancies. -/ -abbrev Histogram (I A : Type*) [Fintype I] [Fintype A] [DecidableEq A] := - Set.range (count (I := I) (A := A)) - -instance : Finite (Histogram I A) := Finite.Set.finite_range _ -noncomputable instance : Fintype (Histogram I A) := Fintype.ofFinite _ - -def histogram (w : I → A) : Histogram I A := ⟨count w, w, rfl⟩ - -omit [DecidableEq I] in -lemma histogram_surjective : Function.Surjective (histogram (I := I) (A := A)) := by - rintro ⟨h,⟨w,hw⟩⟩ - exact ⟨w,Subtype.ext hw⟩ - -omit [DecidableEq I] in -lemma histogram_card_le : Fintype.card (Histogram I A) ≤ (Fintype.card I+1)^Fintype.card A := by - let f : Histogram I A → (A → Fin (Fintype.card I+1)) := fun h a => - ⟨h.val a, by obtain ⟨w,hw⟩ := h.property; rw [← hw]; exact Nat.lt_succ_of_le (count_le w a)⟩ - have hf : Function.Injective f := by - intro h k he - apply Subtype.ext - funext a - exact congrArg Fin.val (congrFun he a) - simpa only [Fintype.card_fun, Fintype.card_fin] using Fintype.card_le_of_injective f hf - -/- The individual multinomial type of a word, evaluated at any integer weights. -/ -def typeWeight (r : A → ℕ) (u : I → A) : ℕ := - Fintype.card {w : I → A // count w = count u} * ∏ a, r a ^ count u a - -lemma typeWeight_mul_factorials (r : A → ℕ) (u : I → A) : - typeWeight r u * (∏ a, (count u a).factorial) = - (Fintype.card I).factorial * (∏ a, r a ^ count u a) := by - rw [typeWeight, mul_right_comm, orbit_card_mul_factorials] - -/- Empirical occupancies maximize their own exact multinomial type weight. -/ -lemma typeWeight_empirical_max (u w : I → A) : typeWeight (count u) w ≤ typeWeight (count u) u := by - have hu : 0 < ∏ a : A, (count u a).factorial := - Finset.prod_pos (fun a _ => Nat.factorial_pos _) - have hw : 0 < ∏ a : A, (count w a).factorial := - Finset.prod_pos (fun a _ => Nat.factorial_pos _) - apply Nat.le_of_mul_le_mul_right (c := ∏ a, (count w a).factorial) _ hw - apply Nat.le_of_mul_le_mul_right (c := ∏ a, (count u a).factorial) _ hu - calc - _ = (Fintype.card I).factorial * - ((∏ a, count u a ^ count w a) * (∏ a, (count u a).factorial)) := by - rw [typeWeight_mul_factorials, mul_assoc] - _ ≤ (Fintype.card I).factorial * - ((∏ a, count u a ^ count u a) * (∏ a, (count w a).factorial)) := by - apply Nat.mul_le_mul_left - rw [← Finset.prod_mul_distrib, ← Finset.prod_mul_distrib] - exact Finset.prod_le_prod (fun a _ => factorial_mode (count u a) (count w a)) - _ = _ := by rw [mul_right_comm (typeWeight _ _), typeWeight_mul_factorials, mul_assoc] - -/- Type weight on the finite, attained histogram space. -/ -def histogramWeight (r : A → ℕ) (h : Histogram I A) : ℕ := - Fintype.card {w : I → A // histogram w = h} * ∏ a, r a ^ h.val a - -lemma histogramWeight_mk (r : A → ℕ) (u : I → A) : - histogramWeight r (histogram u) = typeWeight r u := by - unfold histogramWeight typeWeight - congr 1 - apply Fintype.card_congr - exact { toFun := fun w => ⟨w.val, congrArg Subtype.val w.property⟩ - invFun := fun w => ⟨w.val, Subtype.ext w.property⟩ - left_inv := fun w => Subtype.ext rfl - right_inv := fun w => Subtype.ext rfl } - -lemma sum_histogramWeight (r : A → ℕ) : - (∑ h : Histogram I A, histogramWeight r h) = (∑ a, r a)^Fintype.card I := by - have ht := Finset.sum_prod_piFinset (Finset.univ : Finset A) (fun _i : I => r) - simp only [Fintype.piFinset_univ, Finset.prod_const, Finset.card_univ] at ht - rw [← ht, ← Fintype.sum_fiberwise (histogram (I := I) (A := A))] - apply Finset.sum_congr rfl - intro h _ - change Fintype.card {w : I → A // histogram w = h} * (∏ a, r a^h.val a) = - ∑ w : {w : I → A // histogram w = h}, ∏ i, r (w.val i) - have he (w : {w : I → A // histogram w = h}) : - (∏ i, r (w.val i)) = ∏ a, r a ^ h.val a := by - rw [prod_word_eq_counts, show count w.val = h.val from congrArg Subtype.val w.property] - simp_rw [he] - simp only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, Nat.cast_id] - -/- Exact polynomial empirical multinomial lower bound. It includes zero -occupancies and avoids Stirling errors and asymptotic hypotheses. -/ -theorem empirical_type_mass (u : I → A) : - (Fintype.card I)^Fintype.card I ≤ - (Fintype.card I+1)^Fintype.card A * typeWeight (count u) u := by - have he := sum_histogramWeight (I := I) (count u) - rw [sum_count] at he - calc - _ = ∑ h : Histogram I A, histogramWeight (count u) h := he.symm - _ ≤ ∑ _h : Histogram I A, typeWeight (count u) u := by - apply Finset.sum_le_sum - intro h _ - obtain ⟨w,rfl⟩ := histogram_surjective h - rw [histogramWeight_mk] - exact typeWeight_empirical_max u w - _ = Fintype.card (Histogram I A) * typeWeight (count u) u := by - simp only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, Nat.cast_id] - _ ≤ _ := Nat.mul_le_mul_right _ (histogram_card_le (I := I) (A := A)) -end CoordinateSweeps.OrdinaryTensor - -namespace CoordinateSweeps.OrdinaryTensor -open AddChar -variable {I A : Type*} [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] - -/- Finite independent root phases. The modulus is strictly larger than -any occupancy, so it distinguishes every histogram without an analytic limit. -/ -abbrev PhaseSpace (I A : Type*) [Fintype I] := A → ZMod (Fintype.card I+1) - -def wordPhase (t : PhaseSpace I A) (w : I → A) : ℂ := - ∏ a, ZMod.stdAddChar (t a * (count w a : ZMod (Fintype.card I+1))) - -omit [DecidableEq I] in -lemma wordPhase_eq_prod (t : PhaseSpace I A) (w : I → A) : - wordPhase t w = ∏ i, ZMod.stdAddChar (t (w i)) := by - rw [prod_word_eq_counts (fun a : A => ZMod.stdAddChar (t a)) w] - unfold wordPhase - apply Finset.prod_congr rfl - intro a _ - simpa only [nsmul_eq_mul, mul_comm] using - (map_nsmul_eq_pow (ZMod.stdAddChar (N := Fintype.card I+1)) (count w a) (t a)) - -omit [DecidableEq I] in -lemma phase_conjugate_sum (c d : A → ℕ) (hc : ∀ a, c a ≤ Fintype.card I) - (hd : ∀ a, d a ≤ Fintype.card I) : - (∑ t : PhaseSpace I A, - (∏ a, ZMod.stdAddChar (t a * (c a : ZMod (Fintype.card I+1)))) * - star (∏ a, ZMod.stdAddChar (t a * (d a : ZMod (Fintype.card I+1))))) = - if c = d then (Fintype.card (PhaseSpace I A) : ℂ) else 0 := by - simp only [star_prod] - simp_rw [← Finset.prod_mul_distrib, Complex.star_def, ← AddChar.map_neg_eq_conj, - ← map_add_eq_mul, ← sub_eq_add_neg, ← mul_sub] - have hf := Finset.sum_prod_piFinset (Finset.univ : Finset (ZMod (Fintype.card I+1))) - (fun a x => ZMod.stdAddChar (x * ((c a : ZMod (Fintype.card I+1)) - (d a : ZMod (Fintype.card I+1))))) - simp only [Fintype.piFinset_univ] at hf - rw [hf] - simp_rw [AddChar.sum_mulShift _ (ZMod.isPrimitive_stdAddChar _)] - have he (a : A) : (c a : ZMod (Fintype.card I+1)) - (d a : ZMod (Fintype.card I+1)) = 0 ↔ c a = d a := by - rw [sub_eq_zero, ZMod.natCast_eq_natCast_iff'] - rw [Nat.mod_eq_of_lt (Nat.lt_succ_of_le (hc a)), Nat.mod_eq_of_lt (Nat.lt_succ_of_le (hd a))] - simp_rw [he] - by_cases h : c = d - · simp [h, ZMod.card] - · rw [ite_eq_right h] - obtain ⟨a,ha⟩ := Function.ne_iff.mp h - exact Finset.prod_eq_zero (Finset.mem_univ a) (by simp [ha]) - -/- Exact finite orthogonality of different empirical type phases. -/ -omit [DecidableEq I] in -lemma wordPhase_orthogonality (u w : I → A) : - (∑ t : PhaseSpace I A, wordPhase t u * star (wordPhase t w)) = - if count u = count w then (Fintype.card (PhaseSpace I A) : ℂ) else 0 := - phase_conjugate_sum (count u) (count w) (count_le u) (count_le w) - -/- Every root-phase component has unit modulus. -/ -omit [DecidableEq I] in -lemma wordPhase_star_mul (t : PhaseSpace I A) (w : I → A) : - wordPhase t w * star (wordPhase t w) = 1 := by - simp only [wordPhase, star_prod, ← Finset.prod_mul_distrib] - apply Finset.prod_eq_one - intro a _ - rw [Complex.star_def, ← AddChar.map_neg_eq_conj, ← map_add_eq_mul] - simp -end CoordinateSweeps.OrdinaryTensor - -namespace CoordinateSweeps.OrdinaryTensor -open AddChar -open scoped ComplexOrder -variable {I A : Type*} [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] - -def tensorVector (z : A → ℂ) (w : I → A) : ℂ := ∏ i, z (w i) -def outer {J : Type*} (v : J → ℂ) : Matrix J J ℂ := Matrix.vecMulVec v (star v) - -lemma outer_posSemidef {J : Type*} [Finite J] (v : J → ℂ) : (outer v).PosSemidef := - Matrix.posSemidef_vecMulVec_self_star v - -lemma outer_apply {J : Type*} (v : J → ℂ) (i j : J) : outer v i j = v i * star (v j) := rfl - -/- Empirical-site amplitudes. Their exact squared norm is one when there is -at least one slot. Zero-count letters are allowed and have zero amplitude. -/ -def empiricalVector (h : Histogram I A) (t : PhaseSpace I A) (a : A) : ℂ := - (Real.sqrt ((h.val a : ℝ)/Fintype.card I) : ℂ) * ZMod.stdAddChar (t a) - -def amplitude (h : Histogram I A) (w : I → A) : ℝ := - ∏ i, Real.sqrt ((h.val (w i) : ℝ)/Fintype.card I) - -omit [DecidableEq I] in -lemma char_star_mul (t : ZMod (Fintype.card I+1)) : - ZMod.stdAddChar t * star (ZMod.stdAddChar t) = 1 := by - rw [Complex.star_def, ← AddChar.map_neg_eq_conj, ← map_add_eq_mul] - simp - -omit [DecidableEq I] in -lemma empiricalVector_square (h : Histogram I A) (t : PhaseSpace I A) (a : A) : - empiricalVector h t a * star (empiricalVector h t a) = - (((h.val a : ℝ)/Fintype.card I : ℝ) : ℂ) := by - unfold empiricalVector - simp only [star_mul, RCLike.star_def, Complex.conj_ofReal] - calc - _ = (Real.sqrt ((h.val a : ℝ)/Fintype.card I) : ℂ)^2 * - (ZMod.stdAddChar (t a) * star (ZMod.stdAddChar (t a))) := by - simp only [Complex.star_def]; ring - _ = _ := by - rw [char_star_mul, mul_one, ← Complex.ofReal_pow, Real.sq_sqrt (by positivity)] - -omit [DecidableEq I] in -lemma empiricalVector_unit (hn : 0 < Fintype.card I) (h : Histogram I A) (t : PhaseSpace I A) : - (∑ a, empiricalVector h t a * star (empiricalVector h t a)) = 1 := by - simp_rw [empiricalVector_square] - rw [← Complex.ofReal_sum, ← Finset.sum_div] - obtain ⟨w,hw⟩ := h.property - rw [← hw, ← Nat.cast_sum, sum_count, div_self (Nat.cast_ne_zero.mpr (Nat.ne_of_gt hn))] - rfl - -omit [DecidableEq I] in -lemma amplitude_eq_counts (h : Histogram I A) (w : I → A) : - amplitude h w = ∏ a, (Real.sqrt ((h.val a : ℝ)/Fintype.card I)) ^ count w a := -by - unfold amplitude - exact prod_word_eq_counts (fun a => Real.sqrt ((h.val a : ℝ)/Fintype.card I)) w - -omit [DecidableEq I] in -lemma amplitude_congr (h : Histogram I A) {u w : I → A} (he : count u = count w) : - amplitude h u = amplitude h w := by rw [amplitude_eq_counts, amplitude_eq_counts, he] - -omit [DecidableEq I] in -lemma tensorVector_empirical (h : Histogram I A) (t : PhaseSpace I A) (w : I → A) : - tensorVector (empiricalVector h t) w = (amplitude h w : ℂ) * wordPhase t w := by - rw [wordPhase_eq_prod] - simp only [tensorVector, empiricalVector, amplitude, Complex.ofReal_prod, Finset.prod_mul_distrib] - -omit [DecidableEq I] in -lemma amplitude_square (h : Histogram I A) (w : I → A) : - amplitude h w ^ 2 = (∏ a, (h.val a : ℝ) ^ count w a) / - (Fintype.card I : ℝ) ^ Fintype.card I := by - rw [amplitude_eq_counts, ← Finset.prod_pow] - simp_rw [← pow_mul, mul_comm _ 2, pow_mul, Real.sq_sqrt (by positivity : - 0 ≤ (h.val _ : ℝ)/Fintype.card I), div_pow] - rw [Finset.prod_div_distrib, Finset.prod_pow_eq_pow_sum, sum_count] - -/- Finite phase average of actual pure product states. -/ -def phaseFrame (h : Histogram I A) : Matrix (I → A) (I → A) ℂ := - (Fintype.card (PhaseSpace I A) : ℂ)⁻¹ • - ∑ t : PhaseSpace I A, outer (tensorVector (empiricalVector h t)) - -omit [DecidableEq I] in -lemma phaseSpace_card_pos : 0 < Fintype.card (PhaseSpace I A) := by - rw [Fintype.card_fun, ZMod.card] - positivity - -omit [DecidableEq I] in -lemma phaseFrame_posSemidef (h : Histogram I A) : (phaseFrame h).PosSemidef := by - apply Matrix.PosSemidef.smul - · exact Matrix.posSemidef_sum _ (fun t _ => outer_posSemidef _) - · exact inv_nonneg.mpr (Nat.cast_nonneg _) - -omit [DecidableEq I] in -lemma phaseFrame_entry (h : Histogram I A) (u w : I → A) : - phaseFrame h u w = if count u = count w then ((amplitude h u : ℂ)^2) else 0 := by - simp only [phaseFrame, Matrix.smul_apply, smul_eq_mul, Matrix.sum_apply, outer_apply, - tensorVector_empirical, star_mul, RCLike.star_def, Complex.conj_ofReal] - have he (t : PhaseSpace I A) : - ((amplitude h u : ℂ)*wordPhase t u) * - (star (wordPhase t w)*(amplitude h w : ℂ)) = - ((amplitude h u : ℂ)*(amplitude h w : ℂ)) * (wordPhase t u * star (wordPhase t w)) := by ring - simp only [← Complex.star_def] - simp_rw [he] - rw [← Finset.mul_sum, wordPhase_orthogonality] - split_ifs with hc - · rw [amplitude_congr h hc] - have hn : (Fintype.card (PhaseSpace I A) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr (Nat.ne_of_gt phaseSpace_card_pos) - field_simp - · simp -end CoordinateSweeps.OrdinaryTensor - -namespace CoordinateSweeps.OrdinaryTensor -open scoped ComplexOrder -variable {I A : Type*} [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] - -def orbitSize (h : Histogram I A) : ℕ := Fintype.card {w : I → A // histogram w = h} -def representative (h : Histogram I A) : I → A := Classical.choose h.property - -omit [DecidableEq I] in -lemma count_representative (h : Histogram I A) : count (representative h) = h.val := - Classical.choose_spec h.property -omit [DecidableEq I] in -lemma histogram_representative (h : Histogram I A) : histogram (representative h) = h := - Subtype.ext (count_representative h) - -lemma orbitSize_pos (h : Histogram I A) : 0 < orbitSize h := by - have : Nonempty {w : I → A // histogram w = h} := ⟨⟨representative h, histogram_representative h⟩⟩ - exact Fintype.card_pos - -lemma orbitSize_mk (w : I → A) : - orbitSize (histogram w) = Fintype.card {u : I → A // count u = count w} := by - have he := histogramWeight_mk (fun _ : A => 1) w - simpa only [histogramWeight,typeWeight,one_pow,Finset.prod_const_one,mul_one,orbitSize] using he - -def block (h : Histogram I A) : Matrix (I → A) (I → A) ℂ := - outer (fun w => if histogram w = h then 1 else 0) - -omit [DecidableEq I] in -lemma block_posSemidef (h : Histogram I A) : (block h).PosSemidef := outer_posSemidef _ - -omit [DecidableEq I] in -lemma block_entry (h : Histogram I A) (u w : I → A) : - block h u w = if histogram u = h ∧ histogram w = h then (1 : ℂ) else 0 := by - simp only [block,outer_apply] - split_ifs <;> simp_all - -/- Orthogonal projection onto vectors invariant under ordinary slot -permutations, implemented by their exact histogram blocks. -/ -def symProjector : Matrix (I → A) (I → A) ℂ := - ∑ h : Histogram I A, (orbitSize h : ℂ)⁻¹ • block h - -lemma symProjector_posSemidef : (symProjector (I := I) (A := A)).PosSemidef := by - apply Matrix.posSemidef_sum - intro h _ - exact (block_posSemidef h).smul (inv_nonneg.mpr (Nat.cast_nonneg _)) - -lemma symProjector_entry (u w : I → A) : symProjector u w = - if histogram u = histogram w then (orbitSize (histogram u) : ℂ)⁻¹ else 0 := by - simp only [symProjector, Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, block_entry] - rw [Finset.sum_eq_single (histogram u)] - · by_cases h : histogram u = histogram w <;> simp [h,eq_comm] - · intro h _ hne - have he : histogram u ≠ h := Ne.symm hne - simp [he] - · simp - -lemma symProjector_mulVec_of_constant (v : (I → A) → ℂ) - (hv : ∀ u w, count u = count w → v u = v w) : - (symProjector (I := I) (A := A)).mulVec v = v := by - ext u - simp only [Matrix.mulVec, dotProduct, symProjector_entry, ite_mul, zero_mul] - rw [← Finset.sum_filter] - have he (w : I → A) (hw : w ∈ Finset.univ.filter (fun w => histogram u = histogram w)) : v w = v u := - (hv u w (congrArg Subtype.val (Finset.mem_filter.mp hw).2)).symm - rw [Finset.sum_congr rfl (fun w hw => congrArg ((orbitSize (histogram u) : ℂ)⁻¹ * ·) (he w hw))] - simp only [Finset.sum_const, nsmul_eq_mul, ← Fintype.card_subtype] - have hc : Fintype.card {w : I → A // histogram u = histogram w} = orbitSize (histogram u) := by - unfold orbitSize - apply Fintype.card_congr - exact { toFun := fun w => ⟨w.val,w.property.symm⟩ - invFun := fun w => ⟨w.val,w.property.symm⟩ - left_inv := fun w => Subtype.ext rfl - right_inv := fun w => Subtype.ext rfl } - rw [hc] - have ho : (orbitSize (histogram u) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr (Nat.ne_of_gt (orbitSize_pos _)) - field_simp - -lemma symProjector_idempotent : (symProjector (I := I) (A := A)) * symProjector = symProjector := by - ext u w - have he := symProjector_mulVec_of_constant (fun v : I → A => symProjector v w) (fun v v' h => by - have hh : histogram v = histogram v' := Subtype.ext h - simp only [symProjector_entry, hh]) - exact congrFun he u - -def histogramAmplitude (h k : Histogram I A) : ℝ := amplitude h (representative k) - -omit [DecidableEq I] in -lemma histogramAmplitude_mk (h : Histogram I A) (w : I → A) : - histogramAmplitude h (histogram w) = amplitude h w := by - apply amplitude_congr - exact count_representative _ - -omit [DecidableEq I] in -lemma phaseFrame_blocks (h : Histogram I A) : - phaseFrame h = ∑ k : Histogram I A, ((histogramAmplitude h k : ℂ)^2) • block k := by - ext u w - rw [phaseFrame_entry] - simp only [Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, block_entry] - rw [Finset.sum_eq_single (histogram u)] - · have he : (count u = count w) ↔ histogram w = histogram u := - ⟨fun h => Subtype.ext h.symm, fun h => (congrArg Subtype.val h).symm⟩ - rw [histogramAmplitude_mk] - simp only [true_and, he] - split_ifs <;> simp - · intro k _ hk - have he : histogram u ≠ k := Ne.symm hk - simp [he] - · simp - -/- Polynomial inverse-orbit bound for the **actual** empirical phase frame. -/ -lemma inverse_orbit_le_empirical (hn : 0 < Fintype.card I) (h : Histogram I A) : - (orbitSize h : ℝ)⁻¹ ≤ ((Fintype.card I+1)^Fintype.card A : ℕ) * histogramAmplitude h h ^ 2 := by - obtain ⟨u,rfl⟩ := histogram_surjective h - rw [histogramAmplitude_mk, orbitSize_mk, amplitude_square] - have ho : (0 : ℝ) < Fintype.card {w : I → A // count w = count u} := by - simpa only [← orbitSize_mk] using (Nat.cast_pos.mpr (orbitSize_pos (histogram u)) : - (0 : ℝ) < orbitSize (histogram u)) - have hn' : (0 : ℝ) < (Fintype.card I : ℝ)^Fintype.card I := pow_pos (Nat.cast_pos.mpr hn) _ - have hm := empirical_type_mass u - have hr : (Fintype.card I : ℝ)^Fintype.card I ≤ - (((Fintype.card I+1)^Fintype.card A : ℕ) : ℝ) * - ((Fintype.card {w : I → A // count w = count u} : ℝ) * ∏ a, (count u a : ℝ)^count u a) := by - exact_mod_cast hm - change _ ≤ (((Fintype.card I+1)^Fintype.card A : ℕ) : ℝ) * - ((∏ a, (count u a : ℝ)^count u a) / (Fintype.card I : ℝ)^Fintype.card I) - rw [← mul_div_assoc, le_div_iff₀ hn', inv_mul_eq_div, div_le_iff₀ ho] - nlinarith [hr] -end CoordinateSweeps.OrdinaryTensor - -namespace CoordinateSweeps.OrdinaryTensor -open scoped ComplexOrder -variable {I A : Type*} [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] - -omit [DecidableEq I] in -lemma phaseFrame_sum_blocks : - (∑ h : Histogram I A, phaseFrame h) = ∑ k : Histogram I A, - (∑ h : Histogram I A, (histogramAmplitude h k : ℂ)^2) • block k := by - simp_rw [phaseFrame_blocks] - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro k _ - exact Finset.sum_smul.symm - -/- Constructive finite postselection before normalizing the histogram sum. -/ -theorem phaseFrame_sum_domination (hn : 0 < Fintype.card I) : - ((((Fintype.card I+1)^Fintype.card A : ℕ) : ℂ) • - (∑ h : Histogram I A, phaseFrame h) - symProjector).PosSemidef := by - let P : ℕ := (Fintype.card I+1)^Fintype.card A - have hc (k : Histogram I A) : - 0 ≤ (P : ℝ) * (∑ h : Histogram I A, histogramAmplitude h k ^ 2) - (orbitSize k : ℝ)⁻¹ := by - apply sub_nonneg.mpr - apply (inverse_orbit_le_empirical hn k).trans - exact mul_le_mul_of_nonneg_left - (Finset.single_le_sum (fun h _ => sq_nonneg (histogramAmplitude h k)) (Finset.mem_univ k)) - (Nat.cast_nonneg P) - have he : (P : ℂ) • (∑ h : Histogram I A, phaseFrame h) - symProjector = - ∑ k : Histogram I A, - (((P : ℝ) * (∑ h : Histogram I A, histogramAmplitude h k ^ 2) - - (orbitSize k : ℝ)⁻¹ : ℝ) : ℂ) • block k := by - rw [phaseFrame_sum_blocks, symProjector, Finset.smul_sum, ← Finset.sum_sub_distrib] - apply Finset.sum_congr rfl - intro k _ - rw [smul_smul, ← sub_smul] - congr 1 - push_cast - rfl - rw [show (((Fintype.card I+1)^Fintype.card A : ℕ) : ℂ) = (P : ℂ) from rfl, he] - apply Matrix.posSemidef_sum - intro k _ - exact (block_posSemidef k).smul (by exact_mod_cast hc k) - -instance [Nonempty A] : Nonempty (Histogram I A) := ⟨histogram (fun _ => Classical.arbitrary A)⟩ - -/- Literal finite average of empirical pure product tensors, grouped first -by histogram and then by independent roots. -/ -def finiteMixture : Matrix (I → A) (I → A) ℂ := - (Fintype.card (Histogram I A) : ℂ)⁻¹ • ∑ h : Histogram I A, phaseFrame h - -omit [DecidableEq I] in -lemma finiteMixture_posSemidef : (finiteMixture (I := I) (A := A)).PosSemidef := by - exact (Matrix.posSemidef_sum _ (fun h _ => phaseFrame_posSemidef h)).smul - (inv_nonneg.mpr (Nat.cast_nonneg _)) - -/- Finite, normalized tensor postselection with explicit polynomial overhead. -Every product in finiteMixture comes from squared-norm-one empirical vectors; -there is no de Finetti theorem or independent density assumption. -/ -theorem finite_postselection [Nonempty A] (hn : 0 < Fintype.card I) : - ((((Fintype.card I+1)^(2*Fintype.card A) : ℕ) : ℂ) • - (finiteMixture (I := I) (A := A)) - symProjector).PosSemidef := by - let P : ℕ := (Fintype.card I+1)^Fintype.card A - let H : ℕ := Fintype.card (Histogram I A) - have hH : (H : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr (Nat.ne_of_gt Fintype.card_pos) - have h := phaseFrame_sum_domination (I := I) (A := A) hn - have he : ((P*H : ℕ) : ℂ) • (finiteMixture (I := I) (A := A)) = - (P : ℂ) • ∑ h : Histogram I A, phaseFrame h := by - unfold finiteMixture - rw [smul_smul, Nat.cast_mul] - congr 1 - change (P : ℂ)*(H : ℂ)*(H : ℂ)⁻¹ = (P : ℂ) - field_simp - have hm : (P*H : ℕ) ≤ (Fintype.card I+1)^(2*Fintype.card A) := by - have hle := Nat.mul_le_mul_left P (histogram_card_le (I := I) (A := A)) - simpa only [P,H,← pow_two,← pow_mul, mul_comm 2] using hle - have hp : (0 : ℂ) ≤ (((Fintype.card I+1)^(2*Fintype.card A) : ℕ) : ℂ) - ((P*H : ℕ) : ℂ) := by - exact sub_nonneg.mpr (by exact_mod_cast hm) - have hh := (finiteMixture_posSemidef (I := I) (A := A)).smul hp - have hf := hh.add h - rw [← he] at hf - convert hf using 1 - module - -omit [DecidableEq A] in -lemma outer_tensorVector_trace (z : A → ℂ) : - Matrix.trace (outer (tensorVector (I := I) z)) = - (∑ a, z a * star (z a))^Fintype.card I := by - have ht := Finset.sum_prod_piFinset (Finset.univ : Finset A) - (fun _i : I => fun a : A => z a * star (z a)) - simp only [Fintype.piFinset_univ, Finset.prod_const, Finset.card_univ] at ht - change (∑ w : I → A, tensorVector z w * star (tensorVector z w)) = _ - simp only [tensorVector,star_prod,← Finset.prod_mul_distrib] - exact ht - -lemma phaseFrame_trace [Nonempty A] (hn : 0 < Fintype.card I) (h : Histogram I A) : - Matrix.trace (phaseFrame h) = 1 := by - rw [phaseFrame, Matrix.trace_smul, Matrix.trace_sum] - simp_rw [outer_tensorVector_trace, empiricalVector_unit hn, one_pow] - simp only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, mul_one, smul_eq_mul] - exact inv_mul_cancel₀ (Nat.cast_ne_zero.mpr (Nat.ne_of_gt phaseSpace_card_pos)) - -lemma finiteMixture_trace [Nonempty A] (hn : 0 < Fintype.card I) : - Matrix.trace (finiteMixture (I := I) (A := A)) = 1 := by - rw [finiteMixture, Matrix.trace_smul, Matrix.trace_sum] - simp_rw [phaseFrame_trace hn] - simp only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, mul_one, smul_eq_mul] - exact inv_mul_cancel₀ (Nat.cast_ne_zero.mpr (Nat.ne_of_gt Fintype.card_pos)) -end CoordinateSweeps.OrdinaryTensor - -/- Positive-operator inequalities needed for the actual purification proof -of signed tensor density domination (05:eq13), not standalone main results. -/ -noncomputable section -open scoped BigOperators ComplexOrder MatrixOrder -attribute [local instance] Classical.propDecidable -namespace CoordinateSweeps.OrdinaryTensor -variable {I A : Type*} [Fintype I] [DecidableEq I] [Fintype A] [DecidableEq A] - -omit [DecidableEq A] in -lemma outer_trace_nonneg (v : (I → A) → ℂ) : 0 ≤ Matrix.trace (outer v) := by - exact (outer_posSemidef v).trace_nonneg - -/- The ordinary finite postselection theorem applied to an actual invariant -purification vector, rather than an assumed projection inequality. -/ -theorem invariant_vector_postselection [Nonempty A] (hn : 0 < Fintype.card I) - (v : (I → A) → ℂ) (hv : ∀ σ : Equiv.Perm I, ∀ w, v (permute σ w) = v w) : - ((Matrix.trace (outer v) * ((Fintype.card I+1 : ℕ) : ℂ)^(2*Fintype.card A)) • - finiteMixture - outer v).PosSemidef := by - have hfix : symProjector.mulVec v = v := by - apply symProjector_mulVec_of_constant - intro u w he - obtain ⟨σ,hσ⟩ := counts_eq_exists_perm he - rw [← hσ,hv] - have hPA : symProjector * outer v = outer v := by - ext i j - rw [Matrix.mul_apply] - change (∑ k, symProjector i k * (v k * star (v j))) = v i * star (v j) - simp_rw [← mul_assoc] - rw [← Finset.sum_mul] - exact congrArg (fun z : ℂ => z*star (v j)) (congrFun hfix i) - have h1 := PositiveTensor.projection_trace_domination (outer v) symProjector - (outer_posSemidef v) symProjector_posSemidef.isHermitian symProjector_idempotent hPA - have h2 := (finite_postselection (I := I) (A := A) hn).smul (outer_trace_nonneg v) - have hh := h2.add h1 - simpa only [smul_sub,smul_smul,sub_add_sub_cancel,Nat.cast_pow] using hh -end CoordinateSweeps.OrdinaryTensor -namespace CoordinateSweeps.OrdinaryTensor -variable {I A : Type*} [Fintype I] [DecidableEq I] [Fintype A] [DecidableEq A] - -def rawMixture : Matrix (I → A) (I → A) ℂ := - ∑ h : Histogram I A, ∑ t : PhaseSpace I A, outer (tensorVector (empiricalVector h t)) -omit [DecidableEq I] in -lemma rawMixture_posSemidef : (rawMixture (I := I) (A := A)).PosSemidef := by - exact Matrix.posSemidef_sum _ (fun h _ => Matrix.posSemidef_sum _ (fun t _ => outer_posSemidef _)) -omit [DecidableEq I] in -lemma rawMixture_eq : rawMixture (I := I) (A := A) = - ((Fintype.card (Histogram I A) : ℂ)*(Fintype.card (PhaseSpace I A) : ℂ)) • finiteMixture := by - have hP : (Fintype.card (PhaseSpace I A) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr phaseSpace_card_pos.ne' - by_cases hH : (Fintype.card (Histogram I A) : ℂ) = 0 - · have he : IsEmpty (Histogram I A) := Fintype.card_eq_zero_iff.mp (Nat.cast_eq_zero.mp hH) - let := he - simp [rawMixture,finiteMixture] - · unfold finiteMixture phaseFrame rawMixture - rw [smul_smul,← Finset.smul_sum,smul_smul] - have hc : ((Fintype.card (Histogram I A) : ℂ)*(Fintype.card (PhaseSpace I A) : ℂ)) * - (Fintype.card (Histogram I A) : ℂ)⁻¹ * (Fintype.card (PhaseSpace I A) : ℂ)⁻¹ = 1 := by field_simp - rw [hc,one_smul] -omit [DecidableEq I] in -lemma rawMixture_domination [Nonempty A] : - (rawMixture (I := I) (A := A) - finiteMixture).PosSemidef := by - rw [rawMixture_eq] - have hH : (1 : ℂ) ≤ (Fintype.card (Histogram I A) : ℂ) := by exact_mod_cast Fintype.card_pos - have hP : (1 : ℂ) ≤ (Fintype.card (PhaseSpace I A) : ℂ) := by exact_mod_cast phaseSpace_card_pos - have hp : (0 : ℂ) ≤ (Fintype.card (Histogram I A) : ℂ)*(Fintype.card (PhaseSpace I A) : ℂ)-1 := - sub_nonneg.mpr (one_le_mul_of_one_le_of_one_le hH hP) - simpa only [sub_smul,one_smul] using finiteMixture_posSemidef.smul hp -end CoordinateSweeps.OrdinaryTensor -end -end -end -open scoped Matrix.Norms.L2Operator - -end OAI +import Mathlib +import OAI.Analysis.Matrix.TensorMoment + +namespace OAI + +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ComplexConjugate Matrix.Norms.L2Operator +attribute [local instance] Classical.propDecidable + +namespace CoordinateSweeps.OrdinaryTensor +variable {I A : Type*} [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] + +/- Occupancies of single alphabet symbols in an ordinary tensor word. -/ +def count (w : I → A) (a : A) : ℕ := Fintype.card {i : I // w i = a} + +/- Ordinary tensor permutation, with the manuscript's product convention. -/ +def permute (σ : Equiv.Perm I) : Equiv.Perm (I → A) where + toFun w i := w (σ⁻¹ i) + invFun w i := w (σ i) + left_inv w := by ext i; simp + right_inv w := by ext i; simp + +omit [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] in +lemma permute_mul (σ τ : Equiv.Perm I) : + permute (A := A) (σ*τ) = permute σ * permute τ := by + ext w i; simp [permute] + +omit [Fintype A] [DecidableEq I] in +lemma count_le (w : I → A) (a : A) : count w a ≤ Fintype.card I := Fintype.card_subtype_le _ + +omit [DecidableEq I] in +lemma sum_count (w : I → A) : ∑ a, count w a = Fintype.card I := by + classical + simpa only [count, Fintype.card_sigma] using Fintype.card_congr (Equiv.sigmaFiberEquiv w) + +omit [Fintype A] [DecidableEq I] in +lemma counts_eq_exists_perm {u w : I → A} (h : count u = count w) : + ∃ σ : Equiv.Perm I, permute σ u = w := by + let e (a : A) : {i : I // u i = a} ≃ {i : I // w i = a} := + Fintype.equivOfCardEq (congrFun h a) + let σ : Equiv.Perm I := Equiv.ofFiberEquiv e + refine ⟨σ, ?_⟩ + ext i + have hi : w (σ (σ⁻¹ i)) = u (σ⁻¹ i) := Equiv.ofFiberEquiv_map e (σ⁻¹ i) + change u (σ⁻¹ i) = w i + simpa using hi.symm + +/- Word-preserving permutations and independent permutations of its fibers +are literally equivalent finite sets. This yields the factorial frame moments. -/ +def fiberPermEquiv (w : I → A) : + {σ : Equiv.Perm I // ∀ i, w (σ i) = w i} ≃ (∀ a : A, Equiv.Perm {i : I // w i = a}) where + toFun σ a := σ.val.subtypePerm (fun i => by rw [σ.property i]) + invFun τ := ⟨Equiv.ofFiberEquiv τ, Equiv.ofFiberEquiv_map τ⟩ + left_inv σ := by + apply Subtype.ext + ext i + rfl + right_inv τ := by + funext a + apply Equiv.ext + rintro ⟨i,hi⟩ + apply Subtype.ext + subst a + rfl + +lemma card_wordStabilizer (w : I → A) : + Fintype.card {σ : Equiv.Perm I // ∀ i, w (σ i) = w i} = + ∏ a : A, (count w a).factorial := by + rw [Fintype.card_congr (fiberPermEquiv w), Fintype.card_pi] + simp only [Fintype.card_perm, count] + +/- A transporter fiber is a coset of the literal word stabilizer. -/ +def transporterEquiv (u w : I → A) (σ : Equiv.Perm I) (hσ : permute σ u = w) : + {g : Equiv.Perm I // permute g u = w} ≃ + {g : Equiv.Perm I // ∀ i, u (g i) = u i} where + toFun g := ⟨σ⁻¹*g.val, by + intro i + have hg : u (g.val⁻¹ (g.val i)) = w (g.val i) := congrFun g.property (g.val i) + have hs : u (σ⁻¹ (g.val i)) = w (g.val i) := congrFun hσ (g.val i) + simpa using hs.trans hg.symm⟩ + invFun g := ⟨σ*g.val, by + ext i + change u (g.val⁻¹ (σ⁻¹ i)) = w i + have hg := g.property (g.val⁻¹ (σ⁻¹ i)) + have hs : u (σ⁻¹ i) = w i := congrFun hσ i + have hh : u (g.val⁻¹ (σ⁻¹ i)) = u (σ⁻¹ i) := by simpa using hg.symm + exact hh.trans hs⟩ + left_inv g := Subtype.ext (by simp) + right_inv g := Subtype.ext (by simp) + +omit [Fintype A] [DecidableEq I] in +lemma permute_count (σ : Equiv.Perm I) (w : I → A) : count (permute σ w) = count w := by + ext a + apply Fintype.card_congr + exact + { toFun := fun i => ⟨σ⁻¹ i.val, i.property⟩ + invFun := fun i => ⟨σ i.val, by simpa [permute] using i.property⟩ + left_inv := fun i => Subtype.ext (by simp) + right_inv := fun i => Subtype.ext (by simp) } + +lemma card_transporter (u w : I → A) : + Fintype.card {g : Equiv.Perm I // permute g u = w} = + if count u = count w then ∏ a, (count u a).factorial else 0 := by + split_ifs with h + · obtain ⟨σ,hσ⟩ := counts_eq_exists_perm h + rw [Fintype.card_congr (transporterEquiv u w σ hσ), card_wordStabilizer] + · have : IsEmpty {g : Equiv.Perm I // permute g u = w} := + ⟨fun g => h (by rw [← g.property, permute_count])⟩ + exact Fintype.card_eq_zero + +/- The finite moment matrix which will be realized by actual radial Gamma +variables and root phases rather than an assumed de Finetti density. -/ +def momentFrame : Matrix (I → A) (I → A) ℂ := fun u w => + if count u = count w then (∏ a, ((count u a).factorial : ℂ)) else 0 + +lemma momentFrame_eq_perm_sum : + (momentFrame (I := I) (A := A)) = + ∑ σ : Equiv.Perm I, (fun u w => if permute σ w = u then (1 : ℂ) else 0 : Matrix _ _ ℂ) := by + apply Matrix.ext + intro u w + simp only [momentFrame, Finset.sum_apply] + rw [← Finset.sum_filter] + simp only [Finset.sum_const, nsmul_eq_mul, mul_one, ← Fintype.card_subtype, + card_transporter] + split_ifs with h hw <;> simp_all [eq_comm, Nat.cast_prod] +end CoordinateSweeps.OrdinaryTensor + +namespace CoordinateSweeps.OrdinaryTensor + +/- A factorial ratio is bounded by the largest factor; used to avoid +any assumed entropy/Stirling estimate in the empirical postselection measure. -/ +lemma factorial_step_upper (t k : ℕ) : (t+k).factorial ≤ t.factorial * (t+k)^k := by + induction k with + | zero => simp + | succ k ih => + calc + (t+(k+1)).factorial = (t+k+1)*(t+k).factorial := by rw [← Nat.add_assoc, Nat.factorial_succ] + _ ≤ (t+k+1)*(t.factorial*(t+k)^k) := Nat.mul_le_mul_left _ ih + _ ≤ (t+k+1)*(t.factorial*(t+k+1)^k) := + Nat.mul_le_mul_left _ (Nat.mul_le_mul_left _ (Nat.pow_le_pow_left (by omega) _)) + _ = t.factorial*(t+(k+1))^(k+1) := by rw [pow_succ]; ring + +/- For any integral Poisson mean n, n is a mode. This elementary exact +inequality is the only numerical ingredient for the finite tensor mixture. -/ +lemma factorial_mode (n t : ℕ) : n^t * n.factorial ≤ n^n * t.factorial := by + rcases le_total t n with h | h + · have hu : n.factorial ≤ t.factorial*n^(n-t) := by + simpa only [Nat.add_sub_of_le h] using factorial_step_upper t (n-t) + calc + _ ≤ n^t * (t.factorial*n^(n-t)) := Nat.mul_le_mul_left _ hu + _ = n^n*t.factorial := by rw [mul_left_comm, ← pow_add, Nat.add_sub_of_le h]; ring + · have hl := Nat.factorial_mul_pow_sub_le_factorial h + calc + n^t*n.factorial = n^n*(n.factorial*n^(t-n)) := by + rw [mul_left_comm, ← pow_add, Nat.add_sub_of_le h]; ring + _ ≤ n^n*t.factorial := Nat.mul_le_mul_left _ hl + +variable {I A : Type*} [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] + +omit [DecidableEq I] in +lemma prod_word_eq_counts {R : Type*} [CommMonoid R] (r : A → R) (w : I → A) : + (∏ i, r (w i)) = ∏ a, r a ^ count w a := by + rw [← Finset.prod_fiberwise' Finset.univ w r] + simp only [Finset.prod_const, ← Fintype.card_subtype, count] + +/- Exact sigma decomposition of a word orbit and its transporter fibers. -/ +def orbitFiberEquiv (u : I → A) : + (Σ w : {w : I → A // count w = count u}, {σ : Equiv.Perm I // permute σ u = w.val}) ≃ + Equiv.Perm I where + toFun x := x.2.val + invFun σ := ⟨⟨permute σ u, permute_count σ u⟩,⟨σ,rfl⟩⟩ + left_inv := by + rintro ⟨⟨w,hw⟩,⟨σ,hσ⟩⟩ + change permute σ u = w at hσ + subst w + rfl + right_inv σ := rfl + +lemma orbit_card_mul_factorials (u : I → A) : + Fintype.card {w : I → A // count w = count u} * (∏ a, (count u a).factorial) = + (Fintype.card I).factorial := by + have he := Fintype.card_congr (orbitFiberEquiv u) + rw [Fintype.card_sigma, Fintype.card_perm] at he + calc + _ = ∑ _w : {w : I → A // count w = count u}, (∏ a, (count u a).factorial) := by + simp only [Finset.sum_const, Finset.card_univ, smul_eq_mul] + _ = ∑ w : {w : I → A // count w = count u}, + Fintype.card {σ : Equiv.Perm I // permute σ u = w.val} := by + apply Finset.sum_congr rfl + intro w _ + rw [card_transporter, ite_eq_left w.property.symm] + _ = _ := he + +/- Histogram space is an actual finite set of attained occupancies. -/ +abbrev Histogram (I A : Type*) [Fintype I] [Fintype A] [DecidableEq A] := + Set.range (count (I := I) (A := A)) + +instance : Finite (Histogram I A) := Finite.Set.finite_range _ +noncomputable instance : Fintype (Histogram I A) := Fintype.ofFinite _ + +def histogram (w : I → A) : Histogram I A := ⟨count w, w, rfl⟩ + +omit [DecidableEq I] in +lemma histogram_surjective : Function.Surjective (histogram (I := I) (A := A)) := by + rintro ⟨h,⟨w,hw⟩⟩ + exact ⟨w,Subtype.ext hw⟩ + +omit [DecidableEq I] in +lemma histogram_card_le : Fintype.card (Histogram I A) ≤ (Fintype.card I+1)^Fintype.card A := by + let f : Histogram I A → (A → Fin (Fintype.card I+1)) := fun h a => + ⟨h.val a, by obtain ⟨w,hw⟩ := h.property; rw [← hw]; exact Nat.lt_succ_of_le (count_le w a)⟩ + have hf : Function.Injective f := by + intro h k he + apply Subtype.ext + funext a + exact congrArg Fin.val (congrFun he a) + simpa only [Fintype.card_fun, Fintype.card_fin] using Fintype.card_le_of_injective f hf + +/- The individual multinomial type of a word, evaluated at any integer weights. -/ +def typeWeight (r : A → ℕ) (u : I → A) : ℕ := + Fintype.card {w : I → A // count w = count u} * ∏ a, r a ^ count u a + +lemma typeWeight_mul_factorials (r : A → ℕ) (u : I → A) : + typeWeight r u * (∏ a, (count u a).factorial) = + (Fintype.card I).factorial * (∏ a, r a ^ count u a) := by + rw [typeWeight, mul_right_comm, orbit_card_mul_factorials] + +/- Empirical occupancies maximize their own exact multinomial type weight. -/ +lemma typeWeight_empirical_max (u w : I → A) : typeWeight (count u) w ≤ typeWeight (count u) u := by + have hu : 0 < ∏ a : A, (count u a).factorial := + Finset.prod_pos (fun a _ => Nat.factorial_pos _) + have hw : 0 < ∏ a : A, (count w a).factorial := + Finset.prod_pos (fun a _ => Nat.factorial_pos _) + apply Nat.le_of_mul_le_mul_right (c := ∏ a, (count w a).factorial) _ hw + apply Nat.le_of_mul_le_mul_right (c := ∏ a, (count u a).factorial) _ hu + calc + _ = (Fintype.card I).factorial * + ((∏ a, count u a ^ count w a) * (∏ a, (count u a).factorial)) := by + rw [typeWeight_mul_factorials, mul_assoc] + _ ≤ (Fintype.card I).factorial * + ((∏ a, count u a ^ count u a) * (∏ a, (count w a).factorial)) := by + apply Nat.mul_le_mul_left + rw [← Finset.prod_mul_distrib, ← Finset.prod_mul_distrib] + exact Finset.prod_le_prod (fun a _ => factorial_mode (count u a) (count w a)) + _ = _ := by rw [mul_right_comm (typeWeight _ _), typeWeight_mul_factorials, mul_assoc] + +/- Type weight on the finite, attained histogram space. -/ +def histogramWeight (r : A → ℕ) (h : Histogram I A) : ℕ := + Fintype.card {w : I → A // histogram w = h} * ∏ a, r a ^ h.val a + +lemma histogramWeight_mk (r : A → ℕ) (u : I → A) : + histogramWeight r (histogram u) = typeWeight r u := by + unfold histogramWeight typeWeight + congr 1 + apply Fintype.card_congr + exact { toFun := fun w => ⟨w.val, congrArg Subtype.val w.property⟩ + invFun := fun w => ⟨w.val, Subtype.ext w.property⟩ + left_inv := fun w => Subtype.ext rfl + right_inv := fun w => Subtype.ext rfl } + +lemma sum_histogramWeight (r : A → ℕ) : + (∑ h : Histogram I A, histogramWeight r h) = (∑ a, r a)^Fintype.card I := by + have ht := Finset.sum_prod_piFinset (Finset.univ : Finset A) (fun _i : I => r) + simp only [Fintype.piFinset_univ, Finset.prod_const, Finset.card_univ] at ht + rw [← ht, ← Fintype.sum_fiberwise (histogram (I := I) (A := A))] + apply Finset.sum_congr rfl + intro h _ + change Fintype.card {w : I → A // histogram w = h} * (∏ a, r a^h.val a) = + ∑ w : {w : I → A // histogram w = h}, ∏ i, r (w.val i) + have he (w : {w : I → A // histogram w = h}) : + (∏ i, r (w.val i)) = ∏ a, r a ^ h.val a := by + rw [prod_word_eq_counts, show count w.val = h.val from congrArg Subtype.val w.property] + simp_rw [he] + simp only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, Nat.cast_id] + +/- Exact polynomial empirical multinomial lower bound. It includes zero +occupancies and avoids Stirling errors and asymptotic hypotheses. -/ +theorem empirical_type_mass (u : I → A) : + (Fintype.card I)^Fintype.card I ≤ + (Fintype.card I+1)^Fintype.card A * typeWeight (count u) u := by + have he := sum_histogramWeight (I := I) (count u) + rw [sum_count] at he + calc + _ = ∑ h : Histogram I A, histogramWeight (count u) h := he.symm + _ ≤ ∑ _h : Histogram I A, typeWeight (count u) u := by + apply Finset.sum_le_sum + intro h _ + obtain ⟨w,rfl⟩ := histogram_surjective h + rw [histogramWeight_mk] + exact typeWeight_empirical_max u w + _ = Fintype.card (Histogram I A) * typeWeight (count u) u := by + simp only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, Nat.cast_id] + _ ≤ _ := Nat.mul_le_mul_right _ (histogram_card_le (I := I) (A := A)) +end CoordinateSweeps.OrdinaryTensor + +namespace CoordinateSweeps.OrdinaryTensor +open AddChar +variable {I A : Type*} [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] + +/- Finite independent root phases. The modulus is strictly larger than +any occupancy, so it distinguishes every histogram without an analytic limit. -/ +abbrev PhaseSpace (I A : Type*) [Fintype I] := A → ZMod (Fintype.card I+1) + +def wordPhase (t : PhaseSpace I A) (w : I → A) : ℂ := + ∏ a, ZMod.stdAddChar (t a * (count w a : ZMod (Fintype.card I+1))) + +omit [DecidableEq I] in +lemma wordPhase_eq_prod (t : PhaseSpace I A) (w : I → A) : + wordPhase t w = ∏ i, ZMod.stdAddChar (t (w i)) := by + rw [prod_word_eq_counts (fun a : A => ZMod.stdAddChar (t a)) w] + unfold wordPhase + apply Finset.prod_congr rfl + intro a _ + simpa only [nsmul_eq_mul, mul_comm] using + (map_nsmul_eq_pow (ZMod.stdAddChar (N := Fintype.card I+1)) (count w a) (t a)) + +omit [DecidableEq I] in +lemma phase_conjugate_sum (c d : A → ℕ) (hc : ∀ a, c a ≤ Fintype.card I) + (hd : ∀ a, d a ≤ Fintype.card I) : + (∑ t : PhaseSpace I A, + (∏ a, ZMod.stdAddChar (t a * (c a : ZMod (Fintype.card I+1)))) * + star (∏ a, ZMod.stdAddChar (t a * (d a : ZMod (Fintype.card I+1))))) = + if c = d then (Fintype.card (PhaseSpace I A) : ℂ) else 0 := by + simp only [star_prod] + simp_rw [← Finset.prod_mul_distrib, Complex.star_def, ← AddChar.map_neg_eq_conj, + ← map_add_eq_mul, ← sub_eq_add_neg, ← mul_sub] + have hf := Finset.sum_prod_piFinset (Finset.univ : Finset (ZMod (Fintype.card I+1))) + (fun a x => ZMod.stdAddChar (x * ((c a : ZMod (Fintype.card I+1)) - (d a : ZMod (Fintype.card I+1))))) + simp only [Fintype.piFinset_univ] at hf + rw [hf] + simp_rw [AddChar.sum_mulShift _ (ZMod.isPrimitive_stdAddChar _)] + have he (a : A) : (c a : ZMod (Fintype.card I+1)) - (d a : ZMod (Fintype.card I+1)) = 0 ↔ c a = d a := by + rw [sub_eq_zero, ZMod.natCast_eq_natCast_iff'] + rw [Nat.mod_eq_of_lt (Nat.lt_succ_of_le (hc a)), Nat.mod_eq_of_lt (Nat.lt_succ_of_le (hd a))] + simp_rw [he] + by_cases h : c = d + · simp [h, ZMod.card] + · rw [ite_eq_right h] + obtain ⟨a,ha⟩ := Function.ne_iff.mp h + exact Finset.prod_eq_zero (Finset.mem_univ a) (by simp [ha]) + +/- Exact finite orthogonality of different empirical type phases. -/ +omit [DecidableEq I] in +lemma wordPhase_orthogonality (u w : I → A) : + (∑ t : PhaseSpace I A, wordPhase t u * star (wordPhase t w)) = + if count u = count w then (Fintype.card (PhaseSpace I A) : ℂ) else 0 := + phase_conjugate_sum (count u) (count w) (count_le u) (count_le w) + +/- Every root-phase component has unit modulus. -/ +omit [DecidableEq I] in +lemma wordPhase_star_mul (t : PhaseSpace I A) (w : I → A) : + wordPhase t w * star (wordPhase t w) = 1 := by + simp only [wordPhase, star_prod, ← Finset.prod_mul_distrib] + apply Finset.prod_eq_one + intro a _ + rw [Complex.star_def, ← AddChar.map_neg_eq_conj, ← map_add_eq_mul] + simp +end CoordinateSweeps.OrdinaryTensor + +namespace CoordinateSweeps.OrdinaryTensor +open AddChar +open scoped ComplexOrder +variable {I A : Type*} [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] + +def tensorVector (z : A → ℂ) (w : I → A) : ℂ := ∏ i, z (w i) +def outer {J : Type*} (v : J → ℂ) : Matrix J J ℂ := Matrix.vecMulVec v (star v) + +lemma outer_posSemidef {J : Type*} [Finite J] (v : J → ℂ) : (outer v).PosSemidef := + Matrix.posSemidef_vecMulVec_self_star v + +lemma outer_apply {J : Type*} (v : J → ℂ) (i j : J) : outer v i j = v i * star (v j) := rfl + +/- Empirical-site amplitudes. Their exact squared norm is one when there is +at least one slot. Zero-count letters are allowed and have zero amplitude. -/ +def empiricalVector (h : Histogram I A) (t : PhaseSpace I A) (a : A) : ℂ := + (Real.sqrt ((h.val a : ℝ)/Fintype.card I) : ℂ) * ZMod.stdAddChar (t a) + +def amplitude (h : Histogram I A) (w : I → A) : ℝ := + ∏ i, Real.sqrt ((h.val (w i) : ℝ)/Fintype.card I) + +omit [DecidableEq I] in +lemma char_star_mul (t : ZMod (Fintype.card I+1)) : + ZMod.stdAddChar t * star (ZMod.stdAddChar t) = 1 := by + rw [Complex.star_def, ← AddChar.map_neg_eq_conj, ← map_add_eq_mul] + simp + +omit [DecidableEq I] in +lemma empiricalVector_square (h : Histogram I A) (t : PhaseSpace I A) (a : A) : + empiricalVector h t a * star (empiricalVector h t a) = + (((h.val a : ℝ)/Fintype.card I : ℝ) : ℂ) := by + unfold empiricalVector + simp only [star_mul, RCLike.star_def, Complex.conj_ofReal] + calc + _ = (Real.sqrt ((h.val a : ℝ)/Fintype.card I) : ℂ)^2 * + (ZMod.stdAddChar (t a) * star (ZMod.stdAddChar (t a))) := by + simp only [Complex.star_def]; ring + _ = _ := by + rw [char_star_mul, mul_one, ← Complex.ofReal_pow, Real.sq_sqrt (by positivity)] + +omit [DecidableEq I] in +lemma empiricalVector_unit (hn : 0 < Fintype.card I) (h : Histogram I A) (t : PhaseSpace I A) : + (∑ a, empiricalVector h t a * star (empiricalVector h t a)) = 1 := by + simp_rw [empiricalVector_square] + rw [← Complex.ofReal_sum, ← Finset.sum_div] + obtain ⟨w,hw⟩ := h.property + rw [← hw, ← Nat.cast_sum, sum_count, div_self (Nat.cast_ne_zero.mpr (Nat.ne_of_gt hn))] + rfl + +omit [DecidableEq I] in +lemma amplitude_eq_counts (h : Histogram I A) (w : I → A) : + amplitude h w = ∏ a, (Real.sqrt ((h.val a : ℝ)/Fintype.card I)) ^ count w a := +by + unfold amplitude + exact prod_word_eq_counts (fun a => Real.sqrt ((h.val a : ℝ)/Fintype.card I)) w + +omit [DecidableEq I] in +lemma amplitude_congr (h : Histogram I A) {u w : I → A} (he : count u = count w) : + amplitude h u = amplitude h w := by rw [amplitude_eq_counts, amplitude_eq_counts, he] + +omit [DecidableEq I] in +lemma tensorVector_empirical (h : Histogram I A) (t : PhaseSpace I A) (w : I → A) : + tensorVector (empiricalVector h t) w = (amplitude h w : ℂ) * wordPhase t w := by + rw [wordPhase_eq_prod] + simp only [tensorVector, empiricalVector, amplitude, Complex.ofReal_prod, Finset.prod_mul_distrib] + +omit [DecidableEq I] in +lemma amplitude_square (h : Histogram I A) (w : I → A) : + amplitude h w ^ 2 = (∏ a, (h.val a : ℝ) ^ count w a) / + (Fintype.card I : ℝ) ^ Fintype.card I := by + rw [amplitude_eq_counts, ← Finset.prod_pow] + simp_rw [← pow_mul, mul_comm _ 2, pow_mul, Real.sq_sqrt (by positivity : + 0 ≤ (h.val _ : ℝ)/Fintype.card I), div_pow] + rw [Finset.prod_div_distrib, Finset.prod_pow_eq_pow_sum, sum_count] + +/- Finite phase average of actual pure product states. -/ +def phaseFrame (h : Histogram I A) : Matrix (I → A) (I → A) ℂ := + (Fintype.card (PhaseSpace I A) : ℂ)⁻¹ • + ∑ t : PhaseSpace I A, outer (tensorVector (empiricalVector h t)) + +omit [DecidableEq I] in +lemma phaseSpace_card_pos : 0 < Fintype.card (PhaseSpace I A) := by + rw [Fintype.card_fun, ZMod.card] + positivity + +omit [DecidableEq I] in +lemma phaseFrame_posSemidef (h : Histogram I A) : (phaseFrame h).PosSemidef := by + apply Matrix.PosSemidef.smul + · exact Matrix.posSemidef_sum _ (fun t _ => outer_posSemidef _) + · exact inv_nonneg.mpr (Nat.cast_nonneg _) + +omit [DecidableEq I] in +lemma phaseFrame_entry (h : Histogram I A) (u w : I → A) : + phaseFrame h u w = if count u = count w then ((amplitude h u : ℂ)^2) else 0 := by + simp only [phaseFrame, Matrix.smul_apply, smul_eq_mul, Matrix.sum_apply, outer_apply, + tensorVector_empirical, star_mul, RCLike.star_def, Complex.conj_ofReal] + have he (t : PhaseSpace I A) : + ((amplitude h u : ℂ)*wordPhase t u) * + (star (wordPhase t w)*(amplitude h w : ℂ)) = + ((amplitude h u : ℂ)*(amplitude h w : ℂ)) * (wordPhase t u * star (wordPhase t w)) := by ring + simp only [← Complex.star_def] + simp_rw [he] + rw [← Finset.mul_sum, wordPhase_orthogonality] + split_ifs with hc + · rw [amplitude_congr h hc] + have hn : (Fintype.card (PhaseSpace I A) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr (Nat.ne_of_gt phaseSpace_card_pos) + field_simp + · simp +end CoordinateSweeps.OrdinaryTensor + +namespace CoordinateSweeps.OrdinaryTensor +open scoped ComplexOrder +variable {I A : Type*} [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] + +def orbitSize (h : Histogram I A) : ℕ := Fintype.card {w : I → A // histogram w = h} +def representative (h : Histogram I A) : I → A := Classical.choose h.property + +omit [DecidableEq I] in +lemma count_representative (h : Histogram I A) : count (representative h) = h.val := + Classical.choose_spec h.property +omit [DecidableEq I] in +lemma histogram_representative (h : Histogram I A) : histogram (representative h) = h := + Subtype.ext (count_representative h) + +lemma orbitSize_pos (h : Histogram I A) : 0 < orbitSize h := by + have : Nonempty {w : I → A // histogram w = h} := ⟨⟨representative h, histogram_representative h⟩⟩ + exact Fintype.card_pos + +lemma orbitSize_mk (w : I → A) : + orbitSize (histogram w) = Fintype.card {u : I → A // count u = count w} := by + have he := histogramWeight_mk (fun _ : A => 1) w + simpa only [histogramWeight,typeWeight,one_pow,Finset.prod_const_one,mul_one,orbitSize] using he + +def block (h : Histogram I A) : Matrix (I → A) (I → A) ℂ := + outer (fun w => if histogram w = h then 1 else 0) + +omit [DecidableEq I] in +lemma block_posSemidef (h : Histogram I A) : (block h).PosSemidef := outer_posSemidef _ + +omit [DecidableEq I] in +lemma block_entry (h : Histogram I A) (u w : I → A) : + block h u w = if histogram u = h ∧ histogram w = h then (1 : ℂ) else 0 := by + simp only [block,outer_apply] + split_ifs <;> simp_all + +/- Orthogonal projection onto vectors invariant under ordinary slot +permutations, implemented by their exact histogram blocks. -/ +def symProjector : Matrix (I → A) (I → A) ℂ := + ∑ h : Histogram I A, (orbitSize h : ℂ)⁻¹ • block h + +lemma symProjector_posSemidef : (symProjector (I := I) (A := A)).PosSemidef := by + apply Matrix.posSemidef_sum + intro h _ + exact (block_posSemidef h).smul (inv_nonneg.mpr (Nat.cast_nonneg _)) + +lemma symProjector_entry (u w : I → A) : symProjector u w = + if histogram u = histogram w then (orbitSize (histogram u) : ℂ)⁻¹ else 0 := by + simp only [symProjector, Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, block_entry] + rw [Finset.sum_eq_single (histogram u)] + · by_cases h : histogram u = histogram w <;> simp [h,eq_comm] + · intro h _ hne + have he : histogram u ≠ h := Ne.symm hne + simp [he] + · simp + +lemma symProjector_mulVec_of_constant (v : (I → A) → ℂ) + (hv : ∀ u w, count u = count w → v u = v w) : + (symProjector (I := I) (A := A)).mulVec v = v := by + ext u + simp only [Matrix.mulVec, dotProduct, symProjector_entry, ite_mul, zero_mul] + rw [← Finset.sum_filter] + have he (w : I → A) (hw : w ∈ Finset.univ.filter (fun w => histogram u = histogram w)) : v w = v u := + (hv u w (congrArg Subtype.val (Finset.mem_filter.mp hw).2)).symm + rw [Finset.sum_congr rfl (fun w hw => congrArg ((orbitSize (histogram u) : ℂ)⁻¹ * ·) (he w hw))] + simp only [Finset.sum_const, nsmul_eq_mul, ← Fintype.card_subtype] + have hc : Fintype.card {w : I → A // histogram u = histogram w} = orbitSize (histogram u) := by + unfold orbitSize + apply Fintype.card_congr + exact { toFun := fun w => ⟨w.val,w.property.symm⟩ + invFun := fun w => ⟨w.val,w.property.symm⟩ + left_inv := fun w => Subtype.ext rfl + right_inv := fun w => Subtype.ext rfl } + rw [hc] + have ho : (orbitSize (histogram u) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr (Nat.ne_of_gt (orbitSize_pos _)) + field_simp + +lemma symProjector_idempotent : (symProjector (I := I) (A := A)) * symProjector = symProjector := by + ext u w + have he := symProjector_mulVec_of_constant (fun v : I → A => symProjector v w) (fun v v' h => by + have hh : histogram v = histogram v' := Subtype.ext h + simp only [symProjector_entry, hh]) + exact congrFun he u + +def histogramAmplitude (h k : Histogram I A) : ℝ := amplitude h (representative k) + +omit [DecidableEq I] in +lemma histogramAmplitude_mk (h : Histogram I A) (w : I → A) : + histogramAmplitude h (histogram w) = amplitude h w := by + apply amplitude_congr + exact count_representative _ + +omit [DecidableEq I] in +lemma phaseFrame_blocks (h : Histogram I A) : + phaseFrame h = ∑ k : Histogram I A, ((histogramAmplitude h k : ℂ)^2) • block k := by + ext u w + rw [phaseFrame_entry] + simp only [Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, block_entry] + rw [Finset.sum_eq_single (histogram u)] + · have he : (count u = count w) ↔ histogram w = histogram u := + ⟨fun h => Subtype.ext h.symm, fun h => (congrArg Subtype.val h).symm⟩ + rw [histogramAmplitude_mk] + simp only [true_and, he] + split_ifs <;> simp + · intro k _ hk + have he : histogram u ≠ k := Ne.symm hk + simp [he] + · simp + +/- Polynomial inverse-orbit bound for the **actual** empirical phase frame. -/ +lemma inverse_orbit_le_empirical (hn : 0 < Fintype.card I) (h : Histogram I A) : + (orbitSize h : ℝ)⁻¹ ≤ ((Fintype.card I+1)^Fintype.card A : ℕ) * histogramAmplitude h h ^ 2 := by + obtain ⟨u,rfl⟩ := histogram_surjective h + rw [histogramAmplitude_mk, orbitSize_mk, amplitude_square] + have ho : (0 : ℝ) < Fintype.card {w : I → A // count w = count u} := by + simpa only [← orbitSize_mk] using (Nat.cast_pos.mpr (orbitSize_pos (histogram u)) : + (0 : ℝ) < orbitSize (histogram u)) + have hn' : (0 : ℝ) < (Fintype.card I : ℝ)^Fintype.card I := pow_pos (Nat.cast_pos.mpr hn) _ + have hm := empirical_type_mass u + have hr : (Fintype.card I : ℝ)^Fintype.card I ≤ + (((Fintype.card I+1)^Fintype.card A : ℕ) : ℝ) * + ((Fintype.card {w : I → A // count w = count u} : ℝ) * ∏ a, (count u a : ℝ)^count u a) := by + exact_mod_cast hm + change _ ≤ (((Fintype.card I+1)^Fintype.card A : ℕ) : ℝ) * + ((∏ a, (count u a : ℝ)^count u a) / (Fintype.card I : ℝ)^Fintype.card I) + rw [← mul_div_assoc, le_div_iff₀ hn', inv_mul_eq_div, div_le_iff₀ ho] + nlinarith [hr] +end CoordinateSweeps.OrdinaryTensor + +namespace CoordinateSweeps.OrdinaryTensor +open scoped ComplexOrder +variable {I A : Type*} [Fintype I] [Fintype A] [DecidableEq I] [DecidableEq A] + +omit [DecidableEq I] in +lemma phaseFrame_sum_blocks : + (∑ h : Histogram I A, phaseFrame h) = ∑ k : Histogram I A, + (∑ h : Histogram I A, (histogramAmplitude h k : ℂ)^2) • block k := by + simp_rw [phaseFrame_blocks] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro k _ + exact Finset.sum_smul.symm + +/- Constructive finite postselection before normalizing the histogram sum. -/ +theorem phaseFrame_sum_domination (hn : 0 < Fintype.card I) : + ((((Fintype.card I+1)^Fintype.card A : ℕ) : ℂ) • + (∑ h : Histogram I A, phaseFrame h) - symProjector).PosSemidef := by + let P : ℕ := (Fintype.card I+1)^Fintype.card A + have hc (k : Histogram I A) : + 0 ≤ (P : ℝ) * (∑ h : Histogram I A, histogramAmplitude h k ^ 2) - (orbitSize k : ℝ)⁻¹ := by + apply sub_nonneg.mpr + apply (inverse_orbit_le_empirical hn k).trans + exact mul_le_mul_of_nonneg_left + (Finset.single_le_sum (fun h _ => sq_nonneg (histogramAmplitude h k)) (Finset.mem_univ k)) + (Nat.cast_nonneg P) + have he : (P : ℂ) • (∑ h : Histogram I A, phaseFrame h) - symProjector = + ∑ k : Histogram I A, + (((P : ℝ) * (∑ h : Histogram I A, histogramAmplitude h k ^ 2) - + (orbitSize k : ℝ)⁻¹ : ℝ) : ℂ) • block k := by + rw [phaseFrame_sum_blocks, symProjector, Finset.smul_sum, ← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro k _ + rw [smul_smul, ← sub_smul] + congr 1 + push_cast + rfl + rw [show (((Fintype.card I+1)^Fintype.card A : ℕ) : ℂ) = (P : ℂ) from rfl, he] + apply Matrix.posSemidef_sum + intro k _ + exact (block_posSemidef k).smul (by exact_mod_cast hc k) + +instance [Nonempty A] : Nonempty (Histogram I A) := ⟨histogram (fun _ => Classical.arbitrary A)⟩ + +/- Literal finite average of empirical pure product tensors, grouped first +by histogram and then by independent roots. -/ +def finiteMixture : Matrix (I → A) (I → A) ℂ := + (Fintype.card (Histogram I A) : ℂ)⁻¹ • ∑ h : Histogram I A, phaseFrame h + +omit [DecidableEq I] in +lemma finiteMixture_posSemidef : (finiteMixture (I := I) (A := A)).PosSemidef := by + exact (Matrix.posSemidef_sum _ (fun h _ => phaseFrame_posSemidef h)).smul + (inv_nonneg.mpr (Nat.cast_nonneg _)) + +/- Finite, normalized tensor postselection with explicit polynomial overhead. +Every product in finiteMixture comes from squared-norm-one empirical vectors; +there is no de Finetti theorem or independent density assumption. -/ +theorem finite_postselection [Nonempty A] (hn : 0 < Fintype.card I) : + ((((Fintype.card I+1)^(2*Fintype.card A) : ℕ) : ℂ) • + (finiteMixture (I := I) (A := A)) - symProjector).PosSemidef := by + let P : ℕ := (Fintype.card I+1)^Fintype.card A + let H : ℕ := Fintype.card (Histogram I A) + have hH : (H : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr (Nat.ne_of_gt Fintype.card_pos) + have h := phaseFrame_sum_domination (I := I) (A := A) hn + have he : ((P*H : ℕ) : ℂ) • (finiteMixture (I := I) (A := A)) = + (P : ℂ) • ∑ h : Histogram I A, phaseFrame h := by + unfold finiteMixture + rw [smul_smul, Nat.cast_mul] + congr 1 + change (P : ℂ)*(H : ℂ)*(H : ℂ)⁻¹ = (P : ℂ) + field_simp + have hm : (P*H : ℕ) ≤ (Fintype.card I+1)^(2*Fintype.card A) := by + have hle := Nat.mul_le_mul_left P (histogram_card_le (I := I) (A := A)) + simpa only [P,H,← pow_two,← pow_mul, mul_comm 2] using hle + have hp : (0 : ℂ) ≤ (((Fintype.card I+1)^(2*Fintype.card A) : ℕ) : ℂ) - ((P*H : ℕ) : ℂ) := by + exact sub_nonneg.mpr (by exact_mod_cast hm) + have hh := (finiteMixture_posSemidef (I := I) (A := A)).smul hp + have hf := hh.add h + rw [← he] at hf + convert hf using 1 + module + +omit [DecidableEq A] in +lemma outer_tensorVector_trace (z : A → ℂ) : + Matrix.trace (outer (tensorVector (I := I) z)) = + (∑ a, z a * star (z a))^Fintype.card I := by + have ht := Finset.sum_prod_piFinset (Finset.univ : Finset A) + (fun _i : I => fun a : A => z a * star (z a)) + simp only [Fintype.piFinset_univ, Finset.prod_const, Finset.card_univ] at ht + change (∑ w : I → A, tensorVector z w * star (tensorVector z w)) = _ + simp only [tensorVector,star_prod,← Finset.prod_mul_distrib] + exact ht + +lemma phaseFrame_trace [Nonempty A] (hn : 0 < Fintype.card I) (h : Histogram I A) : + Matrix.trace (phaseFrame h) = 1 := by + rw [phaseFrame, Matrix.trace_smul, Matrix.trace_sum] + simp_rw [outer_tensorVector_trace, empiricalVector_unit hn, one_pow] + simp only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, mul_one, smul_eq_mul] + exact inv_mul_cancel₀ (Nat.cast_ne_zero.mpr (Nat.ne_of_gt phaseSpace_card_pos)) + +lemma finiteMixture_trace [Nonempty A] (hn : 0 < Fintype.card I) : + Matrix.trace (finiteMixture (I := I) (A := A)) = 1 := by + rw [finiteMixture, Matrix.trace_smul, Matrix.trace_sum] + simp_rw [phaseFrame_trace hn] + simp only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, mul_one, smul_eq_mul] + exact inv_mul_cancel₀ (Nat.cast_ne_zero.mpr (Nat.ne_of_gt Fintype.card_pos)) +end CoordinateSweeps.OrdinaryTensor + +/- Positive-operator inequalities needed for the actual purification proof +of signed tensor density domination (05:eq13), not standalone main results. -/ +noncomputable section +open scoped BigOperators ComplexOrder MatrixOrder +attribute [local instance] Classical.propDecidable +namespace CoordinateSweeps.OrdinaryTensor +variable {I A : Type*} [Fintype I] [DecidableEq I] [Fintype A] [DecidableEq A] + +omit [DecidableEq A] in +lemma outer_trace_nonneg (v : (I → A) → ℂ) : 0 ≤ Matrix.trace (outer v) := by + exact (outer_posSemidef v).trace_nonneg + +/- The ordinary finite postselection theorem applied to an actual invariant +purification vector, rather than an assumed projection inequality. -/ +theorem invariant_vector_postselection [Nonempty A] (hn : 0 < Fintype.card I) + (v : (I → A) → ℂ) (hv : ∀ σ : Equiv.Perm I, ∀ w, v (permute σ w) = v w) : + ((Matrix.trace (outer v) * ((Fintype.card I+1 : ℕ) : ℂ)^(2*Fintype.card A)) • + finiteMixture - outer v).PosSemidef := by + have hfix : symProjector.mulVec v = v := by + apply symProjector_mulVec_of_constant + intro u w he + obtain ⟨σ,hσ⟩ := counts_eq_exists_perm he + rw [← hσ,hv] + have hPA : symProjector * outer v = outer v := by + ext i j + rw [Matrix.mul_apply] + change (∑ k, symProjector i k * (v k * star (v j))) = v i * star (v j) + simp_rw [← mul_assoc] + rw [← Finset.sum_mul] + exact congrArg (fun z : ℂ => z*star (v j)) (congrFun hfix i) + have h1 := PositiveTensor.projection_trace_domination (outer v) symProjector + (outer_posSemidef v) symProjector_posSemidef.isHermitian symProjector_idempotent hPA + have h2 := (finite_postselection (I := I) (A := A) hn).smul (outer_trace_nonneg v) + have hh := h2.add h1 + simpa only [smul_sub,smul_smul,sub_add_sub_cancel,Nat.cast_pow] using hh +end CoordinateSweeps.OrdinaryTensor +namespace CoordinateSweeps.OrdinaryTensor +variable {I A : Type*} [Fintype I] [DecidableEq I] [Fintype A] [DecidableEq A] + +def rawMixture : Matrix (I → A) (I → A) ℂ := + ∑ h : Histogram I A, ∑ t : PhaseSpace I A, outer (tensorVector (empiricalVector h t)) +omit [DecidableEq I] in +lemma rawMixture_posSemidef : (rawMixture (I := I) (A := A)).PosSemidef := by + exact Matrix.posSemidef_sum _ (fun h _ => Matrix.posSemidef_sum _ (fun t _ => outer_posSemidef _)) +omit [DecidableEq I] in +lemma rawMixture_eq : rawMixture (I := I) (A := A) = + ((Fintype.card (Histogram I A) : ℂ)*(Fintype.card (PhaseSpace I A) : ℂ)) • finiteMixture := by + have hP : (Fintype.card (PhaseSpace I A) : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr phaseSpace_card_pos.ne' + by_cases hH : (Fintype.card (Histogram I A) : ℂ) = 0 + · have he : IsEmpty (Histogram I A) := Fintype.card_eq_zero_iff.mp (Nat.cast_eq_zero.mp hH) + let := he + simp [rawMixture,finiteMixture] + · unfold finiteMixture phaseFrame rawMixture + rw [smul_smul,← Finset.smul_sum,smul_smul] + have hc : ((Fintype.card (Histogram I A) : ℂ)*(Fintype.card (PhaseSpace I A) : ℂ)) * + (Fintype.card (Histogram I A) : ℂ)⁻¹ * (Fintype.card (PhaseSpace I A) : ℂ)⁻¹ = 1 := by field_simp + rw [hc,one_smul] +omit [DecidableEq I] in +lemma rawMixture_domination [Nonempty A] : + (rawMixture (I := I) (A := A) - finiteMixture).PosSemidef := by + rw [rawMixture_eq] + have hH : (1 : ℂ) ≤ (Fintype.card (Histogram I A) : ℂ) := by exact_mod_cast Fintype.card_pos + have hP : (1 : ℂ) ≤ (Fintype.card (PhaseSpace I A) : ℂ) := by exact_mod_cast phaseSpace_card_pos + have hp : (0 : ℂ) ≤ (Fintype.card (Histogram I A) : ℂ)*(Fintype.card (PhaseSpace I A) : ℂ)-1 := + sub_nonneg.mpr (one_le_mul_of_one_le_of_one_le hH hP) + simpa only [sub_smul,one_smul] using finiteMixture_posSemidef.smul hp +end CoordinateSweeps.OrdinaryTensor +end +end +end +open scoped Matrix.Norms.L2Operator + +end OAI diff --git a/lean/OAI/RepresentationTheory/TensorSquares/Arithmetic.lean b/lean/OAI/RepresentationTheory/TensorSquares/Arithmetic.lean index fd5a4c418efb13df7ce27f00dfa8e92410a5b017..2f29c2778873449804a45734ca276821ab4b7bd1 100644 --- a/lean/OAI/RepresentationTheory/TensorSquares/Arithmetic.lean +++ b/lean/OAI/RepresentationTheory/TensorSquares/Arithmetic.lean @@ -1,102 +1,102 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Basic - -namespace OAI - -/-! Parity-compatible triangular degrees and remainder bounds. -/ - -noncomputable section -open scoped TensorProduct -namespace UniversalTensorSquares - -def triangular (m : ℕ) : ℕ := m * (m + 1) / 2 - -lemma triangular_eq_staircase_card (m : ℕ) : triangular m = (Saxl.staircase m).card := - (Saxl.staircase_card m).symm - -@[simp] lemma triangular_zero : triangular 0 = 0 := rfl -@[simp] lemma triangular_one : triangular 1 = 1 := rfl - -lemma triangular_succ (m : ℕ) : triangular (m + 1) = triangular m + m + 1 := by - simpa only [triangular_eq_staircase_card, Nat.add_assoc] using Saxl.staircase_card_succ m - -lemma index_le_triangular (m : ℕ) : m ≤ triangular m := by - induction m with - | zero => simp - | succ m ih => rw [triangular_succ]; omega - -lemma triangular_add_three (m : ℕ) : triangular (m + 3) = triangular m + 3 * m + 6 := by - have h1 := triangular_succ m - have h2 := triangular_succ (m + 1) - have h3 := triangular_succ (m + 2) - norm_num [Nat.add_assoc] at h1 h2 h3 - omega - -def largestIndex (n : ℕ) : ℕ := - Nat.findGreatest (fun m => triangular m ≤ n ∧ triangular m % 2 = n % 2) n - -lemma largestIndex_spec (n : ℕ) : - triangular (largestIndex n) ≤ n ∧ triangular (largestIndex n) % 2 = n % 2 := by - unfold largestIndex - rcases Nat.mod_two_eq_zero_or_one n with hn | hn - · apply Nat.findGreatest_spec (P := fun m => triangular m ≤ n ∧ triangular m % 2 = n % 2) (m := 0) (Nat.zero_le n) - exact ⟨by simp, by simpa using hn.symm⟩ - · have h1 : 1 ≤ n := by omega - apply Nat.findGreatest_spec (P := fun m => triangular m ≤ n ∧ triangular m % 2 = n % 2) (m := 1) h1 - exact ⟨by simpa using h1, by simpa using hn.symm⟩ - -lemma largestIndex_maximal {n m : ℕ} (hmn : triangular m ≤ n) - (hp : triangular m % 2 = n % 2) : m ≤ largestIndex n := - Nat.le_findGreatest ((index_le_triangular m).trans hmn) ⟨hmn, hp⟩ - -def remainderPairs (n : ℕ) : ℕ := (n - triangular (largestIndex n)) / 2 - -lemma degree_decomposition (n : ℕ) : - triangular (largestIndex n) + 2 * remainderPairs n = n := by - have h := largestIndex_spec n - unfold remainderPairs - omega - -lemma odd_index_remainder_bound (n : ℕ) (hodd : largestIndex n % 2 = 1) : - 2 * remainderPairs n ≤ largestIndex n - 1 := by - have hs := (largestIndex_spec n).2 - have ht := triangular_succ (largestIndex n) - have hp : triangular (largestIndex n + 1) % 2 = n % 2 := by omega - have hn : n < triangular (largestIndex n + 1) := by - by_contra h - have hmax := largestIndex_maximal (Nat.ge_of_not_lt h) hp - omega - have hd := degree_decomposition n - omega - -lemma even_index_remainder_bound (n : ℕ) (heven : largestIndex n % 2 = 0) : - 2 * remainderPairs n ≤ 3 * largestIndex n + 4 := by - have hs := (largestIndex_spec n).2 - have ht := triangular_add_three (largestIndex n) - have hp : triangular (largestIndex n + 3) % 2 = n % 2 := by omega - have hn : n < triangular (largestIndex n + 3) := by - by_contra h - have hmax := largestIndex_maximal (Nat.ge_of_not_lt h) hp - omega - have hd := degree_decomposition n - omega - -lemma small_index_degree_bound (n : ℕ) (hsmall : largestIndex n < 9) : n ≤ 64 := by - by_contra hn - rcases Nat.mod_two_eq_zero_or_one n with heven | hodd - · have h66 : 66 ≤ n := by omega - have hmax : 11 ≤ largestIndex n := largestIndex_maximal - (by norm_num [triangular]; exact h66) - (by norm_num [triangular]; exact heven.symm) - omega - · have h45 : 45 ≤ n := by omega - have hmax : 9 ≤ largestIndex n := largestIndex_maximal - (by norm_num [triangular]; exact h45) - (by norm_num [triangular]; exact hodd.symm) - omega -end UniversalTensorSquares - - -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Basic + +namespace OAI + +/-! Parity-compatible triangular degrees and remainder bounds. -/ + +noncomputable section +open scoped TensorProduct +namespace UniversalTensorSquares + +def triangular (m : ℕ) : ℕ := m * (m + 1) / 2 + +lemma triangular_eq_staircase_card (m : ℕ) : triangular m = (Saxl.staircase m).card := + (Saxl.staircase_card m).symm + +@[simp] lemma triangular_zero : triangular 0 = 0 := rfl +@[simp] lemma triangular_one : triangular 1 = 1 := rfl + +lemma triangular_succ (m : ℕ) : triangular (m + 1) = triangular m + m + 1 := by + simpa only [triangular_eq_staircase_card, Nat.add_assoc] using Saxl.staircase_card_succ m + +lemma index_le_triangular (m : ℕ) : m ≤ triangular m := by + induction m with + | zero => simp + | succ m ih => rw [triangular_succ]; omega + +lemma triangular_add_three (m : ℕ) : triangular (m + 3) = triangular m + 3 * m + 6 := by + have h1 := triangular_succ m + have h2 := triangular_succ (m + 1) + have h3 := triangular_succ (m + 2) + norm_num [Nat.add_assoc] at h1 h2 h3 + omega + +def largestIndex (n : ℕ) : ℕ := + Nat.findGreatest (fun m => triangular m ≤ n ∧ triangular m % 2 = n % 2) n + +lemma largestIndex_spec (n : ℕ) : + triangular (largestIndex n) ≤ n ∧ triangular (largestIndex n) % 2 = n % 2 := by + unfold largestIndex + rcases Nat.mod_two_eq_zero_or_one n with hn | hn + · apply Nat.findGreatest_spec (P := fun m => triangular m ≤ n ∧ triangular m % 2 = n % 2) (m := 0) (Nat.zero_le n) + exact ⟨by simp, by simpa using hn.symm⟩ + · have h1 : 1 ≤ n := by omega + apply Nat.findGreatest_spec (P := fun m => triangular m ≤ n ∧ triangular m % 2 = n % 2) (m := 1) h1 + exact ⟨by simpa using h1, by simpa using hn.symm⟩ + +lemma largestIndex_maximal {n m : ℕ} (hmn : triangular m ≤ n) + (hp : triangular m % 2 = n % 2) : m ≤ largestIndex n := + Nat.le_findGreatest ((index_le_triangular m).trans hmn) ⟨hmn, hp⟩ + +def remainderPairs (n : ℕ) : ℕ := (n - triangular (largestIndex n)) / 2 + +lemma degree_decomposition (n : ℕ) : + triangular (largestIndex n) + 2 * remainderPairs n = n := by + have h := largestIndex_spec n + unfold remainderPairs + omega + +lemma odd_index_remainder_bound (n : ℕ) (hodd : largestIndex n % 2 = 1) : + 2 * remainderPairs n ≤ largestIndex n - 1 := by + have hs := (largestIndex_spec n).2 + have ht := triangular_succ (largestIndex n) + have hp : triangular (largestIndex n + 1) % 2 = n % 2 := by omega + have hn : n < triangular (largestIndex n + 1) := by + by_contra h + have hmax := largestIndex_maximal (Nat.ge_of_not_lt h) hp + omega + have hd := degree_decomposition n + omega + +lemma even_index_remainder_bound (n : ℕ) (heven : largestIndex n % 2 = 0) : + 2 * remainderPairs n ≤ 3 * largestIndex n + 4 := by + have hs := (largestIndex_spec n).2 + have ht := triangular_add_three (largestIndex n) + have hp : triangular (largestIndex n + 3) % 2 = n % 2 := by omega + have hn : n < triangular (largestIndex n + 3) := by + by_contra h + have hmax := largestIndex_maximal (Nat.ge_of_not_lt h) hp + omega + have hd := degree_decomposition n + omega + +lemma small_index_degree_bound (n : ℕ) (hsmall : largestIndex n < 9) : n ≤ 64 := by + by_contra hn + rcases Nat.mod_two_eq_zero_or_one n with heven | hodd + · have h66 : 66 ≤ n := by omega + have hmax : 11 ≤ largestIndex n := largestIndex_maximal + (by norm_num [triangular]; exact h66) + (by norm_num [triangular]; exact heven.symm) + omega + · have h45 : 45 ≤ n := by omega + have hmax : 9 ≤ largestIndex n := largestIndex_maximal + (by norm_num [triangular]; exact h45) + (by norm_num [triangular]; exact hodd.symm) + omega +end UniversalTensorSquares + + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/TensorSquares/Candidate.lean b/lean/OAI/RepresentationTheory/TensorSquares/Candidate.lean index a54da4412f2db37d12f71787c65d059629cad2b2..def8c1c3c978c0a97147eb990834b306851efe90 100644 --- a/lean/OAI/RepresentationTheory/TensorSquares/Candidate.lean +++ b/lean/OAI/RepresentationTheory/TensorSquares/Candidate.lean @@ -1,141 +1,141 @@ -import Mathlib -import OAI.RepresentationTheory.TensorSquares.Arithmetic -import OAI.RepresentationTheory.Saxl.Model - -namespace OAI - -/-! Self-conjugate Young diagrams with prescribed size. -/ - -noncomputable section -open scoped TensorProduct -namespace UniversalTensorSquares -def rectangle (a b : ℕ) : YoungDiagram where - cells := Finset.range a ×ˢ Finset.range b - isLowerSet := by - intro x y hxy hy - simp only [Finset.mem_coe, Finset.mem_product, Finset.mem_range] at hy ⊢ - exact ⟨lt_of_le_of_lt hxy.1 hy.1, lt_of_le_of_lt hxy.2 hy.2⟩ - -@[simp] lemma mem_rectangle {a b i j : ℕ} : - (i, j) ∈ rectangle a b ↔ i < a ∧ j < b := by - change (i, j) ∈ Finset.range a ×ˢ Finset.range b ↔ _ - simp - -def candidateArm (m r : ℕ) : YoungDiagram := - rectangle 1 (m + r / 2 + r % 2) ⊔ rectangle 2 (m - 1 + r / 2) - -def candidate (m r : ℕ) : YoungDiagram := - Saxl.staircase m ⊔ candidateArm m r ⊔ (candidateArm m r).transpose - -lemma mem_candidate {m r i j : ℕ} : - (i, j) ∈ candidate m r ↔ - (i + j < m ∨ - (i < 1 ∧ j < m + r / 2 + r % 2 ∨ i < 2 ∧ j < m - 1 + r / 2)) ∨ - (j < 1 ∧ i < m + r / 2 + r % 2 ∨ j < 2 ∧ i < m - 1 + r / 2) := by - simp only [candidate, candidateArm, YoungDiagram.mem_sup, Saxl.mem_staircase, - YoungDiagram.mem_transpose, Prod.swap_prod_mk, mem_rectangle] - -@[simp] lemma candidate_transpose (m r : ℕ) : (candidate m r).transpose = candidate m r := by - apply SetLike.ext - rintro ⟨i, j⟩ - simp only [YoungDiagram.mem_transpose, Prod.swap_prod_mk, mem_candidate] - omega - -@[simp] lemma candidate_zero (m : ℕ) : candidate m 0 = Saxl.staircase m := by - apply SetLike.ext - rintro ⟨i, j⟩ - simp only [mem_candidate, Saxl.mem_staircase, Nat.zero_div, Nat.zero_mod, Nat.add_zero] - omega - -def rightCells (m r : ℕ) : Finset (ℕ × ℕ) := - ({0} ×ˢ Finset.Ico m (m + r / 2 + r % 2)) ∪ - ({1} ×ˢ Finset.Ico (m - 1) (m - 1 + r / 2)) - -lemma mem_rightCells {m r i j : ℕ} : - (i, j) ∈ rightCells m r ↔ - (i = 0 ∧ m ≤ j ∧ j < m + r / 2 + r % 2) ∨ - (i = 1 ∧ m - 1 ≤ j ∧ j < m - 1 + r / 2) := by - simp only [rightCells, Finset.mem_union, Finset.mem_product, Finset.mem_singleton, - Finset.mem_Ico] - -lemma rightCells_card (m r : ℕ) : (rightCells m r).card = r := by - have hd : Disjoint - ({0} ×ˢ Finset.Ico m (m + r / 2 + r % 2)) - ({1} ×ˢ Finset.Ico (m - 1) (m - 1 + r / 2)) := by - apply Finset.disjoint_left.mpr - rintro ⟨i, j⟩ hi hj - simp only [Finset.mem_product, Finset.mem_singleton] at hi hj - omega - rw [rightCells, Finset.card_union_of_disjoint hd] - simp only [Finset.card_product, Finset.card_singleton, one_mul, Nat.card_Ico] - omega - -lemma candidate_cells (m r : ℕ) (hm : 3 ≤ m) : - (candidate m r).cells = - ((Saxl.staircase m).cells ∪ rightCells m r) ∪ - (rightCells m r).map (Equiv.prodComm ℕ ℕ).toEmbedding := by - ext ⟨i, j⟩ - simp only [YoungDiagram.mem_cells, mem_candidate, Finset.mem_union, Saxl.mem_staircase, - Finset.mem_map_equiv, Equiv.prodComm_symm, Equiv.prodComm_apply, Prod.swap_prod_mk, - mem_rightCells] - omega - -lemma candidate_card (m r : ℕ) (hm : 3 ≤ m) : - (candidate m r).card = triangular m + 2 * r := by - have hd₁ : Disjoint (Saxl.staircase m).cells (rightCells m r) := by - apply Finset.disjoint_left.mpr - rintro ⟨i, j⟩ hi hj - simp only [YoungDiagram.mem_cells, Saxl.mem_staircase] at hi - rw [mem_rightCells] at hj - omega - have hd₂ : Disjoint ((Saxl.staircase m).cells ∪ rightCells m r) - ((rightCells m r).map (Equiv.prodComm ℕ ℕ).toEmbedding) := by - apply Finset.disjoint_left.mpr - rintro ⟨i, j⟩ hi hj - simp only [Finset.mem_union, YoungDiagram.mem_cells, Saxl.mem_staircase, - mem_rightCells] at hi - simp only [Finset.mem_map_equiv, Equiv.prodComm_symm, Equiv.prodComm_apply, - Prod.swap_prod_mk, mem_rightCells] at hj - omega - change (candidate m r).cells.card = _ - rw [candidate_cells m r hm, Finset.card_union_of_disjoint hd₂, - Finset.card_union_of_disjoint hd₁, Finset.card_map, rightCells_card] - change (Saxl.staircase m).card + r + r = _ - rw [← triangular_eq_staircase_card m] - omega - -lemma candidate_rowLen (m r : ℕ) (hm : 4 ≤ m) (i : ℕ) : - (candidate m r).rowLen i = - if i = 0 then m + r / 2 + r % 2 else - if i = 1 then m - 1 + r / 2 else - if i < m - 2 then m - i else - if i < m - 1 + r / 2 then 2 else - if i < m + r / 2 + r % 2 then 1 else 0 := by - apply eq_of_forall_lt_iff - intro j - rw [← YoungDiagram.mem_iff_lt_rowLen, mem_candidate] - split_ifs <;> omega - -lemma candidate_colLen (m r : ℕ) (hm : 4 ≤ m) (i : ℕ) : - (candidate m r).colLen i = - if i = 0 then m + r / 2 + r % 2 else - if i = 1 then m - 1 + r / 2 else - if i < m - 2 then m - i else - if i < m - 1 + r / 2 then 2 else - if i < m + r / 2 + r % 2 then 1 else 0 := by - rw [← YoungDiagram.rowLen_transpose, candidate_transpose] - exact candidate_rowLen m r hm i - -theorem candidate_size_and_self_conjugacy (n : ℕ) (hn : 9 ≤ largestIndex n) : - (candidate (largestIndex n) (remainderPairs n)).card = n ∧ - (candidate (largestIndex n) (remainderPairs n)).transpose = - candidate (largestIndex n) (remainderPairs n) := by - constructor - · rw [candidate_card _ _ (by omega), degree_decomposition] - · exact candidate_transpose _ _ - -end UniversalTensorSquares - -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.TensorSquares.Arithmetic +import OAI.RepresentationTheory.Saxl.Model + +namespace OAI + +/-! Self-conjugate Young diagrams with prescribed size. -/ + +noncomputable section +open scoped TensorProduct +namespace UniversalTensorSquares +def rectangle (a b : ℕ) : YoungDiagram where + cells := Finset.range a ×ˢ Finset.range b + isLowerSet := by + intro x y hxy hy + simp only [Finset.mem_coe, Finset.mem_product, Finset.mem_range] at hy ⊢ + exact ⟨lt_of_le_of_lt hxy.1 hy.1, lt_of_le_of_lt hxy.2 hy.2⟩ + +@[simp] lemma mem_rectangle {a b i j : ℕ} : + (i, j) ∈ rectangle a b ↔ i < a ∧ j < b := by + change (i, j) ∈ Finset.range a ×ˢ Finset.range b ↔ _ + simp + +def candidateArm (m r : ℕ) : YoungDiagram := + rectangle 1 (m + r / 2 + r % 2) ⊔ rectangle 2 (m - 1 + r / 2) + +def candidate (m r : ℕ) : YoungDiagram := + Saxl.staircase m ⊔ candidateArm m r ⊔ (candidateArm m r).transpose + +lemma mem_candidate {m r i j : ℕ} : + (i, j) ∈ candidate m r ↔ + (i + j < m ∨ + (i < 1 ∧ j < m + r / 2 + r % 2 ∨ i < 2 ∧ j < m - 1 + r / 2)) ∨ + (j < 1 ∧ i < m + r / 2 + r % 2 ∨ j < 2 ∧ i < m - 1 + r / 2) := by + simp only [candidate, candidateArm, YoungDiagram.mem_sup, Saxl.mem_staircase, + YoungDiagram.mem_transpose, Prod.swap_prod_mk, mem_rectangle] + +@[simp] lemma candidate_transpose (m r : ℕ) : (candidate m r).transpose = candidate m r := by + apply SetLike.ext + rintro ⟨i, j⟩ + simp only [YoungDiagram.mem_transpose, Prod.swap_prod_mk, mem_candidate] + omega + +@[simp] lemma candidate_zero (m : ℕ) : candidate m 0 = Saxl.staircase m := by + apply SetLike.ext + rintro ⟨i, j⟩ + simp only [mem_candidate, Saxl.mem_staircase, Nat.zero_div, Nat.zero_mod, Nat.add_zero] + omega + +def rightCells (m r : ℕ) : Finset (ℕ × ℕ) := + ({0} ×ˢ Finset.Ico m (m + r / 2 + r % 2)) ∪ + ({1} ×ˢ Finset.Ico (m - 1) (m - 1 + r / 2)) + +lemma mem_rightCells {m r i j : ℕ} : + (i, j) ∈ rightCells m r ↔ + (i = 0 ∧ m ≤ j ∧ j < m + r / 2 + r % 2) ∨ + (i = 1 ∧ m - 1 ≤ j ∧ j < m - 1 + r / 2) := by + simp only [rightCells, Finset.mem_union, Finset.mem_product, Finset.mem_singleton, + Finset.mem_Ico] + +lemma rightCells_card (m r : ℕ) : (rightCells m r).card = r := by + have hd : Disjoint + ({0} ×ˢ Finset.Ico m (m + r / 2 + r % 2)) + ({1} ×ˢ Finset.Ico (m - 1) (m - 1 + r / 2)) := by + apply Finset.disjoint_left.mpr + rintro ⟨i, j⟩ hi hj + simp only [Finset.mem_product, Finset.mem_singleton] at hi hj + omega + rw [rightCells, Finset.card_union_of_disjoint hd] + simp only [Finset.card_product, Finset.card_singleton, one_mul, Nat.card_Ico] + omega + +lemma candidate_cells (m r : ℕ) (hm : 3 ≤ m) : + (candidate m r).cells = + ((Saxl.staircase m).cells ∪ rightCells m r) ∪ + (rightCells m r).map (Equiv.prodComm ℕ ℕ).toEmbedding := by + ext ⟨i, j⟩ + simp only [YoungDiagram.mem_cells, mem_candidate, Finset.mem_union, Saxl.mem_staircase, + Finset.mem_map_equiv, Equiv.prodComm_symm, Equiv.prodComm_apply, Prod.swap_prod_mk, + mem_rightCells] + omega + +lemma candidate_card (m r : ℕ) (hm : 3 ≤ m) : + (candidate m r).card = triangular m + 2 * r := by + have hd₁ : Disjoint (Saxl.staircase m).cells (rightCells m r) := by + apply Finset.disjoint_left.mpr + rintro ⟨i, j⟩ hi hj + simp only [YoungDiagram.mem_cells, Saxl.mem_staircase] at hi + rw [mem_rightCells] at hj + omega + have hd₂ : Disjoint ((Saxl.staircase m).cells ∪ rightCells m r) + ((rightCells m r).map (Equiv.prodComm ℕ ℕ).toEmbedding) := by + apply Finset.disjoint_left.mpr + rintro ⟨i, j⟩ hi hj + simp only [Finset.mem_union, YoungDiagram.mem_cells, Saxl.mem_staircase, + mem_rightCells] at hi + simp only [Finset.mem_map_equiv, Equiv.prodComm_symm, Equiv.prodComm_apply, + Prod.swap_prod_mk, mem_rightCells] at hj + omega + change (candidate m r).cells.card = _ + rw [candidate_cells m r hm, Finset.card_union_of_disjoint hd₂, + Finset.card_union_of_disjoint hd₁, Finset.card_map, rightCells_card] + change (Saxl.staircase m).card + r + r = _ + rw [← triangular_eq_staircase_card m] + omega + +lemma candidate_rowLen (m r : ℕ) (hm : 4 ≤ m) (i : ℕ) : + (candidate m r).rowLen i = + if i = 0 then m + r / 2 + r % 2 else + if i = 1 then m - 1 + r / 2 else + if i < m - 2 then m - i else + if i < m - 1 + r / 2 then 2 else + if i < m + r / 2 + r % 2 then 1 else 0 := by + apply eq_of_forall_lt_iff + intro j + rw [← YoungDiagram.mem_iff_lt_rowLen, mem_candidate] + split_ifs <;> omega + +lemma candidate_colLen (m r : ℕ) (hm : 4 ≤ m) (i : ℕ) : + (candidate m r).colLen i = + if i = 0 then m + r / 2 + r % 2 else + if i = 1 then m - 1 + r / 2 else + if i < m - 2 then m - i else + if i < m - 1 + r / 2 then 2 else + if i < m + r / 2 + r % 2 then 1 else 0 := by + rw [← YoungDiagram.rowLen_transpose, candidate_transpose] + exact candidate_rowLen m r hm i + +theorem candidate_size_and_self_conjugacy (n : ℕ) (hn : 9 ≤ largestIndex n) : + (candidate (largestIndex n) (remainderPairs n)).card = n ∧ + (candidate (largestIndex n) (remainderPairs n)).transpose = + candidate (largestIndex n) (remainderPairs n) := by + constructor + · rw [candidate_card _ _ (by omega), degree_decomposition] + · exact candidate_transpose _ _ + +end UniversalTensorSquares + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/TensorSquares/Main.lean b/lean/OAI/RepresentationTheory/TensorSquares/Main.lean index 86a4d3a3d89a59c401e0859da31e2d2223f8e21a..bd265c5fb63bc7a2381ebcbbed3d0af417d1e8ed 100644 --- a/lean/OAI/RepresentationTheory/TensorSquares/Main.lean +++ b/lean/OAI/RepresentationTheory/TensorSquares/Main.lean @@ -1,37 +1,37 @@ -import Mathlib -import OAI.RepresentationTheory.TensorSquares.Triangular -import OAI.RepresentationTheory.TensorSquares.Candidate -import OAI.RepresentationTheory.TensorSquares.Transpose -import OAI.RepresentationTheory.Saxl.Model - -namespace OAI - -/-! The prescribed self-conjugate candidate and its tensor-square support. -/ - -noncomputable section -open scoped TensorProduct -namespace UniversalTensorSquares - -theorem candidate_with_transpose_support (n : ℕ) (hM : 9 ≤ largestIndex n) : - ∃ hL : (candidate (largestIndex n) (remainderPairs n)).card = n, - (candidate (largestIndex n) (remainderPairs n)).transpose = - candidate (largestIndex n) (remainderPairs n) ∧ - ∀ (nu : YoungDiagram) (hnu : nu.card = n), - (0 < Saxl.kronecker - (Saxl.canonicalTableau (candidate (largestIndex n) (remainderPairs n)) hL) - (Saxl.canonicalTableau (candidate (largestIndex n) (remainderPairs n)) hL) - (Saxl.canonicalTableau nu hnu)) ↔ - (0 < Saxl.kronecker - (Saxl.canonicalTableau (candidate (largestIndex n) (remainderPairs n)) hL) - (Saxl.canonicalTableau (candidate (largestIndex n) (remainderPairs n)) hL) - (Saxl.canonicalTableau nu.transpose ((Saxl.transpose_card nu).trans hnu))) := by - obtain ⟨hcard, hself⟩ := candidate_size_and_self_conjugacy n hM - refine ⟨hcard, hself, ?_⟩ - intro nu hnu - exact transpose_support_of_self_conjugate _ hcard hself nu hnu - -end UniversalTensorSquares - -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.TensorSquares.Triangular +import OAI.RepresentationTheory.TensorSquares.Candidate +import OAI.RepresentationTheory.TensorSquares.Transpose +import OAI.RepresentationTheory.Saxl.Model + +namespace OAI + +/-! The prescribed self-conjugate candidate and its tensor-square support. -/ + +noncomputable section +open scoped TensorProduct +namespace UniversalTensorSquares + +theorem candidate_with_transpose_support (n : ℕ) (hM : 9 ≤ largestIndex n) : + ∃ hL : (candidate (largestIndex n) (remainderPairs n)).card = n, + (candidate (largestIndex n) (remainderPairs n)).transpose = + candidate (largestIndex n) (remainderPairs n) ∧ + ∀ (nu : YoungDiagram) (hnu : nu.card = n), + (0 < Saxl.kronecker + (Saxl.canonicalTableau (candidate (largestIndex n) (remainderPairs n)) hL) + (Saxl.canonicalTableau (candidate (largestIndex n) (remainderPairs n)) hL) + (Saxl.canonicalTableau nu hnu)) ↔ + (0 < Saxl.kronecker + (Saxl.canonicalTableau (candidate (largestIndex n) (remainderPairs n)) hL) + (Saxl.canonicalTableau (candidate (largestIndex n) (remainderPairs n)) hL) + (Saxl.canonicalTableau nu.transpose ((Saxl.transpose_card nu).trans hnu))) := by + obtain ⟨hcard, hself⟩ := candidate_size_and_self_conjugacy n hM + refine ⟨hcard, hself, ?_⟩ + intro nu hnu + exact transpose_support_of_self_conjugate _ hcard hself nu hnu + +end UniversalTensorSquares + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/TensorSquares/Transpose.lean b/lean/OAI/RepresentationTheory/TensorSquares/Transpose.lean index ee029c9843fa6c18a63c43de54205e67f9abf41f..162f1bd4a4cec7c8e9cd57004a5714939428f9fe 100644 --- a/lean/OAI/RepresentationTheory/TensorSquares/Transpose.lean +++ b/lean/OAI/RepresentationTheory/TensorSquares/Transpose.lean @@ -1,100 +1,100 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.DominatedSupport - -namespace OAI - -/-! Sign twisting and transpose-invariant tensor-square support. -/ - -noncomputable section -open scoped TensorProduct -open scoped TensorProduct -namespace UniversalTensorSquares -open Saxl - -def signTwistEquiv {n : ℕ} {X Y : Type*} [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] - {ρ : Representation ℂ (Equiv.Perm (Fin n)) X} - {σ : Representation ℂ (Equiv.Perm (Fin n)) Y} (e : ρ.Equiv σ) : - (signTwist ρ).Equiv (signTwist σ) where - toLinearEquiv := e.toLinearEquiv - isIntertwining' := (signTwistMap e.toIntertwiningMap).isIntertwining' - -def signCancelEquiv {n : ℕ} {X Y : Type*} [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] - {ρ : Representation ℂ (Equiv.Perm (Fin n)) X} - {σ : Representation ℂ (Equiv.Perm (Fin n)) Y} (e : (signTwist ρ).Equiv σ) : - ρ.Equiv (signTwist σ) where - toLinearEquiv := e.toLinearEquiv - isIntertwining' := (signCancelMap e.toIntertwiningMap).isIntertwining' - -def spechtTableauEquiv {n : ℕ} {mu : YoungDiagram} (s t : Tableau n mu) : - (spechtRep s).Equiv (spechtRep t) := - equivOfSubrepEq (spechtSub s) (spechtSub t) (spechtSub_tableau_independent s t) - -def spechtShapeEquiv {n : ℕ} {mu nu : YoungDiagram} (s : Tableau n mu) - (t : Tableau n nu) (h : mu = nu) : (spechtRep s).Equiv (spechtRep t) := by - subst nu - exact spechtTableauEquiv s t - -lemma canonical_sign_transpose {n : ℕ} (mu : YoungDiagram) (hmu : mu.card = n) : - Nonempty ((spechtRep (canonicalTableau mu hmu)).Equiv - (signTwist (spechtRep (canonicalTableau mu.transpose ((transpose_card mu).trans hmu))))) := by - obtain ⟨e⟩ := specht_sign_transpose (canonicalTableau mu hmu) - exact ⟨e.trans (signTwistEquiv (spechtTableauEquiv - (transposeTableau (canonicalTableau mu hmu)) - (canonicalTableau mu.transpose ((transpose_card mu).trans hmu))))⟩ - -lemma canonical_self_sign {n : ℕ} (lam : YoungDiagram) (hlam : lam.card = n) - (hself : lam.transpose = lam) : - Nonempty ((spechtRep (canonicalTableau lam hlam)).Equiv - (signTwist (spechtRep (canonicalTableau lam hlam)))) := by - obtain ⟨e⟩ := specht_sign_transpose (canonicalTableau lam hlam) - exact ⟨e.trans (signTwistEquiv (spechtShapeEquiv - (transposeTableau (canonicalTableau lam hlam)) (canonicalTableau lam hlam) hself))⟩ - -lemma support_sign_transfer {n : ℕ} {X Y Z : Type*} - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - [AddCommGroup Z] [Module ℂ Z] - {ρ : Representation ℂ (Equiv.Perm (Fin n)) X} - {σ : Representation ℂ (Equiv.Perm (Fin n)) Y} - {τ : Representation ℂ (Equiv.Perm (Fin n)) Z} - (a : ρ.Equiv (signTwist ρ)) (e : σ.Equiv (signTwist τ)) - (f : Representation.IntertwiningMap σ (ρ.tprod ρ)) (hf : f ≠ 0) : - ∃ F : Representation.IntertwiningMap τ (ρ.tprod ρ), F ≠ 0 := by - let T := tensorAnti ρ a.toIntertwiningMap - have hT : Function.Injective T := by - change Function.Injective (TensorProduct.congr (LinearEquiv.refl ℂ X) a.toLinearEquiv) - exact (TensorProduct.congr (LinearEquiv.refl ℂ X) a.toLinearEquiv).injective - let F := signCancelMap (ρ := τ) (σ := ρ.tprod ρ) (f.comp e.symm.toIntertwiningMap) - refine ⟨T.comp F, ?_⟩ - intro hz - apply hf - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - have he := congrArg (fun F => F (e x)) hz - change T (f (e.symm (e x))) = 0 at he - rw [e.symm_apply_apply] at he - exact hT (he.trans (map_zero T).symm) - -theorem transpose_support_of_self_conjugate {n : ℕ} (lam : YoungDiagram) - (hlam : lam.card = n) (hself : lam.transpose = lam) - (nu : YoungDiagram) (hnu : nu.card = n) : - (0 < kronecker (canonicalTableau lam hlam) - (canonicalTableau lam hlam) (canonicalTableau nu hnu)) ↔ - (0 < kronecker (canonicalTableau lam hlam) (canonicalTableau lam hlam) - (canonicalTableau nu.transpose ((transpose_card nu).trans hnu))) := by - obtain ⟨a⟩ := canonical_self_sign lam hlam hself - obtain ⟨e⟩ := canonical_sign_transpose nu hnu - rw [kronecker_pos_iff, kronecker_pos_iff] - constructor - · rintro ⟨f, hf⟩ - exact support_sign_transfer a e f hf - · rintro ⟨f, hf⟩ - exact support_sign_transfer a (signCancelEquiv e.symm) f hf - -end UniversalTensorSquares - -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.DominatedSupport + +namespace OAI + +/-! Sign twisting and transpose-invariant tensor-square support. -/ + +noncomputable section +open scoped TensorProduct +open scoped TensorProduct +namespace UniversalTensorSquares +open Saxl + +def signTwistEquiv {n : ℕ} {X Y : Type*} [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] + {ρ : Representation ℂ (Equiv.Perm (Fin n)) X} + {σ : Representation ℂ (Equiv.Perm (Fin n)) Y} (e : ρ.Equiv σ) : + (signTwist ρ).Equiv (signTwist σ) where + toLinearEquiv := e.toLinearEquiv + isIntertwining' := (signTwistMap e.toIntertwiningMap).isIntertwining' + +def signCancelEquiv {n : ℕ} {X Y : Type*} [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] + {ρ : Representation ℂ (Equiv.Perm (Fin n)) X} + {σ : Representation ℂ (Equiv.Perm (Fin n)) Y} (e : (signTwist ρ).Equiv σ) : + ρ.Equiv (signTwist σ) where + toLinearEquiv := e.toLinearEquiv + isIntertwining' := (signCancelMap e.toIntertwiningMap).isIntertwining' + +def spechtTableauEquiv {n : ℕ} {mu : YoungDiagram} (s t : Tableau n mu) : + (spechtRep s).Equiv (spechtRep t) := + equivOfSubrepEq (spechtSub s) (spechtSub t) (spechtSub_tableau_independent s t) + +def spechtShapeEquiv {n : ℕ} {mu nu : YoungDiagram} (s : Tableau n mu) + (t : Tableau n nu) (h : mu = nu) : (spechtRep s).Equiv (spechtRep t) := by + subst nu + exact spechtTableauEquiv s t + +lemma canonical_sign_transpose {n : ℕ} (mu : YoungDiagram) (hmu : mu.card = n) : + Nonempty ((spechtRep (canonicalTableau mu hmu)).Equiv + (signTwist (spechtRep (canonicalTableau mu.transpose ((transpose_card mu).trans hmu))))) := by + obtain ⟨e⟩ := specht_sign_transpose (canonicalTableau mu hmu) + exact ⟨e.trans (signTwistEquiv (spechtTableauEquiv + (transposeTableau (canonicalTableau mu hmu)) + (canonicalTableau mu.transpose ((transpose_card mu).trans hmu))))⟩ + +lemma canonical_self_sign {n : ℕ} (lam : YoungDiagram) (hlam : lam.card = n) + (hself : lam.transpose = lam) : + Nonempty ((spechtRep (canonicalTableau lam hlam)).Equiv + (signTwist (spechtRep (canonicalTableau lam hlam)))) := by + obtain ⟨e⟩ := specht_sign_transpose (canonicalTableau lam hlam) + exact ⟨e.trans (signTwistEquiv (spechtShapeEquiv + (transposeTableau (canonicalTableau lam hlam)) (canonicalTableau lam hlam) hself))⟩ + +lemma support_sign_transfer {n : ℕ} {X Y Z : Type*} + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + [AddCommGroup Z] [Module ℂ Z] + {ρ : Representation ℂ (Equiv.Perm (Fin n)) X} + {σ : Representation ℂ (Equiv.Perm (Fin n)) Y} + {τ : Representation ℂ (Equiv.Perm (Fin n)) Z} + (a : ρ.Equiv (signTwist ρ)) (e : σ.Equiv (signTwist τ)) + (f : Representation.IntertwiningMap σ (ρ.tprod ρ)) (hf : f ≠ 0) : + ∃ F : Representation.IntertwiningMap τ (ρ.tprod ρ), F ≠ 0 := by + let T := tensorAnti ρ a.toIntertwiningMap + have hT : Function.Injective T := by + change Function.Injective (TensorProduct.congr (LinearEquiv.refl ℂ X) a.toLinearEquiv) + exact (TensorProduct.congr (LinearEquiv.refl ℂ X) a.toLinearEquiv).injective + let F := signCancelMap (ρ := τ) (σ := ρ.tprod ρ) (f.comp e.symm.toIntertwiningMap) + refine ⟨T.comp F, ?_⟩ + intro hz + apply hf + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + have he := congrArg (fun F => F (e x)) hz + change T (f (e.symm (e x))) = 0 at he + rw [e.symm_apply_apply] at he + exact hT (he.trans (map_zero T).symm) + +theorem transpose_support_of_self_conjugate {n : ℕ} (lam : YoungDiagram) + (hlam : lam.card = n) (hself : lam.transpose = lam) + (nu : YoungDiagram) (hnu : nu.card = n) : + (0 < kronecker (canonicalTableau lam hlam) + (canonicalTableau lam hlam) (canonicalTableau nu hnu)) ↔ + (0 < kronecker (canonicalTableau lam hlam) (canonicalTableau lam hlam) + (canonicalTableau nu.transpose ((transpose_card nu).trans hnu))) := by + obtain ⟨a⟩ := canonical_self_sign lam hlam hself + obtain ⟨e⟩ := canonical_sign_transpose nu hnu + rw [kronecker_pos_iff, kronecker_pos_iff] + constructor + · rintro ⟨f, hf⟩ + exact support_sign_transfer a e f hf + · rintro ⟨f, hf⟩ + exact support_sign_transfer a (signCancelEquiv e.symm) f hf + +end UniversalTensorSquares + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/TensorSquares/Triangular.lean b/lean/OAI/RepresentationTheory/TensorSquares/Triangular.lean index fc0a9a552af9738d1c67f4437150b3d7a4f898f8..476f27456e3e0b3aa1f8273a0164f6b634eb76a1 100644 --- a/lean/OAI/RepresentationTheory/TensorSquares/Triangular.lean +++ b/lean/OAI/RepresentationTheory/TensorSquares/Triangular.lean @@ -1,65 +1,65 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main - -namespace OAI - -/-! Irreducible embeddings and staircase tensor squares. -/ - -noncomputable section -open scoped TensorProduct -open scoped TensorProduct -universe u - -namespace UniversalTensorSquares - -theorem contains_every_irreducible_of_positive {n : ℕ} - (lam : YoungDiagram) (hlam : lam.card = n) - (h : ∀ (nu : YoungDiagram) (hnu : nu.card = n), - 0 < Saxl.kronecker (Saxl.canonicalTableau lam hlam) - (Saxl.canonicalTableau lam hlam) (Saxl.canonicalTableau nu hnu)) - {V : Type u} [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) - [Representation.IsIrreducible ρ] : - ∃ F : Representation.IntertwiningMap ρ - ((Saxl.spechtRep (Saxl.canonicalTableau lam hlam)).tprod - (Saxl.spechtRep (Saxl.canonicalTableau lam hlam))), Function.Injective F := by - obtain ⟨p, ⟨e⟩⟩ := Saxl.irreducible_equiv_specht ρ - obtain ⟨f, hf⟩ := (Saxl.kronecker_pos_iff (Saxl.canonicalTableau lam hlam) - (Saxl.canonicalTableau lam hlam) (Saxl.partitionTableau p)).mp - (h (Saxl.partitionDiagram p) (Saxl.partitionDiagram_card p)) - let := Saxl.specht_irreducible (Saxl.partitionTableau p) - have hi : Function.Injective f := by - have hi' := @Representation.IsIrreducible.injective_or_eq_zero - (Equiv.Perm (Fin n)) ℂ (Saxl.Specht (Saxl.partitionTableau p)) - (Saxl.Specht (Saxl.canonicalTableau lam hlam) ⊗[ℂ] - Saxl.Specht (Saxl.canonicalTableau lam hlam)) _ _ _ _ _ _ - (Saxl.spechtRep (Saxl.partitionTableau p)) - ((Saxl.spechtRep (Saxl.canonicalTableau lam hlam)).tprod - (Saxl.spechtRep (Saxl.canonicalTableau lam hlam))) f inferInstance - exact hi'.resolve_right hf - exact ⟨f.comp e.toIntertwiningMap, hi.comp e.injective⟩ - -theorem universal_tensor_square_triangular (m : ℕ) (hm : 1 ≤ m) : - ∃ (lam : YoungDiagram) (hlam : lam.card = m * (m + 1) / 2), - (∀ (nu : YoungDiagram) (hnu : nu.card = m * (m + 1) / 2), - 0 < Saxl.kronecker (Saxl.canonicalTableau lam hlam) - (Saxl.canonicalTableau lam hlam) (Saxl.canonicalTableau nu hnu)) ∧ - Representation.IsIrreducible (Saxl.spechtRep (Saxl.canonicalTableau lam hlam)) ∧ - ∀ {V : Type u} [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin (m * (m + 1) / 2))) V) - [Representation.IsIrreducible ρ], - ∃ F : Representation.IntertwiningMap ρ - ((Saxl.spechtRep (Saxl.canonicalTableau lam hlam)).tprod - (Saxl.spechtRep (Saxl.canonicalTableau lam hlam))), - Function.Injective F := by - rw [← Saxl.staircase_card m] - refine ⟨Saxl.staircase m, rfl, ?_, Saxl.specht_irreducible _, ?_⟩ - · exact Saxl.saxl_conjecture m hm - · intro V _ _ _ ρ _ - exact Saxl.saxl_contains_every_irreducible m hm ρ - -end UniversalTensorSquares - -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main + +namespace OAI + +/-! Irreducible embeddings and staircase tensor squares. -/ + +noncomputable section +open scoped TensorProduct +open scoped TensorProduct +universe u + +namespace UniversalTensorSquares + +theorem contains_every_irreducible_of_positive {n : ℕ} + (lam : YoungDiagram) (hlam : lam.card = n) + (h : ∀ (nu : YoungDiagram) (hnu : nu.card = n), + 0 < Saxl.kronecker (Saxl.canonicalTableau lam hlam) + (Saxl.canonicalTableau lam hlam) (Saxl.canonicalTableau nu hnu)) + {V : Type u} [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) + [Representation.IsIrreducible ρ] : + ∃ F : Representation.IntertwiningMap ρ + ((Saxl.spechtRep (Saxl.canonicalTableau lam hlam)).tprod + (Saxl.spechtRep (Saxl.canonicalTableau lam hlam))), Function.Injective F := by + obtain ⟨p, ⟨e⟩⟩ := Saxl.irreducible_equiv_specht ρ + obtain ⟨f, hf⟩ := (Saxl.kronecker_pos_iff (Saxl.canonicalTableau lam hlam) + (Saxl.canonicalTableau lam hlam) (Saxl.partitionTableau p)).mp + (h (Saxl.partitionDiagram p) (Saxl.partitionDiagram_card p)) + let := Saxl.specht_irreducible (Saxl.partitionTableau p) + have hi : Function.Injective f := by + have hi' := @Representation.IsIrreducible.injective_or_eq_zero + (Equiv.Perm (Fin n)) ℂ (Saxl.Specht (Saxl.partitionTableau p)) + (Saxl.Specht (Saxl.canonicalTableau lam hlam) ⊗[ℂ] + Saxl.Specht (Saxl.canonicalTableau lam hlam)) _ _ _ _ _ _ + (Saxl.spechtRep (Saxl.partitionTableau p)) + ((Saxl.spechtRep (Saxl.canonicalTableau lam hlam)).tprod + (Saxl.spechtRep (Saxl.canonicalTableau lam hlam))) f inferInstance + exact hi'.resolve_right hf + exact ⟨f.comp e.toIntertwiningMap, hi.comp e.injective⟩ + +theorem universal_tensor_square_triangular (m : ℕ) (hm : 1 ≤ m) : + ∃ (lam : YoungDiagram) (hlam : lam.card = m * (m + 1) / 2), + (∀ (nu : YoungDiagram) (hnu : nu.card = m * (m + 1) / 2), + 0 < Saxl.kronecker (Saxl.canonicalTableau lam hlam) + (Saxl.canonicalTableau lam hlam) (Saxl.canonicalTableau nu hnu)) ∧ + Representation.IsIrreducible (Saxl.spechtRep (Saxl.canonicalTableau lam hlam)) ∧ + ∀ {V : Type u} [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin (m * (m + 1) / 2))) V) + [Representation.IsIrreducible ρ], + ∃ F : Representation.IntertwiningMap ρ + ((Saxl.spechtRep (Saxl.canonicalTableau lam hlam)).tprod + (Saxl.spechtRep (Saxl.canonicalTableau lam hlam))), + Function.Injective F := by + rw [← Saxl.staircase_card m] + refine ⟨Saxl.staircase m, rfl, ?_, Saxl.specht_irreducible _, ?_⟩ + · exact Saxl.saxl_conjecture m hm + · intro V _ _ _ ρ _ + exact Saxl.saxl_contains_every_irreducible m hm ρ + +end UniversalTensorSquares + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Torus/ConvexWeights.lean b/lean/OAI/RepresentationTheory/Torus/ConvexWeights.lean index 5df4f1a4fe17851d5efd65ac6534130e5db549cd..3bc9963814692cea2ac56af1d912f65fef9ad74b 100644 --- a/lean/OAI/RepresentationTheory/Torus/ConvexWeights.lean +++ b/lean/OAI/RepresentationTheory/Torus/ConvexWeights.lean @@ -1,264 +1,264 @@ -import Mathlib - -namespace OAI - -/-! Invariant products from convex relations among integral characters. -/ - -noncomputable section -open scoped BigOperators - -namespace ExactOrders.Partial - -def realVector {δ : Type*} (p : δ → ℚ) : δ → ℝ := fun j => p j - -lemma rational_barycentric_coordinates - {ι δ : Type*} [Fintype ι] [Fintype δ] - (p : ι → δ → ℚ) (w : ι → ℝ) - (hp : AffineIndependent ℝ (fun i => realVector (p i))) - (hw : ∑ i, w i = 1) - (hz : ∑ i, w i • realVector (p i) = 0) : - ∃ q : ι → ℚ, ∀ i, (q i : ℝ) = w i := by - classical - let u : ι → Option δ → ℚ := fun i j => j.elim 1 (p i) - let A : (ι → ℚ) →ₗ[ℚ] (Option δ → ℚ) := - { toFun := fun a => ∑ i, a i • u i - map_add' := by - intro a b - simp [add_smul, Finset.sum_add_distrib] - map_smul' := by - intro c a - simp [Finset.smul_sum, mul_smul] } - have hker : LinearMap.ker A = ⊥ := by - apply LinearMap.ker_eq_bot'.mpr - intro a ha - have hsum : ∑ i, (a i : ℝ) = 0 := by - have h := congrFun ha none - simp only [A, LinearMap.coe_mk, AddHom.coe_mk, Finset.sum_apply, - Pi.smul_apply, smul_eq_mul, u, Option.elim_none, mul_one, Pi.zero_apply] at h - exact_mod_cast h - have hlin : ∑ i, (a i : ℝ) • realVector (p i) = 0 := by - ext j - have h := congrFun ha (some j) - simp only [A, LinearMap.coe_mk, AddHom.coe_mk, Finset.sum_apply, - Pi.smul_apply, smul_eq_mul, u, Option.elim_some, Pi.zero_apply] at h - simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul, - realVector, Pi.zero_apply] - exact_mod_cast h - have hzero := hp.eq_zero_of_sum_eq_zero hsum hlin - ext i - exact_mod_cast hzero i (Finset.mem_univ i) - obtain ⟨B, hBA⟩ := A.exists_leftInverse_of_injective hker - let e : Option δ → Option δ → ℚ := fun j k => if j = k then 1 else 0 - have hBu (k : ι) : B (u k) = fun i => if k = i then 1 else 0 := by - have h := LinearMap.congr_fun hBA (fun i => if k = i then 1 else 0) - simpa [A] using h - have hcoef (k i : ι) : - ∑ j, (u k j : ℝ) * (B (e j) i : ℝ) = if k = i then 1 else 0 := by - have h := congrFun (hBu k) i - rw [B.pi_apply_eq_sum_univ] at h - simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul] at h - by_cases hki : k = i <;> - simpa [e, hki] using congrArg (fun x : ℚ => (x : ℝ)) h - have haug (j : Option δ) : - (e none j : ℝ) = ∑ k, w k * (u k j : ℝ) := by - cases j with - | none => simpa [e, u] using hw.symm - | some j => - have h := congrFun hz j - simpa [e, u, realVector] using h.symm - refine ⟨B (e none), fun i => ?_⟩ - calc - (B (e none) i : ℝ) = ∑ j, (e none j : ℝ) * (B (e j) i : ℝ) := by - simp [e] - _ = ∑ j, (∑ k, w k * (u k j : ℝ)) * (B (e j) i : ℝ) := by - simp_rw [haug] - _ = ∑ k, w k * (∑ j, (u k j : ℝ) * (B (e j) i : ℝ)) := by - simp only [Finset.sum_mul, Finset.mul_sum, mul_assoc] - exact Finset.sum_comm - _ = ∑ k, w k * (if k = i then 1 else 0) := by simp_rw [hcoef] - _ = w i := by simp - -theorem zero_mem_rational_convexHull - {δ : Type*} [Fintype δ] (s : Set (δ → ℚ)) - (h : (0 : δ → ℝ) ∈ convexHull ℝ (realVector '' s)) : - (0 : δ → ℚ) ∈ convexHull ℚ s := by - classical - obtain ⟨ι, _, z, w, hzs, hz, hwpos, hw, hwz⟩ := - eq_pos_convex_span_of_mem_convexHull h - have hpre : ∀ i, ∃ p ∈ s, realVector p = z i := - fun i => hzs ⟨i, rfl⟩ - choose p hps hpz using hpre - have hpz' : (fun i => realVector (p i)) = z := funext hpz - rw [← hpz'] at hz hwz - obtain ⟨q, hq⟩ := rational_barycentric_coordinates p w hz hw hwz - apply mem_convexHull_of_exists_fintype q p - · intro i - have : 0 < (q i : ℝ) := by rw [hq]; exact hwpos i - exact_mod_cast this.le - · have : ∑ i, (q i : ℝ) = 1 := by simp_rw [hq]; exact hw - exact_mod_cast this - · exact hps - · ext j - have h := congrFun hwz j - simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul, realVector, - Pi.zero_apply] at h ⊢ - simp_rw [← hq] at h - exact_mod_cast h - -lemma natural_common_denominator - {ι : Type*} [Fintype ι] (a : ι → ℚ) (ha : ∀ i, 0 ≤ a i) : - ∃ d : ℕ, 0 < d ∧ ∃ n : ι → ℕ, ∀ i, (n i : ℚ) = d * a i := by - classical - let d := ∏ i, (a i).den - let n : ι → ℕ := fun i => (a i).num.toNat * - ∏ j ∈ Finset.univ.erase i, (a j).den - refine ⟨d, Finset.prod_pos (fun i _ => (a i).den_pos), n, fun i => ?_⟩ - have hnum : ((a i).num.toNat : ℚ) = (a i).num := by - exact_mod_cast Int.toNat_of_nonneg (Rat.num_nonneg.mpr (ha i)) - have hd : (a i).den * (∏ j ∈ Finset.univ.erase i, (a j).den) = d := - Finset.mul_prod_erase Finset.univ (fun j => (a j).den) (Finset.mem_univ i) - calc - (n i : ℚ) = (a i).num * (∏ j ∈ Finset.univ.erase i, (a j).den : ℕ) := by - simp only [n, Nat.cast_mul, hnum] - _ = (a i * (a i).den) * (∏ j ∈ Finset.univ.erase i, (a j).den : ℕ) := by - rw [Rat.mul_den_eq_num] - _ = a i * ((a i).den * (∏ j ∈ Finset.univ.erase i, (a j).den) : ℕ) := by - push_cast - ring - _ = d * a i := by rw [hd, mul_comm] - -lemma integral_weight_relation - {ι δ : Type*} [Fintype ι] - (r : ι → ℕ) (α : ι → δ → ℤ) (c : ι → ℚ) - (hr : ∀ i, 0 < r i) (hc : ∀ i, 0 ≤ c i) - (hc1 : ∑ i, c i = 1) - (hzero : ∑ i, c i • (fun j => (α i j : ℚ) / r i) = 0) : - ∃ n : ι → ℕ, 0 < ∑ i, n i * r i ∧ ∑ i, n i • α i = 0 := by - classical - let a : ι → ℚ := fun i => c i / r i - have hri (i : ι) : (r i : ℚ) ≠ 0 := by exact_mod_cast (hr i).ne' - obtain ⟨d, hd, n, hn⟩ := natural_common_denominator a - (fun i => div_nonneg (hc i) (by positivity)) - have hdeg : (∑ i, n i * r i : ℕ) = d := by - apply Nat.cast_injective (R := ℚ) - push_cast - calc - ∑ i, (n i : ℚ) * r i = ∑ i, (d : ℚ) * c i := by - apply Finset.sum_congr rfl - intro i _ - rw [hn] - dsimp [a] - field_simp [hri i] - _ = d := by rw [← Finset.mul_sum, hc1, mul_one] - refine ⟨n, hdeg ▸ hd, ?_⟩ - ext j - have hz := congrFun hzero j - simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul, Pi.zero_apply] at hz - have hsum : ∑ i, (n i : ℚ) * (α i j : ℚ) = 0 := by - calc - ∑ i, (n i : ℚ) * (α i j : ℚ) = - ∑ i, (d : ℚ) * (c i * ((α i j : ℚ) / r i)) := by - apply Finset.sum_congr rfl - intro i _ - rw [hn] - dsimp [a] - ring - _ = 0 := by rw [← Finset.mul_sum, hz, mul_zero] - simpa only [Finset.sum_apply, Pi.smul_apply, nsmul_eq_mul, Pi.mul_apply, - Pi.zero_apply, Pi.natCast_apply] using - (show ∑ i, (n i : ℤ) * α i j = 0 by exact_mod_cast hsum) - -def character {δ : Type*} [Fintype δ] (α : δ → ℤ) : (δ → ℂˣ) →* ℂˣ where - toFun t := ∏ j, t j ^ α j - map_one' := by simp - map_mul' t u := by simp [mul_zpow, Finset.prod_mul_distrib] - -@[simp] lemma character_zero {δ : Type*} [Fintype δ] (t : δ → ℂˣ) : - character (0 : δ → ℤ) t = 1 := by - simp [character] - -lemma character_add {δ : Type*} [Fintype δ] (α β : δ → ℤ) (t : δ → ℂˣ) : - character (α + β) t = character α t * character β t := by - simp [character, zpow_add, Finset.prod_mul_distrib] - -lemma character_nsmul {δ : Type*} [Fintype δ] - (n : ℕ) (α : δ → ℤ) (t : δ → ℂˣ) : - character (n • α) t = character α t ^ n := by - induction n with - | zero => simp - | succ n ih => rw [succ_nsmul, character_add, ih, pow_succ] - -lemma character_sum {ι δ : Type*} [Fintype δ] - (F : Finset ι) (α : ι → δ → ℤ) (t : δ → ℂˣ) : - character (∑ i ∈ F, α i) t = ∏ i ∈ F, character (α i) t := by - classical - induction F using Finset.induction_on with - | empty => simp - | @insert i F hi ih => simp only [Finset.sum_insert hi, character_add, ih, - Finset.prod_insert hi] - -theorem invariant_product_of_integral_relation - {ι δ R : Type*} [Fintype ι] [Fintype δ] - [CommRing R] [IsDomain R] [Algebra ℂ R] - (A : ℕ → Submodule ℂ R) [SetLike.GradedMonoid A] - (ρ : (δ → ℂˣ) →* (R ≃ₐ[ℂ] R)) - (r : ι → ℕ) (α : ι → δ → ℤ) (s : ι → R) - (hmem : ∀ i, s i ∈ A (r i)) (hne : ∀ i, s i ≠ 0) - (heigen : ∀ t i, ρ t (s i) = (character (α i) t : ℂ) • s i) - (n : ι → ℕ) (hdeg : 0 < ∑ i, n i * r i) - (hweight : ∑ i, n i • α i = 0) : - ∃ m : ℕ, 0 < m ∧ ∃ z : R, z ∈ A m ∧ z ≠ 0 ∧ ∀ t, ρ t z = z := by - classical - refine ⟨∑ i, n i * r i, hdeg, ∏ i, s i ^ n i, ?_, ?_, ?_⟩ - · simpa only [Nat.nsmul_eq_mul] using - (SetLike.prod_pow_mem_graded A r s n (fun i _ => hmem i)) - · exact Finset.prod_ne_zero_iff.mpr (fun i _ => pow_ne_zero _ (hne i)) - · intro t - have hchar : ∏ i, character (α i) t ^ n i = 1 := by - rw [← character_zero t, ← hweight, character_sum] - simp_rw [character_nsmul] - have hscalar : ∏ i, (character (α i) t : ℂ) ^ n i = 1 := by - have h := congrArg (Units.coeHom ℂ) hchar - simpa only [map_prod, map_pow, map_one, Units.coeHom_apply] using h - calc - ρ t (∏ i, s i ^ n i) = ∏ i, (ρ t (s i)) ^ n i := by simp only [map_prod, map_pow] - _ = ∏ i, ((character (α i) t : ℂ) • s i) ^ n i := by simp_rw [heigen] - _ = (∏ i, (character (α i) t : ℂ) ^ n i) • ∏ i, s i ^ n i := by - simp only [smul_pow, Finset.prod_smul] - _ = ∏ i, s i ^ n i := by rw [hscalar, one_smul] - -theorem invariant_of_zero_mem_convexHull - {κ δ R : Type*} [Fintype δ] - [CommRing R] [IsDomain R] [Algebra ℂ R] - (A : ℕ → Submodule ℂ R) [SetLike.GradedMonoid A] - (ρ : (δ → ℂˣ) →* (R ≃ₐ[ℂ] R)) - (r : κ → ℕ) (α : κ → δ → ℤ) (s : κ → R) - (hr : ∀ i, 0 < r i) - (hmem : ∀ i, s i ∈ A (r i)) (hne : ∀ i, s i ≠ 0) - (heigen : ∀ t i, ρ t (s i) = (character (α i) t : ℂ) • s i) - (hconvex : (0 : δ → ℝ) ∈ convexHull ℝ - (Set.range (fun i j => (α i j : ℝ) / r i))) : - ∃ m : ℕ, 0 < m ∧ ∃ z : R, z ∈ A m ∧ z ≠ 0 ∧ ∀ t, ρ t z = z := by - classical - let p : κ → δ → ℚ := fun i j => (α i j : ℚ) / r i - have hrat : (0 : δ → ℚ) ∈ convexHull ℚ (Set.range p) := by - apply zero_mem_rational_convexHull - rw [← Set.range_comp'] - change (0 : δ → ℝ) ∈ convexHull ℝ - (Set.range (fun i j => (((α i j : ℚ) / r i : ℚ) : ℝ))) - simpa only [Rat.cast_div, Rat.cast_intCast, Rat.cast_natCast] using hconvex - obtain ⟨ι, _, c, q, hc, hc1, hq, hzero⟩ := - mem_convexHull_iff_exists_fintype.mp hrat - choose f hf using hq - have hzero' : ∑ i, c i • (fun j => (α (f i) j : ℚ) / r (f i)) = 0 := by - simpa only [← hf, p] using hzero - obtain ⟨n, hn, hα⟩ := integral_weight_relation (r ∘ f) (α ∘ f) c - (fun i => hr (f i)) hc hc1 hzero' - exact invariant_product_of_integral_relation A ρ (r ∘ f) (α ∘ f) (s ∘ f) - (fun i => hmem (f i)) (fun i => hne (f i)) (fun t i => heigen t (f i)) n hn hα - -end ExactOrders.Partial - -end - -end OAI +import Mathlib + +namespace OAI + +/-! Invariant products from convex relations among integral characters. -/ + +noncomputable section +open scoped BigOperators + +namespace ExactOrders.Partial + +def realVector {δ : Type*} (p : δ → ℚ) : δ → ℝ := fun j => p j + +lemma rational_barycentric_coordinates + {ι δ : Type*} [Fintype ι] [Fintype δ] + (p : ι → δ → ℚ) (w : ι → ℝ) + (hp : AffineIndependent ℝ (fun i => realVector (p i))) + (hw : ∑ i, w i = 1) + (hz : ∑ i, w i • realVector (p i) = 0) : + ∃ q : ι → ℚ, ∀ i, (q i : ℝ) = w i := by + classical + let u : ι → Option δ → ℚ := fun i j => j.elim 1 (p i) + let A : (ι → ℚ) →ₗ[ℚ] (Option δ → ℚ) := + { toFun := fun a => ∑ i, a i • u i + map_add' := by + intro a b + simp [add_smul, Finset.sum_add_distrib] + map_smul' := by + intro c a + simp [Finset.smul_sum, mul_smul] } + have hker : LinearMap.ker A = ⊥ := by + apply LinearMap.ker_eq_bot'.mpr + intro a ha + have hsum : ∑ i, (a i : ℝ) = 0 := by + have h := congrFun ha none + simp only [A, LinearMap.coe_mk, AddHom.coe_mk, Finset.sum_apply, + Pi.smul_apply, smul_eq_mul, u, Option.elim_none, mul_one, Pi.zero_apply] at h + exact_mod_cast h + have hlin : ∑ i, (a i : ℝ) • realVector (p i) = 0 := by + ext j + have h := congrFun ha (some j) + simp only [A, LinearMap.coe_mk, AddHom.coe_mk, Finset.sum_apply, + Pi.smul_apply, smul_eq_mul, u, Option.elim_some, Pi.zero_apply] at h + simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul, + realVector, Pi.zero_apply] + exact_mod_cast h + have hzero := hp.eq_zero_of_sum_eq_zero hsum hlin + ext i + exact_mod_cast hzero i (Finset.mem_univ i) + obtain ⟨B, hBA⟩ := A.exists_leftInverse_of_injective hker + let e : Option δ → Option δ → ℚ := fun j k => if j = k then 1 else 0 + have hBu (k : ι) : B (u k) = fun i => if k = i then 1 else 0 := by + have h := LinearMap.congr_fun hBA (fun i => if k = i then 1 else 0) + simpa [A] using h + have hcoef (k i : ι) : + ∑ j, (u k j : ℝ) * (B (e j) i : ℝ) = if k = i then 1 else 0 := by + have h := congrFun (hBu k) i + rw [B.pi_apply_eq_sum_univ] at h + simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul] at h + by_cases hki : k = i <;> + simpa [e, hki] using congrArg (fun x : ℚ => (x : ℝ)) h + have haug (j : Option δ) : + (e none j : ℝ) = ∑ k, w k * (u k j : ℝ) := by + cases j with + | none => simpa [e, u] using hw.symm + | some j => + have h := congrFun hz j + simpa [e, u, realVector] using h.symm + refine ⟨B (e none), fun i => ?_⟩ + calc + (B (e none) i : ℝ) = ∑ j, (e none j : ℝ) * (B (e j) i : ℝ) := by + simp [e] + _ = ∑ j, (∑ k, w k * (u k j : ℝ)) * (B (e j) i : ℝ) := by + simp_rw [haug] + _ = ∑ k, w k * (∑ j, (u k j : ℝ) * (B (e j) i : ℝ)) := by + simp only [Finset.sum_mul, Finset.mul_sum, mul_assoc] + exact Finset.sum_comm + _ = ∑ k, w k * (if k = i then 1 else 0) := by simp_rw [hcoef] + _ = w i := by simp + +theorem zero_mem_rational_convexHull + {δ : Type*} [Fintype δ] (s : Set (δ → ℚ)) + (h : (0 : δ → ℝ) ∈ convexHull ℝ (realVector '' s)) : + (0 : δ → ℚ) ∈ convexHull ℚ s := by + classical + obtain ⟨ι, _, z, w, hzs, hz, hwpos, hw, hwz⟩ := + eq_pos_convex_span_of_mem_convexHull h + have hpre : ∀ i, ∃ p ∈ s, realVector p = z i := + fun i => hzs ⟨i, rfl⟩ + choose p hps hpz using hpre + have hpz' : (fun i => realVector (p i)) = z := funext hpz + rw [← hpz'] at hz hwz + obtain ⟨q, hq⟩ := rational_barycentric_coordinates p w hz hw hwz + apply mem_convexHull_of_exists_fintype q p + · intro i + have : 0 < (q i : ℝ) := by rw [hq]; exact hwpos i + exact_mod_cast this.le + · have : ∑ i, (q i : ℝ) = 1 := by simp_rw [hq]; exact hw + exact_mod_cast this + · exact hps + · ext j + have h := congrFun hwz j + simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul, realVector, + Pi.zero_apply] at h ⊢ + simp_rw [← hq] at h + exact_mod_cast h + +lemma natural_common_denominator + {ι : Type*} [Fintype ι] (a : ι → ℚ) (ha : ∀ i, 0 ≤ a i) : + ∃ d : ℕ, 0 < d ∧ ∃ n : ι → ℕ, ∀ i, (n i : ℚ) = d * a i := by + classical + let d := ∏ i, (a i).den + let n : ι → ℕ := fun i => (a i).num.toNat * + ∏ j ∈ Finset.univ.erase i, (a j).den + refine ⟨d, Finset.prod_pos (fun i _ => (a i).den_pos), n, fun i => ?_⟩ + have hnum : ((a i).num.toNat : ℚ) = (a i).num := by + exact_mod_cast Int.toNat_of_nonneg (Rat.num_nonneg.mpr (ha i)) + have hd : (a i).den * (∏ j ∈ Finset.univ.erase i, (a j).den) = d := + Finset.mul_prod_erase Finset.univ (fun j => (a j).den) (Finset.mem_univ i) + calc + (n i : ℚ) = (a i).num * (∏ j ∈ Finset.univ.erase i, (a j).den : ℕ) := by + simp only [n, Nat.cast_mul, hnum] + _ = (a i * (a i).den) * (∏ j ∈ Finset.univ.erase i, (a j).den : ℕ) := by + rw [Rat.mul_den_eq_num] + _ = a i * ((a i).den * (∏ j ∈ Finset.univ.erase i, (a j).den) : ℕ) := by + push_cast + ring + _ = d * a i := by rw [hd, mul_comm] + +lemma integral_weight_relation + {ι δ : Type*} [Fintype ι] + (r : ι → ℕ) (α : ι → δ → ℤ) (c : ι → ℚ) + (hr : ∀ i, 0 < r i) (hc : ∀ i, 0 ≤ c i) + (hc1 : ∑ i, c i = 1) + (hzero : ∑ i, c i • (fun j => (α i j : ℚ) / r i) = 0) : + ∃ n : ι → ℕ, 0 < ∑ i, n i * r i ∧ ∑ i, n i • α i = 0 := by + classical + let a : ι → ℚ := fun i => c i / r i + have hri (i : ι) : (r i : ℚ) ≠ 0 := by exact_mod_cast (hr i).ne' + obtain ⟨d, hd, n, hn⟩ := natural_common_denominator a + (fun i => div_nonneg (hc i) (by positivity)) + have hdeg : (∑ i, n i * r i : ℕ) = d := by + apply Nat.cast_injective (R := ℚ) + push_cast + calc + ∑ i, (n i : ℚ) * r i = ∑ i, (d : ℚ) * c i := by + apply Finset.sum_congr rfl + intro i _ + rw [hn] + dsimp [a] + field_simp [hri i] + _ = d := by rw [← Finset.mul_sum, hc1, mul_one] + refine ⟨n, hdeg ▸ hd, ?_⟩ + ext j + have hz := congrFun hzero j + simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul, Pi.zero_apply] at hz + have hsum : ∑ i, (n i : ℚ) * (α i j : ℚ) = 0 := by + calc + ∑ i, (n i : ℚ) * (α i j : ℚ) = + ∑ i, (d : ℚ) * (c i * ((α i j : ℚ) / r i)) := by + apply Finset.sum_congr rfl + intro i _ + rw [hn] + dsimp [a] + ring + _ = 0 := by rw [← Finset.mul_sum, hz, mul_zero] + simpa only [Finset.sum_apply, Pi.smul_apply, nsmul_eq_mul, Pi.mul_apply, + Pi.zero_apply, Pi.natCast_apply] using + (show ∑ i, (n i : ℤ) * α i j = 0 by exact_mod_cast hsum) + +def character {δ : Type*} [Fintype δ] (α : δ → ℤ) : (δ → ℂˣ) →* ℂˣ where + toFun t := ∏ j, t j ^ α j + map_one' := by simp + map_mul' t u := by simp [mul_zpow, Finset.prod_mul_distrib] + +@[simp] lemma character_zero {δ : Type*} [Fintype δ] (t : δ → ℂˣ) : + character (0 : δ → ℤ) t = 1 := by + simp [character] + +lemma character_add {δ : Type*} [Fintype δ] (α β : δ → ℤ) (t : δ → ℂˣ) : + character (α + β) t = character α t * character β t := by + simp [character, zpow_add, Finset.prod_mul_distrib] + +lemma character_nsmul {δ : Type*} [Fintype δ] + (n : ℕ) (α : δ → ℤ) (t : δ → ℂˣ) : + character (n • α) t = character α t ^ n := by + induction n with + | zero => simp + | succ n ih => rw [succ_nsmul, character_add, ih, pow_succ] + +lemma character_sum {ι δ : Type*} [Fintype δ] + (F : Finset ι) (α : ι → δ → ℤ) (t : δ → ℂˣ) : + character (∑ i ∈ F, α i) t = ∏ i ∈ F, character (α i) t := by + classical + induction F using Finset.induction_on with + | empty => simp + | @insert i F hi ih => simp only [Finset.sum_insert hi, character_add, ih, + Finset.prod_insert hi] + +theorem invariant_product_of_integral_relation + {ι δ R : Type*} [Fintype ι] [Fintype δ] + [CommRing R] [IsDomain R] [Algebra ℂ R] + (A : ℕ → Submodule ℂ R) [SetLike.GradedMonoid A] + (ρ : (δ → ℂˣ) →* (R ≃ₐ[ℂ] R)) + (r : ι → ℕ) (α : ι → δ → ℤ) (s : ι → R) + (hmem : ∀ i, s i ∈ A (r i)) (hne : ∀ i, s i ≠ 0) + (heigen : ∀ t i, ρ t (s i) = (character (α i) t : ℂ) • s i) + (n : ι → ℕ) (hdeg : 0 < ∑ i, n i * r i) + (hweight : ∑ i, n i • α i = 0) : + ∃ m : ℕ, 0 < m ∧ ∃ z : R, z ∈ A m ∧ z ≠ 0 ∧ ∀ t, ρ t z = z := by + classical + refine ⟨∑ i, n i * r i, hdeg, ∏ i, s i ^ n i, ?_, ?_, ?_⟩ + · simpa only [Nat.nsmul_eq_mul] using + (SetLike.prod_pow_mem_graded A r s n (fun i _ => hmem i)) + · exact Finset.prod_ne_zero_iff.mpr (fun i _ => pow_ne_zero _ (hne i)) + · intro t + have hchar : ∏ i, character (α i) t ^ n i = 1 := by + rw [← character_zero t, ← hweight, character_sum] + simp_rw [character_nsmul] + have hscalar : ∏ i, (character (α i) t : ℂ) ^ n i = 1 := by + have h := congrArg (Units.coeHom ℂ) hchar + simpa only [map_prod, map_pow, map_one, Units.coeHom_apply] using h + calc + ρ t (∏ i, s i ^ n i) = ∏ i, (ρ t (s i)) ^ n i := by simp only [map_prod, map_pow] + _ = ∏ i, ((character (α i) t : ℂ) • s i) ^ n i := by simp_rw [heigen] + _ = (∏ i, (character (α i) t : ℂ) ^ n i) • ∏ i, s i ^ n i := by + simp only [smul_pow, Finset.prod_smul] + _ = ∏ i, s i ^ n i := by rw [hscalar, one_smul] + +theorem invariant_of_zero_mem_convexHull + {κ δ R : Type*} [Fintype δ] + [CommRing R] [IsDomain R] [Algebra ℂ R] + (A : ℕ → Submodule ℂ R) [SetLike.GradedMonoid A] + (ρ : (δ → ℂˣ) →* (R ≃ₐ[ℂ] R)) + (r : κ → ℕ) (α : κ → δ → ℤ) (s : κ → R) + (hr : ∀ i, 0 < r i) + (hmem : ∀ i, s i ∈ A (r i)) (hne : ∀ i, s i ≠ 0) + (heigen : ∀ t i, ρ t (s i) = (character (α i) t : ℂ) • s i) + (hconvex : (0 : δ → ℝ) ∈ convexHull ℝ + (Set.range (fun i j => (α i j : ℝ) / r i))) : + ∃ m : ℕ, 0 < m ∧ ∃ z : R, z ∈ A m ∧ z ≠ 0 ∧ ∀ t, ρ t z = z := by + classical + let p : κ → δ → ℚ := fun i j => (α i j : ℚ) / r i + have hrat : (0 : δ → ℚ) ∈ convexHull ℚ (Set.range p) := by + apply zero_mem_rational_convexHull + rw [← Set.range_comp'] + change (0 : δ → ℝ) ∈ convexHull ℝ + (Set.range (fun i j => (((α i j : ℚ) / r i : ℚ) : ℝ))) + simpa only [Rat.cast_div, Rat.cast_intCast, Rat.cast_natCast] using hconvex + obtain ⟨ι, _, c, q, hc, hc1, hq, hzero⟩ := + mem_convexHull_iff_exists_fintype.mp hrat + choose f hf using hq + have hzero' : ∑ i, c i • (fun j => (α (f i) j : ℚ) / r (f i)) = 0 := by + simpa only [← hf, p] using hzero + obtain ⟨n, hn, hα⟩ := integral_weight_relation (r ∘ f) (α ∘ f) c + (fun i => hr (f i)) hc hc1 hzero' + exact invariant_product_of_integral_relation A ρ (r ∘ f) (α ∘ f) (s ∘ f) + (fun i => hmem (f i)) (fun i => hne (f i)) (fun t i => heigen t (f i)) n hn hα + +end ExactOrders.Partial + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/Unitary/Basic.lean b/lean/OAI/RepresentationTheory/Unitary/Basic.lean index 33a2909153d56cd82fce94ee9a94d1df8d1ba6f5..cb38de9a5bd6deb0ab30d66a2f7f2e37e2cd5564 100644 --- a/lean/OAI/RepresentationTheory/Unitary/Basic.lean +++ b/lean/OAI/RepresentationTheory/Unitary/Basic.lean @@ -1,731 +1,731 @@ -import Mathlib -import OAI.Analysis.Matrix.TensorMoment - -namespace OAI - -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable -namespace CoordinateSweeps -structure UnitaryIrrep (Γ : Type*) [Group Γ] where - dimension : ℕ - positive : 0 < dimension - matrix : Γ →* Matrix (Fin dimension) (Fin dimension) ℂ - unitary : ∀ g, (matrix g).conjTranspose * matrix g = 1 - irreducible : ∀ S : Submodule ℂ (Fin dimension → ℂ), - (∀ g v, v ∈ S → (matrix g).mulVec v ∈ S) → S = ⊥ ∨ S = ⊤ -end CoordinateSweeps -namespace CoordinateSweeps -namespace UnitaryIrrep -variable {Γ : Type*} [Group Γ] (ρ : UnitaryIrrep Γ) - -def asRepresentation : Representation ℂ Γ (Fin ρ.dimension → ℂ) := - Matrix.toLinAlgEquiv'.toMonoidHom.comp ρ.matrix - -@[simp] lemma asRepresentation_apply (g : Γ) (v : Fin ρ.dimension → ℂ) : - ρ.asRepresentation g v=(ρ.matrix g).mulVec v := rfl - -instance asRepresentation_irreducible : ρ.asRepresentation.IsIrreducible := by - let : NeZero ρ.dimension := ⟨ρ.positive.ne'⟩ - have hn : (⊥ : Subrepresentation ρ.asRepresentation) ≠ ⊤ := by - intro hh - have h := congrArg Subrepresentation.toSubmodule hh - exact bot_ne_top h - refine { exists_pair_ne := ⟨⊥,⊤,hn⟩, eq_bot_or_eq_top := ?_ } - intro S - rcases ρ.irreducible S.toSubmodule (fun g v hv => S.apply_mem_toSubmodule g hv) with hh | hh - · exact Or.inl (Subrepresentation.toSubmodule_injective hh) - · exact Or.inr (Subrepresentation.toSubmodule_injective hh) - -lemma character_asRepresentation (g : Γ) : - ρ.asRepresentation.character g=Matrix.trace (ρ.matrix g) := - Matrix.trace_toLin'_eq _ - -/- Schur's scalar-commutant statement with all irreducibility obligations -proved directly from the exact source realization. -/ -theorem commuting_scalar (A : Matrix (Fin ρ.dimension) (Fin ρ.dimension) ℂ) - (hA : ∀ g, A*ρ.matrix g=ρ.matrix g*A) : ∃ c : ℂ, A=c • (1 : Matrix _ _ ℂ) := by - let F : Representation.IntertwiningMap ρ.asRepresentation ρ.asRepresentation := - { toLinearMap := Matrix.toLinAlgEquiv' A - isIntertwining' := by - intro g - change Matrix.toLinAlgEquiv' A * Matrix.toLinAlgEquiv' (ρ.matrix g)= - Matrix.toLinAlgEquiv' (ρ.matrix g) * Matrix.toLinAlgEquiv' A - rw [← map_mul,← map_mul,hA g] } - obtain ⟨c,hc⟩ := Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed - (ρ := ρ.asRepresentation) |>.2 F - refine ⟨c,?_⟩ - apply Matrix.toLinAlgEquiv'.injective - have hh := congrArg Representation.IntertwiningMap.toLinearMap hc - change c • (1 : Module.End ℂ (Fin ρ.dimension → ℂ))=Matrix.toLinAlgEquiv' A at hh - simpa using hh.symm - -variable [Fintype Γ] - -/- Character normalization in exactly the unnormalized trace convention. -/ -theorem character_norm : - (Fintype.card Γ : ℂ)⁻¹ * - ∑ g : Γ, Matrix.trace (ρ.matrix g)*Matrix.trace (ρ.matrix g⁻¹)=1 := by - let : Invertible (Nat.card Γ : ℂ) := invertibleOfNonzero (by - rw [Nat.card_eq_fintype_card] - exact_mod_cast Fintype.card_ne_zero) - have : Nonempty (Representation.Equiv ρ.asRepresentation ρ.asRepresentation) := - ⟨Representation.Equiv.refl _⟩ - have h := Representation.char_orthonormal ρ.asRepresentation ρ.asRepresentation - rw [ite_eq_left (show Nonempty (Representation.Equiv ρ.asRepresentation ρ.asRepresentation) - from inferInstance)] at h - simpa [character_asRepresentation, Nat.card_eq_fintype_card] using h - -omit [Fintype Γ] in -lemma matrix_inv (g : Γ) : ρ.matrix g⁻¹=(ρ.matrix g).conjTranspose := by - calc - ρ.matrix g⁻¹=1*ρ.matrix g⁻¹ := (one_mul _).symm - _ = ((ρ.matrix g).conjTranspose*ρ.matrix g)*ρ.matrix g⁻¹ := by rw [ρ.unitary g] - _ = (ρ.matrix g).conjTranspose := by rw [mul_assoc,← map_mul,mul_inv_cancel,map_one,mul_one] - -/- Coefficients of the central isotypic projector, in unnormalized trace -convention. They are derived from an actual irrep, not supplied as character -data satisfying unproved orthogonality equations. -/ -def coefficient (g : Γ) : ℂ := - (ρ.dimension : ℂ)/(Fintype.card Γ : ℂ) * Matrix.trace (ρ.matrix g⁻¹) - -lemma coefficient_conj (k g : Γ) : ρ.coefficient (k*g*k⁻¹)=ρ.coefficient g := by - unfold coefficient - congr 1 - have h := Representation.char_conj ρ.asRepresentation g⁻¹ k - simpa [character_asRepresentation,mul_inv_rev,mul_assoc] using h - -lemma coefficient_star (g : Γ) : star (ρ.coefficient g)=ρ.coefficient g⁻¹ := by - simp only [coefficient,star_mul,star_div₀,star_natCast,inv_inv] - rw [← Matrix.trace_conjTranspose,← ρ.matrix_inv,inv_inv,mul_comm] - -variable {A : Type*} [Semiring A] [Algebra ℂ A] - -def projector (τ : Γ →* A) : A := ∑ g, ρ.coefficient g • τ g - -lemma projector_commute (τ : Γ →* A) (k : Γ) : - τ k * ρ.projector τ=ρ.projector τ * τ k := by - have hcoef (g : Γ) : ρ.coefficient (k*(g*k⁻¹))=ρ.coefficient g := by - simpa only [mul_assoc] using ρ.coefficient_conj k g - have hh := Equiv.sum_comp (MulAut.conj k).toEquiv - (fun g => ρ.coefficient g • (τ g * τ k)) - simpa [projector,Finset.mul_sum,Finset.sum_mul,mul_smul_comm,smul_mul_assoc, - MulAut.conj_apply,hcoef,coefficient_conj,← map_mul,mul_assoc] using hh - -/- The isotypic projector acts as identity in its own irreducible. -/ -theorem projector_self : ρ.projector ρ.matrix=1 := by - obtain ⟨c,hc⟩ := ρ.commuting_scalar (ρ.projector ρ.matrix) - (fun g => (ρ.projector_commute ρ.matrix g).symm) - have ht : Matrix.trace (ρ.projector ρ.matrix)=(ρ.dimension : ℂ) := by - simp only [projector,Matrix.trace_sum,Matrix.trace_smul,coefficient] - calc - _ = (ρ.dimension : ℂ)*((Fintype.card Γ : ℂ)⁻¹ * - ∑ g, Matrix.trace (ρ.matrix g)*Matrix.trace (ρ.matrix g⁻¹)) := by - simp only [Finset.mul_sum] - apply Finset.sum_congr rfl - intro g hg - ring - _ = _ := by rw [ρ.character_norm,mul_one] - rw [hc,Matrix.trace_smul,Matrix.trace_one,Fintype.card_fin,smul_eq_mul] at ht - have hD : (ρ.dimension : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr ρ.positive.ne' - have hcone : c=1 := (mul_right_cancel₀ hD (by simpa using ht)) - simpa [hcone] using hc - -lemma coefficient_convolution (k : Γ) : - ∑ g, ρ.coefficient g * ρ.coefficient (g⁻¹*k)=ρ.coefficient k := by - calc - _ = ((ρ.dimension : ℂ)/(Fintype.card Γ : ℂ)) * - Matrix.trace (ρ.matrix k⁻¹ * ρ.projector ρ.matrix) := by - simp only [projector,Finset.mul_sum,mul_smul_comm,Matrix.trace_sum, - Matrix.trace_smul,smul_eq_mul,coefficient,mul_inv_rev,inv_inv,map_mul] - apply Finset.sum_congr rfl - intro g hg - ring - _ = _ := by rw [ρ.projector_self,mul_one]; rfl - -/- Idempotence in every genuine representation, including absent types. -/ -theorem projector_idempotent (τ : Γ →* A) : ρ.projector τ * ρ.projector τ=ρ.projector τ := by - calc - _ = ∑ g, ∑ h, (ρ.coefficient g * ρ.coefficient h) • τ (g*h) := by - change (∑ g, ρ.coefficient g • τ g) * (∑ h, ρ.coefficient h • τ h)=_ - rw [Finset.sum_mul] - apply Finset.sum_congr rfl - intro g hg - rw [Finset.mul_sum] - apply Finset.sum_congr rfl - intro h hh - rw [smul_mul_smul_comm,← map_mul] - _ = ∑ g, ∑ k, (ρ.coefficient g * ρ.coefficient (g⁻¹*k)) • τ k := by - apply Finset.sum_congr rfl - intro g hg - simpa using Equiv.sum_comp (Equiv.mulLeft g) - (fun k => (ρ.coefficient g * ρ.coefficient (g⁻¹*k)) • τ k) - _ = ∑ k, ∑ g, (ρ.coefficient g * ρ.coefficient (g⁻¹*k)) • τ k := Finset.sum_comm - _ = ∑ k, (∑ g, ρ.coefficient g * ρ.coefficient (g⁻¹*k)) • τ k := by - simp only [Finset.sum_smul] - _ = _ := by simp only [projector,coefficient_convolution] - -variable {n : Type*} [Fintype n] [DecidableEq n] - -theorem projector_hermitian (τ : Γ →* Matrix n n ℂ) - (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) : - (ρ.projector τ).conjTranspose=ρ.projector τ := by - simp only [projector,Matrix.conjTranspose_sum,Matrix.conjTranspose_smul, - coefficient_star,hu] - exact Equiv.sum_comp (Equiv.inv Γ) (fun g => ρ.coefficient g • τ g) - -theorem projector_posSemidef (τ : Γ →* Matrix n n ℂ) - (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) : - (ρ.projector τ).PosSemidef := by - have h := Matrix.posSemidef_conjTranspose_mul_self (ρ.projector τ) - rwa [ρ.projector_hermitian τ hu,ρ.projector_idempotent] at h - -end UnitaryIrrep -end CoordinateSweeps - -/- Multiplicity in a unitary matrix representation is controlled by the -commutant dimension, with exact (unnormalized) character conventions. -/ -namespace CoordinateSweeps -namespace UnitaryIrrep -variable {Γ : Type*} [Group Γ] [Fintype Γ] -variable {n : Type*} [Fintype n] [DecidableEq n] - -def matrixRepresentation (τ : Γ →* Matrix n n ℂ) : Representation ℂ Γ (n → ℂ) := - Matrix.toLinAlgEquiv'.toMonoidHom.comp τ - -omit [Fintype Γ] in -lemma matrixRepresentation_character (τ : Γ →* Matrix n n ℂ) (g : Γ) : - (matrixRepresentation τ).character g=Matrix.trace (τ g) := - Matrix.trace_toLin'_eq _ - -lemma character_sum_multiplicity (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) : - ∑ g, Matrix.trace (τ g)*Matrix.trace (ρ.matrix g⁻¹)= - (Fintype.card Γ : ℂ) * - Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) := by - let : Invertible (Nat.card Γ : ℂ) := invertibleOfNonzero (by - rw [Nat.card_eq_fintype_card] - exact_mod_cast Fintype.card_ne_zero) - have hc := Representation.card_inv_mul_sum_char_mul_char_eq_finrank - ρ.asRepresentation (matrixRepresentation τ) - simp only [character_asRepresentation,matrixRepresentation_character, - Nat.card_eq_fintype_card] at hc - have hN : (Fintype.card Γ : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - calc - _ = (Fintype.card Γ : ℂ) * ((Fintype.card Γ : ℂ)⁻¹ * - ∑ g, Matrix.trace (τ g)*Matrix.trace (ρ.matrix g⁻¹)) := by - rw [← mul_assoc,mul_inv_cancel₀ hN,one_mul] - _ = _ := by rw [hc] - -lemma sum_trace_norm_sq (τ : Γ →* Matrix n n ℂ) - (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) : - ∑ g, ‖Matrix.trace (τ g)‖^2=(Fintype.card Γ : ℝ) * - Module.finrank ℂ ((matrixRepresentation τ).IntertwiningMap (matrixRepresentation τ)) := by - let : Invertible (Nat.card Γ : ℂ) := invertibleOfNonzero (by - rw [Nat.card_eq_fintype_card] - exact_mod_cast Fintype.card_ne_zero) - have hc := Representation.card_inv_mul_sum_char_mul_char_eq_finrank - (matrixRepresentation τ) (matrixRepresentation τ) - simp only [matrixRepresentation_character,Nat.card_eq_fintype_card] at hc - have hN : (Fintype.card Γ : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - have hcs : ∑ g, Matrix.trace (τ g)*Matrix.trace (τ g⁻¹)= - (Fintype.card Γ : ℂ)* - Module.finrank ℂ ((matrixRepresentation τ).IntertwiningMap (matrixRepresentation τ)) := by - rw [← hc,← mul_assoc,mul_inv_cancel₀ hN,one_mul] - have hstar (g : Γ) : Matrix.trace (τ g⁻¹)=star (Matrix.trace (τ g)) := by - rw [← hu,Matrix.trace_conjTranspose] - simp only [hstar,Complex.star_def,Complex.mul_conj'] at hcs - exact_mod_cast hcs - -lemma irrep_sum_trace_norm_sq (ρ : UnitaryIrrep Γ) : - ∑ g, ‖Matrix.trace (ρ.matrix g)‖^2=(Fintype.card Γ : ℝ) := by - have hc := ρ.character_norm - have hN : (Fintype.card Γ : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - have hcs : ∑ g, Matrix.trace (ρ.matrix g)*Matrix.trace (ρ.matrix g⁻¹)= - (Fintype.card Γ : ℂ) := by - calc - _ = (Fintype.card Γ : ℂ)*((Fintype.card Γ : ℂ)⁻¹ * - ∑ g, Matrix.trace (ρ.matrix g)*Matrix.trace (ρ.matrix g⁻¹)) := by - rw [← mul_assoc,mul_inv_cancel₀ hN,one_mul] - _ = _ := by rw [hc,mul_one] - simp only [ρ.matrix_inv,Matrix.trace_conjTranspose,Complex.star_def,Complex.mul_conj'] at hcs - exact_mod_cast hcs - -/- No decomposition/classification hypothesis is needed for this character -Cauchy--Schwarz bound. It applies also to absent types (multiplicity zero). -/ -theorem multiplicity_sq_le_commutant (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) : - (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)))^2 ≤ - Module.finrank ℂ ((matrixRepresentation τ).IntertwiningMap (matrixRepresentation τ)) := by - let m := Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) - let e := Module.finrank ℂ ((matrixRepresentation τ).IntertwiningMap (matrixRepresentation τ)) - have hs : (Fintype.card Γ : ℝ)*(m : ℝ) ≤ - ∑ g, ‖Matrix.trace (τ g)‖*‖Matrix.trace (ρ.matrix g)‖ := by - have hh := norm_sum_le (Finset.univ : Finset Γ) - (fun g => Matrix.trace (τ g)*Matrix.trace (ρ.matrix g⁻¹)) - rw [ρ.character_sum_multiplicity τ] at hh - simpa only [norm_mul,Complex.norm_natCast,ρ.matrix_inv,Matrix.trace_conjTranspose, - norm_star,m] using hh - have hcs := Finset.sum_mul_sq_le_sq_mul_sq (Finset.univ : Finset Γ) - (fun g => ‖Matrix.trace (τ g)‖) (fun g => ‖Matrix.trace (ρ.matrix g)‖) - rw [sum_trace_norm_sq τ hu,ρ.irrep_sum_trace_norm_sq] at hcs - have hN : (0 : ℝ) f g • (τ g*τ k)) - simpa [Finset.mul_sum,Finset.sum_mul,mul_smul_comm,smul_mul_assoc, - MulAut.conj_apply,hcoef,hf,← map_mul,mul_assoc] using hh - -omit [Fintype Γ] in -lemma trace_conj (τ : Γ →* Matrix n n ℂ) (k g : Γ) : - Matrix.trace (τ (k*g*k⁻¹))=Matrix.trace (τ g) := by - rw [map_mul,map_mul,Matrix.trace_mul_cycle,← map_mul,inv_mul_cancel,map_one,one_mul] - -lemma central_character_operator (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) : - ∑ g, Matrix.trace (τ g⁻¹) • ρ.matrix g = - ((Fintype.card Γ : ℂ) * Module.finrank ℂ - (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) / ρ.dimension) • - (1 : Matrix (Fin ρ.dimension) (Fin ρ.dimension) ℂ) := by - let S := ∑ g, Matrix.trace (τ g⁻¹) • ρ.matrix g - have hcomm (k : Γ) : ρ.matrix k*S=S*ρ.matrix k := - central_sum_commute ρ.matrix _ (fun k g => by - simpa only [mul_inv_rev,inv_inv,mul_assoc] using trace_conj τ k g⁻¹) k - obtain ⟨c,hc⟩ := ρ.commuting_scalar S (fun k => (hcomm k).symm) - have hs : Matrix.trace S=(Fintype.card Γ : ℂ) * Module.finrank ℂ - (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) := by - dsimp [S] - rw [Matrix.trace_sum] - simp only [Matrix.trace_smul,smul_eq_mul] - have hh := Equiv.sum_comp (Equiv.inv Γ) - (fun g => Matrix.trace (τ g)*Matrix.trace (ρ.matrix g⁻¹)) - simp only [Equiv.inv_apply,inv_inv] at hh - rw [hh,ρ.character_sum_multiplicity τ] - rw [hc,Matrix.trace_smul,Matrix.trace_one,Fintype.card_fin,smul_eq_mul] at hs - have hD : (ρ.dimension : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr ρ.positive.ne' - have hce : c=(Fintype.card Γ : ℂ) * Module.finrank ℂ - (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) / ρ.dimension := - (eq_div_iff hD).mpr hs - exact hc.trans (congrArg (fun c : ℂ => c • (1 : Matrix (Fin ρ.dimension) (Fin ρ.dimension) ℂ)) hce) - -/- Exact projected character, with the genuine Hom-space multiplicity. -/ -theorem projector_twisted_trace (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) (k : Γ) : - Matrix.trace (ρ.projector τ*τ k) = - (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) : ℂ) * - Matrix.trace (ρ.matrix k) := by - let M : ℂ := Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) - have hN : (Fintype.card Γ : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - have hD : (ρ.dimension : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr ρ.positive.ne' - calc - _ = ((ρ.dimension : ℂ)/(Fintype.card Γ : ℂ)) * - ∑ g, Matrix.trace (ρ.matrix g⁻¹)*Matrix.trace (τ (g*k)) := by - simp only [projector,Finset.sum_mul,smul_mul_assoc,Matrix.trace_sum,Matrix.trace_smul, - smul_eq_mul,coefficient,Finset.mul_sum,map_mul] - apply Finset.sum_congr rfl - intro g hg - ring - _ = ((ρ.dimension : ℂ)/(Fintype.card Γ : ℂ)) * - ∑ g, Matrix.trace (τ g⁻¹)*Matrix.trace (ρ.matrix (k*g)) := by - congr 1 - have hh := Equiv.sum_comp ((Equiv.mulRight k).trans (Equiv.inv Γ)) - (fun g => Matrix.trace (τ g⁻¹)*Matrix.trace (ρ.matrix (k*g))) - convert hh using 1 - apply Finset.sum_congr rfl - intro g hg - change Matrix.trace (ρ.matrix g⁻¹)*Matrix.trace (τ (g*k)) = - Matrix.trace (τ ((g*k)⁻¹)⁻¹)*Matrix.trace (ρ.matrix (k*(g*k)⁻¹)) - simp only [inv_inv,mul_inv_rev,← mul_assoc,mul_inv_cancel,one_mul] - ring - _ = ((ρ.dimension : ℂ)/(Fintype.card Γ : ℂ)) * - Matrix.trace (ρ.matrix k*(∑ g, Matrix.trace (τ g⁻¹) • ρ.matrix g)) := by - simp only [Matrix.mul_sum,Matrix.mul_smul,Matrix.trace_sum,Matrix.trace_smul,smul_eq_mul,map_mul] - _ = M*Matrix.trace (ρ.matrix k) := by - rw [ρ.central_character_operator τ,Matrix.mul_smul,mul_one,Matrix.trace_smul,smul_eq_mul] - change _*( ((Fintype.card Γ : ℂ)*M/(ρ.dimension : ℂ))*_)=_ - field_simp - -end CoordinateSweeps.UnitaryIrrep - -namespace CoordinateSweeps.UnitaryIrrep -variable {Γ n : Type*} [Group Γ] [Fintype Γ] [Fintype n] [DecidableEq n] - -/- The projected trace formula applies to actual elements of the group algebra, -not just to individual group elements. -/ -theorem projector_lift_trace (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - (x : MonoidAlgebra ℂ Γ) : - Matrix.trace (ρ.projector τ*((MonoidAlgebra.lift ℂ _ Γ) τ x)) = - (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) : ℂ) * - Matrix.trace ((MonoidAlgebra.lift ℂ _ Γ) ρ.matrix x) := by - induction x using MonoidAlgebra.induction_on with - | of g => simpa using ρ.projector_twisted_trace τ g - | add x y hx hy => simp only [map_add,mul_add,Matrix.trace_add,hx,hy] - | smul c x hx => simp only [map_smul,Matrix.mul_smul,Matrix.trace_smul,smul_eq_mul,hx]; ring - -/- Literal finite averages and their adjoints have the same group-algebra -word in every unitary representation. -/ -def averageMatrix {Ω : Type*} [Fintype Ω] (τ : Γ →* Matrix n n ℂ) - (w : Ω → ℂ) (g : Ω → Γ) : Matrix n n ℂ := ∑ ω, w ω • τ (g ω) - -def averageAlgebra {Ω : Type*} [Fintype Ω] (w : Ω → ℂ) (g : Ω → Γ) : - MonoidAlgebra ℂ Γ := ∑ ω, MonoidAlgebra.single (g ω) (w ω) - -omit [Fintype Γ] in -lemma lift_averageAlgebra {Ω : Type*} [Fintype Ω] (τ : Γ →* Matrix n n ℂ) - (w : Ω → ℂ) (g : Ω → Γ) : - (MonoidAlgebra.lift ℂ _ Γ) τ (averageAlgebra w g)=averageMatrix τ w g := by - simp only [averageAlgebra,map_sum,MonoidAlgebra.lift_single,averageMatrix] - -omit [Fintype Γ] in -lemma averageMatrix_star {Ω : Type*} [Fintype Ω] (τ : Γ →* Matrix n n ℂ) - (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) (w : Ω → ℂ) (g : Ω → Γ) : - (averageMatrix τ w g).conjTranspose = averageMatrix τ (fun ω => star (w ω)) - (fun ω => (g ω)⁻¹) := by - simp only [averageMatrix,Matrix.conjTranspose_sum,Matrix.conjTranspose_smul,hu] - -/- Exact unnormalized even moment trace on a genuine isotypic component. -/ -theorem projected_average_moment {Ω : Type*} [Fintype Ω] - (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) (w : Ω → ℂ) (g : Ω → Γ) (q : ℕ) : - Matrix.trace (ρ.projector τ*((averageMatrix τ w g).conjTranspose*averageMatrix τ w g)^q) = - (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) : ℂ) * - Matrix.trace (((averageMatrix ρ.matrix w g).conjTranspose*averageMatrix ρ.matrix w g)^q) := by - have hr (k : Γ) : (ρ.matrix k).conjTranspose=ρ.matrix k⁻¹ := (ρ.matrix_inv k).symm - have hh := ρ.projector_lift_trace τ - ((averageAlgebra (fun ω => star (w ω)) (fun ω => (g ω)⁻¹)*averageAlgebra w g)^q) - simpa only [map_pow,map_mul,lift_averageAlgebra,← averageMatrix_star τ hu, - ← averageMatrix_star ρ.matrix hr] using hh - -end CoordinateSweeps.UnitaryIrrep - -namespace CoordinateSweeps.UnitaryIrrep -variable {Γ n : Type*} [Group Γ] [Fintype Γ] [Fintype n] [DecidableEq n] - -lemma projector_commute_average {Ω : Type*} [Fintype Ω] (ρ : UnitaryIrrep Γ) - (τ : Γ →* Matrix n n ℂ) (w : Ω → ℂ) (g : Ω → Γ) : - ρ.projector τ*averageMatrix τ w g=averageMatrix τ w g*ρ.projector τ := by - simp only [averageMatrix,Matrix.mul_sum,Matrix.sum_mul,Matrix.mul_smul,Matrix.smul_mul, - ρ.projector_commute τ] - -open scoped MatrixOrder in -lemma trace_positive_product {A B : Matrix n n ℂ} (hA : A.PosSemidef) (hB : B.PosSemidef) : - 0 ≤ Matrix.trace (A*B) := by - obtain ⟨C,rfl⟩:=CStarAlgebra.nonneg_iff_eq_star_mul_self.mp hA.nonneg - rw [Matrix.star_eq_conjTranspose,Matrix.trace_mul_cycle,Matrix.trace_mul_cycle] - exact (hB.mul_mul_conjTranspose_same C).trace_nonneg - -lemma projector_complement_posSemidef (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) : (1-ρ.projector τ).PosSemidef := by - have h := Matrix.posSemidef_conjTranspose_mul_self (1-ρ.projector τ) - convert h using 1 - rw [Matrix.conjTranspose_sub,Matrix.conjTranspose_one,ρ.projector_hermitian τ hu] - simp only [sub_mul,mul_sub,one_mul,mul_one,ρ.projector_idempotent] - module - -/- Genuine occurrence gives a lower bound for the encompassing unnormalized -moment, with its actual Hom multiplicity and no missing dimension factor. -/ -theorem multiplicity_moment_le {Ω : Type*} [Fintype Ω] - (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) (w : Ω → ℂ) (g : Ω → Γ) (q : ℕ) : - (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) : ℝ) * - (Matrix.trace (((averageMatrix ρ.matrix w g).conjTranspose*averageMatrix ρ.matrix w g)^q)).re ≤ - (Matrix.trace (((averageMatrix τ w g).conjTranspose*averageMatrix τ w g)^q)).re := by - have hB := (Matrix.posSemidef_conjTranspose_mul_self (averageMatrix τ w g)).pow q - have hh := trace_positive_product (ρ.projector_complement_posSemidef τ hu) hB - rw [sub_mul,one_mul,Matrix.trace_sub,ρ.projected_average_moment τ hu w g q] at hh - simpa only [Complex.sub_re,Complex.mul_re,Complex.natCast_re,Complex.natCast_im,zero_mul,sub_zero, - sub_nonneg] using (Complex.nonneg_iff.mp hh).1 - -/- The Schatten moment of the projected average, rather than merely an -inserted projector in the trace, is exactly the same multiplicity formula. -/ -theorem projected_operator_moment {Ω : Type*} [Fintype Ω] - (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) (w : Ω → ℂ) (g : Ω → Γ) {q : ℕ} (hq : q ≠ 0) : - Matrix.trace (((ρ.projector τ*averageMatrix τ w g).conjTranspose* - (ρ.projector τ*averageMatrix τ w g))^q) = - (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) : ℂ) * - Matrix.trace (((averageMatrix ρ.matrix w g).conjTranspose*averageMatrix ρ.matrix w g)^q) := by - let P := ρ.projector τ - let K := averageMatrix τ w g - have hP2 : P*P=P := ρ.projector_idempotent τ - have hPK : P*K=K*P := ρ.projector_commute_average τ w g - have hPs : P.conjTranspose=P := ρ.projector_hermitian τ hu - have hPa : P*K.conjTranspose=K.conjTranspose*P := by - have hh := congrArg Matrix.conjTranspose hPK - simpa only [Matrix.conjTranspose_mul,hPs] using hh.symm - have he : (P*K).conjTranspose*(P*K)=P*(K.conjTranspose*K) := by - rw [Matrix.conjTranspose_mul,hPs] - calc - _ = K.conjTranspose*(P*P)*K := by noncomm_ring - _ = P*(K.conjTranspose*K) := by rw [hP2,← hPa,mul_assoc] - have hc : Commute P (K.conjTranspose*K) := by - show P*(K.conjTranspose*K)=(K.conjTranspose*K)*P - rw [← mul_assoc,hPa,mul_assoc,hPK,← mul_assoc] - change Matrix.trace (((P*K).conjTranspose*(P*K))^q)=_ - rw [he,hc.mul_pow,(show IsIdempotentElem P from hP2).pow_eq hq] - exact ρ.projected_average_moment τ hu w g q - -end CoordinateSweeps.UnitaryIrrep -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable -noncomputable section -attribute [local instance] Classical.propDecidable -namespace CoordinateSweeps.UnitaryIrrep -variable {Γ Λ : Type*} [Group Γ] [Group Λ] - -def pullback (ρ : UnitaryIrrep Λ) (e : Γ ≃* Λ) : UnitaryIrrep Γ where - dimension := ρ.dimension - positive := ρ.positive - matrix := ρ.matrix.comp e.toMonoidHom - unitary g := ρ.unitary (e g) - irreducible S hS := ρ.irreducible S (by - intro g v hv - have hh := hS (e.symm g) v hv - change (ρ.matrix (e (e.symm g))).mulVec v ∈ S at hh - rwa [MulEquiv.apply_symm_apply] at hh) - -end CoordinateSweeps.UnitaryIrrep -noncomputable section -open Set Complex -open scoped BigOperators Topology -open scoped Matrix.Norms.L2Operator -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -namespace CoordinateSweeps.UnitaryRealization -variable {G J : Type*} [Group G] [Fintype G] [Fintype J] [DecidableEq J] - -/- Gram averaging produces the invariant positive form directly from the -finite action; no invariant inner product is postulated. -/ -lemma gram_posDef (τ : G →* Matrix J J ℂ) : - (∑ g, (τ g).conjTranspose * τ g).PosDef := by - apply Matrix.posDef_sum Finset.univ_nonempty - intro g hg - apply Matrix.PosDef.conjTranspose_mul_self - intro x y h - have hh := congrArg (fun v => (τ g⁻¹).mulVec v) h - simpa only [Matrix.mulVec_mulVec,← map_mul,inv_mul_cancel,map_one,Matrix.one_mulVec] using hh - -lemma gram_invariant (τ : G →* Matrix J J ℂ) (h : G) : - (τ h).conjTranspose*(∑ g, (τ g).conjTranspose*τ g)*τ h= - ∑ g, (τ g).conjTranspose*τ g := by - have hh := Equiv.sum_comp (Equiv.mulRight h) (fun g => (τ g).conjTranspose*τ g) - calc - _ = ∑ g, (τ (g*h)).conjTranspose * τ (g*h) := by - simp only [Matrix.mul_sum,Matrix.sum_mul,map_mul,Matrix.conjTranspose_mul] - apply Finset.sum_congr rfl - intro g hg - simp only [mul_assoc] - _ = _ := hh - -/- Actual conjugating matrices and a unitary action for any finite complex -matrix representation. -/ -theorem unitarize (τ : G →* Matrix J J ℂ) : - ∃ A B : Matrix J J ℂ, A*B=1 ∧ B*A=1 ∧ A.IsHermitian ∧ B.IsHermitian ∧ - (∀ g, (B*τ g*A).conjTranspose*(B*τ g*A)=1) := by - let M : Matrix J J ℂ := ∑ g, (τ g).conjTranspose*τ g - obtain ⟨A,hA,hAMA,hcomm⟩ := TensorBoard.exists_whitening M (gram_posDef τ) - have hAM : A*M=M*A := (hcomm M (Commute.refl M)).eq - let B := M*A - have hAB : A*B=1 := by simpa only [B,mul_assoc] using hAMA - have hBA : B*A=1 := by change M*A*A=1; rw [← hAM]; exact hAMA - have hB : B.IsHermitian := by - change (M*A).conjTranspose=M*A - rw [Matrix.conjTranspose_mul,hA.isHermitian.eq,(gram_posDef τ).isHermitian.eq,hAM] - have hB2 : B*B=M := by - calc - _ = M*(A*B) := by simp only [B,mul_assoc] - _ = M := by rw [hAB,mul_one] - refine ⟨A,B,hAB,hBA,hA.isHermitian,hB,?_⟩ - intro g - calc - _ = A*((τ g).conjTranspose*(B*B)*τ g)*A := by - rw [Matrix.conjTranspose_mul,Matrix.conjTranspose_mul,hA.isHermitian.eq,hB.eq] - simp only [mul_assoc] - _ = A*M*A := by rw [hB2,gram_invariant τ g] - _ = 1 := hAMA - -variable {V : Type*} [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] - -/- A genuine irreducible representation has a unitary finite matrix -realization, with the intertwining equivalence retained. -/ -theorem exists_unitary (σ : Representation ℂ G V) [σ.IsIrreducible] : - ∃ ρ : UnitaryIrrep G, Nonempty (Representation.Equiv σ ρ.asRepresentation) := by - let d := Module.finrank ℂ V - let e : V ≃ₗ[ℂ] (Fin d → ℂ) := (Module.finBasis ℂ V).equivFun - let τ : G →* Matrix (Fin d) (Fin d) ℂ := - LinearMap.toMatrixAlgEquiv'.toMonoidHom.comp ((e.conjAlgEquiv ℂ).toMonoidHom.comp σ) - obtain ⟨A,B,hAB,hBA,hA,hB,hu⟩ := unitarize τ - let f : (Fin d → ℂ) ≃ₗ[ℂ] (Fin d → ℂ) := LinearEquiv.ofLinearMap - (Matrix.toLinAlgEquiv' B) (Matrix.toLinAlgEquiv' A) - (by change Matrix.toLinAlgEquiv' B * Matrix.toLinAlgEquiv' A=1 - rw [← map_mul,hBA,map_one]) - (by change Matrix.toLinAlgEquiv' A * Matrix.toLinAlgEquiv' B=1 - rw [← map_mul,hAB,map_one]) - let E := e.trans f - let ν : G →* Matrix (Fin d) (Fin d) ℂ := - { toFun := fun g => B*τ g*A - map_one' := by rw [map_one,mul_one,hBA] - map_mul' := by intro g h; rw [map_mul]; simp only [mul_assoc]; - rw [← mul_assoc A B,hAB,one_mul] } - have he (g : G) (v : V) : (τ g).mulVec (e v)=e (σ g v) := by - change (LinearMap.toMatrix' (e.conj (σ g))).mulVec (e v)=_ - rw [LinearMap.toMatrix'_mulVec] - simp - have hE (g : G) (v : V) : (ν g).mulVec (E v)=E (σ g v) := by - change (B*τ g*A).mulVec (B.mulVec (e v))=B.mulVec (e (σ g v)) - rw [Matrix.mulVec_mulVec] - have hh : B*τ g*A*B=B*τ g := by simp only [mul_assoc,hAB,mul_one] - rw [hh,← Matrix.mulVec_mulVec,he] - have hd : 0 < d := by - have : Nontrivial σ.asModule := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) σ.asModule - have : Nontrivial V := inferInstanceAs (Nontrivial σ.asModule) - exact Module.finrank_pos - let ρ : UnitaryIrrep G := - { dimension := d - positive := hd - matrix := ν - unitary := hu - irreducible := by - intro S hS - let T : Subrepresentation σ := - { toSubmodule := S.comap E.toLinearMap - apply_mem_toSubmodule := by - intro g v hv - change E (σ g v) ∈ S - rw [← hE] - exact hS g (E v) hv } - rcases eq_bot_or_eq_top T with ht | ht - · left - apply le_antisymm _ bot_le - intro w hw - have hv : E.symm w ∈ T := by change E (E.symm w)∈S; simpa using hw - rw [ht] at hv - have hh : E.symm w=0 := hv - simpa using congrArg E hh - · right - apply le_antisymm le_top - intro w hw - have hv : E.symm w ∈ T := by rw [ht]; trivial - change E (E.symm w) ∈ S at hv - simpa using hv } - refine ⟨ρ,⟨Representation.Equiv.mk E ?_⟩⟩ - intro g - apply LinearMap.ext - intro v - exact (hE g v).symm - -end CoordinateSweeps.UnitaryRealization - -namespace CoordinateSweeps.UnitaryIrrep -variable {G : Type*} [Group G] [Fintype G] - -lemma projector_other (ρ σ : UnitaryIrrep G) - (hne : ¬Nonempty (Representation.Equiv ρ.asRepresentation σ.asRepresentation)) : - ρ.projector σ.matrix=0 := by - obtain ⟨c,hc⟩ := σ.commuting_scalar (ρ.projector σ.matrix) - (fun g => (ρ.projector_commute σ.matrix g).symm) - let : Invertible (Nat.card G : ℂ) := invertibleOfNonzero (by - rw [Nat.card_eq_fintype_card]; exact_mod_cast Fintype.card_ne_zero) - have horth := Representation.char_orthonormal σ.asRepresentation ρ.asRepresentation - rw [ite_eq_right hne] at horth - have ht : Matrix.trace (ρ.projector σ.matrix)=0 := by - simp only [projector,Matrix.trace_sum,Matrix.trace_smul,coefficient] - calc - _ = (ρ.dimension : ℂ)*((Fintype.card G : ℂ)⁻¹ * - ∑ g, Matrix.trace (ρ.matrix g⁻¹)*Matrix.trace (σ.matrix g)) := by - simp only [Finset.mul_sum]; apply Finset.sum_congr rfl - intro g hg; simp only [smul_eq_mul]; ring - _ = 0 := by - have hh := horth - simpa [character_asRepresentation,Nat.card_eq_fintype_card, - ← Finset.mul_sum,mul_comm] using congrArg (fun z : ℂ => (ρ.dimension : ℂ)*z) hh - rw [hc,Matrix.trace_smul,Matrix.trace_one,Fintype.card_fin,smul_eq_mul] at ht - have hc0 : c=0 := (mul_eq_zero.mp ht).resolve_right - (Nat.cast_ne_zero.mpr σ.positive.ne') - simpa [hc0] using hc - -lemma cross_convolution (ρ σ : UnitaryIrrep G) - (hne : ¬Nonempty (Representation.Equiv σ.asRepresentation ρ.asRepresentation)) (k : G) : - ∑ g, ρ.coefficient g*σ.coefficient (g⁻¹*k)=0 := by - calc - _ = ((σ.dimension : ℂ)/(Fintype.card G : ℂ)) * - Matrix.trace (σ.matrix k⁻¹ * ρ.projector σ.matrix) := by - simp only [projector,Finset.mul_sum,mul_smul_comm,Matrix.trace_sum, - Matrix.trace_smul,smul_eq_mul,coefficient,mul_inv_rev,inv_inv,map_mul] - apply Finset.sum_congr rfl; intro g hg; ring - _ = 0 := by - rw [projector_other ρ σ (fun ⟨e⟩ => hne ⟨e.symm⟩),mul_zero,Matrix.trace_zero,mul_zero] - -lemma projector_orthogonal {A : Type*} [Semiring A] [Algebra ℂ A] - (ρ σ : UnitaryIrrep G) - (hne : ¬Nonempty (Representation.Equiv σ.asRepresentation ρ.asRepresentation)) - (τ : G →* A) : ρ.projector τ*σ.projector τ=0 := by - calc - _ = ∑ g, ∑ h, (ρ.coefficient g*σ.coefficient h) • τ (g*h) := by - simp only [projector,Finset.sum_mul,Finset.mul_sum,smul_mul_smul_comm,map_mul] - exact Finset.sum_comm - _ = ∑ g, ∑ k, (ρ.coefficient g*σ.coefficient (g⁻¹*k)) • τ k := by - apply Finset.sum_congr rfl; intro g hg - simpa using Equiv.sum_comp (Equiv.mulLeft g) - (fun k => (ρ.coefficient g*σ.coefficient (g⁻¹*k)) • τ k) - _ = ∑ k, (∑ g, ρ.coefficient g*σ.coefficient (g⁻¹*k)) • τ k := by - rw [Finset.sum_comm]; simp only [Finset.sum_smul] - _ = 0 := by simp only [cross_convolution ρ σ hne,zero_smul,Finset.sum_const_zero] - -lemma projector_intertwiner {V W : Type*} [AddCommGroup V] [Module ℂ V] - [AddCommGroup W] [Module ℂ W] (ρ : UnitaryIrrep G) - (τ : Representation ℂ G V) (ν : Representation ℂ G W) - (F : Representation.IntertwiningMap τ ν) (v : V) : - (ρ.projector ν) (F v)=F ((ρ.projector τ) v) := by - simp only [projector,LinearMap.sum_apply,LinearMap.smul_apply, - map_sum,map_smul,Representation.IntertwiningMap.isIntertwining] - -lemma projector_matrix_asRepresentation (ρ σ : UnitaryIrrep G) : - ρ.projector σ.asRepresentation=Matrix.toLinAlgEquiv' (ρ.projector σ.matrix) := by - simp only [projector,map_sum,map_smul] - rfl - -end CoordinateSweeps.UnitaryIrrep -end -end -end -end -end -end -end -end -end -end -open scoped Matrix.Norms.L2Operator - -end OAI +import Mathlib +import OAI.Analysis.Matrix.TensorMoment + +namespace OAI + +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable +namespace CoordinateSweeps +structure UnitaryIrrep (Γ : Type*) [Group Γ] where + dimension : ℕ + positive : 0 < dimension + matrix : Γ →* Matrix (Fin dimension) (Fin dimension) ℂ + unitary : ∀ g, (matrix g).conjTranspose * matrix g = 1 + irreducible : ∀ S : Submodule ℂ (Fin dimension → ℂ), + (∀ g v, v ∈ S → (matrix g).mulVec v ∈ S) → S = ⊥ ∨ S = ⊤ +end CoordinateSweeps +namespace CoordinateSweeps +namespace UnitaryIrrep +variable {Γ : Type*} [Group Γ] (ρ : UnitaryIrrep Γ) + +def asRepresentation : Representation ℂ Γ (Fin ρ.dimension → ℂ) := + Matrix.toLinAlgEquiv'.toMonoidHom.comp ρ.matrix + +@[simp] lemma asRepresentation_apply (g : Γ) (v : Fin ρ.dimension → ℂ) : + ρ.asRepresentation g v=(ρ.matrix g).mulVec v := rfl + +instance asRepresentation_irreducible : ρ.asRepresentation.IsIrreducible := by + let : NeZero ρ.dimension := ⟨ρ.positive.ne'⟩ + have hn : (⊥ : Subrepresentation ρ.asRepresentation) ≠ ⊤ := by + intro hh + have h := congrArg Subrepresentation.toSubmodule hh + exact bot_ne_top h + refine { exists_pair_ne := ⟨⊥,⊤,hn⟩, eq_bot_or_eq_top := ?_ } + intro S + rcases ρ.irreducible S.toSubmodule (fun g v hv => S.apply_mem_toSubmodule g hv) with hh | hh + · exact Or.inl (Subrepresentation.toSubmodule_injective hh) + · exact Or.inr (Subrepresentation.toSubmodule_injective hh) + +lemma character_asRepresentation (g : Γ) : + ρ.asRepresentation.character g=Matrix.trace (ρ.matrix g) := + Matrix.trace_toLin'_eq _ + +/- Schur's scalar-commutant statement with all irreducibility obligations +proved directly from the exact source realization. -/ +theorem commuting_scalar (A : Matrix (Fin ρ.dimension) (Fin ρ.dimension) ℂ) + (hA : ∀ g, A*ρ.matrix g=ρ.matrix g*A) : ∃ c : ℂ, A=c • (1 : Matrix _ _ ℂ) := by + let F : Representation.IntertwiningMap ρ.asRepresentation ρ.asRepresentation := + { toLinearMap := Matrix.toLinAlgEquiv' A + isIntertwining' := by + intro g + change Matrix.toLinAlgEquiv' A * Matrix.toLinAlgEquiv' (ρ.matrix g)= + Matrix.toLinAlgEquiv' (ρ.matrix g) * Matrix.toLinAlgEquiv' A + rw [← map_mul,← map_mul,hA g] } + obtain ⟨c,hc⟩ := Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed + (ρ := ρ.asRepresentation) |>.2 F + refine ⟨c,?_⟩ + apply Matrix.toLinAlgEquiv'.injective + have hh := congrArg Representation.IntertwiningMap.toLinearMap hc + change c • (1 : Module.End ℂ (Fin ρ.dimension → ℂ))=Matrix.toLinAlgEquiv' A at hh + simpa using hh.symm + +variable [Fintype Γ] + +/- Character normalization in exactly the unnormalized trace convention. -/ +theorem character_norm : + (Fintype.card Γ : ℂ)⁻¹ * + ∑ g : Γ, Matrix.trace (ρ.matrix g)*Matrix.trace (ρ.matrix g⁻¹)=1 := by + let : Invertible (Nat.card Γ : ℂ) := invertibleOfNonzero (by + rw [Nat.card_eq_fintype_card] + exact_mod_cast Fintype.card_ne_zero) + have : Nonempty (Representation.Equiv ρ.asRepresentation ρ.asRepresentation) := + ⟨Representation.Equiv.refl _⟩ + have h := Representation.char_orthonormal ρ.asRepresentation ρ.asRepresentation + rw [ite_eq_left (show Nonempty (Representation.Equiv ρ.asRepresentation ρ.asRepresentation) + from inferInstance)] at h + simpa [character_asRepresentation, Nat.card_eq_fintype_card] using h + +omit [Fintype Γ] in +lemma matrix_inv (g : Γ) : ρ.matrix g⁻¹=(ρ.matrix g).conjTranspose := by + calc + ρ.matrix g⁻¹=1*ρ.matrix g⁻¹ := (one_mul _).symm + _ = ((ρ.matrix g).conjTranspose*ρ.matrix g)*ρ.matrix g⁻¹ := by rw [ρ.unitary g] + _ = (ρ.matrix g).conjTranspose := by rw [mul_assoc,← map_mul,mul_inv_cancel,map_one,mul_one] + +/- Coefficients of the central isotypic projector, in unnormalized trace +convention. They are derived from an actual irrep, not supplied as character +data satisfying unproved orthogonality equations. -/ +def coefficient (g : Γ) : ℂ := + (ρ.dimension : ℂ)/(Fintype.card Γ : ℂ) * Matrix.trace (ρ.matrix g⁻¹) + +lemma coefficient_conj (k g : Γ) : ρ.coefficient (k*g*k⁻¹)=ρ.coefficient g := by + unfold coefficient + congr 1 + have h := Representation.char_conj ρ.asRepresentation g⁻¹ k + simpa [character_asRepresentation,mul_inv_rev,mul_assoc] using h + +lemma coefficient_star (g : Γ) : star (ρ.coefficient g)=ρ.coefficient g⁻¹ := by + simp only [coefficient,star_mul,star_div₀,star_natCast,inv_inv] + rw [← Matrix.trace_conjTranspose,← ρ.matrix_inv,inv_inv,mul_comm] + +variable {A : Type*} [Semiring A] [Algebra ℂ A] + +def projector (τ : Γ →* A) : A := ∑ g, ρ.coefficient g • τ g + +lemma projector_commute (τ : Γ →* A) (k : Γ) : + τ k * ρ.projector τ=ρ.projector τ * τ k := by + have hcoef (g : Γ) : ρ.coefficient (k*(g*k⁻¹))=ρ.coefficient g := by + simpa only [mul_assoc] using ρ.coefficient_conj k g + have hh := Equiv.sum_comp (MulAut.conj k).toEquiv + (fun g => ρ.coefficient g • (τ g * τ k)) + simpa [projector,Finset.mul_sum,Finset.sum_mul,mul_smul_comm,smul_mul_assoc, + MulAut.conj_apply,hcoef,coefficient_conj,← map_mul,mul_assoc] using hh + +/- The isotypic projector acts as identity in its own irreducible. -/ +theorem projector_self : ρ.projector ρ.matrix=1 := by + obtain ⟨c,hc⟩ := ρ.commuting_scalar (ρ.projector ρ.matrix) + (fun g => (ρ.projector_commute ρ.matrix g).symm) + have ht : Matrix.trace (ρ.projector ρ.matrix)=(ρ.dimension : ℂ) := by + simp only [projector,Matrix.trace_sum,Matrix.trace_smul,coefficient] + calc + _ = (ρ.dimension : ℂ)*((Fintype.card Γ : ℂ)⁻¹ * + ∑ g, Matrix.trace (ρ.matrix g)*Matrix.trace (ρ.matrix g⁻¹)) := by + simp only [Finset.mul_sum] + apply Finset.sum_congr rfl + intro g hg + ring + _ = _ := by rw [ρ.character_norm,mul_one] + rw [hc,Matrix.trace_smul,Matrix.trace_one,Fintype.card_fin,smul_eq_mul] at ht + have hD : (ρ.dimension : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr ρ.positive.ne' + have hcone : c=1 := (mul_right_cancel₀ hD (by simpa using ht)) + simpa [hcone] using hc + +lemma coefficient_convolution (k : Γ) : + ∑ g, ρ.coefficient g * ρ.coefficient (g⁻¹*k)=ρ.coefficient k := by + calc + _ = ((ρ.dimension : ℂ)/(Fintype.card Γ : ℂ)) * + Matrix.trace (ρ.matrix k⁻¹ * ρ.projector ρ.matrix) := by + simp only [projector,Finset.mul_sum,mul_smul_comm,Matrix.trace_sum, + Matrix.trace_smul,smul_eq_mul,coefficient,mul_inv_rev,inv_inv,map_mul] + apply Finset.sum_congr rfl + intro g hg + ring + _ = _ := by rw [ρ.projector_self,mul_one]; rfl + +/- Idempotence in every genuine representation, including absent types. -/ +theorem projector_idempotent (τ : Γ →* A) : ρ.projector τ * ρ.projector τ=ρ.projector τ := by + calc + _ = ∑ g, ∑ h, (ρ.coefficient g * ρ.coefficient h) • τ (g*h) := by + change (∑ g, ρ.coefficient g • τ g) * (∑ h, ρ.coefficient h • τ h)=_ + rw [Finset.sum_mul] + apply Finset.sum_congr rfl + intro g hg + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro h hh + rw [smul_mul_smul_comm,← map_mul] + _ = ∑ g, ∑ k, (ρ.coefficient g * ρ.coefficient (g⁻¹*k)) • τ k := by + apply Finset.sum_congr rfl + intro g hg + simpa using Equiv.sum_comp (Equiv.mulLeft g) + (fun k => (ρ.coefficient g * ρ.coefficient (g⁻¹*k)) • τ k) + _ = ∑ k, ∑ g, (ρ.coefficient g * ρ.coefficient (g⁻¹*k)) • τ k := Finset.sum_comm + _ = ∑ k, (∑ g, ρ.coefficient g * ρ.coefficient (g⁻¹*k)) • τ k := by + simp only [Finset.sum_smul] + _ = _ := by simp only [projector,coefficient_convolution] + +variable {n : Type*} [Fintype n] [DecidableEq n] + +theorem projector_hermitian (τ : Γ →* Matrix n n ℂ) + (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) : + (ρ.projector τ).conjTranspose=ρ.projector τ := by + simp only [projector,Matrix.conjTranspose_sum,Matrix.conjTranspose_smul, + coefficient_star,hu] + exact Equiv.sum_comp (Equiv.inv Γ) (fun g => ρ.coefficient g • τ g) + +theorem projector_posSemidef (τ : Γ →* Matrix n n ℂ) + (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) : + (ρ.projector τ).PosSemidef := by + have h := Matrix.posSemidef_conjTranspose_mul_self (ρ.projector τ) + rwa [ρ.projector_hermitian τ hu,ρ.projector_idempotent] at h + +end UnitaryIrrep +end CoordinateSweeps + +/- Multiplicity in a unitary matrix representation is controlled by the +commutant dimension, with exact (unnormalized) character conventions. -/ +namespace CoordinateSweeps +namespace UnitaryIrrep +variable {Γ : Type*} [Group Γ] [Fintype Γ] +variable {n : Type*} [Fintype n] [DecidableEq n] + +def matrixRepresentation (τ : Γ →* Matrix n n ℂ) : Representation ℂ Γ (n → ℂ) := + Matrix.toLinAlgEquiv'.toMonoidHom.comp τ + +omit [Fintype Γ] in +lemma matrixRepresentation_character (τ : Γ →* Matrix n n ℂ) (g : Γ) : + (matrixRepresentation τ).character g=Matrix.trace (τ g) := + Matrix.trace_toLin'_eq _ + +lemma character_sum_multiplicity (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) : + ∑ g, Matrix.trace (τ g)*Matrix.trace (ρ.matrix g⁻¹)= + (Fintype.card Γ : ℂ) * + Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) := by + let : Invertible (Nat.card Γ : ℂ) := invertibleOfNonzero (by + rw [Nat.card_eq_fintype_card] + exact_mod_cast Fintype.card_ne_zero) + have hc := Representation.card_inv_mul_sum_char_mul_char_eq_finrank + ρ.asRepresentation (matrixRepresentation τ) + simp only [character_asRepresentation,matrixRepresentation_character, + Nat.card_eq_fintype_card] at hc + have hN : (Fintype.card Γ : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + calc + _ = (Fintype.card Γ : ℂ) * ((Fintype.card Γ : ℂ)⁻¹ * + ∑ g, Matrix.trace (τ g)*Matrix.trace (ρ.matrix g⁻¹)) := by + rw [← mul_assoc,mul_inv_cancel₀ hN,one_mul] + _ = _ := by rw [hc] + +lemma sum_trace_norm_sq (τ : Γ →* Matrix n n ℂ) + (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) : + ∑ g, ‖Matrix.trace (τ g)‖^2=(Fintype.card Γ : ℝ) * + Module.finrank ℂ ((matrixRepresentation τ).IntertwiningMap (matrixRepresentation τ)) := by + let : Invertible (Nat.card Γ : ℂ) := invertibleOfNonzero (by + rw [Nat.card_eq_fintype_card] + exact_mod_cast Fintype.card_ne_zero) + have hc := Representation.card_inv_mul_sum_char_mul_char_eq_finrank + (matrixRepresentation τ) (matrixRepresentation τ) + simp only [matrixRepresentation_character,Nat.card_eq_fintype_card] at hc + have hN : (Fintype.card Γ : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + have hcs : ∑ g, Matrix.trace (τ g)*Matrix.trace (τ g⁻¹)= + (Fintype.card Γ : ℂ)* + Module.finrank ℂ ((matrixRepresentation τ).IntertwiningMap (matrixRepresentation τ)) := by + rw [← hc,← mul_assoc,mul_inv_cancel₀ hN,one_mul] + have hstar (g : Γ) : Matrix.trace (τ g⁻¹)=star (Matrix.trace (τ g)) := by + rw [← hu,Matrix.trace_conjTranspose] + simp only [hstar,Complex.star_def,Complex.mul_conj'] at hcs + exact_mod_cast hcs + +lemma irrep_sum_trace_norm_sq (ρ : UnitaryIrrep Γ) : + ∑ g, ‖Matrix.trace (ρ.matrix g)‖^2=(Fintype.card Γ : ℝ) := by + have hc := ρ.character_norm + have hN : (Fintype.card Γ : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + have hcs : ∑ g, Matrix.trace (ρ.matrix g)*Matrix.trace (ρ.matrix g⁻¹)= + (Fintype.card Γ : ℂ) := by + calc + _ = (Fintype.card Γ : ℂ)*((Fintype.card Γ : ℂ)⁻¹ * + ∑ g, Matrix.trace (ρ.matrix g)*Matrix.trace (ρ.matrix g⁻¹)) := by + rw [← mul_assoc,mul_inv_cancel₀ hN,one_mul] + _ = _ := by rw [hc,mul_one] + simp only [ρ.matrix_inv,Matrix.trace_conjTranspose,Complex.star_def,Complex.mul_conj'] at hcs + exact_mod_cast hcs + +/- No decomposition/classification hypothesis is needed for this character +Cauchy--Schwarz bound. It applies also to absent types (multiplicity zero). -/ +theorem multiplicity_sq_le_commutant (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) : + (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)))^2 ≤ + Module.finrank ℂ ((matrixRepresentation τ).IntertwiningMap (matrixRepresentation τ)) := by + let m := Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) + let e := Module.finrank ℂ ((matrixRepresentation τ).IntertwiningMap (matrixRepresentation τ)) + have hs : (Fintype.card Γ : ℝ)*(m : ℝ) ≤ + ∑ g, ‖Matrix.trace (τ g)‖*‖Matrix.trace (ρ.matrix g)‖ := by + have hh := norm_sum_le (Finset.univ : Finset Γ) + (fun g => Matrix.trace (τ g)*Matrix.trace (ρ.matrix g⁻¹)) + rw [ρ.character_sum_multiplicity τ] at hh + simpa only [norm_mul,Complex.norm_natCast,ρ.matrix_inv,Matrix.trace_conjTranspose, + norm_star,m] using hh + have hcs := Finset.sum_mul_sq_le_sq_mul_sq (Finset.univ : Finset Γ) + (fun g => ‖Matrix.trace (τ g)‖) (fun g => ‖Matrix.trace (ρ.matrix g)‖) + rw [sum_trace_norm_sq τ hu,ρ.irrep_sum_trace_norm_sq] at hcs + have hN : (0 : ℝ) f g • (τ g*τ k)) + simpa [Finset.mul_sum,Finset.sum_mul,mul_smul_comm,smul_mul_assoc, + MulAut.conj_apply,hcoef,hf,← map_mul,mul_assoc] using hh + +omit [Fintype Γ] in +lemma trace_conj (τ : Γ →* Matrix n n ℂ) (k g : Γ) : + Matrix.trace (τ (k*g*k⁻¹))=Matrix.trace (τ g) := by + rw [map_mul,map_mul,Matrix.trace_mul_cycle,← map_mul,inv_mul_cancel,map_one,one_mul] + +lemma central_character_operator (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) : + ∑ g, Matrix.trace (τ g⁻¹) • ρ.matrix g = + ((Fintype.card Γ : ℂ) * Module.finrank ℂ + (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) / ρ.dimension) • + (1 : Matrix (Fin ρ.dimension) (Fin ρ.dimension) ℂ) := by + let S := ∑ g, Matrix.trace (τ g⁻¹) • ρ.matrix g + have hcomm (k : Γ) : ρ.matrix k*S=S*ρ.matrix k := + central_sum_commute ρ.matrix _ (fun k g => by + simpa only [mul_inv_rev,inv_inv,mul_assoc] using trace_conj τ k g⁻¹) k + obtain ⟨c,hc⟩ := ρ.commuting_scalar S (fun k => (hcomm k).symm) + have hs : Matrix.trace S=(Fintype.card Γ : ℂ) * Module.finrank ℂ + (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) := by + dsimp [S] + rw [Matrix.trace_sum] + simp only [Matrix.trace_smul,smul_eq_mul] + have hh := Equiv.sum_comp (Equiv.inv Γ) + (fun g => Matrix.trace (τ g)*Matrix.trace (ρ.matrix g⁻¹)) + simp only [Equiv.inv_apply,inv_inv] at hh + rw [hh,ρ.character_sum_multiplicity τ] + rw [hc,Matrix.trace_smul,Matrix.trace_one,Fintype.card_fin,smul_eq_mul] at hs + have hD : (ρ.dimension : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr ρ.positive.ne' + have hce : c=(Fintype.card Γ : ℂ) * Module.finrank ℂ + (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) / ρ.dimension := + (eq_div_iff hD).mpr hs + exact hc.trans (congrArg (fun c : ℂ => c • (1 : Matrix (Fin ρ.dimension) (Fin ρ.dimension) ℂ)) hce) + +/- Exact projected character, with the genuine Hom-space multiplicity. -/ +theorem projector_twisted_trace (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) (k : Γ) : + Matrix.trace (ρ.projector τ*τ k) = + (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) : ℂ) * + Matrix.trace (ρ.matrix k) := by + let M : ℂ := Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) + have hN : (Fintype.card Γ : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + have hD : (ρ.dimension : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr ρ.positive.ne' + calc + _ = ((ρ.dimension : ℂ)/(Fintype.card Γ : ℂ)) * + ∑ g, Matrix.trace (ρ.matrix g⁻¹)*Matrix.trace (τ (g*k)) := by + simp only [projector,Finset.sum_mul,smul_mul_assoc,Matrix.trace_sum,Matrix.trace_smul, + smul_eq_mul,coefficient,Finset.mul_sum,map_mul] + apply Finset.sum_congr rfl + intro g hg + ring + _ = ((ρ.dimension : ℂ)/(Fintype.card Γ : ℂ)) * + ∑ g, Matrix.trace (τ g⁻¹)*Matrix.trace (ρ.matrix (k*g)) := by + congr 1 + have hh := Equiv.sum_comp ((Equiv.mulRight k).trans (Equiv.inv Γ)) + (fun g => Matrix.trace (τ g⁻¹)*Matrix.trace (ρ.matrix (k*g))) + convert hh using 1 + apply Finset.sum_congr rfl + intro g hg + change Matrix.trace (ρ.matrix g⁻¹)*Matrix.trace (τ (g*k)) = + Matrix.trace (τ ((g*k)⁻¹)⁻¹)*Matrix.trace (ρ.matrix (k*(g*k)⁻¹)) + simp only [inv_inv,mul_inv_rev,← mul_assoc,mul_inv_cancel,one_mul] + ring + _ = ((ρ.dimension : ℂ)/(Fintype.card Γ : ℂ)) * + Matrix.trace (ρ.matrix k*(∑ g, Matrix.trace (τ g⁻¹) • ρ.matrix g)) := by + simp only [Matrix.mul_sum,Matrix.mul_smul,Matrix.trace_sum,Matrix.trace_smul,smul_eq_mul,map_mul] + _ = M*Matrix.trace (ρ.matrix k) := by + rw [ρ.central_character_operator τ,Matrix.mul_smul,mul_one,Matrix.trace_smul,smul_eq_mul] + change _*( ((Fintype.card Γ : ℂ)*M/(ρ.dimension : ℂ))*_)=_ + field_simp + +end CoordinateSweeps.UnitaryIrrep + +namespace CoordinateSweeps.UnitaryIrrep +variable {Γ n : Type*} [Group Γ] [Fintype Γ] [Fintype n] [DecidableEq n] + +/- The projected trace formula applies to actual elements of the group algebra, +not just to individual group elements. -/ +theorem projector_lift_trace (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + (x : MonoidAlgebra ℂ Γ) : + Matrix.trace (ρ.projector τ*((MonoidAlgebra.lift ℂ _ Γ) τ x)) = + (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) : ℂ) * + Matrix.trace ((MonoidAlgebra.lift ℂ _ Γ) ρ.matrix x) := by + induction x using MonoidAlgebra.induction_on with + | of g => simpa using ρ.projector_twisted_trace τ g + | add x y hx hy => simp only [map_add,mul_add,Matrix.trace_add,hx,hy] + | smul c x hx => simp only [map_smul,Matrix.mul_smul,Matrix.trace_smul,smul_eq_mul,hx]; ring + +/- Literal finite averages and their adjoints have the same group-algebra +word in every unitary representation. -/ +def averageMatrix {Ω : Type*} [Fintype Ω] (τ : Γ →* Matrix n n ℂ) + (w : Ω → ℂ) (g : Ω → Γ) : Matrix n n ℂ := ∑ ω, w ω • τ (g ω) + +def averageAlgebra {Ω : Type*} [Fintype Ω] (w : Ω → ℂ) (g : Ω → Γ) : + MonoidAlgebra ℂ Γ := ∑ ω, MonoidAlgebra.single (g ω) (w ω) + +omit [Fintype Γ] in +lemma lift_averageAlgebra {Ω : Type*} [Fintype Ω] (τ : Γ →* Matrix n n ℂ) + (w : Ω → ℂ) (g : Ω → Γ) : + (MonoidAlgebra.lift ℂ _ Γ) τ (averageAlgebra w g)=averageMatrix τ w g := by + simp only [averageAlgebra,map_sum,MonoidAlgebra.lift_single,averageMatrix] + +omit [Fintype Γ] in +lemma averageMatrix_star {Ω : Type*} [Fintype Ω] (τ : Γ →* Matrix n n ℂ) + (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) (w : Ω → ℂ) (g : Ω → Γ) : + (averageMatrix τ w g).conjTranspose = averageMatrix τ (fun ω => star (w ω)) + (fun ω => (g ω)⁻¹) := by + simp only [averageMatrix,Matrix.conjTranspose_sum,Matrix.conjTranspose_smul,hu] + +/- Exact unnormalized even moment trace on a genuine isotypic component. -/ +theorem projected_average_moment {Ω : Type*} [Fintype Ω] + (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) (w : Ω → ℂ) (g : Ω → Γ) (q : ℕ) : + Matrix.trace (ρ.projector τ*((averageMatrix τ w g).conjTranspose*averageMatrix τ w g)^q) = + (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) : ℂ) * + Matrix.trace (((averageMatrix ρ.matrix w g).conjTranspose*averageMatrix ρ.matrix w g)^q) := by + have hr (k : Γ) : (ρ.matrix k).conjTranspose=ρ.matrix k⁻¹ := (ρ.matrix_inv k).symm + have hh := ρ.projector_lift_trace τ + ((averageAlgebra (fun ω => star (w ω)) (fun ω => (g ω)⁻¹)*averageAlgebra w g)^q) + simpa only [map_pow,map_mul,lift_averageAlgebra,← averageMatrix_star τ hu, + ← averageMatrix_star ρ.matrix hr] using hh + +end CoordinateSweeps.UnitaryIrrep + +namespace CoordinateSweeps.UnitaryIrrep +variable {Γ n : Type*} [Group Γ] [Fintype Γ] [Fintype n] [DecidableEq n] + +lemma projector_commute_average {Ω : Type*} [Fintype Ω] (ρ : UnitaryIrrep Γ) + (τ : Γ →* Matrix n n ℂ) (w : Ω → ℂ) (g : Ω → Γ) : + ρ.projector τ*averageMatrix τ w g=averageMatrix τ w g*ρ.projector τ := by + simp only [averageMatrix,Matrix.mul_sum,Matrix.sum_mul,Matrix.mul_smul,Matrix.smul_mul, + ρ.projector_commute τ] + +open scoped MatrixOrder in +lemma trace_positive_product {A B : Matrix n n ℂ} (hA : A.PosSemidef) (hB : B.PosSemidef) : + 0 ≤ Matrix.trace (A*B) := by + obtain ⟨C,rfl⟩:=CStarAlgebra.nonneg_iff_eq_star_mul_self.mp hA.nonneg + rw [Matrix.star_eq_conjTranspose,Matrix.trace_mul_cycle,Matrix.trace_mul_cycle] + exact (hB.mul_mul_conjTranspose_same C).trace_nonneg + +lemma projector_complement_posSemidef (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) : (1-ρ.projector τ).PosSemidef := by + have h := Matrix.posSemidef_conjTranspose_mul_self (1-ρ.projector τ) + convert h using 1 + rw [Matrix.conjTranspose_sub,Matrix.conjTranspose_one,ρ.projector_hermitian τ hu] + simp only [sub_mul,mul_sub,one_mul,mul_one,ρ.projector_idempotent] + module + +/- Genuine occurrence gives a lower bound for the encompassing unnormalized +moment, with its actual Hom multiplicity and no missing dimension factor. -/ +theorem multiplicity_moment_le {Ω : Type*} [Fintype Ω] + (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) (w : Ω → ℂ) (g : Ω → Γ) (q : ℕ) : + (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) : ℝ) * + (Matrix.trace (((averageMatrix ρ.matrix w g).conjTranspose*averageMatrix ρ.matrix w g)^q)).re ≤ + (Matrix.trace (((averageMatrix τ w g).conjTranspose*averageMatrix τ w g)^q)).re := by + have hB := (Matrix.posSemidef_conjTranspose_mul_self (averageMatrix τ w g)).pow q + have hh := trace_positive_product (ρ.projector_complement_posSemidef τ hu) hB + rw [sub_mul,one_mul,Matrix.trace_sub,ρ.projected_average_moment τ hu w g q] at hh + simpa only [Complex.sub_re,Complex.mul_re,Complex.natCast_re,Complex.natCast_im,zero_mul,sub_zero, + sub_nonneg] using (Complex.nonneg_iff.mp hh).1 + +/- The Schatten moment of the projected average, rather than merely an +inserted projector in the trace, is exactly the same multiplicity formula. -/ +theorem projected_operator_moment {Ω : Type*} [Fintype Ω] + (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) (w : Ω → ℂ) (g : Ω → Γ) {q : ℕ} (hq : q ≠ 0) : + Matrix.trace (((ρ.projector τ*averageMatrix τ w g).conjTranspose* + (ρ.projector τ*averageMatrix τ w g))^q) = + (Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) : ℂ) * + Matrix.trace (((averageMatrix ρ.matrix w g).conjTranspose*averageMatrix ρ.matrix w g)^q) := by + let P := ρ.projector τ + let K := averageMatrix τ w g + have hP2 : P*P=P := ρ.projector_idempotent τ + have hPK : P*K=K*P := ρ.projector_commute_average τ w g + have hPs : P.conjTranspose=P := ρ.projector_hermitian τ hu + have hPa : P*K.conjTranspose=K.conjTranspose*P := by + have hh := congrArg Matrix.conjTranspose hPK + simpa only [Matrix.conjTranspose_mul,hPs] using hh.symm + have he : (P*K).conjTranspose*(P*K)=P*(K.conjTranspose*K) := by + rw [Matrix.conjTranspose_mul,hPs] + calc + _ = K.conjTranspose*(P*P)*K := by noncomm_ring + _ = P*(K.conjTranspose*K) := by rw [hP2,← hPa,mul_assoc] + have hc : Commute P (K.conjTranspose*K) := by + show P*(K.conjTranspose*K)=(K.conjTranspose*K)*P + rw [← mul_assoc,hPa,mul_assoc,hPK,← mul_assoc] + change Matrix.trace (((P*K).conjTranspose*(P*K))^q)=_ + rw [he,hc.mul_pow,(show IsIdempotentElem P from hP2).pow_eq hq] + exact ρ.projected_average_moment τ hu w g q + +end CoordinateSweeps.UnitaryIrrep +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable +noncomputable section +attribute [local instance] Classical.propDecidable +namespace CoordinateSweeps.UnitaryIrrep +variable {Γ Λ : Type*} [Group Γ] [Group Λ] + +def pullback (ρ : UnitaryIrrep Λ) (e : Γ ≃* Λ) : UnitaryIrrep Γ where + dimension := ρ.dimension + positive := ρ.positive + matrix := ρ.matrix.comp e.toMonoidHom + unitary g := ρ.unitary (e g) + irreducible S hS := ρ.irreducible S (by + intro g v hv + have hh := hS (e.symm g) v hv + change (ρ.matrix (e (e.symm g))).mulVec v ∈ S at hh + rwa [MulEquiv.apply_symm_apply] at hh) + +end CoordinateSweeps.UnitaryIrrep +noncomputable section +open Set Complex +open scoped BigOperators Topology +open scoped Matrix.Norms.L2Operator +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +namespace CoordinateSweeps.UnitaryRealization +variable {G J : Type*} [Group G] [Fintype G] [Fintype J] [DecidableEq J] + +/- Gram averaging produces the invariant positive form directly from the +finite action; no invariant inner product is postulated. -/ +lemma gram_posDef (τ : G →* Matrix J J ℂ) : + (∑ g, (τ g).conjTranspose * τ g).PosDef := by + apply Matrix.posDef_sum Finset.univ_nonempty + intro g hg + apply Matrix.PosDef.conjTranspose_mul_self + intro x y h + have hh := congrArg (fun v => (τ g⁻¹).mulVec v) h + simpa only [Matrix.mulVec_mulVec,← map_mul,inv_mul_cancel,map_one,Matrix.one_mulVec] using hh + +lemma gram_invariant (τ : G →* Matrix J J ℂ) (h : G) : + (τ h).conjTranspose*(∑ g, (τ g).conjTranspose*τ g)*τ h= + ∑ g, (τ g).conjTranspose*τ g := by + have hh := Equiv.sum_comp (Equiv.mulRight h) (fun g => (τ g).conjTranspose*τ g) + calc + _ = ∑ g, (τ (g*h)).conjTranspose * τ (g*h) := by + simp only [Matrix.mul_sum,Matrix.sum_mul,map_mul,Matrix.conjTranspose_mul] + apply Finset.sum_congr rfl + intro g hg + simp only [mul_assoc] + _ = _ := hh + +/- Actual conjugating matrices and a unitary action for any finite complex +matrix representation. -/ +theorem unitarize (τ : G →* Matrix J J ℂ) : + ∃ A B : Matrix J J ℂ, A*B=1 ∧ B*A=1 ∧ A.IsHermitian ∧ B.IsHermitian ∧ + (∀ g, (B*τ g*A).conjTranspose*(B*τ g*A)=1) := by + let M : Matrix J J ℂ := ∑ g, (τ g).conjTranspose*τ g + obtain ⟨A,hA,hAMA,hcomm⟩ := TensorBoard.exists_whitening M (gram_posDef τ) + have hAM : A*M=M*A := (hcomm M (Commute.refl M)).eq + let B := M*A + have hAB : A*B=1 := by simpa only [B,mul_assoc] using hAMA + have hBA : B*A=1 := by change M*A*A=1; rw [← hAM]; exact hAMA + have hB : B.IsHermitian := by + change (M*A).conjTranspose=M*A + rw [Matrix.conjTranspose_mul,hA.isHermitian.eq,(gram_posDef τ).isHermitian.eq,hAM] + have hB2 : B*B=M := by + calc + _ = M*(A*B) := by simp only [B,mul_assoc] + _ = M := by rw [hAB,mul_one] + refine ⟨A,B,hAB,hBA,hA.isHermitian,hB,?_⟩ + intro g + calc + _ = A*((τ g).conjTranspose*(B*B)*τ g)*A := by + rw [Matrix.conjTranspose_mul,Matrix.conjTranspose_mul,hA.isHermitian.eq,hB.eq] + simp only [mul_assoc] + _ = A*M*A := by rw [hB2,gram_invariant τ g] + _ = 1 := hAMA + +variable {V : Type*} [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] + +/- A genuine irreducible representation has a unitary finite matrix +realization, with the intertwining equivalence retained. -/ +theorem exists_unitary (σ : Representation ℂ G V) [σ.IsIrreducible] : + ∃ ρ : UnitaryIrrep G, Nonempty (Representation.Equiv σ ρ.asRepresentation) := by + let d := Module.finrank ℂ V + let e : V ≃ₗ[ℂ] (Fin d → ℂ) := (Module.finBasis ℂ V).equivFun + let τ : G →* Matrix (Fin d) (Fin d) ℂ := + LinearMap.toMatrixAlgEquiv'.toMonoidHom.comp ((e.conjAlgEquiv ℂ).toMonoidHom.comp σ) + obtain ⟨A,B,hAB,hBA,hA,hB,hu⟩ := unitarize τ + let f : (Fin d → ℂ) ≃ₗ[ℂ] (Fin d → ℂ) := LinearEquiv.ofLinearMap + (Matrix.toLinAlgEquiv' B) (Matrix.toLinAlgEquiv' A) + (by change Matrix.toLinAlgEquiv' B * Matrix.toLinAlgEquiv' A=1 + rw [← map_mul,hBA,map_one]) + (by change Matrix.toLinAlgEquiv' A * Matrix.toLinAlgEquiv' B=1 + rw [← map_mul,hAB,map_one]) + let E := e.trans f + let ν : G →* Matrix (Fin d) (Fin d) ℂ := + { toFun := fun g => B*τ g*A + map_one' := by rw [map_one,mul_one,hBA] + map_mul' := by intro g h; rw [map_mul]; simp only [mul_assoc]; + rw [← mul_assoc A B,hAB,one_mul] } + have he (g : G) (v : V) : (τ g).mulVec (e v)=e (σ g v) := by + change (LinearMap.toMatrix' (e.conj (σ g))).mulVec (e v)=_ + rw [LinearMap.toMatrix'_mulVec] + simp + have hE (g : G) (v : V) : (ν g).mulVec (E v)=E (σ g v) := by + change (B*τ g*A).mulVec (B.mulVec (e v))=B.mulVec (e (σ g v)) + rw [Matrix.mulVec_mulVec] + have hh : B*τ g*A*B=B*τ g := by simp only [mul_assoc,hAB,mul_one] + rw [hh,← Matrix.mulVec_mulVec,he] + have hd : 0 < d := by + have : Nontrivial σ.asModule := IsSimpleModule.nontrivial (MonoidAlgebra ℂ G) σ.asModule + have : Nontrivial V := inferInstanceAs (Nontrivial σ.asModule) + exact Module.finrank_pos + let ρ : UnitaryIrrep G := + { dimension := d + positive := hd + matrix := ν + unitary := hu + irreducible := by + intro S hS + let T : Subrepresentation σ := + { toSubmodule := S.comap E.toLinearMap + apply_mem_toSubmodule := by + intro g v hv + change E (σ g v) ∈ S + rw [← hE] + exact hS g (E v) hv } + rcases eq_bot_or_eq_top T with ht | ht + · left + apply le_antisymm _ bot_le + intro w hw + have hv : E.symm w ∈ T := by change E (E.symm w)∈S; simpa using hw + rw [ht] at hv + have hh : E.symm w=0 := hv + simpa using congrArg E hh + · right + apply le_antisymm le_top + intro w hw + have hv : E.symm w ∈ T := by rw [ht]; trivial + change E (E.symm w) ∈ S at hv + simpa using hv } + refine ⟨ρ,⟨Representation.Equiv.mk E ?_⟩⟩ + intro g + apply LinearMap.ext + intro v + exact (hE g v).symm + +end CoordinateSweeps.UnitaryRealization + +namespace CoordinateSweeps.UnitaryIrrep +variable {G : Type*} [Group G] [Fintype G] + +lemma projector_other (ρ σ : UnitaryIrrep G) + (hne : ¬Nonempty (Representation.Equiv ρ.asRepresentation σ.asRepresentation)) : + ρ.projector σ.matrix=0 := by + obtain ⟨c,hc⟩ := σ.commuting_scalar (ρ.projector σ.matrix) + (fun g => (ρ.projector_commute σ.matrix g).symm) + let : Invertible (Nat.card G : ℂ) := invertibleOfNonzero (by + rw [Nat.card_eq_fintype_card]; exact_mod_cast Fintype.card_ne_zero) + have horth := Representation.char_orthonormal σ.asRepresentation ρ.asRepresentation + rw [ite_eq_right hne] at horth + have ht : Matrix.trace (ρ.projector σ.matrix)=0 := by + simp only [projector,Matrix.trace_sum,Matrix.trace_smul,coefficient] + calc + _ = (ρ.dimension : ℂ)*((Fintype.card G : ℂ)⁻¹ * + ∑ g, Matrix.trace (ρ.matrix g⁻¹)*Matrix.trace (σ.matrix g)) := by + simp only [Finset.mul_sum]; apply Finset.sum_congr rfl + intro g hg; simp only [smul_eq_mul]; ring + _ = 0 := by + have hh := horth + simpa [character_asRepresentation,Nat.card_eq_fintype_card, + ← Finset.mul_sum,mul_comm] using congrArg (fun z : ℂ => (ρ.dimension : ℂ)*z) hh + rw [hc,Matrix.trace_smul,Matrix.trace_one,Fintype.card_fin,smul_eq_mul] at ht + have hc0 : c=0 := (mul_eq_zero.mp ht).resolve_right + (Nat.cast_ne_zero.mpr σ.positive.ne') + simpa [hc0] using hc + +lemma cross_convolution (ρ σ : UnitaryIrrep G) + (hne : ¬Nonempty (Representation.Equiv σ.asRepresentation ρ.asRepresentation)) (k : G) : + ∑ g, ρ.coefficient g*σ.coefficient (g⁻¹*k)=0 := by + calc + _ = ((σ.dimension : ℂ)/(Fintype.card G : ℂ)) * + Matrix.trace (σ.matrix k⁻¹ * ρ.projector σ.matrix) := by + simp only [projector,Finset.mul_sum,mul_smul_comm,Matrix.trace_sum, + Matrix.trace_smul,smul_eq_mul,coefficient,mul_inv_rev,inv_inv,map_mul] + apply Finset.sum_congr rfl; intro g hg; ring + _ = 0 := by + rw [projector_other ρ σ (fun ⟨e⟩ => hne ⟨e.symm⟩),mul_zero,Matrix.trace_zero,mul_zero] + +lemma projector_orthogonal {A : Type*} [Semiring A] [Algebra ℂ A] + (ρ σ : UnitaryIrrep G) + (hne : ¬Nonempty (Representation.Equiv σ.asRepresentation ρ.asRepresentation)) + (τ : G →* A) : ρ.projector τ*σ.projector τ=0 := by + calc + _ = ∑ g, ∑ h, (ρ.coefficient g*σ.coefficient h) • τ (g*h) := by + simp only [projector,Finset.sum_mul,Finset.mul_sum,smul_mul_smul_comm,map_mul] + exact Finset.sum_comm + _ = ∑ g, ∑ k, (ρ.coefficient g*σ.coefficient (g⁻¹*k)) • τ k := by + apply Finset.sum_congr rfl; intro g hg + simpa using Equiv.sum_comp (Equiv.mulLeft g) + (fun k => (ρ.coefficient g*σ.coefficient (g⁻¹*k)) • τ k) + _ = ∑ k, (∑ g, ρ.coefficient g*σ.coefficient (g⁻¹*k)) • τ k := by + rw [Finset.sum_comm]; simp only [Finset.sum_smul] + _ = 0 := by simp only [cross_convolution ρ σ hne,zero_smul,Finset.sum_const_zero] + +lemma projector_intertwiner {V W : Type*} [AddCommGroup V] [Module ℂ V] + [AddCommGroup W] [Module ℂ W] (ρ : UnitaryIrrep G) + (τ : Representation ℂ G V) (ν : Representation ℂ G W) + (F : Representation.IntertwiningMap τ ν) (v : V) : + (ρ.projector ν) (F v)=F ((ρ.projector τ) v) := by + simp only [projector,LinearMap.sum_apply,LinearMap.smul_apply, + map_sum,map_smul,Representation.IntertwiningMap.isIntertwining] + +lemma projector_matrix_asRepresentation (ρ σ : UnitaryIrrep G) : + ρ.projector σ.asRepresentation=Matrix.toLinAlgEquiv' (ρ.projector σ.matrix) := by + simp only [projector,map_sum,map_smul] + rfl + +end CoordinateSweeps.UnitaryIrrep +end +end +end +end +end +end +end +end +end +end +open scoped Matrix.Norms.L2Operator + +end OAI diff --git a/lean/OAI/RepresentationTheory/Unitary/Spectral.lean b/lean/OAI/RepresentationTheory/Unitary/Spectral.lean index 2b117417cdaee5757cb416baaa6680a84f843102..0a66668f80350c056a44a76b7d13fcc9c464d423 100644 --- a/lean/OAI/RepresentationTheory/Unitary/Spectral.lean +++ b/lean/OAI/RepresentationTheory/Unitary/Spectral.lean @@ -1,422 +1,422 @@ -import Mathlib -import OAI.RepresentationTheory.Unitary.Basic -import OAI.Analysis.Matrix.TensorMoment - -namespace OAI - -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ComplexConjugate Matrix.Norms.L2Operator -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ComplexOrder MatrixOrder -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators ENNReal -open MeasureTheory -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -noncomputable section -open scoped BigOperators -attribute [local instance] Classical.propDecidable -noncomputable section -open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder -attribute [local instance] Classical.propDecidable -noncomputable section -attribute [local instance] Classical.propDecidable - -namespace CoordinateSweeps.UnitaryIrrep -variable {Γ : Type*} [Group Γ] [Fintype Γ] -variable {n : Type*} [Fintype n] [DecidableEq n] - -lemma projector_trace (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) : - Matrix.trace (ρ.projector τ) = (ρ.dimension : ℂ) * - Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) := by - simp only [projector,Matrix.trace_sum,Matrix.trace_smul,coefficient,smul_eq_mul] - calc - _ = ((ρ.dimension : ℂ)/(Fintype.card Γ : ℂ)) * - ∑ g, Matrix.trace (τ g)*Matrix.trace (ρ.matrix g⁻¹) := by - rw [Finset.mul_sum] - apply Finset.sum_congr rfl - intro g _ - ring - _ = _ := by - rw [ρ.character_sum_multiplicity τ] - have hN : (Fintype.card Γ : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero - field_simp - -lemma dimension_le_of_projector_one (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - [Nonempty n] (h : ρ.projector τ = 1) : ρ.dimension ≤ Fintype.card n := by - have he := ρ.projector_trace τ - rw [h,Matrix.trace_one] at he - have he' : Fintype.card n = ρ.dimension * - Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) := by exact_mod_cast he - have hm : 0 < Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) := by - have hn := Fintype.card_pos (α := n) - by_contra hh - have hz := Nat.eq_zero_of_not_pos hh - rw [hz,mul_zero] at he' - omega - rw [he'] - exact Nat.le_mul_of_pos_right _ hm - -lemma projector_map (ρ : UnitaryIrrep Γ) {m : Type*} [Fintype m] [DecidableEq m] - (e : Matrix n n ℂ →ₐ[ℂ] Matrix m m ℂ) (τ : Γ →* Matrix n n ℂ) : - ρ.projector (e.toMonoidHom.comp τ) = e (ρ.projector τ) := by - change (∑ g, ρ.coefficient g • e (τ g)) = e (∑ g, ρ.coefficient g • τ g) - simp only [map_sum,map_smul] - -end CoordinateSweeps.UnitaryIrrep - -namespace CoordinateSweeps.SpectralBlock -variable {Γ : Type*} [Group Γ] [Fintype Γ] -variable {n : Type*} [Fintype n] [DecidableEq n] - -abbrev Level (r : n → ℝ) (v : ℝ) := {i : n // r i=v} - -omit [DecidableEq n] in -lemma mul_restrict (r : n → ℝ) (v : ℝ) (A B : Matrix n n ℂ) - (hA : ∀ i j, r i ≠ r j → A i j=0) : - (A*B).submatrix (Subtype.val : Level r v → n) (Subtype.val : Level r v → n) = - A.submatrix (Subtype.val : Level r v → n) (Subtype.val : Level r v → n) * B.submatrix (Subtype.val : Level r v → n) (Subtype.val : Level r v → n) := by - ext i j - rw [Matrix.submatrix_apply,Matrix.mul_apply,Matrix.mul_apply] - rw [← Fintype.sum_subtype_add_sum_subtype (fun k => r k=v)] - have hz : ∑ k : {k : n // ¬ r k=v}, A i.val k.val * B k.val j.val = 0 := by - apply Finset.sum_eq_zero - intro k _ - have hne : r i.val ≠ r k.val := by rw [i.property]; exact Ne.symm k.property - rw [hA _ _ hne,zero_mul] - rw [hz,add_zero] - rfl - -def representation (τ : Γ →* Matrix n n ℂ) (r : n → ℝ) (v : ℝ) - (hτ : ∀ g i j, r i ≠ r j → τ g i j=0) : Γ →* Matrix (Level r v) (Level r v) ℂ where - toFun g := (τ g).submatrix Subtype.val Subtype.val - map_one' := by - rw [map_one] - ext i j - simp [Matrix.one_apply,Subtype.val_inj] - map_mul' g h := by - rw [map_mul] - exact mul_restrict r v (τ g) (τ h) (hτ g) - -lemma projector_representation (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - (r : n → ℝ) (v : ℝ) (hτ : ∀ g i j, r i ≠ r j → τ g i j=0) : - ρ.projector (representation τ r v hτ) = - (ρ.projector τ).submatrix (Subtype.val : Level r v → n) (Subtype.val : Level r v → n) := by - ext i j - simp [UnitaryIrrep.projector,Matrix.sum_apply,representation] - -omit [Fintype Γ] in -lemma offDiagonal_zero (τ : Γ →* Matrix n n ℂ) (r : n → ℝ) - (hτ : ∀ g, τ g * Matrix.diagonal (fun i => (r i : ℂ)) = - Matrix.diagonal (fun i => (r i : ℂ)) * τ g) : - ∀ g i j, r i ≠ r j → τ g i j=0 := by - intro g i j hij - have he := congrArg (fun M : Matrix n n ℂ => M i j) (hτ g) - simp only [Matrix.mul_diagonal,Matrix.diagonal_mul] at he - by_contra hn - apply hij - exact Complex.ofReal_injective (mul_left_cancel₀ hn (he.trans (mul_comm _ _))).symm - -lemma projector_on_level (P : Matrix n n ℂ) (r : n → ℝ) (v : ℝ) (hv : v ≠ 0) - (hP : P * Matrix.diagonal (fun i => (r i : ℂ)) = Matrix.diagonal (fun i => (r i : ℂ))) : - P.submatrix (Subtype.val : Level r v → n) (Subtype.val : Level r v → n) = 1 := by - ext i j - have he := congrArg (fun M : Matrix n n ℂ => M i.val j.val) hP - simp only [Matrix.mul_diagonal,Matrix.diagonal_apply] at he - have hv' : (v : ℂ) ≠ 0 := by exact_mod_cast hv - apply mul_right_cancel₀ hv' - change P i.val j.val * (v : ℂ) = (1 : Matrix (Level r v) (Level r v) ℂ) i j * (v : ℂ) - simpa only [i.property,j.property,Matrix.one_apply,Subtype.val_inj,ite_mul,one_mul,zero_mul] using he - -omit [DecidableEq n] in -lemma level_card_le_trace (r : n → ℝ) (hr : ∀ i, 0 ≤ r i) (v : ℝ) : - Fintype.card (Level r v) * v ≤ ∑ i, r i := by - rw [← Fintype.sum_subtype_add_sum_subtype (fun i => r i=v)] - have he : ∑ i : Level r v, r i.val = Fintype.card (Level r v) * v := by - simp_rw [show ∀ i : Level r v, r i.val = v from fun i => i.property] - simp - rw [he] - exact le_add_of_nonneg_right (Finset.sum_nonneg (fun i _ => hr i.val)) - -/- Positive spectral blocks supported on an actual character projector have -at least the actual irreducible dimension. No decomposition is assumed. -/ -lemma dimension_mul_eigenvalue_le_trace (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - (r : n → ℝ) (hr : ∀ i, 0 ≤ r i) - (hτ : ∀ g, τ g * Matrix.diagonal (fun i => (r i : ℂ)) = - Matrix.diagonal (fun i => (r i : ℂ)) * τ g) - (hP : ρ.projector τ * Matrix.diagonal (fun i => (r i : ℂ)) = Matrix.diagonal (fun i => (r i : ℂ))) - (i : n) : (ρ.dimension : ℝ)*r i ≤ ∑ j, r j := by - by_cases hi : r i=0 - · simp only [hi,mul_zero] - exact Finset.sum_nonneg (fun j _ => hr j) - · let : Nonempty (Level r (r i)) := ⟨⟨i,rfl⟩⟩ - have hzero := offDiagonal_zero τ r hτ - have hproj : ρ.projector (representation τ r (r i) hzero) = 1 := by - rw [projector_representation] - exact projector_on_level _ _ _ hi hP - have hc := ρ.dimension_le_of_projector_one (representation τ r (r i) hzero) hproj - exact (mul_le_mul_of_nonneg_right (by exact_mod_cast hc) (hr i)).trans - (level_card_le_trace r hr (r i)) -end CoordinateSweeps.SpectralBlock - -namespace CoordinateSweeps.UnitaryIrrep -variable {Γ : Type*} [Group Γ] [Fintype Γ] -variable {n : Type*} [Fintype n] [DecidableEq n] - -/- Source06's dimension-normalized spectral estimate, for every genuine -finite group representation. A is supported on the actual central projection. -/ -theorem supported_trace_domination (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - (A : Matrix n n ℂ) (hA : A.PosSemidef) - (hcomm : ∀ g, τ g * A = A * τ g) (hP : ρ.projector τ * A = A) : - (Matrix.trace A • (1 : Matrix n n ℂ) - (ρ.dimension : ℂ) • A).PosSemidef := by - let U := hA.isHermitian.eigenvectorUnitary - let e := (Unitary.conjStarAlgAut ℂ (Matrix n n ℂ) (star U)).toAlgEquiv.toAlgHom - let r := hA.isHermitian.eigenvalues - let d : n → ℂ := RCLike.ofReal ∘ r - let τ' : Γ →* Matrix n n ℂ := e.toMonoidHom.comp τ - have hdiag : e A = Matrix.diagonal d := hA.isHermitian.conjStarAlgAut_star_eigenvectorUnitary - have hcomm' (g : Γ) : τ' g * Matrix.diagonal d = Matrix.diagonal d * τ' g := by - change e (τ g) * Matrix.diagonal d = Matrix.diagonal d * e (τ g) - rw [← hdiag,← map_mul,← map_mul,hcomm g] - have hP' : ρ.projector τ' * Matrix.diagonal d = Matrix.diagonal d := by - rw [ρ.projector_map e τ,← hdiag,← map_mul,hP] - have hi (i : n) : (ρ.dimension : ℝ)*r i ≤ ∑ j, r j := - SpectralBlock.dimension_mul_eigenvalue_le_trace ρ τ' r hA.eigenvalues_nonneg hcomm' hP' i - have hd (i : n) : (0 : ℂ) ≤ Matrix.trace A - (ρ.dimension : ℂ)*d i := by - rw [hA.isHermitian.trace_eq_sum_eigenvalues] - change (0 : ℂ) ≤ (∑ j, (r j : ℂ)) - (ρ.dimension : ℂ)*(r i : ℂ) - exact_mod_cast sub_nonneg.mpr (hi i) - have hD := Matrix.PosSemidef.diagonal hd - have h := hD.mul_mul_conjTranspose_same (U : Matrix n n ℂ) - have hU : (U : Matrix n n ℂ) * (U : Matrix n n ℂ).conjTranspose = 1 := by - simpa only [Unitary.coe_star,Matrix.star_eq_conjTranspose] using Unitary.coe_mul_star_self U - have hspec : (U : Matrix n n ℂ) * Matrix.diagonal d * (U : Matrix n n ℂ).conjTranspose = A := by - simpa only [U,d,r,Function.comp_def,Unitary.conjStarAlgAut_apply,Matrix.star_eq_conjTranspose] using hA.isHermitian.spectral_theorem.symm - have he : Matrix.diagonal (fun i => Matrix.trace A - (ρ.dimension : ℂ)*d i) = - Matrix.trace A • (1 : Matrix n n ℂ) - (ρ.dimension : ℂ) • Matrix.diagonal d := by - ext i j - by_cases hij : i=j <;> simp [Matrix.diagonal,hij] - simpa only [he,Matrix.mul_sub,Matrix.sub_mul,Matrix.mul_smul,Matrix.smul_mul, - Matrix.mul_one,hU,hspec] using h - -/- Compression of a positive invariant unit-trace operator to any isotypic -type is at most inverse irreducible dimension in operator order. -/ -theorem invariant_projector_trace_domination (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) (T : Matrix n n ℂ) (hT : T.PosSemidef) - (hcomm : ∀ g, τ g*T=T*τ g) : - (Matrix.trace T • (1 : Matrix n n ℂ) - (ρ.dimension : ℂ) • - (ρ.projector τ * T * ρ.projector τ)).PosSemidef := by - let P := ρ.projector τ - have hP : P.conjTranspose=P := ρ.projector_hermitian τ hu - have hP2 : P*P=P := ρ.projector_idempotent τ - let A := P*T*P - have hA : A.PosSemidef := by - simpa only [hP] using hT.mul_mul_conjTranspose_same P - have hAc (g : Γ) : τ g*A=A*τ g := by - dsimp [A] - calc - _ = (τ g*P)*T*P := by noncomm_ring - _ = (P*τ g)*T*P := by rw [ρ.projector_commute τ g] - _ = P*(τ g*T)*P := by noncomm_ring - _ = P*(T*τ g)*P := by rw [hcomm] - _ = P*T*(τ g*P) := by noncomm_ring - _ = P*T*(P*τ g) := by rw [ρ.projector_commute τ g] - _ = _ := by noncomm_ring - have hPA : P*A=A := by dsimp [A]; rw [← mul_assoc,← mul_assoc,hP2] - have hbound := ρ.supported_trace_domination τ A hA hAc hPA - have htrace : Matrix.trace A ≤ Matrix.trace T := by - have hc := hT.mul_mul_conjTranspose_same (1-P) - rw [Matrix.conjTranspose_sub,Matrix.conjTranspose_one,hP] at hc - have hh := hc.trace_nonneg - have he : Matrix.trace ((1-P)*T*(1-P)) = Matrix.trace T-Matrix.trace A := by - dsimp [A] - have hx : (1-P)*(1-P) = 1-P := by - calc - _ = 1-P-P+P*P := by noncomm_ring - _ = _ := by rw [hP2]; module - rw [Matrix.trace_mul_cycle,hx,sub_mul,one_mul,Matrix.trace_sub] - rw [Matrix.trace_mul_cycle P T P,hP2] - - rw [he] at hh - exact sub_nonneg.mp hh - have hpad := (Matrix.PosSemidef.one (n := n) (R := ℂ)).smul (sub_nonneg.mpr htrace) - have h := hpad.add hbound - change (Matrix.trace T • (1 : Matrix n n ℂ) - (ρ.dimension : ℂ) • A).PosSemidef - convert h using 1 - module -end CoordinateSweeps.UnitaryIrrep -namespace CoordinateSweeps.Overlap -open TensorBoard -variable {n Γ : Type*} [Fintype n] [DecidableEq n] [Nonempty n] [Group Γ] [Fintype Γ] - -open scoped MatrixOrder in -lemma norm_le_trace (A : Matrix n n ℂ) (hA : A.PosSemidef) : ‖A‖ ≤ (Matrix.trace A).re := by - have hh := PositiveTensor.trace_domination A hA - have hn := CStarAlgebra.norm_le_norm_of_le_of_nonneg - (show A ≤ Matrix.trace A • (1 : Matrix n n ℂ) from sub_nonneg.mp hh.nonneg) hA.nonneg - have htr := Complex.nonneg_iff.mp hA.trace_nonneg - have he : ((Matrix.trace A).re : ℂ)=Matrix.trace A := by - apply Complex.ext <;> simp [htr.2] - rw [← he,norm_smul,Complex.norm_of_nonneg htr.1,norm_one,mul_one] at hn - exact hn - -lemma norm_sq_le_trace (A : Matrix n n ℂ) : - ‖A‖^2 ≤ (Matrix.trace (A.conjTranspose*A)).re := by - have hh := norm_le_trace _ (Matrix.posSemidef_conjTranspose_mul_self A) - simpa only [Matrix.l2_opNorm_conjTranspose_mul_self,pow_two] using hh - -omit [DecidableEq n] [Nonempty n] in -lemma projection_product_posSemidef (P Q : Matrix n n ℂ) - (hP : P.IsHermitian) (hP2 : P*P=P) (hQ : Q.PosSemidef) (hPQ : P*Q=Q*P) : - (P*Q).PosSemidef := by - have hh := hQ.mul_mul_conjTranspose_same P - rwa [hP.eq,hPQ,mul_assoc,hP2,← hPQ] at hh - -lemma overlap_norm_sq_le_trace (R Q P : Matrix n n ℂ) - (hR : R.IsHermitian) (hR2 : R*R=R) (hQ : Q.IsHermitian) (hQ2 : Q*Q=Q) - (hP : P.IsHermitian) (hP2 : P*P=P) (hPQ : P*Q=Q*P) : - ‖Q*P*R‖^2 ≤ (Matrix.trace (R*(Q*P))).re := by - have hh := norm_sq_le_trace (Q*P*R) - have he : (Q*P*R).conjTranspose*(Q*P*R)=R*Q*P*R := by - rw [Matrix.conjTranspose_mul,Matrix.conjTranspose_mul,hR.eq,hP.eq,hQ.eq] - calc - _ = R*P*(Q*Q)*P*R := by noncomm_ring - _ = R*(P*Q)*P*R := by rw [hQ2]; noncomm_ring - _ = R*Q*(P*P)*R := by rw [hPQ]; noncomm_ring - _ = _ := by rw [hP2] - rw [he,mul_assoc R Q P,Matrix.trace_mul_cycle R (Q*P) R,hR2] at hh - simpa only [mul_assoc] using hh - -/- Whitening of genuine isotypic trace domination. All projections and -commutations are explicit algebraic obligations; no spectral conclusion assumed. -/ -omit [Nonempty n] in -lemma whitened_projector_domination (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) - (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) - (T A Q : Matrix n n ℂ) (hT : T.PosSemidef) - (hcomm : ∀ g, τ g*T=T*τ g) (hA : A.IsHermitian) - (hATA : A*T*A=1) (hAP : A*ρ.projector τ=ρ.projector τ*A) - (hAQ : A*Q=Q*A) (hQ : Q.IsHermitian) (hQ2 : Q*Q=Q) - (hPQ : ρ.projector τ*Q= Q*ρ.projector τ) : - (Matrix.trace T • (A*Q*A) - (ρ.dimension : ℂ) • (Q*ρ.projector τ)).PosSemidef := by - let P := ρ.projector τ - change A*P=P*A at hAP - change P*Q=Q*P at hPQ - have hP2 : P*P=P := ρ.projector_idempotent τ - have hh := ρ.invariant_projector_trace_domination τ hu T hT hcomm - change (Matrix.trace T • (1 : Matrix n n ℂ) - (ρ.dimension : ℂ) • (P*T*P)).PosSemidef at hh - have hk := (hh.mul_mul_conjTranspose_same Q).mul_mul_conjTranspose_same A - simp only [hA.eq,hQ.eq,Matrix.mul_sub,Matrix.sub_mul,Matrix.mul_smul,Matrix.smul_mul] at hk - have hAQP : A*(Q*P)=(Q*P)*A := by - rw [← mul_assoc,hAQ,mul_assoc Q A P,hAP,← mul_assoc] - have hPQA : (P*Q)*A=A*(P*Q) := by - rw [mul_assoc,← hAQ,← mul_assoc P A Q,← hAP,mul_assoc] - have ht : A*(Q*(P*T*P)*Q)*A=Q*P := by - calc - _ = (A*(Q*P))*T*((P*Q)*A) := by noncomm_ring - _ = (Q*P)*(A*T*A)*(P*Q) := by rw [hAQP,hPQA]; noncomm_ring - _ = Q*(P*P)*Q := by rw [hATA]; noncomm_ring - _ = Q*(P*Q) := by rw [hP2,mul_assoc] - _ = Q*(Q*P) := by rw [hPQ] - _ = Q*P := by rw [← mul_assoc,hQ2] - have he : A*(Q*1*Q)*A=A*Q*A := by rw [mul_one,hQ2] - rw [he,ht] at hk - exact hk - -end CoordinateSweeps.Overlap - -namespace CoordinateSweeps.Overlap -open TensorBoard -variable {n I J : Type*} [Fintype n] [DecidableEq n] [Nonempty n] [Fintype I] [Fintype J] - -omit [DecidableEq n] [Nonempty n] in -lemma trace_mixture_re (w : I → ℝ) (U : I → Matrix n n ℂ) (W : Matrix n n ℂ) : - (Matrix.trace ((∑ i, (w i : ℂ) • U i)*W)).re = ∑ i, w i*(Matrix.trace (U i*W)).re := by - simp only [Matrix.sum_mul,Matrix.smul_mul,Matrix.trace_sum,Matrix.trace_smul,Complex.re_sum, - smul_eq_mul,Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im,zero_mul,sub_zero] - -omit [DecidableEq n] [Nonempty n] in -lemma trace_smul_re (t : ℝ) (W : Matrix n n ℂ) : - (Matrix.trace ((t : ℂ) • W)).re=t*(Matrix.trace W).re := by - simp [Matrix.trace_smul] - -omit [DecidableEq n] [Nonempty n] in -lemma trace_four_swap (A Q U : Matrix n n ℂ) : - Matrix.trace (A*Q*A*U)=Matrix.trace (A*U*A*Q) := by - calc - _ = Matrix.trace ((A*Q)*(A*U)) := congrArg Matrix.trace (by noncomm_ring) - _ = Matrix.trace ((A*U)*(A*Q)) := Matrix.trace_mul_comm _ _ - _ = _ := congrArg Matrix.trace (by noncomm_ring) - -/- Finite density mixtures plus genuine whitened isotypic domination give -the row-column overlap bound, before the harmless epsilon limit. -/ -theorem finite_mixture_overlap (R Q P : Matrix n n ℂ) - (hR : R.IsHermitian) (hR2 : R*R=R) (hQ : Q.IsHermitian) (hQ2 : Q*Q=Q) - (hP : P.IsHermitian) (hP2 : P*P=P) (hPQ : P*Q=Q*P) - (u : I → ℝ) (v : J → ℝ) (hu : ∀ i, 0 ≤ u i) (hv : ∀ j, 0 ≤ v j) - (hsu : ∑ i, u i=1) (hsv : ∑ j, v j=1) - (U : I → Matrix n n ℂ) (V : J → Matrix n n ℂ) (A : I → Matrix n n ℂ) - (hU : ∀ i, (U i).PosSemidef) (hA : ∀ i, (A i).IsHermitian) - (cr cc D t E : ℝ) (hcr : 0 ≤ cr) (hcc : 0 ≤ cc) (hD : 0 ≤ D) (ht : 0 ≤ t) - (hrow : ((cr : ℂ) • (∑ i, (u i : ℂ) • U i)-R).PosSemidef) - (hcol : ((cc : ℂ) • (∑ j, (v j : ℂ) • V j)-Q).PosSemidef) - (hwhite : ∀ i, ((t : ℂ) • (A i*Q*A i)-(D : ℂ) • (Q*P)).PosSemidef) - (hpair : ∀ i j, (Matrix.trace (A i*U i*A i*V j)).re ≤ E) : - D*‖Q*P*R‖^2 ≤ cr*cc*t*E := by - have hQpos : Q.PosSemidef := by - simpa only [hQ.eq,hQ2] using Matrix.posSemidef_conjTranspose_mul_self Q - have hQP : (Q*P).PosSemidef := by - rw [← hPQ] - exact projection_product_posSemidef P Q hP hP2 hQpos hPQ - have hlocal (i : I) : D*(Matrix.trace (U i*(Q*P))).re ≤ t*cc*E := by - let W := A i*U i*A i - have hW : W.PosSemidef := by - simpa only [(hA i).eq] using (hU i).mul_mul_conjTranspose_same (A i) - have hc := (Complex.le_def.mp (trace_mono_right hcol hW)).1 - rw [Matrix.smul_mul,trace_smul_re,trace_mixture_re] at hc - have hpair' (j : J) : (Matrix.trace (V j*W)).re ≤ E := by - rw [Matrix.trace_mul_comm] - exact hpair i j - have hc' : (Matrix.trace (W*Q)).re ≤ cc*E := by - rw [Matrix.trace_mul_comm] - apply hc.trans - apply mul_le_mul_of_nonneg_left _ hcc - calc - _ ≤ ∑ j, v j*E := Finset.sum_le_sum (fun j _ => mul_le_mul_of_nonneg_left (hpair' j) (hv j)) - _ = E := by rw [← Finset.sum_mul,hsv,one_mul] - have hw := (Complex.le_def.mp (trace_mono_right (hwhite i) (hU i))).1 - rw [Matrix.smul_mul,Matrix.smul_mul,trace_smul_re,trace_smul_re, - trace_four_swap,Matrix.trace_mul_comm (Q*P)] at hw - exact hw.trans (by simpa only [W,mul_assoc] using mul_le_mul_of_nonneg_left hc' ht) - have hr := (Complex.le_def.mp (trace_mono_right hrow hQP)).1 - rw [Matrix.smul_mul,trace_smul_re,trace_mixture_re] at hr - calc - _ ≤ D*(Matrix.trace (R*(Q*P))).re := mul_le_mul_of_nonneg_left - (overlap_norm_sq_le_trace R Q P hR hR2 hQ hQ2 hP hP2 hPQ) hD - _ ≤ D*(cr*∑ i, u i*(Matrix.trace (U i*(Q*P))).re) := mul_le_mul_of_nonneg_left hr hD - _ = cr*(∑ i, u i*(D*(Matrix.trace (U i*(Q*P))).re)) := by - rw [Finset.mul_sum,Finset.mul_sum,Finset.mul_sum] - apply Finset.sum_congr rfl - intro i hi - ring - _ ≤ cr*(∑ i, u i*(t*cc*E)) := mul_le_mul_of_nonneg_left - (Finset.sum_le_sum (fun i _ => mul_le_mul_of_nonneg_left (hlocal i) (hu i))) hcr - _ = cr*cc*t*E := by rw [← Finset.sum_mul,hsu,one_mul]; ring - -end CoordinateSweeps.Overlap - -end -end -end -end -end -end -end -end -open scoped Matrix.Norms.L2Operator - -end OAI +import Mathlib +import OAI.RepresentationTheory.Unitary.Basic +import OAI.Analysis.Matrix.TensorMoment + +namespace OAI + +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ComplexConjugate Matrix.Norms.L2Operator +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ComplexOrder MatrixOrder +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators ENNReal +open MeasureTheory +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +noncomputable section +open scoped BigOperators +attribute [local instance] Classical.propDecidable +noncomputable section +open scoped BigOperators Matrix.Norms.L2Operator ComplexOrder +attribute [local instance] Classical.propDecidable +noncomputable section +attribute [local instance] Classical.propDecidable + +namespace CoordinateSweeps.UnitaryIrrep +variable {Γ : Type*} [Group Γ] [Fintype Γ] +variable {n : Type*} [Fintype n] [DecidableEq n] + +lemma projector_trace (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) : + Matrix.trace (ρ.projector τ) = (ρ.dimension : ℂ) * + Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) := by + simp only [projector,Matrix.trace_sum,Matrix.trace_smul,coefficient,smul_eq_mul] + calc + _ = ((ρ.dimension : ℂ)/(Fintype.card Γ : ℂ)) * + ∑ g, Matrix.trace (τ g)*Matrix.trace (ρ.matrix g⁻¹) := by + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro g _ + ring + _ = _ := by + rw [ρ.character_sum_multiplicity τ] + have hN : (Fintype.card Γ : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr Fintype.card_ne_zero + field_simp + +lemma dimension_le_of_projector_one (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + [Nonempty n] (h : ρ.projector τ = 1) : ρ.dimension ≤ Fintype.card n := by + have he := ρ.projector_trace τ + rw [h,Matrix.trace_one] at he + have he' : Fintype.card n = ρ.dimension * + Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) := by exact_mod_cast he + have hm : 0 < Module.finrank ℂ (ρ.asRepresentation.IntertwiningMap (matrixRepresentation τ)) := by + have hn := Fintype.card_pos (α := n) + by_contra hh + have hz := Nat.eq_zero_of_not_pos hh + rw [hz,mul_zero] at he' + omega + rw [he'] + exact Nat.le_mul_of_pos_right _ hm + +lemma projector_map (ρ : UnitaryIrrep Γ) {m : Type*} [Fintype m] [DecidableEq m] + (e : Matrix n n ℂ →ₐ[ℂ] Matrix m m ℂ) (τ : Γ →* Matrix n n ℂ) : + ρ.projector (e.toMonoidHom.comp τ) = e (ρ.projector τ) := by + change (∑ g, ρ.coefficient g • e (τ g)) = e (∑ g, ρ.coefficient g • τ g) + simp only [map_sum,map_smul] + +end CoordinateSweeps.UnitaryIrrep + +namespace CoordinateSweeps.SpectralBlock +variable {Γ : Type*} [Group Γ] [Fintype Γ] +variable {n : Type*} [Fintype n] [DecidableEq n] + +abbrev Level (r : n → ℝ) (v : ℝ) := {i : n // r i=v} + +omit [DecidableEq n] in +lemma mul_restrict (r : n → ℝ) (v : ℝ) (A B : Matrix n n ℂ) + (hA : ∀ i j, r i ≠ r j → A i j=0) : + (A*B).submatrix (Subtype.val : Level r v → n) (Subtype.val : Level r v → n) = + A.submatrix (Subtype.val : Level r v → n) (Subtype.val : Level r v → n) * B.submatrix (Subtype.val : Level r v → n) (Subtype.val : Level r v → n) := by + ext i j + rw [Matrix.submatrix_apply,Matrix.mul_apply,Matrix.mul_apply] + rw [← Fintype.sum_subtype_add_sum_subtype (fun k => r k=v)] + have hz : ∑ k : {k : n // ¬ r k=v}, A i.val k.val * B k.val j.val = 0 := by + apply Finset.sum_eq_zero + intro k _ + have hne : r i.val ≠ r k.val := by rw [i.property]; exact Ne.symm k.property + rw [hA _ _ hne,zero_mul] + rw [hz,add_zero] + rfl + +def representation (τ : Γ →* Matrix n n ℂ) (r : n → ℝ) (v : ℝ) + (hτ : ∀ g i j, r i ≠ r j → τ g i j=0) : Γ →* Matrix (Level r v) (Level r v) ℂ where + toFun g := (τ g).submatrix Subtype.val Subtype.val + map_one' := by + rw [map_one] + ext i j + simp [Matrix.one_apply,Subtype.val_inj] + map_mul' g h := by + rw [map_mul] + exact mul_restrict r v (τ g) (τ h) (hτ g) + +lemma projector_representation (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + (r : n → ℝ) (v : ℝ) (hτ : ∀ g i j, r i ≠ r j → τ g i j=0) : + ρ.projector (representation τ r v hτ) = + (ρ.projector τ).submatrix (Subtype.val : Level r v → n) (Subtype.val : Level r v → n) := by + ext i j + simp [UnitaryIrrep.projector,Matrix.sum_apply,representation] + +omit [Fintype Γ] in +lemma offDiagonal_zero (τ : Γ →* Matrix n n ℂ) (r : n → ℝ) + (hτ : ∀ g, τ g * Matrix.diagonal (fun i => (r i : ℂ)) = + Matrix.diagonal (fun i => (r i : ℂ)) * τ g) : + ∀ g i j, r i ≠ r j → τ g i j=0 := by + intro g i j hij + have he := congrArg (fun M : Matrix n n ℂ => M i j) (hτ g) + simp only [Matrix.mul_diagonal,Matrix.diagonal_mul] at he + by_contra hn + apply hij + exact Complex.ofReal_injective (mul_left_cancel₀ hn (he.trans (mul_comm _ _))).symm + +lemma projector_on_level (P : Matrix n n ℂ) (r : n → ℝ) (v : ℝ) (hv : v ≠ 0) + (hP : P * Matrix.diagonal (fun i => (r i : ℂ)) = Matrix.diagonal (fun i => (r i : ℂ))) : + P.submatrix (Subtype.val : Level r v → n) (Subtype.val : Level r v → n) = 1 := by + ext i j + have he := congrArg (fun M : Matrix n n ℂ => M i.val j.val) hP + simp only [Matrix.mul_diagonal,Matrix.diagonal_apply] at he + have hv' : (v : ℂ) ≠ 0 := by exact_mod_cast hv + apply mul_right_cancel₀ hv' + change P i.val j.val * (v : ℂ) = (1 : Matrix (Level r v) (Level r v) ℂ) i j * (v : ℂ) + simpa only [i.property,j.property,Matrix.one_apply,Subtype.val_inj,ite_mul,one_mul,zero_mul] using he + +omit [DecidableEq n] in +lemma level_card_le_trace (r : n → ℝ) (hr : ∀ i, 0 ≤ r i) (v : ℝ) : + Fintype.card (Level r v) * v ≤ ∑ i, r i := by + rw [← Fintype.sum_subtype_add_sum_subtype (fun i => r i=v)] + have he : ∑ i : Level r v, r i.val = Fintype.card (Level r v) * v := by + simp_rw [show ∀ i : Level r v, r i.val = v from fun i => i.property] + simp + rw [he] + exact le_add_of_nonneg_right (Finset.sum_nonneg (fun i _ => hr i.val)) + +/- Positive spectral blocks supported on an actual character projector have +at least the actual irreducible dimension. No decomposition is assumed. -/ +lemma dimension_mul_eigenvalue_le_trace (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + (r : n → ℝ) (hr : ∀ i, 0 ≤ r i) + (hτ : ∀ g, τ g * Matrix.diagonal (fun i => (r i : ℂ)) = + Matrix.diagonal (fun i => (r i : ℂ)) * τ g) + (hP : ρ.projector τ * Matrix.diagonal (fun i => (r i : ℂ)) = Matrix.diagonal (fun i => (r i : ℂ))) + (i : n) : (ρ.dimension : ℝ)*r i ≤ ∑ j, r j := by + by_cases hi : r i=0 + · simp only [hi,mul_zero] + exact Finset.sum_nonneg (fun j _ => hr j) + · let : Nonempty (Level r (r i)) := ⟨⟨i,rfl⟩⟩ + have hzero := offDiagonal_zero τ r hτ + have hproj : ρ.projector (representation τ r (r i) hzero) = 1 := by + rw [projector_representation] + exact projector_on_level _ _ _ hi hP + have hc := ρ.dimension_le_of_projector_one (representation τ r (r i) hzero) hproj + exact (mul_le_mul_of_nonneg_right (by exact_mod_cast hc) (hr i)).trans + (level_card_le_trace r hr (r i)) +end CoordinateSweeps.SpectralBlock + +namespace CoordinateSweeps.UnitaryIrrep +variable {Γ : Type*} [Group Γ] [Fintype Γ] +variable {n : Type*} [Fintype n] [DecidableEq n] + +/- Source06's dimension-normalized spectral estimate, for every genuine +finite group representation. A is supported on the actual central projection. -/ +theorem supported_trace_domination (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + (A : Matrix n n ℂ) (hA : A.PosSemidef) + (hcomm : ∀ g, τ g * A = A * τ g) (hP : ρ.projector τ * A = A) : + (Matrix.trace A • (1 : Matrix n n ℂ) - (ρ.dimension : ℂ) • A).PosSemidef := by + let U := hA.isHermitian.eigenvectorUnitary + let e := (Unitary.conjStarAlgAut ℂ (Matrix n n ℂ) (star U)).toAlgEquiv.toAlgHom + let r := hA.isHermitian.eigenvalues + let d : n → ℂ := RCLike.ofReal ∘ r + let τ' : Γ →* Matrix n n ℂ := e.toMonoidHom.comp τ + have hdiag : e A = Matrix.diagonal d := hA.isHermitian.conjStarAlgAut_star_eigenvectorUnitary + have hcomm' (g : Γ) : τ' g * Matrix.diagonal d = Matrix.diagonal d * τ' g := by + change e (τ g) * Matrix.diagonal d = Matrix.diagonal d * e (τ g) + rw [← hdiag,← map_mul,← map_mul,hcomm g] + have hP' : ρ.projector τ' * Matrix.diagonal d = Matrix.diagonal d := by + rw [ρ.projector_map e τ,← hdiag,← map_mul,hP] + have hi (i : n) : (ρ.dimension : ℝ)*r i ≤ ∑ j, r j := + SpectralBlock.dimension_mul_eigenvalue_le_trace ρ τ' r hA.eigenvalues_nonneg hcomm' hP' i + have hd (i : n) : (0 : ℂ) ≤ Matrix.trace A - (ρ.dimension : ℂ)*d i := by + rw [hA.isHermitian.trace_eq_sum_eigenvalues] + change (0 : ℂ) ≤ (∑ j, (r j : ℂ)) - (ρ.dimension : ℂ)*(r i : ℂ) + exact_mod_cast sub_nonneg.mpr (hi i) + have hD := Matrix.PosSemidef.diagonal hd + have h := hD.mul_mul_conjTranspose_same (U : Matrix n n ℂ) + have hU : (U : Matrix n n ℂ) * (U : Matrix n n ℂ).conjTranspose = 1 := by + simpa only [Unitary.coe_star,Matrix.star_eq_conjTranspose] using Unitary.coe_mul_star_self U + have hspec : (U : Matrix n n ℂ) * Matrix.diagonal d * (U : Matrix n n ℂ).conjTranspose = A := by + simpa only [U,d,r,Function.comp_def,Unitary.conjStarAlgAut_apply,Matrix.star_eq_conjTranspose] using hA.isHermitian.spectral_theorem.symm + have he : Matrix.diagonal (fun i => Matrix.trace A - (ρ.dimension : ℂ)*d i) = + Matrix.trace A • (1 : Matrix n n ℂ) - (ρ.dimension : ℂ) • Matrix.diagonal d := by + ext i j + by_cases hij : i=j <;> simp [Matrix.diagonal,hij] + simpa only [he,Matrix.mul_sub,Matrix.sub_mul,Matrix.mul_smul,Matrix.smul_mul, + Matrix.mul_one,hU,hspec] using h + +/- Compression of a positive invariant unit-trace operator to any isotypic +type is at most inverse irreducible dimension in operator order. -/ +theorem invariant_projector_trace_domination (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) (T : Matrix n n ℂ) (hT : T.PosSemidef) + (hcomm : ∀ g, τ g*T=T*τ g) : + (Matrix.trace T • (1 : Matrix n n ℂ) - (ρ.dimension : ℂ) • + (ρ.projector τ * T * ρ.projector τ)).PosSemidef := by + let P := ρ.projector τ + have hP : P.conjTranspose=P := ρ.projector_hermitian τ hu + have hP2 : P*P=P := ρ.projector_idempotent τ + let A := P*T*P + have hA : A.PosSemidef := by + simpa only [hP] using hT.mul_mul_conjTranspose_same P + have hAc (g : Γ) : τ g*A=A*τ g := by + dsimp [A] + calc + _ = (τ g*P)*T*P := by noncomm_ring + _ = (P*τ g)*T*P := by rw [ρ.projector_commute τ g] + _ = P*(τ g*T)*P := by noncomm_ring + _ = P*(T*τ g)*P := by rw [hcomm] + _ = P*T*(τ g*P) := by noncomm_ring + _ = P*T*(P*τ g) := by rw [ρ.projector_commute τ g] + _ = _ := by noncomm_ring + have hPA : P*A=A := by dsimp [A]; rw [← mul_assoc,← mul_assoc,hP2] + have hbound := ρ.supported_trace_domination τ A hA hAc hPA + have htrace : Matrix.trace A ≤ Matrix.trace T := by + have hc := hT.mul_mul_conjTranspose_same (1-P) + rw [Matrix.conjTranspose_sub,Matrix.conjTranspose_one,hP] at hc + have hh := hc.trace_nonneg + have he : Matrix.trace ((1-P)*T*(1-P)) = Matrix.trace T-Matrix.trace A := by + dsimp [A] + have hx : (1-P)*(1-P) = 1-P := by + calc + _ = 1-P-P+P*P := by noncomm_ring + _ = _ := by rw [hP2]; module + rw [Matrix.trace_mul_cycle,hx,sub_mul,one_mul,Matrix.trace_sub] + rw [Matrix.trace_mul_cycle P T P,hP2] + + rw [he] at hh + exact sub_nonneg.mp hh + have hpad := (Matrix.PosSemidef.one (n := n) (R := ℂ)).smul (sub_nonneg.mpr htrace) + have h := hpad.add hbound + change (Matrix.trace T • (1 : Matrix n n ℂ) - (ρ.dimension : ℂ) • A).PosSemidef + convert h using 1 + module +end CoordinateSweeps.UnitaryIrrep +namespace CoordinateSweeps.Overlap +open TensorBoard +variable {n Γ : Type*} [Fintype n] [DecidableEq n] [Nonempty n] [Group Γ] [Fintype Γ] + +open scoped MatrixOrder in +lemma norm_le_trace (A : Matrix n n ℂ) (hA : A.PosSemidef) : ‖A‖ ≤ (Matrix.trace A).re := by + have hh := PositiveTensor.trace_domination A hA + have hn := CStarAlgebra.norm_le_norm_of_le_of_nonneg + (show A ≤ Matrix.trace A • (1 : Matrix n n ℂ) from sub_nonneg.mp hh.nonneg) hA.nonneg + have htr := Complex.nonneg_iff.mp hA.trace_nonneg + have he : ((Matrix.trace A).re : ℂ)=Matrix.trace A := by + apply Complex.ext <;> simp [htr.2] + rw [← he,norm_smul,Complex.norm_of_nonneg htr.1,norm_one,mul_one] at hn + exact hn + +lemma norm_sq_le_trace (A : Matrix n n ℂ) : + ‖A‖^2 ≤ (Matrix.trace (A.conjTranspose*A)).re := by + have hh := norm_le_trace _ (Matrix.posSemidef_conjTranspose_mul_self A) + simpa only [Matrix.l2_opNorm_conjTranspose_mul_self,pow_two] using hh + +omit [DecidableEq n] [Nonempty n] in +lemma projection_product_posSemidef (P Q : Matrix n n ℂ) + (hP : P.IsHermitian) (hP2 : P*P=P) (hQ : Q.PosSemidef) (hPQ : P*Q=Q*P) : + (P*Q).PosSemidef := by + have hh := hQ.mul_mul_conjTranspose_same P + rwa [hP.eq,hPQ,mul_assoc,hP2,← hPQ] at hh + +lemma overlap_norm_sq_le_trace (R Q P : Matrix n n ℂ) + (hR : R.IsHermitian) (hR2 : R*R=R) (hQ : Q.IsHermitian) (hQ2 : Q*Q=Q) + (hP : P.IsHermitian) (hP2 : P*P=P) (hPQ : P*Q=Q*P) : + ‖Q*P*R‖^2 ≤ (Matrix.trace (R*(Q*P))).re := by + have hh := norm_sq_le_trace (Q*P*R) + have he : (Q*P*R).conjTranspose*(Q*P*R)=R*Q*P*R := by + rw [Matrix.conjTranspose_mul,Matrix.conjTranspose_mul,hR.eq,hP.eq,hQ.eq] + calc + _ = R*P*(Q*Q)*P*R := by noncomm_ring + _ = R*(P*Q)*P*R := by rw [hQ2]; noncomm_ring + _ = R*Q*(P*P)*R := by rw [hPQ]; noncomm_ring + _ = _ := by rw [hP2] + rw [he,mul_assoc R Q P,Matrix.trace_mul_cycle R (Q*P) R,hR2] at hh + simpa only [mul_assoc] using hh + +/- Whitening of genuine isotypic trace domination. All projections and +commutations are explicit algebraic obligations; no spectral conclusion assumed. -/ +omit [Nonempty n] in +lemma whitened_projector_domination (ρ : UnitaryIrrep Γ) (τ : Γ →* Matrix n n ℂ) + (hu : ∀ g, (τ g).conjTranspose=τ g⁻¹) + (T A Q : Matrix n n ℂ) (hT : T.PosSemidef) + (hcomm : ∀ g, τ g*T=T*τ g) (hA : A.IsHermitian) + (hATA : A*T*A=1) (hAP : A*ρ.projector τ=ρ.projector τ*A) + (hAQ : A*Q=Q*A) (hQ : Q.IsHermitian) (hQ2 : Q*Q=Q) + (hPQ : ρ.projector τ*Q= Q*ρ.projector τ) : + (Matrix.trace T • (A*Q*A) - (ρ.dimension : ℂ) • (Q*ρ.projector τ)).PosSemidef := by + let P := ρ.projector τ + change A*P=P*A at hAP + change P*Q=Q*P at hPQ + have hP2 : P*P=P := ρ.projector_idempotent τ + have hh := ρ.invariant_projector_trace_domination τ hu T hT hcomm + change (Matrix.trace T • (1 : Matrix n n ℂ) - (ρ.dimension : ℂ) • (P*T*P)).PosSemidef at hh + have hk := (hh.mul_mul_conjTranspose_same Q).mul_mul_conjTranspose_same A + simp only [hA.eq,hQ.eq,Matrix.mul_sub,Matrix.sub_mul,Matrix.mul_smul,Matrix.smul_mul] at hk + have hAQP : A*(Q*P)=(Q*P)*A := by + rw [← mul_assoc,hAQ,mul_assoc Q A P,hAP,← mul_assoc] + have hPQA : (P*Q)*A=A*(P*Q) := by + rw [mul_assoc,← hAQ,← mul_assoc P A Q,← hAP,mul_assoc] + have ht : A*(Q*(P*T*P)*Q)*A=Q*P := by + calc + _ = (A*(Q*P))*T*((P*Q)*A) := by noncomm_ring + _ = (Q*P)*(A*T*A)*(P*Q) := by rw [hAQP,hPQA]; noncomm_ring + _ = Q*(P*P)*Q := by rw [hATA]; noncomm_ring + _ = Q*(P*Q) := by rw [hP2,mul_assoc] + _ = Q*(Q*P) := by rw [hPQ] + _ = Q*P := by rw [← mul_assoc,hQ2] + have he : A*(Q*1*Q)*A=A*Q*A := by rw [mul_one,hQ2] + rw [he,ht] at hk + exact hk + +end CoordinateSweeps.Overlap + +namespace CoordinateSweeps.Overlap +open TensorBoard +variable {n I J : Type*} [Fintype n] [DecidableEq n] [Nonempty n] [Fintype I] [Fintype J] + +omit [DecidableEq n] [Nonempty n] in +lemma trace_mixture_re (w : I → ℝ) (U : I → Matrix n n ℂ) (W : Matrix n n ℂ) : + (Matrix.trace ((∑ i, (w i : ℂ) • U i)*W)).re = ∑ i, w i*(Matrix.trace (U i*W)).re := by + simp only [Matrix.sum_mul,Matrix.smul_mul,Matrix.trace_sum,Matrix.trace_smul,Complex.re_sum, + smul_eq_mul,Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im,zero_mul,sub_zero] + +omit [DecidableEq n] [Nonempty n] in +lemma trace_smul_re (t : ℝ) (W : Matrix n n ℂ) : + (Matrix.trace ((t : ℂ) • W)).re=t*(Matrix.trace W).re := by + simp [Matrix.trace_smul] + +omit [DecidableEq n] [Nonempty n] in +lemma trace_four_swap (A Q U : Matrix n n ℂ) : + Matrix.trace (A*Q*A*U)=Matrix.trace (A*U*A*Q) := by + calc + _ = Matrix.trace ((A*Q)*(A*U)) := congrArg Matrix.trace (by noncomm_ring) + _ = Matrix.trace ((A*U)*(A*Q)) := Matrix.trace_mul_comm _ _ + _ = _ := congrArg Matrix.trace (by noncomm_ring) + +/- Finite density mixtures plus genuine whitened isotypic domination give +the row-column overlap bound, before the harmless epsilon limit. -/ +theorem finite_mixture_overlap (R Q P : Matrix n n ℂ) + (hR : R.IsHermitian) (hR2 : R*R=R) (hQ : Q.IsHermitian) (hQ2 : Q*Q=Q) + (hP : P.IsHermitian) (hP2 : P*P=P) (hPQ : P*Q=Q*P) + (u : I → ℝ) (v : J → ℝ) (hu : ∀ i, 0 ≤ u i) (hv : ∀ j, 0 ≤ v j) + (hsu : ∑ i, u i=1) (hsv : ∑ j, v j=1) + (U : I → Matrix n n ℂ) (V : J → Matrix n n ℂ) (A : I → Matrix n n ℂ) + (hU : ∀ i, (U i).PosSemidef) (hA : ∀ i, (A i).IsHermitian) + (cr cc D t E : ℝ) (hcr : 0 ≤ cr) (hcc : 0 ≤ cc) (hD : 0 ≤ D) (ht : 0 ≤ t) + (hrow : ((cr : ℂ) • (∑ i, (u i : ℂ) • U i)-R).PosSemidef) + (hcol : ((cc : ℂ) • (∑ j, (v j : ℂ) • V j)-Q).PosSemidef) + (hwhite : ∀ i, ((t : ℂ) • (A i*Q*A i)-(D : ℂ) • (Q*P)).PosSemidef) + (hpair : ∀ i j, (Matrix.trace (A i*U i*A i*V j)).re ≤ E) : + D*‖Q*P*R‖^2 ≤ cr*cc*t*E := by + have hQpos : Q.PosSemidef := by + simpa only [hQ.eq,hQ2] using Matrix.posSemidef_conjTranspose_mul_self Q + have hQP : (Q*P).PosSemidef := by + rw [← hPQ] + exact projection_product_posSemidef P Q hP hP2 hQpos hPQ + have hlocal (i : I) : D*(Matrix.trace (U i*(Q*P))).re ≤ t*cc*E := by + let W := A i*U i*A i + have hW : W.PosSemidef := by + simpa only [(hA i).eq] using (hU i).mul_mul_conjTranspose_same (A i) + have hc := (Complex.le_def.mp (trace_mono_right hcol hW)).1 + rw [Matrix.smul_mul,trace_smul_re,trace_mixture_re] at hc + have hpair' (j : J) : (Matrix.trace (V j*W)).re ≤ E := by + rw [Matrix.trace_mul_comm] + exact hpair i j + have hc' : (Matrix.trace (W*Q)).re ≤ cc*E := by + rw [Matrix.trace_mul_comm] + apply hc.trans + apply mul_le_mul_of_nonneg_left _ hcc + calc + _ ≤ ∑ j, v j*E := Finset.sum_le_sum (fun j _ => mul_le_mul_of_nonneg_left (hpair' j) (hv j)) + _ = E := by rw [← Finset.sum_mul,hsv,one_mul] + have hw := (Complex.le_def.mp (trace_mono_right (hwhite i) (hU i))).1 + rw [Matrix.smul_mul,Matrix.smul_mul,trace_smul_re,trace_smul_re, + trace_four_swap,Matrix.trace_mul_comm (Q*P)] at hw + exact hw.trans (by simpa only [W,mul_assoc] using mul_le_mul_of_nonneg_left hc' ht) + have hr := (Complex.le_def.mp (trace_mono_right hrow hQP)).1 + rw [Matrix.smul_mul,trace_smul_re,trace_mixture_re] at hr + calc + _ ≤ D*(Matrix.trace (R*(Q*P))).re := mul_le_mul_of_nonneg_left + (overlap_norm_sq_le_trace R Q P hR hR2 hQ hQ2 hP hP2 hPQ) hD + _ ≤ D*(cr*∑ i, u i*(Matrix.trace (U i*(Q*P))).re) := mul_le_mul_of_nonneg_left hr hD + _ = cr*(∑ i, u i*(D*(Matrix.trace (U i*(Q*P))).re)) := by + rw [Finset.mul_sum,Finset.mul_sum,Finset.mul_sum] + apply Finset.sum_congr rfl + intro i hi + ring + _ ≤ cr*(∑ i, u i*(t*cc*E)) := mul_le_mul_of_nonneg_left + (Finset.sum_le_sum (fun i _ => mul_le_mul_of_nonneg_left (hlocal i) (hu i))) hcr + _ = cr*cc*t*E := by rw [← Finset.sum_mul,hsu,one_mul]; ring + +end CoordinateSweeps.Overlap + +end +end +end +end +end +end +end +end +open scoped Matrix.Norms.L2Operator + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceAssembly.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceAssembly.lean index ec60054495440008b632fe157477848323ee4fa4..b5e9b458a061984669cb759791755fd0ad198e86 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceAssembly.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceAssembly.lean @@ -1,148 +1,148 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Band.RunBands -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceBlocks - -namespace OAI - -/-! Balance Assembly. -/ - -section - -noncomputable section -namespace Saxl.Balance -open FlagColumns Columns - -def balanceColumns (M b δ τ ε m : ℕ) : List ℕ := - ((bigColumns (M-1+b) δ ++ shortColumns (b+1) τ) ++ - pairColumns (3+τ+ε) m) ++ oneIf (3+τ) ε - -def balanceParts (M b δ τ ε m : ℕ) : List ℕ := - ((bigParts (M-1+b) δ ++ shortParts (b+1) τ) ++ - pairParts (3+τ+ε) m) ++ oneIf (3+τ) ε - -theorem balancePacking {M b δ τ ε m : ℕ} - (hM : 4 ≤ M) (hδ : δ ≤ 1) (hτ : τ ≤ 1) (hε : ε ≤ 1) - (heq : M = 4+τ+ε+2*m) (hshort : τ ≠ 0 → 1 ≤ b) : - ∃ (A : Fin ((M+b+δ)*(M+b+δ)) → Prop) - (label : Fin ((M+b+δ)*(M+b+δ)) → ℕ) (marks : Finset ℕ), - (∀ x y, A x → A y → label x < label y → output x < output y) ∧ - Nonempty (WordPacking (balanceColumns M b δ τ ε m) - (balanceParts M b δ τ ε m) (M+b+δ) A label marks) := by - let a := 3+τ+ε - let q := M-1+b - let lo := 3+τ - let d := M+b+δ - have hg : a+2*m ≤ q := by dsimp [a,q]; omega - have hU : q ≤ bigUpper q δ := by unfold bigUpper; split_ifs <;> omega - let B := runBands a m q (bigUpper q δ) hg hU - let A := B.alphabet d - let label := B.letterLabel d - have he1 : ∀ z, (A z ∧ label z = 1) ↔ output z = 1 := - fun z => runBands_low_iff hg hU (by dsimp [a]; omega) z - obtain ⟨P⟩ := WordPacking.bigBlock (by dsimp [q]; omega : 3 ≤ q) hδ - (by dsimp [q,d]; omega) A label (fun z => runBands_top_iff hg hU z) he1 - have he2 : ∀ z, (A z ∧ label z = 2) ↔ output z = 2 := - fun z => runBands_low_iff hg hU (by dsimp [a]; omega) z - obtain ⟨Q⟩ := WordPacking.shortBlock (by omega : 1 ≤ b+1) - (by intro h; have := hshort h; omega) (by dsimp [d]; omega) - A label he2 (by - intro ht z - exact runBands_low_iff hg hU (by dsimp [a]; omega) z) - obtain ⟨R⟩ := WordPacking.pairRunAny (by dsimp [a]; omega : 2 ≤ a) - (by dsimp [a,d]; omega) A label - (fun k hk z => runBands_pair_iff hg hU hk z) - obtain ⟨S⟩ := WordPacking.optional (by dsimp [lo]; omega : 0 < lo) - (by dsimp [lo,d]; omega) A label (ε := ε) (by - intro h z - exact runBands_low_iff hg hU (by dsimp [lo,a]; omega) z) - have hpq : Disjoint ({q,1}:Finset ℕ) (shortMarks τ) := by - apply Finset.disjoint_left.mpr - intro k hk hl - have hl := mem_shortMarks hl - simp only [Finset.mem_insert,Finset.mem_singleton] at hk - dsimp [q] at hk - omega - have hpqr : Disjoint (({q,1}:Finset ℕ) ∪ shortMarks τ) (pairMarks a m) := by - apply Finset.disjoint_left.mpr - intro k hk hl - have hh := pairMarks_bound hl - rcases Finset.mem_union.mp hk with hk | hk - · simp only [Finset.mem_insert,Finset.mem_singleton] at hk - dsimp [a,q] at hh hk - omega - · have hk := mem_shortMarks hk - dsimp [a] at hh - omega - have hd : Disjoint ((({q,1}:Finset ℕ) ∪ shortMarks τ) ∪ pairMarks a m) - (markIf lo ε) := by - apply Finset.disjoint_left.mpr - intro k hk hl - have hl := mem_markIf hl - rcases Finset.mem_union.mp hk with hk | hk - · rcases Finset.mem_union.mp hk with hk | hk - · simp only [Finset.mem_insert,Finset.mem_singleton] at hk - dsimp [q,lo] at hk hl - omega - · have hk := mem_shortMarks hk - dsimp [lo] at hl - omega - · have hh := pairMarks_bound hk - dsimp [a,lo] at hh hl - omega - exact ⟨A,label,_,B.letter_ordered _,⟨((P.join Q hpq).join R hpqr).join S hd⟩⟩ - -lemma balanceParts_length {M b δ τ ε m : ℕ} - (hδ : δ ≤ 1) (hτ : τ ≤ 1) (hε : ε ≤ 1) (heq : M = 4+τ+ε+2*m) : - 2*M-5 ≤ (balanceParts M b δ τ ε m).length := by - rw [balanceParts,List.length_append,List.length_append,List.length_append, - bigParts_length hδ,shortParts_length hτ,pairParts_length,oneIf_length hε] - omega - -lemma oneIf_mem {x ε p : ℕ} (hp : p ∈ oneIf x ε) : p = x := by - unfold oneIf at hp - split_ifs at hp - · simp at hp - · exact List.mem_singleton.mp hp - -lemma balanceParts_positive {M b δ τ ε m : ℕ} (hM : 4 ≤ M) : - ∀ p ∈ balanceParts M b δ τ ε m, 0 < p := by - intro p hp - simp only [balanceParts,List.mem_append] at hp - rcases hp with ((hp | hp) | hp) | hp - · rcases List.mem_append.mp hp with hp | hp - · exact balancedParts_pos (by decide) (by omega) p hp - · have := oneIf_mem hp; omega - · unfold shortParts at hp - split_ifs at hp - · have := List.mem_singleton.mp hp; omega - · exact balancedParts_pos (by decide) (by omega) p hp - · exact pairParts_positive (by omega) p hp - · have := oneIf_mem hp; omega - -lemma balanceParts_bound {M b δ τ ε m p : ℕ} - (hM : 4 ≤ M) (hb : b ≤ M-2) (hδ : δ ≤ 1) (hτ : τ ≤ 1) (hε : ε ≤ 1) - (heq : M = 4+τ+ε+2*m) (hsmall : τ = 0 → 2*(b+1) ≤ M) - (hp : p ∈ balanceParts M b δ τ ε m) : p ≤ M+1 := by - simp only [balanceParts,List.mem_append] at hp - rcases hp with ((hp | hp) | hp) | hp - · rcases List.mem_append.mp hp with hp | hp - · have hh := (balancedParts_part hp).2 - omega - · have := oneIf_mem hp; omega - · unfold shortParts at hp - split_ifs at hp with ht - · have := List.mem_singleton.mp hp - have := hsmall ht - omega - · have hh := (balancedParts_part hp).2 - omega - · have := pairParts_bound (by omega : 2 ≤ 3+τ+ε) hp - omega - · have := oneIf_mem hp; omega - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Band.RunBands +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceBlocks + +namespace OAI + +/-! Balance Assembly. -/ + +section + +noncomputable section +namespace Saxl.Balance +open FlagColumns Columns + +def balanceColumns (M b δ τ ε m : ℕ) : List ℕ := + ((bigColumns (M-1+b) δ ++ shortColumns (b+1) τ) ++ + pairColumns (3+τ+ε) m) ++ oneIf (3+τ) ε + +def balanceParts (M b δ τ ε m : ℕ) : List ℕ := + ((bigParts (M-1+b) δ ++ shortParts (b+1) τ) ++ + pairParts (3+τ+ε) m) ++ oneIf (3+τ) ε + +theorem balancePacking {M b δ τ ε m : ℕ} + (hM : 4 ≤ M) (hδ : δ ≤ 1) (hτ : τ ≤ 1) (hε : ε ≤ 1) + (heq : M = 4+τ+ε+2*m) (hshort : τ ≠ 0 → 1 ≤ b) : + ∃ (A : Fin ((M+b+δ)*(M+b+δ)) → Prop) + (label : Fin ((M+b+δ)*(M+b+δ)) → ℕ) (marks : Finset ℕ), + (∀ x y, A x → A y → label x < label y → output x < output y) ∧ + Nonempty (WordPacking (balanceColumns M b δ τ ε m) + (balanceParts M b δ τ ε m) (M+b+δ) A label marks) := by + let a := 3+τ+ε + let q := M-1+b + let lo := 3+τ + let d := M+b+δ + have hg : a+2*m ≤ q := by dsimp [a,q]; omega + have hU : q ≤ bigUpper q δ := by unfold bigUpper; split_ifs <;> omega + let B := runBands a m q (bigUpper q δ) hg hU + let A := B.alphabet d + let label := B.letterLabel d + have he1 : ∀ z, (A z ∧ label z = 1) ↔ output z = 1 := + fun z => runBands_low_iff hg hU (by dsimp [a]; omega) z + obtain ⟨P⟩ := WordPacking.bigBlock (by dsimp [q]; omega : 3 ≤ q) hδ + (by dsimp [q,d]; omega) A label (fun z => runBands_top_iff hg hU z) he1 + have he2 : ∀ z, (A z ∧ label z = 2) ↔ output z = 2 := + fun z => runBands_low_iff hg hU (by dsimp [a]; omega) z + obtain ⟨Q⟩ := WordPacking.shortBlock (by omega : 1 ≤ b+1) + (by intro h; have := hshort h; omega) (by dsimp [d]; omega) + A label he2 (by + intro ht z + exact runBands_low_iff hg hU (by dsimp [a]; omega) z) + obtain ⟨R⟩ := WordPacking.pairRunAny (by dsimp [a]; omega : 2 ≤ a) + (by dsimp [a,d]; omega) A label + (fun k hk z => runBands_pair_iff hg hU hk z) + obtain ⟨S⟩ := WordPacking.optional (by dsimp [lo]; omega : 0 < lo) + (by dsimp [lo,d]; omega) A label (ε := ε) (by + intro h z + exact runBands_low_iff hg hU (by dsimp [lo,a]; omega) z) + have hpq : Disjoint ({q,1}:Finset ℕ) (shortMarks τ) := by + apply Finset.disjoint_left.mpr + intro k hk hl + have hl := mem_shortMarks hl + simp only [Finset.mem_insert,Finset.mem_singleton] at hk + dsimp [q] at hk + omega + have hpqr : Disjoint (({q,1}:Finset ℕ) ∪ shortMarks τ) (pairMarks a m) := by + apply Finset.disjoint_left.mpr + intro k hk hl + have hh := pairMarks_bound hl + rcases Finset.mem_union.mp hk with hk | hk + · simp only [Finset.mem_insert,Finset.mem_singleton] at hk + dsimp [a,q] at hh hk + omega + · have hk := mem_shortMarks hk + dsimp [a] at hh + omega + have hd : Disjoint ((({q,1}:Finset ℕ) ∪ shortMarks τ) ∪ pairMarks a m) + (markIf lo ε) := by + apply Finset.disjoint_left.mpr + intro k hk hl + have hl := mem_markIf hl + rcases Finset.mem_union.mp hk with hk | hk + · rcases Finset.mem_union.mp hk with hk | hk + · simp only [Finset.mem_insert,Finset.mem_singleton] at hk + dsimp [q,lo] at hk hl + omega + · have hk := mem_shortMarks hk + dsimp [lo] at hl + omega + · have hh := pairMarks_bound hk + dsimp [a,lo] at hh hl + omega + exact ⟨A,label,_,B.letter_ordered _,⟨((P.join Q hpq).join R hpqr).join S hd⟩⟩ + +lemma balanceParts_length {M b δ τ ε m : ℕ} + (hδ : δ ≤ 1) (hτ : τ ≤ 1) (hε : ε ≤ 1) (heq : M = 4+τ+ε+2*m) : + 2*M-5 ≤ (balanceParts M b δ τ ε m).length := by + rw [balanceParts,List.length_append,List.length_append,List.length_append, + bigParts_length hδ,shortParts_length hτ,pairParts_length,oneIf_length hε] + omega + +lemma oneIf_mem {x ε p : ℕ} (hp : p ∈ oneIf x ε) : p = x := by + unfold oneIf at hp + split_ifs at hp + · simp at hp + · exact List.mem_singleton.mp hp + +lemma balanceParts_positive {M b δ τ ε m : ℕ} (hM : 4 ≤ M) : + ∀ p ∈ balanceParts M b δ τ ε m, 0 < p := by + intro p hp + simp only [balanceParts,List.mem_append] at hp + rcases hp with ((hp | hp) | hp) | hp + · rcases List.mem_append.mp hp with hp | hp + · exact balancedParts_pos (by decide) (by omega) p hp + · have := oneIf_mem hp; omega + · unfold shortParts at hp + split_ifs at hp + · have := List.mem_singleton.mp hp; omega + · exact balancedParts_pos (by decide) (by omega) p hp + · exact pairParts_positive (by omega) p hp + · have := oneIf_mem hp; omega + +lemma balanceParts_bound {M b δ τ ε m p : ℕ} + (hM : 4 ≤ M) (hb : b ≤ M-2) (hδ : δ ≤ 1) (hτ : τ ≤ 1) (hε : ε ≤ 1) + (heq : M = 4+τ+ε+2*m) (hsmall : τ = 0 → 2*(b+1) ≤ M) + (hp : p ∈ balanceParts M b δ τ ε m) : p ≤ M+1 := by + simp only [balanceParts,List.mem_append] at hp + rcases hp with ((hp | hp) | hp) | hp + · rcases List.mem_append.mp hp with hp | hp + · have hh := (balancedParts_part hp).2 + omega + · have := oneIf_mem hp; omega + · unfold shortParts at hp + split_ifs at hp with ht + · have := List.mem_singleton.mp hp + have := hsmall ht + omega + · have hh := (balancedParts_part hp).2 + omega + · have := pairParts_bound (by omega : 2 ≤ 3+τ+ε) hp + omega + · have := oneIf_mem hp; omega + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceBlocks.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceBlocks.lean index 553fb27f9ac813115a652ee4b8bb54823d3f3f83..ec2c08f538374deed8a633481a01356330fe860a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceBlocks.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceBlocks.lean @@ -1,97 +1,97 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingPieri -import OAI.RepresentationTheory.UniversalSquare.Balance.EmptyPacking - -namespace OAI - -/-! Balance Blocks. -/ - -section - -noncomputable section -namespace Saxl.Balance - -def bigColumns (q δ : ℕ) : List ℕ := [q+1+δ,q] ++ List.replicate (1+δ) 1 - -def bigParts (q δ : ℕ) : List ℕ := balancedParts (2*q+1+3*δ) 4 ++ oneIf 1 (1-δ) - -def bigUpper (q δ : ℕ) : ℕ := if δ = 0 then q+1 else 2*q+3 - -theorem WordPacking.bigBlock {q δ d : ℕ} (hq : 3 ≤ q) (hδ : δ ≤ 1) - (hd : q+1+δ ≤ d) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ z, (A z ∧ label z = q) ↔ output z ∈ Set.Icc q (bigUpper q δ)) - (he1 : ∀ z, (A z ∧ label z = 1) ↔ output z = 1) : - Nonempty (WordPacking (bigColumns q δ) (bigParts q δ) d A label {q,1}) := by - rcases (by omega : δ = 0 ∨ δ = 1) with rfl | rfl - · obtain ⟨P⟩ := WordPacking.neighbor (by omega : 0 < q) (by omega) - (balancedParts_sum (2*q+1) 4 (by decide)) (by simp) q A label he - obtain ⟨Q⟩ := WordPacking.repeated (m := 1) (k := 1) (by decide) (by decide) - (by omega) 1 A label he1 - have hh : Disjoint ({q}:Finset ℕ) {1} := by simp; omega - simpa [bigColumns,bigParts,oneIf] using Nonempty.intro (P.join Q hh) - · have heq : 2*q+1+3*1 = 2*q+4 := by omega - have heq' : q+1+1 = q+2 := by omega - obtain ⟨P⟩ := WordPacking.twoPaths hq (by omega) - (balancedParts_sum (2*q+4) 4 (by decide)) (by simp) q 1 (by omega) A label he he1 - simpa [bigColumns,bigParts,heq,heq',oneIf] - using Nonempty.intro P - -def shortColumns (m τ : ℕ) : List ℕ := List.replicate m 2 ++ oneIf 3 τ - -def shortParts (m τ : ℕ) : List ℕ := if τ = 0 then [2*m] else balancedParts (2*m+3) 2 - -def shortMarks (τ : ℕ) : Finset ℕ := if τ = 0 then {2} else {2,3} - -theorem WordPacking.shortBlock {m τ d : ℕ} (hm : 1 ≤ m) (hτm : τ ≠ 0 → 2 ≤ m) (hd : 3 ≤ d) - (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he2 : ∀ z, (A z ∧ label z = 2) ↔ output z = 2) - (he3 : τ ≠ 0 → ∀ z, (A z ∧ label z = 3) ↔ output z = 3) : - Nonempty (WordPacking (shortColumns m τ) (shortParts m τ) d A label (shortMarks τ)) := by - by_cases hτ : τ = 0 - · obtain ⟨P⟩ := WordPacking.repeated (m := m) (k := 2) (by omega) (by decide) - (by omega) 2 A label he2 - simpa only [shortColumns,shortParts,shortMarks,oneIf,ite_eq_left hτ,List.append_nil, - Nat.mul_comm m 2] using Nonempty.intro P - · have hm2 := hτm hτ - obtain ⟨P⟩ := WordPacking.twosOdd (m := m) (x := 3) (by omega) (by decide) - (by omega) (by omega) hd (balancedParts_sum (2*m+3) 2 (by decide)) (by simp) - 2 3 (by decide) A label he2 (he3 hτ) - simpa only [shortColumns,shortParts,shortMarks,oneIf,ite_eq_right hτ] using Nonempty.intro P - -lemma bigParts_length {q δ : ℕ} (hδ : δ ≤ 1) : (bigParts q δ).length = 5-δ := by - simp only [bigParts,List.length_append,balancedParts_length,oneIf] - split_ifs <;> simp_all <;> omega - -lemma shortParts_length {m τ : ℕ} (hτ : τ ≤ 1) : (shortParts m τ).length = 1+τ := by - simp only [shortParts] - split_ifs <;> simp_all - omega - -lemma oneIf_length {x ε : ℕ} (hε : ε ≤ 1) : (oneIf x ε).length = ε := by - unfold oneIf - split_ifs <;> simp_all - omega - -lemma mem_shortMarks {τ k : ℕ} (hk : k ∈ shortMarks τ) : k = 2 ∨ (τ ≠ 0 ∧ k = 3) := by - unfold shortMarks at hk - split_ifs at hk with hτ - · simp only [Finset.mem_singleton] at hk - exact Or.inl hk - · simpa only [Finset.mem_insert,Finset.mem_singleton,hτ,true_and] using - (show k = 2 ∨ (τ ≠ 0 ∧ k = 3) from - (by rcases Finset.mem_insert.mp hk with h | h - · exact Or.inl h - · exact Or.inr ⟨hτ, Finset.mem_singleton.mp h⟩)) - -lemma mem_markIf {x ε k : ℕ} (hk : k ∈ markIf x ε) : ε ≠ 0 ∧ k = x := by - unfold markIf at hk - split_ifs at hk with hε - · simp at hk - · exact ⟨hε,Finset.mem_singleton.mp hk⟩ - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingPieri +import OAI.RepresentationTheory.UniversalSquare.Balance.EmptyPacking + +namespace OAI + +/-! Balance Blocks. -/ + +section + +noncomputable section +namespace Saxl.Balance + +def bigColumns (q δ : ℕ) : List ℕ := [q+1+δ,q] ++ List.replicate (1+δ) 1 + +def bigParts (q δ : ℕ) : List ℕ := balancedParts (2*q+1+3*δ) 4 ++ oneIf 1 (1-δ) + +def bigUpper (q δ : ℕ) : ℕ := if δ = 0 then q+1 else 2*q+3 + +theorem WordPacking.bigBlock {q δ d : ℕ} (hq : 3 ≤ q) (hδ : δ ≤ 1) + (hd : q+1+δ ≤ d) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ z, (A z ∧ label z = q) ↔ output z ∈ Set.Icc q (bigUpper q δ)) + (he1 : ∀ z, (A z ∧ label z = 1) ↔ output z = 1) : + Nonempty (WordPacking (bigColumns q δ) (bigParts q δ) d A label {q,1}) := by + rcases (by omega : δ = 0 ∨ δ = 1) with rfl | rfl + · obtain ⟨P⟩ := WordPacking.neighbor (by omega : 0 < q) (by omega) + (balancedParts_sum (2*q+1) 4 (by decide)) (by simp) q A label he + obtain ⟨Q⟩ := WordPacking.repeated (m := 1) (k := 1) (by decide) (by decide) + (by omega) 1 A label he1 + have hh : Disjoint ({q}:Finset ℕ) {1} := by simp; omega + simpa [bigColumns,bigParts,oneIf] using Nonempty.intro (P.join Q hh) + · have heq : 2*q+1+3*1 = 2*q+4 := by omega + have heq' : q+1+1 = q+2 := by omega + obtain ⟨P⟩ := WordPacking.twoPaths hq (by omega) + (balancedParts_sum (2*q+4) 4 (by decide)) (by simp) q 1 (by omega) A label he he1 + simpa [bigColumns,bigParts,heq,heq',oneIf] + using Nonempty.intro P + +def shortColumns (m τ : ℕ) : List ℕ := List.replicate m 2 ++ oneIf 3 τ + +def shortParts (m τ : ℕ) : List ℕ := if τ = 0 then [2*m] else balancedParts (2*m+3) 2 + +def shortMarks (τ : ℕ) : Finset ℕ := if τ = 0 then {2} else {2,3} + +theorem WordPacking.shortBlock {m τ d : ℕ} (hm : 1 ≤ m) (hτm : τ ≠ 0 → 2 ≤ m) (hd : 3 ≤ d) + (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he2 : ∀ z, (A z ∧ label z = 2) ↔ output z = 2) + (he3 : τ ≠ 0 → ∀ z, (A z ∧ label z = 3) ↔ output z = 3) : + Nonempty (WordPacking (shortColumns m τ) (shortParts m τ) d A label (shortMarks τ)) := by + by_cases hτ : τ = 0 + · obtain ⟨P⟩ := WordPacking.repeated (m := m) (k := 2) (by omega) (by decide) + (by omega) 2 A label he2 + simpa only [shortColumns,shortParts,shortMarks,oneIf,ite_eq_left hτ,List.append_nil, + Nat.mul_comm m 2] using Nonempty.intro P + · have hm2 := hτm hτ + obtain ⟨P⟩ := WordPacking.twosOdd (m := m) (x := 3) (by omega) (by decide) + (by omega) (by omega) hd (balancedParts_sum (2*m+3) 2 (by decide)) (by simp) + 2 3 (by decide) A label he2 (he3 hτ) + simpa only [shortColumns,shortParts,shortMarks,oneIf,ite_eq_right hτ] using Nonempty.intro P + +lemma bigParts_length {q δ : ℕ} (hδ : δ ≤ 1) : (bigParts q δ).length = 5-δ := by + simp only [bigParts,List.length_append,balancedParts_length,oneIf] + split_ifs <;> simp_all <;> omega + +lemma shortParts_length {m τ : ℕ} (hτ : τ ≤ 1) : (shortParts m τ).length = 1+τ := by + simp only [shortParts] + split_ifs <;> simp_all + omega + +lemma oneIf_length {x ε : ℕ} (hε : ε ≤ 1) : (oneIf x ε).length = ε := by + unfold oneIf + split_ifs <;> simp_all + omega + +lemma mem_shortMarks {τ k : ℕ} (hk : k ∈ shortMarks τ) : k = 2 ∨ (τ ≠ 0 ∧ k = 3) := by + unfold shortMarks at hk + split_ifs at hk with hτ + · simp only [Finset.mem_singleton] at hk + exact Or.inl hk + · simpa only [Finset.mem_insert,Finset.mem_singleton,hτ,true_and] using + (show k = 2 ∨ (τ ≠ 0 ∧ k = 3) from + (by rcases Finset.mem_insert.mp hk with h | h + · exact Or.inl h + · exact Or.inr ⟨hτ, Finset.mem_singleton.mp h⟩)) + +lemma mem_markIf {x ε k : ℕ} (hk : k ∈ markIf x ε) : ε ≠ 0 ∧ k = x := by + unfold markIf at hk + split_ifs at hk with hε + · simp at hk + · exact ⟨hε,Finset.mem_singleton.mp hk⟩ + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceColumns.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceColumns.lean index cafe468932edcaf6c6fb27b30376d290540c5f63..52f40ad0c2459e0893f456a717dbd878c5f2cbc5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceColumns.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceColumns.lean @@ -1,309 +1,309 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceProjection -import OAI.RepresentationTheory.UniversalSquare.Support.Neighboring - -namespace OAI - -/-! Balance Columns. -/ - -section - -noncomputable section -open scoped TensorProduct - -namespace Saxl.Balance - -def fixedSumSpace {n d : ℕ} (c : Fin n → ℕ) (z : Fin d → ℤ) - (σ : ℕ → ℤ) : Submodule ℂ (WordSpace n d) where - carrier := {x | FixedComponentSums c z σ x} - zero_mem' := by intro w h; exact False.elim (h rfl) - add_mem' := by - intro x y hx hy w hw - by_cases hh : x w = 0 - · exact hy w (by intro hz; apply hw; simp [hh,hz]) - · exact hx w hh - smul_mem' := by - intro a x hx w hw - exact hx w (by intro hz; apply hw; simp [hz]) - -lemma component_sum_perm {n : ℕ} (c : Fin n → ℕ) (g : Equiv.Perm (Fin n)) - (hg : g ∈ fiberGroup c) (z : Fin n → ℤ) (k : ℕ) : - ∑ i ∈ Finset.univ.filter (fun i => c i = k), z (g i) = - ∑ i ∈ Finset.univ.filter (fun i => c i = k), z i := by - classical - have hh : ∀ i, c (g i) = c i := hg - simpa only [hh] using perm_filter_sum g (fun i => c i = k) z - -lemma fixedSumSpace_invariant {n d : ℕ} (c : Fin n → ℕ) (z : Fin d → ℤ) - (σ : ℕ → ℤ) (g : Equiv.Perm (Fin n)) (hg : g ∈ fiberGroup c) - (x : WordSpace n d) (hx : x ∈ fixedSumSpace c z σ) : - wordRep n d g x ∈ fixedSumSpace c z σ := by - intro w hw k - have hh := hx (w ∘ g) hw k - simpa only [Function.comp_apply, component_sum_perm c g hg (fun i => z (w i)) k] using hh - -def columnRowSums {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (c : Fin n → ℕ) (k : ℕ) : ℤ := - ∑ i ∈ Finset.univ.filter (fun i => c i = k), (rowWord t i).val - -def localColumnSub {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) (c : Fin n → ℕ) := - cyclic ((wordRep n (μ.colLen 0)).comp (fiberGroup c).subtype) (polytabloid t) - -lemma localColumnSub_mem_specht {n : ℕ} {μ : YoungDiagram} - (t : Tableau n μ) (c : Fin n → ℕ) - (x : (localColumnSub t c).toSubmodule) : x.val ∈ spechtSub t := by - rcases x with ⟨x,hx⟩ - change x ∈ Submodule.span ℂ (Set.range fun g : fiberGroup c => - wordRep n (μ.colLen 0) g.val (polytabloid t)) at hx - induction hx using Submodule.span_induction with - | mem y hy => - obtain ⟨g,rfl⟩ := hy - exact (spechtSub t).apply_mem_toSubmodule g.val (mem_cyclic _ _) - | zero => exact Submodule.zero_mem _ - | add y z hy hz iy iz => exact Submodule.add_mem _ iy iz - | smul a y hy iy => exact Submodule.smul_mem _ a iy - -lemma polytabloid_fixed_column_sums {n : ℕ} {μ : YoungDiagram} - (t : Tableau n μ) (c : Fin n → ℕ) - (hc : ∀ i j, (t i).val.2 = (t j).val.2 → c i = c j) : - polytabloid t ∈ fixedSumSpace c (fun a : Fin (μ.colLen 0) => a.val) - (columnRowSums t c) := by - classical - have hbase : (Pi.single (rowWord t) (1 : ℂ)) ∈ - fixedSumSpace c (fun a : Fin (μ.colLen 0) => a.val) (columnRowSums t c) := by - intro w hw k - have he : w = rowWord t := by - by_contra hn - exact hw (Pi.single_eq_of_ne hn _) - subst w - rfl - unfold polytabloid - apply Submodule.sum_mem - intro g hg - apply Submodule.smul_mem - apply fixedSumSpace_invariant _ _ _ _ ?_ _ hbase - intro i - exact hc _ _ (g.property i) - -lemma localColumnSub_fixed_sums {n : ℕ} {μ : YoungDiagram} - (t : Tableau n μ) (c : Fin n → ℕ) - (hc : ∀ i j, (t i).val.2 = (t j).val.2 → c i = c j) - (x : (localColumnSub t c).toSubmodule) : - x.val ∈ fixedSumSpace c (fun a : Fin (μ.colLen 0) => a.val) (columnRowSums t c) := by - rcases x with ⟨x,hx⟩ - change x ∈ Submodule.span ℂ (Set.range fun g : fiberGroup c => - wordRep n (μ.colLen 0) g.val (polytabloid t)) at hx - induction hx using Submodule.span_induction with - | mem y hy => - obtain ⟨g,rfl⟩ := hy - exact fixedSumSpace_invariant _ _ _ g.val g.property _ - (polytabloid_fixed_column_sums t c hc) - | zero => exact Submodule.zero_mem _ - | add y z hy hz iy iz => exact Submodule.add_mem _ iy iz - | smul a y hy iy => exact Submodule.smul_mem _ a iy - -def localColumnTensorMap {n : ℕ} {μ : YoungDiagram} - (t : Tableau n μ) (c : Fin n → ℕ) : - Representation.IntertwiningMap - ((localColumnSub t c).toRepresentation.tprod (localColumnSub t c).toRepresentation) - ((wordRep n (μ.colLen 0 * μ.colLen 0)).comp (fiberGroup c).subtype) where - toLinearMap := (wordTensor n (μ.colLen 0) (μ.colLen 0)).toLinearMap.comp - (TensorProduct.map (localColumnSub t c).toSubmodule.subtype - (localColumnSub t c).toSubmodule.subtype) - isIntertwining' g := by - apply LinearMap.ext - intro x - induction x using TensorProduct.inductionOn with - | add x y hx hy => simp only [map_add, hx, hy] - | tmul x y => - change wordTensor _ _ _ - (wordRep n (μ.colLen 0) g.val x.val ⊗ₜ[ℂ] wordRep n (μ.colLen 0) g.val y.val) = _ - exact wordTensor_equivariant g.val (x.val ⊗ₜ[ℂ] y.val) - -lemma localColumnTensorMap_tmul {n : ℕ} {μ : YoungDiagram} - (t : Tableau n μ) (c : Fin n → ℕ) - (x y : (localColumnSub t c).toSubmodule) : - localColumnTensorMap t c (x ⊗ₜ[ℂ] y) = wordTensor _ _ _ (x.val ⊗ₜ[ℂ] y.val) := rfl - -lemma localColumnTensorMap_mem {n : ℕ} {μ : YoungDiagram} - (t : Tableau n μ) (c : Fin n → ℕ) - (x : (localColumnSub t c).toSubmodule ⊗[ℂ] (localColumnSub t c).toSubmodule) : - localColumnTensorMap t c x ∈ (spechtTensorMap t t).range := by - change localColumnTensorMap t c x ∈ (spechtTensorMap t t).range.toSubmodule - induction x using TensorProduct.inductionOn with - | add x y hx hy => simpa only [map_add] using Submodule.add_mem _ hx hy - | tmul x y => - refine ⟨(⟨x.val,localColumnSub_mem_specht t c x⟩ : Specht t) ⊗ₜ[ℂ] - (⟨y.val,localColumnSub_mem_specht t c y⟩ : Specht t), ?_⟩ - rw [spechtTensorMap] - rfl - -def columnOutputSums {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (c : Fin n → ℕ) (k : ℕ) : ℤ := - 2 * columnRowSums t c k + (Finset.univ.filter (fun i => c i = k)).card - -theorem localColumnTensorMap_fixed_sums {n : ℕ} {μ : YoungDiagram} - (t : Tableau n μ) (c : Fin n → ℕ) - (hc : ∀ i j, (t i).val.2 = (t j).val.2 → c i = c j) - (x : (localColumnSub t c).toSubmodule ⊗[ℂ] (localColumnSub t c).toSubmodule) : - localColumnTensorMap t c x ∈ fixedSumSpace c - (fun a : Fin (μ.colLen 0 * μ.colLen 0) => (output a : ℤ)) (columnOutputSums t c) := by - classical - induction x using TensorProduct.inductionOn with - | add x y hx hy => simpa only [map_add] using Submodule.add_mem _ hx hy - | tmul x y => - intro w hw k - rw [localColumnTensorMap_tmul, wordTensor_tmul] at hw - obtain ⟨hx,hy⟩ := mul_ne_zero_iff.mp hw - have hs₁ := localColumnSub_fixed_sums t c hc x (splitLeft w) hx k - have hs₂ := localColumnSub_fixed_sums t c hc y (splitRight w) hy k - change (∑ i ∈ Finset.univ.filter (fun i => c i = k), - (output (w i) : ℤ)) = _ - simp only [output, Nat.cast_add, Nat.cast_one, Finset.sum_add_distrib, - Finset.sum_const, nsmul_eq_mul, mul_one] - change (∑ i ∈ Finset.univ.filter (fun i => c i = k), ((splitLeft w i).val : ℤ)) + - (∑ i ∈ Finset.univ.filter (fun i => c i = k), ((splitRight w i).val : ℤ)) + - _ = _ - rw [hs₁,hs₂] - dsimp only [columnOutputSums] - ring - -lemma componentWords_invariant_fiber {n d : ℕ} (c : Fin n → ℕ) - (A : Fin d → Prop) (label : Fin d → ℕ) (g : Equiv.Perm (Fin n)) - (hg : g ∈ fiberGroup c) (w : Fin n → Fin d) : - componentWords c A label (w ∘ g) ↔ componentWords c A label w := by - constructor - · rintro ⟨hA,hl⟩ - refine ⟨?_, fun i => ?_⟩ - · intro i - simpa only [Function.comp_apply, Equiv.apply_symm_apply] using hA (g.symm i) - · have he := hl (g.symm i) - have hc := hg (g.symm i) - simpa only [Function.comp_apply, Equiv.apply_symm_apply] using he.trans hc.symm - · rintro ⟨hA,hl⟩ - exact ⟨fun i => hA (g i),fun i => (hl (g i)).trans (hg i)⟩ - -def componentProjection {n d : ℕ} (c : Fin n → ℕ) - (A : Fin d → Prop) (label : Fin d → ℕ) : - Representation.IntertwiningMap - ((wordRep n d).comp (fiberGroup c).subtype) - ((wordRep n d).comp (fiberGroup c).subtype) where - toLinearMap := coordinateProjection (componentWords c A label) - isIntertwining' g := by - classical - apply LinearMap.ext - intro x - funext w - change (if componentWords c A label w then x (w ∘ g.val) else 0) = - (if componentWords c A label (w ∘ g.val) then x (w ∘ g.val) else 0) - rw [componentWords_invariant_fiber c A label g.val g.property] - -def projectedColumnSquare {n : ℕ} {μ : YoungDiagram} - (t : Tableau n μ) (c : Fin n → ℕ) - (A : Fin (μ.colLen 0 * μ.colLen 0) → Prop) - (label : Fin (μ.colLen 0 * μ.colLen 0) → ℕ) := - ((componentProjection c A label).comp (localColumnTensorMap t c)).range - -def rangeQuotient {G X Y : Type*} [Group G] - [AddCommMonoid X] [Module ℂ X] [AddCommMonoid Y] [Module ℂ Y] - {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} - (F : Representation.IntertwiningMap ρ σ) : - Representation.IntertwiningMap ρ F.range.toRepresentation where - toLinearMap := F.toLinearMap.rangeRestrict - isIntertwining' g := by - apply LinearMap.ext - intro x - apply Subtype.ext - exact LinearMap.congr_fun (F.isIntertwining' g) x - -lemma rangeQuotient_surjective {G X Y : Type*} [Group G] - [AddCommMonoid X] [Module ℂ X] [AddCommMonoid Y] [Module ℂ Y] - {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} - (F : Representation.IntertwiningMap ρ σ) : Function.Surjective (rangeQuotient F) := by - rintro ⟨y,x,rfl⟩ - exact ⟨x,rfl⟩ - -theorem projected_range_support {n d : ℕ} {X Y : Type*} - [AddCommGroup X] [Module ℂ X] [AddCommMonoid Y] [Module ℂ Y] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (W : Subrepresentation (wordRep n d)) - (c : Fin n → ℕ) (A : Fin d → Prop) (label : Fin d → ℕ) - (z : Fin d → ℤ) (σ : ℕ → ℤ) - (ho : ∀ a b, A a → A b → label a < label b → z a < z b) - (τ : Representation ℂ (fiberGroup c) Y) - (J : Representation.IntertwiningMap τ ((wordRep n d).comp (fiberGroup c).subtype)) - (hm : ∀ y, J y ∈ W) (hs : ∀ y, FixedComponentSums c z σ (J y)) - (f : Representation.IntertwiningMap (ρ.comp (fiberGroup c).subtype) - ((componentProjection c A label).comp J).range.toRepresentation) (hf : f ≠ 0) : - ∃ F : Representation.IntertwiningMap ρ W.toRepresentation, F ≠ 0 := by - let : AddCommGroup Y := Module.addCommMonoidToAddCommGroup ℂ - let Q := (componentProjection c A label).comp J - obtain ⟨h,hh⟩ := intertwining_lift_surjective (rangeQuotient Q) - (rangeQuotient_surjective Q) f - let L := J.toLinearMap.comp h.toLinearMap - have he (x : X) : coordinateProjection (componentWords c A label) (L x) = (f x).val := - congrArg Subtype.val (congrArg (fun T : Representation.IntertwiningMap - (ρ.comp (fiberGroup c).subtype) Q.range.toRepresentation => T x) hh) - have hL : (coordinateProjection (componentWords c A label)).comp L ≠ 0 := by - intro hz - apply hf - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - apply Subtype.ext - exact (he x).symm.trans (LinearMap.congr_fun hz x) - have heq (g : Equiv.Perm (Fin n)) (hg : g ∈ fiberGroup c) (x : X) : - coordinateProjection (componentWords c A label) (L (ρ g x)) = - wordRep n d g (coordinateProjection (componentWords c A label) (L x)) := by - rw [he,he] - exact congrArg Subtype.val (LinearMap.congr_fun (f.isIntertwining' ⟨g,hg⟩) x) - exact balance_support_transfer ρ W c A label z σ ho L - (fun x => hm (h x)) (fun x => hs (h x)) hL heq - -theorem projected_columns_support {n : ℕ} {μ : YoungDiagram} {X : Type*} - [AddCommGroup X] [Module ℂ X] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (t : Tableau n μ) (c : Fin n → ℕ) - (hc : ∀ i j, (t i).val.2 = (t j).val.2 → c i = c j) - (A : Fin (μ.colLen 0 * μ.colLen 0) → Prop) - (label : Fin (μ.colLen 0 * μ.colLen 0) → ℕ) - (ho : ∀ a b, A a → A b → label a < label b → output a < output b) - (f : Representation.IntertwiningMap (ρ.comp (fiberGroup c).subtype) - (projectedColumnSquare t c A label).toRepresentation) (hf : f ≠ 0) : - ∃ F : Representation.IntertwiningMap ρ ((spechtRep t).tprod (spechtRep t)), F ≠ 0 := by - have hR : ∃ F : Representation.IntertwiningMap ρ (spechtTensorMap t t).range.toRepresentation, - F ≠ 0 := by - apply projected_range_support ρ (spechtTensorMap t t).range c A label - (fun a => (output (d := μ.colLen 0) (e := μ.colLen 0) a : ℤ)) - (columnOutputSums t c) _ - ((localColumnSub t c).toRepresentation.tprod (localColumnSub t c).toRepresentation) - (localColumnTensorMap t c) _ _ f hf - · intro a b ha hb hab - exact_mod_cast ho a b ha hb hab - · intro y - exact localColumnTensorMap_mem t c y - · intro y - exact localColumnTensorMap_fixed_sums t c hc y - obtain ⟨F,hF⟩ := hR - let : AddCommGroup (Specht t ⊗[ℂ] Specht t) := Module.addCommMonoidToAddCommGroup ℂ - obtain ⟨i,hi⟩ := subrepresentation_embeds_of_le_range (spechtTensorMap t t) - (spechtTensorMap t t).range le_rfl - exact ⟨i.comp F,intertwining_comp_ne_zero i hi F hF⟩ - -theorem kronecker_pos_of_projected_columns {n : ℕ} {μ ν : YoungDiagram} - (t : Tableau n μ) (s : Tableau n ν) (c : Fin n → ℕ) - (hc : ∀ i j, (t i).val.2 = (t j).val.2 → c i = c j) - (A : Fin (μ.colLen 0 * μ.colLen 0) → Prop) - (label : Fin (μ.colLen 0 * μ.colLen 0) → ℕ) - (ho : ∀ a b, A a → A b → label a < label b → output a < output b) - (f : Representation.IntertwiningMap ((spechtRep s).comp (fiberGroup c).subtype) - (projectedColumnSquare t c A label).toRepresentation) (hf : f ≠ 0) : - 0 < kronecker t t s := - (kronecker_pos_iff t t s).mpr (projected_columns_support (spechtRep s) t c hc A label ho f hf) - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceProjection +import OAI.RepresentationTheory.UniversalSquare.Support.Neighboring + +namespace OAI + +/-! Balance Columns. -/ + +section + +noncomputable section +open scoped TensorProduct + +namespace Saxl.Balance + +def fixedSumSpace {n d : ℕ} (c : Fin n → ℕ) (z : Fin d → ℤ) + (σ : ℕ → ℤ) : Submodule ℂ (WordSpace n d) where + carrier := {x | FixedComponentSums c z σ x} + zero_mem' := by intro w h; exact False.elim (h rfl) + add_mem' := by + intro x y hx hy w hw + by_cases hh : x w = 0 + · exact hy w (by intro hz; apply hw; simp [hh,hz]) + · exact hx w hh + smul_mem' := by + intro a x hx w hw + exact hx w (by intro hz; apply hw; simp [hz]) + +lemma component_sum_perm {n : ℕ} (c : Fin n → ℕ) (g : Equiv.Perm (Fin n)) + (hg : g ∈ fiberGroup c) (z : Fin n → ℤ) (k : ℕ) : + ∑ i ∈ Finset.univ.filter (fun i => c i = k), z (g i) = + ∑ i ∈ Finset.univ.filter (fun i => c i = k), z i := by + classical + have hh : ∀ i, c (g i) = c i := hg + simpa only [hh] using perm_filter_sum g (fun i => c i = k) z + +lemma fixedSumSpace_invariant {n d : ℕ} (c : Fin n → ℕ) (z : Fin d → ℤ) + (σ : ℕ → ℤ) (g : Equiv.Perm (Fin n)) (hg : g ∈ fiberGroup c) + (x : WordSpace n d) (hx : x ∈ fixedSumSpace c z σ) : + wordRep n d g x ∈ fixedSumSpace c z σ := by + intro w hw k + have hh := hx (w ∘ g) hw k + simpa only [Function.comp_apply, component_sum_perm c g hg (fun i => z (w i)) k] using hh + +def columnRowSums {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (c : Fin n → ℕ) (k : ℕ) : ℤ := + ∑ i ∈ Finset.univ.filter (fun i => c i = k), (rowWord t i).val + +def localColumnSub {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) (c : Fin n → ℕ) := + cyclic ((wordRep n (μ.colLen 0)).comp (fiberGroup c).subtype) (polytabloid t) + +lemma localColumnSub_mem_specht {n : ℕ} {μ : YoungDiagram} + (t : Tableau n μ) (c : Fin n → ℕ) + (x : (localColumnSub t c).toSubmodule) : x.val ∈ spechtSub t := by + rcases x with ⟨x,hx⟩ + change x ∈ Submodule.span ℂ (Set.range fun g : fiberGroup c => + wordRep n (μ.colLen 0) g.val (polytabloid t)) at hx + induction hx using Submodule.span_induction with + | mem y hy => + obtain ⟨g,rfl⟩ := hy + exact (spechtSub t).apply_mem_toSubmodule g.val (mem_cyclic _ _) + | zero => exact Submodule.zero_mem _ + | add y z hy hz iy iz => exact Submodule.add_mem _ iy iz + | smul a y hy iy => exact Submodule.smul_mem _ a iy + +lemma polytabloid_fixed_column_sums {n : ℕ} {μ : YoungDiagram} + (t : Tableau n μ) (c : Fin n → ℕ) + (hc : ∀ i j, (t i).val.2 = (t j).val.2 → c i = c j) : + polytabloid t ∈ fixedSumSpace c (fun a : Fin (μ.colLen 0) => a.val) + (columnRowSums t c) := by + classical + have hbase : (Pi.single (rowWord t) (1 : ℂ)) ∈ + fixedSumSpace c (fun a : Fin (μ.colLen 0) => a.val) (columnRowSums t c) := by + intro w hw k + have he : w = rowWord t := by + by_contra hn + exact hw (Pi.single_eq_of_ne hn _) + subst w + rfl + unfold polytabloid + apply Submodule.sum_mem + intro g hg + apply Submodule.smul_mem + apply fixedSumSpace_invariant _ _ _ _ ?_ _ hbase + intro i + exact hc _ _ (g.property i) + +lemma localColumnSub_fixed_sums {n : ℕ} {μ : YoungDiagram} + (t : Tableau n μ) (c : Fin n → ℕ) + (hc : ∀ i j, (t i).val.2 = (t j).val.2 → c i = c j) + (x : (localColumnSub t c).toSubmodule) : + x.val ∈ fixedSumSpace c (fun a : Fin (μ.colLen 0) => a.val) (columnRowSums t c) := by + rcases x with ⟨x,hx⟩ + change x ∈ Submodule.span ℂ (Set.range fun g : fiberGroup c => + wordRep n (μ.colLen 0) g.val (polytabloid t)) at hx + induction hx using Submodule.span_induction with + | mem y hy => + obtain ⟨g,rfl⟩ := hy + exact fixedSumSpace_invariant _ _ _ g.val g.property _ + (polytabloid_fixed_column_sums t c hc) + | zero => exact Submodule.zero_mem _ + | add y z hy hz iy iz => exact Submodule.add_mem _ iy iz + | smul a y hy iy => exact Submodule.smul_mem _ a iy + +def localColumnTensorMap {n : ℕ} {μ : YoungDiagram} + (t : Tableau n μ) (c : Fin n → ℕ) : + Representation.IntertwiningMap + ((localColumnSub t c).toRepresentation.tprod (localColumnSub t c).toRepresentation) + ((wordRep n (μ.colLen 0 * μ.colLen 0)).comp (fiberGroup c).subtype) where + toLinearMap := (wordTensor n (μ.colLen 0) (μ.colLen 0)).toLinearMap.comp + (TensorProduct.map (localColumnSub t c).toSubmodule.subtype + (localColumnSub t c).toSubmodule.subtype) + isIntertwining' g := by + apply LinearMap.ext + intro x + induction x using TensorProduct.inductionOn with + | add x y hx hy => simp only [map_add, hx, hy] + | tmul x y => + change wordTensor _ _ _ + (wordRep n (μ.colLen 0) g.val x.val ⊗ₜ[ℂ] wordRep n (μ.colLen 0) g.val y.val) = _ + exact wordTensor_equivariant g.val (x.val ⊗ₜ[ℂ] y.val) + +lemma localColumnTensorMap_tmul {n : ℕ} {μ : YoungDiagram} + (t : Tableau n μ) (c : Fin n → ℕ) + (x y : (localColumnSub t c).toSubmodule) : + localColumnTensorMap t c (x ⊗ₜ[ℂ] y) = wordTensor _ _ _ (x.val ⊗ₜ[ℂ] y.val) := rfl + +lemma localColumnTensorMap_mem {n : ℕ} {μ : YoungDiagram} + (t : Tableau n μ) (c : Fin n → ℕ) + (x : (localColumnSub t c).toSubmodule ⊗[ℂ] (localColumnSub t c).toSubmodule) : + localColumnTensorMap t c x ∈ (spechtTensorMap t t).range := by + change localColumnTensorMap t c x ∈ (spechtTensorMap t t).range.toSubmodule + induction x using TensorProduct.inductionOn with + | add x y hx hy => simpa only [map_add] using Submodule.add_mem _ hx hy + | tmul x y => + refine ⟨(⟨x.val,localColumnSub_mem_specht t c x⟩ : Specht t) ⊗ₜ[ℂ] + (⟨y.val,localColumnSub_mem_specht t c y⟩ : Specht t), ?_⟩ + rw [spechtTensorMap] + rfl + +def columnOutputSums {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (c : Fin n → ℕ) (k : ℕ) : ℤ := + 2 * columnRowSums t c k + (Finset.univ.filter (fun i => c i = k)).card + +theorem localColumnTensorMap_fixed_sums {n : ℕ} {μ : YoungDiagram} + (t : Tableau n μ) (c : Fin n → ℕ) + (hc : ∀ i j, (t i).val.2 = (t j).val.2 → c i = c j) + (x : (localColumnSub t c).toSubmodule ⊗[ℂ] (localColumnSub t c).toSubmodule) : + localColumnTensorMap t c x ∈ fixedSumSpace c + (fun a : Fin (μ.colLen 0 * μ.colLen 0) => (output a : ℤ)) (columnOutputSums t c) := by + classical + induction x using TensorProduct.inductionOn with + | add x y hx hy => simpa only [map_add] using Submodule.add_mem _ hx hy + | tmul x y => + intro w hw k + rw [localColumnTensorMap_tmul, wordTensor_tmul] at hw + obtain ⟨hx,hy⟩ := mul_ne_zero_iff.mp hw + have hs₁ := localColumnSub_fixed_sums t c hc x (splitLeft w) hx k + have hs₂ := localColumnSub_fixed_sums t c hc y (splitRight w) hy k + change (∑ i ∈ Finset.univ.filter (fun i => c i = k), + (output (w i) : ℤ)) = _ + simp only [output, Nat.cast_add, Nat.cast_one, Finset.sum_add_distrib, + Finset.sum_const, nsmul_eq_mul, mul_one] + change (∑ i ∈ Finset.univ.filter (fun i => c i = k), ((splitLeft w i).val : ℤ)) + + (∑ i ∈ Finset.univ.filter (fun i => c i = k), ((splitRight w i).val : ℤ)) + + _ = _ + rw [hs₁,hs₂] + dsimp only [columnOutputSums] + ring + +lemma componentWords_invariant_fiber {n d : ℕ} (c : Fin n → ℕ) + (A : Fin d → Prop) (label : Fin d → ℕ) (g : Equiv.Perm (Fin n)) + (hg : g ∈ fiberGroup c) (w : Fin n → Fin d) : + componentWords c A label (w ∘ g) ↔ componentWords c A label w := by + constructor + · rintro ⟨hA,hl⟩ + refine ⟨?_, fun i => ?_⟩ + · intro i + simpa only [Function.comp_apply, Equiv.apply_symm_apply] using hA (g.symm i) + · have he := hl (g.symm i) + have hc := hg (g.symm i) + simpa only [Function.comp_apply, Equiv.apply_symm_apply] using he.trans hc.symm + · rintro ⟨hA,hl⟩ + exact ⟨fun i => hA (g i),fun i => (hl (g i)).trans (hg i)⟩ + +def componentProjection {n d : ℕ} (c : Fin n → ℕ) + (A : Fin d → Prop) (label : Fin d → ℕ) : + Representation.IntertwiningMap + ((wordRep n d).comp (fiberGroup c).subtype) + ((wordRep n d).comp (fiberGroup c).subtype) where + toLinearMap := coordinateProjection (componentWords c A label) + isIntertwining' g := by + classical + apply LinearMap.ext + intro x + funext w + change (if componentWords c A label w then x (w ∘ g.val) else 0) = + (if componentWords c A label (w ∘ g.val) then x (w ∘ g.val) else 0) + rw [componentWords_invariant_fiber c A label g.val g.property] + +def projectedColumnSquare {n : ℕ} {μ : YoungDiagram} + (t : Tableau n μ) (c : Fin n → ℕ) + (A : Fin (μ.colLen 0 * μ.colLen 0) → Prop) + (label : Fin (μ.colLen 0 * μ.colLen 0) → ℕ) := + ((componentProjection c A label).comp (localColumnTensorMap t c)).range + +def rangeQuotient {G X Y : Type*} [Group G] + [AddCommMonoid X] [Module ℂ X] [AddCommMonoid Y] [Module ℂ Y] + {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} + (F : Representation.IntertwiningMap ρ σ) : + Representation.IntertwiningMap ρ F.range.toRepresentation where + toLinearMap := F.toLinearMap.rangeRestrict + isIntertwining' g := by + apply LinearMap.ext + intro x + apply Subtype.ext + exact LinearMap.congr_fun (F.isIntertwining' g) x + +lemma rangeQuotient_surjective {G X Y : Type*} [Group G] + [AddCommMonoid X] [Module ℂ X] [AddCommMonoid Y] [Module ℂ Y] + {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} + (F : Representation.IntertwiningMap ρ σ) : Function.Surjective (rangeQuotient F) := by + rintro ⟨y,x,rfl⟩ + exact ⟨x,rfl⟩ + +theorem projected_range_support {n d : ℕ} {X Y : Type*} + [AddCommGroup X] [Module ℂ X] [AddCommMonoid Y] [Module ℂ Y] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (W : Subrepresentation (wordRep n d)) + (c : Fin n → ℕ) (A : Fin d → Prop) (label : Fin d → ℕ) + (z : Fin d → ℤ) (σ : ℕ → ℤ) + (ho : ∀ a b, A a → A b → label a < label b → z a < z b) + (τ : Representation ℂ (fiberGroup c) Y) + (J : Representation.IntertwiningMap τ ((wordRep n d).comp (fiberGroup c).subtype)) + (hm : ∀ y, J y ∈ W) (hs : ∀ y, FixedComponentSums c z σ (J y)) + (f : Representation.IntertwiningMap (ρ.comp (fiberGroup c).subtype) + ((componentProjection c A label).comp J).range.toRepresentation) (hf : f ≠ 0) : + ∃ F : Representation.IntertwiningMap ρ W.toRepresentation, F ≠ 0 := by + let : AddCommGroup Y := Module.addCommMonoidToAddCommGroup ℂ + let Q := (componentProjection c A label).comp J + obtain ⟨h,hh⟩ := intertwining_lift_surjective (rangeQuotient Q) + (rangeQuotient_surjective Q) f + let L := J.toLinearMap.comp h.toLinearMap + have he (x : X) : coordinateProjection (componentWords c A label) (L x) = (f x).val := + congrArg Subtype.val (congrArg (fun T : Representation.IntertwiningMap + (ρ.comp (fiberGroup c).subtype) Q.range.toRepresentation => T x) hh) + have hL : (coordinateProjection (componentWords c A label)).comp L ≠ 0 := by + intro hz + apply hf + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + apply Subtype.ext + exact (he x).symm.trans (LinearMap.congr_fun hz x) + have heq (g : Equiv.Perm (Fin n)) (hg : g ∈ fiberGroup c) (x : X) : + coordinateProjection (componentWords c A label) (L (ρ g x)) = + wordRep n d g (coordinateProjection (componentWords c A label) (L x)) := by + rw [he,he] + exact congrArg Subtype.val (LinearMap.congr_fun (f.isIntertwining' ⟨g,hg⟩) x) + exact balance_support_transfer ρ W c A label z σ ho L + (fun x => hm (h x)) (fun x => hs (h x)) hL heq + +theorem projected_columns_support {n : ℕ} {μ : YoungDiagram} {X : Type*} + [AddCommGroup X] [Module ℂ X] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (t : Tableau n μ) (c : Fin n → ℕ) + (hc : ∀ i j, (t i).val.2 = (t j).val.2 → c i = c j) + (A : Fin (μ.colLen 0 * μ.colLen 0) → Prop) + (label : Fin (μ.colLen 0 * μ.colLen 0) → ℕ) + (ho : ∀ a b, A a → A b → label a < label b → output a < output b) + (f : Representation.IntertwiningMap (ρ.comp (fiberGroup c).subtype) + (projectedColumnSquare t c A label).toRepresentation) (hf : f ≠ 0) : + ∃ F : Representation.IntertwiningMap ρ ((spechtRep t).tprod (spechtRep t)), F ≠ 0 := by + have hR : ∃ F : Representation.IntertwiningMap ρ (spechtTensorMap t t).range.toRepresentation, + F ≠ 0 := by + apply projected_range_support ρ (spechtTensorMap t t).range c A label + (fun a => (output (d := μ.colLen 0) (e := μ.colLen 0) a : ℤ)) + (columnOutputSums t c) _ + ((localColumnSub t c).toRepresentation.tprod (localColumnSub t c).toRepresentation) + (localColumnTensorMap t c) _ _ f hf + · intro a b ha hb hab + exact_mod_cast ho a b ha hb hab + · intro y + exact localColumnTensorMap_mem t c y + · intro y + exact localColumnTensorMap_fixed_sums t c hc y + obtain ⟨F,hF⟩ := hR + let : AddCommGroup (Specht t ⊗[ℂ] Specht t) := Module.addCommMonoidToAddCommGroup ℂ + obtain ⟨i,hi⟩ := subrepresentation_embeds_of_le_range (spechtTensorMap t t) + (spechtTensorMap t t).range le_rfl + exact ⟨i.comp F,intertwining_comp_ne_zero i hi F hF⟩ + +theorem kronecker_pos_of_projected_columns {n : ℕ} {μ ν : YoungDiagram} + (t : Tableau n μ) (s : Tableau n ν) (c : Fin n → ℕ) + (hc : ∀ i j, (t i).val.2 = (t j).val.2 → c i = c j) + (A : Fin (μ.colLen 0 * μ.colLen 0) → Prop) + (label : Fin (μ.colLen 0 * μ.colLen 0) → ℕ) + (ho : ∀ a b, A a → A b → label a < label b → output a < output b) + (f : Representation.IntertwiningMap ((spechtRep s).comp (fiberGroup c).subtype) + (projectedColumnSquare t c A label).toRepresentation) (hf : f ≠ 0) : + 0 < kronecker t t s := + (kronecker_pos_iff t t s).mpr (projected_columns_support (spechtRep s) t c hc A label ho f hf) + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceDominance.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceDominance.lean index cd78a37b3439c72e1b53f8a3e3f792d59cf521da..c69dc9ec2ceeb0c90e1af55d162a1d50256ebf1b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceDominance.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceDominance.lean @@ -1,142 +1,142 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Capacity.Capacity - -namespace OAI - -/-! Balance Dominance. -/ - -section - -noncomputable section - -namespace UniversalTensorSquare -open Saxl - -lemma rowPrefix_scaled_mono (μ : YoungDiagram) {k l : ℕ} (hkl : k ≤ l) : - k * rowPrefix μ l ≤ l * rowPrefix μ k := by - induction l, hkl using Nat.le_induction with - | base => exact le_rfl - | succ l hl ih => - have hlast : k * μ.rowLen l ≤ rowPrefix μ k := by - have h := Finset.sum_le_sum (s := Finset.range k) (f := fun _ => μ.rowLen l) - (g := μ.rowLen) (by - intro i hi - exact μ.rowLen_anti _ _ (by have := Finset.mem_range.mp hi; omega)) - simpa only [Finset.sum_const, Finset.card_range, smul_eq_mul, rowPrefix] using h - rw [rowPrefix_succ] - nlinarith - -lemma colPrefix_eq_min_sum (μ : YoungDiagram) (k : ℕ) : - colPrefix μ k = ∑ i ∈ Finset.range (μ.colLen 0), min k (μ.rowLen i) := by - rw [← colTruncate_card, ← rowPrefix_eq_card _ (colTruncate_height μ k)] - exact Finset.sum_congr rfl (fun i _ => colTruncate_rowLen μ k i) - -lemma scaled_colPrefix_lower (A : YoungDiagram) {k B : ℕ} - (hB : A.rowLen 0 ≤ B) (hk : k ≤ B) : - k*A.card ≤ B*colPrefix A k := by - rw [colPrefix_eq_min_sum, ← rowPrefix_eq_card A le_rfl] - simp only [rowPrefix, Finset.mul_sum] - apply Finset.sum_le_sum - intro i _ - have hi : A.rowLen i ≤ B := (A.rowLen_anti _ _ (Nat.zero_le _)).trans hB - by_cases hh : k ≤ A.rowLen i - · rw [min_eq_left hh] - nlinarith - · rw [min_eq_right (by omega)] - exact Nat.mul_le_mul_right _ hk - -theorem balance_dominance (M : ℕ) (hM : 9 ≤ M) (μ A : YoungDiagram) - (hc : μ.card = A.card) (hn : (staircase M).card ≤ μ.card) - (hμ : colPrefix μ 4 ≤ 2*M-2) - (hparts : 2*M-5 ≤ A.colLen 0) (hmax : A.rowLen 0 ≤ M+1) - (hfour : 2 ≤ A.rowLen 3) : Dominates μ A := by - have hdouble := staircase_card_double M - have hn' : M*(M+1) ≤ 2*μ.card := by omega - have hlarge : 2*M-2 < μ.card := by - have hs : M*M ≥ 9*M := Nat.mul_le_mul_right M hM - have hsub : 2*M-2 ≤ 2*M := Nat.sub_le _ _ - nlinarith - have hwidth : 4 ≤ μ.rowLen 0 := by - by_contra hh - have he : colPrefix μ 4 = μ.card := by - simpa only [colPrefix, YoungDiagram.colLen_transpose, transpose_card] using - rowPrefix_eq_card μ.transpose (by simpa using (show μ.rowLen 0 ≤ 4 by omega)) - omega - have hpos (i : ℕ) (hi : i < 4) : 1 ≤ μ.colLen i := by - have hh := YoungDiagram.mem_iff_lt_colLen.mp - (YoungDiagram.mem_iff_lt_rowLen.mpr (show i < μ.rowLen 0 by omega)) - omega - have hheight : μ.colLen 0 ≤ 2*M-5 := by - have hp1 := hpos 1 (by decide) - have hp2 := hpos 2 (by decide) - have hp3 := hpos 3 (by decide) - rw [colPrefix_eq_sum] at hμ - simp only [Finset.sum_range_succ, Finset.sum_range_zero, zero_add] at hμ - omega - have hA1 : 4 ≤ A.colLen 1 := by - have h := YoungDiagram.mem_iff_lt_colLen.mp - (YoungDiagram.mem_iff_lt_rowLen.mpr (show 1 < A.rowLen 3 by omega)) - omega - have hA2 : 2*M-1 ≤ colPrefix A 2 := by - rw [colPrefix_eq_sum] - simp only [Finset.sum_range_succ, Finset.sum_range_zero, zero_add] - omega - have hdual : Dominates A.transpose μ.transpose := by - intro k - change colPrefix μ k ≤ colPrefix A k - by_cases hk : k < 4 - · interval_cases k - · simp [colPrefix, rowPrefix] - · simpa only [colPrefix_eq_sum, Finset.sum_range_one] using hheight.trans hparts - · exact ((rowPrefix_mono μ.transpose (by omega)).trans hμ).trans (by omega) - · have hA3 := rowPrefix_mono A.transpose (show 2 ≤ 3 by omega) - change colPrefix A 2 ≤ colPrefix A 3 at hA3 - exact ((rowPrefix_mono μ.transpose (by omega)).trans hμ).trans (by omega) - · by_cases hB : A.rowLen 0 ≤ k - · have he : colPrefix A k = A.card := by - simpa only [colPrefix, transpose_card] using - rowPrefix_eq_card A.transpose (by simpa using hB) - rw [he, ← hc] - exact (rowPrefix_le_card μ.transpose k).trans_eq (transpose_card _) - · let B := A.rowLen 0 - have hBp : 0 < B := by dsimp only [B]; omega - have hupper : 4*colPrefix μ k ≤ k*(2*M-2) := - (rowPrefix_scaled_mono μ.transpose (by omega)).trans - (Nat.mul_le_mul_left k hμ) - have hlower := scaled_colPrefix_lower A le_rfl (show k ≤ B by dsimp [B]; omega) - have hratio : B*(2*M-2) ≤ 4*A.card := by - have hmul := Nat.mul_le_mul_right (2*M-2) hmax - dsimp only [B] - have hsub : 2*M-2+2 = 2*M := by omega - nlinarith - have hbound : (4*B)*colPrefix μ k ≤ (4*B)*colPrefix A k := calc - (4*B)*colPrefix μ k = B*(4*colPrefix μ k) := by ring - _ ≤ B*(k*(2*M-2)) := Nat.mul_le_mul_left B hupper - _ = k*(B*(2*M-2)) := by ring - _ ≤ k*(4*A.card) := Nat.mul_le_mul_left k hratio - _ = 4*(k*A.card) := by ring - _ ≤ 4*(B*colPrefix A k) := Nat.mul_le_mul_left 4 hlower - _ = (4*B)*colPrefix A k := by ring - exact (mul_le_mul_iff_right₀ (show 0 < 4*B by omega)).mp hbound - simpa only [YoungDiagram.transpose_transpose] using - dominates_transpose (by simpa only [transpose_card] using hc.symm) hdual - -theorem balance_invariant_functional (M : ℕ) (hM : 9 ≤ M) (μ A : YoungDiagram) - (hc : μ.card = A.card) (hn : (staircase M).card ≤ μ.card) - (hμ : colPrefix μ 4 ≤ 2*M-2) - (hparts : 2*M-5 ≤ A.colLen 0) (hmax : A.rowLen 0 ≤ M+1) - (hfour : 2 ≤ A.rowLen 3) : - ∃ (a : Fin μ.card → Fin (A.colLen 0)) (l : Module.Dual ℂ (Specht (shapeTableau μ))), - l ≠ 0 ∧ - (∀ j, (Finset.univ.filter (fun i => a i = j)).card = A.rowLen j) ∧ - (∀ g : Equiv.Perm (Fin μ.card), a ∘ g = a → - ∀ x, l (spechtRep (shapeTableau μ) g x) = l x) := by - exact young_invariant_functional A μ hc - (balance_dominance M hM μ A hc hn hμ hparts hmax hfour) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Capacity.Capacity + +namespace OAI + +/-! Balance Dominance. -/ + +section + +noncomputable section + +namespace UniversalTensorSquare +open Saxl + +lemma rowPrefix_scaled_mono (μ : YoungDiagram) {k l : ℕ} (hkl : k ≤ l) : + k * rowPrefix μ l ≤ l * rowPrefix μ k := by + induction l, hkl using Nat.le_induction with + | base => exact le_rfl + | succ l hl ih => + have hlast : k * μ.rowLen l ≤ rowPrefix μ k := by + have h := Finset.sum_le_sum (s := Finset.range k) (f := fun _ => μ.rowLen l) + (g := μ.rowLen) (by + intro i hi + exact μ.rowLen_anti _ _ (by have := Finset.mem_range.mp hi; omega)) + simpa only [Finset.sum_const, Finset.card_range, smul_eq_mul, rowPrefix] using h + rw [rowPrefix_succ] + nlinarith + +lemma colPrefix_eq_min_sum (μ : YoungDiagram) (k : ℕ) : + colPrefix μ k = ∑ i ∈ Finset.range (μ.colLen 0), min k (μ.rowLen i) := by + rw [← colTruncate_card, ← rowPrefix_eq_card _ (colTruncate_height μ k)] + exact Finset.sum_congr rfl (fun i _ => colTruncate_rowLen μ k i) + +lemma scaled_colPrefix_lower (A : YoungDiagram) {k B : ℕ} + (hB : A.rowLen 0 ≤ B) (hk : k ≤ B) : + k*A.card ≤ B*colPrefix A k := by + rw [colPrefix_eq_min_sum, ← rowPrefix_eq_card A le_rfl] + simp only [rowPrefix, Finset.mul_sum] + apply Finset.sum_le_sum + intro i _ + have hi : A.rowLen i ≤ B := (A.rowLen_anti _ _ (Nat.zero_le _)).trans hB + by_cases hh : k ≤ A.rowLen i + · rw [min_eq_left hh] + nlinarith + · rw [min_eq_right (by omega)] + exact Nat.mul_le_mul_right _ hk + +theorem balance_dominance (M : ℕ) (hM : 9 ≤ M) (μ A : YoungDiagram) + (hc : μ.card = A.card) (hn : (staircase M).card ≤ μ.card) + (hμ : colPrefix μ 4 ≤ 2*M-2) + (hparts : 2*M-5 ≤ A.colLen 0) (hmax : A.rowLen 0 ≤ M+1) + (hfour : 2 ≤ A.rowLen 3) : Dominates μ A := by + have hdouble := staircase_card_double M + have hn' : M*(M+1) ≤ 2*μ.card := by omega + have hlarge : 2*M-2 < μ.card := by + have hs : M*M ≥ 9*M := Nat.mul_le_mul_right M hM + have hsub : 2*M-2 ≤ 2*M := Nat.sub_le _ _ + nlinarith + have hwidth : 4 ≤ μ.rowLen 0 := by + by_contra hh + have he : colPrefix μ 4 = μ.card := by + simpa only [colPrefix, YoungDiagram.colLen_transpose, transpose_card] using + rowPrefix_eq_card μ.transpose (by simpa using (show μ.rowLen 0 ≤ 4 by omega)) + omega + have hpos (i : ℕ) (hi : i < 4) : 1 ≤ μ.colLen i := by + have hh := YoungDiagram.mem_iff_lt_colLen.mp + (YoungDiagram.mem_iff_lt_rowLen.mpr (show i < μ.rowLen 0 by omega)) + omega + have hheight : μ.colLen 0 ≤ 2*M-5 := by + have hp1 := hpos 1 (by decide) + have hp2 := hpos 2 (by decide) + have hp3 := hpos 3 (by decide) + rw [colPrefix_eq_sum] at hμ + simp only [Finset.sum_range_succ, Finset.sum_range_zero, zero_add] at hμ + omega + have hA1 : 4 ≤ A.colLen 1 := by + have h := YoungDiagram.mem_iff_lt_colLen.mp + (YoungDiagram.mem_iff_lt_rowLen.mpr (show 1 < A.rowLen 3 by omega)) + omega + have hA2 : 2*M-1 ≤ colPrefix A 2 := by + rw [colPrefix_eq_sum] + simp only [Finset.sum_range_succ, Finset.sum_range_zero, zero_add] + omega + have hdual : Dominates A.transpose μ.transpose := by + intro k + change colPrefix μ k ≤ colPrefix A k + by_cases hk : k < 4 + · interval_cases k + · simp [colPrefix, rowPrefix] + · simpa only [colPrefix_eq_sum, Finset.sum_range_one] using hheight.trans hparts + · exact ((rowPrefix_mono μ.transpose (by omega)).trans hμ).trans (by omega) + · have hA3 := rowPrefix_mono A.transpose (show 2 ≤ 3 by omega) + change colPrefix A 2 ≤ colPrefix A 3 at hA3 + exact ((rowPrefix_mono μ.transpose (by omega)).trans hμ).trans (by omega) + · by_cases hB : A.rowLen 0 ≤ k + · have he : colPrefix A k = A.card := by + simpa only [colPrefix, transpose_card] using + rowPrefix_eq_card A.transpose (by simpa using hB) + rw [he, ← hc] + exact (rowPrefix_le_card μ.transpose k).trans_eq (transpose_card _) + · let B := A.rowLen 0 + have hBp : 0 < B := by dsimp only [B]; omega + have hupper : 4*colPrefix μ k ≤ k*(2*M-2) := + (rowPrefix_scaled_mono μ.transpose (by omega)).trans + (Nat.mul_le_mul_left k hμ) + have hlower := scaled_colPrefix_lower A le_rfl (show k ≤ B by dsimp [B]; omega) + have hratio : B*(2*M-2) ≤ 4*A.card := by + have hmul := Nat.mul_le_mul_right (2*M-2) hmax + dsimp only [B] + have hsub : 2*M-2+2 = 2*M := by omega + nlinarith + have hbound : (4*B)*colPrefix μ k ≤ (4*B)*colPrefix A k := calc + (4*B)*colPrefix μ k = B*(4*colPrefix μ k) := by ring + _ ≤ B*(k*(2*M-2)) := Nat.mul_le_mul_left B hupper + _ = k*(B*(2*M-2)) := by ring + _ ≤ k*(4*A.card) := Nat.mul_le_mul_left k hratio + _ = 4*(k*A.card) := by ring + _ ≤ 4*(B*colPrefix A k) := Nat.mul_le_mul_left 4 hlower + _ = (4*B)*colPrefix A k := by ring + exact (mul_le_mul_iff_right₀ (show 0 < 4*B by omega)).mp hbound + simpa only [YoungDiagram.transpose_transpose] using + dominates_transpose (by simpa only [transpose_card] using hc.symm) hdual + +theorem balance_invariant_functional (M : ℕ) (hM : 9 ≤ M) (μ A : YoungDiagram) + (hc : μ.card = A.card) (hn : (staircase M).card ≤ μ.card) + (hμ : colPrefix μ 4 ≤ 2*M-2) + (hparts : 2*M-5 ≤ A.colLen 0) (hmax : A.rowLen 0 ≤ M+1) + (hfour : 2 ≤ A.rowLen 3) : + ∃ (a : Fin μ.card → Fin (A.colLen 0)) (l : Module.Dual ℂ (Specht (shapeTableau μ))), + l ≠ 0 ∧ + (∀ j, (Finset.univ.filter (fun i => a i = j)).card = A.rowLen j) ∧ + (∀ g : Equiv.Perm (Fin μ.card), a ∘ g = a → + ∀ x, l (spechtRep (shapeTableau μ) g x) = l x) := by + exact young_invariant_functional A μ hc + (balance_dominance M hM μ A hc hn hμ hparts hmax hfour) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceFour.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceFour.lean index 89eb1d44f68a320677e4eb867fab611c700b6f25..6878637a1ad97fd23d7ffd075342ad8113345dc5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceFour.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceFour.lean @@ -1,121 +1,121 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceDominance -import OAI.RepresentationTheory.UniversalSquare.Specht.CandidateColumns - -namespace OAI - -/-! Balance Four. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns Saxl.FlagColumns - -lemma balanceParts_shape_bounds {M b δ τ ε m : ℕ} - (hM : 9 ≤ M) (hb : b ≤ M-2) (hδ : δ ≤ 1) (hτ : τ ≤ 1) (hε : ε ≤ 1) - (heq : M = 4+τ+ε+2*m) (hsmall : τ = 0 → 2*(b+1) ≤ M) : - let θ := (columnShape (balanceParts M b δ τ ε m)).transpose - 2*M-5 ≤ θ.colLen 0 ∧ θ.rowLen 0 ≤ M+1 ∧ 2 ≤ θ.rowLen 3 := by - let ps := balanceParts M b δ τ ε m - let θ := (columnShape ps).transpose - have hp := balanceParts_positive (M := M) (b := b) (δ := δ) (τ := τ) (ε := ε) (m := m) (by omega) - have hperm := columnShape_rows_permutation ps hp - have hlen : ps.length = θ.colLen 0 := by - simpa only [YoungDiagram.length_rowLens] using hperm.length_eq - have hlower : 2*M-5 ≤ θ.colLen 0 := hlen ▸ balanceParts_length hδ hτ hε heq - refine ⟨hlower,?_,?_⟩ - · have hzero : 0 < θ.rowLens.length := by rw [YoungDiagram.length_rowLens]; omega - have hh : θ.rowLen 0 ∈ ps := by - apply hperm.mem_iff.mpr - rw [← YoungDiagram.get_rowLens (h := hzero)] - exact List.getElem_mem hzero - exact balanceParts_bound (by omega) hb hδ hτ hε heq hsmall hh - · rw [YoungDiagram.rowLen_transpose] - change 2 ≤ (columnShape ps).colLen 3 - suffices h : 3 < (columnShape ps).rowLen 1 from - YoungDiagram.mem_iff_lt_colLen.mp (YoungDiagram.mem_iff_lt_rowLen.mpr h) - rw [columnShape_rowLen] - have hfour : List.countP (fun p => decide (1 < p)) - (balancedParts (2*(M-1+b)+1+3*δ) 4) = 4 := by - rw [List.countP_eq_length.mpr ?_,balancedParts_length] - intro p hp - simp only [decide_eq_true_eq] - have hh := (balancedParts_part hp).1 - omega - dsimp only [ps,balanceParts,bigParts] - simp only [List.countP_append,hfour] - omega - -theorem balance_kronecker_pos {n M b δ : ℕ} (hM : 9 ≤ M) - (hb : b ≤ M-2) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (μ : YoungDiagram) (s : Tableau n μ) - (hμ : colPrefix μ 4 ≤ 2*M-2) : 0 < kronecker t t s := by - let τ := if 2*(b+1) ≤ M then 0 else 1 - let ε := (M-4-τ)%2 - let m := (M-4-τ)/2 - have hτ : τ ≤ 1 := by dsimp [τ]; split_ifs <;> omega - have hε : ε ≤ 1 := by dsimp [ε]; omega - have heq : M = 4+τ+ε+2*m := by dsimp [ε,m]; omega - have hsmall : τ = 0 → 2*(b+1) ≤ M := by - intro ht - by_contra h - have hh : τ = 1 := ite_eq_right h - omega - have hshort : τ ≠ 0 → 1 ≤ b := by - intro ht - have hn : ¬ 2*(b+1) ≤ M := by - intro h - exact ht (ite_eq_left h) - omega - have hheight : (candidate M b δ).colLen 0 = M+b+δ := by - rw [candidate_colLen _ _ _ _ (by omega)] - simp [candidateLengths] - have hpack := balancePacking (by omega) hδ hτ hε heq hshort - rw [← hheight] at hpack - obtain ⟨A,label,marks,hordered,⟨P⟩⟩ := hpack - let rs := balanceColumns M b δ τ ε m - let ps := balanceParts M b δ τ ε m - have hperm := balanceColumns_perm (b := b) (δ := δ) (by omega) hτ hε heq - obtain ⟨e,hr,hc⟩ := place_columns (candidate M b δ) hperm - have hdegree : rs.sum = n := by - simpa only [Fintype.card_fin] using - Fintype.card_congr (((enumerate rs).trans e).trans t.symm) - subst n - let a := (enumerate rs).trans e - have hcand : (candidate M b δ).card = rs.sum := by - simpa only [Fintype.card_fin,Fintype.card_coe] using (Fintype.card_congr a).symm - have htarget : μ.card = rs.sum := by - simpa only [Fintype.card_fin,Fintype.card_coe] using (Fintype.card_congr s).symm - have hparts : μ.card = (columnShape ps).transpose.card := by - rw [htarget,transpose_card,columnShape_card] - exact P.total.symm - have hn : (staircase M).card ≤ μ.card := by - rw [htarget,← hcand,candidate_card _ _ _ (by omega)] - omega - obtain ⟨hcount,hmax,hfour⟩ := balanceParts_shape_bounds hM hb hδ hτ hε heq hsmall - have hdom := balance_dominance M hM μ (columnShape ps).transpose hparts hn hμ hcount hmax hfour - have hpos := P.kronecker_pos a s (standard_placed_self e hr hc) - (balanceParts_positive (by omega)) hordered hdom - unfold kronecker spechtRep Specht at hpos ⊢ - rw [spechtSub_tableau_independent a t] at hpos - exact hpos - -theorem balance_kronecker_pos_or_transpose {n M b δ : ℕ} (hM : 9 ≤ M) - (hb : b ≤ M-2) (hδ : δ ≤ 1) (hn : (candidate M b δ).card = n) - (μ : YoungDiagram) (hμ : μ.card = n) - (hsmall : colPrefix μ 4 ≤ 2*M-2 ∨ colPrefix μ.transpose 4 ≤ 2*M-2) : - 0 < kronecker (canonicalTableau (candidate M b δ) hn) - (canonicalTableau (candidate M b δ) hn) (canonicalTableau μ hμ) := by - rcases hsmall with h | h - · exact balance_kronecker_pos hM hb hδ _ μ _ h - · have hpos := balance_kronecker_pos hM hb hδ (canonicalTableau (candidate M b δ) hn) - μ.transpose (canonicalTableau μ.transpose ((transpose_card μ).trans hμ)) h - exact (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr hpos - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceDominance +import OAI.RepresentationTheory.UniversalSquare.Specht.CandidateColumns + +namespace OAI + +/-! Balance Four. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns Saxl.FlagColumns + +lemma balanceParts_shape_bounds {M b δ τ ε m : ℕ} + (hM : 9 ≤ M) (hb : b ≤ M-2) (hδ : δ ≤ 1) (hτ : τ ≤ 1) (hε : ε ≤ 1) + (heq : M = 4+τ+ε+2*m) (hsmall : τ = 0 → 2*(b+1) ≤ M) : + let θ := (columnShape (balanceParts M b δ τ ε m)).transpose + 2*M-5 ≤ θ.colLen 0 ∧ θ.rowLen 0 ≤ M+1 ∧ 2 ≤ θ.rowLen 3 := by + let ps := balanceParts M b δ τ ε m + let θ := (columnShape ps).transpose + have hp := balanceParts_positive (M := M) (b := b) (δ := δ) (τ := τ) (ε := ε) (m := m) (by omega) + have hperm := columnShape_rows_permutation ps hp + have hlen : ps.length = θ.colLen 0 := by + simpa only [YoungDiagram.length_rowLens] using hperm.length_eq + have hlower : 2*M-5 ≤ θ.colLen 0 := hlen ▸ balanceParts_length hδ hτ hε heq + refine ⟨hlower,?_,?_⟩ + · have hzero : 0 < θ.rowLens.length := by rw [YoungDiagram.length_rowLens]; omega + have hh : θ.rowLen 0 ∈ ps := by + apply hperm.mem_iff.mpr + rw [← YoungDiagram.get_rowLens (h := hzero)] + exact List.getElem_mem hzero + exact balanceParts_bound (by omega) hb hδ hτ hε heq hsmall hh + · rw [YoungDiagram.rowLen_transpose] + change 2 ≤ (columnShape ps).colLen 3 + suffices h : 3 < (columnShape ps).rowLen 1 from + YoungDiagram.mem_iff_lt_colLen.mp (YoungDiagram.mem_iff_lt_rowLen.mpr h) + rw [columnShape_rowLen] + have hfour : List.countP (fun p => decide (1 < p)) + (balancedParts (2*(M-1+b)+1+3*δ) 4) = 4 := by + rw [List.countP_eq_length.mpr ?_,balancedParts_length] + intro p hp + simp only [decide_eq_true_eq] + have hh := (balancedParts_part hp).1 + omega + dsimp only [ps,balanceParts,bigParts] + simp only [List.countP_append,hfour] + omega + +theorem balance_kronecker_pos {n M b δ : ℕ} (hM : 9 ≤ M) + (hb : b ≤ M-2) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (μ : YoungDiagram) (s : Tableau n μ) + (hμ : colPrefix μ 4 ≤ 2*M-2) : 0 < kronecker t t s := by + let τ := if 2*(b+1) ≤ M then 0 else 1 + let ε := (M-4-τ)%2 + let m := (M-4-τ)/2 + have hτ : τ ≤ 1 := by dsimp [τ]; split_ifs <;> omega + have hε : ε ≤ 1 := by dsimp [ε]; omega + have heq : M = 4+τ+ε+2*m := by dsimp [ε,m]; omega + have hsmall : τ = 0 → 2*(b+1) ≤ M := by + intro ht + by_contra h + have hh : τ = 1 := ite_eq_right h + omega + have hshort : τ ≠ 0 → 1 ≤ b := by + intro ht + have hn : ¬ 2*(b+1) ≤ M := by + intro h + exact ht (ite_eq_left h) + omega + have hheight : (candidate M b δ).colLen 0 = M+b+δ := by + rw [candidate_colLen _ _ _ _ (by omega)] + simp [candidateLengths] + have hpack := balancePacking (by omega) hδ hτ hε heq hshort + rw [← hheight] at hpack + obtain ⟨A,label,marks,hordered,⟨P⟩⟩ := hpack + let rs := balanceColumns M b δ τ ε m + let ps := balanceParts M b δ τ ε m + have hperm := balanceColumns_perm (b := b) (δ := δ) (by omega) hτ hε heq + obtain ⟨e,hr,hc⟩ := place_columns (candidate M b δ) hperm + have hdegree : rs.sum = n := by + simpa only [Fintype.card_fin] using + Fintype.card_congr (((enumerate rs).trans e).trans t.symm) + subst n + let a := (enumerate rs).trans e + have hcand : (candidate M b δ).card = rs.sum := by + simpa only [Fintype.card_fin,Fintype.card_coe] using (Fintype.card_congr a).symm + have htarget : μ.card = rs.sum := by + simpa only [Fintype.card_fin,Fintype.card_coe] using (Fintype.card_congr s).symm + have hparts : μ.card = (columnShape ps).transpose.card := by + rw [htarget,transpose_card,columnShape_card] + exact P.total.symm + have hn : (staircase M).card ≤ μ.card := by + rw [htarget,← hcand,candidate_card _ _ _ (by omega)] + omega + obtain ⟨hcount,hmax,hfour⟩ := balanceParts_shape_bounds hM hb hδ hτ hε heq hsmall + have hdom := balance_dominance M hM μ (columnShape ps).transpose hparts hn hμ hcount hmax hfour + have hpos := P.kronecker_pos a s (standard_placed_self e hr hc) + (balanceParts_positive (by omega)) hordered hdom + unfold kronecker spechtRep Specht at hpos ⊢ + rw [spechtSub_tableau_independent a t] at hpos + exact hpos + +theorem balance_kronecker_pos_or_transpose {n M b δ : ℕ} (hM : 9 ≤ M) + (hb : b ≤ M-2) (hδ : δ ≤ 1) (hn : (candidate M b δ).card = n) + (μ : YoungDiagram) (hμ : μ.card = n) + (hsmall : colPrefix μ 4 ≤ 2*M-2 ∨ colPrefix μ.transpose 4 ≤ 2*M-2) : + 0 < kronecker (canonicalTableau (candidate M b δ) hn) + (canonicalTableau (candidate M b δ) hn) (canonicalTableau μ hμ) := by + rcases hsmall with h | h + · exact balance_kronecker_pos hM hb hδ _ μ _ h + · have hpos := balance_kronecker_pos hM hb hδ (canonicalTableau (candidate M b δ) hn) + μ.transpose (canonicalTableau μ.transpose ((transpose_card μ).trans hμ)) h + exact (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr hpos + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceGluing.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceGluing.lean index 6b3ec46fcb176572b0655ec3c77c1d57f4245343..ac66c6bc8644d4c9107e8256954d49a909c493cf 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceGluing.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceGluing.lean @@ -1,129 +1,129 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceColumns -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceInduction -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceProduct - -namespace OAI - -/-! Balance Gluing. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl.Balance - -structure Piece {n d : ℕ} {G Y : Type*} [Group G] [AddCommGroup Y] [Module ℂ Y] - (v : WordSpace n d) (c : Fin n → ℕ) - (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) (σ : ℕ → ℤ) - (φ : G →* fiberGroup c) (τ : Representation ℂ G Y) where - surj : Function.Surjective φ - raw : Y →ₗ[ℂ] WordSpace n (d*d) - raw_mem : ∀ y, raw y ∈ (cyclicSquareMap v).range - raw_sums : ∀ y, FixedComponentSums c (fun a => (output a : ℤ)) σ (raw y) - projected : Representation.IntertwiningMap τ - ((wordRep n (d*d)).comp ((fiberGroup c).subtype.comp φ)) - injective : Function.Injective projected - projection_eq : ∀ y, coordinateProjection (componentWords c A label) (raw y) = projected y - -def Piece.join {n a b d : ℕ} {G H X Y : Type*} [Group G] [Group H] - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - {v : WordSpace a d} {u : WordSpace b d} - {c : Fin a → ℕ} {c' : Fin b → ℕ} - {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {σ σ' : ℕ → ℤ} - {φ : G →* fiberGroup c} {ψ : H →* fiberGroup c'} - {ρ : Representation ℂ G X} {τ : Representation ℂ H Y} - (P : Piece v c A label σ φ ρ) (Q : Piece u c' A label σ' ψ τ) - (e : Fin n ≃ Fin a ⊕ Fin b) (hd : ∀ i j, c i ≠ c' j) : - letI : AddCommGroup (X ⊗[ℂ] Y) := Module.addCommMonoidToAddCommGroup ℂ - Piece (positionProduct e v u) (joinedLabels e c c') A label (σ+σ') - ((joinedFiberHom e c c').comp (φ.prodMap ψ)) (outer ρ τ) := by - letI : AddCommGroup (X ⊗[ℂ] Y) := Module.addCommMonoidToAddCommGroup ℂ - let L := (positionTensor e).toLinearMap.comp (TensorProduct.map P.raw Q.raw) - let T := outerWordMap e ((fiberGroup c).subtype.comp φ) - ((fiberGroup c').subtype.comp ψ) P.projected Q.projected - refine { - surj := (joinedFiberHom_surjective e c c' hd).comp (P.surj.prodMap Q.surj) - raw := L - raw_mem := ?_ - raw_sums := ?_ - projected := T - injective := outerWordMap_injective e _ _ P.projected Q.projected P.injective Q.injective - projection_eq := ?_ } - · intro z - change L z ∈ (cyclicSquareMap (positionProduct e v u)).range.toSubmodule - induction z using TensorProduct.inductionOn with - | add x y hx hy => simpa only [map_add] using Submodule.add_mem _ hx hy - | tmul x y => - change positionTensor e (P.raw x ⊗ₜ[ℂ] Q.raw y) ∈ _ - rw [positionTensor_tmul] - exact product_mem_square e v u _ _ (P.raw_mem x) (Q.raw_mem y) - · intro z - change L z ∈ fixedSumSpace (joinedLabels e c c') (fun a => (output a : ℤ)) (σ+σ') - induction z using TensorProduct.inductionOn with - | add x y hx hy => simpa only [map_add] using Submodule.add_mem _ hx hy - | tmul x y => - change positionTensor e (P.raw x ⊗ₜ[ℂ] Q.raw y) ∈ _ - rw [positionTensor_tmul] - exact product_fixed_sums e c c' _ σ σ' _ _ (P.raw_sums x) (Q.raw_sums y) - · intro z - induction z using TensorProduct.inductionOn with - | add x y hx hy => - change coordinateProjection _ (L (x+y)) = T.toLinearMap (x+y) - rw [map_add,map_add,hx,hy,map_add] - rfl - | tmul x y => - change coordinateProjection (componentWords (joinedLabels e c c') A label) - (positionTensor e (P.raw x ⊗ₜ[ℂ] Q.raw y)) = - positionTensor e (P.projected x ⊗ₜ[ℂ] Q.projected y) - rw [positionTensor_tmul,positionTensor_tmul,component_projection_product, - P.projection_eq,Q.projection_eq] - -theorem Piece.support {n d : ℕ} {G X Y : Type*} - [Group G] [Finite G] [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - {v : WordSpace n d} {c : Fin n → ℕ} - {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {σ : ℕ → ℤ} - {φ : G →* fiberGroup c} {τ : Representation ℂ G Y} - (P : Piece v c A label σ φ τ) - (ho : ∀ a b, A a → A b → label a < label b → output a < output b) - (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (F : Representation.IntertwiningMap ρ (Representation.coind ((fiberGroup c).subtype.comp φ) τ)) - (hF : F ≠ 0) : - ∃ T : Representation.IntertwiningMap ρ (cyclicSquareMap v).range.toRepresentation, T ≠ 0 := by - exact balance_support_of_surjective ρ (cyclicSquareMap v).range c A label - (fun a => (output a : ℤ)) σ (by intro a b ha hb hl; exact_mod_cast ho a b ha hb hl) - φ P.surj τ P.raw P.raw_mem P.raw_sums P.projected P.injective P.projection_eq - (coindEval ((fiberGroup c).subtype.comp φ) F) - (coindEval_ne_zero ((fiberGroup c).subtype.comp φ) F hF) - -lemma cyclicSquareMap_polytabloid {n : ℕ} {lam : YoungDiagram} (a : Tableau n lam) : - cyclicSquareMap (polytabloid a) = spechtTensorMap a a := by - unfold spechtTensorMap - rfl - -theorem Piece.kronecker_pos {n : ℕ} {G Y : Type*} - [Group G] [Finite G] [AddCommGroup Y] [Module ℂ Y] - {lam μ : YoungDiagram} (a : Tableau n lam) (t : Tableau n μ) - {c : Fin n → ℕ} {A : Fin (lam.colLen 0 * lam.colLen 0) → Prop} - {label : Fin (lam.colLen 0 * lam.colLen 0) → ℕ} {σ : ℕ → ℤ} - {φ : G →* fiberGroup c} {τ : Representation ℂ G Y} - (P : Piece (polytabloid a) c A label σ φ τ) - (ho : ∀ a b, A a → A b → label a < label b → output a < output b) - (θ : YoungDiagram) (hc : μ.card = θ.card) (hd : Dominates μ θ) - (w : Fin n → Fin (θ.colLen 0)) (e : Equiv.Perm (Fin (θ.colLen 0))) - (hw : ∀ j, (Finset.univ.filter (fun i => w i = e j)).card = θ.rowLen j) - (hpack : SupportLE (cyclic (wordRep n (θ.colLen 0)) (Pi.single w 1)).toRepresentation - (Representation.coind ((fiberGroup c).subtype.comp φ) τ)) : - 0 < kronecker a a t := by - exact kronecker_pos_of_packing a t c A label σ ho φ P.surj τ P.raw (by - intro y - obtain ⟨z,hz⟩ := P.raw_mem y - exact ⟨z, by rw [←cyclicSquareMap_polytabloid]; exact hz⟩) - P.raw_sums P.projected P.injective P.projection_eq θ hc hd w e hw hpack - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceColumns +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceInduction +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceProduct + +namespace OAI + +/-! Balance Gluing. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl.Balance + +structure Piece {n d : ℕ} {G Y : Type*} [Group G] [AddCommGroup Y] [Module ℂ Y] + (v : WordSpace n d) (c : Fin n → ℕ) + (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) (σ : ℕ → ℤ) + (φ : G →* fiberGroup c) (τ : Representation ℂ G Y) where + surj : Function.Surjective φ + raw : Y →ₗ[ℂ] WordSpace n (d*d) + raw_mem : ∀ y, raw y ∈ (cyclicSquareMap v).range + raw_sums : ∀ y, FixedComponentSums c (fun a => (output a : ℤ)) σ (raw y) + projected : Representation.IntertwiningMap τ + ((wordRep n (d*d)).comp ((fiberGroup c).subtype.comp φ)) + injective : Function.Injective projected + projection_eq : ∀ y, coordinateProjection (componentWords c A label) (raw y) = projected y + +def Piece.join {n a b d : ℕ} {G H X Y : Type*} [Group G] [Group H] + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + {v : WordSpace a d} {u : WordSpace b d} + {c : Fin a → ℕ} {c' : Fin b → ℕ} + {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {σ σ' : ℕ → ℤ} + {φ : G →* fiberGroup c} {ψ : H →* fiberGroup c'} + {ρ : Representation ℂ G X} {τ : Representation ℂ H Y} + (P : Piece v c A label σ φ ρ) (Q : Piece u c' A label σ' ψ τ) + (e : Fin n ≃ Fin a ⊕ Fin b) (hd : ∀ i j, c i ≠ c' j) : + letI : AddCommGroup (X ⊗[ℂ] Y) := Module.addCommMonoidToAddCommGroup ℂ + Piece (positionProduct e v u) (joinedLabels e c c') A label (σ+σ') + ((joinedFiberHom e c c').comp (φ.prodMap ψ)) (outer ρ τ) := by + letI : AddCommGroup (X ⊗[ℂ] Y) := Module.addCommMonoidToAddCommGroup ℂ + let L := (positionTensor e).toLinearMap.comp (TensorProduct.map P.raw Q.raw) + let T := outerWordMap e ((fiberGroup c).subtype.comp φ) + ((fiberGroup c').subtype.comp ψ) P.projected Q.projected + refine { + surj := (joinedFiberHom_surjective e c c' hd).comp (P.surj.prodMap Q.surj) + raw := L + raw_mem := ?_ + raw_sums := ?_ + projected := T + injective := outerWordMap_injective e _ _ P.projected Q.projected P.injective Q.injective + projection_eq := ?_ } + · intro z + change L z ∈ (cyclicSquareMap (positionProduct e v u)).range.toSubmodule + induction z using TensorProduct.inductionOn with + | add x y hx hy => simpa only [map_add] using Submodule.add_mem _ hx hy + | tmul x y => + change positionTensor e (P.raw x ⊗ₜ[ℂ] Q.raw y) ∈ _ + rw [positionTensor_tmul] + exact product_mem_square e v u _ _ (P.raw_mem x) (Q.raw_mem y) + · intro z + change L z ∈ fixedSumSpace (joinedLabels e c c') (fun a => (output a : ℤ)) (σ+σ') + induction z using TensorProduct.inductionOn with + | add x y hx hy => simpa only [map_add] using Submodule.add_mem _ hx hy + | tmul x y => + change positionTensor e (P.raw x ⊗ₜ[ℂ] Q.raw y) ∈ _ + rw [positionTensor_tmul] + exact product_fixed_sums e c c' _ σ σ' _ _ (P.raw_sums x) (Q.raw_sums y) + · intro z + induction z using TensorProduct.inductionOn with + | add x y hx hy => + change coordinateProjection _ (L (x+y)) = T.toLinearMap (x+y) + rw [map_add,map_add,hx,hy,map_add] + rfl + | tmul x y => + change coordinateProjection (componentWords (joinedLabels e c c') A label) + (positionTensor e (P.raw x ⊗ₜ[ℂ] Q.raw y)) = + positionTensor e (P.projected x ⊗ₜ[ℂ] Q.projected y) + rw [positionTensor_tmul,positionTensor_tmul,component_projection_product, + P.projection_eq,Q.projection_eq] + +theorem Piece.support {n d : ℕ} {G X Y : Type*} + [Group G] [Finite G] [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + {v : WordSpace n d} {c : Fin n → ℕ} + {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {σ : ℕ → ℤ} + {φ : G →* fiberGroup c} {τ : Representation ℂ G Y} + (P : Piece v c A label σ φ τ) + (ho : ∀ a b, A a → A b → label a < label b → output a < output b) + (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (F : Representation.IntertwiningMap ρ (Representation.coind ((fiberGroup c).subtype.comp φ) τ)) + (hF : F ≠ 0) : + ∃ T : Representation.IntertwiningMap ρ (cyclicSquareMap v).range.toRepresentation, T ≠ 0 := by + exact balance_support_of_surjective ρ (cyclicSquareMap v).range c A label + (fun a => (output a : ℤ)) σ (by intro a b ha hb hl; exact_mod_cast ho a b ha hb hl) + φ P.surj τ P.raw P.raw_mem P.raw_sums P.projected P.injective P.projection_eq + (coindEval ((fiberGroup c).subtype.comp φ) F) + (coindEval_ne_zero ((fiberGroup c).subtype.comp φ) F hF) + +lemma cyclicSquareMap_polytabloid {n : ℕ} {lam : YoungDiagram} (a : Tableau n lam) : + cyclicSquareMap (polytabloid a) = spechtTensorMap a a := by + unfold spechtTensorMap + rfl + +theorem Piece.kronecker_pos {n : ℕ} {G Y : Type*} + [Group G] [Finite G] [AddCommGroup Y] [Module ℂ Y] + {lam μ : YoungDiagram} (a : Tableau n lam) (t : Tableau n μ) + {c : Fin n → ℕ} {A : Fin (lam.colLen 0 * lam.colLen 0) → Prop} + {label : Fin (lam.colLen 0 * lam.colLen 0) → ℕ} {σ : ℕ → ℤ} + {φ : G →* fiberGroup c} {τ : Representation ℂ G Y} + (P : Piece (polytabloid a) c A label σ φ τ) + (ho : ∀ a b, A a → A b → label a < label b → output a < output b) + (θ : YoungDiagram) (hc : μ.card = θ.card) (hd : Dominates μ θ) + (w : Fin n → Fin (θ.colLen 0)) (e : Equiv.Perm (Fin (θ.colLen 0))) + (hw : ∀ j, (Finset.univ.filter (fun i => w i = e j)).card = θ.rowLen j) + (hpack : SupportLE (cyclic (wordRep n (θ.colLen 0)) (Pi.single w 1)).toRepresentation + (Representation.coind ((fiberGroup c).subtype.comp φ) τ)) : + 0 < kronecker a a t := by + exact kronecker_pos_of_packing a t c A label σ ho φ P.surj τ P.raw (by + intro y + obtain ⟨z,hz⟩ := P.raw_mem y + exact ⟨z, by rw [←cyclicSquareMap_polytabloid]; exact hz⟩) + P.raw_sums P.projected P.injective P.projection_eq θ hc hd w e hw hpack + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceInduction.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceInduction.lean index 0c88be302cd87d4a8bf1c429d8affaf535600fb4..a68deb8353e65ddcf870b19029e076965535c35b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceInduction.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceInduction.lean @@ -1,97 +1,97 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceProjection -import OAI.RepresentationTheory.UniversalSquare.Support.Neighboring -import OAI.RepresentationTheory.UniversalSquare.Balance.PackingSupport - -namespace OAI - -/-! Balance Induction. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl.Balance - -theorem balance_support_of_surjective {n d : ℕ} {G X Y : Type*} - [Group G] [Finite G] [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (W : Subrepresentation (wordRep n d)) - (c : Fin n → ℕ) (A : Fin d → Prop) (label : Fin d → ℕ) - (z : Fin d → ℤ) (σ : ℕ → ℤ) - (ho : ∀ a b, A a → A b → label a < label b → z a < z b) - (φ : G →* fiberGroup c) (hφ : Function.Surjective φ) - (τ : Representation ℂ G Y) - (L : Y →ₗ[ℂ] WordSpace n d) - (hm : ∀ y, L y ∈ W) (hs : ∀ y, FixedComponentSums c z σ (L y)) - (T : Representation.IntertwiningMap τ - ((wordRep n d).comp ((fiberGroup c).subtype.comp φ))) - (hT : Function.Injective T) - (he : ∀ y, coordinateProjection (componentWords c A label) (L y) = T y) - (f : Representation.IntertwiningMap - (ρ.comp ((fiberGroup c).subtype.comp φ)) τ) (hf : f ≠ 0) : - ∃ F : Representation.IntertwiningMap ρ W.toRepresentation, F ≠ 0 := by - let K := L.comp f.toLinearMap - have hK : (coordinateProjection (componentWords c A label)).comp K ≠ 0 := by - intro h0 - apply hf - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - apply hT - change T (f x) = T 0 - rw [map_zero, ← he] - exact LinearMap.congr_fun h0 x - apply balance_support_transfer ρ W c A label z σ ho K - (fun x => hm (f x)) (fun x => hs (f x)) hK - intro g hg x - obtain ⟨a,ha⟩ := hφ ⟨g,hg⟩ - have hval : (φ a).val = g := congrArg Subtype.val ha - change coordinateProjection (componentWords c A label) (L (f (ρ g x))) = - wordRep n d g (coordinateProjection (componentWords c A label) (L (f x))) - rw [he,he,← hval] - exact LinearMap.congr_fun ((T.comp f).isIntertwining' a) x - -theorem kronecker_pos_of_packing {n : ℕ} {G Y : Type*} - [Group G] [Finite G] [AddCommGroup Y] [Module ℂ Y] - {lam μ : YoungDiagram} (a : Tableau n lam) (t : Tableau n μ) - (c : Fin n → ℕ) - (A : Fin (lam.colLen 0 * lam.colLen 0) → Prop) - (label : Fin (lam.colLen 0 * lam.colLen 0) → ℕ) (σ : ℕ → ℤ) - (ho : ∀ a b, A a → A b → label a < label b → output a < output b) - (φ : G →* fiberGroup c) (hφ : Function.Surjective φ) - (τ : Representation ℂ G Y) - (L : Y →ₗ[ℂ] WordSpace n (lam.colLen 0 * lam.colLen 0)) - (hm : ∀ y, L y ∈ (spechtTensorMap a a).range) - (hs : ∀ y, FixedComponentSums c (fun a => (output a : ℤ)) σ (L y)) - (T : Representation.IntertwiningMap τ - ((wordRep n (lam.colLen 0 * lam.colLen 0)).comp ((fiberGroup c).subtype.comp φ))) - (hT : Function.Injective T) - (he : ∀ y, coordinateProjection (componentWords c A label) (L y) = T y) - (θ : YoungDiagram) (hc : μ.card = θ.card) (hd : Dominates μ θ) - (w : Fin n → Fin (θ.colLen 0)) (e : Equiv.Perm (Fin (θ.colLen 0))) - (hw : ∀ j, (Finset.univ.filter (fun i => w i = e j)).card = θ.rowLen j) - (hpack : SupportLE (cyclic (wordRep n (θ.colLen 0)) (Pi.single w 1)).toRepresentation - (Representation.coind ((fiberGroup c).subtype.comp φ) τ)) : - 0 < kronecker a a t := by - obtain ⟨F,hF⟩ := young_cyclic_support θ μ t hc hd w e hw - obtain ⟨Q,hQ⟩ := hpack.detects_map F hF - obtain ⟨R,hR⟩ := balance_support_of_surjective (spechtRep t) - (spechtTensorMap a a).range c A label (fun a => (output a : ℤ)) σ - (fun a b ha hb hab => by exact_mod_cast ho a b ha hb hab) - φ hφ τ L hm hs T hT he - (coindEval ((fiberGroup c).subtype.comp φ) Q) - (coindEval_ne_zero ((fiberGroup c).subtype.comp φ) Q hQ) - let : AddCommGroup (Specht a ⊗[ℂ] Specht a) := Module.addCommMonoidToAddCommGroup ℂ - obtain ⟨i,hi⟩ := subrepresentation_embeds_of_le_range (spechtTensorMap a a) - (spechtTensorMap a a).range le_rfl - exact (kronecker_pos_iff a a t).mpr - ⟨i.comp R,intertwining_comp_ne_zero i hi R hR⟩ - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceProjection +import OAI.RepresentationTheory.UniversalSquare.Support.Neighboring +import OAI.RepresentationTheory.UniversalSquare.Balance.PackingSupport + +namespace OAI + +/-! Balance Induction. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl.Balance + +theorem balance_support_of_surjective {n d : ℕ} {G X Y : Type*} + [Group G] [Finite G] [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (W : Subrepresentation (wordRep n d)) + (c : Fin n → ℕ) (A : Fin d → Prop) (label : Fin d → ℕ) + (z : Fin d → ℤ) (σ : ℕ → ℤ) + (ho : ∀ a b, A a → A b → label a < label b → z a < z b) + (φ : G →* fiberGroup c) (hφ : Function.Surjective φ) + (τ : Representation ℂ G Y) + (L : Y →ₗ[ℂ] WordSpace n d) + (hm : ∀ y, L y ∈ W) (hs : ∀ y, FixedComponentSums c z σ (L y)) + (T : Representation.IntertwiningMap τ + ((wordRep n d).comp ((fiberGroup c).subtype.comp φ))) + (hT : Function.Injective T) + (he : ∀ y, coordinateProjection (componentWords c A label) (L y) = T y) + (f : Representation.IntertwiningMap + (ρ.comp ((fiberGroup c).subtype.comp φ)) τ) (hf : f ≠ 0) : + ∃ F : Representation.IntertwiningMap ρ W.toRepresentation, F ≠ 0 := by + let K := L.comp f.toLinearMap + have hK : (coordinateProjection (componentWords c A label)).comp K ≠ 0 := by + intro h0 + apply hf + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + apply hT + change T (f x) = T 0 + rw [map_zero, ← he] + exact LinearMap.congr_fun h0 x + apply balance_support_transfer ρ W c A label z σ ho K + (fun x => hm (f x)) (fun x => hs (f x)) hK + intro g hg x + obtain ⟨a,ha⟩ := hφ ⟨g,hg⟩ + have hval : (φ a).val = g := congrArg Subtype.val ha + change coordinateProjection (componentWords c A label) (L (f (ρ g x))) = + wordRep n d g (coordinateProjection (componentWords c A label) (L (f x))) + rw [he,he,← hval] + exact LinearMap.congr_fun ((T.comp f).isIntertwining' a) x + +theorem kronecker_pos_of_packing {n : ℕ} {G Y : Type*} + [Group G] [Finite G] [AddCommGroup Y] [Module ℂ Y] + {lam μ : YoungDiagram} (a : Tableau n lam) (t : Tableau n μ) + (c : Fin n → ℕ) + (A : Fin (lam.colLen 0 * lam.colLen 0) → Prop) + (label : Fin (lam.colLen 0 * lam.colLen 0) → ℕ) (σ : ℕ → ℤ) + (ho : ∀ a b, A a → A b → label a < label b → output a < output b) + (φ : G →* fiberGroup c) (hφ : Function.Surjective φ) + (τ : Representation ℂ G Y) + (L : Y →ₗ[ℂ] WordSpace n (lam.colLen 0 * lam.colLen 0)) + (hm : ∀ y, L y ∈ (spechtTensorMap a a).range) + (hs : ∀ y, FixedComponentSums c (fun a => (output a : ℤ)) σ (L y)) + (T : Representation.IntertwiningMap τ + ((wordRep n (lam.colLen 0 * lam.colLen 0)).comp ((fiberGroup c).subtype.comp φ))) + (hT : Function.Injective T) + (he : ∀ y, coordinateProjection (componentWords c A label) (L y) = T y) + (θ : YoungDiagram) (hc : μ.card = θ.card) (hd : Dominates μ θ) + (w : Fin n → Fin (θ.colLen 0)) (e : Equiv.Perm (Fin (θ.colLen 0))) + (hw : ∀ j, (Finset.univ.filter (fun i => w i = e j)).card = θ.rowLen j) + (hpack : SupportLE (cyclic (wordRep n (θ.colLen 0)) (Pi.single w 1)).toRepresentation + (Representation.coind ((fiberGroup c).subtype.comp φ) τ)) : + 0 < kronecker a a t := by + obtain ⟨F,hF⟩ := young_cyclic_support θ μ t hc hd w e hw + obtain ⟨Q,hQ⟩ := hpack.detects_map F hF + obtain ⟨R,hR⟩ := balance_support_of_surjective (spechtRep t) + (spechtTensorMap a a).range c A label (fun a => (output a : ℤ)) σ + (fun a b ha hb hab => by exact_mod_cast ho a b ha hb hab) + φ hφ τ L hm hs T hT he + (coindEval ((fiberGroup c).subtype.comp φ) Q) + (coindEval_ne_zero ((fiberGroup c).subtype.comp φ) Q hQ) + let : AddCommGroup (Specht a ⊗[ℂ] Specht a) := Module.addCommMonoidToAddCommGroup ℂ + obtain ⟨i,hi⟩ := subrepresentation_embeds_of_le_range (spechtTensorMap a a) + (spechtTensorMap a a).range le_rfl + exact (kronecker_pos_iff a a t).mpr + ⟨i.comp R,intertwining_comp_ne_zero i hi R hR⟩ + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceLeaves.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceLeaves.lean index 34c45834be340e94ed0d306f4b4d202b2e39f48f..f592aaa2f76ac4fd2eee79862dbec83e6aba8f39 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceLeaves.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceLeaves.lean @@ -1,125 +1,125 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceGluing - -namespace OAI - -/-! Balance Leaves. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl.Balance - -def singleFiberHom (n k : ℕ) : Equiv.Perm (Fin n) →* fiberGroup (fun _ : Fin n => k) where - toFun g := ⟨g,fun _ => rfl⟩ - map_one' := rfl - map_mul' _ _ := rfl - -lemma singleFiberHom_surjective (n k : ℕ) : Function.Surjective (singleFiberHom n k) := - fun g => ⟨g.val,Subtype.ext rfl⟩ - -lemma specht_fixed_single_sum {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (k : ℕ) (x : Specht t) : - x.val ∈ fixedSumSpace (fun _ : Fin n => k) (fun a : Fin (μ.colLen 0) => a.val) - (columnRowSums t (fun _ => k)) := by - rcases x with ⟨x,hx⟩ - change x ∈ Submodule.span ℂ (Set.range fun g : Equiv.Perm (Fin n) => - wordRep n (μ.colLen 0) g (polytabloid t)) at hx - induction hx using Submodule.span_induction with - | mem y hy => - obtain ⟨g,rfl⟩ := hy - exact fixedSumSpace_invariant _ _ _ g (fun _ => rfl) _ - (polytabloid_fixed_column_sums t _ (fun _ _ _ => rfl)) - | zero => exact Submodule.zero_mem _ - | add x y hx hy ihx ihy => exact Submodule.add_mem _ ihx ihy - | smul a x hx ih => exact Submodule.smul_mem _ a ih - -lemma spechtTensor_fixed_single_sum {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (k : ℕ) (x : Specht t ⊗[ℂ] Specht t) : - FixedComponentSums (fun _ : Fin n => k) (fun a => (output a : ℤ)) - (columnOutputSums t (fun _ => k)) (spechtTensorMap t t x) := by - classical - change spechtTensorMap t t x ∈ fixedSumSpace (fun _ : Fin n => k) - (fun a => (output a : ℤ)) (columnOutputSums t (fun _ => k)) - induction x using TensorProduct.inductionOn with - | add x y hx hy => simpa only [map_add] using Submodule.add_mem _ hx hy - | tmul x y => - intro w hw i - rw [spechtTensorMap] at hw - change wordTensor _ _ _ (x.val ⊗ₜ[ℂ] y.val) w ≠ 0 at hw - rw [wordTensor_tmul] at hw - obtain ⟨hx,hy⟩ := mul_ne_zero_iff.mp hw - have hs₁ := specht_fixed_single_sum t k x (splitLeft w) hx i - have hs₂ := specht_fixed_single_sum t k y (splitRight w) hy i - change (∑ p ∈ Finset.univ.filter (fun _ : Fin n => k = i), (output (w p) : ℤ)) = _ - simp only [output, Nat.cast_add, Nat.cast_one, Finset.sum_add_distrib, - Finset.sum_const, nsmul_eq_mul, mul_one] - change (∑ p ∈ Finset.univ.filter (fun _ : Fin n => k = i), ((splitLeft w p).val : ℤ)) + - (∑ p ∈ Finset.univ.filter (fun _ : Fin n => k = i), ((splitRight w p).val : ℤ)) + _ = _ - rw [hs₁,hs₂] - dsimp only [columnOutputSums] - ring - -lemma componentWords_single {n d : ℕ} (k : ℕ) (I : Set ℕ) - (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (h : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) (w : Fin n → Fin (d*d)) : - componentWords (fun _ : Fin n => k) A label w ↔ inOutputs I w := by - constructor - · rintro ⟨hA,hl⟩ i - exact (h _).mp ⟨hA i,hl i⟩ - · intro hw - exact ⟨fun i => ((h _).mpr (hw i)).1,fun i => ((h _).mpr (hw i)).2⟩ - -def projectedPiece {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (k : ℕ) (I : Set ℕ) - (A : Fin (μ.colLen 0 * μ.colLen 0) → Prop) - (label : Fin (μ.colLen 0 * μ.colLen 0) → ℕ) - (h : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) : - Piece (polytabloid t) (fun _ : Fin n => k) A label - (columnOutputSums t (fun _ => k)) (singleFiberHom n k) - (projectedSpechtTensor t t (inOutputs I) (inOutputs_invariant I)).toRepresentation := by - let W := projectedSpechtTensor t t (inOutputs I) (inOutputs_invariant I) - let Q := projectedTensorQuotient t t (inOutputs I) (inOutputs_invariant I) - have hQ : Function.Surjective Q := by - rintro ⟨y,x,rfl⟩ - exact ⟨x,rfl⟩ - letI : AddCommGroup (Specht t ⊗[ℂ] Specht t) := Module.addCommMonoidToAddCommGroup ℂ - let s := Classical.choose (intertwining_lift_surjective Q hQ - (Representation.IntertwiningMap.id W.toRepresentation)) - have hs := Classical.choose_spec (intertwining_lift_surjective Q hQ - (Representation.IntertwiningMap.id W.toRepresentation)) - let T : Representation.IntertwiningMap W.toRepresentation - ((wordRep n (μ.colLen 0 * μ.colLen 0)).comp - ((fiberGroup (fun _ : Fin n => k)).subtype.comp (singleFiberHom n k))) := - subrepInclusion W - refine { - surj := singleFiberHom_surjective n k - raw := (spechtTensorMap t t).toLinearMap.comp s.toLinearMap - raw_mem := ?_ - raw_sums := fun y => spechtTensor_fixed_single_sum t k (s y) - projected := T - injective := Subtype.val_injective - projection_eq := ?_ } - · intro y - refine ⟨s y,?_⟩ - change cyclicSquareMap (polytabloid t) (s y) = spechtTensorMap t t (s y) - rw [cyclicSquareMap_polytabloid] - rfl - · intro y - have he := congrArg Subtype.val (congrArg (fun F : Representation.IntertwiningMap - W.toRepresentation W.toRepresentation => F y) hs) - change coordinateProjection (inOutputs I) (spechtTensorMap t t (s y)) = y.val at he - change coordinateProjection (componentWords (fun _ : Fin n => k) A label) - (spechtTensorMap t t (s y)) = y.val - convert he using 2 - apply congrArg coordinateProjection - funext w - exact propext (componentWords_single k I A label h w) - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceGluing + +namespace OAI + +/-! Balance Leaves. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl.Balance + +def singleFiberHom (n k : ℕ) : Equiv.Perm (Fin n) →* fiberGroup (fun _ : Fin n => k) where + toFun g := ⟨g,fun _ => rfl⟩ + map_one' := rfl + map_mul' _ _ := rfl + +lemma singleFiberHom_surjective (n k : ℕ) : Function.Surjective (singleFiberHom n k) := + fun g => ⟨g.val,Subtype.ext rfl⟩ + +lemma specht_fixed_single_sum {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (k : ℕ) (x : Specht t) : + x.val ∈ fixedSumSpace (fun _ : Fin n => k) (fun a : Fin (μ.colLen 0) => a.val) + (columnRowSums t (fun _ => k)) := by + rcases x with ⟨x,hx⟩ + change x ∈ Submodule.span ℂ (Set.range fun g : Equiv.Perm (Fin n) => + wordRep n (μ.colLen 0) g (polytabloid t)) at hx + induction hx using Submodule.span_induction with + | mem y hy => + obtain ⟨g,rfl⟩ := hy + exact fixedSumSpace_invariant _ _ _ g (fun _ => rfl) _ + (polytabloid_fixed_column_sums t _ (fun _ _ _ => rfl)) + | zero => exact Submodule.zero_mem _ + | add x y hx hy ihx ihy => exact Submodule.add_mem _ ihx ihy + | smul a x hx ih => exact Submodule.smul_mem _ a ih + +lemma spechtTensor_fixed_single_sum {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (k : ℕ) (x : Specht t ⊗[ℂ] Specht t) : + FixedComponentSums (fun _ : Fin n => k) (fun a => (output a : ℤ)) + (columnOutputSums t (fun _ => k)) (spechtTensorMap t t x) := by + classical + change spechtTensorMap t t x ∈ fixedSumSpace (fun _ : Fin n => k) + (fun a => (output a : ℤ)) (columnOutputSums t (fun _ => k)) + induction x using TensorProduct.inductionOn with + | add x y hx hy => simpa only [map_add] using Submodule.add_mem _ hx hy + | tmul x y => + intro w hw i + rw [spechtTensorMap] at hw + change wordTensor _ _ _ (x.val ⊗ₜ[ℂ] y.val) w ≠ 0 at hw + rw [wordTensor_tmul] at hw + obtain ⟨hx,hy⟩ := mul_ne_zero_iff.mp hw + have hs₁ := specht_fixed_single_sum t k x (splitLeft w) hx i + have hs₂ := specht_fixed_single_sum t k y (splitRight w) hy i + change (∑ p ∈ Finset.univ.filter (fun _ : Fin n => k = i), (output (w p) : ℤ)) = _ + simp only [output, Nat.cast_add, Nat.cast_one, Finset.sum_add_distrib, + Finset.sum_const, nsmul_eq_mul, mul_one] + change (∑ p ∈ Finset.univ.filter (fun _ : Fin n => k = i), ((splitLeft w p).val : ℤ)) + + (∑ p ∈ Finset.univ.filter (fun _ : Fin n => k = i), ((splitRight w p).val : ℤ)) + _ = _ + rw [hs₁,hs₂] + dsimp only [columnOutputSums] + ring + +lemma componentWords_single {n d : ℕ} (k : ℕ) (I : Set ℕ) + (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (h : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) (w : Fin n → Fin (d*d)) : + componentWords (fun _ : Fin n => k) A label w ↔ inOutputs I w := by + constructor + · rintro ⟨hA,hl⟩ i + exact (h _).mp ⟨hA i,hl i⟩ + · intro hw + exact ⟨fun i => ((h _).mpr (hw i)).1,fun i => ((h _).mpr (hw i)).2⟩ + +def projectedPiece {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (k : ℕ) (I : Set ℕ) + (A : Fin (μ.colLen 0 * μ.colLen 0) → Prop) + (label : Fin (μ.colLen 0 * μ.colLen 0) → ℕ) + (h : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) : + Piece (polytabloid t) (fun _ : Fin n => k) A label + (columnOutputSums t (fun _ => k)) (singleFiberHom n k) + (projectedSpechtTensor t t (inOutputs I) (inOutputs_invariant I)).toRepresentation := by + let W := projectedSpechtTensor t t (inOutputs I) (inOutputs_invariant I) + let Q := projectedTensorQuotient t t (inOutputs I) (inOutputs_invariant I) + have hQ : Function.Surjective Q := by + rintro ⟨y,x,rfl⟩ + exact ⟨x,rfl⟩ + letI : AddCommGroup (Specht t ⊗[ℂ] Specht t) := Module.addCommMonoidToAddCommGroup ℂ + let s := Classical.choose (intertwining_lift_surjective Q hQ + (Representation.IntertwiningMap.id W.toRepresentation)) + have hs := Classical.choose_spec (intertwining_lift_surjective Q hQ + (Representation.IntertwiningMap.id W.toRepresentation)) + let T : Representation.IntertwiningMap W.toRepresentation + ((wordRep n (μ.colLen 0 * μ.colLen 0)).comp + ((fiberGroup (fun _ : Fin n => k)).subtype.comp (singleFiberHom n k))) := + subrepInclusion W + refine { + surj := singleFiberHom_surjective n k + raw := (spechtTensorMap t t).toLinearMap.comp s.toLinearMap + raw_mem := ?_ + raw_sums := fun y => spechtTensor_fixed_single_sum t k (s y) + projected := T + injective := Subtype.val_injective + projection_eq := ?_ } + · intro y + refine ⟨s y,?_⟩ + change cyclicSquareMap (polytabloid t) (s y) = spechtTensorMap t t (s y) + rw [cyclicSquareMap_polytabloid] + rfl + · intro y + have he := congrArg Subtype.val (congrArg (fun F : Representation.IntertwiningMap + W.toRepresentation W.toRepresentation => F y) hs) + change coordinateProjection (inOutputs I) (spechtTensorMap t t (s y)) = y.val at he + change coordinateProjection (componentWords (fun _ : Fin n => k) A label) + (spechtTensorMap t t (s y)) = y.val + convert he using 2 + apply congrArg coordinateProjection + funext w + exact propext (componentWords_single k I A label h w) + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceLift.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceLift.lean index 999bc1baf5982866a4cea29691aaffaec54128bf..cb26e57753bea5dc14046c34952aefecd89d3384 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceLift.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceLift.lean @@ -1,104 +1,104 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceGluing - -namespace OAI - -/-! Balance Lift. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl - -lemma coordinateProjection_letterLift {n d D : ℕ} (f : Fin d → Fin D) - (P : (Fin n → Fin d) → Prop) (Q : (Fin n → Fin D) → Prop) - (h : ∀ w, Q (f ∘ w) ↔ P w) (x : WordSpace n d) : - coordinateProjection Q (letterLift f x) = letterLift f (coordinateProjection P x) := by - classical - conv_lhs => rw [← (Pi.basisFun ℂ (Fin n → Fin d)).sum_repr x] - conv_rhs => rw [← (Pi.basisFun ℂ (Fin n → Fin d)).sum_repr x] - simp only [map_sum,map_smul,Pi.basisFun_apply,letterLift_single, - coordinateProjection_single,h] - apply Finset.sum_congr rfl - intro w hw - by_cases hp : P w <;> simp [hp,letterLift_single] - -lemma letterLift_nonzero_word {n d D : ℕ} (f : Fin d → Fin D) (hf : Function.Injective f) - (x : WordSpace n d) (w : Fin n → Fin D) (hw : letterLift f x w ≠ 0) : - ∃ a : Fin n → Fin d, f ∘ a = w ∧ x a ≠ 0 := by - classical - have hm := letterLift_mem_alphabet (Set.range f) f (fun a => ⟨a,rfl⟩) x - have hr : ∀ i, ∃ a, f a = w i := by - intro i - by_contra hi - exact hw (hm w ⟨i,hi⟩) - choose a ha using hr - have he : f ∘ a = w := funext ha - refine ⟨a,he,?_⟩ - rw [←he,letterLift_eval f hf] at hw - exact hw - -namespace Balance - -lemma output_pairLetterMap {d D : ℕ} (f : Fin d → Fin D) - (hf : ∀ a, (f a).val = a.val) (a : Fin (d*d)) : - output (pairLetterMap f f a) = output a := by - simp only [output,pairLetterMap,Equiv.symm_apply_apply,hf] - -lemma cyclicSquareMap_lift_mem {n d D : ℕ} (f : Fin d → Fin D) - (v : WordSpace n d) (x : WordSpace n (d*d)) - (hx : x ∈ (cyclicSquareMap v).range) : - letterLift (pairLetterMap f f) x ∈ (cyclicSquareMap (letterLift f v)).range := by - obtain ⟨z,rfl⟩ := hx - let F := cyclicMap (letterLift f) v - refine ⟨TensorProduct.map F.toLinearMap F.toLinearMap z,?_⟩ - induction z using TensorProduct.inductionOn with - | add x y hx hy => simp only [map_add,hx,hy] - | tmul x y => - change wordTensor _ _ _ (letterLift f x.val ⊗ₜ[ℂ] letterLift f y.val) = - letterLift (pairLetterMap f f) (wordTensor _ _ _ (x.val ⊗ₜ[ℂ] y.val)) - exact (letterLift_wordTensor f f x.val y.val).symm - -def Piece.lift {n d D : ℕ} {G Y : Type*} [Group G] [AddCommGroup Y] [Module ℂ Y] - {v : WordSpace n d} {c : Fin n → ℕ} {σ : ℕ → ℤ} - {φ : G →* fiberGroup c} {τ : Representation ℂ G Y} - (f : Fin d → Fin D) (hf : ∀ a, (f a).val = a.val) - (A : Fin (D*D) → Prop) (label : Fin (D*D) → ℕ) - (P : Piece v c (A ∘ pairLetterMap f f) (label ∘ pairLetterMap f f) σ φ τ) : - Piece (letterLift f v) c A label σ φ τ := by - have hfi : Function.Injective f := by - intro a b he - apply Fin.ext - simpa only [hf] using congrArg Fin.val he - let J := pairLetterMap f f - have hJi : Function.Injective J := pairLetterMap_injective f f hfi hfi - let T : Representation.IntertwiningMap - ((wordRep n (d*d)).comp ((fiberGroup c).subtype.comp φ)) - ((wordRep n (D*D)).comp ((fiberGroup c).subtype.comp φ)) := - ⟨(letterLift J).toLinearMap, fun g => (letterLift J).isIntertwining' (φ g).val⟩ - refine { - surj := P.surj - raw := (letterLift J).toLinearMap.comp P.raw - raw_mem := fun y => cyclicSquareMap_lift_mem f v _ (P.raw_mem y) - raw_sums := ?_ - projected := T.comp P.projected - injective := (letterLift_injective J hJi).comp P.injective - projection_eq := ?_ } - · intro y w hw k - obtain ⟨a,rfl,ha⟩ := letterLift_nonzero_word J hJi (P.raw y) w hw - have he := P.raw_sums y a ha k - simpa only [J, Function.comp_apply,output_pairLetterMap f hf] using he - · intro y - change coordinateProjection (componentWords c A label) (letterLift J (P.raw y)) = - letterLift J (P.projected y) - rw [coordinateProjection_letterLift J (componentWords c (A ∘ J) (label ∘ J)) - (componentWords c A label) (fun _ => Iff.rfl),P.projection_eq] - -end Balance -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceGluing + +namespace OAI + +/-! Balance Lift. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl + +lemma coordinateProjection_letterLift {n d D : ℕ} (f : Fin d → Fin D) + (P : (Fin n → Fin d) → Prop) (Q : (Fin n → Fin D) → Prop) + (h : ∀ w, Q (f ∘ w) ↔ P w) (x : WordSpace n d) : + coordinateProjection Q (letterLift f x) = letterLift f (coordinateProjection P x) := by + classical + conv_lhs => rw [← (Pi.basisFun ℂ (Fin n → Fin d)).sum_repr x] + conv_rhs => rw [← (Pi.basisFun ℂ (Fin n → Fin d)).sum_repr x] + simp only [map_sum,map_smul,Pi.basisFun_apply,letterLift_single, + coordinateProjection_single,h] + apply Finset.sum_congr rfl + intro w hw + by_cases hp : P w <;> simp [hp,letterLift_single] + +lemma letterLift_nonzero_word {n d D : ℕ} (f : Fin d → Fin D) (hf : Function.Injective f) + (x : WordSpace n d) (w : Fin n → Fin D) (hw : letterLift f x w ≠ 0) : + ∃ a : Fin n → Fin d, f ∘ a = w ∧ x a ≠ 0 := by + classical + have hm := letterLift_mem_alphabet (Set.range f) f (fun a => ⟨a,rfl⟩) x + have hr : ∀ i, ∃ a, f a = w i := by + intro i + by_contra hi + exact hw (hm w ⟨i,hi⟩) + choose a ha using hr + have he : f ∘ a = w := funext ha + refine ⟨a,he,?_⟩ + rw [←he,letterLift_eval f hf] at hw + exact hw + +namespace Balance + +lemma output_pairLetterMap {d D : ℕ} (f : Fin d → Fin D) + (hf : ∀ a, (f a).val = a.val) (a : Fin (d*d)) : + output (pairLetterMap f f a) = output a := by + simp only [output,pairLetterMap,Equiv.symm_apply_apply,hf] + +lemma cyclicSquareMap_lift_mem {n d D : ℕ} (f : Fin d → Fin D) + (v : WordSpace n d) (x : WordSpace n (d*d)) + (hx : x ∈ (cyclicSquareMap v).range) : + letterLift (pairLetterMap f f) x ∈ (cyclicSquareMap (letterLift f v)).range := by + obtain ⟨z,rfl⟩ := hx + let F := cyclicMap (letterLift f) v + refine ⟨TensorProduct.map F.toLinearMap F.toLinearMap z,?_⟩ + induction z using TensorProduct.inductionOn with + | add x y hx hy => simp only [map_add,hx,hy] + | tmul x y => + change wordTensor _ _ _ (letterLift f x.val ⊗ₜ[ℂ] letterLift f y.val) = + letterLift (pairLetterMap f f) (wordTensor _ _ _ (x.val ⊗ₜ[ℂ] y.val)) + exact (letterLift_wordTensor f f x.val y.val).symm + +def Piece.lift {n d D : ℕ} {G Y : Type*} [Group G] [AddCommGroup Y] [Module ℂ Y] + {v : WordSpace n d} {c : Fin n → ℕ} {σ : ℕ → ℤ} + {φ : G →* fiberGroup c} {τ : Representation ℂ G Y} + (f : Fin d → Fin D) (hf : ∀ a, (f a).val = a.val) + (A : Fin (D*D) → Prop) (label : Fin (D*D) → ℕ) + (P : Piece v c (A ∘ pairLetterMap f f) (label ∘ pairLetterMap f f) σ φ τ) : + Piece (letterLift f v) c A label σ φ τ := by + have hfi : Function.Injective f := by + intro a b he + apply Fin.ext + simpa only [hf] using congrArg Fin.val he + let J := pairLetterMap f f + have hJi : Function.Injective J := pairLetterMap_injective f f hfi hfi + let T : Representation.IntertwiningMap + ((wordRep n (d*d)).comp ((fiberGroup c).subtype.comp φ)) + ((wordRep n (D*D)).comp ((fiberGroup c).subtype.comp φ)) := + ⟨(letterLift J).toLinearMap, fun g => (letterLift J).isIntertwining' (φ g).val⟩ + refine { + surj := P.surj + raw := (letterLift J).toLinearMap.comp P.raw + raw_mem := fun y => cyclicSquareMap_lift_mem f v _ (P.raw_mem y) + raw_sums := ?_ + projected := T.comp P.projected + injective := (letterLift_injective J hJi).comp P.injective + projection_eq := ?_ } + · intro y w hw k + obtain ⟨a,rfl,ha⟩ := letterLift_nonzero_word J hJi (P.raw y) w hw + have he := P.raw_sums y a ha k + simpa only [J, Function.comp_apply,output_pairLetterMap f hf] using he + · intro y + change coordinateProjection (componentWords c A label) (letterLift J (P.raw y)) = + letterLift J (P.projected y) + rw [coordinateProjection_letterLift J (componentWords c (A ∘ J) (label ∘ J)) + (componentWords c A label) (fun _ => Iff.rfl),P.projection_eq] + +end Balance +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalancePacking.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalancePacking.lean index 92a60e90e7e9aa5f15a58fdf607a05bd064d27f0..27a927af41d3e2c189af24703ef6dd6efdb3ea64 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalancePacking.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalancePacking.lean @@ -1,119 +1,119 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceLeaves -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceLift - -namespace OAI - -/-! Balance Packing. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl.Balance - -structure Packing {n d e : ℕ} (v : WordSpace n d) - (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) (w : WordSpace n e) where - G : Type - [groupG : Group G] - [finiteG : Finite G] - Y : Type - [addY : AddCommGroup Y] - [moduleY : Module ℂ Y] - [finiteY : FiniteDimensional ℂ Y] - c : Fin n → ℕ - σ : ℕ → ℤ - φ : G →* fiberGroup c - τ : Representation ℂ G Y - piece : Piece v c A label σ φ τ - support : SupportLE (cyclic (wordRep n e) w).toRepresentation - (Representation.coind ((fiberGroup c).subtype.comp φ) τ) - -attribute [instance] Packing.groupG Packing.finiteG Packing.addY Packing.moduleY Packing.finiteY - -def Packing.join {n a b d E : ℕ} {v : WordSpace a d} {u : WordSpace b d} - {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} - {w : WordSpace a E} {z : WordSpace b E} - (P : Packing v A label w) (Q : Packing u A label z) - (e : Fin n ≃ Fin a ⊕ Fin b) (hd : ∀ i j, P.c i ≠ Q.c j) : - Packing (positionProduct e v u) A label (positionProduct e w z) := by - letI : AddCommGroup (P.Y ⊗[ℂ] Q.Y) := Module.addCommMonoidToAddCommGroup ℂ - exact { - G := P.G × Q.G - Y := P.Y ⊗[ℂ] Q.Y - c := joinedLabels e P.c Q.c - σ := P.σ + Q.σ - φ := (joinedFiberHom e P.c Q.c).comp (P.φ.prodMap Q.φ) - τ := outer P.τ Q.τ - piece := P.piece.join Q.piece e hd - support := product_supportLE_coind - ((fiberGroup P.c).subtype.comp P.φ) ((fiberGroup Q.c).subtype.comp Q.φ) - P.τ Q.τ e w z P.support Q.support } - -def Packing.map {n d e E : ℕ} {v : WordSpace n d} - {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {w : WordSpace n e} - (P : Packing v A label w) - (T : Representation.IntertwiningMap (wordRep n e) (wordRep n E)) : - Packing v A label (T w) := - { P with support := P.support.cyclic_image w T } - -def Packing.lift {n d D e : ℕ} {v : WordSpace n d} {w : WordSpace n e} - (f : Fin d → Fin D) (hf : ∀ a, (f a).val = a.val) - (A : Fin (D*D) → Prop) (label : Fin (D*D) → ℕ) - (P : Packing v (A ∘ pairLetterMap f f) (label ∘ pairLetterMap f f) w) : - Packing (letterLift f v) A label w := - { P with piece := P.piece.lift f hf A label } - -def Packing.replace {n d e E : ℕ} {v : WordSpace n d} - {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} - {w : WordSpace n e} (P : Packing v A label w) (z : WordSpace n E) - (h : SupportLE (cyclic (wordRep n E) z).toRepresentation - (cyclic (wordRep n e) w).toRepresentation) : Packing v A label z := - { P with support := h.trans P.support } - -def boundedPacking {n e : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (k : ℕ) (I : Set ℕ) - (A : Fin (μ.colLen 0 * μ.colLen 0) → Prop) - (label : Fin (μ.colLen 0 * μ.colLen 0) → ℕ) - (h : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) - (hs : SupportLE (wordRep n e) - (projectedSpechtTensor t t (inOutputs I) (inOutputs_invariant I)).toRepresentation) - (w : WordSpace n e) : Packing (polytabloid t) A label w := by - let W := projectedSpechtTensor t t (inOutputs I) (inOutputs_invariant I) - let φ := (fiberGroup (fun _ : Fin n => k)).subtype.comp (singleFiberHom n k) - have hi : Function.Injective (coindLift (ρ := W.toRepresentation) φ (Representation.IntertwiningMap.id W.toRepresentation)) := by - intro x y hxy - have he := congrArg (fun z : Representation.coindV φ W.toRepresentation => z.val 1) hxy - change W.toRepresentation 1 x = W.toRepresentation 1 y at he - simpa only [map_one,Module.End.one_apply] using he - refine { - G := Equiv.Perm (Fin n) - Y := W.toSubmodule - c := fun _ => k - σ := columnOutputSums t (fun _ => k) - φ := singleFiberHom n k - τ := W.toRepresentation - piece := projectedPiece t k I A label h - support := ?_ } - exact ((SupportLE.of_injective (subrepInclusion (cyclic (wordRep n e) w)) - Subtype.val_injective).trans hs).trans (SupportLE.of_injective _ hi) - -theorem Packing.kronecker_pos {n : ℕ} {lam μ θ : YoungDiagram} - (a : Tableau n lam) (t : Tableau n μ) - {A : Fin (lam.colLen 0 * lam.colLen 0) → Prop} - {label : Fin (lam.colLen 0 * lam.colLen 0) → ℕ} - (w : Fin n → Fin (θ.colLen 0)) - (P : Packing (polytabloid a) A label (Pi.single w 1)) - (ho : ∀ x y, A x → A y → label x < label y → output x < output y) - (hc : μ.card = θ.card) (hd : Dominates μ θ) - (e : Equiv.Perm (Fin (θ.colLen 0))) - (hw : ∀ j, (Finset.univ.filter (fun i => w i = e j)).card = θ.rowLen j) : - 0 < kronecker a a t := - P.piece.kronecker_pos a t ho θ hc hd w e hw P.support - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceLeaves +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceLift + +namespace OAI + +/-! Balance Packing. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl.Balance + +structure Packing {n d e : ℕ} (v : WordSpace n d) + (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) (w : WordSpace n e) where + G : Type + [groupG : Group G] + [finiteG : Finite G] + Y : Type + [addY : AddCommGroup Y] + [moduleY : Module ℂ Y] + [finiteY : FiniteDimensional ℂ Y] + c : Fin n → ℕ + σ : ℕ → ℤ + φ : G →* fiberGroup c + τ : Representation ℂ G Y + piece : Piece v c A label σ φ τ + support : SupportLE (cyclic (wordRep n e) w).toRepresentation + (Representation.coind ((fiberGroup c).subtype.comp φ) τ) + +attribute [instance] Packing.groupG Packing.finiteG Packing.addY Packing.moduleY Packing.finiteY + +def Packing.join {n a b d E : ℕ} {v : WordSpace a d} {u : WordSpace b d} + {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} + {w : WordSpace a E} {z : WordSpace b E} + (P : Packing v A label w) (Q : Packing u A label z) + (e : Fin n ≃ Fin a ⊕ Fin b) (hd : ∀ i j, P.c i ≠ Q.c j) : + Packing (positionProduct e v u) A label (positionProduct e w z) := by + letI : AddCommGroup (P.Y ⊗[ℂ] Q.Y) := Module.addCommMonoidToAddCommGroup ℂ + exact { + G := P.G × Q.G + Y := P.Y ⊗[ℂ] Q.Y + c := joinedLabels e P.c Q.c + σ := P.σ + Q.σ + φ := (joinedFiberHom e P.c Q.c).comp (P.φ.prodMap Q.φ) + τ := outer P.τ Q.τ + piece := P.piece.join Q.piece e hd + support := product_supportLE_coind + ((fiberGroup P.c).subtype.comp P.φ) ((fiberGroup Q.c).subtype.comp Q.φ) + P.τ Q.τ e w z P.support Q.support } + +def Packing.map {n d e E : ℕ} {v : WordSpace n d} + {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {w : WordSpace n e} + (P : Packing v A label w) + (T : Representation.IntertwiningMap (wordRep n e) (wordRep n E)) : + Packing v A label (T w) := + { P with support := P.support.cyclic_image w T } + +def Packing.lift {n d D e : ℕ} {v : WordSpace n d} {w : WordSpace n e} + (f : Fin d → Fin D) (hf : ∀ a, (f a).val = a.val) + (A : Fin (D*D) → Prop) (label : Fin (D*D) → ℕ) + (P : Packing v (A ∘ pairLetterMap f f) (label ∘ pairLetterMap f f) w) : + Packing (letterLift f v) A label w := + { P with piece := P.piece.lift f hf A label } + +def Packing.replace {n d e E : ℕ} {v : WordSpace n d} + {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} + {w : WordSpace n e} (P : Packing v A label w) (z : WordSpace n E) + (h : SupportLE (cyclic (wordRep n E) z).toRepresentation + (cyclic (wordRep n e) w).toRepresentation) : Packing v A label z := + { P with support := h.trans P.support } + +def boundedPacking {n e : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (k : ℕ) (I : Set ℕ) + (A : Fin (μ.colLen 0 * μ.colLen 0) → Prop) + (label : Fin (μ.colLen 0 * μ.colLen 0) → ℕ) + (h : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) + (hs : SupportLE (wordRep n e) + (projectedSpechtTensor t t (inOutputs I) (inOutputs_invariant I)).toRepresentation) + (w : WordSpace n e) : Packing (polytabloid t) A label w := by + let W := projectedSpechtTensor t t (inOutputs I) (inOutputs_invariant I) + let φ := (fiberGroup (fun _ : Fin n => k)).subtype.comp (singleFiberHom n k) + have hi : Function.Injective (coindLift (ρ := W.toRepresentation) φ (Representation.IntertwiningMap.id W.toRepresentation)) := by + intro x y hxy + have he := congrArg (fun z : Representation.coindV φ W.toRepresentation => z.val 1) hxy + change W.toRepresentation 1 x = W.toRepresentation 1 y at he + simpa only [map_one,Module.End.one_apply] using he + refine { + G := Equiv.Perm (Fin n) + Y := W.toSubmodule + c := fun _ => k + σ := columnOutputSums t (fun _ => k) + φ := singleFiberHom n k + τ := W.toRepresentation + piece := projectedPiece t k I A label h + support := ?_ } + exact ((SupportLE.of_injective (subrepInclusion (cyclic (wordRep n e) w)) + Subtype.val_injective).trans hs).trans (SupportLE.of_injective _ hi) + +theorem Packing.kronecker_pos {n : ℕ} {lam μ θ : YoungDiagram} + (a : Tableau n lam) (t : Tableau n μ) + {A : Fin (lam.colLen 0 * lam.colLen 0) → Prop} + {label : Fin (lam.colLen 0 * lam.colLen 0) → ℕ} + (w : Fin n → Fin (θ.colLen 0)) + (P : Packing (polytabloid a) A label (Pi.single w 1)) + (ho : ∀ x y, A x → A y → label x < label y → output x < output y) + (hc : μ.card = θ.card) (hd : Dominates μ θ) + (e : Equiv.Perm (Fin (θ.colLen 0))) + (hw : ∀ j, (Finset.univ.filter (fun i => w i = e j)).card = θ.rowLen j) : + 0 < kronecker a a t := + P.piece.kronecker_pos a t ho θ hc hd w e hw P.support + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceProduct.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceProduct.lean index c0ef1f35bcb8a80c47624e85bda890490fac4b33..05025f0dd6479997b39ee3fcec35d77543274751 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceProduct.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceProduct.lean @@ -1,195 +1,195 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ProductInduction -import OAI.RepresentationTheory.UniversalSquare.Support.WordRelabel -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceProjection -import OAI.RepresentationTheory.UniversalSquare.Support.SupportTransport - -namespace OAI - -/-! Balance Product. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl.Balance - -def cyclicSquareMap {n d : ℕ} (v : WordSpace n d) : - Representation.IntertwiningMap - ((cyclic (wordRep n d) v).toRepresentation.tprod (cyclic (wordRep n d) v).toRepresentation) - (wordRep n (d*d)) where - toLinearMap := (wordTensor n d d).toLinearMap.comp - (TensorProduct.map (cyclic (wordRep n d) v).toSubmodule.subtype - (cyclic (wordRep n d) v).toSubmodule.subtype) - isIntertwining' g := by - ext x y w - exact congrFun (wordTensor_equivariant g (x.val ⊗ₜ[ℂ] y.val)) w - -@[simp] lemma cyclicSquareMap_tmul {n d : ℕ} (v : WordSpace n d) - (x y : (cyclic (wordRep n d) v).toSubmodule) : - cyclicSquareMap v (x ⊗ₜ[ℂ] y) = wordTensor n d d (x.val ⊗ₜ[ℂ] y.val) := rfl - -theorem product_mem_square {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (v : WordSpace a d) (u : WordSpace b d) - (x : WordSpace a (d*d)) (y : WordSpace b (d*d)) - (hx : x ∈ (cyclicSquareMap v).range) (hy : y ∈ (cyclicSquareMap u).range) : - positionProduct e x y ∈ (cyclicSquareMap (positionProduct e v u)).range := by - obtain ⟨X,rfl⟩ := hx - obtain ⟨Y,rfl⟩ := hy - let W := (cyclicSquareMap (positionProduct e v u)).range.toSubmodule - change positionProduct e (cyclicSquareMap v X) (cyclicSquareMap u Y) ∈ W - rw [← positionTensor_tmul e (cyclicSquareMap v X) (cyclicSquareMap u Y)] - induction X using TensorProduct.inductionOn with - | add X X' h h' => simpa only [map_add,TensorProduct.add_tmul] using W.add_mem h h' - | tmul x x' => - induction Y using TensorProduct.inductionOn with - | add Y Y' h h' => simpa only [map_add,TensorProduct.tmul_add] using W.add_mem h h' - | tmul y y' => - rw [cyclicSquareMap_tmul,cyclicSquareMap_tmul,positionTensor_tmul, - ← wordTensor_positionProduct] - refine ⟨(⟨positionProduct e x.val y.val,product_mem_cyclic e v u _ _ x.property y.property⟩ : - (cyclic (wordRep n d) (positionProduct e v u)).toSubmodule) ⊗ₜ[ℂ] - (⟨positionProduct e x'.val y'.val,product_mem_cyclic e v u _ _ x'.property y'.property⟩ : - (cyclic (wordRep n d) (positionProduct e v u)).toSubmodule), rfl⟩ - -def joinedLabels {n a b : ℕ} {α : Type*} (e : Fin n ≃ Fin a ⊕ Fin b) - (c : Fin a → α) (c' : Fin b → α) : Fin n → α := fun i => Sum.elim c c' (e i) - -@[simp] lemma joinedLabels_left {n a b : ℕ} {α : Type*} (e : Fin n ≃ Fin a ⊕ Fin b) - (c : Fin a → α) (c' : Fin b → α) (i : Fin a) : - joinedLabels e c c' (e.symm (Sum.inl i)) = c i := by simp [joinedLabels] - -@[simp] lemma joinedLabels_right {n a b : ℕ} {α : Type*} (e : Fin n ≃ Fin a ⊕ Fin b) - (c : Fin a → α) (c' : Fin b → α) (i : Fin b) : - joinedLabels e c c' (e.symm (Sum.inr i)) = c' i := by simp [joinedLabels] - -def joinedFiberHom {n a b : ℕ} {α : Type*} (e : Fin n ≃ Fin a ⊕ Fin b) - (c : Fin a → α) (c' : Fin b → α) : - (fiberGroup c × fiberGroup c') →* fiberGroup (joinedLabels e c c') where - toFun g := ⟨sumPerm e g.1.val g.2.val,by - intro i - obtain ⟨j,rfl⟩ := e.symm.surjective i - cases j with - | inl j => simpa only [sumPerm_left,joinedLabels_left] using g.1.property j - | inr j => simpa only [sumPerm_right,joinedLabels_right] using g.2.property j⟩ - map_one' := Subtype.ext (sumPerm_one e) - map_mul' g h := Subtype.ext (sumPerm_mul e g.1.val h.1.val g.2.val h.2.val) - -lemma joinedFiberHom_surjective {n a b : ℕ} {α : Type*} (e : Fin n ≃ Fin a ⊕ Fin b) - (c : Fin a → α) (c' : Fin b → α) (hd : ∀ i j, c i ≠ c' j) : - Function.Surjective (joinedFiberHom e c c') := by - intro g - have hg : g.val ∈ sectorGroup (fun i => (e i).isLeft = true) := by - intro i - have h := g.property i - change Sum.elim c c' (e (g.val i)) = Sum.elim c c' (e i) at h - cases he : e i with - | inl j => - cases hf : e (g.val i) with - | inl k => simp only [he,hf,Sum.isLeft_inl] - | inr k => simp only [he,hf,Sum.elim_inl,Sum.elim_inr] at h; exact False.elim (hd j k h.symm) - | inr j => - cases hf : e (g.val i) with - | inl k => simp only [he,hf,Sum.elim_inl,Sum.elim_inr] at h; exact False.elim (hd k j h) - | inr k => simp only [he,hf,Sum.isLeft_inr] - let g' : sectorGroup (fun i => (e i).isLeft = true) := ⟨g.val,hg⟩ - have hl : leftRestriction e g' ∈ fiberGroup c := by - intro i - have hh := g.property (e.symm (Sum.inl i)) - rw [← leftRestriction_apply e g',joinedLabels_left,joinedLabels_left] at hh - exact hh - have hr : rightRestriction e g' ∈ fiberGroup c' := by - intro i - have hh := g.property (e.symm (Sum.inr i)) - rw [← rightRestriction_apply e g',joinedLabels_right,joinedLabels_right] at hh - exact hh - exact ⟨(⟨_,hl⟩,⟨_,hr⟩),Subtype.ext (sumPerm_restrictions e g')⟩ - -lemma componentWords_joined {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (c : Fin a → ℕ) (c' : Fin b → ℕ) (A : Fin d → Prop) (label : Fin d → ℕ) - (w : Fin n → Fin d) : - componentWords (joinedLabels e c c') A label w ↔ - componentWords c A label (leftWord e w) ∧ componentWords c' A label (rightWord e w) := by - constructor - · rintro ⟨hA,hl⟩ - exact ⟨⟨fun i => hA _,fun i => (hl _).trans (joinedLabels_left e c c' i)⟩, - ⟨fun i => hA _,fun i => (hl _).trans (joinedLabels_right e c c' i)⟩⟩ - · rintro ⟨⟨hA,hl⟩,⟨hA',hl'⟩⟩ - constructor - · intro i - obtain ⟨j,rfl⟩ := e.symm.surjective i - cases j with - | inl j => exact hA j - | inr j => exact hA' j - · intro i - obtain ⟨j,rfl⟩ := e.symm.surjective i - cases j with - | inl j => exact (hl j).trans (joinedLabels_left e c c' j).symm - | inr j => exact (hl' j).trans (joinedLabels_right e c c' j).symm - -lemma component_projection_product {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (c : Fin a → ℕ) (c' : Fin b → ℕ) (A : Fin d → Prop) (label : Fin d → ℕ) - (x : WordSpace a d) (y : WordSpace b d) : - coordinateProjection (componentWords (joinedLabels e c c') A label) (positionProduct e x y) = - positionProduct e (coordinateProjection (componentWords c A label) x) - (coordinateProjection (componentWords c' A label) y) := by - classical - ext w - simp only [coordinateProjection_apply,componentWords_joined,positionProduct] - split_ifs <;> simp_all - -lemma joined_component_sum {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (c : Fin a → ℕ) (c' : Fin b → ℕ) (z : Fin d → ℤ) - (w : Fin n → Fin d) (k : ℕ) : - ∑ i ∈ Finset.univ.filter (fun i => joinedLabels e c c' i = k), z (w i) = - (∑ i ∈ Finset.univ.filter (fun i => c i = k), z (leftWord e w i)) + - ∑ i ∈ Finset.univ.filter (fun i => c' i = k), z (rightWord e w i) := by - classical - simp only [Finset.sum_filter] - rw [← Equiv.sum_comp e.symm, Fintype.sum_sum_type] - simp only [joinedLabels_left,joinedLabels_right,leftWord,rightWord] - -lemma product_fixed_sums {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (c : Fin a → ℕ) (c' : Fin b → ℕ) (z : Fin d → ℤ) - (σ σ' : ℕ → ℤ) (x : WordSpace a d) (y : WordSpace b d) - (hx : FixedComponentSums c z σ x) (hy : FixedComponentSums c' z σ' y) : - FixedComponentSums (joinedLabels e c c') z (σ+σ') (positionProduct e x y) := by - intro w hw k - obtain ⟨hxw,hyw⟩ := mul_ne_zero_iff.mp hw - rw [joined_component_sum,hx _ hxw k,hy _ hyw k,Pi.add_apply] - -def outerWordMap {n a b d : ℕ} {G H X Y : Type*} [Group G] [Group H] - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - {ρ : Representation ℂ G X} {σ : Representation ℂ H Y} - (e : Fin n ≃ Fin a ⊕ Fin b) - (φ : G →* Equiv.Perm (Fin a)) (ψ : H →* Equiv.Perm (Fin b)) - (F : Representation.IntertwiningMap ρ ((wordRep a d).comp φ)) - (Q : Representation.IntertwiningMap σ ((wordRep b d).comp ψ)) : - Representation.IntertwiningMap (outer ρ σ) - ((wordRep n d).comp ((sumPermHom e).comp (φ.prodMap ψ))) where - toLinearMap := (positionTensor e).toLinearMap.comp (TensorProduct.map F.toLinearMap Q.toLinearMap) - isIntertwining' g := by - ext x y w - apply congrFun (a := w) - change positionTensor e (F (ρ g.1 x) ⊗ₜ[ℂ] Q (σ g.2 y)) = - wordRep n d (sumPerm e (φ g.1) (ψ g.2)) (positionTensor e (F x ⊗ₜ[ℂ] Q y)) - rw [F.isIntertwining,Q.isIntertwining,positionTensor_tmul,positionTensor_tmul] - exact (positionProduct_equivariant e (φ g.1) (ψ g.2) (F x) (Q y)).symm - -lemma outerWordMap_injective {n a b d : ℕ} {G H X Y : Type*} [Group G] [Group H] - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - {ρ : Representation ℂ G X} {σ : Representation ℂ H Y} - (e : Fin n ≃ Fin a ⊕ Fin b) - (φ : G →* Equiv.Perm (Fin a)) (ψ : H →* Equiv.Perm (Fin b)) - (F : Representation.IntertwiningMap ρ ((wordRep a d).comp φ)) - (Q : Representation.IntertwiningMap σ ((wordRep b d).comp ψ)) - (hF : Function.Injective F) (hQ : Function.Injective Q) : - Function.Injective (outerWordMap e φ ψ F Q) := - (positionTensor e).injective.comp (TensorProduct.map_injective_of_flat_flat _ _ hF hQ) - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ProductInduction +import OAI.RepresentationTheory.UniversalSquare.Support.WordRelabel +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceProjection +import OAI.RepresentationTheory.UniversalSquare.Support.SupportTransport + +namespace OAI + +/-! Balance Product. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl.Balance + +def cyclicSquareMap {n d : ℕ} (v : WordSpace n d) : + Representation.IntertwiningMap + ((cyclic (wordRep n d) v).toRepresentation.tprod (cyclic (wordRep n d) v).toRepresentation) + (wordRep n (d*d)) where + toLinearMap := (wordTensor n d d).toLinearMap.comp + (TensorProduct.map (cyclic (wordRep n d) v).toSubmodule.subtype + (cyclic (wordRep n d) v).toSubmodule.subtype) + isIntertwining' g := by + ext x y w + exact congrFun (wordTensor_equivariant g (x.val ⊗ₜ[ℂ] y.val)) w + +@[simp] lemma cyclicSquareMap_tmul {n d : ℕ} (v : WordSpace n d) + (x y : (cyclic (wordRep n d) v).toSubmodule) : + cyclicSquareMap v (x ⊗ₜ[ℂ] y) = wordTensor n d d (x.val ⊗ₜ[ℂ] y.val) := rfl + +theorem product_mem_square {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (v : WordSpace a d) (u : WordSpace b d) + (x : WordSpace a (d*d)) (y : WordSpace b (d*d)) + (hx : x ∈ (cyclicSquareMap v).range) (hy : y ∈ (cyclicSquareMap u).range) : + positionProduct e x y ∈ (cyclicSquareMap (positionProduct e v u)).range := by + obtain ⟨X,rfl⟩ := hx + obtain ⟨Y,rfl⟩ := hy + let W := (cyclicSquareMap (positionProduct e v u)).range.toSubmodule + change positionProduct e (cyclicSquareMap v X) (cyclicSquareMap u Y) ∈ W + rw [← positionTensor_tmul e (cyclicSquareMap v X) (cyclicSquareMap u Y)] + induction X using TensorProduct.inductionOn with + | add X X' h h' => simpa only [map_add,TensorProduct.add_tmul] using W.add_mem h h' + | tmul x x' => + induction Y using TensorProduct.inductionOn with + | add Y Y' h h' => simpa only [map_add,TensorProduct.tmul_add] using W.add_mem h h' + | tmul y y' => + rw [cyclicSquareMap_tmul,cyclicSquareMap_tmul,positionTensor_tmul, + ← wordTensor_positionProduct] + refine ⟨(⟨positionProduct e x.val y.val,product_mem_cyclic e v u _ _ x.property y.property⟩ : + (cyclic (wordRep n d) (positionProduct e v u)).toSubmodule) ⊗ₜ[ℂ] + (⟨positionProduct e x'.val y'.val,product_mem_cyclic e v u _ _ x'.property y'.property⟩ : + (cyclic (wordRep n d) (positionProduct e v u)).toSubmodule), rfl⟩ + +def joinedLabels {n a b : ℕ} {α : Type*} (e : Fin n ≃ Fin a ⊕ Fin b) + (c : Fin a → α) (c' : Fin b → α) : Fin n → α := fun i => Sum.elim c c' (e i) + +@[simp] lemma joinedLabels_left {n a b : ℕ} {α : Type*} (e : Fin n ≃ Fin a ⊕ Fin b) + (c : Fin a → α) (c' : Fin b → α) (i : Fin a) : + joinedLabels e c c' (e.symm (Sum.inl i)) = c i := by simp [joinedLabels] + +@[simp] lemma joinedLabels_right {n a b : ℕ} {α : Type*} (e : Fin n ≃ Fin a ⊕ Fin b) + (c : Fin a → α) (c' : Fin b → α) (i : Fin b) : + joinedLabels e c c' (e.symm (Sum.inr i)) = c' i := by simp [joinedLabels] + +def joinedFiberHom {n a b : ℕ} {α : Type*} (e : Fin n ≃ Fin a ⊕ Fin b) + (c : Fin a → α) (c' : Fin b → α) : + (fiberGroup c × fiberGroup c') →* fiberGroup (joinedLabels e c c') where + toFun g := ⟨sumPerm e g.1.val g.2.val,by + intro i + obtain ⟨j,rfl⟩ := e.symm.surjective i + cases j with + | inl j => simpa only [sumPerm_left,joinedLabels_left] using g.1.property j + | inr j => simpa only [sumPerm_right,joinedLabels_right] using g.2.property j⟩ + map_one' := Subtype.ext (sumPerm_one e) + map_mul' g h := Subtype.ext (sumPerm_mul e g.1.val h.1.val g.2.val h.2.val) + +lemma joinedFiberHom_surjective {n a b : ℕ} {α : Type*} (e : Fin n ≃ Fin a ⊕ Fin b) + (c : Fin a → α) (c' : Fin b → α) (hd : ∀ i j, c i ≠ c' j) : + Function.Surjective (joinedFiberHom e c c') := by + intro g + have hg : g.val ∈ sectorGroup (fun i => (e i).isLeft = true) := by + intro i + have h := g.property i + change Sum.elim c c' (e (g.val i)) = Sum.elim c c' (e i) at h + cases he : e i with + | inl j => + cases hf : e (g.val i) with + | inl k => simp only [he,hf,Sum.isLeft_inl] + | inr k => simp only [he,hf,Sum.elim_inl,Sum.elim_inr] at h; exact False.elim (hd j k h.symm) + | inr j => + cases hf : e (g.val i) with + | inl k => simp only [he,hf,Sum.elim_inl,Sum.elim_inr] at h; exact False.elim (hd k j h) + | inr k => simp only [he,hf,Sum.isLeft_inr] + let g' : sectorGroup (fun i => (e i).isLeft = true) := ⟨g.val,hg⟩ + have hl : leftRestriction e g' ∈ fiberGroup c := by + intro i + have hh := g.property (e.symm (Sum.inl i)) + rw [← leftRestriction_apply e g',joinedLabels_left,joinedLabels_left] at hh + exact hh + have hr : rightRestriction e g' ∈ fiberGroup c' := by + intro i + have hh := g.property (e.symm (Sum.inr i)) + rw [← rightRestriction_apply e g',joinedLabels_right,joinedLabels_right] at hh + exact hh + exact ⟨(⟨_,hl⟩,⟨_,hr⟩),Subtype.ext (sumPerm_restrictions e g')⟩ + +lemma componentWords_joined {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (c : Fin a → ℕ) (c' : Fin b → ℕ) (A : Fin d → Prop) (label : Fin d → ℕ) + (w : Fin n → Fin d) : + componentWords (joinedLabels e c c') A label w ↔ + componentWords c A label (leftWord e w) ∧ componentWords c' A label (rightWord e w) := by + constructor + · rintro ⟨hA,hl⟩ + exact ⟨⟨fun i => hA _,fun i => (hl _).trans (joinedLabels_left e c c' i)⟩, + ⟨fun i => hA _,fun i => (hl _).trans (joinedLabels_right e c c' i)⟩⟩ + · rintro ⟨⟨hA,hl⟩,⟨hA',hl'⟩⟩ + constructor + · intro i + obtain ⟨j,rfl⟩ := e.symm.surjective i + cases j with + | inl j => exact hA j + | inr j => exact hA' j + · intro i + obtain ⟨j,rfl⟩ := e.symm.surjective i + cases j with + | inl j => exact (hl j).trans (joinedLabels_left e c c' j).symm + | inr j => exact (hl' j).trans (joinedLabels_right e c c' j).symm + +lemma component_projection_product {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (c : Fin a → ℕ) (c' : Fin b → ℕ) (A : Fin d → Prop) (label : Fin d → ℕ) + (x : WordSpace a d) (y : WordSpace b d) : + coordinateProjection (componentWords (joinedLabels e c c') A label) (positionProduct e x y) = + positionProduct e (coordinateProjection (componentWords c A label) x) + (coordinateProjection (componentWords c' A label) y) := by + classical + ext w + simp only [coordinateProjection_apply,componentWords_joined,positionProduct] + split_ifs <;> simp_all + +lemma joined_component_sum {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (c : Fin a → ℕ) (c' : Fin b → ℕ) (z : Fin d → ℤ) + (w : Fin n → Fin d) (k : ℕ) : + ∑ i ∈ Finset.univ.filter (fun i => joinedLabels e c c' i = k), z (w i) = + (∑ i ∈ Finset.univ.filter (fun i => c i = k), z (leftWord e w i)) + + ∑ i ∈ Finset.univ.filter (fun i => c' i = k), z (rightWord e w i) := by + classical + simp only [Finset.sum_filter] + rw [← Equiv.sum_comp e.symm, Fintype.sum_sum_type] + simp only [joinedLabels_left,joinedLabels_right,leftWord,rightWord] + +lemma product_fixed_sums {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (c : Fin a → ℕ) (c' : Fin b → ℕ) (z : Fin d → ℤ) + (σ σ' : ℕ → ℤ) (x : WordSpace a d) (y : WordSpace b d) + (hx : FixedComponentSums c z σ x) (hy : FixedComponentSums c' z σ' y) : + FixedComponentSums (joinedLabels e c c') z (σ+σ') (positionProduct e x y) := by + intro w hw k + obtain ⟨hxw,hyw⟩ := mul_ne_zero_iff.mp hw + rw [joined_component_sum,hx _ hxw k,hy _ hyw k,Pi.add_apply] + +def outerWordMap {n a b d : ℕ} {G H X Y : Type*} [Group G] [Group H] + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + {ρ : Representation ℂ G X} {σ : Representation ℂ H Y} + (e : Fin n ≃ Fin a ⊕ Fin b) + (φ : G →* Equiv.Perm (Fin a)) (ψ : H →* Equiv.Perm (Fin b)) + (F : Representation.IntertwiningMap ρ ((wordRep a d).comp φ)) + (Q : Representation.IntertwiningMap σ ((wordRep b d).comp ψ)) : + Representation.IntertwiningMap (outer ρ σ) + ((wordRep n d).comp ((sumPermHom e).comp (φ.prodMap ψ))) where + toLinearMap := (positionTensor e).toLinearMap.comp (TensorProduct.map F.toLinearMap Q.toLinearMap) + isIntertwining' g := by + ext x y w + apply congrFun (a := w) + change positionTensor e (F (ρ g.1 x) ⊗ₜ[ℂ] Q (σ g.2 y)) = + wordRep n d (sumPerm e (φ g.1) (ψ g.2)) (positionTensor e (F x ⊗ₜ[ℂ] Q y)) + rw [F.isIntertwining,Q.isIntertwining,positionTensor_tmul,positionTensor_tmul] + exact (positionProduct_equivariant e (φ g.1) (ψ g.2) (F x) (Q y)).symm + +lemma outerWordMap_injective {n a b d : ℕ} {G H X Y : Type*} [Group G] [Group H] + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + {ρ : Representation ℂ G X} {σ : Representation ℂ H Y} + (e : Fin n ≃ Fin a ⊕ Fin b) + (φ : G →* Equiv.Perm (Fin a)) (ψ : H →* Equiv.Perm (Fin b)) + (F : Representation.IntertwiningMap ρ ((wordRep a d).comp φ)) + (Q : Representation.IntertwiningMap σ ((wordRep b d).comp ψ)) + (hF : Function.Injective F) (hQ : Function.Injective Q) : + Function.Injective (outerWordMap e φ ψ F Q) := + (positionTensor e).injective.comp (TensorProduct.map_injective_of_flat_flat _ _ hF hQ) + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceProjection.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceProjection.lean index 2c221171274b099eb23aa4e57a7f171090002112..b7ed07378028224007fcdc74bb69cc962ebfecd8 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceProjection.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceProjection.lean @@ -1,194 +1,194 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceSeparation -import OAI.RepresentationTheory.UniversalSquare.Support.ProjectedTensor - -namespace OAI - -/-! Balance Projection. -/ - -section - -noncomputable section -namespace Saxl.Balance - -def FixedComponentSums {n d : ℕ} (c : Fin n → ℕ) (z : Fin d → ℤ) - (σ : ℕ → ℤ) (x : WordSpace n d) : Prop := - ∀ w, x w ≠ 0 → ∀ k, ∑ i ∈ Finset.univ.filter (fun i => c i = k), z (w i) = σ k - -def balanceWords {n d : ℕ} (c : Fin n → ℕ) (A : Fin d → Prop) - (label : Fin d → ℕ) (z : Fin d → ℤ) (σ : ℕ → ℤ) - (w : Fin n → Fin d) : Prop := - (∀ i, A (w i)) ∧ ∀ k, - (Finset.univ.filter (fun i => label (w i) = k)).card = - (Finset.univ.filter (fun i => c i = k)).card ∧ - ∑ i ∈ Finset.univ.filter (fun i => label (w i) = k), z (w i) = σ k - -def componentWords {n d : ℕ} (c : Fin n → ℕ) (A : Fin d → Prop) - (label : Fin d → ℕ) (w : Fin n → Fin d) : Prop := - (∀ i, A (w i)) ∧ ∀ i, label (w i) = c i - -lemma perm_filter_card {X : Type*} [Fintype X] [DecidableEq X] - (g : Equiv.Perm X) (p : X → Prop) [DecidablePred p] : - (Finset.univ.filter (fun x => p (g x))).card = (Finset.univ.filter p).card := by - classical - apply Finset.card_bij (fun x _ => g x) - · intro x hx - exact Finset.mem_filter.mpr ⟨Finset.mem_univ _, (Finset.mem_filter.mp hx).2⟩ - · intro x hx y hy hxy - exact g.injective hxy - · intro y hy - refine ⟨g.symm y, ?_, g.apply_symm_apply y⟩ - simpa only [Finset.mem_filter, Finset.mem_univ, true_and, Equiv.apply_symm_apply] - using (Finset.mem_filter.mp hy).2 - -lemma perm_filter_sum {X : Type*} [Fintype X] [DecidableEq X] - (g : Equiv.Perm X) (p : X → Prop) [DecidablePred p] (f : X → ℤ) : - ∑ i ∈ Finset.univ.filter (fun i => p (g i)), f (g i) = - ∑ i ∈ Finset.univ.filter p, f i := by - simpa only [Finset.sum_filter] using - Equiv.sum_comp g (fun i => if p i then f i else 0) - -lemma balanceWords_invariant {n d : ℕ} (c : Fin n → ℕ) (A : Fin d → Prop) - (label : Fin d → ℕ) (z : Fin d → ℤ) (σ : ℕ → ℤ) - (g : Equiv.Perm (Fin n)) (w : Fin n → Fin d) : - balanceWords c A label z σ (w ∘ g) ↔ balanceWords c A label z σ w := by - classical - unfold balanceWords - have hc (k) := perm_filter_card g (fun i => label (w i) = k) - have hs (k) := perm_filter_sum g (fun i => label (w i) = k) (fun i => z (w i)) - simp only [Function.comp_apply, hc, hs] - constructor - · rintro ⟨h,hc⟩ - exact ⟨fun i => by simpa using h (g.symm i),hc⟩ - · rintro ⟨h,hc⟩ - exact ⟨fun i => h (g i),hc⟩ - -lemma balanceWords_iff_components {n d : ℕ} (c : Fin n → ℕ) (A : Fin d → Prop) - (label : Fin d → ℕ) (z : Fin d → ℤ) (σ : ℕ → ℤ) - (ho : ∀ a b, A a → A b → label a < label b → z a < z b) - (w : Fin n → Fin d) - (hw : ∀ k, ∑ i ∈ Finset.univ.filter (fun i => c i = k), z (w i) = σ k) : - balanceWords c A label z σ w ↔ componentWords c A label w := by - classical - constructor - · rintro ⟨hA,hcs⟩ - refine ⟨hA,fun i => ?_⟩ - exact (ordered_output_labels_eq Finset.univ c (fun i => label (w i)) - (fun i => z (w i)) (fun i hi j hj hh => ho _ _ (hA i) (hA j) hh) - (fun k => (hcs k).1.symm) (fun k => (hw k).trans (hcs k).2.symm) - i (Finset.mem_univ i)).symm - · rintro ⟨hA,hl⟩ - refine ⟨hA, fun k => ?_⟩ - simp only [hl] - exact ⟨True.intro,hw k⟩ - -theorem balance_projection_eq {n d : ℕ} (c : Fin n → ℕ) (A : Fin d → Prop) - (label : Fin d → ℕ) (z : Fin d → ℤ) (σ : ℕ → ℤ) - (ho : ∀ a b, A a → A b → label a < label b → z a < z b) - (x : WordSpace n d) (hx : FixedComponentSums c z σ x) : - coordinateProjection (balanceWords c A label z σ) x = - coordinateProjection (componentWords c A label) x := by - classical - funext w - by_cases hw : x w = 0 - · simp only [coordinateProjection_apply, hw, ite_self] - · simp only [coordinateProjection_apply, - balanceWords_iff_components c A label z σ ho w (hx w hw)] - -theorem component_projection_mem {n d : ℕ} (c : Fin n → ℕ) (A : Fin d → Prop) - (label : Fin d → ℕ) (z : Fin d → ℤ) (σ : ℕ → ℤ) - (ho : ∀ a b, A a → A b → label a < label b → z a < z b) - (W : Subrepresentation (wordRep n d)) (x : WordSpace n d) - (hxW : x ∈ W) (hx : FixedComponentSums c z σ x) : - coordinateProjection (componentWords c A label) x ∈ - ((invariantCoordinateProjection (balanceWords c A label z σ) - (balanceWords_invariant c A label z σ)).comp (subrepInclusion W)).range := by - refine ⟨⟨x,hxW⟩, ?_⟩ - exact balance_projection_eq c A label z σ ho x hx - -theorem components_support_transfer {n d : ℕ} {X : Type*} - [AddCommGroup X] [Module ℂ X] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (W : Subrepresentation (wordRep n d)) - (c : Fin n → ℕ) (A : Fin d → Prop) (label : Fin d → ℕ) - (f : X →ₗ[ℂ] WordSpace n d) (hf : f ≠ 0) - (he : ∀ g ∈ fiberGroup c, ∀ x, f (ρ g x) = wordRep n d g (f x)) - (hm : ∀ x, f x ∈ W) - (hs : ∀ x w, f x w ≠ 0 → componentWords c A label w) : - ∃ F : Representation.IntertwiningMap ρ W.toRepresentation, F ≠ 0 := by - classical - let P := coordinateProjection (componentWords c A label) - have hP (x) : P (f x) = f x := by - ext w - change (if componentWords c A label w then f x w else 0) = _ - split_ifs with h - · rfl - · exact (not_ne_iff.mp (fun hh => h (hs x w hh))).symm - have hk (g : Equiv.Perm (Fin n)) (hg : g ∉ fiberGroup c) (x) : - P (wordRep n d g (f x)) = 0 := by - ext w - change (if componentWords c A label w then f x (w ∘ g) else 0) = 0 - split_ifs with hw - · by_contra hn - have hh := hs x (w ∘ g) hn - apply hg - intro i - exact (hw.2 (g i)).symm.trans (hh.2 i) - · rfl - let F := averagedMap ρ (wordRep n d) f - have hF : F ≠ 0 := sector_average_nonzero ρ (wordRep n d) (fiberGroup c) f hf he P hP hk - have hmem (x) : F x ∈ W := by - rw [show F x = _ from averagedMap_apply ρ (wordRep n d) f x] - apply Submodule.sum_mem - intro g hg - exact W.apply_mem_toSubmodule g (hm _) - let T : Representation.IntertwiningMap ρ W.toRepresentation := - { toLinearMap := F.toLinearMap.codRestrict _ hmem - isIntertwining' := by - intro g - apply LinearMap.ext - intro x - apply Subtype.ext - exact LinearMap.congr_fun (F.isIntertwining' g) x } - refine ⟨T, ?_⟩ - intro hz - apply hF - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - exact congrArg Subtype.val (congrArg (fun l => l x) hz) - -theorem balance_support_transfer {n d : ℕ} {X : Type*} - [AddCommGroup X] [Module ℂ X] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (W : Subrepresentation (wordRep n d)) - (c : Fin n → ℕ) (A : Fin d → Prop) (label : Fin d → ℕ) - (z : Fin d → ℤ) (σ : ℕ → ℤ) - (ho : ∀ a b, A a → A b → label a < label b → z a < z b) - (L : X →ₗ[ℂ] WordSpace n d) - (hm : ∀ x, L x ∈ W) (hσ : ∀ x, FixedComponentSums c z σ (L x)) - (hf : (coordinateProjection (componentWords c A label)).comp L ≠ 0) - (he : ∀ g ∈ fiberGroup c, ∀ x, - coordinateProjection (componentWords c A label) (L (ρ g x)) = - wordRep n d g (coordinateProjection (componentWords c A label) (L x))) : - ∃ F : Representation.IntertwiningMap ρ W.toRepresentation, F ≠ 0 := by - classical - let P := (invariantCoordinateProjection (balanceWords c A label z σ) - (balanceWords_invariant c A label z σ)).comp (subrepInclusion W) - let f := (coordinateProjection (componentWords c A label)).comp L - have hmem (x) : f x ∈ P.range := - component_projection_mem c A label z σ ho W (L x) (hm x) (hσ x) - have hsector (x w) (hw : f x w ≠ 0) : componentWords c A label w := by - by_contra hn - exact hw (by change (if componentWords c A label w then L x w else 0) = 0; rw [ite_eq_right hn]) - obtain ⟨T,hT⟩ := components_support_transfer ρ P.range c A label f hf he hmem hsector - obtain ⟨i,hi⟩ := subrepresentation_embeds_of_le_range P P.range le_rfl - refine ⟨i.comp T, ?_⟩ - exact intertwining_comp_ne_zero i hi T hT - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceSeparation +import OAI.RepresentationTheory.UniversalSquare.Support.ProjectedTensor + +namespace OAI + +/-! Balance Projection. -/ + +section + +noncomputable section +namespace Saxl.Balance + +def FixedComponentSums {n d : ℕ} (c : Fin n → ℕ) (z : Fin d → ℤ) + (σ : ℕ → ℤ) (x : WordSpace n d) : Prop := + ∀ w, x w ≠ 0 → ∀ k, ∑ i ∈ Finset.univ.filter (fun i => c i = k), z (w i) = σ k + +def balanceWords {n d : ℕ} (c : Fin n → ℕ) (A : Fin d → Prop) + (label : Fin d → ℕ) (z : Fin d → ℤ) (σ : ℕ → ℤ) + (w : Fin n → Fin d) : Prop := + (∀ i, A (w i)) ∧ ∀ k, + (Finset.univ.filter (fun i => label (w i) = k)).card = + (Finset.univ.filter (fun i => c i = k)).card ∧ + ∑ i ∈ Finset.univ.filter (fun i => label (w i) = k), z (w i) = σ k + +def componentWords {n d : ℕ} (c : Fin n → ℕ) (A : Fin d → Prop) + (label : Fin d → ℕ) (w : Fin n → Fin d) : Prop := + (∀ i, A (w i)) ∧ ∀ i, label (w i) = c i + +lemma perm_filter_card {X : Type*} [Fintype X] [DecidableEq X] + (g : Equiv.Perm X) (p : X → Prop) [DecidablePred p] : + (Finset.univ.filter (fun x => p (g x))).card = (Finset.univ.filter p).card := by + classical + apply Finset.card_bij (fun x _ => g x) + · intro x hx + exact Finset.mem_filter.mpr ⟨Finset.mem_univ _, (Finset.mem_filter.mp hx).2⟩ + · intro x hx y hy hxy + exact g.injective hxy + · intro y hy + refine ⟨g.symm y, ?_, g.apply_symm_apply y⟩ + simpa only [Finset.mem_filter, Finset.mem_univ, true_and, Equiv.apply_symm_apply] + using (Finset.mem_filter.mp hy).2 + +lemma perm_filter_sum {X : Type*} [Fintype X] [DecidableEq X] + (g : Equiv.Perm X) (p : X → Prop) [DecidablePred p] (f : X → ℤ) : + ∑ i ∈ Finset.univ.filter (fun i => p (g i)), f (g i) = + ∑ i ∈ Finset.univ.filter p, f i := by + simpa only [Finset.sum_filter] using + Equiv.sum_comp g (fun i => if p i then f i else 0) + +lemma balanceWords_invariant {n d : ℕ} (c : Fin n → ℕ) (A : Fin d → Prop) + (label : Fin d → ℕ) (z : Fin d → ℤ) (σ : ℕ → ℤ) + (g : Equiv.Perm (Fin n)) (w : Fin n → Fin d) : + balanceWords c A label z σ (w ∘ g) ↔ balanceWords c A label z σ w := by + classical + unfold balanceWords + have hc (k) := perm_filter_card g (fun i => label (w i) = k) + have hs (k) := perm_filter_sum g (fun i => label (w i) = k) (fun i => z (w i)) + simp only [Function.comp_apply, hc, hs] + constructor + · rintro ⟨h,hc⟩ + exact ⟨fun i => by simpa using h (g.symm i),hc⟩ + · rintro ⟨h,hc⟩ + exact ⟨fun i => h (g i),hc⟩ + +lemma balanceWords_iff_components {n d : ℕ} (c : Fin n → ℕ) (A : Fin d → Prop) + (label : Fin d → ℕ) (z : Fin d → ℤ) (σ : ℕ → ℤ) + (ho : ∀ a b, A a → A b → label a < label b → z a < z b) + (w : Fin n → Fin d) + (hw : ∀ k, ∑ i ∈ Finset.univ.filter (fun i => c i = k), z (w i) = σ k) : + balanceWords c A label z σ w ↔ componentWords c A label w := by + classical + constructor + · rintro ⟨hA,hcs⟩ + refine ⟨hA,fun i => ?_⟩ + exact (ordered_output_labels_eq Finset.univ c (fun i => label (w i)) + (fun i => z (w i)) (fun i hi j hj hh => ho _ _ (hA i) (hA j) hh) + (fun k => (hcs k).1.symm) (fun k => (hw k).trans (hcs k).2.symm) + i (Finset.mem_univ i)).symm + · rintro ⟨hA,hl⟩ + refine ⟨hA, fun k => ?_⟩ + simp only [hl] + exact ⟨True.intro,hw k⟩ + +theorem balance_projection_eq {n d : ℕ} (c : Fin n → ℕ) (A : Fin d → Prop) + (label : Fin d → ℕ) (z : Fin d → ℤ) (σ : ℕ → ℤ) + (ho : ∀ a b, A a → A b → label a < label b → z a < z b) + (x : WordSpace n d) (hx : FixedComponentSums c z σ x) : + coordinateProjection (balanceWords c A label z σ) x = + coordinateProjection (componentWords c A label) x := by + classical + funext w + by_cases hw : x w = 0 + · simp only [coordinateProjection_apply, hw, ite_self] + · simp only [coordinateProjection_apply, + balanceWords_iff_components c A label z σ ho w (hx w hw)] + +theorem component_projection_mem {n d : ℕ} (c : Fin n → ℕ) (A : Fin d → Prop) + (label : Fin d → ℕ) (z : Fin d → ℤ) (σ : ℕ → ℤ) + (ho : ∀ a b, A a → A b → label a < label b → z a < z b) + (W : Subrepresentation (wordRep n d)) (x : WordSpace n d) + (hxW : x ∈ W) (hx : FixedComponentSums c z σ x) : + coordinateProjection (componentWords c A label) x ∈ + ((invariantCoordinateProjection (balanceWords c A label z σ) + (balanceWords_invariant c A label z σ)).comp (subrepInclusion W)).range := by + refine ⟨⟨x,hxW⟩, ?_⟩ + exact balance_projection_eq c A label z σ ho x hx + +theorem components_support_transfer {n d : ℕ} {X : Type*} + [AddCommGroup X] [Module ℂ X] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (W : Subrepresentation (wordRep n d)) + (c : Fin n → ℕ) (A : Fin d → Prop) (label : Fin d → ℕ) + (f : X →ₗ[ℂ] WordSpace n d) (hf : f ≠ 0) + (he : ∀ g ∈ fiberGroup c, ∀ x, f (ρ g x) = wordRep n d g (f x)) + (hm : ∀ x, f x ∈ W) + (hs : ∀ x w, f x w ≠ 0 → componentWords c A label w) : + ∃ F : Representation.IntertwiningMap ρ W.toRepresentation, F ≠ 0 := by + classical + let P := coordinateProjection (componentWords c A label) + have hP (x) : P (f x) = f x := by + ext w + change (if componentWords c A label w then f x w else 0) = _ + split_ifs with h + · rfl + · exact (not_ne_iff.mp (fun hh => h (hs x w hh))).symm + have hk (g : Equiv.Perm (Fin n)) (hg : g ∉ fiberGroup c) (x) : + P (wordRep n d g (f x)) = 0 := by + ext w + change (if componentWords c A label w then f x (w ∘ g) else 0) = 0 + split_ifs with hw + · by_contra hn + have hh := hs x (w ∘ g) hn + apply hg + intro i + exact (hw.2 (g i)).symm.trans (hh.2 i) + · rfl + let F := averagedMap ρ (wordRep n d) f + have hF : F ≠ 0 := sector_average_nonzero ρ (wordRep n d) (fiberGroup c) f hf he P hP hk + have hmem (x) : F x ∈ W := by + rw [show F x = _ from averagedMap_apply ρ (wordRep n d) f x] + apply Submodule.sum_mem + intro g hg + exact W.apply_mem_toSubmodule g (hm _) + let T : Representation.IntertwiningMap ρ W.toRepresentation := + { toLinearMap := F.toLinearMap.codRestrict _ hmem + isIntertwining' := by + intro g + apply LinearMap.ext + intro x + apply Subtype.ext + exact LinearMap.congr_fun (F.isIntertwining' g) x } + refine ⟨T, ?_⟩ + intro hz + apply hF + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + exact congrArg Subtype.val (congrArg (fun l => l x) hz) + +theorem balance_support_transfer {n d : ℕ} {X : Type*} + [AddCommGroup X] [Module ℂ X] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (W : Subrepresentation (wordRep n d)) + (c : Fin n → ℕ) (A : Fin d → Prop) (label : Fin d → ℕ) + (z : Fin d → ℤ) (σ : ℕ → ℤ) + (ho : ∀ a b, A a → A b → label a < label b → z a < z b) + (L : X →ₗ[ℂ] WordSpace n d) + (hm : ∀ x, L x ∈ W) (hσ : ∀ x, FixedComponentSums c z σ (L x)) + (hf : (coordinateProjection (componentWords c A label)).comp L ≠ 0) + (he : ∀ g ∈ fiberGroup c, ∀ x, + coordinateProjection (componentWords c A label) (L (ρ g x)) = + wordRep n d g (coordinateProjection (componentWords c A label) (L x))) : + ∃ F : Representation.IntertwiningMap ρ W.toRepresentation, F ≠ 0 := by + classical + let P := (invariantCoordinateProjection (balanceWords c A label z σ) + (balanceWords_invariant c A label z σ)).comp (subrepInclusion W) + let f := (coordinateProjection (componentWords c A label)).comp L + have hmem (x) : f x ∈ P.range := + component_projection_mem c A label z σ ho W (L x) (hm x) (hσ x) + have hsector (x w) (hw : f x w ≠ 0) : componentWords c A label w := by + by_contra hn + exact hw (by change (if componentWords c A label w then L x w else 0) = 0; rw [ite_eq_right hn]) + obtain ⟨T,hT⟩ := components_support_transfer ρ P.range c A label f hf he hmem hsector + obtain ⟨i,hi⟩ := subrepresentation_embeds_of_le_range P P.range le_rfl + refine ⟨i.comp T, ?_⟩ + exact intertwining_comp_ne_zero i hi T hT + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceSeparation.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceSeparation.lean index bd3e22afab5625117ecdefe463e08e312f7bc42a..35c84168ded43feae01b48e1db934ebeb7c53e74 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceSeparation.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalanceSeparation.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.SquareDetection - -namespace OAI - -/-! Balance Separation. -/ - -section - -noncomputable section -namespace Saxl - -lemma equal_sets_of_card_sum_gap {X : Type*} [DecidableEq X] - (A B : Finset X) (z : X → ℤ) (hc : A.card = B.card) - (hz : ∑ x ∈ A, z x = ∑ x ∈ B, z x) - (hgap : ∀ x ∈ A \ B, ∀ y ∈ B \ A, z y < z x) : A = B := by - classical - have he := Finset.card_sdiff_comm hc - let e : ↥(A \ B) ≃ ↥(B \ A) := Finset.equivOfCardEq he - have hsum : ∑ x ∈ A \ B, z x = ∑ x ∈ B \ A, z x := by - have h₁ := Finset.sum_sdiff_eq_sub (f := z) (Finset.inter_subset_left (s₁ := A) (s₂ := B)) - have h₂ := Finset.sum_sdiff_eq_sub (f := z) (Finset.inter_subset_right (s₁ := A) (s₂ := B)) - simp only [Finset.sdiff_inter_self_left, Finset.sdiff_inter_self_right] at h₁ h₂ - rw [h₁, h₂, hz] - have hn : A \ B = ∅ := by - by_contra hn - have hs : (Finset.univ : Finset ↥(A \ B)).Nonempty := by - obtain ⟨x,hx⟩ := Finset.nonempty_iff_ne_empty.mpr hn - exact ⟨⟨x,hx⟩,Finset.mem_univ _⟩ - have hh : (∑ x : ↥(A \ B), z (e x)) < ∑ x : ↥(A \ B), z x := by - apply Finset.sum_lt_sum_of_nonempty hs - intro x hx - exact hgap x.val x.property (e x).val (e x).property - rw [Equiv.sum_comp e (fun y : ↥(B \ A) => z y), - Finset.sum_coe_sort, Finset.sum_coe_sort, hsum] at hh - exact lt_irrefl _ hh - exact Finset.eq_of_subset_of_card_le (Finset.sdiff_eq_empty_iff_subset.mp hn) hc.ge - -theorem ordered_output_fibers_eq {X : Type*} [DecidableEq X] - (s : Finset X) (a b : X → ℕ) (z : X → ℤ) - (ho : ∀ x ∈ s, ∀ y ∈ s, b x < b y → z x < z y) - (hc : ∀ k, (s.filter (fun x => a x = k)).card = - (s.filter (fun x => b x = k)).card) - (hz : ∀ k, ∑ x ∈ s.filter (fun x => a x = k), z x = - ∑ x ∈ s.filter (fun x => b x = k), z x) : - ∀ k, s.filter (fun x => a x = k) = s.filter (fun x => b x = k) := by - classical - intro k - induction k using Nat.strong_induction_on with - | h k ih => - apply equal_sets_of_card_sum_gap _ _ z (hc k) (hz k) - intro x hx y hy - obtain ⟨hxA,hxB⟩ := Finset.mem_sdiff.mp hx - obtain ⟨hyB,hyA⟩ := Finset.mem_sdiff.mp hy - obtain ⟨hxs,hxa⟩ := Finset.mem_filter.mp hxA - obtain ⟨hys,hyb⟩ := Finset.mem_filter.mp hyB - have hxne : b x ≠ k := by - intro hh - exact hxB (Finset.mem_filter.mpr ⟨hxs,hh⟩) - have hxge : k ≤ b x := by - by_contra hh - have hh' : b x < k := Nat.lt_of_not_ge hh - have hi := ih (b x) hh' - have hx' : x ∈ s.filter (fun w => a w = b x) := by - rw [hi] - exact Finset.mem_filter.mpr ⟨hxs,rfl⟩ - have ha := (Finset.mem_filter.mp hx').2 - omega - exact ho y hys x hxs (by omega) - -lemma ordered_output_labels_eq {X : Type*} [DecidableEq X] - (s : Finset X) (a b : X → ℕ) (z : X → ℤ) - (ho : ∀ x ∈ s, ∀ y ∈ s, b x < b y → z x < z y) - (hc : ∀ k, (s.filter (fun x => a x = k)).card = - (s.filter (fun x => b x = k)).card) - (hz : ∀ k, ∑ x ∈ s.filter (fun x => a x = k), z x = - ∑ x ∈ s.filter (fun x => b x = k), z x) : - ∀ x ∈ s, a x = b x := by - intro x hx - have he := ordered_output_fibers_eq s a b z ho hc hz (b x) - have hh : x ∈ s.filter (fun w => a w = b x) := by - rw [he] - exact Finset.mem_filter.mpr ⟨hx,rfl⟩ - exact (Finset.mem_filter.mp hh).2 - -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.SquareDetection + +namespace OAI + +/-! Balance Separation. -/ + +section + +noncomputable section +namespace Saxl + +lemma equal_sets_of_card_sum_gap {X : Type*} [DecidableEq X] + (A B : Finset X) (z : X → ℤ) (hc : A.card = B.card) + (hz : ∑ x ∈ A, z x = ∑ x ∈ B, z x) + (hgap : ∀ x ∈ A \ B, ∀ y ∈ B \ A, z y < z x) : A = B := by + classical + have he := Finset.card_sdiff_comm hc + let e : ↥(A \ B) ≃ ↥(B \ A) := Finset.equivOfCardEq he + have hsum : ∑ x ∈ A \ B, z x = ∑ x ∈ B \ A, z x := by + have h₁ := Finset.sum_sdiff_eq_sub (f := z) (Finset.inter_subset_left (s₁ := A) (s₂ := B)) + have h₂ := Finset.sum_sdiff_eq_sub (f := z) (Finset.inter_subset_right (s₁ := A) (s₂ := B)) + simp only [Finset.sdiff_inter_self_left, Finset.sdiff_inter_self_right] at h₁ h₂ + rw [h₁, h₂, hz] + have hn : A \ B = ∅ := by + by_contra hn + have hs : (Finset.univ : Finset ↥(A \ B)).Nonempty := by + obtain ⟨x,hx⟩ := Finset.nonempty_iff_ne_empty.mpr hn + exact ⟨⟨x,hx⟩,Finset.mem_univ _⟩ + have hh : (∑ x : ↥(A \ B), z (e x)) < ∑ x : ↥(A \ B), z x := by + apply Finset.sum_lt_sum_of_nonempty hs + intro x hx + exact hgap x.val x.property (e x).val (e x).property + rw [Equiv.sum_comp e (fun y : ↥(B \ A) => z y), + Finset.sum_coe_sort, Finset.sum_coe_sort, hsum] at hh + exact lt_irrefl _ hh + exact Finset.eq_of_subset_of_card_le (Finset.sdiff_eq_empty_iff_subset.mp hn) hc.ge + +theorem ordered_output_fibers_eq {X : Type*} [DecidableEq X] + (s : Finset X) (a b : X → ℕ) (z : X → ℤ) + (ho : ∀ x ∈ s, ∀ y ∈ s, b x < b y → z x < z y) + (hc : ∀ k, (s.filter (fun x => a x = k)).card = + (s.filter (fun x => b x = k)).card) + (hz : ∀ k, ∑ x ∈ s.filter (fun x => a x = k), z x = + ∑ x ∈ s.filter (fun x => b x = k), z x) : + ∀ k, s.filter (fun x => a x = k) = s.filter (fun x => b x = k) := by + classical + intro k + induction k using Nat.strong_induction_on with + | h k ih => + apply equal_sets_of_card_sum_gap _ _ z (hc k) (hz k) + intro x hx y hy + obtain ⟨hxA,hxB⟩ := Finset.mem_sdiff.mp hx + obtain ⟨hyB,hyA⟩ := Finset.mem_sdiff.mp hy + obtain ⟨hxs,hxa⟩ := Finset.mem_filter.mp hxA + obtain ⟨hys,hyb⟩ := Finset.mem_filter.mp hyB + have hxne : b x ≠ k := by + intro hh + exact hxB (Finset.mem_filter.mpr ⟨hxs,hh⟩) + have hxge : k ≤ b x := by + by_contra hh + have hh' : b x < k := Nat.lt_of_not_ge hh + have hi := ih (b x) hh' + have hx' : x ∈ s.filter (fun w => a w = b x) := by + rw [hi] + exact Finset.mem_filter.mpr ⟨hxs,rfl⟩ + have ha := (Finset.mem_filter.mp hx').2 + omega + exact ho y hys x hxs (by omega) + +lemma ordered_output_labels_eq {X : Type*} [DecidableEq X] + (s : Finset X) (a b : X → ℕ) (z : X → ℤ) + (ho : ∀ x ∈ s, ∀ y ∈ s, b x < b y → z x < z y) + (hc : ∀ k, (s.filter (fun x => a x = k)).card = + (s.filter (fun x => b x = k)).card) + (hz : ∀ k, ∑ x ∈ s.filter (fun x => a x = k), z x = + ∑ x ∈ s.filter (fun x => b x = k), z x) : + ∀ x ∈ s, a x = b x := by + intro x hx + have he := ordered_output_fibers_eq s a b z ho hc hz (b x) + have hh : x ∈ s.filter (fun w => a w = b x) := by + rw [he] + exact Finset.mem_filter.mpr ⟨hx,rfl⟩ + exact (Finset.mem_filter.mp hh).2 + +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalancedColumns.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalancedColumns.lean index c437fd7f0832a33f33e51759d407d317d07df7e7..7dd00d57219ebf2508916af9ffda6ddeb813d706 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalancedColumns.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalancedColumns.lean @@ -1,236 +1,236 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Specht.ZeroColumns -import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking - -namespace OAI - -/-! Balanced Columns. -/ - -section - -noncomputable section -namespace Saxl.Columns - -def doubled {α : Type*} (xs : List α) : List α := xs.flatMap (fun x => [x,x]) - -@[simp] lemma doubled_nil {α : Type*} : doubled ([] : List α) = [] := rfl -@[simp] lemma doubled_cons {α : Type*} (x : α) (xs : List α) : - doubled (x::xs) = x::x::doubled xs := rfl - -lemma doubled_map {α β : Type*} (f : α → β) (xs : List α) : - (doubled xs).map f = doubled (xs.map f) := by - induction xs with - | nil => rfl - | cons x xs ih => simp only [doubled_cons, List.map_cons, ih] - -lemma doubled_sum (xs : List ℕ) : (doubled xs).sum = 2*xs.sum := by - induction xs with - | nil => rfl - | cons x xs ih => simp only [doubled_cons, List.sum_cons, ih]; omega - -lemma doubled_countP {α : Type*} (p : α → Bool) (xs : List α) : - (doubled xs).countP p = 2*xs.countP p := by - induction xs with - | nil => rfl - | cons x xs ih => simp only [doubled_cons, List.countP_cons, ih]; split <;> omega - -lemma doubled_mem {α : Type*} (x : α) (xs : List α) : x ∈ doubled xs ↔ x ∈ xs := by - induction xs with - | nil => simp - | cons a xs ih => simp only [doubled_cons, List.mem_cons, ih, or_self_left] - -lemma doubled_perm {α : Type*} {xs ys : List α} (h : xs.Perm ys) : - (doubled xs).Perm (doubled ys) := - h.flatMap (fun _ _ => List.Perm.refl _) - -theorem balanced_heights (xs : List ℕ) (D : ℕ) (hD : ∀ h ∈ xs, h ≤ 2*D) : - ∃ ps : List (ℕ × ℕ), - ps.map (fun p => p.1+p.2) = xs ∧ - (∀ p ∈ ps, p.1 ≤ D ∧ p.2 ≤ D) ∧ - (ps.map Prod.fst).sum = xs.sum/2 ∧ - (ps.map Prod.snd).sum = (xs.sum+1)/2 := by - induction xs with - | nil => exact ⟨[],rfl,by simp,by simp,by simp⟩ - | cons j xs ih => - obtain ⟨ps,ht,hp,ha,hb⟩ := ih (fun h hh => hD h (by simp [hh])) - let a := if xs.sum % 2 = 0 then j/2 else (j+1)/2 - let b := j-a - have hj := hD j (by simp) - have hab : a + b = j := by unfold b a; split_ifs <;> omega - have haD : a ≤ D := by unfold a; split_ifs <;> omega - have hbD : b ≤ D := by unfold b a; split_ifs <;> omega - refine ⟨(a,b)::ps,?_,?_,?_,?_⟩ - · simp only [List.map_cons, hab, ht] - · intro p hp' - rcases List.mem_cons.mp hp' with rfl | hp' - · exact ⟨haD,hbD⟩ - · exact hp p hp' - · simp only [List.map_cons, List.sum_cons, ha] - unfold a; split_ifs <;> omega - · simp only [List.map_cons, List.sum_cons, hb] - unfold b a; split_ifs <;> omega - -lemma odd_sum_has_odd (xs : List ℕ) (h : xs.sum % 2 = 1) : - ∃ j ∈ xs, j % 2 = 1 := by - induction xs with - | nil => simp at h - | cons j xs ih => - by_cases hj : j % 2 = 1 - · exact ⟨j,by simp,hj⟩ - · have ht : xs.sum % 2 = 1 := by simp only [List.sum_cons] at h; omega - obtain ⟨k,hk,hko⟩ := ih ht - exact ⟨k,List.mem_cons_of_mem _ hk,hko⟩ - -theorem balanced_even_splits (xs : List ℕ) (D : ℕ) - (hD : ∀ h ∈ xs, h ≤ 2*D) (he : xs.sum % 2 = 0) : - ∃ ps : List (ℕ × ℕ), - ps.map (fun p => p.1+p.2) = doubled xs ∧ - (∀ p ∈ ps, p.1 ≤ D ∧ p.2 ≤ D) ∧ - (ps.map Prod.fst).sum = xs.sum ∧ - (ps.map Prod.snd).sum = xs.sum ∧ - (∀ i, Even ((ps.map Prod.fst).countP (fun h => decide (i decide (i p.1+p.2)).Perm (doubled xs) ∧ - (∀ p ∈ ps, p.1 ≤ D ∧ p.2 ≤ D) ∧ - (ps.map Prod.fst).sum = xs.sum ∧ - (ps.map Prod.snd).sum = xs.sum ∧ - ShortColumns.RowParity (xs.sum%2) (columnShape (ps.map Prod.fst)) ∧ - ShortColumns.RowParity (xs.sum%2) (columnShape (ps.map Prod.snd)) := by - by_cases he : xs.sum % 2 = 0 - · obtain ⟨ps,ht,hp,ha,hb,hra,hrb⟩ := balanced_even_splits xs D hD he - refine ⟨ps,ht ▸ List.Perm.refl _,hp,ha,hb,?_,?_⟩ - · simpa only [he, ShortColumns.RowParity, ↓reduceIte, columnShape_rowLen] using hra - · simpa only [he, ShortColumns.RowParity, ↓reduceIte, columnShape_rowLen] using hrb - · have ho : xs.sum % 2 = 1 := by omega - obtain ⟨j,hj,hjo⟩ := odd_sum_has_odd xs ho - let ys := xs.erase j - have hperm : xs.Perm (j::ys) := List.perm_cons_erase hj - have hsum : xs.sum = j + ys.sum := by simpa only [List.sum_cons] using hperm.sum_eq - have hys : ys.sum % 2 = 0 := by omega - have hDy : ∀ h ∈ ys, h ≤ 2*D := by - intro h hh; exact hD h ((hperm.mem_iff).mpr (List.mem_cons_of_mem _ hh)) - obtain ⟨ps,ht,hp,ha,hb,hra,hrb⟩ := balanced_even_splits ys D hDy hys - let k := j/2 - have hjk : j = 2*k+1 := by dsimp [k]; omega - have hkD : k+1 ≤ D := by have := hD j hj; omega - let qs := (k+1,k)::(k,k+1)::ps - have hta : (qs.map Prod.fst) = (k+1)::k::(ps.map Prod.fst) := rfl - have htb : (qs.map Prod.snd) = k::(k+1)::(ps.map Prod.snd) := rfl - have rowVals (zs : List ℕ) (i : ℕ) : - ((k+1)::k::zs).countP (fun h => decide (i decide (i omega - have hpA : ShortColumns.RowParity 1 (columnShape (qs.map Prod.fst)) := by - simp only [ShortColumns.RowParity, Nat.one_ne_zero, ite_false] - refine ⟨k,?_,?_⟩ - · rw [columnShape_rowLen,hta,rowVals] - simp only [lt_self_iff_false, ite_false] - exact (hra k).add_odd odd_one - · intro i hi - rw [columnShape_rowLen,hta,rowVals] - simp only [hi, ite_false] - split_ifs - · exact (hra i).add (by decide : Even 2) - · simpa using hra i - have countSwap (i : ℕ) : - (qs.map Prod.snd).countP (fun h => decide (i decide (i p.1+p.2) = doubled (j::ys) := by - simp only [qs,List.map_cons,ht,doubled_cons] - rw [show k+1+k = j by omega, show k+(k+1) = j by omega] - exact ht' ▸ (doubled_perm hperm).symm - · intro p hh - rcases List.mem_cons.mp hh with rfl | hh - · exact ⟨hkD,by omega⟩ - · rcases List.mem_cons.mp hh with rfl | hh - · exact ⟨by omega,hkD⟩ - · exact hp p hh - · rw [hta,List.sum_cons,List.sum_cons,ha]; omega - · rw [htb,List.sum_cons,List.sum_cons,hb]; omega - -lemma columnShape_perm {xs ys : List ℕ} (hp : xs.Perm ys) : - columnShape xs = columnShape ys := by - apply YoungDiagram.ext - apply Finset.ext - rintro ⟨i,j⟩ - change (i,j) ∈ columnShape xs ↔ (i,j) ∈ columnShape ys - rw [YoungDiagram.mem_iff_lt_rowLen, YoungDiagram.mem_iff_lt_rowLen, - columnShape_rowLen, columnShape_rowLen, hp.countP_eq] - -lemma count_columns (μ : YoungDiagram) (i : ℕ) : - μ.transpose.rowLens.countP (fun h => decide (i rfl) i).symm - -lemma columnShape_doubled_halfRows (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) : - columnShape (doubled (halfRows μ).transpose.rowLens) = μ := by - apply YoungDiagram.ext - apply Finset.ext - rintro ⟨i,j⟩ - change (i,j) ∈ columnShape _ ↔ (i,j) ∈ μ - rw [YoungDiagram.mem_iff_lt_rowLen, YoungDiagram.mem_iff_lt_rowLen, - columnShape_rowLen,doubled_countP,count_columns,halfRows_rowLen] - have hh := (Nat.even_iff.mp (he i)) - omega - -lemma columns_bounded (μ : YoungDiagram) (D : ℕ) (hD : μ.colLen 0 ≤ D) : - ∀ h ∈ μ.transpose.rowLens, h ≤ D := by - intro h hh - obtain ⟨i,hi,rfl⟩ := List.mem_map.mp hh - exact le_trans (by simpa only [YoungDiagram.rowLen_transpose] using μ.colLen_anti 0 i (Nat.zero_le _)) hD - -theorem even_rows_allocation (r D : ℕ) (μ : YoungDiagram) (hm : μ.card = 2*r) - (he : ∀ i, Even (μ.rowLen i)) (hD : μ.colLen 0 ≤ 2*D) : - ∃ ps : List (ℕ × ℕ), - columnShape (ps.map (fun p => p.1+p.2)) = μ ∧ - (∀ p ∈ ps, p.1 ≤ D ∧ p.2 ≤ D) ∧ - (ps.map Prod.fst).sum = r ∧ (ps.map Prod.snd).sum = r ∧ - ShortColumns.RowParity (r%2) (columnShape (ps.map Prod.fst)) ∧ - ShortColumns.RowParity (r%2) (columnShape (ps.map Prod.snd)) := by - let xs := (halfRows μ).transpose.rowLens - have hx : xs.sum = r := by - have hc := placed_card (toYoung (halfRows μ)) - have hc' := halfRows_card μ he - change (halfRows μ).card = xs.sum at hc - omega - obtain ⟨ps,ht,hp,ha,hb,hpa,hpb⟩ := balanced_double_splits xs D - (columns_bounded (halfRows μ) (2*D) (by rwa [halfRows_height μ he])) - refine ⟨ps,?_,hp,ha.trans hx,hb.trans hx,?_,?_⟩ - · exact (columnShape_perm ht).trans (columnShape_doubled_halfRows μ he) - · rwa [hx] at hpa - · rwa [hx] at hpb - -end Saxl.Columns -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Specht.ZeroColumns +import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking + +namespace OAI + +/-! Balanced Columns. -/ + +section + +noncomputable section +namespace Saxl.Columns + +def doubled {α : Type*} (xs : List α) : List α := xs.flatMap (fun x => [x,x]) + +@[simp] lemma doubled_nil {α : Type*} : doubled ([] : List α) = [] := rfl +@[simp] lemma doubled_cons {α : Type*} (x : α) (xs : List α) : + doubled (x::xs) = x::x::doubled xs := rfl + +lemma doubled_map {α β : Type*} (f : α → β) (xs : List α) : + (doubled xs).map f = doubled (xs.map f) := by + induction xs with + | nil => rfl + | cons x xs ih => simp only [doubled_cons, List.map_cons, ih] + +lemma doubled_sum (xs : List ℕ) : (doubled xs).sum = 2*xs.sum := by + induction xs with + | nil => rfl + | cons x xs ih => simp only [doubled_cons, List.sum_cons, ih]; omega + +lemma doubled_countP {α : Type*} (p : α → Bool) (xs : List α) : + (doubled xs).countP p = 2*xs.countP p := by + induction xs with + | nil => rfl + | cons x xs ih => simp only [doubled_cons, List.countP_cons, ih]; split <;> omega + +lemma doubled_mem {α : Type*} (x : α) (xs : List α) : x ∈ doubled xs ↔ x ∈ xs := by + induction xs with + | nil => simp + | cons a xs ih => simp only [doubled_cons, List.mem_cons, ih, or_self_left] + +lemma doubled_perm {α : Type*} {xs ys : List α} (h : xs.Perm ys) : + (doubled xs).Perm (doubled ys) := + h.flatMap (fun _ _ => List.Perm.refl _) + +theorem balanced_heights (xs : List ℕ) (D : ℕ) (hD : ∀ h ∈ xs, h ≤ 2*D) : + ∃ ps : List (ℕ × ℕ), + ps.map (fun p => p.1+p.2) = xs ∧ + (∀ p ∈ ps, p.1 ≤ D ∧ p.2 ≤ D) ∧ + (ps.map Prod.fst).sum = xs.sum/2 ∧ + (ps.map Prod.snd).sum = (xs.sum+1)/2 := by + induction xs with + | nil => exact ⟨[],rfl,by simp,by simp,by simp⟩ + | cons j xs ih => + obtain ⟨ps,ht,hp,ha,hb⟩ := ih (fun h hh => hD h (by simp [hh])) + let a := if xs.sum % 2 = 0 then j/2 else (j+1)/2 + let b := j-a + have hj := hD j (by simp) + have hab : a + b = j := by unfold b a; split_ifs <;> omega + have haD : a ≤ D := by unfold a; split_ifs <;> omega + have hbD : b ≤ D := by unfold b a; split_ifs <;> omega + refine ⟨(a,b)::ps,?_,?_,?_,?_⟩ + · simp only [List.map_cons, hab, ht] + · intro p hp' + rcases List.mem_cons.mp hp' with rfl | hp' + · exact ⟨haD,hbD⟩ + · exact hp p hp' + · simp only [List.map_cons, List.sum_cons, ha] + unfold a; split_ifs <;> omega + · simp only [List.map_cons, List.sum_cons, hb] + unfold b a; split_ifs <;> omega + +lemma odd_sum_has_odd (xs : List ℕ) (h : xs.sum % 2 = 1) : + ∃ j ∈ xs, j % 2 = 1 := by + induction xs with + | nil => simp at h + | cons j xs ih => + by_cases hj : j % 2 = 1 + · exact ⟨j,by simp,hj⟩ + · have ht : xs.sum % 2 = 1 := by simp only [List.sum_cons] at h; omega + obtain ⟨k,hk,hko⟩ := ih ht + exact ⟨k,List.mem_cons_of_mem _ hk,hko⟩ + +theorem balanced_even_splits (xs : List ℕ) (D : ℕ) + (hD : ∀ h ∈ xs, h ≤ 2*D) (he : xs.sum % 2 = 0) : + ∃ ps : List (ℕ × ℕ), + ps.map (fun p => p.1+p.2) = doubled xs ∧ + (∀ p ∈ ps, p.1 ≤ D ∧ p.2 ≤ D) ∧ + (ps.map Prod.fst).sum = xs.sum ∧ + (ps.map Prod.snd).sum = xs.sum ∧ + (∀ i, Even ((ps.map Prod.fst).countP (fun h => decide (i decide (i p.1+p.2)).Perm (doubled xs) ∧ + (∀ p ∈ ps, p.1 ≤ D ∧ p.2 ≤ D) ∧ + (ps.map Prod.fst).sum = xs.sum ∧ + (ps.map Prod.snd).sum = xs.sum ∧ + ShortColumns.RowParity (xs.sum%2) (columnShape (ps.map Prod.fst)) ∧ + ShortColumns.RowParity (xs.sum%2) (columnShape (ps.map Prod.snd)) := by + by_cases he : xs.sum % 2 = 0 + · obtain ⟨ps,ht,hp,ha,hb,hra,hrb⟩ := balanced_even_splits xs D hD he + refine ⟨ps,ht ▸ List.Perm.refl _,hp,ha,hb,?_,?_⟩ + · simpa only [he, ShortColumns.RowParity, ↓reduceIte, columnShape_rowLen] using hra + · simpa only [he, ShortColumns.RowParity, ↓reduceIte, columnShape_rowLen] using hrb + · have ho : xs.sum % 2 = 1 := by omega + obtain ⟨j,hj,hjo⟩ := odd_sum_has_odd xs ho + let ys := xs.erase j + have hperm : xs.Perm (j::ys) := List.perm_cons_erase hj + have hsum : xs.sum = j + ys.sum := by simpa only [List.sum_cons] using hperm.sum_eq + have hys : ys.sum % 2 = 0 := by omega + have hDy : ∀ h ∈ ys, h ≤ 2*D := by + intro h hh; exact hD h ((hperm.mem_iff).mpr (List.mem_cons_of_mem _ hh)) + obtain ⟨ps,ht,hp,ha,hb,hra,hrb⟩ := balanced_even_splits ys D hDy hys + let k := j/2 + have hjk : j = 2*k+1 := by dsimp [k]; omega + have hkD : k+1 ≤ D := by have := hD j hj; omega + let qs := (k+1,k)::(k,k+1)::ps + have hta : (qs.map Prod.fst) = (k+1)::k::(ps.map Prod.fst) := rfl + have htb : (qs.map Prod.snd) = k::(k+1)::(ps.map Prod.snd) := rfl + have rowVals (zs : List ℕ) (i : ℕ) : + ((k+1)::k::zs).countP (fun h => decide (i decide (i omega + have hpA : ShortColumns.RowParity 1 (columnShape (qs.map Prod.fst)) := by + simp only [ShortColumns.RowParity, Nat.one_ne_zero, ite_false] + refine ⟨k,?_,?_⟩ + · rw [columnShape_rowLen,hta,rowVals] + simp only [lt_self_iff_false, ite_false] + exact (hra k).add_odd odd_one + · intro i hi + rw [columnShape_rowLen,hta,rowVals] + simp only [hi, ite_false] + split_ifs + · exact (hra i).add (by decide : Even 2) + · simpa using hra i + have countSwap (i : ℕ) : + (qs.map Prod.snd).countP (fun h => decide (i decide (i p.1+p.2) = doubled (j::ys) := by + simp only [qs,List.map_cons,ht,doubled_cons] + rw [show k+1+k = j by omega, show k+(k+1) = j by omega] + exact ht' ▸ (doubled_perm hperm).symm + · intro p hh + rcases List.mem_cons.mp hh with rfl | hh + · exact ⟨hkD,by omega⟩ + · rcases List.mem_cons.mp hh with rfl | hh + · exact ⟨by omega,hkD⟩ + · exact hp p hh + · rw [hta,List.sum_cons,List.sum_cons,ha]; omega + · rw [htb,List.sum_cons,List.sum_cons,hb]; omega + +lemma columnShape_perm {xs ys : List ℕ} (hp : xs.Perm ys) : + columnShape xs = columnShape ys := by + apply YoungDiagram.ext + apply Finset.ext + rintro ⟨i,j⟩ + change (i,j) ∈ columnShape xs ↔ (i,j) ∈ columnShape ys + rw [YoungDiagram.mem_iff_lt_rowLen, YoungDiagram.mem_iff_lt_rowLen, + columnShape_rowLen, columnShape_rowLen, hp.countP_eq] + +lemma count_columns (μ : YoungDiagram) (i : ℕ) : + μ.transpose.rowLens.countP (fun h => decide (i rfl) i).symm + +lemma columnShape_doubled_halfRows (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) : + columnShape (doubled (halfRows μ).transpose.rowLens) = μ := by + apply YoungDiagram.ext + apply Finset.ext + rintro ⟨i,j⟩ + change (i,j) ∈ columnShape _ ↔ (i,j) ∈ μ + rw [YoungDiagram.mem_iff_lt_rowLen, YoungDiagram.mem_iff_lt_rowLen, + columnShape_rowLen,doubled_countP,count_columns,halfRows_rowLen] + have hh := (Nat.even_iff.mp (he i)) + omega + +lemma columns_bounded (μ : YoungDiagram) (D : ℕ) (hD : μ.colLen 0 ≤ D) : + ∀ h ∈ μ.transpose.rowLens, h ≤ D := by + intro h hh + obtain ⟨i,hi,rfl⟩ := List.mem_map.mp hh + exact le_trans (by simpa only [YoungDiagram.rowLen_transpose] using μ.colLen_anti 0 i (Nat.zero_le _)) hD + +theorem even_rows_allocation (r D : ℕ) (μ : YoungDiagram) (hm : μ.card = 2*r) + (he : ∀ i, Even (μ.rowLen i)) (hD : μ.colLen 0 ≤ 2*D) : + ∃ ps : List (ℕ × ℕ), + columnShape (ps.map (fun p => p.1+p.2)) = μ ∧ + (∀ p ∈ ps, p.1 ≤ D ∧ p.2 ≤ D) ∧ + (ps.map Prod.fst).sum = r ∧ (ps.map Prod.snd).sum = r ∧ + ShortColumns.RowParity (r%2) (columnShape (ps.map Prod.fst)) ∧ + ShortColumns.RowParity (r%2) (columnShape (ps.map Prod.snd)) := by + let xs := (halfRows μ).transpose.rowLens + have hx : xs.sum = r := by + have hc := placed_card (toYoung (halfRows μ)) + have hc' := halfRows_card μ he + change (halfRows μ).card = xs.sum at hc + omega + obtain ⟨ps,ht,hp,ha,hb,hpa,hpb⟩ := balanced_double_splits xs D + (columns_bounded (halfRows μ) (2*D) (by rwa [halfRows_height μ he])) + refine ⟨ps,?_,hp,ha.trans hx,hb.trans hx,?_,?_⟩ + · exact (columnShape_perm ht).trans (columnShape_doubled_halfRows μ he) + · rwa [hx] at hpa + · rwa [hx] at hpb + +end Saxl.Columns +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalancedPairs.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalancedPairs.lean index e55f9970fe2e58b07901ab034ba1f4f4f77c2088..0ee129ad72838ddc996e30bbd11b59a04bdccf9d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalancedPairs.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/BalancedPairs.lean @@ -1,125 +1,125 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking - -namespace OAI - -/-! Balanced Pairs. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl.Balance - -lemma short_height_ge_two (m : ℕ) (hm : 1 ≤ m) : - 2 ≤ (ShortColumns.shape m 0).colLen 0 := by - have hc : (1,0) ∈ ShortColumns.shape m 0 := - (ShortColumns.mem_shape m 0 1 0).mpr (Or.inr ⟨rfl, by omega⟩) - have hh := YoungDiagram.mem_iff_lt_colLen.mp hc - omega - -def pairAtOutputTwo (m : ℕ) (hm : 1 ≤ m) (i : Fin 2) : - Fin ((ShortColumns.shape m 0).colLen 0 * (ShortColumns.shape m 0).colLen 0) := - finProdFinEquiv (Fin.castLE (short_height_ge_two m hm) i, - Fin.castLE (short_height_ge_two m hm) (Fin.rev i)) - -lemma pairAtOutputTwo_output (m : ℕ) (hm : 1 ≤ m) (i : Fin 2) : - output (pairAtOutputTwo m hm i) = 2 := by - simp only [output, pairAtOutputTwo, Equiv.symm_apply_apply, Fin.val_castLE, Fin.val_rev] - have hi := i.isLt - omega - -lemma evenTableau_eval (m : ℕ) (w : Fin (2*m) → Fin ((ShortColumns.shape m 0).colLen 0)) : - polytabloid (ShortColumns.evenTableau m) w = - ShortColumns.evenAlt m (Fin.castLE (ShortColumns.height_le m 0) ∘ w) := by - have he := congrFun (ShortColumns.evenTableau_polytabloid m) - (Fin.castLE (ShortColumns.height_le m 0) ∘ w) - rw [letterLift_eval _ (Fin.castLE_injective _) _ w] at he - exact he - -lemma outputTwo_pair_entry (i j : Fin 2) : - PathLayer.J i j * PathLayer.J (Fin.rev i) (Fin.rev j) = - (-1 : ℂ) * outputTwoForm i j := by - fin_cases i <;> fin_cases j <;> norm_num [PathLayer.J, outputTwoForm, Fin.rev] - -lemma outputTwo_squared_polytabloid (m : ℕ) (hm : 1 ≤ m) - (w : Fin (2*m) → Fin 2) : - wordTensor (2*m) _ _ (polytabloid (ShortColumns.evenTableau m) ⊗ₜ[ℂ] - polytabloid (ShortColumns.evenTableau m)) (pairAtOutputTwo m hm ∘ w) = - ((-1 : ℂ)^m • pairFormTensor (ShortColumns.pairSplit m) outputTwoForm) w := by - rw [wordTensor_tmul, evenTableau_eval, evenTableau_eval] - have hl : Fin.castLE (ShortColumns.height_le m 0) ∘ - splitLeft (pairAtOutputTwo m hm ∘ w) = w := by - funext i - apply Fin.ext - simp [splitLeft, pairAtOutputTwo] - have hr : Fin.castLE (ShortColumns.height_le m 0) ∘ - splitRight (pairAtOutputTwo m hm ∘ w) = Fin.rev ∘ w := by - funext i - apply Fin.ext - simp [splitRight, pairAtOutputTwo] - rw [hl,hr, ShortColumns.evenAlt_formula, ShortColumns.evenAlt_formula, - ← Finset.prod_mul_distrib] - simp only [Function.comp_apply, outputTwo_pair_entry, Finset.prod_mul_distrib, - Finset.prod_const, Finset.card_univ, Fintype.card_fin] - rfl - -theorem repeated_twos (m : ℕ) (hm : 1 ≤ m) - (a b : Tableau (2*m) (ShortColumns.shape m 0)) - (μ : YoungDiagram) (t : Tableau (2*m) μ) - (he : ∀ i, Even (μ.rowLen i)) (hμ : μ.colLen 0 ≤ 2) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (projectedSpechtTensor a b (inOutputs ({2} : Set ℕ)) - (inOutputs_invariant ({2} : Set ℕ))).toRepresentation, Function.Injective F := by - classical - let P := inOutputs (n := 2*m) (d := (ShortColumns.shape m 0).colLen 0) - (e := (ShortColumns.shape m 0).colLen 0) ({2} : Set ℕ) - let hP := inOutputs_invariant (n := 2*m) (d := (ShortColumns.shape m 0).colLen 0) - (e := (ShortColumns.shape m 0).colLen 0) ({2} : Set ℕ) - let W := projectedSpechtTensor a b P hP - have hma : polytabloid (ShortColumns.evenTableau m) ∈ spechtSub a := by - rw [← spechtSub_tableau_independent (ShortColumns.evenTableau m) a] - exact mem_cyclic _ _ - have hmb : polytabloid (ShortColumns.evenTableau m) ∈ spechtSub b := by - rw [← spechtSub_tableau_independent (ShortColumns.evenTableau m) b] - exact mem_cyclic _ _ - let z : W.toSubmodule := projectedTensorQuotient a b P hP - (⟨polytabloid (ShortColumns.evenTableau m),hma⟩ ⊗ₜ[ℂ] - ⟨polytabloid (ShortColumns.evenTableau m),hmb⟩) - let D : Representation.IntertwiningMap W.toRepresentation (wordRep (2*m) 2) := - (restrictLetters (pairAtOutputTwo m hm)).comp (subrepInclusion W) - have hz : D z = (-1 : ℂ)^m • pairFormTensor (ShortColumns.pairSplit m) outputTwoForm := by - funext w - change coordinateProjection P (spechtTensorMap a b - (⟨polytabloid (ShortColumns.evenTableau m),hma⟩ ⊗ₜ[ℂ] - ⟨polytabloid (ShortColumns.evenTableau m),hmb⟩)) - (pairAtOutputTwo m hm ∘ w) = _ - rw [spechtTensorMap, coordinateProjection_apply, ite_eq_left] - · exact outputTwo_squared_polytabloid m hm w - · intro i - exact pairAtOutputTwo_output m hm (w i) - have hs := even_rows_outputTwo_support (ShortColumns.pairSplit m) μ t he hμ - have hc : cyclic (wordRep (2*m) 2) (D z) = - cyclic (wordRep (2*m) 2) (pairFormTensor (ShortColumns.pairSplit m) outputTwoForm) := by - rw [hz, cyclic_smul_eq _ _ _ (pow_ne_zero m (by norm_num))] - rw [← hc] at hs - obtain ⟨f,hf⟩ := hs - obtain ⟨g,hg⟩ := cyclic_projection_support D z f hf - let F := (subrepInclusion (cyclic W.toRepresentation z)).comp g - have hF : F ≠ 0 := by - intro hz - apply hg - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - apply Subtype.ext - exact congrArg (fun H => H x) hz - let := specht_irreducible t - exact ⟨F, (Representation.IsIrreducible.injective_or_eq_zero F).resolve_right hF⟩ - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking + +namespace OAI + +/-! Balanced Pairs. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl.Balance + +lemma short_height_ge_two (m : ℕ) (hm : 1 ≤ m) : + 2 ≤ (ShortColumns.shape m 0).colLen 0 := by + have hc : (1,0) ∈ ShortColumns.shape m 0 := + (ShortColumns.mem_shape m 0 1 0).mpr (Or.inr ⟨rfl, by omega⟩) + have hh := YoungDiagram.mem_iff_lt_colLen.mp hc + omega + +def pairAtOutputTwo (m : ℕ) (hm : 1 ≤ m) (i : Fin 2) : + Fin ((ShortColumns.shape m 0).colLen 0 * (ShortColumns.shape m 0).colLen 0) := + finProdFinEquiv (Fin.castLE (short_height_ge_two m hm) i, + Fin.castLE (short_height_ge_two m hm) (Fin.rev i)) + +lemma pairAtOutputTwo_output (m : ℕ) (hm : 1 ≤ m) (i : Fin 2) : + output (pairAtOutputTwo m hm i) = 2 := by + simp only [output, pairAtOutputTwo, Equiv.symm_apply_apply, Fin.val_castLE, Fin.val_rev] + have hi := i.isLt + omega + +lemma evenTableau_eval (m : ℕ) (w : Fin (2*m) → Fin ((ShortColumns.shape m 0).colLen 0)) : + polytabloid (ShortColumns.evenTableau m) w = + ShortColumns.evenAlt m (Fin.castLE (ShortColumns.height_le m 0) ∘ w) := by + have he := congrFun (ShortColumns.evenTableau_polytabloid m) + (Fin.castLE (ShortColumns.height_le m 0) ∘ w) + rw [letterLift_eval _ (Fin.castLE_injective _) _ w] at he + exact he + +lemma outputTwo_pair_entry (i j : Fin 2) : + PathLayer.J i j * PathLayer.J (Fin.rev i) (Fin.rev j) = + (-1 : ℂ) * outputTwoForm i j := by + fin_cases i <;> fin_cases j <;> norm_num [PathLayer.J, outputTwoForm, Fin.rev] + +lemma outputTwo_squared_polytabloid (m : ℕ) (hm : 1 ≤ m) + (w : Fin (2*m) → Fin 2) : + wordTensor (2*m) _ _ (polytabloid (ShortColumns.evenTableau m) ⊗ₜ[ℂ] + polytabloid (ShortColumns.evenTableau m)) (pairAtOutputTwo m hm ∘ w) = + ((-1 : ℂ)^m • pairFormTensor (ShortColumns.pairSplit m) outputTwoForm) w := by + rw [wordTensor_tmul, evenTableau_eval, evenTableau_eval] + have hl : Fin.castLE (ShortColumns.height_le m 0) ∘ + splitLeft (pairAtOutputTwo m hm ∘ w) = w := by + funext i + apply Fin.ext + simp [splitLeft, pairAtOutputTwo] + have hr : Fin.castLE (ShortColumns.height_le m 0) ∘ + splitRight (pairAtOutputTwo m hm ∘ w) = Fin.rev ∘ w := by + funext i + apply Fin.ext + simp [splitRight, pairAtOutputTwo] + rw [hl,hr, ShortColumns.evenAlt_formula, ShortColumns.evenAlt_formula, + ← Finset.prod_mul_distrib] + simp only [Function.comp_apply, outputTwo_pair_entry, Finset.prod_mul_distrib, + Finset.prod_const, Finset.card_univ, Fintype.card_fin] + rfl + +theorem repeated_twos (m : ℕ) (hm : 1 ≤ m) + (a b : Tableau (2*m) (ShortColumns.shape m 0)) + (μ : YoungDiagram) (t : Tableau (2*m) μ) + (he : ∀ i, Even (μ.rowLen i)) (hμ : μ.colLen 0 ≤ 2) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (projectedSpechtTensor a b (inOutputs ({2} : Set ℕ)) + (inOutputs_invariant ({2} : Set ℕ))).toRepresentation, Function.Injective F := by + classical + let P := inOutputs (n := 2*m) (d := (ShortColumns.shape m 0).colLen 0) + (e := (ShortColumns.shape m 0).colLen 0) ({2} : Set ℕ) + let hP := inOutputs_invariant (n := 2*m) (d := (ShortColumns.shape m 0).colLen 0) + (e := (ShortColumns.shape m 0).colLen 0) ({2} : Set ℕ) + let W := projectedSpechtTensor a b P hP + have hma : polytabloid (ShortColumns.evenTableau m) ∈ spechtSub a := by + rw [← spechtSub_tableau_independent (ShortColumns.evenTableau m) a] + exact mem_cyclic _ _ + have hmb : polytabloid (ShortColumns.evenTableau m) ∈ spechtSub b := by + rw [← spechtSub_tableau_independent (ShortColumns.evenTableau m) b] + exact mem_cyclic _ _ + let z : W.toSubmodule := projectedTensorQuotient a b P hP + (⟨polytabloid (ShortColumns.evenTableau m),hma⟩ ⊗ₜ[ℂ] + ⟨polytabloid (ShortColumns.evenTableau m),hmb⟩) + let D : Representation.IntertwiningMap W.toRepresentation (wordRep (2*m) 2) := + (restrictLetters (pairAtOutputTwo m hm)).comp (subrepInclusion W) + have hz : D z = (-1 : ℂ)^m • pairFormTensor (ShortColumns.pairSplit m) outputTwoForm := by + funext w + change coordinateProjection P (spechtTensorMap a b + (⟨polytabloid (ShortColumns.evenTableau m),hma⟩ ⊗ₜ[ℂ] + ⟨polytabloid (ShortColumns.evenTableau m),hmb⟩)) + (pairAtOutputTwo m hm ∘ w) = _ + rw [spechtTensorMap, coordinateProjection_apply, ite_eq_left] + · exact outputTwo_squared_polytabloid m hm w + · intro i + exact pairAtOutputTwo_output m hm (w i) + have hs := even_rows_outputTwo_support (ShortColumns.pairSplit m) μ t he hμ + have hc : cyclic (wordRep (2*m) 2) (D z) = + cyclic (wordRep (2*m) 2) (pairFormTensor (ShortColumns.pairSplit m) outputTwoForm) := by + rw [hz, cyclic_smul_eq _ _ _ (pow_ne_zero m (by norm_num))] + rw [← hc] at hs + obtain ⟨f,hf⟩ := hs + obtain ⟨g,hg⟩ := cyclic_projection_support D z f hf + let F := (subrepInclusion (cyclic W.toRepresentation z)).comp g + have hF : F ≠ 0 := by + intro hz + apply hg + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + apply Subtype.ext + exact congrArg (fun H => H x) hz + let := specht_irreducible t + exact ⟨F, (Representation.IsIrreducible.injective_or_eq_zero F).resolve_right hF⟩ + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/ConstantOutputs.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/ConstantOutputs.lean index 422ee82c6f4caf3c8e44a08fa211e3e73fb4a1d1..4c7c978a8e277f5338c11d6013b4a33eb9b36b3d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/ConstantOutputs.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/ConstantOutputs.lean @@ -1,117 +1,117 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPacking - -namespace OAI - -/-! Constant Outputs. -/ - -section - -noncomputable section -open scoped TensorProduct Classical -namespace Saxl.Balance - -def constantOutputMap (n d k : ℕ) : - Representation.IntertwiningMap (wordRep n (d*d)) (wordRep n 1) := - wordMap (fun a _ => if output a = k then 1 else 0) - -lemma constantOutputMap_single {n d : ℕ} (k : ℕ) (w : Fin n → Fin (d*d)) - (z : Fin n → Fin 1) : - constantOutputMap n d k (Pi.single w 1) z = - if inOutputs {k} w then 1 else 0 := by - classical - rw [constantOutputMap,wordMap_single] - by_cases h : inOutputs {k} w - · rw [ite_eq_left h] - have he : ∀ i, output (w i) = k := h - simp only [he,ite_true,Finset.prod_const_one] - · rw [ite_eq_right h] - change ¬ ∀ i, output (w i) = k at h - push Not at h - obtain ⟨i,hi⟩ := h - exact Finset.prod_eq_zero (Finset.mem_univ i) (ite_eq_right hi) - -lemma constantOutputMap_projection {n d : ℕ} (k : ℕ) (x : WordSpace n (d*d)) : - constantOutputMap n d k (coordinateProjection (inOutputs {k}) x) = - constantOutputMap n d k x := by - classical - rw [← (Pi.basisFun ℂ (Fin n → Fin (d*d))).sum_repr x] - simp only [map_sum,map_smul,Pi.basisFun_apply,coordinateProjection_single] - apply Finset.sum_congr rfl - intro w hw - by_cases h : inOutputs {k} w - · rw [ite_eq_left h] - · rw [ite_eq_right h,map_zero,smul_zero] - funext z - simp only [Pi.zero_apply,Pi.smul_apply,smul_eq_mul,constantOutputMap_single,ite_eq_right h,mul_zero] - -lemma constantOutputMap_pairSum {n d e : ℕ} (k : ℕ) - (t : Fin n → Fin e) (ht : ∀ i, (t i).val+1 = k) - (x : WordSpace n (d*d)) (z : Fin n → Fin 1) : - constantOutputMap n d k x z = pairSumMap n d e x t := by - classical - rw [← (Pi.basisFun ℂ (Fin n → Fin (d*d))).sum_repr x] - simp only [map_sum,map_smul,Pi.basisFun_apply,Finset.sum_apply,Pi.smul_apply,smul_eq_mul] - apply Finset.sum_congr rfl - intro w hw - congr 1 - rw [constantOutputMap_single,← merge_split w,pairSumMap_single] - congr 1 - apply propext - change (∀ i, output (mergeWords (splitLeft w) (splitRight w) i) = k) ↔ _ - simp only [mergeWords,output,Equiv.symm_apply_apply] - constructor <;> intro h i <;> have hi := ht i <;> have he := h i <;> omega - -theorem constant_output_support {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (k : ℕ) (hk : ∀ i, (columnLengthWord t i).val+1 = k) : - SupportLE (wordRep n 1) - (projectedSpechtTensor t t (inOutputs {k}) (inOutputs_invariant {k})).toRepresentation := by - classical - let W := projectedSpechtTensor t t (inOutputs {k}) (inOutputs_invariant {k}) - let Q := (constantOutputMap n (μ.colLen 0) k).comp (subrepInclusion W) - let v : Specht t := ⟨polytabloid t,mem_cyclic _ _⟩ - let y := projectedTensorQuotient t t (inOutputs {k}) (inOutputs_invariant {k}) (v ⊗ₜ[ℂ] v) - let C : ℂ := (Nat.card (columnGroup t) : ℂ) * signC (columnReversal t).val - have hC : C ≠ 0 := column_projection_coefficient_ne_zero t - have hy (z : Fin n → Fin 1) : Q y z = C := by - change constantOutputMap n (μ.colLen 0) k - (coordinateProjection (inOutputs {k}) (spechtTensorMap t t (v ⊗ₜ[ℂ] v))) z = C - rw [constantOutputMap_projection,constantOutputMap_pairSum k (columnLengthWord t) hk] - have he := congrFun (squared_polytabloid_projection t) (columnLengthWord t) - change (if wordOrbit (columnLengthWord t) (columnLengthWord t) then - pairSumMap n (μ.colLen 0) (μ.colLen 0) - (wordTensor _ _ _ (polytabloid t ⊗ₜ[ℂ] polytabloid t)) (columnLengthWord t) else 0) = _ at he - rw [ite_eq_left ⟨1,rfl⟩,Pi.smul_apply,Pi.single_eq_same,smul_eq_mul,mul_one] at he - unfold spechtTensorMap - exact he - have hQ : Function.Surjective Q := by - intro x - let z : Fin n → Fin 1 := fun _ => 0 - refine ⟨(x z / C) • y,?_⟩ - funext w - rw [map_smul,Pi.smul_apply,smul_eq_mul,hy] - have he : z = w := Subsingleton.elim _ _ - rw [div_mul_cancel₀ _ hC,he] - obtain ⟨s,hs⟩ := intertwining_lift_surjective Q hQ - (Representation.IntertwiningMap.id (wordRep n 1)) - apply SupportLE.of_injective s - intro x y hxy - have he := congrArg Q hxy - change (Q.comp s) x = (Q.comp s) y at he - rw [hs] at he - exact he - -def constantPacking {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) (k : ℕ) - (hk : ∀ i, (columnLengthWord t i).val+1 = k) - (j : ℕ) (A : Fin (μ.colLen 0 * μ.colLen 0) → Prop) - (label : Fin (μ.colLen 0 * μ.colLen 0) → ℕ) - (h : ∀ a, (A a ∧ label a = j) ↔ output a = k) : - Packing (polytabloid t) A label (Pi.single (fun _ : Fin n => (0 : Fin 1)) 1) := - boundedPacking t j {k} A label h (constant_output_support t k hk) _ - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPacking + +namespace OAI + +/-! Constant Outputs. -/ + +section + +noncomputable section +open scoped TensorProduct Classical +namespace Saxl.Balance + +def constantOutputMap (n d k : ℕ) : + Representation.IntertwiningMap (wordRep n (d*d)) (wordRep n 1) := + wordMap (fun a _ => if output a = k then 1 else 0) + +lemma constantOutputMap_single {n d : ℕ} (k : ℕ) (w : Fin n → Fin (d*d)) + (z : Fin n → Fin 1) : + constantOutputMap n d k (Pi.single w 1) z = + if inOutputs {k} w then 1 else 0 := by + classical + rw [constantOutputMap,wordMap_single] + by_cases h : inOutputs {k} w + · rw [ite_eq_left h] + have he : ∀ i, output (w i) = k := h + simp only [he,ite_true,Finset.prod_const_one] + · rw [ite_eq_right h] + change ¬ ∀ i, output (w i) = k at h + push Not at h + obtain ⟨i,hi⟩ := h + exact Finset.prod_eq_zero (Finset.mem_univ i) (ite_eq_right hi) + +lemma constantOutputMap_projection {n d : ℕ} (k : ℕ) (x : WordSpace n (d*d)) : + constantOutputMap n d k (coordinateProjection (inOutputs {k}) x) = + constantOutputMap n d k x := by + classical + rw [← (Pi.basisFun ℂ (Fin n → Fin (d*d))).sum_repr x] + simp only [map_sum,map_smul,Pi.basisFun_apply,coordinateProjection_single] + apply Finset.sum_congr rfl + intro w hw + by_cases h : inOutputs {k} w + · rw [ite_eq_left h] + · rw [ite_eq_right h,map_zero,smul_zero] + funext z + simp only [Pi.zero_apply,Pi.smul_apply,smul_eq_mul,constantOutputMap_single,ite_eq_right h,mul_zero] + +lemma constantOutputMap_pairSum {n d e : ℕ} (k : ℕ) + (t : Fin n → Fin e) (ht : ∀ i, (t i).val+1 = k) + (x : WordSpace n (d*d)) (z : Fin n → Fin 1) : + constantOutputMap n d k x z = pairSumMap n d e x t := by + classical + rw [← (Pi.basisFun ℂ (Fin n → Fin (d*d))).sum_repr x] + simp only [map_sum,map_smul,Pi.basisFun_apply,Finset.sum_apply,Pi.smul_apply,smul_eq_mul] + apply Finset.sum_congr rfl + intro w hw + congr 1 + rw [constantOutputMap_single,← merge_split w,pairSumMap_single] + congr 1 + apply propext + change (∀ i, output (mergeWords (splitLeft w) (splitRight w) i) = k) ↔ _ + simp only [mergeWords,output,Equiv.symm_apply_apply] + constructor <;> intro h i <;> have hi := ht i <;> have he := h i <;> omega + +theorem constant_output_support {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (k : ℕ) (hk : ∀ i, (columnLengthWord t i).val+1 = k) : + SupportLE (wordRep n 1) + (projectedSpechtTensor t t (inOutputs {k}) (inOutputs_invariant {k})).toRepresentation := by + classical + let W := projectedSpechtTensor t t (inOutputs {k}) (inOutputs_invariant {k}) + let Q := (constantOutputMap n (μ.colLen 0) k).comp (subrepInclusion W) + let v : Specht t := ⟨polytabloid t,mem_cyclic _ _⟩ + let y := projectedTensorQuotient t t (inOutputs {k}) (inOutputs_invariant {k}) (v ⊗ₜ[ℂ] v) + let C : ℂ := (Nat.card (columnGroup t) : ℂ) * signC (columnReversal t).val + have hC : C ≠ 0 := column_projection_coefficient_ne_zero t + have hy (z : Fin n → Fin 1) : Q y z = C := by + change constantOutputMap n (μ.colLen 0) k + (coordinateProjection (inOutputs {k}) (spechtTensorMap t t (v ⊗ₜ[ℂ] v))) z = C + rw [constantOutputMap_projection,constantOutputMap_pairSum k (columnLengthWord t) hk] + have he := congrFun (squared_polytabloid_projection t) (columnLengthWord t) + change (if wordOrbit (columnLengthWord t) (columnLengthWord t) then + pairSumMap n (μ.colLen 0) (μ.colLen 0) + (wordTensor _ _ _ (polytabloid t ⊗ₜ[ℂ] polytabloid t)) (columnLengthWord t) else 0) = _ at he + rw [ite_eq_left ⟨1,rfl⟩,Pi.smul_apply,Pi.single_eq_same,smul_eq_mul,mul_one] at he + unfold spechtTensorMap + exact he + have hQ : Function.Surjective Q := by + intro x + let z : Fin n → Fin 1 := fun _ => 0 + refine ⟨(x z / C) • y,?_⟩ + funext w + rw [map_smul,Pi.smul_apply,smul_eq_mul,hy] + have he : z = w := Subsingleton.elim _ _ + rw [div_mul_cancel₀ _ hC,he] + obtain ⟨s,hs⟩ := intertwining_lift_surjective Q hQ + (Representation.IntertwiningMap.id (wordRep n 1)) + apply SupportLE.of_injective s + intro x y hxy + have he := congrArg Q hxy + change (Q.comp s) x = (Q.comp s) y at he + rw [hs] at he + exact he + +def constantPacking {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) (k : ℕ) + (hk : ∀ i, (columnLengthWord t i).val+1 = k) + (j : ℕ) (A : Fin (μ.colLen 0 * μ.colLen 0) → Prop) + (label : Fin (μ.colLen 0 * μ.colLen 0) → ℕ) + (h : ∀ a, (A a ∧ label a = j) ↔ output a = k) : + Packing (polytabloid t) A label (Pi.single (fun _ : Fin n => (0 : Fin 1)) 1) := + boundedPacking t j {k} A label h (constant_output_support t k hk) _ + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/EmptyPacking.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/EmptyPacking.lean index 5dd72863cfecf1b111b87f39fdbe77ff5292b862..5af33047f36e7d1cdb455a79f4b02879b8eef77a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/EmptyPacking.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/EmptyPacking.lean @@ -1,68 +1,68 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingGeometry -import OAI.RepresentationTheory.UniversalSquare.Band.OutputBands - -namespace OAI - -/-! Empty Packing. -/ - -section - -noncomputable section -namespace Saxl.Balance -open FlagColumns Columns - -def WordPacking.empty (d : ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) : - WordPacking [] [] d A label ∅ := by - classical - let e := Classical.choose (columnShape_placement []) - have hr := (Classical.choose_spec (columnShape_placement [])).1 - have hc := (Classical.choose_spec (columnShape_placement [])).2 - let μ := columnShape [] - have h0 : μ.colLen 0 = 0 := by - apply Nat.eq_zero_of_not_pos - intro h - have hmem : (0,0) ∈ μ := YoungDiagram.mem_iff_lt_colLen.mpr h - exact isEmptyElim (e.symm ⟨(0,0),hmem⟩) - let t := (enumerate []).trans e - let f := Fin.castLE (show μ.colLen 0 ≤ d by omega) - have he : ∀ a, ((A ∘ pairLetterMap f f) a ∧ - (label ∘ pairLetterMap f f) a = 0) ↔ output a ∈ ({0}:Set ℕ) := by - intro a - have hh := a.isLt - simp only [h0,Nat.zero_mul] at hh - omega - have hs : SupportLE (wordRep 0 0) - (projectedSpechtTensor t t (inOutputs {0}) (inOutputs_invariant {0})).toRepresentation := - (SupportLE.of_injective (letterLift (Fin.castLE (show 0 ≤ 1 by omega))) - (letterLift_injective _ (Fin.castLE_injective _))).trans - (constant_output_support t 0 (fun i => Fin.elim0 i)) - let w : Fin 0 → Fin 0 := Fin.elim0 - let P := boundedPacking t 0 {0} (A ∘ pairLetterMap f f) (label ∘ pairLetterMap f f) - he hs (Pi.single w 1) - let Q := P.lift f (fun _ => rfl) A label - exact { - word := w - counts := fun j => Fin.elim0 j - packing := Q.congr (standard_placed e hr hc (show μ.colLen 0 ≤ d by omega)).symm rfl - marksBound := fun i => Fin.elim0 i } - -def oneIf (x ε : ℕ) : List ℕ := if ε = 0 then [] else [x] - -def markIf (x ε : ℕ) : Finset ℕ := if ε = 0 then ∅ else {x} - -theorem WordPacking.optional {x ε d : ℕ} (hx : 0 < x) (hd : x ≤ d) - (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ε ≠ 0 → ∀ a, (A a ∧ label a = x) ↔ output a = x) : - Nonempty (WordPacking (oneIf x ε) (oneIf x ε) d A label (markIf x ε)) := by - by_cases hε : ε = 0 - · simpa only [oneIf,markIf,ite_eq_left hε] using Nonempty.intro (WordPacking.empty d A label) - · obtain ⟨P⟩ := WordPacking.repeated (m := 1) (by decide) hx hd x A label (he hε) - simpa only [oneIf,markIf,ite_eq_right hε,List.replicate_one,one_mul] using Nonempty.intro P - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingGeometry +import OAI.RepresentationTheory.UniversalSquare.Band.OutputBands + +namespace OAI + +/-! Empty Packing. -/ + +section + +noncomputable section +namespace Saxl.Balance +open FlagColumns Columns + +def WordPacking.empty (d : ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) : + WordPacking [] [] d A label ∅ := by + classical + let e := Classical.choose (columnShape_placement []) + have hr := (Classical.choose_spec (columnShape_placement [])).1 + have hc := (Classical.choose_spec (columnShape_placement [])).2 + let μ := columnShape [] + have h0 : μ.colLen 0 = 0 := by + apply Nat.eq_zero_of_not_pos + intro h + have hmem : (0,0) ∈ μ := YoungDiagram.mem_iff_lt_colLen.mpr h + exact isEmptyElim (e.symm ⟨(0,0),hmem⟩) + let t := (enumerate []).trans e + let f := Fin.castLE (show μ.colLen 0 ≤ d by omega) + have he : ∀ a, ((A ∘ pairLetterMap f f) a ∧ + (label ∘ pairLetterMap f f) a = 0) ↔ output a ∈ ({0}:Set ℕ) := by + intro a + have hh := a.isLt + simp only [h0,Nat.zero_mul] at hh + omega + have hs : SupportLE (wordRep 0 0) + (projectedSpechtTensor t t (inOutputs {0}) (inOutputs_invariant {0})).toRepresentation := + (SupportLE.of_injective (letterLift (Fin.castLE (show 0 ≤ 1 by omega))) + (letterLift_injective _ (Fin.castLE_injective _))).trans + (constant_output_support t 0 (fun i => Fin.elim0 i)) + let w : Fin 0 → Fin 0 := Fin.elim0 + let P := boundedPacking t 0 {0} (A ∘ pairLetterMap f f) (label ∘ pairLetterMap f f) + he hs (Pi.single w 1) + let Q := P.lift f (fun _ => rfl) A label + exact { + word := w + counts := fun j => Fin.elim0 j + packing := Q.congr (standard_placed e hr hc (show μ.colLen 0 ≤ d by omega)).symm rfl + marksBound := fun i => Fin.elim0 i } + +def oneIf (x ε : ℕ) : List ℕ := if ε = 0 then [] else [x] + +def markIf (x ε : ℕ) : Finset ℕ := if ε = 0 then ∅ else {x} + +theorem WordPacking.optional {x ε d : ℕ} (hx : 0 < x) (hd : x ≤ d) + (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ε ≠ 0 → ∀ a, (A a ∧ label a = x) ↔ output a = x) : + Nonempty (WordPacking (oneIf x ε) (oneIf x ε) d A label (markIf x ε)) := by + by_cases hε : ε = 0 + · simpa only [oneIf,markIf,ite_eq_left hε] using Nonempty.intro (WordPacking.empty d A label) + · obtain ⟨P⟩ := WordPacking.repeated (m := 1) (by decide) hx hd x A label (he hε) + simpa only [oneIf,markIf,ite_eq_right hε,List.replicate_one,one_mul] using Nonempty.intro P + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/ExceptionalPacking.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/ExceptionalPacking.lean index 8a0abb4c6a96231d4133f2ae7d0fb94274d43734..4792d1ba85ed2039210b0adf6d0a50c3cdc2cb39 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/ExceptionalPacking.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/ExceptionalPacking.lean @@ -1,67 +1,67 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceFour -import OAI.RepresentationTheory.UniversalSquare.Balance.PackingPlans - -namespace OAI - -/-! Exceptional Packing. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -theorem candidate_refined_pos {n M b δ r : ℕ} (hM : 9 ≤ M) (hb : b ≤ M-2) - (hδ : δ ≤ 1) (hr : r = 2*b+δ) (hrpos : 0 < r) - (hn : (candidate M b δ).card = n) - (q : List ℕ) (hq : q.SortedGE) (hqp : ∀ a ∈ q, 0 < a) (hqn : q.sum = n) - (p : PackingPlan) (hv : p.Valid (M+b+δ)) (hbands : BandsValid p.bands) - (hcols : p.columns.Perm ([M+b+δ,M-1+b] ++ - (List.range' 3 (M-4)).reverse ++ List.replicate (b+1) 2 ++ List.replicate (1+δ) 1)) - (hparts : p.parts.Perm q) - (check : ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, - ∀ a ∈ List.range q.length, ∀ c ∈ List.range q.length, - refinedCheck n M r (d+1) (e+1) (a+1) (c+1) q) - (μ : YoungDiagram) (hμ : μ.card = n) : - 0 < kronecker (canonicalTableau (candidate M b δ) hn) - (canonicalTableau (candidate M b δ) hn) (canonicalTableau μ hμ) := by - let θ := YoungDiagram.ofRowLens q hq - have hrows : θ.rowLens = q := YoungDiagram.rowLens_ofRowLens_eq_self hqp - have ht : θ.card = n := by rw [card_eq_sum_rowLens, hrows, hqn] - have hposn : 0 < n := by rw [← hn,candidate_card _ _ _ (by omega)]; omega - have hp : ∀ a ∈ p.parts, 0 < a := fun a ha => hqp a (hparts.mem_iff.mp ha) - have hshape : (columnShape p.parts).transpose = θ := by - rw [columnShape_perm hparts, columnShape_sorted q hq hqp, YoungDiagram.transpose_transpose] - have hh : (candidate M b δ).colLen 0 = M+b+δ := by - rw [candidate_colLen _ _ _ _ (by omega)] - simp [candidateLengths] - have hc : p.columns.Perm (candidate M b δ).transpose.rowLens := by - rw [candidate_transpose, candidate_rowLens (by omega)] - exact hcols - have cone (ν : YoungDiagram) (hν : ν.card = n) (hd : Dominates ν θ) : - 0 < kronecker (canonicalTableau (candidate M b δ) hn) - (canonicalTableau (candidate M b δ) hn) (canonicalTableau ν hν) := by - apply packingPlan_pos p hv hbands hh hc hp - simpa only [hshape] using hd - have htcheck : ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, - ∀ a ∈ List.range θ.rowLens.length, ∀ c ∈ List.range θ.rowLens.length, - refinedCheck n M r (d+1) (e+1) (a+1) (c+1) θ.rowLens := by - simpa only [hrows] using check - rcases refined_capacity_dichotomy μ θ hposn hM hrpos hμ ht htcheck with - h | h | h | h | h | h - · exact balance_kronecker_pos hM hb hδ _ μ _ h - · exact balance_kronecker_pos_or_transpose hM hb hδ hn μ hμ (Or.inr h) - · exact band_kronecker_pos (by omega) hδ hr _ μ _ h - · apply (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr - exact band_kronecker_pos (by omega) hδ hr _ μ.transpose _ h - · exact cone μ hμ h - · apply (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr - exact cone μ.transpose ((transpose_card μ).trans hμ) h - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalanceFour +import OAI.RepresentationTheory.UniversalSquare.Balance.PackingPlans + +namespace OAI + +/-! Exceptional Packing. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +theorem candidate_refined_pos {n M b δ r : ℕ} (hM : 9 ≤ M) (hb : b ≤ M-2) + (hδ : δ ≤ 1) (hr : r = 2*b+δ) (hrpos : 0 < r) + (hn : (candidate M b δ).card = n) + (q : List ℕ) (hq : q.SortedGE) (hqp : ∀ a ∈ q, 0 < a) (hqn : q.sum = n) + (p : PackingPlan) (hv : p.Valid (M+b+δ)) (hbands : BandsValid p.bands) + (hcols : p.columns.Perm ([M+b+δ,M-1+b] ++ + (List.range' 3 (M-4)).reverse ++ List.replicate (b+1) 2 ++ List.replicate (1+δ) 1)) + (hparts : p.parts.Perm q) + (check : ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, + ∀ a ∈ List.range q.length, ∀ c ∈ List.range q.length, + refinedCheck n M r (d+1) (e+1) (a+1) (c+1) q) + (μ : YoungDiagram) (hμ : μ.card = n) : + 0 < kronecker (canonicalTableau (candidate M b δ) hn) + (canonicalTableau (candidate M b δ) hn) (canonicalTableau μ hμ) := by + let θ := YoungDiagram.ofRowLens q hq + have hrows : θ.rowLens = q := YoungDiagram.rowLens_ofRowLens_eq_self hqp + have ht : θ.card = n := by rw [card_eq_sum_rowLens, hrows, hqn] + have hposn : 0 < n := by rw [← hn,candidate_card _ _ _ (by omega)]; omega + have hp : ∀ a ∈ p.parts, 0 < a := fun a ha => hqp a (hparts.mem_iff.mp ha) + have hshape : (columnShape p.parts).transpose = θ := by + rw [columnShape_perm hparts, columnShape_sorted q hq hqp, YoungDiagram.transpose_transpose] + have hh : (candidate M b δ).colLen 0 = M+b+δ := by + rw [candidate_colLen _ _ _ _ (by omega)] + simp [candidateLengths] + have hc : p.columns.Perm (candidate M b δ).transpose.rowLens := by + rw [candidate_transpose, candidate_rowLens (by omega)] + exact hcols + have cone (ν : YoungDiagram) (hν : ν.card = n) (hd : Dominates ν θ) : + 0 < kronecker (canonicalTableau (candidate M b δ) hn) + (canonicalTableau (candidate M b δ) hn) (canonicalTableau ν hν) := by + apply packingPlan_pos p hv hbands hh hc hp + simpa only [hshape] using hd + have htcheck : ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, + ∀ a ∈ List.range θ.rowLens.length, ∀ c ∈ List.range θ.rowLens.length, + refinedCheck n M r (d+1) (e+1) (a+1) (c+1) θ.rowLens := by + simpa only [hrows] using check + rcases refined_capacity_dichotomy μ θ hposn hM hrpos hμ ht htcheck with + h | h | h | h | h | h + · exact balance_kronecker_pos hM hb hδ _ μ _ h + · exact balance_kronecker_pos_or_transpose hM hb hδ hn μ hμ (Or.inr h) + · exact band_kronecker_pos (by omega) hδ hr _ μ _ h + · apply (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr + exact band_kronecker_pos (by omega) hδ hr _ μ.transpose _ h + · exact cone μ hμ h + · apply (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr + exact cone μ.transpose ((transpose_card μ).trans hμ) h + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/PackingPlans.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/PackingPlans.lean index 7bcb13ca79a03db7efa463aa1b81fa7eb35bc479..919f670366e1b27562304344a3717e3affdbd6d0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/PackingPlans.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/PackingPlans.lean @@ -1,150 +1,150 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingPieri -import OAI.RepresentationTheory.UniversalSquare.Balance.EmptyPacking -import OAI.RepresentationTheory.UniversalSquare.Specht.ThreeRowMasks - -namespace OAI - -/-! Packing Plans. -/ - -section - -noncomputable section -namespace Saxl.Balance -open Columns FlagColumns - -inductive PackingPlan where - | empty - | neighbor (r : ℕ) (parts : List ℕ) - | repeated (m k : ℕ) - | twosOdd (m x : ℕ) (parts : List ℕ) - | twoPaths (q : ℕ) (parts : List ℕ) - | threeRows (m s : ℕ) (parts : List ℕ) (strips : List UniversalTensorSquare.ThreeRowEntry) - | join (p q : PackingPlan) - deriving DecidableEq - -namespace PackingPlan - -def columns : PackingPlan → List ℕ - | .empty => [] - | .neighbor r _ => [r+1,r] - | .repeated m k => List.replicate m k - | .twosOdd m x _ => List.replicate m 2 ++ [x] - | .twoPaths q _ => [q+2,q] ++ List.replicate 2 1 - | .threeRows m s _ _ => ThreeRow.columns m s - | .join p q => p.columns ++ q.columns - -def parts : PackingPlan → List ℕ - | .empty => [] - | .neighbor _ ps => ps - | .repeated m k => [m*k] - | .twosOdd _ _ ps => ps - | .twoPaths _ ps => ps - | .threeRows _ _ ps _ => ps - | .join p q => p.parts ++ q.parts - -def bands : PackingPlan → List (ℕ × ℕ) - | .empty => [] - | .neighbor r _ => [(r,r+1)] - | .repeated _ k => [(k,k)] - | .twosOdd _ x _ => [(2,2),(x,x)] - | .twoPaths q _ => [(q,2*q+3),(1,1)] - | .threeRows _ _ _ _ => [(1,3)] - | .join p q => p.bands ++ q.bands - -def marks (p : PackingPlan) : Finset ℕ := bandStarts p.bands - -def Valid : PackingPlan → ℕ → Prop - | .empty,_ => True - | .neighbor r ps,d => 0 < r ∧ r+1 ≤ d ∧ ps.sum = 2*r+1 ∧ ps.length ≤ 4 - | .repeated m k,d => 0 < m ∧ 0 < k ∧ k ≤ d - | .twosOdd m x ps,d => 1 ≤ m ∧ Odd x ∧ x ≤ 2*m ∧ 2 ≤ d ∧ x ≤ d ∧ - ps.sum = 2*m+x ∧ ps.length ≤ 2 - | .twoPaths q ps,d => 3 ≤ q ∧ q+2 ≤ d ∧ ps.sum = 2*q+4 ∧ ps.length ≤ 4 - | .threeRows m s ps cs,d => 3 ≤ d ∧ UniversalTensorSquare.ThreeRowMask m s ps cs - | .join p q,d => p.Valid d ∧ q.Valid d ∧ Disjoint p.marks q.marks - -instance (p : PackingPlan) (d : ℕ) : Decidable (p.Valid d) := by - induction p with - | empty => exact isTrue True.intro - | neighbor r ps => unfold Valid; infer_instance - | repeated m k => unfold Valid; infer_instance - | twosOdd m x ps => unfold Valid; infer_instance - | twoPaths q ps => unfold Valid; infer_instance - | threeRows m s ps cs => unfold Valid; infer_instance - | join p q ip iq => unfold Valid; infer_instance - -theorem realize (p : PackingPlan) {d : ℕ} (h : p.Valid d) - (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ e ∈ p.bands, ∀ z, (A z ∧ label z = e.1) ↔ output z ∈ Set.Icc e.1 e.2) : - Nonempty (WordPacking p.columns p.parts d A label p.marks) := by - induction p with - | empty => simpa [columns,parts,marks,bands,bandStarts] using - Nonempty.intro (WordPacking.empty d A label) - | neighbor r ps => - rcases h with ⟨hr,hd,hs,hl⟩ - simpa [columns,parts,marks,bands,bandStarts] using - WordPacking.neighbor hr hd hs hl r A label (he (r,r+1) (by simp [bands])) - | repeated m k => - rcases h with ⟨hm,hk,hd⟩ - have hei : ∀ z, (A z ∧ label z = k) ↔ output z = k := by - intro z - rw [he (k,k) (by simp [bands]) z] - simp only [Set.mem_Icc]; omega - simpa [columns,parts,marks,bands,bandStarts] using WordPacking.repeated hm hk hd k A label hei - | twosOdd m x ps => - rcases h with ⟨hm,hx,hxc,hd,hd',hs,hl⟩ - have hne : 2 ≠ x := by intro heq; rw [← heq] at hx; norm_num at hx - have hei : ∀ k, (k,k) ∈ (PackingPlan.twosOdd m x ps).bands → - ∀ z, (A z ∧ label z = k) ↔ output z = k := by - intro k hk z - rw [he (k,k) hk z] - simp only [Set.mem_Icc]; omega - simpa [columns,parts,marks,bands,bandStarts] using WordPacking.twosOdd hm hx hxc hd hd' hs hl - 2 x hne A label (hei 2 (by simp [bands])) (hei x (by simp [bands])) - | twoPaths q ps => - rcases h with ⟨hq,hd,hs,hl⟩ - have he1 : ∀ z, (A z ∧ label z = 1) ↔ output z = 1 := by - intro z - rw [he (1,1) (by simp [bands]) z] - simp only [Set.mem_Icc]; omega - simpa [columns,parts,marks,bands,bandStarts] using WordPacking.twoPaths hq hd hs hl - q 1 (by omega) A label (he (q,2*q+3) (by simp [bands])) he1 - | threeRows m s ps cs => - simpa [columns,parts,marks,bands,bandStarts] using - WordPacking.threeRows h.1 h.2 A label (he (1,3) (by simp [bands])) - | join p q ip iq => - obtain ⟨P⟩ := ip h.1 (by intro e he' z; exact he e (List.mem_append_left _ he') z) - obtain ⟨Q⟩ := iq h.2.1 (by intro e he' z; exact he e (List.mem_append_right _ he') z) - simpa only [columns,parts,marks,bands,bandStarts,List.map_append,List.toFinset_append] using - Nonempty.intro (P.join Q h.2.2) - -end PackingPlan -end Saxl.Balance - -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns Saxl.FlagColumns - -theorem packingPlan_pos {n d : ℕ} (p : PackingPlan) {lam μ : YoungDiagram} - (hv : p.Valid d) (hb : BandsValid p.bands) (hheight : lam.colLen 0 = d) - (hc : p.columns.Perm lam.transpose.rowLens) (hp : ∀ x ∈ p.parts, 0 < x) - (a : Tableau n lam) (t : Tableau n μ) - (hd : Dominates μ (columnShape p.parts).transpose) : 0 < kronecker a a t := by - obtain ⟨e,hr,hc'⟩ := place_columns lam hc - have hn : p.columns.sum = n := by - simpa only [Fintype.card_fin] using Fintype.card_congr (((enumerate p.columns).trans e).trans a.symm) - subst n - let B := numericBands p.bands hb - obtain ⟨P⟩ := p.realize hv (B.alphabet d) (B.letterLabel d) - (fun e he z => numericBands_iff hb he z) - rw [← hheight] at P - let a' := (enumerate p.columns).trans e - exact kronecker_pos_of_shapes rfl rfl rfl a' a' t a a t - (P.kronecker_pos a' t (standard_placed_self e hr hc') hp (B.letter_ordered _) hd) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingPieri +import OAI.RepresentationTheory.UniversalSquare.Balance.EmptyPacking +import OAI.RepresentationTheory.UniversalSquare.Specht.ThreeRowMasks + +namespace OAI + +/-! Packing Plans. -/ + +section + +noncomputable section +namespace Saxl.Balance +open Columns FlagColumns + +inductive PackingPlan where + | empty + | neighbor (r : ℕ) (parts : List ℕ) + | repeated (m k : ℕ) + | twosOdd (m x : ℕ) (parts : List ℕ) + | twoPaths (q : ℕ) (parts : List ℕ) + | threeRows (m s : ℕ) (parts : List ℕ) (strips : List UniversalTensorSquare.ThreeRowEntry) + | join (p q : PackingPlan) + deriving DecidableEq + +namespace PackingPlan + +def columns : PackingPlan → List ℕ + | .empty => [] + | .neighbor r _ => [r+1,r] + | .repeated m k => List.replicate m k + | .twosOdd m x _ => List.replicate m 2 ++ [x] + | .twoPaths q _ => [q+2,q] ++ List.replicate 2 1 + | .threeRows m s _ _ => ThreeRow.columns m s + | .join p q => p.columns ++ q.columns + +def parts : PackingPlan → List ℕ + | .empty => [] + | .neighbor _ ps => ps + | .repeated m k => [m*k] + | .twosOdd _ _ ps => ps + | .twoPaths _ ps => ps + | .threeRows _ _ ps _ => ps + | .join p q => p.parts ++ q.parts + +def bands : PackingPlan → List (ℕ × ℕ) + | .empty => [] + | .neighbor r _ => [(r,r+1)] + | .repeated _ k => [(k,k)] + | .twosOdd _ x _ => [(2,2),(x,x)] + | .twoPaths q _ => [(q,2*q+3),(1,1)] + | .threeRows _ _ _ _ => [(1,3)] + | .join p q => p.bands ++ q.bands + +def marks (p : PackingPlan) : Finset ℕ := bandStarts p.bands + +def Valid : PackingPlan → ℕ → Prop + | .empty,_ => True + | .neighbor r ps,d => 0 < r ∧ r+1 ≤ d ∧ ps.sum = 2*r+1 ∧ ps.length ≤ 4 + | .repeated m k,d => 0 < m ∧ 0 < k ∧ k ≤ d + | .twosOdd m x ps,d => 1 ≤ m ∧ Odd x ∧ x ≤ 2*m ∧ 2 ≤ d ∧ x ≤ d ∧ + ps.sum = 2*m+x ∧ ps.length ≤ 2 + | .twoPaths q ps,d => 3 ≤ q ∧ q+2 ≤ d ∧ ps.sum = 2*q+4 ∧ ps.length ≤ 4 + | .threeRows m s ps cs,d => 3 ≤ d ∧ UniversalTensorSquare.ThreeRowMask m s ps cs + | .join p q,d => p.Valid d ∧ q.Valid d ∧ Disjoint p.marks q.marks + +instance (p : PackingPlan) (d : ℕ) : Decidable (p.Valid d) := by + induction p with + | empty => exact isTrue True.intro + | neighbor r ps => unfold Valid; infer_instance + | repeated m k => unfold Valid; infer_instance + | twosOdd m x ps => unfold Valid; infer_instance + | twoPaths q ps => unfold Valid; infer_instance + | threeRows m s ps cs => unfold Valid; infer_instance + | join p q ip iq => unfold Valid; infer_instance + +theorem realize (p : PackingPlan) {d : ℕ} (h : p.Valid d) + (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ e ∈ p.bands, ∀ z, (A z ∧ label z = e.1) ↔ output z ∈ Set.Icc e.1 e.2) : + Nonempty (WordPacking p.columns p.parts d A label p.marks) := by + induction p with + | empty => simpa [columns,parts,marks,bands,bandStarts] using + Nonempty.intro (WordPacking.empty d A label) + | neighbor r ps => + rcases h with ⟨hr,hd,hs,hl⟩ + simpa [columns,parts,marks,bands,bandStarts] using + WordPacking.neighbor hr hd hs hl r A label (he (r,r+1) (by simp [bands])) + | repeated m k => + rcases h with ⟨hm,hk,hd⟩ + have hei : ∀ z, (A z ∧ label z = k) ↔ output z = k := by + intro z + rw [he (k,k) (by simp [bands]) z] + simp only [Set.mem_Icc]; omega + simpa [columns,parts,marks,bands,bandStarts] using WordPacking.repeated hm hk hd k A label hei + | twosOdd m x ps => + rcases h with ⟨hm,hx,hxc,hd,hd',hs,hl⟩ + have hne : 2 ≠ x := by intro heq; rw [← heq] at hx; norm_num at hx + have hei : ∀ k, (k,k) ∈ (PackingPlan.twosOdd m x ps).bands → + ∀ z, (A z ∧ label z = k) ↔ output z = k := by + intro k hk z + rw [he (k,k) hk z] + simp only [Set.mem_Icc]; omega + simpa [columns,parts,marks,bands,bandStarts] using WordPacking.twosOdd hm hx hxc hd hd' hs hl + 2 x hne A label (hei 2 (by simp [bands])) (hei x (by simp [bands])) + | twoPaths q ps => + rcases h with ⟨hq,hd,hs,hl⟩ + have he1 : ∀ z, (A z ∧ label z = 1) ↔ output z = 1 := by + intro z + rw [he (1,1) (by simp [bands]) z] + simp only [Set.mem_Icc]; omega + simpa [columns,parts,marks,bands,bandStarts] using WordPacking.twoPaths hq hd hs hl + q 1 (by omega) A label (he (q,2*q+3) (by simp [bands])) he1 + | threeRows m s ps cs => + simpa [columns,parts,marks,bands,bandStarts] using + WordPacking.threeRows h.1 h.2 A label (he (1,3) (by simp [bands])) + | join p q ip iq => + obtain ⟨P⟩ := ip h.1 (by intro e he' z; exact he e (List.mem_append_left _ he') z) + obtain ⟨Q⟩ := iq h.2.1 (by intro e he' z; exact he e (List.mem_append_right _ he') z) + simpa only [columns,parts,marks,bands,bandStarts,List.map_append,List.toFinset_append] using + Nonempty.intro (P.join Q h.2.2) + +end PackingPlan +end Saxl.Balance + +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns Saxl.FlagColumns + +theorem packingPlan_pos {n d : ℕ} (p : PackingPlan) {lam μ : YoungDiagram} + (hv : p.Valid d) (hb : BandsValid p.bands) (hheight : lam.colLen 0 = d) + (hc : p.columns.Perm lam.transpose.rowLens) (hp : ∀ x ∈ p.parts, 0 < x) + (a : Tableau n lam) (t : Tableau n μ) + (hd : Dominates μ (columnShape p.parts).transpose) : 0 < kronecker a a t := by + obtain ⟨e,hr,hc'⟩ := place_columns lam hc + have hn : p.columns.sum = n := by + simpa only [Fintype.card_fin] using Fintype.card_congr (((enumerate p.columns).trans e).trans a.symm) + subst n + let B := numericBands p.bands hb + obtain ⟨P⟩ := p.realize hv (B.alphabet d) (B.letterLabel d) + (fun e he z => numericBands_iff hb he z) + rw [← hheight] at P + let a' := (enumerate p.columns).trans e + exact kronecker_pos_of_shapes rfl rfl rfl a' a' t a a t + (P.kronecker_pos a' t (standard_placed_self e hr hc') hp (B.letter_ordered _) hd) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/PackingSupport.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/PackingSupport.lean index e9a05b33498f54fde91fbf47d046a75dcf0b8487..9e88af7f69422b2918eb5ed4eae1688b0ae7b659 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/PackingSupport.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/PackingSupport.lean @@ -1,112 +1,112 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ProductInduction -import OAI.RepresentationTheory.UniversalSquare.Specht.CyclicRestriction -import OAI.RepresentationTheory.UniversalSquare.Support.CoindProduct - -namespace OAI - -/-! Packing Support. -/ - -section - -noncomputable section -open scoped TensorProduct MonoidAlgebra -namespace Saxl - -theorem cyclic_supportLE_coind {G H X Y : Type*} - [Group G] [Finite G] [Group H] [Finite H] - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - (ρ : Representation ℂ G X) (σ : Representation ℂ H Y) - (φ : H →* G) (v : X) - (T : Representation.IntertwiningMap σ (ρ.comp φ)) (hv : v ∈ T.range) : - SupportLE (cyclic ρ v).toRepresentation (Representation.coind φ σ) := by - apply intertwining_separates_of_simple_support - intro S hS - let := hS - have hi : subrepInclusion S ≠ 0 := by - intro hz - let : Nontrivial S.toRepresentation.asModule := - IsSimpleModule.nontrivial ℂ[G] S.toRepresentation.asModule - let : Nontrivial S.toSubmodule := S.toRepresentation.asModuleEquiv.symm.toEquiv.nontrivial - obtain ⟨x,hx⟩ := exists_ne (0 : S.toSubmodule) - apply hx - apply Subtype.ext - exact congrArg (fun f : Representation.IntertwiningMap S.toRepresentation - (cyclic ρ v).toRepresentation => f x) hz - obtain ⟨F,hF⟩ := cyclic_restriction_support S.toRepresentation σ ρ φ v T hv - (subrepInclusion S) hi - exact ⟨coindLift φ F,coindLift_ne_zero φ F hF⟩ - -theorem SupportLE.cyclic_image {G X Y Z : Type*} [Group G] [Finite G] - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - [AddCommGroup Z] [Module ℂ Z] - {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} - {τ : Representation ℂ G Z} (v : X) - (T : Representation.IntertwiningMap ρ σ) (h : SupportLE (cyclic ρ v).toRepresentation τ) : - SupportLE (cyclic σ (T v)).toRepresentation τ := by - let Q := T.comp (subrepInclusion (cyclic ρ v)) - have hm : T v ∈ Q.range := ⟨⟨v,mem_cyclic ρ v⟩,rfl⟩ - obtain ⟨i,hi⟩ := subrepresentation_embeds_of_le_range Q (cyclic σ (T v)) - ((cyclic_le _ _ _).mpr hm) - exact (SupportLE.of_injective i hi).trans h - -def cyclicProductMap {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (v : WordSpace a d) (u : WordSpace b d) : - Representation.IntertwiningMap - (outer (cyclic (wordRep a d) v).toRepresentation (cyclic (wordRep b d) u).toRepresentation) - ((wordRep n d).comp (sumPermHom e)) := - externalWordMap e (subrepInclusion (cyclic (wordRep a d) v)) - (subrepInclusion (cyclic (wordRep b d) u)) - -lemma cyclicProduct_mem_range {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (v : WordSpace a d) (u : WordSpace b d) : - positionProduct e v u ∈ (cyclicProductMap e v u).range := by - refine ⟨(⟨v,mem_cyclic _ _⟩ : (cyclic (wordRep a d) v).toSubmodule) ⊗ₜ[ℂ] - (⟨u,mem_cyclic _ _⟩ : (cyclic (wordRep b d) u).toSubmodule), ?_⟩ - exact positionTensor_tmul e v u - -theorem product_supportLE_coind {n a b d : ℕ} {G H X Y : Type*} - [Group G] [Finite G] [Group H] [Finite H] - [AddCommGroup X] [Module ℂ X] [FiniteDimensional ℂ X] - [AddCommGroup Y] [Module ℂ Y] [FiniteDimensional ℂ Y] - (φ : G →* Equiv.Perm (Fin a)) (ψ : H →* Equiv.Perm (Fin b)) - (ρ : Representation ℂ G X) (σ : Representation ℂ H Y) - (e : Fin n ≃ Fin a ⊕ Fin b) (v : WordSpace a d) (u : WordSpace b d) - (hv : SupportLE (cyclic (wordRep a d) v).toRepresentation (Representation.coind φ ρ)) - (hu : SupportLE (cyclic (wordRep b d) u).toRepresentation (Representation.coind ψ σ)) : - SupportLE (cyclic (wordRep n d) (positionProduct e v u)).toRepresentation - (Representation.coind ((sumPermHom e).comp (φ.prodMap ψ)) (outer ρ σ)) := by - classical - let : AddCommGroup ((cyclic (wordRep a d) v).toSubmodule ⊗[ℂ] - (cyclic (wordRep b d) u).toSubmodule) := Module.addCommMonoidToAddCommGroup ℂ - have h₀ := cyclic_supportLE_coind (wordRep n d) - (outer (cyclic (wordRep a d) v).toRepresentation (cyclic (wordRep b d) u).toRepresentation) - (sumPermHom e) (positionProduct e v u) (cyclicProductMap e v u) (cyclicProduct_mem_range e v u) - have h₁ := (hv.outer hu).coind (sumPermHom e) - have h₂ := (SupportLE.of_injective (coindOuter φ ψ ρ σ) - (coindOuter_injective φ ψ ρ σ)).coind (sumPermHom e) - have h₃ := SupportLE.of_injective (coindTrans (φ.prodMap ψ) (sumPermHom e) (outer ρ σ)) - (coindTrans_injective (φ.prodMap ψ) (sumPermHom e) (outer ρ σ)) - exact ((h₀.trans h₁).trans h₂).trans h₃ - -theorem young_cyclic_support {n : ℕ} (θ μ : YoungDiagram) (t : Tableau n μ) - (hc : μ.card = θ.card) (hd : Dominates μ θ) - (w : Fin n → Fin (θ.colLen 0)) (f : Equiv.Perm (Fin (θ.colLen 0))) - (hw : ∀ j, (Finset.univ.filter (fun i => w i = f j)).card = θ.rowLen j) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n (θ.colLen 0)) (Pi.single w 1)).toRepresentation, F ≠ 0 := by - obtain ⟨F,hF⟩ := young_orbit_map θ μ t hc hd w f hw - let Q := F.comp (subrepInclusion (cyclic (wordRep n (θ.colLen 0)) (Pi.single w 1))) - have hQ : Q ≠ 0 := by - intro h0 - exact hF (congrArg (fun T : Representation.IntertwiningMap - (cyclic (wordRep n (θ.colLen 0)) (Pi.single w 1)).toRepresentation (spechtRep t) => - T ⟨Pi.single w 1,mem_cyclic _ _⟩) h0) - exact intertwining_reverse_nonzero Q hQ - -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ProductInduction +import OAI.RepresentationTheory.UniversalSquare.Specht.CyclicRestriction +import OAI.RepresentationTheory.UniversalSquare.Support.CoindProduct + +namespace OAI + +/-! Packing Support. -/ + +section + +noncomputable section +open scoped TensorProduct MonoidAlgebra +namespace Saxl + +theorem cyclic_supportLE_coind {G H X Y : Type*} + [Group G] [Finite G] [Group H] [Finite H] + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + (ρ : Representation ℂ G X) (σ : Representation ℂ H Y) + (φ : H →* G) (v : X) + (T : Representation.IntertwiningMap σ (ρ.comp φ)) (hv : v ∈ T.range) : + SupportLE (cyclic ρ v).toRepresentation (Representation.coind φ σ) := by + apply intertwining_separates_of_simple_support + intro S hS + let := hS + have hi : subrepInclusion S ≠ 0 := by + intro hz + let : Nontrivial S.toRepresentation.asModule := + IsSimpleModule.nontrivial ℂ[G] S.toRepresentation.asModule + let : Nontrivial S.toSubmodule := S.toRepresentation.asModuleEquiv.symm.toEquiv.nontrivial + obtain ⟨x,hx⟩ := exists_ne (0 : S.toSubmodule) + apply hx + apply Subtype.ext + exact congrArg (fun f : Representation.IntertwiningMap S.toRepresentation + (cyclic ρ v).toRepresentation => f x) hz + obtain ⟨F,hF⟩ := cyclic_restriction_support S.toRepresentation σ ρ φ v T hv + (subrepInclusion S) hi + exact ⟨coindLift φ F,coindLift_ne_zero φ F hF⟩ + +theorem SupportLE.cyclic_image {G X Y Z : Type*} [Group G] [Finite G] + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + [AddCommGroup Z] [Module ℂ Z] + {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} + {τ : Representation ℂ G Z} (v : X) + (T : Representation.IntertwiningMap ρ σ) (h : SupportLE (cyclic ρ v).toRepresentation τ) : + SupportLE (cyclic σ (T v)).toRepresentation τ := by + let Q := T.comp (subrepInclusion (cyclic ρ v)) + have hm : T v ∈ Q.range := ⟨⟨v,mem_cyclic ρ v⟩,rfl⟩ + obtain ⟨i,hi⟩ := subrepresentation_embeds_of_le_range Q (cyclic σ (T v)) + ((cyclic_le _ _ _).mpr hm) + exact (SupportLE.of_injective i hi).trans h + +def cyclicProductMap {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (v : WordSpace a d) (u : WordSpace b d) : + Representation.IntertwiningMap + (outer (cyclic (wordRep a d) v).toRepresentation (cyclic (wordRep b d) u).toRepresentation) + ((wordRep n d).comp (sumPermHom e)) := + externalWordMap e (subrepInclusion (cyclic (wordRep a d) v)) + (subrepInclusion (cyclic (wordRep b d) u)) + +lemma cyclicProduct_mem_range {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (v : WordSpace a d) (u : WordSpace b d) : + positionProduct e v u ∈ (cyclicProductMap e v u).range := by + refine ⟨(⟨v,mem_cyclic _ _⟩ : (cyclic (wordRep a d) v).toSubmodule) ⊗ₜ[ℂ] + (⟨u,mem_cyclic _ _⟩ : (cyclic (wordRep b d) u).toSubmodule), ?_⟩ + exact positionTensor_tmul e v u + +theorem product_supportLE_coind {n a b d : ℕ} {G H X Y : Type*} + [Group G] [Finite G] [Group H] [Finite H] + [AddCommGroup X] [Module ℂ X] [FiniteDimensional ℂ X] + [AddCommGroup Y] [Module ℂ Y] [FiniteDimensional ℂ Y] + (φ : G →* Equiv.Perm (Fin a)) (ψ : H →* Equiv.Perm (Fin b)) + (ρ : Representation ℂ G X) (σ : Representation ℂ H Y) + (e : Fin n ≃ Fin a ⊕ Fin b) (v : WordSpace a d) (u : WordSpace b d) + (hv : SupportLE (cyclic (wordRep a d) v).toRepresentation (Representation.coind φ ρ)) + (hu : SupportLE (cyclic (wordRep b d) u).toRepresentation (Representation.coind ψ σ)) : + SupportLE (cyclic (wordRep n d) (positionProduct e v u)).toRepresentation + (Representation.coind ((sumPermHom e).comp (φ.prodMap ψ)) (outer ρ σ)) := by + classical + let : AddCommGroup ((cyclic (wordRep a d) v).toSubmodule ⊗[ℂ] + (cyclic (wordRep b d) u).toSubmodule) := Module.addCommMonoidToAddCommGroup ℂ + have h₀ := cyclic_supportLE_coind (wordRep n d) + (outer (cyclic (wordRep a d) v).toRepresentation (cyclic (wordRep b d) u).toRepresentation) + (sumPermHom e) (positionProduct e v u) (cyclicProductMap e v u) (cyclicProduct_mem_range e v u) + have h₁ := (hv.outer hu).coind (sumPermHom e) + have h₂ := (SupportLE.of_injective (coindOuter φ ψ ρ σ) + (coindOuter_injective φ ψ ρ σ)).coind (sumPermHom e) + have h₃ := SupportLE.of_injective (coindTrans (φ.prodMap ψ) (sumPermHom e) (outer ρ σ)) + (coindTrans_injective (φ.prodMap ψ) (sumPermHom e) (outer ρ σ)) + exact ((h₀.trans h₁).trans h₂).trans h₃ + +theorem young_cyclic_support {n : ℕ} (θ μ : YoungDiagram) (t : Tableau n μ) + (hc : μ.card = θ.card) (hd : Dominates μ θ) + (w : Fin n → Fin (θ.colLen 0)) (f : Equiv.Perm (Fin (θ.colLen 0))) + (hw : ∀ j, (Finset.univ.filter (fun i => w i = f j)).card = θ.rowLen j) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n (θ.colLen 0)) (Pi.single w 1)).toRepresentation, F ≠ 0 := by + obtain ⟨F,hF⟩ := young_orbit_map θ μ t hc hd w f hw + let Q := F.comp (subrepInclusion (cyclic (wordRep n (θ.colLen 0)) (Pi.single w 1))) + have hQ : Q ≠ 0 := by + intro h0 + exact hF (congrArg (fun T : Representation.IntertwiningMap + (cyclic (wordRep n (θ.colLen 0)) (Pi.single w 1)).toRepresentation (spechtRep t) => + T ⟨Pi.single w 1,mem_cyclic _ _⟩) h0) + exact intertwining_reverse_nonzero Q hQ + +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPacking.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPacking.lean index bb67e9821e16dafdd71cecd79f4d69aaf05c7c62..8372805a629a7b5558643f6e8f92dd2b9844bfab 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPacking.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPacking.lean @@ -1,152 +1,152 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Specht.StandardColumns -import OAI.RepresentationTheory.UniversalSquare.Support.WordContents - -namespace OAI - -/-! Word Packing. -/ - -section - -noncomputable section -namespace Saxl -open scoped BigOperators - -lemma sum_wordContent {n d : ℕ} (w : Fin n → Fin d) : - ∑ j, wordContent w j = n := by - classical - simp only [wordContent,Finset.card_filter] - rw [Finset.sum_comm] - simp - -lemma single_joinPositions {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (w : Fin a → Fin d) (z : Fin b → Fin d) : - positionProduct e (Pi.single w 1) (Pi.single z 1) = - Pi.single ((positionWordsEquiv e).symm (w,z)) 1 := by - have hl := congrArg Prod.fst ((positionWordsEquiv e).apply_symm_apply (w,z)) - have hr := congrArg Prod.snd ((positionWordsEquiv e).apply_symm_apply (w,z)) - change leftWord e ((positionWordsEquiv e).symm (w,z)) = w at hl - change rightWord e ((positionWordsEquiv e).symm (w,z)) = z at hr - rw [single_positionProduct e,hl,hr] - -namespace Balance -open FlagColumns Columns - -def Packing.congr {n d e : ℕ} {v u : WordSpace n d} - {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {w z : WordSpace n e} - (P : Packing v A label w) (hv : v = u) (hw : w = z) : Packing u A label z where - G := P.G - Y := P.Y - c := P.c - σ := P.σ - φ := P.φ - τ := P.τ - piece := by rw [← hv]; exact P.piece - support := by rw [← hw]; exact P.support - -structure WordPacking (rs ps : List ℕ) (d : ℕ) - (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) (marks : Finset ℕ) where - word : Fin rs.sum → Fin ps.length - counts : ∀ j, wordContent word j = ps.get j - packing : Packing (blocks rs (standard d)) A label (Pi.single word 1) - marksBound : ∀ i, packing.c i ∈ marks - -lemma WordPacking.total {rs ps : List ℕ} {d : ℕ} - {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {marks : Finset ℕ} - (P : WordPacking rs ps d A label marks) : ps.sum = rs.sum := by - calc - ps.sum = ∑ j, ps.get j := by rw [← List.sum_ofFn, List.ofFn_get] - _ = ∑ j, wordContent P.word j := Finset.sum_congr rfl (fun j _ => (P.counts j).symm) - _ = rs.sum := sum_wordContent P.word - -def WordPacking.join {rs ss ps qs : List ℕ} {d : ℕ} - {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {marks marks' : Finset ℕ} - (P : WordPacking rs ps d A label marks) (Q : WordPacking ss qs d A label marks') - (hdis : Disjoint marks marks') : WordPacking (rs++ss) (ps++qs) d A label (marks ∪ marks') := by - classical - let e := appendPositions rs ss - let f := appendLetters ps qs - let wi := f.symm ∘ Sum.inl ∘ P.word - let zi := f.symm ∘ Sum.inr ∘ Q.word - let P' := P.packing.map (letterLift (f.symm ∘ Sum.inl)) - let Q' := Q.packing.map (letterLift (f.symm ∘ Sum.inr)) - have hd : ∀ i j, P'.c i ≠ Q'.c j := by - intro i j hij - have h₁ := P.marksBound i - have h₂ := Q.marksBound j - change P.packing.c i = Q.packing.c j at hij - rw [← hij] at h₂ - exact Finset.disjoint_left.mp hdis h₁ h₂ - let R := P'.join Q' e hd - have hv : positionProduct e (blocks rs (standard d)) (blocks ss (standard d)) = - blocks (rs++ss) (standard d) := (blocks_append rs ss _).symm - have hw : positionProduct e (letterLift (f.symm ∘ Sum.inl) (Pi.single P.word 1)) - (letterLift (f.symm ∘ Sum.inr) (Pi.single Q.word 1)) = - Pi.single ((positionWordsEquiv e).symm (wi,zi)) 1 := by - rw [letterLift_single,letterLift_single,single_joinPositions] - rfl - refine { - word := (positionWordsEquiv e).symm (wi,zi) - counts := ?_ - packing := R.congr hv hw - marksBound := ?_ } - · intro j - change wordContent ((positionWordsEquiv e).symm - ((fun i => f.symm (Sum.inl (P.word i))), (fun i => f.symm (Sum.inr (Q.word i))))) j = _ - rw [wordContent_position_join e f P.word Q.word j, get_appendLetters] - rcases h : f j with j | j - · exact P.counts j - · exact Q.counts j - · intro i - change joinedLabels e P.packing.c Q.packing.c i ∈ marks ∪ marks' - unfold joinedLabels - rcases e i with i | i - · exact Finset.mem_union_left _ (P.marksBound i) - · exact Finset.mem_union_right _ (Q.marksBound i) - -def WordPacking.sorted {rs ps : List ℕ} {d : ℕ} - {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {marks : Finset ℕ} - (P : WordPacking rs ps d A label marks) (hp : ∀ p ∈ ps, 0 < p) : - WordPacking rs (columnShape ps).transpose.rowLens d A label marks := by - classical - let q := Classical.choose (list_get_equiv (columnShape_rows_permutation ps hp)) - have hq := Classical.choose_spec (list_get_equiv (columnShape_rows_permutation ps hp)) - refine { - word := q ∘ P.word - counts := ?_ - packing := (P.packing.map (letterLift q)).congr rfl (letterLift_single q P.word) - marksBound := P.marksBound } - intro j - rw [wordContent_lift_equiv,P.counts,← hq,Equiv.apply_symm_apply] - -theorem WordPacking.kronecker_pos {rs ps : List ℕ} {lam μ : YoungDiagram} - (a : Tableau rs.sum lam) (t : Tableau rs.sum μ) - {A : Fin (lam.colLen 0 * lam.colLen 0) → Prop} - {label : Fin (lam.colLen 0 * lam.colLen 0) → ℕ} {marks : Finset ℕ} - (P : WordPacking rs ps (lam.colLen 0) A label marks) - (hv : blocks rs (standard (lam.colLen 0)) = polytabloid a) - (hp : ∀ p ∈ ps, 0 < p) - (ho : ∀ x y, A x → A y → label x < label y → output x < output y) - (hd : Dominates μ (columnShape ps).transpose) : 0 < kronecker a a t := by - let θ := (columnShape ps).transpose - let Q := P.sorted hp - let q : Fin θ.rowLens.length ≃ Fin (θ.colLen 0) := finCongr YoungDiagram.length_rowLens - let w := q ∘ Q.word - let R := (Q.packing.map (letterLift q)).congr hv (letterLift_single q Q.word) - apply R.kronecker_pos a t w ho _ hd (Equiv.refl _) _ - · have hc : μ.card = rs.sum := by - simpa only [Fintype.card_fin,Fintype.card_coe] using (Fintype.card_congr t).symm - rw [hc, show θ.card = ps.sum from by simp only [θ,transpose_card,columnShape_card]] - exact P.total.symm - · intro j - change wordContent w j = θ.rowLen j - rw [wordContent_lift_equiv,Q.counts] - exact YoungDiagram.get_rowLens - -end Balance -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Specht.StandardColumns +import OAI.RepresentationTheory.UniversalSquare.Support.WordContents + +namespace OAI + +/-! Word Packing. -/ + +section + +noncomputable section +namespace Saxl +open scoped BigOperators + +lemma sum_wordContent {n d : ℕ} (w : Fin n → Fin d) : + ∑ j, wordContent w j = n := by + classical + simp only [wordContent,Finset.card_filter] + rw [Finset.sum_comm] + simp + +lemma single_joinPositions {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (w : Fin a → Fin d) (z : Fin b → Fin d) : + positionProduct e (Pi.single w 1) (Pi.single z 1) = + Pi.single ((positionWordsEquiv e).symm (w,z)) 1 := by + have hl := congrArg Prod.fst ((positionWordsEquiv e).apply_symm_apply (w,z)) + have hr := congrArg Prod.snd ((positionWordsEquiv e).apply_symm_apply (w,z)) + change leftWord e ((positionWordsEquiv e).symm (w,z)) = w at hl + change rightWord e ((positionWordsEquiv e).symm (w,z)) = z at hr + rw [single_positionProduct e,hl,hr] + +namespace Balance +open FlagColumns Columns + +def Packing.congr {n d e : ℕ} {v u : WordSpace n d} + {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {w z : WordSpace n e} + (P : Packing v A label w) (hv : v = u) (hw : w = z) : Packing u A label z where + G := P.G + Y := P.Y + c := P.c + σ := P.σ + φ := P.φ + τ := P.τ + piece := by rw [← hv]; exact P.piece + support := by rw [← hw]; exact P.support + +structure WordPacking (rs ps : List ℕ) (d : ℕ) + (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) (marks : Finset ℕ) where + word : Fin rs.sum → Fin ps.length + counts : ∀ j, wordContent word j = ps.get j + packing : Packing (blocks rs (standard d)) A label (Pi.single word 1) + marksBound : ∀ i, packing.c i ∈ marks + +lemma WordPacking.total {rs ps : List ℕ} {d : ℕ} + {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {marks : Finset ℕ} + (P : WordPacking rs ps d A label marks) : ps.sum = rs.sum := by + calc + ps.sum = ∑ j, ps.get j := by rw [← List.sum_ofFn, List.ofFn_get] + _ = ∑ j, wordContent P.word j := Finset.sum_congr rfl (fun j _ => (P.counts j).symm) + _ = rs.sum := sum_wordContent P.word + +def WordPacking.join {rs ss ps qs : List ℕ} {d : ℕ} + {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {marks marks' : Finset ℕ} + (P : WordPacking rs ps d A label marks) (Q : WordPacking ss qs d A label marks') + (hdis : Disjoint marks marks') : WordPacking (rs++ss) (ps++qs) d A label (marks ∪ marks') := by + classical + let e := appendPositions rs ss + let f := appendLetters ps qs + let wi := f.symm ∘ Sum.inl ∘ P.word + let zi := f.symm ∘ Sum.inr ∘ Q.word + let P' := P.packing.map (letterLift (f.symm ∘ Sum.inl)) + let Q' := Q.packing.map (letterLift (f.symm ∘ Sum.inr)) + have hd : ∀ i j, P'.c i ≠ Q'.c j := by + intro i j hij + have h₁ := P.marksBound i + have h₂ := Q.marksBound j + change P.packing.c i = Q.packing.c j at hij + rw [← hij] at h₂ + exact Finset.disjoint_left.mp hdis h₁ h₂ + let R := P'.join Q' e hd + have hv : positionProduct e (blocks rs (standard d)) (blocks ss (standard d)) = + blocks (rs++ss) (standard d) := (blocks_append rs ss _).symm + have hw : positionProduct e (letterLift (f.symm ∘ Sum.inl) (Pi.single P.word 1)) + (letterLift (f.symm ∘ Sum.inr) (Pi.single Q.word 1)) = + Pi.single ((positionWordsEquiv e).symm (wi,zi)) 1 := by + rw [letterLift_single,letterLift_single,single_joinPositions] + rfl + refine { + word := (positionWordsEquiv e).symm (wi,zi) + counts := ?_ + packing := R.congr hv hw + marksBound := ?_ } + · intro j + change wordContent ((positionWordsEquiv e).symm + ((fun i => f.symm (Sum.inl (P.word i))), (fun i => f.symm (Sum.inr (Q.word i))))) j = _ + rw [wordContent_position_join e f P.word Q.word j, get_appendLetters] + rcases h : f j with j | j + · exact P.counts j + · exact Q.counts j + · intro i + change joinedLabels e P.packing.c Q.packing.c i ∈ marks ∪ marks' + unfold joinedLabels + rcases e i with i | i + · exact Finset.mem_union_left _ (P.marksBound i) + · exact Finset.mem_union_right _ (Q.marksBound i) + +def WordPacking.sorted {rs ps : List ℕ} {d : ℕ} + {A : Fin (d*d) → Prop} {label : Fin (d*d) → ℕ} {marks : Finset ℕ} + (P : WordPacking rs ps d A label marks) (hp : ∀ p ∈ ps, 0 < p) : + WordPacking rs (columnShape ps).transpose.rowLens d A label marks := by + classical + let q := Classical.choose (list_get_equiv (columnShape_rows_permutation ps hp)) + have hq := Classical.choose_spec (list_get_equiv (columnShape_rows_permutation ps hp)) + refine { + word := q ∘ P.word + counts := ?_ + packing := (P.packing.map (letterLift q)).congr rfl (letterLift_single q P.word) + marksBound := P.marksBound } + intro j + rw [wordContent_lift_equiv,P.counts,← hq,Equiv.apply_symm_apply] + +theorem WordPacking.kronecker_pos {rs ps : List ℕ} {lam μ : YoungDiagram} + (a : Tableau rs.sum lam) (t : Tableau rs.sum μ) + {A : Fin (lam.colLen 0 * lam.colLen 0) → Prop} + {label : Fin (lam.colLen 0 * lam.colLen 0) → ℕ} {marks : Finset ℕ} + (P : WordPacking rs ps (lam.colLen 0) A label marks) + (hv : blocks rs (standard (lam.colLen 0)) = polytabloid a) + (hp : ∀ p ∈ ps, 0 < p) + (ho : ∀ x y, A x → A y → label x < label y → output x < output y) + (hd : Dominates μ (columnShape ps).transpose) : 0 < kronecker a a t := by + let θ := (columnShape ps).transpose + let Q := P.sorted hp + let q : Fin θ.rowLens.length ≃ Fin (θ.colLen 0) := finCongr YoungDiagram.length_rowLens + let w := q ∘ Q.word + let R := (Q.packing.map (letterLift q)).congr hv (letterLift_single q Q.word) + apply R.kronecker_pos a t w ho _ hd (Equiv.refl _) _ + · have hc : μ.card = rs.sum := by + simpa only [Fintype.card_fin,Fintype.card_coe] using (Fintype.card_congr t).symm + rw [hc, show θ.card = ps.sum from by simp only [θ,transpose_card,columnShape_card]] + exact P.total.symm + · intro j + change wordContent w j = θ.rowLen j + rw [wordContent_lift_equiv,Q.counts] + exact YoungDiagram.get_rowLens + +end Balance +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingCone.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingCone.lean index e233cb8dbbb1827e93b48ed0f7bd52714b4c3534..4a7b7d88e1d6d06764ca6c82de21679dfd8cb6af 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingCone.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingCone.lean @@ -1,83 +1,83 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingPairs -import OAI.RepresentationTheory.UniversalSquare.Support.CountedGluing -import OAI.RepresentationTheory.UniversalSquare.Specht.YoungConverse - -namespace OAI - -/-! Word Packing Cone. -/ - -section - -noncomputable section -namespace Saxl.Balance -open FlagColumns Columns - -def WordPacking.cone {rs : List ℕ} {μ θ : YoungDiagram} {d : ℕ} - (e : Cells rs ≃ μ.cells) - (hr : ∀ c, (e c).val.1 = row c) - (hc : ∀ c c', (e c).val.2 = (e c').val.2 ↔ col c = col c') - (hD : μ.colLen 0 ≤ d) (ht : θ.card = rs.sum) - (k : ℕ) (I : Set ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) - (hs : ∀ (ν : YoungDiagram) (t : Tableau rs.sum ν), Dominates ν θ → - ∃ F : Representation.IntertwiningMap (spechtRep t) - (projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) - (inOutputs I) (inOutputs_invariant I)).toRepresentation, F ≠ 0) : - WordPacking rs θ.rowLens d A label {k} := by - classical - let W := projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) - (inOutputs I) (inOutputs_invariant I) - let φ := (fiberGroup (fun _ : Fin rs.sum => k)).subtype.comp (singleFiberHom rs.sum k) - letI : AddCommGroup (Representation.coindV φ W.toRepresentation) := Module.addCommMonoidToAddCommGroup ℂ - let u := canonicalTableau θ ht - let q : Fin (θ.colLen 0) ≃ Fin θ.rowLens.length := finCongr YoungDiagram.length_rowLens.symm - let w := q ∘ rowWord u - let P := placedPiece e hr hc hD k I A label he - have hh : SupportLE (tabloidSub u).toRepresentation (Representation.coind φ W.toRepresentation) := - (tabloid_supportLE u W.toRepresentation hs).trans - (SupportLE.of_injective _ (single_coindLift_injective W.toRepresentation k)) - change SupportLE (cyclic (wordRep rs.sum (θ.colLen 0)) - (Pi.single (rowWord u) 1)).toRepresentation (Representation.coind φ W.toRepresentation) at hh - have hi : SupportLE - (cyclic (wordRep rs.sum θ.rowLens.length) ((letterLift q) (Pi.single (rowWord u) 1))).toRepresentation - (Representation.coind φ W.toRepresentation) := by - apply SupportLE.cyclic_image (Pi.single (rowWord u) 1) (letterLift q) - exact hh - rw [letterLift_single] at hi - refine { - word := w - counts := ?_ - packing := { - G := Equiv.Perm (Fin rs.sum) - Y := W.toSubmodule - c := fun _ => k - σ := columnOutputSums ((enumerate rs).trans e) (fun _ => k) - φ := singleFiberHom rs.sum k - τ := W.toRepresentation - piece := P - support := hi } - marksBound := fun _ => Finset.mem_singleton_self k } - intro j - rw [wordContent_lift_equiv] - change (Finset.univ.filter (fun i => rowWord u i = q.symm j)).card = θ.rowLens.get j - rw [rowWord_content] - exact YoungDiagram.get_rowLens.symm - -theorem WordPacking.of_cone_shape {rs : List ℕ} {μ θ : YoungDiagram} {d : ℕ} - (hp : rs.Perm μ.transpose.rowLens) (hd : μ.colLen 0 ≤ d) (ht : θ.card = rs.sum) - (k : ℕ) (I : Set ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) - (hs : ∀ (u : Tableau rs.sum μ) (ν : YoungDiagram) (t : Tableau rs.sum ν), Dominates ν θ → - ∃ F : Representation.IntertwiningMap (spechtRep t) - (projectedSpechtTensor u u (inOutputs I) (inOutputs_invariant I)).toRepresentation, F ≠ 0) : - Nonempty (WordPacking rs θ.rowLens d A label {k}) := by - obtain ⟨e,hr,hc⟩ := place_columns μ hp - exact ⟨WordPacking.cone e hr hc hd ht k I A label he (hs _)⟩ - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingPairs +import OAI.RepresentationTheory.UniversalSquare.Support.CountedGluing +import OAI.RepresentationTheory.UniversalSquare.Specht.YoungConverse + +namespace OAI + +/-! Word Packing Cone. -/ + +section + +noncomputable section +namespace Saxl.Balance +open FlagColumns Columns + +def WordPacking.cone {rs : List ℕ} {μ θ : YoungDiagram} {d : ℕ} + (e : Cells rs ≃ μ.cells) + (hr : ∀ c, (e c).val.1 = row c) + (hc : ∀ c c', (e c).val.2 = (e c').val.2 ↔ col c = col c') + (hD : μ.colLen 0 ≤ d) (ht : θ.card = rs.sum) + (k : ℕ) (I : Set ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) + (hs : ∀ (ν : YoungDiagram) (t : Tableau rs.sum ν), Dominates ν θ → + ∃ F : Representation.IntertwiningMap (spechtRep t) + (projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) + (inOutputs I) (inOutputs_invariant I)).toRepresentation, F ≠ 0) : + WordPacking rs θ.rowLens d A label {k} := by + classical + let W := projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) + (inOutputs I) (inOutputs_invariant I) + let φ := (fiberGroup (fun _ : Fin rs.sum => k)).subtype.comp (singleFiberHom rs.sum k) + letI : AddCommGroup (Representation.coindV φ W.toRepresentation) := Module.addCommMonoidToAddCommGroup ℂ + let u := canonicalTableau θ ht + let q : Fin (θ.colLen 0) ≃ Fin θ.rowLens.length := finCongr YoungDiagram.length_rowLens.symm + let w := q ∘ rowWord u + let P := placedPiece e hr hc hD k I A label he + have hh : SupportLE (tabloidSub u).toRepresentation (Representation.coind φ W.toRepresentation) := + (tabloid_supportLE u W.toRepresentation hs).trans + (SupportLE.of_injective _ (single_coindLift_injective W.toRepresentation k)) + change SupportLE (cyclic (wordRep rs.sum (θ.colLen 0)) + (Pi.single (rowWord u) 1)).toRepresentation (Representation.coind φ W.toRepresentation) at hh + have hi : SupportLE + (cyclic (wordRep rs.sum θ.rowLens.length) ((letterLift q) (Pi.single (rowWord u) 1))).toRepresentation + (Representation.coind φ W.toRepresentation) := by + apply SupportLE.cyclic_image (Pi.single (rowWord u) 1) (letterLift q) + exact hh + rw [letterLift_single] at hi + refine { + word := w + counts := ?_ + packing := { + G := Equiv.Perm (Fin rs.sum) + Y := W.toSubmodule + c := fun _ => k + σ := columnOutputSums ((enumerate rs).trans e) (fun _ => k) + φ := singleFiberHom rs.sum k + τ := W.toRepresentation + piece := P + support := hi } + marksBound := fun _ => Finset.mem_singleton_self k } + intro j + rw [wordContent_lift_equiv] + change (Finset.univ.filter (fun i => rowWord u i = q.symm j)).card = θ.rowLens.get j + rw [rowWord_content] + exact YoungDiagram.get_rowLens.symm + +theorem WordPacking.of_cone_shape {rs : List ℕ} {μ θ : YoungDiagram} {d : ℕ} + (hp : rs.Perm μ.transpose.rowLens) (hd : μ.colLen 0 ≤ d) (ht : θ.card = rs.sum) + (k : ℕ) (I : Set ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) + (hs : ∀ (u : Tableau rs.sum μ) (ν : YoungDiagram) (t : Tableau rs.sum ν), Dominates ν θ → + ∃ F : Representation.IntertwiningMap (spechtRep t) + (projectedSpechtTensor u u (inOutputs I) (inOutputs_invariant I)).toRepresentation, F ≠ 0) : + Nonempty (WordPacking rs θ.rowLens d A label {k}) := by + obtain ⟨e,hr,hc⟩ := place_columns μ hp + exact ⟨WordPacking.cone e hr hc hd ht k I A label he (hs _)⟩ + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingGeometry.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingGeometry.lean index 24d1fa5829ce701db140d2842172f483f6ac77a7..777a6154542f739b2dcf53fbb88bb903b4c72773 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingGeometry.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingGeometry.lean @@ -1,89 +1,89 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.ConstantOutputs -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingLeaves - -namespace OAI - -/-! Word Packing Geometry. -/ - -section - -noncomputable section -namespace Saxl.Balance -open FlagColumns Columns - -theorem WordPacking.of_bounded_shape {rs ps : List ℕ} {μ : YoungDiagram} {d E : ℕ} - (hp : rs.Perm μ.transpose.rowLens) (hd : μ.colLen 0 ≤ d) - (hsum : ps.sum = rs.sum) (hlen : ps.length ≤ E) - (k : ℕ) (I : Set ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) - (hs : ∀ t : Tableau rs.sum μ, SupportLE (wordRep rs.sum E) - (projectedSpechtTensor t t (inOutputs I) (inOutputs_invariant I)).toRepresentation) : - Nonempty (WordPacking rs ps d A label {k}) := by - obtain ⟨e,hr,hc⟩ := place_columns μ hp - exact ⟨WordPacking.bounded e hr hc hd hsum hlen k I A label he (hs _)⟩ - -theorem WordPacking.neighbor {r d : ℕ} (hr : 0 < r) (hd : r+1 ≤ d) - {ps : List ℕ} (hsum : ps.sum = 2*r+1) (hlen : ps.length ≤ 4) - (k : ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ Set.Icc r (r+1)) : - Nonempty (WordPacking [r+1,r] ps d A label {k}) := by - have hrow : (ShortColumns.shape r 1).rowLens = [r+1,r] := - YoungDiagram.rowLens_ofRowLens_eq_self (by simp; omega) - have hD : (ShortColumns.shape r 1).transpose.colLen 0 ≤ d := by - rw [YoungDiagram.colLen_transpose] - have hh := YoungDiagram.rowLen_ofRowLens (hw := by apply List.Pairwise.sortedGE; simp) - (show Fin [r+1,r].length from ⟨0,by simp⟩) - change (ShortColumns.shape r 1).rowLen 0 = r+1 at hh - rw [hh] - exact hd - apply WordPacking.of_bounded_shape (μ := (ShortColumns.shape r 1).transpose) - (by rw [YoungDiagram.transpose_transpose,hrow]) hD (by simp; omega) hlen k _ A label he - intro t - exact neighboring_word_support (by simp; omega) t - -lemma replicate_sorted (m k : ℕ) : (List.replicate m k).SortedGE := - List.Pairwise.sortedGE (List.pairwise_replicate.mpr (Or.inr le_rfl)) - -lemma repeated_column_length {m k n : ℕ} (hk : 0 < k) - (t : Tableau n (YoungDiagram.ofRowLens (List.replicate m k) (replicate_sorted m k)).transpose) - (i : Fin n) : (columnLengthWord t i).val+1 = k := by - have hm := YoungDiagram.mem_transpose.mp (t i).property - obtain ⟨hj,hi⟩ := YoungDiagram.mem_ofRowLens.mp hm - have he := YoungDiagram.rowLen_ofRowLens (hw := replicate_sorted m k) - (show Fin (List.replicate m k).length from ⟨(t i).val.2,hj⟩) - simp only [Fin.getElem_fin, List.getElem_replicate] at he - change (YoungDiagram.ofRowLens (List.replicate m k) (replicate_sorted m k)).transpose.colLen - (t i).val.2 - 1 + 1 = k - rw [YoungDiagram.colLen_transpose,he] - omega - -theorem WordPacking.repeated {m k d : ℕ} (hm : 0 < m) (hk : 0 < k) (hd : k ≤ d) - (j : ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ a, (A a ∧ label a = j) ↔ output a = k) : - Nonempty (WordPacking (List.replicate m k) [m*k] d A label {j}) := by - let μ := (YoungDiagram.ofRowLens (List.replicate m k) (replicate_sorted m k)).transpose - have hrow : μ.transpose.rowLens = List.replicate m k := by - rw [YoungDiagram.transpose_transpose] - apply YoungDiagram.rowLens_ofRowLens_eq_self - intro x hx - rw [(List.mem_replicate.mp hx).2] - exact hk - have hD : μ.colLen 0 ≤ d := by - rw [YoungDiagram.colLen_transpose] - have hh := YoungDiagram.rowLen_ofRowLens (hw := replicate_sorted m k) - (show Fin (List.replicate m k).length from ⟨0,by simpa⟩) - simp only [Fin.getElem_fin, List.getElem_replicate] at hh - rw [hh] - exact hd - apply WordPacking.of_bounded_shape (μ := μ) (E := 1) (by rw [hrow]) hD - (by simp) (by simp) j {k} A label he - intro t - exact constant_output_support t k (repeated_column_length hk t) - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.ConstantOutputs +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingLeaves + +namespace OAI + +/-! Word Packing Geometry. -/ + +section + +noncomputable section +namespace Saxl.Balance +open FlagColumns Columns + +theorem WordPacking.of_bounded_shape {rs ps : List ℕ} {μ : YoungDiagram} {d E : ℕ} + (hp : rs.Perm μ.transpose.rowLens) (hd : μ.colLen 0 ≤ d) + (hsum : ps.sum = rs.sum) (hlen : ps.length ≤ E) + (k : ℕ) (I : Set ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) + (hs : ∀ t : Tableau rs.sum μ, SupportLE (wordRep rs.sum E) + (projectedSpechtTensor t t (inOutputs I) (inOutputs_invariant I)).toRepresentation) : + Nonempty (WordPacking rs ps d A label {k}) := by + obtain ⟨e,hr,hc⟩ := place_columns μ hp + exact ⟨WordPacking.bounded e hr hc hd hsum hlen k I A label he (hs _)⟩ + +theorem WordPacking.neighbor {r d : ℕ} (hr : 0 < r) (hd : r+1 ≤ d) + {ps : List ℕ} (hsum : ps.sum = 2*r+1) (hlen : ps.length ≤ 4) + (k : ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ Set.Icc r (r+1)) : + Nonempty (WordPacking [r+1,r] ps d A label {k}) := by + have hrow : (ShortColumns.shape r 1).rowLens = [r+1,r] := + YoungDiagram.rowLens_ofRowLens_eq_self (by simp; omega) + have hD : (ShortColumns.shape r 1).transpose.colLen 0 ≤ d := by + rw [YoungDiagram.colLen_transpose] + have hh := YoungDiagram.rowLen_ofRowLens (hw := by apply List.Pairwise.sortedGE; simp) + (show Fin [r+1,r].length from ⟨0,by simp⟩) + change (ShortColumns.shape r 1).rowLen 0 = r+1 at hh + rw [hh] + exact hd + apply WordPacking.of_bounded_shape (μ := (ShortColumns.shape r 1).transpose) + (by rw [YoungDiagram.transpose_transpose,hrow]) hD (by simp; omega) hlen k _ A label he + intro t + exact neighboring_word_support (by simp; omega) t + +lemma replicate_sorted (m k : ℕ) : (List.replicate m k).SortedGE := + List.Pairwise.sortedGE (List.pairwise_replicate.mpr (Or.inr le_rfl)) + +lemma repeated_column_length {m k n : ℕ} (hk : 0 < k) + (t : Tableau n (YoungDiagram.ofRowLens (List.replicate m k) (replicate_sorted m k)).transpose) + (i : Fin n) : (columnLengthWord t i).val+1 = k := by + have hm := YoungDiagram.mem_transpose.mp (t i).property + obtain ⟨hj,hi⟩ := YoungDiagram.mem_ofRowLens.mp hm + have he := YoungDiagram.rowLen_ofRowLens (hw := replicate_sorted m k) + (show Fin (List.replicate m k).length from ⟨(t i).val.2,hj⟩) + simp only [Fin.getElem_fin, List.getElem_replicate] at he + change (YoungDiagram.ofRowLens (List.replicate m k) (replicate_sorted m k)).transpose.colLen + (t i).val.2 - 1 + 1 = k + rw [YoungDiagram.colLen_transpose,he] + omega + +theorem WordPacking.repeated {m k d : ℕ} (hm : 0 < m) (hk : 0 < k) (hd : k ≤ d) + (j : ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ a, (A a ∧ label a = j) ↔ output a = k) : + Nonempty (WordPacking (List.replicate m k) [m*k] d A label {j}) := by + let μ := (YoungDiagram.ofRowLens (List.replicate m k) (replicate_sorted m k)).transpose + have hrow : μ.transpose.rowLens = List.replicate m k := by + rw [YoungDiagram.transpose_transpose] + apply YoungDiagram.rowLens_ofRowLens_eq_self + intro x hx + rw [(List.mem_replicate.mp hx).2] + exact hk + have hD : μ.colLen 0 ≤ d := by + rw [YoungDiagram.colLen_transpose] + have hh := YoungDiagram.rowLen_ofRowLens (hw := replicate_sorted m k) + (show Fin (List.replicate m k).length from ⟨0,by simpa⟩) + simp only [Fin.getElem_fin, List.getElem_replicate] at hh + rw [hh] + exact hd + apply WordPacking.of_bounded_shape (μ := μ) (E := 1) (by rw [hrow]) hD + (by simp) (by simp) j {k} A label he + intro t + exact constant_output_support t k (repeated_column_length hk t) + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingLeaves.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingLeaves.lean index f9a330174b28eea4c171a3835eb00e5a530f321f..279574e106bc261701ddcbde8870bffef44e0a87 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingLeaves.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingLeaves.lean @@ -1,70 +1,70 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPacking -import OAI.RepresentationTheory.UniversalSquare.Support.PartWords - -namespace OAI - -/-! Word Packing Leaves. -/ - -section - -noncomputable section -namespace Saxl.Balance -open FlagColumns Columns - -def WordPacking.bounded {rs ps : List ℕ} {μ : YoungDiagram} {d E : ℕ} - (e : Cells rs ≃ μ.cells) - (hr : ∀ c, (e c).val.1 = row c) - (hc : ∀ c c', (e c).val.2 = (e c').val.2 ↔ col c = col c') - (hD : μ.colLen 0 ≤ d) (hps : ps.sum = rs.sum) (hone : ps.length ≤ E) - (k : ℕ) (I : Set ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) - (hs : SupportLE (wordRep rs.sum E) - (projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) - (inOutputs I) (inOutputs_invariant I)).toRepresentation) : - WordPacking rs ps d A label {k} := by - classical - let f := Fin.castLE hD - let w := Classical.choose (exists_word_of_parts ps hps) - have hw := Classical.choose_spec (exists_word_of_parts ps hps) - have hlocal : ∀ a, ((A ∘ pairLetterMap f f) a ∧ - (label ∘ pairLetterMap f f) a = k) ↔ output a ∈ I := by - intro a - rw [Function.comp_apply,Function.comp_apply,he,output_pairLetterMap f (fun _ => rfl)] - have hs' : SupportLE (wordRep rs.sum ps.length) - (projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) - (inOutputs I) (inOutputs_invariant I)).toRepresentation := - (SupportLE.of_injective (letterLift (Fin.castLE hone)) - (letterLift_injective _ (Fin.castLE_injective hone))).trans hs - let P := boundedPacking ((enumerate rs).trans e) k I - (A ∘ pairLetterMap f f) (label ∘ pairLetterMap f f) hlocal hs' (Pi.single w 1) - let Q := P.lift f (fun _ => rfl) A label - refine { - word := w - counts := hw - packing := Q.congr (standard_placed e hr hc hD).symm rfl - marksBound := ?_ } - intro i - change k ∈ ({k} : Finset ℕ) - simp - -theorem neighboring_word_support {n r : ℕ} (hn : n = 2*r+1) - (a : Tableau n (ShortColumns.shape r 1).transpose) : - SupportLE (wordRep n 4) - (projectedSpechtTensor a a (inOutputs (Set.Icc r (r+1))) - (inOutputs_invariant (Set.Icc r (r+1)))).toRepresentation := by - subst n - apply word_supportLE - intro μ t hμ - obtain ⟨F,hF⟩ := neighboring r a a μ t hμ - refine ⟨F,?_⟩ - intro h0 - have hzero := hF (show F ⟨polytabloid t,mem_cyclic _ _⟩ = F 0 by rw [h0]; rfl) - exact polytabloid_ne_zero t (congrArg Subtype.val hzero) - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPacking +import OAI.RepresentationTheory.UniversalSquare.Support.PartWords + +namespace OAI + +/-! Word Packing Leaves. -/ + +section + +noncomputable section +namespace Saxl.Balance +open FlagColumns Columns + +def WordPacking.bounded {rs ps : List ℕ} {μ : YoungDiagram} {d E : ℕ} + (e : Cells rs ≃ μ.cells) + (hr : ∀ c, (e c).val.1 = row c) + (hc : ∀ c c', (e c).val.2 = (e c').val.2 ↔ col c = col c') + (hD : μ.colLen 0 ≤ d) (hps : ps.sum = rs.sum) (hone : ps.length ≤ E) + (k : ℕ) (I : Set ℕ) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) + (hs : SupportLE (wordRep rs.sum E) + (projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) + (inOutputs I) (inOutputs_invariant I)).toRepresentation) : + WordPacking rs ps d A label {k} := by + classical + let f := Fin.castLE hD + let w := Classical.choose (exists_word_of_parts ps hps) + have hw := Classical.choose_spec (exists_word_of_parts ps hps) + have hlocal : ∀ a, ((A ∘ pairLetterMap f f) a ∧ + (label ∘ pairLetterMap f f) a = k) ↔ output a ∈ I := by + intro a + rw [Function.comp_apply,Function.comp_apply,he,output_pairLetterMap f (fun _ => rfl)] + have hs' : SupportLE (wordRep rs.sum ps.length) + (projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) + (inOutputs I) (inOutputs_invariant I)).toRepresentation := + (SupportLE.of_injective (letterLift (Fin.castLE hone)) + (letterLift_injective _ (Fin.castLE_injective hone))).trans hs + let P := boundedPacking ((enumerate rs).trans e) k I + (A ∘ pairLetterMap f f) (label ∘ pairLetterMap f f) hlocal hs' (Pi.single w 1) + let Q := P.lift f (fun _ => rfl) A label + refine { + word := w + counts := hw + packing := Q.congr (standard_placed e hr hc hD).symm rfl + marksBound := ?_ } + intro i + change k ∈ ({k} : Finset ℕ) + simp + +theorem neighboring_word_support {n r : ℕ} (hn : n = 2*r+1) + (a : Tableau n (ShortColumns.shape r 1).transpose) : + SupportLE (wordRep n 4) + (projectedSpechtTensor a a (inOutputs (Set.Icc r (r+1))) + (inOutputs_invariant (Set.Icc r (r+1)))).toRepresentation := by + subst n + apply word_supportLE + intro μ t hμ + obtain ⟨F,hF⟩ := neighboring r a a μ t hμ + refine ⟨F,?_⟩ + intro h0 + have hzero := hF (show F ⟨polytabloid t,mem_cyclic _ _⟩ = F 0 by rw [h0]; rfl) + exact polytabloid_ne_zero t (congrArg Subtype.val hzero) + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingPairs.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingPairs.lean index f3e7eb310ce7e812ff0b8f228399234c721ed05c..abc94dd2ed1687bb9c9e29e4938d9716b0dc2ccc 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingPairs.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingPairs.lean @@ -1,116 +1,116 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPacking -import OAI.RepresentationTheory.UniversalSquare.Support.PartWords - -namespace OAI - -/-! Word Packing Pairs. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl.Balance -open FlagColumns Columns - -def placedPiece {rs : List ℕ} {μ : YoungDiagram} {d : ℕ} - (e : Cells rs ≃ μ.cells) - (hr : ∀ c, (e c).val.1 = row c) - (hc : ∀ c c', (e c).val.2 = (e c').val.2 ↔ col c = col c') - (hd : μ.colLen 0 ≤ d) (k : ℕ) (I : Set ℕ) - (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) : - Piece (blocks rs (standard d)) (fun _ => k) A label - (columnOutputSums ((enumerate rs).trans e) (fun _ => k)) (singleFiberHom rs.sum k) - (projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) - (inOutputs I) (inOutputs_invariant I)).toRepresentation := by - let f := Fin.castLE hd - have hlocal : ∀ a, ((A ∘ pairLetterMap f f) a ∧ - (label ∘ pairLetterMap f f) a = k) ↔ output a ∈ I := by - intro a - rw [Function.comp_apply,Function.comp_apply,he,output_pairLetterMap f (fun _ => rfl)] - rw [standard_placed e hr hc hd] - exact (projectedPiece ((enumerate rs).trans e) k I _ _ hlocal).lift f (fun _ => rfl) A label - -def WordPacking.binaryBounded {rs ss ps : List ℕ} {μ ν : YoungDiagram} {d E : ℕ} - (e : Cells rs ≃ μ.cells) (f : Cells ss ≃ ν.cells) - (hr : ∀ c, (e c).val.1 = row c) - (hc : ∀ c c', (e c).val.2 = (e c').val.2 ↔ col c = col c') - (hr' : ∀ c, (f c).val.1 = row c) - (hc' : ∀ c c', (f c).val.2 = (f c').val.2 ↔ col c = col c') - (hd : μ.colLen 0 ≤ d) (hd' : ν.colLen 0 ≤ d) - (hsum : ps.sum = (rs++ss).sum) (hlen : ps.length ≤ E) - (k l : ℕ) (hne : k ≠ l) (I J : Set ℕ) - (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) - (he' : ∀ a, (A a ∧ label a = l) ↔ output a ∈ J) - (hs : SupportLE (wordRep (rs++ss).sum E) - (Representation.coind (sumPermHom (appendPositions rs ss)) - (outer (projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) - (inOutputs I) (inOutputs_invariant I)).toRepresentation - (projectedSpechtTensor ((enumerate ss).trans f) ((enumerate ss).trans f) - (inOutputs J) (inOutputs_invariant J)).toRepresentation))) : - WordPacking (rs++ss) ps d A label {k,l} := by - classical - let W := projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) - (inOutputs I) (inOutputs_invariant I) - let X := projectedSpechtTensor ((enumerate ss).trans f) ((enumerate ss).trans f) - (inOutputs J) (inOutputs_invariant J) - letI : AddCommGroup (W.toSubmodule ⊗[ℂ] X.toSubmodule) := Module.addCommMonoidToAddCommGroup ℂ - let P := placedPiece e hr hc hd k I A label he - let Q := placedPiece f hr' hc' hd' l J A label he' - let w := Classical.choose (exists_word_of_parts ps hsum) - have hw := Classical.choose_spec (exists_word_of_parts ps hsum) - let R := P.join Q (appendPositions rs ss) (fun _ _ => hne) - have ht : SupportLE (cyclic (wordRep (rs++ss).sum ps.length) (Pi.single w 1)).toRepresentation - (wordRep (rs++ss).sum E) := - (SupportLE.of_injective (subrepInclusion (cyclic (wordRep (rs++ss).sum _) (Pi.single w 1))) - Subtype.val_injective).trans (SupportLE.of_injective (letterLift (Fin.castLE hlen)) - (letterLift_injective _ (Fin.castLE_injective hlen))) - refine { - word := w - counts := hw - packing := { - G := Equiv.Perm (Fin rs.sum) × Equiv.Perm (Fin ss.sum) - Y := W.toSubmodule ⊗[ℂ] X.toSubmodule - c := joinedLabels (appendPositions rs ss) (fun _ => k) (fun _ => l) - σ := columnOutputSums ((enumerate rs).trans e) (fun _ => k) + - columnOutputSums ((enumerate ss).trans f) (fun _ => l) - φ := (joinedFiberHom (appendPositions rs ss) (fun _ => k) (fun _ => l)).comp - ((singleFiberHom rs.sum k).prodMap (singleFiberHom ss.sum l)) - τ := outer W.toRepresentation X.toRepresentation - piece := ?_ - support := ht.trans hs } - marksBound := ?_ } - · rw [blocks_append] - exact R - · intro i - change joinedLabels (appendPositions rs ss) (fun _ => k) (fun _ => l) i ∈ ({k,l} : Finset ℕ) - unfold joinedLabels - cases appendPositions rs ss i <;> simp - -theorem WordPacking.of_binary_shapes {rs ss ps : List ℕ} {μ ν : YoungDiagram} {d E : ℕ} - (hp : rs.Perm μ.transpose.rowLens) (hp' : ss.Perm ν.transpose.rowLens) - (hd : μ.colLen 0 ≤ d) (hd' : ν.colLen 0 ≤ d) - (hsum : ps.sum = (rs++ss).sum) (hlen : ps.length ≤ E) - (k l : ℕ) (hne : k ≠ l) (I J : Set ℕ) - (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) - (he' : ∀ a, (A a ∧ label a = l) ↔ output a ∈ J) - (hs : ∀ (t : Tableau rs.sum μ) (u : Tableau ss.sum ν), - SupportLE (wordRep (rs++ss).sum E) - (Representation.coind (sumPermHom (appendPositions rs ss)) - (outer (projectedSpechtTensor t t (inOutputs I) (inOutputs_invariant I)).toRepresentation - (projectedSpechtTensor u u (inOutputs J) (inOutputs_invariant J)).toRepresentation))) : - Nonempty (WordPacking (rs++ss) ps d A label {k,l}) := by - obtain ⟨e,hr,hc⟩ := place_columns μ hp - obtain ⟨f,hr',hc'⟩ := place_columns ν hp' - exact ⟨WordPacking.binaryBounded e f hr hc hr' hc' hd hd' hsum hlen - k l hne I J A label he he' (hs _ _)⟩ - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPacking +import OAI.RepresentationTheory.UniversalSquare.Support.PartWords + +namespace OAI + +/-! Word Packing Pairs. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl.Balance +open FlagColumns Columns + +def placedPiece {rs : List ℕ} {μ : YoungDiagram} {d : ℕ} + (e : Cells rs ≃ μ.cells) + (hr : ∀ c, (e c).val.1 = row c) + (hc : ∀ c c', (e c).val.2 = (e c').val.2 ↔ col c = col c') + (hd : μ.colLen 0 ≤ d) (k : ℕ) (I : Set ℕ) + (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) : + Piece (blocks rs (standard d)) (fun _ => k) A label + (columnOutputSums ((enumerate rs).trans e) (fun _ => k)) (singleFiberHom rs.sum k) + (projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) + (inOutputs I) (inOutputs_invariant I)).toRepresentation := by + let f := Fin.castLE hd + have hlocal : ∀ a, ((A ∘ pairLetterMap f f) a ∧ + (label ∘ pairLetterMap f f) a = k) ↔ output a ∈ I := by + intro a + rw [Function.comp_apply,Function.comp_apply,he,output_pairLetterMap f (fun _ => rfl)] + rw [standard_placed e hr hc hd] + exact (projectedPiece ((enumerate rs).trans e) k I _ _ hlocal).lift f (fun _ => rfl) A label + +def WordPacking.binaryBounded {rs ss ps : List ℕ} {μ ν : YoungDiagram} {d E : ℕ} + (e : Cells rs ≃ μ.cells) (f : Cells ss ≃ ν.cells) + (hr : ∀ c, (e c).val.1 = row c) + (hc : ∀ c c', (e c).val.2 = (e c').val.2 ↔ col c = col c') + (hr' : ∀ c, (f c).val.1 = row c) + (hc' : ∀ c c', (f c).val.2 = (f c').val.2 ↔ col c = col c') + (hd : μ.colLen 0 ≤ d) (hd' : ν.colLen 0 ≤ d) + (hsum : ps.sum = (rs++ss).sum) (hlen : ps.length ≤ E) + (k l : ℕ) (hne : k ≠ l) (I J : Set ℕ) + (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) + (he' : ∀ a, (A a ∧ label a = l) ↔ output a ∈ J) + (hs : SupportLE (wordRep (rs++ss).sum E) + (Representation.coind (sumPermHom (appendPositions rs ss)) + (outer (projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) + (inOutputs I) (inOutputs_invariant I)).toRepresentation + (projectedSpechtTensor ((enumerate ss).trans f) ((enumerate ss).trans f) + (inOutputs J) (inOutputs_invariant J)).toRepresentation))) : + WordPacking (rs++ss) ps d A label {k,l} := by + classical + let W := projectedSpechtTensor ((enumerate rs).trans e) ((enumerate rs).trans e) + (inOutputs I) (inOutputs_invariant I) + let X := projectedSpechtTensor ((enumerate ss).trans f) ((enumerate ss).trans f) + (inOutputs J) (inOutputs_invariant J) + letI : AddCommGroup (W.toSubmodule ⊗[ℂ] X.toSubmodule) := Module.addCommMonoidToAddCommGroup ℂ + let P := placedPiece e hr hc hd k I A label he + let Q := placedPiece f hr' hc' hd' l J A label he' + let w := Classical.choose (exists_word_of_parts ps hsum) + have hw := Classical.choose_spec (exists_word_of_parts ps hsum) + let R := P.join Q (appendPositions rs ss) (fun _ _ => hne) + have ht : SupportLE (cyclic (wordRep (rs++ss).sum ps.length) (Pi.single w 1)).toRepresentation + (wordRep (rs++ss).sum E) := + (SupportLE.of_injective (subrepInclusion (cyclic (wordRep (rs++ss).sum _) (Pi.single w 1))) + Subtype.val_injective).trans (SupportLE.of_injective (letterLift (Fin.castLE hlen)) + (letterLift_injective _ (Fin.castLE_injective hlen))) + refine { + word := w + counts := hw + packing := { + G := Equiv.Perm (Fin rs.sum) × Equiv.Perm (Fin ss.sum) + Y := W.toSubmodule ⊗[ℂ] X.toSubmodule + c := joinedLabels (appendPositions rs ss) (fun _ => k) (fun _ => l) + σ := columnOutputSums ((enumerate rs).trans e) (fun _ => k) + + columnOutputSums ((enumerate ss).trans f) (fun _ => l) + φ := (joinedFiberHom (appendPositions rs ss) (fun _ => k) (fun _ => l)).comp + ((singleFiberHom rs.sum k).prodMap (singleFiberHom ss.sum l)) + τ := outer W.toRepresentation X.toRepresentation + piece := ?_ + support := ht.trans hs } + marksBound := ?_ } + · rw [blocks_append] + exact R + · intro i + change joinedLabels (appendPositions rs ss) (fun _ => k) (fun _ => l) i ∈ ({k,l} : Finset ℕ) + unfold joinedLabels + cases appendPositions rs ss i <;> simp + +theorem WordPacking.of_binary_shapes {rs ss ps : List ℕ} {μ ν : YoungDiagram} {d E : ℕ} + (hp : rs.Perm μ.transpose.rowLens) (hp' : ss.Perm ν.transpose.rowLens) + (hd : μ.colLen 0 ≤ d) (hd' : ν.colLen 0 ≤ d) + (hsum : ps.sum = (rs++ss).sum) (hlen : ps.length ≤ E) + (k l : ℕ) (hne : k ≠ l) (I J : Set ℕ) + (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ I) + (he' : ∀ a, (A a ∧ label a = l) ↔ output a ∈ J) + (hs : ∀ (t : Tableau rs.sum μ) (u : Tableau ss.sum ν), + SupportLE (wordRep (rs++ss).sum E) + (Representation.coind (sumPermHom (appendPositions rs ss)) + (outer (projectedSpechtTensor t t (inOutputs I) (inOutputs_invariant I)).toRepresentation + (projectedSpechtTensor u u (inOutputs J) (inOutputs_invariant J)).toRepresentation))) : + Nonempty (WordPacking (rs++ss) ps d A label {k,l}) := by + obtain ⟨e,hr,hc⟩ := place_columns μ hp + obtain ⟨f,hr',hc'⟩ := place_columns ν hp' + exact ⟨WordPacking.binaryBounded e f hr hc hr' hc' hd hd' hsum hlen + k l hne I J A label he he' (hs _ _)⟩ + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingPieri.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingPieri.lean index 9ecfcf2b20c5b1b73d2e313c29bd839b494d9c43..30fb06a800944ae20c0cd347716482816bfc5b9c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingPieri.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Balance/WordPackingPieri.lean @@ -1,123 +1,123 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingGeometry -import OAI.RepresentationTheory.UniversalSquare.Specht.PieriInduction -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingPairs - -namespace OAI - -/-! Word Packing Pieri. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl.Balance -open FlagColumns Columns - -lemma short_transpose_height (r δ : ℕ) : (ShortColumns.shape r δ).transpose.colLen 0 = r+δ := by - rw [YoungDiagram.colLen_transpose] - exact YoungDiagram.rowLen_ofRowLens (hw := by apply List.Pairwise.sortedGE; simp) - (show Fin [r+δ,r].length from ⟨0,by simp⟩) - -lemma repeat_transpose_height {m k : ℕ} (hm : 0 < m) : - (YoungDiagram.ofRowLens (List.replicate m k) (replicate_sorted m k)).transpose.colLen 0 = k := by - rw [YoungDiagram.colLen_transpose] - simpa only [Fin.getElem_fin,List.getElem_replicate] using - YoungDiagram.rowLen_ofRowLens (hw := replicate_sorted m k) - (show Fin (List.replicate m k).length from ⟨0,by simpa⟩) - -lemma repeat_transpose_rows {m k : ℕ} (hk : 0 < k) : - (YoungDiagram.ofRowLens (List.replicate m k) (replicate_sorted m k)).transpose.transpose.rowLens = - List.replicate m k := by - rw [YoungDiagram.transpose_transpose] - apply YoungDiagram.rowLens_ofRowLens_eq_self - intro x hx - rw [(List.mem_replicate.mp hx).2] - exact hk - -lemma repeated_twos_shape (m : ℕ) : - (YoungDiagram.ofRowLens (List.replicate m 2) (replicate_sorted m 2)).transpose = - ShortColumns.shape m 0 := by - apply YoungDiagram.ext - apply Finset.ext - intro x - rcases x with ⟨i,j⟩ - change (i,j) ∈ (YoungDiagram.ofRowLens (List.replicate m 2) (replicate_sorted m 2)).transpose ↔ - (i,j) ∈ ShortColumns.shape m 0 - simp only [YoungDiagram.mem_transpose,YoungDiagram.mem_ofRowLens, - List.length_replicate,List.getElem_replicate,ShortColumns.mem_shape,Prod.swap_prod_mk] - simp only [exists_prop,Nat.add_zero] - omega - -lemma two_paths_two_support_sizes {n a b q : ℕ} {ν : YoungDiagram} - (hn : n = 2*q+4) (ha : a = 2*q+2) (hb : b = 2) (hq : 3 ≤ q) - (t : Tableau a (ShortColumns.shape q 2).transpose) (u : Tableau b ν) - (e : Fin n ≃ Fin a ⊕ Fin b) - (hu : ∀ i, (columnLengthWord u i).val+1 = 1) : - SupportLE (wordRep n 4) - (Representation.coind (sumPermHom e) - (outer (projectedSpechtTensor t t (inOutputs (Set.Icc q (2*q+3))) - (inOutputs_invariant (Set.Icc q (2*q+3)))).toRepresentation - (projectedSpechtTensor u u (inOutputs {1}) (inOutputs_invariant {1})).toRepresentation)) := by - subst n a b - exact (two_paths_two_coind q hq t e).trans - (SupportLE.coind _ ((SupportLE.refl _).outer (constant_output_support u 1 hu))) - -theorem WordPacking.twoPaths {q d : ℕ} (hq : 3 ≤ q) (hd : q+2 ≤ d) - {ps : List ℕ} (hsum : ps.sum = 2*q+4) (hlen : ps.length ≤ 4) - (k l : ℕ) (hne : k ≠ l) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ Set.Icc q (2*q+3)) - (he' : ∀ a, (A a ∧ label a = l) ↔ output a = 1) : - Nonempty (WordPacking ([q+2,q] ++ List.replicate 2 1) ps d A label {k,l}) := by - have hrow : (ShortColumns.shape q 2).rowLens = [q+2,q] := - YoungDiagram.rowLens_ofRowLens_eq_self (by simp; omega) - let ν := (YoungDiagram.ofRowLens (List.replicate 2 1) (replicate_sorted 2 1)).transpose - apply WordPacking.of_binary_shapes (μ := (ShortColumns.shape q 2).transpose) (ν := ν) - (by rw [YoungDiagram.transpose_transpose,hrow]) (by rw [repeat_transpose_rows (by decide)]) - (by rw [short_transpose_height]; exact hd) - (by rw [repeat_transpose_height (by decide)]; omega) - (by simp; omega) hlen k l hne _ {1} A label he he' - intro t u - exact two_paths_two_support_sizes (by simp; omega) (by simp; omega) (by simp) - hq t u (appendPositions _ _) (repeated_column_length (by decide) u) - -lemma even_twos_odd_support_sizes {n a b m x : ℕ} {ν : YoungDiagram} - (hn : n = 2*m+x) (ha : a = 2*m) (hb : b = x) - (hm : 1 ≤ m) (hx : Odd x) (hxc : x ≤ 2*m) - (t : Tableau a (ShortColumns.shape m 0)) (u : Tableau b ν) - (e : Fin n ≃ Fin a ⊕ Fin b) (hu : ∀ i, (columnLengthWord u i).val+1 = x) : - SupportLE (wordRep n 2) - (Representation.coind (sumPermHom e) - (outer (projectedSpechtTensor t t (inOutputs {2}) (inOutputs_invariant {2})).toRepresentation - (projectedSpechtTensor u u (inOutputs {x}) (inOutputs_invariant {x})).toRepresentation)) := by - subst n a b - exact (even_twos_odd_coind m x hm hx hxc t e).trans - (SupportLE.coind _ ((SupportLE.refl _).outer (constant_output_support u x hu))) - -theorem WordPacking.twosOdd {m x d : ℕ} (hm : 1 ≤ m) (hx : Odd x) (hxc : x ≤ 2*m) - (hd : 2 ≤ d) (hd' : x ≤ d) - {ps : List ℕ} (hsum : ps.sum = 2*m+x) (hlen : ps.length ≤ 2) - (k l : ℕ) (hne : k ≠ l) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ a, (A a ∧ label a = k) ↔ output a = 2) - (he' : ∀ a, (A a ∧ label a = l) ↔ output a = x) : - Nonempty (WordPacking (List.replicate m 2 ++ [x]) ps d A label {k,l}) := by - let ν := (YoungDiagram.ofRowLens (List.replicate 1 x) (replicate_sorted 1 x)).transpose - have hxpos : 0 < x := hx.pos - have hp : (List.replicate m 2).Perm (ShortColumns.shape m 0).transpose.rowLens := by - rw [← repeated_twos_shape,repeat_transpose_rows (by decide)] - apply WordPacking.of_binary_shapes (μ := ShortColumns.shape m 0) (ν := ν) hp - (by rw [repeat_transpose_rows hxpos]; rfl) - ((ShortColumns.height_le m 0).trans hd) - (by rw [repeat_transpose_height (by decide)]; exact hd') - (by simp only [List.sum_append,List.sum_replicate,List.sum_singleton,smul_eq_mul]; omega) - hlen k l hne {2} {x} A label he he' - intro t u - exact even_twos_odd_support_sizes (by simp; omega) (by simp; omega) (by simp) - hm hx hxc t u (appendPositions _ _) (repeated_column_length hxpos u) - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingGeometry +import OAI.RepresentationTheory.UniversalSquare.Specht.PieriInduction +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPackingPairs + +namespace OAI + +/-! Word Packing Pieri. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl.Balance +open FlagColumns Columns + +lemma short_transpose_height (r δ : ℕ) : (ShortColumns.shape r δ).transpose.colLen 0 = r+δ := by + rw [YoungDiagram.colLen_transpose] + exact YoungDiagram.rowLen_ofRowLens (hw := by apply List.Pairwise.sortedGE; simp) + (show Fin [r+δ,r].length from ⟨0,by simp⟩) + +lemma repeat_transpose_height {m k : ℕ} (hm : 0 < m) : + (YoungDiagram.ofRowLens (List.replicate m k) (replicate_sorted m k)).transpose.colLen 0 = k := by + rw [YoungDiagram.colLen_transpose] + simpa only [Fin.getElem_fin,List.getElem_replicate] using + YoungDiagram.rowLen_ofRowLens (hw := replicate_sorted m k) + (show Fin (List.replicate m k).length from ⟨0,by simpa⟩) + +lemma repeat_transpose_rows {m k : ℕ} (hk : 0 < k) : + (YoungDiagram.ofRowLens (List.replicate m k) (replicate_sorted m k)).transpose.transpose.rowLens = + List.replicate m k := by + rw [YoungDiagram.transpose_transpose] + apply YoungDiagram.rowLens_ofRowLens_eq_self + intro x hx + rw [(List.mem_replicate.mp hx).2] + exact hk + +lemma repeated_twos_shape (m : ℕ) : + (YoungDiagram.ofRowLens (List.replicate m 2) (replicate_sorted m 2)).transpose = + ShortColumns.shape m 0 := by + apply YoungDiagram.ext + apply Finset.ext + intro x + rcases x with ⟨i,j⟩ + change (i,j) ∈ (YoungDiagram.ofRowLens (List.replicate m 2) (replicate_sorted m 2)).transpose ↔ + (i,j) ∈ ShortColumns.shape m 0 + simp only [YoungDiagram.mem_transpose,YoungDiagram.mem_ofRowLens, + List.length_replicate,List.getElem_replicate,ShortColumns.mem_shape,Prod.swap_prod_mk] + simp only [exists_prop,Nat.add_zero] + omega + +lemma two_paths_two_support_sizes {n a b q : ℕ} {ν : YoungDiagram} + (hn : n = 2*q+4) (ha : a = 2*q+2) (hb : b = 2) (hq : 3 ≤ q) + (t : Tableau a (ShortColumns.shape q 2).transpose) (u : Tableau b ν) + (e : Fin n ≃ Fin a ⊕ Fin b) + (hu : ∀ i, (columnLengthWord u i).val+1 = 1) : + SupportLE (wordRep n 4) + (Representation.coind (sumPermHom e) + (outer (projectedSpechtTensor t t (inOutputs (Set.Icc q (2*q+3))) + (inOutputs_invariant (Set.Icc q (2*q+3)))).toRepresentation + (projectedSpechtTensor u u (inOutputs {1}) (inOutputs_invariant {1})).toRepresentation)) := by + subst n a b + exact (two_paths_two_coind q hq t e).trans + (SupportLE.coind _ ((SupportLE.refl _).outer (constant_output_support u 1 hu))) + +theorem WordPacking.twoPaths {q d : ℕ} (hq : 3 ≤ q) (hd : q+2 ≤ d) + {ps : List ℕ} (hsum : ps.sum = 2*q+4) (hlen : ps.length ≤ 4) + (k l : ℕ) (hne : k ≠ l) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ a, (A a ∧ label a = k) ↔ output a ∈ Set.Icc q (2*q+3)) + (he' : ∀ a, (A a ∧ label a = l) ↔ output a = 1) : + Nonempty (WordPacking ([q+2,q] ++ List.replicate 2 1) ps d A label {k,l}) := by + have hrow : (ShortColumns.shape q 2).rowLens = [q+2,q] := + YoungDiagram.rowLens_ofRowLens_eq_self (by simp; omega) + let ν := (YoungDiagram.ofRowLens (List.replicate 2 1) (replicate_sorted 2 1)).transpose + apply WordPacking.of_binary_shapes (μ := (ShortColumns.shape q 2).transpose) (ν := ν) + (by rw [YoungDiagram.transpose_transpose,hrow]) (by rw [repeat_transpose_rows (by decide)]) + (by rw [short_transpose_height]; exact hd) + (by rw [repeat_transpose_height (by decide)]; omega) + (by simp; omega) hlen k l hne _ {1} A label he he' + intro t u + exact two_paths_two_support_sizes (by simp; omega) (by simp; omega) (by simp) + hq t u (appendPositions _ _) (repeated_column_length (by decide) u) + +lemma even_twos_odd_support_sizes {n a b m x : ℕ} {ν : YoungDiagram} + (hn : n = 2*m+x) (ha : a = 2*m) (hb : b = x) + (hm : 1 ≤ m) (hx : Odd x) (hxc : x ≤ 2*m) + (t : Tableau a (ShortColumns.shape m 0)) (u : Tableau b ν) + (e : Fin n ≃ Fin a ⊕ Fin b) (hu : ∀ i, (columnLengthWord u i).val+1 = x) : + SupportLE (wordRep n 2) + (Representation.coind (sumPermHom e) + (outer (projectedSpechtTensor t t (inOutputs {2}) (inOutputs_invariant {2})).toRepresentation + (projectedSpechtTensor u u (inOutputs {x}) (inOutputs_invariant {x})).toRepresentation)) := by + subst n a b + exact (even_twos_odd_coind m x hm hx hxc t e).trans + (SupportLE.coind _ ((SupportLE.refl _).outer (constant_output_support u x hu))) + +theorem WordPacking.twosOdd {m x d : ℕ} (hm : 1 ≤ m) (hx : Odd x) (hxc : x ≤ 2*m) + (hd : 2 ≤ d) (hd' : x ≤ d) + {ps : List ℕ} (hsum : ps.sum = 2*m+x) (hlen : ps.length ≤ 2) + (k l : ℕ) (hne : k ≠ l) (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ a, (A a ∧ label a = k) ↔ output a = 2) + (he' : ∀ a, (A a ∧ label a = l) ↔ output a = x) : + Nonempty (WordPacking (List.replicate m 2 ++ [x]) ps d A label {k,l}) := by + let ν := (YoungDiagram.ofRowLens (List.replicate 1 x) (replicate_sorted 1 x)).transpose + have hxpos : 0 < x := hx.pos + have hp : (List.replicate m 2).Perm (ShortColumns.shape m 0).transpose.rowLens := by + rw [← repeated_twos_shape,repeat_transpose_rows (by decide)] + apply WordPacking.of_binary_shapes (μ := ShortColumns.shape m 0) (ν := ν) hp + (by rw [repeat_transpose_rows hxpos]; rfl) + ((ShortColumns.height_le m 0).trans hd) + (by rw [repeat_transpose_height (by decide)]; exact hd') + (by simp only [List.sum_append,List.sum_replicate,List.sum_singleton,smul_eq_mul]; omega) + hlen k l hne {2} {x} A label he he' + intro t u + exact even_twos_odd_support_sizes (by simp; omega) (by simp; omega) (by simp) + hm hx hxc t u (appendPositions _ _) (repeated_column_length hxpos u) + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandAllocation.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandAllocation.lean index 808698684dc2817c0ee39bdbe4fbdd8e6e4ceb89..c47f4143f40c31f23ee50addc2df2e1975b75116 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandAllocation.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandAllocation.lean @@ -1,215 +1,215 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Capacity.Capacity - -namespace OAI - -/-! Band Allocation. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -def prefixFill (f : ℕ → ℕ) (r i : ℕ) : ℕ := - min (f i) (r - ∑ j ∈ Finset.range i, f j) - -lemma prefixFill_le (f : ℕ → ℕ) (r i : ℕ) : prefixFill f r i ≤ f i := min_le_left _ _ - -lemma prefixFill_antitone {f : ℕ → ℕ} (hf : Antitone f) (r : ℕ) : - Antitone (prefixFill f r) := by - intro i j hij - apply min_le_min (hf hij) - apply Nat.sub_le_sub_left - exact Finset.sum_le_sum_of_subset (Finset.range_mono hij) - -lemma prefixFill_sum (f : ℕ → ℕ) (r k : ℕ) : - (∑ i ∈ Finset.range k, prefixFill f r i) = min r (∑ i ∈ Finset.range k, f i) := by - induction k with - | zero => simp - | succ k ih => - rw [Finset.sum_range_succ, Finset.sum_range_succ, ih, prefixFill] - omega - -def columnCut (μ : YoungDiagram) (f : ℕ → ℕ) (hf : Antitone f) : YoungDiagram where - cells := μ.cells.filter (fun c => c.1 < f c.2) - isLowerSet := by - intro x y hxy hy - simp only [Finset.mem_coe, Finset.mem_filter] at hy ⊢ - exact ⟨μ.isLowerSet hxy hy.1, hxy.1.trans_lt (hy.2.trans_le (hf hxy.2))⟩ - -lemma columnCut_le (μ : YoungDiagram) (f : ℕ → ℕ) (hf : Antitone f) : - columnCut μ f hf ≤ μ := fun _ h => (Finset.mem_filter.mp h).1 - -lemma columnCut_colLen (μ : YoungDiagram) (f : ℕ → ℕ) (hf : Antitone f) - (hb : ∀ i, f i ≤ μ.colLen i) (i : ℕ) : (columnCut μ f hf).colLen i = f i := by - have H (j : ℕ) : j < (columnCut μ f hf).colLen i ↔ j < f i := by - rw [← YoungDiagram.mem_iff_lt_colLen] - change ((j,i) ∈ μ.cells.filter _) ↔ _ - simp only [Finset.mem_filter, YoungDiagram.mem_cells] - exact ⟨And.right, fun h => ⟨YoungDiagram.mem_iff_lt_colLen.mpr (h.trans_le (hb i)),h⟩⟩ - have h₁ := H ((columnCut μ f hf).colLen i) - have h₂ := H (f i) - omega - -lemma columnCut_card (μ : YoungDiagram) (f : ℕ → ℕ) (hf : Antitone f) - (hb : ∀ i, f i ≤ μ.colLen i) : - (columnCut μ f hf).card = ∑ i ∈ Finset.range (μ.rowLen 0), f i := by - have hw : (columnCut μ f hf).rowLen 0 ≤ μ.rowLen 0 := by - by_contra hh - have he := columnCut_le μ f hf (YoungDiagram.mem_iff_lt_rowLen.mpr (Nat.lt_of_not_ge hh)) - exact Nat.lt_irrefl _ (YoungDiagram.mem_iff_lt_rowLen.mp he) - rw [← transpose_card, ← rowPrefix_eq_card _ (by simpa using hw)] - simp only [rowPrefix, YoungDiagram.rowLen_transpose, columnCut_colLen μ f hf hb] - -def extraCapacity (μ : YoungDiagram) (d q i : ℕ) : ℕ := - if i < q then (μ.colLen i-d)/2 else 0 - -lemma extraCapacity_antitone (μ : YoungDiagram) (d q : ℕ) : - Antitone (extraCapacity μ d q) := by - intro i j hij - dsimp only [extraCapacity] - split_ifs with hj hi hi - · exact Nat.div_le_div_right (Nat.sub_le_sub_right (μ.colLen_anti i j hij) d) - · omega - · exact Nat.zero_le _ - · exact le_rfl - -lemma extraCapacity_sum (μ : YoungDiagram) (d q : ℕ) : - (∑ i ∈ Finset.range (μ.rowLen 0), extraCapacity μ d q i) = bandCapacity μ d q := by - classical - have hs : ∀ i, μ.rowLen 0 ≤ i → μ.colLen i = 0 := by - intro i hi - simpa only [YoungDiagram.rowLen_transpose, YoungDiagram.colLen_transpose] using - rowLen_zero_of_height_le μ.transpose (by simpa using hi) - unfold bandCapacity - by_cases hq : q ≤ μ.rowLen 0 - · rw [← Finset.sum_subset (Finset.range_mono hq) (by - intro i hi hni - simp only [Finset.mem_range] at hni - simp [extraCapacity, hni])] - apply Finset.sum_congr rfl - intro i hi - simp only [extraCapacity, Finset.mem_range.mp hi, ite_true] - · have hh : μ.rowLen 0 ≤ q := by omega - rw [← Finset.sum_subset (Finset.range_mono hh) (by - intro i hi hni - simp only [Finset.mem_range, not_lt] at hni - simp only [hs i hni, Nat.zero_sub, Nat.zero_div])] - apply Finset.sum_congr rfl - intro i hi - simp only [extraCapacity, (Finset.mem_range.mp hi).trans_le hh, ite_true] - -lemma pathCapacity_sum (μ : YoungDiagram) (d : ℕ) : - (∑ i ∈ Finset.range (μ.rowLen 0), min d (μ.colLen i)) = rowPrefix μ d := by - rw [← rowTruncate_card, ← transpose_card] - have hw : (rowTruncate μ d).rowLen 0 ≤ μ.rowLen 0 := by - rw [rowTruncate_rowLen] - split_ifs <;> omega - rw [← rowPrefix_eq_card _ (by simpa using hw)] - simp only [rowPrefix, YoungDiagram.rowLen_transpose] - apply Finset.sum_congr rfl - intro i hi - apply Nat.le_antisymm - · by_contra hn - have hh : ((rowTruncate μ d).colLen i,i) ∈ rowTruncate μ d := - mem_rowTruncate.mpr ⟨YoungDiagram.mem_iff_lt_colLen.mpr (by omega), by omega⟩ - exact Nat.lt_irrefl _ (YoungDiagram.mem_iff_lt_colLen.mp hh) - · by_contra hn - have hh : (min d (μ.colLen i),i) ∈ rowTruncate μ d := - YoungDiagram.mem_iff_lt_colLen.mpr (by omega) - have ht := mem_rowTruncate.mp hh - have hc := YoungDiagram.mem_iff_lt_colLen.mp ht.1 - omega - -theorem band_subdiagram_allocation (lam : YoungDiagram) (K r d q : ℕ) - (hK : K ≤ rowPrefix lam d) (hclear : d*q+7+d ≤ K) - (hr : r ≤ bandCapacity lam d q) : - ∃ π η μ : YoungDiagram, - μ ≤ lam ∧ π.card = K ∧ η.card = 2*r ∧ μ.card = K+2*r ∧ - (∀ i, μ.colLen i = π.colLen i + η.colLen i) ∧ - (∀ i, π.colLen i ≤ d) ∧ - (∀ i, Even (η.colLen i)) ∧ η.rowLen 0 ≤ q ∧ - (∀ i, 0 < η.colLen i → π.colLen i = d) := by - let p := prefixFill (fun i => min d (lam.colLen i)) K - let e := fun i => 2*prefixFill (extraCapacity lam d q) r i - have hpanti : Antitone p := prefixFill_antitone (fun _ _ h => min_le_min le_rfl (lam.colLen_anti _ _ h)) K - have heanti : Antitone e := fun _ _ h => Nat.mul_le_mul_left 2 - (prefixFill_antitone (extraCapacity_antitone lam d q) r h) - have hpbound (i : ℕ) : p i ≤ min d (lam.colLen i) := prefixFill_le _ _ _ - have hebound (i : ℕ) : e i ≤ lam.colLen i-d := by - have hh := Nat.mul_le_mul_left 2 (prefixFill_le (extraCapacity lam d q) r i) - have hc : extraCapacity lam d q i ≤ (lam.colLen i-d)/2 := by - dsimp [extraCapacity] - split_ifs <;> omega - dsimp only [e] - omega - have hpb (i : ℕ) : p i ≤ lam.colLen i := (hpbound i).trans (min_le_right _ _) - have heb (i : ℕ) : e i ≤ lam.colLen i := (hebound i).trans (Nat.sub_le _ _) - have hpos (i : ℕ) (hi : 0 < e i) : i < q ∧ d ≤ lam.colLen i := by - have hh := prefixFill_le (extraCapacity lam d q) r i - have hc : 0 < extraCapacity lam d q i := by dsimp [e] at hi; omega - dsimp only [extraCapacity] at hc - split_ifs at hc with h - · exact ⟨h, by omega⟩ - · omega - have hsbound (i : ℕ) : p i+e i ≤ lam.colLen i := by - by_cases hi : 0 < e i - · have hh := (hpos i hi).2 - have hp := (hpbound i).trans (min_le_left _ _) - have he := hebound i - omega - · have hp := hpb i - omega - let π := columnCut lam p hpanti - let η := columnCut lam e heanti - let μ := columnCut lam (fun i => p i+e i) (fun _ _ h => Nat.add_le_add (hpanti h) (heanti h)) - have hπ (i) : π.colLen i = p i := columnCut_colLen _ _ _ hpb i - have hη (i) : η.colLen i = e i := columnCut_colLen _ _ _ heb i - have hμ (i) : μ.colLen i = p i+e i := columnCut_colLen _ _ _ hsbound i - have hpSum : (∑ i ∈ Finset.range (lam.rowLen 0), p i) = K := by - rw [prefixFill_sum, pathCapacity_sum, min_eq_left hK] - have heSum : (∑ i ∈ Finset.range (lam.rowLen 0), e i) = 2*r := by - rw [← Finset.mul_sum, prefixFill_sum, extraCapacity_sum, min_eq_left hr] - refine ⟨π,η,μ,columnCut_le _ _ _, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩ - · exact (columnCut_card _ _ _ hpb).trans hpSum - · exact (columnCut_card _ _ _ heb).trans heSum - · refine (columnCut_card lam (fun i => p i+e i) - (fun _ _ h => Nat.add_le_add (hpanti h) (heanti h)) hsbound).trans ?_ - rw [Finset.sum_add_distrib, hpSum, heSum] - · intro i - rw [hμ,hπ,hη] - · intro i - exact (hπ i).le.trans ((hpbound i).trans (min_le_left _ _)) - · intro i - rw [hη] - exact even_two_mul _ - · by_contra hh - have h : 0 < η.colLen q := YoungDiagram.mem_iff_lt_colLen.mp - (YoungDiagram.mem_iff_lt_rowLen.mpr (Nat.lt_of_not_ge hh)) - rw [hη] at h - exact Nat.lt_irrefl _ (hpos q h).1 - · intro i hi - rw [hπ] - rw [hη] at hi - obtain ⟨hiq,hid⟩ := hpos i hi - have hs : (∑ j ∈ Finset.range i, min d (lam.colLen j)) ≤ i*d := by - simpa only [Finset.sum_const, Finset.card_range, smul_eq_mul] using - (Finset.sum_le_sum (s := Finset.range i) (fun j _ => min_le_left d (lam.colLen j))) - have hmul : (i+1)*d ≤ q*d := Nat.mul_le_mul_right d hiq - dsimp only [p, prefixFill] - rw [min_eq_left hid] - apply min_eq_left - apply Nat.le_sub_of_add_le - have hc : q*d ≤ K := by simpa only [Nat.mul_comm] using (show d*q ≤ K by omega) - calc d + (∑ j ∈ Finset.range i, min d (lam.colLen j)) ≤ d+i*d := Nat.add_le_add_left hs _ - _ = (i+1)*d := by ring - _ ≤ q*d := hmul - _ ≤ K := hc - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Capacity.Capacity + +namespace OAI + +/-! Band Allocation. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +def prefixFill (f : ℕ → ℕ) (r i : ℕ) : ℕ := + min (f i) (r - ∑ j ∈ Finset.range i, f j) + +lemma prefixFill_le (f : ℕ → ℕ) (r i : ℕ) : prefixFill f r i ≤ f i := min_le_left _ _ + +lemma prefixFill_antitone {f : ℕ → ℕ} (hf : Antitone f) (r : ℕ) : + Antitone (prefixFill f r) := by + intro i j hij + apply min_le_min (hf hij) + apply Nat.sub_le_sub_left + exact Finset.sum_le_sum_of_subset (Finset.range_mono hij) + +lemma prefixFill_sum (f : ℕ → ℕ) (r k : ℕ) : + (∑ i ∈ Finset.range k, prefixFill f r i) = min r (∑ i ∈ Finset.range k, f i) := by + induction k with + | zero => simp + | succ k ih => + rw [Finset.sum_range_succ, Finset.sum_range_succ, ih, prefixFill] + omega + +def columnCut (μ : YoungDiagram) (f : ℕ → ℕ) (hf : Antitone f) : YoungDiagram where + cells := μ.cells.filter (fun c => c.1 < f c.2) + isLowerSet := by + intro x y hxy hy + simp only [Finset.mem_coe, Finset.mem_filter] at hy ⊢ + exact ⟨μ.isLowerSet hxy hy.1, hxy.1.trans_lt (hy.2.trans_le (hf hxy.2))⟩ + +lemma columnCut_le (μ : YoungDiagram) (f : ℕ → ℕ) (hf : Antitone f) : + columnCut μ f hf ≤ μ := fun _ h => (Finset.mem_filter.mp h).1 + +lemma columnCut_colLen (μ : YoungDiagram) (f : ℕ → ℕ) (hf : Antitone f) + (hb : ∀ i, f i ≤ μ.colLen i) (i : ℕ) : (columnCut μ f hf).colLen i = f i := by + have H (j : ℕ) : j < (columnCut μ f hf).colLen i ↔ j < f i := by + rw [← YoungDiagram.mem_iff_lt_colLen] + change ((j,i) ∈ μ.cells.filter _) ↔ _ + simp only [Finset.mem_filter, YoungDiagram.mem_cells] + exact ⟨And.right, fun h => ⟨YoungDiagram.mem_iff_lt_colLen.mpr (h.trans_le (hb i)),h⟩⟩ + have h₁ := H ((columnCut μ f hf).colLen i) + have h₂ := H (f i) + omega + +lemma columnCut_card (μ : YoungDiagram) (f : ℕ → ℕ) (hf : Antitone f) + (hb : ∀ i, f i ≤ μ.colLen i) : + (columnCut μ f hf).card = ∑ i ∈ Finset.range (μ.rowLen 0), f i := by + have hw : (columnCut μ f hf).rowLen 0 ≤ μ.rowLen 0 := by + by_contra hh + have he := columnCut_le μ f hf (YoungDiagram.mem_iff_lt_rowLen.mpr (Nat.lt_of_not_ge hh)) + exact Nat.lt_irrefl _ (YoungDiagram.mem_iff_lt_rowLen.mp he) + rw [← transpose_card, ← rowPrefix_eq_card _ (by simpa using hw)] + simp only [rowPrefix, YoungDiagram.rowLen_transpose, columnCut_colLen μ f hf hb] + +def extraCapacity (μ : YoungDiagram) (d q i : ℕ) : ℕ := + if i < q then (μ.colLen i-d)/2 else 0 + +lemma extraCapacity_antitone (μ : YoungDiagram) (d q : ℕ) : + Antitone (extraCapacity μ d q) := by + intro i j hij + dsimp only [extraCapacity] + split_ifs with hj hi hi + · exact Nat.div_le_div_right (Nat.sub_le_sub_right (μ.colLen_anti i j hij) d) + · omega + · exact Nat.zero_le _ + · exact le_rfl + +lemma extraCapacity_sum (μ : YoungDiagram) (d q : ℕ) : + (∑ i ∈ Finset.range (μ.rowLen 0), extraCapacity μ d q i) = bandCapacity μ d q := by + classical + have hs : ∀ i, μ.rowLen 0 ≤ i → μ.colLen i = 0 := by + intro i hi + simpa only [YoungDiagram.rowLen_transpose, YoungDiagram.colLen_transpose] using + rowLen_zero_of_height_le μ.transpose (by simpa using hi) + unfold bandCapacity + by_cases hq : q ≤ μ.rowLen 0 + · rw [← Finset.sum_subset (Finset.range_mono hq) (by + intro i hi hni + simp only [Finset.mem_range] at hni + simp [extraCapacity, hni])] + apply Finset.sum_congr rfl + intro i hi + simp only [extraCapacity, Finset.mem_range.mp hi, ite_true] + · have hh : μ.rowLen 0 ≤ q := by omega + rw [← Finset.sum_subset (Finset.range_mono hh) (by + intro i hi hni + simp only [Finset.mem_range, not_lt] at hni + simp only [hs i hni, Nat.zero_sub, Nat.zero_div])] + apply Finset.sum_congr rfl + intro i hi + simp only [extraCapacity, (Finset.mem_range.mp hi).trans_le hh, ite_true] + +lemma pathCapacity_sum (μ : YoungDiagram) (d : ℕ) : + (∑ i ∈ Finset.range (μ.rowLen 0), min d (μ.colLen i)) = rowPrefix μ d := by + rw [← rowTruncate_card, ← transpose_card] + have hw : (rowTruncate μ d).rowLen 0 ≤ μ.rowLen 0 := by + rw [rowTruncate_rowLen] + split_ifs <;> omega + rw [← rowPrefix_eq_card _ (by simpa using hw)] + simp only [rowPrefix, YoungDiagram.rowLen_transpose] + apply Finset.sum_congr rfl + intro i hi + apply Nat.le_antisymm + · by_contra hn + have hh : ((rowTruncate μ d).colLen i,i) ∈ rowTruncate μ d := + mem_rowTruncate.mpr ⟨YoungDiagram.mem_iff_lt_colLen.mpr (by omega), by omega⟩ + exact Nat.lt_irrefl _ (YoungDiagram.mem_iff_lt_colLen.mp hh) + · by_contra hn + have hh : (min d (μ.colLen i),i) ∈ rowTruncate μ d := + YoungDiagram.mem_iff_lt_colLen.mpr (by omega) + have ht := mem_rowTruncate.mp hh + have hc := YoungDiagram.mem_iff_lt_colLen.mp ht.1 + omega + +theorem band_subdiagram_allocation (lam : YoungDiagram) (K r d q : ℕ) + (hK : K ≤ rowPrefix lam d) (hclear : d*q+7+d ≤ K) + (hr : r ≤ bandCapacity lam d q) : + ∃ π η μ : YoungDiagram, + μ ≤ lam ∧ π.card = K ∧ η.card = 2*r ∧ μ.card = K+2*r ∧ + (∀ i, μ.colLen i = π.colLen i + η.colLen i) ∧ + (∀ i, π.colLen i ≤ d) ∧ + (∀ i, Even (η.colLen i)) ∧ η.rowLen 0 ≤ q ∧ + (∀ i, 0 < η.colLen i → π.colLen i = d) := by + let p := prefixFill (fun i => min d (lam.colLen i)) K + let e := fun i => 2*prefixFill (extraCapacity lam d q) r i + have hpanti : Antitone p := prefixFill_antitone (fun _ _ h => min_le_min le_rfl (lam.colLen_anti _ _ h)) K + have heanti : Antitone e := fun _ _ h => Nat.mul_le_mul_left 2 + (prefixFill_antitone (extraCapacity_antitone lam d q) r h) + have hpbound (i : ℕ) : p i ≤ min d (lam.colLen i) := prefixFill_le _ _ _ + have hebound (i : ℕ) : e i ≤ lam.colLen i-d := by + have hh := Nat.mul_le_mul_left 2 (prefixFill_le (extraCapacity lam d q) r i) + have hc : extraCapacity lam d q i ≤ (lam.colLen i-d)/2 := by + dsimp [extraCapacity] + split_ifs <;> omega + dsimp only [e] + omega + have hpb (i : ℕ) : p i ≤ lam.colLen i := (hpbound i).trans (min_le_right _ _) + have heb (i : ℕ) : e i ≤ lam.colLen i := (hebound i).trans (Nat.sub_le _ _) + have hpos (i : ℕ) (hi : 0 < e i) : i < q ∧ d ≤ lam.colLen i := by + have hh := prefixFill_le (extraCapacity lam d q) r i + have hc : 0 < extraCapacity lam d q i := by dsimp [e] at hi; omega + dsimp only [extraCapacity] at hc + split_ifs at hc with h + · exact ⟨h, by omega⟩ + · omega + have hsbound (i : ℕ) : p i+e i ≤ lam.colLen i := by + by_cases hi : 0 < e i + · have hh := (hpos i hi).2 + have hp := (hpbound i).trans (min_le_left _ _) + have he := hebound i + omega + · have hp := hpb i + omega + let π := columnCut lam p hpanti + let η := columnCut lam e heanti + let μ := columnCut lam (fun i => p i+e i) (fun _ _ h => Nat.add_le_add (hpanti h) (heanti h)) + have hπ (i) : π.colLen i = p i := columnCut_colLen _ _ _ hpb i + have hη (i) : η.colLen i = e i := columnCut_colLen _ _ _ heb i + have hμ (i) : μ.colLen i = p i+e i := columnCut_colLen _ _ _ hsbound i + have hpSum : (∑ i ∈ Finset.range (lam.rowLen 0), p i) = K := by + rw [prefixFill_sum, pathCapacity_sum, min_eq_left hK] + have heSum : (∑ i ∈ Finset.range (lam.rowLen 0), e i) = 2*r := by + rw [← Finset.mul_sum, prefixFill_sum, extraCapacity_sum, min_eq_left hr] + refine ⟨π,η,μ,columnCut_le _ _ _, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩ + · exact (columnCut_card _ _ _ hpb).trans hpSum + · exact (columnCut_card _ _ _ heb).trans heSum + · refine (columnCut_card lam (fun i => p i+e i) + (fun _ _ h => Nat.add_le_add (hpanti h) (heanti h)) hsbound).trans ?_ + rw [Finset.sum_add_distrib, hpSum, heSum] + · intro i + rw [hμ,hπ,hη] + · intro i + exact (hπ i).le.trans ((hpbound i).trans (min_le_left _ _)) + · intro i + rw [hη] + exact even_two_mul _ + · by_contra hh + have h : 0 < η.colLen q := YoungDiagram.mem_iff_lt_colLen.mp + (YoungDiagram.mem_iff_lt_rowLen.mpr (Nat.lt_of_not_ge hh)) + rw [hη] at h + exact Nat.lt_irrefl _ (hpos q h).1 + · intro i hi + rw [hπ] + rw [hη] at hi + obtain ⟨hiq,hid⟩ := hpos i hi + have hs : (∑ j ∈ Finset.range i, min d (lam.colLen j)) ≤ i*d := by + simpa only [Finset.sum_const, Finset.card_range, smul_eq_mul] using + (Finset.sum_le_sum (s := Finset.range i) (fun j _ => min_le_left d (lam.colLen j))) + have hmul : (i+1)*d ≤ q*d := Nat.mul_le_mul_right d hiq + dsimp only [p, prefixFill] + rw [min_eq_left hid] + apply min_eq_left + apply Nat.le_sub_of_add_le + have hc : q*d ≤ K := by simpa only [Nat.mul_comm] using (show d*q ≤ K by omega) + calc d + (∑ j ∈ Finset.range i, min d (lam.colLen j)) ≤ d+i*d := Nat.add_le_add_left hs _ + _ = (i+1)*d := by ring + _ ≤ q*d := hmul + _ ≤ K := hc + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandAllocationLists.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandAllocationLists.lean index 33e087b3df62aaa0f8f1ada32aa865b9adedd1c6..fb9bf4a40f4fb8f9c23a7baa5f7e260dd9d260f0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandAllocationLists.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandAllocationLists.lean @@ -1,132 +1,132 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Band.BandAllocation -import OAI.RepresentationTheory.UniversalSquare.Specht.ColumnClearance - -namespace OAI - -/-! Band Allocation Lists. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -lemma colLen_pos_iff (μ : YoungDiagram) (i : ℕ) : - 0 < μ.colLen i ↔ i < μ.rowLen 0 := by - rw [← YoungDiagram.mem_iff_lt_colLen, YoungDiagram.mem_iff_lt_rowLen] - -lemma positive_column_list (μ : YoungDiagram) (W : ℕ) (hW : μ.rowLen 0 ≤ W) : - ((List.range W).map μ.colLen).filter (fun a => 0 < a) = μ.transpose.rowLens := by - rw [List.filter_map] - have h : (List.range W).filter ((fun a => decide (0 < a)) ∘ μ.colLen) = - List.range (μ.rowLen 0) := by - calc _ = (List.range W).filter (fun i => decide (i < μ.rowLen 0)) := by - apply List.filter_congr - intro i hi - simp only [Function.comp_apply, colLen_pos_iff] - _ = List.range (μ.rowLen 0) := by - rw [← List.Ico.zero_bot W, List.Ico.filter_lt_of_ge hW, List.Ico.zero_bot] - rw [h] - simp only [YoungDiagram.rowLens, YoungDiagram.colLen_transpose] - apply List.map_congr_left - intro i hi - exact (YoungDiagram.rowLen_transpose μ i).symm - -lemma column_list_sum (μ : YoungDiagram) (W : ℕ) (hW : μ.rowLen 0 ≤ W) : - ((List.range W).map μ.colLen).sum = μ.card := by - rw [← List.sum_toFinset μ.colLen List.nodup_range] - simpa only [List.toFinset_range, rowPrefix, YoungDiagram.rowLen_transpose, transpose_card] - using rowPrefix_eq_card μ.transpose (by simpa using hW) - -lemma place_padded_columns (μ : YoungDiagram) (W : ℕ) (hW : μ.rowLen 0 ≤ W) - (rs : List ℕ) (h : rs.Perm ((List.range W).map μ.colLen)) : - ∃ e : Columns.Cells rs ≃ μ.cells, - (∀ c, (e c).val.1 = Columns.row c) ∧ - (∀ c d, (e c).val.2 = (e d).val.2 ↔ Columns.col c = Columns.col d) := by - obtain ⟨e,hr,hc⟩ := Columns.discard_zero_columns rs - have hh := h.filter (fun a => decide (0 < a)) - rw [positive_column_list μ W hW] at hh - obtain ⟨f,hr',hc'⟩ := Columns.place_columns μ hh - exact ⟨e.trans f,fun c => (hr' (e c)).trans (hr c), - fun c d => (hc' (e c) (e d)).trans (hc c d)⟩ - -lemma width_le_of_cols {π μ : YoungDiagram} (h : ∀ i, π.colLen i ≤ μ.colLen i) : - π.rowLen 0 ≤ μ.rowLen 0 := by - by_contra hh - have hi : 0 < π.colLen (μ.rowLen 0) := (colLen_pos_iff _ _).mpr (by omega) - have hi' : 0 < μ.colLen (μ.rowLen 0) := hi.trans_le (h _) - exact Nat.lt_irrefl _ ((colLen_pos_iff _ _).mp hi') - -theorem band_subdiagram_columns (lam : YoungDiagram) (K r d q : ℕ) - (hd : 1 ≤ d) (hK : K ≤ rowPrefix lam d) (hclear : d*q+7+d ≤ K) - (hr : r ≤ bandCapacity lam d q) : - ∃ μ η : YoungDiagram, ∃ ps : List (ℕ × ℕ), - μ ≤ lam ∧ μ.card = K+2*r ∧ η.card = 2*r ∧ - (ps.map Prod.fst).sum = K ∧ (ps.map Prod.snd).sum = 2*r ∧ - (∀ p ∈ ps, 1 ≤ p.1 ∧ p.1 ≤ d) ∧ - (∀ p ∈ ps, p.2 ≠ 0 → p.1 = d) ∧ - Saxl.FlagColumns.columnsAway K ps 0 ∧ - (∀ i, Even (η.colLen i)) ∧ η.rowLen 0 ≤ q ∧ - (∃ e : Columns.Cells (ps.map (fun p => p.1+p.2)) ≃ μ.cells, - (∀ c, (e c).val.1 = Columns.row c) ∧ - (∀ c c', (e c).val.2 = (e c').val.2 ↔ Columns.col c = Columns.col c')) ∧ - (∃ e : Columns.Cells (ps.map Prod.snd) ≃ η.cells, - (∀ c, (e c).val.1 = Columns.row c) ∧ - (∀ c c', (e c).val.2 = (e c').val.2 ↔ Columns.col c = Columns.col c')) := by - obtain ⟨π,η,μ,hμlam,hπcard,hηcard,hμcard,hcolsh,hplen,heven,hηw,hchosen⟩ := - band_subdiagram_allocation lam K r d q hK hclear hr - let W := μ.rowLen 0 - let ps := (List.range W).map (fun i => (π.colLen i, η.colLen i)) - have hπw : π.rowLen 0 ≤ W := width_le_of_cols (fun i => by rw [hcolsh]; omega) - have hηw' : η.rowLen 0 ≤ W := width_le_of_cols (fun i => by rw [hcolsh]; omega) - have hs₁ : (ps.map Prod.fst).sum = K := by - simpa only [ps,List.map_map,Function.comp_def] using - (column_list_sum π W hπw).trans hπcard - have hs₂ : (ps.map Prod.snd).sum = 2*r := by - simpa only [ps,List.map_map,Function.comp_def] using - (column_list_sum η W hηw').trans hηcard - have ha : ∀ p ∈ ps, 1 ≤ p.1 ∧ p.1 ≤ d := by - intro p hp - obtain ⟨i,hi,rfl⟩ := List.mem_map.mp hp - have hm : 0 < μ.colLen i := (colLen_pos_iff μ i).mpr (List.mem_range.mp hi) - rw [hcolsh] at hm - by_cases he : 0 < η.colLen i - · exact ⟨by rw [hchosen i he]; exact hd,hplen i⟩ - · exact ⟨by omega,hplen i⟩ - have hb : ∀ p ∈ ps, p.2 ≠ 0 → p.1 = d := by - intro p hp hn - obtain ⟨i,hi,rfl⟩ := List.mem_map.mp hp - exact hchosen i (Nat.pos_of_ne_zero hn) - have hlen : (ps.filter (fun p => p.2 ≠ 0)).length ≤ q := by - have hh : (ps.filter (fun p => p.2 ≠ 0)).length = η.rowLen 0 := by - dsimp only [ps] - rw [List.filter_map, List.length_map] - have hh : (List.range W).filter ((fun p : ℕ × ℕ => decide (p.2 ≠ 0)) ∘ - (fun i => (π.colLen i,η.colLen i))) = List.range (η.rowLen 0) := by - calc _ = (List.range W).filter (fun i => decide (i < η.rowLen 0)) := by - apply List.filter_congr - intro i hi - simp only [Function.comp_apply, Nat.pos_iff_ne_zero.symm, colLen_pos_iff] - _ = List.range (η.rowLen 0) := by - rw [← List.Ico.zero_bot W,List.Ico.filter_lt_of_ge hηw',List.Ico.zero_bot] - rw [hh,List.length_range] - exact hh.le.trans hηw - obtain ⟨qs,hqs,hqc⟩ := Saxl.FlagColumns.reorder_columns_away ps d K q hs₁ - (fun p hp => (ha p hp).2) hb hlen hclear - refine ⟨μ,η,qs,hμlam,hμcard,hηcard,(hqs.map Prod.fst).sum_eq.trans hs₁, - (hqs.map Prod.snd).sum_eq.trans hs₂, - fun p hp => ha p (hqs.mem_iff.mp hp),fun p hp => hb p (hqs.mem_iff.mp hp), - hqc,heven,hηw,?_,?_⟩ - · apply place_padded_columns μ W le_rfl - have hh := hqs.map (fun p => p.1+p.2) - simpa only [ps,List.map_map,Function.comp_def,← hcolsh] using hh - · apply place_padded_columns η W hηw' - simpa only [ps,List.map_map,Function.comp_def] using hqs.map Prod.snd - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Band.BandAllocation +import OAI.RepresentationTheory.UniversalSquare.Specht.ColumnClearance + +namespace OAI + +/-! Band Allocation Lists. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +lemma colLen_pos_iff (μ : YoungDiagram) (i : ℕ) : + 0 < μ.colLen i ↔ i < μ.rowLen 0 := by + rw [← YoungDiagram.mem_iff_lt_colLen, YoungDiagram.mem_iff_lt_rowLen] + +lemma positive_column_list (μ : YoungDiagram) (W : ℕ) (hW : μ.rowLen 0 ≤ W) : + ((List.range W).map μ.colLen).filter (fun a => 0 < a) = μ.transpose.rowLens := by + rw [List.filter_map] + have h : (List.range W).filter ((fun a => decide (0 < a)) ∘ μ.colLen) = + List.range (μ.rowLen 0) := by + calc _ = (List.range W).filter (fun i => decide (i < μ.rowLen 0)) := by + apply List.filter_congr + intro i hi + simp only [Function.comp_apply, colLen_pos_iff] + _ = List.range (μ.rowLen 0) := by + rw [← List.Ico.zero_bot W, List.Ico.filter_lt_of_ge hW, List.Ico.zero_bot] + rw [h] + simp only [YoungDiagram.rowLens, YoungDiagram.colLen_transpose] + apply List.map_congr_left + intro i hi + exact (YoungDiagram.rowLen_transpose μ i).symm + +lemma column_list_sum (μ : YoungDiagram) (W : ℕ) (hW : μ.rowLen 0 ≤ W) : + ((List.range W).map μ.colLen).sum = μ.card := by + rw [← List.sum_toFinset μ.colLen List.nodup_range] + simpa only [List.toFinset_range, rowPrefix, YoungDiagram.rowLen_transpose, transpose_card] + using rowPrefix_eq_card μ.transpose (by simpa using hW) + +lemma place_padded_columns (μ : YoungDiagram) (W : ℕ) (hW : μ.rowLen 0 ≤ W) + (rs : List ℕ) (h : rs.Perm ((List.range W).map μ.colLen)) : + ∃ e : Columns.Cells rs ≃ μ.cells, + (∀ c, (e c).val.1 = Columns.row c) ∧ + (∀ c d, (e c).val.2 = (e d).val.2 ↔ Columns.col c = Columns.col d) := by + obtain ⟨e,hr,hc⟩ := Columns.discard_zero_columns rs + have hh := h.filter (fun a => decide (0 < a)) + rw [positive_column_list μ W hW] at hh + obtain ⟨f,hr',hc'⟩ := Columns.place_columns μ hh + exact ⟨e.trans f,fun c => (hr' (e c)).trans (hr c), + fun c d => (hc' (e c) (e d)).trans (hc c d)⟩ + +lemma width_le_of_cols {π μ : YoungDiagram} (h : ∀ i, π.colLen i ≤ μ.colLen i) : + π.rowLen 0 ≤ μ.rowLen 0 := by + by_contra hh + have hi : 0 < π.colLen (μ.rowLen 0) := (colLen_pos_iff _ _).mpr (by omega) + have hi' : 0 < μ.colLen (μ.rowLen 0) := hi.trans_le (h _) + exact Nat.lt_irrefl _ ((colLen_pos_iff _ _).mp hi') + +theorem band_subdiagram_columns (lam : YoungDiagram) (K r d q : ℕ) + (hd : 1 ≤ d) (hK : K ≤ rowPrefix lam d) (hclear : d*q+7+d ≤ K) + (hr : r ≤ bandCapacity lam d q) : + ∃ μ η : YoungDiagram, ∃ ps : List (ℕ × ℕ), + μ ≤ lam ∧ μ.card = K+2*r ∧ η.card = 2*r ∧ + (ps.map Prod.fst).sum = K ∧ (ps.map Prod.snd).sum = 2*r ∧ + (∀ p ∈ ps, 1 ≤ p.1 ∧ p.1 ≤ d) ∧ + (∀ p ∈ ps, p.2 ≠ 0 → p.1 = d) ∧ + Saxl.FlagColumns.columnsAway K ps 0 ∧ + (∀ i, Even (η.colLen i)) ∧ η.rowLen 0 ≤ q ∧ + (∃ e : Columns.Cells (ps.map (fun p => p.1+p.2)) ≃ μ.cells, + (∀ c, (e c).val.1 = Columns.row c) ∧ + (∀ c c', (e c).val.2 = (e c').val.2 ↔ Columns.col c = Columns.col c')) ∧ + (∃ e : Columns.Cells (ps.map Prod.snd) ≃ η.cells, + (∀ c, (e c).val.1 = Columns.row c) ∧ + (∀ c c', (e c).val.2 = (e c').val.2 ↔ Columns.col c = Columns.col c')) := by + obtain ⟨π,η,μ,hμlam,hπcard,hηcard,hμcard,hcolsh,hplen,heven,hηw,hchosen⟩ := + band_subdiagram_allocation lam K r d q hK hclear hr + let W := μ.rowLen 0 + let ps := (List.range W).map (fun i => (π.colLen i, η.colLen i)) + have hπw : π.rowLen 0 ≤ W := width_le_of_cols (fun i => by rw [hcolsh]; omega) + have hηw' : η.rowLen 0 ≤ W := width_le_of_cols (fun i => by rw [hcolsh]; omega) + have hs₁ : (ps.map Prod.fst).sum = K := by + simpa only [ps,List.map_map,Function.comp_def] using + (column_list_sum π W hπw).trans hπcard + have hs₂ : (ps.map Prod.snd).sum = 2*r := by + simpa only [ps,List.map_map,Function.comp_def] using + (column_list_sum η W hηw').trans hηcard + have ha : ∀ p ∈ ps, 1 ≤ p.1 ∧ p.1 ≤ d := by + intro p hp + obtain ⟨i,hi,rfl⟩ := List.mem_map.mp hp + have hm : 0 < μ.colLen i := (colLen_pos_iff μ i).mpr (List.mem_range.mp hi) + rw [hcolsh] at hm + by_cases he : 0 < η.colLen i + · exact ⟨by rw [hchosen i he]; exact hd,hplen i⟩ + · exact ⟨by omega,hplen i⟩ + have hb : ∀ p ∈ ps, p.2 ≠ 0 → p.1 = d := by + intro p hp hn + obtain ⟨i,hi,rfl⟩ := List.mem_map.mp hp + exact hchosen i (Nat.pos_of_ne_zero hn) + have hlen : (ps.filter (fun p => p.2 ≠ 0)).length ≤ q := by + have hh : (ps.filter (fun p => p.2 ≠ 0)).length = η.rowLen 0 := by + dsimp only [ps] + rw [List.filter_map, List.length_map] + have hh : (List.range W).filter ((fun p : ℕ × ℕ => decide (p.2 ≠ 0)) ∘ + (fun i => (π.colLen i,η.colLen i))) = List.range (η.rowLen 0) := by + calc _ = (List.range W).filter (fun i => decide (i < η.rowLen 0)) := by + apply List.filter_congr + intro i hi + simp only [Function.comp_apply, Nat.pos_iff_ne_zero.symm, colLen_pos_iff] + _ = List.range (η.rowLen 0) := by + rw [← List.Ico.zero_bot W,List.Ico.filter_lt_of_ge hηw',List.Ico.zero_bot] + rw [hh,List.length_range] + exact hh.le.trans hηw + obtain ⟨qs,hqs,hqc⟩ := Saxl.FlagColumns.reorder_columns_away ps d K q hs₁ + (fun p hp => (ha p hp).2) hb hlen hclear + refine ⟨μ,η,qs,hμlam,hμcard,hηcard,(hqs.map Prod.fst).sum_eq.trans hs₁, + (hqs.map Prod.snd).sum_eq.trans hs₂, + fun p hp => ha p (hqs.mem_iff.mp hp),fun p hp => hb p (hqs.mem_iff.mp hp), + hqc,heven,hηw,?_,?_⟩ + · apply place_padded_columns μ W le_rfl + have hh := hqs.map (fun p => p.1+p.2) + simpa only [ps,List.map_map,Function.comp_def,← hcolsh] using hh + · apply place_padded_columns η W hηw' + simpa only [ps,List.map_map,Function.comp_def] using hqs.map Prod.snd + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandCriterion.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandCriterion.lean index f207ff409ca7cd511225e84051b7f291e90fba8e..37fdfbfd0ab17e29d21b63a3b3058ce72d71f28f 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandCriterion.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandCriterion.lean @@ -1,65 +1,65 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.SubdiagramSupport -import OAI.RepresentationTheory.UniversalSquare.Band.BandAllocationLists - -namespace OAI - -/-! Band Criterion. -/ - -section - -noncomputable section -namespace Saxl.ShortColumns - -lemma card (b δ : ℕ) (hδ : δ ≤ 1) : (shape b δ).card = 2*b+δ := by - have h (n : ℕ) (t : Tableau n (shape b δ)) : (shape b δ).card = n := by - simpa only [Fintype.card_fin, Fintype.card_coe, YoungDiagram.card] using - (Fintype.card_congr t).symm - rcases (by omega : δ = 0 ∨ δ = 1) with rfl | rfl - · simpa only [Nat.add_zero] using h _ (evenTableau b) - · exact h _ (oddTableau b) - -end Saxl.ShortColumns -namespace UniversalTensorSquare -open Saxl - -lemma candidateBandSize_eq {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (hr : r = 2*b+δ) (t : Tableau n (candidate M b δ)) : - candidateBandSize t = 2*M-1+2*r := by - let s := canonicalTableau (ShortColumns.shape b δ) ((ShortColumns.card b δ hδ).trans hr.symm) - simpa only [Fintype.card_fin, Fintype.card_sum] using - Fintype.card_congr (candidateBandSplit hM t s s) - -theorem band_kronecker_pos {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (hr : r = 2*b+δ) (t : Tableau n (candidate M b δ)) - (lam : YoungDiagram) (s : Tableau n lam) (hband : BandTest M r lam) : - 0 < kronecker t t s := by - obtain ⟨d,hd₁,hd₄,q,hq,hK,hclear,hrcap⟩ := hband - obtain ⟨μ,η,ps,hμlam,hμcard,hηcard,hp,he,ha,hb,hc,hηe,hηw, - ⟨Eμ,Eμr,Eμc⟩,⟨Eη,Eηr,Eηc⟩⟩ := - band_subdiagram_columns lam (2*M-1) r d q hd₁ hK hclear hrcap - let a := canonicalTableau (ShortColumns.shape b δ) ((ShortColumns.card b δ hδ).trans hr.symm) - let v := canonicalTableau μ (hμcard.trans (candidateBandSize_eq hM hδ hr t).symm) - obtain ⟨F,hF⟩ := candidateBandWord_support_of_columns hM hδ hr hd₄ t a a ps hp he ha hb hc - μ η hηcard hηe (hηw.trans hq) Eμ Eμr Eμc Eη Eηr Eηc v - exact candidate_kronecker_pos_of_subdiagram hM t hμlam v s F hF - -theorem fixedCandidate_band_pos (n : ℕ) (hM : 4 ≤ staircaseIndex n) - (μ : YoungDiagram) (hμ : μ.card = n) - (hband : BandTest (staircaseIndex n) (remainderPairs n) μ) : - 0 < kronecker (canonicalTableau (fixedCandidate n) (fixedCandidate_card n (by omega))) - (canonicalTableau (fixedCandidate n) (fixedCandidate_card n (by omega))) - (canonicalTableau μ hμ) := by - have hδ : remainderPairs n % 2 ≤ 1 := by omega - have hr : remainderPairs n = 2 * (remainderPairs n / 2) + remainderPairs n % 2 := by omega - exact band_kronecker_pos (M := staircaseIndex n) (b := remainderPairs n / 2) - (δ := remainderPairs n % 2) (r := remainderPairs n) hM hδ hr - (canonicalTableau (fixedCandidate n) (fixedCandidate_card n (by omega))) - μ (canonicalTableau μ hμ) hband - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.SubdiagramSupport +import OAI.RepresentationTheory.UniversalSquare.Band.BandAllocationLists + +namespace OAI + +/-! Band Criterion. -/ + +section + +noncomputable section +namespace Saxl.ShortColumns + +lemma card (b δ : ℕ) (hδ : δ ≤ 1) : (shape b δ).card = 2*b+δ := by + have h (n : ℕ) (t : Tableau n (shape b δ)) : (shape b δ).card = n := by + simpa only [Fintype.card_fin, Fintype.card_coe, YoungDiagram.card] using + (Fintype.card_congr t).symm + rcases (by omega : δ = 0 ∨ δ = 1) with rfl | rfl + · simpa only [Nat.add_zero] using h _ (evenTableau b) + · exact h _ (oddTableau b) + +end Saxl.ShortColumns +namespace UniversalTensorSquare +open Saxl + +lemma candidateBandSize_eq {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (hr : r = 2*b+δ) (t : Tableau n (candidate M b δ)) : + candidateBandSize t = 2*M-1+2*r := by + let s := canonicalTableau (ShortColumns.shape b δ) ((ShortColumns.card b δ hδ).trans hr.symm) + simpa only [Fintype.card_fin, Fintype.card_sum] using + Fintype.card_congr (candidateBandSplit hM t s s) + +theorem band_kronecker_pos {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (hr : r = 2*b+δ) (t : Tableau n (candidate M b δ)) + (lam : YoungDiagram) (s : Tableau n lam) (hband : BandTest M r lam) : + 0 < kronecker t t s := by + obtain ⟨d,hd₁,hd₄,q,hq,hK,hclear,hrcap⟩ := hband + obtain ⟨μ,η,ps,hμlam,hμcard,hηcard,hp,he,ha,hb,hc,hηe,hηw, + ⟨Eμ,Eμr,Eμc⟩,⟨Eη,Eηr,Eηc⟩⟩ := + band_subdiagram_columns lam (2*M-1) r d q hd₁ hK hclear hrcap + let a := canonicalTableau (ShortColumns.shape b δ) ((ShortColumns.card b δ hδ).trans hr.symm) + let v := canonicalTableau μ (hμcard.trans (candidateBandSize_eq hM hδ hr t).symm) + obtain ⟨F,hF⟩ := candidateBandWord_support_of_columns hM hδ hr hd₄ t a a ps hp he ha hb hc + μ η hηcard hηe (hηw.trans hq) Eμ Eμr Eμc Eη Eηr Eηc v + exact candidate_kronecker_pos_of_subdiagram hM t hμlam v s F hF + +theorem fixedCandidate_band_pos (n : ℕ) (hM : 4 ≤ staircaseIndex n) + (μ : YoungDiagram) (hμ : μ.card = n) + (hband : BandTest (staircaseIndex n) (remainderPairs n) μ) : + 0 < kronecker (canonicalTableau (fixedCandidate n) (fixedCandidate_card n (by omega))) + (canonicalTableau (fixedCandidate n) (fixedCandidate_card n (by omega))) + (canonicalTableau μ hμ) := by + have hδ : remainderPairs n % 2 ≤ 1 := by omega + have hr : remainderPairs n = 2 * (remainderPairs n / 2) + remainderPairs n % 2 := by omega + exact band_kronecker_pos (M := staircaseIndex n) (b := remainderPairs n / 2) + (δ := remainderPairs n % 2) (r := remainderPairs n) hM hδ hr + (canonicalTableau (fixedCandidate n) (fixedCandidate_card n (by omega))) + μ (canonicalTableau μ hμ) hband + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandExtras.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandExtras.lean index 4d7748e9e7038e5b4b2243146da5e7778f621445..1d7a5ff3af8b53eac0bf2d20075307ae5e3aefe6 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandExtras.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandExtras.lean @@ -1,81 +1,81 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Band.BandSeparated -import OAI.RepresentationTheory.UniversalSquare.Band.TwoExtras - -namespace OAI - -/-! Band Extras. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl -open scoped TensorProduct - -def bandNELetter {M b δ : ℕ} (hM : 4 ≤ M) := - pairLetterMap (bandLongRowLetter (b := b) (δ := δ) hM) (bandShortColLetter (b := b) (δ := δ) hM) - -def bandSWLetter {M b δ : ℕ} (hM : 4 ≤ M) := - pairLetterMap ((bandShortRowLetter (b := b) (δ := δ) hM) ∘ Fin.cast - (congrArg (fun ν : YoungDiagram => ν.colLen 0) - (YoungDiagram.transpose_transpose (ShortColumns.shape b δ)))) (bandLongColLetter (b := b) (δ := δ) hM) - -lemma bandNELetter_injective {M b δ : ℕ} (hM : 4 ≤ M) : - Function.Injective (@bandNELetter M b δ hM) := - pairLetterMap_injective _ _ (bandExtraLetter_injective _) (Fin.castLE_injective _) - -lemma bandSWLetter_injective {M b δ : ℕ} (hM : 4 ≤ M) : - Function.Injective (@bandSWLetter M b δ hM) := - pairLetterMap_injective _ _ ((Fin.castLE_injective _).comp (Fin.cast_injective _)) - (bandExtraLetter_injective _) - -lemma candidateExtrasWord_eq {M b δ r : ℕ} (hM : 4 ≤ M) - (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - candidateExtrasWord hM s₁ s₂ = positionProduct (candidateExtraSplit r) - (letterLift (bandNELetter hM) (rowColumnWord s₁)) - (letterLift (bandSWLetter hM) (rowColumnWord (transposeTableau s₂))) := by - unfold candidateExtrasWord rowColumnWord bandNELetter bandSWLetter - rw [letterLift_wordTensor, letterLift_wordTensor, ← letterLift_comp] - rw [polytabloid_doubleTranspose] - -lemma bandNELetter_high {M b δ : ℕ} (hM : 4 ≤ M) (x) : - 2 ≤ ((finProdFinEquiv.symm (@bandNELetter M b δ hM x)).1).val := by - simpa only [bandNELetter, pairLetterMap, Equiv.symm_apply_apply, bandLongRowLetter] - using bandExtraLetter_high hM _ (finProdFinEquiv.symm x).1 - -lemma bandSWLetter_low {M b δ : ℕ} (hM : 4 ≤ M) (x) : - ((finProdFinEquiv.symm (@bandSWLetter M b δ hM x)).1).val < 2 := by - simp only [bandSWLetter, pairLetterMap, Equiv.symm_apply_apply, - Function.comp_apply, bandShortRowLetter, Fin.val_castLE, Fin.val_cast] - have h := (finProdFinEquiv.symm x).1.isLt - have he := congrArg (fun μ : YoungDiagram => μ.colLen 0) - (YoungDiagram.transpose_transpose (ShortColumns.shape b δ)) - have hh := ShortColumns.height_le b δ - omega - -theorem candidateExtrasWord_support {M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (hr : r = 2*b+δ) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) - (η : YoungDiagram) (hη : η.card = 2*r) (t : Tableau (2*r) η) - (he : ∀ i, Even (η.colLen i)) (hd : η.rowLen 0 ≤ 8) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep (2*r) _) (candidateExtrasWord hM s₁ s₂)).toRepresentation, - F ≠ 0 := by - rw [candidateExtrasWord_eq] - have hb : r/2 = b := by omega - have hδ' : r%2 = δ := by omega - have H := ShortColumns.two_extras r - ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0) - rw [hb,hδ'] at H - exact H s₁ s₂ (bandNELetter hM) (bandSWLetter hM) - (bandNELetter_injective hM) (bandSWLetter_injective hM) - (fun a => 2 ≤ (finProdFinEquiv.symm a).1.val) - (bandNELetter_high hM) (fun a => Nat.not_le.mpr (bandSWLetter_low hM a)) - (candidateExtraSplit r) η hη t he hd - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Band.BandSeparated +import OAI.RepresentationTheory.UniversalSquare.Band.TwoExtras + +namespace OAI + +/-! Band Extras. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl +open scoped TensorProduct + +def bandNELetter {M b δ : ℕ} (hM : 4 ≤ M) := + pairLetterMap (bandLongRowLetter (b := b) (δ := δ) hM) (bandShortColLetter (b := b) (δ := δ) hM) + +def bandSWLetter {M b δ : ℕ} (hM : 4 ≤ M) := + pairLetterMap ((bandShortRowLetter (b := b) (δ := δ) hM) ∘ Fin.cast + (congrArg (fun ν : YoungDiagram => ν.colLen 0) + (YoungDiagram.transpose_transpose (ShortColumns.shape b δ)))) (bandLongColLetter (b := b) (δ := δ) hM) + +lemma bandNELetter_injective {M b δ : ℕ} (hM : 4 ≤ M) : + Function.Injective (@bandNELetter M b δ hM) := + pairLetterMap_injective _ _ (bandExtraLetter_injective _) (Fin.castLE_injective _) + +lemma bandSWLetter_injective {M b δ : ℕ} (hM : 4 ≤ M) : + Function.Injective (@bandSWLetter M b δ hM) := + pairLetterMap_injective _ _ ((Fin.castLE_injective _).comp (Fin.cast_injective _)) + (bandExtraLetter_injective _) + +lemma candidateExtrasWord_eq {M b δ r : ℕ} (hM : 4 ≤ M) + (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + candidateExtrasWord hM s₁ s₂ = positionProduct (candidateExtraSplit r) + (letterLift (bandNELetter hM) (rowColumnWord s₁)) + (letterLift (bandSWLetter hM) (rowColumnWord (transposeTableau s₂))) := by + unfold candidateExtrasWord rowColumnWord bandNELetter bandSWLetter + rw [letterLift_wordTensor, letterLift_wordTensor, ← letterLift_comp] + rw [polytabloid_doubleTranspose] + +lemma bandNELetter_high {M b δ : ℕ} (hM : 4 ≤ M) (x) : + 2 ≤ ((finProdFinEquiv.symm (@bandNELetter M b δ hM x)).1).val := by + simpa only [bandNELetter, pairLetterMap, Equiv.symm_apply_apply, bandLongRowLetter] + using bandExtraLetter_high hM _ (finProdFinEquiv.symm x).1 + +lemma bandSWLetter_low {M b δ : ℕ} (hM : 4 ≤ M) (x) : + ((finProdFinEquiv.symm (@bandSWLetter M b δ hM x)).1).val < 2 := by + simp only [bandSWLetter, pairLetterMap, Equiv.symm_apply_apply, + Function.comp_apply, bandShortRowLetter, Fin.val_castLE, Fin.val_cast] + have h := (finProdFinEquiv.symm x).1.isLt + have he := congrArg (fun μ : YoungDiagram => μ.colLen 0) + (YoungDiagram.transpose_transpose (ShortColumns.shape b δ)) + have hh := ShortColumns.height_le b δ + omega + +theorem candidateExtrasWord_support {M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (hr : r = 2*b+δ) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) + (η : YoungDiagram) (hη : η.card = 2*r) (t : Tableau (2*r) η) + (he : ∀ i, Even (η.colLen i)) (hd : η.rowLen 0 ≤ 8) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep (2*r) _) (candidateExtrasWord hM s₁ s₂)).toRepresentation, + F ≠ 0 := by + rw [candidateExtrasWord_eq] + have hb : r/2 = b := by omega + have hδ' : r%2 = δ := by omega + have H := ShortColumns.two_extras r + ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0) + rw [hb,hδ'] at H + exact H s₁ s₂ (bandNELetter hM) (bandSWLetter hM) + (bandNELetter_injective hM) (bandSWLetter_injective hM) + (fun a => 2 ≤ (finProdFinEquiv.symm a).1.val) + (bandNELetter_high hM) (fun a => Nat.not_le.mpr (bandSWLetter_low hM a)) + (candidateExtraSplit r) η hη t he hd + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandFactor.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandFactor.lean index 5f577915aa020cd6f20e0f1247f7d148b6bf9d80..16cd4173c9f47e3140b6d076bb8df1852c4fd94e 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandFactor.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandFactor.lean @@ -1,103 +1,103 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Band.BandLetters -import OAI.RepresentationTheory.UniversalSquare.Band.BandGroups - -namespace OAI - -/-! Band Factor. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl -open scoped TensorProduct - -def candidatePathRow {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) := - altWord (fiberGroup (fun i => (candidateBandTableau t - ((candidateBandSplit hM t s₁ s₂).symm (Sum.inl i))).val.1)) - (leftWord (candidateBandSplit hM t s₁ s₂) (candidateBandRowSeed hM t)) - -def candidatePathCol {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) := - altWord (fiberGroup (fun i => (candidateBandTableau t - ((candidateBandSplit hM t s₁ s₂).symm (Sum.inl i))).val.2)) - (leftWord (candidateBandSplit hM t s₁ s₂) (candidateBandColSeed hM t)) - -def bandLongRowLetter {M b δ : ℕ} (hM : 4 ≤ M) : - Fin ((ShortColumns.shape b δ).transpose.colLen 0) → Fin ((candidate M b δ).transpose.colLen 0) := - bandExtraLetter (le_of_eq (candidateRowAlphabet_size hM).symm) - -def bandShortRowLetter {M b δ : ℕ} (hM : 4 ≤ M) : - Fin ((ShortColumns.shape b δ).colLen 0) → Fin ((candidate M b δ).transpose.colLen 0) := - Fin.castLE ((ShortColumns.height_le b δ).trans (by rw [candidateRowAlphabet_size hM]; omega)) - -def bandLongColLetter {M b δ : ℕ} (hM : 4 ≤ M) : - Fin ((ShortColumns.shape b δ).transpose.colLen 0) → Fin ((candidate M b δ).colLen 0) := - bandExtraLetter (le_of_eq (candidateColAlphabet_size hM).symm) - -def bandShortColLetter {M b δ : ℕ} (hM : 4 ≤ M) : - Fin ((ShortColumns.shape b δ).colLen 0) → Fin ((candidate M b δ).colLen 0) := - Fin.castLE ((ShortColumns.height_le b δ).trans (by rw [candidateColAlphabet_size hM]; omega)) - -lemma candidateBandRow_extras {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - altWord (fiberGroup (fun i => (candidateBandTableau t - ((candidateBandSplit hM t s₁ s₂).symm (Sum.inr i))).val.1)) - (rightWord (candidateBandSplit hM t s₁ s₂) (candidateBandRowSeed hM t)) = - positionProduct (candidateExtraSplit r) - (letterLift (bandLongRowLetter hM) (polytabloid (transposeTableau s₁))) - (letterLift (bandShortRowLetter hM) (polytabloid s₂)) := by - rw [candidateBand_extra_sector hM t s₁ s₂ Prod.fst (Or.inl rfl), altWord_fiber_split, - candidateBandRow_NE_group, candidateBandRow_SW_group, - candidateBandRowSeed_NE hM hδ, candidateBandRowSeed_SW hM hδ] - simp only [polytabloid_eq_altWord, letterLift_altWord] - rfl - -lemma candidateBandCol_extras {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - altWord (fiberGroup (fun i => (candidateBandTableau t - ((candidateBandSplit hM t s₁ s₂).symm (Sum.inr i))).val.2)) - (rightWord (candidateBandSplit hM t s₁ s₂) (candidateBandColSeed hM t)) = - positionProduct (candidateExtraSplit r) - (letterLift (bandShortColLetter hM) (polytabloid s₁)) - (letterLift (bandLongColLetter hM) (polytabloid (transposeTableau s₂))) := by - rw [candidateBand_extra_sector hM t s₁ s₂ Prod.snd (Or.inr rfl), altWord_fiber_split, - candidateBandCol_NE_group, candidateBandCol_SW_group, - candidateBandColSeed_NE hM hδ, candidateBandColSeed_SW hM hδ] - simp only [polytabloid_eq_altWord, letterLift_altWord] - rfl - -lemma candidateBandRow_factor {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - coordinateProjection (fun w => ∀ i, 2 ≤ (w i).val ↔ - (candidateBandTableau t i).val ∈ attachmentNE M b δ) (candidateBandRow hM t) = - signC (candidateBandRowShuffle hM t).val • - positionProduct (candidateBandSplit hM t s₁ s₂) (candidatePathRow hM t s₁ s₂) - (positionProduct (candidateExtraSplit r) - (letterLift (bandLongRowLetter hM) (polytabloid (transposeTableau s₁))) - (letterLift (bandShortRowLetter hM) (polytabloid s₂))) := by - rw [candidateBandRow_project_extra hM hδ, candidateBandRow_sector_eq hM t s₁ s₂, - altWord_fiber_split, candidateBandRow_extras hM hδ] - rfl - -lemma candidateBandCol_factor {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - coordinateProjection (fun w => ∀ i, 2 ≤ (w i).val ↔ - (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ) (candidateBandCol hM t) = - signC (candidateBandColShuffle hM t).val • - positionProduct (candidateBandSplit hM t s₁ s₂) (candidatePathCol hM t s₁ s₂) - (positionProduct (candidateExtraSplit r) - (letterLift (bandShortColLetter hM) (polytabloid s₁)) - (letterLift (bandLongColLetter hM) (polytabloid (transposeTableau s₂)))) := by - rw [candidateBandCol_project_extra hM hδ, candidateBandCol_sector_eq hM t s₁ s₂, - altWord_fiber_split, candidateBandCol_extras hM hδ] - rfl - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Band.BandLetters +import OAI.RepresentationTheory.UniversalSquare.Band.BandGroups + +namespace OAI + +/-! Band Factor. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl +open scoped TensorProduct + +def candidatePathRow {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) := + altWord (fiberGroup (fun i => (candidateBandTableau t + ((candidateBandSplit hM t s₁ s₂).symm (Sum.inl i))).val.1)) + (leftWord (candidateBandSplit hM t s₁ s₂) (candidateBandRowSeed hM t)) + +def candidatePathCol {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) := + altWord (fiberGroup (fun i => (candidateBandTableau t + ((candidateBandSplit hM t s₁ s₂).symm (Sum.inl i))).val.2)) + (leftWord (candidateBandSplit hM t s₁ s₂) (candidateBandColSeed hM t)) + +def bandLongRowLetter {M b δ : ℕ} (hM : 4 ≤ M) : + Fin ((ShortColumns.shape b δ).transpose.colLen 0) → Fin ((candidate M b δ).transpose.colLen 0) := + bandExtraLetter (le_of_eq (candidateRowAlphabet_size hM).symm) + +def bandShortRowLetter {M b δ : ℕ} (hM : 4 ≤ M) : + Fin ((ShortColumns.shape b δ).colLen 0) → Fin ((candidate M b δ).transpose.colLen 0) := + Fin.castLE ((ShortColumns.height_le b δ).trans (by rw [candidateRowAlphabet_size hM]; omega)) + +def bandLongColLetter {M b δ : ℕ} (hM : 4 ≤ M) : + Fin ((ShortColumns.shape b δ).transpose.colLen 0) → Fin ((candidate M b δ).colLen 0) := + bandExtraLetter (le_of_eq (candidateColAlphabet_size hM).symm) + +def bandShortColLetter {M b δ : ℕ} (hM : 4 ≤ M) : + Fin ((ShortColumns.shape b δ).colLen 0) → Fin ((candidate M b δ).colLen 0) := + Fin.castLE ((ShortColumns.height_le b δ).trans (by rw [candidateColAlphabet_size hM]; omega)) + +lemma candidateBandRow_extras {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + altWord (fiberGroup (fun i => (candidateBandTableau t + ((candidateBandSplit hM t s₁ s₂).symm (Sum.inr i))).val.1)) + (rightWord (candidateBandSplit hM t s₁ s₂) (candidateBandRowSeed hM t)) = + positionProduct (candidateExtraSplit r) + (letterLift (bandLongRowLetter hM) (polytabloid (transposeTableau s₁))) + (letterLift (bandShortRowLetter hM) (polytabloid s₂)) := by + rw [candidateBand_extra_sector hM t s₁ s₂ Prod.fst (Or.inl rfl), altWord_fiber_split, + candidateBandRow_NE_group, candidateBandRow_SW_group, + candidateBandRowSeed_NE hM hδ, candidateBandRowSeed_SW hM hδ] + simp only [polytabloid_eq_altWord, letterLift_altWord] + rfl + +lemma candidateBandCol_extras {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + altWord (fiberGroup (fun i => (candidateBandTableau t + ((candidateBandSplit hM t s₁ s₂).symm (Sum.inr i))).val.2)) + (rightWord (candidateBandSplit hM t s₁ s₂) (candidateBandColSeed hM t)) = + positionProduct (candidateExtraSplit r) + (letterLift (bandShortColLetter hM) (polytabloid s₁)) + (letterLift (bandLongColLetter hM) (polytabloid (transposeTableau s₂))) := by + rw [candidateBand_extra_sector hM t s₁ s₂ Prod.snd (Or.inr rfl), altWord_fiber_split, + candidateBandCol_NE_group, candidateBandCol_SW_group, + candidateBandColSeed_NE hM hδ, candidateBandColSeed_SW hM hδ] + simp only [polytabloid_eq_altWord, letterLift_altWord] + rfl + +lemma candidateBandRow_factor {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + coordinateProjection (fun w => ∀ i, 2 ≤ (w i).val ↔ + (candidateBandTableau t i).val ∈ attachmentNE M b δ) (candidateBandRow hM t) = + signC (candidateBandRowShuffle hM t).val • + positionProduct (candidateBandSplit hM t s₁ s₂) (candidatePathRow hM t s₁ s₂) + (positionProduct (candidateExtraSplit r) + (letterLift (bandLongRowLetter hM) (polytabloid (transposeTableau s₁))) + (letterLift (bandShortRowLetter hM) (polytabloid s₂))) := by + rw [candidateBandRow_project_extra hM hδ, candidateBandRow_sector_eq hM t s₁ s₂, + altWord_fiber_split, candidateBandRow_extras hM hδ] + rfl + +lemma candidateBandCol_factor {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + coordinateProjection (fun w => ∀ i, 2 ≤ (w i).val ↔ + (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ) (candidateBandCol hM t) = + signC (candidateBandColShuffle hM t).val • + positionProduct (candidateBandSplit hM t s₁ s₂) (candidatePathCol hM t s₁ s₂) + (positionProduct (candidateExtraSplit r) + (letterLift (bandShortColLetter hM) (polytabloid s₁)) + (letterLift (bandLongColLetter hM) (polytabloid (transposeTableau s₂)))) := by + rw [candidateBandCol_project_extra hM hδ, candidateBandCol_sector_eq hM t s₁ s₂, + altWord_fiber_split, candidateBandCol_extras hM hδ] + rfl + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandGluing.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandGluing.lean index 7d7cd5bd22cba839d5c21059eed38c71cedbef6d..12d46088dd7c1d181c2d025ce1761f69b7d86ec0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandGluing.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandGluing.lean @@ -1,191 +1,191 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Specht.NoMixedColumns -import OAI.RepresentationTheory.UniversalSquare.Contraction.BandContractions - -namespace OAI - -/-! Band Gluing. -/ - -section - -noncomputable section -namespace Saxl.FlagColumns - -def columnsAway (K : ℕ) : List (ℕ × ℕ) → ℕ → Prop - | [], _ => True - | (a,b)::ps, o => (b ≠ 0 → 4 ≤ o ∧ o+a+4 ≤ K) ∧ columnsAway K ps (o+a) - -lemma clearSlots_of_columnsAway {D K : ℕ} (P : Fin D → Prop) - (ps : List (ℕ × ℕ)) (o : ℕ) (hs : columnsAway K ps o) - (w : Fin (ps.map (fun p => p.1+p.2)).sum → Fin D) - (hw : ∀ i : Fin (ps.map Prod.fst).sum, 4 ≤ o+i.val → o+i.val+4 < K → - P (w ((splitPositions ps).symm (Sum.inl i)))) : clearSlots P ps w := by - induction ps generalizing o with - | nil => trivial - | cons p ps ih => - obtain ⟨a,b⟩ := p - constructor - · intro hb i - have hi := i.isLt - have h₁ := (hs.1 hb).1 - have h₂ := (hs.1 hb).2 - have H := hw (Fin.castAdd (ps.map Prod.fst).sum i) (by simp only [Fin.val_castAdd]; omega) - (by simp only [Fin.val_castAdd]; omega) - erw [splitPositions_left_first] at H - exact H - · apply ih (o+a) hs.2 (rightWord finSumFinEquiv.symm w) - intro i h₁ h₂ - have H := hw (Fin.natAdd a i) (by change 4 ≤ o+(a+i.val); omega) - (by change o+(a+i.val)+4 < K; omega) - erw [splitPositions_left_rest] at H - exact H - -end Saxl.FlagColumns -namespace Saxl - -def joinedPositionEquiv {n m a b A B : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) - (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) : Fin n ≃ Fin m := - e.trans ((p.sumCongr q).trans f.symm) - -lemma joinedPositionEquiv_left {n m a b A B : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) - (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) (i : Fin a) : - joinedPositionEquiv e f p q (e.symm (Sum.inl i)) = f.symm (Sum.inl (p i)) := by - simp [joinedPositionEquiv] - -lemma joinedPositionEquiv_right {n m a b A B : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) - (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) (i : Fin b) : - joinedPositionEquiv e f p q (e.symm (Sum.inr i)) = f.symm (Sum.inr (q i)) := by - simp [joinedPositionEquiv] - -lemma relabelWord_positionProduct {n m a b A B D : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) - (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) - (v : WordSpace a D) (u : WordSpace b D) : - relabelWord (joinedPositionEquiv e f p q) (positionProduct e v u) = - positionProduct f (relabelWord p v) (relabelWord q u) := by - ext w - change v _ * u _ = v _ * u _ - congr 1 - · congr 1 - funext i - exact congrArg w (joinedPositionEquiv_left e f p q i) - · congr 1 - funext i - exact congrArg w (joinedPositionEquiv_right e f p q i) - -lemma joinedPositionEquiv_isLeft {n m a b A B : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) - (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) (i : Fin n) : - (f (joinedPositionEquiv e f p q i)).isLeft = (e i).isLeft := by - simp only [joinedPositionEquiv, Equiv.trans_apply, Equiv.apply_symm_apply] - cases e i <;> rfl - -lemma wordSector_joinedPositionEquiv {n m a b A B D : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) - (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) (P : Fin D → Prop) - (w : Fin m → Fin D) : - wordSector (fun i => (e i).isLeft = true) P (w ∘ joinedPositionEquiv e f p q) ↔ - wordSector (fun i => (f i).isLeft = true) P w := by - change (∀ i, P (w (joinedPositionEquiv e f p q i)) ↔ (e i).isLeft = true) ↔ _ - simp only [← joinedPositionEquiv_isLeft e f p q] - exact ((joinedPositionEquiv e f p q).surjective.forall - (p := fun i => P (w i) ↔ (f i).isLeft = true)).symm - -lemma coordinateProjection_relabel_split {n m a b A B D : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) - (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) (P : Fin D → Prop) - (z : WordSpace n D) : - coordinateProjection (wordSector (fun i => (f i).isLeft = true) P) - (relabelWord (joinedPositionEquiv e f p q) z) = - relabelWord (joinedPositionEquiv e f p q) - (coordinateProjection (wordSector (fun i => (e i).isLeft = true) P) z) := by - classical - ext w - simp only [relabelWord_apply, coordinateProjection_apply, - wordSector_joinedPositionEquiv e f p q P w] - -end Saxl - -namespace UniversalTensorSquare -open Saxl Saxl.FlagColumns - -theorem candidateBandWord_support_of_columns {n M b δ r d : ℕ} - (hM : 4 ≤ M) (hδ : δ ≤ 1) (hr : r = 2*b+δ) (hd : d ≤ 4) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) - (ps : List (ℕ × ℕ)) (hp : (ps.map Prod.fst).sum = 2*M-1) - (he : (ps.map Prod.snd).sum = 2*r) - (ha : ∀ p ∈ ps, 1 ≤ p.1 ∧ p.1 ≤ d) - (hb : ∀ p ∈ ps, p.2 ≠ 0 → p.1 = d) (hc : columnsAway (2*M-1) ps 0) - (μ η : YoungDiagram) (hη : η.card = 2*r) - (hηe : ∀ i, Even (η.colLen i)) (hηw : η.rowLen 0 ≤ 8) - (Eμ : Columns.Cells (ps.map (fun p => p.1+p.2)) ≃ μ.cells) - (Eμr : ∀ c, (Eμ c).val.1 = Columns.row c) - (Eμc : ∀ c c', (Eμ c).val.2 = (Eμ c').val.2 ↔ Columns.col c = Columns.col c') - (Eη : Columns.Cells (ps.map Prod.snd) ≃ η.cells) - (Eηr : ∀ c, (Eη c).val.1 = Columns.row c) - (Eηc : ∀ c c', (Eη c).val.2 = (Eη c').val.2 ↔ Columns.col c = Columns.col c') - (s : Tableau (candidateBandSize t) μ) : - ∃ F : Representation.IntertwiningMap (spechtRep s) - (cyclic (wordRep _ _) (candidateBandWord hM t)).toRepresentation, F ≠ 0 := by - obtain ⟨N,hN,hNp⟩ := candidatePathWord_contraction hM hδ t s₁ s₂ (ps.map Prod.fst) (by - intro a ha' - obtain ⟨p,hp',rfl⟩ := List.mem_map.mp ha' - exact ⟨(ha p hp').1,(ha p hp').2.trans hd⟩) hp - obtain ⟨g,Q,hQ,hQp⟩ := candidateExtrasWord_contraction hM hδ hr s₁ s₂ η hη hηe hηw - (ps.map Prod.snd) he Eη Eηr Eηc - let e := candidateBandSplit hM t s₁ s₂ - let f := splitPositions ps - let p := (finCongr hp).symm - let q := (finCongr he).symm.trans g - let E := joinedPositionEquiv e f p q - let z := relabelWord E (candidateBandWord hM t) - let v := relabelWord p (candidatePathWord hM t s₁ s₂) - let u := relabelWord q (candidateExtrasWord hM s₁ s₂) - let c := signC (candidateBandRowShuffle hM t).val * signC (candidateBandColShuffle hM t).val - have hz : ∀ w, z w ≠ 0 → clearSlots (candidatePathAlphabet M b δ) ps w := by - intro w hw - apply clearSlots_of_columnsAway (candidatePathAlphabet M b δ) ps 0 hc w - intro i h₁ h₂ - have H := candidateBandWord_path_clearance hM t (w ∘ E) hw - (e.symm (Sum.inl (finCongr hp i))) (finCongr hp i) - (candidateBandSplit_path hM t s₁ s₂ _) (by change 4 ≤ i.val; omega) - (by change i.val+4 < 2*M-1; omega) - change candidatePathAlphabet M b δ (w (E (e.symm (Sum.inl (finCongr hp i))))) at H - dsimp only [E] at H - rw [joinedPositionEquiv_left, show p (finCongr hp i) = i from - (finCongr hp).symm_apply_apply i] at H - exact H - have hsep : coordinateProjection - (wordSector (fun i => (f i).isLeft = true) (candidatePathAlphabet M b δ)) z = - c • positionProduct f v u := by - rw [coordinateProjection_relabel_split e f p q, candidateBandWord_separated hM hδ t s₁ s₂, - map_smul, relabelWord_positionProduct] - have hsign {k : ℕ} (g : Equiv.Perm (Fin k)) : signC g ≠ 0 := by - have H := signC_mul_self g - intro hz - rw [hz,zero_mul] at H - exact zero_ne_one H - have hc' : c ≠ 0 := mul_ne_zero (hsign _) (hsign _) - have Hpair := band_contraction_factor N Q (candidatePathAlphabet M b δ) ps - (fun p hp => (ha p hp).2) hb hN hQ z hz v u c hsep - have hnon : dotProduct (blocks (ps.map (fun p => p.1+p.2)) (joinedFlag d N Q)) z ≠ 0 := by - rw [Hpair] - exact mul_ne_zero hc' (mul_ne_zero hNp (by - change dotProduct (blocks (ps.map Prod.snd) Q) - (relabelWord ((finCongr he).symm.trans g) (candidateExtrasWord hM s₁ s₂)) ≠ 0 - rw [← relabelWord_trans] - exact hQp)) - have hs := columns_sufficient Eμ Eμr Eμc ((Columns.enumerate _).trans Eμ) z - (joinedFlag d N Q) hnon - exact (cyclic_support_relabel_iff E s ((Columns.enumerate _).trans Eμ) - (candidateBandWord hM t)).mp hs - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Specht.NoMixedColumns +import OAI.RepresentationTheory.UniversalSquare.Contraction.BandContractions + +namespace OAI + +/-! Band Gluing. -/ + +section + +noncomputable section +namespace Saxl.FlagColumns + +def columnsAway (K : ℕ) : List (ℕ × ℕ) → ℕ → Prop + | [], _ => True + | (a,b)::ps, o => (b ≠ 0 → 4 ≤ o ∧ o+a+4 ≤ K) ∧ columnsAway K ps (o+a) + +lemma clearSlots_of_columnsAway {D K : ℕ} (P : Fin D → Prop) + (ps : List (ℕ × ℕ)) (o : ℕ) (hs : columnsAway K ps o) + (w : Fin (ps.map (fun p => p.1+p.2)).sum → Fin D) + (hw : ∀ i : Fin (ps.map Prod.fst).sum, 4 ≤ o+i.val → o+i.val+4 < K → + P (w ((splitPositions ps).symm (Sum.inl i)))) : clearSlots P ps w := by + induction ps generalizing o with + | nil => trivial + | cons p ps ih => + obtain ⟨a,b⟩ := p + constructor + · intro hb i + have hi := i.isLt + have h₁ := (hs.1 hb).1 + have h₂ := (hs.1 hb).2 + have H := hw (Fin.castAdd (ps.map Prod.fst).sum i) (by simp only [Fin.val_castAdd]; omega) + (by simp only [Fin.val_castAdd]; omega) + erw [splitPositions_left_first] at H + exact H + · apply ih (o+a) hs.2 (rightWord finSumFinEquiv.symm w) + intro i h₁ h₂ + have H := hw (Fin.natAdd a i) (by change 4 ≤ o+(a+i.val); omega) + (by change o+(a+i.val)+4 < K; omega) + erw [splitPositions_left_rest] at H + exact H + +end Saxl.FlagColumns +namespace Saxl + +def joinedPositionEquiv {n m a b A B : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) + (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) : Fin n ≃ Fin m := + e.trans ((p.sumCongr q).trans f.symm) + +lemma joinedPositionEquiv_left {n m a b A B : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) + (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) (i : Fin a) : + joinedPositionEquiv e f p q (e.symm (Sum.inl i)) = f.symm (Sum.inl (p i)) := by + simp [joinedPositionEquiv] + +lemma joinedPositionEquiv_right {n m a b A B : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) + (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) (i : Fin b) : + joinedPositionEquiv e f p q (e.symm (Sum.inr i)) = f.symm (Sum.inr (q i)) := by + simp [joinedPositionEquiv] + +lemma relabelWord_positionProduct {n m a b A B D : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) + (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) + (v : WordSpace a D) (u : WordSpace b D) : + relabelWord (joinedPositionEquiv e f p q) (positionProduct e v u) = + positionProduct f (relabelWord p v) (relabelWord q u) := by + ext w + change v _ * u _ = v _ * u _ + congr 1 + · congr 1 + funext i + exact congrArg w (joinedPositionEquiv_left e f p q i) + · congr 1 + funext i + exact congrArg w (joinedPositionEquiv_right e f p q i) + +lemma joinedPositionEquiv_isLeft {n m a b A B : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) + (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) (i : Fin n) : + (f (joinedPositionEquiv e f p q i)).isLeft = (e i).isLeft := by + simp only [joinedPositionEquiv, Equiv.trans_apply, Equiv.apply_symm_apply] + cases e i <;> rfl + +lemma wordSector_joinedPositionEquiv {n m a b A B D : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) + (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) (P : Fin D → Prop) + (w : Fin m → Fin D) : + wordSector (fun i => (e i).isLeft = true) P (w ∘ joinedPositionEquiv e f p q) ↔ + wordSector (fun i => (f i).isLeft = true) P w := by + change (∀ i, P (w (joinedPositionEquiv e f p q i)) ↔ (e i).isLeft = true) ↔ _ + simp only [← joinedPositionEquiv_isLeft e f p q] + exact ((joinedPositionEquiv e f p q).surjective.forall + (p := fun i => P (w i) ↔ (f i).isLeft = true)).symm + +lemma coordinateProjection_relabel_split {n m a b A B D : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin b) (f : Fin m ≃ Fin A ⊕ Fin B) + (p : Fin a ≃ Fin A) (q : Fin b ≃ Fin B) (P : Fin D → Prop) + (z : WordSpace n D) : + coordinateProjection (wordSector (fun i => (f i).isLeft = true) P) + (relabelWord (joinedPositionEquiv e f p q) z) = + relabelWord (joinedPositionEquiv e f p q) + (coordinateProjection (wordSector (fun i => (e i).isLeft = true) P) z) := by + classical + ext w + simp only [relabelWord_apply, coordinateProjection_apply, + wordSector_joinedPositionEquiv e f p q P w] + +end Saxl + +namespace UniversalTensorSquare +open Saxl Saxl.FlagColumns + +theorem candidateBandWord_support_of_columns {n M b δ r d : ℕ} + (hM : 4 ≤ M) (hδ : δ ≤ 1) (hr : r = 2*b+δ) (hd : d ≤ 4) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) + (ps : List (ℕ × ℕ)) (hp : (ps.map Prod.fst).sum = 2*M-1) + (he : (ps.map Prod.snd).sum = 2*r) + (ha : ∀ p ∈ ps, 1 ≤ p.1 ∧ p.1 ≤ d) + (hb : ∀ p ∈ ps, p.2 ≠ 0 → p.1 = d) (hc : columnsAway (2*M-1) ps 0) + (μ η : YoungDiagram) (hη : η.card = 2*r) + (hηe : ∀ i, Even (η.colLen i)) (hηw : η.rowLen 0 ≤ 8) + (Eμ : Columns.Cells (ps.map (fun p => p.1+p.2)) ≃ μ.cells) + (Eμr : ∀ c, (Eμ c).val.1 = Columns.row c) + (Eμc : ∀ c c', (Eμ c).val.2 = (Eμ c').val.2 ↔ Columns.col c = Columns.col c') + (Eη : Columns.Cells (ps.map Prod.snd) ≃ η.cells) + (Eηr : ∀ c, (Eη c).val.1 = Columns.row c) + (Eηc : ∀ c c', (Eη c).val.2 = (Eη c').val.2 ↔ Columns.col c = Columns.col c') + (s : Tableau (candidateBandSize t) μ) : + ∃ F : Representation.IntertwiningMap (spechtRep s) + (cyclic (wordRep _ _) (candidateBandWord hM t)).toRepresentation, F ≠ 0 := by + obtain ⟨N,hN,hNp⟩ := candidatePathWord_contraction hM hδ t s₁ s₂ (ps.map Prod.fst) (by + intro a ha' + obtain ⟨p,hp',rfl⟩ := List.mem_map.mp ha' + exact ⟨(ha p hp').1,(ha p hp').2.trans hd⟩) hp + obtain ⟨g,Q,hQ,hQp⟩ := candidateExtrasWord_contraction hM hδ hr s₁ s₂ η hη hηe hηw + (ps.map Prod.snd) he Eη Eηr Eηc + let e := candidateBandSplit hM t s₁ s₂ + let f := splitPositions ps + let p := (finCongr hp).symm + let q := (finCongr he).symm.trans g + let E := joinedPositionEquiv e f p q + let z := relabelWord E (candidateBandWord hM t) + let v := relabelWord p (candidatePathWord hM t s₁ s₂) + let u := relabelWord q (candidateExtrasWord hM s₁ s₂) + let c := signC (candidateBandRowShuffle hM t).val * signC (candidateBandColShuffle hM t).val + have hz : ∀ w, z w ≠ 0 → clearSlots (candidatePathAlphabet M b δ) ps w := by + intro w hw + apply clearSlots_of_columnsAway (candidatePathAlphabet M b δ) ps 0 hc w + intro i h₁ h₂ + have H := candidateBandWord_path_clearance hM t (w ∘ E) hw + (e.symm (Sum.inl (finCongr hp i))) (finCongr hp i) + (candidateBandSplit_path hM t s₁ s₂ _) (by change 4 ≤ i.val; omega) + (by change i.val+4 < 2*M-1; omega) + change candidatePathAlphabet M b δ (w (E (e.symm (Sum.inl (finCongr hp i))))) at H + dsimp only [E] at H + rw [joinedPositionEquiv_left, show p (finCongr hp i) = i from + (finCongr hp).symm_apply_apply i] at H + exact H + have hsep : coordinateProjection + (wordSector (fun i => (f i).isLeft = true) (candidatePathAlphabet M b δ)) z = + c • positionProduct f v u := by + rw [coordinateProjection_relabel_split e f p q, candidateBandWord_separated hM hδ t s₁ s₂, + map_smul, relabelWord_positionProduct] + have hsign {k : ℕ} (g : Equiv.Perm (Fin k)) : signC g ≠ 0 := by + have H := signC_mul_self g + intro hz + rw [hz,zero_mul] at H + exact zero_ne_one H + have hc' : c ≠ 0 := mul_ne_zero (hsign _) (hsign _) + have Hpair := band_contraction_factor N Q (candidatePathAlphabet M b δ) ps + (fun p hp => (ha p hp).2) hb hN hQ z hz v u c hsep + have hnon : dotProduct (blocks (ps.map (fun p => p.1+p.2)) (joinedFlag d N Q)) z ≠ 0 := by + rw [Hpair] + exact mul_ne_zero hc' (mul_ne_zero hNp (by + change dotProduct (blocks (ps.map Prod.snd) Q) + (relabelWord ((finCongr he).symm.trans g) (candidateExtrasWord hM s₁ s₂)) ≠ 0 + rw [← relabelWord_trans] + exact hQp)) + have hs := columns_sufficient Eμ Eμr Eμc ((Columns.enumerate _).trans Eμ) z + (joinedFlag d N Q) hnon + exact (cyclic_support_relabel_iff E s ((Columns.enumerate _).trans Eμ) + (candidateBandWord hM t)).mp hs + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandGroups.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandGroups.lean index 543a4eb1a4fbd82454d44ad50bb861f11f3eb771..ccb89bbf9e9b8f85330debe4846180be9690b390 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandGroups.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandGroups.lean @@ -1,153 +1,153 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Band.BandSplit - -namespace OAI - -/-! Band Groups. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -def candidatePartsSwap {M b δ : ℕ} : CandidateBandParts M b δ → CandidateBandParts M b δ - | .inl q => .inl q.rev - | .inr (.inl x) => .inr (.inr x) - | .inr (.inr x) => .inr (.inl x) - -lemma candidatePartsCell_swap {M b δ : ℕ} (hM : 4 ≤ M) (x : CandidateBandParts M b δ) : - (candidatePartsCell M b δ hM (candidatePartsSwap x)).val.val = - (candidatePartsCell M b δ hM x).val.val.swap := by - rcases x with q | (z | z) - · exact (candidatePathCell_swap hM q).symm - · rfl - · exact Prod.swap_swap _ |>.symm - -lemma candidateParts_col_sectors {M b δ : ℕ} (hM : 4 ≤ M) - (x y : CandidateBandParts M b δ) - (hcol : (candidatePartsCell M b δ hM x).val.val.2 = - (candidatePartsCell M b δ hM y).val.val.2) : - (Sum.isLeft x = true ↔ Sum.isLeft y = true) ↔ - ((candidatePartsCell M b δ hM x).val.val.swap ∈ attachmentNE M b δ ↔ - (candidatePartsCell M b δ hM y).val.val.swap ∈ attachmentNE M b δ) := by - have H := candidateParts_row_sectors hM (candidatePartsSwap x) (candidatePartsSwap y) - (by simpa only [candidatePartsCell_swap, Prod.fst_swap] using hcol) - rw [candidatePartsCell_swap, candidatePartsCell_swap] at H - have he (z : CandidateBandParts M b δ) : (candidatePartsSwap z).isLeft = z.isLeft := by - rcases z with z | (z | z) <;> rfl - simpa only [he] using H - -lemma candidateBandCol_sector_eq {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - fiberGroup (fun i => (candidateBandTableau t i).val.2) ⊓ - sectorGroup (fun i => (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ) = - fiberGroup (fun i => (candidateBandTableau t i).val.2) ⊓ - sectorGroup (fun i => ((candidateBandSplit hM t s₁ s₂) i).isLeft = true) := by - apply Subgroup.ext - intro g - change ((∀ i, (candidateBandTableau t (g i)).val.2 = (candidateBandTableau t i).val.2) ∧ _) ↔ - ((∀ i, (candidateBandTableau t (g i)).val.2 = (candidateBandTableau t i).val.2) ∧ _) - apply and_congr_right - intro hg - change (∀ i, _ ↔ _) ↔ (∀ i, _ ↔ _) - apply forall_congr' - intro i - let E := candidateBandPartsEquiv hM t s₁ s₂ - let f := Equiv.sumCongr (Equiv.refl (Fin (2*M-1))) (Equiv.sumCongr s₁ s₂) - have H (i) : (candidateBandTableau t i).val = - (candidatePartsCell M b δ hM (f (E i))).val.val := by - rw [← candidateBandParts_cell hM t s₁ s₂, Equiv.symm_apply_apply] - have hh := candidateParts_col_sectors hM (f (E (g i))) (f (E i)) (by - rw [← H, ← H]; exact hg i) - dsimp only at * - simp_rw [H] - have hside (j) : (f (E j)).isLeft = ((candidateBandSplit hM t s₁ s₂) j).isLeft := by - dsimp only [candidateBandSplit, Equiv.trans_apply, f] - cases E j <;> rfl - rw [hside, hside] at hh - exact hh.symm - -lemma candidateBand_extra_sector {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) - (p : (ℕ × ℕ) → ℕ) (hp : p = Prod.fst ∨ p = Prod.snd) : - fiberGroup (fun i => p (candidateBandTableau t - ((candidateBandSplit hM t s₁ s₂).symm (Sum.inr i))).val) = - fiberGroup (fun i => p (candidateBandTableau t - ((candidateBandSplit hM t s₁ s₂).symm (Sum.inr i))).val) ⊓ - sectorGroup (fun i => (candidateExtraSplit r i).isLeft = true) := by - apply le_antisymm - · intro g hg - refine ⟨hg, ?_⟩ - intro i - have H := hg i - obtain ⟨j,hj⟩ := (candidateExtraSplit r).symm.surjective i - obtain ⟨k,hk⟩ := (candidateExtraSplit r).symm.surjective (g i) - change (candidateExtraSplit r (g i)).isLeft = true ↔ (candidateExtraSplit r i).isLeft = true - rw [← hk, ← hj, Equiv.apply_symm_apply, Equiv.apply_symm_apply] - change p (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm (Sum.inr (g i)))).val = - p (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm (Sum.inr i))).val at H - rw [← hk, ← hj] at H - cases k with - | inl k => - cases j with - | inl j => rfl - | inr j => - rw [candidateBandSplit_NE, candidateBandSplit_SW] at H - have hx := (ShortColumns.mem_shape b δ (s₁ k).val.1 (s₁ k).val.2).mp (s₁ k).property - have hy := (ShortColumns.mem_shape b δ (s₂ j).val.1 (s₂ j).val.2).mp (s₂ j).property - rcases hp with rfl | rfl <;> dsimp only [candidateNECell, Prod.swap] at H <;> omega - | inr k => - cases j with - | inr j => rfl - | inl j => - rw [candidateBandSplit_SW, candidateBandSplit_NE] at H - have hx := (ShortColumns.mem_shape b δ (s₂ k).val.1 (s₂ k).val.2).mp (s₂ k).property - have hy := (ShortColumns.mem_shape b δ (s₁ j).val.1 (s₁ j).val.2).mp (s₁ j).property - rcases hp with rfl | rfl <;> dsimp only [candidateNECell, Prod.swap] at H <;> omega - · exact inf_le_left - -lemma candidateBandRow_NE_group {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - fiberGroup (fun i => (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm - (Sum.inr ((candidateExtraSplit r).symm (Sum.inl i))))).val.1) = - columnGroup (transposeTableau s₁) := by - simp_rw [candidateBandSplit_NE] - rfl - -lemma candidateBandRow_SW_group {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - fiberGroup (fun i => (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm - (Sum.inr ((candidateExtraSplit r).symm (Sum.inr i))))).val.1) = - columnGroup s₂ := by - simp_rw [candidateBandSplit_SW] - apply Subgroup.ext - intro g - change (∀ i, M-1+(s₂ (g i)).val.2 = M-1+(s₂ i).val.2) ↔ (∀ i, (s₂ (g i)).val.2 = (s₂ i).val.2) - simp only [Nat.add_left_cancel_iff] - -lemma candidateBandCol_NE_group {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - fiberGroup (fun i => (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm - (Sum.inr ((candidateExtraSplit r).symm (Sum.inl i))))).val.2) = - columnGroup s₁ := by - simp_rw [candidateBandSplit_NE] - apply Subgroup.ext - intro g - change (∀ i, M-1+(s₁ (g i)).val.2 = M-1+(s₁ i).val.2) ↔ (∀ i, (s₁ (g i)).val.2 = (s₁ i).val.2) - simp only [Nat.add_left_cancel_iff] - -lemma candidateBandCol_SW_group {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - fiberGroup (fun i => (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm - (Sum.inr ((candidateExtraSplit r).symm (Sum.inr i))))).val.2) = - columnGroup (transposeTableau s₂) := by - simp_rw [candidateBandSplit_SW] - rfl - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Band.BandSplit + +namespace OAI + +/-! Band Groups. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +def candidatePartsSwap {M b δ : ℕ} : CandidateBandParts M b δ → CandidateBandParts M b δ + | .inl q => .inl q.rev + | .inr (.inl x) => .inr (.inr x) + | .inr (.inr x) => .inr (.inl x) + +lemma candidatePartsCell_swap {M b δ : ℕ} (hM : 4 ≤ M) (x : CandidateBandParts M b δ) : + (candidatePartsCell M b δ hM (candidatePartsSwap x)).val.val = + (candidatePartsCell M b δ hM x).val.val.swap := by + rcases x with q | (z | z) + · exact (candidatePathCell_swap hM q).symm + · rfl + · exact Prod.swap_swap _ |>.symm + +lemma candidateParts_col_sectors {M b δ : ℕ} (hM : 4 ≤ M) + (x y : CandidateBandParts M b δ) + (hcol : (candidatePartsCell M b δ hM x).val.val.2 = + (candidatePartsCell M b δ hM y).val.val.2) : + (Sum.isLeft x = true ↔ Sum.isLeft y = true) ↔ + ((candidatePartsCell M b δ hM x).val.val.swap ∈ attachmentNE M b δ ↔ + (candidatePartsCell M b δ hM y).val.val.swap ∈ attachmentNE M b δ) := by + have H := candidateParts_row_sectors hM (candidatePartsSwap x) (candidatePartsSwap y) + (by simpa only [candidatePartsCell_swap, Prod.fst_swap] using hcol) + rw [candidatePartsCell_swap, candidatePartsCell_swap] at H + have he (z : CandidateBandParts M b δ) : (candidatePartsSwap z).isLeft = z.isLeft := by + rcases z with z | (z | z) <;> rfl + simpa only [he] using H + +lemma candidateBandCol_sector_eq {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + fiberGroup (fun i => (candidateBandTableau t i).val.2) ⊓ + sectorGroup (fun i => (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ) = + fiberGroup (fun i => (candidateBandTableau t i).val.2) ⊓ + sectorGroup (fun i => ((candidateBandSplit hM t s₁ s₂) i).isLeft = true) := by + apply Subgroup.ext + intro g + change ((∀ i, (candidateBandTableau t (g i)).val.2 = (candidateBandTableau t i).val.2) ∧ _) ↔ + ((∀ i, (candidateBandTableau t (g i)).val.2 = (candidateBandTableau t i).val.2) ∧ _) + apply and_congr_right + intro hg + change (∀ i, _ ↔ _) ↔ (∀ i, _ ↔ _) + apply forall_congr' + intro i + let E := candidateBandPartsEquiv hM t s₁ s₂ + let f := Equiv.sumCongr (Equiv.refl (Fin (2*M-1))) (Equiv.sumCongr s₁ s₂) + have H (i) : (candidateBandTableau t i).val = + (candidatePartsCell M b δ hM (f (E i))).val.val := by + rw [← candidateBandParts_cell hM t s₁ s₂, Equiv.symm_apply_apply] + have hh := candidateParts_col_sectors hM (f (E (g i))) (f (E i)) (by + rw [← H, ← H]; exact hg i) + dsimp only at * + simp_rw [H] + have hside (j) : (f (E j)).isLeft = ((candidateBandSplit hM t s₁ s₂) j).isLeft := by + dsimp only [candidateBandSplit, Equiv.trans_apply, f] + cases E j <;> rfl + rw [hside, hside] at hh + exact hh.symm + +lemma candidateBand_extra_sector {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) + (p : (ℕ × ℕ) → ℕ) (hp : p = Prod.fst ∨ p = Prod.snd) : + fiberGroup (fun i => p (candidateBandTableau t + ((candidateBandSplit hM t s₁ s₂).symm (Sum.inr i))).val) = + fiberGroup (fun i => p (candidateBandTableau t + ((candidateBandSplit hM t s₁ s₂).symm (Sum.inr i))).val) ⊓ + sectorGroup (fun i => (candidateExtraSplit r i).isLeft = true) := by + apply le_antisymm + · intro g hg + refine ⟨hg, ?_⟩ + intro i + have H := hg i + obtain ⟨j,hj⟩ := (candidateExtraSplit r).symm.surjective i + obtain ⟨k,hk⟩ := (candidateExtraSplit r).symm.surjective (g i) + change (candidateExtraSplit r (g i)).isLeft = true ↔ (candidateExtraSplit r i).isLeft = true + rw [← hk, ← hj, Equiv.apply_symm_apply, Equiv.apply_symm_apply] + change p (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm (Sum.inr (g i)))).val = + p (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm (Sum.inr i))).val at H + rw [← hk, ← hj] at H + cases k with + | inl k => + cases j with + | inl j => rfl + | inr j => + rw [candidateBandSplit_NE, candidateBandSplit_SW] at H + have hx := (ShortColumns.mem_shape b δ (s₁ k).val.1 (s₁ k).val.2).mp (s₁ k).property + have hy := (ShortColumns.mem_shape b δ (s₂ j).val.1 (s₂ j).val.2).mp (s₂ j).property + rcases hp with rfl | rfl <;> dsimp only [candidateNECell, Prod.swap] at H <;> omega + | inr k => + cases j with + | inr j => rfl + | inl j => + rw [candidateBandSplit_SW, candidateBandSplit_NE] at H + have hx := (ShortColumns.mem_shape b δ (s₂ k).val.1 (s₂ k).val.2).mp (s₂ k).property + have hy := (ShortColumns.mem_shape b δ (s₁ j).val.1 (s₁ j).val.2).mp (s₁ j).property + rcases hp with rfl | rfl <;> dsimp only [candidateNECell, Prod.swap] at H <;> omega + · exact inf_le_left + +lemma candidateBandRow_NE_group {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + fiberGroup (fun i => (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm + (Sum.inr ((candidateExtraSplit r).symm (Sum.inl i))))).val.1) = + columnGroup (transposeTableau s₁) := by + simp_rw [candidateBandSplit_NE] + rfl + +lemma candidateBandRow_SW_group {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + fiberGroup (fun i => (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm + (Sum.inr ((candidateExtraSplit r).symm (Sum.inr i))))).val.1) = + columnGroup s₂ := by + simp_rw [candidateBandSplit_SW] + apply Subgroup.ext + intro g + change (∀ i, M-1+(s₂ (g i)).val.2 = M-1+(s₂ i).val.2) ↔ (∀ i, (s₂ (g i)).val.2 = (s₂ i).val.2) + simp only [Nat.add_left_cancel_iff] + +lemma candidateBandCol_NE_group {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + fiberGroup (fun i => (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm + (Sum.inr ((candidateExtraSplit r).symm (Sum.inl i))))).val.2) = + columnGroup s₁ := by + simp_rw [candidateBandSplit_NE] + apply Subgroup.ext + intro g + change (∀ i, M-1+(s₁ (g i)).val.2 = M-1+(s₁ i).val.2) ↔ (∀ i, (s₁ (g i)).val.2 = (s₁ i).val.2) + simp only [Nat.add_left_cancel_iff] + +lemma candidateBandCol_SW_group {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + fiberGroup (fun i => (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm + (Sum.inr ((candidateExtraSplit r).symm (Sum.inr i))))).val.2) = + columnGroup (transposeTableau s₂) := by + simp_rw [candidateBandSplit_SW] + rfl + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandLetters.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandLetters.lean index be884ea4d6f697fa111673001383e634e4fbf510..fbb32cdb4ad654e3aba33fd581fd84a2942a26bf 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandLetters.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandLetters.lean @@ -1,138 +1,138 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Band.BandSeeds -import OAI.RepresentationTheory.UniversalSquare.Band.BandSplit - -namespace OAI - -/-! Band Letters. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -lemma candidateSeparatedRow_NE {M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (x : (candidate M b δ).cells) (z : (ShortColumns.shape b δ).cells) - (hx : x.val = candidateNECell M z) : - (candidateSeparatedRow M b δ hM x).val.2 = - if z.val.2 < b then M-1+z.val.2 else M+z.val.2 := by - classical - have hz := (ShortColumns.mem_shape b δ z.val.1 z.val.2).mp z.property - rw [candidateSeparatedRow_band M b δ hM hδ x (by rw [hx]; dsimp [candidateNECell]; omega), hx] - dsimp +instances only [candidateNECell] - split_ifs <;> omega - -lemma candidateSeparatedRow_SW {M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (x : (candidate M b δ).cells) (z : (ShortColumns.shape b δ).cells) - (hx : x.val = (candidateNECell M z).swap) : - (candidateSeparatedRow M b δ hM x).val.2 = z.val.1 := by - classical - have hz := (ShortColumns.mem_shape b δ z.val.1 z.val.2).mp z.property - rw [candidateSeparatedRow_band M b δ hM hδ x (by rw [hx]; dsimp [candidateNECell]; omega), hx] - dsimp +instances only [candidateNECell, Prod.swap] - split_ifs <;> omega - -lemma shortColumns_width (b δ : ℕ) : (ShortColumns.shape b δ).transpose.colLen 0 = b+δ := by - rw [YoungDiagram.colLen_transpose] - have H (j : ℕ) : j < (ShortColumns.shape b δ).rowLen 0 ↔ j < b+δ := by - rw [← YoungDiagram.mem_iff_lt_rowLen, ShortColumns.mem_shape] - simp only [true_and, zero_ne_one, false_and, or_false] - have h₁ := H (b+δ) - have h₂ := H ((ShortColumns.shape b δ).rowLen 0) - omega - -def bandSmallLetter {D : ℕ} (hD : 2 ≤ D) : Fin 2 → Fin D := Fin.castLE hD - -lemma bandSmallLetter_injective {D : ℕ} (hD : 2 ≤ D) : - Function.Injective (bandSmallLetter hD) := Fin.castLE_injective hD - -def bandExtraLetter {M b δ D : ℕ} (hD : M+b+δ ≤ D) : - Fin ((ShortColumns.shape b δ).transpose.colLen 0) → Fin D := - fun c => ⟨if c.val < b then M-1+c.val else M+c.val, by - have hc := c.isLt - have hc' : c.val < b+δ := by simpa only [shortColumns_width] using hc - split_ifs <;> omega⟩ - -lemma bandExtraLetter_injective {M b δ D : ℕ} (hD : M+b+δ ≤ D) : - Function.Injective (@bandExtraLetter M b δ D hD) := by - intro i j he - have hv := congrArg Fin.val he - apply Fin.ext - dsimp only [bandExtraLetter] at hv - split_ifs at hv <;> omega - -lemma bandExtraLetter_high {M b δ D : ℕ} (hM : 4 ≤ M) (hD : M+b+δ ≤ D) - (c : Fin ((ShortColumns.shape b δ).transpose.colLen 0)) : - 2 ≤ (bandExtraLetter hD c).val := by - dsimp only [bandExtraLetter] - split_ifs <;> omega - -lemma candidateRowAlphabet_size {M b δ : ℕ} (hM : 4 ≤ M) : - (candidate M b δ).transpose.colLen 0 = M+b+δ := by - rw [candidate_transpose, candidate_colLen M b δ 0 hM] - rfl - -lemma candidateColAlphabet_size {M b δ : ℕ} (hM : 4 ≤ M) : - (candidate M b δ).colLen 0 = M+b+δ := by - rw [candidate_colLen M b δ 0 hM] - rfl - -lemma candidateBandRowSeed_NE {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - leftWord (candidateExtraSplit r) - (rightWord (candidateBandSplit hM t s₁ s₂) (candidateBandRowSeed hM t)) = - bandExtraLetter (le_of_eq (candidateRowAlphabet_size hM).symm) ∘ - rowWord (transposeTableau s₁) := by - funext i - apply Fin.ext - rw [leftWord, rightWord, candidateBandRowSeed_val] - exact candidateSeparatedRow_NE hM hδ _ (s₁ i) (candidateBandSplit_NE hM t s₁ s₂ i) - -lemma candidateBandRowSeed_SW {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - rightWord (candidateExtraSplit r) - (rightWord (candidateBandSplit hM t s₁ s₂) (candidateBandRowSeed hM t)) = - Fin.castLE (show (ShortColumns.shape b δ).colLen 0 ≤ - (candidate M b δ).transpose.colLen 0 from - (ShortColumns.height_le b δ).trans (by rw [candidateRowAlphabet_size hM]; omega)) ∘ - rowWord s₂ := by - funext i - apply Fin.ext - rw [rightWord, rightWord, candidateBandRowSeed_val] - exact candidateSeparatedRow_SW hM hδ _ (s₂ i) (candidateBandSplit_SW hM t s₁ s₂ i) - -lemma candidateBandColSeed_NE {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - leftWord (candidateExtraSplit r) - (rightWord (candidateBandSplit hM t s₁ s₂) (candidateBandColSeed hM t)) = - Fin.castLE (show (ShortColumns.shape b δ).colLen 0 ≤ - (candidate M b δ).colLen 0 from - (ShortColumns.height_le b δ).trans (by rw [candidateColAlphabet_size hM]; omega)) ∘ - rowWord s₁ := by - funext i - apply Fin.ext - rw [leftWord, rightWord, candidateBandColSeed_val] - apply candidateSeparatedRow_SW hM hδ _ (s₁ i) - change (candidateBandTableau t _).val.swap = _ - rw [candidateBandSplit_NE] - -lemma candidateBandColSeed_SW {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - rightWord (candidateExtraSplit r) - (rightWord (candidateBandSplit hM t s₁ s₂) (candidateBandColSeed hM t)) = - bandExtraLetter (le_of_eq (candidateColAlphabet_size hM).symm) ∘ - rowWord (transposeTableau s₂) := by - funext i - apply Fin.ext - rw [rightWord, rightWord, candidateBandColSeed_val] - apply candidateSeparatedRow_NE hM hδ _ (s₂ i) - change (candidateBandTableau t _).val.swap = _ - rw [candidateBandSplit_SW, Prod.swap_swap] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Band.BandSeeds +import OAI.RepresentationTheory.UniversalSquare.Band.BandSplit + +namespace OAI + +/-! Band Letters. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +lemma candidateSeparatedRow_NE {M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (x : (candidate M b δ).cells) (z : (ShortColumns.shape b δ).cells) + (hx : x.val = candidateNECell M z) : + (candidateSeparatedRow M b δ hM x).val.2 = + if z.val.2 < b then M-1+z.val.2 else M+z.val.2 := by + classical + have hz := (ShortColumns.mem_shape b δ z.val.1 z.val.2).mp z.property + rw [candidateSeparatedRow_band M b δ hM hδ x (by rw [hx]; dsimp [candidateNECell]; omega), hx] + dsimp +instances only [candidateNECell] + split_ifs <;> omega + +lemma candidateSeparatedRow_SW {M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (x : (candidate M b δ).cells) (z : (ShortColumns.shape b δ).cells) + (hx : x.val = (candidateNECell M z).swap) : + (candidateSeparatedRow M b δ hM x).val.2 = z.val.1 := by + classical + have hz := (ShortColumns.mem_shape b δ z.val.1 z.val.2).mp z.property + rw [candidateSeparatedRow_band M b δ hM hδ x (by rw [hx]; dsimp [candidateNECell]; omega), hx] + dsimp +instances only [candidateNECell, Prod.swap] + split_ifs <;> omega + +lemma shortColumns_width (b δ : ℕ) : (ShortColumns.shape b δ).transpose.colLen 0 = b+δ := by + rw [YoungDiagram.colLen_transpose] + have H (j : ℕ) : j < (ShortColumns.shape b δ).rowLen 0 ↔ j < b+δ := by + rw [← YoungDiagram.mem_iff_lt_rowLen, ShortColumns.mem_shape] + simp only [true_and, zero_ne_one, false_and, or_false] + have h₁ := H (b+δ) + have h₂ := H ((ShortColumns.shape b δ).rowLen 0) + omega + +def bandSmallLetter {D : ℕ} (hD : 2 ≤ D) : Fin 2 → Fin D := Fin.castLE hD + +lemma bandSmallLetter_injective {D : ℕ} (hD : 2 ≤ D) : + Function.Injective (bandSmallLetter hD) := Fin.castLE_injective hD + +def bandExtraLetter {M b δ D : ℕ} (hD : M+b+δ ≤ D) : + Fin ((ShortColumns.shape b δ).transpose.colLen 0) → Fin D := + fun c => ⟨if c.val < b then M-1+c.val else M+c.val, by + have hc := c.isLt + have hc' : c.val < b+δ := by simpa only [shortColumns_width] using hc + split_ifs <;> omega⟩ + +lemma bandExtraLetter_injective {M b δ D : ℕ} (hD : M+b+δ ≤ D) : + Function.Injective (@bandExtraLetter M b δ D hD) := by + intro i j he + have hv := congrArg Fin.val he + apply Fin.ext + dsimp only [bandExtraLetter] at hv + split_ifs at hv <;> omega + +lemma bandExtraLetter_high {M b δ D : ℕ} (hM : 4 ≤ M) (hD : M+b+δ ≤ D) + (c : Fin ((ShortColumns.shape b δ).transpose.colLen 0)) : + 2 ≤ (bandExtraLetter hD c).val := by + dsimp only [bandExtraLetter] + split_ifs <;> omega + +lemma candidateRowAlphabet_size {M b δ : ℕ} (hM : 4 ≤ M) : + (candidate M b δ).transpose.colLen 0 = M+b+δ := by + rw [candidate_transpose, candidate_colLen M b δ 0 hM] + rfl + +lemma candidateColAlphabet_size {M b δ : ℕ} (hM : 4 ≤ M) : + (candidate M b δ).colLen 0 = M+b+δ := by + rw [candidate_colLen M b δ 0 hM] + rfl + +lemma candidateBandRowSeed_NE {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + leftWord (candidateExtraSplit r) + (rightWord (candidateBandSplit hM t s₁ s₂) (candidateBandRowSeed hM t)) = + bandExtraLetter (le_of_eq (candidateRowAlphabet_size hM).symm) ∘ + rowWord (transposeTableau s₁) := by + funext i + apply Fin.ext + rw [leftWord, rightWord, candidateBandRowSeed_val] + exact candidateSeparatedRow_NE hM hδ _ (s₁ i) (candidateBandSplit_NE hM t s₁ s₂ i) + +lemma candidateBandRowSeed_SW {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + rightWord (candidateExtraSplit r) + (rightWord (candidateBandSplit hM t s₁ s₂) (candidateBandRowSeed hM t)) = + Fin.castLE (show (ShortColumns.shape b δ).colLen 0 ≤ + (candidate M b δ).transpose.colLen 0 from + (ShortColumns.height_le b δ).trans (by rw [candidateRowAlphabet_size hM]; omega)) ∘ + rowWord s₂ := by + funext i + apply Fin.ext + rw [rightWord, rightWord, candidateBandRowSeed_val] + exact candidateSeparatedRow_SW hM hδ _ (s₂ i) (candidateBandSplit_SW hM t s₁ s₂ i) + +lemma candidateBandColSeed_NE {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + leftWord (candidateExtraSplit r) + (rightWord (candidateBandSplit hM t s₁ s₂) (candidateBandColSeed hM t)) = + Fin.castLE (show (ShortColumns.shape b δ).colLen 0 ≤ + (candidate M b δ).colLen 0 from + (ShortColumns.height_le b δ).trans (by rw [candidateColAlphabet_size hM]; omega)) ∘ + rowWord s₁ := by + funext i + apply Fin.ext + rw [leftWord, rightWord, candidateBandColSeed_val] + apply candidateSeparatedRow_SW hM hδ _ (s₁ i) + change (candidateBandTableau t _).val.swap = _ + rw [candidateBandSplit_NE] + +lemma candidateBandColSeed_SW {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + rightWord (candidateExtraSplit r) + (rightWord (candidateBandSplit hM t s₁ s₂) (candidateBandColSeed hM t)) = + bandExtraLetter (le_of_eq (candidateColAlphabet_size hM).symm) ∘ + rowWord (transposeTableau s₂) := by + funext i + apply Fin.ext + rw [rightWord, rightWord, candidateBandColSeed_val] + apply candidateSeparatedRow_NE hM hδ _ (s₂ i) + change (candidateBandTableau t _).val.swap = _ + rw [candidateBandSplit_SW, Prod.swap_swap] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandPath.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandPath.lean index 21c448c4a7c3df3646f53d822ebf2364413ebdd1..0cd0b0de964d5f39f592f22fb6e0c60577336ea8 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandPath.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandPath.lean @@ -1,140 +1,140 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPacking -import OAI.RepresentationTheory.UniversalSquare.Band.BandSeparated - -namespace OAI - -/-! Band Path. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl -open scoped TensorProduct - -def candidatePathEquiv {M : ℕ} (hM : 4 ≤ M) : Fin (2*(M-1)+1) ≃ Fin (2*M-1) := - finCongr (by omega) - -def bandSmallRowLetter {M b δ : ℕ} (hM : 4 ≤ M) : - Fin 2 → Fin ((candidate M b δ).transpose.colLen 0) := - bandSmallLetter (by rw [candidateRowAlphabet_size hM]; omega) - -def bandSmallColLetter {M b δ : ℕ} (hM : 4 ≤ M) : - Fin 2 → Fin ((candidate M b δ).colLen 0) := - bandSmallLetter (by rw [candidateColAlphabet_size hM]; omega) - -lemma candidatePathRow_eq {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - candidatePathRow hM t s₁ s₂ = - letterLift (bandSmallRowLetter hM) - (relabelWord (candidatePathEquiv hM) (PathLayer.rowAlt (M-1))) := by - unfold PathLayer.rowAlt - rw [altWord_relabel, letterLift_altWord] - unfold candidatePathRow - congr 1 - · apply Subgroup.ext - intro g - change (∀ i, _ = _) ↔ (∀ i, _ = _) - apply forall_congr' - intro i - simp only [candidateBandSplit_path] - exact candidatePathCell_row_tag hM _ _ - · funext i - apply Fin.ext - rw [Function.comp_apply] - change (candidateBandRowSeed hM t ((candidateBandSplit hM t s₁ s₂).symm (Sum.inl i))).val = _ - rw [candidateBandRowSeed_val, candidateSeparatedRow_path hM hδ _ i - (candidateBandSplit_path hM t s₁ s₂ i)] - simp only [bandSmallRowLetter, bandSmallLetter, Fin.val_castLE, Function.comp_apply, - PathLayer.base, candidatePathEquiv, finCongr_symm, finCongr_apply, Fin.val_cast] - split_ifs <;> rfl - -lemma candidatePathCol_eq {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - candidatePathCol hM t s₁ s₂ = - letterLift (bandSmallColLetter hM) - (relabelWord ((Fin.revPerm).trans (candidatePathEquiv hM)) (PathLayer.rowAlt (M-1))) := by - unfold PathLayer.rowAlt - rw [altWord_relabel, letterLift_altWord] - unfold candidatePathCol - congr 1 - · apply Subgroup.ext - intro g - change (∀ i, _ = _) ↔ (∀ i, _ = _) - apply forall_congr' - intro i - simp only [candidateBandSplit_path] - have hh := candidatePathCell_row_tag (b := b) (δ := δ) hM (g i).rev i.rev - rw [← candidatePathCell_swap hM, ← candidatePathCell_swap hM] at hh - simpa only [Prod.fst_swap, Function.comp_apply, PathLayer.tag, Equiv.symm_trans, - Equiv.trans_apply, candidatePathEquiv, finCongr_symm, finCongr_apply, - Fin.revPerm_symm, Fin.revPerm_apply, Fin.val_rev, Fin.val_cast, - show 2*(M-1)+1 = 2*M-1 from by omega] using hh - · funext i - apply Fin.ext - rw [Function.comp_apply] - change (candidateBandColSeed hM t ((candidateBandSplit hM t s₁ s₂).symm (Sum.inl i))).val = _ - rw [candidateBandColSeed_val, candidateSeparatedRow_path hM hδ _ i.rev (by - change (candidateBandTableau t _).val.swap = _ - rw [candidateBandSplit_path, candidatePathCell_swap hM])] - simp only [bandSmallColLetter, bandSmallLetter, Fin.val_castLE, Function.comp_apply, - PathLayer.base, candidatePathEquiv, Equiv.symm_trans, Equiv.trans_apply, - finCongr_symm, finCongr_apply, Fin.revPerm_symm, Fin.revPerm_apply, Fin.val_cast, Fin.val_rev, - show 2*(M-1)+1 = 2*M-1 from by omega] - split_ifs <;> rfl - -def bandPairSmallLetter {M b δ : ℕ} (hM : 4 ≤ M) : - Fin 4 → Fin ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0) := - pairLetterMap (bandSmallRowLetter hM) (bandSmallColLetter hM) - -lemma bandPairSmallLetter_injective {M b δ : ℕ} (hM : 4 ≤ M) : - Function.Injective (@bandPairSmallLetter M b δ hM) := - pairLetterMap_injective _ _ (bandSmallLetter_injective _) (bandSmallLetter_injective _) - -theorem candidatePathWord_eq {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - candidatePathWord hM t s₁ s₂ = - (-1 : ℂ)^(M-1) • letterLift (bandPairSmallLetter hM) - (relabelWord (candidatePathEquiv hM) (Path.bandWord (M-1))) := by - rw [candidatePathWord, candidatePathRow_eq hM hδ, candidatePathCol_eq hM hδ, - ← letterLift_wordTensor, ← map_smul, ← map_smul] - congr 1 - ext w - simp only [wordTensor_tmul, relabelWord_apply, Pi.smul_apply, smul_eq_mul] - have hr : (splitRight w) ∘ (Fin.revPerm.trans (candidatePathEquiv hM)) = - (fun i => (Path.parts ((w ∘ candidatePathEquiv hM) i)).2) ∘ Fin.rev := rfl - rw [hr] - exact PathLayer.paired_rowAlt (M-1) (w ∘ candidatePathEquiv hM) - -theorem candidatePathWord_support {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) - (μ : YoungDiagram) (u : Tableau (2*M-1) μ) (hd : μ.colLen 0 ≤ 4) : - ∃ F : Representation.IntertwiningMap (spechtRep u) - (cyclic (wordRep (2*M-1) _) - (candidatePathWord hM t s₁ s₂)).toRepresentation, F ≠ 0 := by - rw [candidatePathWord_eq hM hδ, cyclic_smul_eq _ _ _ (pow_ne_zero _ (by norm_num))] - obtain ⟨f,hf⟩ := support_relabel (candidatePathEquiv hM) (Path.bandWord (M-1)) - (fun μ u hd => Path.odd_path_support (M-1) μ u hd) μ u hd - let v := relabelWord (candidatePathEquiv hM) (Path.bandWord (M-1)) - let G := cyclicMap (letterLift (bandPairSmallLetter (b := b) (δ := δ) hM)) v - refine ⟨G.comp f, ?_⟩ - intro h0 - apply hf - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - have hz : G (f x) = 0 := congrArg (fun H => H x) h0 - have hGi : Function.Injective G := by - intro a c he - apply Subtype.ext - exact letterLift_injective _ (bandPairSmallLetter_injective hM) - (congrArg Subtype.val he) - exact hGi (hz.trans (map_zero G).symm) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPacking +import OAI.RepresentationTheory.UniversalSquare.Band.BandSeparated + +namespace OAI + +/-! Band Path. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl +open scoped TensorProduct + +def candidatePathEquiv {M : ℕ} (hM : 4 ≤ M) : Fin (2*(M-1)+1) ≃ Fin (2*M-1) := + finCongr (by omega) + +def bandSmallRowLetter {M b δ : ℕ} (hM : 4 ≤ M) : + Fin 2 → Fin ((candidate M b δ).transpose.colLen 0) := + bandSmallLetter (by rw [candidateRowAlphabet_size hM]; omega) + +def bandSmallColLetter {M b δ : ℕ} (hM : 4 ≤ M) : + Fin 2 → Fin ((candidate M b δ).colLen 0) := + bandSmallLetter (by rw [candidateColAlphabet_size hM]; omega) + +lemma candidatePathRow_eq {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + candidatePathRow hM t s₁ s₂ = + letterLift (bandSmallRowLetter hM) + (relabelWord (candidatePathEquiv hM) (PathLayer.rowAlt (M-1))) := by + unfold PathLayer.rowAlt + rw [altWord_relabel, letterLift_altWord] + unfold candidatePathRow + congr 1 + · apply Subgroup.ext + intro g + change (∀ i, _ = _) ↔ (∀ i, _ = _) + apply forall_congr' + intro i + simp only [candidateBandSplit_path] + exact candidatePathCell_row_tag hM _ _ + · funext i + apply Fin.ext + rw [Function.comp_apply] + change (candidateBandRowSeed hM t ((candidateBandSplit hM t s₁ s₂).symm (Sum.inl i))).val = _ + rw [candidateBandRowSeed_val, candidateSeparatedRow_path hM hδ _ i + (candidateBandSplit_path hM t s₁ s₂ i)] + simp only [bandSmallRowLetter, bandSmallLetter, Fin.val_castLE, Function.comp_apply, + PathLayer.base, candidatePathEquiv, finCongr_symm, finCongr_apply, Fin.val_cast] + split_ifs <;> rfl + +lemma candidatePathCol_eq {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + candidatePathCol hM t s₁ s₂ = + letterLift (bandSmallColLetter hM) + (relabelWord ((Fin.revPerm).trans (candidatePathEquiv hM)) (PathLayer.rowAlt (M-1))) := by + unfold PathLayer.rowAlt + rw [altWord_relabel, letterLift_altWord] + unfold candidatePathCol + congr 1 + · apply Subgroup.ext + intro g + change (∀ i, _ = _) ↔ (∀ i, _ = _) + apply forall_congr' + intro i + simp only [candidateBandSplit_path] + have hh := candidatePathCell_row_tag (b := b) (δ := δ) hM (g i).rev i.rev + rw [← candidatePathCell_swap hM, ← candidatePathCell_swap hM] at hh + simpa only [Prod.fst_swap, Function.comp_apply, PathLayer.tag, Equiv.symm_trans, + Equiv.trans_apply, candidatePathEquiv, finCongr_symm, finCongr_apply, + Fin.revPerm_symm, Fin.revPerm_apply, Fin.val_rev, Fin.val_cast, + show 2*(M-1)+1 = 2*M-1 from by omega] using hh + · funext i + apply Fin.ext + rw [Function.comp_apply] + change (candidateBandColSeed hM t ((candidateBandSplit hM t s₁ s₂).symm (Sum.inl i))).val = _ + rw [candidateBandColSeed_val, candidateSeparatedRow_path hM hδ _ i.rev (by + change (candidateBandTableau t _).val.swap = _ + rw [candidateBandSplit_path, candidatePathCell_swap hM])] + simp only [bandSmallColLetter, bandSmallLetter, Fin.val_castLE, Function.comp_apply, + PathLayer.base, candidatePathEquiv, Equiv.symm_trans, Equiv.trans_apply, + finCongr_symm, finCongr_apply, Fin.revPerm_symm, Fin.revPerm_apply, Fin.val_cast, Fin.val_rev, + show 2*(M-1)+1 = 2*M-1 from by omega] + split_ifs <;> rfl + +def bandPairSmallLetter {M b δ : ℕ} (hM : 4 ≤ M) : + Fin 4 → Fin ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0) := + pairLetterMap (bandSmallRowLetter hM) (bandSmallColLetter hM) + +lemma bandPairSmallLetter_injective {M b δ : ℕ} (hM : 4 ≤ M) : + Function.Injective (@bandPairSmallLetter M b δ hM) := + pairLetterMap_injective _ _ (bandSmallLetter_injective _) (bandSmallLetter_injective _) + +theorem candidatePathWord_eq {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + candidatePathWord hM t s₁ s₂ = + (-1 : ℂ)^(M-1) • letterLift (bandPairSmallLetter hM) + (relabelWord (candidatePathEquiv hM) (Path.bandWord (M-1))) := by + rw [candidatePathWord, candidatePathRow_eq hM hδ, candidatePathCol_eq hM hδ, + ← letterLift_wordTensor, ← map_smul, ← map_smul] + congr 1 + ext w + simp only [wordTensor_tmul, relabelWord_apply, Pi.smul_apply, smul_eq_mul] + have hr : (splitRight w) ∘ (Fin.revPerm.trans (candidatePathEquiv hM)) = + (fun i => (Path.parts ((w ∘ candidatePathEquiv hM) i)).2) ∘ Fin.rev := rfl + rw [hr] + exact PathLayer.paired_rowAlt (M-1) (w ∘ candidatePathEquiv hM) + +theorem candidatePathWord_support {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) + (μ : YoungDiagram) (u : Tableau (2*M-1) μ) (hd : μ.colLen 0 ≤ 4) : + ∃ F : Representation.IntertwiningMap (spechtRep u) + (cyclic (wordRep (2*M-1) _) + (candidatePathWord hM t s₁ s₂)).toRepresentation, F ≠ 0 := by + rw [candidatePathWord_eq hM hδ, cyclic_smul_eq _ _ _ (pow_ne_zero _ (by norm_num))] + obtain ⟨f,hf⟩ := support_relabel (candidatePathEquiv hM) (Path.bandWord (M-1)) + (fun μ u hd => Path.odd_path_support (M-1) μ u hd) μ u hd + let v := relabelWord (candidatePathEquiv hM) (Path.bandWord (M-1)) + let G := cyclicMap (letterLift (bandPairSmallLetter (b := b) (δ := δ) hM)) v + refine ⟨G.comp f, ?_⟩ + intro h0 + apply hf + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + have hz : G (f x) = 0 := congrArg (fun H => H x) h0 + have hGi : Function.Injective G := by + intro a c he + apply Subtype.ext + exact letterLift_injective _ (bandPairSmallLetter_injective hM) + (congrArg Subtype.val he) + exact hGi (hz.trans (map_zero G).symm) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandPositions.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandPositions.lean index b43b9accc95669852385897303db1d1136da600e..5e3a0c6dfe5520350d7b3efb6efd95f22475a16c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandPositions.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandPositions.lean @@ -1,157 +1,157 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CandidateClearance - -namespace OAI - -/-! Band Positions. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -lemma candidateBandTableau_injective {n M b δ : ℕ} (t : Tableau n (candidate M b δ)) : - Function.Injective (candidateBandTableau t) := by - intro i j h - have h₁ := t.injective h - exact Sum.inr_injective ((candidateCutPositions t).symm.injective h₁) - -lemma candidateBandTableau_surjective {n M b δ : ℕ} (t : Tableau n (candidate M b δ)) - (x : (candidate M b δ).cells) (hx : M-2 ≤ x.val.1+x.val.2) : - ∃ i, candidateBandTableau t i = x := by - cases he : candidateCutPositions t (t.symm x) with - | inl i => - have ht := (candidateCutPositions_high t (t.symm x)).mp (by rw [he]; rfl) - change (t (t.symm x)).val.1 + (t (t.symm x)).val.2 < M-2 at ht - rw [Equiv.apply_symm_apply] at ht - omega - | inr i => - refine ⟨i, ?_⟩ - change t ((candidateCutPositions t).symm (Sum.inr i)) = x - rw [← he, Equiv.symm_apply_apply, Equiv.apply_symm_apply] - -abbrev candidateComplement (M b δ : ℕ) := - {x : (candidate M b δ).cells // M-2 ≤ x.val.1+x.val.2} - -def candidateComplementEquiv {n M b δ : ℕ} (t : Tableau n (candidate M b δ)) : - Fin (candidateBandSize t) ≃ candidateComplement M b δ := - Equiv.ofBijective (fun i => ⟨candidateBandTableau t i, candidateBandTableau_outside t i⟩) - ⟨fun _ _ h => candidateBandTableau_injective t (congrArg Subtype.val h), by - intro x - obtain ⟨i,hi⟩ := candidateBandTableau_surjective t x.val x.property - exact ⟨i, Subtype.ext hi⟩⟩ - -def candidateNECell (M : ℕ) {b δ : ℕ} (x : (ShortColumns.shape b δ).cells) : ℕ × ℕ := - (x.val.1,M-1+x.val.2) - -lemma candidateNECell_mem {M b δ : ℕ} (hM : 4 ≤ M) - (x : (ShortColumns.shape b δ).cells) : candidateNECell M x ∈ attachmentNE M b δ := by - have hx := (ShortColumns.mem_shape b δ x.val.1 x.val.2).mp x.property - change (x.val.1,M-1+x.val.2) ∈ attachmentNE M b δ - rw [mem_attachmentNE] - omega - -lemma candidateNECell_injective (M b δ : ℕ) : - Function.Injective (candidateNECell M (b := b) (δ := δ)) := by - intro x y h - apply Subtype.ext - have h₁ := congrArg Prod.fst h - have h₂ := congrArg Prod.snd h - apply Prod.ext - · exact h₁ - change M-1+x.val.2 = M-1+y.val.2 at h₂ - omega - -lemma candidateNECell_surjective {M b δ : ℕ} (hM : 4 ≤ M) (i j : ℕ) - (hx : (i,j) ∈ attachmentNE M b δ) : - ∃ x : (ShortColumns.shape b δ).cells, candidateNECell M x = (i,j) := by - rw [mem_attachmentNE] at hx - have hs : (i,j-(M-1)) ∈ ShortColumns.shape b δ := by - rw [ShortColumns.mem_shape] - omega - refine ⟨⟨(i,j-(M-1)),hs⟩, ?_⟩ - apply Prod.ext - · rfl - change M-1 + (j-(M-1)) = j - omega - -abbrev CandidateBandParts (M b δ : ℕ) := - Fin (2*M-1) ⊕ (ShortColumns.shape b δ).cells ⊕ (ShortColumns.shape b δ).cells - -def candidatePartsCell (M b δ : ℕ) (hM : 4 ≤ M) : - CandidateBandParts M b δ → candidateComplement M b δ - | .inl q => ⟨⟨candidatePathCell M b δ q, (candidatePathCell_mem M b δ hM q).1⟩, - (candidatePathCell_mem M b δ hM q).2⟩ - | .inr (.inl x) => ⟨⟨candidateNECell M x, - (attachmentNE_mem M b δ hM (candidateNECell_mem hM x)).1⟩, - (attachmentNE_mem M b δ hM (candidateNECell_mem hM x)).2⟩ - | .inr (.inr x) => ⟨⟨(candidateNECell M x).swap, by - have hx := (attachmentNE_mem M b δ hM (candidateNECell_mem hM x)).1 - have ht : (candidateNECell M x).swap ∈ (candidate M b δ).transpose := by - simpa only [YoungDiagram.mem_transpose, Prod.swap_swap, candidateNECell] using hx - simpa only [candidate_transpose, YoungDiagram.mem_cells] using ht⟩, by - have hx := (attachmentNE_mem M b δ hM (candidateNECell_mem hM x)).2 - change M-2 ≤ (candidateNECell M x).2 + (candidateNECell M x).1 - dsimp only [candidateNECell] at * - omega⟩ - -lemma candidatePartsCell_injective (M b δ : ℕ) (hM : 4 ≤ M) : - Function.Injective (candidatePartsCell M b δ hM) := by - intro x y he - have h := congrArg (fun z : candidateComplement M b δ => z.val.val) he - rcases x with i | (x | x) <;> rcases y with j | (y | y) <;> - dsimp only [candidatePartsCell] at h - · exact congrArg Sum.inl (candidatePathCell_injective M b δ hM h) - · exact False.elim ((pathCell_not_attachment M b δ hM i).1 - (h.symm ▸ candidateNECell_mem hM y)) - · have hh := congrArg Prod.swap h - rw [Prod.swap_swap] at hh - exact False.elim ((pathCell_not_attachment M b δ hM i).2 - (hh.symm ▸ candidateNECell_mem hM y)) - · exact False.elim ((pathCell_not_attachment M b δ hM j).1 - (h ▸ candidateNECell_mem hM x)) - · exact congrArg (Sum.inr ∘ Sum.inl) (candidateNECell_injective M b δ h) - · have hx := candidateNECell_mem hM x - have hy := candidateNECell_mem hM y - have hd := attachment_disjoint_transpose M b δ hM - exact False.elim (Finset.disjoint_left.mp hd hx - (h.symm ▸ Finset.mem_map.mpr ⟨candidateNECell M y,hy,rfl⟩)) - · have hh := congrArg Prod.swap h - rw [Prod.swap_swap] at hh - exact False.elim ((pathCell_not_attachment M b δ hM j).2 - (hh ▸ candidateNECell_mem hM x)) - · have hx := candidateNECell_mem hM x - have hy := candidateNECell_mem hM y - have hd := attachment_disjoint_transpose M b δ hM - exact False.elim (Finset.disjoint_left.mp hd hy - (h ▸ Finset.mem_map.mpr ⟨candidateNECell M x,hx,rfl⟩)) - · have hh := congrArg Prod.swap h - simp only [Prod.swap_swap] at hh - exact congrArg (Sum.inr ∘ Sum.inr) (candidateNECell_injective M b δ hh) - -lemma candidatePartsCell_surjective (M b δ : ℕ) (hM : 4 ≤ M) : - Function.Surjective (candidatePartsCell M b δ hM) := by - intro x - obtain ⟨⟨⟨i,j⟩,hx⟩,ht⟩ := x - rcases candidate_band_cell_decomposition M b δ hM i j hx ht with ⟨q,hq⟩ | hn | hs - · exact ⟨Sum.inl q, Subtype.ext (Subtype.ext hq)⟩ - · obtain ⟨y,hy⟩ := candidateNECell_surjective hM i j hn - exact ⟨Sum.inr (Sum.inl y), Subtype.ext (Subtype.ext hy)⟩ - · obtain ⟨y,hy⟩ := candidateNECell_surjective hM j i hs - exact ⟨Sum.inr (Sum.inr y), Subtype.ext (Subtype.ext (congrArg Prod.swap hy))⟩ - -def candidateBandPartsEquiv {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - Fin (candidateBandSize t) ≃ Fin (2*M-1) ⊕ (Fin r ⊕ Fin r) := - ((candidateComplementEquiv t).trans - (Equiv.ofBijective (candidatePartsCell M b δ hM) - ⟨candidatePartsCell_injective M b δ hM,candidatePartsCell_surjective M b δ hM⟩).symm).trans - (Equiv.sumCongr (Equiv.refl _) (Equiv.sumCongr s₁.symm s₂.symm)) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CandidateClearance + +namespace OAI + +/-! Band Positions. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +lemma candidateBandTableau_injective {n M b δ : ℕ} (t : Tableau n (candidate M b δ)) : + Function.Injective (candidateBandTableau t) := by + intro i j h + have h₁ := t.injective h + exact Sum.inr_injective ((candidateCutPositions t).symm.injective h₁) + +lemma candidateBandTableau_surjective {n M b δ : ℕ} (t : Tableau n (candidate M b δ)) + (x : (candidate M b δ).cells) (hx : M-2 ≤ x.val.1+x.val.2) : + ∃ i, candidateBandTableau t i = x := by + cases he : candidateCutPositions t (t.symm x) with + | inl i => + have ht := (candidateCutPositions_high t (t.symm x)).mp (by rw [he]; rfl) + change (t (t.symm x)).val.1 + (t (t.symm x)).val.2 < M-2 at ht + rw [Equiv.apply_symm_apply] at ht + omega + | inr i => + refine ⟨i, ?_⟩ + change t ((candidateCutPositions t).symm (Sum.inr i)) = x + rw [← he, Equiv.symm_apply_apply, Equiv.apply_symm_apply] + +abbrev candidateComplement (M b δ : ℕ) := + {x : (candidate M b δ).cells // M-2 ≤ x.val.1+x.val.2} + +def candidateComplementEquiv {n M b δ : ℕ} (t : Tableau n (candidate M b δ)) : + Fin (candidateBandSize t) ≃ candidateComplement M b δ := + Equiv.ofBijective (fun i => ⟨candidateBandTableau t i, candidateBandTableau_outside t i⟩) + ⟨fun _ _ h => candidateBandTableau_injective t (congrArg Subtype.val h), by + intro x + obtain ⟨i,hi⟩ := candidateBandTableau_surjective t x.val x.property + exact ⟨i, Subtype.ext hi⟩⟩ + +def candidateNECell (M : ℕ) {b δ : ℕ} (x : (ShortColumns.shape b δ).cells) : ℕ × ℕ := + (x.val.1,M-1+x.val.2) + +lemma candidateNECell_mem {M b δ : ℕ} (hM : 4 ≤ M) + (x : (ShortColumns.shape b δ).cells) : candidateNECell M x ∈ attachmentNE M b δ := by + have hx := (ShortColumns.mem_shape b δ x.val.1 x.val.2).mp x.property + change (x.val.1,M-1+x.val.2) ∈ attachmentNE M b δ + rw [mem_attachmentNE] + omega + +lemma candidateNECell_injective (M b δ : ℕ) : + Function.Injective (candidateNECell M (b := b) (δ := δ)) := by + intro x y h + apply Subtype.ext + have h₁ := congrArg Prod.fst h + have h₂ := congrArg Prod.snd h + apply Prod.ext + · exact h₁ + change M-1+x.val.2 = M-1+y.val.2 at h₂ + omega + +lemma candidateNECell_surjective {M b δ : ℕ} (hM : 4 ≤ M) (i j : ℕ) + (hx : (i,j) ∈ attachmentNE M b δ) : + ∃ x : (ShortColumns.shape b δ).cells, candidateNECell M x = (i,j) := by + rw [mem_attachmentNE] at hx + have hs : (i,j-(M-1)) ∈ ShortColumns.shape b δ := by + rw [ShortColumns.mem_shape] + omega + refine ⟨⟨(i,j-(M-1)),hs⟩, ?_⟩ + apply Prod.ext + · rfl + change M-1 + (j-(M-1)) = j + omega + +abbrev CandidateBandParts (M b δ : ℕ) := + Fin (2*M-1) ⊕ (ShortColumns.shape b δ).cells ⊕ (ShortColumns.shape b δ).cells + +def candidatePartsCell (M b δ : ℕ) (hM : 4 ≤ M) : + CandidateBandParts M b δ → candidateComplement M b δ + | .inl q => ⟨⟨candidatePathCell M b δ q, (candidatePathCell_mem M b δ hM q).1⟩, + (candidatePathCell_mem M b δ hM q).2⟩ + | .inr (.inl x) => ⟨⟨candidateNECell M x, + (attachmentNE_mem M b δ hM (candidateNECell_mem hM x)).1⟩, + (attachmentNE_mem M b δ hM (candidateNECell_mem hM x)).2⟩ + | .inr (.inr x) => ⟨⟨(candidateNECell M x).swap, by + have hx := (attachmentNE_mem M b δ hM (candidateNECell_mem hM x)).1 + have ht : (candidateNECell M x).swap ∈ (candidate M b δ).transpose := by + simpa only [YoungDiagram.mem_transpose, Prod.swap_swap, candidateNECell] using hx + simpa only [candidate_transpose, YoungDiagram.mem_cells] using ht⟩, by + have hx := (attachmentNE_mem M b δ hM (candidateNECell_mem hM x)).2 + change M-2 ≤ (candidateNECell M x).2 + (candidateNECell M x).1 + dsimp only [candidateNECell] at * + omega⟩ + +lemma candidatePartsCell_injective (M b δ : ℕ) (hM : 4 ≤ M) : + Function.Injective (candidatePartsCell M b δ hM) := by + intro x y he + have h := congrArg (fun z : candidateComplement M b δ => z.val.val) he + rcases x with i | (x | x) <;> rcases y with j | (y | y) <;> + dsimp only [candidatePartsCell] at h + · exact congrArg Sum.inl (candidatePathCell_injective M b δ hM h) + · exact False.elim ((pathCell_not_attachment M b δ hM i).1 + (h.symm ▸ candidateNECell_mem hM y)) + · have hh := congrArg Prod.swap h + rw [Prod.swap_swap] at hh + exact False.elim ((pathCell_not_attachment M b δ hM i).2 + (hh.symm ▸ candidateNECell_mem hM y)) + · exact False.elim ((pathCell_not_attachment M b δ hM j).1 + (h ▸ candidateNECell_mem hM x)) + · exact congrArg (Sum.inr ∘ Sum.inl) (candidateNECell_injective M b δ h) + · have hx := candidateNECell_mem hM x + have hy := candidateNECell_mem hM y + have hd := attachment_disjoint_transpose M b δ hM + exact False.elim (Finset.disjoint_left.mp hd hx + (h.symm ▸ Finset.mem_map.mpr ⟨candidateNECell M y,hy,rfl⟩)) + · have hh := congrArg Prod.swap h + rw [Prod.swap_swap] at hh + exact False.elim ((pathCell_not_attachment M b δ hM j).2 + (hh ▸ candidateNECell_mem hM x)) + · have hx := candidateNECell_mem hM x + have hy := candidateNECell_mem hM y + have hd := attachment_disjoint_transpose M b δ hM + exact False.elim (Finset.disjoint_left.mp hd hy + (h ▸ Finset.mem_map.mpr ⟨candidateNECell M x,hx,rfl⟩)) + · have hh := congrArg Prod.swap h + simp only [Prod.swap_swap] at hh + exact congrArg (Sum.inr ∘ Sum.inr) (candidateNECell_injective M b δ hh) + +lemma candidatePartsCell_surjective (M b δ : ℕ) (hM : 4 ≤ M) : + Function.Surjective (candidatePartsCell M b δ hM) := by + intro x + obtain ⟨⟨⟨i,j⟩,hx⟩,ht⟩ := x + rcases candidate_band_cell_decomposition M b δ hM i j hx ht with ⟨q,hq⟩ | hn | hs + · exact ⟨Sum.inl q, Subtype.ext (Subtype.ext hq)⟩ + · obtain ⟨y,hy⟩ := candidateNECell_surjective hM i j hn + exact ⟨Sum.inr (Sum.inl y), Subtype.ext (Subtype.ext hy)⟩ + · obtain ⟨y,hy⟩ := candidateNECell_surjective hM j i hs + exact ⟨Sum.inr (Sum.inr y), Subtype.ext (Subtype.ext (congrArg Prod.swap hy))⟩ + +def candidateBandPartsEquiv {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + Fin (candidateBandSize t) ≃ Fin (2*M-1) ⊕ (Fin r ⊕ Fin r) := + ((candidateComplementEquiv t).trans + (Equiv.ofBijective (candidatePartsCell M b δ hM) + ⟨candidatePartsCell_injective M b δ hM,candidatePartsCell_surjective M b δ hM⟩).symm).trans + (Equiv.sumCongr (Equiv.refl _) (Equiv.sumCongr s₁.symm s₂.symm)) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandSeeds.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandSeeds.lean index c9934f5bd86de8931b5a20a78980a4fb9015abe6..8c6af04e3c2b5948df95f3fe78fb3a1fddc88277 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandSeeds.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandSeeds.lean @@ -1,167 +1,167 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CandidateShuffle -import OAI.RepresentationTheory.UniversalSquare.Band.BandPositions - -namespace OAI - -/-! Band Seeds. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -lemma candidateSeparatedRow_extra {M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (x : (candidate M b δ).cells) (hx : M-2 ≤ x.val.1+x.val.2) : - 2 ≤ (candidateSeparatedRow M b δ hM x).val.2 ↔ x.val ∈ attachmentNE M b δ := by - rw [candidateSeparatedRow_band M b δ hM hδ x hx] - have hm := mem_candidate.mp x.property - rcases x with ⟨⟨i,j⟩,hm0⟩ - simp only [mem_attachmentNE] - dsimp only at * - split_ifs <;> omega - -def candidateComplementRowShuffle (M b δ : ℕ) (hM : 4 ≤ M) : - Equiv.Perm (candidateComplement M b δ) := - (candidateRowShuffle M b δ hM).subtypePerm (fun x => by - have h := candidateRowShuffle_triangle M b δ hM x - omega) - -lemma candidateComplementRowShuffle_val (M b δ : ℕ) (hM : 4 ≤ M) - (x : candidateComplement M b δ) : - (candidateComplementRowShuffle M b δ hM x).val = - candidateRowShuffle M b δ hM x.val := rfl - -def candidateBandRowShuffle {n M b δ : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) : - fiberGroup (fun i => (candidateBandTableau t i).val.1) := - ⟨((candidateComplementEquiv t).trans (candidateComplementRowShuffle M b δ hM)).trans - (candidateComplementEquiv t).symm, by - intro i - have he := (candidateComplementEquiv t).apply_symm_apply - (candidateComplementRowShuffle M b δ hM (candidateComplementEquiv t i)) - exact congrArg (fun x : candidateComplement M b δ => x.val.val.1) he⟩ - -lemma candidateBandRowShuffle_cell {n M b δ : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (i : Fin (candidateBandSize t)) : - candidateBandTableau t ((candidateBandRowShuffle hM t).val i) = - candidateRowShuffle M b δ hM (candidateBandTableau t i) := by - exact congrArg (fun x : candidateComplement M b δ => x.val) - ((candidateComplementEquiv t).apply_symm_apply - (candidateComplementRowShuffle M b δ hM (candidateComplementEquiv t i))) - -def candidateBandRowSeed {n M b δ : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) := - (rightWord (candidateCutPositions t) - (rowWord (transposeTableau t) ∘ (candidateRotateRowPositions hM t).val)) ∘ - (candidateBandRowShuffle hM t).val - -lemma candidateBandRowSeed_val {n M b δ : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (i : Fin (candidateBandSize t)) : - (candidateBandRowSeed hM t i).val = - (candidateSeparatedRow M b δ hM (candidateBandTableau t i)).val.2 := by - rw [candidateBandRowSeed, Function.comp_apply, candidateBandRow_seed, - candidateBandRowShuffle_cell] - rfl - -lemma candidateBandRowSeed_extra {n M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (i : Fin (candidateBandSize t)) : - 2 ≤ (candidateBandRowSeed hM t i).val ↔ - (candidateBandTableau t i).val ∈ attachmentNE M b δ := by - rw [candidateBandRowSeed_val] - exact candidateSeparatedRow_extra hM hδ _ (candidateBandTableau_outside t i) - -theorem candidateBandRow_project_extra {n M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) : - coordinateProjection (fun w => ∀ i, 2 ≤ (w i).val ↔ - (candidateBandTableau t i).val ∈ attachmentNE M b δ) (candidateBandRow hM t) = - signC (candidateBandRowShuffle hM t).val • - altWord (fiberGroup (fun i => (candidateBandTableau t i).val.1) ⊓ - sectorGroup (fun i => (candidateBandTableau t i).val ∈ attachmentNE M b δ)) - (candidateBandRowSeed hM t) := by - exact altWord_sector_rotated _ _ (fun a => 2 ≤ a.val) _ - (candidateBandRowShuffle hM t) (candidateBandRowSeed_extra hM hδ t) - -def candidateColShuffle (M b δ : ℕ) (hM : 4 ≤ M) : - Equiv.Perm (candidate M b δ).cells := - ((candidateSwap M b δ).trans (candidateRowShuffle M b δ hM)).trans - (candidateSwap M b δ) - -lemma candidateColShuffle_triangle (M b δ : ℕ) (hM : 4 ≤ M) - (x : (candidate M b δ).cells) : - (candidateColShuffle M b δ hM x).val.1 + (candidateColShuffle M b δ hM x).val.2 < M-2 ↔ - x.val.1+x.val.2 < M-2 := by - have h := candidateRowShuffle_triangle M b δ hM (candidateSwap M b δ x) - change (candidateRowShuffle M b δ hM (candidateSwap M b δ x)).val.2 + - (candidateRowShuffle M b δ hM (candidateSwap M b δ x)).val.1 < M-2 ↔ _ - change _ ↔ x.val.2+x.val.1 < M-2 at h - simpa only [Nat.add_comm] using h - -def candidateComplementColShuffle (M b δ : ℕ) (hM : 4 ≤ M) : - Equiv.Perm (candidateComplement M b δ) := - (candidateColShuffle M b δ hM).subtypePerm (fun x => by - have h := candidateColShuffle_triangle M b δ hM x - omega) - -def candidateBandColShuffle {n M b δ : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) : - fiberGroup (fun i => (candidateBandTableau t i).val.2) := - ⟨((candidateComplementEquiv t).trans (candidateComplementColShuffle M b δ hM)).trans - (candidateComplementEquiv t).symm, by - intro i - have he := (candidateComplementEquiv t).apply_symm_apply - (candidateComplementColShuffle M b δ hM (candidateComplementEquiv t i)) - exact congrArg (fun x : candidateComplement M b δ => x.val.val.2) he⟩ - -lemma candidateBandColShuffle_cell {n M b δ : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (i : Fin (candidateBandSize t)) : - candidateBandTableau t ((candidateBandColShuffle hM t).val i) = - candidateColShuffle M b δ hM (candidateBandTableau t i) := by - exact congrArg (fun x : candidateComplement M b δ => x.val) - ((candidateComplementEquiv t).apply_symm_apply - (candidateComplementColShuffle M b δ hM (candidateComplementEquiv t i))) - -def candidateBandColSeed {n M b δ : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) := - (rightWord (candidateCutPositions t) - (rowWord t ∘ (candidateRotateColPositions hM t).val)) ∘ - (candidateBandColShuffle hM t).val - -lemma candidateBandColSeed_val {n M b δ : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (i : Fin (candidateBandSize t)) : - (candidateBandColSeed hM t i).val = - (candidateSeparatedRow M b δ hM (candidateSwap M b δ (candidateBandTableau t i))).val.2 := by - rw [candidateBandColSeed, Function.comp_apply, candidateBandCol_seed, - candidateBandColShuffle_cell] - simp only [candidateRotateCol, candidateColShuffle, candidateSeparatedRow, - Equiv.trans_apply] - rfl - -lemma candidateBandColSeed_extra {n M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (i : Fin (candidateBandSize t)) : - 2 ≤ (candidateBandColSeed hM t i).val ↔ - (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ := by - rw [candidateBandColSeed_val] - apply candidateSeparatedRow_extra hM hδ - have h := candidateBandTableau_outside t i - change M-2 ≤ (candidateBandTableau t i).val.2+(candidateBandTableau t i).val.1 - omega - -theorem candidateBandCol_project_extra {n M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) : - coordinateProjection (fun w => ∀ i, 2 ≤ (w i).val ↔ - (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ) (candidateBandCol hM t) = - signC (candidateBandColShuffle hM t).val • - altWord (fiberGroup (fun i => (candidateBandTableau t i).val.2) ⊓ - sectorGroup (fun i => (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ)) - (candidateBandColSeed hM t) := by - exact altWord_sector_rotated _ _ (fun a => 2 ≤ a.val) _ - (candidateBandColShuffle hM t) (candidateBandColSeed_extra hM hδ t) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CandidateShuffle +import OAI.RepresentationTheory.UniversalSquare.Band.BandPositions + +namespace OAI + +/-! Band Seeds. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +lemma candidateSeparatedRow_extra {M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (x : (candidate M b δ).cells) (hx : M-2 ≤ x.val.1+x.val.2) : + 2 ≤ (candidateSeparatedRow M b δ hM x).val.2 ↔ x.val ∈ attachmentNE M b δ := by + rw [candidateSeparatedRow_band M b δ hM hδ x hx] + have hm := mem_candidate.mp x.property + rcases x with ⟨⟨i,j⟩,hm0⟩ + simp only [mem_attachmentNE] + dsimp only at * + split_ifs <;> omega + +def candidateComplementRowShuffle (M b δ : ℕ) (hM : 4 ≤ M) : + Equiv.Perm (candidateComplement M b δ) := + (candidateRowShuffle M b δ hM).subtypePerm (fun x => by + have h := candidateRowShuffle_triangle M b δ hM x + omega) + +lemma candidateComplementRowShuffle_val (M b δ : ℕ) (hM : 4 ≤ M) + (x : candidateComplement M b δ) : + (candidateComplementRowShuffle M b δ hM x).val = + candidateRowShuffle M b δ hM x.val := rfl + +def candidateBandRowShuffle {n M b δ : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) : + fiberGroup (fun i => (candidateBandTableau t i).val.1) := + ⟨((candidateComplementEquiv t).trans (candidateComplementRowShuffle M b δ hM)).trans + (candidateComplementEquiv t).symm, by + intro i + have he := (candidateComplementEquiv t).apply_symm_apply + (candidateComplementRowShuffle M b δ hM (candidateComplementEquiv t i)) + exact congrArg (fun x : candidateComplement M b δ => x.val.val.1) he⟩ + +lemma candidateBandRowShuffle_cell {n M b δ : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (i : Fin (candidateBandSize t)) : + candidateBandTableau t ((candidateBandRowShuffle hM t).val i) = + candidateRowShuffle M b δ hM (candidateBandTableau t i) := by + exact congrArg (fun x : candidateComplement M b δ => x.val) + ((candidateComplementEquiv t).apply_symm_apply + (candidateComplementRowShuffle M b δ hM (candidateComplementEquiv t i))) + +def candidateBandRowSeed {n M b δ : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) := + (rightWord (candidateCutPositions t) + (rowWord (transposeTableau t) ∘ (candidateRotateRowPositions hM t).val)) ∘ + (candidateBandRowShuffle hM t).val + +lemma candidateBandRowSeed_val {n M b δ : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (i : Fin (candidateBandSize t)) : + (candidateBandRowSeed hM t i).val = + (candidateSeparatedRow M b δ hM (candidateBandTableau t i)).val.2 := by + rw [candidateBandRowSeed, Function.comp_apply, candidateBandRow_seed, + candidateBandRowShuffle_cell] + rfl + +lemma candidateBandRowSeed_extra {n M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (i : Fin (candidateBandSize t)) : + 2 ≤ (candidateBandRowSeed hM t i).val ↔ + (candidateBandTableau t i).val ∈ attachmentNE M b δ := by + rw [candidateBandRowSeed_val] + exact candidateSeparatedRow_extra hM hδ _ (candidateBandTableau_outside t i) + +theorem candidateBandRow_project_extra {n M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) : + coordinateProjection (fun w => ∀ i, 2 ≤ (w i).val ↔ + (candidateBandTableau t i).val ∈ attachmentNE M b δ) (candidateBandRow hM t) = + signC (candidateBandRowShuffle hM t).val • + altWord (fiberGroup (fun i => (candidateBandTableau t i).val.1) ⊓ + sectorGroup (fun i => (candidateBandTableau t i).val ∈ attachmentNE M b δ)) + (candidateBandRowSeed hM t) := by + exact altWord_sector_rotated _ _ (fun a => 2 ≤ a.val) _ + (candidateBandRowShuffle hM t) (candidateBandRowSeed_extra hM hδ t) + +def candidateColShuffle (M b δ : ℕ) (hM : 4 ≤ M) : + Equiv.Perm (candidate M b δ).cells := + ((candidateSwap M b δ).trans (candidateRowShuffle M b δ hM)).trans + (candidateSwap M b δ) + +lemma candidateColShuffle_triangle (M b δ : ℕ) (hM : 4 ≤ M) + (x : (candidate M b δ).cells) : + (candidateColShuffle M b δ hM x).val.1 + (candidateColShuffle M b δ hM x).val.2 < M-2 ↔ + x.val.1+x.val.2 < M-2 := by + have h := candidateRowShuffle_triangle M b δ hM (candidateSwap M b δ x) + change (candidateRowShuffle M b δ hM (candidateSwap M b δ x)).val.2 + + (candidateRowShuffle M b δ hM (candidateSwap M b δ x)).val.1 < M-2 ↔ _ + change _ ↔ x.val.2+x.val.1 < M-2 at h + simpa only [Nat.add_comm] using h + +def candidateComplementColShuffle (M b δ : ℕ) (hM : 4 ≤ M) : + Equiv.Perm (candidateComplement M b δ) := + (candidateColShuffle M b δ hM).subtypePerm (fun x => by + have h := candidateColShuffle_triangle M b δ hM x + omega) + +def candidateBandColShuffle {n M b δ : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) : + fiberGroup (fun i => (candidateBandTableau t i).val.2) := + ⟨((candidateComplementEquiv t).trans (candidateComplementColShuffle M b δ hM)).trans + (candidateComplementEquiv t).symm, by + intro i + have he := (candidateComplementEquiv t).apply_symm_apply + (candidateComplementColShuffle M b δ hM (candidateComplementEquiv t i)) + exact congrArg (fun x : candidateComplement M b δ => x.val.val.2) he⟩ + +lemma candidateBandColShuffle_cell {n M b δ : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (i : Fin (candidateBandSize t)) : + candidateBandTableau t ((candidateBandColShuffle hM t).val i) = + candidateColShuffle M b δ hM (candidateBandTableau t i) := by + exact congrArg (fun x : candidateComplement M b δ => x.val) + ((candidateComplementEquiv t).apply_symm_apply + (candidateComplementColShuffle M b δ hM (candidateComplementEquiv t i))) + +def candidateBandColSeed {n M b δ : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) := + (rightWord (candidateCutPositions t) + (rowWord t ∘ (candidateRotateColPositions hM t).val)) ∘ + (candidateBandColShuffle hM t).val + +lemma candidateBandColSeed_val {n M b δ : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (i : Fin (candidateBandSize t)) : + (candidateBandColSeed hM t i).val = + (candidateSeparatedRow M b δ hM (candidateSwap M b δ (candidateBandTableau t i))).val.2 := by + rw [candidateBandColSeed, Function.comp_apply, candidateBandCol_seed, + candidateBandColShuffle_cell] + simp only [candidateRotateCol, candidateColShuffle, candidateSeparatedRow, + Equiv.trans_apply] + rfl + +lemma candidateBandColSeed_extra {n M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (i : Fin (candidateBandSize t)) : + 2 ≤ (candidateBandColSeed hM t i).val ↔ + (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ := by + rw [candidateBandColSeed_val] + apply candidateSeparatedRow_extra hM hδ + have h := candidateBandTableau_outside t i + change M-2 ≤ (candidateBandTableau t i).val.2+(candidateBandTableau t i).val.1 + omega + +theorem candidateBandCol_project_extra {n M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) : + coordinateProjection (fun w => ∀ i, 2 ≤ (w i).val ↔ + (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ) (candidateBandCol hM t) = + signC (candidateBandColShuffle hM t).val • + altWord (fiberGroup (fun i => (candidateBandTableau t i).val.2) ⊓ + sectorGroup (fun i => (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ)) + (candidateBandColSeed hM t) := by + exact altWord_sector_rotated _ _ (fun a => 2 ≤ a.val) _ + (candidateBandColShuffle hM t) (candidateBandColSeed_extra hM hδ t) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandSeparated.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandSeparated.lean index 3883d1082a76109e5373d081d4e3cef193e832fc..77e168d5f9e3c948adee7ab6145204594435ee93 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandSeparated.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandSeparated.lean @@ -1,139 +1,139 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Band.BandFactor - -namespace OAI - -/-! Band Separated. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl -open scoped TensorProduct - -def candidateBandPattern {n M b δ : ℕ} (t : Tableau n (candidate M b δ)) - (w : Fin (candidateBandSize t) → - Fin ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0)) : Prop := - (∀ i, 2 ≤ (splitLeft w i).val ↔ (candidateBandTableau t i).val ∈ attachmentNE M b δ) ∧ - (∀ i, 2 ≤ (splitRight w i).val ↔ (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ) - -def candidatePathWord {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) := - wordTensor _ _ _ (candidatePathRow hM t s₁ s₂ ⊗ₜ[ℂ] candidatePathCol hM t s₁ s₂) - -def candidateExtrasWord {M b δ r : ℕ} (hM : 4 ≤ M) - (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) := - positionProduct (candidateExtraSplit r) - (wordTensor _ _ _ - (letterLift (bandLongRowLetter hM) (polytabloid (transposeTableau s₁)) ⊗ₜ[ℂ] - letterLift (bandShortColLetter hM) (polytabloid s₁))) - (wordTensor _ _ _ - (letterLift (bandShortRowLetter hM) (polytabloid s₂) ⊗ₜ[ℂ] - letterLift (bandLongColLetter hM) (polytabloid (transposeTableau s₂)))) - -theorem candidateBandPattern_factor {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - coordinateProjection (candidateBandPattern t) (candidateBandWord hM t) = - (signC (candidateBandRowShuffle hM t).val * signC (candidateBandColShuffle hM t).val) • - positionProduct (candidateBandSplit hM t s₁ s₂) (candidatePathWord hM t s₁ s₂) - (candidateExtrasWord hM s₁ s₂) := by - change coordinateProjection (fun w => - (fun v => ∀ i, 2 ≤ (v i).val ↔ (candidateBandTableau t i).val ∈ attachmentNE M b δ) - (splitLeft w) ∧ - (fun v => ∀ i, 2 ≤ (v i).val ↔ (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ) - (splitRight w)) _ = _ - rw [candidateBandWord, coordinateProjection_wordTensor - (fun v => ∀ i, 2 ≤ (v i).val ↔ (candidateBandTableau t i).val ∈ attachmentNE M b δ) - (fun v => ∀ i, 2 ≤ (v i).val ↔ (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ), - candidateBandRow_factor hM hδ t s₁ s₂, candidateBandCol_factor hM hδ t s₁ s₂, - TensorProduct.smul_tmul_smul, map_smul, wordTensor_positionProduct, - wordTensor_positionProduct] - rfl - -lemma candidateNECell_swap_not_mem {M b δ : ℕ} (hM : 4 ≤ M) - (z : (ShortColumns.shape b δ).cells) : - (candidateNECell M z).swap ∉ attachmentNE M b δ := by - have hz := (ShortColumns.mem_shape b δ z.val.1 z.val.2).mp z.property - rw [mem_attachmentNE] - dsimp only [candidateNECell, Prod.swap] - omega - -lemma candidateBandWord_sector_iff {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) - (w : Fin (candidateBandSize t) → - Fin ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0)) - (hw : candidateBandWord hM t w ≠ 0) : - wordSector (fun i => ((candidateBandSplit hM t s₁ s₂) i).isLeft = true) - (candidatePathAlphabet M b δ) w ↔ candidateBandPattern t w := by - have hw' := hw - rw [candidateBandWord, wordTensor_tmul] at hw' - have hr := (mul_ne_zero_iff.mp hw').1 - have hc := (mul_ne_zero_iff.mp hw').2 - have H (i : Fin (candidateBandSize t)) : - (candidatePathAlphabet M b δ (w i) ↔ - ((candidateBandSplit hM t s₁ s₂) i).isLeft = true) ↔ - ((2 ≤ (splitLeft w i).val ↔ (candidateBandTableau t i).val ∈ attachmentNE M b δ) ∧ - (2 ≤ (splitRight w i).val ↔ (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ)) := by - obtain ⟨p,rfl⟩ := (candidateBandSplit hM t s₁ s₂).symm.surjective i - cases p with - | inl q => - rw [candidateBandSplit_path] - simp only [Equiv.apply_symm_apply, Sum.isLeft_inl, iff_true, - (pathCell_not_attachment M b δ hM q).1, - (pathCell_not_attachment M b δ hM q).2, iff_false, - not_le, candidatePathAlphabet, splitLeft, splitRight] - | inr j => - obtain ⟨p,rfl⟩ := (candidateExtraSplit r).symm.surjective j - cases p with - | inl z => - have hc' := candidateBandCol_clearance hM t _ hc - ((candidateBandSplit hM t s₁ s₂).symm - (Sum.inr ((candidateExtraSplit r).symm (Sum.inl z)))) (by - rw [candidateBandSplit_NE] - dsimp only [candidateNECell] - omega) - rw [candidateBandSplit_NE] - simp only [Equiv.apply_symm_apply, Sum.isLeft_inr, Bool.false_eq_true, iff_false, - candidateNECell_mem hM, candidateNECell_swap_not_mem hM, iff_true] - change (¬ ((splitLeft w _).val < 2 ∧ (splitRight w _).val < 2)) ↔ - (2 ≤ (splitLeft w _).val ∧ ¬2 ≤ (splitRight w _).val) - omega - | inr z => - have hr' := candidateBandRow_clearance hM t _ hr - ((candidateBandSplit hM t s₁ s₂).symm - (Sum.inr ((candidateExtraSplit r).symm (Sum.inr z)))) (by - rw [candidateBandSplit_SW] - dsimp only [candidateNECell, Prod.swap] - omega) - rw [candidateBandSplit_SW] - simp only [Equiv.apply_symm_apply, Sum.isLeft_inr, Bool.false_eq_true, iff_false, - Prod.swap_swap, candidateNECell_mem hM, candidateNECell_swap_not_mem hM, iff_true] - change (¬ ((splitLeft w _).val < 2 ∧ (splitRight w _).val < 2)) ↔ - (¬2 ≤ (splitLeft w _).val ∧ 2 ≤ (splitRight w _).val) - omega - change (∀ i, _) ↔ ((∀ i, _) ∧ ∀ i, _) - exact (forall_congr' H).trans forall_and - -theorem candidateBandWord_separated {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - coordinateProjection - (wordSector (fun i => ((candidateBandSplit hM t s₁ s₂) i).isLeft = true) - (candidatePathAlphabet M b δ)) (candidateBandWord hM t) = - (signC (candidateBandRowShuffle hM t).val * signC (candidateBandColShuffle hM t).val) • - positionProduct (candidateBandSplit hM t s₁ s₂) (candidatePathWord hM t s₁ s₂) - (candidateExtrasWord hM s₁ s₂) := by - classical - rw [← candidateBandPattern_factor hM hδ t s₁ s₂] - ext w - simp only [coordinateProjection_apply] - by_cases hw : candidateBandWord hM t w = 0 - · simp only [hw, ite_self] - · rw [candidateBandWord_sector_iff hM t s₁ s₂ w hw] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Band.BandFactor + +namespace OAI + +/-! Band Separated. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl +open scoped TensorProduct + +def candidateBandPattern {n M b δ : ℕ} (t : Tableau n (candidate M b δ)) + (w : Fin (candidateBandSize t) → + Fin ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0)) : Prop := + (∀ i, 2 ≤ (splitLeft w i).val ↔ (candidateBandTableau t i).val ∈ attachmentNE M b δ) ∧ + (∀ i, 2 ≤ (splitRight w i).val ↔ (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ) + +def candidatePathWord {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) := + wordTensor _ _ _ (candidatePathRow hM t s₁ s₂ ⊗ₜ[ℂ] candidatePathCol hM t s₁ s₂) + +def candidateExtrasWord {M b δ r : ℕ} (hM : 4 ≤ M) + (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) := + positionProduct (candidateExtraSplit r) + (wordTensor _ _ _ + (letterLift (bandLongRowLetter hM) (polytabloid (transposeTableau s₁)) ⊗ₜ[ℂ] + letterLift (bandShortColLetter hM) (polytabloid s₁))) + (wordTensor _ _ _ + (letterLift (bandShortRowLetter hM) (polytabloid s₂) ⊗ₜ[ℂ] + letterLift (bandLongColLetter hM) (polytabloid (transposeTableau s₂)))) + +theorem candidateBandPattern_factor {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + coordinateProjection (candidateBandPattern t) (candidateBandWord hM t) = + (signC (candidateBandRowShuffle hM t).val * signC (candidateBandColShuffle hM t).val) • + positionProduct (candidateBandSplit hM t s₁ s₂) (candidatePathWord hM t s₁ s₂) + (candidateExtrasWord hM s₁ s₂) := by + change coordinateProjection (fun w => + (fun v => ∀ i, 2 ≤ (v i).val ↔ (candidateBandTableau t i).val ∈ attachmentNE M b δ) + (splitLeft w) ∧ + (fun v => ∀ i, 2 ≤ (v i).val ↔ (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ) + (splitRight w)) _ = _ + rw [candidateBandWord, coordinateProjection_wordTensor + (fun v => ∀ i, 2 ≤ (v i).val ↔ (candidateBandTableau t i).val ∈ attachmentNE M b δ) + (fun v => ∀ i, 2 ≤ (v i).val ↔ (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ), + candidateBandRow_factor hM hδ t s₁ s₂, candidateBandCol_factor hM hδ t s₁ s₂, + TensorProduct.smul_tmul_smul, map_smul, wordTensor_positionProduct, + wordTensor_positionProduct] + rfl + +lemma candidateNECell_swap_not_mem {M b δ : ℕ} (hM : 4 ≤ M) + (z : (ShortColumns.shape b δ).cells) : + (candidateNECell M z).swap ∉ attachmentNE M b δ := by + have hz := (ShortColumns.mem_shape b δ z.val.1 z.val.2).mp z.property + rw [mem_attachmentNE] + dsimp only [candidateNECell, Prod.swap] + omega + +lemma candidateBandWord_sector_iff {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) + (w : Fin (candidateBandSize t) → + Fin ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0)) + (hw : candidateBandWord hM t w ≠ 0) : + wordSector (fun i => ((candidateBandSplit hM t s₁ s₂) i).isLeft = true) + (candidatePathAlphabet M b δ) w ↔ candidateBandPattern t w := by + have hw' := hw + rw [candidateBandWord, wordTensor_tmul] at hw' + have hr := (mul_ne_zero_iff.mp hw').1 + have hc := (mul_ne_zero_iff.mp hw').2 + have H (i : Fin (candidateBandSize t)) : + (candidatePathAlphabet M b δ (w i) ↔ + ((candidateBandSplit hM t s₁ s₂) i).isLeft = true) ↔ + ((2 ≤ (splitLeft w i).val ↔ (candidateBandTableau t i).val ∈ attachmentNE M b δ) ∧ + (2 ≤ (splitRight w i).val ↔ (candidateBandTableau t i).val.swap ∈ attachmentNE M b δ)) := by + obtain ⟨p,rfl⟩ := (candidateBandSplit hM t s₁ s₂).symm.surjective i + cases p with + | inl q => + rw [candidateBandSplit_path] + simp only [Equiv.apply_symm_apply, Sum.isLeft_inl, iff_true, + (pathCell_not_attachment M b δ hM q).1, + (pathCell_not_attachment M b δ hM q).2, iff_false, + not_le, candidatePathAlphabet, splitLeft, splitRight] + | inr j => + obtain ⟨p,rfl⟩ := (candidateExtraSplit r).symm.surjective j + cases p with + | inl z => + have hc' := candidateBandCol_clearance hM t _ hc + ((candidateBandSplit hM t s₁ s₂).symm + (Sum.inr ((candidateExtraSplit r).symm (Sum.inl z)))) (by + rw [candidateBandSplit_NE] + dsimp only [candidateNECell] + omega) + rw [candidateBandSplit_NE] + simp only [Equiv.apply_symm_apply, Sum.isLeft_inr, Bool.false_eq_true, iff_false, + candidateNECell_mem hM, candidateNECell_swap_not_mem hM, iff_true] + change (¬ ((splitLeft w _).val < 2 ∧ (splitRight w _).val < 2)) ↔ + (2 ≤ (splitLeft w _).val ∧ ¬2 ≤ (splitRight w _).val) + omega + | inr z => + have hr' := candidateBandRow_clearance hM t _ hr + ((candidateBandSplit hM t s₁ s₂).symm + (Sum.inr ((candidateExtraSplit r).symm (Sum.inr z)))) (by + rw [candidateBandSplit_SW] + dsimp only [candidateNECell, Prod.swap] + omega) + rw [candidateBandSplit_SW] + simp only [Equiv.apply_symm_apply, Sum.isLeft_inr, Bool.false_eq_true, iff_false, + Prod.swap_swap, candidateNECell_mem hM, candidateNECell_swap_not_mem hM, iff_true] + change (¬ ((splitLeft w _).val < 2 ∧ (splitRight w _).val < 2)) ↔ + (¬2 ≤ (splitLeft w _).val ∧ 2 ≤ (splitRight w _).val) + omega + change (∀ i, _) ↔ ((∀ i, _) ∧ ∀ i, _) + exact (forall_congr' H).trans forall_and + +theorem candidateBandWord_separated {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + coordinateProjection + (wordSector (fun i => ((candidateBandSplit hM t s₁ s₂) i).isLeft = true) + (candidatePathAlphabet M b δ)) (candidateBandWord hM t) = + (signC (candidateBandRowShuffle hM t).val * signC (candidateBandColShuffle hM t).val) • + positionProduct (candidateBandSplit hM t s₁ s₂) (candidatePathWord hM t s₁ s₂) + (candidateExtrasWord hM s₁ s₂) := by + classical + rw [← candidateBandPattern_factor hM hδ t s₁ s₂] + ext w + simp only [coordinateProjection_apply] + by_cases hw : candidateBandWord hM t w = 0 + · simp only [hw, ite_self] + · rw [candidateBandWord_sector_iff hM t s₁ s₂ w hw] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandSplit.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandSplit.lean index 7288983255de0a179a7e40d1c8144c81bc9f5ba8..e38aef816405aec2304bd07b252e104a69889b1a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandSplit.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/BandSplit.lean @@ -1,157 +1,157 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CandidateShuffle -import OAI.RepresentationTheory.UniversalSquare.Band.BandPositions - -namespace OAI - -/-! Band Split. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -lemma candidateBandParts_cell {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) - (x : Fin (2*M-1) ⊕ (Fin r ⊕ Fin r)) : - (candidateBandTableau t ((candidateBandPartsEquiv hM t s₁ s₂).symm x)).val = - (candidatePartsCell M b δ hM - ((Equiv.sumCongr (Equiv.refl _) (Equiv.sumCongr s₁ s₂)) x)).val.val := by - change ((candidateComplementEquiv t) - (((candidateComplementEquiv t).symm) - (candidatePartsCell M b δ hM _))).val.val = _ - rw [Equiv.apply_symm_apply] - rfl - -def candidateBandSplit {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - Fin (candidateBandSize t) ≃ Fin (2*M-1) ⊕ Fin (2*r) := - (candidateBandPartsEquiv hM t s₁ s₂).trans - (Equiv.sumCongr (Equiv.refl _) (finSumFinEquiv.trans (finCongr (by omega)))) - -def candidateExtraSplit (r : ℕ) : Fin (2*r) ≃ Fin r ⊕ Fin r := - (finCongr (by omega)).trans finSumFinEquiv.symm - -lemma candidateBandSplit_path {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) - (q : Fin (2*M-1)) : - (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm (Sum.inl q))).val = - candidatePathCell M b δ q := - candidateBandParts_cell hM t s₁ s₂ (Sum.inl q) - -lemma candidateBandSplit_NE {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) - (i : Fin r) : - (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm - (Sum.inr ((candidateExtraSplit r).symm (Sum.inl i))))).val = - candidateNECell M (s₁ i) := by - simpa only [candidateBandSplit, candidateExtraSplit, Equiv.symm_trans, Equiv.trans_apply, - Equiv.sumCongr_symm, Equiv.sumCongr_apply, Sum.map_inr, candidatePartsCell, - Sum.map_inl, Equiv.symm_apply_apply, Equiv.apply_symm_apply, Equiv.symm_symm, finCongr_symm, finCongr_apply, Fin.cast_cast, Fin.cast_eq_self] - using candidateBandParts_cell hM t s₁ s₂ (Sum.inr (Sum.inl i)) - -lemma candidateBandSplit_SW {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) - (i : Fin r) : - (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm - (Sum.inr ((candidateExtraSplit r).symm (Sum.inr i))))).val = - (candidateNECell M (s₂ i)).swap := by - simpa only [candidateBandSplit, candidateExtraSplit, Equiv.symm_trans, Equiv.trans_apply, - Equiv.sumCongr_symm, Equiv.sumCongr_apply, Sum.map_inr, candidatePartsCell, - Sum.map_inl, Equiv.symm_apply_apply, Equiv.apply_symm_apply, Equiv.symm_symm, finCongr_symm, finCongr_apply, Fin.cast_cast, Fin.cast_eq_self] - using candidateBandParts_cell hM t s₁ s₂ (Sum.inr (Sum.inr i)) - -lemma candidatePathCell_row_tag {M b δ : ℕ} (hM : 4 ≤ M) - (i j : Fin (2*M-1)) : - (candidatePathCell M b δ i).1 = (candidatePathCell M b δ j).1 ↔ - (i.val+1)/2 = (j.val+1)/2 := by - have hi := i.isLt - have hj := j.isLt - unfold candidatePathCell - split_ifs <;> dsimp only <;> omega - -lemma candidatePathCell_swap {M b δ : ℕ} (hM : 4 ≤ M) - (i : Fin (2*M-1)) : - (candidatePathCell M b δ i).swap = candidatePathCell M b δ i.rev := by - have hi := i.isLt - unfold candidatePathCell - simp only [Fin.val_rev] - split_ifs <;> simp only [Prod.swap_prod_mk, Prod.mk.injEq] <;> omega - -lemma candidateSeparatedRow_path {M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (x : (candidate M b δ).cells) (q : Fin (2*M-1)) - (hx : x.val = candidatePathCell M b δ q) : - (candidateSeparatedRow M b δ hM x).val.2 = if q.val = 0 then 0 else (q.val+1)%2 := by - have hq := q.isLt - rw [candidateSeparatedRow_band M b δ hM hδ x (by - rw [hx]; exact (candidatePathCell_mem M b δ hM q).2), hx] - unfold candidatePathCell - split_ifs <;> dsimp only at * <;> omega - -lemma candidateParts_row_sectors {M b δ : ℕ} (hM : 4 ≤ M) - (x y : CandidateBandParts M b δ) - (hrow : (candidatePartsCell M b δ hM x).val.val.1 = - (candidatePartsCell M b δ hM y).val.val.1) : - (Sum.isLeft x = true ↔ Sum.isLeft y = true) ↔ - ((candidatePartsCell M b δ hM x).val.val ∈ attachmentNE M b δ ↔ - (candidatePartsCell M b δ hM y).val.val ∈ attachmentNE M b δ) := by - have H (q : Fin (2*M-1)) (z : (ShortColumns.shape b δ).cells) : - (candidatePathCell M b δ q).1 ≠ (candidateNECell M z).2 := by - have hz := (ShortColumns.mem_shape b δ z.val.1 z.val.2).mp z.property - have hq := q.isLt - unfold candidatePathCell candidateNECell - split_ifs <;> dsimp only <;> omega - have N (z : (ShortColumns.shape b δ).cells) : - (candidateNECell M z).swap ∉ attachmentNE M b δ := by - have hz := candidateNECell_mem hM z - simp only [mem_attachmentNE, candidateNECell, Prod.swap_prod_mk] at hz ⊢ - omega - rcases x with x | (x | x) <;> rcases y with y | (y | y) <;> - dsimp only [candidatePartsCell] at hrow ⊢ - all_goals try simp only [Sum.isLeft_inl, Sum.isLeft_inr, Bool.false_eq_true, - true_iff, false_iff, (pathCell_not_attachment M b δ hM _).1, - candidateNECell_mem hM, N, iff_self] - all_goals try first | exact False.elim (H _ _ hrow) | - exact False.elim (H _ _ hrow.symm) | trivial - all_goals have hx := (ShortColumns.mem_shape b δ x.val.1 x.val.2).mp x.property - all_goals have hy := (ShortColumns.mem_shape b δ y.val.1 y.val.2).mp y.property - all_goals dsimp only [candidateNECell, Prod.swap] at hrow - all_goals omega - -lemma candidateBandRow_sector_eq {n M b δ r : ℕ} (hM : 4 ≤ M) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - fiberGroup (fun i => (candidateBandTableau t i).val.1) ⊓ - sectorGroup (fun i => (candidateBandTableau t i).val ∈ attachmentNE M b δ) = - fiberGroup (fun i => (candidateBandTableau t i).val.1) ⊓ - sectorGroup (fun i => ((candidateBandSplit hM t s₁ s₂) i).isLeft = true) := by - apply Subgroup.ext - intro g - change ((∀ i, (candidateBandTableau t (g i)).val.1 = (candidateBandTableau t i).val.1) ∧ _) ↔ - ((∀ i, (candidateBandTableau t (g i)).val.1 = (candidateBandTableau t i).val.1) ∧ _) - apply and_congr_right - intro hg - change (∀ i, _ ↔ _) ↔ (∀ i, _ ↔ _) - apply forall_congr' - intro i - let E := candidateBandPartsEquiv hM t s₁ s₂ - let f := Equiv.sumCongr (Equiv.refl (Fin (2*M-1))) (Equiv.sumCongr s₁ s₂) - have H (i) : (candidateBandTableau t i).val = - (candidatePartsCell M b δ hM (f (E i))).val.val := by - rw [← candidateBandParts_cell hM t s₁ s₂, Equiv.symm_apply_apply] - have hh := candidateParts_row_sectors hM (f (E (g i))) (f (E i)) (by - rw [← H, ← H]; exact hg i) - dsimp only at * - simp_rw [H] - have hside (j) : (f (E j)).isLeft = ((candidateBandSplit hM t s₁ s₂) j).isLeft := by - dsimp only [candidateBandSplit, Equiv.trans_apply, f] - cases E j <;> rfl - rw [hside, hside] at hh - exact hh.symm - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CandidateShuffle +import OAI.RepresentationTheory.UniversalSquare.Band.BandPositions + +namespace OAI + +/-! Band Split. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +lemma candidateBandParts_cell {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) + (x : Fin (2*M-1) ⊕ (Fin r ⊕ Fin r)) : + (candidateBandTableau t ((candidateBandPartsEquiv hM t s₁ s₂).symm x)).val = + (candidatePartsCell M b δ hM + ((Equiv.sumCongr (Equiv.refl _) (Equiv.sumCongr s₁ s₂)) x)).val.val := by + change ((candidateComplementEquiv t) + (((candidateComplementEquiv t).symm) + (candidatePartsCell M b δ hM _))).val.val = _ + rw [Equiv.apply_symm_apply] + rfl + +def candidateBandSplit {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + Fin (candidateBandSize t) ≃ Fin (2*M-1) ⊕ Fin (2*r) := + (candidateBandPartsEquiv hM t s₁ s₂).trans + (Equiv.sumCongr (Equiv.refl _) (finSumFinEquiv.trans (finCongr (by omega)))) + +def candidateExtraSplit (r : ℕ) : Fin (2*r) ≃ Fin r ⊕ Fin r := + (finCongr (by omega)).trans finSumFinEquiv.symm + +lemma candidateBandSplit_path {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) + (q : Fin (2*M-1)) : + (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm (Sum.inl q))).val = + candidatePathCell M b δ q := + candidateBandParts_cell hM t s₁ s₂ (Sum.inl q) + +lemma candidateBandSplit_NE {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) + (i : Fin r) : + (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm + (Sum.inr ((candidateExtraSplit r).symm (Sum.inl i))))).val = + candidateNECell M (s₁ i) := by + simpa only [candidateBandSplit, candidateExtraSplit, Equiv.symm_trans, Equiv.trans_apply, + Equiv.sumCongr_symm, Equiv.sumCongr_apply, Sum.map_inr, candidatePartsCell, + Sum.map_inl, Equiv.symm_apply_apply, Equiv.apply_symm_apply, Equiv.symm_symm, finCongr_symm, finCongr_apply, Fin.cast_cast, Fin.cast_eq_self] + using candidateBandParts_cell hM t s₁ s₂ (Sum.inr (Sum.inl i)) + +lemma candidateBandSplit_SW {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) + (i : Fin r) : + (candidateBandTableau t ((candidateBandSplit hM t s₁ s₂).symm + (Sum.inr ((candidateExtraSplit r).symm (Sum.inr i))))).val = + (candidateNECell M (s₂ i)).swap := by + simpa only [candidateBandSplit, candidateExtraSplit, Equiv.symm_trans, Equiv.trans_apply, + Equiv.sumCongr_symm, Equiv.sumCongr_apply, Sum.map_inr, candidatePartsCell, + Sum.map_inl, Equiv.symm_apply_apply, Equiv.apply_symm_apply, Equiv.symm_symm, finCongr_symm, finCongr_apply, Fin.cast_cast, Fin.cast_eq_self] + using candidateBandParts_cell hM t s₁ s₂ (Sum.inr (Sum.inr i)) + +lemma candidatePathCell_row_tag {M b δ : ℕ} (hM : 4 ≤ M) + (i j : Fin (2*M-1)) : + (candidatePathCell M b δ i).1 = (candidatePathCell M b δ j).1 ↔ + (i.val+1)/2 = (j.val+1)/2 := by + have hi := i.isLt + have hj := j.isLt + unfold candidatePathCell + split_ifs <;> dsimp only <;> omega + +lemma candidatePathCell_swap {M b δ : ℕ} (hM : 4 ≤ M) + (i : Fin (2*M-1)) : + (candidatePathCell M b δ i).swap = candidatePathCell M b δ i.rev := by + have hi := i.isLt + unfold candidatePathCell + simp only [Fin.val_rev] + split_ifs <;> simp only [Prod.swap_prod_mk, Prod.mk.injEq] <;> omega + +lemma candidateSeparatedRow_path {M b δ : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (x : (candidate M b δ).cells) (q : Fin (2*M-1)) + (hx : x.val = candidatePathCell M b δ q) : + (candidateSeparatedRow M b δ hM x).val.2 = if q.val = 0 then 0 else (q.val+1)%2 := by + have hq := q.isLt + rw [candidateSeparatedRow_band M b δ hM hδ x (by + rw [hx]; exact (candidatePathCell_mem M b δ hM q).2), hx] + unfold candidatePathCell + split_ifs <;> dsimp only at * <;> omega + +lemma candidateParts_row_sectors {M b δ : ℕ} (hM : 4 ≤ M) + (x y : CandidateBandParts M b δ) + (hrow : (candidatePartsCell M b δ hM x).val.val.1 = + (candidatePartsCell M b δ hM y).val.val.1) : + (Sum.isLeft x = true ↔ Sum.isLeft y = true) ↔ + ((candidatePartsCell M b δ hM x).val.val ∈ attachmentNE M b δ ↔ + (candidatePartsCell M b δ hM y).val.val ∈ attachmentNE M b δ) := by + have H (q : Fin (2*M-1)) (z : (ShortColumns.shape b δ).cells) : + (candidatePathCell M b δ q).1 ≠ (candidateNECell M z).2 := by + have hz := (ShortColumns.mem_shape b δ z.val.1 z.val.2).mp z.property + have hq := q.isLt + unfold candidatePathCell candidateNECell + split_ifs <;> dsimp only <;> omega + have N (z : (ShortColumns.shape b δ).cells) : + (candidateNECell M z).swap ∉ attachmentNE M b δ := by + have hz := candidateNECell_mem hM z + simp only [mem_attachmentNE, candidateNECell, Prod.swap_prod_mk] at hz ⊢ + omega + rcases x with x | (x | x) <;> rcases y with y | (y | y) <;> + dsimp only [candidatePartsCell] at hrow ⊢ + all_goals try simp only [Sum.isLeft_inl, Sum.isLeft_inr, Bool.false_eq_true, + true_iff, false_iff, (pathCell_not_attachment M b δ hM _).1, + candidateNECell_mem hM, N, iff_self] + all_goals try first | exact False.elim (H _ _ hrow) | + exact False.elim (H _ _ hrow.symm) | trivial + all_goals have hx := (ShortColumns.mem_shape b δ x.val.1 x.val.2).mp x.property + all_goals have hy := (ShortColumns.mem_shape b δ y.val.1 y.val.2).mp y.property + all_goals dsimp only [candidateNECell, Prod.swap] at hrow + all_goals omega + +lemma candidateBandRow_sector_eq {n M b δ r : ℕ} (hM : 4 ≤ M) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + fiberGroup (fun i => (candidateBandTableau t i).val.1) ⊓ + sectorGroup (fun i => (candidateBandTableau t i).val ∈ attachmentNE M b δ) = + fiberGroup (fun i => (candidateBandTableau t i).val.1) ⊓ + sectorGroup (fun i => ((candidateBandSplit hM t s₁ s₂) i).isLeft = true) := by + apply Subgroup.ext + intro g + change ((∀ i, (candidateBandTableau t (g i)).val.1 = (candidateBandTableau t i).val.1) ∧ _) ↔ + ((∀ i, (candidateBandTableau t (g i)).val.1 = (candidateBandTableau t i).val.1) ∧ _) + apply and_congr_right + intro hg + change (∀ i, _ ↔ _) ↔ (∀ i, _ ↔ _) + apply forall_congr' + intro i + let E := candidateBandPartsEquiv hM t s₁ s₂ + let f := Equiv.sumCongr (Equiv.refl (Fin (2*M-1))) (Equiv.sumCongr s₁ s₂) + have H (i) : (candidateBandTableau t i).val = + (candidatePartsCell M b δ hM (f (E i))).val.val := by + rw [← candidateBandParts_cell hM t s₁ s₂, Equiv.symm_apply_apply] + have hh := candidateParts_row_sectors hM (f (E (g i))) (f (E i)) (by + rw [← H, ← H]; exact hg i) + dsimp only at * + simp_rw [H] + have hside (j) : (f (E j)).isLeft = ((candidateBandSplit hM t s₁ s₂) j).isLeft := by + dsimp only [candidateBandSplit, Equiv.trans_apply, f] + cases E j <;> rfl + rw [hside, hside] at hh + exact hh.symm + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/CommonPath.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/CommonPath.lean index 27ab8d8c0a38b97350d0f16ba76ba8a0d656cc77..9c7ff8f98105d7860e8dca0b408d74c1f24e1557 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/CommonPath.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/CommonPath.lean @@ -1,45 +1,45 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Band.OddPath - -namespace OAI - -/-! Common Path. -/ - -section - -noncomputable section -namespace Saxl.Band - -def extendFourBasis (N : Module.Basis (Fin 4) ℂ Mat) (i : ℕ) : Mat := - if h : i < 4 then N ⟨i,h⟩ else N 3 - -lemma extendFourBasis_pathBasis (i : ℕ) : - extendFourBasis pathBasis i = conjugation (basis i) := by - unfold extendFourBasis - split_ifs with h - · exact pathBasis_apply ⟨i,h⟩ - · rw [pathBasis_apply] - congr 1 - obtain ⟨k,rfl⟩ := Nat.exists_eq_add_of_le (show 4 ≤ i by omega) - simp [basis, Nat.add_comm] - -theorem odd_path_common_basis : - ∃ N : Module.Basis (Fin 4) ℂ Mat, - ∀ (r : ℕ) (rs : List ℕ), - (∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) → ∀ hn : rs.sum = 2*r+1, - dotProduct - (fun w : Fin (2*r+1) → Fin 4 => - Columns.dualBlockWord rs (extendFourBasis N) (w ∘ Fin.cast hn)) - (Path.bandWord r) ≠ 0 := by - refine ⟨pathBasis, ?_⟩ - intro r rs hrs hn - rw [show extendFourBasis pathBasis = (fun i => conjugation (basis i)) from - funext extendFourBasis_pathBasis] - exact Columns.odd_path_ordered_contraction r rs hrs hn - -end Saxl.Band -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Band.OddPath + +namespace OAI + +/-! Common Path. -/ + +section + +noncomputable section +namespace Saxl.Band + +def extendFourBasis (N : Module.Basis (Fin 4) ℂ Mat) (i : ℕ) : Mat := + if h : i < 4 then N ⟨i,h⟩ else N 3 + +lemma extendFourBasis_pathBasis (i : ℕ) : + extendFourBasis pathBasis i = conjugation (basis i) := by + unfold extendFourBasis + split_ifs with h + · exact pathBasis_apply ⟨i,h⟩ + · rw [pathBasis_apply] + congr 1 + obtain ⟨k,rfl⟩ := Nat.exists_eq_add_of_le (show 4 ≤ i by omega) + simp [basis, Nat.add_comm] + +theorem odd_path_common_basis : + ∃ N : Module.Basis (Fin 4) ℂ Mat, + ∀ (r : ℕ) (rs : List ℕ), + (∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) → ∀ hn : rs.sum = 2*r+1, + dotProduct + (fun w : Fin (2*r+1) → Fin 4 => + Columns.dualBlockWord rs (extendFourBasis N) (w ∘ Fin.cast hn)) + (Path.bandWord r) ≠ 0 := by + refine ⟨pathBasis, ?_⟩ + intro r rs hrs hn + rw [show extendFourBasis pathBasis = (fun i => conjugation (basis i)) from + funext extendFourBasis_pathBasis] + exact Columns.odd_path_ordered_contraction r rs hrs hn + +end Saxl.Band +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/OddPath.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/OddPath.lean index da527aafdf3c5f1b5cb4a3f0bdbf2545b3d747fe..5aab7f7db44d60d7948ccc23c778d80e30ec60f0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/OddPath.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/OddPath.lean @@ -1,99 +1,99 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main - -namespace OAI - -/-! Odd Path. -/ - -section - -noncomputable section -namespace Saxl.Band - -def basisCoordinates : Mat →ₗ[ℂ] (Fin 4 → ℂ) where - toFun X := ![(X 0 0 + X 1 1)/2, (X 0 0 - X 1 1)/2, - (X 0 1 + X 1 0)/2, (X 0 1 - X 1 0)/2] - map_add' X Y := by - ext i - fin_cases i <;> simp <;> ring - map_smul' c X := by - ext i - fin_cases i <;> simp <;> ring - -def matrixBasisEquiv : (Fin 4 → ℂ) ≃ₗ[ℂ] Mat where - toFun c := ∑ i : Fin 4, c i • basis i.val - invFun := basisCoordinates - map_add' c d := by simp [add_smul, Finset.sum_add_distrib] - map_smul' c d := by simp [smul_smul, Finset.smul_sum] - left_inv c := by - ext i - fin_cases i <;> - simp [basisCoordinates, Fin.sum_univ_succ, basis] <;> ring - right_inv X := by - ext i j - fin_cases i <;> fin_cases j <;> - simp [basisCoordinates, Fin.sum_univ_succ, basis] <;> ring - -def conjugationEquiv : Mat ≃ₗ[ℂ] Mat where - toLinearMap := conjugation - invFun X := Qinv * X * Q - left_inv X := by - change Qinv * (Q * X * Qinv) * Q = X - simp only [mul_assoc, Qinv_mul_Q, mul_one] - rw [← mul_assoc Qinv Q X, Qinv_mul_Q, one_mul] - right_inv X := by - change Q * (Qinv * X * Q) * Qinv = X - simp only [mul_assoc, Q_mul_Qinv, mul_one] - rw [← mul_assoc Q Qinv X, Q_mul_Qinv, one_mul] - -def pathBasis : Module.Basis (Fin 4) ℂ Mat := - (Pi.basisFun ℂ (Fin 4)).map (matrixBasisEquiv.trans conjugationEquiv) - -lemma pathBasis_apply (i : Fin 4) : pathBasis i = conjugation (basis i.val) := by - simp [pathBasis, matrixBasisEquiv, Pi.basisFun_apply, - Pi.single_apply, conjugationEquiv] - -end Saxl.Band - -namespace Saxl.Columns - -def dualBlockWord (rs : List ℕ) (N : ℕ → Band.Mat) : WordSpace rs.sum 4 := - ∑ π : Perms rs, sg π • Path.pureWord - (fun q => N (row (perm π (enumerate rs q)))) - -lemma chainFunctional_dualBlockWord (rs : List ℕ) (N : ℕ → Band.Mat) (p : ℕ) : - Path.chainFunctional rs.sum p (dualBlockWord rs N) = segments p rs N := by - rw [dualBlockWord, map_sum] - simp_rw [map_smul, Path.chainFunctional_pure] - exact sum_chain rs p N - -theorem odd_path_ordered_contraction (r : ℕ) (rs : List ℕ) - (hrs : ∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) (hn : rs.sum = 2*r+1) : - dotProduct - (fun w : Fin (2*r+1) → Fin 4 => - dualBlockWord rs (fun i => Band.conjugation (Band.basis i)) - (w ∘ Fin.cast hn)) - (Path.bandWord r) ≠ 0 := by - have h := Band.conjugation_blocks_ne_zero rs hrs - rw [← Band.segments_conjugation rs 1, - ← chainFunctional_dualBlockWord rs (fun i => Band.conjugation (Band.basis i)) 1] at h - have hc : Path.chainFunctional (2*r+1) 1 - (fun w => dualBlockWord rs (fun i => Band.conjugation (Band.basis i)) - (w ∘ Fin.cast hn)) = - Path.chainFunctional rs.sum 1 - (dualBlockWord rs (fun i => Band.conjugation (Band.basis i))) := by - have aux : ∀ (m n : ℕ) (h : m = n) (x : WordSpace m 4), - Path.chainFunctional n 1 (fun w => x (w ∘ Fin.cast h)) = - Path.chainFunctional m 1 x := by - intro m n h x - subst n - rfl - exact aux _ _ hn _ - rw [← hc, Path.chainFunctional_endpoint] at h - exact (mul_ne_zero_iff.mp h).2 - -end Saxl.Columns -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main + +namespace OAI + +/-! Odd Path. -/ + +section + +noncomputable section +namespace Saxl.Band + +def basisCoordinates : Mat →ₗ[ℂ] (Fin 4 → ℂ) where + toFun X := ![(X 0 0 + X 1 1)/2, (X 0 0 - X 1 1)/2, + (X 0 1 + X 1 0)/2, (X 0 1 - X 1 0)/2] + map_add' X Y := by + ext i + fin_cases i <;> simp <;> ring + map_smul' c X := by + ext i + fin_cases i <;> simp <;> ring + +def matrixBasisEquiv : (Fin 4 → ℂ) ≃ₗ[ℂ] Mat where + toFun c := ∑ i : Fin 4, c i • basis i.val + invFun := basisCoordinates + map_add' c d := by simp [add_smul, Finset.sum_add_distrib] + map_smul' c d := by simp [smul_smul, Finset.smul_sum] + left_inv c := by + ext i + fin_cases i <;> + simp [basisCoordinates, Fin.sum_univ_succ, basis] <;> ring + right_inv X := by + ext i j + fin_cases i <;> fin_cases j <;> + simp [basisCoordinates, Fin.sum_univ_succ, basis] <;> ring + +def conjugationEquiv : Mat ≃ₗ[ℂ] Mat where + toLinearMap := conjugation + invFun X := Qinv * X * Q + left_inv X := by + change Qinv * (Q * X * Qinv) * Q = X + simp only [mul_assoc, Qinv_mul_Q, mul_one] + rw [← mul_assoc Qinv Q X, Qinv_mul_Q, one_mul] + right_inv X := by + change Q * (Qinv * X * Q) * Qinv = X + simp only [mul_assoc, Q_mul_Qinv, mul_one] + rw [← mul_assoc Q Qinv X, Q_mul_Qinv, one_mul] + +def pathBasis : Module.Basis (Fin 4) ℂ Mat := + (Pi.basisFun ℂ (Fin 4)).map (matrixBasisEquiv.trans conjugationEquiv) + +lemma pathBasis_apply (i : Fin 4) : pathBasis i = conjugation (basis i.val) := by + simp [pathBasis, matrixBasisEquiv, Pi.basisFun_apply, + Pi.single_apply, conjugationEquiv] + +end Saxl.Band + +namespace Saxl.Columns + +def dualBlockWord (rs : List ℕ) (N : ℕ → Band.Mat) : WordSpace rs.sum 4 := + ∑ π : Perms rs, sg π • Path.pureWord + (fun q => N (row (perm π (enumerate rs q)))) + +lemma chainFunctional_dualBlockWord (rs : List ℕ) (N : ℕ → Band.Mat) (p : ℕ) : + Path.chainFunctional rs.sum p (dualBlockWord rs N) = segments p rs N := by + rw [dualBlockWord, map_sum] + simp_rw [map_smul, Path.chainFunctional_pure] + exact sum_chain rs p N + +theorem odd_path_ordered_contraction (r : ℕ) (rs : List ℕ) + (hrs : ∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) (hn : rs.sum = 2*r+1) : + dotProduct + (fun w : Fin (2*r+1) → Fin 4 => + dualBlockWord rs (fun i => Band.conjugation (Band.basis i)) + (w ∘ Fin.cast hn)) + (Path.bandWord r) ≠ 0 := by + have h := Band.conjugation_blocks_ne_zero rs hrs + rw [← Band.segments_conjugation rs 1, + ← chainFunctional_dualBlockWord rs (fun i => Band.conjugation (Band.basis i)) 1] at h + have hc : Path.chainFunctional (2*r+1) 1 + (fun w => dualBlockWord rs (fun i => Band.conjugation (Band.basis i)) + (w ∘ Fin.cast hn)) = + Path.chainFunctional rs.sum 1 + (dualBlockWord rs (fun i => Band.conjugation (Band.basis i))) := by + have aux : ∀ (m n : ℕ) (h : m = n) (x : WordSpace m 4), + Path.chainFunctional n 1 (fun w => x (w ∘ Fin.cast h)) = + Path.chainFunctional m 1 x := by + intro m n h x + subst n + rfl + exact aux _ _ hn _ + rw [← hc, Path.chainFunctional_endpoint] at h + exact (mul_ne_zero_iff.mp h).2 + +end Saxl.Columns +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/OddStrip.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/OddStrip.lean index 919910993ddc892994a14cba71b30e5ec27864c1..0c043b503148146ad1ab0b83372ce6f33b386eba 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/OddStrip.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/OddStrip.lean @@ -1,116 +1,116 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking - -namespace OAI - -/-! Odd Strip. -/ - -section - -noncomputable section - -namespace Saxl.Balance - -lemma card_of_height_two (μ : YoungDiagram) (hμ : μ.colLen 0 ≤ 2) : - μ.card = μ.rowLen 0 + μ.rowLen 1 := by - rw [← rowPrefix_eq_card μ hμ] - simp [rowPrefix, Finset.sum_range_succ] - -lemma short_rowLen (b δ i : ℕ) : - (ShortColumns.shape b δ).rowLen i = if i = 0 then b+δ else if i = 1 then b else 0 := by - apply eq_of_forall_lt_iff - intro j - rw [← YoungDiagram.mem_iff_lt_rowLen, ShortColumns.mem_shape] - split_ifs <;> simp_all - -lemma short_card (b δ : ℕ) : - (ShortColumns.shape b δ).card = 2*b+δ := by - rw [card_of_height_two _ (ShortColumns.height_le b δ)] - simp [short_rowLen] - omega - -lemma horizontal_two_rows (ν μ : YoungDiagram) - (hν : ν.colLen 0 ≤ 2) (hμ : μ.colLen 0 ≤ 2) - (h0 : ν.rowLen 0 ≤ μ.rowLen 0) (h1 : ν.rowLen 1 ≤ μ.rowLen 1) - (hm : μ.rowLen 1 ≤ ν.rowLen 0) : HorizontalStrip ν μ := by - have row_lt (η : YoungDiagram) (hη : η.colLen 0 ≤ 2) (x : ℕ × ℕ) - (hx : x ∈ η) : x.1 = 0 ∨ x.1 = 1 := by - have hh := YoungDiagram.mem_iff_lt_colLen.mp - (η.up_left_mem (le_refl x.1) (Nat.zero_le x.2) hx) - omega - constructor - · intro x hx - rw [YoungDiagram.mem_iff_lt_rowLen] at hx ⊢ - rcases row_lt ν hν x (YoungDiagram.mem_iff_lt_rowLen.mpr hx) with h | h - · simpa only [h] using lt_of_lt_of_le (by simpa only [h] using hx) h0 - · simpa only [h] using lt_of_lt_of_le (by simpa only [h] using hx) h1 - · intro x hx hxn y hy hyn hxy - apply Prod.ext _ hxy - have hxr := row_lt μ hμ x hx - have hyr := row_lt μ hμ y hy - rw [YoungDiagram.mem_iff_lt_rowLen] at hx hy hxn hyn - rcases hxr with hxr | hxr <;> rcases hyr with hyr | hyr - · omega - · simp only [hxr, hyr] at hx hy hxn hyn - omega - · simp only [hxr, hyr] at hx hy hxn hyn - omega - · omega - -theorem odd_strip_precursor (c x : ℕ) (hc : Even c) (hx : Odd x) - (hxc : x ≤ c) (μ : YoungDiagram) (hsize : μ.card = c+x) - (hμ : μ.colLen 0 ≤ 2) : - ∃ ν : YoungDiagram, ν.card = c ∧ ν.colLen 0 ≤ 2 ∧ - (∀ i, Even (ν.rowLen i)) ∧ HorizontalStrip ν μ := by - let β := μ.rowLen 1 - let U := min β (c-β) - let y := 2*(U/2) - have hm := μ.rowLen_anti 0 1 (by omega) - have hcard := card_of_height_two μ hμ - have hcp := Nat.even_iff.mp hc - have hxp := Nat.odd_iff.mp hx - have hβ : β ≤ c := by dsimp only [β]; omega - have huβ : U ≤ β := min_le_left _ _ - have huc : U ≤ c-β := min_le_right _ _ - have hyu : y ≤ U := by dsimp only [y]; omega - have hyc : 2*y ≤ c := by omega - have hyβ : β ≤ y+x := by - dsimp only [β, U, y] at * - omega - have hyp : y % 2 = 0 := by dsimp only [y]; omega - refine ⟨ShortColumns.shape y (c-2*y), ?_, ShortColumns.height_le _ _, ?_, ?_⟩ - · rw [short_card] - omega - · intro i - rw [short_rowLen, Nat.even_iff] - split_ifs <;> omega - · apply horizontal_two_rows _ _ (ShortColumns.height_le _ _) hμ - · simp only [short_rowLen, ite_true] - dsimp only [β] at * - omega - · simpa only [short_rowLen, Nat.one_ne_zero, ite_false, ite_true] using - hyu.trans huβ - · simp only [short_rowLen, ite_true] - dsimp only [β] at * - omega - -theorem odd_strip_restriction (c x : ℕ) (hc : Even c) (hx : Odd x) - (hxc : x ≤ c) (μ : YoungDiagram) (hsize : μ.card = c+x) - (hμ : μ.colLen 0 ≤ 2) (t : Tableau (c+x) μ) : - ∃ (ν : YoungDiagram) (hν : ν.card = c) (hs : HorizontalStrip ν μ), - ν.colLen 0 ≤ 2 ∧ (∀ i, Even (ν.rowLen i)) ∧ - ∃ F : Specht t →ₗ[ℂ] Specht (canonicalTableau ν hν), Function.Surjective F ∧ - ∀ (g : Equiv.Perm (Fin (c+x))) (h : Equiv.Perm (Fin c)), - (∀ k, g (tableauInclusion (canonicalTableau ν hν) t hs.1 k) = - tableauInclusion (canonicalTableau ν hν) t hs.1 (h k)) → - ∀ v, F (spechtRep t g v) = spechtRep (canonicalTableau ν hν) h (F v) := by - obtain ⟨ν,hν,hheight,he,hs⟩ := odd_strip_precursor c x hc hx hxc μ hsize hμ - obtain ⟨f,hf,heq⟩ := pieri_strip_surjective (canonicalTableau ν hν) t hs - exact ⟨ν,hν,hs,hheight,he,f,hf,heq⟩ - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking + +namespace OAI + +/-! Odd Strip. -/ + +section + +noncomputable section + +namespace Saxl.Balance + +lemma card_of_height_two (μ : YoungDiagram) (hμ : μ.colLen 0 ≤ 2) : + μ.card = μ.rowLen 0 + μ.rowLen 1 := by + rw [← rowPrefix_eq_card μ hμ] + simp [rowPrefix, Finset.sum_range_succ] + +lemma short_rowLen (b δ i : ℕ) : + (ShortColumns.shape b δ).rowLen i = if i = 0 then b+δ else if i = 1 then b else 0 := by + apply eq_of_forall_lt_iff + intro j + rw [← YoungDiagram.mem_iff_lt_rowLen, ShortColumns.mem_shape] + split_ifs <;> simp_all + +lemma short_card (b δ : ℕ) : + (ShortColumns.shape b δ).card = 2*b+δ := by + rw [card_of_height_two _ (ShortColumns.height_le b δ)] + simp [short_rowLen] + omega + +lemma horizontal_two_rows (ν μ : YoungDiagram) + (hν : ν.colLen 0 ≤ 2) (hμ : μ.colLen 0 ≤ 2) + (h0 : ν.rowLen 0 ≤ μ.rowLen 0) (h1 : ν.rowLen 1 ≤ μ.rowLen 1) + (hm : μ.rowLen 1 ≤ ν.rowLen 0) : HorizontalStrip ν μ := by + have row_lt (η : YoungDiagram) (hη : η.colLen 0 ≤ 2) (x : ℕ × ℕ) + (hx : x ∈ η) : x.1 = 0 ∨ x.1 = 1 := by + have hh := YoungDiagram.mem_iff_lt_colLen.mp + (η.up_left_mem (le_refl x.1) (Nat.zero_le x.2) hx) + omega + constructor + · intro x hx + rw [YoungDiagram.mem_iff_lt_rowLen] at hx ⊢ + rcases row_lt ν hν x (YoungDiagram.mem_iff_lt_rowLen.mpr hx) with h | h + · simpa only [h] using lt_of_lt_of_le (by simpa only [h] using hx) h0 + · simpa only [h] using lt_of_lt_of_le (by simpa only [h] using hx) h1 + · intro x hx hxn y hy hyn hxy + apply Prod.ext _ hxy + have hxr := row_lt μ hμ x hx + have hyr := row_lt μ hμ y hy + rw [YoungDiagram.mem_iff_lt_rowLen] at hx hy hxn hyn + rcases hxr with hxr | hxr <;> rcases hyr with hyr | hyr + · omega + · simp only [hxr, hyr] at hx hy hxn hyn + omega + · simp only [hxr, hyr] at hx hy hxn hyn + omega + · omega + +theorem odd_strip_precursor (c x : ℕ) (hc : Even c) (hx : Odd x) + (hxc : x ≤ c) (μ : YoungDiagram) (hsize : μ.card = c+x) + (hμ : μ.colLen 0 ≤ 2) : + ∃ ν : YoungDiagram, ν.card = c ∧ ν.colLen 0 ≤ 2 ∧ + (∀ i, Even (ν.rowLen i)) ∧ HorizontalStrip ν μ := by + let β := μ.rowLen 1 + let U := min β (c-β) + let y := 2*(U/2) + have hm := μ.rowLen_anti 0 1 (by omega) + have hcard := card_of_height_two μ hμ + have hcp := Nat.even_iff.mp hc + have hxp := Nat.odd_iff.mp hx + have hβ : β ≤ c := by dsimp only [β]; omega + have huβ : U ≤ β := min_le_left _ _ + have huc : U ≤ c-β := min_le_right _ _ + have hyu : y ≤ U := by dsimp only [y]; omega + have hyc : 2*y ≤ c := by omega + have hyβ : β ≤ y+x := by + dsimp only [β, U, y] at * + omega + have hyp : y % 2 = 0 := by dsimp only [y]; omega + refine ⟨ShortColumns.shape y (c-2*y), ?_, ShortColumns.height_le _ _, ?_, ?_⟩ + · rw [short_card] + omega + · intro i + rw [short_rowLen, Nat.even_iff] + split_ifs <;> omega + · apply horizontal_two_rows _ _ (ShortColumns.height_le _ _) hμ + · simp only [short_rowLen, ite_true] + dsimp only [β] at * + omega + · simpa only [short_rowLen, Nat.one_ne_zero, ite_false, ite_true] using + hyu.trans huβ + · simp only [short_rowLen, ite_true] + dsimp only [β] at * + omega + +theorem odd_strip_restriction (c x : ℕ) (hc : Even c) (hx : Odd x) + (hxc : x ≤ c) (μ : YoungDiagram) (hsize : μ.card = c+x) + (hμ : μ.colLen 0 ≤ 2) (t : Tableau (c+x) μ) : + ∃ (ν : YoungDiagram) (hν : ν.card = c) (hs : HorizontalStrip ν μ), + ν.colLen 0 ≤ 2 ∧ (∀ i, Even (ν.rowLen i)) ∧ + ∃ F : Specht t →ₗ[ℂ] Specht (canonicalTableau ν hν), Function.Surjective F ∧ + ∀ (g : Equiv.Perm (Fin (c+x))) (h : Equiv.Perm (Fin c)), + (∀ k, g (tableauInclusion (canonicalTableau ν hν) t hs.1 k) = + tableauInclusion (canonicalTableau ν hν) t hs.1 (h k)) → + ∀ v, F (spechtRep t g v) = spechtRep (canonicalTableau ν hν) h (F v) := by + obtain ⟨ν,hν,hheight,he,hs⟩ := odd_strip_precursor c x hc hx hxc μ hsize hμ + obtain ⟨f,hf,heq⟩ := pieri_strip_surjective (canonicalTableau ν hν) t hs + exact ⟨ν,hν,hs,hheight,he,f,hf,heq⟩ + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/OneExtra.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/OneExtra.lean index 82e94c78532aee7dc7c0e9988d7fd40bbcd0ac4c..7f2ef3cb9984398ea91cafca04412f003ca8e49d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/OneExtra.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/OneExtra.lean @@ -1,201 +1,201 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.PairSwap -import OAI.RepresentationTheory.UniversalSquare.Specht.ShortColumns - -namespace OAI - -/-! One Extra. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl - -lemma intertwining_comp_ne_zero {G X Y Z : Type*} [Group G] - [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] - [AddCommGroup Z] [Module ℂ Z] - {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} {τ : Representation ℂ G Z} - (F : Representation.IntertwiningMap σ τ) (hF : Function.Injective F) - (f : Representation.IntertwiningMap ρ σ) (hf : f ≠ 0) : F.comp f ≠ 0 := by - intro hz - apply hf - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - apply hF - have hh := congrArg (fun H => H x) hz - exact hh.trans (map_zero F).symm - -def columnSquareWord {n : ℕ} {α : YoungDiagram} (t : Tableau n α) : - WordSpace n (α.colLen 0 * α.colLen 0) := - wordTensor _ _ _ (polytabloid t ⊗ₜ[ℂ] polytabloid t) - -def columnSquareCyclic {n : ℕ} {α : YoungDiagram} (t : Tableau n α) := - cyclic (wordRep n (α.colLen 0 * α.colLen 0)) (columnSquareWord t) - -def rowColumnTransposeCyclicMap {n : ℕ} {α : YoungDiagram} (t : Tableau n α) : - Representation.IntertwiningMap (rowColumnCyclic (transposeTableau t)).toRepresentation - (rowColumnCyclic t).toRepresentation where - toLinearMap := ((rowColumnTransposeMap t).toLinearMap.comp - (rowColumnCyclic (transposeTableau t)).toSubmodule.subtype).codRestrict _ (by - intro x - have h := intertwiner_cyclic_mem (rowColumnTransposeMap t) - (rowColumnWord (transposeTableau t)) x.val x.property - rw [rowColumnTransposeMap_word t] at h - exact h) - isIntertwining' g := by - apply LinearMap.ext - intro x - apply Subtype.ext - exact LinearMap.congr_fun ((rowColumnTransposeMap t).isIntertwining' g) x.val - -lemma rowColumnTransposeCyclicMap_injective {n : ℕ} {α : YoungDiagram} (t : Tableau n α) : - Function.Injective (rowColumnTransposeCyclicMap t) := by - intro x y h - apply Subtype.ext - exact rowColumnTransposeMap_injective t (congrArg Subtype.val h) - -theorem sign_rowColumn_support_of_columnSquare {n : ℕ} {α : YoungDiagram} (t : Tableau n α) - {X : Type*} [AddCommGroup X] [Module ℂ X] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (f : Representation.IntertwiningMap ρ (columnSquareCyclic t).toRepresentation) (hf : f ≠ 0) : - ∃ g : Representation.IntertwiningMap ρ (signTwist (rowColumnCyclic t).toRepresentation), - g ≠ 0 := by - let T := transposeTableau (transposeTableau t) - let F := pairWordMap (n := n) (letterLift (Fin.cast (congrArg (fun ν : YoungDiagram => ν.colLen 0) - (YoungDiagram.transpose_transpose α)))) - (letterLift (Fin.cast (congrArg (fun ν : YoungDiagram => ν.colLen 0) - (YoungDiagram.transpose_transpose α)))) - have hF : F (columnSquareWord T) = columnSquareWord t := by - change pairWordMap _ _ (wordTensor _ _ _ (_ ⊗ₜ[ℂ] _)) = _ - rw [pairWordMap_tensor, polytabloid_doubleTranspose] - rfl - have hs : ∃ g : Representation.IntertwiningMap ρ - (cyclic (wordRep n (α.colLen 0 * α.colLen 0)) (F (columnSquareWord T))).toRepresentation, - g ≠ 0 := by - rw [hF] - exact ⟨f,hf⟩ - obtain ⟨f',hf'⟩ := hs - obtain ⟨f'',hf''⟩ := cyclic_projection_support F (columnSquareWord T) f' hf' - obtain ⟨A,hA⟩ := square_cyclic_embeds_sign_rowColumn (transposeTableau t) - let B := signTwistMap (rowColumnTransposeCyclicMap t) - refine ⟨B.comp (A.comp f''), intertwining_comp_ne_zero B ?_ _ - (intertwining_comp_ne_zero A hA f'' hf'')⟩ - exact rowColumnTransposeCyclicMap_injective t - -lemma transposeTableau_move {n : ℕ} {α : YoungDiagram} (s t : Tableau n α) : - tableauMove (transposeTableau s) (transposeTableau t) = tableauMove s t := by - ext i - rfl - -lemma rowColumnWord_move {n : ℕ} {α : YoungDiagram} (s t : Tableau n α) : - wordRep n _ (tableauMove s t) (rowColumnWord s) = rowColumnWord t := by - unfold rowColumnWord - rw [← wordTensor_equivariant] - change wordTensor _ _ _ (wordRep _ _ (tableauMove s t) (polytabloid (transposeTableau s)) - ⊗ₜ[ℂ] wordRep _ _ (tableauMove s t) (polytabloid s)) = _ - rw [← polytabloid_move s t, ← transposeTableau_move s t, - ← polytabloid_move (transposeTableau s) (transposeTableau t)] - -lemma cyclic_translate_eq {G X : Type*} [Group G] [AddCommGroup X] [Module ℂ X] - (ρ : Representation ℂ G X) (g : G) (v : X) : cyclic ρ (ρ g v) = cyclic ρ v := by - apply le_antisymm - · exact (cyclic_le _ _ _).mpr ((cyclic ρ v).apply_mem_toSubmodule g (mem_cyclic _ _)) - · apply (cyclic_le _ _ _).mpr - have h := (cyclic ρ (ρ g v)).apply_mem_toSubmodule g⁻¹ (mem_cyclic _ _) - change v ∈ (cyclic ρ (ρ g v)).toSubmodule - simpa only [← Module.End.mul_apply, ← map_mul, inv_mul_cancel, map_one, - Module.End.one_apply] using h - -lemma rowColumnCyclic_tableau_independent {n : ℕ} {α : YoungDiagram} (s t : Tableau n α) : - rowColumnCyclic s = rowColumnCyclic t := by - unfold rowColumnCyclic - rw [← rowColumnWord_move s t, cyclic_translate_eq] - -theorem rowColumn_support_change_tableau {n : ℕ} {α : YoungDiagram} (s t : Tableau n α) - {X : Type*} [AddCommGroup X] [Module ℂ X] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) - (f : Representation.IntertwiningMap ρ (signTwist (rowColumnCyclic s).toRepresentation)) - (hf : f ≠ 0) : - ∃ g : Representation.IntertwiningMap ρ (signTwist (rowColumnCyclic t).toRepresentation), - g ≠ 0 := by - rw [← rowColumnCyclic_tableau_independent s t] - exact ⟨f,hf⟩ - -namespace ShortColumns - -theorem even_columnSquare_support (b : ℕ) (μ : YoungDiagram) (t : Tableau (2*b) μ) - (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ 4) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (columnSquareCyclic (evenTableau b)).toRepresentation, F ≠ 0 := by - let F := pairWordMap (n := 2*b) (letterLift (Fin.castLE (height_le b 0))) - (letterLift (Fin.castLE (height_le b 0))) - have hF : F (columnSquareWord (evenTableau b)) = - pairFormTensor (pairSplit b) shortPairForm := by - change pairWordMap _ _ (wordTensor _ _ _ (_ ⊗ₜ[ℂ] _)) = _ - rw [pairWordMap_tensor, evenTableau_polytabloid, even_square] - have hs := even_rows_shortPair_support (pairSplit b) μ t he hd - rw [← hF] at hs - obtain ⟨g,hg⟩ := hs - exact cyclic_projection_support F (columnSquareWord (evenTableau b)) g hg - -theorem odd_columnSquare_support (b : ℕ) (μ : YoungDiagram) (t : Tableau (2*b+1) μ) - (k : ℕ) (hk : Odd (μ.rowLen k)) (he : ∀ l, l ≠ k → Even (μ.rowLen l)) - (hd : μ.colLen 0 ≤ 4) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (columnSquareCyclic (oddTableau b)).toRepresentation, F ≠ 0 := by - let F := pairWordMap (n := 2*b+1) (letterLift (Fin.castLE (height_le b 1))) - (letterLift (Fin.castLE (height_le b 1))) - have hF : F (columnSquareWord (oddTableau b)) = - pairSingletonTensor (oddSplit b) (pairSplit b) shortPairForm (Pi.single 0 1) := by - change pairWordMap _ _ (wordTensor _ _ _ (_ ⊗ₜ[ℂ] _)) = _ - rw [pairWordMap_tensor, oddTableau_polytabloid, odd_square] - have hs := one_odd_row_shortPair_support (oddSplit b) (pairSplit b) μ t k hk he hd - rw [← hF] at hs - obtain ⟨g,hg⟩ := hs - exact cyclic_projection_support F (columnSquareWord (oddTableau b)) g hg - -theorem one_extra_even (b : ℕ) (s : Tableau (2*b) (shape b 0)) - (μ : YoungDiagram) (t : Tableau (2*b) μ) - (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ 4) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (signTwist (rowColumnCyclic s).toRepresentation), F ≠ 0 := by - obtain ⟨f,hf⟩ := even_columnSquare_support b μ t he hd - obtain ⟨g,hg⟩ := sign_rowColumn_support_of_columnSquare (evenTableau b) (spechtRep t) f hf - exact rowColumn_support_change_tableau (evenTableau b) s (spechtRep t) g hg - -theorem one_extra_odd (b : ℕ) (s : Tableau (2*b+1) (shape b 1)) - (μ : YoungDiagram) (t : Tableau (2*b+1) μ) - (k : ℕ) (hk : Odd (μ.rowLen k)) (he : ∀ l, l ≠ k → Even (μ.rowLen l)) - (hd : μ.colLen 0 ≤ 4) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (signTwist (rowColumnCyclic s).toRepresentation), F ≠ 0 := by - obtain ⟨f,hf⟩ := odd_columnSquare_support b μ t k hk he hd - obtain ⟨g,hg⟩ := sign_rowColumn_support_of_columnSquare (oddTableau b) (spechtRep t) f hf - exact rowColumn_support_change_tableau (oddTableau b) s (spechtRep t) g hg - -def RowParity (δ : ℕ) (μ : YoungDiagram) : Prop := - if δ = 0 then ∀ i, Even (μ.rowLen i) - else ∃ k, Odd (μ.rowLen k) ∧ ∀ l, l ≠ k → Even (μ.rowLen l) - -theorem one_extra (b δ : ℕ) (hδ : δ ≤ 1) (s : Tableau (2*b+δ) (shape b δ)) - (μ : YoungDiagram) (t : Tableau (2*b+δ) μ) (hp : RowParity δ μ) - (hd : μ.colLen 0 ≤ 4) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (signTwist (rowColumnCyclic s).toRepresentation), F ≠ 0 := by - have h : δ = 0 ∨ δ = 1 := by omega - rcases h with rfl | rfl - · simp only [RowParity, ↓reduceIte] at hp - exact one_extra_even b s μ t hp hd - · simp only [RowParity, Nat.one_ne_zero, ↓reduceIte] at hp - obtain ⟨k,hk,he⟩ := hp - exact one_extra_odd b s μ t k hk he hd - -end ShortColumns -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.PairSwap +import OAI.RepresentationTheory.UniversalSquare.Specht.ShortColumns + +namespace OAI + +/-! One Extra. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl + +lemma intertwining_comp_ne_zero {G X Y Z : Type*} [Group G] + [AddCommGroup X] [Module ℂ X] [AddCommGroup Y] [Module ℂ Y] + [AddCommGroup Z] [Module ℂ Z] + {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} {τ : Representation ℂ G Z} + (F : Representation.IntertwiningMap σ τ) (hF : Function.Injective F) + (f : Representation.IntertwiningMap ρ σ) (hf : f ≠ 0) : F.comp f ≠ 0 := by + intro hz + apply hf + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + apply hF + have hh := congrArg (fun H => H x) hz + exact hh.trans (map_zero F).symm + +def columnSquareWord {n : ℕ} {α : YoungDiagram} (t : Tableau n α) : + WordSpace n (α.colLen 0 * α.colLen 0) := + wordTensor _ _ _ (polytabloid t ⊗ₜ[ℂ] polytabloid t) + +def columnSquareCyclic {n : ℕ} {α : YoungDiagram} (t : Tableau n α) := + cyclic (wordRep n (α.colLen 0 * α.colLen 0)) (columnSquareWord t) + +def rowColumnTransposeCyclicMap {n : ℕ} {α : YoungDiagram} (t : Tableau n α) : + Representation.IntertwiningMap (rowColumnCyclic (transposeTableau t)).toRepresentation + (rowColumnCyclic t).toRepresentation where + toLinearMap := ((rowColumnTransposeMap t).toLinearMap.comp + (rowColumnCyclic (transposeTableau t)).toSubmodule.subtype).codRestrict _ (by + intro x + have h := intertwiner_cyclic_mem (rowColumnTransposeMap t) + (rowColumnWord (transposeTableau t)) x.val x.property + rw [rowColumnTransposeMap_word t] at h + exact h) + isIntertwining' g := by + apply LinearMap.ext + intro x + apply Subtype.ext + exact LinearMap.congr_fun ((rowColumnTransposeMap t).isIntertwining' g) x.val + +lemma rowColumnTransposeCyclicMap_injective {n : ℕ} {α : YoungDiagram} (t : Tableau n α) : + Function.Injective (rowColumnTransposeCyclicMap t) := by + intro x y h + apply Subtype.ext + exact rowColumnTransposeMap_injective t (congrArg Subtype.val h) + +theorem sign_rowColumn_support_of_columnSquare {n : ℕ} {α : YoungDiagram} (t : Tableau n α) + {X : Type*} [AddCommGroup X] [Module ℂ X] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (f : Representation.IntertwiningMap ρ (columnSquareCyclic t).toRepresentation) (hf : f ≠ 0) : + ∃ g : Representation.IntertwiningMap ρ (signTwist (rowColumnCyclic t).toRepresentation), + g ≠ 0 := by + let T := transposeTableau (transposeTableau t) + let F := pairWordMap (n := n) (letterLift (Fin.cast (congrArg (fun ν : YoungDiagram => ν.colLen 0) + (YoungDiagram.transpose_transpose α)))) + (letterLift (Fin.cast (congrArg (fun ν : YoungDiagram => ν.colLen 0) + (YoungDiagram.transpose_transpose α)))) + have hF : F (columnSquareWord T) = columnSquareWord t := by + change pairWordMap _ _ (wordTensor _ _ _ (_ ⊗ₜ[ℂ] _)) = _ + rw [pairWordMap_tensor, polytabloid_doubleTranspose] + rfl + have hs : ∃ g : Representation.IntertwiningMap ρ + (cyclic (wordRep n (α.colLen 0 * α.colLen 0)) (F (columnSquareWord T))).toRepresentation, + g ≠ 0 := by + rw [hF] + exact ⟨f,hf⟩ + obtain ⟨f',hf'⟩ := hs + obtain ⟨f'',hf''⟩ := cyclic_projection_support F (columnSquareWord T) f' hf' + obtain ⟨A,hA⟩ := square_cyclic_embeds_sign_rowColumn (transposeTableau t) + let B := signTwistMap (rowColumnTransposeCyclicMap t) + refine ⟨B.comp (A.comp f''), intertwining_comp_ne_zero B ?_ _ + (intertwining_comp_ne_zero A hA f'' hf'')⟩ + exact rowColumnTransposeCyclicMap_injective t + +lemma transposeTableau_move {n : ℕ} {α : YoungDiagram} (s t : Tableau n α) : + tableauMove (transposeTableau s) (transposeTableau t) = tableauMove s t := by + ext i + rfl + +lemma rowColumnWord_move {n : ℕ} {α : YoungDiagram} (s t : Tableau n α) : + wordRep n _ (tableauMove s t) (rowColumnWord s) = rowColumnWord t := by + unfold rowColumnWord + rw [← wordTensor_equivariant] + change wordTensor _ _ _ (wordRep _ _ (tableauMove s t) (polytabloid (transposeTableau s)) + ⊗ₜ[ℂ] wordRep _ _ (tableauMove s t) (polytabloid s)) = _ + rw [← polytabloid_move s t, ← transposeTableau_move s t, + ← polytabloid_move (transposeTableau s) (transposeTableau t)] + +lemma cyclic_translate_eq {G X : Type*} [Group G] [AddCommGroup X] [Module ℂ X] + (ρ : Representation ℂ G X) (g : G) (v : X) : cyclic ρ (ρ g v) = cyclic ρ v := by + apply le_antisymm + · exact (cyclic_le _ _ _).mpr ((cyclic ρ v).apply_mem_toSubmodule g (mem_cyclic _ _)) + · apply (cyclic_le _ _ _).mpr + have h := (cyclic ρ (ρ g v)).apply_mem_toSubmodule g⁻¹ (mem_cyclic _ _) + change v ∈ (cyclic ρ (ρ g v)).toSubmodule + simpa only [← Module.End.mul_apply, ← map_mul, inv_mul_cancel, map_one, + Module.End.one_apply] using h + +lemma rowColumnCyclic_tableau_independent {n : ℕ} {α : YoungDiagram} (s t : Tableau n α) : + rowColumnCyclic s = rowColumnCyclic t := by + unfold rowColumnCyclic + rw [← rowColumnWord_move s t, cyclic_translate_eq] + +theorem rowColumn_support_change_tableau {n : ℕ} {α : YoungDiagram} (s t : Tableau n α) + {X : Type*} [AddCommGroup X] [Module ℂ X] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) X) + (f : Representation.IntertwiningMap ρ (signTwist (rowColumnCyclic s).toRepresentation)) + (hf : f ≠ 0) : + ∃ g : Representation.IntertwiningMap ρ (signTwist (rowColumnCyclic t).toRepresentation), + g ≠ 0 := by + rw [← rowColumnCyclic_tableau_independent s t] + exact ⟨f,hf⟩ + +namespace ShortColumns + +theorem even_columnSquare_support (b : ℕ) (μ : YoungDiagram) (t : Tableau (2*b) μ) + (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ 4) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (columnSquareCyclic (evenTableau b)).toRepresentation, F ≠ 0 := by + let F := pairWordMap (n := 2*b) (letterLift (Fin.castLE (height_le b 0))) + (letterLift (Fin.castLE (height_le b 0))) + have hF : F (columnSquareWord (evenTableau b)) = + pairFormTensor (pairSplit b) shortPairForm := by + change pairWordMap _ _ (wordTensor _ _ _ (_ ⊗ₜ[ℂ] _)) = _ + rw [pairWordMap_tensor, evenTableau_polytabloid, even_square] + have hs := even_rows_shortPair_support (pairSplit b) μ t he hd + rw [← hF] at hs + obtain ⟨g,hg⟩ := hs + exact cyclic_projection_support F (columnSquareWord (evenTableau b)) g hg + +theorem odd_columnSquare_support (b : ℕ) (μ : YoungDiagram) (t : Tableau (2*b+1) μ) + (k : ℕ) (hk : Odd (μ.rowLen k)) (he : ∀ l, l ≠ k → Even (μ.rowLen l)) + (hd : μ.colLen 0 ≤ 4) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (columnSquareCyclic (oddTableau b)).toRepresentation, F ≠ 0 := by + let F := pairWordMap (n := 2*b+1) (letterLift (Fin.castLE (height_le b 1))) + (letterLift (Fin.castLE (height_le b 1))) + have hF : F (columnSquareWord (oddTableau b)) = + pairSingletonTensor (oddSplit b) (pairSplit b) shortPairForm (Pi.single 0 1) := by + change pairWordMap _ _ (wordTensor _ _ _ (_ ⊗ₜ[ℂ] _)) = _ + rw [pairWordMap_tensor, oddTableau_polytabloid, odd_square] + have hs := one_odd_row_shortPair_support (oddSplit b) (pairSplit b) μ t k hk he hd + rw [← hF] at hs + obtain ⟨g,hg⟩ := hs + exact cyclic_projection_support F (columnSquareWord (oddTableau b)) g hg + +theorem one_extra_even (b : ℕ) (s : Tableau (2*b) (shape b 0)) + (μ : YoungDiagram) (t : Tableau (2*b) μ) + (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ 4) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (signTwist (rowColumnCyclic s).toRepresentation), F ≠ 0 := by + obtain ⟨f,hf⟩ := even_columnSquare_support b μ t he hd + obtain ⟨g,hg⟩ := sign_rowColumn_support_of_columnSquare (evenTableau b) (spechtRep t) f hf + exact rowColumn_support_change_tableau (evenTableau b) s (spechtRep t) g hg + +theorem one_extra_odd (b : ℕ) (s : Tableau (2*b+1) (shape b 1)) + (μ : YoungDiagram) (t : Tableau (2*b+1) μ) + (k : ℕ) (hk : Odd (μ.rowLen k)) (he : ∀ l, l ≠ k → Even (μ.rowLen l)) + (hd : μ.colLen 0 ≤ 4) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (signTwist (rowColumnCyclic s).toRepresentation), F ≠ 0 := by + obtain ⟨f,hf⟩ := odd_columnSquare_support b μ t k hk he hd + obtain ⟨g,hg⟩ := sign_rowColumn_support_of_columnSquare (oddTableau b) (spechtRep t) f hf + exact rowColumn_support_change_tableau (oddTableau b) s (spechtRep t) g hg + +def RowParity (δ : ℕ) (μ : YoungDiagram) : Prop := + if δ = 0 then ∀ i, Even (μ.rowLen i) + else ∃ k, Odd (μ.rowLen k) ∧ ∀ l, l ≠ k → Even (μ.rowLen l) + +theorem one_extra (b δ : ℕ) (hδ : δ ≤ 1) (s : Tableau (2*b+δ) (shape b δ)) + (μ : YoungDiagram) (t : Tableau (2*b+δ) μ) (hp : RowParity δ μ) + (hd : μ.colLen 0 ≤ 4) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (signTwist (rowColumnCyclic s).toRepresentation), F ≠ 0 := by + have h : δ = 0 ∨ δ = 1 := by omega + rcases h with rfl | rfl + · simp only [RowParity, ↓reduceIte] at hp + exact one_extra_even b s μ t hp hd + · simp only [RowParity, Nat.one_ne_zero, ↓reduceIte] at hp + obtain ⟨k,hk,he⟩ := hp + exact one_extra_odd b s μ t k hk he hd + +end ShortColumns +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/OutputBands.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/OutputBands.lean index c6569b1f0ab214387cdc7f33b81d7bb19af27740..91b019a081731da254724355d90c367d2dad89c6 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/OutputBands.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/OutputBands.lean @@ -1,81 +1,81 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking - -namespace OAI - -/-! Output Bands. -/ - -section - -noncomputable section -namespace Saxl.Balance - -structure OutputBands where - starts : Finset ℕ - upper : ℕ → ℕ - nonempty : ∀ k ∈ starts, k ≤ upper k - separated : ∀ k ∈ starts, ∀ l ∈ starts, k < l → upper k < l - -def OutputBands.Allows (B : OutputBands) (x : ℕ) : Prop := - ∃ k ∈ B.starts, k ≤ x ∧ x ≤ B.upper k - -def OutputBands.label (B : OutputBands) (x : ℕ) : ℕ := by - classical - exact if h : B.Allows x then Classical.choose h else 0 - -lemma OutputBands.label_spec (B : OutputBands) {x : ℕ} (h : B.Allows x) : - B.label x ∈ B.starts ∧ B.label x ≤ x ∧ x ≤ B.upper (B.label x) := by - rw [OutputBands.label,dite_eq_left h] - exact Classical.choose_spec h - -lemma OutputBands.unique (B : OutputBands) {x k l : ℕ} - (hk : k ∈ B.starts) (hl : l ∈ B.starts) - (hkx : k ≤ x) (hxk : x ≤ B.upper k) (hlx : l ≤ x) (hxl : x ≤ B.upper l) : k = l := by - rcases lt_trichotomy k l with h | h | h - · have := B.separated k hk l hl h - omega - · exact h - · have := B.separated l hl k hk h - omega - -lemma OutputBands.label_iff (B : OutputBands) {k x : ℕ} (hk : k ∈ B.starts) : - (B.Allows x ∧ B.label x = k) ↔ x ∈ Set.Icc k (B.upper k) := by - constructor - · rintro ⟨hx,hk'⟩ - have h := B.label_spec hx - rw [hk'] at h - exact h.2 - · rintro ⟨hkx,hxk⟩ - have hx : B.Allows x := ⟨k,hk,hkx,hxk⟩ - have h := B.label_spec hx - exact ⟨hx,B.unique h.1 hk h.2.1 h.2.2 hkx hxk⟩ - -lemma OutputBands.ordered (B : OutputBands) {x y : ℕ} - (hx : B.Allows x) (hy : B.Allows y) (hxy : B.label x < B.label y) : x < y := by - have hx' := B.label_spec hx - have hy' := B.label_spec hy - exact lt_of_le_of_lt hx'.2.2 ((B.separated _ hx'.1 _ hy'.1 hxy).trans_le hy'.2.1) - -def OutputBands.alphabet (B : OutputBands) (d : ℕ) : Fin (d*d) → Prop := - fun a => B.Allows (output a) - -def OutputBands.letterLabel (B : OutputBands) (d : ℕ) : Fin (d*d) → ℕ := - fun a => B.label (output a) - -lemma OutputBands.letter_iff (B : OutputBands) {d k : ℕ} (hk : k ∈ B.starts) - (a : Fin (d*d)) : - (B.alphabet d a ∧ B.letterLabel d a = k) ↔ output a ∈ Set.Icc k (B.upper k) := - B.label_iff hk - -lemma OutputBands.letter_ordered (B : OutputBands) (d : ℕ) : - ∀ x y, B.alphabet d x → B.alphabet d y → - B.letterLabel d x < B.letterLabel d y → output x < output y := by - intro x y hx hy h - exact B.ordered hx hy h - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking + +namespace OAI + +/-! Output Bands. -/ + +section + +noncomputable section +namespace Saxl.Balance + +structure OutputBands where + starts : Finset ℕ + upper : ℕ → ℕ + nonempty : ∀ k ∈ starts, k ≤ upper k + separated : ∀ k ∈ starts, ∀ l ∈ starts, k < l → upper k < l + +def OutputBands.Allows (B : OutputBands) (x : ℕ) : Prop := + ∃ k ∈ B.starts, k ≤ x ∧ x ≤ B.upper k + +def OutputBands.label (B : OutputBands) (x : ℕ) : ℕ := by + classical + exact if h : B.Allows x then Classical.choose h else 0 + +lemma OutputBands.label_spec (B : OutputBands) {x : ℕ} (h : B.Allows x) : + B.label x ∈ B.starts ∧ B.label x ≤ x ∧ x ≤ B.upper (B.label x) := by + rw [OutputBands.label,dite_eq_left h] + exact Classical.choose_spec h + +lemma OutputBands.unique (B : OutputBands) {x k l : ℕ} + (hk : k ∈ B.starts) (hl : l ∈ B.starts) + (hkx : k ≤ x) (hxk : x ≤ B.upper k) (hlx : l ≤ x) (hxl : x ≤ B.upper l) : k = l := by + rcases lt_trichotomy k l with h | h | h + · have := B.separated k hk l hl h + omega + · exact h + · have := B.separated l hl k hk h + omega + +lemma OutputBands.label_iff (B : OutputBands) {k x : ℕ} (hk : k ∈ B.starts) : + (B.Allows x ∧ B.label x = k) ↔ x ∈ Set.Icc k (B.upper k) := by + constructor + · rintro ⟨hx,hk'⟩ + have h := B.label_spec hx + rw [hk'] at h + exact h.2 + · rintro ⟨hkx,hxk⟩ + have hx : B.Allows x := ⟨k,hk,hkx,hxk⟩ + have h := B.label_spec hx + exact ⟨hx,B.unique h.1 hk h.2.1 h.2.2 hkx hxk⟩ + +lemma OutputBands.ordered (B : OutputBands) {x y : ℕ} + (hx : B.Allows x) (hy : B.Allows y) (hxy : B.label x < B.label y) : x < y := by + have hx' := B.label_spec hx + have hy' := B.label_spec hy + exact lt_of_le_of_lt hx'.2.2 ((B.separated _ hx'.1 _ hy'.1 hxy).trans_le hy'.2.1) + +def OutputBands.alphabet (B : OutputBands) (d : ℕ) : Fin (d*d) → Prop := + fun a => B.Allows (output a) + +def OutputBands.letterLabel (B : OutputBands) (d : ℕ) : Fin (d*d) → ℕ := + fun a => B.label (output a) + +lemma OutputBands.letter_iff (B : OutputBands) {d k : ℕ} (hk : k ∈ B.starts) + (a : Fin (d*d)) : + (B.alphabet d a ∧ B.letterLabel d a = k) ↔ output a ∈ Set.Icc k (B.upper k) := + B.label_iff hk + +lemma OutputBands.letter_ordered (B : OutputBands) (d : ℕ) : + ∀ x y, B.alphabet d x → B.alphabet d y → + B.letterLabel d x < B.letterLabel d y → output x < output y := by + intro x y hx hy h + exact B.ordered hx hy h + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/PathGeometry.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/PathGeometry.lean index e2c36b3bfbb037a427d45e4368bcc2fdf0c8c6c7..43259cadbe722bb69640707889f6474a6a7e61f1 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/PathGeometry.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/PathGeometry.lean @@ -1,169 +1,169 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.Candidate -import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking - -namespace OAI - -/-! Path Geometry. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -def candidatePathCell (M b δ : ℕ) (q : Fin (2*M-1)) : ℕ × ℕ := - if q.val = 0 then (M+b+δ-1,0) else - if q.val = 2*M-2 then (0,M+b+δ-1) else - (M-1-(q.val+1)/2, q.val/2) - -def attachmentNE (M b δ : ℕ) : Finset (ℕ × ℕ) := - {0} ×ˢ Finset.Ico (M-1) (M+b+δ-1) ∪ - {1} ×ˢ Finset.Ico (M-1) (M+b-1) - -lemma mem_attachmentNE {M b δ i j : ℕ} : - (i,j) ∈ attachmentNE M b δ ↔ - (i = 0 ∧ M-1 ≤ j ∧ j < M+b+δ-1) ∨ - (i = 1 ∧ M-1 ≤ j ∧ j < M+b-1) := by - simp only [attachmentNE, Finset.mem_union, Finset.mem_product, - Finset.mem_singleton, Finset.mem_Ico] - -lemma attachmentNE_card (M b δ : ℕ) (hM : 1 ≤ M) : - (attachmentNE M b δ).card = 2*b+δ := by - unfold attachmentNE - rw [Finset.card_union_of_disjoint] - · simp only [Finset.card_product, Finset.card_singleton, Nat.card_Ico, one_mul] - omega - · apply Finset.disjoint_left.mpr - rintro ⟨i,j⟩ hi hj - simp only [Finset.mem_product, Finset.mem_singleton] at hi hj - omega - -lemma candidatePathCell_mem (M b δ : ℕ) (hM : 4 ≤ M) (q : Fin (2*M-1)) : - candidatePathCell M b δ q ∈ candidate M b δ ∧ - M-2 ≤ (candidatePathCell M b δ q).1 + (candidatePathCell M b δ q).2 := by - have hq := q.isLt - unfold candidatePathCell - split_ifs with h₀ h₁ - · simp only [ add_zero, mem_candidate] - omega - · simp only [ zero_add, mem_candidate] - omega - · simp only [ mem_candidate] - omega - -lemma candidatePathCell_injective (M b δ : ℕ) (hM : 4 ≤ M) : - Function.Injective (candidatePathCell M b δ) := by - intro q t he - have hq := q.isLt - have ht := t.isLt - apply Fin.ext - unfold candidatePathCell at he - split_ifs at he <;> simp only [Prod.mk.injEq] at he <;> omega - -lemma pathCell_not_attachment (M b δ : ℕ) (hM : 4 ≤ M) (q : Fin (2*M-1)) : - candidatePathCell M b δ q ∉ attachmentNE M b δ ∧ - (candidatePathCell M b δ q).swap ∉ attachmentNE M b δ := by - have hq := q.isLt - unfold candidatePathCell - split_ifs <;> simp only [Prod.swap_prod_mk, mem_attachmentNE] <;> omega - -lemma attachment_disjoint_transpose (M b δ : ℕ) (hM : 4 ≤ M) : - Disjoint (attachmentNE M b δ) - ((attachmentNE M b δ).map (Equiv.prodComm ℕ ℕ).toEmbedding) := by - apply Finset.disjoint_left.mpr - rintro ⟨i,j⟩ hi hj - simp only [Finset.mem_map_equiv, Equiv.prodComm_symm, Equiv.prodComm_apply, - Prod.swap_prod_mk, mem_attachmentNE] at hi hj - omega - -lemma attachmentNE_mem (M b δ : ℕ) (hM : 4 ≤ M) {i j : ℕ} - (hx : (i,j) ∈ attachmentNE M b δ) : - (i,j) ∈ candidate M b δ ∧ M-2 ≤ i+j := by - rw [mem_attachmentNE] at hx - rw [mem_candidate] - omega - -lemma candidate_band_indices (M b δ : ℕ) (hM : 4 ≤ M) (i j : ℕ) - (hc : (i,j) ∈ candidate M b δ) (ht : M-2 ≤ i+j) - (hne : (i,j) ∉ attachmentNE M b δ) (hsw : (j,i) ∉ attachmentNE M b δ) - (h₀ : ¬ (j = 0 ∧ i = M+b+δ-1)) (h₁ : ¬ (i = 0 ∧ j = M+b+δ-1)) : - i+j = M-2 ∨ (i+j = M-1 ∧ 0 < i ∧ 0 < j) := by - rw [mem_candidate] at hc - rw [mem_attachmentNE] at hne hsw - omega - -lemma candidatePathCell_odd (M b δ : ℕ) (hM : 4 ≤ M) (i j : ℕ) - (hs : i+j = M-2) : - ∃ q : Fin (2*M-1), candidatePathCell M b δ q = (i,j) := by - refine ⟨⟨2*j+1,by omega⟩, ?_⟩ - simp only [candidatePathCell] - rw [ite_eq_right (by omega), ite_eq_right (by omega)] - apply Prod.ext <;> dsimp only <;> omega - -lemma candidatePathCell_even (M b δ : ℕ) (hM : 4 ≤ M) (i j : ℕ) - (hs : i+j = M-1) (hi : 0 < i) (hj : 0 < j) : - ∃ q : Fin (2*M-1), candidatePathCell M b δ q = (i,j) := by - refine ⟨⟨2*j,by omega⟩, ?_⟩ - simp only [candidatePathCell] - rw [ite_eq_right (by omega), ite_eq_right (by omega)] - apply Prod.ext <;> dsimp only <;> omega - -theorem candidate_band_cell_decomposition (M b δ : ℕ) (hM : 4 ≤ M) (i j : ℕ) - (hc : (i,j) ∈ candidate M b δ) (ht : M-2 ≤ i+j) : - (∃ q : Fin (2*M-1), candidatePathCell M b δ q = (i,j)) ∨ - (i,j) ∈ attachmentNE M b δ ∨ (j,i) ∈ attachmentNE M b δ := by - by_cases hne : (i,j) ∈ attachmentNE M b δ - · exact Or.inr (Or.inl hne) - by_cases hsw : (j,i) ∈ attachmentNE M b δ - · exact Or.inr (Or.inr hsw) - apply Or.inl - by_cases h₀ : j = 0 ∧ i = M+b+δ-1 - · refine ⟨⟨0,by omega⟩, ?_⟩ - simp only [candidatePathCell, ite_true] - exact Prod.ext (by omega) (by omega) - by_cases h₁ : i = 0 ∧ j = M+b+δ-1 - · refine ⟨⟨2*M-2,by omega⟩, ?_⟩ - simp only [candidatePathCell, ite_eq_right (show 2*M-2 ≠ 0 by omega), ite_true] - exact Prod.ext (by omega) (by omega) - rcases candidate_band_indices M b δ hM i j hc ht hne hsw h₀ h₁ with hs | ⟨hs,hi,hj⟩ - · exact candidatePathCell_odd M b δ hM i j hs - · exact candidatePathCell_even M b δ hM i j hs hi hj - -theorem candidate_band_cells (M b δ : ℕ) (hM : 4 ≤ M) : - (candidate M b δ).cells \ (staircase (M-2)).cells = - Finset.univ.image (candidatePathCell M b δ) ∪ attachmentNE M b δ ∪ - (attachmentNE M b δ).map (Equiv.prodComm ℕ ℕ).toEmbedding := by - ext ⟨i,j⟩ - simp only [Finset.mem_sdiff, YoungDiagram.mem_cells, mem_staircase, not_lt, - Finset.mem_union, Finset.mem_image, Finset.mem_univ, true_and, - Finset.mem_map_equiv, Equiv.prodComm_symm, Equiv.prodComm_apply, Prod.swap_prod_mk] - constructor - · rintro ⟨hc,ht⟩ - exact (or_assoc).mpr (candidate_band_cell_decomposition M b δ hM i j hc ht) - · rintro ((⟨q,hq⟩ | hn) | hs) - · have h := candidatePathCell_mem M b δ hM q - simpa only [hq] using h - · exact attachmentNE_mem M b δ hM hn - · have h := attachmentNE_mem M b δ hM hs - constructor - · have hx : (i,j) ∈ (candidate M b δ).transpose := by - simpa only [YoungDiagram.mem_transpose, Prod.swap_prod_mk] using h.1 - simpa only [candidate_transpose] using hx - · omega - -theorem path_endpoint_clearance (M b δ : ℕ) (hM : 4 ≤ M) - (q : Fin (2*M-1)) (hle : 4 ≤ q.val) (hri : q.val+4 < 2*M-1) : - 2 ≤ (candidatePathCell M b δ q).1 ∧ - 2 ≤ (candidatePathCell M b δ q).2 := by - simp only [candidatePathCell] - rw [ite_eq_right (by omega), ite_eq_right (by omega)] - dsimp only - omega - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.Candidate +import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking + +namespace OAI + +/-! Path Geometry. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +def candidatePathCell (M b δ : ℕ) (q : Fin (2*M-1)) : ℕ × ℕ := + if q.val = 0 then (M+b+δ-1,0) else + if q.val = 2*M-2 then (0,M+b+δ-1) else + (M-1-(q.val+1)/2, q.val/2) + +def attachmentNE (M b δ : ℕ) : Finset (ℕ × ℕ) := + {0} ×ˢ Finset.Ico (M-1) (M+b+δ-1) ∪ + {1} ×ˢ Finset.Ico (M-1) (M+b-1) + +lemma mem_attachmentNE {M b δ i j : ℕ} : + (i,j) ∈ attachmentNE M b δ ↔ + (i = 0 ∧ M-1 ≤ j ∧ j < M+b+δ-1) ∨ + (i = 1 ∧ M-1 ≤ j ∧ j < M+b-1) := by + simp only [attachmentNE, Finset.mem_union, Finset.mem_product, + Finset.mem_singleton, Finset.mem_Ico] + +lemma attachmentNE_card (M b δ : ℕ) (hM : 1 ≤ M) : + (attachmentNE M b δ).card = 2*b+δ := by + unfold attachmentNE + rw [Finset.card_union_of_disjoint] + · simp only [Finset.card_product, Finset.card_singleton, Nat.card_Ico, one_mul] + omega + · apply Finset.disjoint_left.mpr + rintro ⟨i,j⟩ hi hj + simp only [Finset.mem_product, Finset.mem_singleton] at hi hj + omega + +lemma candidatePathCell_mem (M b δ : ℕ) (hM : 4 ≤ M) (q : Fin (2*M-1)) : + candidatePathCell M b δ q ∈ candidate M b δ ∧ + M-2 ≤ (candidatePathCell M b δ q).1 + (candidatePathCell M b δ q).2 := by + have hq := q.isLt + unfold candidatePathCell + split_ifs with h₀ h₁ + · simp only [ add_zero, mem_candidate] + omega + · simp only [ zero_add, mem_candidate] + omega + · simp only [ mem_candidate] + omega + +lemma candidatePathCell_injective (M b δ : ℕ) (hM : 4 ≤ M) : + Function.Injective (candidatePathCell M b δ) := by + intro q t he + have hq := q.isLt + have ht := t.isLt + apply Fin.ext + unfold candidatePathCell at he + split_ifs at he <;> simp only [Prod.mk.injEq] at he <;> omega + +lemma pathCell_not_attachment (M b δ : ℕ) (hM : 4 ≤ M) (q : Fin (2*M-1)) : + candidatePathCell M b δ q ∉ attachmentNE M b δ ∧ + (candidatePathCell M b δ q).swap ∉ attachmentNE M b δ := by + have hq := q.isLt + unfold candidatePathCell + split_ifs <;> simp only [Prod.swap_prod_mk, mem_attachmentNE] <;> omega + +lemma attachment_disjoint_transpose (M b δ : ℕ) (hM : 4 ≤ M) : + Disjoint (attachmentNE M b δ) + ((attachmentNE M b δ).map (Equiv.prodComm ℕ ℕ).toEmbedding) := by + apply Finset.disjoint_left.mpr + rintro ⟨i,j⟩ hi hj + simp only [Finset.mem_map_equiv, Equiv.prodComm_symm, Equiv.prodComm_apply, + Prod.swap_prod_mk, mem_attachmentNE] at hi hj + omega + +lemma attachmentNE_mem (M b δ : ℕ) (hM : 4 ≤ M) {i j : ℕ} + (hx : (i,j) ∈ attachmentNE M b δ) : + (i,j) ∈ candidate M b δ ∧ M-2 ≤ i+j := by + rw [mem_attachmentNE] at hx + rw [mem_candidate] + omega + +lemma candidate_band_indices (M b δ : ℕ) (hM : 4 ≤ M) (i j : ℕ) + (hc : (i,j) ∈ candidate M b δ) (ht : M-2 ≤ i+j) + (hne : (i,j) ∉ attachmentNE M b δ) (hsw : (j,i) ∉ attachmentNE M b δ) + (h₀ : ¬ (j = 0 ∧ i = M+b+δ-1)) (h₁ : ¬ (i = 0 ∧ j = M+b+δ-1)) : + i+j = M-2 ∨ (i+j = M-1 ∧ 0 < i ∧ 0 < j) := by + rw [mem_candidate] at hc + rw [mem_attachmentNE] at hne hsw + omega + +lemma candidatePathCell_odd (M b δ : ℕ) (hM : 4 ≤ M) (i j : ℕ) + (hs : i+j = M-2) : + ∃ q : Fin (2*M-1), candidatePathCell M b δ q = (i,j) := by + refine ⟨⟨2*j+1,by omega⟩, ?_⟩ + simp only [candidatePathCell] + rw [ite_eq_right (by omega), ite_eq_right (by omega)] + apply Prod.ext <;> dsimp only <;> omega + +lemma candidatePathCell_even (M b δ : ℕ) (hM : 4 ≤ M) (i j : ℕ) + (hs : i+j = M-1) (hi : 0 < i) (hj : 0 < j) : + ∃ q : Fin (2*M-1), candidatePathCell M b δ q = (i,j) := by + refine ⟨⟨2*j,by omega⟩, ?_⟩ + simp only [candidatePathCell] + rw [ite_eq_right (by omega), ite_eq_right (by omega)] + apply Prod.ext <;> dsimp only <;> omega + +theorem candidate_band_cell_decomposition (M b δ : ℕ) (hM : 4 ≤ M) (i j : ℕ) + (hc : (i,j) ∈ candidate M b δ) (ht : M-2 ≤ i+j) : + (∃ q : Fin (2*M-1), candidatePathCell M b δ q = (i,j)) ∨ + (i,j) ∈ attachmentNE M b δ ∨ (j,i) ∈ attachmentNE M b δ := by + by_cases hne : (i,j) ∈ attachmentNE M b δ + · exact Or.inr (Or.inl hne) + by_cases hsw : (j,i) ∈ attachmentNE M b δ + · exact Or.inr (Or.inr hsw) + apply Or.inl + by_cases h₀ : j = 0 ∧ i = M+b+δ-1 + · refine ⟨⟨0,by omega⟩, ?_⟩ + simp only [candidatePathCell, ite_true] + exact Prod.ext (by omega) (by omega) + by_cases h₁ : i = 0 ∧ j = M+b+δ-1 + · refine ⟨⟨2*M-2,by omega⟩, ?_⟩ + simp only [candidatePathCell, ite_eq_right (show 2*M-2 ≠ 0 by omega), ite_true] + exact Prod.ext (by omega) (by omega) + rcases candidate_band_indices M b δ hM i j hc ht hne hsw h₀ h₁ with hs | ⟨hs,hi,hj⟩ + · exact candidatePathCell_odd M b δ hM i j hs + · exact candidatePathCell_even M b δ hM i j hs hi hj + +theorem candidate_band_cells (M b δ : ℕ) (hM : 4 ≤ M) : + (candidate M b δ).cells \ (staircase (M-2)).cells = + Finset.univ.image (candidatePathCell M b δ) ∪ attachmentNE M b δ ∪ + (attachmentNE M b δ).map (Equiv.prodComm ℕ ℕ).toEmbedding := by + ext ⟨i,j⟩ + simp only [Finset.mem_sdiff, YoungDiagram.mem_cells, mem_staircase, not_lt, + Finset.mem_union, Finset.mem_image, Finset.mem_univ, true_and, + Finset.mem_map_equiv, Equiv.prodComm_symm, Equiv.prodComm_apply, Prod.swap_prod_mk] + constructor + · rintro ⟨hc,ht⟩ + exact (or_assoc).mpr (candidate_band_cell_decomposition M b δ hM i j hc ht) + · rintro ((⟨q,hq⟩ | hn) | hs) + · have h := candidatePathCell_mem M b δ hM q + simpa only [hq] using h + · exact attachmentNE_mem M b δ hM hn + · have h := attachmentNE_mem M b δ hM hs + constructor + · have hx : (i,j) ∈ (candidate M b δ).transpose := by + simpa only [YoungDiagram.mem_transpose, Prod.swap_prod_mk] using h.1 + simpa only [candidate_transpose] using hx + · omega + +theorem path_endpoint_clearance (M b δ : ℕ) (hM : 4 ≤ M) + (q : Fin (2*M-1)) (hle : 4 ≤ q.val) (hri : q.val+4 < 2*M-1) : + 2 ≤ (candidatePathCell M b δ q).1 ∧ + 2 ≤ (candidatePathCell M b δ q).2 := by + simp only [candidatePathCell] + rw [ite_eq_right (by omega), ite_eq_right (by omega)] + dsimp only + omega + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/RunBands.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/RunBands.lean index e31b9cf3fd63730aebb0b8cf598ab6168a10981d..445d1476adf8e043c8026327c4f2584bf33f97b5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/RunBands.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/RunBands.lean @@ -1,109 +1,109 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.PairRun -import OAI.RepresentationTheory.UniversalSquare.Balance.EmptyPacking - -namespace OAI - -/-! Run Bands. -/ - -section - -noncomputable section -namespace Saxl.Balance - -theorem WordPacking.pairRunAny {a m d : ℕ} (ha : 2 ≤ a) - (hd : a+2*m-1 ≤ d) - (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) - (he : ∀ k ∈ pairMarks a m, ∀ z, - (A z ∧ label z = k) ↔ output z ∈ Set.Icc k (k+1)) : - Nonempty (WordPacking (pairColumns a m) (pairParts a m) d A label (pairMarks a m)) := by - by_cases hm : m = 0 - · subst m - simpa [pairColumns,pairParts,pairMarks] using Nonempty.intro (WordPacking.empty d A label) - · exact WordPacking.pairRun ha (by omega) hd A label he - -def runBands (a m q U : ℕ) (hg : a+2*m ≤ q) (hU : q ≤ U) : OutputBands where - starts := Finset.range a ∪ pairMarks a m ∪ {q} - upper k := if k = q then U else if k ∈ pairMarks a m then k+1 else k - nonempty := by - intro k hk - split_ifs with h h - · omega - · omega - · omega - separated := by - intro k hk l hl hkl - have hk' : k < a ∨ k ∈ pairMarks a m ∨ k = q := by - simpa only [Finset.mem_union,Finset.mem_range,Finset.mem_singleton,or_assoc] using hk - have hl' : l < a ∨ l ∈ pairMarks a m ∨ l = q := by - simpa only [Finset.mem_union,Finset.mem_range,Finset.mem_singleton,or_assoc] using hl - have hle : l ≤ q := by - rcases hl' with h | h | h - · omega - · have := pairMarks_bound h; omega - · omega - rw [ite_eq_right (by omega)] - split_ifs with hm - · have hb := pairMarks_bound hm - rcases hl' with h | h | h - · omega - · exact pairMarks_separated hm h hkl - · omega - · exact hkl - -lemma runBands_low {a m q U k : ℕ} (hg : a+2*m ≤ q) (hU : q ≤ U) (hk : k < a) : - k ∈ (runBands a m q U hg hU).starts ∧ (runBands a m q U hg hU).upper k = k := by - constructor - · apply Finset.mem_union_left - exact Finset.mem_union_left _ (Finset.mem_range.mpr hk) - · change (if k=q then U else if k ∈ pairMarks a m then k+1 else k) = k - have hn : k ∉ pairMarks a m := by - intro hh - have := pairMarks_bound hh - omega - rw [ite_eq_right (by omega),ite_eq_right hn] - -lemma runBands_pair {a m q U k : ℕ} (hg : a+2*m ≤ q) (hU : q ≤ U) - (hk : k ∈ pairMarks a m) : - k ∈ (runBands a m q U hg hU).starts ∧ (runBands a m q U hg hU).upper k = k+1 := by - constructor - · exact Finset.mem_union_left _ (Finset.mem_union_right _ hk) - · have hh := pairMarks_bound hk - change (if k=q then U else if k ∈ pairMarks a m then k+1 else k) = k+1 - rw [ite_eq_right (by omega),ite_eq_left hk] - -lemma runBands_top {a m q U : ℕ} (hg : a+2*m ≤ q) (hU : q ≤ U) : - q ∈ (runBands a m q U hg hU).starts ∧ (runBands a m q U hg hU).upper q = U := by - constructor - · exact Finset.mem_union_right _ (Finset.mem_singleton_self q) - · simp [runBands] - -lemma runBands_low_iff {a m q U k d : ℕ} (hg : a+2*m ≤ q) (hU : q ≤ U) (hk : k < a) - (z : Fin (d*d)) : - ((runBands a m q U hg hU).alphabet d z ∧ - (runBands a m q U hg hU).letterLabel d z = k) ↔ output z = k := by - rw [(runBands a m q U hg hU).letter_iff (runBands_low hg hU hk).1, - (runBands_low hg hU hk).2] - simp only [Set.mem_Icc] - omega - -lemma runBands_pair_iff {a m q U k d : ℕ} (hg : a+2*m ≤ q) (hU : q ≤ U) - (hk : k ∈ pairMarks a m) (z : Fin (d*d)) : - ((runBands a m q U hg hU).alphabet d z ∧ - (runBands a m q U hg hU).letterLabel d z = k) ↔ output z ∈ Set.Icc k (k+1) := by - rw [(runBands a m q U hg hU).letter_iff (runBands_pair hg hU hk).1, - (runBands_pair hg hU hk).2] - -lemma runBands_top_iff {a m q U d : ℕ} (hg : a+2*m ≤ q) (hU : q ≤ U) - (z : Fin (d*d)) : - ((runBands a m q U hg hU).alphabet d z ∧ - (runBands a m q U hg hU).letterLabel d z = q) ↔ output z ∈ Set.Icc q U := by - rw [(runBands a m q U hg hU).letter_iff (runBands_top hg hU).1, - (runBands_top hg hU).2] - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.PairRun +import OAI.RepresentationTheory.UniversalSquare.Balance.EmptyPacking + +namespace OAI + +/-! Run Bands. -/ + +section + +noncomputable section +namespace Saxl.Balance + +theorem WordPacking.pairRunAny {a m d : ℕ} (ha : 2 ≤ a) + (hd : a+2*m-1 ≤ d) + (A : Fin (d*d) → Prop) (label : Fin (d*d) → ℕ) + (he : ∀ k ∈ pairMarks a m, ∀ z, + (A z ∧ label z = k) ↔ output z ∈ Set.Icc k (k+1)) : + Nonempty (WordPacking (pairColumns a m) (pairParts a m) d A label (pairMarks a m)) := by + by_cases hm : m = 0 + · subst m + simpa [pairColumns,pairParts,pairMarks] using Nonempty.intro (WordPacking.empty d A label) + · exact WordPacking.pairRun ha (by omega) hd A label he + +def runBands (a m q U : ℕ) (hg : a+2*m ≤ q) (hU : q ≤ U) : OutputBands where + starts := Finset.range a ∪ pairMarks a m ∪ {q} + upper k := if k = q then U else if k ∈ pairMarks a m then k+1 else k + nonempty := by + intro k hk + split_ifs with h h + · omega + · omega + · omega + separated := by + intro k hk l hl hkl + have hk' : k < a ∨ k ∈ pairMarks a m ∨ k = q := by + simpa only [Finset.mem_union,Finset.mem_range,Finset.mem_singleton,or_assoc] using hk + have hl' : l < a ∨ l ∈ pairMarks a m ∨ l = q := by + simpa only [Finset.mem_union,Finset.mem_range,Finset.mem_singleton,or_assoc] using hl + have hle : l ≤ q := by + rcases hl' with h | h | h + · omega + · have := pairMarks_bound h; omega + · omega + rw [ite_eq_right (by omega)] + split_ifs with hm + · have hb := pairMarks_bound hm + rcases hl' with h | h | h + · omega + · exact pairMarks_separated hm h hkl + · omega + · exact hkl + +lemma runBands_low {a m q U k : ℕ} (hg : a+2*m ≤ q) (hU : q ≤ U) (hk : k < a) : + k ∈ (runBands a m q U hg hU).starts ∧ (runBands a m q U hg hU).upper k = k := by + constructor + · apply Finset.mem_union_left + exact Finset.mem_union_left _ (Finset.mem_range.mpr hk) + · change (if k=q then U else if k ∈ pairMarks a m then k+1 else k) = k + have hn : k ∉ pairMarks a m := by + intro hh + have := pairMarks_bound hh + omega + rw [ite_eq_right (by omega),ite_eq_right hn] + +lemma runBands_pair {a m q U k : ℕ} (hg : a+2*m ≤ q) (hU : q ≤ U) + (hk : k ∈ pairMarks a m) : + k ∈ (runBands a m q U hg hU).starts ∧ (runBands a m q U hg hU).upper k = k+1 := by + constructor + · exact Finset.mem_union_left _ (Finset.mem_union_right _ hk) + · have hh := pairMarks_bound hk + change (if k=q then U else if k ∈ pairMarks a m then k+1 else k) = k+1 + rw [ite_eq_right (by omega),ite_eq_left hk] + +lemma runBands_top {a m q U : ℕ} (hg : a+2*m ≤ q) (hU : q ≤ U) : + q ∈ (runBands a m q U hg hU).starts ∧ (runBands a m q U hg hU).upper q = U := by + constructor + · exact Finset.mem_union_right _ (Finset.mem_singleton_self q) + · simp [runBands] + +lemma runBands_low_iff {a m q U k d : ℕ} (hg : a+2*m ≤ q) (hU : q ≤ U) (hk : k < a) + (z : Fin (d*d)) : + ((runBands a m q U hg hU).alphabet d z ∧ + (runBands a m q U hg hU).letterLabel d z = k) ↔ output z = k := by + rw [(runBands a m q U hg hU).letter_iff (runBands_low hg hU hk).1, + (runBands_low hg hU hk).2] + simp only [Set.mem_Icc] + omega + +lemma runBands_pair_iff {a m q U k d : ℕ} (hg : a+2*m ≤ q) (hU : q ≤ U) + (hk : k ∈ pairMarks a m) (z : Fin (d*d)) : + ((runBands a m q U hg hU).alphabet d z ∧ + (runBands a m q U hg hU).letterLabel d z = k) ↔ output z ∈ Set.Icc k (k+1) := by + rw [(runBands a m q U hg hU).letter_iff (runBands_pair hg hU hk).1, + (runBands_pair hg hU hk).2] + +lemma runBands_top_iff {a m q U d : ℕ} (hg : a+2*m ≤ q) (hU : q ≤ U) + (z : Fin (d*d)) : + ((runBands a m q U hg hU).alphabet d z ∧ + (runBands a m q U hg hU).letterLabel d z = q) ↔ output z ∈ Set.Icc q U := by + rw [(runBands a m q U hg hU).letter_iff (runBands_top hg hU).1, + (runBands_top hg hU).2] + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/TwoExtras.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/TwoExtras.lean index eea6e5e88a2e9ee44f5d64294f476bc4be5fdb81..f2a2620a89fd38dd67c983b01d667926975515d9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/TwoExtras.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/TwoExtras.lean @@ -1,222 +1,222 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Specht.ColumnRestriction -import OAI.RepresentationTheory.UniversalSquare.Balance.BalancedColumns -import OAI.RepresentationTheory.UniversalSquare.Support.SignedInduction - -namespace OAI - -/-! Two Extras. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl - -lemma cyclicMap_injective {G X Y : Type*} [Group G] [AddCommGroup X] [Module ℂ X] - [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} - (F : Representation.IntertwiningMap ρ σ) (v : X) (hF : Function.Injective F) : - Function.Injective (cyclicMap F v) := by - intro x y h - apply Subtype.ext - exact hF (congrArg Subtype.val h) - -lemma cyclic_positionProduct_eq {n a b d : ℕ} (e e' : Fin n ≃ Fin a ⊕ Fin b) - (v : WordSpace a d) (w : WordSpace b d) : - cyclic (wordRep n d) (positionProduct e v w) = - cyclic (wordRep n d) (positionProduct e' v w) := by - have h : wordRep n d (e'.trans e.symm) (positionProduct e' v w) = - positionProduct e v w := by - ext x - change v (fun i => x ((e'.trans e.symm) (e'.symm (Sum.inl i)))) * - w (fun i => x ((e'.trans e.symm) (e'.symm (Sum.inr i)))) = _ - - simp only [Equiv.trans_apply, Equiv.apply_symm_apply] - rfl - rw [← h, cyclic_translate_eq] - -lemma restriction_equal_degrees {n a b n' a' b' : ℕ} {α β γ : YoungDiagram} - (ha : a = a') (hb : b = b') (hn : n = n') - (ta : Tableau a α) (tb : Tableau b β) (tt : Tableau n γ) - (e : Fin n ≃ Fin a ⊕ Fin b) - (F : Representation.IntertwiningMap ((spechtRep tt).comp (sumPermHom e)) - (externalTensor (spechtRep ta) (spechtRep tb))) (hF : F ≠ 0) : - ∃ (sa : Tableau a' α) (sb : Tableau b' β) (st : Tableau n' γ) - (e' : Fin n' ≃ Fin a' ⊕ Fin b'), - ∃ G : Representation.IntertwiningMap ((spechtRep st).comp (sumPermHom e')) - (externalTensor (spechtRep sa) (spechtRep sb)), G ≠ 0 := by - subst a'; subst b'; subst n' - exact ⟨ta,tb,tt,e,F,hF⟩ - -theorem even_rows_restriction (r D : ℕ) (θ : YoungDiagram) (hθ : θ.card = 2*r) - (he : ∀ i, Even (θ.rowLen i)) (hd : θ.colLen 0 ≤ 2*D) : - ∃ (α β : YoungDiagram) (ta : Tableau r α) (tb : Tableau r β) - (tt : Tableau (2*r) θ) (e : Fin (2*r) ≃ Fin r ⊕ Fin r), - α.colLen 0 ≤ D ∧ β.colLen 0 ≤ D ∧ - ShortColumns.RowParity (r%2) α ∧ ShortColumns.RowParity (r%2) β ∧ - ∃ F : Representation.IntertwiningMap ((spechtRep tt).comp (sumPermHom e)) - (externalTensor (spechtRep ta) (spechtRep tb)), F ≠ 0 := by - obtain ⟨ps,ht,hp,ha,hb,hpa,hpb⟩ := Columns.even_rows_allocation r D θ hθ he hd - let α := Columns.columnShape (ps.map Prod.fst) - let β := Columns.columnShape (ps.map Prod.snd) - obtain ⟨ea,hra,hca⟩ := Columns.columnShape_placement (ps.map Prod.fst) - obtain ⟨eb,hrb,hcb⟩ := Columns.columnShape_placement (ps.map Prod.snd) - have heθ := Columns.columnShape_placement (ps.map (fun p => p.1+p.2)) - rw [ht] at heθ - obtain ⟨et,hrt,hct⟩ := heθ - obtain ⟨F,hF⟩ := FlagColumns.column_split_restriction ps α β θ ea eb et - hra hrb hrt hca hcb hct D D (fun p h => (hp p h).1) (fun p h => (hp p h).2) - have hn : (ps.map (fun p => p.1+p.2)).sum = 2*r := - (Columns.placed_card et).symm.trans hθ - obtain ⟨ta,tb,tt,e,G,hG⟩ := restriction_equal_degrees ha hb hn _ _ _ _ F hF - refine ⟨α,β,ta,tb,tt,e,?_,?_,hpa,hpb,G,hG⟩ - · exact Columns.placed_height ea hra D (by - intro h hh; obtain ⟨p,hp',rfl⟩ := List.mem_map.mp hh; exact (hp p hp').1) - · exact Columns.placed_height eb hrb D (by - intro h hh; obtain ⟨p,hp',rfl⟩ := List.mem_map.mp hh; exact (hp p hp').2) - -lemma rowColumnTransposeCyclicMap_surjective {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - Function.Surjective (rowColumnTransposeCyclicMap t) := by - intro y - let y' : (cyclic (wordRep n (μ.transpose.colLen 0 * μ.colLen 0)) - (rowColumnTransposeMap t (rowColumnWord (transposeTableau t)))).toSubmodule := - ⟨y.val, by simpa only [rowColumnCyclic, rowColumnTransposeMap_word] using y.property⟩ - obtain ⟨x,hx⟩ := cyclicMap_surjective (rowColumnTransposeMap t) - (rowColumnWord (transposeTableau t)) y' - have hv : rowColumnTransposeMap t x.val = y.val := congrArg (fun z => z.val) hx - exact ⟨x, Subtype.ext hv⟩ - -def rowColumnTransposeCyclicEquiv {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : - (rowColumnCyclic (transposeTableau t)).toRepresentation.Equiv - (rowColumnCyclic t).toRepresentation := - (rowColumnTransposeCyclicMap t).ofBijective - ⟨rowColumnTransposeCyclicMap_injective t, rowColumnTransposeCyclicMap_surjective t⟩ - -namespace ShortColumns - -lemma one_extra_degree (b δ n : ℕ) (hδ : δ ≤ 1) (hn : 2*b+δ = n) - (s : Tableau n (shape b δ)) (μ : YoungDiagram) (t : Tableau n μ) - (hp : RowParity δ μ) (hd : μ.colLen 0 ≤ 4) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (signTwist (rowColumnCyclic s).toRepresentation), F ≠ 0 := by - subst n - exact one_extra b δ hδ s μ t hp hd - -lemma one_extra_lifted (r d : ℕ) (s : Tableau r (shape (r/2) (r%2))) - (φ : Fin ((shape (r/2) (r%2)).transpose.colLen 0 * - (shape (r/2) (r%2)).colLen 0) → Fin d) (hφ : Function.Injective φ) - (μ : YoungDiagram) (t : Tableau r μ) (hp : RowParity (r%2) μ) - (hd : μ.colLen 0 ≤ 4) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (signTwist (cyclic (wordRep r d) (letterLift φ (rowColumnWord s))).toRepresentation), - Function.Injective F := by - obtain ⟨f,hf⟩ := one_extra_degree (r/2) (r%2) r (by omega) (by omega) s μ t hp hd - let G := signTwistMap (cyclicMap (letterLift φ) (rowColumnWord s)) - have hG : Function.Injective G := cyclicMap_injective _ _ (letterLift_injective φ hφ) - let := specht_irreducible t - exact ⟨G.comp f, hG.comp ((Representation.IsIrreducible.injective_or_eq_zero f).resolve_right hf)⟩ - -theorem two_extras_lifted (r d : ℕ) (s₁ s₂ : Tableau r (shape (r/2) (r%2))) - (φ ψ : Fin ((shape (r/2) (r%2)).transpose.colLen 0 * - (shape (r/2) (r%2)).colLen 0) → Fin d) - (hφ : Function.Injective φ) (hψ : Function.Injective ψ) - (A : Fin d → Prop) (hA : ∀ x, A (φ x)) (hB : ∀ x, ¬ A (ψ x)) - (e : Fin (2*r) ≃ Fin r ⊕ Fin r) - (η : YoungDiagram) (hη : η.card = 2*r) (t : Tableau (2*r) η) - (he : ∀ i, Even (η.colLen i)) (hd : η.rowLen 0 ≤ 8) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep (2*r) d) (positionProduct e - (letterLift φ (rowColumnWord s₁)) (letterLift ψ (rowColumnWord s₂)))).toRepresentation, - F ≠ 0 := by - obtain ⟨α,β,ta,tb,tt,e₀,ha,hb,hpa,hpb,f,hf⟩ := - even_rows_restriction r 4 η.transpose (by rwa [transpose_card]) - (by simpa only [YoungDiagram.rowLen_transpose] using he) - (by simpa only [YoungDiagram.colLen_transpose] using hd) - obtain ⟨Fa,hFa⟩ := one_extra_lifted r d s₁ φ hφ α ta hpa ha - obtain ⟨Fb,hFb⟩ := one_extra_lifted r d s₂ ψ hψ β tb hpb hb - have hs := signed_external_cyclic_support (spechtRep tt) (spechtRep ta) (spechtRep tb) - e₀ (letterLift φ (rowColumnWord s₁)) (letterLift ψ (rowColumnWord s₂)) A - (letterLift_mem_alphabet A φ hA _) (letterLift_mem_alphabet (fun x => ¬ A x) ψ hB _) - Fa Fb hFa hFb f hf - rw [cyclic_positionProduct_eq e₀ e] at hs - obtain ⟨H,hH⟩ := hs - have hEq := specht_sign_transpose t - change Nonempty ((spechtRep t).Equiv - (signTwist (spechtSub (transposeTableau t)).toRepresentation)) at hEq - rw [spechtSub_tableau_independent (transposeTableau t) tt] at hEq - obtain ⟨E⟩ := hEq - refine ⟨H.comp E.toIntertwiningMap, ?_⟩ - intro hz - apply hH - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - obtain ⟨y,rfl⟩ := E.surjective x - exact congrArg (fun K => K y) hz - -lemma one_extra_transpose_lifted (r d : ℕ) (s : Tableau r (shape (r/2) (r%2))) - (φ : Fin ((shape (r/2) (r%2)).transpose.transpose.colLen 0 * - (shape (r/2) (r%2)).transpose.colLen 0) → Fin d) (hφ : Function.Injective φ) - (μ : YoungDiagram) (t : Tableau r μ) (hp : RowParity (r%2) μ) - (hd : μ.colLen 0 ≤ 4) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (signTwist (cyclic (wordRep r d) - (letterLift φ (rowColumnWord (transposeTableau s)))).toRepresentation), - Function.Injective F := by - obtain ⟨f,hf⟩ := one_extra_degree (r/2) (r%2) r (by omega) (by omega) s μ t hp hd - let E := (rowColumnTransposeCyclicEquiv s).symm - let G := signTwistMap ((cyclicMap (letterLift φ) (rowColumnWord (transposeTableau s))).comp - E.toIntertwiningMap) - have hG : Function.Injective G := - (cyclicMap_injective _ _ (letterLift_injective φ hφ)).comp E.injective - let := specht_irreducible t - exact ⟨G.comp f, hG.comp ((Representation.IsIrreducible.injective_or_eq_zero f).resolve_right hf)⟩ - -theorem two_extras (r d : ℕ) (s₁ s₂ : Tableau r (shape (r/2) (r%2))) - (φ : Fin ((shape (r/2) (r%2)).transpose.colLen 0 * - (shape (r/2) (r%2)).colLen 0) → Fin d) - (ψ : Fin ((shape (r/2) (r%2)).transpose.transpose.colLen 0 * - (shape (r/2) (r%2)).transpose.colLen 0) → Fin d) - (hφ : Function.Injective φ) (hψ : Function.Injective ψ) - (A : Fin d → Prop) (hA : ∀ x, A (φ x)) (hB : ∀ x, ¬ A (ψ x)) - (e : Fin (2*r) ≃ Fin r ⊕ Fin r) - (η : YoungDiagram) (hη : η.card = 2*r) (t : Tableau (2*r) η) - (he : ∀ i, Even (η.colLen i)) (hd : η.rowLen 0 ≤ 8) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep (2*r) d) (positionProduct e - (letterLift φ (rowColumnWord s₁)) - (letterLift ψ (rowColumnWord (transposeTableau s₂))))).toRepresentation, - F ≠ 0 := by - obtain ⟨α,β,ta,tb,tt,e₀,ha,hb,hpa,hpb,f,hf⟩ := - even_rows_restriction r 4 η.transpose (by rwa [transpose_card]) - (by simpa only [YoungDiagram.rowLen_transpose] using he) - (by simpa only [YoungDiagram.colLen_transpose] using hd) - obtain ⟨Fa,hFa⟩ := one_extra_lifted r d s₁ φ hφ α ta hpa ha - obtain ⟨Fb,hFb⟩ := one_extra_transpose_lifted r d s₂ ψ hψ β tb hpb hb - have hs := signed_external_cyclic_support (spechtRep tt) (spechtRep ta) (spechtRep tb) - e₀ (letterLift φ (rowColumnWord s₁)) (letterLift ψ (rowColumnWord (transposeTableau s₂))) A - (letterLift_mem_alphabet A φ hA _) (letterLift_mem_alphabet (fun x => ¬ A x) ψ hB _) - Fa Fb hFa hFb f hf - rw [cyclic_positionProduct_eq e₀ e] at hs - obtain ⟨H,hH⟩ := hs - have hEq := specht_sign_transpose t - change Nonempty ((spechtRep t).Equiv - (signTwist (spechtSub (transposeTableau t)).toRepresentation)) at hEq - rw [spechtSub_tableau_independent (transposeTableau t) tt] at hEq - obtain ⟨E⟩ := hEq - refine ⟨H.comp E.toIntertwiningMap, ?_⟩ - intro hz - apply hH - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - obtain ⟨y,rfl⟩ := E.surjective x - exact congrArg (fun K => K y) hz - -end ShortColumns -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Specht.ColumnRestriction +import OAI.RepresentationTheory.UniversalSquare.Balance.BalancedColumns +import OAI.RepresentationTheory.UniversalSquare.Support.SignedInduction + +namespace OAI + +/-! Two Extras. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl + +lemma cyclicMap_injective {G X Y : Type*} [Group G] [AddCommGroup X] [Module ℂ X] + [AddCommGroup Y] [Module ℂ Y] {ρ : Representation ℂ G X} {σ : Representation ℂ G Y} + (F : Representation.IntertwiningMap ρ σ) (v : X) (hF : Function.Injective F) : + Function.Injective (cyclicMap F v) := by + intro x y h + apply Subtype.ext + exact hF (congrArg Subtype.val h) + +lemma cyclic_positionProduct_eq {n a b d : ℕ} (e e' : Fin n ≃ Fin a ⊕ Fin b) + (v : WordSpace a d) (w : WordSpace b d) : + cyclic (wordRep n d) (positionProduct e v w) = + cyclic (wordRep n d) (positionProduct e' v w) := by + have h : wordRep n d (e'.trans e.symm) (positionProduct e' v w) = + positionProduct e v w := by + ext x + change v (fun i => x ((e'.trans e.symm) (e'.symm (Sum.inl i)))) * + w (fun i => x ((e'.trans e.symm) (e'.symm (Sum.inr i)))) = _ + + simp only [Equiv.trans_apply, Equiv.apply_symm_apply] + rfl + rw [← h, cyclic_translate_eq] + +lemma restriction_equal_degrees {n a b n' a' b' : ℕ} {α β γ : YoungDiagram} + (ha : a = a') (hb : b = b') (hn : n = n') + (ta : Tableau a α) (tb : Tableau b β) (tt : Tableau n γ) + (e : Fin n ≃ Fin a ⊕ Fin b) + (F : Representation.IntertwiningMap ((spechtRep tt).comp (sumPermHom e)) + (externalTensor (spechtRep ta) (spechtRep tb))) (hF : F ≠ 0) : + ∃ (sa : Tableau a' α) (sb : Tableau b' β) (st : Tableau n' γ) + (e' : Fin n' ≃ Fin a' ⊕ Fin b'), + ∃ G : Representation.IntertwiningMap ((spechtRep st).comp (sumPermHom e')) + (externalTensor (spechtRep sa) (spechtRep sb)), G ≠ 0 := by + subst a'; subst b'; subst n' + exact ⟨ta,tb,tt,e,F,hF⟩ + +theorem even_rows_restriction (r D : ℕ) (θ : YoungDiagram) (hθ : θ.card = 2*r) + (he : ∀ i, Even (θ.rowLen i)) (hd : θ.colLen 0 ≤ 2*D) : + ∃ (α β : YoungDiagram) (ta : Tableau r α) (tb : Tableau r β) + (tt : Tableau (2*r) θ) (e : Fin (2*r) ≃ Fin r ⊕ Fin r), + α.colLen 0 ≤ D ∧ β.colLen 0 ≤ D ∧ + ShortColumns.RowParity (r%2) α ∧ ShortColumns.RowParity (r%2) β ∧ + ∃ F : Representation.IntertwiningMap ((spechtRep tt).comp (sumPermHom e)) + (externalTensor (spechtRep ta) (spechtRep tb)), F ≠ 0 := by + obtain ⟨ps,ht,hp,ha,hb,hpa,hpb⟩ := Columns.even_rows_allocation r D θ hθ he hd + let α := Columns.columnShape (ps.map Prod.fst) + let β := Columns.columnShape (ps.map Prod.snd) + obtain ⟨ea,hra,hca⟩ := Columns.columnShape_placement (ps.map Prod.fst) + obtain ⟨eb,hrb,hcb⟩ := Columns.columnShape_placement (ps.map Prod.snd) + have heθ := Columns.columnShape_placement (ps.map (fun p => p.1+p.2)) + rw [ht] at heθ + obtain ⟨et,hrt,hct⟩ := heθ + obtain ⟨F,hF⟩ := FlagColumns.column_split_restriction ps α β θ ea eb et + hra hrb hrt hca hcb hct D D (fun p h => (hp p h).1) (fun p h => (hp p h).2) + have hn : (ps.map (fun p => p.1+p.2)).sum = 2*r := + (Columns.placed_card et).symm.trans hθ + obtain ⟨ta,tb,tt,e,G,hG⟩ := restriction_equal_degrees ha hb hn _ _ _ _ F hF + refine ⟨α,β,ta,tb,tt,e,?_,?_,hpa,hpb,G,hG⟩ + · exact Columns.placed_height ea hra D (by + intro h hh; obtain ⟨p,hp',rfl⟩ := List.mem_map.mp hh; exact (hp p hp').1) + · exact Columns.placed_height eb hrb D (by + intro h hh; obtain ⟨p,hp',rfl⟩ := List.mem_map.mp hh; exact (hp p hp').2) + +lemma rowColumnTransposeCyclicMap_surjective {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + Function.Surjective (rowColumnTransposeCyclicMap t) := by + intro y + let y' : (cyclic (wordRep n (μ.transpose.colLen 0 * μ.colLen 0)) + (rowColumnTransposeMap t (rowColumnWord (transposeTableau t)))).toSubmodule := + ⟨y.val, by simpa only [rowColumnCyclic, rowColumnTransposeMap_word] using y.property⟩ + obtain ⟨x,hx⟩ := cyclicMap_surjective (rowColumnTransposeMap t) + (rowColumnWord (transposeTableau t)) y' + have hv : rowColumnTransposeMap t x.val = y.val := congrArg (fun z => z.val) hx + exact ⟨x, Subtype.ext hv⟩ + +def rowColumnTransposeCyclicEquiv {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) : + (rowColumnCyclic (transposeTableau t)).toRepresentation.Equiv + (rowColumnCyclic t).toRepresentation := + (rowColumnTransposeCyclicMap t).ofBijective + ⟨rowColumnTransposeCyclicMap_injective t, rowColumnTransposeCyclicMap_surjective t⟩ + +namespace ShortColumns + +lemma one_extra_degree (b δ n : ℕ) (hδ : δ ≤ 1) (hn : 2*b+δ = n) + (s : Tableau n (shape b δ)) (μ : YoungDiagram) (t : Tableau n μ) + (hp : RowParity δ μ) (hd : μ.colLen 0 ≤ 4) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (signTwist (rowColumnCyclic s).toRepresentation), F ≠ 0 := by + subst n + exact one_extra b δ hδ s μ t hp hd + +lemma one_extra_lifted (r d : ℕ) (s : Tableau r (shape (r/2) (r%2))) + (φ : Fin ((shape (r/2) (r%2)).transpose.colLen 0 * + (shape (r/2) (r%2)).colLen 0) → Fin d) (hφ : Function.Injective φ) + (μ : YoungDiagram) (t : Tableau r μ) (hp : RowParity (r%2) μ) + (hd : μ.colLen 0 ≤ 4) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (signTwist (cyclic (wordRep r d) (letterLift φ (rowColumnWord s))).toRepresentation), + Function.Injective F := by + obtain ⟨f,hf⟩ := one_extra_degree (r/2) (r%2) r (by omega) (by omega) s μ t hp hd + let G := signTwistMap (cyclicMap (letterLift φ) (rowColumnWord s)) + have hG : Function.Injective G := cyclicMap_injective _ _ (letterLift_injective φ hφ) + let := specht_irreducible t + exact ⟨G.comp f, hG.comp ((Representation.IsIrreducible.injective_or_eq_zero f).resolve_right hf)⟩ + +theorem two_extras_lifted (r d : ℕ) (s₁ s₂ : Tableau r (shape (r/2) (r%2))) + (φ ψ : Fin ((shape (r/2) (r%2)).transpose.colLen 0 * + (shape (r/2) (r%2)).colLen 0) → Fin d) + (hφ : Function.Injective φ) (hψ : Function.Injective ψ) + (A : Fin d → Prop) (hA : ∀ x, A (φ x)) (hB : ∀ x, ¬ A (ψ x)) + (e : Fin (2*r) ≃ Fin r ⊕ Fin r) + (η : YoungDiagram) (hη : η.card = 2*r) (t : Tableau (2*r) η) + (he : ∀ i, Even (η.colLen i)) (hd : η.rowLen 0 ≤ 8) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep (2*r) d) (positionProduct e + (letterLift φ (rowColumnWord s₁)) (letterLift ψ (rowColumnWord s₂)))).toRepresentation, + F ≠ 0 := by + obtain ⟨α,β,ta,tb,tt,e₀,ha,hb,hpa,hpb,f,hf⟩ := + even_rows_restriction r 4 η.transpose (by rwa [transpose_card]) + (by simpa only [YoungDiagram.rowLen_transpose] using he) + (by simpa only [YoungDiagram.colLen_transpose] using hd) + obtain ⟨Fa,hFa⟩ := one_extra_lifted r d s₁ φ hφ α ta hpa ha + obtain ⟨Fb,hFb⟩ := one_extra_lifted r d s₂ ψ hψ β tb hpb hb + have hs := signed_external_cyclic_support (spechtRep tt) (spechtRep ta) (spechtRep tb) + e₀ (letterLift φ (rowColumnWord s₁)) (letterLift ψ (rowColumnWord s₂)) A + (letterLift_mem_alphabet A φ hA _) (letterLift_mem_alphabet (fun x => ¬ A x) ψ hB _) + Fa Fb hFa hFb f hf + rw [cyclic_positionProduct_eq e₀ e] at hs + obtain ⟨H,hH⟩ := hs + have hEq := specht_sign_transpose t + change Nonempty ((spechtRep t).Equiv + (signTwist (spechtSub (transposeTableau t)).toRepresentation)) at hEq + rw [spechtSub_tableau_independent (transposeTableau t) tt] at hEq + obtain ⟨E⟩ := hEq + refine ⟨H.comp E.toIntertwiningMap, ?_⟩ + intro hz + apply hH + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + obtain ⟨y,rfl⟩ := E.surjective x + exact congrArg (fun K => K y) hz + +lemma one_extra_transpose_lifted (r d : ℕ) (s : Tableau r (shape (r/2) (r%2))) + (φ : Fin ((shape (r/2) (r%2)).transpose.transpose.colLen 0 * + (shape (r/2) (r%2)).transpose.colLen 0) → Fin d) (hφ : Function.Injective φ) + (μ : YoungDiagram) (t : Tableau r μ) (hp : RowParity (r%2) μ) + (hd : μ.colLen 0 ≤ 4) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (signTwist (cyclic (wordRep r d) + (letterLift φ (rowColumnWord (transposeTableau s)))).toRepresentation), + Function.Injective F := by + obtain ⟨f,hf⟩ := one_extra_degree (r/2) (r%2) r (by omega) (by omega) s μ t hp hd + let E := (rowColumnTransposeCyclicEquiv s).symm + let G := signTwistMap ((cyclicMap (letterLift φ) (rowColumnWord (transposeTableau s))).comp + E.toIntertwiningMap) + have hG : Function.Injective G := + (cyclicMap_injective _ _ (letterLift_injective φ hφ)).comp E.injective + let := specht_irreducible t + exact ⟨G.comp f, hG.comp ((Representation.IsIrreducible.injective_or_eq_zero f).resolve_right hf)⟩ + +theorem two_extras (r d : ℕ) (s₁ s₂ : Tableau r (shape (r/2) (r%2))) + (φ : Fin ((shape (r/2) (r%2)).transpose.colLen 0 * + (shape (r/2) (r%2)).colLen 0) → Fin d) + (ψ : Fin ((shape (r/2) (r%2)).transpose.transpose.colLen 0 * + (shape (r/2) (r%2)).transpose.colLen 0) → Fin d) + (hφ : Function.Injective φ) (hψ : Function.Injective ψ) + (A : Fin d → Prop) (hA : ∀ x, A (φ x)) (hB : ∀ x, ¬ A (ψ x)) + (e : Fin (2*r) ≃ Fin r ⊕ Fin r) + (η : YoungDiagram) (hη : η.card = 2*r) (t : Tableau (2*r) η) + (he : ∀ i, Even (η.colLen i)) (hd : η.rowLen 0 ≤ 8) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep (2*r) d) (positionProduct e + (letterLift φ (rowColumnWord s₁)) + (letterLift ψ (rowColumnWord (transposeTableau s₂))))).toRepresentation, + F ≠ 0 := by + obtain ⟨α,β,ta,tb,tt,e₀,ha,hb,hpa,hpb,f,hf⟩ := + even_rows_restriction r 4 η.transpose (by rwa [transpose_card]) + (by simpa only [YoungDiagram.rowLen_transpose] using he) + (by simpa only [YoungDiagram.colLen_transpose] using hd) + obtain ⟨Fa,hFa⟩ := one_extra_lifted r d s₁ φ hφ α ta hpa ha + obtain ⟨Fb,hFb⟩ := one_extra_transpose_lifted r d s₂ ψ hψ β tb hpb hb + have hs := signed_external_cyclic_support (spechtRep tt) (spechtRep ta) (spechtRep tb) + e₀ (letterLift φ (rowColumnWord s₁)) (letterLift ψ (rowColumnWord (transposeTableau s₂))) A + (letterLift_mem_alphabet A φ hA _) (letterLift_mem_alphabet (fun x => ¬ A x) ψ hB _) + Fa Fb hFa hFb f hf + rw [cyclic_positionProduct_eq e₀ e] at hs + obtain ⟨H,hH⟩ := hs + have hEq := specht_sign_transpose t + change Nonempty ((spechtRep t).Equiv + (signTwist (spechtSub (transposeTableau t)).toRepresentation)) at hEq + rw [spechtSub_tableau_independent (transposeTableau t) tt] at hEq + obtain ⟨E⟩ := hEq + refine ⟨H.comp E.toIntertwiningMap, ?_⟩ + intro hz + apply hH + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + obtain ⟨y,rfl⟩ := E.surjective x + exact congrArg (fun K => K y) hz + +end ShortColumns +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/TwoPathGeometry.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/TwoPathGeometry.lean index f0b99d26558f352853c178dc3c6d997b11ad5b9f..1a98e554f46200d95ad0b7854c5c07e8495ed3a5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/TwoPathGeometry.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/TwoPathGeometry.lean @@ -1,398 +1,398 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.SubdiagramSupport -import OAI.RepresentationTheory.UniversalSquare.Band.OddStrip -import OAI.RepresentationTheory.UniversalSquare.Contraction.TwoPathContraction - -namespace OAI - -/-! Two Path Geometry. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl.Balance - -def appendShortMap (p r q : ℕ) (hq : p+r=q) : - (ShortColumns.shape p 1).cells ⊕ (ShortColumns.shape r 1).cells → - (ShortColumns.shape q 2).cells := - Sum.elim - (fun c => ⟨(c.val.1, if c.val.2 = p then q else c.val.2), by - have hc := (ShortColumns.mem_shape p 1 c.val.1 c.val.2).mp c.property - apply (ShortColumns.mem_shape q 2 _ _).mpr - split_ifs <;> omega⟩) - (fun c => ⟨(c.val.1, if c.val.2 = r then q+1 else p+c.val.2), by - have hc := (ShortColumns.mem_shape r 1 c.val.1 c.val.2).mp c.property - apply (ShortColumns.mem_shape q 2 _ _).mpr - split_ifs <;> omega⟩) - -lemma appendShortMap_injective (p r q : ℕ) (hq : p+r=q) : - Function.Injective (appendShortMap p r q hq) := by - intro x y he - have hh := congrArg Subtype.val he - cases x with - | inl x => - have hx := (ShortColumns.mem_shape p 1 x.val.1 x.val.2).mp x.property - cases y with - | inl y => - have hy := (ShortColumns.mem_shape p 1 y.val.1 y.val.2).mp y.property - apply congrArg Sum.inl - apply Subtype.ext - apply Prod.ext - · simpa only [appendShortMap, Sum.elim_inl, Sum.elim_inr] using congrArg Prod.fst hh - · have ht := congrArg Prod.snd hh - change (if x.val.2 = p then q else x.val.2) = - (if y.val.2 = p then q else y.val.2) at ht - split_ifs at ht <;> omega - | inr y => - have hy := (ShortColumns.mem_shape r 1 y.val.1 y.val.2).mp y.property - have ht := congrArg Prod.snd hh - change (if x.val.2 = p then q else x.val.2) = - (if y.val.2 = r then q+1 else p+y.val.2) at ht - split_ifs at ht <;> omega - | inr x => - have hx := (ShortColumns.mem_shape r 1 x.val.1 x.val.2).mp x.property - cases y with - | inl y => - have hy := (ShortColumns.mem_shape p 1 y.val.1 y.val.2).mp y.property - have ht := congrArg Prod.snd hh - change (if x.val.2 = r then q+1 else p+x.val.2) = - (if y.val.2 = p then q else y.val.2) at ht - split_ifs at ht <;> omega - | inr y => - have hy := (ShortColumns.mem_shape r 1 y.val.1 y.val.2).mp y.property - apply congrArg Sum.inr - apply Subtype.ext - apply Prod.ext - · simpa only [appendShortMap, Sum.elim_inl, Sum.elim_inr] using congrArg Prod.fst hh - · have ht := congrArg Prod.snd hh - change (if x.val.2 = r then q+1 else p+x.val.2) = - (if y.val.2 = r then q+1 else p+y.val.2) at ht - split_ifs at ht <;> omega - -def appendShortCells (p r q : ℕ) (hq : p+r=q) : - (ShortColumns.shape p 1).cells ⊕ (ShortColumns.shape r 1).cells ≃ - (ShortColumns.shape q 2).cells := - Equiv.ofBijective (appendShortMap p r q hq) - ((Fintype.bijective_iff_injective_and_card _).mpr - ⟨appendShortMap_injective p r q hq, by - rw [Fintype.card_sum, Fintype.card_coe, Fintype.card_coe, Fintype.card_coe] - change (ShortColumns.shape p 1).card + (ShortColumns.shape r 1).card = - (ShortColumns.shape q 2).card - rw [short_card, short_card, short_card] - omega⟩) - -@[simp] lemma appendShortCells_left (p r q : ℕ) (hq : p+r=q) - (c : (ShortColumns.shape p 1).cells) : - (appendShortCells p r q hq (Sum.inl c)).val = - (c.val.1, if c.val.2 = p then q else c.val.2) := rfl - -@[simp] lemma appendShortCells_right (p r q : ℕ) (hq : p+r=q) - (c : (ShortColumns.shape r 1).cells) : - (appendShortCells p r q hq (Sum.inr c)).val = - (c.val.1, if c.val.2 = r then q+1 else p+c.val.2) := rfl - -lemma appendShortCells_column_same (p r q : ℕ) (hq : p+r=q) - (x y : (ShortColumns.shape p 1).cells ⊕ (ShortColumns.shape r 1).cells) - (h : (appendShortCells p r q hq x).val.2 = - (appendShortCells p r q hq y).val.2) : x.isLeft = y.isLeft := by - cases x with - | inl x => - cases y with - | inl y => rfl - | inr y => - have hx := (ShortColumns.mem_shape p 1 x.val.1 x.val.2).mp x.property - have hy := (ShortColumns.mem_shape r 1 y.val.1 y.val.2).mp y.property - simp only [appendShortCells_left, appendShortCells_right] at h - split_ifs at h <;> omega - | inr x => - cases y with - | inr y => rfl - | inl y => - have hx := (ShortColumns.mem_shape r 1 x.val.1 x.val.2).mp x.property - have hy := (ShortColumns.mem_shape p 1 y.val.1 y.val.2).mp y.property - simp only [appendShortCells_left, appendShortCells_right] at h - split_ifs at h <;> omega - -lemma appendShortCells_left_col (p r q : ℕ) (hq : p+r=q) - (x y : (ShortColumns.shape p 1).cells) : - (appendShortCells p r q hq (Sum.inl x)).val.2 = - (appendShortCells p r q hq (Sum.inl y)).val.2 ↔ x.val.2 = y.val.2 := by - have hx := (ShortColumns.mem_shape p 1 x.val.1 x.val.2).mp x.property - have hy := (ShortColumns.mem_shape p 1 y.val.1 y.val.2).mp y.property - simp only [appendShortCells_left] - split_ifs <;> omega - -lemma appendShortCells_right_col (p r q : ℕ) (hq : p+r=q) - (x y : (ShortColumns.shape r 1).cells) : - (appendShortCells p r q hq (Sum.inr x)).val.2 = - (appendShortCells p r q hq (Sum.inr y)).val.2 ↔ x.val.2 = y.val.2 := by - have hx := (ShortColumns.mem_shape r 1 x.val.1 x.val.2).mp x.property - have hy := (ShortColumns.mem_shape r 1 y.val.1 y.val.2).mp y.property - simp only [appendShortCells_right] - split_ifs <;> omega - -def appendShortTableau {n a b : ℕ} (p r q : ℕ) (hq : p+r=q) - (e : Fin n ≃ Fin a ⊕ Fin b) - (s : Tableau a (ShortColumns.shape p 1)) - (t : Tableau b (ShortColumns.shape r 1)) : Tableau n (ShortColumns.shape q 2) := - e.trans ((s.sumCongr t).trans (appendShortCells p r q hq)) - -lemma appendShort_polytabloid {n a b : ℕ} (p r q : ℕ) (hq : p+r=q) - (e : Fin n ≃ Fin a ⊕ Fin b) - (s : Tableau a (ShortColumns.shape p 1)) - (t : Tableau b (ShortColumns.shape r 1)) : - letterLift (Fin.castLE (ShortColumns.height_le q 2)) - (polytabloid (appendShortTableau p r q hq e s t)) = - positionProduct e - (letterLift (Fin.castLE (ShortColumns.height_le p 1)) (polytabloid s)) - (letterLift (Fin.castLE (ShortColumns.height_le r 1)) (polytabloid t)) := by - let T := appendShortTableau p r q hq e s t - let f := fun i => (T i).val.2 - have hs (i : Fin a) : T (e.symm (Sum.inl i)) = - appendShortCells p r q hq (Sum.inl (s i)) := by simp [T, appendShortTableau] - have ht (i : Fin b) : T (e.symm (Sum.inr i)) = - appendShortCells p r q hq (Sum.inr (t i)) := by simp [T, appendShortTableau] - have hf : fiberGroup f = fiberGroup f ⊓ sectorGroup (fun i => (e i).isLeft = true) := by - apply le_antisymm - · intro g hg - refine ⟨hg, ?_⟩ - intro i - have hh := appendShortCells_column_same p r q hq - ((s.sumCongr t) (e (g i))) ((s.sumCongr t) (e i)) (hg i) - have he (i : Fin n) : ((s.sumCongr t) (e i)).isLeft = (e i).isLeft := by - cases e i <;> rfl - rw [he, he] at hh - change (e (g i)).isLeft = true ↔ (e i).isLeft = true - rw [hh] - · exact inf_le_left - have hl : fiberGroup (fun i => f (e.symm (Sum.inl i))) = columnGroup s := by - apply Subgroup.ext - intro g - change (∀ i, (T (e.symm (Sum.inl (g i)))).val.2 = - (T (e.symm (Sum.inl i))).val.2) ↔ (∀ i, (s (g i)).val.2 = (s i).val.2) - simp only [hs, appendShortCells_left_col] - have hr : fiberGroup (fun i => f (e.symm (Sum.inr i))) = columnGroup t := by - apply Subgroup.ext - intro g - change (∀ i, (T (e.symm (Sum.inr (g i)))).val.2 = - (T (e.symm (Sum.inr i))).val.2) ↔ (∀ i, (t (g i)).val.2 = (t i).val.2) - simp only [ht, appendShortCells_right_col] - rw [polytabloid_eq_altWord, letterLift_altWord] - change altWord (fiberGroup f) _ = _ - rw [hf, altWord_fiber_split, hl, hr, - polytabloid_eq_altWord, polytabloid_eq_altWord, letterLift_altWord, letterLift_altWord] - congr 2 - · funext i - apply Fin.ext - change (T (e.symm (Sum.inl i))).val.1 = (s i).val.1 - rw [hs] - rfl - · funext i - apply Fin.ext - change (T (e.symm (Sum.inr i))).val.1 = (t i).val.1 - rw [ht] - rfl - -def twoPathLeft {n : ℕ} (p r q : ℕ) (hq : p+r=q) - (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : - Tableau n (ShortColumns.shape q 2) := - appendShortTableau p r q hq e (neighborLayer p) (neighborLayer r) - -def twoPathRight {n : ℕ} (p r q : ℕ) (hq : p+r=q) - (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : - Tableau n (ShortColumns.shape q 2) := - appendShortTableau r p q (by omega) (e.trans (Equiv.sumComm _ _)) - (Fin.revPerm.trans (neighborLayer r)) (Fin.revPerm.trans (neighborLayer p)) - -lemma appendShortCells_left_neighbor (p r q : ℕ) (hq : p+r=q) - (i : Fin (2*p+1)) : - (appendShortCells p r q hq (Sum.inl (neighborLayer p i))).val.2 = - if i.val = 0 then q else p-1-(i.val-1)/2 := by - rw [appendShortCells_left, neighborLayer_col] - have hi := i.isLt - split_ifs <;> omega - -lemma appendShortCells_right_neighbor (p r q : ℕ) (hq : p+r=q) - (i : Fin (2*r+1)) : - (appendShortCells p r q hq (Sum.inr (neighborLayer r i))).val.2 = - if i.val = 0 then q+1 else p+(r-1-(i.val-1)/2) := by - rw [appendShortCells_right, neighborLayer_col] - have hi := i.isLt - split_ifs <;> omega - -lemma twoPathLeft_col_left {n : ℕ} (p r q : ℕ) (hq : p+r=q) - (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) (i : Fin (2*p+1)) : - (twoPathLeft p r q hq e (e.symm (Sum.inl i))).val.2 = - if i.val = 0 then q else p-1-(i.val-1)/2 := by - simp only [twoPathLeft, appendShortTableau, Equiv.trans_apply, - Equiv.apply_symm_apply, Equiv.sumCongr_apply, Sum.map_inl] - exact appendShortCells_left_neighbor p r q hq i - -lemma twoPathLeft_col_right {n : ℕ} (p r q : ℕ) (hq : p+r=q) - (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) (i : Fin (2*r+1)) : - (twoPathLeft p r q hq e (e.symm (Sum.inr i))).val.2 = - if i.val = 0 then q+1 else p+(r-1-(i.val-1)/2) := by - simp only [twoPathLeft, appendShortTableau, Equiv.trans_apply, - Equiv.apply_symm_apply, Equiv.sumCongr_apply, Sum.map_inr] - exact appendShortCells_right_neighbor p r q hq i - -lemma twoPathRight_col_left {n : ℕ} (p r q : ℕ) (hq : p+r=q) - (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) (i : Fin (2*p+1)) : - (twoPathRight p r q hq e (e.symm (Sum.inl i))).val.2 = - if i.rev.val = 0 then q+1 else r+(p-1-(i.rev.val-1)/2) := by - simp only [twoPathRight, appendShortTableau, Equiv.trans_apply, - Equiv.apply_symm_apply, Equiv.sumComm_apply, Sum.swap_inl, - Equiv.sumCongr_apply, Sum.map_inr] - exact appendShortCells_right_neighbor r p q (by omega) i.rev - -lemma twoPathRight_col_right {n : ℕ} (p r q : ℕ) (hq : p+r=q) - (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) (i : Fin (2*r+1)) : - (twoPathRight p r q hq e (e.symm (Sum.inr i))).val.2 = - if i.rev.val = 0 then q else r-1-(i.rev.val-1)/2 := by - simp only [twoPathRight, appendShortTableau, Equiv.trans_apply, - Equiv.apply_symm_apply, Equiv.sumComm_apply, Sum.swap_inr, - Equiv.sumCongr_apply, Sum.map_inl] - exact appendShortCells_left_neighbor r p q (by omega) i.rev - -theorem twoPath_outputs {n : ℕ} (p r q : ℕ) (hq : p+r=q) - (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : - inOutputs (Set.Icc q (2*q+3)) - (mergeWords (rowWord (transposeTableau (twoPathLeft p r q hq e))) - (rowWord (transposeTableau (twoPathRight p r q hq e)))) := by - intro i - simp only [output, mergeWords, Equiv.symm_apply_apply] - change (twoPathLeft p r q hq e i).val.2 + - (twoPathRight p r q hq e i).val.2 + 1 ∈ Set.Icc q (2*q+3) - obtain ⟨j,rfl⟩ := e.symm.surjective i - cases j with - | inl j => - rw [twoPathLeft_col_left, twoPathRight_col_left] - simp only [Set.mem_Icc, Fin.val_rev] - have hj := j.isLt - split_ifs <;> omega - | inr j => - rw [twoPathLeft_col_right, twoPathRight_col_right] - simp only [Set.mem_Icc, Fin.val_rev] - have hj := j.isLt - split_ifs <;> omega - -lemma positionProduct_swap {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (x : WordSpace a d) (y : WordSpace b d) : - positionProduct (e.trans (Equiv.sumComm _ _)) y x = positionProduct e x y := by - funext w - exact mul_comm _ _ - -lemma neighborLayer_reverse_word (r : ℕ) : - letterLift (Fin.castLE (ShortColumns.height_le r 1)) - (polytabloid (Fin.revPerm.trans (neighborLayer r))) = - wordRep (2*r+1) 2 Fin.revPerm (PathLayer.rowAlt r) := by - rw [polytabloid_move (neighborLayer r) (Fin.revPerm.trans (neighborLayer r))] - have he : tableauMove (neighborLayer r) (Fin.revPerm.trans (neighborLayer r)) = - Fin.revPerm := by - apply Equiv.ext - intro i - simp only [tableauMove, Equiv.trans_apply, Equiv.symm_trans_apply, - Equiv.symm_apply_apply] - rfl - rw [he, Representation.IntertwiningMap.isIntertwining, neighborLayer_polytabloid] - -lemma twoPathLeft_word {n : ℕ} (p r q : ℕ) (hq : p+r=q) - (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : - letterLift (Fin.castLE (ShortColumns.height_le q 2)) - (polytabloid (twoPathLeft p r q hq e)) = - positionProduct e (PathLayer.rowAlt p) (PathLayer.rowAlt r) := by - rw [twoPathLeft, appendShort_polytabloid, - neighborLayer_polytabloid, neighborLayer_polytabloid] - -lemma twoPathRight_word {n : ℕ} (p r q : ℕ) (hq : p+r=q) - (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : - letterLift (Fin.castLE (ShortColumns.height_le q 2)) - (polytabloid (twoPathRight p r q hq e)) = - positionProduct e (wordRep (2*p+1) 2 Fin.revPerm (PathLayer.rowAlt p)) - (wordRep (2*r+1) 2 Fin.revPerm (PathLayer.rowAlt r)) := by - rw [twoPathRight, appendShort_polytabloid, - neighborLayer_reverse_word, neighborLayer_reverse_word, positionProduct_swap] - -def twoPathLetter (q : ℕ) : - Fin ((ShortColumns.shape q 2).transpose.transpose.colLen 0) → Fin 2 := - (Fin.castLE (ShortColumns.height_le q 2)) ∘ Fin.cast - (congrArg (fun ν : YoungDiagram => ν.colLen 0) - (YoungDiagram.transpose_transpose (ShortColumns.shape q 2))) - -lemma twoPath_doubleTranspose_word {n : ℕ} (q : ℕ) - (t : Tableau n (ShortColumns.shape q 2)) : - letterLift (twoPathLetter q) (polytabloid (transposeTableau (transposeTableau t))) = - letterLift (Fin.castLE (ShortColumns.height_le q 2)) (polytabloid t) := by - rw [twoPathLetter, letterLift_comp] - change letterLift _ (letterLift _ (polytabloid (transposeTableau (transposeTableau t)))) = _ - rw [polytabloid_doubleTranspose] - -lemma twoPath_pair_word {n : ℕ} (p r q : ℕ) (hq : p+r=q) - (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : - pairWordMap (letterLift (twoPathLetter q)) (letterLift (twoPathLetter q)) - (wordTensor _ _ _ - (polytabloid (transposeTableau (transposeTableau (twoPathLeft p r q hq e))) ⊗ₜ[ℂ] - polytabloid (transposeTableau (transposeTableau (twoPathRight p r q hq e))))) = - (-1 : ℂ)^q • positionProduct e (Path.bandWord p) (Path.bandWord r) := by - rw [pairWordMap_tensor, twoPath_doubleTranspose_word, twoPath_doubleTranspose_word, - twoPathLeft_word, twoPathRight_word] - funext w - rw [wordTensor_tmul] - change (PathLayer.rowAlt p (leftWord e (splitLeft w)) * - PathLayer.rowAlt r (rightWord e (splitLeft w))) * - (PathLayer.rowAlt p (leftWord e (splitRight w) ∘ Fin.rev) * - PathLayer.rowAlt r (rightWord e (splitRight w) ∘ Fin.rev)) = - (-1 : ℂ)^q * (Path.bandWord p (leftWord e w) * Path.bandWord r (rightWord e w)) - have hp := PathLayer.paired_rowAlt p (leftWord e w) - have hr := PathLayer.paired_rowAlt r (rightWord e w) - change PathLayer.rowAlt p (leftWord e (splitLeft w)) * - PathLayer.rowAlt p (leftWord e (splitRight w) ∘ Fin.rev) = _ at hp - change PathLayer.rowAlt r (rightWord e (splitLeft w)) * - PathLayer.rowAlt r (rightWord e (splitRight w) ∘ Fin.rev) = _ at hr - calc - _ = (PathLayer.rowAlt p (leftWord e (splitLeft w)) * - PathLayer.rowAlt p (leftWord e (splitRight w) ∘ Fin.rev)) * - (PathLayer.rowAlt r (rightWord e (splitLeft w)) * - PathLayer.rowAlt r (rightWord e (splitRight w) ∘ Fin.rev)) := by ring - _ = _ := by rw [hp, hr, ← hq, pow_add]; ring - -theorem two_paths (q : ℕ) - (a b : Tableau (2*q+2) (ShortColumns.shape q 2).transpose) - (μ : YoungDiagram) (t : Tableau (2*q+2) μ) (hμ : μ.colLen 0 ≤ 4) - (ho : ∃ j, μ.colLen j % 2 = 1) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (projectedSpechtTensor a b (inOutputs (Set.Icc q (2*q+3))) - (inOutputs_invariant (Set.Icc q (2*q+3)))).toRepresentation, - Function.Injective F := by - have hn : μ.card = 2*q+2 := by - have h := Fintype.card_congr t - simpa only [Fintype.card_fin, Fintype.card_coe] using h.symm - obtain ⟨p,rs,hpq,hp,hrs,hr,hc⟩ := Columns.odd_column_split q μ hn hμ ho - let r := q-p - have hrq : p+r=q := by omega - have heq : 2*q+2 = (2*p+1)+(2*r+1) := by omega - let e : Fin (2*q+2) ≃ Fin (2*p+1) ⊕ Fin (2*r+1) := - (finCongr heq).trans finSumFinEquiv.symm - let s := transposeTableau (twoPathLeft p r q hrq e) - let u := transposeTableau (twoPathRight p r q hrq e) - let D := pairWordMap (n := 2*q+2) - (letterLift (twoPathLetter q)) (letterLift (twoPathLetter q)) - let v := wordTensor _ _ _ - (polytabloid (transposeTableau s) ⊗ₜ[ℂ] polytabloid (transposeTableau u)) - have hs : ∃ f : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep (2*q+2) 4) (D v)).toRepresentation, f ≠ 0 := by - dsimp only [D, v, s, u] - rw [twoPath_pair_word, cyclic_smul_eq _ _ _ (pow_ne_zero q (by norm_num))] - exact Columns.two_path_cyclic_support_placed p r rs hp hrs hr μ hc t e - obtain ⟨f,hf⟩ := hs - obtain ⟨g,hg⟩ := cyclic_projection_support D v f hf - exact projectedTensor_support_of_coordinate a s b u t _ _ - (twoPath_outputs p r q hrq e) g hg - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.SubdiagramSupport +import OAI.RepresentationTheory.UniversalSquare.Band.OddStrip +import OAI.RepresentationTheory.UniversalSquare.Contraction.TwoPathContraction + +namespace OAI + +/-! Two Path Geometry. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl.Balance + +def appendShortMap (p r q : ℕ) (hq : p+r=q) : + (ShortColumns.shape p 1).cells ⊕ (ShortColumns.shape r 1).cells → + (ShortColumns.shape q 2).cells := + Sum.elim + (fun c => ⟨(c.val.1, if c.val.2 = p then q else c.val.2), by + have hc := (ShortColumns.mem_shape p 1 c.val.1 c.val.2).mp c.property + apply (ShortColumns.mem_shape q 2 _ _).mpr + split_ifs <;> omega⟩) + (fun c => ⟨(c.val.1, if c.val.2 = r then q+1 else p+c.val.2), by + have hc := (ShortColumns.mem_shape r 1 c.val.1 c.val.2).mp c.property + apply (ShortColumns.mem_shape q 2 _ _).mpr + split_ifs <;> omega⟩) + +lemma appendShortMap_injective (p r q : ℕ) (hq : p+r=q) : + Function.Injective (appendShortMap p r q hq) := by + intro x y he + have hh := congrArg Subtype.val he + cases x with + | inl x => + have hx := (ShortColumns.mem_shape p 1 x.val.1 x.val.2).mp x.property + cases y with + | inl y => + have hy := (ShortColumns.mem_shape p 1 y.val.1 y.val.2).mp y.property + apply congrArg Sum.inl + apply Subtype.ext + apply Prod.ext + · simpa only [appendShortMap, Sum.elim_inl, Sum.elim_inr] using congrArg Prod.fst hh + · have ht := congrArg Prod.snd hh + change (if x.val.2 = p then q else x.val.2) = + (if y.val.2 = p then q else y.val.2) at ht + split_ifs at ht <;> omega + | inr y => + have hy := (ShortColumns.mem_shape r 1 y.val.1 y.val.2).mp y.property + have ht := congrArg Prod.snd hh + change (if x.val.2 = p then q else x.val.2) = + (if y.val.2 = r then q+1 else p+y.val.2) at ht + split_ifs at ht <;> omega + | inr x => + have hx := (ShortColumns.mem_shape r 1 x.val.1 x.val.2).mp x.property + cases y with + | inl y => + have hy := (ShortColumns.mem_shape p 1 y.val.1 y.val.2).mp y.property + have ht := congrArg Prod.snd hh + change (if x.val.2 = r then q+1 else p+x.val.2) = + (if y.val.2 = p then q else y.val.2) at ht + split_ifs at ht <;> omega + | inr y => + have hy := (ShortColumns.mem_shape r 1 y.val.1 y.val.2).mp y.property + apply congrArg Sum.inr + apply Subtype.ext + apply Prod.ext + · simpa only [appendShortMap, Sum.elim_inl, Sum.elim_inr] using congrArg Prod.fst hh + · have ht := congrArg Prod.snd hh + change (if x.val.2 = r then q+1 else p+x.val.2) = + (if y.val.2 = r then q+1 else p+y.val.2) at ht + split_ifs at ht <;> omega + +def appendShortCells (p r q : ℕ) (hq : p+r=q) : + (ShortColumns.shape p 1).cells ⊕ (ShortColumns.shape r 1).cells ≃ + (ShortColumns.shape q 2).cells := + Equiv.ofBijective (appendShortMap p r q hq) + ((Fintype.bijective_iff_injective_and_card _).mpr + ⟨appendShortMap_injective p r q hq, by + rw [Fintype.card_sum, Fintype.card_coe, Fintype.card_coe, Fintype.card_coe] + change (ShortColumns.shape p 1).card + (ShortColumns.shape r 1).card = + (ShortColumns.shape q 2).card + rw [short_card, short_card, short_card] + omega⟩) + +@[simp] lemma appendShortCells_left (p r q : ℕ) (hq : p+r=q) + (c : (ShortColumns.shape p 1).cells) : + (appendShortCells p r q hq (Sum.inl c)).val = + (c.val.1, if c.val.2 = p then q else c.val.2) := rfl + +@[simp] lemma appendShortCells_right (p r q : ℕ) (hq : p+r=q) + (c : (ShortColumns.shape r 1).cells) : + (appendShortCells p r q hq (Sum.inr c)).val = + (c.val.1, if c.val.2 = r then q+1 else p+c.val.2) := rfl + +lemma appendShortCells_column_same (p r q : ℕ) (hq : p+r=q) + (x y : (ShortColumns.shape p 1).cells ⊕ (ShortColumns.shape r 1).cells) + (h : (appendShortCells p r q hq x).val.2 = + (appendShortCells p r q hq y).val.2) : x.isLeft = y.isLeft := by + cases x with + | inl x => + cases y with + | inl y => rfl + | inr y => + have hx := (ShortColumns.mem_shape p 1 x.val.1 x.val.2).mp x.property + have hy := (ShortColumns.mem_shape r 1 y.val.1 y.val.2).mp y.property + simp only [appendShortCells_left, appendShortCells_right] at h + split_ifs at h <;> omega + | inr x => + cases y with + | inr y => rfl + | inl y => + have hx := (ShortColumns.mem_shape r 1 x.val.1 x.val.2).mp x.property + have hy := (ShortColumns.mem_shape p 1 y.val.1 y.val.2).mp y.property + simp only [appendShortCells_left, appendShortCells_right] at h + split_ifs at h <;> omega + +lemma appendShortCells_left_col (p r q : ℕ) (hq : p+r=q) + (x y : (ShortColumns.shape p 1).cells) : + (appendShortCells p r q hq (Sum.inl x)).val.2 = + (appendShortCells p r q hq (Sum.inl y)).val.2 ↔ x.val.2 = y.val.2 := by + have hx := (ShortColumns.mem_shape p 1 x.val.1 x.val.2).mp x.property + have hy := (ShortColumns.mem_shape p 1 y.val.1 y.val.2).mp y.property + simp only [appendShortCells_left] + split_ifs <;> omega + +lemma appendShortCells_right_col (p r q : ℕ) (hq : p+r=q) + (x y : (ShortColumns.shape r 1).cells) : + (appendShortCells p r q hq (Sum.inr x)).val.2 = + (appendShortCells p r q hq (Sum.inr y)).val.2 ↔ x.val.2 = y.val.2 := by + have hx := (ShortColumns.mem_shape r 1 x.val.1 x.val.2).mp x.property + have hy := (ShortColumns.mem_shape r 1 y.val.1 y.val.2).mp y.property + simp only [appendShortCells_right] + split_ifs <;> omega + +def appendShortTableau {n a b : ℕ} (p r q : ℕ) (hq : p+r=q) + (e : Fin n ≃ Fin a ⊕ Fin b) + (s : Tableau a (ShortColumns.shape p 1)) + (t : Tableau b (ShortColumns.shape r 1)) : Tableau n (ShortColumns.shape q 2) := + e.trans ((s.sumCongr t).trans (appendShortCells p r q hq)) + +lemma appendShort_polytabloid {n a b : ℕ} (p r q : ℕ) (hq : p+r=q) + (e : Fin n ≃ Fin a ⊕ Fin b) + (s : Tableau a (ShortColumns.shape p 1)) + (t : Tableau b (ShortColumns.shape r 1)) : + letterLift (Fin.castLE (ShortColumns.height_le q 2)) + (polytabloid (appendShortTableau p r q hq e s t)) = + positionProduct e + (letterLift (Fin.castLE (ShortColumns.height_le p 1)) (polytabloid s)) + (letterLift (Fin.castLE (ShortColumns.height_le r 1)) (polytabloid t)) := by + let T := appendShortTableau p r q hq e s t + let f := fun i => (T i).val.2 + have hs (i : Fin a) : T (e.symm (Sum.inl i)) = + appendShortCells p r q hq (Sum.inl (s i)) := by simp [T, appendShortTableau] + have ht (i : Fin b) : T (e.symm (Sum.inr i)) = + appendShortCells p r q hq (Sum.inr (t i)) := by simp [T, appendShortTableau] + have hf : fiberGroup f = fiberGroup f ⊓ sectorGroup (fun i => (e i).isLeft = true) := by + apply le_antisymm + · intro g hg + refine ⟨hg, ?_⟩ + intro i + have hh := appendShortCells_column_same p r q hq + ((s.sumCongr t) (e (g i))) ((s.sumCongr t) (e i)) (hg i) + have he (i : Fin n) : ((s.sumCongr t) (e i)).isLeft = (e i).isLeft := by + cases e i <;> rfl + rw [he, he] at hh + change (e (g i)).isLeft = true ↔ (e i).isLeft = true + rw [hh] + · exact inf_le_left + have hl : fiberGroup (fun i => f (e.symm (Sum.inl i))) = columnGroup s := by + apply Subgroup.ext + intro g + change (∀ i, (T (e.symm (Sum.inl (g i)))).val.2 = + (T (e.symm (Sum.inl i))).val.2) ↔ (∀ i, (s (g i)).val.2 = (s i).val.2) + simp only [hs, appendShortCells_left_col] + have hr : fiberGroup (fun i => f (e.symm (Sum.inr i))) = columnGroup t := by + apply Subgroup.ext + intro g + change (∀ i, (T (e.symm (Sum.inr (g i)))).val.2 = + (T (e.symm (Sum.inr i))).val.2) ↔ (∀ i, (t (g i)).val.2 = (t i).val.2) + simp only [ht, appendShortCells_right_col] + rw [polytabloid_eq_altWord, letterLift_altWord] + change altWord (fiberGroup f) _ = _ + rw [hf, altWord_fiber_split, hl, hr, + polytabloid_eq_altWord, polytabloid_eq_altWord, letterLift_altWord, letterLift_altWord] + congr 2 + · funext i + apply Fin.ext + change (T (e.symm (Sum.inl i))).val.1 = (s i).val.1 + rw [hs] + rfl + · funext i + apply Fin.ext + change (T (e.symm (Sum.inr i))).val.1 = (t i).val.1 + rw [ht] + rfl + +def twoPathLeft {n : ℕ} (p r q : ℕ) (hq : p+r=q) + (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : + Tableau n (ShortColumns.shape q 2) := + appendShortTableau p r q hq e (neighborLayer p) (neighborLayer r) + +def twoPathRight {n : ℕ} (p r q : ℕ) (hq : p+r=q) + (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : + Tableau n (ShortColumns.shape q 2) := + appendShortTableau r p q (by omega) (e.trans (Equiv.sumComm _ _)) + (Fin.revPerm.trans (neighborLayer r)) (Fin.revPerm.trans (neighborLayer p)) + +lemma appendShortCells_left_neighbor (p r q : ℕ) (hq : p+r=q) + (i : Fin (2*p+1)) : + (appendShortCells p r q hq (Sum.inl (neighborLayer p i))).val.2 = + if i.val = 0 then q else p-1-(i.val-1)/2 := by + rw [appendShortCells_left, neighborLayer_col] + have hi := i.isLt + split_ifs <;> omega + +lemma appendShortCells_right_neighbor (p r q : ℕ) (hq : p+r=q) + (i : Fin (2*r+1)) : + (appendShortCells p r q hq (Sum.inr (neighborLayer r i))).val.2 = + if i.val = 0 then q+1 else p+(r-1-(i.val-1)/2) := by + rw [appendShortCells_right, neighborLayer_col] + have hi := i.isLt + split_ifs <;> omega + +lemma twoPathLeft_col_left {n : ℕ} (p r q : ℕ) (hq : p+r=q) + (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) (i : Fin (2*p+1)) : + (twoPathLeft p r q hq e (e.symm (Sum.inl i))).val.2 = + if i.val = 0 then q else p-1-(i.val-1)/2 := by + simp only [twoPathLeft, appendShortTableau, Equiv.trans_apply, + Equiv.apply_symm_apply, Equiv.sumCongr_apply, Sum.map_inl] + exact appendShortCells_left_neighbor p r q hq i + +lemma twoPathLeft_col_right {n : ℕ} (p r q : ℕ) (hq : p+r=q) + (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) (i : Fin (2*r+1)) : + (twoPathLeft p r q hq e (e.symm (Sum.inr i))).val.2 = + if i.val = 0 then q+1 else p+(r-1-(i.val-1)/2) := by + simp only [twoPathLeft, appendShortTableau, Equiv.trans_apply, + Equiv.apply_symm_apply, Equiv.sumCongr_apply, Sum.map_inr] + exact appendShortCells_right_neighbor p r q hq i + +lemma twoPathRight_col_left {n : ℕ} (p r q : ℕ) (hq : p+r=q) + (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) (i : Fin (2*p+1)) : + (twoPathRight p r q hq e (e.symm (Sum.inl i))).val.2 = + if i.rev.val = 0 then q+1 else r+(p-1-(i.rev.val-1)/2) := by + simp only [twoPathRight, appendShortTableau, Equiv.trans_apply, + Equiv.apply_symm_apply, Equiv.sumComm_apply, Sum.swap_inl, + Equiv.sumCongr_apply, Sum.map_inr] + exact appendShortCells_right_neighbor r p q (by omega) i.rev + +lemma twoPathRight_col_right {n : ℕ} (p r q : ℕ) (hq : p+r=q) + (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) (i : Fin (2*r+1)) : + (twoPathRight p r q hq e (e.symm (Sum.inr i))).val.2 = + if i.rev.val = 0 then q else r-1-(i.rev.val-1)/2 := by + simp only [twoPathRight, appendShortTableau, Equiv.trans_apply, + Equiv.apply_symm_apply, Equiv.sumComm_apply, Sum.swap_inr, + Equiv.sumCongr_apply, Sum.map_inl] + exact appendShortCells_left_neighbor r p q (by omega) i.rev + +theorem twoPath_outputs {n : ℕ} (p r q : ℕ) (hq : p+r=q) + (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : + inOutputs (Set.Icc q (2*q+3)) + (mergeWords (rowWord (transposeTableau (twoPathLeft p r q hq e))) + (rowWord (transposeTableau (twoPathRight p r q hq e)))) := by + intro i + simp only [output, mergeWords, Equiv.symm_apply_apply] + change (twoPathLeft p r q hq e i).val.2 + + (twoPathRight p r q hq e i).val.2 + 1 ∈ Set.Icc q (2*q+3) + obtain ⟨j,rfl⟩ := e.symm.surjective i + cases j with + | inl j => + rw [twoPathLeft_col_left, twoPathRight_col_left] + simp only [Set.mem_Icc, Fin.val_rev] + have hj := j.isLt + split_ifs <;> omega + | inr j => + rw [twoPathLeft_col_right, twoPathRight_col_right] + simp only [Set.mem_Icc, Fin.val_rev] + have hj := j.isLt + split_ifs <;> omega + +lemma positionProduct_swap {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (x : WordSpace a d) (y : WordSpace b d) : + positionProduct (e.trans (Equiv.sumComm _ _)) y x = positionProduct e x y := by + funext w + exact mul_comm _ _ + +lemma neighborLayer_reverse_word (r : ℕ) : + letterLift (Fin.castLE (ShortColumns.height_le r 1)) + (polytabloid (Fin.revPerm.trans (neighborLayer r))) = + wordRep (2*r+1) 2 Fin.revPerm (PathLayer.rowAlt r) := by + rw [polytabloid_move (neighborLayer r) (Fin.revPerm.trans (neighborLayer r))] + have he : tableauMove (neighborLayer r) (Fin.revPerm.trans (neighborLayer r)) = + Fin.revPerm := by + apply Equiv.ext + intro i + simp only [tableauMove, Equiv.trans_apply, Equiv.symm_trans_apply, + Equiv.symm_apply_apply] + rfl + rw [he, Representation.IntertwiningMap.isIntertwining, neighborLayer_polytabloid] + +lemma twoPathLeft_word {n : ℕ} (p r q : ℕ) (hq : p+r=q) + (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : + letterLift (Fin.castLE (ShortColumns.height_le q 2)) + (polytabloid (twoPathLeft p r q hq e)) = + positionProduct e (PathLayer.rowAlt p) (PathLayer.rowAlt r) := by + rw [twoPathLeft, appendShort_polytabloid, + neighborLayer_polytabloid, neighborLayer_polytabloid] + +lemma twoPathRight_word {n : ℕ} (p r q : ℕ) (hq : p+r=q) + (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : + letterLift (Fin.castLE (ShortColumns.height_le q 2)) + (polytabloid (twoPathRight p r q hq e)) = + positionProduct e (wordRep (2*p+1) 2 Fin.revPerm (PathLayer.rowAlt p)) + (wordRep (2*r+1) 2 Fin.revPerm (PathLayer.rowAlt r)) := by + rw [twoPathRight, appendShort_polytabloid, + neighborLayer_reverse_word, neighborLayer_reverse_word, positionProduct_swap] + +def twoPathLetter (q : ℕ) : + Fin ((ShortColumns.shape q 2).transpose.transpose.colLen 0) → Fin 2 := + (Fin.castLE (ShortColumns.height_le q 2)) ∘ Fin.cast + (congrArg (fun ν : YoungDiagram => ν.colLen 0) + (YoungDiagram.transpose_transpose (ShortColumns.shape q 2))) + +lemma twoPath_doubleTranspose_word {n : ℕ} (q : ℕ) + (t : Tableau n (ShortColumns.shape q 2)) : + letterLift (twoPathLetter q) (polytabloid (transposeTableau (transposeTableau t))) = + letterLift (Fin.castLE (ShortColumns.height_le q 2)) (polytabloid t) := by + rw [twoPathLetter, letterLift_comp] + change letterLift _ (letterLift _ (polytabloid (transposeTableau (transposeTableau t)))) = _ + rw [polytabloid_doubleTranspose] + +lemma twoPath_pair_word {n : ℕ} (p r q : ℕ) (hq : p+r=q) + (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : + pairWordMap (letterLift (twoPathLetter q)) (letterLift (twoPathLetter q)) + (wordTensor _ _ _ + (polytabloid (transposeTableau (transposeTableau (twoPathLeft p r q hq e))) ⊗ₜ[ℂ] + polytabloid (transposeTableau (transposeTableau (twoPathRight p r q hq e))))) = + (-1 : ℂ)^q • positionProduct e (Path.bandWord p) (Path.bandWord r) := by + rw [pairWordMap_tensor, twoPath_doubleTranspose_word, twoPath_doubleTranspose_word, + twoPathLeft_word, twoPathRight_word] + funext w + rw [wordTensor_tmul] + change (PathLayer.rowAlt p (leftWord e (splitLeft w)) * + PathLayer.rowAlt r (rightWord e (splitLeft w))) * + (PathLayer.rowAlt p (leftWord e (splitRight w) ∘ Fin.rev) * + PathLayer.rowAlt r (rightWord e (splitRight w) ∘ Fin.rev)) = + (-1 : ℂ)^q * (Path.bandWord p (leftWord e w) * Path.bandWord r (rightWord e w)) + have hp := PathLayer.paired_rowAlt p (leftWord e w) + have hr := PathLayer.paired_rowAlt r (rightWord e w) + change PathLayer.rowAlt p (leftWord e (splitLeft w)) * + PathLayer.rowAlt p (leftWord e (splitRight w) ∘ Fin.rev) = _ at hp + change PathLayer.rowAlt r (rightWord e (splitLeft w)) * + PathLayer.rowAlt r (rightWord e (splitRight w) ∘ Fin.rev) = _ at hr + calc + _ = (PathLayer.rowAlt p (leftWord e (splitLeft w)) * + PathLayer.rowAlt p (leftWord e (splitRight w) ∘ Fin.rev)) * + (PathLayer.rowAlt r (rightWord e (splitLeft w)) * + PathLayer.rowAlt r (rightWord e (splitRight w) ∘ Fin.rev)) := by ring + _ = _ := by rw [hp, hr, ← hq, pow_add]; ring + +theorem two_paths (q : ℕ) + (a b : Tableau (2*q+2) (ShortColumns.shape q 2).transpose) + (μ : YoungDiagram) (t : Tableau (2*q+2) μ) (hμ : μ.colLen 0 ≤ 4) + (ho : ∃ j, μ.colLen j % 2 = 1) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (projectedSpechtTensor a b (inOutputs (Set.Icc q (2*q+3))) + (inOutputs_invariant (Set.Icc q (2*q+3)))).toRepresentation, + Function.Injective F := by + have hn : μ.card = 2*q+2 := by + have h := Fintype.card_congr t + simpa only [Fintype.card_fin, Fintype.card_coe] using h.symm + obtain ⟨p,rs,hpq,hp,hrs,hr,hc⟩ := Columns.odd_column_split q μ hn hμ ho + let r := q-p + have hrq : p+r=q := by omega + have heq : 2*q+2 = (2*p+1)+(2*r+1) := by omega + let e : Fin (2*q+2) ≃ Fin (2*p+1) ⊕ Fin (2*r+1) := + (finCongr heq).trans finSumFinEquiv.symm + let s := transposeTableau (twoPathLeft p r q hrq e) + let u := transposeTableau (twoPathRight p r q hrq e) + let D := pairWordMap (n := 2*q+2) + (letterLift (twoPathLetter q)) (letterLift (twoPathLetter q)) + let v := wordTensor _ _ _ + (polytabloid (transposeTableau s) ⊗ₜ[ℂ] polytabloid (transposeTableau u)) + have hs : ∃ f : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep (2*q+2) 4) (D v)).toRepresentation, f ≠ 0 := by + dsimp only [D, v, s, u] + rw [twoPath_pair_word, cyclic_smul_eq _ _ _ (pow_ne_zero q (by norm_num))] + exact Columns.two_path_cyclic_support_placed p r rs hp hrs hr μ hc t e + obtain ⟨f,hf⟩ := hs + obtain ⟨g,hg⟩ := cyclic_projection_support D v f hf + exact projectedTensor_support_of_coordinate a s b u t _ _ + (twoPath_outputs p r q hrq e) g hg + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Band/TwoStrip.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Band/TwoStrip.lean index 2a0da1317535435bb59a09debda3b594d4b22cd5..354e981b5781fb980f6ca605812cc43bb71eff51 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Band/TwoStrip.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Band/TwoStrip.lean @@ -1,166 +1,166 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking - -namespace OAI - -/-! Two Strip. -/ - -section - -noncomputable section - -namespace Saxl.Balance - -def FourInterlacing (a b c d x y z w : ℕ) : Prop := - x ≤ a ∧ b ≤ x ∧ y ≤ b ∧ c ≤ y ∧ z ≤ c ∧ d ≤ z ∧ w ≤ d ∧ - x+y+z+w+2 = a+b+c+d ∧ (y < x ∨ w < z) - -lemma four_interlacing_exists (a b c d : ℕ) (hab : b ≤ a) (hbc : c ≤ b) - (hcd : d ≤ c) (ha : 3 ≤ a) : - ∃ x y z w, FourInterlacing a b c d x y z w := by - by_cases hd2 : 2 ≤ d - · exact ⟨a,b,c,d-2,by unfold FourInterlacing; omega⟩ - by_cases hd1 : d = 1 - · by_cases hab' : b < a - · exact ⟨a-1,b,c,d-1,by unfold FourInterlacing; omega⟩ - · by_cases hbc' : c < b - · exact ⟨a,b-1,c,d-1,by unfold FourInterlacing; omega⟩ - · exact ⟨a,b,c-1,d-1,by unfold FourInterlacing; omega⟩ - have hd0 : d = 0 := by omega - by_cases hc3 : 3 ≤ c - · exact ⟨a,b,c-2,d,by unfold FourInterlacing; omega⟩ - by_cases hc2 : c = 2 - · by_cases hab' : b < a - · exact ⟨a,b,c-2,d,by unfold FourInterlacing; omega⟩ - · exact ⟨a,b-1,c-1,d,by unfold FourInterlacing; omega⟩ - by_cases hc1 : c = 1 - · by_cases hb2 : 2 ≤ b - · exact ⟨a,b-1,c-1,d,by unfold FourInterlacing; omega⟩ - · exact ⟨a-1,b,c-1,d,by unfold FourInterlacing; omega⟩ - by_cases hb2 : 2 ≤ b - · exact ⟨a,b-2,c,d,by unfold FourInterlacing; omega⟩ - by_cases hb1 : b = 1 - · exact ⟨a-1,b-1,c,d,by unfold FourInterlacing; omega⟩ - · exact ⟨a-2,b,c,d,by unfold FourInterlacing; omega⟩ - -lemma horizontal_of_interlacing (ν μ : YoungDiagram) - (hsub : ∀ i, ν.rowLen i ≤ μ.rowLen i) - (hbtw : ∀ i, μ.rowLen (i+1) ≤ ν.rowLen i) : HorizontalStrip ν μ := by - constructor - · intro x hx - exact YoungDiagram.mem_iff_lt_rowLen.mpr - ((YoungDiagram.mem_iff_lt_rowLen.mp hx).trans_le (hsub x.1)) - · intro x hx hxν y hy hyν hxy - apply Prod.ext _ hxy - have hh : ∀ (p q : ℕ × ℕ), p ∈ μ → p ∉ ν → q ∈ μ → q ∉ ν → - p.2 = q.2 → ¬ p.1 < q.1 := by - intro p q _ hp hq _ hpq hlt - have hp' := mt YoungDiagram.mem_iff_lt_rowLen.mpr hp - have hq' := YoungDiagram.mem_iff_lt_rowLen.mp hq - have hb := (μ.rowLen_anti _ _ (show p.1+1 ≤ q.1 by omega)).trans (hbtw p.1) - omega - exact Nat.le_antisymm (Nat.le_of_not_gt (hh y x hy hyν hx hxν hxy.symm)) - (Nat.le_of_not_gt (hh x y hx hxν hy hyν hxy)) - -lemma sorted_four (x y z w : ℕ) (hxy : y ≤ x) (hyz : z ≤ y) (hzw : w ≤ z) : - [x,y,z,w].SortedGE := by - simp [List.sortedGE_iff_pairwise, List.pairwise_cons] - omega - -lemma ofRowLens_height (A : List ℕ) (hA : A.SortedGE) : - (YoungDiagram.ofRowLens A hA).colLen 0 ≤ A.length := by - by_contra hh - have h := YoungDiagram.mem_iff_lt_colLen.mpr - (show A.length < (YoungDiagram.ofRowLens A hA).colLen 0 by omega) - obtain ⟨h',_⟩ := YoungDiagram.mem_ofRowLens.mp h - exact (Nat.lt_irrefl _) h' - -lemma ofRowLens_rowLen (A : List ℕ) (hA : A.SortedGE) (i : ℕ) : - (YoungDiagram.ofRowLens A hA).rowLen i = A[i]?.getD 0 := by - by_cases hi : i < A.length - · simpa [hi] using YoungDiagram.rowLen_ofRowLens (hw := hA) ⟨i,hi⟩ - · rw [rowLen_zero_of_height_le _ ((ofRowLens_height A hA).trans (by omega))] - simp [List.getElem?_eq_none (by omega : A.length ≤ i)] - -lemma card_of_height_four (μ : YoungDiagram) (hμ : μ.colLen 0 ≤ 4) : - μ.card = μ.rowLen 0 + μ.rowLen 1 + μ.rowLen 2 + μ.rowLen 3 := by - rw [← rowPrefix_eq_card μ hμ] - simp [rowPrefix, Finset.sum_range_succ, add_assoc] - -lemma odd_column_of_row_gap (μ : YoungDiagram) (i : ℕ) (hi : Even i) - (hgap : μ.rowLen (i+1) < μ.rowLen i) : ∃ j, Odd (μ.colLen j) := by - let j := μ.rowLen (i+1) - have h₁ : i < μ.colLen j := YoungDiagram.mem_iff_lt_colLen.mp - (YoungDiagram.mem_iff_lt_rowLen.mpr hgap) - have h₂ : ¬ i+1 < μ.colLen j := by - intro h - have hh := YoungDiagram.mem_iff_lt_rowLen.mp (YoungDiagram.mem_iff_lt_colLen.mpr h) - exact Nat.lt_irrefl j hh - refine ⟨j, ?_⟩ - have hlen : μ.colLen j = i+1 := by omega - rw [hlen, Nat.odd_iff] - have := Nat.even_iff.mp hi - omega - -theorem horizontal_two_odd_precursor (μ : YoungDiagram) (hμ : μ.colLen 0 ≤ 4) - (hw : 3 ≤ μ.rowLen 0) : - ∃ ν : YoungDiagram, ν.card+2 = μ.card ∧ ν.colLen 0 ≤ 4 ∧ - (∃ j, Odd (ν.colLen j)) ∧ HorizontalStrip ν μ := by - obtain ⟨x,y,z,w,hh⟩ := four_interlacing_exists - (μ.rowLen 0) (μ.rowLen 1) (μ.rowLen 2) (μ.rowLen 3) - (μ.rowLen_anti _ _ (by omega)) (μ.rowLen_anti _ _ (by omega)) - (μ.rowLen_anti _ _ (by omega)) hw - have hs := sorted_four x y z w (hh.2.2.1.trans hh.2.1) - (hh.2.2.2.2.1.trans hh.2.2.2.1) (hh.2.2.2.2.2.2.1.trans hh.2.2.2.2.2.1) - let ν := YoungDiagram.ofRowLens [x,y,z,w] hs - have hheight : ν.colLen 0 ≤ 4 := ofRowLens_height [x,y,z,w] hs - have hrows (i : ℕ) : ν.rowLen i = [x,y,z,w][i]?.getD 0 := ofRowLens_rowLen _ _ _ - have h0 : ν.rowLen 0 = x := by simp [hrows] - have h1 : ν.rowLen 1 = y := by simp [hrows] - have h2 : ν.rowLen 2 = z := by simp [hrows] - have h3 : ν.rowLen 3 = w := by simp [hrows] - refine ⟨ν, ?_, hheight, ?_, ?_⟩ - · rw [card_of_height_four _ hheight, card_of_height_four μ hμ, h0, h1, h2, h3] - exact hh.2.2.2.2.2.2.2.1 - · rcases hh.2.2.2.2.2.2.2.2 with h | h - · exact odd_column_of_row_gap ν 0 (by decide) (by simpa only [h0,h1] using h) - · exact odd_column_of_row_gap ν 2 (by decide) (by simpa only [h2,h3] using h) - · apply horizontal_of_interlacing - · intro i - by_cases hi : i < 4 - · interval_cases i <;> simp only [h0,h1,h2,h3] <;> unfold FourInterlacing at hh <;> omega - · rw [rowLen_zero_of_height_le _ (hheight.trans (by omega))] - exact Nat.zero_le _ - · intro i - by_cases hi : i < 3 - · interval_cases i <;> simp only [Nat.reduceAdd, h0,h1,h2] <;> unfold FourInterlacing at hh <;> omega - · rw [rowLen_zero_of_height_le _ (hμ.trans (by omega))] - exact Nat.zero_le _ - -theorem two_path_strip_restriction (q : ℕ) (hq : 3 ≤ q) - (μ : YoungDiagram) (hsize : μ.card = 2*q+4) (hμ : μ.colLen 0 ≤ 4) - (t : Tableau (2*q+4) μ) : - ∃ (ν : YoungDiagram) (hν : ν.card = 2*q+2) (hs : HorizontalStrip ν μ), - ν.colLen 0 ≤ 4 ∧ (∃ j, Odd (ν.colLen j)) ∧ - ∃ F : Specht t →ₗ[ℂ] Specht (canonicalTableau ν hν), Function.Surjective F ∧ - ∀ (g : Equiv.Perm (Fin (2*q+4))) (h : Equiv.Perm (Fin (2*q+2))), - (∀ k, g (tableauInclusion (canonicalTableau ν hν) t hs.1 k) = - tableauInclusion (canonicalTableau ν hν) t hs.1 (h k)) → - ∀ v, F (spechtRep t g v) = spechtRep (canonicalTableau ν hν) h (F v) := by - have hw : 3 ≤ μ.rowLen 0 := by - have hc := card_of_height_four μ hμ - have h1 := μ.rowLen_anti 0 1 (by omega) - have h2 := μ.rowLen_anti 0 2 (by omega) - have h3 := μ.rowLen_anti 0 3 (by omega) - omega - obtain ⟨ν,hcard,hheight,hodd,hs⟩ := horizontal_two_odd_precursor μ hμ hw - have hν : ν.card = 2*q+2 := by omega - obtain ⟨F,hF,hFeq⟩ := pieri_strip_surjective (canonicalTableau ν hν) t hs - exact ⟨ν,hν,hs,hheight,hodd,F,hF,hFeq⟩ - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking + +namespace OAI + +/-! Two Strip. -/ + +section + +noncomputable section + +namespace Saxl.Balance + +def FourInterlacing (a b c d x y z w : ℕ) : Prop := + x ≤ a ∧ b ≤ x ∧ y ≤ b ∧ c ≤ y ∧ z ≤ c ∧ d ≤ z ∧ w ≤ d ∧ + x+y+z+w+2 = a+b+c+d ∧ (y < x ∨ w < z) + +lemma four_interlacing_exists (a b c d : ℕ) (hab : b ≤ a) (hbc : c ≤ b) + (hcd : d ≤ c) (ha : 3 ≤ a) : + ∃ x y z w, FourInterlacing a b c d x y z w := by + by_cases hd2 : 2 ≤ d + · exact ⟨a,b,c,d-2,by unfold FourInterlacing; omega⟩ + by_cases hd1 : d = 1 + · by_cases hab' : b < a + · exact ⟨a-1,b,c,d-1,by unfold FourInterlacing; omega⟩ + · by_cases hbc' : c < b + · exact ⟨a,b-1,c,d-1,by unfold FourInterlacing; omega⟩ + · exact ⟨a,b,c-1,d-1,by unfold FourInterlacing; omega⟩ + have hd0 : d = 0 := by omega + by_cases hc3 : 3 ≤ c + · exact ⟨a,b,c-2,d,by unfold FourInterlacing; omega⟩ + by_cases hc2 : c = 2 + · by_cases hab' : b < a + · exact ⟨a,b,c-2,d,by unfold FourInterlacing; omega⟩ + · exact ⟨a,b-1,c-1,d,by unfold FourInterlacing; omega⟩ + by_cases hc1 : c = 1 + · by_cases hb2 : 2 ≤ b + · exact ⟨a,b-1,c-1,d,by unfold FourInterlacing; omega⟩ + · exact ⟨a-1,b,c-1,d,by unfold FourInterlacing; omega⟩ + by_cases hb2 : 2 ≤ b + · exact ⟨a,b-2,c,d,by unfold FourInterlacing; omega⟩ + by_cases hb1 : b = 1 + · exact ⟨a-1,b-1,c,d,by unfold FourInterlacing; omega⟩ + · exact ⟨a-2,b,c,d,by unfold FourInterlacing; omega⟩ + +lemma horizontal_of_interlacing (ν μ : YoungDiagram) + (hsub : ∀ i, ν.rowLen i ≤ μ.rowLen i) + (hbtw : ∀ i, μ.rowLen (i+1) ≤ ν.rowLen i) : HorizontalStrip ν μ := by + constructor + · intro x hx + exact YoungDiagram.mem_iff_lt_rowLen.mpr + ((YoungDiagram.mem_iff_lt_rowLen.mp hx).trans_le (hsub x.1)) + · intro x hx hxν y hy hyν hxy + apply Prod.ext _ hxy + have hh : ∀ (p q : ℕ × ℕ), p ∈ μ → p ∉ ν → q ∈ μ → q ∉ ν → + p.2 = q.2 → ¬ p.1 < q.1 := by + intro p q _ hp hq _ hpq hlt + have hp' := mt YoungDiagram.mem_iff_lt_rowLen.mpr hp + have hq' := YoungDiagram.mem_iff_lt_rowLen.mp hq + have hb := (μ.rowLen_anti _ _ (show p.1+1 ≤ q.1 by omega)).trans (hbtw p.1) + omega + exact Nat.le_antisymm (Nat.le_of_not_gt (hh y x hy hyν hx hxν hxy.symm)) + (Nat.le_of_not_gt (hh x y hx hxν hy hyν hxy)) + +lemma sorted_four (x y z w : ℕ) (hxy : y ≤ x) (hyz : z ≤ y) (hzw : w ≤ z) : + [x,y,z,w].SortedGE := by + simp [List.sortedGE_iff_pairwise, List.pairwise_cons] + omega + +lemma ofRowLens_height (A : List ℕ) (hA : A.SortedGE) : + (YoungDiagram.ofRowLens A hA).colLen 0 ≤ A.length := by + by_contra hh + have h := YoungDiagram.mem_iff_lt_colLen.mpr + (show A.length < (YoungDiagram.ofRowLens A hA).colLen 0 by omega) + obtain ⟨h',_⟩ := YoungDiagram.mem_ofRowLens.mp h + exact (Nat.lt_irrefl _) h' + +lemma ofRowLens_rowLen (A : List ℕ) (hA : A.SortedGE) (i : ℕ) : + (YoungDiagram.ofRowLens A hA).rowLen i = A[i]?.getD 0 := by + by_cases hi : i < A.length + · simpa [hi] using YoungDiagram.rowLen_ofRowLens (hw := hA) ⟨i,hi⟩ + · rw [rowLen_zero_of_height_le _ ((ofRowLens_height A hA).trans (by omega))] + simp [List.getElem?_eq_none (by omega : A.length ≤ i)] + +lemma card_of_height_four (μ : YoungDiagram) (hμ : μ.colLen 0 ≤ 4) : + μ.card = μ.rowLen 0 + μ.rowLen 1 + μ.rowLen 2 + μ.rowLen 3 := by + rw [← rowPrefix_eq_card μ hμ] + simp [rowPrefix, Finset.sum_range_succ, add_assoc] + +lemma odd_column_of_row_gap (μ : YoungDiagram) (i : ℕ) (hi : Even i) + (hgap : μ.rowLen (i+1) < μ.rowLen i) : ∃ j, Odd (μ.colLen j) := by + let j := μ.rowLen (i+1) + have h₁ : i < μ.colLen j := YoungDiagram.mem_iff_lt_colLen.mp + (YoungDiagram.mem_iff_lt_rowLen.mpr hgap) + have h₂ : ¬ i+1 < μ.colLen j := by + intro h + have hh := YoungDiagram.mem_iff_lt_rowLen.mp (YoungDiagram.mem_iff_lt_colLen.mpr h) + exact Nat.lt_irrefl j hh + refine ⟨j, ?_⟩ + have hlen : μ.colLen j = i+1 := by omega + rw [hlen, Nat.odd_iff] + have := Nat.even_iff.mp hi + omega + +theorem horizontal_two_odd_precursor (μ : YoungDiagram) (hμ : μ.colLen 0 ≤ 4) + (hw : 3 ≤ μ.rowLen 0) : + ∃ ν : YoungDiagram, ν.card+2 = μ.card ∧ ν.colLen 0 ≤ 4 ∧ + (∃ j, Odd (ν.colLen j)) ∧ HorizontalStrip ν μ := by + obtain ⟨x,y,z,w,hh⟩ := four_interlacing_exists + (μ.rowLen 0) (μ.rowLen 1) (μ.rowLen 2) (μ.rowLen 3) + (μ.rowLen_anti _ _ (by omega)) (μ.rowLen_anti _ _ (by omega)) + (μ.rowLen_anti _ _ (by omega)) hw + have hs := sorted_four x y z w (hh.2.2.1.trans hh.2.1) + (hh.2.2.2.2.1.trans hh.2.2.2.1) (hh.2.2.2.2.2.2.1.trans hh.2.2.2.2.2.1) + let ν := YoungDiagram.ofRowLens [x,y,z,w] hs + have hheight : ν.colLen 0 ≤ 4 := ofRowLens_height [x,y,z,w] hs + have hrows (i : ℕ) : ν.rowLen i = [x,y,z,w][i]?.getD 0 := ofRowLens_rowLen _ _ _ + have h0 : ν.rowLen 0 = x := by simp [hrows] + have h1 : ν.rowLen 1 = y := by simp [hrows] + have h2 : ν.rowLen 2 = z := by simp [hrows] + have h3 : ν.rowLen 3 = w := by simp [hrows] + refine ⟨ν, ?_, hheight, ?_, ?_⟩ + · rw [card_of_height_four _ hheight, card_of_height_four μ hμ, h0, h1, h2, h3] + exact hh.2.2.2.2.2.2.2.1 + · rcases hh.2.2.2.2.2.2.2.2 with h | h + · exact odd_column_of_row_gap ν 0 (by decide) (by simpa only [h0,h1] using h) + · exact odd_column_of_row_gap ν 2 (by decide) (by simpa only [h2,h3] using h) + · apply horizontal_of_interlacing + · intro i + by_cases hi : i < 4 + · interval_cases i <;> simp only [h0,h1,h2,h3] <;> unfold FourInterlacing at hh <;> omega + · rw [rowLen_zero_of_height_le _ (hheight.trans (by omega))] + exact Nat.zero_le _ + · intro i + by_cases hi : i < 3 + · interval_cases i <;> simp only [Nat.reduceAdd, h0,h1,h2] <;> unfold FourInterlacing at hh <;> omega + · rw [rowLen_zero_of_height_le _ (hμ.trans (by omega))] + exact Nat.zero_le _ + +theorem two_path_strip_restriction (q : ℕ) (hq : 3 ≤ q) + (μ : YoungDiagram) (hsize : μ.card = 2*q+4) (hμ : μ.colLen 0 ≤ 4) + (t : Tableau (2*q+4) μ) : + ∃ (ν : YoungDiagram) (hν : ν.card = 2*q+2) (hs : HorizontalStrip ν μ), + ν.colLen 0 ≤ 4 ∧ (∃ j, Odd (ν.colLen j)) ∧ + ∃ F : Specht t →ₗ[ℂ] Specht (canonicalTableau ν hν), Function.Surjective F ∧ + ∀ (g : Equiv.Perm (Fin (2*q+4))) (h : Equiv.Perm (Fin (2*q+2))), + (∀ k, g (tableauInclusion (canonicalTableau ν hν) t hs.1 k) = + tableauInclusion (canonicalTableau ν hν) t hs.1 (h k)) → + ∀ v, F (spechtRep t g v) = spechtRep (canonicalTableau ν hν) h (F v) := by + have hw : 3 ≤ μ.rowLen 0 := by + have hc := card_of_height_four μ hμ + have h1 := μ.rowLen_anti 0 1 (by omega) + have h2 := μ.rowLen_anti 0 2 (by omega) + have h3 := μ.rowLen_anti 0 3 (by omega) + omega + obtain ⟨ν,hcard,hheight,hodd,hs⟩ := horizontal_two_odd_precursor μ hμ hw + have hν : ν.card = 2*q+2 := by omega + obtain ⟨F,hF,hFeq⟩ := pieri_strip_surjective (canonicalTableau ν hν) t hs + exact ⟨ν,hν,hs,hheight,hodd,F,hF,hFeq⟩ + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/Capacity.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/Capacity.lean index df86bee13488b301c88d2b7bd0afe8caca9b8951..26bbfdec91b46277889a9a2c50413dad7562134a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/Capacity.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/Capacity.lean @@ -1,213 +1,213 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.Candidate -import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking - -namespace OAI - -/-! Capacity. -/ - -section - -noncomputable section - -namespace UniversalTensorSquare - -open Saxl - -def colPrefix (μ : YoungDiagram) (i : ℕ) : ℕ := rowPrefix μ.transpose i - -lemma colPrefix_eq_sum (μ : YoungDiagram) (i : ℕ) : - colPrefix μ i = ∑ k ∈ Finset.range i, μ.colLen k := by - simp only [colPrefix, rowPrefix, YoungDiagram.rowLen_transpose] - -lemma mem_colTruncate (μ : YoungDiagram) (i : ℕ) (a b : ℕ) : - (a,b) ∈ colTruncate μ i ↔ (a,b) ∈ μ ∧ b < i := by - simp only [colTruncate, YoungDiagram.mem_transpose, Prod.swap_prod_mk, - Saxl.mem_rowTruncate] - -lemma rowTruncate_subset (μ : YoungDiagram) (j : ℕ) : - (rowTruncate μ j).cells ⊆ μ.cells := by - intro p hp - exact (Saxl.mem_rowTruncate.mp hp).1 - -lemma colTruncate_subset (μ : YoungDiagram) (i : ℕ) : - (colTruncate μ i).cells ⊆ μ.cells := by - rintro ⟨a,b⟩ hp - exact ((mem_colTruncate μ i a b).mp hp).1 - -lemma colTruncate_card (μ : YoungDiagram) (i : ℕ) : - (colTruncate μ i).card = colPrefix μ i := by - rw [colTruncate, Saxl.transpose_card, rowTruncate_card, colPrefix] - -lemma strip_area_identity (μ : YoungDiagram) (i j : ℕ) : - μ.card + ((rowTruncate μ j).cells ∩ (colTruncate μ i).cells).card = - rowPrefix μ j + colPrefix μ i + - (μ.cells \ ((rowTruncate μ j).cells ∪ (colTruncate μ i).cells)).card := by - have hu : (rowTruncate μ j).cells ∪ (colTruncate μ i).cells ⊆ μ.cells := - Finset.union_subset (rowTruncate_subset μ j) (colTruncate_subset μ i) - have h₁ := Finset.card_sdiff_add_card_eq_card hu - have h₂ := Finset.card_union_add_card_inter - (rowTruncate μ j).cells (colTruncate μ i).cells - have h₃ := rowTruncate_card μ j - have h₄ := colTruncate_card μ i - change (rowTruncate μ j).cells.card = _ at h₃ - change (colTruncate μ i).cells.card = _ at h₄ - change μ.cells.card + _ = _ - omega - -lemma corner_subset_rectangle (μ : YoungDiagram) {i j : ℕ} (hi : 0 < i) (hj : 0 < j) : - μ.cells \ ((rowTruncate μ j).cells ∪ (colTruncate μ i).cells) ⊆ - Finset.Ico j (μ.colLen (i-1)) ×ˢ Finset.Ico i (μ.rowLen (j-1)) := by - rintro ⟨a,b⟩ hp - simp only [Finset.mem_sdiff, Finset.mem_union, YoungDiagram.mem_cells, - mem_rowTruncate, mem_colTruncate, not_or] at hp - have ha : j ≤ a := Nat.le_of_not_gt fun ha => hp.2.1 ⟨hp.1, ha⟩ - have hb : i ≤ b := Nat.le_of_not_gt fun hb => hp.2.2 ⟨hp.1, hb⟩ - have ha' : a < μ.colLen (i-1) := YoungDiagram.mem_iff_lt_colLen.mp - (μ.up_left_mem le_rfl (by omega) hp.1) - have hb' : b < μ.rowLen (j-1) := YoungDiagram.mem_iff_lt_rowLen.mp - (μ.up_left_mem (by omega) le_rfl hp.1) - simpa only [Finset.mem_product, Finset.mem_Ico] using And.intro ⟨ha, ha'⟩ ⟨hb,hb'⟩ - -lemma prefix_last_mul_le (μ : YoungDiagram) {j : ℕ} (hj : 0 < j) : - j * μ.rowLen (j-1) ≤ rowPrefix μ j := by - have h := Finset.sum_le_sum (s := Finset.range j) (f := fun _ => μ.rowLen (j-1)) - (g := fun a => μ.rowLen a) (by - intro a ha - exact μ.rowLen_anti a (j-1) (by have := Finset.mem_range.mp ha; omega)) - simpa only [Finset.sum_const, Finset.card_range, smul_eq_mul, rowPrefix] using h - -theorem capacity_rectangle (μ : YoungDiagram) {i j U V : ℕ} - (hi : 0 < i) (hj : 0 < j) (hU : colPrefix μ i ≤ U) (hV : rowPrefix μ j ≤ V) : - μ.card ≤ max (U+V-1) (U*V/(i*j)) := by - classical - by_cases hcell : (j-1,i-1) ∈ μ - · have heq : (rowTruncate μ j).cells ∩ (colTruncate μ i).cells = - (rectangle j i).cells := by - ext ⟨a,b⟩ - simp only [Finset.mem_inter, YoungDiagram.mem_cells, Saxl.mem_rowTruncate, - mem_colTruncate, mem_rectangle] - constructor - · tauto - · rintro ⟨ha,hb⟩ - have hx := μ.up_left_mem (by omega : a ≤ j-1) (by omega : b ≤ i-1) hcell - tauto - have hint : ((rowTruncate μ j).cells ∩ (colTruncate μ i).cells).card = j*i := by - rw [heq] - simp only [rectangle, Finset.card_product, Finset.card_range] - have hcorner := Finset.card_le_card (corner_subset_rectangle μ hi hj) - simp only [Finset.card_product, Nat.card_Ico] at hcorner - have hid := strip_area_identity μ i j - rw [hint, Nat.mul_comm j i] at hid - have harea : μ.card + i*j ≤ U+V + (μ.colLen (i-1)-j)*(μ.rowLen (j-1)-i) := by - omega - have hx : j ≤ μ.colLen (i-1) := by - have := YoungDiagram.mem_iff_lt_colLen.mp hcell - omega - have hy : i ≤ μ.rowLen (j-1) := by - have := YoungDiagram.mem_iff_lt_rowLen.mp hcell - omega - have hxu : i*μ.colLen (i-1) ≤ U := by - simpa only [YoungDiagram.rowLen_transpose] using - (prefix_last_mul_le μ.transpose hi).trans hU - have hyv : j*μ.rowLen (j-1) ≤ V := (prefix_last_mul_le μ hj).trans hV - have hu : i*j ≤ U := (Nat.mul_le_mul_left i hx).trans hxu - have hv : i*j ≤ V := by nlinarith - have ha : i*(μ.colLen (i-1)-j) ≤ U-i*j := by - rw [Nat.mul_sub_left_distrib] - exact Nat.sub_le_sub_right hxu _ - have hb : j*(μ.rowLen (j-1)-i) ≤ V-i*j := by - rw [Nat.mul_sub_left_distrib, Nat.mul_comm j i] - exact Nat.sub_le_sub_right hyv _ - have hprod := Nat.mul_le_mul ha hb - have hscaled := Nat.mul_le_mul_left (i*j) harea - have hmul : μ.card * (i*j) ≤ U*V := by - have hU' := Nat.sub_add_cancel hu - have hV' := Nat.sub_add_cancel hv - nlinarith - exact (Nat.le_div_iff_mul_le (Nat.mul_pos hi hj)).mpr hmul |>.trans (le_max_right _ _) - · have hcorner : μ.cells \ ((rowTruncate μ j).cells ∪ (colTruncate μ i).cells) = ∅ := by - apply Finset.eq_empty_iff_forall_notMem.mpr - rintro ⟨a,b⟩ hp - simp only [Finset.mem_sdiff, Finset.mem_union, YoungDiagram.mem_cells, - mem_rowTruncate, mem_colTruncate, not_or] at hp - have ha : j ≤ a := Nat.le_of_not_gt fun ha => hp.2.1 ⟨hp.1, ha⟩ - have hb : i ≤ b := Nat.le_of_not_gt fun hb => hp.2.2 ⟨hp.1, hb⟩ - exact hcell (μ.up_left_mem (by omega) (by omega) hp.1) - by_cases hn : μ.card = 0 - · simp [hn] - have hzero : (0,0) ∈ μ := by - obtain ⟨⟨a,b⟩,hp⟩ := Finset.card_pos.mp (show 0 < μ.cells.card from Nat.pos_of_ne_zero hn) - exact μ.up_left_mem (Nat.zero_le _) (Nat.zero_le _) hp - have hzmem : (0,0) ∈ (rowTruncate μ j).cells ∩ (colTruncate μ i).cells := by - simpa only [Finset.mem_inter, YoungDiagram.mem_cells, mem_rowTruncate, - mem_colTruncate, and_self] using And.intro ⟨hzero,hj⟩ ⟨hzero,hi⟩ - have hpos := Finset.card_pos.mpr ⟨(0,0),hzmem⟩ - have hid := strip_area_identity μ i j - rw [hcorner, Finset.card_empty, add_zero] at hid - exact (show μ.card ≤ U+V-1 by omega).trans (le_max_left _ _) - -def bandCapacity (μ : YoungDiagram) (d q : ℕ) : ℕ := - ∑ k ∈ Finset.range q, (μ.colLen k - d) / 2 - -def BandTest (M r : ℕ) (μ : YoungDiagram) : Prop := - ∃ d, 1 ≤ d ∧ d ≤ 4 ∧ ∃ q, q ≤ 8 ∧ - 2*M-1 ≤ rowPrefix μ d ∧ d*q+7+d ≤ 2*M-1 ∧ r ≤ bandCapacity μ d q - -lemma capacity_floor_bound (x f : ℕ) : x ≤ 2*((x-f)/2)+f+1 := by omega - -lemma prefix_le_capacity (μ : YoungDiagram) (d q : ℕ) : - colPrefix μ q ≤ 2*bandCapacity μ d q + q*(d+1) := by - rw [colPrefix_eq_sum, bandCapacity] - have h := Finset.sum_le_sum (s := Finset.range q) - (fun k _ => capacity_floor_bound (μ.colLen k) d) - simpa only [Finset.sum_add_distrib, ← Finset.mul_sum, - Finset.sum_const, Finset.card_range, smul_eq_mul, Nat.mul_add, Nat.mul_one, - Nat.add_assoc] using h - -lemma capacity_large_numeric (M r n : ℕ) (hM : 22 ≤ M) (hr : 2*r ≤ 3*M+4) - (hn : 2*n = M*(M+1)+4*r) : - 2*(2*r+38) < n ∧ (2*r+38)*(2*r+38) < 64*n := by - have hM2 := Nat.mul_le_mul_left M hM - have hr2 := Nat.mul_le_mul hr hr - constructor <;> nlinarith - -theorem capacity_large (μ : YoungDiagram) (M r : ℕ) (hM : 22 ≤ M) - (hr : 2*r ≤ 3*M+4) - (hn : μ.card = (staircase M).card + 2*r) - (hH : 2*M-1 ≤ colPrefix μ 4) (hW : 2*M-1 ≤ rowPrefix μ 4) : - BandTest M r μ ∨ BandTest M r μ.transpose := by - classical - by_contra hh - push Not at hh - have ha : (4:ℕ)*8+7+4 ≤ 2*M-1 := by omega - have hc : bandCapacity μ 4 8 < r := by - by_contra hc - exact hh.1 ⟨4, by omega, by omega, 8, by omega, hW, ha, by omega⟩ - have hct : bandCapacity μ.transpose 4 8 < r := by - by_contra hc - exact hh.2 ⟨4, by omega, by omega, 8, by omega, hH, ha, by omega⟩ - have h₁ : colPrefix μ 8 ≤ 2*r+38 := by - have := prefix_le_capacity μ 4 8 - omega - have h₂ : rowPrefix μ 8 ≤ 2*r+38 := by - have hp := prefix_le_capacity μ.transpose 4 8 - simp only [colPrefix, YoungDiagram.transpose_transpose] at hp - omega - have hb := capacity_rectangle μ (by omega : 0 < 8) (by omega : 0 < 8) h₁ h₂ - have he : 2*μ.card = M*(M+1)+4*r := by - have hx := staircase_card_double M - nlinarith - obtain ⟨hl,hu⟩ := capacity_large_numeric M r μ.card hM hr he - have hdiv : (2*r+38)*(2*r+38)/(8*8) < μ.card := by - exact (Nat.div_lt_iff_lt_mul (by norm_num)).mpr (by nlinarith) - have hmax : max (2*r+38+(2*r+38)-1) ((2*r+38)*(2*r+38)/(8*8)) < μ.card := - max_lt (by omega) hdiv - omega - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.Candidate +import OAI.RepresentationTheory.UniversalSquare.Balance.BalancePacking + +namespace OAI + +/-! Capacity. -/ + +section + +noncomputable section + +namespace UniversalTensorSquare + +open Saxl + +def colPrefix (μ : YoungDiagram) (i : ℕ) : ℕ := rowPrefix μ.transpose i + +lemma colPrefix_eq_sum (μ : YoungDiagram) (i : ℕ) : + colPrefix μ i = ∑ k ∈ Finset.range i, μ.colLen k := by + simp only [colPrefix, rowPrefix, YoungDiagram.rowLen_transpose] + +lemma mem_colTruncate (μ : YoungDiagram) (i : ℕ) (a b : ℕ) : + (a,b) ∈ colTruncate μ i ↔ (a,b) ∈ μ ∧ b < i := by + simp only [colTruncate, YoungDiagram.mem_transpose, Prod.swap_prod_mk, + Saxl.mem_rowTruncate] + +lemma rowTruncate_subset (μ : YoungDiagram) (j : ℕ) : + (rowTruncate μ j).cells ⊆ μ.cells := by + intro p hp + exact (Saxl.mem_rowTruncate.mp hp).1 + +lemma colTruncate_subset (μ : YoungDiagram) (i : ℕ) : + (colTruncate μ i).cells ⊆ μ.cells := by + rintro ⟨a,b⟩ hp + exact ((mem_colTruncate μ i a b).mp hp).1 + +lemma colTruncate_card (μ : YoungDiagram) (i : ℕ) : + (colTruncate μ i).card = colPrefix μ i := by + rw [colTruncate, Saxl.transpose_card, rowTruncate_card, colPrefix] + +lemma strip_area_identity (μ : YoungDiagram) (i j : ℕ) : + μ.card + ((rowTruncate μ j).cells ∩ (colTruncate μ i).cells).card = + rowPrefix μ j + colPrefix μ i + + (μ.cells \ ((rowTruncate μ j).cells ∪ (colTruncate μ i).cells)).card := by + have hu : (rowTruncate μ j).cells ∪ (colTruncate μ i).cells ⊆ μ.cells := + Finset.union_subset (rowTruncate_subset μ j) (colTruncate_subset μ i) + have h₁ := Finset.card_sdiff_add_card_eq_card hu + have h₂ := Finset.card_union_add_card_inter + (rowTruncate μ j).cells (colTruncate μ i).cells + have h₃ := rowTruncate_card μ j + have h₄ := colTruncate_card μ i + change (rowTruncate μ j).cells.card = _ at h₃ + change (colTruncate μ i).cells.card = _ at h₄ + change μ.cells.card + _ = _ + omega + +lemma corner_subset_rectangle (μ : YoungDiagram) {i j : ℕ} (hi : 0 < i) (hj : 0 < j) : + μ.cells \ ((rowTruncate μ j).cells ∪ (colTruncate μ i).cells) ⊆ + Finset.Ico j (μ.colLen (i-1)) ×ˢ Finset.Ico i (μ.rowLen (j-1)) := by + rintro ⟨a,b⟩ hp + simp only [Finset.mem_sdiff, Finset.mem_union, YoungDiagram.mem_cells, + mem_rowTruncate, mem_colTruncate, not_or] at hp + have ha : j ≤ a := Nat.le_of_not_gt fun ha => hp.2.1 ⟨hp.1, ha⟩ + have hb : i ≤ b := Nat.le_of_not_gt fun hb => hp.2.2 ⟨hp.1, hb⟩ + have ha' : a < μ.colLen (i-1) := YoungDiagram.mem_iff_lt_colLen.mp + (μ.up_left_mem le_rfl (by omega) hp.1) + have hb' : b < μ.rowLen (j-1) := YoungDiagram.mem_iff_lt_rowLen.mp + (μ.up_left_mem (by omega) le_rfl hp.1) + simpa only [Finset.mem_product, Finset.mem_Ico] using And.intro ⟨ha, ha'⟩ ⟨hb,hb'⟩ + +lemma prefix_last_mul_le (μ : YoungDiagram) {j : ℕ} (hj : 0 < j) : + j * μ.rowLen (j-1) ≤ rowPrefix μ j := by + have h := Finset.sum_le_sum (s := Finset.range j) (f := fun _ => μ.rowLen (j-1)) + (g := fun a => μ.rowLen a) (by + intro a ha + exact μ.rowLen_anti a (j-1) (by have := Finset.mem_range.mp ha; omega)) + simpa only [Finset.sum_const, Finset.card_range, smul_eq_mul, rowPrefix] using h + +theorem capacity_rectangle (μ : YoungDiagram) {i j U V : ℕ} + (hi : 0 < i) (hj : 0 < j) (hU : colPrefix μ i ≤ U) (hV : rowPrefix μ j ≤ V) : + μ.card ≤ max (U+V-1) (U*V/(i*j)) := by + classical + by_cases hcell : (j-1,i-1) ∈ μ + · have heq : (rowTruncate μ j).cells ∩ (colTruncate μ i).cells = + (rectangle j i).cells := by + ext ⟨a,b⟩ + simp only [Finset.mem_inter, YoungDiagram.mem_cells, Saxl.mem_rowTruncate, + mem_colTruncate, mem_rectangle] + constructor + · tauto + · rintro ⟨ha,hb⟩ + have hx := μ.up_left_mem (by omega : a ≤ j-1) (by omega : b ≤ i-1) hcell + tauto + have hint : ((rowTruncate μ j).cells ∩ (colTruncate μ i).cells).card = j*i := by + rw [heq] + simp only [rectangle, Finset.card_product, Finset.card_range] + have hcorner := Finset.card_le_card (corner_subset_rectangle μ hi hj) + simp only [Finset.card_product, Nat.card_Ico] at hcorner + have hid := strip_area_identity μ i j + rw [hint, Nat.mul_comm j i] at hid + have harea : μ.card + i*j ≤ U+V + (μ.colLen (i-1)-j)*(μ.rowLen (j-1)-i) := by + omega + have hx : j ≤ μ.colLen (i-1) := by + have := YoungDiagram.mem_iff_lt_colLen.mp hcell + omega + have hy : i ≤ μ.rowLen (j-1) := by + have := YoungDiagram.mem_iff_lt_rowLen.mp hcell + omega + have hxu : i*μ.colLen (i-1) ≤ U := by + simpa only [YoungDiagram.rowLen_transpose] using + (prefix_last_mul_le μ.transpose hi).trans hU + have hyv : j*μ.rowLen (j-1) ≤ V := (prefix_last_mul_le μ hj).trans hV + have hu : i*j ≤ U := (Nat.mul_le_mul_left i hx).trans hxu + have hv : i*j ≤ V := by nlinarith + have ha : i*(μ.colLen (i-1)-j) ≤ U-i*j := by + rw [Nat.mul_sub_left_distrib] + exact Nat.sub_le_sub_right hxu _ + have hb : j*(μ.rowLen (j-1)-i) ≤ V-i*j := by + rw [Nat.mul_sub_left_distrib, Nat.mul_comm j i] + exact Nat.sub_le_sub_right hyv _ + have hprod := Nat.mul_le_mul ha hb + have hscaled := Nat.mul_le_mul_left (i*j) harea + have hmul : μ.card * (i*j) ≤ U*V := by + have hU' := Nat.sub_add_cancel hu + have hV' := Nat.sub_add_cancel hv + nlinarith + exact (Nat.le_div_iff_mul_le (Nat.mul_pos hi hj)).mpr hmul |>.trans (le_max_right _ _) + · have hcorner : μ.cells \ ((rowTruncate μ j).cells ∪ (colTruncate μ i).cells) = ∅ := by + apply Finset.eq_empty_iff_forall_notMem.mpr + rintro ⟨a,b⟩ hp + simp only [Finset.mem_sdiff, Finset.mem_union, YoungDiagram.mem_cells, + mem_rowTruncate, mem_colTruncate, not_or] at hp + have ha : j ≤ a := Nat.le_of_not_gt fun ha => hp.2.1 ⟨hp.1, ha⟩ + have hb : i ≤ b := Nat.le_of_not_gt fun hb => hp.2.2 ⟨hp.1, hb⟩ + exact hcell (μ.up_left_mem (by omega) (by omega) hp.1) + by_cases hn : μ.card = 0 + · simp [hn] + have hzero : (0,0) ∈ μ := by + obtain ⟨⟨a,b⟩,hp⟩ := Finset.card_pos.mp (show 0 < μ.cells.card from Nat.pos_of_ne_zero hn) + exact μ.up_left_mem (Nat.zero_le _) (Nat.zero_le _) hp + have hzmem : (0,0) ∈ (rowTruncate μ j).cells ∩ (colTruncate μ i).cells := by + simpa only [Finset.mem_inter, YoungDiagram.mem_cells, mem_rowTruncate, + mem_colTruncate, and_self] using And.intro ⟨hzero,hj⟩ ⟨hzero,hi⟩ + have hpos := Finset.card_pos.mpr ⟨(0,0),hzmem⟩ + have hid := strip_area_identity μ i j + rw [hcorner, Finset.card_empty, add_zero] at hid + exact (show μ.card ≤ U+V-1 by omega).trans (le_max_left _ _) + +def bandCapacity (μ : YoungDiagram) (d q : ℕ) : ℕ := + ∑ k ∈ Finset.range q, (μ.colLen k - d) / 2 + +def BandTest (M r : ℕ) (μ : YoungDiagram) : Prop := + ∃ d, 1 ≤ d ∧ d ≤ 4 ∧ ∃ q, q ≤ 8 ∧ + 2*M-1 ≤ rowPrefix μ d ∧ d*q+7+d ≤ 2*M-1 ∧ r ≤ bandCapacity μ d q + +lemma capacity_floor_bound (x f : ℕ) : x ≤ 2*((x-f)/2)+f+1 := by omega + +lemma prefix_le_capacity (μ : YoungDiagram) (d q : ℕ) : + colPrefix μ q ≤ 2*bandCapacity μ d q + q*(d+1) := by + rw [colPrefix_eq_sum, bandCapacity] + have h := Finset.sum_le_sum (s := Finset.range q) + (fun k _ => capacity_floor_bound (μ.colLen k) d) + simpa only [Finset.sum_add_distrib, ← Finset.mul_sum, + Finset.sum_const, Finset.card_range, smul_eq_mul, Nat.mul_add, Nat.mul_one, + Nat.add_assoc] using h + +lemma capacity_large_numeric (M r n : ℕ) (hM : 22 ≤ M) (hr : 2*r ≤ 3*M+4) + (hn : 2*n = M*(M+1)+4*r) : + 2*(2*r+38) < n ∧ (2*r+38)*(2*r+38) < 64*n := by + have hM2 := Nat.mul_le_mul_left M hM + have hr2 := Nat.mul_le_mul hr hr + constructor <;> nlinarith + +theorem capacity_large (μ : YoungDiagram) (M r : ℕ) (hM : 22 ≤ M) + (hr : 2*r ≤ 3*M+4) + (hn : μ.card = (staircase M).card + 2*r) + (hH : 2*M-1 ≤ colPrefix μ 4) (hW : 2*M-1 ≤ rowPrefix μ 4) : + BandTest M r μ ∨ BandTest M r μ.transpose := by + classical + by_contra hh + push Not at hh + have ha : (4:ℕ)*8+7+4 ≤ 2*M-1 := by omega + have hc : bandCapacity μ 4 8 < r := by + by_contra hc + exact hh.1 ⟨4, by omega, by omega, 8, by omega, hW, ha, by omega⟩ + have hct : bandCapacity μ.transpose 4 8 < r := by + by_contra hc + exact hh.2 ⟨4, by omega, by omega, 8, by omega, hH, ha, by omega⟩ + have h₁ : colPrefix μ 8 ≤ 2*r+38 := by + have := prefix_le_capacity μ 4 8 + omega + have h₂ : rowPrefix μ 8 ≤ 2*r+38 := by + have hp := prefix_le_capacity μ.transpose 4 8 + simp only [colPrefix, YoungDiagram.transpose_transpose] at hp + omega + have hb := capacity_rectangle μ (by omega : 0 < 8) (by omega : 0 < 8) h₁ h₂ + have he : 2*μ.card = M*(M+1)+4*r := by + have hx := staircase_card_double M + nlinarith + obtain ⟨hl,hu⟩ := capacity_large_numeric M r μ.card hM hr he + have hdiv : (2*r+38)*(2*r+38)/(8*8) < μ.card := by + exact (Nat.div_lt_iff_lt_mul (by norm_num)).mpr (by nlinarith) + have hmax : max (2*r+38+(2*r+38)-1) ((2*r+38)*(2*r+38)/(8*8)) < μ.card := + max_lt (by omega) hdiv + omega + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/CapacityDichotomy.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/CapacityDichotomy.lean index db5346137b672ac896caa1ae59876835925022f6..cf4720e8bbf34110e42e8da469693b575ab332f9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/CapacityDichotomy.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/CapacityDichotomy.lean @@ -1,59 +1,59 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Capacity.Intermediate - -namespace OAI - -/-! Capacity Dichotomy. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -theorem capacity_dichotomy (μ : YoungDiagram) {M r : ℕ} - (hM : 9 ≤ M) (hr : 0 < r) - (hbound : if M % 2 = 1 then 2*r ≤ M-1 else 2*r ≤ 3*M+4) - (hexc : ¬exceptionalPair M r) - (hn : μ.card = (staircase M).card + 2*r) : - colPrefix μ 4 ≤ 2*M-2 ∨ colPrefix μ.transpose 4 ≤ 2*M-2 ∨ - BandTest M r μ ∨ BandTest M r μ.transpose := by - by_cases hs : colPrefix μ 4 ≤ 2*M-2 - · exact Or.inl hs - apply Or.inr - by_cases ht : colPrefix μ.transpose 4 ≤ 2*M-2 - · exact Or.inl ht - apply Or.inr - have hH : 2*M-1 ≤ colPrefix μ 4 := by omega - have hW : 2*M-1 ≤ rowPrefix μ 4 := by - simp only [colPrefix, YoungDiagram.transpose_transpose] at ht - omega - by_cases hlarge : 22 ≤ M - · apply capacity_large μ M r hlarge _ hn hH hW - split_ifs at hbound <;> omega - · exact capacity_intermediate μ hM (by omega) ⟨hr,hbound,hexc⟩ hn hH hW - -theorem fixed_degree_capacity_dichotomy (n : ℕ) (hn : 64 < n) - (hr : 0 < remainderPairs n) - (hexc : ¬exceptionalPair (staircaseIndex n) (remainderPairs n)) - (μ : YoungDiagram) (hμ : μ.card = n) : - colPrefix μ 4 ≤ 2*staircaseIndex n-2 ∨ - colPrefix μ.transpose 4 ≤ 2*staircaseIndex n-2 ∨ - BandTest (staircaseIndex n) (remainderPairs n) μ ∨ - BandTest (staircaseIndex n) (remainderPairs n) μ.transpose := by - have hM : 9 ≤ staircaseIndex n := by - by_contra h - have := degree_le_64_of_small_index n (by omega) - omega - apply capacity_dichotomy μ hM hr _ hexc - (hμ.trans (degree_eq n).symm) - split_ifs with ho - · exact remainderPairs_bound_odd n ho - · exact remainderPairs_bound_even n (by omega) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Capacity.Intermediate + +namespace OAI + +/-! Capacity Dichotomy. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +theorem capacity_dichotomy (μ : YoungDiagram) {M r : ℕ} + (hM : 9 ≤ M) (hr : 0 < r) + (hbound : if M % 2 = 1 then 2*r ≤ M-1 else 2*r ≤ 3*M+4) + (hexc : ¬exceptionalPair M r) + (hn : μ.card = (staircase M).card + 2*r) : + colPrefix μ 4 ≤ 2*M-2 ∨ colPrefix μ.transpose 4 ≤ 2*M-2 ∨ + BandTest M r μ ∨ BandTest M r μ.transpose := by + by_cases hs : colPrefix μ 4 ≤ 2*M-2 + · exact Or.inl hs + apply Or.inr + by_cases ht : colPrefix μ.transpose 4 ≤ 2*M-2 + · exact Or.inl ht + apply Or.inr + have hH : 2*M-1 ≤ colPrefix μ 4 := by omega + have hW : 2*M-1 ≤ rowPrefix μ 4 := by + simp only [colPrefix, YoungDiagram.transpose_transpose] at ht + omega + by_cases hlarge : 22 ≤ M + · apply capacity_large μ M r hlarge _ hn hH hW + split_ifs at hbound <;> omega + · exact capacity_intermediate μ hM (by omega) ⟨hr,hbound,hexc⟩ hn hH hW + +theorem fixed_degree_capacity_dichotomy (n : ℕ) (hn : 64 < n) + (hr : 0 < remainderPairs n) + (hexc : ¬exceptionalPair (staircaseIndex n) (remainderPairs n)) + (μ : YoungDiagram) (hμ : μ.card = n) : + colPrefix μ 4 ≤ 2*staircaseIndex n-2 ∨ + colPrefix μ.transpose 4 ≤ 2*staircaseIndex n-2 ∨ + BandTest (staircaseIndex n) (remainderPairs n) μ ∨ + BandTest (staircaseIndex n) (remainderPairs n) μ.transpose := by + have hM : 9 ≤ staircaseIndex n := by + by_contra h + have := degree_le_64_of_small_index n (by omega) + omega + apply capacity_dichotomy μ hM hr _ hexc + (hμ.trans (degree_eq n).symm) + split_ifs with ho + · exact remainderPairs_bound_odd n ho + · exact remainderPairs_bound_even n (by omega) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/Intermediate.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/Intermediate.lean index 8385b8f01e49552b3d205221ff0b19c81c7ffc53..d8e6c81f58d95ed7360ea3d19b8a0b53ad78b17c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/Intermediate.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/Intermediate.lean @@ -1,191 +1,191 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Band.BandCriterion - -namespace OAI - -/-! Intermediate. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -def testWidth (M f : ℕ) : ℕ := min 8 ((2*M-8-f)/f) - -lemma testWidth_valid {M f : ℕ} (hM : 9 ≤ M) (hf : 1 ≤ f) (hf' : f ≤ 4) : - testWidth M f ≤ 8 ∧ f * testWidth M f + 7 + f ≤ 2*M-1 := by - refine ⟨min_le_left _ _, ?_⟩ - have h := Nat.mul_le_mul_left f (min_le_right 8 ((2*M-8-f)/f)) - have h' := Nat.div_mul_le_self (2*M-8-f) f - unfold testWidth - nlinarith [Nat.sub_add_cancel (show f ≤ 2*M-8 by omega), - Nat.sub_add_cancel (show 8 ≤ 2*M by omega), - Nat.sub_add_cancel (show 1 ≤ 2*M by omega)] - -def prefixBounds (M r d e : ℕ) : List (ℕ × ℕ) := - (if 1 < d then [(d-1,2*M-2)] else []) ++ - ((List.range 4).filterMap fun k => - let f := k+1 - let q := testWidth M f - if e ≤ f ∧ 0 < q then some (q,2*r-2+q*(f+1)) else none) - -lemma prefixBounds_sound (μ : YoungDiagram) {M r d e : ℕ} - (hM : 9 ≤ M) (hr : 0 < r) - (hd : 1 < d → colPrefix μ (d-1) < 2*M-1) - (he : 2*M-1 ≤ rowPrefix μ e) (hfail : ¬BandTest M r μ) : - ∀ p ∈ prefixBounds M r d e, 0 < p.1 ∧ colPrefix μ p.1 ≤ p.2 := by - intro p hp - simp only [prefixBounds, List.mem_append] at hp - rcases hp with hp | hp - · split_ifs at hp with hd' - · simp only [List.mem_cons, List.not_mem_nil, or_false] at hp - subst p - exact ⟨by omega, by have := hd hd'; dsimp; omega⟩ - · simp at hp - · obtain ⟨k,hk,hkp⟩ := List.mem_filterMap.mp hp - simp only [List.mem_range] at hk - split_ifs at hkp with hke - · have hp' := Option.some.inj hkp - subst p - have hw := testWidth_valid hM (by omega : 1 ≤ k+1) (by omega : k+1 ≤ 4) - have hc : bandCapacity μ (k+1) (testWidth M (k+1)) < r := by - by_contra hh - apply hfail - exact ⟨k+1, by omega, by omega, testWidth M (k+1), hw.1, - he.trans (rowPrefix_mono μ hke.1), hw.2, by omega⟩ - have hb := prefix_le_capacity μ (k+1) (testWidth M (k+1)) - exact ⟨hke.2, by dsimp; omega⟩ - -def exceptionalPair (M r : ℕ) : Prop := - (M = 10 ∧ 8 ≤ r ∧ r ≤ 17) ∨ (M = 12 ∧ 14 ≤ r ∧ r ≤ 20) ∨ - (M = 14 ∧ 22 ≤ r ∧ r ≤ 23) - -instance (M r : ℕ) : Decidable (exceptionalPair M r) := inferInstanceAs - (Decidable ((M = 10 ∧ 8 ≤ r ∧ r ≤ 17) ∨ (M = 12 ∧ 14 ≤ r ∧ r ≤ 20) ∨ - (M = 14 ∧ 22 ≤ r ∧ r ≤ 23))) - -def admissibleR (M r : ℕ) : Prop := 0 < r ∧ - (if M % 2 = 1 then 2*r ≤ M-1 else 2*r ≤ 3*M+4) ∧ ¬exceptionalPair M r - -instance (M r : ℕ) : Decidable (admissibleR M r) := inferInstanceAs - (Decidable (0 < r ∧ (if M % 2 = 1 then 2*r ≤ M-1 else 2*r ≤ 3*M+4) ∧ - ¬exceptionalPair M r)) - -def intermediateCheck (M r d e : ℕ) : Prop := - ∃ p ∈ prefixBounds M r d e, ∃ q ∈ prefixBounds M r e d, - max (p.2+q.2-1) (p.2*q.2/(p.1*q.1)) < M*(M+1)/2+2*r - -instance (M r d e : ℕ) : Decidable (intermediateCheck M r d e) := - inferInstanceAs (Decidable (∃ p ∈ prefixBounds M r d e, - ∃ q ∈ prefixBounds M r e d, - max (p.2+q.2-1) (p.2*q.2/(p.1*q.1)) < M*(M+1)/2+2*r)) - -lemma intermediate9 : ∀ r ∈ List.range 34, admissibleR 9 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 9 r (d+1) (e+1) := by decide - -lemma intermediate10 : ∀ r ∈ List.range 34, admissibleR 10 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 10 r (d+1) (e+1) := by decide - -lemma intermediate11 : ∀ r ∈ List.range 34, admissibleR 11 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 11 r (d+1) (e+1) := by decide - -lemma intermediate12 : ∀ r ∈ List.range 34, admissibleR 12 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 12 r (d+1) (e+1) := by decide - -lemma intermediate13 : ∀ r ∈ List.range 34, admissibleR 13 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 13 r (d+1) (e+1) := by decide - -lemma intermediate14 : ∀ r ∈ List.range 34, admissibleR 14 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 14 r (d+1) (e+1) := by decide - -lemma intermediate15 : ∀ r ∈ List.range 34, admissibleR 15 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 15 r (d+1) (e+1) := by decide - -lemma intermediate16 : ∀ r ∈ List.range 34, admissibleR 16 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 16 r (d+1) (e+1) := by decide - -lemma intermediate17 : ∀ r ∈ List.range 34, admissibleR 17 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 17 r (d+1) (e+1) := by decide - -lemma intermediate18 : ∀ r ∈ List.range 34, admissibleR 18 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 18 r (d+1) (e+1) := by decide - -lemma intermediate19 : ∀ r ∈ List.range 34, admissibleR 19 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 19 r (d+1) (e+1) := by decide - -lemma intermediate20 : ∀ r ∈ List.range 34, admissibleR 20 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 20 r (d+1) (e+1) := by decide - -lemma intermediate21 : ∀ r ∈ List.range 34, admissibleR 21 r → - ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 21 r (d+1) (e+1) := by decide - -lemma capacity_intermediate_numeric {M r d e : ℕ} - (hM : 9 ≤ M) (hM' : M ≤ 21) (hr : admissibleR M r) - (hd : 1 ≤ d) (hd' : d ≤ 4) (he : 1 ≤ e) (he' : e ≤ 4) : - intermediateCheck M r d e := by - have hr' : r ∈ List.range 34 := by - have hb := hr.2.1 - split_ifs at hb <;> simp only [List.mem_range] <;> omega - have hdd : d-1 ∈ List.range 4 := by simp only [List.mem_range]; omega - have hee : e-1 ∈ List.range 4 := by simp only [List.mem_range]; omega - have hde : d = (d-1)+1 := by omega - have hee' : e = (e-1)+1 := by omega - rw [hde, hee'] - interval_cases M - · exact intermediate9 r hr' hr _ hdd _ hee - · exact intermediate10 r hr' hr _ hdd _ hee - · exact intermediate11 r hr' hr _ hdd _ hee - · exact intermediate12 r hr' hr _ hdd _ hee - · exact intermediate13 r hr' hr _ hdd _ hee - · exact intermediate14 r hr' hr _ hdd _ hee - · exact intermediate15 r hr' hr _ hdd _ hee - · exact intermediate16 r hr' hr _ hdd _ hee - · exact intermediate17 r hr' hr _ hdd _ hee - · exact intermediate18 r hr' hr _ hdd _ hee - · exact intermediate19 r hr' hr _ hdd _ hee - · exact intermediate20 r hr' hr _ hdd _ hee - · exact intermediate21 r hr' hr _ hdd _ hee - -lemma first_prefix_height (μ : YoungDiagram) {K : ℕ} (hK : 0 < K) - (h : K ≤ rowPrefix μ 4) : - ∃ d, 1 ≤ d ∧ d ≤ 4 ∧ K ≤ rowPrefix μ d ∧ - (1 < d → rowPrefix μ (d-1) < K) := by - let h' : ∃ d, K ≤ rowPrefix μ d := ⟨4,h⟩ - refine ⟨Nat.find h', ?_, Nat.find_min' h' h, Nat.find_spec h', ?_⟩ - · have hx := Nat.find_spec h' - by_contra hh - have hd : Nat.find h' = 0 := by omega - change K ≤ rowPrefix μ (Nat.find h') at hx - rw [hd] at hx - simp only [rowPrefix, Finset.range_zero, Finset.sum_empty] at hx - omega - · intro hd - exact Nat.lt_of_not_ge (Nat.find_min h' (by omega)) - -theorem capacity_intermediate (μ : YoungDiagram) {M r : ℕ} - (hM : 9 ≤ M) (hM' : M ≤ 21) (hr : admissibleR M r) - (hn : μ.card = (staircase M).card + 2*r) - (hH : 2*M-1 ≤ colPrefix μ 4) (hW : 2*M-1 ≤ rowPrefix μ 4) : - BandTest M r μ ∨ BandTest M r μ.transpose := by - classical - by_contra hh - push Not at hh - obtain ⟨d,hd,hd',hHd,hHd'⟩ := first_prefix_height μ.transpose (by omega) hH - obtain ⟨e,he,he',hWe,hWe'⟩ := first_prefix_height μ (by omega) hW - obtain ⟨p,hp,q,hq,hpq⟩ := capacity_intermediate_numeric hM hM' hr hd hd' he he' - have hp' := prefixBounds_sound μ hM hr.1 hHd' hWe hh.1 p hp - have hq' := prefixBounds_sound μ.transpose hM hr.1 - (by simpa only [colPrefix, YoungDiagram.transpose_transpose] using hWe') - hHd hh.2 q hq - have hb := capacity_rectangle μ hp'.1 hq'.1 hp'.2 - (by simpa only [colPrefix, YoungDiagram.transpose_transpose] using hq'.2) - have hn' : μ.card = M*(M+1)/2+2*r := by rw [hn, staircase_card] - omega - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Band.BandCriterion + +namespace OAI + +/-! Intermediate. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +def testWidth (M f : ℕ) : ℕ := min 8 ((2*M-8-f)/f) + +lemma testWidth_valid {M f : ℕ} (hM : 9 ≤ M) (hf : 1 ≤ f) (hf' : f ≤ 4) : + testWidth M f ≤ 8 ∧ f * testWidth M f + 7 + f ≤ 2*M-1 := by + refine ⟨min_le_left _ _, ?_⟩ + have h := Nat.mul_le_mul_left f (min_le_right 8 ((2*M-8-f)/f)) + have h' := Nat.div_mul_le_self (2*M-8-f) f + unfold testWidth + nlinarith [Nat.sub_add_cancel (show f ≤ 2*M-8 by omega), + Nat.sub_add_cancel (show 8 ≤ 2*M by omega), + Nat.sub_add_cancel (show 1 ≤ 2*M by omega)] + +def prefixBounds (M r d e : ℕ) : List (ℕ × ℕ) := + (if 1 < d then [(d-1,2*M-2)] else []) ++ + ((List.range 4).filterMap fun k => + let f := k+1 + let q := testWidth M f + if e ≤ f ∧ 0 < q then some (q,2*r-2+q*(f+1)) else none) + +lemma prefixBounds_sound (μ : YoungDiagram) {M r d e : ℕ} + (hM : 9 ≤ M) (hr : 0 < r) + (hd : 1 < d → colPrefix μ (d-1) < 2*M-1) + (he : 2*M-1 ≤ rowPrefix μ e) (hfail : ¬BandTest M r μ) : + ∀ p ∈ prefixBounds M r d e, 0 < p.1 ∧ colPrefix μ p.1 ≤ p.2 := by + intro p hp + simp only [prefixBounds, List.mem_append] at hp + rcases hp with hp | hp + · split_ifs at hp with hd' + · simp only [List.mem_cons, List.not_mem_nil, or_false] at hp + subst p + exact ⟨by omega, by have := hd hd'; dsimp; omega⟩ + · simp at hp + · obtain ⟨k,hk,hkp⟩ := List.mem_filterMap.mp hp + simp only [List.mem_range] at hk + split_ifs at hkp with hke + · have hp' := Option.some.inj hkp + subst p + have hw := testWidth_valid hM (by omega : 1 ≤ k+1) (by omega : k+1 ≤ 4) + have hc : bandCapacity μ (k+1) (testWidth M (k+1)) < r := by + by_contra hh + apply hfail + exact ⟨k+1, by omega, by omega, testWidth M (k+1), hw.1, + he.trans (rowPrefix_mono μ hke.1), hw.2, by omega⟩ + have hb := prefix_le_capacity μ (k+1) (testWidth M (k+1)) + exact ⟨hke.2, by dsimp; omega⟩ + +def exceptionalPair (M r : ℕ) : Prop := + (M = 10 ∧ 8 ≤ r ∧ r ≤ 17) ∨ (M = 12 ∧ 14 ≤ r ∧ r ≤ 20) ∨ + (M = 14 ∧ 22 ≤ r ∧ r ≤ 23) + +instance (M r : ℕ) : Decidable (exceptionalPair M r) := inferInstanceAs + (Decidable ((M = 10 ∧ 8 ≤ r ∧ r ≤ 17) ∨ (M = 12 ∧ 14 ≤ r ∧ r ≤ 20) ∨ + (M = 14 ∧ 22 ≤ r ∧ r ≤ 23))) + +def admissibleR (M r : ℕ) : Prop := 0 < r ∧ + (if M % 2 = 1 then 2*r ≤ M-1 else 2*r ≤ 3*M+4) ∧ ¬exceptionalPair M r + +instance (M r : ℕ) : Decidable (admissibleR M r) := inferInstanceAs + (Decidable (0 < r ∧ (if M % 2 = 1 then 2*r ≤ M-1 else 2*r ≤ 3*M+4) ∧ + ¬exceptionalPair M r)) + +def intermediateCheck (M r d e : ℕ) : Prop := + ∃ p ∈ prefixBounds M r d e, ∃ q ∈ prefixBounds M r e d, + max (p.2+q.2-1) (p.2*q.2/(p.1*q.1)) < M*(M+1)/2+2*r + +instance (M r d e : ℕ) : Decidable (intermediateCheck M r d e) := + inferInstanceAs (Decidable (∃ p ∈ prefixBounds M r d e, + ∃ q ∈ prefixBounds M r e d, + max (p.2+q.2-1) (p.2*q.2/(p.1*q.1)) < M*(M+1)/2+2*r)) + +lemma intermediate9 : ∀ r ∈ List.range 34, admissibleR 9 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 9 r (d+1) (e+1) := by decide + +lemma intermediate10 : ∀ r ∈ List.range 34, admissibleR 10 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 10 r (d+1) (e+1) := by decide + +lemma intermediate11 : ∀ r ∈ List.range 34, admissibleR 11 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 11 r (d+1) (e+1) := by decide + +lemma intermediate12 : ∀ r ∈ List.range 34, admissibleR 12 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 12 r (d+1) (e+1) := by decide + +lemma intermediate13 : ∀ r ∈ List.range 34, admissibleR 13 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 13 r (d+1) (e+1) := by decide + +lemma intermediate14 : ∀ r ∈ List.range 34, admissibleR 14 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 14 r (d+1) (e+1) := by decide + +lemma intermediate15 : ∀ r ∈ List.range 34, admissibleR 15 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 15 r (d+1) (e+1) := by decide + +lemma intermediate16 : ∀ r ∈ List.range 34, admissibleR 16 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 16 r (d+1) (e+1) := by decide + +lemma intermediate17 : ∀ r ∈ List.range 34, admissibleR 17 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 17 r (d+1) (e+1) := by decide + +lemma intermediate18 : ∀ r ∈ List.range 34, admissibleR 18 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 18 r (d+1) (e+1) := by decide + +lemma intermediate19 : ∀ r ∈ List.range 34, admissibleR 19 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 19 r (d+1) (e+1) := by decide + +lemma intermediate20 : ∀ r ∈ List.range 34, admissibleR 20 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 20 r (d+1) (e+1) := by decide + +lemma intermediate21 : ∀ r ∈ List.range 34, admissibleR 21 r → + ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, intermediateCheck 21 r (d+1) (e+1) := by decide + +lemma capacity_intermediate_numeric {M r d e : ℕ} + (hM : 9 ≤ M) (hM' : M ≤ 21) (hr : admissibleR M r) + (hd : 1 ≤ d) (hd' : d ≤ 4) (he : 1 ≤ e) (he' : e ≤ 4) : + intermediateCheck M r d e := by + have hr' : r ∈ List.range 34 := by + have hb := hr.2.1 + split_ifs at hb <;> simp only [List.mem_range] <;> omega + have hdd : d-1 ∈ List.range 4 := by simp only [List.mem_range]; omega + have hee : e-1 ∈ List.range 4 := by simp only [List.mem_range]; omega + have hde : d = (d-1)+1 := by omega + have hee' : e = (e-1)+1 := by omega + rw [hde, hee'] + interval_cases M + · exact intermediate9 r hr' hr _ hdd _ hee + · exact intermediate10 r hr' hr _ hdd _ hee + · exact intermediate11 r hr' hr _ hdd _ hee + · exact intermediate12 r hr' hr _ hdd _ hee + · exact intermediate13 r hr' hr _ hdd _ hee + · exact intermediate14 r hr' hr _ hdd _ hee + · exact intermediate15 r hr' hr _ hdd _ hee + · exact intermediate16 r hr' hr _ hdd _ hee + · exact intermediate17 r hr' hr _ hdd _ hee + · exact intermediate18 r hr' hr _ hdd _ hee + · exact intermediate19 r hr' hr _ hdd _ hee + · exact intermediate20 r hr' hr _ hdd _ hee + · exact intermediate21 r hr' hr _ hdd _ hee + +lemma first_prefix_height (μ : YoungDiagram) {K : ℕ} (hK : 0 < K) + (h : K ≤ rowPrefix μ 4) : + ∃ d, 1 ≤ d ∧ d ≤ 4 ∧ K ≤ rowPrefix μ d ∧ + (1 < d → rowPrefix μ (d-1) < K) := by + let h' : ∃ d, K ≤ rowPrefix μ d := ⟨4,h⟩ + refine ⟨Nat.find h', ?_, Nat.find_min' h' h, Nat.find_spec h', ?_⟩ + · have hx := Nat.find_spec h' + by_contra hh + have hd : Nat.find h' = 0 := by omega + change K ≤ rowPrefix μ (Nat.find h') at hx + rw [hd] at hx + simp only [rowPrefix, Finset.range_zero, Finset.sum_empty] at hx + omega + · intro hd + exact Nat.lt_of_not_ge (Nat.find_min h' (by omega)) + +theorem capacity_intermediate (μ : YoungDiagram) {M r : ℕ} + (hM : 9 ≤ M) (hM' : M ≤ 21) (hr : admissibleR M r) + (hn : μ.card = (staircase M).card + 2*r) + (hH : 2*M-1 ≤ colPrefix μ 4) (hW : 2*M-1 ≤ rowPrefix μ 4) : + BandTest M r μ ∨ BandTest M r μ.transpose := by + classical + by_contra hh + push Not at hh + obtain ⟨d,hd,hd',hHd,hHd'⟩ := first_prefix_height μ.transpose (by omega) hH + obtain ⟨e,he,he',hWe,hWe'⟩ := first_prefix_height μ (by omega) hW + obtain ⟨p,hp,q,hq,hpq⟩ := capacity_intermediate_numeric hM hM' hr hd hd' he he' + have hp' := prefixBounds_sound μ hM hr.1 hHd' hWe hh.1 p hp + have hq' := prefixBounds_sound μ.transpose hM hr.1 + (by simpa only [colPrefix, YoungDiagram.transpose_transpose] using hWe') + hHd hh.2 q hq + have hb := capacity_rectangle μ hp'.1 hq'.1 hp'.2 + (by simpa only [colPrefix, YoungDiagram.transpose_transpose] using hq'.2) + have hn' : μ.card = M*(M+1)/2+2*r := by rw [hn, staircase_card] + omega + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/NumericBands.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/NumericBands.lean index 77fabd05cc5d34dbfb7571d6a8a9f5a8fa37b14d..3f1262527d21c89f824c0c88219979a641633b8a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/NumericBands.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/NumericBands.lean @@ -1,70 +1,70 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Band.OutputBands -import OAI.RepresentationTheory.UniversalSquare.Capacity.RefinedExhaustion - -namespace OAI - -/-! Numeric Bands. -/ - -section - -noncomputable section -namespace Saxl.Balance - -def BandsValid (es : List (ℕ × ℕ)) : Prop := - (∀ e ∈ es, e.1 ≤ e.2) ∧ ∀ e ∈ es, ∀ f ∈ es, - (e.1 = f.1 → e.2 = f.2) ∧ (e.1 < f.1 → e.2 < f.1) - -instance (es : List (ℕ × ℕ)) : Decidable (BandsValid es) := by - unfold BandsValid - infer_instance - -def bandStarts (es : List (ℕ × ℕ)) : Finset ℕ := (es.map Prod.fst).toFinset - -def bandUpper (es : List (ℕ × ℕ)) (k : ℕ) : ℕ := - es.toFinset.sup (fun e => if e.1 = k then e.2 else 0) - -lemma bandUpper_eq {es : List (ℕ × ℕ)} (h : BandsValid es) {e : ℕ × ℕ} - (he : e ∈ es) : bandUpper es e.1 = e.2 := by - apply le_antisymm - · apply Finset.sup_le - intro f hf - by_cases hf' : f.1 = e.1 - · simp only [ite_eq_left hf'] - exact ((h.2 f (List.mem_toFinset.mp hf) e he).1 hf').le - · simp only [ite_eq_right hf']; exact Nat.zero_le _ - · have hh := Finset.le_sup (f := fun f : ℕ × ℕ => if f.1 = e.1 then f.2 else 0) - (List.mem_toFinset.mpr he) - simpa only [bandUpper, ite_true] using hh - -lemma mem_bandStarts {es : List (ℕ × ℕ)} {k : ℕ} : - k ∈ bandStarts es ↔ ∃ e ∈ es, e.1 = k := by simp [bandStarts] - -def numericBands (es : List (ℕ × ℕ)) (h : BandsValid es) : OutputBands where - starts := bandStarts es - upper := bandUpper es - nonempty := by - intro k hk - obtain ⟨e,he,rfl⟩ := mem_bandStarts.mp hk - rw [bandUpper_eq h he] - exact h.1 e he - separated := by - intro k hk l hl hkl - obtain ⟨e,he,rfl⟩ := mem_bandStarts.mp hk - obtain ⟨f,hf,rfl⟩ := mem_bandStarts.mp hl - rw [bandUpper_eq h he] - exact (h.2 e he f hf).2 hkl - -lemma numericBands_iff {es : List (ℕ × ℕ)} (h : BandsValid es) {e : ℕ × ℕ} - (he : e ∈ es) {d : ℕ} (z : Fin (d*d)) : - ((numericBands es h).alphabet d z ∧ (numericBands es h).letterLabel d z = e.1) ↔ - output z ∈ Set.Icc e.1 e.2 := by - rw [(numericBands es h).letter_iff (mem_bandStarts.mpr ⟨e,he,rfl⟩)] - rw [show (numericBands es h).upper e.1 = e.2 from bandUpper_eq h he] - -end Saxl.Balance -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Band.OutputBands +import OAI.RepresentationTheory.UniversalSquare.Capacity.RefinedExhaustion + +namespace OAI + +/-! Numeric Bands. -/ + +section + +noncomputable section +namespace Saxl.Balance + +def BandsValid (es : List (ℕ × ℕ)) : Prop := + (∀ e ∈ es, e.1 ≤ e.2) ∧ ∀ e ∈ es, ∀ f ∈ es, + (e.1 = f.1 → e.2 = f.2) ∧ (e.1 < f.1 → e.2 < f.1) + +instance (es : List (ℕ × ℕ)) : Decidable (BandsValid es) := by + unfold BandsValid + infer_instance + +def bandStarts (es : List (ℕ × ℕ)) : Finset ℕ := (es.map Prod.fst).toFinset + +def bandUpper (es : List (ℕ × ℕ)) (k : ℕ) : ℕ := + es.toFinset.sup (fun e => if e.1 = k then e.2 else 0) + +lemma bandUpper_eq {es : List (ℕ × ℕ)} (h : BandsValid es) {e : ℕ × ℕ} + (he : e ∈ es) : bandUpper es e.1 = e.2 := by + apply le_antisymm + · apply Finset.sup_le + intro f hf + by_cases hf' : f.1 = e.1 + · simp only [ite_eq_left hf'] + exact ((h.2 f (List.mem_toFinset.mp hf) e he).1 hf').le + · simp only [ite_eq_right hf']; exact Nat.zero_le _ + · have hh := Finset.le_sup (f := fun f : ℕ × ℕ => if f.1 = e.1 then f.2 else 0) + (List.mem_toFinset.mpr he) + simpa only [bandUpper, ite_true] using hh + +lemma mem_bandStarts {es : List (ℕ × ℕ)} {k : ℕ} : + k ∈ bandStarts es ↔ ∃ e ∈ es, e.1 = k := by simp [bandStarts] + +def numericBands (es : List (ℕ × ℕ)) (h : BandsValid es) : OutputBands where + starts := bandStarts es + upper := bandUpper es + nonempty := by + intro k hk + obtain ⟨e,he,rfl⟩ := mem_bandStarts.mp hk + rw [bandUpper_eq h he] + exact h.1 e he + separated := by + intro k hk l hl hkl + obtain ⟨e,he,rfl⟩ := mem_bandStarts.mp hk + obtain ⟨f,hf,rfl⟩ := mem_bandStarts.mp hl + rw [bandUpper_eq h he] + exact (h.2 e he f hf).2 hkl + +lemma numericBands_iff {es : List (ℕ × ℕ)} (h : BandsValid es) {e : ℕ × ℕ} + (he : e ∈ es) {d : ℕ} (z : Fin (d*d)) : + ((numericBands es h).alphabet d z ∧ (numericBands es h).letterLabel d z = e.1) ↔ + output z ∈ Set.Icc e.1 e.2 := by + rw [(numericBands es h).letter_iff (mem_bandStarts.mpr ⟨e,he,rfl⟩)] + rw [show (numericBands es h).upper e.1 = e.2 from bandUpper_eq h he] + +end Saxl.Balance +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/RefinedCapacity.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/RefinedCapacity.lean index 4f94d76b9d420b4221cffc9f01f56219314090c3..f726266b85c2a10f124afc4898e10bfffe7074d6 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/RefinedCapacity.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/RefinedCapacity.lean @@ -1,146 +1,146 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Capacity.Intermediate - -namespace OAI - -/-! Refined Capacity. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -lemma prefix_last_after_first (μ : YoungDiagram) {j : ℕ} (hj : 0 < j) : - μ.rowLen 0 + (j-1)*μ.rowLen (j-1) ≤ rowPrefix μ j := by - have he : j = (j-1)+1 := by omega - unfold rowPrefix - conv_rhs => rw [he, Finset.sum_range_succ'] - have hh := Finset.sum_le_sum (s := Finset.range (j-1)) - (f := fun _ => μ.rowLen (j-1)) (g := fun a => μ.rowLen (a+1)) (by - intro a ha - exact μ.rowLen_anti _ _ (by have := Finset.mem_range.mp ha; omega)) - simp only [Finset.sum_const, Finset.card_range, smul_eq_mul] at hh - omega - -def endpointBound (i U H : ℕ) : ℕ := - if i = 1 then U else min (U/i) ((U-H)/(i-1)) - -lemma endpointBound_sound (μ : YoungDiagram) {i U H : ℕ} (hi : 0 < i) - (hU : rowPrefix μ i ≤ U) (hH : H ≤ μ.rowLen 0) : - μ.rowLen (i-1) ≤ endpointBound i U H := by - unfold endpointBound - split_ifs with he - · subst i - simpa [rowPrefix] using hU - · apply le_min - · apply (Nat.le_div_iff_mul_le hi).mpr - simpa [Nat.mul_comm] using (prefix_last_mul_le μ hi).trans hU - · apply (Nat.le_div_iff_mul_le (by omega : 0 < i-1)).mpr - have h := prefix_last_after_first μ hi - have hx : (i-1)*μ.rowLen (i-1) ≤ U-H := by omega - simpa [Nat.mul_comm] using hx - -lemma prefix_intersection_hook (μ : YoungDiagram) {i j H W : ℕ} - (hi : 0 < i) (hj : 0 < j) (hH : H ≤ μ.colLen 0) (hW : W ≤ μ.rowLen 0) - (hHp : 0 < H) (hWp : 0 < W) : - min i W + min j H - 1 ≤ - ((rowTruncate μ j).cells ∩ (colTruncate μ i).cells).card := by - let A := (rectangle 1 (min i W)).cells - let B := (rectangle (min j H) 1).cells - have hA : A ⊆ (rowTruncate μ j).cells ∩ (colTruncate μ i).cells := by - rintro ⟨a,b⟩ hp - have hx : a < 1 ∧ b < min i W := mem_rectangle.mp hp - have ha : a = 0 := by omega - subst a - have hc : (0,b) ∈ μ := YoungDiagram.mem_iff_lt_rowLen.mpr (by omega) - simpa only [Finset.mem_inter,YoungDiagram.mem_cells,mem_rowTruncate,mem_colTruncate] - using And.intro ⟨hc,hj⟩ ⟨hc,lt_of_lt_of_le hx.2 (min_le_left _ _)⟩ - have hB : B ⊆ (rowTruncate μ j).cells ∩ (colTruncate μ i).cells := by - rintro ⟨a,b⟩ hp - have hx : a < min j H ∧ b < 1 := mem_rectangle.mp hp - have hb : b = 0 := by omega - subst b - have hc : (a,0) ∈ μ := YoungDiagram.mem_iff_lt_colLen.mpr (by omega) - simpa only [Finset.mem_inter,YoungDiagram.mem_cells,mem_rowTruncate,mem_colTruncate] - using And.intro ⟨hc,lt_of_lt_of_le hx.1 (min_le_left _ _)⟩ ⟨hc,hi⟩ - have hAB : A ∩ B = {(0,0)} := by - ext ⟨a,b⟩ - simp only [Finset.mem_inter,Finset.mem_singleton,Prod.mk.injEq] - simp only [A,B,rectangle,Finset.mem_product,Finset.mem_range] - omega - have he := Finset.card_union_add_card_inter A B - have ha : A.card = min i W := by simp [A,rectangle] - have hb : B.card = min j H := by simp [B,rectangle] - rw [hAB,Finset.card_singleton,ha,hb] at he - have h := Finset.card_le_card (Finset.union_subset hA hB) - omega - -def refinedArea (i j U V X Y H W : ℕ) : ℕ := - if j ≤ X ∧ i ≤ Y then - max (U+V-(min i W + min j H - 1)) (U+V-i*j+(X-j)*(Y-i)) - else U+V-(min i W + min j H - 1) - -lemma area_le_refined (μ : YoungDiagram) {i j U V X Y H W : ℕ} - (hi : 0 < i) (hj : 0 < j) (hU : colPrefix μ i ≤ U) (hV : rowPrefix μ j ≤ V) - (hX : μ.colLen (i-1) ≤ X) (hY : μ.rowLen (j-1) ≤ Y) - (hH : H ≤ μ.colLen 0) (hW : W ≤ μ.rowLen 0) (hHp : 0 < H) (hWp : 0 < W) : - μ.card ≤ refinedArea i j U V X Y H W := by - classical - have hid := strip_area_identity μ i j - have hh := prefix_intersection_hook μ hi hj hH hW hHp hWp - by_cases hcell : (j-1,i-1) ∈ μ - · have heq : (rowTruncate μ j).cells ∩ (colTruncate μ i).cells = - (rectangle j i).cells := by - ext ⟨a,b⟩ - simp only [Finset.mem_inter, YoungDiagram.mem_cells, mem_rowTruncate, - mem_colTruncate, mem_rectangle] - constructor - · tauto - · rintro ⟨ha,hb⟩ - have hx := μ.up_left_mem (by omega : a ≤ j-1) (by omega : b ≤ i-1) hcell - tauto - have hint : ((rowTruncate μ j).cells ∩ (colTruncate μ i).cells).card = j*i := by - rw [heq] - simp only [rectangle,Finset.card_product,Finset.card_range] - have hcor := Finset.card_le_card (corner_subset_rectangle μ hi hj) - simp only [Finset.card_product,Nat.card_Ico] at hcor - have hmul := Nat.mul_le_mul (Nat.sub_le_sub_right hX j) (Nat.sub_le_sub_right hY i) - have hx : j ≤ μ.colLen (i-1) := by - have := YoungDiagram.mem_iff_lt_colLen.mp hcell; omega - have hy : i ≤ μ.rowLen (j-1) := by - have := YoungDiagram.mem_iff_lt_rowLen.mp hcell; omega - rw [hint] at hid - have hup : i*j ≤ U+V := by - have ht := prefix_last_mul_le μ.transpose hi - simp only [YoungDiagram.rowLen_transpose] at ht - change i * μ.colLen (i-1) ≤ colPrefix μ i at ht - nlinarith - have hsub := Nat.sub_add_cancel hup - have ha : μ.card ≤ U+V-i*j+(X-j)*(Y-i) := by - rw [Nat.mul_comm j i] at hid - omega - unfold refinedArea - rw [ite_eq_left ⟨hx.trans hX,hy.trans hY⟩] - exact ha.trans (le_max_right _ _) - · have hz : μ.cells \ ((rowTruncate μ j).cells ∪ (colTruncate μ i).cells) = ∅ := by - apply Finset.eq_empty_iff_forall_notMem.mpr - rintro ⟨a,b⟩ hp - simp only [Finset.mem_sdiff,Finset.mem_union,YoungDiagram.mem_cells, - mem_rowTruncate,mem_colTruncate,not_or] at hp - have ha : j ≤ a := Nat.le_of_not_gt fun ha => hp.2.1 ⟨hp.1,ha⟩ - have hb : i ≤ b := Nat.le_of_not_gt fun hb => hp.2.2 ⟨hp.1,hb⟩ - exact hcell (μ.up_left_mem (by omega) (by omega) hp.1) - rw [hz,Finset.card_empty,add_zero] at hid - have ha : μ.card ≤ U+V-(min i W+min j H-1) := by omega - unfold refinedArea - split_ifs - · exact ha.trans (le_max_left _ _) - · exact ha - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Capacity.Intermediate + +namespace OAI + +/-! Refined Capacity. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +lemma prefix_last_after_first (μ : YoungDiagram) {j : ℕ} (hj : 0 < j) : + μ.rowLen 0 + (j-1)*μ.rowLen (j-1) ≤ rowPrefix μ j := by + have he : j = (j-1)+1 := by omega + unfold rowPrefix + conv_rhs => rw [he, Finset.sum_range_succ'] + have hh := Finset.sum_le_sum (s := Finset.range (j-1)) + (f := fun _ => μ.rowLen (j-1)) (g := fun a => μ.rowLen (a+1)) (by + intro a ha + exact μ.rowLen_anti _ _ (by have := Finset.mem_range.mp ha; omega)) + simp only [Finset.sum_const, Finset.card_range, smul_eq_mul] at hh + omega + +def endpointBound (i U H : ℕ) : ℕ := + if i = 1 then U else min (U/i) ((U-H)/(i-1)) + +lemma endpointBound_sound (μ : YoungDiagram) {i U H : ℕ} (hi : 0 < i) + (hU : rowPrefix μ i ≤ U) (hH : H ≤ μ.rowLen 0) : + μ.rowLen (i-1) ≤ endpointBound i U H := by + unfold endpointBound + split_ifs with he + · subst i + simpa [rowPrefix] using hU + · apply le_min + · apply (Nat.le_div_iff_mul_le hi).mpr + simpa [Nat.mul_comm] using (prefix_last_mul_le μ hi).trans hU + · apply (Nat.le_div_iff_mul_le (by omega : 0 < i-1)).mpr + have h := prefix_last_after_first μ hi + have hx : (i-1)*μ.rowLen (i-1) ≤ U-H := by omega + simpa [Nat.mul_comm] using hx + +lemma prefix_intersection_hook (μ : YoungDiagram) {i j H W : ℕ} + (hi : 0 < i) (hj : 0 < j) (hH : H ≤ μ.colLen 0) (hW : W ≤ μ.rowLen 0) + (hHp : 0 < H) (hWp : 0 < W) : + min i W + min j H - 1 ≤ + ((rowTruncate μ j).cells ∩ (colTruncate μ i).cells).card := by + let A := (rectangle 1 (min i W)).cells + let B := (rectangle (min j H) 1).cells + have hA : A ⊆ (rowTruncate μ j).cells ∩ (colTruncate μ i).cells := by + rintro ⟨a,b⟩ hp + have hx : a < 1 ∧ b < min i W := mem_rectangle.mp hp + have ha : a = 0 := by omega + subst a + have hc : (0,b) ∈ μ := YoungDiagram.mem_iff_lt_rowLen.mpr (by omega) + simpa only [Finset.mem_inter,YoungDiagram.mem_cells,mem_rowTruncate,mem_colTruncate] + using And.intro ⟨hc,hj⟩ ⟨hc,lt_of_lt_of_le hx.2 (min_le_left _ _)⟩ + have hB : B ⊆ (rowTruncate μ j).cells ∩ (colTruncate μ i).cells := by + rintro ⟨a,b⟩ hp + have hx : a < min j H ∧ b < 1 := mem_rectangle.mp hp + have hb : b = 0 := by omega + subst b + have hc : (a,0) ∈ μ := YoungDiagram.mem_iff_lt_colLen.mpr (by omega) + simpa only [Finset.mem_inter,YoungDiagram.mem_cells,mem_rowTruncate,mem_colTruncate] + using And.intro ⟨hc,lt_of_lt_of_le hx.1 (min_le_left _ _)⟩ ⟨hc,hi⟩ + have hAB : A ∩ B = {(0,0)} := by + ext ⟨a,b⟩ + simp only [Finset.mem_inter,Finset.mem_singleton,Prod.mk.injEq] + simp only [A,B,rectangle,Finset.mem_product,Finset.mem_range] + omega + have he := Finset.card_union_add_card_inter A B + have ha : A.card = min i W := by simp [A,rectangle] + have hb : B.card = min j H := by simp [B,rectangle] + rw [hAB,Finset.card_singleton,ha,hb] at he + have h := Finset.card_le_card (Finset.union_subset hA hB) + omega + +def refinedArea (i j U V X Y H W : ℕ) : ℕ := + if j ≤ X ∧ i ≤ Y then + max (U+V-(min i W + min j H - 1)) (U+V-i*j+(X-j)*(Y-i)) + else U+V-(min i W + min j H - 1) + +lemma area_le_refined (μ : YoungDiagram) {i j U V X Y H W : ℕ} + (hi : 0 < i) (hj : 0 < j) (hU : colPrefix μ i ≤ U) (hV : rowPrefix μ j ≤ V) + (hX : μ.colLen (i-1) ≤ X) (hY : μ.rowLen (j-1) ≤ Y) + (hH : H ≤ μ.colLen 0) (hW : W ≤ μ.rowLen 0) (hHp : 0 < H) (hWp : 0 < W) : + μ.card ≤ refinedArea i j U V X Y H W := by + classical + have hid := strip_area_identity μ i j + have hh := prefix_intersection_hook μ hi hj hH hW hHp hWp + by_cases hcell : (j-1,i-1) ∈ μ + · have heq : (rowTruncate μ j).cells ∩ (colTruncate μ i).cells = + (rectangle j i).cells := by + ext ⟨a,b⟩ + simp only [Finset.mem_inter, YoungDiagram.mem_cells, mem_rowTruncate, + mem_colTruncate, mem_rectangle] + constructor + · tauto + · rintro ⟨ha,hb⟩ + have hx := μ.up_left_mem (by omega : a ≤ j-1) (by omega : b ≤ i-1) hcell + tauto + have hint : ((rowTruncate μ j).cells ∩ (colTruncate μ i).cells).card = j*i := by + rw [heq] + simp only [rectangle,Finset.card_product,Finset.card_range] + have hcor := Finset.card_le_card (corner_subset_rectangle μ hi hj) + simp only [Finset.card_product,Nat.card_Ico] at hcor + have hmul := Nat.mul_le_mul (Nat.sub_le_sub_right hX j) (Nat.sub_le_sub_right hY i) + have hx : j ≤ μ.colLen (i-1) := by + have := YoungDiagram.mem_iff_lt_colLen.mp hcell; omega + have hy : i ≤ μ.rowLen (j-1) := by + have := YoungDiagram.mem_iff_lt_rowLen.mp hcell; omega + rw [hint] at hid + have hup : i*j ≤ U+V := by + have ht := prefix_last_mul_le μ.transpose hi + simp only [YoungDiagram.rowLen_transpose] at ht + change i * μ.colLen (i-1) ≤ colPrefix μ i at ht + nlinarith + have hsub := Nat.sub_add_cancel hup + have ha : μ.card ≤ U+V-i*j+(X-j)*(Y-i) := by + rw [Nat.mul_comm j i] at hid + omega + unfold refinedArea + rw [ite_eq_left ⟨hx.trans hX,hy.trans hY⟩] + exact ha.trans (le_max_right _ _) + · have hz : μ.cells \ ((rowTruncate μ j).cells ∪ (colTruncate μ i).cells) = ∅ := by + apply Finset.eq_empty_iff_forall_notMem.mpr + rintro ⟨a,b⟩ hp + simp only [Finset.mem_sdiff,Finset.mem_union,YoungDiagram.mem_cells, + mem_rowTruncate,mem_colTruncate,not_or] at hp + have ha : j ≤ a := Nat.le_of_not_gt fun ha => hp.2.1 ⟨hp.1,ha⟩ + have hb : i ≤ b := Nat.le_of_not_gt fun hb => hp.2.2 ⟨hp.1,hb⟩ + exact hcell (μ.up_left_mem (by omega) (by omega) hp.1) + rw [hz,Finset.card_empty,add_zero] at hid + have ha : μ.card ≤ U+V-(min i W+min j H-1) := by omega + unfold refinedArea + split_ifs + · exact ha.trans (le_max_left _ _) + · exact ha + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/RefinedExhaustion.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/RefinedExhaustion.lean index 7960b9bb043ad90b136cb3083dbe71385875c765..ee7f19b230acd0502b3183dbc45f090af9d910db 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/RefinedExhaustion.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/RefinedExhaustion.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Capacity.RefinedCapacity - -namespace OAI - -/-! Refined Exhaustion. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -def RowBounds (μ : YoungDiagram) (B : List (ℕ × ℕ)) : Prop := - ∀ p ∈ B, 0 < p.1 ∧ rowPrefix μ p.1 ≤ p.2 - -def minHeight (n : ℕ) (B : List (ℕ × ℕ)) : ℕ := - B.foldr (fun p h => if p.2 < n then max (p.1+1) h else h) 1 - -lemma minHeight_pos (n : ℕ) (B : List (ℕ × ℕ)) : 0 < minHeight n B := by - induction B with - | nil => simp [minHeight] - | cons p B ih => - simp only [minHeight,List.foldr_cons] - split_ifs - · exact lt_of_lt_of_le ih (le_max_right _ _) - · exact ih - -lemma minHeight_sound {n : ℕ} (hn : 0 < n) (μ : YoungDiagram) - (hcard : μ.card = n) {B : List (ℕ × ℕ)} (hb : RowBounds μ B) : - minHeight n B ≤ μ.colLen 0 := by - have hpos : 0 < μ.colLen 0 := by - have hc := rowPrefix_eq_card μ (k := 0) - by_contra h - have hz := hc (by omega) - simp only [rowPrefix,Finset.range_zero,Finset.sum_empty] at hz - omega - induction B with - | nil => exact hpos - | cons p B ih => - have hp := hb p (by simp) - have htail : RowBounds μ B := fun q hq => hb q (by simp [hq]) - simp only [minHeight,List.foldr_cons] - split_ifs with hh - · apply max_le _ (ih htail) - by_contra h - have := rowPrefix_eq_card μ (show μ.colLen 0 ≤ p.1 by omega) - omega - · exact ih htail - -lemma rowLen_first_le_prefix (μ : YoungDiagram) {i : ℕ} (hi : 0 < i) : - μ.rowLen 0 ≤ rowPrefix μ i := by - have h := rowPrefix_mono μ (show 1 ≤ i from hi) - simpa [rowPrefix] using h - -def impossibleBounds (n : ℕ) (A B : List (ℕ × ℕ)) : Prop := - (∃ p ∈ A, p.2 < minHeight n B) ∨ - (∃ q ∈ B, q.2 < minHeight n A) ∨ - ∃ p ∈ A, ∃ q ∈ B, - refinedArea p.1 q.1 p.2 q.2 - (endpointBound p.1 p.2 (minHeight n B)) - (endpointBound q.1 q.2 (minHeight n A)) - (minHeight n B) (minHeight n A) < n - -instance (n : ℕ) (A B : List (ℕ × ℕ)) : Decidable (impossibleBounds n A B) := - inferInstanceAs (Decidable ((∃ p ∈ A, p.2 < minHeight n B) ∨ - (∃ q ∈ B, q.2 < minHeight n A) ∨ - ∃ p ∈ A, ∃ q ∈ B, refinedArea p.1 q.1 p.2 q.2 - (endpointBound p.1 p.2 (minHeight n B)) - (endpointBound q.1 q.2 (minHeight n A)) - (minHeight n B) (minHeight n A) < n)) - -lemma impossibleBounds_false {n : ℕ} (hn : 0 < n) (μ : YoungDiagram) - (hcard : μ.card = n) {A B : List (ℕ × ℕ)} - (ha : RowBounds μ.transpose A) (hb : RowBounds μ B) - (h : impossibleBounds n A B) : False := by - have hH := minHeight_sound hn μ hcard hb - have hW := minHeight_sound hn μ.transpose ((transpose_card _).trans hcard) ha - simp only [YoungDiagram.colLen_transpose] at hW - rcases h with ⟨p,hp,h⟩ | ⟨q,hq,h⟩ | ⟨p,hp,q,hq,h⟩ - · have hs := (rowLen_first_le_prefix μ.transpose (ha p hp).1).trans (ha p hp).2 - simp only [YoungDiagram.rowLen_transpose] at hs - omega - · have hs := (rowLen_first_le_prefix μ (hb q hq).1).trans (hb q hq).2 - omega - · have hX := endpointBound_sound μ.transpose (ha p hp).1 (ha p hp).2 - (show minHeight n B ≤ μ.transpose.rowLen 0 by simpa using hH) - have hY := endpointBound_sound μ (hb q hq).1 (hb q hq).2 hW - have ht := area_le_refined μ (ha p hp).1 (hb q hq).1 (ha p hp).2 - (hb q hq).2 (by simpa using hX) hY hH hW (minHeight_pos n B) (minHeight_pos n A) - omega - -lemma rowPrefix_eq_take (μ : YoungDiagram) (k : ℕ) : - rowPrefix μ k = (μ.rowLens.take k).sum := by - induction k with - | zero => simp [rowPrefix] - | succ k ih => - rw [rowPrefix_succ,ih] - by_cases hk : k < μ.rowLens.length - · rw [List.take_succ_eq_append_getElem hk, List.sum_append, List.sum_singleton] - congr 1 - exact YoungDiagram.get_rowLens.symm - · have hh : μ.colLen 0 ≤ k := by simpa only [YoungDiagram.length_rowLens] using Nat.le_of_not_gt hk - rw [rowLen_zero_of_height_le μ hh,add_zero] - rw [List.take_of_length_le (Nat.le_of_not_gt hk), - List.take_of_length_le (by omega : μ.rowLens.length ≤ k+1)] - -lemma not_dominates_witness {μ θ : YoungDiagram} (hc : μ.card = θ.card) - (h : ¬ Dominates μ θ) : - ∃ k, 1 ≤ k ∧ k ≤ θ.colLen 0 ∧ rowPrefix μ k < rowPrefix θ k := by - classical - obtain ⟨k,hk⟩ := not_forall.mp h - have hk' : rowPrefix μ k < rowPrefix θ k := Nat.lt_of_not_ge hk - by_cases hb : k ≤ θ.colLen 0 - · refine ⟨k,?_,hb,hk'⟩ - by_contra ht - have hz : k = 0 := by omega - simp [hz,rowPrefix] at hk' - · refine ⟨θ.colLen 0,?_,le_rfl,?_⟩ - · by_contra ht - have hz : θ.colLen 0 = 0 := by omega - have hs := rowPrefix_eq_card θ (le_of_eq hz) - simp only [rowPrefix,Finset.range_zero,Finset.sum_empty] at hs - have hu := rowPrefix_le_card θ k - omega - · have hle := rowPrefix_mono μ (show θ.colLen 0 ≤ k by omega) - rw [rowPrefix_eq_card θ (by omega), ← hc] at hk' - rw [rowPrefix_eq_card θ le_rfl, ← hc] - omega - -def coreImpossible (K d : ℕ) (A : List (ℕ × ℕ)) : Prop := - ∃ p ∈ A, d ≤ p.1 ∧ p.2 < K - -instance (K d : ℕ) (A : List (ℕ × ℕ)) : Decidable (coreImpossible K d A) := - inferInstanceAs (Decidable (∃ p ∈ A, d ≤ p.1 ∧ p.2 < K)) - -lemma coreImpossible_false (μ : YoungDiagram) {K d : ℕ} - (hd : K ≤ rowPrefix μ d) {A : List (ℕ × ℕ)} (ha : RowBounds μ A) - (h : coreImpossible K d A) : False := by - obtain ⟨p,hp,hpd,hpK⟩ := h - have hle := (hd.trans (rowPrefix_mono μ hpd)).trans (ha p hp).2 - omega - -def refinedCheck (n M r d e a b : ℕ) (q : List ℕ) : Prop := - let A := prefixBounds M r d e ++ [(a,(q.take a).sum-1)] - let B := prefixBounds M r e d ++ [(b,(q.take b).sum-1)] - coreImpossible (2*M-1) d A ∨ coreImpossible (2*M-1) e B ∨ impossibleBounds n A B - -instance (n M r d e a b : ℕ) (q : List ℕ) : Decidable (refinedCheck n M r d e a b q) := by - unfold refinedCheck; infer_instance - -theorem refined_capacity_dichotomy (μ θ : YoungDiagram) {n M r : ℕ} - (hn : 0 < n) (hM : 9 ≤ M) (hr : 0 < r) (hc : μ.card = n) (ht : θ.card = n) - (check : ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, - ∀ a ∈ List.range θ.rowLens.length, ∀ b ∈ List.range θ.rowLens.length, - refinedCheck n M r (d+1) (e+1) (a+1) (b+1) θ.rowLens) : - colPrefix μ 4 ≤ 2*M-2 ∨ colPrefix μ.transpose 4 ≤ 2*M-2 ∨ - BandTest M r μ ∨ BandTest M r μ.transpose ∨ Dominates μ θ ∨ Dominates μ.transpose θ := by - classical - by_contra hh - push Not at hh - rcases hh with ⟨hfour,hfour',hband,hband',hdom,hdom'⟩ - have hK : 0 < 2*M-1 := by omega - obtain ⟨d,hd,hd',hHd,hHd'⟩ := first_prefix_height μ.transpose hK (by unfold colPrefix at hfour; omega) - obtain ⟨e,he,he',hWe,hWe'⟩ := first_prefix_height μ hK (by - simp only [colPrefix,YoungDiagram.transpose_transpose] at hfour'; omega) - obtain ⟨a,ha,ha',hA⟩ := not_dominates_witness ((transpose_card _).trans hc |>.trans ht.symm) hdom' - obtain ⟨b,hb,hb',hB⟩ := not_dominates_witness (hc.trans ht.symm) hdom - have hAf := prefixBounds_sound μ hM hr hHd' hWe hband - have hBf := prefixBounds_sound μ.transpose hM hr - (by simpa only [colPrefix,YoungDiagram.transpose_transpose] using hWe') hHd hband' - let A := prefixBounds M r d e ++ [(a,(θ.rowLens.take a).sum-1)] - let B := prefixBounds M r e d ++ [(b,(θ.rowLens.take b).sum-1)] - have hAbb : RowBounds μ.transpose A := by - intro p hp - rcases List.mem_append.mp hp with hp | hp - · exact hAf p hp - · have heq : p = (a,(θ.rowLens.take a).sum-1) := by simpa using hp - subst p - rw [rowPrefix_eq_take θ] at hA - exact ⟨ha,by dsimp; omega⟩ - have hBbb : RowBounds μ B := by - intro p hp - rcases List.mem_append.mp hp with hp | hp - · simpa only [colPrefix,YoungDiagram.transpose_transpose] using hBf p hp - · have heq : p = (b,(θ.rowLens.take b).sum-1) := by simpa using hp - subst p - rw [rowPrefix_eq_take θ] at hB - exact ⟨hb,by dsimp; omega⟩ - have h := check (d-1) (by simp; omega) (e-1) (by simp; omega) - (a-1) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) - (b-1) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) - have hde : d-1+1 = d := by omega - have hee : e-1+1 = e := by omega - have hae : a-1+1 = a := by omega - have hbe : b-1+1 = b := by omega - rw [hde,hee,hae,hbe] at h - rcases h with h | h | h - · exact coreImpossible_false μ.transpose hHd hAbb h - · exact coreImpossible_false μ hWe hBbb h - · exact impossibleBounds_false hn μ hc hAbb hBbb h - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Capacity.RefinedCapacity + +namespace OAI + +/-! Refined Exhaustion. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +def RowBounds (μ : YoungDiagram) (B : List (ℕ × ℕ)) : Prop := + ∀ p ∈ B, 0 < p.1 ∧ rowPrefix μ p.1 ≤ p.2 + +def minHeight (n : ℕ) (B : List (ℕ × ℕ)) : ℕ := + B.foldr (fun p h => if p.2 < n then max (p.1+1) h else h) 1 + +lemma minHeight_pos (n : ℕ) (B : List (ℕ × ℕ)) : 0 < minHeight n B := by + induction B with + | nil => simp [minHeight] + | cons p B ih => + simp only [minHeight,List.foldr_cons] + split_ifs + · exact lt_of_lt_of_le ih (le_max_right _ _) + · exact ih + +lemma minHeight_sound {n : ℕ} (hn : 0 < n) (μ : YoungDiagram) + (hcard : μ.card = n) {B : List (ℕ × ℕ)} (hb : RowBounds μ B) : + minHeight n B ≤ μ.colLen 0 := by + have hpos : 0 < μ.colLen 0 := by + have hc := rowPrefix_eq_card μ (k := 0) + by_contra h + have hz := hc (by omega) + simp only [rowPrefix,Finset.range_zero,Finset.sum_empty] at hz + omega + induction B with + | nil => exact hpos + | cons p B ih => + have hp := hb p (by simp) + have htail : RowBounds μ B := fun q hq => hb q (by simp [hq]) + simp only [minHeight,List.foldr_cons] + split_ifs with hh + · apply max_le _ (ih htail) + by_contra h + have := rowPrefix_eq_card μ (show μ.colLen 0 ≤ p.1 by omega) + omega + · exact ih htail + +lemma rowLen_first_le_prefix (μ : YoungDiagram) {i : ℕ} (hi : 0 < i) : + μ.rowLen 0 ≤ rowPrefix μ i := by + have h := rowPrefix_mono μ (show 1 ≤ i from hi) + simpa [rowPrefix] using h + +def impossibleBounds (n : ℕ) (A B : List (ℕ × ℕ)) : Prop := + (∃ p ∈ A, p.2 < minHeight n B) ∨ + (∃ q ∈ B, q.2 < minHeight n A) ∨ + ∃ p ∈ A, ∃ q ∈ B, + refinedArea p.1 q.1 p.2 q.2 + (endpointBound p.1 p.2 (minHeight n B)) + (endpointBound q.1 q.2 (minHeight n A)) + (minHeight n B) (minHeight n A) < n + +instance (n : ℕ) (A B : List (ℕ × ℕ)) : Decidable (impossibleBounds n A B) := + inferInstanceAs (Decidable ((∃ p ∈ A, p.2 < minHeight n B) ∨ + (∃ q ∈ B, q.2 < minHeight n A) ∨ + ∃ p ∈ A, ∃ q ∈ B, refinedArea p.1 q.1 p.2 q.2 + (endpointBound p.1 p.2 (minHeight n B)) + (endpointBound q.1 q.2 (minHeight n A)) + (minHeight n B) (minHeight n A) < n)) + +lemma impossibleBounds_false {n : ℕ} (hn : 0 < n) (μ : YoungDiagram) + (hcard : μ.card = n) {A B : List (ℕ × ℕ)} + (ha : RowBounds μ.transpose A) (hb : RowBounds μ B) + (h : impossibleBounds n A B) : False := by + have hH := minHeight_sound hn μ hcard hb + have hW := minHeight_sound hn μ.transpose ((transpose_card _).trans hcard) ha + simp only [YoungDiagram.colLen_transpose] at hW + rcases h with ⟨p,hp,h⟩ | ⟨q,hq,h⟩ | ⟨p,hp,q,hq,h⟩ + · have hs := (rowLen_first_le_prefix μ.transpose (ha p hp).1).trans (ha p hp).2 + simp only [YoungDiagram.rowLen_transpose] at hs + omega + · have hs := (rowLen_first_le_prefix μ (hb q hq).1).trans (hb q hq).2 + omega + · have hX := endpointBound_sound μ.transpose (ha p hp).1 (ha p hp).2 + (show minHeight n B ≤ μ.transpose.rowLen 0 by simpa using hH) + have hY := endpointBound_sound μ (hb q hq).1 (hb q hq).2 hW + have ht := area_le_refined μ (ha p hp).1 (hb q hq).1 (ha p hp).2 + (hb q hq).2 (by simpa using hX) hY hH hW (minHeight_pos n B) (minHeight_pos n A) + omega + +lemma rowPrefix_eq_take (μ : YoungDiagram) (k : ℕ) : + rowPrefix μ k = (μ.rowLens.take k).sum := by + induction k with + | zero => simp [rowPrefix] + | succ k ih => + rw [rowPrefix_succ,ih] + by_cases hk : k < μ.rowLens.length + · rw [List.take_succ_eq_append_getElem hk, List.sum_append, List.sum_singleton] + congr 1 + exact YoungDiagram.get_rowLens.symm + · have hh : μ.colLen 0 ≤ k := by simpa only [YoungDiagram.length_rowLens] using Nat.le_of_not_gt hk + rw [rowLen_zero_of_height_le μ hh,add_zero] + rw [List.take_of_length_le (Nat.le_of_not_gt hk), + List.take_of_length_le (by omega : μ.rowLens.length ≤ k+1)] + +lemma not_dominates_witness {μ θ : YoungDiagram} (hc : μ.card = θ.card) + (h : ¬ Dominates μ θ) : + ∃ k, 1 ≤ k ∧ k ≤ θ.colLen 0 ∧ rowPrefix μ k < rowPrefix θ k := by + classical + obtain ⟨k,hk⟩ := not_forall.mp h + have hk' : rowPrefix μ k < rowPrefix θ k := Nat.lt_of_not_ge hk + by_cases hb : k ≤ θ.colLen 0 + · refine ⟨k,?_,hb,hk'⟩ + by_contra ht + have hz : k = 0 := by omega + simp [hz,rowPrefix] at hk' + · refine ⟨θ.colLen 0,?_,le_rfl,?_⟩ + · by_contra ht + have hz : θ.colLen 0 = 0 := by omega + have hs := rowPrefix_eq_card θ (le_of_eq hz) + simp only [rowPrefix,Finset.range_zero,Finset.sum_empty] at hs + have hu := rowPrefix_le_card θ k + omega + · have hle := rowPrefix_mono μ (show θ.colLen 0 ≤ k by omega) + rw [rowPrefix_eq_card θ (by omega), ← hc] at hk' + rw [rowPrefix_eq_card θ le_rfl, ← hc] + omega + +def coreImpossible (K d : ℕ) (A : List (ℕ × ℕ)) : Prop := + ∃ p ∈ A, d ≤ p.1 ∧ p.2 < K + +instance (K d : ℕ) (A : List (ℕ × ℕ)) : Decidable (coreImpossible K d A) := + inferInstanceAs (Decidable (∃ p ∈ A, d ≤ p.1 ∧ p.2 < K)) + +lemma coreImpossible_false (μ : YoungDiagram) {K d : ℕ} + (hd : K ≤ rowPrefix μ d) {A : List (ℕ × ℕ)} (ha : RowBounds μ A) + (h : coreImpossible K d A) : False := by + obtain ⟨p,hp,hpd,hpK⟩ := h + have hle := (hd.trans (rowPrefix_mono μ hpd)).trans (ha p hp).2 + omega + +def refinedCheck (n M r d e a b : ℕ) (q : List ℕ) : Prop := + let A := prefixBounds M r d e ++ [(a,(q.take a).sum-1)] + let B := prefixBounds M r e d ++ [(b,(q.take b).sum-1)] + coreImpossible (2*M-1) d A ∨ coreImpossible (2*M-1) e B ∨ impossibleBounds n A B + +instance (n M r d e a b : ℕ) (q : List ℕ) : Decidable (refinedCheck n M r d e a b q) := by + unfold refinedCheck; infer_instance + +theorem refined_capacity_dichotomy (μ θ : YoungDiagram) {n M r : ℕ} + (hn : 0 < n) (hM : 9 ≤ M) (hr : 0 < r) (hc : μ.card = n) (ht : θ.card = n) + (check : ∀ d ∈ List.range 4, ∀ e ∈ List.range 4, + ∀ a ∈ List.range θ.rowLens.length, ∀ b ∈ List.range θ.rowLens.length, + refinedCheck n M r (d+1) (e+1) (a+1) (b+1) θ.rowLens) : + colPrefix μ 4 ≤ 2*M-2 ∨ colPrefix μ.transpose 4 ≤ 2*M-2 ∨ + BandTest M r μ ∨ BandTest M r μ.transpose ∨ Dominates μ θ ∨ Dominates μ.transpose θ := by + classical + by_contra hh + push Not at hh + rcases hh with ⟨hfour,hfour',hband,hband',hdom,hdom'⟩ + have hK : 0 < 2*M-1 := by omega + obtain ⟨d,hd,hd',hHd,hHd'⟩ := first_prefix_height μ.transpose hK (by unfold colPrefix at hfour; omega) + obtain ⟨e,he,he',hWe,hWe'⟩ := first_prefix_height μ hK (by + simp only [colPrefix,YoungDiagram.transpose_transpose] at hfour'; omega) + obtain ⟨a,ha,ha',hA⟩ := not_dominates_witness ((transpose_card _).trans hc |>.trans ht.symm) hdom' + obtain ⟨b,hb,hb',hB⟩ := not_dominates_witness (hc.trans ht.symm) hdom + have hAf := prefixBounds_sound μ hM hr hHd' hWe hband + have hBf := prefixBounds_sound μ.transpose hM hr + (by simpa only [colPrefix,YoungDiagram.transpose_transpose] using hWe') hHd hband' + let A := prefixBounds M r d e ++ [(a,(θ.rowLens.take a).sum-1)] + let B := prefixBounds M r e d ++ [(b,(θ.rowLens.take b).sum-1)] + have hAbb : RowBounds μ.transpose A := by + intro p hp + rcases List.mem_append.mp hp with hp | hp + · exact hAf p hp + · have heq : p = (a,(θ.rowLens.take a).sum-1) := by simpa using hp + subst p + rw [rowPrefix_eq_take θ] at hA + exact ⟨ha,by dsimp; omega⟩ + have hBbb : RowBounds μ B := by + intro p hp + rcases List.mem_append.mp hp with hp | hp + · simpa only [colPrefix,YoungDiagram.transpose_transpose] using hBf p hp + · have heq : p = (b,(θ.rowLens.take b).sum-1) := by simpa using hp + subst p + rw [rowPrefix_eq_take θ] at hB + exact ⟨hb,by dsimp; omega⟩ + have h := check (d-1) (by simp; omega) (e-1) (by simp; omega) + (a-1) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) + (b-1) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) + have hde : d-1+1 = d := by omega + have hee : e-1+1 = e := by omega + have hae : a-1+1 = a := by omega + have hbe : b-1+1 = b := by omega + rw [hde,hee,hae,hbe] at h + rcases h with h | h | h + · exact coreImpossible_false μ.transpose hHd hAbb h + · exact coreImpossible_false μ hWe hBbb h + · exact impossibleBounds_false hn μ hc hAbb hBbb h + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/RegionExhaustion.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/RegionExhaustion.lean index 8ac30eb47948d17f5b65f54510734352808f673d..ab31957365fe755db5ec1e90c61e7b284423b118 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/RegionExhaustion.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/RegionExhaustion.lean @@ -1,169 +1,169 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.RowSquareTools - -namespace OAI - -/-! Region Exhaustion. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def semanticResidualCheck (n M r d e a b : ℕ) (q : List ℕ) (P : List ℕ → Prop) : Prop := - let A := prefixBounds M r d e ++ [(a,(q.take a).sum-1)] - let B := prefixBounds M r e d ++ [(b,(q.take b).sum-1)] - (d ≤ 4 ∧ coreImpossible (2*M-1) d A) ∨ - (e ≤ 4 ∧ coreImpossible (2*M-1) e B) ∨ impossibleBounds n A B ∨ - ∀ μ : YoungDiagram, μ.card = n → RowBounds μ.transpose A → RowBounds μ B → P μ.rowLens - -def boundsEntail (A B : List (ℕ × ℕ)) : Prop := - ∀ p ∈ B, 0 < p.1 ∧ ∃ q ∈ A, p.1 ≤ q.1 ∧ q.2 ≤ p.2 - -instance (A B : List (ℕ × ℕ)) : Decidable (boundsEntail A B) := by - unfold boundsEntail; infer_instance - -lemma boundsEntail_sound {A B : List (ℕ × ℕ)} (h : boundsEntail A B) - (μ : YoungDiagram) (ha : RowBounds μ A) : RowBounds μ B := by - intro p hp - obtain ⟨hpos,q,hq,hk,hv⟩ := h p hp - exact ⟨hpos,((rowPrefix_mono μ hk).trans (ha q hq).2).trans hv⟩ - -abbrev PrefixRegion := List (ℕ × ℕ) × List (ℕ × ℕ) - -def regionCheck (n M r d e a b : ℕ) (q : List ℕ) (regions : List PrefixRegion) : Prop := - let A := prefixBounds M r d e ++ [(a,(q.take a).sum-1)] - let B := prefixBounds M r e d ++ [(b,(q.take b).sum-1)] - (d ≤ 4 ∧ coreImpossible (2*M-1) d A) ∨ - (e ≤ 4 ∧ coreImpossible (2*M-1) e B) ∨ impossibleBounds n A B ∨ - ∃ R ∈ regions, boundsEntail A R.1 ∧ boundsEntail B R.2 - -instance (n M r d e a b : ℕ) (q : List ℕ) (regions : List PrefixRegion) : - Decidable (regionCheck n M r d e a b q regions) := by - unfold regionCheck; infer_instance - -lemma regionCheck_sound {n M r d e a b : ℕ} {q : List ℕ} {regions : List PrefixRegion} - (hn : 0 < n) {P : List ℕ → Prop} - (hc : ∀ R ∈ regions, ∀ rs ∈ rowsWithin n R.1 R.2, P rs) - (h : regionCheck n M r d e a b q regions) : - semanticResidualCheck n M r d e a b q P := by - rcases h with h | h | h | ⟨R,hR,hA,hB⟩ - · exact Or.inl h - · exact Or.inr (Or.inl h) - · exact Or.inr (Or.inr (Or.inl h)) - · refine Or.inr (Or.inr (Or.inr ?_)) - intro μ hμ ha hb - exact rowsWithin_sound hn μ hμ (boundsEntail_sound hA _ ha) - (boundsEntail_sound hB _ hb) (hc R hR) - -lemma rowsWithin_of_checks {n : ℕ} {A B : List (ℕ × ℕ)} {P : List ℕ → Prop} - (hc : ∀ h ∈ List.range' (minHeight n B) (firstBound n A+1-minHeight n B), - ∀ rs ∈ constrainedRows h n (firstBound n B) A B, P rs) : - ∀ rs ∈ rowsWithin n A B, P rs := by - intro rs hrs - obtain ⟨h,hh,hrs⟩ := List.mem_flatMap.mp hrs - exact hc h hh rs hrs - -theorem semantic_capacity_dichotomy (μ θ : YoungDiagram) {n M r : ℕ} - (hn : 0 < n) (hM : 1 ≤ M) (hr : 0 < r) (hc : μ.card = n) (ht : θ.card = n) - (P : List ℕ → Prop) - (check : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range θ.rowLens.length, ∀ b ∈ List.range θ.rowLens.length, - semanticResidualCheck n M r (d+1) (e+1) (a+1) (b+1) θ.rowLens P) : - BandTest M r μ ∨ BandTest M r μ.transpose ∨ Dominates μ θ ∨ - Dominates μ.transpose θ ∨ P μ.rowLens := by - classical - by_contra hh - push Not at hh - rcases hh with ⟨hband,hband',hdom,hdom',hP⟩ - obtain ⟨d,hd,hd',hHd,hHd'⟩ := sentinel_height μ.transpose (show 0 < 2*M-1 by omega) - obtain ⟨e,he,he',hWe,hWe'⟩ := sentinel_height μ (show 0 < 2*M-1 by omega) - obtain ⟨a,ha,ha',hA⟩ := not_dominates_witness ((transpose_card _).trans hc |>.trans ht.symm) hdom' - obtain ⟨b,hb,hb',hB⟩ := not_dominates_witness (hc.trans ht.symm) hdom - have hAf := prefixBounds_sound_sentinel μ hM hr hHd' hWe hband - have hBf := prefixBounds_sound_sentinel μ.transpose hM hr - (by simpa only [colPrefix,YoungDiagram.transpose_transpose] using hWe') hHd hband' - let A := prefixBounds M r d e ++ [(a,(θ.rowLens.take a).sum-1)] - let B := prefixBounds M r e d ++ [(b,(θ.rowLens.take b).sum-1)] - have hAbb : RowBounds μ.transpose A := by - intro p hp - rcases List.mem_append.mp hp with hp | hp - · exact hAf p hp - · have heq : p = (a,(θ.rowLens.take a).sum-1) := by simpa using hp - subst p - rw [rowPrefix_eq_take θ] at hA - exact ⟨ha,by dsimp; omega⟩ - have hBbb : RowBounds μ B := by - intro p hp - rcases List.mem_append.mp hp with hp | hp - · simpa only [colPrefix,YoungDiagram.transpose_transpose] using hBf p hp - · have heq : p = (b,(θ.rowLens.take b).sum-1) := by simpa using hp - subst p - rw [rowPrefix_eq_take θ] at hB - exact ⟨hb,by dsimp; omega⟩ - have h := check (d-1) (by simp; omega) (e-1) (by simp; omega) - (a-1) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) - (b-1) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) - have hde : d-1+1 = d := by omega - have hee : e-1+1 = e := by omega - have hae : a-1+1 = a := by omega - have hbe : b-1+1 = b := by omega - rw [hde,hee,hae,hbe] at h - rcases h with ⟨h4,h⟩ | ⟨h4,h⟩ | h | h - · exact coreImpossible_false μ.transpose (hHd h4) hAbb h - · exact coreImpossible_false μ (hWe h4) hBbb h - · exact impossibleBounds_false hn μ hc hAbb hBbb h - · exact hP (h μ hc hAbb hBbb) - -theorem candidate_semantic_pos {n M b δ r : ℕ} (hM : 4 ≤ M) - (hδ : δ ≤ 1) (hr : r = 2*b+δ) (hrpos : 0 < r) - (hn : (candidate M b δ).card = n) - (q : List ℕ) (hq : GoodRows q) (hqn : q.sum = n) - (p : PackingPlan) (hv : p.Valid (M+b+δ)) (hbands : BandsValid p.bands) - (hcols : p.columns.Perm ([M+b+δ,M-1+b] ++ - (List.range' 3 (M-4)).reverse ++ List.replicate (b+1) 2 ++ List.replicate (1+δ) 1)) - (hparts : p.parts.Perm q) (P : List ℕ → Prop) - (hP : ∀ rs, GoodRows rs → rs.sum = n → P rs → SquareOccurs (candidate M b δ) (rowDiagram rs)) - (check : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range q.length, ∀ c ∈ List.range q.length, - semanticResidualCheck n M r (d+1) (e+1) (a+1) (c+1) q P) - (μ : YoungDiagram) (hμ : μ.card = n) : - 0 < kronecker (canonicalTableau (candidate M b δ) hn) - (canonicalTableau (candidate M b δ) hn) (canonicalTableau μ hμ) := by - have hposn : 0 < n := by rw [← hn,candidate_card _ _ _ (by omega)]; omega - have hp : ∀ a ∈ p.parts, 0 < a := fun a ha => hq.2 a (hparts.mem_iff.mp ha) - have hshape : (columnShape p.parts).transpose = rowDiagram q := by - rw [columnShape_perm hparts]; rfl - have hh : (candidate M b δ).colLen 0 = M+b+δ := by - rw [candidate_colLen _ _ _ _ hM]; simp [candidateLengths] - have hc : p.columns.Perm (candidate M b δ).transpose.rowLens := by - rw [candidate_transpose,candidate_rowLens hM]; exact hcols - have cone (ν : YoungDiagram) (hν : ν.card = n) (hd : Dominates ν (rowDiagram q)) : - 0 < kronecker (canonicalTableau (candidate M b δ) hn) - (canonicalTableau (candidate M b δ) hn) (canonicalTableau ν hν) := by - apply packingPlan_pos p hv hbands hh hc hp - simpa only [hshape] using hd - have htcheck : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range (rowDiagram q).rowLens.length, ∀ c ∈ List.range (rowDiagram q).rowLens.length, - semanticResidualCheck n M r (d+1) (e+1) (a+1) (c+1) (rowDiagram q).rowLens P := by - simpa only [rowDiagram_rows hq] using check - rcases semantic_capacity_dichotomy μ (rowDiagram q) hposn (by omega) hrpos hμ - ((rowDiagram_card q).trans hqn) P htcheck with h | h | h | h | h - · exact band_kronecker_pos hM hδ hr _ μ _ h - · apply (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr - exact band_kronecker_pos hM hδ hr _ μ.transpose _ h - · exact cone μ hμ h - · apply (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr - exact cone μ.transpose ((transpose_card μ).trans hμ) h - · have ht := hP μ.rowLens ⟨μ.rowLens_sorted,μ.pos_of_mem_rowLens⟩ - ((card_eq_sum_rowLens μ).symm.trans hμ) h - rw [rowDiagram_rowLens] at ht - exact ht.pos _ _ - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.RowSquareTools + +namespace OAI + +/-! Region Exhaustion. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def semanticResidualCheck (n M r d e a b : ℕ) (q : List ℕ) (P : List ℕ → Prop) : Prop := + let A := prefixBounds M r d e ++ [(a,(q.take a).sum-1)] + let B := prefixBounds M r e d ++ [(b,(q.take b).sum-1)] + (d ≤ 4 ∧ coreImpossible (2*M-1) d A) ∨ + (e ≤ 4 ∧ coreImpossible (2*M-1) e B) ∨ impossibleBounds n A B ∨ + ∀ μ : YoungDiagram, μ.card = n → RowBounds μ.transpose A → RowBounds μ B → P μ.rowLens + +def boundsEntail (A B : List (ℕ × ℕ)) : Prop := + ∀ p ∈ B, 0 < p.1 ∧ ∃ q ∈ A, p.1 ≤ q.1 ∧ q.2 ≤ p.2 + +instance (A B : List (ℕ × ℕ)) : Decidable (boundsEntail A B) := by + unfold boundsEntail; infer_instance + +lemma boundsEntail_sound {A B : List (ℕ × ℕ)} (h : boundsEntail A B) + (μ : YoungDiagram) (ha : RowBounds μ A) : RowBounds μ B := by + intro p hp + obtain ⟨hpos,q,hq,hk,hv⟩ := h p hp + exact ⟨hpos,((rowPrefix_mono μ hk).trans (ha q hq).2).trans hv⟩ + +abbrev PrefixRegion := List (ℕ × ℕ) × List (ℕ × ℕ) + +def regionCheck (n M r d e a b : ℕ) (q : List ℕ) (regions : List PrefixRegion) : Prop := + let A := prefixBounds M r d e ++ [(a,(q.take a).sum-1)] + let B := prefixBounds M r e d ++ [(b,(q.take b).sum-1)] + (d ≤ 4 ∧ coreImpossible (2*M-1) d A) ∨ + (e ≤ 4 ∧ coreImpossible (2*M-1) e B) ∨ impossibleBounds n A B ∨ + ∃ R ∈ regions, boundsEntail A R.1 ∧ boundsEntail B R.2 + +instance (n M r d e a b : ℕ) (q : List ℕ) (regions : List PrefixRegion) : + Decidable (regionCheck n M r d e a b q regions) := by + unfold regionCheck; infer_instance + +lemma regionCheck_sound {n M r d e a b : ℕ} {q : List ℕ} {regions : List PrefixRegion} + (hn : 0 < n) {P : List ℕ → Prop} + (hc : ∀ R ∈ regions, ∀ rs ∈ rowsWithin n R.1 R.2, P rs) + (h : regionCheck n M r d e a b q regions) : + semanticResidualCheck n M r d e a b q P := by + rcases h with h | h | h | ⟨R,hR,hA,hB⟩ + · exact Or.inl h + · exact Or.inr (Or.inl h) + · exact Or.inr (Or.inr (Or.inl h)) + · refine Or.inr (Or.inr (Or.inr ?_)) + intro μ hμ ha hb + exact rowsWithin_sound hn μ hμ (boundsEntail_sound hA _ ha) + (boundsEntail_sound hB _ hb) (hc R hR) + +lemma rowsWithin_of_checks {n : ℕ} {A B : List (ℕ × ℕ)} {P : List ℕ → Prop} + (hc : ∀ h ∈ List.range' (minHeight n B) (firstBound n A+1-minHeight n B), + ∀ rs ∈ constrainedRows h n (firstBound n B) A B, P rs) : + ∀ rs ∈ rowsWithin n A B, P rs := by + intro rs hrs + obtain ⟨h,hh,hrs⟩ := List.mem_flatMap.mp hrs + exact hc h hh rs hrs + +theorem semantic_capacity_dichotomy (μ θ : YoungDiagram) {n M r : ℕ} + (hn : 0 < n) (hM : 1 ≤ M) (hr : 0 < r) (hc : μ.card = n) (ht : θ.card = n) + (P : List ℕ → Prop) + (check : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range θ.rowLens.length, ∀ b ∈ List.range θ.rowLens.length, + semanticResidualCheck n M r (d+1) (e+1) (a+1) (b+1) θ.rowLens P) : + BandTest M r μ ∨ BandTest M r μ.transpose ∨ Dominates μ θ ∨ + Dominates μ.transpose θ ∨ P μ.rowLens := by + classical + by_contra hh + push Not at hh + rcases hh with ⟨hband,hband',hdom,hdom',hP⟩ + obtain ⟨d,hd,hd',hHd,hHd'⟩ := sentinel_height μ.transpose (show 0 < 2*M-1 by omega) + obtain ⟨e,he,he',hWe,hWe'⟩ := sentinel_height μ (show 0 < 2*M-1 by omega) + obtain ⟨a,ha,ha',hA⟩ := not_dominates_witness ((transpose_card _).trans hc |>.trans ht.symm) hdom' + obtain ⟨b,hb,hb',hB⟩ := not_dominates_witness (hc.trans ht.symm) hdom + have hAf := prefixBounds_sound_sentinel μ hM hr hHd' hWe hband + have hBf := prefixBounds_sound_sentinel μ.transpose hM hr + (by simpa only [colPrefix,YoungDiagram.transpose_transpose] using hWe') hHd hband' + let A := prefixBounds M r d e ++ [(a,(θ.rowLens.take a).sum-1)] + let B := prefixBounds M r e d ++ [(b,(θ.rowLens.take b).sum-1)] + have hAbb : RowBounds μ.transpose A := by + intro p hp + rcases List.mem_append.mp hp with hp | hp + · exact hAf p hp + · have heq : p = (a,(θ.rowLens.take a).sum-1) := by simpa using hp + subst p + rw [rowPrefix_eq_take θ] at hA + exact ⟨ha,by dsimp; omega⟩ + have hBbb : RowBounds μ B := by + intro p hp + rcases List.mem_append.mp hp with hp | hp + · simpa only [colPrefix,YoungDiagram.transpose_transpose] using hBf p hp + · have heq : p = (b,(θ.rowLens.take b).sum-1) := by simpa using hp + subst p + rw [rowPrefix_eq_take θ] at hB + exact ⟨hb,by dsimp; omega⟩ + have h := check (d-1) (by simp; omega) (e-1) (by simp; omega) + (a-1) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) + (b-1) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) + have hde : d-1+1 = d := by omega + have hee : e-1+1 = e := by omega + have hae : a-1+1 = a := by omega + have hbe : b-1+1 = b := by omega + rw [hde,hee,hae,hbe] at h + rcases h with ⟨h4,h⟩ | ⟨h4,h⟩ | h | h + · exact coreImpossible_false μ.transpose (hHd h4) hAbb h + · exact coreImpossible_false μ (hWe h4) hBbb h + · exact impossibleBounds_false hn μ hc hAbb hBbb h + · exact hP (h μ hc hAbb hBbb) + +theorem candidate_semantic_pos {n M b δ r : ℕ} (hM : 4 ≤ M) + (hδ : δ ≤ 1) (hr : r = 2*b+δ) (hrpos : 0 < r) + (hn : (candidate M b δ).card = n) + (q : List ℕ) (hq : GoodRows q) (hqn : q.sum = n) + (p : PackingPlan) (hv : p.Valid (M+b+δ)) (hbands : BandsValid p.bands) + (hcols : p.columns.Perm ([M+b+δ,M-1+b] ++ + (List.range' 3 (M-4)).reverse ++ List.replicate (b+1) 2 ++ List.replicate (1+δ) 1)) + (hparts : p.parts.Perm q) (P : List ℕ → Prop) + (hP : ∀ rs, GoodRows rs → rs.sum = n → P rs → SquareOccurs (candidate M b δ) (rowDiagram rs)) + (check : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range q.length, ∀ c ∈ List.range q.length, + semanticResidualCheck n M r (d+1) (e+1) (a+1) (c+1) q P) + (μ : YoungDiagram) (hμ : μ.card = n) : + 0 < kronecker (canonicalTableau (candidate M b δ) hn) + (canonicalTableau (candidate M b δ) hn) (canonicalTableau μ hμ) := by + have hposn : 0 < n := by rw [← hn,candidate_card _ _ _ (by omega)]; omega + have hp : ∀ a ∈ p.parts, 0 < a := fun a ha => hq.2 a (hparts.mem_iff.mp ha) + have hshape : (columnShape p.parts).transpose = rowDiagram q := by + rw [columnShape_perm hparts]; rfl + have hh : (candidate M b δ).colLen 0 = M+b+δ := by + rw [candidate_colLen _ _ _ _ hM]; simp [candidateLengths] + have hc : p.columns.Perm (candidate M b δ).transpose.rowLens := by + rw [candidate_transpose,candidate_rowLens hM]; exact hcols + have cone (ν : YoungDiagram) (hν : ν.card = n) (hd : Dominates ν (rowDiagram q)) : + 0 < kronecker (canonicalTableau (candidate M b δ) hn) + (canonicalTableau (candidate M b δ) hn) (canonicalTableau ν hν) := by + apply packingPlan_pos p hv hbands hh hc hp + simpa only [hshape] using hd + have htcheck : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range (rowDiagram q).rowLens.length, ∀ c ∈ List.range (rowDiagram q).rowLens.length, + semanticResidualCheck n M r (d+1) (e+1) (a+1) (c+1) (rowDiagram q).rowLens P := by + simpa only [rowDiagram_rows hq] using check + rcases semantic_capacity_dichotomy μ (rowDiagram q) hposn (by omega) hrpos hμ + ((rowDiagram_card q).trans hqn) P htcheck with h | h | h | h | h + · exact band_kronecker_pos hM hδ hr _ μ _ h + · apply (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr + exact band_kronecker_pos hM hδ hr _ μ.transpose _ h + · exact cone μ hμ h + · apply (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr + exact cone μ.transpose ((transpose_card μ).trans hμ) h + · have ht := hP μ.rowLens ⟨μ.rowLens_sorted,μ.pos_of_mem_rowLens⟩ + ((card_eq_sum_rowLens μ).symm.trans hμ) h + rw [rowDiagram_rowLens] at ht + exact ht.pos _ _ + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/SentinelExhaustion.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/SentinelExhaustion.lean index 5a710370c40979ad2e8c003b2d64c1ac82657783..d1ac323b97566da75a35ce7150c9f1cafe8f7509 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/SentinelExhaustion.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Capacity/SentinelExhaustion.lean @@ -1,175 +1,175 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Specht.CandidateColumns -import OAI.RepresentationTheory.UniversalSquare.Support.ConstrainedDiagrams -import OAI.RepresentationTheory.UniversalSquare.Balance.PackingPlans - -namespace OAI - -/-! Sentinel Exhaustion. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma testWidth_valid_pos {M f : ℕ} (hf : 1 ≤ f) (hw : 0 < testWidth M f) : - testWidth M f ≤ 8 ∧ f * testWidth M f + 7 + f ≤ 2*M-1 := by - refine ⟨min_le_left _ _, ?_⟩ - have hh := Nat.mul_le_mul_left f (min_le_right 8 ((2*M-8-f)/f)) - have hh' := Nat.div_mul_le_self (2*M-8-f) f - have hq : 0 < (2*M-8-f)/f := lt_of_lt_of_le hw (min_le_right _ _) - have hn : f ≤ 2*M-8-f := by simpa using (Nat.le_div_iff_mul_le (by omega)).mp hq - unfold testWidth - nlinarith [Nat.sub_add_cancel (show f ≤ 2*M-8 by omega), - Nat.sub_add_cancel (show 8 ≤ 2*M by omega), - Nat.sub_add_cancel (show 1 ≤ 2*M by omega)] - -lemma sentinel_height (μ : YoungDiagram) {K : ℕ} (hK : 0 < K) : - ∃ d, 1 ≤ d ∧ d ≤ 5 ∧ (d ≤ 4 → K ≤ rowPrefix μ d) ∧ - (1 < d → rowPrefix μ (d-1) < K) := by - by_cases hh : K ≤ rowPrefix μ 4 - · obtain ⟨d,hd,h4,hp,hl⟩ := first_prefix_height μ hK hh - exact ⟨d,hd,by omega,fun _ => hp,hl⟩ - · exact ⟨5,by decide,le_rfl,by omega,by simpa using Nat.lt_of_not_ge hh⟩ - -lemma prefixBounds_sound_sentinel (μ : YoungDiagram) {M r d e : ℕ} - (hM : 1 ≤ M) (hr : 0 < r) - (hd : 1 < d → colPrefix μ (d-1) < 2*M-1) - (he : e ≤ 4 → 2*M-1 ≤ rowPrefix μ e) (hfail : ¬BandTest M r μ) : - ∀ p ∈ prefixBounds M r d e, 0 < p.1 ∧ colPrefix μ p.1 ≤ p.2 := by - intro p hp - simp only [prefixBounds,List.mem_append] at hp - rcases hp with hp | hp - · split_ifs at hp with hd' - · simp only [List.mem_cons,List.not_mem_nil,or_false] at hp - subst p - exact ⟨by omega,by have := hd hd'; dsimp; omega⟩ - · simp at hp - · obtain ⟨k,hk,hkp⟩ := List.mem_filterMap.mp hp - simp only [List.mem_range] at hk - split_ifs at hkp with hke - · have hp' := Option.some.inj hkp - subst p - have hw := testWidth_valid_pos (by omega : 1 ≤ k+1) hke.2 - have hc : bandCapacity μ (k+1) (testWidth M (k+1)) < r := by - by_contra hh - apply hfail - exact ⟨k+1,by omega,by omega,testWidth M (k+1),hw.1, - (he (by omega)).trans (rowPrefix_mono μ hke.1),hw.2,by omega⟩ - have hb := prefix_le_capacity μ (k+1) (testWidth M (k+1)) - exact ⟨hke.2,by dsimp; omega⟩ - -def residualCheck (n M r d e a b : ℕ) (q : List ℕ) (P : List ℕ → Prop) : Prop := - let A := prefixBounds M r d e ++ [(a,(q.take a).sum-1)] - let B := prefixBounds M r e d ++ [(b,(q.take b).sum-1)] - (d ≤ 4 ∧ coreImpossible (2*M-1) d A) ∨ - (e ≤ 4 ∧ coreImpossible (2*M-1) e B) ∨ impossibleBounds n A B ∨ - ∀ rs ∈ rowsWithin n A B, P rs - -instance (n M r d e a b : ℕ) (q : List ℕ) (P : List ℕ → Prop) [DecidablePred P] : - Decidable (residualCheck n M r d e a b q P) := by - unfold residualCheck; infer_instance - -theorem sentinel_capacity_dichotomy (μ θ : YoungDiagram) {n M r : ℕ} - (hn : 0 < n) (hM : 1 ≤ M) (hr : 0 < r) (hc : μ.card = n) (ht : θ.card = n) - (P : List ℕ → Prop) - (check : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range θ.rowLens.length, ∀ b ∈ List.range θ.rowLens.length, - residualCheck n M r (d+1) (e+1) (a+1) (b+1) θ.rowLens P) : - BandTest M r μ ∨ BandTest M r μ.transpose ∨ Dominates μ θ ∨ - Dominates μ.transpose θ ∨ P μ.rowLens := by - classical - by_contra hh - push Not at hh - rcases hh with ⟨hband,hband',hdom,hdom',hP⟩ - obtain ⟨d,hd,hd',hHd,hHd'⟩ := sentinel_height μ.transpose (show 0 < 2*M-1 by omega) - obtain ⟨e,he,he',hWe,hWe'⟩ := sentinel_height μ (show 0 < 2*M-1 by omega) - obtain ⟨a,ha,ha',hA⟩ := not_dominates_witness ((transpose_card _).trans hc |>.trans ht.symm) hdom' - obtain ⟨b,hb,hb',hB⟩ := not_dominates_witness (hc.trans ht.symm) hdom - have hAf := prefixBounds_sound_sentinel μ hM hr hHd' hWe hband - have hBf := prefixBounds_sound_sentinel μ.transpose hM hr - (by simpa only [colPrefix,YoungDiagram.transpose_transpose] using hWe') hHd hband' - let A := prefixBounds M r d e ++ [(a,(θ.rowLens.take a).sum-1)] - let B := prefixBounds M r e d ++ [(b,(θ.rowLens.take b).sum-1)] - have hAbb : RowBounds μ.transpose A := by - intro p hp - rcases List.mem_append.mp hp with hp | hp - · exact hAf p hp - · have heq : p = (a,(θ.rowLens.take a).sum-1) := by simpa using hp - subst p - rw [rowPrefix_eq_take θ] at hA - exact ⟨ha,by dsimp; omega⟩ - have hBbb : RowBounds μ B := by - intro p hp - rcases List.mem_append.mp hp with hp | hp - · simpa only [colPrefix,YoungDiagram.transpose_transpose] using hBf p hp - · have heq : p = (b,(θ.rowLens.take b).sum-1) := by simpa using hp - subst p - rw [rowPrefix_eq_take θ] at hB - exact ⟨hb,by dsimp; omega⟩ - have h := check (d-1) (by simp; omega) (e-1) (by simp; omega) - (a-1) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) - (b-1) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) - have hde : d-1+1 = d := by omega - have hee : e-1+1 = e := by omega - have hae : a-1+1 = a := by omega - have hbe : b-1+1 = b := by omega - rw [hde,hee,hae,hbe] at h - rcases h with ⟨h4,h⟩ | ⟨h4,h⟩ | h | h - · exact coreImpossible_false μ.transpose (hHd h4) hAbb h - · exact coreImpossible_false μ (hWe h4) hBbb h - · exact impossibleBounds_false hn μ hc hAbb hBbb h - · exact hP (rowsWithin_sound hn μ hc hAbb hBbb h) - -theorem candidate_residual_pos {n M b δ r : ℕ} (hM : 4 ≤ M) - (hδ : δ ≤ 1) (hr : r = 2*b+δ) (hrpos : 0 < r) - (hn : (candidate M b δ).card = n) - (q : List ℕ) (hq : GoodRows q) (hqn : q.sum = n) - (p : PackingPlan) (hv : p.Valid (M+b+δ)) (hbands : BandsValid p.bands) - (hcols : p.columns.Perm ([M+b+δ,M-1+b] ++ - (List.range' 3 (M-4)).reverse ++ List.replicate (b+1) 2 ++ List.replicate (1+δ) 1)) - (hparts : p.parts.Perm q) (P : List ℕ → Prop) - (hP : ∀ rs, GoodRows rs → rs.sum = n → P rs → SquareOccurs (candidate M b δ) (rowDiagram rs)) - (check : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range q.length, ∀ c ∈ List.range q.length, - residualCheck n M r (d+1) (e+1) (a+1) (c+1) q P) - (μ : YoungDiagram) (hμ : μ.card = n) : - 0 < kronecker (canonicalTableau (candidate M b δ) hn) - (canonicalTableau (candidate M b δ) hn) (canonicalTableau μ hμ) := by - have hposn : 0 < n := by rw [← hn,candidate_card _ _ _ (by omega)]; omega - have hp : ∀ a ∈ p.parts, 0 < a := fun a ha => hq.2 a (hparts.mem_iff.mp ha) - have hshape : (columnShape p.parts).transpose = rowDiagram q := by - rw [columnShape_perm hparts]; rfl - have hh : (candidate M b δ).colLen 0 = M+b+δ := by - rw [candidate_colLen _ _ _ _ hM]; simp [candidateLengths] - have hc : p.columns.Perm (candidate M b δ).transpose.rowLens := by - rw [candidate_transpose,candidate_rowLens hM]; exact hcols - have cone (ν : YoungDiagram) (hν : ν.card = n) (hd : Dominates ν (rowDiagram q)) : - 0 < kronecker (canonicalTableau (candidate M b δ) hn) - (canonicalTableau (candidate M b δ) hn) (canonicalTableau ν hν) := by - apply packingPlan_pos p hv hbands hh hc hp - simpa only [hshape] using hd - have htcheck : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range (rowDiagram q).rowLens.length, ∀ c ∈ List.range (rowDiagram q).rowLens.length, - residualCheck n M r (d+1) (e+1) (a+1) (c+1) (rowDiagram q).rowLens P := by - simpa only [rowDiagram_rows hq] using check - rcases sentinel_capacity_dichotomy μ (rowDiagram q) hposn (by omega) hrpos hμ - ((rowDiagram_card q).trans hqn) P htcheck with h | h | h | h | h - · exact band_kronecker_pos hM hδ hr _ μ _ h - · apply (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr - exact band_kronecker_pos hM hδ hr _ μ.transpose _ h - · exact cone μ hμ h - · apply (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr - exact cone μ.transpose ((transpose_card μ).trans hμ) h - · have ht := hP μ.rowLens ⟨μ.rowLens_sorted,μ.pos_of_mem_rowLens⟩ - ((card_eq_sum_rowLens μ).symm.trans hμ) h - rw [rowDiagram_rowLens] at ht - exact ht.pos _ _ - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Specht.CandidateColumns +import OAI.RepresentationTheory.UniversalSquare.Support.ConstrainedDiagrams +import OAI.RepresentationTheory.UniversalSquare.Balance.PackingPlans + +namespace OAI + +/-! Sentinel Exhaustion. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma testWidth_valid_pos {M f : ℕ} (hf : 1 ≤ f) (hw : 0 < testWidth M f) : + testWidth M f ≤ 8 ∧ f * testWidth M f + 7 + f ≤ 2*M-1 := by + refine ⟨min_le_left _ _, ?_⟩ + have hh := Nat.mul_le_mul_left f (min_le_right 8 ((2*M-8-f)/f)) + have hh' := Nat.div_mul_le_self (2*M-8-f) f + have hq : 0 < (2*M-8-f)/f := lt_of_lt_of_le hw (min_le_right _ _) + have hn : f ≤ 2*M-8-f := by simpa using (Nat.le_div_iff_mul_le (by omega)).mp hq + unfold testWidth + nlinarith [Nat.sub_add_cancel (show f ≤ 2*M-8 by omega), + Nat.sub_add_cancel (show 8 ≤ 2*M by omega), + Nat.sub_add_cancel (show 1 ≤ 2*M by omega)] + +lemma sentinel_height (μ : YoungDiagram) {K : ℕ} (hK : 0 < K) : + ∃ d, 1 ≤ d ∧ d ≤ 5 ∧ (d ≤ 4 → K ≤ rowPrefix μ d) ∧ + (1 < d → rowPrefix μ (d-1) < K) := by + by_cases hh : K ≤ rowPrefix μ 4 + · obtain ⟨d,hd,h4,hp,hl⟩ := first_prefix_height μ hK hh + exact ⟨d,hd,by omega,fun _ => hp,hl⟩ + · exact ⟨5,by decide,le_rfl,by omega,by simpa using Nat.lt_of_not_ge hh⟩ + +lemma prefixBounds_sound_sentinel (μ : YoungDiagram) {M r d e : ℕ} + (hM : 1 ≤ M) (hr : 0 < r) + (hd : 1 < d → colPrefix μ (d-1) < 2*M-1) + (he : e ≤ 4 → 2*M-1 ≤ rowPrefix μ e) (hfail : ¬BandTest M r μ) : + ∀ p ∈ prefixBounds M r d e, 0 < p.1 ∧ colPrefix μ p.1 ≤ p.2 := by + intro p hp + simp only [prefixBounds,List.mem_append] at hp + rcases hp with hp | hp + · split_ifs at hp with hd' + · simp only [List.mem_cons,List.not_mem_nil,or_false] at hp + subst p + exact ⟨by omega,by have := hd hd'; dsimp; omega⟩ + · simp at hp + · obtain ⟨k,hk,hkp⟩ := List.mem_filterMap.mp hp + simp only [List.mem_range] at hk + split_ifs at hkp with hke + · have hp' := Option.some.inj hkp + subst p + have hw := testWidth_valid_pos (by omega : 1 ≤ k+1) hke.2 + have hc : bandCapacity μ (k+1) (testWidth M (k+1)) < r := by + by_contra hh + apply hfail + exact ⟨k+1,by omega,by omega,testWidth M (k+1),hw.1, + (he (by omega)).trans (rowPrefix_mono μ hke.1),hw.2,by omega⟩ + have hb := prefix_le_capacity μ (k+1) (testWidth M (k+1)) + exact ⟨hke.2,by dsimp; omega⟩ + +def residualCheck (n M r d e a b : ℕ) (q : List ℕ) (P : List ℕ → Prop) : Prop := + let A := prefixBounds M r d e ++ [(a,(q.take a).sum-1)] + let B := prefixBounds M r e d ++ [(b,(q.take b).sum-1)] + (d ≤ 4 ∧ coreImpossible (2*M-1) d A) ∨ + (e ≤ 4 ∧ coreImpossible (2*M-1) e B) ∨ impossibleBounds n A B ∨ + ∀ rs ∈ rowsWithin n A B, P rs + +instance (n M r d e a b : ℕ) (q : List ℕ) (P : List ℕ → Prop) [DecidablePred P] : + Decidable (residualCheck n M r d e a b q P) := by + unfold residualCheck; infer_instance + +theorem sentinel_capacity_dichotomy (μ θ : YoungDiagram) {n M r : ℕ} + (hn : 0 < n) (hM : 1 ≤ M) (hr : 0 < r) (hc : μ.card = n) (ht : θ.card = n) + (P : List ℕ → Prop) + (check : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range θ.rowLens.length, ∀ b ∈ List.range θ.rowLens.length, + residualCheck n M r (d+1) (e+1) (a+1) (b+1) θ.rowLens P) : + BandTest M r μ ∨ BandTest M r μ.transpose ∨ Dominates μ θ ∨ + Dominates μ.transpose θ ∨ P μ.rowLens := by + classical + by_contra hh + push Not at hh + rcases hh with ⟨hband,hband',hdom,hdom',hP⟩ + obtain ⟨d,hd,hd',hHd,hHd'⟩ := sentinel_height μ.transpose (show 0 < 2*M-1 by omega) + obtain ⟨e,he,he',hWe,hWe'⟩ := sentinel_height μ (show 0 < 2*M-1 by omega) + obtain ⟨a,ha,ha',hA⟩ := not_dominates_witness ((transpose_card _).trans hc |>.trans ht.symm) hdom' + obtain ⟨b,hb,hb',hB⟩ := not_dominates_witness (hc.trans ht.symm) hdom + have hAf := prefixBounds_sound_sentinel μ hM hr hHd' hWe hband + have hBf := prefixBounds_sound_sentinel μ.transpose hM hr + (by simpa only [colPrefix,YoungDiagram.transpose_transpose] using hWe') hHd hband' + let A := prefixBounds M r d e ++ [(a,(θ.rowLens.take a).sum-1)] + let B := prefixBounds M r e d ++ [(b,(θ.rowLens.take b).sum-1)] + have hAbb : RowBounds μ.transpose A := by + intro p hp + rcases List.mem_append.mp hp with hp | hp + · exact hAf p hp + · have heq : p = (a,(θ.rowLens.take a).sum-1) := by simpa using hp + subst p + rw [rowPrefix_eq_take θ] at hA + exact ⟨ha,by dsimp; omega⟩ + have hBbb : RowBounds μ B := by + intro p hp + rcases List.mem_append.mp hp with hp | hp + · simpa only [colPrefix,YoungDiagram.transpose_transpose] using hBf p hp + · have heq : p = (b,(θ.rowLens.take b).sum-1) := by simpa using hp + subst p + rw [rowPrefix_eq_take θ] at hB + exact ⟨hb,by dsimp; omega⟩ + have h := check (d-1) (by simp; omega) (e-1) (by simp; omega) + (a-1) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) + (b-1) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) + have hde : d-1+1 = d := by omega + have hee : e-1+1 = e := by omega + have hae : a-1+1 = a := by omega + have hbe : b-1+1 = b := by omega + rw [hde,hee,hae,hbe] at h + rcases h with ⟨h4,h⟩ | ⟨h4,h⟩ | h | h + · exact coreImpossible_false μ.transpose (hHd h4) hAbb h + · exact coreImpossible_false μ (hWe h4) hBbb h + · exact impossibleBounds_false hn μ hc hAbb hBbb h + · exact hP (rowsWithin_sound hn μ hc hAbb hBbb h) + +theorem candidate_residual_pos {n M b δ r : ℕ} (hM : 4 ≤ M) + (hδ : δ ≤ 1) (hr : r = 2*b+δ) (hrpos : 0 < r) + (hn : (candidate M b δ).card = n) + (q : List ℕ) (hq : GoodRows q) (hqn : q.sum = n) + (p : PackingPlan) (hv : p.Valid (M+b+δ)) (hbands : BandsValid p.bands) + (hcols : p.columns.Perm ([M+b+δ,M-1+b] ++ + (List.range' 3 (M-4)).reverse ++ List.replicate (b+1) 2 ++ List.replicate (1+δ) 1)) + (hparts : p.parts.Perm q) (P : List ℕ → Prop) + (hP : ∀ rs, GoodRows rs → rs.sum = n → P rs → SquareOccurs (candidate M b δ) (rowDiagram rs)) + (check : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range q.length, ∀ c ∈ List.range q.length, + residualCheck n M r (d+1) (e+1) (a+1) (c+1) q P) + (μ : YoungDiagram) (hμ : μ.card = n) : + 0 < kronecker (canonicalTableau (candidate M b δ) hn) + (canonicalTableau (candidate M b δ) hn) (canonicalTableau μ hμ) := by + have hposn : 0 < n := by rw [← hn,candidate_card _ _ _ (by omega)]; omega + have hp : ∀ a ∈ p.parts, 0 < a := fun a ha => hq.2 a (hparts.mem_iff.mp ha) + have hshape : (columnShape p.parts).transpose = rowDiagram q := by + rw [columnShape_perm hparts]; rfl + have hh : (candidate M b δ).colLen 0 = M+b+δ := by + rw [candidate_colLen _ _ _ _ hM]; simp [candidateLengths] + have hc : p.columns.Perm (candidate M b δ).transpose.rowLens := by + rw [candidate_transpose,candidate_rowLens hM]; exact hcols + have cone (ν : YoungDiagram) (hν : ν.card = n) (hd : Dominates ν (rowDiagram q)) : + 0 < kronecker (canonicalTableau (candidate M b δ) hn) + (canonicalTableau (candidate M b δ) hn) (canonicalTableau ν hν) := by + apply packingPlan_pos p hv hbands hh hc hp + simpa only [hshape] using hd + have htcheck : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range (rowDiagram q).rowLens.length, ∀ c ∈ List.range (rowDiagram q).rowLens.length, + residualCheck n M r (d+1) (e+1) (a+1) (c+1) (rowDiagram q).rowLens P := by + simpa only [rowDiagram_rows hq] using check + rcases sentinel_capacity_dichotomy μ (rowDiagram q) hposn (by omega) hrpos hμ + ((rowDiagram_card q).trans hqn) P htcheck with h | h | h | h | h + · exact band_kronecker_pos hM hδ hr _ μ _ h + · apply (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr + exact band_kronecker_pos hM hδ hr _ μ.transpose _ h + · exact cone μ hμ h + · apply (kronecker_pos_transpose_iff _ hn (candidate_transpose M b δ) μ hμ).mpr + exact cone μ.transpose ((transpose_card μ).trans hμ) h + · have ht := hP μ.rowLens ⟨μ.rowLens_sorted,μ.pos_of_mem_rowLens⟩ + ((card_eq_sum_rowLens μ).symm.trans hμ) h + rw [rowDiagram_rowLens] at ht + exact ht.pos _ _ + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/BandContractions.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/BandContractions.lean index 0c47e5186e2a9bb5bda6a5bb254b7643779c40cf..a428f1341adfa5280a98a9c3677fa9fb7584cbe3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/BandContractions.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/BandContractions.lean @@ -1,151 +1,151 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Band.CommonPath -import OAI.RepresentationTheory.UniversalSquare.Band.BandPath -import OAI.RepresentationTheory.UniversalSquare.Band.BandExtras -import OAI.RepresentationTheory.UniversalSquare.Contraction.FlagDetection - -namespace OAI - -/-! Band Contractions. -/ - -section - -noncomputable section -namespace Saxl - -lemma relabelWord_trans {n m k d : ℕ} (e : Fin n ≃ Fin m) (f : Fin m ≃ Fin k) - (v : WordSpace n d) : relabelWord f (relabelWord e v) = relabelWord (e.trans f) v := rfl - -lemma positionProduct_alphabet {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) - (P : Fin d → Prop) (v : WordSpace a d) (u : WordSpace b d) - (hv : v ∈ alphabetSub a d P) (hu : u ∈ alphabetSub b d P) : - positionProduct e v u ∈ alphabetSub n d P := by - intro w hw - obtain ⟨i,hi⟩ := hw - obtain ⟨j,rfl⟩ := e.symm.surjective i - cases j with - | inl j => - change v (leftWord e w) * u (rightWord e w) = 0 - rw [hv _ ⟨j,hi⟩, zero_mul] - | inr j => - change v (leftWord e w) * u (rightWord e w) = 0 - rw [hu _ ⟨j,hi⟩, mul_zero] - -end Saxl -namespace Saxl.FlagColumns - -lemma blocks_comp {a b : ℕ} (rs : List ℕ) (N : ℕ → Fin b → ℂ) - (φ : Fin a → Fin b) (w : Fin rs.sum → Fin a) : - blocks rs N (φ ∘ w) = blocks rs (fun i x => N i (φ x)) w := by - simp only [blocks, Finset.sum_apply, Pi.smul_apply, smul_eq_mul, pure, Function.comp_apply] - -lemma blocks_lift_relabel_pair {n a b : ℕ} (rs : List ℕ) - (e : Fin rs.sum ≃ Fin n) (φ : Fin a → Fin b) - (N : ℕ → Fin b → ℂ) (B : ℕ → Fin a → ℂ) - (hN : ∀ i x, N i (φ x) = B i x) (v : WordSpace n a) : - dotProduct (blocks rs N) (relabelWord e.symm (letterLift φ v)) = - dotProduct (fun w => blocks rs B (w ∘ e)) v := by - rw [relabelWord_symm_pair e.symm, Equiv.symm_symm, - dotProduct_comm, letterLift_pair, dotProduct_comm] - congr 1 - funext w - change blocks rs N (φ ∘ (w ∘ e)) = _ - rw [blocks_comp, show (fun i x => N i (φ x)) = B from funext (fun i => funext (hN i))] - -end Saxl.FlagColumns -namespace UniversalTensorSquare -open Saxl -open Saxl.FlagColumns - -lemma bandPairSmallLetter_range {M b δ : ℕ} (hM : 4 ≤ M) (a) : - candidatePathAlphabet M b δ a ↔ ∃ x, bandPairSmallLetter hM x = a := by - constructor - · intro ha - refine ⟨finProdFinEquiv (⟨(finProdFinEquiv.symm a).1.val,ha.1⟩, - ⟨(finProdFinEquiv.symm a).2.val,ha.2⟩), ?_⟩ - apply finProdFinEquiv.symm.injective - simp only [bandPairSmallLetter, pairLetterMap, Equiv.symm_apply_apply, - bandSmallRowLetter, bandSmallColLetter, bandSmallLetter] - exact Prod.ext (Fin.ext rfl) (Fin.ext rfl) - · rintro ⟨x,rfl⟩ - simp only [candidatePathAlphabet, bandPairSmallLetter, pairLetterMap, - Equiv.symm_apply_apply, bandSmallRowLetter, bandSmallColLetter, - bandSmallLetter, Fin.val_castLE] - exact ⟨(finProdFinEquiv.symm x : Fin 2 × Fin 2).1.isLt, - (finProdFinEquiv.symm x : Fin 2 × Fin 2).2.isLt⟩ - -theorem candidatePathWord_contraction {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) - (rs : List ℕ) (hrs : ∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) (hn : rs.sum = 2*M-1) : - ∃ N : ℕ → Fin ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0) → ℂ, - (∀ i a, ¬candidatePathAlphabet M b δ a → N i a = 0) ∧ - dotProduct (blocks rs N) - (relabelWord (finCongr hn).symm (candidatePathWord hM t s₁ s₂)) ≠ 0 := by - classical - obtain ⟨B,hB⟩ := Band.odd_path_common_basis - let C : ℕ → Fin 4 → ℂ := fun i a => Band.extendFourBasis B i - (Path.parts a).1 (Path.parts a).2 - let N : ℕ → Fin ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0) → ℂ := - fun i => Function.extend (bandPairSmallLetter hM) (C i) 0 - have hN : ∀ i a, N i (bandPairSmallLetter hM a) = C i a := fun i a => - (bandPairSmallLetter_injective hM).extend_apply (C i) 0 a - refine ⟨N,?_,?_⟩ - · intro i a ha - exact Function.extend_apply' (f := bandPairSmallLetter hM) (C i) (fun _ => 0) a ((bandPairSmallLetter_range hM a).not.mp ha) - · rw [candidatePathWord_eq hM hδ, map_smul, dotProduct_smul, smul_eq_mul] - apply mul_ne_zero (pow_ne_zero _ (by norm_num)) - rw [relabelWord_letterLift, relabelWord_trans, ← relabelWord_letterLift] - let e : Fin rs.sum ≃ Fin (2*(M-1)+1) := (finCongr hn).trans (candidatePathEquiv hM).symm - change dotProduct (blocks rs N) (relabelWord e.symm (letterLift (bandPairSmallLetter hM) - (Path.bandWord (M-1)))) ≠ 0 - rw [blocks_lift_relabel_pair rs e (bandPairSmallLetter hM) N C hN] - have hraw : rs.sum = 2*(M-1)+1 := by omega - convert hB (M-1) rs hrs hraw using 1 - congr 1 - -lemma bandSWLetter_high {M b δ : ℕ} (hM : 4 ≤ M) (x) : - 2 ≤ ((finProdFinEquiv.symm (@bandSWLetter M b δ hM x)).2).val := by - simpa only [bandSWLetter, pairLetterMap, Equiv.symm_apply_apply, bandLongColLetter] - using bandExtraLetter_high hM _ (finProdFinEquiv.symm x).2 - -lemma candidateExtrasWord_alphabet {M b δ r : ℕ} (hM : 4 ≤ M) - (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : - candidateExtrasWord hM s₁ s₂ ∈ alphabetSub (2*r) _ - (fun a => ¬candidatePathAlphabet M b δ a) := by - rw [candidateExtrasWord_eq] - apply positionProduct_alphabet - · apply letterLift_mem_alphabet - intro a ha - exact Nat.not_lt.mpr (bandNELetter_high hM a) ha.1 - · apply letterLift_mem_alphabet - intro a ha - exact Nat.not_lt.mpr (bandSWLetter_high hM a) ha.2 - -theorem candidateExtrasWord_contraction {M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) - (hr : r = 2*b+δ) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) - (η : YoungDiagram) (hη : η.card = 2*r) - (he : ∀ i, Even (η.colLen i)) (hd : η.rowLen 0 ≤ 8) - (rs : List ℕ) (hn : rs.sum = 2*r) (e : Columns.Cells rs ≃ η.cells) - (er : ∀ c, (e c).val.1 = Columns.row c) - (ec : ∀ c c', (e c).val.2 = (e c').val.2 ↔ Columns.col c = Columns.col c') : - ∃ (g : Equiv.Perm (Fin rs.sum)) - (Q : ℕ → Fin ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0) → ℂ), - (∀ i a, candidatePathAlphabet M b δ a → Q i a = 0) ∧ - dotProduct (blocks rs Q) (relabelWord g - (relabelWord (finCongr hn).symm (candidateExtrasWord hM s₁ s₂))) ≠ 0 := by - let u := canonicalTableau η hη - have hs := candidateExtrasWord_support hM hδ hr s₁ s₂ η hη u he hd - let v : Tableau rs.sum η := (Columns.enumerate rs).trans e - have hs' := (cyclic_support_relabel_iff (finCongr hn).symm u v - (candidateExtrasWord hM s₁ s₂)).mpr hs - obtain ⟨g,Q,hQ,hp⟩ := columns_necessary e er ec v _ - (fun a => ¬candidatePathAlphabet M b δ a) - (relabelWord_alphabet _ _ _ (candidateExtrasWord_alphabet hM s₁ s₂)) hs' - exact ⟨g,Q,fun i a ha => hQ i a (not_not_intro ha),hp⟩ - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Band.CommonPath +import OAI.RepresentationTheory.UniversalSquare.Band.BandPath +import OAI.RepresentationTheory.UniversalSquare.Band.BandExtras +import OAI.RepresentationTheory.UniversalSquare.Contraction.FlagDetection + +namespace OAI + +/-! Band Contractions. -/ + +section + +noncomputable section +namespace Saxl + +lemma relabelWord_trans {n m k d : ℕ} (e : Fin n ≃ Fin m) (f : Fin m ≃ Fin k) + (v : WordSpace n d) : relabelWord f (relabelWord e v) = relabelWord (e.trans f) v := rfl + +lemma positionProduct_alphabet {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) + (P : Fin d → Prop) (v : WordSpace a d) (u : WordSpace b d) + (hv : v ∈ alphabetSub a d P) (hu : u ∈ alphabetSub b d P) : + positionProduct e v u ∈ alphabetSub n d P := by + intro w hw + obtain ⟨i,hi⟩ := hw + obtain ⟨j,rfl⟩ := e.symm.surjective i + cases j with + | inl j => + change v (leftWord e w) * u (rightWord e w) = 0 + rw [hv _ ⟨j,hi⟩, zero_mul] + | inr j => + change v (leftWord e w) * u (rightWord e w) = 0 + rw [hu _ ⟨j,hi⟩, mul_zero] + +end Saxl +namespace Saxl.FlagColumns + +lemma blocks_comp {a b : ℕ} (rs : List ℕ) (N : ℕ → Fin b → ℂ) + (φ : Fin a → Fin b) (w : Fin rs.sum → Fin a) : + blocks rs N (φ ∘ w) = blocks rs (fun i x => N i (φ x)) w := by + simp only [blocks, Finset.sum_apply, Pi.smul_apply, smul_eq_mul, pure, Function.comp_apply] + +lemma blocks_lift_relabel_pair {n a b : ℕ} (rs : List ℕ) + (e : Fin rs.sum ≃ Fin n) (φ : Fin a → Fin b) + (N : ℕ → Fin b → ℂ) (B : ℕ → Fin a → ℂ) + (hN : ∀ i x, N i (φ x) = B i x) (v : WordSpace n a) : + dotProduct (blocks rs N) (relabelWord e.symm (letterLift φ v)) = + dotProduct (fun w => blocks rs B (w ∘ e)) v := by + rw [relabelWord_symm_pair e.symm, Equiv.symm_symm, + dotProduct_comm, letterLift_pair, dotProduct_comm] + congr 1 + funext w + change blocks rs N (φ ∘ (w ∘ e)) = _ + rw [blocks_comp, show (fun i x => N i (φ x)) = B from funext (fun i => funext (hN i))] + +end Saxl.FlagColumns +namespace UniversalTensorSquare +open Saxl +open Saxl.FlagColumns + +lemma bandPairSmallLetter_range {M b δ : ℕ} (hM : 4 ≤ M) (a) : + candidatePathAlphabet M b δ a ↔ ∃ x, bandPairSmallLetter hM x = a := by + constructor + · intro ha + refine ⟨finProdFinEquiv (⟨(finProdFinEquiv.symm a).1.val,ha.1⟩, + ⟨(finProdFinEquiv.symm a).2.val,ha.2⟩), ?_⟩ + apply finProdFinEquiv.symm.injective + simp only [bandPairSmallLetter, pairLetterMap, Equiv.symm_apply_apply, + bandSmallRowLetter, bandSmallColLetter, bandSmallLetter] + exact Prod.ext (Fin.ext rfl) (Fin.ext rfl) + · rintro ⟨x,rfl⟩ + simp only [candidatePathAlphabet, bandPairSmallLetter, pairLetterMap, + Equiv.symm_apply_apply, bandSmallRowLetter, bandSmallColLetter, + bandSmallLetter, Fin.val_castLE] + exact ⟨(finProdFinEquiv.symm x : Fin 2 × Fin 2).1.isLt, + (finProdFinEquiv.symm x : Fin 2 × Fin 2).2.isLt⟩ + +theorem candidatePathWord_contraction {n M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (t : Tableau n (candidate M b δ)) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) + (rs : List ℕ) (hrs : ∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) (hn : rs.sum = 2*M-1) : + ∃ N : ℕ → Fin ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0) → ℂ, + (∀ i a, ¬candidatePathAlphabet M b δ a → N i a = 0) ∧ + dotProduct (blocks rs N) + (relabelWord (finCongr hn).symm (candidatePathWord hM t s₁ s₂)) ≠ 0 := by + classical + obtain ⟨B,hB⟩ := Band.odd_path_common_basis + let C : ℕ → Fin 4 → ℂ := fun i a => Band.extendFourBasis B i + (Path.parts a).1 (Path.parts a).2 + let N : ℕ → Fin ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0) → ℂ := + fun i => Function.extend (bandPairSmallLetter hM) (C i) 0 + have hN : ∀ i a, N i (bandPairSmallLetter hM a) = C i a := fun i a => + (bandPairSmallLetter_injective hM).extend_apply (C i) 0 a + refine ⟨N,?_,?_⟩ + · intro i a ha + exact Function.extend_apply' (f := bandPairSmallLetter hM) (C i) (fun _ => 0) a ((bandPairSmallLetter_range hM a).not.mp ha) + · rw [candidatePathWord_eq hM hδ, map_smul, dotProduct_smul, smul_eq_mul] + apply mul_ne_zero (pow_ne_zero _ (by norm_num)) + rw [relabelWord_letterLift, relabelWord_trans, ← relabelWord_letterLift] + let e : Fin rs.sum ≃ Fin (2*(M-1)+1) := (finCongr hn).trans (candidatePathEquiv hM).symm + change dotProduct (blocks rs N) (relabelWord e.symm (letterLift (bandPairSmallLetter hM) + (Path.bandWord (M-1)))) ≠ 0 + rw [blocks_lift_relabel_pair rs e (bandPairSmallLetter hM) N C hN] + have hraw : rs.sum = 2*(M-1)+1 := by omega + convert hB (M-1) rs hrs hraw using 1 + congr 1 + +lemma bandSWLetter_high {M b δ : ℕ} (hM : 4 ≤ M) (x) : + 2 ≤ ((finProdFinEquiv.symm (@bandSWLetter M b δ hM x)).2).val := by + simpa only [bandSWLetter, pairLetterMap, Equiv.symm_apply_apply, bandLongColLetter] + using bandExtraLetter_high hM _ (finProdFinEquiv.symm x).2 + +lemma candidateExtrasWord_alphabet {M b δ r : ℕ} (hM : 4 ≤ M) + (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) : + candidateExtrasWord hM s₁ s₂ ∈ alphabetSub (2*r) _ + (fun a => ¬candidatePathAlphabet M b δ a) := by + rw [candidateExtrasWord_eq] + apply positionProduct_alphabet + · apply letterLift_mem_alphabet + intro a ha + exact Nat.not_lt.mpr (bandNELetter_high hM a) ha.1 + · apply letterLift_mem_alphabet + intro a ha + exact Nat.not_lt.mpr (bandSWLetter_high hM a) ha.2 + +theorem candidateExtrasWord_contraction {M b δ r : ℕ} (hM : 4 ≤ M) (hδ : δ ≤ 1) + (hr : r = 2*b+δ) (s₁ s₂ : Tableau r (ShortColumns.shape b δ)) + (η : YoungDiagram) (hη : η.card = 2*r) + (he : ∀ i, Even (η.colLen i)) (hd : η.rowLen 0 ≤ 8) + (rs : List ℕ) (hn : rs.sum = 2*r) (e : Columns.Cells rs ≃ η.cells) + (er : ∀ c, (e c).val.1 = Columns.row c) + (ec : ∀ c c', (e c).val.2 = (e c').val.2 ↔ Columns.col c = Columns.col c') : + ∃ (g : Equiv.Perm (Fin rs.sum)) + (Q : ℕ → Fin ((candidate M b δ).transpose.colLen 0 * (candidate M b δ).colLen 0) → ℂ), + (∀ i a, candidatePathAlphabet M b δ a → Q i a = 0) ∧ + dotProduct (blocks rs Q) (relabelWord g + (relabelWord (finCongr hn).symm (candidateExtrasWord hM s₁ s₂))) ≠ 0 := by + let u := canonicalTableau η hη + have hs := candidateExtrasWord_support hM hδ hr s₁ s₂ η hη u he hd + let v : Tableau rs.sum η := (Columns.enumerate rs).trans e + have hs' := (cyclic_support_relabel_iff (finCongr hn).symm u v + (candidateExtrasWord hM s₁ s₂)).mpr hs + obtain ⟨g,Q,hQ,hp⟩ := columns_necessary e er ec v _ + (fun a => ¬candidatePathAlphabet M b δ a) + (relabelWord_alphabet _ _ _ (candidateExtrasWord_alphabet hM s₁ s₂)) hs' + exact ⟨g,Q,fun i a ha => hQ i a (not_not_intro ha),hp⟩ + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/ChoiceContractions.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/ChoiceContractions.lean index 67e41da3c9f45ea53cc53a5325929df5f0e6d5e5..bee67a309d22062fcef6d04326fc22c9dbc736cd 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/ChoiceContractions.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/ChoiceContractions.lean @@ -1,87 +1,87 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.RowSquareTools - -namespace OAI - -/-! Choice Contractions. -/ - -section - -open scoped BigOperators -namespace Saxl.Columns - -inductive EdgeChoices where - | fallback - | node (index : ℕ) (next : (ℕ × ℕ × ℕ) → EdgeChoices) - -def solveChoices {rsT rsA rsB : List ℕ} : EdgeChoices → CompactDomains rsT → - CompactDomains rsA → CompactDomains rsB → List (Edge rsT rsA rsB) → - Finset (ℕ × ℕ × ℕ) → ℤ - | .fallback, D, E, F, edges, flag => solveCompact edges.length D E F edges flag - | .node i next, D, E, F, edges, flag => - if D.vanished || E.vanished || F.vanished then 0 - else match edges.rotate i with - | [] => D.mass * E.mass * F.mass - | c :: cs => ∑ v ∈ compactEdgeOptions D E F c flag, - solveChoices (next v) (D.atValue c.1 v.1) (E.atValue c.2.1 v.2.1) - (F.atValue c.2.2 v.2.2) cs flag - -lemma solveChoices_correct {rsT rsA rsB : List ℕ} (ch : EdgeChoices) - (D : CompactDomains rsT) (E : CompactDomains rsA) (F : CompactDomains rsB) - (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : - solveChoices ch D E F edges flag = - domainContraction D.describe E.describe F.describe edges flag := by - induction ch generalizing D E F edges with - | fallback => - rw [solveChoices, ← solveCompact_describe] - exact solveDomains_correct _ _ _ _ _ _ le_rfl - | node i next ih => - rw [solveChoices] - split_ifs with hv - · apply Eq.symm - apply domainContraction_zero - simpa only [CompactDomains.describe_vanished] using hv - · rw [← domainContraction_perm D.describe E.describe F.describe (edges.rotate_perm i) flag] - cases he : edges.rotate i with - | nil => simp only [domainContraction_nil, CompactDomains.describe_mass] - | cons c cs => - rw [domainContraction_cons_options, compactEdgeOptions_describe] - apply Finset.sum_congr rfl - intro v hv - rw [ih] - simp only [CompactDomains.describe_atValue] - -lemma contractionInteger_choices {n : ℕ} (rsA rsB rsT : List ℕ) - (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) - (flag : Finset (ℕ × ℕ × ℕ)) (ch : EdgeChoices) : - contractionInteger rsA rsB rsT ea eb et (fun r a b => if (r,a,b) ∈ flag then 1 else 0) = - solveChoices ch (.full rsT) (.full rsA) (.full rsB) - (certificateEdges rsA rsB rsT ea eb et) flag := by - rw [solveChoices_correct, CompactDomains.describe_full, CompactDomains.describe_full, - CompactDomains.describe_full] - exact contractionInteger_domains .. - -end Saxl.Columns - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma rowSquare_choices {n : ℕ} {p q cs ts : List ℕ} - (hp : GoodRows p) (hq : GoodRows q) (hcs : GoodRows cs) (hts : GoodRows ts) - (he : cs = transposeRows p ∨ cs = p) (ht : ts = transposeRows q) - (hn : cs.sum = n) (hn' : ts.sum = n) - (eb : Fin n ≃ Fin cs.sum) (et : Fin n ≃ Fin ts.sum) - (flag : Finset (ℕ × ℕ × ℕ)) (ch : EdgeChoices) - (hcert : solveChoices ch (.full ts) (.full cs) (.full cs) - (certificateEdges cs cs ts (finCongr hn.symm) eb et) flag ≠ 0) : RowSquare p q := by - apply rowSquare_domain hp hq hcs hts he ht hn hn' eb et flag - rw [← contractionInteger_solve, contractionInteger_choices _ _ _ _ _ _ flag ch] - exact hcert - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.RowSquareTools + +namespace OAI + +/-! Choice Contractions. -/ + +section + +open scoped BigOperators +namespace Saxl.Columns + +inductive EdgeChoices where + | fallback + | node (index : ℕ) (next : (ℕ × ℕ × ℕ) → EdgeChoices) + +def solveChoices {rsT rsA rsB : List ℕ} : EdgeChoices → CompactDomains rsT → + CompactDomains rsA → CompactDomains rsB → List (Edge rsT rsA rsB) → + Finset (ℕ × ℕ × ℕ) → ℤ + | .fallback, D, E, F, edges, flag => solveCompact edges.length D E F edges flag + | .node i next, D, E, F, edges, flag => + if D.vanished || E.vanished || F.vanished then 0 + else match edges.rotate i with + | [] => D.mass * E.mass * F.mass + | c :: cs => ∑ v ∈ compactEdgeOptions D E F c flag, + solveChoices (next v) (D.atValue c.1 v.1) (E.atValue c.2.1 v.2.1) + (F.atValue c.2.2 v.2.2) cs flag + +lemma solveChoices_correct {rsT rsA rsB : List ℕ} (ch : EdgeChoices) + (D : CompactDomains rsT) (E : CompactDomains rsA) (F : CompactDomains rsB) + (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : + solveChoices ch D E F edges flag = + domainContraction D.describe E.describe F.describe edges flag := by + induction ch generalizing D E F edges with + | fallback => + rw [solveChoices, ← solveCompact_describe] + exact solveDomains_correct _ _ _ _ _ _ le_rfl + | node i next ih => + rw [solveChoices] + split_ifs with hv + · apply Eq.symm + apply domainContraction_zero + simpa only [CompactDomains.describe_vanished] using hv + · rw [← domainContraction_perm D.describe E.describe F.describe (edges.rotate_perm i) flag] + cases he : edges.rotate i with + | nil => simp only [domainContraction_nil, CompactDomains.describe_mass] + | cons c cs => + rw [domainContraction_cons_options, compactEdgeOptions_describe] + apply Finset.sum_congr rfl + intro v hv + rw [ih] + simp only [CompactDomains.describe_atValue] + +lemma contractionInteger_choices {n : ℕ} (rsA rsB rsT : List ℕ) + (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) + (flag : Finset (ℕ × ℕ × ℕ)) (ch : EdgeChoices) : + contractionInteger rsA rsB rsT ea eb et (fun r a b => if (r,a,b) ∈ flag then 1 else 0) = + solveChoices ch (.full rsT) (.full rsA) (.full rsB) + (certificateEdges rsA rsB rsT ea eb et) flag := by + rw [solveChoices_correct, CompactDomains.describe_full, CompactDomains.describe_full, + CompactDomains.describe_full] + exact contractionInteger_domains .. + +end Saxl.Columns + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma rowSquare_choices {n : ℕ} {p q cs ts : List ℕ} + (hp : GoodRows p) (hq : GoodRows q) (hcs : GoodRows cs) (hts : GoodRows ts) + (he : cs = transposeRows p ∨ cs = p) (ht : ts = transposeRows q) + (hn : cs.sum = n) (hn' : ts.sum = n) + (eb : Fin n ≃ Fin cs.sum) (et : Fin n ≃ Fin ts.sum) + (flag : Finset (ℕ × ℕ × ℕ)) (ch : EdgeChoices) + (hcert : solveChoices ch (.full ts) (.full cs) (.full cs) + (certificateEdges cs cs ts (finCongr hn.symm) eb et) flag ≠ 0) : RowSquare p q := by + apply rowSquare_domain hp hq hcs hts he ht hn hn' eb et flag + rw [← contractionInteger_solve, contractionInteger_choices _ _ _ _ _ _ flag ch] + exact hcert + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/ColumnCertificates.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/ColumnCertificates.lean index 55350a9fe2454073c951cba98b3f1375adf7a303..fc776e500783d97f3a2521d0fe6a68da33cda349 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/ColumnCertificates.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/ColumnCertificates.lean @@ -1,143 +1,143 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Capacity.NumericBands - -namespace OAI - -/-! Column Certificates. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl - -lemma polytabloid_reindex {n m : ℕ} {μ : YoungDiagram} (t : Tableau m μ) - (e : Fin n ≃ Fin m) (w : Fin n → Fin (μ.colLen 0)) : - polytabloid (e.trans t) w = polytabloid t (w ∘ e.symm) := by - rw [polytabloid_eq_altWord, polytabloid_eq_altWord] - exact (altWord_fiber_relabel e (fun i => (t i).val.2) (rowWord t) w).symm - -namespace Columns - -def signedRowWord (μ : YoungDiagram) (π : Perms μ.transpose.rowLens) : - Fin μ.transpose.rowLens.sum → Fin (μ.colLen 0) := - fun q => ⟨row (perm π (enumerate μ.transpose.rowLens q)), row_lt μ _⟩ - -lemma polytabloid_column_expansion (μ : YoungDiagram) : - polytabloid (columnTableau μ) = - ∑ π : Perms μ.transpose.rowLens, sg π • Pi.single (signedRowWord μ π) 1 := by - classical - let := Fintype.ofFinite (columnGroup (columnTableau μ)) - rw [polytabloid_eq_altWord, altWord_inverse_sum] - symm - apply Fintype.sum_equiv (columnEquiv μ) - intro π - rw [← columnPerm_sign μ π] - congr 2 - funext q - apply Fin.ext - change row (perm π (enumerate μ.transpose.rowLens q)) = - ((columnTableau μ) ((columnEquiv μ π).val q)).val.1 - rw [columnTableau_val] - simp only [columnEquiv, Equiv.ofBijective_apply, columnPerm, Equiv.permCongr_apply, - Equiv.symm_symm, Equiv.apply_symm_apply] - -lemma polytabloid_placed_expansion {n : ℕ} (μ : YoungDiagram) - (e : Fin n ≃ Fin μ.transpose.rowLens.sum) : - polytabloid (e.trans (columnTableau μ)) = - ∑ π : Perms μ.transpose.rowLens, sg π • Pi.single (signedRowWord μ π ∘ e) 1 := by - classical - funext w - rw [polytabloid_reindex, polytabloid_column_expansion] - simp only [Finset.sum_apply, Pi.smul_apply] - apply Finset.sum_congr rfl - intro π hπ - congr 1 - simp only [Pi.single_apply] - congr 1 - apply propext - constructor - · intro hw - funext q - have h := congrFun hw (e q) - simpa using h - · intro hw - funext q - have h := congrFun hw (e.symm q) - simpa using h - -def sgInteger : {rs : List ℕ} → Perms rs → ℤ - | [], _ => 1 - | _ :: _, (π, σ) => (Equiv.Perm.sign π : ℤ) * sgInteger σ - -lemma sgInteger_cast {rs : List ℕ} (π : Perms rs) : (sgInteger π : ℂ) = sg π := by - induction rs with - | nil => simp [sgInteger, sg] - | cons r rs ih => simp only [sgInteger, sg, Int.cast_mul, ih] - -def tableFor {n : ℕ} (μ : YoungDiagram) (rs : List ℕ) - (h : μ.transpose.rowLens = rs) (e : Fin n ≃ Fin rs.sum) : Tableau n μ := - e.trans (h ▸ columnTableau μ) - -def contractionInteger {n : ℕ} (rsA rsB rsT : List ℕ) - (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) - (L : ℕ → ℕ → ℕ → ℤ) : ℤ := - ∑ π : Perms rsT, ∑ σ : Perms rsA, ∑ τ : Perms rsB, - sgInteger π * sgInteger σ * sgInteger τ * - ∏ i : Fin n, L (row (perm π (enumerate rsT (et i)))) - (row (perm σ (enumerate rsA (ea i)))) - (row (perm τ (enumerate rsB (eb i)))) - -def pairFlag {d a b : ℕ} (L : ℕ → ℕ → ℕ → ℤ) : Fin d → Fin (a*b) → ℂ := - fun r c => (L r.val (finProdFinEquiv.symm c).1.val (finProdFinEquiv.symm c).2.val : ℂ) - -lemma contractionInteger_correct {n : ℕ} (α β μ : YoungDiagram) - (rsA rsB rsT : List ℕ) (ha : α.transpose.rowLens = rsA) - (hb : β.transpose.rowLens = rsB) (ht : μ.transpose.rowLens = rsT) - (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) - (L : ℕ → ℕ → ℕ → ℤ) : - dotProduct (wordMap (pairFlag L) (polytabloid (tableFor μ rsT ht et))) - (wordTensor _ _ _ (polytabloid (tableFor α rsA ha ea) ⊗ₜ[ℂ] - polytabloid (tableFor β rsB hb eb))) = - (contractionInteger rsA rsB rsT ea eb et L : ℂ) := by - subst rsA rsB rsT - simp only [tableFor, polytabloid_placed_expansion, map_sum, map_smul, - sum_dotProduct, smul_dotProduct] - simp only [TensorProduct.sum_tmul, TensorProduct.tmul_sum, - TensorProduct.smul_tmul_smul, map_sum, map_smul, wordTensor_single, - dotProduct_sum, dotProduct_smul, smul_eq_mul, - dotProduct_single_one, wordMap_single, - contractionInteger, Int.cast_sum, Int.cast_mul, Int.cast_prod, sgInteger_cast] - apply Finset.sum_congr rfl - intro π hπ - conv_lhs => arg 2; rw [Finset.sum_comm] - simp only [Finset.mul_sum] - apply Finset.sum_congr rfl - intro σ hσ - apply Finset.sum_congr rfl - intro τ hτ - simp only [mul_assoc] - congr 3 - apply Finset.prod_congr rfl - intro q hq - simp only [pairFlag, mergeWords, Equiv.symm_apply_apply, signedRowWord, Function.comp_apply] - -theorem kronecker_pos_of_integer_certificate {n : ℕ} {α β μ : YoungDiagram} - (a : Tableau n α) (b : Tableau n β) (t : Tableau n μ) - (rsA rsB rsT : List ℕ) (ha : α.transpose.rowLens = rsA) - (hb : β.transpose.rowLens = rsB) (ht : μ.transpose.rowLens = rsT) - (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) - (L : ℕ → ℕ → ℕ → ℤ) (hcert : contractionInteger rsA rsB rsT ea eb et L ≠ 0) : - 0 < kronecker a b t := by - apply kronecker_pos_of_contraction a (tableFor α rsA ha ea) - b (tableFor β rsB hb eb) t (tableFor μ rsT ht et) (pairFlag L) - rw [contractionInteger_correct] - exact_mod_cast hcert - -end Columns -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Capacity.NumericBands + +namespace OAI + +/-! Column Certificates. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl + +lemma polytabloid_reindex {n m : ℕ} {μ : YoungDiagram} (t : Tableau m μ) + (e : Fin n ≃ Fin m) (w : Fin n → Fin (μ.colLen 0)) : + polytabloid (e.trans t) w = polytabloid t (w ∘ e.symm) := by + rw [polytabloid_eq_altWord, polytabloid_eq_altWord] + exact (altWord_fiber_relabel e (fun i => (t i).val.2) (rowWord t) w).symm + +namespace Columns + +def signedRowWord (μ : YoungDiagram) (π : Perms μ.transpose.rowLens) : + Fin μ.transpose.rowLens.sum → Fin (μ.colLen 0) := + fun q => ⟨row (perm π (enumerate μ.transpose.rowLens q)), row_lt μ _⟩ + +lemma polytabloid_column_expansion (μ : YoungDiagram) : + polytabloid (columnTableau μ) = + ∑ π : Perms μ.transpose.rowLens, sg π • Pi.single (signedRowWord μ π) 1 := by + classical + let := Fintype.ofFinite (columnGroup (columnTableau μ)) + rw [polytabloid_eq_altWord, altWord_inverse_sum] + symm + apply Fintype.sum_equiv (columnEquiv μ) + intro π + rw [← columnPerm_sign μ π] + congr 2 + funext q + apply Fin.ext + change row (perm π (enumerate μ.transpose.rowLens q)) = + ((columnTableau μ) ((columnEquiv μ π).val q)).val.1 + rw [columnTableau_val] + simp only [columnEquiv, Equiv.ofBijective_apply, columnPerm, Equiv.permCongr_apply, + Equiv.symm_symm, Equiv.apply_symm_apply] + +lemma polytabloid_placed_expansion {n : ℕ} (μ : YoungDiagram) + (e : Fin n ≃ Fin μ.transpose.rowLens.sum) : + polytabloid (e.trans (columnTableau μ)) = + ∑ π : Perms μ.transpose.rowLens, sg π • Pi.single (signedRowWord μ π ∘ e) 1 := by + classical + funext w + rw [polytabloid_reindex, polytabloid_column_expansion] + simp only [Finset.sum_apply, Pi.smul_apply] + apply Finset.sum_congr rfl + intro π hπ + congr 1 + simp only [Pi.single_apply] + congr 1 + apply propext + constructor + · intro hw + funext q + have h := congrFun hw (e q) + simpa using h + · intro hw + funext q + have h := congrFun hw (e.symm q) + simpa using h + +def sgInteger : {rs : List ℕ} → Perms rs → ℤ + | [], _ => 1 + | _ :: _, (π, σ) => (Equiv.Perm.sign π : ℤ) * sgInteger σ + +lemma sgInteger_cast {rs : List ℕ} (π : Perms rs) : (sgInteger π : ℂ) = sg π := by + induction rs with + | nil => simp [sgInteger, sg] + | cons r rs ih => simp only [sgInteger, sg, Int.cast_mul, ih] + +def tableFor {n : ℕ} (μ : YoungDiagram) (rs : List ℕ) + (h : μ.transpose.rowLens = rs) (e : Fin n ≃ Fin rs.sum) : Tableau n μ := + e.trans (h ▸ columnTableau μ) + +def contractionInteger {n : ℕ} (rsA rsB rsT : List ℕ) + (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) + (L : ℕ → ℕ → ℕ → ℤ) : ℤ := + ∑ π : Perms rsT, ∑ σ : Perms rsA, ∑ τ : Perms rsB, + sgInteger π * sgInteger σ * sgInteger τ * + ∏ i : Fin n, L (row (perm π (enumerate rsT (et i)))) + (row (perm σ (enumerate rsA (ea i)))) + (row (perm τ (enumerate rsB (eb i)))) + +def pairFlag {d a b : ℕ} (L : ℕ → ℕ → ℕ → ℤ) : Fin d → Fin (a*b) → ℂ := + fun r c => (L r.val (finProdFinEquiv.symm c).1.val (finProdFinEquiv.symm c).2.val : ℂ) + +lemma contractionInteger_correct {n : ℕ} (α β μ : YoungDiagram) + (rsA rsB rsT : List ℕ) (ha : α.transpose.rowLens = rsA) + (hb : β.transpose.rowLens = rsB) (ht : μ.transpose.rowLens = rsT) + (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) + (L : ℕ → ℕ → ℕ → ℤ) : + dotProduct (wordMap (pairFlag L) (polytabloid (tableFor μ rsT ht et))) + (wordTensor _ _ _ (polytabloid (tableFor α rsA ha ea) ⊗ₜ[ℂ] + polytabloid (tableFor β rsB hb eb))) = + (contractionInteger rsA rsB rsT ea eb et L : ℂ) := by + subst rsA rsB rsT + simp only [tableFor, polytabloid_placed_expansion, map_sum, map_smul, + sum_dotProduct, smul_dotProduct] + simp only [TensorProduct.sum_tmul, TensorProduct.tmul_sum, + TensorProduct.smul_tmul_smul, map_sum, map_smul, wordTensor_single, + dotProduct_sum, dotProduct_smul, smul_eq_mul, + dotProduct_single_one, wordMap_single, + contractionInteger, Int.cast_sum, Int.cast_mul, Int.cast_prod, sgInteger_cast] + apply Finset.sum_congr rfl + intro π hπ + conv_lhs => arg 2; rw [Finset.sum_comm] + simp only [Finset.mul_sum] + apply Finset.sum_congr rfl + intro σ hσ + apply Finset.sum_congr rfl + intro τ hτ + simp only [mul_assoc] + congr 3 + apply Finset.prod_congr rfl + intro q hq + simp only [pairFlag, mergeWords, Equiv.symm_apply_apply, signedRowWord, Function.comp_apply] + +theorem kronecker_pos_of_integer_certificate {n : ℕ} {α β μ : YoungDiagram} + (a : Tableau n α) (b : Tableau n β) (t : Tableau n μ) + (rsA rsB rsT : List ℕ) (ha : α.transpose.rowLens = rsA) + (hb : β.transpose.rowLens = rsB) (ht : μ.transpose.rowLens = rsT) + (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) + (L : ℕ → ℕ → ℕ → ℤ) (hcert : contractionInteger rsA rsB rsT ea eb et L ≠ 0) : + 0 < kronecker a b t := by + apply kronecker_pos_of_contraction a (tableFor α rsA ha ea) + b (tableFor β rsB hb eb) t (tableFor μ rsT ht et) (pairFlag L) + rw [contractionInteger_correct] + exact_mod_cast hcert + +end Columns +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/CompactDomains.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/CompactDomains.lean index a5faf61000b5731c31f86f414bce6750835888de..07b03ba801aa48020bbaab5a1ffd7dcc0565239b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/CompactDomains.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/CompactDomains.lean @@ -1,30 +1,30 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.RowSquareTools - -namespace OAI - -/-! Compact Domains. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma rowSquare_compact {n : ℕ} {p q cs ts : List ℕ} - (hp : GoodRows p) (hq : GoodRows q) (hcs : GoodRows cs) (hts : GoodRows ts) - (he : cs = transposeRows p ∨ cs = p) (ht : ts = transposeRows q) - (hn : cs.sum = n) (hn' : ts.sum = n) - (eb : Fin n ≃ Fin cs.sum) (et : Fin n ≃ Fin ts.sum) - (flag : Finset (ℕ × ℕ × ℕ)) - (hcert : solveCompact n (.full ts) (.full cs) (.full cs) - (certificateEdges cs cs ts (finCongr hn.symm) eb et) flag ≠ 0) : RowSquare p q := by - apply rowSquare_domain hp hq hcs hts he ht hn hn' eb et flag - simpa only [← CompactDomains.describe_full,solveCompact_describe] using hcert - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.RowSquareTools + +namespace OAI + +/-! Compact Domains. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma rowSquare_compact {n : ℕ} {p q cs ts : List ℕ} + (hp : GoodRows p) (hq : GoodRows q) (hcs : GoodRows cs) (hts : GoodRows ts) + (he : cs = transposeRows p ∨ cs = p) (ht : ts = transposeRows q) + (hn : cs.sum = n) (hn' : ts.sum = n) + (eb : Fin n ≃ Fin cs.sum) (et : Fin n ≃ Fin ts.sum) + (flag : Finset (ℕ × ℕ × ℕ)) + (hcert : solveCompact n (.full ts) (.full cs) (.full cs) + (certificateEdges cs cs ts (finCongr hn.symm) eb et) flag ≠ 0) : RowSquare p q := by + apply rowSquare_domain hp hq hcs hts he ht hn hn' eb et flag + simpa only [← CompactDomains.describe_full,solveCompact_describe] using hcert + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/CompactDomainsCore.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/CompactDomainsCore.lean index 1d942a773f4a42a1da22f79f00344c836970a29c..35c24c2542c402c76066c5fd890eae692d72eb64 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/CompactDomainsCore.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/CompactDomainsCore.lean @@ -1,287 +1,287 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.VectorDomainsCore - -namespace OAI - -/-! Compact Domains Core. -/ - -section - -open scoped BigOperators -namespace Saxl.Columns - -abbrev CompactDomain (n : ℕ) := Option (Equiv.Perm (Fin n) × Finset (Fin n)) - -def CompactDomain.describe {n : ℕ} : CompactDomain n → Finset (Equiv.Perm (Fin n)) - | none => ∅ - | some (π,s) => Finset.univ.filter (fun σ => ∀ i, i ∉ s → σ i = π i) - -lemma CompactDomain.mem_describe {n : ℕ} (π σ : Equiv.Perm (Fin n)) (s : Finset (Fin n)) : - σ ∈ CompactDomain.describe (some (π,s)) ↔ ∀ i, i ∉ s → σ i = π i := by - simp [describe] - -def CompactDomain.full (n : ℕ) : CompactDomain n := some (1,Finset.univ) - -lemma CompactDomain.describe_full (n : ℕ) : (full n).describe = Finset.univ := by - ext σ; simp [full,mem_describe] - -def CompactDomain.atValue {n : ℕ} : CompactDomain n → Fin n → ℕ → CompactDomain n - | none, _, _ => none - | some (π,s), i, j => - if hj : j < n then - let k := π.symm ⟨j,hj⟩ - if i ∈ s then - if k ∈ s then some (π * Equiv.swap i k,s.erase i) else none - else if (π i).val = j then some (π,s) else none - else none - -lemma CompactDomain.describe_atValue {n : ℕ} (D : CompactDomain n) (i : Fin n) (j : ℕ) : - (D.atValue i j).describe = D.describe.filter (fun σ => (σ i).val = j) := by - cases D with - | none => simp [atValue,describe] - | some ds => - rcases ds with ⟨π,s⟩ - ext σ - simp only [Finset.mem_filter,mem_describe] - by_cases hj : j < n - · let k := π.symm ⟨j,hj⟩ - have hk : π k = ⟨j,hj⟩ := π.apply_symm_apply _ - by_cases hi : i ∈ s - · by_cases hks : k ∈ s - · simp only [atValue,dite_eq_left hj,ite_eq_left hi,show π.symm ⟨j,hj⟩ ∈ s from hks, - ite_true,mem_describe] - constructor - · intro h - constructor - · intro x hx - have hxi : x ≠ i := by intro he; subst x; exact hx hi - have hxk : x ≠ π.symm ⟨j,hj⟩ := by intro he; subst x; exact hx hks - simpa only [Equiv.Perm.mul_apply,Equiv.swap_apply_of_ne_of_ne hxi hxk] using - h x (by simp [hx]) - · have hh := h i (by simp) - simpa [Equiv.Perm.mul_apply,k] using congrArg Fin.val hh - · rintro ⟨h,hv⟩ x hx - by_cases hxi : x = i - · subst x - simpa [Equiv.Perm.mul_apply,k] using (Fin.ext hv : σ i = ⟨j,hj⟩) - · have hxs : x ∉ s := by simpa [Finset.mem_erase,hxi] using hx - have hxk : x ≠ π.symm ⟨j,hj⟩ := by intro he; subst x; exact hxs hks - simpa only [Equiv.Perm.mul_apply,Equiv.swap_apply_of_ne_of_ne hxi hxk] using h x hxs - · simp only [atValue,dite_eq_left hj,ite_eq_left hi,show π.symm ⟨j,hj⟩ ∉ s from hks, - ite_false,describe,Finset.notMem_empty,false_iff,not_and] - intro h hv - have hki : k = i := σ.injective ((h k hks).trans (hk.trans (Fin.ext hv).symm)) - exact hks (hki.symm ▸ hi) - · by_cases hv : (π i).val = j - · simp only [atValue,dite_eq_left hj,ite_eq_right hi,ite_eq_left hv,mem_describe] - exact ⟨fun h => ⟨h,(congrArg Fin.val (h i hi)).trans hv⟩,fun h => h.1⟩ - · simp only [atValue,dite_eq_left hj,ite_eq_right hi,ite_eq_right hv,describe,Finset.notMem_empty, - false_iff,not_and] - intro h he - exact hv ((congrArg Fin.val (h i hi)).symm.trans he) - · simp only [atValue,dite_eq_right hj,describe,Finset.notMem_empty,false_iff,not_and] - intro h hv - exact hj (hv ▸ (σ i).isLt) - -def CompactDomain.vanished {n : ℕ} (D : CompactDomain n) : Bool := D.isNone - -lemma CompactDomain.describe_vanished {n : ℕ} (D : CompactDomain n) : - decide (D.describe = ∅) = D.vanished := by - cases D with - | none => rfl - | some ds => - rcases ds with ⟨π,s⟩ - have hh : π ∈ CompactDomain.describe (some (π,s)) := by simp only [mem_describe]; tauto - have hn := Finset.ne_empty_of_mem hh - simp only [hn,decide_false,vanished,Option.isNone_some] - -lemma compact_sum_sign {n : ℕ} (π : Equiv.Perm (Fin n)) (s : Finset (Fin n)) : - (∑ σ ∈ CompactDomain.describe (some (π,s)), (Equiv.Perm.sign σ : ℤ)) = - if s.card ≤ 1 then (Equiv.Perm.sign π : ℤ) else 0 := by - by_cases hs : s.card ≤ 1 - · rw [ite_eq_left hs] - have he : CompactDomain.describe (some (π,s)) = {π} := by - ext σ - rw [CompactDomain.mem_describe,Finset.mem_singleton] - constructor - · intro h - apply Equiv.ext - intro i - by_cases hi : i ∈ s - · let k := π.symm (σ i) - have hk : π k = σ i := π.apply_symm_apply _ - by_cases hks : k ∈ s - · have hki : k = i := Finset.card_le_one.mp hs k hks i hi - exact (hki ▸ hk).symm - · have hki : k = i := σ.injective ((h k hks).trans hk) - exact (hki ▸ hk).symm - · exact h i hi - · rintro rfl i hi; rfl - simp only [he,Finset.sum_singleton] - · rw [ite_eq_right hs] - obtain ⟨i,hi,k,hk,hik⟩ := Finset.one_lt_card.mp (by omega : 1 < s.card) - let τ := Equiv.swap i k - have ht : Equiv.Perm.sign τ = -1 := Equiv.Perm.sign_swap hik - have hm (σ : Equiv.Perm (Fin n)) : - σ * τ ∈ CompactDomain.describe (some (π,s)) ↔ - σ ∈ CompactDomain.describe (some (π,s)) := by - simp only [CompactDomain.mem_describe] - have hh (x : Fin n) (hx : x ∉ s) : τ x = x := by - apply Equiv.swap_apply_of_ne_of_ne - · intro he; subst x; exact hx hi - · intro he; subst x; exact hx hk - simp only [Equiv.Perm.mul_apply] - constructor <;> intro h x hx <;> simpa only [hh x hx] using h x hx - have he : (∑ σ ∈ CompactDomain.describe (some (π,s)), (Equiv.Perm.sign σ : ℤ)) = - ∑ σ ∈ CompactDomain.describe (some (π,s)), (Equiv.Perm.sign (σ * τ) : ℤ) := by - apply Finset.sum_bij (fun σ _ => σ * τ) - · intro σ hσ; exact (hm σ).mpr hσ - · intro σ hσ ρ hρ h; exact mul_right_cancel h - · intro σ hσ - refine ⟨σ * τ,(hm σ).mpr hσ,?_⟩ - simp [τ,mul_assoc] - · intro σ hσ - simp [τ,mul_assoc] - have hn : (∑ σ ∈ CompactDomain.describe (some (π,s)), (Equiv.Perm.sign (σ * τ) : ℤ)) = - -(∑ σ ∈ CompactDomain.describe (some (π,s)), (Equiv.Perm.sign σ : ℤ)) := by - simp only [Equiv.Perm.sign_mul,ht,Units.val_neg,mul_neg_one, - Finset.sum_neg_distrib] - omega - -def CompactDomain.mass {n : ℕ} : CompactDomain n → ℤ - | none => 0 - | some (π,s) => if s.card ≤ 1 then vectorSign n (permVector π) else 0 - -lemma CompactDomain.describe_mass {n : ℕ} (D : CompactDomain n) : - (∑ σ ∈ D.describe, (Equiv.Perm.sign σ : ℤ)) = D.mass := by - cases D with - | none => simp [describe,mass] - | some ds => - rcases ds with ⟨π,s⟩ - simp only [mass,vectorSign_perm,compact_sum_sign] - -def CompactDomains : List ℕ → Type - | [] => Unit - | r :: rs => CompactDomain r × CompactDomains rs - -def CompactDomains.full : (rs : List ℕ) → CompactDomains rs - | [] => () - | r :: rs => (CompactDomain.full r,full rs) - -def CompactDomains.describe : {rs : List ℕ} → CompactDomains rs → Domains rs - | [], _ => () - | _ :: _, (s,D) => (s.describe,describe D) - -def CompactDomains.atValue : {rs : List ℕ} → CompactDomains rs → Cells rs → ℕ → CompactDomains rs - | _ :: _, (s,D), .inl i, j => (s.atValue i j,D) - | _ :: _, (s,D), .inr c, j => (s,atValue D c j) - -def CompactDomains.vanished : {rs : List ℕ} → CompactDomains rs → Bool - | [], _ => false - | _ :: _, (s,D) => s.vanished || vanished D - -def CompactDomains.mass : {rs : List ℕ} → CompactDomains rs → ℤ - | [], _ => 1 - | _ :: _, (s,D) => s.mass * mass D - -lemma CompactDomains.describe_full (rs : List ℕ) : (full rs).describe = Domains.full rs := by - induction rs with - | nil => rfl - | cons r rs ih => simp only [full,describe,Domains.full,CompactDomain.describe_full,ih]; rfl - -lemma CompactDomains.describe_atValue {rs : List ℕ} (D : CompactDomains rs) (c : Cells rs) (j : ℕ) : - (D.atValue c j).describe = D.describe.atValue c j := by - induction rs with - | nil => exact c.elim - | cons r rs ih => - rcases D with ⟨s,D⟩ - cases c with - | inl i => simp only [atValue,describe,Domains.atValue,CompactDomain.describe_atValue]; rfl - | inr c => simp only [atValue,describe,Domains.atValue,ih]; rfl - -lemma CompactDomains.describe_vanished {rs : List ℕ} (D : CompactDomains rs) : - D.describe.vanished = D.vanished := by - induction rs with - | nil => rfl - | cons r rs ih => - rcases D with ⟨s,D⟩ - simp only [describe,Domains.vanished,vanished,CompactDomain.describe_vanished,ih] - -lemma CompactDomains.describe_mass {rs : List ℕ} (D : CompactDomains rs) : - D.describe.mass = D.mass := by - induction rs with - | nil => rfl - | cons r rs ih => - rcases D with ⟨s,D⟩ - simp only [describe,Domains.mass,mass,CompactDomain.describe_mass,ih] - -def compactEdgeOptions {rsT rsA rsB : List ℕ} - (D : CompactDomains rsT) (E : CompactDomains rsA) (F : CompactDomains rsB) - (c : Edge rsT rsA rsB) (flag : Finset (ℕ × ℕ × ℕ)) : Finset (ℕ × ℕ × ℕ) := - flag.filter (fun v => (D.atValue c.1 v.1).vanished = false ∧ - (E.atValue c.2.1 v.2.1).vanished = false ∧ (F.atValue c.2.2 v.2.2).vanished = false) - -lemma compactEdgeOptions_describe {rsT rsA rsB : List ℕ} - (D : CompactDomains rsT) (E : CompactDomains rsA) (F : CompactDomains rsB) - (c : Edge rsT rsA rsB) (flag : Finset (ℕ × ℕ × ℕ)) : - edgeOptions D.describe E.describe F.describe c flag = compactEdgeOptions D E F c flag := by - simp only [compactEdgeOptions,edgeOptions,← CompactDomains.describe_atValue, - CompactDomains.describe_vanished] - -def compactOrderEdges {rsT rsA rsB : List ℕ} - (D : CompactDomains rsT) (E : CompactDomains rsA) (F : CompactDomains rsB) - (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : List (Edge rsT rsA rsB) := - bringBest (fun c => (compactEdgeOptions D E F c flag).card) edges - -lemma compactOrderEdges_describe {rsT rsA rsB : List ℕ} - (D : CompactDomains rsT) (E : CompactDomains rsA) (F : CompactDomains rsB) - (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : - orderEdges D.describe E.describe F.describe edges flag = compactOrderEdges D E F edges flag := by - simp only [compactOrderEdges,orderEdges,compactEdgeOptions_describe] - -def solveCompact {rsT rsA rsB : List ℕ} : ℕ → CompactDomains rsT → CompactDomains rsA → - CompactDomains rsB → List (Edge rsT rsA rsB) → Finset (ℕ × ℕ × ℕ) → ℤ - | fuel, D, E, F, edges, flag => - if D.vanished || E.vanished || F.vanished then 0 - else match compactOrderEdges D E F edges flag with - | [] => D.mass * E.mass * F.mass - | c :: cs => match fuel with - | 0 => 0 - | k+1 => ∑ v ∈ compactEdgeOptions D E F c flag, - solveCompact k (D.atValue c.1 v.1) (E.atValue c.2.1 v.2.1) - (F.atValue c.2.2 v.2.2) cs flag - -lemma solveCompact_describe {rsT rsA rsB : List ℕ} (fuel : ℕ) - (D : CompactDomains rsT) (E : CompactDomains rsA) (F : CompactDomains rsB) - (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : - solveDomains fuel D.describe E.describe F.describe edges flag = solveCompact fuel D E F edges flag := by - induction fuel generalizing D E F edges with - | zero => - rw [solveCompact,solveDomains] - simp only [CompactDomains.describe_vanished,compactOrderEdges_describe,CompactDomains.describe_mass] - split <;> rfl - | succ fuel ih => - rw [solveCompact,solveDomains] - simp only [CompactDomains.describe_vanished,compactOrderEdges_describe,CompactDomains.describe_mass] - split - · rfl - · cases he : compactOrderEdges D E F edges flag with - | nil => rfl - | cons c cs => - simp only [compactEdgeOptions_describe,← CompactDomains.describe_atValue,ih] - -lemma contractionInteger_compact {n : ℕ} (rsA rsB rsT : List ℕ) - (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) - (flag : Finset (ℕ × ℕ × ℕ)) : - contractionInteger rsA rsB rsT ea eb et (fun r a b => if (r,a,b) ∈ flag then 1 else 0) = - solveCompact n (.full rsT) (.full rsA) (.full rsB) - (certificateEdges rsA rsB rsT ea eb et) flag := by - rw [contractionInteger_solve,← CompactDomains.describe_full,← CompactDomains.describe_full, - ← CompactDomains.describe_full,solveCompact_describe] - -end Saxl.Columns - -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.VectorDomainsCore + +namespace OAI + +/-! Compact Domains Core. -/ + +section + +open scoped BigOperators +namespace Saxl.Columns + +abbrev CompactDomain (n : ℕ) := Option (Equiv.Perm (Fin n) × Finset (Fin n)) + +def CompactDomain.describe {n : ℕ} : CompactDomain n → Finset (Equiv.Perm (Fin n)) + | none => ∅ + | some (π,s) => Finset.univ.filter (fun σ => ∀ i, i ∉ s → σ i = π i) + +lemma CompactDomain.mem_describe {n : ℕ} (π σ : Equiv.Perm (Fin n)) (s : Finset (Fin n)) : + σ ∈ CompactDomain.describe (some (π,s)) ↔ ∀ i, i ∉ s → σ i = π i := by + simp [describe] + +def CompactDomain.full (n : ℕ) : CompactDomain n := some (1,Finset.univ) + +lemma CompactDomain.describe_full (n : ℕ) : (full n).describe = Finset.univ := by + ext σ; simp [full,mem_describe] + +def CompactDomain.atValue {n : ℕ} : CompactDomain n → Fin n → ℕ → CompactDomain n + | none, _, _ => none + | some (π,s), i, j => + if hj : j < n then + let k := π.symm ⟨j,hj⟩ + if i ∈ s then + if k ∈ s then some (π * Equiv.swap i k,s.erase i) else none + else if (π i).val = j then some (π,s) else none + else none + +lemma CompactDomain.describe_atValue {n : ℕ} (D : CompactDomain n) (i : Fin n) (j : ℕ) : + (D.atValue i j).describe = D.describe.filter (fun σ => (σ i).val = j) := by + cases D with + | none => simp [atValue,describe] + | some ds => + rcases ds with ⟨π,s⟩ + ext σ + simp only [Finset.mem_filter,mem_describe] + by_cases hj : j < n + · let k := π.symm ⟨j,hj⟩ + have hk : π k = ⟨j,hj⟩ := π.apply_symm_apply _ + by_cases hi : i ∈ s + · by_cases hks : k ∈ s + · simp only [atValue,dite_eq_left hj,ite_eq_left hi,show π.symm ⟨j,hj⟩ ∈ s from hks, + ite_true,mem_describe] + constructor + · intro h + constructor + · intro x hx + have hxi : x ≠ i := by intro he; subst x; exact hx hi + have hxk : x ≠ π.symm ⟨j,hj⟩ := by intro he; subst x; exact hx hks + simpa only [Equiv.Perm.mul_apply,Equiv.swap_apply_of_ne_of_ne hxi hxk] using + h x (by simp [hx]) + · have hh := h i (by simp) + simpa [Equiv.Perm.mul_apply,k] using congrArg Fin.val hh + · rintro ⟨h,hv⟩ x hx + by_cases hxi : x = i + · subst x + simpa [Equiv.Perm.mul_apply,k] using (Fin.ext hv : σ i = ⟨j,hj⟩) + · have hxs : x ∉ s := by simpa [Finset.mem_erase,hxi] using hx + have hxk : x ≠ π.symm ⟨j,hj⟩ := by intro he; subst x; exact hxs hks + simpa only [Equiv.Perm.mul_apply,Equiv.swap_apply_of_ne_of_ne hxi hxk] using h x hxs + · simp only [atValue,dite_eq_left hj,ite_eq_left hi,show π.symm ⟨j,hj⟩ ∉ s from hks, + ite_false,describe,Finset.notMem_empty,false_iff,not_and] + intro h hv + have hki : k = i := σ.injective ((h k hks).trans (hk.trans (Fin.ext hv).symm)) + exact hks (hki.symm ▸ hi) + · by_cases hv : (π i).val = j + · simp only [atValue,dite_eq_left hj,ite_eq_right hi,ite_eq_left hv,mem_describe] + exact ⟨fun h => ⟨h,(congrArg Fin.val (h i hi)).trans hv⟩,fun h => h.1⟩ + · simp only [atValue,dite_eq_left hj,ite_eq_right hi,ite_eq_right hv,describe,Finset.notMem_empty, + false_iff,not_and] + intro h he + exact hv ((congrArg Fin.val (h i hi)).symm.trans he) + · simp only [atValue,dite_eq_right hj,describe,Finset.notMem_empty,false_iff,not_and] + intro h hv + exact hj (hv ▸ (σ i).isLt) + +def CompactDomain.vanished {n : ℕ} (D : CompactDomain n) : Bool := D.isNone + +lemma CompactDomain.describe_vanished {n : ℕ} (D : CompactDomain n) : + decide (D.describe = ∅) = D.vanished := by + cases D with + | none => rfl + | some ds => + rcases ds with ⟨π,s⟩ + have hh : π ∈ CompactDomain.describe (some (π,s)) := by simp only [mem_describe]; tauto + have hn := Finset.ne_empty_of_mem hh + simp only [hn,decide_false,vanished,Option.isNone_some] + +lemma compact_sum_sign {n : ℕ} (π : Equiv.Perm (Fin n)) (s : Finset (Fin n)) : + (∑ σ ∈ CompactDomain.describe (some (π,s)), (Equiv.Perm.sign σ : ℤ)) = + if s.card ≤ 1 then (Equiv.Perm.sign π : ℤ) else 0 := by + by_cases hs : s.card ≤ 1 + · rw [ite_eq_left hs] + have he : CompactDomain.describe (some (π,s)) = {π} := by + ext σ + rw [CompactDomain.mem_describe,Finset.mem_singleton] + constructor + · intro h + apply Equiv.ext + intro i + by_cases hi : i ∈ s + · let k := π.symm (σ i) + have hk : π k = σ i := π.apply_symm_apply _ + by_cases hks : k ∈ s + · have hki : k = i := Finset.card_le_one.mp hs k hks i hi + exact (hki ▸ hk).symm + · have hki : k = i := σ.injective ((h k hks).trans hk) + exact (hki ▸ hk).symm + · exact h i hi + · rintro rfl i hi; rfl + simp only [he,Finset.sum_singleton] + · rw [ite_eq_right hs] + obtain ⟨i,hi,k,hk,hik⟩ := Finset.one_lt_card.mp (by omega : 1 < s.card) + let τ := Equiv.swap i k + have ht : Equiv.Perm.sign τ = -1 := Equiv.Perm.sign_swap hik + have hm (σ : Equiv.Perm (Fin n)) : + σ * τ ∈ CompactDomain.describe (some (π,s)) ↔ + σ ∈ CompactDomain.describe (some (π,s)) := by + simp only [CompactDomain.mem_describe] + have hh (x : Fin n) (hx : x ∉ s) : τ x = x := by + apply Equiv.swap_apply_of_ne_of_ne + · intro he; subst x; exact hx hi + · intro he; subst x; exact hx hk + simp only [Equiv.Perm.mul_apply] + constructor <;> intro h x hx <;> simpa only [hh x hx] using h x hx + have he : (∑ σ ∈ CompactDomain.describe (some (π,s)), (Equiv.Perm.sign σ : ℤ)) = + ∑ σ ∈ CompactDomain.describe (some (π,s)), (Equiv.Perm.sign (σ * τ) : ℤ) := by + apply Finset.sum_bij (fun σ _ => σ * τ) + · intro σ hσ; exact (hm σ).mpr hσ + · intro σ hσ ρ hρ h; exact mul_right_cancel h + · intro σ hσ + refine ⟨σ * τ,(hm σ).mpr hσ,?_⟩ + simp [τ,mul_assoc] + · intro σ hσ + simp [τ,mul_assoc] + have hn : (∑ σ ∈ CompactDomain.describe (some (π,s)), (Equiv.Perm.sign (σ * τ) : ℤ)) = + -(∑ σ ∈ CompactDomain.describe (some (π,s)), (Equiv.Perm.sign σ : ℤ)) := by + simp only [Equiv.Perm.sign_mul,ht,Units.val_neg,mul_neg_one, + Finset.sum_neg_distrib] + omega + +def CompactDomain.mass {n : ℕ} : CompactDomain n → ℤ + | none => 0 + | some (π,s) => if s.card ≤ 1 then vectorSign n (permVector π) else 0 + +lemma CompactDomain.describe_mass {n : ℕ} (D : CompactDomain n) : + (∑ σ ∈ D.describe, (Equiv.Perm.sign σ : ℤ)) = D.mass := by + cases D with + | none => simp [describe,mass] + | some ds => + rcases ds with ⟨π,s⟩ + simp only [mass,vectorSign_perm,compact_sum_sign] + +def CompactDomains : List ℕ → Type + | [] => Unit + | r :: rs => CompactDomain r × CompactDomains rs + +def CompactDomains.full : (rs : List ℕ) → CompactDomains rs + | [] => () + | r :: rs => (CompactDomain.full r,full rs) + +def CompactDomains.describe : {rs : List ℕ} → CompactDomains rs → Domains rs + | [], _ => () + | _ :: _, (s,D) => (s.describe,describe D) + +def CompactDomains.atValue : {rs : List ℕ} → CompactDomains rs → Cells rs → ℕ → CompactDomains rs + | _ :: _, (s,D), .inl i, j => (s.atValue i j,D) + | _ :: _, (s,D), .inr c, j => (s,atValue D c j) + +def CompactDomains.vanished : {rs : List ℕ} → CompactDomains rs → Bool + | [], _ => false + | _ :: _, (s,D) => s.vanished || vanished D + +def CompactDomains.mass : {rs : List ℕ} → CompactDomains rs → ℤ + | [], _ => 1 + | _ :: _, (s,D) => s.mass * mass D + +lemma CompactDomains.describe_full (rs : List ℕ) : (full rs).describe = Domains.full rs := by + induction rs with + | nil => rfl + | cons r rs ih => simp only [full,describe,Domains.full,CompactDomain.describe_full,ih]; rfl + +lemma CompactDomains.describe_atValue {rs : List ℕ} (D : CompactDomains rs) (c : Cells rs) (j : ℕ) : + (D.atValue c j).describe = D.describe.atValue c j := by + induction rs with + | nil => exact c.elim + | cons r rs ih => + rcases D with ⟨s,D⟩ + cases c with + | inl i => simp only [atValue,describe,Domains.atValue,CompactDomain.describe_atValue]; rfl + | inr c => simp only [atValue,describe,Domains.atValue,ih]; rfl + +lemma CompactDomains.describe_vanished {rs : List ℕ} (D : CompactDomains rs) : + D.describe.vanished = D.vanished := by + induction rs with + | nil => rfl + | cons r rs ih => + rcases D with ⟨s,D⟩ + simp only [describe,Domains.vanished,vanished,CompactDomain.describe_vanished,ih] + +lemma CompactDomains.describe_mass {rs : List ℕ} (D : CompactDomains rs) : + D.describe.mass = D.mass := by + induction rs with + | nil => rfl + | cons r rs ih => + rcases D with ⟨s,D⟩ + simp only [describe,Domains.mass,mass,CompactDomain.describe_mass,ih] + +def compactEdgeOptions {rsT rsA rsB : List ℕ} + (D : CompactDomains rsT) (E : CompactDomains rsA) (F : CompactDomains rsB) + (c : Edge rsT rsA rsB) (flag : Finset (ℕ × ℕ × ℕ)) : Finset (ℕ × ℕ × ℕ) := + flag.filter (fun v => (D.atValue c.1 v.1).vanished = false ∧ + (E.atValue c.2.1 v.2.1).vanished = false ∧ (F.atValue c.2.2 v.2.2).vanished = false) + +lemma compactEdgeOptions_describe {rsT rsA rsB : List ℕ} + (D : CompactDomains rsT) (E : CompactDomains rsA) (F : CompactDomains rsB) + (c : Edge rsT rsA rsB) (flag : Finset (ℕ × ℕ × ℕ)) : + edgeOptions D.describe E.describe F.describe c flag = compactEdgeOptions D E F c flag := by + simp only [compactEdgeOptions,edgeOptions,← CompactDomains.describe_atValue, + CompactDomains.describe_vanished] + +def compactOrderEdges {rsT rsA rsB : List ℕ} + (D : CompactDomains rsT) (E : CompactDomains rsA) (F : CompactDomains rsB) + (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : List (Edge rsT rsA rsB) := + bringBest (fun c => (compactEdgeOptions D E F c flag).card) edges + +lemma compactOrderEdges_describe {rsT rsA rsB : List ℕ} + (D : CompactDomains rsT) (E : CompactDomains rsA) (F : CompactDomains rsB) + (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : + orderEdges D.describe E.describe F.describe edges flag = compactOrderEdges D E F edges flag := by + simp only [compactOrderEdges,orderEdges,compactEdgeOptions_describe] + +def solveCompact {rsT rsA rsB : List ℕ} : ℕ → CompactDomains rsT → CompactDomains rsA → + CompactDomains rsB → List (Edge rsT rsA rsB) → Finset (ℕ × ℕ × ℕ) → ℤ + | fuel, D, E, F, edges, flag => + if D.vanished || E.vanished || F.vanished then 0 + else match compactOrderEdges D E F edges flag with + | [] => D.mass * E.mass * F.mass + | c :: cs => match fuel with + | 0 => 0 + | k+1 => ∑ v ∈ compactEdgeOptions D E F c flag, + solveCompact k (D.atValue c.1 v.1) (E.atValue c.2.1 v.2.1) + (F.atValue c.2.2 v.2.2) cs flag + +lemma solveCompact_describe {rsT rsA rsB : List ℕ} (fuel : ℕ) + (D : CompactDomains rsT) (E : CompactDomains rsA) (F : CompactDomains rsB) + (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : + solveDomains fuel D.describe E.describe F.describe edges flag = solveCompact fuel D E F edges flag := by + induction fuel generalizing D E F edges with + | zero => + rw [solveCompact,solveDomains] + simp only [CompactDomains.describe_vanished,compactOrderEdges_describe,CompactDomains.describe_mass] + split <;> rfl + | succ fuel ih => + rw [solveCompact,solveDomains] + simp only [CompactDomains.describe_vanished,compactOrderEdges_describe,CompactDomains.describe_mass] + split + · rfl + · cases he : compactOrderEdges D E F edges flag with + | nil => rfl + | cons c cs => + simp only [compactEdgeOptions_describe,← CompactDomains.describe_atValue,ih] + +lemma contractionInteger_compact {n : ℕ} (rsA rsB rsT : List ℕ) + (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) + (flag : Finset (ℕ × ℕ × ℕ)) : + contractionInteger rsA rsB rsT ea eb et (fun r a b => if (r,a,b) ∈ flag then 1 else 0) = + solveCompact n (.full rsT) (.full rsA) (.full rsB) + (certificateEdges rsA rsB rsT ea eb et) flag := by + rw [contractionInteger_solve,← CompactDomains.describe_full,← CompactDomains.describe_full, + ← CompactDomains.describe_full,solveCompact_describe] + +end Saxl.Columns + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/ContractionNecessary.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/ContractionNecessary.lean index 4f5a4a67016da62521cd7cbcf743223e8c1b8fd9..a7a3059d668e1ba1b6579c91b7d956764f975f57 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/ContractionNecessary.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/ContractionNecessary.lean @@ -1,95 +1,95 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Capacity.NumericBands - -namespace OAI - -/-! Contraction Necessary. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl - -lemma polytabloid_action {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) - (g : Equiv.Perm (Fin n)) : - polytabloid (g.symm.trans t) = wordRep n (μ.colLen 0) g (polytabloid t) := by - rw [polytabloid_move t (g.symm.trans t)] - have he : tableauMove t (g.symm.trans t) = g := by - ext i - simp [tableauMove] - rw [he] - -lemma spechtTensor_linear_ext {n : ℕ} {α β : YoungDiagram} - (a : Tableau n α) (b : Tableau n β) {Z : Type*} [AddCommGroup Z] [Module ℂ Z] - (R : WordSpace n (α.colLen 0 * β.colLen 0) →ₗ[ℂ] Z) - (h : ∀ (a' : Tableau n α) (b' : Tableau n β), - R (wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b')) = 0) - (z : Specht a ⊗[ℂ] Specht b) : R (spechtTensorMap a b z) = 0 := by - have aux (x : WordSpace n (α.colLen 0)) (hx : x ∈ spechtSub a) - (y : WordSpace n (β.colLen 0)) (hy : y ∈ spechtSub b) : - R (wordTensor _ _ _ (x ⊗ₜ[ℂ] y)) = 0 := by - induction hx using Submodule.span_induction with - | mem x hx => - obtain ⟨g,rfl⟩ := hx - induction hy using Submodule.span_induction with - | mem y hy => - obtain ⟨k,rfl⟩ := hy - dsimp only - rw [←polytabloid_action,←polytabloid_action] - exact h _ _ - | zero => simp - | add y w hy hw ihy ihw => simp only [TensorProduct.tmul_add,map_add,ihy,ihw,add_zero] - | smul c y hy ih => simp only [TensorProduct.tmul_smul,map_smul,ih,smul_zero] - | zero => simp - | add x w hx hw ihx ihw => simp only [TensorProduct.add_tmul,map_add,ihx,ihw,add_zero] - | smul c x hx ih => simp only [TensorProduct.smul_tmul,TensorProduct.tmul_smul,map_smul,ih,smul_zero] - induction z using TensorProduct.inductionOn with - | add x y hx hy => simp only [map_add,hx,hy,add_zero] - | tmul x y => - unfold spechtTensorMap - change R (wordTensor _ _ _ (x.val ⊗ₜ[ℂ] y.val)) = 0 - exact aux x.val x.property y.val y.property - -theorem kronecker_contraction_necessary {n : ℕ} {α β μ : YoungDiagram} - (a : Tableau n α) (b : Tableau n β) (t : Tableau n μ) - (h : 0 < kronecker a b t) : - ∃ (a' : Tableau n α) (b' : Tableau n β) (s : Tableau n μ) - (L : Fin (μ.colLen 0) → Fin (α.colLen 0 * β.colLen 0) → ℂ), - dotProduct (wordMap L (polytabloid s)) - (wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b')) ≠ 0 := by - classical - obtain ⟨F,hF⟩ := (kronecker_pos_iff a b t).mp h - let := specht_irreducible t - have hFi : Function.Injective F := (Representation.IsIrreducible.injective_or_eq_zero (W := Specht a ⊗[ℂ] Specht b) F).resolve_right hF - let E := (spechtTensorMap a b).comp F - have hEi : Function.Injective E := (spechtTensorMap_injective a b).comp hFi - obtain ⟨R,hR⟩ := intertwining_extend_injective E hEi - (Representation.IntertwiningMap.id (spechtRep t)) - have he : ∃ (a' : Tableau n α) (b' : Tableau n β), - R (wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b')) ≠ 0 := by - by_contra hn - push Not at hn - let p : Specht t := ⟨polytabloid t,mem_cyclic _ _⟩ - have hz := spechtTensor_linear_ext a b R.toLinearMap hn (F p) - have hi := congrArg (fun H : Representation.IntertwiningMap (spechtRep t) (spechtRep t) => H p) hR - change R (spechtTensorMap a b (F p)) = p at hi - change R (spechtTensorMap a b (F p)) = 0 at hz - have hp : p = 0 := hi.symm.trans hz - exact polytabloid_ne_zero t (congrArg Subtype.val hp) - obtain ⟨a',b',hab⟩ := he - let y := wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b') - have hv : (R y).val ≠ 0 := fun hz => hab (Subtype.ext hz) - obtain ⟨g,hg⟩ := specht_detect t (R y).property hv - rw [wordPair_move] at hg - let H := (spechtInclusion t).comp R - obtain ⟨L,hL⟩ := wordMap_detects_intertwiner H y _ hg - rw [wordMap_pair_transpose,dotProduct_comm,←polytabloid_action] at hL - exact ⟨a',b',g.trans t,fun a b => L b a,hL⟩ - -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Capacity.NumericBands + +namespace OAI + +/-! Contraction Necessary. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl + +lemma polytabloid_action {n : ℕ} {μ : YoungDiagram} (t : Tableau n μ) + (g : Equiv.Perm (Fin n)) : + polytabloid (g.symm.trans t) = wordRep n (μ.colLen 0) g (polytabloid t) := by + rw [polytabloid_move t (g.symm.trans t)] + have he : tableauMove t (g.symm.trans t) = g := by + ext i + simp [tableauMove] + rw [he] + +lemma spechtTensor_linear_ext {n : ℕ} {α β : YoungDiagram} + (a : Tableau n α) (b : Tableau n β) {Z : Type*} [AddCommGroup Z] [Module ℂ Z] + (R : WordSpace n (α.colLen 0 * β.colLen 0) →ₗ[ℂ] Z) + (h : ∀ (a' : Tableau n α) (b' : Tableau n β), + R (wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b')) = 0) + (z : Specht a ⊗[ℂ] Specht b) : R (spechtTensorMap a b z) = 0 := by + have aux (x : WordSpace n (α.colLen 0)) (hx : x ∈ spechtSub a) + (y : WordSpace n (β.colLen 0)) (hy : y ∈ spechtSub b) : + R (wordTensor _ _ _ (x ⊗ₜ[ℂ] y)) = 0 := by + induction hx using Submodule.span_induction with + | mem x hx => + obtain ⟨g,rfl⟩ := hx + induction hy using Submodule.span_induction with + | mem y hy => + obtain ⟨k,rfl⟩ := hy + dsimp only + rw [←polytabloid_action,←polytabloid_action] + exact h _ _ + | zero => simp + | add y w hy hw ihy ihw => simp only [TensorProduct.tmul_add,map_add,ihy,ihw,add_zero] + | smul c y hy ih => simp only [TensorProduct.tmul_smul,map_smul,ih,smul_zero] + | zero => simp + | add x w hx hw ihx ihw => simp only [TensorProduct.add_tmul,map_add,ihx,ihw,add_zero] + | smul c x hx ih => simp only [TensorProduct.smul_tmul,TensorProduct.tmul_smul,map_smul,ih,smul_zero] + induction z using TensorProduct.inductionOn with + | add x y hx hy => simp only [map_add,hx,hy,add_zero] + | tmul x y => + unfold spechtTensorMap + change R (wordTensor _ _ _ (x.val ⊗ₜ[ℂ] y.val)) = 0 + exact aux x.val x.property y.val y.property + +theorem kronecker_contraction_necessary {n : ℕ} {α β μ : YoungDiagram} + (a : Tableau n α) (b : Tableau n β) (t : Tableau n μ) + (h : 0 < kronecker a b t) : + ∃ (a' : Tableau n α) (b' : Tableau n β) (s : Tableau n μ) + (L : Fin (μ.colLen 0) → Fin (α.colLen 0 * β.colLen 0) → ℂ), + dotProduct (wordMap L (polytabloid s)) + (wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b')) ≠ 0 := by + classical + obtain ⟨F,hF⟩ := (kronecker_pos_iff a b t).mp h + let := specht_irreducible t + have hFi : Function.Injective F := (Representation.IsIrreducible.injective_or_eq_zero (W := Specht a ⊗[ℂ] Specht b) F).resolve_right hF + let E := (spechtTensorMap a b).comp F + have hEi : Function.Injective E := (spechtTensorMap_injective a b).comp hFi + obtain ⟨R,hR⟩ := intertwining_extend_injective E hEi + (Representation.IntertwiningMap.id (spechtRep t)) + have he : ∃ (a' : Tableau n α) (b' : Tableau n β), + R (wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b')) ≠ 0 := by + by_contra hn + push Not at hn + let p : Specht t := ⟨polytabloid t,mem_cyclic _ _⟩ + have hz := spechtTensor_linear_ext a b R.toLinearMap hn (F p) + have hi := congrArg (fun H : Representation.IntertwiningMap (spechtRep t) (spechtRep t) => H p) hR + change R (spechtTensorMap a b (F p)) = p at hi + change R (spechtTensorMap a b (F p)) = 0 at hz + have hp : p = 0 := hi.symm.trans hz + exact polytabloid_ne_zero t (congrArg Subtype.val hp) + obtain ⟨a',b',hab⟩ := he + let y := wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b') + have hv : (R y).val ≠ 0 := fun hz => hab (Subtype.ext hz) + obtain ⟨g,hg⟩ := specht_detect t (R y).property hv + rw [wordPair_move] at hg + let H := (spechtInclusion t).comp R + obtain ⟨L,hL⟩ := wordMap_detects_intertwiner H y _ hg + rw [wordMap_pair_transpose,dotProduct_comm,←polytabloid_action] at hL + exact ⟨a',b',g.trans t,fun a b => L b a,hL⟩ + +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/DomainContractions.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/DomainContractions.lean index 1cd4c873c83c55f1c677842e89ae4bda69714d4f..4773c338dce620ce397ca356f41d54be7702b707 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/DomainContractions.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/DomainContractions.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ColumnCertificates -import OAI.RepresentationTheory.UniversalSquare.Balance.PackingPlans - -namespace OAI - -/-! Domain Contractions. -/ - -section - -open scoped BigOperators -namespace Saxl.Columns - -def Domains : List ℕ → Type - | [] => Unit - | r :: rs => Finset (Equiv.Perm (Fin r)) × Domains rs - -def Domains.full : (rs : List ℕ) → Domains rs - | [] => () - | _ :: rs => (Finset.univ, full rs) - -def Domains.weight : {rs : List ℕ} → Domains rs → Perms rs → ℤ - | [], _, _ => 1 - | _ :: _, (s,D), (π,σ) => (if π ∈ s then (Equiv.Perm.sign π : ℤ) else 0) * weight D σ - -lemma Domains.full_weight {rs : List ℕ} (σ : Perms rs) : - (full rs).weight σ = sgInteger σ := by - induction rs with - | nil => rfl - | cons r rs ih => simp only [full, weight, sgInteger, Finset.mem_univ, ite_true, ih] - -def Domains.atValue : {rs : List ℕ} → Domains rs → Cells rs → ℕ → Domains rs - | _ :: _, (s,D), .inl i, j => (s.filter (fun π => (π i).val = j),D) - | _ :: _, (s,D), .inr c, j => (s,atValue D c j) - -lemma Domains.atValue_weight {rs : List ℕ} (D : Domains rs) (c : Cells rs) - (j : ℕ) (σ : Perms rs) : - (D.atValue c j).weight σ = D.weight σ * - (if row (perm σ c) = j then 1 else 0) := by - induction rs with - | nil => exact c.elim - | cons r rs ih => - rcases D with ⟨s,D⟩ - rcases σ with ⟨π,σ⟩ - cases c with - | inl i => - simp only [atValue, weight, Finset.mem_filter, perm, Equiv.sumCongr_apply, - Sum.map_inl, row] - split_ifs <;> simp_all - | inr c => - simp only [atValue, weight, perm, Equiv.sumCongr_apply, Sum.map_inr, row, ih, - mul_assoc] - -def Domains.vanished : {rs : List ℕ} → Domains rs → Bool - | [], _ => false - | _ :: _, (s,D) => decide (s = ∅) || vanished D - -lemma Domains.weight_eq_zero {rs : List ℕ} (D : Domains rs) - (h : D.vanished = true) (σ : Perms rs) : D.weight σ = 0 := by - induction rs with - | nil => simp [vanished] at h - | cons r rs ih => - rcases D with ⟨s,D⟩ - rcases σ with ⟨π,σ⟩ - simp only [vanished, Bool.or_eq_true] at h - rcases h with h | h - · have hs : s = ∅ := of_decide_eq_true h - simp [weight, hs] - · simp only [weight, ih D h σ, mul_zero] - -def Domains.mass : {rs : List ℕ} → Domains rs → ℤ - | [], _ => 1 - | _ :: _, (s,D) => (∑ π ∈ s, (Equiv.Perm.sign π : ℤ)) * mass D - -lemma Domains.mass_eq_sum {rs : List ℕ} (D : Domains rs) : - D.mass = ∑ σ : Perms rs, D.weight σ := by - classical - induction rs with - | nil => simp [mass, weight, Perms] - | cons r rs ih => - rcases D with ⟨s,D⟩ - simp only [Perms, Fintype.sum_prod_type, weight, ← Finset.mul_sum, ← ih, - ← Finset.sum_mul, mass] - congr 1 - simp - -abbrev Edge (rsT rsA rsB : List ℕ) := Cells rsT × Cells rsA × Cells rsB - -def domainContraction {rsT rsA rsB : List ℕ} - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : ℤ := - ∑ π : Perms rsT, ∑ σ : Perms rsA, ∑ τ : Perms rsB, - D.weight π * E.weight σ * F.weight τ * - (edges.map (fun c => if (row (perm π c.1), row (perm σ c.2.1), - row (perm τ c.2.2)) ∈ flag then (1 : ℤ) else 0)).prod - -lemma domainContraction_nil {rsT rsA rsB : List ℕ} - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - (flag : Finset (ℕ × ℕ × ℕ)) : - domainContraction D E F [] flag = D.mass * E.mass * F.mass := by - simp only [domainContraction, List.map_nil, List.prod_nil, mul_one, - ← Finset.mul_sum, ← Finset.sum_mul, ← Domains.mass_eq_sum] - -lemma domainContraction_zero {rsT rsA rsB : List ℕ} - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) - (h : (D.vanished || E.vanished || F.vanished) = true) : - domainContraction D E F edges flag = 0 := by - rw [domainContraction] - simp only [Bool.or_eq_true] at h - rcases h with (h | h) | h - · simp only [Domains.weight_eq_zero D h, zero_mul, Finset.sum_const_zero] - · simp only [Domains.weight_eq_zero E h, mul_zero, zero_mul, Finset.sum_const_zero] - · simp only [Domains.weight_eq_zero F h, mul_zero, zero_mul, Finset.sum_const_zero] - -lemma triple_indicator_sum (flag : Finset (ℕ × ℕ × ℕ)) (a b c : ℕ) : - (∑ v ∈ flag, (if a = v.1 then (1 : ℤ) else 0) * - (if b = v.2.1 then 1 else 0) * (if c = v.2.2 then 1 else 0)) = - if (a,b,c) ∈ flag then 1 else 0 := by - have hh : ∀ v : ℕ × ℕ × ℕ, (if a = v.1 then (1 : ℤ) else 0) * - (if b = v.2.1 then 1 else 0) * (if c = v.2.2 then 1 else 0) = - if (a,b,c) = v then 1 else 0 := by - rintro ⟨x,y,z⟩ - simp only [Prod.mk.injEq] - split_ifs <;> simp_all - simp only [hh] - rw [Finset.sum_ite_eq] - -lemma domainContraction_cons {rsT rsA rsB : List ℕ} - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - (c : Edge rsT rsA rsB) (edges : List (Edge rsT rsA rsB)) - (flag : Finset (ℕ × ℕ × ℕ)) : - domainContraction D E F (c::edges) flag = - ∑ v ∈ flag, domainContraction (D.atValue c.1 v.1) - (E.atValue c.2.1 v.2.1) (F.atValue c.2.2 v.2.2) edges flag := by - classical - simp only [domainContraction, List.map_cons, List.prod_cons, Domains.atValue_weight] - conv_rhs => rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro π _ - conv_rhs => rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro σ _ - conv_rhs => rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro τ _ - trans (D.weight π * E.weight σ * F.weight τ) * - (∑ v ∈ flag, (if row (perm π c.1) = v.1 then (1 : ℤ) else 0) * - (if row (perm σ c.2.1) = v.2.1 then 1 else 0) * - (if row (perm τ c.2.2) = v.2.2 then 1 else 0)) * - (edges.map (fun e => if (row (perm π e.1), row (perm σ e.2.1), - row (perm τ e.2.2)) ∈ flag then (1 : ℤ) else 0)).prod - · rw [triple_indicator_sum] - ring - · simp only [Finset.mul_sum, Finset.sum_mul] - apply Finset.sum_congr rfl - intro v _ - ring - -lemma domainContraction_perm {rsT rsA rsB : List ℕ} - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - {cs es : List (Edge rsT rsA rsB)} (hp : cs.Perm es) - (flag : Finset (ℕ × ℕ × ℕ)) : - domainContraction D E F cs flag = domainContraction D E F es flag := by - simp only [domainContraction] - apply Finset.sum_congr rfl - intro π _ - apply Finset.sum_congr rfl - intro σ _ - apply Finset.sum_congr rfl - intro τ _ - exact congrArg (_ * ·) ((hp.map _).prod_eq) - -end Saxl.Columns -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ColumnCertificates +import OAI.RepresentationTheory.UniversalSquare.Balance.PackingPlans + +namespace OAI + +/-! Domain Contractions. -/ + +section + +open scoped BigOperators +namespace Saxl.Columns + +def Domains : List ℕ → Type + | [] => Unit + | r :: rs => Finset (Equiv.Perm (Fin r)) × Domains rs + +def Domains.full : (rs : List ℕ) → Domains rs + | [] => () + | _ :: rs => (Finset.univ, full rs) + +def Domains.weight : {rs : List ℕ} → Domains rs → Perms rs → ℤ + | [], _, _ => 1 + | _ :: _, (s,D), (π,σ) => (if π ∈ s then (Equiv.Perm.sign π : ℤ) else 0) * weight D σ + +lemma Domains.full_weight {rs : List ℕ} (σ : Perms rs) : + (full rs).weight σ = sgInteger σ := by + induction rs with + | nil => rfl + | cons r rs ih => simp only [full, weight, sgInteger, Finset.mem_univ, ite_true, ih] + +def Domains.atValue : {rs : List ℕ} → Domains rs → Cells rs → ℕ → Domains rs + | _ :: _, (s,D), .inl i, j => (s.filter (fun π => (π i).val = j),D) + | _ :: _, (s,D), .inr c, j => (s,atValue D c j) + +lemma Domains.atValue_weight {rs : List ℕ} (D : Domains rs) (c : Cells rs) + (j : ℕ) (σ : Perms rs) : + (D.atValue c j).weight σ = D.weight σ * + (if row (perm σ c) = j then 1 else 0) := by + induction rs with + | nil => exact c.elim + | cons r rs ih => + rcases D with ⟨s,D⟩ + rcases σ with ⟨π,σ⟩ + cases c with + | inl i => + simp only [atValue, weight, Finset.mem_filter, perm, Equiv.sumCongr_apply, + Sum.map_inl, row] + split_ifs <;> simp_all + | inr c => + simp only [atValue, weight, perm, Equiv.sumCongr_apply, Sum.map_inr, row, ih, + mul_assoc] + +def Domains.vanished : {rs : List ℕ} → Domains rs → Bool + | [], _ => false + | _ :: _, (s,D) => decide (s = ∅) || vanished D + +lemma Domains.weight_eq_zero {rs : List ℕ} (D : Domains rs) + (h : D.vanished = true) (σ : Perms rs) : D.weight σ = 0 := by + induction rs with + | nil => simp [vanished] at h + | cons r rs ih => + rcases D with ⟨s,D⟩ + rcases σ with ⟨π,σ⟩ + simp only [vanished, Bool.or_eq_true] at h + rcases h with h | h + · have hs : s = ∅ := of_decide_eq_true h + simp [weight, hs] + · simp only [weight, ih D h σ, mul_zero] + +def Domains.mass : {rs : List ℕ} → Domains rs → ℤ + | [], _ => 1 + | _ :: _, (s,D) => (∑ π ∈ s, (Equiv.Perm.sign π : ℤ)) * mass D + +lemma Domains.mass_eq_sum {rs : List ℕ} (D : Domains rs) : + D.mass = ∑ σ : Perms rs, D.weight σ := by + classical + induction rs with + | nil => simp [mass, weight, Perms] + | cons r rs ih => + rcases D with ⟨s,D⟩ + simp only [Perms, Fintype.sum_prod_type, weight, ← Finset.mul_sum, ← ih, + ← Finset.sum_mul, mass] + congr 1 + simp + +abbrev Edge (rsT rsA rsB : List ℕ) := Cells rsT × Cells rsA × Cells rsB + +def domainContraction {rsT rsA rsB : List ℕ} + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : ℤ := + ∑ π : Perms rsT, ∑ σ : Perms rsA, ∑ τ : Perms rsB, + D.weight π * E.weight σ * F.weight τ * + (edges.map (fun c => if (row (perm π c.1), row (perm σ c.2.1), + row (perm τ c.2.2)) ∈ flag then (1 : ℤ) else 0)).prod + +lemma domainContraction_nil {rsT rsA rsB : List ℕ} + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + (flag : Finset (ℕ × ℕ × ℕ)) : + domainContraction D E F [] flag = D.mass * E.mass * F.mass := by + simp only [domainContraction, List.map_nil, List.prod_nil, mul_one, + ← Finset.mul_sum, ← Finset.sum_mul, ← Domains.mass_eq_sum] + +lemma domainContraction_zero {rsT rsA rsB : List ℕ} + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) + (h : (D.vanished || E.vanished || F.vanished) = true) : + domainContraction D E F edges flag = 0 := by + rw [domainContraction] + simp only [Bool.or_eq_true] at h + rcases h with (h | h) | h + · simp only [Domains.weight_eq_zero D h, zero_mul, Finset.sum_const_zero] + · simp only [Domains.weight_eq_zero E h, mul_zero, zero_mul, Finset.sum_const_zero] + · simp only [Domains.weight_eq_zero F h, mul_zero, zero_mul, Finset.sum_const_zero] + +lemma triple_indicator_sum (flag : Finset (ℕ × ℕ × ℕ)) (a b c : ℕ) : + (∑ v ∈ flag, (if a = v.1 then (1 : ℤ) else 0) * + (if b = v.2.1 then 1 else 0) * (if c = v.2.2 then 1 else 0)) = + if (a,b,c) ∈ flag then 1 else 0 := by + have hh : ∀ v : ℕ × ℕ × ℕ, (if a = v.1 then (1 : ℤ) else 0) * + (if b = v.2.1 then 1 else 0) * (if c = v.2.2 then 1 else 0) = + if (a,b,c) = v then 1 else 0 := by + rintro ⟨x,y,z⟩ + simp only [Prod.mk.injEq] + split_ifs <;> simp_all + simp only [hh] + rw [Finset.sum_ite_eq] + +lemma domainContraction_cons {rsT rsA rsB : List ℕ} + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + (c : Edge rsT rsA rsB) (edges : List (Edge rsT rsA rsB)) + (flag : Finset (ℕ × ℕ × ℕ)) : + domainContraction D E F (c::edges) flag = + ∑ v ∈ flag, domainContraction (D.atValue c.1 v.1) + (E.atValue c.2.1 v.2.1) (F.atValue c.2.2 v.2.2) edges flag := by + classical + simp only [domainContraction, List.map_cons, List.prod_cons, Domains.atValue_weight] + conv_rhs => rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro π _ + conv_rhs => rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro σ _ + conv_rhs => rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro τ _ + trans (D.weight π * E.weight σ * F.weight τ) * + (∑ v ∈ flag, (if row (perm π c.1) = v.1 then (1 : ℤ) else 0) * + (if row (perm σ c.2.1) = v.2.1 then 1 else 0) * + (if row (perm τ c.2.2) = v.2.2 then 1 else 0)) * + (edges.map (fun e => if (row (perm π e.1), row (perm σ e.2.1), + row (perm τ e.2.2)) ∈ flag then (1 : ℤ) else 0)).prod + · rw [triple_indicator_sum] + ring + · simp only [Finset.mul_sum, Finset.sum_mul] + apply Finset.sum_congr rfl + intro v _ + ring + +lemma domainContraction_perm {rsT rsA rsB : List ℕ} + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + {cs es : List (Edge rsT rsA rsB)} (hp : cs.Perm es) + (flag : Finset (ℕ × ℕ × ℕ)) : + domainContraction D E F cs flag = domainContraction D E F es flag := by + simp only [domainContraction] + apply Finset.sum_congr rfl + intro π _ + apply Finset.sum_congr rfl + intro σ _ + apply Finset.sum_congr rfl + intro τ _ + exact congrArg (_ * ·) ((hp.map _).prod_eq) + +end Saxl.Columns +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/DomainSolver.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/DomainSolver.lean index d5ebb814f2b134e2a6858fec2c6536316ca49de0..43f4d7d0f55b4484d72c2a912ccd591ad455c2b6 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/DomainSolver.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/DomainSolver.lean @@ -1,141 +1,141 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.DomainContractions - -namespace OAI - -/-! Domain Solver. -/ - -section - -open scoped BigOperators -namespace Saxl.Columns - -def edgeOptions {rsT rsA rsB : List ℕ} - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - (c : Edge rsT rsA rsB) (flag : Finset (ℕ × ℕ × ℕ)) : Finset (ℕ × ℕ × ℕ) := - flag.filter (fun v => (D.atValue c.1 v.1).vanished = false ∧ - (E.atValue c.2.1 v.2.1).vanished = false ∧ (F.atValue c.2.2 v.2.2).vanished = false) - -lemma domainContraction_cons_options {rsT rsA rsB : List ℕ} - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - (c : Edge rsT rsA rsB) (edges : List (Edge rsT rsA rsB)) - (flag : Finset (ℕ × ℕ × ℕ)) : - domainContraction D E F (c::edges) flag = - ∑ v ∈ edgeOptions D E F c flag, domainContraction (D.atValue c.1 v.1) - (E.atValue c.2.1 v.2.1) (F.atValue c.2.2 v.2.2) edges flag := by - rw [domainContraction_cons, edgeOptions, Finset.sum_filter] - apply Finset.sum_congr rfl - intro v hv - split_ifs with h - · rfl - · apply domainContraction_zero - simpa only [Bool.or_eq_true, Bool.not_eq_false, not_and_or, or_assoc] using h - -def bringBest {α : Type*} (score : α → ℕ) : List α → List α - | [] => [] - | c :: cs => match bringBest score cs with - | [] => [c] - | d :: ds => if score c ≤ score d then c :: d :: ds else d :: c :: ds - -lemma bringBest_perm {α : Type*} (score : α → ℕ) (cs : List α) : - (bringBest score cs).Perm cs := by - induction cs with - | nil => exact List.Perm.refl _ - | cons c cs ih => - rw [bringBest] - cases he : bringBest score cs with - | nil => - rw [he] at ih - exact List.Perm.cons c ih - | cons d ds => - rw [he] at ih - simp only - split_ifs - · exact List.Perm.cons c ih - · exact (List.Perm.swap _ _ _).trans (List.Perm.cons c ih) - -def orderEdges {rsT rsA rsB : List ℕ} - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : List (Edge rsT rsA rsB) := - bringBest (fun c => (edgeOptions D E F c flag).card) edges - -lemma orderEdges_perm {rsT rsA rsB : List ℕ} - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : - (orderEdges D E F edges flag).Perm edges := bringBest_perm _ _ - -def solveDomains {rsT rsA rsB : List ℕ} : ℕ → Domains rsT → Domains rsA → Domains rsB → - List (Edge rsT rsA rsB) → Finset (ℕ × ℕ × ℕ) → ℤ - | fuel, D, E, F, edges, flag => - if D.vanished || E.vanished || F.vanished then 0 - else match orderEdges D E F edges flag with - | [] => D.mass * E.mass * F.mass - | c :: cs => match fuel with - | 0 => 0 - | k+1 => ∑ v ∈ edgeOptions D E F c flag, - solveDomains k (D.atValue c.1 v.1) (E.atValue c.2.1 v.2.1) - (F.atValue c.2.2 v.2.2) cs flag - -theorem solveDomains_correct {rsT rsA rsB : List ℕ} (fuel : ℕ) - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) - (h : edges.length ≤ fuel) : - solveDomains fuel D E F edges flag = domainContraction D E F edges flag := by - induction fuel generalizing D E F edges with - | zero => - have hh : orderEdges D E F edges flag = [] := by - apply List.length_eq_zero_iff.mp - rw [(orderEdges_perm D E F edges flag).length_eq] - omega - rw [solveDomains] - split_ifs with hv - · exact (domainContraction_zero D E F edges flag hv).symm - · rw [hh] - rw [← domainContraction_perm D E F (orderEdges_perm D E F edges flag) flag, hh] - exact (domainContraction_nil D E F flag).symm - | succ fuel ih => - rw [solveDomains] - split_ifs with hv - · exact (domainContraction_zero D E F edges flag hv).symm - · have hp := orderEdges_perm D E F edges flag - rw [← domainContraction_perm D E F hp flag] - cases he : orderEdges D E F edges flag with - | nil => exact (domainContraction_nil D E F flag).symm - | cons c cs => - have hlen : cs.length ≤ fuel := by - have hl := hp.length_eq - rw [he, List.length_cons] at hl - omega - rw [domainContraction_cons_options] - apply Finset.sum_congr rfl - intro v hv - exact ih _ _ _ _ hlen - -def certificateEdges {n : ℕ} (rsA rsB rsT : List ℕ) - (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) : - List (Edge rsT rsA rsB) := - List.ofFn (fun i => (enumerate rsT (et i), enumerate rsA (ea i), enumerate rsB (eb i))) - -lemma contractionInteger_domains {n : ℕ} (rsA rsB rsT : List ℕ) - (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) - (flag : Finset (ℕ × ℕ × ℕ)) : - contractionInteger rsA rsB rsT ea eb et (fun r a b => if (r,a,b) ∈ flag then 1 else 0) = - domainContraction (.full rsT) (.full rsA) (.full rsB) - (certificateEdges rsA rsB rsT ea eb et) flag := by - simp only [contractionInteger, domainContraction, Domains.full_weight, - certificateEdges, List.map_ofFn, List.prod_ofFn, Function.comp_apply] - -theorem contractionInteger_solve {n : ℕ} (rsA rsB rsT : List ℕ) - (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) - (flag : Finset (ℕ × ℕ × ℕ)) : - contractionInteger rsA rsB rsT ea eb et (fun r a b => if (r,a,b) ∈ flag then 1 else 0) = - solveDomains n (.full rsT) (.full rsA) (.full rsB) - (certificateEdges rsA rsB rsT ea eb et) flag := by - rw [solveDomains_correct n _ _ _ _ _ (by simp [certificateEdges])] - exact contractionInteger_domains .. - -end Saxl.Columns -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.DomainContractions + +namespace OAI + +/-! Domain Solver. -/ + +section + +open scoped BigOperators +namespace Saxl.Columns + +def edgeOptions {rsT rsA rsB : List ℕ} + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + (c : Edge rsT rsA rsB) (flag : Finset (ℕ × ℕ × ℕ)) : Finset (ℕ × ℕ × ℕ) := + flag.filter (fun v => (D.atValue c.1 v.1).vanished = false ∧ + (E.atValue c.2.1 v.2.1).vanished = false ∧ (F.atValue c.2.2 v.2.2).vanished = false) + +lemma domainContraction_cons_options {rsT rsA rsB : List ℕ} + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + (c : Edge rsT rsA rsB) (edges : List (Edge rsT rsA rsB)) + (flag : Finset (ℕ × ℕ × ℕ)) : + domainContraction D E F (c::edges) flag = + ∑ v ∈ edgeOptions D E F c flag, domainContraction (D.atValue c.1 v.1) + (E.atValue c.2.1 v.2.1) (F.atValue c.2.2 v.2.2) edges flag := by + rw [domainContraction_cons, edgeOptions, Finset.sum_filter] + apply Finset.sum_congr rfl + intro v hv + split_ifs with h + · rfl + · apply domainContraction_zero + simpa only [Bool.or_eq_true, Bool.not_eq_false, not_and_or, or_assoc] using h + +def bringBest {α : Type*} (score : α → ℕ) : List α → List α + | [] => [] + | c :: cs => match bringBest score cs with + | [] => [c] + | d :: ds => if score c ≤ score d then c :: d :: ds else d :: c :: ds + +lemma bringBest_perm {α : Type*} (score : α → ℕ) (cs : List α) : + (bringBest score cs).Perm cs := by + induction cs with + | nil => exact List.Perm.refl _ + | cons c cs ih => + rw [bringBest] + cases he : bringBest score cs with + | nil => + rw [he] at ih + exact List.Perm.cons c ih + | cons d ds => + rw [he] at ih + simp only + split_ifs + · exact List.Perm.cons c ih + · exact (List.Perm.swap _ _ _).trans (List.Perm.cons c ih) + +def orderEdges {rsT rsA rsB : List ℕ} + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : List (Edge rsT rsA rsB) := + bringBest (fun c => (edgeOptions D E F c flag).card) edges + +lemma orderEdges_perm {rsT rsA rsB : List ℕ} + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : + (orderEdges D E F edges flag).Perm edges := bringBest_perm _ _ + +def solveDomains {rsT rsA rsB : List ℕ} : ℕ → Domains rsT → Domains rsA → Domains rsB → + List (Edge rsT rsA rsB) → Finset (ℕ × ℕ × ℕ) → ℤ + | fuel, D, E, F, edges, flag => + if D.vanished || E.vanished || F.vanished then 0 + else match orderEdges D E F edges flag with + | [] => D.mass * E.mass * F.mass + | c :: cs => match fuel with + | 0 => 0 + | k+1 => ∑ v ∈ edgeOptions D E F c flag, + solveDomains k (D.atValue c.1 v.1) (E.atValue c.2.1 v.2.1) + (F.atValue c.2.2 v.2.2) cs flag + +theorem solveDomains_correct {rsT rsA rsB : List ℕ} (fuel : ℕ) + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) + (h : edges.length ≤ fuel) : + solveDomains fuel D E F edges flag = domainContraction D E F edges flag := by + induction fuel generalizing D E F edges with + | zero => + have hh : orderEdges D E F edges flag = [] := by + apply List.length_eq_zero_iff.mp + rw [(orderEdges_perm D E F edges flag).length_eq] + omega + rw [solveDomains] + split_ifs with hv + · exact (domainContraction_zero D E F edges flag hv).symm + · rw [hh] + rw [← domainContraction_perm D E F (orderEdges_perm D E F edges flag) flag, hh] + exact (domainContraction_nil D E F flag).symm + | succ fuel ih => + rw [solveDomains] + split_ifs with hv + · exact (domainContraction_zero D E F edges flag hv).symm + · have hp := orderEdges_perm D E F edges flag + rw [← domainContraction_perm D E F hp flag] + cases he : orderEdges D E F edges flag with + | nil => exact (domainContraction_nil D E F flag).symm + | cons c cs => + have hlen : cs.length ≤ fuel := by + have hl := hp.length_eq + rw [he, List.length_cons] at hl + omega + rw [domainContraction_cons_options] + apply Finset.sum_congr rfl + intro v hv + exact ih _ _ _ _ hlen + +def certificateEdges {n : ℕ} (rsA rsB rsT : List ℕ) + (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) : + List (Edge rsT rsA rsB) := + List.ofFn (fun i => (enumerate rsT (et i), enumerate rsA (ea i), enumerate rsB (eb i))) + +lemma contractionInteger_domains {n : ℕ} (rsA rsB rsT : List ℕ) + (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) + (flag : Finset (ℕ × ℕ × ℕ)) : + contractionInteger rsA rsB rsT ea eb et (fun r a b => if (r,a,b) ∈ flag then 1 else 0) = + domainContraction (.full rsT) (.full rsA) (.full rsB) + (certificateEdges rsA rsB rsT ea eb et) flag := by + simp only [contractionInteger, domainContraction, Domains.full_weight, + certificateEdges, List.map_ofFn, List.prod_ofFn, Function.comp_apply] + +theorem contractionInteger_solve {n : ℕ} (rsA rsB rsT : List ℕ) + (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) + (flag : Finset (ℕ × ℕ × ℕ)) : + contractionInteger rsA rsB rsT ea eb et (fun r a b => if (r,a,b) ∈ flag then 1 else 0) = + solveDomains n (.full rsT) (.full rsA) (.full rsB) + (certificateEdges rsA rsB rsT ea eb et) flag := by + rw [solveDomains_correct n _ _ _ _ _ (by simp [certificateEdges])] + exact contractionInteger_domains .. + +end Saxl.Columns +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/EncodedDomains.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/EncodedDomains.lean index 907bf514ff75293dcd000b8b4a0c4c8d29801977..8ad9e1aacf1616ce8230ee8fab03921f9b4b0559 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/EncodedDomains.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/EncodedDomains.lean @@ -1,30 +1,30 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.RowSquareTools - -namespace OAI - -/-! Encoded Domains. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma rowSquare_vectors {n : ℕ} {p q cs ts : List ℕ} - (hp : GoodRows p) (hq : GoodRows q) (hcs : GoodRows cs) (hts : GoodRows ts) - (he : cs = transposeRows p ∨ cs = p) (ht : ts = transposeRows q) - (hn : cs.sum = n) (hn' : ts.sum = n) - (eb : Fin n ≃ Fin cs.sum) (et : Fin n ≃ Fin ts.sum) - (flag : Finset (ℕ × ℕ × ℕ)) - (hcert : solveVectors n (.full ts) (.full cs) (.full cs) - (certificateEdges cs cs ts (finCongr hn.symm) eb et) flag ≠ 0) : RowSquare p q := by - apply rowSquare_domain hp hq hcs hts he ht hn hn' eb et flag - simpa only [← solveVectors_encode, Domains.encode_full] using hcert - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.RowSquareTools + +namespace OAI + +/-! Encoded Domains. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma rowSquare_vectors {n : ℕ} {p q cs ts : List ℕ} + (hp : GoodRows p) (hq : GoodRows q) (hcs : GoodRows cs) (hts : GoodRows ts) + (he : cs = transposeRows p ∨ cs = p) (ht : ts = transposeRows q) + (hn : cs.sum = n) (hn' : ts.sum = n) + (eb : Fin n ≃ Fin cs.sum) (et : Fin n ≃ Fin ts.sum) + (flag : Finset (ℕ × ℕ × ℕ)) + (hcert : solveVectors n (.full ts) (.full cs) (.full cs) + (certificateEdges cs cs ts (finCongr hn.symm) eb et) flag ≠ 0) : RowSquare p q := by + apply rowSquare_domain hp hq hcs hts he ht hn hn' eb et flag + simpa only [← solveVectors_encode, Domains.encode_full] using hcert + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/FactoredCertificates.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/FactoredCertificates.lean index 6e95c7e589420954e2037ecec8986e6ae3c1dad6..9bac7d74e90e114b6b7e72db15caa60f2cb501f8 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/FactoredCertificates.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/FactoredCertificates.lean @@ -1,102 +1,102 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ColumnCertificates -import OAI.RepresentationTheory.UniversalSquare.Support.NumericalSupport - -namespace OAI - -/-! Factored Certificates. -/ - -section - -namespace Saxl.Columns - -def integralWedge (r : ℕ) (L : ℕ → Fin r → ℤ) : ℤ := - ∑ π : Equiv.Perm (Fin r), (Equiv.Perm.sign π : ℤ) * ∏ i, L (π i).val i - -def integralBlocks : (rs : List ℕ) → (ℕ → Fin rs.sum → ℤ) → ℤ - | [], _ => 1 - | r :: rs, L => integralWedge r (fun a i => L a (Fin.castAdd rs.sum i)) * - integralBlocks rs (fun a i => L a (Fin.natAdd r i)) - -lemma integralBlocks_eq (rs : List ℕ) (L : ℕ → Fin rs.sum → ℤ) : - integralBlocks rs L = ∑ π : Perms rs, sgInteger π * - ∏ i, L (row (perm π (enumerate rs i))) i := by - induction rs with - | nil => - change 1 = ∑ π : PUnit, sgInteger (rs := []) π * ∏ i : Fin 0, - L (row (perm (rs := []) π (enumerate [] i))) i - simp [sgInteger] - | cons r rs ih => - change ℕ → Fin (r + rs.sum) → ℤ at L - simp only [integralBlocks, ih, integralWedge, Perms, Fintype.sum_prod_type, - sgInteger, Finset.sum_mul_sum, List.sum_cons] - apply Finset.sum_congr rfl - intro π hπ - apply Finset.sum_congr rfl - intro σ hσ - have hprod : (∏ i : Fin (r + rs.sum), L (row (perm (rs := r::rs) (π,σ) - (enumerate (r::rs) i))) i) = - (∏ i : Fin r, L (row (perm (rs := r::rs) (π,σ) - (enumerate (r::rs) (Fin.castAdd rs.sum i)))) (Fin.castAdd rs.sum i)) * - ∏ i : Fin rs.sum, L (row (perm (rs := r::rs) (π,σ) - (enumerate (r::rs) (Fin.natAdd r i)))) (Fin.natAdd r i) := - Fin.prod_univ_add _ - erw [hprod] - have hl : (∏ i : Fin r, L (row (perm (rs := r::rs) (π,σ) - (enumerate (r::rs) (Fin.castAdd rs.sum i)))) (Fin.castAdd rs.sum i)) = - ∏ i : Fin r, L (π i).val (Fin.castAdd rs.sum i) := by - apply Finset.prod_congr rfl - intro i hi - erw [enumerate_left r rs i] - rfl - have hr : (∏ i : Fin rs.sum, L (row (perm (rs := r::rs) (π,σ) - (enumerate (r::rs) (Fin.natAdd r i)))) (Fin.natAdd r i)) = - ∏ i : Fin rs.sum, L (row (perm σ (enumerate rs i))) (Fin.natAdd r i) := by - apply Finset.prod_congr rfl - intro i hi - erw [enumerate_right r rs i] - rfl - erw [hl, hr] - ring_nf - rfl - -def factoredContraction {n : ℕ} (rsA rsB rsT : List ℕ) - (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) - (L : ℕ → ℕ → ℕ → ℤ) : ℤ := - ∑ σ : Perms rsA, ∑ τ : Perms rsB, sgInteger σ * sgInteger τ * - integralBlocks rsT (fun r i => - L r (row (perm σ (enumerate rsA (ea (et.symm i))))) - (row (perm τ (enumerate rsB (eb (et.symm i)))))) - -lemma contractionInteger_eq_factored {n : ℕ} (rsA rsB rsT : List ℕ) - (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) - (L : ℕ → ℕ → ℕ → ℤ) : - contractionInteger rsA rsB rsT ea eb et L = - factoredContraction rsA rsB rsT ea eb et L := by - unfold contractionInteger factoredContraction - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro σ hσ - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro τ hτ - rw [integralBlocks_eq, Finset.mul_sum] - apply Finset.sum_congr rfl - intro π hπ - have he : (∏ i, L (row (perm π (enumerate rsT (et i)))) - (row (perm σ (enumerate rsA (ea i)))) - (row (perm τ (enumerate rsB (eb i))))) = - ∏ i, L (row (perm π (enumerate rsT i))) - (row (perm σ (enumerate rsA (ea (et.symm i))))) - (row (perm τ (enumerate rsB (eb (et.symm i))))) := by - apply Fintype.prod_equiv et - intro i - simp only [Equiv.symm_apply_apply] - rw [he] - ring - -end Saxl.Columns -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ColumnCertificates +import OAI.RepresentationTheory.UniversalSquare.Support.NumericalSupport + +namespace OAI + +/-! Factored Certificates. -/ + +section + +namespace Saxl.Columns + +def integralWedge (r : ℕ) (L : ℕ → Fin r → ℤ) : ℤ := + ∑ π : Equiv.Perm (Fin r), (Equiv.Perm.sign π : ℤ) * ∏ i, L (π i).val i + +def integralBlocks : (rs : List ℕ) → (ℕ → Fin rs.sum → ℤ) → ℤ + | [], _ => 1 + | r :: rs, L => integralWedge r (fun a i => L a (Fin.castAdd rs.sum i)) * + integralBlocks rs (fun a i => L a (Fin.natAdd r i)) + +lemma integralBlocks_eq (rs : List ℕ) (L : ℕ → Fin rs.sum → ℤ) : + integralBlocks rs L = ∑ π : Perms rs, sgInteger π * + ∏ i, L (row (perm π (enumerate rs i))) i := by + induction rs with + | nil => + change 1 = ∑ π : PUnit, sgInteger (rs := []) π * ∏ i : Fin 0, + L (row (perm (rs := []) π (enumerate [] i))) i + simp [sgInteger] + | cons r rs ih => + change ℕ → Fin (r + rs.sum) → ℤ at L + simp only [integralBlocks, ih, integralWedge, Perms, Fintype.sum_prod_type, + sgInteger, Finset.sum_mul_sum, List.sum_cons] + apply Finset.sum_congr rfl + intro π hπ + apply Finset.sum_congr rfl + intro σ hσ + have hprod : (∏ i : Fin (r + rs.sum), L (row (perm (rs := r::rs) (π,σ) + (enumerate (r::rs) i))) i) = + (∏ i : Fin r, L (row (perm (rs := r::rs) (π,σ) + (enumerate (r::rs) (Fin.castAdd rs.sum i)))) (Fin.castAdd rs.sum i)) * + ∏ i : Fin rs.sum, L (row (perm (rs := r::rs) (π,σ) + (enumerate (r::rs) (Fin.natAdd r i)))) (Fin.natAdd r i) := + Fin.prod_univ_add _ + erw [hprod] + have hl : (∏ i : Fin r, L (row (perm (rs := r::rs) (π,σ) + (enumerate (r::rs) (Fin.castAdd rs.sum i)))) (Fin.castAdd rs.sum i)) = + ∏ i : Fin r, L (π i).val (Fin.castAdd rs.sum i) := by + apply Finset.prod_congr rfl + intro i hi + erw [enumerate_left r rs i] + rfl + have hr : (∏ i : Fin rs.sum, L (row (perm (rs := r::rs) (π,σ) + (enumerate (r::rs) (Fin.natAdd r i)))) (Fin.natAdd r i)) = + ∏ i : Fin rs.sum, L (row (perm σ (enumerate rs i))) (Fin.natAdd r i) := by + apply Finset.prod_congr rfl + intro i hi + erw [enumerate_right r rs i] + rfl + erw [hl, hr] + ring_nf + rfl + +def factoredContraction {n : ℕ} (rsA rsB rsT : List ℕ) + (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) + (L : ℕ → ℕ → ℕ → ℤ) : ℤ := + ∑ σ : Perms rsA, ∑ τ : Perms rsB, sgInteger σ * sgInteger τ * + integralBlocks rsT (fun r i => + L r (row (perm σ (enumerate rsA (ea (et.symm i))))) + (row (perm τ (enumerate rsB (eb (et.symm i)))))) + +lemma contractionInteger_eq_factored {n : ℕ} (rsA rsB rsT : List ℕ) + (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) + (L : ℕ → ℕ → ℕ → ℤ) : + contractionInteger rsA rsB rsT ea eb et L = + factoredContraction rsA rsB rsT ea eb et L := by + unfold contractionInteger factoredContraction + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro σ hσ + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro τ hτ + rw [integralBlocks_eq, Finset.mul_sum] + apply Finset.sum_congr rfl + intro π hπ + have he : (∏ i, L (row (perm π (enumerate rsT (et i)))) + (row (perm σ (enumerate rsA (ea i)))) + (row (perm τ (enumerate rsB (eb i))))) = + ∏ i, L (row (perm π (enumerate rsT i))) + (row (perm σ (enumerate rsA (ea (et.symm i))))) + (row (perm τ (enumerate rsB (eb (et.symm i))))) := by + apply Fintype.prod_equiv et + intro i + simp only [Equiv.symm_apply_apply] + rw [he] + ring + +end Saxl.Columns +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/FlagDetection.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/FlagDetection.lean index fcedde7ede1cb970e7ff8bc11ae9d7580ac45f95..e787bf19a7662eeebec77b48098045592fb1a1af 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/FlagDetection.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/FlagDetection.lean @@ -1,136 +1,136 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPacking - -namespace OAI - -/-! Flag Detection. -/ - -section - -noncomputable section -namespace Saxl - -lemma cyclic_support_tableau {n d : ℕ} {μ : YoungDiagram} - (s t : Tableau n μ) (u : WordSpace n d) - (h : ∃ f : Representation.IntertwiningMap (spechtRep s) - (cyclic (wordRep n d) u).toRepresentation, f ≠ 0) : - ∃ f : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n d) u).toRepresentation, f ≠ 0 := by - change ∃ f : Representation.IntertwiningMap (spechtSub s).toRepresentation - (cyclic (wordRep n d) u).toRepresentation, f ≠ 0 at h - rw [spechtSub_tableau_independent s t] at h - exact h - -lemma cyclic_support_relabel_iff {n m d : ℕ} {μ : YoungDiagram} - (e : Fin n ≃ Fin m) (s : Tableau n μ) (t : Tableau m μ) (u : WordSpace n d) : - (∃ f : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep m d) (relabelWord e u)).toRepresentation, f ≠ 0) ↔ - (∃ f : Representation.IntertwiningMap (spechtRep s) - (cyclic (wordRep n d) u).toRepresentation, f ≠ 0) := by - have hnm : n = m := by simpa only [Fintype.card_fin] using Fintype.card_congr e - subst m - change (∃ f : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n d) (wordRep n d e u)).toRepresentation, f ≠ 0) ↔ _ - rw [cyclic_action_eq] - constructor - · exact cyclic_support_tableau t s u - · exact cyclic_support_tableau s t u - -lemma relabelWord_pair {n m d : ℕ} (e : Fin n ≃ Fin m) - (x y : WordSpace n d) : - dotProduct (relabelWord e x) (relabelWord e y) = dotProduct x y := by - classical - apply Fintype.sum_equiv ((Equiv.arrowCongr e (Equiv.refl _)).symm) - intro w - rfl - -lemma relabelWord_symm_pair {n m d : ℕ} (e : Fin n ≃ Fin m) - (x : WordSpace m d) (y : WordSpace n d) : - dotProduct x (relabelWord e y) = dotProduct (relabelWord e.symm x) y := by - conv_lhs => rw [← (relabelWord e).apply_symm_apply x] - exact relabelWord_pair e _ _ - -lemma relabelWord_alphabet {n m d : ℕ} (e : Fin n ≃ Fin m) - (P : Fin d → Prop) (u : WordSpace n d) (hu : u ∈ alphabetSub n d P) : - relabelWord e u ∈ alphabetSub m d P := by - intro w hw - obtain ⟨i,hi⟩ := hw - apply hu - exact ⟨e.symm i, by simpa only [Function.comp_apply, Equiv.apply_symm_apply] using hi⟩ - -end Saxl -namespace Saxl.FlagColumns -open Columns - -lemma blocks_congr_word {d : ℕ} (rs : List ℕ) (N Q : ℕ → Fin d → ℂ) - (w : Fin rs.sum → Fin d) (h : ∀ i k, N i (w k) = Q i (w k)) : - blocks rs N w = blocks rs Q w := by - classical - simp only [blocks, Finset.sum_apply, Pi.smul_apply, smul_eq_mul, pure] - apply Finset.sum_congr rfl - intro π hπ - congr 1 - apply Finset.prod_congr rfl - intro i hi - exact h _ _ - -theorem columns_necessary {rs : List ℕ} {μ : YoungDiagram} {d : ℕ} - (e : Cells rs ≃ μ.cells) - (hr : ∀ c, (e c).val.1 = row c) - (hc : ∀ c c', (e c).val.2 = (e c').val.2 ↔ col c = col c') - (s : Tableau rs.sum μ) (u : WordSpace rs.sum d) - (P : Fin d → Prop) (hu : u ∈ alphabetSub rs.sum d P) - (hs : ∃ f : Representation.IntertwiningMap (spechtRep s) - (cyclic (wordRep rs.sum d) u).toRepresentation, f ≠ 0) : - ∃ (g : Equiv.Perm (Fin rs.sum)) (Q : ℕ → Fin d → ℂ), - (∀ i a, ¬P a → Q i a = 0) ∧ - dotProduct (blocks rs Q) (relabelWord g u) ≠ 0 := by - classical - let t := (enumerate rs).trans e - obtain ⟨f,hf⟩ := cyclic_support_tableau s t u hs - obtain ⟨g,L,hL⟩ := dual_polytabloid_necessary t u f hf - rw [(wordMap L).isIntertwining, wordPair_move] at hL - let N : ℕ → Fin d → ℂ := fun i a => if hi : i < μ.colLen 0 then L ⟨i,hi⟩ a else 0 - have hN : wordMap L (polytabloid t) = blocks rs N := by - convert (mapped_placed e hr hc N) using 1 - congr 2 - funext i a - change L i a = if hi : (i : ℕ) < μ.colLen 0 then L ⟨i,hi⟩ a else 0 - simp only [dite_eq_left i.isLt] - rw [hN] at hL - let Q : ℕ → Fin d → ℂ := fun i a => if P a then N i a else 0 - refine ⟨g⁻¹,Q,fun i a ha => ite_eq_right ha,?_⟩ - have hu' := relabelWord_alphabet g⁻¹ P u hu - have he : dotProduct (blocks rs Q) (relabelWord g⁻¹ u) = - dotProduct (blocks rs N) (relabelWord g⁻¹ u) := by - apply Finset.sum_congr rfl - intro w hw - by_cases hz : relabelWord g⁻¹ u w = 0 - · simp only [hz,mul_zero] - · congr 1 - apply blocks_congr_word - intro i k - exact ite_eq_left (by - by_contra hh - exact hz (hu' w ⟨k,hh⟩)) - rw [he] - exact hL - -theorem columns_sufficient {rs : List ℕ} {μ : YoungDiagram} {d : ℕ} - (e : Cells rs ≃ μ.cells) - (hr : ∀ c, (e c).val.1 = row c) - (hc : ∀ c c', (e c).val.2 = (e c').val.2 ↔ col c = col c') - (s : Tableau rs.sum μ) (u : WordSpace rs.sum d) (N : ℕ → Fin d → ℂ) - (h : dotProduct (blocks rs N) u ≠ 0) : - ∃ f : Representation.IntertwiningMap (spechtRep s) - (cyclic (wordRep rs.sum d) u).toRepresentation, f ≠ 0 := by - apply cyclic_support_tableau ((enumerate rs).trans e) s u - apply specht_to_cyclic_of_pair _ (fun i a => N i.val a) u - rwa [mapped_placed e hr hc N] - -end Saxl.FlagColumns -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPacking + +namespace OAI + +/-! Flag Detection. -/ + +section + +noncomputable section +namespace Saxl + +lemma cyclic_support_tableau {n d : ℕ} {μ : YoungDiagram} + (s t : Tableau n μ) (u : WordSpace n d) + (h : ∃ f : Representation.IntertwiningMap (spechtRep s) + (cyclic (wordRep n d) u).toRepresentation, f ≠ 0) : + ∃ f : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n d) u).toRepresentation, f ≠ 0 := by + change ∃ f : Representation.IntertwiningMap (spechtSub s).toRepresentation + (cyclic (wordRep n d) u).toRepresentation, f ≠ 0 at h + rw [spechtSub_tableau_independent s t] at h + exact h + +lemma cyclic_support_relabel_iff {n m d : ℕ} {μ : YoungDiagram} + (e : Fin n ≃ Fin m) (s : Tableau n μ) (t : Tableau m μ) (u : WordSpace n d) : + (∃ f : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep m d) (relabelWord e u)).toRepresentation, f ≠ 0) ↔ + (∃ f : Representation.IntertwiningMap (spechtRep s) + (cyclic (wordRep n d) u).toRepresentation, f ≠ 0) := by + have hnm : n = m := by simpa only [Fintype.card_fin] using Fintype.card_congr e + subst m + change (∃ f : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n d) (wordRep n d e u)).toRepresentation, f ≠ 0) ↔ _ + rw [cyclic_action_eq] + constructor + · exact cyclic_support_tableau t s u + · exact cyclic_support_tableau s t u + +lemma relabelWord_pair {n m d : ℕ} (e : Fin n ≃ Fin m) + (x y : WordSpace n d) : + dotProduct (relabelWord e x) (relabelWord e y) = dotProduct x y := by + classical + apply Fintype.sum_equiv ((Equiv.arrowCongr e (Equiv.refl _)).symm) + intro w + rfl + +lemma relabelWord_symm_pair {n m d : ℕ} (e : Fin n ≃ Fin m) + (x : WordSpace m d) (y : WordSpace n d) : + dotProduct x (relabelWord e y) = dotProduct (relabelWord e.symm x) y := by + conv_lhs => rw [← (relabelWord e).apply_symm_apply x] + exact relabelWord_pair e _ _ + +lemma relabelWord_alphabet {n m d : ℕ} (e : Fin n ≃ Fin m) + (P : Fin d → Prop) (u : WordSpace n d) (hu : u ∈ alphabetSub n d P) : + relabelWord e u ∈ alphabetSub m d P := by + intro w hw + obtain ⟨i,hi⟩ := hw + apply hu + exact ⟨e.symm i, by simpa only [Function.comp_apply, Equiv.apply_symm_apply] using hi⟩ + +end Saxl +namespace Saxl.FlagColumns +open Columns + +lemma blocks_congr_word {d : ℕ} (rs : List ℕ) (N Q : ℕ → Fin d → ℂ) + (w : Fin rs.sum → Fin d) (h : ∀ i k, N i (w k) = Q i (w k)) : + blocks rs N w = blocks rs Q w := by + classical + simp only [blocks, Finset.sum_apply, Pi.smul_apply, smul_eq_mul, pure] + apply Finset.sum_congr rfl + intro π hπ + congr 1 + apply Finset.prod_congr rfl + intro i hi + exact h _ _ + +theorem columns_necessary {rs : List ℕ} {μ : YoungDiagram} {d : ℕ} + (e : Cells rs ≃ μ.cells) + (hr : ∀ c, (e c).val.1 = row c) + (hc : ∀ c c', (e c).val.2 = (e c').val.2 ↔ col c = col c') + (s : Tableau rs.sum μ) (u : WordSpace rs.sum d) + (P : Fin d → Prop) (hu : u ∈ alphabetSub rs.sum d P) + (hs : ∃ f : Representation.IntertwiningMap (spechtRep s) + (cyclic (wordRep rs.sum d) u).toRepresentation, f ≠ 0) : + ∃ (g : Equiv.Perm (Fin rs.sum)) (Q : ℕ → Fin d → ℂ), + (∀ i a, ¬P a → Q i a = 0) ∧ + dotProduct (blocks rs Q) (relabelWord g u) ≠ 0 := by + classical + let t := (enumerate rs).trans e + obtain ⟨f,hf⟩ := cyclic_support_tableau s t u hs + obtain ⟨g,L,hL⟩ := dual_polytabloid_necessary t u f hf + rw [(wordMap L).isIntertwining, wordPair_move] at hL + let N : ℕ → Fin d → ℂ := fun i a => if hi : i < μ.colLen 0 then L ⟨i,hi⟩ a else 0 + have hN : wordMap L (polytabloid t) = blocks rs N := by + convert (mapped_placed e hr hc N) using 1 + congr 2 + funext i a + change L i a = if hi : (i : ℕ) < μ.colLen 0 then L ⟨i,hi⟩ a else 0 + simp only [dite_eq_left i.isLt] + rw [hN] at hL + let Q : ℕ → Fin d → ℂ := fun i a => if P a then N i a else 0 + refine ⟨g⁻¹,Q,fun i a ha => ite_eq_right ha,?_⟩ + have hu' := relabelWord_alphabet g⁻¹ P u hu + have he : dotProduct (blocks rs Q) (relabelWord g⁻¹ u) = + dotProduct (blocks rs N) (relabelWord g⁻¹ u) := by + apply Finset.sum_congr rfl + intro w hw + by_cases hz : relabelWord g⁻¹ u w = 0 + · simp only [hz,mul_zero] + · congr 1 + apply blocks_congr_word + intro i k + exact ite_eq_left (by + by_contra hh + exact hz (hu' w ⟨k,hh⟩)) + rw [he] + exact hL + +theorem columns_sufficient {rs : List ℕ} {μ : YoungDiagram} {d : ℕ} + (e : Cells rs ≃ μ.cells) + (hr : ∀ c, (e c).val.1 = row c) + (hc : ∀ c c', (e c).val.2 = (e c').val.2 ↔ col c = col c') + (s : Tableau rs.sum μ) (u : WordSpace rs.sum d) (N : ℕ → Fin d → ℂ) + (h : dotProduct (blocks rs N) u ≠ 0) : + ∃ f : Representation.IntertwiningMap (spechtRep s) + (cyclic (wordRep rs.sum d) u).toRepresentation, f ≠ 0 := by + apply cyclic_support_tableau ((enumerate rs).trans e) s u + apply specht_to_cyclic_of_pair _ (fun i a => N i.val a) u + rwa [mapped_placed e hr hc N] + +end Saxl.FlagColumns +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/GeneralDetection.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/GeneralDetection.lean index 58335a497d66ae4af8ec3d081f00c20ec5bb035b..a024465c330af43d426e2a1835431708f3509190 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/GeneralDetection.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/GeneralDetection.lean @@ -1,61 +1,61 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Specht.RepeatedColumns - -namespace OAI - -/-! General Detection. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl - -lemma wordMap_pair_transpose {n d e : ℕ} (L : Fin d → Fin e → ℂ) - (x : WordSpace n d) (y : WordSpace n e) : - dotProduct (wordMap L x) y = dotProduct x (wordMap (fun b a => L a b) y) := by - classical - change (∑ b, (∑ a, x a * ∏ i, L (a i) (b i)) * y b) = - ∑ a, x a * ∑ b, y b * ∏ i, L (a i) (b i) - simp_rw [Finset.sum_mul, Finset.mul_sum] - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro a ha - apply Finset.sum_congr rfl - intro b hb - ring - -theorem specht_to_cyclic_of_pair {n d : ℕ} {μ : YoungDiagram} - (t : Tableau n μ) (L : Fin (μ.colLen 0) → Fin d → ℂ) - (u : WordSpace n d) - (h : dotProduct (wordMap L (polytabloid t)) u ≠ 0) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n d) u).toRepresentation, F ≠ 0 := by - let pr := subrepProject (spechtSub t) - (fun _ hx => cyclic_star _ (polytabloid_real t) hx) - let F : Representation.IntertwiningMap - (cyclic (wordRep n d) u).toRepresentation (spechtRep t) := - pr.comp ((wordMap (fun b a => L a b)).comp (subrepInclusion _)) - apply specht_map_back_of_nonzero _ t F - intro hz - have hp := subrepProject_pair (spechtSub t) - (fun _ hx => cyclic_star _ (polytabloid_real t) hx) - (wordMap (fun b a => L a b) u) ⟨polytabloid t, mem_cyclic _ _⟩ - have he : pr (wordMap (fun b a => L a b) u) = 0 := - congrArg (fun H : Representation.IntertwiningMap - (cyclic (wordRep n d) u).toRepresentation (spechtRep t) => - H ⟨u, mem_cyclic _ _⟩) hz - rw [he] at hp - change dotProduct (0 : WordSpace n (μ.colLen 0)) (polytabloid t) = - dotProduct (wordMap (fun b a => L a b) u) (polytabloid t) at hp - rw [zero_dotProduct] at hp - rw [wordMap_pair_transpose, dotProduct_comm] - at h - exact h hp.symm - -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Specht.RepeatedColumns + +namespace OAI + +/-! General Detection. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl + +lemma wordMap_pair_transpose {n d e : ℕ} (L : Fin d → Fin e → ℂ) + (x : WordSpace n d) (y : WordSpace n e) : + dotProduct (wordMap L x) y = dotProduct x (wordMap (fun b a => L a b) y) := by + classical + change (∑ b, (∑ a, x a * ∏ i, L (a i) (b i)) * y b) = + ∑ a, x a * ∑ b, y b * ∏ i, L (a i) (b i) + simp_rw [Finset.sum_mul, Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro a ha + apply Finset.sum_congr rfl + intro b hb + ring + +theorem specht_to_cyclic_of_pair {n d : ℕ} {μ : YoungDiagram} + (t : Tableau n μ) (L : Fin (μ.colLen 0) → Fin d → ℂ) + (u : WordSpace n d) + (h : dotProduct (wordMap L (polytabloid t)) u ≠ 0) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n d) u).toRepresentation, F ≠ 0 := by + let pr := subrepProject (spechtSub t) + (fun _ hx => cyclic_star _ (polytabloid_real t) hx) + let F : Representation.IntertwiningMap + (cyclic (wordRep n d) u).toRepresentation (spechtRep t) := + pr.comp ((wordMap (fun b a => L a b)).comp (subrepInclusion _)) + apply specht_map_back_of_nonzero _ t F + intro hz + have hp := subrepProject_pair (spechtSub t) + (fun _ hx => cyclic_star _ (polytabloid_real t) hx) + (wordMap (fun b a => L a b) u) ⟨polytabloid t, mem_cyclic _ _⟩ + have he : pr (wordMap (fun b a => L a b) u) = 0 := + congrArg (fun H : Representation.IntertwiningMap + (cyclic (wordRep n d) u).toRepresentation (spechtRep t) => + H ⟨u, mem_cyclic _ _⟩) hz + rw [he] at hp + change dotProduct (0 : WordSpace n (μ.colLen 0)) (polytabloid t) = + dotProduct (wordMap (fun b a => L a b) u) (polytabloid t) at hp + rw [zero_dotProduct] at hp + rw [wordMap_pair_transpose, dotProduct_comm] + at h + exact h hp.symm + +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/NondegeneratePairs.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/NondegeneratePairs.lean index 142ce95b84854cd441e850c5a70ae091086d8126..0997893f4d20563fc135ae98d5adc3d46408afa7 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/NondegeneratePairs.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/NondegeneratePairs.lean @@ -1,70 +1,70 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.PairForms - -namespace OAI - -/-! Nondegenerate Pairs. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl - -theorem pairForm_orthonormal {d : ℕ} (B : Matrix (Fin d) (Fin d) ℂ) - (hS : B.IsSymm) (hB : B.Nondegenerate) : - ∃ L : Matrix (Fin d) (Fin d) ℂ, - (fun j k => ∑ p : Fin d × Fin d, B p.1 p.2 * L p.1 j * L p.2 k) = (1 : Matrix (Fin d) (Fin d) ℂ) := by - let A : Matrix (Fin d) (Fin d) ℂ := 1 - have hA : A.IsSymm := by simp [A] - have hAn : A.Nondegenerate := by - rw [Matrix.nondegenerate_iff_det_ne_zero] - simp [A] - have hBs : QuadraticMap.associated B.toBilin'.toQuadraticMap = B.toBilin' := - QuadraticMap.associated_left_inverse ℂ - (fun x y => (Matrix.isSymm_toBilin'_iff_isSymm.mpr hS).eq x y) - have hAs : QuadraticMap.associated A.toBilin'.toQuadraticMap = A.toBilin' := - QuadraticMap.associated_left_inverse ℂ - (fun x y => (Matrix.isSymm_toBilin'_iff_isSymm.mpr hA).eq x y) - obtain ⟨f⟩ := QuadraticForm.equivalent_of_isAlgClosed - A.toBilin'.toQuadraticMap B.toBilin'.toQuadraticMap - (by rw [hAs]; exact hAn.toBilin'.1) (by rw [hBs]; exact hB.toBilin'.1) - have hf (x y : Fin d → ℂ) : B.toBilin' (f x) (f y) = A.toBilin' x y := by - calc - B.toBilin' (f x) (f y) = - QuadraticMap.associated B.toBilin'.toQuadraticMap (f x) (f y) := - congrArg (fun K : LinearMap.BilinForm ℂ (Fin d → ℂ) => K (f x) (f y)) hBs.symm - _ = QuadraticMap.associated A.toBilin'.toQuadraticMap x y := by - simp only [QuadraticMap.associated, QuadraticMap.associated_apply, - ← map_add f, f.map_app] - _ = A.toBilin' x y := congrArg (fun K : LinearMap.BilinForm ℂ (Fin d → ℂ) => K x y) hAs - refine ⟨fun i j => f (Pi.single j 1) i, ?_⟩ - ext j k - have hh := hf (Pi.single j 1) (Pi.single k 1) - rw [Matrix.toBilin'_single, Matrix.toBilin'_apply] at hh - rw [Fintype.sum_prod_type] - change (∑ i, ∑ l, B i l * f (Pi.single j 1) i * f (Pi.single k 1) l) = A j k - convert hh using 1 - apply Finset.sum_congr rfl - intro i hi - apply Finset.sum_congr rfl - intro l hl - ring - -theorem even_rows_nondegenerate_pair_support {n m d : ℕ} - (e : Fin n ≃ Fin m ⊕ Fin m) (B : Matrix (Fin d) (Fin d) ℂ) - (hS : B.IsSymm) (hB : B.Nondegenerate) - (μ : YoungDiagram) (t : Tableau n μ) - (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ d) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n d) (pairFormTensor e B)).toRepresentation, F ≠ 0 := by - obtain ⟨L,hL⟩ := pairForm_orthonormal B hS hB - apply even_rows_pairFormTensor_support e B L 1 one_ne_zero - (by simpa only [one_smul] using hL) μ t he hd - -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.PairForms + +namespace OAI + +/-! Nondegenerate Pairs. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl + +theorem pairForm_orthonormal {d : ℕ} (B : Matrix (Fin d) (Fin d) ℂ) + (hS : B.IsSymm) (hB : B.Nondegenerate) : + ∃ L : Matrix (Fin d) (Fin d) ℂ, + (fun j k => ∑ p : Fin d × Fin d, B p.1 p.2 * L p.1 j * L p.2 k) = (1 : Matrix (Fin d) (Fin d) ℂ) := by + let A : Matrix (Fin d) (Fin d) ℂ := 1 + have hA : A.IsSymm := by simp [A] + have hAn : A.Nondegenerate := by + rw [Matrix.nondegenerate_iff_det_ne_zero] + simp [A] + have hBs : QuadraticMap.associated B.toBilin'.toQuadraticMap = B.toBilin' := + QuadraticMap.associated_left_inverse ℂ + (fun x y => (Matrix.isSymm_toBilin'_iff_isSymm.mpr hS).eq x y) + have hAs : QuadraticMap.associated A.toBilin'.toQuadraticMap = A.toBilin' := + QuadraticMap.associated_left_inverse ℂ + (fun x y => (Matrix.isSymm_toBilin'_iff_isSymm.mpr hA).eq x y) + obtain ⟨f⟩ := QuadraticForm.equivalent_of_isAlgClosed + A.toBilin'.toQuadraticMap B.toBilin'.toQuadraticMap + (by rw [hAs]; exact hAn.toBilin'.1) (by rw [hBs]; exact hB.toBilin'.1) + have hf (x y : Fin d → ℂ) : B.toBilin' (f x) (f y) = A.toBilin' x y := by + calc + B.toBilin' (f x) (f y) = + QuadraticMap.associated B.toBilin'.toQuadraticMap (f x) (f y) := + congrArg (fun K : LinearMap.BilinForm ℂ (Fin d → ℂ) => K (f x) (f y)) hBs.symm + _ = QuadraticMap.associated A.toBilin'.toQuadraticMap x y := by + simp only [QuadraticMap.associated, QuadraticMap.associated_apply, + ← map_add f, f.map_app] + _ = A.toBilin' x y := congrArg (fun K : LinearMap.BilinForm ℂ (Fin d → ℂ) => K x y) hAs + refine ⟨fun i j => f (Pi.single j 1) i, ?_⟩ + ext j k + have hh := hf (Pi.single j 1) (Pi.single k 1) + rw [Matrix.toBilin'_single, Matrix.toBilin'_apply] at hh + rw [Fintype.sum_prod_type] + change (∑ i, ∑ l, B i l * f (Pi.single j 1) i * f (Pi.single k 1) l) = A j k + convert hh using 1 + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro l hl + ring + +theorem even_rows_nondegenerate_pair_support {n m d : ℕ} + (e : Fin n ≃ Fin m ⊕ Fin m) (B : Matrix (Fin d) (Fin d) ℂ) + (hS : B.IsSymm) (hB : B.Nondegenerate) + (μ : YoungDiagram) (t : Tableau n μ) + (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ d) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n d) (pairFormTensor e B)).toRepresentation, F ≠ 0 := by + obtain ⟨L,hL⟩ := pairForm_orthonormal B hS hB + apply even_rows_pairFormTensor_support e B L 1 one_ne_zero + (by simpa only [one_smul] using hL) μ t he hd + +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/PairForms.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/PairForms.lean index 7b9b8c38f856ee02b90fc5cda4da7b275269c511..6ca6c8dcf78d10a7bb6f612506ae0c7d9f5fd48d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/PairForms.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/PairForms.lean @@ -1,147 +1,147 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.SymmetricPairs - -namespace OAI - -/-! Pair Forms. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl - -def pairFormTensor {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) - (B : Matrix (Fin d) (Fin d) ℂ) : WordSpace n d := - fun w => ∏ i, B (leftWord e w i) (rightWord e w i) - -lemma pairFormTensor_one {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) : - pairFormTensor e (1 : Matrix (Fin d) (Fin d) ℂ) = symmetricPairs e d := by - classical - funext w - change (∏ i, if leftWord e w i = rightWord e w i then (1 : ℂ) else 0) = _ - by_cases hw : leftWord e w = rightWord e w - · simp [hw, symmetricPairs] - · have hi : ∃ i, leftWord e w i ≠ rightWord e w i := by - exact not_forall.mp (fun he => hw (funext he)) - obtain ⟨i, hi⟩ := hi - rw [symmetricPairs, ite_eq_right hw] - exact Finset.prod_eq_zero (Finset.mem_univ i) (ite_eq_right hi) - -lemma pairFormTensor_smul {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) - (c : ℂ) (B : Matrix (Fin d) (Fin d) ℂ) : - pairFormTensor e (c • B) = c^m • pairFormTensor e B := by - funext w - simp [pairFormTensor, Finset.prod_mul_distrib] - -def pairWordsEquiv {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) : - (Fin n → Fin d) ≃ (Fin m → Fin d × Fin d) := - (positionWordsEquiv e).trans - (Equiv.arrowProdEquivProdArrow (Fin m) (fun _ => Fin d) (fun _ => Fin d)).symm - -@[simp] lemma pairWordsEquiv_apply {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) - (w : Fin n → Fin d) (i : Fin m) : - pairWordsEquiv e w i = (leftWord e w i, rightWord e w i) := rfl - -lemma wordMap_pairFormTensor {n m a b : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) - (L : Fin a → Fin b → ℂ) (B : Matrix (Fin a) (Fin a) ℂ) : - wordMap L (pairFormTensor e B) = pairFormTensor e - (fun j k => ∑ p : Fin a × Fin a, B p.1 p.2 * L p.1 j * L p.2 k) := by - classical - funext w - change (∑ c, pairFormTensor e B c * ∏ i, L (c i) (w i)) = _ - calc - _ = ∑ c : Fin m → Fin a × Fin a, - ∏ i, B (c i).1 (c i).2 * L (c i).1 (leftWord e w i) * - L (c i).2 (rightWord e w i) := by - apply Fintype.sum_equiv (pairWordsEquiv e) - intro c - simp only [pairWordsEquiv_apply, pairFormTensor, Finset.prod_mul_distrib] - have he : (∏ i, L (c i) (w i)) = - (∏ i, L (leftWord e c i) (leftWord e w i)) * - ∏ i, L (rightWord e c i) (rightWord e w i) := by - calc - _ = ∏ x : Fin m ⊕ Fin m, L (c (e.symm x)) (w (e.symm x)) := - (Equiv.prod_comp e.symm (fun i => L (c i) (w i))).symm - _ = _ := by - rw [Fintype.prod_sum_type] - rfl - rw [he, mul_assoc] - _ = _ := by - change (∑ c : Fin m → Fin a × Fin a, - ∏ i, B (c i).1 (c i).2 * L (c i).1 (leftWord e w i) * - L (c i).2 (rightWord e w i)) = - ∏ i, ∑ p : Fin a × Fin a, - B p.1 p.2 * L p.1 (leftWord e w i) * L p.2 (rightWord e w i) - exact (Fintype.prod_sum (fun (i : Fin m) (p : Fin a × Fin a) => - B p.1 p.2 * L p.1 (leftWord e w i) * L p.2 (rightWord e w i))).symm - -theorem even_rows_pairFormTensor_support {n m a d : ℕ} - (e : Fin n ≃ Fin m ⊕ Fin m) (B : Matrix (Fin a) (Fin a) ℂ) - (L : Fin a → Fin d → ℂ) (c : ℂ) (hc : c ≠ 0) - (hL : (fun j k => ∑ p : Fin a × Fin a, B p.1 p.2 * L p.1 j * L p.2 k) = - c • (1 : Matrix (Fin d) (Fin d) ℂ)) - (μ : YoungDiagram) (t : Tableau n μ) - (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ d) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n a) (pairFormTensor e B)).toRepresentation, F ≠ 0 := by - have hmap : wordMap L (pairFormTensor e B) = c^m • symmetricPairs e d := by - rw [wordMap_pairFormTensor, hL, pairFormTensor_smul, pairFormTensor_one] - have hs := even_rows_symmetricPairs_support e μ t he hd - have hcyc : cyclic (wordRep n d) (wordMap L (pairFormTensor e B)) = - cyclic (wordRep n d) (symmetricPairs e d) := by - rw [hmap, cyclic_smul_eq _ _ _ (pow_ne_zero m hc)] - rw [← hcyc] at hs - obtain ⟨F,hF⟩ := hs - exact cyclic_projection_support (wordMap L) (pairFormTensor e B) F hF - -def shortPairForm : Matrix (Fin 4) (Fin 4) ℂ := - !![0,0,0,1; 0,0,-1,0; 0,-1,0,0; 1,0,0,0] - -def shortPairCongruence : Matrix (Fin 4) (Fin 4) ℂ := - !![1,Complex.I,0,0; 0,0,1,Complex.I; 0,0,-1,Complex.I; 1,-Complex.I,0,0] - -lemma shortPairCongruence_gram : - (fun j k => ∑ p : Fin 4 × Fin 4, - shortPairForm p.1 p.2 * shortPairCongruence p.1 j * shortPairCongruence p.2 k) = - (2 : ℂ) • (1 : Matrix (Fin 4) (Fin 4) ℂ) := by - ext j k - fin_cases j <;> fin_cases k <;> - norm_num [Fintype.sum_prod_type, Fin.sum_univ_succ, shortPairForm, - shortPairCongruence, Matrix.one_apply] - -theorem even_rows_shortPair_support {n m : ℕ} - (e : Fin n ≃ Fin m ⊕ Fin m) (μ : YoungDiagram) (t : Tableau n μ) - (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ 4) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n 4) (pairFormTensor e shortPairForm)).toRepresentation, F ≠ 0 := - even_rows_pairFormTensor_support e shortPairForm shortPairCongruence 2 (by norm_num) - shortPairCongruence_gram μ t he hd - -def outputTwoForm : Matrix (Fin 2) (Fin 2) ℂ := !![0,1; 1,0] - -def outputTwoCongruence : Matrix (Fin 2) (Fin 2) ℂ := !![1,Complex.I; 1,-Complex.I] - -lemma outputTwoCongruence_gram : - (fun j k => ∑ p : Fin 2 × Fin 2, - outputTwoForm p.1 p.2 * outputTwoCongruence p.1 j * outputTwoCongruence p.2 k) = - (2 : ℂ) • (1 : Matrix (Fin 2) (Fin 2) ℂ) := by - ext j k - fin_cases j <;> fin_cases k <;> - norm_num [Fintype.sum_prod_type, Fin.sum_univ_succ, outputTwoForm, - outputTwoCongruence, Matrix.one_apply] - -theorem even_rows_outputTwo_support {n m : ℕ} - (e : Fin n ≃ Fin m ⊕ Fin m) (μ : YoungDiagram) (t : Tableau n μ) - (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ 2) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n 2) (pairFormTensor e outputTwoForm)).toRepresentation, F ≠ 0 := - even_rows_pairFormTensor_support e outputTwoForm outputTwoCongruence 2 (by norm_num) - outputTwoCongruence_gram μ t he hd - -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.SymmetricPairs + +namespace OAI + +/-! Pair Forms. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl + +def pairFormTensor {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) + (B : Matrix (Fin d) (Fin d) ℂ) : WordSpace n d := + fun w => ∏ i, B (leftWord e w i) (rightWord e w i) + +lemma pairFormTensor_one {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) : + pairFormTensor e (1 : Matrix (Fin d) (Fin d) ℂ) = symmetricPairs e d := by + classical + funext w + change (∏ i, if leftWord e w i = rightWord e w i then (1 : ℂ) else 0) = _ + by_cases hw : leftWord e w = rightWord e w + · simp [hw, symmetricPairs] + · have hi : ∃ i, leftWord e w i ≠ rightWord e w i := by + exact not_forall.mp (fun he => hw (funext he)) + obtain ⟨i, hi⟩ := hi + rw [symmetricPairs, ite_eq_right hw] + exact Finset.prod_eq_zero (Finset.mem_univ i) (ite_eq_right hi) + +lemma pairFormTensor_smul {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) + (c : ℂ) (B : Matrix (Fin d) (Fin d) ℂ) : + pairFormTensor e (c • B) = c^m • pairFormTensor e B := by + funext w + simp [pairFormTensor, Finset.prod_mul_distrib] + +def pairWordsEquiv {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) : + (Fin n → Fin d) ≃ (Fin m → Fin d × Fin d) := + (positionWordsEquiv e).trans + (Equiv.arrowProdEquivProdArrow (Fin m) (fun _ => Fin d) (fun _ => Fin d)).symm + +@[simp] lemma pairWordsEquiv_apply {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) + (w : Fin n → Fin d) (i : Fin m) : + pairWordsEquiv e w i = (leftWord e w i, rightWord e w i) := rfl + +lemma wordMap_pairFormTensor {n m a b : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) + (L : Fin a → Fin b → ℂ) (B : Matrix (Fin a) (Fin a) ℂ) : + wordMap L (pairFormTensor e B) = pairFormTensor e + (fun j k => ∑ p : Fin a × Fin a, B p.1 p.2 * L p.1 j * L p.2 k) := by + classical + funext w + change (∑ c, pairFormTensor e B c * ∏ i, L (c i) (w i)) = _ + calc + _ = ∑ c : Fin m → Fin a × Fin a, + ∏ i, B (c i).1 (c i).2 * L (c i).1 (leftWord e w i) * + L (c i).2 (rightWord e w i) := by + apply Fintype.sum_equiv (pairWordsEquiv e) + intro c + simp only [pairWordsEquiv_apply, pairFormTensor, Finset.prod_mul_distrib] + have he : (∏ i, L (c i) (w i)) = + (∏ i, L (leftWord e c i) (leftWord e w i)) * + ∏ i, L (rightWord e c i) (rightWord e w i) := by + calc + _ = ∏ x : Fin m ⊕ Fin m, L (c (e.symm x)) (w (e.symm x)) := + (Equiv.prod_comp e.symm (fun i => L (c i) (w i))).symm + _ = _ := by + rw [Fintype.prod_sum_type] + rfl + rw [he, mul_assoc] + _ = _ := by + change (∑ c : Fin m → Fin a × Fin a, + ∏ i, B (c i).1 (c i).2 * L (c i).1 (leftWord e w i) * + L (c i).2 (rightWord e w i)) = + ∏ i, ∑ p : Fin a × Fin a, + B p.1 p.2 * L p.1 (leftWord e w i) * L p.2 (rightWord e w i) + exact (Fintype.prod_sum (fun (i : Fin m) (p : Fin a × Fin a) => + B p.1 p.2 * L p.1 (leftWord e w i) * L p.2 (rightWord e w i))).symm + +theorem even_rows_pairFormTensor_support {n m a d : ℕ} + (e : Fin n ≃ Fin m ⊕ Fin m) (B : Matrix (Fin a) (Fin a) ℂ) + (L : Fin a → Fin d → ℂ) (c : ℂ) (hc : c ≠ 0) + (hL : (fun j k => ∑ p : Fin a × Fin a, B p.1 p.2 * L p.1 j * L p.2 k) = + c • (1 : Matrix (Fin d) (Fin d) ℂ)) + (μ : YoungDiagram) (t : Tableau n μ) + (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ d) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n a) (pairFormTensor e B)).toRepresentation, F ≠ 0 := by + have hmap : wordMap L (pairFormTensor e B) = c^m • symmetricPairs e d := by + rw [wordMap_pairFormTensor, hL, pairFormTensor_smul, pairFormTensor_one] + have hs := even_rows_symmetricPairs_support e μ t he hd + have hcyc : cyclic (wordRep n d) (wordMap L (pairFormTensor e B)) = + cyclic (wordRep n d) (symmetricPairs e d) := by + rw [hmap, cyclic_smul_eq _ _ _ (pow_ne_zero m hc)] + rw [← hcyc] at hs + obtain ⟨F,hF⟩ := hs + exact cyclic_projection_support (wordMap L) (pairFormTensor e B) F hF + +def shortPairForm : Matrix (Fin 4) (Fin 4) ℂ := + !![0,0,0,1; 0,0,-1,0; 0,-1,0,0; 1,0,0,0] + +def shortPairCongruence : Matrix (Fin 4) (Fin 4) ℂ := + !![1,Complex.I,0,0; 0,0,1,Complex.I; 0,0,-1,Complex.I; 1,-Complex.I,0,0] + +lemma shortPairCongruence_gram : + (fun j k => ∑ p : Fin 4 × Fin 4, + shortPairForm p.1 p.2 * shortPairCongruence p.1 j * shortPairCongruence p.2 k) = + (2 : ℂ) • (1 : Matrix (Fin 4) (Fin 4) ℂ) := by + ext j k + fin_cases j <;> fin_cases k <;> + norm_num [Fintype.sum_prod_type, Fin.sum_univ_succ, shortPairForm, + shortPairCongruence, Matrix.one_apply] + +theorem even_rows_shortPair_support {n m : ℕ} + (e : Fin n ≃ Fin m ⊕ Fin m) (μ : YoungDiagram) (t : Tableau n μ) + (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ 4) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n 4) (pairFormTensor e shortPairForm)).toRepresentation, F ≠ 0 := + even_rows_pairFormTensor_support e shortPairForm shortPairCongruence 2 (by norm_num) + shortPairCongruence_gram μ t he hd + +def outputTwoForm : Matrix (Fin 2) (Fin 2) ℂ := !![0,1; 1,0] + +def outputTwoCongruence : Matrix (Fin 2) (Fin 2) ℂ := !![1,Complex.I; 1,-Complex.I] + +lemma outputTwoCongruence_gram : + (fun j k => ∑ p : Fin 2 × Fin 2, + outputTwoForm p.1 p.2 * outputTwoCongruence p.1 j * outputTwoCongruence p.2 k) = + (2 : ℂ) • (1 : Matrix (Fin 2) (Fin 2) ℂ) := by + ext j k + fin_cases j <;> fin_cases k <;> + norm_num [Fintype.sum_prod_type, Fin.sum_univ_succ, outputTwoForm, + outputTwoCongruence, Matrix.one_apply] + +theorem even_rows_outputTwo_support {n m : ℕ} + (e : Fin n ≃ Fin m ⊕ Fin m) (μ : YoungDiagram) (t : Tableau n μ) + (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ 2) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n 2) (pairFormTensor e outputTwoForm)).toRepresentation, F ≠ 0 := + even_rows_pairFormTensor_support e outputTwoForm outputTwoCongruence 2 (by norm_num) + outputTwoCongruence_gram μ t he hd + +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/PieriCertificates.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/PieriCertificates.lean index 326d9f29db31548e58b63362fdae15f3d01ef742..b396a6a24370d916816527a6ab7c3669b5f675f9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/PieriCertificates.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/PieriCertificates.lean @@ -1,42 +1,42 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Pieri Certificates. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma rowSquare_pieri {p rs ss : List ℕ} {cs : List (List ℕ)} - (plan : PackingPlan) (q δ : ℕ) - (hp : GoodRows p) (hq : 0 < q) (hδ : δ = 1 ∨ δ = 2) - (hv : plan.Valid p.length) (hb : BandsValid ((q,pairUpper q δ)::plan.bands)) - (hk : q ∉ plan.marks) (hd : q+δ ≤ p.length) - (hc : ([q+δ,q]++plan.columns).Perm (transposeRows p)) - (hr : GoodRows rs) (hrl : rs.length ≤ 4) (hrs : rs.sum = 2*q+δ) - (ho : δ = 2 → ∃ j ∈ List.range (rs.sum+1), - (rs.countP (fun x => decide (j < x))) % 2 = 1) - (hchain : ChainValid rs cs ss) (hs : plan.parts.Perm (stripSizes rs cs)) - (hn : ss.sum = p.sum) : RowSquare p ss := by - let a := canonicalTableau (rowDiagram p) (rowDiagram_card p) - let t := canonicalTableau (rowDiagram ss) ((rowDiagram_card ss).trans hn) - refine ⟨p.sum,a,t,?_⟩ - apply pieriPlan_pos plan hq hδ hv hb hk (rowDiagram_height hp) hd - · rwa [← transposeRows_eq hp] - · exact hr - · exact hrl - · exact hrs - · exact ho - · exact hchain - · exact hs - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Pieri Certificates. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma rowSquare_pieri {p rs ss : List ℕ} {cs : List (List ℕ)} + (plan : PackingPlan) (q δ : ℕ) + (hp : GoodRows p) (hq : 0 < q) (hδ : δ = 1 ∨ δ = 2) + (hv : plan.Valid p.length) (hb : BandsValid ((q,pairUpper q δ)::plan.bands)) + (hk : q ∉ plan.marks) (hd : q+δ ≤ p.length) + (hc : ([q+δ,q]++plan.columns).Perm (transposeRows p)) + (hr : GoodRows rs) (hrl : rs.length ≤ 4) (hrs : rs.sum = 2*q+δ) + (ho : δ = 2 → ∃ j ∈ List.range (rs.sum+1), + (rs.countP (fun x => decide (j < x))) % 2 = 1) + (hchain : ChainValid rs cs ss) (hs : plan.parts.Perm (stripSizes rs cs)) + (hn : ss.sum = p.sum) : RowSquare p ss := by + let a := canonicalTableau (rowDiagram p) (rowDiagram_card p) + let t := canonicalTableau (rowDiagram ss) ((rowDiagram_card ss).trans hn) + refine ⟨p.sum,a,t,?_⟩ + apply pieriPlan_pos plan hq hδ hv hb hk (rowDiagram_height hp) hd + · rwa [← transposeRows_eq hp] + · exact hr + · exact hrl + · exact hrs + · exact ho + · exact hchain + · exact hs + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/PolynomialDetection.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/PolynomialDetection.lean index 907e59ea9c3221d5ac034bcaddebbb3c243f4174..f8a1afdce1b4b24b9a9d8845ac329b13dc0e86e3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/PolynomialDetection.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/PolynomialDetection.lean @@ -1,168 +1,168 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.SquareDetection - -namespace OAI - -/-! Polynomial Detection. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl - -def jointContent {n d e : ℕ} (a : Fin n → Fin d) (b : Fin n → Fin e) : - (Fin d × Fin e) →₀ ℕ := ∑ i, Finsupp.single (a i, b i) 1 - -lemma jointContent_apply {n d e : ℕ} (a : Fin n → Fin d) (b : Fin n → Fin e) - (j : Fin d × Fin e) : jointContent a b j = - (Finset.univ.filter (fun i => (a i, b i) = j)).card := by - classical - simp [jointContent, Finsupp.single_apply, eq_comm] - -lemma perm_of_equal_jointContent {n d e : ℕ} - (a a' : Fin n → Fin d) (b b' : Fin n → Fin e) - (h : jointContent a b = jointContent a' b') : - ∃ g : Equiv.Perm (Fin n), a' ∘ g = a ∧ b' ∘ g = b := by - classical - have hc : ∀ j : Fin (d*e), - (Finset.univ.filter (fun i => finProdFinEquiv (a i,b i) = j)).card = - (Finset.univ.filter (fun i => finProdFinEquiv (a' i,b' i) = j)).card := by - intro j - have hh := DFunLike.congr_fun h (finProdFinEquiv.symm j) - simp only [jointContent_apply] at hh - simpa only [← Equiv.eq_symm_apply] using hh - obtain ⟨g, hg⟩ := perm_of_equal_content - (fun i => finProdFinEquiv (a i, b i)) - (fun i => finProdFinEquiv (a' i, b' i)) hc - refine ⟨g, ?_, ?_⟩ - · funext i - exact congrArg Prod.fst (finProdFinEquiv.injective (congrFun hg i)) - · funext i - exact congrArg Prod.snd (finProdFinEquiv.injective (congrFun hg i)) - -lemma intertwiner_jointContent {n d e : ℕ} - (F : Representation.IntertwiningMap (wordRep n d) (wordRep n e)) - (a a' : Fin n → Fin d) (b b' : Fin n → Fin e) - (h : jointContent a b = jointContent a' b') : - F (Pi.single a 1) b = F (Pi.single a' 1) b' := by - classical - obtain ⟨g, ha, hb⟩ := perm_of_equal_jointContent a a' b b' h - have hs : wordRep n d g (Pi.single a 1) = Pi.single a' 1 := by - ext w - change (Pi.single a 1 : WordSpace n d) (w ∘ g) = (Pi.single a' 1 : WordSpace n d) w - simp only [Pi.single_apply] - have he : (w ∘ g = a) ↔ w = a' := by - rw [← ha] - exact ⟨fun h => funext (fun i => by - have hh := congrFun h (g⁻¹ i) - simpa using hh), - fun h => by rw [h]⟩ - simp only [he] - have hh := congrFun (LinearMap.congr_fun (F.isIntertwining' g) (Pi.single a 1)) b' - simp only [LinearMap.comp_apply] at hh - rw [hs] at hh - change F (Pi.single a' 1) b' = F (Pi.single a 1) (b' ∘ g) at hh - rw [hb] at hh - exact hh.symm - -def pairingPolynomial {n d e : ℕ} (x : WordSpace n d) (y : WordSpace n e) : - MvPolynomial (Fin d × Fin e) ℂ := - ∑ a, ∑ b, MvPolynomial.monomial (jointContent a b) (x a * y b) - -lemma eval_jointContent_monomial {n d e : ℕ} - (a : Fin n → Fin d) (b : Fin n → Fin e) - (c : ℂ) (L : Fin d → Fin e → ℂ) : - MvPolynomial.eval (fun j => L j.1 j.2) - (MvPolynomial.monomial (jointContent a b) c) = - c * ∏ i, L (a i) (b i) := by - classical - rw [jointContent, MvPolynomial.monomial_sum_index] - simp only [map_mul, MvPolynomial.eval_C, map_prod] - congr 1 - apply Finset.prod_congr rfl - intro i hi - change MvPolynomial.eval _ (MvPolynomial.X (a i, b i)) = _ - exact MvPolynomial.eval_X _ - -lemma pairingPolynomial_eval {n d e : ℕ} - (x : WordSpace n d) (y : WordSpace n e) (L : Fin d → Fin e → ℂ) : - MvPolynomial.eval (fun j => L j.1 j.2) (pairingPolynomial x y) = - dotProduct (wordMap L x) y := by - classical - simp only [pairingPolynomial, map_sum, eval_jointContent_monomial] - change (∑ a, ∑ b, x a * y b * ∏ i, L (a i) (b i)) = - ∑ b, (∑ a, x a * ∏ i, L (a i) (b i)) * y b - simp_rw [Finset.sum_mul] - rw [Finset.sum_comm] - apply Finset.sum_congr rfl - intro b hb - apply Finset.sum_congr rfl - intro a ha - ring - -def jointContentWeight {n d e : ℕ} - (F : Representation.IntertwiningMap (wordRep n d) (wordRep n e)) - (m : (Fin d × Fin e) →₀ ℕ) : ℂ := - if h : ∃ a b, jointContent a b = m then - F (Pi.single h.choose 1) h.choose_spec.choose else 0 - -lemma jointContentWeight_apply {n d e : ℕ} - (F : Representation.IntertwiningMap (wordRep n d) (wordRep n e)) - (a : Fin n → Fin d) (b : Fin n → Fin e) : - jointContentWeight F (jointContent a b) = F (Pi.single a 1) b := by - classical - unfold jointContentWeight - have hab : ∃ a' b', jointContent a' b' = jointContent a b := ⟨a,b,rfl⟩ - rw [dite_eq_left hab] - exact intertwiner_jointContent F _ a _ b hab.choose_spec.choose_spec - -lemma pairingPolynomial_zero_pair {n d e : ℕ} - (F : Representation.IntertwiningMap (wordRep n d) (wordRep n e)) - (x : WordSpace n d) (y : WordSpace n e) (h : pairingPolynomial x y = 0) : - dotProduct (F x) y = 0 := by - classical - let w : MvPolynomial (Fin d × Fin e) ℂ →ₗ[ℂ] ℂ := - (Finsupp.linearCombination ℂ (jointContentWeight F)).comp - (AddMonoidAlgebra.coeffLinearEquiv ℂ).toLinearMap - have he := congrArg w h - have hw (m : (Fin d × Fin e) →₀ ℕ) (c : ℂ) : - w (MvPolynomial.monomial m c) = c * jointContentWeight F m := by - change Finsupp.linearCombination ℂ (jointContentWeight F) (Finsupp.single m c) = _ - simp - have he' : (∑ a, ∑ b, (x a * y b) * F (Pi.single a 1) b) = 0 := by - simpa only [pairingPolynomial, map_sum, map_zero, hw, jointContentWeight_apply] using he - have hx : x = ∑ a, x a • Pi.single a 1 := by - ext a - simp [Pi.single_apply] - rw [hx, map_sum] - simp only [map_smul, dotProduct, Finset.sum_apply, Pi.smul_apply, smul_eq_mul, - Finset.sum_mul] - rw [Finset.sum_comm] - convert he' using 1 - apply Finset.sum_congr rfl - intro a ha - apply Finset.sum_congr rfl - intro b hb - ring - -theorem wordMap_detects_intertwiner {n d e : ℕ} - (F : Representation.IntertwiningMap (wordRep n d) (wordRep n e)) - (x : WordSpace n d) (y : WordSpace n e) - (h : dotProduct (F x) y ≠ 0) : - ∃ L : Fin d → Fin e → ℂ, dotProduct (wordMap L x) y ≠ 0 := by - by_contra hn - push Not at hn - apply h - apply pairingPolynomial_zero_pair F - apply MvPolynomial.funext - intro L - simpa only [map_zero, pairingPolynomial_eval] using - (pairingPolynomial_eval x y (fun a b => L (a,b))).trans (hn _) - -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.SquareDetection + +namespace OAI + +/-! Polynomial Detection. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl + +def jointContent {n d e : ℕ} (a : Fin n → Fin d) (b : Fin n → Fin e) : + (Fin d × Fin e) →₀ ℕ := ∑ i, Finsupp.single (a i, b i) 1 + +lemma jointContent_apply {n d e : ℕ} (a : Fin n → Fin d) (b : Fin n → Fin e) + (j : Fin d × Fin e) : jointContent a b j = + (Finset.univ.filter (fun i => (a i, b i) = j)).card := by + classical + simp [jointContent, Finsupp.single_apply, eq_comm] + +lemma perm_of_equal_jointContent {n d e : ℕ} + (a a' : Fin n → Fin d) (b b' : Fin n → Fin e) + (h : jointContent a b = jointContent a' b') : + ∃ g : Equiv.Perm (Fin n), a' ∘ g = a ∧ b' ∘ g = b := by + classical + have hc : ∀ j : Fin (d*e), + (Finset.univ.filter (fun i => finProdFinEquiv (a i,b i) = j)).card = + (Finset.univ.filter (fun i => finProdFinEquiv (a' i,b' i) = j)).card := by + intro j + have hh := DFunLike.congr_fun h (finProdFinEquiv.symm j) + simp only [jointContent_apply] at hh + simpa only [← Equiv.eq_symm_apply] using hh + obtain ⟨g, hg⟩ := perm_of_equal_content + (fun i => finProdFinEquiv (a i, b i)) + (fun i => finProdFinEquiv (a' i, b' i)) hc + refine ⟨g, ?_, ?_⟩ + · funext i + exact congrArg Prod.fst (finProdFinEquiv.injective (congrFun hg i)) + · funext i + exact congrArg Prod.snd (finProdFinEquiv.injective (congrFun hg i)) + +lemma intertwiner_jointContent {n d e : ℕ} + (F : Representation.IntertwiningMap (wordRep n d) (wordRep n e)) + (a a' : Fin n → Fin d) (b b' : Fin n → Fin e) + (h : jointContent a b = jointContent a' b') : + F (Pi.single a 1) b = F (Pi.single a' 1) b' := by + classical + obtain ⟨g, ha, hb⟩ := perm_of_equal_jointContent a a' b b' h + have hs : wordRep n d g (Pi.single a 1) = Pi.single a' 1 := by + ext w + change (Pi.single a 1 : WordSpace n d) (w ∘ g) = (Pi.single a' 1 : WordSpace n d) w + simp only [Pi.single_apply] + have he : (w ∘ g = a) ↔ w = a' := by + rw [← ha] + exact ⟨fun h => funext (fun i => by + have hh := congrFun h (g⁻¹ i) + simpa using hh), + fun h => by rw [h]⟩ + simp only [he] + have hh := congrFun (LinearMap.congr_fun (F.isIntertwining' g) (Pi.single a 1)) b' + simp only [LinearMap.comp_apply] at hh + rw [hs] at hh + change F (Pi.single a' 1) b' = F (Pi.single a 1) (b' ∘ g) at hh + rw [hb] at hh + exact hh.symm + +def pairingPolynomial {n d e : ℕ} (x : WordSpace n d) (y : WordSpace n e) : + MvPolynomial (Fin d × Fin e) ℂ := + ∑ a, ∑ b, MvPolynomial.monomial (jointContent a b) (x a * y b) + +lemma eval_jointContent_monomial {n d e : ℕ} + (a : Fin n → Fin d) (b : Fin n → Fin e) + (c : ℂ) (L : Fin d → Fin e → ℂ) : + MvPolynomial.eval (fun j => L j.1 j.2) + (MvPolynomial.monomial (jointContent a b) c) = + c * ∏ i, L (a i) (b i) := by + classical + rw [jointContent, MvPolynomial.monomial_sum_index] + simp only [map_mul, MvPolynomial.eval_C, map_prod] + congr 1 + apply Finset.prod_congr rfl + intro i hi + change MvPolynomial.eval _ (MvPolynomial.X (a i, b i)) = _ + exact MvPolynomial.eval_X _ + +lemma pairingPolynomial_eval {n d e : ℕ} + (x : WordSpace n d) (y : WordSpace n e) (L : Fin d → Fin e → ℂ) : + MvPolynomial.eval (fun j => L j.1 j.2) (pairingPolynomial x y) = + dotProduct (wordMap L x) y := by + classical + simp only [pairingPolynomial, map_sum, eval_jointContent_monomial] + change (∑ a, ∑ b, x a * y b * ∏ i, L (a i) (b i)) = + ∑ b, (∑ a, x a * ∏ i, L (a i) (b i)) * y b + simp_rw [Finset.sum_mul] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro b hb + apply Finset.sum_congr rfl + intro a ha + ring + +def jointContentWeight {n d e : ℕ} + (F : Representation.IntertwiningMap (wordRep n d) (wordRep n e)) + (m : (Fin d × Fin e) →₀ ℕ) : ℂ := + if h : ∃ a b, jointContent a b = m then + F (Pi.single h.choose 1) h.choose_spec.choose else 0 + +lemma jointContentWeight_apply {n d e : ℕ} + (F : Representation.IntertwiningMap (wordRep n d) (wordRep n e)) + (a : Fin n → Fin d) (b : Fin n → Fin e) : + jointContentWeight F (jointContent a b) = F (Pi.single a 1) b := by + classical + unfold jointContentWeight + have hab : ∃ a' b', jointContent a' b' = jointContent a b := ⟨a,b,rfl⟩ + rw [dite_eq_left hab] + exact intertwiner_jointContent F _ a _ b hab.choose_spec.choose_spec + +lemma pairingPolynomial_zero_pair {n d e : ℕ} + (F : Representation.IntertwiningMap (wordRep n d) (wordRep n e)) + (x : WordSpace n d) (y : WordSpace n e) (h : pairingPolynomial x y = 0) : + dotProduct (F x) y = 0 := by + classical + let w : MvPolynomial (Fin d × Fin e) ℂ →ₗ[ℂ] ℂ := + (Finsupp.linearCombination ℂ (jointContentWeight F)).comp + (AddMonoidAlgebra.coeffLinearEquiv ℂ).toLinearMap + have he := congrArg w h + have hw (m : (Fin d × Fin e) →₀ ℕ) (c : ℂ) : + w (MvPolynomial.monomial m c) = c * jointContentWeight F m := by + change Finsupp.linearCombination ℂ (jointContentWeight F) (Finsupp.single m c) = _ + simp + have he' : (∑ a, ∑ b, (x a * y b) * F (Pi.single a 1) b) = 0 := by + simpa only [pairingPolynomial, map_sum, map_zero, hw, jointContentWeight_apply] using he + have hx : x = ∑ a, x a • Pi.single a 1 := by + ext a + simp [Pi.single_apply] + rw [hx, map_sum] + simp only [map_smul, dotProduct, Finset.sum_apply, Pi.smul_apply, smul_eq_mul, + Finset.sum_mul] + rw [Finset.sum_comm] + convert he' using 1 + apply Finset.sum_congr rfl + intro a ha + apply Finset.sum_congr rfl + intro b hb + ring + +theorem wordMap_detects_intertwiner {n d e : ℕ} + (F : Representation.IntertwiningMap (wordRep n d) (wordRep n e)) + (x : WordSpace n d) (y : WordSpace n e) + (h : dotProduct (F x) y ≠ 0) : + ∃ L : Fin d → Fin e → ℂ, dotProduct (wordMap L x) y ≠ 0 := by + by_contra hn + push Not at hn + apply h + apply pairingPolynomial_zero_pair F + apply MvPolynomial.funext + intro L + simpa only [map_zero, pairingPolynomial_eval] using + (pairingPolynomial_eval x y (fun a b => L (a,b))).trans (hn _) + +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/RowCertificates.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/RowCertificates.lean index 99879e28059b35a55402faa5570aa5ad36c97a2e..85203f32e975f56e60f34a3644755f8d1db3e457 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/RowCertificates.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/RowCertificates.lean @@ -1,136 +1,136 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Band.TwoStrip -import OAI.RepresentationTheory.UniversalSquare.Support.SquareSemigroup -import OAI.RepresentationTheory.UniversalSquare.Support.ConstrainedRows - -namespace OAI - -/-! Row Certificates. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def rowDiagram (rs : List ℕ) : YoungDiagram := (columnShape rs).transpose - -def GoodRows (rs : List ℕ) : Prop := rs.SortedGE ∧ ∀ a ∈ rs, 0 < a -instance (rs : List ℕ) : Decidable (GoodRows rs) := by unfold GoodRows; infer_instance - -lemma rowDiagram_eq (rs : List ℕ) (h : GoodRows rs) : - rowDiagram rs = YoungDiagram.ofRowLens rs h.1 := by - rw [rowDiagram,columnShape_sorted rs h.1 h.2,YoungDiagram.transpose_transpose] - -lemma rowDiagram_rows {rs : List ℕ} (h : GoodRows rs) : (rowDiagram rs).rowLens = rs := by - rw [rowDiagram_eq rs h,YoungDiagram.rowLens_ofRowLens_eq_self h.2] - -lemma rowDiagram_card (rs : List ℕ) : (rowDiagram rs).card = rs.sum := by - rw [rowDiagram,transpose_card,columnShape_card] - -lemma rowDiagram_rowLen {rs : List ℕ} (h : GoodRows rs) (i : ℕ) : - (rowDiagram rs).rowLen i = rs[i]?.getD 0 := by - rw [rowDiagram_eq rs h,ofRowLens_rowLen] - -lemma rowDiagram_height {rs : List ℕ} (h : GoodRows rs) : - (rowDiagram rs).colLen 0 = rs.length := by - rw [← YoungDiagram.length_rowLens,rowDiagram_rows h] - -lemma rowDiagram_rowLens (μ : YoungDiagram) : rowDiagram μ.rowLens = μ := by - rw [rowDiagram_eq _ ⟨μ.rowLens_sorted,μ.pos_of_mem_rowLens⟩, - YoungDiagram.ofRowLens_to_rowLens_eq_self] - -def RowsStrip (rs ss : List ℕ) : Prop := - GoodRows rs ∧ GoodRows ss ∧ ∀ i ∈ List.range (max rs.length ss.length), - rs[i]?.getD 0 ≤ ss[i]?.getD 0 ∧ ss[i+1]?.getD 0 ≤ rs[i]?.getD 0 -instance (rs ss : List ℕ) : Decidable (RowsStrip rs ss) := by - unfold RowsStrip; infer_instance - -lemma rowsStrip_sound {rs ss : List ℕ} (h : RowsStrip rs ss) : - HorizontalStrip (rowDiagram rs) (rowDiagram ss) := by - have hb (i : ℕ) : (rowDiagram rs).rowLen i ≤ (rowDiagram ss).rowLen i ∧ - (rowDiagram ss).rowLen (i+1) ≤ (rowDiagram rs).rowLen i := by - rw [rowDiagram_rowLen h.1,rowDiagram_rowLen h.2.1,rowDiagram_rowLen h.2.1] - by_cases hi : i < max rs.length ss.length - · exact h.2.2 i (List.mem_range.mpr hi) - · have hr : rs.length ≤ i := le_trans (le_max_left _ _) (Nat.le_of_not_gt hi) - have hs : ss.length ≤ i := le_trans (le_max_right _ _) (Nat.le_of_not_gt hi) - simp [List.getElem?_eq_none hr,List.getElem?_eq_none hs, - List.getElem?_eq_none (by omega : ss.length ≤ i+1)] - exact horizontal_of_interlacing _ _ (fun i => (hb i).1) (fun i => (hb i).2) - -def RowsChain : List (List ℕ) → List ℕ → List ℕ → List ℕ → Prop - | [],bs,rs,ss => bs = [] ∧ rs = ss - | us::cs,bs,rs,ss => ∃ k ∈ List.range (ss.sum+1), - RowsStrip rs us ∧ rs.sum+k = us.sum ∧ ∃ ks ∈ [bs.drop 1], - bs = k::ks ∧ RowsChain cs ks us ss - -def stripSizes : List ℕ → List (List ℕ) → List ℕ - | _,[] => [] - | rs,ss::cs => (ss.sum-rs.sum)::stripSizes ss cs - -def ChainValid : List ℕ → List (List ℕ) → List ℕ → Prop - | rs,[],ss => rs=ss - | rs,us::cs,ss => RowsStrip rs us ∧ rs.sum ≤ us.sum ∧ ChainValid us cs ss -instance (rs : List ℕ) (cs : List (List ℕ)) (ss : List ℕ) : Decidable (ChainValid rs cs ss) := by - induction cs generalizing rs with - | nil => unfold ChainValid; infer_instance - | cons us cs ih => - letI := ih us - unfold ChainValid - infer_instance - -lemma SizedStripChain.trans {bs cs : List ℕ} {ν η μ : YoungDiagram} - (h : SizedStripChain bs ν η) (h' : SizedStripChain cs η μ) : - SizedStripChain (bs++cs) ν μ := by - induction h' with - | nil => simpa using h - | snoc hs ht hc ih => simpa [List.append_assoc] using Saxl.SizedStripChain.snoc (ih h) ht hc - -lemma chainValid_sound {rs ss : List ℕ} {cs : List (List ℕ)} (h : ChainValid rs cs ss) : - Saxl.SizedStripChain (stripSizes rs cs) (rowDiagram rs) (rowDiagram ss) := by - induction cs generalizing rs with - | nil => have he : rs = ss := h; subst rs; exact Saxl.SizedStripChain.nil _ - | cons us cs ih => - have ht : Saxl.SizedStripChain [us.sum-rs.sum] (rowDiagram rs) (rowDiagram us) := - Saxl.SizedStripChain.snoc (Saxl.SizedStripChain.nil _) (rowsStrip_sound h.1) - (by rw [rowDiagram_card,rowDiagram_card]; exact Nat.add_sub_of_le h.2.1) - exact SizedStripChain.trans ht (ih h.2.2) - -def RowsDom (rs ss : List ℕ) : Prop := - ∀ k ∈ List.range (ss.length+1), (ss.take k).sum ≤ (rs.take k).sum -instance (rs ss : List ℕ) : Decidable (RowsDom rs ss) := by unfold RowsDom; infer_instance - -lemma rowsDom_of_dominates {μ θ : YoungDiagram} (h : Dominates μ θ) : - RowsDom μ.rowLens θ.rowLens := by - intro k _ - simpa only [← rowPrefix_eq_take] using h k - -lemma dominates_of_rowsDom {μ θ : YoungDiagram} (hc : μ.card = θ.card) - (h : RowsDom μ.rowLens θ.rowLens) : Dominates μ θ := by - intro k - by_cases hk : k ≤ θ.colLen 0 - · rw [rowPrefix_eq_take,rowPrefix_eq_take] - exact h k (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) - · have hh := h (θ.colLen 0) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) - rw [← rowPrefix_eq_take,← rowPrefix_eq_take,rowPrefix_eq_card θ le_rfl,← hc] at hh - rw [rowPrefix_eq_card θ (by omega),← hc] - exact hh.trans (rowPrefix_mono μ (by omega)) - -lemma height_le_of_dominates {μ θ : YoungDiagram} (hc : μ.card = θ.card) - (h : Dominates μ θ) : μ.colLen 0 ≤ θ.colLen 0 := by - by_contra hn - have hp : 0 < μ.rowLen (θ.colLen 0) := - YoungDiagram.mem_iff_lt_rowLen.mp (YoungDiagram.mem_iff_lt_colLen.mpr (by omega)) - have hh := h (θ.colLen 0) - rw [rowPrefix_eq_card θ le_rfl] at hh - have hk := rowPrefix_le_card μ (θ.colLen 0+1) - rw [rowPrefix_succ] at hk - omega - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Band.TwoStrip +import OAI.RepresentationTheory.UniversalSquare.Support.SquareSemigroup +import OAI.RepresentationTheory.UniversalSquare.Support.ConstrainedRows + +namespace OAI + +/-! Row Certificates. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def rowDiagram (rs : List ℕ) : YoungDiagram := (columnShape rs).transpose + +def GoodRows (rs : List ℕ) : Prop := rs.SortedGE ∧ ∀ a ∈ rs, 0 < a +instance (rs : List ℕ) : Decidable (GoodRows rs) := by unfold GoodRows; infer_instance + +lemma rowDiagram_eq (rs : List ℕ) (h : GoodRows rs) : + rowDiagram rs = YoungDiagram.ofRowLens rs h.1 := by + rw [rowDiagram,columnShape_sorted rs h.1 h.2,YoungDiagram.transpose_transpose] + +lemma rowDiagram_rows {rs : List ℕ} (h : GoodRows rs) : (rowDiagram rs).rowLens = rs := by + rw [rowDiagram_eq rs h,YoungDiagram.rowLens_ofRowLens_eq_self h.2] + +lemma rowDiagram_card (rs : List ℕ) : (rowDiagram rs).card = rs.sum := by + rw [rowDiagram,transpose_card,columnShape_card] + +lemma rowDiagram_rowLen {rs : List ℕ} (h : GoodRows rs) (i : ℕ) : + (rowDiagram rs).rowLen i = rs[i]?.getD 0 := by + rw [rowDiagram_eq rs h,ofRowLens_rowLen] + +lemma rowDiagram_height {rs : List ℕ} (h : GoodRows rs) : + (rowDiagram rs).colLen 0 = rs.length := by + rw [← YoungDiagram.length_rowLens,rowDiagram_rows h] + +lemma rowDiagram_rowLens (μ : YoungDiagram) : rowDiagram μ.rowLens = μ := by + rw [rowDiagram_eq _ ⟨μ.rowLens_sorted,μ.pos_of_mem_rowLens⟩, + YoungDiagram.ofRowLens_to_rowLens_eq_self] + +def RowsStrip (rs ss : List ℕ) : Prop := + GoodRows rs ∧ GoodRows ss ∧ ∀ i ∈ List.range (max rs.length ss.length), + rs[i]?.getD 0 ≤ ss[i]?.getD 0 ∧ ss[i+1]?.getD 0 ≤ rs[i]?.getD 0 +instance (rs ss : List ℕ) : Decidable (RowsStrip rs ss) := by + unfold RowsStrip; infer_instance + +lemma rowsStrip_sound {rs ss : List ℕ} (h : RowsStrip rs ss) : + HorizontalStrip (rowDiagram rs) (rowDiagram ss) := by + have hb (i : ℕ) : (rowDiagram rs).rowLen i ≤ (rowDiagram ss).rowLen i ∧ + (rowDiagram ss).rowLen (i+1) ≤ (rowDiagram rs).rowLen i := by + rw [rowDiagram_rowLen h.1,rowDiagram_rowLen h.2.1,rowDiagram_rowLen h.2.1] + by_cases hi : i < max rs.length ss.length + · exact h.2.2 i (List.mem_range.mpr hi) + · have hr : rs.length ≤ i := le_trans (le_max_left _ _) (Nat.le_of_not_gt hi) + have hs : ss.length ≤ i := le_trans (le_max_right _ _) (Nat.le_of_not_gt hi) + simp [List.getElem?_eq_none hr,List.getElem?_eq_none hs, + List.getElem?_eq_none (by omega : ss.length ≤ i+1)] + exact horizontal_of_interlacing _ _ (fun i => (hb i).1) (fun i => (hb i).2) + +def RowsChain : List (List ℕ) → List ℕ → List ℕ → List ℕ → Prop + | [],bs,rs,ss => bs = [] ∧ rs = ss + | us::cs,bs,rs,ss => ∃ k ∈ List.range (ss.sum+1), + RowsStrip rs us ∧ rs.sum+k = us.sum ∧ ∃ ks ∈ [bs.drop 1], + bs = k::ks ∧ RowsChain cs ks us ss + +def stripSizes : List ℕ → List (List ℕ) → List ℕ + | _,[] => [] + | rs,ss::cs => (ss.sum-rs.sum)::stripSizes ss cs + +def ChainValid : List ℕ → List (List ℕ) → List ℕ → Prop + | rs,[],ss => rs=ss + | rs,us::cs,ss => RowsStrip rs us ∧ rs.sum ≤ us.sum ∧ ChainValid us cs ss +instance (rs : List ℕ) (cs : List (List ℕ)) (ss : List ℕ) : Decidable (ChainValid rs cs ss) := by + induction cs generalizing rs with + | nil => unfold ChainValid; infer_instance + | cons us cs ih => + letI := ih us + unfold ChainValid + infer_instance + +lemma SizedStripChain.trans {bs cs : List ℕ} {ν η μ : YoungDiagram} + (h : SizedStripChain bs ν η) (h' : SizedStripChain cs η μ) : + SizedStripChain (bs++cs) ν μ := by + induction h' with + | nil => simpa using h + | snoc hs ht hc ih => simpa [List.append_assoc] using Saxl.SizedStripChain.snoc (ih h) ht hc + +lemma chainValid_sound {rs ss : List ℕ} {cs : List (List ℕ)} (h : ChainValid rs cs ss) : + Saxl.SizedStripChain (stripSizes rs cs) (rowDiagram rs) (rowDiagram ss) := by + induction cs generalizing rs with + | nil => have he : rs = ss := h; subst rs; exact Saxl.SizedStripChain.nil _ + | cons us cs ih => + have ht : Saxl.SizedStripChain [us.sum-rs.sum] (rowDiagram rs) (rowDiagram us) := + Saxl.SizedStripChain.snoc (Saxl.SizedStripChain.nil _) (rowsStrip_sound h.1) + (by rw [rowDiagram_card,rowDiagram_card]; exact Nat.add_sub_of_le h.2.1) + exact SizedStripChain.trans ht (ih h.2.2) + +def RowsDom (rs ss : List ℕ) : Prop := + ∀ k ∈ List.range (ss.length+1), (ss.take k).sum ≤ (rs.take k).sum +instance (rs ss : List ℕ) : Decidable (RowsDom rs ss) := by unfold RowsDom; infer_instance + +lemma rowsDom_of_dominates {μ θ : YoungDiagram} (h : Dominates μ θ) : + RowsDom μ.rowLens θ.rowLens := by + intro k _ + simpa only [← rowPrefix_eq_take] using h k + +lemma dominates_of_rowsDom {μ θ : YoungDiagram} (hc : μ.card = θ.card) + (h : RowsDom μ.rowLens θ.rowLens) : Dominates μ θ := by + intro k + by_cases hk : k ≤ θ.colLen 0 + · rw [rowPrefix_eq_take,rowPrefix_eq_take] + exact h k (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) + · have hh := h (θ.colLen 0) (by simp only [List.mem_range,YoungDiagram.length_rowLens]; omega) + rw [← rowPrefix_eq_take,← rowPrefix_eq_take,rowPrefix_eq_card θ le_rfl,← hc] at hh + rw [rowPrefix_eq_card θ (by omega),← hc] + exact hh.trans (rowPrefix_mono μ (by omega)) + +lemma height_le_of_dominates {μ θ : YoungDiagram} (hc : μ.card = θ.card) + (h : Dominates μ θ) : μ.colLen 0 ≤ θ.colLen 0 := by + by_contra hn + have hp : 0 < μ.rowLen (θ.colLen 0) := + YoungDiagram.mem_iff_lt_rowLen.mp (YoungDiagram.mem_iff_lt_colLen.mpr (by omega)) + have hh := h (θ.colLen 0) + rw [rowPrefix_eq_card θ le_rfl] at hh + have hk := rowPrefix_le_card μ (θ.colLen 0+1) + rw [rowPrefix_succ] at hk + omega + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/SingletonForms.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/SingletonForms.lean index c213054358a631efb29b0f70508f5264af0dfe35..5047d91e9f1c4fa258610d3749db09ff2f50ca00 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/SingletonForms.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/SingletonForms.lean @@ -1,159 +1,159 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.PairForms -import OAI.RepresentationTheory.UniversalSquare.Support.SingletonPairs - -namespace OAI - -/-! Singleton Forms. -/ - -section - -noncomputable section -namespace Saxl - -def singleWord {d : ℕ} (v : Fin d → ℂ) : WordSpace 1 d := fun w => v (w 0) - -lemma wordMap_singleWord {a b : ℕ} (L : Fin a → Fin b → ℂ) (v : Fin a → ℂ) : - wordMap L (singleWord v) = singleWord (fun j => ∑ i, v i * L i j) := by - classical - funext w - change (∑ c : Fin 1 → Fin a, v (c 0) * ∏ i, L (c i) (w i)) = _ - simpa only [Fintype.prod_unique, show (default : Fin 1) = 0 from rfl, singleWord] using - (Fintype.sum_equiv (Equiv.funUnique (Fin 1) (Fin a)) - (fun c => v (c 0) * L (c 0) (w 0)) - (fun i => v i * L i (w 0)) (fun _ => rfl)) - -def pairSingletonTensor {n a m d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin 1) - (p : Fin a ≃ Fin m ⊕ Fin m) (B : Matrix (Fin d) (Fin d) ℂ) (v : Fin d → ℂ) : - WordSpace n d := positionProduct e (pairFormTensor p B) (singleWord v) - -lemma wordMap_pairSingletonTensor {n a m d D : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) - (L : Fin d → Fin D → ℂ) (B : Matrix (Fin d) (Fin d) ℂ) (v : Fin d → ℂ) : - wordMap L (pairSingletonTensor e p B v) = pairSingletonTensor e p - (fun j k => ∑ q : Fin d × Fin d, B q.1 q.2 * L q.1 j * L q.2 k) - (fun j => ∑ i, v i * L i j) := by - rw [pairSingletonTensor, wordMap_positionProduct, wordMap_pairFormTensor, - wordMap_singleWord] - rfl - -def pairSingletonEquiv {n a m : ℕ} (e : Fin n ≃ Fin a ⊕ Fin 1) - (p : Fin a ≃ Fin m ⊕ Fin m) : Fin n ≃ Fin (m+1) ⊕ Fin m := - e.trans ((Equiv.sumCongr p (Equiv.refl _)).trans - ((Equiv.sumAssoc _ _ _).trans ((Equiv.sumCongr (Equiv.refl _) - (Equiv.sumComm _ _)).trans ((Equiv.sumAssoc _ _ _).symm.trans - (Equiv.sumCongr finSumFinEquiv (Equiv.refl _)))))) - -@[simp] lemma pairSingletonEquiv_left {n a m : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) (k : Fin m) : - (pairSingletonEquiv e p).symm (Sum.inl k.castSucc) = - e.symm (Sum.inl (p.symm (Sum.inl k))) := by - change (pairSingletonEquiv e p).symm (Sum.inl (Fin.castAdd 1 k)) = _ - simp [pairSingletonEquiv] - -@[simp] lemma pairSingletonEquiv_right {n a m : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) (k : Fin m) : - (pairSingletonEquiv e p).symm (Sum.inr k) = - e.symm (Sum.inl (p.symm (Sum.inr k))) := by - simp [pairSingletonEquiv] - -@[simp] lemma pairSingletonEquiv_last {n a m : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) : - (pairSingletonEquiv e p).symm (Sum.inl (Fin.last m)) = e.symm (Sum.inr 0) := by - have hh : Fin.last m = Fin.natAdd m (0 : Fin 1) := Fin.ext (by simp) - rw [hh] - simp [pairSingletonEquiv] - -lemma pairSingletonTensor_one {n a m d : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) (v : Fin d → ℂ) : - pairSingletonTensor e p (1 : Matrix (Fin d) (Fin d) ℂ) v = - symmetricPartialPairs (pairSingletonEquiv e p) Fin.castSuccEmb v := by - classical - funext w - have ht : leftWord (pairSingletonEquiv e p) w ∘ Fin.castSuccEmb = - leftWord p (leftWord e w) := by - funext k - simp [leftWord] - have hb : rightWord (pairSingletonEquiv e p) w = rightWord p (leftWord e w) := by - funext k - simp [rightWord,leftWord] - have hlast : Fin.last m ∉ Set.range (Fin.castSuccEmb : Fin m ↪ Fin (m+1)) := by - rintro ⟨k,hk⟩ - have hh := congrArg Fin.val hk - have hh' := k.isLt - change k.val = m at hh - omega - have hcast (k : Fin m) : k.castSucc ∈ Set.range (Fin.castSuccEmb : Fin m ↪ Fin (m+1)) := - ⟨k,rfl⟩ - have hprod : (∏ k ∈ Finset.univ.filter - (fun k => k ∉ Set.range (Fin.castSuccEmb : Fin m ↪ Fin (m+1))), - v (leftWord (pairSingletonEquiv e p) w k)) = v (rightWord e w 0) := by - rw [Finset.prod_filter, Fin.prod_univ_castSucc] - simp [leftWord,rightWord] - unfold symmetricPartialPairs - rw [ht,hb,hprod] - unfold pairSingletonTensor - rw [pairFormTensor_one] - change (if leftWord p (leftWord e w) = rightWord p (leftWord e w) then 1 else 0) * - v (rightWord e w 0) = _ - split_ifs <;> simp - -lemma pairSingletonTensor_smul {n a m d : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) - (B : Matrix (Fin d) (Fin d) ℂ) (v : Fin d → ℂ) (c : ℂ) : - pairSingletonTensor e p (c • B) v = c^m • pairSingletonTensor e p B v := by - unfold pairSingletonTensor - rw [pairFormTensor_smul] - funext w - change c^m * pairFormTensor p B (leftWord e w) * singleWord v (rightWord e w) = _ - exact mul_assoc _ _ _ - -theorem one_odd_row_pairSingleton_support {n a m d D : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) - (B : Matrix (Fin d) (Fin d) ℂ) (v : Fin d → ℂ) - (L : Fin d → Fin D → ℂ) (c : ℂ) (hc : c ≠ 0) - (hL : (fun j k => ∑ q : Fin d × Fin d, B q.1 q.2 * L q.1 j * L q.2 k) = - c • (1 : Matrix (Fin D) (Fin D) ℂ)) - (hv : (fun j => ∑ i, v i * L i j) ≠ 0) - (μ : YoungDiagram) (t : Tableau n μ) - (k : ℕ) (hk : Odd (μ.rowLen k)) (he : ∀ l, l ≠ k → Even (μ.rowLen l)) - (hd : μ.colLen 0 ≤ D) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n d) (pairSingletonTensor e p B v)).toRepresentation, F ≠ 0 := by - let v' := fun j => ∑ i, v i * L i j - have hmap : wordMap L (pairSingletonTensor e p B v) = - c^m • symmetricPartialPairs (pairSingletonEquiv e p) Fin.castSuccEmb v' := by - rw [wordMap_pairSingletonTensor, hL, pairSingletonTensor_smul, pairSingletonTensor_one] - have hcyc : cyclic (wordRep n D) (wordMap L (pairSingletonTensor e p B v)) = - cyclic (wordRep n D) (symmetricPartialPairs (pairSingletonEquiv e p) Fin.castSuccEmb v') := by - rw [hmap, cyclic_smul_eq _ _ _ (pow_ne_zero m hc)] - have hs := one_odd_row_symmetricPartialPairs_support (pairSingletonEquiv e p) Fin.castSuccEmb - v' hv μ t k hk he hd - rw [← hcyc] at hs - obtain ⟨F,hF⟩ := hs - exact cyclic_projection_support (wordMap L) (pairSingletonTensor e p B v) F hF - -lemma shortPair_singleton_nonzero : - (fun j => ∑ i : Fin 4, (Pi.single 0 (1 : ℂ) : Fin 4 → ℂ) i * shortPairCongruence i j) ≠ 0 := by - intro h - have hh := congrFun h (0 : Fin 4) - norm_num [shortPairCongruence, Pi.single_apply, Fin.sum_univ_succ] at hh - -theorem one_odd_row_shortPair_support {n a m : ℕ} - (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) - (μ : YoungDiagram) (t : Tableau n μ) - (k : ℕ) (hk : Odd (μ.rowLen k)) (he : ∀ l, l ≠ k → Even (μ.rowLen l)) - (hd : μ.colLen 0 ≤ 4) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n 4) (pairSingletonTensor e p shortPairForm (Pi.single 0 1))).toRepresentation, - F ≠ 0 := - one_odd_row_pairSingleton_support e p shortPairForm (Pi.single 0 1) - shortPairCongruence 2 (by norm_num) shortPairCongruence_gram - shortPair_singleton_nonzero μ t k hk he hd - -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.PairForms +import OAI.RepresentationTheory.UniversalSquare.Support.SingletonPairs + +namespace OAI + +/-! Singleton Forms. -/ + +section + +noncomputable section +namespace Saxl + +def singleWord {d : ℕ} (v : Fin d → ℂ) : WordSpace 1 d := fun w => v (w 0) + +lemma wordMap_singleWord {a b : ℕ} (L : Fin a → Fin b → ℂ) (v : Fin a → ℂ) : + wordMap L (singleWord v) = singleWord (fun j => ∑ i, v i * L i j) := by + classical + funext w + change (∑ c : Fin 1 → Fin a, v (c 0) * ∏ i, L (c i) (w i)) = _ + simpa only [Fintype.prod_unique, show (default : Fin 1) = 0 from rfl, singleWord] using + (Fintype.sum_equiv (Equiv.funUnique (Fin 1) (Fin a)) + (fun c => v (c 0) * L (c 0) (w 0)) + (fun i => v i * L i (w 0)) (fun _ => rfl)) + +def pairSingletonTensor {n a m d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin 1) + (p : Fin a ≃ Fin m ⊕ Fin m) (B : Matrix (Fin d) (Fin d) ℂ) (v : Fin d → ℂ) : + WordSpace n d := positionProduct e (pairFormTensor p B) (singleWord v) + +lemma wordMap_pairSingletonTensor {n a m d D : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) + (L : Fin d → Fin D → ℂ) (B : Matrix (Fin d) (Fin d) ℂ) (v : Fin d → ℂ) : + wordMap L (pairSingletonTensor e p B v) = pairSingletonTensor e p + (fun j k => ∑ q : Fin d × Fin d, B q.1 q.2 * L q.1 j * L q.2 k) + (fun j => ∑ i, v i * L i j) := by + rw [pairSingletonTensor, wordMap_positionProduct, wordMap_pairFormTensor, + wordMap_singleWord] + rfl + +def pairSingletonEquiv {n a m : ℕ} (e : Fin n ≃ Fin a ⊕ Fin 1) + (p : Fin a ≃ Fin m ⊕ Fin m) : Fin n ≃ Fin (m+1) ⊕ Fin m := + e.trans ((Equiv.sumCongr p (Equiv.refl _)).trans + ((Equiv.sumAssoc _ _ _).trans ((Equiv.sumCongr (Equiv.refl _) + (Equiv.sumComm _ _)).trans ((Equiv.sumAssoc _ _ _).symm.trans + (Equiv.sumCongr finSumFinEquiv (Equiv.refl _)))))) + +@[simp] lemma pairSingletonEquiv_left {n a m : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) (k : Fin m) : + (pairSingletonEquiv e p).symm (Sum.inl k.castSucc) = + e.symm (Sum.inl (p.symm (Sum.inl k))) := by + change (pairSingletonEquiv e p).symm (Sum.inl (Fin.castAdd 1 k)) = _ + simp [pairSingletonEquiv] + +@[simp] lemma pairSingletonEquiv_right {n a m : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) (k : Fin m) : + (pairSingletonEquiv e p).symm (Sum.inr k) = + e.symm (Sum.inl (p.symm (Sum.inr k))) := by + simp [pairSingletonEquiv] + +@[simp] lemma pairSingletonEquiv_last {n a m : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) : + (pairSingletonEquiv e p).symm (Sum.inl (Fin.last m)) = e.symm (Sum.inr 0) := by + have hh : Fin.last m = Fin.natAdd m (0 : Fin 1) := Fin.ext (by simp) + rw [hh] + simp [pairSingletonEquiv] + +lemma pairSingletonTensor_one {n a m d : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) (v : Fin d → ℂ) : + pairSingletonTensor e p (1 : Matrix (Fin d) (Fin d) ℂ) v = + symmetricPartialPairs (pairSingletonEquiv e p) Fin.castSuccEmb v := by + classical + funext w + have ht : leftWord (pairSingletonEquiv e p) w ∘ Fin.castSuccEmb = + leftWord p (leftWord e w) := by + funext k + simp [leftWord] + have hb : rightWord (pairSingletonEquiv e p) w = rightWord p (leftWord e w) := by + funext k + simp [rightWord,leftWord] + have hlast : Fin.last m ∉ Set.range (Fin.castSuccEmb : Fin m ↪ Fin (m+1)) := by + rintro ⟨k,hk⟩ + have hh := congrArg Fin.val hk + have hh' := k.isLt + change k.val = m at hh + omega + have hcast (k : Fin m) : k.castSucc ∈ Set.range (Fin.castSuccEmb : Fin m ↪ Fin (m+1)) := + ⟨k,rfl⟩ + have hprod : (∏ k ∈ Finset.univ.filter + (fun k => k ∉ Set.range (Fin.castSuccEmb : Fin m ↪ Fin (m+1))), + v (leftWord (pairSingletonEquiv e p) w k)) = v (rightWord e w 0) := by + rw [Finset.prod_filter, Fin.prod_univ_castSucc] + simp [leftWord,rightWord] + unfold symmetricPartialPairs + rw [ht,hb,hprod] + unfold pairSingletonTensor + rw [pairFormTensor_one] + change (if leftWord p (leftWord e w) = rightWord p (leftWord e w) then 1 else 0) * + v (rightWord e w 0) = _ + split_ifs <;> simp + +lemma pairSingletonTensor_smul {n a m d : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) + (B : Matrix (Fin d) (Fin d) ℂ) (v : Fin d → ℂ) (c : ℂ) : + pairSingletonTensor e p (c • B) v = c^m • pairSingletonTensor e p B v := by + unfold pairSingletonTensor + rw [pairFormTensor_smul] + funext w + change c^m * pairFormTensor p B (leftWord e w) * singleWord v (rightWord e w) = _ + exact mul_assoc _ _ _ + +theorem one_odd_row_pairSingleton_support {n a m d D : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) + (B : Matrix (Fin d) (Fin d) ℂ) (v : Fin d → ℂ) + (L : Fin d → Fin D → ℂ) (c : ℂ) (hc : c ≠ 0) + (hL : (fun j k => ∑ q : Fin d × Fin d, B q.1 q.2 * L q.1 j * L q.2 k) = + c • (1 : Matrix (Fin D) (Fin D) ℂ)) + (hv : (fun j => ∑ i, v i * L i j) ≠ 0) + (μ : YoungDiagram) (t : Tableau n μ) + (k : ℕ) (hk : Odd (μ.rowLen k)) (he : ∀ l, l ≠ k → Even (μ.rowLen l)) + (hd : μ.colLen 0 ≤ D) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n d) (pairSingletonTensor e p B v)).toRepresentation, F ≠ 0 := by + let v' := fun j => ∑ i, v i * L i j + have hmap : wordMap L (pairSingletonTensor e p B v) = + c^m • symmetricPartialPairs (pairSingletonEquiv e p) Fin.castSuccEmb v' := by + rw [wordMap_pairSingletonTensor, hL, pairSingletonTensor_smul, pairSingletonTensor_one] + have hcyc : cyclic (wordRep n D) (wordMap L (pairSingletonTensor e p B v)) = + cyclic (wordRep n D) (symmetricPartialPairs (pairSingletonEquiv e p) Fin.castSuccEmb v') := by + rw [hmap, cyclic_smul_eq _ _ _ (pow_ne_zero m hc)] + have hs := one_odd_row_symmetricPartialPairs_support (pairSingletonEquiv e p) Fin.castSuccEmb + v' hv μ t k hk he hd + rw [← hcyc] at hs + obtain ⟨F,hF⟩ := hs + exact cyclic_projection_support (wordMap L) (pairSingletonTensor e p B v) F hF + +lemma shortPair_singleton_nonzero : + (fun j => ∑ i : Fin 4, (Pi.single 0 (1 : ℂ) : Fin 4 → ℂ) i * shortPairCongruence i j) ≠ 0 := by + intro h + have hh := congrFun h (0 : Fin 4) + norm_num [shortPairCongruence, Pi.single_apply, Fin.sum_univ_succ] at hh + +theorem one_odd_row_shortPair_support {n a m : ℕ} + (e : Fin n ≃ Fin a ⊕ Fin 1) (p : Fin a ≃ Fin m ⊕ Fin m) + (μ : YoungDiagram) (t : Tableau n μ) + (k : ℕ) (hk : Odd (μ.rowLen k)) (he : ∀ l, l ≠ k → Even (μ.rowLen l)) + (hd : μ.colLen 0 ≤ 4) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n 4) (pairSingletonTensor e p shortPairForm (Pi.single 0 1))).toRepresentation, + F ≠ 0 := + one_odd_row_pairSingleton_support e p shortPairForm (Pi.single 0 1) + shortPairCongruence 2 (by norm_num) shortPairCongruence_gram + shortPair_singleton_nonzero μ t k hk he hd + +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/SquareDetection.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/SquareDetection.lean index 0d11b3489fe2a74a980f45124b83aaffb46e98e2..f3b58030a8e97f68717f35b0dcb82a9bd726a81a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/SquareDetection.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/SquareDetection.lean @@ -1,89 +1,89 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main - -namespace OAI - -/-! Square Detection. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl - -def spechtTensorMap {n : ℕ} {α β : YoungDiagram} - (a : Tableau n α) (b : Tableau n β) : - Representation.IntertwiningMap ((spechtRep a).tprod (spechtRep b)) - (wordRep n (α.colLen 0 * β.colLen 0)) := - (wordTensorIntertwiner _ _ _).comp ((spechtInclusion a).tensor (spechtInclusion b)) - -lemma spechtTensorMap_injective {n : ℕ} {α β : YoungDiagram} - (a : Tableau n α) (b : Tableau n β) : Function.Injective (spechtTensorMap a b) := by - apply (wordTensor _ _ _).injective.comp - exact TensorProduct.map_injective_of_flat_flat _ _ - (spechtSub a).toSubmodule.subtype_injective (spechtSub b).toSubmodule.subtype_injective - -lemma polytabloidTensor_real {n : ℕ} {α β : YoungDiagram} - (a : Tableau n α) (b : Tableau n β) : - star (wordTensor _ _ _ (polytabloid a ⊗ₜ[ℂ] polytabloid b)) = - wordTensor _ _ _ (polytabloid a ⊗ₜ[ℂ] polytabloid b) := by - funext w - simp only [Pi.star_apply, wordTensor_tmul, star_mul] - have h₁ := congrFun (polytabloid_real a) (splitLeft w) - have h₂ := congrFun (polytabloid_real b) (splitRight w) - change star (polytabloid b (splitRight w)) * star (polytabloid a (splitLeft w)) = _ - rw [show star (polytabloid a (splitLeft w)) = _ from h₁, - show star (polytabloid b (splitRight w)) = _ from h₂] - exact mul_comm _ _ - -lemma polytabloidTensor_cyclic_le_range {n : ℕ} {α β : YoungDiagram} - (a a' : Tableau n α) (b b' : Tableau n β) : - cyclic (wordRep n (α.colLen 0 * β.colLen 0)) - (wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b')) ≤ - (spechtTensorMap a b).range := by - apply (cyclic_le _ _ _).mpr - exact ⟨(⟨polytabloid a', polytabloid_mem_all a a'⟩ : Specht a) ⊗ₜ[ℂ] - (⟨polytabloid b', polytabloid_mem_all b b'⟩ : Specht b), rfl⟩ - -attribute [irreducible] spechtTensorMap - -theorem kronecker_pos_of_contraction {n : ℕ} {α β μ : YoungDiagram} - (a a' : Tableau n α) (b b' : Tableau n β) (t s : Tableau n μ) - (L : Fin (μ.colLen 0) → Fin (α.colLen 0 * β.colLen 0) → ℂ) - (h : dotProduct (wordMap L (polytabloid s)) - (wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b')) ≠ 0) : - 0 < kronecker a b t := by - let z := wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b') - let S := cyclic (wordRep n (α.colLen 0 * β.colLen 0)) z - obtain ⟨f, hf⟩ := hom_to_cyclic_of_pair L (spechtSub t) - ⟨polytabloid s, polytabloid_mem_all t s⟩ z (polytabloidTensor_real a' b') h - let F := @intertwiningLiftSubrep (Equiv.Perm (Fin n)) - (Specht a ⊗[ℂ] Specht b) (WordSpace n (α.colLen 0 * β.colLen 0)) - _ _ _ _ _ ((spechtRep a).tprod (spechtRep b)) - (wordRep n (α.colLen 0 * β.colLen 0)) - (spechtTensorMap a b) (spechtTensorMap_injective a b) - S (polytabloidTensor_cyclic_le_range a a' b b') - have hF : Function.Injective F := @intertwiningLiftSubrep_injective (Equiv.Perm (Fin n)) - (Specht a ⊗[ℂ] Specht b) (WordSpace n (α.colLen 0 * β.colLen 0)) - _ _ _ _ _ ((spechtRep a).tprod (spechtRep b)) - (wordRep n (α.colLen 0 * β.colLen 0)) - (spechtTensorMap a b) (spechtTensorMap_injective a b) - S (polytabloidTensor_cyclic_le_range a a' b b') - apply (kronecker_pos_iff a b t).mpr - refine ⟨F.comp f, ?_⟩ - intro hz - apply hf - apply Representation.IntertwiningMap.ext - apply LinearMap.ext - intro x - apply hF - have hzero := congrArg (fun H => H x) hz - change F (f x) = 0 at hzero - change F (f x) = F 0 - simpa only [map_zero] using hzero - -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main + +namespace OAI + +/-! Square Detection. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl + +def spechtTensorMap {n : ℕ} {α β : YoungDiagram} + (a : Tableau n α) (b : Tableau n β) : + Representation.IntertwiningMap ((spechtRep a).tprod (spechtRep b)) + (wordRep n (α.colLen 0 * β.colLen 0)) := + (wordTensorIntertwiner _ _ _).comp ((spechtInclusion a).tensor (spechtInclusion b)) + +lemma spechtTensorMap_injective {n : ℕ} {α β : YoungDiagram} + (a : Tableau n α) (b : Tableau n β) : Function.Injective (spechtTensorMap a b) := by + apply (wordTensor _ _ _).injective.comp + exact TensorProduct.map_injective_of_flat_flat _ _ + (spechtSub a).toSubmodule.subtype_injective (spechtSub b).toSubmodule.subtype_injective + +lemma polytabloidTensor_real {n : ℕ} {α β : YoungDiagram} + (a : Tableau n α) (b : Tableau n β) : + star (wordTensor _ _ _ (polytabloid a ⊗ₜ[ℂ] polytabloid b)) = + wordTensor _ _ _ (polytabloid a ⊗ₜ[ℂ] polytabloid b) := by + funext w + simp only [Pi.star_apply, wordTensor_tmul, star_mul] + have h₁ := congrFun (polytabloid_real a) (splitLeft w) + have h₂ := congrFun (polytabloid_real b) (splitRight w) + change star (polytabloid b (splitRight w)) * star (polytabloid a (splitLeft w)) = _ + rw [show star (polytabloid a (splitLeft w)) = _ from h₁, + show star (polytabloid b (splitRight w)) = _ from h₂] + exact mul_comm _ _ + +lemma polytabloidTensor_cyclic_le_range {n : ℕ} {α β : YoungDiagram} + (a a' : Tableau n α) (b b' : Tableau n β) : + cyclic (wordRep n (α.colLen 0 * β.colLen 0)) + (wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b')) ≤ + (spechtTensorMap a b).range := by + apply (cyclic_le _ _ _).mpr + exact ⟨(⟨polytabloid a', polytabloid_mem_all a a'⟩ : Specht a) ⊗ₜ[ℂ] + (⟨polytabloid b', polytabloid_mem_all b b'⟩ : Specht b), rfl⟩ + +attribute [irreducible] spechtTensorMap + +theorem kronecker_pos_of_contraction {n : ℕ} {α β μ : YoungDiagram} + (a a' : Tableau n α) (b b' : Tableau n β) (t s : Tableau n μ) + (L : Fin (μ.colLen 0) → Fin (α.colLen 0 * β.colLen 0) → ℂ) + (h : dotProduct (wordMap L (polytabloid s)) + (wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b')) ≠ 0) : + 0 < kronecker a b t := by + let z := wordTensor _ _ _ (polytabloid a' ⊗ₜ[ℂ] polytabloid b') + let S := cyclic (wordRep n (α.colLen 0 * β.colLen 0)) z + obtain ⟨f, hf⟩ := hom_to_cyclic_of_pair L (spechtSub t) + ⟨polytabloid s, polytabloid_mem_all t s⟩ z (polytabloidTensor_real a' b') h + let F := @intertwiningLiftSubrep (Equiv.Perm (Fin n)) + (Specht a ⊗[ℂ] Specht b) (WordSpace n (α.colLen 0 * β.colLen 0)) + _ _ _ _ _ ((spechtRep a).tprod (spechtRep b)) + (wordRep n (α.colLen 0 * β.colLen 0)) + (spechtTensorMap a b) (spechtTensorMap_injective a b) + S (polytabloidTensor_cyclic_le_range a a' b b') + have hF : Function.Injective F := @intertwiningLiftSubrep_injective (Equiv.Perm (Fin n)) + (Specht a ⊗[ℂ] Specht b) (WordSpace n (α.colLen 0 * β.colLen 0)) + _ _ _ _ _ ((spechtRep a).tprod (spechtRep b)) + (wordRep n (α.colLen 0 * β.colLen 0)) + (spechtTensorMap a b) (spechtTensorMap_injective a b) + S (polytabloidTensor_cyclic_le_range a a' b b') + apply (kronecker_pos_iff a b t).mpr + refine ⟨F.comp f, ?_⟩ + intro hz + apply hf + apply Representation.IntertwiningMap.ext + apply LinearMap.ext + intro x + apply hF + have hzero := congrArg (fun H => H x) hz + change F (f x) = 0 at hzero + change F (f x) = F 0 + simpa only [map_zero] using hzero + +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/SymmetricPairs.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/SymmetricPairs.lean index a0fbd9bcc97f1c259a0dae20cdf1de8704971683..2670cbb002de5a8154e29058397f935242fe9cf2 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/SymmetricPairs.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/SymmetricPairs.lean @@ -1,323 +1,323 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.SquareDetection - -namespace OAI - -/-! Symmetric Pairs. -/ - -section - -noncomputable section -open scoped TensorProduct -namespace Saxl - -def symmetricPairs {n m : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) (d : ℕ) : WordSpace n d := - fun w => if leftWord e w = rightWord e w then 1 else 0 - -lemma symmetricPairs_real {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) : - star (symmetricPairs e d) = symmetricPairs e d := by - ext w - simp only [Pi.star_apply, symmetricPairs] - split_ifs <;> simp - -def positionWordsEquiv {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : - (Fin n → Fin d) ≃ (Fin a → Fin d) × (Fin b → Fin d) where - toFun w := (leftWord e w, rightWord e w) - invFun p := joinPositions e p.1 p.2 - left_inv := joinPositions_parts e - right_inv p := by simp - -lemma symmetricPairs_contraction {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) - (x y : WordSpace m d) : - dotProduct (positionProduct e x y) (symmetricPairs e d) = dotProduct x y := by - classical - unfold dotProduct - calc - _ = ∑ p : (Fin m → Fin d) × (Fin m → Fin d), - x p.1 * y p.2 * (if p.1 = p.2 then 1 else 0) := by - apply Fintype.sum_equiv (positionWordsEquiv e) - intro w - rfl - _ = _ := by - rw [Fintype.sum_prod_type] - simp - -lemma real_self_pair_ne_zero {n d : ℕ} (x : WordSpace n d) - (hr : star x = x) (hx : x ≠ 0) : dotProduct x x ≠ 0 := by - let : PartialOrder ℂ := RCLike.toPartialOrder - let : StarOrderedRing ℂ := RCLike.toStarOrderedRing - intro he - apply hx - exact dotProduct_self_star_eq_zero.mp (by simpa only [hr] using he) - -def halfRows (μ : YoungDiagram) : YoungDiagram where - cells := μ.cells.filter (fun c => 2*c.2+1 < μ.rowLen c.1) - isLowerSet := by - intro x y hxy hy - obtain ⟨hym,hy⟩ := Finset.mem_filter.mp hy - refine Finset.mem_filter.mpr ⟨μ.up_left_mem hxy.1 hxy.2 hym, ?_⟩ - have hm := μ.rowLen_anti _ _ hxy.1 - have hj := hxy.2 - omega - -lemma mem_halfRows (μ : YoungDiagram) (i j : ℕ) : - (i,j) ∈ halfRows μ ↔ 2*j+1 < μ.rowLen i := by - change (i,j) ∈ μ.cells.filter _ ↔ _ - rw [Finset.mem_filter] - exact ⟨And.right, fun h => ⟨YoungDiagram.mem_iff_lt_rowLen.mpr (by omega),h⟩⟩ - -lemma halfRows_rowLen (μ : YoungDiagram) (i : ℕ) : - (halfRows μ).rowLen i = μ.rowLen i / 2 := by - have hh : ∀ j, j < (halfRows μ).rowLen i ↔ j < μ.rowLen i / 2 := by - intro j - rw [← YoungDiagram.mem_iff_lt_rowLen, mem_halfRows] - omega - have h₁ := hh ((halfRows μ).rowLen i) - have h₂ := hh (μ.rowLen i / 2) - omega - -lemma halfRows_height (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) : - (halfRows μ).colLen 0 = μ.colLen 0 := by - have hh : ∀ i, i < (halfRows μ).colLen 0 ↔ i < μ.colLen 0 := by - intro i - rw [← YoungDiagram.mem_iff_lt_colLen, ← YoungDiagram.mem_iff_lt_colLen, - mem_halfRows, YoungDiagram.mem_iff_lt_rowLen] - obtain ⟨k,hk⟩ := he i - omega - have h₁ := hh ((halfRows μ).colLen 0) - have h₂ := hh (μ.colLen 0) - omega - -def pairedCells (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) : - (halfRows μ).cells ⊕ (halfRows μ).cells ≃ μ.cells where - toFun := Sum.elim - (fun c => ⟨(c.val.1,2*c.val.2), YoungDiagram.mem_iff_lt_rowLen.mpr (by - have h : 2*c.val.2+1 < μ.rowLen c.val.1 := (mem_halfRows μ _ _).mp c.property - change 2*c.val.2 < μ.rowLen c.val.1 - omega)⟩) - (fun c => ⟨(c.val.1,2*c.val.2+1), YoungDiagram.mem_iff_lt_rowLen.mpr - ((mem_halfRows μ _ _).mp c.property)⟩) - invFun c := - if h : c.val.2 % 2 = 0 then Sum.inl ⟨(c.val.1,c.val.2/2), (mem_halfRows μ _ _).mpr (by - have hc : c.val.2 < μ.rowLen c.val.1 := YoungDiagram.mem_iff_lt_rowLen.mp c.property - obtain ⟨k,hk⟩ := he c.val.1 - change 2*(c.val.2/2)+1 < μ.rowLen c.val.1 - omega)⟩ - else Sum.inr ⟨(c.val.1,c.val.2/2), (mem_halfRows μ _ _).mpr (by - have hc : c.val.2 < μ.rowLen c.val.1 := YoungDiagram.mem_iff_lt_rowLen.mp c.property - change 2*(c.val.2/2)+1 < μ.rowLen c.val.1 - omega)⟩ - left_inv c := by - cases c with - | inl c => simp - | inr c => - simp - apply Subtype.ext - apply Prod.ext - · rfl - · change (2*c.val.2+1)/2 = c.val.2 - omega - right_inv c := by - dsimp only - split_ifs with h - · apply Subtype.ext - apply Prod.ext - · rfl - · change 2*(c.val.2/2) = c.val.2 - change c.val.2 % 2 = 0 at h - omega - · apply Subtype.ext - apply Prod.ext - · rfl - · change 2*(c.val.2/2)+1 = c.val.2 - change c.val.2 % 2 ≠ 0 at h - omega - -def pairedTableau {n m : ℕ} (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) - (e : Fin n ≃ Fin m ⊕ Fin m) (s : Tableau m (halfRows μ)) : Tableau n μ := - e.trans ((Equiv.sumCongr s s).trans (pairedCells μ he)) - -lemma pairedTableau_left {n m : ℕ} (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) - (e : Fin n ≃ Fin m ⊕ Fin m) (s : Tableau m (halfRows μ)) (i : Fin m) : - (pairedTableau μ he e s (e.symm (Sum.inl i))).val = - ((s i).val.1, 2*(s i).val.2) := by - simp [pairedTableau, pairedCells] - -lemma pairedTableau_right {n m : ℕ} (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) - (e : Fin n ≃ Fin m ⊕ Fin m) (s : Tableau m (halfRows μ)) (i : Fin m) : - (pairedTableau μ he e s (e.symm (Sum.inr i))).val = - ((s i).val.1, 2*(s i).val.2+1) := by - simp [pairedTableau, pairedCells] - -lemma pairedTableau_group_sector {n m : ℕ} (μ : YoungDiagram) - (he : ∀ i, Even (μ.rowLen i)) (e : Fin n ≃ Fin m ⊕ Fin m) - (s : Tableau m (halfRows μ)) : - columnGroup (pairedTableau μ he e s) ≤ sectorGroup (fun i => (e i).isLeft = true) := by - intro g hg i - have hc := hg i - obtain ⟨j,rfl⟩ := e.symm.surjective i - obtain ⟨k,hk⟩ := e.symm.surjective (g (e.symm j)) - rw [← hk] at hc ⊢ - cases j <;> cases k <;> - simp only [Equiv.apply_symm_apply, Sum.isLeft_inl, Sum.isLeft_inr] at * - · rw [pairedTableau_left, pairedTableau_right] at hc - dsimp only at hc - omega - · rw [pairedTableau_left, pairedTableau_right] at hc - dsimp only at hc - omega - -lemma pairedTableau_factor {n m : ℕ} (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) - (e : Fin n ≃ Fin m ⊕ Fin m) (s : Tableau m (halfRows μ)) : - polytabloid (pairedTableau μ he e s) = positionProduct e - (letterLift (Fin.cast (halfRows_height μ he)) (polytabloid s)) - (letterLift (Fin.cast (halfRows_height μ he)) (polytabloid s)) := by - let t := pairedTableau μ he e s - let f : Fin n → ℕ := fun i => (t i).val.2 - have hn : columnGroup t = fiberGroup f := rfl - have hg : columnGroup t = fiberGroup f ⊓ sectorGroup (fun i => (e i).isLeft = true) := by - rw [← hn] - exact (inf_eq_left.mpr (pairedTableau_group_sector μ he e s)).symm - have hl : fiberGroup (fun i => f (e.symm (Sum.inl i))) = columnGroup s := by - apply Subgroup.ext - intro g - change (∀ i, (t (e.symm (Sum.inl (g i)))).val.2 = - (t (e.symm (Sum.inl i))).val.2) ↔ ∀ i, (s (g i)).val.2 = (s i).val.2 - simp only [t, pairedTableau_left, Nat.mul_right_inj (by decide : 2 ≠ 0)] - have hr : fiberGroup (fun i => f (e.symm (Sum.inr i))) = columnGroup s := by - apply Subgroup.ext - intro g - change (∀ i, (t (e.symm (Sum.inr (g i)))).val.2 = - (t (e.symm (Sum.inr i))).val.2) ↔ ∀ i, (s (g i)).val.2 = (s i).val.2 - simp only [t, pairedTableau_right, Nat.add_right_cancel_iff, - Nat.mul_right_inj (by decide : 2 ≠ 0)] - have hw₁ : leftWord e (rowWord t) = Fin.cast (halfRows_height μ he) ∘ rowWord s := by - funext i - apply Fin.ext - change (t (e.symm (Sum.inl i))).val.1 = (s i).val.1 - rw [pairedTableau_left] - have hw₂ : rightWord e (rowWord t) = Fin.cast (halfRows_height μ he) ∘ rowWord s := by - funext i - apply Fin.ext - change (t (e.symm (Sum.inr i))).val.1 = (s i).val.1 - rw [pairedTableau_right] - change polytabloid t = _ - rw [polytabloid_eq_altWord, hg, altWord_fiber_split, hl, hr, hw₁, hw₂, - ← letterLift_altWord, ← polytabloid_eq_altWord] - -lemma letterLift_real {n a b : ℕ} (φ : Fin a → Fin b) (x : WordSpace n a) - (hr : star x = x) : star (letterLift φ x) = letterLift φ x := by - classical - funext w - change star (∑ c, x c * ∏ i, if φ (c i) = w i then (1 : ℂ) else 0) = _ - simp only [star_sum, star_mul, star_prod, apply_ite, star_one, star_zero] - have hx (c) : star (x c) = x c := congrFun hr c - simp_rw [hx] - simp only [letterLift, wordMap, mul_comm] - rfl - -lemma letterLift_pair {n a b : ℕ} (φ : Fin a → Fin b) - (x : WordSpace n a) (y : WordSpace n b) : - dotProduct (letterLift φ x) y = dotProduct x (fun w => y (φ ∘ w)) := by - classical - have hx : x = ∑ w, x w • Pi.single w (1 : ℂ) := by - funext w - simp [Pi.single_apply] - conv_lhs => rw [hx, map_sum] - simp only [dotProduct, Finset.sum_apply, Pi.smul_apply, smul_eq_mul, - map_smul, letterLift_single] - simp_rw [Finset.sum_mul] - rw [Finset.sum_comm] - congr 1 - funext w - simp [Pi.single_apply] - -lemma letterLift_symmetricPairs_pair {n m a b : ℕ} - (e : Fin n ≃ Fin m ⊕ Fin m) (φ : Fin a → Fin b) - (hφ : Function.Injective φ) (x : WordSpace n a) : - dotProduct (letterLift φ x) (symmetricPairs e b) = - dotProduct x (symmetricPairs e a) := by - rw [letterLift_pair] - congr 1 - funext w - have hh : leftWord e (φ ∘ w) = rightWord e (φ ∘ w) ↔ - leftWord e w = rightWord e w := by - constructor - · intro h - funext i - exact hφ (congrFun h i) - · intro h - funext i - exact congrArg φ (congrFun h i) - simp only [symmetricPairs, hh] - -lemma pairedTableau_contraction {n m : ℕ} (μ : YoungDiagram) - (he : ∀ i, Even (μ.rowLen i)) (e : Fin n ≃ Fin m ⊕ Fin m) - (s : Tableau m (halfRows μ)) : - dotProduct (polytabloid (pairedTableau μ he e s)) - (symmetricPairs e (μ.colLen 0)) ≠ 0 := by - rw [pairedTableau_factor, symmetricPairs_contraction] - apply real_self_pair_ne_zero - · exact letterLift_real _ _ (polytabloid_real s) - · intro hz - apply polytabloid_ne_zero s - exact letterLift_injective _ (Fin.cast_injective _) (hz.trans (map_zero _).symm) - -lemma halfRows_card (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) : - 2 * (halfRows μ).card = μ.card := by - have hc := Fintype.card_congr (pairedCells μ he) - simpa only [Fintype.card_sum, Fintype.card_coe, ← two_mul] using hc - -theorem even_rows_symmetricPairs_support {n m d : ℕ} - (e : Fin n ≃ Fin m ⊕ Fin m) (μ : YoungDiagram) (t : Tableau n μ) - (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ d) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n d) (symmetricPairs e d)).toRepresentation, F ≠ 0 := by - have hn : μ.card = n := by - simpa only [Fintype.card_fin, Fintype.card_coe] using (Fintype.card_congr t).symm - have hnm : n = 2*m := by - simpa only [Fintype.card_fin, Fintype.card_sum, ← two_mul] using Fintype.card_congr e - have hm : (halfRows μ).card = m := by - have hc := halfRows_card μ he - omega - let s := canonicalTableau (halfRows μ) hm - let es : Fin n ≃ Fin m ⊕ Fin m := t.trans ((pairedCells μ he).symm.trans - (Equiv.sumCongr s.symm s.symm)) - have ht : pairedTableau μ he es s = t := by - apply Equiv.ext - intro i - change pairedCells μ he ((Equiv.sumCongr s s) - ((Equiv.sumCongr s s).symm ((pairedCells μ he).symm (t i)))) = t i - simp only [Equiv.apply_symm_apply] - let φ : Fin (μ.colLen 0) → Fin d := Fin.castLE hd - have hh : dotProduct (letterLift φ (polytabloid t)) (symmetricPairs es d) ≠ 0 := by - rw [letterLift_symmetricPairs_pair _ φ (Fin.castLE_injective hd), ← ht] - exact pairedTableau_contraction μ he es s - have hsupp := hom_to_cyclic_of_pair - (fun a b => if φ a = b then 1 else 0) (spechtSub t) - ⟨polytabloid t, mem_cyclic _ _⟩ (symmetricPairs es d) (symmetricPairs_real es) hh - let g : Equiv.Perm (Fin n) := e.trans es.symm - have hg : wordRep n d g (symmetricPairs e d) = symmetricPairs es d := by - funext w - have hl : leftWord e (w ∘ g) = leftWord es w := by - funext i - simp [leftWord, g] - have hr : rightWord e (w ∘ g) = rightWord es w := by - funext i - simp [rightWord, g] - change (if leftWord e (w ∘ g) = rightWord e (w ∘ g) then 1 else 0) = _ - simp only [hl, hr, symmetricPairs] - have hc : cyclic (wordRep n d) (symmetricPairs es d) = - cyclic (wordRep n d) (symmetricPairs e d) := by - rw [← hg, cyclic_action_eq] - change ∃ f : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n d) (symmetricPairs es d)).toRepresentation, f ≠ 0 at hsupp - rw [hc] at hsupp - exact hsupp - -end Saxl -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.SquareDetection + +namespace OAI + +/-! Symmetric Pairs. -/ + +section + +noncomputable section +open scoped TensorProduct +namespace Saxl + +def symmetricPairs {n m : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) (d : ℕ) : WordSpace n d := + fun w => if leftWord e w = rightWord e w then 1 else 0 + +lemma symmetricPairs_real {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) : + star (symmetricPairs e d) = symmetricPairs e d := by + ext w + simp only [Pi.star_apply, symmetricPairs] + split_ifs <;> simp + +def positionWordsEquiv {n a b d : ℕ} (e : Fin n ≃ Fin a ⊕ Fin b) : + (Fin n → Fin d) ≃ (Fin a → Fin d) × (Fin b → Fin d) where + toFun w := (leftWord e w, rightWord e w) + invFun p := joinPositions e p.1 p.2 + left_inv := joinPositions_parts e + right_inv p := by simp + +lemma symmetricPairs_contraction {n m d : ℕ} (e : Fin n ≃ Fin m ⊕ Fin m) + (x y : WordSpace m d) : + dotProduct (positionProduct e x y) (symmetricPairs e d) = dotProduct x y := by + classical + unfold dotProduct + calc + _ = ∑ p : (Fin m → Fin d) × (Fin m → Fin d), + x p.1 * y p.2 * (if p.1 = p.2 then 1 else 0) := by + apply Fintype.sum_equiv (positionWordsEquiv e) + intro w + rfl + _ = _ := by + rw [Fintype.sum_prod_type] + simp + +lemma real_self_pair_ne_zero {n d : ℕ} (x : WordSpace n d) + (hr : star x = x) (hx : x ≠ 0) : dotProduct x x ≠ 0 := by + let : PartialOrder ℂ := RCLike.toPartialOrder + let : StarOrderedRing ℂ := RCLike.toStarOrderedRing + intro he + apply hx + exact dotProduct_self_star_eq_zero.mp (by simpa only [hr] using he) + +def halfRows (μ : YoungDiagram) : YoungDiagram where + cells := μ.cells.filter (fun c => 2*c.2+1 < μ.rowLen c.1) + isLowerSet := by + intro x y hxy hy + obtain ⟨hym,hy⟩ := Finset.mem_filter.mp hy + refine Finset.mem_filter.mpr ⟨μ.up_left_mem hxy.1 hxy.2 hym, ?_⟩ + have hm := μ.rowLen_anti _ _ hxy.1 + have hj := hxy.2 + omega + +lemma mem_halfRows (μ : YoungDiagram) (i j : ℕ) : + (i,j) ∈ halfRows μ ↔ 2*j+1 < μ.rowLen i := by + change (i,j) ∈ μ.cells.filter _ ↔ _ + rw [Finset.mem_filter] + exact ⟨And.right, fun h => ⟨YoungDiagram.mem_iff_lt_rowLen.mpr (by omega),h⟩⟩ + +lemma halfRows_rowLen (μ : YoungDiagram) (i : ℕ) : + (halfRows μ).rowLen i = μ.rowLen i / 2 := by + have hh : ∀ j, j < (halfRows μ).rowLen i ↔ j < μ.rowLen i / 2 := by + intro j + rw [← YoungDiagram.mem_iff_lt_rowLen, mem_halfRows] + omega + have h₁ := hh ((halfRows μ).rowLen i) + have h₂ := hh (μ.rowLen i / 2) + omega + +lemma halfRows_height (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) : + (halfRows μ).colLen 0 = μ.colLen 0 := by + have hh : ∀ i, i < (halfRows μ).colLen 0 ↔ i < μ.colLen 0 := by + intro i + rw [← YoungDiagram.mem_iff_lt_colLen, ← YoungDiagram.mem_iff_lt_colLen, + mem_halfRows, YoungDiagram.mem_iff_lt_rowLen] + obtain ⟨k,hk⟩ := he i + omega + have h₁ := hh ((halfRows μ).colLen 0) + have h₂ := hh (μ.colLen 0) + omega + +def pairedCells (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) : + (halfRows μ).cells ⊕ (halfRows μ).cells ≃ μ.cells where + toFun := Sum.elim + (fun c => ⟨(c.val.1,2*c.val.2), YoungDiagram.mem_iff_lt_rowLen.mpr (by + have h : 2*c.val.2+1 < μ.rowLen c.val.1 := (mem_halfRows μ _ _).mp c.property + change 2*c.val.2 < μ.rowLen c.val.1 + omega)⟩) + (fun c => ⟨(c.val.1,2*c.val.2+1), YoungDiagram.mem_iff_lt_rowLen.mpr + ((mem_halfRows μ _ _).mp c.property)⟩) + invFun c := + if h : c.val.2 % 2 = 0 then Sum.inl ⟨(c.val.1,c.val.2/2), (mem_halfRows μ _ _).mpr (by + have hc : c.val.2 < μ.rowLen c.val.1 := YoungDiagram.mem_iff_lt_rowLen.mp c.property + obtain ⟨k,hk⟩ := he c.val.1 + change 2*(c.val.2/2)+1 < μ.rowLen c.val.1 + omega)⟩ + else Sum.inr ⟨(c.val.1,c.val.2/2), (mem_halfRows μ _ _).mpr (by + have hc : c.val.2 < μ.rowLen c.val.1 := YoungDiagram.mem_iff_lt_rowLen.mp c.property + change 2*(c.val.2/2)+1 < μ.rowLen c.val.1 + omega)⟩ + left_inv c := by + cases c with + | inl c => simp + | inr c => + simp + apply Subtype.ext + apply Prod.ext + · rfl + · change (2*c.val.2+1)/2 = c.val.2 + omega + right_inv c := by + dsimp only + split_ifs with h + · apply Subtype.ext + apply Prod.ext + · rfl + · change 2*(c.val.2/2) = c.val.2 + change c.val.2 % 2 = 0 at h + omega + · apply Subtype.ext + apply Prod.ext + · rfl + · change 2*(c.val.2/2)+1 = c.val.2 + change c.val.2 % 2 ≠ 0 at h + omega + +def pairedTableau {n m : ℕ} (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) + (e : Fin n ≃ Fin m ⊕ Fin m) (s : Tableau m (halfRows μ)) : Tableau n μ := + e.trans ((Equiv.sumCongr s s).trans (pairedCells μ he)) + +lemma pairedTableau_left {n m : ℕ} (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) + (e : Fin n ≃ Fin m ⊕ Fin m) (s : Tableau m (halfRows μ)) (i : Fin m) : + (pairedTableau μ he e s (e.symm (Sum.inl i))).val = + ((s i).val.1, 2*(s i).val.2) := by + simp [pairedTableau, pairedCells] + +lemma pairedTableau_right {n m : ℕ} (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) + (e : Fin n ≃ Fin m ⊕ Fin m) (s : Tableau m (halfRows μ)) (i : Fin m) : + (pairedTableau μ he e s (e.symm (Sum.inr i))).val = + ((s i).val.1, 2*(s i).val.2+1) := by + simp [pairedTableau, pairedCells] + +lemma pairedTableau_group_sector {n m : ℕ} (μ : YoungDiagram) + (he : ∀ i, Even (μ.rowLen i)) (e : Fin n ≃ Fin m ⊕ Fin m) + (s : Tableau m (halfRows μ)) : + columnGroup (pairedTableau μ he e s) ≤ sectorGroup (fun i => (e i).isLeft = true) := by + intro g hg i + have hc := hg i + obtain ⟨j,rfl⟩ := e.symm.surjective i + obtain ⟨k,hk⟩ := e.symm.surjective (g (e.symm j)) + rw [← hk] at hc ⊢ + cases j <;> cases k <;> + simp only [Equiv.apply_symm_apply, Sum.isLeft_inl, Sum.isLeft_inr] at * + · rw [pairedTableau_left, pairedTableau_right] at hc + dsimp only at hc + omega + · rw [pairedTableau_left, pairedTableau_right] at hc + dsimp only at hc + omega + +lemma pairedTableau_factor {n m : ℕ} (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) + (e : Fin n ≃ Fin m ⊕ Fin m) (s : Tableau m (halfRows μ)) : + polytabloid (pairedTableau μ he e s) = positionProduct e + (letterLift (Fin.cast (halfRows_height μ he)) (polytabloid s)) + (letterLift (Fin.cast (halfRows_height μ he)) (polytabloid s)) := by + let t := pairedTableau μ he e s + let f : Fin n → ℕ := fun i => (t i).val.2 + have hn : columnGroup t = fiberGroup f := rfl + have hg : columnGroup t = fiberGroup f ⊓ sectorGroup (fun i => (e i).isLeft = true) := by + rw [← hn] + exact (inf_eq_left.mpr (pairedTableau_group_sector μ he e s)).symm + have hl : fiberGroup (fun i => f (e.symm (Sum.inl i))) = columnGroup s := by + apply Subgroup.ext + intro g + change (∀ i, (t (e.symm (Sum.inl (g i)))).val.2 = + (t (e.symm (Sum.inl i))).val.2) ↔ ∀ i, (s (g i)).val.2 = (s i).val.2 + simp only [t, pairedTableau_left, Nat.mul_right_inj (by decide : 2 ≠ 0)] + have hr : fiberGroup (fun i => f (e.symm (Sum.inr i))) = columnGroup s := by + apply Subgroup.ext + intro g + change (∀ i, (t (e.symm (Sum.inr (g i)))).val.2 = + (t (e.symm (Sum.inr i))).val.2) ↔ ∀ i, (s (g i)).val.2 = (s i).val.2 + simp only [t, pairedTableau_right, Nat.add_right_cancel_iff, + Nat.mul_right_inj (by decide : 2 ≠ 0)] + have hw₁ : leftWord e (rowWord t) = Fin.cast (halfRows_height μ he) ∘ rowWord s := by + funext i + apply Fin.ext + change (t (e.symm (Sum.inl i))).val.1 = (s i).val.1 + rw [pairedTableau_left] + have hw₂ : rightWord e (rowWord t) = Fin.cast (halfRows_height μ he) ∘ rowWord s := by + funext i + apply Fin.ext + change (t (e.symm (Sum.inr i))).val.1 = (s i).val.1 + rw [pairedTableau_right] + change polytabloid t = _ + rw [polytabloid_eq_altWord, hg, altWord_fiber_split, hl, hr, hw₁, hw₂, + ← letterLift_altWord, ← polytabloid_eq_altWord] + +lemma letterLift_real {n a b : ℕ} (φ : Fin a → Fin b) (x : WordSpace n a) + (hr : star x = x) : star (letterLift φ x) = letterLift φ x := by + classical + funext w + change star (∑ c, x c * ∏ i, if φ (c i) = w i then (1 : ℂ) else 0) = _ + simp only [star_sum, star_mul, star_prod, apply_ite, star_one, star_zero] + have hx (c) : star (x c) = x c := congrFun hr c + simp_rw [hx] + simp only [letterLift, wordMap, mul_comm] + rfl + +lemma letterLift_pair {n a b : ℕ} (φ : Fin a → Fin b) + (x : WordSpace n a) (y : WordSpace n b) : + dotProduct (letterLift φ x) y = dotProduct x (fun w => y (φ ∘ w)) := by + classical + have hx : x = ∑ w, x w • Pi.single w (1 : ℂ) := by + funext w + simp [Pi.single_apply] + conv_lhs => rw [hx, map_sum] + simp only [dotProduct, Finset.sum_apply, Pi.smul_apply, smul_eq_mul, + map_smul, letterLift_single] + simp_rw [Finset.sum_mul] + rw [Finset.sum_comm] + congr 1 + funext w + simp [Pi.single_apply] + +lemma letterLift_symmetricPairs_pair {n m a b : ℕ} + (e : Fin n ≃ Fin m ⊕ Fin m) (φ : Fin a → Fin b) + (hφ : Function.Injective φ) (x : WordSpace n a) : + dotProduct (letterLift φ x) (symmetricPairs e b) = + dotProduct x (symmetricPairs e a) := by + rw [letterLift_pair] + congr 1 + funext w + have hh : leftWord e (φ ∘ w) = rightWord e (φ ∘ w) ↔ + leftWord e w = rightWord e w := by + constructor + · intro h + funext i + exact hφ (congrFun h i) + · intro h + funext i + exact congrArg φ (congrFun h i) + simp only [symmetricPairs, hh] + +lemma pairedTableau_contraction {n m : ℕ} (μ : YoungDiagram) + (he : ∀ i, Even (μ.rowLen i)) (e : Fin n ≃ Fin m ⊕ Fin m) + (s : Tableau m (halfRows μ)) : + dotProduct (polytabloid (pairedTableau μ he e s)) + (symmetricPairs e (μ.colLen 0)) ≠ 0 := by + rw [pairedTableau_factor, symmetricPairs_contraction] + apply real_self_pair_ne_zero + · exact letterLift_real _ _ (polytabloid_real s) + · intro hz + apply polytabloid_ne_zero s + exact letterLift_injective _ (Fin.cast_injective _) (hz.trans (map_zero _).symm) + +lemma halfRows_card (μ : YoungDiagram) (he : ∀ i, Even (μ.rowLen i)) : + 2 * (halfRows μ).card = μ.card := by + have hc := Fintype.card_congr (pairedCells μ he) + simpa only [Fintype.card_sum, Fintype.card_coe, ← two_mul] using hc + +theorem even_rows_symmetricPairs_support {n m d : ℕ} + (e : Fin n ≃ Fin m ⊕ Fin m) (μ : YoungDiagram) (t : Tableau n μ) + (he : ∀ i, Even (μ.rowLen i)) (hd : μ.colLen 0 ≤ d) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n d) (symmetricPairs e d)).toRepresentation, F ≠ 0 := by + have hn : μ.card = n := by + simpa only [Fintype.card_fin, Fintype.card_coe] using (Fintype.card_congr t).symm + have hnm : n = 2*m := by + simpa only [Fintype.card_fin, Fintype.card_sum, ← two_mul] using Fintype.card_congr e + have hm : (halfRows μ).card = m := by + have hc := halfRows_card μ he + omega + let s := canonicalTableau (halfRows μ) hm + let es : Fin n ≃ Fin m ⊕ Fin m := t.trans ((pairedCells μ he).symm.trans + (Equiv.sumCongr s.symm s.symm)) + have ht : pairedTableau μ he es s = t := by + apply Equiv.ext + intro i + change pairedCells μ he ((Equiv.sumCongr s s) + ((Equiv.sumCongr s s).symm ((pairedCells μ he).symm (t i)))) = t i + simp only [Equiv.apply_symm_apply] + let φ : Fin (μ.colLen 0) → Fin d := Fin.castLE hd + have hh : dotProduct (letterLift φ (polytabloid t)) (symmetricPairs es d) ≠ 0 := by + rw [letterLift_symmetricPairs_pair _ φ (Fin.castLE_injective hd), ← ht] + exact pairedTableau_contraction μ he es s + have hsupp := hom_to_cyclic_of_pair + (fun a b => if φ a = b then 1 else 0) (spechtSub t) + ⟨polytabloid t, mem_cyclic _ _⟩ (symmetricPairs es d) (symmetricPairs_real es) hh + let g : Equiv.Perm (Fin n) := e.trans es.symm + have hg : wordRep n d g (symmetricPairs e d) = symmetricPairs es d := by + funext w + have hl : leftWord e (w ∘ g) = leftWord es w := by + funext i + simp [leftWord, g] + have hr : rightWord e (w ∘ g) = rightWord es w := by + funext i + simp [rightWord, g] + change (if leftWord e (w ∘ g) = rightWord e (w ∘ g) then 1 else 0) = _ + simp only [hl, hr, symmetricPairs] + have hc : cyclic (wordRep n d) (symmetricPairs es d) = + cyclic (wordRep n d) (symmetricPairs e d) := by + rw [← hg, cyclic_action_eq] + change ∃ f : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n d) (symmetricPairs es d)).toRepresentation, f ≠ 0 at hsupp + rw [hc] at hsupp + exact hsupp + +end Saxl +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/TwoPathContraction.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/TwoPathContraction.lean index a41d4704293b0f8dc064b2fa36180c76e6432d06..6a0502d618be09185463bf465cac39b8dc186fad 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/TwoPathContraction.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/TwoPathContraction.lean @@ -1,155 +1,155 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Balance.WordPacking - -namespace OAI - -/-! Two Path Contraction. -/ - -section - -noncomputable section -namespace Saxl.Columns - -lemma dualBlockWord_singleton (r : ℕ) (N : ℕ → Band.Mat) : - dualBlockWord [r] N = columnWedge r N := by - classical - unfold dualBlockWord columnWedge - change (∑ π : Equiv.Perm (Fin r) × Unit, sg (rs := [r]) π • - Path.pureWord (fun q => N (row (perm (rs := [r]) π (enumerate [r] q))))) = _ - rw [Fintype.sum_prod_type] - simp only [Fintype.sum_unique, sg, mul_one] - apply Finset.sum_congr rfl - intro π hπ - congr 2 - funext j - change N (row (perm (rs := [r]) (π, ()) (enumerate [r] (Fin.castAdd 0 j)))) = _ - erw [enumerate_left r [] j] - rfl - -lemma dotProduct_cast {m n d : ℕ} (hn : m = n) - (x : WordSpace m d) (y : WordSpace n d) : - dotProduct (fun w => x (w ∘ Fin.cast hn)) y = - dotProduct x (fun w => y (w ∘ Fin.cast hn.symm)) := by - subst n - rfl - -lemma columnWedge_path_nonzero (r : ℕ) (hr : 2*r+1 ≤ 4) : - dotProduct (columnWedge (2*r+1) (fun i => Band.conjugation (Band.basis i))) - (Path.bandWord r) ≠ 0 := by - have h := odd_path_ordered_contraction r [2*r+1] (by - intro a ha - obtain rfl := List.mem_singleton.mp ha - exact ⟨by omega, hr⟩) - (by simp) - rw [dualBlockWord_singleton] at h - exact h - -theorem two_path_contraction (p r : ℕ) (rs : List ℕ) - (hp : 2*p+1 ≤ 4) (hrs : ∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) - (hr : rs.sum = 2*r+1) : - dotProduct (dualBlockWord ((2*p+1)::rs) - (fun i => Band.conjugation (Band.basis i))) - (positionProduct finSumFinEquiv.symm (Path.bandWord p) - (fun w => Path.bandWord r (w ∘ Fin.cast hr.symm))) ≠ 0 := by - rw [dualBlockWord_cons] - erw [positionProduct_pair] - apply mul_ne_zero (columnWedge_path_nonzero p hp) - erw [← dotProduct_cast hr] - exact odd_path_ordered_contraction r rs hrs hr - -theorem two_path_cyclic_support (p r : ℕ) (rs : List ℕ) - (hp : 2*p+1 ≤ 4) (hrs : ∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) - (hr : rs.sum = 2*r+1) (μ : YoungDiagram) - (hc : ((2*p+1)::rs).Perm μ.transpose.rowLens) - (t : Tableau ((2*p+1)+rs.sum) μ) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep ((2*p+1)+rs.sum) 4) - (positionProduct finSumFinEquiv.symm (Path.bandWord p) - (fun w => Path.bandWord r (w ∘ Fin.cast hr.symm)))).toRepresentation, - F ≠ 0 := by - obtain ⟨e, he, he'⟩ := place_columns μ hc - let s : Tableau ((2*p+1)+rs.sum) μ := (enumerate ((2*p+1)::rs)).trans e - apply specht_to_cyclic_of_vector_pair t - ⟨polytabloid s, polytabloid_mem_all t s⟩ - (fun i a => Band.conjugation (Band.basis i.val) (Path.parts a).1 (Path.parts a).2) - change dotProduct (wordMap _ (polytabloid ((enumerate _).trans e))) _ ≠ 0 - erw [mapped_placed_columns e he he' (fun i => Band.conjugation (Band.basis i))] - exact two_path_contraction p r rs hp hrs hr - -lemma positionProduct_move {n a b d : ℕ} (e f : Fin n ≃ Fin a ⊕ Fin b) - (x : WordSpace a d) (y : WordSpace b d) : - positionProduct f x y = wordRep n d (e.trans f.symm) (positionProduct e x y) := by - funext w - change x (leftWord f w) * y (rightWord f w) = - x (leftWord e (w ∘ (e.trans f.symm))) * y (rightWord e (w ∘ (e.trans f.symm))) - congr 1 <;> apply congrArg - · funext i - simp [leftWord] - · funext i - simp [rightWord] - -theorem two_path_cyclic_support_placed {n : ℕ} (p r : ℕ) (rs : List ℕ) - (hp : 2*p+1 ≤ 4) (hrs : ∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) - (hr : rs.sum = 2*r+1) (μ : YoungDiagram) - (hc : ((2*p+1)::rs).Perm μ.transpose.rowLens) - (t : Tableau n μ) (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : - ∃ F : Representation.IntertwiningMap (spechtRep t) - (cyclic (wordRep n 4) - (positionProduct e (Path.bandWord p) (Path.bandWord r))).toRepresentation, - F ≠ 0 := by - let d : Fin n ≃ Fin (2*p+1) ⊕ Fin rs.sum := - e.trans ((Equiv.refl _).sumCongr (finCongr hr.symm)) - have hd : n = (2*p+1)+rs.sum := by - simpa only [Fintype.card_fin, Fintype.card_sum] using Fintype.card_congr d - subst n - have heq : positionProduct e (Path.bandWord p) (Path.bandWord r) = - positionProduct d (Path.bandWord p) - (fun w => Path.bandWord r (w ∘ Fin.cast hr.symm)) := by - funext w - change Path.bandWord p (leftWord e w) * Path.bandWord r (rightWord e w) = - Path.bandWord p (leftWord d w) * - Path.bandWord r (rightWord d w ∘ Fin.cast hr.symm) - rfl - rw [heq, positionProduct_move finSumFinEquiv.symm d, cyclic_action_eq] - exact two_path_cyclic_support p r rs hp hrs hr μ hc t - -theorem odd_column_split (q : ℕ) (μ : YoungDiagram) - (hn : μ.card = 2*q+2) (hμ : μ.colLen 0 ≤ 4) - (ho : ∃ j, μ.colLen j % 2 = 1) : - ∃ p rs, p ≤ q ∧ 2*p+1 ≤ 4 ∧ - (∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) ∧ rs.sum = 2*(q-p)+1 ∧ - ((2*p+1)::rs).Perm μ.transpose.rowLens := by - classical - obtain ⟨j,hj⟩ := ho - have hp : 0 < μ.colLen j := by omega - have hjlt : j < μ.transpose.colLen 0 := by - rw [YoungDiagram.colLen_transpose] - exact YoungDiagram.mem_iff_lt_rowLen.mp (YoungDiagram.mem_iff_lt_colLen.mpr hp) - have hmem : μ.colLen j ∈ μ.transpose.rowLens := by - have hjl : j < μ.transpose.rowLens.length := by simpa using hjlt - have he := List.getElem_mem hjl - simpa only [YoungDiagram.get_rowLens, YoungDiagram.rowLen_transpose] using he - let rs := μ.transpose.rowLens.erase (μ.colLen j) - have hperm : ((μ.colLen j)::rs).Perm μ.transpose.rowLens := - (List.perm_cons_erase hmem).symm - have hs : μ.colLen j + rs.sum = 2*q+2 := by - have h := hperm.sum_eq - rw [List.sum_cons, ← card_eq_sum_rowLens, transpose_card, hn] at h - exact h - have hu := (μ.colLen_anti 0 j (Nat.zero_le _)).trans hμ - refine ⟨(μ.colLen j)/2, rs, ?_, ?_, ?_, ?_, ?_⟩ - · omega - · omega - · intro a ha - have ha' := List.mem_of_mem_erase ha - exact Path.fourRow_column_lengths μ hμ a ha' - · omega - · have he : 2*(μ.colLen j/2)+1 = μ.colLen j := by omega - simpa only [he] using hperm - -end Saxl.Columns -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Balance.WordPacking + +namespace OAI + +/-! Two Path Contraction. -/ + +section + +noncomputable section +namespace Saxl.Columns + +lemma dualBlockWord_singleton (r : ℕ) (N : ℕ → Band.Mat) : + dualBlockWord [r] N = columnWedge r N := by + classical + unfold dualBlockWord columnWedge + change (∑ π : Equiv.Perm (Fin r) × Unit, sg (rs := [r]) π • + Path.pureWord (fun q => N (row (perm (rs := [r]) π (enumerate [r] q))))) = _ + rw [Fintype.sum_prod_type] + simp only [Fintype.sum_unique, sg, mul_one] + apply Finset.sum_congr rfl + intro π hπ + congr 2 + funext j + change N (row (perm (rs := [r]) (π, ()) (enumerate [r] (Fin.castAdd 0 j)))) = _ + erw [enumerate_left r [] j] + rfl + +lemma dotProduct_cast {m n d : ℕ} (hn : m = n) + (x : WordSpace m d) (y : WordSpace n d) : + dotProduct (fun w => x (w ∘ Fin.cast hn)) y = + dotProduct x (fun w => y (w ∘ Fin.cast hn.symm)) := by + subst n + rfl + +lemma columnWedge_path_nonzero (r : ℕ) (hr : 2*r+1 ≤ 4) : + dotProduct (columnWedge (2*r+1) (fun i => Band.conjugation (Band.basis i))) + (Path.bandWord r) ≠ 0 := by + have h := odd_path_ordered_contraction r [2*r+1] (by + intro a ha + obtain rfl := List.mem_singleton.mp ha + exact ⟨by omega, hr⟩) + (by simp) + rw [dualBlockWord_singleton] at h + exact h + +theorem two_path_contraction (p r : ℕ) (rs : List ℕ) + (hp : 2*p+1 ≤ 4) (hrs : ∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) + (hr : rs.sum = 2*r+1) : + dotProduct (dualBlockWord ((2*p+1)::rs) + (fun i => Band.conjugation (Band.basis i))) + (positionProduct finSumFinEquiv.symm (Path.bandWord p) + (fun w => Path.bandWord r (w ∘ Fin.cast hr.symm))) ≠ 0 := by + rw [dualBlockWord_cons] + erw [positionProduct_pair] + apply mul_ne_zero (columnWedge_path_nonzero p hp) + erw [← dotProduct_cast hr] + exact odd_path_ordered_contraction r rs hrs hr + +theorem two_path_cyclic_support (p r : ℕ) (rs : List ℕ) + (hp : 2*p+1 ≤ 4) (hrs : ∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) + (hr : rs.sum = 2*r+1) (μ : YoungDiagram) + (hc : ((2*p+1)::rs).Perm μ.transpose.rowLens) + (t : Tableau ((2*p+1)+rs.sum) μ) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep ((2*p+1)+rs.sum) 4) + (positionProduct finSumFinEquiv.symm (Path.bandWord p) + (fun w => Path.bandWord r (w ∘ Fin.cast hr.symm)))).toRepresentation, + F ≠ 0 := by + obtain ⟨e, he, he'⟩ := place_columns μ hc + let s : Tableau ((2*p+1)+rs.sum) μ := (enumerate ((2*p+1)::rs)).trans e + apply specht_to_cyclic_of_vector_pair t + ⟨polytabloid s, polytabloid_mem_all t s⟩ + (fun i a => Band.conjugation (Band.basis i.val) (Path.parts a).1 (Path.parts a).2) + change dotProduct (wordMap _ (polytabloid ((enumerate _).trans e))) _ ≠ 0 + erw [mapped_placed_columns e he he' (fun i => Band.conjugation (Band.basis i))] + exact two_path_contraction p r rs hp hrs hr + +lemma positionProduct_move {n a b d : ℕ} (e f : Fin n ≃ Fin a ⊕ Fin b) + (x : WordSpace a d) (y : WordSpace b d) : + positionProduct f x y = wordRep n d (e.trans f.symm) (positionProduct e x y) := by + funext w + change x (leftWord f w) * y (rightWord f w) = + x (leftWord e (w ∘ (e.trans f.symm))) * y (rightWord e (w ∘ (e.trans f.symm))) + congr 1 <;> apply congrArg + · funext i + simp [leftWord] + · funext i + simp [rightWord] + +theorem two_path_cyclic_support_placed {n : ℕ} (p r : ℕ) (rs : List ℕ) + (hp : 2*p+1 ≤ 4) (hrs : ∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) + (hr : rs.sum = 2*r+1) (μ : YoungDiagram) + (hc : ((2*p+1)::rs).Perm μ.transpose.rowLens) + (t : Tableau n μ) (e : Fin n ≃ Fin (2*p+1) ⊕ Fin (2*r+1)) : + ∃ F : Representation.IntertwiningMap (spechtRep t) + (cyclic (wordRep n 4) + (positionProduct e (Path.bandWord p) (Path.bandWord r))).toRepresentation, + F ≠ 0 := by + let d : Fin n ≃ Fin (2*p+1) ⊕ Fin rs.sum := + e.trans ((Equiv.refl _).sumCongr (finCongr hr.symm)) + have hd : n = (2*p+1)+rs.sum := by + simpa only [Fintype.card_fin, Fintype.card_sum] using Fintype.card_congr d + subst n + have heq : positionProduct e (Path.bandWord p) (Path.bandWord r) = + positionProduct d (Path.bandWord p) + (fun w => Path.bandWord r (w ∘ Fin.cast hr.symm)) := by + funext w + change Path.bandWord p (leftWord e w) * Path.bandWord r (rightWord e w) = + Path.bandWord p (leftWord d w) * + Path.bandWord r (rightWord d w ∘ Fin.cast hr.symm) + rfl + rw [heq, positionProduct_move finSumFinEquiv.symm d, cyclic_action_eq] + exact two_path_cyclic_support p r rs hp hrs hr μ hc t + +theorem odd_column_split (q : ℕ) (μ : YoungDiagram) + (hn : μ.card = 2*q+2) (hμ : μ.colLen 0 ≤ 4) + (ho : ∃ j, μ.colLen j % 2 = 1) : + ∃ p rs, p ≤ q ∧ 2*p+1 ≤ 4 ∧ + (∀ a ∈ rs, 1 ≤ a ∧ a ≤ 4) ∧ rs.sum = 2*(q-p)+1 ∧ + ((2*p+1)::rs).Perm μ.transpose.rowLens := by + classical + obtain ⟨j,hj⟩ := ho + have hp : 0 < μ.colLen j := by omega + have hjlt : j < μ.transpose.colLen 0 := by + rw [YoungDiagram.colLen_transpose] + exact YoungDiagram.mem_iff_lt_rowLen.mp (YoungDiagram.mem_iff_lt_colLen.mpr hp) + have hmem : μ.colLen j ∈ μ.transpose.rowLens := by + have hjl : j < μ.transpose.rowLens.length := by simpa using hjlt + have he := List.getElem_mem hjl + simpa only [YoungDiagram.get_rowLens, YoungDiagram.rowLen_transpose] using he + let rs := μ.transpose.rowLens.erase (μ.colLen j) + have hperm : ((μ.colLen j)::rs).Perm μ.transpose.rowLens := + (List.perm_cons_erase hmem).symm + have hs : μ.colLen j + rs.sum = 2*q+2 := by + have h := hperm.sum_eq + rw [List.sum_cons, ← card_eq_sum_rowLens, transpose_card, hn] at h + exact h + have hu := (μ.colLen_anti 0 j (Nat.zero_le _)).trans hμ + refine ⟨(μ.colLen j)/2, rs, ?_, ?_, ?_, ?_, ?_⟩ + · omega + · omega + · intro a ha + have ha' := List.mem_of_mem_erase ha + exact Path.fourRow_column_lengths μ hμ a ha' + · omega + · have he : 2*(μ.colLen j/2)+1 = μ.colLen j := by omega + simpa only [he] using hperm + +end Saxl.Columns +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/VectorDomainsCore.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/VectorDomainsCore.lean index 61c01e12782c29ba971dbd6c194c97c0687d8fa2..32e70a17be9dfef982bce0ba851b0dc3277381e4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/VectorDomainsCore.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Contraction/VectorDomainsCore.lean @@ -1,207 +1,207 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.DomainSolver - -namespace OAI - -/-! Vector Domains Core. -/ - -section - -open scoped BigOperators -namespace Saxl.Columns - -def permVector {n : ℕ} (π : Equiv.Perm (Fin n)) : List ℕ := List.ofFn (fun i => (π i).val) - -lemma permVector_get {n : ℕ} (π : Equiv.Perm (Fin n)) (i : Fin n) : - (permVector π)[i.val]?.getD 0 = (π i).val := by - simp [permVector,i.isLt] - -lemma permVector_injective {n : ℕ} : Function.Injective (@permVector n) := by - intro π σ h - ext i - have hh := congrArg (fun rs : List ℕ => rs[i.val]?.getD 0) h - simpa only [permVector_get] using hh - -lemma ofFn_fin_val (n : ℕ) : List.ofFn (fun i : Fin n => i.val) = List.range n := by - apply List.ext_getElem - · simp - · intro i hi hj; simp - -lemma permVector_perm {n : ℕ} (π : Equiv.Perm (Fin n)) : - (permVector π).Perm (List.range n) := by - simpa only [permVector,Function.comp_def,ofFn_fin_val] using π.ofFn_comp_perm (fun i : Fin n => i.val) - -lemma permVector_surj {n : ℕ} {rs : List ℕ} (h : rs.Perm (List.range n)) : - ∃ π : Equiv.Perm (Fin n), permVector π = rs := by - obtain ⟨e,he⟩ := Saxl.list_get_equiv h - have hl : rs.length = n := h.length_eq.trans (List.length_range) - let π : Equiv.Perm (Fin n) := (finCongr hl.symm).trans (e.trans (finCongr (List.length_range))) - refine ⟨π,?_⟩ - apply List.ext_getElem - · simpa [permVector] using hl.symm - · intro i hi hj - have hin : i < n := by simpa only [permVector,List.length_ofFn] using hi - have hh := he ⟨i,hj⟩ - simpa [permVector,π,List.get_eq_getElem] using hh - -def vectorFull (n : ℕ) : Finset (List ℕ) := - ⟨(List.range n).permutations', (List.permutations_perm_permutations' _).nodup_iff.mp - (List.nodup_permutations _ (List.nodup_range))⟩ - -lemma vectorFull_eq_image (n : ℕ) : - vectorFull n = Finset.univ.image (@permVector n) := by - ext rs - change rs ∈ (List.range n).permutations' ↔ _ - simp only [List.mem_permutations',Finset.mem_image,Finset.mem_univ,true_and] - constructor - · exact permVector_surj - · rintro ⟨π,rfl⟩; exact permVector_perm π - -def vectorSign (n : ℕ) (rs : List ℕ) : ℤ := - ∏ x ∈ Equiv.Perm.finPairsLT n, - if rs[x.1.val]?.getD 0 ≤ rs[x.2.val]?.getD 0 then -1 else 1 - -lemma sign_eq_aux {n : ℕ} (π : Equiv.Perm (Fin n)) : - Equiv.Perm.sign π = Equiv.Perm.signAux π := by - induction π using Equiv.Perm.swap_induction_on with - | one => simp [Equiv.Perm.signAux_one] - | swap_mul π i j hij ih => - rw [Equiv.Perm.sign_mul,Equiv.Perm.signAux_mul,ih, - Equiv.Perm.sign_swap hij,Equiv.Perm.signAux_swap hij] - -lemma vectorSign_perm {n : ℕ} (π : Equiv.Perm (Fin n)) : - vectorSign n (permVector π) = (Equiv.Perm.sign π : ℤ) := by - rw [sign_eq_aux] - simp only [vectorSign,Equiv.Perm.signAux,Units.coe_prod,permVector_get] - apply Finset.prod_congr rfl - intro x hx - simp only [Fin.le_def] - split_ifs <;> rfl - -def VectorDomains : List ℕ → Type - | [] => Unit - | _ :: rs => Finset (List ℕ) × VectorDomains rs - -def VectorDomains.full : (rs : List ℕ) → VectorDomains rs - | [] => () - | r :: rs => (vectorFull r,full rs) - -def VectorDomains.atValue : {rs : List ℕ} → VectorDomains rs → Cells rs → ℕ → VectorDomains rs - | _ :: _, (s,D), .inl i, j => (s.filter (fun π => π[i.val]?.getD 0 = j),D) - | _ :: _, (s,D), .inr c, j => (s,atValue D c j) - -def VectorDomains.vanished : {rs : List ℕ} → VectorDomains rs → Bool - | [], _ => false - | _ :: _, (s,D) => decide (s = ∅) || vanished D - -def VectorDomains.mass : {rs : List ℕ} → VectorDomains rs → ℤ - | [], _ => 1 - | r :: _, (s,D) => (∑ π ∈ s, vectorSign r π) * mass D - -def Domains.encode : {rs : List ℕ} → Domains rs → VectorDomains rs - | [], _ => () - | _ :: _, (s,D) => (s.image permVector,encode D) - -lemma Domains.encode_full (rs : List ℕ) : (Domains.full rs).encode = VectorDomains.full rs := by - induction rs with - | nil => rfl - | cons r rs ih => simp only [full,encode,VectorDomains.full,← vectorFull_eq_image,ih]; rfl - -lemma Domains.encode_atValue {rs : List ℕ} (D : Domains rs) (c : Cells rs) (j : ℕ) : - (D.atValue c j).encode = D.encode.atValue c j := by - induction rs with - | nil => exact c.elim - | cons r rs ih => - rcases D with ⟨s,D⟩ - cases c with - | inl i => simp only [atValue,encode,VectorDomains.atValue,Finset.filter_image,permVector_get]; rfl - | inr c => simp only [atValue,encode,VectorDomains.atValue,ih]; rfl - -lemma Domains.encode_vanished {rs : List ℕ} (D : Domains rs) : D.encode.vanished = D.vanished := by - induction rs with - | nil => rfl - | cons r rs ih => - rcases D with ⟨s,D⟩ - simp only [encode,VectorDomains.vanished,vanished,Finset.image_eq_empty,ih] - -lemma Domains.encode_mass {rs : List ℕ} (D : Domains rs) : D.encode.mass = D.mass := by - induction rs with - | nil => rfl - | cons r rs ih => - rcases D with ⟨s,D⟩ - simp only [encode,VectorDomains.mass,mass,ih] - congr 1 - rw [Finset.sum_image (fun _ _ _ _ h => permVector_injective h)] - apply Finset.sum_congr rfl - intro π hπ - exact vectorSign_perm π - -def vectorEdgeOptions {rsT rsA rsB : List ℕ} - (D : VectorDomains rsT) (E : VectorDomains rsA) (F : VectorDomains rsB) - (c : Edge rsT rsA rsB) (flag : Finset (ℕ × ℕ × ℕ)) : Finset (ℕ × ℕ × ℕ) := - flag.filter (fun v => (D.atValue c.1 v.1).vanished = false ∧ - (E.atValue c.2.1 v.2.1).vanished = false ∧ (F.atValue c.2.2 v.2.2).vanished = false) - -lemma vectorEdgeOptions_encode {rsT rsA rsB : List ℕ} - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - (c : Edge rsT rsA rsB) (flag : Finset (ℕ × ℕ × ℕ)) : - vectorEdgeOptions D.encode E.encode F.encode c flag = edgeOptions D E F c flag := by - simp only [vectorEdgeOptions,edgeOptions,← Domains.encode_atValue, Domains.encode_vanished] - -def vectorOrderEdges {rsT rsA rsB : List ℕ} - (D : VectorDomains rsT) (E : VectorDomains rsA) (F : VectorDomains rsB) - (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : List (Edge rsT rsA rsB) := - bringBest (fun c => (vectorEdgeOptions D E F c flag).card) edges - -lemma vectorOrderEdges_encode {rsT rsA rsB : List ℕ} - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : - vectorOrderEdges D.encode E.encode F.encode edges flag = orderEdges D E F edges flag := by - simp only [vectorOrderEdges,orderEdges,vectorEdgeOptions_encode] - -def solveVectors {rsT rsA rsB : List ℕ} : ℕ → VectorDomains rsT → VectorDomains rsA → - VectorDomains rsB → List (Edge rsT rsA rsB) → Finset (ℕ × ℕ × ℕ) → ℤ - | fuel, D, E, F, edges, flag => - if D.vanished || E.vanished || F.vanished then 0 - else match vectorOrderEdges D E F edges flag with - | [] => D.mass * E.mass * F.mass - | c :: cs => match fuel with - | 0 => 0 - | k+1 => ∑ v ∈ vectorEdgeOptions D E F c flag, - solveVectors k (D.atValue c.1 v.1) (E.atValue c.2.1 v.2.1) - (F.atValue c.2.2 v.2.2) cs flag - -lemma solveVectors_encode {rsT rsA rsB : List ℕ} (fuel : ℕ) - (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) - (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : - solveVectors fuel D.encode E.encode F.encode edges flag = solveDomains fuel D E F edges flag := by - induction fuel generalizing D E F edges with - | zero => - rw [solveVectors,solveDomains] - simp only [Domains.encode_vanished,vectorOrderEdges_encode,Domains.encode_mass] - split <;> rfl - | succ fuel ih => - rw [solveVectors,solveDomains] - simp only [Domains.encode_vanished,vectorOrderEdges_encode,Domains.encode_mass] - split - · rfl - · cases he : orderEdges D E F edges flag with - | nil => rfl - | cons c cs => - simp only [vectorEdgeOptions_encode,← Domains.encode_atValue,ih] - -lemma contractionInteger_vectors {n : ℕ} (rsA rsB rsT : List ℕ) - (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) - (flag : Finset (ℕ × ℕ × ℕ)) : - contractionInteger rsA rsB rsT ea eb et (fun r a b => if (r,a,b) ∈ flag then 1 else 0) = - solveVectors n (.full rsT) (.full rsA) (.full rsB) - (certificateEdges rsA rsB rsT ea eb et) flag := by - rw [← Domains.encode_full,← Domains.encode_full,← Domains.encode_full, solveVectors_encode] - exact contractionInteger_solve .. - -end Saxl.Columns - -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.DomainSolver + +namespace OAI + +/-! Vector Domains Core. -/ + +section + +open scoped BigOperators +namespace Saxl.Columns + +def permVector {n : ℕ} (π : Equiv.Perm (Fin n)) : List ℕ := List.ofFn (fun i => (π i).val) + +lemma permVector_get {n : ℕ} (π : Equiv.Perm (Fin n)) (i : Fin n) : + (permVector π)[i.val]?.getD 0 = (π i).val := by + simp [permVector,i.isLt] + +lemma permVector_injective {n : ℕ} : Function.Injective (@permVector n) := by + intro π σ h + ext i + have hh := congrArg (fun rs : List ℕ => rs[i.val]?.getD 0) h + simpa only [permVector_get] using hh + +lemma ofFn_fin_val (n : ℕ) : List.ofFn (fun i : Fin n => i.val) = List.range n := by + apply List.ext_getElem + · simp + · intro i hi hj; simp + +lemma permVector_perm {n : ℕ} (π : Equiv.Perm (Fin n)) : + (permVector π).Perm (List.range n) := by + simpa only [permVector,Function.comp_def,ofFn_fin_val] using π.ofFn_comp_perm (fun i : Fin n => i.val) + +lemma permVector_surj {n : ℕ} {rs : List ℕ} (h : rs.Perm (List.range n)) : + ∃ π : Equiv.Perm (Fin n), permVector π = rs := by + obtain ⟨e,he⟩ := Saxl.list_get_equiv h + have hl : rs.length = n := h.length_eq.trans (List.length_range) + let π : Equiv.Perm (Fin n) := (finCongr hl.symm).trans (e.trans (finCongr (List.length_range))) + refine ⟨π,?_⟩ + apply List.ext_getElem + · simpa [permVector] using hl.symm + · intro i hi hj + have hin : i < n := by simpa only [permVector,List.length_ofFn] using hi + have hh := he ⟨i,hj⟩ + simpa [permVector,π,List.get_eq_getElem] using hh + +def vectorFull (n : ℕ) : Finset (List ℕ) := + ⟨(List.range n).permutations', (List.permutations_perm_permutations' _).nodup_iff.mp + (List.nodup_permutations _ (List.nodup_range))⟩ + +lemma vectorFull_eq_image (n : ℕ) : + vectorFull n = Finset.univ.image (@permVector n) := by + ext rs + change rs ∈ (List.range n).permutations' ↔ _ + simp only [List.mem_permutations',Finset.mem_image,Finset.mem_univ,true_and] + constructor + · exact permVector_surj + · rintro ⟨π,rfl⟩; exact permVector_perm π + +def vectorSign (n : ℕ) (rs : List ℕ) : ℤ := + ∏ x ∈ Equiv.Perm.finPairsLT n, + if rs[x.1.val]?.getD 0 ≤ rs[x.2.val]?.getD 0 then -1 else 1 + +lemma sign_eq_aux {n : ℕ} (π : Equiv.Perm (Fin n)) : + Equiv.Perm.sign π = Equiv.Perm.signAux π := by + induction π using Equiv.Perm.swap_induction_on with + | one => simp [Equiv.Perm.signAux_one] + | swap_mul π i j hij ih => + rw [Equiv.Perm.sign_mul,Equiv.Perm.signAux_mul,ih, + Equiv.Perm.sign_swap hij,Equiv.Perm.signAux_swap hij] + +lemma vectorSign_perm {n : ℕ} (π : Equiv.Perm (Fin n)) : + vectorSign n (permVector π) = (Equiv.Perm.sign π : ℤ) := by + rw [sign_eq_aux] + simp only [vectorSign,Equiv.Perm.signAux,Units.coe_prod,permVector_get] + apply Finset.prod_congr rfl + intro x hx + simp only [Fin.le_def] + split_ifs <;> rfl + +def VectorDomains : List ℕ → Type + | [] => Unit + | _ :: rs => Finset (List ℕ) × VectorDomains rs + +def VectorDomains.full : (rs : List ℕ) → VectorDomains rs + | [] => () + | r :: rs => (vectorFull r,full rs) + +def VectorDomains.atValue : {rs : List ℕ} → VectorDomains rs → Cells rs → ℕ → VectorDomains rs + | _ :: _, (s,D), .inl i, j => (s.filter (fun π => π[i.val]?.getD 0 = j),D) + | _ :: _, (s,D), .inr c, j => (s,atValue D c j) + +def VectorDomains.vanished : {rs : List ℕ} → VectorDomains rs → Bool + | [], _ => false + | _ :: _, (s,D) => decide (s = ∅) || vanished D + +def VectorDomains.mass : {rs : List ℕ} → VectorDomains rs → ℤ + | [], _ => 1 + | r :: _, (s,D) => (∑ π ∈ s, vectorSign r π) * mass D + +def Domains.encode : {rs : List ℕ} → Domains rs → VectorDomains rs + | [], _ => () + | _ :: _, (s,D) => (s.image permVector,encode D) + +lemma Domains.encode_full (rs : List ℕ) : (Domains.full rs).encode = VectorDomains.full rs := by + induction rs with + | nil => rfl + | cons r rs ih => simp only [full,encode,VectorDomains.full,← vectorFull_eq_image,ih]; rfl + +lemma Domains.encode_atValue {rs : List ℕ} (D : Domains rs) (c : Cells rs) (j : ℕ) : + (D.atValue c j).encode = D.encode.atValue c j := by + induction rs with + | nil => exact c.elim + | cons r rs ih => + rcases D with ⟨s,D⟩ + cases c with + | inl i => simp only [atValue,encode,VectorDomains.atValue,Finset.filter_image,permVector_get]; rfl + | inr c => simp only [atValue,encode,VectorDomains.atValue,ih]; rfl + +lemma Domains.encode_vanished {rs : List ℕ} (D : Domains rs) : D.encode.vanished = D.vanished := by + induction rs with + | nil => rfl + | cons r rs ih => + rcases D with ⟨s,D⟩ + simp only [encode,VectorDomains.vanished,vanished,Finset.image_eq_empty,ih] + +lemma Domains.encode_mass {rs : List ℕ} (D : Domains rs) : D.encode.mass = D.mass := by + induction rs with + | nil => rfl + | cons r rs ih => + rcases D with ⟨s,D⟩ + simp only [encode,VectorDomains.mass,mass,ih] + congr 1 + rw [Finset.sum_image (fun _ _ _ _ h => permVector_injective h)] + apply Finset.sum_congr rfl + intro π hπ + exact vectorSign_perm π + +def vectorEdgeOptions {rsT rsA rsB : List ℕ} + (D : VectorDomains rsT) (E : VectorDomains rsA) (F : VectorDomains rsB) + (c : Edge rsT rsA rsB) (flag : Finset (ℕ × ℕ × ℕ)) : Finset (ℕ × ℕ × ℕ) := + flag.filter (fun v => (D.atValue c.1 v.1).vanished = false ∧ + (E.atValue c.2.1 v.2.1).vanished = false ∧ (F.atValue c.2.2 v.2.2).vanished = false) + +lemma vectorEdgeOptions_encode {rsT rsA rsB : List ℕ} + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + (c : Edge rsT rsA rsB) (flag : Finset (ℕ × ℕ × ℕ)) : + vectorEdgeOptions D.encode E.encode F.encode c flag = edgeOptions D E F c flag := by + simp only [vectorEdgeOptions,edgeOptions,← Domains.encode_atValue, Domains.encode_vanished] + +def vectorOrderEdges {rsT rsA rsB : List ℕ} + (D : VectorDomains rsT) (E : VectorDomains rsA) (F : VectorDomains rsB) + (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : List (Edge rsT rsA rsB) := + bringBest (fun c => (vectorEdgeOptions D E F c flag).card) edges + +lemma vectorOrderEdges_encode {rsT rsA rsB : List ℕ} + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : + vectorOrderEdges D.encode E.encode F.encode edges flag = orderEdges D E F edges flag := by + simp only [vectorOrderEdges,orderEdges,vectorEdgeOptions_encode] + +def solveVectors {rsT rsA rsB : List ℕ} : ℕ → VectorDomains rsT → VectorDomains rsA → + VectorDomains rsB → List (Edge rsT rsA rsB) → Finset (ℕ × ℕ × ℕ) → ℤ + | fuel, D, E, F, edges, flag => + if D.vanished || E.vanished || F.vanished then 0 + else match vectorOrderEdges D E F edges flag with + | [] => D.mass * E.mass * F.mass + | c :: cs => match fuel with + | 0 => 0 + | k+1 => ∑ v ∈ vectorEdgeOptions D E F c flag, + solveVectors k (D.atValue c.1 v.1) (E.atValue c.2.1 v.2.1) + (F.atValue c.2.2 v.2.2) cs flag + +lemma solveVectors_encode {rsT rsA rsB : List ℕ} (fuel : ℕ) + (D : Domains rsT) (E : Domains rsA) (F : Domains rsB) + (edges : List (Edge rsT rsA rsB)) (flag : Finset (ℕ × ℕ × ℕ)) : + solveVectors fuel D.encode E.encode F.encode edges flag = solveDomains fuel D E F edges flag := by + induction fuel generalizing D E F edges with + | zero => + rw [solveVectors,solveDomains] + simp only [Domains.encode_vanished,vectorOrderEdges_encode,Domains.encode_mass] + split <;> rfl + | succ fuel ih => + rw [solveVectors,solveDomains] + simp only [Domains.encode_vanished,vectorOrderEdges_encode,Domains.encode_mass] + split + · rfl + · cases he : orderEdges D E F edges flag with + | nil => rfl + | cons c cs => + simp only [vectorEdgeOptions_encode,← Domains.encode_atValue,ih] + +lemma contractionInteger_vectors {n : ℕ} (rsA rsB rsT : List ℕ) + (ea : Fin n ≃ Fin rsA.sum) (eb : Fin n ≃ Fin rsB.sum) (et : Fin n ≃ Fin rsT.sum) + (flag : Finset (ℕ × ℕ × ℕ)) : + contractionInteger rsA rsB rsT ea eb et (fun r a b => if (r,a,b) ∈ flag then 1 else 0) = + solveVectors n (.full rsT) (.full rsA) (.full rsB) + (certificateEdges rsA rsB rsT ea eb et) flag := by + rw [← Domains.encode_full,← Domains.encode_full,← Domains.encode_full, solveVectors_encode] + exact contractionInteger_solve .. + +end Saxl.Columns + +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/ChoiceCertificates13.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/ChoiceCertificates13.lean index 5c94327dbdeff23ecf5b53461eff612feeefaa41..f6048d51b4fc201ee98c8a401eda64e236b2c837 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/ChoiceCertificates13.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/ChoiceCertificates13.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Choice certificates in degree thirteen. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_0 : Equiv.Perm (Fin 13) := Equiv.swap 1 12 * (Equiv.swap 6 3 * (Equiv.swap 6 5 * (Equiv.swap 6 7 * (Equiv.swap 5 0 * (Equiv.swap 3 9 * (Equiv.swap 2 4 * (Equiv.swap 1 11 * (Equiv.swap 0 8)))))))) -def smallT13_0 : Equiv.Perm (Fin 13) := Equiv.swap 0 12 * (Equiv.swap 6 3 * (Equiv.swap 3 2 * (Equiv.swap 6 9 * (Equiv.swap 6 7 * (Equiv.swap 0 10 * (Equiv.swap 0 5 * (Equiv.swap 3 8 * (Equiv.swap 2 1 * (Equiv.swap 1 11 * (Equiv.swap 0 4)))))))))) -def smallFlag13_0 : Finset (ℕ × ℕ × ℕ) := {(4,0,0),(6,0,1),(5,0,2),(2,0,3),(0,1,0),(0,1,1),(3,1,2),(1,2,0),(0,2,2),(0,2,3),(0,3,1)} - -def smallChoices13_0 : EdgeChoices := (.node 1 (fun v => if v = (0,1,0) then (.node 1 (fun v => if v = (0,2,2) then (.node 6 (fun v => if v = (0,1,0) then (.node 0 (fun v => if v = (6,0,1) then (.node 1 (fun _ => (.node 7 (fun _ => (.node 0 (fun v => if v = (4,0,0) then (.node 0 (fun v => if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if v = (5,0,2) then (.node 0 (fun v => if v = (4,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun v => if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun v => if v = (0,1,0) then (.node 0 (fun v => if v = (6,0,1) then (.node 1 (fun v => if v = (5,0,2) then (.node 0 (fun v => if v = (1,2,0) then (.node 5 (fun v => if v = (2,0,3) then (.node 5 (fun v => if v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if v = (0,2,2) then (.node 6 (fun _ => (.node 0 (fun v => if v = (4,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 6 (fun _ => (.node 5 (fun v => if v = (4,0,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _ => (.node 0 (fun v => if v = (4,0,0) then (.node 0 (fun v => if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if v = (5,0,2) then (.node 0 (fun v => if v = (4,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 5 (fun _ => (.node 5 (fun _ => .fallback)))))))))) else (.node 0 (fun v => if v = (6,0,1) then (.node 1 (fun v => if v = (4,0,0) then (.node 0 (fun v => if v = (1,2,0) then (.node 6 (fun v => if v = (0,1,0) then (.node 0 (fun v => if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if v = (0,1,1) then (.node 0 (fun v => if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (2,0,3) then (.node 0 (fun v => if v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))) else (.node 0 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(fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if v = (6,0,1) then (.node 0 (fun v => if v = (4,0,0) then (.node 0 (fun v => if v = (0,2,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 6 (fun v => if v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 5 (fun v => if v = (4,0,0) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if v = (2,0,3) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 5 (fun v => if v = (6,0,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if v = (2,0,3) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_0 : solveChoices smallChoices13_0 (.full [7,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [7,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_0 smallT13_0) smallFlag13_0 = 116 := by - decide +kernel - -lemma smallSupport13_0 : RowSquare [4,4,3,2] [7,1,1,1,1,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [7,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_0 smallT13_0 smallFlag13_0 smallChoices13_0 - change solveChoices smallChoices13_0 (.full [7,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [7,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_0 smallT13_0) smallFlag13_0 ≠ 0 - rw [smallCert13_0] - norm_num - -def smallB13_1 : Equiv.Perm (Fin 13) := Equiv.swap 9 0 * (Equiv.swap 9 6 * (Equiv.swap 7 10 * (Equiv.swap 6 11 * (Equiv.swap 3 5 * (Equiv.swap 0 12))))) -def smallT13_1 : Equiv.Perm (Fin 13) := Equiv.swap 10 6 * (Equiv.swap 6 3 * (Equiv.swap 6 7 * (Equiv.swap 7 9 * (Equiv.swap 6 5 * (Equiv.swap 5 2 * (Equiv.swap 3 1 * (Equiv.swap 3 4 * (Equiv.swap 2 8 * (Equiv.swap 1 0 * (Equiv.swap 0 11)))))))))) -def smallFlag13_1 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,1),(0,1,1),(3,1,2),(2,1,3),(5,2,0),(0,2,2),(0,2,3),(4,3,1),(1,3,2)} - -def smallChoices13_1 : EdgeChoices := (.node 0 (fun v => if v = (0,0,0) then (.node 5 (fun v => if v = (0,0,1) then (.node 0 (fun v => if v = (0,1,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if v = (0,2,2) then (.node 6 (fun _ => (.node 2 (fun v => if v = (2,1,3) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 4 (fun v => if v = (3,1,2) then (.node 6 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 6 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else if v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun v => if v = (0,2,2) then (.node 6 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 2 (fun v => if v = (3,1,2) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun v => if v = (0,2,2) then (.node 6 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun v => if v = (3,1,2) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun v => if v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun v => if v = (0,2,2) then (.node 6 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 2 (fun v => if v = (3,1,2) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))))) else if v = (0,1,1) then (.node 4 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 4 (fun v => if v = (4,3,1) then (.node 7 (fun v => if v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 7 (fun _ => (.node 0 (fun v => if v = (0,0,0) then (.node 4 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun v => if v = (0,2,2) then (.node 7 (fun _ => (.node 0 (fun v => if v = 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then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun v => if v = (0,1,1) then (.node 0 (fun v => if v = (2,1,3) then (.node 2 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (5,2,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (0,2,2) then (.node 4 (fun v => if v = (0,1,1) then (.node 0 (fun v => if v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 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then (.node 2 (fun v => if v = (3,1,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (2,1,3) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun v => if v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun v => if v = (0,0,0) then (.node 2 (fun v => if v = (3,1,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (2,1,3) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun v => if v = (3,1,2) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun v => if v = (0,1,1) then (.node 5 (fun v => if v = (0,2,2) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if v = (0,2,2) then (.node 5 (fun v => if v = (0,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun v => if v = (0,0,0) then (.node 2 (fun _ => .fallback)) else if v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (0,2,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun v => if v = (0,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 5 (fun v => if v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun v => if v = (1,0,0) then (.node 2 (fun v => if v = (3,1,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (2,1,3) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun v => if v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun v => if v = (1,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun v => if v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 5 (fun v => if v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun v => if v = (1,0,0) then (.node 2 (fun v => if v = (3,1,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (2,1,3) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun v => if v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun v => if v = (0,0,0) then (.node 2 (fun v => if v = (3,1,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (2,1,3) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun v => if v = (3,1,2) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun v => if v = (0,1,1) then (.node 5 (fun v => if v = (0,2,2) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if v = (0,2,2) then (.node 5 (fun v => if v = (0,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun v => if v = (0,0,0) then (.node 2 (fun _ => .fallback)) else if v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (0,2,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun v => if v = (0,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert13_1 : solveChoices smallChoices13_1 (.full [6,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [6,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_1 smallT13_1) smallFlag13_1 = 15 := by - decide +kernel - -lemma smallSupport13_1 : RowSquare [4,4,3,2] [6,3,1,1,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [6,2,2,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_1 smallT13_1 smallFlag13_1 smallChoices13_1 - change solveChoices smallChoices13_1 (.full [6,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [6,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_1 smallT13_1) smallFlag13_1 ≠ 0 - rw [smallCert13_1] - norm_num - -def smallB13_2 : Equiv.Perm (Fin 13) := Equiv.swap 7 12 * (Equiv.swap 7 8 * (Equiv.swap 7 5 * (Equiv.swap 8 4 * (Equiv.swap 7 3 * (Equiv.swap 5 10 * (Equiv.swap 5 6 * (Equiv.swap 4 0 * (Equiv.swap 3 9 * (Equiv.swap 1 2 * (Equiv.swap 0 11)))))))))) -def smallT13_2 : Equiv.Perm (Fin 13) := Equiv.swap 10 5 * (Equiv.swap 5 6 * (Equiv.swap 3 2 * (Equiv.swap 6 12 * (Equiv.swap 5 0 * (Equiv.swap 1 11 * (Equiv.swap 3 7 * (Equiv.swap 2 9 * (Equiv.swap 1 4 * (Equiv.swap 0 8))))))))) -def smallFlag13_2 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(3,1,1),(0,1,2),(4,1,2),(0,1,3),(5,2,0),(0,2,1),(0,2,2),(1,3,1),(2,3,3)} - -def smallChoices13_2 : EdgeChoices := (.node 0 (fun v => if v = (0,0,0) then (.node 10 (fun v => if v = (1,0,1) then (.node 0 (fun v => if v = (0,1,2) then (.node 1 (fun v => if v = (0,1,2) then (.node 0 (fun v => if v = (0,2,1) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun v => if v = (0,0,0) then (.node 0 (fun v => if v = (0,1,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if v = (0,2,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun v => if v = (5,2,0) then (.node 0 (fun v => if v = (0,1,3) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun v => if v = (0,1,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun v => if v = (3,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 2 (fun _ => (.node 1 (fun v => if v = (3,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if v = (0,1,3) then (.node 0 (fun v => if v = (0,2,1) then (.node 7 (fun _ => .fallback)) else if v = (0,2,2) then (.node 7 (fun _ => .fallback)) else (.node 2 (fun v => if v = (0,0,0) then (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun v => if v = (3,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (0,1,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if v = (0,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 0 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))))) else if v = (0,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun v => if v = (0,2,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if v = (0,2,1) then (.node 0 (fun v => if v = (0,1,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 2 (fun v => if v = (0,0,0) then (.node 1 (fun v => if v = (0,1,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 2 (fun v => if v = (0,0,0) then (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun v => if v = (3,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (0,1,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if v = (0,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 0 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else if v = (0,1,2) then (.node 3 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun v => if v = (0,2,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun v => if v = (0,0,0) then (.node 0 (fun v => if v = (3,1,1) then (.node 2 (fun v => if v = (0,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun v => if v = (0,1,2) then (.node 1 (fun _ => .fallback)) else if v = (4,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun v => if v = (0,1,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun v => if v = (3,1,1) then (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun v => if v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun v => if v = (0,1,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))))) else (.node 1 (fun v => if v = (0,1,2) then (.node 0 (fun v => if v = (0,2,1) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if v = (0,2,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun v => if v = (5,2,0) then (.node 0 (fun v => if v = (0,1,3) then (.node 2 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun v => if v = (0,1,3) then (.node 3 (fun _ => .fallback)) else (.node 2 (fun v => if v = (0,1,2) then (.node 2 (fun _ => .fallback)) else if v = (4,1,2) then (.node 0 (fun v => if v = (3,1,1) then (.node 0 (fun _ => 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(.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun v => if v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun v => if v = (3,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))) else (.node 7 (fun _ => (.node 0 (fun v => if v = (0,0,0) then (.node 2 (fun _ => (.node 2 (fun v => if v = (4,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun v => if v = (3,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 8 (fun v => if v = (1,0,1) then (.node 0 (fun _ => (.node 3 (fun v => if v = (4,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 4 (fun _ => (.node 0 (fun v => if v = (4,1,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun v => if v = (4,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 4 (fun _ => .fallback)))))))))))))))))) -lemma smallCert13_2 : solveChoices smallChoices13_2 (.full [6,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [6,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_2 smallT13_2) smallFlag13_2 = -9 := by - decide +kernel - -lemma smallSupport13_2 : RowSquare [4,4,3,2] [7,2,1,1,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [6,2,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_2 smallT13_2 smallFlag13_2 smallChoices13_2 - change solveChoices smallChoices13_2 (.full [6,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [6,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_2 smallT13_2) smallFlag13_2 ≠ 0 - rw [smallCert13_2] - norm_num - -def smallB13_3 : Equiv.Perm (Fin 13) := Equiv.swap 11 2 * (Equiv.swap 2 8 * (Equiv.swap 8 6 * (Equiv.swap 6 3 * (Equiv.swap 1 10 * (Equiv.swap 3 0 * (Equiv.swap 2 9 * (Equiv.swap 1 4 * (Equiv.swap 0 12)))))))) -def smallT13_3 : Equiv.Perm (Fin 13) := Equiv.swap 2 0 * (Equiv.swap 0 6 * (Equiv.swap 0 10 * (Equiv.swap 2 4 * (Equiv.swap 4 5 * (Equiv.swap 6 12 * (Equiv.swap 5 11 * (Equiv.swap 4 7 * (Equiv.swap 0 1 * (Equiv.swap 2 8 * (Equiv.swap 1 9 * (Equiv.swap 0 3))))))))))) -def smallFlag13_3 : Finset (ℕ × ℕ × ℕ) := {(3,0,1),(0,0,2),(4,0,2),(0,1,0),(2,1,0),(0,1,1),(0,2,1),(0,2,3),(1,3,0),(5,3,3)} - -def smallChoices13_3 : EdgeChoices := (.node 2 (fun v => if v = (0,0,2) then (.node 1 (fun v => if v = (0,1,0) then (.node 4 (fun v => if v = (0,1,1) then (.node 0 (fun v => if v = (0,0,2) then (.node 6 (fun v => if v = (0,2,1) then (.node 7 (fun _ => (.node 0 (fun v => if v = (1,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 7 (fun _ => (.node 0 (fun v => if v = (1,3,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else if v = (0,2,1) then (.node 6 (fun v => if v = (0,0,2) then (.node 2 (fun v => if v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun v => if v = (0,1,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _ => (.node 1 (fun _ => (.node 3 (fun v => if v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 6 (fun v => if v = (0,0,2) then (.node 7 (fun v => if v = (0,2,1) then (.node 0 (fun v => if v = (1,3,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 0 (fun v => if v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 4 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 3 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=> (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => .fallback)))) else if v = (2,1,0) then (.node 3 (fun v => if v = (0,1,1) then (.node 0 (fun v => if v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun v => if v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun v => if v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else if v = (0,1,0) then (.node 5 (fun v => if v = (0,0,2) then (.node 2 (fun _ => (.node 3 (fun v => if v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 3 (fun v => if v = (0,1,1) then (.node 3 (fun _ => .fallback)) else 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.fallback)))))))))))))))))) else (.node 6 (fun v => if v = (0,0,2) then (.node 2 (fun v => if v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun v => if v = (0,1,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _ => (.node 1 (fun _ => (.node 3 (fun v => if v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))))) else if v = (0,1,1) then (.node 4 (fun _ => (.node 0 (fun v => if v = (0,0,2) then (.node 6 (fun v => if v = (0,2,1) then (.node 7 (fun _ => 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-lemma smallCert13_3 : solveChoices smallChoices13_3 (.full [6,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [6,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_3 smallT13_3) smallFlag13_3 = -2 := by - decide +kernel - -lemma smallSupport13_3 : RowSquare [4,4,3,2] [8,1,1,1,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [6,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_3 smallT13_3 smallFlag13_3 smallChoices13_3 - change solveChoices smallChoices13_3 (.full [6,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [6,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_3 smallT13_3) smallFlag13_3 ≠ 0 - rw [smallCert13_3] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Choice certificates in degree thirteen. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_0 : Equiv.Perm (Fin 13) := Equiv.swap 1 12 * (Equiv.swap 6 3 * (Equiv.swap 6 5 * (Equiv.swap 6 7 * (Equiv.swap 5 0 * (Equiv.swap 3 9 * (Equiv.swap 2 4 * (Equiv.swap 1 11 * (Equiv.swap 0 8)))))))) +def smallT13_0 : Equiv.Perm (Fin 13) := Equiv.swap 0 12 * (Equiv.swap 6 3 * (Equiv.swap 3 2 * (Equiv.swap 6 9 * (Equiv.swap 6 7 * (Equiv.swap 0 10 * (Equiv.swap 0 5 * (Equiv.swap 3 8 * (Equiv.swap 2 1 * (Equiv.swap 1 11 * (Equiv.swap 0 4)))))))))) +def smallFlag13_0 : Finset (ℕ × ℕ × ℕ) := {(4,0,0),(6,0,1),(5,0,2),(2,0,3),(0,1,0),(0,1,1),(3,1,2),(1,2,0),(0,2,2),(0,2,3),(0,3,1)} + +def smallChoices13_0 : EdgeChoices := (.node 1 (fun v => if v = (0,1,0) then (.node 1 (fun v => if v = (0,2,2) then (.node 6 (fun v => if v = (0,1,0) then (.node 0 (fun v => if v = (6,0,1) then (.node 1 (fun _ => (.node 7 (fun _ => (.node 0 (fun v => if v = (4,0,0) then (.node 0 (fun v => if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if v = (5,0,2) then (.node 0 (fun v => if v = (4,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun v => if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun v => if v = (0,1,0) then (.node 0 (fun v => if v = (6,0,1) then (.node 1 (fun v => if v = (5,0,2) then (.node 0 (fun v => if v = (1,2,0) then (.node 5 (fun v => if v = (2,0,3) then (.node 5 (fun v => if v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if v = (0,2,2) then (.node 6 (fun _ => (.node 0 (fun v => if v = (4,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 6 (fun _ => (.node 5 (fun v => if v = (4,0,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _ => (.node 0 (fun v => if v = (4,0,0) then (.node 0 (fun v => if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if v = (5,0,2) then (.node 0 (fun v => if v = (4,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 5 (fun _ => (.node 5 (fun _ => .fallback)))))))))) else (.node 0 (fun v => if v = (6,0,1) then (.node 1 (fun v => if v = (4,0,0) then (.node 0 (fun v => if v = (1,2,0) then (.node 6 (fun v => if v = (0,1,0) then (.node 0 (fun v => if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if v = (0,1,1) then (.node 0 (fun v => if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (2,0,3) then (.node 0 (fun v => if v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 4 (fun v => if v = (2,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if v = (0,1,0) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if v = (0,2,2) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 6 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun v => if v = (4,0,0) then (.node 6 (fun v => if v = (0,1,0) then (.node 0 (fun v => if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (2,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ 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(fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if v = (0,1,1) then (.node 5 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun v => if v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (0,2,3) then (.node 0 (fun v => if v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 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then (.node 2 (fun v => if v = (0,1,0) then (.node 0 (fun v => if v = (0,2,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun v => if v = (5,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if v = (0,2,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun v => if v = (5,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if v = (5,0,2) then (.node 5 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun v => if v = (4,0,0) then (.node 0 (fun v => if v = (6,0,1) then (.node 0 (fun v => if v = (0,2,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if v = (6,0,1) then (.node 0 (fun v => if v = (4,0,0) then (.node 0 (fun v => if v = (0,2,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 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(.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun v => if v = (6,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 6 (fun _ => .fallback)))))))) else (.node 6 (fun v => if v = (0,1,0) then (.node 0 (fun v => if v = (4,0,0) then (.node 1 (fun v => if v = (5,0,2) then (.node 0 (fun v => if v = (1,2,0) then (.node 6 (fun v => if v = (0,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else if v = (0,1,1) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 4 (fun v => if v = 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(fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun v => if v = (6,0,1) then (.node 0 (fun v => if v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))) else if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 0 (fun v => if v = (4,0,0) then (.node 6 (fun v => if v = (6,0,1) then (.node 0 (fun v => if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (2,0,3) then (.node 0 (fun v => if v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else if v = (5,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun v => if v = (6,0,1) then (.node 0 (fun v => if v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))) else if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if v = (6,0,1) then (.node 2 (fun v => if v = (0,1,0) then (.node 0 (fun v => if v = (0,2,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun v => if v = (5,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if v = (0,2,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun v => if v = (5,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if v = (5,0,2) then (.node 5 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun v => if v = (4,0,0) then (.node 0 (fun v => if v = (6,0,1) then (.node 0 (fun v => if v = (0,2,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if v = (6,0,1) then (.node 0 (fun v => if v = (4,0,0) then (.node 0 (fun v => if v = (0,2,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (5,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 6 (fun v => if v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 5 (fun v => if v = (4,0,0) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if v = (2,0,3) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 5 (fun v => if v = (6,0,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if v = (2,0,3) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_0 : solveChoices smallChoices13_0 (.full [7,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [7,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_0 smallT13_0) smallFlag13_0 = 116 := by + decide +kernel + +lemma smallSupport13_0 : RowSquare [4,4,3,2] [7,1,1,1,1,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [7,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_0 smallT13_0 smallFlag13_0 smallChoices13_0 + change solveChoices smallChoices13_0 (.full [7,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [7,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_0 smallT13_0) smallFlag13_0 ≠ 0 + rw [smallCert13_0] + norm_num + +def smallB13_1 : Equiv.Perm (Fin 13) := Equiv.swap 9 0 * (Equiv.swap 9 6 * (Equiv.swap 7 10 * (Equiv.swap 6 11 * (Equiv.swap 3 5 * (Equiv.swap 0 12))))) +def smallT13_1 : Equiv.Perm (Fin 13) := Equiv.swap 10 6 * (Equiv.swap 6 3 * (Equiv.swap 6 7 * (Equiv.swap 7 9 * (Equiv.swap 6 5 * (Equiv.swap 5 2 * (Equiv.swap 3 1 * (Equiv.swap 3 4 * (Equiv.swap 2 8 * (Equiv.swap 1 0 * (Equiv.swap 0 11)))))))))) +def smallFlag13_1 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,1),(0,1,1),(3,1,2),(2,1,3),(5,2,0),(0,2,2),(0,2,3),(4,3,1),(1,3,2)} + +def smallChoices13_1 : EdgeChoices := (.node 0 (fun v => if v = (0,0,0) then (.node 5 (fun v => if v = (0,0,1) then (.node 0 (fun v => if v = (0,1,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if v = (0,2,2) then (.node 6 (fun _ => (.node 2 (fun v => if v = (2,1,3) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 4 (fun v => if v = (3,1,2) then (.node 6 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 6 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else if v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun v => if v = (0,2,2) then (.node 6 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 2 (fun v => if v = (3,1,2) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun v => if v = (0,2,2) then (.node 6 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun v => if v = (3,1,2) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun v => if v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun v => if v = (0,2,2) then (.node 6 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 2 (fun v => if v = (3,1,2) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))))) else if v = (0,1,1) then (.node 4 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 4 (fun v => if v = (4,3,1) then (.node 7 (fun v => if v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 7 (fun _ => (.node 0 (fun v => if v = (0,0,0) then (.node 4 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun v => if v = (0,2,2) then (.node 7 (fun _ => (.node 0 (fun v => if v = (4,3,1) then (.node 1 (fun v => if v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun v => if v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if v = (0,2,3) then (.node 3 (fun v => if v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun v => if v = (3,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun v => if v = (3,1,2) then (.node 0 (fun v => if v = (4,3,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun v => if v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun v => if v = (0,2,2) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun v => if v = (4,3,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (0,2,3) then (.node 3 (fun _ => (.node 0 (fun v => if v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 2 (fun v => if v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun v => if v = (0,2,2) then (.node 7 (fun _ => (.node 0 (fun v => if v = (4,3,1) then (.node 1 (fun v => if v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun v => if v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if v = (0,2,3) then (.node 3 (fun v => if v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun v => if v = (3,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun v => if v = (3,1,2) then (.node 0 (fun v => if v = (4,3,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun v => if v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 4 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 5 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 2 (fun v => if v = (0,1,1) then (.node 3 (fun _ => .fallback)) else if v = (2,1,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))) else if v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun v => if v = (0,1,1) then (.node 0 (fun v => if v = (0,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if v = (0,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun v => if v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (0,2,2) then (.node 4 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun v => if v = (0,1,1) then (.node 3 (fun _ => 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then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun v => if v = (0,1,1) then (.node 0 (fun v => if v = (2,1,3) then (.node 2 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (5,2,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (0,2,2) then (.node 4 (fun v => if v = (0,1,1) then (.node 0 (fun v => if v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 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else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 5 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun v => if v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if v = (0,0,1) then (.node 0 (fun _ => (.node 5 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun v => if v = (0,1,1) then (.node 1 (fun v => if v = (0,0,0) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 5 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 5 (fun v => if v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun v => if v = (0,1,1) then (.node 1 (fun v => if v = (0,0,0) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 5 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 4 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 5 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => 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(fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun v => if v = (0,1,1) then (.node 5 (fun v => if v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun v => if v = (4,3,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))) else if v = (0,2,2) then (.node 5 (fun v => if v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun v => if v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun v => if v = (0,0,1) then (.node 2 (fun _ => .fallback)) else if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun v => if v = (0,1,1) then (.node 0 (fun v => if v = (4,3,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))) else (.node 1 (fun v => if v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (0,2,2) then (.node 3 (fun v => if v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun v => if v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if v = (0,0,1) then (.node 0 (fun _ => (.node 5 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun v => if v = (1,0,0) then (.node 2 (fun v => if v = (3,1,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (2,1,3) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun v => if v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun v => if v = (0,0,0) then (.node 2 (fun v => if v = (3,1,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (2,1,3) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun v => if v = (3,1,2) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun v => if v = (0,1,1) then (.node 5 (fun v => if v = (0,2,2) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if v = (0,2,2) then (.node 5 (fun v => if v = (0,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun v => if v = (0,0,0) then (.node 2 (fun _ => .fallback)) else if v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (0,2,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun v => if v = (0,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 5 (fun v => if v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun v => if v = (1,0,0) then (.node 2 (fun v => if v = (3,1,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (2,1,3) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun v => if v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun v => if v = (1,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun v => if v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 5 (fun v => if v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun v => if v = (1,0,0) then (.node 2 (fun v => if v = (3,1,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (2,1,3) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun v => if v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun v => if v = (0,0,0) then (.node 2 (fun v => if v = (3,1,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (2,1,3) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun v => if v = (3,1,2) then (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun v => if v = (0,1,1) then (.node 5 (fun v => if v = (0,2,2) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if v = (0,2,2) then (.node 5 (fun v => if v = (0,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun v => if v = (0,0,0) then (.node 2 (fun _ => .fallback)) else if v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if v = (0,2,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun v => if v = (0,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert13_1 : solveChoices smallChoices13_1 (.full [6,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [6,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_1 smallT13_1) smallFlag13_1 = 15 := by + decide +kernel + +lemma smallSupport13_1 : RowSquare [4,4,3,2] [6,3,1,1,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [6,2,2,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_1 smallT13_1 smallFlag13_1 smallChoices13_1 + change solveChoices smallChoices13_1 (.full [6,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [6,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_1 smallT13_1) smallFlag13_1 ≠ 0 + rw [smallCert13_1] + norm_num + +def smallB13_2 : Equiv.Perm (Fin 13) := Equiv.swap 7 12 * (Equiv.swap 7 8 * (Equiv.swap 7 5 * (Equiv.swap 8 4 * (Equiv.swap 7 3 * (Equiv.swap 5 10 * (Equiv.swap 5 6 * (Equiv.swap 4 0 * (Equiv.swap 3 9 * (Equiv.swap 1 2 * (Equiv.swap 0 11)))))))))) +def smallT13_2 : Equiv.Perm (Fin 13) := Equiv.swap 10 5 * (Equiv.swap 5 6 * (Equiv.swap 3 2 * (Equiv.swap 6 12 * (Equiv.swap 5 0 * (Equiv.swap 1 11 * (Equiv.swap 3 7 * (Equiv.swap 2 9 * (Equiv.swap 1 4 * (Equiv.swap 0 8))))))))) +def smallFlag13_2 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(3,1,1),(0,1,2),(4,1,2),(0,1,3),(5,2,0),(0,2,1),(0,2,2),(1,3,1),(2,3,3)} + +def smallChoices13_2 : EdgeChoices := (.node 0 (fun v => if v = (0,0,0) then (.node 10 (fun v => if v = (1,0,1) then (.node 0 (fun v => if v = (0,1,2) then (.node 1 (fun v => if v = (0,1,2) then (.node 0 (fun v => if v = (0,2,1) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun v => if v = (0,0,0) then (.node 0 (fun v => if v = (0,1,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if v = (0,2,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun v => if v = (5,2,0) then (.node 0 (fun v => if v = (0,1,3) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun v => if v = (0,1,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun v => if v = (3,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => 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0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun v => if v = (0,0,0) then (.node 0 (fun v => if v = (0,1,2) then (.node 4 (fun _ => (.node 0 (fun v => if v = (4,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun v => if v = (4,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun v => if v = (3,1,1) then (.node 2 (fun v => if v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun v => if v = (4,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => 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(.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 1 (fun v => if v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun v => if v = (3,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))) else (.node 7 (fun _ => (.node 0 (fun v => if v = (0,0,0) then (.node 2 (fun _ => (.node 2 (fun v => if v = (4,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun v => if v = (3,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 8 (fun v => if v = (1,0,1) then (.node 0 (fun _ => (.node 3 (fun v => if v = (4,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 0 (fun v => if v = (0,0,0) then (.node 4 (fun _ => (.node 0 (fun v => if v = (4,1,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun v => if v = (4,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 4 (fun _ => .fallback)))))))))))))))))) +lemma smallCert13_2 : solveChoices smallChoices13_2 (.full [6,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [6,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_2 smallT13_2) smallFlag13_2 = -9 := by + decide +kernel + +lemma smallSupport13_2 : RowSquare [4,4,3,2] [7,2,1,1,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [6,2,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_2 smallT13_2 smallFlag13_2 smallChoices13_2 + change solveChoices smallChoices13_2 (.full [6,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [6,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_2 smallT13_2) smallFlag13_2 ≠ 0 + rw [smallCert13_2] + norm_num + +def smallB13_3 : Equiv.Perm (Fin 13) := Equiv.swap 11 2 * (Equiv.swap 2 8 * (Equiv.swap 8 6 * (Equiv.swap 6 3 * (Equiv.swap 1 10 * (Equiv.swap 3 0 * (Equiv.swap 2 9 * (Equiv.swap 1 4 * (Equiv.swap 0 12)))))))) +def smallT13_3 : Equiv.Perm (Fin 13) := Equiv.swap 2 0 * (Equiv.swap 0 6 * (Equiv.swap 0 10 * (Equiv.swap 2 4 * (Equiv.swap 4 5 * (Equiv.swap 6 12 * (Equiv.swap 5 11 * (Equiv.swap 4 7 * (Equiv.swap 0 1 * (Equiv.swap 2 8 * (Equiv.swap 1 9 * (Equiv.swap 0 3))))))))))) +def smallFlag13_3 : Finset (ℕ × ℕ × ℕ) := {(3,0,1),(0,0,2),(4,0,2),(0,1,0),(2,1,0),(0,1,1),(0,2,1),(0,2,3),(1,3,0),(5,3,3)} + +def smallChoices13_3 : EdgeChoices := (.node 2 (fun v => if v = (0,0,2) then (.node 1 (fun v => if v = (0,1,0) then (.node 4 (fun v => if v = (0,1,1) then (.node 0 (fun v => if v = (0,0,2) then (.node 6 (fun v => if v = (0,2,1) then (.node 7 (fun _ => (.node 0 (fun v => if v = (1,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 7 (fun _ => (.node 0 (fun v => if v = (1,3,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else if v = (0,2,1) then (.node 6 (fun v => if v = (0,0,2) then (.node 2 (fun v => if v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun v => if v = (0,1,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => 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=> if v = (3,0,1) then (.node 0 (fun _ => (.node 1 (fun v => if v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun v => if v = (3,0,1) then (.node 0 (fun v => if v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun v => if v = (3,0,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun v => if v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun v => if v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _ => (.node 4 (fun v => if v = (0,0,2) then (.node 1 (fun v => if v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun v => if v = (1,3,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun v => if v = (0,1,0) then (.node 0 (fun v => if v = (0,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun v => if v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun v => if v = (0,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun v => if v = (3,0,1) then (.node 0 (fun v => if v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if v = (0,1,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun v => if v = (0,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if v = (0,1,0) then (.node 8 (fun v => if v = (3,0,1) then (.node 0 (fun v => if v = (1,3,0) then (.node 6 (fun v => if v = (0,1,0) then (.node 3 (fun _ => .fallback)) else (.node 5 (fun v => if v = (0,0,2) then (.node 3 (fun _ => .fallback)) else (.node 1 (fun v => if v = (0,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun v => if v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun v => if v = (3,0,1) then (.node 0 (fun v => if v = (0,0,2) then (.node 3 (fun _ => .fallback)) else (.node 1 (fun v => if v = (0,2,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun v => if v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _ => .fallback)))))) else (.node 1 (fun v => if v = (0,0,2) then (.node 0 (fun v => if v = (0,2,1) then (.node 0 (fun v => if v = (1,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun v => if v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun v => if v = (3,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun v => if v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun v => if v = (1,3,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun v => if v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun v => if v = (3,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun v => if v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) +lemma smallCert13_3 : solveChoices smallChoices13_3 (.full [6,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [6,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_3 smallT13_3) smallFlag13_3 = -2 := by + decide +kernel + +lemma smallSupport13_3 : RowSquare [4,4,3,2] [8,1,1,1,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [6,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_3 smallT13_3 smallFlag13_3 smallChoices13_3 + change solveChoices smallChoices13_3 (.full [6,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [6,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_3 smallT13_3) smallFlag13_3 ≠ 0 + rw [smallCert13_3] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks116.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks116.lean index d813fc426e5aa30cd387a6048362b75fce258426..fc757b16ce28742577954c05213f26b04535c763 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks116.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks116.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover116 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions116 - -namespace OAI - -/-! Degree Checks 116. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck116 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - semanticResidualCheck 116 12 19 (d+1) (e+1) (a+1) (c+1) degreeRows116_0 degreeP116 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked116 (degreeCover116 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover116 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions116 + +namespace OAI + +/-! Degree Checks 116. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck116 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + semanticResidualCheck 116 12 19 (d+1) (e+1) (a+1) (c+1) degreeRows116_0 degreeP116 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked116 (degreeCover116 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks118.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks118.lean index b5d1bb91458d753785546e87115017a5cd94a186..cd9e723b11b3f4dc41f5b6bb3cab7545ca649784 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks118.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks118.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover118 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions118 - -namespace OAI - -/-! Degree Checks 118. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck118 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - semanticResidualCheck 118 12 20 (d+1) (e+1) (a+1) (c+1) degreeRows118_0 degreeP118 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked118 (degreeCover118 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover118 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions118 + +namespace OAI + +/-! Degree Checks 118. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck118 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + semanticResidualCheck 118 12 20 (d+1) (e+1) (a+1) (c+1) degreeRows118_0 degreeP118 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked118 (degreeCover118 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks14.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks14.lean index 440f1524a5b6955d13a9a778341a394f933afe22..1bd9a4f9fee479ebc0cc25711abc5507ecf94734 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks14.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks14.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover14 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions14 - -namespace OAI - -/-! Degree Checks 14. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck14 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - semanticResidualCheck 14 4 2 (d+1) (e+1) (a+1) (c+1) degreeRows14_0 degreeP14 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked14 (degreeCover14 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover14 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions14 + +namespace OAI + +/-! Degree Checks 14. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck14 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + semanticResidualCheck 14 4 2 (d+1) (e+1) (a+1) (c+1) degreeRows14_0 degreeP14 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked14 (degreeCover14 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks16.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks16.lean index 9b60fe83c15ea04110fd2c99142ae1af9ae1f8e4..06aff185eb382cee13d6ad5e4365491ec5cfa1a7 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks16.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks16.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover16 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions16 - -namespace OAI - -/-! Degree Checks 16. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck16 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - semanticResidualCheck 16 4 3 (d+1) (e+1) (a+1) (c+1) degreeRows16_0 degreeP16 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked16 (degreeCover16 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover16 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions16 + +namespace OAI + +/-! Degree Checks 16. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck16 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + semanticResidualCheck 16 4 3 (d+1) (e+1) (a+1) (c+1) degreeRows16_0 degreeP16 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked16 (degreeCover16 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks18.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks18.lean index cd98a5c1f39a5a87ee9a990e3d4d336a629c04e6..62007f893688e9ce7b3bea019a2d784c95ed2ada 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks18.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks18.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover18 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions18 - -namespace OAI - -/-! Degree Checks 18. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck18 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - semanticResidualCheck 18 4 4 (d+1) (e+1) (a+1) (c+1) degreeRows18_0 degreeP18 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked18 (degreeCover18 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover18 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions18 + +namespace OAI + +/-! Degree Checks 18. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck18 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + semanticResidualCheck 18 4 4 (d+1) (e+1) (a+1) (c+1) degreeRows18_0 degreeP18 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked18 (degreeCover18 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks19.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks19.lean index 20314e1715dd1d21fac63ab9e2ebcbeb8f7b2f93..651f1ba2b2879d1f4a5ed27b6d378910b61a2a30 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks19.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks19.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover19 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions19 - -namespace OAI - -/-! Degree Checks 19. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck19 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - semanticResidualCheck 19 5 2 (d+1) (e+1) (a+1) (c+1) degreeRows19_0 degreeP19 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked19 (degreeCover19 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover19 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions19 + +namespace OAI + +/-! Degree Checks 19. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck19 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + semanticResidualCheck 19 5 2 (d+1) (e+1) (a+1) (c+1) degreeRows19_0 degreeP19 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked19 (degreeCover19 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks20.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks20.lean index 30921734b7d1a38ac064d900f9bd6ed762d0e1a6..5dc0d537e66a3ea588351c977973248f156d4cd3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks20.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks20.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover20 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions20 - -namespace OAI - -/-! Degree Checks 20. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck20 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - semanticResidualCheck 20 4 5 (d+1) (e+1) (a+1) (c+1) degreeRows20_0 degreeP20 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked20 (degreeCover20 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover20 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions20 + +namespace OAI + +/-! Degree Checks 20. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck20 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + semanticResidualCheck 20 4 5 (d+1) (e+1) (a+1) (c+1) degreeRows20_0 degreeP20 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked20 (degreeCover20 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks22.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks22.lean index f4d7faafbd3e9d2cc74f5639ddb70ce819e35bfa..0b2a5a195b363248625e12ed040636c2c05b7ff7 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks22.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks22.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover22 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions22 - -namespace OAI - -/-! Degree Checks 22. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck22 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - semanticResidualCheck 22 4 6 (d+1) (e+1) (a+1) (c+1) degreeRows22_0 degreeP22 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked22 (degreeCover22 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover22 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions22 + +namespace OAI + +/-! Degree Checks 22. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck22 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + semanticResidualCheck 22 4 6 (d+1) (e+1) (a+1) (c+1) degreeRows22_0 degreeP22 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked22 (degreeCover22 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks24.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks24.lean index e271e4c99618240dfef085ee4e21458c0b2b11eb..44be0718263a17f79aa2c908fe901ec0f7ecb61e 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks24.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks24.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover24 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions24 - -namespace OAI - -/-! Degree Checks 24. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck24 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - semanticResidualCheck 24 4 7 (d+1) (e+1) (a+1) (c+1) degreeRows24_0 degreeP24 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked24 (degreeCover24 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover24 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions24 + +namespace OAI + +/-! Degree Checks 24. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck24 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + semanticResidualCheck 24 4 7 (d+1) (e+1) (a+1) (c+1) degreeRows24_0 degreeP24 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked24 (degreeCover24 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks26.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks26.lean index a1de74ae43ff5c228518b2d35d466185264f3a55..ceed0c97efbe206b297f1f49371405ff62393950 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks26.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks26.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover26 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions26 - -namespace OAI - -/-! Degree Checks 26. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck26 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - semanticResidualCheck 26 4 8 (d+1) (e+1) (a+1) (c+1) degreeRows26_0 degreeP26 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked26 (degreeCover26 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover26 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions26 + +namespace OAI + +/-! Degree Checks 26. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck26 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + semanticResidualCheck 26 4 8 (d+1) (e+1) (a+1) (c+1) degreeRows26_0 degreeP26 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked26 (degreeCover26 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks31.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks31.lean index 0468a60f97b9e16894f93675a866019b7f91b5aa..d243d704e53bb89a46ccce09e76d6d68d6413074 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks31.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks31.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover31 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions31 - -namespace OAI - -/-! Degree Checks 31. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck31 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - semanticResidualCheck 31 6 5 (d+1) (e+1) (a+1) (c+1) degreeRows31_0 degreeP31 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked31 (degreeCover31 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover31 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions31 + +namespace OAI + +/-! Degree Checks 31. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck31 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + semanticResidualCheck 31 6 5 (d+1) (e+1) (a+1) (c+1) degreeRows31_0 degreeP31 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked31 (degreeCover31 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks35.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks35.lean index e9395ce1e2ae6616e734db87cadc57a016f6fbb1..08f620b1d89b9a1f427f2407cb4c22e0ab441aeb 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks35.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks35.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover35 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions35 - -namespace OAI - -/-! Degree Checks 35. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck35 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - semanticResidualCheck 35 6 7 (d+1) (e+1) (a+1) (c+1) degreeRows35_0 degreeP35 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked35 (degreeCover35 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover35 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions35 + +namespace OAI + +/-! Degree Checks 35. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck35 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + semanticResidualCheck 35 6 7 (d+1) (e+1) (a+1) (c+1) degreeRows35_0 degreeP35 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked35 (degreeCover35 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks37.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks37.lean index e3e74e1677580388c637e9591b8f7be5e873bfd9..24651d13974f575730f461e401efd3637e560b35 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks37.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks37.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover37 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions37 - -namespace OAI - -/-! Degree Checks 37. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck37 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - semanticResidualCheck 37 6 8 (d+1) (e+1) (a+1) (c+1) degreeRows37_0 degreeP37 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked37 (degreeCover37 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover37 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions37 + +namespace OAI + +/-! Degree Checks 37. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck37 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + semanticResidualCheck 37 6 8 (d+1) (e+1) (a+1) (c+1) degreeRows37_0 degreeP37 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked37 (degreeCover37 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks39.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks39.lean index 60401ccdb48453afc601f1d16cb6d834c131449f..ffb53f30647b13a9ebbb9afc213cf7b5fa5ba8f0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks39.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks39.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover39 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions39 - -namespace OAI - -/-! Degree Checks 39. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck39 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - semanticResidualCheck 39 6 9 (d+1) (e+1) (a+1) (c+1) degreeRows39_0 degreeP39 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked39 (degreeCover39 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover39 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions39 + +namespace OAI + +/-! Degree Checks 39. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck39 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + semanticResidualCheck 39 6 9 (d+1) (e+1) (a+1) (c+1) degreeRows39_0 degreeP39 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked39 (degreeCover39 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks41.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks41.lean index 69dcf2f71daaefdc4bd8d3c2cf160c135972e4fe..a38a3f01fbc066a9ecaf4bb1a285a6420afc29c2 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks41.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks41.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover41 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions41 - -namespace OAI - -/-! Degree Checks 41. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck41 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - semanticResidualCheck 41 6 10 (d+1) (e+1) (a+1) (c+1) degreeRows41_0 degreeP41 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked41 (degreeCover41 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover41 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions41 + +namespace OAI + +/-! Degree Checks 41. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck41 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + semanticResidualCheck 41 6 10 (d+1) (e+1) (a+1) (c+1) degreeRows41_0 degreeP41 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked41 (degreeCover41 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks43.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks43.lean index a5375e74d5319801715f4ec8449340be7e6e4e05..1078a14a2e82a801841ddc4fba7b39f4bf4cc753 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks43.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks43.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover43 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions43 - -namespace OAI - -/-! Degree Checks 43. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck43 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - semanticResidualCheck 43 6 11 (d+1) (e+1) (a+1) (c+1) degreeRows43_0 degreeP43 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked43 (degreeCover43 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover43 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions43 + +namespace OAI + +/-! Degree Checks 43. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck43 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + semanticResidualCheck 43 6 11 (d+1) (e+1) (a+1) (c+1) degreeRows43_0 degreeP43 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked43 (degreeCover43 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks58.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks58.lean index a902f3752753460d533f80e40abf76217c093a28..555cd3fde3701e6c0544f536a99c3ee27cafe770 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks58.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks58.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover58 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions58 - -namespace OAI - -/-! Degree Checks 58. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck58 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - semanticResidualCheck 58 8 11 (d+1) (e+1) (a+1) (c+1) degreeRows58_0 degreeP58 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked58 (degreeCover58 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover58 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions58 + +namespace OAI + +/-! Degree Checks 58. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck58 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + semanticResidualCheck 58 8 11 (d+1) (e+1) (a+1) (c+1) degreeRows58_0 degreeP58 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked58 (degreeCover58 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks62.lean index ea7c2ef8bbc20460aa577d8a349ea4ee84d1c023..c8e18e8372a972605d891d8c45ac3cce612c02f7 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks62.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover62 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions62 - -namespace OAI - -/-! Degree Checks 62. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck62 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - semanticResidualCheck 62 8 13 (d+1) (e+1) (a+1) (c+1) degreeRows62_0 degreeP62 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked62 (degreeCover62 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover62 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions62 + +namespace OAI + +/-! Degree Checks 62. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck62 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + semanticResidualCheck 62 8 13 (d+1) (e+1) (a+1) (c+1) degreeRows62_0 degreeP62 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked62 (degreeCover62 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks64.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks64.lean index 7cb4278341b4323f63ee2825443c404a95a58629..072bc1658c3280e06622eb3cc4b68550326444f9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks64.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks64.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover64 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions64 - -namespace OAI - -/-! Degree Checks 64. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck64 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - semanticResidualCheck 64 8 14 (d+1) (e+1) (a+1) (c+1) degreeRows64_0 degreeP64 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked64 (degreeCover64 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover64 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions64 + +namespace OAI + +/-! Degree Checks 64. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck64 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + semanticResidualCheck 64 8 14 (d+1) (e+1) (a+1) (c+1) degreeRows64_0 degreeP64 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked64 (degreeCover64 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks89.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks89.lean index c231af96d9bf199a0d0afda0153c1506e7f437ad..579f5800e6bcb1c8c12d2be7d477ebfd7c7445e3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks89.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeChecks89.lean @@ -1,26 +1,26 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover89 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions89 - -namespace OAI - -/-! Degree Checks 89. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCheck89 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - semanticResidualCheck 89 10 17 (d+1) (e+1) (a+1) (c+1) degreeRows89_0 degreeP89 := by - intro d hd e he a ha c hc - exact regionCheck_sound_diagram degreeDiagramRegionsChecked89 (degreeCover89 d hd e he a ha c hc) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeCover89 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegions89 + +namespace OAI + +/-! Degree Checks 89. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCheck89 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + semanticResidualCheck 89 10 17 (d+1) (e+1) (a+1) (c+1) degreeRows89_0 degreeP89 := by + intro d hd e he a ha c hc + exact regionCheck_sound_diagram degreeDiagramRegionsChecked89 (degreeCover89 d hd e he a ha c hc) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover116.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover116.lean index 0ae5242c34c026e52a707ac0ed7ba230ca1f379b..02b04db17d5f7e9a8d39d797f326f8749ec8839c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover116.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover116.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans116 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData116 - -namespace OAI - -/-! Degree Cover 116. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover116_0_0 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 1 1 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_0_1 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 1 2 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_0_2 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 1 3 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_0_3 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 1 4 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_0_4 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 1 5 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_1_0 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 2 1 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_1_1 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 2 2 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_1_2 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 2 3 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_1_3 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 2 4 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_1_4 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 2 5 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_2_0 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 3 1 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_2_1 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 3 2 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_2_2 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 3 3 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_2_3 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 3 4 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_2_4 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 3 5 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_3_0 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 4 1 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_3_1 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 4 2 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_3_2 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 4 3 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_3_3 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 4 4 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_3_4 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 4 5 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_4_0 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 5 1 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_4_1 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 5 2 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_4_2 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 5 3 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_4_3 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 5 4 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116_4_4 : - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 5 5 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - decide +kernel - -lemma degreeCover116 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, - regionCheck 116 12 19 (d+1) (e+1) (a+1) (c+1) degreeRows116_0 degreeRegions116 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover116_0_0 - · exact degreeCover116_0_1 - · exact degreeCover116_0_2 - · exact degreeCover116_0_3 - · exact degreeCover116_0_4 - · exact degreeCover116_1_0 - · exact degreeCover116_1_1 - · exact degreeCover116_1_2 - · exact degreeCover116_1_3 - · exact degreeCover116_1_4 - · exact degreeCover116_2_0 - · exact degreeCover116_2_1 - · exact degreeCover116_2_2 - · exact degreeCover116_2_3 - · exact degreeCover116_2_4 - · exact degreeCover116_3_0 - · exact degreeCover116_3_1 - · exact degreeCover116_3_2 - · exact degreeCover116_3_3 - · exact degreeCover116_3_4 - · exact degreeCover116_4_0 - · exact degreeCover116_4_1 - · exact degreeCover116_4_2 - · exact degreeCover116_4_3 - · exact degreeCover116_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans116 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData116 + +namespace OAI + +/-! Degree Cover 116. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover116_0_0 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 1 1 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_0_1 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 1 2 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_0_2 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 1 3 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_0_3 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 1 4 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_0_4 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 1 5 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_1_0 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 2 1 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_1_1 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 2 2 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_1_2 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 2 3 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_1_3 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 2 4 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_1_4 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 2 5 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_2_0 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 3 1 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_2_1 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 3 2 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_2_2 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 3 3 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_2_3 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 3 4 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_2_4 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 3 5 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_3_0 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 4 1 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_3_1 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 4 2 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_3_2 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 4 3 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_3_3 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 4 4 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_3_4 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 4 5 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_4_0 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 5 1 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_4_1 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 5 2 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_4_2 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 5 3 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_4_3 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 5 4 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116_4_4 : + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 5 5 (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + decide +kernel + +lemma degreeCover116 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows116_0.length, ∀ c ∈ List.range degreeRows116_0.length, + regionCheck 116 12 19 (d+1) (e+1) (a+1) (c+1) degreeRows116_0 degreeRegions116 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover116_0_0 + · exact degreeCover116_0_1 + · exact degreeCover116_0_2 + · exact degreeCover116_0_3 + · exact degreeCover116_0_4 + · exact degreeCover116_1_0 + · exact degreeCover116_1_1 + · exact degreeCover116_1_2 + · exact degreeCover116_1_3 + · exact degreeCover116_1_4 + · exact degreeCover116_2_0 + · exact degreeCover116_2_1 + · exact degreeCover116_2_2 + · exact degreeCover116_2_3 + · exact degreeCover116_2_4 + · exact degreeCover116_3_0 + · exact degreeCover116_3_1 + · exact degreeCover116_3_2 + · exact degreeCover116_3_3 + · exact degreeCover116_3_4 + · exact degreeCover116_4_0 + · exact degreeCover116_4_1 + · exact degreeCover116_4_2 + · exact degreeCover116_4_3 + · exact degreeCover116_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover118.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover118.lean index b786dc0d4ed28b4b86357785ae5d8c3c917c2d11..87c8781213148e675817c2f7dc187a31da59db8f 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover118.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover118.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans118 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData118 - -namespace OAI - -/-! Degree Cover 118. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover118_0_0 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 1 1 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_0_1 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 1 2 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_0_2 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 1 3 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_0_3 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 1 4 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_0_4 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 1 5 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_1_0 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 2 1 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_1_1 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 2 2 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_1_2 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 2 3 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_1_3 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 2 4 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_1_4 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 2 5 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_2_0 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 3 1 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_2_1 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 3 2 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_2_2 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 3 3 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_2_3 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 3 4 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_2_4 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 3 5 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_3_0 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 4 1 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_3_1 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 4 2 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_3_2 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 4 3 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_3_3 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 4 4 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_3_4 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 4 5 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_4_0 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 5 1 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_4_1 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 5 2 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_4_2 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 5 3 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_4_3 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 5 4 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118_4_4 : - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 5 5 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - decide +kernel - -lemma degreeCover118 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, - regionCheck 118 12 20 (d+1) (e+1) (a+1) (c+1) degreeRows118_0 degreeRegions118 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover118_0_0 - · exact degreeCover118_0_1 - · exact degreeCover118_0_2 - · exact degreeCover118_0_3 - · exact degreeCover118_0_4 - · exact degreeCover118_1_0 - · exact degreeCover118_1_1 - · exact degreeCover118_1_2 - · exact degreeCover118_1_3 - · exact degreeCover118_1_4 - · exact degreeCover118_2_0 - · exact degreeCover118_2_1 - · exact degreeCover118_2_2 - · exact degreeCover118_2_3 - · exact degreeCover118_2_4 - · exact degreeCover118_3_0 - · exact degreeCover118_3_1 - · exact degreeCover118_3_2 - · exact degreeCover118_3_3 - · exact degreeCover118_3_4 - · exact degreeCover118_4_0 - · exact degreeCover118_4_1 - · exact degreeCover118_4_2 - · exact degreeCover118_4_3 - · exact degreeCover118_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans118 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData118 + +namespace OAI + +/-! Degree Cover 118. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover118_0_0 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 1 1 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_0_1 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 1 2 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_0_2 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 1 3 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_0_3 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 1 4 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_0_4 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 1 5 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_1_0 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 2 1 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_1_1 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 2 2 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_1_2 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 2 3 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_1_3 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 2 4 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_1_4 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 2 5 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_2_0 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 3 1 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_2_1 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 3 2 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_2_2 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 3 3 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_2_3 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 3 4 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_2_4 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 3 5 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_3_0 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 4 1 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_3_1 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 4 2 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_3_2 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 4 3 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_3_3 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 4 4 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_3_4 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 4 5 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_4_0 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 5 1 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_4_1 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 5 2 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_4_2 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 5 3 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_4_3 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 5 4 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118_4_4 : + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 5 5 (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + decide +kernel + +lemma degreeCover118 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows118_0.length, ∀ c ∈ List.range degreeRows118_0.length, + regionCheck 118 12 20 (d+1) (e+1) (a+1) (c+1) degreeRows118_0 degreeRegions118 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover118_0_0 + · exact degreeCover118_0_1 + · exact degreeCover118_0_2 + · exact degreeCover118_0_3 + · exact degreeCover118_0_4 + · exact degreeCover118_1_0 + · exact degreeCover118_1_1 + · exact degreeCover118_1_2 + · exact degreeCover118_1_3 + · exact degreeCover118_1_4 + · exact degreeCover118_2_0 + · exact degreeCover118_2_1 + · exact degreeCover118_2_2 + · exact degreeCover118_2_3 + · exact degreeCover118_2_4 + · exact degreeCover118_3_0 + · exact degreeCover118_3_1 + · exact degreeCover118_3_2 + · exact degreeCover118_3_3 + · exact degreeCover118_3_4 + · exact degreeCover118_4_0 + · exact degreeCover118_4_1 + · exact degreeCover118_4_2 + · exact degreeCover118_4_3 + · exact degreeCover118_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover14.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover14.lean index 9674f69a3c04b8d50e835db6797e8cc1ce47ae33..8d842ef14595b0b3aece132ef631586cc4c4d998 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover14.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover14.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans14 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData14 - -namespace OAI - -/-! Degree Cover 14. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover14_0_0 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 1 1 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_0_1 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 1 2 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_0_2 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 1 3 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_0_3 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 1 4 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_0_4 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 1 5 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_1_0 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 2 1 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_1_1 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 2 2 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_1_2 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 2 3 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_1_3 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 2 4 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_1_4 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 2 5 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_2_0 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 3 1 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_2_1 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 3 2 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_2_2 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 3 3 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_2_3 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 3 4 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_2_4 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 3 5 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_3_0 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 4 1 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_3_1 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 4 2 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_3_2 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 4 3 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_3_3 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 4 4 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_3_4 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 4 5 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_4_0 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 5 1 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_4_1 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 5 2 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_4_2 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 5 3 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_4_3 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 5 4 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14_4_4 : - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 5 5 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - decide +kernel - -lemma degreeCover14 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, - regionCheck 14 4 2 (d+1) (e+1) (a+1) (c+1) degreeRows14_0 degreeRegions14 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover14_0_0 - · exact degreeCover14_0_1 - · exact degreeCover14_0_2 - · exact degreeCover14_0_3 - · exact degreeCover14_0_4 - · exact degreeCover14_1_0 - · exact degreeCover14_1_1 - · exact degreeCover14_1_2 - · exact degreeCover14_1_3 - · exact degreeCover14_1_4 - · exact degreeCover14_2_0 - · exact degreeCover14_2_1 - · exact degreeCover14_2_2 - · exact degreeCover14_2_3 - · exact degreeCover14_2_4 - · exact degreeCover14_3_0 - · exact degreeCover14_3_1 - · exact degreeCover14_3_2 - · exact degreeCover14_3_3 - · exact degreeCover14_3_4 - · exact degreeCover14_4_0 - · exact degreeCover14_4_1 - · exact degreeCover14_4_2 - · exact degreeCover14_4_3 - · exact degreeCover14_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans14 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData14 + +namespace OAI + +/-! Degree Cover 14. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover14_0_0 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 1 1 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_0_1 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 1 2 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_0_2 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 1 3 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_0_3 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 1 4 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_0_4 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 1 5 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_1_0 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 2 1 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_1_1 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 2 2 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_1_2 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 2 3 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_1_3 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 2 4 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_1_4 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 2 5 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_2_0 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 3 1 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_2_1 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 3 2 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_2_2 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 3 3 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_2_3 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 3 4 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_2_4 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 3 5 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_3_0 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 4 1 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_3_1 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 4 2 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_3_2 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 4 3 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_3_3 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 4 4 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_3_4 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 4 5 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_4_0 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 5 1 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_4_1 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 5 2 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_4_2 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 5 3 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_4_3 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 5 4 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14_4_4 : + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 5 5 (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + decide +kernel + +lemma degreeCover14 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows14_0.length, ∀ c ∈ List.range degreeRows14_0.length, + regionCheck 14 4 2 (d+1) (e+1) (a+1) (c+1) degreeRows14_0 degreeRegions14 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover14_0_0 + · exact degreeCover14_0_1 + · exact degreeCover14_0_2 + · exact degreeCover14_0_3 + · exact degreeCover14_0_4 + · exact degreeCover14_1_0 + · exact degreeCover14_1_1 + · exact degreeCover14_1_2 + · exact degreeCover14_1_3 + · exact degreeCover14_1_4 + · exact degreeCover14_2_0 + · exact degreeCover14_2_1 + · exact degreeCover14_2_2 + · exact degreeCover14_2_3 + · exact degreeCover14_2_4 + · exact degreeCover14_3_0 + · exact degreeCover14_3_1 + · exact degreeCover14_3_2 + · exact degreeCover14_3_3 + · exact degreeCover14_3_4 + · exact degreeCover14_4_0 + · exact degreeCover14_4_1 + · exact degreeCover14_4_2 + · exact degreeCover14_4_3 + · exact degreeCover14_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover16.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover16.lean index 761e317afef03b3abea57716b7579b37d68cd237..1699c0e754a61222d5afc9ca484749133086d5c5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover16.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover16.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans16 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData16 - -namespace OAI - -/-! Degree Cover 16. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover16_0_0 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 1 1 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_0_1 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 1 2 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_0_2 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 1 3 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_0_3 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 1 4 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_0_4 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 1 5 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_1_0 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 2 1 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_1_1 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 2 2 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_1_2 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 2 3 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_1_3 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 2 4 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_1_4 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 2 5 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_2_0 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 3 1 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_2_1 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 3 2 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_2_2 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 3 3 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_2_3 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 3 4 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_2_4 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 3 5 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_3_0 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 4 1 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_3_1 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 4 2 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_3_2 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 4 3 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_3_3 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 4 4 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_3_4 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 4 5 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_4_0 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 5 1 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_4_1 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 5 2 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_4_2 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 5 3 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_4_3 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 5 4 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16_4_4 : - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 5 5 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - decide +kernel - -lemma degreeCover16 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, - regionCheck 16 4 3 (d+1) (e+1) (a+1) (c+1) degreeRows16_0 degreeRegions16 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover16_0_0 - · exact degreeCover16_0_1 - · exact degreeCover16_0_2 - · exact degreeCover16_0_3 - · exact degreeCover16_0_4 - · exact degreeCover16_1_0 - · exact degreeCover16_1_1 - · exact degreeCover16_1_2 - · exact degreeCover16_1_3 - · exact degreeCover16_1_4 - · exact degreeCover16_2_0 - · exact degreeCover16_2_1 - · exact degreeCover16_2_2 - · exact degreeCover16_2_3 - · exact degreeCover16_2_4 - · exact degreeCover16_3_0 - · exact degreeCover16_3_1 - · exact degreeCover16_3_2 - · exact degreeCover16_3_3 - · exact degreeCover16_3_4 - · exact degreeCover16_4_0 - · exact degreeCover16_4_1 - · exact degreeCover16_4_2 - · exact degreeCover16_4_3 - · exact degreeCover16_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans16 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData16 + +namespace OAI + +/-! Degree Cover 16. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover16_0_0 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 1 1 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_0_1 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 1 2 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_0_2 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 1 3 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_0_3 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 1 4 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_0_4 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 1 5 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_1_0 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 2 1 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_1_1 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 2 2 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_1_2 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 2 3 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_1_3 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 2 4 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_1_4 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 2 5 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_2_0 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 3 1 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_2_1 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 3 2 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_2_2 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 3 3 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_2_3 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 3 4 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_2_4 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 3 5 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_3_0 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 4 1 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_3_1 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 4 2 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_3_2 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 4 3 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_3_3 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 4 4 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_3_4 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 4 5 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_4_0 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 5 1 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_4_1 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 5 2 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_4_2 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 5 3 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_4_3 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 5 4 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16_4_4 : + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 5 5 (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + decide +kernel + +lemma degreeCover16 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows16_0.length, ∀ c ∈ List.range degreeRows16_0.length, + regionCheck 16 4 3 (d+1) (e+1) (a+1) (c+1) degreeRows16_0 degreeRegions16 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover16_0_0 + · exact degreeCover16_0_1 + · exact degreeCover16_0_2 + · exact degreeCover16_0_3 + · exact degreeCover16_0_4 + · exact degreeCover16_1_0 + · exact degreeCover16_1_1 + · exact degreeCover16_1_2 + · exact degreeCover16_1_3 + · exact degreeCover16_1_4 + · exact degreeCover16_2_0 + · exact degreeCover16_2_1 + · exact degreeCover16_2_2 + · exact degreeCover16_2_3 + · exact degreeCover16_2_4 + · exact degreeCover16_3_0 + · exact degreeCover16_3_1 + · exact degreeCover16_3_2 + · exact degreeCover16_3_3 + · exact degreeCover16_3_4 + · exact degreeCover16_4_0 + · exact degreeCover16_4_1 + · exact degreeCover16_4_2 + · exact degreeCover16_4_3 + · exact degreeCover16_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover18.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover18.lean index 764cf14f6a47c9915ce7a8b8dbed8ef412740234..936b951021f7629c1010673137bc0e002a6cb526 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover18.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover18.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans18 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData18 - -namespace OAI - -/-! Degree Cover 18. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover18_0_0 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 1 1 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_0_1 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 1 2 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_0_2 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 1 3 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_0_3 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 1 4 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_0_4 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 1 5 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_1_0 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 2 1 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_1_1 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 2 2 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_1_2 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 2 3 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_1_3 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 2 4 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_1_4 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 2 5 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_2_0 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 3 1 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_2_1 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 3 2 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_2_2 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 3 3 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_2_3 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 3 4 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_2_4 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 3 5 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_3_0 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 4 1 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_3_1 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 4 2 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_3_2 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 4 3 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_3_3 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 4 4 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_3_4 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 4 5 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_4_0 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 5 1 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_4_1 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 5 2 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_4_2 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 5 3 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_4_3 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 5 4 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18_4_4 : - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 5 5 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - decide +kernel - -lemma degreeCover18 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, - regionCheck 18 4 4 (d+1) (e+1) (a+1) (c+1) degreeRows18_0 degreeRegions18 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover18_0_0 - · exact degreeCover18_0_1 - · exact degreeCover18_0_2 - · exact degreeCover18_0_3 - · exact degreeCover18_0_4 - · exact degreeCover18_1_0 - · exact degreeCover18_1_1 - · exact degreeCover18_1_2 - · exact degreeCover18_1_3 - · exact degreeCover18_1_4 - · exact degreeCover18_2_0 - · exact degreeCover18_2_1 - · exact degreeCover18_2_2 - · exact degreeCover18_2_3 - · exact degreeCover18_2_4 - · exact degreeCover18_3_0 - · exact degreeCover18_3_1 - · exact degreeCover18_3_2 - · exact degreeCover18_3_3 - · exact degreeCover18_3_4 - · exact degreeCover18_4_0 - · exact degreeCover18_4_1 - · exact degreeCover18_4_2 - · exact degreeCover18_4_3 - · exact degreeCover18_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans18 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData18 + +namespace OAI + +/-! Degree Cover 18. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover18_0_0 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 1 1 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_0_1 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 1 2 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_0_2 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 1 3 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_0_3 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 1 4 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_0_4 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 1 5 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_1_0 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 2 1 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_1_1 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 2 2 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_1_2 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 2 3 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_1_3 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 2 4 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_1_4 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 2 5 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_2_0 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 3 1 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_2_1 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 3 2 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_2_2 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 3 3 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_2_3 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 3 4 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_2_4 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 3 5 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_3_0 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 4 1 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_3_1 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 4 2 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_3_2 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 4 3 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_3_3 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 4 4 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_3_4 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 4 5 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_4_0 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 5 1 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_4_1 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 5 2 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_4_2 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 5 3 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_4_3 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 5 4 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18_4_4 : + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 5 5 (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + decide +kernel + +lemma degreeCover18 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows18_0.length, ∀ c ∈ List.range degreeRows18_0.length, + regionCheck 18 4 4 (d+1) (e+1) (a+1) (c+1) degreeRows18_0 degreeRegions18 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover18_0_0 + · exact degreeCover18_0_1 + · exact degreeCover18_0_2 + · exact degreeCover18_0_3 + · exact degreeCover18_0_4 + · exact degreeCover18_1_0 + · exact degreeCover18_1_1 + · exact degreeCover18_1_2 + · exact degreeCover18_1_3 + · exact degreeCover18_1_4 + · exact degreeCover18_2_0 + · exact degreeCover18_2_1 + · exact degreeCover18_2_2 + · exact degreeCover18_2_3 + · exact degreeCover18_2_4 + · exact degreeCover18_3_0 + · exact degreeCover18_3_1 + · exact degreeCover18_3_2 + · exact degreeCover18_3_3 + · exact degreeCover18_3_4 + · exact degreeCover18_4_0 + · exact degreeCover18_4_1 + · exact degreeCover18_4_2 + · exact degreeCover18_4_3 + · exact degreeCover18_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover19.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover19.lean index 5cb89693cf1b026d8731049f356592ebd1378286..2e1ed3b061ce3fa0d3fa3339cda195c9d6054deb 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover19.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover19.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans19 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData19 - -namespace OAI - -/-! Degree Cover 19. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover19_0_0 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 1 1 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_0_1 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 1 2 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_0_2 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 1 3 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_0_3 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 1 4 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_0_4 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 1 5 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_1_0 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 2 1 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_1_1 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 2 2 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_1_2 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 2 3 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_1_3 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 2 4 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_1_4 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 2 5 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_2_0 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 3 1 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_2_1 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 3 2 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_2_2 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 3 3 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_2_3 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 3 4 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_2_4 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 3 5 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_3_0 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 4 1 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_3_1 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 4 2 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_3_2 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 4 3 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_3_3 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 4 4 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_3_4 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 4 5 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_4_0 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 5 1 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_4_1 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 5 2 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_4_2 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 5 3 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_4_3 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 5 4 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19_4_4 : - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 5 5 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - decide +kernel - -lemma degreeCover19 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, - regionCheck 19 5 2 (d+1) (e+1) (a+1) (c+1) degreeRows19_0 degreeRegions19 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover19_0_0 - · exact degreeCover19_0_1 - · exact degreeCover19_0_2 - · exact degreeCover19_0_3 - · exact degreeCover19_0_4 - · exact degreeCover19_1_0 - · exact degreeCover19_1_1 - · exact degreeCover19_1_2 - · exact degreeCover19_1_3 - · exact degreeCover19_1_4 - · exact degreeCover19_2_0 - · exact degreeCover19_2_1 - · exact degreeCover19_2_2 - · exact degreeCover19_2_3 - · exact degreeCover19_2_4 - · exact degreeCover19_3_0 - · exact degreeCover19_3_1 - · exact degreeCover19_3_2 - · exact degreeCover19_3_3 - · exact degreeCover19_3_4 - · exact degreeCover19_4_0 - · exact degreeCover19_4_1 - · exact degreeCover19_4_2 - · exact degreeCover19_4_3 - · exact degreeCover19_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans19 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData19 + +namespace OAI + +/-! Degree Cover 19. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover19_0_0 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 1 1 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_0_1 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 1 2 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_0_2 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 1 3 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_0_3 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 1 4 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_0_4 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 1 5 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_1_0 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 2 1 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_1_1 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 2 2 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_1_2 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 2 3 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_1_3 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 2 4 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_1_4 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 2 5 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_2_0 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 3 1 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_2_1 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 3 2 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_2_2 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 3 3 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_2_3 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 3 4 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_2_4 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 3 5 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_3_0 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 4 1 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_3_1 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 4 2 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_3_2 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 4 3 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_3_3 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 4 4 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_3_4 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 4 5 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_4_0 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 5 1 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_4_1 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 5 2 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_4_2 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 5 3 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_4_3 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 5 4 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19_4_4 : + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 5 5 (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + decide +kernel + +lemma degreeCover19 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows19_0.length, ∀ c ∈ List.range degreeRows19_0.length, + regionCheck 19 5 2 (d+1) (e+1) (a+1) (c+1) degreeRows19_0 degreeRegions19 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover19_0_0 + · exact degreeCover19_0_1 + · exact degreeCover19_0_2 + · exact degreeCover19_0_3 + · exact degreeCover19_0_4 + · exact degreeCover19_1_0 + · exact degreeCover19_1_1 + · exact degreeCover19_1_2 + · exact degreeCover19_1_3 + · exact degreeCover19_1_4 + · exact degreeCover19_2_0 + · exact degreeCover19_2_1 + · exact degreeCover19_2_2 + · exact degreeCover19_2_3 + · exact degreeCover19_2_4 + · exact degreeCover19_3_0 + · exact degreeCover19_3_1 + · exact degreeCover19_3_2 + · exact degreeCover19_3_3 + · exact degreeCover19_3_4 + · exact degreeCover19_4_0 + · exact degreeCover19_4_1 + · exact degreeCover19_4_2 + · exact degreeCover19_4_3 + · exact degreeCover19_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover20.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover20.lean index bb8b2da930c19c0a276df819b98f8b0f00d9a6a0..beb6e616444af17cfe86d75553551cd9bea48b72 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover20.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover20.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans20 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData20 - -namespace OAI - -/-! Degree Cover 20. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover20_0_0 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 1 1 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_0_1 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 1 2 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_0_2 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 1 3 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_0_3 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 1 4 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_0_4 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 1 5 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_1_0 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 2 1 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_1_1 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 2 2 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_1_2 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 2 3 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_1_3 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 2 4 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_1_4 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 2 5 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_2_0 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 3 1 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_2_1 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 3 2 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_2_2 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 3 3 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_2_3 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 3 4 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_2_4 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 3 5 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_3_0 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 4 1 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_3_1 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 4 2 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_3_2 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 4 3 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_3_3 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 4 4 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_3_4 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 4 5 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_4_0 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 5 1 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_4_1 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 5 2 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_4_2 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 5 3 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_4_3 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 5 4 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20_4_4 : - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 5 5 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - decide +kernel - -lemma degreeCover20 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, - regionCheck 20 4 5 (d+1) (e+1) (a+1) (c+1) degreeRows20_0 degreeRegions20 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover20_0_0 - · exact degreeCover20_0_1 - · exact degreeCover20_0_2 - · exact degreeCover20_0_3 - · exact degreeCover20_0_4 - · exact degreeCover20_1_0 - · exact degreeCover20_1_1 - · exact degreeCover20_1_2 - · exact degreeCover20_1_3 - · exact degreeCover20_1_4 - · exact degreeCover20_2_0 - · exact degreeCover20_2_1 - · exact degreeCover20_2_2 - · exact degreeCover20_2_3 - · exact degreeCover20_2_4 - · exact degreeCover20_3_0 - · exact degreeCover20_3_1 - · exact degreeCover20_3_2 - · exact degreeCover20_3_3 - · exact degreeCover20_3_4 - · exact degreeCover20_4_0 - · exact degreeCover20_4_1 - · exact degreeCover20_4_2 - · exact degreeCover20_4_3 - · exact degreeCover20_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans20 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData20 + +namespace OAI + +/-! Degree Cover 20. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover20_0_0 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 1 1 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_0_1 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 1 2 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_0_2 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 1 3 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_0_3 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 1 4 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_0_4 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 1 5 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_1_0 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 2 1 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_1_1 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 2 2 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_1_2 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 2 3 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_1_3 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 2 4 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_1_4 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 2 5 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_2_0 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 3 1 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_2_1 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 3 2 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_2_2 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 3 3 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_2_3 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 3 4 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_2_4 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 3 5 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_3_0 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 4 1 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_3_1 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 4 2 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_3_2 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 4 3 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_3_3 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 4 4 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_3_4 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 4 5 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_4_0 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 5 1 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_4_1 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 5 2 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_4_2 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 5 3 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_4_3 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 5 4 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20_4_4 : + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 5 5 (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + decide +kernel + +lemma degreeCover20 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows20_0.length, ∀ c ∈ List.range degreeRows20_0.length, + regionCheck 20 4 5 (d+1) (e+1) (a+1) (c+1) degreeRows20_0 degreeRegions20 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover20_0_0 + · exact degreeCover20_0_1 + · exact degreeCover20_0_2 + · exact degreeCover20_0_3 + · exact degreeCover20_0_4 + · exact degreeCover20_1_0 + · exact degreeCover20_1_1 + · exact degreeCover20_1_2 + · exact degreeCover20_1_3 + · exact degreeCover20_1_4 + · exact degreeCover20_2_0 + · exact degreeCover20_2_1 + · exact degreeCover20_2_2 + · exact degreeCover20_2_3 + · exact degreeCover20_2_4 + · exact degreeCover20_3_0 + · exact degreeCover20_3_1 + · exact degreeCover20_3_2 + · exact degreeCover20_3_3 + · exact degreeCover20_3_4 + · exact degreeCover20_4_0 + · exact degreeCover20_4_1 + · exact degreeCover20_4_2 + · exact degreeCover20_4_3 + · exact degreeCover20_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover22.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover22.lean index de4e6af99247ed0504bf1167167e6ff23704d4cc..ed2720f6b91c1582fe816d9695d20b979b633f9a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover22.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover22.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans22 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData22 - -namespace OAI - -/-! Degree Cover 22. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover22_0_0 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 1 1 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_0_1 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 1 2 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_0_2 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 1 3 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_0_3 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 1 4 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_0_4 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 1 5 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_1_0 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 2 1 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_1_1 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 2 2 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_1_2 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 2 3 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_1_3 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 2 4 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_1_4 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 2 5 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_2_0 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 3 1 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_2_1 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 3 2 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_2_2 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 3 3 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_2_3 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 3 4 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_2_4 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 3 5 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_3_0 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 4 1 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_3_1 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 4 2 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_3_2 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 4 3 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_3_3 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 4 4 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_3_4 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 4 5 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_4_0 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 5 1 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_4_1 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 5 2 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_4_2 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 5 3 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_4_3 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 5 4 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22_4_4 : - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 5 5 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - decide +kernel - -lemma degreeCover22 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, - regionCheck 22 4 6 (d+1) (e+1) (a+1) (c+1) degreeRows22_0 degreeRegions22 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover22_0_0 - · exact degreeCover22_0_1 - · exact degreeCover22_0_2 - · exact degreeCover22_0_3 - · exact degreeCover22_0_4 - · exact degreeCover22_1_0 - · exact degreeCover22_1_1 - · exact degreeCover22_1_2 - · exact degreeCover22_1_3 - · exact degreeCover22_1_4 - · exact degreeCover22_2_0 - · exact degreeCover22_2_1 - · exact degreeCover22_2_2 - · exact degreeCover22_2_3 - · exact degreeCover22_2_4 - · exact degreeCover22_3_0 - · exact degreeCover22_3_1 - · exact degreeCover22_3_2 - · exact degreeCover22_3_3 - · exact degreeCover22_3_4 - · exact degreeCover22_4_0 - · exact degreeCover22_4_1 - · exact degreeCover22_4_2 - · exact degreeCover22_4_3 - · exact degreeCover22_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans22 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData22 + +namespace OAI + +/-! Degree Cover 22. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover22_0_0 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 1 1 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_0_1 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 1 2 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_0_2 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 1 3 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_0_3 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 1 4 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_0_4 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 1 5 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_1_0 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 2 1 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_1_1 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 2 2 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_1_2 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 2 3 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_1_3 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 2 4 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_1_4 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 2 5 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_2_0 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 3 1 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_2_1 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 3 2 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_2_2 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 3 3 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_2_3 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 3 4 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_2_4 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 3 5 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_3_0 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 4 1 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_3_1 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 4 2 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_3_2 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 4 3 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_3_3 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 4 4 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_3_4 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 4 5 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_4_0 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 5 1 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_4_1 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 5 2 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_4_2 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 5 3 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_4_3 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 5 4 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22_4_4 : + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 5 5 (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + decide +kernel + +lemma degreeCover22 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows22_0.length, ∀ c ∈ List.range degreeRows22_0.length, + regionCheck 22 4 6 (d+1) (e+1) (a+1) (c+1) degreeRows22_0 degreeRegions22 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover22_0_0 + · exact degreeCover22_0_1 + · exact degreeCover22_0_2 + · exact degreeCover22_0_3 + · exact degreeCover22_0_4 + · exact degreeCover22_1_0 + · exact degreeCover22_1_1 + · exact degreeCover22_1_2 + · exact degreeCover22_1_3 + · exact degreeCover22_1_4 + · exact degreeCover22_2_0 + · exact degreeCover22_2_1 + · exact degreeCover22_2_2 + · exact degreeCover22_2_3 + · exact degreeCover22_2_4 + · exact degreeCover22_3_0 + · exact degreeCover22_3_1 + · exact degreeCover22_3_2 + · exact degreeCover22_3_3 + · exact degreeCover22_3_4 + · exact degreeCover22_4_0 + · exact degreeCover22_4_1 + · exact degreeCover22_4_2 + · exact degreeCover22_4_3 + · exact degreeCover22_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover24.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover24.lean index efa6dc7060c1069c2b84dc76774ae9f53574d7b3..19cf532548fd378f1dc6256869da97ba02f07c57 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover24.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover24.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans24 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData24 - -namespace OAI - -/-! Degree Cover 24. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover24_0_0 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 1 1 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_0_1 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 1 2 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_0_2 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 1 3 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_0_3 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 1 4 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_0_4 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 1 5 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_1_0 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 2 1 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_1_1 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 2 2 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_1_2 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 2 3 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_1_3 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 2 4 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_1_4 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 2 5 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_2_0 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 3 1 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_2_1 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 3 2 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_2_2 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 3 3 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_2_3 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 3 4 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_2_4 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 3 5 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_3_0 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 4 1 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_3_1 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 4 2 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_3_2 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 4 3 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_3_3 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 4 4 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_3_4 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 4 5 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_4_0 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 5 1 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_4_1 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 5 2 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_4_2 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 5 3 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_4_3 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 5 4 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24_4_4 : - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 5 5 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - decide +kernel - -lemma degreeCover24 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, - regionCheck 24 4 7 (d+1) (e+1) (a+1) (c+1) degreeRows24_0 degreeRegions24 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover24_0_0 - · exact degreeCover24_0_1 - · exact degreeCover24_0_2 - · exact degreeCover24_0_3 - · exact degreeCover24_0_4 - · exact degreeCover24_1_0 - · exact degreeCover24_1_1 - · exact degreeCover24_1_2 - · exact degreeCover24_1_3 - · exact degreeCover24_1_4 - · exact degreeCover24_2_0 - · exact degreeCover24_2_1 - · exact degreeCover24_2_2 - · exact degreeCover24_2_3 - · exact degreeCover24_2_4 - · exact degreeCover24_3_0 - · exact degreeCover24_3_1 - · exact degreeCover24_3_2 - · exact degreeCover24_3_3 - · exact degreeCover24_3_4 - · exact degreeCover24_4_0 - · exact degreeCover24_4_1 - · exact degreeCover24_4_2 - · exact degreeCover24_4_3 - · exact degreeCover24_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans24 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData24 + +namespace OAI + +/-! Degree Cover 24. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover24_0_0 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 1 1 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_0_1 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 1 2 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_0_2 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 1 3 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_0_3 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 1 4 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_0_4 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 1 5 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_1_0 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 2 1 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_1_1 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 2 2 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_1_2 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 2 3 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_1_3 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 2 4 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_1_4 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 2 5 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_2_0 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 3 1 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_2_1 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 3 2 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_2_2 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 3 3 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_2_3 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 3 4 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_2_4 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 3 5 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_3_0 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 4 1 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_3_1 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 4 2 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_3_2 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 4 3 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_3_3 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 4 4 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_3_4 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 4 5 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_4_0 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 5 1 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_4_1 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 5 2 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_4_2 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 5 3 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_4_3 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 5 4 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24_4_4 : + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 5 5 (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + decide +kernel + +lemma degreeCover24 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows24_0.length, ∀ c ∈ List.range degreeRows24_0.length, + regionCheck 24 4 7 (d+1) (e+1) (a+1) (c+1) degreeRows24_0 degreeRegions24 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover24_0_0 + · exact degreeCover24_0_1 + · exact degreeCover24_0_2 + · exact degreeCover24_0_3 + · exact degreeCover24_0_4 + · exact degreeCover24_1_0 + · exact degreeCover24_1_1 + · exact degreeCover24_1_2 + · exact degreeCover24_1_3 + · exact degreeCover24_1_4 + · exact degreeCover24_2_0 + · exact degreeCover24_2_1 + · exact degreeCover24_2_2 + · exact degreeCover24_2_3 + · exact degreeCover24_2_4 + · exact degreeCover24_3_0 + · exact degreeCover24_3_1 + · exact degreeCover24_3_2 + · exact degreeCover24_3_3 + · exact degreeCover24_3_4 + · exact degreeCover24_4_0 + · exact degreeCover24_4_1 + · exact degreeCover24_4_2 + · exact degreeCover24_4_3 + · exact degreeCover24_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover26.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover26.lean index a65fa88f1d5d996761812de01b25278253f587ec..bc20df1402c9ed399c9dc5268f26d8e62abfe052 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover26.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover26.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans26 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData26 - -namespace OAI - -/-! Degree Cover 26. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover26_0_0 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 1 1 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_0_1 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 1 2 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_0_2 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 1 3 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_0_3 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 1 4 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_0_4 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 1 5 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_1_0 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 2 1 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_1_1 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 2 2 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_1_2 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 2 3 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_1_3 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 2 4 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_1_4 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 2 5 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_2_0 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 3 1 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_2_1 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 3 2 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_2_2 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 3 3 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_2_3 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 3 4 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_2_4 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 3 5 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_3_0 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 4 1 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_3_1 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 4 2 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_3_2 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 4 3 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_3_3 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 4 4 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_3_4 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 4 5 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_4_0 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 5 1 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_4_1 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 5 2 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_4_2 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 5 3 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_4_3 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 5 4 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26_4_4 : - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 5 5 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - decide +kernel - -lemma degreeCover26 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, - regionCheck 26 4 8 (d+1) (e+1) (a+1) (c+1) degreeRows26_0 degreeRegions26 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover26_0_0 - · exact degreeCover26_0_1 - · exact degreeCover26_0_2 - · exact degreeCover26_0_3 - · exact degreeCover26_0_4 - · exact degreeCover26_1_0 - · exact degreeCover26_1_1 - · exact degreeCover26_1_2 - · exact degreeCover26_1_3 - · exact degreeCover26_1_4 - · exact degreeCover26_2_0 - · exact degreeCover26_2_1 - · exact degreeCover26_2_2 - · exact degreeCover26_2_3 - · exact degreeCover26_2_4 - · exact degreeCover26_3_0 - · exact degreeCover26_3_1 - · exact degreeCover26_3_2 - · exact degreeCover26_3_3 - · exact degreeCover26_3_4 - · exact degreeCover26_4_0 - · exact degreeCover26_4_1 - · exact degreeCover26_4_2 - · exact degreeCover26_4_3 - · exact degreeCover26_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans26 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData26 + +namespace OAI + +/-! Degree Cover 26. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover26_0_0 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 1 1 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_0_1 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 1 2 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_0_2 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 1 3 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_0_3 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 1 4 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_0_4 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 1 5 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_1_0 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 2 1 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_1_1 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 2 2 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_1_2 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 2 3 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_1_3 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 2 4 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_1_4 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 2 5 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_2_0 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 3 1 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_2_1 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 3 2 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_2_2 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 3 3 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_2_3 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 3 4 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_2_4 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 3 5 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_3_0 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 4 1 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_3_1 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 4 2 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_3_2 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 4 3 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_3_3 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 4 4 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_3_4 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 4 5 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_4_0 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 5 1 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_4_1 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 5 2 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_4_2 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 5 3 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_4_3 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 5 4 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26_4_4 : + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 5 5 (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + decide +kernel + +lemma degreeCover26 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows26_0.length, ∀ c ∈ List.range degreeRows26_0.length, + regionCheck 26 4 8 (d+1) (e+1) (a+1) (c+1) degreeRows26_0 degreeRegions26 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover26_0_0 + · exact degreeCover26_0_1 + · exact degreeCover26_0_2 + · exact degreeCover26_0_3 + · exact degreeCover26_0_4 + · exact degreeCover26_1_0 + · exact degreeCover26_1_1 + · exact degreeCover26_1_2 + · exact degreeCover26_1_3 + · exact degreeCover26_1_4 + · exact degreeCover26_2_0 + · exact degreeCover26_2_1 + · exact degreeCover26_2_2 + · exact degreeCover26_2_3 + · exact degreeCover26_2_4 + · exact degreeCover26_3_0 + · exact degreeCover26_3_1 + · exact degreeCover26_3_2 + · exact degreeCover26_3_3 + · exact degreeCover26_3_4 + · exact degreeCover26_4_0 + · exact degreeCover26_4_1 + · exact degreeCover26_4_2 + · exact degreeCover26_4_3 + · exact degreeCover26_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover31.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover31.lean index 95e228a23179b9e1f43e55ca780a8d3d7daa4087..8bec2db60c7df2b20c9883d8442632cf944cebcc 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover31.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover31.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans31 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData31 - -namespace OAI - -/-! Degree Cover 31. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover31_0_0 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 1 1 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_0_1 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 1 2 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_0_2 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 1 3 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_0_3 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 1 4 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_0_4 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 1 5 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_1_0 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 2 1 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_1_1 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 2 2 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_1_2 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 2 3 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_1_3 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 2 4 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_1_4 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 2 5 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_2_0 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 3 1 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_2_1 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 3 2 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_2_2 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 3 3 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_2_3 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 3 4 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_2_4 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 3 5 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_3_0 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 4 1 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_3_1 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 4 2 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_3_2 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 4 3 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_3_3 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 4 4 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_3_4 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 4 5 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_4_0 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 5 1 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_4_1 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 5 2 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_4_2 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 5 3 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_4_3 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 5 4 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31_4_4 : - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 5 5 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - decide +kernel - -lemma degreeCover31 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, - regionCheck 31 6 5 (d+1) (e+1) (a+1) (c+1) degreeRows31_0 degreeRegions31 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover31_0_0 - · exact degreeCover31_0_1 - · exact degreeCover31_0_2 - · exact degreeCover31_0_3 - · exact degreeCover31_0_4 - · exact degreeCover31_1_0 - · exact degreeCover31_1_1 - · exact degreeCover31_1_2 - · exact degreeCover31_1_3 - · exact degreeCover31_1_4 - · exact degreeCover31_2_0 - · exact degreeCover31_2_1 - · exact degreeCover31_2_2 - · exact degreeCover31_2_3 - · exact degreeCover31_2_4 - · exact degreeCover31_3_0 - · exact degreeCover31_3_1 - · exact degreeCover31_3_2 - · exact degreeCover31_3_3 - · exact degreeCover31_3_4 - · exact degreeCover31_4_0 - · exact degreeCover31_4_1 - · exact degreeCover31_4_2 - · exact degreeCover31_4_3 - · exact degreeCover31_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans31 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData31 + +namespace OAI + +/-! Degree Cover 31. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover31_0_0 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 1 1 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_0_1 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 1 2 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_0_2 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 1 3 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_0_3 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 1 4 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_0_4 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 1 5 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_1_0 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 2 1 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_1_1 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 2 2 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_1_2 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 2 3 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_1_3 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 2 4 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_1_4 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 2 5 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_2_0 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 3 1 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_2_1 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 3 2 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_2_2 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 3 3 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_2_3 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 3 4 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_2_4 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 3 5 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_3_0 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 4 1 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_3_1 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 4 2 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_3_2 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 4 3 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_3_3 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 4 4 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_3_4 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 4 5 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_4_0 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 5 1 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_4_1 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 5 2 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_4_2 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 5 3 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_4_3 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 5 4 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31_4_4 : + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 5 5 (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + decide +kernel + +lemma degreeCover31 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows31_0.length, ∀ c ∈ List.range degreeRows31_0.length, + regionCheck 31 6 5 (d+1) (e+1) (a+1) (c+1) degreeRows31_0 degreeRegions31 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover31_0_0 + · exact degreeCover31_0_1 + · exact degreeCover31_0_2 + · exact degreeCover31_0_3 + · exact degreeCover31_0_4 + · exact degreeCover31_1_0 + · exact degreeCover31_1_1 + · exact degreeCover31_1_2 + · exact degreeCover31_1_3 + · exact degreeCover31_1_4 + · exact degreeCover31_2_0 + · exact degreeCover31_2_1 + · exact degreeCover31_2_2 + · exact degreeCover31_2_3 + · exact degreeCover31_2_4 + · exact degreeCover31_3_0 + · exact degreeCover31_3_1 + · exact degreeCover31_3_2 + · exact degreeCover31_3_3 + · exact degreeCover31_3_4 + · exact degreeCover31_4_0 + · exact degreeCover31_4_1 + · exact degreeCover31_4_2 + · exact degreeCover31_4_3 + · exact degreeCover31_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover35.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover35.lean index a98d8e27e9951cd66cefa30bf90e370c75bd2401..e21dd9608c4f0775a864ae2557215987ae892368 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover35.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover35.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans35 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData35 - -namespace OAI - -/-! Degree Cover 35. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover35_0_0 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 1 1 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_0_1 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 1 2 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_0_2 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 1 3 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_0_3 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 1 4 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_0_4 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 1 5 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_1_0 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 2 1 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_1_1 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 2 2 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_1_2 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 2 3 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_1_3 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 2 4 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_1_4 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 2 5 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_2_0 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 3 1 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_2_1 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 3 2 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_2_2 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 3 3 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_2_3 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 3 4 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_2_4 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 3 5 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_3_0 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 4 1 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_3_1 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 4 2 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_3_2 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 4 3 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_3_3 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 4 4 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_3_4 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 4 5 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_4_0 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 5 1 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_4_1 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 5 2 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_4_2 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 5 3 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_4_3 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 5 4 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35_4_4 : - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 5 5 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - decide +kernel - -lemma degreeCover35 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, - regionCheck 35 6 7 (d+1) (e+1) (a+1) (c+1) degreeRows35_0 degreeRegions35 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover35_0_0 - · exact degreeCover35_0_1 - · exact degreeCover35_0_2 - · exact degreeCover35_0_3 - · exact degreeCover35_0_4 - · exact degreeCover35_1_0 - · exact degreeCover35_1_1 - · exact degreeCover35_1_2 - · exact degreeCover35_1_3 - · exact degreeCover35_1_4 - · exact degreeCover35_2_0 - · exact degreeCover35_2_1 - · exact degreeCover35_2_2 - · exact degreeCover35_2_3 - · exact degreeCover35_2_4 - · exact degreeCover35_3_0 - · exact degreeCover35_3_1 - · exact degreeCover35_3_2 - · exact degreeCover35_3_3 - · exact degreeCover35_3_4 - · exact degreeCover35_4_0 - · exact degreeCover35_4_1 - · exact degreeCover35_4_2 - · exact degreeCover35_4_3 - · exact degreeCover35_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans35 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData35 + +namespace OAI + +/-! Degree Cover 35. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover35_0_0 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 1 1 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_0_1 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 1 2 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_0_2 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 1 3 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_0_3 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 1 4 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_0_4 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 1 5 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_1_0 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 2 1 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_1_1 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 2 2 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_1_2 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 2 3 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_1_3 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 2 4 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_1_4 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 2 5 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_2_0 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 3 1 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_2_1 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 3 2 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_2_2 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 3 3 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_2_3 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 3 4 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_2_4 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 3 5 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_3_0 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 4 1 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_3_1 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 4 2 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_3_2 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 4 3 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_3_3 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 4 4 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_3_4 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 4 5 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_4_0 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 5 1 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_4_1 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 5 2 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_4_2 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 5 3 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_4_3 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 5 4 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35_4_4 : + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 5 5 (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + decide +kernel + +lemma degreeCover35 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows35_0.length, ∀ c ∈ List.range degreeRows35_0.length, + regionCheck 35 6 7 (d+1) (e+1) (a+1) (c+1) degreeRows35_0 degreeRegions35 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover35_0_0 + · exact degreeCover35_0_1 + · exact degreeCover35_0_2 + · exact degreeCover35_0_3 + · exact degreeCover35_0_4 + · exact degreeCover35_1_0 + · exact degreeCover35_1_1 + · exact degreeCover35_1_2 + · exact degreeCover35_1_3 + · exact degreeCover35_1_4 + · exact degreeCover35_2_0 + · exact degreeCover35_2_1 + · exact degreeCover35_2_2 + · exact degreeCover35_2_3 + · exact degreeCover35_2_4 + · exact degreeCover35_3_0 + · exact degreeCover35_3_1 + · exact degreeCover35_3_2 + · exact degreeCover35_3_3 + · exact degreeCover35_3_4 + · exact degreeCover35_4_0 + · exact degreeCover35_4_1 + · exact degreeCover35_4_2 + · exact degreeCover35_4_3 + · exact degreeCover35_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover37.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover37.lean index a52e014f742f60634e77df942e4138f6b01ade6a..e0afcb921ba6b0fd591dd7d8616ada46f484b0ee 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover37.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover37.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans37 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData37 - -namespace OAI - -/-! Degree Cover 37. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover37_0_0 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 1 1 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_0_1 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 1 2 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_0_2 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 1 3 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_0_3 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 1 4 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_0_4 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 1 5 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_1_0 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 2 1 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_1_1 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 2 2 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_1_2 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 2 3 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_1_3 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 2 4 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_1_4 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 2 5 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_2_0 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 3 1 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_2_1 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 3 2 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_2_2 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 3 3 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_2_3 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 3 4 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_2_4 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 3 5 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_3_0 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 4 1 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_3_1 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 4 2 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_3_2 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 4 3 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_3_3 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 4 4 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_3_4 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 4 5 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_4_0 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 5 1 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_4_1 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 5 2 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_4_2 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 5 3 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_4_3 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 5 4 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37_4_4 : - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 5 5 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - decide +kernel - -lemma degreeCover37 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, - regionCheck 37 6 8 (d+1) (e+1) (a+1) (c+1) degreeRows37_0 degreeRegions37 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover37_0_0 - · exact degreeCover37_0_1 - · exact degreeCover37_0_2 - · exact degreeCover37_0_3 - · exact degreeCover37_0_4 - · exact degreeCover37_1_0 - · exact degreeCover37_1_1 - · exact degreeCover37_1_2 - · exact degreeCover37_1_3 - · exact degreeCover37_1_4 - · exact degreeCover37_2_0 - · exact degreeCover37_2_1 - · exact degreeCover37_2_2 - · exact degreeCover37_2_3 - · exact degreeCover37_2_4 - · exact degreeCover37_3_0 - · exact degreeCover37_3_1 - · exact degreeCover37_3_2 - · exact degreeCover37_3_3 - · exact degreeCover37_3_4 - · exact degreeCover37_4_0 - · exact degreeCover37_4_1 - · exact degreeCover37_4_2 - · exact degreeCover37_4_3 - · exact degreeCover37_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans37 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData37 + +namespace OAI + +/-! Degree Cover 37. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover37_0_0 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 1 1 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_0_1 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 1 2 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_0_2 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 1 3 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_0_3 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 1 4 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_0_4 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 1 5 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_1_0 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 2 1 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_1_1 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 2 2 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_1_2 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 2 3 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_1_3 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 2 4 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_1_4 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 2 5 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_2_0 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 3 1 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_2_1 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 3 2 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_2_2 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 3 3 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_2_3 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 3 4 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_2_4 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 3 5 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_3_0 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 4 1 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_3_1 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 4 2 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_3_2 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 4 3 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_3_3 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 4 4 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_3_4 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 4 5 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_4_0 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 5 1 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_4_1 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 5 2 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_4_2 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 5 3 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_4_3 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 5 4 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37_4_4 : + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 5 5 (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + decide +kernel + +lemma degreeCover37 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows37_0.length, ∀ c ∈ List.range degreeRows37_0.length, + regionCheck 37 6 8 (d+1) (e+1) (a+1) (c+1) degreeRows37_0 degreeRegions37 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover37_0_0 + · exact degreeCover37_0_1 + · exact degreeCover37_0_2 + · exact degreeCover37_0_3 + · exact degreeCover37_0_4 + · exact degreeCover37_1_0 + · exact degreeCover37_1_1 + · exact degreeCover37_1_2 + · exact degreeCover37_1_3 + · exact degreeCover37_1_4 + · exact degreeCover37_2_0 + · exact degreeCover37_2_1 + · exact degreeCover37_2_2 + · exact degreeCover37_2_3 + · exact degreeCover37_2_4 + · exact degreeCover37_3_0 + · exact degreeCover37_3_1 + · exact degreeCover37_3_2 + · exact degreeCover37_3_3 + · exact degreeCover37_3_4 + · exact degreeCover37_4_0 + · exact degreeCover37_4_1 + · exact degreeCover37_4_2 + · exact degreeCover37_4_3 + · exact degreeCover37_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover39.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover39.lean index d3338d6efec9fdca10f5ec8cb3b1c3b041cabb7d..671039c19d6b5a8a66a62dabe0b5082596578689 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover39.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover39.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans39 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData39 - -namespace OAI - -/-! Degree Cover 39. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover39_0_0 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 1 1 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_0_1 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 1 2 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_0_2 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 1 3 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_0_3 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 1 4 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_0_4 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 1 5 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_1_0 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 2 1 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_1_1 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 2 2 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_1_2 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 2 3 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_1_3 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 2 4 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_1_4 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 2 5 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_2_0 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 3 1 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_2_1 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 3 2 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_2_2 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 3 3 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_2_3 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 3 4 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_2_4 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 3 5 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_3_0 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 4 1 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_3_1 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 4 2 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_3_2 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 4 3 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_3_3 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 4 4 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_3_4 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 4 5 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_4_0 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 5 1 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_4_1 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 5 2 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_4_2 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 5 3 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_4_3 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 5 4 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39_4_4 : - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 5 5 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - decide +kernel - -lemma degreeCover39 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, - regionCheck 39 6 9 (d+1) (e+1) (a+1) (c+1) degreeRows39_0 degreeRegions39 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover39_0_0 - · exact degreeCover39_0_1 - · exact degreeCover39_0_2 - · exact degreeCover39_0_3 - · exact degreeCover39_0_4 - · exact degreeCover39_1_0 - · exact degreeCover39_1_1 - · exact degreeCover39_1_2 - · exact degreeCover39_1_3 - · exact degreeCover39_1_4 - · exact degreeCover39_2_0 - · exact degreeCover39_2_1 - · exact degreeCover39_2_2 - · exact degreeCover39_2_3 - · exact degreeCover39_2_4 - · exact degreeCover39_3_0 - · exact degreeCover39_3_1 - · exact degreeCover39_3_2 - · exact degreeCover39_3_3 - · exact degreeCover39_3_4 - · exact degreeCover39_4_0 - · exact degreeCover39_4_1 - · exact degreeCover39_4_2 - · exact degreeCover39_4_3 - · exact degreeCover39_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans39 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData39 + +namespace OAI + +/-! Degree Cover 39. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover39_0_0 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 1 1 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_0_1 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 1 2 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_0_2 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 1 3 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_0_3 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 1 4 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_0_4 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 1 5 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_1_0 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 2 1 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_1_1 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 2 2 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_1_2 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 2 3 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_1_3 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 2 4 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_1_4 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 2 5 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_2_0 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 3 1 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_2_1 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 3 2 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_2_2 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 3 3 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_2_3 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 3 4 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_2_4 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 3 5 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_3_0 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 4 1 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_3_1 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 4 2 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_3_2 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 4 3 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_3_3 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 4 4 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_3_4 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 4 5 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_4_0 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 5 1 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_4_1 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 5 2 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_4_2 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 5 3 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_4_3 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 5 4 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39_4_4 : + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 5 5 (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + decide +kernel + +lemma degreeCover39 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows39_0.length, ∀ c ∈ List.range degreeRows39_0.length, + regionCheck 39 6 9 (d+1) (e+1) (a+1) (c+1) degreeRows39_0 degreeRegions39 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover39_0_0 + · exact degreeCover39_0_1 + · exact degreeCover39_0_2 + · exact degreeCover39_0_3 + · exact degreeCover39_0_4 + · exact degreeCover39_1_0 + · exact degreeCover39_1_1 + · exact degreeCover39_1_2 + · exact degreeCover39_1_3 + · exact degreeCover39_1_4 + · exact degreeCover39_2_0 + · exact degreeCover39_2_1 + · exact degreeCover39_2_2 + · exact degreeCover39_2_3 + · exact degreeCover39_2_4 + · exact degreeCover39_3_0 + · exact degreeCover39_3_1 + · exact degreeCover39_3_2 + · exact degreeCover39_3_3 + · exact degreeCover39_3_4 + · exact degreeCover39_4_0 + · exact degreeCover39_4_1 + · exact degreeCover39_4_2 + · exact degreeCover39_4_3 + · exact degreeCover39_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover41.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover41.lean index 0383d7fa1356825c1e692cba6463718e6a7ad228..e74297df88f9248d6118b2d2ef97deaebb85f91b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover41.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover41.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans41 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData41 - -namespace OAI - -/-! Degree Cover 41. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover41_0_0 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 1 1 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_0_1 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 1 2 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_0_2 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 1 3 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_0_3 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 1 4 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_0_4 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 1 5 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_1_0 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 2 1 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_1_1 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 2 2 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_1_2 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 2 3 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_1_3 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 2 4 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_1_4 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 2 5 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_2_0 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 3 1 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_2_1 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 3 2 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_2_2 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 3 3 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_2_3 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 3 4 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_2_4 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 3 5 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_3_0 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 4 1 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_3_1 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 4 2 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_3_2 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 4 3 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_3_3 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 4 4 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_3_4 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 4 5 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_4_0 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 5 1 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_4_1 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 5 2 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_4_2 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 5 3 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_4_3 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 5 4 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41_4_4 : - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 5 5 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - decide +kernel - -lemma degreeCover41 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, - regionCheck 41 6 10 (d+1) (e+1) (a+1) (c+1) degreeRows41_0 degreeRegions41 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover41_0_0 - · exact degreeCover41_0_1 - · exact degreeCover41_0_2 - · exact degreeCover41_0_3 - · exact degreeCover41_0_4 - · exact degreeCover41_1_0 - · exact degreeCover41_1_1 - · exact degreeCover41_1_2 - · exact degreeCover41_1_3 - · exact degreeCover41_1_4 - · exact degreeCover41_2_0 - · exact degreeCover41_2_1 - · exact degreeCover41_2_2 - · exact degreeCover41_2_3 - · exact degreeCover41_2_4 - · exact degreeCover41_3_0 - · exact degreeCover41_3_1 - · exact degreeCover41_3_2 - · exact degreeCover41_3_3 - · exact degreeCover41_3_4 - · exact degreeCover41_4_0 - · exact degreeCover41_4_1 - · exact degreeCover41_4_2 - · exact degreeCover41_4_3 - · exact degreeCover41_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans41 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData41 + +namespace OAI + +/-! Degree Cover 41. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover41_0_0 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 1 1 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_0_1 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 1 2 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_0_2 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 1 3 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_0_3 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 1 4 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_0_4 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 1 5 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_1_0 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 2 1 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_1_1 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 2 2 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_1_2 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 2 3 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_1_3 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 2 4 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_1_4 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 2 5 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_2_0 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 3 1 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_2_1 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 3 2 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_2_2 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 3 3 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_2_3 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 3 4 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_2_4 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 3 5 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_3_0 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 4 1 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_3_1 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 4 2 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_3_2 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 4 3 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_3_3 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 4 4 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_3_4 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 4 5 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_4_0 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 5 1 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_4_1 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 5 2 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_4_2 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 5 3 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_4_3 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 5 4 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41_4_4 : + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 5 5 (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + decide +kernel + +lemma degreeCover41 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows41_0.length, ∀ c ∈ List.range degreeRows41_0.length, + regionCheck 41 6 10 (d+1) (e+1) (a+1) (c+1) degreeRows41_0 degreeRegions41 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover41_0_0 + · exact degreeCover41_0_1 + · exact degreeCover41_0_2 + · exact degreeCover41_0_3 + · exact degreeCover41_0_4 + · exact degreeCover41_1_0 + · exact degreeCover41_1_1 + · exact degreeCover41_1_2 + · exact degreeCover41_1_3 + · exact degreeCover41_1_4 + · exact degreeCover41_2_0 + · exact degreeCover41_2_1 + · exact degreeCover41_2_2 + · exact degreeCover41_2_3 + · exact degreeCover41_2_4 + · exact degreeCover41_3_0 + · exact degreeCover41_3_1 + · exact degreeCover41_3_2 + · exact degreeCover41_3_3 + · exact degreeCover41_3_4 + · exact degreeCover41_4_0 + · exact degreeCover41_4_1 + · exact degreeCover41_4_2 + · exact degreeCover41_4_3 + · exact degreeCover41_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover43.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover43.lean index db3285a73c9594f083bebea969c3a43106382978..30fdf8a8f1165691c460610d14ba185f1acbfb95 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover43.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover43.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans43 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData43 - -namespace OAI - -/-! Degree Cover 43. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover43_0_0 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 1 1 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_0_1 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 1 2 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_0_2 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 1 3 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_0_3 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 1 4 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_0_4 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 1 5 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_1_0 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 2 1 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_1_1 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 2 2 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_1_2 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 2 3 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_1_3 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 2 4 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_1_4 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 2 5 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_2_0 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 3 1 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_2_1 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 3 2 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_2_2 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 3 3 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_2_3 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 3 4 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_2_4 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 3 5 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_3_0 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 4 1 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_3_1 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 4 2 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_3_2 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 4 3 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_3_3 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 4 4 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_3_4 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 4 5 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_4_0 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 5 1 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_4_1 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 5 2 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_4_2 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 5 3 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_4_3 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 5 4 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43_4_4 : - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 5 5 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - decide +kernel - -lemma degreeCover43 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, - regionCheck 43 6 11 (d+1) (e+1) (a+1) (c+1) degreeRows43_0 degreeRegions43 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover43_0_0 - · exact degreeCover43_0_1 - · exact degreeCover43_0_2 - · exact degreeCover43_0_3 - · exact degreeCover43_0_4 - · exact degreeCover43_1_0 - · exact degreeCover43_1_1 - · exact degreeCover43_1_2 - · exact degreeCover43_1_3 - · exact degreeCover43_1_4 - · exact degreeCover43_2_0 - · exact degreeCover43_2_1 - · exact degreeCover43_2_2 - · exact degreeCover43_2_3 - · exact degreeCover43_2_4 - · exact degreeCover43_3_0 - · exact degreeCover43_3_1 - · exact degreeCover43_3_2 - · exact degreeCover43_3_3 - · exact degreeCover43_3_4 - · exact degreeCover43_4_0 - · exact degreeCover43_4_1 - · exact degreeCover43_4_2 - · exact degreeCover43_4_3 - · exact degreeCover43_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans43 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData43 + +namespace OAI + +/-! Degree Cover 43. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover43_0_0 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 1 1 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_0_1 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 1 2 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_0_2 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 1 3 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_0_3 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 1 4 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_0_4 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 1 5 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_1_0 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 2 1 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_1_1 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 2 2 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_1_2 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 2 3 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_1_3 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 2 4 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_1_4 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 2 5 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_2_0 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 3 1 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_2_1 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 3 2 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_2_2 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 3 3 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_2_3 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 3 4 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_2_4 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 3 5 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_3_0 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 4 1 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_3_1 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 4 2 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_3_2 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 4 3 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_3_3 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 4 4 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_3_4 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 4 5 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_4_0 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 5 1 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_4_1 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 5 2 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_4_2 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 5 3 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_4_3 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 5 4 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43_4_4 : + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 5 5 (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + decide +kernel + +lemma degreeCover43 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows43_0.length, ∀ c ∈ List.range degreeRows43_0.length, + regionCheck 43 6 11 (d+1) (e+1) (a+1) (c+1) degreeRows43_0 degreeRegions43 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover43_0_0 + · exact degreeCover43_0_1 + · exact degreeCover43_0_2 + · exact degreeCover43_0_3 + · exact degreeCover43_0_4 + · exact degreeCover43_1_0 + · exact degreeCover43_1_1 + · exact degreeCover43_1_2 + · exact degreeCover43_1_3 + · exact degreeCover43_1_4 + · exact degreeCover43_2_0 + · exact degreeCover43_2_1 + · exact degreeCover43_2_2 + · exact degreeCover43_2_3 + · exact degreeCover43_2_4 + · exact degreeCover43_3_0 + · exact degreeCover43_3_1 + · exact degreeCover43_3_2 + · exact degreeCover43_3_3 + · exact degreeCover43_3_4 + · exact degreeCover43_4_0 + · exact degreeCover43_4_1 + · exact degreeCover43_4_2 + · exact degreeCover43_4_3 + · exact degreeCover43_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover58.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover58.lean index 15a4d925bfdd37380f594f5cd0b320589a17174c..e8c7c1db46a098939fa1b42cd6cc9f8e41ce7b00 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover58.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover58.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans58 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData58 - -namespace OAI - -/-! Degree Cover 58. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover58_0_0 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 1 1 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_0_1 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 1 2 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_0_2 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 1 3 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_0_3 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 1 4 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_0_4 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 1 5 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_1_0 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 2 1 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_1_1 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 2 2 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_1_2 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 2 3 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_1_3 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 2 4 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_1_4 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 2 5 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_2_0 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 3 1 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_2_1 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 3 2 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_2_2 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 3 3 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_2_3 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 3 4 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_2_4 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 3 5 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_3_0 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 4 1 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_3_1 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 4 2 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_3_2 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 4 3 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_3_3 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 4 4 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_3_4 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 4 5 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_4_0 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 5 1 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_4_1 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 5 2 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_4_2 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 5 3 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_4_3 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 5 4 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58_4_4 : - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 5 5 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - decide +kernel - -lemma degreeCover58 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, - regionCheck 58 8 11 (d+1) (e+1) (a+1) (c+1) degreeRows58_0 degreeRegions58 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover58_0_0 - · exact degreeCover58_0_1 - · exact degreeCover58_0_2 - · exact degreeCover58_0_3 - · exact degreeCover58_0_4 - · exact degreeCover58_1_0 - · exact degreeCover58_1_1 - · exact degreeCover58_1_2 - · exact degreeCover58_1_3 - · exact degreeCover58_1_4 - · exact degreeCover58_2_0 - · exact degreeCover58_2_1 - · exact degreeCover58_2_2 - · exact degreeCover58_2_3 - · exact degreeCover58_2_4 - · exact degreeCover58_3_0 - · exact degreeCover58_3_1 - · exact degreeCover58_3_2 - · exact degreeCover58_3_3 - · exact degreeCover58_3_4 - · exact degreeCover58_4_0 - · exact degreeCover58_4_1 - · exact degreeCover58_4_2 - · exact degreeCover58_4_3 - · exact degreeCover58_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans58 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData58 + +namespace OAI + +/-! Degree Cover 58. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover58_0_0 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 1 1 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_0_1 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 1 2 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_0_2 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 1 3 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_0_3 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 1 4 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_0_4 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 1 5 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_1_0 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 2 1 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_1_1 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 2 2 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_1_2 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 2 3 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_1_3 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 2 4 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_1_4 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 2 5 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_2_0 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 3 1 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_2_1 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 3 2 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_2_2 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 3 3 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_2_3 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 3 4 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_2_4 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 3 5 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_3_0 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 4 1 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_3_1 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 4 2 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_3_2 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 4 3 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_3_3 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 4 4 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_3_4 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 4 5 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_4_0 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 5 1 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_4_1 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 5 2 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_4_2 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 5 3 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_4_3 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 5 4 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58_4_4 : + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 5 5 (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + decide +kernel + +lemma degreeCover58 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows58_0.length, ∀ c ∈ List.range degreeRows58_0.length, + regionCheck 58 8 11 (d+1) (e+1) (a+1) (c+1) degreeRows58_0 degreeRegions58 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover58_0_0 + · exact degreeCover58_0_1 + · exact degreeCover58_0_2 + · exact degreeCover58_0_3 + · exact degreeCover58_0_4 + · exact degreeCover58_1_0 + · exact degreeCover58_1_1 + · exact degreeCover58_1_2 + · exact degreeCover58_1_3 + · exact degreeCover58_1_4 + · exact degreeCover58_2_0 + · exact degreeCover58_2_1 + · exact degreeCover58_2_2 + · exact degreeCover58_2_3 + · exact degreeCover58_2_4 + · exact degreeCover58_3_0 + · exact degreeCover58_3_1 + · exact degreeCover58_3_2 + · exact degreeCover58_3_3 + · exact degreeCover58_3_4 + · exact degreeCover58_4_0 + · exact degreeCover58_4_1 + · exact degreeCover58_4_2 + · exact degreeCover58_4_3 + · exact degreeCover58_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover62.lean index 5bf5872852db6455649f5e23e9e94972acbd379b..0416a469a3bf2035b4715c8e12e0814c10e24e9a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover62.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans62 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData62 - -namespace OAI - -/-! Degree Cover 62. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover62_0_0 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 1 1 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_0_1 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 1 2 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_0_2 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 1 3 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_0_3 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 1 4 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_0_4 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 1 5 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_1_0 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 2 1 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_1_1 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 2 2 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_1_2 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 2 3 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_1_3 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 2 4 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_1_4 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 2 5 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_2_0 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 3 1 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_2_1 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 3 2 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_2_2 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 3 3 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_2_3 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 3 4 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_2_4 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 3 5 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_3_0 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 4 1 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_3_1 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 4 2 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_3_2 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 4 3 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_3_3 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 4 4 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_3_4 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 4 5 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_4_0 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 5 1 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_4_1 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 5 2 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_4_2 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 5 3 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_4_3 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 5 4 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62_4_4 : - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 5 5 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - decide +kernel - -lemma degreeCover62 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, - regionCheck 62 8 13 (d+1) (e+1) (a+1) (c+1) degreeRows62_0 degreeRegions62 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover62_0_0 - · exact degreeCover62_0_1 - · exact degreeCover62_0_2 - · exact degreeCover62_0_3 - · exact degreeCover62_0_4 - · exact degreeCover62_1_0 - · exact degreeCover62_1_1 - · exact degreeCover62_1_2 - · exact degreeCover62_1_3 - · exact degreeCover62_1_4 - · exact degreeCover62_2_0 - · exact degreeCover62_2_1 - · exact degreeCover62_2_2 - · exact degreeCover62_2_3 - · exact degreeCover62_2_4 - · exact degreeCover62_3_0 - · exact degreeCover62_3_1 - · exact degreeCover62_3_2 - · exact degreeCover62_3_3 - · exact degreeCover62_3_4 - · exact degreeCover62_4_0 - · exact degreeCover62_4_1 - · exact degreeCover62_4_2 - · exact degreeCover62_4_3 - · exact degreeCover62_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans62 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData62 + +namespace OAI + +/-! Degree Cover 62. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover62_0_0 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 1 1 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_0_1 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 1 2 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_0_2 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 1 3 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_0_3 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 1 4 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_0_4 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 1 5 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_1_0 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 2 1 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_1_1 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 2 2 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_1_2 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 2 3 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_1_3 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 2 4 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_1_4 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 2 5 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_2_0 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 3 1 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_2_1 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 3 2 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_2_2 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 3 3 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_2_3 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 3 4 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_2_4 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 3 5 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_3_0 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 4 1 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_3_1 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 4 2 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_3_2 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 4 3 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_3_3 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 4 4 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_3_4 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 4 5 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_4_0 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 5 1 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_4_1 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 5 2 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_4_2 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 5 3 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_4_3 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 5 4 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62_4_4 : + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 5 5 (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + decide +kernel + +lemma degreeCover62 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows62_0.length, ∀ c ∈ List.range degreeRows62_0.length, + regionCheck 62 8 13 (d+1) (e+1) (a+1) (c+1) degreeRows62_0 degreeRegions62 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover62_0_0 + · exact degreeCover62_0_1 + · exact degreeCover62_0_2 + · exact degreeCover62_0_3 + · exact degreeCover62_0_4 + · exact degreeCover62_1_0 + · exact degreeCover62_1_1 + · exact degreeCover62_1_2 + · exact degreeCover62_1_3 + · exact degreeCover62_1_4 + · exact degreeCover62_2_0 + · exact degreeCover62_2_1 + · exact degreeCover62_2_2 + · exact degreeCover62_2_3 + · exact degreeCover62_2_4 + · exact degreeCover62_3_0 + · exact degreeCover62_3_1 + · exact degreeCover62_3_2 + · exact degreeCover62_3_3 + · exact degreeCover62_3_4 + · exact degreeCover62_4_0 + · exact degreeCover62_4_1 + · exact degreeCover62_4_2 + · exact degreeCover62_4_3 + · exact degreeCover62_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover64.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover64.lean index 2f197a96097437f34c29dc0d5f8981f32efbf8cf..8b1308d647e6ba7ae8067ac291d87a57a1d695e2 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover64.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover64.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans64 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData64 - -namespace OAI - -/-! Degree Cover 64. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover64_0_0 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 1 1 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_0_1 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 1 2 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_0_2 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 1 3 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_0_3 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 1 4 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_0_4 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 1 5 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_1_0 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 2 1 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_1_1 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 2 2 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_1_2 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 2 3 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_1_3 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 2 4 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_1_4 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 2 5 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_2_0 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 3 1 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_2_1 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 3 2 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_2_2 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 3 3 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_2_3 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 3 4 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_2_4 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 3 5 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_3_0 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 4 1 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_3_1 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 4 2 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_3_2 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 4 3 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_3_3 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 4 4 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_3_4 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 4 5 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_4_0 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 5 1 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_4_1 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 5 2 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_4_2 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 5 3 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_4_3 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 5 4 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64_4_4 : - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 5 5 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - decide +kernel - -lemma degreeCover64 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, - regionCheck 64 8 14 (d+1) (e+1) (a+1) (c+1) degreeRows64_0 degreeRegions64 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover64_0_0 - · exact degreeCover64_0_1 - · exact degreeCover64_0_2 - · exact degreeCover64_0_3 - · exact degreeCover64_0_4 - · exact degreeCover64_1_0 - · exact degreeCover64_1_1 - · exact degreeCover64_1_2 - · exact degreeCover64_1_3 - · exact degreeCover64_1_4 - · exact degreeCover64_2_0 - · exact degreeCover64_2_1 - · exact degreeCover64_2_2 - · exact degreeCover64_2_3 - · exact degreeCover64_2_4 - · exact degreeCover64_3_0 - · exact degreeCover64_3_1 - · exact degreeCover64_3_2 - · exact degreeCover64_3_3 - · exact degreeCover64_3_4 - · exact degreeCover64_4_0 - · exact degreeCover64_4_1 - · exact degreeCover64_4_2 - · exact degreeCover64_4_3 - · exact degreeCover64_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans64 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData64 + +namespace OAI + +/-! Degree Cover 64. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover64_0_0 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 1 1 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_0_1 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 1 2 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_0_2 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 1 3 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_0_3 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 1 4 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_0_4 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 1 5 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_1_0 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 2 1 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_1_1 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 2 2 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_1_2 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 2 3 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_1_3 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 2 4 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_1_4 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 2 5 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_2_0 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 3 1 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_2_1 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 3 2 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_2_2 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 3 3 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_2_3 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 3 4 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_2_4 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 3 5 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_3_0 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 4 1 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_3_1 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 4 2 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_3_2 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 4 3 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_3_3 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 4 4 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_3_4 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 4 5 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_4_0 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 5 1 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_4_1 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 5 2 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_4_2 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 5 3 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_4_3 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 5 4 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64_4_4 : + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 5 5 (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + decide +kernel + +lemma degreeCover64 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows64_0.length, ∀ c ∈ List.range degreeRows64_0.length, + regionCheck 64 8 14 (d+1) (e+1) (a+1) (c+1) degreeRows64_0 degreeRegions64 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover64_0_0 + · exact degreeCover64_0_1 + · exact degreeCover64_0_2 + · exact degreeCover64_0_3 + · exact degreeCover64_0_4 + · exact degreeCover64_1_0 + · exact degreeCover64_1_1 + · exact degreeCover64_1_2 + · exact degreeCover64_1_3 + · exact degreeCover64_1_4 + · exact degreeCover64_2_0 + · exact degreeCover64_2_1 + · exact degreeCover64_2_2 + · exact degreeCover64_2_3 + · exact degreeCover64_2_4 + · exact degreeCover64_3_0 + · exact degreeCover64_3_1 + · exact degreeCover64_3_2 + · exact degreeCover64_3_3 + · exact degreeCover64_3_4 + · exact degreeCover64_4_0 + · exact degreeCover64_4_1 + · exact degreeCover64_4_2 + · exact degreeCover64_4_3 + · exact degreeCover64_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover89.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover89.lean index 5721423bd6ddfe87001d08ec74bf2b4922bf7462..a88cba77754c08a32740ebab7176ecd3e1c27f99 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover89.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeCover89.lean @@ -1,178 +1,178 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans89 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData89 - -namespace OAI - -/-! Degree Cover 89. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCover89_0_0 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 1 1 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_0_1 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 1 2 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_0_2 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 1 3 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_0_3 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 1 4 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_0_4 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 1 5 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_1_0 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 2 1 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_1_1 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 2 2 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_1_2 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 2 3 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_1_3 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 2 4 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_1_4 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 2 5 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_2_0 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 3 1 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_2_1 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 3 2 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_2_2 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 3 3 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_2_3 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 3 4 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_2_4 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 3 5 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_3_0 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 4 1 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_3_1 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 4 2 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_3_2 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 4 3 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_3_3 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 4 4 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_3_4 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 4 5 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_4_0 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 5 1 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_4_1 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 5 2 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_4_2 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 5 3 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_4_3 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 5 4 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89_4_4 : - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 5 5 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - decide +kernel - -lemma degreeCover89 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, - regionCheck 89 10 17 (d+1) (e+1) (a+1) (c+1) degreeRows89_0 degreeRegions89 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCover89_0_0 - · exact degreeCover89_0_1 - · exact degreeCover89_0_2 - · exact degreeCover89_0_3 - · exact degreeCover89_0_4 - · exact degreeCover89_1_0 - · exact degreeCover89_1_1 - · exact degreeCover89_1_2 - · exact degreeCover89_1_3 - · exact degreeCover89_1_4 - · exact degreeCover89_2_0 - · exact degreeCover89_2_1 - · exact degreeCover89_2_2 - · exact degreeCover89_2_3 - · exact degreeCover89_2_4 - · exact degreeCover89_3_0 - · exact degreeCover89_3_1 - · exact degreeCover89_3_2 - · exact degreeCover89_3_3 - · exact degreeCover89_3_4 - · exact degreeCover89_4_0 - · exact degreeCover89_4_1 - · exact degreeCover89_4_2 - · exact degreeCover89_4_3 - · exact degreeCover89_4_4 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans89 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData89 + +namespace OAI + +/-! Degree Cover 89. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCover89_0_0 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 1 1 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_0_1 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 1 2 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_0_2 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 1 3 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_0_3 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 1 4 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_0_4 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 1 5 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_1_0 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 2 1 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_1_1 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 2 2 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_1_2 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 2 3 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_1_3 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 2 4 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_1_4 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 2 5 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_2_0 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 3 1 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_2_1 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 3 2 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_2_2 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 3 3 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_2_3 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 3 4 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_2_4 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 3 5 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_3_0 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 4 1 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_3_1 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 4 2 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_3_2 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 4 3 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_3_3 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 4 4 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_3_4 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 4 5 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_4_0 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 5 1 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_4_1 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 5 2 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_4_2 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 5 3 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_4_3 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 5 4 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89_4_4 : + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 5 5 (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + decide +kernel + +lemma degreeCover89 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows89_0.length, ∀ c ∈ List.range degreeRows89_0.length, + regionCheck 89 10 17 (d+1) (e+1) (a+1) (c+1) degreeRows89_0 degreeRegions89 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCover89_0_0 + · exact degreeCover89_0_1 + · exact degreeCover89_0_2 + · exact degreeCover89_0_3 + · exact degreeCover89_0_4 + · exact degreeCover89_1_0 + · exact degreeCover89_1_1 + · exact degreeCover89_1_2 + · exact degreeCover89_1_3 + · exact degreeCover89_1_4 + · exact degreeCover89_2_0 + · exact degreeCover89_2_1 + · exact degreeCover89_2_2 + · exact degreeCover89_2_3 + · exact degreeCover89_2_4 + · exact degreeCover89_3_0 + · exact degreeCover89_3_1 + · exact degreeCover89_3_2 + · exact degreeCover89_3_3 + · exact degreeCover89_3_4 + · exact degreeCover89_4_0 + · exact degreeCover89_4_1 + · exact degreeCover89_4_2 + · exact degreeCover89_4_3 + · exact degreeCover89_4_4 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeEight.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeEight.lean index afbb4f745b6209b3c06ad2f96e704a98af3691a1..3257c693584cb161525c85e66304001b97609c62 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeEight.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeEight.lean @@ -1,482 +1,482 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.EightSplitCertificate - -namespace OAI - -/-! Degree Eight. -/ - -section - -open Saxl Saxl.Columns -namespace UniversalTensorSquare - -def eightWitness : YoungDiagram := diagramOfCols [4,2,1,1] (by decide) - -lemma eightWitness_cols : eightWitness.transpose.rowLens = [4,2,1,1] := - diagramOfCols_cols _ _ (by simp) - -lemma eightWitness_card : eightWitness.card = 8 := - diagramOfCols_card _ _ (by simp) - -lemma eightWitness_self : eightWitness.transpose = eightWitness := by - apply YoungDiagram.ext - decide - -def eightPlaceB0 : Equiv.Perm (Fin 8) := Equiv.swap 5 4 * (Equiv.swap 4 7 * (Equiv.swap 1 6 * (Equiv.swap 1 3 * (Equiv.swap 0 2)))) - -def eightPlaceT0 : Equiv.Perm (Fin 8) := Equiv.swap 0 7 * (Equiv.swap 0 1 * (Equiv.swap 0 3 * (Equiv.swap 1 5 * (Equiv.swap 0 2)))) - -def eightFlag0 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,0,2),(0,1,1),(0,1,3),(0,2,1),(0,3,0)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma eightCertificate0 : contractionInteger [4,2,1,1] [4,2,1,1] [1,1,1,1,1,1,1,1] - (Equiv.refl (Fin 8)) eightPlaceB0 eightPlaceT0 eightFlag0 = 6 := by - unfold eightFlag0 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def eightPlaceB1 : Equiv.Perm (Fin 8) := Equiv.swap 5 3 * (Equiv.swap 5 6 * (Equiv.swap 3 0 * (Equiv.swap 2 4 * (Equiv.swap 0 7 * (Equiv.swap 0 1))))) - -def eightPlaceT1 : Equiv.Perm (Fin 8) := Equiv.swap 5 6 * (Equiv.swap 2 4 * (Equiv.swap 0 3)) - -def eightFlag1 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,1,1),(0,3,3),(1,2,2)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma eightCertificate1 : contractionInteger [4,2,1,1] [4,2,1,1] [2,1,1,1,1,1,1] - (Equiv.refl (Fin 8)) eightPlaceB1 eightPlaceT1 eightFlag1 = -1 := by - unfold eightFlag1 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def eightPlaceB2 : Equiv.Perm (Fin 8) := Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 3 5 * (Equiv.swap 2 0 * (Equiv.swap 0 6)))) - -def eightPlaceT2 : Equiv.Perm (Fin 8) := Equiv.swap 2 5 * (Equiv.swap 5 7 * (Equiv.swap 0 4 * (Equiv.swap 2 1 * (Equiv.swap 1 6 * (Equiv.swap 0 3))))) - -def eightFlag2 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,1),(0,1,0),(0,2,3),(0,3,2),(1,0,0)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma eightCertificate2 : contractionInteger [4,2,1,1] [4,2,1,1] [2,2,1,1,1,1] - (Equiv.refl (Fin 8)) eightPlaceB2 eightPlaceT2 eightFlag2 = -2 := by - unfold eightFlag2 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def eightPlaceB3 : Equiv.Perm (Fin 8) := Equiv.swap 6 1 * (Equiv.swap 3 0 * (Equiv.swap 1 7 * (Equiv.swap 1 2 * (Equiv.swap 0 5)))) - -def eightPlaceT3 : Equiv.Perm (Fin 8) := Equiv.swap 1 7 * (Equiv.swap 1 6 * (Equiv.swap 1 0 * (Equiv.swap 0 5))) - -def eightFlag3 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,1,1),(0,2,3),(0,3,1),(1,1,0),(2,0,2)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma eightCertificate3 : contractionInteger [4,2,1,1] [4,2,1,1] [3,1,1,1,1,1] - (Equiv.refl (Fin 8)) eightPlaceB3 eightPlaceT3 eightFlag3 = -1 := by - unfold eightFlag3 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def eightPlaceB4 : Equiv.Perm (Fin 8) := Equiv.swap 4 1 * (Equiv.swap 4 6 * (Equiv.swap 4 5 * (Equiv.swap 1 0 * (Equiv.swap 0 7 * (Equiv.swap 1 3 * (Equiv.swap 0 2)))))) - -def eightPlaceT4 : Equiv.Perm (Fin 8) := Equiv.swap 1 0 * (Equiv.swap 1 3 * (Equiv.swap 1 5 * (Equiv.swap 3 6 * (Equiv.swap 1 4 * (Equiv.swap 1 2 * (Equiv.swap 0 7)))))) - -def eightFlag4 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,1,1),(0,1,3),(1,0,1),(1,2,0),(1,3,2)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma eightCertificate4 : contractionInteger [4,2,1,1] [4,2,1,1] [2,2,2,1,1] - (Equiv.refl (Fin 8)) eightPlaceB4 eightPlaceT4 eightFlag4 = -2 := by - unfold eightFlag4 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def eightPlaceB5 : Equiv.Perm (Fin 8) := Equiv.swap 5 4 * (Equiv.swap 4 0 * (Equiv.swap 3 6 * (Equiv.swap 0 7 * (Equiv.swap 0 2)))) - -def eightPlaceT5 : Equiv.Perm (Fin 8) := Equiv.swap 6 1 * (Equiv.swap 1 3 * (Equiv.swap 3 2 * (Equiv.swap 2 7 * (Equiv.swap 1 5 * (Equiv.swap 0 4))))) - -def eightFlag5 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,2,3),(0,3,2),(1,0,1),(1,1,0),(2,1,1)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma eightCertificate5 : contractionInteger [4,2,1,1] [4,2,1,1] [3,2,1,1,1] - (Equiv.refl (Fin 8)) eightPlaceB5 eightPlaceT5 eightFlag5 = 2 := by - unfold eightFlag5 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def eightPlaceB6 : Equiv.Perm (Fin 8) := Equiv.swap 1 6 * (Equiv.swap 3 0 * (Equiv.swap 3 4 * (Equiv.swap 1 5 * (Equiv.swap 0 7)))) - -def eightPlaceT6 : Equiv.Perm (Fin 8) := Equiv.swap 3 6 * (Equiv.swap 3 5 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 4)))) - -def eightFlag6 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,1,1),(1,0,3),(2,2,0),(3,3,2)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma eightCertificate6 : contractionInteger [4,2,1,1] [4,2,1,1] [4,1,1,1,1] - (Equiv.refl (Fin 8)) eightPlaceB6 eightPlaceT6 eightFlag6 = -3 := by - unfold eightFlag6 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def eightPlaceB7 : Equiv.Perm (Fin 8) := Equiv.swap 6 3 * (Equiv.swap 3 0 * (Equiv.swap 0 7 * (Equiv.swap 0 2))) - -def eightPlaceT7 : Equiv.Perm (Fin 8) := Equiv.swap 6 4 * (Equiv.swap 4 3 * (Equiv.swap 4 5 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 0 7 * (Equiv.swap 0 1)))))) - -def eightFlag7 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,3,3),(1,0,2),(1,1,1),(1,2,0)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma eightCertificate7 : contractionInteger [4,2,1,1] [4,2,1,1] [2,2,2,2] - (Equiv.refl (Fin 8)) eightPlaceB7 eightPlaceT7 eightFlag7 = 2 := by - unfold eightFlag7 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def eightPlaceB8 : Equiv.Perm (Fin 8) := Equiv.swap 0 4 * (Equiv.swap 4 1 * (Equiv.swap 1 7 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 6))))) - -def eightPlaceT8 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 3 * (Equiv.swap 3 5 * (Equiv.swap 1 6 * (Equiv.swap 1 0 * (Equiv.swap 0 2))))) - -def eightFlag8 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,1,1),(1,0,3),(1,2,0),(1,3,1),(2,1,2)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma eightCertificate8 : contractionInteger [4,2,1,1] [4,2,1,1] [3,2,2,1] - (Equiv.refl (Fin 8)) eightPlaceB8 eightPlaceT8 eightFlag8 = -3 := by - unfold eightFlag8 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def eightPlaceB9 : Equiv.Perm (Fin 8) := Equiv.swap 5 0 * (Equiv.swap 0 7 * (Equiv.swap 2 6 * (Equiv.swap 0 4 * (Equiv.swap 0 1)))) - -def eightPlaceT9 : Equiv.Perm (Fin 8) := Equiv.swap 5 1 * (Equiv.swap 2 3 * (Equiv.swap 1 0 * (Equiv.swap 0 6))) - -def eightFlag9 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,1),(0,2,0),(0,3,2),(1,1,0),(2,0,0),(2,0,3)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma eightCertificate9 : contractionInteger [4,2,1,1] [4,2,1,1] [3,3,1,1] - (Equiv.refl (Fin 8)) eightPlaceB9 eightPlaceT9 eightFlag9 = 3 := by - unfold eightFlag9 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def eightPlaceB11 : Equiv.Perm (Fin 8) := Equiv.swap 2 7 * (Equiv.swap 2 4 * (Equiv.swap 4 3 * (Equiv.swap 3 6 * (Equiv.swap 2 5)))) - -def eightPlaceT11 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 1 * (Equiv.swap 1 2 * (Equiv.swap 2 5 * (Equiv.swap 1 3)))) - -def eightFlag11 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,1,0),(0,2,3),(1,0,0),(1,3,2),(2,0,1)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma eightCertificate11 : contractionInteger [4,2,1,1] [4,2,1,1] [3,3,2] - (Equiv.refl (Fin 8)) eightPlaceB11 eightPlaceT11 eightFlag11 = 1 := by - unfold eightFlag11 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -noncomputable section - -lemma eight_positive_certificate (rs : List ℕ) (hs : rs.SortedGE) - (hp : ∀ a ∈ rs, 0 < a) (hn : rs.sum = 8) - (eb : Equiv.Perm (Fin 8)) (et : Fin 8 ≃ Fin rs.sum) - (L : ℕ → ℕ → ℕ → ℤ) - (hc : contractionInteger [4,2,1,1] [4,2,1,1] rs (Equiv.refl _) eb et L ≠ 0) : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols rs hs) ((diagramOfCols_card rs hs hp).trans hn)) := by - exact kronecker_pos_of_integer_certificate _ _ _ [4,2,1,1] [4,2,1,1] rs - eightWitness_cols eightWitness_cols (diagramOfCols_cols _ _ hp) - (Equiv.refl _) eb et L hc - -lemma eight_positive0 : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols [1,1,1,1,1,1,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply eight_positive_certificate [1,1,1,1,1,1,1,1] (by decide) (by simp) rfl - eightPlaceB0 eightPlaceT0 eightFlag0 - intro hz - have hh : (6 : ℤ) = 0 := eightCertificate0.symm.trans hz - norm_num at hh - -lemma eight_positive1 : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols [2,1,1,1,1,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply eight_positive_certificate [2,1,1,1,1,1,1] (by decide) (by simp) rfl - eightPlaceB1 eightPlaceT1 eightFlag1 - intro hz - have hh : (-1 : ℤ) = 0 := eightCertificate1.symm.trans hz - norm_num at hh - -lemma eight_positive2 : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols [2,2,1,1,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply eight_positive_certificate [2,2,1,1,1,1] (by decide) (by simp) rfl - eightPlaceB2 eightPlaceT2 eightFlag2 - intro hz - have hh : (-2 : ℤ) = 0 := eightCertificate2.symm.trans hz - norm_num at hh - -lemma eight_positive3 : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols [3,1,1,1,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply eight_positive_certificate [3,1,1,1,1,1] (by decide) (by simp) rfl - eightPlaceB3 eightPlaceT3 eightFlag3 - intro hz - have hh : (-1 : ℤ) = 0 := eightCertificate3.symm.trans hz - norm_num at hh - -lemma eight_positive4 : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols [2,2,2,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply eight_positive_certificate [2,2,2,1,1] (by decide) (by simp) rfl - eightPlaceB4 eightPlaceT4 eightFlag4 - intro hz - have hh : (-2 : ℤ) = 0 := eightCertificate4.symm.trans hz - norm_num at hh - -lemma eight_positive5 : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols [3,2,1,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply eight_positive_certificate [3,2,1,1,1] (by decide) (by simp) rfl - eightPlaceB5 eightPlaceT5 eightFlag5 - intro hz - have hh : (2 : ℤ) = 0 := eightCertificate5.symm.trans hz - norm_num at hh - -lemma eight_positive6 : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols [4,1,1,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply eight_positive_certificate [4,1,1,1,1] (by decide) (by simp) rfl - eightPlaceB6 eightPlaceT6 eightFlag6 - intro hz - have hh : (-3 : ℤ) = 0 := eightCertificate6.symm.trans hz - norm_num at hh - -lemma eight_positive7 : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols [2,2,2,2] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply eight_positive_certificate [2,2,2,2] (by decide) (by simp) rfl - eightPlaceB7 eightPlaceT7 eightFlag7 - intro hz - have hh : (2 : ℤ) = 0 := eightCertificate7.symm.trans hz - norm_num at hh - -lemma eight_positive8 : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols [3,2,2,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply eight_positive_certificate [3,2,2,1] (by decide) (by simp) rfl - eightPlaceB8 eightPlaceT8 eightFlag8 - intro hz - have hh : (-3 : ℤ) = 0 := eightCertificate8.symm.trans hz - norm_num at hh - -lemma eight_positive9 : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols [3,3,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply eight_positive_certificate [3,3,1,1] (by decide) (by simp) rfl - eightPlaceB9 eightPlaceT9 eightFlag9 - intro hz - have hh : (3 : ℤ) = 0 := eightCertificate9.symm.trans hz - norm_num at hh - -lemma eight_positive10 : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols [4,2,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply eight_positive_certificate [4,2,1,1] (by decide) (by simp) rfl - eightPlaceB10 eightPlaceT10 eightFlag10 - intro hz - have hh : (-4 : ℤ) = 0 := eightCertificate10.symm.trans hz - norm_num at hh - -lemma eight_positive11 : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau (diagramOfCols [3,3,2] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply eight_positive_certificate [3,3,2] (by decide) (by simp) rfl - eightPlaceB11 eightPlaceT11 eightFlag11 - intro hz - have hh : (1 : ℤ) = 0 := eightCertificate11.symm.trans hz - norm_num at hh - -lemma eight_positive_target_eq {μ ν : YoungDiagram} (hμ : μ.card = 8) (hν : ν.card = 8) - (he : μ = ν) - (hp : 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) (canonicalTableau ν hν)) : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) (canonicalTableau μ hμ) := by - subst ν - exact hp - -lemma partitionLists_eight : partitionLists 8 8 8 = - {[8],[7,1],[6,2],[6,1,1],[5,3],[5,2,1],[5,1,1,1],[4,4],[4,3,1],[4,2,2],[4,2,1,1],[4,1,1,1,1],[3,3,2],[3,3,1,1],[3,2,2,1],[3,2,1,1,1],[3,1,1,1,1,1],[2,2,2,2],[2,2,2,1,1],[2,2,1,1,1,1],[2,1,1,1,1,1,1],[1,1,1,1,1,1,1,1]} := by decide - -theorem eight_kronecker_pos (ν : YoungDiagram) (hν : ν.card = 8) : - 0 < kronecker (canonicalTableau eightWitness eightWitness_card) - (canonicalTableau eightWitness eightWitness_card) (canonicalTableau ν hν) := by - have hc := rowLens_mem_partitionLists ν.transpose - rw [transpose_card, hν, partitionLists_eight] at hc - simp only [Finset.mem_insert, Finset.mem_singleton] at hc - rcases hc with h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h - · have he := eq_diagramOfCols ν [8] (by decide) h - have ht : diagramOfCols [8] (by decide) = - (diagramOfCols [1,1,1,1,1,1,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self - _ _ eight_positive0 - exact eight_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [7,1] (by decide) h - have ht : diagramOfCols [7,1] (by decide) = - (diagramOfCols [2,1,1,1,1,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self - _ _ eight_positive1 - exact eight_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [6,2] (by decide) h - have ht : diagramOfCols [6,2] (by decide) = - (diagramOfCols [2,2,1,1,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self - _ _ eight_positive2 - exact eight_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [6,1,1] (by decide) h - have ht : diagramOfCols [6,1,1] (by decide) = - (diagramOfCols [3,1,1,1,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self - _ _ eight_positive3 - exact eight_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [5,3] (by decide) h - have ht : diagramOfCols [5,3] (by decide) = - (diagramOfCols [2,2,2,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self - _ _ eight_positive4 - exact eight_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [5,2,1] (by decide) h - have ht : diagramOfCols [5,2,1] (by decide) = - (diagramOfCols [3,2,1,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self - _ _ eight_positive5 - exact eight_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [5,1,1,1] (by decide) h - have ht : diagramOfCols [5,1,1,1] (by decide) = - (diagramOfCols [4,1,1,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self - _ _ eight_positive6 - exact eight_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [4,4] (by decide) h - have ht : diagramOfCols [4,4] (by decide) = - (diagramOfCols [2,2,2,2] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self - _ _ eight_positive7 - exact eight_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [4,3,1] (by decide) h - have ht : diagramOfCols [4,3,1] (by decide) = - (diagramOfCols [3,2,2,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self - _ _ eight_positive8 - exact eight_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [4,2,2] (by decide) h - have ht : diagramOfCols [4,2,2] (by decide) = - (diagramOfCols [3,3,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self - _ _ eight_positive9 - exact eight_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [4,2,1,1] (by decide) h - subst ν - exact eight_positive10 - · have he := eq_diagramOfCols ν [4,1,1,1,1] (by decide) h - subst ν - exact eight_positive6 - · have he := eq_diagramOfCols ν [3,3,2] (by decide) h - subst ν - exact eight_positive11 - · have he := eq_diagramOfCols ν [3,3,1,1] (by decide) h - subst ν - exact eight_positive9 - · have he := eq_diagramOfCols ν [3,2,2,1] (by decide) h - subst ν - exact eight_positive8 - · have he := eq_diagramOfCols ν [3,2,1,1,1] (by decide) h - subst ν - exact eight_positive5 - · have he := eq_diagramOfCols ν [3,1,1,1,1,1] (by decide) h - subst ν - exact eight_positive3 - · have he := eq_diagramOfCols ν [2,2,2,2] (by decide) h - subst ν - exact eight_positive7 - · have he := eq_diagramOfCols ν [2,2,2,1,1] (by decide) h - subst ν - exact eight_positive4 - · have he := eq_diagramOfCols ν [2,2,1,1,1,1] (by decide) h - subst ν - exact eight_positive2 - · have he := eq_diagramOfCols ν [2,1,1,1,1,1,1] (by decide) h - subst ν - exact eight_positive1 - · have he := eq_diagramOfCols ν [1,1,1,1,1,1,1,1] (by decide) h - subst ν - exact eight_positive0 - -universe u - -theorem universal_tensor_square_eight : - ∃ (lam : YoungDiagram) (hlam : lam.card = 8), - (∀ (ν : YoungDiagram) (hν : ν.card = 8), - 0 < kronecker (canonicalTableau lam hlam) - (canonicalTableau lam hlam) (canonicalTableau ν hν)) ∧ - Representation.IsIrreducible (spechtRep (canonicalTableau lam hlam)) ∧ - ∀ (V : Type u) [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin 8)) V) [Representation.IsIrreducible ρ], - ∃ F : Representation.IntertwiningMap ρ - ((spechtRep (canonicalTableau lam hlam)).tprod - (spechtRep (canonicalTableau lam hlam))), Function.Injective F := by - exact ⟨eightWitness, eightWitness_card, eight_kronecker_pos, - irreducibles_of_kronecker_pos _ _ eight_kronecker_pos⟩ - -end -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.EightSplitCertificate + +namespace OAI + +/-! Degree Eight. -/ + +section + +open Saxl Saxl.Columns +namespace UniversalTensorSquare + +def eightWitness : YoungDiagram := diagramOfCols [4,2,1,1] (by decide) + +lemma eightWitness_cols : eightWitness.transpose.rowLens = [4,2,1,1] := + diagramOfCols_cols _ _ (by simp) + +lemma eightWitness_card : eightWitness.card = 8 := + diagramOfCols_card _ _ (by simp) + +lemma eightWitness_self : eightWitness.transpose = eightWitness := by + apply YoungDiagram.ext + decide + +def eightPlaceB0 : Equiv.Perm (Fin 8) := Equiv.swap 5 4 * (Equiv.swap 4 7 * (Equiv.swap 1 6 * (Equiv.swap 1 3 * (Equiv.swap 0 2)))) + +def eightPlaceT0 : Equiv.Perm (Fin 8) := Equiv.swap 0 7 * (Equiv.swap 0 1 * (Equiv.swap 0 3 * (Equiv.swap 1 5 * (Equiv.swap 0 2)))) + +def eightFlag0 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,0,2),(0,1,1),(0,1,3),(0,2,1),(0,3,0)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma eightCertificate0 : contractionInteger [4,2,1,1] [4,2,1,1] [1,1,1,1,1,1,1,1] + (Equiv.refl (Fin 8)) eightPlaceB0 eightPlaceT0 eightFlag0 = 6 := by + unfold eightFlag0 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def eightPlaceB1 : Equiv.Perm (Fin 8) := Equiv.swap 5 3 * (Equiv.swap 5 6 * (Equiv.swap 3 0 * (Equiv.swap 2 4 * (Equiv.swap 0 7 * (Equiv.swap 0 1))))) + +def eightPlaceT1 : Equiv.Perm (Fin 8) := Equiv.swap 5 6 * (Equiv.swap 2 4 * (Equiv.swap 0 3)) + +def eightFlag1 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,1,1),(0,3,3),(1,2,2)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma eightCertificate1 : contractionInteger [4,2,1,1] [4,2,1,1] [2,1,1,1,1,1,1] + (Equiv.refl (Fin 8)) eightPlaceB1 eightPlaceT1 eightFlag1 = -1 := by + unfold eightFlag1 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def eightPlaceB2 : Equiv.Perm (Fin 8) := Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 3 5 * (Equiv.swap 2 0 * (Equiv.swap 0 6)))) + +def eightPlaceT2 : Equiv.Perm (Fin 8) := Equiv.swap 2 5 * (Equiv.swap 5 7 * (Equiv.swap 0 4 * (Equiv.swap 2 1 * (Equiv.swap 1 6 * (Equiv.swap 0 3))))) + +def eightFlag2 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,1),(0,1,0),(0,2,3),(0,3,2),(1,0,0)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma eightCertificate2 : contractionInteger [4,2,1,1] [4,2,1,1] [2,2,1,1,1,1] + (Equiv.refl (Fin 8)) eightPlaceB2 eightPlaceT2 eightFlag2 = -2 := by + unfold eightFlag2 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def eightPlaceB3 : Equiv.Perm (Fin 8) := Equiv.swap 6 1 * (Equiv.swap 3 0 * (Equiv.swap 1 7 * (Equiv.swap 1 2 * (Equiv.swap 0 5)))) + +def eightPlaceT3 : Equiv.Perm (Fin 8) := Equiv.swap 1 7 * (Equiv.swap 1 6 * (Equiv.swap 1 0 * (Equiv.swap 0 5))) + +def eightFlag3 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,1,1),(0,2,3),(0,3,1),(1,1,0),(2,0,2)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma eightCertificate3 : contractionInteger [4,2,1,1] [4,2,1,1] [3,1,1,1,1,1] + (Equiv.refl (Fin 8)) eightPlaceB3 eightPlaceT3 eightFlag3 = -1 := by + unfold eightFlag3 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def eightPlaceB4 : Equiv.Perm (Fin 8) := Equiv.swap 4 1 * (Equiv.swap 4 6 * (Equiv.swap 4 5 * (Equiv.swap 1 0 * (Equiv.swap 0 7 * (Equiv.swap 1 3 * (Equiv.swap 0 2)))))) + +def eightPlaceT4 : Equiv.Perm (Fin 8) := Equiv.swap 1 0 * (Equiv.swap 1 3 * (Equiv.swap 1 5 * (Equiv.swap 3 6 * (Equiv.swap 1 4 * (Equiv.swap 1 2 * (Equiv.swap 0 7)))))) + +def eightFlag4 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,1,1),(0,1,3),(1,0,1),(1,2,0),(1,3,2)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma eightCertificate4 : contractionInteger [4,2,1,1] [4,2,1,1] [2,2,2,1,1] + (Equiv.refl (Fin 8)) eightPlaceB4 eightPlaceT4 eightFlag4 = -2 := by + unfold eightFlag4 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def eightPlaceB5 : Equiv.Perm (Fin 8) := Equiv.swap 5 4 * (Equiv.swap 4 0 * (Equiv.swap 3 6 * (Equiv.swap 0 7 * (Equiv.swap 0 2)))) + +def eightPlaceT5 : Equiv.Perm (Fin 8) := Equiv.swap 6 1 * (Equiv.swap 1 3 * (Equiv.swap 3 2 * (Equiv.swap 2 7 * (Equiv.swap 1 5 * (Equiv.swap 0 4))))) + +def eightFlag5 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,2,3),(0,3,2),(1,0,1),(1,1,0),(2,1,1)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma eightCertificate5 : contractionInteger [4,2,1,1] [4,2,1,1] [3,2,1,1,1] + (Equiv.refl (Fin 8)) eightPlaceB5 eightPlaceT5 eightFlag5 = 2 := by + unfold eightFlag5 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def eightPlaceB6 : Equiv.Perm (Fin 8) := Equiv.swap 1 6 * (Equiv.swap 3 0 * (Equiv.swap 3 4 * (Equiv.swap 1 5 * (Equiv.swap 0 7)))) + +def eightPlaceT6 : Equiv.Perm (Fin 8) := Equiv.swap 3 6 * (Equiv.swap 3 5 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 4)))) + +def eightFlag6 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,1,1),(1,0,3),(2,2,0),(3,3,2)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma eightCertificate6 : contractionInteger [4,2,1,1] [4,2,1,1] [4,1,1,1,1] + (Equiv.refl (Fin 8)) eightPlaceB6 eightPlaceT6 eightFlag6 = -3 := by + unfold eightFlag6 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def eightPlaceB7 : Equiv.Perm (Fin 8) := Equiv.swap 6 3 * (Equiv.swap 3 0 * (Equiv.swap 0 7 * (Equiv.swap 0 2))) + +def eightPlaceT7 : Equiv.Perm (Fin 8) := Equiv.swap 6 4 * (Equiv.swap 4 3 * (Equiv.swap 4 5 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 0 7 * (Equiv.swap 0 1)))))) + +def eightFlag7 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,3,3),(1,0,2),(1,1,1),(1,2,0)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma eightCertificate7 : contractionInteger [4,2,1,1] [4,2,1,1] [2,2,2,2] + (Equiv.refl (Fin 8)) eightPlaceB7 eightPlaceT7 eightFlag7 = 2 := by + unfold eightFlag7 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def eightPlaceB8 : Equiv.Perm (Fin 8) := Equiv.swap 0 4 * (Equiv.swap 4 1 * (Equiv.swap 1 7 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 6))))) + +def eightPlaceT8 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 3 * (Equiv.swap 3 5 * (Equiv.swap 1 6 * (Equiv.swap 1 0 * (Equiv.swap 0 2))))) + +def eightFlag8 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,1,1),(1,0,3),(1,2,0),(1,3,1),(2,1,2)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma eightCertificate8 : contractionInteger [4,2,1,1] [4,2,1,1] [3,2,2,1] + (Equiv.refl (Fin 8)) eightPlaceB8 eightPlaceT8 eightFlag8 = -3 := by + unfold eightFlag8 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def eightPlaceB9 : Equiv.Perm (Fin 8) := Equiv.swap 5 0 * (Equiv.swap 0 7 * (Equiv.swap 2 6 * (Equiv.swap 0 4 * (Equiv.swap 0 1)))) + +def eightPlaceT9 : Equiv.Perm (Fin 8) := Equiv.swap 5 1 * (Equiv.swap 2 3 * (Equiv.swap 1 0 * (Equiv.swap 0 6))) + +def eightFlag9 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,1),(0,2,0),(0,3,2),(1,1,0),(2,0,0),(2,0,3)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma eightCertificate9 : contractionInteger [4,2,1,1] [4,2,1,1] [3,3,1,1] + (Equiv.refl (Fin 8)) eightPlaceB9 eightPlaceT9 eightFlag9 = 3 := by + unfold eightFlag9 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def eightPlaceB11 : Equiv.Perm (Fin 8) := Equiv.swap 2 7 * (Equiv.swap 2 4 * (Equiv.swap 4 3 * (Equiv.swap 3 6 * (Equiv.swap 2 5)))) + +def eightPlaceT11 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 1 * (Equiv.swap 1 2 * (Equiv.swap 2 5 * (Equiv.swap 1 3)))) + +def eightFlag11 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,1,0),(0,2,3),(1,0,0),(1,3,2),(2,0,1)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma eightCertificate11 : contractionInteger [4,2,1,1] [4,2,1,1] [3,3,2] + (Equiv.refl (Fin 8)) eightPlaceB11 eightPlaceT11 eightFlag11 = 1 := by + unfold eightFlag11 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +noncomputable section + +lemma eight_positive_certificate (rs : List ℕ) (hs : rs.SortedGE) + (hp : ∀ a ∈ rs, 0 < a) (hn : rs.sum = 8) + (eb : Equiv.Perm (Fin 8)) (et : Fin 8 ≃ Fin rs.sum) + (L : ℕ → ℕ → ℕ → ℤ) + (hc : contractionInteger [4,2,1,1] [4,2,1,1] rs (Equiv.refl _) eb et L ≠ 0) : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols rs hs) ((diagramOfCols_card rs hs hp).trans hn)) := by + exact kronecker_pos_of_integer_certificate _ _ _ [4,2,1,1] [4,2,1,1] rs + eightWitness_cols eightWitness_cols (diagramOfCols_cols _ _ hp) + (Equiv.refl _) eb et L hc + +lemma eight_positive0 : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols [1,1,1,1,1,1,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply eight_positive_certificate [1,1,1,1,1,1,1,1] (by decide) (by simp) rfl + eightPlaceB0 eightPlaceT0 eightFlag0 + intro hz + have hh : (6 : ℤ) = 0 := eightCertificate0.symm.trans hz + norm_num at hh + +lemma eight_positive1 : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols [2,1,1,1,1,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply eight_positive_certificate [2,1,1,1,1,1,1] (by decide) (by simp) rfl + eightPlaceB1 eightPlaceT1 eightFlag1 + intro hz + have hh : (-1 : ℤ) = 0 := eightCertificate1.symm.trans hz + norm_num at hh + +lemma eight_positive2 : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols [2,2,1,1,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply eight_positive_certificate [2,2,1,1,1,1] (by decide) (by simp) rfl + eightPlaceB2 eightPlaceT2 eightFlag2 + intro hz + have hh : (-2 : ℤ) = 0 := eightCertificate2.symm.trans hz + norm_num at hh + +lemma eight_positive3 : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols [3,1,1,1,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply eight_positive_certificate [3,1,1,1,1,1] (by decide) (by simp) rfl + eightPlaceB3 eightPlaceT3 eightFlag3 + intro hz + have hh : (-1 : ℤ) = 0 := eightCertificate3.symm.trans hz + norm_num at hh + +lemma eight_positive4 : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols [2,2,2,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply eight_positive_certificate [2,2,2,1,1] (by decide) (by simp) rfl + eightPlaceB4 eightPlaceT4 eightFlag4 + intro hz + have hh : (-2 : ℤ) = 0 := eightCertificate4.symm.trans hz + norm_num at hh + +lemma eight_positive5 : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols [3,2,1,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply eight_positive_certificate [3,2,1,1,1] (by decide) (by simp) rfl + eightPlaceB5 eightPlaceT5 eightFlag5 + intro hz + have hh : (2 : ℤ) = 0 := eightCertificate5.symm.trans hz + norm_num at hh + +lemma eight_positive6 : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols [4,1,1,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply eight_positive_certificate [4,1,1,1,1] (by decide) (by simp) rfl + eightPlaceB6 eightPlaceT6 eightFlag6 + intro hz + have hh : (-3 : ℤ) = 0 := eightCertificate6.symm.trans hz + norm_num at hh + +lemma eight_positive7 : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols [2,2,2,2] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply eight_positive_certificate [2,2,2,2] (by decide) (by simp) rfl + eightPlaceB7 eightPlaceT7 eightFlag7 + intro hz + have hh : (2 : ℤ) = 0 := eightCertificate7.symm.trans hz + norm_num at hh + +lemma eight_positive8 : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols [3,2,2,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply eight_positive_certificate [3,2,2,1] (by decide) (by simp) rfl + eightPlaceB8 eightPlaceT8 eightFlag8 + intro hz + have hh : (-3 : ℤ) = 0 := eightCertificate8.symm.trans hz + norm_num at hh + +lemma eight_positive9 : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols [3,3,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply eight_positive_certificate [3,3,1,1] (by decide) (by simp) rfl + eightPlaceB9 eightPlaceT9 eightFlag9 + intro hz + have hh : (3 : ℤ) = 0 := eightCertificate9.symm.trans hz + norm_num at hh + +lemma eight_positive10 : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols [4,2,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply eight_positive_certificate [4,2,1,1] (by decide) (by simp) rfl + eightPlaceB10 eightPlaceT10 eightFlag10 + intro hz + have hh : (-4 : ℤ) = 0 := eightCertificate10.symm.trans hz + norm_num at hh + +lemma eight_positive11 : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau (diagramOfCols [3,3,2] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply eight_positive_certificate [3,3,2] (by decide) (by simp) rfl + eightPlaceB11 eightPlaceT11 eightFlag11 + intro hz + have hh : (1 : ℤ) = 0 := eightCertificate11.symm.trans hz + norm_num at hh + +lemma eight_positive_target_eq {μ ν : YoungDiagram} (hμ : μ.card = 8) (hν : ν.card = 8) + (he : μ = ν) + (hp : 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) (canonicalTableau ν hν)) : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) (canonicalTableau μ hμ) := by + subst ν + exact hp + +lemma partitionLists_eight : partitionLists 8 8 8 = + {[8],[7,1],[6,2],[6,1,1],[5,3],[5,2,1],[5,1,1,1],[4,4],[4,3,1],[4,2,2],[4,2,1,1],[4,1,1,1,1],[3,3,2],[3,3,1,1],[3,2,2,1],[3,2,1,1,1],[3,1,1,1,1,1],[2,2,2,2],[2,2,2,1,1],[2,2,1,1,1,1],[2,1,1,1,1,1,1],[1,1,1,1,1,1,1,1]} := by decide + +theorem eight_kronecker_pos (ν : YoungDiagram) (hν : ν.card = 8) : + 0 < kronecker (canonicalTableau eightWitness eightWitness_card) + (canonicalTableau eightWitness eightWitness_card) (canonicalTableau ν hν) := by + have hc := rowLens_mem_partitionLists ν.transpose + rw [transpose_card, hν, partitionLists_eight] at hc + simp only [Finset.mem_insert, Finset.mem_singleton] at hc + rcases hc with h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h | h + · have he := eq_diagramOfCols ν [8] (by decide) h + have ht : diagramOfCols [8] (by decide) = + (diagramOfCols [1,1,1,1,1,1,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self + _ _ eight_positive0 + exact eight_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [7,1] (by decide) h + have ht : diagramOfCols [7,1] (by decide) = + (diagramOfCols [2,1,1,1,1,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self + _ _ eight_positive1 + exact eight_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [6,2] (by decide) h + have ht : diagramOfCols [6,2] (by decide) = + (diagramOfCols [2,2,1,1,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self + _ _ eight_positive2 + exact eight_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [6,1,1] (by decide) h + have ht : diagramOfCols [6,1,1] (by decide) = + (diagramOfCols [3,1,1,1,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self + _ _ eight_positive3 + exact eight_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [5,3] (by decide) h + have ht : diagramOfCols [5,3] (by decide) = + (diagramOfCols [2,2,2,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self + _ _ eight_positive4 + exact eight_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [5,2,1] (by decide) h + have ht : diagramOfCols [5,2,1] (by decide) = + (diagramOfCols [3,2,1,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self + _ _ eight_positive5 + exact eight_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [5,1,1,1] (by decide) h + have ht : diagramOfCols [5,1,1,1] (by decide) = + (diagramOfCols [4,1,1,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self + _ _ eight_positive6 + exact eight_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [4,4] (by decide) h + have ht : diagramOfCols [4,4] (by decide) = + (diagramOfCols [2,2,2,2] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self + _ _ eight_positive7 + exact eight_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [4,3,1] (by decide) h + have ht : diagramOfCols [4,3,1] (by decide) = + (diagramOfCols [3,2,2,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self + _ _ eight_positive8 + exact eight_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [4,2,2] (by decide) h + have ht : diagramOfCols [4,2,2] (by decide) = + (diagramOfCols [3,3,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose eightWitness eightWitness_card eightWitness_self + _ _ eight_positive9 + exact eight_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [4,2,1,1] (by decide) h + subst ν + exact eight_positive10 + · have he := eq_diagramOfCols ν [4,1,1,1,1] (by decide) h + subst ν + exact eight_positive6 + · have he := eq_diagramOfCols ν [3,3,2] (by decide) h + subst ν + exact eight_positive11 + · have he := eq_diagramOfCols ν [3,3,1,1] (by decide) h + subst ν + exact eight_positive9 + · have he := eq_diagramOfCols ν [3,2,2,1] (by decide) h + subst ν + exact eight_positive8 + · have he := eq_diagramOfCols ν [3,2,1,1,1] (by decide) h + subst ν + exact eight_positive5 + · have he := eq_diagramOfCols ν [3,1,1,1,1,1] (by decide) h + subst ν + exact eight_positive3 + · have he := eq_diagramOfCols ν [2,2,2,2] (by decide) h + subst ν + exact eight_positive7 + · have he := eq_diagramOfCols ν [2,2,2,1,1] (by decide) h + subst ν + exact eight_positive4 + · have he := eq_diagramOfCols ν [2,2,1,1,1,1] (by decide) h + subst ν + exact eight_positive2 + · have he := eq_diagramOfCols ν [2,1,1,1,1,1,1] (by decide) h + subst ν + exact eight_positive1 + · have he := eq_diagramOfCols ν [1,1,1,1,1,1,1,1] (by decide) h + subst ν + exact eight_positive0 + +universe u + +theorem universal_tensor_square_eight : + ∃ (lam : YoungDiagram) (hlam : lam.card = 8), + (∀ (ν : YoungDiagram) (hν : ν.card = 8), + 0 < kronecker (canonicalTableau lam hlam) + (canonicalTableau lam hlam) (canonicalTableau ν hν)) ∧ + Representation.IsIrreducible (spechtRep (canonicalTableau lam hlam)) ∧ + ∀ (V : Type u) [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin 8)) V) [Representation.IsIrreducible ρ], + ∃ F : Representation.IntertwiningMap ρ + ((spechtRep (canonicalTableau lam hlam)).tprod + (spechtRep (canonicalTableau lam hlam))), Function.Injective F := by + exact ⟨eightWitness, eightWitness_card, eight_kronecker_pos, + irreducibles_of_kronecker_pos _ _ eight_kronecker_pos⟩ + +end +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeFive.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeFive.lean index f001453c899e91b93930b637bb846ec2959918ef..0183c36e3127d6da94d02114478f712b90f8e787 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeFive.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeFive.lean @@ -1,191 +1,191 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ColumnCertificates -import OAI.RepresentationTheory.UniversalSquare.Support.NumericalSupport - -namespace OAI - -/-! Degree Five. -/ - -section - -open Saxl Saxl.Columns -namespace UniversalTensorSquare - -def fiveWitness : YoungDiagram := diagramOfCols [3,1,1] (by decide) - -lemma fiveWitness_cols : fiveWitness.transpose.rowLens = [3,1,1] := - diagramOfCols_cols _ _ (by simp) - -lemma fiveWitness_card : fiveWitness.card = 5 := - diagramOfCols_card _ _ (by simp) - -lemma fiveWitness_self : fiveWitness.transpose = fiveWitness := by - apply YoungDiagram.ext - decide - -def hookPlacement : Equiv.Perm (Fin 5) := Equiv.swap 1 3 * Equiv.swap 2 4 - -def flag5 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(1,1,0),(2,2,0),(3,0,1),(4,0,2)] : List (ℕ × ℕ × ℕ)) - then 1 else 0 - -def flag41 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(1,1,1),(2,2,0),(3,0,2)] : List (ℕ × ℕ × ℕ)) - then 1 else 0 - -def flag32 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,2),(0,1,1),(1,0,0),(2,2,0)] : List (ℕ × ℕ × ℕ)) - then 1 else 0 - -def flag311 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,1,1),(1,2,0),(2,0,2)] : List (ℕ × ℕ × ℕ)) - then 1 else 0 - -lemma certificate5 : contractionInteger [3,1,1] [3,1,1] [5] - (Equiv.refl (Fin 5)) hookPlacement (Equiv.refl (Fin 5)) flag5 = 20 := by decide +kernel - -lemma certificate41 : contractionInteger [3,1,1] [3,1,1] [4,1] - (Equiv.refl (Fin 5)) hookPlacement (Equiv.refl (Fin 5)) flag41 = 2 := by decide +kernel - -lemma certificate32 : contractionInteger [3,1,1] [3,1,1] [3,2] - (Equiv.refl (Fin 5)) hookPlacement (Equiv.refl (Fin 5)) flag32 = -4 := by decide +kernel - -lemma certificate311 : contractionInteger [3,1,1] [3,1,1] [3,1,1] - (Equiv.refl (Fin 5)) (Equiv.swap (2 : Fin 5) 3) (Equiv.swap (1 : Fin 5) 2 * Equiv.swap (1 : Fin 5) 3) flag311 = 4 := by - decide +kernel - -noncomputable section - -lemma five_positive_certificate (rs : List ℕ) (hs : rs.SortedGE) - (hp : ∀ a ∈ rs, 0 < a) (hn : rs.sum = 5) - (eb : Equiv.Perm (Fin 5)) (et : Fin 5 ≃ Fin rs.sum) - (L : ℕ → ℕ → ℕ → ℤ) - (hc : contractionInteger [3,1,1] [3,1,1] rs (Equiv.refl _) eb et L ≠ 0) : - 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau (diagramOfCols rs hs) ((diagramOfCols_card rs hs hp).trans hn)) := by - exact kronecker_pos_of_integer_certificate _ _ _ [3,1,1] [3,1,1] rs - fiveWitness_cols fiveWitness_cols (diagramOfCols_cols _ _ hp) - (Equiv.refl _) eb et L hc - -lemma five_positive5 : - 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau (diagramOfCols [5] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply five_positive_certificate [5] (by decide) (by simp) rfl - hookPlacement (Equiv.refl _) flag5 - intro hz - have hz' : (20 : ℤ) = 0 := certificate5.symm.trans hz - norm_num at hz' - -lemma five_positive41 : - 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau (diagramOfCols [4,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply five_positive_certificate [4,1] (by decide) (by simp) rfl - hookPlacement (Equiv.refl _) flag41 - intro hz - have hz' : (2 : ℤ) = 0 := certificate41.symm.trans hz - norm_num at hz' - -lemma five_positive32 : - 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau (diagramOfCols [3,2] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply five_positive_certificate [3,2] (by decide) (by simp) rfl - hookPlacement (Equiv.refl _) flag32 - intro hz - have hz' : (-4 : ℤ) = 0 := certificate32.symm.trans hz - norm_num at hz' - -lemma five_positive311 : - 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau fiveWitness fiveWitness_card) := by - apply five_positive_certificate [3,1,1] (by decide) (by simp) rfl - (Equiv.swap 2 3) (Equiv.swap 1 2 * Equiv.swap 1 3) flag311 - intro hz - have hz' : (4 : ℤ) = 0 := certificate311.symm.trans hz - norm_num at hz' - -lemma five_positive_target_eq {μ ν : YoungDiagram} (hμ : μ.card = 5) (hν : ν.card = 5) - (he : μ = ν) - (hp : 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau fiveWitness fiveWitness_card) (canonicalTableau ν hν)) : - 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau fiveWitness fiveWitness_card) (canonicalTableau μ hμ) := by - subst ν - exact hp - -lemma partitionLists_five : partitionLists 5 5 5 = - {[5],[4,1],[3,2],[3,1,1],[2,2,1],[2,1,1,1],[1,1,1,1,1]} := by decide - -theorem five_kronecker_pos (ν : YoungDiagram) (hν : ν.card = 5) : - 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) - (canonicalTableau fiveWitness fiveWitness_card) (canonicalTableau ν hν) := by - have hc := rowLens_mem_partitionLists ν.transpose - rw [transpose_card, hν, partitionLists_five] at hc - simp only [Finset.mem_insert, Finset.mem_singleton] at hc - rcases hc with h | h | h | h | h | h | h - · have he := eq_diagramOfCols ν [5] (by decide) h - subst ν - exact five_positive5 - · have he := eq_diagramOfCols ν [4,1] (by decide) h - subst ν - exact five_positive41 - · have he := eq_diagramOfCols ν [3,2] (by decide) h - subst ν - exact five_positive32 - · have he := eq_diagramOfCols ν [3,1,1] (by decide) h - subst ν - exact five_positive311 - · have he := eq_diagramOfCols ν [2,2,1] (by decide) h - have ht : diagramOfCols [2,2,1] (by decide) = - (diagramOfCols [3,2] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose fiveWitness fiveWitness_card fiveWitness_self - _ _ five_positive32 - exact five_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [2,1,1,1] (by decide) h - have ht : diagramOfCols [2,1,1,1] (by decide) = - (diagramOfCols [4,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose fiveWitness fiveWitness_card fiveWitness_self - _ _ five_positive41 - exact five_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [1,1,1,1,1] (by decide) h - have ht : diagramOfCols [1,1,1,1,1] (by decide) = - (diagramOfCols [5] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose fiveWitness fiveWitness_card fiveWitness_self - _ _ five_positive5 - exact five_positive_target_eq hν _ (he.trans ht) hh - -universe u - -theorem universal_tensor_square_five : - ∃ (lam : YoungDiagram) (hlam : lam.card = 5), - (∀ (ν : YoungDiagram) (hν : ν.card = 5), - 0 < kronecker (canonicalTableau lam hlam) - (canonicalTableau lam hlam) (canonicalTableau ν hν)) ∧ - Representation.IsIrreducible (spechtRep (canonicalTableau lam hlam)) ∧ - ∀ (V : Type u) [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin 5)) V) [Representation.IsIrreducible ρ], - ∃ F : Representation.IntertwiningMap ρ - ((spechtRep (canonicalTableau lam hlam)).tprod - (spechtRep (canonicalTableau lam hlam))), Function.Injective F := by - exact ⟨fiveWitness, fiveWitness_card, five_kronecker_pos, - irreducibles_of_kronecker_pos _ _ five_kronecker_pos⟩ - -end -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ColumnCertificates +import OAI.RepresentationTheory.UniversalSquare.Support.NumericalSupport + +namespace OAI + +/-! Degree Five. -/ + +section + +open Saxl Saxl.Columns +namespace UniversalTensorSquare + +def fiveWitness : YoungDiagram := diagramOfCols [3,1,1] (by decide) + +lemma fiveWitness_cols : fiveWitness.transpose.rowLens = [3,1,1] := + diagramOfCols_cols _ _ (by simp) + +lemma fiveWitness_card : fiveWitness.card = 5 := + diagramOfCols_card _ _ (by simp) + +lemma fiveWitness_self : fiveWitness.transpose = fiveWitness := by + apply YoungDiagram.ext + decide + +def hookPlacement : Equiv.Perm (Fin 5) := Equiv.swap 1 3 * Equiv.swap 2 4 + +def flag5 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(1,1,0),(2,2,0),(3,0,1),(4,0,2)] : List (ℕ × ℕ × ℕ)) + then 1 else 0 + +def flag41 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(1,1,1),(2,2,0),(3,0,2)] : List (ℕ × ℕ × ℕ)) + then 1 else 0 + +def flag32 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,2),(0,1,1),(1,0,0),(2,2,0)] : List (ℕ × ℕ × ℕ)) + then 1 else 0 + +def flag311 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,1,1),(1,2,0),(2,0,2)] : List (ℕ × ℕ × ℕ)) + then 1 else 0 + +lemma certificate5 : contractionInteger [3,1,1] [3,1,1] [5] + (Equiv.refl (Fin 5)) hookPlacement (Equiv.refl (Fin 5)) flag5 = 20 := by decide +kernel + +lemma certificate41 : contractionInteger [3,1,1] [3,1,1] [4,1] + (Equiv.refl (Fin 5)) hookPlacement (Equiv.refl (Fin 5)) flag41 = 2 := by decide +kernel + +lemma certificate32 : contractionInteger [3,1,1] [3,1,1] [3,2] + (Equiv.refl (Fin 5)) hookPlacement (Equiv.refl (Fin 5)) flag32 = -4 := by decide +kernel + +lemma certificate311 : contractionInteger [3,1,1] [3,1,1] [3,1,1] + (Equiv.refl (Fin 5)) (Equiv.swap (2 : Fin 5) 3) (Equiv.swap (1 : Fin 5) 2 * Equiv.swap (1 : Fin 5) 3) flag311 = 4 := by + decide +kernel + +noncomputable section + +lemma five_positive_certificate (rs : List ℕ) (hs : rs.SortedGE) + (hp : ∀ a ∈ rs, 0 < a) (hn : rs.sum = 5) + (eb : Equiv.Perm (Fin 5)) (et : Fin 5 ≃ Fin rs.sum) + (L : ℕ → ℕ → ℕ → ℤ) + (hc : contractionInteger [3,1,1] [3,1,1] rs (Equiv.refl _) eb et L ≠ 0) : + 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau (diagramOfCols rs hs) ((diagramOfCols_card rs hs hp).trans hn)) := by + exact kronecker_pos_of_integer_certificate _ _ _ [3,1,1] [3,1,1] rs + fiveWitness_cols fiveWitness_cols (diagramOfCols_cols _ _ hp) + (Equiv.refl _) eb et L hc + +lemma five_positive5 : + 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau (diagramOfCols [5] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply five_positive_certificate [5] (by decide) (by simp) rfl + hookPlacement (Equiv.refl _) flag5 + intro hz + have hz' : (20 : ℤ) = 0 := certificate5.symm.trans hz + norm_num at hz' + +lemma five_positive41 : + 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau (diagramOfCols [4,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply five_positive_certificate [4,1] (by decide) (by simp) rfl + hookPlacement (Equiv.refl _) flag41 + intro hz + have hz' : (2 : ℤ) = 0 := certificate41.symm.trans hz + norm_num at hz' + +lemma five_positive32 : + 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau (diagramOfCols [3,2] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply five_positive_certificate [3,2] (by decide) (by simp) rfl + hookPlacement (Equiv.refl _) flag32 + intro hz + have hz' : (-4 : ℤ) = 0 := certificate32.symm.trans hz + norm_num at hz' + +lemma five_positive311 : + 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau fiveWitness fiveWitness_card) := by + apply five_positive_certificate [3,1,1] (by decide) (by simp) rfl + (Equiv.swap 2 3) (Equiv.swap 1 2 * Equiv.swap 1 3) flag311 + intro hz + have hz' : (4 : ℤ) = 0 := certificate311.symm.trans hz + norm_num at hz' + +lemma five_positive_target_eq {μ ν : YoungDiagram} (hμ : μ.card = 5) (hν : ν.card = 5) + (he : μ = ν) + (hp : 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau fiveWitness fiveWitness_card) (canonicalTableau ν hν)) : + 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau fiveWitness fiveWitness_card) (canonicalTableau μ hμ) := by + subst ν + exact hp + +lemma partitionLists_five : partitionLists 5 5 5 = + {[5],[4,1],[3,2],[3,1,1],[2,2,1],[2,1,1,1],[1,1,1,1,1]} := by decide + +theorem five_kronecker_pos (ν : YoungDiagram) (hν : ν.card = 5) : + 0 < kronecker (canonicalTableau fiveWitness fiveWitness_card) + (canonicalTableau fiveWitness fiveWitness_card) (canonicalTableau ν hν) := by + have hc := rowLens_mem_partitionLists ν.transpose + rw [transpose_card, hν, partitionLists_five] at hc + simp only [Finset.mem_insert, Finset.mem_singleton] at hc + rcases hc with h | h | h | h | h | h | h + · have he := eq_diagramOfCols ν [5] (by decide) h + subst ν + exact five_positive5 + · have he := eq_diagramOfCols ν [4,1] (by decide) h + subst ν + exact five_positive41 + · have he := eq_diagramOfCols ν [3,2] (by decide) h + subst ν + exact five_positive32 + · have he := eq_diagramOfCols ν [3,1,1] (by decide) h + subst ν + exact five_positive311 + · have he := eq_diagramOfCols ν [2,2,1] (by decide) h + have ht : diagramOfCols [2,2,1] (by decide) = + (diagramOfCols [3,2] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose fiveWitness fiveWitness_card fiveWitness_self + _ _ five_positive32 + exact five_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [2,1,1,1] (by decide) h + have ht : diagramOfCols [2,1,1,1] (by decide) = + (diagramOfCols [4,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose fiveWitness fiveWitness_card fiveWitness_self + _ _ five_positive41 + exact five_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [1,1,1,1,1] (by decide) h + have ht : diagramOfCols [1,1,1,1,1] (by decide) = + (diagramOfCols [5] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose fiveWitness fiveWitness_card fiveWitness_self + _ _ five_positive5 + exact five_positive_target_eq hν _ (he.trans ht) hh + +universe u + +theorem universal_tensor_square_five : + ∃ (lam : YoungDiagram) (hlam : lam.card = 5), + (∀ (ν : YoungDiagram) (hν : ν.card = 5), + 0 < kronecker (canonicalTableau lam hlam) + (canonicalTableau lam hlam) (canonicalTableau ν hν)) ∧ + Representation.IsIrreducible (spechtRep (canonicalTableau lam hlam)) ∧ + ∀ (V : Type u) [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin 5)) V) [Representation.IsIrreducible ρ], + ∃ F : Representation.IntertwiningMap ρ + ((spechtRep (canonicalTableau lam hlam)).tprod + (spechtRep (canonicalTableau lam hlam))), Function.Injective F := by + exact ⟨fiveWitness, fiveWitness_card, five_kronecker_pos, + irreducibles_of_kronecker_pos _ _ five_kronecker_pos⟩ + +end +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves116.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves116.lean index e11ec57048d5fd9b7f72610188a8ef8c960d4103..43b73c76aef136e57176088f227186ab4d9af286 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves116.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves116.lean @@ -1,94 +1,94 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans116 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData116 - -namespace OAI - -/-! Degree Leaves 116. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch116_0 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 0 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_1 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 1 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_2 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 2 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_3 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 3 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_4 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 4 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_5 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 5 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_6 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 6 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_7 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 7 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_8 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 8 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_9 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 9 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_10 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 10 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_11 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 11 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch116_12 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 12 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_13 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 13 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_14 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 14 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_15 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 15 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_16 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 16 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_17 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 17 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_18 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 18 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_19 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 19 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_20 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 20 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_21 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 21 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -lemma degreeUnionBranch116_22 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 22 116 22 degreeHalfRegions116 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans116 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData116 + +namespace OAI + +/-! Degree Leaves 116. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch116_0 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 0 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_1 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 1 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_2 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 2 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_3 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 3 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_4 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 4 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_5 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 5 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_6 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 6 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_7 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 7 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_8 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 8 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_9 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 9 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_10 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 10 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_11 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 11 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch116_12 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 12 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_13 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 13 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_14 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 14 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_15 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 15 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_16 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 16 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_17 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 17 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_18 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 18 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_19 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 19 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_20 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 20 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_21 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 21 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +lemma degreeUnionBranch116_22 : checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) 22 116 22 degreeHalfRegions116 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves118.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves118.lean index 08c7bd4c1ab67d6dab1173ee72f86b8cc1671ff0..c6dfbb4b874aa26a8f3c2e7e60d04244be2dc234 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves118.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves118.lean @@ -1,94 +1,94 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans118 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData118 - -namespace OAI - -/-! Degree Leaves 118. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch118_0 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 0 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_1 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 1 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_2 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 2 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_3 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 3 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_4 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 4 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_5 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 5 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_6 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 6 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_7 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 7 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_8 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 8 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_9 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 9 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_10 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 10 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_11 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 11 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch118_12 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 12 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_13 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 13 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_14 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 14 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_15 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 15 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_16 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 16 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_17 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 17 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_18 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 18 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_19 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 19 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_20 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 20 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_21 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 21 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -lemma degreeUnionBranch118_22 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 22 118 22 degreeHalfRegions118 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans118 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData118 + +namespace OAI + +/-! Degree Leaves 118. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch118_0 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 0 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_1 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 1 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_2 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 2 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_3 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 3 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_4 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 4 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_5 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 5 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_6 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 6 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_7 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 7 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_8 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 8 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_9 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 9 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_10 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 10 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_11 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 11 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch118_12 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 12 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_13 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 13 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_14 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 14 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_15 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 15 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_16 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 16 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_17 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 17 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_18 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 18 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_19 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 19 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_20 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 20 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_21 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 21 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +lemma degreeUnionBranch118_22 : checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) 22 118 22 degreeHalfRegions118 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves14.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves14.lean index caf65dfad1e2ba3bff358fcf494fa26ab8158b89..e89cbaaab02c459453136b7e5b0674b2ba2c109d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves14.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves14.lean @@ -1,67 +1,67 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans14 -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData14 - -namespace OAI - -/-! Degree Leaves 14. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch14_0 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 0 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -lemma degreeUnionBranch14_1 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 1 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -lemma degreeUnionBranch14_2 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 2 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -lemma degreeUnionBranch14_3 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 3 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -lemma degreeUnionBranch14_4 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 4 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -lemma degreeUnionBranch14_5 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 5 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -lemma degreeUnionBranch14_6 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 6 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -lemma degreeUnionBranch14_7 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 7 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -lemma degreeUnionBranch14_8 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 8 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -lemma degreeUnionBranch14_9 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 9 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -lemma degreeUnionBranch14_10 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 10 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -lemma degreeUnionBranch14_11 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 11 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch14_12 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 12 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -lemma degreeUnionBranch14_13 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 13 14 13 degreeHalfRegions14 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans14 +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData14 + +namespace OAI + +/-! Degree Leaves 14. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch14_0 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 0 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +lemma degreeUnionBranch14_1 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 1 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +lemma degreeUnionBranch14_2 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 2 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +lemma degreeUnionBranch14_3 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 3 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +lemma degreeUnionBranch14_4 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 4 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +lemma degreeUnionBranch14_5 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 5 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +lemma degreeUnionBranch14_6 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 6 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +lemma degreeUnionBranch14_7 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 7 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +lemma degreeUnionBranch14_8 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 8 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +lemma degreeUnionBranch14_9 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 9 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +lemma degreeUnionBranch14_10 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 10 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +lemma degreeUnionBranch14_11 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 11 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch14_12 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 12 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +lemma degreeUnionBranch14_13 : checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) 13 14 13 degreeHalfRegions14 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves16.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves16.lean index c0a244eb4c5462550c6f306d33d49129b1732e9f..1501b88a3b3f4f04dbfad8e8ccdf93f8299ed108 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves16.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves16.lean @@ -1,73 +1,73 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans16 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData16 - -namespace OAI - -/-! Degree Leaves 16. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch16_0 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 0 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_1 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 1 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_2 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 2 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_3 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 3 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_4 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 4 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_5 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 5 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_6 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 6 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_7 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 7 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_8 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 8 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_9 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 9 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_10 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 10 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_11 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 11 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch16_12 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 12 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_13 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 13 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_14 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 14 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -lemma degreeUnionBranch16_15 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 15 16 15 degreeHalfRegions16 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans16 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData16 + +namespace OAI + +/-! Degree Leaves 16. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch16_0 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 0 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_1 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 1 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_2 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 2 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_3 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 3 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_4 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 4 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_5 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 5 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_6 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 6 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_7 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 7 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_8 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 8 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_9 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 9 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_10 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 10 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_11 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 11 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch16_12 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 12 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_13 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 13 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_14 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 14 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +lemma degreeUnionBranch16_15 : checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) 15 16 15 degreeHalfRegions16 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves18.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves18.lean index 0d54c8f2d49551c27244af644b65a77d20225e2d..bf4c892d708b902d644d0f6ab987a3225988a354 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves18.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves18.lean @@ -1,79 +1,79 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans18 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData18 - -namespace OAI - -/-! Degree Leaves 18. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch18_0 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 0 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_1 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 1 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_2 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 2 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_3 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 3 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_4 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 4 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_5 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 5 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_6 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 6 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_7 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 7 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_8 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 8 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_9 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 9 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_10 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 10 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_11 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 11 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch18_12 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 12 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_13 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 13 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_14 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 14 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_15 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 15 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_16 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 16 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -lemma degreeUnionBranch18_17 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 17 18 17 degreeHalfRegions18 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans18 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData18 + +namespace OAI + +/-! Degree Leaves 18. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch18_0 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 0 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_1 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 1 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_2 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 2 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_3 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 3 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_4 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 4 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_5 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 5 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_6 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 6 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_7 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 7 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_8 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 8 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_9 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 9 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_10 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 10 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_11 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 11 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch18_12 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 12 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_13 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 13 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_14 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 14 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_15 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 15 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_16 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 16 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +lemma degreeUnionBranch18_17 : checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) 17 18 17 degreeHalfRegions18 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves19.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves19.lean index f41d869d3863c8bfe057832fb0db0096ac1bd263..949736a6f9dc5a3817424d4e790182968c21b4b9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves19.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves19.lean @@ -1,45 +1,45 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans19 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData19 - -namespace OAI - -/-! Degree Leaves 19. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch19_0 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 0 19 8 degreeHalfRegions19 [] = true := by - decide +kernel - -lemma degreeUnionBranch19_1 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 1 19 8 degreeHalfRegions19 [] = true := by - decide +kernel - -lemma degreeUnionBranch19_2 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 2 19 8 degreeHalfRegions19 [] = true := by - decide +kernel - -lemma degreeUnionBranch19_3 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 3 19 8 degreeHalfRegions19 [] = true := by - decide +kernel - -lemma degreeUnionBranch19_4 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 4 19 8 degreeHalfRegions19 [] = true := by - decide +kernel - -lemma degreeUnionBranch19_5 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 5 19 8 degreeHalfRegions19 [] = true := by - decide +kernel - -lemma degreeUnionBranch19_6 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 6 19 8 degreeHalfRegions19 [] = true := by - decide +kernel - -lemma degreeUnionBranch19_7 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 7 19 8 degreeHalfRegions19 [] = true := by - decide +kernel - -lemma degreeUnionBranch19_8 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 8 19 8 degreeHalfRegions19 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans19 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData19 + +namespace OAI + +/-! Degree Leaves 19. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch19_0 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 0 19 8 degreeHalfRegions19 [] = true := by + decide +kernel + +lemma degreeUnionBranch19_1 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 1 19 8 degreeHalfRegions19 [] = true := by + decide +kernel + +lemma degreeUnionBranch19_2 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 2 19 8 degreeHalfRegions19 [] = true := by + decide +kernel + +lemma degreeUnionBranch19_3 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 3 19 8 degreeHalfRegions19 [] = true := by + decide +kernel + +lemma degreeUnionBranch19_4 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 4 19 8 degreeHalfRegions19 [] = true := by + decide +kernel + +lemma degreeUnionBranch19_5 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 5 19 8 degreeHalfRegions19 [] = true := by + decide +kernel + +lemma degreeUnionBranch19_6 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 6 19 8 degreeHalfRegions19 [] = true := by + decide +kernel + +lemma degreeUnionBranch19_7 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 7 19 8 degreeHalfRegions19 [] = true := by + decide +kernel + +lemma degreeUnionBranch19_8 : checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) 8 19 8 degreeHalfRegions19 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves20.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves20.lean index 2cbf58001d9bd0e370bd61f49344504ab6699507..8f0fc87ffecfe7c2f25ac9659cf8cc9f883f69be 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves20.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves20.lean @@ -1,85 +1,85 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans20 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData20 - -namespace OAI - -/-! Degree Leaves 20. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch20_0 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 0 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_1 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 1 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_2 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 2 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_3 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 3 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_4 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 4 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_5 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 5 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_6 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 6 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_7 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 7 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_8 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 8 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_9 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 9 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_10 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 10 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_11 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 11 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch20_12 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 12 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_13 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 13 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_14 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 14 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_15 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 15 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_16 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 16 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_17 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 17 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_18 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 18 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -lemma degreeUnionBranch20_19 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 19 20 19 degreeHalfRegions20 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans20 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData20 + +namespace OAI + +/-! Degree Leaves 20. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch20_0 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 0 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_1 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 1 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_2 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 2 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_3 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 3 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_4 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 4 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_5 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 5 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_6 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 6 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_7 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 7 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_8 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 8 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_9 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 9 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_10 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 10 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_11 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 11 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch20_12 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 12 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_13 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 13 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_14 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 14 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_15 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 15 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_16 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 16 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_17 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 17 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_18 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 18 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +lemma degreeUnionBranch20_19 : checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) 19 20 19 degreeHalfRegions20 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves22.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves22.lean index a636db696236411ab28f910118acfa4413cac205..917f87e1205fa18657529b94aaee5ecdf79d4ca1 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves22.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves22.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans22 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData22 - -namespace OAI - -/-! Degree Leaves 22. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch22_0 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 0 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_1 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 1 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_2 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 2 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_3 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 3 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_4 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 4 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_5 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 5 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_6 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 6 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_7 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 7 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_8 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 8 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_9 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 9 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_10 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 10 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_11 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 11 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch22_12 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 12 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_13 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 13 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_14 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 14 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_15 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 15 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_16 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 16 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_17 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 17 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_18 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 18 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_19 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 19 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_20 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 20 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -lemma degreeUnionBranch22_21 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 21 22 21 degreeHalfRegions22 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans22 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData22 + +namespace OAI + +/-! Degree Leaves 22. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch22_0 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 0 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_1 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 1 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_2 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 2 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_3 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 3 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_4 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 4 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_5 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 5 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_6 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 6 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_7 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 7 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_8 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 8 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_9 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 9 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_10 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 10 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_11 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 11 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch22_12 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 12 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_13 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 13 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_14 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 14 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_15 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 15 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_16 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 16 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_17 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 17 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_18 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 18 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_19 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 19 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_20 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 20 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +lemma degreeUnionBranch22_21 : checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) 21 22 21 degreeHalfRegions22 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves24.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves24.lean index 566dc8d270441b26588d96d23df4f00697853d00..a7e077a0103f3a9cb38ec145fa66d360f8d7e459 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves24.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves24.lean @@ -1,305 +1,305 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans24 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates24 - -namespace OAI - -/-! Degree Leaves 24. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch24_0 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 0 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_1 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 1 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_2 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 2 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_3 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 3 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_4 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 4 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_5 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_7 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 20 4 degreeUnionState24_7 [4] = true := by - decide +kernel - -lemma degreeUnionBranch24_8 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 19 5 degreeUnionState24_8 [5] = true := by - decide +kernel - -lemma degreeUnionBranch24_9 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 18 6 degreeUnionState24_9 [6] = true := by - decide +kernel - -lemma degreeUnionBranch24_10 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 17 7 degreeUnionState24_10 [7] = true := by - decide +kernel - -lemma degreeUnionBranch24_11 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 16 8 degreeUnionState24_11 [8] = true := by - decide +kernel - -lemma degreeUnionBranch24_12 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 15 9 degreeUnionState24_12 [9] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch24_13 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 14 10 degreeUnionState24_13 [10] = true := by - decide +kernel - -lemma degreeUnionBranch24_14 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 13 11 degreeUnionState24_14 [11] = true := by - decide +kernel - -lemma degreeUnionBranch24_15 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 12 12 degreeUnionState24_15 [12] = true := by - decide +kernel - -lemma degreeUnionBranch24_16 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 11 13 degreeUnionState24_16 [13] = true := by - decide +kernel - -lemma degreeUnionBranch24_17 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 10 14 degreeUnionState24_17 [14] = true := by - decide +kernel - -lemma degreeUnionBranch24_18 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 9 15 degreeUnionState24_18 [15] = true := by - decide +kernel - -lemma degreeUnionBranch24_19 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 8 16 degreeUnionState24_19 [16] = true := by - decide +kernel - -lemma degreeUnionBranch24_20 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 7 17 degreeUnionState24_20 [17] = true := by - decide +kernel - -lemma degreeUnionBranch24_21 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 6 18 degreeUnionState24_21 [18] = true := by - decide +kernel - -lemma degreeUnionBranch24_22 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 5 19 degreeUnionState24_22 [19] = true := by - decide +kernel - -lemma degreeUnionBranch24_23 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 4 20 degreeUnionState24_23 [20] = true := by - decide +kernel - -lemma degreeUnionBranch24_24 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 3 21 degreeUnionState24_24 [21] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch24_25 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 2 22 degreeUnionState24_25 [22] = true := by - decide +kernel - -lemma degreeUnionBranch24_26 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 1 23 degreeUnionState24_26 [23] = true := by - decide +kernel - -lemma degreeUnionBranch24_28 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 20 4 degreeUnionState24_28 [4] = true := by - decide +kernel - -lemma degreeUnionBranch24_29 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 19 5 degreeUnionState24_29 [5] = true := by - decide +kernel - -lemma degreeUnionBranch24_30 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 18 6 degreeUnionState24_30 [6] = true := by - decide +kernel - -lemma degreeUnionBranch24_31 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 17 7 degreeUnionState24_31 [7] = true := by - decide +kernel - -lemma degreeUnionBranch24_32 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 16 8 degreeUnionState24_32 [8] = true := by - decide +kernel - -lemma degreeUnionBranch24_33 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 15 9 degreeUnionState24_33 [9] = true := by - decide +kernel - -lemma degreeUnionBranch24_34 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 14 10 degreeUnionState24_34 [10] = true := by - decide +kernel - -lemma degreeUnionBranch24_35 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 13 11 degreeUnionState24_35 [11] = true := by - decide +kernel - -lemma degreeUnionBranch24_36 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 12 12 degreeUnionState24_36 [12] = true := by - decide +kernel - -lemma degreeUnionBranch24_37 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 11 13 degreeUnionState24_37 [13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch24_38 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 10 14 degreeUnionState24_38 [14] = true := by - decide +kernel - -lemma degreeUnionBranch24_39 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 9 15 degreeUnionState24_39 [15] = true := by - decide +kernel - -lemma degreeUnionBranch24_40 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 8 16 degreeUnionState24_40 [16] = true := by - decide +kernel - -lemma degreeUnionBranch24_41 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 7 17 degreeUnionState24_41 [17] = true := by - decide +kernel - -lemma degreeUnionBranch24_42 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 6 18 degreeUnionState24_42 [18] = true := by - decide +kernel - -lemma degreeUnionBranch24_43 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 5 19 degreeUnionState24_43 [19] = true := by - decide +kernel - -lemma degreeUnionBranch24_44 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 4 20 degreeUnionState24_44 [20] = true := by - decide +kernel - -lemma degreeUnionBranch24_45 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 3 21 degreeUnionState24_45 [21] = true := by - decide +kernel - -lemma degreeUnionBranch24_46 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 2 22 degreeUnionState24_46 [22] = true := by - decide +kernel - -lemma degreeUnionBranch24_47 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 1 23 degreeUnionState24_47 [23] = true := by - decide +kernel - -lemma degreeUnionBranch24_49 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 21 3 degreeUnionState24_49 [3] = true := by - decide +kernel - -lemma degreeUnionBranch24_50 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 20 4 degreeUnionState24_50 [4] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch24_51 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 19 5 degreeUnionState24_51 [5] = true := by - decide +kernel - -lemma degreeUnionBranch24_52 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 18 6 degreeUnionState24_52 [6] = true := by - decide +kernel - -lemma degreeUnionBranch24_53 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 17 7 degreeUnionState24_53 [7] = true := by - decide +kernel - -lemma degreeUnionBranch24_54 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 16 8 degreeUnionState24_54 [8] = true := by - decide +kernel - -lemma degreeUnionBranch24_55 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 15 9 degreeUnionState24_55 [9] = true := by - decide +kernel - -lemma degreeUnionBranch24_56 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 14 10 degreeUnionState24_56 [10] = true := by - decide +kernel - -lemma degreeUnionBranch24_57 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 13 11 degreeUnionState24_57 [11] = true := by - decide +kernel - -lemma degreeUnionBranch24_58 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 12 12 degreeUnionState24_58 [12] = true := by - decide +kernel - -lemma degreeUnionBranch24_59 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 11 13 degreeUnionState24_59 [13] = true := by - decide +kernel - -lemma degreeUnionBranch24_60 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 10 14 degreeUnionState24_60 [14] = true := by - decide +kernel - -lemma degreeUnionBranch24_61 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 9 15 degreeUnionState24_61 [15] = true := by - decide +kernel - -lemma degreeUnionBranch24_62 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 8 16 degreeUnionState24_62 [16] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch24_63 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 7 17 degreeUnionState24_63 [17] = true := by - decide +kernel - -lemma degreeUnionBranch24_64 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 6 18 degreeUnionState24_64 [18] = true := by - decide +kernel - -lemma degreeUnionBranch24_65 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 5 19 degreeUnionState24_65 [19] = true := by - decide +kernel - -lemma degreeUnionBranch24_66 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 4 20 degreeUnionState24_66 [20] = true := by - decide +kernel - -lemma degreeUnionBranch24_67 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 3 21 degreeUnionState24_67 [21] = true := by - decide +kernel - -lemma degreeUnionBranch24_68 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 2 22 degreeUnionState24_68 [22] = true := by - decide +kernel - -lemma degreeUnionBranch24_69 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 1 23 degreeUnionState24_69 [23] = true := by - decide +kernel - -lemma degreeUnionBranch24_70 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 9 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_71 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 10 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_72 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 11 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_73 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 12 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_74 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 13 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch24_75 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 14 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_76 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 15 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_77 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 16 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_78 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 17 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_79 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 18 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_80 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 19 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_81 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 20 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_82 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 21 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_83 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 22 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -lemma degreeUnionBranch24_84 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 23 24 23 degreeHalfRegions24 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans24 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates24 + +namespace OAI + +/-! Degree Leaves 24. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch24_0 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 0 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_1 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 1 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_2 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 2 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_3 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 3 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_4 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 4 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_5 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_7 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 20 4 degreeUnionState24_7 [4] = true := by + decide +kernel + +lemma degreeUnionBranch24_8 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 19 5 degreeUnionState24_8 [5] = true := by + decide +kernel + +lemma degreeUnionBranch24_9 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 18 6 degreeUnionState24_9 [6] = true := by + decide +kernel + +lemma degreeUnionBranch24_10 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 17 7 degreeUnionState24_10 [7] = true := by + decide +kernel + +lemma degreeUnionBranch24_11 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 16 8 degreeUnionState24_11 [8] = true := by + decide +kernel + +lemma degreeUnionBranch24_12 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 15 9 degreeUnionState24_12 [9] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch24_13 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 14 10 degreeUnionState24_13 [10] = true := by + decide +kernel + +lemma degreeUnionBranch24_14 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 13 11 degreeUnionState24_14 [11] = true := by + decide +kernel + +lemma degreeUnionBranch24_15 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 12 12 degreeUnionState24_15 [12] = true := by + decide +kernel + +lemma degreeUnionBranch24_16 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 11 13 degreeUnionState24_16 [13] = true := by + decide +kernel + +lemma degreeUnionBranch24_17 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 10 14 degreeUnionState24_17 [14] = true := by + decide +kernel + +lemma degreeUnionBranch24_18 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 9 15 degreeUnionState24_18 [15] = true := by + decide +kernel + +lemma degreeUnionBranch24_19 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 8 16 degreeUnionState24_19 [16] = true := by + decide +kernel + +lemma degreeUnionBranch24_20 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 7 17 degreeUnionState24_20 [17] = true := by + decide +kernel + +lemma degreeUnionBranch24_21 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 6 18 degreeUnionState24_21 [18] = true := by + decide +kernel + +lemma degreeUnionBranch24_22 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 5 19 degreeUnionState24_22 [19] = true := by + decide +kernel + +lemma degreeUnionBranch24_23 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 4 20 degreeUnionState24_23 [20] = true := by + decide +kernel + +lemma degreeUnionBranch24_24 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 3 21 degreeUnionState24_24 [21] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch24_25 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 2 22 degreeUnionState24_25 [22] = true := by + decide +kernel + +lemma degreeUnionBranch24_26 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 5 1 23 degreeUnionState24_26 [23] = true := by + decide +kernel + +lemma degreeUnionBranch24_28 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 20 4 degreeUnionState24_28 [4] = true := by + decide +kernel + +lemma degreeUnionBranch24_29 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 19 5 degreeUnionState24_29 [5] = true := by + decide +kernel + +lemma degreeUnionBranch24_30 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 18 6 degreeUnionState24_30 [6] = true := by + decide +kernel + +lemma degreeUnionBranch24_31 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 17 7 degreeUnionState24_31 [7] = true := by + decide +kernel + +lemma degreeUnionBranch24_32 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 16 8 degreeUnionState24_32 [8] = true := by + decide +kernel + +lemma degreeUnionBranch24_33 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 15 9 degreeUnionState24_33 [9] = true := by + decide +kernel + +lemma degreeUnionBranch24_34 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 14 10 degreeUnionState24_34 [10] = true := by + decide +kernel + +lemma degreeUnionBranch24_35 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 13 11 degreeUnionState24_35 [11] = true := by + decide +kernel + +lemma degreeUnionBranch24_36 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 12 12 degreeUnionState24_36 [12] = true := by + decide +kernel + +lemma degreeUnionBranch24_37 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 11 13 degreeUnionState24_37 [13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch24_38 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 10 14 degreeUnionState24_38 [14] = true := by + decide +kernel + +lemma degreeUnionBranch24_39 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 9 15 degreeUnionState24_39 [15] = true := by + decide +kernel + +lemma degreeUnionBranch24_40 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 8 16 degreeUnionState24_40 [16] = true := by + decide +kernel + +lemma degreeUnionBranch24_41 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 7 17 degreeUnionState24_41 [17] = true := by + decide +kernel + +lemma degreeUnionBranch24_42 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 6 18 degreeUnionState24_42 [18] = true := by + decide +kernel + +lemma degreeUnionBranch24_43 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 5 19 degreeUnionState24_43 [19] = true := by + decide +kernel + +lemma degreeUnionBranch24_44 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 4 20 degreeUnionState24_44 [20] = true := by + decide +kernel + +lemma degreeUnionBranch24_45 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 3 21 degreeUnionState24_45 [21] = true := by + decide +kernel + +lemma degreeUnionBranch24_46 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 2 22 degreeUnionState24_46 [22] = true := by + decide +kernel + +lemma degreeUnionBranch24_47 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 1 23 degreeUnionState24_47 [23] = true := by + decide +kernel + +lemma degreeUnionBranch24_49 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 21 3 degreeUnionState24_49 [3] = true := by + decide +kernel + +lemma degreeUnionBranch24_50 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 20 4 degreeUnionState24_50 [4] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch24_51 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 19 5 degreeUnionState24_51 [5] = true := by + decide +kernel + +lemma degreeUnionBranch24_52 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 18 6 degreeUnionState24_52 [6] = true := by + decide +kernel + +lemma degreeUnionBranch24_53 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 17 7 degreeUnionState24_53 [7] = true := by + decide +kernel + +lemma degreeUnionBranch24_54 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 16 8 degreeUnionState24_54 [8] = true := by + decide +kernel + +lemma degreeUnionBranch24_55 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 15 9 degreeUnionState24_55 [9] = true := by + decide +kernel + +lemma degreeUnionBranch24_56 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 14 10 degreeUnionState24_56 [10] = true := by + decide +kernel + +lemma degreeUnionBranch24_57 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 13 11 degreeUnionState24_57 [11] = true := by + decide +kernel + +lemma degreeUnionBranch24_58 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 12 12 degreeUnionState24_58 [12] = true := by + decide +kernel + +lemma degreeUnionBranch24_59 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 11 13 degreeUnionState24_59 [13] = true := by + decide +kernel + +lemma degreeUnionBranch24_60 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 10 14 degreeUnionState24_60 [14] = true := by + decide +kernel + +lemma degreeUnionBranch24_61 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 9 15 degreeUnionState24_61 [15] = true := by + decide +kernel + +lemma degreeUnionBranch24_62 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 8 16 degreeUnionState24_62 [16] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch24_63 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 7 17 degreeUnionState24_63 [17] = true := by + decide +kernel + +lemma degreeUnionBranch24_64 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 6 18 degreeUnionState24_64 [18] = true := by + decide +kernel + +lemma degreeUnionBranch24_65 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 5 19 degreeUnionState24_65 [19] = true := by + decide +kernel + +lemma degreeUnionBranch24_66 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 4 20 degreeUnionState24_66 [20] = true := by + decide +kernel + +lemma degreeUnionBranch24_67 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 3 21 degreeUnionState24_67 [21] = true := by + decide +kernel + +lemma degreeUnionBranch24_68 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 2 22 degreeUnionState24_68 [22] = true := by + decide +kernel + +lemma degreeUnionBranch24_69 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 1 23 degreeUnionState24_69 [23] = true := by + decide +kernel + +lemma degreeUnionBranch24_70 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 9 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_71 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 10 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_72 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 11 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_73 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 12 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_74 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 13 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch24_75 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 14 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_76 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 15 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_77 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 16 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_78 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 17 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_79 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 18 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_80 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 19 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_81 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 20 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_82 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 21 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_83 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 22 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +lemma degreeUnionBranch24_84 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 23 24 23 degreeHalfRegions24 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves26.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves26.lean index cf34ffed6ba3f6f37b90415d8b343b135ca7fe63..e2f4d59c5dea1225ee2ddb2491098339f73bd86a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves26.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves26.lean @@ -1,336 +1,336 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans26 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates26 - -namespace OAI - -/-! Degree Leaves 26. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch26_0 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 0 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_1 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 1 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_2 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 2 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_3 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 3 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_4 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 4 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_5 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 5 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_6 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_8 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 22 4 degreeUnionState26_8 [4] = true := by - decide +kernel - -lemma degreeUnionBranch26_9 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 21 5 degreeUnionState26_9 [5] = true := by - decide +kernel - -lemma degreeUnionBranch26_10 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 20 6 degreeUnionState26_10 [6] = true := by - decide +kernel - -lemma degreeUnionBranch26_11 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 19 7 degreeUnionState26_11 [7] = true := by - decide +kernel - -lemma degreeUnionBranch26_12 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 18 8 degreeUnionState26_12 [8] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch26_13 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 17 9 degreeUnionState26_13 [9] = true := by - decide +kernel - -lemma degreeUnionBranch26_14 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 16 10 degreeUnionState26_14 [10] = true := by - decide +kernel - -lemma degreeUnionBranch26_15 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 15 11 degreeUnionState26_15 [11] = true := by - decide +kernel - -lemma degreeUnionBranch26_16 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 14 12 degreeUnionState26_16 [12] = true := by - decide +kernel - -lemma degreeUnionBranch26_17 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 13 13 degreeUnionState26_17 [13] = true := by - decide +kernel - -lemma degreeUnionBranch26_18 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 12 14 degreeUnionState26_18 [14] = true := by - decide +kernel - -lemma degreeUnionBranch26_19 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 11 15 degreeUnionState26_19 [15] = true := by - decide +kernel - -lemma degreeUnionBranch26_20 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 10 16 degreeUnionState26_20 [16] = true := by - decide +kernel - -lemma degreeUnionBranch26_21 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 9 17 degreeUnionState26_21 [17] = true := by - decide +kernel - -lemma degreeUnionBranch26_22 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 8 18 degreeUnionState26_22 [18] = true := by - decide +kernel - -lemma degreeUnionBranch26_23 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 7 19 degreeUnionState26_23 [19] = true := by - decide +kernel - -lemma degreeUnionBranch26_24 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 6 20 degreeUnionState26_24 [20] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch26_25 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 5 21 degreeUnionState26_25 [21] = true := by - decide +kernel - -lemma degreeUnionBranch26_26 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 4 22 degreeUnionState26_26 [22] = true := by - decide +kernel - -lemma degreeUnionBranch26_27 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 3 23 degreeUnionState26_27 [23] = true := by - decide +kernel - -lemma degreeUnionBranch26_28 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 2 24 degreeUnionState26_28 [24] = true := by - decide +kernel - -lemma degreeUnionBranch26_29 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 1 25 degreeUnionState26_29 [25] = true := by - decide +kernel - -lemma degreeUnionBranch26_31 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 22 4 degreeUnionState26_31 [4] = true := by - decide +kernel - -lemma degreeUnionBranch26_32 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 21 5 degreeUnionState26_32 [5] = true := by - decide +kernel - -lemma degreeUnionBranch26_33 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 20 6 degreeUnionState26_33 [6] = true := by - decide +kernel - -lemma degreeUnionBranch26_34 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 19 7 degreeUnionState26_34 [7] = true := by - decide +kernel - -lemma degreeUnionBranch26_35 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 18 8 degreeUnionState26_35 [8] = true := by - decide +kernel - -lemma degreeUnionBranch26_36 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 17 9 degreeUnionState26_36 [9] = true := by - decide +kernel - -lemma degreeUnionBranch26_37 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 16 10 degreeUnionState26_37 [10] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch26_38 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 15 11 degreeUnionState26_38 [11] = true := by - decide +kernel - -lemma degreeUnionBranch26_39 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 14 12 degreeUnionState26_39 [12] = true := by - decide +kernel - -lemma degreeUnionBranch26_40 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 13 13 degreeUnionState26_40 [13] = true := by - decide +kernel - -lemma degreeUnionBranch26_41 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 12 14 degreeUnionState26_41 [14] = true := by - decide +kernel - -lemma degreeUnionBranch26_42 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 11 15 degreeUnionState26_42 [15] = true := by - decide +kernel - -lemma degreeUnionBranch26_43 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 10 16 degreeUnionState26_43 [16] = true := by - decide +kernel - -lemma degreeUnionBranch26_44 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 9 17 degreeUnionState26_44 [17] = true := by - decide +kernel - -lemma degreeUnionBranch26_45 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 8 18 degreeUnionState26_45 [18] = true := by - decide +kernel - -lemma degreeUnionBranch26_46 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 7 19 degreeUnionState26_46 [19] = true := by - decide +kernel - -lemma degreeUnionBranch26_47 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 6 20 degreeUnionState26_47 [20] = true := by - decide +kernel - -lemma degreeUnionBranch26_48 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 5 21 degreeUnionState26_48 [21] = true := by - decide +kernel - -lemma degreeUnionBranch26_49 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 4 22 degreeUnionState26_49 [22] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch26_50 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 3 23 degreeUnionState26_50 [23] = true := by - decide +kernel - -lemma degreeUnionBranch26_51 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 2 24 degreeUnionState26_51 [24] = true := by - decide +kernel - -lemma degreeUnionBranch26_52 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 1 25 degreeUnionState26_52 [25] = true := by - decide +kernel - -lemma degreeUnionBranch26_54 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 23 3 degreeUnionState26_54 [3] = true := by - decide +kernel - -lemma degreeUnionBranch26_55 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 22 4 degreeUnionState26_55 [4] = true := by - decide +kernel - -lemma degreeUnionBranch26_56 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 21 5 degreeUnionState26_56 [5] = true := by - decide +kernel - -lemma degreeUnionBranch26_57 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 20 6 degreeUnionState26_57 [6] = true := by - decide +kernel - -lemma degreeUnionBranch26_58 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 19 7 degreeUnionState26_58 [7] = true := by - decide +kernel - -lemma degreeUnionBranch26_59 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 18 8 degreeUnionState26_59 [8] = true := by - decide +kernel - -lemma degreeUnionBranch26_60 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 17 9 degreeUnionState26_60 [9] = true := by - decide +kernel - -lemma degreeUnionBranch26_61 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 16 10 degreeUnionState26_61 [10] = true := by - decide +kernel - -lemma degreeUnionBranch26_62 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 15 11 degreeUnionState26_62 [11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch26_63 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 14 12 degreeUnionState26_63 [12] = true := by - decide +kernel - -lemma degreeUnionBranch26_64 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 13 13 degreeUnionState26_64 [13] = true := by - decide +kernel - -lemma degreeUnionBranch26_65 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 12 14 degreeUnionState26_65 [14] = true := by - decide +kernel - -lemma degreeUnionBranch26_66 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 11 15 degreeUnionState26_66 [15] = true := by - decide +kernel - -lemma degreeUnionBranch26_67 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 10 16 degreeUnionState26_67 [16] = true := by - decide +kernel - -lemma degreeUnionBranch26_68 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 9 17 degreeUnionState26_68 [17] = true := by - decide +kernel - -lemma degreeUnionBranch26_69 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 8 18 degreeUnionState26_69 [18] = true := by - decide +kernel - -lemma degreeUnionBranch26_70 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 7 19 degreeUnionState26_70 [19] = true := by - decide +kernel - -lemma degreeUnionBranch26_71 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 6 20 degreeUnionState26_71 [20] = true := by - decide +kernel - -lemma degreeUnionBranch26_72 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 5 21 degreeUnionState26_72 [21] = true := by - decide +kernel - -lemma degreeUnionBranch26_73 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 4 22 degreeUnionState26_73 [22] = true := by - decide +kernel - -lemma degreeUnionBranch26_74 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 3 23 degreeUnionState26_74 [23] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch26_75 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 2 24 degreeUnionState26_75 [24] = true := by - decide +kernel - -lemma degreeUnionBranch26_76 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 1 25 degreeUnionState26_76 [25] = true := by - decide +kernel - -lemma degreeUnionBranch26_77 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 10 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_78 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 11 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_79 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 12 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_80 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 13 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_81 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 14 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_82 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 15 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_83 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 16 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_84 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 17 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_85 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 18 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_86 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 19 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch26_87 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 20 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_88 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 21 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_89 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 22 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_90 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 23 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_91 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 24 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -lemma degreeUnionBranch26_92 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 25 26 25 degreeHalfRegions26 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans26 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates26 + +namespace OAI + +/-! Degree Leaves 26. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch26_0 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 0 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_1 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 1 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_2 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 2 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_3 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 3 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_4 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 4 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_5 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 5 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_6 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_8 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 22 4 degreeUnionState26_8 [4] = true := by + decide +kernel + +lemma degreeUnionBranch26_9 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 21 5 degreeUnionState26_9 [5] = true := by + decide +kernel + +lemma degreeUnionBranch26_10 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 20 6 degreeUnionState26_10 [6] = true := by + decide +kernel + +lemma degreeUnionBranch26_11 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 19 7 degreeUnionState26_11 [7] = true := by + decide +kernel + +lemma degreeUnionBranch26_12 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 18 8 degreeUnionState26_12 [8] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch26_13 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 17 9 degreeUnionState26_13 [9] = true := by + decide +kernel + +lemma degreeUnionBranch26_14 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 16 10 degreeUnionState26_14 [10] = true := by + decide +kernel + +lemma degreeUnionBranch26_15 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 15 11 degreeUnionState26_15 [11] = true := by + decide +kernel + +lemma degreeUnionBranch26_16 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 14 12 degreeUnionState26_16 [12] = true := by + decide +kernel + +lemma degreeUnionBranch26_17 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 13 13 degreeUnionState26_17 [13] = true := by + decide +kernel + +lemma degreeUnionBranch26_18 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 12 14 degreeUnionState26_18 [14] = true := by + decide +kernel + +lemma degreeUnionBranch26_19 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 11 15 degreeUnionState26_19 [15] = true := by + decide +kernel + +lemma degreeUnionBranch26_20 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 10 16 degreeUnionState26_20 [16] = true := by + decide +kernel + +lemma degreeUnionBranch26_21 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 9 17 degreeUnionState26_21 [17] = true := by + decide +kernel + +lemma degreeUnionBranch26_22 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 8 18 degreeUnionState26_22 [18] = true := by + decide +kernel + +lemma degreeUnionBranch26_23 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 7 19 degreeUnionState26_23 [19] = true := by + decide +kernel + +lemma degreeUnionBranch26_24 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 6 20 degreeUnionState26_24 [20] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch26_25 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 5 21 degreeUnionState26_25 [21] = true := by + decide +kernel + +lemma degreeUnionBranch26_26 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 4 22 degreeUnionState26_26 [22] = true := by + decide +kernel + +lemma degreeUnionBranch26_27 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 3 23 degreeUnionState26_27 [23] = true := by + decide +kernel + +lemma degreeUnionBranch26_28 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 2 24 degreeUnionState26_28 [24] = true := by + decide +kernel + +lemma degreeUnionBranch26_29 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 6 1 25 degreeUnionState26_29 [25] = true := by + decide +kernel + +lemma degreeUnionBranch26_31 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 22 4 degreeUnionState26_31 [4] = true := by + decide +kernel + +lemma degreeUnionBranch26_32 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 21 5 degreeUnionState26_32 [5] = true := by + decide +kernel + +lemma degreeUnionBranch26_33 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 20 6 degreeUnionState26_33 [6] = true := by + decide +kernel + +lemma degreeUnionBranch26_34 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 19 7 degreeUnionState26_34 [7] = true := by + decide +kernel + +lemma degreeUnionBranch26_35 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 18 8 degreeUnionState26_35 [8] = true := by + decide +kernel + +lemma degreeUnionBranch26_36 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 17 9 degreeUnionState26_36 [9] = true := by + decide +kernel + +lemma degreeUnionBranch26_37 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 16 10 degreeUnionState26_37 [10] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch26_38 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 15 11 degreeUnionState26_38 [11] = true := by + decide +kernel + +lemma degreeUnionBranch26_39 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 14 12 degreeUnionState26_39 [12] = true := by + decide +kernel + +lemma degreeUnionBranch26_40 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 13 13 degreeUnionState26_40 [13] = true := by + decide +kernel + +lemma degreeUnionBranch26_41 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 12 14 degreeUnionState26_41 [14] = true := by + decide +kernel + +lemma degreeUnionBranch26_42 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 11 15 degreeUnionState26_42 [15] = true := by + decide +kernel + +lemma degreeUnionBranch26_43 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 10 16 degreeUnionState26_43 [16] = true := by + decide +kernel + +lemma degreeUnionBranch26_44 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 9 17 degreeUnionState26_44 [17] = true := by + decide +kernel + +lemma degreeUnionBranch26_45 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 8 18 degreeUnionState26_45 [18] = true := by + decide +kernel + +lemma degreeUnionBranch26_46 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 7 19 degreeUnionState26_46 [19] = true := by + decide +kernel + +lemma degreeUnionBranch26_47 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 6 20 degreeUnionState26_47 [20] = true := by + decide +kernel + +lemma degreeUnionBranch26_48 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 5 21 degreeUnionState26_48 [21] = true := by + decide +kernel + +lemma degreeUnionBranch26_49 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 4 22 degreeUnionState26_49 [22] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch26_50 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 3 23 degreeUnionState26_50 [23] = true := by + decide +kernel + +lemma degreeUnionBranch26_51 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 2 24 degreeUnionState26_51 [24] = true := by + decide +kernel + +lemma degreeUnionBranch26_52 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 1 25 degreeUnionState26_52 [25] = true := by + decide +kernel + +lemma degreeUnionBranch26_54 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 23 3 degreeUnionState26_54 [3] = true := by + decide +kernel + +lemma degreeUnionBranch26_55 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 22 4 degreeUnionState26_55 [4] = true := by + decide +kernel + +lemma degreeUnionBranch26_56 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 21 5 degreeUnionState26_56 [5] = true := by + decide +kernel + +lemma degreeUnionBranch26_57 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 20 6 degreeUnionState26_57 [6] = true := by + decide +kernel + +lemma degreeUnionBranch26_58 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 19 7 degreeUnionState26_58 [7] = true := by + decide +kernel + +lemma degreeUnionBranch26_59 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 18 8 degreeUnionState26_59 [8] = true := by + decide +kernel + +lemma degreeUnionBranch26_60 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 17 9 degreeUnionState26_60 [9] = true := by + decide +kernel + +lemma degreeUnionBranch26_61 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 16 10 degreeUnionState26_61 [10] = true := by + decide +kernel + +lemma degreeUnionBranch26_62 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 15 11 degreeUnionState26_62 [11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch26_63 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 14 12 degreeUnionState26_63 [12] = true := by + decide +kernel + +lemma degreeUnionBranch26_64 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 13 13 degreeUnionState26_64 [13] = true := by + decide +kernel + +lemma degreeUnionBranch26_65 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 12 14 degreeUnionState26_65 [14] = true := by + decide +kernel + +lemma degreeUnionBranch26_66 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 11 15 degreeUnionState26_66 [15] = true := by + decide +kernel + +lemma degreeUnionBranch26_67 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 10 16 degreeUnionState26_67 [16] = true := by + decide +kernel + +lemma degreeUnionBranch26_68 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 9 17 degreeUnionState26_68 [17] = true := by + decide +kernel + +lemma degreeUnionBranch26_69 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 8 18 degreeUnionState26_69 [18] = true := by + decide +kernel + +lemma degreeUnionBranch26_70 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 7 19 degreeUnionState26_70 [19] = true := by + decide +kernel + +lemma degreeUnionBranch26_71 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 6 20 degreeUnionState26_71 [20] = true := by + decide +kernel + +lemma degreeUnionBranch26_72 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 5 21 degreeUnionState26_72 [21] = true := by + decide +kernel + +lemma degreeUnionBranch26_73 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 4 22 degreeUnionState26_73 [22] = true := by + decide +kernel + +lemma degreeUnionBranch26_74 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 3 23 degreeUnionState26_74 [23] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch26_75 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 2 24 degreeUnionState26_75 [24] = true := by + decide +kernel + +lemma degreeUnionBranch26_76 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 1 25 degreeUnionState26_76 [25] = true := by + decide +kernel + +lemma degreeUnionBranch26_77 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 10 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_78 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 11 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_79 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 12 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_80 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 13 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_81 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 14 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_82 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 15 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_83 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 16 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_84 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 17 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_85 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 18 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_86 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 19 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch26_87 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 20 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_88 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 21 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_89 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 22 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_90 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 23 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_91 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 24 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +lemma degreeUnionBranch26_92 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 25 26 25 degreeHalfRegions26 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves31.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves31.lean index 542b40dc5e7d98216e35e312a428be2d354543e2..bea20d35ceed744511cacb1c851f9df5e6ecfbb6 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves31.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves31.lean @@ -1,333 +1,333 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans31 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates31 - -namespace OAI - -/-! Degree Leaves 31. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch31_0 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 0 31 30 degreeHalfRegions31 [] = true := by - decide +kernel - -lemma degreeUnionBranch31_1 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 1 31 30 degreeHalfRegions31 [] = true := by - decide +kernel - -lemma degreeUnionBranch31_2 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 2 31 30 degreeHalfRegions31 [] = true := by - decide +kernel - -lemma degreeUnionBranch31_3 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 3 31 30 degreeHalfRegions31 [] = true := by - decide +kernel - -lemma degreeUnionBranch31_4 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 4 31 30 degreeHalfRegions31 [] = true := by - decide +kernel - -lemma degreeUnionBranch31_5 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 5 31 30 degreeHalfRegions31 [] = true := by - decide +kernel - -lemma degreeUnionBranch31_6 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 6 31 30 degreeHalfRegions31 [] = true := by - decide +kernel - -lemma degreeUnionBranch31_7 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 31 30 degreeHalfRegions31 [] = true := by - decide +kernel - -lemma degreeUnionBranch31_9 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 27 4 degreeUnionState31_9 [4] = true := by - decide +kernel - -lemma degreeUnionBranch31_10 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 26 5 degreeUnionState31_10 [5] = true := by - decide +kernel - -lemma degreeUnionBranch31_11 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 25 6 degreeUnionState31_11 [6] = true := by - decide +kernel - -lemma degreeUnionBranch31_12 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 24 7 degreeUnionState31_12 [7] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch31_13 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 23 8 degreeUnionState31_13 [8] = true := by - decide +kernel - -lemma degreeUnionBranch31_14 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 22 9 degreeUnionState31_14 [9] = true := by - decide +kernel - -lemma degreeUnionBranch31_15 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 21 10 degreeUnionState31_15 [10] = true := by - decide +kernel - -lemma degreeUnionBranch31_16 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 20 11 degreeUnionState31_16 [11] = true := by - decide +kernel - -lemma degreeUnionBranch31_17 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 19 12 degreeUnionState31_17 [12] = true := by - decide +kernel - -lemma degreeUnionBranch31_18 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 18 13 degreeUnionState31_18 [13] = true := by - decide +kernel - -lemma degreeUnionBranch31_19 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 17 14 degreeUnionState31_19 [14] = true := by - decide +kernel - -lemma degreeUnionBranch31_20 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 16 15 degreeUnionState31_20 [15] = true := by - decide +kernel - -lemma degreeUnionBranch31_21 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 15 16 degreeUnionState31_21 [16] = true := by - decide +kernel - -lemma degreeUnionBranch31_22 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 14 17 degreeUnionState31_22 [17] = true := by - decide +kernel - -lemma degreeUnionBranch31_23 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 13 18 degreeUnionState31_23 [18] = true := by - decide +kernel - -lemma degreeUnionBranch31_24 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 12 19 degreeUnionState31_24 [19] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch31_25 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 11 20 degreeUnionState31_25 [20] = true := by - decide +kernel - -lemma degreeUnionBranch31_26 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 10 21 degreeUnionState31_26 [21] = true := by - decide +kernel - -lemma degreeUnionBranch31_27 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 9 22 degreeUnionState31_27 [22] = true := by - decide +kernel - -lemma degreeUnionBranch31_28 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 8 23 degreeUnionState31_28 [23] = true := by - decide +kernel - -lemma degreeUnionBranch31_29 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 7 24 degreeUnionState31_29 [24] = true := by - decide +kernel - -lemma degreeUnionBranch31_30 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 6 25 degreeUnionState31_30 [25] = true := by - decide +kernel - -lemma degreeUnionBranch31_31 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 5 26 degreeUnionState31_31 [26] = true := by - decide +kernel - -lemma degreeUnionBranch31_32 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 4 27 degreeUnionState31_32 [27] = true := by - decide +kernel - -lemma degreeUnionBranch31_33 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 3 28 degreeUnionState31_33 [28] = true := by - decide +kernel - -lemma degreeUnionBranch31_34 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 2 29 degreeUnionState31_34 [29] = true := by - decide +kernel - -lemma degreeUnionBranch31_35 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 1 30 degreeUnionState31_35 [30] = true := by - decide +kernel - -lemma degreeUnionBranch31_37 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 27 4 degreeUnionState31_37 [4] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch31_38 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 26 5 degreeUnionState31_38 [5] = true := by - decide +kernel - -lemma degreeUnionBranch31_39 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 25 6 degreeUnionState31_39 [6] = true := by - decide +kernel - -lemma degreeUnionBranch31_40 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 24 7 degreeUnionState31_40 [7] = true := by - decide +kernel - -lemma degreeUnionBranch31_41 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 23 8 degreeUnionState31_41 [8] = true := by - decide +kernel - -lemma degreeUnionBranch31_42 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 22 9 degreeUnionState31_42 [9] = true := by - decide +kernel - -lemma degreeUnionBranch31_43 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 21 10 degreeUnionState31_43 [10] = true := by - decide +kernel - -lemma degreeUnionBranch31_44 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 20 11 degreeUnionState31_44 [11] = true := by - decide +kernel - -lemma degreeUnionBranch31_45 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 19 12 degreeUnionState31_45 [12] = true := by - decide +kernel - -lemma degreeUnionBranch31_46 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 18 13 degreeUnionState31_46 [13] = true := by - decide +kernel - -lemma degreeUnionBranch31_47 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 17 14 degreeUnionState31_47 [14] = true := by - decide +kernel - -lemma degreeUnionBranch31_48 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 16 15 degreeUnionState31_48 [15] = true := by - decide +kernel - -lemma degreeUnionBranch31_49 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 15 16 degreeUnionState31_49 [16] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch31_50 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 14 17 degreeUnionState31_50 [17] = true := by - decide +kernel - -lemma degreeUnionBranch31_51 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 13 18 degreeUnionState31_51 [18] = true := by - decide +kernel - -lemma degreeUnionBranch31_52 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 12 19 degreeUnionState31_52 [19] = true := by - decide +kernel - -lemma degreeUnionBranch31_53 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 11 20 degreeUnionState31_53 [20] = true := by - decide +kernel - -lemma degreeUnionBranch31_54 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 10 21 degreeUnionState31_54 [21] = true := by - decide +kernel - -lemma degreeUnionBranch31_55 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 9 22 degreeUnionState31_55 [22] = true := by - decide +kernel - -lemma degreeUnionBranch31_56 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 8 23 degreeUnionState31_56 [23] = true := by - decide +kernel - -lemma degreeUnionBranch31_57 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 7 24 degreeUnionState31_57 [24] = true := by - decide +kernel - -lemma degreeUnionBranch31_58 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 6 25 degreeUnionState31_58 [25] = true := by - decide +kernel - -lemma degreeUnionBranch31_59 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 5 26 degreeUnionState31_59 [26] = true := by - decide +kernel - -lemma degreeUnionBranch31_60 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 4 27 degreeUnionState31_60 [27] = true := by - decide +kernel - -lemma degreeUnionBranch31_61 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 3 28 degreeUnionState31_61 [28] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch31_62 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 2 29 degreeUnionState31_62 [29] = true := by - decide +kernel - -lemma degreeUnionBranch31_63 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 1 30 degreeUnionState31_63 [30] = true := by - decide +kernel - -lemma degreeUnionBranch31_65 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 27 4 degreeUnionState31_65 [4] = true := by - decide +kernel - -lemma degreeUnionBranch31_66 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 26 5 degreeUnionState31_66 [5] = true := by - decide +kernel - -lemma degreeUnionBranch31_67 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 25 6 degreeUnionState31_67 [6] = true := by - decide +kernel - -lemma degreeUnionBranch31_68 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 24 7 degreeUnionState31_68 [7] = true := by - decide +kernel - -lemma degreeUnionBranch31_69 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 23 8 degreeUnionState31_69 [8] = true := by - decide +kernel - -lemma degreeUnionBranch31_70 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 22 9 degreeUnionState31_70 [9] = true := by - decide +kernel - -lemma degreeUnionBranch31_71 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 21 10 degreeUnionState31_71 [10] = true := by - decide +kernel - -lemma degreeUnionBranch31_72 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 20 11 degreeUnionState31_72 [11] = true := by - decide +kernel - -lemma degreeUnionBranch31_73 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 19 12 degreeUnionState31_73 [12] = true := by - decide +kernel - -lemma degreeUnionBranch31_74 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 18 13 degreeUnionState31_74 [13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch31_75 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 17 14 degreeUnionState31_75 [14] = true := by - decide +kernel - -lemma degreeUnionBranch31_76 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 16 15 degreeUnionState31_76 [15] = true := by - decide +kernel - -lemma degreeUnionBranch31_77 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 15 16 degreeUnionState31_77 [16] = true := by - decide +kernel - -lemma degreeUnionBranch31_78 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 14 17 degreeUnionState31_78 [17] = true := by - decide +kernel - -lemma degreeUnionBranch31_79 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 13 18 degreeUnionState31_79 [18] = true := by - decide +kernel - -lemma degreeUnionBranch31_80 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 12 19 degreeUnionState31_80 [19] = true := by - decide +kernel - -lemma degreeUnionBranch31_81 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 11 20 degreeUnionState31_81 [20] = true := by - decide +kernel - -lemma degreeUnionBranch31_82 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 10 21 degreeUnionState31_82 [21] = true := by - decide +kernel - -lemma degreeUnionBranch31_83 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 9 22 degreeUnionState31_83 [22] = true := by - decide +kernel - -lemma degreeUnionBranch31_84 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 8 23 degreeUnionState31_84 [23] = true := by - decide +kernel - -lemma degreeUnionBranch31_85 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 7 24 degreeUnionState31_85 [24] = true := by - decide +kernel - -lemma degreeUnionBranch31_86 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 6 25 degreeUnionState31_86 [25] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch31_87 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 5 26 degreeUnionState31_87 [26] = true := by - decide +kernel - -lemma degreeUnionBranch31_88 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 4 27 degreeUnionState31_88 [27] = true := by - decide +kernel - -lemma degreeUnionBranch31_89 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 3 28 degreeUnionState31_89 [28] = true := by - decide +kernel - -lemma degreeUnionBranch31_90 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 2 29 degreeUnionState31_90 [29] = true := by - decide +kernel - -lemma degreeUnionBranch31_91 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 1 30 degreeUnionState31_91 [30] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans31 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates31 + +namespace OAI + +/-! Degree Leaves 31. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch31_0 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 0 31 30 degreeHalfRegions31 [] = true := by + decide +kernel + +lemma degreeUnionBranch31_1 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 1 31 30 degreeHalfRegions31 [] = true := by + decide +kernel + +lemma degreeUnionBranch31_2 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 2 31 30 degreeHalfRegions31 [] = true := by + decide +kernel + +lemma degreeUnionBranch31_3 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 3 31 30 degreeHalfRegions31 [] = true := by + decide +kernel + +lemma degreeUnionBranch31_4 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 4 31 30 degreeHalfRegions31 [] = true := by + decide +kernel + +lemma degreeUnionBranch31_5 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 5 31 30 degreeHalfRegions31 [] = true := by + decide +kernel + +lemma degreeUnionBranch31_6 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 6 31 30 degreeHalfRegions31 [] = true := by + decide +kernel + +lemma degreeUnionBranch31_7 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 31 30 degreeHalfRegions31 [] = true := by + decide +kernel + +lemma degreeUnionBranch31_9 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 27 4 degreeUnionState31_9 [4] = true := by + decide +kernel + +lemma degreeUnionBranch31_10 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 26 5 degreeUnionState31_10 [5] = true := by + decide +kernel + +lemma degreeUnionBranch31_11 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 25 6 degreeUnionState31_11 [6] = true := by + decide +kernel + +lemma degreeUnionBranch31_12 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 24 7 degreeUnionState31_12 [7] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch31_13 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 23 8 degreeUnionState31_13 [8] = true := by + decide +kernel + +lemma degreeUnionBranch31_14 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 22 9 degreeUnionState31_14 [9] = true := by + decide +kernel + +lemma degreeUnionBranch31_15 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 21 10 degreeUnionState31_15 [10] = true := by + decide +kernel + +lemma degreeUnionBranch31_16 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 20 11 degreeUnionState31_16 [11] = true := by + decide +kernel + +lemma degreeUnionBranch31_17 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 19 12 degreeUnionState31_17 [12] = true := by + decide +kernel + +lemma degreeUnionBranch31_18 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 18 13 degreeUnionState31_18 [13] = true := by + decide +kernel + +lemma degreeUnionBranch31_19 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 17 14 degreeUnionState31_19 [14] = true := by + decide +kernel + +lemma degreeUnionBranch31_20 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 16 15 degreeUnionState31_20 [15] = true := by + decide +kernel + +lemma degreeUnionBranch31_21 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 15 16 degreeUnionState31_21 [16] = true := by + decide +kernel + +lemma degreeUnionBranch31_22 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 14 17 degreeUnionState31_22 [17] = true := by + decide +kernel + +lemma degreeUnionBranch31_23 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 13 18 degreeUnionState31_23 [18] = true := by + decide +kernel + +lemma degreeUnionBranch31_24 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 12 19 degreeUnionState31_24 [19] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch31_25 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 11 20 degreeUnionState31_25 [20] = true := by + decide +kernel + +lemma degreeUnionBranch31_26 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 10 21 degreeUnionState31_26 [21] = true := by + decide +kernel + +lemma degreeUnionBranch31_27 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 9 22 degreeUnionState31_27 [22] = true := by + decide +kernel + +lemma degreeUnionBranch31_28 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 8 23 degreeUnionState31_28 [23] = true := by + decide +kernel + +lemma degreeUnionBranch31_29 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 7 24 degreeUnionState31_29 [24] = true := by + decide +kernel + +lemma degreeUnionBranch31_30 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 6 25 degreeUnionState31_30 [25] = true := by + decide +kernel + +lemma degreeUnionBranch31_31 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 5 26 degreeUnionState31_31 [26] = true := by + decide +kernel + +lemma degreeUnionBranch31_32 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 4 27 degreeUnionState31_32 [27] = true := by + decide +kernel + +lemma degreeUnionBranch31_33 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 3 28 degreeUnionState31_33 [28] = true := by + decide +kernel + +lemma degreeUnionBranch31_34 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 2 29 degreeUnionState31_34 [29] = true := by + decide +kernel + +lemma degreeUnionBranch31_35 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 7 1 30 degreeUnionState31_35 [30] = true := by + decide +kernel + +lemma degreeUnionBranch31_37 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 27 4 degreeUnionState31_37 [4] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch31_38 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 26 5 degreeUnionState31_38 [5] = true := by + decide +kernel + +lemma degreeUnionBranch31_39 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 25 6 degreeUnionState31_39 [6] = true := by + decide +kernel + +lemma degreeUnionBranch31_40 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 24 7 degreeUnionState31_40 [7] = true := by + decide +kernel + +lemma degreeUnionBranch31_41 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 23 8 degreeUnionState31_41 [8] = true := by + decide +kernel + +lemma degreeUnionBranch31_42 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 22 9 degreeUnionState31_42 [9] = true := by + decide +kernel + +lemma degreeUnionBranch31_43 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 21 10 degreeUnionState31_43 [10] = true := by + decide +kernel + +lemma degreeUnionBranch31_44 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 20 11 degreeUnionState31_44 [11] = true := by + decide +kernel + +lemma degreeUnionBranch31_45 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 19 12 degreeUnionState31_45 [12] = true := by + decide +kernel + +lemma degreeUnionBranch31_46 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 18 13 degreeUnionState31_46 [13] = true := by + decide +kernel + +lemma degreeUnionBranch31_47 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 17 14 degreeUnionState31_47 [14] = true := by + decide +kernel + +lemma degreeUnionBranch31_48 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 16 15 degreeUnionState31_48 [15] = true := by + decide +kernel + +lemma degreeUnionBranch31_49 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 15 16 degreeUnionState31_49 [16] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch31_50 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 14 17 degreeUnionState31_50 [17] = true := by + decide +kernel + +lemma degreeUnionBranch31_51 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 13 18 degreeUnionState31_51 [18] = true := by + decide +kernel + +lemma degreeUnionBranch31_52 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 12 19 degreeUnionState31_52 [19] = true := by + decide +kernel + +lemma degreeUnionBranch31_53 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 11 20 degreeUnionState31_53 [20] = true := by + decide +kernel + +lemma degreeUnionBranch31_54 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 10 21 degreeUnionState31_54 [21] = true := by + decide +kernel + +lemma degreeUnionBranch31_55 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 9 22 degreeUnionState31_55 [22] = true := by + decide +kernel + +lemma degreeUnionBranch31_56 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 8 23 degreeUnionState31_56 [23] = true := by + decide +kernel + +lemma degreeUnionBranch31_57 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 7 24 degreeUnionState31_57 [24] = true := by + decide +kernel + +lemma degreeUnionBranch31_58 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 6 25 degreeUnionState31_58 [25] = true := by + decide +kernel + +lemma degreeUnionBranch31_59 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 5 26 degreeUnionState31_59 [26] = true := by + decide +kernel + +lemma degreeUnionBranch31_60 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 4 27 degreeUnionState31_60 [27] = true := by + decide +kernel + +lemma degreeUnionBranch31_61 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 3 28 degreeUnionState31_61 [28] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch31_62 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 2 29 degreeUnionState31_62 [29] = true := by + decide +kernel + +lemma degreeUnionBranch31_63 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 1 30 degreeUnionState31_63 [30] = true := by + decide +kernel + +lemma degreeUnionBranch31_65 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 27 4 degreeUnionState31_65 [4] = true := by + decide +kernel + +lemma degreeUnionBranch31_66 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 26 5 degreeUnionState31_66 [5] = true := by + decide +kernel + +lemma degreeUnionBranch31_67 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 25 6 degreeUnionState31_67 [6] = true := by + decide +kernel + +lemma degreeUnionBranch31_68 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 24 7 degreeUnionState31_68 [7] = true := by + decide +kernel + +lemma degreeUnionBranch31_69 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 23 8 degreeUnionState31_69 [8] = true := by + decide +kernel + +lemma degreeUnionBranch31_70 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 22 9 degreeUnionState31_70 [9] = true := by + decide +kernel + +lemma degreeUnionBranch31_71 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 21 10 degreeUnionState31_71 [10] = true := by + decide +kernel + +lemma degreeUnionBranch31_72 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 20 11 degreeUnionState31_72 [11] = true := by + decide +kernel + +lemma degreeUnionBranch31_73 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 19 12 degreeUnionState31_73 [12] = true := by + decide +kernel + +lemma degreeUnionBranch31_74 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 18 13 degreeUnionState31_74 [13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch31_75 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 17 14 degreeUnionState31_75 [14] = true := by + decide +kernel + +lemma degreeUnionBranch31_76 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 16 15 degreeUnionState31_76 [15] = true := by + decide +kernel + +lemma degreeUnionBranch31_77 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 15 16 degreeUnionState31_77 [16] = true := by + decide +kernel + +lemma degreeUnionBranch31_78 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 14 17 degreeUnionState31_78 [17] = true := by + decide +kernel + +lemma degreeUnionBranch31_79 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 13 18 degreeUnionState31_79 [18] = true := by + decide +kernel + +lemma degreeUnionBranch31_80 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 12 19 degreeUnionState31_80 [19] = true := by + decide +kernel + +lemma degreeUnionBranch31_81 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 11 20 degreeUnionState31_81 [20] = true := by + decide +kernel + +lemma degreeUnionBranch31_82 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 10 21 degreeUnionState31_82 [21] = true := by + decide +kernel + +lemma degreeUnionBranch31_83 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 9 22 degreeUnionState31_83 [22] = true := by + decide +kernel + +lemma degreeUnionBranch31_84 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 8 23 degreeUnionState31_84 [23] = true := by + decide +kernel + +lemma degreeUnionBranch31_85 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 7 24 degreeUnionState31_85 [24] = true := by + decide +kernel + +lemma degreeUnionBranch31_86 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 6 25 degreeUnionState31_86 [25] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch31_87 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 5 26 degreeUnionState31_87 [26] = true := by + decide +kernel + +lemma degreeUnionBranch31_88 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 4 27 degreeUnionState31_88 [27] = true := by + decide +kernel + +lemma degreeUnionBranch31_89 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 3 28 degreeUnionState31_89 [28] = true := by + decide +kernel + +lemma degreeUnionBranch31_90 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 2 29 degreeUnionState31_90 [29] = true := by + decide +kernel + +lemma degreeUnionBranch31_91 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 1 30 degreeUnionState31_91 [30] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves35.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves35.lean index 9bd8236e30e35404add21f4b883eafa0a862aa71..c40383803971ea7501c0b14ba8c91753af45e3be 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves35.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves35.lean @@ -1,548 +1,548 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans35 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates35 - -namespace OAI - -/-! Degree Leaves 35. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_0 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 0 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -lemma degreeUnionBranch35_1 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 1 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -lemma degreeUnionBranch35_2 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 2 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -lemma degreeUnionBranch35_3 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 3 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -lemma degreeUnionBranch35_4 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 4 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -lemma degreeUnionBranch35_5 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 5 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -lemma degreeUnionBranch35_6 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -lemma degreeUnionBranch35_7 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -lemma degreeUnionBranch35_9 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 30 5 degreeUnionState35_9 [5] = true := by - decide +kernel - -lemma degreeUnionBranch35_10 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 29 6 degreeUnionState35_10 [6] = true := by - decide +kernel - -lemma degreeUnionBranch35_11 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 28 7 degreeUnionState35_11 [7] = true := by - decide +kernel - -lemma degreeUnionBranch35_12 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 27 8 degreeUnionState35_12 [8] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_14 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 22 4 degreeUnionState35_14 [4,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_15 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 21 5 degreeUnionState35_15 [5,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_16 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 20 6 degreeUnionState35_16 [6,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_17 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 19 7 degreeUnionState35_17 [7,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_18 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 18 8 degreeUnionState35_18 [8,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_19 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 17 9 degreeUnionState35_19 [9,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_21 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 21 4 degreeUnionState35_21 [4,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_22 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 20 5 degreeUnionState35_22 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_23 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 19 6 degreeUnionState35_23 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_24 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 18 7 degreeUnionState35_24 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_25 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 17 8 degreeUnionState35_25 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_26 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 16 9 degreeUnionState35_26 [9,10] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_27 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 15 10 degreeUnionState35_27 [10,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_28 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 24 11 degreeUnionState35_28 [11] = true := by - decide +kernel - -lemma degreeUnionBranch35_29 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 23 12 degreeUnionState35_29 [12] = true := by - decide +kernel - -lemma degreeUnionBranch35_30 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 22 13 degreeUnionState35_30 [13] = true := by - decide +kernel - -lemma degreeUnionBranch35_31 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 21 14 degreeUnionState35_31 [14] = true := by - decide +kernel - -lemma degreeUnionBranch35_32 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 20 15 degreeUnionState35_32 [15] = true := by - decide +kernel - -lemma degreeUnionBranch35_33 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 19 16 degreeUnionState35_33 [16] = true := by - decide +kernel - -lemma degreeUnionBranch35_34 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 18 17 degreeUnionState35_34 [17] = true := by - decide +kernel - -lemma degreeUnionBranch35_35 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 17 18 degreeUnionState35_35 [18] = true := by - decide +kernel - -lemma degreeUnionBranch35_36 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 16 19 degreeUnionState35_36 [19] = true := by - decide +kernel - -lemma degreeUnionBranch35_37 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 15 20 degreeUnionState35_37 [20] = true := by - decide +kernel - -lemma degreeUnionBranch35_38 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 14 21 degreeUnionState35_38 [21] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_39 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 13 22 degreeUnionState35_39 [22] = true := by - decide +kernel - -lemma degreeUnionBranch35_40 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 12 23 degreeUnionState35_40 [23] = true := by - decide +kernel - -lemma degreeUnionBranch35_41 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 11 24 degreeUnionState35_41 [24] = true := by - decide +kernel - -lemma degreeUnionBranch35_42 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 10 25 degreeUnionState35_42 [25] = true := by - decide +kernel - -lemma degreeUnionBranch35_43 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 9 26 degreeUnionState35_43 [26] = true := by - decide +kernel - -lemma degreeUnionBranch35_44 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 8 27 degreeUnionState35_44 [27] = true := by - decide +kernel - -lemma degreeUnionBranch35_45 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 7 28 degreeUnionState35_45 [28] = true := by - decide +kernel - -lemma degreeUnionBranch35_46 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 6 29 degreeUnionState35_46 [29] = true := by - decide +kernel - -lemma degreeUnionBranch35_47 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 5 30 degreeUnionState35_47 [30] = true := by - decide +kernel - -lemma degreeUnionBranch35_48 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 4 31 degreeUnionState35_48 [31] = true := by - decide +kernel - -lemma degreeUnionBranch35_49 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 3 32 degreeUnionState35_49 [32] = true := by - decide +kernel - -lemma degreeUnionBranch35_50 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 2 33 degreeUnionState35_50 [33] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_51 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 1 34 degreeUnionState35_51 [34] = true := by - decide +kernel - -lemma degreeUnionBranch35_53 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 31 4 degreeUnionState35_53 [4] = true := by - decide +kernel - -lemma degreeUnionBranch35_54 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 30 5 degreeUnionState35_54 [5] = true := by - decide +kernel - -lemma degreeUnionBranch35_55 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 29 6 degreeUnionState35_55 [6] = true := by - decide +kernel - -lemma degreeUnionBranch35_56 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 28 7 degreeUnionState35_56 [7] = true := by - decide +kernel - -lemma degreeUnionBranch35_58 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 23 4 degreeUnionState35_58 [4,8] = true := by - decide +kernel - -lemma degreeUnionBranch35_59 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 22 5 degreeUnionState35_59 [5,8] = true := by - decide +kernel - -lemma degreeUnionBranch35_60 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 21 6 degreeUnionState35_60 [6,8] = true := by - decide +kernel - -lemma degreeUnionBranch35_61 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 20 7 degreeUnionState35_61 [7,8] = true := by - decide +kernel - -lemma degreeUnionBranch35_62 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 19 8 degreeUnionState35_62 [8,8] = true := by - decide +kernel - -lemma degreeUnionBranch35_64 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 22 4 degreeUnionState35_64 [4,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_65 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 21 5 degreeUnionState35_65 [5,9] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_66 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 20 6 degreeUnionState35_66 [6,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_67 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 19 7 degreeUnionState35_67 [7,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_68 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 18 8 degreeUnionState35_68 [8,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_69 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 17 9 degreeUnionState35_69 [9,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_71 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 21 4 degreeUnionState35_71 [4,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_72 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 20 5 degreeUnionState35_72 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_73 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 19 6 degreeUnionState35_73 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_74 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 18 7 degreeUnionState35_74 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_75 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 17 8 degreeUnionState35_75 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_76 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 16 9 degreeUnionState35_76 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_77 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 15 10 degreeUnionState35_77 [10,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_78 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 24 11 degreeUnionState35_78 [11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_79 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 23 12 degreeUnionState35_79 [12] = true := by - decide +kernel - -lemma degreeUnionBranch35_80 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 22 13 degreeUnionState35_80 [13] = true := by - decide +kernel - -lemma degreeUnionBranch35_81 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 21 14 degreeUnionState35_81 [14] = true := by - decide +kernel - -lemma degreeUnionBranch35_82 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 20 15 degreeUnionState35_82 [15] = true := by - decide +kernel - -lemma degreeUnionBranch35_83 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 19 16 degreeUnionState35_83 [16] = true := by - decide +kernel - -lemma degreeUnionBranch35_84 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 18 17 degreeUnionState35_84 [17] = true := by - decide +kernel - -lemma degreeUnionBranch35_85 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 17 18 degreeUnionState35_85 [18] = true := by - decide +kernel - -lemma degreeUnionBranch35_86 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 16 19 degreeUnionState35_86 [19] = true := by - decide +kernel - -lemma degreeUnionBranch35_87 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 15 20 degreeUnionState35_87 [20] = true := by - decide +kernel - -lemma degreeUnionBranch35_88 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 14 21 degreeUnionState35_88 [21] = true := by - decide +kernel - -lemma degreeUnionBranch35_89 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 13 22 degreeUnionState35_89 [22] = true := by - decide +kernel - -lemma degreeUnionBranch35_90 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 12 23 degreeUnionState35_90 [23] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_91 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 11 24 degreeUnionState35_91 [24] = true := by - decide +kernel - -lemma degreeUnionBranch35_92 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 10 25 degreeUnionState35_92 [25] = true := by - decide +kernel - -lemma degreeUnionBranch35_93 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 9 26 degreeUnionState35_93 [26] = true := by - decide +kernel - -lemma degreeUnionBranch35_94 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 8 27 degreeUnionState35_94 [27] = true := by - decide +kernel - -lemma degreeUnionBranch35_95 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 7 28 degreeUnionState35_95 [28] = true := by - decide +kernel - -lemma degreeUnionBranch35_96 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 6 29 degreeUnionState35_96 [29] = true := by - decide +kernel - -lemma degreeUnionBranch35_97 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 5 30 degreeUnionState35_97 [30] = true := by - decide +kernel - -lemma degreeUnionBranch35_98 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 4 31 degreeUnionState35_98 [31] = true := by - decide +kernel - -lemma degreeUnionBranch35_99 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 3 32 degreeUnionState35_99 [32] = true := by - decide +kernel - -lemma degreeUnionBranch35_100 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 2 33 degreeUnionState35_100 [33] = true := by - decide +kernel - -lemma degreeUnionBranch35_101 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 1 34 degreeUnionState35_101 [34] = true := by - decide +kernel - -lemma degreeUnionBranch35_103 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 31 4 degreeUnionState35_103 [4] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_104 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 30 5 degreeUnionState35_104 [5] = true := by - decide +kernel - -lemma degreeUnionBranch35_105 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 29 6 degreeUnionState35_105 [6] = true := by - decide +kernel - -lemma degreeUnionBranch35_106 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 28 7 degreeUnionState35_106 [7] = true := by - decide +kernel - -lemma degreeUnionBranch35_108 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 24 3 degreeUnionState35_108 [3,8] = true := by - decide +kernel - -lemma degreeUnionBranch35_109 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 23 4 degreeUnionState35_109 [4,8] = true := by - decide +kernel - -lemma degreeUnionBranch35_110 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 22 5 degreeUnionState35_110 [5,8] = true := by - decide +kernel - -lemma degreeUnionBranch35_111 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 21 6 degreeUnionState35_111 [6,8] = true := by - decide +kernel - -lemma degreeUnionBranch35_112 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 20 7 degreeUnionState35_112 [7,8] = true := by - decide +kernel - -lemma degreeUnionBranch35_113 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 19 8 degreeUnionState35_113 [8,8] = true := by - decide +kernel - -lemma degreeUnionBranch35_115 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 23 3 degreeUnionState35_115 [3,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_116 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 22 4 degreeUnionState35_116 [4,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_117 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 21 5 degreeUnionState35_117 [5,9] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_118 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 20 6 degreeUnionState35_118 [6,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_119 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 19 7 degreeUnionState35_119 [7,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_120 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 18 8 degreeUnionState35_120 [8,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_121 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 17 9 degreeUnionState35_121 [9,9] = true := by - decide +kernel - -lemma degreeUnionBranch35_123 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 22 3 degreeUnionState35_123 [3,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_124 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 21 4 degreeUnionState35_124 [4,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_125 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 20 5 degreeUnionState35_125 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_126 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 19 6 degreeUnionState35_126 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_127 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 18 7 degreeUnionState35_127 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_128 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 17 8 degreeUnionState35_128 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_129 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 16 9 degreeUnionState35_129 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch35_130 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 15 10 degreeUnionState35_130 [10,10] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_131 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 24 11 degreeUnionState35_131 [11] = true := by - decide +kernel - -lemma degreeUnionBranch35_132 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 23 12 degreeUnionState35_132 [12] = true := by - decide +kernel - -lemma degreeUnionBranch35_133 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 22 13 degreeUnionState35_133 [13] = true := by - decide +kernel - -lemma degreeUnionBranch35_134 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 21 14 degreeUnionState35_134 [14] = true := by - decide +kernel - -lemma degreeUnionBranch35_135 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 20 15 degreeUnionState35_135 [15] = true := by - decide +kernel - -lemma degreeUnionBranch35_136 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 19 16 degreeUnionState35_136 [16] = true := by - decide +kernel - -lemma degreeUnionBranch35_137 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 18 17 degreeUnionState35_137 [17] = true := by - decide +kernel - -lemma degreeUnionBranch35_138 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 17 18 degreeUnionState35_138 [18] = true := by - decide +kernel - -lemma degreeUnionBranch35_139 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 16 19 degreeUnionState35_139 [19] = true := by - decide +kernel - -lemma degreeUnionBranch35_140 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 15 20 degreeUnionState35_140 [20] = true := by - decide +kernel - -lemma degreeUnionBranch35_141 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 14 21 degreeUnionState35_141 [21] = true := by - decide +kernel - -lemma degreeUnionBranch35_142 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 13 22 degreeUnionState35_142 [22] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_143 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 12 23 degreeUnionState35_143 [23] = true := by - decide +kernel - -lemma degreeUnionBranch35_144 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 11 24 degreeUnionState35_144 [24] = true := by - decide +kernel - -lemma degreeUnionBranch35_145 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 10 25 degreeUnionState35_145 [25] = true := by - decide +kernel - -lemma degreeUnionBranch35_146 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 9 26 degreeUnionState35_146 [26] = true := by - decide +kernel - -lemma degreeUnionBranch35_147 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 8 27 degreeUnionState35_147 [27] = true := by - decide +kernel - -lemma degreeUnionBranch35_148 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 7 28 degreeUnionState35_148 [28] = true := by - decide +kernel - -lemma degreeUnionBranch35_149 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 6 29 degreeUnionState35_149 [29] = true := by - decide +kernel - -lemma degreeUnionBranch35_150 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 5 30 degreeUnionState35_150 [30] = true := by - decide +kernel - -lemma degreeUnionBranch35_151 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 4 31 degreeUnionState35_151 [31] = true := by - decide +kernel - -lemma degreeUnionBranch35_152 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 3 32 degreeUnionState35_152 [32] = true := by - decide +kernel - -lemma degreeUnionBranch35_153 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 2 33 degreeUnionState35_153 [33] = true := by - decide +kernel - -lemma degreeUnionBranch35_154 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 1 34 degreeUnionState35_154 [34] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_155 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 11 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -lemma degreeUnionBranch35_156 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 12 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -lemma degreeUnionBranch35_157 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 13 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -lemma degreeUnionBranch35_158 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 14 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -lemma degreeUnionBranch35_159 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 15 35 34 degreeHalfRegions35 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans35 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates35 + +namespace OAI + +/-! Degree Leaves 35. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_0 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 0 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +lemma degreeUnionBranch35_1 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 1 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +lemma degreeUnionBranch35_2 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 2 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +lemma degreeUnionBranch35_3 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 3 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +lemma degreeUnionBranch35_4 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 4 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +lemma degreeUnionBranch35_5 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 5 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +lemma degreeUnionBranch35_6 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +lemma degreeUnionBranch35_7 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +lemma degreeUnionBranch35_9 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 30 5 degreeUnionState35_9 [5] = true := by + decide +kernel + +lemma degreeUnionBranch35_10 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 29 6 degreeUnionState35_10 [6] = true := by + decide +kernel + +lemma degreeUnionBranch35_11 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 28 7 degreeUnionState35_11 [7] = true := by + decide +kernel + +lemma degreeUnionBranch35_12 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 27 8 degreeUnionState35_12 [8] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_14 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 22 4 degreeUnionState35_14 [4,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_15 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 21 5 degreeUnionState35_15 [5,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_16 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 20 6 degreeUnionState35_16 [6,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_17 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 19 7 degreeUnionState35_17 [7,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_18 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 18 8 degreeUnionState35_18 [8,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_19 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 17 9 degreeUnionState35_19 [9,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_21 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 21 4 degreeUnionState35_21 [4,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_22 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 20 5 degreeUnionState35_22 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_23 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 19 6 degreeUnionState35_23 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_24 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 18 7 degreeUnionState35_24 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_25 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 17 8 degreeUnionState35_25 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_26 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 16 9 degreeUnionState35_26 [9,10] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_27 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 6 15 10 degreeUnionState35_27 [10,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_28 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 24 11 degreeUnionState35_28 [11] = true := by + decide +kernel + +lemma degreeUnionBranch35_29 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 23 12 degreeUnionState35_29 [12] = true := by + decide +kernel + +lemma degreeUnionBranch35_30 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 22 13 degreeUnionState35_30 [13] = true := by + decide +kernel + +lemma degreeUnionBranch35_31 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 21 14 degreeUnionState35_31 [14] = true := by + decide +kernel + +lemma degreeUnionBranch35_32 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 20 15 degreeUnionState35_32 [15] = true := by + decide +kernel + +lemma degreeUnionBranch35_33 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 19 16 degreeUnionState35_33 [16] = true := by + decide +kernel + +lemma degreeUnionBranch35_34 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 18 17 degreeUnionState35_34 [17] = true := by + decide +kernel + +lemma degreeUnionBranch35_35 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 17 18 degreeUnionState35_35 [18] = true := by + decide +kernel + +lemma degreeUnionBranch35_36 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 16 19 degreeUnionState35_36 [19] = true := by + decide +kernel + +lemma degreeUnionBranch35_37 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 15 20 degreeUnionState35_37 [20] = true := by + decide +kernel + +lemma degreeUnionBranch35_38 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 14 21 degreeUnionState35_38 [21] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_39 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 13 22 degreeUnionState35_39 [22] = true := by + decide +kernel + +lemma degreeUnionBranch35_40 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 12 23 degreeUnionState35_40 [23] = true := by + decide +kernel + +lemma degreeUnionBranch35_41 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 11 24 degreeUnionState35_41 [24] = true := by + decide +kernel + +lemma degreeUnionBranch35_42 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 10 25 degreeUnionState35_42 [25] = true := by + decide +kernel + +lemma degreeUnionBranch35_43 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 9 26 degreeUnionState35_43 [26] = true := by + decide +kernel + +lemma degreeUnionBranch35_44 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 8 27 degreeUnionState35_44 [27] = true := by + decide +kernel + +lemma degreeUnionBranch35_45 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 7 28 degreeUnionState35_45 [28] = true := by + decide +kernel + +lemma degreeUnionBranch35_46 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 6 29 degreeUnionState35_46 [29] = true := by + decide +kernel + +lemma degreeUnionBranch35_47 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 5 30 degreeUnionState35_47 [30] = true := by + decide +kernel + +lemma degreeUnionBranch35_48 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 4 31 degreeUnionState35_48 [31] = true := by + decide +kernel + +lemma degreeUnionBranch35_49 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 3 32 degreeUnionState35_49 [32] = true := by + decide +kernel + +lemma degreeUnionBranch35_50 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 2 33 degreeUnionState35_50 [33] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_51 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 1 34 degreeUnionState35_51 [34] = true := by + decide +kernel + +lemma degreeUnionBranch35_53 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 31 4 degreeUnionState35_53 [4] = true := by + decide +kernel + +lemma degreeUnionBranch35_54 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 30 5 degreeUnionState35_54 [5] = true := by + decide +kernel + +lemma degreeUnionBranch35_55 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 29 6 degreeUnionState35_55 [6] = true := by + decide +kernel + +lemma degreeUnionBranch35_56 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 28 7 degreeUnionState35_56 [7] = true := by + decide +kernel + +lemma degreeUnionBranch35_58 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 23 4 degreeUnionState35_58 [4,8] = true := by + decide +kernel + +lemma degreeUnionBranch35_59 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 22 5 degreeUnionState35_59 [5,8] = true := by + decide +kernel + +lemma degreeUnionBranch35_60 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 21 6 degreeUnionState35_60 [6,8] = true := by + decide +kernel + +lemma degreeUnionBranch35_61 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 20 7 degreeUnionState35_61 [7,8] = true := by + decide +kernel + +lemma degreeUnionBranch35_62 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 19 8 degreeUnionState35_62 [8,8] = true := by + decide +kernel + +lemma degreeUnionBranch35_64 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 22 4 degreeUnionState35_64 [4,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_65 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 21 5 degreeUnionState35_65 [5,9] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_66 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 20 6 degreeUnionState35_66 [6,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_67 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 19 7 degreeUnionState35_67 [7,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_68 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 18 8 degreeUnionState35_68 [8,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_69 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 17 9 degreeUnionState35_69 [9,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_71 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 21 4 degreeUnionState35_71 [4,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_72 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 20 5 degreeUnionState35_72 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_73 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 19 6 degreeUnionState35_73 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_74 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 18 7 degreeUnionState35_74 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_75 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 17 8 degreeUnionState35_75 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_76 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 16 9 degreeUnionState35_76 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_77 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 15 10 degreeUnionState35_77 [10,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_78 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 24 11 degreeUnionState35_78 [11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_79 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 23 12 degreeUnionState35_79 [12] = true := by + decide +kernel + +lemma degreeUnionBranch35_80 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 22 13 degreeUnionState35_80 [13] = true := by + decide +kernel + +lemma degreeUnionBranch35_81 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 21 14 degreeUnionState35_81 [14] = true := by + decide +kernel + +lemma degreeUnionBranch35_82 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 20 15 degreeUnionState35_82 [15] = true := by + decide +kernel + +lemma degreeUnionBranch35_83 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 19 16 degreeUnionState35_83 [16] = true := by + decide +kernel + +lemma degreeUnionBranch35_84 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 18 17 degreeUnionState35_84 [17] = true := by + decide +kernel + +lemma degreeUnionBranch35_85 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 17 18 degreeUnionState35_85 [18] = true := by + decide +kernel + +lemma degreeUnionBranch35_86 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 16 19 degreeUnionState35_86 [19] = true := by + decide +kernel + +lemma degreeUnionBranch35_87 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 15 20 degreeUnionState35_87 [20] = true := by + decide +kernel + +lemma degreeUnionBranch35_88 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 14 21 degreeUnionState35_88 [21] = true := by + decide +kernel + +lemma degreeUnionBranch35_89 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 13 22 degreeUnionState35_89 [22] = true := by + decide +kernel + +lemma degreeUnionBranch35_90 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 12 23 degreeUnionState35_90 [23] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_91 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 11 24 degreeUnionState35_91 [24] = true := by + decide +kernel + +lemma degreeUnionBranch35_92 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 10 25 degreeUnionState35_92 [25] = true := by + decide +kernel + +lemma degreeUnionBranch35_93 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 9 26 degreeUnionState35_93 [26] = true := by + decide +kernel + +lemma degreeUnionBranch35_94 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 8 27 degreeUnionState35_94 [27] = true := by + decide +kernel + +lemma degreeUnionBranch35_95 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 7 28 degreeUnionState35_95 [28] = true := by + decide +kernel + +lemma degreeUnionBranch35_96 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 6 29 degreeUnionState35_96 [29] = true := by + decide +kernel + +lemma degreeUnionBranch35_97 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 5 30 degreeUnionState35_97 [30] = true := by + decide +kernel + +lemma degreeUnionBranch35_98 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 4 31 degreeUnionState35_98 [31] = true := by + decide +kernel + +lemma degreeUnionBranch35_99 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 3 32 degreeUnionState35_99 [32] = true := by + decide +kernel + +lemma degreeUnionBranch35_100 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 2 33 degreeUnionState35_100 [33] = true := by + decide +kernel + +lemma degreeUnionBranch35_101 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 1 34 degreeUnionState35_101 [34] = true := by + decide +kernel + +lemma degreeUnionBranch35_103 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 31 4 degreeUnionState35_103 [4] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_104 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 30 5 degreeUnionState35_104 [5] = true := by + decide +kernel + +lemma degreeUnionBranch35_105 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 29 6 degreeUnionState35_105 [6] = true := by + decide +kernel + +lemma degreeUnionBranch35_106 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 28 7 degreeUnionState35_106 [7] = true := by + decide +kernel + +lemma degreeUnionBranch35_108 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 24 3 degreeUnionState35_108 [3,8] = true := by + decide +kernel + +lemma degreeUnionBranch35_109 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 23 4 degreeUnionState35_109 [4,8] = true := by + decide +kernel + +lemma degreeUnionBranch35_110 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 22 5 degreeUnionState35_110 [5,8] = true := by + decide +kernel + +lemma degreeUnionBranch35_111 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 21 6 degreeUnionState35_111 [6,8] = true := by + decide +kernel + +lemma degreeUnionBranch35_112 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 20 7 degreeUnionState35_112 [7,8] = true := by + decide +kernel + +lemma degreeUnionBranch35_113 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 19 8 degreeUnionState35_113 [8,8] = true := by + decide +kernel + +lemma degreeUnionBranch35_115 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 23 3 degreeUnionState35_115 [3,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_116 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 22 4 degreeUnionState35_116 [4,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_117 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 21 5 degreeUnionState35_117 [5,9] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_118 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 20 6 degreeUnionState35_118 [6,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_119 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 19 7 degreeUnionState35_119 [7,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_120 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 18 8 degreeUnionState35_120 [8,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_121 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 17 9 degreeUnionState35_121 [9,9] = true := by + decide +kernel + +lemma degreeUnionBranch35_123 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 22 3 degreeUnionState35_123 [3,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_124 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 21 4 degreeUnionState35_124 [4,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_125 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 20 5 degreeUnionState35_125 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_126 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 19 6 degreeUnionState35_126 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_127 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 18 7 degreeUnionState35_127 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_128 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 17 8 degreeUnionState35_128 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_129 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 16 9 degreeUnionState35_129 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch35_130 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 15 10 degreeUnionState35_130 [10,10] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_131 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 24 11 degreeUnionState35_131 [11] = true := by + decide +kernel + +lemma degreeUnionBranch35_132 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 23 12 degreeUnionState35_132 [12] = true := by + decide +kernel + +lemma degreeUnionBranch35_133 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 22 13 degreeUnionState35_133 [13] = true := by + decide +kernel + +lemma degreeUnionBranch35_134 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 21 14 degreeUnionState35_134 [14] = true := by + decide +kernel + +lemma degreeUnionBranch35_135 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 20 15 degreeUnionState35_135 [15] = true := by + decide +kernel + +lemma degreeUnionBranch35_136 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 19 16 degreeUnionState35_136 [16] = true := by + decide +kernel + +lemma degreeUnionBranch35_137 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 18 17 degreeUnionState35_137 [17] = true := by + decide +kernel + +lemma degreeUnionBranch35_138 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 17 18 degreeUnionState35_138 [18] = true := by + decide +kernel + +lemma degreeUnionBranch35_139 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 16 19 degreeUnionState35_139 [19] = true := by + decide +kernel + +lemma degreeUnionBranch35_140 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 15 20 degreeUnionState35_140 [20] = true := by + decide +kernel + +lemma degreeUnionBranch35_141 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 14 21 degreeUnionState35_141 [21] = true := by + decide +kernel + +lemma degreeUnionBranch35_142 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 13 22 degreeUnionState35_142 [22] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_143 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 12 23 degreeUnionState35_143 [23] = true := by + decide +kernel + +lemma degreeUnionBranch35_144 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 11 24 degreeUnionState35_144 [24] = true := by + decide +kernel + +lemma degreeUnionBranch35_145 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 10 25 degreeUnionState35_145 [25] = true := by + decide +kernel + +lemma degreeUnionBranch35_146 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 9 26 degreeUnionState35_146 [26] = true := by + decide +kernel + +lemma degreeUnionBranch35_147 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 8 27 degreeUnionState35_147 [27] = true := by + decide +kernel + +lemma degreeUnionBranch35_148 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 7 28 degreeUnionState35_148 [28] = true := by + decide +kernel + +lemma degreeUnionBranch35_149 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 6 29 degreeUnionState35_149 [29] = true := by + decide +kernel + +lemma degreeUnionBranch35_150 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 5 30 degreeUnionState35_150 [30] = true := by + decide +kernel + +lemma degreeUnionBranch35_151 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 4 31 degreeUnionState35_151 [31] = true := by + decide +kernel + +lemma degreeUnionBranch35_152 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 3 32 degreeUnionState35_152 [32] = true := by + decide +kernel + +lemma degreeUnionBranch35_153 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 2 33 degreeUnionState35_153 [33] = true := by + decide +kernel + +lemma degreeUnionBranch35_154 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 1 34 degreeUnionState35_154 [34] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_155 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 11 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +lemma degreeUnionBranch35_156 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 12 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +lemma degreeUnionBranch35_157 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 13 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +lemma degreeUnionBranch35_158 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 14 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +lemma degreeUnionBranch35_159 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 15 35 34 degreeHalfRegions35 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves37.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves37.lean index e730d20156a2fb09f463656d569a05988c5494f4..7c7313e1ef6f91b36778291c47feca6088165863 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves37.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves37.lean @@ -1,79 +1,79 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans37 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData37 - -namespace OAI - -/-! Degree Leaves 37. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch37_0 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 0 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_1 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 1 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_2 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 2 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_3 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 3 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_4 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 4 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_5 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 5 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_6 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 6 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_7 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 7 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_8 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 8 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_9 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 9 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_10 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 10 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_11 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 11 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch37_12 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 12 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_13 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 13 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_14 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 14 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_15 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 15 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_16 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 16 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -lemma degreeUnionBranch37_17 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 17 37 17 degreeHalfRegions37 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans37 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData37 + +namespace OAI + +/-! Degree Leaves 37. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch37_0 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 0 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_1 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 1 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_2 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 2 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_3 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 3 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_4 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 4 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_5 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 5 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_6 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 6 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_7 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 7 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_8 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 8 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_9 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 9 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_10 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 10 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_11 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 11 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch37_12 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 12 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_13 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 13 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_14 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 14 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_15 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 15 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_16 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 16 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +lemma degreeUnionBranch37_17 : checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) 17 37 17 degreeHalfRegions37 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves39.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves39.lean index 6c9195f509881e09e0fa1b9f8637141c35e7d1cb..cacdc3ce80cb7b1c07fbf7becd4518ff0fbb8b3a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves39.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves39.lean @@ -1,1058 +1,1058 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans39 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates39 - -namespace OAI - -/-! Degree Leaves 39. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_0 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 0 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_1 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 1 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_2 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 2 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_3 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 3 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_4 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 4 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_5 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 5 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_6 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_7 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_9 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 34 5 degreeUnionState39_9 [5] = true := by - decide +kernel - -lemma degreeUnionBranch39_10 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 33 6 degreeUnionState39_10 [6] = true := by - decide +kernel - -lemma degreeUnionBranch39_11 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 32 7 degreeUnionState39_11 [7] = true := by - decide +kernel - -lemma degreeUnionBranch39_13 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 26 5 degreeUnionState39_13 [5,8] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_14 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 25 6 degreeUnionState39_14 [6,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_15 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 24 7 degreeUnionState39_15 [7,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_16 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 23 8 degreeUnionState39_16 [8,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_18 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 25 5 degreeUnionState39_18 [5,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_19 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 24 6 degreeUnionState39_19 [6,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_20 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 23 7 degreeUnionState39_20 [7,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_21 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 22 8 degreeUnionState39_21 [8,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_22 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 21 9 degreeUnionState39_22 [9,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_24 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 24 5 degreeUnionState39_24 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_25 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 23 6 degreeUnionState39_25 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_26 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 22 7 degreeUnionState39_26 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_27 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 21 8 degreeUnionState39_27 [8,10] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_28 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 20 9 degreeUnionState39_28 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_29 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 10 degreeUnionState39_29 [10,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_31 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 24 4 degreeUnionState39_31 [4,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_32 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 23 5 degreeUnionState39_32 [5,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_33 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 22 6 degreeUnionState39_33 [6,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_34 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 21 7 degreeUnionState39_34 [7,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_35 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 20 8 degreeUnionState39_35 [8,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_36 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 9 degreeUnionState39_36 [9,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_37 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 18 10 degreeUnionState39_37 [10,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_38 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 17 11 degreeUnionState39_38 [11,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_40 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 23 4 degreeUnionState39_40 [4,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_41 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 22 5 degreeUnionState39_41 [5,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_42 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 21 6 degreeUnionState39_42 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_43 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 20 7 degreeUnionState39_43 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_44 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 8 degreeUnionState39_44 [8,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_45 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 18 9 degreeUnionState39_45 [9,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_46 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 17 10 degreeUnionState39_46 [10,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_47 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 16 11 degreeUnionState39_47 [11,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_48 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 15 12 degreeUnionState39_48 [12,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_50 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 22 4 degreeUnionState39_50 [4,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_51 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 21 5 degreeUnionState39_51 [5,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_52 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 20 6 degreeUnionState39_52 [6,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_53 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 7 degreeUnionState39_53 [7,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_54 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 18 8 degreeUnionState39_54 [8,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_55 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 17 9 degreeUnionState39_55 [9,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_56 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 16 10 degreeUnionState39_56 [10,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_57 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 15 11 degreeUnionState39_57 [11,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_58 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 14 12 degreeUnionState39_58 [12,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_59 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 13 13 degreeUnionState39_59 [13,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_61 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 21 4 degreeUnionState39_61 [4,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_62 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 20 5 degreeUnionState39_62 [5,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_63 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 6 degreeUnionState39_63 [6,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_64 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 18 7 degreeUnionState39_64 [7,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_65 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 17 8 degreeUnionState39_65 [8,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_66 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 16 9 degreeUnionState39_66 [9,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_67 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 15 10 degreeUnionState39_67 [10,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_68 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 14 11 degreeUnionState39_68 [11,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_69 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 13 12 degreeUnionState39_69 [12,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_70 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 12 13 degreeUnionState39_70 [13,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_71 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 11 14 degreeUnionState39_71 [14,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_73 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 20 4 degreeUnionState39_73 [4,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_74 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 5 degreeUnionState39_74 [5,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_75 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 18 6 degreeUnionState39_75 [6,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_76 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 17 7 degreeUnionState39_76 [7,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_77 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 16 8 degreeUnionState39_77 [8,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_78 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 15 9 degreeUnionState39_78 [9,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_79 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 14 10 degreeUnionState39_79 [10,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_80 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 13 11 degreeUnionState39_80 [11,15] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_81 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 12 12 degreeUnionState39_81 [12,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_82 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 11 13 degreeUnionState39_82 [13,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_83 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 10 14 degreeUnionState39_83 [14,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_84 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 9 15 degreeUnionState39_84 [15,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_86 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 4 degreeUnionState39_86 [4,16] = true := by - decide +kernel - -lemma degreeUnionBranch39_87 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 18 5 degreeUnionState39_87 [5,16] = true := by - decide +kernel - -lemma degreeUnionBranch39_88 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 17 6 degreeUnionState39_88 [6,16] = true := by - decide +kernel - -lemma degreeUnionBranch39_89 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 16 7 degreeUnionState39_89 [7,16] = true := by - decide +kernel - -lemma degreeUnionBranch39_90 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 15 8 degreeUnionState39_90 [8,16] = true := by - decide +kernel - -lemma degreeUnionBranch39_91 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 14 9 degreeUnionState39_91 [9,16] = true := by - decide +kernel - -lemma degreeUnionBranch39_92 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 13 10 degreeUnionState39_92 [10,16] = true := by - decide +kernel - -lemma degreeUnionBranch39_93 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 12 11 degreeUnionState39_93 [11,16] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_94 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 11 12 degreeUnionState39_94 [12,16] = true := by - decide +kernel - -lemma degreeUnionBranch39_95 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 10 13 degreeUnionState39_95 [13,16] = true := by - decide +kernel - -lemma degreeUnionBranch39_96 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 9 14 degreeUnionState39_96 [14,16] = true := by - decide +kernel - -lemma degreeUnionBranch39_97 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 8 15 degreeUnionState39_97 [15,16] = true := by - decide +kernel - -lemma degreeUnionBranch39_98 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 7 16 degreeUnionState39_98 [16,16] = true := by - decide +kernel - -lemma degreeUnionBranch39_99 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 22 17 degreeUnionState39_99 [17] = true := by - decide +kernel - -lemma degreeUnionBranch39_100 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 18 degreeUnionState39_100 [18] = true := by - decide +kernel - -lemma degreeUnionBranch39_101 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 19 degreeUnionState39_101 [19] = true := by - decide +kernel - -lemma degreeUnionBranch39_102 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 20 degreeUnionState39_102 [20] = true := by - decide +kernel - -lemma degreeUnionBranch39_103 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 18 21 degreeUnionState39_103 [21] = true := by - decide +kernel - -lemma degreeUnionBranch39_104 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 17 22 degreeUnionState39_104 [22] = true := by - decide +kernel - -lemma degreeUnionBranch39_105 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 16 23 degreeUnionState39_105 [23] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_106 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 15 24 degreeUnionState39_106 [24] = true := by - decide +kernel - -lemma degreeUnionBranch39_107 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 14 25 degreeUnionState39_107 [25] = true := by - decide +kernel - -lemma degreeUnionBranch39_108 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 13 26 degreeUnionState39_108 [26] = true := by - decide +kernel - -lemma degreeUnionBranch39_109 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 12 27 degreeUnionState39_109 [27] = true := by - decide +kernel - -lemma degreeUnionBranch39_110 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 11 28 degreeUnionState39_110 [28] = true := by - decide +kernel - -lemma degreeUnionBranch39_111 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 10 29 degreeUnionState39_111 [29] = true := by - decide +kernel - -lemma degreeUnionBranch39_112 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 9 30 degreeUnionState39_112 [30] = true := by - decide +kernel - -lemma degreeUnionBranch39_113 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 8 31 degreeUnionState39_113 [31] = true := by - decide +kernel - -lemma degreeUnionBranch39_114 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 7 32 degreeUnionState39_114 [32] = true := by - decide +kernel - -lemma degreeUnionBranch39_115 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 6 33 degreeUnionState39_115 [33] = true := by - decide +kernel - -lemma degreeUnionBranch39_116 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 5 34 degreeUnionState39_116 [34] = true := by - decide +kernel - -lemma degreeUnionBranch39_117 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 4 35 degreeUnionState39_117 [35] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_118 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 3 36 degreeUnionState39_118 [36] = true := by - decide +kernel - -lemma degreeUnionBranch39_119 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 2 37 degreeUnionState39_119 [37] = true := by - decide +kernel - -lemma degreeUnionBranch39_120 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 1 38 degreeUnionState39_120 [38] = true := by - decide +kernel - -lemma degreeUnionBranch39_122 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 34 5 degreeUnionState39_122 [5] = true := by - decide +kernel - -lemma degreeUnionBranch39_123 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 33 6 degreeUnionState39_123 [6] = true := by - decide +kernel - -lemma degreeUnionBranch39_124 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 32 7 degreeUnionState39_124 [7] = true := by - decide +kernel - -lemma degreeUnionBranch39_126 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 27 4 degreeUnionState39_126 [4,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_127 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 26 5 degreeUnionState39_127 [5,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_128 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 25 6 degreeUnionState39_128 [6,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_129 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 24 7 degreeUnionState39_129 [7,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_130 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 23 8 degreeUnionState39_130 [8,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_132 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 26 4 degreeUnionState39_132 [4,9] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_133 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 25 5 degreeUnionState39_133 [5,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_134 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 24 6 degreeUnionState39_134 [6,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_135 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 23 7 degreeUnionState39_135 [7,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_136 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 22 8 degreeUnionState39_136 [8,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_137 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 9 degreeUnionState39_137 [9,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_139 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 25 4 degreeUnionState39_139 [4,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_140 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 24 5 degreeUnionState39_140 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_141 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 23 6 degreeUnionState39_141 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_142 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 22 7 degreeUnionState39_142 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_143 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 8 degreeUnionState39_143 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_144 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 9 degreeUnionState39_144 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_145 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 10 degreeUnionState39_145 [10,10] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_147 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 24 4 degreeUnionState39_147 [4,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_148 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 23 5 degreeUnionState39_148 [5,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_149 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 22 6 degreeUnionState39_149 [6,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_150 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 7 degreeUnionState39_150 [7,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_151 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 8 degreeUnionState39_151 [8,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_152 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 9 degreeUnionState39_152 [9,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_153 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 18 10 degreeUnionState39_153 [10,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_154 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 17 11 degreeUnionState39_154 [11,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_156 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 23 4 degreeUnionState39_156 [4,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_157 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 22 5 degreeUnionState39_157 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_158 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 6 degreeUnionState39_158 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_159 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 7 degreeUnionState39_159 [7,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_160 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 8 degreeUnionState39_160 [8,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_161 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 18 9 degreeUnionState39_161 [9,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_162 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 17 10 degreeUnionState39_162 [10,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_163 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 16 11 degreeUnionState39_163 [11,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_164 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 15 12 degreeUnionState39_164 [12,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_166 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 22 4 degreeUnionState39_166 [4,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_167 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 5 degreeUnionState39_167 [5,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_168 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 6 degreeUnionState39_168 [6,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_169 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 7 degreeUnionState39_169 [7,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_170 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 18 8 degreeUnionState39_170 [8,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_171 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 17 9 degreeUnionState39_171 [9,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_172 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 16 10 degreeUnionState39_172 [10,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_173 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 15 11 degreeUnionState39_173 [11,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_174 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 14 12 degreeUnionState39_174 [12,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_175 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 13 13 degreeUnionState39_175 [13,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_177 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 4 degreeUnionState39_177 [4,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_178 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 5 degreeUnionState39_178 [5,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_179 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 6 degreeUnionState39_179 [6,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_180 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 18 7 degreeUnionState39_180 [7,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_181 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 17 8 degreeUnionState39_181 [8,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_182 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 16 9 degreeUnionState39_182 [9,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_183 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 15 10 degreeUnionState39_183 [10,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_184 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 14 11 degreeUnionState39_184 [11,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_185 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 13 12 degreeUnionState39_185 [12,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_186 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 12 13 degreeUnionState39_186 [13,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_187 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 11 14 degreeUnionState39_187 [14,14] = true := by - decide +kernel - -lemma degreeUnionBranch39_189 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 3 degreeUnionState39_189 [3,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_190 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 4 degreeUnionState39_190 [4,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_191 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 5 degreeUnionState39_191 [5,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_192 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 18 6 degreeUnionState39_192 [6,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_193 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 17 7 degreeUnionState39_193 [7,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_194 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 16 8 degreeUnionState39_194 [8,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_195 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 15 9 degreeUnionState39_195 [9,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_196 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 14 10 degreeUnionState39_196 [10,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_197 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 13 11 degreeUnionState39_197 [11,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_198 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 12 12 degreeUnionState39_198 [12,15] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_199 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 11 13 degreeUnionState39_199 [13,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_200 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 10 14 degreeUnionState39_200 [14,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_201 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 9 15 degreeUnionState39_201 [15,15] = true := by - decide +kernel - -lemma degreeUnionBranch39_202 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 16 degreeUnionState39_202 [16] = true := by - decide +kernel - -lemma degreeUnionBranch39_203 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 22 17 degreeUnionState39_203 [17] = true := by - decide +kernel - -lemma degreeUnionBranch39_204 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 21 18 degreeUnionState39_204 [18] = true := by - decide +kernel - -lemma degreeUnionBranch39_205 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 20 19 degreeUnionState39_205 [19] = true := by - decide +kernel - -lemma degreeUnionBranch39_206 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 19 20 degreeUnionState39_206 [20] = true := by - decide +kernel - -lemma degreeUnionBranch39_207 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 18 21 degreeUnionState39_207 [21] = true := by - decide +kernel - -lemma degreeUnionBranch39_208 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 17 22 degreeUnionState39_208 [22] = true := by - decide +kernel - -lemma degreeUnionBranch39_209 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 16 23 degreeUnionState39_209 [23] = true := by - decide +kernel - -lemma degreeUnionBranch39_210 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 15 24 degreeUnionState39_210 [24] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_211 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 14 25 degreeUnionState39_211 [25] = true := by - decide +kernel - -lemma degreeUnionBranch39_212 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 13 26 degreeUnionState39_212 [26] = true := by - decide +kernel - -lemma degreeUnionBranch39_213 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 12 27 degreeUnionState39_213 [27] = true := by - decide +kernel - -lemma degreeUnionBranch39_214 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 11 28 degreeUnionState39_214 [28] = true := by - decide +kernel - -lemma degreeUnionBranch39_215 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 10 29 degreeUnionState39_215 [29] = true := by - decide +kernel - -lemma degreeUnionBranch39_216 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 9 30 degreeUnionState39_216 [30] = true := by - decide +kernel - -lemma degreeUnionBranch39_217 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 8 31 degreeUnionState39_217 [31] = true := by - decide +kernel - -lemma degreeUnionBranch39_218 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 7 32 degreeUnionState39_218 [32] = true := by - decide +kernel - -lemma degreeUnionBranch39_219 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 6 33 degreeUnionState39_219 [33] = true := by - decide +kernel - -lemma degreeUnionBranch39_220 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 5 34 degreeUnionState39_220 [34] = true := by - decide +kernel - -lemma degreeUnionBranch39_221 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 4 35 degreeUnionState39_221 [35] = true := by - decide +kernel - -lemma degreeUnionBranch39_222 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 3 36 degreeUnionState39_222 [36] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_223 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 2 37 degreeUnionState39_223 [37] = true := by - decide +kernel - -lemma degreeUnionBranch39_224 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 1 38 degreeUnionState39_224 [38] = true := by - decide +kernel - -lemma degreeUnionBranch39_226 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 35 4 degreeUnionState39_226 [4] = true := by - decide +kernel - -lemma degreeUnionBranch39_227 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 34 5 degreeUnionState39_227 [5] = true := by - decide +kernel - -lemma degreeUnionBranch39_228 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 33 6 degreeUnionState39_228 [6] = true := by - decide +kernel - -lemma degreeUnionBranch39_229 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 32 7 degreeUnionState39_229 [7] = true := by - decide +kernel - -lemma degreeUnionBranch39_231 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 27 4 degreeUnionState39_231 [4,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_232 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 26 5 degreeUnionState39_232 [5,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_233 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 25 6 degreeUnionState39_233 [6,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_234 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 24 7 degreeUnionState39_234 [7,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_235 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 8 degreeUnionState39_235 [8,8] = true := by - decide +kernel - -lemma degreeUnionBranch39_237 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 26 4 degreeUnionState39_237 [4,9] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_238 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 25 5 degreeUnionState39_238 [5,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_239 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 24 6 degreeUnionState39_239 [6,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_240 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 7 degreeUnionState39_240 [7,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_241 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 22 8 degreeUnionState39_241 [8,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_242 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 21 9 degreeUnionState39_242 [9,9] = true := by - decide +kernel - -lemma degreeUnionBranch39_244 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 25 4 degreeUnionState39_244 [4,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_245 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 24 5 degreeUnionState39_245 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_246 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 6 degreeUnionState39_246 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_247 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 22 7 degreeUnionState39_247 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_248 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 21 8 degreeUnionState39_248 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_249 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 20 9 degreeUnionState39_249 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch39_250 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 19 10 degreeUnionState39_250 [10,10] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_252 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 24 4 degreeUnionState39_252 [4,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_253 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 5 degreeUnionState39_253 [5,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_254 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 22 6 degreeUnionState39_254 [6,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_255 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 21 7 degreeUnionState39_255 [7,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_256 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 20 8 degreeUnionState39_256 [8,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_257 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 19 9 degreeUnionState39_257 [9,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_258 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 18 10 degreeUnionState39_258 [10,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_259 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 17 11 degreeUnionState39_259 [11,11] = true := by - decide +kernel - -lemma degreeUnionBranch39_261 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 24 3 degreeUnionState39_261 [3,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_262 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 4 degreeUnionState39_262 [4,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_263 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 22 5 degreeUnionState39_263 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_264 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 21 6 degreeUnionState39_264 [6,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_265 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 20 7 degreeUnionState39_265 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_266 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 19 8 degreeUnionState39_266 [8,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_267 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 18 9 degreeUnionState39_267 [9,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_268 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 17 10 degreeUnionState39_268 [10,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_269 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 16 11 degreeUnionState39_269 [11,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_270 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 15 12 degreeUnionState39_270 [12,12] = true := by - decide +kernel - -lemma degreeUnionBranch39_272 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 3 degreeUnionState39_272 [3,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_273 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 22 4 degreeUnionState39_273 [4,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_274 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 21 5 degreeUnionState39_274 [5,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_275 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 20 6 degreeUnionState39_275 [6,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_276 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 19 7 degreeUnionState39_276 [7,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_277 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 18 8 degreeUnionState39_277 [8,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_278 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 17 9 degreeUnionState39_278 [9,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_279 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 16 10 degreeUnionState39_279 [10,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_280 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 15 11 degreeUnionState39_280 [11,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_281 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 14 12 degreeUnionState39_281 [12,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_282 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 13 13 degreeUnionState39_282 [13,13] = true := by - decide +kernel - -lemma degreeUnionBranch39_283 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 25 14 degreeUnionState39_283 [14] = true := by - decide +kernel - -lemma degreeUnionBranch39_284 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 24 15 degreeUnionState39_284 [15] = true := by - decide +kernel - -lemma degreeUnionBranch39_285 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 23 16 degreeUnionState39_285 [16] = true := by - decide +kernel - -lemma degreeUnionBranch39_286 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 22 17 degreeUnionState39_286 [17] = true := by - decide +kernel - -lemma degreeUnionBranch39_287 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 21 18 degreeUnionState39_287 [18] = true := by - decide +kernel - -lemma degreeUnionBranch39_288 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 20 19 degreeUnionState39_288 [19] = true := by - decide +kernel - -lemma degreeUnionBranch39_289 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 19 20 degreeUnionState39_289 [20] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_290 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 18 21 degreeUnionState39_290 [21] = true := by - decide +kernel - -lemma degreeUnionBranch39_291 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 17 22 degreeUnionState39_291 [22] = true := by - decide +kernel - -lemma degreeUnionBranch39_292 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 16 23 degreeUnionState39_292 [23] = true := by - decide +kernel - -lemma degreeUnionBranch39_293 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 15 24 degreeUnionState39_293 [24] = true := by - decide +kernel - -lemma degreeUnionBranch39_294 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 14 25 degreeUnionState39_294 [25] = true := by - decide +kernel - -lemma degreeUnionBranch39_295 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 13 26 degreeUnionState39_295 [26] = true := by - decide +kernel - -lemma degreeUnionBranch39_296 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 12 27 degreeUnionState39_296 [27] = true := by - decide +kernel - -lemma degreeUnionBranch39_297 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 11 28 degreeUnionState39_297 [28] = true := by - decide +kernel - -lemma degreeUnionBranch39_298 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 10 29 degreeUnionState39_298 [29] = true := by - decide +kernel - -lemma degreeUnionBranch39_299 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 9 30 degreeUnionState39_299 [30] = true := by - decide +kernel - -lemma degreeUnionBranch39_300 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 8 31 degreeUnionState39_300 [31] = true := by - decide +kernel - -lemma degreeUnionBranch39_301 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 7 32 degreeUnionState39_301 [32] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_302 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 6 33 degreeUnionState39_302 [33] = true := by - decide +kernel - -lemma degreeUnionBranch39_303 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 5 34 degreeUnionState39_303 [34] = true := by - decide +kernel - -lemma degreeUnionBranch39_304 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 4 35 degreeUnionState39_304 [35] = true := by - decide +kernel - -lemma degreeUnionBranch39_305 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 3 36 degreeUnionState39_305 [36] = true := by - decide +kernel - -lemma degreeUnionBranch39_306 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 2 37 degreeUnionState39_306 [37] = true := by - decide +kernel - -lemma degreeUnionBranch39_307 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 1 38 degreeUnionState39_307 [38] = true := by - decide +kernel - -lemma degreeUnionBranch39_308 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 11 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_309 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 12 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_310 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 13 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_311 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 14 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_312 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 15 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_313 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 16 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_314 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 17 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_315 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 18 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -lemma degreeUnionBranch39_316 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 19 39 38 degreeHalfRegions39 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans39 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates39 + +namespace OAI + +/-! Degree Leaves 39. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_0 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 0 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_1 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 1 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_2 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 2 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_3 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 3 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_4 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 4 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_5 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 5 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_6 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_7 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_9 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 34 5 degreeUnionState39_9 [5] = true := by + decide +kernel + +lemma degreeUnionBranch39_10 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 33 6 degreeUnionState39_10 [6] = true := by + decide +kernel + +lemma degreeUnionBranch39_11 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 32 7 degreeUnionState39_11 [7] = true := by + decide +kernel + +lemma degreeUnionBranch39_13 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 26 5 degreeUnionState39_13 [5,8] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_14 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 25 6 degreeUnionState39_14 [6,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_15 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 24 7 degreeUnionState39_15 [7,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_16 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 23 8 degreeUnionState39_16 [8,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_18 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 25 5 degreeUnionState39_18 [5,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_19 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 24 6 degreeUnionState39_19 [6,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_20 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 23 7 degreeUnionState39_20 [7,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_21 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 22 8 degreeUnionState39_21 [8,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_22 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 21 9 degreeUnionState39_22 [9,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_24 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 24 5 degreeUnionState39_24 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_25 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 23 6 degreeUnionState39_25 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_26 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 22 7 degreeUnionState39_26 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_27 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 21 8 degreeUnionState39_27 [8,10] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_28 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 20 9 degreeUnionState39_28 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_29 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 10 degreeUnionState39_29 [10,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_31 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 24 4 degreeUnionState39_31 [4,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_32 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 23 5 degreeUnionState39_32 [5,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_33 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 22 6 degreeUnionState39_33 [6,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_34 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 21 7 degreeUnionState39_34 [7,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_35 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 20 8 degreeUnionState39_35 [8,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_36 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 9 degreeUnionState39_36 [9,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_37 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 18 10 degreeUnionState39_37 [10,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_38 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 17 11 degreeUnionState39_38 [11,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_40 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 23 4 degreeUnionState39_40 [4,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_41 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 22 5 degreeUnionState39_41 [5,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_42 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 21 6 degreeUnionState39_42 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_43 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 20 7 degreeUnionState39_43 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_44 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 8 degreeUnionState39_44 [8,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_45 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 18 9 degreeUnionState39_45 [9,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_46 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 17 10 degreeUnionState39_46 [10,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_47 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 16 11 degreeUnionState39_47 [11,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_48 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 15 12 degreeUnionState39_48 [12,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_50 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 22 4 degreeUnionState39_50 [4,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_51 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 21 5 degreeUnionState39_51 [5,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_52 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 20 6 degreeUnionState39_52 [6,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_53 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 7 degreeUnionState39_53 [7,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_54 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 18 8 degreeUnionState39_54 [8,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_55 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 17 9 degreeUnionState39_55 [9,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_56 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 16 10 degreeUnionState39_56 [10,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_57 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 15 11 degreeUnionState39_57 [11,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_58 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 14 12 degreeUnionState39_58 [12,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_59 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 13 13 degreeUnionState39_59 [13,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_61 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 21 4 degreeUnionState39_61 [4,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_62 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 20 5 degreeUnionState39_62 [5,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_63 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 6 degreeUnionState39_63 [6,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_64 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 18 7 degreeUnionState39_64 [7,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_65 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 17 8 degreeUnionState39_65 [8,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_66 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 16 9 degreeUnionState39_66 [9,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_67 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 15 10 degreeUnionState39_67 [10,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_68 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 14 11 degreeUnionState39_68 [11,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_69 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 13 12 degreeUnionState39_69 [12,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_70 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 12 13 degreeUnionState39_70 [13,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_71 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 11 14 degreeUnionState39_71 [14,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_73 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 20 4 degreeUnionState39_73 [4,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_74 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 5 degreeUnionState39_74 [5,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_75 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 18 6 degreeUnionState39_75 [6,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_76 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 17 7 degreeUnionState39_76 [7,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_77 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 16 8 degreeUnionState39_77 [8,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_78 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 15 9 degreeUnionState39_78 [9,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_79 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 14 10 degreeUnionState39_79 [10,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_80 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 13 11 degreeUnionState39_80 [11,15] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_81 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 12 12 degreeUnionState39_81 [12,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_82 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 11 13 degreeUnionState39_82 [13,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_83 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 10 14 degreeUnionState39_83 [14,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_84 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 9 15 degreeUnionState39_84 [15,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_86 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 19 4 degreeUnionState39_86 [4,16] = true := by + decide +kernel + +lemma degreeUnionBranch39_87 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 18 5 degreeUnionState39_87 [5,16] = true := by + decide +kernel + +lemma degreeUnionBranch39_88 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 17 6 degreeUnionState39_88 [6,16] = true := by + decide +kernel + +lemma degreeUnionBranch39_89 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 16 7 degreeUnionState39_89 [7,16] = true := by + decide +kernel + +lemma degreeUnionBranch39_90 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 15 8 degreeUnionState39_90 [8,16] = true := by + decide +kernel + +lemma degreeUnionBranch39_91 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 14 9 degreeUnionState39_91 [9,16] = true := by + decide +kernel + +lemma degreeUnionBranch39_92 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 13 10 degreeUnionState39_92 [10,16] = true := by + decide +kernel + +lemma degreeUnionBranch39_93 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 12 11 degreeUnionState39_93 [11,16] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_94 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 11 12 degreeUnionState39_94 [12,16] = true := by + decide +kernel + +lemma degreeUnionBranch39_95 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 10 13 degreeUnionState39_95 [13,16] = true := by + decide +kernel + +lemma degreeUnionBranch39_96 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 9 14 degreeUnionState39_96 [14,16] = true := by + decide +kernel + +lemma degreeUnionBranch39_97 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 8 15 degreeUnionState39_97 [15,16] = true := by + decide +kernel + +lemma degreeUnionBranch39_98 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 6 7 16 degreeUnionState39_98 [16,16] = true := by + decide +kernel + +lemma degreeUnionBranch39_99 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 22 17 degreeUnionState39_99 [17] = true := by + decide +kernel + +lemma degreeUnionBranch39_100 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 18 degreeUnionState39_100 [18] = true := by + decide +kernel + +lemma degreeUnionBranch39_101 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 19 degreeUnionState39_101 [19] = true := by + decide +kernel + +lemma degreeUnionBranch39_102 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 20 degreeUnionState39_102 [20] = true := by + decide +kernel + +lemma degreeUnionBranch39_103 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 18 21 degreeUnionState39_103 [21] = true := by + decide +kernel + +lemma degreeUnionBranch39_104 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 17 22 degreeUnionState39_104 [22] = true := by + decide +kernel + +lemma degreeUnionBranch39_105 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 16 23 degreeUnionState39_105 [23] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_106 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 15 24 degreeUnionState39_106 [24] = true := by + decide +kernel + +lemma degreeUnionBranch39_107 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 14 25 degreeUnionState39_107 [25] = true := by + decide +kernel + +lemma degreeUnionBranch39_108 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 13 26 degreeUnionState39_108 [26] = true := by + decide +kernel + +lemma degreeUnionBranch39_109 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 12 27 degreeUnionState39_109 [27] = true := by + decide +kernel + +lemma degreeUnionBranch39_110 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 11 28 degreeUnionState39_110 [28] = true := by + decide +kernel + +lemma degreeUnionBranch39_111 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 10 29 degreeUnionState39_111 [29] = true := by + decide +kernel + +lemma degreeUnionBranch39_112 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 9 30 degreeUnionState39_112 [30] = true := by + decide +kernel + +lemma degreeUnionBranch39_113 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 8 31 degreeUnionState39_113 [31] = true := by + decide +kernel + +lemma degreeUnionBranch39_114 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 7 32 degreeUnionState39_114 [32] = true := by + decide +kernel + +lemma degreeUnionBranch39_115 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 6 33 degreeUnionState39_115 [33] = true := by + decide +kernel + +lemma degreeUnionBranch39_116 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 5 34 degreeUnionState39_116 [34] = true := by + decide +kernel + +lemma degreeUnionBranch39_117 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 4 35 degreeUnionState39_117 [35] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_118 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 3 36 degreeUnionState39_118 [36] = true := by + decide +kernel + +lemma degreeUnionBranch39_119 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 2 37 degreeUnionState39_119 [37] = true := by + decide +kernel + +lemma degreeUnionBranch39_120 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 1 38 degreeUnionState39_120 [38] = true := by + decide +kernel + +lemma degreeUnionBranch39_122 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 34 5 degreeUnionState39_122 [5] = true := by + decide +kernel + +lemma degreeUnionBranch39_123 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 33 6 degreeUnionState39_123 [6] = true := by + decide +kernel + +lemma degreeUnionBranch39_124 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 32 7 degreeUnionState39_124 [7] = true := by + decide +kernel + +lemma degreeUnionBranch39_126 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 27 4 degreeUnionState39_126 [4,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_127 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 26 5 degreeUnionState39_127 [5,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_128 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 25 6 degreeUnionState39_128 [6,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_129 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 24 7 degreeUnionState39_129 [7,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_130 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 23 8 degreeUnionState39_130 [8,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_132 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 26 4 degreeUnionState39_132 [4,9] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_133 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 25 5 degreeUnionState39_133 [5,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_134 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 24 6 degreeUnionState39_134 [6,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_135 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 23 7 degreeUnionState39_135 [7,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_136 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 22 8 degreeUnionState39_136 [8,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_137 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 9 degreeUnionState39_137 [9,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_139 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 25 4 degreeUnionState39_139 [4,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_140 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 24 5 degreeUnionState39_140 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_141 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 23 6 degreeUnionState39_141 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_142 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 22 7 degreeUnionState39_142 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_143 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 8 degreeUnionState39_143 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_144 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 9 degreeUnionState39_144 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_145 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 10 degreeUnionState39_145 [10,10] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_147 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 24 4 degreeUnionState39_147 [4,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_148 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 23 5 degreeUnionState39_148 [5,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_149 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 22 6 degreeUnionState39_149 [6,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_150 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 7 degreeUnionState39_150 [7,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_151 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 8 degreeUnionState39_151 [8,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_152 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 9 degreeUnionState39_152 [9,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_153 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 18 10 degreeUnionState39_153 [10,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_154 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 17 11 degreeUnionState39_154 [11,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_156 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 23 4 degreeUnionState39_156 [4,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_157 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 22 5 degreeUnionState39_157 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_158 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 6 degreeUnionState39_158 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_159 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 7 degreeUnionState39_159 [7,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_160 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 8 degreeUnionState39_160 [8,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_161 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 18 9 degreeUnionState39_161 [9,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_162 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 17 10 degreeUnionState39_162 [10,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_163 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 16 11 degreeUnionState39_163 [11,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_164 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 15 12 degreeUnionState39_164 [12,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_166 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 22 4 degreeUnionState39_166 [4,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_167 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 5 degreeUnionState39_167 [5,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_168 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 6 degreeUnionState39_168 [6,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_169 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 7 degreeUnionState39_169 [7,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_170 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 18 8 degreeUnionState39_170 [8,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_171 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 17 9 degreeUnionState39_171 [9,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_172 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 16 10 degreeUnionState39_172 [10,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_173 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 15 11 degreeUnionState39_173 [11,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_174 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 14 12 degreeUnionState39_174 [12,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_175 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 13 13 degreeUnionState39_175 [13,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_177 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 4 degreeUnionState39_177 [4,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_178 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 5 degreeUnionState39_178 [5,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_179 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 6 degreeUnionState39_179 [6,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_180 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 18 7 degreeUnionState39_180 [7,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_181 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 17 8 degreeUnionState39_181 [8,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_182 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 16 9 degreeUnionState39_182 [9,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_183 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 15 10 degreeUnionState39_183 [10,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_184 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 14 11 degreeUnionState39_184 [11,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_185 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 13 12 degreeUnionState39_185 [12,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_186 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 12 13 degreeUnionState39_186 [13,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_187 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 11 14 degreeUnionState39_187 [14,14] = true := by + decide +kernel + +lemma degreeUnionBranch39_189 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 21 3 degreeUnionState39_189 [3,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_190 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 20 4 degreeUnionState39_190 [4,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_191 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 19 5 degreeUnionState39_191 [5,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_192 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 18 6 degreeUnionState39_192 [6,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_193 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 17 7 degreeUnionState39_193 [7,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_194 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 16 8 degreeUnionState39_194 [8,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_195 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 15 9 degreeUnionState39_195 [9,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_196 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 14 10 degreeUnionState39_196 [10,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_197 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 13 11 degreeUnionState39_197 [11,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_198 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 12 12 degreeUnionState39_198 [12,15] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_199 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 11 13 degreeUnionState39_199 [13,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_200 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 10 14 degreeUnionState39_200 [14,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_201 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 9 15 degreeUnionState39_201 [15,15] = true := by + decide +kernel + +lemma degreeUnionBranch39_202 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 16 degreeUnionState39_202 [16] = true := by + decide +kernel + +lemma degreeUnionBranch39_203 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 22 17 degreeUnionState39_203 [17] = true := by + decide +kernel + +lemma degreeUnionBranch39_204 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 21 18 degreeUnionState39_204 [18] = true := by + decide +kernel + +lemma degreeUnionBranch39_205 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 20 19 degreeUnionState39_205 [19] = true := by + decide +kernel + +lemma degreeUnionBranch39_206 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 19 20 degreeUnionState39_206 [20] = true := by + decide +kernel + +lemma degreeUnionBranch39_207 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 18 21 degreeUnionState39_207 [21] = true := by + decide +kernel + +lemma degreeUnionBranch39_208 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 17 22 degreeUnionState39_208 [22] = true := by + decide +kernel + +lemma degreeUnionBranch39_209 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 16 23 degreeUnionState39_209 [23] = true := by + decide +kernel + +lemma degreeUnionBranch39_210 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 15 24 degreeUnionState39_210 [24] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_211 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 14 25 degreeUnionState39_211 [25] = true := by + decide +kernel + +lemma degreeUnionBranch39_212 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 13 26 degreeUnionState39_212 [26] = true := by + decide +kernel + +lemma degreeUnionBranch39_213 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 12 27 degreeUnionState39_213 [27] = true := by + decide +kernel + +lemma degreeUnionBranch39_214 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 11 28 degreeUnionState39_214 [28] = true := by + decide +kernel + +lemma degreeUnionBranch39_215 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 10 29 degreeUnionState39_215 [29] = true := by + decide +kernel + +lemma degreeUnionBranch39_216 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 9 30 degreeUnionState39_216 [30] = true := by + decide +kernel + +lemma degreeUnionBranch39_217 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 8 31 degreeUnionState39_217 [31] = true := by + decide +kernel + +lemma degreeUnionBranch39_218 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 7 32 degreeUnionState39_218 [32] = true := by + decide +kernel + +lemma degreeUnionBranch39_219 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 6 33 degreeUnionState39_219 [33] = true := by + decide +kernel + +lemma degreeUnionBranch39_220 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 5 34 degreeUnionState39_220 [34] = true := by + decide +kernel + +lemma degreeUnionBranch39_221 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 4 35 degreeUnionState39_221 [35] = true := by + decide +kernel + +lemma degreeUnionBranch39_222 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 3 36 degreeUnionState39_222 [36] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_223 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 2 37 degreeUnionState39_223 [37] = true := by + decide +kernel + +lemma degreeUnionBranch39_224 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 1 38 degreeUnionState39_224 [38] = true := by + decide +kernel + +lemma degreeUnionBranch39_226 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 35 4 degreeUnionState39_226 [4] = true := by + decide +kernel + +lemma degreeUnionBranch39_227 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 34 5 degreeUnionState39_227 [5] = true := by + decide +kernel + +lemma degreeUnionBranch39_228 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 33 6 degreeUnionState39_228 [6] = true := by + decide +kernel + +lemma degreeUnionBranch39_229 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 32 7 degreeUnionState39_229 [7] = true := by + decide +kernel + +lemma degreeUnionBranch39_231 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 27 4 degreeUnionState39_231 [4,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_232 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 26 5 degreeUnionState39_232 [5,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_233 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 25 6 degreeUnionState39_233 [6,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_234 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 24 7 degreeUnionState39_234 [7,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_235 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 8 degreeUnionState39_235 [8,8] = true := by + decide +kernel + +lemma degreeUnionBranch39_237 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 26 4 degreeUnionState39_237 [4,9] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_238 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 25 5 degreeUnionState39_238 [5,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_239 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 24 6 degreeUnionState39_239 [6,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_240 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 7 degreeUnionState39_240 [7,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_241 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 22 8 degreeUnionState39_241 [8,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_242 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 21 9 degreeUnionState39_242 [9,9] = true := by + decide +kernel + +lemma degreeUnionBranch39_244 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 25 4 degreeUnionState39_244 [4,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_245 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 24 5 degreeUnionState39_245 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_246 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 6 degreeUnionState39_246 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_247 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 22 7 degreeUnionState39_247 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_248 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 21 8 degreeUnionState39_248 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_249 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 20 9 degreeUnionState39_249 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch39_250 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 19 10 degreeUnionState39_250 [10,10] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_252 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 24 4 degreeUnionState39_252 [4,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_253 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 5 degreeUnionState39_253 [5,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_254 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 22 6 degreeUnionState39_254 [6,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_255 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 21 7 degreeUnionState39_255 [7,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_256 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 20 8 degreeUnionState39_256 [8,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_257 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 19 9 degreeUnionState39_257 [9,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_258 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 18 10 degreeUnionState39_258 [10,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_259 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 17 11 degreeUnionState39_259 [11,11] = true := by + decide +kernel + +lemma degreeUnionBranch39_261 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 24 3 degreeUnionState39_261 [3,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_262 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 4 degreeUnionState39_262 [4,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_263 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 22 5 degreeUnionState39_263 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_264 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 21 6 degreeUnionState39_264 [6,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_265 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 20 7 degreeUnionState39_265 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_266 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 19 8 degreeUnionState39_266 [8,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_267 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 18 9 degreeUnionState39_267 [9,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_268 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 17 10 degreeUnionState39_268 [10,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_269 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 16 11 degreeUnionState39_269 [11,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_270 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 15 12 degreeUnionState39_270 [12,12] = true := by + decide +kernel + +lemma degreeUnionBranch39_272 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 23 3 degreeUnionState39_272 [3,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_273 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 22 4 degreeUnionState39_273 [4,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_274 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 21 5 degreeUnionState39_274 [5,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_275 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 20 6 degreeUnionState39_275 [6,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_276 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 19 7 degreeUnionState39_276 [7,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_277 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 18 8 degreeUnionState39_277 [8,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_278 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 17 9 degreeUnionState39_278 [9,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_279 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 16 10 degreeUnionState39_279 [10,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_280 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 15 11 degreeUnionState39_280 [11,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_281 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 14 12 degreeUnionState39_281 [12,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_282 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 13 13 degreeUnionState39_282 [13,13] = true := by + decide +kernel + +lemma degreeUnionBranch39_283 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 25 14 degreeUnionState39_283 [14] = true := by + decide +kernel + +lemma degreeUnionBranch39_284 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 24 15 degreeUnionState39_284 [15] = true := by + decide +kernel + +lemma degreeUnionBranch39_285 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 23 16 degreeUnionState39_285 [16] = true := by + decide +kernel + +lemma degreeUnionBranch39_286 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 22 17 degreeUnionState39_286 [17] = true := by + decide +kernel + +lemma degreeUnionBranch39_287 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 21 18 degreeUnionState39_287 [18] = true := by + decide +kernel + +lemma degreeUnionBranch39_288 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 20 19 degreeUnionState39_288 [19] = true := by + decide +kernel + +lemma degreeUnionBranch39_289 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 19 20 degreeUnionState39_289 [20] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_290 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 18 21 degreeUnionState39_290 [21] = true := by + decide +kernel + +lemma degreeUnionBranch39_291 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 17 22 degreeUnionState39_291 [22] = true := by + decide +kernel + +lemma degreeUnionBranch39_292 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 16 23 degreeUnionState39_292 [23] = true := by + decide +kernel + +lemma degreeUnionBranch39_293 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 15 24 degreeUnionState39_293 [24] = true := by + decide +kernel + +lemma degreeUnionBranch39_294 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 14 25 degreeUnionState39_294 [25] = true := by + decide +kernel + +lemma degreeUnionBranch39_295 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 13 26 degreeUnionState39_295 [26] = true := by + decide +kernel + +lemma degreeUnionBranch39_296 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 12 27 degreeUnionState39_296 [27] = true := by + decide +kernel + +lemma degreeUnionBranch39_297 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 11 28 degreeUnionState39_297 [28] = true := by + decide +kernel + +lemma degreeUnionBranch39_298 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 10 29 degreeUnionState39_298 [29] = true := by + decide +kernel + +lemma degreeUnionBranch39_299 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 9 30 degreeUnionState39_299 [30] = true := by + decide +kernel + +lemma degreeUnionBranch39_300 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 8 31 degreeUnionState39_300 [31] = true := by + decide +kernel + +lemma degreeUnionBranch39_301 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 7 32 degreeUnionState39_301 [32] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_302 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 6 33 degreeUnionState39_302 [33] = true := by + decide +kernel + +lemma degreeUnionBranch39_303 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 5 34 degreeUnionState39_303 [34] = true := by + decide +kernel + +lemma degreeUnionBranch39_304 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 4 35 degreeUnionState39_304 [35] = true := by + decide +kernel + +lemma degreeUnionBranch39_305 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 3 36 degreeUnionState39_305 [36] = true := by + decide +kernel + +lemma degreeUnionBranch39_306 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 2 37 degreeUnionState39_306 [37] = true := by + decide +kernel + +lemma degreeUnionBranch39_307 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 1 38 degreeUnionState39_307 [38] = true := by + decide +kernel + +lemma degreeUnionBranch39_308 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 11 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_309 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 12 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_310 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 13 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_311 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 14 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_312 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 15 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_313 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 16 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_314 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 17 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_315 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 18 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +lemma degreeUnionBranch39_316 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 19 39 38 degreeHalfRegions39 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves41.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves41.lean index a9adbcda555cd306e0442c6a0407cc003aaa8d9e..eef5bce1737f5d4bc30a55b713c8bb3476002ab4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves41.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves41.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans41 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData41 - -namespace OAI - -/-! Degree Leaves 41. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch41_0 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 0 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_1 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 1 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_2 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 2 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_3 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 3 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_4 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 4 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_5 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 5 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_6 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 6 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_7 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 7 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_8 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 8 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_9 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 9 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_10 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 10 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_11 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 11 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch41_12 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 12 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_13 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 13 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_14 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 14 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_15 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 15 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_16 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 16 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_17 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 17 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_18 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 18 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_19 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 19 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_20 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 20 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -lemma degreeUnionBranch41_21 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 21 41 21 degreeHalfRegions41 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans41 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData41 + +namespace OAI + +/-! Degree Leaves 41. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch41_0 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 0 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_1 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 1 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_2 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 2 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_3 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 3 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_4 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 4 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_5 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 5 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_6 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 6 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_7 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 7 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_8 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 8 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_9 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 9 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_10 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 10 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_11 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 11 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch41_12 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 12 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_13 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 13 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_14 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 14 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_15 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 15 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_16 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 16 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_17 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 17 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_18 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 18 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_19 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 19 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_20 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 20 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +lemma degreeUnionBranch41_21 : checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) 21 41 21 degreeHalfRegions41 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves43.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves43.lean index df58e57de2533a5ecef59c11c11ef7479f03bced..7399ef990fd5214cf36728024904be4cb9c9802e 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves43.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves43.lean @@ -1,3020 +1,3020 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans43 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates43 - -namespace OAI - -/-! Degree Leaves 43. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_0 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 0 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_1 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 1 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_2 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 2 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_3 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 3 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_4 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 4 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_5 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 5 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_6 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_7 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_9 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 37 6 degreeUnionState43_9 [6] = true := by - decide +kernel - -lemma degreeUnionBranch43_10 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 36 7 degreeUnionState43_10 [7] = true := by - decide +kernel - -lemma degreeUnionBranch43_12 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 30 5 degreeUnionState43_12 [5,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_13 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 29 6 degreeUnionState43_13 [6,8] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_14 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 28 7 degreeUnionState43_14 [7,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_15 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 27 8 degreeUnionState43_15 [8,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_17 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 29 5 degreeUnionState43_17 [5,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_18 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 28 6 degreeUnionState43_18 [6,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_19 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 27 7 degreeUnionState43_19 [7,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_20 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 26 8 degreeUnionState43_20 [8,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_21 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 25 9 degreeUnionState43_21 [9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_23 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 28 5 degreeUnionState43_23 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_24 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 27 6 degreeUnionState43_24 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_25 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 26 7 degreeUnionState43_25 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_26 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 25 8 degreeUnionState43_26 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_27 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 24 9 degreeUnionState43_27 [9,10] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_28 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 10 degreeUnionState43_28 [10,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_30 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 27 5 degreeUnionState43_30 [5,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_31 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 26 6 degreeUnionState43_31 [6,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_32 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 25 7 degreeUnionState43_32 [7,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_33 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 24 8 degreeUnionState43_33 [8,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_34 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 9 degreeUnionState43_34 [9,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_35 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 10 degreeUnionState43_35 [10,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_36 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 11 degreeUnionState43_36 [11,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_38 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 26 5 degreeUnionState43_38 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_39 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 25 6 degreeUnionState43_39 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_40 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 24 7 degreeUnionState43_40 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_41 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 8 degreeUnionState43_41 [8,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_42 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 9 degreeUnionState43_42 [9,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_43 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 10 degreeUnionState43_43 [10,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_44 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 11 degreeUnionState43_44 [11,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_45 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 12 degreeUnionState43_45 [12,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_47 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 25 5 degreeUnionState43_47 [5,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_48 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 24 6 degreeUnionState43_48 [6,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_49 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 7 degreeUnionState43_49 [7,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_50 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 8 degreeUnionState43_50 [8,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_51 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 9 degreeUnionState43_51 [9,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_52 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 10 degreeUnionState43_52 [10,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_53 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 11 degreeUnionState43_53 [11,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_54 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 12 degreeUnionState43_54 [12,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_55 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 13 degreeUnionState43_55 [13,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_57 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 24 5 degreeUnionState43_57 [5,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_58 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 6 degreeUnionState43_58 [6,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_59 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 7 degreeUnionState43_59 [7,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_60 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 8 degreeUnionState43_60 [8,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_61 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 9 degreeUnionState43_61 [9,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_62 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 10 degreeUnionState43_62 [10,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_63 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 11 degreeUnionState43_63 [11,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_64 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 12 degreeUnionState43_64 [12,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_65 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 13 degreeUnionState43_65 [13,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_66 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 14 degreeUnionState43_66 [14,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_68 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 24 4 degreeUnionState43_68 [4,15] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_69 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 5 degreeUnionState43_69 [5,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_70 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 6 degreeUnionState43_70 [6,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_71 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 7 degreeUnionState43_71 [7,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_72 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 8 degreeUnionState43_72 [8,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_73 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 9 degreeUnionState43_73 [9,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_74 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 10 degreeUnionState43_74 [10,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_75 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 11 degreeUnionState43_75 [11,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_76 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 12 degreeUnionState43_76 [12,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_77 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 13 degreeUnionState43_77 [13,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_78 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 14 14 degreeUnionState43_78 [14,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_79 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 13 15 degreeUnionState43_79 [15,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_81 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 4 degreeUnionState43_81 [4,16] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_82 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 5 degreeUnionState43_82 [5,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_83 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 6 degreeUnionState43_83 [6,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_84 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 7 degreeUnionState43_84 [7,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_85 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 8 degreeUnionState43_85 [8,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_86 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 9 degreeUnionState43_86 [9,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_87 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 10 degreeUnionState43_87 [10,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_88 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 11 degreeUnionState43_88 [11,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_89 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 12 degreeUnionState43_89 [12,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_90 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 14 13 degreeUnionState43_90 [13,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_91 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 13 14 degreeUnionState43_91 [14,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_92 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 12 15 degreeUnionState43_92 [15,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_93 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 11 16 degreeUnionState43_93 [16,16] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_95 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 4 degreeUnionState43_95 [4,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_96 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 5 degreeUnionState43_96 [5,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_97 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 6 degreeUnionState43_97 [6,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_98 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 7 degreeUnionState43_98 [7,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_99 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 8 degreeUnionState43_99 [8,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_100 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 9 degreeUnionState43_100 [9,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_101 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 10 degreeUnionState43_101 [10,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_102 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 11 degreeUnionState43_102 [11,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_103 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 14 12 degreeUnionState43_103 [12,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_104 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 13 13 degreeUnionState43_104 [13,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_105 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 12 14 degreeUnionState43_105 [14,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_106 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 11 15 degreeUnionState43_106 [15,17] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_107 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 10 16 degreeUnionState43_107 [16,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_108 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 9 17 degreeUnionState43_108 [17,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_110 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 4 degreeUnionState43_110 [4,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_111 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 5 degreeUnionState43_111 [5,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_112 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 6 degreeUnionState43_112 [6,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_113 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 7 degreeUnionState43_113 [7,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_114 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 8 degreeUnionState43_114 [8,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_115 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 9 degreeUnionState43_115 [9,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_116 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 10 degreeUnionState43_116 [10,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_117 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 14 11 degreeUnionState43_117 [11,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_118 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 13 12 degreeUnionState43_118 [12,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_119 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 12 13 degreeUnionState43_119 [13,18] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_120 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 11 14 degreeUnionState43_120 [14,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_121 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 10 15 degreeUnionState43_121 [15,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_122 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 9 16 degreeUnionState43_122 [16,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_123 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 8 17 degreeUnionState43_123 [17,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_124 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 7 18 degreeUnionState43_124 [18,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_126 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 4 degreeUnionState43_126 [4,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_127 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 5 degreeUnionState43_127 [5,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_128 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 6 degreeUnionState43_128 [6,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_129 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 7 degreeUnionState43_129 [7,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_130 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 8 degreeUnionState43_130 [8,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_131 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 9 degreeUnionState43_131 [9,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_132 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 14 10 degreeUnionState43_132 [10,19] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_133 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 13 11 degreeUnionState43_133 [11,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_134 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 12 12 degreeUnionState43_134 [12,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_135 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 11 13 degreeUnionState43_135 [13,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_136 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 10 14 degreeUnionState43_136 [14,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_137 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 9 15 degreeUnionState43_137 [15,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_138 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 8 16 degreeUnionState43_138 [16,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_139 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 7 17 degreeUnionState43_139 [17,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_140 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 6 18 degreeUnionState43_140 [18,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_141 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 5 19 degreeUnionState43_141 [19,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_143 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 4 degreeUnionState43_143 [4,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_144 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 5 degreeUnionState43_144 [5,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_145 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 6 degreeUnionState43_145 [6,20] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_146 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 7 degreeUnionState43_146 [7,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_147 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 8 degreeUnionState43_147 [8,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_148 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 14 9 degreeUnionState43_148 [9,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_149 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 13 10 degreeUnionState43_149 [10,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_150 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 12 11 degreeUnionState43_150 [11,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_151 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 11 12 degreeUnionState43_151 [12,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_152 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 10 13 degreeUnionState43_152 [13,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_153 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 9 14 degreeUnionState43_153 [14,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_154 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 8 15 degreeUnionState43_154 [15,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_155 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 7 16 degreeUnionState43_155 [16,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_156 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 6 17 degreeUnionState43_156 [17,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_157 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 5 18 degreeUnionState43_157 [18,20] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_158 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 4 19 degreeUnionState43_158 [19,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_159 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 3 20 degreeUnionState43_159 [20,20] = true := by - decide +kernel - -lemma degreeUnionBranch43_160 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 21 degreeUnionState43_160 [21] = true := by - decide +kernel - -lemma degreeUnionBranch43_161 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 22 degreeUnionState43_161 [22] = true := by - decide +kernel - -lemma degreeUnionBranch43_162 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 23 degreeUnionState43_162 [23] = true := by - decide +kernel - -lemma degreeUnionBranch43_163 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 24 degreeUnionState43_163 [24] = true := by - decide +kernel - -lemma degreeUnionBranch43_164 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 25 degreeUnionState43_164 [25] = true := by - decide +kernel - -lemma degreeUnionBranch43_165 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 26 degreeUnionState43_165 [26] = true := by - decide +kernel - -lemma degreeUnionBranch43_166 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 27 degreeUnionState43_166 [27] = true := by - decide +kernel - -lemma degreeUnionBranch43_167 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 28 degreeUnionState43_167 [28] = true := by - decide +kernel - -lemma degreeUnionBranch43_168 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 14 29 degreeUnionState43_168 [29] = true := by - decide +kernel - -lemma degreeUnionBranch43_169 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 13 30 degreeUnionState43_169 [30] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_170 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 12 31 degreeUnionState43_170 [31] = true := by - decide +kernel - -lemma degreeUnionBranch43_171 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 11 32 degreeUnionState43_171 [32] = true := by - decide +kernel - -lemma degreeUnionBranch43_172 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 10 33 degreeUnionState43_172 [33] = true := by - decide +kernel - -lemma degreeUnionBranch43_173 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 9 34 degreeUnionState43_173 [34] = true := by - decide +kernel - -lemma degreeUnionBranch43_174 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 8 35 degreeUnionState43_174 [35] = true := by - decide +kernel - -lemma degreeUnionBranch43_175 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 7 36 degreeUnionState43_175 [36] = true := by - decide +kernel - -lemma degreeUnionBranch43_176 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 6 37 degreeUnionState43_176 [37] = true := by - decide +kernel - -lemma degreeUnionBranch43_177 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 5 38 degreeUnionState43_177 [38] = true := by - decide +kernel - -lemma degreeUnionBranch43_178 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 4 39 degreeUnionState43_178 [39] = true := by - decide +kernel - -lemma degreeUnionBranch43_179 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 3 40 degreeUnionState43_179 [40] = true := by - decide +kernel - -lemma degreeUnionBranch43_180 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 2 41 degreeUnionState43_180 [41] = true := by - decide +kernel - -lemma degreeUnionBranch43_181 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 1 42 degreeUnionState43_181 [42] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_183 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 38 5 degreeUnionState43_183 [5] = true := by - decide +kernel - -lemma degreeUnionBranch43_184 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 37 6 degreeUnionState43_184 [6] = true := by - decide +kernel - -lemma degreeUnionBranch43_185 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 36 7 degreeUnionState43_185 [7] = true := by - decide +kernel - -lemma degreeUnionBranch43_187 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 30 5 degreeUnionState43_187 [5,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_188 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 29 6 degreeUnionState43_188 [6,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_189 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 28 7 degreeUnionState43_189 [7,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_190 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 27 8 degreeUnionState43_190 [8,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_192 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 29 5 degreeUnionState43_192 [5,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_193 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 28 6 degreeUnionState43_193 [6,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_194 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 27 7 degreeUnionState43_194 [7,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_195 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 26 8 degreeUnionState43_195 [8,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_197 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 4 degreeUnionState43_197 [4,9,9] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_198 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 5 degreeUnionState43_198 [5,9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_199 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 6 degreeUnionState43_199 [6,9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_200 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 7 degreeUnionState43_200 [7,9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_201 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 8 degreeUnionState43_201 [8,9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_202 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 9 degreeUnionState43_202 [9,9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_204 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 28 5 degreeUnionState43_204 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_205 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 27 6 degreeUnionState43_205 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_206 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 26 7 degreeUnionState43_206 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_207 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 8 degreeUnionState43_207 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_208 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 9 degreeUnionState43_208 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_209 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 10 degreeUnionState43_209 [10,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_211 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 28 4 degreeUnionState43_211 [4,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_212 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 27 5 degreeUnionState43_212 [5,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_213 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 26 6 degreeUnionState43_213 [6,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_214 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 7 degreeUnionState43_214 [7,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_215 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 8 degreeUnionState43_215 [8,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_216 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 9 degreeUnionState43_216 [9,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_217 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 10 degreeUnionState43_217 [10,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_218 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 11 degreeUnionState43_218 [11,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_220 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 27 4 degreeUnionState43_220 [4,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_221 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 26 5 degreeUnionState43_221 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_222 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 6 degreeUnionState43_222 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_223 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 7 degreeUnionState43_223 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_224 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 8 degreeUnionState43_224 [8,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_225 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 9 degreeUnionState43_225 [9,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_226 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 10 degreeUnionState43_226 [10,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_227 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 11 degreeUnionState43_227 [11,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_228 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 12 degreeUnionState43_228 [12,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_230 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 26 4 degreeUnionState43_230 [4,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_231 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 5 degreeUnionState43_231 [5,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_232 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 6 degreeUnionState43_232 [6,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_233 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 7 degreeUnionState43_233 [7,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_234 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 8 degreeUnionState43_234 [8,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_235 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 9 degreeUnionState43_235 [9,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_236 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 10 degreeUnionState43_236 [10,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_237 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 11 degreeUnionState43_237 [11,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_238 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 12 degreeUnionState43_238 [12,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_239 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 13 degreeUnionState43_239 [13,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_241 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 4 degreeUnionState43_241 [4,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_242 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 5 degreeUnionState43_242 [5,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_243 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 6 degreeUnionState43_243 [6,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_244 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 7 degreeUnionState43_244 [7,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_245 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 8 degreeUnionState43_245 [8,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_246 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 9 degreeUnionState43_246 [9,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_247 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 10 degreeUnionState43_247 [10,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_248 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 11 degreeUnionState43_248 [11,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_249 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 12 degreeUnionState43_249 [12,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_250 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 13 degreeUnionState43_250 [13,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_251 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 14 degreeUnionState43_251 [14,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_253 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 4 degreeUnionState43_253 [4,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_254 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 5 degreeUnionState43_254 [5,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_255 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 6 degreeUnionState43_255 [6,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_256 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 7 degreeUnionState43_256 [7,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_257 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 8 degreeUnionState43_257 [8,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_258 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 9 degreeUnionState43_258 [9,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_259 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 10 degreeUnionState43_259 [10,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_260 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 11 degreeUnionState43_260 [11,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_261 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 12 degreeUnionState43_261 [12,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_262 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 13 degreeUnionState43_262 [13,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_263 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 14 14 degreeUnionState43_263 [14,15] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_264 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 13 15 degreeUnionState43_264 [15,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_266 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 4 degreeUnionState43_266 [4,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_267 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 5 degreeUnionState43_267 [5,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_268 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 6 degreeUnionState43_268 [6,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_269 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 7 degreeUnionState43_269 [7,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_270 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 8 degreeUnionState43_270 [8,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_271 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 9 degreeUnionState43_271 [9,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_272 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 10 degreeUnionState43_272 [10,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_273 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 11 degreeUnionState43_273 [11,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_274 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 12 degreeUnionState43_274 [12,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_275 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 14 13 degreeUnionState43_275 [13,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_276 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 13 14 degreeUnionState43_276 [14,16] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_277 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 12 15 degreeUnionState43_277 [15,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_278 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 11 16 degreeUnionState43_278 [16,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_280 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 4 degreeUnionState43_280 [4,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_281 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 5 degreeUnionState43_281 [5,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_282 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 6 degreeUnionState43_282 [6,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_283 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 7 degreeUnionState43_283 [7,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_284 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 8 degreeUnionState43_284 [8,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_285 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 9 degreeUnionState43_285 [9,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_286 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 10 degreeUnionState43_286 [10,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_287 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 11 degreeUnionState43_287 [11,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_288 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 14 12 degreeUnionState43_288 [12,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_289 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 13 13 degreeUnionState43_289 [13,17] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_290 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 12 14 degreeUnionState43_290 [14,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_291 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 11 15 degreeUnionState43_291 [15,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_292 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 10 16 degreeUnionState43_292 [16,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_293 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 9 17 degreeUnionState43_293 [17,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_295 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 4 degreeUnionState43_295 [4,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_296 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 5 degreeUnionState43_296 [5,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_297 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 6 degreeUnionState43_297 [6,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_298 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 7 degreeUnionState43_298 [7,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_299 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 8 degreeUnionState43_299 [8,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_300 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 9 degreeUnionState43_300 [9,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_301 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 10 degreeUnionState43_301 [10,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_302 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 14 11 degreeUnionState43_302 [11,18] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_303 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 13 12 degreeUnionState43_303 [12,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_304 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 12 13 degreeUnionState43_304 [13,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_305 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 11 14 degreeUnionState43_305 [14,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_306 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 10 15 degreeUnionState43_306 [15,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_307 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 9 16 degreeUnionState43_307 [16,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_308 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 8 17 degreeUnionState43_308 [17,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_309 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 7 18 degreeUnionState43_309 [18,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_311 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 3 degreeUnionState43_311 [3,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_312 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 4 degreeUnionState43_312 [4,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_313 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 5 degreeUnionState43_313 [5,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_314 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 6 degreeUnionState43_314 [6,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_315 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 7 degreeUnionState43_315 [7,19] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_316 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 8 degreeUnionState43_316 [8,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_317 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 9 degreeUnionState43_317 [9,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_318 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 14 10 degreeUnionState43_318 [10,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_319 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 13 11 degreeUnionState43_319 [11,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_320 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 12 12 degreeUnionState43_320 [12,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_321 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 11 13 degreeUnionState43_321 [13,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_322 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 10 14 degreeUnionState43_322 [14,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_323 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 9 15 degreeUnionState43_323 [15,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_324 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 8 16 degreeUnionState43_324 [16,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_325 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 7 17 degreeUnionState43_325 [17,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_326 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 6 18 degreeUnionState43_326 [18,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_327 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 5 19 degreeUnionState43_327 [19,19] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_328 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 20 degreeUnionState43_328 [20] = true := by - decide +kernel - -lemma degreeUnionBranch43_329 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 21 degreeUnionState43_329 [21] = true := by - decide +kernel - -lemma degreeUnionBranch43_330 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 22 degreeUnionState43_330 [22] = true := by - decide +kernel - -lemma degreeUnionBranch43_331 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 23 degreeUnionState43_331 [23] = true := by - decide +kernel - -lemma degreeUnionBranch43_332 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 24 degreeUnionState43_332 [24] = true := by - decide +kernel - -lemma degreeUnionBranch43_333 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 25 degreeUnionState43_333 [25] = true := by - decide +kernel - -lemma degreeUnionBranch43_334 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 26 degreeUnionState43_334 [26] = true := by - decide +kernel - -lemma degreeUnionBranch43_335 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 27 degreeUnionState43_335 [27] = true := by - decide +kernel - -lemma degreeUnionBranch43_336 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 28 degreeUnionState43_336 [28] = true := by - decide +kernel - -lemma degreeUnionBranch43_337 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 14 29 degreeUnionState43_337 [29] = true := by - decide +kernel - -lemma degreeUnionBranch43_338 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 13 30 degreeUnionState43_338 [30] = true := by - decide +kernel - -lemma degreeUnionBranch43_339 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 12 31 degreeUnionState43_339 [31] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_340 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 11 32 degreeUnionState43_340 [32] = true := by - decide +kernel - -lemma degreeUnionBranch43_341 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 10 33 degreeUnionState43_341 [33] = true := by - decide +kernel - -lemma degreeUnionBranch43_342 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 9 34 degreeUnionState43_342 [34] = true := by - decide +kernel - -lemma degreeUnionBranch43_343 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 8 35 degreeUnionState43_343 [35] = true := by - decide +kernel - -lemma degreeUnionBranch43_344 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 7 36 degreeUnionState43_344 [36] = true := by - decide +kernel - -lemma degreeUnionBranch43_345 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 6 37 degreeUnionState43_345 [37] = true := by - decide +kernel - -lemma degreeUnionBranch43_346 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 5 38 degreeUnionState43_346 [38] = true := by - decide +kernel - -lemma degreeUnionBranch43_347 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 4 39 degreeUnionState43_347 [39] = true := by - decide +kernel - -lemma degreeUnionBranch43_348 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 3 40 degreeUnionState43_348 [40] = true := by - decide +kernel - -lemma degreeUnionBranch43_349 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 2 41 degreeUnionState43_349 [41] = true := by - decide +kernel - -lemma degreeUnionBranch43_350 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 1 42 degreeUnionState43_350 [42] = true := by - decide +kernel - -lemma degreeUnionBranch43_352 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 38 5 degreeUnionState43_352 [5] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_353 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 37 6 degreeUnionState43_353 [6] = true := by - decide +kernel - -lemma degreeUnionBranch43_354 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 36 7 degreeUnionState43_354 [7] = true := by - decide +kernel - -lemma degreeUnionBranch43_356 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 31 4 degreeUnionState43_356 [4,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_357 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 30 5 degreeUnionState43_357 [5,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_358 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 29 6 degreeUnionState43_358 [6,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_359 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 28 7 degreeUnionState43_359 [7,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_361 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 4 degreeUnionState43_361 [4,8,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_362 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 5 degreeUnionState43_362 [5,8,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_363 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 6 degreeUnionState43_363 [6,8,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_364 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 7 degreeUnionState43_364 [7,8,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_365 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 8 degreeUnionState43_365 [8,8,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_367 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 30 4 degreeUnionState43_367 [4,9] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_368 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 29 5 degreeUnionState43_368 [5,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_369 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 28 6 degreeUnionState43_369 [6,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_370 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 27 7 degreeUnionState43_370 [7,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_372 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 4 degreeUnionState43_372 [4,8,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_373 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 5 degreeUnionState43_373 [5,8,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_374 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 6 degreeUnionState43_374 [6,8,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_375 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 7 degreeUnionState43_375 [7,8,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_376 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 8 degreeUnionState43_376 [8,8,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_378 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 4 degreeUnionState43_378 [4,9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_379 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 5 degreeUnionState43_379 [5,9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_380 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 6 degreeUnionState43_380 [6,9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_381 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 7 degreeUnionState43_381 [7,9,9] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_382 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 8 degreeUnionState43_382 [8,9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_383 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 9 degreeUnionState43_383 [9,9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_385 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 29 4 degreeUnionState43_385 [4,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_386 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 28 5 degreeUnionState43_386 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_387 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 27 6 degreeUnionState43_387 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_388 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 26 7 degreeUnionState43_388 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_389 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 8 degreeUnionState43_389 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_390 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 9 degreeUnionState43_390 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_391 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 10 degreeUnionState43_391 [10,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_393 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 28 4 degreeUnionState43_393 [4,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_394 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 27 5 degreeUnionState43_394 [5,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_395 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 26 6 degreeUnionState43_395 [6,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_396 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 7 degreeUnionState43_396 [7,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_397 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 8 degreeUnionState43_397 [8,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_398 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 9 degreeUnionState43_398 [9,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_399 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 10 degreeUnionState43_399 [10,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_400 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 11 degreeUnionState43_400 [11,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_402 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 27 4 degreeUnionState43_402 [4,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_403 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 26 5 degreeUnionState43_403 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_404 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 6 degreeUnionState43_404 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_405 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 7 degreeUnionState43_405 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_406 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 8 degreeUnionState43_406 [8,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_407 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 9 degreeUnionState43_407 [9,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_408 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 10 degreeUnionState43_408 [10,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_409 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 11 degreeUnionState43_409 [11,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_410 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 12 degreeUnionState43_410 [12,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_412 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 26 4 degreeUnionState43_412 [4,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_413 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 5 degreeUnionState43_413 [5,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_414 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 6 degreeUnionState43_414 [6,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_415 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 7 degreeUnionState43_415 [7,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_416 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 8 degreeUnionState43_416 [8,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_417 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 9 degreeUnionState43_417 [9,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_418 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 10 degreeUnionState43_418 [10,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_419 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 11 degreeUnionState43_419 [11,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_420 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 12 degreeUnionState43_420 [12,13] = true := by - decide +kernel - -lemma degreeUnionBranch43_421 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 13 degreeUnionState43_421 [13,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_423 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 4 degreeUnionState43_423 [4,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_424 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 5 degreeUnionState43_424 [5,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_425 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 6 degreeUnionState43_425 [6,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_426 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 7 degreeUnionState43_426 [7,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_427 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 8 degreeUnionState43_427 [8,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_428 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 9 degreeUnionState43_428 [9,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_429 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 10 degreeUnionState43_429 [10,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_430 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 11 degreeUnionState43_430 [11,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_431 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 12 degreeUnionState43_431 [12,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_432 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 13 degreeUnionState43_432 [13,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_433 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 14 degreeUnionState43_433 [14,14] = true := by - decide +kernel - -lemma degreeUnionBranch43_435 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 4 degreeUnionState43_435 [4,15] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_436 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 5 degreeUnionState43_436 [5,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_437 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 6 degreeUnionState43_437 [6,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_438 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 7 degreeUnionState43_438 [7,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_439 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 8 degreeUnionState43_439 [8,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_440 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 9 degreeUnionState43_440 [9,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_441 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 10 degreeUnionState43_441 [10,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_442 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 11 degreeUnionState43_442 [11,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_443 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 12 degreeUnionState43_443 [12,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_444 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 13 degreeUnionState43_444 [13,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_445 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 14 14 degreeUnionState43_445 [14,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_446 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 13 15 degreeUnionState43_446 [15,15] = true := by - decide +kernel - -lemma degreeUnionBranch43_448 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 3 degreeUnionState43_448 [3,16] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_449 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 4 degreeUnionState43_449 [4,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_450 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 5 degreeUnionState43_450 [5,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_451 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 6 degreeUnionState43_451 [6,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_452 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 7 degreeUnionState43_452 [7,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_453 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 8 degreeUnionState43_453 [8,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_454 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 9 degreeUnionState43_454 [9,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_455 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 10 degreeUnionState43_455 [10,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_456 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 11 degreeUnionState43_456 [11,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_457 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 12 degreeUnionState43_457 [12,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_458 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 14 13 degreeUnionState43_458 [13,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_459 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 13 14 degreeUnionState43_459 [14,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_460 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 12 15 degreeUnionState43_460 [15,16] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_461 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 11 16 degreeUnionState43_461 [16,16] = true := by - decide +kernel - -lemma degreeUnionBranch43_463 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 3 degreeUnionState43_463 [3,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_464 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 4 degreeUnionState43_464 [4,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_465 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 5 degreeUnionState43_465 [5,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_466 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 6 degreeUnionState43_466 [6,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_467 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 7 degreeUnionState43_467 [7,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_468 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 8 degreeUnionState43_468 [8,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_469 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 9 degreeUnionState43_469 [9,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_470 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 10 degreeUnionState43_470 [10,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_471 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 11 degreeUnionState43_471 [11,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_472 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 14 12 degreeUnionState43_472 [12,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_473 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 13 13 degreeUnionState43_473 [13,17] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_474 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 12 14 degreeUnionState43_474 [14,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_475 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 11 15 degreeUnionState43_475 [15,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_476 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 10 16 degreeUnionState43_476 [16,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_477 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 9 17 degreeUnionState43_477 [17,17] = true := by - decide +kernel - -lemma degreeUnionBranch43_479 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 3 degreeUnionState43_479 [3,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_480 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 4 degreeUnionState43_480 [4,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_481 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 5 degreeUnionState43_481 [5,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_482 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 6 degreeUnionState43_482 [6,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_483 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 7 degreeUnionState43_483 [7,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_484 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 8 degreeUnionState43_484 [8,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_485 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 9 degreeUnionState43_485 [9,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_486 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 10 degreeUnionState43_486 [10,18] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_487 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 14 11 degreeUnionState43_487 [11,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_488 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 13 12 degreeUnionState43_488 [12,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_489 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 12 13 degreeUnionState43_489 [13,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_490 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 11 14 degreeUnionState43_490 [14,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_491 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 10 15 degreeUnionState43_491 [15,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_492 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 9 16 degreeUnionState43_492 [16,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_493 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 8 17 degreeUnionState43_493 [17,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_494 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 7 18 degreeUnionState43_494 [18,18] = true := by - decide +kernel - -lemma degreeUnionBranch43_496 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 3 degreeUnionState43_496 [3,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_497 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 4 degreeUnionState43_497 [4,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_498 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 5 degreeUnionState43_498 [5,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_499 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 6 degreeUnionState43_499 [6,19] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_500 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 7 degreeUnionState43_500 [7,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_501 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 8 degreeUnionState43_501 [8,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_502 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 9 degreeUnionState43_502 [9,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_503 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 14 10 degreeUnionState43_503 [10,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_504 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 13 11 degreeUnionState43_504 [11,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_505 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 12 12 degreeUnionState43_505 [12,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_506 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 11 13 degreeUnionState43_506 [13,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_507 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 10 14 degreeUnionState43_507 [14,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_508 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 9 15 degreeUnionState43_508 [15,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_509 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 8 16 degreeUnionState43_509 [16,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_510 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 7 17 degreeUnionState43_510 [17,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_511 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 6 18 degreeUnionState43_511 [18,19] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_512 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 5 19 degreeUnionState43_512 [19,19] = true := by - decide +kernel - -lemma degreeUnionBranch43_513 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 23 20 degreeUnionState43_513 [20] = true := by - decide +kernel - -lemma degreeUnionBranch43_514 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 22 21 degreeUnionState43_514 [21] = true := by - decide +kernel - -lemma degreeUnionBranch43_515 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 21 22 degreeUnionState43_515 [22] = true := by - decide +kernel - -lemma degreeUnionBranch43_516 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 20 23 degreeUnionState43_516 [23] = true := by - decide +kernel - -lemma degreeUnionBranch43_517 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 19 24 degreeUnionState43_517 [24] = true := by - decide +kernel - -lemma degreeUnionBranch43_518 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 18 25 degreeUnionState43_518 [25] = true := by - decide +kernel - -lemma degreeUnionBranch43_519 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 17 26 degreeUnionState43_519 [26] = true := by - decide +kernel - -lemma degreeUnionBranch43_520 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 16 27 degreeUnionState43_520 [27] = true := by - decide +kernel - -lemma degreeUnionBranch43_521 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 15 28 degreeUnionState43_521 [28] = true := by - decide +kernel - -lemma degreeUnionBranch43_522 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 14 29 degreeUnionState43_522 [29] = true := by - decide +kernel - -lemma degreeUnionBranch43_523 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 13 30 degreeUnionState43_523 [30] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_524 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 12 31 degreeUnionState43_524 [31] = true := by - decide +kernel - -lemma degreeUnionBranch43_525 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 11 32 degreeUnionState43_525 [32] = true := by - decide +kernel - -lemma degreeUnionBranch43_526 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 10 33 degreeUnionState43_526 [33] = true := by - decide +kernel - -lemma degreeUnionBranch43_527 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 9 34 degreeUnionState43_527 [34] = true := by - decide +kernel - -lemma degreeUnionBranch43_528 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 8 35 degreeUnionState43_528 [35] = true := by - decide +kernel - -lemma degreeUnionBranch43_529 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 7 36 degreeUnionState43_529 [36] = true := by - decide +kernel - -lemma degreeUnionBranch43_530 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 6 37 degreeUnionState43_530 [37] = true := by - decide +kernel - -lemma degreeUnionBranch43_531 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 5 38 degreeUnionState43_531 [38] = true := by - decide +kernel - -lemma degreeUnionBranch43_532 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 4 39 degreeUnionState43_532 [39] = true := by - decide +kernel - -lemma degreeUnionBranch43_533 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 3 40 degreeUnionState43_533 [40] = true := by - decide +kernel - -lemma degreeUnionBranch43_534 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 2 41 degreeUnionState43_534 [41] = true := by - decide +kernel - -lemma degreeUnionBranch43_535 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 1 42 degreeUnionState43_535 [42] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_537 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 39 4 degreeUnionState43_537 [4] = true := by - decide +kernel - -lemma degreeUnionBranch43_538 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 38 5 degreeUnionState43_538 [5] = true := by - decide +kernel - -lemma degreeUnionBranch43_539 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 37 6 degreeUnionState43_539 [6] = true := by - decide +kernel - -lemma degreeUnionBranch43_540 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 36 7 degreeUnionState43_540 [7] = true := by - decide +kernel - -lemma degreeUnionBranch43_542 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 31 4 degreeUnionState43_542 [4,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_543 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 30 5 degreeUnionState43_543 [5,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_544 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 29 6 degreeUnionState43_544 [6,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_545 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 28 7 degreeUnionState43_545 [7,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_546 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 27 8 degreeUnionState43_546 [8,8] = true := by - decide +kernel - -lemma degreeUnionBranch43_548 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 30 4 degreeUnionState43_548 [4,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_549 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 29 5 degreeUnionState43_549 [5,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_550 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 28 6 degreeUnionState43_550 [6,9] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_551 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 27 7 degreeUnionState43_551 [7,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_552 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 26 8 degreeUnionState43_552 [8,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_553 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 25 9 degreeUnionState43_553 [9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_555 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 29 4 degreeUnionState43_555 [4,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_556 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 28 5 degreeUnionState43_556 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_557 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 27 6 degreeUnionState43_557 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_558 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 26 7 degreeUnionState43_558 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_559 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 25 8 degreeUnionState43_559 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_560 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 24 9 degreeUnionState43_560 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_561 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 23 10 degreeUnionState43_561 [10,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_563 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 28 4 degreeUnionState43_563 [4,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_564 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 27 5 degreeUnionState43_564 [5,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_565 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 26 6 degreeUnionState43_565 [6,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_566 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 25 7 degreeUnionState43_566 [7,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_567 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 24 8 degreeUnionState43_567 [8,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_568 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 23 9 degreeUnionState43_568 [9,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_569 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 22 10 degreeUnionState43_569 [10,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_570 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 21 11 degreeUnionState43_570 [11,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_572 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 27 4 degreeUnionState43_572 [4,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_573 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 26 5 degreeUnionState43_573 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_574 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 25 6 degreeUnionState43_574 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_575 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 24 7 degreeUnionState43_575 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_576 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 23 8 degreeUnionState43_576 [8,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_577 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 22 9 degreeUnionState43_577 [9,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_578 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 21 10 degreeUnionState43_578 [10,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_579 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 20 11 degreeUnionState43_579 [11,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_580 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 19 12 degreeUnionState43_580 [12,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_581 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 30 13 degreeUnionState43_581 [13] = true := by - decide +kernel - -lemma degreeUnionBranch43_582 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 29 14 degreeUnionState43_582 [14] = true := by - decide +kernel - -lemma degreeUnionBranch43_583 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 28 15 degreeUnionState43_583 [15] = true := by - decide +kernel - -lemma degreeUnionBranch43_584 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 27 16 degreeUnionState43_584 [16] = true := by - decide +kernel - -lemma degreeUnionBranch43_585 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 26 17 degreeUnionState43_585 [17] = true := by - decide +kernel - -lemma degreeUnionBranch43_586 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 25 18 degreeUnionState43_586 [18] = true := by - decide +kernel - -lemma degreeUnionBranch43_587 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 24 19 degreeUnionState43_587 [19] = true := by - decide +kernel - -lemma degreeUnionBranch43_588 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 23 20 degreeUnionState43_588 [20] = true := by - decide +kernel - -lemma degreeUnionBranch43_589 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 22 21 degreeUnionState43_589 [21] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_590 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 21 22 degreeUnionState43_590 [22] = true := by - decide +kernel - -lemma degreeUnionBranch43_591 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 20 23 degreeUnionState43_591 [23] = true := by - decide +kernel - -lemma degreeUnionBranch43_592 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 19 24 degreeUnionState43_592 [24] = true := by - decide +kernel - -lemma degreeUnionBranch43_593 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 18 25 degreeUnionState43_593 [25] = true := by - decide +kernel - -lemma degreeUnionBranch43_594 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 17 26 degreeUnionState43_594 [26] = true := by - decide +kernel - -lemma degreeUnionBranch43_595 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 16 27 degreeUnionState43_595 [27] = true := by - decide +kernel - -lemma degreeUnionBranch43_596 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 15 28 degreeUnionState43_596 [28] = true := by - decide +kernel - -lemma degreeUnionBranch43_597 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 14 29 degreeUnionState43_597 [29] = true := by - decide +kernel - -lemma degreeUnionBranch43_598 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 13 30 degreeUnionState43_598 [30] = true := by - decide +kernel - -lemma degreeUnionBranch43_599 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 12 31 degreeUnionState43_599 [31] = true := by - decide +kernel - -lemma degreeUnionBranch43_600 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 11 32 degreeUnionState43_600 [32] = true := by - decide +kernel - -lemma degreeUnionBranch43_601 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 10 33 degreeUnionState43_601 [33] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_602 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 9 34 degreeUnionState43_602 [34] = true := by - decide +kernel - -lemma degreeUnionBranch43_603 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 8 35 degreeUnionState43_603 [35] = true := by - decide +kernel - -lemma degreeUnionBranch43_604 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 7 36 degreeUnionState43_604 [36] = true := by - decide +kernel - -lemma degreeUnionBranch43_605 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 6 37 degreeUnionState43_605 [37] = true := by - decide +kernel - -lemma degreeUnionBranch43_606 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 5 38 degreeUnionState43_606 [38] = true := by - decide +kernel - -lemma degreeUnionBranch43_607 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 4 39 degreeUnionState43_607 [39] = true := by - decide +kernel - -lemma degreeUnionBranch43_608 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 3 40 degreeUnionState43_608 [40] = true := by - decide +kernel - -lemma degreeUnionBranch43_609 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 2 41 degreeUnionState43_609 [41] = true := by - decide +kernel - -lemma degreeUnionBranch43_610 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 1 42 degreeUnionState43_610 [42] = true := by - decide +kernel - -lemma degreeUnionBranch43_612 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 39 4 degreeUnionState43_612 [4] = true := by - decide +kernel - -lemma degreeUnionBranch43_613 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 38 5 degreeUnionState43_613 [5] = true := by - decide +kernel - -lemma degreeUnionBranch43_614 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 37 6 degreeUnionState43_614 [6] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_615 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 36 7 degreeUnionState43_615 [7] = true := by - decide +kernel - -lemma degreeUnionBranch43_616 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 35 8 degreeUnionState43_616 [8] = true := by - decide +kernel - -lemma degreeUnionBranch43_618 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 30 4 degreeUnionState43_618 [4,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_619 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 29 5 degreeUnionState43_619 [5,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_620 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 28 6 degreeUnionState43_620 [6,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_621 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 27 7 degreeUnionState43_621 [7,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_622 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 26 8 degreeUnionState43_622 [8,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_623 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 25 9 degreeUnionState43_623 [9,9] = true := by - decide +kernel - -lemma degreeUnionBranch43_625 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 30 3 degreeUnionState43_625 [3,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_626 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 29 4 degreeUnionState43_626 [4,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_627 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 28 5 degreeUnionState43_627 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_628 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 27 6 degreeUnionState43_628 [6,10] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_629 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 26 7 degreeUnionState43_629 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_630 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 25 8 degreeUnionState43_630 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_631 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 24 9 degreeUnionState43_631 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_632 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 23 10 degreeUnionState43_632 [10,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_634 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 29 3 degreeUnionState43_634 [3,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_635 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 28 4 degreeUnionState43_635 [4,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_636 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 27 5 degreeUnionState43_636 [5,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_637 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 26 6 degreeUnionState43_637 [6,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_638 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 25 7 degreeUnionState43_638 [7,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_639 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 24 8 degreeUnionState43_639 [8,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_640 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 23 9 degreeUnionState43_640 [9,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_641 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 22 10 degreeUnionState43_641 [10,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_642 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 21 11 degreeUnionState43_642 [11,11] = true := by - decide +kernel - -lemma degreeUnionBranch43_644 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 28 3 degreeUnionState43_644 [3,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_645 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 27 4 degreeUnionState43_645 [4,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_646 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 26 5 degreeUnionState43_646 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_647 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 25 6 degreeUnionState43_647 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_648 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 24 7 degreeUnionState43_648 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_649 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 23 8 degreeUnionState43_649 [8,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_650 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 22 9 degreeUnionState43_650 [9,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_651 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 21 10 degreeUnionState43_651 [10,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_652 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 20 11 degreeUnionState43_652 [11,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_653 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 19 12 degreeUnionState43_653 [12,12] = true := by - decide +kernel - -lemma degreeUnionBranch43_654 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 30 13 degreeUnionState43_654 [13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_655 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 29 14 degreeUnionState43_655 [14] = true := by - decide +kernel - -lemma degreeUnionBranch43_656 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 28 15 degreeUnionState43_656 [15] = true := by - decide +kernel - -lemma degreeUnionBranch43_657 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 27 16 degreeUnionState43_657 [16] = true := by - decide +kernel - -lemma degreeUnionBranch43_658 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 26 17 degreeUnionState43_658 [17] = true := by - decide +kernel - -lemma degreeUnionBranch43_659 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 25 18 degreeUnionState43_659 [18] = true := by - decide +kernel - -lemma degreeUnionBranch43_660 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 24 19 degreeUnionState43_660 [19] = true := by - decide +kernel - -lemma degreeUnionBranch43_661 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 23 20 degreeUnionState43_661 [20] = true := by - decide +kernel - -lemma degreeUnionBranch43_662 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 22 21 degreeUnionState43_662 [21] = true := by - decide +kernel - -lemma degreeUnionBranch43_663 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 21 22 degreeUnionState43_663 [22] = true := by - decide +kernel - -lemma degreeUnionBranch43_664 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 20 23 degreeUnionState43_664 [23] = true := by - decide +kernel - -lemma degreeUnionBranch43_665 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 19 24 degreeUnionState43_665 [24] = true := by - decide +kernel - -lemma degreeUnionBranch43_666 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 18 25 degreeUnionState43_666 [25] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_667 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 17 26 degreeUnionState43_667 [26] = true := by - decide +kernel - -lemma degreeUnionBranch43_668 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 16 27 degreeUnionState43_668 [27] = true := by - decide +kernel - -lemma degreeUnionBranch43_669 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 15 28 degreeUnionState43_669 [28] = true := by - decide +kernel - -lemma degreeUnionBranch43_670 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 14 29 degreeUnionState43_670 [29] = true := by - decide +kernel - -lemma degreeUnionBranch43_671 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 13 30 degreeUnionState43_671 [30] = true := by - decide +kernel - -lemma degreeUnionBranch43_672 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 12 31 degreeUnionState43_672 [31] = true := by - decide +kernel - -lemma degreeUnionBranch43_673 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 11 32 degreeUnionState43_673 [32] = true := by - decide +kernel - -lemma degreeUnionBranch43_674 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 10 33 degreeUnionState43_674 [33] = true := by - decide +kernel - -lemma degreeUnionBranch43_675 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 9 34 degreeUnionState43_675 [34] = true := by - decide +kernel - -lemma degreeUnionBranch43_676 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 8 35 degreeUnionState43_676 [35] = true := by - decide +kernel - -lemma degreeUnionBranch43_677 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 7 36 degreeUnionState43_677 [36] = true := by - decide +kernel - -lemma degreeUnionBranch43_678 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 6 37 degreeUnionState43_678 [37] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_679 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 5 38 degreeUnionState43_679 [38] = true := by - decide +kernel - -lemma degreeUnionBranch43_680 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 4 39 degreeUnionState43_680 [39] = true := by - decide +kernel - -lemma degreeUnionBranch43_681 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 3 40 degreeUnionState43_681 [40] = true := by - decide +kernel - -lemma degreeUnionBranch43_682 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 2 41 degreeUnionState43_682 [41] = true := by - decide +kernel - -lemma degreeUnionBranch43_683 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 1 42 degreeUnionState43_683 [42] = true := by - decide +kernel - -lemma degreeUnionBranch43_685 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 39 4 degreeUnionState43_685 [4] = true := by - decide +kernel - -lemma degreeUnionBranch43_686 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 38 5 degreeUnionState43_686 [5] = true := by - decide +kernel - -lemma degreeUnionBranch43_687 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 37 6 degreeUnionState43_687 [6] = true := by - decide +kernel - -lemma degreeUnionBranch43_688 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 36 7 degreeUnionState43_688 [7] = true := by - decide +kernel - -lemma degreeUnionBranch43_689 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 35 8 degreeUnionState43_689 [8] = true := by - decide +kernel - -lemma degreeUnionBranch43_690 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 34 9 degreeUnionState43_690 [9] = true := by - decide +kernel - -lemma degreeUnionBranch43_692 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 30 3 degreeUnionState43_692 [3,10] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_693 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 29 4 degreeUnionState43_693 [4,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_694 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 28 5 degreeUnionState43_694 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_695 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 27 6 degreeUnionState43_695 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_696 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 26 7 degreeUnionState43_696 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_697 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 25 8 degreeUnionState43_697 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_698 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 24 9 degreeUnionState43_698 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_699 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 23 10 degreeUnionState43_699 [10,10] = true := by - decide +kernel - -lemma degreeUnionBranch43_700 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 32 11 degreeUnionState43_700 [11] = true := by - decide +kernel - -lemma degreeUnionBranch43_701 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 31 12 degreeUnionState43_701 [12] = true := by - decide +kernel - -lemma degreeUnionBranch43_702 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 30 13 degreeUnionState43_702 [13] = true := by - decide +kernel - -lemma degreeUnionBranch43_703 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 29 14 degreeUnionState43_703 [14] = true := by - decide +kernel - -lemma degreeUnionBranch43_704 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 28 15 degreeUnionState43_704 [15] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_705 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 27 16 degreeUnionState43_705 [16] = true := by - decide +kernel - -lemma degreeUnionBranch43_706 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 26 17 degreeUnionState43_706 [17] = true := by - decide +kernel - -lemma degreeUnionBranch43_707 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 25 18 degreeUnionState43_707 [18] = true := by - decide +kernel - -lemma degreeUnionBranch43_708 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 24 19 degreeUnionState43_708 [19] = true := by - decide +kernel - -lemma degreeUnionBranch43_709 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 23 20 degreeUnionState43_709 [20] = true := by - decide +kernel - -lemma degreeUnionBranch43_710 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 22 21 degreeUnionState43_710 [21] = true := by - decide +kernel - -lemma degreeUnionBranch43_711 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 21 22 degreeUnionState43_711 [22] = true := by - decide +kernel - -lemma degreeUnionBranch43_712 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 20 23 degreeUnionState43_712 [23] = true := by - decide +kernel - -lemma degreeUnionBranch43_713 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 19 24 degreeUnionState43_713 [24] = true := by - decide +kernel - -lemma degreeUnionBranch43_714 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 18 25 degreeUnionState43_714 [25] = true := by - decide +kernel - -lemma degreeUnionBranch43_715 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 17 26 degreeUnionState43_715 [26] = true := by - decide +kernel - -lemma degreeUnionBranch43_716 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 16 27 degreeUnionState43_716 [27] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_717 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 15 28 degreeUnionState43_717 [28] = true := by - decide +kernel - -lemma degreeUnionBranch43_718 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 14 29 degreeUnionState43_718 [29] = true := by - decide +kernel - -lemma degreeUnionBranch43_719 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 13 30 degreeUnionState43_719 [30] = true := by - decide +kernel - -lemma degreeUnionBranch43_720 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 12 31 degreeUnionState43_720 [31] = true := by - decide +kernel - -lemma degreeUnionBranch43_721 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 11 32 degreeUnionState43_721 [32] = true := by - decide +kernel - -lemma degreeUnionBranch43_722 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 10 33 degreeUnionState43_722 [33] = true := by - decide +kernel - -lemma degreeUnionBranch43_723 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 9 34 degreeUnionState43_723 [34] = true := by - decide +kernel - -lemma degreeUnionBranch43_724 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 8 35 degreeUnionState43_724 [35] = true := by - decide +kernel - -lemma degreeUnionBranch43_725 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 7 36 degreeUnionState43_725 [36] = true := by - decide +kernel - -lemma degreeUnionBranch43_726 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 6 37 degreeUnionState43_726 [37] = true := by - decide +kernel - -lemma degreeUnionBranch43_727 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 5 38 degreeUnionState43_727 [38] = true := by - decide +kernel - -lemma degreeUnionBranch43_728 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 4 39 degreeUnionState43_728 [39] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_729 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 3 40 degreeUnionState43_729 [40] = true := by - decide +kernel - -lemma degreeUnionBranch43_730 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 2 41 degreeUnionState43_730 [41] = true := by - decide +kernel - -lemma degreeUnionBranch43_731 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 1 42 degreeUnionState43_731 [42] = true := by - decide +kernel - -lemma degreeUnionBranch43_733 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 39 4 degreeUnionState43_733 [4] = true := by - decide +kernel - -lemma degreeUnionBranch43_734 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 38 5 degreeUnionState43_734 [5] = true := by - decide +kernel - -lemma degreeUnionBranch43_735 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 37 6 degreeUnionState43_735 [6] = true := by - decide +kernel - -lemma degreeUnionBranch43_736 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 36 7 degreeUnionState43_736 [7] = true := by - decide +kernel - -lemma degreeUnionBranch43_737 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 35 8 degreeUnionState43_737 [8] = true := by - decide +kernel - -lemma degreeUnionBranch43_738 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 34 9 degreeUnionState43_738 [9] = true := by - decide +kernel - -lemma degreeUnionBranch43_739 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 33 10 degreeUnionState43_739 [10] = true := by - decide +kernel - -lemma degreeUnionBranch43_740 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 32 11 degreeUnionState43_740 [11] = true := by - decide +kernel - -lemma degreeUnionBranch43_741 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 31 12 degreeUnionState43_741 [12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_742 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 30 13 degreeUnionState43_742 [13] = true := by - decide +kernel - -lemma degreeUnionBranch43_743 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 29 14 degreeUnionState43_743 [14] = true := by - decide +kernel - -lemma degreeUnionBranch43_744 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 28 15 degreeUnionState43_744 [15] = true := by - decide +kernel - -lemma degreeUnionBranch43_745 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 27 16 degreeUnionState43_745 [16] = true := by - decide +kernel - -lemma degreeUnionBranch43_746 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 26 17 degreeUnionState43_746 [17] = true := by - decide +kernel - -lemma degreeUnionBranch43_747 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 25 18 degreeUnionState43_747 [18] = true := by - decide +kernel - -lemma degreeUnionBranch43_748 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 24 19 degreeUnionState43_748 [19] = true := by - decide +kernel - -lemma degreeUnionBranch43_749 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 23 20 degreeUnionState43_749 [20] = true := by - decide +kernel - -lemma degreeUnionBranch43_750 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 22 21 degreeUnionState43_750 [21] = true := by - decide +kernel - -lemma degreeUnionBranch43_751 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 21 22 degreeUnionState43_751 [22] = true := by - decide +kernel - -lemma degreeUnionBranch43_752 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 20 23 degreeUnionState43_752 [23] = true := by - decide +kernel - -lemma degreeUnionBranch43_753 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 19 24 degreeUnionState43_753 [24] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_754 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 18 25 degreeUnionState43_754 [25] = true := by - decide +kernel - -lemma degreeUnionBranch43_755 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 17 26 degreeUnionState43_755 [26] = true := by - decide +kernel - -lemma degreeUnionBranch43_756 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 16 27 degreeUnionState43_756 [27] = true := by - decide +kernel - -lemma degreeUnionBranch43_757 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 15 28 degreeUnionState43_757 [28] = true := by - decide +kernel - -lemma degreeUnionBranch43_758 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 14 29 degreeUnionState43_758 [29] = true := by - decide +kernel - -lemma degreeUnionBranch43_759 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 13 30 degreeUnionState43_759 [30] = true := by - decide +kernel - -lemma degreeUnionBranch43_760 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 12 31 degreeUnionState43_760 [31] = true := by - decide +kernel - -lemma degreeUnionBranch43_761 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 11 32 degreeUnionState43_761 [32] = true := by - decide +kernel - -lemma degreeUnionBranch43_762 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 10 33 degreeUnionState43_762 [33] = true := by - decide +kernel - -lemma degreeUnionBranch43_763 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 9 34 degreeUnionState43_763 [34] = true := by - decide +kernel - -lemma degreeUnionBranch43_764 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 8 35 degreeUnionState43_764 [35] = true := by - decide +kernel - -lemma degreeUnionBranch43_765 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 7 36 degreeUnionState43_765 [36] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_766 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 6 37 degreeUnionState43_766 [37] = true := by - decide +kernel - -lemma degreeUnionBranch43_767 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 5 38 degreeUnionState43_767 [38] = true := by - decide +kernel - -lemma degreeUnionBranch43_768 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 4 39 degreeUnionState43_768 [39] = true := by - decide +kernel - -lemma degreeUnionBranch43_769 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 3 40 degreeUnionState43_769 [40] = true := by - decide +kernel - -lemma degreeUnionBranch43_770 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 2 41 degreeUnionState43_770 [41] = true := by - decide +kernel - -lemma degreeUnionBranch43_771 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 1 42 degreeUnionState43_771 [42] = true := by - decide +kernel - -lemma degreeUnionBranch43_773 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 40 3 degreeUnionState43_773 [3] = true := by - decide +kernel - -lemma degreeUnionBranch43_774 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 39 4 degreeUnionState43_774 [4] = true := by - decide +kernel - -lemma degreeUnionBranch43_775 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 38 5 degreeUnionState43_775 [5] = true := by - decide +kernel - -lemma degreeUnionBranch43_776 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 37 6 degreeUnionState43_776 [6] = true := by - decide +kernel - -lemma degreeUnionBranch43_777 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 36 7 degreeUnionState43_777 [7] = true := by - decide +kernel - -lemma degreeUnionBranch43_778 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 35 8 degreeUnionState43_778 [8] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_779 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 34 9 degreeUnionState43_779 [9] = true := by - decide +kernel - -lemma degreeUnionBranch43_780 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 33 10 degreeUnionState43_780 [10] = true := by - decide +kernel - -lemma degreeUnionBranch43_781 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 32 11 degreeUnionState43_781 [11] = true := by - decide +kernel - -lemma degreeUnionBranch43_782 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 31 12 degreeUnionState43_782 [12] = true := by - decide +kernel - -lemma degreeUnionBranch43_783 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 30 13 degreeUnionState43_783 [13] = true := by - decide +kernel - -lemma degreeUnionBranch43_784 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 29 14 degreeUnionState43_784 [14] = true := by - decide +kernel - -lemma degreeUnionBranch43_785 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 28 15 degreeUnionState43_785 [15] = true := by - decide +kernel - -lemma degreeUnionBranch43_786 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 27 16 degreeUnionState43_786 [16] = true := by - decide +kernel - -lemma degreeUnionBranch43_787 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 26 17 degreeUnionState43_787 [17] = true := by - decide +kernel - -lemma degreeUnionBranch43_788 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 25 18 degreeUnionState43_788 [18] = true := by - decide +kernel - -lemma degreeUnionBranch43_789 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 24 19 degreeUnionState43_789 [19] = true := by - decide +kernel - -lemma degreeUnionBranch43_790 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 23 20 degreeUnionState43_790 [20] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_791 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 22 21 degreeUnionState43_791 [21] = true := by - decide +kernel - -lemma degreeUnionBranch43_792 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 21 22 degreeUnionState43_792 [22] = true := by - decide +kernel - -lemma degreeUnionBranch43_793 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 20 23 degreeUnionState43_793 [23] = true := by - decide +kernel - -lemma degreeUnionBranch43_794 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 19 24 degreeUnionState43_794 [24] = true := by - decide +kernel - -lemma degreeUnionBranch43_795 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 18 25 degreeUnionState43_795 [25] = true := by - decide +kernel - -lemma degreeUnionBranch43_796 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 17 26 degreeUnionState43_796 [26] = true := by - decide +kernel - -lemma degreeUnionBranch43_797 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 16 27 degreeUnionState43_797 [27] = true := by - decide +kernel - -lemma degreeUnionBranch43_798 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 15 28 degreeUnionState43_798 [28] = true := by - decide +kernel - -lemma degreeUnionBranch43_799 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 14 29 degreeUnionState43_799 [29] = true := by - decide +kernel - -lemma degreeUnionBranch43_800 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 13 30 degreeUnionState43_800 [30] = true := by - decide +kernel - -lemma degreeUnionBranch43_801 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 12 31 degreeUnionState43_801 [31] = true := by - decide +kernel - -lemma degreeUnionBranch43_802 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 11 32 degreeUnionState43_802 [32] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_803 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 10 33 degreeUnionState43_803 [33] = true := by - decide +kernel - -lemma degreeUnionBranch43_804 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 9 34 degreeUnionState43_804 [34] = true := by - decide +kernel - -lemma degreeUnionBranch43_805 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 8 35 degreeUnionState43_805 [35] = true := by - decide +kernel - -lemma degreeUnionBranch43_806 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 7 36 degreeUnionState43_806 [36] = true := by - decide +kernel - -lemma degreeUnionBranch43_807 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 6 37 degreeUnionState43_807 [37] = true := by - decide +kernel - -lemma degreeUnionBranch43_808 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 5 38 degreeUnionState43_808 [38] = true := by - decide +kernel - -lemma degreeUnionBranch43_809 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 4 39 degreeUnionState43_809 [39] = true := by - decide +kernel - -lemma degreeUnionBranch43_810 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 3 40 degreeUnionState43_810 [40] = true := by - decide +kernel - -lemma degreeUnionBranch43_811 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 2 41 degreeUnionState43_811 [41] = true := by - decide +kernel - -lemma degreeUnionBranch43_812 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 1 42 degreeUnionState43_812 [42] = true := by - decide +kernel - -lemma degreeUnionBranch43_814 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 40 3 degreeUnionState43_814 [3] = true := by - decide +kernel - -lemma degreeUnionBranch43_815 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 39 4 degreeUnionState43_815 [4] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_816 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 38 5 degreeUnionState43_816 [5] = true := by - decide +kernel - -lemma degreeUnionBranch43_817 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 37 6 degreeUnionState43_817 [6] = true := by - decide +kernel - -lemma degreeUnionBranch43_818 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 36 7 degreeUnionState43_818 [7] = true := by - decide +kernel - -lemma degreeUnionBranch43_819 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 35 8 degreeUnionState43_819 [8] = true := by - decide +kernel - -lemma degreeUnionBranch43_820 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 34 9 degreeUnionState43_820 [9] = true := by - decide +kernel - -lemma degreeUnionBranch43_821 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 33 10 degreeUnionState43_821 [10] = true := by - decide +kernel - -lemma degreeUnionBranch43_822 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 32 11 degreeUnionState43_822 [11] = true := by - decide +kernel - -lemma degreeUnionBranch43_823 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 31 12 degreeUnionState43_823 [12] = true := by - decide +kernel - -lemma degreeUnionBranch43_824 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 30 13 degreeUnionState43_824 [13] = true := by - decide +kernel - -lemma degreeUnionBranch43_825 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 29 14 degreeUnionState43_825 [14] = true := by - decide +kernel - -lemma degreeUnionBranch43_826 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 28 15 degreeUnionState43_826 [15] = true := by - decide +kernel - -lemma degreeUnionBranch43_827 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 27 16 degreeUnionState43_827 [16] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_828 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 26 17 degreeUnionState43_828 [17] = true := by - decide +kernel - -lemma degreeUnionBranch43_829 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 25 18 degreeUnionState43_829 [18] = true := by - decide +kernel - -lemma degreeUnionBranch43_830 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 24 19 degreeUnionState43_830 [19] = true := by - decide +kernel - -lemma degreeUnionBranch43_831 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 23 20 degreeUnionState43_831 [20] = true := by - decide +kernel - -lemma degreeUnionBranch43_832 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 22 21 degreeUnionState43_832 [21] = true := by - decide +kernel - -lemma degreeUnionBranch43_833 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 21 22 degreeUnionState43_833 [22] = true := by - decide +kernel - -lemma degreeUnionBranch43_834 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 20 23 degreeUnionState43_834 [23] = true := by - decide +kernel - -lemma degreeUnionBranch43_835 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 19 24 degreeUnionState43_835 [24] = true := by - decide +kernel - -lemma degreeUnionBranch43_836 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 18 25 degreeUnionState43_836 [25] = true := by - decide +kernel - -lemma degreeUnionBranch43_837 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 17 26 degreeUnionState43_837 [26] = true := by - decide +kernel - -lemma degreeUnionBranch43_838 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 16 27 degreeUnionState43_838 [27] = true := by - decide +kernel - -lemma degreeUnionBranch43_839 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 15 28 degreeUnionState43_839 [28] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_840 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 14 29 degreeUnionState43_840 [29] = true := by - decide +kernel - -lemma degreeUnionBranch43_841 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 13 30 degreeUnionState43_841 [30] = true := by - decide +kernel - -lemma degreeUnionBranch43_842 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 12 31 degreeUnionState43_842 [31] = true := by - decide +kernel - -lemma degreeUnionBranch43_843 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 11 32 degreeUnionState43_843 [32] = true := by - decide +kernel - -lemma degreeUnionBranch43_844 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 10 33 degreeUnionState43_844 [33] = true := by - decide +kernel - -lemma degreeUnionBranch43_845 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 9 34 degreeUnionState43_845 [34] = true := by - decide +kernel - -lemma degreeUnionBranch43_846 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 8 35 degreeUnionState43_846 [35] = true := by - decide +kernel - -lemma degreeUnionBranch43_847 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 7 36 degreeUnionState43_847 [36] = true := by - decide +kernel - -lemma degreeUnionBranch43_848 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 6 37 degreeUnionState43_848 [37] = true := by - decide +kernel - -lemma degreeUnionBranch43_849 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 5 38 degreeUnionState43_849 [38] = true := by - decide +kernel - -lemma degreeUnionBranch43_850 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 4 39 degreeUnionState43_850 [39] = true := by - decide +kernel - -lemma degreeUnionBranch43_851 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 3 40 degreeUnionState43_851 [40] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_852 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 2 41 degreeUnionState43_852 [41] = true := by - decide +kernel - -lemma degreeUnionBranch43_853 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 1 42 degreeUnionState43_853 [42] = true := by - decide +kernel - -lemma degreeUnionBranch43_855 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 40 3 degreeUnionState43_855 [3] = true := by - decide +kernel - -lemma degreeUnionBranch43_856 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 39 4 degreeUnionState43_856 [4] = true := by - decide +kernel - -lemma degreeUnionBranch43_857 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 38 5 degreeUnionState43_857 [5] = true := by - decide +kernel - -lemma degreeUnionBranch43_858 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 37 6 degreeUnionState43_858 [6] = true := by - decide +kernel - -lemma degreeUnionBranch43_859 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 36 7 degreeUnionState43_859 [7] = true := by - decide +kernel - -lemma degreeUnionBranch43_860 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 35 8 degreeUnionState43_860 [8] = true := by - decide +kernel - -lemma degreeUnionBranch43_861 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 34 9 degreeUnionState43_861 [9] = true := by - decide +kernel - -lemma degreeUnionBranch43_862 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 33 10 degreeUnionState43_862 [10] = true := by - decide +kernel - -lemma degreeUnionBranch43_863 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 32 11 degreeUnionState43_863 [11] = true := by - decide +kernel - -lemma degreeUnionBranch43_864 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 31 12 degreeUnionState43_864 [12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_865 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 30 13 degreeUnionState43_865 [13] = true := by - decide +kernel - -lemma degreeUnionBranch43_866 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 29 14 degreeUnionState43_866 [14] = true := by - decide +kernel - -lemma degreeUnionBranch43_867 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 28 15 degreeUnionState43_867 [15] = true := by - decide +kernel - -lemma degreeUnionBranch43_868 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 27 16 degreeUnionState43_868 [16] = true := by - decide +kernel - -lemma degreeUnionBranch43_869 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 26 17 degreeUnionState43_869 [17] = true := by - decide +kernel - -lemma degreeUnionBranch43_870 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 25 18 degreeUnionState43_870 [18] = true := by - decide +kernel - -lemma degreeUnionBranch43_871 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 24 19 degreeUnionState43_871 [19] = true := by - decide +kernel - -lemma degreeUnionBranch43_872 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 23 20 degreeUnionState43_872 [20] = true := by - decide +kernel - -lemma degreeUnionBranch43_873 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 22 21 degreeUnionState43_873 [21] = true := by - decide +kernel - -lemma degreeUnionBranch43_874 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 21 22 degreeUnionState43_874 [22] = true := by - decide +kernel - -lemma degreeUnionBranch43_875 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 20 23 degreeUnionState43_875 [23] = true := by - decide +kernel - -lemma degreeUnionBranch43_876 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 19 24 degreeUnionState43_876 [24] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_877 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 18 25 degreeUnionState43_877 [25] = true := by - decide +kernel - -lemma degreeUnionBranch43_878 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 17 26 degreeUnionState43_878 [26] = true := by - decide +kernel - -lemma degreeUnionBranch43_879 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 16 27 degreeUnionState43_879 [27] = true := by - decide +kernel - -lemma degreeUnionBranch43_880 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 15 28 degreeUnionState43_880 [28] = true := by - decide +kernel - -lemma degreeUnionBranch43_881 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 14 29 degreeUnionState43_881 [29] = true := by - decide +kernel - -lemma degreeUnionBranch43_882 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 13 30 degreeUnionState43_882 [30] = true := by - decide +kernel - -lemma degreeUnionBranch43_883 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 12 31 degreeUnionState43_883 [31] = true := by - decide +kernel - -lemma degreeUnionBranch43_884 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 11 32 degreeUnionState43_884 [32] = true := by - decide +kernel - -lemma degreeUnionBranch43_885 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 10 33 degreeUnionState43_885 [33] = true := by - decide +kernel - -lemma degreeUnionBranch43_886 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 9 34 degreeUnionState43_886 [34] = true := by - decide +kernel - -lemma degreeUnionBranch43_887 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 8 35 degreeUnionState43_887 [35] = true := by - decide +kernel - -lemma degreeUnionBranch43_888 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 7 36 degreeUnionState43_888 [36] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_889 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 6 37 degreeUnionState43_889 [37] = true := by - decide +kernel - -lemma degreeUnionBranch43_890 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 5 38 degreeUnionState43_890 [38] = true := by - decide +kernel - -lemma degreeUnionBranch43_891 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 4 39 degreeUnionState43_891 [39] = true := by - decide +kernel - -lemma degreeUnionBranch43_892 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 3 40 degreeUnionState43_892 [40] = true := by - decide +kernel - -lemma degreeUnionBranch43_893 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 2 41 degreeUnionState43_893 [41] = true := by - decide +kernel - -lemma degreeUnionBranch43_894 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 1 42 degreeUnionState43_894 [42] = true := by - decide +kernel - -lemma degreeUnionBranch43_895 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 18 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_896 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 19 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_897 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 20 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_898 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 21 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_899 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 22 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -lemma degreeUnionBranch43_900 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 23 43 42 degreeHalfRegions43 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans43 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates43 + +namespace OAI + +/-! Degree Leaves 43. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_0 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 0 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_1 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 1 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_2 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 2 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_3 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 3 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_4 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 4 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_5 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 5 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_6 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_7 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_9 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 37 6 degreeUnionState43_9 [6] = true := by + decide +kernel + +lemma degreeUnionBranch43_10 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 36 7 degreeUnionState43_10 [7] = true := by + decide +kernel + +lemma degreeUnionBranch43_12 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 30 5 degreeUnionState43_12 [5,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_13 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 29 6 degreeUnionState43_13 [6,8] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_14 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 28 7 degreeUnionState43_14 [7,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_15 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 27 8 degreeUnionState43_15 [8,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_17 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 29 5 degreeUnionState43_17 [5,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_18 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 28 6 degreeUnionState43_18 [6,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_19 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 27 7 degreeUnionState43_19 [7,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_20 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 26 8 degreeUnionState43_20 [8,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_21 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 25 9 degreeUnionState43_21 [9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_23 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 28 5 degreeUnionState43_23 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_24 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 27 6 degreeUnionState43_24 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_25 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 26 7 degreeUnionState43_25 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_26 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 25 8 degreeUnionState43_26 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_27 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 24 9 degreeUnionState43_27 [9,10] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_28 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 10 degreeUnionState43_28 [10,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_30 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 27 5 degreeUnionState43_30 [5,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_31 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 26 6 degreeUnionState43_31 [6,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_32 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 25 7 degreeUnionState43_32 [7,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_33 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 24 8 degreeUnionState43_33 [8,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_34 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 9 degreeUnionState43_34 [9,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_35 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 10 degreeUnionState43_35 [10,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_36 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 11 degreeUnionState43_36 [11,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_38 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 26 5 degreeUnionState43_38 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_39 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 25 6 degreeUnionState43_39 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_40 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 24 7 degreeUnionState43_40 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_41 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 8 degreeUnionState43_41 [8,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_42 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 9 degreeUnionState43_42 [9,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_43 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 10 degreeUnionState43_43 [10,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_44 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 11 degreeUnionState43_44 [11,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_45 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 12 degreeUnionState43_45 [12,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_47 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 25 5 degreeUnionState43_47 [5,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_48 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 24 6 degreeUnionState43_48 [6,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_49 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 7 degreeUnionState43_49 [7,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_50 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 8 degreeUnionState43_50 [8,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_51 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 9 degreeUnionState43_51 [9,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_52 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 10 degreeUnionState43_52 [10,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_53 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 11 degreeUnionState43_53 [11,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_54 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 12 degreeUnionState43_54 [12,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_55 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 13 degreeUnionState43_55 [13,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_57 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 24 5 degreeUnionState43_57 [5,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_58 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 6 degreeUnionState43_58 [6,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_59 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 7 degreeUnionState43_59 [7,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_60 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 8 degreeUnionState43_60 [8,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_61 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 9 degreeUnionState43_61 [9,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_62 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 10 degreeUnionState43_62 [10,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_63 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 11 degreeUnionState43_63 [11,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_64 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 12 degreeUnionState43_64 [12,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_65 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 13 degreeUnionState43_65 [13,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_66 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 14 degreeUnionState43_66 [14,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_68 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 24 4 degreeUnionState43_68 [4,15] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_69 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 5 degreeUnionState43_69 [5,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_70 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 6 degreeUnionState43_70 [6,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_71 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 7 degreeUnionState43_71 [7,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_72 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 8 degreeUnionState43_72 [8,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_73 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 9 degreeUnionState43_73 [9,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_74 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 10 degreeUnionState43_74 [10,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_75 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 11 degreeUnionState43_75 [11,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_76 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 12 degreeUnionState43_76 [12,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_77 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 13 degreeUnionState43_77 [13,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_78 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 14 14 degreeUnionState43_78 [14,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_79 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 13 15 degreeUnionState43_79 [15,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_81 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 23 4 degreeUnionState43_81 [4,16] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_82 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 5 degreeUnionState43_82 [5,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_83 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 6 degreeUnionState43_83 [6,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_84 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 7 degreeUnionState43_84 [7,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_85 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 8 degreeUnionState43_85 [8,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_86 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 9 degreeUnionState43_86 [9,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_87 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 10 degreeUnionState43_87 [10,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_88 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 11 degreeUnionState43_88 [11,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_89 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 12 degreeUnionState43_89 [12,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_90 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 14 13 degreeUnionState43_90 [13,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_91 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 13 14 degreeUnionState43_91 [14,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_92 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 12 15 degreeUnionState43_92 [15,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_93 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 11 16 degreeUnionState43_93 [16,16] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_95 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 22 4 degreeUnionState43_95 [4,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_96 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 5 degreeUnionState43_96 [5,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_97 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 6 degreeUnionState43_97 [6,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_98 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 7 degreeUnionState43_98 [7,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_99 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 8 degreeUnionState43_99 [8,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_100 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 9 degreeUnionState43_100 [9,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_101 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 10 degreeUnionState43_101 [10,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_102 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 11 degreeUnionState43_102 [11,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_103 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 14 12 degreeUnionState43_103 [12,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_104 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 13 13 degreeUnionState43_104 [13,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_105 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 12 14 degreeUnionState43_105 [14,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_106 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 11 15 degreeUnionState43_106 [15,17] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_107 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 10 16 degreeUnionState43_107 [16,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_108 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 9 17 degreeUnionState43_108 [17,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_110 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 4 degreeUnionState43_110 [4,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_111 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 5 degreeUnionState43_111 [5,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_112 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 6 degreeUnionState43_112 [6,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_113 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 7 degreeUnionState43_113 [7,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_114 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 8 degreeUnionState43_114 [8,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_115 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 9 degreeUnionState43_115 [9,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_116 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 10 degreeUnionState43_116 [10,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_117 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 14 11 degreeUnionState43_117 [11,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_118 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 13 12 degreeUnionState43_118 [12,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_119 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 12 13 degreeUnionState43_119 [13,18] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_120 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 11 14 degreeUnionState43_120 [14,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_121 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 10 15 degreeUnionState43_121 [15,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_122 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 9 16 degreeUnionState43_122 [16,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_123 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 8 17 degreeUnionState43_123 [17,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_124 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 7 18 degreeUnionState43_124 [18,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_126 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 4 degreeUnionState43_126 [4,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_127 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 5 degreeUnionState43_127 [5,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_128 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 6 degreeUnionState43_128 [6,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_129 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 7 degreeUnionState43_129 [7,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_130 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 8 degreeUnionState43_130 [8,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_131 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 9 degreeUnionState43_131 [9,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_132 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 14 10 degreeUnionState43_132 [10,19] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_133 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 13 11 degreeUnionState43_133 [11,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_134 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 12 12 degreeUnionState43_134 [12,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_135 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 11 13 degreeUnionState43_135 [13,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_136 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 10 14 degreeUnionState43_136 [14,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_137 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 9 15 degreeUnionState43_137 [15,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_138 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 8 16 degreeUnionState43_138 [16,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_139 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 7 17 degreeUnionState43_139 [17,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_140 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 6 18 degreeUnionState43_140 [18,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_141 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 5 19 degreeUnionState43_141 [19,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_143 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 4 degreeUnionState43_143 [4,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_144 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 5 degreeUnionState43_144 [5,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_145 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 6 degreeUnionState43_145 [6,20] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_146 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 7 degreeUnionState43_146 [7,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_147 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 15 8 degreeUnionState43_147 [8,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_148 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 14 9 degreeUnionState43_148 [9,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_149 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 13 10 degreeUnionState43_149 [10,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_150 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 12 11 degreeUnionState43_150 [11,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_151 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 11 12 degreeUnionState43_151 [12,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_152 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 10 13 degreeUnionState43_152 [13,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_153 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 9 14 degreeUnionState43_153 [14,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_154 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 8 15 degreeUnionState43_154 [15,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_155 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 7 16 degreeUnionState43_155 [16,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_156 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 6 17 degreeUnionState43_156 [17,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_157 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 5 18 degreeUnionState43_157 [18,20] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_158 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 4 19 degreeUnionState43_158 [19,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_159 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 3 20 degreeUnionState43_159 [20,20] = true := by + decide +kernel + +lemma degreeUnionBranch43_160 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 21 degreeUnionState43_160 [21] = true := by + decide +kernel + +lemma degreeUnionBranch43_161 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 22 degreeUnionState43_161 [22] = true := by + decide +kernel + +lemma degreeUnionBranch43_162 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 23 degreeUnionState43_162 [23] = true := by + decide +kernel + +lemma degreeUnionBranch43_163 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 24 degreeUnionState43_163 [24] = true := by + decide +kernel + +lemma degreeUnionBranch43_164 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 25 degreeUnionState43_164 [25] = true := by + decide +kernel + +lemma degreeUnionBranch43_165 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 26 degreeUnionState43_165 [26] = true := by + decide +kernel + +lemma degreeUnionBranch43_166 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 27 degreeUnionState43_166 [27] = true := by + decide +kernel + +lemma degreeUnionBranch43_167 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 28 degreeUnionState43_167 [28] = true := by + decide +kernel + +lemma degreeUnionBranch43_168 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 14 29 degreeUnionState43_168 [29] = true := by + decide +kernel + +lemma degreeUnionBranch43_169 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 13 30 degreeUnionState43_169 [30] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_170 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 12 31 degreeUnionState43_170 [31] = true := by + decide +kernel + +lemma degreeUnionBranch43_171 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 11 32 degreeUnionState43_171 [32] = true := by + decide +kernel + +lemma degreeUnionBranch43_172 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 10 33 degreeUnionState43_172 [33] = true := by + decide +kernel + +lemma degreeUnionBranch43_173 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 9 34 degreeUnionState43_173 [34] = true := by + decide +kernel + +lemma degreeUnionBranch43_174 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 8 35 degreeUnionState43_174 [35] = true := by + decide +kernel + +lemma degreeUnionBranch43_175 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 7 36 degreeUnionState43_175 [36] = true := by + decide +kernel + +lemma degreeUnionBranch43_176 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 6 37 degreeUnionState43_176 [37] = true := by + decide +kernel + +lemma degreeUnionBranch43_177 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 5 38 degreeUnionState43_177 [38] = true := by + decide +kernel + +lemma degreeUnionBranch43_178 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 4 39 degreeUnionState43_178 [39] = true := by + decide +kernel + +lemma degreeUnionBranch43_179 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 3 40 degreeUnionState43_179 [40] = true := by + decide +kernel + +lemma degreeUnionBranch43_180 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 2 41 degreeUnionState43_180 [41] = true := by + decide +kernel + +lemma degreeUnionBranch43_181 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 1 42 degreeUnionState43_181 [42] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_183 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 38 5 degreeUnionState43_183 [5] = true := by + decide +kernel + +lemma degreeUnionBranch43_184 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 37 6 degreeUnionState43_184 [6] = true := by + decide +kernel + +lemma degreeUnionBranch43_185 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 36 7 degreeUnionState43_185 [7] = true := by + decide +kernel + +lemma degreeUnionBranch43_187 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 30 5 degreeUnionState43_187 [5,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_188 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 29 6 degreeUnionState43_188 [6,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_189 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 28 7 degreeUnionState43_189 [7,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_190 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 27 8 degreeUnionState43_190 [8,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_192 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 29 5 degreeUnionState43_192 [5,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_193 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 28 6 degreeUnionState43_193 [6,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_194 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 27 7 degreeUnionState43_194 [7,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_195 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 26 8 degreeUnionState43_195 [8,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_197 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 21 4 degreeUnionState43_197 [4,9,9] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_198 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 20 5 degreeUnionState43_198 [5,9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_199 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 19 6 degreeUnionState43_199 [6,9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_200 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 18 7 degreeUnionState43_200 [7,9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_201 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 17 8 degreeUnionState43_201 [8,9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_202 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 6 16 9 degreeUnionState43_202 [9,9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_204 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 28 5 degreeUnionState43_204 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_205 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 27 6 degreeUnionState43_205 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_206 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 26 7 degreeUnionState43_206 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_207 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 8 degreeUnionState43_207 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_208 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 9 degreeUnionState43_208 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_209 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 10 degreeUnionState43_209 [10,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_211 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 28 4 degreeUnionState43_211 [4,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_212 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 27 5 degreeUnionState43_212 [5,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_213 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 26 6 degreeUnionState43_213 [6,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_214 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 7 degreeUnionState43_214 [7,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_215 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 8 degreeUnionState43_215 [8,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_216 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 9 degreeUnionState43_216 [9,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_217 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 10 degreeUnionState43_217 [10,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_218 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 11 degreeUnionState43_218 [11,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_220 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 27 4 degreeUnionState43_220 [4,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_221 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 26 5 degreeUnionState43_221 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_222 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 6 degreeUnionState43_222 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_223 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 7 degreeUnionState43_223 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_224 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 8 degreeUnionState43_224 [8,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_225 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 9 degreeUnionState43_225 [9,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_226 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 10 degreeUnionState43_226 [10,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_227 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 11 degreeUnionState43_227 [11,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_228 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 12 degreeUnionState43_228 [12,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_230 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 26 4 degreeUnionState43_230 [4,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_231 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 5 degreeUnionState43_231 [5,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_232 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 6 degreeUnionState43_232 [6,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_233 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 7 degreeUnionState43_233 [7,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_234 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 8 degreeUnionState43_234 [8,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_235 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 9 degreeUnionState43_235 [9,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_236 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 10 degreeUnionState43_236 [10,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_237 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 11 degreeUnionState43_237 [11,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_238 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 12 degreeUnionState43_238 [12,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_239 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 13 degreeUnionState43_239 [13,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_241 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 4 degreeUnionState43_241 [4,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_242 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 5 degreeUnionState43_242 [5,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_243 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 6 degreeUnionState43_243 [6,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_244 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 7 degreeUnionState43_244 [7,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_245 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 8 degreeUnionState43_245 [8,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_246 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 9 degreeUnionState43_246 [9,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_247 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 10 degreeUnionState43_247 [10,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_248 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 11 degreeUnionState43_248 [11,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_249 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 12 degreeUnionState43_249 [12,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_250 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 13 degreeUnionState43_250 [13,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_251 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 14 degreeUnionState43_251 [14,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_253 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 4 degreeUnionState43_253 [4,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_254 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 5 degreeUnionState43_254 [5,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_255 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 6 degreeUnionState43_255 [6,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_256 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 7 degreeUnionState43_256 [7,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_257 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 8 degreeUnionState43_257 [8,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_258 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 9 degreeUnionState43_258 [9,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_259 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 10 degreeUnionState43_259 [10,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_260 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 11 degreeUnionState43_260 [11,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_261 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 12 degreeUnionState43_261 [12,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_262 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 13 degreeUnionState43_262 [13,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_263 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 14 14 degreeUnionState43_263 [14,15] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_264 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 13 15 degreeUnionState43_264 [15,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_266 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 4 degreeUnionState43_266 [4,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_267 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 5 degreeUnionState43_267 [5,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_268 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 6 degreeUnionState43_268 [6,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_269 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 7 degreeUnionState43_269 [7,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_270 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 8 degreeUnionState43_270 [8,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_271 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 9 degreeUnionState43_271 [9,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_272 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 10 degreeUnionState43_272 [10,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_273 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 11 degreeUnionState43_273 [11,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_274 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 12 degreeUnionState43_274 [12,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_275 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 14 13 degreeUnionState43_275 [13,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_276 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 13 14 degreeUnionState43_276 [14,16] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_277 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 12 15 degreeUnionState43_277 [15,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_278 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 11 16 degreeUnionState43_278 [16,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_280 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 4 degreeUnionState43_280 [4,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_281 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 5 degreeUnionState43_281 [5,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_282 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 6 degreeUnionState43_282 [6,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_283 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 7 degreeUnionState43_283 [7,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_284 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 8 degreeUnionState43_284 [8,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_285 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 9 degreeUnionState43_285 [9,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_286 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 10 degreeUnionState43_286 [10,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_287 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 11 degreeUnionState43_287 [11,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_288 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 14 12 degreeUnionState43_288 [12,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_289 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 13 13 degreeUnionState43_289 [13,17] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_290 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 12 14 degreeUnionState43_290 [14,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_291 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 11 15 degreeUnionState43_291 [15,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_292 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 10 16 degreeUnionState43_292 [16,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_293 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 9 17 degreeUnionState43_293 [17,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_295 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 4 degreeUnionState43_295 [4,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_296 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 5 degreeUnionState43_296 [5,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_297 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 6 degreeUnionState43_297 [6,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_298 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 7 degreeUnionState43_298 [7,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_299 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 8 degreeUnionState43_299 [8,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_300 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 9 degreeUnionState43_300 [9,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_301 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 10 degreeUnionState43_301 [10,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_302 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 14 11 degreeUnionState43_302 [11,18] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_303 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 13 12 degreeUnionState43_303 [12,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_304 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 12 13 degreeUnionState43_304 [13,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_305 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 11 14 degreeUnionState43_305 [14,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_306 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 10 15 degreeUnionState43_306 [15,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_307 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 9 16 degreeUnionState43_307 [16,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_308 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 8 17 degreeUnionState43_308 [17,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_309 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 7 18 degreeUnionState43_309 [18,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_311 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 3 degreeUnionState43_311 [3,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_312 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 4 degreeUnionState43_312 [4,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_313 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 5 degreeUnionState43_313 [5,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_314 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 6 degreeUnionState43_314 [6,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_315 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 7 degreeUnionState43_315 [7,19] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_316 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 8 degreeUnionState43_316 [8,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_317 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 15 9 degreeUnionState43_317 [9,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_318 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 14 10 degreeUnionState43_318 [10,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_319 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 13 11 degreeUnionState43_319 [11,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_320 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 12 12 degreeUnionState43_320 [12,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_321 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 11 13 degreeUnionState43_321 [13,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_322 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 10 14 degreeUnionState43_322 [14,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_323 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 9 15 degreeUnionState43_323 [15,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_324 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 8 16 degreeUnionState43_324 [16,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_325 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 7 17 degreeUnionState43_325 [17,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_326 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 6 18 degreeUnionState43_326 [18,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_327 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 5 19 degreeUnionState43_327 [19,19] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_328 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 20 degreeUnionState43_328 [20] = true := by + decide +kernel + +lemma degreeUnionBranch43_329 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 21 degreeUnionState43_329 [21] = true := by + decide +kernel + +lemma degreeUnionBranch43_330 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 22 degreeUnionState43_330 [22] = true := by + decide +kernel + +lemma degreeUnionBranch43_331 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 23 degreeUnionState43_331 [23] = true := by + decide +kernel + +lemma degreeUnionBranch43_332 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 24 degreeUnionState43_332 [24] = true := by + decide +kernel + +lemma degreeUnionBranch43_333 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 25 degreeUnionState43_333 [25] = true := by + decide +kernel + +lemma degreeUnionBranch43_334 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 26 degreeUnionState43_334 [26] = true := by + decide +kernel + +lemma degreeUnionBranch43_335 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 27 degreeUnionState43_335 [27] = true := by + decide +kernel + +lemma degreeUnionBranch43_336 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 28 degreeUnionState43_336 [28] = true := by + decide +kernel + +lemma degreeUnionBranch43_337 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 14 29 degreeUnionState43_337 [29] = true := by + decide +kernel + +lemma degreeUnionBranch43_338 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 13 30 degreeUnionState43_338 [30] = true := by + decide +kernel + +lemma degreeUnionBranch43_339 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 12 31 degreeUnionState43_339 [31] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_340 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 11 32 degreeUnionState43_340 [32] = true := by + decide +kernel + +lemma degreeUnionBranch43_341 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 10 33 degreeUnionState43_341 [33] = true := by + decide +kernel + +lemma degreeUnionBranch43_342 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 9 34 degreeUnionState43_342 [34] = true := by + decide +kernel + +lemma degreeUnionBranch43_343 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 8 35 degreeUnionState43_343 [35] = true := by + decide +kernel + +lemma degreeUnionBranch43_344 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 7 36 degreeUnionState43_344 [36] = true := by + decide +kernel + +lemma degreeUnionBranch43_345 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 6 37 degreeUnionState43_345 [37] = true := by + decide +kernel + +lemma degreeUnionBranch43_346 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 5 38 degreeUnionState43_346 [38] = true := by + decide +kernel + +lemma degreeUnionBranch43_347 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 4 39 degreeUnionState43_347 [39] = true := by + decide +kernel + +lemma degreeUnionBranch43_348 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 3 40 degreeUnionState43_348 [40] = true := by + decide +kernel + +lemma degreeUnionBranch43_349 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 2 41 degreeUnionState43_349 [41] = true := by + decide +kernel + +lemma degreeUnionBranch43_350 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 1 42 degreeUnionState43_350 [42] = true := by + decide +kernel + +lemma degreeUnionBranch43_352 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 38 5 degreeUnionState43_352 [5] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_353 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 37 6 degreeUnionState43_353 [6] = true := by + decide +kernel + +lemma degreeUnionBranch43_354 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 36 7 degreeUnionState43_354 [7] = true := by + decide +kernel + +lemma degreeUnionBranch43_356 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 31 4 degreeUnionState43_356 [4,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_357 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 30 5 degreeUnionState43_357 [5,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_358 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 29 6 degreeUnionState43_358 [6,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_359 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 28 7 degreeUnionState43_359 [7,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_361 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 4 degreeUnionState43_361 [4,8,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_362 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 5 degreeUnionState43_362 [5,8,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_363 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 6 degreeUnionState43_363 [6,8,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_364 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 7 degreeUnionState43_364 [7,8,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_365 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 8 degreeUnionState43_365 [8,8,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_367 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 30 4 degreeUnionState43_367 [4,9] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_368 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 29 5 degreeUnionState43_368 [5,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_369 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 28 6 degreeUnionState43_369 [6,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_370 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 27 7 degreeUnionState43_370 [7,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_372 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 22 4 degreeUnionState43_372 [4,8,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_373 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 5 degreeUnionState43_373 [5,8,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_374 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 6 degreeUnionState43_374 [6,8,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_375 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 7 degreeUnionState43_375 [7,8,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_376 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 8 degreeUnionState43_376 [8,8,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_378 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 21 4 degreeUnionState43_378 [4,9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_379 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 20 5 degreeUnionState43_379 [5,9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_380 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 19 6 degreeUnionState43_380 [6,9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_381 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 18 7 degreeUnionState43_381 [7,9,9] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_382 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 17 8 degreeUnionState43_382 [8,9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_383 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 16 9 degreeUnionState43_383 [9,9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_385 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 29 4 degreeUnionState43_385 [4,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_386 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 28 5 degreeUnionState43_386 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_387 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 27 6 degreeUnionState43_387 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_388 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 26 7 degreeUnionState43_388 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_389 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 8 degreeUnionState43_389 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_390 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 9 degreeUnionState43_390 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_391 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 10 degreeUnionState43_391 [10,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_393 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 28 4 degreeUnionState43_393 [4,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_394 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 27 5 degreeUnionState43_394 [5,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_395 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 26 6 degreeUnionState43_395 [6,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_396 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 7 degreeUnionState43_396 [7,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_397 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 8 degreeUnionState43_397 [8,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_398 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 9 degreeUnionState43_398 [9,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_399 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 10 degreeUnionState43_399 [10,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_400 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 11 degreeUnionState43_400 [11,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_402 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 27 4 degreeUnionState43_402 [4,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_403 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 26 5 degreeUnionState43_403 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_404 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 6 degreeUnionState43_404 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_405 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 7 degreeUnionState43_405 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_406 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 8 degreeUnionState43_406 [8,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_407 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 9 degreeUnionState43_407 [9,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_408 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 10 degreeUnionState43_408 [10,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_409 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 11 degreeUnionState43_409 [11,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_410 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 12 degreeUnionState43_410 [12,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_412 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 26 4 degreeUnionState43_412 [4,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_413 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 5 degreeUnionState43_413 [5,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_414 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 6 degreeUnionState43_414 [6,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_415 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 7 degreeUnionState43_415 [7,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_416 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 8 degreeUnionState43_416 [8,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_417 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 9 degreeUnionState43_417 [9,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_418 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 10 degreeUnionState43_418 [10,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_419 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 11 degreeUnionState43_419 [11,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_420 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 12 degreeUnionState43_420 [12,13] = true := by + decide +kernel + +lemma degreeUnionBranch43_421 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 13 degreeUnionState43_421 [13,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_423 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 4 degreeUnionState43_423 [4,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_424 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 5 degreeUnionState43_424 [5,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_425 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 6 degreeUnionState43_425 [6,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_426 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 7 degreeUnionState43_426 [7,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_427 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 8 degreeUnionState43_427 [8,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_428 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 9 degreeUnionState43_428 [9,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_429 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 10 degreeUnionState43_429 [10,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_430 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 11 degreeUnionState43_430 [11,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_431 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 12 degreeUnionState43_431 [12,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_432 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 13 degreeUnionState43_432 [13,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_433 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 14 degreeUnionState43_433 [14,14] = true := by + decide +kernel + +lemma degreeUnionBranch43_435 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 4 degreeUnionState43_435 [4,15] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_436 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 5 degreeUnionState43_436 [5,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_437 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 6 degreeUnionState43_437 [6,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_438 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 7 degreeUnionState43_438 [7,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_439 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 8 degreeUnionState43_439 [8,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_440 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 9 degreeUnionState43_440 [9,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_441 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 10 degreeUnionState43_441 [10,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_442 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 11 degreeUnionState43_442 [11,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_443 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 12 degreeUnionState43_443 [12,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_444 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 13 degreeUnionState43_444 [13,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_445 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 14 14 degreeUnionState43_445 [14,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_446 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 13 15 degreeUnionState43_446 [15,15] = true := by + decide +kernel + +lemma degreeUnionBranch43_448 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 3 degreeUnionState43_448 [3,16] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_449 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 4 degreeUnionState43_449 [4,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_450 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 5 degreeUnionState43_450 [5,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_451 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 6 degreeUnionState43_451 [6,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_452 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 7 degreeUnionState43_452 [7,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_453 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 8 degreeUnionState43_453 [8,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_454 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 9 degreeUnionState43_454 [9,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_455 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 10 degreeUnionState43_455 [10,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_456 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 11 degreeUnionState43_456 [11,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_457 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 12 degreeUnionState43_457 [12,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_458 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 14 13 degreeUnionState43_458 [13,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_459 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 13 14 degreeUnionState43_459 [14,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_460 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 12 15 degreeUnionState43_460 [15,16] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_461 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 11 16 degreeUnionState43_461 [16,16] = true := by + decide +kernel + +lemma degreeUnionBranch43_463 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 23 3 degreeUnionState43_463 [3,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_464 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 4 degreeUnionState43_464 [4,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_465 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 5 degreeUnionState43_465 [5,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_466 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 6 degreeUnionState43_466 [6,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_467 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 7 degreeUnionState43_467 [7,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_468 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 8 degreeUnionState43_468 [8,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_469 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 9 degreeUnionState43_469 [9,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_470 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 10 degreeUnionState43_470 [10,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_471 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 11 degreeUnionState43_471 [11,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_472 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 14 12 degreeUnionState43_472 [12,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_473 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 13 13 degreeUnionState43_473 [13,17] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_474 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 12 14 degreeUnionState43_474 [14,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_475 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 11 15 degreeUnionState43_475 [15,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_476 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 10 16 degreeUnionState43_476 [16,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_477 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 9 17 degreeUnionState43_477 [17,17] = true := by + decide +kernel + +lemma degreeUnionBranch43_479 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 22 3 degreeUnionState43_479 [3,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_480 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 4 degreeUnionState43_480 [4,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_481 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 5 degreeUnionState43_481 [5,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_482 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 6 degreeUnionState43_482 [6,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_483 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 7 degreeUnionState43_483 [7,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_484 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 8 degreeUnionState43_484 [8,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_485 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 9 degreeUnionState43_485 [9,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_486 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 10 degreeUnionState43_486 [10,18] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_487 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 14 11 degreeUnionState43_487 [11,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_488 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 13 12 degreeUnionState43_488 [12,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_489 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 12 13 degreeUnionState43_489 [13,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_490 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 11 14 degreeUnionState43_490 [14,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_491 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 10 15 degreeUnionState43_491 [15,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_492 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 9 16 degreeUnionState43_492 [16,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_493 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 8 17 degreeUnionState43_493 [17,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_494 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 7 18 degreeUnionState43_494 [18,18] = true := by + decide +kernel + +lemma degreeUnionBranch43_496 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 21 3 degreeUnionState43_496 [3,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_497 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 20 4 degreeUnionState43_497 [4,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_498 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 19 5 degreeUnionState43_498 [5,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_499 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 18 6 degreeUnionState43_499 [6,19] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_500 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 17 7 degreeUnionState43_500 [7,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_501 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 16 8 degreeUnionState43_501 [8,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_502 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 15 9 degreeUnionState43_502 [9,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_503 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 14 10 degreeUnionState43_503 [10,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_504 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 13 11 degreeUnionState43_504 [11,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_505 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 12 12 degreeUnionState43_505 [12,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_506 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 11 13 degreeUnionState43_506 [13,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_507 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 10 14 degreeUnionState43_507 [14,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_508 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 9 15 degreeUnionState43_508 [15,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_509 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 8 16 degreeUnionState43_509 [16,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_510 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 7 17 degreeUnionState43_510 [17,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_511 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 6 18 degreeUnionState43_511 [18,19] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_512 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 5 19 degreeUnionState43_512 [19,19] = true := by + decide +kernel + +lemma degreeUnionBranch43_513 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 23 20 degreeUnionState43_513 [20] = true := by + decide +kernel + +lemma degreeUnionBranch43_514 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 22 21 degreeUnionState43_514 [21] = true := by + decide +kernel + +lemma degreeUnionBranch43_515 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 21 22 degreeUnionState43_515 [22] = true := by + decide +kernel + +lemma degreeUnionBranch43_516 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 20 23 degreeUnionState43_516 [23] = true := by + decide +kernel + +lemma degreeUnionBranch43_517 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 19 24 degreeUnionState43_517 [24] = true := by + decide +kernel + +lemma degreeUnionBranch43_518 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 18 25 degreeUnionState43_518 [25] = true := by + decide +kernel + +lemma degreeUnionBranch43_519 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 17 26 degreeUnionState43_519 [26] = true := by + decide +kernel + +lemma degreeUnionBranch43_520 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 16 27 degreeUnionState43_520 [27] = true := by + decide +kernel + +lemma degreeUnionBranch43_521 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 15 28 degreeUnionState43_521 [28] = true := by + decide +kernel + +lemma degreeUnionBranch43_522 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 14 29 degreeUnionState43_522 [29] = true := by + decide +kernel + +lemma degreeUnionBranch43_523 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 13 30 degreeUnionState43_523 [30] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_524 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 12 31 degreeUnionState43_524 [31] = true := by + decide +kernel + +lemma degreeUnionBranch43_525 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 11 32 degreeUnionState43_525 [32] = true := by + decide +kernel + +lemma degreeUnionBranch43_526 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 10 33 degreeUnionState43_526 [33] = true := by + decide +kernel + +lemma degreeUnionBranch43_527 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 9 34 degreeUnionState43_527 [34] = true := by + decide +kernel + +lemma degreeUnionBranch43_528 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 8 35 degreeUnionState43_528 [35] = true := by + decide +kernel + +lemma degreeUnionBranch43_529 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 7 36 degreeUnionState43_529 [36] = true := by + decide +kernel + +lemma degreeUnionBranch43_530 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 6 37 degreeUnionState43_530 [37] = true := by + decide +kernel + +lemma degreeUnionBranch43_531 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 5 38 degreeUnionState43_531 [38] = true := by + decide +kernel + +lemma degreeUnionBranch43_532 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 4 39 degreeUnionState43_532 [39] = true := by + decide +kernel + +lemma degreeUnionBranch43_533 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 3 40 degreeUnionState43_533 [40] = true := by + decide +kernel + +lemma degreeUnionBranch43_534 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 2 41 degreeUnionState43_534 [41] = true := by + decide +kernel + +lemma degreeUnionBranch43_535 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 1 42 degreeUnionState43_535 [42] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_537 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 39 4 degreeUnionState43_537 [4] = true := by + decide +kernel + +lemma degreeUnionBranch43_538 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 38 5 degreeUnionState43_538 [5] = true := by + decide +kernel + +lemma degreeUnionBranch43_539 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 37 6 degreeUnionState43_539 [6] = true := by + decide +kernel + +lemma degreeUnionBranch43_540 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 36 7 degreeUnionState43_540 [7] = true := by + decide +kernel + +lemma degreeUnionBranch43_542 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 31 4 degreeUnionState43_542 [4,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_543 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 30 5 degreeUnionState43_543 [5,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_544 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 29 6 degreeUnionState43_544 [6,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_545 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 28 7 degreeUnionState43_545 [7,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_546 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 27 8 degreeUnionState43_546 [8,8] = true := by + decide +kernel + +lemma degreeUnionBranch43_548 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 30 4 degreeUnionState43_548 [4,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_549 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 29 5 degreeUnionState43_549 [5,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_550 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 28 6 degreeUnionState43_550 [6,9] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_551 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 27 7 degreeUnionState43_551 [7,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_552 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 26 8 degreeUnionState43_552 [8,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_553 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 25 9 degreeUnionState43_553 [9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_555 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 29 4 degreeUnionState43_555 [4,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_556 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 28 5 degreeUnionState43_556 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_557 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 27 6 degreeUnionState43_557 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_558 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 26 7 degreeUnionState43_558 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_559 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 25 8 degreeUnionState43_559 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_560 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 24 9 degreeUnionState43_560 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_561 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 23 10 degreeUnionState43_561 [10,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_563 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 28 4 degreeUnionState43_563 [4,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_564 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 27 5 degreeUnionState43_564 [5,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_565 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 26 6 degreeUnionState43_565 [6,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_566 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 25 7 degreeUnionState43_566 [7,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_567 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 24 8 degreeUnionState43_567 [8,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_568 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 23 9 degreeUnionState43_568 [9,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_569 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 22 10 degreeUnionState43_569 [10,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_570 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 21 11 degreeUnionState43_570 [11,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_572 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 27 4 degreeUnionState43_572 [4,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_573 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 26 5 degreeUnionState43_573 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_574 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 25 6 degreeUnionState43_574 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_575 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 24 7 degreeUnionState43_575 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_576 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 23 8 degreeUnionState43_576 [8,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_577 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 22 9 degreeUnionState43_577 [9,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_578 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 21 10 degreeUnionState43_578 [10,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_579 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 20 11 degreeUnionState43_579 [11,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_580 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 19 12 degreeUnionState43_580 [12,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_581 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 30 13 degreeUnionState43_581 [13] = true := by + decide +kernel + +lemma degreeUnionBranch43_582 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 29 14 degreeUnionState43_582 [14] = true := by + decide +kernel + +lemma degreeUnionBranch43_583 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 28 15 degreeUnionState43_583 [15] = true := by + decide +kernel + +lemma degreeUnionBranch43_584 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 27 16 degreeUnionState43_584 [16] = true := by + decide +kernel + +lemma degreeUnionBranch43_585 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 26 17 degreeUnionState43_585 [17] = true := by + decide +kernel + +lemma degreeUnionBranch43_586 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 25 18 degreeUnionState43_586 [18] = true := by + decide +kernel + +lemma degreeUnionBranch43_587 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 24 19 degreeUnionState43_587 [19] = true := by + decide +kernel + +lemma degreeUnionBranch43_588 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 23 20 degreeUnionState43_588 [20] = true := by + decide +kernel + +lemma degreeUnionBranch43_589 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 22 21 degreeUnionState43_589 [21] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_590 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 21 22 degreeUnionState43_590 [22] = true := by + decide +kernel + +lemma degreeUnionBranch43_591 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 20 23 degreeUnionState43_591 [23] = true := by + decide +kernel + +lemma degreeUnionBranch43_592 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 19 24 degreeUnionState43_592 [24] = true := by + decide +kernel + +lemma degreeUnionBranch43_593 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 18 25 degreeUnionState43_593 [25] = true := by + decide +kernel + +lemma degreeUnionBranch43_594 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 17 26 degreeUnionState43_594 [26] = true := by + decide +kernel + +lemma degreeUnionBranch43_595 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 16 27 degreeUnionState43_595 [27] = true := by + decide +kernel + +lemma degreeUnionBranch43_596 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 15 28 degreeUnionState43_596 [28] = true := by + decide +kernel + +lemma degreeUnionBranch43_597 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 14 29 degreeUnionState43_597 [29] = true := by + decide +kernel + +lemma degreeUnionBranch43_598 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 13 30 degreeUnionState43_598 [30] = true := by + decide +kernel + +lemma degreeUnionBranch43_599 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 12 31 degreeUnionState43_599 [31] = true := by + decide +kernel + +lemma degreeUnionBranch43_600 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 11 32 degreeUnionState43_600 [32] = true := by + decide +kernel + +lemma degreeUnionBranch43_601 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 10 33 degreeUnionState43_601 [33] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_602 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 9 34 degreeUnionState43_602 [34] = true := by + decide +kernel + +lemma degreeUnionBranch43_603 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 8 35 degreeUnionState43_603 [35] = true := by + decide +kernel + +lemma degreeUnionBranch43_604 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 7 36 degreeUnionState43_604 [36] = true := by + decide +kernel + +lemma degreeUnionBranch43_605 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 6 37 degreeUnionState43_605 [37] = true := by + decide +kernel + +lemma degreeUnionBranch43_606 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 5 38 degreeUnionState43_606 [38] = true := by + decide +kernel + +lemma degreeUnionBranch43_607 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 4 39 degreeUnionState43_607 [39] = true := by + decide +kernel + +lemma degreeUnionBranch43_608 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 3 40 degreeUnionState43_608 [40] = true := by + decide +kernel + +lemma degreeUnionBranch43_609 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 2 41 degreeUnionState43_609 [41] = true := by + decide +kernel + +lemma degreeUnionBranch43_610 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 1 42 degreeUnionState43_610 [42] = true := by + decide +kernel + +lemma degreeUnionBranch43_612 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 39 4 degreeUnionState43_612 [4] = true := by + decide +kernel + +lemma degreeUnionBranch43_613 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 38 5 degreeUnionState43_613 [5] = true := by + decide +kernel + +lemma degreeUnionBranch43_614 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 37 6 degreeUnionState43_614 [6] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_615 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 36 7 degreeUnionState43_615 [7] = true := by + decide +kernel + +lemma degreeUnionBranch43_616 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 35 8 degreeUnionState43_616 [8] = true := by + decide +kernel + +lemma degreeUnionBranch43_618 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 30 4 degreeUnionState43_618 [4,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_619 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 29 5 degreeUnionState43_619 [5,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_620 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 28 6 degreeUnionState43_620 [6,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_621 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 27 7 degreeUnionState43_621 [7,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_622 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 26 8 degreeUnionState43_622 [8,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_623 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 25 9 degreeUnionState43_623 [9,9] = true := by + decide +kernel + +lemma degreeUnionBranch43_625 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 30 3 degreeUnionState43_625 [3,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_626 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 29 4 degreeUnionState43_626 [4,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_627 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 28 5 degreeUnionState43_627 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_628 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 27 6 degreeUnionState43_628 [6,10] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_629 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 26 7 degreeUnionState43_629 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_630 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 25 8 degreeUnionState43_630 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_631 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 24 9 degreeUnionState43_631 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_632 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 23 10 degreeUnionState43_632 [10,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_634 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 29 3 degreeUnionState43_634 [3,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_635 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 28 4 degreeUnionState43_635 [4,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_636 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 27 5 degreeUnionState43_636 [5,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_637 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 26 6 degreeUnionState43_637 [6,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_638 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 25 7 degreeUnionState43_638 [7,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_639 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 24 8 degreeUnionState43_639 [8,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_640 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 23 9 degreeUnionState43_640 [9,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_641 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 22 10 degreeUnionState43_641 [10,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_642 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 21 11 degreeUnionState43_642 [11,11] = true := by + decide +kernel + +lemma degreeUnionBranch43_644 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 28 3 degreeUnionState43_644 [3,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_645 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 27 4 degreeUnionState43_645 [4,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_646 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 26 5 degreeUnionState43_646 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_647 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 25 6 degreeUnionState43_647 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_648 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 24 7 degreeUnionState43_648 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_649 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 23 8 degreeUnionState43_649 [8,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_650 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 22 9 degreeUnionState43_650 [9,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_651 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 21 10 degreeUnionState43_651 [10,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_652 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 20 11 degreeUnionState43_652 [11,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_653 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 19 12 degreeUnionState43_653 [12,12] = true := by + decide +kernel + +lemma degreeUnionBranch43_654 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 30 13 degreeUnionState43_654 [13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_655 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 29 14 degreeUnionState43_655 [14] = true := by + decide +kernel + +lemma degreeUnionBranch43_656 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 28 15 degreeUnionState43_656 [15] = true := by + decide +kernel + +lemma degreeUnionBranch43_657 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 27 16 degreeUnionState43_657 [16] = true := by + decide +kernel + +lemma degreeUnionBranch43_658 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 26 17 degreeUnionState43_658 [17] = true := by + decide +kernel + +lemma degreeUnionBranch43_659 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 25 18 degreeUnionState43_659 [18] = true := by + decide +kernel + +lemma degreeUnionBranch43_660 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 24 19 degreeUnionState43_660 [19] = true := by + decide +kernel + +lemma degreeUnionBranch43_661 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 23 20 degreeUnionState43_661 [20] = true := by + decide +kernel + +lemma degreeUnionBranch43_662 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 22 21 degreeUnionState43_662 [21] = true := by + decide +kernel + +lemma degreeUnionBranch43_663 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 21 22 degreeUnionState43_663 [22] = true := by + decide +kernel + +lemma degreeUnionBranch43_664 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 20 23 degreeUnionState43_664 [23] = true := by + decide +kernel + +lemma degreeUnionBranch43_665 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 19 24 degreeUnionState43_665 [24] = true := by + decide +kernel + +lemma degreeUnionBranch43_666 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 18 25 degreeUnionState43_666 [25] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_667 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 17 26 degreeUnionState43_667 [26] = true := by + decide +kernel + +lemma degreeUnionBranch43_668 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 16 27 degreeUnionState43_668 [27] = true := by + decide +kernel + +lemma degreeUnionBranch43_669 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 15 28 degreeUnionState43_669 [28] = true := by + decide +kernel + +lemma degreeUnionBranch43_670 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 14 29 degreeUnionState43_670 [29] = true := by + decide +kernel + +lemma degreeUnionBranch43_671 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 13 30 degreeUnionState43_671 [30] = true := by + decide +kernel + +lemma degreeUnionBranch43_672 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 12 31 degreeUnionState43_672 [31] = true := by + decide +kernel + +lemma degreeUnionBranch43_673 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 11 32 degreeUnionState43_673 [32] = true := by + decide +kernel + +lemma degreeUnionBranch43_674 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 10 33 degreeUnionState43_674 [33] = true := by + decide +kernel + +lemma degreeUnionBranch43_675 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 9 34 degreeUnionState43_675 [34] = true := by + decide +kernel + +lemma degreeUnionBranch43_676 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 8 35 degreeUnionState43_676 [35] = true := by + decide +kernel + +lemma degreeUnionBranch43_677 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 7 36 degreeUnionState43_677 [36] = true := by + decide +kernel + +lemma degreeUnionBranch43_678 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 6 37 degreeUnionState43_678 [37] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_679 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 5 38 degreeUnionState43_679 [38] = true := by + decide +kernel + +lemma degreeUnionBranch43_680 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 4 39 degreeUnionState43_680 [39] = true := by + decide +kernel + +lemma degreeUnionBranch43_681 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 3 40 degreeUnionState43_681 [40] = true := by + decide +kernel + +lemma degreeUnionBranch43_682 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 2 41 degreeUnionState43_682 [41] = true := by + decide +kernel + +lemma degreeUnionBranch43_683 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 1 42 degreeUnionState43_683 [42] = true := by + decide +kernel + +lemma degreeUnionBranch43_685 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 39 4 degreeUnionState43_685 [4] = true := by + decide +kernel + +lemma degreeUnionBranch43_686 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 38 5 degreeUnionState43_686 [5] = true := by + decide +kernel + +lemma degreeUnionBranch43_687 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 37 6 degreeUnionState43_687 [6] = true := by + decide +kernel + +lemma degreeUnionBranch43_688 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 36 7 degreeUnionState43_688 [7] = true := by + decide +kernel + +lemma degreeUnionBranch43_689 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 35 8 degreeUnionState43_689 [8] = true := by + decide +kernel + +lemma degreeUnionBranch43_690 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 34 9 degreeUnionState43_690 [9] = true := by + decide +kernel + +lemma degreeUnionBranch43_692 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 30 3 degreeUnionState43_692 [3,10] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_693 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 29 4 degreeUnionState43_693 [4,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_694 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 28 5 degreeUnionState43_694 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_695 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 27 6 degreeUnionState43_695 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_696 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 26 7 degreeUnionState43_696 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_697 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 25 8 degreeUnionState43_697 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_698 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 24 9 degreeUnionState43_698 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_699 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 23 10 degreeUnionState43_699 [10,10] = true := by + decide +kernel + +lemma degreeUnionBranch43_700 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 32 11 degreeUnionState43_700 [11] = true := by + decide +kernel + +lemma degreeUnionBranch43_701 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 31 12 degreeUnionState43_701 [12] = true := by + decide +kernel + +lemma degreeUnionBranch43_702 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 30 13 degreeUnionState43_702 [13] = true := by + decide +kernel + +lemma degreeUnionBranch43_703 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 29 14 degreeUnionState43_703 [14] = true := by + decide +kernel + +lemma degreeUnionBranch43_704 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 28 15 degreeUnionState43_704 [15] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_705 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 27 16 degreeUnionState43_705 [16] = true := by + decide +kernel + +lemma degreeUnionBranch43_706 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 26 17 degreeUnionState43_706 [17] = true := by + decide +kernel + +lemma degreeUnionBranch43_707 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 25 18 degreeUnionState43_707 [18] = true := by + decide +kernel + +lemma degreeUnionBranch43_708 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 24 19 degreeUnionState43_708 [19] = true := by + decide +kernel + +lemma degreeUnionBranch43_709 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 23 20 degreeUnionState43_709 [20] = true := by + decide +kernel + +lemma degreeUnionBranch43_710 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 22 21 degreeUnionState43_710 [21] = true := by + decide +kernel + +lemma degreeUnionBranch43_711 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 21 22 degreeUnionState43_711 [22] = true := by + decide +kernel + +lemma degreeUnionBranch43_712 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 20 23 degreeUnionState43_712 [23] = true := by + decide +kernel + +lemma degreeUnionBranch43_713 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 19 24 degreeUnionState43_713 [24] = true := by + decide +kernel + +lemma degreeUnionBranch43_714 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 18 25 degreeUnionState43_714 [25] = true := by + decide +kernel + +lemma degreeUnionBranch43_715 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 17 26 degreeUnionState43_715 [26] = true := by + decide +kernel + +lemma degreeUnionBranch43_716 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 16 27 degreeUnionState43_716 [27] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_717 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 15 28 degreeUnionState43_717 [28] = true := by + decide +kernel + +lemma degreeUnionBranch43_718 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 14 29 degreeUnionState43_718 [29] = true := by + decide +kernel + +lemma degreeUnionBranch43_719 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 13 30 degreeUnionState43_719 [30] = true := by + decide +kernel + +lemma degreeUnionBranch43_720 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 12 31 degreeUnionState43_720 [31] = true := by + decide +kernel + +lemma degreeUnionBranch43_721 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 11 32 degreeUnionState43_721 [32] = true := by + decide +kernel + +lemma degreeUnionBranch43_722 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 10 33 degreeUnionState43_722 [33] = true := by + decide +kernel + +lemma degreeUnionBranch43_723 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 9 34 degreeUnionState43_723 [34] = true := by + decide +kernel + +lemma degreeUnionBranch43_724 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 8 35 degreeUnionState43_724 [35] = true := by + decide +kernel + +lemma degreeUnionBranch43_725 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 7 36 degreeUnionState43_725 [36] = true := by + decide +kernel + +lemma degreeUnionBranch43_726 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 6 37 degreeUnionState43_726 [37] = true := by + decide +kernel + +lemma degreeUnionBranch43_727 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 5 38 degreeUnionState43_727 [38] = true := by + decide +kernel + +lemma degreeUnionBranch43_728 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 4 39 degreeUnionState43_728 [39] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_729 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 3 40 degreeUnionState43_729 [40] = true := by + decide +kernel + +lemma degreeUnionBranch43_730 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 2 41 degreeUnionState43_730 [41] = true := by + decide +kernel + +lemma degreeUnionBranch43_731 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 1 42 degreeUnionState43_731 [42] = true := by + decide +kernel + +lemma degreeUnionBranch43_733 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 39 4 degreeUnionState43_733 [4] = true := by + decide +kernel + +lemma degreeUnionBranch43_734 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 38 5 degreeUnionState43_734 [5] = true := by + decide +kernel + +lemma degreeUnionBranch43_735 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 37 6 degreeUnionState43_735 [6] = true := by + decide +kernel + +lemma degreeUnionBranch43_736 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 36 7 degreeUnionState43_736 [7] = true := by + decide +kernel + +lemma degreeUnionBranch43_737 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 35 8 degreeUnionState43_737 [8] = true := by + decide +kernel + +lemma degreeUnionBranch43_738 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 34 9 degreeUnionState43_738 [9] = true := by + decide +kernel + +lemma degreeUnionBranch43_739 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 33 10 degreeUnionState43_739 [10] = true := by + decide +kernel + +lemma degreeUnionBranch43_740 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 32 11 degreeUnionState43_740 [11] = true := by + decide +kernel + +lemma degreeUnionBranch43_741 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 31 12 degreeUnionState43_741 [12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_742 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 30 13 degreeUnionState43_742 [13] = true := by + decide +kernel + +lemma degreeUnionBranch43_743 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 29 14 degreeUnionState43_743 [14] = true := by + decide +kernel + +lemma degreeUnionBranch43_744 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 28 15 degreeUnionState43_744 [15] = true := by + decide +kernel + +lemma degreeUnionBranch43_745 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 27 16 degreeUnionState43_745 [16] = true := by + decide +kernel + +lemma degreeUnionBranch43_746 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 26 17 degreeUnionState43_746 [17] = true := by + decide +kernel + +lemma degreeUnionBranch43_747 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 25 18 degreeUnionState43_747 [18] = true := by + decide +kernel + +lemma degreeUnionBranch43_748 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 24 19 degreeUnionState43_748 [19] = true := by + decide +kernel + +lemma degreeUnionBranch43_749 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 23 20 degreeUnionState43_749 [20] = true := by + decide +kernel + +lemma degreeUnionBranch43_750 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 22 21 degreeUnionState43_750 [21] = true := by + decide +kernel + +lemma degreeUnionBranch43_751 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 21 22 degreeUnionState43_751 [22] = true := by + decide +kernel + +lemma degreeUnionBranch43_752 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 20 23 degreeUnionState43_752 [23] = true := by + decide +kernel + +lemma degreeUnionBranch43_753 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 19 24 degreeUnionState43_753 [24] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_754 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 18 25 degreeUnionState43_754 [25] = true := by + decide +kernel + +lemma degreeUnionBranch43_755 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 17 26 degreeUnionState43_755 [26] = true := by + decide +kernel + +lemma degreeUnionBranch43_756 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 16 27 degreeUnionState43_756 [27] = true := by + decide +kernel + +lemma degreeUnionBranch43_757 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 15 28 degreeUnionState43_757 [28] = true := by + decide +kernel + +lemma degreeUnionBranch43_758 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 14 29 degreeUnionState43_758 [29] = true := by + decide +kernel + +lemma degreeUnionBranch43_759 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 13 30 degreeUnionState43_759 [30] = true := by + decide +kernel + +lemma degreeUnionBranch43_760 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 12 31 degreeUnionState43_760 [31] = true := by + decide +kernel + +lemma degreeUnionBranch43_761 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 11 32 degreeUnionState43_761 [32] = true := by + decide +kernel + +lemma degreeUnionBranch43_762 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 10 33 degreeUnionState43_762 [33] = true := by + decide +kernel + +lemma degreeUnionBranch43_763 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 9 34 degreeUnionState43_763 [34] = true := by + decide +kernel + +lemma degreeUnionBranch43_764 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 8 35 degreeUnionState43_764 [35] = true := by + decide +kernel + +lemma degreeUnionBranch43_765 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 7 36 degreeUnionState43_765 [36] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_766 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 6 37 degreeUnionState43_766 [37] = true := by + decide +kernel + +lemma degreeUnionBranch43_767 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 5 38 degreeUnionState43_767 [38] = true := by + decide +kernel + +lemma degreeUnionBranch43_768 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 4 39 degreeUnionState43_768 [39] = true := by + decide +kernel + +lemma degreeUnionBranch43_769 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 3 40 degreeUnionState43_769 [40] = true := by + decide +kernel + +lemma degreeUnionBranch43_770 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 2 41 degreeUnionState43_770 [41] = true := by + decide +kernel + +lemma degreeUnionBranch43_771 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 1 42 degreeUnionState43_771 [42] = true := by + decide +kernel + +lemma degreeUnionBranch43_773 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 40 3 degreeUnionState43_773 [3] = true := by + decide +kernel + +lemma degreeUnionBranch43_774 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 39 4 degreeUnionState43_774 [4] = true := by + decide +kernel + +lemma degreeUnionBranch43_775 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 38 5 degreeUnionState43_775 [5] = true := by + decide +kernel + +lemma degreeUnionBranch43_776 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 37 6 degreeUnionState43_776 [6] = true := by + decide +kernel + +lemma degreeUnionBranch43_777 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 36 7 degreeUnionState43_777 [7] = true := by + decide +kernel + +lemma degreeUnionBranch43_778 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 35 8 degreeUnionState43_778 [8] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_779 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 34 9 degreeUnionState43_779 [9] = true := by + decide +kernel + +lemma degreeUnionBranch43_780 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 33 10 degreeUnionState43_780 [10] = true := by + decide +kernel + +lemma degreeUnionBranch43_781 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 32 11 degreeUnionState43_781 [11] = true := by + decide +kernel + +lemma degreeUnionBranch43_782 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 31 12 degreeUnionState43_782 [12] = true := by + decide +kernel + +lemma degreeUnionBranch43_783 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 30 13 degreeUnionState43_783 [13] = true := by + decide +kernel + +lemma degreeUnionBranch43_784 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 29 14 degreeUnionState43_784 [14] = true := by + decide +kernel + +lemma degreeUnionBranch43_785 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 28 15 degreeUnionState43_785 [15] = true := by + decide +kernel + +lemma degreeUnionBranch43_786 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 27 16 degreeUnionState43_786 [16] = true := by + decide +kernel + +lemma degreeUnionBranch43_787 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 26 17 degreeUnionState43_787 [17] = true := by + decide +kernel + +lemma degreeUnionBranch43_788 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 25 18 degreeUnionState43_788 [18] = true := by + decide +kernel + +lemma degreeUnionBranch43_789 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 24 19 degreeUnionState43_789 [19] = true := by + decide +kernel + +lemma degreeUnionBranch43_790 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 23 20 degreeUnionState43_790 [20] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_791 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 22 21 degreeUnionState43_791 [21] = true := by + decide +kernel + +lemma degreeUnionBranch43_792 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 21 22 degreeUnionState43_792 [22] = true := by + decide +kernel + +lemma degreeUnionBranch43_793 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 20 23 degreeUnionState43_793 [23] = true := by + decide +kernel + +lemma degreeUnionBranch43_794 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 19 24 degreeUnionState43_794 [24] = true := by + decide +kernel + +lemma degreeUnionBranch43_795 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 18 25 degreeUnionState43_795 [25] = true := by + decide +kernel + +lemma degreeUnionBranch43_796 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 17 26 degreeUnionState43_796 [26] = true := by + decide +kernel + +lemma degreeUnionBranch43_797 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 16 27 degreeUnionState43_797 [27] = true := by + decide +kernel + +lemma degreeUnionBranch43_798 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 15 28 degreeUnionState43_798 [28] = true := by + decide +kernel + +lemma degreeUnionBranch43_799 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 14 29 degreeUnionState43_799 [29] = true := by + decide +kernel + +lemma degreeUnionBranch43_800 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 13 30 degreeUnionState43_800 [30] = true := by + decide +kernel + +lemma degreeUnionBranch43_801 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 12 31 degreeUnionState43_801 [31] = true := by + decide +kernel + +lemma degreeUnionBranch43_802 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 11 32 degreeUnionState43_802 [32] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_803 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 10 33 degreeUnionState43_803 [33] = true := by + decide +kernel + +lemma degreeUnionBranch43_804 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 9 34 degreeUnionState43_804 [34] = true := by + decide +kernel + +lemma degreeUnionBranch43_805 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 8 35 degreeUnionState43_805 [35] = true := by + decide +kernel + +lemma degreeUnionBranch43_806 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 7 36 degreeUnionState43_806 [36] = true := by + decide +kernel + +lemma degreeUnionBranch43_807 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 6 37 degreeUnionState43_807 [37] = true := by + decide +kernel + +lemma degreeUnionBranch43_808 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 5 38 degreeUnionState43_808 [38] = true := by + decide +kernel + +lemma degreeUnionBranch43_809 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 4 39 degreeUnionState43_809 [39] = true := by + decide +kernel + +lemma degreeUnionBranch43_810 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 3 40 degreeUnionState43_810 [40] = true := by + decide +kernel + +lemma degreeUnionBranch43_811 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 2 41 degreeUnionState43_811 [41] = true := by + decide +kernel + +lemma degreeUnionBranch43_812 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 1 42 degreeUnionState43_812 [42] = true := by + decide +kernel + +lemma degreeUnionBranch43_814 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 40 3 degreeUnionState43_814 [3] = true := by + decide +kernel + +lemma degreeUnionBranch43_815 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 39 4 degreeUnionState43_815 [4] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_816 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 38 5 degreeUnionState43_816 [5] = true := by + decide +kernel + +lemma degreeUnionBranch43_817 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 37 6 degreeUnionState43_817 [6] = true := by + decide +kernel + +lemma degreeUnionBranch43_818 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 36 7 degreeUnionState43_818 [7] = true := by + decide +kernel + +lemma degreeUnionBranch43_819 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 35 8 degreeUnionState43_819 [8] = true := by + decide +kernel + +lemma degreeUnionBranch43_820 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 34 9 degreeUnionState43_820 [9] = true := by + decide +kernel + +lemma degreeUnionBranch43_821 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 33 10 degreeUnionState43_821 [10] = true := by + decide +kernel + +lemma degreeUnionBranch43_822 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 32 11 degreeUnionState43_822 [11] = true := by + decide +kernel + +lemma degreeUnionBranch43_823 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 31 12 degreeUnionState43_823 [12] = true := by + decide +kernel + +lemma degreeUnionBranch43_824 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 30 13 degreeUnionState43_824 [13] = true := by + decide +kernel + +lemma degreeUnionBranch43_825 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 29 14 degreeUnionState43_825 [14] = true := by + decide +kernel + +lemma degreeUnionBranch43_826 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 28 15 degreeUnionState43_826 [15] = true := by + decide +kernel + +lemma degreeUnionBranch43_827 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 27 16 degreeUnionState43_827 [16] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_828 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 26 17 degreeUnionState43_828 [17] = true := by + decide +kernel + +lemma degreeUnionBranch43_829 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 25 18 degreeUnionState43_829 [18] = true := by + decide +kernel + +lemma degreeUnionBranch43_830 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 24 19 degreeUnionState43_830 [19] = true := by + decide +kernel + +lemma degreeUnionBranch43_831 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 23 20 degreeUnionState43_831 [20] = true := by + decide +kernel + +lemma degreeUnionBranch43_832 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 22 21 degreeUnionState43_832 [21] = true := by + decide +kernel + +lemma degreeUnionBranch43_833 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 21 22 degreeUnionState43_833 [22] = true := by + decide +kernel + +lemma degreeUnionBranch43_834 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 20 23 degreeUnionState43_834 [23] = true := by + decide +kernel + +lemma degreeUnionBranch43_835 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 19 24 degreeUnionState43_835 [24] = true := by + decide +kernel + +lemma degreeUnionBranch43_836 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 18 25 degreeUnionState43_836 [25] = true := by + decide +kernel + +lemma degreeUnionBranch43_837 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 17 26 degreeUnionState43_837 [26] = true := by + decide +kernel + +lemma degreeUnionBranch43_838 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 16 27 degreeUnionState43_838 [27] = true := by + decide +kernel + +lemma degreeUnionBranch43_839 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 15 28 degreeUnionState43_839 [28] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_840 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 14 29 degreeUnionState43_840 [29] = true := by + decide +kernel + +lemma degreeUnionBranch43_841 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 13 30 degreeUnionState43_841 [30] = true := by + decide +kernel + +lemma degreeUnionBranch43_842 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 12 31 degreeUnionState43_842 [31] = true := by + decide +kernel + +lemma degreeUnionBranch43_843 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 11 32 degreeUnionState43_843 [32] = true := by + decide +kernel + +lemma degreeUnionBranch43_844 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 10 33 degreeUnionState43_844 [33] = true := by + decide +kernel + +lemma degreeUnionBranch43_845 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 9 34 degreeUnionState43_845 [34] = true := by + decide +kernel + +lemma degreeUnionBranch43_846 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 8 35 degreeUnionState43_846 [35] = true := by + decide +kernel + +lemma degreeUnionBranch43_847 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 7 36 degreeUnionState43_847 [36] = true := by + decide +kernel + +lemma degreeUnionBranch43_848 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 6 37 degreeUnionState43_848 [37] = true := by + decide +kernel + +lemma degreeUnionBranch43_849 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 5 38 degreeUnionState43_849 [38] = true := by + decide +kernel + +lemma degreeUnionBranch43_850 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 4 39 degreeUnionState43_850 [39] = true := by + decide +kernel + +lemma degreeUnionBranch43_851 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 3 40 degreeUnionState43_851 [40] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_852 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 2 41 degreeUnionState43_852 [41] = true := by + decide +kernel + +lemma degreeUnionBranch43_853 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 1 42 degreeUnionState43_853 [42] = true := by + decide +kernel + +lemma degreeUnionBranch43_855 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 40 3 degreeUnionState43_855 [3] = true := by + decide +kernel + +lemma degreeUnionBranch43_856 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 39 4 degreeUnionState43_856 [4] = true := by + decide +kernel + +lemma degreeUnionBranch43_857 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 38 5 degreeUnionState43_857 [5] = true := by + decide +kernel + +lemma degreeUnionBranch43_858 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 37 6 degreeUnionState43_858 [6] = true := by + decide +kernel + +lemma degreeUnionBranch43_859 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 36 7 degreeUnionState43_859 [7] = true := by + decide +kernel + +lemma degreeUnionBranch43_860 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 35 8 degreeUnionState43_860 [8] = true := by + decide +kernel + +lemma degreeUnionBranch43_861 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 34 9 degreeUnionState43_861 [9] = true := by + decide +kernel + +lemma degreeUnionBranch43_862 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 33 10 degreeUnionState43_862 [10] = true := by + decide +kernel + +lemma degreeUnionBranch43_863 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 32 11 degreeUnionState43_863 [11] = true := by + decide +kernel + +lemma degreeUnionBranch43_864 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 31 12 degreeUnionState43_864 [12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_865 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 30 13 degreeUnionState43_865 [13] = true := by + decide +kernel + +lemma degreeUnionBranch43_866 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 29 14 degreeUnionState43_866 [14] = true := by + decide +kernel + +lemma degreeUnionBranch43_867 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 28 15 degreeUnionState43_867 [15] = true := by + decide +kernel + +lemma degreeUnionBranch43_868 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 27 16 degreeUnionState43_868 [16] = true := by + decide +kernel + +lemma degreeUnionBranch43_869 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 26 17 degreeUnionState43_869 [17] = true := by + decide +kernel + +lemma degreeUnionBranch43_870 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 25 18 degreeUnionState43_870 [18] = true := by + decide +kernel + +lemma degreeUnionBranch43_871 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 24 19 degreeUnionState43_871 [19] = true := by + decide +kernel + +lemma degreeUnionBranch43_872 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 23 20 degreeUnionState43_872 [20] = true := by + decide +kernel + +lemma degreeUnionBranch43_873 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 22 21 degreeUnionState43_873 [21] = true := by + decide +kernel + +lemma degreeUnionBranch43_874 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 21 22 degreeUnionState43_874 [22] = true := by + decide +kernel + +lemma degreeUnionBranch43_875 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 20 23 degreeUnionState43_875 [23] = true := by + decide +kernel + +lemma degreeUnionBranch43_876 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 19 24 degreeUnionState43_876 [24] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_877 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 18 25 degreeUnionState43_877 [25] = true := by + decide +kernel + +lemma degreeUnionBranch43_878 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 17 26 degreeUnionState43_878 [26] = true := by + decide +kernel + +lemma degreeUnionBranch43_879 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 16 27 degreeUnionState43_879 [27] = true := by + decide +kernel + +lemma degreeUnionBranch43_880 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 15 28 degreeUnionState43_880 [28] = true := by + decide +kernel + +lemma degreeUnionBranch43_881 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 14 29 degreeUnionState43_881 [29] = true := by + decide +kernel + +lemma degreeUnionBranch43_882 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 13 30 degreeUnionState43_882 [30] = true := by + decide +kernel + +lemma degreeUnionBranch43_883 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 12 31 degreeUnionState43_883 [31] = true := by + decide +kernel + +lemma degreeUnionBranch43_884 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 11 32 degreeUnionState43_884 [32] = true := by + decide +kernel + +lemma degreeUnionBranch43_885 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 10 33 degreeUnionState43_885 [33] = true := by + decide +kernel + +lemma degreeUnionBranch43_886 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 9 34 degreeUnionState43_886 [34] = true := by + decide +kernel + +lemma degreeUnionBranch43_887 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 8 35 degreeUnionState43_887 [35] = true := by + decide +kernel + +lemma degreeUnionBranch43_888 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 7 36 degreeUnionState43_888 [36] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_889 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 6 37 degreeUnionState43_889 [37] = true := by + decide +kernel + +lemma degreeUnionBranch43_890 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 5 38 degreeUnionState43_890 [38] = true := by + decide +kernel + +lemma degreeUnionBranch43_891 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 4 39 degreeUnionState43_891 [39] = true := by + decide +kernel + +lemma degreeUnionBranch43_892 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 3 40 degreeUnionState43_892 [40] = true := by + decide +kernel + +lemma degreeUnionBranch43_893 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 2 41 degreeUnionState43_893 [41] = true := by + decide +kernel + +lemma degreeUnionBranch43_894 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 1 42 degreeUnionState43_894 [42] = true := by + decide +kernel + +lemma degreeUnionBranch43_895 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 18 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_896 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 19 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_897 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 20 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_898 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 21 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_899 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 22 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +lemma degreeUnionBranch43_900 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 23 43 42 degreeHalfRegions43 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves58.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves58.lean index ec676c5bd740c26d86b44a9e60585c372e51bacc..927e1591ef9190728f4d353a8775226d7e5710c2 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves58.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves58.lean @@ -1,413 +1,413 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans58 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates58 - -namespace OAI - -/-! Degree Leaves 58. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch58_0 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 0 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_1 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 1 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_2 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 2 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_3 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 3 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_4 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 4 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_5 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 5 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_6 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 6 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_7 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 7 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_8 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 8 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_9 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_10 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_11 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch58_13 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 53 5 degreeUnionState58_13 [5] = true := by - decide +kernel - -lemma degreeUnionBranch58_14 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 52 6 degreeUnionState58_14 [6] = true := by - decide +kernel - -lemma degreeUnionBranch58_15 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 51 7 degreeUnionState58_15 [7] = true := by - decide +kernel - -lemma degreeUnionBranch58_16 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 50 8 degreeUnionState58_16 [8] = true := by - decide +kernel - -lemma degreeUnionBranch58_17 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 49 9 degreeUnionState58_17 [9] = true := by - decide +kernel - -lemma degreeUnionBranch58_18 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 48 10 degreeUnionState58_18 [10] = true := by - decide +kernel - -lemma degreeUnionBranch58_19 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 47 11 degreeUnionState58_19 [11] = true := by - decide +kernel - -lemma degreeUnionBranch58_21 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 41 5 degreeUnionState58_21 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_22 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 40 6 degreeUnionState58_22 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_23 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 39 7 degreeUnionState58_23 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_24 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 38 8 degreeUnionState58_24 [8,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_26 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 33 4 degreeUnionState58_26 [4,9,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch58_27 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 32 5 degreeUnionState58_27 [5,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_28 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 31 6 degreeUnionState58_28 [6,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_29 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 30 7 degreeUnionState58_29 [7,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_30 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 29 8 degreeUnionState58_30 [8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_31 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 28 9 degreeUnionState58_31 [9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_32 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 36 10 degreeUnionState58_32 [10,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_33 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 35 11 degreeUnionState58_33 [11,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_34 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 34 12 degreeUnionState58_34 [12,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_36 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 40 5 degreeUnionState58_36 [5,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_37 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 39 6 degreeUnionState58_37 [6,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_38 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 38 7 degreeUnionState58_38 [7,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_40 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 33 4 degreeUnionState58_40 [4,8,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch58_41 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 32 5 degreeUnionState58_41 [5,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_42 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 31 6 degreeUnionState58_42 [6,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_43 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 30 7 degreeUnionState58_43 [7,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_44 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 29 8 degreeUnionState58_44 [8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_45 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 36 9 degreeUnionState58_45 [9,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_46 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 35 10 degreeUnionState58_46 [10,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_47 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 34 11 degreeUnionState58_47 [11,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_48 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 33 12 degreeUnionState58_48 [12,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_49 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 32 13 degreeUnionState58_49 [13,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_51 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 40 4 degreeUnionState58_51 [4,14] = true := by - decide +kernel - -lemma degreeUnionBranch58_52 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 39 5 degreeUnionState58_52 [5,14] = true := by - decide +kernel - -lemma degreeUnionBranch58_53 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 38 6 degreeUnionState58_53 [6,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch58_54 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 37 7 degreeUnionState58_54 [7,14] = true := by - decide +kernel - -lemma degreeUnionBranch58_55 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 36 8 degreeUnionState58_55 [8,14] = true := by - decide +kernel - -lemma degreeUnionBranch58_56 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 35 9 degreeUnionState58_56 [9,14] = true := by - decide +kernel - -lemma degreeUnionBranch58_57 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 34 10 degreeUnionState58_57 [10,14] = true := by - decide +kernel - -lemma degreeUnionBranch58_58 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 33 11 degreeUnionState58_58 [11,14] = true := by - decide +kernel - -lemma degreeUnionBranch58_59 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 32 12 degreeUnionState58_59 [12,14] = true := by - decide +kernel - -lemma degreeUnionBranch58_60 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 31 13 degreeUnionState58_60 [13,14] = true := by - decide +kernel - -lemma degreeUnionBranch58_61 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 30 14 degreeUnionState58_61 [14,14] = true := by - decide +kernel - -lemma degreeUnionBranch58_63 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 53 5 degreeUnionState58_63 [5] = true := by - decide +kernel - -lemma degreeUnionBranch58_64 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 52 6 degreeUnionState58_64 [6] = true := by - decide +kernel - -lemma degreeUnionBranch58_65 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 51 7 degreeUnionState58_65 [7] = true := by - decide +kernel - -lemma degreeUnionBranch58_66 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 50 8 degreeUnionState58_66 [8] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch58_67 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 49 9 degreeUnionState58_67 [9] = true := by - decide +kernel - -lemma degreeUnionBranch58_68 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 48 10 degreeUnionState58_68 [10] = true := by - decide +kernel - -lemma degreeUnionBranch58_69 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 47 11 degreeUnionState58_69 [11] = true := by - decide +kernel - -lemma degreeUnionBranch58_71 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 42 4 degreeUnionState58_71 [4,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_72 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 41 5 degreeUnionState58_72 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_73 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 40 6 degreeUnionState58_73 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_74 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 39 7 degreeUnionState58_74 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_75 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 38 8 degreeUnionState58_75 [8,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_76 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 37 9 degreeUnionState58_76 [9,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_77 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 36 10 degreeUnionState58_77 [10,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_78 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 35 11 degreeUnionState58_78 [11,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_79 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 34 12 degreeUnionState58_79 [12,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch58_81 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 41 4 degreeUnionState58_81 [4,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_82 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 40 5 degreeUnionState58_82 [5,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_83 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 39 6 degreeUnionState58_83 [6,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_84 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 38 7 degreeUnionState58_84 [7,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_85 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 37 8 degreeUnionState58_85 [8,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_86 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 36 9 degreeUnionState58_86 [9,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_87 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 35 10 degreeUnionState58_87 [10,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_88 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 34 11 degreeUnionState58_88 [11,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_89 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 33 12 degreeUnionState58_89 [12,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_90 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 32 13 degreeUnionState58_90 [13,13] = true := by - decide +kernel - -lemma degreeUnionBranch58_91 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 44 14 degreeUnionState58_91 [14] = true := by - decide +kernel - -lemma degreeUnionBranch58_93 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 53 5 degreeUnionState58_93 [5] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch58_94 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 52 6 degreeUnionState58_94 [6] = true := by - decide +kernel - -lemma degreeUnionBranch58_95 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 51 7 degreeUnionState58_95 [7] = true := by - decide +kernel - -lemma degreeUnionBranch58_96 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 50 8 degreeUnionState58_96 [8] = true := by - decide +kernel - -lemma degreeUnionBranch58_97 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 49 9 degreeUnionState58_97 [9] = true := by - decide +kernel - -lemma degreeUnionBranch58_98 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 48 10 degreeUnionState58_98 [10] = true := by - decide +kernel - -lemma degreeUnionBranch58_99 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 47 11 degreeUnionState58_99 [11] = true := by - decide +kernel - -lemma degreeUnionBranch58_101 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 42 4 degreeUnionState58_101 [4,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_102 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 41 5 degreeUnionState58_102 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_103 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 40 6 degreeUnionState58_103 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_104 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 39 7 degreeUnionState58_104 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_105 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 38 8 degreeUnionState58_105 [8,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_106 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 37 9 degreeUnionState58_106 [9,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch58_107 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 36 10 degreeUnionState58_107 [10,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_108 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 35 11 degreeUnionState58_108 [11,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_109 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 34 12 degreeUnionState58_109 [12,12] = true := by - decide +kernel - -lemma degreeUnionBranch58_110 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 45 13 degreeUnionState58_110 [13] = true := by - decide +kernel - -lemma degreeUnionBranch58_111 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 44 14 degreeUnionState58_111 [14] = true := by - decide +kernel - -lemma degreeUnionBranch58_112 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 15 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_113 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 16 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_114 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 17 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_115 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 18 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_116 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 19 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_117 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 20 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_118 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 21 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch58_119 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 22 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_120 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 23 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -lemma degreeUnionBranch58_121 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 24 58 14 degreeHalfRegions58 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans58 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates58 + +namespace OAI + +/-! Degree Leaves 58. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch58_0 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 0 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_1 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 1 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_2 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 2 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_3 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 3 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_4 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 4 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_5 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 5 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_6 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 6 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_7 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 7 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_8 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 8 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_9 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_10 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_11 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch58_13 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 53 5 degreeUnionState58_13 [5] = true := by + decide +kernel + +lemma degreeUnionBranch58_14 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 52 6 degreeUnionState58_14 [6] = true := by + decide +kernel + +lemma degreeUnionBranch58_15 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 51 7 degreeUnionState58_15 [7] = true := by + decide +kernel + +lemma degreeUnionBranch58_16 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 50 8 degreeUnionState58_16 [8] = true := by + decide +kernel + +lemma degreeUnionBranch58_17 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 49 9 degreeUnionState58_17 [9] = true := by + decide +kernel + +lemma degreeUnionBranch58_18 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 48 10 degreeUnionState58_18 [10] = true := by + decide +kernel + +lemma degreeUnionBranch58_19 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 47 11 degreeUnionState58_19 [11] = true := by + decide +kernel + +lemma degreeUnionBranch58_21 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 41 5 degreeUnionState58_21 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_22 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 40 6 degreeUnionState58_22 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_23 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 39 7 degreeUnionState58_23 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_24 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 38 8 degreeUnionState58_24 [8,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_26 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 33 4 degreeUnionState58_26 [4,9,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch58_27 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 32 5 degreeUnionState58_27 [5,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_28 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 31 6 degreeUnionState58_28 [6,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_29 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 30 7 degreeUnionState58_29 [7,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_30 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 29 8 degreeUnionState58_30 [8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_31 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 28 9 degreeUnionState58_31 [9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_32 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 36 10 degreeUnionState58_32 [10,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_33 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 35 11 degreeUnionState58_33 [11,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_34 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 34 12 degreeUnionState58_34 [12,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_36 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 40 5 degreeUnionState58_36 [5,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_37 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 39 6 degreeUnionState58_37 [6,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_38 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 38 7 degreeUnionState58_38 [7,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_40 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 33 4 degreeUnionState58_40 [4,8,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch58_41 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 32 5 degreeUnionState58_41 [5,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_42 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 31 6 degreeUnionState58_42 [6,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_43 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 30 7 degreeUnionState58_43 [7,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_44 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 9 29 8 degreeUnionState58_44 [8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_45 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 36 9 degreeUnionState58_45 [9,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_46 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 35 10 degreeUnionState58_46 [10,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_47 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 34 11 degreeUnionState58_47 [11,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_48 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 33 12 degreeUnionState58_48 [12,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_49 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 32 13 degreeUnionState58_49 [13,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_51 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 40 4 degreeUnionState58_51 [4,14] = true := by + decide +kernel + +lemma degreeUnionBranch58_52 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 39 5 degreeUnionState58_52 [5,14] = true := by + decide +kernel + +lemma degreeUnionBranch58_53 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 38 6 degreeUnionState58_53 [6,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch58_54 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 37 7 degreeUnionState58_54 [7,14] = true := by + decide +kernel + +lemma degreeUnionBranch58_55 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 36 8 degreeUnionState58_55 [8,14] = true := by + decide +kernel + +lemma degreeUnionBranch58_56 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 35 9 degreeUnionState58_56 [9,14] = true := by + decide +kernel + +lemma degreeUnionBranch58_57 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 34 10 degreeUnionState58_57 [10,14] = true := by + decide +kernel + +lemma degreeUnionBranch58_58 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 33 11 degreeUnionState58_58 [11,14] = true := by + decide +kernel + +lemma degreeUnionBranch58_59 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 32 12 degreeUnionState58_59 [12,14] = true := by + decide +kernel + +lemma degreeUnionBranch58_60 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 31 13 degreeUnionState58_60 [13,14] = true := by + decide +kernel + +lemma degreeUnionBranch58_61 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 30 14 degreeUnionState58_61 [14,14] = true := by + decide +kernel + +lemma degreeUnionBranch58_63 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 53 5 degreeUnionState58_63 [5] = true := by + decide +kernel + +lemma degreeUnionBranch58_64 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 52 6 degreeUnionState58_64 [6] = true := by + decide +kernel + +lemma degreeUnionBranch58_65 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 51 7 degreeUnionState58_65 [7] = true := by + decide +kernel + +lemma degreeUnionBranch58_66 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 50 8 degreeUnionState58_66 [8] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch58_67 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 49 9 degreeUnionState58_67 [9] = true := by + decide +kernel + +lemma degreeUnionBranch58_68 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 48 10 degreeUnionState58_68 [10] = true := by + decide +kernel + +lemma degreeUnionBranch58_69 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 47 11 degreeUnionState58_69 [11] = true := by + decide +kernel + +lemma degreeUnionBranch58_71 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 42 4 degreeUnionState58_71 [4,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_72 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 41 5 degreeUnionState58_72 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_73 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 40 6 degreeUnionState58_73 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_74 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 39 7 degreeUnionState58_74 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_75 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 38 8 degreeUnionState58_75 [8,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_76 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 37 9 degreeUnionState58_76 [9,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_77 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 36 10 degreeUnionState58_77 [10,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_78 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 35 11 degreeUnionState58_78 [11,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_79 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 34 12 degreeUnionState58_79 [12,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch58_81 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 41 4 degreeUnionState58_81 [4,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_82 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 40 5 degreeUnionState58_82 [5,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_83 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 39 6 degreeUnionState58_83 [6,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_84 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 38 7 degreeUnionState58_84 [7,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_85 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 37 8 degreeUnionState58_85 [8,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_86 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 36 9 degreeUnionState58_86 [9,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_87 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 35 10 degreeUnionState58_87 [10,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_88 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 34 11 degreeUnionState58_88 [11,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_89 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 33 12 degreeUnionState58_89 [12,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_90 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 32 13 degreeUnionState58_90 [13,13] = true := by + decide +kernel + +lemma degreeUnionBranch58_91 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 44 14 degreeUnionState58_91 [14] = true := by + decide +kernel + +lemma degreeUnionBranch58_93 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 53 5 degreeUnionState58_93 [5] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch58_94 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 52 6 degreeUnionState58_94 [6] = true := by + decide +kernel + +lemma degreeUnionBranch58_95 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 51 7 degreeUnionState58_95 [7] = true := by + decide +kernel + +lemma degreeUnionBranch58_96 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 50 8 degreeUnionState58_96 [8] = true := by + decide +kernel + +lemma degreeUnionBranch58_97 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 49 9 degreeUnionState58_97 [9] = true := by + decide +kernel + +lemma degreeUnionBranch58_98 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 48 10 degreeUnionState58_98 [10] = true := by + decide +kernel + +lemma degreeUnionBranch58_99 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 47 11 degreeUnionState58_99 [11] = true := by + decide +kernel + +lemma degreeUnionBranch58_101 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 42 4 degreeUnionState58_101 [4,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_102 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 41 5 degreeUnionState58_102 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_103 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 40 6 degreeUnionState58_103 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_104 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 39 7 degreeUnionState58_104 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_105 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 38 8 degreeUnionState58_105 [8,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_106 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 37 9 degreeUnionState58_106 [9,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch58_107 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 36 10 degreeUnionState58_107 [10,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_108 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 35 11 degreeUnionState58_108 [11,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_109 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 34 12 degreeUnionState58_109 [12,12] = true := by + decide +kernel + +lemma degreeUnionBranch58_110 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 45 13 degreeUnionState58_110 [13] = true := by + decide +kernel + +lemma degreeUnionBranch58_111 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 44 14 degreeUnionState58_111 [14] = true := by + decide +kernel + +lemma degreeUnionBranch58_112 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 15 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_113 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 16 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_114 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 17 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_115 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 18 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_116 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 19 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_117 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 20 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_118 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 21 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch58_119 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 22 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_120 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 23 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +lemma degreeUnionBranch58_121 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 24 58 14 degreeHalfRegions58 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves62.lean index 6ae9875e05c89f9222b775b130a8f15069d69fbc..316cb0284864007e2fb6a042543344e677b13154 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves62.lean @@ -1,4151 +1,4151 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans62 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates62 - -namespace OAI - -/-! Degree Leaves 62. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_0 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 0 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 1 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_2 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 2 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_3 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 3 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_4 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 4 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_5 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 5 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_6 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 6 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_7 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 7 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_8 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_9 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_10 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_12 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 56 6 degreeUnionState62_12 [6] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_13 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 55 7 degreeUnionState62_13 [7] = true := by - decide +kernel - -lemma degreeUnionBranch62_14 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 54 8 degreeUnionState62_14 [8] = true := by - decide +kernel - -lemma degreeUnionBranch62_15 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 53 9 degreeUnionState62_15 [9] = true := by - decide +kernel - -lemma degreeUnionBranch62_16 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 52 10 degreeUnionState62_16 [10] = true := by - decide +kernel - -lemma degreeUnionBranch62_17 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 51 11 degreeUnionState62_17 [11] = true := by - decide +kernel - -lemma degreeUnionBranch62_19 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 45 5 degreeUnionState62_19 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_20 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 44 6 degreeUnionState62_20 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_21 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 43 7 degreeUnionState62_21 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_22 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 42 8 degreeUnionState62_22 [8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_23 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 41 9 degreeUnionState62_23 [9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_24 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 40 10 degreeUnionState62_24 [10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_25 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 39 11 degreeUnionState62_25 [11,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_26 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 38 12 degreeUnionState62_26 [12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_28 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 44 5 degreeUnionState62_28 [5,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_29 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 43 6 degreeUnionState62_29 [6,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_30 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 42 7 degreeUnionState62_30 [7,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_31 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 41 8 degreeUnionState62_31 [8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_32 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 40 9 degreeUnionState62_32 [9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_33 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 39 10 degreeUnionState62_33 [10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_34 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 38 11 degreeUnionState62_34 [11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_35 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 37 12 degreeUnionState62_35 [12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_36 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 13 degreeUnionState62_36 [13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_38 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 43 5 degreeUnionState62_38 [5,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_39 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 42 6 degreeUnionState62_39 [6,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_40 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 41 7 degreeUnionState62_40 [7,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_41 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 40 8 degreeUnionState62_41 [8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_42 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 39 9 degreeUnionState62_42 [9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_43 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 38 10 degreeUnionState62_43 [10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_44 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 37 11 degreeUnionState62_44 [11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_45 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 12 degreeUnionState62_45 [12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_46 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 13 degreeUnionState62_46 [13,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_47 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 14 degreeUnionState62_47 [14,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_48 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 47 15 degreeUnionState62_48 [15] = true := by - decide +kernel - -lemma degreeUnionBranch62_49 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 46 16 degreeUnionState62_49 [16] = true := by - decide +kernel - -lemma degreeUnionBranch62_50 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 45 17 degreeUnionState62_50 [17] = true := by - decide +kernel - -lemma degreeUnionBranch62_51 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 44 18 degreeUnionState62_51 [18] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_52 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 43 19 degreeUnionState62_52 [19] = true := by - decide +kernel - -lemma degreeUnionBranch62_53 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 42 20 degreeUnionState62_53 [20] = true := by - decide +kernel - -lemma degreeUnionBranch62_54 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 41 21 degreeUnionState62_54 [21] = true := by - decide +kernel - -lemma degreeUnionBranch62_55 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 40 22 degreeUnionState62_55 [22] = true := by - decide +kernel - -lemma degreeUnionBranch62_56 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 39 23 degreeUnionState62_56 [23] = true := by - decide +kernel - -lemma degreeUnionBranch62_57 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 24 degreeUnionState62_57 [24] = true := by - decide +kernel - -lemma degreeUnionBranch62_58 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 25 degreeUnionState62_58 [25] = true := by - decide +kernel - -lemma degreeUnionBranch62_59 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 26 degreeUnionState62_59 [26] = true := by - decide +kernel - -lemma degreeUnionBranch62_60 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 27 degreeUnionState62_60 [27] = true := by - decide +kernel - -lemma degreeUnionBranch62_61 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 28 degreeUnionState62_61 [28] = true := by - decide +kernel - -lemma degreeUnionBranch62_63 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 56 6 degreeUnionState62_63 [6] = true := by - decide +kernel - -lemma degreeUnionBranch62_64 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 55 7 degreeUnionState62_64 [7] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_65 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 54 8 degreeUnionState62_65 [8] = true := by - decide +kernel - -lemma degreeUnionBranch62_66 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 53 9 degreeUnionState62_66 [9] = true := by - decide +kernel - -lemma degreeUnionBranch62_68 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 47 5 degreeUnionState62_68 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_69 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 46 6 degreeUnionState62_69 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_70 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 45 7 degreeUnionState62_70 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_71 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 44 8 degreeUnionState62_71 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_72 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 43 9 degreeUnionState62_72 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_74 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 37 5 degreeUnionState62_74 [5,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_75 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 6 degreeUnionState62_75 [6,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_76 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 7 degreeUnionState62_76 [7,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_77 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 8 degreeUnionState62_77 [8,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_78 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 9 degreeUnionState62_78 [9,10,10] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_80 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_80 [4,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_81 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_81 [5,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_82 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_82 [6,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_83 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_83 [7,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_84 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 8 degreeUnionState62_84 [8,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_85 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 9 degreeUnionState62_85 [9,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_86 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 10 degreeUnionState62_86 [10,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_88 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 46 5 degreeUnionState62_88 [5,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_89 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 45 6 degreeUnionState62_89 [6,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_90 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 44 7 degreeUnionState62_90 [7,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_91 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 43 8 degreeUnionState62_91 [8,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_92 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 42 9 degreeUnionState62_92 [9,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_94 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 5 degreeUnionState62_94 [5,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_95 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 6 degreeUnionState62_95 [6,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_96 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 7 degreeUnionState62_96 [7,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_97 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 8 degreeUnionState62_97 [8,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_98 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 9 degreeUnionState62_98 [9,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_100 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_100 [4,10,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_101 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_101 [5,10,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_102 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_102 [6,10,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_103 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_103 [7,10,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_104 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 8 degreeUnionState62_104 [8,10,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_105 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 9 degreeUnionState62_105 [9,10,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_106 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 10 degreeUnionState62_106 [10,10,10,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_108 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 4 degreeUnionState62_108 [4,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_109 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 5 degreeUnionState62_109 [5,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_110 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 6 degreeUnionState62_110 [6,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_111 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 7 degreeUnionState62_111 [7,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_112 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 8 degreeUnionState62_112 [8,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_113 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 9 degreeUnionState62_113 [9,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_115 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_115 [4,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_116 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_116 [5,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_117 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_117 [6,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_118 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_118 [7,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_119 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_119 [8,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_120 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 9 degreeUnionState62_120 [9,10,11,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_121 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 10 degreeUnionState62_121 [10,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_123 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_123 [4,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_124 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_124 [5,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_125 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_125 [6,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_126 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_126 [7,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_127 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_127 [8,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_128 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 9 degreeUnionState62_128 [9,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_129 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 19 10 degreeUnionState62_129 [10,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_130 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 18 11 degreeUnionState62_130 [11,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_132 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 45 5 degreeUnionState62_132 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_133 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 44 6 degreeUnionState62_133 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_135 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 38 5 degreeUnionState62_135 [5,7,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_136 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 37 6 degreeUnionState62_136 [6,7,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_137 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 7 degreeUnionState62_137 [7,7,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_139 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 37 5 degreeUnionState62_139 [5,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_140 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 6 degreeUnionState62_140 [6,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_142 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 31 4 degreeUnionState62_142 [4,7,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_143 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 30 5 degreeUnionState62_143 [5,7,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_144 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 6 degreeUnionState62_144 [6,7,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_145 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 7 degreeUnionState62_145 [7,7,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_147 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 30 4 degreeUnionState62_147 [4,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_148 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 5 degreeUnionState62_148 [5,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_149 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 6 degreeUnionState62_149 [6,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_150 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 7 degreeUnionState62_150 [7,8,8,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_151 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 8 degreeUnionState62_151 [8,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_153 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 5 degreeUnionState62_153 [5,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_154 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 6 degreeUnionState62_154 [6,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_156 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 30 4 degreeUnionState62_156 [4,7,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_157 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 5 degreeUnionState62_157 [5,7,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_158 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 6 degreeUnionState62_158 [6,7,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_159 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 7 degreeUnionState62_159 [7,7,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_161 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 4 degreeUnionState62_161 [4,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_162 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 5 degreeUnionState62_162 [5,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_163 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 6 degreeUnionState62_163 [6,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_164 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 7 degreeUnionState62_164 [7,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_165 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 8 degreeUnionState62_165 [8,8,9,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_167 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_167 [4,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_168 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_168 [5,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_169 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_169 [6,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_170 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_170 [7,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_171 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 8 degreeUnionState62_171 [8,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_172 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 9 degreeUnionState62_172 [9,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_174 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 4 degreeUnionState62_174 [4,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_175 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 5 degreeUnionState62_175 [5,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_176 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 6 degreeUnionState62_176 [6,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_178 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 4 degreeUnionState62_178 [4,7,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_179 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 5 degreeUnionState62_179 [5,7,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_180 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 6 degreeUnionState62_180 [6,7,10,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_181 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 7 degreeUnionState62_181 [7,7,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_183 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_183 [4,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_184 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_184 [5,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_185 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_185 [6,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_186 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_186 [7,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_187 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 8 degreeUnionState62_187 [8,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_189 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_189 [4,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_190 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_190 [5,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_191 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_191 [6,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_192 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_192 [7,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_193 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 8 degreeUnionState62_193 [8,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_194 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 9 degreeUnionState62_194 [9,9,10,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_196 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_196 [4,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_197 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_197 [5,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_198 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_198 [6,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_199 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_199 [7,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_200 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_200 [8,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_201 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 9 degreeUnionState62_201 [9,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_202 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 10 degreeUnionState62_202 [10,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_204 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 4 degreeUnionState62_204 [4,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_205 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 5 degreeUnionState62_205 [5,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_206 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 6 degreeUnionState62_206 [6,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_208 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_208 [4,7,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_209 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_209 [5,7,11,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_210 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_210 [6,7,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_211 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_211 [7,7,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_213 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_213 [4,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_214 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_214 [5,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_215 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_215 [6,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_216 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_216 [7,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_217 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 8 degreeUnionState62_217 [8,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_219 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_219 [4,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_220 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_220 [5,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_221 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_221 [6,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_222 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_222 [7,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_223 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_223 [8,9,11,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_224 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 9 degreeUnionState62_224 [9,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_226 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_226 [4,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_227 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_227 [5,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_228 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_228 [6,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_229 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_229 [7,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_230 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_230 [8,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_231 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 9 degreeUnionState62_231 [9,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_232 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 19 10 degreeUnionState62_232 [10,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_233 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 11 degreeUnionState62_233 [11,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_235 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 4 degreeUnionState62_235 [4,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_236 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 5 degreeUnionState62_236 [5,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_237 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 6 degreeUnionState62_237 [6,12,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_239 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_239 [4,7,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_240 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_240 [5,7,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_241 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_241 [6,7,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_242 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_242 [7,7,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_244 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_244 [4,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_245 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_245 [5,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_246 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_246 [6,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_247 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_247 [7,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_248 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_248 [8,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_250 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_250 [4,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_251 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_251 [5,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_252 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_252 [6,9,12,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_253 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_253 [7,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_254 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_254 [8,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_255 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 9 degreeUnionState62_255 [9,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_256 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 10 degreeUnionState62_256 [10,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_257 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 11 degreeUnionState62_257 [11,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_258 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 12 degreeUnionState62_258 [12,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_260 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 44 5 degreeUnionState62_260 [5,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_261 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 43 6 degreeUnionState62_261 [6,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_263 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 37 5 degreeUnionState62_263 [5,7,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_264 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 6 degreeUnionState62_264 [6,7,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_266 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 31 4 degreeUnionState62_266 [4,7,7,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_267 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 30 5 degreeUnionState62_267 [5,7,7,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_268 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 6 degreeUnionState62_268 [6,7,7,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_269 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 7 degreeUnionState62_269 [7,7,7,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_271 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 5 degreeUnionState62_271 [5,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_272 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 6 degreeUnionState62_272 [6,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_274 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 30 4 degreeUnionState62_274 [4,7,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_275 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 5 degreeUnionState62_275 [5,7,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_276 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 6 degreeUnionState62_276 [6,7,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_277 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 7 degreeUnionState62_277 [7,7,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_279 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 4 degreeUnionState62_279 [4,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_280 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 5 degreeUnionState62_280 [5,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_281 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 6 degreeUnionState62_281 [6,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_282 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 7 degreeUnionState62_282 [7,8,8,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_283 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 8 degreeUnionState62_283 [8,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_285 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 4 degreeUnionState62_285 [4,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_286 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 5 degreeUnionState62_286 [5,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_287 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 6 degreeUnionState62_287 [6,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_289 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 4 degreeUnionState62_289 [4,7,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_290 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 5 degreeUnionState62_290 [5,7,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_291 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 6 degreeUnionState62_291 [6,7,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_292 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 7 degreeUnionState62_292 [7,7,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_294 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_294 [4,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_295 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_295 [5,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_296 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_296 [6,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_297 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_297 [7,8,9,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_298 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 8 degreeUnionState62_298 [8,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_300 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_300 [4,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_301 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_301 [5,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_302 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_302 [6,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_303 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_303 [7,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_304 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 8 degreeUnionState62_304 [8,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_305 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 9 degreeUnionState62_305 [9,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_307 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 4 degreeUnionState62_307 [4,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_308 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 5 degreeUnionState62_308 [5,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_309 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 6 degreeUnionState62_309 [6,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_311 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_311 [4,7,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_312 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_312 [5,7,10,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_313 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_313 [6,7,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_314 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_314 [7,7,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_316 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_316 [4,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_317 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_317 [5,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_318 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_318 [6,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_319 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_319 [7,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_320 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 8 degreeUnionState62_320 [8,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_322 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_322 [4,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_323 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_323 [5,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_324 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_324 [6,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_325 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_325 [7,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_326 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_326 [8,9,10,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_327 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 9 degreeUnionState62_327 [9,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_329 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_329 [4,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_330 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_330 [5,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_331 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_331 [6,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_332 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_332 [7,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_333 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_333 [8,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_334 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 9 degreeUnionState62_334 [9,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_335 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 19 10 degreeUnionState62_335 [10,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_337 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 4 degreeUnionState62_337 [4,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_338 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 5 degreeUnionState62_338 [5,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_339 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 6 degreeUnionState62_339 [6,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_341 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_341 [4,7,11,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_342 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_342 [5,7,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_343 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_343 [6,7,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_344 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_344 [7,7,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_346 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_346 [4,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_347 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_347 [5,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_348 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_348 [6,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_349 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_349 [7,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_350 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_350 [8,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_352 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_352 [4,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_353 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_353 [5,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_354 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_354 [6,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_355 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_355 [7,9,11,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_356 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_356 [8,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_357 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 9 degreeUnionState62_357 [9,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_358 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 10 degreeUnionState62_358 [10,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_359 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 11 degreeUnionState62_359 [11,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_361 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 4 degreeUnionState62_361 [4,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_362 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 5 degreeUnionState62_362 [5,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_363 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 6 degreeUnionState62_363 [6,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_365 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_365 [4,7,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_366 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_366 [5,7,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_367 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_367 [6,7,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_368 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_368 [7,7,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_370 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_370 [4,8,12,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_371 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_371 [5,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_372 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_372 [6,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_373 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_373 [7,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_374 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_374 [8,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_375 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 9 degreeUnionState62_375 [9,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_376 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 10 degreeUnionState62_376 [10,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_377 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 11 degreeUnionState62_377 [11,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_378 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 12 degreeUnionState62_378 [12,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_380 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 4 degreeUnionState62_380 [4,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_381 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 5 degreeUnionState62_381 [5,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_382 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 6 degreeUnionState62_382 [6,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_384 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_384 [4,7,13,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_385 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_385 [5,7,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_386 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_386 [6,7,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_387 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_387 [7,7,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_388 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 8 degreeUnionState62_388 [8,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_389 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 9 degreeUnionState62_389 [9,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_390 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 10 degreeUnionState62_390 [10,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_391 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 11 degreeUnionState62_391 [11,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_392 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 12 degreeUnionState62_392 [12,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_393 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 13 degreeUnionState62_393 [13,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_395 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 43 5 degreeUnionState62_395 [5,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_396 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 42 6 degreeUnionState62_396 [6,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_398 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 5 degreeUnionState62_398 [5,7,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_399 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 6 degreeUnionState62_399 [6,7,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_401 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 30 4 degreeUnionState62_401 [4,7,7,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_402 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 5 degreeUnionState62_402 [5,7,7,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_403 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 6 degreeUnionState62_403 [6,7,7,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_404 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 7 degreeUnionState62_404 [7,7,7,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_406 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 4 degreeUnionState62_406 [4,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_407 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 5 degreeUnionState62_407 [5,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_408 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 6 degreeUnionState62_408 [6,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_410 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 4 degreeUnionState62_410 [4,7,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_411 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 5 degreeUnionState62_411 [5,7,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_412 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 6 degreeUnionState62_412 [6,7,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_413 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 7 degreeUnionState62_413 [7,7,8,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_415 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_415 [4,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_416 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_416 [5,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_417 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_417 [6,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_418 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_418 [7,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_419 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 8 degreeUnionState62_419 [8,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_421 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 4 degreeUnionState62_421 [4,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_422 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 5 degreeUnionState62_422 [5,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_423 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 6 degreeUnionState62_423 [6,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_425 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_425 [4,7,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_426 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_426 [5,7,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_427 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_427 [6,7,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_428 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_428 [7,7,9,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_430 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_430 [4,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_431 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_431 [5,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_432 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_432 [6,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_433 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_433 [7,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_434 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 8 degreeUnionState62_434 [8,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_436 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_436 [4,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_437 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_437 [5,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_438 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_438 [6,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_439 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_439 [7,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_440 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_440 [8,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_441 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 9 degreeUnionState62_441 [9,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_443 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 4 degreeUnionState62_443 [4,10,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_444 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 5 degreeUnionState62_444 [5,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_445 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 6 degreeUnionState62_445 [6,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_447 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_447 [4,7,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_448 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_448 [5,7,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_449 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_449 [6,7,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_450 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_450 [7,7,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_452 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_452 [4,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_453 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_453 [5,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_454 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_454 [6,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_455 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_455 [7,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_456 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_456 [8,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_458 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_458 [4,9,10,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_459 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_459 [5,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_460 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_460 [6,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_461 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_461 [7,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_462 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_462 [8,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_463 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 9 degreeUnionState62_463 [9,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_464 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 10 degreeUnionState62_464 [10,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_466 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 4 degreeUnionState62_466 [4,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_467 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 5 degreeUnionState62_467 [5,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_468 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 6 degreeUnionState62_468 [6,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_470 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_470 [4,7,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_471 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_471 [5,7,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_472 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_472 [6,7,11,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_473 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_473 [7,7,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_475 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_475 [4,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_476 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_476 [5,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_477 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_477 [6,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_478 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_478 [7,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_479 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_479 [8,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_480 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 9 degreeUnionState62_480 [9,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_481 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 10 degreeUnionState62_481 [10,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_482 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 11 degreeUnionState62_482 [11,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_484 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 4 degreeUnionState62_484 [4,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_485 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 5 degreeUnionState62_485 [5,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_486 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 6 degreeUnionState62_486 [6,12,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_488 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_488 [4,7,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_489 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_489 [5,7,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_490 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_490 [6,7,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_491 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_491 [7,7,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_492 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 8 degreeUnionState62_492 [8,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_493 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 9 degreeUnionState62_493 [9,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_494 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 10 degreeUnionState62_494 [10,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_495 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 11 degreeUnionState62_495 [11,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_496 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 12 degreeUnionState62_496 [12,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_497 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 13 degreeUnionState62_497 [13,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_498 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 14 degreeUnionState62_498 [14,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_499 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 47 15 degreeUnionState62_499 [15] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_500 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 46 16 degreeUnionState62_500 [16] = true := by - decide +kernel - -lemma degreeUnionBranch62_501 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 45 17 degreeUnionState62_501 [17] = true := by - decide +kernel - -lemma degreeUnionBranch62_502 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 44 18 degreeUnionState62_502 [18] = true := by - decide +kernel - -lemma degreeUnionBranch62_503 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 43 19 degreeUnionState62_503 [19] = true := by - decide +kernel - -lemma degreeUnionBranch62_504 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 42 20 degreeUnionState62_504 [20] = true := by - decide +kernel - -lemma degreeUnionBranch62_505 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 41 21 degreeUnionState62_505 [21] = true := by - decide +kernel - -lemma degreeUnionBranch62_506 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 40 22 degreeUnionState62_506 [22] = true := by - decide +kernel - -lemma degreeUnionBranch62_507 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 39 23 degreeUnionState62_507 [23] = true := by - decide +kernel - -lemma degreeUnionBranch62_508 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 38 24 degreeUnionState62_508 [24] = true := by - decide +kernel - -lemma degreeUnionBranch62_509 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 25 degreeUnionState62_509 [25] = true := by - decide +kernel - -lemma degreeUnionBranch62_510 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 26 degreeUnionState62_510 [26] = true := by - decide +kernel - -lemma degreeUnionBranch62_511 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 27 degreeUnionState62_511 [27] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_512 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 28 degreeUnionState62_512 [28] = true := by - decide +kernel - -lemma degreeUnionBranch62_514 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 57 5 degreeUnionState62_514 [5] = true := by - decide +kernel - -lemma degreeUnionBranch62_515 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 56 6 degreeUnionState62_515 [6] = true := by - decide +kernel - -lemma degreeUnionBranch62_516 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 55 7 degreeUnionState62_516 [7] = true := by - decide +kernel - -lemma degreeUnionBranch62_517 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 54 8 degreeUnionState62_517 [8] = true := by - decide +kernel - -lemma degreeUnionBranch62_518 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 53 9 degreeUnionState62_518 [9] = true := by - decide +kernel - -lemma degreeUnionBranch62_520 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 47 5 degreeUnionState62_520 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_521 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 46 6 degreeUnionState62_521 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_522 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 45 7 degreeUnionState62_522 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_523 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 44 8 degreeUnionState62_523 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_524 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 43 9 degreeUnionState62_524 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_526 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 4 degreeUnionState62_526 [4,10,10] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_527 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 5 degreeUnionState62_527 [5,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_528 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 6 degreeUnionState62_528 [6,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_529 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 7 degreeUnionState62_529 [7,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_530 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 8 degreeUnionState62_530 [8,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_531 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 9 degreeUnionState62_531 [9,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_533 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_533 [4,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_534 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_534 [5,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_535 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_535 [6,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_536 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_536 [7,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_537 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 8 degreeUnionState62_537 [8,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_538 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 9 degreeUnionState62_538 [9,10,10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_539 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 10 degreeUnionState62_539 [10,10,10,10] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_541 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 46 5 degreeUnionState62_541 [5,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_542 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 45 6 degreeUnionState62_542 [6,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_543 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 44 7 degreeUnionState62_543 [7,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_544 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 43 8 degreeUnionState62_544 [8,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_545 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 42 9 degreeUnionState62_545 [9,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_547 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 4 degreeUnionState62_547 [4,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_548 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 5 degreeUnionState62_548 [5,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_549 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 6 degreeUnionState62_549 [6,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_550 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 7 degreeUnionState62_550 [7,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_551 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 8 degreeUnionState62_551 [8,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_552 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 9 degreeUnionState62_552 [9,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_554 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_554 [4,10,10,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_555 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_555 [5,10,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_556 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_556 [6,10,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_557 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_557 [7,10,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_558 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 8 degreeUnionState62_558 [8,10,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_559 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 9 degreeUnionState62_559 [9,10,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_560 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 10 degreeUnionState62_560 [10,10,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_562 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 4 degreeUnionState62_562 [4,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_563 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 5 degreeUnionState62_563 [5,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_564 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 6 degreeUnionState62_564 [6,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_565 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 7 degreeUnionState62_565 [7,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_566 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 8 degreeUnionState62_566 [8,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_567 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 9 degreeUnionState62_567 [9,11,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_569 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_569 [3,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_570 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_570 [4,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_571 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_571 [5,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_572 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_572 [6,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_573 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_573 [7,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_574 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_574 [8,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_575 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 9 degreeUnionState62_575 [9,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_576 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 10 degreeUnionState62_576 [10,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_578 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_578 [3,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_579 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_579 [4,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_580 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_580 [5,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_581 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_581 [6,11,11,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_582 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_582 [7,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_583 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_583 [8,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_584 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 9 degreeUnionState62_584 [9,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_585 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 19 10 degreeUnionState62_585 [10,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_586 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 18 11 degreeUnionState62_586 [11,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_588 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 45 5 degreeUnionState62_588 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_589 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 44 6 degreeUnionState62_589 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_590 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 43 7 degreeUnionState62_590 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_592 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 4 degreeUnionState62_592 [4,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_593 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 5 degreeUnionState62_593 [5,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_594 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 6 degreeUnionState62_594 [6,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_595 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 7 degreeUnionState62_595 [7,8,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_597 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 4 degreeUnionState62_597 [4,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_598 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 5 degreeUnionState62_598 [5,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_599 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 6 degreeUnionState62_599 [6,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_600 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 7 degreeUnionState62_600 [7,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_601 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 8 degreeUnionState62_601 [8,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_603 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 4 degreeUnionState62_603 [4,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_604 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 5 degreeUnionState62_604 [5,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_605 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 6 degreeUnionState62_605 [6,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_606 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 7 degreeUnionState62_606 [7,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_608 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 4 degreeUnionState62_608 [4,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_609 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 5 degreeUnionState62_609 [5,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_610 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 6 degreeUnionState62_610 [6,8,9,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_611 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 7 degreeUnionState62_611 [7,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_612 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 8 degreeUnionState62_612 [8,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_614 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_614 [4,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_615 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_615 [5,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_616 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_616 [6,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_617 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_617 [7,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_618 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 8 degreeUnionState62_618 [8,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_619 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 9 degreeUnionState62_619 [9,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_621 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 4 degreeUnionState62_621 [4,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_622 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 5 degreeUnionState62_622 [5,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_623 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 6 degreeUnionState62_623 [6,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_624 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 7 degreeUnionState62_624 [7,10,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_626 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_626 [4,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_627 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_627 [5,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_628 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_628 [6,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_629 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_629 [7,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_630 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 8 degreeUnionState62_630 [8,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_632 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_632 [4,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_633 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_633 [5,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_634 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_634 [6,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_635 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_635 [7,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_636 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 8 degreeUnionState62_636 [8,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_637 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 9 degreeUnionState62_637 [9,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_639 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_639 [3,10,10,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_640 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_640 [4,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_641 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_641 [5,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_642 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_642 [6,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_643 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_643 [7,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_644 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_644 [8,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_645 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 9 degreeUnionState62_645 [9,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_646 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 10 degreeUnionState62_646 [10,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_648 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 4 degreeUnionState62_648 [4,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_649 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 5 degreeUnionState62_649 [5,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_650 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 6 degreeUnionState62_650 [6,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_652 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_652 [4,7,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_653 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_653 [5,7,11,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_654 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_654 [6,7,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_655 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_655 [7,7,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_657 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_657 [4,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_658 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_658 [5,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_659 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_659 [6,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_660 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_660 [7,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_661 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 8 degreeUnionState62_661 [8,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_663 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_663 [3,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_664 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_664 [4,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_665 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_665 [5,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_666 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_666 [6,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_667 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_667 [7,9,11,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_668 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_668 [8,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_669 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 9 degreeUnionState62_669 [9,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_671 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_671 [3,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_672 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_672 [4,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_673 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_673 [5,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_674 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_674 [6,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_675 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_675 [7,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_676 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_676 [8,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_677 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 9 degreeUnionState62_677 [9,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_678 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 19 10 degreeUnionState62_678 [10,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_679 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 11 degreeUnionState62_679 [11,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_681 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 4 degreeUnionState62_681 [4,12,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_682 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 5 degreeUnionState62_682 [5,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_683 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 6 degreeUnionState62_683 [6,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_685 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_685 [4,7,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_686 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_686 [5,7,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_687 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_687 [6,7,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_688 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_688 [7,7,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_690 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_690 [3,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_691 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_691 [4,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_692 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_692 [5,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_693 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_693 [6,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_694 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_694 [7,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_695 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_695 [8,8,12,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_697 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_697 [3,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_698 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_698 [4,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_699 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_699 [5,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_700 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_700 [6,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_701 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_701 [7,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_702 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_702 [8,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_703 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 9 degreeUnionState62_703 [9,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_704 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 10 degreeUnionState62_704 [10,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_705 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 11 degreeUnionState62_705 [11,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_706 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 12 degreeUnionState62_706 [12,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_708 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 44 5 degreeUnionState62_708 [5,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_709 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 43 6 degreeUnionState62_709 [6,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_711 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 4 degreeUnionState62_711 [4,7,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_712 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 5 degreeUnionState62_712 [5,7,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_713 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 6 degreeUnionState62_713 [6,7,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_714 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 7 degreeUnionState62_714 [7,7,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_716 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 4 degreeUnionState62_716 [4,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_717 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 5 degreeUnionState62_717 [5,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_718 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 6 degreeUnionState62_718 [6,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_719 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 7 degreeUnionState62_719 [7,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_721 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 4 degreeUnionState62_721 [4,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_722 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 5 degreeUnionState62_722 [5,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_723 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 6 degreeUnionState62_723 [6,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_724 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 7 degreeUnionState62_724 [7,8,8,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_725 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 8 degreeUnionState62_725 [8,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_727 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 4 degreeUnionState62_727 [4,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_728 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 5 degreeUnionState62_728 [5,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_729 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 6 degreeUnionState62_729 [6,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_730 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 7 degreeUnionState62_730 [7,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_732 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_732 [4,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_733 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_733 [5,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_734 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_734 [6,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_735 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_735 [7,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_736 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 8 degreeUnionState62_736 [8,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_738 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_738 [4,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_739 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_739 [5,9,9,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_740 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_740 [6,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_741 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_741 [7,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_742 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 8 degreeUnionState62_742 [8,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_743 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 9 degreeUnionState62_743 [9,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_745 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 4 degreeUnionState62_745 [4,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_746 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 5 degreeUnionState62_746 [5,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_747 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 6 degreeUnionState62_747 [6,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_749 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_749 [4,7,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_750 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_750 [5,7,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_751 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_751 [6,7,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_752 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_752 [7,7,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_754 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_754 [4,8,10,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_755 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_755 [5,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_756 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_756 [6,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_757 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_757 [7,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_758 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 8 degreeUnionState62_758 [8,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_760 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_760 [3,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_761 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_761 [4,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_762 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_762 [5,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_763 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_763 [6,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_764 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_764 [7,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_765 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_765 [8,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_766 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 9 degreeUnionState62_766 [9,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_768 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_768 [3,10,10,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_769 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_769 [4,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_770 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_770 [5,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_771 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_771 [6,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_772 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_772 [7,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_773 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_773 [8,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_774 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 9 degreeUnionState62_774 [9,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_775 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 19 10 degreeUnionState62_775 [10,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_777 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 4 degreeUnionState62_777 [4,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_778 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 5 degreeUnionState62_778 [5,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_779 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 6 degreeUnionState62_779 [6,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_781 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_781 [4,7,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_782 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_782 [5,7,11,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_783 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_783 [6,7,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_784 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_784 [7,7,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_786 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_786 [3,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_787 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_787 [4,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_788 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_788 [5,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_789 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_789 [6,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_790 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_790 [7,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_791 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_791 [8,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_793 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_793 [3,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_794 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_794 [4,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_795 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_795 [5,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_796 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_796 [6,9,11,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_797 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_797 [7,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_798 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_798 [8,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_799 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 9 degreeUnionState62_799 [9,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_800 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 10 degreeUnionState62_800 [10,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_801 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 11 degreeUnionState62_801 [11,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_803 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 4 degreeUnionState62_803 [4,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_804 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 5 degreeUnionState62_804 [5,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_805 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 6 degreeUnionState62_805 [6,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_807 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_807 [3,7,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_808 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_808 [4,7,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_809 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_809 [5,7,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_810 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_810 [6,7,12,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_811 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_811 [7,7,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_813 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_813 [3,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_814 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_814 [4,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_815 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_815 [5,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_816 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_816 [6,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_817 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_817 [7,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_818 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_818 [8,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_819 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 9 degreeUnionState62_819 [9,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_820 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 10 degreeUnionState62_820 [10,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_821 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 11 degreeUnionState62_821 [11,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_822 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 12 degreeUnionState62_822 [12,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_824 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 4 degreeUnionState62_824 [4,13,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_825 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 5 degreeUnionState62_825 [5,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_826 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 6 degreeUnionState62_826 [6,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_827 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 7 degreeUnionState62_827 [7,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_828 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 8 degreeUnionState62_828 [8,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_829 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 9 degreeUnionState62_829 [9,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_830 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 10 degreeUnionState62_830 [10,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_831 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 11 degreeUnionState62_831 [11,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_832 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 12 degreeUnionState62_832 [12,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_833 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 13 degreeUnionState62_833 [13,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_835 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 44 4 degreeUnionState62_835 [4,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_836 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 43 5 degreeUnionState62_836 [5,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_837 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 42 6 degreeUnionState62_837 [6,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_839 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 4 degreeUnionState62_839 [4,7,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_840 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 5 degreeUnionState62_840 [5,7,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_841 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 6 degreeUnionState62_841 [6,7,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_842 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 7 degreeUnionState62_842 [7,7,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_844 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 4 degreeUnionState62_844 [4,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_845 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 5 degreeUnionState62_845 [5,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_846 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 6 degreeUnionState62_846 [6,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_847 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 7 degreeUnionState62_847 [7,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_849 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_849 [4,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_850 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_850 [5,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_851 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_851 [6,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_852 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_852 [7,8,8,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_853 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 8 degreeUnionState62_853 [8,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_855 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 4 degreeUnionState62_855 [4,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_856 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 5 degreeUnionState62_856 [5,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_857 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 6 degreeUnionState62_857 [6,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_859 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_859 [4,7,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_860 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_860 [5,7,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_861 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_861 [6,7,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_862 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_862 [7,7,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_864 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_864 [4,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_865 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_865 [5,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_866 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_866 [6,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_867 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_867 [7,8,9,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_868 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 8 degreeUnionState62_868 [8,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_870 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_870 [3,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_871 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_871 [4,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_872 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_872 [5,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_873 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_873 [6,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_874 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_874 [7,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_875 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_875 [8,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_876 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 9 degreeUnionState62_876 [9,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_878 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 4 degreeUnionState62_878 [4,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_879 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 5 degreeUnionState62_879 [5,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_880 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 6 degreeUnionState62_880 [6,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_882 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_882 [4,7,10,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_883 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_883 [5,7,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_884 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_884 [6,7,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_885 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_885 [7,7,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_887 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_887 [3,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_888 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_888 [4,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_889 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_889 [5,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_890 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_890 [6,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_891 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_891 [7,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_892 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_892 [8,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_894 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_894 [3,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_895 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_895 [4,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_896 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_896 [5,9,10,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_897 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_897 [6,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_898 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_898 [7,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_899 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_899 [8,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_900 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 9 degreeUnionState62_900 [9,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_901 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 10 degreeUnionState62_901 [10,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_903 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 4 degreeUnionState62_903 [4,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_904 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 5 degreeUnionState62_904 [5,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_905 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 6 degreeUnionState62_905 [6,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_907 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_907 [3,7,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_908 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_908 [4,7,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_909 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_909 [5,7,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_910 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_910 [6,7,11,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_911 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_911 [7,7,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_913 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_913 [3,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_914 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_914 [4,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_915 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_915 [5,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_916 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_916 [6,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_917 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_917 [7,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_918 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_918 [8,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_919 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 9 degreeUnionState62_919 [9,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_920 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 10 degreeUnionState62_920 [10,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_921 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 11 degreeUnionState62_921 [11,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_923 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 4 degreeUnionState62_923 [4,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_924 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 5 degreeUnionState62_924 [5,12,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_925 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 6 degreeUnionState62_925 [6,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_926 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 7 degreeUnionState62_926 [7,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_927 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 8 degreeUnionState62_927 [8,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_928 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 9 degreeUnionState62_928 [9,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_929 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 10 degreeUnionState62_929 [10,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_930 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 11 degreeUnionState62_930 [11,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_931 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 12 degreeUnionState62_931 [12,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_932 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 13 degreeUnionState62_932 [13,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_933 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 14 degreeUnionState62_933 [14,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_934 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 47 15 degreeUnionState62_934 [15] = true := by - decide +kernel - -lemma degreeUnionBranch62_935 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 46 16 degreeUnionState62_935 [16] = true := by - decide +kernel - -lemma degreeUnionBranch62_936 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 45 17 degreeUnionState62_936 [17] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_937 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 44 18 degreeUnionState62_937 [18] = true := by - decide +kernel - -lemma degreeUnionBranch62_938 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 43 19 degreeUnionState62_938 [19] = true := by - decide +kernel - -lemma degreeUnionBranch62_939 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 42 20 degreeUnionState62_939 [20] = true := by - decide +kernel - -lemma degreeUnionBranch62_940 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 41 21 degreeUnionState62_940 [21] = true := by - decide +kernel - -lemma degreeUnionBranch62_941 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 40 22 degreeUnionState62_941 [22] = true := by - decide +kernel - -lemma degreeUnionBranch62_942 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 39 23 degreeUnionState62_942 [23] = true := by - decide +kernel - -lemma degreeUnionBranch62_943 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 38 24 degreeUnionState62_943 [24] = true := by - decide +kernel - -lemma degreeUnionBranch62_944 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 37 25 degreeUnionState62_944 [25] = true := by - decide +kernel - -lemma degreeUnionBranch62_945 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 36 26 degreeUnionState62_945 [26] = true := by - decide +kernel - -lemma degreeUnionBranch62_946 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 35 27 degreeUnionState62_946 [27] = true := by - decide +kernel - -lemma degreeUnionBranch62_947 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 34 28 degreeUnionState62_947 [28] = true := by - decide +kernel - -lemma degreeUnionBranch62_949 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 57 5 degreeUnionState62_949 [5] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_950 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 56 6 degreeUnionState62_950 [6] = true := by - decide +kernel - -lemma degreeUnionBranch62_951 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 55 7 degreeUnionState62_951 [7] = true := by - decide +kernel - -lemma degreeUnionBranch62_952 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 54 8 degreeUnionState62_952 [8] = true := by - decide +kernel - -lemma degreeUnionBranch62_953 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 53 9 degreeUnionState62_953 [9] = true := by - decide +kernel - -lemma degreeUnionBranch62_955 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 48 4 degreeUnionState62_955 [4,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_956 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 47 5 degreeUnionState62_956 [5,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_957 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 46 6 degreeUnionState62_957 [6,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_958 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 45 7 degreeUnionState62_958 [7,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_959 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 44 8 degreeUnionState62_959 [8,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_960 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 43 9 degreeUnionState62_960 [9,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_961 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 42 10 degreeUnionState62_961 [10,10] = true := by - decide +kernel - -lemma degreeUnionBranch62_963 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 47 4 degreeUnionState62_963 [4,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_964 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 46 5 degreeUnionState62_964 [5,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_965 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 45 6 degreeUnionState62_965 [6,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_966 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 44 7 degreeUnionState62_966 [7,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_967 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 43 8 degreeUnionState62_967 [8,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_968 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 42 9 degreeUnionState62_968 [9,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_970 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 4 degreeUnionState62_970 [4,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_971 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 5 degreeUnionState62_971 [5,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_972 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 6 degreeUnionState62_972 [6,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_973 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 7 degreeUnionState62_973 [7,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_974 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 8 degreeUnionState62_974 [8,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_975 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 9 degreeUnionState62_975 [9,10,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_976 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 10 degreeUnionState62_976 [10,10,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_978 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 4 degreeUnionState62_978 [4,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_979 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 5 degreeUnionState62_979 [5,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_980 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 6 degreeUnionState62_980 [6,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_981 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 7 degreeUnionState62_981 [7,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_982 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 8 degreeUnionState62_982 [8,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_983 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 9 degreeUnionState62_983 [9,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_985 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_985 [3,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_986 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_986 [4,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_987 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_987 [5,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_988 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_988 [6,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_989 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_989 [7,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_990 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_990 [8,10,11,11] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_991 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 9 degreeUnionState62_991 [9,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_992 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 10 degreeUnionState62_992 [10,10,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_994 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_994 [3,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_995 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_995 [4,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_996 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_996 [5,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_997 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_997 [6,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_998 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_998 [7,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_999 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_999 [8,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_1000 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 9 degreeUnionState62_1000 [9,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_1001 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 19 10 degreeUnionState62_1001 [10,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_1002 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 18 11 degreeUnionState62_1002 [11,11,11,11] = true := by - decide +kernel - -lemma degreeUnionBranch62_1004 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 46 4 degreeUnionState62_1004 [4,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1005 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 45 5 degreeUnionState62_1005 [5,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1006 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 44 6 degreeUnionState62_1006 [6,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1007 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 43 7 degreeUnionState62_1007 [7,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1009 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 38 4 degreeUnionState62_1009 [4,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1010 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 5 degreeUnionState62_1010 [5,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1011 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 6 degreeUnionState62_1011 [6,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1012 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 7 degreeUnionState62_1012 [7,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1014 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 4 degreeUnionState62_1014 [4,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1015 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 5 degreeUnionState62_1015 [5,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1016 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 6 degreeUnionState62_1016 [6,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1017 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 7 degreeUnionState62_1017 [7,8,8,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1018 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 8 degreeUnionState62_1018 [8,8,8,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1020 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 4 degreeUnionState62_1020 [4,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1021 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 5 degreeUnionState62_1021 [5,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1022 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 6 degreeUnionState62_1022 [6,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1023 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 7 degreeUnionState62_1023 [7,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1025 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 3 degreeUnionState62_1025 [3,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1026 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 4 degreeUnionState62_1026 [4,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1027 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 5 degreeUnionState62_1027 [5,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1028 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 6 degreeUnionState62_1028 [6,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1029 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 7 degreeUnionState62_1029 [7,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1030 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 8 degreeUnionState62_1030 [8,8,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1032 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 3 degreeUnionState62_1032 [3,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1033 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 4 degreeUnionState62_1033 [4,9,9,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1034 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 5 degreeUnionState62_1034 [5,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1035 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 6 degreeUnionState62_1035 [6,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1036 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 7 degreeUnionState62_1036 [7,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1037 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 8 degreeUnionState62_1037 [8,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1038 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 9 degreeUnionState62_1038 [9,9,9,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1040 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 4 degreeUnionState62_1040 [4,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1041 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 5 degreeUnionState62_1041 [5,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1042 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 6 degreeUnionState62_1042 [6,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1043 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 7 degreeUnionState62_1043 [7,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1045 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 3 degreeUnionState62_1045 [3,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1046 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 4 degreeUnionState62_1046 [4,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1047 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 5 degreeUnionState62_1047 [5,8,10,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1048 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 6 degreeUnionState62_1048 [6,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1049 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 7 degreeUnionState62_1049 [7,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1050 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 8 degreeUnionState62_1050 [8,8,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1052 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 3 degreeUnionState62_1052 [3,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1053 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 4 degreeUnionState62_1053 [4,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1054 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 5 degreeUnionState62_1054 [5,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1055 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 6 degreeUnionState62_1055 [6,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1056 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 7 degreeUnionState62_1056 [7,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1057 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 8 degreeUnionState62_1057 [8,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1058 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 9 degreeUnionState62_1058 [9,9,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1060 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1060 [3,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1061 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1061 [4,10,10,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1062 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1062 [5,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1063 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1063 [6,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1064 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1064 [7,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1065 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1065 [8,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1066 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 9 degreeUnionState62_1066 [9,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1067 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 10 degreeUnionState62_1067 [10,10,10,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1069 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 4 degreeUnionState62_1069 [4,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1070 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 5 degreeUnionState62_1070 [5,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1071 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 6 degreeUnionState62_1071 [6,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1072 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 7 degreeUnionState62_1072 [7,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1074 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 3 degreeUnionState62_1074 [3,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1075 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 4 degreeUnionState62_1075 [4,8,11,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1076 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 5 degreeUnionState62_1076 [5,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1077 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 6 degreeUnionState62_1077 [6,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1078 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 7 degreeUnionState62_1078 [7,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1079 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 8 degreeUnionState62_1079 [8,8,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1081 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1081 [3,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1082 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1082 [4,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1083 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1083 [5,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1084 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1084 [6,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1085 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1085 [7,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1086 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1086 [8,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1087 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 9 degreeUnionState62_1087 [9,9,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1089 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1089 [3,10,11,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1090 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1090 [4,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1091 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1091 [5,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1092 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1092 [6,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1093 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1093 [7,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1094 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1094 [8,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1095 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 9 degreeUnionState62_1095 [9,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1096 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 19 10 degreeUnionState62_1096 [10,10,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1097 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 11 degreeUnionState62_1097 [11,11,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1099 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 4 degreeUnionState62_1099 [4,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1100 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 5 degreeUnionState62_1100 [5,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1101 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 6 degreeUnionState62_1101 [6,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1102 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 7 degreeUnionState62_1102 [7,12,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1104 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1104 [3,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1105 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1105 [4,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1106 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1106 [5,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1107 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1107 [6,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1108 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1108 [7,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1109 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1109 [8,8,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1111 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1111 [3,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1112 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1112 [4,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1113 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1113 [5,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1114 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1114 [6,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1115 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1115 [7,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1116 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1116 [8,9,12,12] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1117 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 9 degreeUnionState62_1117 [9,9,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1118 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 10 degreeUnionState62_1118 [10,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1119 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 27 11 degreeUnionState62_1119 [11,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1120 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 26 12 degreeUnionState62_1120 [12,12,12] = true := by - decide +kernel - -lemma degreeUnionBranch62_1122 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 45 4 degreeUnionState62_1122 [4,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1123 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 44 5 degreeUnionState62_1123 [5,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1124 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 43 6 degreeUnionState62_1124 [6,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1125 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 42 7 degreeUnionState62_1125 [7,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1127 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 4 degreeUnionState62_1127 [4,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1128 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 5 degreeUnionState62_1128 [5,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1129 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 6 degreeUnionState62_1129 [6,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1130 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 7 degreeUnionState62_1130 [7,8,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1132 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 3 degreeUnionState62_1132 [3,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1133 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 4 degreeUnionState62_1133 [4,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1134 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 5 degreeUnionState62_1134 [5,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1135 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 6 degreeUnionState62_1135 [6,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1136 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 7 degreeUnionState62_1136 [7,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1137 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 8 degreeUnionState62_1137 [8,8,8,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1139 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 4 degreeUnionState62_1139 [4,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1140 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 5 degreeUnionState62_1140 [5,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1141 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 6 degreeUnionState62_1141 [6,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1142 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 7 degreeUnionState62_1142 [7,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1144 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 3 degreeUnionState62_1144 [3,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1145 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 4 degreeUnionState62_1145 [4,8,9,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1146 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 5 degreeUnionState62_1146 [5,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1147 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 6 degreeUnionState62_1147 [6,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1148 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 7 degreeUnionState62_1148 [7,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1149 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 8 degreeUnionState62_1149 [8,8,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1151 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 3 degreeUnionState62_1151 [3,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1152 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 4 degreeUnionState62_1152 [4,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1153 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 5 degreeUnionState62_1153 [5,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1154 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 6 degreeUnionState62_1154 [6,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1155 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 7 degreeUnionState62_1155 [7,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1156 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 8 degreeUnionState62_1156 [8,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1157 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 9 degreeUnionState62_1157 [9,9,9,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1159 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 4 degreeUnionState62_1159 [4,10,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1160 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 5 degreeUnionState62_1160 [5,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1161 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 6 degreeUnionState62_1161 [6,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1162 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 7 degreeUnionState62_1162 [7,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1164 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 3 degreeUnionState62_1164 [3,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1165 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 4 degreeUnionState62_1165 [4,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1166 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 5 degreeUnionState62_1166 [5,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1167 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 6 degreeUnionState62_1167 [6,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1168 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 7 degreeUnionState62_1168 [7,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1169 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 8 degreeUnionState62_1169 [8,8,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1171 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1171 [3,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1172 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1172 [4,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1173 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1173 [5,9,10,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1174 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1174 [6,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1175 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1175 [7,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1176 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1176 [8,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1177 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 9 degreeUnionState62_1177 [9,9,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1179 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1179 [3,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1180 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1180 [4,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1181 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1181 [5,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1182 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1182 [6,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1183 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1183 [7,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1184 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1184 [8,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1185 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 9 degreeUnionState62_1185 [9,10,10,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1186 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 19 10 degreeUnionState62_1186 [10,10,10,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1188 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 4 degreeUnionState62_1188 [4,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1189 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 5 degreeUnionState62_1189 [5,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1190 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 6 degreeUnionState62_1190 [6,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1191 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 7 degreeUnionState62_1191 [7,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1193 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1193 [3,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1194 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1194 [4,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1195 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1195 [5,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1196 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1196 [6,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1197 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1197 [7,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1198 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1198 [8,8,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1200 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1200 [3,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1201 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1201 [4,9,11,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1202 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1202 [5,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1203 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1203 [6,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1204 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1204 [7,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1205 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1205 [8,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1206 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 9 degreeUnionState62_1206 [9,9,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1207 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 10 degreeUnionState62_1207 [10,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1208 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 27 11 degreeUnionState62_1208 [11,11,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1210 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 4 degreeUnionState62_1210 [4,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1211 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 5 degreeUnionState62_1211 [5,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1212 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 6 degreeUnionState62_1212 [6,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1213 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 7 degreeUnionState62_1213 [7,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1215 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1215 [3,8,12,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1216 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1216 [4,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1217 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1217 [5,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1218 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1218 [6,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1219 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1219 [7,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1220 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1220 [8,8,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1221 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 9 degreeUnionState62_1221 [9,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1222 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 27 10 degreeUnionState62_1222 [10,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1223 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 26 11 degreeUnionState62_1223 [11,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1224 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 25 12 degreeUnionState62_1224 [12,12,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1226 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 3 degreeUnionState62_1226 [3,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1227 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 4 degreeUnionState62_1227 [4,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1228 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 5 degreeUnionState62_1228 [5,13,13] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1229 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 6 degreeUnionState62_1229 [6,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1230 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 7 degreeUnionState62_1230 [7,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1231 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 8 degreeUnionState62_1231 [8,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1232 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 27 9 degreeUnionState62_1232 [9,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1233 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 26 10 degreeUnionState62_1233 [10,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1234 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 25 11 degreeUnionState62_1234 [11,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1235 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 24 12 degreeUnionState62_1235 [12,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1236 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 23 13 degreeUnionState62_1236 [13,13,13] = true := by - decide +kernel - -lemma degreeUnionBranch62_1238 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 44 4 degreeUnionState62_1238 [4,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1239 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 43 5 degreeUnionState62_1239 [5,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1240 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 42 6 degreeUnionState62_1240 [6,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1241 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 41 7 degreeUnionState62_1241 [7,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1243 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 4 degreeUnionState62_1243 [4,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1244 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 5 degreeUnionState62_1244 [5,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1245 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 6 degreeUnionState62_1245 [6,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1246 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 7 degreeUnionState62_1246 [7,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1248 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 3 degreeUnionState62_1248 [3,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1249 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 4 degreeUnionState62_1249 [4,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1250 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 5 degreeUnionState62_1250 [5,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1251 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 6 degreeUnionState62_1251 [6,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1252 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 7 degreeUnionState62_1252 [7,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1253 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 8 degreeUnionState62_1253 [8,8,8,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1255 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 4 degreeUnionState62_1255 [4,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1256 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 5 degreeUnionState62_1256 [5,9,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1257 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 6 degreeUnionState62_1257 [6,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1258 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 7 degreeUnionState62_1258 [7,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1260 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 3 degreeUnionState62_1260 [3,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1261 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 4 degreeUnionState62_1261 [4,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1262 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 5 degreeUnionState62_1262 [5,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1263 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 6 degreeUnionState62_1263 [6,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1264 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 7 degreeUnionState62_1264 [7,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1265 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 8 degreeUnionState62_1265 [8,8,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1267 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1267 [3,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1268 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1268 [4,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1269 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1269 [5,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1270 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1270 [6,9,9,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1271 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1271 [7,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1272 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1272 [8,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1273 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 9 degreeUnionState62_1273 [9,9,9,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1275 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 4 degreeUnionState62_1275 [4,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1276 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 5 degreeUnionState62_1276 [5,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1277 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 6 degreeUnionState62_1277 [6,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1278 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 7 degreeUnionState62_1278 [7,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1280 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1280 [3,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1281 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1281 [4,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1282 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1282 [5,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1283 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1283 [6,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1284 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1284 [7,8,10,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1285 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1285 [8,8,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1287 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1287 [3,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1288 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1288 [4,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1289 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1289 [5,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1290 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1290 [6,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1291 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1291 [7,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1292 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1292 [8,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1293 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 9 degreeUnionState62_1293 [9,9,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1294 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 10 degreeUnionState62_1294 [10,10,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1296 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 4 degreeUnionState62_1296 [4,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1297 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 5 degreeUnionState62_1297 [5,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1298 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 6 degreeUnionState62_1298 [6,11,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1299 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 7 degreeUnionState62_1299 [7,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1301 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1301 [3,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1302 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1302 [4,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1303 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1303 [5,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1304 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1304 [6,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1305 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1305 [7,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1306 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1306 [8,8,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1307 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 9 degreeUnionState62_1307 [9,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1308 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 27 10 degreeUnionState62_1308 [10,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1309 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 26 11 degreeUnionState62_1309 [11,11,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1311 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 3 degreeUnionState62_1311 [3,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1312 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 4 degreeUnionState62_1312 [4,12,14] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1313 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 5 degreeUnionState62_1313 [5,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1314 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 6 degreeUnionState62_1314 [6,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1315 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 7 degreeUnionState62_1315 [7,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1316 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 8 degreeUnionState62_1316 [8,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1317 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 27 9 degreeUnionState62_1317 [9,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1318 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 26 10 degreeUnionState62_1318 [10,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1319 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 25 11 degreeUnionState62_1319 [11,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1320 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 24 12 degreeUnionState62_1320 [12,12,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1321 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 35 13 degreeUnionState62_1321 [13,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1322 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 34 14 degreeUnionState62_1322 [14,14] = true := by - decide +kernel - -lemma degreeUnionBranch62_1323 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 47 15 degreeUnionState62_1323 [15] = true := by - decide +kernel - -lemma degreeUnionBranch62_1324 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 46 16 degreeUnionState62_1324 [16] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1325 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 45 17 degreeUnionState62_1325 [17] = true := by - decide +kernel - -lemma degreeUnionBranch62_1326 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 44 18 degreeUnionState62_1326 [18] = true := by - decide +kernel - -lemma degreeUnionBranch62_1327 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 43 19 degreeUnionState62_1327 [19] = true := by - decide +kernel - -lemma degreeUnionBranch62_1328 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 42 20 degreeUnionState62_1328 [20] = true := by - decide +kernel - -lemma degreeUnionBranch62_1329 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 41 21 degreeUnionState62_1329 [21] = true := by - decide +kernel - -lemma degreeUnionBranch62_1330 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 40 22 degreeUnionState62_1330 [22] = true := by - decide +kernel - -lemma degreeUnionBranch62_1331 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 39 23 degreeUnionState62_1331 [23] = true := by - decide +kernel - -lemma degreeUnionBranch62_1332 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 38 24 degreeUnionState62_1332 [24] = true := by - decide +kernel - -lemma degreeUnionBranch62_1333 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 37 25 degreeUnionState62_1333 [25] = true := by - decide +kernel - -lemma degreeUnionBranch62_1334 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 36 26 degreeUnionState62_1334 [26] = true := by - decide +kernel - -lemma degreeUnionBranch62_1335 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 35 27 degreeUnionState62_1335 [27] = true := by - decide +kernel - -lemma degreeUnionBranch62_1336 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 34 28 degreeUnionState62_1336 [28] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1337 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 15 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1338 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 16 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1339 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 17 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1340 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 18 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1341 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 19 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1342 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 20 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1343 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 21 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1344 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 22 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1345 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 23 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1346 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 24 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1347 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 25 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1348 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 26 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_1349 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 27 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -lemma degreeUnionBranch62_1350 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 28 62 28 degreeHalfRegions62 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans62 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionStates62 + +namespace OAI + +/-! Degree Leaves 62. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_0 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 0 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 1 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_2 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 2 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_3 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 3 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_4 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 4 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_5 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 5 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_6 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 6 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_7 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 7 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_8 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_9 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_10 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_12 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 56 6 degreeUnionState62_12 [6] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_13 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 55 7 degreeUnionState62_13 [7] = true := by + decide +kernel + +lemma degreeUnionBranch62_14 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 54 8 degreeUnionState62_14 [8] = true := by + decide +kernel + +lemma degreeUnionBranch62_15 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 53 9 degreeUnionState62_15 [9] = true := by + decide +kernel + +lemma degreeUnionBranch62_16 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 52 10 degreeUnionState62_16 [10] = true := by + decide +kernel + +lemma degreeUnionBranch62_17 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 51 11 degreeUnionState62_17 [11] = true := by + decide +kernel + +lemma degreeUnionBranch62_19 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 45 5 degreeUnionState62_19 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_20 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 44 6 degreeUnionState62_20 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_21 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 43 7 degreeUnionState62_21 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_22 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 42 8 degreeUnionState62_22 [8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_23 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 41 9 degreeUnionState62_23 [9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_24 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 40 10 degreeUnionState62_24 [10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_25 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 39 11 degreeUnionState62_25 [11,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_26 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 38 12 degreeUnionState62_26 [12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_28 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 44 5 degreeUnionState62_28 [5,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_29 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 43 6 degreeUnionState62_29 [6,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_30 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 42 7 degreeUnionState62_30 [7,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_31 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 41 8 degreeUnionState62_31 [8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_32 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 40 9 degreeUnionState62_32 [9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_33 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 39 10 degreeUnionState62_33 [10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_34 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 38 11 degreeUnionState62_34 [11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_35 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 37 12 degreeUnionState62_35 [12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_36 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 13 degreeUnionState62_36 [13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_38 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 43 5 degreeUnionState62_38 [5,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_39 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 42 6 degreeUnionState62_39 [6,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_40 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 41 7 degreeUnionState62_40 [7,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_41 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 40 8 degreeUnionState62_41 [8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_42 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 39 9 degreeUnionState62_42 [9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_43 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 38 10 degreeUnionState62_43 [10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_44 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 37 11 degreeUnionState62_44 [11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_45 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 12 degreeUnionState62_45 [12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_46 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 13 degreeUnionState62_46 [13,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_47 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 14 degreeUnionState62_47 [14,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_48 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 47 15 degreeUnionState62_48 [15] = true := by + decide +kernel + +lemma degreeUnionBranch62_49 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 46 16 degreeUnionState62_49 [16] = true := by + decide +kernel + +lemma degreeUnionBranch62_50 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 45 17 degreeUnionState62_50 [17] = true := by + decide +kernel + +lemma degreeUnionBranch62_51 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 44 18 degreeUnionState62_51 [18] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_52 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 43 19 degreeUnionState62_52 [19] = true := by + decide +kernel + +lemma degreeUnionBranch62_53 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 42 20 degreeUnionState62_53 [20] = true := by + decide +kernel + +lemma degreeUnionBranch62_54 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 41 21 degreeUnionState62_54 [21] = true := by + decide +kernel + +lemma degreeUnionBranch62_55 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 40 22 degreeUnionState62_55 [22] = true := by + decide +kernel + +lemma degreeUnionBranch62_56 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 39 23 degreeUnionState62_56 [23] = true := by + decide +kernel + +lemma degreeUnionBranch62_57 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 24 degreeUnionState62_57 [24] = true := by + decide +kernel + +lemma degreeUnionBranch62_58 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 25 degreeUnionState62_58 [25] = true := by + decide +kernel + +lemma degreeUnionBranch62_59 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 26 degreeUnionState62_59 [26] = true := by + decide +kernel + +lemma degreeUnionBranch62_60 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 27 degreeUnionState62_60 [27] = true := by + decide +kernel + +lemma degreeUnionBranch62_61 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 28 degreeUnionState62_61 [28] = true := by + decide +kernel + +lemma degreeUnionBranch62_63 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 56 6 degreeUnionState62_63 [6] = true := by + decide +kernel + +lemma degreeUnionBranch62_64 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 55 7 degreeUnionState62_64 [7] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_65 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 54 8 degreeUnionState62_65 [8] = true := by + decide +kernel + +lemma degreeUnionBranch62_66 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 53 9 degreeUnionState62_66 [9] = true := by + decide +kernel + +lemma degreeUnionBranch62_68 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 47 5 degreeUnionState62_68 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_69 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 46 6 degreeUnionState62_69 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_70 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 45 7 degreeUnionState62_70 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_71 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 44 8 degreeUnionState62_71 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_72 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 43 9 degreeUnionState62_72 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_74 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 37 5 degreeUnionState62_74 [5,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_75 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 6 degreeUnionState62_75 [6,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_76 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 7 degreeUnionState62_76 [7,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_77 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 8 degreeUnionState62_77 [8,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_78 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 9 degreeUnionState62_78 [9,10,10] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_80 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_80 [4,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_81 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_81 [5,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_82 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_82 [6,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_83 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_83 [7,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_84 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 8 degreeUnionState62_84 [8,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_85 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 9 degreeUnionState62_85 [9,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_86 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 10 degreeUnionState62_86 [10,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_88 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 46 5 degreeUnionState62_88 [5,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_89 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 45 6 degreeUnionState62_89 [6,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_90 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 44 7 degreeUnionState62_90 [7,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_91 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 43 8 degreeUnionState62_91 [8,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_92 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 42 9 degreeUnionState62_92 [9,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_94 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 5 degreeUnionState62_94 [5,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_95 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 6 degreeUnionState62_95 [6,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_96 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 7 degreeUnionState62_96 [7,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_97 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 8 degreeUnionState62_97 [8,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_98 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 9 degreeUnionState62_98 [9,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_100 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_100 [4,10,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_101 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_101 [5,10,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_102 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_102 [6,10,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_103 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_103 [7,10,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_104 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 8 degreeUnionState62_104 [8,10,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_105 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 9 degreeUnionState62_105 [9,10,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_106 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 10 degreeUnionState62_106 [10,10,10,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_108 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 4 degreeUnionState62_108 [4,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_109 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 5 degreeUnionState62_109 [5,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_110 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 6 degreeUnionState62_110 [6,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_111 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 7 degreeUnionState62_111 [7,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_112 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 8 degreeUnionState62_112 [8,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_113 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 9 degreeUnionState62_113 [9,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_115 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_115 [4,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_116 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_116 [5,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_117 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_117 [6,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_118 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_118 [7,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_119 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_119 [8,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_120 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 9 degreeUnionState62_120 [9,10,11,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_121 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 10 degreeUnionState62_121 [10,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_123 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_123 [4,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_124 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_124 [5,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_125 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_125 [6,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_126 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_126 [7,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_127 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_127 [8,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_128 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 9 degreeUnionState62_128 [9,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_129 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 19 10 degreeUnionState62_129 [10,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_130 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 18 11 degreeUnionState62_130 [11,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_132 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 45 5 degreeUnionState62_132 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_133 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 44 6 degreeUnionState62_133 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_135 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 38 5 degreeUnionState62_135 [5,7,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_136 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 37 6 degreeUnionState62_136 [6,7,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_137 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 7 degreeUnionState62_137 [7,7,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_139 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 37 5 degreeUnionState62_139 [5,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_140 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 6 degreeUnionState62_140 [6,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_142 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 31 4 degreeUnionState62_142 [4,7,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_143 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 30 5 degreeUnionState62_143 [5,7,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_144 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 6 degreeUnionState62_144 [6,7,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_145 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 7 degreeUnionState62_145 [7,7,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_147 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 30 4 degreeUnionState62_147 [4,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_148 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 5 degreeUnionState62_148 [5,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_149 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 6 degreeUnionState62_149 [6,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_150 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 7 degreeUnionState62_150 [7,8,8,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_151 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 8 degreeUnionState62_151 [8,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_153 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 5 degreeUnionState62_153 [5,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_154 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 6 degreeUnionState62_154 [6,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_156 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 30 4 degreeUnionState62_156 [4,7,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_157 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 5 degreeUnionState62_157 [5,7,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_158 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 6 degreeUnionState62_158 [6,7,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_159 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 7 degreeUnionState62_159 [7,7,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_161 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 4 degreeUnionState62_161 [4,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_162 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 5 degreeUnionState62_162 [5,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_163 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 6 degreeUnionState62_163 [6,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_164 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 7 degreeUnionState62_164 [7,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_165 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 8 degreeUnionState62_165 [8,8,9,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_167 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_167 [4,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_168 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_168 [5,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_169 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_169 [6,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_170 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_170 [7,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_171 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 8 degreeUnionState62_171 [8,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_172 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 9 degreeUnionState62_172 [9,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_174 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 4 degreeUnionState62_174 [4,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_175 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 5 degreeUnionState62_175 [5,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_176 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 6 degreeUnionState62_176 [6,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_178 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 4 degreeUnionState62_178 [4,7,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_179 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 5 degreeUnionState62_179 [5,7,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_180 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 6 degreeUnionState62_180 [6,7,10,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_181 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 7 degreeUnionState62_181 [7,7,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_183 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_183 [4,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_184 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_184 [5,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_185 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_185 [6,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_186 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_186 [7,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_187 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 8 degreeUnionState62_187 [8,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_189 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_189 [4,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_190 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_190 [5,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_191 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_191 [6,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_192 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_192 [7,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_193 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 8 degreeUnionState62_193 [8,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_194 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 9 degreeUnionState62_194 [9,9,10,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_196 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_196 [4,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_197 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_197 [5,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_198 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_198 [6,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_199 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_199 [7,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_200 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_200 [8,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_201 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 9 degreeUnionState62_201 [9,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_202 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 10 degreeUnionState62_202 [10,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_204 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 4 degreeUnionState62_204 [4,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_205 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 5 degreeUnionState62_205 [5,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_206 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 6 degreeUnionState62_206 [6,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_208 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_208 [4,7,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_209 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_209 [5,7,11,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_210 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_210 [6,7,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_211 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_211 [7,7,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_213 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_213 [4,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_214 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_214 [5,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_215 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_215 [6,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_216 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_216 [7,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_217 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 8 degreeUnionState62_217 [8,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_219 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_219 [4,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_220 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_220 [5,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_221 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_221 [6,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_222 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_222 [7,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_223 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_223 [8,9,11,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_224 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 9 degreeUnionState62_224 [9,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_226 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_226 [4,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_227 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_227 [5,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_228 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_228 [6,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_229 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_229 [7,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_230 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_230 [8,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_231 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 9 degreeUnionState62_231 [9,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_232 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 19 10 degreeUnionState62_232 [10,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_233 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 11 degreeUnionState62_233 [11,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_235 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 4 degreeUnionState62_235 [4,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_236 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 5 degreeUnionState62_236 [5,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_237 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 6 degreeUnionState62_237 [6,12,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_239 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_239 [4,7,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_240 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_240 [5,7,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_241 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_241 [6,7,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_242 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_242 [7,7,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_244 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_244 [4,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_245 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_245 [5,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_246 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_246 [6,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_247 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_247 [7,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_248 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_248 [8,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_250 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_250 [4,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_251 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_251 [5,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_252 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_252 [6,9,12,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_253 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_253 [7,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_254 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_254 [8,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_255 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 9 degreeUnionState62_255 [9,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_256 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 10 degreeUnionState62_256 [10,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_257 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 11 degreeUnionState62_257 [11,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_258 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 12 degreeUnionState62_258 [12,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_260 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 44 5 degreeUnionState62_260 [5,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_261 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 43 6 degreeUnionState62_261 [6,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_263 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 37 5 degreeUnionState62_263 [5,7,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_264 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 6 degreeUnionState62_264 [6,7,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_266 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 31 4 degreeUnionState62_266 [4,7,7,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_267 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 30 5 degreeUnionState62_267 [5,7,7,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_268 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 6 degreeUnionState62_268 [6,7,7,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_269 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 7 degreeUnionState62_269 [7,7,7,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_271 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 5 degreeUnionState62_271 [5,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_272 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 6 degreeUnionState62_272 [6,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_274 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 30 4 degreeUnionState62_274 [4,7,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_275 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 5 degreeUnionState62_275 [5,7,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_276 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 6 degreeUnionState62_276 [6,7,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_277 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 7 degreeUnionState62_277 [7,7,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_279 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 4 degreeUnionState62_279 [4,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_280 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 5 degreeUnionState62_280 [5,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_281 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 6 degreeUnionState62_281 [6,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_282 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 7 degreeUnionState62_282 [7,8,8,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_283 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 8 degreeUnionState62_283 [8,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_285 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 4 degreeUnionState62_285 [4,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_286 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 5 degreeUnionState62_286 [5,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_287 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 6 degreeUnionState62_287 [6,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_289 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 4 degreeUnionState62_289 [4,7,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_290 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 5 degreeUnionState62_290 [5,7,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_291 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 6 degreeUnionState62_291 [6,7,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_292 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 7 degreeUnionState62_292 [7,7,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_294 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_294 [4,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_295 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_295 [5,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_296 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_296 [6,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_297 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_297 [7,8,9,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_298 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 8 degreeUnionState62_298 [8,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_300 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_300 [4,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_301 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_301 [5,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_302 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_302 [6,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_303 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_303 [7,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_304 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 8 degreeUnionState62_304 [8,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_305 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 9 degreeUnionState62_305 [9,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_307 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 4 degreeUnionState62_307 [4,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_308 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 5 degreeUnionState62_308 [5,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_309 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 6 degreeUnionState62_309 [6,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_311 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_311 [4,7,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_312 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_312 [5,7,10,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_313 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_313 [6,7,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_314 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_314 [7,7,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_316 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_316 [4,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_317 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_317 [5,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_318 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_318 [6,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_319 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_319 [7,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_320 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 8 degreeUnionState62_320 [8,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_322 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_322 [4,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_323 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_323 [5,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_324 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_324 [6,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_325 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_325 [7,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_326 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_326 [8,9,10,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_327 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 9 degreeUnionState62_327 [9,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_329 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_329 [4,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_330 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_330 [5,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_331 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_331 [6,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_332 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_332 [7,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_333 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_333 [8,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_334 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 9 degreeUnionState62_334 [9,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_335 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 19 10 degreeUnionState62_335 [10,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_337 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 4 degreeUnionState62_337 [4,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_338 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 5 degreeUnionState62_338 [5,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_339 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 6 degreeUnionState62_339 [6,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_341 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_341 [4,7,11,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_342 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_342 [5,7,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_343 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_343 [6,7,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_344 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_344 [7,7,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_346 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_346 [4,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_347 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_347 [5,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_348 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_348 [6,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_349 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_349 [7,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_350 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_350 [8,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_352 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_352 [4,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_353 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_353 [5,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_354 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_354 [6,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_355 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_355 [7,9,11,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_356 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_356 [8,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_357 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 9 degreeUnionState62_357 [9,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_358 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 10 degreeUnionState62_358 [10,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_359 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 11 degreeUnionState62_359 [11,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_361 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 4 degreeUnionState62_361 [4,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_362 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 5 degreeUnionState62_362 [5,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_363 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 6 degreeUnionState62_363 [6,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_365 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_365 [4,7,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_366 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_366 [5,7,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_367 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_367 [6,7,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_368 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_368 [7,7,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_370 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_370 [4,8,12,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_371 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_371 [5,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_372 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_372 [6,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_373 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_373 [7,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_374 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_374 [8,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_375 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 9 degreeUnionState62_375 [9,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_376 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 10 degreeUnionState62_376 [10,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_377 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 11 degreeUnionState62_377 [11,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_378 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 12 degreeUnionState62_378 [12,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_380 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 4 degreeUnionState62_380 [4,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_381 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 5 degreeUnionState62_381 [5,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_382 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 6 degreeUnionState62_382 [6,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_384 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_384 [4,7,13,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_385 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_385 [5,7,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_386 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_386 [6,7,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_387 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_387 [7,7,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_388 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 8 degreeUnionState62_388 [8,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_389 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 9 degreeUnionState62_389 [9,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_390 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 10 degreeUnionState62_390 [10,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_391 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 11 degreeUnionState62_391 [11,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_392 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 12 degreeUnionState62_392 [12,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_393 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 13 degreeUnionState62_393 [13,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_395 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 43 5 degreeUnionState62_395 [5,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_396 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 42 6 degreeUnionState62_396 [6,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_398 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 5 degreeUnionState62_398 [5,7,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_399 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 6 degreeUnionState62_399 [6,7,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_401 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 30 4 degreeUnionState62_401 [4,7,7,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_402 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 5 degreeUnionState62_402 [5,7,7,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_403 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 6 degreeUnionState62_403 [6,7,7,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_404 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 7 degreeUnionState62_404 [7,7,7,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_406 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 36 4 degreeUnionState62_406 [4,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_407 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 5 degreeUnionState62_407 [5,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_408 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 6 degreeUnionState62_408 [6,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_410 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 29 4 degreeUnionState62_410 [4,7,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_411 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 5 degreeUnionState62_411 [5,7,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_412 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 6 degreeUnionState62_412 [6,7,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_413 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 7 degreeUnionState62_413 [7,7,8,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_415 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_415 [4,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_416 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_416 [5,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_417 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_417 [6,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_418 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_418 [7,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_419 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 8 degreeUnionState62_419 [8,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_421 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 4 degreeUnionState62_421 [4,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_422 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 5 degreeUnionState62_422 [5,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_423 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 6 degreeUnionState62_423 [6,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_425 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 28 4 degreeUnionState62_425 [4,7,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_426 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 5 degreeUnionState62_426 [5,7,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_427 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 6 degreeUnionState62_427 [6,7,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_428 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 7 degreeUnionState62_428 [7,7,9,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_430 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_430 [4,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_431 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_431 [5,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_432 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_432 [6,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_433 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_433 [7,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_434 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 8 degreeUnionState62_434 [8,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_436 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_436 [4,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_437 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_437 [5,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_438 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_438 [6,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_439 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_439 [7,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_440 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_440 [8,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_441 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 9 degreeUnionState62_441 [9,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_443 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 4 degreeUnionState62_443 [4,10,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_444 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 5 degreeUnionState62_444 [5,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_445 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 6 degreeUnionState62_445 [6,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_447 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 27 4 degreeUnionState62_447 [4,7,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_448 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 5 degreeUnionState62_448 [5,7,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_449 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 6 degreeUnionState62_449 [6,7,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_450 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 7 degreeUnionState62_450 [7,7,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_452 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_452 [4,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_453 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_453 [5,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_454 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_454 [6,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_455 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_455 [7,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_456 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 8 degreeUnionState62_456 [8,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_458 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_458 [4,9,10,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_459 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_459 [5,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_460 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_460 [6,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_461 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_461 [7,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_462 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_462 [8,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_463 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 20 9 degreeUnionState62_463 [9,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_464 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 10 degreeUnionState62_464 [10,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_466 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 4 degreeUnionState62_466 [4,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_467 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 5 degreeUnionState62_467 [5,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_468 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 6 degreeUnionState62_468 [6,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_470 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 26 4 degreeUnionState62_470 [4,7,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_471 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 5 degreeUnionState62_471 [5,7,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_472 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 6 degreeUnionState62_472 [6,7,11,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_473 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 7 degreeUnionState62_473 [7,7,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_475 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_475 [4,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_476 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_476 [5,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_477 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_477 [6,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_478 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_478 [7,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_479 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 21 8 degreeUnionState62_479 [8,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_480 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 9 degreeUnionState62_480 [9,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_481 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 10 degreeUnionState62_481 [10,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_482 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 11 degreeUnionState62_482 [11,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_484 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 4 degreeUnionState62_484 [4,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_485 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 5 degreeUnionState62_485 [5,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_486 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 6 degreeUnionState62_486 [6,12,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_488 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 25 4 degreeUnionState62_488 [4,7,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_489 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 24 5 degreeUnionState62_489 [5,7,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_490 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 23 6 degreeUnionState62_490 [6,7,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_491 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 8 22 7 degreeUnionState62_491 [7,7,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_492 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 8 degreeUnionState62_492 [8,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_493 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 9 degreeUnionState62_493 [9,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_494 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 10 degreeUnionState62_494 [10,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_495 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 11 degreeUnionState62_495 [11,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_496 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 12 degreeUnionState62_496 [12,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_497 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 13 degreeUnionState62_497 [13,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_498 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 14 degreeUnionState62_498 [14,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_499 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 47 15 degreeUnionState62_499 [15] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_500 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 46 16 degreeUnionState62_500 [16] = true := by + decide +kernel + +lemma degreeUnionBranch62_501 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 45 17 degreeUnionState62_501 [17] = true := by + decide +kernel + +lemma degreeUnionBranch62_502 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 44 18 degreeUnionState62_502 [18] = true := by + decide +kernel + +lemma degreeUnionBranch62_503 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 43 19 degreeUnionState62_503 [19] = true := by + decide +kernel + +lemma degreeUnionBranch62_504 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 42 20 degreeUnionState62_504 [20] = true := by + decide +kernel + +lemma degreeUnionBranch62_505 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 41 21 degreeUnionState62_505 [21] = true := by + decide +kernel + +lemma degreeUnionBranch62_506 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 40 22 degreeUnionState62_506 [22] = true := by + decide +kernel + +lemma degreeUnionBranch62_507 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 39 23 degreeUnionState62_507 [23] = true := by + decide +kernel + +lemma degreeUnionBranch62_508 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 38 24 degreeUnionState62_508 [24] = true := by + decide +kernel + +lemma degreeUnionBranch62_509 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 25 degreeUnionState62_509 [25] = true := by + decide +kernel + +lemma degreeUnionBranch62_510 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 26 degreeUnionState62_510 [26] = true := by + decide +kernel + +lemma degreeUnionBranch62_511 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 27 degreeUnionState62_511 [27] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_512 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 28 degreeUnionState62_512 [28] = true := by + decide +kernel + +lemma degreeUnionBranch62_514 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 57 5 degreeUnionState62_514 [5] = true := by + decide +kernel + +lemma degreeUnionBranch62_515 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 56 6 degreeUnionState62_515 [6] = true := by + decide +kernel + +lemma degreeUnionBranch62_516 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 55 7 degreeUnionState62_516 [7] = true := by + decide +kernel + +lemma degreeUnionBranch62_517 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 54 8 degreeUnionState62_517 [8] = true := by + decide +kernel + +lemma degreeUnionBranch62_518 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 53 9 degreeUnionState62_518 [9] = true := by + decide +kernel + +lemma degreeUnionBranch62_520 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 47 5 degreeUnionState62_520 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_521 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 46 6 degreeUnionState62_521 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_522 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 45 7 degreeUnionState62_522 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_523 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 44 8 degreeUnionState62_523 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_524 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 43 9 degreeUnionState62_524 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_526 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 4 degreeUnionState62_526 [4,10,10] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_527 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 5 degreeUnionState62_527 [5,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_528 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 6 degreeUnionState62_528 [6,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_529 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 7 degreeUnionState62_529 [7,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_530 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 8 degreeUnionState62_530 [8,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_531 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 9 degreeUnionState62_531 [9,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_533 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_533 [4,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_534 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_534 [5,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_535 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_535 [6,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_536 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_536 [7,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_537 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 8 degreeUnionState62_537 [8,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_538 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 9 degreeUnionState62_538 [9,10,10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_539 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 10 degreeUnionState62_539 [10,10,10,10] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_541 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 46 5 degreeUnionState62_541 [5,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_542 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 45 6 degreeUnionState62_542 [6,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_543 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 44 7 degreeUnionState62_543 [7,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_544 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 43 8 degreeUnionState62_544 [8,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_545 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 42 9 degreeUnionState62_545 [9,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_547 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 4 degreeUnionState62_547 [4,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_548 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 5 degreeUnionState62_548 [5,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_549 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 6 degreeUnionState62_549 [6,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_550 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 7 degreeUnionState62_550 [7,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_551 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 8 degreeUnionState62_551 [8,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_552 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 9 degreeUnionState62_552 [9,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_554 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_554 [4,10,10,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_555 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_555 [5,10,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_556 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_556 [6,10,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_557 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_557 [7,10,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_558 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 8 degreeUnionState62_558 [8,10,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_559 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 9 degreeUnionState62_559 [9,10,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_560 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 10 degreeUnionState62_560 [10,10,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_562 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 4 degreeUnionState62_562 [4,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_563 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 5 degreeUnionState62_563 [5,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_564 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 6 degreeUnionState62_564 [6,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_565 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 7 degreeUnionState62_565 [7,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_566 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 8 degreeUnionState62_566 [8,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_567 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 9 degreeUnionState62_567 [9,11,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_569 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_569 [3,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_570 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_570 [4,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_571 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_571 [5,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_572 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_572 [6,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_573 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_573 [7,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_574 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_574 [8,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_575 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 9 degreeUnionState62_575 [9,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_576 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 10 degreeUnionState62_576 [10,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_578 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_578 [3,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_579 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_579 [4,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_580 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_580 [5,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_581 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_581 [6,11,11,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_582 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_582 [7,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_583 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_583 [8,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_584 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 9 degreeUnionState62_584 [9,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_585 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 19 10 degreeUnionState62_585 [10,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_586 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 18 11 degreeUnionState62_586 [11,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_588 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 45 5 degreeUnionState62_588 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_589 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 44 6 degreeUnionState62_589 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_590 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 43 7 degreeUnionState62_590 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_592 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 4 degreeUnionState62_592 [4,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_593 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 5 degreeUnionState62_593 [5,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_594 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 6 degreeUnionState62_594 [6,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_595 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 7 degreeUnionState62_595 [7,8,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_597 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 4 degreeUnionState62_597 [4,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_598 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 5 degreeUnionState62_598 [5,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_599 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 6 degreeUnionState62_599 [6,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_600 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 7 degreeUnionState62_600 [7,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_601 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 8 degreeUnionState62_601 [8,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_603 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 4 degreeUnionState62_603 [4,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_604 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 5 degreeUnionState62_604 [5,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_605 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 6 degreeUnionState62_605 [6,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_606 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 7 degreeUnionState62_606 [7,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_608 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 4 degreeUnionState62_608 [4,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_609 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 5 degreeUnionState62_609 [5,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_610 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 6 degreeUnionState62_610 [6,8,9,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_611 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 7 degreeUnionState62_611 [7,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_612 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 8 degreeUnionState62_612 [8,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_614 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_614 [4,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_615 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_615 [5,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_616 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_616 [6,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_617 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_617 [7,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_618 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 8 degreeUnionState62_618 [8,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_619 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 9 degreeUnionState62_619 [9,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_621 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 4 degreeUnionState62_621 [4,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_622 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 5 degreeUnionState62_622 [5,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_623 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 6 degreeUnionState62_623 [6,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_624 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 7 degreeUnionState62_624 [7,10,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_626 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_626 [4,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_627 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_627 [5,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_628 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_628 [6,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_629 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_629 [7,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_630 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 8 degreeUnionState62_630 [8,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_632 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_632 [4,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_633 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_633 [5,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_634 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_634 [6,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_635 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_635 [7,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_636 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 8 degreeUnionState62_636 [8,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_637 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 9 degreeUnionState62_637 [9,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_639 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_639 [3,10,10,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_640 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_640 [4,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_641 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_641 [5,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_642 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_642 [6,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_643 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_643 [7,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_644 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_644 [8,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_645 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 9 degreeUnionState62_645 [9,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_646 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 10 degreeUnionState62_646 [10,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_648 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 4 degreeUnionState62_648 [4,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_649 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 5 degreeUnionState62_649 [5,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_650 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 6 degreeUnionState62_650 [6,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_652 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_652 [4,7,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_653 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_653 [5,7,11,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_654 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_654 [6,7,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_655 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_655 [7,7,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_657 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_657 [4,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_658 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_658 [5,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_659 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_659 [6,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_660 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_660 [7,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_661 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 8 degreeUnionState62_661 [8,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_663 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_663 [3,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_664 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_664 [4,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_665 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_665 [5,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_666 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_666 [6,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_667 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_667 [7,9,11,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_668 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_668 [8,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_669 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 9 degreeUnionState62_669 [9,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_671 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_671 [3,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_672 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_672 [4,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_673 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_673 [5,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_674 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_674 [6,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_675 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_675 [7,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_676 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_676 [8,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_677 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 9 degreeUnionState62_677 [9,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_678 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 19 10 degreeUnionState62_678 [10,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_679 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 11 degreeUnionState62_679 [11,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_681 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 4 degreeUnionState62_681 [4,12,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_682 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 5 degreeUnionState62_682 [5,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_683 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 6 degreeUnionState62_683 [6,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_685 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_685 [4,7,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_686 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_686 [5,7,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_687 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_687 [6,7,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_688 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_688 [7,7,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_690 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_690 [3,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_691 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_691 [4,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_692 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_692 [5,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_693 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_693 [6,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_694 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_694 [7,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_695 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_695 [8,8,12,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_697 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_697 [3,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_698 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_698 [4,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_699 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_699 [5,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_700 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_700 [6,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_701 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_701 [7,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_702 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_702 [8,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_703 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 9 degreeUnionState62_703 [9,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_704 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 10 degreeUnionState62_704 [10,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_705 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 11 degreeUnionState62_705 [11,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_706 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 12 degreeUnionState62_706 [12,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_708 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 44 5 degreeUnionState62_708 [5,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_709 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 43 6 degreeUnionState62_709 [6,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_711 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 4 degreeUnionState62_711 [4,7,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_712 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 5 degreeUnionState62_712 [5,7,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_713 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 6 degreeUnionState62_713 [6,7,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_714 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 7 degreeUnionState62_714 [7,7,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_716 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 4 degreeUnionState62_716 [4,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_717 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 5 degreeUnionState62_717 [5,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_718 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 6 degreeUnionState62_718 [6,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_719 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 7 degreeUnionState62_719 [7,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_721 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 4 degreeUnionState62_721 [4,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_722 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 5 degreeUnionState62_722 [5,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_723 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 6 degreeUnionState62_723 [6,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_724 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 7 degreeUnionState62_724 [7,8,8,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_725 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 8 degreeUnionState62_725 [8,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_727 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 4 degreeUnionState62_727 [4,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_728 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 5 degreeUnionState62_728 [5,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_729 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 6 degreeUnionState62_729 [6,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_730 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 7 degreeUnionState62_730 [7,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_732 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_732 [4,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_733 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_733 [5,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_734 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_734 [6,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_735 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_735 [7,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_736 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 8 degreeUnionState62_736 [8,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_738 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_738 [4,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_739 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_739 [5,9,9,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_740 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_740 [6,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_741 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_741 [7,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_742 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 8 degreeUnionState62_742 [8,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_743 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 9 degreeUnionState62_743 [9,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_745 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 4 degreeUnionState62_745 [4,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_746 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 5 degreeUnionState62_746 [5,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_747 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 6 degreeUnionState62_747 [6,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_749 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_749 [4,7,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_750 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_750 [5,7,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_751 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_751 [6,7,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_752 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_752 [7,7,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_754 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_754 [4,8,10,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_755 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_755 [5,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_756 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_756 [6,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_757 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_757 [7,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_758 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 8 degreeUnionState62_758 [8,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_760 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_760 [3,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_761 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_761 [4,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_762 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_762 [5,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_763 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_763 [6,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_764 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_764 [7,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_765 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_765 [8,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_766 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 9 degreeUnionState62_766 [9,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_768 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_768 [3,10,10,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_769 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_769 [4,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_770 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_770 [5,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_771 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_771 [6,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_772 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_772 [7,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_773 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_773 [8,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_774 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 9 degreeUnionState62_774 [9,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_775 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 19 10 degreeUnionState62_775 [10,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_777 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 4 degreeUnionState62_777 [4,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_778 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 5 degreeUnionState62_778 [5,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_779 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 6 degreeUnionState62_779 [6,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_781 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_781 [4,7,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_782 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_782 [5,7,11,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_783 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_783 [6,7,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_784 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_784 [7,7,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_786 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_786 [3,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_787 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_787 [4,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_788 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_788 [5,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_789 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_789 [6,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_790 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_790 [7,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_791 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_791 [8,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_793 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_793 [3,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_794 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_794 [4,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_795 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_795 [5,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_796 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_796 [6,9,11,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_797 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_797 [7,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_798 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_798 [8,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_799 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 9 degreeUnionState62_799 [9,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_800 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 10 degreeUnionState62_800 [10,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_801 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 11 degreeUnionState62_801 [11,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_803 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 4 degreeUnionState62_803 [4,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_804 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 5 degreeUnionState62_804 [5,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_805 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 6 degreeUnionState62_805 [6,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_807 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_807 [3,7,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_808 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_808 [4,7,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_809 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_809 [5,7,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_810 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_810 [6,7,12,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_811 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_811 [7,7,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_813 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_813 [3,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_814 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_814 [4,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_815 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_815 [5,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_816 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_816 [6,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_817 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_817 [7,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_818 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_818 [8,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_819 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 9 degreeUnionState62_819 [9,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_820 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 10 degreeUnionState62_820 [10,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_821 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 11 degreeUnionState62_821 [11,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_822 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 12 degreeUnionState62_822 [12,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_824 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 4 degreeUnionState62_824 [4,13,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_825 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 5 degreeUnionState62_825 [5,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_826 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 6 degreeUnionState62_826 [6,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_827 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 7 degreeUnionState62_827 [7,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_828 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 8 degreeUnionState62_828 [8,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_829 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 9 degreeUnionState62_829 [9,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_830 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 10 degreeUnionState62_830 [10,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_831 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 11 degreeUnionState62_831 [11,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_832 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 12 degreeUnionState62_832 [12,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_833 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 13 degreeUnionState62_833 [13,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_835 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 44 4 degreeUnionState62_835 [4,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_836 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 43 5 degreeUnionState62_836 [5,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_837 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 42 6 degreeUnionState62_837 [6,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_839 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 4 degreeUnionState62_839 [4,7,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_840 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 5 degreeUnionState62_840 [5,7,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_841 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 6 degreeUnionState62_841 [6,7,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_842 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 7 degreeUnionState62_842 [7,7,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_844 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 4 degreeUnionState62_844 [4,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_845 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 5 degreeUnionState62_845 [5,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_846 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 6 degreeUnionState62_846 [6,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_847 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 7 degreeUnionState62_847 [7,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_849 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_849 [4,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_850 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_850 [5,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_851 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_851 [6,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_852 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_852 [7,8,8,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_853 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 8 degreeUnionState62_853 [8,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_855 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 35 4 degreeUnionState62_855 [4,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_856 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 5 degreeUnionState62_856 [5,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_857 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 6 degreeUnionState62_857 [6,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_859 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 28 4 degreeUnionState62_859 [4,7,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_860 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 5 degreeUnionState62_860 [5,7,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_861 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 6 degreeUnionState62_861 [6,7,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_862 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 7 degreeUnionState62_862 [7,7,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_864 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_864 [4,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_865 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_865 [5,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_866 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_866 [6,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_867 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_867 [7,8,9,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_868 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 8 degreeUnionState62_868 [8,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_870 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_870 [3,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_871 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_871 [4,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_872 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_872 [5,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_873 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_873 [6,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_874 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_874 [7,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_875 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_875 [8,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_876 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 9 degreeUnionState62_876 [9,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_878 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 4 degreeUnionState62_878 [4,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_879 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 5 degreeUnionState62_879 [5,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_880 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 6 degreeUnionState62_880 [6,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_882 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 4 degreeUnionState62_882 [4,7,10,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_883 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 5 degreeUnionState62_883 [5,7,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_884 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 6 degreeUnionState62_884 [6,7,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_885 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 7 degreeUnionState62_885 [7,7,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_887 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_887 [3,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_888 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_888 [4,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_889 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_889 [5,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_890 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_890 [6,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_891 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_891 [7,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_892 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 8 degreeUnionState62_892 [8,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_894 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_894 [3,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_895 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_895 [4,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_896 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_896 [5,9,10,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_897 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_897 [6,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_898 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_898 [7,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_899 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_899 [8,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_900 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 20 9 degreeUnionState62_900 [9,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_901 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 10 degreeUnionState62_901 [10,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_903 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 4 degreeUnionState62_903 [4,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_904 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 5 degreeUnionState62_904 [5,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_905 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 6 degreeUnionState62_905 [6,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_907 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 27 3 degreeUnionState62_907 [3,7,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_908 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 4 degreeUnionState62_908 [4,7,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_909 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 5 degreeUnionState62_909 [5,7,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_910 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 6 degreeUnionState62_910 [6,7,11,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_911 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 7 degreeUnionState62_911 [7,7,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_913 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 26 3 degreeUnionState62_913 [3,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_914 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 25 4 degreeUnionState62_914 [4,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_915 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 24 5 degreeUnionState62_915 [5,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_916 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 23 6 degreeUnionState62_916 [6,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_917 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 22 7 degreeUnionState62_917 [7,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_918 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 21 8 degreeUnionState62_918 [8,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_919 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 9 degreeUnionState62_919 [9,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_920 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 10 degreeUnionState62_920 [10,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_921 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 11 degreeUnionState62_921 [11,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_923 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 4 degreeUnionState62_923 [4,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_924 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 5 degreeUnionState62_924 [5,12,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_925 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 6 degreeUnionState62_925 [6,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_926 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 7 degreeUnionState62_926 [7,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_927 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 8 degreeUnionState62_927 [8,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_928 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 9 degreeUnionState62_928 [9,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_929 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 10 degreeUnionState62_929 [10,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_930 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 11 degreeUnionState62_930 [11,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_931 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 12 degreeUnionState62_931 [12,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_932 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 13 degreeUnionState62_932 [13,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_933 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 14 degreeUnionState62_933 [14,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_934 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 47 15 degreeUnionState62_934 [15] = true := by + decide +kernel + +lemma degreeUnionBranch62_935 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 46 16 degreeUnionState62_935 [16] = true := by + decide +kernel + +lemma degreeUnionBranch62_936 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 45 17 degreeUnionState62_936 [17] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_937 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 44 18 degreeUnionState62_937 [18] = true := by + decide +kernel + +lemma degreeUnionBranch62_938 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 43 19 degreeUnionState62_938 [19] = true := by + decide +kernel + +lemma degreeUnionBranch62_939 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 42 20 degreeUnionState62_939 [20] = true := by + decide +kernel + +lemma degreeUnionBranch62_940 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 41 21 degreeUnionState62_940 [21] = true := by + decide +kernel + +lemma degreeUnionBranch62_941 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 40 22 degreeUnionState62_941 [22] = true := by + decide +kernel + +lemma degreeUnionBranch62_942 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 39 23 degreeUnionState62_942 [23] = true := by + decide +kernel + +lemma degreeUnionBranch62_943 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 38 24 degreeUnionState62_943 [24] = true := by + decide +kernel + +lemma degreeUnionBranch62_944 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 37 25 degreeUnionState62_944 [25] = true := by + decide +kernel + +lemma degreeUnionBranch62_945 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 36 26 degreeUnionState62_945 [26] = true := by + decide +kernel + +lemma degreeUnionBranch62_946 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 35 27 degreeUnionState62_946 [27] = true := by + decide +kernel + +lemma degreeUnionBranch62_947 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 34 28 degreeUnionState62_947 [28] = true := by + decide +kernel + +lemma degreeUnionBranch62_949 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 57 5 degreeUnionState62_949 [5] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_950 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 56 6 degreeUnionState62_950 [6] = true := by + decide +kernel + +lemma degreeUnionBranch62_951 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 55 7 degreeUnionState62_951 [7] = true := by + decide +kernel + +lemma degreeUnionBranch62_952 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 54 8 degreeUnionState62_952 [8] = true := by + decide +kernel + +lemma degreeUnionBranch62_953 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 53 9 degreeUnionState62_953 [9] = true := by + decide +kernel + +lemma degreeUnionBranch62_955 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 48 4 degreeUnionState62_955 [4,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_956 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 47 5 degreeUnionState62_956 [5,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_957 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 46 6 degreeUnionState62_957 [6,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_958 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 45 7 degreeUnionState62_958 [7,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_959 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 44 8 degreeUnionState62_959 [8,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_960 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 43 9 degreeUnionState62_960 [9,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_961 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 42 10 degreeUnionState62_961 [10,10] = true := by + decide +kernel + +lemma degreeUnionBranch62_963 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 47 4 degreeUnionState62_963 [4,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_964 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 46 5 degreeUnionState62_964 [5,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_965 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 45 6 degreeUnionState62_965 [6,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_966 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 44 7 degreeUnionState62_966 [7,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_967 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 43 8 degreeUnionState62_967 [8,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_968 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 42 9 degreeUnionState62_968 [9,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_970 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 4 degreeUnionState62_970 [4,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_971 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 5 degreeUnionState62_971 [5,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_972 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 6 degreeUnionState62_972 [6,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_973 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 7 degreeUnionState62_973 [7,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_974 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 8 degreeUnionState62_974 [8,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_975 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 9 degreeUnionState62_975 [9,10,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_976 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 10 degreeUnionState62_976 [10,10,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_978 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 4 degreeUnionState62_978 [4,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_979 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 5 degreeUnionState62_979 [5,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_980 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 6 degreeUnionState62_980 [6,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_981 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 7 degreeUnionState62_981 [7,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_982 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 8 degreeUnionState62_982 [8,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_983 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 9 degreeUnionState62_983 [9,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_985 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_985 [3,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_986 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_986 [4,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_987 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_987 [5,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_988 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_988 [6,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_989 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_989 [7,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_990 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_990 [8,10,11,11] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_991 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 9 degreeUnionState62_991 [9,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_992 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 10 degreeUnionState62_992 [10,10,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_994 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_994 [3,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_995 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_995 [4,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_996 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_996 [5,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_997 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_997 [6,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_998 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_998 [7,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_999 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_999 [8,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_1000 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 9 degreeUnionState62_1000 [9,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_1001 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 19 10 degreeUnionState62_1001 [10,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_1002 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 18 11 degreeUnionState62_1002 [11,11,11,11] = true := by + decide +kernel + +lemma degreeUnionBranch62_1004 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 46 4 degreeUnionState62_1004 [4,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1005 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 45 5 degreeUnionState62_1005 [5,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1006 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 44 6 degreeUnionState62_1006 [6,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1007 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 43 7 degreeUnionState62_1007 [7,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1009 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 38 4 degreeUnionState62_1009 [4,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1010 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 5 degreeUnionState62_1010 [5,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1011 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 6 degreeUnionState62_1011 [6,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1012 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 7 degreeUnionState62_1012 [7,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1014 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 4 degreeUnionState62_1014 [4,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1015 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 5 degreeUnionState62_1015 [5,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1016 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 6 degreeUnionState62_1016 [6,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1017 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 7 degreeUnionState62_1017 [7,8,8,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1018 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 8 degreeUnionState62_1018 [8,8,8,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1020 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 4 degreeUnionState62_1020 [4,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1021 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 5 degreeUnionState62_1021 [5,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1022 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 6 degreeUnionState62_1022 [6,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1023 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 7 degreeUnionState62_1023 [7,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1025 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 3 degreeUnionState62_1025 [3,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1026 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 4 degreeUnionState62_1026 [4,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1027 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 5 degreeUnionState62_1027 [5,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1028 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 6 degreeUnionState62_1028 [6,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1029 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 7 degreeUnionState62_1029 [7,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1030 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 8 degreeUnionState62_1030 [8,8,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1032 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 3 degreeUnionState62_1032 [3,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1033 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 4 degreeUnionState62_1033 [4,9,9,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1034 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 5 degreeUnionState62_1034 [5,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1035 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 6 degreeUnionState62_1035 [6,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1036 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 7 degreeUnionState62_1036 [7,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1037 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 8 degreeUnionState62_1037 [8,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1038 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 9 degreeUnionState62_1038 [9,9,9,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1040 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 4 degreeUnionState62_1040 [4,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1041 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 5 degreeUnionState62_1041 [5,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1042 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 6 degreeUnionState62_1042 [6,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1043 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 7 degreeUnionState62_1043 [7,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1045 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 3 degreeUnionState62_1045 [3,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1046 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 4 degreeUnionState62_1046 [4,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1047 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 5 degreeUnionState62_1047 [5,8,10,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1048 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 6 degreeUnionState62_1048 [6,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1049 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 7 degreeUnionState62_1049 [7,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1050 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 8 degreeUnionState62_1050 [8,8,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1052 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 3 degreeUnionState62_1052 [3,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1053 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 4 degreeUnionState62_1053 [4,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1054 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 5 degreeUnionState62_1054 [5,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1055 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 6 degreeUnionState62_1055 [6,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1056 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 7 degreeUnionState62_1056 [7,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1057 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 8 degreeUnionState62_1057 [8,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1058 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 9 degreeUnionState62_1058 [9,9,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1060 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1060 [3,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1061 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1061 [4,10,10,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1062 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1062 [5,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1063 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1063 [6,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1064 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1064 [7,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1065 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1065 [8,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1066 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 9 degreeUnionState62_1066 [9,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1067 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 10 degreeUnionState62_1067 [10,10,10,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1069 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 4 degreeUnionState62_1069 [4,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1070 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 5 degreeUnionState62_1070 [5,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1071 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 6 degreeUnionState62_1071 [6,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1072 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 7 degreeUnionState62_1072 [7,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1074 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 3 degreeUnionState62_1074 [3,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1075 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 4 degreeUnionState62_1075 [4,8,11,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1076 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 5 degreeUnionState62_1076 [5,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1077 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 6 degreeUnionState62_1077 [6,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1078 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 7 degreeUnionState62_1078 [7,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1079 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 8 degreeUnionState62_1079 [8,8,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1081 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1081 [3,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1082 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1082 [4,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1083 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1083 [5,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1084 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1084 [6,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1085 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1085 [7,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1086 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1086 [8,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1087 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 9 degreeUnionState62_1087 [9,9,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1089 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1089 [3,10,11,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1090 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1090 [4,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1091 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1091 [5,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1092 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1092 [6,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1093 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1093 [7,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1094 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1094 [8,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1095 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 9 degreeUnionState62_1095 [9,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1096 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 19 10 degreeUnionState62_1096 [10,10,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1097 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 11 degreeUnionState62_1097 [11,11,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1099 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 4 degreeUnionState62_1099 [4,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1100 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 5 degreeUnionState62_1100 [5,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1101 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 6 degreeUnionState62_1101 [6,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1102 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 7 degreeUnionState62_1102 [7,12,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1104 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1104 [3,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1105 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1105 [4,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1106 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1106 [5,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1107 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1107 [6,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1108 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1108 [7,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1109 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1109 [8,8,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1111 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1111 [3,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1112 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1112 [4,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1113 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1113 [5,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1114 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1114 [6,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1115 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1115 [7,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1116 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1116 [8,9,12,12] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1117 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 9 degreeUnionState62_1117 [9,9,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1118 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 10 degreeUnionState62_1118 [10,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1119 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 27 11 degreeUnionState62_1119 [11,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1120 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 26 12 degreeUnionState62_1120 [12,12,12] = true := by + decide +kernel + +lemma degreeUnionBranch62_1122 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 45 4 degreeUnionState62_1122 [4,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1123 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 44 5 degreeUnionState62_1123 [5,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1124 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 43 6 degreeUnionState62_1124 [6,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1125 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 42 7 degreeUnionState62_1125 [7,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1127 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 4 degreeUnionState62_1127 [4,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1128 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 5 degreeUnionState62_1128 [5,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1129 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 6 degreeUnionState62_1129 [6,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1130 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 7 degreeUnionState62_1130 [7,8,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1132 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 3 degreeUnionState62_1132 [3,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1133 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 4 degreeUnionState62_1133 [4,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1134 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 5 degreeUnionState62_1134 [5,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1135 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 6 degreeUnionState62_1135 [6,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1136 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 7 degreeUnionState62_1136 [7,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1137 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 8 degreeUnionState62_1137 [8,8,8,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1139 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 4 degreeUnionState62_1139 [4,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1140 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 5 degreeUnionState62_1140 [5,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1141 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 6 degreeUnionState62_1141 [6,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1142 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 7 degreeUnionState62_1142 [7,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1144 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 3 degreeUnionState62_1144 [3,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1145 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 4 degreeUnionState62_1145 [4,8,9,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1146 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 5 degreeUnionState62_1146 [5,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1147 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 6 degreeUnionState62_1147 [6,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1148 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 7 degreeUnionState62_1148 [7,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1149 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 8 degreeUnionState62_1149 [8,8,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1151 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 3 degreeUnionState62_1151 [3,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1152 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 4 degreeUnionState62_1152 [4,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1153 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 5 degreeUnionState62_1153 [5,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1154 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 6 degreeUnionState62_1154 [6,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1155 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 7 degreeUnionState62_1155 [7,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1156 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 8 degreeUnionState62_1156 [8,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1157 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 9 degreeUnionState62_1157 [9,9,9,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1159 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 4 degreeUnionState62_1159 [4,10,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1160 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 5 degreeUnionState62_1160 [5,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1161 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 6 degreeUnionState62_1161 [6,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1162 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 7 degreeUnionState62_1162 [7,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1164 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 3 degreeUnionState62_1164 [3,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1165 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 4 degreeUnionState62_1165 [4,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1166 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 5 degreeUnionState62_1166 [5,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1167 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 6 degreeUnionState62_1167 [6,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1168 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 7 degreeUnionState62_1168 [7,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1169 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 8 degreeUnionState62_1169 [8,8,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1171 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1171 [3,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1172 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1172 [4,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1173 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1173 [5,9,10,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1174 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1174 [6,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1175 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1175 [7,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1176 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1176 [8,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1177 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 9 degreeUnionState62_1177 [9,9,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1179 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1179 [3,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1180 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1180 [4,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1181 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1181 [5,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1182 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1182 [6,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1183 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1183 [7,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1184 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1184 [8,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1185 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 9 degreeUnionState62_1185 [9,10,10,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1186 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 19 10 degreeUnionState62_1186 [10,10,10,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1188 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 4 degreeUnionState62_1188 [4,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1189 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 5 degreeUnionState62_1189 [5,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1190 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 6 degreeUnionState62_1190 [6,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1191 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 7 degreeUnionState62_1191 [7,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1193 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1193 [3,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1194 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1194 [4,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1195 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1195 [5,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1196 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1196 [6,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1197 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1197 [7,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1198 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1198 [8,8,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1200 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1200 [3,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1201 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1201 [4,9,11,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1202 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1202 [5,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1203 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1203 [6,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1204 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1204 [7,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1205 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1205 [8,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1206 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 9 degreeUnionState62_1206 [9,9,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1207 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 10 degreeUnionState62_1207 [10,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1208 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 27 11 degreeUnionState62_1208 [11,11,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1210 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 4 degreeUnionState62_1210 [4,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1211 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 5 degreeUnionState62_1211 [5,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1212 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 6 degreeUnionState62_1212 [6,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1213 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 7 degreeUnionState62_1213 [7,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1215 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1215 [3,8,12,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1216 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1216 [4,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1217 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1217 [5,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1218 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1218 [6,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1219 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1219 [7,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1220 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1220 [8,8,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1221 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 9 degreeUnionState62_1221 [9,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1222 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 27 10 degreeUnionState62_1222 [10,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1223 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 26 11 degreeUnionState62_1223 [11,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1224 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 25 12 degreeUnionState62_1224 [12,12,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1226 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 3 degreeUnionState62_1226 [3,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1227 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 4 degreeUnionState62_1227 [4,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1228 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 5 degreeUnionState62_1228 [5,13,13] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1229 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 6 degreeUnionState62_1229 [6,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1230 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 7 degreeUnionState62_1230 [7,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1231 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 8 degreeUnionState62_1231 [8,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1232 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 27 9 degreeUnionState62_1232 [9,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1233 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 26 10 degreeUnionState62_1233 [10,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1234 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 25 11 degreeUnionState62_1234 [11,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1235 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 24 12 degreeUnionState62_1235 [12,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1236 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 23 13 degreeUnionState62_1236 [13,13,13] = true := by + decide +kernel + +lemma degreeUnionBranch62_1238 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 44 4 degreeUnionState62_1238 [4,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1239 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 43 5 degreeUnionState62_1239 [5,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1240 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 42 6 degreeUnionState62_1240 [6,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1241 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 41 7 degreeUnionState62_1241 [7,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1243 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 4 degreeUnionState62_1243 [4,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1244 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 5 degreeUnionState62_1244 [5,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1245 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 6 degreeUnionState62_1245 [6,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1246 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 7 degreeUnionState62_1246 [7,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1248 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 3 degreeUnionState62_1248 [3,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1249 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 4 degreeUnionState62_1249 [4,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1250 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 5 degreeUnionState62_1250 [5,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1251 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 6 degreeUnionState62_1251 [6,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1252 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 7 degreeUnionState62_1252 [7,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1253 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 8 degreeUnionState62_1253 [8,8,8,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1255 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 35 4 degreeUnionState62_1255 [4,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1256 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 5 degreeUnionState62_1256 [5,9,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1257 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 6 degreeUnionState62_1257 [6,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1258 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 7 degreeUnionState62_1258 [7,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1260 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 28 3 degreeUnionState62_1260 [3,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1261 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 4 degreeUnionState62_1261 [4,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1262 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 5 degreeUnionState62_1262 [5,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1263 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 6 degreeUnionState62_1263 [6,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1264 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 7 degreeUnionState62_1264 [7,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1265 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 8 degreeUnionState62_1265 [8,8,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1267 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1267 [3,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1268 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1268 [4,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1269 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1269 [5,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1270 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1270 [6,9,9,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1271 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1271 [7,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1272 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1272 [8,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1273 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 9 degreeUnionState62_1273 [9,9,9,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1275 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 4 degreeUnionState62_1275 [4,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1276 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 5 degreeUnionState62_1276 [5,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1277 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 6 degreeUnionState62_1277 [6,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1278 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 7 degreeUnionState62_1278 [7,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1280 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 27 3 degreeUnionState62_1280 [3,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1281 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 4 degreeUnionState62_1281 [4,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1282 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 5 degreeUnionState62_1282 [5,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1283 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 6 degreeUnionState62_1283 [6,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1284 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 7 degreeUnionState62_1284 [7,8,10,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1285 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 8 degreeUnionState62_1285 [8,8,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1287 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1287 [3,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1288 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1288 [4,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1289 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1289 [5,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1290 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1290 [6,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1291 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1291 [7,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1292 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1292 [8,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1293 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 20 9 degreeUnionState62_1293 [9,9,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1294 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 10 degreeUnionState62_1294 [10,10,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1296 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 4 degreeUnionState62_1296 [4,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1297 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 5 degreeUnionState62_1297 [5,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1298 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 6 degreeUnionState62_1298 [6,11,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1299 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 7 degreeUnionState62_1299 [7,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1301 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 26 3 degreeUnionState62_1301 [3,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1302 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 25 4 degreeUnionState62_1302 [4,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1303 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 24 5 degreeUnionState62_1303 [5,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1304 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 23 6 degreeUnionState62_1304 [6,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1305 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 22 7 degreeUnionState62_1305 [7,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1306 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 21 8 degreeUnionState62_1306 [8,8,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1307 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 9 degreeUnionState62_1307 [9,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1308 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 27 10 degreeUnionState62_1308 [10,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1309 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 26 11 degreeUnionState62_1309 [11,11,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1311 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 3 degreeUnionState62_1311 [3,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1312 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 4 degreeUnionState62_1312 [4,12,14] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1313 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 5 degreeUnionState62_1313 [5,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1314 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 6 degreeUnionState62_1314 [6,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1315 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 7 degreeUnionState62_1315 [7,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1316 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 28 8 degreeUnionState62_1316 [8,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1317 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 27 9 degreeUnionState62_1317 [9,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1318 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 26 10 degreeUnionState62_1318 [10,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1319 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 25 11 degreeUnionState62_1319 [11,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1320 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 24 12 degreeUnionState62_1320 [12,12,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1321 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 35 13 degreeUnionState62_1321 [13,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1322 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 34 14 degreeUnionState62_1322 [14,14] = true := by + decide +kernel + +lemma degreeUnionBranch62_1323 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 47 15 degreeUnionState62_1323 [15] = true := by + decide +kernel + +lemma degreeUnionBranch62_1324 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 46 16 degreeUnionState62_1324 [16] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1325 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 45 17 degreeUnionState62_1325 [17] = true := by + decide +kernel + +lemma degreeUnionBranch62_1326 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 44 18 degreeUnionState62_1326 [18] = true := by + decide +kernel + +lemma degreeUnionBranch62_1327 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 43 19 degreeUnionState62_1327 [19] = true := by + decide +kernel + +lemma degreeUnionBranch62_1328 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 42 20 degreeUnionState62_1328 [20] = true := by + decide +kernel + +lemma degreeUnionBranch62_1329 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 41 21 degreeUnionState62_1329 [21] = true := by + decide +kernel + +lemma degreeUnionBranch62_1330 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 40 22 degreeUnionState62_1330 [22] = true := by + decide +kernel + +lemma degreeUnionBranch62_1331 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 39 23 degreeUnionState62_1331 [23] = true := by + decide +kernel + +lemma degreeUnionBranch62_1332 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 38 24 degreeUnionState62_1332 [24] = true := by + decide +kernel + +lemma degreeUnionBranch62_1333 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 37 25 degreeUnionState62_1333 [25] = true := by + decide +kernel + +lemma degreeUnionBranch62_1334 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 36 26 degreeUnionState62_1334 [26] = true := by + decide +kernel + +lemma degreeUnionBranch62_1335 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 35 27 degreeUnionState62_1335 [27] = true := by + decide +kernel + +lemma degreeUnionBranch62_1336 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 34 28 degreeUnionState62_1336 [28] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1337 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 15 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1338 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 16 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1339 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 17 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1340 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 18 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1341 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 19 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1342 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 20 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1343 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 21 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1344 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 22 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1345 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 23 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1346 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 24 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1347 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 25 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1348 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 26 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_1349 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 27 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +lemma degreeUnionBranch62_1350 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 28 62 28 degreeHalfRegions62 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves64.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves64.lean index a81871c1a6f83f6c82088b1fcfeebb56572991ce..835742a9c3c2c05394a3a467c10ccf1e713c48fc 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves64.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves64.lean @@ -1,125 +1,125 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans64 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData64 - -namespace OAI - -/-! Degree Leaves 64. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch64_0 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 0 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_1 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 1 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_2 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 2 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_3 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 3 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_4 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 4 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_5 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 5 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_6 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 6 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_7 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 7 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_8 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 8 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_9 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 9 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_10 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 10 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_11 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 11 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch64_12 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 12 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_13 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 13 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_14 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 14 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_15 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 15 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_16 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 16 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_17 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 17 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_18 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 18 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_19 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 19 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_20 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 20 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_21 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 21 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_22 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 22 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_23 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 23 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch64_24 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 24 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_25 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 25 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_26 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 26 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_27 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 27 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_28 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 28 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_29 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 29 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -lemma degreeUnionBranch64_30 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 30 64 30 degreeHalfRegions64 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans64 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData64 + +namespace OAI + +/-! Degree Leaves 64. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch64_0 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 0 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_1 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 1 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_2 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 2 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_3 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 3 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_4 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 4 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_5 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 5 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_6 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 6 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_7 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 7 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_8 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 8 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_9 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 9 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_10 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 10 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_11 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 11 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch64_12 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 12 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_13 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 13 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_14 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 14 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_15 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 15 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_16 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 16 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_17 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 17 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_18 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 18 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_19 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 19 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_20 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 20 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_21 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 21 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_22 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 22 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_23 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 23 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch64_24 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 24 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_25 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 25 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_26 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 26 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_27 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 27 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_28 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 28 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_29 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 29 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +lemma degreeUnionBranch64_30 : checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) 30 64 30 degreeHalfRegions64 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves89.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves89.lean index 3a7a37afef7ff24089d63728e9371988eca56b7f..e20e8fa417b3a027a0a869df675d6722a7912a48 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves89.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeLeaves89.lean @@ -1,82 +1,82 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans89 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData89 - -namespace OAI - -/-! Degree Leaves 89. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch89_0 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 0 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_1 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 1 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_2 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 2 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_3 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 3 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_4 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 4 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_5 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 5 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_6 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 6 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_7 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 7 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_8 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 8 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_9 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 9 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_10 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 10 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_11 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 11 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch89_12 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 12 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_13 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 13 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_14 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 14 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_15 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 15 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_16 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 16 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_17 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 17 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -lemma degreeUnionBranch89_18 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 18 89 18 degreeHalfRegions89 [] = true := by - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreePlans89 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData89 + +namespace OAI + +/-! Degree Leaves 89. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch89_0 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 0 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_1 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 1 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_2 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 2 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_3 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 3 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_4 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 4 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_5 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 5 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_6 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 6 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_7 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 7 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_8 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 8 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_9 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 9 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_10 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 10 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_11 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 11 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch89_12 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 12 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_13 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 13 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_14 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 14 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_15 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 15 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_16 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 16 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_17 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 17 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +lemma degreeUnionBranch89_18 : checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) 18 89 18 degreeHalfRegions89 [] = true := by + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans116.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans116.lean index a0d0864c1a4032883cadf63cc10be8f334f4d1a9..d6e2fcda22ee2a85d5345f2b13b5e1500431a1e5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans116.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans116.lean @@ -1,49 +1,49 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData116 - -namespace OAI - -/-! Degree Plans 116. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard116 : (candidate 12 9 1).card = 116 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan116_0 : PackingPlan := (.join (.twoPaths 20 [11,11,11,11]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 10 3 [12,11])))))) -def degreeRows116_0 : List ℕ := [12,11,11,11,11,11,5,5,5,4,4,4,4,4,3,3,3,3,2] - -lemma degreeCone116_0 (μ : YoungDiagram) (hμ : μ.card = 116) - (hd : RowsDom μ.rowLens degreeRows116_0) : SquareOccurs (candidate 12 9 1) μ := by - exact candidate_cone (by decide) degreeCard116 degreePlan116_0 degreeRows116_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan116_1 : PackingPlan := (.join (.twoPaths 20 [11,11,11,11]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 10 2)))))) -def degreeRows116_1 : List ℕ := [20,11,11,11,11,5,5,5,4,4,4,4,3,3,3,3,2,2,2,2,1] - -lemma degreeCone116_1 (μ : YoungDiagram) (hμ : μ.card = 116) - (hd : RowsDom μ.rowLens degreeRows116_1) : SquareOccurs (candidate 12 9 1) μ := by - exact candidate_cone (by decide) degreeCard116 degreePlan116_1 degreeRows116_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs116 : List (List ℕ) := [degreeRows116_1] - -lemma degreeCones116 : ∀ q ∈ degreeQs116, ∀ μ : YoungDiagram, μ.card = 116 → - RowsDom μ.rowLens q → SquareOccurs (candidate 12 9 1) μ := by - intro q hq - simp only [degreeQs116,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone116_1 - -abbrev degreeP116 := TreeResidual 12 19 degreeQs116 degreeTree116 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData116 + +namespace OAI + +/-! Degree Plans 116. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard116 : (candidate 12 9 1).card = 116 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan116_0 : PackingPlan := (.join (.twoPaths 20 [11,11,11,11]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 10 3 [12,11])))))) +def degreeRows116_0 : List ℕ := [12,11,11,11,11,11,5,5,5,4,4,4,4,4,3,3,3,3,2] + +lemma degreeCone116_0 (μ : YoungDiagram) (hμ : μ.card = 116) + (hd : RowsDom μ.rowLens degreeRows116_0) : SquareOccurs (candidate 12 9 1) μ := by + exact candidate_cone (by decide) degreeCard116 degreePlan116_0 degreeRows116_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan116_1 : PackingPlan := (.join (.twoPaths 20 [11,11,11,11]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 10 2)))))) +def degreeRows116_1 : List ℕ := [20,11,11,11,11,5,5,5,4,4,4,4,3,3,3,3,2,2,2,2,1] + +lemma degreeCone116_1 (μ : YoungDiagram) (hμ : μ.card = 116) + (hd : RowsDom μ.rowLens degreeRows116_1) : SquareOccurs (candidate 12 9 1) μ := by + exact candidate_cone (by decide) degreeCard116 degreePlan116_1 degreeRows116_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs116 : List (List ℕ) := [degreeRows116_1] + +lemma degreeCones116 : ∀ q ∈ degreeQs116, ∀ μ : YoungDiagram, μ.card = 116 → + RowsDom μ.rowLens q → SquareOccurs (candidate 12 9 1) μ := by + intro q hq + simp only [degreeQs116,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone116_1 + +abbrev degreeP116 := TreeResidual 12 19 degreeQs116 degreeTree116 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans118.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans118.lean index 4ead81e84d55c2be9b2ad5877fe5c46ff99c737f..cf6055d735f358c366ce39a2323358b325674a7a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans118.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans118.lean @@ -1,39 +1,39 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData118 - -namespace OAI - -/-! Degree Plans 118. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard118 : (candidate 12 10 0).card = 118 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan118_0 : PackingPlan := (.join (.neighbor 21 [11,11,11,10]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 11 1 [12,11])))))) -def degreeRows118_0 : List ℕ := [12,11,11,11,11,10,5,5,5,4,4,4,4,3,3,3,3,2,2,2,2,1] - -lemma degreeCone118_0 (μ : YoungDiagram) (hμ : μ.card = 118) - (hd : RowsDom μ.rowLens degreeRows118_0) : SquareOccurs (candidate 12 10 0) μ := by - exact candidate_cone (by decide) degreeCard118 degreePlan118_0 degreeRows118_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs118 : List (List ℕ) := [] - -lemma degreeCones118 : ∀ q ∈ degreeQs118, ∀ μ : YoungDiagram, μ.card = 118 → - RowsDom μ.rowLens q → SquareOccurs (candidate 12 10 0) μ := by - intro q hq - simp only [degreeQs118,List.not_mem_nil] at hq - -abbrev degreeP118 := TreeResidual 12 20 degreeQs118 degreeTree118 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData118 + +namespace OAI + +/-! Degree Plans 118. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard118 : (candidate 12 10 0).card = 118 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan118_0 : PackingPlan := (.join (.neighbor 21 [11,11,11,10]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 11 1 [12,11])))))) +def degreeRows118_0 : List ℕ := [12,11,11,11,11,10,5,5,5,4,4,4,4,3,3,3,3,2,2,2,2,1] + +lemma degreeCone118_0 (μ : YoungDiagram) (hμ : μ.card = 118) + (hd : RowsDom μ.rowLens degreeRows118_0) : SquareOccurs (candidate 12 10 0) μ := by + exact candidate_cone (by decide) degreeCard118 degreePlan118_0 degreeRows118_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs118 : List (List ℕ) := [] + +lemma degreeCones118 : ∀ q ∈ degreeQs118, ∀ μ : YoungDiagram, μ.card = 118 → + RowsDom μ.rowLens q → SquareOccurs (candidate 12 10 0) μ := by + intro q hq + simp only [degreeQs118,List.not_mem_nil] at hq + +abbrev degreeP118 := TreeResidual 12 20 degreeQs118 degreeTree118 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans14.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans14.lean index 8c82cdd83bc3f5d22af27115d5bf7aa5ea03c1e2..0d77222143caf4bfe6749fe64b96acfac282e53b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans14.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans14.lean @@ -1,39 +1,39 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData14 - -namespace OAI - -/-! Degree Plans 14. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard14 : (candidate 4 1 0).card = 14 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan14_0 : PackingPlan := (.join (.neighbor 4 [3,2,2,2]) (.twosOdd 2 1 [3,2])) -def degreeRows14_0 : List ℕ := [3,3,2,2,2,2] - -lemma degreeCone14_0 (μ : YoungDiagram) (hμ : μ.card = 14) - (hd : RowsDom μ.rowLens degreeRows14_0) : SquareOccurs (candidate 4 1 0) μ := by - exact candidate_cone (by decide) degreeCard14 degreePlan14_0 degreeRows14_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs14 : List (List ℕ) := [] - -lemma degreeCones14 : ∀ q ∈ degreeQs14, ∀ μ : YoungDiagram, μ.card = 14 → - RowsDom μ.rowLens q → SquareOccurs (candidate 4 1 0) μ := by - intro q hq - simp only [degreeQs14,List.not_mem_nil] at hq - -abbrev degreeP14 := TreeResidual 4 2 degreeQs14 degreeTree14 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData14 + +namespace OAI + +/-! Degree Plans 14. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard14 : (candidate 4 1 0).card = 14 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan14_0 : PackingPlan := (.join (.neighbor 4 [3,2,2,2]) (.twosOdd 2 1 [3,2])) +def degreeRows14_0 : List ℕ := [3,3,2,2,2,2] + +lemma degreeCone14_0 (μ : YoungDiagram) (hμ : μ.card = 14) + (hd : RowsDom μ.rowLens degreeRows14_0) : SquareOccurs (candidate 4 1 0) μ := by + exact candidate_cone (by decide) degreeCard14 degreePlan14_0 degreeRows14_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs14 : List (List ℕ) := [] + +lemma degreeCones14 : ∀ q ∈ degreeQs14, ∀ μ : YoungDiagram, μ.card = 14 → + RowsDom μ.rowLens q → SquareOccurs (candidate 4 1 0) μ := by + intro q hq + simp only [degreeQs14,List.not_mem_nil] at hq + +abbrev degreeP14 := TreeResidual 4 2 degreeQs14 degreeTree14 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans16.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans16.lean index bc6cebe1e6962cff3f0a0bedc3aab948b0895ea5..9dda47f68c8caead0805c471a5f6659d8d77d415 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans16.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans16.lean @@ -1,39 +1,39 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData16 - -namespace OAI - -/-! Degree Plans 16. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard16 : (candidate 4 1 1).card = 16 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan16_0 : PackingPlan := (.join (.twoPaths 4 [3,3,3,3]) (.repeated 2 2)) -def degreeRows16_0 : List ℕ := [4,3,3,3,3] - -lemma degreeCone16_0 (μ : YoungDiagram) (hμ : μ.card = 16) - (hd : RowsDom μ.rowLens degreeRows16_0) : SquareOccurs (candidate 4 1 1) μ := by - exact candidate_cone (by decide) degreeCard16 degreePlan16_0 degreeRows16_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs16 : List (List ℕ) := [] - -lemma degreeCones16 : ∀ q ∈ degreeQs16, ∀ μ : YoungDiagram, μ.card = 16 → - RowsDom μ.rowLens q → SquareOccurs (candidate 4 1 1) μ := by - intro q hq - simp only [degreeQs16, List.not_mem_nil] at hq - -abbrev degreeP16 := TreeResidual 4 3 degreeQs16 degreeTree16 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData16 + +namespace OAI + +/-! Degree Plans 16. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard16 : (candidate 4 1 1).card = 16 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan16_0 : PackingPlan := (.join (.twoPaths 4 [3,3,3,3]) (.repeated 2 2)) +def degreeRows16_0 : List ℕ := [4,3,3,3,3] + +lemma degreeCone16_0 (μ : YoungDiagram) (hμ : μ.card = 16) + (hd : RowsDom μ.rowLens degreeRows16_0) : SquareOccurs (candidate 4 1 1) μ := by + exact candidate_cone (by decide) degreeCard16 degreePlan16_0 degreeRows16_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs16 : List (List ℕ) := [] + +lemma degreeCones16 : ∀ q ∈ degreeQs16, ∀ μ : YoungDiagram, μ.card = 16 → + RowsDom μ.rowLens q → SquareOccurs (candidate 4 1 1) μ := by + intro q hq + simp only [degreeQs16, List.not_mem_nil] at hq + +abbrev degreeP16 := TreeResidual 4 3 degreeQs16 degreeTree16 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans18.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans18.lean index 93b47ed0f993b0e2aa6ee625461636560151b341..64ec54e8308a79cb612db9581ef7d873a2eb5af1 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans18.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans18.lean @@ -1,39 +1,39 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData18 - -namespace OAI - -/-! Degree Plans 18. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard18 : (candidate 4 2 0).card = 18 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan18_0 : PackingPlan := (.join (.neighbor 5 [3,3,3,2]) (.twosOdd 3 1 [4,3])) -def degreeRows18_0 : List ℕ := [4,3,3,3,3,2] - -lemma degreeCone18_0 (μ : YoungDiagram) (hμ : μ.card = 18) - (hd : RowsDom μ.rowLens degreeRows18_0) : SquareOccurs (candidate 4 2 0) μ := by - exact candidate_cone (by decide) degreeCard18 degreePlan18_0 degreeRows18_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs18 : List (List ℕ) := [] - -lemma degreeCones18 : ∀ q ∈ degreeQs18, ∀ μ : YoungDiagram, μ.card = 18 → - RowsDom μ.rowLens q → SquareOccurs (candidate 4 2 0) μ := by - intro q hq - simp only [degreeQs18,List.not_mem_nil] at hq - -abbrev degreeP18 := TreeResidual 4 4 degreeQs18 degreeTree18 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData18 + +namespace OAI + +/-! Degree Plans 18. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard18 : (candidate 4 2 0).card = 18 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan18_0 : PackingPlan := (.join (.neighbor 5 [3,3,3,2]) (.twosOdd 3 1 [4,3])) +def degreeRows18_0 : List ℕ := [4,3,3,3,3,2] + +lemma degreeCone18_0 (μ : YoungDiagram) (hμ : μ.card = 18) + (hd : RowsDom μ.rowLens degreeRows18_0) : SquareOccurs (candidate 4 2 0) μ := by + exact candidate_cone (by decide) degreeCard18 degreePlan18_0 degreeRows18_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs18 : List (List ℕ) := [] + +lemma degreeCones18 : ∀ q ∈ degreeQs18, ∀ μ : YoungDiagram, μ.card = 18 → + RowsDom μ.rowLens q → SquareOccurs (candidate 4 2 0) μ := by + intro q hq + simp only [degreeQs18,List.not_mem_nil] at hq + +abbrev degreeP18 := TreeResidual 4 4 degreeQs18 degreeTree18 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans19.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans19.lean index 78640fd9aefdb0e1713f40f10746466b6da4f323..4c2fff8b38eb6c79e40fef8b818a939282451650 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans19.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans19.lean @@ -1,39 +1,39 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData19 - -namespace OAI - -/-! Degree Plans 19. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard19 : (candidate 5 1 0).card = 19 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan19_0 : PackingPlan := (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 3) (.twosOdd 2 1 [3,2]))) -def degreeRows19_0 : List ℕ := [3,3,3,3,3,2,2] - -lemma degreeCone19_0 (μ : YoungDiagram) (hμ : μ.card = 19) - (hd : RowsDom μ.rowLens degreeRows19_0) : SquareOccurs (candidate 5 1 0) μ := by - exact candidate_cone (by decide) degreeCard19 degreePlan19_0 degreeRows19_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs19 : List (List ℕ) := [] - -lemma degreeCones19 : ∀ q ∈ degreeQs19, ∀ μ : YoungDiagram, μ.card = 19 → - RowsDom μ.rowLens q → SquareOccurs (candidate 5 1 0) μ := by - intro q hq - simp only [degreeQs19, List.not_mem_nil] at hq - -abbrev degreeP19 := TreeResidual 5 2 degreeQs19 degreeTree19 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData19 + +namespace OAI + +/-! Degree Plans 19. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard19 : (candidate 5 1 0).card = 19 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan19_0 : PackingPlan := (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 3) (.twosOdd 2 1 [3,2]))) +def degreeRows19_0 : List ℕ := [3,3,3,3,3,2,2] + +lemma degreeCone19_0 (μ : YoungDiagram) (hμ : μ.card = 19) + (hd : RowsDom μ.rowLens degreeRows19_0) : SquareOccurs (candidate 5 1 0) μ := by + exact candidate_cone (by decide) degreeCard19 degreePlan19_0 degreeRows19_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs19 : List (List ℕ) := [] + +lemma degreeCones19 : ∀ q ∈ degreeQs19, ∀ μ : YoungDiagram, μ.card = 19 → + RowsDom μ.rowLens q → SquareOccurs (candidate 5 1 0) μ := by + intro q hq + simp only [degreeQs19, List.not_mem_nil] at hq + +abbrev degreeP19 := TreeResidual 5 2 degreeQs19 degreeTree19 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans20.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans20.lean index 4f69ee0bcd94931717ff53babd0a3b2d31dc8c20..c0e4578bce5df3a27d8ceda9bcc1d63d07e2aed4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans20.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans20.lean @@ -1,39 +1,39 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData20 - -namespace OAI - -/-! Degree Plans 20. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard20 : (candidate 4 2 1).card = 20 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan20_0 : PackingPlan := (.join (.twoPaths 5 [4,4,3,3]) (.repeated 3 2)) -def degreeRows20_0 : List ℕ := [6,4,4,3,3] - -lemma degreeCone20_0 (μ : YoungDiagram) (hμ : μ.card = 20) - (hd : RowsDom μ.rowLens degreeRows20_0) : SquareOccurs (candidate 4 2 1) μ := by - exact candidate_cone (by decide) degreeCard20 degreePlan20_0 degreeRows20_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs20 : List (List ℕ) := [] - -lemma degreeCones20 : ∀ q ∈ degreeQs20, ∀ μ : YoungDiagram, μ.card = 20 → - RowsDom μ.rowLens q → SquareOccurs (candidate 4 2 1) μ := by - intro q hq - simp only [degreeQs20,List.not_mem_nil] at hq - -abbrev degreeP20 := TreeResidual 4 5 degreeQs20 degreeTree20 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData20 + +namespace OAI + +/-! Degree Plans 20. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard20 : (candidate 4 2 1).card = 20 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan20_0 : PackingPlan := (.join (.twoPaths 5 [4,4,3,3]) (.repeated 3 2)) +def degreeRows20_0 : List ℕ := [6,4,4,3,3] + +lemma degreeCone20_0 (μ : YoungDiagram) (hμ : μ.card = 20) + (hd : RowsDom μ.rowLens degreeRows20_0) : SquareOccurs (candidate 4 2 1) μ := by + exact candidate_cone (by decide) degreeCard20 degreePlan20_0 degreeRows20_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs20 : List (List ℕ) := [] + +lemma degreeCones20 : ∀ q ∈ degreeQs20, ∀ μ : YoungDiagram, μ.card = 20 → + RowsDom μ.rowLens q → SquareOccurs (candidate 4 2 1) μ := by + intro q hq + simp only [degreeQs20,List.not_mem_nil] at hq + +abbrev degreeP20 := TreeResidual 4 5 degreeQs20 degreeTree20 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans22.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans22.lean index 4d9f024036415c3d759d275aae2f08745a9500d4..d03cfb725ce8eb93d7b2061d7c27426b88527a0d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans22.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans22.lean @@ -1,39 +1,39 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData22 - -namespace OAI - -/-! Degree Plans 22. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard22 : (candidate 4 3 0).card = 22 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan22_0 : PackingPlan := (.join (.neighbor 6 [4,3,3,3]) (.twosOdd 4 1 [5,4])) -def degreeRows22_0 : List ℕ := [5,4,4,3,3,3] - -lemma degreeCone22_0 (μ : YoungDiagram) (hμ : μ.card = 22) - (hd : RowsDom μ.rowLens degreeRows22_0) : SquareOccurs (candidate 4 3 0) μ := by - exact candidate_cone (by decide) degreeCard22 degreePlan22_0 degreeRows22_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs22 : List (List ℕ) := [] - -lemma degreeCones22 : ∀ q ∈ degreeQs22, ∀ μ : YoungDiagram, μ.card = 22 → - RowsDom μ.rowLens q → SquareOccurs (candidate 4 3 0) μ := by - intro q hq - simp only [degreeQs22,List.not_mem_nil] at hq - -abbrev degreeP22 := TreeResidual 4 6 degreeQs22 degreeTree22 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData22 + +namespace OAI + +/-! Degree Plans 22. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard22 : (candidate 4 3 0).card = 22 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan22_0 : PackingPlan := (.join (.neighbor 6 [4,3,3,3]) (.twosOdd 4 1 [5,4])) +def degreeRows22_0 : List ℕ := [5,4,4,3,3,3] + +lemma degreeCone22_0 (μ : YoungDiagram) (hμ : μ.card = 22) + (hd : RowsDom μ.rowLens degreeRows22_0) : SquareOccurs (candidate 4 3 0) μ := by + exact candidate_cone (by decide) degreeCard22 degreePlan22_0 degreeRows22_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs22 : List (List ℕ) := [] + +lemma degreeCones22 : ∀ q ∈ degreeQs22, ∀ μ : YoungDiagram, μ.card = 22 → + RowsDom μ.rowLens q → SquareOccurs (candidate 4 3 0) μ := by + intro q hq + simp only [degreeQs22,List.not_mem_nil] at hq + +abbrev degreeP22 := TreeResidual 4 6 degreeQs22 degreeTree22 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans24.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans24.lean index 8ec9bdc0bef39d5adf4e3aae30379731cf895fdc..856b866f47efebfb2de62c9cb29ed6e00032ccf8 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans24.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans24.lean @@ -1,39 +1,39 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData24 - -namespace OAI - -/-! Degree Plans 24. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard24 : (candidate 4 3 1).card = 24 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan24_0 : PackingPlan := (.join (.twoPaths 6 [4,4,4,4]) (.repeated 4 2)) -def degreeRows24_0 : List ℕ := [8,4,4,4,4] - -lemma degreeCone24_0 (μ : YoungDiagram) (hμ : μ.card = 24) - (hd : RowsDom μ.rowLens degreeRows24_0) : SquareOccurs (candidate 4 3 1) μ := by - exact candidate_cone (by decide) degreeCard24 degreePlan24_0 degreeRows24_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs24 : List (List ℕ) := [] - -lemma degreeCones24 : ∀ q ∈ degreeQs24, ∀ μ : YoungDiagram, μ.card = 24 → - RowsDom μ.rowLens q → SquareOccurs (candidate 4 3 1) μ := by - intro q hq - simp only [degreeQs24,List.not_mem_nil] at hq - -abbrev degreeP24 := TreeResidual 4 7 degreeQs24 degreeTree24 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData24 + +namespace OAI + +/-! Degree Plans 24. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard24 : (candidate 4 3 1).card = 24 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan24_0 : PackingPlan := (.join (.twoPaths 6 [4,4,4,4]) (.repeated 4 2)) +def degreeRows24_0 : List ℕ := [8,4,4,4,4] + +lemma degreeCone24_0 (μ : YoungDiagram) (hμ : μ.card = 24) + (hd : RowsDom μ.rowLens degreeRows24_0) : SquareOccurs (candidate 4 3 1) μ := by + exact candidate_cone (by decide) degreeCard24 degreePlan24_0 degreeRows24_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs24 : List (List ℕ) := [] + +lemma degreeCones24 : ∀ q ∈ degreeQs24, ∀ μ : YoungDiagram, μ.card = 24 → + RowsDom μ.rowLens q → SquareOccurs (candidate 4 3 1) μ := by + intro q hq + simp only [degreeQs24,List.not_mem_nil] at hq + +abbrev degreeP24 := TreeResidual 4 7 degreeQs24 degreeTree24 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans26.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans26.lean index 07a3da7177bc520319e0f3024aca72bda8e4eb38..084f6971628b7b42a2931ed367c82a5d8b0a3a0e 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans26.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans26.lean @@ -1,39 +1,39 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData26 - -namespace OAI - -/-! Degree Plans 26. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard26 : (candidate 4 4 0).card = 26 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan26_0 : PackingPlan := (.join (.neighbor 7 [4,4,4,3]) (.twosOdd 5 1 [6,5])) -def degreeRows26_0 : List ℕ := [6,5,4,4,4,3] - -lemma degreeCone26_0 (μ : YoungDiagram) (hμ : μ.card = 26) - (hd : RowsDom μ.rowLens degreeRows26_0) : SquareOccurs (candidate 4 4 0) μ := by - exact candidate_cone (by decide) degreeCard26 degreePlan26_0 degreeRows26_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs26 : List (List ℕ) := [] - -lemma degreeCones26 : ∀ q ∈ degreeQs26, ∀ μ : YoungDiagram, μ.card = 26 → - RowsDom μ.rowLens q → SquareOccurs (candidate 4 4 0) μ := by - intro q hq - simp only [degreeQs26,List.not_mem_nil] at hq - -abbrev degreeP26 := TreeResidual 4 8 degreeQs26 degreeTree26 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData26 + +namespace OAI + +/-! Degree Plans 26. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard26 : (candidate 4 4 0).card = 26 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan26_0 : PackingPlan := (.join (.neighbor 7 [4,4,4,3]) (.twosOdd 5 1 [6,5])) +def degreeRows26_0 : List ℕ := [6,5,4,4,4,3] + +lemma degreeCone26_0 (μ : YoungDiagram) (hμ : μ.card = 26) + (hd : RowsDom μ.rowLens degreeRows26_0) : SquareOccurs (candidate 4 4 0) μ := by + exact candidate_cone (by decide) degreeCard26 degreePlan26_0 degreeRows26_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs26 : List (List ℕ) := [] + +lemma degreeCones26 : ∀ q ∈ degreeQs26, ∀ μ : YoungDiagram, μ.card = 26 → + RowsDom μ.rowLens q → SquareOccurs (candidate 4 4 0) μ := by + intro q hq + simp only [degreeQs26,List.not_mem_nil] at hq + +abbrev degreeP26 := TreeResidual 4 8 degreeQs26 degreeTree26 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans31.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans31.lean index 06598b7dbf7ac769703e006136a57fa0f13af0d1..b4a0214a994c5dc65b752c798a86aed6433768e8 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans31.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans31.lean @@ -1,49 +1,49 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData31 - -namespace OAI - -/-! Degree Plans 31. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard31 : (candidate 6 2 1).card = 31 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan31_0 : PackingPlan := (.join (.twoPaths 7 [5,5,4,4]) (.join (.repeated 1 4) (.twosOdd 3 3 [5,4]))) -def degreeRows31_0 : List ℕ := [5,5,5,4,4,4,4] - -lemma degreeCone31_0 (μ : YoungDiagram) (hμ : μ.card = 31) - (hd : RowsDom μ.rowLens degreeRows31_0) : SquareOccurs (candidate 6 2 1) μ := by - exact candidate_cone (by decide) degreeCard31 degreePlan31_0 degreeRows31_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan31_1 : PackingPlan := (.join (.twoPaths 7 [5,5,4,4]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 3 2))) -def degreeRows31_1 : List ℕ := [6,5,5,4,4,2,2,2,1] - -lemma degreeCone31_1 (μ : YoungDiagram) (hμ : μ.card = 31) - (hd : RowsDom μ.rowLens degreeRows31_1) : SquareOccurs (candidate 6 2 1) μ := by - exact candidate_cone (by decide) degreeCard31 degreePlan31_1 degreeRows31_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs31 : List (List ℕ) := [degreeRows31_1] - -lemma degreeCones31 : ∀ q ∈ degreeQs31, ∀ μ : YoungDiagram, μ.card = 31 → - RowsDom μ.rowLens q → SquareOccurs (candidate 6 2 1) μ := by - intro q hq - simp only [degreeQs31,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone31_1 - -abbrev degreeP31 := TreeResidual 6 5 degreeQs31 degreeTree31 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData31 + +namespace OAI + +/-! Degree Plans 31. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard31 : (candidate 6 2 1).card = 31 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan31_0 : PackingPlan := (.join (.twoPaths 7 [5,5,4,4]) (.join (.repeated 1 4) (.twosOdd 3 3 [5,4]))) +def degreeRows31_0 : List ℕ := [5,5,5,4,4,4,4] + +lemma degreeCone31_0 (μ : YoungDiagram) (hμ : μ.card = 31) + (hd : RowsDom μ.rowLens degreeRows31_0) : SquareOccurs (candidate 6 2 1) μ := by + exact candidate_cone (by decide) degreeCard31 degreePlan31_0 degreeRows31_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan31_1 : PackingPlan := (.join (.twoPaths 7 [5,5,4,4]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 3 2))) +def degreeRows31_1 : List ℕ := [6,5,5,4,4,2,2,2,1] + +lemma degreeCone31_1 (μ : YoungDiagram) (hμ : μ.card = 31) + (hd : RowsDom μ.rowLens degreeRows31_1) : SquareOccurs (candidate 6 2 1) μ := by + exact candidate_cone (by decide) degreeCard31 degreePlan31_1 degreeRows31_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs31 : List (List ℕ) := [degreeRows31_1] + +lemma degreeCones31 : ∀ q ∈ degreeQs31, ∀ μ : YoungDiagram, μ.card = 31 → + RowsDom μ.rowLens q → SquareOccurs (candidate 6 2 1) μ := by + intro q hq + simp only [degreeQs31,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone31_1 + +abbrev degreeP31 := TreeResidual 6 5 degreeQs31 degreeTree31 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans35.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans35.lean index 8670fa22f9eb1d935a627bc58eacf3260d7ec163..a8f768b7da2acb197f336a38707313acb42d7220 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans35.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans35.lean @@ -1,49 +1,49 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData35 - -namespace OAI - -/-! Degree Plans 35. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard35 : (candidate 6 3 1).card = 35 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan35_0 : PackingPlan := (.join (.twoPaths 8 [5,5,5,5]) (.join (.repeated 1 4) (.twosOdd 4 3 [6,5]))) -def degreeRows35_0 : List ℕ := [6,5,5,5,5,5,4] - -lemma degreeCone35_0 (μ : YoungDiagram) (hμ : μ.card = 35) - (hd : RowsDom μ.rowLens degreeRows35_0) : SquareOccurs (candidate 6 3 1) μ := by - exact candidate_cone (by decide) degreeCard35 degreePlan35_0 degreeRows35_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan35_1 : PackingPlan := (.join (.twoPaths 8 [5,5,5,5]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 4 2))) -def degreeRows35_1 : List ℕ := [8,5,5,5,5,2,2,2,1] - -lemma degreeCone35_1 (μ : YoungDiagram) (hμ : μ.card = 35) - (hd : RowsDom μ.rowLens degreeRows35_1) : SquareOccurs (candidate 6 3 1) μ := by - exact candidate_cone (by decide) degreeCard35 degreePlan35_1 degreeRows35_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs35 : List (List ℕ) := [degreeRows35_1] - -lemma degreeCones35 : ∀ q ∈ degreeQs35, ∀ μ : YoungDiagram, μ.card = 35 → - RowsDom μ.rowLens q → SquareOccurs (candidate 6 3 1) μ := by - intro q hq - simp only [degreeQs35,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone35_1 - -abbrev degreeP35 := TreeResidual 6 7 degreeQs35 degreeTree35 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData35 + +namespace OAI + +/-! Degree Plans 35. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard35 : (candidate 6 3 1).card = 35 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan35_0 : PackingPlan := (.join (.twoPaths 8 [5,5,5,5]) (.join (.repeated 1 4) (.twosOdd 4 3 [6,5]))) +def degreeRows35_0 : List ℕ := [6,5,5,5,5,5,4] + +lemma degreeCone35_0 (μ : YoungDiagram) (hμ : μ.card = 35) + (hd : RowsDom μ.rowLens degreeRows35_0) : SquareOccurs (candidate 6 3 1) μ := by + exact candidate_cone (by decide) degreeCard35 degreePlan35_0 degreeRows35_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan35_1 : PackingPlan := (.join (.twoPaths 8 [5,5,5,5]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 4 2))) +def degreeRows35_1 : List ℕ := [8,5,5,5,5,2,2,2,1] + +lemma degreeCone35_1 (μ : YoungDiagram) (hμ : μ.card = 35) + (hd : RowsDom μ.rowLens degreeRows35_1) : SquareOccurs (candidate 6 3 1) μ := by + exact candidate_cone (by decide) degreeCard35 degreePlan35_1 degreeRows35_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs35 : List (List ℕ) := [degreeRows35_1] + +lemma degreeCones35 : ∀ q ∈ degreeQs35, ∀ μ : YoungDiagram, μ.card = 35 → + RowsDom μ.rowLens q → SquareOccurs (candidate 6 3 1) μ := by + intro q hq + simp only [degreeQs35,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone35_1 + +abbrev degreeP35 := TreeResidual 6 7 degreeQs35 degreeTree35 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans37.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans37.lean index a08b70524e1044a19872e6ef05c8449f1214ff55..0242a141d07e1c58a0653f0e0e3055ac225d9198 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans37.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans37.lean @@ -1,39 +1,39 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData37 - -namespace OAI - -/-! Degree Plans 37. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard37 : (candidate 6 4 0).card = 37 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan37_0 : PackingPlan := (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 5 1 [6,5]))) -def degreeRows37_0 : List ℕ := [6,5,5,5,5,4,2,2,2,1] - -lemma degreeCone37_0 (μ : YoungDiagram) (hμ : μ.card = 37) - (hd : RowsDom μ.rowLens degreeRows37_0) : SquareOccurs (candidate 6 4 0) μ := by - exact candidate_cone (by decide) degreeCard37 degreePlan37_0 degreeRows37_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs37 : List (List ℕ) := [] - -lemma degreeCones37 : ∀ q ∈ degreeQs37, ∀ μ : YoungDiagram, μ.card = 37 → - RowsDom μ.rowLens q → SquareOccurs (candidate 6 4 0) μ := by - intro q hq - simp only [degreeQs37, List.not_mem_nil] at hq - -abbrev degreeP37 := TreeResidual 6 8 degreeQs37 degreeTree37 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData37 + +namespace OAI + +/-! Degree Plans 37. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard37 : (candidate 6 4 0).card = 37 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan37_0 : PackingPlan := (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 5 1 [6,5]))) +def degreeRows37_0 : List ℕ := [6,5,5,5,5,4,2,2,2,1] + +lemma degreeCone37_0 (μ : YoungDiagram) (hμ : μ.card = 37) + (hd : RowsDom μ.rowLens degreeRows37_0) : SquareOccurs (candidate 6 4 0) μ := by + exact candidate_cone (by decide) degreeCard37 degreePlan37_0 degreeRows37_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs37 : List (List ℕ) := [] + +lemma degreeCones37 : ∀ q ∈ degreeQs37, ∀ μ : YoungDiagram, μ.card = 37 → + RowsDom μ.rowLens q → SquareOccurs (candidate 6 4 0) μ := by + intro q hq + simp only [degreeQs37, List.not_mem_nil] at hq + +abbrev degreeP37 := TreeResidual 6 8 degreeQs37 degreeTree37 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans39.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans39.lean index 501b1dbf031a11fed23fb9937fd34beb3e4ffd5b..24fecc8a02cbe34d55e33cc17425e383c869c907 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans39.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans39.lean @@ -1,49 +1,49 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData39 - -namespace OAI - -/-! Degree Plans 39. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard39 : (candidate 6 4 1).card = 39 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan39_0 : PackingPlan := (.join (.twoPaths 9 [6,6,5,5]) (.join (.repeated 1 4) (.twosOdd 5 3 [7,6]))) -def degreeRows39_0 : List ℕ := [7,6,6,6,5,5,4] - -lemma degreeCone39_0 (μ : YoungDiagram) (hμ : μ.card = 39) - (hd : RowsDom μ.rowLens degreeRows39_0) : SquareOccurs (candidate 6 4 1) μ := by - exact candidate_cone (by decide) degreeCard39 degreePlan39_0 degreeRows39_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan39_1 : PackingPlan := (.join (.twoPaths 9 [6,6,5,5]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 5 2))) -def degreeRows39_1 : List ℕ := [10,6,6,5,5,2,2,2,1] - -lemma degreeCone39_1 (μ : YoungDiagram) (hμ : μ.card = 39) - (hd : RowsDom μ.rowLens degreeRows39_1) : SquareOccurs (candidate 6 4 1) μ := by - exact candidate_cone (by decide) degreeCard39 degreePlan39_1 degreeRows39_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs39 : List (List ℕ) := [degreeRows39_1] - -lemma degreeCones39 : ∀ q ∈ degreeQs39, ∀ μ : YoungDiagram, μ.card = 39 → - RowsDom μ.rowLens q → SquareOccurs (candidate 6 4 1) μ := by - intro q hq - simp only [degreeQs39,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone39_1 - -abbrev degreeP39 := TreeResidual 6 9 degreeQs39 degreeTree39 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData39 + +namespace OAI + +/-! Degree Plans 39. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard39 : (candidate 6 4 1).card = 39 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan39_0 : PackingPlan := (.join (.twoPaths 9 [6,6,5,5]) (.join (.repeated 1 4) (.twosOdd 5 3 [7,6]))) +def degreeRows39_0 : List ℕ := [7,6,6,6,5,5,4] + +lemma degreeCone39_0 (μ : YoungDiagram) (hμ : μ.card = 39) + (hd : RowsDom μ.rowLens degreeRows39_0) : SquareOccurs (candidate 6 4 1) μ := by + exact candidate_cone (by decide) degreeCard39 degreePlan39_0 degreeRows39_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan39_1 : PackingPlan := (.join (.twoPaths 9 [6,6,5,5]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 5 2))) +def degreeRows39_1 : List ℕ := [10,6,6,5,5,2,2,2,1] + +lemma degreeCone39_1 (μ : YoungDiagram) (hμ : μ.card = 39) + (hd : RowsDom μ.rowLens degreeRows39_1) : SquareOccurs (candidate 6 4 1) μ := by + exact candidate_cone (by decide) degreeCard39 degreePlan39_1 degreeRows39_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs39 : List (List ℕ) := [degreeRows39_1] + +lemma degreeCones39 : ∀ q ∈ degreeQs39, ∀ μ : YoungDiagram, μ.card = 39 → + RowsDom μ.rowLens q → SquareOccurs (candidate 6 4 1) μ := by + intro q hq + simp only [degreeQs39,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone39_1 + +abbrev degreeP39 := TreeResidual 6 9 degreeQs39 degreeTree39 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans41.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans41.lean index 1a7ea2f029250cb4b226790999029f91183a6285..7c73b83b9cac7e9d443fb073e12a8c27e9e44869 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans41.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans41.lean @@ -1,39 +1,39 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData41 - -namespace OAI - -/-! Degree Plans 41. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard41 : (candidate 6 5 0).card = 41 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan41_0 : PackingPlan := (.join (.neighbor 10 [6,5,5,5]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 6 1 [7,6]))) -def degreeRows41_0 : List ℕ := [7,6,6,5,5,5,2,2,2,1] - -lemma degreeCone41_0 (μ : YoungDiagram) (hμ : μ.card = 41) - (hd : RowsDom μ.rowLens degreeRows41_0) : SquareOccurs (candidate 6 5 0) μ := by - exact candidate_cone (by decide) degreeCard41 degreePlan41_0 degreeRows41_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs41 : List (List ℕ) := [] - -lemma degreeCones41 : ∀ q ∈ degreeQs41, ∀ μ : YoungDiagram, μ.card = 41 → - RowsDom μ.rowLens q → SquareOccurs (candidate 6 5 0) μ := by - intro q hq - simp only [degreeQs41,List.not_mem_nil] at hq - -abbrev degreeP41 := TreeResidual 6 10 degreeQs41 degreeTree41 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData41 + +namespace OAI + +/-! Degree Plans 41. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard41 : (candidate 6 5 0).card = 41 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan41_0 : PackingPlan := (.join (.neighbor 10 [6,5,5,5]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 6 1 [7,6]))) +def degreeRows41_0 : List ℕ := [7,6,6,5,5,5,2,2,2,1] + +lemma degreeCone41_0 (μ : YoungDiagram) (hμ : μ.card = 41) + (hd : RowsDom μ.rowLens degreeRows41_0) : SquareOccurs (candidate 6 5 0) μ := by + exact candidate_cone (by decide) degreeCard41 degreePlan41_0 degreeRows41_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs41 : List (List ℕ) := [] + +lemma degreeCones41 : ∀ q ∈ degreeQs41, ∀ μ : YoungDiagram, μ.card = 41 → + RowsDom μ.rowLens q → SquareOccurs (candidate 6 5 0) μ := by + intro q hq + simp only [degreeQs41,List.not_mem_nil] at hq + +abbrev degreeP41 := TreeResidual 6 10 degreeQs41 degreeTree41 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans43.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans43.lean index 8fc4488cbbd8e50c96300da851dc9435b54ded7a..9dbfa0755719cf0281a4e3a1e396ffc8e4845bd0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans43.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans43.lean @@ -1,49 +1,49 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData43 - -namespace OAI - -/-! Degree Plans 43. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard43 : (candidate 6 5 1).card = 43 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan43_0 : PackingPlan := (.join (.twoPaths 10 [6,6,6,6]) (.join (.repeated 1 4) (.twosOdd 6 3 [8,7]))) -def degreeRows43_0 : List ℕ := [8,7,6,6,6,6,4] - -lemma degreeCone43_0 (μ : YoungDiagram) (hμ : μ.card = 43) - (hd : RowsDom μ.rowLens degreeRows43_0) : SquareOccurs (candidate 6 5 1) μ := by - exact candidate_cone (by decide) degreeCard43 degreePlan43_0 degreeRows43_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan43_1 : PackingPlan := (.join (.twoPaths 10 [6,6,6,6]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 6 2))) -def degreeRows43_1 : List ℕ := [12,6,6,6,6,2,2,2,1] - -lemma degreeCone43_1 (μ : YoungDiagram) (hμ : μ.card = 43) - (hd : RowsDom μ.rowLens degreeRows43_1) : SquareOccurs (candidate 6 5 1) μ := by - exact candidate_cone (by decide) degreeCard43 degreePlan43_1 degreeRows43_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs43 : List (List ℕ) := [degreeRows43_1] - -lemma degreeCones43 : ∀ q ∈ degreeQs43, ∀ μ : YoungDiagram, μ.card = 43 → - RowsDom μ.rowLens q → SquareOccurs (candidate 6 5 1) μ := by - intro q hq - simp only [degreeQs43,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone43_1 - -abbrev degreeP43 := TreeResidual 6 11 degreeQs43 degreeTree43 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData43 + +namespace OAI + +/-! Degree Plans 43. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard43 : (candidate 6 5 1).card = 43 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan43_0 : PackingPlan := (.join (.twoPaths 10 [6,6,6,6]) (.join (.repeated 1 4) (.twosOdd 6 3 [8,7]))) +def degreeRows43_0 : List ℕ := [8,7,6,6,6,6,4] + +lemma degreeCone43_0 (μ : YoungDiagram) (hμ : μ.card = 43) + (hd : RowsDom μ.rowLens degreeRows43_0) : SquareOccurs (candidate 6 5 1) μ := by + exact candidate_cone (by decide) degreeCard43 degreePlan43_0 degreeRows43_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan43_1 : PackingPlan := (.join (.twoPaths 10 [6,6,6,6]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 6 2))) +def degreeRows43_1 : List ℕ := [12,6,6,6,6,2,2,2,1] + +lemma degreeCone43_1 (μ : YoungDiagram) (hμ : μ.card = 43) + (hd : RowsDom μ.rowLens degreeRows43_1) : SquareOccurs (candidate 6 5 1) μ := by + exact candidate_cone (by decide) degreeCard43 degreePlan43_1 degreeRows43_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs43 : List (List ℕ) := [degreeRows43_1] + +lemma degreeCones43 : ∀ q ∈ degreeQs43, ∀ μ : YoungDiagram, μ.card = 43 → + RowsDom μ.rowLens q → SquareOccurs (candidate 6 5 1) μ := by + intro q hq + simp only [degreeQs43,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone43_1 + +abbrev degreeP43 := TreeResidual 6 11 degreeQs43 degreeTree43 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans58.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans58.lean index 07cf5a299cf04b99f63c92421bf5246f0e31e07d..5e23d6658bb38b37203cf5dc8971f4e09b7c8d54 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans58.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans58.lean @@ -1,49 +1,49 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData58 - -namespace OAI - -/-! Degree Plans 58. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard58 : (candidate 8 5 1).card = 58 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan58_0 : PackingPlan := (.join (.twoPaths 12 [7,7,7,7]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 6 3 [8,7])))) -def degreeRows58_0 : List ℕ := [8,7,7,7,7,7,4,3,3,3,2] - -lemma degreeCone58_0 (μ : YoungDiagram) (hμ : μ.card = 58) - (hd : RowsDom μ.rowLens degreeRows58_0) : SquareOccurs (candidate 8 5 1) μ := by - exact candidate_cone (by decide) degreeCard58 degreePlan58_0 degreeRows58_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan58_1 : PackingPlan := (.join (.twoPaths 12 [7,7,7,7]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 6 2)))) -def degreeRows58_1 : List ℕ := [12,7,7,7,7,3,3,3,2,2,2,2,1] - -lemma degreeCone58_1 (μ : YoungDiagram) (hμ : μ.card = 58) - (hd : RowsDom μ.rowLens degreeRows58_1) : SquareOccurs (candidate 8 5 1) μ := by - exact candidate_cone (by decide) degreeCard58 degreePlan58_1 degreeRows58_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs58 : List (List ℕ) := [degreeRows58_1] - -lemma degreeCones58 : ∀ q ∈ degreeQs58, ∀ μ : YoungDiagram, μ.card = 58 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 5 1) μ := by - intro q hq - simp only [degreeQs58,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone58_1 - -abbrev degreeP58 := TreeResidual 8 11 degreeQs58 degreeTree58 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData58 + +namespace OAI + +/-! Degree Plans 58. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard58 : (candidate 8 5 1).card = 58 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan58_0 : PackingPlan := (.join (.twoPaths 12 [7,7,7,7]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 6 3 [8,7])))) +def degreeRows58_0 : List ℕ := [8,7,7,7,7,7,4,3,3,3,2] + +lemma degreeCone58_0 (μ : YoungDiagram) (hμ : μ.card = 58) + (hd : RowsDom μ.rowLens degreeRows58_0) : SquareOccurs (candidate 8 5 1) μ := by + exact candidate_cone (by decide) degreeCard58 degreePlan58_0 degreeRows58_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan58_1 : PackingPlan := (.join (.twoPaths 12 [7,7,7,7]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 6 2)))) +def degreeRows58_1 : List ℕ := [12,7,7,7,7,3,3,3,2,2,2,2,1] + +lemma degreeCone58_1 (μ : YoungDiagram) (hμ : μ.card = 58) + (hd : RowsDom μ.rowLens degreeRows58_1) : SquareOccurs (candidate 8 5 1) μ := by + exact candidate_cone (by decide) degreeCard58 degreePlan58_1 degreeRows58_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs58 : List (List ℕ) := [degreeRows58_1] + +lemma degreeCones58 : ∀ q ∈ degreeQs58, ∀ μ : YoungDiagram, μ.card = 58 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 5 1) μ := by + intro q hq + simp only [degreeQs58,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone58_1 + +abbrev degreeP58 := TreeResidual 8 11 degreeQs58 degreeTree58 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans62.lean index 913fcea0d2d4086428b39b452948815128207dc0..7f6f4403793bea1541a998acca13c2d37ae12ab6 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans62.lean @@ -1,49 +1,49 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData62 - -namespace OAI - -/-! Degree Plans 62. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard62 : (candidate 8 6 1).card = 62 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan62_0 : PackingPlan := (.join (.twoPaths 13 [8,8,7,7]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 7 3 [9,8])))) -def degreeRows62_0 : List ℕ := [9,8,8,8,7,7,4,3,3,3,2] - -lemma degreeCone62_0 (μ : YoungDiagram) (hμ : μ.card = 62) - (hd : RowsDom μ.rowLens degreeRows62_0) : SquareOccurs (candidate 8 6 1) μ := by - exact candidate_cone (by decide) degreeCard62 degreePlan62_0 degreeRows62_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan62_1 : PackingPlan := (.join (.twoPaths 13 [8,8,7,7]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 7 2)))) -def degreeRows62_1 : List ℕ := [14,8,8,7,7,3,3,3,2,2,2,2,1] - -lemma degreeCone62_1 (μ : YoungDiagram) (hμ : μ.card = 62) - (hd : RowsDom μ.rowLens degreeRows62_1) : SquareOccurs (candidate 8 6 1) μ := by - exact candidate_cone (by decide) degreeCard62 degreePlan62_1 degreeRows62_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs62 : List (List ℕ) := [degreeRows62_1] - -lemma degreeCones62 : ∀ q ∈ degreeQs62, ∀ μ : YoungDiagram, μ.card = 62 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 6 1) μ := by - intro q hq - simp only [degreeQs62,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone62_1 - -abbrev degreeP62 := TreeResidual 8 13 degreeQs62 degreeTree62 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData62 + +namespace OAI + +/-! Degree Plans 62. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard62 : (candidate 8 6 1).card = 62 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan62_0 : PackingPlan := (.join (.twoPaths 13 [8,8,7,7]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 7 3 [9,8])))) +def degreeRows62_0 : List ℕ := [9,8,8,8,7,7,4,3,3,3,2] + +lemma degreeCone62_0 (μ : YoungDiagram) (hμ : μ.card = 62) + (hd : RowsDom μ.rowLens degreeRows62_0) : SquareOccurs (candidate 8 6 1) μ := by + exact candidate_cone (by decide) degreeCard62 degreePlan62_0 degreeRows62_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan62_1 : PackingPlan := (.join (.twoPaths 13 [8,8,7,7]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 7 2)))) +def degreeRows62_1 : List ℕ := [14,8,8,7,7,3,3,3,2,2,2,2,1] + +lemma degreeCone62_1 (μ : YoungDiagram) (hμ : μ.card = 62) + (hd : RowsDom μ.rowLens degreeRows62_1) : SquareOccurs (candidate 8 6 1) μ := by + exact candidate_cone (by decide) degreeCard62 degreePlan62_1 degreeRows62_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs62 : List (List ℕ) := [degreeRows62_1] + +lemma degreeCones62 : ∀ q ∈ degreeQs62, ∀ μ : YoungDiagram, μ.card = 62 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 6 1) μ := by + intro q hq + simp only [degreeQs62,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone62_1 + +abbrev degreeP62 := TreeResidual 8 13 degreeQs62 degreeTree62 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans64.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans64.lean index 18ac8654e524ce3fdd98701a3587fb8292faecfc..31145ef3eb2ce3c017b30815c0f1499addd21d84 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans64.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans64.lean @@ -1,39 +1,39 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData64 - -namespace OAI - -/-! Degree Plans 64. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard64 : (candidate 8 7 0).card = 64 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan64_0 : PackingPlan := (.join (.neighbor 14 [8,7,7,7]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 8 1 [9,8])))) -def degreeRows64_0 : List ℕ := [9,8,8,7,7,7,3,3,3,2,2,2,2,1] - -lemma degreeCone64_0 (μ : YoungDiagram) (hμ : μ.card = 64) - (hd : RowsDom μ.rowLens degreeRows64_0) : SquareOccurs (candidate 8 7 0) μ := by - exact candidate_cone (by decide) degreeCard64 degreePlan64_0 degreeRows64_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs64 : List (List ℕ) := [] - -lemma degreeCones64 : ∀ q ∈ degreeQs64, ∀ μ : YoungDiagram, μ.card = 64 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 7 0) μ := by - intro q hq - simp only [degreeQs64, List.not_mem_nil] at hq - -abbrev degreeP64 := TreeResidual 8 14 degreeQs64 degreeTree64 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData64 + +namespace OAI + +/-! Degree Plans 64. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard64 : (candidate 8 7 0).card = 64 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan64_0 : PackingPlan := (.join (.neighbor 14 [8,7,7,7]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 8 1 [9,8])))) +def degreeRows64_0 : List ℕ := [9,8,8,7,7,7,3,3,3,2,2,2,2,1] + +lemma degreeCone64_0 (μ : YoungDiagram) (hμ : μ.card = 64) + (hd : RowsDom μ.rowLens degreeRows64_0) : SquareOccurs (candidate 8 7 0) μ := by + exact candidate_cone (by decide) degreeCard64 degreePlan64_0 degreeRows64_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs64 : List (List ℕ) := [] + +lemma degreeCones64 : ∀ q ∈ degreeQs64, ∀ μ : YoungDiagram, μ.card = 64 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 7 0) μ := by + intro q hq + simp only [degreeQs64, List.not_mem_nil] at hq + +abbrev degreeP64 := TreeResidual 8 14 degreeQs64 degreeTree64 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans89.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans89.lean index ab0da5d1695c5422c374012698936b52b81f0cfd..776c2e4c0d4e21f25ffceba1c177bbc47cf12c22 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans89.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreePlans89.lean @@ -1,49 +1,49 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData89 - -namespace OAI - -/-! Degree Plans 89. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard89 : (candidate 10 8 1).card = 89 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan89_0 : PackingPlan := (.join (.twoPaths 17 [10,10,9,9]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 9 3 [11,10]))))) -def degreeRows89_0 : List ℕ := [11,10,10,10,9,9,4,4,4,4,3,3,3,3,2] - -lemma degreeCone89_0 (μ : YoungDiagram) (hμ : μ.card = 89) - (hd : RowsDom μ.rowLens degreeRows89_0) : SquareOccurs (candidate 10 8 1) μ := by - exact candidate_cone (by decide) degreeCard89 degreePlan89_0 degreeRows89_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan89_1 : PackingPlan := (.join (.twoPaths 17 [10,10,9,9]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 9 2))))) -def degreeRows89_1 : List ℕ := [18,10,10,9,9,4,4,4,3,3,3,3,2,2,2,2,1] - -lemma degreeCone89_1 (μ : YoungDiagram) (hμ : μ.card = 89) - (hd : RowsDom μ.rowLens degreeRows89_1) : SquareOccurs (candidate 10 8 1) μ := by - exact candidate_cone (by decide) degreeCard89 degreePlan89_1 degreeRows89_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs89 : List (List ℕ) := [degreeRows89_1] - -lemma degreeCones89 : ∀ q ∈ degreeQs89, ∀ μ : YoungDiagram, μ.card = 89 → - RowsDom μ.rowLens q → SquareOccurs (candidate 10 8 1) μ := by - intro q hq - simp only [degreeQs89,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone89_1 - -abbrev degreeP89 := TreeResidual 10 17 degreeQs89 degreeTree89 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData89 + +namespace OAI + +/-! Degree Plans 89. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard89 : (candidate 10 8 1).card = 89 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan89_0 : PackingPlan := (.join (.twoPaths 17 [10,10,9,9]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 9 3 [11,10]))))) +def degreeRows89_0 : List ℕ := [11,10,10,10,9,9,4,4,4,4,3,3,3,3,2] + +lemma degreeCone89_0 (μ : YoungDiagram) (hμ : μ.card = 89) + (hd : RowsDom μ.rowLens degreeRows89_0) : SquareOccurs (candidate 10 8 1) μ := by + exact candidate_cone (by decide) degreeCard89 degreePlan89_0 degreeRows89_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan89_1 : PackingPlan := (.join (.twoPaths 17 [10,10,9,9]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 9 2))))) +def degreeRows89_1 : List ℕ := [18,10,10,9,9,4,4,4,3,3,3,3,2,2,2,2,1] + +lemma degreeCone89_1 (μ : YoungDiagram) (hμ : μ.card = 89) + (hd : RowsDom μ.rowLens degreeRows89_1) : SquareOccurs (candidate 10 8 1) μ := by + exact candidate_cone (by decide) degreeCard89 degreePlan89_1 degreeRows89_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs89 : List (List ℕ) := [degreeRows89_1] + +lemma degreeCones89 : ∀ q ∈ degreeQs89, ∀ μ : YoungDiagram, μ.card = 89 → + RowsDom μ.rowLens q → SquareOccurs (candidate 10 8 1) μ := by + intro q hq + simp only [degreeQs89,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone89_1 + +abbrev degreeP89 := TreeResidual 10 17 degreeQs89 degreeTree89 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData116.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData116.lean index 20c6d7db2fba6bd87962a4e498fdcf5ce6668137..6e85a58b27f3c4f50a1c8e724472552921f5daf2 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData116.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData116.lean @@ -1,23 +1,23 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 116. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion116_0 : PrefixRegion := ([(2,22),(3,51),(4,52)], [(2,22),(3,51),(4,52)]) - -def degreeRegions116 : List PrefixRegion := [degreeRegion116_0] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 116. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion116_0 : PrefixRegion := ([(2,22),(3,51),(4,52)], [(2,22),(3,51),(4,52)]) + +def degreeRegions116 : List PrefixRegion := [degreeRegion116_0] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData118.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData118.lean index cff5e2a5cbb4542429463fc2b7ece139e85ce27b..52f4faf370bfbffe2e01f3dba0135421f51bdda7 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData118.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData118.lean @@ -1,23 +1,23 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 118. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion118_0 : PrefixRegion := ([(2,22),(3,53),(4,54)], [(2,22),(3,53),(4,54)]) - -def degreeRegions118 : List PrefixRegion := [degreeRegion118_0] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 118. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion118_0 : PrefixRegion := ([(2,22),(3,53),(4,54)], [(2,22),(3,53),(4,54)]) + +def degreeRegions118 : List PrefixRegion := [degreeRegion118_0] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData14.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData14.lean index d161d279b7fbb7f16a6f33b9184276bfe02b3599..286874407f5714dd7b797de7cb16898789a2ed3e 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData14.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData14.lean @@ -1,25 +1,25 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 14. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion14_0 : PrefixRegion := ([(5,11)], [(6,13)]) -def degreeRegion14_1 : PrefixRegion := ([(6,13)], [(5,11)]) -def degreeRegion14_2 : PrefixRegion := ([(6,13)], [(6,13)]) - -def degreeRegions14 : List PrefixRegion := [degreeRegion14_0,degreeRegion14_1,degreeRegion14_2] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 14. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion14_0 : PrefixRegion := ([(5,11)], [(6,13)]) +def degreeRegion14_1 : PrefixRegion := ([(6,13)], [(5,11)]) +def degreeRegion14_2 : PrefixRegion := ([(6,13)], [(6,13)]) + +def degreeRegions14 : List PrefixRegion := [degreeRegion14_0,degreeRegion14_1,degreeRegion14_2] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData16.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData16.lean index 2c9655ce23e263afcd3f9d90b1ac7de1e4542177..27171d6c8a1a46d7e56f83f88e8e0367728fcf9e 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData16.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData16.lean @@ -1,28 +1,28 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 16. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion16_0 : PrefixRegion := ([(3,9)], [(5,15)]) -def degreeRegion16_1 : PrefixRegion := ([(4,12)], [(4,12)]) -def degreeRegion16_2 : PrefixRegion := ([(4,12)], [(5,15)]) -def degreeRegion16_3 : PrefixRegion := ([(5,15)], [(3,9)]) -def degreeRegion16_4 : PrefixRegion := ([(5,15)], [(4,12)]) -def degreeRegion16_5 : PrefixRegion := ([(5,15)], [(5,15)]) - -def degreeRegions16 : List PrefixRegion := [degreeRegion16_0,degreeRegion16_1,degreeRegion16_2,degreeRegion16_3,degreeRegion16_4,degreeRegion16_5] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 16. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion16_0 : PrefixRegion := ([(3,9)], [(5,15)]) +def degreeRegion16_1 : PrefixRegion := ([(4,12)], [(4,12)]) +def degreeRegion16_2 : PrefixRegion := ([(4,12)], [(5,15)]) +def degreeRegion16_3 : PrefixRegion := ([(5,15)], [(3,9)]) +def degreeRegion16_4 : PrefixRegion := ([(5,15)], [(4,12)]) +def degreeRegion16_5 : PrefixRegion := ([(5,15)], [(5,15)]) + +def degreeRegions16 : List PrefixRegion := [degreeRegion16_0,degreeRegion16_1,degreeRegion16_2,degreeRegion16_3,degreeRegion16_4,degreeRegion16_5] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData18.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData18.lean index 2798063adb9f452ccb3f60bc31435105535b4d9c..533b3e545aaa1e7491b4fb30c240ea8c5e6e2834 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData18.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData18.lean @@ -1,32 +1,32 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 18. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion18_0 : PrefixRegion := ([(3,9)], [(6,17)]) -def degreeRegion18_1 : PrefixRegion := ([(4,12)], [(5,15)]) -def degreeRegion18_2 : PrefixRegion := ([(4,12)], [(6,17)]) -def degreeRegion18_3 : PrefixRegion := ([(5,15)], [(4,12)]) -def degreeRegion18_4 : PrefixRegion := ([(5,15)], [(5,15)]) -def degreeRegion18_5 : PrefixRegion := ([(5,15)], [(6,17)]) -def degreeRegion18_6 : PrefixRegion := ([(6,17)], [(3,9)]) -def degreeRegion18_7 : PrefixRegion := ([(6,17)], [(4,12)]) -def degreeRegion18_8 : PrefixRegion := ([(6,17)], [(5,15)]) -def degreeRegion18_9 : PrefixRegion := ([(6,17)], [(6,17)]) - -def degreeRegions18 : List PrefixRegion := [degreeRegion18_0,degreeRegion18_1,degreeRegion18_2,degreeRegion18_3,degreeRegion18_4,degreeRegion18_5,degreeRegion18_6,degreeRegion18_7,degreeRegion18_8,degreeRegion18_9] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 18. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion18_0 : PrefixRegion := ([(3,9)], [(6,17)]) +def degreeRegion18_1 : PrefixRegion := ([(4,12)], [(5,15)]) +def degreeRegion18_2 : PrefixRegion := ([(4,12)], [(6,17)]) +def degreeRegion18_3 : PrefixRegion := ([(5,15)], [(4,12)]) +def degreeRegion18_4 : PrefixRegion := ([(5,15)], [(5,15)]) +def degreeRegion18_5 : PrefixRegion := ([(5,15)], [(6,17)]) +def degreeRegion18_6 : PrefixRegion := ([(6,17)], [(3,9)]) +def degreeRegion18_7 : PrefixRegion := ([(6,17)], [(4,12)]) +def degreeRegion18_8 : PrefixRegion := ([(6,17)], [(5,15)]) +def degreeRegion18_9 : PrefixRegion := ([(6,17)], [(6,17)]) + +def degreeRegions18 : List PrefixRegion := [degreeRegion18_0,degreeRegion18_1,degreeRegion18_2,degreeRegion18_3,degreeRegion18_4,degreeRegion18_5,degreeRegion18_6,degreeRegion18_7,degreeRegion18_8,degreeRegion18_9] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData19.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData19.lean index a1949bdf9075d2a55b8238f66b80bce86bcd915a..540b6d00f257c276756a9174e68e64059effa801 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData19.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData19.lean @@ -1,24 +1,24 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 19. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion19_0 : PrefixRegion := ([(1,8),(5,14)], [(1,8),(5,14)]) -def degreeRegion19_1 : PrefixRegion := ([(1,8),(7,18)], [(1,8),(7,18)]) - -def degreeRegions19 : List PrefixRegion := [degreeRegion19_0,degreeRegion19_1] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 19. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion19_0 : PrefixRegion := ([(1,8),(5,14)], [(1,8),(5,14)]) +def degreeRegion19_1 : PrefixRegion := ([(1,8),(7,18)], [(1,8),(7,18)]) + +def degreeRegions19 : List PrefixRegion := [degreeRegion19_0,degreeRegion19_1] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData20.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData20.lean index de045413289a69a6f6ac1fc211aa585881e14ad8..3e9b0759fac783c3feebb1fca65cc39d00fc76f3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData20.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData20.lean @@ -1,42 +1,42 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 20. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion20_0 : PrefixRegion := ([(1,5)], [(1,5)]) -def degreeRegion20_1 : PrefixRegion := ([(1,5)], [(2,9)]) -def degreeRegion20_2 : PrefixRegion := ([(1,5)], [(3,13)]) -def degreeRegion20_3 : PrefixRegion := ([(1,5)], [(4,16)]) -def degreeRegion20_4 : PrefixRegion := ([(2,9)], [(1,5)]) -def degreeRegion20_5 : PrefixRegion := ([(2,9)], [(4,16)]) -def degreeRegion20_6 : PrefixRegion := ([(2,9)], [(5,19)]) -def degreeRegion20_7 : PrefixRegion := ([(3,13)], [(1,5)]) -def degreeRegion20_8 : PrefixRegion := ([(3,13)], [(3,13)]) -def degreeRegion20_9 : PrefixRegion := ([(3,13)], [(4,16)]) -def degreeRegion20_10 : PrefixRegion := ([(3,13)], [(5,19)]) -def degreeRegion20_11 : PrefixRegion := ([(4,16)], [(1,5)]) -def degreeRegion20_12 : PrefixRegion := ([(4,16)], [(2,9)]) -def degreeRegion20_13 : PrefixRegion := ([(4,16)], [(3,13)]) -def degreeRegion20_14 : PrefixRegion := ([(4,16)], [(4,16)]) -def degreeRegion20_15 : PrefixRegion := ([(4,16)], [(5,19)]) -def degreeRegion20_16 : PrefixRegion := ([(5,19)], [(2,9)]) -def degreeRegion20_17 : PrefixRegion := ([(5,19)], [(3,13)]) -def degreeRegion20_18 : PrefixRegion := ([(5,19)], [(4,16)]) -def degreeRegion20_19 : PrefixRegion := ([(5,19)], [(5,19)]) - -def degreeRegions20 : List PrefixRegion := [degreeRegion20_0,degreeRegion20_1,degreeRegion20_2,degreeRegion20_3,degreeRegion20_4,degreeRegion20_5,degreeRegion20_6,degreeRegion20_7,degreeRegion20_8,degreeRegion20_9,degreeRegion20_10,degreeRegion20_11,degreeRegion20_12,degreeRegion20_13,degreeRegion20_14,degreeRegion20_15,degreeRegion20_16,degreeRegion20_17,degreeRegion20_18,degreeRegion20_19] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 20. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion20_0 : PrefixRegion := ([(1,5)], [(1,5)]) +def degreeRegion20_1 : PrefixRegion := ([(1,5)], [(2,9)]) +def degreeRegion20_2 : PrefixRegion := ([(1,5)], [(3,13)]) +def degreeRegion20_3 : PrefixRegion := ([(1,5)], [(4,16)]) +def degreeRegion20_4 : PrefixRegion := ([(2,9)], [(1,5)]) +def degreeRegion20_5 : PrefixRegion := ([(2,9)], [(4,16)]) +def degreeRegion20_6 : PrefixRegion := ([(2,9)], [(5,19)]) +def degreeRegion20_7 : PrefixRegion := ([(3,13)], [(1,5)]) +def degreeRegion20_8 : PrefixRegion := ([(3,13)], [(3,13)]) +def degreeRegion20_9 : PrefixRegion := ([(3,13)], [(4,16)]) +def degreeRegion20_10 : PrefixRegion := ([(3,13)], [(5,19)]) +def degreeRegion20_11 : PrefixRegion := ([(4,16)], [(1,5)]) +def degreeRegion20_12 : PrefixRegion := ([(4,16)], [(2,9)]) +def degreeRegion20_13 : PrefixRegion := ([(4,16)], [(3,13)]) +def degreeRegion20_14 : PrefixRegion := ([(4,16)], [(4,16)]) +def degreeRegion20_15 : PrefixRegion := ([(4,16)], [(5,19)]) +def degreeRegion20_16 : PrefixRegion := ([(5,19)], [(2,9)]) +def degreeRegion20_17 : PrefixRegion := ([(5,19)], [(3,13)]) +def degreeRegion20_18 : PrefixRegion := ([(5,19)], [(4,16)]) +def degreeRegion20_19 : PrefixRegion := ([(5,19)], [(5,19)]) + +def degreeRegions20 : List PrefixRegion := [degreeRegion20_0,degreeRegion20_1,degreeRegion20_2,degreeRegion20_3,degreeRegion20_4,degreeRegion20_5,degreeRegion20_6,degreeRegion20_7,degreeRegion20_8,degreeRegion20_9,degreeRegion20_10,degreeRegion20_11,degreeRegion20_12,degreeRegion20_13,degreeRegion20_14,degreeRegion20_15,degreeRegion20_16,degreeRegion20_17,degreeRegion20_18,degreeRegion20_19] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData22.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData22.lean index 7a28e6bc67e3f158fab85c4ca43f3358207890ff..9783686efe783aab68541a4adeeb17361d8fd866 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData22.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData22.lean @@ -1,37 +1,37 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 22. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion22_0 : PrefixRegion := ([(2,8)], [(6,21)]) -def degreeRegion22_1 : PrefixRegion := ([(3,12)], [(5,18)]) -def degreeRegion22_2 : PrefixRegion := ([(3,12)], [(6,21)]) -def degreeRegion22_3 : PrefixRegion := ([(4,15)], [(4,15)]) -def degreeRegion22_4 : PrefixRegion := ([(4,15)], [(5,18)]) -def degreeRegion22_5 : PrefixRegion := ([(4,15)], [(6,21)]) -def degreeRegion22_6 : PrefixRegion := ([(5,18)], [(3,12)]) -def degreeRegion22_7 : PrefixRegion := ([(5,18)], [(4,15)]) -def degreeRegion22_8 : PrefixRegion := ([(5,18)], [(5,18)]) -def degreeRegion22_9 : PrefixRegion := ([(5,18)], [(6,21)]) -def degreeRegion22_10 : PrefixRegion := ([(6,21)], [(2,8)]) -def degreeRegion22_11 : PrefixRegion := ([(6,21)], [(3,12)]) -def degreeRegion22_12 : PrefixRegion := ([(6,21)], [(4,15)]) -def degreeRegion22_13 : PrefixRegion := ([(6,21)], [(5,18)]) -def degreeRegion22_14 : PrefixRegion := ([(6,21)], [(6,21)]) - -def degreeRegions22 : List PrefixRegion := [degreeRegion22_0,degreeRegion22_1,degreeRegion22_2,degreeRegion22_3,degreeRegion22_4,degreeRegion22_5,degreeRegion22_6,degreeRegion22_7,degreeRegion22_8,degreeRegion22_9,degreeRegion22_10,degreeRegion22_11,degreeRegion22_12,degreeRegion22_13,degreeRegion22_14] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 22. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion22_0 : PrefixRegion := ([(2,8)], [(6,21)]) +def degreeRegion22_1 : PrefixRegion := ([(3,12)], [(5,18)]) +def degreeRegion22_2 : PrefixRegion := ([(3,12)], [(6,21)]) +def degreeRegion22_3 : PrefixRegion := ([(4,15)], [(4,15)]) +def degreeRegion22_4 : PrefixRegion := ([(4,15)], [(5,18)]) +def degreeRegion22_5 : PrefixRegion := ([(4,15)], [(6,21)]) +def degreeRegion22_6 : PrefixRegion := ([(5,18)], [(3,12)]) +def degreeRegion22_7 : PrefixRegion := ([(5,18)], [(4,15)]) +def degreeRegion22_8 : PrefixRegion := ([(5,18)], [(5,18)]) +def degreeRegion22_9 : PrefixRegion := ([(5,18)], [(6,21)]) +def degreeRegion22_10 : PrefixRegion := ([(6,21)], [(2,8)]) +def degreeRegion22_11 : PrefixRegion := ([(6,21)], [(3,12)]) +def degreeRegion22_12 : PrefixRegion := ([(6,21)], [(4,15)]) +def degreeRegion22_13 : PrefixRegion := ([(6,21)], [(5,18)]) +def degreeRegion22_14 : PrefixRegion := ([(6,21)], [(6,21)]) + +def degreeRegions22 : List PrefixRegion := [degreeRegion22_0,degreeRegion22_1,degreeRegion22_2,degreeRegion22_3,degreeRegion22_4,degreeRegion22_5,degreeRegion22_6,degreeRegion22_7,degreeRegion22_8,degreeRegion22_9,degreeRegion22_10,degreeRegion22_11,degreeRegion22_12,degreeRegion22_13,degreeRegion22_14] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData24.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData24.lean index c5b02617397900257b4f09451b702112df29b883..033bea1f59a7865cee748d537992af2122c0ac85 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData24.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData24.lean @@ -1,47 +1,47 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 24. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion24_0 : PrefixRegion := ([(1,7)], [(1,7)]) -def degreeRegion24_1 : PrefixRegion := ([(1,7)], [(2,11)]) -def degreeRegion24_2 : PrefixRegion := ([(1,7)], [(3,15)]) -def degreeRegion24_3 : PrefixRegion := ([(1,7)], [(4,19)]) -def degreeRegion24_4 : PrefixRegion := ([(1,7)], [(5,23)]) -def degreeRegion24_5 : PrefixRegion := ([(2,11)], [(1,7)]) -def degreeRegion24_6 : PrefixRegion := ([(2,11)], [(2,11)]) -def degreeRegion24_7 : PrefixRegion := ([(2,11)], [(3,15)]) -def degreeRegion24_8 : PrefixRegion := ([(2,11)], [(4,19)]) -def degreeRegion24_9 : PrefixRegion := ([(2,11)], [(5,23)]) -def degreeRegion24_10 : PrefixRegion := ([(3,15)], [(1,7)]) -def degreeRegion24_11 : PrefixRegion := ([(3,15)], [(2,11)]) -def degreeRegion24_12 : PrefixRegion := ([(3,15)], [(3,15)]) -def degreeRegion24_13 : PrefixRegion := ([(3,15)], [(4,19)]) -def degreeRegion24_14 : PrefixRegion := ([(3,15)], [(5,23)]) -def degreeRegion24_15 : PrefixRegion := ([(4,19)], [(1,7)]) -def degreeRegion24_16 : PrefixRegion := ([(4,19)], [(2,11)]) -def degreeRegion24_17 : PrefixRegion := ([(4,19)], [(3,15)]) -def degreeRegion24_18 : PrefixRegion := ([(4,19)], [(4,19)]) -def degreeRegion24_19 : PrefixRegion := ([(4,19)], [(5,23)]) -def degreeRegion24_20 : PrefixRegion := ([(5,23)], [(1,7)]) -def degreeRegion24_21 : PrefixRegion := ([(5,23)], [(2,11)]) -def degreeRegion24_22 : PrefixRegion := ([(5,23)], [(3,15)]) -def degreeRegion24_23 : PrefixRegion := ([(5,23)], [(4,19)]) -def degreeRegion24_24 : PrefixRegion := ([(5,23)], [(5,23)]) - -def degreeRegions24 : List PrefixRegion := [degreeRegion24_0,degreeRegion24_1,degreeRegion24_2,degreeRegion24_3,degreeRegion24_4,degreeRegion24_5,degreeRegion24_6,degreeRegion24_7,degreeRegion24_8,degreeRegion24_9,degreeRegion24_10,degreeRegion24_11,degreeRegion24_12,degreeRegion24_13,degreeRegion24_14,degreeRegion24_15,degreeRegion24_16,degreeRegion24_17,degreeRegion24_18,degreeRegion24_19,degreeRegion24_20,degreeRegion24_21,degreeRegion24_22,degreeRegion24_23,degreeRegion24_24] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 24. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion24_0 : PrefixRegion := ([(1,7)], [(1,7)]) +def degreeRegion24_1 : PrefixRegion := ([(1,7)], [(2,11)]) +def degreeRegion24_2 : PrefixRegion := ([(1,7)], [(3,15)]) +def degreeRegion24_3 : PrefixRegion := ([(1,7)], [(4,19)]) +def degreeRegion24_4 : PrefixRegion := ([(1,7)], [(5,23)]) +def degreeRegion24_5 : PrefixRegion := ([(2,11)], [(1,7)]) +def degreeRegion24_6 : PrefixRegion := ([(2,11)], [(2,11)]) +def degreeRegion24_7 : PrefixRegion := ([(2,11)], [(3,15)]) +def degreeRegion24_8 : PrefixRegion := ([(2,11)], [(4,19)]) +def degreeRegion24_9 : PrefixRegion := ([(2,11)], [(5,23)]) +def degreeRegion24_10 : PrefixRegion := ([(3,15)], [(1,7)]) +def degreeRegion24_11 : PrefixRegion := ([(3,15)], [(2,11)]) +def degreeRegion24_12 : PrefixRegion := ([(3,15)], [(3,15)]) +def degreeRegion24_13 : PrefixRegion := ([(3,15)], [(4,19)]) +def degreeRegion24_14 : PrefixRegion := ([(3,15)], [(5,23)]) +def degreeRegion24_15 : PrefixRegion := ([(4,19)], [(1,7)]) +def degreeRegion24_16 : PrefixRegion := ([(4,19)], [(2,11)]) +def degreeRegion24_17 : PrefixRegion := ([(4,19)], [(3,15)]) +def degreeRegion24_18 : PrefixRegion := ([(4,19)], [(4,19)]) +def degreeRegion24_19 : PrefixRegion := ([(4,19)], [(5,23)]) +def degreeRegion24_20 : PrefixRegion := ([(5,23)], [(1,7)]) +def degreeRegion24_21 : PrefixRegion := ([(5,23)], [(2,11)]) +def degreeRegion24_22 : PrefixRegion := ([(5,23)], [(3,15)]) +def degreeRegion24_23 : PrefixRegion := ([(5,23)], [(4,19)]) +def degreeRegion24_24 : PrefixRegion := ([(5,23)], [(5,23)]) + +def degreeRegions24 : List PrefixRegion := [degreeRegion24_0,degreeRegion24_1,degreeRegion24_2,degreeRegion24_3,degreeRegion24_4,degreeRegion24_5,degreeRegion24_6,degreeRegion24_7,degreeRegion24_8,degreeRegion24_9,degreeRegion24_10,degreeRegion24_11,degreeRegion24_12,degreeRegion24_13,degreeRegion24_14,degreeRegion24_15,degreeRegion24_16,degreeRegion24_17,degreeRegion24_18,degreeRegion24_19,degreeRegion24_20,degreeRegion24_21,degreeRegion24_22,degreeRegion24_23,degreeRegion24_24] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData26.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData26.lean index e1221b916cf746d647bfcd78f0ca13c1f67643ef..027ed746f361e791af3dc6d823386bf6d6fbe697 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData26.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData26.lean @@ -1,41 +1,41 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 26. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion26_0 : PrefixRegion := ([(2,10)], [(5,22)]) -def degreeRegion26_1 : PrefixRegion := ([(2,10)], [(6,25)]) -def degreeRegion26_2 : PrefixRegion := ([(3,14)], [(4,18)]) -def degreeRegion26_3 : PrefixRegion := ([(3,14)], [(5,22)]) -def degreeRegion26_4 : PrefixRegion := ([(3,14)], [(6,25)]) -def degreeRegion26_5 : PrefixRegion := ([(4,18)], [(3,14)]) -def degreeRegion26_6 : PrefixRegion := ([(4,18)], [(4,18)]) -def degreeRegion26_7 : PrefixRegion := ([(4,18)], [(5,22)]) -def degreeRegion26_8 : PrefixRegion := ([(4,18)], [(6,25)]) -def degreeRegion26_9 : PrefixRegion := ([(5,22)], [(2,10)]) -def degreeRegion26_10 : PrefixRegion := ([(5,22)], [(3,14)]) -def degreeRegion26_11 : PrefixRegion := ([(5,22)], [(4,18)]) -def degreeRegion26_12 : PrefixRegion := ([(5,22)], [(5,22)]) -def degreeRegion26_13 : PrefixRegion := ([(5,22)], [(6,25)]) -def degreeRegion26_14 : PrefixRegion := ([(6,25)], [(2,10)]) -def degreeRegion26_15 : PrefixRegion := ([(6,25)], [(3,14)]) -def degreeRegion26_16 : PrefixRegion := ([(6,25)], [(4,18)]) -def degreeRegion26_17 : PrefixRegion := ([(6,25)], [(5,22)]) -def degreeRegion26_18 : PrefixRegion := ([(6,25)], [(6,25)]) - -def degreeRegions26 : List PrefixRegion := [degreeRegion26_0,degreeRegion26_1,degreeRegion26_2,degreeRegion26_3,degreeRegion26_4,degreeRegion26_5,degreeRegion26_6,degreeRegion26_7,degreeRegion26_8,degreeRegion26_9,degreeRegion26_10,degreeRegion26_11,degreeRegion26_12,degreeRegion26_13,degreeRegion26_14,degreeRegion26_15,degreeRegion26_16,degreeRegion26_17,degreeRegion26_18] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 26. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion26_0 : PrefixRegion := ([(2,10)], [(5,22)]) +def degreeRegion26_1 : PrefixRegion := ([(2,10)], [(6,25)]) +def degreeRegion26_2 : PrefixRegion := ([(3,14)], [(4,18)]) +def degreeRegion26_3 : PrefixRegion := ([(3,14)], [(5,22)]) +def degreeRegion26_4 : PrefixRegion := ([(3,14)], [(6,25)]) +def degreeRegion26_5 : PrefixRegion := ([(4,18)], [(3,14)]) +def degreeRegion26_6 : PrefixRegion := ([(4,18)], [(4,18)]) +def degreeRegion26_7 : PrefixRegion := ([(4,18)], [(5,22)]) +def degreeRegion26_8 : PrefixRegion := ([(4,18)], [(6,25)]) +def degreeRegion26_9 : PrefixRegion := ([(5,22)], [(2,10)]) +def degreeRegion26_10 : PrefixRegion := ([(5,22)], [(3,14)]) +def degreeRegion26_11 : PrefixRegion := ([(5,22)], [(4,18)]) +def degreeRegion26_12 : PrefixRegion := ([(5,22)], [(5,22)]) +def degreeRegion26_13 : PrefixRegion := ([(5,22)], [(6,25)]) +def degreeRegion26_14 : PrefixRegion := ([(6,25)], [(2,10)]) +def degreeRegion26_15 : PrefixRegion := ([(6,25)], [(3,14)]) +def degreeRegion26_16 : PrefixRegion := ([(6,25)], [(4,18)]) +def degreeRegion26_17 : PrefixRegion := ([(6,25)], [(5,22)]) +def degreeRegion26_18 : PrefixRegion := ([(6,25)], [(6,25)]) + +def degreeRegions26 : List PrefixRegion := [degreeRegion26_0,degreeRegion26_1,degreeRegion26_2,degreeRegion26_3,degreeRegion26_4,degreeRegion26_5,degreeRegion26_6,degreeRegion26_7,degreeRegion26_8,degreeRegion26_9,degreeRegion26_10,degreeRegion26_11,degreeRegion26_12,degreeRegion26_13,degreeRegion26_14,degreeRegion26_15,degreeRegion26_16,degreeRegion26_17,degreeRegion26_18] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData31.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData31.lean index 2dd4c8d1b29598524167075c080378fdb6d95bb1..6b2916425b78d9b50802551120c14c900a9ae11a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData31.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData31.lean @@ -1,43 +1,43 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 31. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion31_0 : PrefixRegion := ([(1,10),(3,14)], [(1,11),(6,26)]) -def degreeRegion31_1 : PrefixRegion := ([(1,10),(3,14)], [(1,11),(7,30)]) -def degreeRegion31_2 : PrefixRegion := ([(1,10),(4,18)], [(1,10),(5,22)]) -def degreeRegion31_3 : PrefixRegion := ([(1,10),(4,18)], [(1,10),(6,26)]) -def degreeRegion31_4 : PrefixRegion := ([(1,10),(4,18)], [(1,10),(7,30)]) -def degreeRegion31_5 : PrefixRegion := ([(1,10),(5,22)], [(1,10),(4,18)]) -def degreeRegion31_6 : PrefixRegion := ([(1,10),(5,22)], [(1,10),(5,22)]) -def degreeRegion31_7 : PrefixRegion := ([(1,10),(5,22)], [(1,10),(6,26)]) -def degreeRegion31_8 : PrefixRegion := ([(1,10),(5,22)], [(1,10),(7,30)]) -def degreeRegion31_9 : PrefixRegion := ([(1,10),(6,26)], [(1,10),(4,18)]) -def degreeRegion31_10 : PrefixRegion := ([(1,10),(6,26)], [(1,10),(5,22)]) -def degreeRegion31_11 : PrefixRegion := ([(1,10),(6,26)], [(1,10),(6,26)]) -def degreeRegion31_12 : PrefixRegion := ([(1,10),(6,26)], [(1,10),(7,30)]) -def degreeRegion31_13 : PrefixRegion := ([(1,10),(7,30)], [(1,10),(4,18)]) -def degreeRegion31_14 : PrefixRegion := ([(1,10),(7,30)], [(1,10),(5,22)]) -def degreeRegion31_15 : PrefixRegion := ([(1,10),(7,30)], [(1,10),(6,26)]) -def degreeRegion31_16 : PrefixRegion := ([(1,10),(7,30)], [(1,10),(7,30)]) -def degreeRegion31_17 : PrefixRegion := ([(1,11),(6,26)], [(1,10),(3,14)]) -def degreeRegion31_18 : PrefixRegion := ([(1,11),(7,30)], [(1,10),(3,14)]) -def degreeRegion31_19 : PrefixRegion := ([(2,10),(3,14)], [(7,30)]) -def degreeRegion31_20 : PrefixRegion := ([(7,30)], [(2,10),(3,14)]) - -def degreeRegions31 : List PrefixRegion := [degreeRegion31_0,degreeRegion31_1,degreeRegion31_2,degreeRegion31_3,degreeRegion31_4,degreeRegion31_5,degreeRegion31_6,degreeRegion31_7,degreeRegion31_8,degreeRegion31_9,degreeRegion31_10,degreeRegion31_11,degreeRegion31_12,degreeRegion31_13,degreeRegion31_14,degreeRegion31_15,degreeRegion31_16,degreeRegion31_17,degreeRegion31_18,degreeRegion31_19,degreeRegion31_20] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 31. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion31_0 : PrefixRegion := ([(1,10),(3,14)], [(1,11),(6,26)]) +def degreeRegion31_1 : PrefixRegion := ([(1,10),(3,14)], [(1,11),(7,30)]) +def degreeRegion31_2 : PrefixRegion := ([(1,10),(4,18)], [(1,10),(5,22)]) +def degreeRegion31_3 : PrefixRegion := ([(1,10),(4,18)], [(1,10),(6,26)]) +def degreeRegion31_4 : PrefixRegion := ([(1,10),(4,18)], [(1,10),(7,30)]) +def degreeRegion31_5 : PrefixRegion := ([(1,10),(5,22)], [(1,10),(4,18)]) +def degreeRegion31_6 : PrefixRegion := ([(1,10),(5,22)], [(1,10),(5,22)]) +def degreeRegion31_7 : PrefixRegion := ([(1,10),(5,22)], [(1,10),(6,26)]) +def degreeRegion31_8 : PrefixRegion := ([(1,10),(5,22)], [(1,10),(7,30)]) +def degreeRegion31_9 : PrefixRegion := ([(1,10),(6,26)], [(1,10),(4,18)]) +def degreeRegion31_10 : PrefixRegion := ([(1,10),(6,26)], [(1,10),(5,22)]) +def degreeRegion31_11 : PrefixRegion := ([(1,10),(6,26)], [(1,10),(6,26)]) +def degreeRegion31_12 : PrefixRegion := ([(1,10),(6,26)], [(1,10),(7,30)]) +def degreeRegion31_13 : PrefixRegion := ([(1,10),(7,30)], [(1,10),(4,18)]) +def degreeRegion31_14 : PrefixRegion := ([(1,10),(7,30)], [(1,10),(5,22)]) +def degreeRegion31_15 : PrefixRegion := ([(1,10),(7,30)], [(1,10),(6,26)]) +def degreeRegion31_16 : PrefixRegion := ([(1,10),(7,30)], [(1,10),(7,30)]) +def degreeRegion31_17 : PrefixRegion := ([(1,11),(6,26)], [(1,10),(3,14)]) +def degreeRegion31_18 : PrefixRegion := ([(1,11),(7,30)], [(1,10),(3,14)]) +def degreeRegion31_19 : PrefixRegion := ([(2,10),(3,14)], [(7,30)]) +def degreeRegion31_20 : PrefixRegion := ([(7,30)], [(2,10),(3,14)]) + +def degreeRegions31 : List PrefixRegion := [degreeRegion31_0,degreeRegion31_1,degreeRegion31_2,degreeRegion31_3,degreeRegion31_4,degreeRegion31_5,degreeRegion31_6,degreeRegion31_7,degreeRegion31_8,degreeRegion31_9,degreeRegion31_10,degreeRegion31_11,degreeRegion31_12,degreeRegion31_13,degreeRegion31_14,degreeRegion31_15,degreeRegion31_16,degreeRegion31_17,degreeRegion31_18,degreeRegion31_19,degreeRegion31_20] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData35.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData35.lean index 5f207fc4c530803199a4a3cc75b2d3ba8e5b1e82..60446704a6fcbce10604daaf14fd83a2a6ea1cb9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData35.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData35.lean @@ -1,68 +1,68 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 35. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion35_0 : PrefixRegion := ([(1,10),(3,15)], [(1,15),(6,30)]) -def degreeRegion35_1 : PrefixRegion := ([(1,10),(3,15)], [(1,15),(7,34)]) -def degreeRegion35_2 : PrefixRegion := ([(1,10),(3,18),(4,20)], [(1,15),(5,25)]) -def degreeRegion35_3 : PrefixRegion := ([(1,10),(3,18),(4,20)], [(1,15),(6,30)]) -def degreeRegion35_4 : PrefixRegion := ([(1,10),(3,18),(4,20)], [(1,15),(7,34)]) -def degreeRegion35_5 : PrefixRegion := ([(1,10),(3,18),(5,25)], [(1,15),(5,25)]) -def degreeRegion35_6 : PrefixRegion := ([(1,10),(3,18),(5,25)], [(1,15),(6,30)]) -def degreeRegion35_7 : PrefixRegion := ([(1,10),(3,18),(5,25)], [(1,15),(7,34)]) -def degreeRegion35_8 : PrefixRegion := ([(1,10),(3,18),(6,30)], [(1,15),(5,25)]) -def degreeRegion35_9 : PrefixRegion := ([(1,10),(3,18),(6,30)], [(1,15),(6,30)]) -def degreeRegion35_10 : PrefixRegion := ([(1,10),(3,18),(6,30)], [(1,15),(7,34)]) -def degreeRegion35_11 : PrefixRegion := ([(1,10),(3,18),(7,34)], [(1,15),(5,25)]) -def degreeRegion35_12 : PrefixRegion := ([(1,10),(3,18),(7,34)], [(1,15),(6,30)]) -def degreeRegion35_13 : PrefixRegion := ([(1,10),(3,18),(7,34)], [(1,15),(7,34)]) -def degreeRegion35_14 : PrefixRegion := ([(1,10),(4,20)], [(1,10),(5,25)]) -def degreeRegion35_15 : PrefixRegion := ([(1,10),(4,20)], [(1,10),(6,30)]) -def degreeRegion35_16 : PrefixRegion := ([(1,10),(4,20)], [(1,10),(7,34)]) -def degreeRegion35_17 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(4,20)]) -def degreeRegion35_18 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(5,25)]) -def degreeRegion35_19 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(6,30)]) -def degreeRegion35_20 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(7,34)]) -def degreeRegion35_21 : PrefixRegion := ([(1,10),(6,30)], [(1,10),(4,20)]) -def degreeRegion35_22 : PrefixRegion := ([(1,10),(6,30)], [(1,10),(5,25)]) -def degreeRegion35_23 : PrefixRegion := ([(1,10),(6,30)], [(1,10),(6,30)]) -def degreeRegion35_24 : PrefixRegion := ([(1,10),(6,30)], [(1,10),(7,34)]) -def degreeRegion35_25 : PrefixRegion := ([(1,10),(7,34)], [(1,10),(4,20)]) -def degreeRegion35_26 : PrefixRegion := ([(1,10),(7,34)], [(1,10),(5,25)]) -def degreeRegion35_27 : PrefixRegion := ([(1,10),(7,34)], [(1,10),(6,30)]) -def degreeRegion35_28 : PrefixRegion := ([(1,10),(7,34)], [(1,10),(7,34)]) -def degreeRegion35_29 : PrefixRegion := ([(1,15),(3,18),(5,25)], [(1,15),(3,18),(5,25)]) -def degreeRegion35_30 : PrefixRegion := ([(1,15),(5,25)], [(1,10),(3,18),(4,20)]) -def degreeRegion35_31 : PrefixRegion := ([(1,15),(5,25)], [(1,10),(3,18),(5,25)]) -def degreeRegion35_32 : PrefixRegion := ([(1,15),(5,25)], [(1,10),(3,18),(6,30)]) -def degreeRegion35_33 : PrefixRegion := ([(1,15),(5,25)], [(1,10),(3,18),(7,34)]) -def degreeRegion35_34 : PrefixRegion := ([(1,15),(6,30)], [(1,10),(3,15)]) -def degreeRegion35_35 : PrefixRegion := ([(1,15),(6,30)], [(1,10),(3,18),(4,20)]) -def degreeRegion35_36 : PrefixRegion := ([(1,15),(6,30)], [(1,10),(3,18),(5,25)]) -def degreeRegion35_37 : PrefixRegion := ([(1,15),(6,30)], [(1,10),(3,18),(6,30)]) -def degreeRegion35_38 : PrefixRegion := ([(1,15),(6,30)], [(1,10),(3,18),(7,34)]) -def degreeRegion35_39 : PrefixRegion := ([(1,15),(7,34)], [(1,10),(3,15)]) -def degreeRegion35_40 : PrefixRegion := ([(1,15),(7,34)], [(1,10),(3,18),(4,20)]) -def degreeRegion35_41 : PrefixRegion := ([(1,15),(7,34)], [(1,10),(3,18),(5,25)]) -def degreeRegion35_42 : PrefixRegion := ([(1,15),(7,34)], [(1,10),(3,18),(6,30)]) -def degreeRegion35_43 : PrefixRegion := ([(1,15),(7,34)], [(1,10),(3,18),(7,34)]) -def degreeRegion35_44 : PrefixRegion := ([(2,10),(3,18)], [(7,34)]) -def degreeRegion35_45 : PrefixRegion := ([(7,34)], [(2,10),(3,18)]) - -def degreeRegions35 : List PrefixRegion := [degreeRegion35_0,degreeRegion35_1,degreeRegion35_2,degreeRegion35_3,degreeRegion35_4,degreeRegion35_5,degreeRegion35_6,degreeRegion35_7,degreeRegion35_8,degreeRegion35_9,degreeRegion35_10,degreeRegion35_11,degreeRegion35_12,degreeRegion35_13,degreeRegion35_14,degreeRegion35_15,degreeRegion35_16,degreeRegion35_17,degreeRegion35_18,degreeRegion35_19,degreeRegion35_20,degreeRegion35_21,degreeRegion35_22,degreeRegion35_23,degreeRegion35_24,degreeRegion35_25,degreeRegion35_26,degreeRegion35_27,degreeRegion35_28,degreeRegion35_29,degreeRegion35_30,degreeRegion35_31,degreeRegion35_32,degreeRegion35_33,degreeRegion35_34,degreeRegion35_35,degreeRegion35_36,degreeRegion35_37,degreeRegion35_38,degreeRegion35_39,degreeRegion35_40,degreeRegion35_41,degreeRegion35_42,degreeRegion35_43,degreeRegion35_44,degreeRegion35_45] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 35. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion35_0 : PrefixRegion := ([(1,10),(3,15)], [(1,15),(6,30)]) +def degreeRegion35_1 : PrefixRegion := ([(1,10),(3,15)], [(1,15),(7,34)]) +def degreeRegion35_2 : PrefixRegion := ([(1,10),(3,18),(4,20)], [(1,15),(5,25)]) +def degreeRegion35_3 : PrefixRegion := ([(1,10),(3,18),(4,20)], [(1,15),(6,30)]) +def degreeRegion35_4 : PrefixRegion := ([(1,10),(3,18),(4,20)], [(1,15),(7,34)]) +def degreeRegion35_5 : PrefixRegion := ([(1,10),(3,18),(5,25)], [(1,15),(5,25)]) +def degreeRegion35_6 : PrefixRegion := ([(1,10),(3,18),(5,25)], [(1,15),(6,30)]) +def degreeRegion35_7 : PrefixRegion := ([(1,10),(3,18),(5,25)], [(1,15),(7,34)]) +def degreeRegion35_8 : PrefixRegion := ([(1,10),(3,18),(6,30)], [(1,15),(5,25)]) +def degreeRegion35_9 : PrefixRegion := ([(1,10),(3,18),(6,30)], [(1,15),(6,30)]) +def degreeRegion35_10 : PrefixRegion := ([(1,10),(3,18),(6,30)], [(1,15),(7,34)]) +def degreeRegion35_11 : PrefixRegion := ([(1,10),(3,18),(7,34)], [(1,15),(5,25)]) +def degreeRegion35_12 : PrefixRegion := ([(1,10),(3,18),(7,34)], [(1,15),(6,30)]) +def degreeRegion35_13 : PrefixRegion := ([(1,10),(3,18),(7,34)], [(1,15),(7,34)]) +def degreeRegion35_14 : PrefixRegion := ([(1,10),(4,20)], [(1,10),(5,25)]) +def degreeRegion35_15 : PrefixRegion := ([(1,10),(4,20)], [(1,10),(6,30)]) +def degreeRegion35_16 : PrefixRegion := ([(1,10),(4,20)], [(1,10),(7,34)]) +def degreeRegion35_17 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(4,20)]) +def degreeRegion35_18 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(5,25)]) +def degreeRegion35_19 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(6,30)]) +def degreeRegion35_20 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(7,34)]) +def degreeRegion35_21 : PrefixRegion := ([(1,10),(6,30)], [(1,10),(4,20)]) +def degreeRegion35_22 : PrefixRegion := ([(1,10),(6,30)], [(1,10),(5,25)]) +def degreeRegion35_23 : PrefixRegion := ([(1,10),(6,30)], [(1,10),(6,30)]) +def degreeRegion35_24 : PrefixRegion := ([(1,10),(6,30)], [(1,10),(7,34)]) +def degreeRegion35_25 : PrefixRegion := ([(1,10),(7,34)], [(1,10),(4,20)]) +def degreeRegion35_26 : PrefixRegion := ([(1,10),(7,34)], [(1,10),(5,25)]) +def degreeRegion35_27 : PrefixRegion := ([(1,10),(7,34)], [(1,10),(6,30)]) +def degreeRegion35_28 : PrefixRegion := ([(1,10),(7,34)], [(1,10),(7,34)]) +def degreeRegion35_29 : PrefixRegion := ([(1,15),(3,18),(5,25)], [(1,15),(3,18),(5,25)]) +def degreeRegion35_30 : PrefixRegion := ([(1,15),(5,25)], [(1,10),(3,18),(4,20)]) +def degreeRegion35_31 : PrefixRegion := ([(1,15),(5,25)], [(1,10),(3,18),(5,25)]) +def degreeRegion35_32 : PrefixRegion := ([(1,15),(5,25)], [(1,10),(3,18),(6,30)]) +def degreeRegion35_33 : PrefixRegion := ([(1,15),(5,25)], [(1,10),(3,18),(7,34)]) +def degreeRegion35_34 : PrefixRegion := ([(1,15),(6,30)], [(1,10),(3,15)]) +def degreeRegion35_35 : PrefixRegion := ([(1,15),(6,30)], [(1,10),(3,18),(4,20)]) +def degreeRegion35_36 : PrefixRegion := ([(1,15),(6,30)], [(1,10),(3,18),(5,25)]) +def degreeRegion35_37 : PrefixRegion := ([(1,15),(6,30)], [(1,10),(3,18),(6,30)]) +def degreeRegion35_38 : PrefixRegion := ([(1,15),(6,30)], [(1,10),(3,18),(7,34)]) +def degreeRegion35_39 : PrefixRegion := ([(1,15),(7,34)], [(1,10),(3,15)]) +def degreeRegion35_40 : PrefixRegion := ([(1,15),(7,34)], [(1,10),(3,18),(4,20)]) +def degreeRegion35_41 : PrefixRegion := ([(1,15),(7,34)], [(1,10),(3,18),(5,25)]) +def degreeRegion35_42 : PrefixRegion := ([(1,15),(7,34)], [(1,10),(3,18),(6,30)]) +def degreeRegion35_43 : PrefixRegion := ([(1,15),(7,34)], [(1,10),(3,18),(7,34)]) +def degreeRegion35_44 : PrefixRegion := ([(2,10),(3,18)], [(7,34)]) +def degreeRegion35_45 : PrefixRegion := ([(7,34)], [(2,10),(3,18)]) + +def degreeRegions35 : List PrefixRegion := [degreeRegion35_0,degreeRegion35_1,degreeRegion35_2,degreeRegion35_3,degreeRegion35_4,degreeRegion35_5,degreeRegion35_6,degreeRegion35_7,degreeRegion35_8,degreeRegion35_9,degreeRegion35_10,degreeRegion35_11,degreeRegion35_12,degreeRegion35_13,degreeRegion35_14,degreeRegion35_15,degreeRegion35_16,degreeRegion35_17,degreeRegion35_18,degreeRegion35_19,degreeRegion35_20,degreeRegion35_21,degreeRegion35_22,degreeRegion35_23,degreeRegion35_24,degreeRegion35_25,degreeRegion35_26,degreeRegion35_27,degreeRegion35_28,degreeRegion35_29,degreeRegion35_30,degreeRegion35_31,degreeRegion35_32,degreeRegion35_33,degreeRegion35_34,degreeRegion35_35,degreeRegion35_36,degreeRegion35_37,degreeRegion35_38,degreeRegion35_39,degreeRegion35_40,degreeRegion35_41,degreeRegion35_42,degreeRegion35_43,degreeRegion35_44,degreeRegion35_45] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData37.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData37.lean index 93d7ec661ac00187822114bb8f31e561fac5819d..919fb91fbf8301536863ec5139226db46e27189f 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData37.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData37.lean @@ -1,144 +1,144 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 37. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion37_0 : PrefixRegion := ([(1,10),(3,15)], [(1,17),(7,31)]) -def degreeRegion37_1 : PrefixRegion := ([(1,10),(3,15)], [(1,17),(8,33)]) -def degreeRegion37_2 : PrefixRegion := ([(1,10),(3,15)], [(1,17),(9,35)]) -def degreeRegion37_3 : PrefixRegion := ([(1,10),(3,20),(5,25)], [(1,17),(5,25)]) -def degreeRegion37_4 : PrefixRegion := ([(1,10),(3,20),(5,25)], [(1,17),(6,29)]) -def degreeRegion37_5 : PrefixRegion := ([(1,10),(3,20),(5,25)], [(1,17),(7,31)]) -def degreeRegion37_6 : PrefixRegion := ([(1,10),(3,20),(5,25)], [(1,17),(8,33)]) -def degreeRegion37_7 : PrefixRegion := ([(1,10),(3,20),(5,25)], [(1,17),(9,35)]) -def degreeRegion37_8 : PrefixRegion := ([(1,10),(3,20),(6,29)], [(1,17),(5,25)]) -def degreeRegion37_9 : PrefixRegion := ([(1,10),(3,20),(6,29)], [(1,17),(6,29)]) -def degreeRegion37_10 : PrefixRegion := ([(1,10),(3,20),(6,29)], [(1,17),(7,31)]) -def degreeRegion37_11 : PrefixRegion := ([(1,10),(3,20),(6,29)], [(1,17),(8,33)]) -def degreeRegion37_12 : PrefixRegion := ([(1,10),(3,20),(6,29)], [(1,17),(9,35)]) -def degreeRegion37_13 : PrefixRegion := ([(1,10),(3,20),(7,31)], [(1,17),(5,25)]) -def degreeRegion37_14 : PrefixRegion := ([(1,10),(3,20),(7,31)], [(1,17),(6,29)]) -def degreeRegion37_15 : PrefixRegion := ([(1,10),(3,20),(7,31)], [(1,17),(7,31)]) -def degreeRegion37_16 : PrefixRegion := ([(1,10),(3,20),(7,31)], [(1,17),(8,33)]) -def degreeRegion37_17 : PrefixRegion := ([(1,10),(3,20),(7,31)], [(1,17),(9,35)]) -def degreeRegion37_18 : PrefixRegion := ([(1,10),(3,20),(8,33)], [(1,17),(5,25)]) -def degreeRegion37_19 : PrefixRegion := ([(1,10),(3,20),(8,33)], [(1,17),(6,29)]) -def degreeRegion37_20 : PrefixRegion := ([(1,10),(3,20),(8,33)], [(1,17),(7,31)]) -def degreeRegion37_21 : PrefixRegion := ([(1,10),(3,20),(8,33)], [(1,17),(8,33)]) -def degreeRegion37_22 : PrefixRegion := ([(1,10),(3,20),(8,33)], [(1,17),(9,35)]) -def degreeRegion37_23 : PrefixRegion := ([(1,10),(3,20),(9,35)], [(1,17),(5,25)]) -def degreeRegion37_24 : PrefixRegion := ([(1,10),(3,20),(9,35)], [(1,17),(6,29)]) -def degreeRegion37_25 : PrefixRegion := ([(1,10),(3,20),(9,35)], [(1,17),(7,31)]) -def degreeRegion37_26 : PrefixRegion := ([(1,10),(3,20),(9,35)], [(1,17),(8,33)]) -def degreeRegion37_27 : PrefixRegion := ([(1,10),(3,20),(9,35)], [(1,17),(9,35)]) -def degreeRegion37_28 : PrefixRegion := ([(1,10),(3,20),(10,36)], [(1,17),(5,25)]) -def degreeRegion37_29 : PrefixRegion := ([(1,10),(3,20),(10,36)], [(1,17),(6,29)]) -def degreeRegion37_30 : PrefixRegion := ([(1,10),(3,20),(10,36)], [(1,17),(7,31)]) -def degreeRegion37_31 : PrefixRegion := ([(1,10),(3,20),(10,36)], [(1,17),(8,33)]) -def degreeRegion37_32 : PrefixRegion := ([(1,10),(3,20),(10,36)], [(1,17),(9,35)]) -def degreeRegion37_33 : PrefixRegion := ([(1,10),(4,20)], [(1,17),(5,25)]) -def degreeRegion37_34 : PrefixRegion := ([(1,10),(4,20)], [(1,17),(6,29)]) -def degreeRegion37_35 : PrefixRegion := ([(1,10),(4,20)], [(1,17),(7,31)]) -def degreeRegion37_36 : PrefixRegion := ([(1,10),(4,20)], [(1,17),(8,33)]) -def degreeRegion37_37 : PrefixRegion := ([(1,10),(4,20)], [(1,17),(9,35)]) -def degreeRegion37_38 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(5,25)]) -def degreeRegion37_39 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(6,29)]) -def degreeRegion37_40 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(7,31)]) -def degreeRegion37_41 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(8,33)]) -def degreeRegion37_42 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(9,35)]) -def degreeRegion37_43 : PrefixRegion := ([(1,10),(6,29)], [(1,10),(5,25)]) -def degreeRegion37_44 : PrefixRegion := ([(1,10),(6,29)], [(1,10),(6,29)]) -def degreeRegion37_45 : PrefixRegion := ([(1,10),(6,29)], [(1,10),(7,31)]) -def degreeRegion37_46 : PrefixRegion := ([(1,10),(6,29)], [(1,10),(8,33)]) -def degreeRegion37_47 : PrefixRegion := ([(1,10),(6,29)], [(1,10),(9,35)]) -def degreeRegion37_48 : PrefixRegion := ([(1,10),(7,31)], [(1,10),(5,25)]) -def degreeRegion37_49 : PrefixRegion := ([(1,10),(7,31)], [(1,10),(6,29)]) -def degreeRegion37_50 : PrefixRegion := ([(1,10),(7,31)], [(1,10),(7,31)]) -def degreeRegion37_51 : PrefixRegion := ([(1,10),(7,31)], [(1,10),(8,33)]) -def degreeRegion37_52 : PrefixRegion := ([(1,10),(7,31)], [(1,10),(9,35)]) -def degreeRegion37_53 : PrefixRegion := ([(1,10),(8,33)], [(1,10),(5,25)]) -def degreeRegion37_54 : PrefixRegion := ([(1,10),(8,33)], [(1,10),(6,29)]) -def degreeRegion37_55 : PrefixRegion := ([(1,10),(8,33)], [(1,10),(7,31)]) -def degreeRegion37_56 : PrefixRegion := ([(1,10),(8,33)], [(1,10),(8,33)]) -def degreeRegion37_57 : PrefixRegion := ([(1,10),(8,33)], [(1,10),(9,35)]) -def degreeRegion37_58 : PrefixRegion := ([(1,10),(9,35)], [(1,10),(5,25)]) -def degreeRegion37_59 : PrefixRegion := ([(1,10),(9,35)], [(1,10),(6,29)]) -def degreeRegion37_60 : PrefixRegion := ([(1,10),(9,35)], [(1,10),(7,31)]) -def degreeRegion37_61 : PrefixRegion := ([(1,10),(9,35)], [(1,10),(8,33)]) -def degreeRegion37_62 : PrefixRegion := ([(1,10),(9,35)], [(1,10),(9,35)]) -def degreeRegion37_63 : PrefixRegion := ([(1,17),(3,20),(5,25)], [(1,17),(3,20),(5,25)]) -def degreeRegion37_64 : PrefixRegion := ([(1,17),(3,20),(5,25)], [(1,17),(3,20),(6,29)]) -def degreeRegion37_65 : PrefixRegion := ([(1,17),(3,20),(5,25)], [(1,17),(3,20),(7,31)]) -def degreeRegion37_66 : PrefixRegion := ([(1,17),(3,20),(5,25)], [(1,17),(3,20),(8,33)]) -def degreeRegion37_67 : PrefixRegion := ([(1,17),(3,20),(5,25)], [(1,17),(3,20),(9,35)]) -def degreeRegion37_68 : PrefixRegion := ([(1,17),(3,20),(6,29)], [(1,17),(3,20),(5,25)]) -def degreeRegion37_69 : PrefixRegion := ([(1,17),(3,20),(6,29)], [(1,17),(3,20),(6,29)]) -def degreeRegion37_70 : PrefixRegion := ([(1,17),(3,20),(6,29)], [(1,17),(3,20),(7,31)]) -def degreeRegion37_71 : PrefixRegion := ([(1,17),(3,20),(6,29)], [(1,17),(3,20),(8,33)]) -def degreeRegion37_72 : PrefixRegion := ([(1,17),(3,20),(6,29)], [(1,17),(3,20),(9,35)]) -def degreeRegion37_73 : PrefixRegion := ([(1,17),(3,20),(7,31)], [(1,17),(3,20),(5,25)]) -def degreeRegion37_74 : PrefixRegion := ([(1,17),(3,20),(7,31)], [(1,17),(3,20),(6,29)]) -def degreeRegion37_75 : PrefixRegion := ([(1,17),(3,20),(7,31)], [(1,17),(3,20),(7,31)]) -def degreeRegion37_76 : PrefixRegion := ([(1,17),(3,20),(7,31)], [(1,17),(3,20),(8,33)]) -def degreeRegion37_77 : PrefixRegion := ([(1,17),(3,20),(7,31)], [(1,17),(3,20),(9,35)]) -def degreeRegion37_78 : PrefixRegion := ([(1,17),(3,20),(8,33)], [(1,17),(3,20),(5,25)]) -def degreeRegion37_79 : PrefixRegion := ([(1,17),(3,20),(8,33)], [(1,17),(3,20),(6,29)]) -def degreeRegion37_80 : PrefixRegion := ([(1,17),(3,20),(8,33)], [(1,17),(3,20),(7,31)]) -def degreeRegion37_81 : PrefixRegion := ([(1,17),(3,20),(9,35)], [(1,17),(3,20),(5,25)]) -def degreeRegion37_82 : PrefixRegion := ([(1,17),(3,20),(9,35)], [(1,17),(3,20),(6,29)]) -def degreeRegion37_83 : PrefixRegion := ([(1,17),(3,20),(9,35)], [(1,17),(3,20),(7,31)]) -def degreeRegion37_84 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(3,20),(5,25)]) -def degreeRegion37_85 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(3,20),(6,29)]) -def degreeRegion37_86 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(3,20),(7,31)]) -def degreeRegion37_87 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(3,20),(8,33)]) -def degreeRegion37_88 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(3,20),(9,35)]) -def degreeRegion37_89 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(3,20),(10,36)]) -def degreeRegion37_90 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(4,20)]) -def degreeRegion37_91 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(3,20),(5,25)]) -def degreeRegion37_92 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(3,20),(6,29)]) -def degreeRegion37_93 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(3,20),(7,31)]) -def degreeRegion37_94 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(3,20),(8,33)]) -def degreeRegion37_95 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(3,20),(9,35)]) -def degreeRegion37_96 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(3,20),(10,36)]) -def degreeRegion37_97 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(4,20)]) -def degreeRegion37_98 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,15)]) -def degreeRegion37_99 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,20),(5,25)]) -def degreeRegion37_100 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,20),(6,29)]) -def degreeRegion37_101 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,20),(7,31)]) -def degreeRegion37_102 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,20),(8,33)]) -def degreeRegion37_103 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,20),(9,35)]) -def degreeRegion37_104 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,20),(10,36)]) -def degreeRegion37_105 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(4,20)]) -def degreeRegion37_106 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,15)]) -def degreeRegion37_107 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,20),(5,25)]) -def degreeRegion37_108 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,20),(6,29)]) -def degreeRegion37_109 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,20),(7,31)]) -def degreeRegion37_110 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,20),(8,33)]) -def degreeRegion37_111 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,20),(9,35)]) -def degreeRegion37_112 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,20),(10,36)]) -def degreeRegion37_113 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(4,20)]) -def degreeRegion37_114 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,15)]) -def degreeRegion37_115 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,20),(5,25)]) -def degreeRegion37_116 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,20),(6,29)]) -def degreeRegion37_117 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,20),(7,31)]) -def degreeRegion37_118 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,20),(8,33)]) -def degreeRegion37_119 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,20),(9,35)]) -def degreeRegion37_120 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,20),(10,36)]) -def degreeRegion37_121 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(4,20)]) - -def degreeRegions37 : List PrefixRegion := [degreeRegion37_0,degreeRegion37_1,degreeRegion37_2,degreeRegion37_3,degreeRegion37_4,degreeRegion37_5,degreeRegion37_6,degreeRegion37_7,degreeRegion37_8,degreeRegion37_9,degreeRegion37_10,degreeRegion37_11,degreeRegion37_12,degreeRegion37_13,degreeRegion37_14,degreeRegion37_15,degreeRegion37_16,degreeRegion37_17,degreeRegion37_18,degreeRegion37_19,degreeRegion37_20,degreeRegion37_21,degreeRegion37_22,degreeRegion37_23,degreeRegion37_24,degreeRegion37_25,degreeRegion37_26,degreeRegion37_27,degreeRegion37_28,degreeRegion37_29,degreeRegion37_30,degreeRegion37_31,degreeRegion37_32,degreeRegion37_33,degreeRegion37_34,degreeRegion37_35,degreeRegion37_36,degreeRegion37_37,degreeRegion37_38,degreeRegion37_39,degreeRegion37_40,degreeRegion37_41,degreeRegion37_42,degreeRegion37_43,degreeRegion37_44,degreeRegion37_45,degreeRegion37_46,degreeRegion37_47,degreeRegion37_48,degreeRegion37_49,degreeRegion37_50,degreeRegion37_51,degreeRegion37_52,degreeRegion37_53,degreeRegion37_54,degreeRegion37_55,degreeRegion37_56,degreeRegion37_57,degreeRegion37_58,degreeRegion37_59,degreeRegion37_60,degreeRegion37_61,degreeRegion37_62,degreeRegion37_63,degreeRegion37_64,degreeRegion37_65,degreeRegion37_66,degreeRegion37_67,degreeRegion37_68,degreeRegion37_69,degreeRegion37_70,degreeRegion37_71,degreeRegion37_72,degreeRegion37_73,degreeRegion37_74,degreeRegion37_75,degreeRegion37_76,degreeRegion37_77,degreeRegion37_78,degreeRegion37_79,degreeRegion37_80,degreeRegion37_81,degreeRegion37_82,degreeRegion37_83,degreeRegion37_84,degreeRegion37_85,degreeRegion37_86,degreeRegion37_87,degreeRegion37_88,degreeRegion37_89,degreeRegion37_90,degreeRegion37_91,degreeRegion37_92,degreeRegion37_93,degreeRegion37_94,degreeRegion37_95,degreeRegion37_96,degreeRegion37_97,degreeRegion37_98,degreeRegion37_99,degreeRegion37_100,degreeRegion37_101,degreeRegion37_102,degreeRegion37_103,degreeRegion37_104,degreeRegion37_105,degreeRegion37_106,degreeRegion37_107,degreeRegion37_108,degreeRegion37_109,degreeRegion37_110,degreeRegion37_111,degreeRegion37_112,degreeRegion37_113,degreeRegion37_114,degreeRegion37_115,degreeRegion37_116,degreeRegion37_117,degreeRegion37_118,degreeRegion37_119,degreeRegion37_120,degreeRegion37_121] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 37. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion37_0 : PrefixRegion := ([(1,10),(3,15)], [(1,17),(7,31)]) +def degreeRegion37_1 : PrefixRegion := ([(1,10),(3,15)], [(1,17),(8,33)]) +def degreeRegion37_2 : PrefixRegion := ([(1,10),(3,15)], [(1,17),(9,35)]) +def degreeRegion37_3 : PrefixRegion := ([(1,10),(3,20),(5,25)], [(1,17),(5,25)]) +def degreeRegion37_4 : PrefixRegion := ([(1,10),(3,20),(5,25)], [(1,17),(6,29)]) +def degreeRegion37_5 : PrefixRegion := ([(1,10),(3,20),(5,25)], [(1,17),(7,31)]) +def degreeRegion37_6 : PrefixRegion := ([(1,10),(3,20),(5,25)], [(1,17),(8,33)]) +def degreeRegion37_7 : PrefixRegion := ([(1,10),(3,20),(5,25)], [(1,17),(9,35)]) +def degreeRegion37_8 : PrefixRegion := ([(1,10),(3,20),(6,29)], [(1,17),(5,25)]) +def degreeRegion37_9 : PrefixRegion := ([(1,10),(3,20),(6,29)], [(1,17),(6,29)]) +def degreeRegion37_10 : PrefixRegion := ([(1,10),(3,20),(6,29)], [(1,17),(7,31)]) +def degreeRegion37_11 : PrefixRegion := ([(1,10),(3,20),(6,29)], [(1,17),(8,33)]) +def degreeRegion37_12 : PrefixRegion := ([(1,10),(3,20),(6,29)], [(1,17),(9,35)]) +def degreeRegion37_13 : PrefixRegion := ([(1,10),(3,20),(7,31)], [(1,17),(5,25)]) +def degreeRegion37_14 : PrefixRegion := ([(1,10),(3,20),(7,31)], [(1,17),(6,29)]) +def degreeRegion37_15 : PrefixRegion := ([(1,10),(3,20),(7,31)], [(1,17),(7,31)]) +def degreeRegion37_16 : PrefixRegion := ([(1,10),(3,20),(7,31)], [(1,17),(8,33)]) +def degreeRegion37_17 : PrefixRegion := ([(1,10),(3,20),(7,31)], [(1,17),(9,35)]) +def degreeRegion37_18 : PrefixRegion := ([(1,10),(3,20),(8,33)], [(1,17),(5,25)]) +def degreeRegion37_19 : PrefixRegion := ([(1,10),(3,20),(8,33)], [(1,17),(6,29)]) +def degreeRegion37_20 : PrefixRegion := ([(1,10),(3,20),(8,33)], [(1,17),(7,31)]) +def degreeRegion37_21 : PrefixRegion := ([(1,10),(3,20),(8,33)], [(1,17),(8,33)]) +def degreeRegion37_22 : PrefixRegion := ([(1,10),(3,20),(8,33)], [(1,17),(9,35)]) +def degreeRegion37_23 : PrefixRegion := ([(1,10),(3,20),(9,35)], [(1,17),(5,25)]) +def degreeRegion37_24 : PrefixRegion := ([(1,10),(3,20),(9,35)], [(1,17),(6,29)]) +def degreeRegion37_25 : PrefixRegion := ([(1,10),(3,20),(9,35)], [(1,17),(7,31)]) +def degreeRegion37_26 : PrefixRegion := ([(1,10),(3,20),(9,35)], [(1,17),(8,33)]) +def degreeRegion37_27 : PrefixRegion := ([(1,10),(3,20),(9,35)], [(1,17),(9,35)]) +def degreeRegion37_28 : PrefixRegion := ([(1,10),(3,20),(10,36)], [(1,17),(5,25)]) +def degreeRegion37_29 : PrefixRegion := ([(1,10),(3,20),(10,36)], [(1,17),(6,29)]) +def degreeRegion37_30 : PrefixRegion := ([(1,10),(3,20),(10,36)], [(1,17),(7,31)]) +def degreeRegion37_31 : PrefixRegion := ([(1,10),(3,20),(10,36)], [(1,17),(8,33)]) +def degreeRegion37_32 : PrefixRegion := ([(1,10),(3,20),(10,36)], [(1,17),(9,35)]) +def degreeRegion37_33 : PrefixRegion := ([(1,10),(4,20)], [(1,17),(5,25)]) +def degreeRegion37_34 : PrefixRegion := ([(1,10),(4,20)], [(1,17),(6,29)]) +def degreeRegion37_35 : PrefixRegion := ([(1,10),(4,20)], [(1,17),(7,31)]) +def degreeRegion37_36 : PrefixRegion := ([(1,10),(4,20)], [(1,17),(8,33)]) +def degreeRegion37_37 : PrefixRegion := ([(1,10),(4,20)], [(1,17),(9,35)]) +def degreeRegion37_38 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(5,25)]) +def degreeRegion37_39 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(6,29)]) +def degreeRegion37_40 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(7,31)]) +def degreeRegion37_41 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(8,33)]) +def degreeRegion37_42 : PrefixRegion := ([(1,10),(5,25)], [(1,10),(9,35)]) +def degreeRegion37_43 : PrefixRegion := ([(1,10),(6,29)], [(1,10),(5,25)]) +def degreeRegion37_44 : PrefixRegion := ([(1,10),(6,29)], [(1,10),(6,29)]) +def degreeRegion37_45 : PrefixRegion := ([(1,10),(6,29)], [(1,10),(7,31)]) +def degreeRegion37_46 : PrefixRegion := ([(1,10),(6,29)], [(1,10),(8,33)]) +def degreeRegion37_47 : PrefixRegion := ([(1,10),(6,29)], [(1,10),(9,35)]) +def degreeRegion37_48 : PrefixRegion := ([(1,10),(7,31)], [(1,10),(5,25)]) +def degreeRegion37_49 : PrefixRegion := ([(1,10),(7,31)], [(1,10),(6,29)]) +def degreeRegion37_50 : PrefixRegion := ([(1,10),(7,31)], [(1,10),(7,31)]) +def degreeRegion37_51 : PrefixRegion := ([(1,10),(7,31)], [(1,10),(8,33)]) +def degreeRegion37_52 : PrefixRegion := ([(1,10),(7,31)], [(1,10),(9,35)]) +def degreeRegion37_53 : PrefixRegion := ([(1,10),(8,33)], [(1,10),(5,25)]) +def degreeRegion37_54 : PrefixRegion := ([(1,10),(8,33)], [(1,10),(6,29)]) +def degreeRegion37_55 : PrefixRegion := ([(1,10),(8,33)], [(1,10),(7,31)]) +def degreeRegion37_56 : PrefixRegion := ([(1,10),(8,33)], [(1,10),(8,33)]) +def degreeRegion37_57 : PrefixRegion := ([(1,10),(8,33)], [(1,10),(9,35)]) +def degreeRegion37_58 : PrefixRegion := ([(1,10),(9,35)], [(1,10),(5,25)]) +def degreeRegion37_59 : PrefixRegion := ([(1,10),(9,35)], [(1,10),(6,29)]) +def degreeRegion37_60 : PrefixRegion := ([(1,10),(9,35)], [(1,10),(7,31)]) +def degreeRegion37_61 : PrefixRegion := ([(1,10),(9,35)], [(1,10),(8,33)]) +def degreeRegion37_62 : PrefixRegion := ([(1,10),(9,35)], [(1,10),(9,35)]) +def degreeRegion37_63 : PrefixRegion := ([(1,17),(3,20),(5,25)], [(1,17),(3,20),(5,25)]) +def degreeRegion37_64 : PrefixRegion := ([(1,17),(3,20),(5,25)], [(1,17),(3,20),(6,29)]) +def degreeRegion37_65 : PrefixRegion := ([(1,17),(3,20),(5,25)], [(1,17),(3,20),(7,31)]) +def degreeRegion37_66 : PrefixRegion := ([(1,17),(3,20),(5,25)], [(1,17),(3,20),(8,33)]) +def degreeRegion37_67 : PrefixRegion := ([(1,17),(3,20),(5,25)], [(1,17),(3,20),(9,35)]) +def degreeRegion37_68 : PrefixRegion := ([(1,17),(3,20),(6,29)], [(1,17),(3,20),(5,25)]) +def degreeRegion37_69 : PrefixRegion := ([(1,17),(3,20),(6,29)], [(1,17),(3,20),(6,29)]) +def degreeRegion37_70 : PrefixRegion := ([(1,17),(3,20),(6,29)], [(1,17),(3,20),(7,31)]) +def degreeRegion37_71 : PrefixRegion := ([(1,17),(3,20),(6,29)], [(1,17),(3,20),(8,33)]) +def degreeRegion37_72 : PrefixRegion := ([(1,17),(3,20),(6,29)], [(1,17),(3,20),(9,35)]) +def degreeRegion37_73 : PrefixRegion := ([(1,17),(3,20),(7,31)], [(1,17),(3,20),(5,25)]) +def degreeRegion37_74 : PrefixRegion := ([(1,17),(3,20),(7,31)], [(1,17),(3,20),(6,29)]) +def degreeRegion37_75 : PrefixRegion := ([(1,17),(3,20),(7,31)], [(1,17),(3,20),(7,31)]) +def degreeRegion37_76 : PrefixRegion := ([(1,17),(3,20),(7,31)], [(1,17),(3,20),(8,33)]) +def degreeRegion37_77 : PrefixRegion := ([(1,17),(3,20),(7,31)], [(1,17),(3,20),(9,35)]) +def degreeRegion37_78 : PrefixRegion := ([(1,17),(3,20),(8,33)], [(1,17),(3,20),(5,25)]) +def degreeRegion37_79 : PrefixRegion := ([(1,17),(3,20),(8,33)], [(1,17),(3,20),(6,29)]) +def degreeRegion37_80 : PrefixRegion := ([(1,17),(3,20),(8,33)], [(1,17),(3,20),(7,31)]) +def degreeRegion37_81 : PrefixRegion := ([(1,17),(3,20),(9,35)], [(1,17),(3,20),(5,25)]) +def degreeRegion37_82 : PrefixRegion := ([(1,17),(3,20),(9,35)], [(1,17),(3,20),(6,29)]) +def degreeRegion37_83 : PrefixRegion := ([(1,17),(3,20),(9,35)], [(1,17),(3,20),(7,31)]) +def degreeRegion37_84 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(3,20),(5,25)]) +def degreeRegion37_85 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(3,20),(6,29)]) +def degreeRegion37_86 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(3,20),(7,31)]) +def degreeRegion37_87 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(3,20),(8,33)]) +def degreeRegion37_88 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(3,20),(9,35)]) +def degreeRegion37_89 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(3,20),(10,36)]) +def degreeRegion37_90 : PrefixRegion := ([(1,17),(5,25)], [(1,10),(4,20)]) +def degreeRegion37_91 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(3,20),(5,25)]) +def degreeRegion37_92 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(3,20),(6,29)]) +def degreeRegion37_93 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(3,20),(7,31)]) +def degreeRegion37_94 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(3,20),(8,33)]) +def degreeRegion37_95 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(3,20),(9,35)]) +def degreeRegion37_96 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(3,20),(10,36)]) +def degreeRegion37_97 : PrefixRegion := ([(1,17),(6,29)], [(1,10),(4,20)]) +def degreeRegion37_98 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,15)]) +def degreeRegion37_99 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,20),(5,25)]) +def degreeRegion37_100 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,20),(6,29)]) +def degreeRegion37_101 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,20),(7,31)]) +def degreeRegion37_102 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,20),(8,33)]) +def degreeRegion37_103 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,20),(9,35)]) +def degreeRegion37_104 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(3,20),(10,36)]) +def degreeRegion37_105 : PrefixRegion := ([(1,17),(7,31)], [(1,10),(4,20)]) +def degreeRegion37_106 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,15)]) +def degreeRegion37_107 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,20),(5,25)]) +def degreeRegion37_108 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,20),(6,29)]) +def degreeRegion37_109 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,20),(7,31)]) +def degreeRegion37_110 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,20),(8,33)]) +def degreeRegion37_111 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,20),(9,35)]) +def degreeRegion37_112 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(3,20),(10,36)]) +def degreeRegion37_113 : PrefixRegion := ([(1,17),(8,33)], [(1,10),(4,20)]) +def degreeRegion37_114 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,15)]) +def degreeRegion37_115 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,20),(5,25)]) +def degreeRegion37_116 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,20),(6,29)]) +def degreeRegion37_117 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,20),(7,31)]) +def degreeRegion37_118 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,20),(8,33)]) +def degreeRegion37_119 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,20),(9,35)]) +def degreeRegion37_120 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(3,20),(10,36)]) +def degreeRegion37_121 : PrefixRegion := ([(1,17),(9,35)], [(1,10),(4,20)]) + +def degreeRegions37 : List PrefixRegion := [degreeRegion37_0,degreeRegion37_1,degreeRegion37_2,degreeRegion37_3,degreeRegion37_4,degreeRegion37_5,degreeRegion37_6,degreeRegion37_7,degreeRegion37_8,degreeRegion37_9,degreeRegion37_10,degreeRegion37_11,degreeRegion37_12,degreeRegion37_13,degreeRegion37_14,degreeRegion37_15,degreeRegion37_16,degreeRegion37_17,degreeRegion37_18,degreeRegion37_19,degreeRegion37_20,degreeRegion37_21,degreeRegion37_22,degreeRegion37_23,degreeRegion37_24,degreeRegion37_25,degreeRegion37_26,degreeRegion37_27,degreeRegion37_28,degreeRegion37_29,degreeRegion37_30,degreeRegion37_31,degreeRegion37_32,degreeRegion37_33,degreeRegion37_34,degreeRegion37_35,degreeRegion37_36,degreeRegion37_37,degreeRegion37_38,degreeRegion37_39,degreeRegion37_40,degreeRegion37_41,degreeRegion37_42,degreeRegion37_43,degreeRegion37_44,degreeRegion37_45,degreeRegion37_46,degreeRegion37_47,degreeRegion37_48,degreeRegion37_49,degreeRegion37_50,degreeRegion37_51,degreeRegion37_52,degreeRegion37_53,degreeRegion37_54,degreeRegion37_55,degreeRegion37_56,degreeRegion37_57,degreeRegion37_58,degreeRegion37_59,degreeRegion37_60,degreeRegion37_61,degreeRegion37_62,degreeRegion37_63,degreeRegion37_64,degreeRegion37_65,degreeRegion37_66,degreeRegion37_67,degreeRegion37_68,degreeRegion37_69,degreeRegion37_70,degreeRegion37_71,degreeRegion37_72,degreeRegion37_73,degreeRegion37_74,degreeRegion37_75,degreeRegion37_76,degreeRegion37_77,degreeRegion37_78,degreeRegion37_79,degreeRegion37_80,degreeRegion37_81,degreeRegion37_82,degreeRegion37_83,degreeRegion37_84,degreeRegion37_85,degreeRegion37_86,degreeRegion37_87,degreeRegion37_88,degreeRegion37_89,degreeRegion37_90,degreeRegion37_91,degreeRegion37_92,degreeRegion37_93,degreeRegion37_94,degreeRegion37_95,degreeRegion37_96,degreeRegion37_97,degreeRegion37_98,degreeRegion37_99,degreeRegion37_100,degreeRegion37_101,degreeRegion37_102,degreeRegion37_103,degreeRegion37_104,degreeRegion37_105,degreeRegion37_106,degreeRegion37_107,degreeRegion37_108,degreeRegion37_109,degreeRegion37_110,degreeRegion37_111,degreeRegion37_112,degreeRegion37_113,degreeRegion37_114,degreeRegion37_115,degreeRegion37_116,degreeRegion37_117,degreeRegion37_118,degreeRegion37_119,degreeRegion37_120,degreeRegion37_121] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData39.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData39.lean index 1a53363f4acf73b4b21a2607fd9001bf836e5905..1b0a08a9013778323e213041023eb1a08c04d69c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData39.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData39.lean @@ -1,108 +1,108 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 39. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion39_0 : PrefixRegion := ([(1,10),(2,12)], [(1,10),(6,34)]) -def degreeRegion39_1 : PrefixRegion := ([(1,10),(2,12)], [(1,10),(7,38)]) -def degreeRegion39_2 : PrefixRegion := ([(1,10),(2,12),(3,22)], [(1,19),(6,34)]) -def degreeRegion39_3 : PrefixRegion := ([(1,10),(2,12),(3,22)], [(1,19),(7,38)]) -def degreeRegion39_4 : PrefixRegion := ([(1,10),(3,18)], [(1,19),(5,29)]) -def degreeRegion39_5 : PrefixRegion := ([(1,10),(3,18)], [(1,19),(6,34)]) -def degreeRegion39_6 : PrefixRegion := ([(1,10),(3,18)], [(1,19),(7,38)]) -def degreeRegion39_7 : PrefixRegion := ([(1,10),(3,22),(4,24)], [(1,19),(4,24)]) -def degreeRegion39_8 : PrefixRegion := ([(1,10),(3,22),(4,24)], [(1,19),(5,29)]) -def degreeRegion39_9 : PrefixRegion := ([(1,10),(3,22),(4,24)], [(1,19),(6,34)]) -def degreeRegion39_10 : PrefixRegion := ([(1,10),(3,22),(4,24)], [(1,19),(7,38)]) -def degreeRegion39_11 : PrefixRegion := ([(1,10),(3,22),(5,29)], [(1,19),(4,24)]) -def degreeRegion39_12 : PrefixRegion := ([(1,10),(3,22),(5,29)], [(1,19),(5,29)]) -def degreeRegion39_13 : PrefixRegion := ([(1,10),(3,22),(5,29)], [(1,19),(6,34)]) -def degreeRegion39_14 : PrefixRegion := ([(1,10),(3,22),(5,29)], [(1,19),(7,38)]) -def degreeRegion39_15 : PrefixRegion := ([(1,10),(3,22),(6,34)], [(1,19),(4,24)]) -def degreeRegion39_16 : PrefixRegion := ([(1,10),(3,22),(6,34)], [(1,19),(5,29)]) -def degreeRegion39_17 : PrefixRegion := ([(1,10),(3,22),(6,34)], [(1,19),(6,34)]) -def degreeRegion39_18 : PrefixRegion := ([(1,10),(3,22),(6,34)], [(1,19),(7,38)]) -def degreeRegion39_19 : PrefixRegion := ([(1,10),(3,22),(7,38)], [(1,19),(4,24)]) -def degreeRegion39_20 : PrefixRegion := ([(1,10),(3,22),(7,38)], [(1,19),(5,29)]) -def degreeRegion39_21 : PrefixRegion := ([(1,10),(3,22),(7,38)], [(1,19),(6,34)]) -def degreeRegion39_22 : PrefixRegion := ([(1,10),(3,22),(7,38)], [(1,19),(7,38)]) -def degreeRegion39_23 : PrefixRegion := ([(1,10),(4,24)], [(1,10),(4,24)]) -def degreeRegion39_24 : PrefixRegion := ([(1,10),(4,24)], [(1,10),(5,29)]) -def degreeRegion39_25 : PrefixRegion := ([(1,10),(4,24)], [(1,10),(6,34)]) -def degreeRegion39_26 : PrefixRegion := ([(1,10),(4,24)], [(1,10),(7,38)]) -def degreeRegion39_27 : PrefixRegion := ([(1,10),(5,29)], [(1,10),(4,24)]) -def degreeRegion39_28 : PrefixRegion := ([(1,10),(5,29)], [(1,10),(5,29)]) -def degreeRegion39_29 : PrefixRegion := ([(1,10),(5,29)], [(1,10),(6,34)]) -def degreeRegion39_30 : PrefixRegion := ([(1,10),(5,29)], [(1,10),(7,38)]) -def degreeRegion39_31 : PrefixRegion := ([(1,10),(6,34)], [(1,10),(2,12)]) -def degreeRegion39_32 : PrefixRegion := ([(1,10),(6,34)], [(1,10),(4,24)]) -def degreeRegion39_33 : PrefixRegion := ([(1,10),(6,34)], [(1,10),(5,29)]) -def degreeRegion39_34 : PrefixRegion := ([(1,10),(6,34)], [(1,10),(6,34)]) -def degreeRegion39_35 : PrefixRegion := ([(1,10),(6,34)], [(1,10),(7,38)]) -def degreeRegion39_36 : PrefixRegion := ([(1,10),(7,38)], [(1,10),(2,12)]) -def degreeRegion39_37 : PrefixRegion := ([(1,10),(7,38)], [(1,10),(4,24)]) -def degreeRegion39_38 : PrefixRegion := ([(1,10),(7,38)], [(1,10),(5,29)]) -def degreeRegion39_39 : PrefixRegion := ([(1,10),(7,38)], [(1,10),(6,34)]) -def degreeRegion39_40 : PrefixRegion := ([(1,10),(7,38)], [(1,10),(7,38)]) -def degreeRegion39_41 : PrefixRegion := ([(1,19),(3,22),(4,24)], [(1,19),(3,22),(4,24)]) -def degreeRegion39_42 : PrefixRegion := ([(1,19),(3,22),(4,24)], [(1,19),(3,22),(5,29)]) -def degreeRegion39_43 : PrefixRegion := ([(1,19),(3,22),(4,24)], [(1,19),(3,22),(6,34)]) -def degreeRegion39_44 : PrefixRegion := ([(1,19),(3,22),(4,24)], [(1,19),(3,22),(7,38)]) -def degreeRegion39_45 : PrefixRegion := ([(1,19),(3,22),(5,29)], [(1,19),(3,22),(4,24)]) -def degreeRegion39_46 : PrefixRegion := ([(1,19),(3,22),(5,29)], [(1,19),(3,22),(5,29)]) -def degreeRegion39_47 : PrefixRegion := ([(1,19),(3,22),(5,29)], [(1,19),(3,22),(6,34)]) -def degreeRegion39_48 : PrefixRegion := ([(1,19),(3,22),(5,29)], [(1,19),(3,22),(7,38)]) -def degreeRegion39_49 : PrefixRegion := ([(1,19),(3,22),(5,29)], [(3,18)]) -def degreeRegion39_50 : PrefixRegion := ([(1,19),(3,22),(6,34)], [(1,19),(3,22),(4,24)]) -def degreeRegion39_51 : PrefixRegion := ([(1,19),(3,22),(6,34)], [(1,19),(3,22),(5,29)]) -def degreeRegion39_52 : PrefixRegion := ([(1,19),(3,22),(6,34)], [(1,19),(3,22),(6,34)]) -def degreeRegion39_53 : PrefixRegion := ([(1,19),(3,22),(6,34)], [(1,19),(3,22),(7,38)]) -def degreeRegion39_54 : PrefixRegion := ([(1,19),(3,22),(6,34)], [(3,18)]) -def degreeRegion39_55 : PrefixRegion := ([(1,19),(3,22),(7,38)], [(1,19),(3,22),(4,24)]) -def degreeRegion39_56 : PrefixRegion := ([(1,19),(3,22),(7,38)], [(1,19),(3,22),(5,29)]) -def degreeRegion39_57 : PrefixRegion := ([(1,19),(3,22),(7,38)], [(1,19),(3,22),(6,34)]) -def degreeRegion39_58 : PrefixRegion := ([(1,19),(3,22),(7,38)], [(1,19),(3,22),(7,38)]) -def degreeRegion39_59 : PrefixRegion := ([(1,19),(3,22),(7,38)], [(3,18)]) -def degreeRegion39_60 : PrefixRegion := ([(1,19),(4,24)], [(1,10),(3,22),(4,24)]) -def degreeRegion39_61 : PrefixRegion := ([(1,19),(4,24)], [(1,10),(3,22),(5,29)]) -def degreeRegion39_62 : PrefixRegion := ([(1,19),(4,24)], [(1,10),(3,22),(6,34)]) -def degreeRegion39_63 : PrefixRegion := ([(1,19),(4,24)], [(1,10),(3,22),(7,38)]) -def degreeRegion39_64 : PrefixRegion := ([(1,19),(5,29)], [(1,10),(3,18)]) -def degreeRegion39_65 : PrefixRegion := ([(1,19),(5,29)], [(1,10),(3,22),(4,24)]) -def degreeRegion39_66 : PrefixRegion := ([(1,19),(5,29)], [(1,10),(3,22),(5,29)]) -def degreeRegion39_67 : PrefixRegion := ([(1,19),(5,29)], [(1,10),(3,22),(6,34)]) -def degreeRegion39_68 : PrefixRegion := ([(1,19),(5,29)], [(1,10),(3,22),(7,38)]) -def degreeRegion39_69 : PrefixRegion := ([(1,19),(6,34)], [(1,10),(2,12),(3,22)]) -def degreeRegion39_70 : PrefixRegion := ([(1,19),(6,34)], [(1,10),(3,18)]) -def degreeRegion39_71 : PrefixRegion := ([(1,19),(6,34)], [(1,10),(3,22),(4,24)]) -def degreeRegion39_72 : PrefixRegion := ([(1,19),(6,34)], [(1,10),(3,22),(5,29)]) -def degreeRegion39_73 : PrefixRegion := ([(1,19),(6,34)], [(1,10),(3,22),(6,34)]) -def degreeRegion39_74 : PrefixRegion := ([(1,19),(6,34)], [(1,10),(3,22),(7,38)]) -def degreeRegion39_75 : PrefixRegion := ([(1,19),(7,38)], [(1,10),(2,12),(3,22)]) -def degreeRegion39_76 : PrefixRegion := ([(1,19),(7,38)], [(1,10),(3,18)]) -def degreeRegion39_77 : PrefixRegion := ([(1,19),(7,38)], [(1,10),(3,22),(4,24)]) -def degreeRegion39_78 : PrefixRegion := ([(1,19),(7,38)], [(1,10),(3,22),(5,29)]) -def degreeRegion39_79 : PrefixRegion := ([(1,19),(7,38)], [(1,10),(3,22),(6,34)]) -def degreeRegion39_80 : PrefixRegion := ([(1,19),(7,38)], [(1,10),(3,22),(7,38)]) -def degreeRegion39_81 : PrefixRegion := ([(2,10),(3,22)], [(7,38)]) -def degreeRegion39_82 : PrefixRegion := ([(3,18)], [(1,19),(3,22),(5,29)]) -def degreeRegion39_83 : PrefixRegion := ([(3,18)], [(1,19),(3,22),(6,34)]) -def degreeRegion39_84 : PrefixRegion := ([(3,18)], [(1,19),(3,22),(7,38)]) -def degreeRegion39_85 : PrefixRegion := ([(7,38)], [(2,10),(3,22)]) - -def degreeRegions39 : List PrefixRegion := [degreeRegion39_0,degreeRegion39_1,degreeRegion39_2,degreeRegion39_3,degreeRegion39_4,degreeRegion39_5,degreeRegion39_6,degreeRegion39_7,degreeRegion39_8,degreeRegion39_9,degreeRegion39_10,degreeRegion39_11,degreeRegion39_12,degreeRegion39_13,degreeRegion39_14,degreeRegion39_15,degreeRegion39_16,degreeRegion39_17,degreeRegion39_18,degreeRegion39_19,degreeRegion39_20,degreeRegion39_21,degreeRegion39_22,degreeRegion39_23,degreeRegion39_24,degreeRegion39_25,degreeRegion39_26,degreeRegion39_27,degreeRegion39_28,degreeRegion39_29,degreeRegion39_30,degreeRegion39_31,degreeRegion39_32,degreeRegion39_33,degreeRegion39_34,degreeRegion39_35,degreeRegion39_36,degreeRegion39_37,degreeRegion39_38,degreeRegion39_39,degreeRegion39_40,degreeRegion39_41,degreeRegion39_42,degreeRegion39_43,degreeRegion39_44,degreeRegion39_45,degreeRegion39_46,degreeRegion39_47,degreeRegion39_48,degreeRegion39_49,degreeRegion39_50,degreeRegion39_51,degreeRegion39_52,degreeRegion39_53,degreeRegion39_54,degreeRegion39_55,degreeRegion39_56,degreeRegion39_57,degreeRegion39_58,degreeRegion39_59,degreeRegion39_60,degreeRegion39_61,degreeRegion39_62,degreeRegion39_63,degreeRegion39_64,degreeRegion39_65,degreeRegion39_66,degreeRegion39_67,degreeRegion39_68,degreeRegion39_69,degreeRegion39_70,degreeRegion39_71,degreeRegion39_72,degreeRegion39_73,degreeRegion39_74,degreeRegion39_75,degreeRegion39_76,degreeRegion39_77,degreeRegion39_78,degreeRegion39_79,degreeRegion39_80,degreeRegion39_81,degreeRegion39_82,degreeRegion39_83,degreeRegion39_84,degreeRegion39_85] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 39. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion39_0 : PrefixRegion := ([(1,10),(2,12)], [(1,10),(6,34)]) +def degreeRegion39_1 : PrefixRegion := ([(1,10),(2,12)], [(1,10),(7,38)]) +def degreeRegion39_2 : PrefixRegion := ([(1,10),(2,12),(3,22)], [(1,19),(6,34)]) +def degreeRegion39_3 : PrefixRegion := ([(1,10),(2,12),(3,22)], [(1,19),(7,38)]) +def degreeRegion39_4 : PrefixRegion := ([(1,10),(3,18)], [(1,19),(5,29)]) +def degreeRegion39_5 : PrefixRegion := ([(1,10),(3,18)], [(1,19),(6,34)]) +def degreeRegion39_6 : PrefixRegion := ([(1,10),(3,18)], [(1,19),(7,38)]) +def degreeRegion39_7 : PrefixRegion := ([(1,10),(3,22),(4,24)], [(1,19),(4,24)]) +def degreeRegion39_8 : PrefixRegion := ([(1,10),(3,22),(4,24)], [(1,19),(5,29)]) +def degreeRegion39_9 : PrefixRegion := ([(1,10),(3,22),(4,24)], [(1,19),(6,34)]) +def degreeRegion39_10 : PrefixRegion := ([(1,10),(3,22),(4,24)], [(1,19),(7,38)]) +def degreeRegion39_11 : PrefixRegion := ([(1,10),(3,22),(5,29)], [(1,19),(4,24)]) +def degreeRegion39_12 : PrefixRegion := ([(1,10),(3,22),(5,29)], [(1,19),(5,29)]) +def degreeRegion39_13 : PrefixRegion := ([(1,10),(3,22),(5,29)], [(1,19),(6,34)]) +def degreeRegion39_14 : PrefixRegion := ([(1,10),(3,22),(5,29)], [(1,19),(7,38)]) +def degreeRegion39_15 : PrefixRegion := ([(1,10),(3,22),(6,34)], [(1,19),(4,24)]) +def degreeRegion39_16 : PrefixRegion := ([(1,10),(3,22),(6,34)], [(1,19),(5,29)]) +def degreeRegion39_17 : PrefixRegion := ([(1,10),(3,22),(6,34)], [(1,19),(6,34)]) +def degreeRegion39_18 : PrefixRegion := ([(1,10),(3,22),(6,34)], [(1,19),(7,38)]) +def degreeRegion39_19 : PrefixRegion := ([(1,10),(3,22),(7,38)], [(1,19),(4,24)]) +def degreeRegion39_20 : PrefixRegion := ([(1,10),(3,22),(7,38)], [(1,19),(5,29)]) +def degreeRegion39_21 : PrefixRegion := ([(1,10),(3,22),(7,38)], [(1,19),(6,34)]) +def degreeRegion39_22 : PrefixRegion := ([(1,10),(3,22),(7,38)], [(1,19),(7,38)]) +def degreeRegion39_23 : PrefixRegion := ([(1,10),(4,24)], [(1,10),(4,24)]) +def degreeRegion39_24 : PrefixRegion := ([(1,10),(4,24)], [(1,10),(5,29)]) +def degreeRegion39_25 : PrefixRegion := ([(1,10),(4,24)], [(1,10),(6,34)]) +def degreeRegion39_26 : PrefixRegion := ([(1,10),(4,24)], [(1,10),(7,38)]) +def degreeRegion39_27 : PrefixRegion := ([(1,10),(5,29)], [(1,10),(4,24)]) +def degreeRegion39_28 : PrefixRegion := ([(1,10),(5,29)], [(1,10),(5,29)]) +def degreeRegion39_29 : PrefixRegion := ([(1,10),(5,29)], [(1,10),(6,34)]) +def degreeRegion39_30 : PrefixRegion := ([(1,10),(5,29)], [(1,10),(7,38)]) +def degreeRegion39_31 : PrefixRegion := ([(1,10),(6,34)], [(1,10),(2,12)]) +def degreeRegion39_32 : PrefixRegion := ([(1,10),(6,34)], [(1,10),(4,24)]) +def degreeRegion39_33 : PrefixRegion := ([(1,10),(6,34)], [(1,10),(5,29)]) +def degreeRegion39_34 : PrefixRegion := ([(1,10),(6,34)], [(1,10),(6,34)]) +def degreeRegion39_35 : PrefixRegion := ([(1,10),(6,34)], [(1,10),(7,38)]) +def degreeRegion39_36 : PrefixRegion := ([(1,10),(7,38)], [(1,10),(2,12)]) +def degreeRegion39_37 : PrefixRegion := ([(1,10),(7,38)], [(1,10),(4,24)]) +def degreeRegion39_38 : PrefixRegion := ([(1,10),(7,38)], [(1,10),(5,29)]) +def degreeRegion39_39 : PrefixRegion := ([(1,10),(7,38)], [(1,10),(6,34)]) +def degreeRegion39_40 : PrefixRegion := ([(1,10),(7,38)], [(1,10),(7,38)]) +def degreeRegion39_41 : PrefixRegion := ([(1,19),(3,22),(4,24)], [(1,19),(3,22),(4,24)]) +def degreeRegion39_42 : PrefixRegion := ([(1,19),(3,22),(4,24)], [(1,19),(3,22),(5,29)]) +def degreeRegion39_43 : PrefixRegion := ([(1,19),(3,22),(4,24)], [(1,19),(3,22),(6,34)]) +def degreeRegion39_44 : PrefixRegion := ([(1,19),(3,22),(4,24)], [(1,19),(3,22),(7,38)]) +def degreeRegion39_45 : PrefixRegion := ([(1,19),(3,22),(5,29)], [(1,19),(3,22),(4,24)]) +def degreeRegion39_46 : PrefixRegion := ([(1,19),(3,22),(5,29)], [(1,19),(3,22),(5,29)]) +def degreeRegion39_47 : PrefixRegion := ([(1,19),(3,22),(5,29)], [(1,19),(3,22),(6,34)]) +def degreeRegion39_48 : PrefixRegion := ([(1,19),(3,22),(5,29)], [(1,19),(3,22),(7,38)]) +def degreeRegion39_49 : PrefixRegion := ([(1,19),(3,22),(5,29)], [(3,18)]) +def degreeRegion39_50 : PrefixRegion := ([(1,19),(3,22),(6,34)], [(1,19),(3,22),(4,24)]) +def degreeRegion39_51 : PrefixRegion := ([(1,19),(3,22),(6,34)], [(1,19),(3,22),(5,29)]) +def degreeRegion39_52 : PrefixRegion := ([(1,19),(3,22),(6,34)], [(1,19),(3,22),(6,34)]) +def degreeRegion39_53 : PrefixRegion := ([(1,19),(3,22),(6,34)], [(1,19),(3,22),(7,38)]) +def degreeRegion39_54 : PrefixRegion := ([(1,19),(3,22),(6,34)], [(3,18)]) +def degreeRegion39_55 : PrefixRegion := ([(1,19),(3,22),(7,38)], [(1,19),(3,22),(4,24)]) +def degreeRegion39_56 : PrefixRegion := ([(1,19),(3,22),(7,38)], [(1,19),(3,22),(5,29)]) +def degreeRegion39_57 : PrefixRegion := ([(1,19),(3,22),(7,38)], [(1,19),(3,22),(6,34)]) +def degreeRegion39_58 : PrefixRegion := ([(1,19),(3,22),(7,38)], [(1,19),(3,22),(7,38)]) +def degreeRegion39_59 : PrefixRegion := ([(1,19),(3,22),(7,38)], [(3,18)]) +def degreeRegion39_60 : PrefixRegion := ([(1,19),(4,24)], [(1,10),(3,22),(4,24)]) +def degreeRegion39_61 : PrefixRegion := ([(1,19),(4,24)], [(1,10),(3,22),(5,29)]) +def degreeRegion39_62 : PrefixRegion := ([(1,19),(4,24)], [(1,10),(3,22),(6,34)]) +def degreeRegion39_63 : PrefixRegion := ([(1,19),(4,24)], [(1,10),(3,22),(7,38)]) +def degreeRegion39_64 : PrefixRegion := ([(1,19),(5,29)], [(1,10),(3,18)]) +def degreeRegion39_65 : PrefixRegion := ([(1,19),(5,29)], [(1,10),(3,22),(4,24)]) +def degreeRegion39_66 : PrefixRegion := ([(1,19),(5,29)], [(1,10),(3,22),(5,29)]) +def degreeRegion39_67 : PrefixRegion := ([(1,19),(5,29)], [(1,10),(3,22),(6,34)]) +def degreeRegion39_68 : PrefixRegion := ([(1,19),(5,29)], [(1,10),(3,22),(7,38)]) +def degreeRegion39_69 : PrefixRegion := ([(1,19),(6,34)], [(1,10),(2,12),(3,22)]) +def degreeRegion39_70 : PrefixRegion := ([(1,19),(6,34)], [(1,10),(3,18)]) +def degreeRegion39_71 : PrefixRegion := ([(1,19),(6,34)], [(1,10),(3,22),(4,24)]) +def degreeRegion39_72 : PrefixRegion := ([(1,19),(6,34)], [(1,10),(3,22),(5,29)]) +def degreeRegion39_73 : PrefixRegion := ([(1,19),(6,34)], [(1,10),(3,22),(6,34)]) +def degreeRegion39_74 : PrefixRegion := ([(1,19),(6,34)], [(1,10),(3,22),(7,38)]) +def degreeRegion39_75 : PrefixRegion := ([(1,19),(7,38)], [(1,10),(2,12),(3,22)]) +def degreeRegion39_76 : PrefixRegion := ([(1,19),(7,38)], [(1,10),(3,18)]) +def degreeRegion39_77 : PrefixRegion := ([(1,19),(7,38)], [(1,10),(3,22),(4,24)]) +def degreeRegion39_78 : PrefixRegion := ([(1,19),(7,38)], [(1,10),(3,22),(5,29)]) +def degreeRegion39_79 : PrefixRegion := ([(1,19),(7,38)], [(1,10),(3,22),(6,34)]) +def degreeRegion39_80 : PrefixRegion := ([(1,19),(7,38)], [(1,10),(3,22),(7,38)]) +def degreeRegion39_81 : PrefixRegion := ([(2,10),(3,22)], [(7,38)]) +def degreeRegion39_82 : PrefixRegion := ([(3,18)], [(1,19),(3,22),(5,29)]) +def degreeRegion39_83 : PrefixRegion := ([(3,18)], [(1,19),(3,22),(6,34)]) +def degreeRegion39_84 : PrefixRegion := ([(3,18)], [(1,19),(3,22),(7,38)]) +def degreeRegion39_85 : PrefixRegion := ([(7,38)], [(2,10),(3,22)]) + +def degreeRegions39 : List PrefixRegion := [degreeRegion39_0,degreeRegion39_1,degreeRegion39_2,degreeRegion39_3,degreeRegion39_4,degreeRegion39_5,degreeRegion39_6,degreeRegion39_7,degreeRegion39_8,degreeRegion39_9,degreeRegion39_10,degreeRegion39_11,degreeRegion39_12,degreeRegion39_13,degreeRegion39_14,degreeRegion39_15,degreeRegion39_16,degreeRegion39_17,degreeRegion39_18,degreeRegion39_19,degreeRegion39_20,degreeRegion39_21,degreeRegion39_22,degreeRegion39_23,degreeRegion39_24,degreeRegion39_25,degreeRegion39_26,degreeRegion39_27,degreeRegion39_28,degreeRegion39_29,degreeRegion39_30,degreeRegion39_31,degreeRegion39_32,degreeRegion39_33,degreeRegion39_34,degreeRegion39_35,degreeRegion39_36,degreeRegion39_37,degreeRegion39_38,degreeRegion39_39,degreeRegion39_40,degreeRegion39_41,degreeRegion39_42,degreeRegion39_43,degreeRegion39_44,degreeRegion39_45,degreeRegion39_46,degreeRegion39_47,degreeRegion39_48,degreeRegion39_49,degreeRegion39_50,degreeRegion39_51,degreeRegion39_52,degreeRegion39_53,degreeRegion39_54,degreeRegion39_55,degreeRegion39_56,degreeRegion39_57,degreeRegion39_58,degreeRegion39_59,degreeRegion39_60,degreeRegion39_61,degreeRegion39_62,degreeRegion39_63,degreeRegion39_64,degreeRegion39_65,degreeRegion39_66,degreeRegion39_67,degreeRegion39_68,degreeRegion39_69,degreeRegion39_70,degreeRegion39_71,degreeRegion39_72,degreeRegion39_73,degreeRegion39_74,degreeRegion39_75,degreeRegion39_76,degreeRegion39_77,degreeRegion39_78,degreeRegion39_79,degreeRegion39_80,degreeRegion39_81,degreeRegion39_82,degreeRegion39_83,degreeRegion39_84,degreeRegion39_85] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData41.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData41.lean index 578b052714812cd6d62ee6453e328ae3221b0d88..c1b78cc2781d7cf5252379d76e17594cccf448e0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData41.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData41.lean @@ -1,179 +1,179 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 41. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion41_0 : PrefixRegion := ([(1,10),(2,12),(3,24)], [(1,21),(9,39)]) -def degreeRegion41_1 : PrefixRegion := ([(1,10),(3,18)], [(1,21),(6,33)]) -def degreeRegion41_2 : PrefixRegion := ([(1,10),(3,18)], [(1,21),(7,35)]) -def degreeRegion41_3 : PrefixRegion := ([(1,10),(3,18)], [(1,21),(8,37)]) -def degreeRegion41_4 : PrefixRegion := ([(1,10),(3,18)], [(1,21),(9,39)]) -def degreeRegion41_5 : PrefixRegion := ([(1,10),(3,24),(5,28)], [(1,21),(5,28)]) -def degreeRegion41_6 : PrefixRegion := ([(1,10),(3,24),(5,28)], [(1,21),(6,33)]) -def degreeRegion41_7 : PrefixRegion := ([(1,10),(3,24),(5,28)], [(1,21),(7,35)]) -def degreeRegion41_8 : PrefixRegion := ([(1,10),(3,24),(5,28)], [(1,21),(8,37)]) -def degreeRegion41_9 : PrefixRegion := ([(1,10),(3,24),(5,28)], [(1,21),(9,39)]) -def degreeRegion41_10 : PrefixRegion := ([(1,10),(3,24),(6,33)], [(1,21),(5,28)]) -def degreeRegion41_11 : PrefixRegion := ([(1,10),(3,24),(6,33)], [(1,21),(6,33)]) -def degreeRegion41_12 : PrefixRegion := ([(1,10),(3,24),(6,33)], [(1,21),(7,35)]) -def degreeRegion41_13 : PrefixRegion := ([(1,10),(3,24),(6,33)], [(1,21),(8,37)]) -def degreeRegion41_14 : PrefixRegion := ([(1,10),(3,24),(6,33)], [(1,21),(9,39)]) -def degreeRegion41_15 : PrefixRegion := ([(1,10),(3,24),(7,35)], [(1,21),(5,28)]) -def degreeRegion41_16 : PrefixRegion := ([(1,10),(3,24),(7,35)], [(1,21),(6,33)]) -def degreeRegion41_17 : PrefixRegion := ([(1,10),(3,24),(7,35)], [(1,21),(7,35)]) -def degreeRegion41_18 : PrefixRegion := ([(1,10),(3,24),(7,35)], [(1,21),(8,37)]) -def degreeRegion41_19 : PrefixRegion := ([(1,10),(3,24),(7,35)], [(1,21),(9,39)]) -def degreeRegion41_20 : PrefixRegion := ([(1,10),(3,24),(8,37)], [(1,21),(5,28)]) -def degreeRegion41_21 : PrefixRegion := ([(1,10),(3,24),(8,37)], [(1,21),(6,33)]) -def degreeRegion41_22 : PrefixRegion := ([(1,10),(3,24),(8,37)], [(1,21),(7,35)]) -def degreeRegion41_23 : PrefixRegion := ([(1,10),(3,24),(8,37)], [(1,21),(8,37)]) -def degreeRegion41_24 : PrefixRegion := ([(1,10),(3,24),(8,37)], [(1,21),(9,39)]) -def degreeRegion41_25 : PrefixRegion := ([(1,10),(3,24),(9,39)], [(1,21),(5,28)]) -def degreeRegion41_26 : PrefixRegion := ([(1,10),(3,24),(9,39)], [(1,21),(6,33)]) -def degreeRegion41_27 : PrefixRegion := ([(1,10),(3,24),(9,39)], [(1,21),(7,35)]) -def degreeRegion41_28 : PrefixRegion := ([(1,10),(3,24),(9,39)], [(1,21),(8,37)]) -def degreeRegion41_29 : PrefixRegion := ([(1,10),(3,24),(9,39)], [(1,21),(9,39)]) -def degreeRegion41_30 : PrefixRegion := ([(1,10),(3,24),(10,40)], [(1,21),(5,28)]) -def degreeRegion41_31 : PrefixRegion := ([(1,10),(3,24),(10,40)], [(1,21),(6,33)]) -def degreeRegion41_32 : PrefixRegion := ([(1,10),(3,24),(10,40)], [(1,21),(7,35)]) -def degreeRegion41_33 : PrefixRegion := ([(1,10),(3,24),(10,40)], [(1,21),(8,37)]) -def degreeRegion41_34 : PrefixRegion := ([(1,10),(3,24),(10,40)], [(1,21),(9,39)]) -def degreeRegion41_35 : PrefixRegion := ([(1,10),(4,23)], [(1,21),(5,28)]) -def degreeRegion41_36 : PrefixRegion := ([(1,10),(4,23)], [(1,21),(6,33)]) -def degreeRegion41_37 : PrefixRegion := ([(1,10),(4,23)], [(1,21),(7,35)]) -def degreeRegion41_38 : PrefixRegion := ([(1,10),(4,23)], [(1,21),(8,37)]) -def degreeRegion41_39 : PrefixRegion := ([(1,10),(4,23)], [(1,21),(9,39)]) -def degreeRegion41_40 : PrefixRegion := ([(1,10),(5,28)], [(1,10),(5,28)]) -def degreeRegion41_41 : PrefixRegion := ([(1,10),(5,28)], [(1,10),(6,33)]) -def degreeRegion41_42 : PrefixRegion := ([(1,10),(5,28)], [(1,10),(7,35)]) -def degreeRegion41_43 : PrefixRegion := ([(1,10),(5,28)], [(1,10),(8,37)]) -def degreeRegion41_44 : PrefixRegion := ([(1,10),(5,28)], [(1,10),(9,39)]) -def degreeRegion41_45 : PrefixRegion := ([(1,10),(6,33)], [(1,10),(5,28)]) -def degreeRegion41_46 : PrefixRegion := ([(1,10),(6,33)], [(1,10),(6,33)]) -def degreeRegion41_47 : PrefixRegion := ([(1,10),(6,33)], [(1,10),(7,35)]) -def degreeRegion41_48 : PrefixRegion := ([(1,10),(6,33)], [(1,10),(8,37)]) -def degreeRegion41_49 : PrefixRegion := ([(1,10),(6,33)], [(1,10),(9,39)]) -def degreeRegion41_50 : PrefixRegion := ([(1,10),(7,35)], [(1,10),(5,28)]) -def degreeRegion41_51 : PrefixRegion := ([(1,10),(7,35)], [(1,10),(6,33)]) -def degreeRegion41_52 : PrefixRegion := ([(1,10),(7,35)], [(1,10),(7,35)]) -def degreeRegion41_53 : PrefixRegion := ([(1,10),(7,35)], [(1,10),(8,37)]) -def degreeRegion41_54 : PrefixRegion := ([(1,10),(7,35)], [(1,10),(9,39)]) -def degreeRegion41_55 : PrefixRegion := ([(1,10),(8,37)], [(1,10),(5,28)]) -def degreeRegion41_56 : PrefixRegion := ([(1,10),(8,37)], [(1,10),(6,33)]) -def degreeRegion41_57 : PrefixRegion := ([(1,10),(8,37)], [(1,10),(7,35)]) -def degreeRegion41_58 : PrefixRegion := ([(1,10),(8,37)], [(1,10),(8,37)]) -def degreeRegion41_59 : PrefixRegion := ([(1,10),(8,37)], [(1,10),(9,39)]) -def degreeRegion41_60 : PrefixRegion := ([(1,10),(9,39)], [(1,10),(5,28)]) -def degreeRegion41_61 : PrefixRegion := ([(1,10),(9,39)], [(1,10),(6,33)]) -def degreeRegion41_62 : PrefixRegion := ([(1,10),(9,39)], [(1,10),(7,35)]) -def degreeRegion41_63 : PrefixRegion := ([(1,10),(9,39)], [(1,10),(8,37)]) -def degreeRegion41_64 : PrefixRegion := ([(1,10),(9,39)], [(1,10),(9,39)]) -def degreeRegion41_65 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(3,24),(5,28)]) -def degreeRegion41_66 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(3,24),(6,33)]) -def degreeRegion41_67 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(3,24),(7,35)]) -def degreeRegion41_68 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(3,24),(8,37)]) -def degreeRegion41_69 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(3,24),(9,39)]) -def degreeRegion41_70 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(3,24),(10,40)]) -def degreeRegion41_71 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(4,23)]) -def degreeRegion41_72 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(3,24),(5,28)]) -def degreeRegion41_73 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(3,24),(6,33)]) -def degreeRegion41_74 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(3,24),(7,35)]) -def degreeRegion41_75 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(3,24),(8,37)]) -def degreeRegion41_76 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(3,24),(9,39)]) -def degreeRegion41_77 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(3,24),(10,40)]) -def degreeRegion41_78 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(4,23)]) -def degreeRegion41_79 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(3,18)]) -def degreeRegion41_80 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(3,24),(5,28)]) -def degreeRegion41_81 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(3,24),(6,33)]) -def degreeRegion41_82 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(3,24),(7,35)]) -def degreeRegion41_83 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(3,24),(8,37)]) -def degreeRegion41_84 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(3,24),(9,39)]) -def degreeRegion41_85 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(3,24),(10,40)]) -def degreeRegion41_86 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(4,23)]) -def degreeRegion41_87 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(3,18)]) -def degreeRegion41_88 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(3,24),(5,28)]) -def degreeRegion41_89 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(3,24),(6,33)]) -def degreeRegion41_90 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(3,24),(7,35)]) -def degreeRegion41_91 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(3,24),(8,37)]) -def degreeRegion41_92 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(3,24),(9,39)]) -def degreeRegion41_93 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(3,24),(10,40)]) -def degreeRegion41_94 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(4,23)]) -def degreeRegion41_95 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(3,24),(5,28)]) -def degreeRegion41_96 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(3,24),(6,33)]) -def degreeRegion41_97 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(3,24),(7,35)]) -def degreeRegion41_98 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(3,24),(8,37)]) -def degreeRegion41_99 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(3,24),(9,39)]) -def degreeRegion41_100 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(3,24),(10,40)]) -def degreeRegion41_101 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(4,23)]) -def degreeRegion41_102 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(3,24),(5,28)]) -def degreeRegion41_103 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(3,24),(6,33)]) -def degreeRegion41_104 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(3,24),(7,35)]) -def degreeRegion41_105 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(3,24),(8,37)]) -def degreeRegion41_106 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(3,24),(9,39)]) -def degreeRegion41_107 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(3,24),(10,40)]) -def degreeRegion41_108 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(4,23)]) -def degreeRegion41_109 : PrefixRegion := ([(1,21),(4,23)], [(1,21),(3,24),(5,28)]) -def degreeRegion41_110 : PrefixRegion := ([(1,21),(4,23)], [(1,21),(3,24),(6,33)]) -def degreeRegion41_111 : PrefixRegion := ([(1,21),(4,23)], [(1,21),(3,24),(7,35)]) -def degreeRegion41_112 : PrefixRegion := ([(1,21),(4,23)], [(1,21),(3,24),(8,37)]) -def degreeRegion41_113 : PrefixRegion := ([(1,21),(4,23)], [(1,21),(3,24),(9,39)]) -def degreeRegion41_114 : PrefixRegion := ([(1,21),(4,23)], [(1,21),(3,24),(10,40)]) -def degreeRegion41_115 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(3,24),(5,28)]) -def degreeRegion41_116 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(3,24),(6,33)]) -def degreeRegion41_117 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(3,24),(7,35)]) -def degreeRegion41_118 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(3,24),(8,37)]) -def degreeRegion41_119 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(3,24),(9,39)]) -def degreeRegion41_120 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(3,24),(10,40)]) -def degreeRegion41_121 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(4,23)]) -def degreeRegion41_122 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,18)]) -def degreeRegion41_123 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,24),(5,28)]) -def degreeRegion41_124 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,24),(6,33)]) -def degreeRegion41_125 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,24),(7,35)]) -def degreeRegion41_126 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,24),(8,37)]) -def degreeRegion41_127 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,24),(9,39)]) -def degreeRegion41_128 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,24),(10,40)]) -def degreeRegion41_129 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(4,23)]) -def degreeRegion41_130 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,18)]) -def degreeRegion41_131 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,24),(5,28)]) -def degreeRegion41_132 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,24),(6,33)]) -def degreeRegion41_133 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,24),(7,35)]) -def degreeRegion41_134 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,24),(8,37)]) -def degreeRegion41_135 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,24),(9,39)]) -def degreeRegion41_136 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,24),(10,40)]) -def degreeRegion41_137 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(4,23)]) -def degreeRegion41_138 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,18)]) -def degreeRegion41_139 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,24),(5,28)]) -def degreeRegion41_140 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,24),(6,33)]) -def degreeRegion41_141 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,24),(7,35)]) -def degreeRegion41_142 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,24),(8,37)]) -def degreeRegion41_143 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,24),(9,39)]) -def degreeRegion41_144 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,24),(10,40)]) -def degreeRegion41_145 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(4,23)]) -def degreeRegion41_146 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(2,12),(3,24)]) -def degreeRegion41_147 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,18)]) -def degreeRegion41_148 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,24),(5,28)]) -def degreeRegion41_149 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,24),(6,33)]) -def degreeRegion41_150 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,24),(7,35)]) -def degreeRegion41_151 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,24),(8,37)]) -def degreeRegion41_152 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,24),(9,39)]) -def degreeRegion41_153 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,24),(10,40)]) -def degreeRegion41_154 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(4,23)]) -def degreeRegion41_155 : PrefixRegion := ([(3,18)], [(1,21),(3,24),(6,33)]) -def degreeRegion41_156 : PrefixRegion := ([(3,18)], [(1,21),(3,24),(7,35)]) - -def degreeRegions41 : List PrefixRegion := [degreeRegion41_0,degreeRegion41_1,degreeRegion41_2,degreeRegion41_3,degreeRegion41_4,degreeRegion41_5,degreeRegion41_6,degreeRegion41_7,degreeRegion41_8,degreeRegion41_9,degreeRegion41_10,degreeRegion41_11,degreeRegion41_12,degreeRegion41_13,degreeRegion41_14,degreeRegion41_15,degreeRegion41_16,degreeRegion41_17,degreeRegion41_18,degreeRegion41_19,degreeRegion41_20,degreeRegion41_21,degreeRegion41_22,degreeRegion41_23,degreeRegion41_24,degreeRegion41_25,degreeRegion41_26,degreeRegion41_27,degreeRegion41_28,degreeRegion41_29,degreeRegion41_30,degreeRegion41_31,degreeRegion41_32,degreeRegion41_33,degreeRegion41_34,degreeRegion41_35,degreeRegion41_36,degreeRegion41_37,degreeRegion41_38,degreeRegion41_39,degreeRegion41_40,degreeRegion41_41,degreeRegion41_42,degreeRegion41_43,degreeRegion41_44,degreeRegion41_45,degreeRegion41_46,degreeRegion41_47,degreeRegion41_48,degreeRegion41_49,degreeRegion41_50,degreeRegion41_51,degreeRegion41_52,degreeRegion41_53,degreeRegion41_54,degreeRegion41_55,degreeRegion41_56,degreeRegion41_57,degreeRegion41_58,degreeRegion41_59,degreeRegion41_60,degreeRegion41_61,degreeRegion41_62,degreeRegion41_63,degreeRegion41_64,degreeRegion41_65,degreeRegion41_66,degreeRegion41_67,degreeRegion41_68,degreeRegion41_69,degreeRegion41_70,degreeRegion41_71,degreeRegion41_72,degreeRegion41_73,degreeRegion41_74,degreeRegion41_75,degreeRegion41_76,degreeRegion41_77,degreeRegion41_78,degreeRegion41_79,degreeRegion41_80,degreeRegion41_81,degreeRegion41_82,degreeRegion41_83,degreeRegion41_84,degreeRegion41_85,degreeRegion41_86,degreeRegion41_87,degreeRegion41_88,degreeRegion41_89,degreeRegion41_90,degreeRegion41_91,degreeRegion41_92,degreeRegion41_93,degreeRegion41_94,degreeRegion41_95,degreeRegion41_96,degreeRegion41_97,degreeRegion41_98,degreeRegion41_99,degreeRegion41_100,degreeRegion41_101,degreeRegion41_102,degreeRegion41_103,degreeRegion41_104,degreeRegion41_105,degreeRegion41_106,degreeRegion41_107,degreeRegion41_108,degreeRegion41_109,degreeRegion41_110,degreeRegion41_111,degreeRegion41_112,degreeRegion41_113,degreeRegion41_114,degreeRegion41_115,degreeRegion41_116,degreeRegion41_117,degreeRegion41_118,degreeRegion41_119,degreeRegion41_120,degreeRegion41_121,degreeRegion41_122,degreeRegion41_123,degreeRegion41_124,degreeRegion41_125,degreeRegion41_126,degreeRegion41_127,degreeRegion41_128,degreeRegion41_129,degreeRegion41_130,degreeRegion41_131,degreeRegion41_132,degreeRegion41_133,degreeRegion41_134,degreeRegion41_135,degreeRegion41_136,degreeRegion41_137,degreeRegion41_138,degreeRegion41_139,degreeRegion41_140,degreeRegion41_141,degreeRegion41_142,degreeRegion41_143,degreeRegion41_144,degreeRegion41_145,degreeRegion41_146,degreeRegion41_147,degreeRegion41_148,degreeRegion41_149,degreeRegion41_150,degreeRegion41_151,degreeRegion41_152,degreeRegion41_153,degreeRegion41_154,degreeRegion41_155,degreeRegion41_156] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 41. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion41_0 : PrefixRegion := ([(1,10),(2,12),(3,24)], [(1,21),(9,39)]) +def degreeRegion41_1 : PrefixRegion := ([(1,10),(3,18)], [(1,21),(6,33)]) +def degreeRegion41_2 : PrefixRegion := ([(1,10),(3,18)], [(1,21),(7,35)]) +def degreeRegion41_3 : PrefixRegion := ([(1,10),(3,18)], [(1,21),(8,37)]) +def degreeRegion41_4 : PrefixRegion := ([(1,10),(3,18)], [(1,21),(9,39)]) +def degreeRegion41_5 : PrefixRegion := ([(1,10),(3,24),(5,28)], [(1,21),(5,28)]) +def degreeRegion41_6 : PrefixRegion := ([(1,10),(3,24),(5,28)], [(1,21),(6,33)]) +def degreeRegion41_7 : PrefixRegion := ([(1,10),(3,24),(5,28)], [(1,21),(7,35)]) +def degreeRegion41_8 : PrefixRegion := ([(1,10),(3,24),(5,28)], [(1,21),(8,37)]) +def degreeRegion41_9 : PrefixRegion := ([(1,10),(3,24),(5,28)], [(1,21),(9,39)]) +def degreeRegion41_10 : PrefixRegion := ([(1,10),(3,24),(6,33)], [(1,21),(5,28)]) +def degreeRegion41_11 : PrefixRegion := ([(1,10),(3,24),(6,33)], [(1,21),(6,33)]) +def degreeRegion41_12 : PrefixRegion := ([(1,10),(3,24),(6,33)], [(1,21),(7,35)]) +def degreeRegion41_13 : PrefixRegion := ([(1,10),(3,24),(6,33)], [(1,21),(8,37)]) +def degreeRegion41_14 : PrefixRegion := ([(1,10),(3,24),(6,33)], [(1,21),(9,39)]) +def degreeRegion41_15 : PrefixRegion := ([(1,10),(3,24),(7,35)], [(1,21),(5,28)]) +def degreeRegion41_16 : PrefixRegion := ([(1,10),(3,24),(7,35)], [(1,21),(6,33)]) +def degreeRegion41_17 : PrefixRegion := ([(1,10),(3,24),(7,35)], [(1,21),(7,35)]) +def degreeRegion41_18 : PrefixRegion := ([(1,10),(3,24),(7,35)], [(1,21),(8,37)]) +def degreeRegion41_19 : PrefixRegion := ([(1,10),(3,24),(7,35)], [(1,21),(9,39)]) +def degreeRegion41_20 : PrefixRegion := ([(1,10),(3,24),(8,37)], [(1,21),(5,28)]) +def degreeRegion41_21 : PrefixRegion := ([(1,10),(3,24),(8,37)], [(1,21),(6,33)]) +def degreeRegion41_22 : PrefixRegion := ([(1,10),(3,24),(8,37)], [(1,21),(7,35)]) +def degreeRegion41_23 : PrefixRegion := ([(1,10),(3,24),(8,37)], [(1,21),(8,37)]) +def degreeRegion41_24 : PrefixRegion := ([(1,10),(3,24),(8,37)], [(1,21),(9,39)]) +def degreeRegion41_25 : PrefixRegion := ([(1,10),(3,24),(9,39)], [(1,21),(5,28)]) +def degreeRegion41_26 : PrefixRegion := ([(1,10),(3,24),(9,39)], [(1,21),(6,33)]) +def degreeRegion41_27 : PrefixRegion := ([(1,10),(3,24),(9,39)], [(1,21),(7,35)]) +def degreeRegion41_28 : PrefixRegion := ([(1,10),(3,24),(9,39)], [(1,21),(8,37)]) +def degreeRegion41_29 : PrefixRegion := ([(1,10),(3,24),(9,39)], [(1,21),(9,39)]) +def degreeRegion41_30 : PrefixRegion := ([(1,10),(3,24),(10,40)], [(1,21),(5,28)]) +def degreeRegion41_31 : PrefixRegion := ([(1,10),(3,24),(10,40)], [(1,21),(6,33)]) +def degreeRegion41_32 : PrefixRegion := ([(1,10),(3,24),(10,40)], [(1,21),(7,35)]) +def degreeRegion41_33 : PrefixRegion := ([(1,10),(3,24),(10,40)], [(1,21),(8,37)]) +def degreeRegion41_34 : PrefixRegion := ([(1,10),(3,24),(10,40)], [(1,21),(9,39)]) +def degreeRegion41_35 : PrefixRegion := ([(1,10),(4,23)], [(1,21),(5,28)]) +def degreeRegion41_36 : PrefixRegion := ([(1,10),(4,23)], [(1,21),(6,33)]) +def degreeRegion41_37 : PrefixRegion := ([(1,10),(4,23)], [(1,21),(7,35)]) +def degreeRegion41_38 : PrefixRegion := ([(1,10),(4,23)], [(1,21),(8,37)]) +def degreeRegion41_39 : PrefixRegion := ([(1,10),(4,23)], [(1,21),(9,39)]) +def degreeRegion41_40 : PrefixRegion := ([(1,10),(5,28)], [(1,10),(5,28)]) +def degreeRegion41_41 : PrefixRegion := ([(1,10),(5,28)], [(1,10),(6,33)]) +def degreeRegion41_42 : PrefixRegion := ([(1,10),(5,28)], [(1,10),(7,35)]) +def degreeRegion41_43 : PrefixRegion := ([(1,10),(5,28)], [(1,10),(8,37)]) +def degreeRegion41_44 : PrefixRegion := ([(1,10),(5,28)], [(1,10),(9,39)]) +def degreeRegion41_45 : PrefixRegion := ([(1,10),(6,33)], [(1,10),(5,28)]) +def degreeRegion41_46 : PrefixRegion := ([(1,10),(6,33)], [(1,10),(6,33)]) +def degreeRegion41_47 : PrefixRegion := ([(1,10),(6,33)], [(1,10),(7,35)]) +def degreeRegion41_48 : PrefixRegion := ([(1,10),(6,33)], [(1,10),(8,37)]) +def degreeRegion41_49 : PrefixRegion := ([(1,10),(6,33)], [(1,10),(9,39)]) +def degreeRegion41_50 : PrefixRegion := ([(1,10),(7,35)], [(1,10),(5,28)]) +def degreeRegion41_51 : PrefixRegion := ([(1,10),(7,35)], [(1,10),(6,33)]) +def degreeRegion41_52 : PrefixRegion := ([(1,10),(7,35)], [(1,10),(7,35)]) +def degreeRegion41_53 : PrefixRegion := ([(1,10),(7,35)], [(1,10),(8,37)]) +def degreeRegion41_54 : PrefixRegion := ([(1,10),(7,35)], [(1,10),(9,39)]) +def degreeRegion41_55 : PrefixRegion := ([(1,10),(8,37)], [(1,10),(5,28)]) +def degreeRegion41_56 : PrefixRegion := ([(1,10),(8,37)], [(1,10),(6,33)]) +def degreeRegion41_57 : PrefixRegion := ([(1,10),(8,37)], [(1,10),(7,35)]) +def degreeRegion41_58 : PrefixRegion := ([(1,10),(8,37)], [(1,10),(8,37)]) +def degreeRegion41_59 : PrefixRegion := ([(1,10),(8,37)], [(1,10),(9,39)]) +def degreeRegion41_60 : PrefixRegion := ([(1,10),(9,39)], [(1,10),(5,28)]) +def degreeRegion41_61 : PrefixRegion := ([(1,10),(9,39)], [(1,10),(6,33)]) +def degreeRegion41_62 : PrefixRegion := ([(1,10),(9,39)], [(1,10),(7,35)]) +def degreeRegion41_63 : PrefixRegion := ([(1,10),(9,39)], [(1,10),(8,37)]) +def degreeRegion41_64 : PrefixRegion := ([(1,10),(9,39)], [(1,10),(9,39)]) +def degreeRegion41_65 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(3,24),(5,28)]) +def degreeRegion41_66 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(3,24),(6,33)]) +def degreeRegion41_67 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(3,24),(7,35)]) +def degreeRegion41_68 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(3,24),(8,37)]) +def degreeRegion41_69 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(3,24),(9,39)]) +def degreeRegion41_70 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(3,24),(10,40)]) +def degreeRegion41_71 : PrefixRegion := ([(1,21),(3,24),(5,28)], [(1,21),(4,23)]) +def degreeRegion41_72 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(3,24),(5,28)]) +def degreeRegion41_73 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(3,24),(6,33)]) +def degreeRegion41_74 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(3,24),(7,35)]) +def degreeRegion41_75 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(3,24),(8,37)]) +def degreeRegion41_76 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(3,24),(9,39)]) +def degreeRegion41_77 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(3,24),(10,40)]) +def degreeRegion41_78 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(1,21),(4,23)]) +def degreeRegion41_79 : PrefixRegion := ([(1,21),(3,24),(6,33)], [(3,18)]) +def degreeRegion41_80 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(3,24),(5,28)]) +def degreeRegion41_81 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(3,24),(6,33)]) +def degreeRegion41_82 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(3,24),(7,35)]) +def degreeRegion41_83 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(3,24),(8,37)]) +def degreeRegion41_84 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(3,24),(9,39)]) +def degreeRegion41_85 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(3,24),(10,40)]) +def degreeRegion41_86 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(1,21),(4,23)]) +def degreeRegion41_87 : PrefixRegion := ([(1,21),(3,24),(7,35)], [(3,18)]) +def degreeRegion41_88 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(3,24),(5,28)]) +def degreeRegion41_89 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(3,24),(6,33)]) +def degreeRegion41_90 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(3,24),(7,35)]) +def degreeRegion41_91 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(3,24),(8,37)]) +def degreeRegion41_92 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(3,24),(9,39)]) +def degreeRegion41_93 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(3,24),(10,40)]) +def degreeRegion41_94 : PrefixRegion := ([(1,21),(3,24),(8,37)], [(1,21),(4,23)]) +def degreeRegion41_95 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(3,24),(5,28)]) +def degreeRegion41_96 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(3,24),(6,33)]) +def degreeRegion41_97 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(3,24),(7,35)]) +def degreeRegion41_98 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(3,24),(8,37)]) +def degreeRegion41_99 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(3,24),(9,39)]) +def degreeRegion41_100 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(3,24),(10,40)]) +def degreeRegion41_101 : PrefixRegion := ([(1,21),(3,24),(9,39)], [(1,21),(4,23)]) +def degreeRegion41_102 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(3,24),(5,28)]) +def degreeRegion41_103 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(3,24),(6,33)]) +def degreeRegion41_104 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(3,24),(7,35)]) +def degreeRegion41_105 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(3,24),(8,37)]) +def degreeRegion41_106 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(3,24),(9,39)]) +def degreeRegion41_107 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(3,24),(10,40)]) +def degreeRegion41_108 : PrefixRegion := ([(1,21),(3,24),(10,40)], [(1,21),(4,23)]) +def degreeRegion41_109 : PrefixRegion := ([(1,21),(4,23)], [(1,21),(3,24),(5,28)]) +def degreeRegion41_110 : PrefixRegion := ([(1,21),(4,23)], [(1,21),(3,24),(6,33)]) +def degreeRegion41_111 : PrefixRegion := ([(1,21),(4,23)], [(1,21),(3,24),(7,35)]) +def degreeRegion41_112 : PrefixRegion := ([(1,21),(4,23)], [(1,21),(3,24),(8,37)]) +def degreeRegion41_113 : PrefixRegion := ([(1,21),(4,23)], [(1,21),(3,24),(9,39)]) +def degreeRegion41_114 : PrefixRegion := ([(1,21),(4,23)], [(1,21),(3,24),(10,40)]) +def degreeRegion41_115 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(3,24),(5,28)]) +def degreeRegion41_116 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(3,24),(6,33)]) +def degreeRegion41_117 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(3,24),(7,35)]) +def degreeRegion41_118 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(3,24),(8,37)]) +def degreeRegion41_119 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(3,24),(9,39)]) +def degreeRegion41_120 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(3,24),(10,40)]) +def degreeRegion41_121 : PrefixRegion := ([(1,21),(5,28)], [(1,10),(4,23)]) +def degreeRegion41_122 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,18)]) +def degreeRegion41_123 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,24),(5,28)]) +def degreeRegion41_124 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,24),(6,33)]) +def degreeRegion41_125 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,24),(7,35)]) +def degreeRegion41_126 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,24),(8,37)]) +def degreeRegion41_127 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,24),(9,39)]) +def degreeRegion41_128 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(3,24),(10,40)]) +def degreeRegion41_129 : PrefixRegion := ([(1,21),(6,33)], [(1,10),(4,23)]) +def degreeRegion41_130 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,18)]) +def degreeRegion41_131 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,24),(5,28)]) +def degreeRegion41_132 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,24),(6,33)]) +def degreeRegion41_133 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,24),(7,35)]) +def degreeRegion41_134 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,24),(8,37)]) +def degreeRegion41_135 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,24),(9,39)]) +def degreeRegion41_136 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(3,24),(10,40)]) +def degreeRegion41_137 : PrefixRegion := ([(1,21),(7,35)], [(1,10),(4,23)]) +def degreeRegion41_138 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,18)]) +def degreeRegion41_139 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,24),(5,28)]) +def degreeRegion41_140 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,24),(6,33)]) +def degreeRegion41_141 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,24),(7,35)]) +def degreeRegion41_142 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,24),(8,37)]) +def degreeRegion41_143 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,24),(9,39)]) +def degreeRegion41_144 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(3,24),(10,40)]) +def degreeRegion41_145 : PrefixRegion := ([(1,21),(8,37)], [(1,10),(4,23)]) +def degreeRegion41_146 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(2,12),(3,24)]) +def degreeRegion41_147 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,18)]) +def degreeRegion41_148 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,24),(5,28)]) +def degreeRegion41_149 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,24),(6,33)]) +def degreeRegion41_150 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,24),(7,35)]) +def degreeRegion41_151 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,24),(8,37)]) +def degreeRegion41_152 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,24),(9,39)]) +def degreeRegion41_153 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(3,24),(10,40)]) +def degreeRegion41_154 : PrefixRegion := ([(1,21),(9,39)], [(1,10),(4,23)]) +def degreeRegion41_155 : PrefixRegion := ([(3,18)], [(1,21),(3,24),(6,33)]) +def degreeRegion41_156 : PrefixRegion := ([(3,18)], [(1,21),(3,24),(7,35)]) + +def degreeRegions41 : List PrefixRegion := [degreeRegion41_0,degreeRegion41_1,degreeRegion41_2,degreeRegion41_3,degreeRegion41_4,degreeRegion41_5,degreeRegion41_6,degreeRegion41_7,degreeRegion41_8,degreeRegion41_9,degreeRegion41_10,degreeRegion41_11,degreeRegion41_12,degreeRegion41_13,degreeRegion41_14,degreeRegion41_15,degreeRegion41_16,degreeRegion41_17,degreeRegion41_18,degreeRegion41_19,degreeRegion41_20,degreeRegion41_21,degreeRegion41_22,degreeRegion41_23,degreeRegion41_24,degreeRegion41_25,degreeRegion41_26,degreeRegion41_27,degreeRegion41_28,degreeRegion41_29,degreeRegion41_30,degreeRegion41_31,degreeRegion41_32,degreeRegion41_33,degreeRegion41_34,degreeRegion41_35,degreeRegion41_36,degreeRegion41_37,degreeRegion41_38,degreeRegion41_39,degreeRegion41_40,degreeRegion41_41,degreeRegion41_42,degreeRegion41_43,degreeRegion41_44,degreeRegion41_45,degreeRegion41_46,degreeRegion41_47,degreeRegion41_48,degreeRegion41_49,degreeRegion41_50,degreeRegion41_51,degreeRegion41_52,degreeRegion41_53,degreeRegion41_54,degreeRegion41_55,degreeRegion41_56,degreeRegion41_57,degreeRegion41_58,degreeRegion41_59,degreeRegion41_60,degreeRegion41_61,degreeRegion41_62,degreeRegion41_63,degreeRegion41_64,degreeRegion41_65,degreeRegion41_66,degreeRegion41_67,degreeRegion41_68,degreeRegion41_69,degreeRegion41_70,degreeRegion41_71,degreeRegion41_72,degreeRegion41_73,degreeRegion41_74,degreeRegion41_75,degreeRegion41_76,degreeRegion41_77,degreeRegion41_78,degreeRegion41_79,degreeRegion41_80,degreeRegion41_81,degreeRegion41_82,degreeRegion41_83,degreeRegion41_84,degreeRegion41_85,degreeRegion41_86,degreeRegion41_87,degreeRegion41_88,degreeRegion41_89,degreeRegion41_90,degreeRegion41_91,degreeRegion41_92,degreeRegion41_93,degreeRegion41_94,degreeRegion41_95,degreeRegion41_96,degreeRegion41_97,degreeRegion41_98,degreeRegion41_99,degreeRegion41_100,degreeRegion41_101,degreeRegion41_102,degreeRegion41_103,degreeRegion41_104,degreeRegion41_105,degreeRegion41_106,degreeRegion41_107,degreeRegion41_108,degreeRegion41_109,degreeRegion41_110,degreeRegion41_111,degreeRegion41_112,degreeRegion41_113,degreeRegion41_114,degreeRegion41_115,degreeRegion41_116,degreeRegion41_117,degreeRegion41_118,degreeRegion41_119,degreeRegion41_120,degreeRegion41_121,degreeRegion41_122,degreeRegion41_123,degreeRegion41_124,degreeRegion41_125,degreeRegion41_126,degreeRegion41_127,degreeRegion41_128,degreeRegion41_129,degreeRegion41_130,degreeRegion41_131,degreeRegion41_132,degreeRegion41_133,degreeRegion41_134,degreeRegion41_135,degreeRegion41_136,degreeRegion41_137,degreeRegion41_138,degreeRegion41_139,degreeRegion41_140,degreeRegion41_141,degreeRegion41_142,degreeRegion41_143,degreeRegion41_144,degreeRegion41_145,degreeRegion41_146,degreeRegion41_147,degreeRegion41_148,degreeRegion41_149,degreeRegion41_150,degreeRegion41_151,degreeRegion41_152,degreeRegion41_153,degreeRegion41_154,degreeRegion41_155,degreeRegion41_156] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData43.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData43.lean index f9159884bd7849bfaf1f8dd2ec451b9f5ea0b174..95d3b4854c8665bba3eb9936f1bba85585292abb 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData43.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData43.lean @@ -1,142 +1,142 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 43. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion43_0 : PrefixRegion := ([(1,7)], [(1,7)]) -def degreeRegion43_1 : PrefixRegion := ([(1,7)], [(1,10),(2,14)]) -def degreeRegion43_2 : PrefixRegion := ([(1,7)], [(1,10),(3,20)]) -def degreeRegion43_3 : PrefixRegion := ([(1,7)], [(1,10),(4,26)]) -def degreeRegion43_4 : PrefixRegion := ([(1,7)], [(1,10),(5,32)]) -def degreeRegion43_5 : PrefixRegion := ([(1,7)], [(1,10),(6,38)]) -def degreeRegion43_6 : PrefixRegion := ([(1,7),(3,26)], [(1,23),(4,26)]) -def degreeRegion43_7 : PrefixRegion := ([(1,7),(3,26)], [(1,23),(5,32)]) -def degreeRegion43_8 : PrefixRegion := ([(1,7),(3,26)], [(1,23),(6,38)]) -def degreeRegion43_9 : PrefixRegion := ([(1,7),(3,26)], [(2,14)]) -def degreeRegion43_10 : PrefixRegion := ([(1,7),(3,26)], [(3,20)]) -def degreeRegion43_11 : PrefixRegion := ([(1,10),(2,14)], [(1,7)]) -def degreeRegion43_12 : PrefixRegion := ([(1,10),(2,14)], [(1,10),(2,14)]) -def degreeRegion43_13 : PrefixRegion := ([(1,10),(2,14)], [(1,10),(5,32)]) -def degreeRegion43_14 : PrefixRegion := ([(1,10),(2,14)], [(1,10),(6,38)]) -def degreeRegion43_15 : PrefixRegion := ([(1,10),(2,14)], [(1,10),(7,42)]) -def degreeRegion43_16 : PrefixRegion := ([(1,10),(2,14),(3,26)], [(1,23),(5,32)]) -def degreeRegion43_17 : PrefixRegion := ([(1,10),(2,14),(3,26)], [(1,23),(6,38)]) -def degreeRegion43_18 : PrefixRegion := ([(1,10),(2,14),(3,26)], [(1,23),(7,42)]) -def degreeRegion43_19 : PrefixRegion := ([(1,10),(2,14),(3,26)], [(2,14)]) -def degreeRegion43_20 : PrefixRegion := ([(1,10),(3,20)], [(1,7)]) -def degreeRegion43_21 : PrefixRegion := ([(1,10),(3,20)], [(1,23),(5,32)]) -def degreeRegion43_22 : PrefixRegion := ([(1,10),(3,20)], [(1,23),(6,38)]) -def degreeRegion43_23 : PrefixRegion := ([(1,10),(3,20)], [(1,23),(7,42)]) -def degreeRegion43_24 : PrefixRegion := ([(1,10),(3,20)], [(2,14)]) -def degreeRegion43_25 : PrefixRegion := ([(1,10),(3,26),(5,32)], [(1,23),(5,32)]) -def degreeRegion43_26 : PrefixRegion := ([(1,10),(3,26),(5,32)], [(1,23),(6,38)]) -def degreeRegion43_27 : PrefixRegion := ([(1,10),(3,26),(5,32)], [(1,23),(7,42)]) -def degreeRegion43_28 : PrefixRegion := ([(1,10),(3,26),(5,32)], [(2,14)]) -def degreeRegion43_29 : PrefixRegion := ([(1,10),(3,26),(6,38)], [(1,23),(5,32)]) -def degreeRegion43_30 : PrefixRegion := ([(1,10),(3,26),(6,38)], [(1,23),(6,38)]) -def degreeRegion43_31 : PrefixRegion := ([(1,10),(3,26),(6,38)], [(1,23),(7,42)]) -def degreeRegion43_32 : PrefixRegion := ([(1,10),(3,26),(6,38)], [(2,14)]) -def degreeRegion43_33 : PrefixRegion := ([(1,10),(3,26),(7,42)], [(1,23),(5,32)]) -def degreeRegion43_34 : PrefixRegion := ([(1,10),(3,26),(7,42)], [(1,23),(6,38)]) -def degreeRegion43_35 : PrefixRegion := ([(1,10),(3,26),(7,42)], [(1,23),(7,42)]) -def degreeRegion43_36 : PrefixRegion := ([(1,10),(3,26),(7,42)], [(2,14)]) -def degreeRegion43_37 : PrefixRegion := ([(1,10),(4,26)], [(1,7)]) -def degreeRegion43_38 : PrefixRegion := ([(1,10),(4,26)], [(1,23),(5,32)]) -def degreeRegion43_39 : PrefixRegion := ([(1,10),(4,26)], [(1,23),(6,38)]) -def degreeRegion43_40 : PrefixRegion := ([(1,10),(4,26)], [(1,23),(7,42)]) -def degreeRegion43_41 : PrefixRegion := ([(1,10),(4,26)], [(2,14)]) -def degreeRegion43_42 : PrefixRegion := ([(1,10),(5,32)], [(1,7)]) -def degreeRegion43_43 : PrefixRegion := ([(1,10),(5,32)], [(1,10),(2,14)]) -def degreeRegion43_44 : PrefixRegion := ([(1,10),(5,32)], [(1,10),(5,32)]) -def degreeRegion43_45 : PrefixRegion := ([(1,10),(5,32)], [(1,10),(6,38)]) -def degreeRegion43_46 : PrefixRegion := ([(1,10),(5,32)], [(1,10),(7,42)]) -def degreeRegion43_47 : PrefixRegion := ([(1,10),(6,38)], [(1,7)]) -def degreeRegion43_48 : PrefixRegion := ([(1,10),(6,38)], [(1,10),(2,14)]) -def degreeRegion43_49 : PrefixRegion := ([(1,10),(6,38)], [(1,10),(5,32)]) -def degreeRegion43_50 : PrefixRegion := ([(1,10),(6,38)], [(1,10),(6,38)]) -def degreeRegion43_51 : PrefixRegion := ([(1,10),(6,38)], [(1,10),(7,42)]) -def degreeRegion43_52 : PrefixRegion := ([(1,10),(7,42)], [(1,10),(2,14)]) -def degreeRegion43_53 : PrefixRegion := ([(1,10),(7,42)], [(1,10),(5,32)]) -def degreeRegion43_54 : PrefixRegion := ([(1,10),(7,42)], [(1,10),(6,38)]) -def degreeRegion43_55 : PrefixRegion := ([(1,10),(7,42)], [(1,10),(7,42)]) -def degreeRegion43_56 : PrefixRegion := ([(1,23),(3,26),(5,32)], [(1,23),(3,26),(5,32)]) -def degreeRegion43_57 : PrefixRegion := ([(1,23),(3,26),(5,32)], [(1,23),(3,26),(6,38)]) -def degreeRegion43_58 : PrefixRegion := ([(1,23),(3,26),(5,32)], [(1,23),(3,26),(7,42)]) -def degreeRegion43_59 : PrefixRegion := ([(1,23),(3,26),(5,32)], [(1,23),(4,26)]) -def degreeRegion43_60 : PrefixRegion := ([(1,23),(3,26),(5,32)], [(2,14),(3,26)]) -def degreeRegion43_61 : PrefixRegion := ([(1,23),(3,26),(5,32)], [(3,20)]) -def degreeRegion43_62 : PrefixRegion := ([(1,23),(3,26),(6,38)], [(1,23),(3,26),(5,32)]) -def degreeRegion43_63 : PrefixRegion := ([(1,23),(3,26),(6,38)], [(1,23),(3,26),(6,38)]) -def degreeRegion43_64 : PrefixRegion := ([(1,23),(3,26),(6,38)], [(1,23),(3,26),(7,42)]) -def degreeRegion43_65 : PrefixRegion := ([(1,23),(3,26),(6,38)], [(1,23),(4,26)]) -def degreeRegion43_66 : PrefixRegion := ([(1,23),(3,26),(6,38)], [(2,14),(3,26)]) -def degreeRegion43_67 : PrefixRegion := ([(1,23),(3,26),(6,38)], [(3,20)]) -def degreeRegion43_68 : PrefixRegion := ([(1,23),(3,26),(7,42)], [(1,23),(3,26),(5,32)]) -def degreeRegion43_69 : PrefixRegion := ([(1,23),(3,26),(7,42)], [(1,23),(3,26),(6,38)]) -def degreeRegion43_70 : PrefixRegion := ([(1,23),(3,26),(7,42)], [(1,23),(3,26),(7,42)]) -def degreeRegion43_71 : PrefixRegion := ([(1,23),(3,26),(7,42)], [(1,23),(4,26)]) -def degreeRegion43_72 : PrefixRegion := ([(1,23),(3,26),(7,42)], [(2,14),(3,26)]) -def degreeRegion43_73 : PrefixRegion := ([(1,23),(3,26),(7,42)], [(3,20)]) -def degreeRegion43_74 : PrefixRegion := ([(1,23),(4,26)], [(1,7),(3,26)]) -def degreeRegion43_75 : PrefixRegion := ([(1,23),(4,26)], [(1,23),(3,26),(5,32)]) -def degreeRegion43_76 : PrefixRegion := ([(1,23),(4,26)], [(1,23),(3,26),(6,38)]) -def degreeRegion43_77 : PrefixRegion := ([(1,23),(4,26)], [(1,23),(3,26),(7,42)]) -def degreeRegion43_78 : PrefixRegion := ([(1,23),(4,26)], [(1,23),(4,26)]) -def degreeRegion43_79 : PrefixRegion := ([(1,23),(4,26)], [(2,14),(3,26)]) -def degreeRegion43_80 : PrefixRegion := ([(1,23),(5,32)], [(1,7),(3,26)]) -def degreeRegion43_81 : PrefixRegion := ([(1,23),(5,32)], [(1,10),(2,14),(3,26)]) -def degreeRegion43_82 : PrefixRegion := ([(1,23),(5,32)], [(1,10),(3,20)]) -def degreeRegion43_83 : PrefixRegion := ([(1,23),(5,32)], [(1,10),(3,26),(5,32)]) -def degreeRegion43_84 : PrefixRegion := ([(1,23),(5,32)], [(1,10),(3,26),(6,38)]) -def degreeRegion43_85 : PrefixRegion := ([(1,23),(5,32)], [(1,10),(3,26),(7,42)]) -def degreeRegion43_86 : PrefixRegion := ([(1,23),(5,32)], [(1,10),(4,26)]) -def degreeRegion43_87 : PrefixRegion := ([(1,23),(6,38)], [(1,7),(3,26)]) -def degreeRegion43_88 : PrefixRegion := ([(1,23),(6,38)], [(1,10),(2,14),(3,26)]) -def degreeRegion43_89 : PrefixRegion := ([(1,23),(6,38)], [(1,10),(3,20)]) -def degreeRegion43_90 : PrefixRegion := ([(1,23),(6,38)], [(1,10),(3,26),(5,32)]) -def degreeRegion43_91 : PrefixRegion := ([(1,23),(6,38)], [(1,10),(3,26),(6,38)]) -def degreeRegion43_92 : PrefixRegion := ([(1,23),(6,38)], [(1,10),(3,26),(7,42)]) -def degreeRegion43_93 : PrefixRegion := ([(1,23),(6,38)], [(1,10),(4,26)]) -def degreeRegion43_94 : PrefixRegion := ([(1,23),(7,42)], [(1,10),(2,14),(3,26)]) -def degreeRegion43_95 : PrefixRegion := ([(1,23),(7,42)], [(1,10),(3,20)]) -def degreeRegion43_96 : PrefixRegion := ([(1,23),(7,42)], [(1,10),(3,26),(5,32)]) -def degreeRegion43_97 : PrefixRegion := ([(1,23),(7,42)], [(1,10),(3,26),(6,38)]) -def degreeRegion43_98 : PrefixRegion := ([(1,23),(7,42)], [(1,10),(3,26),(7,42)]) -def degreeRegion43_99 : PrefixRegion := ([(1,23),(7,42)], [(1,10),(4,26)]) -def degreeRegion43_100 : PrefixRegion := ([(2,10),(3,26)], [(7,42)]) -def degreeRegion43_101 : PrefixRegion := ([(2,14)], [(1,7),(3,26)]) -def degreeRegion43_102 : PrefixRegion := ([(2,14)], [(1,10),(2,14),(3,26)]) -def degreeRegion43_103 : PrefixRegion := ([(2,14)], [(1,10),(3,20)]) -def degreeRegion43_104 : PrefixRegion := ([(2,14)], [(1,10),(3,26),(5,32)]) -def degreeRegion43_105 : PrefixRegion := ([(2,14)], [(1,10),(3,26),(6,38)]) -def degreeRegion43_106 : PrefixRegion := ([(2,14)], [(1,10),(3,26),(7,42)]) -def degreeRegion43_107 : PrefixRegion := ([(2,14)], [(1,10),(4,26)]) -def degreeRegion43_108 : PrefixRegion := ([(2,14),(3,26)], [(1,23),(3,26),(5,32)]) -def degreeRegion43_109 : PrefixRegion := ([(2,14),(3,26)], [(1,23),(3,26),(6,38)]) -def degreeRegion43_110 : PrefixRegion := ([(2,14),(3,26)], [(1,23),(3,26),(7,42)]) -def degreeRegion43_111 : PrefixRegion := ([(2,14),(3,26)], [(1,23),(4,26)]) -def degreeRegion43_112 : PrefixRegion := ([(2,14),(3,26)], [(2,14),(3,26)]) -def degreeRegion43_113 : PrefixRegion := ([(2,14),(3,26)], [(3,20)]) -def degreeRegion43_114 : PrefixRegion := ([(3,20)], [(1,7),(3,26)]) -def degreeRegion43_115 : PrefixRegion := ([(3,20)], [(1,23),(3,26),(5,32)]) -def degreeRegion43_116 : PrefixRegion := ([(3,20)], [(1,23),(3,26),(6,38)]) -def degreeRegion43_117 : PrefixRegion := ([(3,20)], [(1,23),(3,26),(7,42)]) -def degreeRegion43_118 : PrefixRegion := ([(3,20)], [(2,14),(3,26)]) -def degreeRegion43_119 : PrefixRegion := ([(7,42)], [(2,10),(3,26)]) - -def degreeRegions43 : List PrefixRegion := [degreeRegion43_0,degreeRegion43_1,degreeRegion43_2,degreeRegion43_3,degreeRegion43_4,degreeRegion43_5,degreeRegion43_6,degreeRegion43_7,degreeRegion43_8,degreeRegion43_9,degreeRegion43_10,degreeRegion43_11,degreeRegion43_12,degreeRegion43_13,degreeRegion43_14,degreeRegion43_15,degreeRegion43_16,degreeRegion43_17,degreeRegion43_18,degreeRegion43_19,degreeRegion43_20,degreeRegion43_21,degreeRegion43_22,degreeRegion43_23,degreeRegion43_24,degreeRegion43_25,degreeRegion43_26,degreeRegion43_27,degreeRegion43_28,degreeRegion43_29,degreeRegion43_30,degreeRegion43_31,degreeRegion43_32,degreeRegion43_33,degreeRegion43_34,degreeRegion43_35,degreeRegion43_36,degreeRegion43_37,degreeRegion43_38,degreeRegion43_39,degreeRegion43_40,degreeRegion43_41,degreeRegion43_42,degreeRegion43_43,degreeRegion43_44,degreeRegion43_45,degreeRegion43_46,degreeRegion43_47,degreeRegion43_48,degreeRegion43_49,degreeRegion43_50,degreeRegion43_51,degreeRegion43_52,degreeRegion43_53,degreeRegion43_54,degreeRegion43_55,degreeRegion43_56,degreeRegion43_57,degreeRegion43_58,degreeRegion43_59,degreeRegion43_60,degreeRegion43_61,degreeRegion43_62,degreeRegion43_63,degreeRegion43_64,degreeRegion43_65,degreeRegion43_66,degreeRegion43_67,degreeRegion43_68,degreeRegion43_69,degreeRegion43_70,degreeRegion43_71,degreeRegion43_72,degreeRegion43_73,degreeRegion43_74,degreeRegion43_75,degreeRegion43_76,degreeRegion43_77,degreeRegion43_78,degreeRegion43_79,degreeRegion43_80,degreeRegion43_81,degreeRegion43_82,degreeRegion43_83,degreeRegion43_84,degreeRegion43_85,degreeRegion43_86,degreeRegion43_87,degreeRegion43_88,degreeRegion43_89,degreeRegion43_90,degreeRegion43_91,degreeRegion43_92,degreeRegion43_93,degreeRegion43_94,degreeRegion43_95,degreeRegion43_96,degreeRegion43_97,degreeRegion43_98,degreeRegion43_99,degreeRegion43_100,degreeRegion43_101,degreeRegion43_102,degreeRegion43_103,degreeRegion43_104,degreeRegion43_105,degreeRegion43_106,degreeRegion43_107,degreeRegion43_108,degreeRegion43_109,degreeRegion43_110,degreeRegion43_111,degreeRegion43_112,degreeRegion43_113,degreeRegion43_114,degreeRegion43_115,degreeRegion43_116,degreeRegion43_117,degreeRegion43_118,degreeRegion43_119] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 43. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion43_0 : PrefixRegion := ([(1,7)], [(1,7)]) +def degreeRegion43_1 : PrefixRegion := ([(1,7)], [(1,10),(2,14)]) +def degreeRegion43_2 : PrefixRegion := ([(1,7)], [(1,10),(3,20)]) +def degreeRegion43_3 : PrefixRegion := ([(1,7)], [(1,10),(4,26)]) +def degreeRegion43_4 : PrefixRegion := ([(1,7)], [(1,10),(5,32)]) +def degreeRegion43_5 : PrefixRegion := ([(1,7)], [(1,10),(6,38)]) +def degreeRegion43_6 : PrefixRegion := ([(1,7),(3,26)], [(1,23),(4,26)]) +def degreeRegion43_7 : PrefixRegion := ([(1,7),(3,26)], [(1,23),(5,32)]) +def degreeRegion43_8 : PrefixRegion := ([(1,7),(3,26)], [(1,23),(6,38)]) +def degreeRegion43_9 : PrefixRegion := ([(1,7),(3,26)], [(2,14)]) +def degreeRegion43_10 : PrefixRegion := ([(1,7),(3,26)], [(3,20)]) +def degreeRegion43_11 : PrefixRegion := ([(1,10),(2,14)], [(1,7)]) +def degreeRegion43_12 : PrefixRegion := ([(1,10),(2,14)], [(1,10),(2,14)]) +def degreeRegion43_13 : PrefixRegion := ([(1,10),(2,14)], [(1,10),(5,32)]) +def degreeRegion43_14 : PrefixRegion := ([(1,10),(2,14)], [(1,10),(6,38)]) +def degreeRegion43_15 : PrefixRegion := ([(1,10),(2,14)], [(1,10),(7,42)]) +def degreeRegion43_16 : PrefixRegion := ([(1,10),(2,14),(3,26)], [(1,23),(5,32)]) +def degreeRegion43_17 : PrefixRegion := ([(1,10),(2,14),(3,26)], [(1,23),(6,38)]) +def degreeRegion43_18 : PrefixRegion := ([(1,10),(2,14),(3,26)], [(1,23),(7,42)]) +def degreeRegion43_19 : PrefixRegion := ([(1,10),(2,14),(3,26)], [(2,14)]) +def degreeRegion43_20 : PrefixRegion := ([(1,10),(3,20)], [(1,7)]) +def degreeRegion43_21 : PrefixRegion := ([(1,10),(3,20)], [(1,23),(5,32)]) +def degreeRegion43_22 : PrefixRegion := ([(1,10),(3,20)], [(1,23),(6,38)]) +def degreeRegion43_23 : PrefixRegion := ([(1,10),(3,20)], [(1,23),(7,42)]) +def degreeRegion43_24 : PrefixRegion := ([(1,10),(3,20)], [(2,14)]) +def degreeRegion43_25 : PrefixRegion := ([(1,10),(3,26),(5,32)], [(1,23),(5,32)]) +def degreeRegion43_26 : PrefixRegion := ([(1,10),(3,26),(5,32)], [(1,23),(6,38)]) +def degreeRegion43_27 : PrefixRegion := ([(1,10),(3,26),(5,32)], [(1,23),(7,42)]) +def degreeRegion43_28 : PrefixRegion := ([(1,10),(3,26),(5,32)], [(2,14)]) +def degreeRegion43_29 : PrefixRegion := ([(1,10),(3,26),(6,38)], [(1,23),(5,32)]) +def degreeRegion43_30 : PrefixRegion := ([(1,10),(3,26),(6,38)], [(1,23),(6,38)]) +def degreeRegion43_31 : PrefixRegion := ([(1,10),(3,26),(6,38)], [(1,23),(7,42)]) +def degreeRegion43_32 : PrefixRegion := ([(1,10),(3,26),(6,38)], [(2,14)]) +def degreeRegion43_33 : PrefixRegion := ([(1,10),(3,26),(7,42)], [(1,23),(5,32)]) +def degreeRegion43_34 : PrefixRegion := ([(1,10),(3,26),(7,42)], [(1,23),(6,38)]) +def degreeRegion43_35 : PrefixRegion := ([(1,10),(3,26),(7,42)], [(1,23),(7,42)]) +def degreeRegion43_36 : PrefixRegion := ([(1,10),(3,26),(7,42)], [(2,14)]) +def degreeRegion43_37 : PrefixRegion := ([(1,10),(4,26)], [(1,7)]) +def degreeRegion43_38 : PrefixRegion := ([(1,10),(4,26)], [(1,23),(5,32)]) +def degreeRegion43_39 : PrefixRegion := ([(1,10),(4,26)], [(1,23),(6,38)]) +def degreeRegion43_40 : PrefixRegion := ([(1,10),(4,26)], [(1,23),(7,42)]) +def degreeRegion43_41 : PrefixRegion := ([(1,10),(4,26)], [(2,14)]) +def degreeRegion43_42 : PrefixRegion := ([(1,10),(5,32)], [(1,7)]) +def degreeRegion43_43 : PrefixRegion := ([(1,10),(5,32)], [(1,10),(2,14)]) +def degreeRegion43_44 : PrefixRegion := ([(1,10),(5,32)], [(1,10),(5,32)]) +def degreeRegion43_45 : PrefixRegion := ([(1,10),(5,32)], [(1,10),(6,38)]) +def degreeRegion43_46 : PrefixRegion := ([(1,10),(5,32)], [(1,10),(7,42)]) +def degreeRegion43_47 : PrefixRegion := ([(1,10),(6,38)], [(1,7)]) +def degreeRegion43_48 : PrefixRegion := ([(1,10),(6,38)], [(1,10),(2,14)]) +def degreeRegion43_49 : PrefixRegion := ([(1,10),(6,38)], [(1,10),(5,32)]) +def degreeRegion43_50 : PrefixRegion := ([(1,10),(6,38)], [(1,10),(6,38)]) +def degreeRegion43_51 : PrefixRegion := ([(1,10),(6,38)], [(1,10),(7,42)]) +def degreeRegion43_52 : PrefixRegion := ([(1,10),(7,42)], [(1,10),(2,14)]) +def degreeRegion43_53 : PrefixRegion := ([(1,10),(7,42)], [(1,10),(5,32)]) +def degreeRegion43_54 : PrefixRegion := ([(1,10),(7,42)], [(1,10),(6,38)]) +def degreeRegion43_55 : PrefixRegion := ([(1,10),(7,42)], [(1,10),(7,42)]) +def degreeRegion43_56 : PrefixRegion := ([(1,23),(3,26),(5,32)], [(1,23),(3,26),(5,32)]) +def degreeRegion43_57 : PrefixRegion := ([(1,23),(3,26),(5,32)], [(1,23),(3,26),(6,38)]) +def degreeRegion43_58 : PrefixRegion := ([(1,23),(3,26),(5,32)], [(1,23),(3,26),(7,42)]) +def degreeRegion43_59 : PrefixRegion := ([(1,23),(3,26),(5,32)], [(1,23),(4,26)]) +def degreeRegion43_60 : PrefixRegion := ([(1,23),(3,26),(5,32)], [(2,14),(3,26)]) +def degreeRegion43_61 : PrefixRegion := ([(1,23),(3,26),(5,32)], [(3,20)]) +def degreeRegion43_62 : PrefixRegion := ([(1,23),(3,26),(6,38)], [(1,23),(3,26),(5,32)]) +def degreeRegion43_63 : PrefixRegion := ([(1,23),(3,26),(6,38)], [(1,23),(3,26),(6,38)]) +def degreeRegion43_64 : PrefixRegion := ([(1,23),(3,26),(6,38)], [(1,23),(3,26),(7,42)]) +def degreeRegion43_65 : PrefixRegion := ([(1,23),(3,26),(6,38)], [(1,23),(4,26)]) +def degreeRegion43_66 : PrefixRegion := ([(1,23),(3,26),(6,38)], [(2,14),(3,26)]) +def degreeRegion43_67 : PrefixRegion := ([(1,23),(3,26),(6,38)], [(3,20)]) +def degreeRegion43_68 : PrefixRegion := ([(1,23),(3,26),(7,42)], [(1,23),(3,26),(5,32)]) +def degreeRegion43_69 : PrefixRegion := ([(1,23),(3,26),(7,42)], [(1,23),(3,26),(6,38)]) +def degreeRegion43_70 : PrefixRegion := ([(1,23),(3,26),(7,42)], [(1,23),(3,26),(7,42)]) +def degreeRegion43_71 : PrefixRegion := ([(1,23),(3,26),(7,42)], [(1,23),(4,26)]) +def degreeRegion43_72 : PrefixRegion := ([(1,23),(3,26),(7,42)], [(2,14),(3,26)]) +def degreeRegion43_73 : PrefixRegion := ([(1,23),(3,26),(7,42)], [(3,20)]) +def degreeRegion43_74 : PrefixRegion := ([(1,23),(4,26)], [(1,7),(3,26)]) +def degreeRegion43_75 : PrefixRegion := ([(1,23),(4,26)], [(1,23),(3,26),(5,32)]) +def degreeRegion43_76 : PrefixRegion := ([(1,23),(4,26)], [(1,23),(3,26),(6,38)]) +def degreeRegion43_77 : PrefixRegion := ([(1,23),(4,26)], [(1,23),(3,26),(7,42)]) +def degreeRegion43_78 : PrefixRegion := ([(1,23),(4,26)], [(1,23),(4,26)]) +def degreeRegion43_79 : PrefixRegion := ([(1,23),(4,26)], [(2,14),(3,26)]) +def degreeRegion43_80 : PrefixRegion := ([(1,23),(5,32)], [(1,7),(3,26)]) +def degreeRegion43_81 : PrefixRegion := ([(1,23),(5,32)], [(1,10),(2,14),(3,26)]) +def degreeRegion43_82 : PrefixRegion := ([(1,23),(5,32)], [(1,10),(3,20)]) +def degreeRegion43_83 : PrefixRegion := ([(1,23),(5,32)], [(1,10),(3,26),(5,32)]) +def degreeRegion43_84 : PrefixRegion := ([(1,23),(5,32)], [(1,10),(3,26),(6,38)]) +def degreeRegion43_85 : PrefixRegion := ([(1,23),(5,32)], [(1,10),(3,26),(7,42)]) +def degreeRegion43_86 : PrefixRegion := ([(1,23),(5,32)], [(1,10),(4,26)]) +def degreeRegion43_87 : PrefixRegion := ([(1,23),(6,38)], [(1,7),(3,26)]) +def degreeRegion43_88 : PrefixRegion := ([(1,23),(6,38)], [(1,10),(2,14),(3,26)]) +def degreeRegion43_89 : PrefixRegion := ([(1,23),(6,38)], [(1,10),(3,20)]) +def degreeRegion43_90 : PrefixRegion := ([(1,23),(6,38)], [(1,10),(3,26),(5,32)]) +def degreeRegion43_91 : PrefixRegion := ([(1,23),(6,38)], [(1,10),(3,26),(6,38)]) +def degreeRegion43_92 : PrefixRegion := ([(1,23),(6,38)], [(1,10),(3,26),(7,42)]) +def degreeRegion43_93 : PrefixRegion := ([(1,23),(6,38)], [(1,10),(4,26)]) +def degreeRegion43_94 : PrefixRegion := ([(1,23),(7,42)], [(1,10),(2,14),(3,26)]) +def degreeRegion43_95 : PrefixRegion := ([(1,23),(7,42)], [(1,10),(3,20)]) +def degreeRegion43_96 : PrefixRegion := ([(1,23),(7,42)], [(1,10),(3,26),(5,32)]) +def degreeRegion43_97 : PrefixRegion := ([(1,23),(7,42)], [(1,10),(3,26),(6,38)]) +def degreeRegion43_98 : PrefixRegion := ([(1,23),(7,42)], [(1,10),(3,26),(7,42)]) +def degreeRegion43_99 : PrefixRegion := ([(1,23),(7,42)], [(1,10),(4,26)]) +def degreeRegion43_100 : PrefixRegion := ([(2,10),(3,26)], [(7,42)]) +def degreeRegion43_101 : PrefixRegion := ([(2,14)], [(1,7),(3,26)]) +def degreeRegion43_102 : PrefixRegion := ([(2,14)], [(1,10),(2,14),(3,26)]) +def degreeRegion43_103 : PrefixRegion := ([(2,14)], [(1,10),(3,20)]) +def degreeRegion43_104 : PrefixRegion := ([(2,14)], [(1,10),(3,26),(5,32)]) +def degreeRegion43_105 : PrefixRegion := ([(2,14)], [(1,10),(3,26),(6,38)]) +def degreeRegion43_106 : PrefixRegion := ([(2,14)], [(1,10),(3,26),(7,42)]) +def degreeRegion43_107 : PrefixRegion := ([(2,14)], [(1,10),(4,26)]) +def degreeRegion43_108 : PrefixRegion := ([(2,14),(3,26)], [(1,23),(3,26),(5,32)]) +def degreeRegion43_109 : PrefixRegion := ([(2,14),(3,26)], [(1,23),(3,26),(6,38)]) +def degreeRegion43_110 : PrefixRegion := ([(2,14),(3,26)], [(1,23),(3,26),(7,42)]) +def degreeRegion43_111 : PrefixRegion := ([(2,14),(3,26)], [(1,23),(4,26)]) +def degreeRegion43_112 : PrefixRegion := ([(2,14),(3,26)], [(2,14),(3,26)]) +def degreeRegion43_113 : PrefixRegion := ([(2,14),(3,26)], [(3,20)]) +def degreeRegion43_114 : PrefixRegion := ([(3,20)], [(1,7),(3,26)]) +def degreeRegion43_115 : PrefixRegion := ([(3,20)], [(1,23),(3,26),(5,32)]) +def degreeRegion43_116 : PrefixRegion := ([(3,20)], [(1,23),(3,26),(6,38)]) +def degreeRegion43_117 : PrefixRegion := ([(3,20)], [(1,23),(3,26),(7,42)]) +def degreeRegion43_118 : PrefixRegion := ([(3,20)], [(2,14),(3,26)]) +def degreeRegion43_119 : PrefixRegion := ([(7,42)], [(2,10),(3,26)]) + +def degreeRegions43 : List PrefixRegion := [degreeRegion43_0,degreeRegion43_1,degreeRegion43_2,degreeRegion43_3,degreeRegion43_4,degreeRegion43_5,degreeRegion43_6,degreeRegion43_7,degreeRegion43_8,degreeRegion43_9,degreeRegion43_10,degreeRegion43_11,degreeRegion43_12,degreeRegion43_13,degreeRegion43_14,degreeRegion43_15,degreeRegion43_16,degreeRegion43_17,degreeRegion43_18,degreeRegion43_19,degreeRegion43_20,degreeRegion43_21,degreeRegion43_22,degreeRegion43_23,degreeRegion43_24,degreeRegion43_25,degreeRegion43_26,degreeRegion43_27,degreeRegion43_28,degreeRegion43_29,degreeRegion43_30,degreeRegion43_31,degreeRegion43_32,degreeRegion43_33,degreeRegion43_34,degreeRegion43_35,degreeRegion43_36,degreeRegion43_37,degreeRegion43_38,degreeRegion43_39,degreeRegion43_40,degreeRegion43_41,degreeRegion43_42,degreeRegion43_43,degreeRegion43_44,degreeRegion43_45,degreeRegion43_46,degreeRegion43_47,degreeRegion43_48,degreeRegion43_49,degreeRegion43_50,degreeRegion43_51,degreeRegion43_52,degreeRegion43_53,degreeRegion43_54,degreeRegion43_55,degreeRegion43_56,degreeRegion43_57,degreeRegion43_58,degreeRegion43_59,degreeRegion43_60,degreeRegion43_61,degreeRegion43_62,degreeRegion43_63,degreeRegion43_64,degreeRegion43_65,degreeRegion43_66,degreeRegion43_67,degreeRegion43_68,degreeRegion43_69,degreeRegion43_70,degreeRegion43_71,degreeRegion43_72,degreeRegion43_73,degreeRegion43_74,degreeRegion43_75,degreeRegion43_76,degreeRegion43_77,degreeRegion43_78,degreeRegion43_79,degreeRegion43_80,degreeRegion43_81,degreeRegion43_82,degreeRegion43_83,degreeRegion43_84,degreeRegion43_85,degreeRegion43_86,degreeRegion43_87,degreeRegion43_88,degreeRegion43_89,degreeRegion43_90,degreeRegion43_91,degreeRegion43_92,degreeRegion43_93,degreeRegion43_94,degreeRegion43_95,degreeRegion43_96,degreeRegion43_97,degreeRegion43_98,degreeRegion43_99,degreeRegion43_100,degreeRegion43_101,degreeRegion43_102,degreeRegion43_103,degreeRegion43_104,degreeRegion43_105,degreeRegion43_106,degreeRegion43_107,degreeRegion43_108,degreeRegion43_109,degreeRegion43_110,degreeRegion43_111,degreeRegion43_112,degreeRegion43_113,degreeRegion43_114,degreeRegion43_115,degreeRegion43_116,degreeRegion43_117,degreeRegion43_118,degreeRegion43_119] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData58.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData58.lean index 3ae5272789a33cad39b9321acc84e6d945eaac37..32cf9e85e208435ce180752c45da3dbe86c3fccc 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData58.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData58.lean @@ -1,85 +1,85 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 58. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion58_0 : PrefixRegion := ([(1,14),(3,21)], [(1,14),(3,29),(7,46)]) -def degreeRegion58_1 : PrefixRegion := ([(1,14),(3,21)], [(1,14),(3,29),(8,49)]) -def degreeRegion58_2 : PrefixRegion := ([(1,14),(3,29),(5,35)], [(1,14),(3,29),(5,35)]) -def degreeRegion58_3 : PrefixRegion := ([(1,14),(3,29),(5,35)], [(1,14),(3,29),(6,42)]) -def degreeRegion58_4 : PrefixRegion := ([(1,14),(3,29),(5,35)], [(1,14),(3,29),(7,46)]) -def degreeRegion58_5 : PrefixRegion := ([(1,14),(3,29),(5,35)], [(1,14),(3,29),(8,49)]) -def degreeRegion58_6 : PrefixRegion := ([(1,14),(3,29),(5,35)], [(1,14),(3,29),(9,52)]) -def degreeRegion58_7 : PrefixRegion := ([(1,14),(3,29),(5,35)], [(1,14),(3,29),(10,55)]) -def degreeRegion58_8 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(5,35)]) -def degreeRegion58_9 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(6,42)]) -def degreeRegion58_10 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(7,46)]) -def degreeRegion58_11 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(8,49)]) -def degreeRegion58_12 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(9,52)]) -def degreeRegion58_13 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(10,55)]) -def degreeRegion58_14 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(11,57)]) -def degreeRegion58_15 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(4,28)]) -def degreeRegion58_16 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,21)]) -def degreeRegion58_17 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(5,35)]) -def degreeRegion58_18 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(6,42)]) -def degreeRegion58_19 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(7,46)]) -def degreeRegion58_20 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(8,49)]) -def degreeRegion58_21 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(9,52)]) -def degreeRegion58_22 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(10,55)]) -def degreeRegion58_23 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(11,57)]) -def degreeRegion58_24 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(4,28)]) -def degreeRegion58_25 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,21)]) -def degreeRegion58_26 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(5,35)]) -def degreeRegion58_27 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(6,42)]) -def degreeRegion58_28 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(7,46)]) -def degreeRegion58_29 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(8,49)]) -def degreeRegion58_30 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(9,52)]) -def degreeRegion58_31 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(10,55)]) -def degreeRegion58_32 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(11,57)]) -def degreeRegion58_33 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(4,28)]) -def degreeRegion58_34 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(5,35)]) -def degreeRegion58_35 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(6,42)]) -def degreeRegion58_36 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(7,46)]) -def degreeRegion58_37 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(8,49)]) -def degreeRegion58_38 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(9,52)]) -def degreeRegion58_39 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(10,55)]) -def degreeRegion58_40 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(11,57)]) -def degreeRegion58_41 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(4,28)]) -def degreeRegion58_42 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(5,35)]) -def degreeRegion58_43 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(6,42)]) -def degreeRegion58_44 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(7,46)]) -def degreeRegion58_45 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(8,49)]) -def degreeRegion58_46 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(9,52)]) -def degreeRegion58_47 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(10,55)]) -def degreeRegion58_48 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(11,57)]) -def degreeRegion58_49 : PrefixRegion := ([(1,14),(3,29),(11,57)], [(1,14),(3,29),(6,42)]) -def degreeRegion58_50 : PrefixRegion := ([(1,14),(3,29),(11,57)], [(1,14),(3,29),(7,46)]) -def degreeRegion58_51 : PrefixRegion := ([(1,14),(3,29),(11,57)], [(1,14),(3,29),(8,49)]) -def degreeRegion58_52 : PrefixRegion := ([(1,14),(3,29),(11,57)], [(1,14),(3,29),(9,52)]) -def degreeRegion58_53 : PrefixRegion := ([(1,14),(3,29),(11,57)], [(1,14),(3,29),(10,55)]) -def degreeRegion58_54 : PrefixRegion := ([(1,14),(3,29),(11,57)], [(1,14),(3,29),(11,57)]) -def degreeRegion58_55 : PrefixRegion := ([(1,14),(4,28)], [(1,14),(3,29),(6,42)]) -def degreeRegion58_56 : PrefixRegion := ([(1,14),(4,28)], [(1,14),(3,29),(7,46)]) -def degreeRegion58_57 : PrefixRegion := ([(1,14),(4,28)], [(1,14),(3,29),(8,49)]) -def degreeRegion58_58 : PrefixRegion := ([(1,14),(4,28)], [(1,14),(3,29),(9,52)]) -def degreeRegion58_59 : PrefixRegion := ([(1,24),(10,55)], [(2,14),(3,29),(7,34)]) -def degreeRegion58_60 : PrefixRegion := ([(1,24),(11,57)], [(2,14),(3,29),(7,34)]) -def degreeRegion58_61 : PrefixRegion := ([(2,14),(3,29),(7,34)], [(1,24),(10,55)]) -def degreeRegion58_62 : PrefixRegion := ([(2,14),(3,29),(7,34)], [(1,24),(11,57)]) - -def degreeRegions58 : List PrefixRegion := [degreeRegion58_0,degreeRegion58_1,degreeRegion58_2,degreeRegion58_3,degreeRegion58_4,degreeRegion58_5,degreeRegion58_6,degreeRegion58_7,degreeRegion58_8,degreeRegion58_9,degreeRegion58_10,degreeRegion58_11,degreeRegion58_12,degreeRegion58_13,degreeRegion58_14,degreeRegion58_15,degreeRegion58_16,degreeRegion58_17,degreeRegion58_18,degreeRegion58_19,degreeRegion58_20,degreeRegion58_21,degreeRegion58_22,degreeRegion58_23,degreeRegion58_24,degreeRegion58_25,degreeRegion58_26,degreeRegion58_27,degreeRegion58_28,degreeRegion58_29,degreeRegion58_30,degreeRegion58_31,degreeRegion58_32,degreeRegion58_33,degreeRegion58_34,degreeRegion58_35,degreeRegion58_36,degreeRegion58_37,degreeRegion58_38,degreeRegion58_39,degreeRegion58_40,degreeRegion58_41,degreeRegion58_42,degreeRegion58_43,degreeRegion58_44,degreeRegion58_45,degreeRegion58_46,degreeRegion58_47,degreeRegion58_48,degreeRegion58_49,degreeRegion58_50,degreeRegion58_51,degreeRegion58_52,degreeRegion58_53,degreeRegion58_54,degreeRegion58_55,degreeRegion58_56,degreeRegion58_57,degreeRegion58_58,degreeRegion58_59,degreeRegion58_60,degreeRegion58_61,degreeRegion58_62] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 58. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion58_0 : PrefixRegion := ([(1,14),(3,21)], [(1,14),(3,29),(7,46)]) +def degreeRegion58_1 : PrefixRegion := ([(1,14),(3,21)], [(1,14),(3,29),(8,49)]) +def degreeRegion58_2 : PrefixRegion := ([(1,14),(3,29),(5,35)], [(1,14),(3,29),(5,35)]) +def degreeRegion58_3 : PrefixRegion := ([(1,14),(3,29),(5,35)], [(1,14),(3,29),(6,42)]) +def degreeRegion58_4 : PrefixRegion := ([(1,14),(3,29),(5,35)], [(1,14),(3,29),(7,46)]) +def degreeRegion58_5 : PrefixRegion := ([(1,14),(3,29),(5,35)], [(1,14),(3,29),(8,49)]) +def degreeRegion58_6 : PrefixRegion := ([(1,14),(3,29),(5,35)], [(1,14),(3,29),(9,52)]) +def degreeRegion58_7 : PrefixRegion := ([(1,14),(3,29),(5,35)], [(1,14),(3,29),(10,55)]) +def degreeRegion58_8 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(5,35)]) +def degreeRegion58_9 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(6,42)]) +def degreeRegion58_10 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(7,46)]) +def degreeRegion58_11 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(8,49)]) +def degreeRegion58_12 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(9,52)]) +def degreeRegion58_13 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(10,55)]) +def degreeRegion58_14 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(3,29),(11,57)]) +def degreeRegion58_15 : PrefixRegion := ([(1,14),(3,29),(6,42)], [(1,14),(4,28)]) +def degreeRegion58_16 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,21)]) +def degreeRegion58_17 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(5,35)]) +def degreeRegion58_18 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(6,42)]) +def degreeRegion58_19 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(7,46)]) +def degreeRegion58_20 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(8,49)]) +def degreeRegion58_21 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(9,52)]) +def degreeRegion58_22 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(10,55)]) +def degreeRegion58_23 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(3,29),(11,57)]) +def degreeRegion58_24 : PrefixRegion := ([(1,14),(3,29),(7,46)], [(1,14),(4,28)]) +def degreeRegion58_25 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,21)]) +def degreeRegion58_26 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(5,35)]) +def degreeRegion58_27 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(6,42)]) +def degreeRegion58_28 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(7,46)]) +def degreeRegion58_29 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(8,49)]) +def degreeRegion58_30 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(9,52)]) +def degreeRegion58_31 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(10,55)]) +def degreeRegion58_32 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(3,29),(11,57)]) +def degreeRegion58_33 : PrefixRegion := ([(1,14),(3,29),(8,49)], [(1,14),(4,28)]) +def degreeRegion58_34 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(5,35)]) +def degreeRegion58_35 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(6,42)]) +def degreeRegion58_36 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(7,46)]) +def degreeRegion58_37 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(8,49)]) +def degreeRegion58_38 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(9,52)]) +def degreeRegion58_39 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(10,55)]) +def degreeRegion58_40 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(3,29),(11,57)]) +def degreeRegion58_41 : PrefixRegion := ([(1,14),(3,29),(9,52)], [(1,14),(4,28)]) +def degreeRegion58_42 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(5,35)]) +def degreeRegion58_43 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(6,42)]) +def degreeRegion58_44 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(7,46)]) +def degreeRegion58_45 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(8,49)]) +def degreeRegion58_46 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(9,52)]) +def degreeRegion58_47 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(10,55)]) +def degreeRegion58_48 : PrefixRegion := ([(1,14),(3,29),(10,55)], [(1,14),(3,29),(11,57)]) +def degreeRegion58_49 : PrefixRegion := ([(1,14),(3,29),(11,57)], [(1,14),(3,29),(6,42)]) +def degreeRegion58_50 : PrefixRegion := ([(1,14),(3,29),(11,57)], [(1,14),(3,29),(7,46)]) +def degreeRegion58_51 : PrefixRegion := ([(1,14),(3,29),(11,57)], [(1,14),(3,29),(8,49)]) +def degreeRegion58_52 : PrefixRegion := ([(1,14),(3,29),(11,57)], [(1,14),(3,29),(9,52)]) +def degreeRegion58_53 : PrefixRegion := ([(1,14),(3,29),(11,57)], [(1,14),(3,29),(10,55)]) +def degreeRegion58_54 : PrefixRegion := ([(1,14),(3,29),(11,57)], [(1,14),(3,29),(11,57)]) +def degreeRegion58_55 : PrefixRegion := ([(1,14),(4,28)], [(1,14),(3,29),(6,42)]) +def degreeRegion58_56 : PrefixRegion := ([(1,14),(4,28)], [(1,14),(3,29),(7,46)]) +def degreeRegion58_57 : PrefixRegion := ([(1,14),(4,28)], [(1,14),(3,29),(8,49)]) +def degreeRegion58_58 : PrefixRegion := ([(1,14),(4,28)], [(1,14),(3,29),(9,52)]) +def degreeRegion58_59 : PrefixRegion := ([(1,24),(10,55)], [(2,14),(3,29),(7,34)]) +def degreeRegion58_60 : PrefixRegion := ([(1,24),(11,57)], [(2,14),(3,29),(7,34)]) +def degreeRegion58_61 : PrefixRegion := ([(2,14),(3,29),(7,34)], [(1,24),(10,55)]) +def degreeRegion58_62 : PrefixRegion := ([(2,14),(3,29),(7,34)], [(1,24),(11,57)]) + +def degreeRegions58 : List PrefixRegion := [degreeRegion58_0,degreeRegion58_1,degreeRegion58_2,degreeRegion58_3,degreeRegion58_4,degreeRegion58_5,degreeRegion58_6,degreeRegion58_7,degreeRegion58_8,degreeRegion58_9,degreeRegion58_10,degreeRegion58_11,degreeRegion58_12,degreeRegion58_13,degreeRegion58_14,degreeRegion58_15,degreeRegion58_16,degreeRegion58_17,degreeRegion58_18,degreeRegion58_19,degreeRegion58_20,degreeRegion58_21,degreeRegion58_22,degreeRegion58_23,degreeRegion58_24,degreeRegion58_25,degreeRegion58_26,degreeRegion58_27,degreeRegion58_28,degreeRegion58_29,degreeRegion58_30,degreeRegion58_31,degreeRegion58_32,degreeRegion58_33,degreeRegion58_34,degreeRegion58_35,degreeRegion58_36,degreeRegion58_37,degreeRegion58_38,degreeRegion58_39,degreeRegion58_40,degreeRegion58_41,degreeRegion58_42,degreeRegion58_43,degreeRegion58_44,degreeRegion58_45,degreeRegion58_46,degreeRegion58_47,degreeRegion58_48,degreeRegion58_49,degreeRegion58_50,degreeRegion58_51,degreeRegion58_52,degreeRegion58_53,degreeRegion58_54,degreeRegion58_55,degreeRegion58_56,degreeRegion58_57,degreeRegion58_58,degreeRegion58_59,degreeRegion58_60,degreeRegion58_61,degreeRegion58_62] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData62.lean index e996f024975d3b61791ea9c4d3de6e483352c53c..b13faea7f192bb275872ec8817158e9b8e7f2c88 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData62.lean @@ -1,134 +1,134 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 62. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion62_0 : PrefixRegion := ([(1,8),(3,33)], [(1,8),(3,33)]) -def degreeRegion62_1 : PrefixRegion := ([(1,8),(3,33)], [(1,14),(2,16),(3,33)]) -def degreeRegion62_2 : PrefixRegion := ([(1,8),(3,33)], [(1,14),(3,24)]) -def degreeRegion62_3 : PrefixRegion := ([(1,8),(3,33)], [(1,14),(4,32)]) -def degreeRegion62_4 : PrefixRegion := ([(1,14),(2,16),(3,33)], [(1,8),(3,33)]) -def degreeRegion62_5 : PrefixRegion := ([(1,14),(2,16),(3,33)], [(1,14),(2,16),(3,33)]) -def degreeRegion62_6 : PrefixRegion := ([(1,14),(2,16),(3,33)], [(1,14),(3,24)]) -def degreeRegion62_7 : PrefixRegion := ([(1,14),(2,16),(3,33)], [(1,14),(3,33),(9,56)]) -def degreeRegion62_8 : PrefixRegion := ([(1,14),(2,16),(3,33)], [(1,14),(4,32)]) -def degreeRegion62_9 : PrefixRegion := ([(1,14),(3,24)], [(1,8),(3,33)]) -def degreeRegion62_10 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(2,16),(3,33)]) -def degreeRegion62_11 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,24)]) -def degreeRegion62_12 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,33),(6,46)]) -def degreeRegion62_13 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,33),(7,50)]) -def degreeRegion62_14 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,33),(8,53)]) -def degreeRegion62_15 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,33),(9,56)]) -def degreeRegion62_16 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,33),(10,59)]) -def degreeRegion62_17 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,33),(11,61)]) -def degreeRegion62_18 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(4,32)]) -def degreeRegion62_19 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(5,39)]) -def degreeRegion62_20 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(6,46)]) -def degreeRegion62_21 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(7,50)]) -def degreeRegion62_22 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(8,53)]) -def degreeRegion62_23 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(9,56)]) -def degreeRegion62_24 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(10,59)]) -def degreeRegion62_25 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(11,61)]) -def degreeRegion62_26 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(4,32)]) -def degreeRegion62_27 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,24)]) -def degreeRegion62_28 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(5,39)]) -def degreeRegion62_29 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(6,46)]) -def degreeRegion62_30 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(7,50)]) -def degreeRegion62_31 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(8,53)]) -def degreeRegion62_32 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(9,56)]) -def degreeRegion62_33 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(10,59)]) -def degreeRegion62_34 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(11,61)]) -def degreeRegion62_35 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(4,32)]) -def degreeRegion62_36 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(5,39)]) -def degreeRegion62_37 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(6,46)]) -def degreeRegion62_38 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(7,50)]) -def degreeRegion62_39 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(8,53)]) -def degreeRegion62_40 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(9,56)]) -def degreeRegion62_41 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(10,59)]) -def degreeRegion62_42 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(11,61)]) -def degreeRegion62_43 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,24)]) -def degreeRegion62_44 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(5,39)]) -def degreeRegion62_45 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(6,46)]) -def degreeRegion62_46 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(7,50)]) -def degreeRegion62_47 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(8,53)]) -def degreeRegion62_48 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(9,56)]) -def degreeRegion62_49 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(10,59)]) -def degreeRegion62_50 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(11,61)]) -def degreeRegion62_51 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(4,32)]) -def degreeRegion62_52 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,24)]) -def degreeRegion62_53 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(5,39)]) -def degreeRegion62_54 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(6,46)]) -def degreeRegion62_55 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(7,50)]) -def degreeRegion62_56 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(8,53)]) -def degreeRegion62_57 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(9,56)]) -def degreeRegion62_58 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(10,59)]) -def degreeRegion62_59 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(11,61)]) -def degreeRegion62_60 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(4,32)]) -def degreeRegion62_61 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(2,16),(3,33)]) -def degreeRegion62_62 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,24)]) -def degreeRegion62_63 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(5,39)]) -def degreeRegion62_64 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(6,46)]) -def degreeRegion62_65 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(7,50)]) -def degreeRegion62_66 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(8,53)]) -def degreeRegion62_67 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(9,56)]) -def degreeRegion62_68 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(10,59)]) -def degreeRegion62_69 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(11,61)]) -def degreeRegion62_70 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(4,32)]) -def degreeRegion62_71 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,24)]) -def degreeRegion62_72 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(5,39)]) -def degreeRegion62_73 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(6,46)]) -def degreeRegion62_74 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(7,50)]) -def degreeRegion62_75 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(8,53)]) -def degreeRegion62_76 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(9,56)]) -def degreeRegion62_77 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(10,59)]) -def degreeRegion62_78 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(11,61)]) -def degreeRegion62_79 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(4,32)]) -def degreeRegion62_80 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,24)]) -def degreeRegion62_81 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(5,39)]) -def degreeRegion62_82 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(6,46)]) -def degreeRegion62_83 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(7,50)]) -def degreeRegion62_84 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(8,53)]) -def degreeRegion62_85 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(9,56)]) -def degreeRegion62_86 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(10,59)]) -def degreeRegion62_87 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(11,61)]) -def degreeRegion62_88 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(4,32)]) -def degreeRegion62_89 : PrefixRegion := ([(1,14),(4,32)], [(1,8),(3,33)]) -def degreeRegion62_90 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(2,16),(3,33)]) -def degreeRegion62_91 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,24)]) -def degreeRegion62_92 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(5,39)]) -def degreeRegion62_93 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(6,46)]) -def degreeRegion62_94 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(7,50)]) -def degreeRegion62_95 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(8,53)]) -def degreeRegion62_96 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(9,56)]) -def degreeRegion62_97 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(10,59)]) -def degreeRegion62_98 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(11,61)]) -def degreeRegion62_99 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(4,32)]) -def degreeRegion62_100 : PrefixRegion := ([(1,28),(3,33),(5,39)], [(1,14),(3,33),(7,38)]) -def degreeRegion62_101 : PrefixRegion := ([(1,28),(3,33),(6,46)], [(1,14),(3,33),(7,38)]) -def degreeRegion62_102 : PrefixRegion := ([(1,28),(3,33),(7,38)], [(1,28),(3,33),(7,38)]) -def degreeRegion62_103 : PrefixRegion := ([(1,28),(3,33),(7,50)], [(1,14),(3,33),(7,38)]) -def degreeRegion62_104 : PrefixRegion := ([(1,28),(3,33),(8,53)], [(1,14),(3,33),(7,38)]) -def degreeRegion62_105 : PrefixRegion := ([(1,28),(3,33),(9,56)], [(1,14),(3,33),(7,38)]) -def degreeRegion62_106 : PrefixRegion := ([(1,28),(3,33),(10,59)], [(1,14),(3,33),(7,38)]) -def degreeRegion62_107 : PrefixRegion := ([(1,28),(3,33),(11,61)], [(1,14),(3,33),(7,38)]) -def degreeRegion62_108 : PrefixRegion := ([(1,28),(10,59)], [(2,14),(3,33),(7,38)]) -def degreeRegion62_109 : PrefixRegion := ([(1,28),(11,61)], [(2,14),(3,33),(7,38)]) -def degreeRegion62_110 : PrefixRegion := ([(2,14),(3,33),(7,38)], [(1,28),(10,59)]) -def degreeRegion62_111 : PrefixRegion := ([(2,14),(3,33),(7,38)], [(1,28),(11,61)]) - -def degreeRegions62 : List PrefixRegion := [degreeRegion62_0,degreeRegion62_1,degreeRegion62_2,degreeRegion62_3,degreeRegion62_4,degreeRegion62_5,degreeRegion62_6,degreeRegion62_7,degreeRegion62_8,degreeRegion62_9,degreeRegion62_10,degreeRegion62_11,degreeRegion62_12,degreeRegion62_13,degreeRegion62_14,degreeRegion62_15,degreeRegion62_16,degreeRegion62_17,degreeRegion62_18,degreeRegion62_19,degreeRegion62_20,degreeRegion62_21,degreeRegion62_22,degreeRegion62_23,degreeRegion62_24,degreeRegion62_25,degreeRegion62_26,degreeRegion62_27,degreeRegion62_28,degreeRegion62_29,degreeRegion62_30,degreeRegion62_31,degreeRegion62_32,degreeRegion62_33,degreeRegion62_34,degreeRegion62_35,degreeRegion62_36,degreeRegion62_37,degreeRegion62_38,degreeRegion62_39,degreeRegion62_40,degreeRegion62_41,degreeRegion62_42,degreeRegion62_43,degreeRegion62_44,degreeRegion62_45,degreeRegion62_46,degreeRegion62_47,degreeRegion62_48,degreeRegion62_49,degreeRegion62_50,degreeRegion62_51,degreeRegion62_52,degreeRegion62_53,degreeRegion62_54,degreeRegion62_55,degreeRegion62_56,degreeRegion62_57,degreeRegion62_58,degreeRegion62_59,degreeRegion62_60,degreeRegion62_61,degreeRegion62_62,degreeRegion62_63,degreeRegion62_64,degreeRegion62_65,degreeRegion62_66,degreeRegion62_67,degreeRegion62_68,degreeRegion62_69,degreeRegion62_70,degreeRegion62_71,degreeRegion62_72,degreeRegion62_73,degreeRegion62_74,degreeRegion62_75,degreeRegion62_76,degreeRegion62_77,degreeRegion62_78,degreeRegion62_79,degreeRegion62_80,degreeRegion62_81,degreeRegion62_82,degreeRegion62_83,degreeRegion62_84,degreeRegion62_85,degreeRegion62_86,degreeRegion62_87,degreeRegion62_88,degreeRegion62_89,degreeRegion62_90,degreeRegion62_91,degreeRegion62_92,degreeRegion62_93,degreeRegion62_94,degreeRegion62_95,degreeRegion62_96,degreeRegion62_97,degreeRegion62_98,degreeRegion62_99,degreeRegion62_100,degreeRegion62_101,degreeRegion62_102,degreeRegion62_103,degreeRegion62_104,degreeRegion62_105,degreeRegion62_106,degreeRegion62_107,degreeRegion62_108,degreeRegion62_109,degreeRegion62_110,degreeRegion62_111] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 62. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion62_0 : PrefixRegion := ([(1,8),(3,33)], [(1,8),(3,33)]) +def degreeRegion62_1 : PrefixRegion := ([(1,8),(3,33)], [(1,14),(2,16),(3,33)]) +def degreeRegion62_2 : PrefixRegion := ([(1,8),(3,33)], [(1,14),(3,24)]) +def degreeRegion62_3 : PrefixRegion := ([(1,8),(3,33)], [(1,14),(4,32)]) +def degreeRegion62_4 : PrefixRegion := ([(1,14),(2,16),(3,33)], [(1,8),(3,33)]) +def degreeRegion62_5 : PrefixRegion := ([(1,14),(2,16),(3,33)], [(1,14),(2,16),(3,33)]) +def degreeRegion62_6 : PrefixRegion := ([(1,14),(2,16),(3,33)], [(1,14),(3,24)]) +def degreeRegion62_7 : PrefixRegion := ([(1,14),(2,16),(3,33)], [(1,14),(3,33),(9,56)]) +def degreeRegion62_8 : PrefixRegion := ([(1,14),(2,16),(3,33)], [(1,14),(4,32)]) +def degreeRegion62_9 : PrefixRegion := ([(1,14),(3,24)], [(1,8),(3,33)]) +def degreeRegion62_10 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(2,16),(3,33)]) +def degreeRegion62_11 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,24)]) +def degreeRegion62_12 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,33),(6,46)]) +def degreeRegion62_13 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,33),(7,50)]) +def degreeRegion62_14 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,33),(8,53)]) +def degreeRegion62_15 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,33),(9,56)]) +def degreeRegion62_16 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,33),(10,59)]) +def degreeRegion62_17 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,33),(11,61)]) +def degreeRegion62_18 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(4,32)]) +def degreeRegion62_19 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(5,39)]) +def degreeRegion62_20 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(6,46)]) +def degreeRegion62_21 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(7,50)]) +def degreeRegion62_22 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(8,53)]) +def degreeRegion62_23 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(9,56)]) +def degreeRegion62_24 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(10,59)]) +def degreeRegion62_25 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(3,33),(11,61)]) +def degreeRegion62_26 : PrefixRegion := ([(1,14),(3,33),(5,39)], [(1,14),(4,32)]) +def degreeRegion62_27 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,24)]) +def degreeRegion62_28 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(5,39)]) +def degreeRegion62_29 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(6,46)]) +def degreeRegion62_30 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(7,50)]) +def degreeRegion62_31 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(8,53)]) +def degreeRegion62_32 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(9,56)]) +def degreeRegion62_33 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(10,59)]) +def degreeRegion62_34 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(3,33),(11,61)]) +def degreeRegion62_35 : PrefixRegion := ([(1,14),(3,33),(6,46)], [(1,14),(4,32)]) +def degreeRegion62_36 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(5,39)]) +def degreeRegion62_37 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(6,46)]) +def degreeRegion62_38 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(7,50)]) +def degreeRegion62_39 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(8,53)]) +def degreeRegion62_40 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(9,56)]) +def degreeRegion62_41 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(10,59)]) +def degreeRegion62_42 : PrefixRegion := ([(1,14),(3,33),(7,38)], [(1,28),(3,33),(11,61)]) +def degreeRegion62_43 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,24)]) +def degreeRegion62_44 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(5,39)]) +def degreeRegion62_45 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(6,46)]) +def degreeRegion62_46 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(7,50)]) +def degreeRegion62_47 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(8,53)]) +def degreeRegion62_48 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(9,56)]) +def degreeRegion62_49 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(10,59)]) +def degreeRegion62_50 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(3,33),(11,61)]) +def degreeRegion62_51 : PrefixRegion := ([(1,14),(3,33),(7,50)], [(1,14),(4,32)]) +def degreeRegion62_52 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,24)]) +def degreeRegion62_53 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(5,39)]) +def degreeRegion62_54 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(6,46)]) +def degreeRegion62_55 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(7,50)]) +def degreeRegion62_56 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(8,53)]) +def degreeRegion62_57 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(9,56)]) +def degreeRegion62_58 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(10,59)]) +def degreeRegion62_59 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(3,33),(11,61)]) +def degreeRegion62_60 : PrefixRegion := ([(1,14),(3,33),(8,53)], [(1,14),(4,32)]) +def degreeRegion62_61 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(2,16),(3,33)]) +def degreeRegion62_62 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,24)]) +def degreeRegion62_63 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(5,39)]) +def degreeRegion62_64 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(6,46)]) +def degreeRegion62_65 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(7,50)]) +def degreeRegion62_66 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(8,53)]) +def degreeRegion62_67 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(9,56)]) +def degreeRegion62_68 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(10,59)]) +def degreeRegion62_69 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(3,33),(11,61)]) +def degreeRegion62_70 : PrefixRegion := ([(1,14),(3,33),(9,56)], [(1,14),(4,32)]) +def degreeRegion62_71 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,24)]) +def degreeRegion62_72 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(5,39)]) +def degreeRegion62_73 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(6,46)]) +def degreeRegion62_74 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(7,50)]) +def degreeRegion62_75 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(8,53)]) +def degreeRegion62_76 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(9,56)]) +def degreeRegion62_77 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(10,59)]) +def degreeRegion62_78 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(3,33),(11,61)]) +def degreeRegion62_79 : PrefixRegion := ([(1,14),(3,33),(10,59)], [(1,14),(4,32)]) +def degreeRegion62_80 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,24)]) +def degreeRegion62_81 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(5,39)]) +def degreeRegion62_82 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(6,46)]) +def degreeRegion62_83 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(7,50)]) +def degreeRegion62_84 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(8,53)]) +def degreeRegion62_85 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(9,56)]) +def degreeRegion62_86 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(10,59)]) +def degreeRegion62_87 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(3,33),(11,61)]) +def degreeRegion62_88 : PrefixRegion := ([(1,14),(3,33),(11,61)], [(1,14),(4,32)]) +def degreeRegion62_89 : PrefixRegion := ([(1,14),(4,32)], [(1,8),(3,33)]) +def degreeRegion62_90 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(2,16),(3,33)]) +def degreeRegion62_91 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,24)]) +def degreeRegion62_92 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(5,39)]) +def degreeRegion62_93 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(6,46)]) +def degreeRegion62_94 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(7,50)]) +def degreeRegion62_95 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(8,53)]) +def degreeRegion62_96 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(9,56)]) +def degreeRegion62_97 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(10,59)]) +def degreeRegion62_98 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(3,33),(11,61)]) +def degreeRegion62_99 : PrefixRegion := ([(1,14),(4,32)], [(1,14),(4,32)]) +def degreeRegion62_100 : PrefixRegion := ([(1,28),(3,33),(5,39)], [(1,14),(3,33),(7,38)]) +def degreeRegion62_101 : PrefixRegion := ([(1,28),(3,33),(6,46)], [(1,14),(3,33),(7,38)]) +def degreeRegion62_102 : PrefixRegion := ([(1,28),(3,33),(7,38)], [(1,28),(3,33),(7,38)]) +def degreeRegion62_103 : PrefixRegion := ([(1,28),(3,33),(7,50)], [(1,14),(3,33),(7,38)]) +def degreeRegion62_104 : PrefixRegion := ([(1,28),(3,33),(8,53)], [(1,14),(3,33),(7,38)]) +def degreeRegion62_105 : PrefixRegion := ([(1,28),(3,33),(9,56)], [(1,14),(3,33),(7,38)]) +def degreeRegion62_106 : PrefixRegion := ([(1,28),(3,33),(10,59)], [(1,14),(3,33),(7,38)]) +def degreeRegion62_107 : PrefixRegion := ([(1,28),(3,33),(11,61)], [(1,14),(3,33),(7,38)]) +def degreeRegion62_108 : PrefixRegion := ([(1,28),(10,59)], [(2,14),(3,33),(7,38)]) +def degreeRegion62_109 : PrefixRegion := ([(1,28),(11,61)], [(2,14),(3,33),(7,38)]) +def degreeRegion62_110 : PrefixRegion := ([(2,14),(3,33),(7,38)], [(1,28),(10,59)]) +def degreeRegion62_111 : PrefixRegion := ([(2,14),(3,33),(7,38)], [(1,28),(11,61)]) + +def degreeRegions62 : List PrefixRegion := [degreeRegion62_0,degreeRegion62_1,degreeRegion62_2,degreeRegion62_3,degreeRegion62_4,degreeRegion62_5,degreeRegion62_6,degreeRegion62_7,degreeRegion62_8,degreeRegion62_9,degreeRegion62_10,degreeRegion62_11,degreeRegion62_12,degreeRegion62_13,degreeRegion62_14,degreeRegion62_15,degreeRegion62_16,degreeRegion62_17,degreeRegion62_18,degreeRegion62_19,degreeRegion62_20,degreeRegion62_21,degreeRegion62_22,degreeRegion62_23,degreeRegion62_24,degreeRegion62_25,degreeRegion62_26,degreeRegion62_27,degreeRegion62_28,degreeRegion62_29,degreeRegion62_30,degreeRegion62_31,degreeRegion62_32,degreeRegion62_33,degreeRegion62_34,degreeRegion62_35,degreeRegion62_36,degreeRegion62_37,degreeRegion62_38,degreeRegion62_39,degreeRegion62_40,degreeRegion62_41,degreeRegion62_42,degreeRegion62_43,degreeRegion62_44,degreeRegion62_45,degreeRegion62_46,degreeRegion62_47,degreeRegion62_48,degreeRegion62_49,degreeRegion62_50,degreeRegion62_51,degreeRegion62_52,degreeRegion62_53,degreeRegion62_54,degreeRegion62_55,degreeRegion62_56,degreeRegion62_57,degreeRegion62_58,degreeRegion62_59,degreeRegion62_60,degreeRegion62_61,degreeRegion62_62,degreeRegion62_63,degreeRegion62_64,degreeRegion62_65,degreeRegion62_66,degreeRegion62_67,degreeRegion62_68,degreeRegion62_69,degreeRegion62_70,degreeRegion62_71,degreeRegion62_72,degreeRegion62_73,degreeRegion62_74,degreeRegion62_75,degreeRegion62_76,degreeRegion62_77,degreeRegion62_78,degreeRegion62_79,degreeRegion62_80,degreeRegion62_81,degreeRegion62_82,degreeRegion62_83,degreeRegion62_84,degreeRegion62_85,degreeRegion62_86,degreeRegion62_87,degreeRegion62_88,degreeRegion62_89,degreeRegion62_90,degreeRegion62_91,degreeRegion62_92,degreeRegion62_93,degreeRegion62_94,degreeRegion62_95,degreeRegion62_96,degreeRegion62_97,degreeRegion62_98,degreeRegion62_99,degreeRegion62_100,degreeRegion62_101,degreeRegion62_102,degreeRegion62_103,degreeRegion62_104,degreeRegion62_105,degreeRegion62_106,degreeRegion62_107,degreeRegion62_108,degreeRegion62_109,degreeRegion62_110,degreeRegion62_111] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData64.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData64.lean index 5460d95c0a681dc7650e5ca3a45b73414a07ea98..4eb31c9abb571047625d0392bbf2e1489b646593 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData64.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData64.lean @@ -1,159 +1,159 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 64. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion64_0 : PrefixRegion := ([(1,8),(3,35)], [(1,8),(3,35)]) -def degreeRegion64_1 : PrefixRegion := ([(1,8),(3,35)], [(1,14),(2,16),(3,35)]) -def degreeRegion64_2 : PrefixRegion := ([(1,8),(3,35)], [(1,14),(3,24)]) -def degreeRegion64_3 : PrefixRegion := ([(1,14),(2,16),(3,35)], [(1,8),(3,35)]) -def degreeRegion64_4 : PrefixRegion := ([(1,14),(2,16),(3,35)], [(1,14),(2,16),(3,35)]) -def degreeRegion64_5 : PrefixRegion := ([(1,14),(2,16),(3,35)], [(1,14),(3,24)]) -def degreeRegion64_6 : PrefixRegion := ([(1,14),(3,24)], [(1,8),(3,35)]) -def degreeRegion64_7 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(2,16),(3,35)]) -def degreeRegion64_8 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,24)]) -def degreeRegion64_9 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,35),(8,51)]) -def degreeRegion64_10 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,35),(9,54)]) -def degreeRegion64_11 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,35),(10,56)]) -def degreeRegion64_12 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,35),(11,58)]) -def degreeRegion64_13 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,35),(12,60)]) -def degreeRegion64_14 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,35),(13,62)]) -def degreeRegion64_15 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(5,38)]) -def degreeRegion64_16 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(6,45)]) -def degreeRegion64_17 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(7,48)]) -def degreeRegion64_18 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(8,51)]) -def degreeRegion64_19 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(9,54)]) -def degreeRegion64_20 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(10,56)]) -def degreeRegion64_21 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(11,58)]) -def degreeRegion64_22 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(12,60)]) -def degreeRegion64_23 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(13,62)]) -def degreeRegion64_24 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(5,38)]) -def degreeRegion64_25 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(6,45)]) -def degreeRegion64_26 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(7,48)]) -def degreeRegion64_27 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(8,51)]) -def degreeRegion64_28 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(9,54)]) -def degreeRegion64_29 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(10,56)]) -def degreeRegion64_30 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(11,58)]) -def degreeRegion64_31 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(12,60)]) -def degreeRegion64_32 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(13,62)]) -def degreeRegion64_33 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(4,31)]) -def degreeRegion64_34 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(5,38)]) -def degreeRegion64_35 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(6,45)]) -def degreeRegion64_36 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(7,48)]) -def degreeRegion64_37 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(8,51)]) -def degreeRegion64_38 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(9,54)]) -def degreeRegion64_39 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(10,56)]) -def degreeRegion64_40 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(11,58)]) -def degreeRegion64_41 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(12,60)]) -def degreeRegion64_42 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(13,62)]) -def degreeRegion64_43 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(5,38)]) -def degreeRegion64_44 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(6,45)]) -def degreeRegion64_45 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(7,48)]) -def degreeRegion64_46 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(8,51)]) -def degreeRegion64_47 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(9,54)]) -def degreeRegion64_48 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(10,56)]) -def degreeRegion64_49 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(11,58)]) -def degreeRegion64_50 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(12,60)]) -def degreeRegion64_51 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(13,62)]) -def degreeRegion64_52 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(4,31)]) -def degreeRegion64_53 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,24)]) -def degreeRegion64_54 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(5,38)]) -def degreeRegion64_55 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(6,45)]) -def degreeRegion64_56 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(7,48)]) -def degreeRegion64_57 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(8,51)]) -def degreeRegion64_58 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(9,54)]) -def degreeRegion64_59 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(10,56)]) -def degreeRegion64_60 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(11,58)]) -def degreeRegion64_61 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(12,60)]) -def degreeRegion64_62 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(13,62)]) -def degreeRegion64_63 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(4,31)]) -def degreeRegion64_64 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,24)]) -def degreeRegion64_65 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(5,38)]) -def degreeRegion64_66 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(6,45)]) -def degreeRegion64_67 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(7,48)]) -def degreeRegion64_68 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(8,51)]) -def degreeRegion64_69 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(9,54)]) -def degreeRegion64_70 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(10,56)]) -def degreeRegion64_71 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(11,58)]) -def degreeRegion64_72 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(12,60)]) -def degreeRegion64_73 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(13,62)]) -def degreeRegion64_74 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(4,31)]) -def degreeRegion64_75 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,24)]) -def degreeRegion64_76 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(5,38)]) -def degreeRegion64_77 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(6,45)]) -def degreeRegion64_78 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(7,48)]) -def degreeRegion64_79 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(8,51)]) -def degreeRegion64_80 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(9,54)]) -def degreeRegion64_81 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(10,56)]) -def degreeRegion64_82 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(11,58)]) -def degreeRegion64_83 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(12,60)]) -def degreeRegion64_84 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(13,62)]) -def degreeRegion64_85 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(4,31)]) -def degreeRegion64_86 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,24)]) -def degreeRegion64_87 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(5,38)]) -def degreeRegion64_88 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(6,45)]) -def degreeRegion64_89 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(7,48)]) -def degreeRegion64_90 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(8,51)]) -def degreeRegion64_91 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(9,54)]) -def degreeRegion64_92 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(10,56)]) -def degreeRegion64_93 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(11,58)]) -def degreeRegion64_94 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(12,60)]) -def degreeRegion64_95 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(13,62)]) -def degreeRegion64_96 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(4,31)]) -def degreeRegion64_97 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,24)]) -def degreeRegion64_98 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(5,38)]) -def degreeRegion64_99 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(6,45)]) -def degreeRegion64_100 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(7,48)]) -def degreeRegion64_101 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(8,51)]) -def degreeRegion64_102 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(9,54)]) -def degreeRegion64_103 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(10,56)]) -def degreeRegion64_104 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(11,58)]) -def degreeRegion64_105 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(12,60)]) -def degreeRegion64_106 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(13,62)]) -def degreeRegion64_107 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(4,31)]) -def degreeRegion64_108 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,24)]) -def degreeRegion64_109 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(5,38)]) -def degreeRegion64_110 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(6,45)]) -def degreeRegion64_111 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(7,48)]) -def degreeRegion64_112 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(8,51)]) -def degreeRegion64_113 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(9,54)]) -def degreeRegion64_114 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(10,56)]) -def degreeRegion64_115 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(11,58)]) -def degreeRegion64_116 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(12,60)]) -def degreeRegion64_117 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(13,62)]) -def degreeRegion64_118 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(4,31)]) -def degreeRegion64_119 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(6,45)]) -def degreeRegion64_120 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(7,48)]) -def degreeRegion64_121 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(8,51)]) -def degreeRegion64_122 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(9,54)]) -def degreeRegion64_123 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(10,56)]) -def degreeRegion64_124 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(11,58)]) -def degreeRegion64_125 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(12,60)]) -def degreeRegion64_126 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(13,62)]) -def degreeRegion64_127 : PrefixRegion := ([(1,30),(3,35),(5,38)], [(1,14),(3,35),(7,40)]) -def degreeRegion64_128 : PrefixRegion := ([(1,30),(3,35),(6,45)], [(1,14),(3,35),(7,40)]) -def degreeRegion64_129 : PrefixRegion := ([(1,30),(3,35),(7,40)], [(1,30),(3,35),(7,40)]) -def degreeRegion64_130 : PrefixRegion := ([(1,30),(3,35),(7,48)], [(1,14),(3,35),(7,40)]) -def degreeRegion64_131 : PrefixRegion := ([(1,30),(3,35),(8,51)], [(1,14),(3,35),(7,40)]) -def degreeRegion64_132 : PrefixRegion := ([(1,30),(3,35),(9,54)], [(1,14),(3,35),(7,40)]) -def degreeRegion64_133 : PrefixRegion := ([(1,30),(3,35),(10,56)], [(1,14),(3,35),(7,40)]) -def degreeRegion64_134 : PrefixRegion := ([(1,30),(3,35),(11,58)], [(1,14),(3,35),(7,40)]) -def degreeRegion64_135 : PrefixRegion := ([(1,30),(3,35),(12,60)], [(1,14),(3,35),(7,40)]) -def degreeRegion64_136 : PrefixRegion := ([(1,30),(3,35),(13,62)], [(1,14),(3,35),(7,40)]) - -def degreeRegions64 : List PrefixRegion := [degreeRegion64_0,degreeRegion64_1,degreeRegion64_2,degreeRegion64_3,degreeRegion64_4,degreeRegion64_5,degreeRegion64_6,degreeRegion64_7,degreeRegion64_8,degreeRegion64_9,degreeRegion64_10,degreeRegion64_11,degreeRegion64_12,degreeRegion64_13,degreeRegion64_14,degreeRegion64_15,degreeRegion64_16,degreeRegion64_17,degreeRegion64_18,degreeRegion64_19,degreeRegion64_20,degreeRegion64_21,degreeRegion64_22,degreeRegion64_23,degreeRegion64_24,degreeRegion64_25,degreeRegion64_26,degreeRegion64_27,degreeRegion64_28,degreeRegion64_29,degreeRegion64_30,degreeRegion64_31,degreeRegion64_32,degreeRegion64_33,degreeRegion64_34,degreeRegion64_35,degreeRegion64_36,degreeRegion64_37,degreeRegion64_38,degreeRegion64_39,degreeRegion64_40,degreeRegion64_41,degreeRegion64_42,degreeRegion64_43,degreeRegion64_44,degreeRegion64_45,degreeRegion64_46,degreeRegion64_47,degreeRegion64_48,degreeRegion64_49,degreeRegion64_50,degreeRegion64_51,degreeRegion64_52,degreeRegion64_53,degreeRegion64_54,degreeRegion64_55,degreeRegion64_56,degreeRegion64_57,degreeRegion64_58,degreeRegion64_59,degreeRegion64_60,degreeRegion64_61,degreeRegion64_62,degreeRegion64_63,degreeRegion64_64,degreeRegion64_65,degreeRegion64_66,degreeRegion64_67,degreeRegion64_68,degreeRegion64_69,degreeRegion64_70,degreeRegion64_71,degreeRegion64_72,degreeRegion64_73,degreeRegion64_74,degreeRegion64_75,degreeRegion64_76,degreeRegion64_77,degreeRegion64_78,degreeRegion64_79,degreeRegion64_80,degreeRegion64_81,degreeRegion64_82,degreeRegion64_83,degreeRegion64_84,degreeRegion64_85,degreeRegion64_86,degreeRegion64_87,degreeRegion64_88,degreeRegion64_89,degreeRegion64_90,degreeRegion64_91,degreeRegion64_92,degreeRegion64_93,degreeRegion64_94,degreeRegion64_95,degreeRegion64_96,degreeRegion64_97,degreeRegion64_98,degreeRegion64_99,degreeRegion64_100,degreeRegion64_101,degreeRegion64_102,degreeRegion64_103,degreeRegion64_104,degreeRegion64_105,degreeRegion64_106,degreeRegion64_107,degreeRegion64_108,degreeRegion64_109,degreeRegion64_110,degreeRegion64_111,degreeRegion64_112,degreeRegion64_113,degreeRegion64_114,degreeRegion64_115,degreeRegion64_116,degreeRegion64_117,degreeRegion64_118,degreeRegion64_119,degreeRegion64_120,degreeRegion64_121,degreeRegion64_122,degreeRegion64_123,degreeRegion64_124,degreeRegion64_125,degreeRegion64_126,degreeRegion64_127,degreeRegion64_128,degreeRegion64_129,degreeRegion64_130,degreeRegion64_131,degreeRegion64_132,degreeRegion64_133,degreeRegion64_134,degreeRegion64_135,degreeRegion64_136] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 64. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion64_0 : PrefixRegion := ([(1,8),(3,35)], [(1,8),(3,35)]) +def degreeRegion64_1 : PrefixRegion := ([(1,8),(3,35)], [(1,14),(2,16),(3,35)]) +def degreeRegion64_2 : PrefixRegion := ([(1,8),(3,35)], [(1,14),(3,24)]) +def degreeRegion64_3 : PrefixRegion := ([(1,14),(2,16),(3,35)], [(1,8),(3,35)]) +def degreeRegion64_4 : PrefixRegion := ([(1,14),(2,16),(3,35)], [(1,14),(2,16),(3,35)]) +def degreeRegion64_5 : PrefixRegion := ([(1,14),(2,16),(3,35)], [(1,14),(3,24)]) +def degreeRegion64_6 : PrefixRegion := ([(1,14),(3,24)], [(1,8),(3,35)]) +def degreeRegion64_7 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(2,16),(3,35)]) +def degreeRegion64_8 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,24)]) +def degreeRegion64_9 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,35),(8,51)]) +def degreeRegion64_10 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,35),(9,54)]) +def degreeRegion64_11 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,35),(10,56)]) +def degreeRegion64_12 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,35),(11,58)]) +def degreeRegion64_13 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,35),(12,60)]) +def degreeRegion64_14 : PrefixRegion := ([(1,14),(3,24)], [(1,14),(3,35),(13,62)]) +def degreeRegion64_15 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(5,38)]) +def degreeRegion64_16 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(6,45)]) +def degreeRegion64_17 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(7,48)]) +def degreeRegion64_18 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(8,51)]) +def degreeRegion64_19 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(9,54)]) +def degreeRegion64_20 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(10,56)]) +def degreeRegion64_21 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(11,58)]) +def degreeRegion64_22 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(12,60)]) +def degreeRegion64_23 : PrefixRegion := ([(1,14),(3,35),(5,38)], [(1,14),(3,35),(13,62)]) +def degreeRegion64_24 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(5,38)]) +def degreeRegion64_25 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(6,45)]) +def degreeRegion64_26 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(7,48)]) +def degreeRegion64_27 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(8,51)]) +def degreeRegion64_28 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(9,54)]) +def degreeRegion64_29 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(10,56)]) +def degreeRegion64_30 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(11,58)]) +def degreeRegion64_31 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(12,60)]) +def degreeRegion64_32 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(3,35),(13,62)]) +def degreeRegion64_33 : PrefixRegion := ([(1,14),(3,35),(6,45)], [(1,14),(4,31)]) +def degreeRegion64_34 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(5,38)]) +def degreeRegion64_35 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(6,45)]) +def degreeRegion64_36 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(7,48)]) +def degreeRegion64_37 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(8,51)]) +def degreeRegion64_38 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(9,54)]) +def degreeRegion64_39 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(10,56)]) +def degreeRegion64_40 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(11,58)]) +def degreeRegion64_41 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(12,60)]) +def degreeRegion64_42 : PrefixRegion := ([(1,14),(3,35),(7,40)], [(1,30),(3,35),(13,62)]) +def degreeRegion64_43 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(5,38)]) +def degreeRegion64_44 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(6,45)]) +def degreeRegion64_45 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(7,48)]) +def degreeRegion64_46 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(8,51)]) +def degreeRegion64_47 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(9,54)]) +def degreeRegion64_48 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(10,56)]) +def degreeRegion64_49 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(11,58)]) +def degreeRegion64_50 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(12,60)]) +def degreeRegion64_51 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(3,35),(13,62)]) +def degreeRegion64_52 : PrefixRegion := ([(1,14),(3,35),(7,48)], [(1,14),(4,31)]) +def degreeRegion64_53 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,24)]) +def degreeRegion64_54 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(5,38)]) +def degreeRegion64_55 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(6,45)]) +def degreeRegion64_56 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(7,48)]) +def degreeRegion64_57 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(8,51)]) +def degreeRegion64_58 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(9,54)]) +def degreeRegion64_59 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(10,56)]) +def degreeRegion64_60 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(11,58)]) +def degreeRegion64_61 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(12,60)]) +def degreeRegion64_62 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(3,35),(13,62)]) +def degreeRegion64_63 : PrefixRegion := ([(1,14),(3,35),(8,51)], [(1,14),(4,31)]) +def degreeRegion64_64 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,24)]) +def degreeRegion64_65 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(5,38)]) +def degreeRegion64_66 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(6,45)]) +def degreeRegion64_67 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(7,48)]) +def degreeRegion64_68 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(8,51)]) +def degreeRegion64_69 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(9,54)]) +def degreeRegion64_70 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(10,56)]) +def degreeRegion64_71 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(11,58)]) +def degreeRegion64_72 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(12,60)]) +def degreeRegion64_73 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(3,35),(13,62)]) +def degreeRegion64_74 : PrefixRegion := ([(1,14),(3,35),(9,54)], [(1,14),(4,31)]) +def degreeRegion64_75 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,24)]) +def degreeRegion64_76 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(5,38)]) +def degreeRegion64_77 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(6,45)]) +def degreeRegion64_78 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(7,48)]) +def degreeRegion64_79 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(8,51)]) +def degreeRegion64_80 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(9,54)]) +def degreeRegion64_81 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(10,56)]) +def degreeRegion64_82 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(11,58)]) +def degreeRegion64_83 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(12,60)]) +def degreeRegion64_84 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(3,35),(13,62)]) +def degreeRegion64_85 : PrefixRegion := ([(1,14),(3,35),(10,56)], [(1,14),(4,31)]) +def degreeRegion64_86 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,24)]) +def degreeRegion64_87 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(5,38)]) +def degreeRegion64_88 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(6,45)]) +def degreeRegion64_89 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(7,48)]) +def degreeRegion64_90 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(8,51)]) +def degreeRegion64_91 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(9,54)]) +def degreeRegion64_92 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(10,56)]) +def degreeRegion64_93 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(11,58)]) +def degreeRegion64_94 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(12,60)]) +def degreeRegion64_95 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(3,35),(13,62)]) +def degreeRegion64_96 : PrefixRegion := ([(1,14),(3,35),(11,58)], [(1,14),(4,31)]) +def degreeRegion64_97 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,24)]) +def degreeRegion64_98 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(5,38)]) +def degreeRegion64_99 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(6,45)]) +def degreeRegion64_100 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(7,48)]) +def degreeRegion64_101 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(8,51)]) +def degreeRegion64_102 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(9,54)]) +def degreeRegion64_103 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(10,56)]) +def degreeRegion64_104 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(11,58)]) +def degreeRegion64_105 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(12,60)]) +def degreeRegion64_106 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(3,35),(13,62)]) +def degreeRegion64_107 : PrefixRegion := ([(1,14),(3,35),(12,60)], [(1,14),(4,31)]) +def degreeRegion64_108 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,24)]) +def degreeRegion64_109 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(5,38)]) +def degreeRegion64_110 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(6,45)]) +def degreeRegion64_111 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(7,48)]) +def degreeRegion64_112 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(8,51)]) +def degreeRegion64_113 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(9,54)]) +def degreeRegion64_114 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(10,56)]) +def degreeRegion64_115 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(11,58)]) +def degreeRegion64_116 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(12,60)]) +def degreeRegion64_117 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(3,35),(13,62)]) +def degreeRegion64_118 : PrefixRegion := ([(1,14),(3,35),(13,62)], [(1,14),(4,31)]) +def degreeRegion64_119 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(6,45)]) +def degreeRegion64_120 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(7,48)]) +def degreeRegion64_121 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(8,51)]) +def degreeRegion64_122 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(9,54)]) +def degreeRegion64_123 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(10,56)]) +def degreeRegion64_124 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(11,58)]) +def degreeRegion64_125 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(12,60)]) +def degreeRegion64_126 : PrefixRegion := ([(1,14),(4,31)], [(1,14),(3,35),(13,62)]) +def degreeRegion64_127 : PrefixRegion := ([(1,30),(3,35),(5,38)], [(1,14),(3,35),(7,40)]) +def degreeRegion64_128 : PrefixRegion := ([(1,30),(3,35),(6,45)], [(1,14),(3,35),(7,40)]) +def degreeRegion64_129 : PrefixRegion := ([(1,30),(3,35),(7,40)], [(1,30),(3,35),(7,40)]) +def degreeRegion64_130 : PrefixRegion := ([(1,30),(3,35),(7,48)], [(1,14),(3,35),(7,40)]) +def degreeRegion64_131 : PrefixRegion := ([(1,30),(3,35),(8,51)], [(1,14),(3,35),(7,40)]) +def degreeRegion64_132 : PrefixRegion := ([(1,30),(3,35),(9,54)], [(1,14),(3,35),(7,40)]) +def degreeRegion64_133 : PrefixRegion := ([(1,30),(3,35),(10,56)], [(1,14),(3,35),(7,40)]) +def degreeRegion64_134 : PrefixRegion := ([(1,30),(3,35),(11,58)], [(1,14),(3,35),(7,40)]) +def degreeRegion64_135 : PrefixRegion := ([(1,30),(3,35),(12,60)], [(1,14),(3,35),(7,40)]) +def degreeRegion64_136 : PrefixRegion := ([(1,30),(3,35),(13,62)], [(1,14),(3,35),(7,40)]) + +def degreeRegions64 : List PrefixRegion := [degreeRegion64_0,degreeRegion64_1,degreeRegion64_2,degreeRegion64_3,degreeRegion64_4,degreeRegion64_5,degreeRegion64_6,degreeRegion64_7,degreeRegion64_8,degreeRegion64_9,degreeRegion64_10,degreeRegion64_11,degreeRegion64_12,degreeRegion64_13,degreeRegion64_14,degreeRegion64_15,degreeRegion64_16,degreeRegion64_17,degreeRegion64_18,degreeRegion64_19,degreeRegion64_20,degreeRegion64_21,degreeRegion64_22,degreeRegion64_23,degreeRegion64_24,degreeRegion64_25,degreeRegion64_26,degreeRegion64_27,degreeRegion64_28,degreeRegion64_29,degreeRegion64_30,degreeRegion64_31,degreeRegion64_32,degreeRegion64_33,degreeRegion64_34,degreeRegion64_35,degreeRegion64_36,degreeRegion64_37,degreeRegion64_38,degreeRegion64_39,degreeRegion64_40,degreeRegion64_41,degreeRegion64_42,degreeRegion64_43,degreeRegion64_44,degreeRegion64_45,degreeRegion64_46,degreeRegion64_47,degreeRegion64_48,degreeRegion64_49,degreeRegion64_50,degreeRegion64_51,degreeRegion64_52,degreeRegion64_53,degreeRegion64_54,degreeRegion64_55,degreeRegion64_56,degreeRegion64_57,degreeRegion64_58,degreeRegion64_59,degreeRegion64_60,degreeRegion64_61,degreeRegion64_62,degreeRegion64_63,degreeRegion64_64,degreeRegion64_65,degreeRegion64_66,degreeRegion64_67,degreeRegion64_68,degreeRegion64_69,degreeRegion64_70,degreeRegion64_71,degreeRegion64_72,degreeRegion64_73,degreeRegion64_74,degreeRegion64_75,degreeRegion64_76,degreeRegion64_77,degreeRegion64_78,degreeRegion64_79,degreeRegion64_80,degreeRegion64_81,degreeRegion64_82,degreeRegion64_83,degreeRegion64_84,degreeRegion64_85,degreeRegion64_86,degreeRegion64_87,degreeRegion64_88,degreeRegion64_89,degreeRegion64_90,degreeRegion64_91,degreeRegion64_92,degreeRegion64_93,degreeRegion64_94,degreeRegion64_95,degreeRegion64_96,degreeRegion64_97,degreeRegion64_98,degreeRegion64_99,degreeRegion64_100,degreeRegion64_101,degreeRegion64_102,degreeRegion64_103,degreeRegion64_104,degreeRegion64_105,degreeRegion64_106,degreeRegion64_107,degreeRegion64_108,degreeRegion64_109,degreeRegion64_110,degreeRegion64_111,degreeRegion64_112,degreeRegion64_113,degreeRegion64_114,degreeRegion64_115,degreeRegion64_116,degreeRegion64_117,degreeRegion64_118,degreeRegion64_119,degreeRegion64_120,degreeRegion64_121,degreeRegion64_122,degreeRegion64_123,degreeRegion64_124,degreeRegion64_125,degreeRegion64_126,degreeRegion64_127,degreeRegion64_128,degreeRegion64_129,degreeRegion64_130,degreeRegion64_131,degreeRegion64_132,degreeRegion64_133,degreeRegion64_134,degreeRegion64_135,degreeRegion64_136] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData89.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData89.lean index f7062957249d8d394b438bf0e97f6c553a9eeb17..4914f202abd7119e2c2b5e00d11b8c381ae10961 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData89.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegionData89.lean @@ -1,30 +1,30 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Region Data 89. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeRegion89_0 : PrefixRegion := ([(1,10),(2,42),(3,44)], [(2,18),(3,44),(5,47)]) -def degreeRegion89_1 : PrefixRegion := ([(1,18),(2,20),(3,44)], [(2,18),(3,44),(5,47)]) -def degreeRegion89_2 : PrefixRegion := ([(1,18),(3,30)], [(2,18),(3,44),(5,47)]) -def degreeRegion89_3 : PrefixRegion := ([(1,18),(4,40)], [(2,18),(3,44),(5,47)]) -def degreeRegion89_4 : PrefixRegion := ([(2,18),(3,44),(5,47)], [(1,10),(2,42),(3,44)]) -def degreeRegion89_5 : PrefixRegion := ([(2,18),(3,44),(5,47)], [(1,18),(2,20),(3,44)]) -def degreeRegion89_6 : PrefixRegion := ([(2,18),(3,44),(5,47)], [(1,18),(3,30)]) -def degreeRegion89_7 : PrefixRegion := ([(2,18),(3,44),(5,47)], [(1,18),(4,40)]) - -def degreeRegions89 : List PrefixRegion := [degreeRegion89_0,degreeRegion89_1,degreeRegion89_2,degreeRegion89_3,degreeRegion89_4,degreeRegion89_5,degreeRegion89_6,degreeRegion89_7] - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Region Data 89. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeRegion89_0 : PrefixRegion := ([(1,10),(2,42),(3,44)], [(2,18),(3,44),(5,47)]) +def degreeRegion89_1 : PrefixRegion := ([(1,18),(2,20),(3,44)], [(2,18),(3,44),(5,47)]) +def degreeRegion89_2 : PrefixRegion := ([(1,18),(3,30)], [(2,18),(3,44),(5,47)]) +def degreeRegion89_3 : PrefixRegion := ([(1,18),(4,40)], [(2,18),(3,44),(5,47)]) +def degreeRegion89_4 : PrefixRegion := ([(2,18),(3,44),(5,47)], [(1,10),(2,42),(3,44)]) +def degreeRegion89_5 : PrefixRegion := ([(2,18),(3,44),(5,47)], [(1,18),(2,20),(3,44)]) +def degreeRegion89_6 : PrefixRegion := ([(2,18),(3,44),(5,47)], [(1,18),(3,30)]) +def degreeRegion89_7 : PrefixRegion := ([(2,18),(3,44),(5,47)], [(1,18),(4,40)]) + +def degreeRegions89 : List PrefixRegion := [degreeRegion89_0,degreeRegion89_1,degreeRegion89_2,degreeRegion89_3,degreeRegion89_4,degreeRegion89_5,degreeRegion89_6,degreeRegion89_7] + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions116.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions116.lean index 685bfbeaeba5487ed9ed748f4a8b3081e7b32086..928aeb6671ac8df21bd5d77bf0f0866b3f05f05c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions116.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions116.lean @@ -1,54 +1,54 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves116 - -namespace OAI - -/-! Degree Regions 116. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionCheck116 : ∀ h ≤ 22, - checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) h 116 22 degreeHalfRegions116 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch116_0 - · exact degreeUnionBranch116_1 - · exact degreeUnionBranch116_2 - · exact degreeUnionBranch116_3 - · exact degreeUnionBranch116_4 - · exact degreeUnionBranch116_5 - · exact degreeUnionBranch116_6 - · exact degreeUnionBranch116_7 - · exact degreeUnionBranch116_8 - · exact degreeUnionBranch116_9 - · exact degreeUnionBranch116_10 - · exact degreeUnionBranch116_11 - · exact degreeUnionBranch116_12 - · exact degreeUnionBranch116_13 - · exact degreeUnionBranch116_14 - · exact degreeUnionBranch116_15 - · exact degreeUnionBranch116_16 - · exact degreeUnionBranch116_17 - · exact degreeUnionBranch116_18 - · exact degreeUnionBranch116_19 - · exact degreeUnionBranch116_20 - · exact degreeUnionBranch116_21 - · exact degreeUnionBranch116_22 - -lemma degreeHalfCover116 : ∀ R ∈ degreeRegions116, - R ∈ degreeHalfRegions116 ∨ (R.2,R.1) ∈ degreeHalfRegions116 := by decide +kernel - -lemma degreeDiagramRegionsChecked116 : ∀ R ∈ degreeRegions116, - ∀ μ : YoungDiagram, μ.card = 116 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP116 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck116 degreeHalfHeight116 degreeHalfWidth116 - degreeHalfCover116 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves116 + +namespace OAI + +/-! Degree Regions 116. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionCheck116 : ∀ h ≤ 22, + checkRegionPrefixes (quickResidual 12 19 degreeQs116 degreeTree116) h 116 22 degreeHalfRegions116 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch116_0 + · exact degreeUnionBranch116_1 + · exact degreeUnionBranch116_2 + · exact degreeUnionBranch116_3 + · exact degreeUnionBranch116_4 + · exact degreeUnionBranch116_5 + · exact degreeUnionBranch116_6 + · exact degreeUnionBranch116_7 + · exact degreeUnionBranch116_8 + · exact degreeUnionBranch116_9 + · exact degreeUnionBranch116_10 + · exact degreeUnionBranch116_11 + · exact degreeUnionBranch116_12 + · exact degreeUnionBranch116_13 + · exact degreeUnionBranch116_14 + · exact degreeUnionBranch116_15 + · exact degreeUnionBranch116_16 + · exact degreeUnionBranch116_17 + · exact degreeUnionBranch116_18 + · exact degreeUnionBranch116_19 + · exact degreeUnionBranch116_20 + · exact degreeUnionBranch116_21 + · exact degreeUnionBranch116_22 + +lemma degreeHalfCover116 : ∀ R ∈ degreeRegions116, + R ∈ degreeHalfRegions116 ∨ (R.2,R.1) ∈ degreeHalfRegions116 := by decide +kernel + +lemma degreeDiagramRegionsChecked116 : ∀ R ∈ degreeRegions116, + ∀ μ : YoungDiagram, μ.card = 116 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP116 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck116 degreeHalfHeight116 degreeHalfWidth116 + degreeHalfCover116 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions118.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions118.lean index 67a2dc0300e7444abf6d0fdb129431a83ef52579..dd8cff743cf2b0888bd7118e41ac6e1cb4805b47 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions118.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions118.lean @@ -1,54 +1,54 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves118 - -namespace OAI - -/-! Degree Regions 118. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionCheck118 : ∀ h ≤ 22, - checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) h 118 22 degreeHalfRegions118 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch118_0 - · exact degreeUnionBranch118_1 - · exact degreeUnionBranch118_2 - · exact degreeUnionBranch118_3 - · exact degreeUnionBranch118_4 - · exact degreeUnionBranch118_5 - · exact degreeUnionBranch118_6 - · exact degreeUnionBranch118_7 - · exact degreeUnionBranch118_8 - · exact degreeUnionBranch118_9 - · exact degreeUnionBranch118_10 - · exact degreeUnionBranch118_11 - · exact degreeUnionBranch118_12 - · exact degreeUnionBranch118_13 - · exact degreeUnionBranch118_14 - · exact degreeUnionBranch118_15 - · exact degreeUnionBranch118_16 - · exact degreeUnionBranch118_17 - · exact degreeUnionBranch118_18 - · exact degreeUnionBranch118_19 - · exact degreeUnionBranch118_20 - · exact degreeUnionBranch118_21 - · exact degreeUnionBranch118_22 - -lemma degreeHalfCover118 : ∀ R ∈ degreeRegions118, - R ∈ degreeHalfRegions118 ∨ (R.2,R.1) ∈ degreeHalfRegions118 := by decide +kernel - -lemma degreeDiagramRegionsChecked118 : ∀ R ∈ degreeRegions118, - ∀ μ : YoungDiagram, μ.card = 118 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP118 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck118 degreeHalfHeight118 degreeHalfWidth118 - degreeHalfCover118 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves118 + +namespace OAI + +/-! Degree Regions 118. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionCheck118 : ∀ h ≤ 22, + checkRegionPrefixes (quickResidual 12 20 degreeQs118 degreeTree118) h 118 22 degreeHalfRegions118 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch118_0 + · exact degreeUnionBranch118_1 + · exact degreeUnionBranch118_2 + · exact degreeUnionBranch118_3 + · exact degreeUnionBranch118_4 + · exact degreeUnionBranch118_5 + · exact degreeUnionBranch118_6 + · exact degreeUnionBranch118_7 + · exact degreeUnionBranch118_8 + · exact degreeUnionBranch118_9 + · exact degreeUnionBranch118_10 + · exact degreeUnionBranch118_11 + · exact degreeUnionBranch118_12 + · exact degreeUnionBranch118_13 + · exact degreeUnionBranch118_14 + · exact degreeUnionBranch118_15 + · exact degreeUnionBranch118_16 + · exact degreeUnionBranch118_17 + · exact degreeUnionBranch118_18 + · exact degreeUnionBranch118_19 + · exact degreeUnionBranch118_20 + · exact degreeUnionBranch118_21 + · exact degreeUnionBranch118_22 + +lemma degreeHalfCover118 : ∀ R ∈ degreeRegions118, + R ∈ degreeHalfRegions118 ∨ (R.2,R.1) ∈ degreeHalfRegions118 := by decide +kernel + +lemma degreeDiagramRegionsChecked118 : ∀ R ∈ degreeRegions118, + ∀ μ : YoungDiagram, μ.card = 118 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP118 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck118 degreeHalfHeight118 degreeHalfWidth118 + degreeHalfCover118 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions14.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions14.lean index adcd8ee2a7f19cd1c1b4ec719562be84fa9738f3..de6648ee5163d7505f51294429c753f2a638a329 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions14.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions14.lean @@ -1,45 +1,45 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves14 - -namespace OAI - -/-! Degree Regions 14. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionCheck14 : ∀ h ≤ 13, - checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) h 14 13 degreeHalfRegions14 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch14_0 - · exact degreeUnionBranch14_1 - · exact degreeUnionBranch14_2 - · exact degreeUnionBranch14_3 - · exact degreeUnionBranch14_4 - · exact degreeUnionBranch14_5 - · exact degreeUnionBranch14_6 - · exact degreeUnionBranch14_7 - · exact degreeUnionBranch14_8 - · exact degreeUnionBranch14_9 - · exact degreeUnionBranch14_10 - · exact degreeUnionBranch14_11 - · exact degreeUnionBranch14_12 - · exact degreeUnionBranch14_13 - -lemma degreeHalfCover14 : ∀ R ∈ degreeRegions14, - R ∈ degreeHalfRegions14 ∨ (R.2,R.1) ∈ degreeHalfRegions14 := by decide +kernel - -lemma degreeDiagramRegionsChecked14 : ∀ R ∈ degreeRegions14, - ∀ μ : YoungDiagram, μ.card = 14 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP14 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck14 degreeHalfHeight14 degreeHalfWidth14 - degreeHalfCover14 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves14 + +namespace OAI + +/-! Degree Regions 14. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionCheck14 : ∀ h ≤ 13, + checkRegionPrefixes (quickResidual 4 2 degreeQs14 degreeTree14) h 14 13 degreeHalfRegions14 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch14_0 + · exact degreeUnionBranch14_1 + · exact degreeUnionBranch14_2 + · exact degreeUnionBranch14_3 + · exact degreeUnionBranch14_4 + · exact degreeUnionBranch14_5 + · exact degreeUnionBranch14_6 + · exact degreeUnionBranch14_7 + · exact degreeUnionBranch14_8 + · exact degreeUnionBranch14_9 + · exact degreeUnionBranch14_10 + · exact degreeUnionBranch14_11 + · exact degreeUnionBranch14_12 + · exact degreeUnionBranch14_13 + +lemma degreeHalfCover14 : ∀ R ∈ degreeRegions14, + R ∈ degreeHalfRegions14 ∨ (R.2,R.1) ∈ degreeHalfRegions14 := by decide +kernel + +lemma degreeDiagramRegionsChecked14 : ∀ R ∈ degreeRegions14, + ∀ μ : YoungDiagram, μ.card = 14 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP14 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck14 degreeHalfHeight14 degreeHalfWidth14 + degreeHalfCover14 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions16.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions16.lean index c7fb25559c8ffedb5379c731a2d930200b74b6fa..4e3de79f395c937a23ef0ccde2411b3732e5c9c5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions16.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions16.lean @@ -1,47 +1,47 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves16 - -namespace OAI - -/-! Degree Regions 16. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionCheck16 : ∀ h ≤ 15, - checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) h 16 15 degreeHalfRegions16 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch16_0 - · exact degreeUnionBranch16_1 - · exact degreeUnionBranch16_2 - · exact degreeUnionBranch16_3 - · exact degreeUnionBranch16_4 - · exact degreeUnionBranch16_5 - · exact degreeUnionBranch16_6 - · exact degreeUnionBranch16_7 - · exact degreeUnionBranch16_8 - · exact degreeUnionBranch16_9 - · exact degreeUnionBranch16_10 - · exact degreeUnionBranch16_11 - · exact degreeUnionBranch16_12 - · exact degreeUnionBranch16_13 - · exact degreeUnionBranch16_14 - · exact degreeUnionBranch16_15 - -lemma degreeHalfCover16 : ∀ R ∈ degreeRegions16, - R ∈ degreeHalfRegions16 ∨ (R.2,R.1) ∈ degreeHalfRegions16 := by decide +kernel - -lemma degreeDiagramRegionsChecked16 : ∀ R ∈ degreeRegions16, - ∀ μ : YoungDiagram, μ.card = 16 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP16 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck16 degreeHalfHeight16 degreeHalfWidth16 - degreeHalfCover16 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves16 + +namespace OAI + +/-! Degree Regions 16. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionCheck16 : ∀ h ≤ 15, + checkRegionPrefixes (quickResidual 4 3 degreeQs16 degreeTree16) h 16 15 degreeHalfRegions16 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch16_0 + · exact degreeUnionBranch16_1 + · exact degreeUnionBranch16_2 + · exact degreeUnionBranch16_3 + · exact degreeUnionBranch16_4 + · exact degreeUnionBranch16_5 + · exact degreeUnionBranch16_6 + · exact degreeUnionBranch16_7 + · exact degreeUnionBranch16_8 + · exact degreeUnionBranch16_9 + · exact degreeUnionBranch16_10 + · exact degreeUnionBranch16_11 + · exact degreeUnionBranch16_12 + · exact degreeUnionBranch16_13 + · exact degreeUnionBranch16_14 + · exact degreeUnionBranch16_15 + +lemma degreeHalfCover16 : ∀ R ∈ degreeRegions16, + R ∈ degreeHalfRegions16 ∨ (R.2,R.1) ∈ degreeHalfRegions16 := by decide +kernel + +lemma degreeDiagramRegionsChecked16 : ∀ R ∈ degreeRegions16, + ∀ μ : YoungDiagram, μ.card = 16 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP16 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck16 degreeHalfHeight16 degreeHalfWidth16 + degreeHalfCover16 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions18.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions18.lean index f57ef4f63776149d9b7f8b7e9d5e5abaa86aa00a..8cc263dad76ab12683ecee6427439d14d1a83ce2 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions18.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions18.lean @@ -1,49 +1,49 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves18 - -namespace OAI - -/-! Degree Regions 18. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionCheck18 : ∀ h ≤ 17, - checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) h 18 17 degreeHalfRegions18 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch18_0 - · exact degreeUnionBranch18_1 - · exact degreeUnionBranch18_2 - · exact degreeUnionBranch18_3 - · exact degreeUnionBranch18_4 - · exact degreeUnionBranch18_5 - · exact degreeUnionBranch18_6 - · exact degreeUnionBranch18_7 - · exact degreeUnionBranch18_8 - · exact degreeUnionBranch18_9 - · exact degreeUnionBranch18_10 - · exact degreeUnionBranch18_11 - · exact degreeUnionBranch18_12 - · exact degreeUnionBranch18_13 - · exact degreeUnionBranch18_14 - · exact degreeUnionBranch18_15 - · exact degreeUnionBranch18_16 - · exact degreeUnionBranch18_17 - -lemma degreeHalfCover18 : ∀ R ∈ degreeRegions18, - R ∈ degreeHalfRegions18 ∨ (R.2,R.1) ∈ degreeHalfRegions18 := by decide +kernel - -lemma degreeDiagramRegionsChecked18 : ∀ R ∈ degreeRegions18, - ∀ μ : YoungDiagram, μ.card = 18 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP18 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck18 degreeHalfHeight18 degreeHalfWidth18 - degreeHalfCover18 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves18 + +namespace OAI + +/-! Degree Regions 18. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionCheck18 : ∀ h ≤ 17, + checkRegionPrefixes (quickResidual 4 4 degreeQs18 degreeTree18) h 18 17 degreeHalfRegions18 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch18_0 + · exact degreeUnionBranch18_1 + · exact degreeUnionBranch18_2 + · exact degreeUnionBranch18_3 + · exact degreeUnionBranch18_4 + · exact degreeUnionBranch18_5 + · exact degreeUnionBranch18_6 + · exact degreeUnionBranch18_7 + · exact degreeUnionBranch18_8 + · exact degreeUnionBranch18_9 + · exact degreeUnionBranch18_10 + · exact degreeUnionBranch18_11 + · exact degreeUnionBranch18_12 + · exact degreeUnionBranch18_13 + · exact degreeUnionBranch18_14 + · exact degreeUnionBranch18_15 + · exact degreeUnionBranch18_16 + · exact degreeUnionBranch18_17 + +lemma degreeHalfCover18 : ∀ R ∈ degreeRegions18, + R ∈ degreeHalfRegions18 ∨ (R.2,R.1) ∈ degreeHalfRegions18 := by decide +kernel + +lemma degreeDiagramRegionsChecked18 : ∀ R ∈ degreeRegions18, + ∀ μ : YoungDiagram, μ.card = 18 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP18 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck18 degreeHalfHeight18 degreeHalfWidth18 + degreeHalfCover18 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions19.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions19.lean index 1f51acff4eeab2c4671683f93f6deb21607a7e35..22c09093e26648042b6776cdec14d3204679aee6 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions19.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions19.lean @@ -1,40 +1,40 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves19 - -namespace OAI - -/-! Degree Regions 19. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionCheck19 : ∀ h ≤ 8, - checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) h 19 8 degreeHalfRegions19 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch19_0 - · exact degreeUnionBranch19_1 - · exact degreeUnionBranch19_2 - · exact degreeUnionBranch19_3 - · exact degreeUnionBranch19_4 - · exact degreeUnionBranch19_5 - · exact degreeUnionBranch19_6 - · exact degreeUnionBranch19_7 - · exact degreeUnionBranch19_8 - -lemma degreeHalfCover19 : ∀ R ∈ degreeRegions19, - R ∈ degreeHalfRegions19 ∨ (R.2,R.1) ∈ degreeHalfRegions19 := by decide +kernel - -lemma degreeDiagramRegionsChecked19 : ∀ R ∈ degreeRegions19, - ∀ μ : YoungDiagram, μ.card = 19 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP19 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck19 degreeHalfHeight19 degreeHalfWidth19 - degreeHalfCover19 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves19 + +namespace OAI + +/-! Degree Regions 19. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionCheck19 : ∀ h ≤ 8, + checkRegionPrefixes (quickResidual 5 2 degreeQs19 degreeTree19) h 19 8 degreeHalfRegions19 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch19_0 + · exact degreeUnionBranch19_1 + · exact degreeUnionBranch19_2 + · exact degreeUnionBranch19_3 + · exact degreeUnionBranch19_4 + · exact degreeUnionBranch19_5 + · exact degreeUnionBranch19_6 + · exact degreeUnionBranch19_7 + · exact degreeUnionBranch19_8 + +lemma degreeHalfCover19 : ∀ R ∈ degreeRegions19, + R ∈ degreeHalfRegions19 ∨ (R.2,R.1) ∈ degreeHalfRegions19 := by decide +kernel + +lemma degreeDiagramRegionsChecked19 : ∀ R ∈ degreeRegions19, + ∀ μ : YoungDiagram, μ.card = 19 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP19 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck19 degreeHalfHeight19 degreeHalfWidth19 + degreeHalfCover19 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions20.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions20.lean index e772abe2774e4eac0a60f7bec3d8b09e0c537f15..fd76bf24ed14bff611b6c1ec442a502df8a504e4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions20.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions20.lean @@ -1,51 +1,51 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves20 - -namespace OAI - -/-! Degree Regions 20. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionCheck20 : ∀ h ≤ 19, - checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) h 20 19 degreeHalfRegions20 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch20_0 - · exact degreeUnionBranch20_1 - · exact degreeUnionBranch20_2 - · exact degreeUnionBranch20_3 - · exact degreeUnionBranch20_4 - · exact degreeUnionBranch20_5 - · exact degreeUnionBranch20_6 - · exact degreeUnionBranch20_7 - · exact degreeUnionBranch20_8 - · exact degreeUnionBranch20_9 - · exact degreeUnionBranch20_10 - · exact degreeUnionBranch20_11 - · exact degreeUnionBranch20_12 - · exact degreeUnionBranch20_13 - · exact degreeUnionBranch20_14 - · exact degreeUnionBranch20_15 - · exact degreeUnionBranch20_16 - · exact degreeUnionBranch20_17 - · exact degreeUnionBranch20_18 - · exact degreeUnionBranch20_19 - -lemma degreeHalfCover20 : ∀ R ∈ degreeRegions20, - R ∈ degreeHalfRegions20 ∨ (R.2,R.1) ∈ degreeHalfRegions20 := by decide +kernel - -lemma degreeDiagramRegionsChecked20 : ∀ R ∈ degreeRegions20, - ∀ μ : YoungDiagram, μ.card = 20 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP20 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck20 degreeHalfHeight20 degreeHalfWidth20 - degreeHalfCover20 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves20 + +namespace OAI + +/-! Degree Regions 20. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionCheck20 : ∀ h ≤ 19, + checkRegionPrefixes (quickResidual 4 5 degreeQs20 degreeTree20) h 20 19 degreeHalfRegions20 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch20_0 + · exact degreeUnionBranch20_1 + · exact degreeUnionBranch20_2 + · exact degreeUnionBranch20_3 + · exact degreeUnionBranch20_4 + · exact degreeUnionBranch20_5 + · exact degreeUnionBranch20_6 + · exact degreeUnionBranch20_7 + · exact degreeUnionBranch20_8 + · exact degreeUnionBranch20_9 + · exact degreeUnionBranch20_10 + · exact degreeUnionBranch20_11 + · exact degreeUnionBranch20_12 + · exact degreeUnionBranch20_13 + · exact degreeUnionBranch20_14 + · exact degreeUnionBranch20_15 + · exact degreeUnionBranch20_16 + · exact degreeUnionBranch20_17 + · exact degreeUnionBranch20_18 + · exact degreeUnionBranch20_19 + +lemma degreeHalfCover20 : ∀ R ∈ degreeRegions20, + R ∈ degreeHalfRegions20 ∨ (R.2,R.1) ∈ degreeHalfRegions20 := by decide +kernel + +lemma degreeDiagramRegionsChecked20 : ∀ R ∈ degreeRegions20, + ∀ μ : YoungDiagram, μ.card = 20 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP20 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck20 degreeHalfHeight20 degreeHalfWidth20 + degreeHalfCover20 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions22.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions22.lean index c9608f4443efe29ad135104bf6f9c6c5078c0fa1..a13c9ba07389d9fa28d9d750fe5e35fc649bd5a9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions22.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions22.lean @@ -1,53 +1,53 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves22 - -namespace OAI - -/-! Degree Regions 22. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionCheck22 : ∀ h ≤ 21, - checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) h 22 21 degreeHalfRegions22 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch22_0 - · exact degreeUnionBranch22_1 - · exact degreeUnionBranch22_2 - · exact degreeUnionBranch22_3 - · exact degreeUnionBranch22_4 - · exact degreeUnionBranch22_5 - · exact degreeUnionBranch22_6 - · exact degreeUnionBranch22_7 - · exact degreeUnionBranch22_8 - · exact degreeUnionBranch22_9 - · exact degreeUnionBranch22_10 - · exact degreeUnionBranch22_11 - · exact degreeUnionBranch22_12 - · exact degreeUnionBranch22_13 - · exact degreeUnionBranch22_14 - · exact degreeUnionBranch22_15 - · exact degreeUnionBranch22_16 - · exact degreeUnionBranch22_17 - · exact degreeUnionBranch22_18 - · exact degreeUnionBranch22_19 - · exact degreeUnionBranch22_20 - · exact degreeUnionBranch22_21 - -lemma degreeHalfCover22 : ∀ R ∈ degreeRegions22, - R ∈ degreeHalfRegions22 ∨ (R.2,R.1) ∈ degreeHalfRegions22 := by decide +kernel - -lemma degreeDiagramRegionsChecked22 : ∀ R ∈ degreeRegions22, - ∀ μ : YoungDiagram, μ.card = 22 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP22 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck22 degreeHalfHeight22 degreeHalfWidth22 - degreeHalfCover22 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves22 + +namespace OAI + +/-! Degree Regions 22. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionCheck22 : ∀ h ≤ 21, + checkRegionPrefixes (quickResidual 4 6 degreeQs22 degreeTree22) h 22 21 degreeHalfRegions22 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch22_0 + · exact degreeUnionBranch22_1 + · exact degreeUnionBranch22_2 + · exact degreeUnionBranch22_3 + · exact degreeUnionBranch22_4 + · exact degreeUnionBranch22_5 + · exact degreeUnionBranch22_6 + · exact degreeUnionBranch22_7 + · exact degreeUnionBranch22_8 + · exact degreeUnionBranch22_9 + · exact degreeUnionBranch22_10 + · exact degreeUnionBranch22_11 + · exact degreeUnionBranch22_12 + · exact degreeUnionBranch22_13 + · exact degreeUnionBranch22_14 + · exact degreeUnionBranch22_15 + · exact degreeUnionBranch22_16 + · exact degreeUnionBranch22_17 + · exact degreeUnionBranch22_18 + · exact degreeUnionBranch22_19 + · exact degreeUnionBranch22_20 + · exact degreeUnionBranch22_21 + +lemma degreeHalfCover22 : ∀ R ∈ degreeRegions22, + R ∈ degreeHalfRegions22 ∨ (R.2,R.1) ∈ degreeHalfRegions22 := by decide +kernel + +lemma degreeDiagramRegionsChecked22 : ∀ R ∈ degreeRegions22, + ∀ μ : YoungDiagram, μ.card = 22 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP22 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck22 degreeHalfHeight22 degreeHalfWidth22 + degreeHalfCover22 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions24.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions24.lean index 2199db56ba9c3cb7f5a19b555d9cea519ce5994e..1ddf7fab99a66f8a0641e5b0e62a1ce4d78a47a1 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions24.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions24.lean @@ -1,144 +1,144 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves24 - -namespace OAI - -/-! Degree Regions 24. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch24_6 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 24 23 degreeHalfRegions24 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 23 at hb - change 24 ≤ 6*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch24_7 - · exact degreeUnionBranch24_8 - · exact degreeUnionBranch24_9 - · exact degreeUnionBranch24_10 - · exact degreeUnionBranch24_11 - · exact degreeUnionBranch24_12 - · exact degreeUnionBranch24_13 - · exact degreeUnionBranch24_14 - · exact degreeUnionBranch24_15 - · exact degreeUnionBranch24_16 - · exact degreeUnionBranch24_17 - · exact degreeUnionBranch24_18 - · exact degreeUnionBranch24_19 - · exact degreeUnionBranch24_20 - · exact degreeUnionBranch24_21 - · exact degreeUnionBranch24_22 - · exact degreeUnionBranch24_23 - · exact degreeUnionBranch24_24 - · exact degreeUnionBranch24_25 - · exact degreeUnionBranch24_26 - -lemma degreeUnionBranch24_27 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 24 23 degreeHalfRegions24 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 23 at hb - change 24 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch24_28 - · exact degreeUnionBranch24_29 - · exact degreeUnionBranch24_30 - · exact degreeUnionBranch24_31 - · exact degreeUnionBranch24_32 - · exact degreeUnionBranch24_33 - · exact degreeUnionBranch24_34 - · exact degreeUnionBranch24_35 - · exact degreeUnionBranch24_36 - · exact degreeUnionBranch24_37 - · exact degreeUnionBranch24_38 - · exact degreeUnionBranch24_39 - · exact degreeUnionBranch24_40 - · exact degreeUnionBranch24_41 - · exact degreeUnionBranch24_42 - · exact degreeUnionBranch24_43 - · exact degreeUnionBranch24_44 - · exact degreeUnionBranch24_45 - · exact degreeUnionBranch24_46 - · exact degreeUnionBranch24_47 - -lemma degreeUnionBranch24_48 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 8 24 23 degreeHalfRegions24 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 23 at hb - change 24 ≤ 8*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch24_49 - · exact degreeUnionBranch24_50 - · exact degreeUnionBranch24_51 - · exact degreeUnionBranch24_52 - · exact degreeUnionBranch24_53 - · exact degreeUnionBranch24_54 - · exact degreeUnionBranch24_55 - · exact degreeUnionBranch24_56 - · exact degreeUnionBranch24_57 - · exact degreeUnionBranch24_58 - · exact degreeUnionBranch24_59 - · exact degreeUnionBranch24_60 - · exact degreeUnionBranch24_61 - · exact degreeUnionBranch24_62 - · exact degreeUnionBranch24_63 - · exact degreeUnionBranch24_64 - · exact degreeUnionBranch24_65 - · exact degreeUnionBranch24_66 - · exact degreeUnionBranch24_67 - · exact degreeUnionBranch24_68 - · exact degreeUnionBranch24_69 - -lemma degreeUnionCheck24 : ∀ h ≤ 23, - checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) h 24 23 degreeHalfRegions24 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch24_0 - · exact degreeUnionBranch24_1 - · exact degreeUnionBranch24_2 - · exact degreeUnionBranch24_3 - · exact degreeUnionBranch24_4 - · exact degreeUnionBranch24_5 - · exact degreeUnionBranch24_6 - · exact degreeUnionBranch24_27 - · exact degreeUnionBranch24_48 - · exact degreeUnionBranch24_70 - · exact degreeUnionBranch24_71 - · exact degreeUnionBranch24_72 - · exact degreeUnionBranch24_73 - · exact degreeUnionBranch24_74 - · exact degreeUnionBranch24_75 - · exact degreeUnionBranch24_76 - · exact degreeUnionBranch24_77 - · exact degreeUnionBranch24_78 - · exact degreeUnionBranch24_79 - · exact degreeUnionBranch24_80 - · exact degreeUnionBranch24_81 - · exact degreeUnionBranch24_82 - · exact degreeUnionBranch24_83 - · exact degreeUnionBranch24_84 - -lemma degreeHalfCover24 : ∀ R ∈ degreeRegions24, - R ∈ degreeHalfRegions24 ∨ (R.2,R.1) ∈ degreeHalfRegions24 := by decide +kernel - -lemma degreeDiagramRegionsChecked24 : ∀ R ∈ degreeRegions24, - ∀ μ : YoungDiagram, μ.card = 24 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP24 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck24 degreeHalfHeight24 degreeHalfWidth24 - degreeHalfCover24 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves24 + +namespace OAI + +/-! Degree Regions 24. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch24_6 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 6 24 23 degreeHalfRegions24 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 23 at hb + change 24 ≤ 6*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch24_7 + · exact degreeUnionBranch24_8 + · exact degreeUnionBranch24_9 + · exact degreeUnionBranch24_10 + · exact degreeUnionBranch24_11 + · exact degreeUnionBranch24_12 + · exact degreeUnionBranch24_13 + · exact degreeUnionBranch24_14 + · exact degreeUnionBranch24_15 + · exact degreeUnionBranch24_16 + · exact degreeUnionBranch24_17 + · exact degreeUnionBranch24_18 + · exact degreeUnionBranch24_19 + · exact degreeUnionBranch24_20 + · exact degreeUnionBranch24_21 + · exact degreeUnionBranch24_22 + · exact degreeUnionBranch24_23 + · exact degreeUnionBranch24_24 + · exact degreeUnionBranch24_25 + · exact degreeUnionBranch24_26 + +lemma degreeUnionBranch24_27 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 7 24 23 degreeHalfRegions24 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 23 at hb + change 24 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch24_28 + · exact degreeUnionBranch24_29 + · exact degreeUnionBranch24_30 + · exact degreeUnionBranch24_31 + · exact degreeUnionBranch24_32 + · exact degreeUnionBranch24_33 + · exact degreeUnionBranch24_34 + · exact degreeUnionBranch24_35 + · exact degreeUnionBranch24_36 + · exact degreeUnionBranch24_37 + · exact degreeUnionBranch24_38 + · exact degreeUnionBranch24_39 + · exact degreeUnionBranch24_40 + · exact degreeUnionBranch24_41 + · exact degreeUnionBranch24_42 + · exact degreeUnionBranch24_43 + · exact degreeUnionBranch24_44 + · exact degreeUnionBranch24_45 + · exact degreeUnionBranch24_46 + · exact degreeUnionBranch24_47 + +lemma degreeUnionBranch24_48 : checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) 8 24 23 degreeHalfRegions24 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 23 at hb + change 24 ≤ 8*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch24_49 + · exact degreeUnionBranch24_50 + · exact degreeUnionBranch24_51 + · exact degreeUnionBranch24_52 + · exact degreeUnionBranch24_53 + · exact degreeUnionBranch24_54 + · exact degreeUnionBranch24_55 + · exact degreeUnionBranch24_56 + · exact degreeUnionBranch24_57 + · exact degreeUnionBranch24_58 + · exact degreeUnionBranch24_59 + · exact degreeUnionBranch24_60 + · exact degreeUnionBranch24_61 + · exact degreeUnionBranch24_62 + · exact degreeUnionBranch24_63 + · exact degreeUnionBranch24_64 + · exact degreeUnionBranch24_65 + · exact degreeUnionBranch24_66 + · exact degreeUnionBranch24_67 + · exact degreeUnionBranch24_68 + · exact degreeUnionBranch24_69 + +lemma degreeUnionCheck24 : ∀ h ≤ 23, + checkRegionPrefixes (quickResidual 4 7 degreeQs24 degreeTree24) h 24 23 degreeHalfRegions24 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch24_0 + · exact degreeUnionBranch24_1 + · exact degreeUnionBranch24_2 + · exact degreeUnionBranch24_3 + · exact degreeUnionBranch24_4 + · exact degreeUnionBranch24_5 + · exact degreeUnionBranch24_6 + · exact degreeUnionBranch24_27 + · exact degreeUnionBranch24_48 + · exact degreeUnionBranch24_70 + · exact degreeUnionBranch24_71 + · exact degreeUnionBranch24_72 + · exact degreeUnionBranch24_73 + · exact degreeUnionBranch24_74 + · exact degreeUnionBranch24_75 + · exact degreeUnionBranch24_76 + · exact degreeUnionBranch24_77 + · exact degreeUnionBranch24_78 + · exact degreeUnionBranch24_79 + · exact degreeUnionBranch24_80 + · exact degreeUnionBranch24_81 + · exact degreeUnionBranch24_82 + · exact degreeUnionBranch24_83 + · exact degreeUnionBranch24_84 + +lemma degreeHalfCover24 : ∀ R ∈ degreeRegions24, + R ∈ degreeHalfRegions24 ∨ (R.2,R.1) ∈ degreeHalfRegions24 := by decide +kernel + +lemma degreeDiagramRegionsChecked24 : ∀ R ∈ degreeRegions24, + ∀ μ : YoungDiagram, μ.card = 24 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP24 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck24 degreeHalfHeight24 degreeHalfWidth24 + degreeHalfCover24 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions26.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions26.lean index f841e0a1488cf2c118dbf6992d5eb7ba87d83120..b37f178212f102e4ea2c2e3c075558aab2147ce4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions26.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions26.lean @@ -1,152 +1,152 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves26 - -namespace OAI - -/-! Degree Regions 26. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch26_7 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 26 25 degreeHalfRegions26 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 25 at hb - change 26 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch26_8 - · exact degreeUnionBranch26_9 - · exact degreeUnionBranch26_10 - · exact degreeUnionBranch26_11 - · exact degreeUnionBranch26_12 - · exact degreeUnionBranch26_13 - · exact degreeUnionBranch26_14 - · exact degreeUnionBranch26_15 - · exact degreeUnionBranch26_16 - · exact degreeUnionBranch26_17 - · exact degreeUnionBranch26_18 - · exact degreeUnionBranch26_19 - · exact degreeUnionBranch26_20 - · exact degreeUnionBranch26_21 - · exact degreeUnionBranch26_22 - · exact degreeUnionBranch26_23 - · exact degreeUnionBranch26_24 - · exact degreeUnionBranch26_25 - · exact degreeUnionBranch26_26 - · exact degreeUnionBranch26_27 - · exact degreeUnionBranch26_28 - · exact degreeUnionBranch26_29 - -lemma degreeUnionBranch26_30 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 26 25 degreeHalfRegions26 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 25 at hb - change 26 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch26_31 - · exact degreeUnionBranch26_32 - · exact degreeUnionBranch26_33 - · exact degreeUnionBranch26_34 - · exact degreeUnionBranch26_35 - · exact degreeUnionBranch26_36 - · exact degreeUnionBranch26_37 - · exact degreeUnionBranch26_38 - · exact degreeUnionBranch26_39 - · exact degreeUnionBranch26_40 - · exact degreeUnionBranch26_41 - · exact degreeUnionBranch26_42 - · exact degreeUnionBranch26_43 - · exact degreeUnionBranch26_44 - · exact degreeUnionBranch26_45 - · exact degreeUnionBranch26_46 - · exact degreeUnionBranch26_47 - · exact degreeUnionBranch26_48 - · exact degreeUnionBranch26_49 - · exact degreeUnionBranch26_50 - · exact degreeUnionBranch26_51 - · exact degreeUnionBranch26_52 - -lemma degreeUnionBranch26_53 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 9 26 25 degreeHalfRegions26 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 25 at hb - change 26 ≤ 9*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch26_54 - · exact degreeUnionBranch26_55 - · exact degreeUnionBranch26_56 - · exact degreeUnionBranch26_57 - · exact degreeUnionBranch26_58 - · exact degreeUnionBranch26_59 - · exact degreeUnionBranch26_60 - · exact degreeUnionBranch26_61 - · exact degreeUnionBranch26_62 - · exact degreeUnionBranch26_63 - · exact degreeUnionBranch26_64 - · exact degreeUnionBranch26_65 - · exact degreeUnionBranch26_66 - · exact degreeUnionBranch26_67 - · exact degreeUnionBranch26_68 - · exact degreeUnionBranch26_69 - · exact degreeUnionBranch26_70 - · exact degreeUnionBranch26_71 - · exact degreeUnionBranch26_72 - · exact degreeUnionBranch26_73 - · exact degreeUnionBranch26_74 - · exact degreeUnionBranch26_75 - · exact degreeUnionBranch26_76 - -lemma degreeUnionCheck26 : ∀ h ≤ 25, - checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) h 26 25 degreeHalfRegions26 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch26_0 - · exact degreeUnionBranch26_1 - · exact degreeUnionBranch26_2 - · exact degreeUnionBranch26_3 - · exact degreeUnionBranch26_4 - · exact degreeUnionBranch26_5 - · exact degreeUnionBranch26_6 - · exact degreeUnionBranch26_7 - · exact degreeUnionBranch26_30 - · exact degreeUnionBranch26_53 - · exact degreeUnionBranch26_77 - · exact degreeUnionBranch26_78 - · exact degreeUnionBranch26_79 - · exact degreeUnionBranch26_80 - · exact degreeUnionBranch26_81 - · exact degreeUnionBranch26_82 - · exact degreeUnionBranch26_83 - · exact degreeUnionBranch26_84 - · exact degreeUnionBranch26_85 - · exact degreeUnionBranch26_86 - · exact degreeUnionBranch26_87 - · exact degreeUnionBranch26_88 - · exact degreeUnionBranch26_89 - · exact degreeUnionBranch26_90 - · exact degreeUnionBranch26_91 - · exact degreeUnionBranch26_92 - -lemma degreeHalfCover26 : ∀ R ∈ degreeRegions26, - R ∈ degreeHalfRegions26 ∨ (R.2,R.1) ∈ degreeHalfRegions26 := by decide +kernel - -lemma degreeDiagramRegionsChecked26 : ∀ R ∈ degreeRegions26, - ∀ μ : YoungDiagram, μ.card = 26 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP26 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck26 degreeHalfHeight26 degreeHalfWidth26 - degreeHalfCover26 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves26 + +namespace OAI + +/-! Degree Regions 26. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch26_7 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 7 26 25 degreeHalfRegions26 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 25 at hb + change 26 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch26_8 + · exact degreeUnionBranch26_9 + · exact degreeUnionBranch26_10 + · exact degreeUnionBranch26_11 + · exact degreeUnionBranch26_12 + · exact degreeUnionBranch26_13 + · exact degreeUnionBranch26_14 + · exact degreeUnionBranch26_15 + · exact degreeUnionBranch26_16 + · exact degreeUnionBranch26_17 + · exact degreeUnionBranch26_18 + · exact degreeUnionBranch26_19 + · exact degreeUnionBranch26_20 + · exact degreeUnionBranch26_21 + · exact degreeUnionBranch26_22 + · exact degreeUnionBranch26_23 + · exact degreeUnionBranch26_24 + · exact degreeUnionBranch26_25 + · exact degreeUnionBranch26_26 + · exact degreeUnionBranch26_27 + · exact degreeUnionBranch26_28 + · exact degreeUnionBranch26_29 + +lemma degreeUnionBranch26_30 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 8 26 25 degreeHalfRegions26 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 25 at hb + change 26 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch26_31 + · exact degreeUnionBranch26_32 + · exact degreeUnionBranch26_33 + · exact degreeUnionBranch26_34 + · exact degreeUnionBranch26_35 + · exact degreeUnionBranch26_36 + · exact degreeUnionBranch26_37 + · exact degreeUnionBranch26_38 + · exact degreeUnionBranch26_39 + · exact degreeUnionBranch26_40 + · exact degreeUnionBranch26_41 + · exact degreeUnionBranch26_42 + · exact degreeUnionBranch26_43 + · exact degreeUnionBranch26_44 + · exact degreeUnionBranch26_45 + · exact degreeUnionBranch26_46 + · exact degreeUnionBranch26_47 + · exact degreeUnionBranch26_48 + · exact degreeUnionBranch26_49 + · exact degreeUnionBranch26_50 + · exact degreeUnionBranch26_51 + · exact degreeUnionBranch26_52 + +lemma degreeUnionBranch26_53 : checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) 9 26 25 degreeHalfRegions26 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 25 at hb + change 26 ≤ 9*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch26_54 + · exact degreeUnionBranch26_55 + · exact degreeUnionBranch26_56 + · exact degreeUnionBranch26_57 + · exact degreeUnionBranch26_58 + · exact degreeUnionBranch26_59 + · exact degreeUnionBranch26_60 + · exact degreeUnionBranch26_61 + · exact degreeUnionBranch26_62 + · exact degreeUnionBranch26_63 + · exact degreeUnionBranch26_64 + · exact degreeUnionBranch26_65 + · exact degreeUnionBranch26_66 + · exact degreeUnionBranch26_67 + · exact degreeUnionBranch26_68 + · exact degreeUnionBranch26_69 + · exact degreeUnionBranch26_70 + · exact degreeUnionBranch26_71 + · exact degreeUnionBranch26_72 + · exact degreeUnionBranch26_73 + · exact degreeUnionBranch26_74 + · exact degreeUnionBranch26_75 + · exact degreeUnionBranch26_76 + +lemma degreeUnionCheck26 : ∀ h ≤ 25, + checkRegionPrefixes (quickResidual 4 8 degreeQs26 degreeTree26) h 26 25 degreeHalfRegions26 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch26_0 + · exact degreeUnionBranch26_1 + · exact degreeUnionBranch26_2 + · exact degreeUnionBranch26_3 + · exact degreeUnionBranch26_4 + · exact degreeUnionBranch26_5 + · exact degreeUnionBranch26_6 + · exact degreeUnionBranch26_7 + · exact degreeUnionBranch26_30 + · exact degreeUnionBranch26_53 + · exact degreeUnionBranch26_77 + · exact degreeUnionBranch26_78 + · exact degreeUnionBranch26_79 + · exact degreeUnionBranch26_80 + · exact degreeUnionBranch26_81 + · exact degreeUnionBranch26_82 + · exact degreeUnionBranch26_83 + · exact degreeUnionBranch26_84 + · exact degreeUnionBranch26_85 + · exact degreeUnionBranch26_86 + · exact degreeUnionBranch26_87 + · exact degreeUnionBranch26_88 + · exact degreeUnionBranch26_89 + · exact degreeUnionBranch26_90 + · exact degreeUnionBranch26_91 + · exact degreeUnionBranch26_92 + +lemma degreeHalfCover26 : ∀ R ∈ degreeRegions26, + R ∈ degreeHalfRegions26 ∨ (R.2,R.1) ∈ degreeHalfRegions26 := by decide +kernel + +lemma degreeDiagramRegionsChecked26 : ∀ R ∈ degreeRegions26, + ∀ μ : YoungDiagram, μ.card = 26 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP26 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck26 degreeHalfHeight26 degreeHalfWidth26 + degreeHalfCover26 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions31.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions31.lean index b715382d93bd050e64a48180b2be35df36b5ad98..23cf0d787ea7919af6339de190c84879eee56f7a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions31.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions31.lean @@ -1,151 +1,151 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves31 - -namespace OAI - -/-! Degree Regions 31. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch31_8 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 31 30 degreeHalfRegions31 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 30 at hb - change 31 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch31_9 - · exact degreeUnionBranch31_10 - · exact degreeUnionBranch31_11 - · exact degreeUnionBranch31_12 - · exact degreeUnionBranch31_13 - · exact degreeUnionBranch31_14 - · exact degreeUnionBranch31_15 - · exact degreeUnionBranch31_16 - · exact degreeUnionBranch31_17 - · exact degreeUnionBranch31_18 - · exact degreeUnionBranch31_19 - · exact degreeUnionBranch31_20 - · exact degreeUnionBranch31_21 - · exact degreeUnionBranch31_22 - · exact degreeUnionBranch31_23 - · exact degreeUnionBranch31_24 - · exact degreeUnionBranch31_25 - · exact degreeUnionBranch31_26 - · exact degreeUnionBranch31_27 - · exact degreeUnionBranch31_28 - · exact degreeUnionBranch31_29 - · exact degreeUnionBranch31_30 - · exact degreeUnionBranch31_31 - · exact degreeUnionBranch31_32 - · exact degreeUnionBranch31_33 - · exact degreeUnionBranch31_34 - · exact degreeUnionBranch31_35 - -lemma degreeUnionBranch31_36 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 31 30 degreeHalfRegions31 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 30 at hb - change 31 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch31_37 - · exact degreeUnionBranch31_38 - · exact degreeUnionBranch31_39 - · exact degreeUnionBranch31_40 - · exact degreeUnionBranch31_41 - · exact degreeUnionBranch31_42 - · exact degreeUnionBranch31_43 - · exact degreeUnionBranch31_44 - · exact degreeUnionBranch31_45 - · exact degreeUnionBranch31_46 - · exact degreeUnionBranch31_47 - · exact degreeUnionBranch31_48 - · exact degreeUnionBranch31_49 - · exact degreeUnionBranch31_50 - · exact degreeUnionBranch31_51 - · exact degreeUnionBranch31_52 - · exact degreeUnionBranch31_53 - · exact degreeUnionBranch31_54 - · exact degreeUnionBranch31_55 - · exact degreeUnionBranch31_56 - · exact degreeUnionBranch31_57 - · exact degreeUnionBranch31_58 - · exact degreeUnionBranch31_59 - · exact degreeUnionBranch31_60 - · exact degreeUnionBranch31_61 - · exact degreeUnionBranch31_62 - · exact degreeUnionBranch31_63 - -lemma degreeUnionBranch31_64 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 10 31 30 degreeHalfRegions31 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 30 at hb - change 31 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch31_65 - · exact degreeUnionBranch31_66 - · exact degreeUnionBranch31_67 - · exact degreeUnionBranch31_68 - · exact degreeUnionBranch31_69 - · exact degreeUnionBranch31_70 - · exact degreeUnionBranch31_71 - · exact degreeUnionBranch31_72 - · exact degreeUnionBranch31_73 - · exact degreeUnionBranch31_74 - · exact degreeUnionBranch31_75 - · exact degreeUnionBranch31_76 - · exact degreeUnionBranch31_77 - · exact degreeUnionBranch31_78 - · exact degreeUnionBranch31_79 - · exact degreeUnionBranch31_80 - · exact degreeUnionBranch31_81 - · exact degreeUnionBranch31_82 - · exact degreeUnionBranch31_83 - · exact degreeUnionBranch31_84 - · exact degreeUnionBranch31_85 - · exact degreeUnionBranch31_86 - · exact degreeUnionBranch31_87 - · exact degreeUnionBranch31_88 - · exact degreeUnionBranch31_89 - · exact degreeUnionBranch31_90 - · exact degreeUnionBranch31_91 - -lemma degreeUnionCheck31 : ∀ h ≤ 10, - checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) h 31 30 degreeHalfRegions31 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch31_0 - · exact degreeUnionBranch31_1 - · exact degreeUnionBranch31_2 - · exact degreeUnionBranch31_3 - · exact degreeUnionBranch31_4 - · exact degreeUnionBranch31_5 - · exact degreeUnionBranch31_6 - · exact degreeUnionBranch31_7 - · exact degreeUnionBranch31_8 - · exact degreeUnionBranch31_36 - · exact degreeUnionBranch31_64 - -lemma degreeHalfCover31 : ∀ R ∈ degreeRegions31, - R ∈ degreeHalfRegions31 ∨ (R.2,R.1) ∈ degreeHalfRegions31 := by decide +kernel - -lemma degreeDiagramRegionsChecked31 : ∀ R ∈ degreeRegions31, - ∀ μ : YoungDiagram, μ.card = 31 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP31 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck31 degreeHalfHeight31 degreeHalfWidth31 - degreeHalfCover31 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves31 + +namespace OAI + +/-! Degree Regions 31. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch31_8 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 8 31 30 degreeHalfRegions31 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 30 at hb + change 31 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch31_9 + · exact degreeUnionBranch31_10 + · exact degreeUnionBranch31_11 + · exact degreeUnionBranch31_12 + · exact degreeUnionBranch31_13 + · exact degreeUnionBranch31_14 + · exact degreeUnionBranch31_15 + · exact degreeUnionBranch31_16 + · exact degreeUnionBranch31_17 + · exact degreeUnionBranch31_18 + · exact degreeUnionBranch31_19 + · exact degreeUnionBranch31_20 + · exact degreeUnionBranch31_21 + · exact degreeUnionBranch31_22 + · exact degreeUnionBranch31_23 + · exact degreeUnionBranch31_24 + · exact degreeUnionBranch31_25 + · exact degreeUnionBranch31_26 + · exact degreeUnionBranch31_27 + · exact degreeUnionBranch31_28 + · exact degreeUnionBranch31_29 + · exact degreeUnionBranch31_30 + · exact degreeUnionBranch31_31 + · exact degreeUnionBranch31_32 + · exact degreeUnionBranch31_33 + · exact degreeUnionBranch31_34 + · exact degreeUnionBranch31_35 + +lemma degreeUnionBranch31_36 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 9 31 30 degreeHalfRegions31 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 30 at hb + change 31 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch31_37 + · exact degreeUnionBranch31_38 + · exact degreeUnionBranch31_39 + · exact degreeUnionBranch31_40 + · exact degreeUnionBranch31_41 + · exact degreeUnionBranch31_42 + · exact degreeUnionBranch31_43 + · exact degreeUnionBranch31_44 + · exact degreeUnionBranch31_45 + · exact degreeUnionBranch31_46 + · exact degreeUnionBranch31_47 + · exact degreeUnionBranch31_48 + · exact degreeUnionBranch31_49 + · exact degreeUnionBranch31_50 + · exact degreeUnionBranch31_51 + · exact degreeUnionBranch31_52 + · exact degreeUnionBranch31_53 + · exact degreeUnionBranch31_54 + · exact degreeUnionBranch31_55 + · exact degreeUnionBranch31_56 + · exact degreeUnionBranch31_57 + · exact degreeUnionBranch31_58 + · exact degreeUnionBranch31_59 + · exact degreeUnionBranch31_60 + · exact degreeUnionBranch31_61 + · exact degreeUnionBranch31_62 + · exact degreeUnionBranch31_63 + +lemma degreeUnionBranch31_64 : checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) 10 31 30 degreeHalfRegions31 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 30 at hb + change 31 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch31_65 + · exact degreeUnionBranch31_66 + · exact degreeUnionBranch31_67 + · exact degreeUnionBranch31_68 + · exact degreeUnionBranch31_69 + · exact degreeUnionBranch31_70 + · exact degreeUnionBranch31_71 + · exact degreeUnionBranch31_72 + · exact degreeUnionBranch31_73 + · exact degreeUnionBranch31_74 + · exact degreeUnionBranch31_75 + · exact degreeUnionBranch31_76 + · exact degreeUnionBranch31_77 + · exact degreeUnionBranch31_78 + · exact degreeUnionBranch31_79 + · exact degreeUnionBranch31_80 + · exact degreeUnionBranch31_81 + · exact degreeUnionBranch31_82 + · exact degreeUnionBranch31_83 + · exact degreeUnionBranch31_84 + · exact degreeUnionBranch31_85 + · exact degreeUnionBranch31_86 + · exact degreeUnionBranch31_87 + · exact degreeUnionBranch31_88 + · exact degreeUnionBranch31_89 + · exact degreeUnionBranch31_90 + · exact degreeUnionBranch31_91 + +lemma degreeUnionCheck31 : ∀ h ≤ 10, + checkRegionPrefixes (quickResidual 6 5 degreeQs31 degreeTree31) h 31 30 degreeHalfRegions31 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch31_0 + · exact degreeUnionBranch31_1 + · exact degreeUnionBranch31_2 + · exact degreeUnionBranch31_3 + · exact degreeUnionBranch31_4 + · exact degreeUnionBranch31_5 + · exact degreeUnionBranch31_6 + · exact degreeUnionBranch31_7 + · exact degreeUnionBranch31_8 + · exact degreeUnionBranch31_36 + · exact degreeUnionBranch31_64 + +lemma degreeHalfCover31 : ∀ R ∈ degreeRegions31, + R ∈ degreeHalfRegions31 ∨ (R.2,R.1) ∈ degreeHalfRegions31 := by decide +kernel + +lemma degreeDiagramRegionsChecked31 : ∀ R ∈ degreeRegions31, + ∀ μ : YoungDiagram, μ.card = 31 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP31 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck31 degreeHalfHeight31 degreeHalfWidth31 + degreeHalfCover31 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions35.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions35.lean index 5b87e15025f85e01d68f98ade4ac4e24d46073ff..aa6920c911f0913ec4524b35fa087f5f62e03abf 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions35.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions35.lean @@ -1,291 +1,291 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves35 - -namespace OAI - -/-! Degree Regions 35. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch35_13 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 26 9 degreeUnionState35_13 [9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 26 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch35_14 - · exact degreeUnionBranch35_15 - · exact degreeUnionBranch35_16 - · exact degreeUnionBranch35_17 - · exact degreeUnionBranch35_18 - · exact degreeUnionBranch35_19 - -lemma degreeUnionBranch35_20 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 25 10 degreeUnionState35_20 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 25 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch35_21 - · exact degreeUnionBranch35_22 - · exact degreeUnionBranch35_23 - · exact degreeUnionBranch35_24 - · exact degreeUnionBranch35_25 - · exact degreeUnionBranch35_26 - · exact degreeUnionBranch35_27 - -lemma degreeUnionBranch35_8 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 35 34 degreeHalfRegions35 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 34 at hb - change 35 ≤ 8*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch35_9 - · exact degreeUnionBranch35_10 - · exact degreeUnionBranch35_11 - · exact degreeUnionBranch35_12 - · exact degreeUnionBranch35_13 - · exact degreeUnionBranch35_20 - · exact degreeUnionBranch35_28 - · exact degreeUnionBranch35_29 - · exact degreeUnionBranch35_30 - · exact degreeUnionBranch35_31 - · exact degreeUnionBranch35_32 - · exact degreeUnionBranch35_33 - · exact degreeUnionBranch35_34 - · exact degreeUnionBranch35_35 - · exact degreeUnionBranch35_36 - · exact degreeUnionBranch35_37 - · exact degreeUnionBranch35_38 - · exact degreeUnionBranch35_39 - · exact degreeUnionBranch35_40 - · exact degreeUnionBranch35_41 - · exact degreeUnionBranch35_42 - · exact degreeUnionBranch35_43 - · exact degreeUnionBranch35_44 - · exact degreeUnionBranch35_45 - · exact degreeUnionBranch35_46 - · exact degreeUnionBranch35_47 - · exact degreeUnionBranch35_48 - · exact degreeUnionBranch35_49 - · exact degreeUnionBranch35_50 - · exact degreeUnionBranch35_51 - -lemma degreeUnionBranch35_57 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 27 8 degreeUnionState35_57 [8] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 27 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch35_58 - · exact degreeUnionBranch35_59 - · exact degreeUnionBranch35_60 - · exact degreeUnionBranch35_61 - · exact degreeUnionBranch35_62 - -lemma degreeUnionBranch35_63 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 26 9 degreeUnionState35_63 [9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 26 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch35_64 - · exact degreeUnionBranch35_65 - · exact degreeUnionBranch35_66 - · exact degreeUnionBranch35_67 - · exact degreeUnionBranch35_68 - · exact degreeUnionBranch35_69 - -lemma degreeUnionBranch35_70 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 25 10 degreeUnionState35_70 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 25 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch35_71 - · exact degreeUnionBranch35_72 - · exact degreeUnionBranch35_73 - · exact degreeUnionBranch35_74 - · exact degreeUnionBranch35_75 - · exact degreeUnionBranch35_76 - · exact degreeUnionBranch35_77 - -lemma degreeUnionBranch35_52 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 35 34 degreeHalfRegions35 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 34 at hb - change 35 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch35_53 - · exact degreeUnionBranch35_54 - · exact degreeUnionBranch35_55 - · exact degreeUnionBranch35_56 - · exact degreeUnionBranch35_57 - · exact degreeUnionBranch35_63 - · exact degreeUnionBranch35_70 - · exact degreeUnionBranch35_78 - · exact degreeUnionBranch35_79 - · exact degreeUnionBranch35_80 - · exact degreeUnionBranch35_81 - · exact degreeUnionBranch35_82 - · exact degreeUnionBranch35_83 - · exact degreeUnionBranch35_84 - · exact degreeUnionBranch35_85 - · exact degreeUnionBranch35_86 - · exact degreeUnionBranch35_87 - · exact degreeUnionBranch35_88 - · exact degreeUnionBranch35_89 - · exact degreeUnionBranch35_90 - · exact degreeUnionBranch35_91 - · exact degreeUnionBranch35_92 - · exact degreeUnionBranch35_93 - · exact degreeUnionBranch35_94 - · exact degreeUnionBranch35_95 - · exact degreeUnionBranch35_96 - · exact degreeUnionBranch35_97 - · exact degreeUnionBranch35_98 - · exact degreeUnionBranch35_99 - · exact degreeUnionBranch35_100 - · exact degreeUnionBranch35_101 - -lemma degreeUnionBranch35_107 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 27 8 degreeUnionState35_107 [8] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 27 ≤ 9*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch35_108 - · exact degreeUnionBranch35_109 - · exact degreeUnionBranch35_110 - · exact degreeUnionBranch35_111 - · exact degreeUnionBranch35_112 - · exact degreeUnionBranch35_113 - -lemma degreeUnionBranch35_114 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 26 9 degreeUnionState35_114 [9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 26 ≤ 9*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch35_115 - · exact degreeUnionBranch35_116 - · exact degreeUnionBranch35_117 - · exact degreeUnionBranch35_118 - · exact degreeUnionBranch35_119 - · exact degreeUnionBranch35_120 - · exact degreeUnionBranch35_121 - -lemma degreeUnionBranch35_122 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 25 10 degreeUnionState35_122 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 10 at hb - change 25 ≤ 9*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch35_123 - · exact degreeUnionBranch35_124 - · exact degreeUnionBranch35_125 - · exact degreeUnionBranch35_126 - · exact degreeUnionBranch35_127 - · exact degreeUnionBranch35_128 - · exact degreeUnionBranch35_129 - · exact degreeUnionBranch35_130 - -lemma degreeUnionBranch35_102 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 10 35 34 degreeHalfRegions35 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 34 at hb - change 35 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch35_103 - · exact degreeUnionBranch35_104 - · exact degreeUnionBranch35_105 - · exact degreeUnionBranch35_106 - · exact degreeUnionBranch35_107 - · exact degreeUnionBranch35_114 - · exact degreeUnionBranch35_122 - · exact degreeUnionBranch35_131 - · exact degreeUnionBranch35_132 - · exact degreeUnionBranch35_133 - · exact degreeUnionBranch35_134 - · exact degreeUnionBranch35_135 - · exact degreeUnionBranch35_136 - · exact degreeUnionBranch35_137 - · exact degreeUnionBranch35_138 - · exact degreeUnionBranch35_139 - · exact degreeUnionBranch35_140 - · exact degreeUnionBranch35_141 - · exact degreeUnionBranch35_142 - · exact degreeUnionBranch35_143 - · exact degreeUnionBranch35_144 - · exact degreeUnionBranch35_145 - · exact degreeUnionBranch35_146 - · exact degreeUnionBranch35_147 - · exact degreeUnionBranch35_148 - · exact degreeUnionBranch35_149 - · exact degreeUnionBranch35_150 - · exact degreeUnionBranch35_151 - · exact degreeUnionBranch35_152 - · exact degreeUnionBranch35_153 - · exact degreeUnionBranch35_154 - -lemma degreeUnionCheck35 : ∀ h ≤ 15, - checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) h 35 34 degreeHalfRegions35 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch35_0 - · exact degreeUnionBranch35_1 - · exact degreeUnionBranch35_2 - · exact degreeUnionBranch35_3 - · exact degreeUnionBranch35_4 - · exact degreeUnionBranch35_5 - · exact degreeUnionBranch35_6 - · exact degreeUnionBranch35_7 - · exact degreeUnionBranch35_8 - · exact degreeUnionBranch35_52 - · exact degreeUnionBranch35_102 - · exact degreeUnionBranch35_155 - · exact degreeUnionBranch35_156 - · exact degreeUnionBranch35_157 - · exact degreeUnionBranch35_158 - · exact degreeUnionBranch35_159 - -lemma degreeHalfCover35 : ∀ R ∈ degreeRegions35, - R ∈ degreeHalfRegions35 ∨ (R.2,R.1) ∈ degreeHalfRegions35 := by decide +kernel - -lemma degreeDiagramRegionsChecked35 : ∀ R ∈ degreeRegions35, - ∀ μ : YoungDiagram, μ.card = 35 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP35 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck35 degreeHalfHeight35 degreeHalfWidth35 - degreeHalfCover35 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves35 + +namespace OAI + +/-! Degree Regions 35. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch35_13 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 26 9 degreeUnionState35_13 [9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 26 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch35_14 + · exact degreeUnionBranch35_15 + · exact degreeUnionBranch35_16 + · exact degreeUnionBranch35_17 + · exact degreeUnionBranch35_18 + · exact degreeUnionBranch35_19 + +lemma degreeUnionBranch35_20 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 7 25 10 degreeUnionState35_20 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 25 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch35_21 + · exact degreeUnionBranch35_22 + · exact degreeUnionBranch35_23 + · exact degreeUnionBranch35_24 + · exact degreeUnionBranch35_25 + · exact degreeUnionBranch35_26 + · exact degreeUnionBranch35_27 + +lemma degreeUnionBranch35_8 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 35 34 degreeHalfRegions35 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 34 at hb + change 35 ≤ 8*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch35_9 + · exact degreeUnionBranch35_10 + · exact degreeUnionBranch35_11 + · exact degreeUnionBranch35_12 + · exact degreeUnionBranch35_13 + · exact degreeUnionBranch35_20 + · exact degreeUnionBranch35_28 + · exact degreeUnionBranch35_29 + · exact degreeUnionBranch35_30 + · exact degreeUnionBranch35_31 + · exact degreeUnionBranch35_32 + · exact degreeUnionBranch35_33 + · exact degreeUnionBranch35_34 + · exact degreeUnionBranch35_35 + · exact degreeUnionBranch35_36 + · exact degreeUnionBranch35_37 + · exact degreeUnionBranch35_38 + · exact degreeUnionBranch35_39 + · exact degreeUnionBranch35_40 + · exact degreeUnionBranch35_41 + · exact degreeUnionBranch35_42 + · exact degreeUnionBranch35_43 + · exact degreeUnionBranch35_44 + · exact degreeUnionBranch35_45 + · exact degreeUnionBranch35_46 + · exact degreeUnionBranch35_47 + · exact degreeUnionBranch35_48 + · exact degreeUnionBranch35_49 + · exact degreeUnionBranch35_50 + · exact degreeUnionBranch35_51 + +lemma degreeUnionBranch35_57 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 27 8 degreeUnionState35_57 [8] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 27 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch35_58 + · exact degreeUnionBranch35_59 + · exact degreeUnionBranch35_60 + · exact degreeUnionBranch35_61 + · exact degreeUnionBranch35_62 + +lemma degreeUnionBranch35_63 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 26 9 degreeUnionState35_63 [9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 26 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch35_64 + · exact degreeUnionBranch35_65 + · exact degreeUnionBranch35_66 + · exact degreeUnionBranch35_67 + · exact degreeUnionBranch35_68 + · exact degreeUnionBranch35_69 + +lemma degreeUnionBranch35_70 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 8 25 10 degreeUnionState35_70 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 25 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch35_71 + · exact degreeUnionBranch35_72 + · exact degreeUnionBranch35_73 + · exact degreeUnionBranch35_74 + · exact degreeUnionBranch35_75 + · exact degreeUnionBranch35_76 + · exact degreeUnionBranch35_77 + +lemma degreeUnionBranch35_52 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 35 34 degreeHalfRegions35 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 34 at hb + change 35 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch35_53 + · exact degreeUnionBranch35_54 + · exact degreeUnionBranch35_55 + · exact degreeUnionBranch35_56 + · exact degreeUnionBranch35_57 + · exact degreeUnionBranch35_63 + · exact degreeUnionBranch35_70 + · exact degreeUnionBranch35_78 + · exact degreeUnionBranch35_79 + · exact degreeUnionBranch35_80 + · exact degreeUnionBranch35_81 + · exact degreeUnionBranch35_82 + · exact degreeUnionBranch35_83 + · exact degreeUnionBranch35_84 + · exact degreeUnionBranch35_85 + · exact degreeUnionBranch35_86 + · exact degreeUnionBranch35_87 + · exact degreeUnionBranch35_88 + · exact degreeUnionBranch35_89 + · exact degreeUnionBranch35_90 + · exact degreeUnionBranch35_91 + · exact degreeUnionBranch35_92 + · exact degreeUnionBranch35_93 + · exact degreeUnionBranch35_94 + · exact degreeUnionBranch35_95 + · exact degreeUnionBranch35_96 + · exact degreeUnionBranch35_97 + · exact degreeUnionBranch35_98 + · exact degreeUnionBranch35_99 + · exact degreeUnionBranch35_100 + · exact degreeUnionBranch35_101 + +lemma degreeUnionBranch35_107 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 27 8 degreeUnionState35_107 [8] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 27 ≤ 9*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch35_108 + · exact degreeUnionBranch35_109 + · exact degreeUnionBranch35_110 + · exact degreeUnionBranch35_111 + · exact degreeUnionBranch35_112 + · exact degreeUnionBranch35_113 + +lemma degreeUnionBranch35_114 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 26 9 degreeUnionState35_114 [9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 26 ≤ 9*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch35_115 + · exact degreeUnionBranch35_116 + · exact degreeUnionBranch35_117 + · exact degreeUnionBranch35_118 + · exact degreeUnionBranch35_119 + · exact degreeUnionBranch35_120 + · exact degreeUnionBranch35_121 + +lemma degreeUnionBranch35_122 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 9 25 10 degreeUnionState35_122 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 10 at hb + change 25 ≤ 9*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch35_123 + · exact degreeUnionBranch35_124 + · exact degreeUnionBranch35_125 + · exact degreeUnionBranch35_126 + · exact degreeUnionBranch35_127 + · exact degreeUnionBranch35_128 + · exact degreeUnionBranch35_129 + · exact degreeUnionBranch35_130 + +lemma degreeUnionBranch35_102 : checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) 10 35 34 degreeHalfRegions35 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 34 at hb + change 35 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch35_103 + · exact degreeUnionBranch35_104 + · exact degreeUnionBranch35_105 + · exact degreeUnionBranch35_106 + · exact degreeUnionBranch35_107 + · exact degreeUnionBranch35_114 + · exact degreeUnionBranch35_122 + · exact degreeUnionBranch35_131 + · exact degreeUnionBranch35_132 + · exact degreeUnionBranch35_133 + · exact degreeUnionBranch35_134 + · exact degreeUnionBranch35_135 + · exact degreeUnionBranch35_136 + · exact degreeUnionBranch35_137 + · exact degreeUnionBranch35_138 + · exact degreeUnionBranch35_139 + · exact degreeUnionBranch35_140 + · exact degreeUnionBranch35_141 + · exact degreeUnionBranch35_142 + · exact degreeUnionBranch35_143 + · exact degreeUnionBranch35_144 + · exact degreeUnionBranch35_145 + · exact degreeUnionBranch35_146 + · exact degreeUnionBranch35_147 + · exact degreeUnionBranch35_148 + · exact degreeUnionBranch35_149 + · exact degreeUnionBranch35_150 + · exact degreeUnionBranch35_151 + · exact degreeUnionBranch35_152 + · exact degreeUnionBranch35_153 + · exact degreeUnionBranch35_154 + +lemma degreeUnionCheck35 : ∀ h ≤ 15, + checkRegionPrefixes (quickResidual 6 7 degreeQs35 degreeTree35) h 35 34 degreeHalfRegions35 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch35_0 + · exact degreeUnionBranch35_1 + · exact degreeUnionBranch35_2 + · exact degreeUnionBranch35_3 + · exact degreeUnionBranch35_4 + · exact degreeUnionBranch35_5 + · exact degreeUnionBranch35_6 + · exact degreeUnionBranch35_7 + · exact degreeUnionBranch35_8 + · exact degreeUnionBranch35_52 + · exact degreeUnionBranch35_102 + · exact degreeUnionBranch35_155 + · exact degreeUnionBranch35_156 + · exact degreeUnionBranch35_157 + · exact degreeUnionBranch35_158 + · exact degreeUnionBranch35_159 + +lemma degreeHalfCover35 : ∀ R ∈ degreeRegions35, + R ∈ degreeHalfRegions35 ∨ (R.2,R.1) ∈ degreeHalfRegions35 := by decide +kernel + +lemma degreeDiagramRegionsChecked35 : ∀ R ∈ degreeRegions35, + ∀ μ : YoungDiagram, μ.card = 35 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP35 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck35 degreeHalfHeight35 degreeHalfWidth35 + degreeHalfCover35 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions37.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions37.lean index 34f299ac296b35f66388cccbe6b0a48cb6119603..709a534aab820be1d6536e34d3408154628260f3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions37.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions37.lean @@ -1,49 +1,49 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves37 - -namespace OAI - -/-! Degree Regions 37. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionCheck37 : ∀ h ≤ 17, - checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) h 37 17 degreeHalfRegions37 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch37_0 - · exact degreeUnionBranch37_1 - · exact degreeUnionBranch37_2 - · exact degreeUnionBranch37_3 - · exact degreeUnionBranch37_4 - · exact degreeUnionBranch37_5 - · exact degreeUnionBranch37_6 - · exact degreeUnionBranch37_7 - · exact degreeUnionBranch37_8 - · exact degreeUnionBranch37_9 - · exact degreeUnionBranch37_10 - · exact degreeUnionBranch37_11 - · exact degreeUnionBranch37_12 - · exact degreeUnionBranch37_13 - · exact degreeUnionBranch37_14 - · exact degreeUnionBranch37_15 - · exact degreeUnionBranch37_16 - · exact degreeUnionBranch37_17 - -lemma degreeHalfCover37 : ∀ R ∈ degreeRegions37, - R ∈ degreeHalfRegions37 ∨ (R.2,R.1) ∈ degreeHalfRegions37 := by decide +kernel - -lemma degreeDiagramRegionsChecked37 : ∀ R ∈ degreeRegions37, - ∀ μ : YoungDiagram, μ.card = 37 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP37 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck37 degreeHalfHeight37 degreeHalfWidth37 - degreeHalfCover37 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves37 + +namespace OAI + +/-! Degree Regions 37. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionCheck37 : ∀ h ≤ 17, + checkRegionPrefixes (quickResidual 6 8 degreeQs37 degreeTree37) h 37 17 degreeHalfRegions37 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch37_0 + · exact degreeUnionBranch37_1 + · exact degreeUnionBranch37_2 + · exact degreeUnionBranch37_3 + · exact degreeUnionBranch37_4 + · exact degreeUnionBranch37_5 + · exact degreeUnionBranch37_6 + · exact degreeUnionBranch37_7 + · exact degreeUnionBranch37_8 + · exact degreeUnionBranch37_9 + · exact degreeUnionBranch37_10 + · exact degreeUnionBranch37_11 + · exact degreeUnionBranch37_12 + · exact degreeUnionBranch37_13 + · exact degreeUnionBranch37_14 + · exact degreeUnionBranch37_15 + · exact degreeUnionBranch37_16 + · exact degreeUnionBranch37_17 + +lemma degreeHalfCover37 : ∀ R ∈ degreeRegions37, + R ∈ degreeHalfRegions37 ∨ (R.2,R.1) ∈ degreeHalfRegions37 := by decide +kernel + +lemma degreeDiagramRegionsChecked37 : ∀ R ∈ degreeRegions37, + ∀ μ : YoungDiagram, μ.card = 37 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP37 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck37 degreeHalfHeight37 degreeHalfWidth37 + degreeHalfCover37 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions39.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions39.lean index 5f7b7502722ede027ca38144801e3e7e841c6a48..92fc64f963d528186a2e9a1dbd8da99b754695e8 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions39.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions39.lean @@ -1,583 +1,583 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves39 - -namespace OAI - -/-! Degree Regions 39. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch39_12 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 31 8 degreeUnionState39_12 [8] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 8 at hb - change 31 ≤ 7*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_13 - · exact degreeUnionBranch39_14 - · exact degreeUnionBranch39_15 - · exact degreeUnionBranch39_16 - -lemma degreeUnionBranch39_17 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 30 9 degreeUnionState39_17 [9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 9 at hb - change 30 ≤ 7*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_18 - · exact degreeUnionBranch39_19 - · exact degreeUnionBranch39_20 - · exact degreeUnionBranch39_21 - · exact degreeUnionBranch39_22 - -lemma degreeUnionBranch39_23 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 29 10 degreeUnionState39_23 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 10 at hb - change 29 ≤ 7*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_24 - · exact degreeUnionBranch39_25 - · exact degreeUnionBranch39_26 - · exact degreeUnionBranch39_27 - · exact degreeUnionBranch39_28 - · exact degreeUnionBranch39_29 - -lemma degreeUnionBranch39_30 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 28 11 degreeUnionState39_30 [11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 11 at hb - change 28 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_31 - · exact degreeUnionBranch39_32 - · exact degreeUnionBranch39_33 - · exact degreeUnionBranch39_34 - · exact degreeUnionBranch39_35 - · exact degreeUnionBranch39_36 - · exact degreeUnionBranch39_37 - · exact degreeUnionBranch39_38 - -lemma degreeUnionBranch39_39 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 27 12 degreeUnionState39_39 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 27 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_40 - · exact degreeUnionBranch39_41 - · exact degreeUnionBranch39_42 - · exact degreeUnionBranch39_43 - · exact degreeUnionBranch39_44 - · exact degreeUnionBranch39_45 - · exact degreeUnionBranch39_46 - · exact degreeUnionBranch39_47 - · exact degreeUnionBranch39_48 - -lemma degreeUnionBranch39_49 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 26 13 degreeUnionState39_49 [13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 13 at hb - change 26 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_50 - · exact degreeUnionBranch39_51 - · exact degreeUnionBranch39_52 - · exact degreeUnionBranch39_53 - · exact degreeUnionBranch39_54 - · exact degreeUnionBranch39_55 - · exact degreeUnionBranch39_56 - · exact degreeUnionBranch39_57 - · exact degreeUnionBranch39_58 - · exact degreeUnionBranch39_59 - -lemma degreeUnionBranch39_60 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 25 14 degreeUnionState39_60 [14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 14 at hb - change 25 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_61 - · exact degreeUnionBranch39_62 - · exact degreeUnionBranch39_63 - · exact degreeUnionBranch39_64 - · exact degreeUnionBranch39_65 - · exact degreeUnionBranch39_66 - · exact degreeUnionBranch39_67 - · exact degreeUnionBranch39_68 - · exact degreeUnionBranch39_69 - · exact degreeUnionBranch39_70 - · exact degreeUnionBranch39_71 - -lemma degreeUnionBranch39_72 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 24 15 degreeUnionState39_72 [15] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 15 at hb - change 24 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_73 - · exact degreeUnionBranch39_74 - · exact degreeUnionBranch39_75 - · exact degreeUnionBranch39_76 - · exact degreeUnionBranch39_77 - · exact degreeUnionBranch39_78 - · exact degreeUnionBranch39_79 - · exact degreeUnionBranch39_80 - · exact degreeUnionBranch39_81 - · exact degreeUnionBranch39_82 - · exact degreeUnionBranch39_83 - · exact degreeUnionBranch39_84 - -lemma degreeUnionBranch39_85 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 23 16 degreeUnionState39_85 [16] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 16 at hb - change 23 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_86 - · exact degreeUnionBranch39_87 - · exact degreeUnionBranch39_88 - · exact degreeUnionBranch39_89 - · exact degreeUnionBranch39_90 - · exact degreeUnionBranch39_91 - · exact degreeUnionBranch39_92 - · exact degreeUnionBranch39_93 - · exact degreeUnionBranch39_94 - · exact degreeUnionBranch39_95 - · exact degreeUnionBranch39_96 - · exact degreeUnionBranch39_97 - · exact degreeUnionBranch39_98 - -lemma degreeUnionBranch39_8 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 39 38 degreeHalfRegions39 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 38 at hb - change 39 ≤ 8*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_9 - · exact degreeUnionBranch39_10 - · exact degreeUnionBranch39_11 - · exact degreeUnionBranch39_12 - · exact degreeUnionBranch39_17 - · exact degreeUnionBranch39_23 - · exact degreeUnionBranch39_30 - · exact degreeUnionBranch39_39 - · exact degreeUnionBranch39_49 - · exact degreeUnionBranch39_60 - · exact degreeUnionBranch39_72 - · exact degreeUnionBranch39_85 - · exact degreeUnionBranch39_99 - · exact degreeUnionBranch39_100 - · exact degreeUnionBranch39_101 - · exact degreeUnionBranch39_102 - · exact degreeUnionBranch39_103 - · exact degreeUnionBranch39_104 - · exact degreeUnionBranch39_105 - · exact degreeUnionBranch39_106 - · exact degreeUnionBranch39_107 - · exact degreeUnionBranch39_108 - · exact degreeUnionBranch39_109 - · exact degreeUnionBranch39_110 - · exact degreeUnionBranch39_111 - · exact degreeUnionBranch39_112 - · exact degreeUnionBranch39_113 - · exact degreeUnionBranch39_114 - · exact degreeUnionBranch39_115 - · exact degreeUnionBranch39_116 - · exact degreeUnionBranch39_117 - · exact degreeUnionBranch39_118 - · exact degreeUnionBranch39_119 - · exact degreeUnionBranch39_120 - -lemma degreeUnionBranch39_125 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 31 8 degreeUnionState39_125 [8] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 31 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_126 - · exact degreeUnionBranch39_127 - · exact degreeUnionBranch39_128 - · exact degreeUnionBranch39_129 - · exact degreeUnionBranch39_130 - -lemma degreeUnionBranch39_131 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 30 9 degreeUnionState39_131 [9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 30 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_132 - · exact degreeUnionBranch39_133 - · exact degreeUnionBranch39_134 - · exact degreeUnionBranch39_135 - · exact degreeUnionBranch39_136 - · exact degreeUnionBranch39_137 - -lemma degreeUnionBranch39_138 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 29 10 degreeUnionState39_138 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 29 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_139 - · exact degreeUnionBranch39_140 - · exact degreeUnionBranch39_141 - · exact degreeUnionBranch39_142 - · exact degreeUnionBranch39_143 - · exact degreeUnionBranch39_144 - · exact degreeUnionBranch39_145 - -lemma degreeUnionBranch39_146 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 28 11 degreeUnionState39_146 [11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 28 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_147 - · exact degreeUnionBranch39_148 - · exact degreeUnionBranch39_149 - · exact degreeUnionBranch39_150 - · exact degreeUnionBranch39_151 - · exact degreeUnionBranch39_152 - · exact degreeUnionBranch39_153 - · exact degreeUnionBranch39_154 - -lemma degreeUnionBranch39_155 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 27 12 degreeUnionState39_155 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 27 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_156 - · exact degreeUnionBranch39_157 - · exact degreeUnionBranch39_158 - · exact degreeUnionBranch39_159 - · exact degreeUnionBranch39_160 - · exact degreeUnionBranch39_161 - · exact degreeUnionBranch39_162 - · exact degreeUnionBranch39_163 - · exact degreeUnionBranch39_164 - -lemma degreeUnionBranch39_165 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 26 13 degreeUnionState39_165 [13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 13 at hb - change 26 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_166 - · exact degreeUnionBranch39_167 - · exact degreeUnionBranch39_168 - · exact degreeUnionBranch39_169 - · exact degreeUnionBranch39_170 - · exact degreeUnionBranch39_171 - · exact degreeUnionBranch39_172 - · exact degreeUnionBranch39_173 - · exact degreeUnionBranch39_174 - · exact degreeUnionBranch39_175 - -lemma degreeUnionBranch39_176 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 25 14 degreeUnionState39_176 [14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 14 at hb - change 25 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_177 - · exact degreeUnionBranch39_178 - · exact degreeUnionBranch39_179 - · exact degreeUnionBranch39_180 - · exact degreeUnionBranch39_181 - · exact degreeUnionBranch39_182 - · exact degreeUnionBranch39_183 - · exact degreeUnionBranch39_184 - · exact degreeUnionBranch39_185 - · exact degreeUnionBranch39_186 - · exact degreeUnionBranch39_187 - -lemma degreeUnionBranch39_188 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 24 15 degreeUnionState39_188 [15] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 15 at hb - change 24 ≤ 8*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_189 - · exact degreeUnionBranch39_190 - · exact degreeUnionBranch39_191 - · exact degreeUnionBranch39_192 - · exact degreeUnionBranch39_193 - · exact degreeUnionBranch39_194 - · exact degreeUnionBranch39_195 - · exact degreeUnionBranch39_196 - · exact degreeUnionBranch39_197 - · exact degreeUnionBranch39_198 - · exact degreeUnionBranch39_199 - · exact degreeUnionBranch39_200 - · exact degreeUnionBranch39_201 - -lemma degreeUnionBranch39_121 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 39 38 degreeHalfRegions39 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 38 at hb - change 39 ≤ 9*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_122 - · exact degreeUnionBranch39_123 - · exact degreeUnionBranch39_124 - · exact degreeUnionBranch39_125 - · exact degreeUnionBranch39_131 - · exact degreeUnionBranch39_138 - · exact degreeUnionBranch39_146 - · exact degreeUnionBranch39_155 - · exact degreeUnionBranch39_165 - · exact degreeUnionBranch39_176 - · exact degreeUnionBranch39_188 - · exact degreeUnionBranch39_202 - · exact degreeUnionBranch39_203 - · exact degreeUnionBranch39_204 - · exact degreeUnionBranch39_205 - · exact degreeUnionBranch39_206 - · exact degreeUnionBranch39_207 - · exact degreeUnionBranch39_208 - · exact degreeUnionBranch39_209 - · exact degreeUnionBranch39_210 - · exact degreeUnionBranch39_211 - · exact degreeUnionBranch39_212 - · exact degreeUnionBranch39_213 - · exact degreeUnionBranch39_214 - · exact degreeUnionBranch39_215 - · exact degreeUnionBranch39_216 - · exact degreeUnionBranch39_217 - · exact degreeUnionBranch39_218 - · exact degreeUnionBranch39_219 - · exact degreeUnionBranch39_220 - · exact degreeUnionBranch39_221 - · exact degreeUnionBranch39_222 - · exact degreeUnionBranch39_223 - · exact degreeUnionBranch39_224 - -lemma degreeUnionBranch39_230 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 31 8 degreeUnionState39_230 [8] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 31 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_231 - · exact degreeUnionBranch39_232 - · exact degreeUnionBranch39_233 - · exact degreeUnionBranch39_234 - · exact degreeUnionBranch39_235 - -lemma degreeUnionBranch39_236 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 30 9 degreeUnionState39_236 [9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 30 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_237 - · exact degreeUnionBranch39_238 - · exact degreeUnionBranch39_239 - · exact degreeUnionBranch39_240 - · exact degreeUnionBranch39_241 - · exact degreeUnionBranch39_242 - -lemma degreeUnionBranch39_243 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 29 10 degreeUnionState39_243 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 29 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_244 - · exact degreeUnionBranch39_245 - · exact degreeUnionBranch39_246 - · exact degreeUnionBranch39_247 - · exact degreeUnionBranch39_248 - · exact degreeUnionBranch39_249 - · exact degreeUnionBranch39_250 - -lemma degreeUnionBranch39_251 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 28 11 degreeUnionState39_251 [11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 28 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_252 - · exact degreeUnionBranch39_253 - · exact degreeUnionBranch39_254 - · exact degreeUnionBranch39_255 - · exact degreeUnionBranch39_256 - · exact degreeUnionBranch39_257 - · exact degreeUnionBranch39_258 - · exact degreeUnionBranch39_259 - -lemma degreeUnionBranch39_260 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 27 12 degreeUnionState39_260 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 27 ≤ 9*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_261 - · exact degreeUnionBranch39_262 - · exact degreeUnionBranch39_263 - · exact degreeUnionBranch39_264 - · exact degreeUnionBranch39_265 - · exact degreeUnionBranch39_266 - · exact degreeUnionBranch39_267 - · exact degreeUnionBranch39_268 - · exact degreeUnionBranch39_269 - · exact degreeUnionBranch39_270 - -lemma degreeUnionBranch39_271 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 26 13 degreeUnionState39_271 [13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 13 at hb - change 26 ≤ 9*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_272 - · exact degreeUnionBranch39_273 - · exact degreeUnionBranch39_274 - · exact degreeUnionBranch39_275 - · exact degreeUnionBranch39_276 - · exact degreeUnionBranch39_277 - · exact degreeUnionBranch39_278 - · exact degreeUnionBranch39_279 - · exact degreeUnionBranch39_280 - · exact degreeUnionBranch39_281 - · exact degreeUnionBranch39_282 - -lemma degreeUnionBranch39_225 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 10 39 38 degreeHalfRegions39 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 38 at hb - change 39 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch39_226 - · exact degreeUnionBranch39_227 - · exact degreeUnionBranch39_228 - · exact degreeUnionBranch39_229 - · exact degreeUnionBranch39_230 - · exact degreeUnionBranch39_236 - · exact degreeUnionBranch39_243 - · exact degreeUnionBranch39_251 - · exact degreeUnionBranch39_260 - · exact degreeUnionBranch39_271 - · exact degreeUnionBranch39_283 - · exact degreeUnionBranch39_284 - · exact degreeUnionBranch39_285 - · exact degreeUnionBranch39_286 - · exact degreeUnionBranch39_287 - · exact degreeUnionBranch39_288 - · exact degreeUnionBranch39_289 - · exact degreeUnionBranch39_290 - · exact degreeUnionBranch39_291 - · exact degreeUnionBranch39_292 - · exact degreeUnionBranch39_293 - · exact degreeUnionBranch39_294 - · exact degreeUnionBranch39_295 - · exact degreeUnionBranch39_296 - · exact degreeUnionBranch39_297 - · exact degreeUnionBranch39_298 - · exact degreeUnionBranch39_299 - · exact degreeUnionBranch39_300 - · exact degreeUnionBranch39_301 - · exact degreeUnionBranch39_302 - · exact degreeUnionBranch39_303 - · exact degreeUnionBranch39_304 - · exact degreeUnionBranch39_305 - · exact degreeUnionBranch39_306 - · exact degreeUnionBranch39_307 - -lemma degreeUnionCheck39 : ∀ h ≤ 19, - checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) h 39 38 degreeHalfRegions39 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch39_0 - · exact degreeUnionBranch39_1 - · exact degreeUnionBranch39_2 - · exact degreeUnionBranch39_3 - · exact degreeUnionBranch39_4 - · exact degreeUnionBranch39_5 - · exact degreeUnionBranch39_6 - · exact degreeUnionBranch39_7 - · exact degreeUnionBranch39_8 - · exact degreeUnionBranch39_121 - · exact degreeUnionBranch39_225 - · exact degreeUnionBranch39_308 - · exact degreeUnionBranch39_309 - · exact degreeUnionBranch39_310 - · exact degreeUnionBranch39_311 - · exact degreeUnionBranch39_312 - · exact degreeUnionBranch39_313 - · exact degreeUnionBranch39_314 - · exact degreeUnionBranch39_315 - · exact degreeUnionBranch39_316 - -lemma degreeHalfCover39 : ∀ R ∈ degreeRegions39, - R ∈ degreeHalfRegions39 ∨ (R.2,R.1) ∈ degreeHalfRegions39 := by decide +kernel - -lemma degreeDiagramRegionsChecked39 : ∀ R ∈ degreeRegions39, - ∀ μ : YoungDiagram, μ.card = 39 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP39 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck39 degreeHalfHeight39 degreeHalfWidth39 - degreeHalfCover39 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves39 + +namespace OAI + +/-! Degree Regions 39. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch39_12 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 31 8 degreeUnionState39_12 [8] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 8 at hb + change 31 ≤ 7*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_13 + · exact degreeUnionBranch39_14 + · exact degreeUnionBranch39_15 + · exact degreeUnionBranch39_16 + +lemma degreeUnionBranch39_17 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 30 9 degreeUnionState39_17 [9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 9 at hb + change 30 ≤ 7*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_18 + · exact degreeUnionBranch39_19 + · exact degreeUnionBranch39_20 + · exact degreeUnionBranch39_21 + · exact degreeUnionBranch39_22 + +lemma degreeUnionBranch39_23 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 29 10 degreeUnionState39_23 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 10 at hb + change 29 ≤ 7*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_24 + · exact degreeUnionBranch39_25 + · exact degreeUnionBranch39_26 + · exact degreeUnionBranch39_27 + · exact degreeUnionBranch39_28 + · exact degreeUnionBranch39_29 + +lemma degreeUnionBranch39_30 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 28 11 degreeUnionState39_30 [11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 11 at hb + change 28 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_31 + · exact degreeUnionBranch39_32 + · exact degreeUnionBranch39_33 + · exact degreeUnionBranch39_34 + · exact degreeUnionBranch39_35 + · exact degreeUnionBranch39_36 + · exact degreeUnionBranch39_37 + · exact degreeUnionBranch39_38 + +lemma degreeUnionBranch39_39 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 27 12 degreeUnionState39_39 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 27 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_40 + · exact degreeUnionBranch39_41 + · exact degreeUnionBranch39_42 + · exact degreeUnionBranch39_43 + · exact degreeUnionBranch39_44 + · exact degreeUnionBranch39_45 + · exact degreeUnionBranch39_46 + · exact degreeUnionBranch39_47 + · exact degreeUnionBranch39_48 + +lemma degreeUnionBranch39_49 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 26 13 degreeUnionState39_49 [13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 13 at hb + change 26 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_50 + · exact degreeUnionBranch39_51 + · exact degreeUnionBranch39_52 + · exact degreeUnionBranch39_53 + · exact degreeUnionBranch39_54 + · exact degreeUnionBranch39_55 + · exact degreeUnionBranch39_56 + · exact degreeUnionBranch39_57 + · exact degreeUnionBranch39_58 + · exact degreeUnionBranch39_59 + +lemma degreeUnionBranch39_60 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 25 14 degreeUnionState39_60 [14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 14 at hb + change 25 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_61 + · exact degreeUnionBranch39_62 + · exact degreeUnionBranch39_63 + · exact degreeUnionBranch39_64 + · exact degreeUnionBranch39_65 + · exact degreeUnionBranch39_66 + · exact degreeUnionBranch39_67 + · exact degreeUnionBranch39_68 + · exact degreeUnionBranch39_69 + · exact degreeUnionBranch39_70 + · exact degreeUnionBranch39_71 + +lemma degreeUnionBranch39_72 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 24 15 degreeUnionState39_72 [15] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 15 at hb + change 24 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_73 + · exact degreeUnionBranch39_74 + · exact degreeUnionBranch39_75 + · exact degreeUnionBranch39_76 + · exact degreeUnionBranch39_77 + · exact degreeUnionBranch39_78 + · exact degreeUnionBranch39_79 + · exact degreeUnionBranch39_80 + · exact degreeUnionBranch39_81 + · exact degreeUnionBranch39_82 + · exact degreeUnionBranch39_83 + · exact degreeUnionBranch39_84 + +lemma degreeUnionBranch39_85 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 7 23 16 degreeUnionState39_85 [16] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 16 at hb + change 23 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_86 + · exact degreeUnionBranch39_87 + · exact degreeUnionBranch39_88 + · exact degreeUnionBranch39_89 + · exact degreeUnionBranch39_90 + · exact degreeUnionBranch39_91 + · exact degreeUnionBranch39_92 + · exact degreeUnionBranch39_93 + · exact degreeUnionBranch39_94 + · exact degreeUnionBranch39_95 + · exact degreeUnionBranch39_96 + · exact degreeUnionBranch39_97 + · exact degreeUnionBranch39_98 + +lemma degreeUnionBranch39_8 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 39 38 degreeHalfRegions39 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 38 at hb + change 39 ≤ 8*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_9 + · exact degreeUnionBranch39_10 + · exact degreeUnionBranch39_11 + · exact degreeUnionBranch39_12 + · exact degreeUnionBranch39_17 + · exact degreeUnionBranch39_23 + · exact degreeUnionBranch39_30 + · exact degreeUnionBranch39_39 + · exact degreeUnionBranch39_49 + · exact degreeUnionBranch39_60 + · exact degreeUnionBranch39_72 + · exact degreeUnionBranch39_85 + · exact degreeUnionBranch39_99 + · exact degreeUnionBranch39_100 + · exact degreeUnionBranch39_101 + · exact degreeUnionBranch39_102 + · exact degreeUnionBranch39_103 + · exact degreeUnionBranch39_104 + · exact degreeUnionBranch39_105 + · exact degreeUnionBranch39_106 + · exact degreeUnionBranch39_107 + · exact degreeUnionBranch39_108 + · exact degreeUnionBranch39_109 + · exact degreeUnionBranch39_110 + · exact degreeUnionBranch39_111 + · exact degreeUnionBranch39_112 + · exact degreeUnionBranch39_113 + · exact degreeUnionBranch39_114 + · exact degreeUnionBranch39_115 + · exact degreeUnionBranch39_116 + · exact degreeUnionBranch39_117 + · exact degreeUnionBranch39_118 + · exact degreeUnionBranch39_119 + · exact degreeUnionBranch39_120 + +lemma degreeUnionBranch39_125 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 31 8 degreeUnionState39_125 [8] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 31 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_126 + · exact degreeUnionBranch39_127 + · exact degreeUnionBranch39_128 + · exact degreeUnionBranch39_129 + · exact degreeUnionBranch39_130 + +lemma degreeUnionBranch39_131 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 30 9 degreeUnionState39_131 [9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 30 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_132 + · exact degreeUnionBranch39_133 + · exact degreeUnionBranch39_134 + · exact degreeUnionBranch39_135 + · exact degreeUnionBranch39_136 + · exact degreeUnionBranch39_137 + +lemma degreeUnionBranch39_138 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 29 10 degreeUnionState39_138 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 29 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_139 + · exact degreeUnionBranch39_140 + · exact degreeUnionBranch39_141 + · exact degreeUnionBranch39_142 + · exact degreeUnionBranch39_143 + · exact degreeUnionBranch39_144 + · exact degreeUnionBranch39_145 + +lemma degreeUnionBranch39_146 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 28 11 degreeUnionState39_146 [11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 28 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_147 + · exact degreeUnionBranch39_148 + · exact degreeUnionBranch39_149 + · exact degreeUnionBranch39_150 + · exact degreeUnionBranch39_151 + · exact degreeUnionBranch39_152 + · exact degreeUnionBranch39_153 + · exact degreeUnionBranch39_154 + +lemma degreeUnionBranch39_155 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 27 12 degreeUnionState39_155 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 27 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_156 + · exact degreeUnionBranch39_157 + · exact degreeUnionBranch39_158 + · exact degreeUnionBranch39_159 + · exact degreeUnionBranch39_160 + · exact degreeUnionBranch39_161 + · exact degreeUnionBranch39_162 + · exact degreeUnionBranch39_163 + · exact degreeUnionBranch39_164 + +lemma degreeUnionBranch39_165 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 26 13 degreeUnionState39_165 [13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 13 at hb + change 26 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_166 + · exact degreeUnionBranch39_167 + · exact degreeUnionBranch39_168 + · exact degreeUnionBranch39_169 + · exact degreeUnionBranch39_170 + · exact degreeUnionBranch39_171 + · exact degreeUnionBranch39_172 + · exact degreeUnionBranch39_173 + · exact degreeUnionBranch39_174 + · exact degreeUnionBranch39_175 + +lemma degreeUnionBranch39_176 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 25 14 degreeUnionState39_176 [14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 14 at hb + change 25 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_177 + · exact degreeUnionBranch39_178 + · exact degreeUnionBranch39_179 + · exact degreeUnionBranch39_180 + · exact degreeUnionBranch39_181 + · exact degreeUnionBranch39_182 + · exact degreeUnionBranch39_183 + · exact degreeUnionBranch39_184 + · exact degreeUnionBranch39_185 + · exact degreeUnionBranch39_186 + · exact degreeUnionBranch39_187 + +lemma degreeUnionBranch39_188 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 8 24 15 degreeUnionState39_188 [15] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 15 at hb + change 24 ≤ 8*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_189 + · exact degreeUnionBranch39_190 + · exact degreeUnionBranch39_191 + · exact degreeUnionBranch39_192 + · exact degreeUnionBranch39_193 + · exact degreeUnionBranch39_194 + · exact degreeUnionBranch39_195 + · exact degreeUnionBranch39_196 + · exact degreeUnionBranch39_197 + · exact degreeUnionBranch39_198 + · exact degreeUnionBranch39_199 + · exact degreeUnionBranch39_200 + · exact degreeUnionBranch39_201 + +lemma degreeUnionBranch39_121 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 39 38 degreeHalfRegions39 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 38 at hb + change 39 ≤ 9*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_122 + · exact degreeUnionBranch39_123 + · exact degreeUnionBranch39_124 + · exact degreeUnionBranch39_125 + · exact degreeUnionBranch39_131 + · exact degreeUnionBranch39_138 + · exact degreeUnionBranch39_146 + · exact degreeUnionBranch39_155 + · exact degreeUnionBranch39_165 + · exact degreeUnionBranch39_176 + · exact degreeUnionBranch39_188 + · exact degreeUnionBranch39_202 + · exact degreeUnionBranch39_203 + · exact degreeUnionBranch39_204 + · exact degreeUnionBranch39_205 + · exact degreeUnionBranch39_206 + · exact degreeUnionBranch39_207 + · exact degreeUnionBranch39_208 + · exact degreeUnionBranch39_209 + · exact degreeUnionBranch39_210 + · exact degreeUnionBranch39_211 + · exact degreeUnionBranch39_212 + · exact degreeUnionBranch39_213 + · exact degreeUnionBranch39_214 + · exact degreeUnionBranch39_215 + · exact degreeUnionBranch39_216 + · exact degreeUnionBranch39_217 + · exact degreeUnionBranch39_218 + · exact degreeUnionBranch39_219 + · exact degreeUnionBranch39_220 + · exact degreeUnionBranch39_221 + · exact degreeUnionBranch39_222 + · exact degreeUnionBranch39_223 + · exact degreeUnionBranch39_224 + +lemma degreeUnionBranch39_230 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 31 8 degreeUnionState39_230 [8] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 31 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_231 + · exact degreeUnionBranch39_232 + · exact degreeUnionBranch39_233 + · exact degreeUnionBranch39_234 + · exact degreeUnionBranch39_235 + +lemma degreeUnionBranch39_236 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 30 9 degreeUnionState39_236 [9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 30 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_237 + · exact degreeUnionBranch39_238 + · exact degreeUnionBranch39_239 + · exact degreeUnionBranch39_240 + · exact degreeUnionBranch39_241 + · exact degreeUnionBranch39_242 + +lemma degreeUnionBranch39_243 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 29 10 degreeUnionState39_243 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 29 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_244 + · exact degreeUnionBranch39_245 + · exact degreeUnionBranch39_246 + · exact degreeUnionBranch39_247 + · exact degreeUnionBranch39_248 + · exact degreeUnionBranch39_249 + · exact degreeUnionBranch39_250 + +lemma degreeUnionBranch39_251 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 28 11 degreeUnionState39_251 [11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 28 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_252 + · exact degreeUnionBranch39_253 + · exact degreeUnionBranch39_254 + · exact degreeUnionBranch39_255 + · exact degreeUnionBranch39_256 + · exact degreeUnionBranch39_257 + · exact degreeUnionBranch39_258 + · exact degreeUnionBranch39_259 + +lemma degreeUnionBranch39_260 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 27 12 degreeUnionState39_260 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 27 ≤ 9*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_261 + · exact degreeUnionBranch39_262 + · exact degreeUnionBranch39_263 + · exact degreeUnionBranch39_264 + · exact degreeUnionBranch39_265 + · exact degreeUnionBranch39_266 + · exact degreeUnionBranch39_267 + · exact degreeUnionBranch39_268 + · exact degreeUnionBranch39_269 + · exact degreeUnionBranch39_270 + +lemma degreeUnionBranch39_271 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 9 26 13 degreeUnionState39_271 [13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 13 at hb + change 26 ≤ 9*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_272 + · exact degreeUnionBranch39_273 + · exact degreeUnionBranch39_274 + · exact degreeUnionBranch39_275 + · exact degreeUnionBranch39_276 + · exact degreeUnionBranch39_277 + · exact degreeUnionBranch39_278 + · exact degreeUnionBranch39_279 + · exact degreeUnionBranch39_280 + · exact degreeUnionBranch39_281 + · exact degreeUnionBranch39_282 + +lemma degreeUnionBranch39_225 : checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) 10 39 38 degreeHalfRegions39 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 38 at hb + change 39 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch39_226 + · exact degreeUnionBranch39_227 + · exact degreeUnionBranch39_228 + · exact degreeUnionBranch39_229 + · exact degreeUnionBranch39_230 + · exact degreeUnionBranch39_236 + · exact degreeUnionBranch39_243 + · exact degreeUnionBranch39_251 + · exact degreeUnionBranch39_260 + · exact degreeUnionBranch39_271 + · exact degreeUnionBranch39_283 + · exact degreeUnionBranch39_284 + · exact degreeUnionBranch39_285 + · exact degreeUnionBranch39_286 + · exact degreeUnionBranch39_287 + · exact degreeUnionBranch39_288 + · exact degreeUnionBranch39_289 + · exact degreeUnionBranch39_290 + · exact degreeUnionBranch39_291 + · exact degreeUnionBranch39_292 + · exact degreeUnionBranch39_293 + · exact degreeUnionBranch39_294 + · exact degreeUnionBranch39_295 + · exact degreeUnionBranch39_296 + · exact degreeUnionBranch39_297 + · exact degreeUnionBranch39_298 + · exact degreeUnionBranch39_299 + · exact degreeUnionBranch39_300 + · exact degreeUnionBranch39_301 + · exact degreeUnionBranch39_302 + · exact degreeUnionBranch39_303 + · exact degreeUnionBranch39_304 + · exact degreeUnionBranch39_305 + · exact degreeUnionBranch39_306 + · exact degreeUnionBranch39_307 + +lemma degreeUnionCheck39 : ∀ h ≤ 19, + checkRegionPrefixes (quickResidual 6 9 degreeQs39 degreeTree39) h 39 38 degreeHalfRegions39 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch39_0 + · exact degreeUnionBranch39_1 + · exact degreeUnionBranch39_2 + · exact degreeUnionBranch39_3 + · exact degreeUnionBranch39_4 + · exact degreeUnionBranch39_5 + · exact degreeUnionBranch39_6 + · exact degreeUnionBranch39_7 + · exact degreeUnionBranch39_8 + · exact degreeUnionBranch39_121 + · exact degreeUnionBranch39_225 + · exact degreeUnionBranch39_308 + · exact degreeUnionBranch39_309 + · exact degreeUnionBranch39_310 + · exact degreeUnionBranch39_311 + · exact degreeUnionBranch39_312 + · exact degreeUnionBranch39_313 + · exact degreeUnionBranch39_314 + · exact degreeUnionBranch39_315 + · exact degreeUnionBranch39_316 + +lemma degreeHalfCover39 : ∀ R ∈ degreeRegions39, + R ∈ degreeHalfRegions39 ∨ (R.2,R.1) ∈ degreeHalfRegions39 := by decide +kernel + +lemma degreeDiagramRegionsChecked39 : ∀ R ∈ degreeRegions39, + ∀ μ : YoungDiagram, μ.card = 39 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP39 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck39 degreeHalfHeight39 degreeHalfWidth39 + degreeHalfCover39 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions41.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions41.lean index 1e004a94fd38b7e41d87ee7fc12aae833b51659f..3c861717a0f5a37479e3f112ed3ca9766350aec6 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions41.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions41.lean @@ -1,53 +1,53 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves41 - -namespace OAI - -/-! Degree Regions 41. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionCheck41 : ∀ h ≤ 21, - checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) h 41 21 degreeHalfRegions41 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch41_0 - · exact degreeUnionBranch41_1 - · exact degreeUnionBranch41_2 - · exact degreeUnionBranch41_3 - · exact degreeUnionBranch41_4 - · exact degreeUnionBranch41_5 - · exact degreeUnionBranch41_6 - · exact degreeUnionBranch41_7 - · exact degreeUnionBranch41_8 - · exact degreeUnionBranch41_9 - · exact degreeUnionBranch41_10 - · exact degreeUnionBranch41_11 - · exact degreeUnionBranch41_12 - · exact degreeUnionBranch41_13 - · exact degreeUnionBranch41_14 - · exact degreeUnionBranch41_15 - · exact degreeUnionBranch41_16 - · exact degreeUnionBranch41_17 - · exact degreeUnionBranch41_18 - · exact degreeUnionBranch41_19 - · exact degreeUnionBranch41_20 - · exact degreeUnionBranch41_21 - -lemma degreeHalfCover41 : ∀ R ∈ degreeRegions41, - R ∈ degreeHalfRegions41 ∨ (R.2,R.1) ∈ degreeHalfRegions41 := by decide +kernel - -lemma degreeDiagramRegionsChecked41 : ∀ R ∈ degreeRegions41, - ∀ μ : YoungDiagram, μ.card = 41 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP41 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck41 degreeHalfHeight41 degreeHalfWidth41 - degreeHalfCover41 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves41 + +namespace OAI + +/-! Degree Regions 41. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionCheck41 : ∀ h ≤ 21, + checkRegionPrefixes (quickResidual 6 10 degreeQs41 degreeTree41) h 41 21 degreeHalfRegions41 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch41_0 + · exact degreeUnionBranch41_1 + · exact degreeUnionBranch41_2 + · exact degreeUnionBranch41_3 + · exact degreeUnionBranch41_4 + · exact degreeUnionBranch41_5 + · exact degreeUnionBranch41_6 + · exact degreeUnionBranch41_7 + · exact degreeUnionBranch41_8 + · exact degreeUnionBranch41_9 + · exact degreeUnionBranch41_10 + · exact degreeUnionBranch41_11 + · exact degreeUnionBranch41_12 + · exact degreeUnionBranch41_13 + · exact degreeUnionBranch41_14 + · exact degreeUnionBranch41_15 + · exact degreeUnionBranch41_16 + · exact degreeUnionBranch41_17 + · exact degreeUnionBranch41_18 + · exact degreeUnionBranch41_19 + · exact degreeUnionBranch41_20 + · exact degreeUnionBranch41_21 + +lemma degreeHalfCover41 : ∀ R ∈ degreeRegions41, + R ∈ degreeHalfRegions41 ∨ (R.2,R.1) ∈ degreeHalfRegions41 := by decide +kernel + +lemma degreeDiagramRegionsChecked41 : ∀ R ∈ degreeRegions41, + ∀ μ : YoungDiagram, μ.card = 41 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP41 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck41 degreeHalfHeight41 degreeHalfWidth41 + degreeHalfCover41 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions43.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions43.lean index d21d2f5d33956abbe9af9f5582168ca0c8ea97f5..52e456218b1a7d13ca55781909cd23e229133e99 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions43.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions43.lean @@ -1,1482 +1,1482 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves43 - -namespace OAI - -/-! Degree Regions 43. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch43_11 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 35 8 degreeUnionState43_11 [8] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 5 ≤ a at ha - change a ≤ 8 at hb - change 35 ≤ 7*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_12 - · exact degreeUnionBranch43_13 - · exact degreeUnionBranch43_14 - · exact degreeUnionBranch43_15 - -lemma degreeUnionBranch43_16 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 34 9 degreeUnionState43_16 [9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 9 at hb - change 34 ≤ 7*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_17 - · exact degreeUnionBranch43_18 - · exact degreeUnionBranch43_19 - · exact degreeUnionBranch43_20 - · exact degreeUnionBranch43_21 - -lemma degreeUnionBranch43_22 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 33 10 degreeUnionState43_22 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 10 at hb - change 33 ≤ 7*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_23 - · exact degreeUnionBranch43_24 - · exact degreeUnionBranch43_25 - · exact degreeUnionBranch43_26 - · exact degreeUnionBranch43_27 - · exact degreeUnionBranch43_28 - -lemma degreeUnionBranch43_29 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 32 11 degreeUnionState43_29 [11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 11 at hb - change 32 ≤ 7*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_30 - · exact degreeUnionBranch43_31 - · exact degreeUnionBranch43_32 - · exact degreeUnionBranch43_33 - · exact degreeUnionBranch43_34 - · exact degreeUnionBranch43_35 - · exact degreeUnionBranch43_36 - -lemma degreeUnionBranch43_37 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 31 12 degreeUnionState43_37 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 12 at hb - change 31 ≤ 7*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_38 - · exact degreeUnionBranch43_39 - · exact degreeUnionBranch43_40 - · exact degreeUnionBranch43_41 - · exact degreeUnionBranch43_42 - · exact degreeUnionBranch43_43 - · exact degreeUnionBranch43_44 - · exact degreeUnionBranch43_45 - -lemma degreeUnionBranch43_46 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 30 13 degreeUnionState43_46 [13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 13 at hb - change 30 ≤ 7*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_47 - · exact degreeUnionBranch43_48 - · exact degreeUnionBranch43_49 - · exact degreeUnionBranch43_50 - · exact degreeUnionBranch43_51 - · exact degreeUnionBranch43_52 - · exact degreeUnionBranch43_53 - · exact degreeUnionBranch43_54 - · exact degreeUnionBranch43_55 - -lemma degreeUnionBranch43_56 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 29 14 degreeUnionState43_56 [14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 14 at hb - change 29 ≤ 7*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_57 - · exact degreeUnionBranch43_58 - · exact degreeUnionBranch43_59 - · exact degreeUnionBranch43_60 - · exact degreeUnionBranch43_61 - · exact degreeUnionBranch43_62 - · exact degreeUnionBranch43_63 - · exact degreeUnionBranch43_64 - · exact degreeUnionBranch43_65 - · exact degreeUnionBranch43_66 - -lemma degreeUnionBranch43_67 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 28 15 degreeUnionState43_67 [15] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 15 at hb - change 28 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_68 - · exact degreeUnionBranch43_69 - · exact degreeUnionBranch43_70 - · exact degreeUnionBranch43_71 - · exact degreeUnionBranch43_72 - · exact degreeUnionBranch43_73 - · exact degreeUnionBranch43_74 - · exact degreeUnionBranch43_75 - · exact degreeUnionBranch43_76 - · exact degreeUnionBranch43_77 - · exact degreeUnionBranch43_78 - · exact degreeUnionBranch43_79 - -lemma degreeUnionBranch43_80 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 27 16 degreeUnionState43_80 [16] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 16 at hb - change 27 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_81 - · exact degreeUnionBranch43_82 - · exact degreeUnionBranch43_83 - · exact degreeUnionBranch43_84 - · exact degreeUnionBranch43_85 - · exact degreeUnionBranch43_86 - · exact degreeUnionBranch43_87 - · exact degreeUnionBranch43_88 - · exact degreeUnionBranch43_89 - · exact degreeUnionBranch43_90 - · exact degreeUnionBranch43_91 - · exact degreeUnionBranch43_92 - · exact degreeUnionBranch43_93 - -lemma degreeUnionBranch43_94 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 26 17 degreeUnionState43_94 [17] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 17 at hb - change 26 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_95 - · exact degreeUnionBranch43_96 - · exact degreeUnionBranch43_97 - · exact degreeUnionBranch43_98 - · exact degreeUnionBranch43_99 - · exact degreeUnionBranch43_100 - · exact degreeUnionBranch43_101 - · exact degreeUnionBranch43_102 - · exact degreeUnionBranch43_103 - · exact degreeUnionBranch43_104 - · exact degreeUnionBranch43_105 - · exact degreeUnionBranch43_106 - · exact degreeUnionBranch43_107 - · exact degreeUnionBranch43_108 - -lemma degreeUnionBranch43_109 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 18 degreeUnionState43_109 [18] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 18 at hb - change 25 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_110 - · exact degreeUnionBranch43_111 - · exact degreeUnionBranch43_112 - · exact degreeUnionBranch43_113 - · exact degreeUnionBranch43_114 - · exact degreeUnionBranch43_115 - · exact degreeUnionBranch43_116 - · exact degreeUnionBranch43_117 - · exact degreeUnionBranch43_118 - · exact degreeUnionBranch43_119 - · exact degreeUnionBranch43_120 - · exact degreeUnionBranch43_121 - · exact degreeUnionBranch43_122 - · exact degreeUnionBranch43_123 - · exact degreeUnionBranch43_124 - -lemma degreeUnionBranch43_125 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 19 degreeUnionState43_125 [19] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 19 at hb - change 24 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_126 - · exact degreeUnionBranch43_127 - · exact degreeUnionBranch43_128 - · exact degreeUnionBranch43_129 - · exact degreeUnionBranch43_130 - · exact degreeUnionBranch43_131 - · exact degreeUnionBranch43_132 - · exact degreeUnionBranch43_133 - · exact degreeUnionBranch43_134 - · exact degreeUnionBranch43_135 - · exact degreeUnionBranch43_136 - · exact degreeUnionBranch43_137 - · exact degreeUnionBranch43_138 - · exact degreeUnionBranch43_139 - · exact degreeUnionBranch43_140 - · exact degreeUnionBranch43_141 - -lemma degreeUnionBranch43_142 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 20 degreeUnionState43_142 [20] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 20 at hb - change 23 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_143 - · exact degreeUnionBranch43_144 - · exact degreeUnionBranch43_145 - · exact degreeUnionBranch43_146 - · exact degreeUnionBranch43_147 - · exact degreeUnionBranch43_148 - · exact degreeUnionBranch43_149 - · exact degreeUnionBranch43_150 - · exact degreeUnionBranch43_151 - · exact degreeUnionBranch43_152 - · exact degreeUnionBranch43_153 - · exact degreeUnionBranch43_154 - · exact degreeUnionBranch43_155 - · exact degreeUnionBranch43_156 - · exact degreeUnionBranch43_157 - · exact degreeUnionBranch43_158 - · exact degreeUnionBranch43_159 - -lemma degreeUnionBranch43_8 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 43 42 degreeHalfRegions43 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 5 ≤ a at ha - change a ≤ 42 at hb - change 43 ≤ 8*a at hn - have hlo : 6 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_9 - · exact degreeUnionBranch43_10 - · exact degreeUnionBranch43_11 - · exact degreeUnionBranch43_16 - · exact degreeUnionBranch43_22 - · exact degreeUnionBranch43_29 - · exact degreeUnionBranch43_37 - · exact degreeUnionBranch43_46 - · exact degreeUnionBranch43_56 - · exact degreeUnionBranch43_67 - · exact degreeUnionBranch43_80 - · exact degreeUnionBranch43_94 - · exact degreeUnionBranch43_109 - · exact degreeUnionBranch43_125 - · exact degreeUnionBranch43_142 - · exact degreeUnionBranch43_160 - · exact degreeUnionBranch43_161 - · exact degreeUnionBranch43_162 - · exact degreeUnionBranch43_163 - · exact degreeUnionBranch43_164 - · exact degreeUnionBranch43_165 - · exact degreeUnionBranch43_166 - · exact degreeUnionBranch43_167 - · exact degreeUnionBranch43_168 - · exact degreeUnionBranch43_169 - · exact degreeUnionBranch43_170 - · exact degreeUnionBranch43_171 - · exact degreeUnionBranch43_172 - · exact degreeUnionBranch43_173 - · exact degreeUnionBranch43_174 - · exact degreeUnionBranch43_175 - · exact degreeUnionBranch43_176 - · exact degreeUnionBranch43_177 - · exact degreeUnionBranch43_178 - · exact degreeUnionBranch43_179 - · exact degreeUnionBranch43_180 - · exact degreeUnionBranch43_181 - -lemma degreeUnionBranch43_186 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 35 8 degreeUnionState43_186 [8] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 8 at hb - change 35 ≤ 8*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_187 - · exact degreeUnionBranch43_188 - · exact degreeUnionBranch43_189 - · exact degreeUnionBranch43_190 - -lemma degreeUnionBranch43_196 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 9 degreeUnionState43_196 [9,9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 25 ≤ 7*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_197 - · exact degreeUnionBranch43_198 - · exact degreeUnionBranch43_199 - · exact degreeUnionBranch43_200 - · exact degreeUnionBranch43_201 - · exact degreeUnionBranch43_202 - -lemma degreeUnionBranch43_191 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 34 9 degreeUnionState43_191 [9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 9 at hb - change 34 ≤ 8*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_192 - · exact degreeUnionBranch43_193 - · exact degreeUnionBranch43_194 - · exact degreeUnionBranch43_195 - · exact degreeUnionBranch43_196 - -lemma degreeUnionBranch43_203 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 33 10 degreeUnionState43_203 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 10 at hb - change 33 ≤ 8*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_204 - · exact degreeUnionBranch43_205 - · exact degreeUnionBranch43_206 - · exact degreeUnionBranch43_207 - · exact degreeUnionBranch43_208 - · exact degreeUnionBranch43_209 - -lemma degreeUnionBranch43_210 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 32 11 degreeUnionState43_210 [11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 11 at hb - change 32 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_211 - · exact degreeUnionBranch43_212 - · exact degreeUnionBranch43_213 - · exact degreeUnionBranch43_214 - · exact degreeUnionBranch43_215 - · exact degreeUnionBranch43_216 - · exact degreeUnionBranch43_217 - · exact degreeUnionBranch43_218 - -lemma degreeUnionBranch43_219 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 31 12 degreeUnionState43_219 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 31 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_220 - · exact degreeUnionBranch43_221 - · exact degreeUnionBranch43_222 - · exact degreeUnionBranch43_223 - · exact degreeUnionBranch43_224 - · exact degreeUnionBranch43_225 - · exact degreeUnionBranch43_226 - · exact degreeUnionBranch43_227 - · exact degreeUnionBranch43_228 - -lemma degreeUnionBranch43_229 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 30 13 degreeUnionState43_229 [13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 13 at hb - change 30 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_230 - · exact degreeUnionBranch43_231 - · exact degreeUnionBranch43_232 - · exact degreeUnionBranch43_233 - · exact degreeUnionBranch43_234 - · exact degreeUnionBranch43_235 - · exact degreeUnionBranch43_236 - · exact degreeUnionBranch43_237 - · exact degreeUnionBranch43_238 - · exact degreeUnionBranch43_239 - -lemma degreeUnionBranch43_240 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 29 14 degreeUnionState43_240 [14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 14 at hb - change 29 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_241 - · exact degreeUnionBranch43_242 - · exact degreeUnionBranch43_243 - · exact degreeUnionBranch43_244 - · exact degreeUnionBranch43_245 - · exact degreeUnionBranch43_246 - · exact degreeUnionBranch43_247 - · exact degreeUnionBranch43_248 - · exact degreeUnionBranch43_249 - · exact degreeUnionBranch43_250 - · exact degreeUnionBranch43_251 - -lemma degreeUnionBranch43_252 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 28 15 degreeUnionState43_252 [15] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 15 at hb - change 28 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_253 - · exact degreeUnionBranch43_254 - · exact degreeUnionBranch43_255 - · exact degreeUnionBranch43_256 - · exact degreeUnionBranch43_257 - · exact degreeUnionBranch43_258 - · exact degreeUnionBranch43_259 - · exact degreeUnionBranch43_260 - · exact degreeUnionBranch43_261 - · exact degreeUnionBranch43_262 - · exact degreeUnionBranch43_263 - · exact degreeUnionBranch43_264 - -lemma degreeUnionBranch43_265 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 27 16 degreeUnionState43_265 [16] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 16 at hb - change 27 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_266 - · exact degreeUnionBranch43_267 - · exact degreeUnionBranch43_268 - · exact degreeUnionBranch43_269 - · exact degreeUnionBranch43_270 - · exact degreeUnionBranch43_271 - · exact degreeUnionBranch43_272 - · exact degreeUnionBranch43_273 - · exact degreeUnionBranch43_274 - · exact degreeUnionBranch43_275 - · exact degreeUnionBranch43_276 - · exact degreeUnionBranch43_277 - · exact degreeUnionBranch43_278 - -lemma degreeUnionBranch43_279 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 26 17 degreeUnionState43_279 [17] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 17 at hb - change 26 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_280 - · exact degreeUnionBranch43_281 - · exact degreeUnionBranch43_282 - · exact degreeUnionBranch43_283 - · exact degreeUnionBranch43_284 - · exact degreeUnionBranch43_285 - · exact degreeUnionBranch43_286 - · exact degreeUnionBranch43_287 - · exact degreeUnionBranch43_288 - · exact degreeUnionBranch43_289 - · exact degreeUnionBranch43_290 - · exact degreeUnionBranch43_291 - · exact degreeUnionBranch43_292 - · exact degreeUnionBranch43_293 - -lemma degreeUnionBranch43_294 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 18 degreeUnionState43_294 [18] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 18 at hb - change 25 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_295 - · exact degreeUnionBranch43_296 - · exact degreeUnionBranch43_297 - · exact degreeUnionBranch43_298 - · exact degreeUnionBranch43_299 - · exact degreeUnionBranch43_300 - · exact degreeUnionBranch43_301 - · exact degreeUnionBranch43_302 - · exact degreeUnionBranch43_303 - · exact degreeUnionBranch43_304 - · exact degreeUnionBranch43_305 - · exact degreeUnionBranch43_306 - · exact degreeUnionBranch43_307 - · exact degreeUnionBranch43_308 - · exact degreeUnionBranch43_309 - -lemma degreeUnionBranch43_310 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 19 degreeUnionState43_310 [19] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 19 at hb - change 24 ≤ 8*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_311 - · exact degreeUnionBranch43_312 - · exact degreeUnionBranch43_313 - · exact degreeUnionBranch43_314 - · exact degreeUnionBranch43_315 - · exact degreeUnionBranch43_316 - · exact degreeUnionBranch43_317 - · exact degreeUnionBranch43_318 - · exact degreeUnionBranch43_319 - · exact degreeUnionBranch43_320 - · exact degreeUnionBranch43_321 - · exact degreeUnionBranch43_322 - · exact degreeUnionBranch43_323 - · exact degreeUnionBranch43_324 - · exact degreeUnionBranch43_325 - · exact degreeUnionBranch43_326 - · exact degreeUnionBranch43_327 - -lemma degreeUnionBranch43_182 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 43 42 degreeHalfRegions43 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 42 at hb - change 43 ≤ 9*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_183 - · exact degreeUnionBranch43_184 - · exact degreeUnionBranch43_185 - · exact degreeUnionBranch43_186 - · exact degreeUnionBranch43_191 - · exact degreeUnionBranch43_203 - · exact degreeUnionBranch43_210 - · exact degreeUnionBranch43_219 - · exact degreeUnionBranch43_229 - · exact degreeUnionBranch43_240 - · exact degreeUnionBranch43_252 - · exact degreeUnionBranch43_265 - · exact degreeUnionBranch43_279 - · exact degreeUnionBranch43_294 - · exact degreeUnionBranch43_310 - · exact degreeUnionBranch43_328 - · exact degreeUnionBranch43_329 - · exact degreeUnionBranch43_330 - · exact degreeUnionBranch43_331 - · exact degreeUnionBranch43_332 - · exact degreeUnionBranch43_333 - · exact degreeUnionBranch43_334 - · exact degreeUnionBranch43_335 - · exact degreeUnionBranch43_336 - · exact degreeUnionBranch43_337 - · exact degreeUnionBranch43_338 - · exact degreeUnionBranch43_339 - · exact degreeUnionBranch43_340 - · exact degreeUnionBranch43_341 - · exact degreeUnionBranch43_342 - · exact degreeUnionBranch43_343 - · exact degreeUnionBranch43_344 - · exact degreeUnionBranch43_345 - · exact degreeUnionBranch43_346 - · exact degreeUnionBranch43_347 - · exact degreeUnionBranch43_348 - · exact degreeUnionBranch43_349 - · exact degreeUnionBranch43_350 - -lemma degreeUnionBranch43_360 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 27 8 degreeUnionState43_360 [8,8] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 27 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_361 - · exact degreeUnionBranch43_362 - · exact degreeUnionBranch43_363 - · exact degreeUnionBranch43_364 - · exact degreeUnionBranch43_365 - -lemma degreeUnionBranch43_355 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 35 8 degreeUnionState43_355 [8] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 35 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_356 - · exact degreeUnionBranch43_357 - · exact degreeUnionBranch43_358 - · exact degreeUnionBranch43_359 - · exact degreeUnionBranch43_360 - -lemma degreeUnionBranch43_371 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 26 8 degreeUnionState43_371 [8,9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 26 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_372 - · exact degreeUnionBranch43_373 - · exact degreeUnionBranch43_374 - · exact degreeUnionBranch43_375 - · exact degreeUnionBranch43_376 - -lemma degreeUnionBranch43_377 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 9 degreeUnionState43_377 [9,9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 25 ≤ 8*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_378 - · exact degreeUnionBranch43_379 - · exact degreeUnionBranch43_380 - · exact degreeUnionBranch43_381 - · exact degreeUnionBranch43_382 - · exact degreeUnionBranch43_383 - -lemma degreeUnionBranch43_366 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 34 9 degreeUnionState43_366 [9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 34 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_367 - · exact degreeUnionBranch43_368 - · exact degreeUnionBranch43_369 - · exact degreeUnionBranch43_370 - · exact degreeUnionBranch43_371 - · exact degreeUnionBranch43_377 - -lemma degreeUnionBranch43_384 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 33 10 degreeUnionState43_384 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 33 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_385 - · exact degreeUnionBranch43_386 - · exact degreeUnionBranch43_387 - · exact degreeUnionBranch43_388 - · exact degreeUnionBranch43_389 - · exact degreeUnionBranch43_390 - · exact degreeUnionBranch43_391 - -lemma degreeUnionBranch43_392 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 32 11 degreeUnionState43_392 [11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 32 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_393 - · exact degreeUnionBranch43_394 - · exact degreeUnionBranch43_395 - · exact degreeUnionBranch43_396 - · exact degreeUnionBranch43_397 - · exact degreeUnionBranch43_398 - · exact degreeUnionBranch43_399 - · exact degreeUnionBranch43_400 - -lemma degreeUnionBranch43_401 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 31 12 degreeUnionState43_401 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 31 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_402 - · exact degreeUnionBranch43_403 - · exact degreeUnionBranch43_404 - · exact degreeUnionBranch43_405 - · exact degreeUnionBranch43_406 - · exact degreeUnionBranch43_407 - · exact degreeUnionBranch43_408 - · exact degreeUnionBranch43_409 - · exact degreeUnionBranch43_410 - -lemma degreeUnionBranch43_411 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 30 13 degreeUnionState43_411 [13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 13 at hb - change 30 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_412 - · exact degreeUnionBranch43_413 - · exact degreeUnionBranch43_414 - · exact degreeUnionBranch43_415 - · exact degreeUnionBranch43_416 - · exact degreeUnionBranch43_417 - · exact degreeUnionBranch43_418 - · exact degreeUnionBranch43_419 - · exact degreeUnionBranch43_420 - · exact degreeUnionBranch43_421 - -lemma degreeUnionBranch43_422 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 29 14 degreeUnionState43_422 [14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 14 at hb - change 29 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_423 - · exact degreeUnionBranch43_424 - · exact degreeUnionBranch43_425 - · exact degreeUnionBranch43_426 - · exact degreeUnionBranch43_427 - · exact degreeUnionBranch43_428 - · exact degreeUnionBranch43_429 - · exact degreeUnionBranch43_430 - · exact degreeUnionBranch43_431 - · exact degreeUnionBranch43_432 - · exact degreeUnionBranch43_433 - -lemma degreeUnionBranch43_434 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 28 15 degreeUnionState43_434 [15] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 15 at hb - change 28 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_435 - · exact degreeUnionBranch43_436 - · exact degreeUnionBranch43_437 - · exact degreeUnionBranch43_438 - · exact degreeUnionBranch43_439 - · exact degreeUnionBranch43_440 - · exact degreeUnionBranch43_441 - · exact degreeUnionBranch43_442 - · exact degreeUnionBranch43_443 - · exact degreeUnionBranch43_444 - · exact degreeUnionBranch43_445 - · exact degreeUnionBranch43_446 - -lemma degreeUnionBranch43_447 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 27 16 degreeUnionState43_447 [16] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 16 at hb - change 27 ≤ 9*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_448 - · exact degreeUnionBranch43_449 - · exact degreeUnionBranch43_450 - · exact degreeUnionBranch43_451 - · exact degreeUnionBranch43_452 - · exact degreeUnionBranch43_453 - · exact degreeUnionBranch43_454 - · exact degreeUnionBranch43_455 - · exact degreeUnionBranch43_456 - · exact degreeUnionBranch43_457 - · exact degreeUnionBranch43_458 - · exact degreeUnionBranch43_459 - · exact degreeUnionBranch43_460 - · exact degreeUnionBranch43_461 - -lemma degreeUnionBranch43_462 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 26 17 degreeUnionState43_462 [17] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 17 at hb - change 26 ≤ 9*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_463 - · exact degreeUnionBranch43_464 - · exact degreeUnionBranch43_465 - · exact degreeUnionBranch43_466 - · exact degreeUnionBranch43_467 - · exact degreeUnionBranch43_468 - · exact degreeUnionBranch43_469 - · exact degreeUnionBranch43_470 - · exact degreeUnionBranch43_471 - · exact degreeUnionBranch43_472 - · exact degreeUnionBranch43_473 - · exact degreeUnionBranch43_474 - · exact degreeUnionBranch43_475 - · exact degreeUnionBranch43_476 - · exact degreeUnionBranch43_477 - -lemma degreeUnionBranch43_478 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 25 18 degreeUnionState43_478 [18] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 18 at hb - change 25 ≤ 9*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_479 - · exact degreeUnionBranch43_480 - · exact degreeUnionBranch43_481 - · exact degreeUnionBranch43_482 - · exact degreeUnionBranch43_483 - · exact degreeUnionBranch43_484 - · exact degreeUnionBranch43_485 - · exact degreeUnionBranch43_486 - · exact degreeUnionBranch43_487 - · exact degreeUnionBranch43_488 - · exact degreeUnionBranch43_489 - · exact degreeUnionBranch43_490 - · exact degreeUnionBranch43_491 - · exact degreeUnionBranch43_492 - · exact degreeUnionBranch43_493 - · exact degreeUnionBranch43_494 - -lemma degreeUnionBranch43_495 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 24 19 degreeUnionState43_495 [19] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 19 at hb - change 24 ≤ 9*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_496 - · exact degreeUnionBranch43_497 - · exact degreeUnionBranch43_498 - · exact degreeUnionBranch43_499 - · exact degreeUnionBranch43_500 - · exact degreeUnionBranch43_501 - · exact degreeUnionBranch43_502 - · exact degreeUnionBranch43_503 - · exact degreeUnionBranch43_504 - · exact degreeUnionBranch43_505 - · exact degreeUnionBranch43_506 - · exact degreeUnionBranch43_507 - · exact degreeUnionBranch43_508 - · exact degreeUnionBranch43_509 - · exact degreeUnionBranch43_510 - · exact degreeUnionBranch43_511 - · exact degreeUnionBranch43_512 - -lemma degreeUnionBranch43_351 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 43 42 degreeHalfRegions43 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 42 at hb - change 43 ≤ 10*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_352 - · exact degreeUnionBranch43_353 - · exact degreeUnionBranch43_354 - · exact degreeUnionBranch43_355 - · exact degreeUnionBranch43_366 - · exact degreeUnionBranch43_384 - · exact degreeUnionBranch43_392 - · exact degreeUnionBranch43_401 - · exact degreeUnionBranch43_411 - · exact degreeUnionBranch43_422 - · exact degreeUnionBranch43_434 - · exact degreeUnionBranch43_447 - · exact degreeUnionBranch43_462 - · exact degreeUnionBranch43_478 - · exact degreeUnionBranch43_495 - · exact degreeUnionBranch43_513 - · exact degreeUnionBranch43_514 - · exact degreeUnionBranch43_515 - · exact degreeUnionBranch43_516 - · exact degreeUnionBranch43_517 - · exact degreeUnionBranch43_518 - · exact degreeUnionBranch43_519 - · exact degreeUnionBranch43_520 - · exact degreeUnionBranch43_521 - · exact degreeUnionBranch43_522 - · exact degreeUnionBranch43_523 - · exact degreeUnionBranch43_524 - · exact degreeUnionBranch43_525 - · exact degreeUnionBranch43_526 - · exact degreeUnionBranch43_527 - · exact degreeUnionBranch43_528 - · exact degreeUnionBranch43_529 - · exact degreeUnionBranch43_530 - · exact degreeUnionBranch43_531 - · exact degreeUnionBranch43_532 - · exact degreeUnionBranch43_533 - · exact degreeUnionBranch43_534 - · exact degreeUnionBranch43_535 - -lemma degreeUnionBranch43_541 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 35 8 degreeUnionState43_541 [8] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 35 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_542 - · exact degreeUnionBranch43_543 - · exact degreeUnionBranch43_544 - · exact degreeUnionBranch43_545 - · exact degreeUnionBranch43_546 - -lemma degreeUnionBranch43_547 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 34 9 degreeUnionState43_547 [9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 34 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_548 - · exact degreeUnionBranch43_549 - · exact degreeUnionBranch43_550 - · exact degreeUnionBranch43_551 - · exact degreeUnionBranch43_552 - · exact degreeUnionBranch43_553 - -lemma degreeUnionBranch43_554 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 33 10 degreeUnionState43_554 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 33 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_555 - · exact degreeUnionBranch43_556 - · exact degreeUnionBranch43_557 - · exact degreeUnionBranch43_558 - · exact degreeUnionBranch43_559 - · exact degreeUnionBranch43_560 - · exact degreeUnionBranch43_561 - -lemma degreeUnionBranch43_562 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 32 11 degreeUnionState43_562 [11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 32 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_563 - · exact degreeUnionBranch43_564 - · exact degreeUnionBranch43_565 - · exact degreeUnionBranch43_566 - · exact degreeUnionBranch43_567 - · exact degreeUnionBranch43_568 - · exact degreeUnionBranch43_569 - · exact degreeUnionBranch43_570 - -lemma degreeUnionBranch43_571 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 31 12 degreeUnionState43_571 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 31 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_572 - · exact degreeUnionBranch43_573 - · exact degreeUnionBranch43_574 - · exact degreeUnionBranch43_575 - · exact degreeUnionBranch43_576 - · exact degreeUnionBranch43_577 - · exact degreeUnionBranch43_578 - · exact degreeUnionBranch43_579 - · exact degreeUnionBranch43_580 - -lemma degreeUnionBranch43_536 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 43 42 degreeHalfRegions43 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 42 at hb - change 43 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_537 - · exact degreeUnionBranch43_538 - · exact degreeUnionBranch43_539 - · exact degreeUnionBranch43_540 - · exact degreeUnionBranch43_541 - · exact degreeUnionBranch43_547 - · exact degreeUnionBranch43_554 - · exact degreeUnionBranch43_562 - · exact degreeUnionBranch43_571 - · exact degreeUnionBranch43_581 - · exact degreeUnionBranch43_582 - · exact degreeUnionBranch43_583 - · exact degreeUnionBranch43_584 - · exact degreeUnionBranch43_585 - · exact degreeUnionBranch43_586 - · exact degreeUnionBranch43_587 - · exact degreeUnionBranch43_588 - · exact degreeUnionBranch43_589 - · exact degreeUnionBranch43_590 - · exact degreeUnionBranch43_591 - · exact degreeUnionBranch43_592 - · exact degreeUnionBranch43_593 - · exact degreeUnionBranch43_594 - · exact degreeUnionBranch43_595 - · exact degreeUnionBranch43_596 - · exact degreeUnionBranch43_597 - · exact degreeUnionBranch43_598 - · exact degreeUnionBranch43_599 - · exact degreeUnionBranch43_600 - · exact degreeUnionBranch43_601 - · exact degreeUnionBranch43_602 - · exact degreeUnionBranch43_603 - · exact degreeUnionBranch43_604 - · exact degreeUnionBranch43_605 - · exact degreeUnionBranch43_606 - · exact degreeUnionBranch43_607 - · exact degreeUnionBranch43_608 - · exact degreeUnionBranch43_609 - · exact degreeUnionBranch43_610 - -lemma degreeUnionBranch43_617 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 34 9 degreeUnionState43_617 [9] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 34 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_618 - · exact degreeUnionBranch43_619 - · exact degreeUnionBranch43_620 - · exact degreeUnionBranch43_621 - · exact degreeUnionBranch43_622 - · exact degreeUnionBranch43_623 - -lemma degreeUnionBranch43_624 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 33 10 degreeUnionState43_624 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 33 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_625 - · exact degreeUnionBranch43_626 - · exact degreeUnionBranch43_627 - · exact degreeUnionBranch43_628 - · exact degreeUnionBranch43_629 - · exact degreeUnionBranch43_630 - · exact degreeUnionBranch43_631 - · exact degreeUnionBranch43_632 - -lemma degreeUnionBranch43_633 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 32 11 degreeUnionState43_633 [11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 11 at hb - change 32 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_634 - · exact degreeUnionBranch43_635 - · exact degreeUnionBranch43_636 - · exact degreeUnionBranch43_637 - · exact degreeUnionBranch43_638 - · exact degreeUnionBranch43_639 - · exact degreeUnionBranch43_640 - · exact degreeUnionBranch43_641 - · exact degreeUnionBranch43_642 - -lemma degreeUnionBranch43_643 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 31 12 degreeUnionState43_643 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 12 at hb - change 31 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_644 - · exact degreeUnionBranch43_645 - · exact degreeUnionBranch43_646 - · exact degreeUnionBranch43_647 - · exact degreeUnionBranch43_648 - · exact degreeUnionBranch43_649 - · exact degreeUnionBranch43_650 - · exact degreeUnionBranch43_651 - · exact degreeUnionBranch43_652 - · exact degreeUnionBranch43_653 - -lemma degreeUnionBranch43_611 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 43 42 degreeHalfRegions43 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 42 at hb - change 43 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_612 - · exact degreeUnionBranch43_613 - · exact degreeUnionBranch43_614 - · exact degreeUnionBranch43_615 - · exact degreeUnionBranch43_616 - · exact degreeUnionBranch43_617 - · exact degreeUnionBranch43_624 - · exact degreeUnionBranch43_633 - · exact degreeUnionBranch43_643 - · exact degreeUnionBranch43_654 - · exact degreeUnionBranch43_655 - · exact degreeUnionBranch43_656 - · exact degreeUnionBranch43_657 - · exact degreeUnionBranch43_658 - · exact degreeUnionBranch43_659 - · exact degreeUnionBranch43_660 - · exact degreeUnionBranch43_661 - · exact degreeUnionBranch43_662 - · exact degreeUnionBranch43_663 - · exact degreeUnionBranch43_664 - · exact degreeUnionBranch43_665 - · exact degreeUnionBranch43_666 - · exact degreeUnionBranch43_667 - · exact degreeUnionBranch43_668 - · exact degreeUnionBranch43_669 - · exact degreeUnionBranch43_670 - · exact degreeUnionBranch43_671 - · exact degreeUnionBranch43_672 - · exact degreeUnionBranch43_673 - · exact degreeUnionBranch43_674 - · exact degreeUnionBranch43_675 - · exact degreeUnionBranch43_676 - · exact degreeUnionBranch43_677 - · exact degreeUnionBranch43_678 - · exact degreeUnionBranch43_679 - · exact degreeUnionBranch43_680 - · exact degreeUnionBranch43_681 - · exact degreeUnionBranch43_682 - · exact degreeUnionBranch43_683 - -lemma degreeUnionBranch43_691 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 33 10 degreeUnionState43_691 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 10 at hb - change 33 ≤ 12*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_692 - · exact degreeUnionBranch43_693 - · exact degreeUnionBranch43_694 - · exact degreeUnionBranch43_695 - · exact degreeUnionBranch43_696 - · exact degreeUnionBranch43_697 - · exact degreeUnionBranch43_698 - · exact degreeUnionBranch43_699 - -lemma degreeUnionBranch43_684 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 43 42 degreeHalfRegions43 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 42 at hb - change 43 ≤ 13*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_685 - · exact degreeUnionBranch43_686 - · exact degreeUnionBranch43_687 - · exact degreeUnionBranch43_688 - · exact degreeUnionBranch43_689 - · exact degreeUnionBranch43_690 - · exact degreeUnionBranch43_691 - · exact degreeUnionBranch43_700 - · exact degreeUnionBranch43_701 - · exact degreeUnionBranch43_702 - · exact degreeUnionBranch43_703 - · exact degreeUnionBranch43_704 - · exact degreeUnionBranch43_705 - · exact degreeUnionBranch43_706 - · exact degreeUnionBranch43_707 - · exact degreeUnionBranch43_708 - · exact degreeUnionBranch43_709 - · exact degreeUnionBranch43_710 - · exact degreeUnionBranch43_711 - · exact degreeUnionBranch43_712 - · exact degreeUnionBranch43_713 - · exact degreeUnionBranch43_714 - · exact degreeUnionBranch43_715 - · exact degreeUnionBranch43_716 - · exact degreeUnionBranch43_717 - · exact degreeUnionBranch43_718 - · exact degreeUnionBranch43_719 - · exact degreeUnionBranch43_720 - · exact degreeUnionBranch43_721 - · exact degreeUnionBranch43_722 - · exact degreeUnionBranch43_723 - · exact degreeUnionBranch43_724 - · exact degreeUnionBranch43_725 - · exact degreeUnionBranch43_726 - · exact degreeUnionBranch43_727 - · exact degreeUnionBranch43_728 - · exact degreeUnionBranch43_729 - · exact degreeUnionBranch43_730 - · exact degreeUnionBranch43_731 - -lemma degreeUnionBranch43_732 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 43 42 degreeHalfRegions43 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 42 at hb - change 43 ≤ 14*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_733 - · exact degreeUnionBranch43_734 - · exact degreeUnionBranch43_735 - · exact degreeUnionBranch43_736 - · exact degreeUnionBranch43_737 - · exact degreeUnionBranch43_738 - · exact degreeUnionBranch43_739 - · exact degreeUnionBranch43_740 - · exact degreeUnionBranch43_741 - · exact degreeUnionBranch43_742 - · exact degreeUnionBranch43_743 - · exact degreeUnionBranch43_744 - · exact degreeUnionBranch43_745 - · exact degreeUnionBranch43_746 - · exact degreeUnionBranch43_747 - · exact degreeUnionBranch43_748 - · exact degreeUnionBranch43_749 - · exact degreeUnionBranch43_750 - · exact degreeUnionBranch43_751 - · exact degreeUnionBranch43_752 - · exact degreeUnionBranch43_753 - · exact degreeUnionBranch43_754 - · exact degreeUnionBranch43_755 - · exact degreeUnionBranch43_756 - · exact degreeUnionBranch43_757 - · exact degreeUnionBranch43_758 - · exact degreeUnionBranch43_759 - · exact degreeUnionBranch43_760 - · exact degreeUnionBranch43_761 - · exact degreeUnionBranch43_762 - · exact degreeUnionBranch43_763 - · exact degreeUnionBranch43_764 - · exact degreeUnionBranch43_765 - · exact degreeUnionBranch43_766 - · exact degreeUnionBranch43_767 - · exact degreeUnionBranch43_768 - · exact degreeUnionBranch43_769 - · exact degreeUnionBranch43_770 - · exact degreeUnionBranch43_771 - -lemma degreeUnionBranch43_772 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 43 42 degreeHalfRegions43 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 42 at hb - change 43 ≤ 15*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_773 - · exact degreeUnionBranch43_774 - · exact degreeUnionBranch43_775 - · exact degreeUnionBranch43_776 - · exact degreeUnionBranch43_777 - · exact degreeUnionBranch43_778 - · exact degreeUnionBranch43_779 - · exact degreeUnionBranch43_780 - · exact degreeUnionBranch43_781 - · exact degreeUnionBranch43_782 - · exact degreeUnionBranch43_783 - · exact degreeUnionBranch43_784 - · exact degreeUnionBranch43_785 - · exact degreeUnionBranch43_786 - · exact degreeUnionBranch43_787 - · exact degreeUnionBranch43_788 - · exact degreeUnionBranch43_789 - · exact degreeUnionBranch43_790 - · exact degreeUnionBranch43_791 - · exact degreeUnionBranch43_792 - · exact degreeUnionBranch43_793 - · exact degreeUnionBranch43_794 - · exact degreeUnionBranch43_795 - · exact degreeUnionBranch43_796 - · exact degreeUnionBranch43_797 - · exact degreeUnionBranch43_798 - · exact degreeUnionBranch43_799 - · exact degreeUnionBranch43_800 - · exact degreeUnionBranch43_801 - · exact degreeUnionBranch43_802 - · exact degreeUnionBranch43_803 - · exact degreeUnionBranch43_804 - · exact degreeUnionBranch43_805 - · exact degreeUnionBranch43_806 - · exact degreeUnionBranch43_807 - · exact degreeUnionBranch43_808 - · exact degreeUnionBranch43_809 - · exact degreeUnionBranch43_810 - · exact degreeUnionBranch43_811 - · exact degreeUnionBranch43_812 - -lemma degreeUnionBranch43_813 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 43 42 degreeHalfRegions43 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 42 at hb - change 43 ≤ 16*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_814 - · exact degreeUnionBranch43_815 - · exact degreeUnionBranch43_816 - · exact degreeUnionBranch43_817 - · exact degreeUnionBranch43_818 - · exact degreeUnionBranch43_819 - · exact degreeUnionBranch43_820 - · exact degreeUnionBranch43_821 - · exact degreeUnionBranch43_822 - · exact degreeUnionBranch43_823 - · exact degreeUnionBranch43_824 - · exact degreeUnionBranch43_825 - · exact degreeUnionBranch43_826 - · exact degreeUnionBranch43_827 - · exact degreeUnionBranch43_828 - · exact degreeUnionBranch43_829 - · exact degreeUnionBranch43_830 - · exact degreeUnionBranch43_831 - · exact degreeUnionBranch43_832 - · exact degreeUnionBranch43_833 - · exact degreeUnionBranch43_834 - · exact degreeUnionBranch43_835 - · exact degreeUnionBranch43_836 - · exact degreeUnionBranch43_837 - · exact degreeUnionBranch43_838 - · exact degreeUnionBranch43_839 - · exact degreeUnionBranch43_840 - · exact degreeUnionBranch43_841 - · exact degreeUnionBranch43_842 - · exact degreeUnionBranch43_843 - · exact degreeUnionBranch43_844 - · exact degreeUnionBranch43_845 - · exact degreeUnionBranch43_846 - · exact degreeUnionBranch43_847 - · exact degreeUnionBranch43_848 - · exact degreeUnionBranch43_849 - · exact degreeUnionBranch43_850 - · exact degreeUnionBranch43_851 - · exact degreeUnionBranch43_852 - · exact degreeUnionBranch43_853 - -lemma degreeUnionBranch43_854 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 17 43 42 degreeHalfRegions43 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 42 at hb - change 43 ≤ 17*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch43_855 - · exact degreeUnionBranch43_856 - · exact degreeUnionBranch43_857 - · exact degreeUnionBranch43_858 - · exact degreeUnionBranch43_859 - · exact degreeUnionBranch43_860 - · exact degreeUnionBranch43_861 - · exact degreeUnionBranch43_862 - · exact degreeUnionBranch43_863 - · exact degreeUnionBranch43_864 - · exact degreeUnionBranch43_865 - · exact degreeUnionBranch43_866 - · exact degreeUnionBranch43_867 - · exact degreeUnionBranch43_868 - · exact degreeUnionBranch43_869 - · exact degreeUnionBranch43_870 - · exact degreeUnionBranch43_871 - · exact degreeUnionBranch43_872 - · exact degreeUnionBranch43_873 - · exact degreeUnionBranch43_874 - · exact degreeUnionBranch43_875 - · exact degreeUnionBranch43_876 - · exact degreeUnionBranch43_877 - · exact degreeUnionBranch43_878 - · exact degreeUnionBranch43_879 - · exact degreeUnionBranch43_880 - · exact degreeUnionBranch43_881 - · exact degreeUnionBranch43_882 - · exact degreeUnionBranch43_883 - · exact degreeUnionBranch43_884 - · exact degreeUnionBranch43_885 - · exact degreeUnionBranch43_886 - · exact degreeUnionBranch43_887 - · exact degreeUnionBranch43_888 - · exact degreeUnionBranch43_889 - · exact degreeUnionBranch43_890 - · exact degreeUnionBranch43_891 - · exact degreeUnionBranch43_892 - · exact degreeUnionBranch43_893 - · exact degreeUnionBranch43_894 - -lemma degreeUnionCheck43 : ∀ h ≤ 23, - checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) h 43 42 degreeHalfRegions43 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch43_0 - · exact degreeUnionBranch43_1 - · exact degreeUnionBranch43_2 - · exact degreeUnionBranch43_3 - · exact degreeUnionBranch43_4 - · exact degreeUnionBranch43_5 - · exact degreeUnionBranch43_6 - · exact degreeUnionBranch43_7 - · exact degreeUnionBranch43_8 - · exact degreeUnionBranch43_182 - · exact degreeUnionBranch43_351 - · exact degreeUnionBranch43_536 - · exact degreeUnionBranch43_611 - · exact degreeUnionBranch43_684 - · exact degreeUnionBranch43_732 - · exact degreeUnionBranch43_772 - · exact degreeUnionBranch43_813 - · exact degreeUnionBranch43_854 - · exact degreeUnionBranch43_895 - · exact degreeUnionBranch43_896 - · exact degreeUnionBranch43_897 - · exact degreeUnionBranch43_898 - · exact degreeUnionBranch43_899 - · exact degreeUnionBranch43_900 - -lemma degreeHalfCover43 : ∀ R ∈ degreeRegions43, - R ∈ degreeHalfRegions43 ∨ (R.2,R.1) ∈ degreeHalfRegions43 := by decide +kernel - -lemma degreeDiagramRegionsChecked43 : ∀ R ∈ degreeRegions43, - ∀ μ : YoungDiagram, μ.card = 43 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP43 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck43 degreeHalfHeight43 degreeHalfWidth43 - degreeHalfCover43 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves43 + +namespace OAI + +/-! Degree Regions 43. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch43_11 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 35 8 degreeUnionState43_11 [8] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 5 ≤ a at ha + change a ≤ 8 at hb + change 35 ≤ 7*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_12 + · exact degreeUnionBranch43_13 + · exact degreeUnionBranch43_14 + · exact degreeUnionBranch43_15 + +lemma degreeUnionBranch43_16 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 34 9 degreeUnionState43_16 [9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 9 at hb + change 34 ≤ 7*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_17 + · exact degreeUnionBranch43_18 + · exact degreeUnionBranch43_19 + · exact degreeUnionBranch43_20 + · exact degreeUnionBranch43_21 + +lemma degreeUnionBranch43_22 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 33 10 degreeUnionState43_22 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 10 at hb + change 33 ≤ 7*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_23 + · exact degreeUnionBranch43_24 + · exact degreeUnionBranch43_25 + · exact degreeUnionBranch43_26 + · exact degreeUnionBranch43_27 + · exact degreeUnionBranch43_28 + +lemma degreeUnionBranch43_29 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 32 11 degreeUnionState43_29 [11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 11 at hb + change 32 ≤ 7*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_30 + · exact degreeUnionBranch43_31 + · exact degreeUnionBranch43_32 + · exact degreeUnionBranch43_33 + · exact degreeUnionBranch43_34 + · exact degreeUnionBranch43_35 + · exact degreeUnionBranch43_36 + +lemma degreeUnionBranch43_37 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 31 12 degreeUnionState43_37 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 12 at hb + change 31 ≤ 7*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_38 + · exact degreeUnionBranch43_39 + · exact degreeUnionBranch43_40 + · exact degreeUnionBranch43_41 + · exact degreeUnionBranch43_42 + · exact degreeUnionBranch43_43 + · exact degreeUnionBranch43_44 + · exact degreeUnionBranch43_45 + +lemma degreeUnionBranch43_46 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 30 13 degreeUnionState43_46 [13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 13 at hb + change 30 ≤ 7*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_47 + · exact degreeUnionBranch43_48 + · exact degreeUnionBranch43_49 + · exact degreeUnionBranch43_50 + · exact degreeUnionBranch43_51 + · exact degreeUnionBranch43_52 + · exact degreeUnionBranch43_53 + · exact degreeUnionBranch43_54 + · exact degreeUnionBranch43_55 + +lemma degreeUnionBranch43_56 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 29 14 degreeUnionState43_56 [14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 14 at hb + change 29 ≤ 7*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_57 + · exact degreeUnionBranch43_58 + · exact degreeUnionBranch43_59 + · exact degreeUnionBranch43_60 + · exact degreeUnionBranch43_61 + · exact degreeUnionBranch43_62 + · exact degreeUnionBranch43_63 + · exact degreeUnionBranch43_64 + · exact degreeUnionBranch43_65 + · exact degreeUnionBranch43_66 + +lemma degreeUnionBranch43_67 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 28 15 degreeUnionState43_67 [15] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 15 at hb + change 28 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_68 + · exact degreeUnionBranch43_69 + · exact degreeUnionBranch43_70 + · exact degreeUnionBranch43_71 + · exact degreeUnionBranch43_72 + · exact degreeUnionBranch43_73 + · exact degreeUnionBranch43_74 + · exact degreeUnionBranch43_75 + · exact degreeUnionBranch43_76 + · exact degreeUnionBranch43_77 + · exact degreeUnionBranch43_78 + · exact degreeUnionBranch43_79 + +lemma degreeUnionBranch43_80 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 27 16 degreeUnionState43_80 [16] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 16 at hb + change 27 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_81 + · exact degreeUnionBranch43_82 + · exact degreeUnionBranch43_83 + · exact degreeUnionBranch43_84 + · exact degreeUnionBranch43_85 + · exact degreeUnionBranch43_86 + · exact degreeUnionBranch43_87 + · exact degreeUnionBranch43_88 + · exact degreeUnionBranch43_89 + · exact degreeUnionBranch43_90 + · exact degreeUnionBranch43_91 + · exact degreeUnionBranch43_92 + · exact degreeUnionBranch43_93 + +lemma degreeUnionBranch43_94 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 26 17 degreeUnionState43_94 [17] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 17 at hb + change 26 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_95 + · exact degreeUnionBranch43_96 + · exact degreeUnionBranch43_97 + · exact degreeUnionBranch43_98 + · exact degreeUnionBranch43_99 + · exact degreeUnionBranch43_100 + · exact degreeUnionBranch43_101 + · exact degreeUnionBranch43_102 + · exact degreeUnionBranch43_103 + · exact degreeUnionBranch43_104 + · exact degreeUnionBranch43_105 + · exact degreeUnionBranch43_106 + · exact degreeUnionBranch43_107 + · exact degreeUnionBranch43_108 + +lemma degreeUnionBranch43_109 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 18 degreeUnionState43_109 [18] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 18 at hb + change 25 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_110 + · exact degreeUnionBranch43_111 + · exact degreeUnionBranch43_112 + · exact degreeUnionBranch43_113 + · exact degreeUnionBranch43_114 + · exact degreeUnionBranch43_115 + · exact degreeUnionBranch43_116 + · exact degreeUnionBranch43_117 + · exact degreeUnionBranch43_118 + · exact degreeUnionBranch43_119 + · exact degreeUnionBranch43_120 + · exact degreeUnionBranch43_121 + · exact degreeUnionBranch43_122 + · exact degreeUnionBranch43_123 + · exact degreeUnionBranch43_124 + +lemma degreeUnionBranch43_125 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 24 19 degreeUnionState43_125 [19] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 19 at hb + change 24 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_126 + · exact degreeUnionBranch43_127 + · exact degreeUnionBranch43_128 + · exact degreeUnionBranch43_129 + · exact degreeUnionBranch43_130 + · exact degreeUnionBranch43_131 + · exact degreeUnionBranch43_132 + · exact degreeUnionBranch43_133 + · exact degreeUnionBranch43_134 + · exact degreeUnionBranch43_135 + · exact degreeUnionBranch43_136 + · exact degreeUnionBranch43_137 + · exact degreeUnionBranch43_138 + · exact degreeUnionBranch43_139 + · exact degreeUnionBranch43_140 + · exact degreeUnionBranch43_141 + +lemma degreeUnionBranch43_142 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 23 20 degreeUnionState43_142 [20] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 20 at hb + change 23 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_143 + · exact degreeUnionBranch43_144 + · exact degreeUnionBranch43_145 + · exact degreeUnionBranch43_146 + · exact degreeUnionBranch43_147 + · exact degreeUnionBranch43_148 + · exact degreeUnionBranch43_149 + · exact degreeUnionBranch43_150 + · exact degreeUnionBranch43_151 + · exact degreeUnionBranch43_152 + · exact degreeUnionBranch43_153 + · exact degreeUnionBranch43_154 + · exact degreeUnionBranch43_155 + · exact degreeUnionBranch43_156 + · exact degreeUnionBranch43_157 + · exact degreeUnionBranch43_158 + · exact degreeUnionBranch43_159 + +lemma degreeUnionBranch43_8 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 43 42 degreeHalfRegions43 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 5 ≤ a at ha + change a ≤ 42 at hb + change 43 ≤ 8*a at hn + have hlo : 6 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_9 + · exact degreeUnionBranch43_10 + · exact degreeUnionBranch43_11 + · exact degreeUnionBranch43_16 + · exact degreeUnionBranch43_22 + · exact degreeUnionBranch43_29 + · exact degreeUnionBranch43_37 + · exact degreeUnionBranch43_46 + · exact degreeUnionBranch43_56 + · exact degreeUnionBranch43_67 + · exact degreeUnionBranch43_80 + · exact degreeUnionBranch43_94 + · exact degreeUnionBranch43_109 + · exact degreeUnionBranch43_125 + · exact degreeUnionBranch43_142 + · exact degreeUnionBranch43_160 + · exact degreeUnionBranch43_161 + · exact degreeUnionBranch43_162 + · exact degreeUnionBranch43_163 + · exact degreeUnionBranch43_164 + · exact degreeUnionBranch43_165 + · exact degreeUnionBranch43_166 + · exact degreeUnionBranch43_167 + · exact degreeUnionBranch43_168 + · exact degreeUnionBranch43_169 + · exact degreeUnionBranch43_170 + · exact degreeUnionBranch43_171 + · exact degreeUnionBranch43_172 + · exact degreeUnionBranch43_173 + · exact degreeUnionBranch43_174 + · exact degreeUnionBranch43_175 + · exact degreeUnionBranch43_176 + · exact degreeUnionBranch43_177 + · exact degreeUnionBranch43_178 + · exact degreeUnionBranch43_179 + · exact degreeUnionBranch43_180 + · exact degreeUnionBranch43_181 + +lemma degreeUnionBranch43_186 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 35 8 degreeUnionState43_186 [8] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 8 at hb + change 35 ≤ 8*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_187 + · exact degreeUnionBranch43_188 + · exact degreeUnionBranch43_189 + · exact degreeUnionBranch43_190 + +lemma degreeUnionBranch43_196 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 7 25 9 degreeUnionState43_196 [9,9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 25 ≤ 7*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_197 + · exact degreeUnionBranch43_198 + · exact degreeUnionBranch43_199 + · exact degreeUnionBranch43_200 + · exact degreeUnionBranch43_201 + · exact degreeUnionBranch43_202 + +lemma degreeUnionBranch43_191 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 34 9 degreeUnionState43_191 [9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 9 at hb + change 34 ≤ 8*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_192 + · exact degreeUnionBranch43_193 + · exact degreeUnionBranch43_194 + · exact degreeUnionBranch43_195 + · exact degreeUnionBranch43_196 + +lemma degreeUnionBranch43_203 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 33 10 degreeUnionState43_203 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 10 at hb + change 33 ≤ 8*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_204 + · exact degreeUnionBranch43_205 + · exact degreeUnionBranch43_206 + · exact degreeUnionBranch43_207 + · exact degreeUnionBranch43_208 + · exact degreeUnionBranch43_209 + +lemma degreeUnionBranch43_210 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 32 11 degreeUnionState43_210 [11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 11 at hb + change 32 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_211 + · exact degreeUnionBranch43_212 + · exact degreeUnionBranch43_213 + · exact degreeUnionBranch43_214 + · exact degreeUnionBranch43_215 + · exact degreeUnionBranch43_216 + · exact degreeUnionBranch43_217 + · exact degreeUnionBranch43_218 + +lemma degreeUnionBranch43_219 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 31 12 degreeUnionState43_219 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 31 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_220 + · exact degreeUnionBranch43_221 + · exact degreeUnionBranch43_222 + · exact degreeUnionBranch43_223 + · exact degreeUnionBranch43_224 + · exact degreeUnionBranch43_225 + · exact degreeUnionBranch43_226 + · exact degreeUnionBranch43_227 + · exact degreeUnionBranch43_228 + +lemma degreeUnionBranch43_229 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 30 13 degreeUnionState43_229 [13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 13 at hb + change 30 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_230 + · exact degreeUnionBranch43_231 + · exact degreeUnionBranch43_232 + · exact degreeUnionBranch43_233 + · exact degreeUnionBranch43_234 + · exact degreeUnionBranch43_235 + · exact degreeUnionBranch43_236 + · exact degreeUnionBranch43_237 + · exact degreeUnionBranch43_238 + · exact degreeUnionBranch43_239 + +lemma degreeUnionBranch43_240 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 29 14 degreeUnionState43_240 [14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 14 at hb + change 29 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_241 + · exact degreeUnionBranch43_242 + · exact degreeUnionBranch43_243 + · exact degreeUnionBranch43_244 + · exact degreeUnionBranch43_245 + · exact degreeUnionBranch43_246 + · exact degreeUnionBranch43_247 + · exact degreeUnionBranch43_248 + · exact degreeUnionBranch43_249 + · exact degreeUnionBranch43_250 + · exact degreeUnionBranch43_251 + +lemma degreeUnionBranch43_252 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 28 15 degreeUnionState43_252 [15] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 15 at hb + change 28 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_253 + · exact degreeUnionBranch43_254 + · exact degreeUnionBranch43_255 + · exact degreeUnionBranch43_256 + · exact degreeUnionBranch43_257 + · exact degreeUnionBranch43_258 + · exact degreeUnionBranch43_259 + · exact degreeUnionBranch43_260 + · exact degreeUnionBranch43_261 + · exact degreeUnionBranch43_262 + · exact degreeUnionBranch43_263 + · exact degreeUnionBranch43_264 + +lemma degreeUnionBranch43_265 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 27 16 degreeUnionState43_265 [16] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 16 at hb + change 27 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_266 + · exact degreeUnionBranch43_267 + · exact degreeUnionBranch43_268 + · exact degreeUnionBranch43_269 + · exact degreeUnionBranch43_270 + · exact degreeUnionBranch43_271 + · exact degreeUnionBranch43_272 + · exact degreeUnionBranch43_273 + · exact degreeUnionBranch43_274 + · exact degreeUnionBranch43_275 + · exact degreeUnionBranch43_276 + · exact degreeUnionBranch43_277 + · exact degreeUnionBranch43_278 + +lemma degreeUnionBranch43_279 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 26 17 degreeUnionState43_279 [17] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 17 at hb + change 26 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_280 + · exact degreeUnionBranch43_281 + · exact degreeUnionBranch43_282 + · exact degreeUnionBranch43_283 + · exact degreeUnionBranch43_284 + · exact degreeUnionBranch43_285 + · exact degreeUnionBranch43_286 + · exact degreeUnionBranch43_287 + · exact degreeUnionBranch43_288 + · exact degreeUnionBranch43_289 + · exact degreeUnionBranch43_290 + · exact degreeUnionBranch43_291 + · exact degreeUnionBranch43_292 + · exact degreeUnionBranch43_293 + +lemma degreeUnionBranch43_294 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 18 degreeUnionState43_294 [18] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 18 at hb + change 25 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_295 + · exact degreeUnionBranch43_296 + · exact degreeUnionBranch43_297 + · exact degreeUnionBranch43_298 + · exact degreeUnionBranch43_299 + · exact degreeUnionBranch43_300 + · exact degreeUnionBranch43_301 + · exact degreeUnionBranch43_302 + · exact degreeUnionBranch43_303 + · exact degreeUnionBranch43_304 + · exact degreeUnionBranch43_305 + · exact degreeUnionBranch43_306 + · exact degreeUnionBranch43_307 + · exact degreeUnionBranch43_308 + · exact degreeUnionBranch43_309 + +lemma degreeUnionBranch43_310 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 24 19 degreeUnionState43_310 [19] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 19 at hb + change 24 ≤ 8*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_311 + · exact degreeUnionBranch43_312 + · exact degreeUnionBranch43_313 + · exact degreeUnionBranch43_314 + · exact degreeUnionBranch43_315 + · exact degreeUnionBranch43_316 + · exact degreeUnionBranch43_317 + · exact degreeUnionBranch43_318 + · exact degreeUnionBranch43_319 + · exact degreeUnionBranch43_320 + · exact degreeUnionBranch43_321 + · exact degreeUnionBranch43_322 + · exact degreeUnionBranch43_323 + · exact degreeUnionBranch43_324 + · exact degreeUnionBranch43_325 + · exact degreeUnionBranch43_326 + · exact degreeUnionBranch43_327 + +lemma degreeUnionBranch43_182 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 43 42 degreeHalfRegions43 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 42 at hb + change 43 ≤ 9*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_183 + · exact degreeUnionBranch43_184 + · exact degreeUnionBranch43_185 + · exact degreeUnionBranch43_186 + · exact degreeUnionBranch43_191 + · exact degreeUnionBranch43_203 + · exact degreeUnionBranch43_210 + · exact degreeUnionBranch43_219 + · exact degreeUnionBranch43_229 + · exact degreeUnionBranch43_240 + · exact degreeUnionBranch43_252 + · exact degreeUnionBranch43_265 + · exact degreeUnionBranch43_279 + · exact degreeUnionBranch43_294 + · exact degreeUnionBranch43_310 + · exact degreeUnionBranch43_328 + · exact degreeUnionBranch43_329 + · exact degreeUnionBranch43_330 + · exact degreeUnionBranch43_331 + · exact degreeUnionBranch43_332 + · exact degreeUnionBranch43_333 + · exact degreeUnionBranch43_334 + · exact degreeUnionBranch43_335 + · exact degreeUnionBranch43_336 + · exact degreeUnionBranch43_337 + · exact degreeUnionBranch43_338 + · exact degreeUnionBranch43_339 + · exact degreeUnionBranch43_340 + · exact degreeUnionBranch43_341 + · exact degreeUnionBranch43_342 + · exact degreeUnionBranch43_343 + · exact degreeUnionBranch43_344 + · exact degreeUnionBranch43_345 + · exact degreeUnionBranch43_346 + · exact degreeUnionBranch43_347 + · exact degreeUnionBranch43_348 + · exact degreeUnionBranch43_349 + · exact degreeUnionBranch43_350 + +lemma degreeUnionBranch43_360 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 27 8 degreeUnionState43_360 [8,8] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 27 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_361 + · exact degreeUnionBranch43_362 + · exact degreeUnionBranch43_363 + · exact degreeUnionBranch43_364 + · exact degreeUnionBranch43_365 + +lemma degreeUnionBranch43_355 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 35 8 degreeUnionState43_355 [8] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 35 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_356 + · exact degreeUnionBranch43_357 + · exact degreeUnionBranch43_358 + · exact degreeUnionBranch43_359 + · exact degreeUnionBranch43_360 + +lemma degreeUnionBranch43_371 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 26 8 degreeUnionState43_371 [8,9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 26 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_372 + · exact degreeUnionBranch43_373 + · exact degreeUnionBranch43_374 + · exact degreeUnionBranch43_375 + · exact degreeUnionBranch43_376 + +lemma degreeUnionBranch43_377 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 8 25 9 degreeUnionState43_377 [9,9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 25 ≤ 8*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_378 + · exact degreeUnionBranch43_379 + · exact degreeUnionBranch43_380 + · exact degreeUnionBranch43_381 + · exact degreeUnionBranch43_382 + · exact degreeUnionBranch43_383 + +lemma degreeUnionBranch43_366 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 34 9 degreeUnionState43_366 [9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 34 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_367 + · exact degreeUnionBranch43_368 + · exact degreeUnionBranch43_369 + · exact degreeUnionBranch43_370 + · exact degreeUnionBranch43_371 + · exact degreeUnionBranch43_377 + +lemma degreeUnionBranch43_384 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 33 10 degreeUnionState43_384 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 33 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_385 + · exact degreeUnionBranch43_386 + · exact degreeUnionBranch43_387 + · exact degreeUnionBranch43_388 + · exact degreeUnionBranch43_389 + · exact degreeUnionBranch43_390 + · exact degreeUnionBranch43_391 + +lemma degreeUnionBranch43_392 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 32 11 degreeUnionState43_392 [11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 32 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_393 + · exact degreeUnionBranch43_394 + · exact degreeUnionBranch43_395 + · exact degreeUnionBranch43_396 + · exact degreeUnionBranch43_397 + · exact degreeUnionBranch43_398 + · exact degreeUnionBranch43_399 + · exact degreeUnionBranch43_400 + +lemma degreeUnionBranch43_401 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 31 12 degreeUnionState43_401 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 31 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_402 + · exact degreeUnionBranch43_403 + · exact degreeUnionBranch43_404 + · exact degreeUnionBranch43_405 + · exact degreeUnionBranch43_406 + · exact degreeUnionBranch43_407 + · exact degreeUnionBranch43_408 + · exact degreeUnionBranch43_409 + · exact degreeUnionBranch43_410 + +lemma degreeUnionBranch43_411 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 30 13 degreeUnionState43_411 [13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 13 at hb + change 30 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_412 + · exact degreeUnionBranch43_413 + · exact degreeUnionBranch43_414 + · exact degreeUnionBranch43_415 + · exact degreeUnionBranch43_416 + · exact degreeUnionBranch43_417 + · exact degreeUnionBranch43_418 + · exact degreeUnionBranch43_419 + · exact degreeUnionBranch43_420 + · exact degreeUnionBranch43_421 + +lemma degreeUnionBranch43_422 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 29 14 degreeUnionState43_422 [14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 14 at hb + change 29 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_423 + · exact degreeUnionBranch43_424 + · exact degreeUnionBranch43_425 + · exact degreeUnionBranch43_426 + · exact degreeUnionBranch43_427 + · exact degreeUnionBranch43_428 + · exact degreeUnionBranch43_429 + · exact degreeUnionBranch43_430 + · exact degreeUnionBranch43_431 + · exact degreeUnionBranch43_432 + · exact degreeUnionBranch43_433 + +lemma degreeUnionBranch43_434 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 28 15 degreeUnionState43_434 [15] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 15 at hb + change 28 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_435 + · exact degreeUnionBranch43_436 + · exact degreeUnionBranch43_437 + · exact degreeUnionBranch43_438 + · exact degreeUnionBranch43_439 + · exact degreeUnionBranch43_440 + · exact degreeUnionBranch43_441 + · exact degreeUnionBranch43_442 + · exact degreeUnionBranch43_443 + · exact degreeUnionBranch43_444 + · exact degreeUnionBranch43_445 + · exact degreeUnionBranch43_446 + +lemma degreeUnionBranch43_447 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 27 16 degreeUnionState43_447 [16] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 16 at hb + change 27 ≤ 9*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_448 + · exact degreeUnionBranch43_449 + · exact degreeUnionBranch43_450 + · exact degreeUnionBranch43_451 + · exact degreeUnionBranch43_452 + · exact degreeUnionBranch43_453 + · exact degreeUnionBranch43_454 + · exact degreeUnionBranch43_455 + · exact degreeUnionBranch43_456 + · exact degreeUnionBranch43_457 + · exact degreeUnionBranch43_458 + · exact degreeUnionBranch43_459 + · exact degreeUnionBranch43_460 + · exact degreeUnionBranch43_461 + +lemma degreeUnionBranch43_462 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 26 17 degreeUnionState43_462 [17] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 17 at hb + change 26 ≤ 9*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_463 + · exact degreeUnionBranch43_464 + · exact degreeUnionBranch43_465 + · exact degreeUnionBranch43_466 + · exact degreeUnionBranch43_467 + · exact degreeUnionBranch43_468 + · exact degreeUnionBranch43_469 + · exact degreeUnionBranch43_470 + · exact degreeUnionBranch43_471 + · exact degreeUnionBranch43_472 + · exact degreeUnionBranch43_473 + · exact degreeUnionBranch43_474 + · exact degreeUnionBranch43_475 + · exact degreeUnionBranch43_476 + · exact degreeUnionBranch43_477 + +lemma degreeUnionBranch43_478 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 25 18 degreeUnionState43_478 [18] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 18 at hb + change 25 ≤ 9*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_479 + · exact degreeUnionBranch43_480 + · exact degreeUnionBranch43_481 + · exact degreeUnionBranch43_482 + · exact degreeUnionBranch43_483 + · exact degreeUnionBranch43_484 + · exact degreeUnionBranch43_485 + · exact degreeUnionBranch43_486 + · exact degreeUnionBranch43_487 + · exact degreeUnionBranch43_488 + · exact degreeUnionBranch43_489 + · exact degreeUnionBranch43_490 + · exact degreeUnionBranch43_491 + · exact degreeUnionBranch43_492 + · exact degreeUnionBranch43_493 + · exact degreeUnionBranch43_494 + +lemma degreeUnionBranch43_495 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 9 24 19 degreeUnionState43_495 [19] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 19 at hb + change 24 ≤ 9*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_496 + · exact degreeUnionBranch43_497 + · exact degreeUnionBranch43_498 + · exact degreeUnionBranch43_499 + · exact degreeUnionBranch43_500 + · exact degreeUnionBranch43_501 + · exact degreeUnionBranch43_502 + · exact degreeUnionBranch43_503 + · exact degreeUnionBranch43_504 + · exact degreeUnionBranch43_505 + · exact degreeUnionBranch43_506 + · exact degreeUnionBranch43_507 + · exact degreeUnionBranch43_508 + · exact degreeUnionBranch43_509 + · exact degreeUnionBranch43_510 + · exact degreeUnionBranch43_511 + · exact degreeUnionBranch43_512 + +lemma degreeUnionBranch43_351 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 43 42 degreeHalfRegions43 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 42 at hb + change 43 ≤ 10*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_352 + · exact degreeUnionBranch43_353 + · exact degreeUnionBranch43_354 + · exact degreeUnionBranch43_355 + · exact degreeUnionBranch43_366 + · exact degreeUnionBranch43_384 + · exact degreeUnionBranch43_392 + · exact degreeUnionBranch43_401 + · exact degreeUnionBranch43_411 + · exact degreeUnionBranch43_422 + · exact degreeUnionBranch43_434 + · exact degreeUnionBranch43_447 + · exact degreeUnionBranch43_462 + · exact degreeUnionBranch43_478 + · exact degreeUnionBranch43_495 + · exact degreeUnionBranch43_513 + · exact degreeUnionBranch43_514 + · exact degreeUnionBranch43_515 + · exact degreeUnionBranch43_516 + · exact degreeUnionBranch43_517 + · exact degreeUnionBranch43_518 + · exact degreeUnionBranch43_519 + · exact degreeUnionBranch43_520 + · exact degreeUnionBranch43_521 + · exact degreeUnionBranch43_522 + · exact degreeUnionBranch43_523 + · exact degreeUnionBranch43_524 + · exact degreeUnionBranch43_525 + · exact degreeUnionBranch43_526 + · exact degreeUnionBranch43_527 + · exact degreeUnionBranch43_528 + · exact degreeUnionBranch43_529 + · exact degreeUnionBranch43_530 + · exact degreeUnionBranch43_531 + · exact degreeUnionBranch43_532 + · exact degreeUnionBranch43_533 + · exact degreeUnionBranch43_534 + · exact degreeUnionBranch43_535 + +lemma degreeUnionBranch43_541 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 35 8 degreeUnionState43_541 [8] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 35 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_542 + · exact degreeUnionBranch43_543 + · exact degreeUnionBranch43_544 + · exact degreeUnionBranch43_545 + · exact degreeUnionBranch43_546 + +lemma degreeUnionBranch43_547 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 34 9 degreeUnionState43_547 [9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 34 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_548 + · exact degreeUnionBranch43_549 + · exact degreeUnionBranch43_550 + · exact degreeUnionBranch43_551 + · exact degreeUnionBranch43_552 + · exact degreeUnionBranch43_553 + +lemma degreeUnionBranch43_554 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 33 10 degreeUnionState43_554 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 33 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_555 + · exact degreeUnionBranch43_556 + · exact degreeUnionBranch43_557 + · exact degreeUnionBranch43_558 + · exact degreeUnionBranch43_559 + · exact degreeUnionBranch43_560 + · exact degreeUnionBranch43_561 + +lemma degreeUnionBranch43_562 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 32 11 degreeUnionState43_562 [11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 32 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_563 + · exact degreeUnionBranch43_564 + · exact degreeUnionBranch43_565 + · exact degreeUnionBranch43_566 + · exact degreeUnionBranch43_567 + · exact degreeUnionBranch43_568 + · exact degreeUnionBranch43_569 + · exact degreeUnionBranch43_570 + +lemma degreeUnionBranch43_571 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 10 31 12 degreeUnionState43_571 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 31 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_572 + · exact degreeUnionBranch43_573 + · exact degreeUnionBranch43_574 + · exact degreeUnionBranch43_575 + · exact degreeUnionBranch43_576 + · exact degreeUnionBranch43_577 + · exact degreeUnionBranch43_578 + · exact degreeUnionBranch43_579 + · exact degreeUnionBranch43_580 + +lemma degreeUnionBranch43_536 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 43 42 degreeHalfRegions43 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 42 at hb + change 43 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_537 + · exact degreeUnionBranch43_538 + · exact degreeUnionBranch43_539 + · exact degreeUnionBranch43_540 + · exact degreeUnionBranch43_541 + · exact degreeUnionBranch43_547 + · exact degreeUnionBranch43_554 + · exact degreeUnionBranch43_562 + · exact degreeUnionBranch43_571 + · exact degreeUnionBranch43_581 + · exact degreeUnionBranch43_582 + · exact degreeUnionBranch43_583 + · exact degreeUnionBranch43_584 + · exact degreeUnionBranch43_585 + · exact degreeUnionBranch43_586 + · exact degreeUnionBranch43_587 + · exact degreeUnionBranch43_588 + · exact degreeUnionBranch43_589 + · exact degreeUnionBranch43_590 + · exact degreeUnionBranch43_591 + · exact degreeUnionBranch43_592 + · exact degreeUnionBranch43_593 + · exact degreeUnionBranch43_594 + · exact degreeUnionBranch43_595 + · exact degreeUnionBranch43_596 + · exact degreeUnionBranch43_597 + · exact degreeUnionBranch43_598 + · exact degreeUnionBranch43_599 + · exact degreeUnionBranch43_600 + · exact degreeUnionBranch43_601 + · exact degreeUnionBranch43_602 + · exact degreeUnionBranch43_603 + · exact degreeUnionBranch43_604 + · exact degreeUnionBranch43_605 + · exact degreeUnionBranch43_606 + · exact degreeUnionBranch43_607 + · exact degreeUnionBranch43_608 + · exact degreeUnionBranch43_609 + · exact degreeUnionBranch43_610 + +lemma degreeUnionBranch43_617 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 34 9 degreeUnionState43_617 [9] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 34 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_618 + · exact degreeUnionBranch43_619 + · exact degreeUnionBranch43_620 + · exact degreeUnionBranch43_621 + · exact degreeUnionBranch43_622 + · exact degreeUnionBranch43_623 + +lemma degreeUnionBranch43_624 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 33 10 degreeUnionState43_624 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 33 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_625 + · exact degreeUnionBranch43_626 + · exact degreeUnionBranch43_627 + · exact degreeUnionBranch43_628 + · exact degreeUnionBranch43_629 + · exact degreeUnionBranch43_630 + · exact degreeUnionBranch43_631 + · exact degreeUnionBranch43_632 + +lemma degreeUnionBranch43_633 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 32 11 degreeUnionState43_633 [11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 11 at hb + change 32 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_634 + · exact degreeUnionBranch43_635 + · exact degreeUnionBranch43_636 + · exact degreeUnionBranch43_637 + · exact degreeUnionBranch43_638 + · exact degreeUnionBranch43_639 + · exact degreeUnionBranch43_640 + · exact degreeUnionBranch43_641 + · exact degreeUnionBranch43_642 + +lemma degreeUnionBranch43_643 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 11 31 12 degreeUnionState43_643 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 12 at hb + change 31 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_644 + · exact degreeUnionBranch43_645 + · exact degreeUnionBranch43_646 + · exact degreeUnionBranch43_647 + · exact degreeUnionBranch43_648 + · exact degreeUnionBranch43_649 + · exact degreeUnionBranch43_650 + · exact degreeUnionBranch43_651 + · exact degreeUnionBranch43_652 + · exact degreeUnionBranch43_653 + +lemma degreeUnionBranch43_611 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 43 42 degreeHalfRegions43 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 42 at hb + change 43 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_612 + · exact degreeUnionBranch43_613 + · exact degreeUnionBranch43_614 + · exact degreeUnionBranch43_615 + · exact degreeUnionBranch43_616 + · exact degreeUnionBranch43_617 + · exact degreeUnionBranch43_624 + · exact degreeUnionBranch43_633 + · exact degreeUnionBranch43_643 + · exact degreeUnionBranch43_654 + · exact degreeUnionBranch43_655 + · exact degreeUnionBranch43_656 + · exact degreeUnionBranch43_657 + · exact degreeUnionBranch43_658 + · exact degreeUnionBranch43_659 + · exact degreeUnionBranch43_660 + · exact degreeUnionBranch43_661 + · exact degreeUnionBranch43_662 + · exact degreeUnionBranch43_663 + · exact degreeUnionBranch43_664 + · exact degreeUnionBranch43_665 + · exact degreeUnionBranch43_666 + · exact degreeUnionBranch43_667 + · exact degreeUnionBranch43_668 + · exact degreeUnionBranch43_669 + · exact degreeUnionBranch43_670 + · exact degreeUnionBranch43_671 + · exact degreeUnionBranch43_672 + · exact degreeUnionBranch43_673 + · exact degreeUnionBranch43_674 + · exact degreeUnionBranch43_675 + · exact degreeUnionBranch43_676 + · exact degreeUnionBranch43_677 + · exact degreeUnionBranch43_678 + · exact degreeUnionBranch43_679 + · exact degreeUnionBranch43_680 + · exact degreeUnionBranch43_681 + · exact degreeUnionBranch43_682 + · exact degreeUnionBranch43_683 + +lemma degreeUnionBranch43_691 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 12 33 10 degreeUnionState43_691 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 10 at hb + change 33 ≤ 12*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_692 + · exact degreeUnionBranch43_693 + · exact degreeUnionBranch43_694 + · exact degreeUnionBranch43_695 + · exact degreeUnionBranch43_696 + · exact degreeUnionBranch43_697 + · exact degreeUnionBranch43_698 + · exact degreeUnionBranch43_699 + +lemma degreeUnionBranch43_684 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 13 43 42 degreeHalfRegions43 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 42 at hb + change 43 ≤ 13*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_685 + · exact degreeUnionBranch43_686 + · exact degreeUnionBranch43_687 + · exact degreeUnionBranch43_688 + · exact degreeUnionBranch43_689 + · exact degreeUnionBranch43_690 + · exact degreeUnionBranch43_691 + · exact degreeUnionBranch43_700 + · exact degreeUnionBranch43_701 + · exact degreeUnionBranch43_702 + · exact degreeUnionBranch43_703 + · exact degreeUnionBranch43_704 + · exact degreeUnionBranch43_705 + · exact degreeUnionBranch43_706 + · exact degreeUnionBranch43_707 + · exact degreeUnionBranch43_708 + · exact degreeUnionBranch43_709 + · exact degreeUnionBranch43_710 + · exact degreeUnionBranch43_711 + · exact degreeUnionBranch43_712 + · exact degreeUnionBranch43_713 + · exact degreeUnionBranch43_714 + · exact degreeUnionBranch43_715 + · exact degreeUnionBranch43_716 + · exact degreeUnionBranch43_717 + · exact degreeUnionBranch43_718 + · exact degreeUnionBranch43_719 + · exact degreeUnionBranch43_720 + · exact degreeUnionBranch43_721 + · exact degreeUnionBranch43_722 + · exact degreeUnionBranch43_723 + · exact degreeUnionBranch43_724 + · exact degreeUnionBranch43_725 + · exact degreeUnionBranch43_726 + · exact degreeUnionBranch43_727 + · exact degreeUnionBranch43_728 + · exact degreeUnionBranch43_729 + · exact degreeUnionBranch43_730 + · exact degreeUnionBranch43_731 + +lemma degreeUnionBranch43_732 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 14 43 42 degreeHalfRegions43 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 42 at hb + change 43 ≤ 14*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_733 + · exact degreeUnionBranch43_734 + · exact degreeUnionBranch43_735 + · exact degreeUnionBranch43_736 + · exact degreeUnionBranch43_737 + · exact degreeUnionBranch43_738 + · exact degreeUnionBranch43_739 + · exact degreeUnionBranch43_740 + · exact degreeUnionBranch43_741 + · exact degreeUnionBranch43_742 + · exact degreeUnionBranch43_743 + · exact degreeUnionBranch43_744 + · exact degreeUnionBranch43_745 + · exact degreeUnionBranch43_746 + · exact degreeUnionBranch43_747 + · exact degreeUnionBranch43_748 + · exact degreeUnionBranch43_749 + · exact degreeUnionBranch43_750 + · exact degreeUnionBranch43_751 + · exact degreeUnionBranch43_752 + · exact degreeUnionBranch43_753 + · exact degreeUnionBranch43_754 + · exact degreeUnionBranch43_755 + · exact degreeUnionBranch43_756 + · exact degreeUnionBranch43_757 + · exact degreeUnionBranch43_758 + · exact degreeUnionBranch43_759 + · exact degreeUnionBranch43_760 + · exact degreeUnionBranch43_761 + · exact degreeUnionBranch43_762 + · exact degreeUnionBranch43_763 + · exact degreeUnionBranch43_764 + · exact degreeUnionBranch43_765 + · exact degreeUnionBranch43_766 + · exact degreeUnionBranch43_767 + · exact degreeUnionBranch43_768 + · exact degreeUnionBranch43_769 + · exact degreeUnionBranch43_770 + · exact degreeUnionBranch43_771 + +lemma degreeUnionBranch43_772 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 15 43 42 degreeHalfRegions43 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 42 at hb + change 43 ≤ 15*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_773 + · exact degreeUnionBranch43_774 + · exact degreeUnionBranch43_775 + · exact degreeUnionBranch43_776 + · exact degreeUnionBranch43_777 + · exact degreeUnionBranch43_778 + · exact degreeUnionBranch43_779 + · exact degreeUnionBranch43_780 + · exact degreeUnionBranch43_781 + · exact degreeUnionBranch43_782 + · exact degreeUnionBranch43_783 + · exact degreeUnionBranch43_784 + · exact degreeUnionBranch43_785 + · exact degreeUnionBranch43_786 + · exact degreeUnionBranch43_787 + · exact degreeUnionBranch43_788 + · exact degreeUnionBranch43_789 + · exact degreeUnionBranch43_790 + · exact degreeUnionBranch43_791 + · exact degreeUnionBranch43_792 + · exact degreeUnionBranch43_793 + · exact degreeUnionBranch43_794 + · exact degreeUnionBranch43_795 + · exact degreeUnionBranch43_796 + · exact degreeUnionBranch43_797 + · exact degreeUnionBranch43_798 + · exact degreeUnionBranch43_799 + · exact degreeUnionBranch43_800 + · exact degreeUnionBranch43_801 + · exact degreeUnionBranch43_802 + · exact degreeUnionBranch43_803 + · exact degreeUnionBranch43_804 + · exact degreeUnionBranch43_805 + · exact degreeUnionBranch43_806 + · exact degreeUnionBranch43_807 + · exact degreeUnionBranch43_808 + · exact degreeUnionBranch43_809 + · exact degreeUnionBranch43_810 + · exact degreeUnionBranch43_811 + · exact degreeUnionBranch43_812 + +lemma degreeUnionBranch43_813 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 16 43 42 degreeHalfRegions43 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 42 at hb + change 43 ≤ 16*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_814 + · exact degreeUnionBranch43_815 + · exact degreeUnionBranch43_816 + · exact degreeUnionBranch43_817 + · exact degreeUnionBranch43_818 + · exact degreeUnionBranch43_819 + · exact degreeUnionBranch43_820 + · exact degreeUnionBranch43_821 + · exact degreeUnionBranch43_822 + · exact degreeUnionBranch43_823 + · exact degreeUnionBranch43_824 + · exact degreeUnionBranch43_825 + · exact degreeUnionBranch43_826 + · exact degreeUnionBranch43_827 + · exact degreeUnionBranch43_828 + · exact degreeUnionBranch43_829 + · exact degreeUnionBranch43_830 + · exact degreeUnionBranch43_831 + · exact degreeUnionBranch43_832 + · exact degreeUnionBranch43_833 + · exact degreeUnionBranch43_834 + · exact degreeUnionBranch43_835 + · exact degreeUnionBranch43_836 + · exact degreeUnionBranch43_837 + · exact degreeUnionBranch43_838 + · exact degreeUnionBranch43_839 + · exact degreeUnionBranch43_840 + · exact degreeUnionBranch43_841 + · exact degreeUnionBranch43_842 + · exact degreeUnionBranch43_843 + · exact degreeUnionBranch43_844 + · exact degreeUnionBranch43_845 + · exact degreeUnionBranch43_846 + · exact degreeUnionBranch43_847 + · exact degreeUnionBranch43_848 + · exact degreeUnionBranch43_849 + · exact degreeUnionBranch43_850 + · exact degreeUnionBranch43_851 + · exact degreeUnionBranch43_852 + · exact degreeUnionBranch43_853 + +lemma degreeUnionBranch43_854 : checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) 17 43 42 degreeHalfRegions43 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 42 at hb + change 43 ≤ 17*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch43_855 + · exact degreeUnionBranch43_856 + · exact degreeUnionBranch43_857 + · exact degreeUnionBranch43_858 + · exact degreeUnionBranch43_859 + · exact degreeUnionBranch43_860 + · exact degreeUnionBranch43_861 + · exact degreeUnionBranch43_862 + · exact degreeUnionBranch43_863 + · exact degreeUnionBranch43_864 + · exact degreeUnionBranch43_865 + · exact degreeUnionBranch43_866 + · exact degreeUnionBranch43_867 + · exact degreeUnionBranch43_868 + · exact degreeUnionBranch43_869 + · exact degreeUnionBranch43_870 + · exact degreeUnionBranch43_871 + · exact degreeUnionBranch43_872 + · exact degreeUnionBranch43_873 + · exact degreeUnionBranch43_874 + · exact degreeUnionBranch43_875 + · exact degreeUnionBranch43_876 + · exact degreeUnionBranch43_877 + · exact degreeUnionBranch43_878 + · exact degreeUnionBranch43_879 + · exact degreeUnionBranch43_880 + · exact degreeUnionBranch43_881 + · exact degreeUnionBranch43_882 + · exact degreeUnionBranch43_883 + · exact degreeUnionBranch43_884 + · exact degreeUnionBranch43_885 + · exact degreeUnionBranch43_886 + · exact degreeUnionBranch43_887 + · exact degreeUnionBranch43_888 + · exact degreeUnionBranch43_889 + · exact degreeUnionBranch43_890 + · exact degreeUnionBranch43_891 + · exact degreeUnionBranch43_892 + · exact degreeUnionBranch43_893 + · exact degreeUnionBranch43_894 + +lemma degreeUnionCheck43 : ∀ h ≤ 23, + checkRegionPrefixes (quickResidual 6 11 degreeQs43 degreeTree43) h 43 42 degreeHalfRegions43 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch43_0 + · exact degreeUnionBranch43_1 + · exact degreeUnionBranch43_2 + · exact degreeUnionBranch43_3 + · exact degreeUnionBranch43_4 + · exact degreeUnionBranch43_5 + · exact degreeUnionBranch43_6 + · exact degreeUnionBranch43_7 + · exact degreeUnionBranch43_8 + · exact degreeUnionBranch43_182 + · exact degreeUnionBranch43_351 + · exact degreeUnionBranch43_536 + · exact degreeUnionBranch43_611 + · exact degreeUnionBranch43_684 + · exact degreeUnionBranch43_732 + · exact degreeUnionBranch43_772 + · exact degreeUnionBranch43_813 + · exact degreeUnionBranch43_854 + · exact degreeUnionBranch43_895 + · exact degreeUnionBranch43_896 + · exact degreeUnionBranch43_897 + · exact degreeUnionBranch43_898 + · exact degreeUnionBranch43_899 + · exact degreeUnionBranch43_900 + +lemma degreeHalfCover43 : ∀ R ∈ degreeRegions43, + R ∈ degreeHalfRegions43 ∨ (R.2,R.1) ∈ degreeHalfRegions43 := by decide +kernel + +lemma degreeDiagramRegionsChecked43 : ∀ R ∈ degreeRegions43, + ∀ μ : YoungDiagram, μ.card = 43 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP43 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck43 degreeHalfHeight43 degreeHalfWidth43 + degreeHalfCover43 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions58.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions58.lean index e318673522a597f79b8a7f48d6308a552e1186d7..f363cd44efd40aa3bd6daed33abeafc95c3709bb 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions58.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions58.lean @@ -1,253 +1,253 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves58 - -namespace OAI - -/-! Degree Regions 58. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch58_25 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 37 9 degreeUnionState58_25 [9,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 37 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch58_26 - · exact degreeUnionBranch58_27 - · exact degreeUnionBranch58_28 - · exact degreeUnionBranch58_29 - · exact degreeUnionBranch58_30 - · exact degreeUnionBranch58_31 - -lemma degreeUnionBranch58_20 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 46 12 degreeUnionState58_20 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 12 at hb - change 46 ≤ 11*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch58_21 - · exact degreeUnionBranch58_22 - · exact degreeUnionBranch58_23 - · exact degreeUnionBranch58_24 - · exact degreeUnionBranch58_25 - · exact degreeUnionBranch58_32 - · exact degreeUnionBranch58_33 - · exact degreeUnionBranch58_34 - -lemma degreeUnionBranch58_39 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 37 8 degreeUnionState58_39 [8,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 37 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch58_40 - · exact degreeUnionBranch58_41 - · exact degreeUnionBranch58_42 - · exact degreeUnionBranch58_43 - · exact degreeUnionBranch58_44 - -lemma degreeUnionBranch58_35 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 45 13 degreeUnionState58_35 [13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 13 at hb - change 45 ≤ 11*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch58_36 - · exact degreeUnionBranch58_37 - · exact degreeUnionBranch58_38 - · exact degreeUnionBranch58_39 - · exact degreeUnionBranch58_45 - · exact degreeUnionBranch58_46 - · exact degreeUnionBranch58_47 - · exact degreeUnionBranch58_48 - · exact degreeUnionBranch58_49 - -lemma degreeUnionBranch58_50 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 44 14 degreeUnionState58_50 [14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 14 at hb - change 44 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch58_51 - · exact degreeUnionBranch58_52 - · exact degreeUnionBranch58_53 - · exact degreeUnionBranch58_54 - · exact degreeUnionBranch58_55 - · exact degreeUnionBranch58_56 - · exact degreeUnionBranch58_57 - · exact degreeUnionBranch58_58 - · exact degreeUnionBranch58_59 - · exact degreeUnionBranch58_60 - · exact degreeUnionBranch58_61 - -lemma degreeUnionBranch58_12 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 58 14 degreeHalfRegions58 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 14 at hb - change 58 ≤ 12*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch58_13 - · exact degreeUnionBranch58_14 - · exact degreeUnionBranch58_15 - · exact degreeUnionBranch58_16 - · exact degreeUnionBranch58_17 - · exact degreeUnionBranch58_18 - · exact degreeUnionBranch58_19 - · exact degreeUnionBranch58_20 - · exact degreeUnionBranch58_35 - · exact degreeUnionBranch58_50 - -lemma degreeUnionBranch58_70 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 46 12 degreeUnionState58_70 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 46 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch58_71 - · exact degreeUnionBranch58_72 - · exact degreeUnionBranch58_73 - · exact degreeUnionBranch58_74 - · exact degreeUnionBranch58_75 - · exact degreeUnionBranch58_76 - · exact degreeUnionBranch58_77 - · exact degreeUnionBranch58_78 - · exact degreeUnionBranch58_79 - -lemma degreeUnionBranch58_80 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 45 13 degreeUnionState58_80 [13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 13 at hb - change 45 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch58_81 - · exact degreeUnionBranch58_82 - · exact degreeUnionBranch58_83 - · exact degreeUnionBranch58_84 - · exact degreeUnionBranch58_85 - · exact degreeUnionBranch58_86 - · exact degreeUnionBranch58_87 - · exact degreeUnionBranch58_88 - · exact degreeUnionBranch58_89 - · exact degreeUnionBranch58_90 - -lemma degreeUnionBranch58_62 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 58 14 degreeHalfRegions58 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 14 at hb - change 58 ≤ 13*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch58_63 - · exact degreeUnionBranch58_64 - · exact degreeUnionBranch58_65 - · exact degreeUnionBranch58_66 - · exact degreeUnionBranch58_67 - · exact degreeUnionBranch58_68 - · exact degreeUnionBranch58_69 - · exact degreeUnionBranch58_70 - · exact degreeUnionBranch58_80 - · exact degreeUnionBranch58_91 - -lemma degreeUnionBranch58_100 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 46 12 degreeUnionState58_100 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 46 ≤ 13*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch58_101 - · exact degreeUnionBranch58_102 - · exact degreeUnionBranch58_103 - · exact degreeUnionBranch58_104 - · exact degreeUnionBranch58_105 - · exact degreeUnionBranch58_106 - · exact degreeUnionBranch58_107 - · exact degreeUnionBranch58_108 - · exact degreeUnionBranch58_109 - -lemma degreeUnionBranch58_92 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 14 58 14 degreeHalfRegions58 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 14 at hb - change 58 ≤ 14*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch58_93 - · exact degreeUnionBranch58_94 - · exact degreeUnionBranch58_95 - · exact degreeUnionBranch58_96 - · exact degreeUnionBranch58_97 - · exact degreeUnionBranch58_98 - · exact degreeUnionBranch58_99 - · exact degreeUnionBranch58_100 - · exact degreeUnionBranch58_110 - · exact degreeUnionBranch58_111 - -lemma degreeUnionCheck58 : ∀ h ≤ 24, - checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) h 58 14 degreeHalfRegions58 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch58_0 - · exact degreeUnionBranch58_1 - · exact degreeUnionBranch58_2 - · exact degreeUnionBranch58_3 - · exact degreeUnionBranch58_4 - · exact degreeUnionBranch58_5 - · exact degreeUnionBranch58_6 - · exact degreeUnionBranch58_7 - · exact degreeUnionBranch58_8 - · exact degreeUnionBranch58_9 - · exact degreeUnionBranch58_10 - · exact degreeUnionBranch58_11 - · exact degreeUnionBranch58_12 - · exact degreeUnionBranch58_62 - · exact degreeUnionBranch58_92 - · exact degreeUnionBranch58_112 - · exact degreeUnionBranch58_113 - · exact degreeUnionBranch58_114 - · exact degreeUnionBranch58_115 - · exact degreeUnionBranch58_116 - · exact degreeUnionBranch58_117 - · exact degreeUnionBranch58_118 - · exact degreeUnionBranch58_119 - · exact degreeUnionBranch58_120 - · exact degreeUnionBranch58_121 - -lemma degreeHalfCover58 : ∀ R ∈ degreeRegions58, - R ∈ degreeHalfRegions58 ∨ (R.2,R.1) ∈ degreeHalfRegions58 := by decide +kernel - -lemma degreeDiagramRegionsChecked58 : ∀ R ∈ degreeRegions58, - ∀ μ : YoungDiagram, μ.card = 58 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP58 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck58 degreeHalfHeight58 degreeHalfWidth58 - degreeHalfCover58 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves58 + +namespace OAI + +/-! Degree Regions 58. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch58_25 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 37 9 degreeUnionState58_25 [9,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 37 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch58_26 + · exact degreeUnionBranch58_27 + · exact degreeUnionBranch58_28 + · exact degreeUnionBranch58_29 + · exact degreeUnionBranch58_30 + · exact degreeUnionBranch58_31 + +lemma degreeUnionBranch58_20 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 46 12 degreeUnionState58_20 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 12 at hb + change 46 ≤ 11*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch58_21 + · exact degreeUnionBranch58_22 + · exact degreeUnionBranch58_23 + · exact degreeUnionBranch58_24 + · exact degreeUnionBranch58_25 + · exact degreeUnionBranch58_32 + · exact degreeUnionBranch58_33 + · exact degreeUnionBranch58_34 + +lemma degreeUnionBranch58_39 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 10 37 8 degreeUnionState58_39 [8,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 37 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch58_40 + · exact degreeUnionBranch58_41 + · exact degreeUnionBranch58_42 + · exact degreeUnionBranch58_43 + · exact degreeUnionBranch58_44 + +lemma degreeUnionBranch58_35 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 45 13 degreeUnionState58_35 [13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 13 at hb + change 45 ≤ 11*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch58_36 + · exact degreeUnionBranch58_37 + · exact degreeUnionBranch58_38 + · exact degreeUnionBranch58_39 + · exact degreeUnionBranch58_45 + · exact degreeUnionBranch58_46 + · exact degreeUnionBranch58_47 + · exact degreeUnionBranch58_48 + · exact degreeUnionBranch58_49 + +lemma degreeUnionBranch58_50 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 11 44 14 degreeUnionState58_50 [14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 14 at hb + change 44 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch58_51 + · exact degreeUnionBranch58_52 + · exact degreeUnionBranch58_53 + · exact degreeUnionBranch58_54 + · exact degreeUnionBranch58_55 + · exact degreeUnionBranch58_56 + · exact degreeUnionBranch58_57 + · exact degreeUnionBranch58_58 + · exact degreeUnionBranch58_59 + · exact degreeUnionBranch58_60 + · exact degreeUnionBranch58_61 + +lemma degreeUnionBranch58_12 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 58 14 degreeHalfRegions58 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 14 at hb + change 58 ≤ 12*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch58_13 + · exact degreeUnionBranch58_14 + · exact degreeUnionBranch58_15 + · exact degreeUnionBranch58_16 + · exact degreeUnionBranch58_17 + · exact degreeUnionBranch58_18 + · exact degreeUnionBranch58_19 + · exact degreeUnionBranch58_20 + · exact degreeUnionBranch58_35 + · exact degreeUnionBranch58_50 + +lemma degreeUnionBranch58_70 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 46 12 degreeUnionState58_70 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 46 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch58_71 + · exact degreeUnionBranch58_72 + · exact degreeUnionBranch58_73 + · exact degreeUnionBranch58_74 + · exact degreeUnionBranch58_75 + · exact degreeUnionBranch58_76 + · exact degreeUnionBranch58_77 + · exact degreeUnionBranch58_78 + · exact degreeUnionBranch58_79 + +lemma degreeUnionBranch58_80 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 12 45 13 degreeUnionState58_80 [13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 13 at hb + change 45 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch58_81 + · exact degreeUnionBranch58_82 + · exact degreeUnionBranch58_83 + · exact degreeUnionBranch58_84 + · exact degreeUnionBranch58_85 + · exact degreeUnionBranch58_86 + · exact degreeUnionBranch58_87 + · exact degreeUnionBranch58_88 + · exact degreeUnionBranch58_89 + · exact degreeUnionBranch58_90 + +lemma degreeUnionBranch58_62 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 58 14 degreeHalfRegions58 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 14 at hb + change 58 ≤ 13*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch58_63 + · exact degreeUnionBranch58_64 + · exact degreeUnionBranch58_65 + · exact degreeUnionBranch58_66 + · exact degreeUnionBranch58_67 + · exact degreeUnionBranch58_68 + · exact degreeUnionBranch58_69 + · exact degreeUnionBranch58_70 + · exact degreeUnionBranch58_80 + · exact degreeUnionBranch58_91 + +lemma degreeUnionBranch58_100 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 13 46 12 degreeUnionState58_100 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 46 ≤ 13*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch58_101 + · exact degreeUnionBranch58_102 + · exact degreeUnionBranch58_103 + · exact degreeUnionBranch58_104 + · exact degreeUnionBranch58_105 + · exact degreeUnionBranch58_106 + · exact degreeUnionBranch58_107 + · exact degreeUnionBranch58_108 + · exact degreeUnionBranch58_109 + +lemma degreeUnionBranch58_92 : checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) 14 58 14 degreeHalfRegions58 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 14 at hb + change 58 ≤ 14*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch58_93 + · exact degreeUnionBranch58_94 + · exact degreeUnionBranch58_95 + · exact degreeUnionBranch58_96 + · exact degreeUnionBranch58_97 + · exact degreeUnionBranch58_98 + · exact degreeUnionBranch58_99 + · exact degreeUnionBranch58_100 + · exact degreeUnionBranch58_110 + · exact degreeUnionBranch58_111 + +lemma degreeUnionCheck58 : ∀ h ≤ 24, + checkRegionPrefixes (quickResidual 8 11 degreeQs58 degreeTree58) h 58 14 degreeHalfRegions58 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch58_0 + · exact degreeUnionBranch58_1 + · exact degreeUnionBranch58_2 + · exact degreeUnionBranch58_3 + · exact degreeUnionBranch58_4 + · exact degreeUnionBranch58_5 + · exact degreeUnionBranch58_6 + · exact degreeUnionBranch58_7 + · exact degreeUnionBranch58_8 + · exact degreeUnionBranch58_9 + · exact degreeUnionBranch58_10 + · exact degreeUnionBranch58_11 + · exact degreeUnionBranch58_12 + · exact degreeUnionBranch58_62 + · exact degreeUnionBranch58_92 + · exact degreeUnionBranch58_112 + · exact degreeUnionBranch58_113 + · exact degreeUnionBranch58_114 + · exact degreeUnionBranch58_115 + · exact degreeUnionBranch58_116 + · exact degreeUnionBranch58_117 + · exact degreeUnionBranch58_118 + · exact degreeUnionBranch58_119 + · exact degreeUnionBranch58_120 + · exact degreeUnionBranch58_121 + +lemma degreeHalfCover58 : ∀ R ∈ degreeRegions58, + R ∈ degreeHalfRegions58 ∨ (R.2,R.1) ∈ degreeHalfRegions58 := by decide +kernel + +lemma degreeDiagramRegionsChecked58 : ∀ R ∈ degreeRegions58, + ∀ μ : YoungDiagram, μ.card = 58 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP58 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck58 degreeHalfHeight58 degreeHalfWidth58 + degreeHalfCover58 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions62.lean index d45981026b49336f45ef75668519d3728eb7a48c..42982859d4f78f9ea4431a8d75e5f72daf9dd91a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions62.lean @@ -1,3156 +1,3156 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves62 - -namespace OAI - -/-! Degree Regions 62. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionBranch62_18 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 50 12 degreeUnionState62_18 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 5 ≤ a at ha - change a ≤ 12 at hb - change 50 ≤ 10*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_19 - · exact degreeUnionBranch62_20 - · exact degreeUnionBranch62_21 - · exact degreeUnionBranch62_22 - · exact degreeUnionBranch62_23 - · exact degreeUnionBranch62_24 - · exact degreeUnionBranch62_25 - · exact degreeUnionBranch62_26 - -lemma degreeUnionBranch62_27 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 49 13 degreeUnionState62_27 [13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 13 at hb - change 49 ≤ 10*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_28 - · exact degreeUnionBranch62_29 - · exact degreeUnionBranch62_30 - · exact degreeUnionBranch62_31 - · exact degreeUnionBranch62_32 - · exact degreeUnionBranch62_33 - · exact degreeUnionBranch62_34 - · exact degreeUnionBranch62_35 - · exact degreeUnionBranch62_36 - -lemma degreeUnionBranch62_37 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 48 14 degreeUnionState62_37 [14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 14 at hb - change 48 ≤ 10*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_38 - · exact degreeUnionBranch62_39 - · exact degreeUnionBranch62_40 - · exact degreeUnionBranch62_41 - · exact degreeUnionBranch62_42 - · exact degreeUnionBranch62_43 - · exact degreeUnionBranch62_44 - · exact degreeUnionBranch62_45 - · exact degreeUnionBranch62_46 - · exact degreeUnionBranch62_47 - -lemma degreeUnionBranch62_11 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 62 28 degreeHalfRegions62 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 5 ≤ a at ha - change a ≤ 28 at hb - change 62 ≤ 11*a at hn - have hlo : 6 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_12 - · exact degreeUnionBranch62_13 - · exact degreeUnionBranch62_14 - · exact degreeUnionBranch62_15 - · exact degreeUnionBranch62_16 - · exact degreeUnionBranch62_17 - · exact degreeUnionBranch62_18 - · exact degreeUnionBranch62_27 - · exact degreeUnionBranch62_37 - · exact degreeUnionBranch62_48 - · exact degreeUnionBranch62_49 - · exact degreeUnionBranch62_50 - · exact degreeUnionBranch62_51 - · exact degreeUnionBranch62_52 - · exact degreeUnionBranch62_53 - · exact degreeUnionBranch62_54 - · exact degreeUnionBranch62_55 - · exact degreeUnionBranch62_56 - · exact degreeUnionBranch62_57 - · exact degreeUnionBranch62_58 - · exact degreeUnionBranch62_59 - · exact degreeUnionBranch62_60 - · exact degreeUnionBranch62_61 - -lemma degreeUnionBranch62_79 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 10 degreeUnionState62_79 [10,10,10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 32 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_80 - · exact degreeUnionBranch62_81 - · exact degreeUnionBranch62_82 - · exact degreeUnionBranch62_83 - · exact degreeUnionBranch62_84 - · exact degreeUnionBranch62_85 - · exact degreeUnionBranch62_86 - -lemma degreeUnionBranch62_73 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 42 10 degreeUnionState62_73 [10,10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 10 at hb - change 42 ≤ 10*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_74 - · exact degreeUnionBranch62_75 - · exact degreeUnionBranch62_76 - · exact degreeUnionBranch62_77 - · exact degreeUnionBranch62_78 - · exact degreeUnionBranch62_79 - -lemma degreeUnionBranch62_67 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 52 10 degreeUnionState62_67 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 10 at hb - change 52 ≤ 11*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_68 - · exact degreeUnionBranch62_69 - · exact degreeUnionBranch62_70 - · exact degreeUnionBranch62_71 - · exact degreeUnionBranch62_72 - · exact degreeUnionBranch62_73 - -lemma degreeUnionBranch62_99 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 10 degreeUnionState62_99 [10,10,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 31 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_100 - · exact degreeUnionBranch62_101 - · exact degreeUnionBranch62_102 - · exact degreeUnionBranch62_103 - · exact degreeUnionBranch62_104 - · exact degreeUnionBranch62_105 - · exact degreeUnionBranch62_106 - -lemma degreeUnionBranch62_93 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 41 10 degreeUnionState62_93 [10,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 10 at hb - change 41 ≤ 10*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_94 - · exact degreeUnionBranch62_95 - · exact degreeUnionBranch62_96 - · exact degreeUnionBranch62_97 - · exact degreeUnionBranch62_98 - · exact degreeUnionBranch62_99 - -lemma degreeUnionBranch62_114 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 10 degreeUnionState62_114 [10,11,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 30 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_115 - · exact degreeUnionBranch62_116 - · exact degreeUnionBranch62_117 - · exact degreeUnionBranch62_118 - · exact degreeUnionBranch62_119 - · exact degreeUnionBranch62_120 - · exact degreeUnionBranch62_121 - -lemma degreeUnionBranch62_122 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 11 degreeUnionState62_122 [11,11,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 29 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_123 - · exact degreeUnionBranch62_124 - · exact degreeUnionBranch62_125 - · exact degreeUnionBranch62_126 - · exact degreeUnionBranch62_127 - · exact degreeUnionBranch62_128 - · exact degreeUnionBranch62_129 - · exact degreeUnionBranch62_130 - -lemma degreeUnionBranch62_107 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 40 11 degreeUnionState62_107 [11,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 11 at hb - change 40 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_108 - · exact degreeUnionBranch62_109 - · exact degreeUnionBranch62_110 - · exact degreeUnionBranch62_111 - · exact degreeUnionBranch62_112 - · exact degreeUnionBranch62_113 - · exact degreeUnionBranch62_114 - · exact degreeUnionBranch62_122 - -lemma degreeUnionBranch62_87 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 51 11 degreeUnionState62_87 [11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 11 at hb - change 51 ≤ 11*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_88 - · exact degreeUnionBranch62_89 - · exact degreeUnionBranch62_90 - · exact degreeUnionBranch62_91 - · exact degreeUnionBranch62_92 - · exact degreeUnionBranch62_93 - · exact degreeUnionBranch62_107 - -lemma degreeUnionBranch62_134 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 43 7 degreeUnionState62_134 [7,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 7 at hb - change 43 ≤ 10*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_135 - · exact degreeUnionBranch62_136 - · exact degreeUnionBranch62_137 - -lemma degreeUnionBranch62_141 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 7 degreeUnionState62_141 [7,8,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 35 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_142 - · exact degreeUnionBranch62_143 - · exact degreeUnionBranch62_144 - · exact degreeUnionBranch62_145 - -lemma degreeUnionBranch62_146 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 8 degreeUnionState62_146 [8,8,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 34 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_147 - · exact degreeUnionBranch62_148 - · exact degreeUnionBranch62_149 - · exact degreeUnionBranch62_150 - · exact degreeUnionBranch62_151 - -lemma degreeUnionBranch62_138 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 42 8 degreeUnionState62_138 [8,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 8 at hb - change 42 ≤ 10*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_139 - · exact degreeUnionBranch62_140 - · exact degreeUnionBranch62_141 - · exact degreeUnionBranch62_146 - -lemma degreeUnionBranch62_155 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 7 degreeUnionState62_155 [7,9,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 34 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_156 - · exact degreeUnionBranch62_157 - · exact degreeUnionBranch62_158 - · exact degreeUnionBranch62_159 - -lemma degreeUnionBranch62_160 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 8 degreeUnionState62_160 [8,9,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 33 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_161 - · exact degreeUnionBranch62_162 - · exact degreeUnionBranch62_163 - · exact degreeUnionBranch62_164 - · exact degreeUnionBranch62_165 - -lemma degreeUnionBranch62_166 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 9 degreeUnionState62_166 [9,9,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 32 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_167 - · exact degreeUnionBranch62_168 - · exact degreeUnionBranch62_169 - · exact degreeUnionBranch62_170 - · exact degreeUnionBranch62_171 - · exact degreeUnionBranch62_172 - -lemma degreeUnionBranch62_152 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 41 9 degreeUnionState62_152 [9,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 9 at hb - change 41 ≤ 10*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_153 - · exact degreeUnionBranch62_154 - · exact degreeUnionBranch62_155 - · exact degreeUnionBranch62_160 - · exact degreeUnionBranch62_166 - -lemma degreeUnionBranch62_177 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 7 degreeUnionState62_177 [7,10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 33 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_178 - · exact degreeUnionBranch62_179 - · exact degreeUnionBranch62_180 - · exact degreeUnionBranch62_181 - -lemma degreeUnionBranch62_182 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 8 degreeUnionState62_182 [8,10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 32 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_183 - · exact degreeUnionBranch62_184 - · exact degreeUnionBranch62_185 - · exact degreeUnionBranch62_186 - · exact degreeUnionBranch62_187 - -lemma degreeUnionBranch62_188 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 9 degreeUnionState62_188 [9,10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 31 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_189 - · exact degreeUnionBranch62_190 - · exact degreeUnionBranch62_191 - · exact degreeUnionBranch62_192 - · exact degreeUnionBranch62_193 - · exact degreeUnionBranch62_194 - -lemma degreeUnionBranch62_195 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 10 degreeUnionState62_195 [10,10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 30 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_196 - · exact degreeUnionBranch62_197 - · exact degreeUnionBranch62_198 - · exact degreeUnionBranch62_199 - · exact degreeUnionBranch62_200 - · exact degreeUnionBranch62_201 - · exact degreeUnionBranch62_202 - -lemma degreeUnionBranch62_173 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 40 10 degreeUnionState62_173 [10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 10 at hb - change 40 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_174 - · exact degreeUnionBranch62_175 - · exact degreeUnionBranch62_176 - · exact degreeUnionBranch62_177 - · exact degreeUnionBranch62_182 - · exact degreeUnionBranch62_188 - · exact degreeUnionBranch62_195 - -lemma degreeUnionBranch62_207 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 7 degreeUnionState62_207 [7,11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 32 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_208 - · exact degreeUnionBranch62_209 - · exact degreeUnionBranch62_210 - · exact degreeUnionBranch62_211 - -lemma degreeUnionBranch62_212 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 8 degreeUnionState62_212 [8,11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 31 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_213 - · exact degreeUnionBranch62_214 - · exact degreeUnionBranch62_215 - · exact degreeUnionBranch62_216 - · exact degreeUnionBranch62_217 - -lemma degreeUnionBranch62_218 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 9 degreeUnionState62_218 [9,11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 30 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_219 - · exact degreeUnionBranch62_220 - · exact degreeUnionBranch62_221 - · exact degreeUnionBranch62_222 - · exact degreeUnionBranch62_223 - · exact degreeUnionBranch62_224 - -lemma degreeUnionBranch62_225 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 10 degreeUnionState62_225 [10,11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 29 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_226 - · exact degreeUnionBranch62_227 - · exact degreeUnionBranch62_228 - · exact degreeUnionBranch62_229 - · exact degreeUnionBranch62_230 - · exact degreeUnionBranch62_231 - · exact degreeUnionBranch62_232 - -lemma degreeUnionBranch62_203 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 39 11 degreeUnionState62_203 [11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 39 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_204 - · exact degreeUnionBranch62_205 - · exact degreeUnionBranch62_206 - · exact degreeUnionBranch62_207 - · exact degreeUnionBranch62_212 - · exact degreeUnionBranch62_218 - · exact degreeUnionBranch62_225 - · exact degreeUnionBranch62_233 - -lemma degreeUnionBranch62_238 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 7 degreeUnionState62_238 [7,12,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 31 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_239 - · exact degreeUnionBranch62_240 - · exact degreeUnionBranch62_241 - · exact degreeUnionBranch62_242 - -lemma degreeUnionBranch62_243 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 8 degreeUnionState62_243 [8,12,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 30 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_244 - · exact degreeUnionBranch62_245 - · exact degreeUnionBranch62_246 - · exact degreeUnionBranch62_247 - · exact degreeUnionBranch62_248 - -lemma degreeUnionBranch62_249 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 9 degreeUnionState62_249 [9,12,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 29 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_250 - · exact degreeUnionBranch62_251 - · exact degreeUnionBranch62_252 - · exact degreeUnionBranch62_253 - · exact degreeUnionBranch62_254 - · exact degreeUnionBranch62_255 - -lemma degreeUnionBranch62_234 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 12 degreeUnionState62_234 [12,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 38 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_235 - · exact degreeUnionBranch62_236 - · exact degreeUnionBranch62_237 - · exact degreeUnionBranch62_238 - · exact degreeUnionBranch62_243 - · exact degreeUnionBranch62_249 - · exact degreeUnionBranch62_256 - · exact degreeUnionBranch62_257 - · exact degreeUnionBranch62_258 - -lemma degreeUnionBranch62_131 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 50 12 degreeUnionState62_131 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 12 at hb - change 50 ≤ 11*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_132 - · exact degreeUnionBranch62_133 - · exact degreeUnionBranch62_134 - · exact degreeUnionBranch62_138 - · exact degreeUnionBranch62_152 - · exact degreeUnionBranch62_173 - · exact degreeUnionBranch62_203 - · exact degreeUnionBranch62_234 - -lemma degreeUnionBranch62_265 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 7 degreeUnionState62_265 [7,7,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 35 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_266 - · exact degreeUnionBranch62_267 - · exact degreeUnionBranch62_268 - · exact degreeUnionBranch62_269 - -lemma degreeUnionBranch62_262 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 42 7 degreeUnionState62_262 [7,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 7 at hb - change 42 ≤ 10*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_263 - · exact degreeUnionBranch62_264 - · exact degreeUnionBranch62_265 - -lemma degreeUnionBranch62_273 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 7 degreeUnionState62_273 [7,8,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 34 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_274 - · exact degreeUnionBranch62_275 - · exact degreeUnionBranch62_276 - · exact degreeUnionBranch62_277 - -lemma degreeUnionBranch62_278 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 8 degreeUnionState62_278 [8,8,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 33 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_279 - · exact degreeUnionBranch62_280 - · exact degreeUnionBranch62_281 - · exact degreeUnionBranch62_282 - · exact degreeUnionBranch62_283 - -lemma degreeUnionBranch62_270 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 41 8 degreeUnionState62_270 [8,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 8 at hb - change 41 ≤ 10*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_271 - · exact degreeUnionBranch62_272 - · exact degreeUnionBranch62_273 - · exact degreeUnionBranch62_278 - -lemma degreeUnionBranch62_288 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 7 degreeUnionState62_288 [7,9,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 33 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_289 - · exact degreeUnionBranch62_290 - · exact degreeUnionBranch62_291 - · exact degreeUnionBranch62_292 - -lemma degreeUnionBranch62_293 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 8 degreeUnionState62_293 [8,9,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 32 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_294 - · exact degreeUnionBranch62_295 - · exact degreeUnionBranch62_296 - · exact degreeUnionBranch62_297 - · exact degreeUnionBranch62_298 - -lemma degreeUnionBranch62_299 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 9 degreeUnionState62_299 [9,9,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 31 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_300 - · exact degreeUnionBranch62_301 - · exact degreeUnionBranch62_302 - · exact degreeUnionBranch62_303 - · exact degreeUnionBranch62_304 - · exact degreeUnionBranch62_305 - -lemma degreeUnionBranch62_284 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 40 9 degreeUnionState62_284 [9,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 9 at hb - change 40 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_285 - · exact degreeUnionBranch62_286 - · exact degreeUnionBranch62_287 - · exact degreeUnionBranch62_288 - · exact degreeUnionBranch62_293 - · exact degreeUnionBranch62_299 - -lemma degreeUnionBranch62_310 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 7 degreeUnionState62_310 [7,10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 32 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_311 - · exact degreeUnionBranch62_312 - · exact degreeUnionBranch62_313 - · exact degreeUnionBranch62_314 - -lemma degreeUnionBranch62_315 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 8 degreeUnionState62_315 [8,10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 31 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_316 - · exact degreeUnionBranch62_317 - · exact degreeUnionBranch62_318 - · exact degreeUnionBranch62_319 - · exact degreeUnionBranch62_320 - -lemma degreeUnionBranch62_321 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 9 degreeUnionState62_321 [9,10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 30 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_322 - · exact degreeUnionBranch62_323 - · exact degreeUnionBranch62_324 - · exact degreeUnionBranch62_325 - · exact degreeUnionBranch62_326 - · exact degreeUnionBranch62_327 - -lemma degreeUnionBranch62_328 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 10 degreeUnionState62_328 [10,10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 29 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_329 - · exact degreeUnionBranch62_330 - · exact degreeUnionBranch62_331 - · exact degreeUnionBranch62_332 - · exact degreeUnionBranch62_333 - · exact degreeUnionBranch62_334 - · exact degreeUnionBranch62_335 - -lemma degreeUnionBranch62_306 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 39 10 degreeUnionState62_306 [10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 39 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_307 - · exact degreeUnionBranch62_308 - · exact degreeUnionBranch62_309 - · exact degreeUnionBranch62_310 - · exact degreeUnionBranch62_315 - · exact degreeUnionBranch62_321 - · exact degreeUnionBranch62_328 - -lemma degreeUnionBranch62_340 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 7 degreeUnionState62_340 [7,11,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 31 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_341 - · exact degreeUnionBranch62_342 - · exact degreeUnionBranch62_343 - · exact degreeUnionBranch62_344 - -lemma degreeUnionBranch62_345 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 8 degreeUnionState62_345 [8,11,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 30 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_346 - · exact degreeUnionBranch62_347 - · exact degreeUnionBranch62_348 - · exact degreeUnionBranch62_349 - · exact degreeUnionBranch62_350 - -lemma degreeUnionBranch62_351 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 9 degreeUnionState62_351 [9,11,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 29 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_352 - · exact degreeUnionBranch62_353 - · exact degreeUnionBranch62_354 - · exact degreeUnionBranch62_355 - · exact degreeUnionBranch62_356 - · exact degreeUnionBranch62_357 - -lemma degreeUnionBranch62_336 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 11 degreeUnionState62_336 [11,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 38 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_337 - · exact degreeUnionBranch62_338 - · exact degreeUnionBranch62_339 - · exact degreeUnionBranch62_340 - · exact degreeUnionBranch62_345 - · exact degreeUnionBranch62_351 - · exact degreeUnionBranch62_358 - · exact degreeUnionBranch62_359 - -lemma degreeUnionBranch62_364 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 7 degreeUnionState62_364 [7,12,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 30 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_365 - · exact degreeUnionBranch62_366 - · exact degreeUnionBranch62_367 - · exact degreeUnionBranch62_368 - -lemma degreeUnionBranch62_369 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 8 degreeUnionState62_369 [8,12,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 29 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_370 - · exact degreeUnionBranch62_371 - · exact degreeUnionBranch62_372 - · exact degreeUnionBranch62_373 - · exact degreeUnionBranch62_374 - -lemma degreeUnionBranch62_360 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 12 degreeUnionState62_360 [12,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 37 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_361 - · exact degreeUnionBranch62_362 - · exact degreeUnionBranch62_363 - · exact degreeUnionBranch62_364 - · exact degreeUnionBranch62_369 - · exact degreeUnionBranch62_375 - · exact degreeUnionBranch62_376 - · exact degreeUnionBranch62_377 - · exact degreeUnionBranch62_378 - -lemma degreeUnionBranch62_383 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 7 degreeUnionState62_383 [7,13,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 29 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_384 - · exact degreeUnionBranch62_385 - · exact degreeUnionBranch62_386 - · exact degreeUnionBranch62_387 - -lemma degreeUnionBranch62_379 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 13 degreeUnionState62_379 [13,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 13 at hb - change 36 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_380 - · exact degreeUnionBranch62_381 - · exact degreeUnionBranch62_382 - · exact degreeUnionBranch62_383 - · exact degreeUnionBranch62_388 - · exact degreeUnionBranch62_389 - · exact degreeUnionBranch62_390 - · exact degreeUnionBranch62_391 - · exact degreeUnionBranch62_392 - · exact degreeUnionBranch62_393 - -lemma degreeUnionBranch62_259 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 49 13 degreeUnionState62_259 [13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 13 at hb - change 49 ≤ 11*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_260 - · exact degreeUnionBranch62_261 - · exact degreeUnionBranch62_262 - · exact degreeUnionBranch62_270 - · exact degreeUnionBranch62_284 - · exact degreeUnionBranch62_306 - · exact degreeUnionBranch62_336 - · exact degreeUnionBranch62_360 - · exact degreeUnionBranch62_379 - -lemma degreeUnionBranch62_400 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 7 degreeUnionState62_400 [7,7,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 34 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_401 - · exact degreeUnionBranch62_402 - · exact degreeUnionBranch62_403 - · exact degreeUnionBranch62_404 - -lemma degreeUnionBranch62_397 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 41 7 degreeUnionState62_397 [7,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 7 at hb - change 41 ≤ 10*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_398 - · exact degreeUnionBranch62_399 - · exact degreeUnionBranch62_400 - -lemma degreeUnionBranch62_409 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 7 degreeUnionState62_409 [7,8,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 33 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_410 - · exact degreeUnionBranch62_411 - · exact degreeUnionBranch62_412 - · exact degreeUnionBranch62_413 - -lemma degreeUnionBranch62_414 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 8 degreeUnionState62_414 [8,8,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 32 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_415 - · exact degreeUnionBranch62_416 - · exact degreeUnionBranch62_417 - · exact degreeUnionBranch62_418 - · exact degreeUnionBranch62_419 - -lemma degreeUnionBranch62_405 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 40 8 degreeUnionState62_405 [8,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 8 at hb - change 40 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_406 - · exact degreeUnionBranch62_407 - · exact degreeUnionBranch62_408 - · exact degreeUnionBranch62_409 - · exact degreeUnionBranch62_414 - -lemma degreeUnionBranch62_424 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 7 degreeUnionState62_424 [7,9,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 32 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_425 - · exact degreeUnionBranch62_426 - · exact degreeUnionBranch62_427 - · exact degreeUnionBranch62_428 - -lemma degreeUnionBranch62_429 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 8 degreeUnionState62_429 [8,9,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 31 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_430 - · exact degreeUnionBranch62_431 - · exact degreeUnionBranch62_432 - · exact degreeUnionBranch62_433 - · exact degreeUnionBranch62_434 - -lemma degreeUnionBranch62_435 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 9 degreeUnionState62_435 [9,9,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 30 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_436 - · exact degreeUnionBranch62_437 - · exact degreeUnionBranch62_438 - · exact degreeUnionBranch62_439 - · exact degreeUnionBranch62_440 - · exact degreeUnionBranch62_441 - -lemma degreeUnionBranch62_420 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 39 9 degreeUnionState62_420 [9,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 39 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_421 - · exact degreeUnionBranch62_422 - · exact degreeUnionBranch62_423 - · exact degreeUnionBranch62_424 - · exact degreeUnionBranch62_429 - · exact degreeUnionBranch62_435 - -lemma degreeUnionBranch62_446 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 7 degreeUnionState62_446 [7,10,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 31 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_447 - · exact degreeUnionBranch62_448 - · exact degreeUnionBranch62_449 - · exact degreeUnionBranch62_450 - -lemma degreeUnionBranch62_451 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 8 degreeUnionState62_451 [8,10,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 30 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_452 - · exact degreeUnionBranch62_453 - · exact degreeUnionBranch62_454 - · exact degreeUnionBranch62_455 - · exact degreeUnionBranch62_456 - -lemma degreeUnionBranch62_457 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 9 degreeUnionState62_457 [9,10,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 29 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_458 - · exact degreeUnionBranch62_459 - · exact degreeUnionBranch62_460 - · exact degreeUnionBranch62_461 - · exact degreeUnionBranch62_462 - · exact degreeUnionBranch62_463 - -lemma degreeUnionBranch62_442 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 10 degreeUnionState62_442 [10,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 38 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_443 - · exact degreeUnionBranch62_444 - · exact degreeUnionBranch62_445 - · exact degreeUnionBranch62_446 - · exact degreeUnionBranch62_451 - · exact degreeUnionBranch62_457 - · exact degreeUnionBranch62_464 - -lemma degreeUnionBranch62_469 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 7 degreeUnionState62_469 [7,11,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 30 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_470 - · exact degreeUnionBranch62_471 - · exact degreeUnionBranch62_472 - · exact degreeUnionBranch62_473 - -lemma degreeUnionBranch62_474 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 8 degreeUnionState62_474 [8,11,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 29 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_475 - · exact degreeUnionBranch62_476 - · exact degreeUnionBranch62_477 - · exact degreeUnionBranch62_478 - · exact degreeUnionBranch62_479 - -lemma degreeUnionBranch62_465 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 11 degreeUnionState62_465 [11,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 37 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_466 - · exact degreeUnionBranch62_467 - · exact degreeUnionBranch62_468 - · exact degreeUnionBranch62_469 - · exact degreeUnionBranch62_474 - · exact degreeUnionBranch62_480 - · exact degreeUnionBranch62_481 - · exact degreeUnionBranch62_482 - -lemma degreeUnionBranch62_487 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 7 degreeUnionState62_487 [7,12,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 29 ≤ 9*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_488 - · exact degreeUnionBranch62_489 - · exact degreeUnionBranch62_490 - · exact degreeUnionBranch62_491 - -lemma degreeUnionBranch62_483 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 12 degreeUnionState62_483 [12,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 36 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_484 - · exact degreeUnionBranch62_485 - · exact degreeUnionBranch62_486 - · exact degreeUnionBranch62_487 - · exact degreeUnionBranch62_492 - · exact degreeUnionBranch62_493 - · exact degreeUnionBranch62_494 - · exact degreeUnionBranch62_495 - · exact degreeUnionBranch62_496 - -lemma degreeUnionBranch62_394 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 48 14 degreeUnionState62_394 [14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 14 at hb - change 48 ≤ 11*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_395 - · exact degreeUnionBranch62_396 - · exact degreeUnionBranch62_397 - · exact degreeUnionBranch62_405 - · exact degreeUnionBranch62_420 - · exact degreeUnionBranch62_442 - · exact degreeUnionBranch62_465 - · exact degreeUnionBranch62_483 - · exact degreeUnionBranch62_497 - · exact degreeUnionBranch62_498 - -lemma degreeUnionBranch62_62 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 62 28 degreeHalfRegions62 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 5 ≤ a at ha - change a ≤ 28 at hb - change 62 ≤ 12*a at hn - have hlo : 6 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_63 - · exact degreeUnionBranch62_64 - · exact degreeUnionBranch62_65 - · exact degreeUnionBranch62_66 - · exact degreeUnionBranch62_67 - · exact degreeUnionBranch62_87 - · exact degreeUnionBranch62_131 - · exact degreeUnionBranch62_259 - · exact degreeUnionBranch62_394 - · exact degreeUnionBranch62_499 - · exact degreeUnionBranch62_500 - · exact degreeUnionBranch62_501 - · exact degreeUnionBranch62_502 - · exact degreeUnionBranch62_503 - · exact degreeUnionBranch62_504 - · exact degreeUnionBranch62_505 - · exact degreeUnionBranch62_506 - · exact degreeUnionBranch62_507 - · exact degreeUnionBranch62_508 - · exact degreeUnionBranch62_509 - · exact degreeUnionBranch62_510 - · exact degreeUnionBranch62_511 - · exact degreeUnionBranch62_512 - -lemma degreeUnionBranch62_532 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 10 degreeUnionState62_532 [10,10,10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 32 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_533 - · exact degreeUnionBranch62_534 - · exact degreeUnionBranch62_535 - · exact degreeUnionBranch62_536 - · exact degreeUnionBranch62_537 - · exact degreeUnionBranch62_538 - · exact degreeUnionBranch62_539 - -lemma degreeUnionBranch62_525 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 42 10 degreeUnionState62_525 [10,10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 42 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_526 - · exact degreeUnionBranch62_527 - · exact degreeUnionBranch62_528 - · exact degreeUnionBranch62_529 - · exact degreeUnionBranch62_530 - · exact degreeUnionBranch62_531 - · exact degreeUnionBranch62_532 - -lemma degreeUnionBranch62_519 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 52 10 degreeUnionState62_519 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 10 at hb - change 52 ≤ 12*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_520 - · exact degreeUnionBranch62_521 - · exact degreeUnionBranch62_522 - · exact degreeUnionBranch62_523 - · exact degreeUnionBranch62_524 - · exact degreeUnionBranch62_525 - -lemma degreeUnionBranch62_553 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 10 degreeUnionState62_553 [10,10,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 31 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_554 - · exact degreeUnionBranch62_555 - · exact degreeUnionBranch62_556 - · exact degreeUnionBranch62_557 - · exact degreeUnionBranch62_558 - · exact degreeUnionBranch62_559 - · exact degreeUnionBranch62_560 - -lemma degreeUnionBranch62_546 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 41 10 degreeUnionState62_546 [10,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 41 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_547 - · exact degreeUnionBranch62_548 - · exact degreeUnionBranch62_549 - · exact degreeUnionBranch62_550 - · exact degreeUnionBranch62_551 - · exact degreeUnionBranch62_552 - · exact degreeUnionBranch62_553 - -lemma degreeUnionBranch62_568 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 10 degreeUnionState62_568 [10,11,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 30 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_569 - · exact degreeUnionBranch62_570 - · exact degreeUnionBranch62_571 - · exact degreeUnionBranch62_572 - · exact degreeUnionBranch62_573 - · exact degreeUnionBranch62_574 - · exact degreeUnionBranch62_575 - · exact degreeUnionBranch62_576 - -lemma degreeUnionBranch62_577 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 11 degreeUnionState62_577 [11,11,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 11 at hb - change 29 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_578 - · exact degreeUnionBranch62_579 - · exact degreeUnionBranch62_580 - · exact degreeUnionBranch62_581 - · exact degreeUnionBranch62_582 - · exact degreeUnionBranch62_583 - · exact degreeUnionBranch62_584 - · exact degreeUnionBranch62_585 - · exact degreeUnionBranch62_586 - -lemma degreeUnionBranch62_561 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 40 11 degreeUnionState62_561 [11,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 40 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_562 - · exact degreeUnionBranch62_563 - · exact degreeUnionBranch62_564 - · exact degreeUnionBranch62_565 - · exact degreeUnionBranch62_566 - · exact degreeUnionBranch62_567 - · exact degreeUnionBranch62_568 - · exact degreeUnionBranch62_577 - -lemma degreeUnionBranch62_540 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 51 11 degreeUnionState62_540 [11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 11 at hb - change 51 ≤ 12*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_541 - · exact degreeUnionBranch62_542 - · exact degreeUnionBranch62_543 - · exact degreeUnionBranch62_544 - · exact degreeUnionBranch62_545 - · exact degreeUnionBranch62_546 - · exact degreeUnionBranch62_561 - -lemma degreeUnionBranch62_596 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 8 degreeUnionState62_596 [8,8,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 34 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_597 - · exact degreeUnionBranch62_598 - · exact degreeUnionBranch62_599 - · exact degreeUnionBranch62_600 - · exact degreeUnionBranch62_601 - -lemma degreeUnionBranch62_591 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 42 8 degreeUnionState62_591 [8,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 42 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_592 - · exact degreeUnionBranch62_593 - · exact degreeUnionBranch62_594 - · exact degreeUnionBranch62_595 - · exact degreeUnionBranch62_596 - -lemma degreeUnionBranch62_607 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 8 degreeUnionState62_607 [8,9,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 33 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_608 - · exact degreeUnionBranch62_609 - · exact degreeUnionBranch62_610 - · exact degreeUnionBranch62_611 - · exact degreeUnionBranch62_612 - -lemma degreeUnionBranch62_613 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 9 degreeUnionState62_613 [9,9,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 32 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_614 - · exact degreeUnionBranch62_615 - · exact degreeUnionBranch62_616 - · exact degreeUnionBranch62_617 - · exact degreeUnionBranch62_618 - · exact degreeUnionBranch62_619 - -lemma degreeUnionBranch62_602 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 41 9 degreeUnionState62_602 [9,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 41 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_603 - · exact degreeUnionBranch62_604 - · exact degreeUnionBranch62_605 - · exact degreeUnionBranch62_606 - · exact degreeUnionBranch62_607 - · exact degreeUnionBranch62_613 - -lemma degreeUnionBranch62_625 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 8 degreeUnionState62_625 [8,10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 32 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_626 - · exact degreeUnionBranch62_627 - · exact degreeUnionBranch62_628 - · exact degreeUnionBranch62_629 - · exact degreeUnionBranch62_630 - -lemma degreeUnionBranch62_631 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 9 degreeUnionState62_631 [9,10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 31 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_632 - · exact degreeUnionBranch62_633 - · exact degreeUnionBranch62_634 - · exact degreeUnionBranch62_635 - · exact degreeUnionBranch62_636 - · exact degreeUnionBranch62_637 - -lemma degreeUnionBranch62_638 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 10 degreeUnionState62_638 [10,10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 30 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_639 - · exact degreeUnionBranch62_640 - · exact degreeUnionBranch62_641 - · exact degreeUnionBranch62_642 - · exact degreeUnionBranch62_643 - · exact degreeUnionBranch62_644 - · exact degreeUnionBranch62_645 - · exact degreeUnionBranch62_646 - -lemma degreeUnionBranch62_620 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 40 10 degreeUnionState62_620 [10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 40 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_621 - · exact degreeUnionBranch62_622 - · exact degreeUnionBranch62_623 - · exact degreeUnionBranch62_624 - · exact degreeUnionBranch62_625 - · exact degreeUnionBranch62_631 - · exact degreeUnionBranch62_638 - -lemma degreeUnionBranch62_651 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 7 degreeUnionState62_651 [7,11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 32 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_652 - · exact degreeUnionBranch62_653 - · exact degreeUnionBranch62_654 - · exact degreeUnionBranch62_655 - -lemma degreeUnionBranch62_656 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 8 degreeUnionState62_656 [8,11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 31 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_657 - · exact degreeUnionBranch62_658 - · exact degreeUnionBranch62_659 - · exact degreeUnionBranch62_660 - · exact degreeUnionBranch62_661 - -lemma degreeUnionBranch62_662 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 9 degreeUnionState62_662 [9,11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 30 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_663 - · exact degreeUnionBranch62_664 - · exact degreeUnionBranch62_665 - · exact degreeUnionBranch62_666 - · exact degreeUnionBranch62_667 - · exact degreeUnionBranch62_668 - · exact degreeUnionBranch62_669 - -lemma degreeUnionBranch62_670 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 10 degreeUnionState62_670 [10,11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 10 at hb - change 29 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_671 - · exact degreeUnionBranch62_672 - · exact degreeUnionBranch62_673 - · exact degreeUnionBranch62_674 - · exact degreeUnionBranch62_675 - · exact degreeUnionBranch62_676 - · exact degreeUnionBranch62_677 - · exact degreeUnionBranch62_678 - -lemma degreeUnionBranch62_647 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 39 11 degreeUnionState62_647 [11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 39 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_648 - · exact degreeUnionBranch62_649 - · exact degreeUnionBranch62_650 - · exact degreeUnionBranch62_651 - · exact degreeUnionBranch62_656 - · exact degreeUnionBranch62_662 - · exact degreeUnionBranch62_670 - · exact degreeUnionBranch62_679 - -lemma degreeUnionBranch62_684 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 7 degreeUnionState62_684 [7,12,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 31 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_685 - · exact degreeUnionBranch62_686 - · exact degreeUnionBranch62_687 - · exact degreeUnionBranch62_688 - -lemma degreeUnionBranch62_689 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 8 degreeUnionState62_689 [8,12,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 30 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_690 - · exact degreeUnionBranch62_691 - · exact degreeUnionBranch62_692 - · exact degreeUnionBranch62_693 - · exact degreeUnionBranch62_694 - · exact degreeUnionBranch62_695 - -lemma degreeUnionBranch62_696 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 9 degreeUnionState62_696 [9,12,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 29 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_697 - · exact degreeUnionBranch62_698 - · exact degreeUnionBranch62_699 - · exact degreeUnionBranch62_700 - · exact degreeUnionBranch62_701 - · exact degreeUnionBranch62_702 - · exact degreeUnionBranch62_703 - -lemma degreeUnionBranch62_680 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 38 12 degreeUnionState62_680 [12,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 38 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_681 - · exact degreeUnionBranch62_682 - · exact degreeUnionBranch62_683 - · exact degreeUnionBranch62_684 - · exact degreeUnionBranch62_689 - · exact degreeUnionBranch62_696 - · exact degreeUnionBranch62_704 - · exact degreeUnionBranch62_705 - · exact degreeUnionBranch62_706 - -lemma degreeUnionBranch62_587 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 50 12 degreeUnionState62_587 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 12 at hb - change 50 ≤ 12*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_588 - · exact degreeUnionBranch62_589 - · exact degreeUnionBranch62_590 - · exact degreeUnionBranch62_591 - · exact degreeUnionBranch62_602 - · exact degreeUnionBranch62_620 - · exact degreeUnionBranch62_647 - · exact degreeUnionBranch62_680 - -lemma degreeUnionBranch62_710 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 42 7 degreeUnionState62_710 [7,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 42 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_711 - · exact degreeUnionBranch62_712 - · exact degreeUnionBranch62_713 - · exact degreeUnionBranch62_714 - -lemma degreeUnionBranch62_720 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 8 degreeUnionState62_720 [8,8,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 33 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_721 - · exact degreeUnionBranch62_722 - · exact degreeUnionBranch62_723 - · exact degreeUnionBranch62_724 - · exact degreeUnionBranch62_725 - -lemma degreeUnionBranch62_715 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 41 8 degreeUnionState62_715 [8,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 41 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_716 - · exact degreeUnionBranch62_717 - · exact degreeUnionBranch62_718 - · exact degreeUnionBranch62_719 - · exact degreeUnionBranch62_720 - -lemma degreeUnionBranch62_731 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 8 degreeUnionState62_731 [8,9,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 32 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_732 - · exact degreeUnionBranch62_733 - · exact degreeUnionBranch62_734 - · exact degreeUnionBranch62_735 - · exact degreeUnionBranch62_736 - -lemma degreeUnionBranch62_737 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 9 degreeUnionState62_737 [9,9,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 31 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_738 - · exact degreeUnionBranch62_739 - · exact degreeUnionBranch62_740 - · exact degreeUnionBranch62_741 - · exact degreeUnionBranch62_742 - · exact degreeUnionBranch62_743 - -lemma degreeUnionBranch62_726 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 40 9 degreeUnionState62_726 [9,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 40 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_727 - · exact degreeUnionBranch62_728 - · exact degreeUnionBranch62_729 - · exact degreeUnionBranch62_730 - · exact degreeUnionBranch62_731 - · exact degreeUnionBranch62_737 - -lemma degreeUnionBranch62_748 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 7 degreeUnionState62_748 [7,10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 32 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_749 - · exact degreeUnionBranch62_750 - · exact degreeUnionBranch62_751 - · exact degreeUnionBranch62_752 - -lemma degreeUnionBranch62_753 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 8 degreeUnionState62_753 [8,10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 31 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_754 - · exact degreeUnionBranch62_755 - · exact degreeUnionBranch62_756 - · exact degreeUnionBranch62_757 - · exact degreeUnionBranch62_758 - -lemma degreeUnionBranch62_759 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 9 degreeUnionState62_759 [9,10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 30 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_760 - · exact degreeUnionBranch62_761 - · exact degreeUnionBranch62_762 - · exact degreeUnionBranch62_763 - · exact degreeUnionBranch62_764 - · exact degreeUnionBranch62_765 - · exact degreeUnionBranch62_766 - -lemma degreeUnionBranch62_767 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 10 degreeUnionState62_767 [10,10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 10 at hb - change 29 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_768 - · exact degreeUnionBranch62_769 - · exact degreeUnionBranch62_770 - · exact degreeUnionBranch62_771 - · exact degreeUnionBranch62_772 - · exact degreeUnionBranch62_773 - · exact degreeUnionBranch62_774 - · exact degreeUnionBranch62_775 - -lemma degreeUnionBranch62_744 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 39 10 degreeUnionState62_744 [10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 39 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_745 - · exact degreeUnionBranch62_746 - · exact degreeUnionBranch62_747 - · exact degreeUnionBranch62_748 - · exact degreeUnionBranch62_753 - · exact degreeUnionBranch62_759 - · exact degreeUnionBranch62_767 - -lemma degreeUnionBranch62_780 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 7 degreeUnionState62_780 [7,11,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 31 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_781 - · exact degreeUnionBranch62_782 - · exact degreeUnionBranch62_783 - · exact degreeUnionBranch62_784 - -lemma degreeUnionBranch62_785 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 8 degreeUnionState62_785 [8,11,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 30 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_786 - · exact degreeUnionBranch62_787 - · exact degreeUnionBranch62_788 - · exact degreeUnionBranch62_789 - · exact degreeUnionBranch62_790 - · exact degreeUnionBranch62_791 - -lemma degreeUnionBranch62_792 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 9 degreeUnionState62_792 [9,11,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 29 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_793 - · exact degreeUnionBranch62_794 - · exact degreeUnionBranch62_795 - · exact degreeUnionBranch62_796 - · exact degreeUnionBranch62_797 - · exact degreeUnionBranch62_798 - · exact degreeUnionBranch62_799 - -lemma degreeUnionBranch62_776 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 38 11 degreeUnionState62_776 [11,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 38 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_777 - · exact degreeUnionBranch62_778 - · exact degreeUnionBranch62_779 - · exact degreeUnionBranch62_780 - · exact degreeUnionBranch62_785 - · exact degreeUnionBranch62_792 - · exact degreeUnionBranch62_800 - · exact degreeUnionBranch62_801 - -lemma degreeUnionBranch62_806 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 7 degreeUnionState62_806 [7,12,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 30 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_807 - · exact degreeUnionBranch62_808 - · exact degreeUnionBranch62_809 - · exact degreeUnionBranch62_810 - · exact degreeUnionBranch62_811 - -lemma degreeUnionBranch62_812 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 8 degreeUnionState62_812 [8,12,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 29 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_813 - · exact degreeUnionBranch62_814 - · exact degreeUnionBranch62_815 - · exact degreeUnionBranch62_816 - · exact degreeUnionBranch62_817 - · exact degreeUnionBranch62_818 - -lemma degreeUnionBranch62_802 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 12 degreeUnionState62_802 [12,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 37 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_803 - · exact degreeUnionBranch62_804 - · exact degreeUnionBranch62_805 - · exact degreeUnionBranch62_806 - · exact degreeUnionBranch62_812 - · exact degreeUnionBranch62_819 - · exact degreeUnionBranch62_820 - · exact degreeUnionBranch62_821 - · exact degreeUnionBranch62_822 - -lemma degreeUnionBranch62_823 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 13 degreeUnionState62_823 [13,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 13 at hb - change 36 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_824 - · exact degreeUnionBranch62_825 - · exact degreeUnionBranch62_826 - · exact degreeUnionBranch62_827 - · exact degreeUnionBranch62_828 - · exact degreeUnionBranch62_829 - · exact degreeUnionBranch62_830 - · exact degreeUnionBranch62_831 - · exact degreeUnionBranch62_832 - · exact degreeUnionBranch62_833 - -lemma degreeUnionBranch62_707 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 49 13 degreeUnionState62_707 [13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 13 at hb - change 49 ≤ 12*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_708 - · exact degreeUnionBranch62_709 - · exact degreeUnionBranch62_710 - · exact degreeUnionBranch62_715 - · exact degreeUnionBranch62_726 - · exact degreeUnionBranch62_744 - · exact degreeUnionBranch62_776 - · exact degreeUnionBranch62_802 - · exact degreeUnionBranch62_823 - -lemma degreeUnionBranch62_838 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 41 7 degreeUnionState62_838 [7,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 41 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_839 - · exact degreeUnionBranch62_840 - · exact degreeUnionBranch62_841 - · exact degreeUnionBranch62_842 - -lemma degreeUnionBranch62_848 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 8 degreeUnionState62_848 [8,8,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 32 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_849 - · exact degreeUnionBranch62_850 - · exact degreeUnionBranch62_851 - · exact degreeUnionBranch62_852 - · exact degreeUnionBranch62_853 - -lemma degreeUnionBranch62_843 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 40 8 degreeUnionState62_843 [8,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 40 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_844 - · exact degreeUnionBranch62_845 - · exact degreeUnionBranch62_846 - · exact degreeUnionBranch62_847 - · exact degreeUnionBranch62_848 - -lemma degreeUnionBranch62_858 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 7 degreeUnionState62_858 [7,9,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 32 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_859 - · exact degreeUnionBranch62_860 - · exact degreeUnionBranch62_861 - · exact degreeUnionBranch62_862 - -lemma degreeUnionBranch62_863 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 8 degreeUnionState62_863 [8,9,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 31 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_864 - · exact degreeUnionBranch62_865 - · exact degreeUnionBranch62_866 - · exact degreeUnionBranch62_867 - · exact degreeUnionBranch62_868 - -lemma degreeUnionBranch62_869 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 9 degreeUnionState62_869 [9,9,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 30 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_870 - · exact degreeUnionBranch62_871 - · exact degreeUnionBranch62_872 - · exact degreeUnionBranch62_873 - · exact degreeUnionBranch62_874 - · exact degreeUnionBranch62_875 - · exact degreeUnionBranch62_876 - -lemma degreeUnionBranch62_854 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 39 9 degreeUnionState62_854 [9,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 39 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_855 - · exact degreeUnionBranch62_856 - · exact degreeUnionBranch62_857 - · exact degreeUnionBranch62_858 - · exact degreeUnionBranch62_863 - · exact degreeUnionBranch62_869 - -lemma degreeUnionBranch62_881 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 7 degreeUnionState62_881 [7,10,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 31 ≤ 10*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_882 - · exact degreeUnionBranch62_883 - · exact degreeUnionBranch62_884 - · exact degreeUnionBranch62_885 - -lemma degreeUnionBranch62_886 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 8 degreeUnionState62_886 [8,10,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 30 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_887 - · exact degreeUnionBranch62_888 - · exact degreeUnionBranch62_889 - · exact degreeUnionBranch62_890 - · exact degreeUnionBranch62_891 - · exact degreeUnionBranch62_892 - -lemma degreeUnionBranch62_893 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 9 degreeUnionState62_893 [9,10,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 29 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_894 - · exact degreeUnionBranch62_895 - · exact degreeUnionBranch62_896 - · exact degreeUnionBranch62_897 - · exact degreeUnionBranch62_898 - · exact degreeUnionBranch62_899 - · exact degreeUnionBranch62_900 - -lemma degreeUnionBranch62_877 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 38 10 degreeUnionState62_877 [10,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 38 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_878 - · exact degreeUnionBranch62_879 - · exact degreeUnionBranch62_880 - · exact degreeUnionBranch62_881 - · exact degreeUnionBranch62_886 - · exact degreeUnionBranch62_893 - · exact degreeUnionBranch62_901 - -lemma degreeUnionBranch62_906 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 7 degreeUnionState62_906 [7,11,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 7 at hb - change 30 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_907 - · exact degreeUnionBranch62_908 - · exact degreeUnionBranch62_909 - · exact degreeUnionBranch62_910 - · exact degreeUnionBranch62_911 - -lemma degreeUnionBranch62_912 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 8 degreeUnionState62_912 [8,11,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 29 ≤ 10*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_913 - · exact degreeUnionBranch62_914 - · exact degreeUnionBranch62_915 - · exact degreeUnionBranch62_916 - · exact degreeUnionBranch62_917 - · exact degreeUnionBranch62_918 - -lemma degreeUnionBranch62_902 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 11 degreeUnionState62_902 [11,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 37 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_903 - · exact degreeUnionBranch62_904 - · exact degreeUnionBranch62_905 - · exact degreeUnionBranch62_906 - · exact degreeUnionBranch62_912 - · exact degreeUnionBranch62_919 - · exact degreeUnionBranch62_920 - · exact degreeUnionBranch62_921 - -lemma degreeUnionBranch62_922 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 12 degreeUnionState62_922 [12,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 36 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_923 - · exact degreeUnionBranch62_924 - · exact degreeUnionBranch62_925 - · exact degreeUnionBranch62_926 - · exact degreeUnionBranch62_927 - · exact degreeUnionBranch62_928 - · exact degreeUnionBranch62_929 - · exact degreeUnionBranch62_930 - · exact degreeUnionBranch62_931 - -lemma degreeUnionBranch62_834 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 48 14 degreeUnionState62_834 [14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 14 at hb - change 48 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_835 - · exact degreeUnionBranch62_836 - · exact degreeUnionBranch62_837 - · exact degreeUnionBranch62_838 - · exact degreeUnionBranch62_843 - · exact degreeUnionBranch62_854 - · exact degreeUnionBranch62_877 - · exact degreeUnionBranch62_902 - · exact degreeUnionBranch62_922 - · exact degreeUnionBranch62_932 - · exact degreeUnionBranch62_933 - -lemma degreeUnionBranch62_513 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 62 28 degreeHalfRegions62 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 28 at hb - change 62 ≤ 13*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_514 - · exact degreeUnionBranch62_515 - · exact degreeUnionBranch62_516 - · exact degreeUnionBranch62_517 - · exact degreeUnionBranch62_518 - · exact degreeUnionBranch62_519 - · exact degreeUnionBranch62_540 - · exact degreeUnionBranch62_587 - · exact degreeUnionBranch62_707 - · exact degreeUnionBranch62_834 - · exact degreeUnionBranch62_934 - · exact degreeUnionBranch62_935 - · exact degreeUnionBranch62_936 - · exact degreeUnionBranch62_937 - · exact degreeUnionBranch62_938 - · exact degreeUnionBranch62_939 - · exact degreeUnionBranch62_940 - · exact degreeUnionBranch62_941 - · exact degreeUnionBranch62_942 - · exact degreeUnionBranch62_943 - · exact degreeUnionBranch62_944 - · exact degreeUnionBranch62_945 - · exact degreeUnionBranch62_946 - · exact degreeUnionBranch62_947 - -lemma degreeUnionBranch62_954 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 52 10 degreeUnionState62_954 [10] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 10 at hb - change 52 ≤ 13*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_955 - · exact degreeUnionBranch62_956 - · exact degreeUnionBranch62_957 - · exact degreeUnionBranch62_958 - · exact degreeUnionBranch62_959 - · exact degreeUnionBranch62_960 - · exact degreeUnionBranch62_961 - -lemma degreeUnionBranch62_969 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 41 10 degreeUnionState62_969 [10,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 41 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_970 - · exact degreeUnionBranch62_971 - · exact degreeUnionBranch62_972 - · exact degreeUnionBranch62_973 - · exact degreeUnionBranch62_974 - · exact degreeUnionBranch62_975 - · exact degreeUnionBranch62_976 - -lemma degreeUnionBranch62_984 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 10 degreeUnionState62_984 [10,11,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 10 at hb - change 30 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_985 - · exact degreeUnionBranch62_986 - · exact degreeUnionBranch62_987 - · exact degreeUnionBranch62_988 - · exact degreeUnionBranch62_989 - · exact degreeUnionBranch62_990 - · exact degreeUnionBranch62_991 - · exact degreeUnionBranch62_992 - -lemma degreeUnionBranch62_993 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 11 degreeUnionState62_993 [11,11,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 11 at hb - change 29 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_994 - · exact degreeUnionBranch62_995 - · exact degreeUnionBranch62_996 - · exact degreeUnionBranch62_997 - · exact degreeUnionBranch62_998 - · exact degreeUnionBranch62_999 - · exact degreeUnionBranch62_1000 - · exact degreeUnionBranch62_1001 - · exact degreeUnionBranch62_1002 - -lemma degreeUnionBranch62_977 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 40 11 degreeUnionState62_977 [11,11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 40 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_978 - · exact degreeUnionBranch62_979 - · exact degreeUnionBranch62_980 - · exact degreeUnionBranch62_981 - · exact degreeUnionBranch62_982 - · exact degreeUnionBranch62_983 - · exact degreeUnionBranch62_984 - · exact degreeUnionBranch62_993 - -lemma degreeUnionBranch62_962 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 51 11 degreeUnionState62_962 [11] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 51 ≤ 13*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_963 - · exact degreeUnionBranch62_964 - · exact degreeUnionBranch62_965 - · exact degreeUnionBranch62_966 - · exact degreeUnionBranch62_967 - · exact degreeUnionBranch62_968 - · exact degreeUnionBranch62_969 - · exact degreeUnionBranch62_977 - -lemma degreeUnionBranch62_1013 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 8 degreeUnionState62_1013 [8,8,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 34 ≤ 11*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1014 - · exact degreeUnionBranch62_1015 - · exact degreeUnionBranch62_1016 - · exact degreeUnionBranch62_1017 - · exact degreeUnionBranch62_1018 - -lemma degreeUnionBranch62_1008 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 42 8 degreeUnionState62_1008 [8,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 42 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1009 - · exact degreeUnionBranch62_1010 - · exact degreeUnionBranch62_1011 - · exact degreeUnionBranch62_1012 - · exact degreeUnionBranch62_1013 - -lemma degreeUnionBranch62_1024 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 8 degreeUnionState62_1024 [8,9,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 33 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1025 - · exact degreeUnionBranch62_1026 - · exact degreeUnionBranch62_1027 - · exact degreeUnionBranch62_1028 - · exact degreeUnionBranch62_1029 - · exact degreeUnionBranch62_1030 - -lemma degreeUnionBranch62_1031 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 9 degreeUnionState62_1031 [9,9,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 32 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1032 - · exact degreeUnionBranch62_1033 - · exact degreeUnionBranch62_1034 - · exact degreeUnionBranch62_1035 - · exact degreeUnionBranch62_1036 - · exact degreeUnionBranch62_1037 - · exact degreeUnionBranch62_1038 - -lemma degreeUnionBranch62_1019 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 41 9 degreeUnionState62_1019 [9,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 41 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1020 - · exact degreeUnionBranch62_1021 - · exact degreeUnionBranch62_1022 - · exact degreeUnionBranch62_1023 - · exact degreeUnionBranch62_1024 - · exact degreeUnionBranch62_1031 - -lemma degreeUnionBranch62_1044 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 8 degreeUnionState62_1044 [8,10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 32 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1045 - · exact degreeUnionBranch62_1046 - · exact degreeUnionBranch62_1047 - · exact degreeUnionBranch62_1048 - · exact degreeUnionBranch62_1049 - · exact degreeUnionBranch62_1050 - -lemma degreeUnionBranch62_1051 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 9 degreeUnionState62_1051 [9,10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 31 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1052 - · exact degreeUnionBranch62_1053 - · exact degreeUnionBranch62_1054 - · exact degreeUnionBranch62_1055 - · exact degreeUnionBranch62_1056 - · exact degreeUnionBranch62_1057 - · exact degreeUnionBranch62_1058 - -lemma degreeUnionBranch62_1059 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 10 degreeUnionState62_1059 [10,10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 10 at hb - change 30 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1060 - · exact degreeUnionBranch62_1061 - · exact degreeUnionBranch62_1062 - · exact degreeUnionBranch62_1063 - · exact degreeUnionBranch62_1064 - · exact degreeUnionBranch62_1065 - · exact degreeUnionBranch62_1066 - · exact degreeUnionBranch62_1067 - -lemma degreeUnionBranch62_1039 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 40 10 degreeUnionState62_1039 [10,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 40 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1040 - · exact degreeUnionBranch62_1041 - · exact degreeUnionBranch62_1042 - · exact degreeUnionBranch62_1043 - · exact degreeUnionBranch62_1044 - · exact degreeUnionBranch62_1051 - · exact degreeUnionBranch62_1059 - -lemma degreeUnionBranch62_1073 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 8 degreeUnionState62_1073 [8,11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 31 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1074 - · exact degreeUnionBranch62_1075 - · exact degreeUnionBranch62_1076 - · exact degreeUnionBranch62_1077 - · exact degreeUnionBranch62_1078 - · exact degreeUnionBranch62_1079 - -lemma degreeUnionBranch62_1080 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 9 degreeUnionState62_1080 [9,11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 30 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1081 - · exact degreeUnionBranch62_1082 - · exact degreeUnionBranch62_1083 - · exact degreeUnionBranch62_1084 - · exact degreeUnionBranch62_1085 - · exact degreeUnionBranch62_1086 - · exact degreeUnionBranch62_1087 - -lemma degreeUnionBranch62_1088 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 10 degreeUnionState62_1088 [10,11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 10 at hb - change 29 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1089 - · exact degreeUnionBranch62_1090 - · exact degreeUnionBranch62_1091 - · exact degreeUnionBranch62_1092 - · exact degreeUnionBranch62_1093 - · exact degreeUnionBranch62_1094 - · exact degreeUnionBranch62_1095 - · exact degreeUnionBranch62_1096 - -lemma degreeUnionBranch62_1068 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 39 11 degreeUnionState62_1068 [11,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 39 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1069 - · exact degreeUnionBranch62_1070 - · exact degreeUnionBranch62_1071 - · exact degreeUnionBranch62_1072 - · exact degreeUnionBranch62_1073 - · exact degreeUnionBranch62_1080 - · exact degreeUnionBranch62_1088 - · exact degreeUnionBranch62_1097 - -lemma degreeUnionBranch62_1103 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 8 degreeUnionState62_1103 [8,12,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 30 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1104 - · exact degreeUnionBranch62_1105 - · exact degreeUnionBranch62_1106 - · exact degreeUnionBranch62_1107 - · exact degreeUnionBranch62_1108 - · exact degreeUnionBranch62_1109 - -lemma degreeUnionBranch62_1110 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 9 degreeUnionState62_1110 [9,12,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 29 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1111 - · exact degreeUnionBranch62_1112 - · exact degreeUnionBranch62_1113 - · exact degreeUnionBranch62_1114 - · exact degreeUnionBranch62_1115 - · exact degreeUnionBranch62_1116 - · exact degreeUnionBranch62_1117 - -lemma degreeUnionBranch62_1098 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 38 12 degreeUnionState62_1098 [12,12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 38 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1099 - · exact degreeUnionBranch62_1100 - · exact degreeUnionBranch62_1101 - · exact degreeUnionBranch62_1102 - · exact degreeUnionBranch62_1103 - · exact degreeUnionBranch62_1110 - · exact degreeUnionBranch62_1118 - · exact degreeUnionBranch62_1119 - · exact degreeUnionBranch62_1120 - -lemma degreeUnionBranch62_1003 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 50 12 degreeUnionState62_1003 [12] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 50 ≤ 13*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1004 - · exact degreeUnionBranch62_1005 - · exact degreeUnionBranch62_1006 - · exact degreeUnionBranch62_1007 - · exact degreeUnionBranch62_1008 - · exact degreeUnionBranch62_1019 - · exact degreeUnionBranch62_1039 - · exact degreeUnionBranch62_1068 - · exact degreeUnionBranch62_1098 - -lemma degreeUnionBranch62_1131 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 8 degreeUnionState62_1131 [8,8,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 33 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1132 - · exact degreeUnionBranch62_1133 - · exact degreeUnionBranch62_1134 - · exact degreeUnionBranch62_1135 - · exact degreeUnionBranch62_1136 - · exact degreeUnionBranch62_1137 - -lemma degreeUnionBranch62_1126 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 41 8 degreeUnionState62_1126 [8,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 41 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1127 - · exact degreeUnionBranch62_1128 - · exact degreeUnionBranch62_1129 - · exact degreeUnionBranch62_1130 - · exact degreeUnionBranch62_1131 - -lemma degreeUnionBranch62_1143 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 8 degreeUnionState62_1143 [8,9,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 32 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1144 - · exact degreeUnionBranch62_1145 - · exact degreeUnionBranch62_1146 - · exact degreeUnionBranch62_1147 - · exact degreeUnionBranch62_1148 - · exact degreeUnionBranch62_1149 - -lemma degreeUnionBranch62_1150 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 9 degreeUnionState62_1150 [9,9,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 31 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1151 - · exact degreeUnionBranch62_1152 - · exact degreeUnionBranch62_1153 - · exact degreeUnionBranch62_1154 - · exact degreeUnionBranch62_1155 - · exact degreeUnionBranch62_1156 - · exact degreeUnionBranch62_1157 - -lemma degreeUnionBranch62_1138 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 40 9 degreeUnionState62_1138 [9,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 40 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1139 - · exact degreeUnionBranch62_1140 - · exact degreeUnionBranch62_1141 - · exact degreeUnionBranch62_1142 - · exact degreeUnionBranch62_1143 - · exact degreeUnionBranch62_1150 - -lemma degreeUnionBranch62_1163 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 8 degreeUnionState62_1163 [8,10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 31 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1164 - · exact degreeUnionBranch62_1165 - · exact degreeUnionBranch62_1166 - · exact degreeUnionBranch62_1167 - · exact degreeUnionBranch62_1168 - · exact degreeUnionBranch62_1169 - -lemma degreeUnionBranch62_1170 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 9 degreeUnionState62_1170 [9,10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 30 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1171 - · exact degreeUnionBranch62_1172 - · exact degreeUnionBranch62_1173 - · exact degreeUnionBranch62_1174 - · exact degreeUnionBranch62_1175 - · exact degreeUnionBranch62_1176 - · exact degreeUnionBranch62_1177 - -lemma degreeUnionBranch62_1178 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 10 degreeUnionState62_1178 [10,10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 10 at hb - change 29 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1179 - · exact degreeUnionBranch62_1180 - · exact degreeUnionBranch62_1181 - · exact degreeUnionBranch62_1182 - · exact degreeUnionBranch62_1183 - · exact degreeUnionBranch62_1184 - · exact degreeUnionBranch62_1185 - · exact degreeUnionBranch62_1186 - -lemma degreeUnionBranch62_1158 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 39 10 degreeUnionState62_1158 [10,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 39 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1159 - · exact degreeUnionBranch62_1160 - · exact degreeUnionBranch62_1161 - · exact degreeUnionBranch62_1162 - · exact degreeUnionBranch62_1163 - · exact degreeUnionBranch62_1170 - · exact degreeUnionBranch62_1178 - -lemma degreeUnionBranch62_1192 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 8 degreeUnionState62_1192 [8,11,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 30 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1193 - · exact degreeUnionBranch62_1194 - · exact degreeUnionBranch62_1195 - · exact degreeUnionBranch62_1196 - · exact degreeUnionBranch62_1197 - · exact degreeUnionBranch62_1198 - -lemma degreeUnionBranch62_1199 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 9 degreeUnionState62_1199 [9,11,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 29 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1200 - · exact degreeUnionBranch62_1201 - · exact degreeUnionBranch62_1202 - · exact degreeUnionBranch62_1203 - · exact degreeUnionBranch62_1204 - · exact degreeUnionBranch62_1205 - · exact degreeUnionBranch62_1206 - -lemma degreeUnionBranch62_1187 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 38 11 degreeUnionState62_1187 [11,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 38 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1188 - · exact degreeUnionBranch62_1189 - · exact degreeUnionBranch62_1190 - · exact degreeUnionBranch62_1191 - · exact degreeUnionBranch62_1192 - · exact degreeUnionBranch62_1199 - · exact degreeUnionBranch62_1207 - · exact degreeUnionBranch62_1208 - -lemma degreeUnionBranch62_1214 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 8 degreeUnionState62_1214 [8,12,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 29 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1215 - · exact degreeUnionBranch62_1216 - · exact degreeUnionBranch62_1217 - · exact degreeUnionBranch62_1218 - · exact degreeUnionBranch62_1219 - · exact degreeUnionBranch62_1220 - -lemma degreeUnionBranch62_1209 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 37 12 degreeUnionState62_1209 [12,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 37 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1210 - · exact degreeUnionBranch62_1211 - · exact degreeUnionBranch62_1212 - · exact degreeUnionBranch62_1213 - · exact degreeUnionBranch62_1214 - · exact degreeUnionBranch62_1221 - · exact degreeUnionBranch62_1222 - · exact degreeUnionBranch62_1223 - · exact degreeUnionBranch62_1224 - -lemma degreeUnionBranch62_1225 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 36 13 degreeUnionState62_1225 [13,13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 13 at hb - change 36 ≤ 12*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1226 - · exact degreeUnionBranch62_1227 - · exact degreeUnionBranch62_1228 - · exact degreeUnionBranch62_1229 - · exact degreeUnionBranch62_1230 - · exact degreeUnionBranch62_1231 - · exact degreeUnionBranch62_1232 - · exact degreeUnionBranch62_1233 - · exact degreeUnionBranch62_1234 - · exact degreeUnionBranch62_1235 - · exact degreeUnionBranch62_1236 - -lemma degreeUnionBranch62_1121 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 49 13 degreeUnionState62_1121 [13] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 13 at hb - change 49 ≤ 13*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1122 - · exact degreeUnionBranch62_1123 - · exact degreeUnionBranch62_1124 - · exact degreeUnionBranch62_1125 - · exact degreeUnionBranch62_1126 - · exact degreeUnionBranch62_1138 - · exact degreeUnionBranch62_1158 - · exact degreeUnionBranch62_1187 - · exact degreeUnionBranch62_1209 - · exact degreeUnionBranch62_1225 - -lemma degreeUnionBranch62_1247 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 8 degreeUnionState62_1247 [8,8,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 32 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1248 - · exact degreeUnionBranch62_1249 - · exact degreeUnionBranch62_1250 - · exact degreeUnionBranch62_1251 - · exact degreeUnionBranch62_1252 - · exact degreeUnionBranch62_1253 - -lemma degreeUnionBranch62_1242 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 40 8 degreeUnionState62_1242 [8,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 8 at hb - change 40 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1243 - · exact degreeUnionBranch62_1244 - · exact degreeUnionBranch62_1245 - · exact degreeUnionBranch62_1246 - · exact degreeUnionBranch62_1247 - -lemma degreeUnionBranch62_1259 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 8 degreeUnionState62_1259 [8,9,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 31 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1260 - · exact degreeUnionBranch62_1261 - · exact degreeUnionBranch62_1262 - · exact degreeUnionBranch62_1263 - · exact degreeUnionBranch62_1264 - · exact degreeUnionBranch62_1265 - -lemma degreeUnionBranch62_1266 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 9 degreeUnionState62_1266 [9,9,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 30 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1267 - · exact degreeUnionBranch62_1268 - · exact degreeUnionBranch62_1269 - · exact degreeUnionBranch62_1270 - · exact degreeUnionBranch62_1271 - · exact degreeUnionBranch62_1272 - · exact degreeUnionBranch62_1273 - -lemma degreeUnionBranch62_1254 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 39 9 degreeUnionState62_1254 [9,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 9 at hb - change 39 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1255 - · exact degreeUnionBranch62_1256 - · exact degreeUnionBranch62_1257 - · exact degreeUnionBranch62_1258 - · exact degreeUnionBranch62_1259 - · exact degreeUnionBranch62_1266 - -lemma degreeUnionBranch62_1279 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 8 degreeUnionState62_1279 [8,10,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 30 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1280 - · exact degreeUnionBranch62_1281 - · exact degreeUnionBranch62_1282 - · exact degreeUnionBranch62_1283 - · exact degreeUnionBranch62_1284 - · exact degreeUnionBranch62_1285 - -lemma degreeUnionBranch62_1286 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 9 degreeUnionState62_1286 [9,10,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 9 at hb - change 29 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1287 - · exact degreeUnionBranch62_1288 - · exact degreeUnionBranch62_1289 - · exact degreeUnionBranch62_1290 - · exact degreeUnionBranch62_1291 - · exact degreeUnionBranch62_1292 - · exact degreeUnionBranch62_1293 - -lemma degreeUnionBranch62_1274 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 38 10 degreeUnionState62_1274 [10,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 10 at hb - change 38 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1275 - · exact degreeUnionBranch62_1276 - · exact degreeUnionBranch62_1277 - · exact degreeUnionBranch62_1278 - · exact degreeUnionBranch62_1279 - · exact degreeUnionBranch62_1286 - · exact degreeUnionBranch62_1294 - -lemma degreeUnionBranch62_1300 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 8 degreeUnionState62_1300 [8,11,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 2 ≤ a at ha - change a ≤ 8 at hb - change 29 ≤ 11*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1301 - · exact degreeUnionBranch62_1302 - · exact degreeUnionBranch62_1303 - · exact degreeUnionBranch62_1304 - · exact degreeUnionBranch62_1305 - · exact degreeUnionBranch62_1306 - -lemma degreeUnionBranch62_1295 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 37 11 degreeUnionState62_1295 [11,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 11 at hb - change 37 ≤ 12*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1296 - · exact degreeUnionBranch62_1297 - · exact degreeUnionBranch62_1298 - · exact degreeUnionBranch62_1299 - · exact degreeUnionBranch62_1300 - · exact degreeUnionBranch62_1307 - · exact degreeUnionBranch62_1308 - · exact degreeUnionBranch62_1309 - -lemma degreeUnionBranch62_1310 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 36 12 degreeUnionState62_1310 [12,14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 12 at hb - change 36 ≤ 12*a at hn - have hlo : 3 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1311 - · exact degreeUnionBranch62_1312 - · exact degreeUnionBranch62_1313 - · exact degreeUnionBranch62_1314 - · exact degreeUnionBranch62_1315 - · exact degreeUnionBranch62_1316 - · exact degreeUnionBranch62_1317 - · exact degreeUnionBranch62_1318 - · exact degreeUnionBranch62_1319 - · exact degreeUnionBranch62_1320 - -lemma degreeUnionBranch62_1237 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 48 14 degreeUnionState62_1237 [14] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 3 ≤ a at ha - change a ≤ 14 at hb - change 48 ≤ 13*a at hn - have hlo : 4 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_1238 - · exact degreeUnionBranch62_1239 - · exact degreeUnionBranch62_1240 - · exact degreeUnionBranch62_1241 - · exact degreeUnionBranch62_1242 - · exact degreeUnionBranch62_1254 - · exact degreeUnionBranch62_1274 - · exact degreeUnionBranch62_1295 - · exact degreeUnionBranch62_1310 - · exact degreeUnionBranch62_1321 - · exact degreeUnionBranch62_1322 - -lemma degreeUnionBranch62_948 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 14 62 28 degreeHalfRegions62 [] = true := by - apply checkRegionPrefixes_step - intro a ha hb hn - change 4 ≤ a at ha - change a ≤ 28 at hb - change 62 ≤ 14*a at hn - have hlo : 5 ≤ a := by omega - interval_cases a - · exact degreeUnionBranch62_949 - · exact degreeUnionBranch62_950 - · exact degreeUnionBranch62_951 - · exact degreeUnionBranch62_952 - · exact degreeUnionBranch62_953 - · exact degreeUnionBranch62_954 - · exact degreeUnionBranch62_962 - · exact degreeUnionBranch62_1003 - · exact degreeUnionBranch62_1121 - · exact degreeUnionBranch62_1237 - · exact degreeUnionBranch62_1323 - · exact degreeUnionBranch62_1324 - · exact degreeUnionBranch62_1325 - · exact degreeUnionBranch62_1326 - · exact degreeUnionBranch62_1327 - · exact degreeUnionBranch62_1328 - · exact degreeUnionBranch62_1329 - · exact degreeUnionBranch62_1330 - · exact degreeUnionBranch62_1331 - · exact degreeUnionBranch62_1332 - · exact degreeUnionBranch62_1333 - · exact degreeUnionBranch62_1334 - · exact degreeUnionBranch62_1335 - · exact degreeUnionBranch62_1336 - -lemma degreeUnionCheck62 : ∀ h ≤ 28, - checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) h 62 28 degreeHalfRegions62 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch62_0 - · exact degreeUnionBranch62_1 - · exact degreeUnionBranch62_2 - · exact degreeUnionBranch62_3 - · exact degreeUnionBranch62_4 - · exact degreeUnionBranch62_5 - · exact degreeUnionBranch62_6 - · exact degreeUnionBranch62_7 - · exact degreeUnionBranch62_8 - · exact degreeUnionBranch62_9 - · exact degreeUnionBranch62_10 - · exact degreeUnionBranch62_11 - · exact degreeUnionBranch62_62 - · exact degreeUnionBranch62_513 - · exact degreeUnionBranch62_948 - · exact degreeUnionBranch62_1337 - · exact degreeUnionBranch62_1338 - · exact degreeUnionBranch62_1339 - · exact degreeUnionBranch62_1340 - · exact degreeUnionBranch62_1341 - · exact degreeUnionBranch62_1342 - · exact degreeUnionBranch62_1343 - · exact degreeUnionBranch62_1344 - · exact degreeUnionBranch62_1345 - · exact degreeUnionBranch62_1346 - · exact degreeUnionBranch62_1347 - · exact degreeUnionBranch62_1348 - · exact degreeUnionBranch62_1349 - · exact degreeUnionBranch62_1350 - -lemma degreeHalfCover62 : ∀ R ∈ degreeRegions62, - R ∈ degreeHalfRegions62 ∨ (R.2,R.1) ∈ degreeHalfRegions62 := by decide +kernel - -lemma degreeDiagramRegionsChecked62 : ∀ R ∈ degreeRegions62, - ∀ μ : YoungDiagram, μ.card = 62 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP62 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck62 degreeHalfHeight62 degreeHalfWidth62 - degreeHalfCover62 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Support.SplitUnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves62 + +namespace OAI + +/-! Degree Regions 62. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionBranch62_18 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 50 12 degreeUnionState62_18 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 5 ≤ a at ha + change a ≤ 12 at hb + change 50 ≤ 10*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_19 + · exact degreeUnionBranch62_20 + · exact degreeUnionBranch62_21 + · exact degreeUnionBranch62_22 + · exact degreeUnionBranch62_23 + · exact degreeUnionBranch62_24 + · exact degreeUnionBranch62_25 + · exact degreeUnionBranch62_26 + +lemma degreeUnionBranch62_27 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 49 13 degreeUnionState62_27 [13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 13 at hb + change 49 ≤ 10*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_28 + · exact degreeUnionBranch62_29 + · exact degreeUnionBranch62_30 + · exact degreeUnionBranch62_31 + · exact degreeUnionBranch62_32 + · exact degreeUnionBranch62_33 + · exact degreeUnionBranch62_34 + · exact degreeUnionBranch62_35 + · exact degreeUnionBranch62_36 + +lemma degreeUnionBranch62_37 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 48 14 degreeUnionState62_37 [14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 14 at hb + change 48 ≤ 10*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_38 + · exact degreeUnionBranch62_39 + · exact degreeUnionBranch62_40 + · exact degreeUnionBranch62_41 + · exact degreeUnionBranch62_42 + · exact degreeUnionBranch62_43 + · exact degreeUnionBranch62_44 + · exact degreeUnionBranch62_45 + · exact degreeUnionBranch62_46 + · exact degreeUnionBranch62_47 + +lemma degreeUnionBranch62_11 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 62 28 degreeHalfRegions62 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 5 ≤ a at ha + change a ≤ 28 at hb + change 62 ≤ 11*a at hn + have hlo : 6 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_12 + · exact degreeUnionBranch62_13 + · exact degreeUnionBranch62_14 + · exact degreeUnionBranch62_15 + · exact degreeUnionBranch62_16 + · exact degreeUnionBranch62_17 + · exact degreeUnionBranch62_18 + · exact degreeUnionBranch62_27 + · exact degreeUnionBranch62_37 + · exact degreeUnionBranch62_48 + · exact degreeUnionBranch62_49 + · exact degreeUnionBranch62_50 + · exact degreeUnionBranch62_51 + · exact degreeUnionBranch62_52 + · exact degreeUnionBranch62_53 + · exact degreeUnionBranch62_54 + · exact degreeUnionBranch62_55 + · exact degreeUnionBranch62_56 + · exact degreeUnionBranch62_57 + · exact degreeUnionBranch62_58 + · exact degreeUnionBranch62_59 + · exact degreeUnionBranch62_60 + · exact degreeUnionBranch62_61 + +lemma degreeUnionBranch62_79 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 10 degreeUnionState62_79 [10,10,10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 32 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_80 + · exact degreeUnionBranch62_81 + · exact degreeUnionBranch62_82 + · exact degreeUnionBranch62_83 + · exact degreeUnionBranch62_84 + · exact degreeUnionBranch62_85 + · exact degreeUnionBranch62_86 + +lemma degreeUnionBranch62_73 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 42 10 degreeUnionState62_73 [10,10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 10 at hb + change 42 ≤ 10*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_74 + · exact degreeUnionBranch62_75 + · exact degreeUnionBranch62_76 + · exact degreeUnionBranch62_77 + · exact degreeUnionBranch62_78 + · exact degreeUnionBranch62_79 + +lemma degreeUnionBranch62_67 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 52 10 degreeUnionState62_67 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 10 at hb + change 52 ≤ 11*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_68 + · exact degreeUnionBranch62_69 + · exact degreeUnionBranch62_70 + · exact degreeUnionBranch62_71 + · exact degreeUnionBranch62_72 + · exact degreeUnionBranch62_73 + +lemma degreeUnionBranch62_99 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 10 degreeUnionState62_99 [10,10,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 31 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_100 + · exact degreeUnionBranch62_101 + · exact degreeUnionBranch62_102 + · exact degreeUnionBranch62_103 + · exact degreeUnionBranch62_104 + · exact degreeUnionBranch62_105 + · exact degreeUnionBranch62_106 + +lemma degreeUnionBranch62_93 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 41 10 degreeUnionState62_93 [10,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 10 at hb + change 41 ≤ 10*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_94 + · exact degreeUnionBranch62_95 + · exact degreeUnionBranch62_96 + · exact degreeUnionBranch62_97 + · exact degreeUnionBranch62_98 + · exact degreeUnionBranch62_99 + +lemma degreeUnionBranch62_114 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 10 degreeUnionState62_114 [10,11,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 30 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_115 + · exact degreeUnionBranch62_116 + · exact degreeUnionBranch62_117 + · exact degreeUnionBranch62_118 + · exact degreeUnionBranch62_119 + · exact degreeUnionBranch62_120 + · exact degreeUnionBranch62_121 + +lemma degreeUnionBranch62_122 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 11 degreeUnionState62_122 [11,11,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 29 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_123 + · exact degreeUnionBranch62_124 + · exact degreeUnionBranch62_125 + · exact degreeUnionBranch62_126 + · exact degreeUnionBranch62_127 + · exact degreeUnionBranch62_128 + · exact degreeUnionBranch62_129 + · exact degreeUnionBranch62_130 + +lemma degreeUnionBranch62_107 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 40 11 degreeUnionState62_107 [11,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 11 at hb + change 40 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_108 + · exact degreeUnionBranch62_109 + · exact degreeUnionBranch62_110 + · exact degreeUnionBranch62_111 + · exact degreeUnionBranch62_112 + · exact degreeUnionBranch62_113 + · exact degreeUnionBranch62_114 + · exact degreeUnionBranch62_122 + +lemma degreeUnionBranch62_87 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 51 11 degreeUnionState62_87 [11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 11 at hb + change 51 ≤ 11*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_88 + · exact degreeUnionBranch62_89 + · exact degreeUnionBranch62_90 + · exact degreeUnionBranch62_91 + · exact degreeUnionBranch62_92 + · exact degreeUnionBranch62_93 + · exact degreeUnionBranch62_107 + +lemma degreeUnionBranch62_134 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 43 7 degreeUnionState62_134 [7,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 7 at hb + change 43 ≤ 10*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_135 + · exact degreeUnionBranch62_136 + · exact degreeUnionBranch62_137 + +lemma degreeUnionBranch62_141 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 7 degreeUnionState62_141 [7,8,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 35 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_142 + · exact degreeUnionBranch62_143 + · exact degreeUnionBranch62_144 + · exact degreeUnionBranch62_145 + +lemma degreeUnionBranch62_146 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 8 degreeUnionState62_146 [8,8,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 34 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_147 + · exact degreeUnionBranch62_148 + · exact degreeUnionBranch62_149 + · exact degreeUnionBranch62_150 + · exact degreeUnionBranch62_151 + +lemma degreeUnionBranch62_138 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 42 8 degreeUnionState62_138 [8,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 8 at hb + change 42 ≤ 10*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_139 + · exact degreeUnionBranch62_140 + · exact degreeUnionBranch62_141 + · exact degreeUnionBranch62_146 + +lemma degreeUnionBranch62_155 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 7 degreeUnionState62_155 [7,9,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 34 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_156 + · exact degreeUnionBranch62_157 + · exact degreeUnionBranch62_158 + · exact degreeUnionBranch62_159 + +lemma degreeUnionBranch62_160 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 8 degreeUnionState62_160 [8,9,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 33 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_161 + · exact degreeUnionBranch62_162 + · exact degreeUnionBranch62_163 + · exact degreeUnionBranch62_164 + · exact degreeUnionBranch62_165 + +lemma degreeUnionBranch62_166 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 9 degreeUnionState62_166 [9,9,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 32 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_167 + · exact degreeUnionBranch62_168 + · exact degreeUnionBranch62_169 + · exact degreeUnionBranch62_170 + · exact degreeUnionBranch62_171 + · exact degreeUnionBranch62_172 + +lemma degreeUnionBranch62_152 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 41 9 degreeUnionState62_152 [9,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 9 at hb + change 41 ≤ 10*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_153 + · exact degreeUnionBranch62_154 + · exact degreeUnionBranch62_155 + · exact degreeUnionBranch62_160 + · exact degreeUnionBranch62_166 + +lemma degreeUnionBranch62_177 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 7 degreeUnionState62_177 [7,10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 33 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_178 + · exact degreeUnionBranch62_179 + · exact degreeUnionBranch62_180 + · exact degreeUnionBranch62_181 + +lemma degreeUnionBranch62_182 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 8 degreeUnionState62_182 [8,10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 32 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_183 + · exact degreeUnionBranch62_184 + · exact degreeUnionBranch62_185 + · exact degreeUnionBranch62_186 + · exact degreeUnionBranch62_187 + +lemma degreeUnionBranch62_188 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 9 degreeUnionState62_188 [9,10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 31 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_189 + · exact degreeUnionBranch62_190 + · exact degreeUnionBranch62_191 + · exact degreeUnionBranch62_192 + · exact degreeUnionBranch62_193 + · exact degreeUnionBranch62_194 + +lemma degreeUnionBranch62_195 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 10 degreeUnionState62_195 [10,10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 30 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_196 + · exact degreeUnionBranch62_197 + · exact degreeUnionBranch62_198 + · exact degreeUnionBranch62_199 + · exact degreeUnionBranch62_200 + · exact degreeUnionBranch62_201 + · exact degreeUnionBranch62_202 + +lemma degreeUnionBranch62_173 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 40 10 degreeUnionState62_173 [10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 10 at hb + change 40 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_174 + · exact degreeUnionBranch62_175 + · exact degreeUnionBranch62_176 + · exact degreeUnionBranch62_177 + · exact degreeUnionBranch62_182 + · exact degreeUnionBranch62_188 + · exact degreeUnionBranch62_195 + +lemma degreeUnionBranch62_207 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 7 degreeUnionState62_207 [7,11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 32 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_208 + · exact degreeUnionBranch62_209 + · exact degreeUnionBranch62_210 + · exact degreeUnionBranch62_211 + +lemma degreeUnionBranch62_212 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 8 degreeUnionState62_212 [8,11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 31 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_213 + · exact degreeUnionBranch62_214 + · exact degreeUnionBranch62_215 + · exact degreeUnionBranch62_216 + · exact degreeUnionBranch62_217 + +lemma degreeUnionBranch62_218 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 9 degreeUnionState62_218 [9,11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 30 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_219 + · exact degreeUnionBranch62_220 + · exact degreeUnionBranch62_221 + · exact degreeUnionBranch62_222 + · exact degreeUnionBranch62_223 + · exact degreeUnionBranch62_224 + +lemma degreeUnionBranch62_225 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 10 degreeUnionState62_225 [10,11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 29 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_226 + · exact degreeUnionBranch62_227 + · exact degreeUnionBranch62_228 + · exact degreeUnionBranch62_229 + · exact degreeUnionBranch62_230 + · exact degreeUnionBranch62_231 + · exact degreeUnionBranch62_232 + +lemma degreeUnionBranch62_203 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 39 11 degreeUnionState62_203 [11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 39 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_204 + · exact degreeUnionBranch62_205 + · exact degreeUnionBranch62_206 + · exact degreeUnionBranch62_207 + · exact degreeUnionBranch62_212 + · exact degreeUnionBranch62_218 + · exact degreeUnionBranch62_225 + · exact degreeUnionBranch62_233 + +lemma degreeUnionBranch62_238 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 7 degreeUnionState62_238 [7,12,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 31 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_239 + · exact degreeUnionBranch62_240 + · exact degreeUnionBranch62_241 + · exact degreeUnionBranch62_242 + +lemma degreeUnionBranch62_243 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 8 degreeUnionState62_243 [8,12,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 30 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_244 + · exact degreeUnionBranch62_245 + · exact degreeUnionBranch62_246 + · exact degreeUnionBranch62_247 + · exact degreeUnionBranch62_248 + +lemma degreeUnionBranch62_249 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 9 degreeUnionState62_249 [9,12,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 29 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_250 + · exact degreeUnionBranch62_251 + · exact degreeUnionBranch62_252 + · exact degreeUnionBranch62_253 + · exact degreeUnionBranch62_254 + · exact degreeUnionBranch62_255 + +lemma degreeUnionBranch62_234 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 12 degreeUnionState62_234 [12,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 38 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_235 + · exact degreeUnionBranch62_236 + · exact degreeUnionBranch62_237 + · exact degreeUnionBranch62_238 + · exact degreeUnionBranch62_243 + · exact degreeUnionBranch62_249 + · exact degreeUnionBranch62_256 + · exact degreeUnionBranch62_257 + · exact degreeUnionBranch62_258 + +lemma degreeUnionBranch62_131 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 50 12 degreeUnionState62_131 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 12 at hb + change 50 ≤ 11*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_132 + · exact degreeUnionBranch62_133 + · exact degreeUnionBranch62_134 + · exact degreeUnionBranch62_138 + · exact degreeUnionBranch62_152 + · exact degreeUnionBranch62_173 + · exact degreeUnionBranch62_203 + · exact degreeUnionBranch62_234 + +lemma degreeUnionBranch62_265 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 35 7 degreeUnionState62_265 [7,7,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 35 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_266 + · exact degreeUnionBranch62_267 + · exact degreeUnionBranch62_268 + · exact degreeUnionBranch62_269 + +lemma degreeUnionBranch62_262 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 42 7 degreeUnionState62_262 [7,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 7 at hb + change 42 ≤ 10*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_263 + · exact degreeUnionBranch62_264 + · exact degreeUnionBranch62_265 + +lemma degreeUnionBranch62_273 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 7 degreeUnionState62_273 [7,8,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 34 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_274 + · exact degreeUnionBranch62_275 + · exact degreeUnionBranch62_276 + · exact degreeUnionBranch62_277 + +lemma degreeUnionBranch62_278 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 8 degreeUnionState62_278 [8,8,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 33 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_279 + · exact degreeUnionBranch62_280 + · exact degreeUnionBranch62_281 + · exact degreeUnionBranch62_282 + · exact degreeUnionBranch62_283 + +lemma degreeUnionBranch62_270 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 41 8 degreeUnionState62_270 [8,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 8 at hb + change 41 ≤ 10*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_271 + · exact degreeUnionBranch62_272 + · exact degreeUnionBranch62_273 + · exact degreeUnionBranch62_278 + +lemma degreeUnionBranch62_288 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 7 degreeUnionState62_288 [7,9,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 33 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_289 + · exact degreeUnionBranch62_290 + · exact degreeUnionBranch62_291 + · exact degreeUnionBranch62_292 + +lemma degreeUnionBranch62_293 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 8 degreeUnionState62_293 [8,9,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 32 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_294 + · exact degreeUnionBranch62_295 + · exact degreeUnionBranch62_296 + · exact degreeUnionBranch62_297 + · exact degreeUnionBranch62_298 + +lemma degreeUnionBranch62_299 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 9 degreeUnionState62_299 [9,9,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 31 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_300 + · exact degreeUnionBranch62_301 + · exact degreeUnionBranch62_302 + · exact degreeUnionBranch62_303 + · exact degreeUnionBranch62_304 + · exact degreeUnionBranch62_305 + +lemma degreeUnionBranch62_284 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 40 9 degreeUnionState62_284 [9,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 9 at hb + change 40 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_285 + · exact degreeUnionBranch62_286 + · exact degreeUnionBranch62_287 + · exact degreeUnionBranch62_288 + · exact degreeUnionBranch62_293 + · exact degreeUnionBranch62_299 + +lemma degreeUnionBranch62_310 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 7 degreeUnionState62_310 [7,10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 32 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_311 + · exact degreeUnionBranch62_312 + · exact degreeUnionBranch62_313 + · exact degreeUnionBranch62_314 + +lemma degreeUnionBranch62_315 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 8 degreeUnionState62_315 [8,10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 31 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_316 + · exact degreeUnionBranch62_317 + · exact degreeUnionBranch62_318 + · exact degreeUnionBranch62_319 + · exact degreeUnionBranch62_320 + +lemma degreeUnionBranch62_321 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 9 degreeUnionState62_321 [9,10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 30 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_322 + · exact degreeUnionBranch62_323 + · exact degreeUnionBranch62_324 + · exact degreeUnionBranch62_325 + · exact degreeUnionBranch62_326 + · exact degreeUnionBranch62_327 + +lemma degreeUnionBranch62_328 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 10 degreeUnionState62_328 [10,10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 29 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_329 + · exact degreeUnionBranch62_330 + · exact degreeUnionBranch62_331 + · exact degreeUnionBranch62_332 + · exact degreeUnionBranch62_333 + · exact degreeUnionBranch62_334 + · exact degreeUnionBranch62_335 + +lemma degreeUnionBranch62_306 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 39 10 degreeUnionState62_306 [10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 39 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_307 + · exact degreeUnionBranch62_308 + · exact degreeUnionBranch62_309 + · exact degreeUnionBranch62_310 + · exact degreeUnionBranch62_315 + · exact degreeUnionBranch62_321 + · exact degreeUnionBranch62_328 + +lemma degreeUnionBranch62_340 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 7 degreeUnionState62_340 [7,11,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 31 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_341 + · exact degreeUnionBranch62_342 + · exact degreeUnionBranch62_343 + · exact degreeUnionBranch62_344 + +lemma degreeUnionBranch62_345 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 8 degreeUnionState62_345 [8,11,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 30 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_346 + · exact degreeUnionBranch62_347 + · exact degreeUnionBranch62_348 + · exact degreeUnionBranch62_349 + · exact degreeUnionBranch62_350 + +lemma degreeUnionBranch62_351 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 9 degreeUnionState62_351 [9,11,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 29 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_352 + · exact degreeUnionBranch62_353 + · exact degreeUnionBranch62_354 + · exact degreeUnionBranch62_355 + · exact degreeUnionBranch62_356 + · exact degreeUnionBranch62_357 + +lemma degreeUnionBranch62_336 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 11 degreeUnionState62_336 [11,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 38 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_337 + · exact degreeUnionBranch62_338 + · exact degreeUnionBranch62_339 + · exact degreeUnionBranch62_340 + · exact degreeUnionBranch62_345 + · exact degreeUnionBranch62_351 + · exact degreeUnionBranch62_358 + · exact degreeUnionBranch62_359 + +lemma degreeUnionBranch62_364 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 7 degreeUnionState62_364 [7,12,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 30 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_365 + · exact degreeUnionBranch62_366 + · exact degreeUnionBranch62_367 + · exact degreeUnionBranch62_368 + +lemma degreeUnionBranch62_369 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 8 degreeUnionState62_369 [8,12,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 29 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_370 + · exact degreeUnionBranch62_371 + · exact degreeUnionBranch62_372 + · exact degreeUnionBranch62_373 + · exact degreeUnionBranch62_374 + +lemma degreeUnionBranch62_360 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 12 degreeUnionState62_360 [12,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 37 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_361 + · exact degreeUnionBranch62_362 + · exact degreeUnionBranch62_363 + · exact degreeUnionBranch62_364 + · exact degreeUnionBranch62_369 + · exact degreeUnionBranch62_375 + · exact degreeUnionBranch62_376 + · exact degreeUnionBranch62_377 + · exact degreeUnionBranch62_378 + +lemma degreeUnionBranch62_383 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 7 degreeUnionState62_383 [7,13,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 29 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_384 + · exact degreeUnionBranch62_385 + · exact degreeUnionBranch62_386 + · exact degreeUnionBranch62_387 + +lemma degreeUnionBranch62_379 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 13 degreeUnionState62_379 [13,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 13 at hb + change 36 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_380 + · exact degreeUnionBranch62_381 + · exact degreeUnionBranch62_382 + · exact degreeUnionBranch62_383 + · exact degreeUnionBranch62_388 + · exact degreeUnionBranch62_389 + · exact degreeUnionBranch62_390 + · exact degreeUnionBranch62_391 + · exact degreeUnionBranch62_392 + · exact degreeUnionBranch62_393 + +lemma degreeUnionBranch62_259 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 49 13 degreeUnionState62_259 [13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 13 at hb + change 49 ≤ 11*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_260 + · exact degreeUnionBranch62_261 + · exact degreeUnionBranch62_262 + · exact degreeUnionBranch62_270 + · exact degreeUnionBranch62_284 + · exact degreeUnionBranch62_306 + · exact degreeUnionBranch62_336 + · exact degreeUnionBranch62_360 + · exact degreeUnionBranch62_379 + +lemma degreeUnionBranch62_400 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 34 7 degreeUnionState62_400 [7,7,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 34 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_401 + · exact degreeUnionBranch62_402 + · exact degreeUnionBranch62_403 + · exact degreeUnionBranch62_404 + +lemma degreeUnionBranch62_397 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 41 7 degreeUnionState62_397 [7,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 7 at hb + change 41 ≤ 10*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_398 + · exact degreeUnionBranch62_399 + · exact degreeUnionBranch62_400 + +lemma degreeUnionBranch62_409 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 33 7 degreeUnionState62_409 [7,8,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 33 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_410 + · exact degreeUnionBranch62_411 + · exact degreeUnionBranch62_412 + · exact degreeUnionBranch62_413 + +lemma degreeUnionBranch62_414 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 8 degreeUnionState62_414 [8,8,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 32 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_415 + · exact degreeUnionBranch62_416 + · exact degreeUnionBranch62_417 + · exact degreeUnionBranch62_418 + · exact degreeUnionBranch62_419 + +lemma degreeUnionBranch62_405 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 40 8 degreeUnionState62_405 [8,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 8 at hb + change 40 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_406 + · exact degreeUnionBranch62_407 + · exact degreeUnionBranch62_408 + · exact degreeUnionBranch62_409 + · exact degreeUnionBranch62_414 + +lemma degreeUnionBranch62_424 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 32 7 degreeUnionState62_424 [7,9,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 32 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_425 + · exact degreeUnionBranch62_426 + · exact degreeUnionBranch62_427 + · exact degreeUnionBranch62_428 + +lemma degreeUnionBranch62_429 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 8 degreeUnionState62_429 [8,9,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 31 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_430 + · exact degreeUnionBranch62_431 + · exact degreeUnionBranch62_432 + · exact degreeUnionBranch62_433 + · exact degreeUnionBranch62_434 + +lemma degreeUnionBranch62_435 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 9 degreeUnionState62_435 [9,9,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 30 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_436 + · exact degreeUnionBranch62_437 + · exact degreeUnionBranch62_438 + · exact degreeUnionBranch62_439 + · exact degreeUnionBranch62_440 + · exact degreeUnionBranch62_441 + +lemma degreeUnionBranch62_420 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 39 9 degreeUnionState62_420 [9,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 39 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_421 + · exact degreeUnionBranch62_422 + · exact degreeUnionBranch62_423 + · exact degreeUnionBranch62_424 + · exact degreeUnionBranch62_429 + · exact degreeUnionBranch62_435 + +lemma degreeUnionBranch62_446 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 31 7 degreeUnionState62_446 [7,10,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 31 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_447 + · exact degreeUnionBranch62_448 + · exact degreeUnionBranch62_449 + · exact degreeUnionBranch62_450 + +lemma degreeUnionBranch62_451 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 8 degreeUnionState62_451 [8,10,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 30 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_452 + · exact degreeUnionBranch62_453 + · exact degreeUnionBranch62_454 + · exact degreeUnionBranch62_455 + · exact degreeUnionBranch62_456 + +lemma degreeUnionBranch62_457 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 9 degreeUnionState62_457 [9,10,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 29 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_458 + · exact degreeUnionBranch62_459 + · exact degreeUnionBranch62_460 + · exact degreeUnionBranch62_461 + · exact degreeUnionBranch62_462 + · exact degreeUnionBranch62_463 + +lemma degreeUnionBranch62_442 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 38 10 degreeUnionState62_442 [10,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 38 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_443 + · exact degreeUnionBranch62_444 + · exact degreeUnionBranch62_445 + · exact degreeUnionBranch62_446 + · exact degreeUnionBranch62_451 + · exact degreeUnionBranch62_457 + · exact degreeUnionBranch62_464 + +lemma degreeUnionBranch62_469 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 30 7 degreeUnionState62_469 [7,11,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 30 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_470 + · exact degreeUnionBranch62_471 + · exact degreeUnionBranch62_472 + · exact degreeUnionBranch62_473 + +lemma degreeUnionBranch62_474 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 8 degreeUnionState62_474 [8,11,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 29 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_475 + · exact degreeUnionBranch62_476 + · exact degreeUnionBranch62_477 + · exact degreeUnionBranch62_478 + · exact degreeUnionBranch62_479 + +lemma degreeUnionBranch62_465 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 37 11 degreeUnionState62_465 [11,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 37 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_466 + · exact degreeUnionBranch62_467 + · exact degreeUnionBranch62_468 + · exact degreeUnionBranch62_469 + · exact degreeUnionBranch62_474 + · exact degreeUnionBranch62_480 + · exact degreeUnionBranch62_481 + · exact degreeUnionBranch62_482 + +lemma degreeUnionBranch62_487 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 9 29 7 degreeUnionState62_487 [7,12,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 29 ≤ 9*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_488 + · exact degreeUnionBranch62_489 + · exact degreeUnionBranch62_490 + · exact degreeUnionBranch62_491 + +lemma degreeUnionBranch62_483 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 36 12 degreeUnionState62_483 [12,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 36 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_484 + · exact degreeUnionBranch62_485 + · exact degreeUnionBranch62_486 + · exact degreeUnionBranch62_487 + · exact degreeUnionBranch62_492 + · exact degreeUnionBranch62_493 + · exact degreeUnionBranch62_494 + · exact degreeUnionBranch62_495 + · exact degreeUnionBranch62_496 + +lemma degreeUnionBranch62_394 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 48 14 degreeUnionState62_394 [14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 14 at hb + change 48 ≤ 11*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_395 + · exact degreeUnionBranch62_396 + · exact degreeUnionBranch62_397 + · exact degreeUnionBranch62_405 + · exact degreeUnionBranch62_420 + · exact degreeUnionBranch62_442 + · exact degreeUnionBranch62_465 + · exact degreeUnionBranch62_483 + · exact degreeUnionBranch62_497 + · exact degreeUnionBranch62_498 + +lemma degreeUnionBranch62_62 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 62 28 degreeHalfRegions62 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 5 ≤ a at ha + change a ≤ 28 at hb + change 62 ≤ 12*a at hn + have hlo : 6 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_63 + · exact degreeUnionBranch62_64 + · exact degreeUnionBranch62_65 + · exact degreeUnionBranch62_66 + · exact degreeUnionBranch62_67 + · exact degreeUnionBranch62_87 + · exact degreeUnionBranch62_131 + · exact degreeUnionBranch62_259 + · exact degreeUnionBranch62_394 + · exact degreeUnionBranch62_499 + · exact degreeUnionBranch62_500 + · exact degreeUnionBranch62_501 + · exact degreeUnionBranch62_502 + · exact degreeUnionBranch62_503 + · exact degreeUnionBranch62_504 + · exact degreeUnionBranch62_505 + · exact degreeUnionBranch62_506 + · exact degreeUnionBranch62_507 + · exact degreeUnionBranch62_508 + · exact degreeUnionBranch62_509 + · exact degreeUnionBranch62_510 + · exact degreeUnionBranch62_511 + · exact degreeUnionBranch62_512 + +lemma degreeUnionBranch62_532 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 10 degreeUnionState62_532 [10,10,10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 32 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_533 + · exact degreeUnionBranch62_534 + · exact degreeUnionBranch62_535 + · exact degreeUnionBranch62_536 + · exact degreeUnionBranch62_537 + · exact degreeUnionBranch62_538 + · exact degreeUnionBranch62_539 + +lemma degreeUnionBranch62_525 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 42 10 degreeUnionState62_525 [10,10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 42 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_526 + · exact degreeUnionBranch62_527 + · exact degreeUnionBranch62_528 + · exact degreeUnionBranch62_529 + · exact degreeUnionBranch62_530 + · exact degreeUnionBranch62_531 + · exact degreeUnionBranch62_532 + +lemma degreeUnionBranch62_519 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 52 10 degreeUnionState62_519 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 10 at hb + change 52 ≤ 12*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_520 + · exact degreeUnionBranch62_521 + · exact degreeUnionBranch62_522 + · exact degreeUnionBranch62_523 + · exact degreeUnionBranch62_524 + · exact degreeUnionBranch62_525 + +lemma degreeUnionBranch62_553 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 10 degreeUnionState62_553 [10,10,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 31 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_554 + · exact degreeUnionBranch62_555 + · exact degreeUnionBranch62_556 + · exact degreeUnionBranch62_557 + · exact degreeUnionBranch62_558 + · exact degreeUnionBranch62_559 + · exact degreeUnionBranch62_560 + +lemma degreeUnionBranch62_546 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 41 10 degreeUnionState62_546 [10,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 41 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_547 + · exact degreeUnionBranch62_548 + · exact degreeUnionBranch62_549 + · exact degreeUnionBranch62_550 + · exact degreeUnionBranch62_551 + · exact degreeUnionBranch62_552 + · exact degreeUnionBranch62_553 + +lemma degreeUnionBranch62_568 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 10 degreeUnionState62_568 [10,11,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 30 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_569 + · exact degreeUnionBranch62_570 + · exact degreeUnionBranch62_571 + · exact degreeUnionBranch62_572 + · exact degreeUnionBranch62_573 + · exact degreeUnionBranch62_574 + · exact degreeUnionBranch62_575 + · exact degreeUnionBranch62_576 + +lemma degreeUnionBranch62_577 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 11 degreeUnionState62_577 [11,11,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 11 at hb + change 29 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_578 + · exact degreeUnionBranch62_579 + · exact degreeUnionBranch62_580 + · exact degreeUnionBranch62_581 + · exact degreeUnionBranch62_582 + · exact degreeUnionBranch62_583 + · exact degreeUnionBranch62_584 + · exact degreeUnionBranch62_585 + · exact degreeUnionBranch62_586 + +lemma degreeUnionBranch62_561 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 40 11 degreeUnionState62_561 [11,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 40 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_562 + · exact degreeUnionBranch62_563 + · exact degreeUnionBranch62_564 + · exact degreeUnionBranch62_565 + · exact degreeUnionBranch62_566 + · exact degreeUnionBranch62_567 + · exact degreeUnionBranch62_568 + · exact degreeUnionBranch62_577 + +lemma degreeUnionBranch62_540 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 51 11 degreeUnionState62_540 [11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 11 at hb + change 51 ≤ 12*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_541 + · exact degreeUnionBranch62_542 + · exact degreeUnionBranch62_543 + · exact degreeUnionBranch62_544 + · exact degreeUnionBranch62_545 + · exact degreeUnionBranch62_546 + · exact degreeUnionBranch62_561 + +lemma degreeUnionBranch62_596 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 34 8 degreeUnionState62_596 [8,8,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 34 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_597 + · exact degreeUnionBranch62_598 + · exact degreeUnionBranch62_599 + · exact degreeUnionBranch62_600 + · exact degreeUnionBranch62_601 + +lemma degreeUnionBranch62_591 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 42 8 degreeUnionState62_591 [8,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 42 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_592 + · exact degreeUnionBranch62_593 + · exact degreeUnionBranch62_594 + · exact degreeUnionBranch62_595 + · exact degreeUnionBranch62_596 + +lemma degreeUnionBranch62_607 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 8 degreeUnionState62_607 [8,9,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 33 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_608 + · exact degreeUnionBranch62_609 + · exact degreeUnionBranch62_610 + · exact degreeUnionBranch62_611 + · exact degreeUnionBranch62_612 + +lemma degreeUnionBranch62_613 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 9 degreeUnionState62_613 [9,9,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 32 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_614 + · exact degreeUnionBranch62_615 + · exact degreeUnionBranch62_616 + · exact degreeUnionBranch62_617 + · exact degreeUnionBranch62_618 + · exact degreeUnionBranch62_619 + +lemma degreeUnionBranch62_602 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 41 9 degreeUnionState62_602 [9,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 41 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_603 + · exact degreeUnionBranch62_604 + · exact degreeUnionBranch62_605 + · exact degreeUnionBranch62_606 + · exact degreeUnionBranch62_607 + · exact degreeUnionBranch62_613 + +lemma degreeUnionBranch62_625 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 8 degreeUnionState62_625 [8,10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 32 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_626 + · exact degreeUnionBranch62_627 + · exact degreeUnionBranch62_628 + · exact degreeUnionBranch62_629 + · exact degreeUnionBranch62_630 + +lemma degreeUnionBranch62_631 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 9 degreeUnionState62_631 [9,10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 31 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_632 + · exact degreeUnionBranch62_633 + · exact degreeUnionBranch62_634 + · exact degreeUnionBranch62_635 + · exact degreeUnionBranch62_636 + · exact degreeUnionBranch62_637 + +lemma degreeUnionBranch62_638 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 10 degreeUnionState62_638 [10,10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 30 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_639 + · exact degreeUnionBranch62_640 + · exact degreeUnionBranch62_641 + · exact degreeUnionBranch62_642 + · exact degreeUnionBranch62_643 + · exact degreeUnionBranch62_644 + · exact degreeUnionBranch62_645 + · exact degreeUnionBranch62_646 + +lemma degreeUnionBranch62_620 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 40 10 degreeUnionState62_620 [10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 40 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_621 + · exact degreeUnionBranch62_622 + · exact degreeUnionBranch62_623 + · exact degreeUnionBranch62_624 + · exact degreeUnionBranch62_625 + · exact degreeUnionBranch62_631 + · exact degreeUnionBranch62_638 + +lemma degreeUnionBranch62_651 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 7 degreeUnionState62_651 [7,11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 32 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_652 + · exact degreeUnionBranch62_653 + · exact degreeUnionBranch62_654 + · exact degreeUnionBranch62_655 + +lemma degreeUnionBranch62_656 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 8 degreeUnionState62_656 [8,11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 31 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_657 + · exact degreeUnionBranch62_658 + · exact degreeUnionBranch62_659 + · exact degreeUnionBranch62_660 + · exact degreeUnionBranch62_661 + +lemma degreeUnionBranch62_662 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 9 degreeUnionState62_662 [9,11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 30 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_663 + · exact degreeUnionBranch62_664 + · exact degreeUnionBranch62_665 + · exact degreeUnionBranch62_666 + · exact degreeUnionBranch62_667 + · exact degreeUnionBranch62_668 + · exact degreeUnionBranch62_669 + +lemma degreeUnionBranch62_670 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 10 degreeUnionState62_670 [10,11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 10 at hb + change 29 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_671 + · exact degreeUnionBranch62_672 + · exact degreeUnionBranch62_673 + · exact degreeUnionBranch62_674 + · exact degreeUnionBranch62_675 + · exact degreeUnionBranch62_676 + · exact degreeUnionBranch62_677 + · exact degreeUnionBranch62_678 + +lemma degreeUnionBranch62_647 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 39 11 degreeUnionState62_647 [11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 39 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_648 + · exact degreeUnionBranch62_649 + · exact degreeUnionBranch62_650 + · exact degreeUnionBranch62_651 + · exact degreeUnionBranch62_656 + · exact degreeUnionBranch62_662 + · exact degreeUnionBranch62_670 + · exact degreeUnionBranch62_679 + +lemma degreeUnionBranch62_684 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 7 degreeUnionState62_684 [7,12,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 31 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_685 + · exact degreeUnionBranch62_686 + · exact degreeUnionBranch62_687 + · exact degreeUnionBranch62_688 + +lemma degreeUnionBranch62_689 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 8 degreeUnionState62_689 [8,12,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 30 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_690 + · exact degreeUnionBranch62_691 + · exact degreeUnionBranch62_692 + · exact degreeUnionBranch62_693 + · exact degreeUnionBranch62_694 + · exact degreeUnionBranch62_695 + +lemma degreeUnionBranch62_696 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 9 degreeUnionState62_696 [9,12,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 29 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_697 + · exact degreeUnionBranch62_698 + · exact degreeUnionBranch62_699 + · exact degreeUnionBranch62_700 + · exact degreeUnionBranch62_701 + · exact degreeUnionBranch62_702 + · exact degreeUnionBranch62_703 + +lemma degreeUnionBranch62_680 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 38 12 degreeUnionState62_680 [12,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 38 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_681 + · exact degreeUnionBranch62_682 + · exact degreeUnionBranch62_683 + · exact degreeUnionBranch62_684 + · exact degreeUnionBranch62_689 + · exact degreeUnionBranch62_696 + · exact degreeUnionBranch62_704 + · exact degreeUnionBranch62_705 + · exact degreeUnionBranch62_706 + +lemma degreeUnionBranch62_587 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 50 12 degreeUnionState62_587 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 12 at hb + change 50 ≤ 12*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_588 + · exact degreeUnionBranch62_589 + · exact degreeUnionBranch62_590 + · exact degreeUnionBranch62_591 + · exact degreeUnionBranch62_602 + · exact degreeUnionBranch62_620 + · exact degreeUnionBranch62_647 + · exact degreeUnionBranch62_680 + +lemma degreeUnionBranch62_710 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 42 7 degreeUnionState62_710 [7,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 42 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_711 + · exact degreeUnionBranch62_712 + · exact degreeUnionBranch62_713 + · exact degreeUnionBranch62_714 + +lemma degreeUnionBranch62_720 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 33 8 degreeUnionState62_720 [8,8,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 33 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_721 + · exact degreeUnionBranch62_722 + · exact degreeUnionBranch62_723 + · exact degreeUnionBranch62_724 + · exact degreeUnionBranch62_725 + +lemma degreeUnionBranch62_715 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 41 8 degreeUnionState62_715 [8,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 41 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_716 + · exact degreeUnionBranch62_717 + · exact degreeUnionBranch62_718 + · exact degreeUnionBranch62_719 + · exact degreeUnionBranch62_720 + +lemma degreeUnionBranch62_731 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 8 degreeUnionState62_731 [8,9,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 32 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_732 + · exact degreeUnionBranch62_733 + · exact degreeUnionBranch62_734 + · exact degreeUnionBranch62_735 + · exact degreeUnionBranch62_736 + +lemma degreeUnionBranch62_737 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 9 degreeUnionState62_737 [9,9,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 31 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_738 + · exact degreeUnionBranch62_739 + · exact degreeUnionBranch62_740 + · exact degreeUnionBranch62_741 + · exact degreeUnionBranch62_742 + · exact degreeUnionBranch62_743 + +lemma degreeUnionBranch62_726 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 40 9 degreeUnionState62_726 [9,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 40 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_727 + · exact degreeUnionBranch62_728 + · exact degreeUnionBranch62_729 + · exact degreeUnionBranch62_730 + · exact degreeUnionBranch62_731 + · exact degreeUnionBranch62_737 + +lemma degreeUnionBranch62_748 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 7 degreeUnionState62_748 [7,10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 32 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_749 + · exact degreeUnionBranch62_750 + · exact degreeUnionBranch62_751 + · exact degreeUnionBranch62_752 + +lemma degreeUnionBranch62_753 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 8 degreeUnionState62_753 [8,10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 31 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_754 + · exact degreeUnionBranch62_755 + · exact degreeUnionBranch62_756 + · exact degreeUnionBranch62_757 + · exact degreeUnionBranch62_758 + +lemma degreeUnionBranch62_759 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 9 degreeUnionState62_759 [9,10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 30 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_760 + · exact degreeUnionBranch62_761 + · exact degreeUnionBranch62_762 + · exact degreeUnionBranch62_763 + · exact degreeUnionBranch62_764 + · exact degreeUnionBranch62_765 + · exact degreeUnionBranch62_766 + +lemma degreeUnionBranch62_767 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 10 degreeUnionState62_767 [10,10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 10 at hb + change 29 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_768 + · exact degreeUnionBranch62_769 + · exact degreeUnionBranch62_770 + · exact degreeUnionBranch62_771 + · exact degreeUnionBranch62_772 + · exact degreeUnionBranch62_773 + · exact degreeUnionBranch62_774 + · exact degreeUnionBranch62_775 + +lemma degreeUnionBranch62_744 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 39 10 degreeUnionState62_744 [10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 39 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_745 + · exact degreeUnionBranch62_746 + · exact degreeUnionBranch62_747 + · exact degreeUnionBranch62_748 + · exact degreeUnionBranch62_753 + · exact degreeUnionBranch62_759 + · exact degreeUnionBranch62_767 + +lemma degreeUnionBranch62_780 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 7 degreeUnionState62_780 [7,11,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 31 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_781 + · exact degreeUnionBranch62_782 + · exact degreeUnionBranch62_783 + · exact degreeUnionBranch62_784 + +lemma degreeUnionBranch62_785 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 8 degreeUnionState62_785 [8,11,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 30 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_786 + · exact degreeUnionBranch62_787 + · exact degreeUnionBranch62_788 + · exact degreeUnionBranch62_789 + · exact degreeUnionBranch62_790 + · exact degreeUnionBranch62_791 + +lemma degreeUnionBranch62_792 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 9 degreeUnionState62_792 [9,11,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 29 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_793 + · exact degreeUnionBranch62_794 + · exact degreeUnionBranch62_795 + · exact degreeUnionBranch62_796 + · exact degreeUnionBranch62_797 + · exact degreeUnionBranch62_798 + · exact degreeUnionBranch62_799 + +lemma degreeUnionBranch62_776 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 38 11 degreeUnionState62_776 [11,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 38 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_777 + · exact degreeUnionBranch62_778 + · exact degreeUnionBranch62_779 + · exact degreeUnionBranch62_780 + · exact degreeUnionBranch62_785 + · exact degreeUnionBranch62_792 + · exact degreeUnionBranch62_800 + · exact degreeUnionBranch62_801 + +lemma degreeUnionBranch62_806 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 7 degreeUnionState62_806 [7,12,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 30 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_807 + · exact degreeUnionBranch62_808 + · exact degreeUnionBranch62_809 + · exact degreeUnionBranch62_810 + · exact degreeUnionBranch62_811 + +lemma degreeUnionBranch62_812 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 8 degreeUnionState62_812 [8,12,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 29 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_813 + · exact degreeUnionBranch62_814 + · exact degreeUnionBranch62_815 + · exact degreeUnionBranch62_816 + · exact degreeUnionBranch62_817 + · exact degreeUnionBranch62_818 + +lemma degreeUnionBranch62_802 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 12 degreeUnionState62_802 [12,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 37 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_803 + · exact degreeUnionBranch62_804 + · exact degreeUnionBranch62_805 + · exact degreeUnionBranch62_806 + · exact degreeUnionBranch62_812 + · exact degreeUnionBranch62_819 + · exact degreeUnionBranch62_820 + · exact degreeUnionBranch62_821 + · exact degreeUnionBranch62_822 + +lemma degreeUnionBranch62_823 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 13 degreeUnionState62_823 [13,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 13 at hb + change 36 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_824 + · exact degreeUnionBranch62_825 + · exact degreeUnionBranch62_826 + · exact degreeUnionBranch62_827 + · exact degreeUnionBranch62_828 + · exact degreeUnionBranch62_829 + · exact degreeUnionBranch62_830 + · exact degreeUnionBranch62_831 + · exact degreeUnionBranch62_832 + · exact degreeUnionBranch62_833 + +lemma degreeUnionBranch62_707 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 49 13 degreeUnionState62_707 [13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 13 at hb + change 49 ≤ 12*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_708 + · exact degreeUnionBranch62_709 + · exact degreeUnionBranch62_710 + · exact degreeUnionBranch62_715 + · exact degreeUnionBranch62_726 + · exact degreeUnionBranch62_744 + · exact degreeUnionBranch62_776 + · exact degreeUnionBranch62_802 + · exact degreeUnionBranch62_823 + +lemma degreeUnionBranch62_838 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 41 7 degreeUnionState62_838 [7,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 41 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_839 + · exact degreeUnionBranch62_840 + · exact degreeUnionBranch62_841 + · exact degreeUnionBranch62_842 + +lemma degreeUnionBranch62_848 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 8 degreeUnionState62_848 [8,8,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 32 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_849 + · exact degreeUnionBranch62_850 + · exact degreeUnionBranch62_851 + · exact degreeUnionBranch62_852 + · exact degreeUnionBranch62_853 + +lemma degreeUnionBranch62_843 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 40 8 degreeUnionState62_843 [8,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 40 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_844 + · exact degreeUnionBranch62_845 + · exact degreeUnionBranch62_846 + · exact degreeUnionBranch62_847 + · exact degreeUnionBranch62_848 + +lemma degreeUnionBranch62_858 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 32 7 degreeUnionState62_858 [7,9,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 32 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_859 + · exact degreeUnionBranch62_860 + · exact degreeUnionBranch62_861 + · exact degreeUnionBranch62_862 + +lemma degreeUnionBranch62_863 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 8 degreeUnionState62_863 [8,9,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 31 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_864 + · exact degreeUnionBranch62_865 + · exact degreeUnionBranch62_866 + · exact degreeUnionBranch62_867 + · exact degreeUnionBranch62_868 + +lemma degreeUnionBranch62_869 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 9 degreeUnionState62_869 [9,9,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 30 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_870 + · exact degreeUnionBranch62_871 + · exact degreeUnionBranch62_872 + · exact degreeUnionBranch62_873 + · exact degreeUnionBranch62_874 + · exact degreeUnionBranch62_875 + · exact degreeUnionBranch62_876 + +lemma degreeUnionBranch62_854 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 39 9 degreeUnionState62_854 [9,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 39 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_855 + · exact degreeUnionBranch62_856 + · exact degreeUnionBranch62_857 + · exact degreeUnionBranch62_858 + · exact degreeUnionBranch62_863 + · exact degreeUnionBranch62_869 + +lemma degreeUnionBranch62_881 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 31 7 degreeUnionState62_881 [7,10,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 31 ≤ 10*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_882 + · exact degreeUnionBranch62_883 + · exact degreeUnionBranch62_884 + · exact degreeUnionBranch62_885 + +lemma degreeUnionBranch62_886 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 8 degreeUnionState62_886 [8,10,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 30 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_887 + · exact degreeUnionBranch62_888 + · exact degreeUnionBranch62_889 + · exact degreeUnionBranch62_890 + · exact degreeUnionBranch62_891 + · exact degreeUnionBranch62_892 + +lemma degreeUnionBranch62_893 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 9 degreeUnionState62_893 [9,10,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 29 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_894 + · exact degreeUnionBranch62_895 + · exact degreeUnionBranch62_896 + · exact degreeUnionBranch62_897 + · exact degreeUnionBranch62_898 + · exact degreeUnionBranch62_899 + · exact degreeUnionBranch62_900 + +lemma degreeUnionBranch62_877 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 38 10 degreeUnionState62_877 [10,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 38 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_878 + · exact degreeUnionBranch62_879 + · exact degreeUnionBranch62_880 + · exact degreeUnionBranch62_881 + · exact degreeUnionBranch62_886 + · exact degreeUnionBranch62_893 + · exact degreeUnionBranch62_901 + +lemma degreeUnionBranch62_906 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 30 7 degreeUnionState62_906 [7,11,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 7 at hb + change 30 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_907 + · exact degreeUnionBranch62_908 + · exact degreeUnionBranch62_909 + · exact degreeUnionBranch62_910 + · exact degreeUnionBranch62_911 + +lemma degreeUnionBranch62_912 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 10 29 8 degreeUnionState62_912 [8,11,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 29 ≤ 10*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_913 + · exact degreeUnionBranch62_914 + · exact degreeUnionBranch62_915 + · exact degreeUnionBranch62_916 + · exact degreeUnionBranch62_917 + · exact degreeUnionBranch62_918 + +lemma degreeUnionBranch62_902 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 37 11 degreeUnionState62_902 [11,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 37 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_903 + · exact degreeUnionBranch62_904 + · exact degreeUnionBranch62_905 + · exact degreeUnionBranch62_906 + · exact degreeUnionBranch62_912 + · exact degreeUnionBranch62_919 + · exact degreeUnionBranch62_920 + · exact degreeUnionBranch62_921 + +lemma degreeUnionBranch62_922 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 36 12 degreeUnionState62_922 [12,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 36 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_923 + · exact degreeUnionBranch62_924 + · exact degreeUnionBranch62_925 + · exact degreeUnionBranch62_926 + · exact degreeUnionBranch62_927 + · exact degreeUnionBranch62_928 + · exact degreeUnionBranch62_929 + · exact degreeUnionBranch62_930 + · exact degreeUnionBranch62_931 + +lemma degreeUnionBranch62_834 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 48 14 degreeUnionState62_834 [14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 14 at hb + change 48 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_835 + · exact degreeUnionBranch62_836 + · exact degreeUnionBranch62_837 + · exact degreeUnionBranch62_838 + · exact degreeUnionBranch62_843 + · exact degreeUnionBranch62_854 + · exact degreeUnionBranch62_877 + · exact degreeUnionBranch62_902 + · exact degreeUnionBranch62_922 + · exact degreeUnionBranch62_932 + · exact degreeUnionBranch62_933 + +lemma degreeUnionBranch62_513 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 62 28 degreeHalfRegions62 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 28 at hb + change 62 ≤ 13*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_514 + · exact degreeUnionBranch62_515 + · exact degreeUnionBranch62_516 + · exact degreeUnionBranch62_517 + · exact degreeUnionBranch62_518 + · exact degreeUnionBranch62_519 + · exact degreeUnionBranch62_540 + · exact degreeUnionBranch62_587 + · exact degreeUnionBranch62_707 + · exact degreeUnionBranch62_834 + · exact degreeUnionBranch62_934 + · exact degreeUnionBranch62_935 + · exact degreeUnionBranch62_936 + · exact degreeUnionBranch62_937 + · exact degreeUnionBranch62_938 + · exact degreeUnionBranch62_939 + · exact degreeUnionBranch62_940 + · exact degreeUnionBranch62_941 + · exact degreeUnionBranch62_942 + · exact degreeUnionBranch62_943 + · exact degreeUnionBranch62_944 + · exact degreeUnionBranch62_945 + · exact degreeUnionBranch62_946 + · exact degreeUnionBranch62_947 + +lemma degreeUnionBranch62_954 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 52 10 degreeUnionState62_954 [10] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 10 at hb + change 52 ≤ 13*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_955 + · exact degreeUnionBranch62_956 + · exact degreeUnionBranch62_957 + · exact degreeUnionBranch62_958 + · exact degreeUnionBranch62_959 + · exact degreeUnionBranch62_960 + · exact degreeUnionBranch62_961 + +lemma degreeUnionBranch62_969 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 41 10 degreeUnionState62_969 [10,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 41 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_970 + · exact degreeUnionBranch62_971 + · exact degreeUnionBranch62_972 + · exact degreeUnionBranch62_973 + · exact degreeUnionBranch62_974 + · exact degreeUnionBranch62_975 + · exact degreeUnionBranch62_976 + +lemma degreeUnionBranch62_984 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 10 degreeUnionState62_984 [10,11,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 10 at hb + change 30 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_985 + · exact degreeUnionBranch62_986 + · exact degreeUnionBranch62_987 + · exact degreeUnionBranch62_988 + · exact degreeUnionBranch62_989 + · exact degreeUnionBranch62_990 + · exact degreeUnionBranch62_991 + · exact degreeUnionBranch62_992 + +lemma degreeUnionBranch62_993 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 11 degreeUnionState62_993 [11,11,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 11 at hb + change 29 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_994 + · exact degreeUnionBranch62_995 + · exact degreeUnionBranch62_996 + · exact degreeUnionBranch62_997 + · exact degreeUnionBranch62_998 + · exact degreeUnionBranch62_999 + · exact degreeUnionBranch62_1000 + · exact degreeUnionBranch62_1001 + · exact degreeUnionBranch62_1002 + +lemma degreeUnionBranch62_977 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 40 11 degreeUnionState62_977 [11,11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 40 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_978 + · exact degreeUnionBranch62_979 + · exact degreeUnionBranch62_980 + · exact degreeUnionBranch62_981 + · exact degreeUnionBranch62_982 + · exact degreeUnionBranch62_983 + · exact degreeUnionBranch62_984 + · exact degreeUnionBranch62_993 + +lemma degreeUnionBranch62_962 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 51 11 degreeUnionState62_962 [11] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 51 ≤ 13*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_963 + · exact degreeUnionBranch62_964 + · exact degreeUnionBranch62_965 + · exact degreeUnionBranch62_966 + · exact degreeUnionBranch62_967 + · exact degreeUnionBranch62_968 + · exact degreeUnionBranch62_969 + · exact degreeUnionBranch62_977 + +lemma degreeUnionBranch62_1013 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 34 8 degreeUnionState62_1013 [8,8,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 34 ≤ 11*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1014 + · exact degreeUnionBranch62_1015 + · exact degreeUnionBranch62_1016 + · exact degreeUnionBranch62_1017 + · exact degreeUnionBranch62_1018 + +lemma degreeUnionBranch62_1008 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 42 8 degreeUnionState62_1008 [8,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 42 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1009 + · exact degreeUnionBranch62_1010 + · exact degreeUnionBranch62_1011 + · exact degreeUnionBranch62_1012 + · exact degreeUnionBranch62_1013 + +lemma degreeUnionBranch62_1024 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 8 degreeUnionState62_1024 [8,9,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 33 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1025 + · exact degreeUnionBranch62_1026 + · exact degreeUnionBranch62_1027 + · exact degreeUnionBranch62_1028 + · exact degreeUnionBranch62_1029 + · exact degreeUnionBranch62_1030 + +lemma degreeUnionBranch62_1031 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 9 degreeUnionState62_1031 [9,9,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 32 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1032 + · exact degreeUnionBranch62_1033 + · exact degreeUnionBranch62_1034 + · exact degreeUnionBranch62_1035 + · exact degreeUnionBranch62_1036 + · exact degreeUnionBranch62_1037 + · exact degreeUnionBranch62_1038 + +lemma degreeUnionBranch62_1019 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 41 9 degreeUnionState62_1019 [9,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 41 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1020 + · exact degreeUnionBranch62_1021 + · exact degreeUnionBranch62_1022 + · exact degreeUnionBranch62_1023 + · exact degreeUnionBranch62_1024 + · exact degreeUnionBranch62_1031 + +lemma degreeUnionBranch62_1044 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 8 degreeUnionState62_1044 [8,10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 32 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1045 + · exact degreeUnionBranch62_1046 + · exact degreeUnionBranch62_1047 + · exact degreeUnionBranch62_1048 + · exact degreeUnionBranch62_1049 + · exact degreeUnionBranch62_1050 + +lemma degreeUnionBranch62_1051 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 9 degreeUnionState62_1051 [9,10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 31 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1052 + · exact degreeUnionBranch62_1053 + · exact degreeUnionBranch62_1054 + · exact degreeUnionBranch62_1055 + · exact degreeUnionBranch62_1056 + · exact degreeUnionBranch62_1057 + · exact degreeUnionBranch62_1058 + +lemma degreeUnionBranch62_1059 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 10 degreeUnionState62_1059 [10,10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 10 at hb + change 30 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1060 + · exact degreeUnionBranch62_1061 + · exact degreeUnionBranch62_1062 + · exact degreeUnionBranch62_1063 + · exact degreeUnionBranch62_1064 + · exact degreeUnionBranch62_1065 + · exact degreeUnionBranch62_1066 + · exact degreeUnionBranch62_1067 + +lemma degreeUnionBranch62_1039 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 40 10 degreeUnionState62_1039 [10,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 40 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1040 + · exact degreeUnionBranch62_1041 + · exact degreeUnionBranch62_1042 + · exact degreeUnionBranch62_1043 + · exact degreeUnionBranch62_1044 + · exact degreeUnionBranch62_1051 + · exact degreeUnionBranch62_1059 + +lemma degreeUnionBranch62_1073 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 8 degreeUnionState62_1073 [8,11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 31 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1074 + · exact degreeUnionBranch62_1075 + · exact degreeUnionBranch62_1076 + · exact degreeUnionBranch62_1077 + · exact degreeUnionBranch62_1078 + · exact degreeUnionBranch62_1079 + +lemma degreeUnionBranch62_1080 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 9 degreeUnionState62_1080 [9,11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 30 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1081 + · exact degreeUnionBranch62_1082 + · exact degreeUnionBranch62_1083 + · exact degreeUnionBranch62_1084 + · exact degreeUnionBranch62_1085 + · exact degreeUnionBranch62_1086 + · exact degreeUnionBranch62_1087 + +lemma degreeUnionBranch62_1088 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 10 degreeUnionState62_1088 [10,11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 10 at hb + change 29 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1089 + · exact degreeUnionBranch62_1090 + · exact degreeUnionBranch62_1091 + · exact degreeUnionBranch62_1092 + · exact degreeUnionBranch62_1093 + · exact degreeUnionBranch62_1094 + · exact degreeUnionBranch62_1095 + · exact degreeUnionBranch62_1096 + +lemma degreeUnionBranch62_1068 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 39 11 degreeUnionState62_1068 [11,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 39 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1069 + · exact degreeUnionBranch62_1070 + · exact degreeUnionBranch62_1071 + · exact degreeUnionBranch62_1072 + · exact degreeUnionBranch62_1073 + · exact degreeUnionBranch62_1080 + · exact degreeUnionBranch62_1088 + · exact degreeUnionBranch62_1097 + +lemma degreeUnionBranch62_1103 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 8 degreeUnionState62_1103 [8,12,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 30 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1104 + · exact degreeUnionBranch62_1105 + · exact degreeUnionBranch62_1106 + · exact degreeUnionBranch62_1107 + · exact degreeUnionBranch62_1108 + · exact degreeUnionBranch62_1109 + +lemma degreeUnionBranch62_1110 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 9 degreeUnionState62_1110 [9,12,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 29 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1111 + · exact degreeUnionBranch62_1112 + · exact degreeUnionBranch62_1113 + · exact degreeUnionBranch62_1114 + · exact degreeUnionBranch62_1115 + · exact degreeUnionBranch62_1116 + · exact degreeUnionBranch62_1117 + +lemma degreeUnionBranch62_1098 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 38 12 degreeUnionState62_1098 [12,12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 38 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1099 + · exact degreeUnionBranch62_1100 + · exact degreeUnionBranch62_1101 + · exact degreeUnionBranch62_1102 + · exact degreeUnionBranch62_1103 + · exact degreeUnionBranch62_1110 + · exact degreeUnionBranch62_1118 + · exact degreeUnionBranch62_1119 + · exact degreeUnionBranch62_1120 + +lemma degreeUnionBranch62_1003 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 50 12 degreeUnionState62_1003 [12] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 50 ≤ 13*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1004 + · exact degreeUnionBranch62_1005 + · exact degreeUnionBranch62_1006 + · exact degreeUnionBranch62_1007 + · exact degreeUnionBranch62_1008 + · exact degreeUnionBranch62_1019 + · exact degreeUnionBranch62_1039 + · exact degreeUnionBranch62_1068 + · exact degreeUnionBranch62_1098 + +lemma degreeUnionBranch62_1131 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 33 8 degreeUnionState62_1131 [8,8,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 33 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1132 + · exact degreeUnionBranch62_1133 + · exact degreeUnionBranch62_1134 + · exact degreeUnionBranch62_1135 + · exact degreeUnionBranch62_1136 + · exact degreeUnionBranch62_1137 + +lemma degreeUnionBranch62_1126 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 41 8 degreeUnionState62_1126 [8,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 41 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1127 + · exact degreeUnionBranch62_1128 + · exact degreeUnionBranch62_1129 + · exact degreeUnionBranch62_1130 + · exact degreeUnionBranch62_1131 + +lemma degreeUnionBranch62_1143 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 8 degreeUnionState62_1143 [8,9,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 32 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1144 + · exact degreeUnionBranch62_1145 + · exact degreeUnionBranch62_1146 + · exact degreeUnionBranch62_1147 + · exact degreeUnionBranch62_1148 + · exact degreeUnionBranch62_1149 + +lemma degreeUnionBranch62_1150 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 9 degreeUnionState62_1150 [9,9,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 31 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1151 + · exact degreeUnionBranch62_1152 + · exact degreeUnionBranch62_1153 + · exact degreeUnionBranch62_1154 + · exact degreeUnionBranch62_1155 + · exact degreeUnionBranch62_1156 + · exact degreeUnionBranch62_1157 + +lemma degreeUnionBranch62_1138 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 40 9 degreeUnionState62_1138 [9,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 40 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1139 + · exact degreeUnionBranch62_1140 + · exact degreeUnionBranch62_1141 + · exact degreeUnionBranch62_1142 + · exact degreeUnionBranch62_1143 + · exact degreeUnionBranch62_1150 + +lemma degreeUnionBranch62_1163 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 8 degreeUnionState62_1163 [8,10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 31 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1164 + · exact degreeUnionBranch62_1165 + · exact degreeUnionBranch62_1166 + · exact degreeUnionBranch62_1167 + · exact degreeUnionBranch62_1168 + · exact degreeUnionBranch62_1169 + +lemma degreeUnionBranch62_1170 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 9 degreeUnionState62_1170 [9,10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 30 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1171 + · exact degreeUnionBranch62_1172 + · exact degreeUnionBranch62_1173 + · exact degreeUnionBranch62_1174 + · exact degreeUnionBranch62_1175 + · exact degreeUnionBranch62_1176 + · exact degreeUnionBranch62_1177 + +lemma degreeUnionBranch62_1178 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 10 degreeUnionState62_1178 [10,10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 10 at hb + change 29 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1179 + · exact degreeUnionBranch62_1180 + · exact degreeUnionBranch62_1181 + · exact degreeUnionBranch62_1182 + · exact degreeUnionBranch62_1183 + · exact degreeUnionBranch62_1184 + · exact degreeUnionBranch62_1185 + · exact degreeUnionBranch62_1186 + +lemma degreeUnionBranch62_1158 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 39 10 degreeUnionState62_1158 [10,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 39 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1159 + · exact degreeUnionBranch62_1160 + · exact degreeUnionBranch62_1161 + · exact degreeUnionBranch62_1162 + · exact degreeUnionBranch62_1163 + · exact degreeUnionBranch62_1170 + · exact degreeUnionBranch62_1178 + +lemma degreeUnionBranch62_1192 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 8 degreeUnionState62_1192 [8,11,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 30 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1193 + · exact degreeUnionBranch62_1194 + · exact degreeUnionBranch62_1195 + · exact degreeUnionBranch62_1196 + · exact degreeUnionBranch62_1197 + · exact degreeUnionBranch62_1198 + +lemma degreeUnionBranch62_1199 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 9 degreeUnionState62_1199 [9,11,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 29 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1200 + · exact degreeUnionBranch62_1201 + · exact degreeUnionBranch62_1202 + · exact degreeUnionBranch62_1203 + · exact degreeUnionBranch62_1204 + · exact degreeUnionBranch62_1205 + · exact degreeUnionBranch62_1206 + +lemma degreeUnionBranch62_1187 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 38 11 degreeUnionState62_1187 [11,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 38 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1188 + · exact degreeUnionBranch62_1189 + · exact degreeUnionBranch62_1190 + · exact degreeUnionBranch62_1191 + · exact degreeUnionBranch62_1192 + · exact degreeUnionBranch62_1199 + · exact degreeUnionBranch62_1207 + · exact degreeUnionBranch62_1208 + +lemma degreeUnionBranch62_1214 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 8 degreeUnionState62_1214 [8,12,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 29 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1215 + · exact degreeUnionBranch62_1216 + · exact degreeUnionBranch62_1217 + · exact degreeUnionBranch62_1218 + · exact degreeUnionBranch62_1219 + · exact degreeUnionBranch62_1220 + +lemma degreeUnionBranch62_1209 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 37 12 degreeUnionState62_1209 [12,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 37 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1210 + · exact degreeUnionBranch62_1211 + · exact degreeUnionBranch62_1212 + · exact degreeUnionBranch62_1213 + · exact degreeUnionBranch62_1214 + · exact degreeUnionBranch62_1221 + · exact degreeUnionBranch62_1222 + · exact degreeUnionBranch62_1223 + · exact degreeUnionBranch62_1224 + +lemma degreeUnionBranch62_1225 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 36 13 degreeUnionState62_1225 [13,13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 13 at hb + change 36 ≤ 12*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1226 + · exact degreeUnionBranch62_1227 + · exact degreeUnionBranch62_1228 + · exact degreeUnionBranch62_1229 + · exact degreeUnionBranch62_1230 + · exact degreeUnionBranch62_1231 + · exact degreeUnionBranch62_1232 + · exact degreeUnionBranch62_1233 + · exact degreeUnionBranch62_1234 + · exact degreeUnionBranch62_1235 + · exact degreeUnionBranch62_1236 + +lemma degreeUnionBranch62_1121 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 49 13 degreeUnionState62_1121 [13] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 13 at hb + change 49 ≤ 13*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1122 + · exact degreeUnionBranch62_1123 + · exact degreeUnionBranch62_1124 + · exact degreeUnionBranch62_1125 + · exact degreeUnionBranch62_1126 + · exact degreeUnionBranch62_1138 + · exact degreeUnionBranch62_1158 + · exact degreeUnionBranch62_1187 + · exact degreeUnionBranch62_1209 + · exact degreeUnionBranch62_1225 + +lemma degreeUnionBranch62_1247 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 32 8 degreeUnionState62_1247 [8,8,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 32 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1248 + · exact degreeUnionBranch62_1249 + · exact degreeUnionBranch62_1250 + · exact degreeUnionBranch62_1251 + · exact degreeUnionBranch62_1252 + · exact degreeUnionBranch62_1253 + +lemma degreeUnionBranch62_1242 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 40 8 degreeUnionState62_1242 [8,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 8 at hb + change 40 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1243 + · exact degreeUnionBranch62_1244 + · exact degreeUnionBranch62_1245 + · exact degreeUnionBranch62_1246 + · exact degreeUnionBranch62_1247 + +lemma degreeUnionBranch62_1259 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 31 8 degreeUnionState62_1259 [8,9,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 31 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1260 + · exact degreeUnionBranch62_1261 + · exact degreeUnionBranch62_1262 + · exact degreeUnionBranch62_1263 + · exact degreeUnionBranch62_1264 + · exact degreeUnionBranch62_1265 + +lemma degreeUnionBranch62_1266 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 9 degreeUnionState62_1266 [9,9,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 30 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1267 + · exact degreeUnionBranch62_1268 + · exact degreeUnionBranch62_1269 + · exact degreeUnionBranch62_1270 + · exact degreeUnionBranch62_1271 + · exact degreeUnionBranch62_1272 + · exact degreeUnionBranch62_1273 + +lemma degreeUnionBranch62_1254 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 39 9 degreeUnionState62_1254 [9,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 9 at hb + change 39 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1255 + · exact degreeUnionBranch62_1256 + · exact degreeUnionBranch62_1257 + · exact degreeUnionBranch62_1258 + · exact degreeUnionBranch62_1259 + · exact degreeUnionBranch62_1266 + +lemma degreeUnionBranch62_1279 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 30 8 degreeUnionState62_1279 [8,10,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 30 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1280 + · exact degreeUnionBranch62_1281 + · exact degreeUnionBranch62_1282 + · exact degreeUnionBranch62_1283 + · exact degreeUnionBranch62_1284 + · exact degreeUnionBranch62_1285 + +lemma degreeUnionBranch62_1286 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 9 degreeUnionState62_1286 [9,10,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 9 at hb + change 29 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1287 + · exact degreeUnionBranch62_1288 + · exact degreeUnionBranch62_1289 + · exact degreeUnionBranch62_1290 + · exact degreeUnionBranch62_1291 + · exact degreeUnionBranch62_1292 + · exact degreeUnionBranch62_1293 + +lemma degreeUnionBranch62_1274 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 38 10 degreeUnionState62_1274 [10,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 10 at hb + change 38 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1275 + · exact degreeUnionBranch62_1276 + · exact degreeUnionBranch62_1277 + · exact degreeUnionBranch62_1278 + · exact degreeUnionBranch62_1279 + · exact degreeUnionBranch62_1286 + · exact degreeUnionBranch62_1294 + +lemma degreeUnionBranch62_1300 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 11 29 8 degreeUnionState62_1300 [8,11,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 2 ≤ a at ha + change a ≤ 8 at hb + change 29 ≤ 11*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1301 + · exact degreeUnionBranch62_1302 + · exact degreeUnionBranch62_1303 + · exact degreeUnionBranch62_1304 + · exact degreeUnionBranch62_1305 + · exact degreeUnionBranch62_1306 + +lemma degreeUnionBranch62_1295 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 37 11 degreeUnionState62_1295 [11,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 11 at hb + change 37 ≤ 12*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1296 + · exact degreeUnionBranch62_1297 + · exact degreeUnionBranch62_1298 + · exact degreeUnionBranch62_1299 + · exact degreeUnionBranch62_1300 + · exact degreeUnionBranch62_1307 + · exact degreeUnionBranch62_1308 + · exact degreeUnionBranch62_1309 + +lemma degreeUnionBranch62_1310 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 12 36 12 degreeUnionState62_1310 [12,14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 12 at hb + change 36 ≤ 12*a at hn + have hlo : 3 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1311 + · exact degreeUnionBranch62_1312 + · exact degreeUnionBranch62_1313 + · exact degreeUnionBranch62_1314 + · exact degreeUnionBranch62_1315 + · exact degreeUnionBranch62_1316 + · exact degreeUnionBranch62_1317 + · exact degreeUnionBranch62_1318 + · exact degreeUnionBranch62_1319 + · exact degreeUnionBranch62_1320 + +lemma degreeUnionBranch62_1237 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 13 48 14 degreeUnionState62_1237 [14] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 3 ≤ a at ha + change a ≤ 14 at hb + change 48 ≤ 13*a at hn + have hlo : 4 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_1238 + · exact degreeUnionBranch62_1239 + · exact degreeUnionBranch62_1240 + · exact degreeUnionBranch62_1241 + · exact degreeUnionBranch62_1242 + · exact degreeUnionBranch62_1254 + · exact degreeUnionBranch62_1274 + · exact degreeUnionBranch62_1295 + · exact degreeUnionBranch62_1310 + · exact degreeUnionBranch62_1321 + · exact degreeUnionBranch62_1322 + +lemma degreeUnionBranch62_948 : checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) 14 62 28 degreeHalfRegions62 [] = true := by + apply checkRegionPrefixes_step + intro a ha hb hn + change 4 ≤ a at ha + change a ≤ 28 at hb + change 62 ≤ 14*a at hn + have hlo : 5 ≤ a := by omega + interval_cases a + · exact degreeUnionBranch62_949 + · exact degreeUnionBranch62_950 + · exact degreeUnionBranch62_951 + · exact degreeUnionBranch62_952 + · exact degreeUnionBranch62_953 + · exact degreeUnionBranch62_954 + · exact degreeUnionBranch62_962 + · exact degreeUnionBranch62_1003 + · exact degreeUnionBranch62_1121 + · exact degreeUnionBranch62_1237 + · exact degreeUnionBranch62_1323 + · exact degreeUnionBranch62_1324 + · exact degreeUnionBranch62_1325 + · exact degreeUnionBranch62_1326 + · exact degreeUnionBranch62_1327 + · exact degreeUnionBranch62_1328 + · exact degreeUnionBranch62_1329 + · exact degreeUnionBranch62_1330 + · exact degreeUnionBranch62_1331 + · exact degreeUnionBranch62_1332 + · exact degreeUnionBranch62_1333 + · exact degreeUnionBranch62_1334 + · exact degreeUnionBranch62_1335 + · exact degreeUnionBranch62_1336 + +lemma degreeUnionCheck62 : ∀ h ≤ 28, + checkRegionPrefixes (quickResidual 8 13 degreeQs62 degreeTree62) h 62 28 degreeHalfRegions62 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch62_0 + · exact degreeUnionBranch62_1 + · exact degreeUnionBranch62_2 + · exact degreeUnionBranch62_3 + · exact degreeUnionBranch62_4 + · exact degreeUnionBranch62_5 + · exact degreeUnionBranch62_6 + · exact degreeUnionBranch62_7 + · exact degreeUnionBranch62_8 + · exact degreeUnionBranch62_9 + · exact degreeUnionBranch62_10 + · exact degreeUnionBranch62_11 + · exact degreeUnionBranch62_62 + · exact degreeUnionBranch62_513 + · exact degreeUnionBranch62_948 + · exact degreeUnionBranch62_1337 + · exact degreeUnionBranch62_1338 + · exact degreeUnionBranch62_1339 + · exact degreeUnionBranch62_1340 + · exact degreeUnionBranch62_1341 + · exact degreeUnionBranch62_1342 + · exact degreeUnionBranch62_1343 + · exact degreeUnionBranch62_1344 + · exact degreeUnionBranch62_1345 + · exact degreeUnionBranch62_1346 + · exact degreeUnionBranch62_1347 + · exact degreeUnionBranch62_1348 + · exact degreeUnionBranch62_1349 + · exact degreeUnionBranch62_1350 + +lemma degreeHalfCover62 : ∀ R ∈ degreeRegions62, + R ∈ degreeHalfRegions62 ∨ (R.2,R.1) ∈ degreeHalfRegions62 := by decide +kernel + +lemma degreeDiagramRegionsChecked62 : ∀ R ∈ degreeRegions62, + ∀ μ : YoungDiagram, μ.card = 62 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP62 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck62 degreeHalfHeight62 degreeHalfWidth62 + degreeHalfCover62 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions64.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions64.lean index a1a97223994c412b99404a7d0cd9e19b10b47919..105ba78f6ed3601fca25a6db62a7900f2f7d1b3a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions64.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions64.lean @@ -1,62 +1,62 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves64 - -namespace OAI - -/-! Degree Regions 64. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionCheck64 : ∀ h ≤ 30, - checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) h 64 30 degreeHalfRegions64 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch64_0 - · exact degreeUnionBranch64_1 - · exact degreeUnionBranch64_2 - · exact degreeUnionBranch64_3 - · exact degreeUnionBranch64_4 - · exact degreeUnionBranch64_5 - · exact degreeUnionBranch64_6 - · exact degreeUnionBranch64_7 - · exact degreeUnionBranch64_8 - · exact degreeUnionBranch64_9 - · exact degreeUnionBranch64_10 - · exact degreeUnionBranch64_11 - · exact degreeUnionBranch64_12 - · exact degreeUnionBranch64_13 - · exact degreeUnionBranch64_14 - · exact degreeUnionBranch64_15 - · exact degreeUnionBranch64_16 - · exact degreeUnionBranch64_17 - · exact degreeUnionBranch64_18 - · exact degreeUnionBranch64_19 - · exact degreeUnionBranch64_20 - · exact degreeUnionBranch64_21 - · exact degreeUnionBranch64_22 - · exact degreeUnionBranch64_23 - · exact degreeUnionBranch64_24 - · exact degreeUnionBranch64_25 - · exact degreeUnionBranch64_26 - · exact degreeUnionBranch64_27 - · exact degreeUnionBranch64_28 - · exact degreeUnionBranch64_29 - · exact degreeUnionBranch64_30 - -lemma degreeHalfCover64 : ∀ R ∈ degreeRegions64, - R ∈ degreeHalfRegions64 ∨ (R.2,R.1) ∈ degreeHalfRegions64 := by decide +kernel - -lemma degreeDiagramRegionsChecked64 : ∀ R ∈ degreeRegions64, - ∀ μ : YoungDiagram, μ.card = 64 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP64 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck64 degreeHalfHeight64 degreeHalfWidth64 - degreeHalfCover64 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves64 + +namespace OAI + +/-! Degree Regions 64. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionCheck64 : ∀ h ≤ 30, + checkRegionPrefixes (quickResidual 8 14 degreeQs64 degreeTree64) h 64 30 degreeHalfRegions64 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch64_0 + · exact degreeUnionBranch64_1 + · exact degreeUnionBranch64_2 + · exact degreeUnionBranch64_3 + · exact degreeUnionBranch64_4 + · exact degreeUnionBranch64_5 + · exact degreeUnionBranch64_6 + · exact degreeUnionBranch64_7 + · exact degreeUnionBranch64_8 + · exact degreeUnionBranch64_9 + · exact degreeUnionBranch64_10 + · exact degreeUnionBranch64_11 + · exact degreeUnionBranch64_12 + · exact degreeUnionBranch64_13 + · exact degreeUnionBranch64_14 + · exact degreeUnionBranch64_15 + · exact degreeUnionBranch64_16 + · exact degreeUnionBranch64_17 + · exact degreeUnionBranch64_18 + · exact degreeUnionBranch64_19 + · exact degreeUnionBranch64_20 + · exact degreeUnionBranch64_21 + · exact degreeUnionBranch64_22 + · exact degreeUnionBranch64_23 + · exact degreeUnionBranch64_24 + · exact degreeUnionBranch64_25 + · exact degreeUnionBranch64_26 + · exact degreeUnionBranch64_27 + · exact degreeUnionBranch64_28 + · exact degreeUnionBranch64_29 + · exact degreeUnionBranch64_30 + +lemma degreeHalfCover64 : ∀ R ∈ degreeRegions64, + R ∈ degreeHalfRegions64 ∨ (R.2,R.1) ∈ degreeHalfRegions64 := by decide +kernel + +lemma degreeDiagramRegionsChecked64 : ∀ R ∈ degreeRegions64, + ∀ μ : YoungDiagram, μ.card = 64 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP64 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck64 degreeHalfHeight64 degreeHalfWidth64 + degreeHalfCover64 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions89.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions89.lean index 7a7b5a2b0bb7f3e2894b41dedffaf80cac43b332..457cc122de8e8b5076412aa984f35ce7c75bfd78 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions89.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeRegions89.lean @@ -1,50 +1,50 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves89 - -namespace OAI - -/-! Degree Regions 89. -/ - -section - -namespace UniversalTensorSquare - -lemma degreeUnionCheck89 : ∀ h ≤ 18, - checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) h 89 18 degreeHalfRegions89 [] = true := by - intro h hh - interval_cases h - · exact degreeUnionBranch89_0 - · exact degreeUnionBranch89_1 - · exact degreeUnionBranch89_2 - · exact degreeUnionBranch89_3 - · exact degreeUnionBranch89_4 - · exact degreeUnionBranch89_5 - · exact degreeUnionBranch89_6 - · exact degreeUnionBranch89_7 - · exact degreeUnionBranch89_8 - · exact degreeUnionBranch89_9 - · exact degreeUnionBranch89_10 - · exact degreeUnionBranch89_11 - · exact degreeUnionBranch89_12 - · exact degreeUnionBranch89_13 - · exact degreeUnionBranch89_14 - · exact degreeUnionBranch89_15 - · exact degreeUnionBranch89_16 - · exact degreeUnionBranch89_17 - · exact degreeUnionBranch89_18 - -lemma degreeHalfCover89 : ∀ R ∈ degreeRegions89, - R ∈ degreeHalfRegions89 ∨ (R.2,R.1) ∈ degreeHalfRegions89 := by decide +kernel - -lemma degreeDiagramRegionsChecked89 : ∀ R ∈ degreeRegions89, - ∀ μ : YoungDiagram, μ.card = 89 → RowBounds μ.transpose R.1 → - RowBounds μ R.2 → degreeP89 μ.rowLens := - checkedUnion_symmetric degreeUnionCheck89 degreeHalfHeight89 degreeHalfWidth89 - degreeHalfCover89 - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.CheckedUnionSymmetry +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeLeaves89 + +namespace OAI + +/-! Degree Regions 89. -/ + +section + +namespace UniversalTensorSquare + +lemma degreeUnionCheck89 : ∀ h ≤ 18, + checkRegionPrefixes (quickResidual 10 17 degreeQs89 degreeTree89) h 89 18 degreeHalfRegions89 [] = true := by + intro h hh + interval_cases h + · exact degreeUnionBranch89_0 + · exact degreeUnionBranch89_1 + · exact degreeUnionBranch89_2 + · exact degreeUnionBranch89_3 + · exact degreeUnionBranch89_4 + · exact degreeUnionBranch89_5 + · exact degreeUnionBranch89_6 + · exact degreeUnionBranch89_7 + · exact degreeUnionBranch89_8 + · exact degreeUnionBranch89_9 + · exact degreeUnionBranch89_10 + · exact degreeUnionBranch89_11 + · exact degreeUnionBranch89_12 + · exact degreeUnionBranch89_13 + · exact degreeUnionBranch89_14 + · exact degreeUnionBranch89_15 + · exact degreeUnionBranch89_16 + · exact degreeUnionBranch89_17 + · exact degreeUnionBranch89_18 + +lemma degreeHalfCover89 : ∀ R ∈ degreeRegions89, + R ∈ degreeHalfRegions89 ∨ (R.2,R.1) ∈ degreeHalfRegions89 := by decide +kernel + +lemma degreeDiagramRegionsChecked89 : ∀ R ∈ degreeRegions89, + ∀ μ : YoungDiagram, μ.card = 89 → RowBounds μ.transpose R.1 → + RowBounds μ R.2 → degreeP89 μ.rowLens := + checkedUnion_symmetric degreeUnionCheck89 degreeHalfHeight89 degreeHalfWidth89 + degreeHalfCover89 + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeSeven.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeSeven.lean index 74c20d52aa1cabec9f9c0783a58c652c87fab3ec..2a997e4cbde05fb48487a21f10807e18c1c00f26 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeSeven.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeSeven.lean @@ -1,361 +1,361 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomainsCore -import OAI.RepresentationTheory.UniversalSquare.Support.NumericalSupport - -namespace OAI - -/-! Degree Seven. -/ - -section - -open Saxl Saxl.Columns -namespace UniversalTensorSquare - -def sevenWitness : YoungDiagram := diagramOfCols [4,1,1,1] (by decide) - -lemma sevenWitness_cols : sevenWitness.transpose.rowLens = [4,1,1,1] := - diagramOfCols_cols _ _ (by simp) - -lemma sevenWitness_card : sevenWitness.card = 7 := - diagramOfCols_card _ _ (by simp) - -lemma sevenWitness_self : sevenWitness.transpose = sevenWitness := by - apply YoungDiagram.ext - decide - -def sevenPlaceB0 : Equiv.Perm (Fin 7) := Equiv.swap 5 6 * (Equiv.swap 2 1 * (Equiv.swap 2 3 * (Equiv.swap 1 4))) - -def sevenPlaceT0 : Equiv.Perm (Fin 7) := Equiv.swap 1 2 * (Equiv.swap 2 6 * (Equiv.swap 1 0 * (Equiv.swap 0 4))) - -def sevenFlag0 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,1,3),(0,2,2),(0,3,1)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma sevenCertificate0 : contractionInteger [4,1,1,1] [4,1,1,1] [1,1,1,1,1,1,1] - (Equiv.refl (Fin 7)) sevenPlaceB0 sevenPlaceT0 sevenFlag0 = -6 := by - unfold sevenFlag0 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def sevenPlaceB1 : Equiv.Perm (Fin 7) := Equiv.swap 4 1 * (Equiv.swap 1 5 * (Equiv.swap 1 0 * (Equiv.swap 0 2))) - -def sevenPlaceT1 : Equiv.Perm (Fin 7) := Equiv.swap 3 6 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 5)))) - -def sevenFlag1 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,0,2),(0,2,3),(0,3,0),(1,1,1)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma sevenCertificate1 : contractionInteger [4,1,1,1] [4,1,1,1] [2,1,1,1,1,1] - (Equiv.refl (Fin 7)) sevenPlaceB1 sevenPlaceT1 sevenFlag1 = -2 := by - unfold sevenFlag1 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def sevenPlaceB2 : Equiv.Perm (Fin 7) := Equiv.swap 4 2 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 5))) - -def sevenPlaceT2 : Equiv.Perm (Fin 7) := Equiv.swap 4 2 * (Equiv.swap 2 5 * (Equiv.swap 2 3 * (Equiv.swap 0 1))) - -def sevenFlag2 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,1,2),(1,2,1),(1,3,3)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma sevenCertificate2 : contractionInteger [4,1,1,1] [4,1,1,1] [2,2,1,1,1] - (Equiv.refl (Fin 7)) sevenPlaceB2 sevenPlaceT2 sevenFlag2 = 2 := by - unfold sevenFlag2 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def sevenPlaceB3 : Equiv.Perm (Fin 7) := Equiv.swap 3 6 * (Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 1 2))) - -def sevenPlaceT3 : Equiv.Perm (Fin 7) := Equiv.swap 2 6 * (Equiv.swap 2 3 * (Equiv.swap 3 0 * (Equiv.swap 2 4 * (Equiv.swap 0 5)))) - -def sevenFlag3 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,0,3),(0,2,3),(0,3,1),(1,0,2),(2,1,0)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma sevenCertificate3 : contractionInteger [4,1,1,1] [4,1,1,1] [3,1,1,1,1] - (Equiv.refl (Fin 7)) sevenPlaceB3 sevenPlaceT3 sevenFlag3 = -10 := by - unfold sevenFlag3 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def sevenPlaceB4 : Equiv.Perm (Fin 7) := Equiv.swap 2 0 * (Equiv.swap 2 1 * (Equiv.swap 2 3 * (Equiv.swap 1 5 * (Equiv.swap 0 6)))) - -def sevenPlaceT4 : Equiv.Perm (Fin 7) := Equiv.swap 4 5 * (Equiv.swap 3 6 * (Equiv.swap 0 2 * (Equiv.swap 0 1))) - -def sevenFlag4 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,1),(0,1,2),(0,2,0),(0,3,3),(1,0,0)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma sevenCertificate4 : contractionInteger [4,1,1,1] [4,1,1,1] [2,2,2,1] - (Equiv.refl (Fin 7)) sevenPlaceB4 sevenPlaceT4 sevenFlag4 = 2 := by - unfold sevenFlag4 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def sevenPlaceB5 : Equiv.Perm (Fin 7) := Equiv.swap 2 6 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 3))) - -def sevenPlaceT5 : Equiv.Perm (Fin 7) := Equiv.swap 4 0 * (Equiv.swap 1 2 * (Equiv.swap 0 5)) - -def sevenFlag5 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,2,2),(0,3,1),(1,1,3),(1,3,0),(2,0,1)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma sevenCertificate5 : contractionInteger [4,1,1,1] [4,1,1,1] [3,2,1,1] - (Equiv.refl (Fin 7)) sevenPlaceB5 sevenPlaceT5 sevenFlag5 = -2 := by - unfold sevenFlag5 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def sevenPlaceB6 : Equiv.Perm (Fin 7) := Equiv.swap 5 3 * (Equiv.swap 3 6 * (Equiv.swap 3 0 * (Equiv.swap 0 4 * (Equiv.swap 0 2)))) - -def sevenPlaceT6 : Equiv.Perm (Fin 7) := Equiv.swap 2 4 * (Equiv.swap 2 3 * (Equiv.swap 0 5)) - -def sevenFlag6 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,0,2),(0,1,1),(1,0,2),(2,3,0),(3,2,3)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma sevenCertificate6 : contractionInteger [4,1,1,1] [4,1,1,1] [4,1,1,1] - (Equiv.refl (Fin 7)) sevenPlaceB6 sevenPlaceT6 sevenFlag6 = 2 := by - unfold sevenFlag6 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -def sevenPlaceB7 : Equiv.Perm (Fin 7) := Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 2 6 * (Equiv.swap 0 5))) - -def sevenPlaceT7 : Equiv.Perm (Fin 7) := Equiv.swap 4 6 * (Equiv.swap 1 5 * (Equiv.swap 1 3 * (Equiv.swap 1 0 * (Equiv.swap 0 2)))) - -def sevenFlag7 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,0,2),(0,0,3),(1,0,3),(1,2,1),(1,3,2),(2,1,0)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma sevenCertificate7 : contractionInteger [4,1,1,1] [4,1,1,1] [3,2,2] - (Equiv.refl (Fin 7)) sevenPlaceB7 sevenPlaceT7 sevenFlag7 = 2 := by - unfold sevenFlag7 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -noncomputable section - -lemma seven_positive_certificate (rs : List ℕ) (hs : rs.SortedGE) - (hp : ∀ a ∈ rs, 0 < a) (hn : rs.sum = 7) - (eb : Equiv.Perm (Fin 7)) (et : Fin 7 ≃ Fin rs.sum) - (L : ℕ → ℕ → ℕ → ℤ) - (hc : contractionInteger [4,1,1,1] [4,1,1,1] rs (Equiv.refl _) eb et L ≠ 0) : - 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau (diagramOfCols rs hs) ((diagramOfCols_card rs hs hp).trans hn)) := by - exact kronecker_pos_of_integer_certificate _ _ _ [4,1,1,1] [4,1,1,1] rs - sevenWitness_cols sevenWitness_cols (diagramOfCols_cols _ _ hp) - (Equiv.refl _) eb et L hc - -lemma seven_positive0 : - 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau (diagramOfCols [1,1,1,1,1,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply seven_positive_certificate [1,1,1,1,1,1,1] (by decide) (by simp) rfl - sevenPlaceB0 sevenPlaceT0 sevenFlag0 - intro hz - have hh : (-6 : ℤ) = 0 := sevenCertificate0.symm.trans hz - norm_num at hh - -lemma seven_positive1 : - 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau (diagramOfCols [2,1,1,1,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply seven_positive_certificate [2,1,1,1,1,1] (by decide) (by simp) rfl - sevenPlaceB1 sevenPlaceT1 sevenFlag1 - intro hz - have hh : (-2 : ℤ) = 0 := sevenCertificate1.symm.trans hz - norm_num at hh - -lemma seven_positive2 : - 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau (diagramOfCols [2,2,1,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply seven_positive_certificate [2,2,1,1,1] (by decide) (by simp) rfl - sevenPlaceB2 sevenPlaceT2 sevenFlag2 - intro hz - have hh : (2 : ℤ) = 0 := sevenCertificate2.symm.trans hz - norm_num at hh - -lemma seven_positive3 : - 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau (diagramOfCols [3,1,1,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply seven_positive_certificate [3,1,1,1,1] (by decide) (by simp) rfl - sevenPlaceB3 sevenPlaceT3 sevenFlag3 - intro hz - have hh : (-10 : ℤ) = 0 := sevenCertificate3.symm.trans hz - norm_num at hh - -lemma seven_positive4 : - 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau (diagramOfCols [2,2,2,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply seven_positive_certificate [2,2,2,1] (by decide) (by simp) rfl - sevenPlaceB4 sevenPlaceT4 sevenFlag4 - intro hz - have hh : (2 : ℤ) = 0 := sevenCertificate4.symm.trans hz - norm_num at hh - -lemma seven_positive5 : - 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau (diagramOfCols [3,2,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply seven_positive_certificate [3,2,1,1] (by decide) (by simp) rfl - sevenPlaceB5 sevenPlaceT5 sevenFlag5 - intro hz - have hh : (-2 : ℤ) = 0 := sevenCertificate5.symm.trans hz - norm_num at hh - -lemma seven_positive6 : - 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau (diagramOfCols [4,1,1,1] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply seven_positive_certificate [4,1,1,1] (by decide) (by simp) rfl - sevenPlaceB6 sevenPlaceT6 sevenFlag6 - intro hz - have hh : (2 : ℤ) = 0 := sevenCertificate6.symm.trans hz - norm_num at hh - -lemma seven_positive7 : - 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau (diagramOfCols [3,2,2] (by decide)) - (by exact diagramOfCols_card _ _ (by simp))) := by - apply seven_positive_certificate [3,2,2] (by decide) (by simp) rfl - sevenPlaceB7 sevenPlaceT7 sevenFlag7 - intro hz - have hh : (2 : ℤ) = 0 := sevenCertificate7.symm.trans hz - norm_num at hh - -lemma seven_positive_target_eq {μ ν : YoungDiagram} (hμ : μ.card = 7) (hν : ν.card = 7) - (he : μ = ν) - (hp : 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau sevenWitness sevenWitness_card) (canonicalTableau ν hν)) : - 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau sevenWitness sevenWitness_card) (canonicalTableau μ hμ) := by - subst ν - exact hp - -lemma partitionLists_seven : partitionLists 7 7 7 = - {[7],[6,1],[5,2],[5,1,1],[4,3],[4,2,1],[4,1,1,1],[3,3,1],[3,2,2],[3,2,1,1],[3,1,1,1,1],[2,2,2,1],[2,2,1,1,1],[2,1,1,1,1,1],[1,1,1,1,1,1,1]} := by decide - -theorem seven_kronecker_pos (ν : YoungDiagram) (hν : ν.card = 7) : - 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) - (canonicalTableau sevenWitness sevenWitness_card) (canonicalTableau ν hν) := by - have hc := rowLens_mem_partitionLists ν.transpose - rw [transpose_card, hν, partitionLists_seven] at hc - simp only [Finset.mem_insert, Finset.mem_singleton] at hc - rcases hc with h | h | h | h | h | h | h | h | h | h | h | h | h | h | h - · have he := eq_diagramOfCols ν [7] (by decide) h - have ht : diagramOfCols [7] (by decide) = - (diagramOfCols [1,1,1,1,1,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self - _ _ seven_positive0 - exact seven_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [6,1] (by decide) h - have ht : diagramOfCols [6,1] (by decide) = - (diagramOfCols [2,1,1,1,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self - _ _ seven_positive1 - exact seven_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [5,2] (by decide) h - have ht : diagramOfCols [5,2] (by decide) = - (diagramOfCols [2,2,1,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self - _ _ seven_positive2 - exact seven_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [5,1,1] (by decide) h - have ht : diagramOfCols [5,1,1] (by decide) = - (diagramOfCols [3,1,1,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self - _ _ seven_positive3 - exact seven_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [4,3] (by decide) h - have ht : diagramOfCols [4,3] (by decide) = - (diagramOfCols [2,2,2,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self - _ _ seven_positive4 - exact seven_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [4,2,1] (by decide) h - have ht : diagramOfCols [4,2,1] (by decide) = - (diagramOfCols [3,2,1,1] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self - _ _ seven_positive5 - exact seven_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [4,1,1,1] (by decide) h - subst ν - exact seven_positive6 - · have he := eq_diagramOfCols ν [3,3,1] (by decide) h - have ht : diagramOfCols [3,3,1] (by decide) = - (diagramOfCols [3,2,2] (by decide)).transpose := by - apply YoungDiagram.ext - decide - have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self - _ _ seven_positive7 - exact seven_positive_target_eq hν _ (he.trans ht) hh - · have he := eq_diagramOfCols ν [3,2,2] (by decide) h - subst ν - exact seven_positive7 - · have he := eq_diagramOfCols ν [3,2,1,1] (by decide) h - subst ν - exact seven_positive5 - · have he := eq_diagramOfCols ν [3,1,1,1,1] (by decide) h - subst ν - exact seven_positive3 - · have he := eq_diagramOfCols ν [2,2,2,1] (by decide) h - subst ν - exact seven_positive4 - · have he := eq_diagramOfCols ν [2,2,1,1,1] (by decide) h - subst ν - exact seven_positive2 - · have he := eq_diagramOfCols ν [2,1,1,1,1,1] (by decide) h - subst ν - exact seven_positive1 - · have he := eq_diagramOfCols ν [1,1,1,1,1,1,1] (by decide) h - subst ν - exact seven_positive0 - -universe u - -theorem universal_tensor_square_seven : - ∃ (lam : YoungDiagram) (hlam : lam.card = 7), - (∀ (ν : YoungDiagram) (hν : ν.card = 7), - 0 < kronecker (canonicalTableau lam hlam) - (canonicalTableau lam hlam) (canonicalTableau ν hν)) ∧ - Representation.IsIrreducible (spechtRep (canonicalTableau lam hlam)) ∧ - ∀ (V : Type u) [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin 7)) V) [Representation.IsIrreducible ρ], - ∃ F : Representation.IntertwiningMap ρ - ((spechtRep (canonicalTableau lam hlam)).tprod - (spechtRep (canonicalTableau lam hlam))), Function.Injective F := by - exact ⟨sevenWitness, sevenWitness_card, seven_kronecker_pos, - irreducibles_of_kronecker_pos _ _ seven_kronecker_pos⟩ - -end -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomainsCore +import OAI.RepresentationTheory.UniversalSquare.Support.NumericalSupport + +namespace OAI + +/-! Degree Seven. -/ + +section + +open Saxl Saxl.Columns +namespace UniversalTensorSquare + +def sevenWitness : YoungDiagram := diagramOfCols [4,1,1,1] (by decide) + +lemma sevenWitness_cols : sevenWitness.transpose.rowLens = [4,1,1,1] := + diagramOfCols_cols _ _ (by simp) + +lemma sevenWitness_card : sevenWitness.card = 7 := + diagramOfCols_card _ _ (by simp) + +lemma sevenWitness_self : sevenWitness.transpose = sevenWitness := by + apply YoungDiagram.ext + decide + +def sevenPlaceB0 : Equiv.Perm (Fin 7) := Equiv.swap 5 6 * (Equiv.swap 2 1 * (Equiv.swap 2 3 * (Equiv.swap 1 4))) + +def sevenPlaceT0 : Equiv.Perm (Fin 7) := Equiv.swap 1 2 * (Equiv.swap 2 6 * (Equiv.swap 1 0 * (Equiv.swap 0 4))) + +def sevenFlag0 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,1,3),(0,2,2),(0,3,1)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma sevenCertificate0 : contractionInteger [4,1,1,1] [4,1,1,1] [1,1,1,1,1,1,1] + (Equiv.refl (Fin 7)) sevenPlaceB0 sevenPlaceT0 sevenFlag0 = -6 := by + unfold sevenFlag0 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def sevenPlaceB1 : Equiv.Perm (Fin 7) := Equiv.swap 4 1 * (Equiv.swap 1 5 * (Equiv.swap 1 0 * (Equiv.swap 0 2))) + +def sevenPlaceT1 : Equiv.Perm (Fin 7) := Equiv.swap 3 6 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 5)))) + +def sevenFlag1 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,0,2),(0,2,3),(0,3,0),(1,1,1)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma sevenCertificate1 : contractionInteger [4,1,1,1] [4,1,1,1] [2,1,1,1,1,1] + (Equiv.refl (Fin 7)) sevenPlaceB1 sevenPlaceT1 sevenFlag1 = -2 := by + unfold sevenFlag1 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def sevenPlaceB2 : Equiv.Perm (Fin 7) := Equiv.swap 4 2 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 5))) + +def sevenPlaceT2 : Equiv.Perm (Fin 7) := Equiv.swap 4 2 * (Equiv.swap 2 5 * (Equiv.swap 2 3 * (Equiv.swap 0 1))) + +def sevenFlag2 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,1,2),(1,2,1),(1,3,3)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma sevenCertificate2 : contractionInteger [4,1,1,1] [4,1,1,1] [2,2,1,1,1] + (Equiv.refl (Fin 7)) sevenPlaceB2 sevenPlaceT2 sevenFlag2 = 2 := by + unfold sevenFlag2 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def sevenPlaceB3 : Equiv.Perm (Fin 7) := Equiv.swap 3 6 * (Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 1 2))) + +def sevenPlaceT3 : Equiv.Perm (Fin 7) := Equiv.swap 2 6 * (Equiv.swap 2 3 * (Equiv.swap 3 0 * (Equiv.swap 2 4 * (Equiv.swap 0 5)))) + +def sevenFlag3 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,0,3),(0,2,3),(0,3,1),(1,0,2),(2,1,0)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma sevenCertificate3 : contractionInteger [4,1,1,1] [4,1,1,1] [3,1,1,1,1] + (Equiv.refl (Fin 7)) sevenPlaceB3 sevenPlaceT3 sevenFlag3 = -10 := by + unfold sevenFlag3 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def sevenPlaceB4 : Equiv.Perm (Fin 7) := Equiv.swap 2 0 * (Equiv.swap 2 1 * (Equiv.swap 2 3 * (Equiv.swap 1 5 * (Equiv.swap 0 6)))) + +def sevenPlaceT4 : Equiv.Perm (Fin 7) := Equiv.swap 4 5 * (Equiv.swap 3 6 * (Equiv.swap 0 2 * (Equiv.swap 0 1))) + +def sevenFlag4 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,1),(0,1,2),(0,2,0),(0,3,3),(1,0,0)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma sevenCertificate4 : contractionInteger [4,1,1,1] [4,1,1,1] [2,2,2,1] + (Equiv.refl (Fin 7)) sevenPlaceB4 sevenPlaceT4 sevenFlag4 = 2 := by + unfold sevenFlag4 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def sevenPlaceB5 : Equiv.Perm (Fin 7) := Equiv.swap 2 6 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 3))) + +def sevenPlaceT5 : Equiv.Perm (Fin 7) := Equiv.swap 4 0 * (Equiv.swap 1 2 * (Equiv.swap 0 5)) + +def sevenFlag5 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,2,2),(0,3,1),(1,1,3),(1,3,0),(2,0,1)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma sevenCertificate5 : contractionInteger [4,1,1,1] [4,1,1,1] [3,2,1,1] + (Equiv.refl (Fin 7)) sevenPlaceB5 sevenPlaceT5 sevenFlag5 = -2 := by + unfold sevenFlag5 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def sevenPlaceB6 : Equiv.Perm (Fin 7) := Equiv.swap 5 3 * (Equiv.swap 3 6 * (Equiv.swap 3 0 * (Equiv.swap 0 4 * (Equiv.swap 0 2)))) + +def sevenPlaceT6 : Equiv.Perm (Fin 7) := Equiv.swap 2 4 * (Equiv.swap 2 3 * (Equiv.swap 0 5)) + +def sevenFlag6 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,0,2),(0,1,1),(1,0,2),(2,3,0),(3,2,3)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma sevenCertificate6 : contractionInteger [4,1,1,1] [4,1,1,1] [4,1,1,1] + (Equiv.refl (Fin 7)) sevenPlaceB6 sevenPlaceT6 sevenFlag6 = 2 := by + unfold sevenFlag6 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +def sevenPlaceB7 : Equiv.Perm (Fin 7) := Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 2 6 * (Equiv.swap 0 5))) + +def sevenPlaceT7 : Equiv.Perm (Fin 7) := Equiv.swap 4 6 * (Equiv.swap 1 5 * (Equiv.swap 1 3 * (Equiv.swap 1 0 * (Equiv.swap 0 2)))) + +def sevenFlag7 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,0,2),(0,0,3),(1,0,3),(1,2,1),(1,3,2),(2,1,0)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma sevenCertificate7 : contractionInteger [4,1,1,1] [4,1,1,1] [3,2,2] + (Equiv.refl (Fin 7)) sevenPlaceB7 sevenPlaceT7 sevenFlag7 = 2 := by + unfold sevenFlag7 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +noncomputable section + +lemma seven_positive_certificate (rs : List ℕ) (hs : rs.SortedGE) + (hp : ∀ a ∈ rs, 0 < a) (hn : rs.sum = 7) + (eb : Equiv.Perm (Fin 7)) (et : Fin 7 ≃ Fin rs.sum) + (L : ℕ → ℕ → ℕ → ℤ) + (hc : contractionInteger [4,1,1,1] [4,1,1,1] rs (Equiv.refl _) eb et L ≠ 0) : + 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau (diagramOfCols rs hs) ((diagramOfCols_card rs hs hp).trans hn)) := by + exact kronecker_pos_of_integer_certificate _ _ _ [4,1,1,1] [4,1,1,1] rs + sevenWitness_cols sevenWitness_cols (diagramOfCols_cols _ _ hp) + (Equiv.refl _) eb et L hc + +lemma seven_positive0 : + 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau (diagramOfCols [1,1,1,1,1,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply seven_positive_certificate [1,1,1,1,1,1,1] (by decide) (by simp) rfl + sevenPlaceB0 sevenPlaceT0 sevenFlag0 + intro hz + have hh : (-6 : ℤ) = 0 := sevenCertificate0.symm.trans hz + norm_num at hh + +lemma seven_positive1 : + 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau (diagramOfCols [2,1,1,1,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply seven_positive_certificate [2,1,1,1,1,1] (by decide) (by simp) rfl + sevenPlaceB1 sevenPlaceT1 sevenFlag1 + intro hz + have hh : (-2 : ℤ) = 0 := sevenCertificate1.symm.trans hz + norm_num at hh + +lemma seven_positive2 : + 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau (diagramOfCols [2,2,1,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply seven_positive_certificate [2,2,1,1,1] (by decide) (by simp) rfl + sevenPlaceB2 sevenPlaceT2 sevenFlag2 + intro hz + have hh : (2 : ℤ) = 0 := sevenCertificate2.symm.trans hz + norm_num at hh + +lemma seven_positive3 : + 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau (diagramOfCols [3,1,1,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply seven_positive_certificate [3,1,1,1,1] (by decide) (by simp) rfl + sevenPlaceB3 sevenPlaceT3 sevenFlag3 + intro hz + have hh : (-10 : ℤ) = 0 := sevenCertificate3.symm.trans hz + norm_num at hh + +lemma seven_positive4 : + 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau (diagramOfCols [2,2,2,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply seven_positive_certificate [2,2,2,1] (by decide) (by simp) rfl + sevenPlaceB4 sevenPlaceT4 sevenFlag4 + intro hz + have hh : (2 : ℤ) = 0 := sevenCertificate4.symm.trans hz + norm_num at hh + +lemma seven_positive5 : + 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau (diagramOfCols [3,2,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply seven_positive_certificate [3,2,1,1] (by decide) (by simp) rfl + sevenPlaceB5 sevenPlaceT5 sevenFlag5 + intro hz + have hh : (-2 : ℤ) = 0 := sevenCertificate5.symm.trans hz + norm_num at hh + +lemma seven_positive6 : + 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau (diagramOfCols [4,1,1,1] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply seven_positive_certificate [4,1,1,1] (by decide) (by simp) rfl + sevenPlaceB6 sevenPlaceT6 sevenFlag6 + intro hz + have hh : (2 : ℤ) = 0 := sevenCertificate6.symm.trans hz + norm_num at hh + +lemma seven_positive7 : + 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau (diagramOfCols [3,2,2] (by decide)) + (by exact diagramOfCols_card _ _ (by simp))) := by + apply seven_positive_certificate [3,2,2] (by decide) (by simp) rfl + sevenPlaceB7 sevenPlaceT7 sevenFlag7 + intro hz + have hh : (2 : ℤ) = 0 := sevenCertificate7.symm.trans hz + norm_num at hh + +lemma seven_positive_target_eq {μ ν : YoungDiagram} (hμ : μ.card = 7) (hν : ν.card = 7) + (he : μ = ν) + (hp : 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau sevenWitness sevenWitness_card) (canonicalTableau ν hν)) : + 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau sevenWitness sevenWitness_card) (canonicalTableau μ hμ) := by + subst ν + exact hp + +lemma partitionLists_seven : partitionLists 7 7 7 = + {[7],[6,1],[5,2],[5,1,1],[4,3],[4,2,1],[4,1,1,1],[3,3,1],[3,2,2],[3,2,1,1],[3,1,1,1,1],[2,2,2,1],[2,2,1,1,1],[2,1,1,1,1,1],[1,1,1,1,1,1,1]} := by decide + +theorem seven_kronecker_pos (ν : YoungDiagram) (hν : ν.card = 7) : + 0 < kronecker (canonicalTableau sevenWitness sevenWitness_card) + (canonicalTableau sevenWitness sevenWitness_card) (canonicalTableau ν hν) := by + have hc := rowLens_mem_partitionLists ν.transpose + rw [transpose_card, hν, partitionLists_seven] at hc + simp only [Finset.mem_insert, Finset.mem_singleton] at hc + rcases hc with h | h | h | h | h | h | h | h | h | h | h | h | h | h | h + · have he := eq_diagramOfCols ν [7] (by decide) h + have ht : diagramOfCols [7] (by decide) = + (diagramOfCols [1,1,1,1,1,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self + _ _ seven_positive0 + exact seven_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [6,1] (by decide) h + have ht : diagramOfCols [6,1] (by decide) = + (diagramOfCols [2,1,1,1,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self + _ _ seven_positive1 + exact seven_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [5,2] (by decide) h + have ht : diagramOfCols [5,2] (by decide) = + (diagramOfCols [2,2,1,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self + _ _ seven_positive2 + exact seven_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [5,1,1] (by decide) h + have ht : diagramOfCols [5,1,1] (by decide) = + (diagramOfCols [3,1,1,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self + _ _ seven_positive3 + exact seven_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [4,3] (by decide) h + have ht : diagramOfCols [4,3] (by decide) = + (diagramOfCols [2,2,2,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self + _ _ seven_positive4 + exact seven_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [4,2,1] (by decide) h + have ht : diagramOfCols [4,2,1] (by decide) = + (diagramOfCols [3,2,1,1] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self + _ _ seven_positive5 + exact seven_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [4,1,1,1] (by decide) h + subst ν + exact seven_positive6 + · have he := eq_diagramOfCols ν [3,3,1] (by decide) h + have ht : diagramOfCols [3,3,1] (by decide) = + (diagramOfCols [3,2,2] (by decide)).transpose := by + apply YoungDiagram.ext + decide + have hh := kronecker_pos_transpose sevenWitness sevenWitness_card sevenWitness_self + _ _ seven_positive7 + exact seven_positive_target_eq hν _ (he.trans ht) hh + · have he := eq_diagramOfCols ν [3,2,2] (by decide) h + subst ν + exact seven_positive7 + · have he := eq_diagramOfCols ν [3,2,1,1] (by decide) h + subst ν + exact seven_positive5 + · have he := eq_diagramOfCols ν [3,1,1,1,1] (by decide) h + subst ν + exact seven_positive3 + · have he := eq_diagramOfCols ν [2,2,2,1] (by decide) h + subst ν + exact seven_positive4 + · have he := eq_diagramOfCols ν [2,2,1,1,1] (by decide) h + subst ν + exact seven_positive2 + · have he := eq_diagramOfCols ν [2,1,1,1,1,1] (by decide) h + subst ν + exact seven_positive1 + · have he := eq_diagramOfCols ν [1,1,1,1,1,1,1] (by decide) h + subst ν + exact seven_positive0 + +universe u + +theorem universal_tensor_square_seven : + ∃ (lam : YoungDiagram) (hlam : lam.card = 7), + (∀ (ν : YoungDiagram) (hν : ν.card = 7), + 0 < kronecker (canonicalTableau lam hlam) + (canonicalTableau lam hlam) (canonicalTableau ν hν)) ∧ + Representation.IsIrreducible (spechtRep (canonicalTableau lam hlam)) ∧ + ∀ (V : Type u) [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin 7)) V) [Representation.IsIrreducible ρ], + ∃ F : Representation.IntertwiningMap ρ + ((spechtRep (canonicalTableau lam hlam)).tprod + (spechtRep (canonicalTableau lam hlam))), Function.Injective F := by + exact ⟨sevenWitness, sevenWitness_card, seven_kronecker_pos, + irreducibles_of_kronecker_pos _ _ seven_kronecker_pos⟩ + +end +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData116.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData116.lean index 2fa2857e669485761e61ef51ad5a73b87c8bbdd4..0d1df4b8de59be5f9348dee45ff4cd3097549649 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData116.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData116.lean @@ -1,23 +1,23 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 116. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree116_0 : RowTree := (.node [11,11,11,11,11,11,11,11,10,9,9] (.node [11,11,11,11,11,11,11,10,10,10,9] (.node [11,11,11,11,11,11,10,10,10,10,10] .empty .empty) .empty) (.node [11,11,11,11,11,11,11,11,10,10,8] .empty .empty)) - -def degreeTree116 : RowTree := degreeTree116_0 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 116. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree116_0 : RowTree := (.node [11,11,11,11,11,11,11,11,10,9,9] (.node [11,11,11,11,11,11,11,10,10,10,9] (.node [11,11,11,11,11,11,10,10,10,10,10] .empty .empty) .empty) (.node [11,11,11,11,11,11,11,11,10,10,8] .empty .empty)) + +def degreeTree116 : RowTree := degreeTree116_0 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData118.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData118.lean index 16fb32ce29f3aa531e80363451bcf1741449eec9..586feeab14f4b359a9c1c81b18168c8bbcf70429 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData118.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData118.lean @@ -1,23 +1,23 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 118. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree118_0 : RowTree := (.node [11,11,11,11,11,11,11,11,11,10,9] (.node [11,11,11,11,11,11,11,11,10,10,10] .empty .empty) .empty) - -def degreeTree118 : RowTree := degreeTree118_0 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 118. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree118_0 : RowTree := (.node [11,11,11,11,11,11,11,11,11,10,9] (.node [11,11,11,11,11,11,11,11,10,10,10] .empty .empty) .empty) + +def degreeTree118 : RowTree := degreeTree118_0 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData14.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData14.lean index 9982be34224820e3eda4999e4037a1c139831ae8..9b20652b8fcd74951416a04b1a508be64faecfc9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData14.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData14.lean @@ -1,23 +1,23 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 14. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree14_0 : RowTree := (.node [7,2,1,1,1,1,1] (.node [7,1,1,1,1,1,1,1] .empty .empty) .empty) - -def degreeTree14 : RowTree := degreeTree14_0 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 14. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree14_0 : RowTree := (.node [7,2,1,1,1,1,1] (.node [7,1,1,1,1,1,1,1] .empty .empty) .empty) + +def degreeTree14 : RowTree := degreeTree14_0 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData16.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData16.lean index 29fea53b3f0bffd0d120d5daa4bee93d818f9c91..516e66f93abccbc6766d2b60dd5e0219b73cbe43 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData16.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData16.lean @@ -1,23 +1,23 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 16. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree16_0 : RowTree := (.node [6,4,1,1,1,1,1,1] (.node [6,3,1,1,1,1,1,1,1] (.node [6,2,2,2,1,1,1,1] (.node [6,2,1,1,1,1,1,1,1,1] (.node [6,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,2,2,1,1,1,1,1,1] .empty .empty)) (.node [6,2,2,2,2,2] (.node [6,2,2,2,2,1,1] .empty .empty) .empty)) (.node [6,3,2,2,2,1] (.node [6,3,2,2,1,1,1] (.node [6,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [6,3,3,2,1,1] (.node [6,3,3,1,1,1,1] .empty .empty) .empty))) (.node [7,2,2,1,1,1,1,1] (.node [6,5,1,1,1,1,1] (.node [6,4,2,2,1,1] (.node [6,4,2,1,1,1,1] .empty .empty) .empty) (.node [7,2,1,1,1,1,1,1,1] (.node [7,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [7,3,2,1,1,1,1] (.node [7,3,1,1,1,1,1,1] (.node [7,2,2,2,1,1,1] .empty .empty) .empty) (.node [8,2,1,1,1,1,1,1] (.node [8,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree16 : RowTree := degreeTree16_0 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 16. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree16_0 : RowTree := (.node [6,4,1,1,1,1,1,1] (.node [6,3,1,1,1,1,1,1,1] (.node [6,2,2,2,1,1,1,1] (.node [6,2,1,1,1,1,1,1,1,1] (.node [6,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,2,2,1,1,1,1,1,1] .empty .empty)) (.node [6,2,2,2,2,2] (.node [6,2,2,2,2,1,1] .empty .empty) .empty)) (.node [6,3,2,2,2,1] (.node [6,3,2,2,1,1,1] (.node [6,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [6,3,3,2,1,1] (.node [6,3,3,1,1,1,1] .empty .empty) .empty))) (.node [7,2,2,1,1,1,1,1] (.node [6,5,1,1,1,1,1] (.node [6,4,2,2,1,1] (.node [6,4,2,1,1,1,1] .empty .empty) .empty) (.node [7,2,1,1,1,1,1,1,1] (.node [7,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [7,3,2,1,1,1,1] (.node [7,3,1,1,1,1,1,1] (.node [7,2,2,2,1,1,1] .empty .empty) .empty) (.node [8,2,1,1,1,1,1,1] (.node [8,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree16 : RowTree := degreeTree16_0 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData18.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData18.lean index 568fbfc89988b33697da606bf0f5d88a1ca1ef9b..8313ff119c404c8306ac9cb9d8103b92854745f6 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData18.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData18.lean @@ -1,23 +1,23 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 18. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree18_0 : RowTree := (.node [7,4,1,1,1,1,1,1,1] (.node [7,3,1,1,1,1,1,1,1,1] (.node [7,2,2,2,1,1,1,1,1] (.node [7,2,1,1,1,1,1,1,1,1,1] (.node [7,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [7,2,2,2,2,2,1] (.node [7,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [7,3,2,2,2,1,1] (.node [7,3,2,2,1,1,1,1] (.node [7,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [7,3,3,2,1,1,1] (.node [7,3,3,1,1,1,1,1] .empty .empty) .empty))) (.node [8,2,2,1,1,1,1,1,1] (.node [7,5,1,1,1,1,1,1] (.node [7,4,2,2,1,1,1] (.node [7,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [8,2,1,1,1,1,1,1,1,1] (.node [8,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [8,3,2,1,1,1,1,1] (.node [8,3,1,1,1,1,1,1,1] (.node [8,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [9,2,1,1,1,1,1,1,1] (.node [9,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree18 : RowTree := degreeTree18_0 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 18. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree18_0 : RowTree := (.node [7,4,1,1,1,1,1,1,1] (.node [7,3,1,1,1,1,1,1,1,1] (.node [7,2,2,2,1,1,1,1,1] (.node [7,2,1,1,1,1,1,1,1,1,1] (.node [7,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [7,2,2,2,2,2,1] (.node [7,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [7,3,2,2,2,1,1] (.node [7,3,2,2,1,1,1,1] (.node [7,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [7,3,3,2,1,1,1] (.node [7,3,3,1,1,1,1,1] .empty .empty) .empty))) (.node [8,2,2,1,1,1,1,1,1] (.node [7,5,1,1,1,1,1,1] (.node [7,4,2,2,1,1,1] (.node [7,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [8,2,1,1,1,1,1,1,1,1] (.node [8,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [8,3,2,1,1,1,1,1] (.node [8,3,1,1,1,1,1,1,1] (.node [8,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [9,2,1,1,1,1,1,1,1] (.node [9,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree18 : RowTree := degreeTree18_0 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData19.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData19.lean index 8df3a2e5b70ce42794f806cd7ea762e5a4ef9274..bfb2c597e272bb2cc0669c62d29fbbf365c51db9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData19.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData19.lean @@ -1,23 +1,23 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 19. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree19_0 : RowTree := (.node [8,3,2,2,1,1,1,1] (.node [8,2,2,2,2,1,1,1] .empty .empty) (.node [8,3,3,1,1,1,1,1] .empty .empty)) - -def degreeTree19 : RowTree := degreeTree19_0 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 19. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree19_0 : RowTree := (.node [8,3,2,2,1,1,1,1] (.node [8,2,2,2,2,1,1,1] .empty .empty) (.node [8,3,3,1,1,1,1,1] .empty .empty)) + +def degreeTree19 : RowTree := degreeTree19_0 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData20.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData20.lean index 9bd8dabd1a7381ffaefd05cfc71e192cb12dd30c..15aaa7db6eb64eb41281f16a150edbe81f855888 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData20.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData20.lean @@ -1,51 +1,51 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 20. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree20_0 : RowTree := (.node [6,2,2,2,2,1,1,1,1,1,1] (.node [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [5,5,4,3,3] (.node [5,4,4,4,3] (.node [4,4,4,4,4] .empty .empty) .empty) (.node [5,5,4,4,2] .empty .empty)) (.node [6,2,2,1,1,1,1,1,1,1,1,1,1] (.node [6,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [6,3,1,1,1,1,1,1,1,1,1,1,1] (.node [6,2,2,2,2,2,2,1,1] (.node [6,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [6,2,2,2,2,2,2,2] .empty .empty)) (.node [6,3,2,2,1,1,1,1,1,1,1] (.node [6,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,3,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree20_1 : RowTree := (.node [6,3,3,3,2,2,1] (.node [6,3,3,2,2,2,1,1] (.node [6,3,3,2,1,1,1,1,1,1] (.node [6,3,3,1,1,1,1,1,1,1,1] (.node [6,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [6,3,3,2,2,1,1,1,1] .empty .empty)) (.node [6,3,3,3,1,1,1,1,1] (.node [6,3,3,2,2,2,2] .empty .empty) (.node [6,3,3,3,2,1,1,1] .empty .empty))) (.node [6,4,2,1,1,1,1,1,1,1,1] (.node [6,3,3,3,3,2] (.node [6,3,3,3,3,1,1] .empty .empty) (.node [6,4,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [6,4,2,2,2,1,1,1,1] (.node [6,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [6,4,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree20_2 : RowTree := (.node [6,3,2,2,2,2,1,1,1] degreeTree20_0 degreeTree20_1) - -def degreeTree20_3 : RowTree := (.node [6,4,4,1,1,1,1,1,1] (.node [6,4,3,3,1,1,1,1] (.node [6,4,3,2,2,1,1,1] (.node [6,4,3,2,1,1,1,1,1] (.node [6,4,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [6,4,3,2,2,2,1] .empty .empty)) (.node [6,4,3,3,2,2] (.node [6,4,3,3,2,1,1] .empty .empty) (.node [6,4,3,3,3,1] .empty .empty))) (.node [6,4,4,3,1,1,1] (.node [6,4,4,2,2,1,1] (.node [6,4,4,2,1,1,1,1] .empty .empty) (.node [6,4,4,2,2,2] .empty .empty)) (.node [6,4,4,4,1,1] (.node [6,4,4,3,2,1] .empty .empty) (.node [6,5,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree20_4 : RowTree := (.node [6,5,3,3,1,1,1] (.node [6,5,3,1,1,1,1,1,1] (.node [6,5,2,2,2,1,1,1] (.node [6,5,2,2,1,1,1,1,1] .empty .empty) (.node [6,5,2,2,2,2,1] .empty .empty)) (.node [6,5,3,2,2,1,1] (.node [6,5,3,2,1,1,1,1] .empty .empty) (.node [6,5,3,2,2,2] .empty .empty))) (.node [6,5,5,1,1,1,1] (.node [6,5,4,1,1,1,1,1] (.node [6,5,3,3,2,1] .empty .empty) (.node [6,5,4,2,1,1,1] .empty .empty)) (.node [6,6,2,1,1,1,1,1,1] (.node [6,6,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,6,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree20_5 : RowTree := (.node [6,5,2,1,1,1,1,1,1,1] degreeTree20_3 degreeTree20_4) - -def degreeTree20_6 : RowTree := (.node [6,4,2,2,2,2,2] degreeTree20_2 degreeTree20_5) - -def degreeTree20_7 : RowTree := (.node [7,2,2,2,2,1,1,1,1,1] (.node [7,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [6,6,3,2,1,1,1] (.node [6,6,3,1,1,1,1,1] (.node [6,6,2,2,2,2] .empty .empty) .empty) (.node [6,6,4,1,1,1,1] .empty .empty)) (.node [7,2,2,1,1,1,1,1,1,1,1,1] (.node [7,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [7,3,2,1,1,1,1,1,1,1,1] (.node [7,2,2,2,2,2,2,1] (.node [7,2,2,2,2,2,1,1,1] .empty .empty) (.node [7,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,3,2,2,2,1,1,1,1] (.node [7,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [7,3,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree20_8 : RowTree := (.node [7,4,2,1,1,1,1,1,1,1] (.node [7,3,3,2,2,2,1] (.node [7,3,3,2,1,1,1,1,1] (.node [7,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [7,3,3,2,2,1,1,1] .empty .empty)) (.node [7,3,3,3,2,1,1] (.node [7,3,3,3,1,1,1,1] .empty .empty) (.node [7,4,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,4,3,1,1,1,1,1,1] (.node [7,4,2,2,2,1,1,1] (.node [7,4,2,2,1,1,1,1,1] .empty .empty) (.node [7,4,2,2,2,2,1] .empty .empty)) (.node [7,4,3,2,2,1,1] (.node [7,4,3,2,1,1,1,1] .empty .empty) (.node [7,4,3,3,1,1,1] .empty .empty)))) - -def degreeTree20_9 : RowTree := (.node [7,3,2,2,2,2,2] degreeTree20_7 degreeTree20_8) - -def degreeTree20_10 : RowTree := (.node [8,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,5,3,1,1,1,1,1] (.node [7,5,2,2,1,1,1,1] (.node [7,5,2,1,1,1,1,1,1] (.node [7,5,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [7,5,2,2,2,1,1] .empty .empty)) (.node [7,6,2,1,1,1,1,1] (.node [7,6,1,1,1,1,1,1,1] .empty .empty) (.node [7,7,1,1,1,1,1,1] .empty .empty))) (.node [8,2,2,2,2,1,1,1,1] (.node [8,2,2,1,1,1,1,1,1,1,1] (.node [8,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [8,3,1,1,1,1,1,1,1,1,1] (.node [8,2,2,2,2,2,1,1] .empty .empty) (.node [8,3,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree20_11 : RowTree := (.node [9,1,1,1,1,1,1,1,1,1,1,1] (.node [8,4,1,1,1,1,1,1,1,1] (.node [8,3,3,1,1,1,1,1,1] (.node [8,3,2,2,2,1,1,1] .empty .empty) (.node [8,3,3,2,1,1,1,1] .empty .empty)) (.node [8,4,2,2,1,1,1,1] (.node [8,4,2,1,1,1,1,1,1] .empty .empty) (.node [8,5,1,1,1,1,1,1,1] .empty .empty))) (.node [9,3,1,1,1,1,1,1,1,1] (.node [9,2,2,1,1,1,1,1,1,1] (.node [9,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,1,1,1,1,1,1,1,1,1,1] (.node [9,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,2,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree20_12 : RowTree := (.node [8,3,2,2,1,1,1,1,1] degreeTree20_10 degreeTree20_11) - -def degreeTree20_13 : RowTree := (.node [7,4,4,1,1,1,1,1] degreeTree20_9 degreeTree20_12) - -def degreeTree20_14 : RowTree := (.node [6,6,2,2,2,1,1] degreeTree20_6 degreeTree20_13) - -def degreeTree20 : RowTree := degreeTree20_14 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 20. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree20_0 : RowTree := (.node [6,2,2,2,2,1,1,1,1,1,1] (.node [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [5,5,4,3,3] (.node [5,4,4,4,3] (.node [4,4,4,4,4] .empty .empty) .empty) (.node [5,5,4,4,2] .empty .empty)) (.node [6,2,2,1,1,1,1,1,1,1,1,1,1] (.node [6,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [6,3,1,1,1,1,1,1,1,1,1,1,1] (.node [6,2,2,2,2,2,2,1,1] (.node [6,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [6,2,2,2,2,2,2,2] .empty .empty)) (.node [6,3,2,2,1,1,1,1,1,1,1] (.node [6,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,3,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree20_1 : RowTree := (.node [6,3,3,3,2,2,1] (.node [6,3,3,2,2,2,1,1] (.node [6,3,3,2,1,1,1,1,1,1] (.node [6,3,3,1,1,1,1,1,1,1,1] (.node [6,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [6,3,3,2,2,1,1,1,1] .empty .empty)) (.node [6,3,3,3,1,1,1,1,1] (.node [6,3,3,2,2,2,2] .empty .empty) (.node [6,3,3,3,2,1,1,1] .empty .empty))) (.node [6,4,2,1,1,1,1,1,1,1,1] (.node [6,3,3,3,3,2] (.node [6,3,3,3,3,1,1] .empty .empty) (.node [6,4,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [6,4,2,2,2,1,1,1,1] (.node [6,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [6,4,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree20_2 : RowTree := (.node [6,3,2,2,2,2,1,1,1] degreeTree20_0 degreeTree20_1) + +def degreeTree20_3 : RowTree := (.node [6,4,4,1,1,1,1,1,1] (.node [6,4,3,3,1,1,1,1] (.node [6,4,3,2,2,1,1,1] (.node [6,4,3,2,1,1,1,1,1] (.node [6,4,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [6,4,3,2,2,2,1] .empty .empty)) (.node [6,4,3,3,2,2] (.node [6,4,3,3,2,1,1] .empty .empty) (.node [6,4,3,3,3,1] .empty .empty))) (.node [6,4,4,3,1,1,1] (.node [6,4,4,2,2,1,1] (.node [6,4,4,2,1,1,1,1] .empty .empty) (.node [6,4,4,2,2,2] .empty .empty)) (.node [6,4,4,4,1,1] (.node [6,4,4,3,2,1] .empty .empty) (.node [6,5,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree20_4 : RowTree := (.node [6,5,3,3,1,1,1] (.node [6,5,3,1,1,1,1,1,1] (.node [6,5,2,2,2,1,1,1] (.node [6,5,2,2,1,1,1,1,1] .empty .empty) (.node [6,5,2,2,2,2,1] .empty .empty)) (.node [6,5,3,2,2,1,1] (.node [6,5,3,2,1,1,1,1] .empty .empty) (.node [6,5,3,2,2,2] .empty .empty))) (.node [6,5,5,1,1,1,1] (.node [6,5,4,1,1,1,1,1] (.node [6,5,3,3,2,1] .empty .empty) (.node [6,5,4,2,1,1,1] .empty .empty)) (.node [6,6,2,1,1,1,1,1,1] (.node [6,6,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,6,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree20_5 : RowTree := (.node [6,5,2,1,1,1,1,1,1,1] degreeTree20_3 degreeTree20_4) + +def degreeTree20_6 : RowTree := (.node [6,4,2,2,2,2,2] degreeTree20_2 degreeTree20_5) + +def degreeTree20_7 : RowTree := (.node [7,2,2,2,2,1,1,1,1,1] (.node [7,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [6,6,3,2,1,1,1] (.node [6,6,3,1,1,1,1,1] (.node [6,6,2,2,2,2] .empty .empty) .empty) (.node [6,6,4,1,1,1,1] .empty .empty)) (.node [7,2,2,1,1,1,1,1,1,1,1,1] (.node [7,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [7,3,2,1,1,1,1,1,1,1,1] (.node [7,2,2,2,2,2,2,1] (.node [7,2,2,2,2,2,1,1,1] .empty .empty) (.node [7,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,3,2,2,2,1,1,1,1] (.node [7,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [7,3,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree20_8 : RowTree := (.node [7,4,2,1,1,1,1,1,1,1] (.node [7,3,3,2,2,2,1] (.node [7,3,3,2,1,1,1,1,1] (.node [7,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [7,3,3,2,2,1,1,1] .empty .empty)) (.node [7,3,3,3,2,1,1] (.node [7,3,3,3,1,1,1,1] .empty .empty) (.node [7,4,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,4,3,1,1,1,1,1,1] (.node [7,4,2,2,2,1,1,1] (.node [7,4,2,2,1,1,1,1,1] .empty .empty) (.node [7,4,2,2,2,2,1] .empty .empty)) (.node [7,4,3,2,2,1,1] (.node [7,4,3,2,1,1,1,1] .empty .empty) (.node [7,4,3,3,1,1,1] .empty .empty)))) + +def degreeTree20_9 : RowTree := (.node [7,3,2,2,2,2,2] degreeTree20_7 degreeTree20_8) + +def degreeTree20_10 : RowTree := (.node [8,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,5,3,1,1,1,1,1] (.node [7,5,2,2,1,1,1,1] (.node [7,5,2,1,1,1,1,1,1] (.node [7,5,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [7,5,2,2,2,1,1] .empty .empty)) (.node [7,6,2,1,1,1,1,1] (.node [7,6,1,1,1,1,1,1,1] .empty .empty) (.node [7,7,1,1,1,1,1,1] .empty .empty))) (.node [8,2,2,2,2,1,1,1,1] (.node [8,2,2,1,1,1,1,1,1,1,1] (.node [8,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [8,3,1,1,1,1,1,1,1,1,1] (.node [8,2,2,2,2,2,1,1] .empty .empty) (.node [8,3,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree20_11 : RowTree := (.node [9,1,1,1,1,1,1,1,1,1,1,1] (.node [8,4,1,1,1,1,1,1,1,1] (.node [8,3,3,1,1,1,1,1,1] (.node [8,3,2,2,2,1,1,1] .empty .empty) (.node [8,3,3,2,1,1,1,1] .empty .empty)) (.node [8,4,2,2,1,1,1,1] (.node [8,4,2,1,1,1,1,1,1] .empty .empty) (.node [8,5,1,1,1,1,1,1,1] .empty .empty))) (.node [9,3,1,1,1,1,1,1,1,1] (.node [9,2,2,1,1,1,1,1,1,1] (.node [9,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,1,1,1,1,1,1,1,1,1,1] (.node [9,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,2,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree20_12 : RowTree := (.node [8,3,2,2,1,1,1,1,1] degreeTree20_10 degreeTree20_11) + +def degreeTree20_13 : RowTree := (.node [7,4,4,1,1,1,1,1] degreeTree20_9 degreeTree20_12) + +def degreeTree20_14 : RowTree := (.node [6,6,2,2,2,1,1] degreeTree20_6 degreeTree20_13) + +def degreeTree20 : RowTree := degreeTree20_14 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData22.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData22.lean index 1f5aaccb9ea2ecafdcc9cc5de7efd81417dd4c92..ee79ca7b44fca3e9cba603b7df75c5df38472da3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData22.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData22.lean @@ -1,51 +1,51 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 22. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree22_0 : RowTree := (.node [7,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,2,2,2,2,1,1,1,1,1,1,1] (.node [7,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [7,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,2,2,2,2,2,2,1,1,1] (.node [7,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [7,2,2,2,2,2,2,2,1] .empty .empty))) (.node [7,3,2,2,2,2,2,1,1] (.node [7,3,2,2,2,1,1,1,1,1,1] (.node [7,3,2,2,1,1,1,1,1,1,1,1] (.node [7,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [7,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [7,3,3,1,1,1,1,1,1,1,1,1] (.node [7,3,2,2,2,2,2,2] .empty .empty) (.node [7,3,3,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree22_1 : RowTree := (.node [7,4,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,3,3,2,2,1,1] (.node [7,3,3,3,1,1,1,1,1,1] (.node [7,3,3,2,2,2,2,1] (.node [7,3,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [7,3,3,3,2,1,1,1,1] .empty .empty)) (.node [7,3,3,3,3,1,1,1] (.node [7,3,3,3,2,2,2] .empty .empty) (.node [7,3,3,3,3,2,1] .empty .empty))) (.node [7,4,2,2,2,2,1,1,1] (.node [7,4,2,2,1,1,1,1,1,1,1] (.node [7,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,4,2,2,2,1,1,1,1,1] .empty .empty)) (.node [7,4,3,1,1,1,1,1,1,1,1] (.node [7,4,2,2,2,2,2,1] .empty .empty) (.node [7,4,3,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree22_2 : RowTree := (.node [7,3,3,2,2,1,1,1,1,1] degreeTree22_0 degreeTree22_1) - -def degreeTree22_3 : RowTree := (.node [7,4,4,2,2,1,1,1] (.node [7,4,3,3,2,2,1] (.node [7,4,3,3,1,1,1,1,1] (.node [7,4,3,2,2,2,2] (.node [7,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [7,4,3,3,2,1,1,1] .empty .empty)) (.node [7,4,4,1,1,1,1,1,1,1] (.node [7,4,3,3,3,1,1] .empty .empty) (.node [7,4,4,2,1,1,1,1,1] .empty .empty))) (.node [7,4,4,4,1,1,1] (.node [7,4,4,3,1,1,1,1] (.node [7,4,4,2,2,2,1] .empty .empty) (.node [7,4,4,3,2,1,1] .empty .empty)) (.node [7,5,2,1,1,1,1,1,1,1,1] (.node [7,5,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,5,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree22_4 : RowTree := (.node [7,5,4,1,1,1,1,1,1] (.node [7,5,3,2,2,1,1,1] (.node [7,5,3,1,1,1,1,1,1,1] (.node [7,5,2,2,2,2,2] (.node [7,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [7,5,3,2,1,1,1,1,1] .empty .empty)) (.node [7,5,3,3,1,1,1,1] (.node [7,5,3,2,2,2,1] .empty .empty) (.node [7,5,3,3,2,1,1] .empty .empty))) (.node [7,6,2,1,1,1,1,1,1,1] (.node [7,5,5,1,1,1,1,1] (.node [7,5,4,2,1,1,1,1] .empty .empty) (.node [7,6,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,6,2,2,2,1,1,1] (.node [7,6,2,2,1,1,1,1,1] .empty .empty) (.node [7,6,2,2,2,2,1] .empty .empty)))) - -def degreeTree22_5 : RowTree := (.node [7,5,2,2,2,1,1,1,1] degreeTree22_3 degreeTree22_4) - -def degreeTree22_6 : RowTree := (.node [7,4,3,2,2,1,1,1,1] degreeTree22_2 degreeTree22_5) - -def degreeTree22_7 : RowTree := (.node [8,2,2,1,1,1,1,1,1,1,1,1,1] (.node [7,7,2,2,1,1,1,1] (.node [7,7,1,1,1,1,1,1,1,1] (.node [7,6,4,1,1,1,1,1] (.node [7,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [7,7,2,1,1,1,1,1,1] .empty .empty)) (.node [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,7,3,1,1,1,1,1] .empty .empty) (.node [8,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,2,2,2,2,2,2,2] (.node [8,2,2,2,2,2,1,1,1,1] (.node [8,2,2,2,2,1,1,1,1,1,1] (.node [8,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,2,2,2,2,2,2,1,1] .empty .empty)) (.node [8,3,2,1,1,1,1,1,1,1,1,1] (.node [8,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,3,2,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree22_8 : RowTree := (.node [8,4,1,1,1,1,1,1,1,1,1,1] (.node [8,3,3,2,2,1,1,1,1] (.node [8,3,3,1,1,1,1,1,1,1,1] (.node [8,3,2,2,2,2,2,1] (.node [8,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [8,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [8,3,3,3,1,1,1,1,1] (.node [8,3,3,2,2,2,1,1] .empty .empty) (.node [8,3,3,3,2,1,1,1] .empty .empty))) (.node [8,4,2,2,2,2,1,1] (.node [8,4,2,2,1,1,1,1,1,1] (.node [8,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,4,2,2,2,1,1,1,1] .empty .empty)) (.node [8,4,3,2,1,1,1,1,1] (.node [8,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [8,4,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree22_9 : RowTree := (.node [8,3,2,2,2,1,1,1,1,1] degreeTree22_7 degreeTree22_8) - -def degreeTree22_10 : RowTree := (.node [8,7,1,1,1,1,1,1,1] (.node [8,5,2,2,2,1,1,1] (.node [8,5,2,1,1,1,1,1,1,1] (.node [8,5,1,1,1,1,1,1,1,1,1] (.node [8,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,5,2,2,1,1,1,1,1] .empty .empty)) (.node [8,6,1,1,1,1,1,1,1,1] (.node [8,5,3,1,1,1,1,1,1] .empty .empty) (.node [8,6,2,1,1,1,1,1,1] .empty .empty))) (.node [9,2,2,2,1,1,1,1,1,1,1] (.node [9,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,2,2,2,2,2,1,1,1] (.node [9,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [9,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree22_11 : RowTree := (.node [10,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,4,1,1,1,1,1,1,1,1,1] (.node [9,3,3,1,1,1,1,1,1,1] (.node [9,3,2,2,2,1,1,1,1] (.node [9,3,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,3,3,2,1,1,1,1,1] .empty .empty)) (.node [9,4,2,2,1,1,1,1,1] (.node [9,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,5,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,1,1,1,1,1,1,1,1,1] (.node [10,2,2,1,1,1,1,1,1,1,1] (.node [10,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [11,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [11,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree22_12 : RowTree := (.node [9,3,2,1,1,1,1,1,1,1,1] degreeTree22_10 degreeTree22_11) - -def degreeTree22_13 : RowTree := (.node [8,4,3,3,1,1,1,1] degreeTree22_9 degreeTree22_12) - -def degreeTree22_14 : RowTree := (.node [7,6,3,1,1,1,1,1,1] degreeTree22_6 degreeTree22_13) - -def degreeTree22 : RowTree := degreeTree22_14 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 22. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree22_0 : RowTree := (.node [7,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,2,2,2,2,1,1,1,1,1,1,1] (.node [7,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [7,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,2,2,2,2,2,2,1,1,1] (.node [7,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [7,2,2,2,2,2,2,2,1] .empty .empty))) (.node [7,3,2,2,2,2,2,1,1] (.node [7,3,2,2,2,1,1,1,1,1,1] (.node [7,3,2,2,1,1,1,1,1,1,1,1] (.node [7,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [7,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [7,3,3,1,1,1,1,1,1,1,1,1] (.node [7,3,2,2,2,2,2,2] .empty .empty) (.node [7,3,3,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree22_1 : RowTree := (.node [7,4,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,3,3,2,2,1,1] (.node [7,3,3,3,1,1,1,1,1,1] (.node [7,3,3,2,2,2,2,1] (.node [7,3,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [7,3,3,3,2,1,1,1,1] .empty .empty)) (.node [7,3,3,3,3,1,1,1] (.node [7,3,3,3,2,2,2] .empty .empty) (.node [7,3,3,3,3,2,1] .empty .empty))) (.node [7,4,2,2,2,2,1,1,1] (.node [7,4,2,2,1,1,1,1,1,1,1] (.node [7,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,4,2,2,2,1,1,1,1,1] .empty .empty)) (.node [7,4,3,1,1,1,1,1,1,1,1] (.node [7,4,2,2,2,2,2,1] .empty .empty) (.node [7,4,3,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree22_2 : RowTree := (.node [7,3,3,2,2,1,1,1,1,1] degreeTree22_0 degreeTree22_1) + +def degreeTree22_3 : RowTree := (.node [7,4,4,2,2,1,1,1] (.node [7,4,3,3,2,2,1] (.node [7,4,3,3,1,1,1,1,1] (.node [7,4,3,2,2,2,2] (.node [7,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [7,4,3,3,2,1,1,1] .empty .empty)) (.node [7,4,4,1,1,1,1,1,1,1] (.node [7,4,3,3,3,1,1] .empty .empty) (.node [7,4,4,2,1,1,1,1,1] .empty .empty))) (.node [7,4,4,4,1,1,1] (.node [7,4,4,3,1,1,1,1] (.node [7,4,4,2,2,2,1] .empty .empty) (.node [7,4,4,3,2,1,1] .empty .empty)) (.node [7,5,2,1,1,1,1,1,1,1,1] (.node [7,5,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,5,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree22_4 : RowTree := (.node [7,5,4,1,1,1,1,1,1] (.node [7,5,3,2,2,1,1,1] (.node [7,5,3,1,1,1,1,1,1,1] (.node [7,5,2,2,2,2,2] (.node [7,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [7,5,3,2,1,1,1,1,1] .empty .empty)) (.node [7,5,3,3,1,1,1,1] (.node [7,5,3,2,2,2,1] .empty .empty) (.node [7,5,3,3,2,1,1] .empty .empty))) (.node [7,6,2,1,1,1,1,1,1,1] (.node [7,5,5,1,1,1,1,1] (.node [7,5,4,2,1,1,1,1] .empty .empty) (.node [7,6,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,6,2,2,2,1,1,1] (.node [7,6,2,2,1,1,1,1,1] .empty .empty) (.node [7,6,2,2,2,2,1] .empty .empty)))) + +def degreeTree22_5 : RowTree := (.node [7,5,2,2,2,1,1,1,1] degreeTree22_3 degreeTree22_4) + +def degreeTree22_6 : RowTree := (.node [7,4,3,2,2,1,1,1,1] degreeTree22_2 degreeTree22_5) + +def degreeTree22_7 : RowTree := (.node [8,2,2,1,1,1,1,1,1,1,1,1,1] (.node [7,7,2,2,1,1,1,1] (.node [7,7,1,1,1,1,1,1,1,1] (.node [7,6,4,1,1,1,1,1] (.node [7,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [7,7,2,1,1,1,1,1,1] .empty .empty)) (.node [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,7,3,1,1,1,1,1] .empty .empty) (.node [8,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,2,2,2,2,2,2,2] (.node [8,2,2,2,2,2,1,1,1,1] (.node [8,2,2,2,2,1,1,1,1,1,1] (.node [8,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,2,2,2,2,2,2,1,1] .empty .empty)) (.node [8,3,2,1,1,1,1,1,1,1,1,1] (.node [8,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,3,2,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree22_8 : RowTree := (.node [8,4,1,1,1,1,1,1,1,1,1,1] (.node [8,3,3,2,2,1,1,1,1] (.node [8,3,3,1,1,1,1,1,1,1,1] (.node [8,3,2,2,2,2,2,1] (.node [8,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [8,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [8,3,3,3,1,1,1,1,1] (.node [8,3,3,2,2,2,1,1] .empty .empty) (.node [8,3,3,3,2,1,1,1] .empty .empty))) (.node [8,4,2,2,2,2,1,1] (.node [8,4,2,2,1,1,1,1,1,1] (.node [8,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,4,2,2,2,1,1,1,1] .empty .empty)) (.node [8,4,3,2,1,1,1,1,1] (.node [8,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [8,4,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree22_9 : RowTree := (.node [8,3,2,2,2,1,1,1,1,1] degreeTree22_7 degreeTree22_8) + +def degreeTree22_10 : RowTree := (.node [8,7,1,1,1,1,1,1,1] (.node [8,5,2,2,2,1,1,1] (.node [8,5,2,1,1,1,1,1,1,1] (.node [8,5,1,1,1,1,1,1,1,1,1] (.node [8,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,5,2,2,1,1,1,1,1] .empty .empty)) (.node [8,6,1,1,1,1,1,1,1,1] (.node [8,5,3,1,1,1,1,1,1] .empty .empty) (.node [8,6,2,1,1,1,1,1,1] .empty .empty))) (.node [9,2,2,2,1,1,1,1,1,1,1] (.node [9,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,2,2,2,2,2,1,1,1] (.node [9,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [9,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree22_11 : RowTree := (.node [10,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,4,1,1,1,1,1,1,1,1,1] (.node [9,3,3,1,1,1,1,1,1,1] (.node [9,3,2,2,2,1,1,1,1] (.node [9,3,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,3,3,2,1,1,1,1,1] .empty .empty)) (.node [9,4,2,2,1,1,1,1,1] (.node [9,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,5,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,1,1,1,1,1,1,1,1,1] (.node [10,2,2,1,1,1,1,1,1,1,1] (.node [10,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [11,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [11,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree22_12 : RowTree := (.node [9,3,2,1,1,1,1,1,1,1,1] degreeTree22_10 degreeTree22_11) + +def degreeTree22_13 : RowTree := (.node [8,4,3,3,1,1,1,1] degreeTree22_9 degreeTree22_12) + +def degreeTree22_14 : RowTree := (.node [7,6,3,1,1,1,1,1,1] degreeTree22_6 degreeTree22_13) + +def degreeTree22 : RowTree := degreeTree22_14 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData24.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData24.lean index 3de1838cabedc342eadbaeb8b1cca6e7681e9603..4429434f47a4a29e1a4baacf91ae4f5751864c0b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData24.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData24.lean @@ -1,83 +1,83 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 24. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree24_0 : RowTree := (.node [5,5,4,4,3,2,1] (.node [5,4,4,4,3,2,2] (.node [4,4,4,4,4,3,1] (.node [4,4,4,4,3,3,2] (.node [4,4,4,3,3,3,3] .empty .empty) (.node [4,4,4,4,4,2,2] .empty .empty)) (.node [5,4,3,3,3,3,3] (.node [4,4,4,4,4,4] .empty .empty) (.node [5,4,4,3,3,3,2] .empty .empty))) (.node [5,5,3,3,3,3,2] (.node [5,4,4,4,4,2,1] (.node [5,4,4,4,3,3,1] .empty .empty) (.node [5,4,4,4,4,3] .empty .empty)) (.node [5,5,4,3,3,3,1] (.node [5,5,4,3,3,2,2] .empty .empty) (.node [5,5,4,4,2,2,2] .empty .empty)))) (.node [5,5,5,4,3,1,1] (.node [5,5,5,3,2,2,2] (.node [5,5,4,4,4,1,1] (.node [5,5,4,4,3,3] .empty .empty) (.node [5,5,4,4,4,2] .empty .empty)) (.node [5,5,5,3,3,3] (.node [5,5,5,3,3,2,1] .empty .empty) (.node [5,5,5,4,2,2,1] .empty .empty))) (.node [5,5,5,5,2,2] (.node [5,5,5,4,4,1] (.node [5,5,5,4,3,2] .empty .empty) (.node [5,5,5,5,2,1,1] .empty .empty)) (.node [5,5,5,5,4] (.node [5,5,5,5,3,1] .empty .empty) .empty)))) - -def degreeTree24_1 : RowTree := (.node [6,3,2,2,2,2,2,2,1,1,1] (.node [6,2,2,2,2,2,2,2,2,1,1] (.node [6,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [6,2,2,2,2,2,2,1,1,1,1,1,1] (.node [6,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [6,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [6,3,2,2,2,2,1,1,1,1,1,1,1] (.node [6,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)))) (.node [6,3,3,2,2,2,2,2,2] (.node [6,3,3,2,2,1,1,1,1,1,1,1,1] (.node [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [6,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [6,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [6,3,3,2,2,2,2,1,1,1,1] (.node [6,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [6,3,3,2,2,2,2,2,1,1] .empty .empty))) (.node [6,3,3,3,2,2,2,1,1,1] (.node [6,3,3,3,2,1,1,1,1,1,1,1] (.node [6,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,3,3,3,2,2,1,1,1,1,1] .empty .empty)) (.node [6,3,3,3,3,1,1,1,1,1,1] (.node [6,3,3,3,2,2,2,2,1] .empty .empty) .empty)))) - -def degreeTree24_2 : RowTree := (.node [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree24_0 degreeTree24_1) - -def degreeTree24_3 : RowTree := (.node [6,4,3,2,2,1,1,1,1,1,1,1] (.node [6,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [6,3,3,3,3,3,2,1] (.node [6,3,3,3,3,2,2,2] (.node [6,3,3,3,3,2,2,1,1] .empty .empty) (.node [6,3,3,3,3,3,1,1,1] .empty .empty)) (.node [6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [6,3,3,3,3,3,3] .empty .empty) (.node [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [6,4,2,2,2,2,2,2,1,1] (.node [6,4,2,2,2,2,1,1,1,1,1,1] (.node [6,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,4,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [6,4,3,1,1,1,1,1,1,1,1,1,1,1] (.node [6,4,2,2,2,2,2,2,2] .empty .empty) (.node [6,4,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [6,4,3,3,2,2,2,2] (.node [6,4,3,3,1,1,1,1,1,1,1,1] (.node [6,4,3,2,2,2,2,1,1,1] (.node [6,4,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [6,4,3,2,2,2,2,2,1] .empty .empty)) (.node [6,4,3,3,2,2,1,1,1,1] (.node [6,4,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [6,4,3,3,2,2,2,1,1] .empty .empty))) (.node [6,4,3,3,3,3,1,1] (.node [6,4,3,3,3,2,1,1,1] (.node [6,4,3,3,3,1,1,1,1,1] .empty .empty) (.node [6,4,3,3,3,2,2,1] .empty .empty)) (.node [6,4,4,1,1,1,1,1,1,1,1,1,1] (.node [6,4,3,3,3,3,2] .empty .empty) .empty)))) - -def degreeTree24_4 : RowTree := (.node [6,4,4,4,2,2,1,1] (.node [6,4,4,3,2,2,2,1] (.node [6,4,4,2,2,2,2,2] (.node [6,4,4,2,2,2,1,1,1,1] (.node [6,4,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [6,4,4,2,2,2,2,1,1] .empty .empty)) (.node [6,4,4,3,2,1,1,1,1,1] (.node [6,4,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [6,4,4,3,2,2,1,1,1] .empty .empty))) (.node [6,4,4,3,3,3,1] (.node [6,4,4,3,3,2,1,1] (.node [6,4,4,3,3,1,1,1,1] .empty .empty) (.node [6,4,4,3,3,2,2] .empty .empty)) (.node [6,4,4,4,2,1,1,1,1] (.node [6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty))) (.node [6,5,2,1,1,1,1,1,1,1,1,1,1,1] (.node [6,4,4,4,3,3] (.node [6,4,4,4,3,1,1,1] (.node [6,4,4,4,2,2,2] .empty .empty) (.node [6,4,4,4,3,2,1] .empty .empty)) (.node [6,4,4,4,4,2] (.node [6,4,4,4,4,1,1] .empty .empty) (.node [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [6,5,2,2,2,2,2,1,1,1] (.node [6,5,2,2,2,1,1,1,1,1,1,1] (.node [6,5,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,5,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [6,5,3,1,1,1,1,1,1,1,1,1,1] (.node [6,5,2,2,2,2,2,2,1] .empty .empty) .empty)))) - -def degreeTree24_5 : RowTree := (.node [6,4,4,2,1,1,1,1,1,1,1,1] degreeTree24_3 degreeTree24_4) - -def degreeTree24_6 : RowTree := (.node [6,3,3,3,3,2,1,1,1,1] degreeTree24_2 degreeTree24_5) - -def degreeTree24_7 : RowTree := (.node [6,5,4,2,2,2,1,1,1] (.node [6,5,3,3,2,2,2,1] (.node [6,5,3,2,2,2,2,2] (.node [6,5,3,2,2,2,1,1,1,1] (.node [6,5,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [6,5,3,2,2,2,2,1,1] .empty .empty)) (.node [6,5,3,3,2,1,1,1,1,1] (.node [6,5,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [6,5,3,3,2,2,1,1,1] .empty .empty))) (.node [6,5,3,3,3,3,1] (.node [6,5,3,3,3,2,1,1] (.node [6,5,3,3,3,1,1,1,1] .empty .empty) (.node [6,5,3,3,3,2,2] .empty .empty)) (.node [6,5,4,2,1,1,1,1,1,1,1] (.node [6,5,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,5,4,2,2,1,1,1,1,1] .empty .empty)))) (.node [6,5,4,3,3,3] (.node [6,5,4,3,2,2,1,1] (.node [6,5,4,3,1,1,1,1,1,1] (.node [6,5,4,2,2,2,2,1] .empty .empty) (.node [6,5,4,3,2,1,1,1,1] .empty .empty)) (.node [6,5,4,3,3,1,1,1] (.node [6,5,4,3,2,2,2] .empty .empty) (.node [6,5,4,3,3,2,1] .empty .empty))) (.node [6,5,4,4,3,1,1] (.node [6,5,4,4,2,1,1,1] (.node [6,5,4,4,1,1,1,1,1] .empty .empty) (.node [6,5,4,4,2,2,1] .empty .empty)) (.node [6,5,4,4,4,1] (.node [6,5,4,4,3,2] .empty .empty) .empty)))) - -def degreeTree24_8 : RowTree := (.node [6,6,2,1,1,1,1,1,1,1,1,1,1] (.node [6,5,5,3,3,1,1] (.node [6,5,5,2,2,2,2] (.node [6,5,5,2,2,1,1,1,1] (.node [6,5,5,2,1,1,1,1,1,1] .empty .empty) (.node [6,5,5,2,2,2,1,1] .empty .empty)) (.node [6,5,5,3,2,1,1,1] (.node [6,5,5,3,1,1,1,1,1] .empty .empty) (.node [6,5,5,3,2,2,1] .empty .empty))) (.node [6,5,5,4,2,2] (.node [6,5,5,4,1,1,1,1] (.node [6,5,5,3,3,2] .empty .empty) (.node [6,5,5,4,2,1,1] .empty .empty)) (.node [6,5,5,5,1,1,1] (.node [6,5,5,4,3,1] .empty .empty) (.node [6,6,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [6,6,3,2,2,1,1,1,1,1] (.node [6,6,2,2,2,2,2,1,1] (.node [6,6,2,2,2,1,1,1,1,1,1] (.node [6,6,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,6,2,2,2,2,1,1,1,1] .empty .empty)) (.node [6,6,3,1,1,1,1,1,1,1,1,1] (.node [6,6,2,2,2,2,2,2] .empty .empty) (.node [6,6,3,2,1,1,1,1,1,1,1] .empty .empty))) (.node [6,6,3,3,2,1,1,1,1] (.node [6,6,3,2,2,2,2,1] (.node [6,6,3,2,2,2,1,1,1] .empty .empty) (.node [6,6,3,3,1,1,1,1,1,1] .empty .empty)) (.node [6,6,3,3,2,2,2] (.node [6,6,3,3,2,2,1,1] .empty .empty) .empty)))) - -def degreeTree24_9 : RowTree := (.node [6,5,5,1,1,1,1,1,1,1,1] degreeTree24_7 degreeTree24_8) - -def degreeTree24_10 : RowTree := (.node [6,6,5,1,1,1,1,1,1,1] (.node [6,6,4,3,1,1,1,1,1] (.node [6,6,4,2,1,1,1,1,1,1] (.node [6,6,3,3,3,3] (.node [6,6,3,3,3,2,1] .empty .empty) (.node [6,6,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [6,6,4,2,2,2,1,1] (.node [6,6,4,2,2,1,1,1,1] .empty .empty) (.node [6,6,4,2,2,2,2] .empty .empty))) (.node [6,6,4,3,3,2] (.node [6,6,4,3,2,2,1] (.node [6,6,4,3,2,1,1,1] .empty .empty) (.node [6,6,4,3,3,1,1] .empty .empty)) (.node [6,6,4,4,2,1,1] (.node [6,6,4,4,1,1,1,1] .empty .empty) (.node [6,6,4,4,2,2] .empty .empty)))) (.node [6,6,6,2,1,1,1,1] (.node [6,6,5,3,1,1,1,1] (.node [6,6,5,2,2,1,1,1] (.node [6,6,5,2,1,1,1,1,1] .empty .empty) (.node [6,6,5,2,2,2,1] .empty .empty)) (.node [6,6,5,4,1,1,1] (.node [6,6,5,3,2,1,1] .empty .empty) (.node [6,6,6,1,1,1,1,1,1] .empty .empty))) (.node [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [6,6,6,3,1,1,1] (.node [6,6,6,2,2,1,1] .empty .empty) (.node [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree24_11 : RowTree := (.node [7,3,3,2,2,1,1,1,1,1,1,1] (.node [7,3,2,2,2,1,1,1,1,1,1,1,1] (.node [7,2,2,2,2,2,2,2,2,1] (.node [7,2,2,2,2,2,2,1,1,1,1,1] (.node [7,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [7,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,3,2,2,2,2,2,2,2] (.node [7,3,2,2,2,2,2,1,1,1,1] (.node [7,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [7,3,2,2,2,2,2,2,1,1] .empty .empty)) (.node [7,3,3,2,1,1,1,1,1,1,1,1,1] (.node [7,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [7,3,3,3,2,2,2,2] (.node [7,3,3,3,1,1,1,1,1,1,1,1] (.node [7,3,3,2,2,2,2,1,1,1] (.node [7,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [7,3,3,2,2,2,2,2,1] .empty .empty)) (.node [7,3,3,3,2,2,1,1,1,1] (.node [7,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [7,3,3,3,2,2,2,1,1] .empty .empty))) (.node [7,3,3,3,3,3,1,1] (.node [7,3,3,3,3,2,1,1,1] (.node [7,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [7,3,3,3,3,2,2,1] .empty .empty)) (.node [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,3,3,3,3,2] .empty .empty) .empty)))) - -def degreeTree24_12 : RowTree := (.node [7,2,2,2,2,1,1,1,1,1,1,1,1,1] degreeTree24_10 degreeTree24_11) - -def degreeTree24_13 : RowTree := (.node [6,6,3,3,3,1,1,1] degreeTree24_9 degreeTree24_12) - -def degreeTree24_14 : RowTree := (.node [6,5,3,2,1,1,1,1,1,1,1,1] degreeTree24_6 degreeTree24_13) - -def degreeTree24_15 : RowTree := (.node [7,4,3,3,3,1,1,1,1] (.node [7,4,3,2,2,1,1,1,1,1,1] (.node [7,4,2,2,2,2,2,1,1,1] (.node [7,4,2,2,2,1,1,1,1,1,1,1] (.node [7,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,4,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [7,4,3,1,1,1,1,1,1,1,1,1,1] (.node [7,4,2,2,2,2,2,2,1] .empty .empty) (.node [7,4,3,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,4,3,3,1,1,1,1,1,1,1] (.node [7,4,3,2,2,2,2,1,1] (.node [7,4,3,2,2,2,1,1,1,1] .empty .empty) (.node [7,4,3,2,2,2,2,2] .empty .empty)) (.node [7,4,3,3,2,2,1,1,1] (.node [7,4,3,3,2,1,1,1,1,1] .empty .empty) (.node [7,4,3,3,2,2,2,1] .empty .empty)))) (.node [7,4,4,2,2,2,2,1] (.node [7,4,4,1,1,1,1,1,1,1,1,1] (.node [7,4,3,3,3,2,2] (.node [7,4,3,3,3,2,1,1] .empty .empty) (.node [7,4,3,3,3,3,1] .empty .empty)) (.node [7,4,4,2,2,1,1,1,1,1] (.node [7,4,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [7,4,4,2,2,2,1,1,1] .empty .empty))) (.node [7,4,4,3,2,2,2] (.node [7,4,4,3,2,1,1,1,1] (.node [7,4,4,3,1,1,1,1,1,1] .empty .empty) (.node [7,4,4,3,2,2,1,1] .empty .empty)) (.node [7,4,4,3,3,2,1] (.node [7,4,4,3,3,1,1,1] .empty .empty) .empty)))) - -def degreeTree24_16 : RowTree := (.node [7,5,3,3,1,1,1,1,1,1] (.node [7,5,2,2,2,2,1,1,1,1] (.node [7,5,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,4,4,4,2,2,1] (.node [7,4,4,4,2,1,1,1] .empty .empty) (.node [7,4,4,4,3,1,1] .empty .empty)) (.node [7,5,2,2,1,1,1,1,1,1,1,1] (.node [7,5,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,5,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [7,5,3,2,1,1,1,1,1,1,1] (.node [7,5,2,2,2,2,2,2] (.node [7,5,2,2,2,2,2,1,1] .empty .empty) (.node [7,5,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,5,3,2,2,2,1,1,1] (.node [7,5,3,2,2,1,1,1,1,1] .empty .empty) (.node [7,5,3,2,2,2,2,1] .empty .empty)))) (.node [7,5,4,2,2,1,1,1,1] (.node [7,5,3,3,3,1,1,1] (.node [7,5,3,3,2,2,1,1] (.node [7,5,3,3,2,1,1,1,1] .empty .empty) (.node [7,5,3,3,2,2,2] .empty .empty)) (.node [7,5,4,1,1,1,1,1,1,1,1] (.node [7,5,3,3,3,2,1] .empty .empty) (.node [7,5,4,2,1,1,1,1,1,1] .empty .empty))) (.node [7,5,4,3,2,1,1,1] (.node [7,5,4,2,2,2,2] (.node [7,5,4,2,2,2,1,1] .empty .empty) (.node [7,5,4,3,1,1,1,1,1] .empty .empty)) (.node [7,5,4,3,3,1,1] (.node [7,5,4,3,2,2,1] .empty .empty) .empty)))) - -def degreeTree24_17 : RowTree := (.node [7,4,4,4,1,1,1,1,1] degreeTree24_15 degreeTree24_16) - -def degreeTree24_18 : RowTree := (.node [7,6,3,2,2,2,1,1] (.node [7,6,2,1,1,1,1,1,1,1,1,1] (.node [7,5,5,2,2,1,1,1] (.node [7,5,5,1,1,1,1,1,1,1] (.node [7,5,4,4,2,1,1] .empty .empty) (.node [7,5,5,2,1,1,1,1,1] .empty .empty)) (.node [7,5,5,3,1,1,1,1] (.node [7,5,5,2,2,2,1] .empty .empty) (.node [7,6,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,6,2,2,2,2,2,1] (.node [7,6,2,2,2,1,1,1,1,1] (.node [7,6,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [7,6,2,2,2,2,1,1,1] .empty .empty)) (.node [7,6,3,2,1,1,1,1,1,1] (.node [7,6,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,6,3,2,2,1,1,1,1] .empty .empty)))) (.node [7,6,4,3,1,1,1,1] (.node [7,6,3,3,2,2,1] (.node [7,6,3,3,1,1,1,1,1] (.node [7,6,3,2,2,2,2] .empty .empty) (.node [7,6,3,3,2,1,1,1] .empty .empty)) (.node [7,6,4,2,1,1,1,1,1] (.node [7,6,4,1,1,1,1,1,1,1] .empty .empty) (.node [7,6,4,2,2,1,1,1] .empty .empty))) (.node [7,7,1,1,1,1,1,1,1,1,1,1] (.node [7,6,5,2,1,1,1,1] (.node [7,6,5,1,1,1,1,1,1] .empty .empty) (.node [7,6,6,1,1,1,1,1] .empty .empty)) (.node [7,7,2,2,1,1,1,1,1,1] (.node [7,7,2,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree24_19 : RowTree := (.node [8,2,2,2,2,2,1,1,1,1,1,1] (.node [7,7,4,2,1,1,1,1] (.node [7,7,3,2,1,1,1,1,1] (.node [7,7,2,2,2,2,2] (.node [7,7,2,2,2,2,1,1] .empty .empty) (.node [7,7,3,1,1,1,1,1,1,1] .empty .empty)) (.node [7,7,3,3,1,1,1,1] (.node [7,7,3,2,2,1,1,1] .empty .empty) (.node [7,7,4,1,1,1,1,1,1] .empty .empty))) (.node [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,7,5,1,1,1,1,1] .empty .empty) (.node [8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,2,2,2,2,1,1,1,1,1,1,1,1] (.node [8,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [8,3,2,2,2,2,1,1,1,1,1] (.node [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,2,2,2,2,2,2,2,1,1] (.node [8,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [8,2,2,2,2,2,2,2,2] .empty .empty)) (.node [8,3,2,2,1,1,1,1,1,1,1,1,1] (.node [8,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,3,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [8,3,3,2,1,1,1,1,1,1,1,1] (.node [8,3,2,2,2,2,2,2,1] (.node [8,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [8,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,3,3,2,2,2,1,1,1,1] (.node [8,3,3,2,2,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree24_20 : RowTree := (.node [7,7,2,2,2,1,1,1,1] degreeTree24_18 degreeTree24_19) - -def degreeTree24_21 : RowTree := (.node [7,5,4,4,1,1,1,1] degreeTree24_17 degreeTree24_20) - -def degreeTree24_22 : RowTree := (.node [8,4,3,2,1,1,1,1,1,1,1] (.node [8,4,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,3,3,3,2,2,1,1,1] (.node [8,3,3,3,1,1,1,1,1,1,1] (.node [8,3,3,2,2,2,2,2] .empty .empty) (.node [8,3,3,3,2,1,1,1,1,1] .empty .empty)) (.node [8,3,3,3,3,1,1,1,1] (.node [8,3,3,3,2,2,2,1] .empty .empty) (.node [8,3,3,3,3,2,1,1] .empty .empty))) (.node [8,4,2,2,2,2,1,1,1,1] (.node [8,4,2,2,1,1,1,1,1,1,1,1] (.node [8,4,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,4,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [8,4,2,2,2,2,2,2] (.node [8,4,2,2,2,2,2,1,1] .empty .empty) (.node [8,4,3,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,4,4,1,1,1,1,1,1,1,1] (.node [8,4,3,3,1,1,1,1,1,1] (.node [8,4,3,2,2,2,1,1,1] (.node [8,4,3,2,2,1,1,1,1,1] .empty .empty) (.node [8,4,3,2,2,2,2,1] .empty .empty)) (.node [8,4,3,3,2,2,1,1] (.node [8,4,3,3,2,1,1,1,1] .empty .empty) (.node [8,4,3,3,3,1,1,1] .empty .empty))) (.node [8,4,4,3,1,1,1,1,1] (.node [8,4,4,2,2,1,1,1,1] (.node [8,4,4,2,1,1,1,1,1,1] .empty .empty) (.node [8,4,4,2,2,2,1,1] .empty .empty)) (.node [8,4,4,4,1,1,1,1] (.node [8,4,4,3,2,1,1,1] .empty .empty) .empty)))) - -def degreeTree24_23 : RowTree := (.node [8,6,1,1,1,1,1,1,1,1,1,1] (.node [8,5,3,2,2,1,1,1,1] (.node [8,5,2,2,2,2,1,1,1] (.node [8,5,2,2,1,1,1,1,1,1,1] (.node [8,5,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,5,2,2,2,1,1,1,1,1] .empty .empty)) (.node [8,5,3,1,1,1,1,1,1,1,1] (.node [8,5,2,2,2,2,2,1] .empty .empty) (.node [8,5,3,2,1,1,1,1,1,1] .empty .empty))) (.node [8,5,4,1,1,1,1,1,1,1] (.node [8,5,3,3,1,1,1,1,1] (.node [8,5,3,2,2,2,1,1] .empty .empty) (.node [8,5,3,3,2,1,1,1] .empty .empty)) (.node [8,5,5,1,1,1,1,1,1] (.node [8,5,4,2,1,1,1,1,1] .empty .empty) .empty))) (.node [8,7,1,1,1,1,1,1,1,1,1] (.node [8,6,2,2,2,2,1,1] (.node [8,6,2,2,1,1,1,1,1,1] (.node [8,6,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,6,2,2,2,1,1,1,1] .empty .empty)) (.node [8,6,3,2,1,1,1,1,1] (.node [8,6,3,1,1,1,1,1,1,1] .empty .empty) (.node [8,6,4,1,1,1,1,1,1] .empty .empty))) (.node [8,8,1,1,1,1,1,1,1,1] (.node [8,7,2,2,1,1,1,1,1] (.node [8,7,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,3,1,1,1,1,1,1] .empty .empty)) (.node [9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,2,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree24_24 : RowTree := (.node [8,5,1,1,1,1,1,1,1,1,1,1,1] degreeTree24_22 degreeTree24_23) - -def degreeTree24_25 : RowTree := (.node [9,3,3,2,2,2,1,1,1] (.node [9,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,2,2,2,2,2,1,1,1,1,1] (.node [9,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,2,2,2,2,2,2,2,1] (.node [9,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,3,2,2,2,2,2,1,1] (.node [9,3,2,2,2,1,1,1,1,1,1] (.node [9,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [9,3,3,2,1,1,1,1,1,1,1] (.node [9,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,3,3,2,2,1,1,1,1,1] .empty .empty)))) (.node [9,4,3,1,1,1,1,1,1,1,1] (.node [9,4,2,1,1,1,1,1,1,1,1,1] (.node [9,3,3,3,2,1,1,1,1] (.node [9,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,4,2,2,2,1,1,1,1,1] (.node [9,4,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,4,2,2,2,2,1,1,1] .empty .empty))) (.node [9,4,4,1,1,1,1,1,1,1] (.node [9,4,3,2,2,1,1,1,1] (.node [9,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [9,4,3,3,1,1,1,1,1] .empty .empty)) (.node [9,5,2,1,1,1,1,1,1,1,1] (.node [9,5,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree24_26 : RowTree := (.node [10,3,2,2,2,1,1,1,1,1] (.node [10,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,6,2,1,1,1,1,1,1,1] (.node [9,5,3,1,1,1,1,1,1,1] (.node [9,5,2,2,2,1,1,1,1] .empty .empty) (.node [9,6,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,2,2,2,2,1,1,1,1,1,1] (.node [10,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,3,2,2,1,1,1,1,1,1,1] (.node [10,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [11,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,2,1,1,1,1,1,1,1,1] (.node [10,3,3,2,1,1,1,1,1,1] (.node [10,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,1,1,1,1,1,1,1,1,1] (.node [10,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [11,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [11,3,2,1,1,1,1,1,1,1,1] (.node [11,2,2,2,1,1,1,1,1,1,1] (.node [11,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,2,1,1,1,1,1,1,1,1,1,1] (.node [12,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree24_27 : RowTree := (.node [9,5,2,2,1,1,1,1,1,1] degreeTree24_25 degreeTree24_26) - -def degreeTree24_28 : RowTree := (.node [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree24_24 degreeTree24_27) - -def degreeTree24_29 : RowTree := (.node [8,3,3,2,2,2,2,1,1] degreeTree24_21 degreeTree24_28) - -def degreeTree24_30 : RowTree := (.node [7,4,2,1,1,1,1,1,1,1,1,1,1,1] degreeTree24_14 degreeTree24_29) - -def degreeTree24 : RowTree := degreeTree24_30 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 24. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree24_0 : RowTree := (.node [5,5,4,4,3,2,1] (.node [5,4,4,4,3,2,2] (.node [4,4,4,4,4,3,1] (.node [4,4,4,4,3,3,2] (.node [4,4,4,3,3,3,3] .empty .empty) (.node [4,4,4,4,4,2,2] .empty .empty)) (.node [5,4,3,3,3,3,3] (.node [4,4,4,4,4,4] .empty .empty) (.node [5,4,4,3,3,3,2] .empty .empty))) (.node [5,5,3,3,3,3,2] (.node [5,4,4,4,4,2,1] (.node [5,4,4,4,3,3,1] .empty .empty) (.node [5,4,4,4,4,3] .empty .empty)) (.node [5,5,4,3,3,3,1] (.node [5,5,4,3,3,2,2] .empty .empty) (.node [5,5,4,4,2,2,2] .empty .empty)))) (.node [5,5,5,4,3,1,1] (.node [5,5,5,3,2,2,2] (.node [5,5,4,4,4,1,1] (.node [5,5,4,4,3,3] .empty .empty) (.node [5,5,4,4,4,2] .empty .empty)) (.node [5,5,5,3,3,3] (.node [5,5,5,3,3,2,1] .empty .empty) (.node [5,5,5,4,2,2,1] .empty .empty))) (.node [5,5,5,5,2,2] (.node [5,5,5,4,4,1] (.node [5,5,5,4,3,2] .empty .empty) (.node [5,5,5,5,2,1,1] .empty .empty)) (.node [5,5,5,5,4] (.node [5,5,5,5,3,1] .empty .empty) .empty)))) + +def degreeTree24_1 : RowTree := (.node [6,3,2,2,2,2,2,2,1,1,1] (.node [6,2,2,2,2,2,2,2,2,1,1] (.node [6,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [6,2,2,2,2,2,2,1,1,1,1,1,1] (.node [6,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [6,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [6,3,2,2,2,2,1,1,1,1,1,1,1] (.node [6,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)))) (.node [6,3,3,2,2,2,2,2,2] (.node [6,3,3,2,2,1,1,1,1,1,1,1,1] (.node [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [6,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [6,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [6,3,3,2,2,2,2,1,1,1,1] (.node [6,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [6,3,3,2,2,2,2,2,1,1] .empty .empty))) (.node [6,3,3,3,2,2,2,1,1,1] (.node [6,3,3,3,2,1,1,1,1,1,1,1] (.node [6,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,3,3,3,2,2,1,1,1,1,1] .empty .empty)) (.node [6,3,3,3,3,1,1,1,1,1,1] (.node [6,3,3,3,2,2,2,2,1] .empty .empty) .empty)))) + +def degreeTree24_2 : RowTree := (.node [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree24_0 degreeTree24_1) + +def degreeTree24_3 : RowTree := (.node [6,4,3,2,2,1,1,1,1,1,1,1] (.node [6,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [6,3,3,3,3,3,2,1] (.node [6,3,3,3,3,2,2,2] (.node [6,3,3,3,3,2,2,1,1] .empty .empty) (.node [6,3,3,3,3,3,1,1,1] .empty .empty)) (.node [6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [6,3,3,3,3,3,3] .empty .empty) (.node [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [6,4,2,2,2,2,2,2,1,1] (.node [6,4,2,2,2,2,1,1,1,1,1,1] (.node [6,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,4,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [6,4,3,1,1,1,1,1,1,1,1,1,1,1] (.node [6,4,2,2,2,2,2,2,2] .empty .empty) (.node [6,4,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [6,4,3,3,2,2,2,2] (.node [6,4,3,3,1,1,1,1,1,1,1,1] (.node [6,4,3,2,2,2,2,1,1,1] (.node [6,4,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [6,4,3,2,2,2,2,2,1] .empty .empty)) (.node [6,4,3,3,2,2,1,1,1,1] (.node [6,4,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [6,4,3,3,2,2,2,1,1] .empty .empty))) (.node [6,4,3,3,3,3,1,1] (.node [6,4,3,3,3,2,1,1,1] (.node [6,4,3,3,3,1,1,1,1,1] .empty .empty) (.node [6,4,3,3,3,2,2,1] .empty .empty)) (.node [6,4,4,1,1,1,1,1,1,1,1,1,1] (.node [6,4,3,3,3,3,2] .empty .empty) .empty)))) + +def degreeTree24_4 : RowTree := (.node [6,4,4,4,2,2,1,1] (.node [6,4,4,3,2,2,2,1] (.node [6,4,4,2,2,2,2,2] (.node [6,4,4,2,2,2,1,1,1,1] (.node [6,4,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [6,4,4,2,2,2,2,1,1] .empty .empty)) (.node [6,4,4,3,2,1,1,1,1,1] (.node [6,4,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [6,4,4,3,2,2,1,1,1] .empty .empty))) (.node [6,4,4,3,3,3,1] (.node [6,4,4,3,3,2,1,1] (.node [6,4,4,3,3,1,1,1,1] .empty .empty) (.node [6,4,4,3,3,2,2] .empty .empty)) (.node [6,4,4,4,2,1,1,1,1] (.node [6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty))) (.node [6,5,2,1,1,1,1,1,1,1,1,1,1,1] (.node [6,4,4,4,3,3] (.node [6,4,4,4,3,1,1,1] (.node [6,4,4,4,2,2,2] .empty .empty) (.node [6,4,4,4,3,2,1] .empty .empty)) (.node [6,4,4,4,4,2] (.node [6,4,4,4,4,1,1] .empty .empty) (.node [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [6,5,2,2,2,2,2,1,1,1] (.node [6,5,2,2,2,1,1,1,1,1,1,1] (.node [6,5,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,5,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [6,5,3,1,1,1,1,1,1,1,1,1,1] (.node [6,5,2,2,2,2,2,2,1] .empty .empty) .empty)))) + +def degreeTree24_5 : RowTree := (.node [6,4,4,2,1,1,1,1,1,1,1,1] degreeTree24_3 degreeTree24_4) + +def degreeTree24_6 : RowTree := (.node [6,3,3,3,3,2,1,1,1,1] degreeTree24_2 degreeTree24_5) + +def degreeTree24_7 : RowTree := (.node [6,5,4,2,2,2,1,1,1] (.node [6,5,3,3,2,2,2,1] (.node [6,5,3,2,2,2,2,2] (.node [6,5,3,2,2,2,1,1,1,1] (.node [6,5,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [6,5,3,2,2,2,2,1,1] .empty .empty)) (.node [6,5,3,3,2,1,1,1,1,1] (.node [6,5,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [6,5,3,3,2,2,1,1,1] .empty .empty))) (.node [6,5,3,3,3,3,1] (.node [6,5,3,3,3,2,1,1] (.node [6,5,3,3,3,1,1,1,1] .empty .empty) (.node [6,5,3,3,3,2,2] .empty .empty)) (.node [6,5,4,2,1,1,1,1,1,1,1] (.node [6,5,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,5,4,2,2,1,1,1,1,1] .empty .empty)))) (.node [6,5,4,3,3,3] (.node [6,5,4,3,2,2,1,1] (.node [6,5,4,3,1,1,1,1,1,1] (.node [6,5,4,2,2,2,2,1] .empty .empty) (.node [6,5,4,3,2,1,1,1,1] .empty .empty)) (.node [6,5,4,3,3,1,1,1] (.node [6,5,4,3,2,2,2] .empty .empty) (.node [6,5,4,3,3,2,1] .empty .empty))) (.node [6,5,4,4,3,1,1] (.node [6,5,4,4,2,1,1,1] (.node [6,5,4,4,1,1,1,1,1] .empty .empty) (.node [6,5,4,4,2,2,1] .empty .empty)) (.node [6,5,4,4,4,1] (.node [6,5,4,4,3,2] .empty .empty) .empty)))) + +def degreeTree24_8 : RowTree := (.node [6,6,2,1,1,1,1,1,1,1,1,1,1] (.node [6,5,5,3,3,1,1] (.node [6,5,5,2,2,2,2] (.node [6,5,5,2,2,1,1,1,1] (.node [6,5,5,2,1,1,1,1,1,1] .empty .empty) (.node [6,5,5,2,2,2,1,1] .empty .empty)) (.node [6,5,5,3,2,1,1,1] (.node [6,5,5,3,1,1,1,1,1] .empty .empty) (.node [6,5,5,3,2,2,1] .empty .empty))) (.node [6,5,5,4,2,2] (.node [6,5,5,4,1,1,1,1] (.node [6,5,5,3,3,2] .empty .empty) (.node [6,5,5,4,2,1,1] .empty .empty)) (.node [6,5,5,5,1,1,1] (.node [6,5,5,4,3,1] .empty .empty) (.node [6,6,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [6,6,3,2,2,1,1,1,1,1] (.node [6,6,2,2,2,2,2,1,1] (.node [6,6,2,2,2,1,1,1,1,1,1] (.node [6,6,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [6,6,2,2,2,2,1,1,1,1] .empty .empty)) (.node [6,6,3,1,1,1,1,1,1,1,1,1] (.node [6,6,2,2,2,2,2,2] .empty .empty) (.node [6,6,3,2,1,1,1,1,1,1,1] .empty .empty))) (.node [6,6,3,3,2,1,1,1,1] (.node [6,6,3,2,2,2,2,1] (.node [6,6,3,2,2,2,1,1,1] .empty .empty) (.node [6,6,3,3,1,1,1,1,1,1] .empty .empty)) (.node [6,6,3,3,2,2,2] (.node [6,6,3,3,2,2,1,1] .empty .empty) .empty)))) + +def degreeTree24_9 : RowTree := (.node [6,5,5,1,1,1,1,1,1,1,1] degreeTree24_7 degreeTree24_8) + +def degreeTree24_10 : RowTree := (.node [6,6,5,1,1,1,1,1,1,1] (.node [6,6,4,3,1,1,1,1,1] (.node [6,6,4,2,1,1,1,1,1,1] (.node [6,6,3,3,3,3] (.node [6,6,3,3,3,2,1] .empty .empty) (.node [6,6,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [6,6,4,2,2,2,1,1] (.node [6,6,4,2,2,1,1,1,1] .empty .empty) (.node [6,6,4,2,2,2,2] .empty .empty))) (.node [6,6,4,3,3,2] (.node [6,6,4,3,2,2,1] (.node [6,6,4,3,2,1,1,1] .empty .empty) (.node [6,6,4,3,3,1,1] .empty .empty)) (.node [6,6,4,4,2,1,1] (.node [6,6,4,4,1,1,1,1] .empty .empty) (.node [6,6,4,4,2,2] .empty .empty)))) (.node [6,6,6,2,1,1,1,1] (.node [6,6,5,3,1,1,1,1] (.node [6,6,5,2,2,1,1,1] (.node [6,6,5,2,1,1,1,1,1] .empty .empty) (.node [6,6,5,2,2,2,1] .empty .empty)) (.node [6,6,5,4,1,1,1] (.node [6,6,5,3,2,1,1] .empty .empty) (.node [6,6,6,1,1,1,1,1,1] .empty .empty))) (.node [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [6,6,6,3,1,1,1] (.node [6,6,6,2,2,1,1] .empty .empty) (.node [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree24_11 : RowTree := (.node [7,3,3,2,2,1,1,1,1,1,1,1] (.node [7,3,2,2,2,1,1,1,1,1,1,1,1] (.node [7,2,2,2,2,2,2,2,2,1] (.node [7,2,2,2,2,2,2,1,1,1,1,1] (.node [7,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [7,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,3,2,2,2,2,2,2,2] (.node [7,3,2,2,2,2,2,1,1,1,1] (.node [7,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [7,3,2,2,2,2,2,2,1,1] .empty .empty)) (.node [7,3,3,2,1,1,1,1,1,1,1,1,1] (.node [7,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [7,3,3,3,2,2,2,2] (.node [7,3,3,3,1,1,1,1,1,1,1,1] (.node [7,3,3,2,2,2,2,1,1,1] (.node [7,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [7,3,3,2,2,2,2,2,1] .empty .empty)) (.node [7,3,3,3,2,2,1,1,1,1] (.node [7,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [7,3,3,3,2,2,2,1,1] .empty .empty))) (.node [7,3,3,3,3,3,1,1] (.node [7,3,3,3,3,2,1,1,1] (.node [7,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [7,3,3,3,3,2,2,1] .empty .empty)) (.node [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,3,3,3,3,2] .empty .empty) .empty)))) + +def degreeTree24_12 : RowTree := (.node [7,2,2,2,2,1,1,1,1,1,1,1,1,1] degreeTree24_10 degreeTree24_11) + +def degreeTree24_13 : RowTree := (.node [6,6,3,3,3,1,1,1] degreeTree24_9 degreeTree24_12) + +def degreeTree24_14 : RowTree := (.node [6,5,3,2,1,1,1,1,1,1,1,1] degreeTree24_6 degreeTree24_13) + +def degreeTree24_15 : RowTree := (.node [7,4,3,3,3,1,1,1,1] (.node [7,4,3,2,2,1,1,1,1,1,1] (.node [7,4,2,2,2,2,2,1,1,1] (.node [7,4,2,2,2,1,1,1,1,1,1,1] (.node [7,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,4,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [7,4,3,1,1,1,1,1,1,1,1,1,1] (.node [7,4,2,2,2,2,2,2,1] .empty .empty) (.node [7,4,3,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,4,3,3,1,1,1,1,1,1,1] (.node [7,4,3,2,2,2,2,1,1] (.node [7,4,3,2,2,2,1,1,1,1] .empty .empty) (.node [7,4,3,2,2,2,2,2] .empty .empty)) (.node [7,4,3,3,2,2,1,1,1] (.node [7,4,3,3,2,1,1,1,1,1] .empty .empty) (.node [7,4,3,3,2,2,2,1] .empty .empty)))) (.node [7,4,4,2,2,2,2,1] (.node [7,4,4,1,1,1,1,1,1,1,1,1] (.node [7,4,3,3,3,2,2] (.node [7,4,3,3,3,2,1,1] .empty .empty) (.node [7,4,3,3,3,3,1] .empty .empty)) (.node [7,4,4,2,2,1,1,1,1,1] (.node [7,4,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [7,4,4,2,2,2,1,1,1] .empty .empty))) (.node [7,4,4,3,2,2,2] (.node [7,4,4,3,2,1,1,1,1] (.node [7,4,4,3,1,1,1,1,1,1] .empty .empty) (.node [7,4,4,3,2,2,1,1] .empty .empty)) (.node [7,4,4,3,3,2,1] (.node [7,4,4,3,3,1,1,1] .empty .empty) .empty)))) + +def degreeTree24_16 : RowTree := (.node [7,5,3,3,1,1,1,1,1,1] (.node [7,5,2,2,2,2,1,1,1,1] (.node [7,5,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,4,4,4,2,2,1] (.node [7,4,4,4,2,1,1,1] .empty .empty) (.node [7,4,4,4,3,1,1] .empty .empty)) (.node [7,5,2,2,1,1,1,1,1,1,1,1] (.node [7,5,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,5,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [7,5,3,2,1,1,1,1,1,1,1] (.node [7,5,2,2,2,2,2,2] (.node [7,5,2,2,2,2,2,1,1] .empty .empty) (.node [7,5,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,5,3,2,2,2,1,1,1] (.node [7,5,3,2,2,1,1,1,1,1] .empty .empty) (.node [7,5,3,2,2,2,2,1] .empty .empty)))) (.node [7,5,4,2,2,1,1,1,1] (.node [7,5,3,3,3,1,1,1] (.node [7,5,3,3,2,2,1,1] (.node [7,5,3,3,2,1,1,1,1] .empty .empty) (.node [7,5,3,3,2,2,2] .empty .empty)) (.node [7,5,4,1,1,1,1,1,1,1,1] (.node [7,5,3,3,3,2,1] .empty .empty) (.node [7,5,4,2,1,1,1,1,1,1] .empty .empty))) (.node [7,5,4,3,2,1,1,1] (.node [7,5,4,2,2,2,2] (.node [7,5,4,2,2,2,1,1] .empty .empty) (.node [7,5,4,3,1,1,1,1,1] .empty .empty)) (.node [7,5,4,3,3,1,1] (.node [7,5,4,3,2,2,1] .empty .empty) .empty)))) + +def degreeTree24_17 : RowTree := (.node [7,4,4,4,1,1,1,1,1] degreeTree24_15 degreeTree24_16) + +def degreeTree24_18 : RowTree := (.node [7,6,3,2,2,2,1,1] (.node [7,6,2,1,1,1,1,1,1,1,1,1] (.node [7,5,5,2,2,1,1,1] (.node [7,5,5,1,1,1,1,1,1,1] (.node [7,5,4,4,2,1,1] .empty .empty) (.node [7,5,5,2,1,1,1,1,1] .empty .empty)) (.node [7,5,5,3,1,1,1,1] (.node [7,5,5,2,2,2,1] .empty .empty) (.node [7,6,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,6,2,2,2,2,2,1] (.node [7,6,2,2,2,1,1,1,1,1] (.node [7,6,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [7,6,2,2,2,2,1,1,1] .empty .empty)) (.node [7,6,3,2,1,1,1,1,1,1] (.node [7,6,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,6,3,2,2,1,1,1,1] .empty .empty)))) (.node [7,6,4,3,1,1,1,1] (.node [7,6,3,3,2,2,1] (.node [7,6,3,3,1,1,1,1,1] (.node [7,6,3,2,2,2,2] .empty .empty) (.node [7,6,3,3,2,1,1,1] .empty .empty)) (.node [7,6,4,2,1,1,1,1,1] (.node [7,6,4,1,1,1,1,1,1,1] .empty .empty) (.node [7,6,4,2,2,1,1,1] .empty .empty))) (.node [7,7,1,1,1,1,1,1,1,1,1,1] (.node [7,6,5,2,1,1,1,1] (.node [7,6,5,1,1,1,1,1,1] .empty .empty) (.node [7,6,6,1,1,1,1,1] .empty .empty)) (.node [7,7,2,2,1,1,1,1,1,1] (.node [7,7,2,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree24_19 : RowTree := (.node [8,2,2,2,2,2,1,1,1,1,1,1] (.node [7,7,4,2,1,1,1,1] (.node [7,7,3,2,1,1,1,1,1] (.node [7,7,2,2,2,2,2] (.node [7,7,2,2,2,2,1,1] .empty .empty) (.node [7,7,3,1,1,1,1,1,1,1] .empty .empty)) (.node [7,7,3,3,1,1,1,1] (.node [7,7,3,2,2,1,1,1] .empty .empty) (.node [7,7,4,1,1,1,1,1,1] .empty .empty))) (.node [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,7,5,1,1,1,1,1] .empty .empty) (.node [8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,2,2,2,2,1,1,1,1,1,1,1,1] (.node [8,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [8,3,2,2,2,2,1,1,1,1,1] (.node [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,2,2,2,2,2,2,2,1,1] (.node [8,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [8,2,2,2,2,2,2,2,2] .empty .empty)) (.node [8,3,2,2,1,1,1,1,1,1,1,1,1] (.node [8,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,3,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [8,3,3,2,1,1,1,1,1,1,1,1] (.node [8,3,2,2,2,2,2,2,1] (.node [8,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [8,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,3,3,2,2,2,1,1,1,1] (.node [8,3,3,2,2,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree24_20 : RowTree := (.node [7,7,2,2,2,1,1,1,1] degreeTree24_18 degreeTree24_19) + +def degreeTree24_21 : RowTree := (.node [7,5,4,4,1,1,1,1] degreeTree24_17 degreeTree24_20) + +def degreeTree24_22 : RowTree := (.node [8,4,3,2,1,1,1,1,1,1,1] (.node [8,4,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,3,3,3,2,2,1,1,1] (.node [8,3,3,3,1,1,1,1,1,1,1] (.node [8,3,3,2,2,2,2,2] .empty .empty) (.node [8,3,3,3,2,1,1,1,1,1] .empty .empty)) (.node [8,3,3,3,3,1,1,1,1] (.node [8,3,3,3,2,2,2,1] .empty .empty) (.node [8,3,3,3,3,2,1,1] .empty .empty))) (.node [8,4,2,2,2,2,1,1,1,1] (.node [8,4,2,2,1,1,1,1,1,1,1,1] (.node [8,4,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,4,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [8,4,2,2,2,2,2,2] (.node [8,4,2,2,2,2,2,1,1] .empty .empty) (.node [8,4,3,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,4,4,1,1,1,1,1,1,1,1] (.node [8,4,3,3,1,1,1,1,1,1] (.node [8,4,3,2,2,2,1,1,1] (.node [8,4,3,2,2,1,1,1,1,1] .empty .empty) (.node [8,4,3,2,2,2,2,1] .empty .empty)) (.node [8,4,3,3,2,2,1,1] (.node [8,4,3,3,2,1,1,1,1] .empty .empty) (.node [8,4,3,3,3,1,1,1] .empty .empty))) (.node [8,4,4,3,1,1,1,1,1] (.node [8,4,4,2,2,1,1,1,1] (.node [8,4,4,2,1,1,1,1,1,1] .empty .empty) (.node [8,4,4,2,2,2,1,1] .empty .empty)) (.node [8,4,4,4,1,1,1,1] (.node [8,4,4,3,2,1,1,1] .empty .empty) .empty)))) + +def degreeTree24_23 : RowTree := (.node [8,6,1,1,1,1,1,1,1,1,1,1] (.node [8,5,3,2,2,1,1,1,1] (.node [8,5,2,2,2,2,1,1,1] (.node [8,5,2,2,1,1,1,1,1,1,1] (.node [8,5,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,5,2,2,2,1,1,1,1,1] .empty .empty)) (.node [8,5,3,1,1,1,1,1,1,1,1] (.node [8,5,2,2,2,2,2,1] .empty .empty) (.node [8,5,3,2,1,1,1,1,1,1] .empty .empty))) (.node [8,5,4,1,1,1,1,1,1,1] (.node [8,5,3,3,1,1,1,1,1] (.node [8,5,3,2,2,2,1,1] .empty .empty) (.node [8,5,3,3,2,1,1,1] .empty .empty)) (.node [8,5,5,1,1,1,1,1,1] (.node [8,5,4,2,1,1,1,1,1] .empty .empty) .empty))) (.node [8,7,1,1,1,1,1,1,1,1,1] (.node [8,6,2,2,2,2,1,1] (.node [8,6,2,2,1,1,1,1,1,1] (.node [8,6,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,6,2,2,2,1,1,1,1] .empty .empty)) (.node [8,6,3,2,1,1,1,1,1] (.node [8,6,3,1,1,1,1,1,1,1] .empty .empty) (.node [8,6,4,1,1,1,1,1,1] .empty .empty))) (.node [8,8,1,1,1,1,1,1,1,1] (.node [8,7,2,2,1,1,1,1,1] (.node [8,7,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,3,1,1,1,1,1,1] .empty .empty)) (.node [9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,2,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree24_24 : RowTree := (.node [8,5,1,1,1,1,1,1,1,1,1,1,1] degreeTree24_22 degreeTree24_23) + +def degreeTree24_25 : RowTree := (.node [9,3,3,2,2,2,1,1,1] (.node [9,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,2,2,2,2,2,1,1,1,1,1] (.node [9,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,2,2,2,2,2,2,2,1] (.node [9,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,3,2,2,2,2,2,1,1] (.node [9,3,2,2,2,1,1,1,1,1,1] (.node [9,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [9,3,3,2,1,1,1,1,1,1,1] (.node [9,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,3,3,2,2,1,1,1,1,1] .empty .empty)))) (.node [9,4,3,1,1,1,1,1,1,1,1] (.node [9,4,2,1,1,1,1,1,1,1,1,1] (.node [9,3,3,3,2,1,1,1,1] (.node [9,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,4,2,2,2,1,1,1,1,1] (.node [9,4,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,4,2,2,2,2,1,1,1] .empty .empty))) (.node [9,4,4,1,1,1,1,1,1,1] (.node [9,4,3,2,2,1,1,1,1] (.node [9,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [9,4,3,3,1,1,1,1,1] .empty .empty)) (.node [9,5,2,1,1,1,1,1,1,1,1] (.node [9,5,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree24_26 : RowTree := (.node [10,3,2,2,2,1,1,1,1,1] (.node [10,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,6,2,1,1,1,1,1,1,1] (.node [9,5,3,1,1,1,1,1,1,1] (.node [9,5,2,2,2,1,1,1,1] .empty .empty) (.node [9,6,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,2,2,2,2,1,1,1,1,1,1] (.node [10,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,3,2,2,1,1,1,1,1,1,1] (.node [10,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [11,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,2,1,1,1,1,1,1,1,1] (.node [10,3,3,2,1,1,1,1,1,1] (.node [10,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,1,1,1,1,1,1,1,1,1] (.node [10,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [11,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [11,3,2,1,1,1,1,1,1,1,1] (.node [11,2,2,2,1,1,1,1,1,1,1] (.node [11,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,2,1,1,1,1,1,1,1,1,1,1] (.node [12,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree24_27 : RowTree := (.node [9,5,2,2,1,1,1,1,1,1] degreeTree24_25 degreeTree24_26) + +def degreeTree24_28 : RowTree := (.node [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree24_24 degreeTree24_27) + +def degreeTree24_29 : RowTree := (.node [8,3,3,2,2,2,2,1,1] degreeTree24_21 degreeTree24_28) + +def degreeTree24_30 : RowTree := (.node [7,4,2,1,1,1,1,1,1,1,1,1,1,1] degreeTree24_14 degreeTree24_29) + +def degreeTree24 : RowTree := degreeTree24_30 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData26.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData26.lean index cc511a709ffc1ff66e43ef2bb3a1ddc4ef5b0686..1c76191d0558f831c039086f5134d838cbb2b726 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData26.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData26.lean @@ -1,147 +1,147 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 26. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree26_0 : RowTree := (.node [7,2,2,2,2,2,2,2,2,1,1,1] (.node [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [7,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [7,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_1 : RowTree := (.node [7,3,3,2,2,2,2,2,2,1] (.node [7,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,2,2,2,2,2,2,2,2] (.node [7,3,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [7,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,3,3,2,2,2,2,1,1,1,1,1] (.node [7,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [7,3,3,2,2,2,2,2,1,1,1] .empty .empty))) (.node [7,3,3,3,2,2,2,1,1,1,1] (.node [7,3,3,3,2,1,1,1,1,1,1,1,1] (.node [7,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,3,3,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [7,3,3,3,2,2,2,2,2] (.node [7,3,3,3,2,2,2,2,1,1] .empty .empty) (.node [7,3,3,3,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_2 : RowTree := (.node [7,3,2,2,2,2,2,2,1,1,1,1] degreeTree26_0 degreeTree26_1) - -def degreeTree26_3 : RowTree := (.node [7,4,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,3,3,3,3,2,2] (.node [7,3,3,3,3,3,1,1,1,1] (.node [7,3,3,3,3,2,2,2,1] (.node [7,3,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [7,3,3,3,3,3,2,1,1] .empty .empty)) (.node [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,3,3,3,3,3,1] .empty .empty) (.node [7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,4,2,2,2,2,2,2,1,1,1] (.node [7,4,2,2,2,2,1,1,1,1,1,1,1] (.node [7,4,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,4,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [7,4,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,4,2,2,2,2,2,2,2,1] .empty .empty) (.node [7,4,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_4 : RowTree := (.node [7,4,3,3,2,2,2,1,1,1] (.node [7,4,3,2,2,2,2,2,2] (.node [7,4,3,2,2,2,2,1,1,1,1] (.node [7,4,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [7,4,3,2,2,2,2,2,1,1] .empty .empty)) (.node [7,4,3,3,2,1,1,1,1,1,1,1] (.node [7,4,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,4,3,3,2,2,1,1,1,1,1] .empty .empty))) (.node [7,4,3,3,3,2,2,1,1] (.node [7,4,3,3,3,1,1,1,1,1,1] (.node [7,4,3,3,2,2,2,2,1] .empty .empty) (.node [7,4,3,3,3,2,1,1,1,1] .empty .empty)) (.node [7,4,3,3,3,3,1,1,1] (.node [7,4,3,3,3,2,2,2] .empty .empty) (.node [7,4,3,3,3,3,2,1] .empty .empty)))) - -def degreeTree26_5 : RowTree := (.node [7,4,3,2,2,1,1,1,1,1,1,1,1] degreeTree26_3 degreeTree26_4) - -def degreeTree26_6 : RowTree := (.node [7,3,3,3,3,2,1,1,1,1,1] degreeTree26_2 degreeTree26_5) - -def degreeTree26_7 : RowTree := (.node [7,4,4,3,2,2,1,1,1,1] (.node [7,4,4,2,2,2,2,1,1,1] (.node [7,4,4,2,2,1,1,1,1,1,1,1] (.node [7,4,4,2,1,1,1,1,1,1,1,1,1] (.node [7,4,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [7,4,4,2,2,2,1,1,1,1,1] .empty .empty)) (.node [7,4,4,3,1,1,1,1,1,1,1,1] (.node [7,4,4,2,2,2,2,2,1] .empty .empty) (.node [7,4,4,3,2,1,1,1,1,1,1] .empty .empty))) (.node [7,4,4,3,3,2,1,1,1] (.node [7,4,4,3,2,2,2,2] (.node [7,4,4,3,2,2,2,1,1] .empty .empty) (.node [7,4,4,3,3,1,1,1,1,1] .empty .empty)) (.node [7,4,4,3,3,3,1,1] (.node [7,4,4,3,3,2,2,1] .empty .empty) (.node [7,4,4,3,3,3,2] .empty .empty)))) - -def degreeTree26_8 : RowTree := (.node [7,4,4,4,4,1,1,1] (.node [7,4,4,4,3,1,1,1,1] (.node [7,4,4,4,2,2,1,1,1] (.node [7,4,4,4,2,1,1,1,1,1] .empty .empty) (.node [7,4,4,4,2,2,2,1] .empty .empty)) (.node [7,4,4,4,3,2,2] (.node [7,4,4,4,3,2,1,1] .empty .empty) (.node [7,4,4,4,3,3,1] .empty .empty))) (.node [7,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,4,4,4,4,2,1] .empty .empty) (.node [7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,5,2,2,2,2,1,1,1,1,1,1] (.node [7,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,5,2,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree26_9 : RowTree := (.node [7,4,4,4,1,1,1,1,1,1,1] degreeTree26_7 degreeTree26_8) - -def degreeTree26_10 : RowTree := (.node [7,5,3,3,2,1,1,1,1,1,1] (.node [7,5,3,2,2,2,1,1,1,1,1] (.node [7,5,3,2,1,1,1,1,1,1,1,1,1] (.node [7,5,3,1,1,1,1,1,1,1,1,1,1,1] (.node [7,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [7,5,3,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [7,5,3,2,2,2,2,2,1] (.node [7,5,3,2,2,2,2,1,1,1] .empty .empty) (.node [7,5,3,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,5,3,3,3,1,1,1,1,1] (.node [7,5,3,3,2,2,2,1,1] (.node [7,5,3,3,2,2,1,1,1,1] .empty .empty) (.node [7,5,3,3,2,2,2,2] .empty .empty)) (.node [7,5,3,3,3,2,2,1] (.node [7,5,3,3,3,2,1,1,1] .empty .empty) (.node [7,5,3,3,3,3,1,1] .empty .empty)))) - -def degreeTree26_11 : RowTree := (.node [7,5,4,3,2,1,1,1,1,1] (.node [7,5,4,2,2,2,1,1,1,1] (.node [7,5,4,2,1,1,1,1,1,1,1,1] (.node [7,5,4,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,5,4,2,2,1,1,1,1,1,1] .empty .empty)) (.node [7,5,4,2,2,2,2,2] (.node [7,5,4,2,2,2,2,1,1] .empty .empty) (.node [7,5,4,3,1,1,1,1,1,1,1] .empty .empty))) (.node [7,5,4,3,3,2,1,1] (.node [7,5,4,3,2,2,2,1] (.node [7,5,4,3,2,2,1,1,1] .empty .empty) (.node [7,5,4,3,3,1,1,1,1] .empty .empty)) (.node [7,5,4,3,3,3,1] (.node [7,5,4,3,3,2,2] .empty .empty) (.node [7,5,4,4,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_12 : RowTree := (.node [7,5,3,3,3,3,2] degreeTree26_10 degreeTree26_11) - -def degreeTree26_13 : RowTree := (.node [7,5,2,2,2,2,2,2,1,1] degreeTree26_9 degreeTree26_12) - -def degreeTree26_14 : RowTree := (.node [7,4,3,3,3,3,3] degreeTree26_6 degreeTree26_13) - -def degreeTree26_15 : RowTree := (.node [7,5,5,2,2,2,1,1,1] (.node [7,5,4,4,4,1,1] (.node [7,5,4,4,3,1,1,1] (.node [7,5,4,4,2,2,2] (.node [7,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [7,5,4,4,3,2,1] .empty .empty)) (.node [7,5,5,2,1,1,1,1,1,1,1] (.node [7,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,5,5,2,2,1,1,1,1,1] .empty .empty))) (.node [7,5,5,3,2,2,1,1] (.node [7,5,5,3,1,1,1,1,1,1] (.node [7,5,5,2,2,2,2,1] .empty .empty) (.node [7,5,5,3,2,1,1,1,1] .empty .empty)) (.node [7,5,5,3,3,1,1,1] (.node [7,5,5,3,2,2,2] .empty .empty) (.node [7,5,5,3,3,2,1] .empty .empty)))) - -def degreeTree26_16 : RowTree := (.node [7,6,2,2,2,1,1,1,1,1,1,1] (.node [7,5,5,5,1,1,1,1] (.node [7,5,5,4,2,2,1] (.node [7,5,5,4,2,1,1,1] .empty .empty) (.node [7,5,5,4,3,1,1] .empty .empty)) (.node [7,6,2,1,1,1,1,1,1,1,1,1,1,1] (.node [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,6,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,6,3,1,1,1,1,1,1,1,1,1,1] (.node [7,6,2,2,2,2,2,1,1,1] (.node [7,6,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [7,6,2,2,2,2,2,2,1] .empty .empty)) (.node [7,6,3,2,2,1,1,1,1,1,1] (.node [7,6,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,6,3,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree26_17 : RowTree := (.node [7,5,5,4,1,1,1,1,1] degreeTree26_15 degreeTree26_16) - -def degreeTree26_18 : RowTree := (.node [7,6,3,3,3,3,1] (.node [7,6,3,3,2,2,2,1] (.node [7,6,3,3,2,1,1,1,1,1] (.node [7,6,3,3,1,1,1,1,1,1,1] (.node [7,6,3,2,2,2,2,2] .empty .empty) .empty) (.node [7,6,3,3,2,2,1,1,1] .empty .empty)) (.node [7,6,3,3,3,2,1,1] (.node [7,6,3,3,3,1,1,1,1] .empty .empty) (.node [7,6,3,3,3,2,2] .empty .empty))) (.node [7,6,4,2,2,2,1,1,1] (.node [7,6,4,2,1,1,1,1,1,1,1] (.node [7,6,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,6,4,2,2,1,1,1,1,1] .empty .empty)) (.node [7,6,4,3,1,1,1,1,1,1] (.node [7,6,4,2,2,2,2,1] .empty .empty) (.node [7,6,4,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree26_19 : RowTree := (.node [7,6,5,2,1,1,1,1,1,1] (.node [7,6,4,4,1,1,1,1,1] (.node [7,6,4,3,3,1,1,1] (.node [7,6,4,3,2,2,2] .empty .empty) (.node [7,6,4,3,3,2,1] .empty .empty)) (.node [7,6,4,4,2,2,1] (.node [7,6,4,4,2,1,1,1] .empty .empty) (.node [7,6,5,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,6,5,3,1,1,1,1,1] (.node [7,6,5,2,2,2,1,1] (.node [7,6,5,2,2,1,1,1,1] .empty .empty) (.node [7,6,5,2,2,2,2] .empty .empty)) (.node [7,6,5,4,1,1,1,1] (.node [7,6,5,3,2,1,1,1] .empty .empty) (.node [7,6,6,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_20 : RowTree := (.node [7,6,4,3,2,2,1,1] degreeTree26_18 degreeTree26_19) - -def degreeTree26_21 : RowTree := (.node [7,6,3,2,2,2,2,1,1] degreeTree26_17 degreeTree26_20) - -def degreeTree26_22 : RowTree := (.node [7,7,2,2,2,2,2,2] (.node [7,7,2,2,1,1,1,1,1,1,1,1] (.node [7,7,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,6,6,3,1,1,1,1] (.node [7,6,6,2,2,1,1,1] .empty .empty) .empty) (.node [7,7,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,7,2,2,2,2,1,1,1,1] (.node [7,7,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [7,7,2,2,2,2,2,1,1] .empty .empty))) (.node [7,7,3,2,2,2,1,1,1] (.node [7,7,3,2,1,1,1,1,1,1,1] (.node [7,7,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,7,3,2,2,1,1,1,1,1] .empty .empty)) (.node [7,7,3,3,1,1,1,1,1,1] (.node [7,7,3,2,2,2,2,1] .empty .empty) (.node [7,7,3,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree26_23 : RowTree := (.node [7,7,4,3,2,1,1,1] (.node [7,7,4,2,1,1,1,1,1,1] (.node [7,7,3,3,3,1,1,1] (.node [7,7,3,3,2,2,2] .empty .empty) (.node [7,7,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,7,4,2,2,2,1,1] (.node [7,7,4,2,2,1,1,1,1] .empty .empty) (.node [7,7,4,3,1,1,1,1,1] .empty .empty))) (.node [7,7,5,2,2,1,1,1] (.node [7,7,5,1,1,1,1,1,1,1] (.node [7,7,4,4,1,1,1,1] .empty .empty) (.node [7,7,5,2,1,1,1,1,1] .empty .empty)) (.node [7,7,6,1,1,1,1,1,1] (.node [7,7,5,3,1,1,1,1] .empty .empty) (.node [7,7,6,2,1,1,1,1] .empty .empty)))) - -def degreeTree26_24 : RowTree := (.node [7,7,3,3,2,2,1,1] degreeTree26_22 degreeTree26_23) - -def degreeTree26_25 : RowTree := (.node [8,2,2,2,2,2,2,2,2,1,1] (.node [8,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,2,2,2,2,2,2,1,1,1,1,1,1] (.node [8,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [8,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,3,2,2,2,2,1,1,1,1,1,1,1] (.node [8,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_26 : RowTree := (.node [8,3,3,2,2,2,2,2,2] (.node [8,3,3,2,2,1,1,1,1,1,1,1,1] (.node [8,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [8,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,3,3,2,2,2,2,1,1,1,1] (.node [8,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [8,3,3,2,2,2,2,2,1,1] .empty .empty))) (.node [8,3,3,3,2,2,2,1,1,1] (.node [8,3,3,3,2,1,1,1,1,1,1,1] (.node [8,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,3,3,3,2,2,1,1,1,1,1] .empty .empty)) (.node [8,3,3,3,3,1,1,1,1,1,1] (.node [8,3,3,3,2,2,2,2,1] .empty .empty) (.node [8,3,3,3,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree26_27 : RowTree := (.node [8,3,2,2,2,2,2,2,1,1,1] degreeTree26_25 degreeTree26_26) - -def degreeTree26_28 : RowTree := (.node [7,7,7,1,1,1,1,1] degreeTree26_24 degreeTree26_27) - -def degreeTree26_29 : RowTree := (.node [7,6,6,2,1,1,1,1,1] degreeTree26_21 degreeTree26_28) - -def degreeTree26_30 : RowTree := (.node [7,5,4,4,2,1,1,1,1] degreeTree26_14 degreeTree26_29) - -def degreeTree26_31 : RowTree := (.node [8,4,2,2,2,2,2,1,1,1,1] (.node [8,4,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,3,3,3,3,3,2,1] (.node [8,3,3,3,3,3,1,1,1] (.node [8,3,3,3,3,2,2,2] .empty .empty) .empty) (.node [8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,4,2,2,2,1,1,1,1,1,1,1,1] (.node [8,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,4,2,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [8,4,3,2,1,1,1,1,1,1,1,1,1] (.node [8,4,2,2,2,2,2,2,2] (.node [8,4,2,2,2,2,2,2,1,1] .empty .empty) (.node [8,4,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,4,3,2,2,2,1,1,1,1,1] (.node [8,4,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,4,3,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree26_32 : RowTree := (.node [8,4,3,3,3,2,2,1] (.node [8,4,3,3,2,2,2,1,1] (.node [8,4,3,3,2,1,1,1,1,1,1] (.node [8,4,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,4,3,3,2,2,1,1,1,1] .empty .empty)) (.node [8,4,3,3,3,1,1,1,1,1] (.node [8,4,3,3,2,2,2,2] .empty .empty) (.node [8,4,3,3,3,2,1,1,1] .empty .empty))) (.node [8,4,4,2,2,1,1,1,1,1,1] (.node [8,4,4,1,1,1,1,1,1,1,1,1,1] (.node [8,4,3,3,3,3,1,1] .empty .empty) (.node [8,4,4,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,4,4,2,2,2,2,1,1] (.node [8,4,4,2,2,2,1,1,1,1] .empty .empty) (.node [8,4,4,2,2,2,2,2] .empty .empty)))) - -def degreeTree26_33 : RowTree := (.node [8,4,3,2,2,2,2,2,1] degreeTree26_31 degreeTree26_32) - -def degreeTree26_34 : RowTree := (.node [8,4,4,4,3,1,1,1] (.node [8,4,4,3,3,2,1,1] (.node [8,4,4,3,2,2,2,1] (.node [8,4,4,3,2,2,1,1,1] (.node [8,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [8,4,4,3,3,1,1,1,1] .empty .empty)) (.node [8,4,4,4,2,1,1,1,1] (.node [8,4,4,4,1,1,1,1,1,1] .empty .empty) (.node [8,4,4,4,2,2,1,1] .empty .empty))) (.node [8,5,2,2,2,1,1,1,1,1,1,1] (.node [8,5,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,5,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,5,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,5,2,2,2,2,2,1,1,1] (.node [8,5,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [8,5,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree26_35 : RowTree := (.node [8,5,3,3,2,2,1,1,1] (.node [8,5,3,2,2,2,2,1,1] (.node [8,5,3,2,2,1,1,1,1,1,1] (.node [8,5,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,5,3,2,2,2,1,1,1,1] .empty .empty)) (.node [8,5,3,3,1,1,1,1,1,1,1] (.node [8,5,3,2,2,2,2,2] .empty .empty) (.node [8,5,3,3,2,1,1,1,1,1] .empty .empty))) (.node [8,5,4,1,1,1,1,1,1,1,1,1] (.node [8,5,3,3,3,1,1,1,1] (.node [8,5,3,3,2,2,2,1] .empty .empty) (.node [8,5,3,3,3,2,1,1] .empty .empty)) (.node [8,5,4,2,2,1,1,1,1,1] (.node [8,5,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,5,4,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree26_36 : RowTree := (.node [8,5,3,1,1,1,1,1,1,1,1,1,1] degreeTree26_34 degreeTree26_35) - -def degreeTree26_37 : RowTree := (.node [8,4,4,3,1,1,1,1,1,1,1] degreeTree26_33 degreeTree26_36) - -def degreeTree26_38 : RowTree := (.node [8,5,5,2,2,1,1,1,1] (.node [8,5,4,4,1,1,1,1,1] (.node [8,5,4,3,2,2,1,1] (.node [8,5,4,3,2,1,1,1,1] (.node [8,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,5,4,3,3,1,1,1] .empty .empty)) (.node [8,5,5,1,1,1,1,1,1,1,1] (.node [8,5,4,4,2,1,1,1] .empty .empty) (.node [8,5,5,2,1,1,1,1,1,1] .empty .empty))) (.node [8,6,2,1,1,1,1,1,1,1,1,1,1] (.node [8,5,5,3,1,1,1,1,1] (.node [8,5,5,2,2,2,1,1] .empty .empty) (.node [8,6,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,6,2,2,2,1,1,1,1,1,1] (.node [8,6,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,6,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree26_39 : RowTree := (.node [8,6,3,3,2,1,1,1,1] (.node [8,6,3,2,2,1,1,1,1,1] (.node [8,6,3,1,1,1,1,1,1,1,1,1] (.node [8,6,2,2,2,2,2,2] .empty .empty) (.node [8,6,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [8,6,3,2,2,2,2,1] (.node [8,6,3,2,2,2,1,1,1] .empty .empty) (.node [8,6,3,3,1,1,1,1,1,1] .empty .empty))) (.node [8,6,4,2,2,1,1,1,1] (.node [8,6,4,1,1,1,1,1,1,1,1] (.node [8,6,3,3,2,2,1,1] .empty .empty) (.node [8,6,4,2,1,1,1,1,1,1] .empty .empty)) (.node [8,6,5,1,1,1,1,1,1,1] (.node [8,6,4,3,1,1,1,1,1] .empty .empty) (.node [8,6,5,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_40 : RowTree := (.node [8,6,2,2,2,2,2,1,1] degreeTree26_38 degreeTree26_39) - -def degreeTree26_41 : RowTree := (.node [8,7,3,2,2,1,1,1,1] (.node [8,7,2,2,2,2,1,1,1] (.node [8,7,2,2,1,1,1,1,1,1,1] (.node [8,7,2,1,1,1,1,1,1,1,1,1] (.node [8,7,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,7,2,2,2,1,1,1,1,1] .empty .empty)) (.node [8,7,3,1,1,1,1,1,1,1,1] (.node [8,7,2,2,2,2,2,1] .empty .empty) (.node [8,7,3,2,1,1,1,1,1,1] .empty .empty))) (.node [8,7,5,1,1,1,1,1,1] (.node [8,7,4,1,1,1,1,1,1,1] (.node [8,7,3,3,1,1,1,1,1] .empty .empty) (.node [8,7,4,2,1,1,1,1,1] .empty .empty)) (.node [8,8,2,1,1,1,1,1,1,1,1] (.node [8,8,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_42 : RowTree := (.node [9,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,3,2,1,1,1,1,1] (.node [8,8,3,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,4,1,1,1,1,1,1] .empty .empty)) (.node [9,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,2,2,2,2,2,2,2,2,1] (.node [9,2,2,2,2,2,2,1,1,1,1,1] (.node [9,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_43 : RowTree := (.node [8,8,2,2,2,1,1,1,1] degreeTree26_41 degreeTree26_42) - -def degreeTree26_44 : RowTree := (.node [8,6,6,1,1,1,1,1,1] degreeTree26_40 degreeTree26_43) - -def degreeTree26_45 : RowTree := (.node [8,5,4,2,2,2,2,1] degreeTree26_37 degreeTree26_44) - -def degreeTree26_46 : RowTree := (.node [9,3,3,2,2,2,2,1,1,1] (.node [9,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [9,3,2,2,2,2,2,2,1,1] (.node [9,3,2,2,2,2,2,1,1,1,1] (.node [9,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,3,2,2,2,2,2,2,2] .empty .empty)) (.node [9,3,3,2,2,1,1,1,1,1,1,1] (.node [9,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,3,3,2,2,2,1,1,1,1,1] .empty .empty))) (.node [9,3,3,3,2,2,1,1,1,1] (.node [9,3,3,3,1,1,1,1,1,1,1,1] (.node [9,3,3,2,2,2,2,2,1] .empty .empty) (.node [9,3,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [9,3,3,3,3,1,1,1,1,1] (.node [9,3,3,3,2,2,2,1,1] .empty .empty) (.node [9,3,3,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree26_47 : RowTree := (.node [9,4,3,2,1,1,1,1,1,1,1,1] (.node [9,4,2,2,2,2,1,1,1,1,1] (.node [9,4,2,2,1,1,1,1,1,1,1,1,1] (.node [9,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,4,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,4,2,2,2,2,2,2,1] (.node [9,4,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,4,3,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,4,3,3,1,1,1,1,1,1,1] (.node [9,4,3,2,2,2,1,1,1,1] (.node [9,4,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,4,3,2,2,2,2,1,1] .empty .empty)) (.node [9,4,3,3,2,2,1,1,1] (.node [9,4,3,3,2,1,1,1,1,1] .empty .empty) (.node [9,4,3,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree26_48 : RowTree := (.node [9,4,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree26_46 degreeTree26_47) - -def degreeTree26_49 : RowTree := (.node [9,5,2,2,1,1,1,1,1,1,1,1] (.node [9,4,4,3,2,1,1,1,1] (.node [9,4,4,2,2,2,1,1,1] (.node [9,4,4,2,2,1,1,1,1,1] (.node [9,4,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,4,4,3,1,1,1,1,1,1] .empty .empty)) (.node [9,5,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,4,4,4,1,1,1,1,1] .empty .empty) (.node [9,5,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,5,3,1,1,1,1,1,1,1,1,1] (.node [9,5,2,2,2,2,1,1,1,1] (.node [9,5,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,5,2,2,2,2,2,1,1] .empty .empty)) (.node [9,5,3,2,2,1,1,1,1,1] (.node [9,5,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,5,3,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree26_50 : RowTree := (.node [9,6,2,2,2,1,1,1,1,1] (.node [9,5,5,1,1,1,1,1,1,1] (.node [9,5,4,1,1,1,1,1,1,1,1] (.node [9,5,3,3,2,1,1,1,1] .empty .empty) (.node [9,5,4,2,1,1,1,1,1,1] .empty .empty)) (.node [9,6,2,1,1,1,1,1,1,1,1,1] (.node [9,6,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,6,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,6,4,1,1,1,1,1,1,1] (.node [9,6,3,1,1,1,1,1,1,1,1] (.node [9,6,2,2,2,2,1,1,1] .empty .empty) (.node [9,6,3,2,1,1,1,1,1,1] .empty .empty)) (.node [9,7,2,1,1,1,1,1,1,1,1] (.node [9,7,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_51 : RowTree := (.node [9,5,3,3,1,1,1,1,1,1] degreeTree26_49 degreeTree26_50) - -def degreeTree26_52 : RowTree := (.node [9,4,4,1,1,1,1,1,1,1,1,1] degreeTree26_48 degreeTree26_51) - -def degreeTree26_53 : RowTree := (.node [10,2,2,2,2,2,1,1,1,1,1,1] (.node [10,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,1,1,1,1,1,1,1,1] (.node [9,8,2,1,1,1,1,1,1,1] (.node [9,8,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,2,2,2,2,2,2,2,1,1] (.node [10,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,3,2,2,2,1,1,1,1,1,1,1] (.node [10,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,2,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_54 : RowTree := (.node [10,4,2,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,2,2,2,1,1,1,1] (.node [10,3,3,2,1,1,1,1,1,1,1,1] (.node [10,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,2,1,1,1,1,1] (.node [10,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,3,1,1,1,1,1,1,1,1,1] (.node [10,4,2,2,2,1,1,1,1,1,1] (.node [10,4,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,4,3,2,2,1,1,1,1,1] (.node [10,4,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_55 : RowTree := (.node [10,3,2,2,2,2,2,1,1,1] degreeTree26_53 degreeTree26_54) - -def degreeTree26_56 : RowTree := (.node [11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,1,1,1,1,1,1,1,1] (.node [10,5,2,2,1,1,1,1,1,1,1] (.node [10,5,2,1,1,1,1,1,1,1,1,1] (.node [10,5,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,5,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,2,1,1,1,1,1,1,1,1] (.node [10,6,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [11,2,2,2,2,1,1,1,1,1,1,1] (.node [11,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [11,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [11,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_57 : RowTree := (.node [12,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,4,1,1,1,1,1,1,1,1,1,1,1] (.node [11,3,3,1,1,1,1,1,1,1,1,1] (.node [11,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [11,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [11,4,2,2,1,1,1,1,1,1,1] (.node [11,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,5,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [12,3,1,1,1,1,1,1,1,1,1,1,1] (.node [12,2,2,1,1,1,1,1,1,1,1,1,1] (.node [12,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [13,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree26_58 : RowTree := (.node [11,3,2,2,1,1,1,1,1,1,1,1] degreeTree26_56 degreeTree26_57) - -def degreeTree26_59 : RowTree := (.node [10,4,4,1,1,1,1,1,1,1,1] degreeTree26_55 degreeTree26_58) - -def degreeTree26_60 : RowTree := (.node [9,7,3,1,1,1,1,1,1,1] degreeTree26_52 degreeTree26_59) - -def degreeTree26_61 : RowTree := (.node [9,3,2,2,2,1,1,1,1,1,1,1,1] degreeTree26_45 degreeTree26_60) - -def degreeTree26_62 : RowTree := (.node [8,3,3,3,3,2,2,1,1] degreeTree26_30 degreeTree26_61) - -def degreeTree26 : RowTree := degreeTree26_62 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 26. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree26_0 : RowTree := (.node [7,2,2,2,2,2,2,2,2,1,1,1] (.node [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [7,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [7,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_1 : RowTree := (.node [7,3,3,2,2,2,2,2,2,1] (.node [7,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,2,2,2,2,2,2,2,2] (.node [7,3,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [7,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,3,3,2,2,2,2,1,1,1,1,1] (.node [7,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [7,3,3,2,2,2,2,2,1,1,1] .empty .empty))) (.node [7,3,3,3,2,2,2,1,1,1,1] (.node [7,3,3,3,2,1,1,1,1,1,1,1,1] (.node [7,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,3,3,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [7,3,3,3,2,2,2,2,2] (.node [7,3,3,3,2,2,2,2,1,1] .empty .empty) (.node [7,3,3,3,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_2 : RowTree := (.node [7,3,2,2,2,2,2,2,1,1,1,1] degreeTree26_0 degreeTree26_1) + +def degreeTree26_3 : RowTree := (.node [7,4,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,3,3,3,3,2,2] (.node [7,3,3,3,3,3,1,1,1,1] (.node [7,3,3,3,3,2,2,2,1] (.node [7,3,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [7,3,3,3,3,3,2,1,1] .empty .empty)) (.node [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,3,3,3,3,3,3,1] .empty .empty) (.node [7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,4,2,2,2,2,2,2,1,1,1] (.node [7,4,2,2,2,2,1,1,1,1,1,1,1] (.node [7,4,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,4,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [7,4,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,4,2,2,2,2,2,2,2,1] .empty .empty) (.node [7,4,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_4 : RowTree := (.node [7,4,3,3,2,2,2,1,1,1] (.node [7,4,3,2,2,2,2,2,2] (.node [7,4,3,2,2,2,2,1,1,1,1] (.node [7,4,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [7,4,3,2,2,2,2,2,1,1] .empty .empty)) (.node [7,4,3,3,2,1,1,1,1,1,1,1] (.node [7,4,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,4,3,3,2,2,1,1,1,1,1] .empty .empty))) (.node [7,4,3,3,3,2,2,1,1] (.node [7,4,3,3,3,1,1,1,1,1,1] (.node [7,4,3,3,2,2,2,2,1] .empty .empty) (.node [7,4,3,3,3,2,1,1,1,1] .empty .empty)) (.node [7,4,3,3,3,3,1,1,1] (.node [7,4,3,3,3,2,2,2] .empty .empty) (.node [7,4,3,3,3,3,2,1] .empty .empty)))) + +def degreeTree26_5 : RowTree := (.node [7,4,3,2,2,1,1,1,1,1,1,1,1] degreeTree26_3 degreeTree26_4) + +def degreeTree26_6 : RowTree := (.node [7,3,3,3,3,2,1,1,1,1,1] degreeTree26_2 degreeTree26_5) + +def degreeTree26_7 : RowTree := (.node [7,4,4,3,2,2,1,1,1,1] (.node [7,4,4,2,2,2,2,1,1,1] (.node [7,4,4,2,2,1,1,1,1,1,1,1] (.node [7,4,4,2,1,1,1,1,1,1,1,1,1] (.node [7,4,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [7,4,4,2,2,2,1,1,1,1,1] .empty .empty)) (.node [7,4,4,3,1,1,1,1,1,1,1,1] (.node [7,4,4,2,2,2,2,2,1] .empty .empty) (.node [7,4,4,3,2,1,1,1,1,1,1] .empty .empty))) (.node [7,4,4,3,3,2,1,1,1] (.node [7,4,4,3,2,2,2,2] (.node [7,4,4,3,2,2,2,1,1] .empty .empty) (.node [7,4,4,3,3,1,1,1,1,1] .empty .empty)) (.node [7,4,4,3,3,3,1,1] (.node [7,4,4,3,3,2,2,1] .empty .empty) (.node [7,4,4,3,3,3,2] .empty .empty)))) + +def degreeTree26_8 : RowTree := (.node [7,4,4,4,4,1,1,1] (.node [7,4,4,4,3,1,1,1,1] (.node [7,4,4,4,2,2,1,1,1] (.node [7,4,4,4,2,1,1,1,1,1] .empty .empty) (.node [7,4,4,4,2,2,2,1] .empty .empty)) (.node [7,4,4,4,3,2,2] (.node [7,4,4,4,3,2,1,1] .empty .empty) (.node [7,4,4,4,3,3,1] .empty .empty))) (.node [7,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,4,4,4,4,2,1] .empty .empty) (.node [7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,5,2,2,2,2,1,1,1,1,1,1] (.node [7,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,5,2,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree26_9 : RowTree := (.node [7,4,4,4,1,1,1,1,1,1,1] degreeTree26_7 degreeTree26_8) + +def degreeTree26_10 : RowTree := (.node [7,5,3,3,2,1,1,1,1,1,1] (.node [7,5,3,2,2,2,1,1,1,1,1] (.node [7,5,3,2,1,1,1,1,1,1,1,1,1] (.node [7,5,3,1,1,1,1,1,1,1,1,1,1,1] (.node [7,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [7,5,3,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [7,5,3,2,2,2,2,2,1] (.node [7,5,3,2,2,2,2,1,1,1] .empty .empty) (.node [7,5,3,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,5,3,3,3,1,1,1,1,1] (.node [7,5,3,3,2,2,2,1,1] (.node [7,5,3,3,2,2,1,1,1,1] .empty .empty) (.node [7,5,3,3,2,2,2,2] .empty .empty)) (.node [7,5,3,3,3,2,2,1] (.node [7,5,3,3,3,2,1,1,1] .empty .empty) (.node [7,5,3,3,3,3,1,1] .empty .empty)))) + +def degreeTree26_11 : RowTree := (.node [7,5,4,3,2,1,1,1,1,1] (.node [7,5,4,2,2,2,1,1,1,1] (.node [7,5,4,2,1,1,1,1,1,1,1,1] (.node [7,5,4,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,5,4,2,2,1,1,1,1,1,1] .empty .empty)) (.node [7,5,4,2,2,2,2,2] (.node [7,5,4,2,2,2,2,1,1] .empty .empty) (.node [7,5,4,3,1,1,1,1,1,1,1] .empty .empty))) (.node [7,5,4,3,3,2,1,1] (.node [7,5,4,3,2,2,2,1] (.node [7,5,4,3,2,2,1,1,1] .empty .empty) (.node [7,5,4,3,3,1,1,1,1] .empty .empty)) (.node [7,5,4,3,3,3,1] (.node [7,5,4,3,3,2,2] .empty .empty) (.node [7,5,4,4,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_12 : RowTree := (.node [7,5,3,3,3,3,2] degreeTree26_10 degreeTree26_11) + +def degreeTree26_13 : RowTree := (.node [7,5,2,2,2,2,2,2,1,1] degreeTree26_9 degreeTree26_12) + +def degreeTree26_14 : RowTree := (.node [7,4,3,3,3,3,3] degreeTree26_6 degreeTree26_13) + +def degreeTree26_15 : RowTree := (.node [7,5,5,2,2,2,1,1,1] (.node [7,5,4,4,4,1,1] (.node [7,5,4,4,3,1,1,1] (.node [7,5,4,4,2,2,2] (.node [7,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [7,5,4,4,3,2,1] .empty .empty)) (.node [7,5,5,2,1,1,1,1,1,1,1] (.node [7,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,5,5,2,2,1,1,1,1,1] .empty .empty))) (.node [7,5,5,3,2,2,1,1] (.node [7,5,5,3,1,1,1,1,1,1] (.node [7,5,5,2,2,2,2,1] .empty .empty) (.node [7,5,5,3,2,1,1,1,1] .empty .empty)) (.node [7,5,5,3,3,1,1,1] (.node [7,5,5,3,2,2,2] .empty .empty) (.node [7,5,5,3,3,2,1] .empty .empty)))) + +def degreeTree26_16 : RowTree := (.node [7,6,2,2,2,1,1,1,1,1,1,1] (.node [7,5,5,5,1,1,1,1] (.node [7,5,5,4,2,2,1] (.node [7,5,5,4,2,1,1,1] .empty .empty) (.node [7,5,5,4,3,1,1] .empty .empty)) (.node [7,6,2,1,1,1,1,1,1,1,1,1,1,1] (.node [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,6,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,6,3,1,1,1,1,1,1,1,1,1,1] (.node [7,6,2,2,2,2,2,1,1,1] (.node [7,6,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [7,6,2,2,2,2,2,2,1] .empty .empty)) (.node [7,6,3,2,2,1,1,1,1,1,1] (.node [7,6,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,6,3,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree26_17 : RowTree := (.node [7,5,5,4,1,1,1,1,1] degreeTree26_15 degreeTree26_16) + +def degreeTree26_18 : RowTree := (.node [7,6,3,3,3,3,1] (.node [7,6,3,3,2,2,2,1] (.node [7,6,3,3,2,1,1,1,1,1] (.node [7,6,3,3,1,1,1,1,1,1,1] (.node [7,6,3,2,2,2,2,2] .empty .empty) .empty) (.node [7,6,3,3,2,2,1,1,1] .empty .empty)) (.node [7,6,3,3,3,2,1,1] (.node [7,6,3,3,3,1,1,1,1] .empty .empty) (.node [7,6,3,3,3,2,2] .empty .empty))) (.node [7,6,4,2,2,2,1,1,1] (.node [7,6,4,2,1,1,1,1,1,1,1] (.node [7,6,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,6,4,2,2,1,1,1,1,1] .empty .empty)) (.node [7,6,4,3,1,1,1,1,1,1] (.node [7,6,4,2,2,2,2,1] .empty .empty) (.node [7,6,4,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree26_19 : RowTree := (.node [7,6,5,2,1,1,1,1,1,1] (.node [7,6,4,4,1,1,1,1,1] (.node [7,6,4,3,3,1,1,1] (.node [7,6,4,3,2,2,2] .empty .empty) (.node [7,6,4,3,3,2,1] .empty .empty)) (.node [7,6,4,4,2,2,1] (.node [7,6,4,4,2,1,1,1] .empty .empty) (.node [7,6,5,1,1,1,1,1,1,1,1] .empty .empty))) (.node [7,6,5,3,1,1,1,1,1] (.node [7,6,5,2,2,2,1,1] (.node [7,6,5,2,2,1,1,1,1] .empty .empty) (.node [7,6,5,2,2,2,2] .empty .empty)) (.node [7,6,5,4,1,1,1,1] (.node [7,6,5,3,2,1,1,1] .empty .empty) (.node [7,6,6,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_20 : RowTree := (.node [7,6,4,3,2,2,1,1] degreeTree26_18 degreeTree26_19) + +def degreeTree26_21 : RowTree := (.node [7,6,3,2,2,2,2,1,1] degreeTree26_17 degreeTree26_20) + +def degreeTree26_22 : RowTree := (.node [7,7,2,2,2,2,2,2] (.node [7,7,2,2,1,1,1,1,1,1,1,1] (.node [7,7,1,1,1,1,1,1,1,1,1,1,1,1] (.node [7,6,6,3,1,1,1,1] (.node [7,6,6,2,2,1,1,1] .empty .empty) .empty) (.node [7,7,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,7,2,2,2,2,1,1,1,1] (.node [7,7,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [7,7,2,2,2,2,2,1,1] .empty .empty))) (.node [7,7,3,2,2,2,1,1,1] (.node [7,7,3,2,1,1,1,1,1,1,1] (.node [7,7,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [7,7,3,2,2,1,1,1,1,1] .empty .empty)) (.node [7,7,3,3,1,1,1,1,1,1] (.node [7,7,3,2,2,2,2,1] .empty .empty) (.node [7,7,3,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree26_23 : RowTree := (.node [7,7,4,3,2,1,1,1] (.node [7,7,4,2,1,1,1,1,1,1] (.node [7,7,3,3,3,1,1,1] (.node [7,7,3,3,2,2,2] .empty .empty) (.node [7,7,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [7,7,4,2,2,2,1,1] (.node [7,7,4,2,2,1,1,1,1] .empty .empty) (.node [7,7,4,3,1,1,1,1,1] .empty .empty))) (.node [7,7,5,2,2,1,1,1] (.node [7,7,5,1,1,1,1,1,1,1] (.node [7,7,4,4,1,1,1,1] .empty .empty) (.node [7,7,5,2,1,1,1,1,1] .empty .empty)) (.node [7,7,6,1,1,1,1,1,1] (.node [7,7,5,3,1,1,1,1] .empty .empty) (.node [7,7,6,2,1,1,1,1] .empty .empty)))) + +def degreeTree26_24 : RowTree := (.node [7,7,3,3,2,2,1,1] degreeTree26_22 degreeTree26_23) + +def degreeTree26_25 : RowTree := (.node [8,2,2,2,2,2,2,2,2,1,1] (.node [8,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,2,2,2,2,2,2,1,1,1,1,1,1] (.node [8,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [8,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,3,2,2,2,2,1,1,1,1,1,1,1] (.node [8,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_26 : RowTree := (.node [8,3,3,2,2,2,2,2,2] (.node [8,3,3,2,2,1,1,1,1,1,1,1,1] (.node [8,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [8,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,3,3,2,2,2,2,1,1,1,1] (.node [8,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [8,3,3,2,2,2,2,2,1,1] .empty .empty))) (.node [8,3,3,3,2,2,2,1,1,1] (.node [8,3,3,3,2,1,1,1,1,1,1,1] (.node [8,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,3,3,3,2,2,1,1,1,1,1] .empty .empty)) (.node [8,3,3,3,3,1,1,1,1,1,1] (.node [8,3,3,3,2,2,2,2,1] .empty .empty) (.node [8,3,3,3,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree26_27 : RowTree := (.node [8,3,2,2,2,2,2,2,1,1,1] degreeTree26_25 degreeTree26_26) + +def degreeTree26_28 : RowTree := (.node [7,7,7,1,1,1,1,1] degreeTree26_24 degreeTree26_27) + +def degreeTree26_29 : RowTree := (.node [7,6,6,2,1,1,1,1,1] degreeTree26_21 degreeTree26_28) + +def degreeTree26_30 : RowTree := (.node [7,5,4,4,2,1,1,1,1] degreeTree26_14 degreeTree26_29) + +def degreeTree26_31 : RowTree := (.node [8,4,2,2,2,2,2,1,1,1,1] (.node [8,4,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,3,3,3,3,3,2,1] (.node [8,3,3,3,3,3,1,1,1] (.node [8,3,3,3,3,2,2,2] .empty .empty) .empty) (.node [8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,4,2,2,2,1,1,1,1,1,1,1,1] (.node [8,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,4,2,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [8,4,3,2,1,1,1,1,1,1,1,1,1] (.node [8,4,2,2,2,2,2,2,2] (.node [8,4,2,2,2,2,2,2,1,1] .empty .empty) (.node [8,4,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,4,3,2,2,2,1,1,1,1,1] (.node [8,4,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,4,3,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree26_32 : RowTree := (.node [8,4,3,3,3,2,2,1] (.node [8,4,3,3,2,2,2,1,1] (.node [8,4,3,3,2,1,1,1,1,1,1] (.node [8,4,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,4,3,3,2,2,1,1,1,1] .empty .empty)) (.node [8,4,3,3,3,1,1,1,1,1] (.node [8,4,3,3,2,2,2,2] .empty .empty) (.node [8,4,3,3,3,2,1,1,1] .empty .empty))) (.node [8,4,4,2,2,1,1,1,1,1,1] (.node [8,4,4,1,1,1,1,1,1,1,1,1,1] (.node [8,4,3,3,3,3,1,1] .empty .empty) (.node [8,4,4,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,4,4,2,2,2,2,1,1] (.node [8,4,4,2,2,2,1,1,1,1] .empty .empty) (.node [8,4,4,2,2,2,2,2] .empty .empty)))) + +def degreeTree26_33 : RowTree := (.node [8,4,3,2,2,2,2,2,1] degreeTree26_31 degreeTree26_32) + +def degreeTree26_34 : RowTree := (.node [8,4,4,4,3,1,1,1] (.node [8,4,4,3,3,2,1,1] (.node [8,4,4,3,2,2,2,1] (.node [8,4,4,3,2,2,1,1,1] (.node [8,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [8,4,4,3,3,1,1,1,1] .empty .empty)) (.node [8,4,4,4,2,1,1,1,1] (.node [8,4,4,4,1,1,1,1,1,1] .empty .empty) (.node [8,4,4,4,2,2,1,1] .empty .empty))) (.node [8,5,2,2,2,1,1,1,1,1,1,1] (.node [8,5,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,5,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,5,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,5,2,2,2,2,2,1,1,1] (.node [8,5,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [8,5,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree26_35 : RowTree := (.node [8,5,3,3,2,2,1,1,1] (.node [8,5,3,2,2,2,2,1,1] (.node [8,5,3,2,2,1,1,1,1,1,1] (.node [8,5,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,5,3,2,2,2,1,1,1,1] .empty .empty)) (.node [8,5,3,3,1,1,1,1,1,1,1] (.node [8,5,3,2,2,2,2,2] .empty .empty) (.node [8,5,3,3,2,1,1,1,1,1] .empty .empty))) (.node [8,5,4,1,1,1,1,1,1,1,1,1] (.node [8,5,3,3,3,1,1,1,1] (.node [8,5,3,3,2,2,2,1] .empty .empty) (.node [8,5,3,3,3,2,1,1] .empty .empty)) (.node [8,5,4,2,2,1,1,1,1,1] (.node [8,5,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,5,4,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree26_36 : RowTree := (.node [8,5,3,1,1,1,1,1,1,1,1,1,1] degreeTree26_34 degreeTree26_35) + +def degreeTree26_37 : RowTree := (.node [8,4,4,3,1,1,1,1,1,1,1] degreeTree26_33 degreeTree26_36) + +def degreeTree26_38 : RowTree := (.node [8,5,5,2,2,1,1,1,1] (.node [8,5,4,4,1,1,1,1,1] (.node [8,5,4,3,2,2,1,1] (.node [8,5,4,3,2,1,1,1,1] (.node [8,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,5,4,3,3,1,1,1] .empty .empty)) (.node [8,5,5,1,1,1,1,1,1,1,1] (.node [8,5,4,4,2,1,1,1] .empty .empty) (.node [8,5,5,2,1,1,1,1,1,1] .empty .empty))) (.node [8,6,2,1,1,1,1,1,1,1,1,1,1] (.node [8,5,5,3,1,1,1,1,1] (.node [8,5,5,2,2,2,1,1] .empty .empty) (.node [8,6,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,6,2,2,2,1,1,1,1,1,1] (.node [8,6,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,6,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree26_39 : RowTree := (.node [8,6,3,3,2,1,1,1,1] (.node [8,6,3,2,2,1,1,1,1,1] (.node [8,6,3,1,1,1,1,1,1,1,1,1] (.node [8,6,2,2,2,2,2,2] .empty .empty) (.node [8,6,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [8,6,3,2,2,2,2,1] (.node [8,6,3,2,2,2,1,1,1] .empty .empty) (.node [8,6,3,3,1,1,1,1,1,1] .empty .empty))) (.node [8,6,4,2,2,1,1,1,1] (.node [8,6,4,1,1,1,1,1,1,1,1] (.node [8,6,3,3,2,2,1,1] .empty .empty) (.node [8,6,4,2,1,1,1,1,1,1] .empty .empty)) (.node [8,6,5,1,1,1,1,1,1,1] (.node [8,6,4,3,1,1,1,1,1] .empty .empty) (.node [8,6,5,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_40 : RowTree := (.node [8,6,2,2,2,2,2,1,1] degreeTree26_38 degreeTree26_39) + +def degreeTree26_41 : RowTree := (.node [8,7,3,2,2,1,1,1,1] (.node [8,7,2,2,2,2,1,1,1] (.node [8,7,2,2,1,1,1,1,1,1,1] (.node [8,7,2,1,1,1,1,1,1,1,1,1] (.node [8,7,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,7,2,2,2,1,1,1,1,1] .empty .empty)) (.node [8,7,3,1,1,1,1,1,1,1,1] (.node [8,7,2,2,2,2,2,1] .empty .empty) (.node [8,7,3,2,1,1,1,1,1,1] .empty .empty))) (.node [8,7,5,1,1,1,1,1,1] (.node [8,7,4,1,1,1,1,1,1,1] (.node [8,7,3,3,1,1,1,1,1] .empty .empty) (.node [8,7,4,2,1,1,1,1,1] .empty .empty)) (.node [8,8,2,1,1,1,1,1,1,1,1] (.node [8,8,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_42 : RowTree := (.node [9,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,3,2,1,1,1,1,1] (.node [8,8,3,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,4,1,1,1,1,1,1] .empty .empty)) (.node [9,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,2,2,2,2,2,2,2,2,1] (.node [9,2,2,2,2,2,2,1,1,1,1,1] (.node [9,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_43 : RowTree := (.node [8,8,2,2,2,1,1,1,1] degreeTree26_41 degreeTree26_42) + +def degreeTree26_44 : RowTree := (.node [8,6,6,1,1,1,1,1,1] degreeTree26_40 degreeTree26_43) + +def degreeTree26_45 : RowTree := (.node [8,5,4,2,2,2,2,1] degreeTree26_37 degreeTree26_44) + +def degreeTree26_46 : RowTree := (.node [9,3,3,2,2,2,2,1,1,1] (.node [9,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [9,3,2,2,2,2,2,2,1,1] (.node [9,3,2,2,2,2,2,1,1,1,1] (.node [9,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,3,2,2,2,2,2,2,2] .empty .empty)) (.node [9,3,3,2,2,1,1,1,1,1,1,1] (.node [9,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,3,3,2,2,2,1,1,1,1,1] .empty .empty))) (.node [9,3,3,3,2,2,1,1,1,1] (.node [9,3,3,3,1,1,1,1,1,1,1,1] (.node [9,3,3,2,2,2,2,2,1] .empty .empty) (.node [9,3,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [9,3,3,3,3,1,1,1,1,1] (.node [9,3,3,3,2,2,2,1,1] .empty .empty) (.node [9,3,3,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree26_47 : RowTree := (.node [9,4,3,2,1,1,1,1,1,1,1,1] (.node [9,4,2,2,2,2,1,1,1,1,1] (.node [9,4,2,2,1,1,1,1,1,1,1,1,1] (.node [9,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,4,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,4,2,2,2,2,2,2,1] (.node [9,4,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,4,3,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,4,3,3,1,1,1,1,1,1,1] (.node [9,4,3,2,2,2,1,1,1,1] (.node [9,4,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,4,3,2,2,2,2,1,1] .empty .empty)) (.node [9,4,3,3,2,2,1,1,1] (.node [9,4,3,3,2,1,1,1,1,1] .empty .empty) (.node [9,4,3,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree26_48 : RowTree := (.node [9,4,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree26_46 degreeTree26_47) + +def degreeTree26_49 : RowTree := (.node [9,5,2,2,1,1,1,1,1,1,1,1] (.node [9,4,4,3,2,1,1,1,1] (.node [9,4,4,2,2,2,1,1,1] (.node [9,4,4,2,2,1,1,1,1,1] (.node [9,4,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,4,4,3,1,1,1,1,1,1] .empty .empty)) (.node [9,5,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,4,4,4,1,1,1,1,1] .empty .empty) (.node [9,5,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,5,3,1,1,1,1,1,1,1,1,1] (.node [9,5,2,2,2,2,1,1,1,1] (.node [9,5,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,5,2,2,2,2,2,1,1] .empty .empty)) (.node [9,5,3,2,2,1,1,1,1,1] (.node [9,5,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,5,3,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree26_50 : RowTree := (.node [9,6,2,2,2,1,1,1,1,1] (.node [9,5,5,1,1,1,1,1,1,1] (.node [9,5,4,1,1,1,1,1,1,1,1] (.node [9,5,3,3,2,1,1,1,1] .empty .empty) (.node [9,5,4,2,1,1,1,1,1,1] .empty .empty)) (.node [9,6,2,1,1,1,1,1,1,1,1,1] (.node [9,6,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,6,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,6,4,1,1,1,1,1,1,1] (.node [9,6,3,1,1,1,1,1,1,1,1] (.node [9,6,2,2,2,2,1,1,1] .empty .empty) (.node [9,6,3,2,1,1,1,1,1,1] .empty .empty)) (.node [9,7,2,1,1,1,1,1,1,1,1] (.node [9,7,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_51 : RowTree := (.node [9,5,3,3,1,1,1,1,1,1] degreeTree26_49 degreeTree26_50) + +def degreeTree26_52 : RowTree := (.node [9,4,4,1,1,1,1,1,1,1,1,1] degreeTree26_48 degreeTree26_51) + +def degreeTree26_53 : RowTree := (.node [10,2,2,2,2,2,1,1,1,1,1,1] (.node [10,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,1,1,1,1,1,1,1,1] (.node [9,8,2,1,1,1,1,1,1,1] (.node [9,8,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,2,2,2,2,2,2,2,1,1] (.node [10,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,3,2,2,2,1,1,1,1,1,1,1] (.node [10,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,2,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_54 : RowTree := (.node [10,4,2,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,2,2,2,1,1,1,1] (.node [10,3,3,2,1,1,1,1,1,1,1,1] (.node [10,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,2,1,1,1,1,1] (.node [10,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,3,1,1,1,1,1,1,1,1,1] (.node [10,4,2,2,2,1,1,1,1,1,1] (.node [10,4,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,4,3,2,2,1,1,1,1,1] (.node [10,4,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_55 : RowTree := (.node [10,3,2,2,2,2,2,1,1,1] degreeTree26_53 degreeTree26_54) + +def degreeTree26_56 : RowTree := (.node [11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,1,1,1,1,1,1,1,1] (.node [10,5,2,2,1,1,1,1,1,1,1] (.node [10,5,2,1,1,1,1,1,1,1,1,1] (.node [10,5,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,5,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,2,1,1,1,1,1,1,1,1] (.node [10,6,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [11,2,2,2,2,1,1,1,1,1,1,1] (.node [11,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [11,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [11,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_57 : RowTree := (.node [12,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,4,1,1,1,1,1,1,1,1,1,1,1] (.node [11,3,3,1,1,1,1,1,1,1,1,1] (.node [11,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [11,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [11,4,2,2,1,1,1,1,1,1,1] (.node [11,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,5,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [12,3,1,1,1,1,1,1,1,1,1,1,1] (.node [12,2,2,1,1,1,1,1,1,1,1,1,1] (.node [12,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [13,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree26_58 : RowTree := (.node [11,3,2,2,1,1,1,1,1,1,1,1] degreeTree26_56 degreeTree26_57) + +def degreeTree26_59 : RowTree := (.node [10,4,4,1,1,1,1,1,1,1,1] degreeTree26_55 degreeTree26_58) + +def degreeTree26_60 : RowTree := (.node [9,7,3,1,1,1,1,1,1,1] degreeTree26_52 degreeTree26_59) + +def degreeTree26_61 : RowTree := (.node [9,3,2,2,2,1,1,1,1,1,1,1,1] degreeTree26_45 degreeTree26_60) + +def degreeTree26_62 : RowTree := (.node [8,3,3,3,3,2,2,1,1] degreeTree26_30 degreeTree26_61) + +def degreeTree26 : RowTree := degreeTree26_62 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData31.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData31.lean index 57037fa5441d647000e2b585baa5dc0eeb2ba3df..86efdbfba03fb32b8a4e57ccb949aea1c2e156cc 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData31.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData31.lean @@ -1,27 +1,27 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 31. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree31_0 : RowTree := (.node [10,3,3,3,2,2,2,2,2,2] (.node [9,9,3,2,2,2,1,1,1,1] (.node [9,8,6,2,1,1,1,1,1,1] (.node [8,8,8,1,1,1,1,1,1,1] (.node [8,8,7,2,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,2,1,1,1,1,1,1] .empty .empty)) (.node [9,9,2,2,2,2,2,1,1,1] (.node [9,8,7,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [9,9,4,3,1,1,1,1,1,1] (.node [9,9,4,2,2,1,1,1,1,1] (.node [9,9,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [9,9,6,1,1,1,1,1,1,1] (.node [9,9,5,2,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,4,3,3,3,2,2,2,1,1] (.node [10,3,3,3,3,3,3,1,1,1] (.node [10,3,3,3,3,3,2,2,1,1] (.node [10,3,3,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [10,4,3,3,2,2,2,2,2,1] (.node [10,4,3,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [10,4,4,3,2,2,2,2,1,1] (.node [10,4,4,2,2,2,2,2,2,1] (.node [10,4,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [10,4,4,3,3,3,1,1,1,1] (.node [10,4,4,3,3,2,2,1,1,1] .empty .empty) .empty)))) - -def degreeTree31_1 : RowTree := (.node [10,5,4,4,3,1,1,1,1,1] (.node [10,5,3,3,3,2,2,1,1,1] (.node [10,5,2,2,2,2,2,2,2,2] (.node [10,4,4,4,4,1,1,1,1,1] (.node [10,4,4,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,5,3,3,2,2,2,2,1,1] (.node [10,5,3,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [10,5,4,3,2,2,2,1,1,1] (.node [10,5,4,2,2,2,2,2,1,1] (.node [10,5,3,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [10,5,4,4,2,2,1,1,1,1] (.node [10,5,4,3,3,2,1,1,1,1] .empty .empty) .empty))) (.node [10,6,3,3,2,2,2,1,1,1] (.node [10,5,5,3,3,1,1,1,1,1] (.node [10,5,5,3,2,2,1,1,1,1] (.node [10,5,5,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,6,3,2,2,2,2,2,1,1] (.node [10,6,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [10,6,4,3,2,2,1,1,1,1] (.node [10,6,4,2,2,2,2,1,1,1] (.node [10,6,3,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,7,3,2,2,2,2,1,1,1] (.node [10,7,2,2,2,2,2,2,1,1] .empty .empty) .empty)))) - -def degreeTree31_2 : RowTree := (.node [10,4,4,4,2,2,2,1,1,1] degreeTree31_0 degreeTree31_1) - -def degreeTree31 : RowTree := degreeTree31_2 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 31. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree31_0 : RowTree := (.node [10,3,3,3,2,2,2,2,2,2] (.node [9,9,3,2,2,2,1,1,1,1] (.node [9,8,6,2,1,1,1,1,1,1] (.node [8,8,8,1,1,1,1,1,1,1] (.node [8,8,7,2,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,2,1,1,1,1,1,1] .empty .empty)) (.node [9,9,2,2,2,2,2,1,1,1] (.node [9,8,7,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [9,9,4,3,1,1,1,1,1,1] (.node [9,9,4,2,2,1,1,1,1,1] (.node [9,9,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [9,9,6,1,1,1,1,1,1,1] (.node [9,9,5,2,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,4,3,3,3,2,2,2,1,1] (.node [10,3,3,3,3,3,3,1,1,1] (.node [10,3,3,3,3,3,2,2,1,1] (.node [10,3,3,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [10,4,3,3,2,2,2,2,2,1] (.node [10,4,3,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [10,4,4,3,2,2,2,2,1,1] (.node [10,4,4,2,2,2,2,2,2,1] (.node [10,4,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [10,4,4,3,3,3,1,1,1,1] (.node [10,4,4,3,3,2,2,1,1,1] .empty .empty) .empty)))) + +def degreeTree31_1 : RowTree := (.node [10,5,4,4,3,1,1,1,1,1] (.node [10,5,3,3,3,2,2,1,1,1] (.node [10,5,2,2,2,2,2,2,2,2] (.node [10,4,4,4,4,1,1,1,1,1] (.node [10,4,4,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,5,3,3,2,2,2,2,1,1] (.node [10,5,3,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [10,5,4,3,2,2,2,1,1,1] (.node [10,5,4,2,2,2,2,2,1,1] (.node [10,5,3,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [10,5,4,4,2,2,1,1,1,1] (.node [10,5,4,3,3,2,1,1,1,1] .empty .empty) .empty))) (.node [10,6,3,3,2,2,2,1,1,1] (.node [10,5,5,3,3,1,1,1,1,1] (.node [10,5,5,3,2,2,1,1,1,1] (.node [10,5,5,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,6,3,2,2,2,2,2,1,1] (.node [10,6,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [10,6,4,3,2,2,1,1,1,1] (.node [10,6,4,2,2,2,2,1,1,1] (.node [10,6,3,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,7,3,2,2,2,2,1,1,1] (.node [10,7,2,2,2,2,2,2,1,1] .empty .empty) .empty)))) + +def degreeTree31_2 : RowTree := (.node [10,4,4,4,2,2,2,1,1,1] degreeTree31_0 degreeTree31_1) + +def degreeTree31 : RowTree := degreeTree31_2 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData35.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData35.lean index 45e5f55609f733113b51507d1985295a5faf225f..9dc0701902716f5dfe4af126b3542f76ab494e85 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData35.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData35.lean @@ -1,71 +1,71 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 35. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree35_0 : RowTree := (.node [8,8,7,4,3,1,1,1,1,1] (.node [8,8,7,2,2,2,2,2,2] (.node [8,8,6,6,2,1,1,1,1,1] (.node [8,7,7,7,1,1,1,1,1,1] (.node [8,7,7,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [8,8,7,2,2,2,2,2,1,1] .empty .empty)) (.node [8,8,7,3,3,2,1,1,1,1] (.node [8,8,7,3,2,2,2,1,1,1] .empty .empty) (.node [8,8,7,4,2,2,1,1,1,1] .empty .empty))) (.node [8,8,8,3,2,2,1,1,1,1] (.node [8,8,7,6,1,1,1,1,1,1] (.node [8,8,7,5,2,1,1,1,1,1] .empty .empty) (.node [8,8,8,2,2,2,2,1,1,1] .empty .empty)) (.node [8,8,8,4,2,1,1,1,1,1] (.node [8,8,8,3,3,1,1,1,1,1] .empty .empty) (.node [8,8,8,5,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree35_1 : RowTree := (.node [9,7,7,6,1,1,1,1,1,1] (.node [9,7,7,3,3,2,1,1,1,1] (.node [9,7,7,2,2,2,2,2,2] (.node [9,7,7,2,2,2,2,2,1,1] .empty .empty) (.node [9,7,7,3,2,2,2,1,1,1] .empty .empty)) (.node [9,7,7,4,3,1,1,1,1,1] (.node [9,7,7,4,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,5,2,1,1,1,1,1] .empty .empty))) (.node [9,8,6,3,3,2,1,1,1,1] (.node [9,8,6,2,2,2,2,2,2] (.node [9,8,6,2,2,2,2,2,1,1] .empty .empty) (.node [9,8,6,3,2,2,2,1,1,1] .empty .empty)) (.node [9,8,6,4,3,1,1,1,1,1] (.node [9,8,6,4,2,2,1,1,1,1] .empty .empty) (.node [9,8,6,5,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree35_2 : RowTree := (.node [9,7,6,6,2,1,1,1,1,1] degreeTree35_0 degreeTree35_1) - -def degreeTree35_3 : RowTree := (.node [9,9,3,2,2,2,2,2,2,2] (.node [9,8,7,5,1,1,1,1,1,1] (.node [9,8,7,3,3,1,1,1,1,1] (.node [9,8,7,3,2,2,1,1,1,1] (.node [9,8,7,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [9,8,7,4,2,1,1,1,1,1] .empty .empty)) (.node [9,8,8,3,2,1,1,1,1,1] (.node [9,8,8,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,4,1,1,1,1,1,1] .empty .empty))) (.node [9,9,3,3,3,3,2,1,1,1] (.node [9,9,3,3,3,2,2,2,1,1] (.node [9,9,3,3,2,2,2,2,2,1] .empty .empty) (.node [9,9,3,3,3,2,2,2,2] .empty .empty)) (.node [9,9,4,3,2,2,2,2,1,1] (.node [9,9,4,2,2,2,2,2,2,1] .empty .empty) (.node [9,9,4,3,2,2,2,2,2] .empty .empty)))) - -def degreeTree35_4 : RowTree := (.node [9,9,5,4,2,2,1,1,1,1] (.node [9,9,4,4,4,1,1,1,1,1] (.node [9,9,4,4,2,2,2,1,1,1] (.node [9,9,4,3,3,3,1,1,1,1] .empty .empty) (.node [9,9,4,4,3,2,1,1,1,1] .empty .empty)) (.node [9,9,5,3,2,2,2,1,1,1] (.node [9,9,5,2,2,2,2,2,1,1] .empty .empty) (.node [9,9,5,3,3,2,1,1,1,1] .empty .empty))) (.node [9,9,6,3,2,2,1,1,1,1] (.node [9,9,5,5,2,1,1,1,1,1] (.node [9,9,5,4,3,1,1,1,1,1] .empty .empty) (.node [9,9,6,2,2,2,2,1,1,1] .empty .empty)) (.node [9,9,6,4,2,1,1,1,1,1] (.node [9,9,6,3,3,1,1,1,1,1] .empty .empty) (.node [9,9,6,5,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree35_5 : RowTree := (.node [9,9,4,3,3,2,2,1,1,1] degreeTree35_3 degreeTree35_4) - -def degreeTree35_6 : RowTree := (.node [9,8,6,6,1,1,1,1,1,1] degreeTree35_2 degreeTree35_5) - -def degreeTree35_7 : RowTree := (.node [10,3,2,2,2,2,2,2,2,2,2,2,1,1] (.node [9,9,9,2,1,1,1,1,1,1] (.node [9,9,8,2,2,1,1,1,1,1] (.node [9,9,7,4,1,1,1,1,1,1] (.node [9,9,7,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [9,9,8,3,1,1,1,1,1,1] .empty .empty)) (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,3,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,3,3,2,2,2,2,2,2,2,2,2,1] (.node [10,3,3,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,3,2,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,3,3,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,3,3,3,2,2,2,2,2,2,1,1,1,1] (.node [10,3,3,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,2,2,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree35_8 : RowTree := (.node [10,3,3,3,3,3,2,2,2,2,1,1] (.node [10,3,3,3,3,2,2,2,2,2,2,1] (.node [10,3,3,3,3,2,2,2,2,1,1,1,1,1] (.node [10,3,3,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,2,2,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,2,2,2,1,1,1,1] .empty .empty))) (.node [10,3,3,3,3,3,3,2,2,1,1,1] (.node [10,3,3,3,3,3,3,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,2,2,2,2] .empty .empty) (.node [10,3,3,3,3,3,3,2,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,3,1,1,1,1] (.node [10,3,3,3,3,3,3,2,2,2,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,2,1,1] .empty .empty)))) - -def degreeTree35_9 : RowTree := (.node [10,3,3,3,2,2,2,2,2,2,2,2] degreeTree35_7 degreeTree35_8) - -def degreeTree35_10 : RowTree := (.node [10,4,3,3,3,2,2,2,2,2,1,1] (.node [10,4,3,2,2,2,2,2,2,2,2,2] (.node [10,4,2,2,2,2,2,2,2,2,2,2,1] (.node [10,4,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,3,3,3,3,3,3,3,3,1] .empty .empty) (.node [10,4,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,4,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,4,3,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,2,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [10,4,3,3,2,2,2,2,2,2,2,1] (.node [10,4,3,3,2,2,2,2,2,1,1,1,1,1] (.node [10,4,3,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,4,3,3,3,2,2,2,1,1,1,1,1,1] (.node [10,4,3,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,2,2,2,2,1,1,1,1] .empty .empty)))) (.node [10,4,3,3,3,3,3,2,1,1,1,1] (.node [10,4,3,3,3,3,2,2,1,1,1,1,1] (.node [10,4,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,4,3,3,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,3,2,2,2,2,1] (.node [10,4,3,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,4,3,3,3,3,3,3,2,1] (.node [10,4,3,3,3,3,3,2,2,2] (.node [10,4,3,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,3,1,1,1] .empty .empty)) (.node [10,4,4,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,4,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,2,2,2,2,2,2,2,1,1,1] .empty .empty))))) - -def degreeTree35_11 : RowTree := (.node [10,3,3,3,3,3,3,3,2,2] degreeTree35_9 degreeTree35_10) - -def degreeTree35_12 : RowTree := (.node [9,9,7,2,2,2,1,1,1,1] degreeTree35_6 degreeTree35_11) - -def degreeTree35_13 : RowTree := (.node [10,4,4,3,3,2,2,2,2,1,1,1] (.node [10,4,4,3,2,2,2,2,2,2,2] (.node [10,4,4,3,2,2,2,2,2,1,1,1,1] (.node [10,4,4,3,2,2,2,2,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,4,4,3,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,4,4,3,3,2,2,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,4,4,3,3,3,2,2,1,1,1,1] (.node [10,4,4,3,3,3,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,2,2,2,2,1] .empty .empty) (.node [10,4,4,3,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,3,3,3,2,2,2,2] (.node [10,4,4,3,3,3,2,2,2,1,1] .empty .empty) (.node [10,4,4,3,3,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree35_14 : RowTree := (.node [10,4,4,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,2,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,3,3,1,1] (.node [10,4,4,3,3,3,3,2,2,1] .empty .empty) (.node [10,4,4,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,2,2,2,2,2,1,1,1] (.node [10,4,4,4,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,2,2,2,2,2,2,1] .empty .empty))) (.node [10,4,4,4,3,2,2,2,2,1,1] (.node [10,4,4,4,3,2,2,1,1,1,1,1,1] (.node [10,4,4,4,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,3,2,2,2,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,3,1,1,1,1,1,1,1] (.node [10,4,4,4,3,2,2,2,2,2] .empty .empty) (.node [10,4,4,4,3,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree35_15 : RowTree := (.node [10,4,4,3,3,3,3,2,1,1,1] degreeTree35_13 degreeTree35_14) - -def degreeTree35_16 : RowTree := (.node [10,5,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,4,4,4,4,2,2,2,2,1] (.node [10,4,4,4,4,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,1,1,1,1] (.node [10,4,4,4,3,3,2,2,2,1] .empty .empty) (.node [10,4,4,4,3,3,3,2,1,1] .empty .empty)) (.node [10,4,4,4,4,2,2,1,1,1,1,1] (.node [10,4,4,4,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,2,2,2,1,1,1] .empty .empty))) (.node [10,4,4,4,4,3,3,1,1,1] (.node [10,4,4,4,4,3,2,1,1,1,1] (.node [10,4,4,4,4,3,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,3,2,2,1,1] .empty .empty)) (.node [10,4,4,4,4,4,2,1,1,1] (.node [10,4,4,4,4,4,1,1,1,1,1] .empty .empty) (.node [10,5,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,4,3,3,3,3,2,1,1] (.node [10,5,3,3,3,3,3,2,2,1] (.node [10,5,2,2,2,2,2,2,2,2,2,2] (.node [10,5,2,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,3,3,3,3,2,2,2,2] .empty .empty)) (.node [10,5,4,3,3,2,2,2,2,2] (.node [10,5,3,3,3,3,3,3,1,1] .empty .empty) (.node [10,5,4,3,3,3,2,2,2,1] .empty .empty))) (.node [10,5,4,4,3,3,3,1,1,1] (.node [10,5,4,4,3,2,2,2,2,1] (.node [10,5,4,4,2,2,2,2,2,2] .empty .empty) (.node [10,5,4,4,3,3,2,2,1,1] .empty .empty)) (.node [10,5,4,4,4,3,2,1,1,1] (.node [10,5,4,4,4,2,2,2,1,1] .empty .empty) (.node [10,5,4,4,4,4,1,1,1,1] .empty .empty))))) - -def degreeTree35_17 : RowTree := (.node [10,4,4,4,3,3,2,2,1,1,1] degreeTree35_15 degreeTree35_16) - -def degreeTree35_18 : RowTree := (.node [10,5,5,5,2,2,2,2,1,1] (.node [10,5,5,4,3,2,2,2,1,1] (.node [10,5,5,3,3,3,3,1,1,1] (.node [10,5,5,3,3,3,2,2,1,1] (.node [10,5,5,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [10,5,5,4,2,2,2,2,2,1] .empty .empty)) (.node [10,5,5,4,4,2,2,1,1,1] (.node [10,5,5,4,3,3,2,1,1,1] .empty .empty) (.node [10,5,5,4,4,3,1,1,1,1] .empty .empty))) (.node [10,5,5,5,5,1,1,1,1,1] (.node [10,5,5,5,3,3,1,1,1,1] (.node [10,5,5,5,3,2,2,1,1,1] .empty .empty) (.node [10,5,5,5,4,2,1,1,1,1] .empty .empty)) (.node [10,6,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree35_19 : RowTree := (.node [10,6,4,4,2,2,2,2,2,1] (.node [10,6,4,3,2,2,2,2,2,2] (.node [10,6,3,3,3,3,2,2,2,1] (.node [10,6,3,3,3,2,2,2,2,2] .empty .empty) (.node [10,6,3,3,3,3,3,2,1,1] .empty .empty)) (.node [10,6,4,3,3,3,2,2,1,1] (.node [10,6,4,3,3,2,2,2,2,1] .empty .empty) (.node [10,6,4,3,3,3,3,1,1,1] .empty .empty))) (.node [10,6,4,4,4,3,1,1,1,1] (.node [10,6,4,4,3,3,2,1,1,1] (.node [10,6,4,4,3,2,2,2,1,1] .empty .empty) (.node [10,6,4,4,4,2,2,1,1,1] .empty .empty)) (.node [10,6,5,3,2,2,2,2,2,1] (.node [10,6,5,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,5,3,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree35_20 : RowTree := (.node [10,6,2,2,2,2,2,2,2,2,2,1] degreeTree35_18 degreeTree35_19) - -def degreeTree35_21 : RowTree := (.node [10,7,4,3,2,2,2,2,2,1] (.node [10,6,6,3,3,2,2,1,1,1] (.node [10,6,5,4,4,2,1,1,1,1] (.node [10,6,5,4,3,2,2,1,1,1] (.node [10,6,5,4,2,2,2,2,1,1] .empty .empty) (.node [10,6,5,4,3,3,1,1,1,1] .empty .empty)) (.node [10,6,6,2,2,2,2,2,2,1] (.node [10,6,5,5,2,2,2,1,1,1] .empty .empty) (.node [10,6,6,3,2,2,2,2,1,1] .empty .empty))) (.node [10,7,3,3,3,2,2,2,2,1] (.node [10,6,6,4,2,2,2,1,1,1] (.node [10,6,6,3,3,3,1,1,1,1] .empty .empty) (.node [10,7,3,3,2,2,2,2,2,2] .empty .empty)) (.node [10,7,3,3,3,3,3,1,1,1] (.node [10,7,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,7,4,2,2,2,2,2,2,2] .empty .empty)))) (.node [10,7,6,2,2,2,2,2,1,1] (.node [10,7,4,4,3,2,2,1,1,1] (.node [10,7,4,3,3,3,2,1,1,1] (.node [10,7,4,3,3,2,2,2,1,1] .empty .empty) (.node [10,7,4,4,2,2,2,2,1,1] .empty .empty)) (.node [10,7,5,3,2,2,2,2,1,1] (.node [10,7,5,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,5,3,3,2,2,1,1,1] .empty .empty))) (.node [10,8,4,2,2,2,2,2,2,1] (.node [10,8,3,3,2,2,2,2,2,1] (.node [10,8,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,8,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,9,2,2,2,2,2,2,2,2] (.node [10,8,4,3,2,2,2,2,1,1] .empty .empty) (.node [10,9,3,2,2,2,2,2,2,1] .empty .empty))))) - -def degreeTree35_22 : RowTree := (.node [10,6,5,3,3,3,2,1,1,1] degreeTree35_20 degreeTree35_21) - -def degreeTree35_23 : RowTree := (.node [10,5,5,3,2,2,2,2,2,2] degreeTree35_17 degreeTree35_22) - -def degreeTree35_24 : RowTree := (.node [10,4,4,2,2,2,2,2,2,2,2,1] degreeTree35_12 degreeTree35_23) - -def degreeTree35 : RowTree := degreeTree35_24 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 35. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree35_0 : RowTree := (.node [8,8,7,4,3,1,1,1,1,1] (.node [8,8,7,2,2,2,2,2,2] (.node [8,8,6,6,2,1,1,1,1,1] (.node [8,7,7,7,1,1,1,1,1,1] (.node [8,7,7,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [8,8,7,2,2,2,2,2,1,1] .empty .empty)) (.node [8,8,7,3,3,2,1,1,1,1] (.node [8,8,7,3,2,2,2,1,1,1] .empty .empty) (.node [8,8,7,4,2,2,1,1,1,1] .empty .empty))) (.node [8,8,8,3,2,2,1,1,1,1] (.node [8,8,7,6,1,1,1,1,1,1] (.node [8,8,7,5,2,1,1,1,1,1] .empty .empty) (.node [8,8,8,2,2,2,2,1,1,1] .empty .empty)) (.node [8,8,8,4,2,1,1,1,1,1] (.node [8,8,8,3,3,1,1,1,1,1] .empty .empty) (.node [8,8,8,5,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree35_1 : RowTree := (.node [9,7,7,6,1,1,1,1,1,1] (.node [9,7,7,3,3,2,1,1,1,1] (.node [9,7,7,2,2,2,2,2,2] (.node [9,7,7,2,2,2,2,2,1,1] .empty .empty) (.node [9,7,7,3,2,2,2,1,1,1] .empty .empty)) (.node [9,7,7,4,3,1,1,1,1,1] (.node [9,7,7,4,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,5,2,1,1,1,1,1] .empty .empty))) (.node [9,8,6,3,3,2,1,1,1,1] (.node [9,8,6,2,2,2,2,2,2] (.node [9,8,6,2,2,2,2,2,1,1] .empty .empty) (.node [9,8,6,3,2,2,2,1,1,1] .empty .empty)) (.node [9,8,6,4,3,1,1,1,1,1] (.node [9,8,6,4,2,2,1,1,1,1] .empty .empty) (.node [9,8,6,5,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree35_2 : RowTree := (.node [9,7,6,6,2,1,1,1,1,1] degreeTree35_0 degreeTree35_1) + +def degreeTree35_3 : RowTree := (.node [9,9,3,2,2,2,2,2,2,2] (.node [9,8,7,5,1,1,1,1,1,1] (.node [9,8,7,3,3,1,1,1,1,1] (.node [9,8,7,3,2,2,1,1,1,1] (.node [9,8,7,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [9,8,7,4,2,1,1,1,1,1] .empty .empty)) (.node [9,8,8,3,2,1,1,1,1,1] (.node [9,8,8,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,4,1,1,1,1,1,1] .empty .empty))) (.node [9,9,3,3,3,3,2,1,1,1] (.node [9,9,3,3,3,2,2,2,1,1] (.node [9,9,3,3,2,2,2,2,2,1] .empty .empty) (.node [9,9,3,3,3,2,2,2,2] .empty .empty)) (.node [9,9,4,3,2,2,2,2,1,1] (.node [9,9,4,2,2,2,2,2,2,1] .empty .empty) (.node [9,9,4,3,2,2,2,2,2] .empty .empty)))) + +def degreeTree35_4 : RowTree := (.node [9,9,5,4,2,2,1,1,1,1] (.node [9,9,4,4,4,1,1,1,1,1] (.node [9,9,4,4,2,2,2,1,1,1] (.node [9,9,4,3,3,3,1,1,1,1] .empty .empty) (.node [9,9,4,4,3,2,1,1,1,1] .empty .empty)) (.node [9,9,5,3,2,2,2,1,1,1] (.node [9,9,5,2,2,2,2,2,1,1] .empty .empty) (.node [9,9,5,3,3,2,1,1,1,1] .empty .empty))) (.node [9,9,6,3,2,2,1,1,1,1] (.node [9,9,5,5,2,1,1,1,1,1] (.node [9,9,5,4,3,1,1,1,1,1] .empty .empty) (.node [9,9,6,2,2,2,2,1,1,1] .empty .empty)) (.node [9,9,6,4,2,1,1,1,1,1] (.node [9,9,6,3,3,1,1,1,1,1] .empty .empty) (.node [9,9,6,5,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree35_5 : RowTree := (.node [9,9,4,3,3,2,2,1,1,1] degreeTree35_3 degreeTree35_4) + +def degreeTree35_6 : RowTree := (.node [9,8,6,6,1,1,1,1,1,1] degreeTree35_2 degreeTree35_5) + +def degreeTree35_7 : RowTree := (.node [10,3,2,2,2,2,2,2,2,2,2,2,1,1] (.node [9,9,9,2,1,1,1,1,1,1] (.node [9,9,8,2,2,1,1,1,1,1] (.node [9,9,7,4,1,1,1,1,1,1] (.node [9,9,7,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [9,9,8,3,1,1,1,1,1,1] .empty .empty)) (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,3,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,3,3,2,2,2,2,2,2,2,2,2,1] (.node [10,3,3,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,3,2,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,3,3,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,3,3,3,2,2,2,2,2,2,1,1,1,1] (.node [10,3,3,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,2,2,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree35_8 : RowTree := (.node [10,3,3,3,3,3,2,2,2,2,1,1] (.node [10,3,3,3,3,2,2,2,2,2,2,1] (.node [10,3,3,3,3,2,2,2,2,1,1,1,1,1] (.node [10,3,3,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,2,2,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,2,2,2,1,1,1,1] .empty .empty))) (.node [10,3,3,3,3,3,3,2,2,1,1,1] (.node [10,3,3,3,3,3,3,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,2,2,2,2] .empty .empty) (.node [10,3,3,3,3,3,3,2,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,3,1,1,1,1] (.node [10,3,3,3,3,3,3,2,2,2,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,2,1,1] .empty .empty)))) + +def degreeTree35_9 : RowTree := (.node [10,3,3,3,2,2,2,2,2,2,2,2] degreeTree35_7 degreeTree35_8) + +def degreeTree35_10 : RowTree := (.node [10,4,3,3,3,2,2,2,2,2,1,1] (.node [10,4,3,2,2,2,2,2,2,2,2,2] (.node [10,4,2,2,2,2,2,2,2,2,2,2,1] (.node [10,4,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,3,3,3,3,3,3,3,3,1] .empty .empty) (.node [10,4,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,4,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,4,3,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,2,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [10,4,3,3,2,2,2,2,2,2,2,1] (.node [10,4,3,3,2,2,2,2,2,1,1,1,1,1] (.node [10,4,3,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,4,3,3,3,2,2,2,1,1,1,1,1,1] (.node [10,4,3,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,2,2,2,2,1,1,1,1] .empty .empty)))) (.node [10,4,3,3,3,3,3,2,1,1,1,1] (.node [10,4,3,3,3,3,2,2,1,1,1,1,1] (.node [10,4,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,4,3,3,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,3,2,2,2,2,1] (.node [10,4,3,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,4,3,3,3,3,3,3,2,1] (.node [10,4,3,3,3,3,3,2,2,2] (.node [10,4,3,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,3,1,1,1] .empty .empty)) (.node [10,4,4,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,4,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,2,2,2,2,2,2,2,1,1,1] .empty .empty))))) + +def degreeTree35_11 : RowTree := (.node [10,3,3,3,3,3,3,3,2,2] degreeTree35_9 degreeTree35_10) + +def degreeTree35_12 : RowTree := (.node [9,9,7,2,2,2,1,1,1,1] degreeTree35_6 degreeTree35_11) + +def degreeTree35_13 : RowTree := (.node [10,4,4,3,3,2,2,2,2,1,1,1] (.node [10,4,4,3,2,2,2,2,2,2,2] (.node [10,4,4,3,2,2,2,2,2,1,1,1,1] (.node [10,4,4,3,2,2,2,2,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,4,4,3,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,4,4,3,3,2,2,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,4,4,3,3,3,2,2,1,1,1,1] (.node [10,4,4,3,3,3,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,2,2,2,2,1] .empty .empty) (.node [10,4,4,3,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,3,3,3,2,2,2,2] (.node [10,4,4,3,3,3,2,2,2,1,1] .empty .empty) (.node [10,4,4,3,3,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree35_14 : RowTree := (.node [10,4,4,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,2,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,3,3,1,1] (.node [10,4,4,3,3,3,3,2,2,1] .empty .empty) (.node [10,4,4,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,2,2,2,2,2,1,1,1] (.node [10,4,4,4,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,2,2,2,2,2,2,1] .empty .empty))) (.node [10,4,4,4,3,2,2,2,2,1,1] (.node [10,4,4,4,3,2,2,1,1,1,1,1,1] (.node [10,4,4,4,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,3,2,2,2,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,3,1,1,1,1,1,1,1] (.node [10,4,4,4,3,2,2,2,2,2] .empty .empty) (.node [10,4,4,4,3,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree35_15 : RowTree := (.node [10,4,4,3,3,3,3,2,1,1,1] degreeTree35_13 degreeTree35_14) + +def degreeTree35_16 : RowTree := (.node [10,5,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,4,4,4,4,2,2,2,2,1] (.node [10,4,4,4,4,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,1,1,1,1] (.node [10,4,4,4,3,3,2,2,2,1] .empty .empty) (.node [10,4,4,4,3,3,3,2,1,1] .empty .empty)) (.node [10,4,4,4,4,2,2,1,1,1,1,1] (.node [10,4,4,4,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,2,2,2,1,1,1] .empty .empty))) (.node [10,4,4,4,4,3,3,1,1,1] (.node [10,4,4,4,4,3,2,1,1,1,1] (.node [10,4,4,4,4,3,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,3,2,2,1,1] .empty .empty)) (.node [10,4,4,4,4,4,2,1,1,1] (.node [10,4,4,4,4,4,1,1,1,1,1] .empty .empty) (.node [10,5,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,4,3,3,3,3,2,1,1] (.node [10,5,3,3,3,3,3,2,2,1] (.node [10,5,2,2,2,2,2,2,2,2,2,2] (.node [10,5,2,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,3,3,3,3,2,2,2,2] .empty .empty)) (.node [10,5,4,3,3,2,2,2,2,2] (.node [10,5,3,3,3,3,3,3,1,1] .empty .empty) (.node [10,5,4,3,3,3,2,2,2,1] .empty .empty))) (.node [10,5,4,4,3,3,3,1,1,1] (.node [10,5,4,4,3,2,2,2,2,1] (.node [10,5,4,4,2,2,2,2,2,2] .empty .empty) (.node [10,5,4,4,3,3,2,2,1,1] .empty .empty)) (.node [10,5,4,4,4,3,2,1,1,1] (.node [10,5,4,4,4,2,2,2,1,1] .empty .empty) (.node [10,5,4,4,4,4,1,1,1,1] .empty .empty))))) + +def degreeTree35_17 : RowTree := (.node [10,4,4,4,3,3,2,2,1,1,1] degreeTree35_15 degreeTree35_16) + +def degreeTree35_18 : RowTree := (.node [10,5,5,5,2,2,2,2,1,1] (.node [10,5,5,4,3,2,2,2,1,1] (.node [10,5,5,3,3,3,3,1,1,1] (.node [10,5,5,3,3,3,2,2,1,1] (.node [10,5,5,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [10,5,5,4,2,2,2,2,2,1] .empty .empty)) (.node [10,5,5,4,4,2,2,1,1,1] (.node [10,5,5,4,3,3,2,1,1,1] .empty .empty) (.node [10,5,5,4,4,3,1,1,1,1] .empty .empty))) (.node [10,5,5,5,5,1,1,1,1,1] (.node [10,5,5,5,3,3,1,1,1,1] (.node [10,5,5,5,3,2,2,1,1,1] .empty .empty) (.node [10,5,5,5,4,2,1,1,1,1] .empty .empty)) (.node [10,6,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree35_19 : RowTree := (.node [10,6,4,4,2,2,2,2,2,1] (.node [10,6,4,3,2,2,2,2,2,2] (.node [10,6,3,3,3,3,2,2,2,1] (.node [10,6,3,3,3,2,2,2,2,2] .empty .empty) (.node [10,6,3,3,3,3,3,2,1,1] .empty .empty)) (.node [10,6,4,3,3,3,2,2,1,1] (.node [10,6,4,3,3,2,2,2,2,1] .empty .empty) (.node [10,6,4,3,3,3,3,1,1,1] .empty .empty))) (.node [10,6,4,4,4,3,1,1,1,1] (.node [10,6,4,4,3,3,2,1,1,1] (.node [10,6,4,4,3,2,2,2,1,1] .empty .empty) (.node [10,6,4,4,4,2,2,1,1,1] .empty .empty)) (.node [10,6,5,3,2,2,2,2,2,1] (.node [10,6,5,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,5,3,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree35_20 : RowTree := (.node [10,6,2,2,2,2,2,2,2,2,2,1] degreeTree35_18 degreeTree35_19) + +def degreeTree35_21 : RowTree := (.node [10,7,4,3,2,2,2,2,2,1] (.node [10,6,6,3,3,2,2,1,1,1] (.node [10,6,5,4,4,2,1,1,1,1] (.node [10,6,5,4,3,2,2,1,1,1] (.node [10,6,5,4,2,2,2,2,1,1] .empty .empty) (.node [10,6,5,4,3,3,1,1,1,1] .empty .empty)) (.node [10,6,6,2,2,2,2,2,2,1] (.node [10,6,5,5,2,2,2,1,1,1] .empty .empty) (.node [10,6,6,3,2,2,2,2,1,1] .empty .empty))) (.node [10,7,3,3,3,2,2,2,2,1] (.node [10,6,6,4,2,2,2,1,1,1] (.node [10,6,6,3,3,3,1,1,1,1] .empty .empty) (.node [10,7,3,3,2,2,2,2,2,2] .empty .empty)) (.node [10,7,3,3,3,3,3,1,1,1] (.node [10,7,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,7,4,2,2,2,2,2,2,2] .empty .empty)))) (.node [10,7,6,2,2,2,2,2,1,1] (.node [10,7,4,4,3,2,2,1,1,1] (.node [10,7,4,3,3,3,2,1,1,1] (.node [10,7,4,3,3,2,2,2,1,1] .empty .empty) (.node [10,7,4,4,2,2,2,2,1,1] .empty .empty)) (.node [10,7,5,3,2,2,2,2,1,1] (.node [10,7,5,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,5,3,3,2,2,1,1,1] .empty .empty))) (.node [10,8,4,2,2,2,2,2,2,1] (.node [10,8,3,3,2,2,2,2,2,1] (.node [10,8,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,8,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,9,2,2,2,2,2,2,2,2] (.node [10,8,4,3,2,2,2,2,1,1] .empty .empty) (.node [10,9,3,2,2,2,2,2,2,1] .empty .empty))))) + +def degreeTree35_22 : RowTree := (.node [10,6,5,3,3,3,2,1,1,1] degreeTree35_20 degreeTree35_21) + +def degreeTree35_23 : RowTree := (.node [10,5,5,3,2,2,2,2,2,2] degreeTree35_17 degreeTree35_22) + +def degreeTree35_24 : RowTree := (.node [10,4,4,2,2,2,2,2,2,2,2,1] degreeTree35_12 degreeTree35_23) + +def degreeTree35 : RowTree := degreeTree35_24 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData37.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData37.lean index 06c368aebbc4faf91f341a9e6fd280ead971cb2c..98e82bf4b0c0bfb8aa3b45430d4ebf2e0c63e974 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData37.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData37.lean @@ -1,23 +1,23 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 37. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree37_0 : RowTree := (.node [10,10,3,2,2,2,2,2,2,2] .empty .empty) - -def degreeTree37 : RowTree := degreeTree37_0 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 37. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree37_0 : RowTree := (.node [10,10,3,2,2,2,2,2,2,2] .empty .empty) + +def degreeTree37 : RowTree := degreeTree37_0 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData39.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData39.lean index a551d75812302c7dac9d4e7e7b30f87801ead0a9..1188cbebc130b113cd49eb53060a200ab772cd2f 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData39.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData39.lean @@ -1,275 +1,275 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 39. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree39_0 : RowTree := (.node [8,5,5,5,5,4,3,2,2] (.node [8,5,5,4,4,4,4,4,1] (.node [8,5,4,4,4,4,4,3,3] (.node [7,7,7,7,7,2,1,1] (.node [7,7,7,7,7,1,1,1,1] .empty .empty) (.node [8,4,4,4,4,4,4,4,3] .empty .empty)) (.node [8,5,5,4,4,4,3,3,3] (.node [8,5,4,4,4,4,4,4,2] .empty .empty) (.node [8,5,5,4,4,4,4,3,2] .empty .empty))) (.node [8,5,5,5,4,4,4,3,1] (.node [8,5,5,5,4,4,3,3,2] (.node [8,5,5,5,4,3,3,3,3] .empty .empty) (.node [8,5,5,5,4,4,4,2,2] .empty .empty)) (.node [8,5,5,5,5,3,3,3,2] (.node [8,5,5,5,4,4,4,4] .empty .empty) .empty))) (.node [8,5,5,5,5,5,4,2] (.node [8,5,5,5,5,5,2,2,2] (.node [8,5,5,5,5,4,4,2,1] (.node [8,5,5,5,5,4,3,3,1] .empty .empty) (.node [8,5,5,5,5,4,4,3] .empty .empty)) (.node [8,5,5,5,5,5,3,3] (.node [8,5,5,5,5,5,3,2,1] .empty .empty) (.node [8,5,5,5,5,5,4,1,1] .empty .empty))) (.node [8,6,4,4,4,4,4,4,1] (.node [8,6,4,4,4,4,3,3,3] (.node [8,5,5,5,5,5,5,1] .empty .empty) (.node [8,6,4,4,4,4,4,3,2] .empty .empty)) (.node [8,6,5,4,4,4,3,3,2] (.node [8,6,5,4,4,3,3,3,3] .empty .empty) .empty)))) - -def degreeTree39_1 : RowTree := (.node [8,6,5,5,5,4,4,2] (.node [8,6,5,5,4,4,4,3] (.node [8,6,5,5,4,3,3,3,2] (.node [8,6,5,4,4,4,4,4] (.node [8,6,5,4,4,4,4,3,1] .empty .empty) (.node [8,6,5,5,3,3,3,3,3] .empty .empty)) (.node [8,6,5,5,4,4,3,3,1] (.node [8,6,5,5,4,4,3,2,2] .empty .empty) (.node [8,6,5,5,4,4,4,2,1] .empty .empty))) (.node [8,6,5,5,5,4,3,2,1] (.node [8,6,5,5,5,3,3,3,1] (.node [8,6,5,5,5,3,3,2,2] .empty .empty) (.node [8,6,5,5,5,4,2,2,2] .empty .empty)) (.node [8,6,5,5,5,4,4,1,1] (.node [8,6,5,5,5,4,3,3] .empty .empty) .empty))) (.node [8,6,6,4,4,4,3,2,2] (.node [8,6,5,5,5,5,4,1] (.node [8,6,5,5,5,5,3,1,1] (.node [8,6,5,5,5,5,2,2,1] .empty .empty) (.node [8,6,5,5,5,5,3,2] .empty .empty)) (.node [8,6,6,4,4,3,3,3,2] (.node [8,6,6,4,3,3,3,3,3] .empty .empty) .empty)) (.node [8,6,6,5,3,3,3,3,2] (.node [8,6,6,4,4,4,4,2,1] (.node [8,6,6,4,4,4,3,3,1] .empty .empty) (.node [8,6,6,4,4,4,4,3] .empty .empty)) (.node [8,6,6,5,4,3,3,3,1] (.node [8,6,6,5,4,3,3,2,2] .empty .empty) .empty)))) - -def degreeTree39_2 : RowTree := (.node [8,6,5,4,4,4,4,2,2] degreeTree39_0 degreeTree39_1) - -def degreeTree39_3 : RowTree := (.node [8,6,6,6,3,3,3,2,2] (.node [8,6,6,5,5,4,2,2,1] (.node [8,6,6,5,4,4,4,2] (.node [8,6,6,5,4,4,3,3] (.node [8,6,6,5,4,4,3,2,1] .empty .empty) (.node [8,6,6,5,4,4,4,1,1] .empty .empty)) (.node [8,6,6,5,5,3,3,2,1] (.node [8,6,6,5,5,3,2,2,2] .empty .empty) (.node [8,6,6,5,5,3,3,3] .empty .empty))) (.node [8,6,6,5,5,5,2,1,1] (.node [8,6,6,5,5,4,3,2] (.node [8,6,6,5,5,4,3,1,1] .empty .empty) (.node [8,6,6,5,5,4,4,1] .empty .empty)) (.node [8,6,6,5,5,5,3,1] (.node [8,6,6,5,5,5,2,2] .empty .empty) .empty))) (.node [8,6,6,6,4,4,3,2] (.node [8,6,6,6,4,3,3,3] (.node [8,6,6,6,4,3,2,2,2] (.node [8,6,6,6,3,3,3,3,1] .empty .empty) (.node [8,6,6,6,4,3,3,2,1] .empty .empty)) (.node [8,6,6,6,4,4,3,1,1] (.node [8,6,6,6,4,4,2,2,1] .empty .empty) .empty)) (.node [8,6,6,6,5,3,3,1,1] (.node [8,6,6,6,5,2,2,2,2] (.node [8,6,6,6,4,4,4,1] .empty .empty) (.node [8,6,6,6,5,3,2,2,1] .empty .empty)) (.node [8,6,6,6,5,4,2,1,1] (.node [8,6,6,6,5,3,3,2] .empty .empty) .empty)))) - -def degreeTree39_4 : RowTree := (.node [8,7,4,4,4,4,4,4] (.node [8,6,6,6,6,4,1,1,1] (.node [8,6,6,6,6,2,2,2,1] (.node [8,6,6,6,5,5,1,1,1] (.node [8,6,6,6,5,4,3,1] .empty .empty) (.node [8,6,6,6,5,5,2,1] .empty .empty)) (.node [8,6,6,6,6,3,2,2] (.node [8,6,6,6,6,3,2,1,1] .empty .empty) (.node [8,6,6,6,6,3,3,1] .empty .empty))) (.node [8,7,4,4,4,4,3,3,2] (.node [8,6,6,6,6,5,1,1] (.node [8,6,6,6,6,4,2,1] .empty .empty) (.node [8,7,4,4,4,3,3,3,3] .empty .empty)) (.node [8,7,4,4,4,4,4,3,1] (.node [8,7,4,4,4,4,4,2,2] .empty .empty) .empty))) (.node [8,7,5,5,3,3,3,3,2] (.node [8,7,5,4,4,4,3,3,1] (.node [8,7,5,4,4,3,3,3,2] (.node [8,7,5,4,3,3,3,3,3] .empty .empty) (.node [8,7,5,4,4,4,3,2,2] .empty .empty)) (.node [8,7,5,4,4,4,4,3] (.node [8,7,5,4,4,4,4,2,1] .empty .empty) .empty)) (.node [8,7,5,5,4,4,3,2,1] (.node [8,7,5,5,4,3,3,3,1] (.node [8,7,5,5,4,3,3,2,2] .empty .empty) (.node [8,7,5,5,4,4,2,2,2] .empty .empty)) (.node [8,7,5,5,4,4,4,1,1] (.node [8,7,5,5,4,4,3,3] .empty .empty) .empty)))) - -def degreeTree39_5 : RowTree := (.node [8,6,6,6,5,4,2,2] degreeTree39_3 degreeTree39_4) - -def degreeTree39_6 : RowTree := (.node [8,6,6,5,4,4,2,2,2] degreeTree39_2 degreeTree39_5) - -def degreeTree39_7 : RowTree := (.node [8,7,6,4,4,4,2,2,2] (.node [8,7,5,5,5,5,2,1,1] (.node [8,7,5,5,5,4,2,2,1] (.node [8,7,5,5,5,3,3,2,1] (.node [8,7,5,5,5,3,2,2,2] .empty .empty) (.node [8,7,5,5,5,3,3,3] .empty .empty)) (.node [8,7,5,5,5,4,3,2] (.node [8,7,5,5,5,4,3,1,1] .empty .empty) (.node [8,7,5,5,5,4,4,1] .empty .empty))) (.node [8,7,6,4,3,3,3,3,2] (.node [8,7,5,5,5,5,3,1] (.node [8,7,5,5,5,5,2,2] .empty .empty) (.node [8,7,6,3,3,3,3,3,3] .empty .empty)) (.node [8,7,6,4,4,3,3,3,1] (.node [8,7,6,4,4,3,3,2,2] .empty .empty) .empty))) (.node [8,7,6,5,4,3,2,2,2] (.node [8,7,6,4,4,4,4,2] (.node [8,7,6,4,4,4,3,3] (.node [8,7,6,4,4,4,3,2,1] .empty .empty) (.node [8,7,6,4,4,4,4,1,1] .empty .empty)) (.node [8,7,6,5,3,3,3,3,1] (.node [8,7,6,5,3,3,3,2,2] .empty .empty) .empty)) (.node [8,7,6,5,4,4,3,1,1] (.node [8,7,6,5,4,3,3,3] (.node [8,7,6,5,4,3,3,2,1] .empty .empty) (.node [8,7,6,5,4,4,2,2,1] .empty .empty)) (.node [8,7,6,5,4,4,4,1] (.node [8,7,6,5,4,4,3,2] .empty .empty) .empty)))) - -def degreeTree39_8 : RowTree := (.node [8,7,6,6,4,3,3,2] (.node [8,7,6,5,5,5,2,1] (.node [8,7,6,5,5,4,2,1,1] (.node [8,7,6,5,5,3,3,1,1] (.node [8,7,6,5,5,3,2,2,1] .empty .empty) (.node [8,7,6,5,5,3,3,2] .empty .empty)) (.node [8,7,6,5,5,4,3,1] (.node [8,7,6,5,5,4,2,2] .empty .empty) (.node [8,7,6,5,5,5,1,1,1] .empty .empty))) (.node [8,7,6,6,4,2,2,2,2] (.node [8,7,6,6,3,3,3,2,1] (.node [8,7,6,6,3,3,2,2,2] .empty .empty) (.node [8,7,6,6,3,3,3,3] .empty .empty)) (.node [8,7,6,6,4,3,3,1,1] (.node [8,7,6,6,4,3,2,2,1] .empty .empty) .empty))) (.node [8,7,6,6,5,3,3,1] (.node [8,7,6,6,5,2,2,2,1] (.node [8,7,6,6,4,4,2,2] (.node [8,7,6,6,4,4,2,1,1] .empty .empty) (.node [8,7,6,6,4,4,3,1] .empty .empty)) (.node [8,7,6,6,5,3,2,2] (.node [8,7,6,6,5,3,2,1,1] .empty .empty) .empty)) (.node [8,7,6,6,6,2,1,1,1,1] (.node [8,7,6,6,5,4,2,1] (.node [8,7,6,6,5,4,1,1,1] .empty .empty) (.node [8,7,6,6,6,1,1,1,1,1,1] .empty .empty)) (.node [8,7,6,6,6,2,2,2] (.node [8,7,6,6,6,2,2,1,1] .empty .empty) .empty)))) - -def degreeTree39_9 : RowTree := (.node [8,7,6,5,5,2,2,2,2] degreeTree39_7 degreeTree39_8) - -def degreeTree39_10 : RowTree := (.node [8,7,7,5,4,3,2,2,1] (.node [8,7,7,4,4,4,3,1,1] (.node [8,7,7,4,4,3,2,2,2] (.node [8,7,7,4,3,3,3,2,2] (.node [8,7,7,3,3,3,3,3,2] .empty .empty) (.node [8,7,7,4,3,3,3,3,1] .empty .empty)) (.node [8,7,7,4,4,3,3,3] (.node [8,7,7,4,4,3,3,2,1] .empty .empty) (.node [8,7,7,4,4,4,2,2,1] .empty .empty))) (.node [8,7,7,5,3,3,3,2,1] (.node [8,7,7,4,4,4,4,1] (.node [8,7,7,4,4,4,3,2] .empty .empty) (.node [8,7,7,5,3,3,2,2,2] .empty .empty)) (.node [8,7,7,5,4,2,2,2,2] (.node [8,7,7,5,3,3,3,3] .empty .empty) .empty))) (.node [8,7,7,5,5,3,2,1,1] (.node [8,7,7,5,4,4,2,2] (.node [8,7,7,5,4,3,3,2] (.node [8,7,7,5,4,3,3,1,1] .empty .empty) (.node [8,7,7,5,4,4,2,1,1] .empty .empty)) (.node [8,7,7,5,5,2,2,2,1] (.node [8,7,7,5,4,4,3,1] .empty .empty) .empty)) (.node [8,7,7,6,2,2,2,2,2,1] (.node [8,7,7,5,5,3,3,1] (.node [8,7,7,5,5,3,2,2] .empty .empty) (.node [8,7,7,5,5,4,1,1,1] .empty .empty)) (.node [8,7,7,6,3,2,2,2,2] (.node [8,7,7,6,3,2,2,2,1,1] .empty .empty) .empty)))) - -def degreeTree39_11 : RowTree := (.node [8,7,7,6,6,2,1,1,1] (.node [8,7,7,6,4,3,2,2] (.node [8,7,7,6,4,2,2,1,1,1] (.node [8,7,7,6,3,3,3,1,1] (.node [8,7,7,6,3,3,2,2,1] .empty .empty) (.node [8,7,7,6,3,3,3,2] .empty .empty)) (.node [8,7,7,6,4,3,1,1,1,1] (.node [8,7,7,6,4,2,2,2,1] .empty .empty) (.node [8,7,7,6,4,3,2,1,1] .empty .empty))) (.node [8,7,7,6,5,2,2,2] (.node [8,7,7,6,5,2,1,1,1,1] (.node [8,7,7,6,4,4,1,1,1] .empty .empty) (.node [8,7,7,6,5,2,2,1,1] .empty .empty)) (.node [8,7,7,6,6,1,1,1,1,1] (.node [8,7,7,6,5,3,1,1,1] .empty .empty) .empty))) (.node [8,7,7,7,3,3,2,2] (.node [8,7,7,7,3,2,2,2,1] (.node [8,7,7,7,2,2,2,2,2] (.node [8,7,7,7,2,2,2,2,1,1] .empty .empty) (.node [8,7,7,7,3,2,2,1,1,1] .empty .empty)) (.node [8,7,7,7,3,3,2,1,1] (.node [8,7,7,7,3,3,1,1,1,1] .empty .empty) .empty)) (.node [8,7,7,7,4,3,1,1,1] (.node [8,7,7,7,4,2,2,1,1] (.node [8,7,7,7,4,2,1,1,1,1] .empty .empty) (.node [8,7,7,7,4,2,2,2] .empty .empty)) (.node [8,7,7,7,5,2,1,1,1] (.node [8,7,7,7,5,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_12 : RowTree := (.node [8,7,7,6,3,3,2,1,1,1] degreeTree39_10 degreeTree39_11) - -def degreeTree39_13 : RowTree := (.node [8,7,6,6,6,3,1,1,1] degreeTree39_9 degreeTree39_12) - -def degreeTree39_14 : RowTree := (.node [8,7,5,5,4,4,4,2] degreeTree39_6 degreeTree39_13) - -def degreeTree39_15 : RowTree := (.node [8,8,5,4,4,4,4,2] (.node [8,8,5,4,3,3,3,3,2] (.node [8,8,4,4,4,4,3,3,1] (.node [8,8,4,4,4,3,3,3,2] (.node [8,8,4,4,3,3,3,3,3] .empty .empty) (.node [8,8,4,4,4,4,3,2,2] .empty .empty)) (.node [8,8,4,4,4,4,4,3] (.node [8,8,4,4,4,4,4,2,1] .empty .empty) (.node [8,8,5,3,3,3,3,3,3] .empty .empty))) (.node [8,8,5,4,4,4,3,2,1] (.node [8,8,5,4,4,3,3,3,1] (.node [8,8,5,4,4,3,3,2,2] .empty .empty) (.node [8,8,5,4,4,4,2,2,2] .empty .empty)) (.node [8,8,5,4,4,4,4,1,1] (.node [8,8,5,4,4,4,3,3] .empty .empty) .empty))) (.node [8,8,5,5,4,4,3,1,1] (.node [8,8,5,5,4,3,3,2,1] (.node [8,8,5,5,3,3,3,3,1] (.node [8,8,5,5,3,3,3,2,2] .empty .empty) (.node [8,8,5,5,4,3,2,2,2] .empty .empty)) (.node [8,8,5,5,4,4,2,2,1] (.node [8,8,5,5,4,3,3,3] .empty .empty) .empty)) (.node [8,8,5,5,5,3,3,1,1] (.node [8,8,5,5,5,2,2,2,2] (.node [8,8,5,5,4,4,3,2] .empty .empty) (.node [8,8,5,5,5,3,2,2,1] .empty .empty)) (.node [8,8,5,5,5,4,2,1,1] (.node [8,8,5,5,5,3,3,2] .empty .empty) .empty)))) - -def degreeTree39_16 : RowTree := (.node [8,8,6,5,4,3,2,2,1] (.node [8,8,6,4,4,4,2,2,1] (.node [8,8,6,4,3,3,3,3,1] (.node [8,8,6,3,3,3,3,3,2] (.node [8,8,5,5,5,5,1,1,1] .empty .empty) (.node [8,8,6,4,3,3,3,2,2] .empty .empty)) (.node [8,8,6,4,4,3,3,2,1] (.node [8,8,6,4,4,3,2,2,2] .empty .empty) (.node [8,8,6,4,4,3,3,3] .empty .empty))) (.node [8,8,6,5,3,3,3,2,1] (.node [8,8,6,4,4,4,3,2] (.node [8,8,6,4,4,4,3,1,1] .empty .empty) (.node [8,8,6,5,3,3,2,2,2] .empty .empty)) (.node [8,8,6,5,4,2,2,2,2] (.node [8,8,6,5,3,3,3,3] .empty .empty) .empty))) (.node [8,8,6,5,5,3,2,2] (.node [8,8,6,5,4,4,2,2] (.node [8,8,6,5,4,3,3,2] (.node [8,8,6,5,4,3,3,1,1] .empty .empty) (.node [8,8,6,5,4,4,2,1,1] .empty .empty)) (.node [8,8,6,5,5,3,2,1,1] (.node [8,8,6,5,5,2,2,2,1] .empty .empty) .empty)) (.node [8,8,6,6,2,2,1,1,1,1,1,1,1] (.node [8,8,6,6,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,6,5,5,4,1,1,1] .empty .empty) (.node [8,8,6,6,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,6,6,2,2,2,2,1,1,1] (.node [8,8,6,6,2,2,2,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_17 : RowTree := (.node [8,8,5,5,5,4,2,2] degreeTree39_15 degreeTree39_16) - -def degreeTree39_18 : RowTree := (.node [8,8,6,6,4,3,1,1,1,1] (.node [8,8,6,6,3,3,2,2,1] (.node [8,8,6,6,3,2,2,2,1,1] (.node [8,8,6,6,3,2,1,1,1,1,1,1] (.node [8,8,6,6,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,3,2,2,1,1,1,1] .empty .empty)) (.node [8,8,6,6,3,3,1,1,1,1,1] (.node [8,8,6,6,3,2,2,2,2] .empty .empty) (.node [8,8,6,6,3,3,2,1,1,1] .empty .empty))) (.node [8,8,6,6,4,2,1,1,1,1,1] (.node [8,8,6,6,3,3,3,2] (.node [8,8,6,6,3,3,3,1,1] .empty .empty) (.node [8,8,6,6,4,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,6,6,4,2,2,2,1] (.node [8,8,6,6,4,2,2,1,1,1] .empty .empty) .empty))) (.node [8,8,6,6,6,1,1,1,1,1] (.node [8,8,6,6,5,2,1,1,1,1] (.node [8,8,6,6,4,4,1,1,1] (.node [8,8,6,6,4,3,2,1,1] .empty .empty) (.node [8,8,6,6,5,1,1,1,1,1,1] .empty .empty)) (.node [8,8,6,6,5,3,1,1,1] (.node [8,8,6,6,5,2,2,1,1] .empty .empty) .empty)) (.node [8,8,7,3,3,3,3,2,1,1] (.node [8,8,7,3,3,2,2,2,2,2] (.node [8,8,6,6,6,2,1,1,1] .empty .empty) (.node [8,8,7,3,3,3,2,2,2,1] .empty .empty)) (.node [8,8,7,3,3,3,3,3,1] (.node [8,8,7,3,3,3,3,2,2] .empty .empty) .empty)))) - -def degreeTree39_19 : RowTree := (.node [8,8,7,5,2,2,2,2,2,1] (.node [8,8,7,4,4,2,2,2,2] (.node [8,8,7,4,3,3,3,1,1,1] (.node [8,8,7,4,3,3,2,2,1,1] (.node [8,8,7,4,3,2,2,2,2,1] .empty .empty) (.node [8,8,7,4,3,3,2,2,2] .empty .empty)) (.node [8,8,7,4,3,3,3,3] (.node [8,8,7,4,3,3,3,2,1] .empty .empty) (.node [8,8,7,4,4,2,2,2,1,1] .empty .empty))) (.node [8,8,7,4,4,3,3,2] (.node [8,8,7,4,4,3,2,2,1] (.node [8,8,7,4,4,3,2,1,1,1] .empty .empty) (.node [8,8,7,4,4,3,3,1,1] .empty .empty)) (.node [8,8,7,4,4,4,2,1,1] (.node [8,8,7,4,4,4,1,1,1,1] .empty .empty) .empty))) (.node [8,8,7,5,4,2,2,2,1] (.node [8,8,7,5,3,3,2,2,1] (.node [8,8,7,5,3,2,2,2,2] (.node [8,8,7,5,3,2,2,2,1,1] .empty .empty) (.node [8,8,7,5,3,3,2,1,1,1] .empty .empty)) (.node [8,8,7,5,4,2,2,1,1,1] (.node [8,8,7,5,3,3,3,1,1] .empty .empty) .empty)) (.node [8,8,7,5,5,2,1,1,1,1] (.node [8,8,7,5,4,3,2,1,1] (.node [8,8,7,5,4,3,1,1,1,1] .empty .empty) (.node [8,8,7,5,4,4,1,1,1] .empty .empty)) (.node [8,8,7,5,5,3,1,1,1] (.node [8,8,7,5,5,2,2,1,1] .empty .empty) .empty)))) - -def degreeTree39_20 : RowTree := (.node [8,8,7,4,2,2,2,2,2,2] degreeTree39_18 degreeTree39_19) - -def degreeTree39_21 : RowTree := (.node [8,8,6,6,2,2,2,2,2,1] degreeTree39_17 degreeTree39_20) - -def degreeTree39_22 : RowTree := (.node [8,8,7,7,3,2,2,1,1] (.node [8,8,7,6,4,3,1,1,1] (.node [8,8,7,6,3,3,1,1,1,1] (.node [8,8,7,6,3,2,2,1,1,1] (.node [8,8,7,6,2,2,2,2,2] .empty .empty) (.node [8,8,7,6,3,2,2,2,1] .empty .empty)) (.node [8,8,7,6,4,2,1,1,1,1] (.node [8,8,7,6,3,3,2,1,1] .empty .empty) (.node [8,8,7,6,4,2,2,1,1] .empty .empty))) (.node [8,8,7,7,2,2,2,1,1,1] (.node [8,8,7,6,5,2,1,1,1] (.node [8,8,7,6,5,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,6,1,1,1,1] .empty .empty)) (.node [8,8,7,7,3,2,1,1,1,1] (.node [8,8,7,7,2,2,2,2,1] .empty .empty) .empty))) (.node [8,8,8,3,3,3,2,2,1,1] (.node [8,8,7,7,5,1,1,1,1] (.node [8,8,7,7,4,1,1,1,1,1] (.node [8,8,7,7,3,3,1,1,1] .empty .empty) (.node [8,8,7,7,4,2,1,1,1] .empty .empty)) (.node [8,8,8,3,3,2,2,2,2,1] (.node [8,8,8,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [8,8,8,3,3,3,3,3] (.node [8,8,8,3,3,3,3,1,1,1] (.node [8,8,8,3,3,3,2,2,2] .empty .empty) (.node [8,8,8,3,3,3,3,2,1] .empty .empty)) (.node [8,8,8,4,3,2,2,2,1,1] (.node [8,8,8,4,2,2,2,2,2,1] .empty .empty) .empty)))) - -def degreeTree39_23 : RowTree := (.node [8,8,8,5,4,2,1,1,1,1] (.node [8,8,8,4,4,4,1,1,1] (.node [8,8,8,4,4,2,2,1,1,1] (.node [8,8,8,4,3,3,2,2,1] (.node [8,8,8,4,3,3,2,1,1,1] .empty .empty) (.node [8,8,8,4,3,3,3,1,1] .empty .empty)) (.node [8,8,8,4,4,3,1,1,1,1] (.node [8,8,8,4,4,2,2,2,1] .empty .empty) (.node [8,8,8,4,4,3,2,1,1] .empty .empty))) (.node [8,8,8,5,3,2,2,2,1] (.node [8,8,8,5,2,2,2,2,2] (.node [8,8,8,5,2,2,2,2,1,1] .empty .empty) (.node [8,8,8,5,3,2,2,1,1,1] .empty .empty)) (.node [8,8,8,5,3,3,2,1,1] (.node [8,8,8,5,3,3,1,1,1,1] .empty .empty) .empty))) (.node [8,8,8,6,3,2,1,1,1,1] (.node [8,8,8,5,5,2,1,1,1] (.node [8,8,8,5,4,3,1,1,1] (.node [8,8,8,5,4,2,2,1,1] .empty .empty) (.node [8,8,8,5,5,1,1,1,1,1] .empty .empty)) (.node [8,8,8,6,2,2,2,2,1] (.node [8,8,8,6,2,2,2,1,1,1] .empty .empty) .empty)) (.node [8,8,8,6,4,2,1,1,1] (.node [8,8,8,6,3,3,1,1,1] (.node [8,8,8,6,3,2,2,1,1] .empty .empty) (.node [8,8,8,6,4,1,1,1,1,1] .empty .empty)) (.node [8,8,8,7,2,2,1,1,1,1] (.node [8,8,8,6,5,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_24 : RowTree := (.node [8,8,8,4,3,2,2,2,2] degreeTree39_22 degreeTree39_23) - -def degreeTree39_25 : RowTree := (.node [9,5,5,4,4,4,4,3,1] (.node [9,4,4,4,4,4,4,4,2] (.node [8,8,8,8,2,1,1,1,1,1] (.node [8,8,8,7,3,2,1,1,1] (.node [8,8,8,7,3,1,1,1,1,1] .empty .empty) (.node [8,8,8,7,4,1,1,1,1] .empty .empty)) (.node [8,8,8,8,3,1,1,1,1] (.node [8,8,8,8,2,2,1,1,1] .empty .empty) (.node [9,4,4,4,4,4,4,3,3] .empty .empty))) (.node [9,5,5,4,4,3,3,3,3] (.node [9,5,4,4,4,4,4,3,2] (.node [9,5,4,4,4,4,3,3,3] .empty .empty) (.node [9,5,4,4,4,4,4,4,1] .empty .empty)) (.node [9,5,5,4,4,4,4,2,2] (.node [9,5,5,4,4,4,3,3,2] .empty .empty) .empty))) (.node [9,5,5,5,5,3,3,3,1] (.node [9,5,5,5,4,4,3,3,1] (.node [9,5,5,5,4,3,3,3,2] (.node [9,5,5,5,3,3,3,3,3] .empty .empty) (.node [9,5,5,5,4,4,3,2,2] .empty .empty)) (.node [9,5,5,5,5,3,3,2,2] (.node [9,5,5,5,4,4,4,2,1] .empty .empty) .empty)) (.node [9,5,5,5,5,5,2,2,1] (.node [9,5,5,5,5,4,3,2,1] (.node [9,5,5,5,5,4,2,2,2] .empty .empty) (.node [9,5,5,5,5,4,4,1,1] .empty .empty)) (.node [9,6,4,4,4,3,3,3,3] (.node [9,5,5,5,5,5,3,1,1] .empty .empty) .empty)))) - -def degreeTree39_26 : RowTree := (.node [9,6,5,5,5,3,3,2,1] (.node [9,6,5,5,3,3,3,3,2] (.node [9,6,5,4,4,3,3,3,2] (.node [9,6,4,4,4,4,4,3,1] (.node [9,6,4,4,4,4,4,2,2] .empty .empty) (.node [9,6,5,4,3,3,3,3,3] .empty .empty)) (.node [9,6,5,4,4,4,3,3,1] (.node [9,6,5,4,4,4,3,2,2] .empty .empty) (.node [9,6,5,4,4,4,4,2,1] .empty .empty))) (.node [9,6,5,5,4,4,3,2,1] (.node [9,6,5,5,4,3,3,3,1] (.node [9,6,5,5,4,3,3,2,2] .empty .empty) (.node [9,6,5,5,4,4,2,2,2] .empty .empty)) (.node [9,6,5,5,5,3,2,2,2] (.node [9,6,5,5,4,4,4,1,1] .empty .empty) .empty))) (.node [9,6,6,4,4,3,3,3,1] (.node [9,6,6,3,3,3,3,3,3] (.node [9,6,5,5,5,4,3,1,1] (.node [9,6,5,5,5,4,2,2,1] .empty .empty) (.node [9,6,5,5,5,5,2,1,1] .empty .empty)) (.node [9,6,6,4,4,3,3,2,2] (.node [9,6,6,4,3,3,3,3,2] .empty .empty) .empty)) (.node [9,6,6,5,3,3,3,2,2] (.node [9,6,6,4,4,4,3,2,1] (.node [9,6,6,4,4,4,2,2,2] .empty .empty) (.node [9,6,6,4,4,4,4,1,1] .empty .empty)) (.node [9,6,6,5,4,3,2,2,2] (.node [9,6,6,5,3,3,3,3,1] .empty .empty) .empty)))) - -def degreeTree39_27 : RowTree := (.node [9,6,4,4,4,4,3,3,2] degreeTree39_25 degreeTree39_26) - -def degreeTree39_28 : RowTree := (.node [8,8,8,7,2,2,2,1,1] degreeTree39_24 degreeTree39_27) - -def degreeTree39_29 : RowTree := (.node [8,8,7,6,2,2,2,2,1,1] degreeTree39_21 degreeTree39_28) - -def degreeTree39_30 : RowTree := (.node [8,7,7,7,6,1,1,1,1] degreeTree39_14 degreeTree39_29) - -def degreeTree39_31 : RowTree := (.node [9,6,6,6,5,3,2,1,1] (.node [9,6,6,6,3,3,2,2,2] (.node [9,6,6,5,5,3,2,2,1] (.node [9,6,6,5,4,4,3,1,1] (.node [9,6,6,5,4,4,2,2,1] .empty .empty) (.node [9,6,6,5,5,2,2,2,2] .empty .empty)) (.node [9,6,6,5,5,4,2,1,1] (.node [9,6,6,5,5,3,3,1,1] .empty .empty) (.node [9,6,6,5,5,5,1,1,1] .empty .empty))) (.node [9,6,6,6,4,3,3,1,1] (.node [9,6,6,6,4,2,2,2,2] (.node [9,6,6,6,3,3,3,2,1] .empty .empty) (.node [9,6,6,6,4,3,2,2,1] .empty .empty)) (.node [9,6,6,6,5,2,2,2,1] (.node [9,6,6,6,4,4,2,1,1] .empty .empty) .empty))) (.node [9,7,4,4,4,4,3,3,1] (.node [9,6,6,6,6,2,2,1,1] (.node [9,6,6,6,6,1,1,1,1,1,1] (.node [9,6,6,6,5,4,1,1,1] .empty .empty) (.node [9,6,6,6,6,2,1,1,1,1] .empty .empty)) (.node [9,7,4,4,4,3,3,3,2] (.node [9,7,4,4,3,3,3,3,3] .empty .empty) (.node [9,7,4,4,4,4,3,2,2] .empty .empty))) (.node [9,7,5,4,4,3,3,2,2] (.node [9,7,5,3,3,3,3,3,3] (.node [9,7,4,4,4,4,4,2,1] .empty .empty) (.node [9,7,5,4,3,3,3,3,2] .empty .empty)) (.node [9,7,5,4,4,4,2,2,2] (.node [9,7,5,4,4,3,3,3,1] .empty .empty) .empty)))) - -def degreeTree39_32 : RowTree := (.node [9,7,6,4,4,3,2,2,2] (.node [9,7,5,5,5,2,2,2,2] (.node [9,7,5,5,4,3,2,2,2] (.node [9,7,5,5,3,3,3,2,2] (.node [9,7,5,4,4,4,4,1,1] .empty .empty) (.node [9,7,5,5,3,3,3,3,1] .empty .empty)) (.node [9,7,5,5,4,4,2,2,1] (.node [9,7,5,5,4,3,3,2,1] .empty .empty) (.node [9,7,5,5,4,4,3,1,1] .empty .empty))) (.node [9,7,6,3,3,3,3,3,2] (.node [9,7,5,5,5,3,3,1,1] (.node [9,7,5,5,5,3,2,2,1] .empty .empty) (.node [9,7,5,5,5,4,2,1,1] .empty .empty)) (.node [9,7,6,4,3,3,3,3,1] (.node [9,7,6,4,3,3,3,2,2] .empty .empty) .empty))) (.node [9,7,6,5,4,3,2,2,1] (.node [9,7,6,5,3,3,2,2,2] (.node [9,7,6,4,4,4,2,2,1] (.node [9,7,6,4,4,3,3,2,1] .empty .empty) (.node [9,7,6,4,4,4,3,1,1] .empty .empty)) (.node [9,7,6,5,4,2,2,2,2] (.node [9,7,6,5,3,3,3,2,1] .empty .empty) .empty)) (.node [9,7,6,5,5,3,2,1,1] (.node [9,7,6,5,4,4,2,1,1] (.node [9,7,6,5,4,3,3,1,1] .empty .empty) (.node [9,7,6,5,5,2,2,2,1] .empty .empty)) (.node [9,7,6,6,3,2,2,2,1,1] (.node [9,7,6,6,2,2,2,2,2,1] .empty .empty) .empty)))) - -def degreeTree39_33 : RowTree := (.node [9,7,5,4,4,4,3,2,1] degreeTree39_31 degreeTree39_32) - -def degreeTree39_34 : RowTree := (.node [9,7,7,4,3,2,2,2,2,1] (.node [9,7,6,6,6,1,1,1,1,1] (.node [9,7,6,6,4,2,2,1,1,1] (.node [9,7,6,6,3,3,2,2,1] (.node [9,7,6,6,3,3,2,1,1,1] .empty .empty) (.node [9,7,6,6,3,3,3,1,1] .empty .empty)) (.node [9,7,6,6,4,3,1,1,1,1] (.node [9,7,6,6,4,2,2,2,1] .empty .empty) (.node [9,7,6,6,5,2,1,1,1,1] .empty .empty))) (.node [9,7,7,3,3,3,3,2,2] (.node [9,7,7,3,3,3,2,2,2,1] (.node [9,7,7,3,3,2,2,2,2,2] .empty .empty) (.node [9,7,7,3,3,3,3,2,1,1] .empty .empty)) (.node [9,7,7,4,2,2,2,2,2,2] (.node [9,7,7,3,3,3,3,3,1] .empty .empty) .empty))) (.node [9,7,7,4,4,3,2,1,1,1] (.node [9,7,7,4,3,3,3,2,1] (.node [9,7,7,4,3,3,2,2,2] (.node [9,7,7,4,3,3,2,2,1,1] .empty .empty) (.node [9,7,7,4,3,3,3,1,1,1] .empty .empty)) (.node [9,7,7,4,4,2,2,2,2] (.node [9,7,7,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [9,7,7,5,2,2,2,2,2,1] (.node [9,7,7,4,4,3,3,1,1] (.node [9,7,7,4,4,3,2,2,1] .empty .empty) (.node [9,7,7,4,4,4,1,1,1,1] .empty .empty)) (.node [9,7,7,5,3,2,2,2,2] (.node [9,7,7,5,3,2,2,2,1,1] .empty .empty) .empty)))) - -def degreeTree39_35 : RowTree := (.node [9,7,7,7,3,2,1,1,1,1] (.node [9,7,7,6,3,2,2,1,1,1] (.node [9,7,7,5,4,3,1,1,1,1] (.node [9,7,7,5,4,2,2,1,1,1] (.node [9,7,7,5,3,3,2,2,1] .empty .empty) (.node [9,7,7,5,4,2,2,2,1] .empty .empty)) (.node [9,7,7,6,2,2,2,2,1,1] (.node [9,7,7,5,5,2,1,1,1,1] .empty .empty) (.node [9,7,7,6,2,2,2,2,2] .empty .empty))) (.node [9,7,7,6,5,1,1,1,1,1] (.node [9,7,7,6,3,3,1,1,1,1] (.node [9,7,7,6,3,2,2,2,1] .empty .empty) (.node [9,7,7,6,4,2,1,1,1,1] .empty .empty)) (.node [9,7,7,7,2,2,2,2,1] (.node [9,7,7,7,2,2,2,1,1,1] .empty .empty) .empty))) (.node [9,8,4,4,4,4,3,2,1] (.node [9,8,4,4,4,3,3,2,2] (.node [9,8,4,3,3,3,3,3,3] (.node [9,7,7,7,4,1,1,1,1,1] .empty .empty) (.node [9,8,4,4,3,3,3,3,2] .empty .empty)) (.node [9,8,4,4,4,4,2,2,2] (.node [9,8,4,4,4,3,3,3,1] .empty .empty) .empty)) (.node [9,8,5,4,4,3,2,2,2] (.node [9,8,5,4,3,3,3,2,2] (.node [9,8,5,3,3,3,3,3,2] .empty .empty) (.node [9,8,5,4,3,3,3,3,1] .empty .empty)) (.node [9,8,5,4,4,4,2,2,1] (.node [9,8,5,4,4,3,3,2,1] .empty .empty) .empty)))) - -def degreeTree39_36 : RowTree := (.node [9,7,7,5,3,3,2,1,1,1] degreeTree39_34 degreeTree39_35) - -def degreeTree39_37 : RowTree := (.node [9,7,6,6,3,2,2,2,2] degreeTree39_33 degreeTree39_36) - -def degreeTree39_38 : RowTree := (.node [9,8,6,4,3,3,3,2,1] (.node [9,8,6,3,3,3,3,2,2] (.node [9,8,5,5,5,2,2,2,1] (.node [9,8,5,5,4,2,2,2,2] (.node [9,8,5,5,3,3,3,2,1] .empty .empty) (.node [9,8,5,5,4,3,2,2,1] .empty .empty)) (.node [9,8,6,3,3,3,2,2,2,1] (.node [9,8,6,3,3,2,2,2,2,2] .empty .empty) (.node [9,8,6,3,3,3,3,2,1,1] .empty .empty))) (.node [9,8,6,4,3,3,2,2,1,1] (.node [9,8,6,4,2,2,2,2,2,2] (.node [9,8,6,3,3,3,3,3,1] .empty .empty) (.node [9,8,6,4,3,2,2,2,2,1] .empty .empty)) (.node [9,8,6,4,3,3,3,1,1,1] (.node [9,8,6,4,3,3,2,2,2] .empty .empty) .empty))) (.node [9,8,6,5,3,2,2,2,1,1] (.node [9,8,6,4,4,3,2,2,1] (.node [9,8,6,4,4,2,2,2,2] (.node [9,8,6,4,4,2,2,2,1,1] .empty .empty) (.node [9,8,6,4,4,3,2,1,1,1] .empty .empty)) (.node [9,8,6,5,2,2,2,2,2,1] (.node [9,8,6,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [9,8,6,5,4,3,1,1,1,1] (.node [9,8,6,5,3,3,2,1,1,1] (.node [9,8,6,5,3,2,2,2,2] .empty .empty) (.node [9,8,6,5,4,2,2,1,1,1] .empty .empty)) (.node [9,8,6,6,2,2,2,2,1,1] (.node [9,8,6,5,5,2,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_39 : RowTree := (.node [9,8,7,4,4,2,2,1,1,1] (.node [9,8,7,3,3,3,2,2,2] (.node [9,8,6,6,5,1,1,1,1,1] (.node [9,8,6,6,3,3,1,1,1,1] (.node [9,8,6,6,3,2,2,1,1,1] .empty .empty) (.node [9,8,6,6,4,2,1,1,1,1] .empty .empty)) (.node [9,8,7,3,3,2,2,2,2,1] (.node [9,8,7,3,2,2,2,2,2,2] .empty .empty) (.node [9,8,7,3,3,3,2,2,1,1] .empty .empty))) (.node [9,8,7,4,3,2,2,2,1,1] (.node [9,8,7,3,3,3,3,2,1] (.node [9,8,7,3,3,3,3,1,1,1] .empty .empty) (.node [9,8,7,4,2,2,2,2,2,1] .empty .empty)) (.node [9,8,7,4,3,3,2,1,1,1] (.node [9,8,7,4,3,2,2,2,2] .empty .empty) .empty))) (.node [9,8,7,5,5,1,1,1,1,1] (.node [9,8,7,5,3,2,2,1,1,1] (.node [9,8,7,5,2,2,2,2,1,1] (.node [9,8,7,4,4,3,1,1,1,1] .empty .empty) (.node [9,8,7,5,2,2,2,2,2] .empty .empty)) (.node [9,8,7,5,4,2,1,1,1,1] (.node [9,8,7,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [9,8,7,7,2,2,1,1,1,1] (.node [9,8,7,6,3,2,1,1,1,1] (.node [9,8,7,6,2,2,2,1,1,1] .empty .empty) (.node [9,8,7,6,4,1,1,1,1,1] .empty .empty)) (.node [9,8,8,2,2,2,2,2,2,2] (.node [9,8,7,7,3,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_40 : RowTree := (.node [9,8,6,6,2,2,2,2,2] degreeTree39_38 degreeTree39_39) - -def degreeTree39_41 : RowTree := (.node [9,8,8,8,1,1,1,1,1,1] (.node [9,8,8,4,4,2,1,1,1,1] (.node [9,8,8,4,2,2,2,2,1,1] (.node [9,8,8,3,3,2,2,2,2] (.node [9,8,8,3,3,2,2,2,1,1] .empty .empty) (.node [9,8,8,3,3,3,2,1,1,1] .empty .empty)) (.node [9,8,8,4,3,2,2,1,1,1] (.node [9,8,8,4,2,2,2,2,2] .empty .empty) (.node [9,8,8,4,3,3,1,1,1,1] .empty .empty))) (.node [9,8,8,6,2,2,1,1,1,1] (.node [9,8,8,5,3,2,1,1,1,1] (.node [9,8,8,5,2,2,2,1,1,1] .empty .empty) (.node [9,8,8,5,4,1,1,1,1,1] .empty .empty)) (.node [9,8,8,7,2,1,1,1,1,1] (.node [9,8,8,6,3,1,1,1,1,1] .empty .empty) .empty))) (.node [9,9,2,2,2,2,2,2,2,2,2,2,1] (.node [9,9,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [9,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,2,2,2,2,2,2,2,2,2,1,1,1] (.node [9,9,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [9,9,4,3,3,3,2,2,2,2] (.node [9,9,3,3,3,3,3,3,2,1] (.node [9,9,3,3,3,3,3,2,2,2] .empty .empty) (.node [9,9,3,3,3,3,3,3,3] .empty .empty)) (.node [9,9,4,3,3,3,3,3,1,1] (.node [9,9,4,3,3,3,3,2,2,1] .empty .empty) .empty)))) - -def degreeTree39_42 : RowTree := (.node [9,9,5,4,3,2,2,2,2,1] (.node [9,9,4,4,4,3,3,1,1,1] (.node [9,9,4,4,3,3,3,2,2] (.node [9,9,4,4,3,3,2,2,2,1] (.node [9,9,4,4,3,2,2,2,2,2] .empty .empty) (.node [9,9,4,4,3,3,3,2,1,1] .empty .empty)) (.node [9,9,4,4,4,3,2,2,1,1] (.node [9,9,4,4,4,2,2,2,2,1] .empty .empty) (.node [9,9,4,4,4,3,2,2,2] .empty .empty))) (.node [9,9,5,3,3,3,3,2,1,1] (.node [9,9,5,3,3,2,2,2,2,2] (.node [9,9,4,4,4,4,2,1,1,1] .empty .empty) (.node [9,9,5,3,3,3,2,2,2,1] .empty .empty)) (.node [9,9,5,4,2,2,2,2,2,2] (.node [9,9,5,3,3,3,3,2,2] .empty .empty) .empty))) (.node [9,9,5,4,4,4,1,1,1,1] (.node [9,9,5,4,4,2,2,2,1,1] (.node [9,9,5,4,3,3,2,2,2] (.node [9,9,5,4,3,3,2,2,1,1] .empty .empty) (.node [9,9,5,4,3,3,3,1,1,1] .empty .empty)) (.node [9,9,5,4,4,3,2,1,1,1] (.node [9,9,5,4,4,2,2,2,2] .empty .empty) .empty)) (.node [9,9,5,5,4,2,2,1,1,1] (.node [9,9,5,5,3,2,2,2,1,1] (.node [9,9,5,5,2,2,2,2,2,1] .empty .empty) (.node [9,9,5,5,3,3,2,1,1,1] .empty .empty)) (.node [9,9,5,5,5,2,1,1,1,1] (.node [9,9,5,5,4,3,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_43 : RowTree := (.node [9,9,4,3,3,3,3,3,2] degreeTree39_41 degreeTree39_42) - -def degreeTree39_44 : RowTree := (.node [9,8,8,3,2,2,2,2,2,1] degreeTree39_40 degreeTree39_43) - -def degreeTree39_45 : RowTree := (.node [9,8,5,5,3,3,2,2,2] degreeTree39_37 degreeTree39_44) - -def degreeTree39_46 : RowTree := (.node [9,9,6,6,2,2,2,1,1,1] (.node [9,9,6,4,4,2,2,1,1,1] (.node [9,9,6,3,3,3,3,1,1,1] (.node [9,9,6,3,3,3,2,2,1,1] (.node [9,9,6,3,3,2,2,2,2,1] .empty .empty) (.node [9,9,6,3,3,3,2,2,2] .empty .empty)) (.node [9,9,6,4,3,2,2,2,1,1] (.node [9,9,6,4,2,2,2,2,2,1] .empty .empty) (.node [9,9,6,4,3,3,2,1,1,1] .empty .empty))) (.node [9,9,6,5,3,3,1,1,1,1] (.node [9,9,6,5,2,2,2,2,1,1] (.node [9,9,6,4,4,3,1,1,1,1] .empty .empty) (.node [9,9,6,5,3,2,2,1,1,1] .empty .empty)) (.node [9,9,6,5,5,1,1,1,1,1] (.node [9,9,6,5,4,2,1,1,1,1] .empty .empty) .empty))) (.node [9,9,7,4,2,2,2,2,1,1] (.node [9,9,7,3,2,2,2,2,2,1] (.node [9,9,6,6,4,1,1,1,1,1] (.node [9,9,6,6,3,2,1,1,1,1] .empty .empty) (.node [9,9,7,2,2,2,2,2,2,2] .empty .empty)) (.node [9,9,7,3,3,3,2,1,1,1] (.node [9,9,7,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [9,9,7,5,2,2,2,1,1,1] (.node [9,9,7,4,3,3,1,1,1,1] (.node [9,9,7,4,3,2,2,1,1,1] .empty .empty) (.node [9,9,7,4,4,2,1,1,1,1] .empty .empty)) (.node [9,9,7,5,4,1,1,1,1,1] (.node [9,9,7,5,3,2,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_47 : RowTree := (.node [9,9,9,3,2,2,2,1,1,1] (.node [9,9,8,4,3,2,1,1,1,1] (.node [9,9,8,3,2,2,2,2,1,1] (.node [9,9,7,7,2,1,1,1,1,1] (.node [9,9,7,6,3,1,1,1,1,1] .empty .empty) (.node [9,9,8,2,2,2,2,2,2,1] .empty .empty)) (.node [9,9,8,3,3,3,1,1,1,1] (.node [9,9,8,3,3,2,2,1,1,1] .empty .empty) (.node [9,9,8,4,2,2,2,1,1,1] .empty .empty))) (.node [9,9,8,6,2,1,1,1,1,1] (.node [9,9,8,5,2,2,1,1,1,1] (.node [9,9,8,4,4,1,1,1,1,1] .empty .empty) (.node [9,9,8,5,3,1,1,1,1,1] .empty .empty)) (.node [9,9,9,2,2,2,2,2,1,1] (.node [9,9,8,7,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [9,9,9,5,2,1,1,1,1,1] (.node [9,9,9,4,2,2,1,1,1,1] (.node [9,9,9,3,3,2,1,1,1,1] .empty .empty) (.node [9,9,9,4,3,1,1,1,1,1] .empty .empty)) (.node [10,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [9,9,9,6,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_48 : RowTree := (.node [9,9,7,6,2,2,1,1,1,1] degreeTree39_46 degreeTree39_47) - -def degreeTree39_49 : RowTree := (.node [10,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1] (.node [10,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,2,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,2,2,2,2,2,2,2,2,2,1,1] (.node [10,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,3,3,3,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,3,3,3,3,3,2,2,2,2,2,1,1,1,1] (.node [10,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,2,2,2,2,2,2,2,2,1] (.node [10,3,3,3,3,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,2,2,2,2,2,2] (.node [10,3,3,3,3,3,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,2,2,2,1,1,1,1,1] (.node [10,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_50 : RowTree := (.node [10,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,3,3,3,3,3,3,3,3,2,1,1,1] (.node [10,3,3,3,3,3,3,3,2,2,1,1,1,1] (.node [10,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,2,2,2,2,2,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,3,2,2,2,2] (.node [10,3,3,3,3,3,3,3,2,2,2,1,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,3,1,1,1,1,1] .empty .empty))) (.node [10,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,3,3,3,1,1] (.node [10,3,3,3,3,3,3,3,3,2,2,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,3,3,2] .empty .empty)) (.node [10,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,4,3,2,2,2,2,2,2,2,2,2,2,2] (.node [10,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,4,2,2,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,4,3,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,4,3,3,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,2,2,2,2,2,2,2,2,2,1] (.node [10,4,3,3,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_51 : RowTree := (.node [10,3,3,3,3,3,3,2,2,2,2,1,1,1] degreeTree39_49 degreeTree39_50) - -def degreeTree39_52 : RowTree := (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2] degreeTree39_48 degreeTree39_51) - -def degreeTree39_53 : RowTree := (.node [10,4,3,3,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,2,2,2,2,2,2,1,1,1,1] (.node [10,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,2,2,2,2,2,2,2,2] (.node [10,4,3,3,3,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,3,3,3,3,2,2,2,2,2,1,1,1] (.node [10,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,2,2,2,2,2,2,1] .empty .empty) .empty))) (.node [10,4,3,3,3,3,3,3,2,2,1,1,1] (.node [10,4,3,3,3,3,3,2,2,2,2,2] (.node [10,4,3,3,3,3,3,2,2,2,1,1,1,1] (.node [10,4,3,3,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,2,2,2,2,1,1] .empty .empty)) (.node [10,4,3,3,3,3,3,3,2,1,1,1,1,1] (.node [10,4,3,3,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,4,3,3,3,3,3,3,3,2,2] (.node [10,4,3,3,3,3,3,3,3,1,1,1,1] (.node [10,4,3,3,3,3,3,3,2,2,2,1] .empty .empty) (.node [10,4,3,3,3,3,3,3,3,2,1,1] .empty .empty)) (.node [10,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,3,3,3,3,1] .empty .empty) .empty)))) - -def degreeTree39_54 : RowTree := (.node [10,4,4,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,4,4,2,2,2,2,2,2,2,2,2,2,1] (.node [10,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,2,2,2,2,2,1,1] (.node [10,4,4,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,4,4,3,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,4,4,3,3,3,2,2,2,1,1,1,1,1,1] (.node [10,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,2,2,2,2,2,1,1,1] (.node [10,4,4,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,4,4,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,4,4,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,2,2,2,2,2,1,1] (.node [10,4,4,3,3,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,2,2,2,2,2,2] .empty .empty)) (.node [10,4,4,3,3,3,3,2,2,1,1,1,1,1] (.node [10,4,4,3,3,3,3,2,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_55 : RowTree := (.node [10,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] degreeTree39_53 degreeTree39_54) - -def degreeTree39_56 : RowTree := (.node [10,4,4,4,2,2,2,2,2,2,2,2,1] (.node [10,4,4,3,3,3,3,3,3,3] (.node [10,4,4,3,3,3,3,3,2,2,1,1] (.node [10,4,4,3,3,3,3,3,1,1,1,1,1,1] (.node [10,4,4,3,3,3,3,2,2,2,2,1] .empty .empty) (.node [10,4,4,3,3,3,3,3,2,1,1,1,1] .empty .empty)) (.node [10,4,4,3,3,3,3,3,3,1,1,1] (.node [10,4,4,3,3,3,3,3,2,2,2] .empty .empty) (.node [10,4,4,3,3,3,3,3,3,2,1] .empty .empty))) (.node [10,4,4,4,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,2,2,2,2,2,2,2,1,1,1] (.node [10,4,4,4,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) .empty))) (.node [10,4,4,4,3,2,2,2,2,2,2,1,1] (.node [10,4,4,4,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,2,2,2,2,2,1,1,1,1] (.node [10,4,4,4,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,4,4,4,3,3,2,2,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,4,4,4,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,3,2,2,2,2,1,1,1] (.node [10,4,4,4,3,3,2,2,2,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_57 : RowTree := (.node [10,4,4,4,4,2,2,2,2,1,1,1,1,1] (.node [10,4,4,4,3,3,3,3,2,2,1] (.node [10,4,4,4,3,3,3,2,2,2,1,1] (.node [10,4,4,4,3,3,3,2,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,3,3,3,2,2,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,3,3,3,1,1,1,1,1] (.node [10,4,4,4,3,3,3,2,2,2,2] .empty .empty) (.node [10,4,4,4,3,3,3,3,2,1,1,1] .empty .empty))) (.node [10,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,3,3,2] (.node [10,4,4,4,3,3,3,3,3,1,1] .empty .empty) (.node [10,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,2,2,2,1,1,1,1,1,1,1] (.node [10,4,4,4,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,4,4,4,4,3,2,2,2,2,1,1] (.node [10,4,4,4,4,3,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,2,2,2,2,2,2,1] (.node [10,4,4,4,4,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,4,4,4,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,3,2,2,2,1,1,1,1] (.node [10,4,4,4,4,3,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,4,4,4,4,3,3,2,2,1,1,1] (.node [10,4,4,4,4,3,3,1,1,1,1,1,1,1] (.node [10,4,4,4,4,3,2,2,2,2,2] .empty .empty) (.node [10,4,4,4,4,3,3,2,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,3,3,3,1,1,1,1] (.node [10,4,4,4,4,3,3,2,2,2,1] .empty .empty) .empty)))) - -def degreeTree39_58 : RowTree := (.node [10,4,4,4,3,3,2,2,2,2,2,1] degreeTree39_56 degreeTree39_57) - -def degreeTree39_59 : RowTree := (.node [10,4,4,3,3,3,3,2,2,2,1,1,1] degreeTree39_55 degreeTree39_58) - -def degreeTree39_60 : RowTree := (.node [10,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree39_52 degreeTree39_59) - -def degreeTree39_61 : RowTree := (.node [9,9,6,3,2,2,2,2,2,2] degreeTree39_45 degreeTree39_60) - -def degreeTree39_62 : RowTree := (.node [9,6,6,5,4,3,3,2,1] degreeTree39_30 degreeTree39_61) - -def degreeTree39_63 : RowTree := (.node [10,4,4,4,4,4,4,2,1,1,1] (.node [10,4,4,4,4,4,3,1,1,1,1,1,1] (.node [10,4,4,4,4,4,2,1,1,1,1,1,1,1] (.node [10,4,4,4,4,3,3,3,3,1] (.node [10,4,4,4,4,3,3,3,2,2] .empty .empty) (.node [10,4,4,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,4,2,2,2,1,1,1] (.node [10,4,4,4,4,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,2,2,2,2,1] .empty .empty))) (.node [10,4,4,4,4,4,3,3,1,1,1] (.node [10,4,4,4,4,4,3,2,2,1,1] (.node [10,4,4,4,4,4,3,2,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,3,2,2,2] .empty .empty)) (.node [10,4,4,4,4,4,4,1,1,1,1,1] (.node [10,4,4,4,4,4,3,3,2,1] .empty .empty) .empty))) (.node [10,5,2,2,2,2,2,2,2,2,2,2,2,2] (.node [10,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,4,4,3,1,1] (.node [10,4,4,4,4,4,4,2,2,1] .empty .empty) (.node [10,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,2,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,2,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [10,5,3,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,3,2,2,2,2,2,2,2,2,2,2,1] (.node [10,5,3,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_64 : RowTree := (.node [10,5,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,3,3,2,2,2,2,2,2,2,2,2] (.node [10,5,3,3,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,3,3,3,2,2,2,2,2,2,1,1,1] (.node [10,5,3,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,2,2,2,2,2,2,2,1] .empty .empty) .empty))) (.node [10,5,3,3,3,3,3,2,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,2,2,2,2,2,1,1] (.node [10,5,3,3,3,3,2,2,2,1,1,1,1,1,1] (.node [10,5,3,3,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,3,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [10,5,3,3,3,3,3,3,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,2,2,2,1,1,1] (.node [10,5,3,3,3,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,2,2,2,2,1] .empty .empty)) (.node [10,5,3,3,3,3,3,3,2,2,1,1] (.node [10,5,3,3,3,3,3,3,2,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_65 : RowTree := (.node [10,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree39_63 degreeTree39_64) - -def degreeTree39_66 : RowTree := (.node [10,5,4,3,2,2,2,2,2,2,1,1,1,1,1] (.node [10,5,4,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,3,3,2,1] (.node [10,5,3,3,3,3,3,3,3,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,3,3,3] .empty .empty)) (.node [10,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,2,2,2,2,2,2,2,2,2,2] (.node [10,5,4,2,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,5,4,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,2,2,2,2,2,2,2,2,1] (.node [10,5,4,3,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,2,2,2,2,2,2,1,1] (.node [10,5,4,3,3,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,2,2,2,2,2,2,2] .empty .empty)) (.node [10,5,4,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_67 : RowTree := (.node [10,5,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,3,3,1,1,1,1,1] (.node [10,5,4,3,3,3,3,2,1,1,1,1,1,1] (.node [10,5,4,3,3,3,2,2,2,2,2,1] (.node [10,5,4,3,3,3,2,2,2,2,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,3,3,3,2,2,2,1,1] (.node [10,5,4,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,2,2,2,2] .empty .empty))) (.node [10,5,4,3,3,3,3,3,3,2] (.node [10,5,4,3,3,3,3,3,2,2,1] (.node [10,5,4,3,3,3,3,3,2,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,3,3,1,1] .empty .empty)) (.node [10,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,5,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,2,2,2,2,2,2,2,1,1] (.node [10,5,4,4,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,4,4,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,2,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [10,5,4,4,3,2,2,2,2,2,1,1,1] (.node [10,5,4,4,3,2,2,2,1,1,1,1,1,1,1] (.node [10,5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,3,2,2,2,2,2,2,1] .empty .empty) .empty)))) - -def degreeTree39_68 : RowTree := (.node [10,5,4,3,3,3,2,2,2,1,1,1,1,1] degreeTree39_66 degreeTree39_67) - -def degreeTree39_69 : RowTree := (.node [10,5,3,3,3,3,3,3,2,2,2] degreeTree39_65 degreeTree39_68) - -def degreeTree39_70 : RowTree := (.node [10,5,4,4,4,2,2,1,1,1,1,1,1,1,1] (.node [10,5,4,4,3,3,3,2,2,2,1] (.node [10,5,4,4,3,3,2,2,2,2,2] (.node [10,5,4,4,3,3,2,2,2,1,1,1,1] (.node [10,5,4,4,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,3,2,2,2,2,1,1] .empty .empty)) (.node [10,5,4,4,3,3,3,2,1,1,1,1,1] (.node [10,5,4,4,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,3,3,2,2,1,1,1] .empty .empty))) (.node [10,5,4,4,3,3,3,3,3,1] (.node [10,5,4,4,3,3,3,3,2,1,1] (.node [10,5,4,4,3,3,3,3,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,3,3,3,2,2] .empty .empty)) (.node [10,5,4,4,4,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,5,4,4,4,3,2,2,1,1,1,1,1] (.node [10,5,4,4,4,2,2,2,2,2,2] (.node [10,5,4,4,4,2,2,2,2,1,1,1,1] (.node [10,5,4,4,4,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,4,2,2,2,2,2,1,1] .empty .empty)) (.node [10,5,4,4,4,3,2,1,1,1,1,1,1,1] (.node [10,5,4,4,4,3,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,4,4,4,3,3,2,1,1,1,1] (.node [10,5,4,4,4,3,2,2,2,2,1] (.node [10,5,4,4,4,3,2,2,2,1,1,1] .empty .empty) (.node [10,5,4,4,4,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,3,3,2,2,2] (.node [10,5,4,4,4,3,3,2,2,1,1] .empty .empty) .empty)))) - -def degreeTree39_71 : RowTree := (.node [10,5,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,4,3,2,1,1,1] (.node [10,5,4,4,4,4,2,2,1,1,1,1] (.node [10,5,4,4,4,4,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,3,3,3,2,1] .empty .empty) (.node [10,5,4,4,4,4,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,4,2,2,2,2] (.node [10,5,4,4,4,4,2,2,2,1,1] .empty .empty) (.node [10,5,4,4,4,4,3,1,1,1,1,1] .empty .empty))) (.node [10,5,4,4,4,4,4,2,1,1] (.node [10,5,4,4,4,4,3,3,1,1] (.node [10,5,4,4,4,4,3,2,2,1] .empty .empty) (.node [10,5,4,4,4,4,4,1,1,1,1] .empty .empty)) (.node [10,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,5,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,2,2,2,2,2,2,2,2,2,1] (.node [10,5,5,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,5,5,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,5,3,2,2,2,2,2,2,2,1,1] (.node [10,5,5,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,5,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,2,2,2,2,2,2,2,2] .empty .empty) .empty)))) - -def degreeTree39_72 : RowTree := (.node [10,5,4,4,4,3,3,3,1,1,1] degreeTree39_70 degreeTree39_71) - -def degreeTree39_73 : RowTree := (.node [10,5,5,3,3,3,3,2,2,2,1] (.node [10,5,5,3,3,3,2,2,1,1,1,1,1,1] (.node [10,5,5,3,3,2,2,2,2,2,1,1,1] (.node [10,5,5,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,5,5,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,3,3,3,3,1,1,1,1,1,1,1] (.node [10,5,5,3,3,3,2,2,2,2,1,1] (.node [10,5,5,3,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,3,2,2,2,2,2] .empty .empty)) (.node [10,5,5,3,3,3,3,2,2,1,1,1] (.node [10,5,5,3,3,3,3,2,1,1,1,1,1] .empty .empty) .empty))) (.node [10,5,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,3,3,3,3,1] (.node [10,5,5,3,3,3,3,3,2,1,1] (.node [10,5,5,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,3,3,3,2,2] .empty .empty)) (.node [10,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,5,4,2,2,2,2,2,2,1,1,1] (.node [10,5,5,4,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,5,4,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,2,2,2,2,2,2,2,1] .empty .empty) .empty)))) - -def degreeTree39_74 : RowTree := (.node [10,5,5,4,3,3,3,3,1,1,1] (.node [10,5,5,4,3,3,2,2,1,1,1,1,1] (.node [10,5,5,4,3,2,2,2,2,2,1,1] (.node [10,5,5,4,3,2,2,2,1,1,1,1,1,1] (.node [10,5,5,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,3,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,2,2,2,2,2,2] .empty .empty) (.node [10,5,5,4,3,3,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,4,3,3,3,2,1,1,1,1] (.node [10,5,5,4,3,3,2,2,2,2,1] (.node [10,5,5,4,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,5,5,4,3,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,3,3,2,2,2] (.node [10,5,5,4,3,3,3,2,2,1,1] .empty .empty) .empty))) (.node [10,5,5,4,4,2,2,2,2,2,1] (.node [10,5,5,4,4,2,2,1,1,1,1,1,1,1] (.node [10,5,5,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,3,3,3,2,1] .empty .empty) (.node [10,5,5,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,2,2,2,2,1,1,1] (.node [10,5,5,4,4,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,5,4,4,3,2,2,2,1,1] (.node [10,5,5,4,4,3,2,1,1,1,1,1,1] (.node [10,5,5,4,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,4,3,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,3,3,1,1,1,1,1] (.node [10,5,5,4,4,3,2,2,2,2] .empty .empty) .empty)))) - -def degreeTree39_75 : RowTree := (.node [10,5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] degreeTree39_73 degreeTree39_74) - -def degreeTree39_76 : RowTree := (.node [10,5,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1] degreeTree39_72 degreeTree39_75) - -def degreeTree39_77 : RowTree := (.node [10,5,4,4,3,3,2,1,1,1,1,1,1,1,1] degreeTree39_69 degreeTree39_76) - -def degreeTree39_78 : RowTree := (.node [10,5,5,5,2,2,2,2,2,1,1,1,1] (.node [10,5,5,4,4,4,3,2,1,1] (.node [10,5,5,4,4,4,2,1,1,1,1,1] (.node [10,5,5,4,4,3,3,3,1,1] (.node [10,5,5,4,4,3,3,2,2,1] .empty .empty) (.node [10,5,5,4,4,4,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,4,2,2,2,1] (.node [10,5,5,4,4,4,2,2,1,1,1] .empty .empty) (.node [10,5,5,4,4,4,3,1,1,1,1] .empty .empty))) (.node [10,5,5,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,4,4,1,1,1] .empty .empty) (.node [10,5,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,2,2,2,2,1,1,1,1,1,1] (.node [10,5,5,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,5,5,5,3,2,2,2,2,1,1,1] (.node [10,5,5,5,3,2,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,2,2,2,2,2,2,2] (.node [10,5,5,5,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,5,5,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,3,2,2,2,1,1,1,1,1] (.node [10,5,5,5,3,2,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,5,5,3,3,2,2,1,1,1,1] (.node [10,5,5,5,3,3,1,1,1,1,1,1,1,1] (.node [10,5,5,5,3,2,2,2,2,2,1] .empty .empty) (.node [10,5,5,5,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,3,3,2,2,2,2] (.node [10,5,5,5,3,3,2,2,2,1,1] .empty .empty) .empty)))) - -def degreeTree39_79 : RowTree := (.node [10,5,5,5,4,3,3,2,1,1] (.node [10,5,5,5,4,2,2,2,2,1,1] (.node [10,5,5,5,4,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,3,3,3,2,2,1] (.node [10,5,5,5,3,3,3,2,1,1,1] .empty .empty) (.node [10,5,5,5,3,3,3,3,1,1] .empty .empty)) (.node [10,5,5,5,4,2,2,1,1,1,1,1,1] (.node [10,5,5,5,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,4,2,2,2,1,1,1,1] .empty .empty))) (.node [10,5,5,5,4,3,2,2,1,1,1] (.node [10,5,5,5,4,3,1,1,1,1,1,1,1] (.node [10,5,5,5,4,2,2,2,2,2] .empty .empty) (.node [10,5,5,5,4,3,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,4,3,3,1,1,1,1] (.node [10,5,5,5,4,3,2,2,2,1] .empty .empty) .empty))) (.node [10,5,5,5,5,2,2,1,1,1,1,1] (.node [10,5,5,5,4,4,3,1,1,1] (.node [10,5,5,5,4,4,2,1,1,1,1] (.node [10,5,5,5,4,4,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,4,4,2,2,1,1] .empty .empty)) (.node [10,5,5,5,5,2,1,1,1,1,1,1,1] (.node [10,5,5,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,5,5,5,3,2,1,1,1,1] (.node [10,5,5,5,5,2,2,2,2,1] (.node [10,5,5,5,5,2,2,2,1,1,1] .empty .empty) (.node [10,5,5,5,5,3,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,5,3,3,1,1,1] (.node [10,5,5,5,5,3,2,2,1,1] .empty .empty) .empty)))) - -def degreeTree39_80 : RowTree := (.node [10,5,5,5,3,3,3,1,1,1,1,1] degreeTree39_78 degreeTree39_79) - -def degreeTree39_81 : RowTree := (.node [10,6,3,2,2,2,2,2,2,2,2,2,2] (.node [10,6,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,5,5,1,1,1,1] (.node [10,5,5,5,5,4,2,1,1,1] .empty .empty) (.node [10,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,6,3,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,2,2,2,2,2,2,2,2,2,1,1] (.node [10,6,3,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) .empty))) (.node [10,6,3,3,2,2,2,2,2,2,2,2,1] (.node [10,6,3,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,2,2,2,2,2,2,2,1,1,1] (.node [10,6,3,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,6,3,3,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,3,2,2,2,2,2,1,1,1,1] (.node [10,6,3,3,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_82 : RowTree := (.node [10,6,3,3,3,3,3,3,2,2,1] (.node [10,6,3,3,3,3,3,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,3,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,3,3,2,2,2,2,1,1,1] (.node [10,6,3,3,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,3,2,2,2,2,2,1] .empty .empty))) (.node [10,6,3,3,3,3,3,2,2,2,2] (.node [10,6,3,3,3,3,3,2,2,1,1,1,1] (.node [10,6,3,3,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,6,3,3,3,3,3,3,2,1,1,1] (.node [10,6,3,3,3,3,3,3,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,4,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,3,3,3,2] (.node [10,6,3,3,3,3,3,3,3,1,1] .empty .empty) (.node [10,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,2,2,2,2,2,2,2,2,2,1] (.node [10,6,4,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_83 : RowTree := (.node [10,6,3,3,3,2,2,2,2,2,2,1,1] degreeTree39_81 degreeTree39_82) - -def degreeTree39_84 : RowTree := (.node [10,5,5,5,5,4,1,1,1,1,1] degreeTree39_80 degreeTree39_83) - -def degreeTree39_85 : RowTree := (.node [10,6,4,3,3,3,2,2,2,2,1,1] (.node [10,6,4,3,3,2,2,2,2,1,1,1,1,1] (.node [10,6,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,2,2,2,2,2,2,2,1,1] (.node [10,6,4,3,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,6,4,3,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,6,4,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,4,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,2,2,2,2,2,2,1] (.node [10,6,4,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,4,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,3,3,3,2,2,2,1,1,1,1] (.node [10,6,4,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,4,3,3,3,3,3,2,1,1] (.node [10,6,4,3,3,3,3,2,2,1,1,1] (.node [10,6,4,3,3,3,3,1,1,1,1,1,1,1] (.node [10,6,4,3,3,3,2,2,2,2,2] .empty .empty) (.node [10,6,4,3,3,3,3,2,1,1,1,1,1] .empty .empty)) (.node [10,6,4,3,3,3,3,3,1,1,1,1] (.node [10,6,4,3,3,3,3,2,2,2,1] .empty .empty) .empty)) (.node [10,6,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,3,3,3,3,1] (.node [10,6,4,3,3,3,3,3,2,2] .empty .empty) (.node [10,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_86 : RowTree := (.node [10,6,4,4,3,3,2,2,2,2,1] (.node [10,6,4,4,3,2,2,2,2,1,1,1,1] (.node [10,6,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,2,2,2,2,2,2,1,1,1] (.node [10,6,4,4,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,6,4,4,3,2,2,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,3,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,6,4,4,3,3,2,1,1,1,1,1,1,1] (.node [10,6,4,4,3,2,2,2,2,2,2] (.node [10,6,4,4,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,6,4,4,3,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,3,3,2,2,2,1,1,1] (.node [10,6,4,4,3,3,2,2,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,4,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,3,3,2,2,2] (.node [10,6,4,4,3,3,3,2,1,1,1,1] (.node [10,6,4,4,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,3,3,3,2,2,1,1] .empty .empty)) (.node [10,6,4,4,3,3,3,3,2,1] (.node [10,6,4,4,3,3,3,3,1,1,1] .empty .empty) .empty)) (.node [10,6,4,4,4,2,2,2,2,1,1,1] (.node [10,6,4,4,4,2,2,1,1,1,1,1,1,1] (.node [10,6,4,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,4,3,1,1,1,1,1,1,1,1] (.node [10,6,4,4,4,2,2,2,2,2,1] .empty .empty) .empty)))) - -def degreeTree39_87 : RowTree := (.node [10,6,4,4,2,2,2,2,1,1,1,1,1,1,1] degreeTree39_85 degreeTree39_86) - -def degreeTree39_88 : RowTree := (.node [10,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,4,4,1,1,1,1,1,1,1] (.node [10,6,4,4,4,3,3,1,1,1,1,1] (.node [10,6,4,4,4,3,2,2,2,1,1] (.node [10,6,4,4,4,3,2,2,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,3,2,2,2,2] .empty .empty)) (.node [10,6,4,4,4,3,3,2,2,1] (.node [10,6,4,4,4,3,3,2,1,1,1] .empty .empty) (.node [10,6,4,4,4,3,3,3,1,1] .empty .empty))) (.node [10,6,4,4,4,4,3,1,1,1,1] (.node [10,6,4,4,4,4,2,2,1,1,1] (.node [10,6,4,4,4,4,2,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,2,2,2,1] .empty .empty)) (.node [10,6,4,4,4,4,4,1,1,1] (.node [10,6,4,4,4,4,3,2,1,1] .empty .empty) .empty))) (.node [10,6,5,2,2,2,2,2,2,2,2,2] (.node [10,6,5,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,2,2,2,2,2,2,2,2,1,1] (.node [10,6,5,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,6,5,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,3,2,2,2,2,2,1,1,1,1,1] (.node [10,6,5,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_89 : RowTree := (.node [10,6,5,3,3,3,3,2,1,1,1,1] (.node [10,6,5,3,3,2,2,2,2,2,2] (.node [10,6,5,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,6,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,6,5,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,3,3,2,2,2,2,1,1,1,1] (.node [10,6,5,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,2,2,2,2,2,1,1] .empty .empty))) (.node [10,6,5,3,3,3,2,2,2,1,1,1] (.node [10,6,5,3,3,3,2,1,1,1,1,1,1,1] (.node [10,6,5,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,3,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,5,3,3,3,3,1,1,1,1,1,1] (.node [10,6,5,3,3,3,2,2,2,2,1] .empty .empty) .empty))) (.node [10,6,5,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,3,3,3,3,2,1] (.node [10,6,5,3,3,3,3,2,2,2] (.node [10,6,5,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,6,5,3,3,3,3,3,1,1,1] .empty .empty)) (.node [10,6,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,6,5,4,2,2,2,2,2,2,1,1] (.node [10,6,5,4,2,2,2,2,1,1,1,1,1,1] (.node [10,6,5,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,6,5,4,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,2,2,2,2,2,2,2] .empty .empty) .empty)))) - -def degreeTree39_90 : RowTree := (.node [10,6,5,3,2,2,2,2,2,2,1,1,1] degreeTree39_88 degreeTree39_89) - -def degreeTree39_91 : RowTree := (.node [10,6,4,4,4,3,2,1,1,1,1,1,1] degreeTree39_87 degreeTree39_90) - -def degreeTree39_92 : RowTree := (.node [10,6,4,3,2,2,2,2,2,1,1,1,1,1,1] degreeTree39_84 degreeTree39_91) - -def degreeTree39_93 : RowTree := (.node [10,5,5,4,4,3,3,2,1,1,1] degreeTree39_77 degreeTree39_92) - -def degreeTree39_94 : RowTree := (.node [10,6,5,4,4,2,1,1,1,1,1,1,1,1] (.node [10,6,5,4,3,3,2,2,2,1,1] (.node [10,6,5,4,3,2,2,2,2,2,1] (.node [10,6,5,4,3,2,2,2,1,1,1,1,1] (.node [10,6,5,4,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,3,2,2,2,2,1,1,1] .empty .empty)) (.node [10,6,5,4,3,3,2,1,1,1,1,1,1] (.node [10,6,5,4,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,3,3,2,2,1,1,1,1] .empty .empty))) (.node [10,6,5,4,3,3,3,2,2,1] (.node [10,6,5,4,3,3,3,1,1,1,1,1] (.node [10,6,5,4,3,3,2,2,2,2] .empty .empty) (.node [10,6,5,4,3,3,3,2,1,1,1] .empty .empty)) (.node [10,6,5,4,4,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,3,3,3,3,1,1] .empty .empty) .empty))) (.node [10,6,5,4,4,3,2,2,2,1] (.node [10,6,5,4,4,2,2,2,2,2] (.node [10,6,5,4,4,2,2,2,1,1,1,1] (.node [10,6,5,4,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,2,2,2,2,1,1] .empty .empty)) (.node [10,6,5,4,4,3,2,1,1,1,1,1] (.node [10,6,5,4,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,3,2,2,1,1,1] .empty .empty))) (.node [10,6,5,4,4,4,2,1,1,1,1] (.node [10,6,5,4,4,3,3,2,1,1] (.node [10,6,5,4,4,3,3,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,4,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,4,4,3,1,1,1] (.node [10,6,5,4,4,4,2,2,1,1] .empty .empty) .empty)))) - -def degreeTree39_95 : RowTree := (.node [10,6,5,5,3,3,2,2,1,1,1] (.node [10,6,5,5,3,2,1,1,1,1,1,1,1,1] (.node [10,6,5,5,2,2,2,2,1,1,1,1,1] (.node [10,6,5,5,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,5,2,2,2,2,2,2,1] (.node [10,6,5,5,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,5,3,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,5,3,2,2,2,2,2] (.node [10,6,5,5,3,2,2,2,1,1,1,1] (.node [10,6,5,5,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,3,2,2,2,2,1,1] .empty .empty)) (.node [10,6,5,5,3,3,2,1,1,1,1,1] (.node [10,6,5,5,3,3,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,5,5,4,2,2,2,1,1,1] (.node [10,6,5,5,4,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,3,3,3,1,1,1,1] (.node [10,6,5,5,3,3,2,2,2,1] .empty .empty) (.node [10,6,5,5,3,3,3,2,1,1] .empty .empty)) (.node [10,6,5,5,4,2,2,1,1,1,1,1] (.node [10,6,5,5,4,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,6,5,5,4,3,2,2,1,1] (.node [10,6,5,5,4,3,1,1,1,1,1,1] (.node [10,6,5,5,4,2,2,2,2,1] .empty .empty) (.node [10,6,5,5,4,3,2,1,1,1,1] .empty .empty)) (.node [10,6,5,5,4,4,1,1,1,1,1] (.node [10,6,5,5,4,3,3,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_96 : RowTree := (.node [10,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree39_94 degreeTree39_95) - -def degreeTree39_97 : RowTree := (.node [10,6,6,2,2,2,2,2,2,2,2,1] (.node [10,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,5,2,2,2,1,1] (.node [10,6,5,5,5,2,1,1,1,1,1,1] (.node [10,6,5,5,5,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,5,2,2,1,1,1,1] .empty .empty)) (.node [10,6,5,5,5,3,2,1,1,1] (.node [10,6,5,5,5,3,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,5,4,1,1,1,1] .empty .empty))) (.node [10,6,6,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,2,2,2,2,2,2,2,1,1,1] (.node [10,6,6,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,6,3,2,2,2,2,2,2,1,1] (.node [10,6,6,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,3,2,2,2,2,2,1,1,1,1] (.node [10,6,6,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,6,6,3,3,2,2,1,1,1,1,1,1,1] (.node [10,6,6,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,6,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,3,3,2,2,2,2,1,1,1] (.node [10,6,6,3,3,2,2,2,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_98 : RowTree := (.node [10,6,6,4,2,2,2,2,2,1,1,1] (.node [10,6,6,3,3,3,3,2,2,1] (.node [10,6,6,3,3,3,2,2,2,1,1] (.node [10,6,6,3,3,3,2,1,1,1,1,1,1] (.node [10,6,6,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,3,3,2,2,1,1,1,1] .empty .empty)) (.node [10,6,6,3,3,3,3,1,1,1,1,1] (.node [10,6,6,3,3,3,2,2,2,2] .empty .empty) (.node [10,6,6,3,3,3,3,2,1,1,1] .empty .empty))) (.node [10,6,6,4,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,3,3,3,3,1,1] .empty .empty) (.node [10,6,6,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,4,2,2,2,2,1,1,1,1,1] (.node [10,6,6,4,2,2,2,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,6,4,3,2,2,2,2,2] (.node [10,6,6,4,3,2,2,1,1,1,1,1,1] (.node [10,6,6,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,2,2,2,2,2,2,1] .empty .empty) (.node [10,6,6,4,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,4,3,2,2,2,2,1,1] (.node [10,6,6,4,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,6,6,4,3,3,2,2,2,1] (.node [10,6,6,4,3,3,2,1,1,1,1,1] (.node [10,6,6,4,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,3,3,2,2,1,1,1] .empty .empty)) (.node [10,6,6,4,3,3,3,2,1,1] (.node [10,6,6,4,3,3,3,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_99 : RowTree := (.node [10,6,6,3,3,2,2,2,2,2,1] degreeTree39_97 degreeTree39_98) - -def degreeTree39_100 : RowTree := (.node [10,6,5,5,4,4,2,1,1,1] degreeTree39_96 degreeTree39_99) - -def degreeTree39_101 : RowTree := (.node [10,6,6,5,2,2,2,2,1,1,1,1] (.node [10,6,6,4,4,3,3,1,1,1] (.node [10,6,6,4,4,2,2,2,2,1] (.node [10,6,6,4,4,2,2,1,1,1,1,1] (.node [10,6,6,4,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,4,2,2,2,1,1,1] .empty .empty)) (.node [10,6,6,4,4,3,2,1,1,1,1] (.node [10,6,6,4,4,3,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,4,3,2,2,1,1] .empty .empty))) (.node [10,6,6,5,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,4,4,2,1,1,1] (.node [10,6,6,4,4,4,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,2,2,2,1,1,1,1,1,1] (.node [10,6,6,5,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,6,5,3,2,2,2,2,1] (.node [10,6,6,5,3,2,1,1,1,1,1,1,1] (.node [10,6,6,5,2,2,2,2,2,2] (.node [10,6,6,5,2,2,2,2,2,1,1] .empty .empty) (.node [10,6,6,5,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,3,2,2,2,1,1,1] (.node [10,6,6,5,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,6,6,5,3,3,3,1,1,1] (.node [10,6,6,5,3,3,2,1,1,1,1] (.node [10,6,6,5,3,3,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,3,3,2,2,1,1] .empty .empty)) (.node [10,6,6,5,4,2,1,1,1,1,1,1] (.node [10,6,6,5,4,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_102 : RowTree := (.node [10,6,6,6,3,1,1,1,1,1,1,1,1] (.node [10,6,6,5,5,3,1,1,1,1] (.node [10,6,6,5,4,4,1,1,1,1] (.node [10,6,6,5,4,3,1,1,1,1,1] (.node [10,6,6,5,4,2,2,2,1,1] .empty .empty) (.node [10,6,6,5,4,3,2,1,1,1] .empty .empty)) (.node [10,6,6,5,5,2,1,1,1,1,1] (.node [10,6,6,5,5,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,5,2,2,1,1,1] .empty .empty))) (.node [10,6,6,6,2,2,2,1,1,1,1,1] (.node [10,6,6,6,2,1,1,1,1,1,1,1,1,1] (.node [10,6,6,6,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,6,2,2,2,2,2,1] (.node [10,6,6,6,2,2,2,2,1,1,1] .empty .empty) .empty))) (.node [10,6,6,6,4,2,1,1,1,1,1] (.node [10,6,6,6,3,3,1,1,1,1,1] (.node [10,6,6,6,3,2,2,1,1,1,1] (.node [10,6,6,6,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,3,2,2,2,1,1] .empty .empty)) (.node [10,6,6,6,4,1,1,1,1,1,1,1] (.node [10,6,6,6,3,3,2,1,1,1] .empty .empty) .empty)) (.node [10,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,6,5,1,1,1,1,1,1] (.node [10,6,6,6,4,2,2,1,1,1] .empty .empty) (.node [10,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,7,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_103 : RowTree := (.node [10,6,6,5,4,2,2,1,1,1,1] degreeTree39_101 degreeTree39_102) - -def degreeTree39_104 : RowTree := (.node [10,7,3,3,2,2,2,2,2,2,1,1,1,1] (.node [10,7,3,2,2,2,2,2,2,2,2,1,1,1] (.node [10,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,2,2,2,2,2,2,2,2,2,2,2] (.node [10,7,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,7,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,7,3,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,7,3,3,3,2,2,2,2,1,1,1,1,1] (.node [10,7,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,2,2,2,2,2,2,2,2] (.node [10,7,3,3,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,7,3,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,7,3,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,2,2,2,2,2,2,1] (.node [10,7,3,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,7,3,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,3,2,2,2,1,1,1,1] (.node [10,7,3,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_105 : RowTree := (.node [10,7,4,2,2,2,2,2,2,2,1,1,1,1] (.node [10,7,3,3,3,3,3,3,2,2] (.node [10,7,3,3,3,3,3,2,2,1,1,1] (.node [10,7,3,3,3,3,3,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,2,2,2,2,2] .empty .empty) (.node [10,7,3,3,3,3,3,2,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,3,3,3,1,1,1,1] (.node [10,7,3,3,3,3,3,2,2,2,1] .empty .empty) (.node [10,7,3,3,3,3,3,3,2,1,1] .empty .empty))) (.node [10,7,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,3,3,3,1] .empty .empty) (.node [10,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,7,4,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,7,4,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,2,2,2,2,2,2,2,2,2] (.node [10,7,4,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,7,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,2,2,2,2,2,2,1,1,1] (.node [10,7,4,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,7,4,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_106 : RowTree := (.node [10,7,3,3,3,3,2,2,2,2,1,1] degreeTree39_104 degreeTree39_105) - -def degreeTree39_107 : RowTree := (.node [10,7,2,2,2,2,2,2,2,2,2,1,1,1,1] degreeTree39_103 degreeTree39_106) - -def degreeTree39_108 : RowTree := (.node [10,6,6,4,4,1,1,1,1,1,1,1,1,1] degreeTree39_100 degreeTree39_107) - -def degreeTree39_109 : RowTree := (.node [10,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,3,2,2,2,2,1] (.node [10,7,4,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,2,2,2,2,2,1,1] (.node [10,7,4,3,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,2,2,2,2,2,2] .empty .empty)) (.node [10,7,4,3,3,3,2,2,1,1,1,1,1] (.node [10,7,4,3,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,2,2,2,1,1,1] .empty .empty))) (.node [10,7,4,3,3,3,3,2,2,2] (.node [10,7,4,3,3,3,3,2,1,1,1,1] (.node [10,7,4,3,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,3,2,2,1,1] .empty .empty)) (.node [10,7,4,3,3,3,3,3,2,1] (.node [10,7,4,3,3,3,3,3,1,1,1] .empty .empty) .empty))) (.node [10,7,4,4,2,2,2,2,2,2,2] (.node [10,7,4,4,2,2,2,2,1,1,1,1,1,1] (.node [10,7,4,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,2,2,2,2,2,2,1,1] (.node [10,7,4,4,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,7,4,4,3,2,2,2,1,1,1,1,1] (.node [10,7,4,4,3,2,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,3,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,3,2,2,2,2,2,1] (.node [10,7,4,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_110 : RowTree := (.node [10,7,4,4,4,3,1,1,1,1,1,1,1] (.node [10,7,4,4,3,3,3,3,1,1] (.node [10,7,4,4,3,3,2,2,2,2] (.node [10,7,4,4,3,3,2,2,1,1,1,1] (.node [10,7,4,4,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,3,3,2,2,2,1,1] .empty .empty)) (.node [10,7,4,4,3,3,3,2,1,1,1] (.node [10,7,4,4,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,3,3,3,2,2,1] .empty .empty))) (.node [10,7,4,4,4,2,2,2,1,1,1,1] (.node [10,7,4,4,4,2,1,1,1,1,1,1,1,1] (.node [10,7,4,4,4,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,4,2,2,2,2,2] (.node [10,7,4,4,4,2,2,2,2,1,1] .empty .empty) .empty))) (.node [10,7,4,4,4,4,2,1,1,1,1] (.node [10,7,4,4,4,3,3,1,1,1,1] (.node [10,7,4,4,4,3,2,2,1,1,1] (.node [10,7,4,4,4,3,2,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,3,2,2,2,1] .empty .empty)) (.node [10,7,4,4,4,4,1,1,1,1,1,1] (.node [10,7,4,4,4,3,3,2,1,1] .empty .empty) .empty)) (.node [10,7,5,3,3,3,3,2,2,1] (.node [10,7,4,4,4,4,3,1,1,1] (.node [10,7,4,4,4,4,2,2,1,1] .empty .empty) (.node [10,7,5,3,3,3,2,2,2,2] .empty .empty)) (.node [10,7,5,4,3,2,2,2,2,2] (.node [10,7,5,3,3,3,3,3,1,1] .empty .empty) .empty)))) - -def degreeTree39_111 : RowTree := (.node [10,7,4,4,3,3,1,1,1,1,1,1,1,1] degreeTree39_109 degreeTree39_110) - -def degreeTree39_112 : RowTree := (.node [10,7,6,3,3,3,3,2,1,1] (.node [10,7,5,5,3,3,2,2,1,1] (.node [10,7,5,4,4,3,3,1,1,1] (.node [10,7,5,4,4,2,2,2,2,1] (.node [10,7,5,4,3,3,3,2,1,1] .empty .empty) (.node [10,7,5,4,4,3,2,2,1,1] .empty .empty)) (.node [10,7,5,5,2,2,2,2,2,2] (.node [10,7,5,4,4,4,2,1,1,1] .empty .empty) (.node [10,7,5,5,3,2,2,2,2,1] .empty .empty))) (.node [10,7,5,5,5,2,2,1,1,1] (.node [10,7,5,5,4,2,2,2,1,1] (.node [10,7,5,5,3,3,3,1,1,1] .empty .empty) (.node [10,7,5,5,4,3,2,1,1,1] .empty .empty)) (.node [10,7,6,3,3,3,2,2,2,1] (.node [10,7,6,3,3,2,2,2,2,2] .empty .empty) .empty))) (.node [10,7,6,5,2,2,2,2,2,1] (.node [10,7,6,4,3,3,3,1,1,1] (.node [10,7,6,4,3,2,2,2,2,1] (.node [10,7,6,4,2,2,2,2,2,2] .empty .empty) (.node [10,7,6,4,3,3,2,2,1,1] .empty .empty)) (.node [10,7,6,4,4,3,2,1,1,1] (.node [10,7,6,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [10,7,7,3,3,2,2,2,2,1] (.node [10,7,6,6,2,2,2,2,1,1] (.node [10,7,6,5,3,2,2,2,1,1] .empty .empty) (.node [10,7,7,3,2,2,2,2,2,2] .empty .empty)) (.node [10,7,7,3,3,3,3,1,1,1] (.node [10,7,7,3,3,3,2,2,1,1] .empty .empty) .empty)))) - -def degreeTree39_113 : RowTree := (.node [10,8,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,8,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,8,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,5,2,2,2,2,1,1] (.node [10,7,7,4,3,2,2,2,1,1] .empty .empty) (.node [10,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,8,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,8,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,8,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,2,2,2,2,2,2,2,2,2] (.node [10,8,3,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,3,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,8,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,2,2,2,2,2,2,1,1,1] (.node [10,8,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,8,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_114 : RowTree := (.node [10,7,7,4,2,2,2,2,2,1] degreeTree39_112 degreeTree39_113) - -def degreeTree39_115 : RowTree := (.node [10,7,5,4,3,3,2,2,2,1] degreeTree39_111 degreeTree39_114) - -def degreeTree39_116 : RowTree := (.node [10,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,3,2,2,2,2,1] (.node [10,8,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,2,2,2,2,2,1,1] (.node [10,8,3,3,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,8,3,3,3,2,2,2,2,2,2] .empty .empty)) (.node [10,8,3,3,3,3,2,2,1,1,1,1,1] (.node [10,8,3,3,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,3,3,2,2,2,1,1,1] .empty .empty))) (.node [10,8,3,3,3,3,3,2,2,2] (.node [10,8,3,3,3,3,3,2,1,1,1,1] (.node [10,8,3,3,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,3,3,3,2,2,1,1] .empty .empty)) (.node [10,8,3,3,3,3,3,3,2,1] (.node [10,8,3,3,3,3,3,3,1,1,1] .empty .empty) .empty))) (.node [10,8,4,2,2,2,2,2,2,2,2,1] (.node [10,8,4,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,2,2,2,2,2,2,2,1,1,1] (.node [10,8,4,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,8,4,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,3,2,2,2,2,2,1,1,1,1] (.node [10,8,4,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_117 : RowTree := (.node [10,8,4,3,3,3,3,2,2,1] (.node [10,8,4,3,3,3,1,1,1,1,1,1,1,1] (.node [10,8,4,3,3,2,2,1,1,1,1,1,1,1] (.node [10,8,4,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,8,4,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,3,3,2,2,2,2,1,1,1] (.node [10,8,4,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,3,2,2,2,2,2,1] .empty .empty))) (.node [10,8,4,3,3,3,2,2,2,2] (.node [10,8,4,3,3,3,2,2,1,1,1,1] (.node [10,8,4,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,8,4,3,3,3,3,2,1,1,1] (.node [10,8,4,3,3,3,3,1,1,1,1,1] .empty .empty) .empty))) (.node [10,8,4,4,2,2,2,2,2,1,1,1] (.node [10,8,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,3,3,3,3,1,1] .empty .empty) (.node [10,8,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,2,2,2,2,1,1,1,1,1] (.node [10,8,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,8,4,4,3,2,2,1,1,1,1,1,1] (.node [10,8,4,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,4,4,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,3,2,2,2,2,1,1] (.node [10,8,4,4,3,2,2,2,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree39_118 : RowTree := (.node [10,8,4,3,2,2,2,2,2,2,1,1] degreeTree39_116 degreeTree39_117) - -def degreeTree39_119 : RowTree := (.node [10,8,4,4,4,4,1,1,1,1,1] (.node [10,8,4,4,4,2,1,1,1,1,1,1,1] (.node [10,8,4,4,3,3,2,2,2,1] (.node [10,8,4,4,3,3,2,1,1,1,1,1] (.node [10,8,4,4,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,3,3,2,2,1,1,1] .empty .empty)) (.node [10,8,4,4,3,3,3,2,1,1] (.node [10,8,4,4,3,3,3,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,4,4,4,3,1,1,1,1,1,1] (.node [10,8,4,4,4,2,2,2,1,1,1] (.node [10,8,4,4,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,2,2,2,2,1] .empty .empty)) (.node [10,8,4,4,4,3,2,2,1,1] (.node [10,8,4,4,4,3,2,1,1,1,1] .empty .empty) .empty))) (.node [10,8,5,4,4,2,2,2,1,1] (.node [10,8,5,4,2,2,2,2,2,2] (.node [10,8,5,3,3,3,2,2,2,1] (.node [10,8,5,3,3,2,2,2,2,2] .empty .empty) (.node [10,8,5,3,3,3,3,2,1,1] .empty .empty)) (.node [10,8,5,4,3,3,2,2,1,1] (.node [10,8,5,4,3,2,2,2,2,1] .empty .empty) .empty)) (.node [10,8,6,3,3,3,2,2,1,1] (.node [10,8,6,3,2,2,2,2,2,2] (.node [10,8,5,5,2,2,2,2,2,1] .empty .empty) (.node [10,8,6,3,3,2,2,2,2,1] .empty .empty)) (.node [10,8,7,2,2,2,2,2,2,2] (.node [10,8,6,4,2,2,2,2,2,1] .empty .empty) .empty)))) - -def degreeTree39_120 : RowTree := (.node [10,9,4,4,3,2,2,2,2,1] (.node [10,9,2,2,2,2,2,2,2,2,2,1,1] (.node [10,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,2,2,2,2,2,2,1] .empty .empty) (.node [10,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,9,4,3,3,2,2,2,2,2] (.node [10,9,3,3,3,3,2,2,2,2] (.node [10,9,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,9,3,3,3,3,3,2,2,1] .empty .empty)) (.node [10,9,4,4,2,2,2,2,2,2] (.node [10,9,4,3,3,3,2,2,2,1] .empty .empty) .empty))) (.node [10,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,3,3,2,2,2,2,1] (.node [10,9,5,3,2,2,2,2,2,2] .empty .empty) (.node [10,9,6,2,2,2,2,2,2,2] .empty .empty)) (.node [10,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,2,2,2,2,2,2,2,2,2,1] (.node [10,10,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,10,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,10,4,3,2,2,2,2,2,2] (.node [10,10,3,3,3,2,2,2,2,2] .empty .empty) .empty)))) - -def degreeTree39_121 : RowTree := (.node [10,8,7,3,2,2,2,2,2,1] degreeTree39_119 degreeTree39_120) - -def degreeTree39_122 : RowTree := (.node [10,8,4,4,3,2,2,2,2,2] degreeTree39_118 degreeTree39_121) - -def degreeTree39_123 : RowTree := (.node [10,8,3,3,3,2,2,2,1,1,1,1,1,1] degreeTree39_115 degreeTree39_122) - -def degreeTree39_124 : RowTree := (.node [10,7,4,3,3,2,2,2,1,1,1,1,1,1] degreeTree39_108 degreeTree39_123) - -def degreeTree39_125 : RowTree := (.node [10,6,5,4,3,2,1,1,1,1,1,1,1,1,1] degreeTree39_93 degreeTree39_124) - -def degreeTree39_126 : RowTree := (.node [10,4,4,4,4,3,3,3,2,1,1] degreeTree39_62 degreeTree39_125) - -def degreeTree39 : RowTree := degreeTree39_126 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 39. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree39_0 : RowTree := (.node [8,5,5,5,5,4,3,2,2] (.node [8,5,5,4,4,4,4,4,1] (.node [8,5,4,4,4,4,4,3,3] (.node [7,7,7,7,7,2,1,1] (.node [7,7,7,7,7,1,1,1,1] .empty .empty) (.node [8,4,4,4,4,4,4,4,3] .empty .empty)) (.node [8,5,5,4,4,4,3,3,3] (.node [8,5,4,4,4,4,4,4,2] .empty .empty) (.node [8,5,5,4,4,4,4,3,2] .empty .empty))) (.node [8,5,5,5,4,4,4,3,1] (.node [8,5,5,5,4,4,3,3,2] (.node [8,5,5,5,4,3,3,3,3] .empty .empty) (.node [8,5,5,5,4,4,4,2,2] .empty .empty)) (.node [8,5,5,5,5,3,3,3,2] (.node [8,5,5,5,4,4,4,4] .empty .empty) .empty))) (.node [8,5,5,5,5,5,4,2] (.node [8,5,5,5,5,5,2,2,2] (.node [8,5,5,5,5,4,4,2,1] (.node [8,5,5,5,5,4,3,3,1] .empty .empty) (.node [8,5,5,5,5,4,4,3] .empty .empty)) (.node [8,5,5,5,5,5,3,3] (.node [8,5,5,5,5,5,3,2,1] .empty .empty) (.node [8,5,5,5,5,5,4,1,1] .empty .empty))) (.node [8,6,4,4,4,4,4,4,1] (.node [8,6,4,4,4,4,3,3,3] (.node [8,5,5,5,5,5,5,1] .empty .empty) (.node [8,6,4,4,4,4,4,3,2] .empty .empty)) (.node [8,6,5,4,4,4,3,3,2] (.node [8,6,5,4,4,3,3,3,3] .empty .empty) .empty)))) + +def degreeTree39_1 : RowTree := (.node [8,6,5,5,5,4,4,2] (.node [8,6,5,5,4,4,4,3] (.node [8,6,5,5,4,3,3,3,2] (.node [8,6,5,4,4,4,4,4] (.node [8,6,5,4,4,4,4,3,1] .empty .empty) (.node [8,6,5,5,3,3,3,3,3] .empty .empty)) (.node [8,6,5,5,4,4,3,3,1] (.node [8,6,5,5,4,4,3,2,2] .empty .empty) (.node [8,6,5,5,4,4,4,2,1] .empty .empty))) (.node [8,6,5,5,5,4,3,2,1] (.node [8,6,5,5,5,3,3,3,1] (.node [8,6,5,5,5,3,3,2,2] .empty .empty) (.node [8,6,5,5,5,4,2,2,2] .empty .empty)) (.node [8,6,5,5,5,4,4,1,1] (.node [8,6,5,5,5,4,3,3] .empty .empty) .empty))) (.node [8,6,6,4,4,4,3,2,2] (.node [8,6,5,5,5,5,4,1] (.node [8,6,5,5,5,5,3,1,1] (.node [8,6,5,5,5,5,2,2,1] .empty .empty) (.node [8,6,5,5,5,5,3,2] .empty .empty)) (.node [8,6,6,4,4,3,3,3,2] (.node [8,6,6,4,3,3,3,3,3] .empty .empty) .empty)) (.node [8,6,6,5,3,3,3,3,2] (.node [8,6,6,4,4,4,4,2,1] (.node [8,6,6,4,4,4,3,3,1] .empty .empty) (.node [8,6,6,4,4,4,4,3] .empty .empty)) (.node [8,6,6,5,4,3,3,3,1] (.node [8,6,6,5,4,3,3,2,2] .empty .empty) .empty)))) + +def degreeTree39_2 : RowTree := (.node [8,6,5,4,4,4,4,2,2] degreeTree39_0 degreeTree39_1) + +def degreeTree39_3 : RowTree := (.node [8,6,6,6,3,3,3,2,2] (.node [8,6,6,5,5,4,2,2,1] (.node [8,6,6,5,4,4,4,2] (.node [8,6,6,5,4,4,3,3] (.node [8,6,6,5,4,4,3,2,1] .empty .empty) (.node [8,6,6,5,4,4,4,1,1] .empty .empty)) (.node [8,6,6,5,5,3,3,2,1] (.node [8,6,6,5,5,3,2,2,2] .empty .empty) (.node [8,6,6,5,5,3,3,3] .empty .empty))) (.node [8,6,6,5,5,5,2,1,1] (.node [8,6,6,5,5,4,3,2] (.node [8,6,6,5,5,4,3,1,1] .empty .empty) (.node [8,6,6,5,5,4,4,1] .empty .empty)) (.node [8,6,6,5,5,5,3,1] (.node [8,6,6,5,5,5,2,2] .empty .empty) .empty))) (.node [8,6,6,6,4,4,3,2] (.node [8,6,6,6,4,3,3,3] (.node [8,6,6,6,4,3,2,2,2] (.node [8,6,6,6,3,3,3,3,1] .empty .empty) (.node [8,6,6,6,4,3,3,2,1] .empty .empty)) (.node [8,6,6,6,4,4,3,1,1] (.node [8,6,6,6,4,4,2,2,1] .empty .empty) .empty)) (.node [8,6,6,6,5,3,3,1,1] (.node [8,6,6,6,5,2,2,2,2] (.node [8,6,6,6,4,4,4,1] .empty .empty) (.node [8,6,6,6,5,3,2,2,1] .empty .empty)) (.node [8,6,6,6,5,4,2,1,1] (.node [8,6,6,6,5,3,3,2] .empty .empty) .empty)))) + +def degreeTree39_4 : RowTree := (.node [8,7,4,4,4,4,4,4] (.node [8,6,6,6,6,4,1,1,1] (.node [8,6,6,6,6,2,2,2,1] (.node [8,6,6,6,5,5,1,1,1] (.node [8,6,6,6,5,4,3,1] .empty .empty) (.node [8,6,6,6,5,5,2,1] .empty .empty)) (.node [8,6,6,6,6,3,2,2] (.node [8,6,6,6,6,3,2,1,1] .empty .empty) (.node [8,6,6,6,6,3,3,1] .empty .empty))) (.node [8,7,4,4,4,4,3,3,2] (.node [8,6,6,6,6,5,1,1] (.node [8,6,6,6,6,4,2,1] .empty .empty) (.node [8,7,4,4,4,3,3,3,3] .empty .empty)) (.node [8,7,4,4,4,4,4,3,1] (.node [8,7,4,4,4,4,4,2,2] .empty .empty) .empty))) (.node [8,7,5,5,3,3,3,3,2] (.node [8,7,5,4,4,4,3,3,1] (.node [8,7,5,4,4,3,3,3,2] (.node [8,7,5,4,3,3,3,3,3] .empty .empty) (.node [8,7,5,4,4,4,3,2,2] .empty .empty)) (.node [8,7,5,4,4,4,4,3] (.node [8,7,5,4,4,4,4,2,1] .empty .empty) .empty)) (.node [8,7,5,5,4,4,3,2,1] (.node [8,7,5,5,4,3,3,3,1] (.node [8,7,5,5,4,3,3,2,2] .empty .empty) (.node [8,7,5,5,4,4,2,2,2] .empty .empty)) (.node [8,7,5,5,4,4,4,1,1] (.node [8,7,5,5,4,4,3,3] .empty .empty) .empty)))) + +def degreeTree39_5 : RowTree := (.node [8,6,6,6,5,4,2,2] degreeTree39_3 degreeTree39_4) + +def degreeTree39_6 : RowTree := (.node [8,6,6,5,4,4,2,2,2] degreeTree39_2 degreeTree39_5) + +def degreeTree39_7 : RowTree := (.node [8,7,6,4,4,4,2,2,2] (.node [8,7,5,5,5,5,2,1,1] (.node [8,7,5,5,5,4,2,2,1] (.node [8,7,5,5,5,3,3,2,1] (.node [8,7,5,5,5,3,2,2,2] .empty .empty) (.node [8,7,5,5,5,3,3,3] .empty .empty)) (.node [8,7,5,5,5,4,3,2] (.node [8,7,5,5,5,4,3,1,1] .empty .empty) (.node [8,7,5,5,5,4,4,1] .empty .empty))) (.node [8,7,6,4,3,3,3,3,2] (.node [8,7,5,5,5,5,3,1] (.node [8,7,5,5,5,5,2,2] .empty .empty) (.node [8,7,6,3,3,3,3,3,3] .empty .empty)) (.node [8,7,6,4,4,3,3,3,1] (.node [8,7,6,4,4,3,3,2,2] .empty .empty) .empty))) (.node [8,7,6,5,4,3,2,2,2] (.node [8,7,6,4,4,4,4,2] (.node [8,7,6,4,4,4,3,3] (.node [8,7,6,4,4,4,3,2,1] .empty .empty) (.node [8,7,6,4,4,4,4,1,1] .empty .empty)) (.node [8,7,6,5,3,3,3,3,1] (.node [8,7,6,5,3,3,3,2,2] .empty .empty) .empty)) (.node [8,7,6,5,4,4,3,1,1] (.node [8,7,6,5,4,3,3,3] (.node [8,7,6,5,4,3,3,2,1] .empty .empty) (.node [8,7,6,5,4,4,2,2,1] .empty .empty)) (.node [8,7,6,5,4,4,4,1] (.node [8,7,6,5,4,4,3,2] .empty .empty) .empty)))) + +def degreeTree39_8 : RowTree := (.node [8,7,6,6,4,3,3,2] (.node [8,7,6,5,5,5,2,1] (.node [8,7,6,5,5,4,2,1,1] (.node [8,7,6,5,5,3,3,1,1] (.node [8,7,6,5,5,3,2,2,1] .empty .empty) (.node [8,7,6,5,5,3,3,2] .empty .empty)) (.node [8,7,6,5,5,4,3,1] (.node [8,7,6,5,5,4,2,2] .empty .empty) (.node [8,7,6,5,5,5,1,1,1] .empty .empty))) (.node [8,7,6,6,4,2,2,2,2] (.node [8,7,6,6,3,3,3,2,1] (.node [8,7,6,6,3,3,2,2,2] .empty .empty) (.node [8,7,6,6,3,3,3,3] .empty .empty)) (.node [8,7,6,6,4,3,3,1,1] (.node [8,7,6,6,4,3,2,2,1] .empty .empty) .empty))) (.node [8,7,6,6,5,3,3,1] (.node [8,7,6,6,5,2,2,2,1] (.node [8,7,6,6,4,4,2,2] (.node [8,7,6,6,4,4,2,1,1] .empty .empty) (.node [8,7,6,6,4,4,3,1] .empty .empty)) (.node [8,7,6,6,5,3,2,2] (.node [8,7,6,6,5,3,2,1,1] .empty .empty) .empty)) (.node [8,7,6,6,6,2,1,1,1,1] (.node [8,7,6,6,5,4,2,1] (.node [8,7,6,6,5,4,1,1,1] .empty .empty) (.node [8,7,6,6,6,1,1,1,1,1,1] .empty .empty)) (.node [8,7,6,6,6,2,2,2] (.node [8,7,6,6,6,2,2,1,1] .empty .empty) .empty)))) + +def degreeTree39_9 : RowTree := (.node [8,7,6,5,5,2,2,2,2] degreeTree39_7 degreeTree39_8) + +def degreeTree39_10 : RowTree := (.node [8,7,7,5,4,3,2,2,1] (.node [8,7,7,4,4,4,3,1,1] (.node [8,7,7,4,4,3,2,2,2] (.node [8,7,7,4,3,3,3,2,2] (.node [8,7,7,3,3,3,3,3,2] .empty .empty) (.node [8,7,7,4,3,3,3,3,1] .empty .empty)) (.node [8,7,7,4,4,3,3,3] (.node [8,7,7,4,4,3,3,2,1] .empty .empty) (.node [8,7,7,4,4,4,2,2,1] .empty .empty))) (.node [8,7,7,5,3,3,3,2,1] (.node [8,7,7,4,4,4,4,1] (.node [8,7,7,4,4,4,3,2] .empty .empty) (.node [8,7,7,5,3,3,2,2,2] .empty .empty)) (.node [8,7,7,5,4,2,2,2,2] (.node [8,7,7,5,3,3,3,3] .empty .empty) .empty))) (.node [8,7,7,5,5,3,2,1,1] (.node [8,7,7,5,4,4,2,2] (.node [8,7,7,5,4,3,3,2] (.node [8,7,7,5,4,3,3,1,1] .empty .empty) (.node [8,7,7,5,4,4,2,1,1] .empty .empty)) (.node [8,7,7,5,5,2,2,2,1] (.node [8,7,7,5,4,4,3,1] .empty .empty) .empty)) (.node [8,7,7,6,2,2,2,2,2,1] (.node [8,7,7,5,5,3,3,1] (.node [8,7,7,5,5,3,2,2] .empty .empty) (.node [8,7,7,5,5,4,1,1,1] .empty .empty)) (.node [8,7,7,6,3,2,2,2,2] (.node [8,7,7,6,3,2,2,2,1,1] .empty .empty) .empty)))) + +def degreeTree39_11 : RowTree := (.node [8,7,7,6,6,2,1,1,1] (.node [8,7,7,6,4,3,2,2] (.node [8,7,7,6,4,2,2,1,1,1] (.node [8,7,7,6,3,3,3,1,1] (.node [8,7,7,6,3,3,2,2,1] .empty .empty) (.node [8,7,7,6,3,3,3,2] .empty .empty)) (.node [8,7,7,6,4,3,1,1,1,1] (.node [8,7,7,6,4,2,2,2,1] .empty .empty) (.node [8,7,7,6,4,3,2,1,1] .empty .empty))) (.node [8,7,7,6,5,2,2,2] (.node [8,7,7,6,5,2,1,1,1,1] (.node [8,7,7,6,4,4,1,1,1] .empty .empty) (.node [8,7,7,6,5,2,2,1,1] .empty .empty)) (.node [8,7,7,6,6,1,1,1,1,1] (.node [8,7,7,6,5,3,1,1,1] .empty .empty) .empty))) (.node [8,7,7,7,3,3,2,2] (.node [8,7,7,7,3,2,2,2,1] (.node [8,7,7,7,2,2,2,2,2] (.node [8,7,7,7,2,2,2,2,1,1] .empty .empty) (.node [8,7,7,7,3,2,2,1,1,1] .empty .empty)) (.node [8,7,7,7,3,3,2,1,1] (.node [8,7,7,7,3,3,1,1,1,1] .empty .empty) .empty)) (.node [8,7,7,7,4,3,1,1,1] (.node [8,7,7,7,4,2,2,1,1] (.node [8,7,7,7,4,2,1,1,1,1] .empty .empty) (.node [8,7,7,7,4,2,2,2] .empty .empty)) (.node [8,7,7,7,5,2,1,1,1] (.node [8,7,7,7,5,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_12 : RowTree := (.node [8,7,7,6,3,3,2,1,1,1] degreeTree39_10 degreeTree39_11) + +def degreeTree39_13 : RowTree := (.node [8,7,6,6,6,3,1,1,1] degreeTree39_9 degreeTree39_12) + +def degreeTree39_14 : RowTree := (.node [8,7,5,5,4,4,4,2] degreeTree39_6 degreeTree39_13) + +def degreeTree39_15 : RowTree := (.node [8,8,5,4,4,4,4,2] (.node [8,8,5,4,3,3,3,3,2] (.node [8,8,4,4,4,4,3,3,1] (.node [8,8,4,4,4,3,3,3,2] (.node [8,8,4,4,3,3,3,3,3] .empty .empty) (.node [8,8,4,4,4,4,3,2,2] .empty .empty)) (.node [8,8,4,4,4,4,4,3] (.node [8,8,4,4,4,4,4,2,1] .empty .empty) (.node [8,8,5,3,3,3,3,3,3] .empty .empty))) (.node [8,8,5,4,4,4,3,2,1] (.node [8,8,5,4,4,3,3,3,1] (.node [8,8,5,4,4,3,3,2,2] .empty .empty) (.node [8,8,5,4,4,4,2,2,2] .empty .empty)) (.node [8,8,5,4,4,4,4,1,1] (.node [8,8,5,4,4,4,3,3] .empty .empty) .empty))) (.node [8,8,5,5,4,4,3,1,1] (.node [8,8,5,5,4,3,3,2,1] (.node [8,8,5,5,3,3,3,3,1] (.node [8,8,5,5,3,3,3,2,2] .empty .empty) (.node [8,8,5,5,4,3,2,2,2] .empty .empty)) (.node [8,8,5,5,4,4,2,2,1] (.node [8,8,5,5,4,3,3,3] .empty .empty) .empty)) (.node [8,8,5,5,5,3,3,1,1] (.node [8,8,5,5,5,2,2,2,2] (.node [8,8,5,5,4,4,3,2] .empty .empty) (.node [8,8,5,5,5,3,2,2,1] .empty .empty)) (.node [8,8,5,5,5,4,2,1,1] (.node [8,8,5,5,5,3,3,2] .empty .empty) .empty)))) + +def degreeTree39_16 : RowTree := (.node [8,8,6,5,4,3,2,2,1] (.node [8,8,6,4,4,4,2,2,1] (.node [8,8,6,4,3,3,3,3,1] (.node [8,8,6,3,3,3,3,3,2] (.node [8,8,5,5,5,5,1,1,1] .empty .empty) (.node [8,8,6,4,3,3,3,2,2] .empty .empty)) (.node [8,8,6,4,4,3,3,2,1] (.node [8,8,6,4,4,3,2,2,2] .empty .empty) (.node [8,8,6,4,4,3,3,3] .empty .empty))) (.node [8,8,6,5,3,3,3,2,1] (.node [8,8,6,4,4,4,3,2] (.node [8,8,6,4,4,4,3,1,1] .empty .empty) (.node [8,8,6,5,3,3,2,2,2] .empty .empty)) (.node [8,8,6,5,4,2,2,2,2] (.node [8,8,6,5,3,3,3,3] .empty .empty) .empty))) (.node [8,8,6,5,5,3,2,2] (.node [8,8,6,5,4,4,2,2] (.node [8,8,6,5,4,3,3,2] (.node [8,8,6,5,4,3,3,1,1] .empty .empty) (.node [8,8,6,5,4,4,2,1,1] .empty .empty)) (.node [8,8,6,5,5,3,2,1,1] (.node [8,8,6,5,5,2,2,2,1] .empty .empty) .empty)) (.node [8,8,6,6,2,2,1,1,1,1,1,1,1] (.node [8,8,6,6,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,6,5,5,4,1,1,1] .empty .empty) (.node [8,8,6,6,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,6,6,2,2,2,2,1,1,1] (.node [8,8,6,6,2,2,2,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_17 : RowTree := (.node [8,8,5,5,5,4,2,2] degreeTree39_15 degreeTree39_16) + +def degreeTree39_18 : RowTree := (.node [8,8,6,6,4,3,1,1,1,1] (.node [8,8,6,6,3,3,2,2,1] (.node [8,8,6,6,3,2,2,2,1,1] (.node [8,8,6,6,3,2,1,1,1,1,1,1] (.node [8,8,6,6,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,3,2,2,1,1,1,1] .empty .empty)) (.node [8,8,6,6,3,3,1,1,1,1,1] (.node [8,8,6,6,3,2,2,2,2] .empty .empty) (.node [8,8,6,6,3,3,2,1,1,1] .empty .empty))) (.node [8,8,6,6,4,2,1,1,1,1,1] (.node [8,8,6,6,3,3,3,2] (.node [8,8,6,6,3,3,3,1,1] .empty .empty) (.node [8,8,6,6,4,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,6,6,4,2,2,2,1] (.node [8,8,6,6,4,2,2,1,1,1] .empty .empty) .empty))) (.node [8,8,6,6,6,1,1,1,1,1] (.node [8,8,6,6,5,2,1,1,1,1] (.node [8,8,6,6,4,4,1,1,1] (.node [8,8,6,6,4,3,2,1,1] .empty .empty) (.node [8,8,6,6,5,1,1,1,1,1,1] .empty .empty)) (.node [8,8,6,6,5,3,1,1,1] (.node [8,8,6,6,5,2,2,1,1] .empty .empty) .empty)) (.node [8,8,7,3,3,3,3,2,1,1] (.node [8,8,7,3,3,2,2,2,2,2] (.node [8,8,6,6,6,2,1,1,1] .empty .empty) (.node [8,8,7,3,3,3,2,2,2,1] .empty .empty)) (.node [8,8,7,3,3,3,3,3,1] (.node [8,8,7,3,3,3,3,2,2] .empty .empty) .empty)))) + +def degreeTree39_19 : RowTree := (.node [8,8,7,5,2,2,2,2,2,1] (.node [8,8,7,4,4,2,2,2,2] (.node [8,8,7,4,3,3,3,1,1,1] (.node [8,8,7,4,3,3,2,2,1,1] (.node [8,8,7,4,3,2,2,2,2,1] .empty .empty) (.node [8,8,7,4,3,3,2,2,2] .empty .empty)) (.node [8,8,7,4,3,3,3,3] (.node [8,8,7,4,3,3,3,2,1] .empty .empty) (.node [8,8,7,4,4,2,2,2,1,1] .empty .empty))) (.node [8,8,7,4,4,3,3,2] (.node [8,8,7,4,4,3,2,2,1] (.node [8,8,7,4,4,3,2,1,1,1] .empty .empty) (.node [8,8,7,4,4,3,3,1,1] .empty .empty)) (.node [8,8,7,4,4,4,2,1,1] (.node [8,8,7,4,4,4,1,1,1,1] .empty .empty) .empty))) (.node [8,8,7,5,4,2,2,2,1] (.node [8,8,7,5,3,3,2,2,1] (.node [8,8,7,5,3,2,2,2,2] (.node [8,8,7,5,3,2,2,2,1,1] .empty .empty) (.node [8,8,7,5,3,3,2,1,1,1] .empty .empty)) (.node [8,8,7,5,4,2,2,1,1,1] (.node [8,8,7,5,3,3,3,1,1] .empty .empty) .empty)) (.node [8,8,7,5,5,2,1,1,1,1] (.node [8,8,7,5,4,3,2,1,1] (.node [8,8,7,5,4,3,1,1,1,1] .empty .empty) (.node [8,8,7,5,4,4,1,1,1] .empty .empty)) (.node [8,8,7,5,5,3,1,1,1] (.node [8,8,7,5,5,2,2,1,1] .empty .empty) .empty)))) + +def degreeTree39_20 : RowTree := (.node [8,8,7,4,2,2,2,2,2,2] degreeTree39_18 degreeTree39_19) + +def degreeTree39_21 : RowTree := (.node [8,8,6,6,2,2,2,2,2,1] degreeTree39_17 degreeTree39_20) + +def degreeTree39_22 : RowTree := (.node [8,8,7,7,3,2,2,1,1] (.node [8,8,7,6,4,3,1,1,1] (.node [8,8,7,6,3,3,1,1,1,1] (.node [8,8,7,6,3,2,2,1,1,1] (.node [8,8,7,6,2,2,2,2,2] .empty .empty) (.node [8,8,7,6,3,2,2,2,1] .empty .empty)) (.node [8,8,7,6,4,2,1,1,1,1] (.node [8,8,7,6,3,3,2,1,1] .empty .empty) (.node [8,8,7,6,4,2,2,1,1] .empty .empty))) (.node [8,8,7,7,2,2,2,1,1,1] (.node [8,8,7,6,5,2,1,1,1] (.node [8,8,7,6,5,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,6,1,1,1,1] .empty .empty)) (.node [8,8,7,7,3,2,1,1,1,1] (.node [8,8,7,7,2,2,2,2,1] .empty .empty) .empty))) (.node [8,8,8,3,3,3,2,2,1,1] (.node [8,8,7,7,5,1,1,1,1] (.node [8,8,7,7,4,1,1,1,1,1] (.node [8,8,7,7,3,3,1,1,1] .empty .empty) (.node [8,8,7,7,4,2,1,1,1] .empty .empty)) (.node [8,8,8,3,3,2,2,2,2,1] (.node [8,8,8,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [8,8,8,3,3,3,3,3] (.node [8,8,8,3,3,3,3,1,1,1] (.node [8,8,8,3,3,3,2,2,2] .empty .empty) (.node [8,8,8,3,3,3,3,2,1] .empty .empty)) (.node [8,8,8,4,3,2,2,2,1,1] (.node [8,8,8,4,2,2,2,2,2,1] .empty .empty) .empty)))) + +def degreeTree39_23 : RowTree := (.node [8,8,8,5,4,2,1,1,1,1] (.node [8,8,8,4,4,4,1,1,1] (.node [8,8,8,4,4,2,2,1,1,1] (.node [8,8,8,4,3,3,2,2,1] (.node [8,8,8,4,3,3,2,1,1,1] .empty .empty) (.node [8,8,8,4,3,3,3,1,1] .empty .empty)) (.node [8,8,8,4,4,3,1,1,1,1] (.node [8,8,8,4,4,2,2,2,1] .empty .empty) (.node [8,8,8,4,4,3,2,1,1] .empty .empty))) (.node [8,8,8,5,3,2,2,2,1] (.node [8,8,8,5,2,2,2,2,2] (.node [8,8,8,5,2,2,2,2,1,1] .empty .empty) (.node [8,8,8,5,3,2,2,1,1,1] .empty .empty)) (.node [8,8,8,5,3,3,2,1,1] (.node [8,8,8,5,3,3,1,1,1,1] .empty .empty) .empty))) (.node [8,8,8,6,3,2,1,1,1,1] (.node [8,8,8,5,5,2,1,1,1] (.node [8,8,8,5,4,3,1,1,1] (.node [8,8,8,5,4,2,2,1,1] .empty .empty) (.node [8,8,8,5,5,1,1,1,1,1] .empty .empty)) (.node [8,8,8,6,2,2,2,2,1] (.node [8,8,8,6,2,2,2,1,1,1] .empty .empty) .empty)) (.node [8,8,8,6,4,2,1,1,1] (.node [8,8,8,6,3,3,1,1,1] (.node [8,8,8,6,3,2,2,1,1] .empty .empty) (.node [8,8,8,6,4,1,1,1,1,1] .empty .empty)) (.node [8,8,8,7,2,2,1,1,1,1] (.node [8,8,8,6,5,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_24 : RowTree := (.node [8,8,8,4,3,2,2,2,2] degreeTree39_22 degreeTree39_23) + +def degreeTree39_25 : RowTree := (.node [9,5,5,4,4,4,4,3,1] (.node [9,4,4,4,4,4,4,4,2] (.node [8,8,8,8,2,1,1,1,1,1] (.node [8,8,8,7,3,2,1,1,1] (.node [8,8,8,7,3,1,1,1,1,1] .empty .empty) (.node [8,8,8,7,4,1,1,1,1] .empty .empty)) (.node [8,8,8,8,3,1,1,1,1] (.node [8,8,8,8,2,2,1,1,1] .empty .empty) (.node [9,4,4,4,4,4,4,3,3] .empty .empty))) (.node [9,5,5,4,4,3,3,3,3] (.node [9,5,4,4,4,4,4,3,2] (.node [9,5,4,4,4,4,3,3,3] .empty .empty) (.node [9,5,4,4,4,4,4,4,1] .empty .empty)) (.node [9,5,5,4,4,4,4,2,2] (.node [9,5,5,4,4,4,3,3,2] .empty .empty) .empty))) (.node [9,5,5,5,5,3,3,3,1] (.node [9,5,5,5,4,4,3,3,1] (.node [9,5,5,5,4,3,3,3,2] (.node [9,5,5,5,3,3,3,3,3] .empty .empty) (.node [9,5,5,5,4,4,3,2,2] .empty .empty)) (.node [9,5,5,5,5,3,3,2,2] (.node [9,5,5,5,4,4,4,2,1] .empty .empty) .empty)) (.node [9,5,5,5,5,5,2,2,1] (.node [9,5,5,5,5,4,3,2,1] (.node [9,5,5,5,5,4,2,2,2] .empty .empty) (.node [9,5,5,5,5,4,4,1,1] .empty .empty)) (.node [9,6,4,4,4,3,3,3,3] (.node [9,5,5,5,5,5,3,1,1] .empty .empty) .empty)))) + +def degreeTree39_26 : RowTree := (.node [9,6,5,5,5,3,3,2,1] (.node [9,6,5,5,3,3,3,3,2] (.node [9,6,5,4,4,3,3,3,2] (.node [9,6,4,4,4,4,4,3,1] (.node [9,6,4,4,4,4,4,2,2] .empty .empty) (.node [9,6,5,4,3,3,3,3,3] .empty .empty)) (.node [9,6,5,4,4,4,3,3,1] (.node [9,6,5,4,4,4,3,2,2] .empty .empty) (.node [9,6,5,4,4,4,4,2,1] .empty .empty))) (.node [9,6,5,5,4,4,3,2,1] (.node [9,6,5,5,4,3,3,3,1] (.node [9,6,5,5,4,3,3,2,2] .empty .empty) (.node [9,6,5,5,4,4,2,2,2] .empty .empty)) (.node [9,6,5,5,5,3,2,2,2] (.node [9,6,5,5,4,4,4,1,1] .empty .empty) .empty))) (.node [9,6,6,4,4,3,3,3,1] (.node [9,6,6,3,3,3,3,3,3] (.node [9,6,5,5,5,4,3,1,1] (.node [9,6,5,5,5,4,2,2,1] .empty .empty) (.node [9,6,5,5,5,5,2,1,1] .empty .empty)) (.node [9,6,6,4,4,3,3,2,2] (.node [9,6,6,4,3,3,3,3,2] .empty .empty) .empty)) (.node [9,6,6,5,3,3,3,2,2] (.node [9,6,6,4,4,4,3,2,1] (.node [9,6,6,4,4,4,2,2,2] .empty .empty) (.node [9,6,6,4,4,4,4,1,1] .empty .empty)) (.node [9,6,6,5,4,3,2,2,2] (.node [9,6,6,5,3,3,3,3,1] .empty .empty) .empty)))) + +def degreeTree39_27 : RowTree := (.node [9,6,4,4,4,4,3,3,2] degreeTree39_25 degreeTree39_26) + +def degreeTree39_28 : RowTree := (.node [8,8,8,7,2,2,2,1,1] degreeTree39_24 degreeTree39_27) + +def degreeTree39_29 : RowTree := (.node [8,8,7,6,2,2,2,2,1,1] degreeTree39_21 degreeTree39_28) + +def degreeTree39_30 : RowTree := (.node [8,7,7,7,6,1,1,1,1] degreeTree39_14 degreeTree39_29) + +def degreeTree39_31 : RowTree := (.node [9,6,6,6,5,3,2,1,1] (.node [9,6,6,6,3,3,2,2,2] (.node [9,6,6,5,5,3,2,2,1] (.node [9,6,6,5,4,4,3,1,1] (.node [9,6,6,5,4,4,2,2,1] .empty .empty) (.node [9,6,6,5,5,2,2,2,2] .empty .empty)) (.node [9,6,6,5,5,4,2,1,1] (.node [9,6,6,5,5,3,3,1,1] .empty .empty) (.node [9,6,6,5,5,5,1,1,1] .empty .empty))) (.node [9,6,6,6,4,3,3,1,1] (.node [9,6,6,6,4,2,2,2,2] (.node [9,6,6,6,3,3,3,2,1] .empty .empty) (.node [9,6,6,6,4,3,2,2,1] .empty .empty)) (.node [9,6,6,6,5,2,2,2,1] (.node [9,6,6,6,4,4,2,1,1] .empty .empty) .empty))) (.node [9,7,4,4,4,4,3,3,1] (.node [9,6,6,6,6,2,2,1,1] (.node [9,6,6,6,6,1,1,1,1,1,1] (.node [9,6,6,6,5,4,1,1,1] .empty .empty) (.node [9,6,6,6,6,2,1,1,1,1] .empty .empty)) (.node [9,7,4,4,4,3,3,3,2] (.node [9,7,4,4,3,3,3,3,3] .empty .empty) (.node [9,7,4,4,4,4,3,2,2] .empty .empty))) (.node [9,7,5,4,4,3,3,2,2] (.node [9,7,5,3,3,3,3,3,3] (.node [9,7,4,4,4,4,4,2,1] .empty .empty) (.node [9,7,5,4,3,3,3,3,2] .empty .empty)) (.node [9,7,5,4,4,4,2,2,2] (.node [9,7,5,4,4,3,3,3,1] .empty .empty) .empty)))) + +def degreeTree39_32 : RowTree := (.node [9,7,6,4,4,3,2,2,2] (.node [9,7,5,5,5,2,2,2,2] (.node [9,7,5,5,4,3,2,2,2] (.node [9,7,5,5,3,3,3,2,2] (.node [9,7,5,4,4,4,4,1,1] .empty .empty) (.node [9,7,5,5,3,3,3,3,1] .empty .empty)) (.node [9,7,5,5,4,4,2,2,1] (.node [9,7,5,5,4,3,3,2,1] .empty .empty) (.node [9,7,5,5,4,4,3,1,1] .empty .empty))) (.node [9,7,6,3,3,3,3,3,2] (.node [9,7,5,5,5,3,3,1,1] (.node [9,7,5,5,5,3,2,2,1] .empty .empty) (.node [9,7,5,5,5,4,2,1,1] .empty .empty)) (.node [9,7,6,4,3,3,3,3,1] (.node [9,7,6,4,3,3,3,2,2] .empty .empty) .empty))) (.node [9,7,6,5,4,3,2,2,1] (.node [9,7,6,5,3,3,2,2,2] (.node [9,7,6,4,4,4,2,2,1] (.node [9,7,6,4,4,3,3,2,1] .empty .empty) (.node [9,7,6,4,4,4,3,1,1] .empty .empty)) (.node [9,7,6,5,4,2,2,2,2] (.node [9,7,6,5,3,3,3,2,1] .empty .empty) .empty)) (.node [9,7,6,5,5,3,2,1,1] (.node [9,7,6,5,4,4,2,1,1] (.node [9,7,6,5,4,3,3,1,1] .empty .empty) (.node [9,7,6,5,5,2,2,2,1] .empty .empty)) (.node [9,7,6,6,3,2,2,2,1,1] (.node [9,7,6,6,2,2,2,2,2,1] .empty .empty) .empty)))) + +def degreeTree39_33 : RowTree := (.node [9,7,5,4,4,4,3,2,1] degreeTree39_31 degreeTree39_32) + +def degreeTree39_34 : RowTree := (.node [9,7,7,4,3,2,2,2,2,1] (.node [9,7,6,6,6,1,1,1,1,1] (.node [9,7,6,6,4,2,2,1,1,1] (.node [9,7,6,6,3,3,2,2,1] (.node [9,7,6,6,3,3,2,1,1,1] .empty .empty) (.node [9,7,6,6,3,3,3,1,1] .empty .empty)) (.node [9,7,6,6,4,3,1,1,1,1] (.node [9,7,6,6,4,2,2,2,1] .empty .empty) (.node [9,7,6,6,5,2,1,1,1,1] .empty .empty))) (.node [9,7,7,3,3,3,3,2,2] (.node [9,7,7,3,3,3,2,2,2,1] (.node [9,7,7,3,3,2,2,2,2,2] .empty .empty) (.node [9,7,7,3,3,3,3,2,1,1] .empty .empty)) (.node [9,7,7,4,2,2,2,2,2,2] (.node [9,7,7,3,3,3,3,3,1] .empty .empty) .empty))) (.node [9,7,7,4,4,3,2,1,1,1] (.node [9,7,7,4,3,3,3,2,1] (.node [9,7,7,4,3,3,2,2,2] (.node [9,7,7,4,3,3,2,2,1,1] .empty .empty) (.node [9,7,7,4,3,3,3,1,1,1] .empty .empty)) (.node [9,7,7,4,4,2,2,2,2] (.node [9,7,7,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [9,7,7,5,2,2,2,2,2,1] (.node [9,7,7,4,4,3,3,1,1] (.node [9,7,7,4,4,3,2,2,1] .empty .empty) (.node [9,7,7,4,4,4,1,1,1,1] .empty .empty)) (.node [9,7,7,5,3,2,2,2,2] (.node [9,7,7,5,3,2,2,2,1,1] .empty .empty) .empty)))) + +def degreeTree39_35 : RowTree := (.node [9,7,7,7,3,2,1,1,1,1] (.node [9,7,7,6,3,2,2,1,1,1] (.node [9,7,7,5,4,3,1,1,1,1] (.node [9,7,7,5,4,2,2,1,1,1] (.node [9,7,7,5,3,3,2,2,1] .empty .empty) (.node [9,7,7,5,4,2,2,2,1] .empty .empty)) (.node [9,7,7,6,2,2,2,2,1,1] (.node [9,7,7,5,5,2,1,1,1,1] .empty .empty) (.node [9,7,7,6,2,2,2,2,2] .empty .empty))) (.node [9,7,7,6,5,1,1,1,1,1] (.node [9,7,7,6,3,3,1,1,1,1] (.node [9,7,7,6,3,2,2,2,1] .empty .empty) (.node [9,7,7,6,4,2,1,1,1,1] .empty .empty)) (.node [9,7,7,7,2,2,2,2,1] (.node [9,7,7,7,2,2,2,1,1,1] .empty .empty) .empty))) (.node [9,8,4,4,4,4,3,2,1] (.node [9,8,4,4,4,3,3,2,2] (.node [9,8,4,3,3,3,3,3,3] (.node [9,7,7,7,4,1,1,1,1,1] .empty .empty) (.node [9,8,4,4,3,3,3,3,2] .empty .empty)) (.node [9,8,4,4,4,4,2,2,2] (.node [9,8,4,4,4,3,3,3,1] .empty .empty) .empty)) (.node [9,8,5,4,4,3,2,2,2] (.node [9,8,5,4,3,3,3,2,2] (.node [9,8,5,3,3,3,3,3,2] .empty .empty) (.node [9,8,5,4,3,3,3,3,1] .empty .empty)) (.node [9,8,5,4,4,4,2,2,1] (.node [9,8,5,4,4,3,3,2,1] .empty .empty) .empty)))) + +def degreeTree39_36 : RowTree := (.node [9,7,7,5,3,3,2,1,1,1] degreeTree39_34 degreeTree39_35) + +def degreeTree39_37 : RowTree := (.node [9,7,6,6,3,2,2,2,2] degreeTree39_33 degreeTree39_36) + +def degreeTree39_38 : RowTree := (.node [9,8,6,4,3,3,3,2,1] (.node [9,8,6,3,3,3,3,2,2] (.node [9,8,5,5,5,2,2,2,1] (.node [9,8,5,5,4,2,2,2,2] (.node [9,8,5,5,3,3,3,2,1] .empty .empty) (.node [9,8,5,5,4,3,2,2,1] .empty .empty)) (.node [9,8,6,3,3,3,2,2,2,1] (.node [9,8,6,3,3,2,2,2,2,2] .empty .empty) (.node [9,8,6,3,3,3,3,2,1,1] .empty .empty))) (.node [9,8,6,4,3,3,2,2,1,1] (.node [9,8,6,4,2,2,2,2,2,2] (.node [9,8,6,3,3,3,3,3,1] .empty .empty) (.node [9,8,6,4,3,2,2,2,2,1] .empty .empty)) (.node [9,8,6,4,3,3,3,1,1,1] (.node [9,8,6,4,3,3,2,2,2] .empty .empty) .empty))) (.node [9,8,6,5,3,2,2,2,1,1] (.node [9,8,6,4,4,3,2,2,1] (.node [9,8,6,4,4,2,2,2,2] (.node [9,8,6,4,4,2,2,2,1,1] .empty .empty) (.node [9,8,6,4,4,3,2,1,1,1] .empty .empty)) (.node [9,8,6,5,2,2,2,2,2,1] (.node [9,8,6,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [9,8,6,5,4,3,1,1,1,1] (.node [9,8,6,5,3,3,2,1,1,1] (.node [9,8,6,5,3,2,2,2,2] .empty .empty) (.node [9,8,6,5,4,2,2,1,1,1] .empty .empty)) (.node [9,8,6,6,2,2,2,2,1,1] (.node [9,8,6,5,5,2,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_39 : RowTree := (.node [9,8,7,4,4,2,2,1,1,1] (.node [9,8,7,3,3,3,2,2,2] (.node [9,8,6,6,5,1,1,1,1,1] (.node [9,8,6,6,3,3,1,1,1,1] (.node [9,8,6,6,3,2,2,1,1,1] .empty .empty) (.node [9,8,6,6,4,2,1,1,1,1] .empty .empty)) (.node [9,8,7,3,3,2,2,2,2,1] (.node [9,8,7,3,2,2,2,2,2,2] .empty .empty) (.node [9,8,7,3,3,3,2,2,1,1] .empty .empty))) (.node [9,8,7,4,3,2,2,2,1,1] (.node [9,8,7,3,3,3,3,2,1] (.node [9,8,7,3,3,3,3,1,1,1] .empty .empty) (.node [9,8,7,4,2,2,2,2,2,1] .empty .empty)) (.node [9,8,7,4,3,3,2,1,1,1] (.node [9,8,7,4,3,2,2,2,2] .empty .empty) .empty))) (.node [9,8,7,5,5,1,1,1,1,1] (.node [9,8,7,5,3,2,2,1,1,1] (.node [9,8,7,5,2,2,2,2,1,1] (.node [9,8,7,4,4,3,1,1,1,1] .empty .empty) (.node [9,8,7,5,2,2,2,2,2] .empty .empty)) (.node [9,8,7,5,4,2,1,1,1,1] (.node [9,8,7,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [9,8,7,7,2,2,1,1,1,1] (.node [9,8,7,6,3,2,1,1,1,1] (.node [9,8,7,6,2,2,2,1,1,1] .empty .empty) (.node [9,8,7,6,4,1,1,1,1,1] .empty .empty)) (.node [9,8,8,2,2,2,2,2,2,2] (.node [9,8,7,7,3,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_40 : RowTree := (.node [9,8,6,6,2,2,2,2,2] degreeTree39_38 degreeTree39_39) + +def degreeTree39_41 : RowTree := (.node [9,8,8,8,1,1,1,1,1,1] (.node [9,8,8,4,4,2,1,1,1,1] (.node [9,8,8,4,2,2,2,2,1,1] (.node [9,8,8,3,3,2,2,2,2] (.node [9,8,8,3,3,2,2,2,1,1] .empty .empty) (.node [9,8,8,3,3,3,2,1,1,1] .empty .empty)) (.node [9,8,8,4,3,2,2,1,1,1] (.node [9,8,8,4,2,2,2,2,2] .empty .empty) (.node [9,8,8,4,3,3,1,1,1,1] .empty .empty))) (.node [9,8,8,6,2,2,1,1,1,1] (.node [9,8,8,5,3,2,1,1,1,1] (.node [9,8,8,5,2,2,2,1,1,1] .empty .empty) (.node [9,8,8,5,4,1,1,1,1,1] .empty .empty)) (.node [9,8,8,7,2,1,1,1,1,1] (.node [9,8,8,6,3,1,1,1,1,1] .empty .empty) .empty))) (.node [9,9,2,2,2,2,2,2,2,2,2,2,1] (.node [9,9,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [9,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,2,2,2,2,2,2,2,2,2,1,1,1] (.node [9,9,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [9,9,4,3,3,3,2,2,2,2] (.node [9,9,3,3,3,3,3,3,2,1] (.node [9,9,3,3,3,3,3,2,2,2] .empty .empty) (.node [9,9,3,3,3,3,3,3,3] .empty .empty)) (.node [9,9,4,3,3,3,3,3,1,1] (.node [9,9,4,3,3,3,3,2,2,1] .empty .empty) .empty)))) + +def degreeTree39_42 : RowTree := (.node [9,9,5,4,3,2,2,2,2,1] (.node [9,9,4,4,4,3,3,1,1,1] (.node [9,9,4,4,3,3,3,2,2] (.node [9,9,4,4,3,3,2,2,2,1] (.node [9,9,4,4,3,2,2,2,2,2] .empty .empty) (.node [9,9,4,4,3,3,3,2,1,1] .empty .empty)) (.node [9,9,4,4,4,3,2,2,1,1] (.node [9,9,4,4,4,2,2,2,2,1] .empty .empty) (.node [9,9,4,4,4,3,2,2,2] .empty .empty))) (.node [9,9,5,3,3,3,3,2,1,1] (.node [9,9,5,3,3,2,2,2,2,2] (.node [9,9,4,4,4,4,2,1,1,1] .empty .empty) (.node [9,9,5,3,3,3,2,2,2,1] .empty .empty)) (.node [9,9,5,4,2,2,2,2,2,2] (.node [9,9,5,3,3,3,3,2,2] .empty .empty) .empty))) (.node [9,9,5,4,4,4,1,1,1,1] (.node [9,9,5,4,4,2,2,2,1,1] (.node [9,9,5,4,3,3,2,2,2] (.node [9,9,5,4,3,3,2,2,1,1] .empty .empty) (.node [9,9,5,4,3,3,3,1,1,1] .empty .empty)) (.node [9,9,5,4,4,3,2,1,1,1] (.node [9,9,5,4,4,2,2,2,2] .empty .empty) .empty)) (.node [9,9,5,5,4,2,2,1,1,1] (.node [9,9,5,5,3,2,2,2,1,1] (.node [9,9,5,5,2,2,2,2,2,1] .empty .empty) (.node [9,9,5,5,3,3,2,1,1,1] .empty .empty)) (.node [9,9,5,5,5,2,1,1,1,1] (.node [9,9,5,5,4,3,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_43 : RowTree := (.node [9,9,4,3,3,3,3,3,2] degreeTree39_41 degreeTree39_42) + +def degreeTree39_44 : RowTree := (.node [9,8,8,3,2,2,2,2,2,1] degreeTree39_40 degreeTree39_43) + +def degreeTree39_45 : RowTree := (.node [9,8,5,5,3,3,2,2,2] degreeTree39_37 degreeTree39_44) + +def degreeTree39_46 : RowTree := (.node [9,9,6,6,2,2,2,1,1,1] (.node [9,9,6,4,4,2,2,1,1,1] (.node [9,9,6,3,3,3,3,1,1,1] (.node [9,9,6,3,3,3,2,2,1,1] (.node [9,9,6,3,3,2,2,2,2,1] .empty .empty) (.node [9,9,6,3,3,3,2,2,2] .empty .empty)) (.node [9,9,6,4,3,2,2,2,1,1] (.node [9,9,6,4,2,2,2,2,2,1] .empty .empty) (.node [9,9,6,4,3,3,2,1,1,1] .empty .empty))) (.node [9,9,6,5,3,3,1,1,1,1] (.node [9,9,6,5,2,2,2,2,1,1] (.node [9,9,6,4,4,3,1,1,1,1] .empty .empty) (.node [9,9,6,5,3,2,2,1,1,1] .empty .empty)) (.node [9,9,6,5,5,1,1,1,1,1] (.node [9,9,6,5,4,2,1,1,1,1] .empty .empty) .empty))) (.node [9,9,7,4,2,2,2,2,1,1] (.node [9,9,7,3,2,2,2,2,2,1] (.node [9,9,6,6,4,1,1,1,1,1] (.node [9,9,6,6,3,2,1,1,1,1] .empty .empty) (.node [9,9,7,2,2,2,2,2,2,2] .empty .empty)) (.node [9,9,7,3,3,3,2,1,1,1] (.node [9,9,7,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [9,9,7,5,2,2,2,1,1,1] (.node [9,9,7,4,3,3,1,1,1,1] (.node [9,9,7,4,3,2,2,1,1,1] .empty .empty) (.node [9,9,7,4,4,2,1,1,1,1] .empty .empty)) (.node [9,9,7,5,4,1,1,1,1,1] (.node [9,9,7,5,3,2,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_47 : RowTree := (.node [9,9,9,3,2,2,2,1,1,1] (.node [9,9,8,4,3,2,1,1,1,1] (.node [9,9,8,3,2,2,2,2,1,1] (.node [9,9,7,7,2,1,1,1,1,1] (.node [9,9,7,6,3,1,1,1,1,1] .empty .empty) (.node [9,9,8,2,2,2,2,2,2,1] .empty .empty)) (.node [9,9,8,3,3,3,1,1,1,1] (.node [9,9,8,3,3,2,2,1,1,1] .empty .empty) (.node [9,9,8,4,2,2,2,1,1,1] .empty .empty))) (.node [9,9,8,6,2,1,1,1,1,1] (.node [9,9,8,5,2,2,1,1,1,1] (.node [9,9,8,4,4,1,1,1,1,1] .empty .empty) (.node [9,9,8,5,3,1,1,1,1,1] .empty .empty)) (.node [9,9,9,2,2,2,2,2,1,1] (.node [9,9,8,7,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [9,9,9,5,2,1,1,1,1,1] (.node [9,9,9,4,2,2,1,1,1,1] (.node [9,9,9,3,3,2,1,1,1,1] .empty .empty) (.node [9,9,9,4,3,1,1,1,1,1] .empty .empty)) (.node [10,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [9,9,9,6,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_48 : RowTree := (.node [9,9,7,6,2,2,1,1,1,1] degreeTree39_46 degreeTree39_47) + +def degreeTree39_49 : RowTree := (.node [10,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1] (.node [10,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,2,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,2,2,2,2,2,2,2,2,2,1,1] (.node [10,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,3,3,3,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,3,3,3,3,3,2,2,2,2,2,1,1,1,1] (.node [10,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,2,2,2,2,2,2,2,2,1] (.node [10,3,3,3,3,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,2,2,2,2,2,2] (.node [10,3,3,3,3,3,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,2,2,2,1,1,1,1,1] (.node [10,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_50 : RowTree := (.node [10,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,3,3,3,3,3,3,3,3,2,1,1,1] (.node [10,3,3,3,3,3,3,3,2,2,1,1,1,1] (.node [10,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,2,2,2,2,2,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,3,2,2,2,2] (.node [10,3,3,3,3,3,3,3,2,2,2,1,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,3,1,1,1,1,1] .empty .empty))) (.node [10,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,3,3,3,1,1] (.node [10,3,3,3,3,3,3,3,3,2,2,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,3,3,2] .empty .empty)) (.node [10,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,4,3,2,2,2,2,2,2,2,2,2,2,2] (.node [10,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,4,2,2,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,4,3,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,4,3,3,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,2,2,2,2,2,2,2,2,2,1] (.node [10,4,3,3,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_51 : RowTree := (.node [10,3,3,3,3,3,3,2,2,2,2,1,1,1] degreeTree39_49 degreeTree39_50) + +def degreeTree39_52 : RowTree := (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2] degreeTree39_48 degreeTree39_51) + +def degreeTree39_53 : RowTree := (.node [10,4,3,3,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,2,2,2,2,2,2,1,1,1,1] (.node [10,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,2,2,2,2,2,2,2,2] (.node [10,4,3,3,3,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,3,3,3,3,2,2,2,2,2,1,1,1] (.node [10,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,2,2,2,2,2,2,1] .empty .empty) .empty))) (.node [10,4,3,3,3,3,3,3,2,2,1,1,1] (.node [10,4,3,3,3,3,3,2,2,2,2,2] (.node [10,4,3,3,3,3,3,2,2,2,1,1,1,1] (.node [10,4,3,3,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,2,2,2,2,1,1] .empty .empty)) (.node [10,4,3,3,3,3,3,3,2,1,1,1,1,1] (.node [10,4,3,3,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,4,3,3,3,3,3,3,3,2,2] (.node [10,4,3,3,3,3,3,3,3,1,1,1,1] (.node [10,4,3,3,3,3,3,3,2,2,2,1] .empty .empty) (.node [10,4,3,3,3,3,3,3,3,2,1,1] .empty .empty)) (.node [10,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,3,3,3,3,1] .empty .empty) .empty)))) + +def degreeTree39_54 : RowTree := (.node [10,4,4,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,4,4,2,2,2,2,2,2,2,2,2,2,1] (.node [10,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,2,2,2,2,2,1,1] (.node [10,4,4,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,4,4,3,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,4,4,3,3,3,2,2,2,1,1,1,1,1,1] (.node [10,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,2,2,2,2,2,1,1,1] (.node [10,4,4,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,4,4,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,4,4,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,2,2,2,2,2,1,1] (.node [10,4,4,3,3,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,2,2,2,2,2,2] .empty .empty)) (.node [10,4,4,3,3,3,3,2,2,1,1,1,1,1] (.node [10,4,4,3,3,3,3,2,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_55 : RowTree := (.node [10,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] degreeTree39_53 degreeTree39_54) + +def degreeTree39_56 : RowTree := (.node [10,4,4,4,2,2,2,2,2,2,2,2,1] (.node [10,4,4,3,3,3,3,3,3,3] (.node [10,4,4,3,3,3,3,3,2,2,1,1] (.node [10,4,4,3,3,3,3,3,1,1,1,1,1,1] (.node [10,4,4,3,3,3,3,2,2,2,2,1] .empty .empty) (.node [10,4,4,3,3,3,3,3,2,1,1,1,1] .empty .empty)) (.node [10,4,4,3,3,3,3,3,3,1,1,1] (.node [10,4,4,3,3,3,3,3,2,2,2] .empty .empty) (.node [10,4,4,3,3,3,3,3,3,2,1] .empty .empty))) (.node [10,4,4,4,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,2,2,2,2,2,2,2,1,1,1] (.node [10,4,4,4,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) .empty))) (.node [10,4,4,4,3,2,2,2,2,2,2,1,1] (.node [10,4,4,4,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,2,2,2,2,2,1,1,1,1] (.node [10,4,4,4,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,4,4,4,3,3,2,2,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,4,4,4,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,3,2,2,2,2,1,1,1] (.node [10,4,4,4,3,3,2,2,2,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_57 : RowTree := (.node [10,4,4,4,4,2,2,2,2,1,1,1,1,1] (.node [10,4,4,4,3,3,3,3,2,2,1] (.node [10,4,4,4,3,3,3,2,2,2,1,1] (.node [10,4,4,4,3,3,3,2,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,3,3,3,2,2,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,3,3,3,1,1,1,1,1] (.node [10,4,4,4,3,3,3,2,2,2,2] .empty .empty) (.node [10,4,4,4,3,3,3,3,2,1,1,1] .empty .empty))) (.node [10,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,3,3,2] (.node [10,4,4,4,3,3,3,3,3,1,1] .empty .empty) (.node [10,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,2,2,2,1,1,1,1,1,1,1] (.node [10,4,4,4,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,4,4,4,4,3,2,2,2,2,1,1] (.node [10,4,4,4,4,3,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,2,2,2,2,2,2,1] (.node [10,4,4,4,4,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,4,4,4,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,3,2,2,2,1,1,1,1] (.node [10,4,4,4,4,3,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,4,4,4,4,3,3,2,2,1,1,1] (.node [10,4,4,4,4,3,3,1,1,1,1,1,1,1] (.node [10,4,4,4,4,3,2,2,2,2,2] .empty .empty) (.node [10,4,4,4,4,3,3,2,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,3,3,3,1,1,1,1] (.node [10,4,4,4,4,3,3,2,2,2,1] .empty .empty) .empty)))) + +def degreeTree39_58 : RowTree := (.node [10,4,4,4,3,3,2,2,2,2,2,1] degreeTree39_56 degreeTree39_57) + +def degreeTree39_59 : RowTree := (.node [10,4,4,3,3,3,3,2,2,2,1,1,1] degreeTree39_55 degreeTree39_58) + +def degreeTree39_60 : RowTree := (.node [10,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree39_52 degreeTree39_59) + +def degreeTree39_61 : RowTree := (.node [9,9,6,3,2,2,2,2,2,2] degreeTree39_45 degreeTree39_60) + +def degreeTree39_62 : RowTree := (.node [9,6,6,5,4,3,3,2,1] degreeTree39_30 degreeTree39_61) + +def degreeTree39_63 : RowTree := (.node [10,4,4,4,4,4,4,2,1,1,1] (.node [10,4,4,4,4,4,3,1,1,1,1,1,1] (.node [10,4,4,4,4,4,2,1,1,1,1,1,1,1] (.node [10,4,4,4,4,3,3,3,3,1] (.node [10,4,4,4,4,3,3,3,2,2] .empty .empty) (.node [10,4,4,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,4,2,2,2,1,1,1] (.node [10,4,4,4,4,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,2,2,2,2,1] .empty .empty))) (.node [10,4,4,4,4,4,3,3,1,1,1] (.node [10,4,4,4,4,4,3,2,2,1,1] (.node [10,4,4,4,4,4,3,2,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,3,2,2,2] .empty .empty)) (.node [10,4,4,4,4,4,4,1,1,1,1,1] (.node [10,4,4,4,4,4,3,3,2,1] .empty .empty) .empty))) (.node [10,5,2,2,2,2,2,2,2,2,2,2,2,2] (.node [10,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,4,4,3,1,1] (.node [10,4,4,4,4,4,4,2,2,1] .empty .empty) (.node [10,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,2,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,2,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [10,5,3,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,3,2,2,2,2,2,2,2,2,2,2,1] (.node [10,5,3,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_64 : RowTree := (.node [10,5,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,3,3,2,2,2,2,2,2,2,2,2] (.node [10,5,3,3,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,3,3,3,2,2,2,2,2,2,1,1,1] (.node [10,5,3,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,2,2,2,2,2,2,2,1] .empty .empty) .empty))) (.node [10,5,3,3,3,3,3,2,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,2,2,2,2,2,1,1] (.node [10,5,3,3,3,3,2,2,2,1,1,1,1,1,1] (.node [10,5,3,3,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,3,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [10,5,3,3,3,3,3,3,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,2,2,2,1,1,1] (.node [10,5,3,3,3,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,2,2,2,2,1] .empty .empty)) (.node [10,5,3,3,3,3,3,3,2,2,1,1] (.node [10,5,3,3,3,3,3,3,2,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_65 : RowTree := (.node [10,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree39_63 degreeTree39_64) + +def degreeTree39_66 : RowTree := (.node [10,5,4,3,2,2,2,2,2,2,1,1,1,1,1] (.node [10,5,4,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,3,3,2,1] (.node [10,5,3,3,3,3,3,3,3,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,3,3,3] .empty .empty)) (.node [10,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,2,2,2,2,2,2,2,2,2,2] (.node [10,5,4,2,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,5,4,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,2,2,2,2,2,2,2,2,1] (.node [10,5,4,3,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,2,2,2,2,2,2,1,1] (.node [10,5,4,3,3,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,2,2,2,2,2,2,2] .empty .empty)) (.node [10,5,4,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_67 : RowTree := (.node [10,5,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,3,3,1,1,1,1,1] (.node [10,5,4,3,3,3,3,2,1,1,1,1,1,1] (.node [10,5,4,3,3,3,2,2,2,2,2,1] (.node [10,5,4,3,3,3,2,2,2,2,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,3,3,3,2,2,2,1,1] (.node [10,5,4,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,2,2,2,2] .empty .empty))) (.node [10,5,4,3,3,3,3,3,3,2] (.node [10,5,4,3,3,3,3,3,2,2,1] (.node [10,5,4,3,3,3,3,3,2,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,3,3,1,1] .empty .empty)) (.node [10,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,5,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,2,2,2,2,2,2,2,1,1] (.node [10,5,4,4,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,4,4,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,2,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [10,5,4,4,3,2,2,2,2,2,1,1,1] (.node [10,5,4,4,3,2,2,2,1,1,1,1,1,1,1] (.node [10,5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,3,2,2,2,2,2,2,1] .empty .empty) .empty)))) + +def degreeTree39_68 : RowTree := (.node [10,5,4,3,3,3,2,2,2,1,1,1,1,1] degreeTree39_66 degreeTree39_67) + +def degreeTree39_69 : RowTree := (.node [10,5,3,3,3,3,3,3,2,2,2] degreeTree39_65 degreeTree39_68) + +def degreeTree39_70 : RowTree := (.node [10,5,4,4,4,2,2,1,1,1,1,1,1,1,1] (.node [10,5,4,4,3,3,3,2,2,2,1] (.node [10,5,4,4,3,3,2,2,2,2,2] (.node [10,5,4,4,3,3,2,2,2,1,1,1,1] (.node [10,5,4,4,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,3,2,2,2,2,1,1] .empty .empty)) (.node [10,5,4,4,3,3,3,2,1,1,1,1,1] (.node [10,5,4,4,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,3,3,2,2,1,1,1] .empty .empty))) (.node [10,5,4,4,3,3,3,3,3,1] (.node [10,5,4,4,3,3,3,3,2,1,1] (.node [10,5,4,4,3,3,3,3,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,3,3,3,2,2] .empty .empty)) (.node [10,5,4,4,4,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,5,4,4,4,3,2,2,1,1,1,1,1] (.node [10,5,4,4,4,2,2,2,2,2,2] (.node [10,5,4,4,4,2,2,2,2,1,1,1,1] (.node [10,5,4,4,4,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,4,2,2,2,2,2,1,1] .empty .empty)) (.node [10,5,4,4,4,3,2,1,1,1,1,1,1,1] (.node [10,5,4,4,4,3,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,4,4,4,3,3,2,1,1,1,1] (.node [10,5,4,4,4,3,2,2,2,2,1] (.node [10,5,4,4,4,3,2,2,2,1,1,1] .empty .empty) (.node [10,5,4,4,4,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,3,3,2,2,2] (.node [10,5,4,4,4,3,3,2,2,1,1] .empty .empty) .empty)))) + +def degreeTree39_71 : RowTree := (.node [10,5,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,4,3,2,1,1,1] (.node [10,5,4,4,4,4,2,2,1,1,1,1] (.node [10,5,4,4,4,4,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,3,3,3,2,1] .empty .empty) (.node [10,5,4,4,4,4,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,4,2,2,2,2] (.node [10,5,4,4,4,4,2,2,2,1,1] .empty .empty) (.node [10,5,4,4,4,4,3,1,1,1,1,1] .empty .empty))) (.node [10,5,4,4,4,4,4,2,1,1] (.node [10,5,4,4,4,4,3,3,1,1] (.node [10,5,4,4,4,4,3,2,2,1] .empty .empty) (.node [10,5,4,4,4,4,4,1,1,1,1] .empty .empty)) (.node [10,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,5,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,2,2,2,2,2,2,2,2,2,1] (.node [10,5,5,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,5,5,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,5,3,2,2,2,2,2,2,2,1,1] (.node [10,5,5,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,5,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,2,2,2,2,2,2,2,2] .empty .empty) .empty)))) + +def degreeTree39_72 : RowTree := (.node [10,5,4,4,4,3,3,3,1,1,1] degreeTree39_70 degreeTree39_71) + +def degreeTree39_73 : RowTree := (.node [10,5,5,3,3,3,3,2,2,2,1] (.node [10,5,5,3,3,3,2,2,1,1,1,1,1,1] (.node [10,5,5,3,3,2,2,2,2,2,1,1,1] (.node [10,5,5,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,5,5,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,3,3,3,3,1,1,1,1,1,1,1] (.node [10,5,5,3,3,3,2,2,2,2,1,1] (.node [10,5,5,3,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,3,2,2,2,2,2] .empty .empty)) (.node [10,5,5,3,3,3,3,2,2,1,1,1] (.node [10,5,5,3,3,3,3,2,1,1,1,1,1] .empty .empty) .empty))) (.node [10,5,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,3,3,3,3,1] (.node [10,5,5,3,3,3,3,3,2,1,1] (.node [10,5,5,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,3,3,3,2,2] .empty .empty)) (.node [10,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,5,4,2,2,2,2,2,2,1,1,1] (.node [10,5,5,4,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,5,4,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,2,2,2,2,2,2,2,1] .empty .empty) .empty)))) + +def degreeTree39_74 : RowTree := (.node [10,5,5,4,3,3,3,3,1,1,1] (.node [10,5,5,4,3,3,2,2,1,1,1,1,1] (.node [10,5,5,4,3,2,2,2,2,2,1,1] (.node [10,5,5,4,3,2,2,2,1,1,1,1,1,1] (.node [10,5,5,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,3,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,2,2,2,2,2,2] .empty .empty) (.node [10,5,5,4,3,3,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,4,3,3,3,2,1,1,1,1] (.node [10,5,5,4,3,3,2,2,2,2,1] (.node [10,5,5,4,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,5,5,4,3,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,3,3,2,2,2] (.node [10,5,5,4,3,3,3,2,2,1,1] .empty .empty) .empty))) (.node [10,5,5,4,4,2,2,2,2,2,1] (.node [10,5,5,4,4,2,2,1,1,1,1,1,1,1] (.node [10,5,5,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,3,3,3,2,1] .empty .empty) (.node [10,5,5,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,2,2,2,2,1,1,1] (.node [10,5,5,4,4,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,5,4,4,3,2,2,2,1,1] (.node [10,5,5,4,4,3,2,1,1,1,1,1,1] (.node [10,5,5,4,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,4,3,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,3,3,1,1,1,1,1] (.node [10,5,5,4,4,3,2,2,2,2] .empty .empty) .empty)))) + +def degreeTree39_75 : RowTree := (.node [10,5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] degreeTree39_73 degreeTree39_74) + +def degreeTree39_76 : RowTree := (.node [10,5,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1] degreeTree39_72 degreeTree39_75) + +def degreeTree39_77 : RowTree := (.node [10,5,4,4,3,3,2,1,1,1,1,1,1,1,1] degreeTree39_69 degreeTree39_76) + +def degreeTree39_78 : RowTree := (.node [10,5,5,5,2,2,2,2,2,1,1,1,1] (.node [10,5,5,4,4,4,3,2,1,1] (.node [10,5,5,4,4,4,2,1,1,1,1,1] (.node [10,5,5,4,4,3,3,3,1,1] (.node [10,5,5,4,4,3,3,2,2,1] .empty .empty) (.node [10,5,5,4,4,4,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,4,2,2,2,1] (.node [10,5,5,4,4,4,2,2,1,1,1] .empty .empty) (.node [10,5,5,4,4,4,3,1,1,1,1] .empty .empty))) (.node [10,5,5,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,4,4,1,1,1] .empty .empty) (.node [10,5,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,2,2,2,2,1,1,1,1,1,1] (.node [10,5,5,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,5,5,5,3,2,2,2,2,1,1,1] (.node [10,5,5,5,3,2,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,2,2,2,2,2,2,2] (.node [10,5,5,5,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,5,5,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,3,2,2,2,1,1,1,1,1] (.node [10,5,5,5,3,2,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,5,5,3,3,2,2,1,1,1,1] (.node [10,5,5,5,3,3,1,1,1,1,1,1,1,1] (.node [10,5,5,5,3,2,2,2,2,2,1] .empty .empty) (.node [10,5,5,5,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,3,3,2,2,2,2] (.node [10,5,5,5,3,3,2,2,2,1,1] .empty .empty) .empty)))) + +def degreeTree39_79 : RowTree := (.node [10,5,5,5,4,3,3,2,1,1] (.node [10,5,5,5,4,2,2,2,2,1,1] (.node [10,5,5,5,4,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,3,3,3,2,2,1] (.node [10,5,5,5,3,3,3,2,1,1,1] .empty .empty) (.node [10,5,5,5,3,3,3,3,1,1] .empty .empty)) (.node [10,5,5,5,4,2,2,1,1,1,1,1,1] (.node [10,5,5,5,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,4,2,2,2,1,1,1,1] .empty .empty))) (.node [10,5,5,5,4,3,2,2,1,1,1] (.node [10,5,5,5,4,3,1,1,1,1,1,1,1] (.node [10,5,5,5,4,2,2,2,2,2] .empty .empty) (.node [10,5,5,5,4,3,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,4,3,3,1,1,1,1] (.node [10,5,5,5,4,3,2,2,2,1] .empty .empty) .empty))) (.node [10,5,5,5,5,2,2,1,1,1,1,1] (.node [10,5,5,5,4,4,3,1,1,1] (.node [10,5,5,5,4,4,2,1,1,1,1] (.node [10,5,5,5,4,4,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,4,4,2,2,1,1] .empty .empty)) (.node [10,5,5,5,5,2,1,1,1,1,1,1,1] (.node [10,5,5,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,5,5,5,5,3,2,1,1,1,1] (.node [10,5,5,5,5,2,2,2,2,1] (.node [10,5,5,5,5,2,2,2,1,1,1] .empty .empty) (.node [10,5,5,5,5,3,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,5,3,3,1,1,1] (.node [10,5,5,5,5,3,2,2,1,1] .empty .empty) .empty)))) + +def degreeTree39_80 : RowTree := (.node [10,5,5,5,3,3,3,1,1,1,1,1] degreeTree39_78 degreeTree39_79) + +def degreeTree39_81 : RowTree := (.node [10,6,3,2,2,2,2,2,2,2,2,2,2] (.node [10,6,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,5,5,1,1,1,1] (.node [10,5,5,5,5,4,2,1,1,1] .empty .empty) (.node [10,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,6,3,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,2,2,2,2,2,2,2,2,2,1,1] (.node [10,6,3,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) .empty))) (.node [10,6,3,3,2,2,2,2,2,2,2,2,1] (.node [10,6,3,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,2,2,2,2,2,2,2,1,1,1] (.node [10,6,3,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,6,3,3,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,3,2,2,2,2,2,1,1,1,1] (.node [10,6,3,3,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_82 : RowTree := (.node [10,6,3,3,3,3,3,3,2,2,1] (.node [10,6,3,3,3,3,3,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,3,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,3,3,2,2,2,2,1,1,1] (.node [10,6,3,3,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,3,2,2,2,2,2,1] .empty .empty))) (.node [10,6,3,3,3,3,3,2,2,2,2] (.node [10,6,3,3,3,3,3,2,2,1,1,1,1] (.node [10,6,3,3,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,6,3,3,3,3,3,3,2,1,1,1] (.node [10,6,3,3,3,3,3,3,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,4,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,3,3,3,2] (.node [10,6,3,3,3,3,3,3,3,1,1] .empty .empty) (.node [10,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,2,2,2,2,2,2,2,2,2,1] (.node [10,6,4,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_83 : RowTree := (.node [10,6,3,3,3,2,2,2,2,2,2,1,1] degreeTree39_81 degreeTree39_82) + +def degreeTree39_84 : RowTree := (.node [10,5,5,5,5,4,1,1,1,1,1] degreeTree39_80 degreeTree39_83) + +def degreeTree39_85 : RowTree := (.node [10,6,4,3,3,3,2,2,2,2,1,1] (.node [10,6,4,3,3,2,2,2,2,1,1,1,1,1] (.node [10,6,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,2,2,2,2,2,2,2,1,1] (.node [10,6,4,3,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,6,4,3,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,6,4,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,4,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,2,2,2,2,2,2,1] (.node [10,6,4,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,4,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,3,3,3,2,2,2,1,1,1,1] (.node [10,6,4,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,4,3,3,3,3,3,2,1,1] (.node [10,6,4,3,3,3,3,2,2,1,1,1] (.node [10,6,4,3,3,3,3,1,1,1,1,1,1,1] (.node [10,6,4,3,3,3,2,2,2,2,2] .empty .empty) (.node [10,6,4,3,3,3,3,2,1,1,1,1,1] .empty .empty)) (.node [10,6,4,3,3,3,3,3,1,1,1,1] (.node [10,6,4,3,3,3,3,2,2,2,1] .empty .empty) .empty)) (.node [10,6,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,3,3,3,3,1] (.node [10,6,4,3,3,3,3,3,2,2] .empty .empty) (.node [10,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_86 : RowTree := (.node [10,6,4,4,3,3,2,2,2,2,1] (.node [10,6,4,4,3,2,2,2,2,1,1,1,1] (.node [10,6,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,2,2,2,2,2,2,1,1,1] (.node [10,6,4,4,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,6,4,4,3,2,2,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,3,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,6,4,4,3,3,2,1,1,1,1,1,1,1] (.node [10,6,4,4,3,2,2,2,2,2,2] (.node [10,6,4,4,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,6,4,4,3,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,3,3,2,2,2,1,1,1] (.node [10,6,4,4,3,3,2,2,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,4,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,3,3,2,2,2] (.node [10,6,4,4,3,3,3,2,1,1,1,1] (.node [10,6,4,4,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,3,3,3,2,2,1,1] .empty .empty)) (.node [10,6,4,4,3,3,3,3,2,1] (.node [10,6,4,4,3,3,3,3,1,1,1] .empty .empty) .empty)) (.node [10,6,4,4,4,2,2,2,2,1,1,1] (.node [10,6,4,4,4,2,2,1,1,1,1,1,1,1] (.node [10,6,4,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,4,3,1,1,1,1,1,1,1,1] (.node [10,6,4,4,4,2,2,2,2,2,1] .empty .empty) .empty)))) + +def degreeTree39_87 : RowTree := (.node [10,6,4,4,2,2,2,2,1,1,1,1,1,1,1] degreeTree39_85 degreeTree39_86) + +def degreeTree39_88 : RowTree := (.node [10,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,4,4,1,1,1,1,1,1,1] (.node [10,6,4,4,4,3,3,1,1,1,1,1] (.node [10,6,4,4,4,3,2,2,2,1,1] (.node [10,6,4,4,4,3,2,2,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,3,2,2,2,2] .empty .empty)) (.node [10,6,4,4,4,3,3,2,2,1] (.node [10,6,4,4,4,3,3,2,1,1,1] .empty .empty) (.node [10,6,4,4,4,3,3,3,1,1] .empty .empty))) (.node [10,6,4,4,4,4,3,1,1,1,1] (.node [10,6,4,4,4,4,2,2,1,1,1] (.node [10,6,4,4,4,4,2,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,2,2,2,1] .empty .empty)) (.node [10,6,4,4,4,4,4,1,1,1] (.node [10,6,4,4,4,4,3,2,1,1] .empty .empty) .empty))) (.node [10,6,5,2,2,2,2,2,2,2,2,2] (.node [10,6,5,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,2,2,2,2,2,2,2,2,1,1] (.node [10,6,5,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,6,5,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,3,2,2,2,2,2,1,1,1,1,1] (.node [10,6,5,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_89 : RowTree := (.node [10,6,5,3,3,3,3,2,1,1,1,1] (.node [10,6,5,3,3,2,2,2,2,2,2] (.node [10,6,5,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,6,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,6,5,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,3,3,2,2,2,2,1,1,1,1] (.node [10,6,5,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,2,2,2,2,2,1,1] .empty .empty))) (.node [10,6,5,3,3,3,2,2,2,1,1,1] (.node [10,6,5,3,3,3,2,1,1,1,1,1,1,1] (.node [10,6,5,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,3,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,5,3,3,3,3,1,1,1,1,1,1] (.node [10,6,5,3,3,3,2,2,2,2,1] .empty .empty) .empty))) (.node [10,6,5,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,3,3,3,3,2,1] (.node [10,6,5,3,3,3,3,2,2,2] (.node [10,6,5,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,6,5,3,3,3,3,3,1,1,1] .empty .empty)) (.node [10,6,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,6,5,4,2,2,2,2,2,2,1,1] (.node [10,6,5,4,2,2,2,2,1,1,1,1,1,1] (.node [10,6,5,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,6,5,4,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,2,2,2,2,2,2,2] .empty .empty) .empty)))) + +def degreeTree39_90 : RowTree := (.node [10,6,5,3,2,2,2,2,2,2,1,1,1] degreeTree39_88 degreeTree39_89) + +def degreeTree39_91 : RowTree := (.node [10,6,4,4,4,3,2,1,1,1,1,1,1] degreeTree39_87 degreeTree39_90) + +def degreeTree39_92 : RowTree := (.node [10,6,4,3,2,2,2,2,2,1,1,1,1,1,1] degreeTree39_84 degreeTree39_91) + +def degreeTree39_93 : RowTree := (.node [10,5,5,4,4,3,3,2,1,1,1] degreeTree39_77 degreeTree39_92) + +def degreeTree39_94 : RowTree := (.node [10,6,5,4,4,2,1,1,1,1,1,1,1,1] (.node [10,6,5,4,3,3,2,2,2,1,1] (.node [10,6,5,4,3,2,2,2,2,2,1] (.node [10,6,5,4,3,2,2,2,1,1,1,1,1] (.node [10,6,5,4,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,3,2,2,2,2,1,1,1] .empty .empty)) (.node [10,6,5,4,3,3,2,1,1,1,1,1,1] (.node [10,6,5,4,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,3,3,2,2,1,1,1,1] .empty .empty))) (.node [10,6,5,4,3,3,3,2,2,1] (.node [10,6,5,4,3,3,3,1,1,1,1,1] (.node [10,6,5,4,3,3,2,2,2,2] .empty .empty) (.node [10,6,5,4,3,3,3,2,1,1,1] .empty .empty)) (.node [10,6,5,4,4,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,3,3,3,3,1,1] .empty .empty) .empty))) (.node [10,6,5,4,4,3,2,2,2,1] (.node [10,6,5,4,4,2,2,2,2,2] (.node [10,6,5,4,4,2,2,2,1,1,1,1] (.node [10,6,5,4,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,2,2,2,2,1,1] .empty .empty)) (.node [10,6,5,4,4,3,2,1,1,1,1,1] (.node [10,6,5,4,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,3,2,2,1,1,1] .empty .empty))) (.node [10,6,5,4,4,4,2,1,1,1,1] (.node [10,6,5,4,4,3,3,2,1,1] (.node [10,6,5,4,4,3,3,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,4,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,4,4,3,1,1,1] (.node [10,6,5,4,4,4,2,2,1,1] .empty .empty) .empty)))) + +def degreeTree39_95 : RowTree := (.node [10,6,5,5,3,3,2,2,1,1,1] (.node [10,6,5,5,3,2,1,1,1,1,1,1,1,1] (.node [10,6,5,5,2,2,2,2,1,1,1,1,1] (.node [10,6,5,5,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,5,2,2,2,2,2,2,1] (.node [10,6,5,5,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,5,3,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,5,3,2,2,2,2,2] (.node [10,6,5,5,3,2,2,2,1,1,1,1] (.node [10,6,5,5,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,3,2,2,2,2,1,1] .empty .empty)) (.node [10,6,5,5,3,3,2,1,1,1,1,1] (.node [10,6,5,5,3,3,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,5,5,4,2,2,2,1,1,1] (.node [10,6,5,5,4,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,3,3,3,1,1,1,1] (.node [10,6,5,5,3,3,2,2,2,1] .empty .empty) (.node [10,6,5,5,3,3,3,2,1,1] .empty .empty)) (.node [10,6,5,5,4,2,2,1,1,1,1,1] (.node [10,6,5,5,4,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,6,5,5,4,3,2,2,1,1] (.node [10,6,5,5,4,3,1,1,1,1,1,1] (.node [10,6,5,5,4,2,2,2,2,1] .empty .empty) (.node [10,6,5,5,4,3,2,1,1,1,1] .empty .empty)) (.node [10,6,5,5,4,4,1,1,1,1,1] (.node [10,6,5,5,4,3,3,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_96 : RowTree := (.node [10,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree39_94 degreeTree39_95) + +def degreeTree39_97 : RowTree := (.node [10,6,6,2,2,2,2,2,2,2,2,1] (.node [10,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,5,2,2,2,1,1] (.node [10,6,5,5,5,2,1,1,1,1,1,1] (.node [10,6,5,5,5,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,5,2,2,1,1,1,1] .empty .empty)) (.node [10,6,5,5,5,3,2,1,1,1] (.node [10,6,5,5,5,3,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,5,4,1,1,1,1] .empty .empty))) (.node [10,6,6,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,2,2,2,2,2,2,2,1,1,1] (.node [10,6,6,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,6,3,2,2,2,2,2,2,1,1] (.node [10,6,6,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,3,2,2,2,2,2,1,1,1,1] (.node [10,6,6,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,6,6,3,3,2,2,1,1,1,1,1,1,1] (.node [10,6,6,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,6,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,3,3,2,2,2,2,1,1,1] (.node [10,6,6,3,3,2,2,2,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_98 : RowTree := (.node [10,6,6,4,2,2,2,2,2,1,1,1] (.node [10,6,6,3,3,3,3,2,2,1] (.node [10,6,6,3,3,3,2,2,2,1,1] (.node [10,6,6,3,3,3,2,1,1,1,1,1,1] (.node [10,6,6,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,3,3,2,2,1,1,1,1] .empty .empty)) (.node [10,6,6,3,3,3,3,1,1,1,1,1] (.node [10,6,6,3,3,3,2,2,2,2] .empty .empty) (.node [10,6,6,3,3,3,3,2,1,1,1] .empty .empty))) (.node [10,6,6,4,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,3,3,3,3,1,1] .empty .empty) (.node [10,6,6,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,4,2,2,2,2,1,1,1,1,1] (.node [10,6,6,4,2,2,2,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,6,4,3,2,2,2,2,2] (.node [10,6,6,4,3,2,2,1,1,1,1,1,1] (.node [10,6,6,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,2,2,2,2,2,2,1] .empty .empty) (.node [10,6,6,4,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,4,3,2,2,2,2,1,1] (.node [10,6,6,4,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,6,6,4,3,3,2,2,2,1] (.node [10,6,6,4,3,3,2,1,1,1,1,1] (.node [10,6,6,4,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,3,3,2,2,1,1,1] .empty .empty)) (.node [10,6,6,4,3,3,3,2,1,1] (.node [10,6,6,4,3,3,3,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_99 : RowTree := (.node [10,6,6,3,3,2,2,2,2,2,1] degreeTree39_97 degreeTree39_98) + +def degreeTree39_100 : RowTree := (.node [10,6,5,5,4,4,2,1,1,1] degreeTree39_96 degreeTree39_99) + +def degreeTree39_101 : RowTree := (.node [10,6,6,5,2,2,2,2,1,1,1,1] (.node [10,6,6,4,4,3,3,1,1,1] (.node [10,6,6,4,4,2,2,2,2,1] (.node [10,6,6,4,4,2,2,1,1,1,1,1] (.node [10,6,6,4,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,4,2,2,2,1,1,1] .empty .empty)) (.node [10,6,6,4,4,3,2,1,1,1,1] (.node [10,6,6,4,4,3,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,4,3,2,2,1,1] .empty .empty))) (.node [10,6,6,5,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,4,4,2,1,1,1] (.node [10,6,6,4,4,4,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,2,2,2,1,1,1,1,1,1] (.node [10,6,6,5,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,6,6,5,3,2,2,2,2,1] (.node [10,6,6,5,3,2,1,1,1,1,1,1,1] (.node [10,6,6,5,2,2,2,2,2,2] (.node [10,6,6,5,2,2,2,2,2,1,1] .empty .empty) (.node [10,6,6,5,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,3,2,2,2,1,1,1] (.node [10,6,6,5,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,6,6,5,3,3,3,1,1,1] (.node [10,6,6,5,3,3,2,1,1,1,1] (.node [10,6,6,5,3,3,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,3,3,2,2,1,1] .empty .empty)) (.node [10,6,6,5,4,2,1,1,1,1,1,1] (.node [10,6,6,5,4,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_102 : RowTree := (.node [10,6,6,6,3,1,1,1,1,1,1,1,1] (.node [10,6,6,5,5,3,1,1,1,1] (.node [10,6,6,5,4,4,1,1,1,1] (.node [10,6,6,5,4,3,1,1,1,1,1] (.node [10,6,6,5,4,2,2,2,1,1] .empty .empty) (.node [10,6,6,5,4,3,2,1,1,1] .empty .empty)) (.node [10,6,6,5,5,2,1,1,1,1,1] (.node [10,6,6,5,5,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,5,2,2,1,1,1] .empty .empty))) (.node [10,6,6,6,2,2,2,1,1,1,1,1] (.node [10,6,6,6,2,1,1,1,1,1,1,1,1,1] (.node [10,6,6,6,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,6,2,2,2,2,2,1] (.node [10,6,6,6,2,2,2,2,1,1,1] .empty .empty) .empty))) (.node [10,6,6,6,4,2,1,1,1,1,1] (.node [10,6,6,6,3,3,1,1,1,1,1] (.node [10,6,6,6,3,2,2,1,1,1,1] (.node [10,6,6,6,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,3,2,2,2,1,1] .empty .empty)) (.node [10,6,6,6,4,1,1,1,1,1,1,1] (.node [10,6,6,6,3,3,2,1,1,1] .empty .empty) .empty)) (.node [10,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,6,5,1,1,1,1,1,1] (.node [10,6,6,6,4,2,2,1,1,1] .empty .empty) (.node [10,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,7,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_103 : RowTree := (.node [10,6,6,5,4,2,2,1,1,1,1] degreeTree39_101 degreeTree39_102) + +def degreeTree39_104 : RowTree := (.node [10,7,3,3,2,2,2,2,2,2,1,1,1,1] (.node [10,7,3,2,2,2,2,2,2,2,2,1,1,1] (.node [10,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,2,2,2,2,2,2,2,2,2,2,2] (.node [10,7,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,7,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,7,3,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,7,3,3,3,2,2,2,2,1,1,1,1,1] (.node [10,7,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,2,2,2,2,2,2,2,2] (.node [10,7,3,3,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,7,3,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,7,3,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,2,2,2,2,2,2,1] (.node [10,7,3,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,7,3,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,3,2,2,2,1,1,1,1] (.node [10,7,3,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_105 : RowTree := (.node [10,7,4,2,2,2,2,2,2,2,1,1,1,1] (.node [10,7,3,3,3,3,3,3,2,2] (.node [10,7,3,3,3,3,3,2,2,1,1,1] (.node [10,7,3,3,3,3,3,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,2,2,2,2,2] .empty .empty) (.node [10,7,3,3,3,3,3,2,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,3,3,3,1,1,1,1] (.node [10,7,3,3,3,3,3,2,2,2,1] .empty .empty) (.node [10,7,3,3,3,3,3,3,2,1,1] .empty .empty))) (.node [10,7,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,3,3,3,1] .empty .empty) (.node [10,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,7,4,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,7,4,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,2,2,2,2,2,2,2,2,2] (.node [10,7,4,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,7,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,2,2,2,2,2,2,1,1,1] (.node [10,7,4,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,7,4,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_106 : RowTree := (.node [10,7,3,3,3,3,2,2,2,2,1,1] degreeTree39_104 degreeTree39_105) + +def degreeTree39_107 : RowTree := (.node [10,7,2,2,2,2,2,2,2,2,2,1,1,1,1] degreeTree39_103 degreeTree39_106) + +def degreeTree39_108 : RowTree := (.node [10,6,6,4,4,1,1,1,1,1,1,1,1,1] degreeTree39_100 degreeTree39_107) + +def degreeTree39_109 : RowTree := (.node [10,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,3,2,2,2,2,1] (.node [10,7,4,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,2,2,2,2,2,1,1] (.node [10,7,4,3,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,2,2,2,2,2,2] .empty .empty)) (.node [10,7,4,3,3,3,2,2,1,1,1,1,1] (.node [10,7,4,3,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,2,2,2,1,1,1] .empty .empty))) (.node [10,7,4,3,3,3,3,2,2,2] (.node [10,7,4,3,3,3,3,2,1,1,1,1] (.node [10,7,4,3,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,3,2,2,1,1] .empty .empty)) (.node [10,7,4,3,3,3,3,3,2,1] (.node [10,7,4,3,3,3,3,3,1,1,1] .empty .empty) .empty))) (.node [10,7,4,4,2,2,2,2,2,2,2] (.node [10,7,4,4,2,2,2,2,1,1,1,1,1,1] (.node [10,7,4,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,2,2,2,2,2,2,1,1] (.node [10,7,4,4,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,7,4,4,3,2,2,2,1,1,1,1,1] (.node [10,7,4,4,3,2,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,3,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,3,2,2,2,2,2,1] (.node [10,7,4,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_110 : RowTree := (.node [10,7,4,4,4,3,1,1,1,1,1,1,1] (.node [10,7,4,4,3,3,3,3,1,1] (.node [10,7,4,4,3,3,2,2,2,2] (.node [10,7,4,4,3,3,2,2,1,1,1,1] (.node [10,7,4,4,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,3,3,2,2,2,1,1] .empty .empty)) (.node [10,7,4,4,3,3,3,2,1,1,1] (.node [10,7,4,4,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,3,3,3,2,2,1] .empty .empty))) (.node [10,7,4,4,4,2,2,2,1,1,1,1] (.node [10,7,4,4,4,2,1,1,1,1,1,1,1,1] (.node [10,7,4,4,4,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,4,2,2,2,2,2] (.node [10,7,4,4,4,2,2,2,2,1,1] .empty .empty) .empty))) (.node [10,7,4,4,4,4,2,1,1,1,1] (.node [10,7,4,4,4,3,3,1,1,1,1] (.node [10,7,4,4,4,3,2,2,1,1,1] (.node [10,7,4,4,4,3,2,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,3,2,2,2,1] .empty .empty)) (.node [10,7,4,4,4,4,1,1,1,1,1,1] (.node [10,7,4,4,4,3,3,2,1,1] .empty .empty) .empty)) (.node [10,7,5,3,3,3,3,2,2,1] (.node [10,7,4,4,4,4,3,1,1,1] (.node [10,7,4,4,4,4,2,2,1,1] .empty .empty) (.node [10,7,5,3,3,3,2,2,2,2] .empty .empty)) (.node [10,7,5,4,3,2,2,2,2,2] (.node [10,7,5,3,3,3,3,3,1,1] .empty .empty) .empty)))) + +def degreeTree39_111 : RowTree := (.node [10,7,4,4,3,3,1,1,1,1,1,1,1,1] degreeTree39_109 degreeTree39_110) + +def degreeTree39_112 : RowTree := (.node [10,7,6,3,3,3,3,2,1,1] (.node [10,7,5,5,3,3,2,2,1,1] (.node [10,7,5,4,4,3,3,1,1,1] (.node [10,7,5,4,4,2,2,2,2,1] (.node [10,7,5,4,3,3,3,2,1,1] .empty .empty) (.node [10,7,5,4,4,3,2,2,1,1] .empty .empty)) (.node [10,7,5,5,2,2,2,2,2,2] (.node [10,7,5,4,4,4,2,1,1,1] .empty .empty) (.node [10,7,5,5,3,2,2,2,2,1] .empty .empty))) (.node [10,7,5,5,5,2,2,1,1,1] (.node [10,7,5,5,4,2,2,2,1,1] (.node [10,7,5,5,3,3,3,1,1,1] .empty .empty) (.node [10,7,5,5,4,3,2,1,1,1] .empty .empty)) (.node [10,7,6,3,3,3,2,2,2,1] (.node [10,7,6,3,3,2,2,2,2,2] .empty .empty) .empty))) (.node [10,7,6,5,2,2,2,2,2,1] (.node [10,7,6,4,3,3,3,1,1,1] (.node [10,7,6,4,3,2,2,2,2,1] (.node [10,7,6,4,2,2,2,2,2,2] .empty .empty) (.node [10,7,6,4,3,3,2,2,1,1] .empty .empty)) (.node [10,7,6,4,4,3,2,1,1,1] (.node [10,7,6,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [10,7,7,3,3,2,2,2,2,1] (.node [10,7,6,6,2,2,2,2,1,1] (.node [10,7,6,5,3,2,2,2,1,1] .empty .empty) (.node [10,7,7,3,2,2,2,2,2,2] .empty .empty)) (.node [10,7,7,3,3,3,3,1,1,1] (.node [10,7,7,3,3,3,2,2,1,1] .empty .empty) .empty)))) + +def degreeTree39_113 : RowTree := (.node [10,8,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,8,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,8,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,5,2,2,2,2,1,1] (.node [10,7,7,4,3,2,2,2,1,1] .empty .empty) (.node [10,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,8,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,8,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty))) (.node [10,8,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,2,2,2,2,2,2,2,2,2] (.node [10,8,3,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,3,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,8,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,2,2,2,2,2,2,1,1,1] (.node [10,8,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,8,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_114 : RowTree := (.node [10,7,7,4,2,2,2,2,2,1] degreeTree39_112 degreeTree39_113) + +def degreeTree39_115 : RowTree := (.node [10,7,5,4,3,3,2,2,2,1] degreeTree39_111 degreeTree39_114) + +def degreeTree39_116 : RowTree := (.node [10,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,3,2,2,2,2,1] (.node [10,8,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,2,2,2,2,2,1,1] (.node [10,8,3,3,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,8,3,3,3,2,2,2,2,2,2] .empty .empty)) (.node [10,8,3,3,3,3,2,2,1,1,1,1,1] (.node [10,8,3,3,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,3,3,2,2,2,1,1,1] .empty .empty))) (.node [10,8,3,3,3,3,3,2,2,2] (.node [10,8,3,3,3,3,3,2,1,1,1,1] (.node [10,8,3,3,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,3,3,3,2,2,1,1] .empty .empty)) (.node [10,8,3,3,3,3,3,3,2,1] (.node [10,8,3,3,3,3,3,3,1,1,1] .empty .empty) .empty))) (.node [10,8,4,2,2,2,2,2,2,2,2,1] (.node [10,8,4,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,2,2,2,2,2,2,2,1,1,1] (.node [10,8,4,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,8,4,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,3,2,2,2,2,2,1,1,1,1] (.node [10,8,4,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_117 : RowTree := (.node [10,8,4,3,3,3,3,2,2,1] (.node [10,8,4,3,3,3,1,1,1,1,1,1,1,1] (.node [10,8,4,3,3,2,2,1,1,1,1,1,1,1] (.node [10,8,4,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,8,4,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,3,3,2,2,2,2,1,1,1] (.node [10,8,4,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,3,2,2,2,2,2,1] .empty .empty))) (.node [10,8,4,3,3,3,2,2,2,2] (.node [10,8,4,3,3,3,2,2,1,1,1,1] (.node [10,8,4,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,8,4,3,3,3,3,2,1,1,1] (.node [10,8,4,3,3,3,3,1,1,1,1,1] .empty .empty) .empty))) (.node [10,8,4,4,2,2,2,2,2,1,1,1] (.node [10,8,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,3,3,3,3,1,1] .empty .empty) (.node [10,8,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,2,2,2,2,1,1,1,1,1] (.node [10,8,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,8,4,4,3,2,2,1,1,1,1,1,1] (.node [10,8,4,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,4,4,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,3,2,2,2,2,1,1] (.node [10,8,4,4,3,2,2,2,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree39_118 : RowTree := (.node [10,8,4,3,2,2,2,2,2,2,1,1] degreeTree39_116 degreeTree39_117) + +def degreeTree39_119 : RowTree := (.node [10,8,4,4,4,4,1,1,1,1,1] (.node [10,8,4,4,4,2,1,1,1,1,1,1,1] (.node [10,8,4,4,3,3,2,2,2,1] (.node [10,8,4,4,3,3,2,1,1,1,1,1] (.node [10,8,4,4,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,3,3,2,2,1,1,1] .empty .empty)) (.node [10,8,4,4,3,3,3,2,1,1] (.node [10,8,4,4,3,3,3,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,4,4,4,3,1,1,1,1,1,1] (.node [10,8,4,4,4,2,2,2,1,1,1] (.node [10,8,4,4,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,2,2,2,2,1] .empty .empty)) (.node [10,8,4,4,4,3,2,2,1,1] (.node [10,8,4,4,4,3,2,1,1,1,1] .empty .empty) .empty))) (.node [10,8,5,4,4,2,2,2,1,1] (.node [10,8,5,4,2,2,2,2,2,2] (.node [10,8,5,3,3,3,2,2,2,1] (.node [10,8,5,3,3,2,2,2,2,2] .empty .empty) (.node [10,8,5,3,3,3,3,2,1,1] .empty .empty)) (.node [10,8,5,4,3,3,2,2,1,1] (.node [10,8,5,4,3,2,2,2,2,1] .empty .empty) .empty)) (.node [10,8,6,3,3,3,2,2,1,1] (.node [10,8,6,3,2,2,2,2,2,2] (.node [10,8,5,5,2,2,2,2,2,1] .empty .empty) (.node [10,8,6,3,3,2,2,2,2,1] .empty .empty)) (.node [10,8,7,2,2,2,2,2,2,2] (.node [10,8,6,4,2,2,2,2,2,1] .empty .empty) .empty)))) + +def degreeTree39_120 : RowTree := (.node [10,9,4,4,3,2,2,2,2,1] (.node [10,9,2,2,2,2,2,2,2,2,2,1,1] (.node [10,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,2,2,2,2,2,2,1] .empty .empty) (.node [10,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,9,4,3,3,2,2,2,2,2] (.node [10,9,3,3,3,3,2,2,2,2] (.node [10,9,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,9,3,3,3,3,3,2,2,1] .empty .empty)) (.node [10,9,4,4,2,2,2,2,2,2] (.node [10,9,4,3,3,3,2,2,2,1] .empty .empty) .empty))) (.node [10,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,3,3,2,2,2,2,1] (.node [10,9,5,3,2,2,2,2,2,2] .empty .empty) (.node [10,9,6,2,2,2,2,2,2,2] .empty .empty)) (.node [10,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,2,2,2,2,2,2,2,2,2,1] (.node [10,10,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,10,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,10,4,3,2,2,2,2,2,2] (.node [10,10,3,3,3,2,2,2,2,2] .empty .empty) .empty)))) + +def degreeTree39_121 : RowTree := (.node [10,8,7,3,2,2,2,2,2,1] degreeTree39_119 degreeTree39_120) + +def degreeTree39_122 : RowTree := (.node [10,8,4,4,3,2,2,2,2,2] degreeTree39_118 degreeTree39_121) + +def degreeTree39_123 : RowTree := (.node [10,8,3,3,3,2,2,2,1,1,1,1,1,1] degreeTree39_115 degreeTree39_122) + +def degreeTree39_124 : RowTree := (.node [10,7,4,3,3,2,2,2,1,1,1,1,1,1] degreeTree39_108 degreeTree39_123) + +def degreeTree39_125 : RowTree := (.node [10,6,5,4,3,2,1,1,1,1,1,1,1,1,1] degreeTree39_93 degreeTree39_124) + +def degreeTree39_126 : RowTree := (.node [10,4,4,4,4,3,3,3,2,1,1] degreeTree39_62 degreeTree39_125) + +def degreeTree39 : RowTree := degreeTree39_126 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData41.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData41.lean index fafd8ab319743b1e3297962eb711ed95f4b87418..3be89dbfe0c799c70e0f79f2996b6f00f26ce432 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData41.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData41.lean @@ -1,51 +1,51 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 41. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree41_0 : RowTree := (.node [10,9,8,2,2,2,2,2,2,2] (.node [9,9,8,3,2,2,2,2,2,2] (.node [8,8,8,8,2,2,1,1,1,1,1] (.node [8,8,8,8,2,1,1,1,1,1,1,1] (.node [8,8,8,8,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,8,8,8,3,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,3,2,2,2,2,2,2] (.node [9,9,9,2,2,2,2,2,2,2] .empty .empty) (.node [10,9,7,3,2,2,2,2,2,2] .empty .empty))) (.node [10,10,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,10,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree41_1 : RowTree := (.node [10,10,3,2,2,2,2,2,2,2,2,1,1] (.node [10,10,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,10,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,10,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,10,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,10,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree41_2 : RowTree := (.node [10,10,2,2,2,2,2,2,2,2,2,2,1] degreeTree41_0 degreeTree41_1) - -def degreeTree41_3 : RowTree := (.node [10,10,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,3,2,2,2,1,1,1,1,1,1] (.node [10,10,3,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,3,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,3,3,3,2,2,2,2,2,1,1] (.node [10,10,3,3,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,10,3,3,3,2,2,2,2,2,2] .empty .empty))) (.node [10,10,3,3,3,3,3,1,1,1,1,1,1] (.node [10,10,3,3,3,3,2,2,2,1,1,1] (.node [10,10,3,3,3,3,2,2,1,1,1,1,1] (.node [10,10,3,3,3,3,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,3,3,3,3,2,2,2,2,1] .empty .empty)) (.node [10,10,3,3,3,3,3,2,2,1,1] (.node [10,10,3,3,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,10,3,3,3,3,3,2,2,2] .empty .empty)))) - -def degreeTree41_4 : RowTree := (.node [10,10,4,2,2,2,2,2,2,2,2,1] (.node [10,10,4,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,2,2,2,2,2,2,1,1,1,1,1] (.node [10,10,4,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,10,4,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,10,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,3,2,2,2,2,2,1,1,1,1] (.node [10,10,4,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,3,2,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree41_5 : RowTree := (.node [10,10,3,3,3,3,3,3,1,1,1] degreeTree41_3 degreeTree41_4) - -def degreeTree41_6 : RowTree := (.node [10,10,3,3,2,2,2,2,2,2,1,1,1] degreeTree41_2 degreeTree41_5) - -def degreeTree41_7 : RowTree := (.node [10,10,4,3,3,3,2,2,1,1,1,1] (.node [10,10,4,3,3,2,2,2,2,1,1,1] (.node [10,10,4,3,3,2,2,1,1,1,1,1,1,1] (.node [10,10,4,3,3,2,1,1,1,1,1,1,1,1,1] (.node [10,10,4,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,4,3,3,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,10,4,3,3,3,1,1,1,1,1,1,1,1] (.node [10,10,4,3,3,2,2,2,2,2,1] .empty .empty) (.node [10,10,4,3,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [10,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,3,3,3,3,1,1,1,1,1] (.node [10,10,4,3,3,3,2,2,2,2] (.node [10,10,4,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,4,3,3,3,3,2,1,1,1] .empty .empty)) (.node [10,10,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree41_8 : RowTree := (.node [10,10,4,4,3,3,1,1,1,1,1,1,1] (.node [10,10,4,4,3,2,2,1,1,1,1,1,1] (.node [10,10,4,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,2,2,2,2,2,2,1] (.node [10,10,4,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,4,4,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,4,3,2,2,2,2,1,1] (.node [10,10,4,4,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,10,4,4,3,2,2,2,2,2] .empty .empty))) (.node [10,10,4,4,4,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,3,3,2,2,1,1,1] (.node [10,10,4,4,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,3,3,3,1,1,1,1] .empty .empty)) (.node [10,10,4,4,4,2,2,1,1,1,1,1] (.node [10,10,4,4,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,4,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree41_9 : RowTree := (.node [10,10,4,4,2,2,2,2,1,1,1,1,1] degreeTree41_7 degreeTree41_8) - -def degreeTree41_10 : RowTree := (.node [11,6,6,4,4,4,1,1,1,1,1,1] (.node [11,5,5,5,5,5,1,1,1,1,1] (.node [10,10,5,3,3,2,2,2,2,2] (.node [10,10,4,4,4,4,1,1,1,1,1] (.node [10,10,4,4,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,5,5,5,5,4,1,1,1,1,1,1] .empty .empty)) (.node [11,6,5,5,5,3,1,1,1,1,1,1] (.node [11,6,5,5,4,4,1,1,1,1,1,1] .empty .empty) (.node [11,6,5,5,5,4,1,1,1,1,1] .empty .empty))) (.node [11,6,6,5,5,3,1,1,1,1,1] (.node [11,6,6,5,4,4,1,1,1,1,1] (.node [11,6,6,5,4,3,1,1,1,1,1,1] .empty .empty) (.node [11,6,6,5,5,2,1,1,1,1,1,1] .empty .empty)) (.node [11,6,6,6,2,2,1,1,1,1,1,1,1,1] (.node [11,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,6,6,6,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree41_11 : RowTree := (.node [12,6,6,4,4,3,1,1,1,1,1,1] (.node [12,5,5,5,5,3,1,1,1,1,1,1] (.node [11,8,4,4,4,4,1,1,1,1,1,1] (.node [11,6,6,6,5,1,1,1,1,1,1,1] (.node [11,6,6,6,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,5,5,5,4,4,1,1,1,1,1,1] .empty .empty)) (.node [12,6,5,5,4,3,1,1,1,1,1,1] (.node [12,6,5,4,4,4,1,1,1,1,1,1] .empty .empty) (.node [12,6,5,5,5,2,1,1,1,1,1,1] .empty .empty))) (.node [12,6,6,6,1,1,1,1,1,1,1,1,1,1,1] (.node [12,6,6,5,2,2,1,1,1,1,1,1,1,1] (.node [12,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,5,2,2,2,2,1,1,1,1] .empty .empty)) (.node [12,6,6,6,2,2,1,1,1,1,1,1,1] (.node [12,6,6,6,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,6,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree41_12 : RowTree := (.node [11,6,6,6,3,3,1,1,1,1,1,1] degreeTree41_10 degreeTree41_11) - -def degreeTree41_13 : RowTree := (.node [10,10,4,4,4,3,1,1,1,1,1,1] degreeTree41_9 degreeTree41_12) - -def degreeTree41_14 : RowTree := (.node [10,10,4,3,2,2,2,2,2,2,2] degreeTree41_6 degreeTree41_13) - -def degreeTree41 : RowTree := degreeTree41_14 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 41. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree41_0 : RowTree := (.node [10,9,8,2,2,2,2,2,2,2] (.node [9,9,8,3,2,2,2,2,2,2] (.node [8,8,8,8,2,2,1,1,1,1,1] (.node [8,8,8,8,2,1,1,1,1,1,1,1] (.node [8,8,8,8,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,8,8,8,3,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,3,2,2,2,2,2,2] (.node [9,9,9,2,2,2,2,2,2,2] .empty .empty) (.node [10,9,7,3,2,2,2,2,2,2] .empty .empty))) (.node [10,10,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,10,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree41_1 : RowTree := (.node [10,10,3,2,2,2,2,2,2,2,2,1,1] (.node [10,10,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,10,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,10,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,10,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,10,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree41_2 : RowTree := (.node [10,10,2,2,2,2,2,2,2,2,2,2,1] degreeTree41_0 degreeTree41_1) + +def degreeTree41_3 : RowTree := (.node [10,10,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,3,2,2,2,1,1,1,1,1,1] (.node [10,10,3,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,3,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,3,3,3,2,2,2,2,2,1,1] (.node [10,10,3,3,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,10,3,3,3,2,2,2,2,2,2] .empty .empty))) (.node [10,10,3,3,3,3,3,1,1,1,1,1,1] (.node [10,10,3,3,3,3,2,2,2,1,1,1] (.node [10,10,3,3,3,3,2,2,1,1,1,1,1] (.node [10,10,3,3,3,3,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,3,3,3,3,2,2,2,2,1] .empty .empty)) (.node [10,10,3,3,3,3,3,2,2,1,1] (.node [10,10,3,3,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,10,3,3,3,3,3,2,2,2] .empty .empty)))) + +def degreeTree41_4 : RowTree := (.node [10,10,4,2,2,2,2,2,2,2,2,1] (.node [10,10,4,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,2,2,2,2,2,2,1,1,1,1,1] (.node [10,10,4,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,10,4,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,10,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,3,2,2,2,2,2,1,1,1,1] (.node [10,10,4,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,3,2,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree41_5 : RowTree := (.node [10,10,3,3,3,3,3,3,1,1,1] degreeTree41_3 degreeTree41_4) + +def degreeTree41_6 : RowTree := (.node [10,10,3,3,2,2,2,2,2,2,1,1,1] degreeTree41_2 degreeTree41_5) + +def degreeTree41_7 : RowTree := (.node [10,10,4,3,3,3,2,2,1,1,1,1] (.node [10,10,4,3,3,2,2,2,2,1,1,1] (.node [10,10,4,3,3,2,2,1,1,1,1,1,1,1] (.node [10,10,4,3,3,2,1,1,1,1,1,1,1,1,1] (.node [10,10,4,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,4,3,3,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,10,4,3,3,3,1,1,1,1,1,1,1,1] (.node [10,10,4,3,3,2,2,2,2,2,1] .empty .empty) (.node [10,10,4,3,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [10,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,3,3,3,3,1,1,1,1,1] (.node [10,10,4,3,3,3,2,2,2,2] (.node [10,10,4,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,4,3,3,3,3,2,1,1,1] .empty .empty)) (.node [10,10,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree41_8 : RowTree := (.node [10,10,4,4,3,3,1,1,1,1,1,1,1] (.node [10,10,4,4,3,2,2,1,1,1,1,1,1] (.node [10,10,4,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,2,2,2,2,2,2,1] (.node [10,10,4,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,4,4,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,4,3,2,2,2,2,1,1] (.node [10,10,4,4,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,10,4,4,3,2,2,2,2,2] .empty .empty))) (.node [10,10,4,4,4,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,3,3,2,2,1,1,1] (.node [10,10,4,4,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,3,3,3,1,1,1,1] .empty .empty)) (.node [10,10,4,4,4,2,2,1,1,1,1,1] (.node [10,10,4,4,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,4,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree41_9 : RowTree := (.node [10,10,4,4,2,2,2,2,1,1,1,1,1] degreeTree41_7 degreeTree41_8) + +def degreeTree41_10 : RowTree := (.node [11,6,6,4,4,4,1,1,1,1,1,1] (.node [11,5,5,5,5,5,1,1,1,1,1] (.node [10,10,5,3,3,2,2,2,2,2] (.node [10,10,4,4,4,4,1,1,1,1,1] (.node [10,10,4,4,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,5,5,5,5,4,1,1,1,1,1,1] .empty .empty)) (.node [11,6,5,5,5,3,1,1,1,1,1,1] (.node [11,6,5,5,4,4,1,1,1,1,1,1] .empty .empty) (.node [11,6,5,5,5,4,1,1,1,1,1] .empty .empty))) (.node [11,6,6,5,5,3,1,1,1,1,1] (.node [11,6,6,5,4,4,1,1,1,1,1] (.node [11,6,6,5,4,3,1,1,1,1,1,1] .empty .empty) (.node [11,6,6,5,5,2,1,1,1,1,1,1] .empty .empty)) (.node [11,6,6,6,2,2,1,1,1,1,1,1,1,1] (.node [11,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,6,6,6,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree41_11 : RowTree := (.node [12,6,6,4,4,3,1,1,1,1,1,1] (.node [12,5,5,5,5,3,1,1,1,1,1,1] (.node [11,8,4,4,4,4,1,1,1,1,1,1] (.node [11,6,6,6,5,1,1,1,1,1,1,1] (.node [11,6,6,6,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,5,5,5,4,4,1,1,1,1,1,1] .empty .empty)) (.node [12,6,5,5,4,3,1,1,1,1,1,1] (.node [12,6,5,4,4,4,1,1,1,1,1,1] .empty .empty) (.node [12,6,5,5,5,2,1,1,1,1,1,1] .empty .empty))) (.node [12,6,6,6,1,1,1,1,1,1,1,1,1,1,1] (.node [12,6,6,5,2,2,1,1,1,1,1,1,1,1] (.node [12,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,5,2,2,2,2,1,1,1,1] .empty .empty)) (.node [12,6,6,6,2,2,1,1,1,1,1,1,1] (.node [12,6,6,6,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,6,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree41_12 : RowTree := (.node [11,6,6,6,3,3,1,1,1,1,1,1] degreeTree41_10 degreeTree41_11) + +def degreeTree41_13 : RowTree := (.node [10,10,4,4,4,3,1,1,1,1,1,1] degreeTree41_9 degreeTree41_12) + +def degreeTree41_14 : RowTree := (.node [10,10,4,3,2,2,2,2,2,2,2] degreeTree41_6 degreeTree41_13) + +def degreeTree41 : RowTree := degreeTree41_14 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData43.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData43.lean index 90f835a50a4dde40c1e04ef1972bf6147157264a..3009ddd9372145ec3796eb62a4198d52d4b42f42 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData43.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData43.lean @@ -1,1319 +1,1319 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 43. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree43_0 : RowTree := (.node [7,7,7,7,7,2,2,1,1,1,1] (.node [7,7,7,7,5,5,5] (.node [7,7,7,6,6,5,5] (.node [7,7,6,6,6,6,5] (.node [7,6,6,6,6,6,6] .empty .empty) .empty) (.node [7,7,7,6,6,6,4] .empty .empty)) (.node [7,7,7,7,7,1,1,1,1,1,1,1,1] (.node [7,7,7,7,6,5,4] .empty .empty) (.node [7,7,7,7,7,2,1,1,1,1,1,1] .empty .empty))) (.node [7,7,7,7,7,3,2,1,1,1] (.node [7,7,7,7,7,2,2,2,2] (.node [7,7,7,7,7,2,2,2,1,1] .empty .empty) (.node [7,7,7,7,7,3,1,1,1,1,1] .empty .empty)) (.node [7,7,7,7,7,3,3,1,1] (.node [7,7,7,7,7,3,2,2,1] .empty .empty) (.node [7,7,7,7,7,3,3,2] .empty .empty)))) - -def degreeTree43_1 : RowTree := (.node [8,4,4,4,4,4,4,3,3,3,2] (.node [7,7,7,7,7,5,1,1,1] (.node [7,7,7,7,7,4,2,2] (.node [7,7,7,7,7,4,2,1,1] .empty .empty) (.node [7,7,7,7,7,4,3,1] .empty .empty)) (.node [7,7,7,7,7,6,1,1] (.node [7,7,7,7,7,5,2,1] .empty .empty) (.node [8,4,4,4,4,4,3,3,3,3,3] .empty .empty))) (.node [8,4,4,4,4,4,4,4,4,3] (.node [8,4,4,4,4,4,4,4,3,3,1] (.node [8,4,4,4,4,4,4,4,3,2,2] .empty .empty) (.node [8,4,4,4,4,4,4,4,4,2,1] .empty .empty)) (.node [8,5,4,4,4,4,3,3,3,3,2] (.node [8,5,4,4,4,3,3,3,3,3,3] .empty .empty) (.node [8,5,4,4,4,4,4,3,3,2,2] .empty .empty)))) - -def degreeTree43_2 : RowTree := (.node [7,7,7,7,7,4,1,1,1,1] degreeTree43_0 degreeTree43_1) - -def degreeTree43_3 : RowTree := (.node [8,5,5,4,4,4,4,4,4,1] (.node [8,5,5,4,4,4,3,3,3,2,2] (.node [8,5,4,4,4,4,4,4,4,1,1] (.node [8,5,4,4,4,4,4,4,3,2,1] (.node [8,5,4,4,4,4,4,4,2,2,2] .empty .empty) (.node [8,5,4,4,4,4,4,4,3,3] .empty .empty)) (.node [8,5,5,4,3,3,3,3,3,3,3] (.node [8,5,4,4,4,4,4,4,4,2] .empty .empty) (.node [8,5,5,4,4,3,3,3,3,3,2] .empty .empty))) (.node [8,5,5,4,4,4,4,3,3,3] (.node [8,5,5,4,4,4,4,3,2,2,2] (.node [8,5,5,4,4,4,3,3,3,3,1] .empty .empty) (.node [8,5,5,4,4,4,4,3,3,2,1] .empty .empty)) (.node [8,5,5,4,4,4,4,4,3,1,1] (.node [8,5,5,4,4,4,4,4,2,2,1] .empty .empty) (.node [8,5,5,4,4,4,4,4,3,2] .empty .empty)))) (.node [8,5,5,5,4,4,4,3,2,2,1] (.node [8,5,5,5,4,4,3,3,2,2,2] (.node [8,5,5,5,4,3,3,3,3,2,2] (.node [8,5,5,5,3,3,3,3,3,3,2] .empty .empty) (.node [8,5,5,5,4,3,3,3,3,3,1] .empty .empty)) (.node [8,5,5,5,4,4,3,3,3,3] (.node [8,5,5,5,4,4,3,3,3,2,1] .empty .empty) (.node [8,5,5,5,4,4,4,2,2,2,2] .empty .empty))) (.node [8,5,5,5,4,4,4,4,2,2] (.node [8,5,5,5,4,4,4,3,3,2] (.node [8,5,5,5,4,4,4,3,3,1,1] .empty .empty) (.node [8,5,5,5,4,4,4,4,2,1,1] .empty .empty)) (.node [8,5,5,5,4,4,4,4,4] (.node [8,5,5,5,4,4,4,4,3,1] .empty .empty) (.node [8,5,5,5,5,3,3,3,2,2,2] .empty .empty))))) - -def degreeTree43_4 : RowTree := (.node [8,5,4,4,4,4,4,3,3,3,1] degreeTree43_2 degreeTree43_3) - -def degreeTree43_5 : RowTree := (.node [8,5,5,5,5,4,4,3,3,1] (.node [8,5,5,5,5,4,3,3,3,2] (.node [8,5,5,5,5,4,3,3,2,2,1] (.node [8,5,5,5,5,4,3,2,2,2,2] (.node [8,5,5,5,5,3,3,3,3,3] .empty .empty) .empty) (.node [8,5,5,5,5,4,3,3,3,1,1] .empty .empty)) (.node [8,5,5,5,5,4,4,3,2,1,1] (.node [8,5,5,5,5,4,4,2,2,2,1] .empty .empty) (.node [8,5,5,5,5,4,4,3,2,2] .empty .empty))) (.node [8,5,5,5,5,5,2,2,2,2,2] (.node [8,5,5,5,5,4,4,4,2,1] (.node [8,5,5,5,5,4,4,4,1,1,1] .empty .empty) (.node [8,5,5,5,5,4,4,4,3] .empty .empty)) (.node [8,5,5,5,5,5,3,3,2,1,1] (.node [8,5,5,5,5,5,3,2,2,2,1] .empty .empty) (.node [8,5,5,5,5,5,3,3,2,2] .empty .empty)))) - -def degreeTree43_6 : RowTree := (.node [8,5,5,5,5,5,5,2,1,1,1] (.node [8,5,5,5,5,5,4,3,2,1] (.node [8,5,5,5,5,5,4,2,2,2] (.node [8,5,5,5,5,5,4,2,2,1,1] .empty .empty) (.node [8,5,5,5,5,5,4,3,1,1,1] .empty .empty)) (.node [8,5,5,5,5,5,4,4,1,1] (.node [8,5,5,5,5,5,4,3,3] .empty .empty) (.node [8,5,5,5,5,5,4,4,2] .empty .empty))) (.node [8,5,5,5,5,5,5,4,1] (.node [8,5,5,5,5,5,5,3,1,1] (.node [8,5,5,5,5,5,5,2,2,1] .empty .empty) (.node [8,5,5,5,5,5,5,3,2] .empty .empty)) (.node [8,6,4,4,3,3,3,3,3,3,3] (.node [8,5,5,5,5,5,5,5] .empty .empty) (.node [8,6,4,4,4,3,3,3,3,3,2] .empty .empty)))) - -def degreeTree43_7 : RowTree := (.node [8,5,5,5,5,5,3,3,3,1] degreeTree43_5 degreeTree43_6) - -def degreeTree43_8 : RowTree := (.node [8,6,5,4,4,4,4,2,2,2,2] (.node [8,6,4,4,4,4,4,4,4,1] (.node [8,6,4,4,4,4,4,3,3,3] (.node [8,6,4,4,4,4,4,3,2,2,2] (.node [8,6,4,4,4,4,3,3,3,3,1] .empty .empty) (.node [8,6,4,4,4,4,4,3,3,2,1] .empty .empty)) (.node [8,6,4,4,4,4,4,4,3,1,1] (.node [8,6,4,4,4,4,4,4,2,2,1] .empty .empty) (.node [8,6,4,4,4,4,4,4,3,2] .empty .empty))) (.node [8,6,5,4,4,3,3,3,3,3,1] (.node [8,6,5,4,3,3,3,3,3,3,2] (.node [8,6,5,3,3,3,3,3,3,3,3] .empty .empty) (.node [8,6,5,4,4,3,3,3,3,2,2] .empty .empty)) (.node [8,6,5,4,4,4,3,3,3,2,1] (.node [8,6,5,4,4,4,3,3,2,2,2] .empty .empty) (.node [8,6,5,4,4,4,3,3,3,3] .empty .empty)))) (.node [8,6,5,5,3,3,3,3,3,2,2] (.node [8,6,5,4,4,4,4,4,2,1,1] (.node [8,6,5,4,4,4,4,3,3,1,1] (.node [8,6,5,4,4,4,4,3,2,2,1] .empty .empty) (.node [8,6,5,4,4,4,4,3,3,2] .empty .empty)) (.node [8,6,5,4,4,4,4,4,3,1] (.node [8,6,5,4,4,4,4,4,2,2] .empty .empty) (.node [8,6,5,4,4,4,4,4,4] .empty .empty))) (.node [8,6,5,5,4,3,3,3,3,3] (.node [8,6,5,5,4,3,3,3,2,2,2] (.node [8,6,5,5,3,3,3,3,3,3,1] .empty .empty) (.node [8,6,5,5,4,3,3,3,3,2,1] .empty .empty)) (.node [8,6,5,5,4,4,3,3,2,2,1] (.node [8,6,5,5,4,4,3,2,2,2,2] .empty .empty) (.node [8,6,5,5,4,4,3,3,3,1,1] .empty .empty))))) - -def degreeTree43_9 : RowTree := (.node [8,6,4,4,4,4,3,3,3,2,2] degreeTree43_7 degreeTree43_8) - -def degreeTree43_10 : RowTree := (.node [8,5,5,5,5,3,3,3,3,2,1] degreeTree43_4 degreeTree43_9) - -def degreeTree43_11 : RowTree := (.node [8,6,5,5,5,3,3,3,2,2,1] (.node [8,6,5,5,4,4,4,4,1,1,1] (.node [8,6,5,5,4,4,4,3,2,2] (.node [8,6,5,5,4,4,4,3,2,1,1] (.node [8,6,5,5,4,4,4,2,2,2,1] .empty .empty) .empty) (.node [8,6,5,5,4,4,4,3,3,1] .empty .empty)) (.node [8,6,5,5,4,4,4,4,3] (.node [8,6,5,5,4,4,4,4,2,1] .empty .empty) (.node [8,6,5,5,5,3,3,2,2,2,2] .empty .empty))) (.node [8,6,5,5,5,4,3,2,2,2,1] (.node [8,6,5,5,5,3,3,3,3,2] (.node [8,6,5,5,5,3,3,3,3,1,1] .empty .empty) (.node [8,6,5,5,5,4,2,2,2,2,2] .empty .empty)) (.node [8,6,5,5,5,4,3,3,2,2] (.node [8,6,5,5,5,4,3,3,2,1,1] .empty .empty) (.node [8,6,5,5,5,4,3,3,3,1] .empty .empty)))) - -def degreeTree43_12 : RowTree := (.node [8,6,5,5,5,5,3,2,2,1,1] (.node [8,6,5,5,5,4,4,3,3] (.node [8,6,5,5,5,4,4,3,1,1,1] (.node [8,6,5,5,5,4,4,2,2,2] .empty .empty) (.node [8,6,5,5,5,4,4,3,2,1] .empty .empty)) (.node [8,6,5,5,5,4,4,4,2] (.node [8,6,5,5,5,4,4,4,1,1] .empty .empty) (.node [8,6,5,5,5,5,2,2,2,2,1] .empty .empty))) (.node [8,6,5,5,5,5,3,3,3] (.node [8,6,5,5,5,5,3,3,1,1,1] (.node [8,6,5,5,5,5,3,2,2,2] .empty .empty) (.node [8,6,5,5,5,5,3,3,2,1] .empty .empty)) (.node [8,6,5,5,5,5,4,2,2,1] (.node [8,6,5,5,5,5,4,2,1,1,1] .empty .empty) (.node [8,6,5,5,5,5,4,3,1,1] .empty .empty)))) - -def degreeTree43_13 : RowTree := (.node [8,6,5,5,5,4,4,2,2,1,1] degreeTree43_11 degreeTree43_12) - -def degreeTree43_14 : RowTree := (.node [8,6,6,4,4,4,3,3,3,2] (.node [8,6,6,4,3,3,3,3,3,2,2] (.node [8,6,5,5,5,5,5,2,2] (.node [8,6,5,5,5,5,5,1,1,1,1] (.node [8,6,5,5,5,5,4,4,1] .empty .empty) (.node [8,6,5,5,5,5,5,2,1,1] .empty .empty)) (.node [8,6,5,5,5,5,5,4] (.node [8,6,5,5,5,5,5,3,1] .empty .empty) (.node [8,6,6,3,3,3,3,3,3,3,2] .empty .empty))) (.node [8,6,6,4,4,3,3,3,3,3] (.node [8,6,6,4,4,3,3,3,2,2,2] (.node [8,6,6,4,3,3,3,3,3,3,1] .empty .empty) (.node [8,6,6,4,4,3,3,3,3,2,1] .empty .empty)) (.node [8,6,6,4,4,4,3,3,2,2,1] (.node [8,6,6,4,4,4,3,2,2,2,2] .empty .empty) (.node [8,6,6,4,4,4,3,3,3,1,1] .empty .empty)))) (.node [8,6,6,5,3,3,3,3,2,2,2] (.node [8,6,6,4,4,4,4,3,3,1] (.node [8,6,6,4,4,4,4,3,2,1,1] (.node [8,6,6,4,4,4,4,2,2,2,1] .empty .empty) (.node [8,6,6,4,4,4,4,3,2,2] .empty .empty)) (.node [8,6,6,4,4,4,4,4,2,1] (.node [8,6,6,4,4,4,4,4,1,1,1] .empty .empty) (.node [8,6,6,4,4,4,4,4,3] .empty .empty))) (.node [8,6,6,5,4,3,3,3,2,2,1] (.node [8,6,6,5,3,3,3,3,3,3] (.node [8,6,6,5,3,3,3,3,3,2,1] .empty .empty) (.node [8,6,6,5,4,3,3,2,2,2,2] .empty .empty)) (.node [8,6,6,5,4,3,3,3,3,2] (.node [8,6,6,5,4,3,3,3,3,1,1] .empty .empty) (.node [8,6,6,5,4,4,2,2,2,2,2] .empty .empty))))) - -def degreeTree43_15 : RowTree := (.node [8,6,5,5,5,5,4,3,2] degreeTree43_13 degreeTree43_14) - -def degreeTree43_16 : RowTree := (.node [8,6,6,5,5,4,2,2,2,2,1] (.node [8,6,6,5,4,4,4,3,3] (.node [8,6,6,5,4,4,4,2,2,1,1] (.node [8,6,6,5,4,4,3,3,2,2] (.node [8,6,6,5,4,4,3,3,2,1,1] .empty .empty) (.node [8,6,6,5,4,4,3,3,3,1] .empty .empty)) (.node [8,6,6,5,4,4,4,3,1,1,1] (.node [8,6,6,5,4,4,4,2,2,2] .empty .empty) (.node [8,6,6,5,4,4,4,3,2,1] .empty .empty))) (.node [8,6,6,5,5,3,3,2,2,2,1] (.node [8,6,6,5,4,4,4,4,2] (.node [8,6,6,5,4,4,4,4,1,1] .empty .empty) (.node [8,6,6,5,5,3,2,2,2,2,2] .empty .empty)) (.node [8,6,6,5,5,3,3,3,2,2] (.node [8,6,6,5,5,3,3,3,2,1,1] .empty .empty) (.node [8,6,6,5,5,3,3,3,3,1] .empty .empty)))) (.node [8,6,6,5,5,4,4,3,1,1] (.node [8,6,6,5,5,4,3,3,2,1] (.node [8,6,6,5,5,4,3,2,2,2] (.node [8,6,6,5,5,4,3,2,2,1,1] .empty .empty) (.node [8,6,6,5,5,4,3,3,1,1,1] .empty .empty)) (.node [8,6,6,5,5,4,4,2,1,1,1] (.node [8,6,6,5,5,4,3,3,3] .empty .empty) (.node [8,6,6,5,5,4,4,2,2,1] .empty .empty))) (.node [8,6,6,5,5,5,2,2,2,2] (.node [8,6,6,5,5,4,4,4,1] (.node [8,6,6,5,5,4,4,3,2] .empty .empty) (.node [8,6,6,5,5,5,2,2,2,1,1] .empty .empty)) (.node [8,6,6,5,5,5,3,2,2,1] (.node [8,6,6,5,5,5,3,2,1,1,1] .empty .empty) (.node [8,6,6,5,5,5,3,3,1,1] .empty .empty))))) - -def degreeTree43_17 : RowTree := (.node [8,6,6,6,4,3,3,3,2,2] (.node [8,6,6,5,5,5,5,3] (.node [8,6,6,5,5,5,4,3,1] (.node [8,6,6,5,5,5,4,2,1,1] (.node [8,6,6,5,5,5,4,1,1,1,1] .empty .empty) (.node [8,6,6,5,5,5,4,2,2] .empty .empty)) (.node [8,6,6,5,5,5,5,1,1,1] (.node [8,6,6,5,5,5,4,4] .empty .empty) (.node [8,6,6,5,5,5,5,2,1] .empty .empty))) (.node [8,6,6,6,3,3,3,3,3,2] (.node [8,6,6,6,3,3,3,3,2,2,1] (.node [8,6,6,6,3,3,3,2,2,2,2] .empty .empty) (.node [8,6,6,6,3,3,3,3,3,1,1] .empty .empty)) (.node [8,6,6,6,4,3,3,2,2,2,1] (.node [8,6,6,6,4,3,2,2,2,2,2] .empty .empty) (.node [8,6,6,6,4,3,3,3,2,1,1] .empty .empty)))) (.node [8,6,6,6,4,4,4,2,1,1,1] (.node [8,6,6,6,4,4,3,2,2,2] (.node [8,6,6,6,4,4,2,2,2,2,1] (.node [8,6,6,6,4,3,3,3,3,1] .empty .empty) (.node [8,6,6,6,4,4,3,2,2,1,1] .empty .empty)) (.node [8,6,6,6,4,4,3,3,2,1] (.node [8,6,6,6,4,4,3,3,1,1,1] .empty .empty) (.node [8,6,6,6,4,4,3,3,3] .empty .empty))) (.node [8,6,6,6,4,4,4,4,1] (.node [8,6,6,6,4,4,4,3,1,1] (.node [8,6,6,6,4,4,4,2,2,1] .empty .empty) (.node [8,6,6,6,4,4,4,3,2] .empty .empty)) (.node [8,6,6,6,5,3,2,2,2,2,1] (.node [8,6,6,6,5,2,2,2,2,2,2] .empty .empty) (.node [8,6,6,6,5,3,3,2,2,1,1] .empty .empty))))) - -def degreeTree43_18 : RowTree := (.node [8,6,6,5,5,5,3,3,2] degreeTree43_16 degreeTree43_17) - -def degreeTree43_19 : RowTree := (.node [8,6,6,5,4,4,3,2,2,2,1] degreeTree43_15 degreeTree43_18) - -def degreeTree43_20 : RowTree := (.node [8,6,5,5,4,4,3,3,3,2] degreeTree43_10 degreeTree43_19) - -def degreeTree43_21 : RowTree := (.node [8,6,6,6,5,4,3,3,2] (.node [8,6,6,6,5,4,2,2,2,2] (.node [8,6,6,6,5,3,3,3,3] (.node [8,6,6,6,5,3,3,3,2,1] (.node [8,6,6,6,5,3,3,3,1,1,1] .empty .empty) .empty) (.node [8,6,6,6,5,4,2,2,2,1,1] .empty .empty)) (.node [8,6,6,6,5,4,3,2,2,1] (.node [8,6,6,6,5,4,3,2,1,1,1] .empty .empty) (.node [8,6,6,6,5,4,3,3,1,1] .empty .empty))) (.node [8,6,6,6,5,4,4,3,1] (.node [8,6,6,6,5,4,4,2,1,1] (.node [8,6,6,6,5,4,4,1,1,1,1] .empty .empty) (.node [8,6,6,6,5,4,4,2,2] .empty .empty)) (.node [8,6,6,6,5,5,2,2,1,1,1] (.node [8,6,6,6,5,4,4,4] .empty .empty) (.node [8,6,6,6,5,5,2,2,2,1] .empty .empty)))) - -def degreeTree43_22 : RowTree := (.node [8,6,6,6,5,5,5,2] (.node [8,6,6,6,5,5,4,1,1,1] (.node [8,6,6,6,5,5,3,2,2] (.node [8,6,6,6,5,5,3,2,1,1] .empty .empty) (.node [8,6,6,6,5,5,3,3,1] .empty .empty)) (.node [8,6,6,6,5,5,4,3] (.node [8,6,6,6,5,5,4,2,1] .empty .empty) (.node [8,6,6,6,5,5,5,1,1] .empty .empty))) (.node [8,6,6,6,6,3,3,2,1,1,1] (.node [8,6,6,6,6,3,2,2,2,1,1] (.node [8,6,6,6,6,2,2,2,2,2,1] .empty .empty) (.node [8,6,6,6,6,3,2,2,2,2] .empty .empty)) (.node [8,6,6,6,6,3,3,3,1,1] (.node [8,6,6,6,6,3,3,2,2,1] .empty .empty) (.node [8,6,6,6,6,3,3,3,2] .empty .empty)))) - -def degreeTree43_23 : RowTree := (.node [8,6,6,6,5,5,3,1,1,1,1] degreeTree43_21 degreeTree43_22) - -def degreeTree43_24 : RowTree := (.node [8,6,6,6,6,5,4,2] (.node [8,6,6,6,6,4,4,3] (.node [8,6,6,6,6,4,3,2,2] (.node [8,6,6,6,6,4,3,1,1,1,1] (.node [8,6,6,6,6,4,2,2,2,1] .empty .empty) (.node [8,6,6,6,6,4,3,2,1,1] .empty .empty)) (.node [8,6,6,6,6,4,4,1,1,1] (.node [8,6,6,6,6,4,3,3,1] .empty .empty) (.node [8,6,6,6,6,4,4,2,1] .empty .empty))) (.node [8,6,6,6,6,5,3,1,1,1] (.node [8,6,6,6,6,5,2,2,1,1] (.node [8,6,6,6,6,5,2,1,1,1,1] .empty .empty) (.node [8,6,6,6,6,5,2,2,2] .empty .empty)) (.node [8,6,6,6,6,5,3,3] (.node [8,6,6,6,6,5,3,2,1] .empty .empty) (.node [8,6,6,6,6,5,4,1,1] .empty .empty)))) (.node [8,7,4,3,3,3,3,3,3,3,3] (.node [8,6,6,6,6,6,2,2,1] (.node [8,6,6,6,6,6,1,1,1,1,1] (.node [8,6,6,6,6,5,5,1] .empty .empty) (.node [8,6,6,6,6,6,2,1,1,1] .empty .empty)) (.node [8,6,6,6,6,6,3,2] (.node [8,6,6,6,6,6,3,1,1] .empty .empty) (.node [8,6,6,6,6,6,4,1] .empty .empty))) (.node [8,7,4,4,4,4,3,3,2,2,2] (.node [8,7,4,4,4,3,3,3,3,2,2] (.node [8,7,4,4,3,3,3,3,3,3,2] .empty .empty) (.node [8,7,4,4,4,3,3,3,3,3,1] .empty .empty)) (.node [8,7,4,4,4,4,3,3,3,3] (.node [8,7,4,4,4,4,3,3,3,2,1] .empty .empty) (.node [8,7,4,4,4,4,4,2,2,2,2] .empty .empty))))) - -def degreeTree43_25 : RowTree := (.node [8,6,6,6,6,4,2,2,1,1,1] degreeTree43_23 degreeTree43_24) - -def degreeTree43_26 : RowTree := (.node [8,7,5,4,4,4,3,3,3,2] (.node [8,7,5,4,3,3,3,3,3,2,2] (.node [8,7,4,4,4,4,4,4,2,2] (.node [8,7,4,4,4,4,4,3,3,2] (.node [8,7,4,4,4,4,4,3,3,1,1] .empty .empty) (.node [8,7,4,4,4,4,4,4,2,1,1] .empty .empty)) (.node [8,7,4,4,4,4,4,4,4] (.node [8,7,4,4,4,4,4,4,3,1] .empty .empty) (.node [8,7,5,3,3,3,3,3,3,3,2] .empty .empty))) (.node [8,7,5,4,4,3,3,3,3,3] (.node [8,7,5,4,4,3,3,3,2,2,2] (.node [8,7,5,4,3,3,3,3,3,3,1] .empty .empty) (.node [8,7,5,4,4,3,3,3,3,2,1] .empty .empty)) (.node [8,7,5,4,4,4,3,3,2,2,1] (.node [8,7,5,4,4,4,3,2,2,2,2] .empty .empty) (.node [8,7,5,4,4,4,3,3,3,1,1] .empty .empty)))) (.node [8,7,5,5,3,3,3,3,2,2,2] (.node [8,7,5,4,4,4,4,3,3,1] (.node [8,7,5,4,4,4,4,3,2,1,1] (.node [8,7,5,4,4,4,4,2,2,2,1] .empty .empty) (.node [8,7,5,4,4,4,4,3,2,2] .empty .empty)) (.node [8,7,5,4,4,4,4,4,2,1] (.node [8,7,5,4,4,4,4,4,1,1,1] .empty .empty) (.node [8,7,5,4,4,4,4,4,3] .empty .empty))) (.node [8,7,5,5,4,3,3,3,2,2,1] (.node [8,7,5,5,3,3,3,3,3,3] (.node [8,7,5,5,3,3,3,3,3,2,1] .empty .empty) (.node [8,7,5,5,4,3,3,2,2,2,2] .empty .empty)) (.node [8,7,5,5,4,3,3,3,3,2] (.node [8,7,5,5,4,3,3,3,3,1,1] .empty .empty) (.node [8,7,5,5,4,4,2,2,2,2,2] .empty .empty))))) - -def degreeTree43_27 : RowTree := (.node [8,7,5,5,5,4,2,2,2,2,1] (.node [8,7,5,5,4,4,4,3,3] (.node [8,7,5,5,4,4,4,2,2,1,1] (.node [8,7,5,5,4,4,3,3,2,2] (.node [8,7,5,5,4,4,3,3,2,1,1] .empty .empty) (.node [8,7,5,5,4,4,3,3,3,1] .empty .empty)) (.node [8,7,5,5,4,4,4,3,1,1,1] (.node [8,7,5,5,4,4,4,2,2,2] .empty .empty) (.node [8,7,5,5,4,4,4,3,2,1] .empty .empty))) (.node [8,7,5,5,5,3,3,2,2,2,1] (.node [8,7,5,5,4,4,4,4,2] (.node [8,7,5,5,4,4,4,4,1,1] .empty .empty) (.node [8,7,5,5,5,3,2,2,2,2,2] .empty .empty)) (.node [8,7,5,5,5,3,3,3,2,2] (.node [8,7,5,5,5,3,3,3,2,1,1] .empty .empty) (.node [8,7,5,5,5,3,3,3,3,1] .empty .empty)))) (.node [8,7,5,5,5,4,4,3,1,1] (.node [8,7,5,5,5,4,3,3,2,1] (.node [8,7,5,5,5,4,3,2,2,2] (.node [8,7,5,5,5,4,3,2,2,1,1] .empty .empty) (.node [8,7,5,5,5,4,3,3,1,1,1] .empty .empty)) (.node [8,7,5,5,5,4,4,2,1,1,1] (.node [8,7,5,5,5,4,3,3,3] .empty .empty) (.node [8,7,5,5,5,4,4,2,2,1] .empty .empty))) (.node [8,7,5,5,5,5,2,2,2,2] (.node [8,7,5,5,5,4,4,4,1] (.node [8,7,5,5,5,4,4,3,2] .empty .empty) (.node [8,7,5,5,5,5,2,2,2,1,1] .empty .empty)) (.node [8,7,5,5,5,5,3,2,2,1] (.node [8,7,5,5,5,5,3,2,1,1,1] .empty .empty) (.node [8,7,5,5,5,5,3,3,1,1] .empty .empty))))) - -def degreeTree43_28 : RowTree := (.node [8,7,5,5,4,4,3,2,2,2,1] degreeTree43_26 degreeTree43_27) - -def degreeTree43_29 : RowTree := (.node [8,7,4,4,4,4,4,3,2,2,1] degreeTree43_25 degreeTree43_28) - -def degreeTree43_30 : RowTree := (.node [8,7,6,3,3,3,3,3,3,2,2] (.node [8,7,5,5,5,5,4,4] (.node [8,7,5,5,5,5,4,2,2] (.node [8,7,5,5,5,5,4,2,1,1] (.node [8,7,5,5,5,5,4,1,1,1,1] .empty .empty) .empty) (.node [8,7,5,5,5,5,4,3,1] .empty .empty)) (.node [8,7,5,5,5,5,5,2,1] (.node [8,7,5,5,5,5,5,1,1,1] .empty .empty) (.node [8,7,5,5,5,5,5,3] .empty .empty))) (.node [8,7,6,4,3,3,3,3,3,3] (.node [8,7,6,4,3,3,3,3,2,2,2] (.node [8,7,6,3,3,3,3,3,3,3,1] .empty .empty) (.node [8,7,6,4,3,3,3,3,3,2,1] .empty .empty)) (.node [8,7,6,4,4,3,3,3,2,2,1] (.node [8,7,6,4,4,3,3,2,2,2,2] .empty .empty) (.node [8,7,6,4,4,3,3,3,3,1,1] .empty .empty)))) - -def degreeTree43_31 : RowTree := (.node [8,7,6,4,4,4,4,3,1,1,1] (.node [8,7,6,4,4,4,3,3,2,2] (.node [8,7,6,4,4,4,3,2,2,2,1] (.node [8,7,6,4,4,4,2,2,2,2,2] .empty .empty) (.node [8,7,6,4,4,4,3,3,2,1,1] .empty .empty)) (.node [8,7,6,4,4,4,4,2,2,1,1] (.node [8,7,6,4,4,4,3,3,3,1] .empty .empty) (.node [8,7,6,4,4,4,4,2,2,2] .empty .empty))) (.node [8,7,6,4,4,4,4,4,2] (.node [8,7,6,4,4,4,4,3,3] (.node [8,7,6,4,4,4,4,3,2,1] .empty .empty) (.node [8,7,6,4,4,4,4,4,1,1] .empty .empty)) (.node [8,7,6,5,3,3,3,3,2,2,1] (.node [8,7,6,5,3,3,3,2,2,2,2] .empty .empty) (.node [8,7,6,5,3,3,3,3,3,1,1] .empty .empty)))) - -def degreeTree43_32 : RowTree := (.node [8,7,6,4,4,3,3,3,3,2] degreeTree43_30 degreeTree43_31) - -def degreeTree43_33 : RowTree := (.node [8,7,6,5,4,4,4,4,1] (.node [8,7,6,5,4,4,3,2,2,2] (.node [8,7,6,5,4,3,3,3,2,2] (.node [8,7,6,5,4,3,3,2,2,2,1] (.node [8,7,6,5,4,3,2,2,2,2,2] .empty .empty) (.node [8,7,6,5,4,3,3,3,2,1,1] .empty .empty)) (.node [8,7,6,5,4,4,2,2,2,2,1] (.node [8,7,6,5,4,3,3,3,3,1] .empty .empty) (.node [8,7,6,5,4,4,3,2,2,1,1] .empty .empty))) (.node [8,7,6,5,4,4,4,2,1,1,1] (.node [8,7,6,5,4,4,3,3,2,1] (.node [8,7,6,5,4,4,3,3,1,1,1] .empty .empty) (.node [8,7,6,5,4,4,3,3,3] .empty .empty)) (.node [8,7,6,5,4,4,4,3,1,1] (.node [8,7,6,5,4,4,4,2,2,1] .empty .empty) (.node [8,7,6,5,4,4,4,3,2] .empty .empty)))) (.node [8,7,6,5,5,4,2,2,2,1,1] (.node [8,7,6,5,5,3,3,2,2,2] (.node [8,7,6,5,5,3,2,2,2,2,1] (.node [8,7,6,5,5,2,2,2,2,2,2] .empty .empty) (.node [8,7,6,5,5,3,3,2,2,1,1] .empty .empty)) (.node [8,7,6,5,5,3,3,3,2,1] (.node [8,7,6,5,5,3,3,3,1,1,1] .empty .empty) (.node [8,7,6,5,5,3,3,3,3] .empty .empty))) (.node [8,7,6,5,5,4,3,3,1,1] (.node [8,7,6,5,5,4,3,2,1,1,1] (.node [8,7,6,5,5,4,2,2,2,2] .empty .empty) (.node [8,7,6,5,5,4,3,2,2,1] .empty .empty)) (.node [8,7,6,5,5,4,4,1,1,1,1] (.node [8,7,6,5,5,4,3,3,2] .empty .empty) (.node [8,7,6,5,5,4,4,2,1,1] .empty .empty))))) - -def degreeTree43_34 : RowTree := (.node [8,7,6,5,3,3,3,3,3,2] degreeTree43_32 degreeTree43_33) - -def degreeTree43_35 : RowTree := (.node [8,7,6,6,3,3,3,3,2,1,1] (.node [8,7,6,5,5,5,3,3,1] (.node [8,7,6,5,5,5,2,2,2,1] (.node [8,7,6,5,5,4,4,4] (.node [8,7,6,5,5,4,4,3,1] .empty .empty) (.node [8,7,6,5,5,5,2,2,1,1,1] .empty .empty)) (.node [8,7,6,5,5,5,3,2,1,1] (.node [8,7,6,5,5,5,3,1,1,1,1] .empty .empty) (.node [8,7,6,5,5,5,3,2,2] .empty .empty))) (.node [8,7,6,5,5,5,5,1,1] (.node [8,7,6,5,5,5,4,2,1] (.node [8,7,6,5,5,5,4,1,1,1] .empty .empty) (.node [8,7,6,5,5,5,4,3] .empty .empty)) (.node [8,7,6,6,3,3,2,2,2,2,2] (.node [8,7,6,5,5,5,5,2] .empty .empty) (.node [8,7,6,6,3,3,3,2,2,2,1] .empty .empty)))) (.node [8,7,6,6,4,3,3,3,2,1] (.node [8,7,6,6,4,3,2,2,2,2,1] (.node [8,7,6,6,3,3,3,3,3,1] (.node [8,7,6,6,3,3,3,3,2,2] .empty .empty) (.node [8,7,6,6,4,2,2,2,2,2,2] .empty .empty)) (.node [8,7,6,6,4,3,3,2,2,2] (.node [8,7,6,6,4,3,3,2,2,1,1] .empty .empty) (.node [8,7,6,6,4,3,3,3,1,1,1] .empty .empty))) (.node [8,7,6,6,4,4,3,2,1,1,1] (.node [8,7,6,6,4,4,2,2,2,1,1] (.node [8,7,6,6,4,3,3,3,3] .empty .empty) (.node [8,7,6,6,4,4,2,2,2,2] .empty .empty)) (.node [8,7,6,6,4,4,3,3,1,1] (.node [8,7,6,6,4,4,3,2,2,1] .empty .empty) (.node [8,7,6,6,4,4,3,3,2] .empty .empty))))) - -def degreeTree43_36 : RowTree := (.node [8,7,6,6,5,4,3,2,2] (.node [8,7,6,6,5,3,3,2,1,1,1] (.node [8,7,6,6,4,4,4,4] (.node [8,7,6,6,4,4,4,2,2] (.node [8,7,6,6,4,4,4,2,1,1] .empty .empty) (.node [8,7,6,6,4,4,4,3,1] .empty .empty)) (.node [8,7,6,6,5,3,2,2,2,1,1] (.node [8,7,6,6,5,2,2,2,2,2,1] .empty .empty) (.node [8,7,6,6,5,3,2,2,2,2] .empty .empty))) (.node [8,7,6,6,5,4,2,2,1,1,1] (.node [8,7,6,6,5,3,3,3,1,1] (.node [8,7,6,6,5,3,3,2,2,1] .empty .empty) (.node [8,7,6,6,5,3,3,3,2] .empty .empty)) (.node [8,7,6,6,5,4,3,1,1,1,1] (.node [8,7,6,6,5,4,2,2,2,1] .empty .empty) (.node [8,7,6,6,5,4,3,2,1,1] .empty .empty)))) (.node [8,7,6,6,5,5,3,1,1,1] (.node [8,7,6,6,5,4,4,3] (.node [8,7,6,6,5,4,4,1,1,1] (.node [8,7,6,6,5,4,3,3,1] .empty .empty) (.node [8,7,6,6,5,4,4,2,1] .empty .empty)) (.node [8,7,6,6,5,5,2,2,1,1] (.node [8,7,6,6,5,5,2,1,1,1,1] .empty .empty) (.node [8,7,6,6,5,5,2,2,2] .empty .empty))) (.node [8,7,6,6,5,5,4,2] (.node [8,7,6,6,5,5,3,3] (.node [8,7,6,6,5,5,3,2,1] .empty .empty) (.node [8,7,6,6,5,5,4,1,1] .empty .empty)) (.node [8,7,6,6,6,1,1,1,1,1,1,1,1,1,1] (.node [8,7,6,6,5,5,5,1] .empty .empty) (.node [8,7,6,6,6,2,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_37 : RowTree := (.node [8,7,6,6,4,4,4,1,1,1,1] degreeTree43_35 degreeTree43_36) - -def degreeTree43_38 : RowTree := (.node [8,7,6,5,5,4,4,2,2] degreeTree43_34 degreeTree43_37) - -def degreeTree43_39 : RowTree := (.node [8,7,5,5,5,5,3,3,2] degreeTree43_29 degreeTree43_38) - -def degreeTree43_40 : RowTree := (.node [8,6,6,6,5,3,3,2,2,2] degreeTree43_20 degreeTree43_39) - -def degreeTree43_41 : RowTree := (.node [8,7,6,6,6,3,3,2,1,1] (.node [8,7,6,6,6,3,2,1,1,1,1,1] (.node [8,7,6,6,6,2,2,2,2,2] (.node [8,7,6,6,6,2,2,2,2,1,1] (.node [8,7,6,6,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [8,7,6,6,6,3,1,1,1,1,1,1,1] .empty .empty)) (.node [8,7,6,6,6,3,2,2,2,1] (.node [8,7,6,6,6,3,2,2,1,1,1] .empty .empty) (.node [8,7,6,6,6,3,3,1,1,1,1] .empty .empty))) (.node [8,7,6,6,6,4,2,1,1,1,1] (.node [8,7,6,6,6,3,3,3,1] (.node [8,7,6,6,6,3,3,2,2] .empty .empty) (.node [8,7,6,6,6,4,1,1,1,1,1,1] .empty .empty)) (.node [8,7,6,6,6,4,2,2,2] (.node [8,7,6,6,6,4,2,2,1,1] .empty .empty) (.node [8,7,6,6,6,4,3,1,1,1] .empty .empty)))) - -def degreeTree43_42 : RowTree := (.node [8,7,6,6,6,5,3,2] (.node [8,7,6,6,6,5,1,1,1,1,1] (.node [8,7,6,6,6,4,4,1,1] (.node [8,7,6,6,6,4,3,3] .empty .empty) (.node [8,7,6,6,6,4,4,2] .empty .empty)) (.node [8,7,6,6,6,5,2,2,1] (.node [8,7,6,6,6,5,2,1,1,1] .empty .empty) (.node [8,7,6,6,6,5,3,1,1] .empty .empty))) (.node [8,7,6,6,6,6,2,2] (.node [8,7,6,6,6,6,1,1,1,1] (.node [8,7,6,6,6,5,4,1] .empty .empty) (.node [8,7,6,6,6,6,2,1,1] .empty .empty)) (.node [8,7,7,3,3,3,3,3,2,2,2] (.node [8,7,6,6,6,6,3,1] .empty .empty) (.node [8,7,7,3,3,3,3,3,3,2,1] .empty .empty)))) - -def degreeTree43_43 : RowTree := (.node [8,7,6,6,6,4,3,2,1] degreeTree43_41 degreeTree43_42) - -def degreeTree43_44 : RowTree := (.node [8,7,7,4,4,4,4,2,1,1,1] (.node [8,7,7,4,4,3,3,3,2,2] (.node [8,7,7,4,3,3,3,3,3,2] (.node [8,7,7,4,3,3,3,3,2,2,1] (.node [8,7,7,4,3,3,3,2,2,2,2] .empty .empty) (.node [8,7,7,4,3,3,3,3,3,1,1] .empty .empty)) (.node [8,7,7,4,4,3,3,2,2,2,1] (.node [8,7,7,4,4,3,2,2,2,2,2] .empty .empty) (.node [8,7,7,4,4,3,3,3,2,1,1] .empty .empty))) (.node [8,7,7,4,4,4,3,2,2,2] (.node [8,7,7,4,4,4,2,2,2,2,1] (.node [8,7,7,4,4,3,3,3,3,1] .empty .empty) (.node [8,7,7,4,4,4,3,2,2,1,1] .empty .empty)) (.node [8,7,7,4,4,4,3,3,2,1] (.node [8,7,7,4,4,4,3,3,1,1,1] .empty .empty) (.node [8,7,7,4,4,4,3,3,3] .empty .empty)))) (.node [8,7,7,5,3,3,3,3,2,2] (.node [8,7,7,4,4,4,4,4,1] (.node [8,7,7,4,4,4,4,3,1,1] (.node [8,7,7,4,4,4,4,2,2,1] .empty .empty) (.node [8,7,7,4,4,4,4,3,2] .empty .empty)) (.node [8,7,7,5,3,3,3,2,2,2,1] (.node [8,7,7,5,3,3,2,2,2,2,2] .empty .empty) (.node [8,7,7,5,3,3,3,3,2,1,1] .empty .empty))) (.node [8,7,7,5,4,3,3,2,2,1,1] (.node [8,7,7,5,4,2,2,2,2,2,2] (.node [8,7,7,5,3,3,3,3,3,1] .empty .empty) (.node [8,7,7,5,4,3,2,2,2,2,1] .empty .empty)) (.node [8,7,7,5,4,3,3,3,1,1,1] (.node [8,7,7,5,4,3,3,2,2,2] .empty .empty) (.node [8,7,7,5,4,3,3,3,2,1] .empty .empty))))) - -def degreeTree43_45 : RowTree := (.node [8,7,7,3,3,3,3,3,3,3] degreeTree43_43 degreeTree43_44) - -def degreeTree43_46 : RowTree := (.node [8,7,7,5,5,3,3,2,2,1] (.node [8,7,7,5,4,4,4,2,1,1] (.node [8,7,7,5,4,4,3,2,2,1] (.node [8,7,7,5,4,4,2,2,2,2] (.node [8,7,7,5,4,4,2,2,2,1,1] .empty .empty) (.node [8,7,7,5,4,4,3,2,1,1,1] .empty .empty)) (.node [8,7,7,5,4,4,3,3,2] (.node [8,7,7,5,4,4,3,3,1,1] .empty .empty) (.node [8,7,7,5,4,4,4,1,1,1,1] .empty .empty))) (.node [8,7,7,5,5,2,2,2,2,2,1] (.node [8,7,7,5,4,4,4,3,1] (.node [8,7,7,5,4,4,4,2,2] .empty .empty) (.node [8,7,7,5,4,4,4,4] .empty .empty)) (.node [8,7,7,5,5,3,2,2,2,2] (.node [8,7,7,5,5,3,2,2,2,1,1] .empty .empty) (.node [8,7,7,5,5,3,3,2,1,1,1] .empty .empty)))) (.node [8,7,7,5,5,4,3,3,1] (.node [8,7,7,5,5,4,2,2,2,1] (.node [8,7,7,5,5,3,3,3,2] (.node [8,7,7,5,5,3,3,3,1,1] .empty .empty) (.node [8,7,7,5,5,4,2,2,1,1,1] .empty .empty)) (.node [8,7,7,5,5,4,3,2,1,1] (.node [8,7,7,5,5,4,3,1,1,1,1] .empty .empty) (.node [8,7,7,5,5,4,3,2,2] .empty .empty))) (.node [8,7,7,5,5,5,2,1,1,1,1] (.node [8,7,7,5,5,4,4,2,1] (.node [8,7,7,5,5,4,4,1,1,1] .empty .empty) (.node [8,7,7,5,5,4,4,3] .empty .empty)) (.node [8,7,7,5,5,5,2,2,2] (.node [8,7,7,5,5,5,2,2,1,1] .empty .empty) (.node [8,7,7,5,5,5,3,1,1,1] .empty .empty))))) - -def degreeTree43_47 : RowTree := (.node [8,7,7,6,3,2,2,2,1,1,1,1,1,1] (.node [8,7,7,6,2,2,2,1,1,1,1,1,1,1,1,1] (.node [8,7,7,5,5,5,5,1] (.node [8,7,7,5,5,5,4,1,1] (.node [8,7,7,5,5,5,3,3] .empty .empty) (.node [8,7,7,5,5,5,4,2] .empty .empty)) (.node [8,7,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,7,7,6,2,2,2,2,2,2,2,1] (.node [8,7,7,6,2,2,2,2,2,1,1,1,1,1] (.node [8,7,7,6,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [8,7,7,6,3,2,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,6,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,3,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,7,7,6,3,3,2,2,2,2,1] (.node [8,7,7,6,3,3,1,1,1,1,1,1,1,1,1] (.node [8,7,7,6,3,2,2,2,2,2,1,1] (.node [8,7,7,6,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [8,7,7,6,3,2,2,2,2,2,2] .empty .empty)) (.node [8,7,7,6,3,3,2,2,1,1,1,1,1] (.node [8,7,7,6,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,3,3,2,2,2,1,1,1] .empty .empty))) (.node [8,7,7,6,3,3,3,2,2,2] (.node [8,7,7,6,3,3,3,2,1,1,1,1] (.node [8,7,7,6,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,3,3,3,2,2,1,1] .empty .empty)) (.node [8,7,7,6,3,3,3,3,2,1] (.node [8,7,7,6,3,3,3,3,1,1,1] .empty .empty) (.node [8,7,7,6,3,3,3,3,3] .empty .empty))))) - -def degreeTree43_48 : RowTree := (.node [8,7,7,5,5,5,3,2,1] degreeTree43_46 degreeTree43_47) - -def degreeTree43_49 : RowTree := (.node [8,7,7,5,4,3,3,3,3] degreeTree43_45 degreeTree43_48) - -def degreeTree43_50 : RowTree := (.node [8,7,7,6,4,3,2,2,2,1,1] (.node [8,7,7,6,4,2,2,2,2,2,1] (.node [8,7,7,6,4,2,2,2,1,1,1,1,1] (.node [8,7,7,6,4,2,2,1,1,1,1,1,1,1] (.node [8,7,7,6,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,7,7,6,4,2,2,2,2,1,1,1] .empty .empty)) (.node [8,7,7,6,4,3,2,1,1,1,1,1,1] (.node [8,7,7,6,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,4,3,2,2,1,1,1,1] .empty .empty))) (.node [8,7,7,6,4,3,3,2,2,1] (.node [8,7,7,6,4,3,3,1,1,1,1,1] (.node [8,7,7,6,4,3,2,2,2,2] .empty .empty) (.node [8,7,7,6,4,3,3,2,1,1,1] .empty .empty)) (.node [8,7,7,6,4,3,3,3,2] (.node [8,7,7,6,4,3,3,3,1,1] .empty .empty) (.node [8,7,7,6,4,4,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_51 : RowTree := (.node [8,7,7,6,4,4,4,2,1] (.node [8,7,7,6,4,4,3,2,1,1] (.node [8,7,7,6,4,4,2,2,2,1] (.node [8,7,7,6,4,4,2,2,1,1,1] .empty .empty) (.node [8,7,7,6,4,4,3,1,1,1,1] .empty .empty)) (.node [8,7,7,6,4,4,3,3,1] (.node [8,7,7,6,4,4,3,2,2] .empty .empty) (.node [8,7,7,6,4,4,4,1,1,1] .empty .empty))) (.node [8,7,7,6,5,2,2,1,1,1,1,1,1] (.node [8,7,7,6,5,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,6,4,4,4,3] .empty .empty) (.node [8,7,7,6,5,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,7,7,6,5,2,2,2,2,1,1] (.node [8,7,7,6,5,2,2,2,1,1,1,1] .empty .empty) (.node [8,7,7,6,5,2,2,2,2,2] .empty .empty)))) - -def degreeTree43_52 : RowTree := (.node [8,7,7,6,4,4,2,1,1,1,1,1] degreeTree43_50 degreeTree43_51) - -def degreeTree43_53 : RowTree := (.node [8,7,7,6,5,4,4,2] (.node [8,7,7,6,5,4,1,1,1,1,1,1] (.node [8,7,7,6,5,3,3,1,1,1,1] (.node [8,7,7,6,5,3,2,2,1,1,1] (.node [8,7,7,6,5,3,2,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,5,3,2,2,2,1] .empty .empty)) (.node [8,7,7,6,5,3,3,2,2] (.node [8,7,7,6,5,3,3,2,1,1] .empty .empty) (.node [8,7,7,6,5,3,3,3,1] .empty .empty))) (.node [8,7,7,6,5,4,3,1,1,1] (.node [8,7,7,6,5,4,2,2,1,1] (.node [8,7,7,6,5,4,2,1,1,1,1] .empty .empty) (.node [8,7,7,6,5,4,2,2,2] .empty .empty)) (.node [8,7,7,6,5,4,3,3] (.node [8,7,7,6,5,4,3,2,1] .empty .empty) (.node [8,7,7,6,5,4,4,1,1] .empty .empty)))) (.node [8,7,7,6,6,2,1,1,1,1,1,1,1] (.node [8,7,7,6,5,5,3,1,1] (.node [8,7,7,6,5,5,2,1,1,1] (.node [8,7,7,6,5,5,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,5,5,2,2,1] .empty .empty)) (.node [8,7,7,6,5,5,4,1] (.node [8,7,7,6,5,5,3,2] .empty .empty) (.node [8,7,7,6,6,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,7,7,6,6,3,1,1,1,1,1,1] (.node [8,7,7,6,6,2,2,2,1,1,1] (.node [8,7,7,6,6,2,2,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,6,2,2,2,2,1] .empty .empty)) (.node [8,7,7,6,6,3,2,2,1,1] (.node [8,7,7,6,6,3,2,1,1,1,1] .empty .empty) (.node [8,7,7,6,6,3,2,2,2] .empty .empty))))) - -def degreeTree43_54 : RowTree := (.node [8,7,7,6,5,3,1,1,1,1,1,1,1] degreeTree43_52 degreeTree43_53) - -def degreeTree43_55 : RowTree := (.node [8,7,7,7,2,2,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,6,6,4,4,1] (.node [8,7,7,6,6,4,2,1,1,1] (.node [8,7,7,6,6,3,3,3] (.node [8,7,7,6,6,3,3,2,1] .empty .empty) (.node [8,7,7,6,6,4,1,1,1,1,1] .empty .empty)) (.node [8,7,7,6,6,4,3,1,1] (.node [8,7,7,6,6,4,2,2,1] .empty .empty) (.node [8,7,7,6,6,4,3,2] .empty .empty))) (.node [8,7,7,6,6,5,3,1] (.node [8,7,7,6,6,5,2,1,1] (.node [8,7,7,6,6,5,1,1,1,1] .empty .empty) (.node [8,7,7,6,6,5,2,2] .empty .empty)) (.node [8,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,6,6,6,1,1,1] .empty .empty) (.node [8,7,7,7,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,7,7,7,3,2,2,1,1,1,1,1,1,1] (.node [8,7,7,7,2,2,2,2,2,2,1,1] (.node [8,7,7,7,2,2,2,2,1,1,1,1,1,1] (.node [8,7,7,7,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [8,7,7,7,3,1,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,7,2,2,2,2,2,2,2] .empty .empty) (.node [8,7,7,7,3,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,7,7,7,3,3,1,1,1,1,1,1,1,1] (.node [8,7,7,7,3,2,2,2,2,1,1,1] (.node [8,7,7,7,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,3,2,2,2,2,2,1] .empty .empty)) (.node [8,7,7,7,3,3,2,2,1,1,1,1] (.node [8,7,7,7,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,3,3,2,2,2,1,1] .empty .empty))))) - -def degreeTree43_56 : RowTree := (.node [8,7,7,7,4,3,3,1,1,1,1] (.node [8,7,7,7,4,2,2,1,1,1,1,1,1] (.node [8,7,7,7,3,3,3,3,1,1] (.node [8,7,7,7,3,3,3,2,1,1,1] (.node [8,7,7,7,3,3,3,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,3,3,3,2,2,1] .empty .empty)) (.node [8,7,7,7,4,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,7,3,3,3,3,2] .empty .empty) (.node [8,7,7,7,4,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,7,7,7,4,3,1,1,1,1,1,1,1] (.node [8,7,7,7,4,2,2,2,2,1,1] (.node [8,7,7,7,4,2,2,2,1,1,1,1] .empty .empty) (.node [8,7,7,7,4,2,2,2,2,2] .empty .empty)) (.node [8,7,7,7,4,3,2,2,1,1,1] (.node [8,7,7,7,4,3,2,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,4,3,2,2,2,1] .empty .empty)))) (.node [8,7,7,7,4,4,3,1,1,1] (.node [8,7,7,7,4,4,1,1,1,1,1,1] (.node [8,7,7,7,4,3,3,2,2] (.node [8,7,7,7,4,3,3,2,1,1] .empty .empty) (.node [8,7,7,7,4,3,3,3,1] .empty .empty)) (.node [8,7,7,7,4,4,2,2,1,1] (.node [8,7,7,7,4,4,2,1,1,1,1] .empty .empty) (.node [8,7,7,7,4,4,2,2,2] .empty .empty))) (.node [8,7,7,7,4,4,4,2] (.node [8,7,7,7,4,4,3,3] (.node [8,7,7,7,4,4,3,2,1] .empty .empty) (.node [8,7,7,7,4,4,4,1,1] .empty .empty)) (.node [8,7,7,7,5,2,1,1,1,1,1,1,1] (.node [8,7,7,7,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,5,2,2,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_57 : RowTree := (.node [8,7,7,7,3,3,2,2,2,2] degreeTree43_55 degreeTree43_56) - -def degreeTree43_58 : RowTree := (.node [8,7,7,6,6,3,3,1,1,1] degreeTree43_54 degreeTree43_57) - -def degreeTree43_59 : RowTree := (.node [8,7,7,6,4,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_49 degreeTree43_58) - -def degreeTree43_60 : RowTree := (.node [8,7,7,7,5,4,1,1,1,1,1] (.node [8,7,7,7,5,3,2,2,2] (.node [8,7,7,7,5,3,2,1,1,1,1] (.node [8,7,7,7,5,3,1,1,1,1,1,1] (.node [8,7,7,7,5,2,2,2,2,1] .empty .empty) .empty) (.node [8,7,7,7,5,3,2,2,1,1] .empty .empty)) (.node [8,7,7,7,5,3,3,2,1] (.node [8,7,7,7,5,3,3,1,1,1] .empty .empty) (.node [8,7,7,7,5,3,3,3] .empty .empty))) (.node [8,7,7,7,5,4,3,2] (.node [8,7,7,7,5,4,2,2,1] (.node [8,7,7,7,5,4,2,1,1,1] .empty .empty) (.node [8,7,7,7,5,4,3,1,1] .empty .empty)) (.node [8,7,7,7,5,5,1,1,1,1] (.node [8,7,7,7,5,4,4,1] .empty .empty) (.node [8,7,7,7,5,5,2,1,1] .empty .empty)))) - -def degreeTree43_61 : RowTree := (.node [8,7,7,7,6,3,2,2,1] (.node [8,7,7,7,6,2,2,2,1,1] (.node [8,7,7,7,6,2,1,1,1,1,1,1] (.node [8,7,7,7,6,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,6,2,2,1,1,1,1] .empty .empty)) (.node [8,7,7,7,6,3,1,1,1,1,1] (.node [8,7,7,7,6,2,2,2,2] .empty .empty) (.node [8,7,7,7,6,3,2,1,1,1] .empty .empty))) (.node [8,7,7,7,6,4,2,1,1] (.node [8,7,7,7,6,3,3,2] (.node [8,7,7,7,6,3,3,1,1] .empty .empty) (.node [8,7,7,7,6,4,1,1,1,1] .empty .empty)) (.node [8,7,7,7,6,5,1,1,1] (.node [8,7,7,7,6,4,2,2] .empty .empty) (.node [8,7,7,7,7,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_62 : RowTree := (.node [8,7,7,7,5,5,2,2] degreeTree43_60 degreeTree43_61) - -def degreeTree43_63 : RowTree := (.node [8,8,4,4,4,4,3,3,3,1,1] (.node [8,8,4,3,3,3,3,3,3,3,2] (.node [8,7,7,7,7,3,2,1,1] (.node [8,7,7,7,7,2,2,2,1] (.node [8,7,7,7,7,2,2,1,1,1] .empty .empty) (.node [8,7,7,7,7,3,1,1,1,1] .empty .empty)) (.node [8,7,7,7,7,4,1,1,1] (.node [8,7,7,7,7,3,2,2] .empty .empty) (.node [8,8,3,3,3,3,3,3,3,3,3] .empty .empty))) (.node [8,8,4,4,4,3,3,3,3,2,1] (.node [8,8,4,4,3,3,3,3,3,3,1] (.node [8,8,4,4,3,3,3,3,3,2,2] .empty .empty) (.node [8,8,4,4,4,3,3,3,2,2,2] .empty .empty)) (.node [8,8,4,4,4,4,3,2,2,2,2] (.node [8,8,4,4,4,3,3,3,3,3] .empty .empty) (.node [8,8,4,4,4,4,3,3,2,2,1] .empty .empty)))) (.node [8,8,4,4,4,4,4,4,3] (.node [8,8,4,4,4,4,4,3,2,2] (.node [8,8,4,4,4,4,4,2,2,2,1] (.node [8,8,4,4,4,4,3,3,3,2] .empty .empty) (.node [8,8,4,4,4,4,4,3,2,1,1] .empty .empty)) (.node [8,8,4,4,4,4,4,4,1,1,1] (.node [8,8,4,4,4,4,4,3,3,1] .empty .empty) (.node [8,8,4,4,4,4,4,4,2,1] .empty .empty))) (.node [8,8,5,4,3,3,3,3,3,2,1] (.node [8,8,5,3,3,3,3,3,3,3,1] (.node [8,8,5,3,3,3,3,3,3,2,2] .empty .empty) (.node [8,8,5,4,3,3,3,3,2,2,2] .empty .empty)) (.node [8,8,5,4,4,3,3,2,2,2,2] (.node [8,8,5,4,3,3,3,3,3,3] .empty .empty) (.node [8,8,5,4,4,3,3,3,2,2,1] .empty .empty))))) - -def degreeTree43_64 : RowTree := (.node [8,7,7,7,7,2,1,1,1,1,1] degreeTree43_62 degreeTree43_63) - -def degreeTree43_65 : RowTree := (.node [8,8,5,5,3,3,3,3,3,1,1] (.node [8,8,5,4,4,4,4,2,2,2] (.node [8,8,5,4,4,4,3,3,2,1,1] (.node [8,8,5,4,4,4,2,2,2,2,2] (.node [8,8,5,4,4,3,3,3,3,2] .empty .empty) (.node [8,8,5,4,4,4,3,2,2,2,1] .empty .empty)) (.node [8,8,5,4,4,4,3,3,3,1] (.node [8,8,5,4,4,4,3,3,2,2] .empty .empty) (.node [8,8,5,4,4,4,4,2,2,1,1] .empty .empty))) (.node [8,8,5,4,4,4,4,4,1,1] (.node [8,8,5,4,4,4,4,3,2,1] (.node [8,8,5,4,4,4,4,3,1,1,1] .empty .empty) (.node [8,8,5,4,4,4,4,3,3] .empty .empty)) (.node [8,8,5,5,3,3,3,2,2,2,2] (.node [8,8,5,4,4,4,4,4,2] .empty .empty) (.node [8,8,5,5,3,3,3,3,2,2,1] .empty .empty)))) (.node [8,8,5,5,4,4,3,2,2,1,1] (.node [8,8,5,5,4,3,3,3,2,1,1] (.node [8,8,5,5,4,3,2,2,2,2,2] (.node [8,8,5,5,3,3,3,3,3,2] .empty .empty) (.node [8,8,5,5,4,3,3,2,2,2,1] .empty .empty)) (.node [8,8,5,5,4,3,3,3,3,1] (.node [8,8,5,5,4,3,3,3,2,2] .empty .empty) (.node [8,8,5,5,4,4,2,2,2,2,1] .empty .empty))) (.node [8,8,5,5,4,4,3,3,3] (.node [8,8,5,5,4,4,3,3,1,1,1] (.node [8,8,5,5,4,4,3,2,2,2] .empty .empty) (.node [8,8,5,5,4,4,3,3,2,1] .empty .empty)) (.node [8,8,5,5,4,4,4,2,2,1] (.node [8,8,5,5,4,4,4,2,1,1,1] .empty .empty) (.node [8,8,5,5,4,4,4,3,1,1] .empty .empty))))) - -def degreeTree43_66 : RowTree := (.node [8,8,5,5,5,4,4,2,1,1] (.node [8,8,5,5,5,3,3,3,3] (.node [8,8,5,5,5,3,3,2,2,1,1] (.node [8,8,5,5,5,2,2,2,2,2,2] (.node [8,8,5,5,4,4,4,4,1] .empty .empty) (.node [8,8,5,5,5,3,2,2,2,2,1] .empty .empty)) (.node [8,8,5,5,5,3,3,3,1,1,1] (.node [8,8,5,5,5,3,3,2,2,2] .empty .empty) (.node [8,8,5,5,5,3,3,3,2,1] .empty .empty))) (.node [8,8,5,5,5,4,3,2,2,1] (.node [8,8,5,5,5,4,2,2,2,2] (.node [8,8,5,5,5,4,2,2,2,1,1] .empty .empty) (.node [8,8,5,5,5,4,3,2,1,1,1] .empty .empty)) (.node [8,8,5,5,5,4,3,3,2] (.node [8,8,5,5,5,4,3,3,1,1] .empty .empty) (.node [8,8,5,5,5,4,4,1,1,1,1] .empty .empty)))) (.node [8,8,5,5,5,5,3,2,2] (.node [8,8,5,5,5,5,2,2,1,1,1] (.node [8,8,5,5,5,4,4,3,1] (.node [8,8,5,5,5,4,4,2,2] .empty .empty) (.node [8,8,5,5,5,4,4,4] .empty .empty)) (.node [8,8,5,5,5,5,3,1,1,1,1] (.node [8,8,5,5,5,5,2,2,2,1] .empty .empty) (.node [8,8,5,5,5,5,3,2,1,1] .empty .empty))) (.node [8,8,5,5,5,5,4,3] (.node [8,8,5,5,5,5,4,1,1,1] (.node [8,8,5,5,5,5,3,3,1] .empty .empty) (.node [8,8,5,5,5,5,4,2,1] .empty .empty)) (.node [8,8,5,5,5,5,5,2] (.node [8,8,5,5,5,5,5,1,1] .empty .empty) (.node [8,8,6,3,3,3,3,3,2,2,2] .empty .empty))))) - -def degreeTree43_67 : RowTree := (.node [8,8,5,5,4,4,4,3,2] degreeTree43_65 degreeTree43_66) - -def degreeTree43_68 : RowTree := (.node [8,8,5,4,4,3,3,3,3,1,1] degreeTree43_64 degreeTree43_67) - -def degreeTree43_69 : RowTree := (.node [8,8,6,4,4,3,3,3,2,2] (.node [8,8,6,4,3,3,3,3,3,2] (.node [8,8,6,4,3,3,3,3,2,2,1] (.node [8,8,6,4,3,3,3,2,2,2,2] (.node [8,8,6,3,3,3,3,3,3,3] .empty .empty) .empty) (.node [8,8,6,4,3,3,3,3,3,1,1] .empty .empty)) (.node [8,8,6,4,4,3,3,2,2,2,1] (.node [8,8,6,4,4,3,2,2,2,2,2] .empty .empty) (.node [8,8,6,4,4,3,3,3,2,1,1] .empty .empty))) (.node [8,8,6,4,4,4,3,2,2,2] (.node [8,8,6,4,4,4,2,2,2,2,1] (.node [8,8,6,4,4,3,3,3,3,1] .empty .empty) (.node [8,8,6,4,4,4,3,2,2,1,1] .empty .empty)) (.node [8,8,6,4,4,4,3,3,2,1] (.node [8,8,6,4,4,4,3,3,1,1,1] .empty .empty) (.node [8,8,6,4,4,4,3,3,3] .empty .empty)))) - -def degreeTree43_70 : RowTree := (.node [8,8,6,5,3,3,3,3,2,2] (.node [8,8,6,4,4,4,4,4,1] (.node [8,8,6,4,4,4,4,3,1,1] (.node [8,8,6,4,4,4,4,2,2,1] .empty .empty) (.node [8,8,6,4,4,4,4,3,2] .empty .empty)) (.node [8,8,6,5,3,3,3,2,2,2,1] (.node [8,8,6,5,3,3,2,2,2,2,2] .empty .empty) (.node [8,8,6,5,3,3,3,3,2,1,1] .empty .empty))) (.node [8,8,6,5,4,3,3,2,2,1,1] (.node [8,8,6,5,4,2,2,2,2,2,2] (.node [8,8,6,5,3,3,3,3,3,1] .empty .empty) (.node [8,8,6,5,4,3,2,2,2,2,1] .empty .empty)) (.node [8,8,6,5,4,3,3,3,1,1,1] (.node [8,8,6,5,4,3,3,2,2,2] .empty .empty) (.node [8,8,6,5,4,3,3,3,2,1] .empty .empty)))) - -def degreeTree43_71 : RowTree := (.node [8,8,6,4,4,4,4,2,1,1,1] degreeTree43_69 degreeTree43_70) - -def degreeTree43_72 : RowTree := (.node [8,8,6,5,5,3,3,2,2,1] (.node [8,8,6,5,4,4,4,2,1,1] (.node [8,8,6,5,4,4,3,2,2,1] (.node [8,8,6,5,4,4,2,2,2,2] (.node [8,8,6,5,4,4,2,2,2,1,1] .empty .empty) (.node [8,8,6,5,4,4,3,2,1,1,1] .empty .empty)) (.node [8,8,6,5,4,4,3,3,2] (.node [8,8,6,5,4,4,3,3,1,1] .empty .empty) (.node [8,8,6,5,4,4,4,1,1,1,1] .empty .empty))) (.node [8,8,6,5,5,2,2,2,2,2,1] (.node [8,8,6,5,4,4,4,3,1] (.node [8,8,6,5,4,4,4,2,2] .empty .empty) (.node [8,8,6,5,4,4,4,4] .empty .empty)) (.node [8,8,6,5,5,3,2,2,2,2] (.node [8,8,6,5,5,3,2,2,2,1,1] .empty .empty) (.node [8,8,6,5,5,3,3,2,1,1,1] .empty .empty)))) (.node [8,8,6,5,5,4,3,3,1] (.node [8,8,6,5,5,4,2,2,2,1] (.node [8,8,6,5,5,3,3,3,2] (.node [8,8,6,5,5,3,3,3,1,1] .empty .empty) (.node [8,8,6,5,5,4,2,2,1,1,1] .empty .empty)) (.node [8,8,6,5,5,4,3,2,1,1] (.node [8,8,6,5,5,4,3,1,1,1,1] .empty .empty) (.node [8,8,6,5,5,4,3,2,2] .empty .empty))) (.node [8,8,6,5,5,5,2,1,1,1,1] (.node [8,8,6,5,5,4,4,2,1] (.node [8,8,6,5,5,4,4,1,1,1] .empty .empty) (.node [8,8,6,5,5,4,4,3] .empty .empty)) (.node [8,8,6,5,5,5,2,2,2] (.node [8,8,6,5,5,5,2,2,1,1] .empty .empty) (.node [8,8,6,5,5,5,3,1,1,1] .empty .empty))))) - -def degreeTree43_73 : RowTree := (.node [8,8,6,5,4,3,3,3,3] degreeTree43_71 degreeTree43_72) - -def degreeTree43_74 : RowTree := (.node [8,8,6,6,3,2,2,2,2,1,1,1,1] (.node [8,8,6,6,2,2,2,2,1,1,1,1,1,1,1] (.node [8,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,6,5,5,5,4,1,1] (.node [8,8,6,5,5,5,3,3] .empty .empty) (.node [8,8,6,5,5,5,4,2] .empty .empty)) (.node [8,8,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,6,6,2,2,2,2,2,2,1,1,1] (.node [8,8,6,6,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,2,2,2,2,2,2,2,1] .empty .empty)) (.node [8,8,6,6,3,2,2,1,1,1,1,1,1,1,1] (.node [8,8,6,6,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,3,2,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,6,6,3,3,3,1,1,1,1,1,1] (.node [8,8,6,6,3,3,2,1,1,1,1,1,1,1] (.node [8,8,6,6,3,2,2,2,2,2,2] (.node [8,8,6,6,3,2,2,2,2,2,1,1] .empty .empty) (.node [8,8,6,6,3,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,6,6,3,3,2,2,2,1,1,1] (.node [8,8,6,6,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,3,3,2,2,2,2,1] .empty .empty))) (.node [8,8,6,6,3,3,3,3,1,1,1] (.node [8,8,6,6,3,3,3,2,2,1,1] (.node [8,8,6,6,3,3,3,2,1,1,1,1] .empty .empty) (.node [8,8,6,6,3,3,3,2,2,2] .empty .empty)) (.node [8,8,6,6,3,3,3,3,3] (.node [8,8,6,6,3,3,3,3,2,1] .empty .empty) (.node [8,8,6,6,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_75 : RowTree := (.node [8,8,6,6,4,4,2,1,1,1,1,1] (.node [8,8,6,6,4,3,2,2,2,1,1] (.node [8,8,6,6,4,2,2,2,2,2,1] (.node [8,8,6,6,4,2,2,2,1,1,1,1,1] (.node [8,8,6,6,4,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,4,2,2,2,2,1,1,1] .empty .empty)) (.node [8,8,6,6,4,3,2,1,1,1,1,1,1] (.node [8,8,6,6,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,4,3,2,2,1,1,1,1] .empty .empty))) (.node [8,8,6,6,4,3,3,2,2,1] (.node [8,8,6,6,4,3,3,1,1,1,1,1] (.node [8,8,6,6,4,3,2,2,2,2] .empty .empty) (.node [8,8,6,6,4,3,3,2,1,1,1] .empty .empty)) (.node [8,8,6,6,4,3,3,3,2] (.node [8,8,6,6,4,3,3,3,1,1] .empty .empty) (.node [8,8,6,6,4,4,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,6,6,4,4,4,2,1] (.node [8,8,6,6,4,4,3,2,1,1] (.node [8,8,6,6,4,4,2,2,2,1] (.node [8,8,6,6,4,4,2,2,1,1,1] .empty .empty) (.node [8,8,6,6,4,4,3,1,1,1,1] .empty .empty)) (.node [8,8,6,6,4,4,3,3,1] (.node [8,8,6,6,4,4,3,2,2] .empty .empty) (.node [8,8,6,6,4,4,4,1,1,1] .empty .empty))) (.node [8,8,6,6,5,2,2,1,1,1,1,1,1] (.node [8,8,6,6,5,1,1,1,1,1,1,1,1,1,1] (.node [8,8,6,6,4,4,4,3] .empty .empty) (.node [8,8,6,6,5,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,6,6,5,2,2,2,2,1,1] (.node [8,8,6,6,5,2,2,2,1,1,1,1] .empty .empty) (.node [8,8,6,6,5,2,2,2,2,2] .empty .empty))))) - -def degreeTree43_76 : RowTree := (.node [8,8,6,6,4,2,1,1,1,1,1,1,1,1,1] degreeTree43_74 degreeTree43_75) - -def degreeTree43_77 : RowTree := (.node [8,8,6,5,5,5,3,2,1] degreeTree43_73 degreeTree43_76) - -def degreeTree43_78 : RowTree := (.node [8,8,6,3,3,3,3,3,3,2,1] degreeTree43_68 degreeTree43_77) - -def degreeTree43_79 : RowTree := (.node [8,7,7,7,5,2,2,2,1,1,1] degreeTree43_59 degreeTree43_78) - -def degreeTree43_80 : RowTree := (.node [8,7,6,6,6,2,2,1,1,1,1,1,1] degreeTree43_40 degreeTree43_79) - -def degreeTree43_81 : RowTree := (.node [8,8,6,6,5,4,2,1,1,1,1] (.node [8,8,6,6,5,3,3,2,1,1] (.node [8,8,6,6,5,3,2,2,2,1] (.node [8,8,6,6,5,3,2,2,1,1,1] (.node [8,8,6,6,5,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [8,8,6,6,5,3,3,1,1,1,1] .empty .empty)) (.node [8,8,6,6,5,3,3,3,1] (.node [8,8,6,6,5,3,3,2,2] .empty .empty) (.node [8,8,6,6,5,4,1,1,1,1,1,1] .empty .empty))) (.node [8,8,6,6,5,4,3,2,1] (.node [8,8,6,6,5,4,2,2,2] (.node [8,8,6,6,5,4,2,2,1,1] .empty .empty) (.node [8,8,6,6,5,4,3,1,1,1] .empty .empty)) (.node [8,8,6,6,5,4,4,1,1] (.node [8,8,6,6,5,4,3,3] .empty .empty) (.node [8,8,6,6,5,4,4,2] .empty .empty)))) - -def degreeTree43_82 : RowTree := (.node [8,8,6,6,6,2,2,2,1,1,1] (.node [8,8,6,6,5,5,3,2] (.node [8,8,6,6,5,5,2,2,1] (.node [8,8,6,6,5,5,2,1,1,1] .empty .empty) (.node [8,8,6,6,5,5,3,1,1] .empty .empty)) (.node [8,8,6,6,6,2,1,1,1,1,1,1,1] (.node [8,8,6,6,6,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,6,2,2,1,1,1,1,1] .empty .empty))) (.node [8,8,6,6,6,3,2,2,1,1] (.node [8,8,6,6,6,3,1,1,1,1,1,1] (.node [8,8,6,6,6,2,2,2,2,1] .empty .empty) (.node [8,8,6,6,6,3,2,1,1,1,1] .empty .empty)) (.node [8,8,6,6,6,3,3,1,1,1] (.node [8,8,6,6,6,3,2,2,2] .empty .empty) (.node [8,8,6,6,6,3,3,2,1] .empty .empty)))) - -def degreeTree43_83 : RowTree := (.node [8,8,6,6,5,5,1,1,1,1,1] degreeTree43_81 degreeTree43_82) - -def degreeTree43_84 : RowTree := (.node [8,8,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [8,8,6,6,6,5,2,2] (.node [8,8,6,6,6,4,3,1,1] (.node [8,8,6,6,6,4,2,1,1,1] (.node [8,8,6,6,6,4,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,6,4,2,2,1] .empty .empty)) (.node [8,8,6,6,6,5,1,1,1,1] (.node [8,8,6,6,6,4,3,2] .empty .empty) (.node [8,8,6,6,6,5,2,1,1] .empty .empty))) (.node [8,8,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,6,6,6,6,1,1,1] .empty .empty) (.node [8,8,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,2,2,2,2,2,2,2,2,2,2] (.node [8,8,7,2,2,2,2,2,2,2,2,1,1,1,1] (.node [8,8,7,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [8,8,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,3,2,2,2,2,2,2,2,1,1,1] (.node [8,8,7,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [8,8,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [8,8,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,3,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [8,8,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_85 : RowTree := (.node [8,8,6,6,6,3,3,3] degreeTree43_83 degreeTree43_84) - -def degreeTree43_86 : RowTree := (.node [8,8,7,3,3,3,2,2,2,1,1,1,1,1] (.node [8,8,7,3,3,2,2,2,2,2,2,2] (.node [8,8,7,3,3,2,2,2,2,2,1,1,1,1] (.node [8,8,7,3,3,2,2,2,2,1,1,1,1,1,1] (.node [8,8,7,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,8,7,3,3,2,2,2,2,2,2,1,1] .empty .empty)) (.node [8,8,7,3,3,3,2,1,1,1,1,1,1,1,1,1] (.node [8,8,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,3,3,3,3,2,1,1,1,1,1,1] (.node [8,8,7,3,3,3,2,2,2,2,2,1] (.node [8,8,7,3,3,3,2,2,2,2,1,1,1] .empty .empty) (.node [8,8,7,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,3,3,3,3,2,2,2,1,1] (.node [8,8,7,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [8,8,7,3,3,3,3,2,2,2,2] .empty .empty)))) - -def degreeTree43_87 : RowTree := (.node [8,8,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,3,3,3,3,3,3,2] (.node [8,8,7,3,3,3,3,3,2,2,1] (.node [8,8,7,3,3,3,3,3,2,1,1,1] .empty .empty) (.node [8,8,7,3,3,3,3,3,3,1,1] .empty .empty)) (.node [8,8,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,4,2,2,2,2,2,2,2,1,1] (.node [8,8,7,4,2,2,2,2,2,1,1,1,1,1,1] (.node [8,8,7,4,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,4,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [8,8,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,4,2,2,2,2,2,2,2,2] .empty .empty) (.node [8,8,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_88 : RowTree := (.node [8,8,7,3,3,3,3,3,1,1,1,1,1] degreeTree43_86 degreeTree43_87) - -def degreeTree43_89 : RowTree := (.node [8,8,7,4,3,3,3,3,2,1,1] (.node [8,8,7,4,3,3,2,2,2,1,1,1,1] (.node [8,8,7,4,3,2,2,2,2,2,2,1] (.node [8,8,7,4,3,2,2,2,2,1,1,1,1,1] (.node [8,8,7,4,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,4,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [8,8,7,4,3,3,2,1,1,1,1,1,1,1,1] (.node [8,8,7,4,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,4,3,3,2,2,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,4,3,3,3,2,1,1,1,1,1] (.node [8,8,7,4,3,3,2,2,2,2,2] (.node [8,8,7,4,3,3,2,2,2,2,1,1] .empty .empty) (.node [8,8,7,4,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,4,3,3,3,2,2,2,1] (.node [8,8,7,4,3,3,3,2,2,1,1,1] .empty .empty) (.node [8,8,7,4,3,3,3,3,1,1,1,1] .empty .empty)))) (.node [8,8,7,4,4,2,2,2,2,2,1,1] (.node [8,8,7,4,4,2,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,4,3,3,3,3,3,1] (.node [8,8,7,4,3,3,3,3,2,2] .empty .empty) (.node [8,8,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,4,4,2,2,2,1,1,1,1,1,1] (.node [8,8,7,4,4,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,4,4,2,2,2,2,1,1,1,1] .empty .empty))) (.node [8,8,7,4,4,3,2,2,1,1,1,1,1] (.node [8,8,7,4,4,3,1,1,1,1,1,1,1,1,1] (.node [8,8,7,4,4,2,2,2,2,2,2] .empty .empty) (.node [8,8,7,4,4,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,4,4,3,2,2,2,2,1] (.node [8,8,7,4,4,3,2,2,2,1,1,1] .empty .empty) (.node [8,8,7,4,4,3,3,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_90 : RowTree := (.node [8,8,7,4,3,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_88 degreeTree43_89) - -def degreeTree43_91 : RowTree := (.node [8,8,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_85 degreeTree43_90) - -def degreeTree43_92 : RowTree := (.node [8,8,7,4,4,4,2,2,2,1,1] (.node [8,8,7,4,4,3,3,3,3] (.node [8,8,7,4,4,3,3,3,1,1,1] (.node [8,8,7,4,4,3,3,2,2,2] (.node [8,8,7,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [8,8,7,4,4,3,3,3,2,1] .empty .empty)) (.node [8,8,7,4,4,4,2,1,1,1,1,1,1] (.node [8,8,7,4,4,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,4,4,4,2,2,1,1,1,1] .empty .empty))) (.node [8,8,7,4,4,4,3,2,2,1] (.node [8,8,7,4,4,4,3,1,1,1,1,1] (.node [8,8,7,4,4,4,2,2,2,2] .empty .empty) (.node [8,8,7,4,4,4,3,2,1,1,1] .empty .empty)) (.node [8,8,7,4,4,4,3,3,2] (.node [8,8,7,4,4,4,3,3,1,1] .empty .empty) (.node [8,8,7,4,4,4,4,1,1,1,1] .empty .empty)))) - -def degreeTree43_93 : RowTree := (.node [8,8,7,5,2,2,2,2,1,1,1,1,1,1,1] (.node [8,8,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,4,4,4,4,3,1] (.node [8,8,7,4,4,4,4,2,2] .empty .empty) (.node [8,8,7,4,4,4,4,4] .empty .empty)) (.node [8,8,7,5,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,5,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,5,2,2,2,2,2,2,1,1,1] (.node [8,8,7,5,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,2,2,2,2,2,2,2,1] .empty .empty)) (.node [8,8,7,5,3,2,2,1,1,1,1,1,1,1,1] (.node [8,8,7,5,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,3,2,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_94 : RowTree := (.node [8,8,7,4,4,4,4,2,1,1] degreeTree43_92 degreeTree43_93) - -def degreeTree43_95 : RowTree := (.node [8,8,7,5,4,2,1,1,1,1,1,1,1,1,1] (.node [8,8,7,5,3,3,3,1,1,1,1,1,1] (.node [8,8,7,5,3,3,2,1,1,1,1,1,1,1] (.node [8,8,7,5,3,2,2,2,2,2,2] (.node [8,8,7,5,3,2,2,2,2,2,1,1] .empty .empty) (.node [8,8,7,5,3,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,5,3,3,2,2,2,1,1,1] (.node [8,8,7,5,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,3,3,2,2,2,2,1] .empty .empty))) (.node [8,8,7,5,3,3,3,3,1,1,1] (.node [8,8,7,5,3,3,3,2,2,1,1] (.node [8,8,7,5,3,3,3,2,1,1,1,1] .empty .empty) (.node [8,8,7,5,3,3,3,2,2,2] .empty .empty)) (.node [8,8,7,5,3,3,3,3,3] (.node [8,8,7,5,3,3,3,3,2,1] .empty .empty) (.node [8,8,7,5,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,7,5,4,3,2,2,2,1,1] (.node [8,8,7,5,4,2,2,2,2,2,1] (.node [8,8,7,5,4,2,2,2,1,1,1,1,1] (.node [8,8,7,5,4,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,4,2,2,2,2,1,1,1] .empty .empty)) (.node [8,8,7,5,4,3,2,1,1,1,1,1,1] (.node [8,8,7,5,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,4,3,2,2,1,1,1,1] .empty .empty))) (.node [8,8,7,5,4,3,3,2,2,1] (.node [8,8,7,5,4,3,3,1,1,1,1,1] (.node [8,8,7,5,4,3,2,2,2,2] .empty .empty) (.node [8,8,7,5,4,3,3,2,1,1,1] .empty .empty)) (.node [8,8,7,5,4,3,3,3,2] (.node [8,8,7,5,4,3,3,3,1,1] .empty .empty) (.node [8,8,7,5,4,4,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_96 : RowTree := (.node [8,8,7,5,3,2,2,2,2,1,1,1,1] degreeTree43_94 degreeTree43_95) - -def degreeTree43_97 : RowTree := (.node [8,8,7,5,5,3,1,1,1,1,1,1,1] (.node [8,8,7,5,4,4,4,2,1] (.node [8,8,7,5,4,4,3,2,1,1] (.node [8,8,7,5,4,4,2,2,2,1] (.node [8,8,7,5,4,4,2,2,1,1,1] .empty .empty) (.node [8,8,7,5,4,4,3,1,1,1,1] .empty .empty)) (.node [8,8,7,5,4,4,3,3,1] (.node [8,8,7,5,4,4,3,2,2] .empty .empty) (.node [8,8,7,5,4,4,4,1,1,1] .empty .empty))) (.node [8,8,7,5,5,2,2,1,1,1,1,1,1] (.node [8,8,7,5,5,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,5,4,4,4,3] .empty .empty) (.node [8,8,7,5,5,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,5,5,2,2,2,2,1,1] (.node [8,8,7,5,5,2,2,2,1,1,1,1] .empty .empty) (.node [8,8,7,5,5,2,2,2,2,2] .empty .empty)))) (.node [8,8,7,5,5,4,1,1,1,1,1,1] (.node [8,8,7,5,5,3,3,1,1,1,1] (.node [8,8,7,5,5,3,2,2,1,1,1] (.node [8,8,7,5,5,3,2,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,5,3,2,2,2,1] .empty .empty)) (.node [8,8,7,5,5,3,3,2,2] (.node [8,8,7,5,5,3,3,2,1,1] .empty .empty) (.node [8,8,7,5,5,3,3,3,1] .empty .empty))) (.node [8,8,7,5,5,4,3,1,1,1] (.node [8,8,7,5,5,4,2,2,1,1] (.node [8,8,7,5,5,4,2,1,1,1,1] .empty .empty) (.node [8,8,7,5,5,4,2,2,2] .empty .empty)) (.node [8,8,7,5,5,4,3,3] (.node [8,8,7,5,5,4,3,2,1] .empty .empty) (.node [8,8,7,5,5,4,4,1,1] .empty .empty))))) - -def degreeTree43_98 : RowTree := (.node [8,8,7,6,3,2,2,1,1,1,1,1,1,1] (.node [8,8,7,6,2,2,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,5,5,5,3,1,1] (.node [8,8,7,5,5,5,2,1,1,1] (.node [8,8,7,5,5,5,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,5,5,2,2,1] .empty .empty)) (.node [8,8,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,5,5,5,3,2] .empty .empty) (.node [8,8,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,6,2,2,2,2,2,2,1,1] (.node [8,8,7,6,2,2,2,2,1,1,1,1,1,1] (.node [8,8,7,6,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [8,8,7,6,3,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,6,2,2,2,2,2,2,2] .empty .empty) (.node [8,8,7,6,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,7,6,3,3,2,2,2,2] (.node [8,8,7,6,3,3,1,1,1,1,1,1,1,1] (.node [8,8,7,6,3,2,2,2,2,1,1,1] (.node [8,8,7,6,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,3,2,2,2,2,2,1] .empty .empty)) (.node [8,8,7,6,3,3,2,2,1,1,1,1] (.node [8,8,7,6,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,3,3,2,2,2,1,1] .empty .empty))) (.node [8,8,7,6,3,3,3,3,1,1] (.node [8,8,7,6,3,3,3,2,1,1,1] (.node [8,8,7,6,3,3,3,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,3,3,3,2,2,1] .empty .empty)) (.node [8,8,7,6,4,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,6,3,3,3,3,2] .empty .empty) (.node [8,8,7,6,4,2,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_99 : RowTree := (.node [8,8,7,5,5,4,4,2] degreeTree43_97 degreeTree43_98) - -def degreeTree43_100 : RowTree := (.node [8,8,7,5,4,4,2,1,1,1,1,1] degreeTree43_96 degreeTree43_99) - -def degreeTree43_101 : RowTree := (.node [8,8,7,4,4,3,3,2,1,1,1,1] degreeTree43_91 degreeTree43_100) - -def degreeTree43_102 : RowTree := (.node [8,8,7,6,4,3,3,2,1,1] (.node [8,8,7,6,4,3,2,1,1,1,1,1] (.node [8,8,7,6,4,2,2,2,2,2] (.node [8,8,7,6,4,2,2,2,2,1,1] (.node [8,8,7,6,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [8,8,7,6,4,3,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,6,4,3,2,2,2,1] (.node [8,8,7,6,4,3,2,2,1,1,1] .empty .empty) (.node [8,8,7,6,4,3,3,1,1,1,1] .empty .empty))) (.node [8,8,7,6,4,4,2,1,1,1,1] (.node [8,8,7,6,4,3,3,3,1] (.node [8,8,7,6,4,3,3,2,2] .empty .empty) (.node [8,8,7,6,4,4,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,6,4,4,2,2,2] (.node [8,8,7,6,4,4,2,2,1,1] .empty .empty) (.node [8,8,7,6,4,4,3,1,1,1] .empty .empty)))) - -def degreeTree43_103 : RowTree := (.node [8,8,7,6,5,2,2,2,2,1] (.node [8,8,7,6,5,1,1,1,1,1,1,1,1,1] (.node [8,8,7,6,4,4,4,1,1] (.node [8,8,7,6,4,4,3,3] .empty .empty) (.node [8,8,7,6,4,4,4,2] .empty .empty)) (.node [8,8,7,6,5,2,2,1,1,1,1,1] (.node [8,8,7,6,5,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,5,2,2,2,1,1,1] .empty .empty))) (.node [8,8,7,6,5,3,2,2,2] (.node [8,8,7,6,5,3,2,1,1,1,1] (.node [8,8,7,6,5,3,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,5,3,2,2,1,1] .empty .empty)) (.node [8,8,7,6,5,3,3,2,1] (.node [8,8,7,6,5,3,3,1,1,1] .empty .empty) (.node [8,8,7,6,5,3,3,3] .empty .empty)))) - -def degreeTree43_104 : RowTree := (.node [8,8,7,6,4,4,3,2,1] degreeTree43_102 degreeTree43_103) - -def degreeTree43_105 : RowTree := (.node [8,8,7,6,6,4,1,1,1,1] (.node [8,8,7,6,6,2,1,1,1,1,1,1] (.node [8,8,7,6,5,4,3,2] (.node [8,8,7,6,5,4,2,2,1] (.node [8,8,7,6,5,4,2,1,1,1] .empty .empty) (.node [8,8,7,6,5,4,3,1,1] .empty .empty)) (.node [8,8,7,6,5,5,2,1,1] (.node [8,8,7,6,5,5,1,1,1,1] .empty .empty) (.node [8,8,7,6,6,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,6,6,3,1,1,1,1,1] (.node [8,8,7,6,6,2,2,2,1,1] (.node [8,8,7,6,6,2,2,1,1,1,1] .empty .empty) (.node [8,8,7,6,6,2,2,2,2] .empty .empty)) (.node [8,8,7,6,6,3,2,2,1] (.node [8,8,7,6,6,3,2,1,1,1] .empty .empty) (.node [8,8,7,6,6,3,3,1,1] .empty .empty)))) (.node [8,8,7,7,2,2,2,2,2,1,1,1] (.node [8,8,7,7,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,6,6,5,1,1,1] (.node [8,8,7,6,6,4,2,1,1] .empty .empty) (.node [8,8,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,7,2,2,2,1,1,1,1,1,1,1] (.node [8,8,7,7,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [8,8,7,7,3,2,2,1,1,1,1,1,1] (.node [8,8,7,7,3,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,7,2,2,2,2,2,2,1] .empty .empty) (.node [8,8,7,7,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,7,3,2,2,2,2,1,1] (.node [8,8,7,7,3,2,2,2,1,1,1,1] .empty .empty) (.node [8,8,7,7,3,2,2,2,2,2] .empty .empty))))) - -def degreeTree43_106 : RowTree := (.node [8,8,7,6,5,4,1,1,1,1,1] degreeTree43_104 degreeTree43_105) - -def degreeTree43_107 : RowTree := (.node [8,8,7,7,4,3,2,2,2] (.node [8,8,7,7,4,1,1,1,1,1,1,1,1,1] (.node [8,8,7,7,3,3,3,1,1,1,1] (.node [8,8,7,7,3,3,2,2,1,1,1] (.node [8,8,7,7,3,3,2,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,3,3,2,2,2,1] .empty .empty)) (.node [8,8,7,7,3,3,3,2,2] (.node [8,8,7,7,3,3,3,2,1,1] .empty .empty) (.node [8,8,7,7,3,3,3,3,1] .empty .empty))) (.node [8,8,7,7,4,2,2,2,2,1] (.node [8,8,7,7,4,2,2,1,1,1,1,1] (.node [8,8,7,7,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,4,2,2,2,1,1,1] .empty .empty)) (.node [8,8,7,7,4,3,2,1,1,1,1] (.node [8,8,7,7,4,3,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,4,3,2,2,1,1] .empty .empty)))) (.node [8,8,7,7,5,1,1,1,1,1,1,1,1] (.node [8,8,7,7,4,4,1,1,1,1,1] (.node [8,8,7,7,4,3,3,2,1] (.node [8,8,7,7,4,3,3,1,1,1] .empty .empty) (.node [8,8,7,7,4,3,3,3] .empty .empty)) (.node [8,8,7,7,4,4,2,2,1] (.node [8,8,7,7,4,4,2,1,1,1] .empty .empty) (.node [8,8,7,7,4,4,3,1,1] .empty .empty))) (.node [8,8,7,7,5,2,2,2,2] (.node [8,8,7,7,5,2,2,1,1,1,1] (.node [8,8,7,7,5,2,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,5,2,2,2,1,1] .empty .empty)) (.node [8,8,7,7,5,3,2,1,1,1] (.node [8,8,7,7,5,3,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,5,3,2,2,1] .empty .empty))))) - -def degreeTree43_108 : RowTree := (.node [8,8,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,7,6,3,1,1,1,1] (.node [8,8,7,7,6,1,1,1,1,1,1,1] (.node [8,8,7,7,5,4,2,1,1] (.node [8,8,7,7,5,4,1,1,1,1] .empty .empty) (.node [8,8,7,7,5,5,1,1,1] .empty .empty)) (.node [8,8,7,7,6,2,2,1,1,1] (.node [8,8,7,7,6,2,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,6,2,2,2,1] .empty .empty))) (.node [8,8,7,7,7,2,1,1,1,1] (.node [8,8,7,7,6,4,1,1,1] (.node [8,8,7,7,6,3,2,1,1] .empty .empty) (.node [8,8,7,7,7,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,7,7,3,1,1,1] (.node [8,8,7,7,7,2,2,1,1] .empty .empty) (.node [8,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,8,2,2,2,2,2,2,2,2,2,1] (.node [8,8,8,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [8,8,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,2,2,2,2,2,2,2,1,1,1,1,1] (.node [8,8,8,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,2,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [8,8,8,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,3,2,2,2,2,2,1,1,1,1,1,1] (.node [8,8,8,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,3,2,2,2,2,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_109 : RowTree := (.node [8,8,7,7,5,3,3,1,1] degreeTree43_107 degreeTree43_108) - -def degreeTree43_110 : RowTree := (.node [8,8,7,7,3,3,1,1,1,1,1,1,1] degreeTree43_106 degreeTree43_109) - -def degreeTree43_111 : RowTree := (.node [8,8,8,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,3,2,2,2,1,1,1,1,1,1,1] (.node [8,8,8,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [8,8,8,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,3,3,2,2,2,2,2,1,1,1] (.node [8,8,8,3,3,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [8,8,8,3,3,2,2,2,2,2,2,1] .empty .empty))) (.node [8,8,8,3,3,3,2,2,2,2,1,1] (.node [8,8,8,3,3,3,2,2,1,1,1,1,1,1] (.node [8,8,8,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,3,3,3,2,2,2,1,1,1,1] .empty .empty)) (.node [8,8,8,3,3,3,3,1,1,1,1,1,1,1] (.node [8,8,8,3,3,3,2,2,2,2,2] .empty .empty) (.node [8,8,8,3,3,3,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_112 : RowTree := (.node [8,8,8,4,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,3,3,3,3,2,2] (.node [8,8,8,3,3,3,3,3,1,1,1,1] (.node [8,8,8,3,3,3,3,2,2,2,1] .empty .empty) (.node [8,8,8,3,3,3,3,3,2,1,1] .empty .empty)) (.node [8,8,8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,3,3,3,3,3,1] .empty .empty) (.node [8,8,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,8,4,2,2,2,2,2,2,1,1,1] (.node [8,8,8,4,2,2,2,2,1,1,1,1,1,1,1] (.node [8,8,8,4,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,4,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [8,8,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,4,2,2,2,2,2,2,2,1] .empty .empty) (.node [8,8,8,4,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_113 : RowTree := (.node [8,8,8,3,3,3,3,2,2,1,1,1] degreeTree43_111 degreeTree43_112) - -def degreeTree43_114 : RowTree := (.node [8,8,8,4,3,3,3,3,3] (.node [8,8,8,4,3,3,2,2,2,1,1,1] (.node [8,8,8,4,3,2,2,2,2,2,2] (.node [8,8,8,4,3,2,2,2,2,1,1,1,1] (.node [8,8,8,4,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,4,3,2,2,2,2,2,1,1] .empty .empty)) (.node [8,8,8,4,3,3,2,1,1,1,1,1,1,1] (.node [8,8,8,4,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,4,3,3,2,2,1,1,1,1,1] .empty .empty))) (.node [8,8,8,4,3,3,3,2,2,1,1] (.node [8,8,8,4,3,3,3,1,1,1,1,1,1] (.node [8,8,8,4,3,3,2,2,2,2,1] .empty .empty) (.node [8,8,8,4,3,3,3,2,1,1,1,1] .empty .empty)) (.node [8,8,8,4,3,3,3,3,1,1,1] (.node [8,8,8,4,3,3,3,2,2,2] .empty .empty) (.node [8,8,8,4,3,3,3,3,2,1] .empty .empty)))) (.node [8,8,8,4,4,3,2,1,1,1,1,1,1] (.node [8,8,8,4,4,2,2,2,1,1,1,1,1] (.node [8,8,8,4,4,2,1,1,1,1,1,1,1,1,1] (.node [8,8,8,4,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,4,4,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,4,4,2,2,2,2,2,1] (.node [8,8,8,4,4,2,2,2,2,1,1,1] .empty .empty) (.node [8,8,8,4,4,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,8,4,4,3,3,1,1,1,1,1] (.node [8,8,8,4,4,3,2,2,2,1,1] (.node [8,8,8,4,4,3,2,2,1,1,1,1] .empty .empty) (.node [8,8,8,4,4,3,2,2,2,2] .empty .empty)) (.node [8,8,8,4,4,3,3,2,2,1] (.node [8,8,8,4,4,3,3,2,1,1,1] .empty .empty) (.node [8,8,8,4,4,3,3,3,1,1] .empty .empty))))) - -def degreeTree43_115 : RowTree := (.node [8,8,8,4,3,2,2,1,1,1,1,1,1,1,1] degreeTree43_113 degreeTree43_114) - -def degreeTree43_116 : RowTree := (.node [8,8,8,5,2,2,2,2,1,1,1,1,1,1] (.node [8,8,8,4,4,4,3,3,1] (.node [8,8,8,4,4,4,2,2,2,1] (.node [8,8,8,4,4,4,2,1,1,1,1,1] (.node [8,8,8,4,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,4,4,4,2,2,1,1,1] .empty .empty)) (.node [8,8,8,4,4,4,3,2,1,1] (.node [8,8,8,4,4,4,3,1,1,1,1] .empty .empty) (.node [8,8,8,4,4,4,3,2,2] .empty .empty))) (.node [8,8,8,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,4,4,4,4,2,1] (.node [8,8,8,4,4,4,4,1,1,1] .empty .empty) (.node [8,8,8,4,4,4,4,3] .empty .empty)) (.node [8,8,8,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,8,5,3,2,2,2,2,1,1,1] (.node [8,8,8,5,3,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,5,2,2,2,2,2,2,1,1] (.node [8,8,8,5,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [8,8,8,5,2,2,2,2,2,2,2] .empty .empty)) (.node [8,8,8,5,3,2,2,1,1,1,1,1,1,1] (.node [8,8,8,5,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,5,3,2,2,2,1,1,1,1,1] .empty .empty))) (.node [8,8,8,5,3,3,2,2,1,1,1,1] (.node [8,8,8,5,3,3,1,1,1,1,1,1,1,1] (.node [8,8,8,5,3,2,2,2,2,2,1] .empty .empty) (.node [8,8,8,5,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,5,3,3,2,2,2,2] (.node [8,8,8,5,3,3,2,2,2,1,1] .empty .empty) (.node [8,8,8,5,3,3,3,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_117 : RowTree := (.node [8,8,8,5,4,3,3,2,2] (.node [8,8,8,5,4,2,2,2,2,1,1] (.node [8,8,8,5,4,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,5,3,3,3,3,1,1] (.node [8,8,8,5,3,3,3,2,2,1] .empty .empty) (.node [8,8,8,5,3,3,3,3,2] .empty .empty)) (.node [8,8,8,5,4,2,2,1,1,1,1,1,1] (.node [8,8,8,5,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,5,4,2,2,2,1,1,1,1] .empty .empty))) (.node [8,8,8,5,4,3,2,2,1,1,1] (.node [8,8,8,5,4,3,1,1,1,1,1,1,1] (.node [8,8,8,5,4,2,2,2,2,2] .empty .empty) (.node [8,8,8,5,4,3,2,1,1,1,1,1] .empty .empty)) (.node [8,8,8,5,4,3,3,1,1,1,1] (.node [8,8,8,5,4,3,2,2,2,1] .empty .empty) (.node [8,8,8,5,4,3,3,2,1,1] .empty .empty)))) (.node [8,8,8,5,4,4,3,3] (.node [8,8,8,5,4,4,2,2,1,1] (.node [8,8,8,5,4,4,1,1,1,1,1,1] (.node [8,8,8,5,4,3,3,3,1] .empty .empty) (.node [8,8,8,5,4,4,2,1,1,1,1] .empty .empty)) (.node [8,8,8,5,4,4,3,1,1,1] (.node [8,8,8,5,4,4,2,2,2] .empty .empty) (.node [8,8,8,5,4,4,3,2,1] .empty .empty))) (.node [8,8,8,5,5,2,2,1,1,1,1,1] (.node [8,8,8,5,5,1,1,1,1,1,1,1,1,1] (.node [8,8,8,5,4,4,4,1,1] .empty .empty) (.node [8,8,8,5,5,2,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,5,5,2,2,2,2,1] (.node [8,8,8,5,5,2,2,2,1,1,1] .empty .empty) (.node [8,8,8,5,5,3,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_118 : RowTree := (.node [8,8,8,5,3,3,3,2,1,1,1] degreeTree43_116 degreeTree43_117) - -def degreeTree43_119 : RowTree := (.node [8,8,8,4,4,3,3,3,2] degreeTree43_115 degreeTree43_118) - -def degreeTree43_120 : RowTree := (.node [8,8,8,3,2,2,2,2,2,2,2,1,1] degreeTree43_110 degreeTree43_119) - -def degreeTree43_121 : RowTree := (.node [8,8,7,6,4,2,2,1,1,1,1,1,1] degreeTree43_101 degreeTree43_120) - -def degreeTree43_122 : RowTree := (.node [8,8,8,5,5,4,3,1,1] (.node [8,8,8,5,5,3,3,3] (.node [8,8,8,5,5,3,3,1,1,1] (.node [8,8,8,5,5,3,2,2,2] (.node [8,8,8,5,5,3,2,2,1,1] .empty .empty) .empty) (.node [8,8,8,5,5,3,3,2,1] .empty .empty)) (.node [8,8,8,5,5,4,2,1,1,1] (.node [8,8,8,5,5,4,1,1,1,1,1] .empty .empty) (.node [8,8,8,5,5,4,2,2,1] .empty .empty))) (.node [8,8,8,6,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,5,5,5,2,1,1] (.node [8,8,8,5,5,5,1,1,1,1] .empty .empty) (.node [8,8,8,6,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,6,2,2,2,1,1,1,1,1,1,1] (.node [8,8,8,6,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,6,2,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_123 : RowTree := (.node [8,8,8,6,3,3,1,1,1,1,1,1,1] (.node [8,8,8,6,3,2,2,1,1,1,1,1,1] (.node [8,8,8,6,3,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,6,2,2,2,2,2,2,1] .empty .empty) (.node [8,8,8,6,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,6,3,2,2,2,2,1,1] (.node [8,8,8,6,3,2,2,2,1,1,1,1] .empty .empty) (.node [8,8,8,6,3,2,2,2,2,2] .empty .empty))) (.node [8,8,8,6,3,3,3,1,1,1,1] (.node [8,8,8,6,3,3,2,2,1,1,1] (.node [8,8,8,6,3,3,2,1,1,1,1,1] .empty .empty) (.node [8,8,8,6,3,3,2,2,2,1] .empty .empty)) (.node [8,8,8,6,3,3,3,2,2] (.node [8,8,8,6,3,3,3,2,1,1] .empty .empty) (.node [8,8,8,6,3,3,3,3,1] .empty .empty)))) - -def degreeTree43_124 : RowTree := (.node [8,8,8,6,2,2,2,2,2,1,1,1] degreeTree43_122 degreeTree43_123) - -def degreeTree43_125 : RowTree := (.node [8,8,8,6,5,2,1,1,1,1,1,1] (.node [8,8,8,6,4,3,2,2,2] (.node [8,8,8,6,4,2,2,2,2,1] (.node [8,8,8,6,4,2,2,1,1,1,1,1] (.node [8,8,8,6,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,6,4,2,2,2,1,1,1] .empty .empty)) (.node [8,8,8,6,4,3,2,1,1,1,1] (.node [8,8,8,6,4,3,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,6,4,3,2,2,1,1] .empty .empty))) (.node [8,8,8,6,4,4,2,1,1,1] (.node [8,8,8,6,4,3,3,2,1] (.node [8,8,8,6,4,3,3,1,1,1] .empty .empty) (.node [8,8,8,6,4,4,1,1,1,1,1] .empty .empty)) (.node [8,8,8,6,4,4,3,1,1] (.node [8,8,8,6,4,4,2,2,1] .empty .empty) (.node [8,8,8,6,5,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,8,6,5,4,1,1,1,1] (.node [8,8,8,6,5,3,1,1,1,1,1] (.node [8,8,8,6,5,2,2,2,1,1] (.node [8,8,8,6,5,2,2,1,1,1,1] .empty .empty) (.node [8,8,8,6,5,2,2,2,2] .empty .empty)) (.node [8,8,8,6,5,3,2,2,1] (.node [8,8,8,6,5,3,2,1,1,1] .empty .empty) (.node [8,8,8,6,5,3,3,1,1] .empty .empty))) (.node [8,8,8,6,6,2,1,1,1,1,1] (.node [8,8,8,6,5,5,1,1,1] (.node [8,8,8,6,5,4,2,1,1] .empty .empty) (.node [8,8,8,6,6,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,6,6,2,2,2,1] (.node [8,8,8,6,6,2,2,1,1,1] .empty .empty) (.node [8,8,8,6,6,3,1,1,1,1] .empty .empty))))) - -def degreeTree43_126 : RowTree := (.node [8,8,8,6,4,1,1,1,1,1,1,1,1,1] degreeTree43_124 degreeTree43_125) - -def degreeTree43_127 : RowTree := (.node [8,8,8,7,3,3,2,2,1,1] (.node [8,8,8,7,2,2,2,2,2,2] (.node [8,8,8,7,2,2,1,1,1,1,1,1,1,1] (.node [8,8,8,7,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,6,6,4,1,1,1] .empty .empty) (.node [8,8,8,7,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,7,2,2,2,2,1,1,1,1] (.node [8,8,8,7,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,7,2,2,2,2,2,1,1] .empty .empty))) (.node [8,8,8,7,3,2,2,2,1,1,1] (.node [8,8,8,7,3,2,1,1,1,1,1,1,1] (.node [8,8,8,7,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,7,3,2,2,1,1,1,1,1] .empty .empty)) (.node [8,8,8,7,3,3,1,1,1,1,1,1] (.node [8,8,8,7,3,2,2,2,2,1] .empty .empty) (.node [8,8,8,7,3,3,2,1,1,1,1] .empty .empty)))) (.node [8,8,8,7,4,2,2,2,2] (.node [8,8,8,7,4,1,1,1,1,1,1,1,1] (.node [8,8,8,7,3,3,3,1,1,1] (.node [8,8,8,7,3,3,2,2,2] .empty .empty) (.node [8,8,8,7,3,3,3,2,1] .empty .empty)) (.node [8,8,8,7,4,2,2,1,1,1,1] (.node [8,8,8,7,4,2,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,7,4,2,2,2,1,1] .empty .empty))) (.node [8,8,8,7,4,3,3,1,1] (.node [8,8,8,7,4,3,2,1,1,1] (.node [8,8,8,7,4,3,1,1,1,1,1] .empty .empty) (.node [8,8,8,7,4,3,2,2,1] .empty .empty)) (.node [8,8,8,7,4,4,2,1,1] (.node [8,8,8,7,4,4,1,1,1,1] .empty .empty) (.node [8,8,8,7,5,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_128 : RowTree := (.node [8,8,8,8,2,2,2,2,1,1,1] (.node [8,8,8,7,6,2,2,1,1] (.node [8,8,8,7,5,3,2,1,1] (.node [8,8,8,7,5,2,2,2,1] (.node [8,8,8,7,5,2,2,1,1,1] .empty .empty) (.node [8,8,8,7,5,3,1,1,1,1] .empty .empty)) (.node [8,8,8,7,6,1,1,1,1,1,1] (.node [8,8,8,7,5,4,1,1,1] .empty .empty) (.node [8,8,8,7,6,2,1,1,1,1] .empty .empty))) (.node [8,8,8,8,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,7,7,1,1,1,1,1] (.node [8,8,8,7,6,3,1,1,1] .empty .empty) (.node [8,8,8,7,7,2,1,1,1] .empty .empty)) (.node [8,8,8,8,2,2,1,1,1,1,1,1,1] (.node [8,8,8,8,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,8,2,2,2,1,1,1,1,1] .empty .empty)))) (.node [8,8,8,8,3,3,2,1,1,1] (.node [8,8,8,8,3,2,2,1,1,1,1] (.node [8,8,8,8,3,1,1,1,1,1,1,1,1] (.node [8,8,8,8,2,2,2,2,2,1] .empty .empty) (.node [8,8,8,8,3,2,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,8,3,2,2,2,2] (.node [8,8,8,8,3,2,2,2,1,1] .empty .empty) (.node [8,8,8,8,3,3,1,1,1,1,1] .empty .empty))) (.node [8,8,8,8,4,2,1,1,1,1,1] (.node [8,8,8,8,3,3,3,1,1] (.node [8,8,8,8,3,3,2,2,1] .empty .empty) (.node [8,8,8,8,4,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,8,4,2,2,2,1] (.node [8,8,8,8,4,2,2,1,1,1] .empty .empty) (.node [8,8,8,8,4,3,1,1,1,1] .empty .empty))))) - -def degreeTree43_129 : RowTree := (.node [8,8,8,7,5,2,1,1,1,1,1] degreeTree43_127 degreeTree43_128) - -def degreeTree43_130 : RowTree := (.node [8,8,8,6,6,3,2,1,1] degreeTree43_126 degreeTree43_129) - -def degreeTree43_131 : RowTree := (.node [9,4,4,4,4,3,3,3,3,3,3] (.node [8,8,8,8,5,3,1,1,1] (.node [8,8,8,8,5,2,1,1,1,1] (.node [8,8,8,8,5,1,1,1,1,1,1] (.node [8,8,8,8,4,4,1,1,1] .empty .empty) .empty) (.node [8,8,8,8,5,2,2,1,1] .empty .empty)) (.node [8,8,8,8,6,2,1,1,1] (.node [8,8,8,8,6,1,1,1,1,1] .empty .empty) (.node [8,8,8,8,7,1,1,1,1] .empty .empty))) (.node [9,4,4,4,4,4,4,4,2,2,2] (.node [9,4,4,4,4,4,4,3,3,2,2] (.node [9,4,4,4,4,4,3,3,3,3,2] .empty .empty) (.node [9,4,4,4,4,4,4,3,3,3,1] .empty .empty)) (.node [9,4,4,4,4,4,4,4,3,3] (.node [9,4,4,4,4,4,4,4,3,2,1] .empty .empty) (.node [9,4,4,4,4,4,4,4,4,1,1] .empty .empty)))) - -def degreeTree43_132 : RowTree := (.node [9,5,4,4,4,4,4,4,2,2,1] (.node [9,5,4,4,4,4,3,3,3,3,1] (.node [9,5,4,4,4,3,3,3,3,3,2] (.node [9,5,4,4,3,3,3,3,3,3,3] .empty .empty) (.node [9,5,4,4,4,4,3,3,3,2,2] .empty .empty)) (.node [9,5,4,4,4,4,4,3,3,2,1] (.node [9,5,4,4,4,4,4,3,2,2,2] .empty .empty) (.node [9,5,4,4,4,4,4,3,3,3] .empty .empty))) (.node [9,5,5,3,3,3,3,3,3,3,3] (.node [9,5,4,4,4,4,4,4,3,2] (.node [9,5,4,4,4,4,4,4,3,1,1] .empty .empty) (.node [9,5,4,4,4,4,4,4,4,1] .empty .empty)) (.node [9,5,5,4,4,3,3,3,3,2,2] (.node [9,5,5,4,3,3,3,3,3,3,2] .empty .empty) (.node [9,5,5,4,4,3,3,3,3,3,1] .empty .empty)))) - -def degreeTree43_133 : RowTree := (.node [9,4,4,4,4,4,4,4,4,2] degreeTree43_131 degreeTree43_132) - -def degreeTree43_134 : RowTree := (.node [9,5,5,5,4,4,3,2,2,2,2] (.node [9,5,5,4,4,4,4,4,2,2] (.node [9,5,5,4,4,4,4,3,2,2,1] (.node [9,5,5,4,4,4,3,3,3,3] (.node [9,5,5,4,4,4,3,3,3,2,1] .empty .empty) (.node [9,5,5,4,4,4,4,2,2,2,2] .empty .empty)) (.node [9,5,5,4,4,4,4,3,3,2] (.node [9,5,5,4,4,4,4,3,3,1,1] .empty .empty) (.node [9,5,5,4,4,4,4,4,2,1,1] .empty .empty))) (.node [9,5,5,5,3,3,3,3,3,3,1] (.node [9,5,5,4,4,4,4,4,4] (.node [9,5,5,4,4,4,4,4,3,1] .empty .empty) (.node [9,5,5,5,3,3,3,3,3,2,2] .empty .empty)) (.node [9,5,5,5,4,3,3,3,3,2,1] (.node [9,5,5,5,4,3,3,3,2,2,2] .empty .empty) (.node [9,5,5,5,4,3,3,3,3,3] .empty .empty)))) (.node [9,5,5,5,4,4,4,4,1,1,1] (.node [9,5,5,5,4,4,4,2,2,2,1] (.node [9,5,5,5,4,4,3,3,3,1,1] (.node [9,5,5,5,4,4,3,3,2,2,1] .empty .empty) (.node [9,5,5,5,4,4,3,3,3,2] .empty .empty)) (.node [9,5,5,5,4,4,4,3,2,2] (.node [9,5,5,5,4,4,4,3,2,1,1] .empty .empty) (.node [9,5,5,5,4,4,4,3,3,1] .empty .empty))) (.node [9,5,5,5,5,3,3,3,2,2,1] (.node [9,5,5,5,4,4,4,4,3] (.node [9,5,5,5,4,4,4,4,2,1] .empty .empty) (.node [9,5,5,5,5,3,3,2,2,2,2] .empty .empty)) (.node [9,5,5,5,5,3,3,3,3,2] (.node [9,5,5,5,5,3,3,3,3,1,1] .empty .empty) (.node [9,5,5,5,5,4,2,2,2,2,2] .empty .empty))))) - -def degreeTree43_135 : RowTree := (.node [9,5,5,4,4,4,3,3,2,2,2] degreeTree43_133 degreeTree43_134) - -def degreeTree43_136 : RowTree := (.node [9,5,5,5,5,5,3,3,3] (.node [9,5,5,5,5,4,4,3,3] (.node [9,5,5,5,5,4,4,2,2,1,1] (.node [9,5,5,5,5,4,3,3,2,2] (.node [9,5,5,5,5,4,3,3,2,1,1] .empty .empty) (.node [9,5,5,5,5,4,3,3,3,1] .empty .empty)) (.node [9,5,5,5,5,4,4,3,1,1,1] (.node [9,5,5,5,5,4,4,2,2,2] .empty .empty) (.node [9,5,5,5,5,4,4,3,2,1] .empty .empty))) (.node [9,5,5,5,5,5,3,2,2,1,1] (.node [9,5,5,5,5,4,4,4,2] (.node [9,5,5,5,5,4,4,4,1,1] .empty .empty) (.node [9,5,5,5,5,5,2,2,2,2,1] .empty .empty)) (.node [9,5,5,5,5,5,3,3,1,1,1] (.node [9,5,5,5,5,5,3,2,2,2] .empty .empty) (.node [9,5,5,5,5,5,3,3,2,1] .empty .empty)))) (.node [9,5,5,5,5,5,5,2,2] (.node [9,5,5,5,5,5,4,3,2] (.node [9,5,5,5,5,5,4,2,2,1] (.node [9,5,5,5,5,5,4,2,1,1,1] .empty .empty) (.node [9,5,5,5,5,5,4,3,1,1] .empty .empty)) (.node [9,5,5,5,5,5,5,1,1,1,1] (.node [9,5,5,5,5,5,4,4,1] .empty .empty) (.node [9,5,5,5,5,5,5,2,1,1] .empty .empty))) (.node [9,6,4,4,4,3,3,3,3,2,2] (.node [9,6,4,3,3,3,3,3,3,3,3] (.node [9,5,5,5,5,5,5,3,1] .empty .empty) (.node [9,6,4,4,3,3,3,3,3,3,2] .empty .empty)) (.node [9,6,4,4,4,4,3,3,2,2,2] (.node [9,6,4,4,4,3,3,3,3,3,1] .empty .empty) (.node [9,6,4,4,4,4,3,3,3,2,1] .empty .empty))))) - -def degreeTree43_137 : RowTree := (.node [9,6,5,4,4,4,3,3,2,2,1] (.node [9,6,4,4,4,4,4,4,4] (.node [9,6,4,4,4,4,4,3,3,2] (.node [9,6,4,4,4,4,4,3,2,2,1] (.node [9,6,4,4,4,4,4,2,2,2,2] .empty .empty) (.node [9,6,4,4,4,4,4,3,3,1,1] .empty .empty)) (.node [9,6,4,4,4,4,4,4,2,2] (.node [9,6,4,4,4,4,4,4,2,1,1] .empty .empty) (.node [9,6,4,4,4,4,4,4,3,1] .empty .empty))) (.node [9,6,5,4,4,3,3,3,2,2,2] (.node [9,6,5,4,3,3,3,3,3,2,2] (.node [9,6,5,3,3,3,3,3,3,3,2] .empty .empty) (.node [9,6,5,4,3,3,3,3,3,3,1] .empty .empty)) (.node [9,6,5,4,4,3,3,3,3,3] (.node [9,6,5,4,4,3,3,3,3,2,1] .empty .empty) (.node [9,6,5,4,4,4,3,2,2,2,2] .empty .empty)))) (.node [9,6,5,4,4,4,4,4,2,1] (.node [9,6,5,4,4,4,4,3,2,1,1] (.node [9,6,5,4,4,4,3,3,3,2] (.node [9,6,5,4,4,4,3,3,3,1,1] .empty .empty) (.node [9,6,5,4,4,4,4,2,2,2,1] .empty .empty)) (.node [9,6,5,4,4,4,4,3,3,1] (.node [9,6,5,4,4,4,4,3,2,2] .empty .empty) (.node [9,6,5,4,4,4,4,4,1,1,1] .empty .empty))) (.node [9,6,5,5,3,3,3,3,3,3] (.node [9,6,5,5,3,3,3,3,2,2,2] (.node [9,6,5,4,4,4,4,4,3] .empty .empty) (.node [9,6,5,5,3,3,3,3,3,2,1] .empty .empty)) (.node [9,6,5,5,4,3,3,3,2,2,1] (.node [9,6,5,5,4,3,3,2,2,2,2] .empty .empty) (.node [9,6,5,5,4,3,3,3,3,1,1] .empty .empty))))) - -def degreeTree43_138 : RowTree := (.node [9,6,4,4,4,4,3,3,3,3] degreeTree43_136 degreeTree43_137) - -def degreeTree43_139 : RowTree := (.node [9,5,5,5,5,4,3,2,2,2,1] degreeTree43_135 degreeTree43_138) - -def degreeTree43_140 : RowTree := (.node [8,8,8,8,4,3,2,1,1] degreeTree43_130 degreeTree43_139) - -def degreeTree43_141 : RowTree := (.node [9,6,5,5,4,4,4,3,2,1] (.node [9,6,5,5,4,4,3,3,3,1] (.node [9,6,5,5,4,4,3,3,2,1,1] (.node [9,6,5,5,4,4,3,2,2,2,1] (.node [9,6,5,5,4,4,2,2,2,2,2] .empty .empty) .empty) (.node [9,6,5,5,4,4,3,3,2,2] .empty .empty)) (.node [9,6,5,5,4,4,4,2,2,2] (.node [9,6,5,5,4,4,4,2,2,1,1] .empty .empty) (.node [9,6,5,5,4,4,4,3,1,1,1] .empty .empty))) (.node [9,6,5,5,5,3,2,2,2,2,2] (.node [9,6,5,5,4,4,4,4,1,1] (.node [9,6,5,5,4,4,4,3,3] .empty .empty) (.node [9,6,5,5,4,4,4,4,2] .empty .empty)) (.node [9,6,5,5,5,3,3,3,2,1,1] (.node [9,6,5,5,5,3,3,2,2,2,1] .empty .empty) (.node [9,6,5,5,5,3,3,3,2,2] .empty .empty)))) - -def degreeTree43_142 : RowTree := (.node [9,6,5,5,5,4,4,2,2,1] (.node [9,6,5,5,5,4,3,3,1,1,1] (.node [9,6,5,5,5,4,3,2,2,1,1] (.node [9,6,5,5,5,4,2,2,2,2,1] .empty .empty) (.node [9,6,5,5,5,4,3,2,2,2] .empty .empty)) (.node [9,6,5,5,5,4,3,3,3] (.node [9,6,5,5,5,4,3,3,2,1] .empty .empty) (.node [9,6,5,5,5,4,4,2,1,1,1] .empty .empty))) (.node [9,6,5,5,5,5,2,2,2,1,1] (.node [9,6,5,5,5,4,4,3,2] (.node [9,6,5,5,5,4,4,3,1,1] .empty .empty) (.node [9,6,5,5,5,4,4,4,1] .empty .empty)) (.node [9,6,5,5,5,5,3,2,1,1,1] (.node [9,6,5,5,5,5,2,2,2,2] .empty .empty) (.node [9,6,5,5,5,5,3,2,2,1] .empty .empty)))) - -def degreeTree43_143 : RowTree := (.node [9,6,5,5,5,3,3,3,3,1] degreeTree43_141 degreeTree43_142) - -def degreeTree43_144 : RowTree := (.node [9,6,6,4,4,3,3,3,3,2] (.node [9,6,6,3,3,3,3,3,3,2,2] (.node [9,6,5,5,5,5,4,2,2] (.node [9,6,5,5,5,5,4,1,1,1,1] (.node [9,6,5,5,5,5,3,3,2] .empty .empty) (.node [9,6,5,5,5,5,4,2,1,1] .empty .empty)) (.node [9,6,5,5,5,5,5,1,1,1] (.node [9,6,5,5,5,5,4,3,1] .empty .empty) (.node [9,6,5,5,5,5,5,2,1] .empty .empty))) (.node [9,6,6,4,3,3,3,3,3,3] (.node [9,6,6,4,3,3,3,3,2,2,2] (.node [9,6,6,3,3,3,3,3,3,3,1] .empty .empty) (.node [9,6,6,4,3,3,3,3,3,2,1] .empty .empty)) (.node [9,6,6,4,4,3,3,3,2,2,1] (.node [9,6,6,4,4,3,3,2,2,2,2] .empty .empty) (.node [9,6,6,4,4,3,3,3,3,1,1] .empty .empty)))) (.node [9,6,6,4,4,4,4,3,1,1,1] (.node [9,6,6,4,4,4,3,3,2,2] (.node [9,6,6,4,4,4,3,2,2,2,1] (.node [9,6,6,4,4,4,2,2,2,2,2] .empty .empty) (.node [9,6,6,4,4,4,3,3,2,1,1] .empty .empty)) (.node [9,6,6,4,4,4,4,2,2,1,1] (.node [9,6,6,4,4,4,3,3,3,1] .empty .empty) (.node [9,6,6,4,4,4,4,2,2,2] .empty .empty))) (.node [9,6,6,4,4,4,4,4,2] (.node [9,6,6,4,4,4,4,3,3] (.node [9,6,6,4,4,4,4,3,2,1] .empty .empty) (.node [9,6,6,4,4,4,4,4,1,1] .empty .empty)) (.node [9,6,6,5,3,3,3,3,2,2,1] (.node [9,6,6,5,3,3,3,2,2,2,2] .empty .empty) (.node [9,6,6,5,3,3,3,3,3,1,1] .empty .empty))))) - -def degreeTree43_145 : RowTree := (.node [9,6,5,5,5,5,3,3,1,1] degreeTree43_143 degreeTree43_144) - -def degreeTree43_146 : RowTree := (.node [9,6,6,5,4,4,4,4,1] (.node [9,6,6,5,4,4,3,2,2,2] (.node [9,6,6,5,4,3,3,3,2,2] (.node [9,6,6,5,4,3,3,2,2,2,1] (.node [9,6,6,5,4,3,2,2,2,2,2] .empty .empty) (.node [9,6,6,5,4,3,3,3,2,1,1] .empty .empty)) (.node [9,6,6,5,4,4,2,2,2,2,1] (.node [9,6,6,5,4,3,3,3,3,1] .empty .empty) (.node [9,6,6,5,4,4,3,2,2,1,1] .empty .empty))) (.node [9,6,6,5,4,4,4,2,1,1,1] (.node [9,6,6,5,4,4,3,3,2,1] (.node [9,6,6,5,4,4,3,3,1,1,1] .empty .empty) (.node [9,6,6,5,4,4,3,3,3] .empty .empty)) (.node [9,6,6,5,4,4,4,3,1,1] (.node [9,6,6,5,4,4,4,2,2,1] .empty .empty) (.node [9,6,6,5,4,4,4,3,2] .empty .empty)))) (.node [9,6,6,5,5,4,2,2,2,1,1] (.node [9,6,6,5,5,3,3,2,2,2] (.node [9,6,6,5,5,3,2,2,2,2,1] (.node [9,6,6,5,5,2,2,2,2,2,2] .empty .empty) (.node [9,6,6,5,5,3,3,2,2,1,1] .empty .empty)) (.node [9,6,6,5,5,3,3,3,2,1] (.node [9,6,6,5,5,3,3,3,1,1,1] .empty .empty) (.node [9,6,6,5,5,3,3,3,3] .empty .empty))) (.node [9,6,6,5,5,4,3,3,1,1] (.node [9,6,6,5,5,4,3,2,1,1,1] (.node [9,6,6,5,5,4,2,2,2,2] .empty .empty) (.node [9,6,6,5,5,4,3,2,2,1] .empty .empty)) (.node [9,6,6,5,5,4,4,1,1,1,1] (.node [9,6,6,5,5,4,3,3,2] .empty .empty) (.node [9,6,6,5,5,4,4,2,1,1] .empty .empty))))) - -def degreeTree43_147 : RowTree := (.node [9,6,6,6,4,2,2,2,2,2,2] (.node [9,6,6,5,5,5,4,1,1,1] (.node [9,6,6,5,5,5,3,1,1,1,1] (.node [9,6,6,5,5,5,2,2,1,1,1] (.node [9,6,6,5,5,4,4,3,1] .empty .empty) (.node [9,6,6,5,5,5,2,2,2,1] .empty .empty)) (.node [9,6,6,5,5,5,3,2,2] (.node [9,6,6,5,5,5,3,2,1,1] .empty .empty) (.node [9,6,6,5,5,5,3,3,1] .empty .empty))) (.node [9,6,6,6,3,3,3,2,2,2,1] (.node [9,6,6,5,5,5,5,1,1] (.node [9,6,6,5,5,5,4,2,1] .empty .empty) (.node [9,6,6,6,3,3,2,2,2,2,2] .empty .empty)) (.node [9,6,6,6,3,3,3,3,2,2] (.node [9,6,6,6,3,3,3,3,2,1,1] .empty .empty) (.node [9,6,6,6,3,3,3,3,3,1] .empty .empty)))) (.node [9,6,6,6,4,4,2,2,2,2] (.node [9,6,6,6,4,3,3,3,1,1,1] (.node [9,6,6,6,4,3,3,2,2,1,1] (.node [9,6,6,6,4,3,2,2,2,2,1] .empty .empty) (.node [9,6,6,6,4,3,3,2,2,2] .empty .empty)) (.node [9,6,6,6,4,3,3,3,3] (.node [9,6,6,6,4,3,3,3,2,1] .empty .empty) (.node [9,6,6,6,4,4,2,2,2,1,1] .empty .empty))) (.node [9,6,6,6,4,4,3,3,2] (.node [9,6,6,6,4,4,3,2,2,1] (.node [9,6,6,6,4,4,3,2,1,1,1] .empty .empty) (.node [9,6,6,6,4,4,3,3,1,1] .empty .empty)) (.node [9,6,6,6,4,4,4,2,1,1] (.node [9,6,6,6,4,4,4,1,1,1,1] .empty .empty) (.node [9,6,6,6,4,4,4,2,2] .empty .empty))))) - -def degreeTree43_148 : RowTree := (.node [9,6,6,5,5,4,4,2,2] degreeTree43_146 degreeTree43_147) - -def degreeTree43_149 : RowTree := (.node [9,6,6,5,3,3,3,3,3,2] degreeTree43_145 degreeTree43_148) - -def degreeTree43_150 : RowTree := (.node [9,6,6,6,5,4,2,2,2,1] (.node [9,6,6,6,5,3,3,2,2,1] (.node [9,6,6,6,5,3,2,2,2,2] (.node [9,6,6,6,5,3,2,2,2,1,1] (.node [9,6,6,6,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [9,6,6,6,5,3,3,2,1,1,1] .empty .empty)) (.node [9,6,6,6,5,3,3,3,2] (.node [9,6,6,6,5,3,3,3,1,1] .empty .empty) (.node [9,6,6,6,5,4,2,2,1,1,1] .empty .empty))) (.node [9,6,6,6,5,4,3,3,1] (.node [9,6,6,6,5,4,3,2,1,1] (.node [9,6,6,6,5,4,3,1,1,1,1] .empty .empty) (.node [9,6,6,6,5,4,3,2,2] .empty .empty)) (.node [9,6,6,6,5,4,4,2,1] (.node [9,6,6,6,5,4,4,1,1,1] .empty .empty) (.node [9,6,6,6,5,5,2,1,1,1,1] .empty .empty)))) - -def degreeTree43_151 : RowTree := (.node [9,6,6,6,6,2,2,2,1,1,1,1] (.node [9,6,6,6,5,5,4,1,1] (.node [9,6,6,6,5,5,3,1,1,1] (.node [9,6,6,6,5,5,2,2,2] .empty .empty) (.node [9,6,6,6,5,5,3,2,1] .empty .empty)) (.node [9,6,6,6,6,2,1,1,1,1,1,1,1,1] (.node [9,6,6,6,6,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,6,6,6,6,2,2,1,1,1,1,1,1] .empty .empty))) (.node [9,6,6,6,6,3,2,1,1,1,1,1] (.node [9,6,6,6,6,2,2,2,2,2] (.node [9,6,6,6,6,2,2,2,2,1,1] .empty .empty) (.node [9,6,6,6,6,3,1,1,1,1,1,1,1] .empty .empty)) (.node [9,6,6,6,6,3,2,2,2,1] (.node [9,6,6,6,6,3,2,2,1,1,1] .empty .empty) (.node [9,6,6,6,6,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree43_152 : RowTree := (.node [9,6,6,6,5,5,2,2,1,1] degreeTree43_150 degreeTree43_151) - -def degreeTree43_153 : RowTree := (.node [9,7,3,3,3,3,3,3,3,3,3] (.node [9,6,6,6,6,4,3,2,1] (.node [9,6,6,6,6,4,2,1,1,1,1] (.node [9,6,6,6,6,3,3,3,1] (.node [9,6,6,6,6,3,3,2,2] .empty .empty) (.node [9,6,6,6,6,4,1,1,1,1,1,1] .empty .empty)) (.node [9,6,6,6,6,4,2,2,2] (.node [9,6,6,6,6,4,2,2,1,1] .empty .empty) (.node [9,6,6,6,6,4,3,1,1,1] .empty .empty))) (.node [9,6,6,6,6,5,2,2,1] (.node [9,6,6,6,6,5,1,1,1,1,1] (.node [9,6,6,6,6,4,4,1,1] .empty .empty) (.node [9,6,6,6,6,5,2,1,1,1] .empty .empty)) (.node [9,6,6,6,6,6,1,1,1,1] (.node [9,6,6,6,6,5,3,1,1] .empty .empty) (.node [9,6,6,6,6,6,2,1,1] .empty .empty)))) (.node [9,7,4,4,4,4,3,3,2,2,1] (.node [9,7,4,4,4,3,3,3,2,2,2] (.node [9,7,4,4,3,3,3,3,3,2,2] (.node [9,7,4,3,3,3,3,3,3,3,2] .empty .empty) (.node [9,7,4,4,3,3,3,3,3,3,1] .empty .empty)) (.node [9,7,4,4,4,3,3,3,3,3] (.node [9,7,4,4,4,3,3,3,3,2,1] .empty .empty) (.node [9,7,4,4,4,4,3,2,2,2,2] .empty .empty))) (.node [9,7,4,4,4,4,4,3,2,1,1] (.node [9,7,4,4,4,4,3,3,3,2] (.node [9,7,4,4,4,4,3,3,3,1,1] .empty .empty) (.node [9,7,4,4,4,4,4,2,2,2,1] .empty .empty)) (.node [9,7,4,4,4,4,4,3,3,1] (.node [9,7,4,4,4,4,4,3,2,2] .empty .empty) (.node [9,7,4,4,4,4,4,4,1,1,1] .empty .empty))))) - -def degreeTree43_154 : RowTree := (.node [9,6,6,6,6,3,3,2,1,1] degreeTree43_152 degreeTree43_153) - -def degreeTree43_155 : RowTree := (.node [9,7,5,4,4,4,4,2,2,1,1] (.node [9,7,5,4,4,3,3,3,2,2,1] (.node [9,7,5,4,3,3,3,3,2,2,2] (.node [9,7,5,3,3,3,3,3,3,2,2] (.node [9,7,4,4,4,4,4,4,3] .empty .empty) (.node [9,7,5,3,3,3,3,3,3,3,1] .empty .empty)) (.node [9,7,5,4,3,3,3,3,3,3] (.node [9,7,5,4,3,3,3,3,3,2,1] .empty .empty) (.node [9,7,5,4,4,3,3,2,2,2,2] .empty .empty))) (.node [9,7,5,4,4,4,3,2,2,2,1] (.node [9,7,5,4,4,3,3,3,3,2] (.node [9,7,5,4,4,3,3,3,3,1,1] .empty .empty) (.node [9,7,5,4,4,4,2,2,2,2,2] .empty .empty)) (.node [9,7,5,4,4,4,3,3,2,2] (.node [9,7,5,4,4,4,3,3,2,1,1] .empty .empty) (.node [9,7,5,4,4,4,3,3,3,1] .empty .empty)))) (.node [9,7,5,5,3,3,3,3,2,2,1] (.node [9,7,5,4,4,4,4,3,3] (.node [9,7,5,4,4,4,4,3,1,1,1] (.node [9,7,5,4,4,4,4,2,2,2] .empty .empty) (.node [9,7,5,4,4,4,4,3,2,1] .empty .empty)) (.node [9,7,5,4,4,4,4,4,2] (.node [9,7,5,4,4,4,4,4,1,1] .empty .empty) (.node [9,7,5,5,3,3,3,2,2,2,2] .empty .empty))) (.node [9,7,5,5,4,3,3,2,2,2,1] (.node [9,7,5,5,3,3,3,3,3,2] (.node [9,7,5,5,3,3,3,3,3,1,1] .empty .empty) (.node [9,7,5,5,4,3,2,2,2,2,2] .empty .empty)) (.node [9,7,5,5,4,3,3,3,2,2] (.node [9,7,5,5,4,3,3,3,2,1,1] .empty .empty) (.node [9,7,5,5,4,3,3,3,3,1] .empty .empty))))) - -def degreeTree43_156 : RowTree := (.node [9,7,5,5,5,3,3,3,2,1] (.node [9,7,5,5,4,4,4,3,1,1] (.node [9,7,5,5,4,4,3,3,2,1] (.node [9,7,5,5,4,4,3,2,2,2] (.node [9,7,5,5,4,4,3,2,2,1,1] .empty .empty) (.node [9,7,5,5,4,4,3,3,1,1,1] .empty .empty)) (.node [9,7,5,5,4,4,4,2,1,1,1] (.node [9,7,5,5,4,4,3,3,3] .empty .empty) (.node [9,7,5,5,4,4,4,2,2,1] .empty .empty))) (.node [9,7,5,5,5,3,2,2,2,2,1] (.node [9,7,5,5,4,4,4,4,1] (.node [9,7,5,5,4,4,4,3,2] .empty .empty) (.node [9,7,5,5,5,2,2,2,2,2,2] .empty .empty)) (.node [9,7,5,5,5,3,3,2,2,2] (.node [9,7,5,5,5,3,3,2,2,1,1] .empty .empty) (.node [9,7,5,5,5,3,3,3,1,1,1] .empty .empty)))) (.node [9,7,5,5,5,4,4,1,1,1,1] (.node [9,7,5,5,5,4,3,2,1,1,1] (.node [9,7,5,5,5,4,2,2,2,1,1] (.node [9,7,5,5,5,3,3,3,3] .empty .empty) (.node [9,7,5,5,5,4,2,2,2,2] .empty .empty)) (.node [9,7,5,5,5,4,3,3,1,1] (.node [9,7,5,5,5,4,3,2,2,1] .empty .empty) (.node [9,7,5,5,5,4,3,3,2] .empty .empty))) (.node [9,7,5,5,5,5,2,2,1,1,1] (.node [9,7,5,5,5,4,4,2,2] (.node [9,7,5,5,5,4,4,2,1,1] .empty .empty) (.node [9,7,5,5,5,4,4,3,1] .empty .empty)) (.node [9,7,5,5,5,5,3,1,1,1,1] (.node [9,7,5,5,5,5,2,2,2,1] .empty .empty) (.node [9,7,5,5,5,5,3,2,1,1] .empty .empty))))) - -def degreeTree43_157 : RowTree := (.node [9,7,5,5,4,4,2,2,2,2,1] degreeTree43_155 degreeTree43_156) - -def degreeTree43_158 : RowTree := (.node [9,7,4,4,4,4,4,4,2,1] degreeTree43_154 degreeTree43_157) - -def degreeTree43_159 : RowTree := (.node [9,6,6,6,4,4,4,3,1] degreeTree43_149 degreeTree43_158) - -def degreeTree43_160 : RowTree := (.node [9,6,5,5,4,3,3,3,3,2] degreeTree43_140 degreeTree43_159) - -def degreeTree43_161 : RowTree := (.node [8,8,8,5,5,3,2,1,1,1,1] degreeTree43_121 degreeTree43_160) - -def degreeTree43_162 : RowTree := (.node [8,8,6,6,5,3,1,1,1,1,1,1,1] degreeTree43_80 degreeTree43_161) - -def degreeTree43_163 : RowTree := (.node [9,7,6,4,3,3,3,3,2,2,1] (.node [9,7,6,3,3,3,3,3,2,2,2] (.node [9,7,5,5,5,5,4,2,1] (.node [9,7,5,5,5,5,4,1,1,1] (.node [9,7,5,5,5,5,3,3,1] .empty .empty) .empty) (.node [9,7,5,5,5,5,5,1,1] .empty .empty)) (.node [9,7,6,3,3,3,3,3,3,3] (.node [9,7,6,3,3,3,3,3,3,2,1] .empty .empty) (.node [9,7,6,4,3,3,3,2,2,2,2] .empty .empty))) (.node [9,7,6,4,4,3,3,2,2,2,1] (.node [9,7,6,4,3,3,3,3,3,2] (.node [9,7,6,4,3,3,3,3,3,1,1] .empty .empty) (.node [9,7,6,4,4,3,2,2,2,2,2] .empty .empty)) (.node [9,7,6,4,4,3,3,3,2,2] (.node [9,7,6,4,4,3,3,3,2,1,1] .empty .empty) (.node [9,7,6,4,4,3,3,3,3,1] .empty .empty)))) - -def degreeTree43_164 : RowTree := (.node [9,7,6,4,4,4,4,3,1,1] (.node [9,7,6,4,4,4,3,3,2,1] (.node [9,7,6,4,4,4,3,2,2,2] (.node [9,7,6,4,4,4,3,2,2,1,1] .empty .empty) (.node [9,7,6,4,4,4,3,3,1,1,1] .empty .empty)) (.node [9,7,6,4,4,4,4,2,1,1,1] (.node [9,7,6,4,4,4,3,3,3] .empty .empty) (.node [9,7,6,4,4,4,4,2,2,1] .empty .empty))) (.node [9,7,6,5,3,3,3,2,2,2,1] (.node [9,7,6,4,4,4,4,4,1] (.node [9,7,6,4,4,4,4,3,2] .empty .empty) (.node [9,7,6,5,3,3,2,2,2,2,2] .empty .empty)) (.node [9,7,6,5,3,3,3,3,2,2] (.node [9,7,6,5,3,3,3,3,2,1,1] .empty .empty) (.node [9,7,6,5,3,3,3,3,3,1] .empty .empty)))) - -def degreeTree43_165 : RowTree := (.node [9,7,6,4,4,4,2,2,2,2,1] degreeTree43_163 degreeTree43_164) - -def degreeTree43_166 : RowTree := (.node [9,7,6,5,4,4,4,3,1] (.node [9,7,6,5,4,4,2,2,2,2] (.node [9,7,6,5,4,3,3,3,1,1,1] (.node [9,7,6,5,4,3,3,2,2,1,1] (.node [9,7,6,5,4,3,2,2,2,2,1] .empty .empty) (.node [9,7,6,5,4,3,3,2,2,2] .empty .empty)) (.node [9,7,6,5,4,3,3,3,3] (.node [9,7,6,5,4,3,3,3,2,1] .empty .empty) (.node [9,7,6,5,4,4,2,2,2,1,1] .empty .empty))) (.node [9,7,6,5,4,4,3,3,2] (.node [9,7,6,5,4,4,3,2,2,1] (.node [9,7,6,5,4,4,3,2,1,1,1] .empty .empty) (.node [9,7,6,5,4,4,3,3,1,1] .empty .empty)) (.node [9,7,6,5,4,4,4,2,1,1] (.node [9,7,6,5,4,4,4,1,1,1,1] .empty .empty) (.node [9,7,6,5,4,4,4,2,2] .empty .empty)))) (.node [9,7,6,5,5,4,2,2,1,1,1] (.node [9,7,6,5,5,3,3,2,1,1,1] (.node [9,7,6,5,5,3,2,2,2,1,1] (.node [9,7,6,5,5,2,2,2,2,2,1] .empty .empty) (.node [9,7,6,5,5,3,2,2,2,2] .empty .empty)) (.node [9,7,6,5,5,3,3,3,1,1] (.node [9,7,6,5,5,3,3,2,2,1] .empty .empty) (.node [9,7,6,5,5,3,3,3,2] .empty .empty))) (.node [9,7,6,5,5,4,3,2,2] (.node [9,7,6,5,5,4,3,1,1,1,1] (.node [9,7,6,5,5,4,2,2,2,1] .empty .empty) (.node [9,7,6,5,5,4,3,2,1,1] .empty .empty)) (.node [9,7,6,5,5,4,4,1,1,1] (.node [9,7,6,5,5,4,3,3,1] .empty .empty) (.node [9,7,6,5,5,4,4,2,1] .empty .empty))))) - -def degreeTree43_167 : RowTree := (.node [9,7,6,5,4,2,2,2,2,2,2] degreeTree43_165 degreeTree43_166) - -def degreeTree43_168 : RowTree := (.node [9,7,6,6,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,7,6,5,5,5,4,1,1] (.node [9,7,6,5,5,5,3,1,1,1] (.node [9,7,6,5,5,5,2,2,2] (.node [9,7,6,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [9,7,6,5,5,5,3,2,1] .empty .empty)) (.node [9,7,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,6,6,2,2,2,2,2,2,2,1] (.node [9,7,6,6,2,2,2,2,2,1,1,1,1,1] (.node [9,7,6,6,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,7,6,6,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,7,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,3,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_169 : RowTree := (.node [9,7,6,6,3,3,2,2,2,2,1] (.node [9,7,6,6,3,3,1,1,1,1,1,1,1,1,1] (.node [9,7,6,6,3,2,2,2,2,2,1,1] (.node [9,7,6,6,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,7,6,6,3,2,2,2,2,2,2] .empty .empty)) (.node [9,7,6,6,3,3,2,2,1,1,1,1,1] (.node [9,7,6,6,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,3,3,2,2,2,1,1,1] .empty .empty))) (.node [9,7,6,6,3,3,3,2,2,2] (.node [9,7,6,6,3,3,3,2,1,1,1,1] (.node [9,7,6,6,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,3,3,3,2,2,1,1] .empty .empty)) (.node [9,7,6,6,3,3,3,3,2,1] (.node [9,7,6,6,3,3,3,3,1,1,1] .empty .empty) (.node [9,7,6,6,3,3,3,3,3] .empty .empty)))) - -def degreeTree43_170 : RowTree := (.node [9,7,6,6,3,2,2,2,1,1,1,1,1,1] degreeTree43_168 degreeTree43_169) - -def degreeTree43_171 : RowTree := (.node [9,7,6,6,4,4,1,1,1,1,1,1,1] (.node [9,7,6,6,4,3,2,2,1,1,1,1] (.node [9,7,6,6,4,2,2,2,2,1,1,1] (.node [9,7,6,6,4,2,2,1,1,1,1,1,1,1] (.node [9,7,6,6,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,4,2,2,2,1,1,1,1,1] .empty .empty)) (.node [9,7,6,6,4,3,1,1,1,1,1,1,1,1] (.node [9,7,6,6,4,2,2,2,2,2,1] .empty .empty) (.node [9,7,6,6,4,3,2,1,1,1,1,1,1] .empty .empty))) (.node [9,7,6,6,4,3,3,2,1,1,1] (.node [9,7,6,6,4,3,2,2,2,2] (.node [9,7,6,6,4,3,2,2,2,1,1] .empty .empty) (.node [9,7,6,6,4,3,3,1,1,1,1,1] .empty .empty)) (.node [9,7,6,6,4,3,3,3,1,1] (.node [9,7,6,6,4,3,3,2,2,1] .empty .empty) (.node [9,7,6,6,4,3,3,3,2] .empty .empty)))) (.node [9,7,6,6,4,4,4,1,1,1] (.node [9,7,6,6,4,4,3,1,1,1,1] (.node [9,7,6,6,4,4,2,2,1,1,1] (.node [9,7,6,6,4,4,2,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,4,4,2,2,2,1] .empty .empty)) (.node [9,7,6,6,4,4,3,2,2] (.node [9,7,6,6,4,4,3,2,1,1] .empty .empty) (.node [9,7,6,6,4,4,3,3,1] .empty .empty))) (.node [9,7,6,6,5,2,2,1,1,1,1,1,1] (.node [9,7,6,6,5,1,1,1,1,1,1,1,1,1,1] (.node [9,7,6,6,4,4,4,2,1] .empty .empty) (.node [9,7,6,6,5,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,6,6,5,2,2,2,2,1,1] (.node [9,7,6,6,5,2,2,2,1,1,1,1] .empty .empty) (.node [9,7,6,6,5,2,2,2,2,2] .empty .empty))))) - -def degreeTree43_172 : RowTree := (.node [9,7,6,6,4,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_170 degreeTree43_171) - -def degreeTree43_173 : RowTree := (.node [9,7,6,5,5,5,2,1,1,1,1] degreeTree43_167 degreeTree43_172) - -def degreeTree43_174 : RowTree := (.node [9,7,6,6,5,4,2,1,1,1,1] (.node [9,7,6,6,5,3,3,2,1,1] (.node [9,7,6,6,5,3,2,2,2,1] (.node [9,7,6,6,5,3,2,2,1,1,1] (.node [9,7,6,6,5,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [9,7,6,6,5,3,3,1,1,1,1] .empty .empty)) (.node [9,7,6,6,5,3,3,3,1] (.node [9,7,6,6,5,3,3,2,2] .empty .empty) (.node [9,7,6,6,5,4,1,1,1,1,1,1] .empty .empty))) (.node [9,7,6,6,5,4,3,2,1] (.node [9,7,6,6,5,4,2,2,2] (.node [9,7,6,6,5,4,2,2,1,1] .empty .empty) (.node [9,7,6,6,5,4,3,1,1,1] .empty .empty)) (.node [9,7,6,6,5,5,1,1,1,1,1] (.node [9,7,6,6,5,4,4,1,1] .empty .empty) (.node [9,7,6,6,5,5,2,1,1,1] .empty .empty)))) - -def degreeTree43_175 : RowTree := (.node [9,7,6,6,6,3,2,1,1,1,1] (.node [9,7,6,6,6,2,2,1,1,1,1,1] (.node [9,7,6,6,6,1,1,1,1,1,1,1,1,1] (.node [9,7,6,6,5,5,3,1,1] .empty .empty) (.node [9,7,6,6,6,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,6,6,6,2,2,2,2,1] (.node [9,7,6,6,6,2,2,2,1,1,1] .empty .empty) (.node [9,7,6,6,6,3,1,1,1,1,1,1] .empty .empty))) (.node [9,7,6,6,6,3,3,2,1] (.node [9,7,6,6,6,3,2,2,2] (.node [9,7,6,6,6,3,2,2,1,1] .empty .empty) (.node [9,7,6,6,6,3,3,1,1,1] .empty .empty)) (.node [9,7,6,6,6,4,2,1,1,1] (.node [9,7,6,6,6,4,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,6,4,2,2,1] .empty .empty)))) - -def degreeTree43_176 : RowTree := (.node [9,7,6,6,5,5,2,2,1] degreeTree43_174 degreeTree43_175) - -def degreeTree43_177 : RowTree := (.node [9,7,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,6,6,6,5,2,1,1] (.node [9,7,6,6,6,5,1,1,1,1] .empty .empty) (.node [9,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,7,2,2,2,2,2,2,2,2,2,1,1] (.node [9,7,7,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [9,7,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [9,7,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [9,7,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,7,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,3,2,2,2,2,2,2,1,1,1,1,1] (.node [9,7,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,7,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,3,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,3,2,2,2,2,2,2,2,2,1] (.node [9,7,7,3,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,7,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,7,3,3,2,2,2,2,2,1,1,1,1] (.node [9,7,7,3,3,2,2,2,1,1,1,1,1,1,1,1] (.node [9,7,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,3,3,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,3,3,2,2,2,2,2,2,2] (.node [9,7,7,3,3,2,2,2,2,2,2,1,1] .empty .empty) (.node [9,7,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_178 : RowTree := (.node [9,7,6,6,6,4,3,1,1] degreeTree43_176 degreeTree43_177) - -def degreeTree43_179 : RowTree := (.node [9,7,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,3,3,3,3,2,2,2,1,1] (.node [9,7,7,3,3,3,2,2,2,2,2,1] (.node [9,7,7,3,3,3,2,2,2,1,1,1,1,1] (.node [9,7,7,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,3,3,3,2,2,2,2,1,1,1] .empty .empty)) (.node [9,7,7,3,3,3,3,2,1,1,1,1,1,1] (.node [9,7,7,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,3,3,3,3,2,2,1,1,1,1] .empty .empty))) (.node [9,7,7,3,3,3,3,3,2,2,1] (.node [9,7,7,3,3,3,3,3,1,1,1,1,1] (.node [9,7,7,3,3,3,3,2,2,2,2] .empty .empty) (.node [9,7,7,3,3,3,3,3,2,1,1,1] .empty .empty)) (.node [9,7,7,3,3,3,3,3,3,2] (.node [9,7,7,3,3,3,3,3,3,1,1] .empty .empty) (.node [9,7,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,7,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,4,2,2,2,2,2,1,1,1,1,1,1] (.node [9,7,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,4,2,2,2,2,2,2,2,1,1] (.node [9,7,7,4,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,4,2,2,2,2,2,2,2,2] .empty .empty))) (.node [9,7,7,4,3,2,2,2,2,1,1,1,1,1] (.node [9,7,7,4,3,2,2,1,1,1,1,1,1,1,1,1] (.node [9,7,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,3,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,4,3,2,2,2,2,2,2,1] (.node [9,7,7,4,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,7,7,4,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_180 : RowTree := (.node [9,7,7,4,4,2,2,2,1,1,1,1,1,1] (.node [9,7,7,4,3,3,3,2,2,2,1] (.node [9,7,7,4,3,3,2,2,2,2,2] (.node [9,7,7,4,3,3,2,2,2,1,1,1,1] (.node [9,7,7,4,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,3,3,2,2,2,2,1,1] .empty .empty)) (.node [9,7,7,4,3,3,3,2,1,1,1,1,1] (.node [9,7,7,4,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,3,3,3,2,2,1,1,1] .empty .empty))) (.node [9,7,7,4,3,3,3,3,3,1] (.node [9,7,7,4,3,3,3,3,2,1,1] (.node [9,7,7,4,3,3,3,3,1,1,1,1] .empty .empty) (.node [9,7,7,4,3,3,3,3,2,2] .empty .empty)) (.node [9,7,7,4,4,2,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,4,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,7,7,4,4,3,2,2,2,2,1] (.node [9,7,7,4,4,3,1,1,1,1,1,1,1,1,1] (.node [9,7,7,4,4,2,2,2,2,2,1,1] (.node [9,7,7,4,4,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,4,4,2,2,2,2,2,2] .empty .empty)) (.node [9,7,7,4,4,3,2,2,1,1,1,1,1] (.node [9,7,7,4,4,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,4,3,2,2,2,1,1,1] .empty .empty))) (.node [9,7,7,4,4,3,3,2,2,2] (.node [9,7,7,4,4,3,3,2,1,1,1,1] (.node [9,7,7,4,4,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,4,3,3,2,2,1,1] .empty .empty)) (.node [9,7,7,4,4,3,3,3,2,1] (.node [9,7,7,4,4,3,3,3,1,1,1] .empty .empty) (.node [9,7,7,4,4,3,3,3,3] .empty .empty))))) - -def degreeTree43_181 : RowTree := (.node [9,7,7,4,3,3,2,1,1,1,1,1,1,1,1] degreeTree43_179 degreeTree43_180) - -def degreeTree43_182 : RowTree := (.node [9,7,7,3,3,3,2,1,1,1,1,1,1,1,1,1] degreeTree43_178 degreeTree43_181) - -def degreeTree43_183 : RowTree := (.node [9,7,6,6,5,3,1,1,1,1,1,1,1] degreeTree43_173 degreeTree43_182) - -def degreeTree43_184 : RowTree := (.node [9,7,7,4,4,4,3,3,2] (.node [9,7,7,4,4,4,3,1,1,1,1,1] (.node [9,7,7,4,4,4,2,2,2,1,1] (.node [9,7,7,4,4,4,2,2,1,1,1,1] (.node [9,7,7,4,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,7,7,4,4,4,2,2,2,2] .empty .empty)) (.node [9,7,7,4,4,4,3,2,2,1] (.node [9,7,7,4,4,4,3,2,1,1,1] .empty .empty) (.node [9,7,7,4,4,4,3,3,1,1] .empty .empty))) (.node [9,7,7,4,4,4,4,3,1] (.node [9,7,7,4,4,4,4,2,1,1] (.node [9,7,7,4,4,4,4,1,1,1,1] .empty .empty) (.node [9,7,7,4,4,4,4,2,2] .empty .empty)) (.node [9,7,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_185 : RowTree := (.node [9,7,7,5,3,2,2,2,1,1,1,1,1,1] (.node [9,7,7,5,2,2,2,2,2,2,2,1] (.node [9,7,7,5,2,2,2,2,2,1,1,1,1,1] (.node [9,7,7,5,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,7,7,5,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,5,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,3,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,7,5,3,3,1,1,1,1,1,1,1,1,1] (.node [9,7,7,5,3,2,2,2,2,2,1,1] (.node [9,7,7,5,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,5,3,2,2,2,2,2,2] .empty .empty)) (.node [9,7,7,5,3,3,2,2,1,1,1,1,1] (.node [9,7,7,5,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,3,3,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree43_186 : RowTree := (.node [9,7,7,5,2,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_184 degreeTree43_185) - -def degreeTree43_187 : RowTree := (.node [9,7,7,5,4,3,2,2,1,1,1,1] (.node [9,7,7,5,4,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,5,3,3,3,2,2,2] (.node [9,7,7,5,3,3,3,2,1,1,1,1] (.node [9,7,7,5,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,3,3,3,2,2,1,1] .empty .empty)) (.node [9,7,7,5,3,3,3,3,2,1] (.node [9,7,7,5,3,3,3,3,1,1,1] .empty .empty) (.node [9,7,7,5,3,3,3,3,3] .empty .empty))) (.node [9,7,7,5,4,2,2,2,2,1,1,1] (.node [9,7,7,5,4,2,2,1,1,1,1,1,1,1] (.node [9,7,7,5,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,4,2,2,2,1,1,1,1,1] .empty .empty)) (.node [9,7,7,5,4,3,1,1,1,1,1,1,1,1] (.node [9,7,7,5,4,2,2,2,2,2,1] .empty .empty) (.node [9,7,7,5,4,3,2,1,1,1,1,1,1] .empty .empty)))) (.node [9,7,7,5,4,4,1,1,1,1,1,1,1] (.node [9,7,7,5,4,3,3,2,1,1,1] (.node [9,7,7,5,4,3,2,2,2,2] (.node [9,7,7,5,4,3,2,2,2,1,1] .empty .empty) (.node [9,7,7,5,4,3,3,1,1,1,1,1] .empty .empty)) (.node [9,7,7,5,4,3,3,3,1,1] (.node [9,7,7,5,4,3,3,2,2,1] .empty .empty) (.node [9,7,7,5,4,3,3,3,2] .empty .empty))) (.node [9,7,7,5,4,4,3,1,1,1,1] (.node [9,7,7,5,4,4,2,2,1,1,1] (.node [9,7,7,5,4,4,2,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,4,4,2,2,2,1] .empty .empty)) (.node [9,7,7,5,4,4,3,2,2] (.node [9,7,7,5,4,4,3,2,1,1] .empty .empty) (.node [9,7,7,5,4,4,3,3,1] .empty .empty))))) - -def degreeTree43_188 : RowTree := (.node [9,7,7,5,3,3,2,2,2,2,1] degreeTree43_186 degreeTree43_187) - -def degreeTree43_189 : RowTree := (.node [9,7,7,5,5,4,1,1,1,1,1,1] (.node [9,7,7,5,5,3,1,1,1,1,1,1,1] (.node [9,7,7,5,5,2,2,1,1,1,1,1,1] (.node [9,7,7,5,5,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,5,4,4,4,2,1] .empty .empty) (.node [9,7,7,5,5,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,5,5,2,2,2,2,1,1] (.node [9,7,7,5,5,2,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,5,5,2,2,2,2,2] .empty .empty))) (.node [9,7,7,5,5,3,3,1,1,1,1] (.node [9,7,7,5,5,3,2,2,1,1,1] (.node [9,7,7,5,5,3,2,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,5,3,2,2,2,1] .empty .empty)) (.node [9,7,7,5,5,3,3,2,2] (.node [9,7,7,5,5,3,3,2,1,1] .empty .empty) (.node [9,7,7,5,5,3,3,3,1] .empty .empty)))) (.node [9,7,7,5,5,5,2,1,1,1] (.node [9,7,7,5,5,4,3,1,1,1] (.node [9,7,7,5,5,4,2,2,1,1] (.node [9,7,7,5,5,4,2,1,1,1,1] .empty .empty) (.node [9,7,7,5,5,4,2,2,2] .empty .empty)) (.node [9,7,7,5,5,4,4,1,1] (.node [9,7,7,5,5,4,3,2,1] .empty .empty) (.node [9,7,7,5,5,5,1,1,1,1,1] .empty .empty))) (.node [9,7,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,5,5,5,3,1,1] (.node [9,7,7,5,5,5,2,2,1] .empty .empty) (.node [9,7,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,6,2,2,2,1,1,1,1,1,1,1,1] (.node [9,7,7,6,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,6,2,2,2,2,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_190 : RowTree := (.node [9,7,7,6,3,3,3,2,2,1] (.node [9,7,7,6,3,2,2,2,2,2,1] (.node [9,7,7,6,3,2,1,1,1,1,1,1,1,1,1] (.node [9,7,7,6,2,2,2,2,2,2,2] (.node [9,7,7,6,2,2,2,2,2,2,1,1] .empty .empty) (.node [9,7,7,6,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,6,3,2,2,2,1,1,1,1,1] (.node [9,7,7,6,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,6,3,2,2,2,2,1,1,1] .empty .empty))) (.node [9,7,7,6,3,3,2,2,2,1,1] (.node [9,7,7,6,3,3,2,1,1,1,1,1,1] (.node [9,7,7,6,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,6,3,3,2,2,1,1,1,1] .empty .empty)) (.node [9,7,7,6,3,3,3,1,1,1,1,1] (.node [9,7,7,6,3,3,2,2,2,2] .empty .empty) (.node [9,7,7,6,3,3,3,2,1,1,1] .empty .empty)))) (.node [9,7,7,6,4,2,2,2,2,2] (.node [9,7,7,6,4,2,1,1,1,1,1,1,1,1] (.node [9,7,7,6,3,3,3,3,2] (.node [9,7,7,6,3,3,3,3,1,1] .empty .empty) (.node [9,7,7,6,4,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,6,4,2,2,2,1,1,1,1] (.node [9,7,7,6,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,6,4,2,2,2,2,1,1] .empty .empty))) (.node [9,7,7,6,4,3,2,2,2,1] (.node [9,7,7,6,4,3,2,1,1,1,1,1] (.node [9,7,7,6,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,6,4,3,2,2,1,1,1] .empty .empty)) (.node [9,7,7,6,4,3,3,2,1,1] (.node [9,7,7,6,4,3,3,1,1,1,1] .empty .empty) (.node [9,7,7,6,4,3,3,2,2] .empty .empty))))) - -def degreeTree43_191 : RowTree := (.node [9,7,7,6,2,2,2,2,2,1,1,1,1] degreeTree43_189 degreeTree43_190) - -def degreeTree43_192 : RowTree := (.node [9,7,7,5,4,4,4,1,1,1] degreeTree43_188 degreeTree43_191) - -def degreeTree43_193 : RowTree := (.node [9,7,7,6,5,2,1,1,1,1,1,1,1] (.node [9,7,7,6,4,4,3,1,1,1] (.node [9,7,7,6,4,4,2,2,1,1] (.node [9,7,7,6,4,4,2,1,1,1,1] (.node [9,7,7,6,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,7,7,6,4,4,2,2,2] .empty .empty)) (.node [9,7,7,6,4,4,4,1,1] (.node [9,7,7,6,4,4,3,2,1] .empty .empty) (.node [9,7,7,6,5,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,7,6,5,3,1,1,1,1,1,1] (.node [9,7,7,6,5,2,2,2,1,1,1] (.node [9,7,7,6,5,2,2,1,1,1,1,1] .empty .empty) (.node [9,7,7,6,5,2,2,2,2,1] .empty .empty)) (.node [9,7,7,6,5,3,2,2,1,1] (.node [9,7,7,6,5,3,2,1,1,1,1] .empty .empty) (.node [9,7,7,6,5,3,2,2,2] .empty .empty)))) - -def degreeTree43_194 : RowTree := (.node [9,7,7,6,6,2,1,1,1,1,1,1] (.node [9,7,7,6,5,4,2,2,1] (.node [9,7,7,6,5,4,1,1,1,1,1] (.node [9,7,7,6,5,3,3,2,1] .empty .empty) (.node [9,7,7,6,5,4,2,1,1,1] .empty .empty)) (.node [9,7,7,6,5,5,1,1,1,1] (.node [9,7,7,6,5,4,3,1,1] .empty .empty) (.node [9,7,7,6,6,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,7,6,6,3,1,1,1,1,1] (.node [9,7,7,6,6,2,2,2,1,1] (.node [9,7,7,6,6,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,6,6,2,2,2,2] .empty .empty)) (.node [9,7,7,6,6,3,2,2,1] (.node [9,7,7,6,6,3,2,1,1,1] .empty .empty) (.node [9,7,7,6,6,4,1,1,1,1] .empty .empty)))) - -def degreeTree43_195 : RowTree := (.node [9,7,7,6,5,3,3,1,1,1] degreeTree43_193 degreeTree43_194) - -def degreeTree43_196 : RowTree := (.node [9,7,7,7,3,3,2,2,2,1] (.node [9,7,7,7,3,2,1,1,1,1,1,1,1,1] (.node [9,7,7,7,2,2,2,2,1,1,1,1,1] (.node [9,7,7,7,2,2,1,1,1,1,1,1,1,1,1] (.node [9,7,7,7,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,7,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,7,2,2,2,2,2,2,1] (.node [9,7,7,7,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,7,7,7,3,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,7,7,3,2,2,2,2,2] (.node [9,7,7,7,3,2,2,2,1,1,1,1] (.node [9,7,7,7,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,7,3,2,2,2,2,1,1] .empty .empty)) (.node [9,7,7,7,3,3,2,1,1,1,1,1] (.node [9,7,7,7,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,7,3,3,2,2,1,1,1] .empty .empty)))) (.node [9,7,7,7,4,2,2,2,1,1,1] (.node [9,7,7,7,3,3,3,3,1] (.node [9,7,7,7,3,3,3,2,1,1] (.node [9,7,7,7,3,3,3,1,1,1,1] .empty .empty) (.node [9,7,7,7,3,3,3,2,2] .empty .empty)) (.node [9,7,7,7,4,2,1,1,1,1,1,1,1] (.node [9,7,7,7,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,7,4,2,2,1,1,1,1,1] .empty .empty))) (.node [9,7,7,7,4,3,2,2,1,1] (.node [9,7,7,7,4,3,1,1,1,1,1,1] (.node [9,7,7,7,4,2,2,2,2,1] .empty .empty) (.node [9,7,7,7,4,3,2,1,1,1,1] .empty .empty)) (.node [9,7,7,7,4,3,3,1,1,1] (.node [9,7,7,7,4,3,2,2,2] .empty .empty) (.node [9,7,7,7,4,3,3,2,1] .empty .empty))))) - -def degreeTree43_197 : RowTree := (.node [9,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_195 degreeTree43_196) - -def degreeTree43_198 : RowTree := (.node [9,7,7,7,6,3,1,1,1,1] (.node [9,7,7,7,5,3,1,1,1,1,1] (.node [9,7,7,7,5,2,1,1,1,1,1,1] (.node [9,7,7,7,4,4,2,2,1] (.node [9,7,7,7,4,4,2,1,1,1] .empty .empty) (.node [9,7,7,7,5,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,7,5,2,2,2,1,1] (.node [9,7,7,7,5,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,7,5,2,2,2,2] .empty .empty))) (.node [9,7,7,7,6,1,1,1,1,1,1,1] (.node [9,7,7,7,5,3,2,2,1] (.node [9,7,7,7,5,3,2,1,1,1] .empty .empty) (.node [9,7,7,7,5,4,1,1,1,1] .empty .empty)) (.node [9,7,7,7,6,2,2,1,1,1] (.node [9,7,7,7,6,2,1,1,1,1,1] .empty .empty) (.node [9,7,7,7,6,2,2,2,1] .empty .empty)))) (.node [9,8,4,4,3,3,3,3,3,3] (.node [9,8,4,3,3,3,3,3,3,2,2] (.node [9,7,7,7,7,2,1,1,1,1] (.node [9,7,7,7,7,1,1,1,1,1,1] .empty .empty) (.node [9,8,3,3,3,3,3,3,3,3,2] .empty .empty)) (.node [9,8,4,4,3,3,3,3,2,2,2] (.node [9,8,4,3,3,3,3,3,3,3,1] .empty .empty) (.node [9,8,4,4,3,3,3,3,3,2,1] .empty .empty))) (.node [9,8,4,4,4,3,3,3,3,2] (.node [9,8,4,4,4,3,3,3,2,2,1] (.node [9,8,4,4,4,3,3,2,2,2,2] .empty .empty) (.node [9,8,4,4,4,3,3,3,3,1,1] .empty .empty)) (.node [9,8,4,4,4,4,3,2,2,2,1] (.node [9,8,4,4,4,4,2,2,2,2,2] .empty .empty) (.node [9,8,4,4,4,4,3,3,2,1,1] .empty .empty))))) - -def degreeTree43_199 : RowTree := (.node [9,8,5,4,4,3,2,2,2,2,2] (.node [9,8,4,4,4,4,4,4,2] (.node [9,8,4,4,4,4,4,3,1,1,1] (.node [9,8,4,4,4,4,4,2,2,1,1] (.node [9,8,4,4,4,4,3,3,3,1] .empty .empty) (.node [9,8,4,4,4,4,4,2,2,2] .empty .empty)) (.node [9,8,4,4,4,4,4,3,3] (.node [9,8,4,4,4,4,4,3,2,1] .empty .empty) (.node [9,8,4,4,4,4,4,4,1,1] .empty .empty))) (.node [9,8,5,4,3,3,3,2,2,2,2] (.node [9,8,5,3,3,3,3,3,3,2,1] (.node [9,8,5,3,3,3,3,3,2,2,2] .empty .empty) (.node [9,8,5,3,3,3,3,3,3,3] .empty .empty)) (.node [9,8,5,4,3,3,3,3,3,1,1] (.node [9,8,5,4,3,3,3,3,2,2,1] .empty .empty) (.node [9,8,5,4,3,3,3,3,3,2] .empty .empty)))) (.node [9,8,5,4,4,4,3,3,1,1,1] (.node [9,8,5,4,4,3,3,3,3,1] (.node [9,8,5,4,4,3,3,3,2,1,1] (.node [9,8,5,4,4,3,3,2,2,2,1] .empty .empty) (.node [9,8,5,4,4,3,3,3,2,2] .empty .empty)) (.node [9,8,5,4,4,4,3,2,2,1,1] (.node [9,8,5,4,4,4,2,2,2,2,1] .empty .empty) (.node [9,8,5,4,4,4,3,2,2,2] .empty .empty))) (.node [9,8,5,4,4,4,4,2,2,1] (.node [9,8,5,4,4,4,3,3,3] (.node [9,8,5,4,4,4,3,3,2,1] .empty .empty) (.node [9,8,5,4,4,4,4,2,1,1,1] .empty .empty)) (.node [9,8,5,4,4,4,4,3,2] (.node [9,8,5,4,4,4,4,3,1,1] .empty .empty) (.node [9,8,5,4,4,4,4,4,1] .empty .empty))))) - -def degreeTree43_200 : RowTree := (.node [9,8,4,4,4,4,3,3,2,2] degreeTree43_198 degreeTree43_199) - -def degreeTree43_201 : RowTree := (.node [9,7,7,7,4,4,1,1,1,1,1] degreeTree43_197 degreeTree43_200) - -def degreeTree43_202 : RowTree := (.node [9,7,7,6,4,3,3,3,1] degreeTree43_192 degreeTree43_201) - -def degreeTree43_203 : RowTree := (.node [9,7,7,4,4,4,1,1,1,1,1,1,1,1] degreeTree43_183 degreeTree43_202) - -def degreeTree43_204 : RowTree := (.node [9,8,5,5,4,3,3,3,1,1,1] (.node [9,8,5,5,4,2,2,2,2,2,2] (.node [9,8,5,5,3,3,3,3,2,2] (.node [9,8,5,5,3,3,3,3,2,1,1] (.node [9,8,5,5,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [9,8,5,5,3,3,3,3,3,1] .empty .empty)) (.node [9,8,5,5,4,3,3,2,2,1,1] (.node [9,8,5,5,4,3,2,2,2,2,1] .empty .empty) (.node [9,8,5,5,4,3,3,2,2,2] .empty .empty))) (.node [9,8,5,5,4,4,2,2,2,2] (.node [9,8,5,5,4,3,3,3,3] (.node [9,8,5,5,4,3,3,3,2,1] .empty .empty) (.node [9,8,5,5,4,4,2,2,2,1,1] .empty .empty)) (.node [9,8,5,5,4,4,3,2,2,1] (.node [9,8,5,5,4,4,3,2,1,1,1] .empty .empty) (.node [9,8,5,5,4,4,3,3,1,1] .empty .empty)))) - -def degreeTree43_205 : RowTree := (.node [9,8,5,5,5,3,3,2,1,1,1] (.node [9,8,5,5,4,4,4,3,1] (.node [9,8,5,5,4,4,4,2,1,1] (.node [9,8,5,5,4,4,4,1,1,1,1] .empty .empty) (.node [9,8,5,5,4,4,4,2,2] .empty .empty)) (.node [9,8,5,5,5,3,2,2,2,1,1] (.node [9,8,5,5,5,2,2,2,2,2,1] .empty .empty) (.node [9,8,5,5,5,3,2,2,2,2] .empty .empty))) (.node [9,8,5,5,5,4,2,2,1,1,1] (.node [9,8,5,5,5,3,3,3,1,1] (.node [9,8,5,5,5,3,3,2,2,1] .empty .empty) (.node [9,8,5,5,5,3,3,3,2] .empty .empty)) (.node [9,8,5,5,5,4,3,1,1,1,1] (.node [9,8,5,5,5,4,2,2,2,1] .empty .empty) (.node [9,8,5,5,5,4,3,2,1,1] .empty .empty)))) - -def degreeTree43_206 : RowTree := (.node [9,8,5,5,4,4,3,3,2] degreeTree43_204 degreeTree43_205) - -def degreeTree43_207 : RowTree := (.node [9,8,6,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [9,8,5,5,5,5,3,2,1] (.node [9,8,5,5,5,5,2,1,1,1,1] (.node [9,8,5,5,5,4,4,1,1,1] (.node [9,8,5,5,5,4,3,3,1] .empty .empty) (.node [9,8,5,5,5,4,4,2,1] .empty .empty)) (.node [9,8,5,5,5,5,2,2,2] (.node [9,8,5,5,5,5,2,2,1,1] .empty .empty) (.node [9,8,5,5,5,5,3,1,1,1] .empty .empty))) (.node [9,8,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,8,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,8,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,2,2,2,2,2,2,2,2,2,1,1] (.node [9,8,6,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,6,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [9,8,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,3,2,2,2,2,2,2,2,2,1] (.node [9,8,6,3,2,2,2,2,2,2,1,1,1,1,1] (.node [9,8,6,3,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,3,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,8,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_208 : RowTree := (.node [9,8,5,5,5,4,3,2,2] degreeTree43_206 degreeTree43_207) - -def degreeTree43_209 : RowTree := (.node [9,8,6,3,3,3,3,3,1,1,1,1,1] (.node [9,8,6,3,3,3,2,2,2,1,1,1,1,1] (.node [9,8,6,3,3,2,2,2,2,2,2,2] (.node [9,8,6,3,3,2,2,2,2,2,1,1,1,1] (.node [9,8,6,3,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,3,3,2,2,2,2,2,2,1,1] .empty .empty)) (.node [9,8,6,3,3,3,2,1,1,1,1,1,1,1,1,1] (.node [9,8,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,3,3,3,3,2,1,1,1,1,1,1] (.node [9,8,6,3,3,3,2,2,2,2,2,1] (.node [9,8,6,3,3,3,2,2,2,2,1,1,1] .empty .empty) (.node [9,8,6,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,3,3,3,3,2,2,2,1,1] (.node [9,8,6,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [9,8,6,3,3,3,3,2,2,2,2] .empty .empty)))) (.node [9,8,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,3,3,3,3,3,3,2] (.node [9,8,6,3,3,3,3,3,2,2,1] (.node [9,8,6,3,3,3,3,3,2,1,1,1] .empty .empty) (.node [9,8,6,3,3,3,3,3,3,1,1] .empty .empty)) (.node [9,8,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,4,2,2,2,2,2,2,2,1,1] (.node [9,8,6,4,2,2,2,2,2,1,1,1,1,1,1] (.node [9,8,6,4,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,4,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [9,8,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,4,2,2,2,2,2,2,2,2] .empty .empty) (.node [9,8,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_210 : RowTree := (.node [9,8,6,4,3,3,3,3,2,1,1] (.node [9,8,6,4,3,3,2,2,2,1,1,1,1] (.node [9,8,6,4,3,2,2,2,2,2,2,1] (.node [9,8,6,4,3,2,2,2,2,1,1,1,1,1] (.node [9,8,6,4,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,4,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,8,6,4,3,3,2,1,1,1,1,1,1,1,1] (.node [9,8,6,4,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,4,3,3,2,2,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,4,3,3,3,2,1,1,1,1,1] (.node [9,8,6,4,3,3,2,2,2,2,2] (.node [9,8,6,4,3,3,2,2,2,2,1,1] .empty .empty) (.node [9,8,6,4,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,4,3,3,3,2,2,2,1] (.node [9,8,6,4,3,3,3,2,2,1,1,1] .empty .empty) (.node [9,8,6,4,3,3,3,3,1,1,1,1] .empty .empty)))) (.node [9,8,6,4,4,2,2,2,2,2,1,1] (.node [9,8,6,4,4,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,4,3,3,3,3,3,1] (.node [9,8,6,4,3,3,3,3,2,2] .empty .empty) (.node [9,8,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,4,4,2,2,2,1,1,1,1,1,1] (.node [9,8,6,4,4,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,4,4,2,2,2,2,1,1,1,1] .empty .empty))) (.node [9,8,6,4,4,3,2,2,1,1,1,1,1] (.node [9,8,6,4,4,3,1,1,1,1,1,1,1,1,1] (.node [9,8,6,4,4,2,2,2,2,2,2] .empty .empty) (.node [9,8,6,4,4,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,4,4,3,2,2,2,2,1] (.node [9,8,6,4,4,3,2,2,2,1,1,1] .empty .empty) (.node [9,8,6,4,4,3,3,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_211 : RowTree := (.node [9,8,6,4,3,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_209 degreeTree43_210) - -def degreeTree43_212 : RowTree := (.node [9,8,6,3,3,2,2,2,1,1,1,1,1,1,1,1] degreeTree43_208 degreeTree43_211) - -def degreeTree43_213 : RowTree := (.node [9,8,6,4,4,4,2,2,2,1,1] (.node [9,8,6,4,4,3,3,3,3] (.node [9,8,6,4,4,3,3,3,1,1,1] (.node [9,8,6,4,4,3,3,2,2,2] (.node [9,8,6,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [9,8,6,4,4,3,3,3,2,1] .empty .empty)) (.node [9,8,6,4,4,4,2,1,1,1,1,1,1] (.node [9,8,6,4,4,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,4,4,4,2,2,1,1,1,1] .empty .empty))) (.node [9,8,6,4,4,4,3,2,2,1] (.node [9,8,6,4,4,4,3,1,1,1,1,1] (.node [9,8,6,4,4,4,2,2,2,2] .empty .empty) (.node [9,8,6,4,4,4,3,2,1,1,1] .empty .empty)) (.node [9,8,6,4,4,4,3,3,2] (.node [9,8,6,4,4,4,3,3,1,1] .empty .empty) (.node [9,8,6,4,4,4,4,1,1,1,1] .empty .empty)))) - -def degreeTree43_214 : RowTree := (.node [9,8,6,5,2,2,2,2,2,1,1,1,1,1] (.node [9,8,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,4,4,4,4,3,1] (.node [9,8,6,4,4,4,4,2,2] .empty .empty) (.node [9,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,5,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,8,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,5,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,5,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,5,2,2,2,2,2,2,2,1] (.node [9,8,6,5,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,8,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,5,3,2,2,2,1,1,1,1,1,1] (.node [9,8,6,5,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,5,3,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree43_215 : RowTree := (.node [9,8,6,4,4,4,4,2,1,1] degreeTree43_213 degreeTree43_214) - -def degreeTree43_216 : RowTree := (.node [9,8,6,5,4,2,2,1,1,1,1,1,1,1] (.node [9,8,6,5,3,3,3,2,1,1,1,1] (.node [9,8,6,5,3,3,2,2,1,1,1,1,1] (.node [9,8,6,5,3,3,1,1,1,1,1,1,1,1,1] (.node [9,8,6,5,3,2,2,2,2,2,2] .empty .empty) (.node [9,8,6,5,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,5,3,3,2,2,2,2,1] (.node [9,8,6,5,3,3,2,2,2,1,1,1] .empty .empty) (.node [9,8,6,5,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,5,3,3,3,3,2,1] (.node [9,8,6,5,3,3,3,2,2,2] (.node [9,8,6,5,3,3,3,2,2,1,1] .empty .empty) (.node [9,8,6,5,3,3,3,3,1,1,1] .empty .empty)) (.node [9,8,6,5,4,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,5,3,3,3,3,3] .empty .empty) (.node [9,8,6,5,4,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,8,6,5,4,3,2,2,2,2] (.node [9,8,6,5,4,3,1,1,1,1,1,1,1,1] (.node [9,8,6,5,4,2,2,2,2,1,1,1] (.node [9,8,6,5,4,2,2,2,1,1,1,1,1] .empty .empty) (.node [9,8,6,5,4,2,2,2,2,2,1] .empty .empty)) (.node [9,8,6,5,4,3,2,2,1,1,1,1] (.node [9,8,6,5,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,5,4,3,2,2,2,1,1] .empty .empty))) (.node [9,8,6,5,4,3,3,3,1,1] (.node [9,8,6,5,4,3,3,2,1,1,1] (.node [9,8,6,5,4,3,3,1,1,1,1,1] .empty .empty) (.node [9,8,6,5,4,3,3,2,2,1] .empty .empty)) (.node [9,8,6,5,4,4,1,1,1,1,1,1,1] (.node [9,8,6,5,4,3,3,3,2] .empty .empty) (.node [9,8,6,5,4,4,2,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_217 : RowTree := (.node [9,8,6,5,3,2,2,2,2,2,1,1] degreeTree43_215 degreeTree43_216) - -def degreeTree43_218 : RowTree := (.node [9,8,6,5,5,3,2,2,1,1,1] (.node [9,8,6,5,5,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,5,4,4,3,2,2] (.node [9,8,6,5,4,4,3,1,1,1,1] (.node [9,8,6,5,4,4,2,2,2,1] .empty .empty) (.node [9,8,6,5,4,4,3,2,1,1] .empty .empty)) (.node [9,8,6,5,4,4,4,1,1,1] (.node [9,8,6,5,4,4,3,3,1] .empty .empty) (.node [9,8,6,5,4,4,4,2,1] .empty .empty))) (.node [9,8,6,5,5,2,2,2,2,1,1] (.node [9,8,6,5,5,2,2,1,1,1,1,1,1] (.node [9,8,6,5,5,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,5,5,2,2,2,1,1,1,1] .empty .empty)) (.node [9,8,6,5,5,3,1,1,1,1,1,1,1] (.node [9,8,6,5,5,2,2,2,2,2] .empty .empty) (.node [9,8,6,5,5,3,2,1,1,1,1,1] .empty .empty)))) (.node [9,8,6,5,5,4,2,2,1,1] (.node [9,8,6,5,5,3,3,2,2] (.node [9,8,6,5,5,3,3,1,1,1,1] (.node [9,8,6,5,5,3,2,2,2,1] .empty .empty) (.node [9,8,6,5,5,3,3,2,1,1] .empty .empty)) (.node [9,8,6,5,5,4,1,1,1,1,1,1] (.node [9,8,6,5,5,3,3,3,1] .empty .empty) (.node [9,8,6,5,5,4,2,1,1,1,1] .empty .empty))) (.node [9,8,6,5,5,5,1,1,1,1,1] (.node [9,8,6,5,5,4,3,1,1,1] (.node [9,8,6,5,5,4,2,2,2] .empty .empty) (.node [9,8,6,5,5,4,3,2,1] .empty .empty)) (.node [9,8,6,5,5,5,2,2,1] (.node [9,8,6,5,5,5,2,1,1,1] .empty .empty) (.node [9,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_219 : RowTree := (.node [9,8,6,6,3,3,2,2,2,1,1] (.node [9,8,6,6,3,2,1,1,1,1,1,1,1,1,1] (.node [9,8,6,6,2,2,2,2,2,1,1,1,1] (.node [9,8,6,6,2,2,2,1,1,1,1,1,1,1,1] (.node [9,8,6,6,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,6,2,2,2,2,2,2,2] (.node [9,8,6,6,2,2,2,2,2,2,1,1] .empty .empty) (.node [9,8,6,6,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,6,3,2,2,2,2,2,1] (.node [9,8,6,6,3,2,2,2,1,1,1,1,1] (.node [9,8,6,6,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,3,2,2,2,2,1,1,1] .empty .empty)) (.node [9,8,6,6,3,3,2,1,1,1,1,1,1] (.node [9,8,6,6,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,3,3,2,2,1,1,1,1] .empty .empty)))) (.node [9,8,6,6,4,2,1,1,1,1,1,1,1,1] (.node [9,8,6,6,3,3,3,2,2,1] (.node [9,8,6,6,3,3,3,1,1,1,1,1] (.node [9,8,6,6,3,3,2,2,2,2] .empty .empty) (.node [9,8,6,6,3,3,3,2,1,1,1] .empty .empty)) (.node [9,8,6,6,3,3,3,3,2] (.node [9,8,6,6,3,3,3,3,1,1] .empty .empty) (.node [9,8,6,6,4,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,6,4,2,2,2,2,2] (.node [9,8,6,6,4,2,2,2,1,1,1,1] (.node [9,8,6,6,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,4,2,2,2,2,1,1] .empty .empty)) (.node [9,8,6,6,4,3,2,1,1,1,1,1] (.node [9,8,6,6,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,4,3,2,2,1,1,1] .empty .empty))))) - -def degreeTree43_220 : RowTree := (.node [9,8,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_218 degreeTree43_219) - -def degreeTree43_221 : RowTree := (.node [9,8,6,5,4,4,2,2,1,1,1] degreeTree43_217 degreeTree43_220) - -def degreeTree43_222 : RowTree := (.node [9,8,6,4,4,3,3,2,1,1,1,1] degreeTree43_212 degreeTree43_221) - -def degreeTree43_223 : RowTree := (.node [9,8,6,6,4,4,3,1,1,1] (.node [9,8,6,6,4,4,1,1,1,1,1,1] (.node [9,8,6,6,4,3,3,2,2] (.node [9,8,6,6,4,3,3,2,1,1] (.node [9,8,6,6,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [9,8,6,6,4,3,3,3,1] .empty .empty)) (.node [9,8,6,6,4,4,2,2,1,1] (.node [9,8,6,6,4,4,2,1,1,1,1] .empty .empty) (.node [9,8,6,6,4,4,2,2,2] .empty .empty))) (.node [9,8,6,6,5,2,2,1,1,1,1,1] (.node [9,8,6,6,5,1,1,1,1,1,1,1,1,1] (.node [9,8,6,6,4,4,3,2,1] .empty .empty) (.node [9,8,6,6,5,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,6,5,2,2,2,2,1] (.node [9,8,6,6,5,2,2,2,1,1,1] .empty .empty) (.node [9,8,6,6,5,3,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_224 : RowTree := (.node [9,8,6,6,5,5,1,1,1,1] (.node [9,8,6,6,5,3,3,2,1] (.node [9,8,6,6,5,3,2,2,2] (.node [9,8,6,6,5,3,2,2,1,1] .empty .empty) (.node [9,8,6,6,5,3,3,1,1,1] .empty .empty)) (.node [9,8,6,6,5,4,2,1,1,1] (.node [9,8,6,6,5,4,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,5,4,2,2,1] .empty .empty))) (.node [9,8,6,6,6,2,2,2,1,1] (.node [9,8,6,6,6,2,1,1,1,1,1,1] (.node [9,8,6,6,6,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,6,2,2,1,1,1,1] .empty .empty)) (.node [9,8,6,6,6,3,1,1,1,1,1] (.node [9,8,6,6,6,2,2,2,2] .empty .empty) (.node [9,8,6,6,6,3,2,1,1,1] .empty .empty)))) - -def degreeTree43_225 : RowTree := (.node [9,8,6,6,5,3,2,1,1,1,1] degreeTree43_223 degreeTree43_224) - -def degreeTree43_226 : RowTree := (.node [9,8,7,3,2,2,2,2,2,1,1,1,1,1,1] (.node [9,8,7,2,2,2,2,2,2,2,1,1,1,1,1] (.node [9,8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,8,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,2,2,2,2,2,2,2,2,2,1] (.node [9,8,7,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,8,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,8,7,3,3,2,2,2,2,1,1,1,1,1] (.node [9,8,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,3,2,2,2,2,2,2,2,1,1] (.node [9,8,7,3,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,7,3,2,2,2,2,2,2,2,2] .empty .empty)) (.node [9,8,7,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [9,8,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,7,3,3,3,2,1,1,1,1,1,1,1,1] (.node [9,8,7,3,3,2,2,2,2,2,2,1] (.node [9,8,7,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,8,7,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,3,3,3,2,2,2,1,1,1,1] (.node [9,8,7,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,3,3,3,2,2,2,2,1,1] .empty .empty))))) - -def degreeTree43_227 : RowTree := (.node [9,8,6,6,6,4,1,1,1,1] degreeTree43_225 degreeTree43_226) - -def degreeTree43_228 : RowTree := (.node [9,8,7,4,2,2,2,2,2,2,2,1] (.node [9,8,7,3,3,3,3,3,3,1] (.node [9,8,7,3,3,3,3,2,2,2,1] (.node [9,8,7,3,3,3,3,2,1,1,1,1,1] (.node [9,8,7,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,3,3,3,3,2,2,1,1,1] .empty .empty)) (.node [9,8,7,3,3,3,3,3,2,1,1] (.node [9,8,7,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [9,8,7,3,3,3,3,3,2,2] .empty .empty))) (.node [9,8,7,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,8,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,4,2,2,2,2,2,1,1,1,1,1] (.node [9,8,7,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,2,2,2,2,2,2,1,1,1] .empty .empty)))) (.node [9,8,7,4,3,3,1,1,1,1,1,1,1,1,1] (.node [9,8,7,4,3,2,2,2,1,1,1,1,1,1] (.node [9,8,7,4,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,4,3,2,2,2,2,2,1,1] (.node [9,8,7,4,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,7,4,3,2,2,2,2,2,2] .empty .empty))) (.node [9,8,7,4,3,3,2,2,2,2,1] (.node [9,8,7,4,3,3,2,2,1,1,1,1,1] (.node [9,8,7,4,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,3,3,2,2,2,1,1,1] .empty .empty)) (.node [9,8,7,4,3,3,3,2,1,1,1,1] (.node [9,8,7,4,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,3,3,3,2,2,1,1] .empty .empty))))) - -def degreeTree43_229 : RowTree := (.node [9,8,7,4,4,3,3,2,1,1,1] (.node [9,8,7,4,4,2,2,2,2,1,1,1] (.node [9,8,7,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,4,3,3,3,3,2,1] (.node [9,8,7,4,3,3,3,3,1,1,1] .empty .empty) (.node [9,8,7,4,3,3,3,3,3] .empty .empty)) (.node [9,8,7,4,4,2,2,1,1,1,1,1,1,1] (.node [9,8,7,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,4,2,2,2,1,1,1,1,1] .empty .empty))) (.node [9,8,7,4,4,3,2,2,1,1,1,1] (.node [9,8,7,4,4,3,1,1,1,1,1,1,1,1] (.node [9,8,7,4,4,2,2,2,2,2,1] .empty .empty) (.node [9,8,7,4,4,3,2,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,4,4,3,2,2,2,2] (.node [9,8,7,4,4,3,2,2,2,1,1] .empty .empty) (.node [9,8,7,4,4,3,3,1,1,1,1,1] .empty .empty)))) (.node [9,8,7,4,4,4,3,1,1,1,1] (.node [9,8,7,4,4,4,1,1,1,1,1,1,1] (.node [9,8,7,4,4,3,3,3,1,1] (.node [9,8,7,4,4,3,3,2,2,1] .empty .empty) (.node [9,8,7,4,4,3,3,3,2] .empty .empty)) (.node [9,8,7,4,4,4,2,2,1,1,1] (.node [9,8,7,4,4,4,2,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,4,4,2,2,2,1] .empty .empty))) (.node [9,8,7,4,4,4,4,1,1,1] (.node [9,8,7,4,4,4,3,2,2] (.node [9,8,7,4,4,4,3,2,1,1] .empty .empty) (.node [9,8,7,4,4,4,3,3,1] .empty .empty)) (.node [9,8,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,4,4,4,4,2,1] .empty .empty) (.node [9,8,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_230 : RowTree := (.node [9,8,7,4,3,3,3,2,2,2] degreeTree43_228 degreeTree43_229) - -def degreeTree43_231 : RowTree := (.node [9,8,7,3,3,3,2,2,2,2,2] degreeTree43_227 degreeTree43_230) - -def degreeTree43_232 : RowTree := (.node [9,8,7,5,3,2,2,2,1,1,1,1,1] (.node [9,8,7,5,2,2,2,2,2,2,2] (.node [9,8,7,5,2,2,2,2,2,1,1,1,1] (.node [9,8,7,5,2,2,2,2,1,1,1,1,1,1] (.node [9,8,7,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,8,7,5,2,2,2,2,2,2,1,1] .empty .empty)) (.node [9,8,7,5,3,2,1,1,1,1,1,1,1,1,1] (.node [9,8,7,5,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,5,3,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,7,5,3,3,2,1,1,1,1,1,1] (.node [9,8,7,5,3,2,2,2,2,2,1] (.node [9,8,7,5,3,2,2,2,2,1,1,1] .empty .empty) (.node [9,8,7,5,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,5,3,3,2,2,2,1,1] (.node [9,8,7,5,3,3,2,2,1,1,1,1] .empty .empty) (.node [9,8,7,5,3,3,2,2,2,2] .empty .empty)))) - -def degreeTree43_233 : RowTree := (.node [9,8,7,5,4,2,2,2,1,1,1,1] (.node [9,8,7,5,3,3,3,3,2] (.node [9,8,7,5,3,3,3,2,2,1] (.node [9,8,7,5,3,3,3,2,1,1,1] .empty .empty) (.node [9,8,7,5,3,3,3,3,1,1] .empty .empty)) (.node [9,8,7,5,4,2,1,1,1,1,1,1,1,1] (.node [9,8,7,5,4,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,5,4,2,2,1,1,1,1,1,1] .empty .empty))) (.node [9,8,7,5,4,3,2,1,1,1,1,1] (.node [9,8,7,5,4,2,2,2,2,2] (.node [9,8,7,5,4,2,2,2,2,1,1] .empty .empty) (.node [9,8,7,5,4,3,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,5,4,3,2,2,2,1] (.node [9,8,7,5,4,3,2,2,1,1,1] .empty .empty) (.node [9,8,7,5,4,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree43_234 : RowTree := (.node [9,8,7,5,3,3,3,1,1,1,1,1] degreeTree43_232 degreeTree43_233) - -def degreeTree43_235 : RowTree := (.node [9,8,7,5,5,3,2,2,1,1] (.node [9,8,7,5,4,4,3,2,1] (.node [9,8,7,5,4,4,2,1,1,1,1] (.node [9,8,7,5,4,3,3,3,1] (.node [9,8,7,5,4,3,3,2,2] .empty .empty) (.node [9,8,7,5,4,4,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,5,4,4,2,2,2] (.node [9,8,7,5,4,4,2,2,1,1] .empty .empty) (.node [9,8,7,5,4,4,3,1,1,1] .empty .empty))) (.node [9,8,7,5,5,2,2,2,1,1,1] (.node [9,8,7,5,5,2,1,1,1,1,1,1,1] (.node [9,8,7,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,5,5,2,2,1,1,1,1,1] .empty .empty)) (.node [9,8,7,5,5,3,1,1,1,1,1,1] (.node [9,8,7,5,5,2,2,2,2,1] .empty .empty) (.node [9,8,7,5,5,3,2,1,1,1,1] .empty .empty)))) (.node [9,8,7,6,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,5,5,4,1,1,1,1,1] (.node [9,8,7,5,5,3,3,1,1,1] (.node [9,8,7,5,5,3,2,2,2] .empty .empty) (.node [9,8,7,5,5,3,3,2,1] .empty .empty)) (.node [9,8,7,5,5,5,1,1,1,1] (.node [9,8,7,5,5,4,2,1,1,1] .empty .empty) (.node [9,8,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,7,6,2,2,2,2,2,1,1,1] (.node [9,8,7,6,2,2,2,1,1,1,1,1,1,1] (.node [9,8,7,6,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [9,8,7,6,3,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,6,2,2,2,2,2,2,1] .empty .empty) (.node [9,8,7,6,3,2,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_236 : RowTree := (.node [9,8,7,5,4,3,3,2,1,1] degreeTree43_234 degreeTree43_235) - -def degreeTree43_237 : RowTree := (.node [9,8,7,6,4,2,2,2,2,1] (.node [9,8,7,6,3,3,3,1,1,1,1] (.node [9,8,7,6,3,3,1,1,1,1,1,1,1] (.node [9,8,7,6,3,2,2,2,2,1,1] (.node [9,8,7,6,3,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,7,6,3,2,2,2,2,2] .empty .empty)) (.node [9,8,7,6,3,3,2,2,1,1,1] (.node [9,8,7,6,3,3,2,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,3,3,2,2,2,1] .empty .empty))) (.node [9,8,7,6,4,1,1,1,1,1,1,1,1,1] (.node [9,8,7,6,3,3,3,2,2] (.node [9,8,7,6,3,3,3,2,1,1] .empty .empty) (.node [9,8,7,6,3,3,3,3,1] .empty .empty)) (.node [9,8,7,6,4,2,2,1,1,1,1,1] (.node [9,8,7,6,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,4,2,2,2,1,1,1] .empty .empty)))) (.node [9,8,7,6,5,1,1,1,1,1,1,1,1] (.node [9,8,7,6,4,3,2,2,2] (.node [9,8,7,6,4,3,2,1,1,1,1] (.node [9,8,7,6,4,3,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,4,3,2,2,1,1] .empty .empty)) (.node [9,8,7,6,4,4,1,1,1,1,1] (.node [9,8,7,6,4,3,3,1,1,1] .empty .empty) (.node [9,8,7,6,4,4,2,1,1,1] .empty .empty))) (.node [9,8,7,6,5,2,2,2,2] (.node [9,8,7,6,5,2,2,1,1,1,1] (.node [9,8,7,6,5,2,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,5,2,2,2,1,1] .empty .empty)) (.node [9,8,7,6,5,3,2,1,1,1] (.node [9,8,7,6,5,3,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,5,4,1,1,1,1] .empty .empty))))) - -def degreeTree43_238 : RowTree := (.node [9,8,7,7,3,3,1,1,1,1,1,1] (.node [9,8,7,7,2,2,2,2,1,1,1,1] (.node [9,8,7,7,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,6,6,2,2,1,1,1] (.node [9,8,7,6,6,2,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,6,3,1,1,1,1] .empty .empty)) (.node [9,8,7,7,2,2,1,1,1,1,1,1,1,1] (.node [9,8,7,7,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,7,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [9,8,7,7,3,2,1,1,1,1,1,1,1] (.node [9,8,7,7,2,2,2,2,2,2] (.node [9,8,7,7,2,2,2,2,2,1,1] .empty .empty) (.node [9,8,7,7,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,7,3,2,2,2,1,1,1] (.node [9,8,7,7,3,2,2,1,1,1,1,1] .empty .empty) (.node [9,8,7,7,3,2,2,2,2,1] .empty .empty)))) (.node [9,8,7,7,4,2,2,2,1,1] (.node [9,8,7,7,3,3,3,1,1,1] (.node [9,8,7,7,3,3,2,2,1,1] (.node [9,8,7,7,3,3,2,1,1,1,1] .empty .empty) (.node [9,8,7,7,3,3,2,2,2] .empty .empty)) (.node [9,8,7,7,4,2,1,1,1,1,1,1] (.node [9,8,7,7,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,7,4,2,2,1,1,1,1] .empty .empty))) (.node [9,8,7,7,4,4,1,1,1,1] (.node [9,8,7,7,4,3,1,1,1,1,1] (.node [9,8,7,7,4,2,2,2,2] .empty .empty) (.node [9,8,7,7,4,3,2,1,1,1] .empty .empty)) (.node [9,8,7,7,5,2,1,1,1,1,1] (.node [9,8,7,7,5,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,7,5,2,2,1,1,1] .empty .empty))))) - -def degreeTree43_239 : RowTree := (.node [9,8,7,6,6,1,1,1,1,1,1,1] degreeTree43_237 degreeTree43_238) - -def degreeTree43_240 : RowTree := (.node [9,8,7,6,3,2,2,1,1,1,1,1,1] degreeTree43_236 degreeTree43_239) - -def degreeTree43_241 : RowTree := (.node [9,8,7,5,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_231 degreeTree43_240) - -def degreeTree43_242 : RowTree := (.node [9,8,6,6,4,3,2,2,2,1] degreeTree43_222 degreeTree43_241) - -def degreeTree43_243 : RowTree := (.node [9,8,5,5,3,3,2,2,2,2,2] degreeTree43_203 degreeTree43_242) - -def degreeTree43_244 : RowTree := (.node [9,8,8,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [9,8,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,7,7,1,1,1,1,1] (.node [9,8,7,7,6,2,1,1,1,1] (.node [9,8,7,7,6,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,8,2,2,2,2,2,2,2,2,2] (.node [9,8,8,2,2,2,2,2,2,2,1,1,1,1] (.node [9,8,8,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [9,8,8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_245 : RowTree := (.node [9,8,8,3,3,2,2,2,1,1,1,1,1,1] (.node [9,8,8,3,2,2,2,2,2,2,2,1] (.node [9,8,8,3,2,2,2,2,2,1,1,1,1,1] (.node [9,8,8,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,3,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,8,8,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,8,3,3,3,1,1,1,1,1,1,1,1,1] (.node [9,8,8,3,3,2,2,2,2,2,1,1] (.node [9,8,8,3,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,3,3,2,2,2,2,2,2] .empty .empty)) (.node [9,8,8,3,3,3,2,2,1,1,1,1,1] (.node [9,8,8,3,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,3,3,3,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree43_246 : RowTree := (.node [9,8,8,3,2,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_244 degreeTree43_245) - -def degreeTree43_247 : RowTree := (.node [9,8,8,4,3,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,3,3,3,3,2,2,2] (.node [9,8,8,3,3,3,3,2,1,1,1,1] (.node [9,8,8,3,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,3,3,3,3,2,2,1,1] .empty .empty)) (.node [9,8,8,3,3,3,3,3,2,1] (.node [9,8,8,3,3,3,3,3,1,1,1] .empty .empty) (.node [9,8,8,3,3,3,3,3,3] .empty .empty))) (.node [9,8,8,4,2,2,2,2,1,1,1,1,1,1] (.node [9,8,8,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,4,2,2,2,2,2,2,1,1] (.node [9,8,8,4,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,4,2,2,2,2,2,2,2] .empty .empty)))) (.node [9,8,8,4,3,3,2,2,1,1,1,1] (.node [9,8,8,4,3,2,2,2,2,1,1,1] (.node [9,8,8,4,3,2,2,1,1,1,1,1,1,1] (.node [9,8,8,4,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,4,3,2,2,2,1,1,1,1,1] .empty .empty)) (.node [9,8,8,4,3,3,1,1,1,1,1,1,1,1] (.node [9,8,8,4,3,2,2,2,2,2,1] .empty .empty) (.node [9,8,8,4,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [9,8,8,4,3,3,3,2,1,1,1] (.node [9,8,8,4,3,3,2,2,2,2] (.node [9,8,8,4,3,3,2,2,2,1,1] .empty .empty) (.node [9,8,8,4,3,3,3,1,1,1,1,1] .empty .empty)) (.node [9,8,8,4,3,3,3,3,1,1] (.node [9,8,8,4,3,3,3,2,2,1] .empty .empty) (.node [9,8,8,4,3,3,3,3,2] .empty .empty))))) - -def degreeTree43_248 : RowTree := (.node [9,8,8,3,3,3,2,2,2,2,1] degreeTree43_246 degreeTree43_247) - -def degreeTree43_249 : RowTree := (.node [9,8,8,4,4,4,2,2,1,1] (.node [9,8,8,4,4,3,2,2,1,1,1] (.node [9,8,8,4,4,2,2,2,2,1,1] (.node [9,8,8,4,4,2,2,1,1,1,1,1,1] (.node [9,8,8,4,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,4,4,2,2,2,1,1,1,1] .empty .empty)) (.node [9,8,8,4,4,3,1,1,1,1,1,1,1] (.node [9,8,8,4,4,2,2,2,2,2] .empty .empty) (.node [9,8,8,4,4,3,2,1,1,1,1,1] .empty .empty))) (.node [9,8,8,4,4,3,3,2,2] (.node [9,8,8,4,4,3,3,1,1,1,1] (.node [9,8,8,4,4,3,2,2,2,1] .empty .empty) (.node [9,8,8,4,4,3,3,2,1,1] .empty .empty)) (.node [9,8,8,4,4,4,1,1,1,1,1,1] (.node [9,8,8,4,4,3,3,3,1] .empty .empty) (.node [9,8,8,4,4,4,2,1,1,1,1] .empty .empty)))) (.node [9,8,8,5,2,2,2,2,2,1,1,1] (.node [9,8,8,5,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,4,4,4,3,1,1,1] (.node [9,8,8,4,4,4,2,2,2] .empty .empty) (.node [9,8,8,5,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,5,2,2,2,1,1,1,1,1,1,1] (.node [9,8,8,5,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,5,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [9,8,8,5,3,2,2,1,1,1,1,1,1] (.node [9,8,8,5,3,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,5,2,2,2,2,2,2,1] .empty .empty) (.node [9,8,8,5,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,5,3,2,2,2,2,1,1] (.node [9,8,8,5,3,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,5,3,2,2,2,2,2] .empty .empty))))) - -def degreeTree43_250 : RowTree := (.node [9,8,8,5,4,3,3,1,1,1] (.node [9,8,8,5,4,2,1,1,1,1,1,1,1] (.node [9,8,8,5,3,3,3,1,1,1,1] (.node [9,8,8,5,3,3,2,2,1,1,1] (.node [9,8,8,5,3,3,2,1,1,1,1,1] .empty .empty) (.node [9,8,8,5,3,3,2,2,2,1] .empty .empty)) (.node [9,8,8,5,3,3,3,2,2] (.node [9,8,8,5,3,3,3,2,1,1] .empty .empty) (.node [9,8,8,5,4,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,8,5,4,3,1,1,1,1,1,1] (.node [9,8,8,5,4,2,2,2,1,1,1] (.node [9,8,8,5,4,2,2,1,1,1,1,1] .empty .empty) (.node [9,8,8,5,4,2,2,2,2,1] .empty .empty)) (.node [9,8,8,5,4,3,2,2,1,1] (.node [9,8,8,5,4,3,2,1,1,1,1] .empty .empty) (.node [9,8,8,5,4,3,2,2,2] .empty .empty)))) (.node [9,8,8,5,5,3,1,1,1,1,1] (.node [9,8,8,5,5,2,1,1,1,1,1,1] (.node [9,8,8,5,4,4,2,1,1,1] (.node [9,8,8,5,4,4,1,1,1,1,1] .empty .empty) (.node [9,8,8,5,5,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,5,5,2,2,2,1,1] (.node [9,8,8,5,5,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,5,5,2,2,2,2] .empty .empty))) (.node [9,8,8,6,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,5,5,4,1,1,1,1] (.node [9,8,8,5,5,3,2,1,1,1] .empty .empty) (.node [9,8,8,6,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,6,2,2,2,1,1,1,1,1,1] (.node [9,8,8,6,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,6,2,2,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_251 : RowTree := (.node [9,8,8,5,3,3,1,1,1,1,1,1,1] degreeTree43_249 degreeTree43_250) - -def degreeTree43_252 : RowTree := (.node [9,8,8,4,4,1,1,1,1,1,1,1,1,1,1] degreeTree43_248 degreeTree43_251) - -def degreeTree43_253 : RowTree := (.node [9,8,8,6,3,3,2,2,1,1] (.node [9,8,8,6,3,2,2,2,1,1,1] (.node [9,8,8,6,3,2,1,1,1,1,1,1,1] (.node [9,8,8,6,3,1,1,1,1,1,1,1,1,1] (.node [9,8,8,6,2,2,2,2,2,2] .empty .empty) .empty) (.node [9,8,8,6,3,2,2,1,1,1,1,1] .empty .empty)) (.node [9,8,8,6,3,3,1,1,1,1,1,1] (.node [9,8,8,6,3,2,2,2,2,1] .empty .empty) (.node [9,8,8,6,3,3,2,1,1,1,1] .empty .empty))) (.node [9,8,8,6,4,2,1,1,1,1,1,1] (.node [9,8,8,6,3,3,3,1,1,1] (.node [9,8,8,6,3,3,2,2,2] .empty .empty) (.node [9,8,8,6,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,6,4,2,2,2,1,1] (.node [9,8,8,6,4,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,6,4,2,2,2,2] .empty .empty)))) - -def degreeTree43_254 : RowTree := (.node [9,8,8,6,6,2,1,1,1,1] (.node [9,8,8,6,5,2,1,1,1,1,1] (.node [9,8,8,6,4,4,1,1,1,1] (.node [9,8,8,6,4,3,2,1,1,1] .empty .empty) (.node [9,8,8,6,5,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,6,5,3,1,1,1,1] (.node [9,8,8,6,5,2,2,1,1,1] .empty .empty) (.node [9,8,8,6,6,1,1,1,1,1,1] .empty .empty))) (.node [9,8,8,7,2,2,2,1,1,1,1,1] (.node [9,8,8,7,2,1,1,1,1,1,1,1,1,1] (.node [9,8,8,7,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,7,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,7,2,2,2,2,2,1] (.node [9,8,8,7,2,2,2,2,1,1,1] .empty .empty) (.node [9,8,8,7,3,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_255 : RowTree := (.node [9,8,8,6,4,3,1,1,1,1,1] degreeTree43_253 degreeTree43_254) - -def degreeTree43_256 : RowTree := (.node [9,8,8,8,2,2,2,1,1,1,1] (.node [9,8,8,7,4,2,2,1,1,1] (.node [9,8,8,7,3,3,1,1,1,1,1] (.node [9,8,8,7,3,2,2,2,1,1] (.node [9,8,8,7,3,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,7,3,2,2,2,2] .empty .empty)) (.node [9,8,8,7,4,1,1,1,1,1,1,1] (.node [9,8,8,7,3,3,2,1,1,1] .empty .empty) (.node [9,8,8,7,4,2,1,1,1,1,1] .empty .empty))) (.node [9,8,8,7,6,1,1,1,1,1] (.node [9,8,8,7,5,1,1,1,1,1,1] (.node [9,8,8,7,4,3,1,1,1,1] .empty .empty) (.node [9,8,8,7,5,2,1,1,1,1] .empty .empty)) (.node [9,8,8,8,2,1,1,1,1,1,1,1,1] (.node [9,8,8,8,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,8,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [9,8,8,8,4,2,1,1,1,1] (.node [9,8,8,8,3,2,1,1,1,1,1] (.node [9,8,8,8,2,2,2,2,2] (.node [9,8,8,8,2,2,2,2,1,1] .empty .empty) (.node [9,8,8,8,3,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,8,3,3,1,1,1,1] (.node [9,8,8,8,3,2,2,1,1,1] .empty .empty) (.node [9,8,8,8,4,1,1,1,1,1,1] .empty .empty))) (.node [9,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,8,5,1,1,1,1,1] .empty .empty) (.node [9,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_257 : RowTree := (.node [9,8,8,7,3,2,1,1,1,1,1,1] degreeTree43_255 degreeTree43_256) - -def degreeTree43_258 : RowTree := (.node [9,9,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [9,9,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [9,9,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,3,2,2,2,2,2,2,2,2,2,2,2] (.node [9,9,3,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [9,9,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [9,9,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,9,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,3,3,2,2,2,2,2,2,2,1,1,1,1,1] (.node [9,9,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,3,3,2,2,2,2,2,2,2,2,2,1] (.node [9,9,3,3,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,3,3,3,2,2,2,2,2,1,1,1,1,1,1] (.node [9,9,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,3,3,3,2,2,2,2,2,2,2,1,1] (.node [9,9,3,3,3,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,9,3,3,3,2,2,2,2,2,2,2,2] .empty .empty))))) - -def degreeTree43_259 : RowTree := (.node [9,9,3,3,3,3,3,3,2,2,2,1] (.node [9,9,3,3,3,3,3,2,1,1,1,1,1,1,1,1] (.node [9,9,3,3,3,3,2,2,2,2,1,1,1,1,1] (.node [9,9,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,3,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,3,3,3,3,2,2,2,2,2,2,1] (.node [9,9,3,3,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,3,3,3,3,3,2,2,2,2,2] (.node [9,9,3,3,3,3,3,2,2,2,1,1,1,1] (.node [9,9,3,3,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,3,3,3,3,2,2,2,2,1,1] .empty .empty)) (.node [9,9,3,3,3,3,3,3,2,1,1,1,1,1] (.node [9,9,3,3,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,3,3,3,3,3,2,2,1,1,1] .empty .empty)))) (.node [9,9,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,3,3,3,3,3,3,3,3,1] (.node [9,9,3,3,3,3,3,3,3,2,1,1] (.node [9,9,3,3,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [9,9,3,3,3,3,3,3,3,2,2] .empty .empty)) (.node [9,9,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,4,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [9,9,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,2,2,2,2,2,2,2,2,2,2,1] (.node [9,9,4,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_260 : RowTree := (.node [9,9,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_258 degreeTree43_259) - -def degreeTree43_261 : RowTree := (.node [9,9,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] degreeTree43_257 degreeTree43_260) - -def degreeTree43_262 : RowTree := (.node [9,8,8,6,2,2,2,2,2,1,1] degreeTree43_252 degreeTree43_261) - -def degreeTree43_263 : RowTree := (.node [9,9,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [9,9,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,9,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,3,2,2,2,2,2,2,2,2,1,1] (.node [9,9,4,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,9,4,3,2,2,2,2,2,2,2,2,2] .empty .empty))) (.node [9,9,4,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [9,9,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,3,3,2,2,2,2,2,2,1,1,1] (.node [9,9,4,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [9,9,4,3,3,2,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree43_264 : RowTree := (.node [9,9,4,3,3,3,3,2,1,1,1,1,1,1,1] (.node [9,9,4,3,3,3,2,2,2,2,1,1,1,1] (.node [9,9,4,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [9,9,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,3,3,3,2,2,2,2,2,2] (.node [9,9,4,3,3,3,2,2,2,2,2,1,1] .empty .empty) (.node [9,9,4,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,4,3,3,3,3,3,1,1,1,1,1,1] (.node [9,9,4,3,3,3,3,2,2,2,1,1,1] (.node [9,9,4,3,3,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [9,9,4,3,3,3,3,2,2,2,2,1] .empty .empty)) (.node [9,9,4,3,3,3,3,3,2,2,1,1] (.node [9,9,4,3,3,3,3,3,2,1,1,1,1] .empty .empty) (.node [9,9,4,3,3,3,3,3,2,2,2] .empty .empty)))) - -def degreeTree43_265 : RowTree := (.node [9,9,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_263 degreeTree43_264) - -def degreeTree43_266 : RowTree := (.node [9,9,4,4,3,2,2,2,2,1,1,1,1,1,1] (.node [9,9,4,4,2,2,2,2,2,1,1,1,1,1,1,1] (.node [9,9,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,3,3,3,3,3,3,3] (.node [9,9,4,3,3,3,3,3,3,2,1] .empty .empty) (.node [9,9,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,2,2,2,2,2,2,2,1,1,1] (.node [9,9,4,4,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,2,2,2,2,2,2,2,2,1] .empty .empty)) (.node [9,9,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,9,4,4,3,3,2,2,2,2,1,1,1] (.node [9,9,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,3,2,2,2,2,2,2,1,1] (.node [9,9,4,4,3,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,9,4,4,3,2,2,2,2,2,2,2] .empty .empty)) (.node [9,9,4,4,3,3,2,2,1,1,1,1,1,1,1] (.node [9,9,4,4,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,3,3,2,2,2,1,1,1,1,1] .empty .empty))) (.node [9,9,4,4,3,3,3,2,2,1,1,1,1] (.node [9,9,4,4,3,3,3,1,1,1,1,1,1,1,1] (.node [9,9,4,4,3,3,2,2,2,2,2,1] .empty .empty) (.node [9,9,4,4,3,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,4,3,3,3,2,2,2,2] (.node [9,9,4,4,3,3,3,2,2,2,1,1] .empty .empty) (.node [9,9,4,4,3,3,3,3,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_267 : RowTree := (.node [9,9,4,3,3,3,3,3,3,1,1,1] degreeTree43_265 degreeTree43_266) - -def degreeTree43_268 : RowTree := (.node [9,9,4,4,4,3,2,2,2,2,2] (.node [9,9,4,4,4,2,2,2,2,1,1,1,1,1] (.node [9,9,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,3,3,3,3,3,1,1] (.node [9,9,4,4,3,3,3,3,2,2,1] .empty .empty) (.node [9,9,4,4,3,3,3,3,3,2] .empty .empty)) (.node [9,9,4,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,4,4,4,3,2,1,1,1,1,1,1,1,1] (.node [9,9,4,4,4,2,2,2,2,2,2,1] (.node [9,9,4,4,4,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,4,4,4,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,4,4,3,2,2,2,1,1,1,1] (.node [9,9,4,4,4,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,4,3,2,2,2,2,1,1] .empty .empty)))) (.node [9,9,4,4,4,3,3,3,3,1] (.node [9,9,4,4,4,3,3,2,2,2,1] (.node [9,9,4,4,4,3,3,2,1,1,1,1,1] (.node [9,9,4,4,4,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,4,3,3,2,2,1,1,1] .empty .empty)) (.node [9,9,4,4,4,3,3,3,2,1,1] (.node [9,9,4,4,4,3,3,3,1,1,1,1] .empty .empty) (.node [9,9,4,4,4,3,3,3,2,2] .empty .empty))) (.node [9,9,4,4,4,4,2,2,2,1,1,1] (.node [9,9,4,4,4,4,2,1,1,1,1,1,1,1] (.node [9,9,4,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,4,4,2,2,1,1,1,1,1] .empty .empty)) (.node [9,9,4,4,4,4,3,1,1,1,1,1,1] (.node [9,9,4,4,4,4,2,2,2,2,1] .empty .empty) (.node [9,9,4,4,4,4,3,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_269 : RowTree := (.node [9,9,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [9,9,4,4,4,4,4,3,1,1] (.node [9,9,4,4,4,4,3,3,3] (.node [9,9,4,4,4,4,3,3,1,1,1] (.node [9,9,4,4,4,4,3,2,2,2] .empty .empty) (.node [9,9,4,4,4,4,3,3,2,1] .empty .empty)) (.node [9,9,4,4,4,4,4,2,1,1,1] (.node [9,9,4,4,4,4,4,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,4,4,4,2,2,1] .empty .empty))) (.node [9,9,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,4,4,4,3,2] .empty .empty) (.node [9,9,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,9,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,2,2,2,2,2,2,2,2,2,2] (.node [9,9,5,2,2,2,2,2,2,2,2,1,1,1,1] (.node [9,9,5,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [9,9,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,3,2,2,2,2,2,2,2,1,1,1] (.node [9,9,5,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [9,9,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [9,9,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,3,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [9,9,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_270 : RowTree := (.node [9,9,4,4,4,4,3,2,2,1,1] degreeTree43_268 degreeTree43_269) - -def degreeTree43_271 : RowTree := (.node [9,9,4,4,3,3,3,3,2,1,1,1] degreeTree43_267 degreeTree43_270) - -def degreeTree43_272 : RowTree := (.node [9,9,5,3,3,3,2,2,2,1,1,1,1,1] (.node [9,9,5,3,3,2,2,2,2,2,2,2] (.node [9,9,5,3,3,2,2,2,2,2,1,1,1,1] (.node [9,9,5,3,3,2,2,2,2,1,1,1,1,1,1] (.node [9,9,5,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,9,5,3,3,2,2,2,2,2,2,1,1] .empty .empty)) (.node [9,9,5,3,3,3,2,1,1,1,1,1,1,1,1,1] (.node [9,9,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,3,3,3,3,2,1,1,1,1,1,1] (.node [9,9,5,3,3,3,2,2,2,2,2,1] (.node [9,9,5,3,3,3,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,5,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,3,3,3,3,2,2,2,1,1] (.node [9,9,5,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [9,9,5,3,3,3,3,2,2,2,2] .empty .empty)))) - -def degreeTree43_273 : RowTree := (.node [9,9,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,3,3,3,3,3,3,2] (.node [9,9,5,3,3,3,3,3,2,2,1] (.node [9,9,5,3,3,3,3,3,2,1,1,1] .empty .empty) (.node [9,9,5,3,3,3,3,3,3,1,1] .empty .empty)) (.node [9,9,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,4,2,2,2,2,2,2,2,1,1] (.node [9,9,5,4,2,2,2,2,2,1,1,1,1,1,1] (.node [9,9,5,4,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,4,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [9,9,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,4,2,2,2,2,2,2,2,2] .empty .empty) (.node [9,9,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_274 : RowTree := (.node [9,9,5,3,3,3,3,3,1,1,1,1,1] degreeTree43_272 degreeTree43_273) - -def degreeTree43_275 : RowTree := (.node [9,9,5,4,3,3,3,3,2,1,1] (.node [9,9,5,4,3,3,2,2,2,1,1,1,1] (.node [9,9,5,4,3,2,2,2,2,2,2,1] (.node [9,9,5,4,3,2,2,2,2,1,1,1,1,1] (.node [9,9,5,4,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,4,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,9,5,4,3,3,2,1,1,1,1,1,1,1,1] (.node [9,9,5,4,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,4,3,3,2,2,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,4,3,3,3,2,1,1,1,1,1] (.node [9,9,5,4,3,3,2,2,2,2,2] (.node [9,9,5,4,3,3,2,2,2,2,1,1] .empty .empty) (.node [9,9,5,4,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,4,3,3,3,2,2,2,1] (.node [9,9,5,4,3,3,3,2,2,1,1,1] .empty .empty) (.node [9,9,5,4,3,3,3,3,1,1,1,1] .empty .empty)))) (.node [9,9,5,4,4,2,2,2,2,2,1,1] (.node [9,9,5,4,4,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,4,3,3,3,3,3,1] (.node [9,9,5,4,3,3,3,3,2,2] .empty .empty) (.node [9,9,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,4,4,2,2,2,1,1,1,1,1,1] (.node [9,9,5,4,4,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,4,4,2,2,2,2,1,1,1,1] .empty .empty))) (.node [9,9,5,4,4,3,2,2,1,1,1,1,1] (.node [9,9,5,4,4,3,1,1,1,1,1,1,1,1,1] (.node [9,9,5,4,4,2,2,2,2,2,2] .empty .empty) (.node [9,9,5,4,4,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,4,4,3,2,2,2,2,1] (.node [9,9,5,4,4,3,2,2,2,1,1,1] .empty .empty) (.node [9,9,5,4,4,3,3,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_276 : RowTree := (.node [9,9,5,4,3,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_274 degreeTree43_275) - -def degreeTree43_277 : RowTree := (.node [9,9,5,4,4,4,4,1,1,1,1] (.node [9,9,5,4,4,4,2,2,1,1,1,1] (.node [9,9,5,4,4,3,3,3,2,1] (.node [9,9,5,4,4,3,3,2,2,2] (.node [9,9,5,4,4,3,3,2,2,1,1] .empty .empty) (.node [9,9,5,4,4,3,3,3,1,1,1] .empty .empty)) (.node [9,9,5,4,4,4,1,1,1,1,1,1,1,1] (.node [9,9,5,4,4,3,3,3,3] .empty .empty) (.node [9,9,5,4,4,4,2,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,4,4,4,3,2,1,1,1] (.node [9,9,5,4,4,4,2,2,2,2] (.node [9,9,5,4,4,4,2,2,2,1,1] .empty .empty) (.node [9,9,5,4,4,4,3,1,1,1,1,1] .empty .empty)) (.node [9,9,5,4,4,4,3,3,1,1] (.node [9,9,5,4,4,4,3,2,2,1] .empty .empty) (.node [9,9,5,4,4,4,3,3,2] .empty .empty)))) (.node [9,9,5,5,2,2,2,2,2,1,1,1,1,1] (.node [9,9,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,4,4,4,4,2,2] (.node [9,9,5,4,4,4,4,2,1,1] .empty .empty) (.node [9,9,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,5,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,5,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,5,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,5,2,2,2,2,2,2,2,1] (.node [9,9,5,5,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,5,3,2,2,2,1,1,1,1,1,1] (.node [9,9,5,5,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,5,3,2,2,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_278 : RowTree := (.node [9,9,5,5,4,2,2,1,1,1,1,1,1,1] (.node [9,9,5,5,3,3,3,2,1,1,1,1] (.node [9,9,5,5,3,3,2,2,1,1,1,1,1] (.node [9,9,5,5,3,3,1,1,1,1,1,1,1,1,1] (.node [9,9,5,5,3,2,2,2,2,2,2] .empty .empty) (.node [9,9,5,5,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,5,3,3,2,2,2,2,1] (.node [9,9,5,5,3,3,2,2,2,1,1,1] .empty .empty) (.node [9,9,5,5,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,5,3,3,3,3,2,1] (.node [9,9,5,5,3,3,3,2,2,2] (.node [9,9,5,5,3,3,3,2,2,1,1] .empty .empty) (.node [9,9,5,5,3,3,3,3,1,1,1] .empty .empty)) (.node [9,9,5,5,4,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,5,3,3,3,3,3] .empty .empty) (.node [9,9,5,5,4,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,9,5,5,4,3,2,2,2,2] (.node [9,9,5,5,4,3,1,1,1,1,1,1,1,1] (.node [9,9,5,5,4,2,2,2,2,1,1,1] (.node [9,9,5,5,4,2,2,2,1,1,1,1,1] .empty .empty) (.node [9,9,5,5,4,2,2,2,2,2,1] .empty .empty)) (.node [9,9,5,5,4,3,2,2,1,1,1,1] (.node [9,9,5,5,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,5,4,3,2,2,2,1,1] .empty .empty))) (.node [9,9,5,5,4,3,3,3,1,1] (.node [9,9,5,5,4,3,3,2,1,1,1] (.node [9,9,5,5,4,3,3,1,1,1,1,1] .empty .empty) (.node [9,9,5,5,4,3,3,2,2,1] .empty .empty)) (.node [9,9,5,5,4,4,1,1,1,1,1,1,1] (.node [9,9,5,5,4,3,3,3,2] .empty .empty) (.node [9,9,5,5,4,4,2,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_279 : RowTree := (.node [9,9,5,5,3,2,2,2,2,2,1,1] degreeTree43_277 degreeTree43_278) - -def degreeTree43_280 : RowTree := (.node [9,9,5,4,4,3,3,2,1,1,1,1] degreeTree43_276 degreeTree43_279) - -def degreeTree43_281 : RowTree := (.node [9,9,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_271 degreeTree43_280) - -def degreeTree43_282 : RowTree := (.node [9,9,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_262 degreeTree43_281) - -def degreeTree43_283 : RowTree := (.node [9,9,5,5,5,2,2,2,1,1,1,1] (.node [9,9,5,5,4,4,4,1,1,1] (.node [9,9,5,5,4,4,3,2,1,1] (.node [9,9,5,5,4,4,3,1,1,1,1] (.node [9,9,5,5,4,4,2,2,2,1] .empty .empty) .empty) (.node [9,9,5,5,4,4,3,2,2] .empty .empty)) (.node [9,9,5,5,5,2,1,1,1,1,1,1,1,1] (.node [9,9,5,5,5,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,5,5,2,2,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,5,5,3,2,1,1,1,1,1] (.node [9,9,5,5,5,2,2,2,2,2] (.node [9,9,5,5,5,2,2,2,2,1,1] .empty .empty) (.node [9,9,5,5,5,3,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,5,5,3,2,2,2,1] (.node [9,9,5,5,5,3,2,2,1,1,1] .empty .empty) (.node [9,9,5,5,5,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree43_284 : RowTree := (.node [9,9,5,5,5,5,2,1,1,1] (.node [9,9,5,5,5,4,2,2,1,1] (.node [9,9,5,5,5,4,1,1,1,1,1,1] (.node [9,9,5,5,5,3,3,2,2] .empty .empty) (.node [9,9,5,5,5,4,2,1,1,1,1] .empty .empty)) (.node [9,9,5,5,5,4,3,1,1,1] (.node [9,9,5,5,5,4,2,2,2] .empty .empty) (.node [9,9,5,5,5,5,1,1,1,1,1] .empty .empty))) (.node [9,9,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_285 : RowTree := (.node [9,9,5,5,5,3,3,2,1,1] degreeTree43_283 degreeTree43_284) - -def degreeTree43_286 : RowTree := (.node [9,9,6,3,3,2,2,2,2,1,1,1,1,1] (.node [9,9,6,3,2,2,2,2,2,1,1,1,1,1,1] (.node [9,9,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,2,2,2,2,2,2,2,2,2,1] (.node [9,9,6,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,3,2,2,2,2,2,2,2,1,1] (.node [9,9,6,3,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,9,6,3,2,2,2,2,2,2,2,2] .empty .empty)) (.node [9,9,6,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,9,6,3,3,3,2,2,2,2,2] (.node [9,9,6,3,3,3,2,1,1,1,1,1,1,1,1] (.node [9,9,6,3,3,2,2,2,2,2,2,1] (.node [9,9,6,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,6,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,3,3,3,2,2,2,1,1,1,1] (.node [9,9,6,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,3,3,3,2,2,2,2,1,1] .empty .empty))) (.node [9,9,6,3,3,3,3,2,2,2,1] (.node [9,9,6,3,3,3,3,2,1,1,1,1,1] (.node [9,9,6,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,3,3,3,3,2,2,1,1,1] .empty .empty)) (.node [9,9,6,3,3,3,3,3,2,1,1] (.node [9,9,6,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [9,9,6,3,3,3,3,3,2,2] .empty .empty))))) - -def degreeTree43_287 : RowTree := (.node [9,9,6,2,2,2,2,2,2,2,1,1,1,1,1] degreeTree43_285 degreeTree43_286) - -def degreeTree43_288 : RowTree := (.node [9,9,6,4,3,3,1,1,1,1,1,1,1,1,1] (.node [9,9,6,4,2,2,2,2,2,2,2,1] (.node [9,9,6,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,4,2,2,2,2,2,1,1,1,1,1] (.node [9,9,6,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [9,9,6,4,3,2,2,2,1,1,1,1,1,1] (.node [9,9,6,4,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,4,3,2,2,2,2,2,1,1] (.node [9,9,6,4,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,9,6,4,3,2,2,2,2,2,2] .empty .empty)))) (.node [9,9,6,4,3,3,3,2,2,2] (.node [9,9,6,4,3,3,2,2,2,2,1] (.node [9,9,6,4,3,3,2,2,1,1,1,1,1] (.node [9,9,6,4,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,3,3,2,2,2,1,1,1] .empty .empty)) (.node [9,9,6,4,3,3,3,2,1,1,1,1] (.node [9,9,6,4,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,3,3,3,2,2,1,1] .empty .empty))) (.node [9,9,6,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,4,3,3,3,3,2,1] (.node [9,9,6,4,3,3,3,3,1,1,1] .empty .empty) (.node [9,9,6,4,3,3,3,3,3] .empty .empty)) (.node [9,9,6,4,4,2,2,1,1,1,1,1,1,1] (.node [9,9,6,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,4,2,2,2,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_289 : RowTree := (.node [9,9,6,4,4,4,3,1,1,1,1] (.node [9,9,6,4,4,3,3,2,1,1,1] (.node [9,9,6,4,4,3,2,2,1,1,1,1] (.node [9,9,6,4,4,3,1,1,1,1,1,1,1,1] (.node [9,9,6,4,4,2,2,2,2,2,1] .empty .empty) (.node [9,9,6,4,4,3,2,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,4,4,3,2,2,2,2] (.node [9,9,6,4,4,3,2,2,2,1,1] .empty .empty) (.node [9,9,6,4,4,3,3,1,1,1,1,1] .empty .empty))) (.node [9,9,6,4,4,4,1,1,1,1,1,1,1] (.node [9,9,6,4,4,3,3,3,1,1] (.node [9,9,6,4,4,3,3,2,2,1] .empty .empty) (.node [9,9,6,4,4,3,3,3,2] .empty .empty)) (.node [9,9,6,4,4,4,2,2,1,1,1] (.node [9,9,6,4,4,4,2,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,4,4,2,2,2,1] .empty .empty)))) (.node [9,9,6,5,2,2,2,2,1,1,1,1,1,1] (.node [9,9,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,4,4,4,3,2,2] (.node [9,9,6,4,4,4,3,2,1,1] .empty .empty) (.node [9,9,6,4,4,4,4,1,1,1] .empty .empty)) (.node [9,9,6,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,6,5,3,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,5,2,2,2,2,2,2,1,1] (.node [9,9,6,5,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,9,6,5,2,2,2,2,2,2,2] .empty .empty)) (.node [9,9,6,5,3,2,2,1,1,1,1,1,1,1] (.node [9,9,6,5,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,5,3,2,2,2,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_290 : RowTree := (.node [9,9,6,4,4,2,2,2,2,1,1,1] degreeTree43_288 degreeTree43_289) - -def degreeTree43_291 : RowTree := (.node [9,9,6,3,3,3,3,3,3,1] degreeTree43_287 degreeTree43_290) - -def degreeTree43_292 : RowTree := (.node [9,9,6,5,3,3,3,2,2,1] (.node [9,9,6,5,3,3,2,2,2,1,1] (.node [9,9,6,5,3,3,2,1,1,1,1,1,1] (.node [9,9,6,5,3,3,1,1,1,1,1,1,1,1] (.node [9,9,6,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [9,9,6,5,3,3,2,2,1,1,1,1] .empty .empty)) (.node [9,9,6,5,3,3,3,1,1,1,1,1] (.node [9,9,6,5,3,3,2,2,2,2] .empty .empty) (.node [9,9,6,5,3,3,3,2,1,1,1] .empty .empty))) (.node [9,9,6,5,4,2,1,1,1,1,1,1,1,1] (.node [9,9,6,5,3,3,3,3,2] (.node [9,9,6,5,3,3,3,3,1,1] .empty .empty) (.node [9,9,6,5,4,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,5,4,2,2,2,1,1,1,1] (.node [9,9,6,5,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,5,4,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree43_293 : RowTree := (.node [9,9,6,5,4,4,1,1,1,1,1,1] (.node [9,9,6,5,4,3,2,2,2,1] (.node [9,9,6,5,4,3,2,1,1,1,1,1] (.node [9,9,6,5,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,5,4,3,2,2,1,1,1] .empty .empty)) (.node [9,9,6,5,4,3,3,2,1,1] (.node [9,9,6,5,4,3,3,1,1,1,1] .empty .empty) (.node [9,9,6,5,4,3,3,2,2] .empty .empty))) (.node [9,9,6,5,4,4,3,1,1,1] (.node [9,9,6,5,4,4,2,2,1,1] (.node [9,9,6,5,4,4,2,1,1,1,1] .empty .empty) (.node [9,9,6,5,4,4,2,2,2] .empty .empty)) (.node [9,9,6,5,5,2,1,1,1,1,1,1,1] (.node [9,9,6,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,5,5,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_294 : RowTree := (.node [9,9,6,5,4,2,2,2,2,2] degreeTree43_292 degreeTree43_293) - -def degreeTree43_295 : RowTree := (.node [9,9,6,6,2,2,2,2,2,2,1] (.node [9,9,6,5,5,4,2,1,1,1] (.node [9,9,6,5,5,3,2,2,1,1] (.node [9,9,6,5,5,3,1,1,1,1,1,1] (.node [9,9,6,5,5,2,2,2,2,1] .empty .empty) (.node [9,9,6,5,5,3,2,1,1,1,1] .empty .empty)) (.node [9,9,6,5,5,3,3,1,1,1] (.node [9,9,6,5,5,3,2,2,2] .empty .empty) (.node [9,9,6,5,5,4,1,1,1,1,1] .empty .empty))) (.node [9,9,6,6,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,5,5,5,1,1,1,1] .empty .empty) (.node [9,9,6,6,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,6,2,2,2,2,1,1,1,1,1] (.node [9,9,6,6,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,6,2,2,2,2,2,1,1,1] .empty .empty)))) (.node [9,9,6,6,3,3,2,1,1,1,1,1] (.node [9,9,6,6,3,2,2,2,1,1,1,1] (.node [9,9,6,6,3,2,1,1,1,1,1,1,1,1] (.node [9,9,6,6,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,6,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,6,3,2,2,2,2,2] (.node [9,9,6,6,3,2,2,2,2,1,1] .empty .empty) (.node [9,9,6,6,3,3,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,6,6,3,3,3,2,1,1] (.node [9,9,6,6,3,3,2,2,2,1] (.node [9,9,6,6,3,3,2,2,1,1,1] .empty .empty) (.node [9,9,6,6,3,3,3,1,1,1,1] .empty .empty)) (.node [9,9,6,6,4,1,1,1,1,1,1,1,1,1] (.node [9,9,6,6,3,3,3,2,2] .empty .empty) (.node [9,9,6,6,4,2,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_296 : RowTree := (.node [9,9,6,5,5,2,2,2,1,1,1] degreeTree43_294 degreeTree43_295) - -def degreeTree43_297 : RowTree := (.node [9,9,6,6,6,1,1,1,1,1,1,1] (.node [9,9,6,6,4,4,2,1,1,1] (.node [9,9,6,6,4,3,2,1,1,1,1] (.node [9,9,6,6,4,2,2,2,2,1] (.node [9,9,6,6,4,2,2,2,1,1,1] .empty .empty) (.node [9,9,6,6,4,3,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,6,4,3,3,1,1,1] (.node [9,9,6,6,4,3,2,2,1,1] .empty .empty) (.node [9,9,6,6,4,4,1,1,1,1,1] .empty .empty))) (.node [9,9,6,6,5,2,2,2,1,1] (.node [9,9,6,6,5,2,1,1,1,1,1,1] (.node [9,9,6,6,5,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,6,5,2,2,1,1,1,1] .empty .empty)) (.node [9,9,6,6,5,3,2,1,1,1] (.node [9,9,6,6,5,3,1,1,1,1,1] .empty .empty) (.node [9,9,6,6,5,4,1,1,1,1] .empty .empty)))) (.node [9,9,7,4,3,3,3,2,2,1] (.node [9,9,7,3,3,3,3,2,2,2] (.node [9,9,6,6,6,2,2,1,1,1] (.node [9,9,6,6,6,2,1,1,1,1,1] .empty .empty) (.node [9,9,6,6,6,3,1,1,1,1] .empty .empty)) (.node [9,9,7,3,3,3,3,3,3] (.node [9,9,7,3,3,3,3,3,2,1] .empty .empty) (.node [9,9,7,4,3,3,2,2,2,2] .empty .empty))) (.node [9,9,7,4,4,3,2,2,2,1] (.node [9,9,7,4,3,3,3,3,2] (.node [9,9,7,4,3,3,3,3,1,1] .empty .empty) (.node [9,9,7,4,4,2,2,2,2,2] .empty .empty)) (.node [9,9,7,4,4,3,3,2,2] (.node [9,9,7,4,4,3,3,2,1,1] .empty .empty) (.node [9,9,7,4,4,4,2,2,1,1] .empty .empty))))) - -def degreeTree43_298 : RowTree := (.node [9,9,7,6,4,3,2,1,1,1] (.node [9,9,7,5,5,2,2,2,1,1] (.node [9,9,7,5,4,2,2,2,2,1] (.node [9,9,7,5,3,3,2,2,2,1] (.node [9,9,7,5,3,2,2,2,2,2] .empty .empty) (.node [9,9,7,5,3,3,3,2,1,1] .empty .empty)) (.node [9,9,7,5,4,3,3,1,1,1] (.node [9,9,7,5,4,3,2,2,1,1] .empty .empty) (.node [9,9,7,5,4,4,2,1,1,1] .empty .empty))) (.node [9,9,7,6,3,2,2,2,2,1] (.node [9,9,7,5,5,4,1,1,1,1] (.node [9,9,7,5,5,3,2,1,1,1] .empty .empty) (.node [9,9,7,6,2,2,2,2,2,2] .empty .empty)) (.node [9,9,7,6,3,3,3,1,1,1] (.node [9,9,7,6,3,3,2,2,1,1] .empty .empty) (.node [9,9,7,6,4,2,2,2,1,1] .empty .empty)))) (.node [9,9,7,7,4,2,2,1,1,1] (.node [9,9,7,6,6,2,1,1,1,1] (.node [9,9,7,6,5,2,2,1,1,1] (.node [9,9,7,6,4,4,1,1,1,1] .empty .empty) (.node [9,9,7,6,5,3,1,1,1,1] .empty .empty)) (.node [9,9,7,7,3,2,2,2,1,1] (.node [9,9,7,7,2,2,2,2,2,1] .empty .empty) (.node [9,9,7,7,3,3,2,1,1,1] .empty .empty))) (.node [9,9,8,3,3,3,2,2,2,2] (.node [9,9,7,7,5,2,1,1,1,1] (.node [9,9,7,7,4,3,1,1,1,1] .empty .empty) (.node [9,9,7,7,6,1,1,1,1,1] .empty .empty)) (.node [9,9,8,3,3,3,3,3,1,1] (.node [9,9,8,3,3,3,3,2,2,1] .empty .empty) (.node [9,9,8,3,3,3,3,3,2] .empty .empty))))) - -def degreeTree43_299 : RowTree := (.node [9,9,7,4,4,4,3,1,1,1] degreeTree43_297 degreeTree43_298) - -def degreeTree43_300 : RowTree := (.node [9,9,6,6,4,2,2,1,1,1,1,1] degreeTree43_296 degreeTree43_299) - -def degreeTree43_301 : RowTree := (.node [9,9,6,5,3,2,2,2,2,1,1,1] degreeTree43_291 degreeTree43_300) - -def degreeTree43_302 : RowTree := (.node [9,9,8,5,3,3,2,2,1,1] (.node [9,9,8,4,4,3,3,1,1,1] (.node [9,9,8,4,4,2,2,2,2,1] (.node [9,9,8,4,3,3,3,2,1,1] (.node [9,9,8,4,3,3,2,2,2,1] .empty .empty) .empty) (.node [9,9,8,4,4,3,2,2,1,1] .empty .empty)) (.node [9,9,8,5,2,2,2,2,2,2] (.node [9,9,8,4,4,4,2,1,1,1] .empty .empty) (.node [9,9,8,5,3,2,2,2,2,1] .empty .empty))) (.node [9,9,8,5,4,4,1,1,1,1] (.node [9,9,8,5,4,2,2,2,1,1] (.node [9,9,8,5,3,3,3,1,1,1] .empty .empty) (.node [9,9,8,5,4,3,2,1,1,1] .empty .empty)) (.node [9,9,8,5,5,3,1,1,1,1] (.node [9,9,8,5,5,2,2,1,1,1] .empty .empty) (.node [9,9,8,6,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree43_303 : RowTree := (.node [9,9,8,7,3,3,1,1,1,1] (.node [9,9,8,6,5,2,1,1,1,1] (.node [9,9,8,6,4,2,2,1,1,1] (.node [9,9,8,6,3,3,2,1,1,1] .empty .empty) (.node [9,9,8,6,4,3,1,1,1,1] .empty .empty)) (.node [9,9,8,7,2,2,2,2,1,1] (.node [9,9,8,6,6,1,1,1,1,1] .empty .empty) (.node [9,9,8,7,3,2,2,1,1,1] .empty .empty))) (.node [9,9,8,8,3,2,1,1,1,1] (.node [9,9,8,7,5,1,1,1,1,1] (.node [9,9,8,7,4,2,1,1,1,1] .empty .empty) (.node [9,9,8,8,2,2,2,1,1,1] .empty .empty)) (.node [9,9,9,3,3,2,2,2,2,2] (.node [9,9,8,8,4,1,1,1,1,1] .empty .empty) (.node [9,9,9,3,3,3,2,2,2,1] .empty .empty)))) - -def degreeTree43_304 : RowTree := (.node [9,9,8,6,3,2,2,2,1,1] degreeTree43_302 degreeTree43_303) - -def degreeTree43_305 : RowTree := (.node [9,9,9,6,3,3,1,1,1,1] (.node [9,9,9,5,2,2,2,2,2,1] (.node [9,9,9,4,3,3,3,1,1,1] (.node [9,9,9,4,3,2,2,2,2,1] (.node [9,9,9,4,2,2,2,2,2,2] .empty .empty) (.node [9,9,9,4,3,3,2,2,1,1] .empty .empty)) (.node [9,9,9,4,4,3,2,1,1,1] (.node [9,9,9,4,4,2,2,2,1,1] .empty .empty) (.node [9,9,9,4,4,4,1,1,1,1] .empty .empty))) (.node [9,9,9,5,4,3,1,1,1,1] (.node [9,9,9,5,3,3,2,1,1,1] (.node [9,9,9,5,3,2,2,2,1,1] .empty .empty) (.node [9,9,9,5,4,2,2,1,1,1] .empty .empty)) (.node [9,9,9,6,2,2,2,2,1,1] (.node [9,9,9,5,5,2,1,1,1,1] .empty .empty) (.node [9,9,9,6,3,2,2,1,1,1] .empty .empty)))) (.node [9,9,9,9,2,1,1,1,1,1] (.node [9,9,9,7,3,2,1,1,1,1] (.node [9,9,9,6,5,1,1,1,1,1] (.node [9,9,9,6,4,2,1,1,1,1] .empty .empty) (.node [9,9,9,7,2,2,2,1,1,1] .empty .empty)) (.node [9,9,9,8,2,2,1,1,1,1] (.node [9,9,9,7,4,1,1,1,1,1] .empty .empty) (.node [9,9,9,8,3,1,1,1,1,1] .empty .empty))) (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_306 : RowTree := (.node [9,9,9,3,3,3,3,2,1,1] degreeTree43_304 degreeTree43_305) - -def degreeTree43_307 : RowTree := (.node [10,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,3,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2] (.node [10,3,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,3,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,2,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,3,3,3,2,2,2,2,2,2,2,2,2,2,1] (.node [10,3,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,3,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_308 : RowTree := (.node [10,3,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,2,2,2,2,2,2,2,1,1] (.node [10,3,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,3,3,3,3,3,2,2,2,2,2,2,1,1,1] (.node [10,3,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,3,3,3,3,3,3,3,3,2,2,2,1,1,1] (.node [10,3,3,3,3,3,3,3,2,2,2,2,2,2] (.node [10,3,3,3,3,3,3,3,2,2,2,2,1,1,1,1] (.node [10,3,3,3,3,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,2,2,2,2,2,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,3,3,2,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,3,2,2,1,1,1,1,1] .empty .empty))) (.node [10,3,3,3,3,3,3,3,3,3,2,2,1,1] (.node [10,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,3,3,2,2,2,2,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,3,3,2,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,3,3,3,3,1,1,1] (.node [10,3,3,3,3,3,3,3,3,3,2,2,2] .empty .empty) (.node [10,3,3,3,3,3,3,3,3,3,3,2,1] .empty .empty))))) - -def degreeTree43_309 : RowTree := (.node [10,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_307 degreeTree43_308) - -def degreeTree43_310 : RowTree := (.node [10,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_306 degreeTree43_309) - -def degreeTree43_311 : RowTree := (.node [10,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,4,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,4,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,2,2,2,2,2,2,2,2,2,2,2,2,2] (.node [10,4,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_312 : RowTree := (.node [10,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,4,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,4,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,2,2,2,2,2,2,2,2,2,1,1] (.node [10,4,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,2,2,2,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree43_313 : RowTree := (.node [10,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_311 degreeTree43_312) - -def degreeTree43_314 : RowTree := (.node [10,4,3,3,3,3,3,2,2,2,2,2,2,2] (.node [10,4,3,3,3,3,2,2,2,2,2,2,2,2,1] (.node [10,4,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,4,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,3,3,2,2,2,2,2,1,1,1,1] (.node [10,4,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,2,2,2,2,2,2,1,1] .empty .empty)))) (.node [10,4,3,3,3,3,3,3,3,2,1,1,1,1,1,1] (.node [10,4,3,3,3,3,3,3,2,2,2,1,1,1,1,1] (.node [10,4,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,3,3,3,2,2,2,2,2,1] (.node [10,4,3,3,3,3,3,3,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,3,3,3,3,3,3,3,3,1,1,1,1,1] (.node [10,4,3,3,3,3,3,3,3,2,2,2,1,1] (.node [10,4,3,3,3,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,3,3,2,2,2,2] .empty .empty)) (.node [10,4,3,3,3,3,3,3,3,3,2,2,1] (.node [10,4,3,3,3,3,3,3,3,3,2,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,3,3,3,3,1,1] .empty .empty))))) - -def degreeTree43_315 : RowTree := (.node [10,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_313 degreeTree43_314) - -def degreeTree43_316 : RowTree := (.node [10,4,4,3,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,4,4,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,4,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)))) (.node [10,4,4,3,3,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,2,2,2,2,2,2,2,2,1] (.node [10,4,4,3,3,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_317 : RowTree := (.node [10,4,4,3,3,3,3,3,2,2,2,2,2] (.node [10,4,4,3,3,3,3,2,2,2,2,1,1,1,1,1] (.node [10,4,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,2,2,2,2,2,2,2,1,1] (.node [10,4,4,3,3,3,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,4,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,3,3,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,3,2,2,2,2,2,2,1] (.node [10,4,4,3,3,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,3,3,3,3,3,2,2,2,1,1,1,1] (.node [10,4,4,3,3,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,3,3,2,2,2,2,1,1] .empty .empty)))) (.node [10,4,4,3,3,3,3,3,3,3,3,1] (.node [10,4,4,3,3,3,3,3,3,2,2,2,1] (.node [10,4,4,3,3,3,3,3,3,2,1,1,1,1,1] (.node [10,4,4,3,3,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,3,3,3,2,2,1,1,1] .empty .empty)) (.node [10,4,4,3,3,3,3,3,3,3,2,1,1] (.node [10,4,4,3,3,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,3,3,3,3,2,2] .empty .empty))) (.node [10,4,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_318 : RowTree := (.node [10,4,4,3,3,3,2,2,2,2,2,1,1,1,1,1,1] degreeTree43_316 degreeTree43_317) - -def degreeTree43_319 : RowTree := (.node [10,4,3,3,3,3,3,3,3,3,3,2] degreeTree43_315 degreeTree43_318) - -def degreeTree43_320 : RowTree := (.node [10,3,3,3,3,3,3,3,3,3,3,3] degreeTree43_310 degreeTree43_319) - -def degreeTree43_321 : RowTree := (.node [9,9,8,4,3,2,2,2,2,2] degreeTree43_301 degreeTree43_320) - -def degreeTree43_322 : RowTree := (.node [9,9,5,5,4,4,2,2,1,1,1] degreeTree43_282 degreeTree43_321) - -def degreeTree43_323 : RowTree := (.node [9,8,7,7,5,3,1,1,1,1] degreeTree43_243 degreeTree43_322) - -def degreeTree43_324 : RowTree := (.node [9,7,5,5,5,5,3,2,2] degreeTree43_162 degreeTree43_323) - -def degreeTree43_325 : RowTree := (.node [10,4,4,4,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,4,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,3,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,2,2,2,2,2,2,2,2,2] (.node [10,4,4,4,3,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,3,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_326 : RowTree := (.node [10,4,4,4,3,3,3,2,2,2,2,2,1,1] (.node [10,4,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,2,2,2,2,2,2,2,1] (.node [10,4,4,4,3,3,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,3,3,2,2,2,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,3,3,3,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,4,4,4,3,3,3,3,2,2,1,1,1,1,1] (.node [10,4,4,4,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,4,4,4,3,3,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,3,3,3,2,2,2,2,1] (.node [10,4,4,4,3,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,4,4,4,3,3,3,3,3,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_327 : RowTree := (.node [10,4,4,4,3,3,2,2,2,2,2,1,1,1,1,1] degreeTree43_325 degreeTree43_326) - -def degreeTree43_328 : RowTree := (.node [10,4,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,3,3,3,2,1] (.node [10,4,4,4,3,3,3,3,3,2,2,2] (.node [10,4,4,4,3,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,4,4,4,3,3,3,3,3,3,1,1,1] .empty .empty)) (.node [10,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,3,3,3,3] .empty .empty) (.node [10,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,4,4,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,2,2,2,2,2,2,2,2,1] (.node [10,4,4,4,4,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,4,4,4,4,3,3,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,3,2,2,2,2,2,1,1,1,1] (.node [10,4,4,4,4,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,3,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,3,2,2,2,2,2,2,2] (.node [10,4,4,4,4,3,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,4,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,4,4,3,3,2,2,2,2,2,1] (.node [10,4,4,4,4,3,3,2,2,2,1,1,1,1,1] (.node [10,4,4,4,4,3,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,3,3,2,2,2,2,1,1,1] .empty .empty)) (.node [10,4,4,4,4,3,3,3,2,1,1,1,1,1,1] (.node [10,4,4,4,4,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,3,3,3,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_329 : RowTree := (.node [10,4,4,4,3,3,3,3,3,2,1,1,1,1] degreeTree43_327 degreeTree43_328) - -def degreeTree43_330 : RowTree := (.node [10,4,4,4,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,3,3,3,3,3,1,1] (.node [10,4,4,4,4,3,3,3,3,2,1,1,1] (.node [10,4,4,4,4,3,3,3,3,1,1,1,1,1] (.node [10,4,4,4,4,3,3,3,2,2,2,2] .empty .empty) .empty) (.node [10,4,4,4,4,3,3,3,3,2,2,1] .empty .empty)) (.node [10,4,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,3,3,3,3,3,2] .empty .empty) (.node [10,4,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,4,4,4,2,2,2,2,2,2,1] (.node [10,4,4,4,4,4,2,2,2,2,1,1,1,1,1] (.node [10,4,4,4,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,4,4,4,4,4,3,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,4,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,3,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_331 : RowTree := (.node [10,4,4,4,4,4,3,3,3,2,1,1] (.node [10,4,4,4,4,4,3,3,2,1,1,1,1,1] (.node [10,4,4,4,4,4,3,2,2,2,2,2] (.node [10,4,4,4,4,4,3,2,2,2,2,1,1] .empty .empty) (.node [10,4,4,4,4,4,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,4,3,3,2,2,2,1] (.node [10,4,4,4,4,4,3,3,2,2,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,3,3,3,1,1,1,1] .empty .empty))) (.node [10,4,4,4,4,4,4,2,1,1,1,1,1,1,1] (.node [10,4,4,4,4,4,3,3,3,3,1] (.node [10,4,4,4,4,4,3,3,3,2,2] .empty .empty) (.node [10,4,4,4,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,4,4,2,2,2,1,1,1] (.node [10,4,4,4,4,4,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,4,2,2,2,2,1] .empty .empty)))) - -def degreeTree43_332 : RowTree := (.node [10,4,4,4,4,4,3,2,2,2,1,1,1,1] degreeTree43_330 degreeTree43_331) - -def degreeTree43_333 : RowTree := (.node [10,5,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,4,4,4,2,1,1,1] (.node [10,4,4,4,4,4,4,3,3,1,1,1] (.node [10,4,4,4,4,4,4,3,2,2,1,1] (.node [10,4,4,4,4,4,4,3,2,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,4,3,2,2,2] .empty .empty)) (.node [10,4,4,4,4,4,4,3,3,3] (.node [10,4,4,4,4,4,4,3,3,2,1] .empty .empty) (.node [10,4,4,4,4,4,4,4,1,1,1,1,1] .empty .empty))) (.node [10,4,4,4,4,4,4,4,4,1] (.node [10,4,4,4,4,4,4,4,3,1,1] (.node [10,4,4,4,4,4,4,4,2,2,1] .empty .empty) (.node [10,4,4,4,4,4,4,4,3,2] .empty .empty)) (.node [10,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,2,2,2,2,2,2,2,2,2,2,2,2,2,2] (.node [10,5,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,3,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,5,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,5,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_334 : RowTree := (.node [10,4,4,4,4,4,4,3,1,1,1,1,1,1] degreeTree43_332 degreeTree43_333) - -def degreeTree43_335 : RowTree := (.node [10,4,4,4,4,3,3,3,2,2,2,1,1] degreeTree43_329 degreeTree43_334) - -def degreeTree43_336 : RowTree := (.node [10,5,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,2,2,2,2,2,2,2,2,2,2,2] (.node [10,5,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,5,3,3,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,3,3,3,2,2,2,2,2,2,2,2,1,1,1] (.node [10,5,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,5,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_337 : RowTree := (.node [10,5,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,2,2,2,2,2,2,1,1,1,1] (.node [10,5,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,3,3,3,3,2,2,2,2,2,2,2,2] (.node [10,5,3,3,3,3,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,3,3,3,3,3,2,2,2,2,2,1,1,1] (.node [10,5,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,5,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_338 : RowTree := (.node [10,5,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_336 degreeTree43_337) - -def degreeTree43_339 : RowTree := (.node [10,5,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,3,3,3,1,1,1,1] (.node [10,5,3,3,3,3,3,3,3,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,3,2,2,2,2,1,1] (.node [10,5,3,3,3,3,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,3,2,2,2,2,2] .empty .empty)) (.node [10,5,3,3,3,3,3,3,3,2,2,1,1,1] (.node [10,5,3,3,3,3,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,3,3,2,2,2,1] .empty .empty))) (.node [10,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,3,3,3,2,2] (.node [10,5,3,3,3,3,3,3,3,3,2,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,3,3,3,3,1] .empty .empty)) (.node [10,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,2,2,2,2,2,2,2,2,2,2,2,2] (.node [10,5,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,2,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,3,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,5,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_340 : RowTree := (.node [10,5,3,3,3,3,3,3,2,2,1,1,1,1,1,1] degreeTree43_338 degreeTree43_339) - -def degreeTree43_341 : RowTree := (.node [10,5,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,3,2,2,2,2,2,2,2,2,1,1] (.node [10,5,4,3,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,2,2,2,2,2,2,2,2,2] .empty .empty))) (.node [10,5,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,3,3,2,2,2,2,2,2,1,1,1] (.node [10,5,4,3,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,2,2,2,2,2,2,2,1] .empty .empty)))) (.node [10,5,4,3,3,3,3,3,2,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,3,2,2,2,2,1,1,1,1] (.node [10,5,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,3,3,3,2,2,2,2,2,2] (.node [10,5,4,3,3,3,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,3,3,3,3,3,3,1,1,1,1,1,1] (.node [10,5,4,3,3,3,3,3,2,2,2,1,1,1] (.node [10,5,4,3,3,3,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,3,2,2,2,2,1] .empty .empty)) (.node [10,5,4,3,3,3,3,3,3,2,2,1,1] (.node [10,5,4,3,3,3,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,3,3,2,2,2] .empty .empty))))) - -def degreeTree43_342 : RowTree := (.node [10,5,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,3,3,3,3,3] (.node [10,5,4,3,3,3,3,3,3,3,2,1] .empty .empty) (.node [10,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,4,2,2,2,2,2,2,2,2,2,2] (.node [10,5,4,4,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,5,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,3,2,2,2,2,2,2,2,1,1,1] (.node [10,5,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,3,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,5,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,4,3,3,2,2,2,2,2,2,1,1] (.node [10,5,4,4,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,5,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,3,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,3,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,5,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_343 : RowTree := (.node [10,5,4,3,3,3,3,3,3,3,1,1,1] degreeTree43_341 degreeTree43_342) - -def degreeTree43_344 : RowTree := (.node [10,5,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_340 degreeTree43_343) - -def degreeTree43_345 : RowTree := (.node [10,5,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_335 degreeTree43_344) - -def degreeTree43_346 : RowTree := (.node [10,5,4,4,3,3,3,3,3,1,1,1,1,1] (.node [10,5,4,4,3,3,3,3,2,1,1,1,1,1,1] (.node [10,5,4,4,3,3,3,2,2,2,2,2,1] (.node [10,5,4,4,3,3,3,2,2,2,2,1,1,1] (.node [10,5,4,4,3,3,3,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,5,4,4,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,3,3,3,3,2,2,2,1,1] (.node [10,5,4,4,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,3,3,3,2,2,2,2] .empty .empty))) (.node [10,5,4,4,3,3,3,3,3,3,2] (.node [10,5,4,4,3,3,3,3,3,2,2,1] (.node [10,5,4,4,3,3,3,3,3,2,1,1,1] .empty .empty) (.node [10,5,4,4,3,3,3,3,3,3,1,1] .empty .empty)) (.node [10,5,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_347 : RowTree := (.node [10,5,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,2,2,2,2,2,2,2,1,1] (.node [10,5,4,4,4,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,4,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,5,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,4,4,3,2,2,2,2,2,2,1] (.node [10,5,4,4,4,3,2,2,2,2,1,1,1,1,1] (.node [10,5,4,4,4,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,4,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,5,4,4,4,3,3,2,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,4,3,3,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_348 : RowTree := (.node [10,5,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_346 degreeTree43_347) - -def degreeTree43_349 : RowTree := (.node [10,5,4,4,4,4,2,2,2,2,2,1,1] (.node [10,5,4,4,4,3,3,3,3,2,1,1] (.node [10,5,4,4,4,3,3,3,2,1,1,1,1,1] (.node [10,5,4,4,4,3,3,2,2,2,2,2] (.node [10,5,4,4,4,3,3,2,2,2,2,1,1] .empty .empty) (.node [10,5,4,4,4,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,3,3,3,2,2,2,1] (.node [10,5,4,4,4,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,5,4,4,4,3,3,3,3,1,1,1,1] .empty .empty))) (.node [10,5,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,3,3,3,3,3,1] (.node [10,5,4,4,4,3,3,3,3,2,2] .empty .empty) (.node [10,5,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,4,2,2,2,1,1,1,1,1,1] (.node [10,5,4,4,4,4,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,4,4,2,2,2,2,1,1,1,1] .empty .empty)))) (.node [10,5,4,4,4,4,3,3,2,1,1,1,1] (.node [10,5,4,4,4,4,3,2,2,1,1,1,1,1] (.node [10,5,4,4,4,4,3,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,4,2,2,2,2,2,2] .empty .empty) (.node [10,5,4,4,4,4,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,4,3,2,2,2,2,1] (.node [10,5,4,4,4,4,3,2,2,2,1,1,1] .empty .empty) (.node [10,5,4,4,4,4,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,4,4,4,3,3,3,2,1] (.node [10,5,4,4,4,4,3,3,2,2,2] (.node [10,5,4,4,4,4,3,3,2,2,1,1] .empty .empty) (.node [10,5,4,4,4,4,3,3,3,1,1,1] .empty .empty)) (.node [10,5,4,4,4,4,4,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,4,3,3,3,3] .empty .empty) (.node [10,5,4,4,4,4,4,2,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_350 : RowTree := (.node [10,5,4,4,4,3,3,2,2,2,1,1,1,1] degreeTree43_348 degreeTree43_349) - -def degreeTree43_351 : RowTree := (.node [10,5,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,4,4,4,1,1,1,1] (.node [10,5,4,4,4,4,4,3,2,1,1,1] (.node [10,5,4,4,4,4,4,2,2,2,2] (.node [10,5,4,4,4,4,4,2,2,2,1,1] .empty .empty) (.node [10,5,4,4,4,4,4,3,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,4,4,3,3,1,1] (.node [10,5,4,4,4,4,4,3,2,2,1] .empty .empty) (.node [10,5,4,4,4,4,4,3,3,2] .empty .empty))) (.node [10,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,4,4,4,2,2] (.node [10,5,4,4,4,4,4,4,2,1,1] .empty .empty) (.node [10,5,4,4,4,4,4,4,3,1] .empty .empty)) (.node [10,5,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,5,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,5,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,3,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,3,2,2,2,2,2,2,2,2,2,2] (.node [10,5,5,3,2,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_352 : RowTree := (.node [10,5,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,3,3,2,2,2,2,2,2,2,1,1,1] (.node [10,5,5,3,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,2,2,2,2,2,2,2,2,1] .empty .empty))) (.node [10,5,5,3,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,5,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,3,3,3,2,2,2,2,2,2,1,1] (.node [10,5,5,3,3,3,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,3,2,2,2,2,2,2,2] .empty .empty)))) (.node [10,5,5,3,3,3,3,3,2,2,1,1,1,1] (.node [10,5,5,3,3,3,3,2,2,2,2,1,1,1] (.node [10,5,5,3,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,5,5,3,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,3,3,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,3,3,3,3,3,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,3,3,2,2,2,2,2,1] .empty .empty) (.node [10,5,5,3,3,3,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,3,3,3,3,3,3,2,1,1,1] (.node [10,5,5,3,3,3,3,3,2,2,2,2] (.node [10,5,5,3,3,3,3,3,2,2,2,1,1] .empty .empty) (.node [10,5,5,3,3,3,3,3,3,1,1,1,1,1] .empty .empty)) (.node [10,5,5,3,3,3,3,3,3,3,1,1] (.node [10,5,5,3,3,3,3,3,3,2,2,1] .empty .empty) (.node [10,5,5,3,3,3,3,3,3,3,2] .empty .empty))))) - -def degreeTree43_353 : RowTree := (.node [10,5,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_351 degreeTree43_352) - -def degreeTree43_354 : RowTree := (.node [10,5,4,4,4,4,4,2,2,1,1,1,1] degreeTree43_350 degreeTree43_353) - -def degreeTree43_355 : RowTree := (.node [10,5,5,4,2,2,2,2,2,2,2,2,2,1] (.node [10,5,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,5,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,5,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,2,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,5,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,5,4,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,3,2,2,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree43_356 : RowTree := (.node [10,5,5,4,3,3,2,2,2,2,2,2,1] (.node [10,5,5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,5,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,3,2,2,2,2,1,1,1,1,1] (.node [10,5,5,4,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,3,3,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,5,5,4,3,3,3,2,2,2,1,1,1,1] (.node [10,5,5,4,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,3,3,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,3,3,2,2,2,2,2] (.node [10,5,5,4,3,3,3,2,2,2,2,1,1] .empty .empty) (.node [10,5,5,4,3,3,3,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_357 : RowTree := (.node [10,5,5,4,3,2,2,2,2,2,2,2,1,1] degreeTree43_355 degreeTree43_356) - -def degreeTree43_358 : RowTree := (.node [10,5,5,4,4,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,3,3,3,3,2,1,1] (.node [10,5,5,4,3,3,3,3,2,2,2,1] (.node [10,5,5,4,3,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,5,5,4,3,3,3,3,3,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,3,3,3,3,3,1] (.node [10,5,5,4,3,3,3,3,3,2,2] .empty .empty) (.node [10,5,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,4,4,2,2,2,2,2,1,1,1,1,1] (.node [10,5,5,4,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,2,2,2,2,2,2,2,1] (.node [10,5,5,4,4,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,5,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,5,4,4,3,3,2,2,1,1,1,1,1] (.node [10,5,5,4,4,3,2,2,2,2,2,1,1] (.node [10,5,5,4,4,3,2,2,2,1,1,1,1,1,1] (.node [10,5,5,4,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,4,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,3,3,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,3,2,2,2,2,2,2] .empty .empty) (.node [10,5,5,4,4,3,3,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,4,4,3,3,3,2,1,1,1,1] (.node [10,5,5,4,4,3,3,2,2,2,2,1] (.node [10,5,5,4,4,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,5,5,4,4,3,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,3,3,3,2,2,2] (.node [10,5,5,4,4,3,3,3,2,2,1,1] .empty .empty) (.node [10,5,5,4,4,3,3,3,3,1,1,1] .empty .empty))))) - -def degreeTree43_359 : RowTree := (.node [10,5,5,4,3,3,3,3,2,1,1,1,1,1] degreeTree43_357 degreeTree43_358) - -def degreeTree43_360 : RowTree := (.node [10,5,5,4,4,4,3,3,3,1,1] (.node [10,5,5,4,4,4,3,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,4,2,2,1,1,1,1,1,1,1] (.node [10,5,5,4,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,3,3,3,3,3] .empty .empty) (.node [10,5,5,4,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,4,2,2,2,2,1,1,1] (.node [10,5,5,4,4,4,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,4,4,2,2,2,2,2,1] .empty .empty))) (.node [10,5,5,4,4,4,3,2,2,2,2] (.node [10,5,5,4,4,4,3,2,2,1,1,1,1] (.node [10,5,5,4,4,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,4,4,3,2,2,2,1,1] .empty .empty)) (.node [10,5,5,4,4,4,3,3,2,1,1,1] (.node [10,5,5,4,4,4,3,3,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,4,4,3,3,2,2,1] .empty .empty)))) (.node [10,5,5,4,4,4,4,3,2,2] (.node [10,5,5,4,4,4,4,2,2,1,1,1] (.node [10,5,5,4,4,4,4,1,1,1,1,1,1,1] (.node [10,5,5,4,4,4,3,3,3,2] .empty .empty) (.node [10,5,5,4,4,4,4,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,4,4,3,1,1,1,1] (.node [10,5,5,4,4,4,4,2,2,2,1] .empty .empty) (.node [10,5,5,4,4,4,4,3,2,1,1] .empty .empty))) (.node [10,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,4,4,4,1,1,1] (.node [10,5,5,4,4,4,4,3,3,1] .empty .empty) (.node [10,5,5,4,4,4,4,4,2,1] .empty .empty)) (.node [10,5,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_361 : RowTree := (.node [10,5,5,5,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,5,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,2,2,2,2,2,2,2,2,1,1] (.node [10,5,5,5,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,5,5,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,5,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,5,3,2,2,2,2,2,2,1,1,1] (.node [10,5,5,5,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,5,5,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,5,5,5,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,5,5,3,3,3,2,2,2,1,1,1] (.node [10,5,5,5,3,3,2,2,2,2,2,2] (.node [10,5,5,5,3,3,2,2,2,2,1,1,1,1] (.node [10,5,5,5,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,3,3,2,2,2,2,2,1,1] .empty .empty)) (.node [10,5,5,5,3,3,3,2,1,1,1,1,1,1,1] (.node [10,5,5,5,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,3,3,3,2,2,1,1,1,1,1] .empty .empty))) (.node [10,5,5,5,3,3,3,3,2,2,1,1] (.node [10,5,5,5,3,3,3,3,1,1,1,1,1,1] (.node [10,5,5,5,3,3,3,2,2,2,2,1] .empty .empty) (.node [10,5,5,5,3,3,3,3,2,1,1,1,1] .empty .empty)) (.node [10,5,5,5,3,3,3,3,3,1,1,1] (.node [10,5,5,5,3,3,3,3,2,2,2] .empty .empty) (.node [10,5,5,5,3,3,3,3,3,2,1] .empty .empty))))) - -def degreeTree43_362 : RowTree := (.node [10,5,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_360 degreeTree43_361) - -def degreeTree43_363 : RowTree := (.node [10,5,5,4,4,3,3,3,3,2,1] degreeTree43_359 degreeTree43_362) - -def degreeTree43_364 : RowTree := (.node [10,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_354 degreeTree43_363) - -def degreeTree43_365 : RowTree := (.node [10,5,4,4,3,3,3,2,2,1,1,1,1,1,1,1] degreeTree43_345 degreeTree43_364) - -def degreeTree43_366 : RowTree := (.node [10,5,5,5,4,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,4,2,2,2,2,1,1,1,1,1,1] (.node [10,5,5,5,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,5,5,5,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,4,2,2,2,2,2,2,1,1] (.node [10,5,5,5,4,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,5,5,5,4,2,2,2,2,2,2,2] .empty .empty))) (.node [10,5,5,5,4,3,2,2,2,2,1,1,1] (.node [10,5,5,5,4,3,2,2,1,1,1,1,1,1,1] (.node [10,5,5,5,4,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,4,3,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,4,3,3,1,1,1,1,1,1,1,1] (.node [10,5,5,5,4,3,2,2,2,2,2,1] .empty .empty) (.node [10,5,5,5,4,3,3,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_367 : RowTree := (.node [10,5,5,5,4,4,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,4,3,3,3,2,1,1,1] (.node [10,5,5,5,4,3,3,2,2,2,2] (.node [10,5,5,5,4,3,3,2,2,2,1,1] .empty .empty) (.node [10,5,5,5,4,3,3,3,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,4,3,3,3,3,1,1] (.node [10,5,5,5,4,3,3,3,2,2,1] .empty .empty) (.node [10,5,5,5,4,3,3,3,3,2] .empty .empty))) (.node [10,5,5,5,4,4,2,2,2,2,1,1] (.node [10,5,5,5,4,4,2,2,1,1,1,1,1,1] (.node [10,5,5,5,4,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,4,4,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,5,4,4,3,1,1,1,1,1,1,1] (.node [10,5,5,5,4,4,2,2,2,2,2] .empty .empty) (.node [10,5,5,5,4,4,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_368 : RowTree := (.node [10,5,5,5,4,3,3,2,2,1,1,1,1] degreeTree43_366 degreeTree43_367) - -def degreeTree43_369 : RowTree := (.node [10,5,5,5,5,2,2,2,1,1,1,1,1,1,1] (.node [10,5,5,5,4,4,4,2,2,1,1] (.node [10,5,5,5,4,4,3,3,2,2] (.node [10,5,5,5,4,4,3,3,1,1,1,1] (.node [10,5,5,5,4,4,3,2,2,2,1] .empty .empty) (.node [10,5,5,5,4,4,3,3,2,1,1] .empty .empty)) (.node [10,5,5,5,4,4,4,1,1,1,1,1,1] (.node [10,5,5,5,4,4,3,3,3,1] .empty .empty) (.node [10,5,5,5,4,4,4,2,1,1,1,1] .empty .empty))) (.node [10,5,5,5,4,4,4,4,1,1] (.node [10,5,5,5,4,4,4,3,1,1,1] (.node [10,5,5,5,4,4,4,2,2,2] .empty .empty) (.node [10,5,5,5,4,4,4,3,2,1] .empty .empty)) (.node [10,5,5,5,5,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,5,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,5,5,5,3,2,2,2,2,1,1] (.node [10,5,5,5,5,3,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,5,2,2,2,2,2,1,1,1] (.node [10,5,5,5,5,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,5,2,2,2,2,2,2,1] .empty .empty)) (.node [10,5,5,5,5,3,2,2,1,1,1,1,1,1] (.node [10,5,5,5,5,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,5,3,2,2,2,1,1,1,1] .empty .empty))) (.node [10,5,5,5,5,3,3,2,2,1,1,1] (.node [10,5,5,5,5,3,3,1,1,1,1,1,1,1] (.node [10,5,5,5,5,3,2,2,2,2,2] .empty .empty) (.node [10,5,5,5,5,3,3,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,5,3,3,3,1,1,1,1] (.node [10,5,5,5,5,3,3,2,2,2,1] .empty .empty) (.node [10,5,5,5,5,3,3,3,2,1,1] .empty .empty))))) - -def degreeTree43_370 : RowTree := (.node [10,5,5,5,4,4,3,2,2,1,1,1] degreeTree43_368 degreeTree43_369) - -def degreeTree43_371 : RowTree := (.node [10,5,5,5,5,4,4,3,1,1] (.node [10,5,5,5,5,4,3,2,1,1,1,1] (.node [10,5,5,5,5,4,2,2,1,1,1,1,1] (.node [10,5,5,5,5,4,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,5,3,3,3,3,1] .empty .empty) (.node [10,5,5,5,5,4,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,5,4,2,2,2,2,1] (.node [10,5,5,5,5,4,2,2,2,1,1,1] .empty .empty) (.node [10,5,5,5,5,4,3,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,5,5,4,3,3,2,1] (.node [10,5,5,5,5,4,3,2,2,2] (.node [10,5,5,5,5,4,3,2,2,1,1] .empty .empty) (.node [10,5,5,5,5,4,3,3,1,1,1] .empty .empty)) (.node [10,5,5,5,5,4,4,2,1,1,1] (.node [10,5,5,5,5,4,4,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,5,4,4,2,2,1] .empty .empty)))) (.node [10,5,5,5,5,5,3,2,2,1] (.node [10,5,5,5,5,5,2,2,2,1,1] (.node [10,5,5,5,5,5,2,1,1,1,1,1,1] (.node [10,5,5,5,5,5,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,5,5,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,5,5,5,3,1,1,1,1,1] (.node [10,5,5,5,5,5,2,2,2,2] .empty .empty) (.node [10,5,5,5,5,5,3,2,1,1,1] .empty .empty))) (.node [10,5,5,5,5,5,5,1,1,1] (.node [10,5,5,5,5,5,4,1,1,1,1] (.node [10,5,5,5,5,5,3,3,1,1] .empty .empty) (.node [10,5,5,5,5,5,4,2,1,1] .empty .empty)) (.node [10,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_372 : RowTree := (.node [10,6,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,2,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,3,2,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,6,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,2,2,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,2,2,2,2,2,2,2,2,2,2,1] (.node [10,6,3,3,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,6,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,2,2,2,2,2,2,2,2,1,1] .empty .empty))))) - -def degreeTree43_373 : RowTree := (.node [10,6,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_371 degreeTree43_372) - -def degreeTree43_374 : RowTree := (.node [10,5,5,5,5,3,3,3,2,2] degreeTree43_370 degreeTree43_373) - -def degreeTree43_375 : RowTree := (.node [10,6,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,6,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,3,3,2,2,2,2,2,2,1,1,1] (.node [10,6,3,3,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,3,2,2,2,2,2,2,2,1] .empty .empty))) (.node [10,6,3,3,3,3,3,2,2,2,2,1,1,1,1] (.node [10,6,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,3,3,3,2,2,2,2,2,2] (.node [10,6,3,3,3,3,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,6,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_376 : RowTree := (.node [10,6,3,3,3,3,3,3,3,3,1,1,1] (.node [10,6,3,3,3,3,3,3,3,1,1,1,1,1,1] (.node [10,6,3,3,3,3,3,3,2,2,2,1,1,1] (.node [10,6,3,3,3,3,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,3,3,3,2,2,2,2,1] .empty .empty)) (.node [10,6,3,3,3,3,3,3,3,2,2,1,1] (.node [10,6,3,3,3,3,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,3,3,3,3,2,2,2] .empty .empty))) (.node [10,6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,3,3,3,3,3] (.node [10,6,3,3,3,3,3,3,3,3,2,1] .empty .empty) (.node [10,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_377 : RowTree := (.node [10,6,3,3,3,3,3,3,2,1,1,1,1,1,1,1] degreeTree43_375 degreeTree43_376) - -def degreeTree43_378 : RowTree := (.node [10,6,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,2,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,6,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,4,2,2,2,2,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,6,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,4,3,2,2,2,2,2,2,2,2,2,1,1] (.node [10,6,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,6,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,3,3,2,2,2,2,2,2,2,2,1] (.node [10,6,4,3,3,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,4,3,3,3,2,2,2,2,2,1,1,1,1] (.node [10,6,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,3,3,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,3,3,3,2,2,2,2,2,2,2] (.node [10,6,4,3,3,3,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,6,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_379 : RowTree := (.node [10,6,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] degreeTree43_377 degreeTree43_378) - -def degreeTree43_380 : RowTree := (.node [10,6,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,3,3,3,2,2,2,1,1] (.node [10,6,4,3,3,3,3,2,2,2,2,2,1] (.node [10,6,4,3,3,3,3,2,2,2,1,1,1,1,1] (.node [10,6,4,3,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,3,3,3,2,2,2,2,1,1,1] .empty .empty)) (.node [10,6,4,3,3,3,3,3,2,1,1,1,1,1,1] (.node [10,6,4,3,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,3,3,3,3,2,2,1,1,1,1] .empty .empty))) (.node [10,6,4,3,3,3,3,3,3,2,2,1] (.node [10,6,4,3,3,3,3,3,3,1,1,1,1,1] (.node [10,6,4,3,3,3,3,3,2,2,2,2] .empty .empty) (.node [10,6,4,3,3,3,3,3,3,2,1,1,1] .empty .empty)) (.node [10,6,4,3,3,3,3,3,3,3,2] (.node [10,6,4,3,3,3,3,3,3,3,1,1] .empty .empty) (.node [10,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,4,4,2,2,2,2,2,2,2,2,2,1] (.node [10,6,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,2,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,6,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,3,2,2,2,2,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_381 : RowTree := (.node [10,6,4,4,3,3,3,3,2,1,1,1,1,1] (.node [10,6,4,4,3,3,2,2,2,2,2,2,1] (.node [10,6,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,3,3,2,2,2,2,1,1,1,1,1] (.node [10,6,4,4,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,3,3,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,6,4,4,3,3,3,2,2,2,1,1,1,1] (.node [10,6,4,4,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,3,3,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,3,3,3,2,2,2,2,2] (.node [10,6,4,4,3,3,3,2,2,2,2,1,1] .empty .empty) (.node [10,6,4,4,3,3,3,3,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,3,3,3,3,2,1,1] (.node [10,6,4,4,3,3,3,3,2,2,2,1] (.node [10,6,4,4,3,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,6,4,4,3,3,3,3,3,1,1,1,1] .empty .empty)) (.node [10,6,4,4,3,3,3,3,3,3,1] (.node [10,6,4,4,3,3,3,3,3,2,2] .empty .empty) (.node [10,6,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,4,4,4,2,2,2,2,2,1,1,1,1,1] (.node [10,6,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,4,2,2,2,2,2,2,2,1] (.node [10,6,4,4,4,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_382 : RowTree := (.node [10,6,4,4,3,2,2,2,2,2,2,2,1,1] degreeTree43_380 degreeTree43_381) - -def degreeTree43_383 : RowTree := (.node [10,6,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] degreeTree43_379 degreeTree43_382) - -def degreeTree43_384 : RowTree := (.node [10,6,3,3,3,2,2,2,2,2,2,2,2,2] degreeTree43_374 degreeTree43_383) - -def degreeTree43_385 : RowTree := (.node [10,6,4,4,4,3,3,2,2,2,1,1,1] (.node [10,6,4,4,4,3,2,2,2,2,2,2] (.node [10,6,4,4,4,3,2,2,2,2,1,1,1,1] (.node [10,6,4,4,4,3,2,2,2,1,1,1,1,1,1] (.node [10,6,4,4,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,6,4,4,4,3,2,2,2,2,2,1,1] .empty .empty)) (.node [10,6,4,4,4,3,3,2,1,1,1,1,1,1,1] (.node [10,6,4,4,4,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,3,3,2,2,1,1,1,1,1] .empty .empty))) (.node [10,6,4,4,4,3,3,3,2,2,1,1] (.node [10,6,4,4,4,3,3,3,1,1,1,1,1,1] (.node [10,6,4,4,4,3,3,2,2,2,2,1] .empty .empty) (.node [10,6,4,4,4,3,3,3,2,1,1,1,1] .empty .empty)) (.node [10,6,4,4,4,3,3,3,3,1,1,1] (.node [10,6,4,4,4,3,3,3,2,2,2] .empty .empty) (.node [10,6,4,4,4,3,3,3,3,2,1] .empty .empty)))) - -def degreeTree43_386 : RowTree := (.node [10,6,4,4,4,4,3,2,1,1,1,1,1,1] (.node [10,6,4,4,4,4,2,2,2,1,1,1,1,1] (.node [10,6,4,4,4,4,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,4,4,2,2,2,2,2,1] (.node [10,6,4,4,4,4,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,4,4,4,4,3,3,1,1,1,1,1] (.node [10,6,4,4,4,4,3,2,2,2,1,1] (.node [10,6,4,4,4,4,3,2,2,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,3,2,2,2,2] .empty .empty)) (.node [10,6,4,4,4,4,3,3,2,2,1] (.node [10,6,4,4,4,4,3,3,2,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,3,3,3,1,1] .empty .empty)))) - -def degreeTree43_387 : RowTree := (.node [10,6,4,4,4,3,3,3,3,3] degreeTree43_385 degreeTree43_386) - -def degreeTree43_388 : RowTree := (.node [10,6,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,4,4,4,4,4,3,3,1] (.node [10,6,4,4,4,4,4,2,2,2,1] (.node [10,6,4,4,4,4,4,2,1,1,1,1,1] (.node [10,6,4,4,4,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,4,2,2,1,1,1] .empty .empty)) (.node [10,6,4,4,4,4,4,3,2,1,1] (.node [10,6,4,4,4,4,4,3,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,4,3,2,2] .empty .empty))) (.node [10,6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,4,4,4,4,2,1] (.node [10,6,4,4,4,4,4,4,1,1,1] .empty .empty) (.node [10,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,2,2,2,2,2,2,2,2,2,2,2] (.node [10,6,5,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,6,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,6,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,3,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,3,2,2,2,2,2,2,2,2,2,1] (.node [10,6,5,3,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_389 : RowTree := (.node [10,6,4,4,4,4,3,3,3,2] degreeTree43_387 degreeTree43_388) - -def degreeTree43_390 : RowTree := (.node [10,6,5,3,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,6,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,3,3,2,2,2,2,2,2,2,1,1] (.node [10,6,5,3,3,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,2,2,2,2,2,2,2,2] .empty .empty))) (.node [10,6,5,3,3,3,2,2,2,2,1,1,1,1,1] (.node [10,6,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,3,3,3,2,2,2,2,2,2,1] (.node [10,6,5,3,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,5,3,3,3,3,3,2,2,2,1] (.node [10,6,5,3,3,3,3,2,2,2,2,2] (.node [10,6,5,3,3,3,3,2,2,2,1,1,1,1] (.node [10,6,5,3,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,3,3,2,2,2,2,1,1] .empty .empty)) (.node [10,6,5,3,3,3,3,3,2,1,1,1,1,1] (.node [10,6,5,3,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,3,3,3,2,2,1,1,1] .empty .empty))) (.node [10,6,5,3,3,3,3,3,3,3,1] (.node [10,6,5,3,3,3,3,3,3,2,1,1] (.node [10,6,5,3,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,3,3,3,3,2,2] .empty .empty)) (.node [10,6,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_391 : RowTree := (.node [10,6,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,2,2,2,2,2,2,2,1,1,1,1] (.node [10,6,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,2,2,2,2,2,2,2,2,2] (.node [10,6,5,4,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,6,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,4,3,2,2,2,2,2,1,1,1,1,1] (.node [10,6,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,3,2,2,2,2,2,2,2,1] (.node [10,6,5,4,3,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,5,4,3,3,3,2,2,1,1,1,1,1] (.node [10,6,5,4,3,3,2,2,2,2,2,1,1] (.node [10,6,5,4,3,3,2,2,2,1,1,1,1,1,1] (.node [10,6,5,4,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,3,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,6,5,4,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,6,5,4,3,3,3,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,4,3,3,3,3,2,1,1,1,1] (.node [10,6,5,4,3,3,3,2,2,2,2,1] (.node [10,6,5,4,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,4,3,3,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,3,3,3,3,2,2,2] (.node [10,6,5,4,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,6,5,4,3,3,3,3,3,1,1,1] .empty .empty))))) - -def degreeTree43_392 : RowTree := (.node [10,6,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_390 degreeTree43_391) - -def degreeTree43_393 : RowTree := (.node [10,6,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_389 degreeTree43_392) - -def degreeTree43_394 : RowTree := (.node [10,6,5,4,4,2,2,2,2,2,2,2] (.node [10,6,5,4,4,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,3,3,3,3,3,3] .empty .empty) .empty) (.node [10,6,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,4,2,2,2,2,2,1,1,1,1] (.node [10,6,5,4,4,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,2,2,2,2,2,2,1,1] .empty .empty))) (.node [10,6,5,4,4,3,2,2,2,1,1,1,1,1] (.node [10,6,5,4,4,3,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,3,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,4,3,2,2,2,2,2,1] (.node [10,6,5,4,4,3,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,4,4,3,3,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_395 : RowTree := (.node [10,6,5,4,4,3,3,3,3,2] (.node [10,6,5,4,4,3,3,3,1,1,1,1,1] (.node [10,6,5,4,4,3,3,2,2,2,1,1] (.node [10,6,5,4,4,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,3,3,2,2,2,2] .empty .empty)) (.node [10,6,5,4,4,3,3,3,2,2,1] (.node [10,6,5,4,4,3,3,3,2,1,1,1] .empty .empty) (.node [10,6,5,4,4,3,3,3,3,1,1] .empty .empty))) (.node [10,6,5,4,4,4,2,2,2,1,1,1,1] (.node [10,6,5,4,4,4,2,1,1,1,1,1,1,1,1] (.node [10,6,5,4,4,4,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,4,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,4,4,2,2,2,2,2] (.node [10,6,5,4,4,4,2,2,2,2,1,1] .empty .empty) (.node [10,6,5,4,4,4,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_396 : RowTree := (.node [10,6,5,4,4,3,3,2,1,1,1,1,1,1] degreeTree43_394 degreeTree43_395) - -def degreeTree43_397 : RowTree := (.node [10,6,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,4,4,4,2,1,1,1,1] (.node [10,6,5,4,4,4,3,3,2,1,1] (.node [10,6,5,4,4,4,3,2,2,2,1] (.node [10,6,5,4,4,4,3,2,2,1,1,1] .empty .empty) (.node [10,6,5,4,4,4,3,3,1,1,1,1] .empty .empty)) (.node [10,6,5,4,4,4,3,3,3,1] (.node [10,6,5,4,4,4,3,3,2,2] .empty .empty) (.node [10,6,5,4,4,4,4,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,4,4,4,4,3,2,1] (.node [10,6,5,4,4,4,4,2,2,2] (.node [10,6,5,4,4,4,4,2,2,1,1] .empty .empty) (.node [10,6,5,4,4,4,4,3,1,1,1] .empty .empty)) (.node [10,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,4,4,4,4,1,1] .empty .empty) (.node [10,6,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,5,2,2,2,2,2,2,2,2,1] (.node [10,6,5,5,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,5,3,2,2,2,2,2,1,1,1,1] (.node [10,6,5,5,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,3,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,5,3,2,2,2,2,2,2,2] (.node [10,6,5,5,3,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,6,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_398 : RowTree := (.node [10,6,5,4,4,4,3,2,1,1,1,1,1] degreeTree43_396 degreeTree43_397) - -def degreeTree43_399 : RowTree := (.node [10,6,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,3,3,3,2,2,2,1,1] (.node [10,6,5,5,3,3,2,2,2,2,2,1] (.node [10,6,5,5,3,3,2,2,2,1,1,1,1,1] (.node [10,6,5,5,3,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,3,3,2,2,2,2,1,1,1] .empty .empty)) (.node [10,6,5,5,3,3,3,2,1,1,1,1,1,1] (.node [10,6,5,5,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,3,3,3,2,2,1,1,1,1] .empty .empty))) (.node [10,6,5,5,3,3,3,3,2,2,1] (.node [10,6,5,5,3,3,3,3,1,1,1,1,1] (.node [10,6,5,5,3,3,3,2,2,2,2] .empty .empty) (.node [10,6,5,5,3,3,3,3,2,1,1,1] .empty .empty)) (.node [10,6,5,5,3,3,3,3,3,2] (.node [10,6,5,5,3,3,3,3,3,1,1] .empty .empty) (.node [10,6,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,5,5,4,3,2,2,1,1,1,1,1,1] (.node [10,6,5,5,4,2,2,2,2,2,1,1,1] (.node [10,6,5,5,4,2,2,2,1,1,1,1,1,1,1] (.node [10,6,5,5,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,4,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,5,5,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,4,2,2,2,2,2,2,1] .empty .empty) (.node [10,6,5,5,4,3,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,5,4,3,3,1,1,1,1,1,1,1] (.node [10,6,5,5,4,3,2,2,2,2,1,1] (.node [10,6,5,5,4,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,6,5,5,4,3,2,2,2,2,2] .empty .empty)) (.node [10,6,5,5,4,3,3,2,2,1,1,1] (.node [10,6,5,5,4,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,4,3,3,2,2,2,1] .empty .empty))))) - -def degreeTree43_400 : RowTree := (.node [10,6,5,5,4,4,4,2,1,1,1] (.node [10,6,5,5,4,4,2,2,2,2,1] (.node [10,6,5,5,4,4,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,4,3,3,3,2,2] (.node [10,6,5,5,4,3,3,3,2,1,1] .empty .empty) (.node [10,6,5,5,4,3,3,3,3,1] .empty .empty)) (.node [10,6,5,5,4,4,2,2,1,1,1,1,1] (.node [10,6,5,5,4,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,4,4,2,2,2,1,1,1] .empty .empty))) (.node [10,6,5,5,4,4,3,2,2,2] (.node [10,6,5,5,4,4,3,2,1,1,1,1] (.node [10,6,5,5,4,4,3,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,4,4,3,2,2,1,1] .empty .empty)) (.node [10,6,5,5,4,4,3,3,2,1] (.node [10,6,5,5,4,4,3,3,1,1,1] .empty .empty) (.node [10,6,5,5,4,4,4,1,1,1,1,1] .empty .empty)))) (.node [10,6,5,5,5,2,2,2,2,2,1,1] (.node [10,6,5,5,5,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,4,4,4,3,1,1] (.node [10,6,5,5,4,4,4,2,2,1] .empty .empty) (.node [10,6,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,5,5,2,2,2,1,1,1,1,1,1] (.node [10,6,5,5,5,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,5,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,6,5,5,5,3,2,2,1,1,1,1,1] (.node [10,6,5,5,5,3,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,5,2,2,2,2,2,2] .empty .empty) (.node [10,6,5,5,5,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,5,5,3,2,2,2,2,1] (.node [10,6,5,5,5,3,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,5,5,3,3,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_401 : RowTree := (.node [10,6,5,5,4,3,3,3,1,1,1,1] degreeTree43_399 degreeTree43_400) - -def degreeTree43_402 : RowTree := (.node [10,6,5,5,3,3,2,1,1,1,1,1,1,1,1,1] degreeTree43_398 degreeTree43_401) - -def degreeTree43_403 : RowTree := (.node [10,6,5,4,3,3,3,3,3,2,1] degreeTree43_393 degreeTree43_402) - -def degreeTree43_404 : RowTree := (.node [10,6,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_384 degreeTree43_403) - -def degreeTree43_405 : RowTree := (.node [10,5,5,5,3,3,3,3,3,3] degreeTree43_365 degreeTree43_404) - -def degreeTree43_406 : RowTree := (.node [10,6,5,5,5,4,2,2,2,2] (.node [10,6,5,5,5,4,1,1,1,1,1,1,1,1] (.node [10,6,5,5,5,3,3,3,1,1,1] (.node [10,6,5,5,5,3,3,2,2,2] (.node [10,6,5,5,5,3,3,2,2,1,1] .empty .empty) .empty) (.node [10,6,5,5,5,3,3,3,2,1] .empty .empty)) (.node [10,6,5,5,5,4,2,2,1,1,1,1] (.node [10,6,5,5,5,4,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,5,4,2,2,2,1,1] .empty .empty))) (.node [10,6,5,5,5,4,3,3,1,1] (.node [10,6,5,5,5,4,3,2,1,1,1] (.node [10,6,5,5,5,4,3,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,5,4,3,2,2,1] .empty .empty)) (.node [10,6,5,5,5,4,4,2,1,1] (.node [10,6,5,5,5,4,4,1,1,1,1] .empty .empty) (.node [10,6,5,5,5,5,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_407 : RowTree := (.node [10,6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,5,5,3,2,1,1] (.node [10,6,5,5,5,5,2,2,2,1] (.node [10,6,5,5,5,5,2,2,1,1,1] .empty .empty) (.node [10,6,5,5,5,5,3,1,1,1,1] .empty .empty)) (.node [10,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,5,5,4,1,1,1] .empty .empty) (.node [10,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,6,6,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,6,2,2,2,2,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree43_408 : RowTree := (.node [10,6,5,5,5,5,2,1,1,1,1,1] degreeTree43_406 degreeTree43_407) - -def degreeTree43_409 : RowTree := (.node [10,6,6,3,3,2,2,2,2,2,2,1,1,1] (.node [10,6,6,3,2,2,2,2,2,2,2,2,1,1] (.node [10,6,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,6,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,6,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)))) (.node [10,6,6,3,3,3,2,2,2,2,2,2] (.node [10,6,6,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,6,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,6,6,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,3,3,3,2,2,2,2,1,1,1,1] (.node [10,6,6,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,3,3,2,2,2,2,2,1,1] .empty .empty))) (.node [10,6,6,3,3,3,3,2,2,2,1,1,1] (.node [10,6,6,3,3,3,3,2,1,1,1,1,1,1,1] (.node [10,6,6,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,3,3,3,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,6,3,3,3,3,3,1,1,1,1,1,1] (.node [10,6,6,3,3,3,3,2,2,2,2,1] .empty .empty) (.node [10,6,6,3,3,3,3,3,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_410 : RowTree := (.node [10,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_408 degreeTree43_409) - -def degreeTree43_411 : RowTree := (.node [10,6,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,3,3,3,3,3,3] (.node [10,6,6,3,3,3,3,3,3,1,1,1] (.node [10,6,6,3,3,3,3,3,2,2,2] .empty .empty) (.node [10,6,6,3,3,3,3,3,3,2,1] .empty .empty)) (.node [10,6,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,6,4,2,2,2,2,2,2,2,1,1,1] (.node [10,6,6,4,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,6,4,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,6,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,6,4,3,3,2,2,1,1,1,1,1,1,1] (.node [10,6,6,4,3,2,2,2,2,2,2,1,1] (.node [10,6,6,4,3,2,2,2,2,1,1,1,1,1,1] (.node [10,6,6,4,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,3,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,6,6,4,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,6,4,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,6,4,3,3,3,1,1,1,1,1,1,1,1] (.node [10,6,6,4,3,3,2,2,2,2,1,1,1] (.node [10,6,6,4,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,3,3,2,2,2,2,2,1] .empty .empty)) (.node [10,6,6,4,3,3,3,2,2,1,1,1,1] (.node [10,6,6,4,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,3,3,3,2,2,2,1,1] .empty .empty))))) - -def degreeTree43_412 : RowTree := (.node [10,6,6,4,4,3,2,2,2,1,1,1,1] (.node [10,6,6,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,3,3,3,3,3,1,1] (.node [10,6,6,4,3,3,3,3,2,1,1,1] (.node [10,6,6,4,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,3,3,3,3,2,2,1] .empty .empty)) (.node [10,6,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,3,3,3,3,3,2] .empty .empty) (.node [10,6,6,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,6,4,4,2,2,2,2,2,2,1] (.node [10,6,6,4,4,2,2,2,2,1,1,1,1,1] (.node [10,6,6,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,4,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,6,6,4,4,3,2,1,1,1,1,1,1,1,1] (.node [10,6,6,4,4,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,4,3,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,6,4,4,3,3,3,2,1,1] (.node [10,6,6,4,4,3,3,2,1,1,1,1,1] (.node [10,6,6,4,4,3,2,2,2,2,2] (.node [10,6,6,4,4,3,2,2,2,2,1,1] .empty .empty) (.node [10,6,6,4,4,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,4,4,3,3,2,2,2,1] (.node [10,6,6,4,4,3,3,2,2,1,1,1] .empty .empty) (.node [10,6,6,4,4,3,3,3,1,1,1,1] .empty .empty))) (.node [10,6,6,4,4,4,2,1,1,1,1,1,1,1] (.node [10,6,6,4,4,3,3,3,3,1] (.node [10,6,6,4,4,3,3,3,2,2] .empty .empty) (.node [10,6,6,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,4,4,4,2,2,2,1,1,1] (.node [10,6,6,4,4,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,4,4,2,2,2,2,1] .empty .empty))))) - -def degreeTree43_413 : RowTree := (.node [10,6,6,4,3,3,3,2,2,2,2] degreeTree43_411 degreeTree43_412) - -def degreeTree43_414 : RowTree := (.node [10,6,6,3,3,3,3,3,2,2,1,1] degreeTree43_410 degreeTree43_413) - -def degreeTree43_415 : RowTree := (.node [10,6,6,4,4,4,4,3,1,1] (.node [10,6,6,4,4,4,3,3,2,1] (.node [10,6,6,4,4,4,3,2,2,2] (.node [10,6,6,4,4,4,3,2,2,1,1] (.node [10,6,6,4,4,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,6,6,4,4,4,3,3,1,1,1] .empty .empty)) (.node [10,6,6,4,4,4,4,2,1,1,1] (.node [10,6,6,4,4,4,4,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,4,4,4,2,2,1] .empty .empty))) (.node [10,6,6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,6,5,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,2,2,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree43_416 : RowTree := (.node [10,6,6,5,3,2,2,2,2,2,2,1] (.node [10,6,6,5,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,3,2,2,2,2,1,1,1,1,1] (.node [10,6,6,5,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,3,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,6,6,5,3,3,2,2,2,1,1,1,1] (.node [10,6,6,5,3,3,2,1,1,1,1,1,1,1,1] (.node [10,6,6,5,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,3,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,3,3,2,2,2,2,2] (.node [10,6,6,5,3,3,2,2,2,2,1,1] .empty .empty) (.node [10,6,6,5,3,3,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_417 : RowTree := (.node [10,6,6,5,2,2,2,2,2,2,2,1,1] degreeTree43_415 degreeTree43_416) - -def degreeTree43_418 : RowTree := (.node [10,6,6,5,4,3,2,2,1,1,1,1,1] (.node [10,6,6,5,4,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,3,3,3,3,2,1,1] (.node [10,6,6,5,3,3,3,2,2,2,1] (.node [10,6,6,5,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,6,6,5,3,3,3,3,1,1,1,1] .empty .empty)) (.node [10,6,6,5,3,3,3,3,3,1] (.node [10,6,6,5,3,3,3,3,2,2] .empty .empty) (.node [10,6,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,6,5,4,2,2,2,2,2,1,1] (.node [10,6,6,5,4,2,2,2,1,1,1,1,1,1] (.node [10,6,6,5,4,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,4,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,6,6,5,4,3,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,4,2,2,2,2,2,2] .empty .empty) (.node [10,6,6,5,4,3,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,6,5,4,3,3,3,2,1] (.node [10,6,6,5,4,3,3,2,1,1,1,1] (.node [10,6,6,5,4,3,2,2,2,2,1] (.node [10,6,6,5,4,3,2,2,2,1,1,1] .empty .empty) (.node [10,6,6,5,4,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,4,3,3,2,2,2] (.node [10,6,6,5,4,3,3,2,2,1,1] .empty .empty) (.node [10,6,6,5,4,3,3,3,1,1,1] .empty .empty))) (.node [10,6,6,5,4,4,2,2,2,1,1] (.node [10,6,6,5,4,4,2,1,1,1,1,1,1] (.node [10,6,6,5,4,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,4,4,2,2,1,1,1,1] .empty .empty)) (.node [10,6,6,5,4,4,3,1,1,1,1,1] (.node [10,6,6,5,4,4,2,2,2,2] .empty .empty) (.node [10,6,6,5,4,4,3,2,1,1,1] .empty .empty))))) - -def degreeTree43_419 : RowTree := (.node [10,6,6,5,3,3,3,2,1,1,1,1,1] degreeTree43_417 degreeTree43_418) - -def degreeTree43_420 : RowTree := (.node [10,6,6,5,5,3,3,2,1,1,1] (.node [10,6,6,5,5,2,2,2,2,1,1,1] (.node [10,6,6,5,5,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,4,4,4,1,1,1,1] (.node [10,6,6,5,4,4,3,3,1,1] .empty .empty) (.node [10,6,6,5,4,4,4,2,1,1] .empty .empty)) (.node [10,6,6,5,5,2,2,1,1,1,1,1,1,1] (.node [10,6,6,5,5,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,5,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,6,6,5,5,3,2,2,1,1,1,1] (.node [10,6,6,5,5,3,1,1,1,1,1,1,1,1] (.node [10,6,6,5,5,2,2,2,2,2,1] .empty .empty) (.node [10,6,6,5,5,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,5,3,2,2,2,2] (.node [10,6,6,5,5,3,2,2,2,1,1] .empty .empty) (.node [10,6,6,5,5,3,3,1,1,1,1,1] .empty .empty)))) (.node [10,6,6,5,5,4,3,2,1,1] (.node [10,6,6,5,5,4,2,1,1,1,1,1] (.node [10,6,6,5,5,3,3,3,1,1] (.node [10,6,6,5,5,3,3,2,2,1] .empty .empty) (.node [10,6,6,5,5,4,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,5,4,2,2,2,1] (.node [10,6,6,5,5,4,2,2,1,1,1] .empty .empty) (.node [10,6,6,5,5,4,3,1,1,1,1] .empty .empty))) (.node [10,6,6,5,5,5,2,2,1,1] (.node [10,6,6,5,5,5,1,1,1,1,1,1] (.node [10,6,6,5,5,4,4,1,1,1] .empty .empty) (.node [10,6,6,5,5,5,2,1,1,1,1] .empty .empty)) (.node [10,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,5,5,3,1,1,1] .empty .empty) (.node [10,6,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_421 : RowTree := (.node [10,6,6,6,3,3,2,2,2,1,1,1] (.node [10,6,6,6,3,2,2,1,1,1,1,1,1,1,1] (.node [10,6,6,6,2,2,2,2,2,2,1,1,1] (.node [10,6,6,6,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,6,6,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,6,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,6,6,6,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,6,6,3,2,2,2,2,2,2] (.node [10,6,6,6,3,2,2,2,2,1,1,1,1] (.node [10,6,6,6,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,3,2,2,2,2,2,1,1] .empty .empty)) (.node [10,6,6,6,3,3,2,1,1,1,1,1,1,1] (.node [10,6,6,6,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,3,3,2,2,1,1,1,1,1] .empty .empty)))) (.node [10,6,6,6,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,6,3,3,3,2,2,1,1] (.node [10,6,6,6,3,3,3,1,1,1,1,1,1] (.node [10,6,6,6,3,3,2,2,2,2,1] .empty .empty) (.node [10,6,6,6,3,3,3,2,1,1,1,1] .empty .empty)) (.node [10,6,6,6,3,3,3,3,1,1,1] (.node [10,6,6,6,3,3,3,2,2,2] .empty .empty) (.node [10,6,6,6,3,3,3,3,2,1] .empty .empty))) (.node [10,6,6,6,4,2,2,2,2,1,1,1] (.node [10,6,6,6,4,2,2,1,1,1,1,1,1,1] (.node [10,6,6,6,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,4,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,6,6,4,3,1,1,1,1,1,1,1,1] (.node [10,6,6,6,4,2,2,2,2,2,1] .empty .empty) (.node [10,6,6,6,4,3,2,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_422 : RowTree := (.node [10,6,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_420 degreeTree43_421) - -def degreeTree43_423 : RowTree := (.node [10,6,6,5,4,4,3,2,2,1] degreeTree43_419 degreeTree43_422) - -def degreeTree43_424 : RowTree := (.node [10,6,6,4,4,4,3,1,1,1,1,1,1] degreeTree43_414 degreeTree43_423) - -def degreeTree43_425 : RowTree := (.node [10,6,6,6,4,4,2,2,1,1,1] (.node [10,6,6,6,4,3,3,2,2,1] (.node [10,6,6,6,4,3,3,1,1,1,1,1] (.node [10,6,6,6,4,3,2,2,2,2] (.node [10,6,6,6,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [10,6,6,6,4,3,3,2,1,1,1] .empty .empty)) (.node [10,6,6,6,4,4,1,1,1,1,1,1,1] (.node [10,6,6,6,4,3,3,3,1,1] .empty .empty) (.node [10,6,6,6,4,4,2,1,1,1,1,1] .empty .empty))) (.node [10,6,6,6,4,4,4,1,1,1] (.node [10,6,6,6,4,4,3,1,1,1,1] (.node [10,6,6,6,4,4,2,2,2,1] .empty .empty) (.node [10,6,6,6,4,4,3,2,1,1] .empty .empty)) (.node [10,6,6,6,5,2,1,1,1,1,1,1,1,1] (.node [10,6,6,6,5,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,5,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_426 : RowTree := (.node [10,6,6,6,5,3,3,2,1,1] (.node [10,6,6,6,5,3,2,1,1,1,1,1] (.node [10,6,6,6,5,2,2,2,2,2] (.node [10,6,6,6,5,2,2,2,2,1,1] .empty .empty) (.node [10,6,6,6,5,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,6,5,3,2,2,2,1] (.node [10,6,6,6,5,3,2,2,1,1,1] .empty .empty) (.node [10,6,6,6,5,3,3,1,1,1,1] .empty .empty))) (.node [10,6,6,6,5,4,3,1,1,1] (.node [10,6,6,6,5,4,2,1,1,1,1] (.node [10,6,6,6,5,4,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,5,4,2,2,1,1] .empty .empty)) (.node [10,6,6,6,5,5,2,1,1,1] (.node [10,6,6,6,5,5,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,6,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_427 : RowTree := (.node [10,6,6,6,5,2,2,2,1,1,1,1] degreeTree43_425 degreeTree43_426) - -def degreeTree43_428 : RowTree := (.node [10,7,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,6,6,6,4,1,1,1,1,1] (.node [10,6,6,6,6,3,1,1,1,1,1,1] (.node [10,6,6,6,6,2,2,2,1,1,1] (.node [10,6,6,6,6,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,6,2,2,2,2,1] .empty .empty)) (.node [10,6,6,6,6,3,2,2,1,1] (.node [10,6,6,6,6,3,2,1,1,1,1] .empty .empty) (.node [10,6,6,6,6,3,3,1,1,1] .empty .empty))) (.node [10,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,6,6,5,1,1,1,1] (.node [10,6,6,6,6,4,2,1,1,1] .empty .empty) (.node [10,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,7,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,2,2,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,7,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,2,2,2,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,7,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,3,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,7,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,7,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_429 : RowTree := (.node [10,6,6,6,6,2,1,1,1,1,1,1,1] degreeTree43_427 degreeTree43_428) - -def degreeTree43_430 : RowTree := (.node [10,7,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,7,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,2,2,2,2,2,2,2,2,2,2] (.node [10,7,3,3,2,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,2,2,2,2,2,2,2,1,1,1] (.node [10,7,3,3,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,3,3,3,2,2,2,2,2,2,2,2,1] .empty .empty)))) (.node [10,7,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,7,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,3,2,2,2,2,2,2,1,1] (.node [10,7,3,3,3,3,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,3,3,3,3,2,2,2,2,2,2,2] .empty .empty))) (.node [10,7,3,3,3,3,3,2,2,2,2,1,1,1] (.node [10,7,3,3,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,3,3,3,3,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,3,3,3,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,3,2,2,2,2,2,1] .empty .empty) (.node [10,7,3,3,3,3,3,3,2,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_431 : RowTree := (.node [10,7,4,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,3,3,3,2,1,1,1] (.node [10,7,3,3,3,3,3,3,2,2,2,2] (.node [10,7,3,3,3,3,3,3,2,2,2,1,1] .empty .empty) (.node [10,7,3,3,3,3,3,3,3,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,3,3,3,3,3,1,1] (.node [10,7,3,3,3,3,3,3,3,2,2,1] .empty .empty) (.node [10,7,3,3,3,3,3,3,3,3,2] .empty .empty))) (.node [10,7,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,7,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)))) (.node [10,7,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,2,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,2,2,2,2,2,2,2,2,1,1,1] (.node [10,7,4,3,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,2,2,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,7,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_432 : RowTree := (.node [10,7,3,3,3,3,3,3,2,2,1,1,1,1] degreeTree43_430 degreeTree43_431) - -def degreeTree43_433 : RowTree := (.node [10,7,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_429 degreeTree43_432) - -def degreeTree43_434 : RowTree := (.node [10,7,4,3,3,3,2,2,2,2,1,1,1,1,1] (.node [10,7,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,2,2,2,2,2,2,2,1,1] (.node [10,7,4,3,3,2,2,2,2,2,2,1,1,1,1] (.node [10,7,4,3,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,7,4,3,3,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,7,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,4,3,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,3,2,2,2,2,2,2,1] (.node [10,7,4,3,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,3,3,3,3,2,2,2,1,1,1,1] (.node [10,7,4,3,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,3,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree43_435 : RowTree := (.node [10,7,4,3,3,3,3,3,3,3,1] (.node [10,7,4,3,3,3,3,3,2,2,2,1] (.node [10,7,4,3,3,3,3,3,2,1,1,1,1,1] (.node [10,7,4,3,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,3,3,2,2,1,1,1] .empty .empty)) (.node [10,7,4,3,3,3,3,3,3,2,1,1] (.node [10,7,4,3,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,3,3,3,2,2] .empty .empty))) (.node [10,7,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_436 : RowTree := (.node [10,7,4,3,3,3,3,2,2,2,2,2] degreeTree43_434 degreeTree43_435) - -def degreeTree43_437 : RowTree := (.node [10,7,4,4,3,3,2,2,2,2,2,1,1] (.node [10,7,4,4,3,2,2,2,2,2,1,1,1,1,1] (.node [10,7,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,2,2,2,2,2,2,2,2,2] (.node [10,7,4,4,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,3,2,2,2,2,2,2,2,1] (.node [10,7,4,4,3,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,7,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,3,3,2,2,2,1,1,1,1,1,1] (.node [10,7,4,4,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,3,3,2,2,2,2,1,1,1,1] .empty .empty)))) (.node [10,7,4,4,3,3,3,3,2,1,1,1,1] (.node [10,7,4,4,3,3,3,2,2,1,1,1,1,1] (.node [10,7,4,4,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,7,4,4,3,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,3,3,3,2,2,2,2,1] (.node [10,7,4,4,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,7,4,4,3,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,7,4,4,3,3,3,3,3,2,1] (.node [10,7,4,4,3,3,3,3,2,2,2] (.node [10,7,4,4,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,7,4,4,3,3,3,3,3,1,1,1] .empty .empty)) (.node [10,7,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,3,3,3,3,3,3] .empty .empty) (.node [10,7,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_438 : RowTree := (.node [10,7,4,4,2,2,2,2,2,2,2,1,1,1,1] degreeTree43_436 degreeTree43_437) - -def degreeTree43_439 : RowTree := (.node [10,7,4,4,4,3,3,2,2,2,2] (.node [10,7,4,4,4,3,2,2,1,1,1,1,1,1,1] (.node [10,7,4,4,4,2,2,2,2,2,2,1,1] (.node [10,7,4,4,4,2,2,2,2,1,1,1,1,1,1] (.node [10,7,4,4,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,7,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,4,2,2,2,2,2,2,2] .empty .empty) (.node [10,7,4,4,4,3,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,4,4,4,3,3,1,1,1,1,1,1,1,1] (.node [10,7,4,4,4,3,2,2,2,2,1,1,1] (.node [10,7,4,4,4,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,3,2,2,2,2,2,1] .empty .empty)) (.node [10,7,4,4,4,3,3,2,2,1,1,1,1] (.node [10,7,4,4,4,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,3,3,2,2,2,1,1] .empty .empty)))) (.node [10,7,4,4,4,4,2,2,1,1,1,1,1,1] (.node [10,7,4,4,4,3,3,3,3,1,1] (.node [10,7,4,4,4,3,3,3,2,1,1,1] (.node [10,7,4,4,4,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,3,3,3,2,2,1] .empty .empty)) (.node [10,7,4,4,4,4,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,4,3,3,3,3,2] .empty .empty) (.node [10,7,4,4,4,4,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,4,4,4,4,3,1,1,1,1,1,1,1] (.node [10,7,4,4,4,4,2,2,2,2,1,1] (.node [10,7,4,4,4,4,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,4,2,2,2,2,2] .empty .empty)) (.node [10,7,4,4,4,4,3,2,2,1,1,1] (.node [10,7,4,4,4,4,3,2,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,4,3,2,2,2,1] .empty .empty))))) - -def degreeTree43_440 : RowTree := (.node [10,7,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,4,4,4,3,1,1,1] (.node [10,7,4,4,4,4,4,1,1,1,1,1,1] (.node [10,7,4,4,4,4,3,3,2,2] (.node [10,7,4,4,4,4,3,3,2,1,1] .empty .empty) (.node [10,7,4,4,4,4,3,3,3,1] .empty .empty)) (.node [10,7,4,4,4,4,4,2,2,1,1] (.node [10,7,4,4,4,4,4,2,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,4,4,2,2,2] .empty .empty))) (.node [10,7,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,4,4,4,4,1,1] (.node [10,7,4,4,4,4,4,3,2,1] .empty .empty) (.node [10,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,7,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,2,2,2,2,2,2,2,2,2,2,1] (.node [10,7,5,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,7,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,7,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,5,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,7,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,3,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,3,2,2,2,2,2,2,2,2,2] (.node [10,7,5,3,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_441 : RowTree := (.node [10,7,4,4,4,4,3,3,1,1,1,1] degreeTree43_439 degreeTree43_440) - -def degreeTree43_442 : RowTree := (.node [10,7,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_438 degreeTree43_441) - -def degreeTree43_443 : RowTree := (.node [10,7,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1] degreeTree43_433 degreeTree43_442) - -def degreeTree43_444 : RowTree := (.node [10,6,6,6,4,3,2,2,1,1,1,1] degreeTree43_424 degreeTree43_443) - -def degreeTree43_445 : RowTree := (.node [10,7,5,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,7,5,3,3,2,2,2,2,2,2,1,1,1] (.node [10,7,5,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,7,5,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,3,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,5,3,3,3,2,2,2,2,2,2] (.node [10,7,5,3,3,3,2,2,2,2,1,1,1,1] (.node [10,7,5,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,3,3,3,2,2,2,2,2,1,1] .empty .empty)) (.node [10,7,5,3,3,3,3,2,1,1,1,1,1,1,1] (.node [10,7,5,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,3,3,3,3,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_446 : RowTree := (.node [10,7,5,3,3,3,3,3,3,3] (.node [10,7,5,3,3,3,3,3,2,2,1,1] (.node [10,7,5,3,3,3,3,3,1,1,1,1,1,1] (.node [10,7,5,3,3,3,3,2,2,2,2,1] .empty .empty) (.node [10,7,5,3,3,3,3,3,2,1,1,1,1] .empty .empty)) (.node [10,7,5,3,3,3,3,3,3,1,1,1] (.node [10,7,5,3,3,3,3,3,2,2,2] .empty .empty) (.node [10,7,5,3,3,3,3,3,3,2,1] .empty .empty))) (.node [10,7,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,4,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_447 : RowTree := (.node [10,7,5,3,3,3,3,2,2,2,1,1,1] degreeTree43_445 degreeTree43_446) - -def degreeTree43_448 : RowTree := (.node [10,7,5,4,3,3,3,1,1,1,1,1,1,1,1] (.node [10,7,5,4,3,2,2,2,2,2,2,1,1] (.node [10,7,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,4,3,2,2,2,2,1,1,1,1,1,1] (.node [10,7,5,4,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,3,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,7,5,4,3,3,2,2,1,1,1,1,1,1,1] (.node [10,7,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,7,5,4,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,4,3,3,2,2,2,2,1,1,1] (.node [10,7,5,4,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,3,3,2,2,2,2,2,1] .empty .empty)))) (.node [10,7,5,4,3,3,3,3,3,1,1] (.node [10,7,5,4,3,3,3,2,2,2,2] (.node [10,7,5,4,3,3,3,2,2,1,1,1,1] (.node [10,7,5,4,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,7,5,4,3,3,3,3,2,1,1,1] (.node [10,7,5,4,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,3,3,3,3,2,2,1] .empty .empty))) (.node [10,7,5,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,3,3,3,3,3,2] .empty .empty) (.node [10,7,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,4,4,2,2,2,2,1,1,1,1,1] (.node [10,7,5,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,4,2,2,2,2,2,1,1,1] .empty .empty))))) - -def degreeTree43_449 : RowTree := (.node [10,7,5,4,2,2,2,2,2,2,2,1,1,1] degreeTree43_447 degreeTree43_448) - -def degreeTree43_450 : RowTree := (.node [10,7,5,4,4,4,2,1,1,1,1,1,1,1] (.node [10,7,5,4,4,3,3,2,1,1,1,1,1] (.node [10,7,5,4,4,3,2,2,2,1,1,1,1] (.node [10,7,5,4,4,3,2,1,1,1,1,1,1,1,1] (.node [10,7,5,4,4,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,4,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,4,4,3,2,2,2,2,2] (.node [10,7,5,4,4,3,2,2,2,2,1,1] .empty .empty) (.node [10,7,5,4,4,3,3,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,5,4,4,3,3,3,2,1,1] (.node [10,7,5,4,4,3,3,2,2,2,1] (.node [10,7,5,4,4,3,3,2,2,1,1,1] .empty .empty) (.node [10,7,5,4,4,3,3,3,1,1,1,1] .empty .empty)) (.node [10,7,5,4,4,3,3,3,3,1] (.node [10,7,5,4,4,3,3,3,2,2] .empty .empty) (.node [10,7,5,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,7,5,4,4,4,3,3,1,1,1] (.node [10,7,5,4,4,4,3,1,1,1,1,1,1] (.node [10,7,5,4,4,4,2,2,2,1,1,1] (.node [10,7,5,4,4,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,4,4,2,2,2,2,1] .empty .empty)) (.node [10,7,5,4,4,4,3,2,2,1,1] (.node [10,7,5,4,4,4,3,2,1,1,1,1] .empty .empty) (.node [10,7,5,4,4,4,3,2,2,2] .empty .empty))) (.node [10,7,5,4,4,4,4,2,2,1] (.node [10,7,5,4,4,4,4,1,1,1,1,1] (.node [10,7,5,4,4,4,3,3,2,1] .empty .empty) (.node [10,7,5,4,4,4,4,2,1,1,1] .empty .empty)) (.node [10,7,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,4,4,4,3,1,1] .empty .empty) (.node [10,7,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_451 : RowTree := (.node [10,7,5,5,3,3,2,2,1,1,1,1,1,1] (.node [10,7,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,5,2,2,2,2,2,2,1,1,1,1] (.node [10,7,5,5,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,5,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,5,2,2,2,2,2,2,2,2] (.node [10,7,5,5,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,5,5,3,2,2,2,2,2,1,1,1] (.node [10,7,5,5,3,2,2,2,1,1,1,1,1,1,1] (.node [10,7,5,5,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,5,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,5,5,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,5,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,5,5,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,7,5,5,3,3,3,3,1,1,1,1] (.node [10,7,5,5,3,3,3,1,1,1,1,1,1,1] (.node [10,7,5,5,3,3,2,2,2,2,1,1] (.node [10,7,5,5,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,5,5,3,3,2,2,2,2,2] .empty .empty)) (.node [10,7,5,5,3,3,3,2,2,1,1,1] (.node [10,7,5,5,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,7,5,5,3,3,3,2,2,2,1] .empty .empty))) (.node [10,7,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,5,3,3,3,3,2,2] (.node [10,7,5,5,3,3,3,3,2,1,1] .empty .empty) (.node [10,7,5,5,3,3,3,3,3,1] .empty .empty)) (.node [10,7,5,5,4,2,2,1,1,1,1,1,1,1,1] (.node [10,7,5,5,4,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,5,4,2,2,2,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_452 : RowTree := (.node [10,7,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_450 degreeTree43_451) - -def degreeTree43_453 : RowTree := (.node [10,7,5,4,4,2,2,2,2,2,2,1] degreeTree43_449 degreeTree43_452) - -def degreeTree43_454 : RowTree := (.node [10,7,5,5,4,3,3,2,1,1,1,1] (.node [10,7,5,5,4,3,2,2,1,1,1,1,1] (.node [10,7,5,5,4,3,1,1,1,1,1,1,1,1,1] (.node [10,7,5,5,4,2,2,2,2,2,2] (.node [10,7,5,5,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,7,5,5,4,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,5,4,3,2,2,2,2,1] (.node [10,7,5,5,4,3,2,2,2,1,1,1] .empty .empty) (.node [10,7,5,5,4,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,7,5,5,4,3,3,3,2,1] (.node [10,7,5,5,4,3,3,2,2,2] (.node [10,7,5,5,4,3,3,2,2,1,1] .empty .empty) (.node [10,7,5,5,4,3,3,3,1,1,1] .empty .empty)) (.node [10,7,5,5,4,4,2,1,1,1,1,1,1] (.node [10,7,5,5,4,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,5,4,4,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree43_455 : RowTree := (.node [10,7,5,5,5,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,5,4,4,3,2,2,1] (.node [10,7,5,5,4,4,3,1,1,1,1,1] (.node [10,7,5,5,4,4,2,2,2,2] .empty .empty) (.node [10,7,5,5,4,4,3,2,1,1,1] .empty .empty)) (.node [10,7,5,5,4,4,4,1,1,1,1] (.node [10,7,5,5,4,4,3,3,1,1] .empty .empty) (.node [10,7,5,5,4,4,4,2,1,1] .empty .empty))) (.node [10,7,5,5,5,2,2,2,2,1,1,1] (.node [10,7,5,5,5,2,2,1,1,1,1,1,1,1] (.node [10,7,5,5,5,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,5,5,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,5,5,5,3,1,1,1,1,1,1,1,1] (.node [10,7,5,5,5,2,2,2,2,2,1] .empty .empty) (.node [10,7,5,5,5,3,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_456 : RowTree := (.node [10,7,5,5,4,4,2,2,2,1,1] degreeTree43_454 degreeTree43_455) - -def degreeTree43_457 : RowTree := (.node [10,7,5,5,5,5,2,2,1,1] (.node [10,7,5,5,5,4,2,1,1,1,1,1] (.node [10,7,5,5,5,3,3,2,1,1,1] (.node [10,7,5,5,5,3,2,2,2,2] (.node [10,7,5,5,5,3,2,2,2,1,1] .empty .empty) (.node [10,7,5,5,5,3,3,1,1,1,1,1] .empty .empty)) (.node [10,7,5,5,5,3,3,3,1,1] (.node [10,7,5,5,5,3,3,2,2,1] .empty .empty) (.node [10,7,5,5,5,4,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,5,5,5,4,3,2,1,1] (.node [10,7,5,5,5,4,2,2,2,1] (.node [10,7,5,5,5,4,2,2,1,1,1] .empty .empty) (.node [10,7,5,5,5,4,3,1,1,1,1] .empty .empty)) (.node [10,7,5,5,5,5,1,1,1,1,1,1] (.node [10,7,5,5,5,4,4,1,1,1] .empty .empty) (.node [10,7,5,5,5,5,2,1,1,1,1] .empty .empty)))) (.node [10,7,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,5,5,5,3,1,1,1] .empty .empty) (.node [10,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,6,2,2,2,2,2,2,2,2,2,2] (.node [10,7,6,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,7,6,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,7,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_458 : RowTree := (.node [10,7,5,5,5,3,2,2,1,1,1,1] degreeTree43_456 degreeTree43_457) - -def degreeTree43_459 : RowTree := (.node [10,7,6,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,7,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,3,2,2,2,2,2,2,2,1,1,1] (.node [10,7,6,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,3,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,6,3,3,2,2,2,2,2,2,1,1] (.node [10,7,6,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,7,6,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,3,3,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,7,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,3,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,7,6,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,7,6,3,3,3,3,2,2,2,2] (.node [10,7,6,3,3,3,3,1,1,1,1,1,1,1,1] (.node [10,7,6,3,3,3,2,2,2,2,1,1,1] (.node [10,7,6,3,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,6,3,3,3,2,2,2,2,2,1] .empty .empty)) (.node [10,7,6,3,3,3,3,2,2,1,1,1,1] (.node [10,7,6,3,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,3,3,3,3,2,2,2,1,1] .empty .empty))) (.node [10,7,6,3,3,3,3,3,3,1,1] (.node [10,7,6,3,3,3,3,3,2,1,1,1] (.node [10,7,6,3,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,6,3,3,3,3,3,2,2,1] .empty .empty)) (.node [10,7,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,3,3,3,3,3,3,2] .empty .empty) (.node [10,7,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_460 : RowTree := (.node [10,7,6,4,3,3,2,2,1,1,1,1,1,1] (.node [10,7,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,4,2,2,2,2,2,2,1,1,1,1] (.node [10,7,6,4,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,4,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,4,2,2,2,2,2,2,2,2] (.node [10,7,6,4,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,6,4,3,2,2,2,2,2,1,1,1] (.node [10,7,6,4,3,2,2,2,1,1,1,1,1,1,1] (.node [10,7,6,4,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,4,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,6,4,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,4,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,6,4,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,7,6,4,3,3,3,3,1,1,1,1] (.node [10,7,6,4,3,3,3,1,1,1,1,1,1,1] (.node [10,7,6,4,3,3,2,2,2,2,1,1] (.node [10,7,6,4,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,6,4,3,3,2,2,2,2,2] .empty .empty)) (.node [10,7,6,4,3,3,3,2,2,1,1,1] (.node [10,7,6,4,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,7,6,4,3,3,3,2,2,2,1] .empty .empty))) (.node [10,7,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,4,3,3,3,3,2,2] (.node [10,7,6,4,3,3,3,3,2,1,1] .empty .empty) (.node [10,7,6,4,3,3,3,3,3,1] .empty .empty)) (.node [10,7,6,4,4,2,2,1,1,1,1,1,1,1,1] (.node [10,7,6,4,4,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,4,4,2,2,2,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_461 : RowTree := (.node [10,7,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_459 degreeTree43_460) - -def degreeTree43_462 : RowTree := (.node [10,7,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_458 degreeTree43_461) - -def degreeTree43_463 : RowTree := (.node [10,7,5,5,4,2,2,2,2,1,1,1,1] degreeTree43_453 degreeTree43_462) - -def degreeTree43_464 : RowTree := (.node [10,7,6,4,4,3,3,2,1,1,1,1] (.node [10,7,6,4,4,3,2,2,1,1,1,1,1] (.node [10,7,6,4,4,3,1,1,1,1,1,1,1,1,1] (.node [10,7,6,4,4,2,2,2,2,2,2] (.node [10,7,6,4,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,7,6,4,4,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,4,4,3,2,2,2,2,1] (.node [10,7,6,4,4,3,2,2,2,1,1,1] .empty .empty) (.node [10,7,6,4,4,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,7,6,4,4,3,3,3,2,1] (.node [10,7,6,4,4,3,3,2,2,2] (.node [10,7,6,4,4,3,3,2,2,1,1] .empty .empty) (.node [10,7,6,4,4,3,3,3,1,1,1] .empty .empty)) (.node [10,7,6,4,4,4,2,1,1,1,1,1,1] (.node [10,7,6,4,4,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,4,4,4,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree43_465 : RowTree := (.node [10,7,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,4,4,4,3,2,2,1] (.node [10,7,6,4,4,4,3,1,1,1,1,1] (.node [10,7,6,4,4,4,2,2,2,2] .empty .empty) (.node [10,7,6,4,4,4,3,2,1,1,1] .empty .empty)) (.node [10,7,6,4,4,4,4,1,1,1,1] (.node [10,7,6,4,4,4,3,3,1,1] .empty .empty) (.node [10,7,6,4,4,4,4,2,1,1] .empty .empty))) (.node [10,7,6,5,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,5,2,2,2,2,2,2,1,1,1] (.node [10,7,6,5,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,2,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree43_466 : RowTree := (.node [10,7,6,4,4,4,2,2,2,1,1] degreeTree43_464 degreeTree43_465) - -def degreeTree43_467 : RowTree := (.node [10,7,6,5,3,3,3,3,1,1,1] (.node [10,7,6,5,3,3,2,1,1,1,1,1,1,1] (.node [10,7,6,5,3,2,2,2,2,1,1,1,1] (.node [10,7,6,5,3,2,2,1,1,1,1,1,1,1,1] (.node [10,7,6,5,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,3,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,5,3,2,2,2,2,2,2] (.node [10,7,6,5,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,6,5,3,3,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,6,5,3,3,3,1,1,1,1,1,1] (.node [10,7,6,5,3,3,2,2,2,1,1,1] (.node [10,7,6,5,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,3,3,2,2,2,2,1] .empty .empty)) (.node [10,7,6,5,3,3,3,2,2,1,1] (.node [10,7,6,5,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,7,6,5,3,3,3,2,2,2] .empty .empty)))) (.node [10,7,6,5,4,3,1,1,1,1,1,1,1,1] (.node [10,7,6,5,4,2,2,1,1,1,1,1,1,1] (.node [10,7,6,5,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,5,3,3,3,3,2,1] .empty .empty) (.node [10,7,6,5,4,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,5,4,2,2,2,2,1,1,1] (.node [10,7,6,5,4,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,4,2,2,2,2,2,1] .empty .empty))) (.node [10,7,6,5,4,3,2,2,2,2] (.node [10,7,6,5,4,3,2,2,1,1,1,1] (.node [10,7,6,5,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,4,3,2,2,2,1,1] .empty .empty)) (.node [10,7,6,5,4,3,3,2,1,1,1] (.node [10,7,6,5,4,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,4,3,3,2,2,1] .empty .empty))))) - -def degreeTree43_468 : RowTree := (.node [10,7,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_466 degreeTree43_467) - -def degreeTree43_469 : RowTree := (.node [10,7,6,5,5,3,2,2,1,1,1] (.node [10,7,6,5,5,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,5,4,4,2,2,2,1] (.node [10,7,6,5,4,4,2,1,1,1,1,1] (.node [10,7,6,5,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,4,4,2,2,1,1,1] .empty .empty)) (.node [10,7,6,5,4,4,3,2,1,1] (.node [10,7,6,5,4,4,3,1,1,1,1] .empty .empty) (.node [10,7,6,5,4,4,4,1,1,1] .empty .empty))) (.node [10,7,6,5,5,2,2,2,2,1,1] (.node [10,7,6,5,5,2,2,1,1,1,1,1,1] (.node [10,7,6,5,5,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,5,2,2,2,1,1,1,1] .empty .empty)) (.node [10,7,6,5,5,3,1,1,1,1,1,1,1] (.node [10,7,6,5,5,2,2,2,2,2] .empty .empty) (.node [10,7,6,5,5,3,2,1,1,1,1,1] .empty .empty)))) (.node [10,7,6,5,5,5,1,1,1,1,1] (.node [10,7,6,5,5,4,1,1,1,1,1,1] (.node [10,7,6,5,5,3,3,1,1,1,1] (.node [10,7,6,5,5,3,2,2,2,1] .empty .empty) (.node [10,7,6,5,5,3,3,2,1,1] .empty .empty)) (.node [10,7,6,5,5,4,2,2,1,1] (.node [10,7,6,5,5,4,2,1,1,1,1] .empty .empty) (.node [10,7,6,5,5,4,3,1,1,1] .empty .empty))) (.node [10,7,6,6,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,5,5,5,2,1,1,1] .empty .empty) (.node [10,7,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,6,2,2,2,2,1,1,1,1,1,1] (.node [10,7,6,6,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,2,2,2,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_470 : RowTree := (.node [10,7,6,6,3,3,3,3,1,1] (.node [10,7,6,6,3,3,1,1,1,1,1,1,1,1] (.node [10,7,6,6,3,2,2,1,1,1,1,1,1,1] (.node [10,7,6,6,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,6,2,2,2,2,2,2,2] .empty .empty) (.node [10,7,6,6,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,6,3,2,2,2,2,1,1,1] (.node [10,7,6,6,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,3,2,2,2,2,2,1] .empty .empty))) (.node [10,7,6,6,3,3,2,2,2,2] (.node [10,7,6,6,3,3,2,2,1,1,1,1] (.node [10,7,6,6,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,3,3,2,2,2,1,1] .empty .empty)) (.node [10,7,6,6,3,3,3,2,1,1,1] (.node [10,7,6,6,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,3,3,3,2,2,1] .empty .empty)))) (.node [10,7,6,6,4,3,2,1,1,1,1,1] (.node [10,7,6,6,4,2,2,2,1,1,1,1] (.node [10,7,6,6,4,2,1,1,1,1,1,1,1,1] (.node [10,7,6,6,4,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,4,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,6,4,2,2,2,2,2] (.node [10,7,6,6,4,2,2,2,2,1,1] .empty .empty) (.node [10,7,6,6,4,3,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,6,6,4,3,3,2,1,1] (.node [10,7,6,6,4,3,2,2,2,1] (.node [10,7,6,6,4,3,2,2,1,1,1] .empty .empty) (.node [10,7,6,6,4,3,3,1,1,1,1] .empty .empty)) (.node [10,7,6,6,4,4,2,1,1,1,1] (.node [10,7,6,6,4,4,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,4,4,2,2,1,1] .empty .empty))))) - -def degreeTree43_471 : RowTree := (.node [10,7,6,6,2,2,2,2,2,2,1,1] degreeTree43_469 degreeTree43_470) - -def degreeTree43_472 : RowTree := (.node [10,7,6,5,4,3,3,3,1,1] degreeTree43_468 degreeTree43_471) - -def degreeTree43_473 : RowTree := (.node [10,7,6,6,5,3,3,1,1,1] (.node [10,7,6,6,5,2,2,2,2,1] (.node [10,7,6,6,5,2,2,1,1,1,1,1] (.node [10,7,6,6,5,2,1,1,1,1,1,1,1] (.node [10,7,6,6,5,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,7,6,6,5,2,2,2,1,1,1] .empty .empty)) (.node [10,7,6,6,5,3,2,1,1,1,1] (.node [10,7,6,6,5,3,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,5,3,2,2,1,1] .empty .empty))) (.node [10,7,6,6,6,2,1,1,1,1,1,1] (.node [10,7,6,6,5,4,2,1,1,1] (.node [10,7,6,6,5,4,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,6,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,6,6,2,2,2,1,1] (.node [10,7,6,6,6,2,2,1,1,1,1] .empty .empty) (.node [10,7,6,6,6,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_474 : RowTree := (.node [10,7,7,2,2,2,2,2,2,2,2,1,1,1] (.node [10,7,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,7,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_475 : RowTree := (.node [10,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_473 degreeTree43_474) - -def degreeTree43_476 : RowTree := (.node [10,7,7,3,3,3,3,1,1,1,1,1,1,1] (.node [10,7,7,3,3,2,2,2,2,2,1,1,1] (.node [10,7,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,3,2,2,2,2,2,2,2,2] (.node [10,7,7,3,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,7,7,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,3,3,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,7,7,3,3,3,2,2,1,1,1,1,1,1] (.node [10,7,7,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,3,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,7,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,3,3,3,2,2,2,2,1,1] (.node [10,7,7,3,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,7,3,3,3,2,2,2,2,2] .empty .empty)))) (.node [10,7,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,3,3,3,3,3,1,1,1,1] (.node [10,7,7,3,3,3,3,2,2,1,1,1] (.node [10,7,7,3,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,7,7,3,3,3,3,2,2,2,1] .empty .empty)) (.node [10,7,7,3,3,3,3,3,2,2] (.node [10,7,7,3,3,3,3,3,2,1,1] .empty .empty) (.node [10,7,7,3,3,3,3,3,3,1] .empty .empty))) (.node [10,7,7,4,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,4,2,2,2,2,2,2,1,1,1] (.node [10,7,7,4,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,2,2,2,2,2,2,2,1] .empty .empty))))) - -def degreeTree43_477 : RowTree := (.node [10,7,7,3,2,2,2,2,2,2,1,1,1,1] degreeTree43_475 degreeTree43_476) - -def degreeTree43_478 : RowTree := (.node [10,7,7,4,3,3,3,3,1,1,1] (.node [10,7,7,4,3,3,2,1,1,1,1,1,1,1] (.node [10,7,7,4,3,2,2,2,2,1,1,1,1] (.node [10,7,7,4,3,2,2,1,1,1,1,1,1,1,1] (.node [10,7,7,4,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,3,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,4,3,2,2,2,2,2,2] (.node [10,7,7,4,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,7,4,3,3,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,7,4,3,3,3,1,1,1,1,1,1] (.node [10,7,7,4,3,3,2,2,2,1,1,1] (.node [10,7,7,4,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,3,3,2,2,2,2,1] .empty .empty)) (.node [10,7,7,4,3,3,3,2,2,1,1] (.node [10,7,7,4,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,7,7,4,3,3,3,2,2,2] .empty .empty)))) (.node [10,7,7,4,4,3,1,1,1,1,1,1,1,1] (.node [10,7,7,4,4,2,2,1,1,1,1,1,1,1] (.node [10,7,7,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,4,3,3,3,3,2,1] .empty .empty) (.node [10,7,7,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,4,4,2,2,2,2,1,1,1] (.node [10,7,7,4,4,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,4,2,2,2,2,2,1] .empty .empty))) (.node [10,7,7,4,4,3,2,2,2,2] (.node [10,7,7,4,4,3,2,2,1,1,1,1] (.node [10,7,7,4,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,4,3,2,2,2,1,1] .empty .empty)) (.node [10,7,7,4,4,3,3,2,1,1,1] (.node [10,7,7,4,4,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,4,3,3,2,2,1] .empty .empty))))) - -def degreeTree43_479 : RowTree := (.node [10,7,7,5,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,4,4,4,2,2,2,1] (.node [10,7,7,4,4,4,2,1,1,1,1,1] (.node [10,7,7,4,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,4,4,2,2,1,1,1] .empty .empty)) (.node [10,7,7,4,4,4,3,2,1,1] (.node [10,7,7,4,4,4,3,1,1,1,1] .empty .empty) (.node [10,7,7,4,4,4,4,1,1,1] .empty .empty))) (.node [10,7,7,5,2,2,2,2,1,1,1,1,1,1] (.node [10,7,7,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,5,2,2,2,2,2,2,1,1] (.node [10,7,7,5,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,7,5,2,2,2,2,2,2,2] .empty .empty)))) (.node [10,7,7,5,3,3,2,2,1,1,1,1] (.node [10,7,7,5,3,2,2,2,2,1,1,1] (.node [10,7,7,5,3,2,2,1,1,1,1,1,1,1] (.node [10,7,7,5,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,5,3,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,7,5,3,3,1,1,1,1,1,1,1,1] (.node [10,7,7,5,3,2,2,2,2,2,1] .empty .empty) (.node [10,7,7,5,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [10,7,7,5,3,3,3,2,1,1,1] (.node [10,7,7,5,3,3,2,2,2,2] (.node [10,7,7,5,3,3,2,2,2,1,1] .empty .empty) (.node [10,7,7,5,3,3,3,1,1,1,1,1] .empty .empty)) (.node [10,7,7,5,3,3,3,3,1,1] (.node [10,7,7,5,3,3,3,2,2,1] .empty .empty) (.node [10,7,7,5,4,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_480 : RowTree := (.node [10,7,7,4,4,3,3,3,1,1] degreeTree43_478 degreeTree43_479) - -def degreeTree43_481 : RowTree := (.node [10,7,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_477 degreeTree43_480) - -def degreeTree43_482 : RowTree := (.node [10,7,6,6,4,4,3,1,1,1] degreeTree43_472 degreeTree43_481) - -def degreeTree43_483 : RowTree := (.node [10,7,6,4,4,2,2,2,2,1,1,1,1] degreeTree43_463 degreeTree43_482) - -def degreeTree43_484 : RowTree := (.node [10,7,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_444 degreeTree43_483) - -def degreeTree43_485 : RowTree := (.node [10,6,5,5,5,3,3,2,1,1,1,1] degreeTree43_405 degreeTree43_484) - -def degreeTree43_486 : RowTree := (.node [10,7,7,5,4,3,3,1,1,1,1] (.node [10,7,7,5,4,3,1,1,1,1,1,1,1] (.node [10,7,7,5,4,2,2,2,2,1,1] (.node [10,7,7,5,4,2,2,2,1,1,1,1] (.node [10,7,7,5,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,7,7,5,4,2,2,2,2,2] .empty .empty)) (.node [10,7,7,5,4,3,2,2,1,1,1] (.node [10,7,7,5,4,3,2,1,1,1,1,1] .empty .empty) (.node [10,7,7,5,4,3,2,2,2,1] .empty .empty))) (.node [10,7,7,5,4,4,2,2,1,1] (.node [10,7,7,5,4,4,1,1,1,1,1,1] (.node [10,7,7,5,4,3,3,2,1,1] .empty .empty) (.node [10,7,7,5,4,4,2,1,1,1,1] .empty .empty)) (.node [10,7,7,5,5,1,1,1,1,1,1,1,1,1] (.node [10,7,7,5,4,4,3,1,1,1] .empty .empty) (.node [10,7,7,5,5,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_487 : RowTree := (.node [10,7,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,5,5,3,2,1,1,1,1] (.node [10,7,7,5,5,2,2,2,2,1] (.node [10,7,7,5,5,2,2,2,1,1,1] .empty .empty) (.node [10,7,7,5,5,3,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,5,5,3,3,1,1,1] (.node [10,7,7,5,5,3,2,2,1,1] .empty .empty) (.node [10,7,7,5,5,4,1,1,1,1,1] .empty .empty))) (.node [10,7,7,6,2,2,2,2,1,1,1,1,1] (.node [10,7,7,6,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,7,6,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,6,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,6,2,2,2,2,2,2,1] (.node [10,7,7,6,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,7,7,6,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_488 : RowTree := (.node [10,7,7,5,5,2,2,1,1,1,1,1] degreeTree43_486 degreeTree43_487) - -def degreeTree43_489 : RowTree := (.node [10,7,7,6,4,3,1,1,1,1,1,1] (.node [10,7,7,6,3,3,2,2,2,1] (.node [10,7,7,6,3,2,2,2,2,2] (.node [10,7,7,6,3,2,2,2,1,1,1,1] (.node [10,7,7,6,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,6,3,2,2,2,2,1,1] .empty .empty)) (.node [10,7,7,6,3,3,2,1,1,1,1,1] (.node [10,7,7,6,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,6,3,3,2,2,1,1,1] .empty .empty))) (.node [10,7,7,6,4,2,1,1,1,1,1,1,1] (.node [10,7,7,6,3,3,3,2,1,1] (.node [10,7,7,6,3,3,3,1,1,1,1] .empty .empty) (.node [10,7,7,6,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,6,4,2,2,2,1,1,1] (.node [10,7,7,6,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,7,6,4,2,2,2,2,1] .empty .empty)))) (.node [10,7,7,6,5,3,1,1,1,1,1] (.node [10,7,7,6,5,1,1,1,1,1,1,1,1] (.node [10,7,7,6,4,3,2,2,1,1] (.node [10,7,7,6,4,3,2,1,1,1,1] .empty .empty) (.node [10,7,7,6,4,4,1,1,1,1,1] .empty .empty)) (.node [10,7,7,6,5,2,2,1,1,1,1] (.node [10,7,7,6,5,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,6,5,2,2,2,1,1] .empty .empty))) (.node [10,7,7,7,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,6,6,2,1,1,1,1,1] (.node [10,7,7,6,6,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,7,2,2,2,1,1,1,1,1,1] (.node [10,7,7,7,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,7,2,2,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_490 : RowTree := (.node [10,7,7,6,3,2,1,1,1,1,1,1,1,1] degreeTree43_488 degreeTree43_489) - -def degreeTree43_491 : RowTree := (.node [10,7,7,7,3,3,2,2,1,1] (.node [10,7,7,7,3,2,2,2,1,1,1] (.node [10,7,7,7,3,2,1,1,1,1,1,1,1] (.node [10,7,7,7,3,1,1,1,1,1,1,1,1,1] (.node [10,7,7,7,2,2,2,2,2,2] .empty .empty) .empty) (.node [10,7,7,7,3,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,7,7,3,3,1,1,1,1,1,1] (.node [10,7,7,7,3,2,2,2,2,1] .empty .empty) (.node [10,7,7,7,3,3,2,1,1,1,1] .empty .empty))) (.node [10,7,7,7,4,2,2,2,1,1] (.node [10,7,7,7,4,2,1,1,1,1,1,1] (.node [10,7,7,7,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,7,4,2,2,1,1,1,1] .empty .empty)) (.node [10,7,7,7,5,1,1,1,1,1,1,1] (.node [10,7,7,7,4,3,1,1,1,1,1] .empty .empty) (.node [10,7,7,7,5,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_492 : RowTree := (.node [10,8,2,2,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,8,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,8,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,2,2,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_493 : RowTree := (.node [10,7,7,7,6,1,1,1,1,1,1] degreeTree43_491 degreeTree43_492) - -def degreeTree43_494 : RowTree := (.node [10,8,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,8,3,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,8,3,2,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,8,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,3,3,2,2,2,2,2,2,2,2,1,1,1] (.node [10,8,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,8,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,2,2,2,2,2,2,1,1,1,1] (.node [10,8,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,8,3,3,3,2,2,2,2,2,2,2,2] (.node [10,8,3,3,3,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,3,3,3,3,2,2,2,2,2,1,1,1] (.node [10,8,3,3,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,8,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,3,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,8,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,3,3,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_495 : RowTree := (.node [10,8,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] degreeTree43_493 degreeTree43_494) - -def degreeTree43_496 : RowTree := (.node [10,7,7,7,2,2,2,2,2,1,1] degreeTree43_490 degreeTree43_495) - -def degreeTree43_497 : RowTree := (.node [10,8,3,3,3,3,3,3,3,2,1,1] (.node [10,8,3,3,3,3,3,3,2,1,1,1,1,1] (.node [10,8,3,3,3,3,3,2,2,2,2,2] (.node [10,8,3,3,3,3,3,2,2,2,2,1,1] (.node [10,8,3,3,3,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,8,3,3,3,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,3,3,3,3,3,3,2,2,2,1] (.node [10,8,3,3,3,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,8,3,3,3,3,3,3,3,1,1,1,1] .empty .empty))) (.node [10,8,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,3,3,3,3,3,1] (.node [10,8,3,3,3,3,3,3,3,2,2] .empty .empty) (.node [10,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_498 : RowTree := (.node [10,8,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,2,2,2,2,2,2,2,2,2,2,1] (.node [10,8,4,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,8,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,8,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,4,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,8,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,3,2,2,2,2,2,2,2,2,2] (.node [10,8,4,3,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_499 : RowTree := (.node [10,8,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_497 degreeTree43_498) - -def degreeTree43_500 : RowTree := (.node [10,8,4,3,3,3,3,2,2,1,1,1,1,1] (.node [10,8,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,3,2,2,2,2,2,1,1,1,1,1] (.node [10,8,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,3,3,2,2,2,2,2,2,2,1] (.node [10,8,4,3,3,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,4,3,3,3,2,2,2,2,2,1,1] (.node [10,8,4,3,3,3,2,2,2,1,1,1,1,1,1] (.node [10,8,4,3,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,3,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,8,4,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,8,4,3,3,3,3,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,4,3,3,3,3,3,3,2,1] (.node [10,8,4,3,3,3,3,3,2,1,1,1,1] (.node [10,8,4,3,3,3,3,2,2,2,2,1] (.node [10,8,4,3,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,8,4,3,3,3,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,3,3,3,3,3,2,2,2] (.node [10,8,4,3,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,8,4,3,3,3,3,3,3,1,1,1] .empty .empty))) (.node [10,8,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,3,3,3,3,3,3] .empty .empty) (.node [10,8,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_501 : RowTree := (.node [10,8,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_499 degreeTree43_500) - -def degreeTree43_502 : RowTree := (.node [10,8,4,4,3,3,2,2,2,2,2,1] (.node [10,8,4,4,3,2,2,2,2,2,1,1,1,1] (.node [10,8,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,2,2,2,2,2,2,2,2,1] (.node [10,8,4,4,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,3,2,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,8,4,4,3,3,2,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,3,2,2,2,2,2,2,2] (.node [10,8,4,4,3,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,3,3,2,2,2,1,1,1,1,1] (.node [10,8,4,4,3,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,3,3,2,2,2,2,1,1,1] .empty .empty)))) (.node [10,8,4,4,3,3,3,3,2,2,1] (.node [10,8,4,4,3,3,3,2,2,2,1,1] (.node [10,8,4,4,3,3,3,2,1,1,1,1,1,1] (.node [10,8,4,4,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,3,3,3,2,2,1,1,1,1] .empty .empty)) (.node [10,8,4,4,3,3,3,3,1,1,1,1,1] (.node [10,8,4,4,3,3,3,2,2,2,2] .empty .empty) (.node [10,8,4,4,3,3,3,3,2,1,1,1] .empty .empty))) (.node [10,8,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,3,3,3,3,3,2] (.node [10,8,4,4,3,3,3,3,3,1,1] .empty .empty) (.node [10,8,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,4,2,2,2,1,1,1,1,1,1,1] (.node [10,8,4,4,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,2,2,2,2,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_503 : RowTree := (.node [10,8,4,4,4,4,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,4,3,3,1,1,1,1,1,1,1] (.node [10,8,4,4,4,3,2,2,1,1,1,1,1,1] (.node [10,8,4,4,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,4,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,4,4,4,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,4,3,2,2,2,2,1,1] (.node [10,8,4,4,4,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,3,2,2,2,2,2] .empty .empty))) (.node [10,8,4,4,4,3,3,3,1,1,1,1] (.node [10,8,4,4,4,3,3,2,2,1,1,1] (.node [10,8,4,4,4,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,3,3,2,2,2,1] .empty .empty)) (.node [10,8,4,4,4,3,3,3,2,2] (.node [10,8,4,4,4,3,3,3,2,1,1] .empty .empty) (.node [10,8,4,4,4,3,3,3,3,1] .empty .empty)))) (.node [10,8,4,4,4,4,3,2,2,2] (.node [10,8,4,4,4,4,2,2,2,2,1] (.node [10,8,4,4,4,4,2,2,1,1,1,1,1] (.node [10,8,4,4,4,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,4,2,2,2,1,1,1] .empty .empty)) (.node [10,8,4,4,4,4,3,2,1,1,1,1] (.node [10,8,4,4,4,4,3,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,4,3,2,2,1,1] .empty .empty))) (.node [10,8,4,4,4,4,4,2,1,1,1] (.node [10,8,4,4,4,4,3,3,2,1] (.node [10,8,4,4,4,4,3,3,1,1,1] .empty .empty) (.node [10,8,4,4,4,4,4,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,4,4,4,3,1,1] (.node [10,8,4,4,4,4,4,2,2,1] .empty .empty) (.node [10,8,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_504 : RowTree := (.node [10,8,4,4,4,2,2,2,2,2,1,1,1] degreeTree43_502 degreeTree43_503) - -def degreeTree43_505 : RowTree := (.node [10,8,4,4,2,2,2,2,2,2,1,1,1,1,1] degreeTree43_501 degreeTree43_504) - -def degreeTree43_506 : RowTree := (.node [10,8,3,3,3,3,3,2,2,1,1,1,1,1,1] degreeTree43_496 degreeTree43_505) - -def degreeTree43_507 : RowTree := (.node [10,8,5,2,2,2,2,2,2,2,2,2,2] (.node [10,8,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,8,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,8,5,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,2,2,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [10,8,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_508 : RowTree := (.node [10,8,5,3,3,2,2,2,2,2,2,1,1] (.node [10,8,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,3,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,8,5,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,3,3,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,8,5,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,8,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,3,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,8,5,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,3,3,3,2,2,2,2,1,1,1] (.node [10,8,5,3,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,5,3,3,3,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree43_509 : RowTree := (.node [10,8,5,3,2,2,2,2,2,2,2,1,1,1] degreeTree43_507 degreeTree43_508) - -def degreeTree43_510 : RowTree := (.node [10,8,5,4,2,2,2,2,2,2,1,1,1,1] (.node [10,8,5,3,3,3,3,3,3,1,1] (.node [10,8,5,3,3,3,3,2,2,2,2] (.node [10,8,5,3,3,3,3,2,2,1,1,1,1] (.node [10,8,5,3,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,3,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,8,5,3,3,3,3,3,2,1,1,1] (.node [10,8,5,3,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,8,5,3,3,3,3,3,2,2,1] .empty .empty))) (.node [10,8,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,3,3,3,3,3,3,2] .empty .empty) (.node [10,8,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,4,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,4,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,5,4,3,2,2,2,2,2,1,1,1] (.node [10,8,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,4,2,2,2,2,2,2,2,2] (.node [10,8,5,4,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,4,3,2,2,2,1,1,1,1,1,1,1] (.node [10,8,5,4,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,4,3,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,8,5,4,3,3,2,2,1,1,1,1,1,1] (.node [10,8,5,4,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,4,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,5,4,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,4,3,3,2,2,2,2,1,1] (.node [10,8,5,4,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,8,5,4,3,3,2,2,2,2,2] .empty .empty))))) - -def degreeTree43_511 : RowTree := (.node [10,8,5,3,3,3,3,1,1,1,1,1,1,1,1] degreeTree43_509 degreeTree43_510) - -def degreeTree43_512 : RowTree := (.node [10,8,5,4,4,3,2,1,1,1,1,1,1,1] (.node [10,8,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,4,3,3,3,3,1,1,1,1] (.node [10,8,5,4,3,3,3,2,2,1,1,1] (.node [10,8,5,4,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,8,5,4,3,3,3,2,2,2,1] .empty .empty)) (.node [10,8,5,4,3,3,3,3,2,2] (.node [10,8,5,4,3,3,3,3,2,1,1] .empty .empty) (.node [10,8,5,4,3,3,3,3,3,1] .empty .empty))) (.node [10,8,5,4,4,2,2,2,2,1,1,1,1] (.node [10,8,5,4,4,2,2,1,1,1,1,1,1,1,1] (.node [10,8,5,4,4,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,4,4,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,4,4,2,2,2,2,2,2] (.node [10,8,5,4,4,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,5,4,4,3,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,5,4,4,3,3,3,1,1,1] (.node [10,8,5,4,4,3,3,1,1,1,1,1,1] (.node [10,8,5,4,4,3,2,2,2,1,1,1] (.node [10,8,5,4,4,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,5,4,4,3,2,2,2,2,1] .empty .empty)) (.node [10,8,5,4,4,3,3,2,2,1,1] (.node [10,8,5,4,4,3,3,2,1,1,1,1] .empty .empty) (.node [10,8,5,4,4,3,3,2,2,2] .empty .empty))) (.node [10,8,5,4,4,4,2,2,1,1,1,1] (.node [10,8,5,4,4,4,1,1,1,1,1,1,1,1] (.node [10,8,5,4,4,3,3,3,2,1] .empty .empty) (.node [10,8,5,4,4,4,2,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,4,4,4,2,2,2,2] (.node [10,8,5,4,4,4,2,2,2,1,1] .empty .empty) (.node [10,8,5,4,4,4,3,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_513 : RowTree := (.node [10,8,5,5,3,2,2,2,1,1,1,1,1,1] (.node [10,8,5,5,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,5,4,4,4,4,2,1,1] (.node [10,8,5,4,4,4,3,3,1,1] (.node [10,8,5,4,4,4,3,2,2,1] .empty .empty) (.node [10,8,5,4,4,4,4,1,1,1,1] .empty .empty)) (.node [10,8,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,5,5,2,2,2,2,2,2,2,1] (.node [10,8,5,5,2,2,2,2,2,1,1,1,1,1] (.node [10,8,5,5,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,8,5,5,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,3,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,5,5,3,3,2,2,2,2,1] (.node [10,8,5,5,3,3,1,1,1,1,1,1,1,1,1] (.node [10,8,5,5,3,2,2,2,2,2,1,1] (.node [10,8,5,5,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,8,5,5,3,2,2,2,2,2,2] .empty .empty)) (.node [10,8,5,5,3,3,2,2,1,1,1,1,1] (.node [10,8,5,5,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,3,3,2,2,2,1,1,1] .empty .empty))) (.node [10,8,5,5,3,3,3,2,2,2] (.node [10,8,5,5,3,3,3,2,1,1,1,1] (.node [10,8,5,5,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,3,3,3,2,2,1,1] .empty .empty)) (.node [10,8,5,5,3,3,3,3,2,1] (.node [10,8,5,5,3,3,3,3,1,1,1] .empty .empty) (.node [10,8,5,5,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_514 : RowTree := (.node [10,8,5,4,4,4,3,2,1,1,1] degreeTree43_512 degreeTree43_513) - -def degreeTree43_515 : RowTree := (.node [10,8,5,4,3,3,3,1,1,1,1,1,1,1] degreeTree43_511 degreeTree43_514) - -def degreeTree43_516 : RowTree := (.node [10,8,5,5,4,3,2,2,2,2] (.node [10,8,5,5,4,3,1,1,1,1,1,1,1,1] (.node [10,8,5,5,4,2,2,2,2,1,1,1] (.node [10,8,5,5,4,2,2,2,1,1,1,1,1] (.node [10,8,5,5,4,2,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,8,5,5,4,2,2,2,2,2,1] .empty .empty)) (.node [10,8,5,5,4,3,2,2,1,1,1,1] (.node [10,8,5,5,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,4,3,2,2,2,1,1] .empty .empty))) (.node [10,8,5,5,4,3,3,3,1,1] (.node [10,8,5,5,4,3,3,2,1,1,1] (.node [10,8,5,5,4,3,3,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,4,3,3,2,2,1] .empty .empty)) (.node [10,8,5,5,4,4,2,1,1,1,1,1] (.node [10,8,5,5,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,4,4,2,2,1,1,1] .empty .empty)))) - -def degreeTree43_517 : RowTree := (.node [10,8,5,5,5,2,2,2,2,2] (.node [10,8,5,5,5,2,1,1,1,1,1,1,1,1] (.node [10,8,5,5,4,4,3,2,1,1] (.node [10,8,5,5,4,4,3,1,1,1,1] .empty .empty) (.node [10,8,5,5,5,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,5,5,2,2,2,1,1,1,1] (.node [10,8,5,5,5,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,5,2,2,2,2,1,1] .empty .empty))) (.node [10,8,5,5,5,3,2,2,2,1] (.node [10,8,5,5,5,3,2,1,1,1,1,1] (.node [10,8,5,5,5,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,5,3,2,2,1,1,1] .empty .empty)) (.node [10,8,5,5,5,3,3,2,1,1] (.node [10,8,5,5,5,3,3,1,1,1,1] .empty .empty) (.node [10,8,5,5,5,4,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_518 : RowTree := (.node [10,8,5,5,4,4,2,2,2,1] degreeTree43_516 degreeTree43_517) - -def degreeTree43_519 : RowTree := (.node [10,8,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,5,5,5,1,1,1,1,1] (.node [10,8,5,5,5,4,2,2,1,1] .empty .empty) (.node [10,8,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,6,2,2,2,2,2,2,2,2,2,1] (.node [10,8,6,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,8,6,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,8,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,6,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,6,3,2,2,2,2,2,2,2,1,1] (.node [10,8,6,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,8,6,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,3,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,8,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,3,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,8,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,6,3,3,2,2,2,2,2,2,1] (.node [10,8,6,3,3,2,2,2,2,1,1,1,1,1] (.node [10,8,6,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,3,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,8,6,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,8,6,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,3,3,3,2,2,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_520 : RowTree := (.node [10,8,5,5,5,4,2,1,1,1,1] degreeTree43_518 degreeTree43_519) - -def degreeTree43_521 : RowTree := (.node [10,8,6,4,2,2,2,2,2,1,1,1,1,1] (.node [10,8,6,3,3,3,3,3,2,1,1] (.node [10,8,6,3,3,3,3,2,1,1,1,1,1] (.node [10,8,6,3,3,3,2,2,2,2,2] (.node [10,8,6,3,3,3,2,2,2,2,1,1] .empty .empty) (.node [10,8,6,3,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,3,3,3,3,2,2,2,1] (.node [10,8,6,3,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,8,6,3,3,3,3,3,1,1,1,1] .empty .empty))) (.node [10,8,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,3,3,3,3,3,3,1] (.node [10,8,6,3,3,3,3,3,2,2] .empty .empty) (.node [10,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,6,4,3,2,2,2,2,2,1,1] (.node [10,8,6,4,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,4,2,2,2,2,2,2,2,1] (.node [10,8,6,4,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,4,3,2,2,2,1,1,1,1,1,1] (.node [10,8,6,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,4,3,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,8,6,4,3,3,2,2,1,1,1,1,1] (.node [10,8,6,4,3,3,1,1,1,1,1,1,1,1,1] (.node [10,8,6,4,3,2,2,2,2,2,2] .empty .empty) (.node [10,8,6,4,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,4,3,3,2,2,2,2,1] (.node [10,8,6,4,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,8,6,4,3,3,3,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_522 : RowTree := (.node [10,8,6,4,4,3,3,1,1,1,1,1] (.node [10,8,6,4,4,2,2,2,1,1,1,1,1] (.node [10,8,6,4,3,3,3,3,2,1] (.node [10,8,6,4,3,3,3,2,2,2] (.node [10,8,6,4,3,3,3,2,2,1,1] .empty .empty) (.node [10,8,6,4,3,3,3,3,1,1,1] .empty .empty)) (.node [10,8,6,4,4,2,1,1,1,1,1,1,1,1,1] (.node [10,8,6,4,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,4,4,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,6,4,4,3,2,1,1,1,1,1,1] (.node [10,8,6,4,4,2,2,2,2,2,1] (.node [10,8,6,4,4,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,6,4,4,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,4,4,3,2,2,2,1,1] (.node [10,8,6,4,4,3,2,2,1,1,1,1] .empty .empty) (.node [10,8,6,4,4,3,2,2,2,2] .empty .empty)))) (.node [10,8,6,4,4,4,3,1,1,1,1] (.node [10,8,6,4,4,4,1,1,1,1,1,1,1] (.node [10,8,6,4,4,3,3,2,2,1] (.node [10,8,6,4,4,3,3,2,1,1,1] .empty .empty) (.node [10,8,6,4,4,3,3,3,1,1] .empty .empty)) (.node [10,8,6,4,4,4,2,2,1,1,1] (.node [10,8,6,4,4,4,2,1,1,1,1,1] .empty .empty) (.node [10,8,6,4,4,4,2,2,2,1] .empty .empty))) (.node [10,8,6,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,4,4,4,3,2,1,1] .empty .empty) (.node [10,8,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,5,2,2,2,2,1,1,1,1,1,1] (.node [10,8,6,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,5,2,2,2,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_523 : RowTree := (.node [10,8,6,4,3,3,3,2,1,1,1,1] degreeTree43_521 degreeTree43_522) - -def degreeTree43_524 : RowTree := (.node [10,8,6,3,3,3,2,2,2,1,1,1,1] degreeTree43_520 degreeTree43_523) - -def degreeTree43_525 : RowTree := (.node [10,8,5,5,4,2,1,1,1,1,1,1,1,1,1] degreeTree43_515 degreeTree43_524) - -def degreeTree43_526 : RowTree := (.node [10,8,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_506 degreeTree43_525) - -def degreeTree43_527 : RowTree := (.node [10,8,6,5,3,3,2,1,1,1,1,1,1] (.node [10,8,6,5,3,2,2,2,1,1,1,1,1] (.node [10,8,6,5,3,2,1,1,1,1,1,1,1,1,1] (.node [10,8,6,5,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [10,8,6,5,3,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,5,3,2,2,2,2,2,1] (.node [10,8,6,5,3,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,6,5,3,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,6,5,3,3,3,1,1,1,1,1] (.node [10,8,6,5,3,3,2,2,2,1,1] (.node [10,8,6,5,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,8,6,5,3,3,2,2,2,2] .empty .empty)) (.node [10,8,6,5,3,3,3,2,2,1] (.node [10,8,6,5,3,3,3,2,1,1,1] .empty .empty) (.node [10,8,6,5,3,3,3,3,1,1] .empty .empty)))) - -def degreeTree43_528 : RowTree := (.node [10,8,6,5,4,3,2,2,1,1,1] (.node [10,8,6,5,4,2,2,2,2,1,1] (.node [10,8,6,5,4,2,2,1,1,1,1,1,1] (.node [10,8,6,5,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,5,4,2,2,2,1,1,1,1] .empty .empty)) (.node [10,8,6,5,4,3,1,1,1,1,1,1,1] (.node [10,8,6,5,4,2,2,2,2,2] .empty .empty) (.node [10,8,6,5,4,3,2,1,1,1,1,1] .empty .empty))) (.node [10,8,6,5,4,4,1,1,1,1,1,1] (.node [10,8,6,5,4,3,3,1,1,1,1] (.node [10,8,6,5,4,3,2,2,2,1] .empty .empty) (.node [10,8,6,5,4,3,3,2,1,1] .empty .empty)) (.node [10,8,6,5,4,4,2,2,1,1] (.node [10,8,6,5,4,4,2,1,1,1,1] .empty .empty) (.node [10,8,6,5,5,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_529 : RowTree := (.node [10,8,6,5,4,1,1,1,1,1,1,1,1,1,1] degreeTree43_527 degreeTree43_528) - -def degreeTree43_530 : RowTree := (.node [10,8,6,6,3,2,1,1,1,1,1,1,1,1] (.node [10,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,5,5,3,1,1,1,1,1,1] (.node [10,8,6,5,5,2,2,2,1,1,1] (.node [10,8,6,5,5,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,6,5,5,2,2,2,2,1] .empty .empty)) (.node [10,8,6,5,5,3,2,2,1,1] (.node [10,8,6,5,5,3,2,1,1,1,1] .empty .empty) (.node [10,8,6,5,5,4,1,1,1,1,1] .empty .empty))) (.node [10,8,6,6,2,2,2,2,1,1,1,1,1] (.node [10,8,6,6,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,6,6,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,6,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,6,2,2,2,2,2,2,1] (.node [10,8,6,6,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,6,6,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,6,6,3,3,2,2,2,1] (.node [10,8,6,6,3,2,2,2,2,2] (.node [10,8,6,6,3,2,2,2,1,1,1,1] (.node [10,8,6,6,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,6,3,2,2,2,2,1,1] .empty .empty)) (.node [10,8,6,6,3,3,2,1,1,1,1,1] (.node [10,8,6,6,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,6,3,3,2,2,1,1,1] .empty .empty))) (.node [10,8,6,6,4,2,1,1,1,1,1,1,1] (.node [10,8,6,6,3,3,3,2,1,1] (.node [10,8,6,6,3,3,3,1,1,1,1] .empty .empty) (.node [10,8,6,6,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,6,4,2,2,2,1,1,1] (.node [10,8,6,6,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,6,6,4,2,2,2,2,1] .empty .empty))))) - -def degreeTree43_531 : RowTree := (.node [10,8,6,5,5,2,1,1,1,1,1,1,1] degreeTree43_529 degreeTree43_530) - -def degreeTree43_532 : RowTree := (.node [10,8,7,2,2,2,2,2,2,2,1,1,1,1] (.node [10,8,6,6,6,2,1,1,1,1,1] (.node [10,8,6,6,5,2,1,1,1,1,1,1] (.node [10,8,6,6,4,4,1,1,1,1,1] (.node [10,8,6,6,4,3,2,1,1,1,1] .empty .empty) (.node [10,8,6,6,5,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,6,5,3,1,1,1,1,1] (.node [10,8,6,6,5,2,2,1,1,1,1] .empty .empty) (.node [10,8,6,6,6,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,7,3,2,2,2,2,2,1,1,1,1,1] (.node [10,8,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,2,2,2,2,2,2,2,2,2] (.node [10,8,7,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,7,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,3,2,2,2,2,2,2,2,1] (.node [10,8,7,3,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,3,3,2,2,2,1,1,1,1,1,1] (.node [10,8,7,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,3,3,2,2,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_533 : RowTree := (.node [10,8,7,4,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,7,3,3,3,3,2,1,1,1,1] (.node [10,8,7,3,3,3,2,2,1,1,1,1,1] (.node [10,8,7,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,8,7,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,8,7,3,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,3,3,3,2,2,2,2,1] (.node [10,8,7,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,8,7,3,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,8,7,3,3,3,3,3,2,1] (.node [10,8,7,3,3,3,3,2,2,2] (.node [10,8,7,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,8,7,3,3,3,3,3,1,1,1] .empty .empty)) (.node [10,8,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,7,4,3,2,2,2,1,1,1,1,1] (.node [10,8,7,4,2,2,2,2,2,2,2] (.node [10,8,7,4,2,2,2,2,2,1,1,1,1] (.node [10,8,7,4,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,4,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,8,7,4,3,2,1,1,1,1,1,1,1,1,1] (.node [10,8,7,4,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,4,3,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,7,4,3,3,2,1,1,1,1,1,1] (.node [10,8,7,4,3,2,2,2,2,2,1] (.node [10,8,7,4,3,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,7,4,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,4,3,3,2,2,2,1,1] (.node [10,8,7,4,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,8,7,4,3,3,2,2,2,2] .empty .empty))))) - -def degreeTree43_534 : RowTree := (.node [10,8,7,3,3,2,2,2,2,2,1,1] degreeTree43_532 degreeTree43_533) - -def degreeTree43_535 : RowTree := (.node [10,8,6,6,4,3,1,1,1,1,1,1] degreeTree43_531 degreeTree43_534) - -def degreeTree43_536 : RowTree := (.node [10,8,7,4,4,2,2,2,2,2] (.node [10,8,7,4,4,2,1,1,1,1,1,1,1,1] (.node [10,8,7,4,3,3,3,3,1,1] (.node [10,8,7,4,3,3,3,2,2,1] (.node [10,8,7,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [10,8,7,4,4,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,4,4,2,2,2,1,1,1,1] (.node [10,8,7,4,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,4,4,2,2,2,2,1,1] .empty .empty))) (.node [10,8,7,4,4,3,2,2,2,1] (.node [10,8,7,4,4,3,2,1,1,1,1,1] (.node [10,8,7,4,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,4,4,3,2,2,1,1,1] .empty .empty)) (.node [10,8,7,4,4,3,3,2,1,1] (.node [10,8,7,4,4,3,3,1,1,1,1] .empty .empty) (.node [10,8,7,4,4,4,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_537 : RowTree := (.node [10,8,7,5,3,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,5,2,2,2,1,1,1,1,1,1,1] (.node [10,8,7,5,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,5,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,5,2,2,2,2,2,1,1,1] (.node [10,8,7,5,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,7,5,2,2,2,2,2,2,1] .empty .empty))) (.node [10,8,7,5,3,2,2,2,2,1,1] (.node [10,8,7,5,3,2,2,1,1,1,1,1,1] (.node [10,8,7,5,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,5,3,2,2,2,1,1,1,1] .empty .empty)) (.node [10,8,7,5,3,3,1,1,1,1,1,1,1] (.node [10,8,7,5,3,2,2,2,2,2] .empty .empty) (.node [10,8,7,5,3,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_538 : RowTree := (.node [10,8,7,4,4,4,2,1,1,1,1] degreeTree43_536 degreeTree43_537) - -def degreeTree43_539 : RowTree := (.node [10,8,7,6,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,5,4,3,1,1,1,1,1,1] (.node [10,8,7,5,4,2,1,1,1,1,1,1,1] (.node [10,8,7,5,3,3,3,1,1,1,1] (.node [10,8,7,5,3,3,2,2,2,1] .empty .empty) (.node [10,8,7,5,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,5,4,2,2,2,1,1,1] (.node [10,8,7,5,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,7,5,4,2,2,2,2,1] .empty .empty))) (.node [10,8,7,5,5,2,1,1,1,1,1,1] (.node [10,8,7,5,4,4,1,1,1,1,1] (.node [10,8,7,5,4,3,2,1,1,1,1] .empty .empty) (.node [10,8,7,5,5,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,5,5,3,1,1,1,1,1] (.node [10,8,7,5,5,2,2,1,1,1,1] .empty .empty) (.node [10,8,7,6,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,7,6,3,2,2,1,1,1,1,1] (.node [10,8,7,6,2,2,2,2,2,1,1] (.node [10,8,7,6,2,2,2,1,1,1,1,1,1] (.node [10,8,7,6,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,6,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,8,7,6,3,1,1,1,1,1,1,1,1,1] (.node [10,8,7,6,2,2,2,2,2,2] .empty .empty) (.node [10,8,7,6,3,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,7,6,3,3,2,1,1,1,1] (.node [10,8,7,6,3,2,2,2,2,1] (.node [10,8,7,6,3,2,2,2,1,1,1] .empty .empty) (.node [10,8,7,6,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,6,4,2,1,1,1,1,1,1] (.node [10,8,7,6,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,6,4,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_540 : RowTree := (.node [10,8,7,5,3,3,2,2,1,1,1] degreeTree43_538 degreeTree43_539) - -def degreeTree43_541 : RowTree := (.node [10,8,7,7,5,1,1,1,1,1,1] (.node [10,8,7,7,2,2,2,2,1,1,1] (.node [10,8,7,7,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,6,5,2,1,1,1,1,1] (.node [10,8,7,6,5,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,6,6,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,7,2,2,1,1,1,1,1,1,1] (.node [10,8,7,7,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,7,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,8,7,7,3,2,2,1,1,1,1] (.node [10,8,7,7,3,1,1,1,1,1,1,1,1] (.node [10,8,7,7,2,2,2,2,2,1] .empty .empty) (.node [10,8,7,7,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,7,4,1,1,1,1,1,1,1] (.node [10,8,7,7,3,3,1,1,1,1,1] .empty .empty) (.node [10,8,7,7,4,2,1,1,1,1,1] .empty .empty)))) (.node [10,8,8,2,2,2,2,2,2,2,1,1,1] (.node [10,8,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,8,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,8,8,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,8,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,3,2,2,2,2,1,1,1,1,1,1] (.node [10,8,8,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,3,2,2,2,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_542 : RowTree := (.node [10,8,8,3,3,3,3,3,1,1] (.node [10,8,8,3,3,3,1,1,1,1,1,1,1,1] (.node [10,8,8,3,3,2,2,1,1,1,1,1,1,1] (.node [10,8,8,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,8,8,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,3,3,2,2,2,2,1,1,1] (.node [10,8,8,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,8,3,3,2,2,2,2,2,1] .empty .empty))) (.node [10,8,8,3,3,3,2,2,2,2] (.node [10,8,8,3,3,3,2,2,1,1,1,1] (.node [10,8,8,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,8,8,3,3,3,3,2,1,1,1] (.node [10,8,8,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,8,8,3,3,3,3,2,2,1] .empty .empty)))) (.node [10,8,8,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,4,2,2,2,1,1,1,1,1,1,1] (.node [10,8,8,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,4,2,2,2,2,2,1,1,1] (.node [10,8,8,4,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,8,4,2,2,2,2,2,2,1] .empty .empty))) (.node [10,8,8,4,3,2,2,2,2,1,1] (.node [10,8,8,4,3,2,2,1,1,1,1,1,1] (.node [10,8,8,4,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,4,3,2,2,2,1,1,1,1] .empty .empty)) (.node [10,8,8,4,3,3,1,1,1,1,1,1,1] (.node [10,8,8,4,3,2,2,2,2,2] .empty .empty) (.node [10,8,8,4,3,3,2,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_543 : RowTree := (.node [10,8,8,3,2,2,2,2,2,2,1,1] degreeTree43_541 degreeTree43_542) - -def degreeTree43_544 : RowTree := (.node [10,8,7,6,4,3,1,1,1,1,1] degreeTree43_540 degreeTree43_543) - -def degreeTree43_545 : RowTree := (.node [10,8,7,4,3,3,3,1,1,1,1,1] degreeTree43_535 degreeTree43_544) - -def degreeTree43_546 : RowTree := (.node [10,8,8,4,4,3,2,1,1,1,1] (.node [10,8,8,4,4,2,2,1,1,1,1,1] (.node [10,8,8,4,4,1,1,1,1,1,1,1,1,1] (.node [10,8,8,4,3,3,3,1,1,1,1] (.node [10,8,8,4,3,3,2,2,2,1] .empty .empty) .empty) (.node [10,8,8,4,4,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,4,4,2,2,2,2,1] (.node [10,8,8,4,4,2,2,2,1,1,1] .empty .empty) (.node [10,8,8,4,4,3,1,1,1,1,1,1] .empty .empty))) (.node [10,8,8,5,2,2,1,1,1,1,1,1,1,1] (.node [10,8,8,5,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,4,4,4,1,1,1,1,1] .empty .empty) (.node [10,8,8,5,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,5,2,2,2,2,1,1,1,1] (.node [10,8,8,5,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,5,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree43_547 : RowTree := (.node [10,8,8,5,4,1,1,1,1,1,1,1,1] (.node [10,8,8,5,3,2,2,2,1,1,1] (.node [10,8,8,5,3,2,1,1,1,1,1,1,1] (.node [10,8,8,5,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,5,3,2,2,1,1,1,1,1] .empty .empty)) (.node [10,8,8,5,3,3,1,1,1,1,1,1] (.node [10,8,8,5,3,2,2,2,2,1] .empty .empty) (.node [10,8,8,5,3,3,2,1,1,1,1] .empty .empty))) (.node [10,8,8,5,5,1,1,1,1,1,1,1] (.node [10,8,8,5,4,2,2,1,1,1,1] (.node [10,8,8,5,4,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,5,4,3,1,1,1,1,1] .empty .empty)) (.node [10,8,8,6,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,5,5,2,1,1,1,1,1] .empty .empty) (.node [10,8,8,6,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_548 : RowTree := (.node [10,8,8,5,2,2,2,2,2,2] degreeTree43_546 degreeTree43_547) - -def degreeTree43_549 : RowTree := (.node [10,8,8,7,3,2,1,1,1,1,1] (.node [10,8,8,6,4,1,1,1,1,1,1,1] (.node [10,8,8,6,3,1,1,1,1,1,1,1,1] (.node [10,8,8,6,2,2,2,2,1,1,1] (.node [10,8,8,6,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,8,6,2,2,2,2,2,1] .empty .empty)) (.node [10,8,8,6,3,2,2,1,1,1,1] (.node [10,8,8,6,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,6,3,3,1,1,1,1,1] .empty .empty))) (.node [10,8,8,7,2,1,1,1,1,1,1,1,1] (.node [10,8,8,6,5,1,1,1,1,1,1] (.node [10,8,8,6,4,2,1,1,1,1,1] .empty .empty) (.node [10,8,8,7,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,7,2,2,2,1,1,1,1] (.node [10,8,8,7,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,7,3,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,8,2,2,1,1,1,1,1] (.node [10,8,8,8,1,1,1,1,1,1,1,1,1] (.node [10,8,8,7,4,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,8,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,8,3,1,1,1,1,1,1] .empty .empty) (.node [10,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,9,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,2,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,9,2,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,9,2,2,2,2,2,2,2,2,2,2,2,2] .empty .empty))))) - -def degreeTree43_550 : RowTree := (.node [10,8,8,6,2,2,1,1,1,1,1,1,1] degreeTree43_548 degreeTree43_549) - -def degreeTree43_551 : RowTree := (.node [10,9,3,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,9,3,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,9,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,9,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,3,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,9,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,9,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,9,3,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,9,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,3,2,2,2,2,2,2,2,2,1,1] (.node [10,9,3,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,9,3,3,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,9,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,3,3,2,2,2,2,2,2,1,1,1] (.node [10,9,3,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,3,3,3,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,9,3,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,9,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,3,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_552 : RowTree := (.node [10,9,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,3,3,3,3,3,1,1,1,1,1,1] (.node [10,9,3,3,3,3,3,2,1,1,1,1,1,1,1] (.node [10,9,3,3,3,3,2,2,2,2,2,2] (.node [10,9,3,3,3,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,9,3,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,3,3,3,3,3,2,2,2,1,1,1] (.node [10,9,3,3,3,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,3,3,3,3,3,2,2,2,2,1] .empty .empty))) (.node [10,9,3,3,3,3,3,3,3,1,1,1] (.node [10,9,3,3,3,3,3,3,2,2,1,1] (.node [10,9,3,3,3,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,9,3,3,3,3,3,3,2,2,2] .empty .empty)) (.node [10,9,3,3,3,3,3,3,3,3] (.node [10,9,3,3,3,3,3,3,3,2,1] .empty .empty) (.node [10,9,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,9,4,2,2,2,2,2,2,2,2,2,1,1] (.node [10,9,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,9,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,9,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,9,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,9,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,3,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_553 : RowTree := (.node [10,9,3,3,3,3,2,2,2,2,1,1,1,1] degreeTree43_551 degreeTree43_552) - -def degreeTree43_554 : RowTree := (.node [10,9,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_550 degreeTree43_553) - -def degreeTree43_555 : RowTree := (.node [10,9,4,3,3,2,2,2,2,2,2,1,1] (.node [10,9,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,3,2,2,2,2,2,2,2,2,1] (.node [10,9,4,3,2,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,9,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,9,4,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,3,3,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,9,4,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,9,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,3,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,9,4,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,3,3,3,2,2,2,2,1,1,1] (.node [10,9,4,3,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,4,3,3,3,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree43_556 : RowTree := (.node [10,9,4,3,3,3,3,3,3,1,1] (.node [10,9,4,3,3,3,3,2,2,2,2] (.node [10,9,4,3,3,3,3,2,2,1,1,1,1] (.node [10,9,4,3,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,3,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,9,4,3,3,3,3,3,2,1,1,1] (.node [10,9,4,3,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,9,4,3,3,3,3,3,2,2,1] .empty .empty))) (.node [10,9,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,3,3,3,3,3,3,2] .empty .empty) (.node [10,9,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,4,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,9,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,4,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_557 : RowTree := (.node [10,9,4,3,3,3,3,1,1,1,1,1,1,1,1] degreeTree43_555 degreeTree43_556) - -def degreeTree43_558 : RowTree := (.node [10,9,4,4,3,3,3,1,1,1,1,1,1,1] (.node [10,9,4,4,3,2,2,2,2,2,1,1,1] (.node [10,9,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,4,2,2,2,2,2,2,2,2] (.node [10,9,4,4,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,9,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,4,3,2,2,2,1,1,1,1,1,1,1] (.node [10,9,4,4,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,4,3,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,9,4,4,3,3,2,2,1,1,1,1,1,1] (.node [10,9,4,4,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,4,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,9,4,4,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,4,3,3,2,2,2,2,1,1] (.node [10,9,4,4,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,9,4,4,3,3,2,2,2,2,2] .empty .empty)))) (.node [10,9,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,4,3,3,3,3,1,1,1,1] (.node [10,9,4,4,3,3,3,2,2,1,1,1] (.node [10,9,4,4,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,9,4,4,3,3,3,2,2,2,1] .empty .empty)) (.node [10,9,4,4,3,3,3,3,2,2] (.node [10,9,4,4,3,3,3,3,2,1,1] .empty .empty) (.node [10,9,4,4,3,3,3,3,3,1] .empty .empty))) (.node [10,9,4,4,4,2,2,2,2,1,1,1,1] (.node [10,9,4,4,4,2,2,1,1,1,1,1,1,1,1] (.node [10,9,4,4,4,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,4,4,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,4,4,2,2,2,2,2,2] (.node [10,9,4,4,4,2,2,2,2,2,1,1] .empty .empty) (.node [10,9,4,4,4,3,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_559 : RowTree := (.node [10,9,4,4,2,2,2,2,2,2,1,1,1,1] degreeTree43_557 degreeTree43_558) - -def degreeTree43_560 : RowTree := (.node [10,9,4,4,4,4,3,2,1,1,1] (.node [10,9,4,4,4,3,3,3,1,1,1] (.node [10,9,4,4,4,3,3,1,1,1,1,1,1] (.node [10,9,4,4,4,3,2,2,2,1,1,1] (.node [10,9,4,4,4,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,4,4,4,3,2,2,2,2,1] .empty .empty)) (.node [10,9,4,4,4,3,3,2,2,1,1] (.node [10,9,4,4,4,3,3,2,1,1,1,1] .empty .empty) (.node [10,9,4,4,4,3,3,2,2,2] .empty .empty))) (.node [10,9,4,4,4,4,2,2,1,1,1,1] (.node [10,9,4,4,4,4,1,1,1,1,1,1,1,1] (.node [10,9,4,4,4,3,3,3,2,1] .empty .empty) (.node [10,9,4,4,4,4,2,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,4,4,4,2,2,2,2] (.node [10,9,4,4,4,4,2,2,2,1,1] .empty .empty) (.node [10,9,4,4,4,4,3,1,1,1,1,1] .empty .empty)))) (.node [10,9,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,9,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,4,4,4,4,1,1,1,1] (.node [10,9,4,4,4,4,3,2,2,1] .empty .empty) (.node [10,9,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,5,2,2,2,2,2,2,2,2,2,1] (.node [10,9,5,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,9,5,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,9,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_561 : RowTree := (.node [10,9,5,3,3,3,2,2,2,1,1,1,1] (.node [10,9,5,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,9,5,3,2,2,2,2,2,2,2,1,1] (.node [10,9,5,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,9,5,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,3,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,9,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,3,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,9,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,5,3,3,2,2,2,2,2,2,1] (.node [10,9,5,3,3,2,2,2,2,1,1,1,1,1] (.node [10,9,5,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,3,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,9,5,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,9,5,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,3,3,3,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [10,9,5,3,3,3,3,3,2,1,1] (.node [10,9,5,3,3,3,3,2,1,1,1,1,1] (.node [10,9,5,3,3,3,2,2,2,2,2] (.node [10,9,5,3,3,3,2,2,2,2,1,1] .empty .empty) (.node [10,9,5,3,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,3,3,3,3,2,2,2,1] (.node [10,9,5,3,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,9,5,3,3,3,3,3,1,1,1,1] .empty .empty))) (.node [10,9,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,3,3,3,3,3,3,1] (.node [10,9,5,3,3,3,3,3,2,2] .empty .empty) (.node [10,9,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,9,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_562 : RowTree := (.node [10,9,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_560 degreeTree43_561) - -def degreeTree43_563 : RowTree := (.node [10,9,4,4,4,3,2,1,1,1,1,1,1,1] degreeTree43_559 degreeTree43_562) - -def degreeTree43_564 : RowTree := (.node [10,9,4,3,2,2,2,2,2,2,1,1,1,1,1] degreeTree43_554 degreeTree43_563) - -def degreeTree43_565 : RowTree := (.node [10,8,8,4,3,3,2,2,1,1,1] degreeTree43_545 degreeTree43_564) - -def degreeTree43_566 : RowTree := (.node [10,8,6,5,2,2,2,2,2,2,1,1] degreeTree43_526 degreeTree43_565) - -def degreeTree43_567 : RowTree := (.node [10,9,5,4,3,2,2,2,2,2,2] (.node [10,9,5,4,3,2,2,1,1,1,1,1,1,1,1] (.node [10,9,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,4,2,2,2,2,2,2,2,1] (.node [10,9,5,4,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,9,5,4,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,4,3,2,2,2,2,1,1,1,1] (.node [10,9,5,4,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,4,3,2,2,2,2,2,1,1] .empty .empty))) (.node [10,9,5,4,3,3,2,2,2,1,1,1] (.node [10,9,5,4,3,3,2,1,1,1,1,1,1,1] (.node [10,9,5,4,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,4,3,3,2,2,1,1,1,1,1] .empty .empty)) (.node [10,9,5,4,3,3,3,1,1,1,1,1,1] (.node [10,9,5,4,3,3,2,2,2,2,1] .empty .empty) (.node [10,9,5,4,3,3,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree43_568 : RowTree := (.node [10,9,5,4,4,2,2,2,2,1,1,1] (.node [10,9,5,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,4,3,3,3,3,1,1,1] (.node [10,9,5,4,3,3,3,2,2,2] .empty .empty) (.node [10,9,5,4,3,3,3,3,2,1] .empty .empty)) (.node [10,9,5,4,4,2,2,1,1,1,1,1,1,1] (.node [10,9,5,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,4,4,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,9,5,4,4,3,2,2,1,1,1,1] (.node [10,9,5,4,4,3,1,1,1,1,1,1,1,1] (.node [10,9,5,4,4,2,2,2,2,2,1] .empty .empty) (.node [10,9,5,4,4,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,4,4,3,2,2,2,2] (.node [10,9,5,4,4,3,2,2,2,1,1] .empty .empty) (.node [10,9,5,4,4,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_569 : RowTree := (.node [10,9,5,4,3,3,3,2,2,1,1] degreeTree43_567 degreeTree43_568) - -def degreeTree43_570 : RowTree := (.node [10,9,5,5,3,2,1,1,1,1,1,1,1,1,1] (.node [10,9,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,4,4,4,2,2,1,1,1] (.node [10,9,5,4,4,4,1,1,1,1,1,1,1] (.node [10,9,5,4,4,3,3,2,2,1] .empty .empty) (.node [10,9,5,4,4,4,2,1,1,1,1,1] .empty .empty)) (.node [10,9,5,4,4,4,3,1,1,1,1] (.node [10,9,5,4,4,4,2,2,2,1] .empty .empty) (.node [10,9,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,5,5,2,2,2,2,2,1,1,1,1] (.node [10,9,5,5,2,2,2,1,1,1,1,1,1,1,1] (.node [10,9,5,5,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,5,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,5,2,2,2,2,2,2,2] (.node [10,9,5,5,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,9,5,5,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,9,5,5,3,3,2,2,2,1,1] (.node [10,9,5,5,3,2,2,2,2,2,1] (.node [10,9,5,5,3,2,2,2,1,1,1,1,1] (.node [10,9,5,5,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,5,3,2,2,2,2,1,1,1] .empty .empty)) (.node [10,9,5,5,3,3,2,1,1,1,1,1,1] (.node [10,9,5,5,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,5,3,3,2,2,1,1,1,1] .empty .empty))) (.node [10,9,5,5,3,3,3,2,2,1] (.node [10,9,5,5,3,3,3,1,1,1,1,1] (.node [10,9,5,5,3,3,2,2,2,2] .empty .empty) (.node [10,9,5,5,3,3,3,2,1,1,1] .empty .empty)) (.node [10,9,5,5,4,2,1,1,1,1,1,1,1,1] (.node [10,9,5,5,4,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,5,4,2,2,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_571 : RowTree := (.node [10,9,5,4,4,3,3,2,1,1,1] degreeTree43_569 degreeTree43_570) - -def degreeTree43_572 : RowTree := (.node [10,9,5,5,5,3,2,1,1,1,1] (.node [10,9,5,5,4,4,1,1,1,1,1,1] (.node [10,9,5,5,4,3,2,1,1,1,1,1] (.node [10,9,5,5,4,2,2,2,2,2] (.node [10,9,5,5,4,2,2,2,2,1,1] .empty .empty) (.node [10,9,5,5,4,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,5,4,3,2,2,2,1] (.node [10,9,5,5,4,3,2,2,1,1,1] .empty .empty) (.node [10,9,5,5,4,3,3,1,1,1,1] .empty .empty))) (.node [10,9,5,5,5,2,2,1,1,1,1,1] (.node [10,9,5,5,5,1,1,1,1,1,1,1,1,1] (.node [10,9,5,5,4,4,2,1,1,1,1] .empty .empty) (.node [10,9,5,5,5,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,5,5,2,2,2,2,1] (.node [10,9,5,5,5,2,2,2,1,1,1] .empty .empty) (.node [10,9,5,5,5,3,1,1,1,1,1,1] .empty .empty)))) (.node [10,9,6,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,9,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,5,5,4,1,1,1,1,1] .empty .empty) (.node [10,9,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,2,2,2,2,2,2,2,2,1,1] (.node [10,9,6,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,9,6,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,9,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_573 : RowTree := (.node [10,9,6,3,3,3,3,1,1,1,1,1,1] (.node [10,9,6,3,3,2,2,2,2,1,1,1,1] (.node [10,9,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,3,2,2,2,2,2,2,1,1,1] (.node [10,9,6,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,6,3,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,9,6,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,9,6,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,3,3,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,9,6,3,3,3,2,1,1,1,1,1,1,1] (.node [10,9,6,3,3,2,2,2,2,2,2] (.node [10,9,6,3,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,9,6,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,6,3,3,3,2,2,2,1,1,1] (.node [10,9,6,3,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,6,3,3,3,2,2,2,2,1] .empty .empty)))) (.node [10,9,6,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,3,3,3,3,3,1,1,1] (.node [10,9,6,3,3,3,3,2,2,1,1] (.node [10,9,6,3,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,9,6,3,3,3,3,2,2,2] .empty .empty)) (.node [10,9,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,3,3,3,3,3,2,1] .empty .empty) (.node [10,9,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,6,4,2,2,2,2,2,2,1,1] (.node [10,9,6,4,2,2,2,2,1,1,1,1,1,1] (.node [10,9,6,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,4,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,9,6,4,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,4,2,2,2,2,2,2,2] .empty .empty) (.node [10,9,6,4,3,2,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_574 : RowTree := (.node [10,9,6,3,2,2,2,2,1,1,1,1,1,1,1] degreeTree43_572 degreeTree43_573) - -def degreeTree43_575 : RowTree := (.node [10,9,5,5,4,2,2,2,1,1,1,1] degreeTree43_571 degreeTree43_574) - -def degreeTree43_576 : RowTree := (.node [10,9,6,4,3,3,3,1,1,1,1,1] (.node [10,9,6,4,3,3,2,1,1,1,1,1,1] (.node [10,9,6,4,3,2,2,2,2,2,1] (.node [10,9,6,4,3,2,2,2,2,1,1,1] (.node [10,9,6,4,3,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,6,4,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,6,4,3,3,2,2,2,1,1] (.node [10,9,6,4,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,9,6,4,3,3,2,2,2,2] .empty .empty))) (.node [10,9,6,4,4,2,1,1,1,1,1,1,1,1] (.node [10,9,6,4,3,3,3,2,2,1] (.node [10,9,6,4,3,3,3,2,1,1,1] .empty .empty) (.node [10,9,6,4,4,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,6,4,4,2,2,2,1,1,1,1] (.node [10,9,6,4,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,4,4,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree43_577 : RowTree := (.node [10,9,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,4,4,3,2,2,2,1] (.node [10,9,6,4,4,3,2,1,1,1,1,1] (.node [10,9,6,4,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,4,4,3,2,2,1,1,1] .empty .empty)) (.node [10,9,6,4,4,4,1,1,1,1,1,1] (.node [10,9,6,4,4,3,3,1,1,1,1] .empty .empty) (.node [10,9,6,4,4,4,2,1,1,1,1] .empty .empty))) (.node [10,9,6,5,2,2,2,2,1,1,1,1,1] (.node [10,9,6,5,2,2,1,1,1,1,1,1,1,1,1] (.node [10,9,6,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,5,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,6,5,2,2,2,2,2,2,1] (.node [10,9,6,5,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,9,6,5,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_578 : RowTree := (.node [10,9,6,4,4,2,2,2,2,2] degreeTree43_576 degreeTree43_577) - -def degreeTree43_579 : RowTree := (.node [10,9,6,5,5,1,1,1,1,1,1,1,1] (.node [10,9,6,5,3,3,3,1,1,1,1] (.node [10,9,6,5,3,2,2,2,2,2] (.node [10,9,6,5,3,2,2,2,1,1,1,1] (.node [10,9,6,5,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,5,3,2,2,2,2,1,1] .empty .empty)) (.node [10,9,6,5,3,3,2,1,1,1,1,1] (.node [10,9,6,5,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,5,3,3,2,2,1,1,1] .empty .empty))) (.node [10,9,6,5,4,2,2,2,1,1,1] (.node [10,9,6,5,4,2,1,1,1,1,1,1,1] (.node [10,9,6,5,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,5,4,2,2,1,1,1,1,1] .empty .empty)) (.node [10,9,6,5,4,3,2,1,1,1,1] (.node [10,9,6,5,4,3,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,5,4,4,1,1,1,1,1] .empty .empty)))) (.node [10,9,6,6,2,2,2,2,1,1,1,1] (.node [10,9,6,6,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,5,5,2,2,1,1,1,1] (.node [10,9,6,5,5,2,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,5,5,3,1,1,1,1,1] .empty .empty)) (.node [10,9,6,6,2,2,1,1,1,1,1,1,1,1] (.node [10,9,6,6,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,6,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,9,6,6,3,2,1,1,1,1,1,1,1] (.node [10,9,6,6,2,2,2,2,2,2] (.node [10,9,6,6,2,2,2,2,2,1,1] .empty .empty) (.node [10,9,6,6,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,6,6,3,2,2,2,1,1,1] (.node [10,9,6,6,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,6,6,3,3,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_580 : RowTree := (.node [10,9,6,5,3,2,1,1,1,1,1,1,1,1] degreeTree43_578 degreeTree43_579) - -def degreeTree43_581 : RowTree := (.node [10,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,7,3,3,3,2,2,2,2] (.node [10,9,6,6,4,3,1,1,1,1,1] (.node [10,9,6,6,4,2,1,1,1,1,1,1] (.node [10,9,6,6,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,6,4,2,2,1,1,1,1] .empty .empty)) (.node [10,9,6,6,5,2,1,1,1,1,1] (.node [10,9,6,6,5,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,6,6,1,1,1,1,1,1] .empty .empty))) (.node [10,9,8,3,3,2,2,2,2,2] (.node [10,9,7,4,3,2,2,2,2,2] (.node [10,9,7,3,3,3,3,2,2,1] .empty .empty) (.node [10,9,7,5,2,2,2,2,2,2] .empty .empty)) (.node [10,9,9,3,2,2,2,2,2,2] (.node [10,9,8,4,2,2,2,2,2,2] .empty .empty) (.node [10,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,10,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,10,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,10,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,10,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_582 : RowTree := (.node [10,10,3,3,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,10,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,2,2,2,2,2,2,2,2,2,1,1] (.node [10,10,3,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,10,3,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,10,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,3,3,2,2,2,2,2,2,2,2,1] (.node [10,10,3,3,2,2,2,2,2,2,1,1,1,1,1] (.node [10,10,3,3,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,3,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,10,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,10,3,3,3,3,2,2,2,1,1,1,1,1] (.node [10,10,3,3,3,2,2,2,2,2,2,2] (.node [10,10,3,3,3,2,2,2,2,2,1,1,1,1] (.node [10,10,3,3,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,3,3,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,10,3,3,3,3,2,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,3,3,3,3,3,2,1,1,1,1,1,1] (.node [10,10,3,3,3,3,2,2,2,2,2,1] (.node [10,10,3,3,3,3,2,2,2,2,1,1,1] .empty .empty) (.node [10,10,3,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,3,3,3,3,3,2,2,2,1,1] (.node [10,10,3,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,10,3,3,3,3,3,2,2,2,2] .empty .empty))))) - -def degreeTree43_583 : RowTree := (.node [10,10,3,2,2,2,2,2,2,2,1,1,1,1,1,1] degreeTree43_581 degreeTree43_582) - -def degreeTree43_584 : RowTree := (.node [10,9,6,6,3,3,2,1,1,1,1] degreeTree43_580 degreeTree43_583) - -def degreeTree43_585 : RowTree := (.node [10,9,6,4,3,2,2,1,1,1,1,1,1,1] degreeTree43_575 degreeTree43_584) - -def degreeTree43_586 : RowTree := (.node [10,10,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,3,3,3,3,3,1,1] (.node [10,10,3,3,3,3,3,3,2,2,1] (.node [10,10,3,3,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [10,10,3,3,3,3,3,3,3,2] .empty .empty)) (.node [10,10,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,4,2,2,2,2,2,2,2,2,1,1,1] (.node [10,10,4,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,10,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,10,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,10,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_587 : RowTree := (.node [10,10,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,3,2,2,2,2,2,2,1,1,1,1] (.node [10,10,4,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,10,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,3,2,2,2,2,2,2,2,2] (.node [10,10,4,3,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,10,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,4,3,3,2,2,2,2,2,1,1,1] (.node [10,10,4,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,10,4,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,3,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,10,4,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,3,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,10,4,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_588 : RowTree := (.node [10,10,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_586 degreeTree43_587) - -def degreeTree43_589 : RowTree := (.node [10,10,4,4,2,2,2,2,2,1,1,1,1,1] (.node [10,10,4,3,3,3,3,3,1,1,1,1] (.node [10,10,4,3,3,3,3,1,1,1,1,1,1,1] (.node [10,10,4,3,3,3,2,2,2,2,1,1] (.node [10,10,4,3,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,10,4,3,3,3,2,2,2,2,2] .empty .empty)) (.node [10,10,4,3,3,3,3,2,2,1,1,1] (.node [10,10,4,3,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,10,4,3,3,3,3,2,2,2,1] .empty .empty))) (.node [10,10,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,3,3,3,3,3,2,2] (.node [10,10,4,3,3,3,3,3,2,1,1] .empty .empty) (.node [10,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,10,4,4,3,2,2,2,2,2,1,1] (.node [10,10,4,4,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,2,2,2,2,2,2,2,1] (.node [10,10,4,4,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,10,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,4,3,2,2,2,1,1,1,1,1,1] (.node [10,10,4,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,3,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,10,4,4,3,3,2,2,1,1,1,1,1] (.node [10,10,4,4,3,3,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,3,2,2,2,2,2,2] .empty .empty) (.node [10,10,4,4,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,4,3,3,2,2,2,2,1] (.node [10,10,4,4,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,10,4,4,3,3,3,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_590 : RowTree := (.node [10,10,4,3,3,3,2,2,1,1,1,1,1,1] degreeTree43_588 degreeTree43_589) - -def degreeTree43_591 : RowTree := (.node [10,10,4,4,4,3,3,2,1,1,1] (.node [10,10,4,4,4,2,2,2,2,1,1,1] (.node [10,10,4,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,3,3,3,2,2,2] (.node [10,10,4,4,3,3,3,2,2,1,1] .empty .empty) (.node [10,10,4,4,3,3,3,3,1,1,1] .empty .empty)) (.node [10,10,4,4,4,2,2,1,1,1,1,1,1,1] (.node [10,10,4,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,4,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,10,4,4,4,3,2,2,1,1,1,1] (.node [10,10,4,4,4,3,1,1,1,1,1,1,1,1] (.node [10,10,4,4,4,2,2,2,2,2,1] .empty .empty) (.node [10,10,4,4,4,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,4,4,3,2,2,2,2] (.node [10,10,4,4,4,3,2,2,2,1,1] .empty .empty) (.node [10,10,4,4,4,3,3,1,1,1,1,1] .empty .empty)))) (.node [10,10,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,4,4,3,1,1,1,1] (.node [10,10,4,4,4,4,2,1,1,1,1,1] (.node [10,10,4,4,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,4,4,2,2,1,1,1] .empty .empty)) (.node [10,10,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,5,2,2,2,2,2,2,2,1,1,1,1] (.node [10,10,5,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,10,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,10,5,2,2,2,2,2,2,2,2,2] (.node [10,10,5,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,10,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_592 : RowTree := (.node [10,10,5,3,3,3,2,2,1,1,1,1,1] (.node [10,10,5,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,3,2,2,2,2,2,1,1,1,1,1] (.node [10,10,5,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,5,3,2,2,2,2,2,2,2,1] (.node [10,10,5,3,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,10,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,5,3,3,2,2,2,2,2,1,1] (.node [10,10,5,3,3,2,2,2,1,1,1,1,1,1] (.node [10,10,5,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,3,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,10,5,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,10,5,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,10,5,3,3,3,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,10,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,3,3,3,3,2,1,1,1,1] (.node [10,10,5,3,3,3,2,2,2,2,1] (.node [10,10,5,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,10,5,3,3,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,10,5,3,3,3,3,2,2,2] (.node [10,10,5,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,10,5,3,3,3,3,3,1,1,1] .empty .empty))) (.node [10,10,5,4,2,2,2,2,1,1,1,1,1,1] (.node [10,10,5,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,5,4,2,2,2,2,2,2,1,1] (.node [10,10,5,4,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,10,5,4,2,2,2,2,2,2,2] .empty .empty))))) - -def degreeTree43_593 : RowTree := (.node [10,10,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_591 degreeTree43_592) - -def degreeTree43_594 : RowTree := (.node [10,10,4,4,3,3,3,2,1,1,1,1] degreeTree43_590 degreeTree43_593) - -def degreeTree43_595 : RowTree := (.node [10,10,5,4,3,3,2,2,2,1,1] (.node [10,10,5,4,3,2,2,2,2,2,1] (.node [10,10,5,4,3,2,2,2,1,1,1,1,1] (.node [10,10,5,4,3,2,2,1,1,1,1,1,1,1] (.node [10,10,5,4,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,5,4,3,2,2,2,2,1,1,1] .empty .empty)) (.node [10,10,5,4,3,3,2,1,1,1,1,1,1] (.node [10,10,5,4,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,4,3,3,2,2,1,1,1,1] .empty .empty))) (.node [10,10,5,4,4,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,4,3,3,3,1,1,1,1,1] (.node [10,10,5,4,3,3,2,2,2,2] .empty .empty) (.node [10,10,5,4,3,3,3,2,1,1,1] .empty .empty)) (.node [10,10,5,4,4,2,2,1,1,1,1,1,1] (.node [10,10,5,4,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,4,4,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree43_596 : RowTree := (.node [10,10,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,4,4,3,2,2,1,1,1] (.node [10,10,5,4,4,3,1,1,1,1,1,1,1] (.node [10,10,5,4,4,2,2,2,2,2] .empty .empty) (.node [10,10,5,4,4,3,2,1,1,1,1,1] .empty .empty)) (.node [10,10,5,4,4,4,1,1,1,1,1,1] (.node [10,10,5,4,4,3,3,1,1,1,1] .empty .empty) (.node [10,10,5,4,4,4,2,1,1,1,1] .empty .empty))) (.node [10,10,5,5,2,2,2,2,1,1,1,1,1] (.node [10,10,5,5,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,5,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,5,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,5,5,2,2,2,2,2,2,1] (.node [10,10,5,5,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,10,5,5,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_597 : RowTree := (.node [10,10,5,4,4,2,2,2,2,1,1] degreeTree43_595 degreeTree43_596) - -def degreeTree43_598 : RowTree := (.node [10,10,5,5,5,2,1,1,1,1,1,1] (.node [10,10,5,5,4,1,1,1,1,1,1,1,1,1] (.node [10,10,5,5,3,3,1,1,1,1,1,1,1] (.node [10,10,5,5,3,2,2,2,1,1,1,1] (.node [10,10,5,5,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,5,3,2,2,2,2,1,1] .empty .empty)) (.node [10,10,5,5,3,3,2,2,1,1,1] (.node [10,10,5,5,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,10,5,5,3,3,3,1,1,1,1] .empty .empty))) (.node [10,10,5,5,4,3,1,1,1,1,1,1] (.node [10,10,5,5,4,2,2,1,1,1,1,1] (.node [10,10,5,5,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,5,4,2,2,2,1,1,1] .empty .empty)) (.node [10,10,5,5,4,4,1,1,1,1,1] (.node [10,10,5,5,4,3,2,1,1,1,1] .empty .empty) (.node [10,10,5,5,5,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,10,6,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,10,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,5,5,3,1,1,1,1,1] (.node [10,10,5,5,5,2,2,1,1,1,1] .empty .empty) (.node [10,10,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,2,2,2,2,2,2,2,1,1,1] (.node [10,10,6,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,10,6,2,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,10,6,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_599 : RowTree := (.node [10,10,5,5,3,2,1,1,1,1,1,1,1,1] degreeTree43_597 degreeTree43_598) - -def degreeTree43_600 : RowTree := (.node [10,10,6,3,3,3,3,2,1,1,1] (.node [10,10,6,3,3,2,2,2,2,1,1,1] (.node [10,10,6,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,3,2,2,2,2,2,2,1,1] (.node [10,10,6,3,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,10,6,3,2,2,2,2,2,2,2] .empty .empty)) (.node [10,10,6,3,3,2,2,1,1,1,1,1,1,1] (.node [10,10,6,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,3,3,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,10,6,3,3,3,2,2,1,1,1,1] (.node [10,10,6,3,3,3,1,1,1,1,1,1,1,1] (.node [10,10,6,3,3,2,2,2,2,2,1] .empty .empty) (.node [10,10,6,3,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,10,6,3,3,3,2,2,2,2] (.node [10,10,6,3,3,3,2,2,2,1,1] .empty .empty) (.node [10,10,6,3,3,3,3,1,1,1,1,1] .empty .empty)))) (.node [10,10,6,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,4,2,2,2,1,1,1,1,1,1,1] (.node [10,10,6,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,6,4,2,2,2,2,2,1,1,1] (.node [10,10,6,4,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,10,6,4,2,2,2,2,2,2,1] .empty .empty))) (.node [10,10,6,4,3,2,2,2,2,1,1] (.node [10,10,6,4,3,2,2,1,1,1,1,1,1] (.node [10,10,6,4,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,4,3,2,2,2,1,1,1,1] .empty .empty)) (.node [10,10,6,4,3,3,2,1,1,1,1,1] (.node [10,10,6,4,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,4,3,3,2,2,1,1,1] .empty .empty))))) - -def degreeTree43_601 : RowTree := (.node [10,10,6,5,3,2,2,1,1,1,1,1] (.node [10,10,6,5,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,4,4,2,2,2,1,1,1] (.node [10,10,6,4,4,2,1,1,1,1,1,1,1] (.node [10,10,6,4,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,4,4,2,2,1,1,1,1,1] .empty .empty)) (.node [10,10,6,4,4,3,2,1,1,1,1] (.node [10,10,6,4,4,3,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,4,4,4,1,1,1,1,1] .empty .empty))) (.node [10,10,6,5,2,2,2,2,1,1,1,1] (.node [10,10,6,5,2,2,1,1,1,1,1,1,1,1] (.node [10,10,6,5,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,5,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,10,6,5,3,1,1,1,1,1,1,1,1,1] (.node [10,10,6,5,2,2,2,2,2,1,1] .empty .empty) (.node [10,10,6,5,3,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,10,6,5,5,1,1,1,1,1,1,1] (.node [10,10,6,5,4,1,1,1,1,1,1,1,1] (.node [10,10,6,5,3,3,1,1,1,1,1,1] (.node [10,10,6,5,3,2,2,2,1,1,1] .empty .empty) (.node [10,10,6,5,3,3,2,1,1,1,1] .empty .empty)) (.node [10,10,6,5,4,2,2,1,1,1,1] (.node [10,10,6,5,4,2,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,5,4,3,1,1,1,1,1] .empty .empty))) (.node [10,10,6,6,2,2,1,1,1,1,1,1,1] (.node [10,10,6,6,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,5,5,2,1,1,1,1,1] .empty .empty) (.node [10,10,6,6,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,6,6,2,2,2,2,1,1,1] (.node [10,10,6,6,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,10,6,6,3,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_602 : RowTree := (.node [10,10,6,4,3,3,3,1,1,1,1] degreeTree43_600 degreeTree43_601) - -def degreeTree43_603 : RowTree := (.node [10,10,6,3,2,2,2,2,1,1,1,1,1,1] degreeTree43_599 degreeTree43_602) - -def degreeTree43_604 : RowTree := (.node [10,10,5,4,3,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_594 degreeTree43_603) - -def degreeTree43_605 : RowTree := (.node [10,10,3,3,3,3,3,3,1,1,1,1,1] degreeTree43_585 degreeTree43_604) - -def degreeTree43_606 : RowTree := (.node [11,5,5,5,5,5,2,1,1,1,1,1] (.node [10,10,6,6,5,1,1,1,1,1,1] (.node [10,10,6,6,4,1,1,1,1,1,1,1] (.node [10,10,6,6,3,3,1,1,1,1,1] (.node [10,10,6,6,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,6,6,4,2,1,1,1,1,1] .empty .empty)) (.node [11,5,5,5,5,4,2,2,1,1,1,1] (.node [11,5,5,5,5,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,5,5,5,5,5,1,1,1,1,1,1,1] .empty .empty))) (.node [11,6,5,5,5,3,1,1,1,1,1,1,1,1] (.node [11,6,5,5,4,4,1,1,1,1,1,1,1,1] (.node [11,5,5,5,5,5,2,2,1,1,1] .empty .empty) (.node [11,6,5,5,4,4,2,2,1,1,1,1] .empty .empty)) (.node [11,6,5,5,5,4,1,1,1,1,1,1,1] (.node [11,6,5,5,5,3,2,2,1,1,1,1] .empty .empty) (.node [11,6,5,5,5,4,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_607 : RowTree := (.node [11,6,6,5,4,4,2,1,1,1,1,1] (.node [11,6,6,4,4,4,2,2,1,1,1,1] (.node [11,6,5,5,5,5,2,1,1,1,1] (.node [11,6,5,5,5,5,1,1,1,1,1,1] .empty .empty) (.node [11,6,6,4,4,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,6,6,5,4,3,2,2,1,1,1,1] (.node [11,6,6,5,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,6,6,5,4,4,1,1,1,1,1,1,1] .empty .empty))) (.node [11,6,6,5,5,3,1,1,1,1,1,1,1] (.node [11,6,6,5,5,2,1,1,1,1,1,1,1,1] (.node [11,6,6,5,4,4,2,2,1,1,1] .empty .empty) (.node [11,6,6,5,5,2,2,2,1,1,1,1] .empty .empty)) (.node [11,6,6,5,5,3,2,2,1,1,1] (.node [11,6,6,5,5,3,2,1,1,1,1,1] .empty .empty) (.node [11,6,6,5,5,4,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_608 : RowTree := (.node [11,6,5,5,5,4,2,2,1,1,1] degreeTree43_606 degreeTree43_607) - -def degreeTree43_609 : RowTree := (.node [11,6,6,6,5,2,1,1,1,1,1,1,1] (.node [11,6,6,6,4,2,1,1,1,1,1,1,1,1] (.node [11,6,6,6,2,2,2,2,1,1,1,1,1,1] (.node [11,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,6,6,5,5,5,1,1,1,1,1] .empty .empty) (.node [11,6,6,6,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,6,6,6,3,3,1,1,1,1,1,1,1,1] (.node [11,6,6,6,2,2,2,2,2,2,1,1] .empty .empty) (.node [11,6,6,6,3,3,2,2,1,1,1,1] .empty .empty))) (.node [11,6,6,6,4,3,2,2,1,1,1] (.node [11,6,6,6,4,3,1,1,1,1,1,1,1] (.node [11,6,6,6,4,2,2,2,1,1,1,1] .empty .empty) (.node [11,6,6,6,4,3,2,1,1,1,1,1] .empty .empty)) (.node [11,6,6,6,4,4,2,1,1,1,1] (.node [11,6,6,6,4,4,1,1,1,1,1,1] .empty .empty) (.node [11,6,6,6,5,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [11,6,6,6,6,2,2,1,1,1,1] (.node [11,6,6,6,5,3,2,1,1,1,1] (.node [11,6,6,6,5,2,2,2,1,1,1] (.node [11,6,6,6,5,2,2,1,1,1,1,1] .empty .empty) (.node [11,6,6,6,5,3,1,1,1,1,1,1] .empty .empty)) (.node [11,6,6,6,6,1,1,1,1,1,1,1,1] (.node [11,6,6,6,5,4,1,1,1,1,1] .empty .empty) (.node [11,6,6,6,6,2,1,1,1,1,1,1] .empty .empty))) (.node [11,7,5,5,4,3,2,2,1,1,1,1] (.node [11,7,5,4,4,4,2,2,1,1,1,1] (.node [11,7,5,4,4,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,7,5,5,4,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,7,5,5,4,4,2,1,1,1,1,1] (.node [11,7,5,5,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [11,7,5,5,4,4,2,2,1,1,1] .empty .empty))))) - -def degreeTree43_610 : RowTree := (.node [11,6,6,5,5,4,2,1,1,1,1] degreeTree43_608 degreeTree43_609) - -def degreeTree43_611 : RowTree := (.node [11,7,6,5,3,3,1,1,1,1,1,1,1,1] (.node [11,7,6,4,4,3,2,2,1,1,1,1] (.node [11,7,5,5,5,3,2,2,1,1,1] (.node [11,7,5,5,5,3,1,1,1,1,1,1,1] (.node [11,7,5,5,5,2,2,2,1,1,1,1] .empty .empty) (.node [11,7,5,5,5,3,2,1,1,1,1,1] .empty .empty)) (.node [11,7,5,5,5,4,2,1,1,1,1] (.node [11,7,5,5,5,4,1,1,1,1,1,1] .empty .empty) (.node [11,7,6,4,4,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [11,7,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,7,6,4,4,4,2,1,1,1,1,1] (.node [11,7,6,4,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [11,7,6,4,4,4,2,2,1,1,1] .empty .empty)) (.node [11,7,6,5,2,2,2,2,1,1,1,1,1,1] (.node [11,7,6,5,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,7,6,5,2,2,2,2,2,2,1,1] .empty .empty)))) (.node [11,7,6,5,4,4,2,1,1,1,1] (.node [11,7,6,5,4,3,1,1,1,1,1,1,1] (.node [11,7,6,5,4,2,1,1,1,1,1,1,1,1] (.node [11,7,6,5,3,3,2,2,1,1,1,1] .empty .empty) (.node [11,7,6,5,4,2,2,2,1,1,1,1] .empty .empty)) (.node [11,7,6,5,4,3,2,2,1,1,1] (.node [11,7,6,5,4,3,2,1,1,1,1,1] .empty .empty) (.node [11,7,6,5,4,4,1,1,1,1,1,1] .empty .empty))) (.node [11,7,6,5,5,2,2,2,1,1,1] (.node [11,7,6,5,5,2,1,1,1,1,1,1,1] (.node [11,7,6,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,7,6,5,5,2,2,1,1,1,1,1] .empty .empty)) (.node [11,7,6,5,5,3,2,1,1,1,1] (.node [11,7,6,5,5,3,1,1,1,1,1,1] .empty .empty) (.node [11,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_612 : RowTree := (.node [11,7,6,6,5,1,1,1,1,1,1,1,1] (.node [11,7,6,6,3,3,1,1,1,1,1,1,1] (.node [11,7,6,6,2,2,2,2,2,1,1,1] (.node [11,7,6,6,2,2,2,1,1,1,1,1,1,1] (.node [11,7,6,6,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,7,6,6,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [11,7,6,6,3,2,1,1,1,1,1,1,1,1] (.node [11,7,6,6,2,2,2,2,2,2,1] .empty .empty) (.node [11,7,6,6,3,2,2,2,1,1,1,1] .empty .empty))) (.node [11,7,6,6,4,2,1,1,1,1,1,1,1] (.node [11,7,6,6,3,3,2,2,1,1,1] (.node [11,7,6,6,3,3,2,1,1,1,1,1] .empty .empty) (.node [11,7,6,6,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,7,6,6,4,2,2,2,1,1,1] (.node [11,7,6,6,4,2,2,1,1,1,1,1] .empty .empty) (.node [11,7,6,6,4,3,1,1,1,1,1,1] .empty .empty)))) (.node [11,8,5,4,4,4,2,1,1,1,1,1] (.node [11,8,4,4,4,4,2,2,1,1,1,1] (.node [11,7,6,6,6,1,1,1,1,1,1,1] (.node [11,7,6,6,5,2,1,1,1,1,1,1] .empty .empty) (.node [11,8,4,4,4,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,8,5,4,4,3,2,2,1,1,1,1] (.node [11,8,5,4,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,5,4,4,4,1,1,1,1,1,1,1] .empty .empty))) (.node [11,8,5,5,2,2,2,2,1,1,1,1,1,1] (.node [11,8,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,8,5,4,4,4,2,2,1,1,1] .empty .empty) (.node [11,8,5,5,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,8,5,5,3,3,1,1,1,1,1,1,1,1] (.node [11,8,5,5,2,2,2,2,2,2,1,1] .empty .empty) (.node [11,8,5,5,3,3,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_613 : RowTree := (.node [11,7,6,6,2,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_611 degreeTree43_612) - -def degreeTree43_614 : RowTree := (.node [11,7,5,5,5,2,1,1,1,1,1,1,1,1] degreeTree43_610 degreeTree43_613) - -def degreeTree43_615 : RowTree := (.node [11,8,5,5,5,2,2,2,1,1,1] (.node [11,8,5,5,4,4,1,1,1,1,1,1] (.node [11,8,5,5,4,3,2,1,1,1,1,1] (.node [11,8,5,5,4,3,1,1,1,1,1,1,1] (.node [11,8,5,5,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,8,5,5,4,3,2,2,1,1,1] .empty .empty)) (.node [11,8,5,5,5,2,1,1,1,1,1,1,1] (.node [11,8,5,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,5,5,5,2,2,1,1,1,1,1] .empty .empty))) (.node [11,8,6,4,2,2,2,2,1,1,1,1,1,1] (.node [11,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,8,5,5,5,3,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,8,6,4,3,3,1,1,1,1,1,1,1,1] (.node [11,8,6,4,2,2,2,2,2,2,1,1] .empty .empty) (.node [11,8,6,4,3,3,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree43_616 : RowTree := (.node [11,8,6,5,2,2,1,1,1,1,1,1,1,1,1] (.node [11,8,6,4,4,3,2,2,1,1,1] (.node [11,8,6,4,4,3,1,1,1,1,1,1,1] (.node [11,8,6,4,4,2,2,2,1,1,1,1] .empty .empty) (.node [11,8,6,4,4,3,2,1,1,1,1,1] .empty .empty)) (.node [11,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,8,6,4,4,4,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [11,8,6,5,2,2,2,2,2,2,1] (.node [11,8,6,5,2,2,2,2,1,1,1,1,1] (.node [11,8,6,5,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,5,2,2,2,2,2,1,1,1] .empty .empty)) (.node [11,8,6,5,3,2,2,2,1,1,1,1] (.node [11,8,6,5,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,5,3,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_617 : RowTree := (.node [11,8,6,4,4,2,1,1,1,1,1,1,1,1] degreeTree43_615 degreeTree43_616) - -def degreeTree43_618 : RowTree := (.node [11,8,6,6,3,3,1,1,1,1,1,1] (.node [11,8,6,6,2,1,1,1,1,1,1,1,1,1,1] (.node [11,8,6,5,4,3,1,1,1,1,1,1] (.node [11,8,6,5,4,2,1,1,1,1,1,1,1] (.node [11,8,6,5,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,5,4,2,2,1,1,1,1,1] .empty .empty)) (.node [11,8,6,5,5,2,1,1,1,1,1,1] (.node [11,8,6,5,5,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [11,8,6,6,2,2,2,2,2,1,1] (.node [11,8,6,6,2,2,2,1,1,1,1,1,1] (.node [11,8,6,6,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,6,2,2,2,2,1,1,1,1] .empty .empty)) (.node [11,8,6,6,3,2,1,1,1,1,1,1,1] (.node [11,8,6,6,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,6,3,2,2,1,1,1,1,1] .empty .empty)))) (.node [11,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,9,4,4,4,3,1,1,1,1,1,1,1,1] (.node [11,8,6,6,4,2,1,1,1,1,1,1] (.node [11,8,6,6,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,6,5,1,1,1,1,1,1,1] .empty .empty)) (.node [11,9,4,4,4,4,1,1,1,1,1,1,1] (.node [11,9,4,4,4,3,2,2,1,1,1,1] .empty .empty) (.node [11,9,4,4,4,4,2,1,1,1,1,1] .empty .empty))) (.node [11,10,4,4,3,3,1,1,1,1,1,1,1,1] (.node [11,10,4,4,2,2,2,2,1,1,1,1,1,1] (.node [11,10,4,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,10,4,4,2,2,2,2,2,2,1,1] .empty .empty)) (.node [11,10,4,4,4,2,1,1,1,1,1,1,1,1] (.node [11,10,4,4,3,3,2,2,1,1,1,1] .empty .empty) (.node [11,10,4,4,4,2,2,2,1,1,1,1] .empty .empty))))) - -def degreeTree43_619 : RowTree := (.node [11,8,6,5,3,3,2,1,1,1,1,1] degreeTree43_617 degreeTree43_618) - -def degreeTree43_620 : RowTree := (.node [12,6,5,5,5,2,1,1,1,1,1,1,1,1] (.node [12,5,5,5,5,4,2,1,1,1,1,1] (.node [12,5,5,5,4,4,2,2,1,1,1,1] (.node [11,10,4,4,4,4,1,1,1,1,1,1] (.node [11,10,4,4,4,3,2,1,1,1,1,1] .empty .empty) (.node [12,5,5,5,4,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,5,5,5,5,3,2,2,1,1,1,1] (.node [12,5,5,5,5,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,5,5,5,5,4,1,1,1,1,1,1,1] .empty .empty))) (.node [12,6,5,5,4,3,1,1,1,1,1,1,1,1] (.node [12,6,5,4,4,4,1,1,1,1,1,1,1,1] (.node [12,5,5,5,5,5,1,1,1,1,1,1] .empty .empty) (.node [12,6,5,4,4,4,2,2,1,1,1,1] .empty .empty)) (.node [12,6,5,5,4,4,1,1,1,1,1,1,1] (.node [12,6,5,5,4,3,2,2,1,1,1,1] .empty .empty) (.node [12,6,5,5,4,4,2,1,1,1,1,1] .empty .empty)))) (.node [12,6,6,4,4,4,2,1,1,1,1,1] (.node [12,6,5,5,5,4,1,1,1,1,1,1] (.node [12,6,5,5,5,3,1,1,1,1,1,1,1] (.node [12,6,5,5,5,2,2,2,1,1,1,1] .empty .empty) (.node [12,6,5,5,5,3,2,1,1,1,1,1] .empty .empty)) (.node [12,6,6,4,4,3,2,2,1,1,1,1] (.node [12,6,6,4,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,4,4,4,1,1,1,1,1,1,1] .empty .empty))) (.node [12,6,6,5,2,2,2,2,2,2,1,1] (.node [12,6,6,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [12,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,5,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [12,6,6,5,3,3,2,2,1,1,1,1] (.node [12,6,6,5,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,5,4,2,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_621 : RowTree := (.node [12,6,6,6,3,3,1,1,1,1,1,1,1] (.node [12,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,6,6,5,5,1,1,1,1,1,1,1,1,1] (.node [12,6,6,5,4,3,2,1,1,1,1,1] (.node [12,6,6,5,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,5,4,4,1,1,1,1,1,1] .empty .empty)) (.node [12,6,6,5,5,2,2,1,1,1,1,1] (.node [12,6,6,5,5,2,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,5,5,3,1,1,1,1,1,1] .empty .empty))) (.node [12,6,6,6,2,2,2,2,1,1,1,1,1] (.node [12,6,6,6,2,2,1,1,1,1,1,1,1,1,1] (.node [12,6,6,6,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,6,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [12,6,6,6,3,2,1,1,1,1,1,1,1,1] (.node [12,6,6,6,2,2,2,2,2,1,1,1] .empty .empty) (.node [12,6,6,6,3,2,2,2,1,1,1,1] .empty .empty)))) (.node [12,7,5,4,4,3,1,1,1,1,1,1,1,1] (.node [12,6,6,6,4,2,2,1,1,1,1,1] (.node [12,6,6,6,4,1,1,1,1,1,1,1,1,1] (.node [12,6,6,6,3,3,2,1,1,1,1,1] .empty .empty) (.node [12,6,6,6,4,2,1,1,1,1,1,1,1] .empty .empty)) (.node [12,7,4,4,4,4,1,1,1,1,1,1,1,1] (.node [12,6,6,6,5,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,7,4,4,4,4,2,2,1,1,1,1] .empty .empty))) (.node [12,7,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,7,5,4,4,4,1,1,1,1,1,1,1] (.node [12,7,5,4,4,3,2,2,1,1,1,1] .empty .empty) (.node [12,7,5,4,4,4,2,1,1,1,1,1] .empty .empty)) (.node [12,7,5,5,2,2,2,2,1,1,1,1,1,1] (.node [12,7,5,5,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,7,5,5,2,2,2,2,2,2,1,1] .empty .empty))))) - -def degreeTree43_622 : RowTree := (.node [12,6,6,5,4,2,2,2,1,1,1,1] degreeTree43_620 degreeTree43_621) - -def degreeTree43_623 : RowTree := (.node [11,10,4,4,4,3,1,1,1,1,1,1,1] degreeTree43_619 degreeTree43_622) - -def degreeTree43_624 : RowTree := (.node [11,8,5,5,4,2,1,1,1,1,1,1,1,1] degreeTree43_614 degreeTree43_623) - -def degreeTree43_625 : RowTree := (.node [12,7,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,7,5,5,4,3,2,1,1,1,1,1] (.node [12,7,5,5,4,2,2,2,1,1,1,1] (.node [12,7,5,5,4,2,1,1,1,1,1,1,1,1] (.node [12,7,5,5,3,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,7,5,5,4,3,1,1,1,1,1,1,1] .empty .empty)) (.node [12,7,5,5,5,2,1,1,1,1,1,1,1] (.node [12,7,5,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,7,5,5,5,2,2,1,1,1,1,1] .empty .empty))) (.node [12,7,6,4,3,3,1,1,1,1,1,1,1,1] (.node [12,7,6,4,2,2,2,2,1,1,1,1,1,1] (.node [12,7,6,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,7,6,4,2,2,2,2,2,2,1,1] .empty .empty)) (.node [12,7,6,4,4,2,1,1,1,1,1,1,1,1] (.node [12,7,6,4,3,3,2,2,1,1,1,1] .empty .empty) (.node [12,7,6,4,4,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree43_626 : RowTree := (.node [12,7,6,5,3,2,1,1,1,1,1,1,1,1] (.node [12,7,6,5,2,2,1,1,1,1,1,1,1,1,1] (.node [12,7,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,7,6,4,4,3,2,1,1,1,1,1] .empty .empty) (.node [12,7,6,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,7,6,5,2,2,2,2,1,1,1,1,1] (.node [12,7,6,5,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [12,7,6,5,2,2,2,2,2,1,1,1] .empty .empty))) (.node [12,7,6,5,4,2,1,1,1,1,1,1,1] (.node [12,7,6,5,3,3,1,1,1,1,1,1,1] (.node [12,7,6,5,3,2,2,2,1,1,1,1] .empty .empty) (.node [12,7,6,5,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,7,6,5,5,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,7,6,6,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_627 : RowTree := (.node [12,7,6,4,4,3,1,1,1,1,1,1,1] degreeTree43_625 degreeTree43_626) - -def degreeTree43_628 : RowTree := (.node [12,8,5,4,4,2,2,2,1,1,1,1] (.node [12,8,4,4,4,4,1,1,1,1,1,1,1] (.node [12,7,6,6,3,2,1,1,1,1,1,1,1] (.node [12,7,6,6,2,2,2,2,1,1,1,1] (.node [12,7,6,6,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [12,7,6,6,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,8,4,4,4,3,1,1,1,1,1,1,1,1] (.node [12,7,6,6,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,4,4,4,3,2,2,1,1,1,1] .empty .empty))) (.node [12,8,5,4,2,2,2,2,2,2,1,1] (.node [12,8,5,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [12,8,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,5,4,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [12,8,5,4,3,3,2,2,1,1,1,1] (.node [12,8,5,4,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,5,4,4,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [12,8,5,5,3,2,1,1,1,1,1,1,1,1] (.node [12,8,5,5,2,2,1,1,1,1,1,1,1,1,1] (.node [12,8,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,8,5,4,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,5,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,8,5,5,2,2,2,2,1,1,1,1,1] (.node [12,8,5,5,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,5,5,2,2,2,2,2,1,1,1] .empty .empty))) (.node [12,8,5,5,5,1,1,1,1,1,1,1,1] (.node [12,8,5,5,4,1,1,1,1,1,1,1,1,1] (.node [12,8,5,5,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,5,5,4,2,1,1,1,1,1,1,1] .empty .empty)) (.node [12,8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [12,8,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,3,2,2,2,2,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_629 : RowTree := (.node [12,7,6,6,2,2,1,1,1,1,1,1,1,1] degreeTree43_627 degreeTree43_628) - -def degreeTree43_630 : RowTree := (.node [12,8,6,5,2,2,2,1,1,1,1,1,1] (.node [12,8,6,4,2,2,2,2,2,1,1,1] (.node [12,8,6,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [12,8,6,3,3,3,2,2,1,1,1,1] (.node [12,8,6,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,8,6,4,2,2,2,1,1,1,1,1,1,1] (.node [12,8,6,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,4,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [12,8,6,4,4,2,1,1,1,1,1,1,1] (.node [12,8,6,4,3,3,1,1,1,1,1,1,1] (.node [12,8,6,4,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,4,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,8,6,5,2,1,1,1,1,1,1,1,1,1,1] (.node [12,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,5,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [12,9,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,8,6,6,1,1,1,1,1,1,1,1,1,1,1] (.node [12,8,6,5,3,2,1,1,1,1,1,1,1] (.node [12,8,6,5,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,5,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,8,6,6,2,2,1,1,1,1,1,1,1] (.node [12,8,6,6,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,6,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [12,9,4,4,3,3,1,1,1,1,1,1,1,1] (.node [12,9,4,4,2,2,2,2,1,1,1,1,1,1] (.node [12,9,4,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,9,4,4,2,2,2,2,2,2,1,1] .empty .empty)) (.node [12,9,4,4,4,3,1,1,1,1,1,1,1] (.node [12,9,4,4,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,10,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_631 : RowTree := (.node [12,11,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [12,10,4,4,2,2,2,2,1,1,1,1,1] (.node [12,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,10,4,3,2,2,2,2,2,2,1,1] (.node [12,10,4,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [12,10,4,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,10,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [12,10,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,10,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [12,10,4,4,4,2,1,1,1,1,1,1,1] (.node [12,10,4,4,3,3,1,1,1,1,1,1,1] (.node [12,10,4,4,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,10,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,11,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,11,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [12,12,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [12,12,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,11,2,2,2,2,2,2,2,2,2,2] (.node [12,11,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [12,12,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,12,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,12,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,12,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [13,5,5,4,4,4,1,1,1,1,1,1,1,1] (.node [12,12,2,2,2,2,2,2,2,1,1,1,1,1] (.node [12,12,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [12,12,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [13,5,5,5,4,4,1,1,1,1,1,1,1] (.node [13,5,5,5,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,5,5,5,5,2,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_632 : RowTree := (.node [12,10,4,3,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_630 degreeTree43_631) - -def degreeTree43_633 : RowTree := (.node [12,8,6,3,2,2,2,2,2,2,1,1] degreeTree43_629 degreeTree43_632) - -def degreeTree43_634 : RowTree := (.node [13,6,5,5,4,3,1,1,1,1,1,1,1] (.node [13,6,5,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [13,6,5,4,4,4,1,1,1,1,1,1,1] (.node [13,6,5,4,4,3,1,1,1,1,1,1,1,1] (.node [13,6,4,4,4,4,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [13,6,5,5,3,3,1,1,1,1,1,1,1,1] (.node [13,6,5,5,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [13,6,5,5,4,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [13,6,6,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [13,6,5,5,5,2,1,1,1,1,1,1,1] (.node [13,6,5,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [13,6,6,4,3,3,1,1,1,1,1,1,1,1] (.node [13,6,6,4,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [13,6,6,4,4,2,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_635 : RowTree := (.node [13,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1] (.node [13,6,6,5,2,2,2,1,1,1,1,1,1,1] (.node [13,6,6,5,2,1,1,1,1,1,1,1,1,1,1,1] (.node [13,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,6,6,5,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [13,6,6,5,3,2,1,1,1,1,1,1,1,1] (.node [13,6,6,5,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [13,6,6,5,4,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [13,6,6,6,3,1,1,1,1,1,1,1,1,1] (.node [13,6,6,6,2,2,1,1,1,1,1,1,1,1] (.node [13,6,6,6,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,6,6,6,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [13,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [13,7,4,4,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,8,4,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree43_636 : RowTree := (.node [13,6,6,4,4,3,1,1,1,1,1,1,1] degreeTree43_634 degreeTree43_635) - -def degreeTree43_637 : RowTree := (.node [14,6,4,4,4,3,1,1,1,1,1,1,1,1] (.node [14,5,4,4,4,4,1,1,1,1,1,1,1,1] (.node [13,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [13,8,4,4,4,2,1,1,1,1,1,1,1,1] (.node [13,8,4,4,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [13,10,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [13,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,10,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [14,5,5,5,2,2,2,2,1,1,1,1,1,1] (.node [14,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,5,5,4,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,5,5,5,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [14,5,5,5,4,2,1,1,1,1,1,1,1,1] (.node [14,5,5,5,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,5,5,5,5,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [14,6,5,5,2,2,1,1,1,1,1,1,1,1,1] (.node [14,6,5,4,3,3,1,1,1,1,1,1,1,1] (.node [14,6,5,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [14,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,6,5,4,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [14,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,6,5,4,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,6,5,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [14,6,6,3,2,2,2,2,1,1,1,1,1,1] (.node [14,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,6,5,5,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [14,6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [14,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,6,6,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,6,6,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_638 : RowTree := (.node [13,8,4,4,2,2,2,2,1,1,1,1,1,1] degreeTree43_636 degreeTree43_637) - -def degreeTree43_639 : RowTree := (.node [14,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,6,6,6,1,1,1,1,1,1,1,1,1,1,1] (.node [14,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,6,6,4,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [14,6,6,5,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [14,7,4,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [14,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,7,4,4,2,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [14,8,4,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [14,8,4,3,2,2,2,2,1,1,1,1,1,1] (.node [14,8,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [14,9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,8,4,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,9,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [14,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [14,10,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,9,2,2,2,2,2,2,2,2,1,1,1,1] (.node [14,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [14,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [15,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [15,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,10,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [15,6,4,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [15,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [15,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [15,8,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_640 : RowTree := (.node [17,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [16,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [16,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [16,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [16,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [16,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [16,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [17,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [17,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [18,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [18,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [18,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [17,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [18,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [18,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [18,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [18,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [20,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [19,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [19,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [20,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [21,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [20,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [22,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) - -def degreeTree43_641 : RowTree := (.node [16,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_639 degreeTree43_640) - -def degreeTree43_642 : RowTree := (.node [14,6,6,4,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_638 degreeTree43_641) - -def degreeTree43_643 : RowTree := (.node [13,5,5,5,5,3,1,1,1,1,1,1,1] degreeTree43_633 degreeTree43_642) - -def degreeTree43_644 : RowTree := (.node [12,7,5,5,3,3,1,1,1,1,1,1,1,1] degreeTree43_624 degreeTree43_643) - -def degreeTree43_645 : RowTree := (.node [10,10,6,6,3,2,1,1,1,1,1,1] degreeTree43_605 degreeTree43_644) - -def degreeTree43_646 : RowTree := (.node [10,9,5,4,2,2,2,2,2,1,1,1,1,1] degreeTree43_566 degreeTree43_645) - -def degreeTree43_647 : RowTree := (.node [10,7,7,5,4,2,1,1,1,1,1,1,1,1] degreeTree43_485 degreeTree43_646) - -def degreeTree43_648 : RowTree := (.node [10,4,4,4,2,2,2,2,2,2,2,2,2,1,1,1] degreeTree43_324 degreeTree43_647) - -def degreeTree43 : RowTree := degreeTree43_648 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 43. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree43_0 : RowTree := (.node [7,7,7,7,7,2,2,1,1,1,1] (.node [7,7,7,7,5,5,5] (.node [7,7,7,6,6,5,5] (.node [7,7,6,6,6,6,5] (.node [7,6,6,6,6,6,6] .empty .empty) .empty) (.node [7,7,7,6,6,6,4] .empty .empty)) (.node [7,7,7,7,7,1,1,1,1,1,1,1,1] (.node [7,7,7,7,6,5,4] .empty .empty) (.node [7,7,7,7,7,2,1,1,1,1,1,1] .empty .empty))) (.node [7,7,7,7,7,3,2,1,1,1] (.node [7,7,7,7,7,2,2,2,2] (.node [7,7,7,7,7,2,2,2,1,1] .empty .empty) (.node [7,7,7,7,7,3,1,1,1,1,1] .empty .empty)) (.node [7,7,7,7,7,3,3,1,1] (.node [7,7,7,7,7,3,2,2,1] .empty .empty) (.node [7,7,7,7,7,3,3,2] .empty .empty)))) + +def degreeTree43_1 : RowTree := (.node [8,4,4,4,4,4,4,3,3,3,2] (.node [7,7,7,7,7,5,1,1,1] (.node [7,7,7,7,7,4,2,2] (.node [7,7,7,7,7,4,2,1,1] .empty .empty) (.node [7,7,7,7,7,4,3,1] .empty .empty)) (.node [7,7,7,7,7,6,1,1] (.node [7,7,7,7,7,5,2,1] .empty .empty) (.node [8,4,4,4,4,4,3,3,3,3,3] .empty .empty))) (.node [8,4,4,4,4,4,4,4,4,3] (.node [8,4,4,4,4,4,4,4,3,3,1] (.node [8,4,4,4,4,4,4,4,3,2,2] .empty .empty) (.node [8,4,4,4,4,4,4,4,4,2,1] .empty .empty)) (.node [8,5,4,4,4,4,3,3,3,3,2] (.node [8,5,4,4,4,3,3,3,3,3,3] .empty .empty) (.node [8,5,4,4,4,4,4,3,3,2,2] .empty .empty)))) + +def degreeTree43_2 : RowTree := (.node [7,7,7,7,7,4,1,1,1,1] degreeTree43_0 degreeTree43_1) + +def degreeTree43_3 : RowTree := (.node [8,5,5,4,4,4,4,4,4,1] (.node [8,5,5,4,4,4,3,3,3,2,2] (.node [8,5,4,4,4,4,4,4,4,1,1] (.node [8,5,4,4,4,4,4,4,3,2,1] (.node [8,5,4,4,4,4,4,4,2,2,2] .empty .empty) (.node [8,5,4,4,4,4,4,4,3,3] .empty .empty)) (.node [8,5,5,4,3,3,3,3,3,3,3] (.node [8,5,4,4,4,4,4,4,4,2] .empty .empty) (.node [8,5,5,4,4,3,3,3,3,3,2] .empty .empty))) (.node [8,5,5,4,4,4,4,3,3,3] (.node [8,5,5,4,4,4,4,3,2,2,2] (.node [8,5,5,4,4,4,3,3,3,3,1] .empty .empty) (.node [8,5,5,4,4,4,4,3,3,2,1] .empty .empty)) (.node [8,5,5,4,4,4,4,4,3,1,1] (.node [8,5,5,4,4,4,4,4,2,2,1] .empty .empty) (.node [8,5,5,4,4,4,4,4,3,2] .empty .empty)))) (.node [8,5,5,5,4,4,4,3,2,2,1] (.node [8,5,5,5,4,4,3,3,2,2,2] (.node [8,5,5,5,4,3,3,3,3,2,2] (.node [8,5,5,5,3,3,3,3,3,3,2] .empty .empty) (.node [8,5,5,5,4,3,3,3,3,3,1] .empty .empty)) (.node [8,5,5,5,4,4,3,3,3,3] (.node [8,5,5,5,4,4,3,3,3,2,1] .empty .empty) (.node [8,5,5,5,4,4,4,2,2,2,2] .empty .empty))) (.node [8,5,5,5,4,4,4,4,2,2] (.node [8,5,5,5,4,4,4,3,3,2] (.node [8,5,5,5,4,4,4,3,3,1,1] .empty .empty) (.node [8,5,5,5,4,4,4,4,2,1,1] .empty .empty)) (.node [8,5,5,5,4,4,4,4,4] (.node [8,5,5,5,4,4,4,4,3,1] .empty .empty) (.node [8,5,5,5,5,3,3,3,2,2,2] .empty .empty))))) + +def degreeTree43_4 : RowTree := (.node [8,5,4,4,4,4,4,3,3,3,1] degreeTree43_2 degreeTree43_3) + +def degreeTree43_5 : RowTree := (.node [8,5,5,5,5,4,4,3,3,1] (.node [8,5,5,5,5,4,3,3,3,2] (.node [8,5,5,5,5,4,3,3,2,2,1] (.node [8,5,5,5,5,4,3,2,2,2,2] (.node [8,5,5,5,5,3,3,3,3,3] .empty .empty) .empty) (.node [8,5,5,5,5,4,3,3,3,1,1] .empty .empty)) (.node [8,5,5,5,5,4,4,3,2,1,1] (.node [8,5,5,5,5,4,4,2,2,2,1] .empty .empty) (.node [8,5,5,5,5,4,4,3,2,2] .empty .empty))) (.node [8,5,5,5,5,5,2,2,2,2,2] (.node [8,5,5,5,5,4,4,4,2,1] (.node [8,5,5,5,5,4,4,4,1,1,1] .empty .empty) (.node [8,5,5,5,5,4,4,4,3] .empty .empty)) (.node [8,5,5,5,5,5,3,3,2,1,1] (.node [8,5,5,5,5,5,3,2,2,2,1] .empty .empty) (.node [8,5,5,5,5,5,3,3,2,2] .empty .empty)))) + +def degreeTree43_6 : RowTree := (.node [8,5,5,5,5,5,5,2,1,1,1] (.node [8,5,5,5,5,5,4,3,2,1] (.node [8,5,5,5,5,5,4,2,2,2] (.node [8,5,5,5,5,5,4,2,2,1,1] .empty .empty) (.node [8,5,5,5,5,5,4,3,1,1,1] .empty .empty)) (.node [8,5,5,5,5,5,4,4,1,1] (.node [8,5,5,5,5,5,4,3,3] .empty .empty) (.node [8,5,5,5,5,5,4,4,2] .empty .empty))) (.node [8,5,5,5,5,5,5,4,1] (.node [8,5,5,5,5,5,5,3,1,1] (.node [8,5,5,5,5,5,5,2,2,1] .empty .empty) (.node [8,5,5,5,5,5,5,3,2] .empty .empty)) (.node [8,6,4,4,3,3,3,3,3,3,3] (.node [8,5,5,5,5,5,5,5] .empty .empty) (.node [8,6,4,4,4,3,3,3,3,3,2] .empty .empty)))) + +def degreeTree43_7 : RowTree := (.node [8,5,5,5,5,5,3,3,3,1] degreeTree43_5 degreeTree43_6) + +def degreeTree43_8 : RowTree := (.node [8,6,5,4,4,4,4,2,2,2,2] (.node [8,6,4,4,4,4,4,4,4,1] (.node [8,6,4,4,4,4,4,3,3,3] (.node [8,6,4,4,4,4,4,3,2,2,2] (.node [8,6,4,4,4,4,3,3,3,3,1] .empty .empty) (.node [8,6,4,4,4,4,4,3,3,2,1] .empty .empty)) (.node [8,6,4,4,4,4,4,4,3,1,1] (.node [8,6,4,4,4,4,4,4,2,2,1] .empty .empty) (.node [8,6,4,4,4,4,4,4,3,2] .empty .empty))) (.node [8,6,5,4,4,3,3,3,3,3,1] (.node [8,6,5,4,3,3,3,3,3,3,2] (.node [8,6,5,3,3,3,3,3,3,3,3] .empty .empty) (.node [8,6,5,4,4,3,3,3,3,2,2] .empty .empty)) (.node [8,6,5,4,4,4,3,3,3,2,1] (.node [8,6,5,4,4,4,3,3,2,2,2] .empty .empty) (.node [8,6,5,4,4,4,3,3,3,3] .empty .empty)))) (.node [8,6,5,5,3,3,3,3,3,2,2] (.node [8,6,5,4,4,4,4,4,2,1,1] (.node [8,6,5,4,4,4,4,3,3,1,1] (.node [8,6,5,4,4,4,4,3,2,2,1] .empty .empty) (.node [8,6,5,4,4,4,4,3,3,2] .empty .empty)) (.node [8,6,5,4,4,4,4,4,3,1] (.node [8,6,5,4,4,4,4,4,2,2] .empty .empty) (.node [8,6,5,4,4,4,4,4,4] .empty .empty))) (.node [8,6,5,5,4,3,3,3,3,3] (.node [8,6,5,5,4,3,3,3,2,2,2] (.node [8,6,5,5,3,3,3,3,3,3,1] .empty .empty) (.node [8,6,5,5,4,3,3,3,3,2,1] .empty .empty)) (.node [8,6,5,5,4,4,3,3,2,2,1] (.node [8,6,5,5,4,4,3,2,2,2,2] .empty .empty) (.node [8,6,5,5,4,4,3,3,3,1,1] .empty .empty))))) + +def degreeTree43_9 : RowTree := (.node [8,6,4,4,4,4,3,3,3,2,2] degreeTree43_7 degreeTree43_8) + +def degreeTree43_10 : RowTree := (.node [8,5,5,5,5,3,3,3,3,2,1] degreeTree43_4 degreeTree43_9) + +def degreeTree43_11 : RowTree := (.node [8,6,5,5,5,3,3,3,2,2,1] (.node [8,6,5,5,4,4,4,4,1,1,1] (.node [8,6,5,5,4,4,4,3,2,2] (.node [8,6,5,5,4,4,4,3,2,1,1] (.node [8,6,5,5,4,4,4,2,2,2,1] .empty .empty) .empty) (.node [8,6,5,5,4,4,4,3,3,1] .empty .empty)) (.node [8,6,5,5,4,4,4,4,3] (.node [8,6,5,5,4,4,4,4,2,1] .empty .empty) (.node [8,6,5,5,5,3,3,2,2,2,2] .empty .empty))) (.node [8,6,5,5,5,4,3,2,2,2,1] (.node [8,6,5,5,5,3,3,3,3,2] (.node [8,6,5,5,5,3,3,3,3,1,1] .empty .empty) (.node [8,6,5,5,5,4,2,2,2,2,2] .empty .empty)) (.node [8,6,5,5,5,4,3,3,2,2] (.node [8,6,5,5,5,4,3,3,2,1,1] .empty .empty) (.node [8,6,5,5,5,4,3,3,3,1] .empty .empty)))) + +def degreeTree43_12 : RowTree := (.node [8,6,5,5,5,5,3,2,2,1,1] (.node [8,6,5,5,5,4,4,3,3] (.node [8,6,5,5,5,4,4,3,1,1,1] (.node [8,6,5,5,5,4,4,2,2,2] .empty .empty) (.node [8,6,5,5,5,4,4,3,2,1] .empty .empty)) (.node [8,6,5,5,5,4,4,4,2] (.node [8,6,5,5,5,4,4,4,1,1] .empty .empty) (.node [8,6,5,5,5,5,2,2,2,2,1] .empty .empty))) (.node [8,6,5,5,5,5,3,3,3] (.node [8,6,5,5,5,5,3,3,1,1,1] (.node [8,6,5,5,5,5,3,2,2,2] .empty .empty) (.node [8,6,5,5,5,5,3,3,2,1] .empty .empty)) (.node [8,6,5,5,5,5,4,2,2,1] (.node [8,6,5,5,5,5,4,2,1,1,1] .empty .empty) (.node [8,6,5,5,5,5,4,3,1,1] .empty .empty)))) + +def degreeTree43_13 : RowTree := (.node [8,6,5,5,5,4,4,2,2,1,1] degreeTree43_11 degreeTree43_12) + +def degreeTree43_14 : RowTree := (.node [8,6,6,4,4,4,3,3,3,2] (.node [8,6,6,4,3,3,3,3,3,2,2] (.node [8,6,5,5,5,5,5,2,2] (.node [8,6,5,5,5,5,5,1,1,1,1] (.node [8,6,5,5,5,5,4,4,1] .empty .empty) (.node [8,6,5,5,5,5,5,2,1,1] .empty .empty)) (.node [8,6,5,5,5,5,5,4] (.node [8,6,5,5,5,5,5,3,1] .empty .empty) (.node [8,6,6,3,3,3,3,3,3,3,2] .empty .empty))) (.node [8,6,6,4,4,3,3,3,3,3] (.node [8,6,6,4,4,3,3,3,2,2,2] (.node [8,6,6,4,3,3,3,3,3,3,1] .empty .empty) (.node [8,6,6,4,4,3,3,3,3,2,1] .empty .empty)) (.node [8,6,6,4,4,4,3,3,2,2,1] (.node [8,6,6,4,4,4,3,2,2,2,2] .empty .empty) (.node [8,6,6,4,4,4,3,3,3,1,1] .empty .empty)))) (.node [8,6,6,5,3,3,3,3,2,2,2] (.node [8,6,6,4,4,4,4,3,3,1] (.node [8,6,6,4,4,4,4,3,2,1,1] (.node [8,6,6,4,4,4,4,2,2,2,1] .empty .empty) (.node [8,6,6,4,4,4,4,3,2,2] .empty .empty)) (.node [8,6,6,4,4,4,4,4,2,1] (.node [8,6,6,4,4,4,4,4,1,1,1] .empty .empty) (.node [8,6,6,4,4,4,4,4,3] .empty .empty))) (.node [8,6,6,5,4,3,3,3,2,2,1] (.node [8,6,6,5,3,3,3,3,3,3] (.node [8,6,6,5,3,3,3,3,3,2,1] .empty .empty) (.node [8,6,6,5,4,3,3,2,2,2,2] .empty .empty)) (.node [8,6,6,5,4,3,3,3,3,2] (.node [8,6,6,5,4,3,3,3,3,1,1] .empty .empty) (.node [8,6,6,5,4,4,2,2,2,2,2] .empty .empty))))) + +def degreeTree43_15 : RowTree := (.node [8,6,5,5,5,5,4,3,2] degreeTree43_13 degreeTree43_14) + +def degreeTree43_16 : RowTree := (.node [8,6,6,5,5,4,2,2,2,2,1] (.node [8,6,6,5,4,4,4,3,3] (.node [8,6,6,5,4,4,4,2,2,1,1] (.node [8,6,6,5,4,4,3,3,2,2] (.node [8,6,6,5,4,4,3,3,2,1,1] .empty .empty) (.node [8,6,6,5,4,4,3,3,3,1] .empty .empty)) (.node [8,6,6,5,4,4,4,3,1,1,1] (.node [8,6,6,5,4,4,4,2,2,2] .empty .empty) (.node [8,6,6,5,4,4,4,3,2,1] .empty .empty))) (.node [8,6,6,5,5,3,3,2,2,2,1] (.node [8,6,6,5,4,4,4,4,2] (.node [8,6,6,5,4,4,4,4,1,1] .empty .empty) (.node [8,6,6,5,5,3,2,2,2,2,2] .empty .empty)) (.node [8,6,6,5,5,3,3,3,2,2] (.node [8,6,6,5,5,3,3,3,2,1,1] .empty .empty) (.node [8,6,6,5,5,3,3,3,3,1] .empty .empty)))) (.node [8,6,6,5,5,4,4,3,1,1] (.node [8,6,6,5,5,4,3,3,2,1] (.node [8,6,6,5,5,4,3,2,2,2] (.node [8,6,6,5,5,4,3,2,2,1,1] .empty .empty) (.node [8,6,6,5,5,4,3,3,1,1,1] .empty .empty)) (.node [8,6,6,5,5,4,4,2,1,1,1] (.node [8,6,6,5,5,4,3,3,3] .empty .empty) (.node [8,6,6,5,5,4,4,2,2,1] .empty .empty))) (.node [8,6,6,5,5,5,2,2,2,2] (.node [8,6,6,5,5,4,4,4,1] (.node [8,6,6,5,5,4,4,3,2] .empty .empty) (.node [8,6,6,5,5,5,2,2,2,1,1] .empty .empty)) (.node [8,6,6,5,5,5,3,2,2,1] (.node [8,6,6,5,5,5,3,2,1,1,1] .empty .empty) (.node [8,6,6,5,5,5,3,3,1,1] .empty .empty))))) + +def degreeTree43_17 : RowTree := (.node [8,6,6,6,4,3,3,3,2,2] (.node [8,6,6,5,5,5,5,3] (.node [8,6,6,5,5,5,4,3,1] (.node [8,6,6,5,5,5,4,2,1,1] (.node [8,6,6,5,5,5,4,1,1,1,1] .empty .empty) (.node [8,6,6,5,5,5,4,2,2] .empty .empty)) (.node [8,6,6,5,5,5,5,1,1,1] (.node [8,6,6,5,5,5,4,4] .empty .empty) (.node [8,6,6,5,5,5,5,2,1] .empty .empty))) (.node [8,6,6,6,3,3,3,3,3,2] (.node [8,6,6,6,3,3,3,3,2,2,1] (.node [8,6,6,6,3,3,3,2,2,2,2] .empty .empty) (.node [8,6,6,6,3,3,3,3,3,1,1] .empty .empty)) (.node [8,6,6,6,4,3,3,2,2,2,1] (.node [8,6,6,6,4,3,2,2,2,2,2] .empty .empty) (.node [8,6,6,6,4,3,3,3,2,1,1] .empty .empty)))) (.node [8,6,6,6,4,4,4,2,1,1,1] (.node [8,6,6,6,4,4,3,2,2,2] (.node [8,6,6,6,4,4,2,2,2,2,1] (.node [8,6,6,6,4,3,3,3,3,1] .empty .empty) (.node [8,6,6,6,4,4,3,2,2,1,1] .empty .empty)) (.node [8,6,6,6,4,4,3,3,2,1] (.node [8,6,6,6,4,4,3,3,1,1,1] .empty .empty) (.node [8,6,6,6,4,4,3,3,3] .empty .empty))) (.node [8,6,6,6,4,4,4,4,1] (.node [8,6,6,6,4,4,4,3,1,1] (.node [8,6,6,6,4,4,4,2,2,1] .empty .empty) (.node [8,6,6,6,4,4,4,3,2] .empty .empty)) (.node [8,6,6,6,5,3,2,2,2,2,1] (.node [8,6,6,6,5,2,2,2,2,2,2] .empty .empty) (.node [8,6,6,6,5,3,3,2,2,1,1] .empty .empty))))) + +def degreeTree43_18 : RowTree := (.node [8,6,6,5,5,5,3,3,2] degreeTree43_16 degreeTree43_17) + +def degreeTree43_19 : RowTree := (.node [8,6,6,5,4,4,3,2,2,2,1] degreeTree43_15 degreeTree43_18) + +def degreeTree43_20 : RowTree := (.node [8,6,5,5,4,4,3,3,3,2] degreeTree43_10 degreeTree43_19) + +def degreeTree43_21 : RowTree := (.node [8,6,6,6,5,4,3,3,2] (.node [8,6,6,6,5,4,2,2,2,2] (.node [8,6,6,6,5,3,3,3,3] (.node [8,6,6,6,5,3,3,3,2,1] (.node [8,6,6,6,5,3,3,3,1,1,1] .empty .empty) .empty) (.node [8,6,6,6,5,4,2,2,2,1,1] .empty .empty)) (.node [8,6,6,6,5,4,3,2,2,1] (.node [8,6,6,6,5,4,3,2,1,1,1] .empty .empty) (.node [8,6,6,6,5,4,3,3,1,1] .empty .empty))) (.node [8,6,6,6,5,4,4,3,1] (.node [8,6,6,6,5,4,4,2,1,1] (.node [8,6,6,6,5,4,4,1,1,1,1] .empty .empty) (.node [8,6,6,6,5,4,4,2,2] .empty .empty)) (.node [8,6,6,6,5,5,2,2,1,1,1] (.node [8,6,6,6,5,4,4,4] .empty .empty) (.node [8,6,6,6,5,5,2,2,2,1] .empty .empty)))) + +def degreeTree43_22 : RowTree := (.node [8,6,6,6,5,5,5,2] (.node [8,6,6,6,5,5,4,1,1,1] (.node [8,6,6,6,5,5,3,2,2] (.node [8,6,6,6,5,5,3,2,1,1] .empty .empty) (.node [8,6,6,6,5,5,3,3,1] .empty .empty)) (.node [8,6,6,6,5,5,4,3] (.node [8,6,6,6,5,5,4,2,1] .empty .empty) (.node [8,6,6,6,5,5,5,1,1] .empty .empty))) (.node [8,6,6,6,6,3,3,2,1,1,1] (.node [8,6,6,6,6,3,2,2,2,1,1] (.node [8,6,6,6,6,2,2,2,2,2,1] .empty .empty) (.node [8,6,6,6,6,3,2,2,2,2] .empty .empty)) (.node [8,6,6,6,6,3,3,3,1,1] (.node [8,6,6,6,6,3,3,2,2,1] .empty .empty) (.node [8,6,6,6,6,3,3,3,2] .empty .empty)))) + +def degreeTree43_23 : RowTree := (.node [8,6,6,6,5,5,3,1,1,1,1] degreeTree43_21 degreeTree43_22) + +def degreeTree43_24 : RowTree := (.node [8,6,6,6,6,5,4,2] (.node [8,6,6,6,6,4,4,3] (.node [8,6,6,6,6,4,3,2,2] (.node [8,6,6,6,6,4,3,1,1,1,1] (.node [8,6,6,6,6,4,2,2,2,1] .empty .empty) (.node [8,6,6,6,6,4,3,2,1,1] .empty .empty)) (.node [8,6,6,6,6,4,4,1,1,1] (.node [8,6,6,6,6,4,3,3,1] .empty .empty) (.node [8,6,6,6,6,4,4,2,1] .empty .empty))) (.node [8,6,6,6,6,5,3,1,1,1] (.node [8,6,6,6,6,5,2,2,1,1] (.node [8,6,6,6,6,5,2,1,1,1,1] .empty .empty) (.node [8,6,6,6,6,5,2,2,2] .empty .empty)) (.node [8,6,6,6,6,5,3,3] (.node [8,6,6,6,6,5,3,2,1] .empty .empty) (.node [8,6,6,6,6,5,4,1,1] .empty .empty)))) (.node [8,7,4,3,3,3,3,3,3,3,3] (.node [8,6,6,6,6,6,2,2,1] (.node [8,6,6,6,6,6,1,1,1,1,1] (.node [8,6,6,6,6,5,5,1] .empty .empty) (.node [8,6,6,6,6,6,2,1,1,1] .empty .empty)) (.node [8,6,6,6,6,6,3,2] (.node [8,6,6,6,6,6,3,1,1] .empty .empty) (.node [8,6,6,6,6,6,4,1] .empty .empty))) (.node [8,7,4,4,4,4,3,3,2,2,2] (.node [8,7,4,4,4,3,3,3,3,2,2] (.node [8,7,4,4,3,3,3,3,3,3,2] .empty .empty) (.node [8,7,4,4,4,3,3,3,3,3,1] .empty .empty)) (.node [8,7,4,4,4,4,3,3,3,3] (.node [8,7,4,4,4,4,3,3,3,2,1] .empty .empty) (.node [8,7,4,4,4,4,4,2,2,2,2] .empty .empty))))) + +def degreeTree43_25 : RowTree := (.node [8,6,6,6,6,4,2,2,1,1,1] degreeTree43_23 degreeTree43_24) + +def degreeTree43_26 : RowTree := (.node [8,7,5,4,4,4,3,3,3,2] (.node [8,7,5,4,3,3,3,3,3,2,2] (.node [8,7,4,4,4,4,4,4,2,2] (.node [8,7,4,4,4,4,4,3,3,2] (.node [8,7,4,4,4,4,4,3,3,1,1] .empty .empty) (.node [8,7,4,4,4,4,4,4,2,1,1] .empty .empty)) (.node [8,7,4,4,4,4,4,4,4] (.node [8,7,4,4,4,4,4,4,3,1] .empty .empty) (.node [8,7,5,3,3,3,3,3,3,3,2] .empty .empty))) (.node [8,7,5,4,4,3,3,3,3,3] (.node [8,7,5,4,4,3,3,3,2,2,2] (.node [8,7,5,4,3,3,3,3,3,3,1] .empty .empty) (.node [8,7,5,4,4,3,3,3,3,2,1] .empty .empty)) (.node [8,7,5,4,4,4,3,3,2,2,1] (.node [8,7,5,4,4,4,3,2,2,2,2] .empty .empty) (.node [8,7,5,4,4,4,3,3,3,1,1] .empty .empty)))) (.node [8,7,5,5,3,3,3,3,2,2,2] (.node [8,7,5,4,4,4,4,3,3,1] (.node [8,7,5,4,4,4,4,3,2,1,1] (.node [8,7,5,4,4,4,4,2,2,2,1] .empty .empty) (.node [8,7,5,4,4,4,4,3,2,2] .empty .empty)) (.node [8,7,5,4,4,4,4,4,2,1] (.node [8,7,5,4,4,4,4,4,1,1,1] .empty .empty) (.node [8,7,5,4,4,4,4,4,3] .empty .empty))) (.node [8,7,5,5,4,3,3,3,2,2,1] (.node [8,7,5,5,3,3,3,3,3,3] (.node [8,7,5,5,3,3,3,3,3,2,1] .empty .empty) (.node [8,7,5,5,4,3,3,2,2,2,2] .empty .empty)) (.node [8,7,5,5,4,3,3,3,3,2] (.node [8,7,5,5,4,3,3,3,3,1,1] .empty .empty) (.node [8,7,5,5,4,4,2,2,2,2,2] .empty .empty))))) + +def degreeTree43_27 : RowTree := (.node [8,7,5,5,5,4,2,2,2,2,1] (.node [8,7,5,5,4,4,4,3,3] (.node [8,7,5,5,4,4,4,2,2,1,1] (.node [8,7,5,5,4,4,3,3,2,2] (.node [8,7,5,5,4,4,3,3,2,1,1] .empty .empty) (.node [8,7,5,5,4,4,3,3,3,1] .empty .empty)) (.node [8,7,5,5,4,4,4,3,1,1,1] (.node [8,7,5,5,4,4,4,2,2,2] .empty .empty) (.node [8,7,5,5,4,4,4,3,2,1] .empty .empty))) (.node [8,7,5,5,5,3,3,2,2,2,1] (.node [8,7,5,5,4,4,4,4,2] (.node [8,7,5,5,4,4,4,4,1,1] .empty .empty) (.node [8,7,5,5,5,3,2,2,2,2,2] .empty .empty)) (.node [8,7,5,5,5,3,3,3,2,2] (.node [8,7,5,5,5,3,3,3,2,1,1] .empty .empty) (.node [8,7,5,5,5,3,3,3,3,1] .empty .empty)))) (.node [8,7,5,5,5,4,4,3,1,1] (.node [8,7,5,5,5,4,3,3,2,1] (.node [8,7,5,5,5,4,3,2,2,2] (.node [8,7,5,5,5,4,3,2,2,1,1] .empty .empty) (.node [8,7,5,5,5,4,3,3,1,1,1] .empty .empty)) (.node [8,7,5,5,5,4,4,2,1,1,1] (.node [8,7,5,5,5,4,3,3,3] .empty .empty) (.node [8,7,5,5,5,4,4,2,2,1] .empty .empty))) (.node [8,7,5,5,5,5,2,2,2,2] (.node [8,7,5,5,5,4,4,4,1] (.node [8,7,5,5,5,4,4,3,2] .empty .empty) (.node [8,7,5,5,5,5,2,2,2,1,1] .empty .empty)) (.node [8,7,5,5,5,5,3,2,2,1] (.node [8,7,5,5,5,5,3,2,1,1,1] .empty .empty) (.node [8,7,5,5,5,5,3,3,1,1] .empty .empty))))) + +def degreeTree43_28 : RowTree := (.node [8,7,5,5,4,4,3,2,2,2,1] degreeTree43_26 degreeTree43_27) + +def degreeTree43_29 : RowTree := (.node [8,7,4,4,4,4,4,3,2,2,1] degreeTree43_25 degreeTree43_28) + +def degreeTree43_30 : RowTree := (.node [8,7,6,3,3,3,3,3,3,2,2] (.node [8,7,5,5,5,5,4,4] (.node [8,7,5,5,5,5,4,2,2] (.node [8,7,5,5,5,5,4,2,1,1] (.node [8,7,5,5,5,5,4,1,1,1,1] .empty .empty) .empty) (.node [8,7,5,5,5,5,4,3,1] .empty .empty)) (.node [8,7,5,5,5,5,5,2,1] (.node [8,7,5,5,5,5,5,1,1,1] .empty .empty) (.node [8,7,5,5,5,5,5,3] .empty .empty))) (.node [8,7,6,4,3,3,3,3,3,3] (.node [8,7,6,4,3,3,3,3,2,2,2] (.node [8,7,6,3,3,3,3,3,3,3,1] .empty .empty) (.node [8,7,6,4,3,3,3,3,3,2,1] .empty .empty)) (.node [8,7,6,4,4,3,3,3,2,2,1] (.node [8,7,6,4,4,3,3,2,2,2,2] .empty .empty) (.node [8,7,6,4,4,3,3,3,3,1,1] .empty .empty)))) + +def degreeTree43_31 : RowTree := (.node [8,7,6,4,4,4,4,3,1,1,1] (.node [8,7,6,4,4,4,3,3,2,2] (.node [8,7,6,4,4,4,3,2,2,2,1] (.node [8,7,6,4,4,4,2,2,2,2,2] .empty .empty) (.node [8,7,6,4,4,4,3,3,2,1,1] .empty .empty)) (.node [8,7,6,4,4,4,4,2,2,1,1] (.node [8,7,6,4,4,4,3,3,3,1] .empty .empty) (.node [8,7,6,4,4,4,4,2,2,2] .empty .empty))) (.node [8,7,6,4,4,4,4,4,2] (.node [8,7,6,4,4,4,4,3,3] (.node [8,7,6,4,4,4,4,3,2,1] .empty .empty) (.node [8,7,6,4,4,4,4,4,1,1] .empty .empty)) (.node [8,7,6,5,3,3,3,3,2,2,1] (.node [8,7,6,5,3,3,3,2,2,2,2] .empty .empty) (.node [8,7,6,5,3,3,3,3,3,1,1] .empty .empty)))) + +def degreeTree43_32 : RowTree := (.node [8,7,6,4,4,3,3,3,3,2] degreeTree43_30 degreeTree43_31) + +def degreeTree43_33 : RowTree := (.node [8,7,6,5,4,4,4,4,1] (.node [8,7,6,5,4,4,3,2,2,2] (.node [8,7,6,5,4,3,3,3,2,2] (.node [8,7,6,5,4,3,3,2,2,2,1] (.node [8,7,6,5,4,3,2,2,2,2,2] .empty .empty) (.node [8,7,6,5,4,3,3,3,2,1,1] .empty .empty)) (.node [8,7,6,5,4,4,2,2,2,2,1] (.node [8,7,6,5,4,3,3,3,3,1] .empty .empty) (.node [8,7,6,5,4,4,3,2,2,1,1] .empty .empty))) (.node [8,7,6,5,4,4,4,2,1,1,1] (.node [8,7,6,5,4,4,3,3,2,1] (.node [8,7,6,5,4,4,3,3,1,1,1] .empty .empty) (.node [8,7,6,5,4,4,3,3,3] .empty .empty)) (.node [8,7,6,5,4,4,4,3,1,1] (.node [8,7,6,5,4,4,4,2,2,1] .empty .empty) (.node [8,7,6,5,4,4,4,3,2] .empty .empty)))) (.node [8,7,6,5,5,4,2,2,2,1,1] (.node [8,7,6,5,5,3,3,2,2,2] (.node [8,7,6,5,5,3,2,2,2,2,1] (.node [8,7,6,5,5,2,2,2,2,2,2] .empty .empty) (.node [8,7,6,5,5,3,3,2,2,1,1] .empty .empty)) (.node [8,7,6,5,5,3,3,3,2,1] (.node [8,7,6,5,5,3,3,3,1,1,1] .empty .empty) (.node [8,7,6,5,5,3,3,3,3] .empty .empty))) (.node [8,7,6,5,5,4,3,3,1,1] (.node [8,7,6,5,5,4,3,2,1,1,1] (.node [8,7,6,5,5,4,2,2,2,2] .empty .empty) (.node [8,7,6,5,5,4,3,2,2,1] .empty .empty)) (.node [8,7,6,5,5,4,4,1,1,1,1] (.node [8,7,6,5,5,4,3,3,2] .empty .empty) (.node [8,7,6,5,5,4,4,2,1,1] .empty .empty))))) + +def degreeTree43_34 : RowTree := (.node [8,7,6,5,3,3,3,3,3,2] degreeTree43_32 degreeTree43_33) + +def degreeTree43_35 : RowTree := (.node [8,7,6,6,3,3,3,3,2,1,1] (.node [8,7,6,5,5,5,3,3,1] (.node [8,7,6,5,5,5,2,2,2,1] (.node [8,7,6,5,5,4,4,4] (.node [8,7,6,5,5,4,4,3,1] .empty .empty) (.node [8,7,6,5,5,5,2,2,1,1,1] .empty .empty)) (.node [8,7,6,5,5,5,3,2,1,1] (.node [8,7,6,5,5,5,3,1,1,1,1] .empty .empty) (.node [8,7,6,5,5,5,3,2,2] .empty .empty))) (.node [8,7,6,5,5,5,5,1,1] (.node [8,7,6,5,5,5,4,2,1] (.node [8,7,6,5,5,5,4,1,1,1] .empty .empty) (.node [8,7,6,5,5,5,4,3] .empty .empty)) (.node [8,7,6,6,3,3,2,2,2,2,2] (.node [8,7,6,5,5,5,5,2] .empty .empty) (.node [8,7,6,6,3,3,3,2,2,2,1] .empty .empty)))) (.node [8,7,6,6,4,3,3,3,2,1] (.node [8,7,6,6,4,3,2,2,2,2,1] (.node [8,7,6,6,3,3,3,3,3,1] (.node [8,7,6,6,3,3,3,3,2,2] .empty .empty) (.node [8,7,6,6,4,2,2,2,2,2,2] .empty .empty)) (.node [8,7,6,6,4,3,3,2,2,2] (.node [8,7,6,6,4,3,3,2,2,1,1] .empty .empty) (.node [8,7,6,6,4,3,3,3,1,1,1] .empty .empty))) (.node [8,7,6,6,4,4,3,2,1,1,1] (.node [8,7,6,6,4,4,2,2,2,1,1] (.node [8,7,6,6,4,3,3,3,3] .empty .empty) (.node [8,7,6,6,4,4,2,2,2,2] .empty .empty)) (.node [8,7,6,6,4,4,3,3,1,1] (.node [8,7,6,6,4,4,3,2,2,1] .empty .empty) (.node [8,7,6,6,4,4,3,3,2] .empty .empty))))) + +def degreeTree43_36 : RowTree := (.node [8,7,6,6,5,4,3,2,2] (.node [8,7,6,6,5,3,3,2,1,1,1] (.node [8,7,6,6,4,4,4,4] (.node [8,7,6,6,4,4,4,2,2] (.node [8,7,6,6,4,4,4,2,1,1] .empty .empty) (.node [8,7,6,6,4,4,4,3,1] .empty .empty)) (.node [8,7,6,6,5,3,2,2,2,1,1] (.node [8,7,6,6,5,2,2,2,2,2,1] .empty .empty) (.node [8,7,6,6,5,3,2,2,2,2] .empty .empty))) (.node [8,7,6,6,5,4,2,2,1,1,1] (.node [8,7,6,6,5,3,3,3,1,1] (.node [8,7,6,6,5,3,3,2,2,1] .empty .empty) (.node [8,7,6,6,5,3,3,3,2] .empty .empty)) (.node [8,7,6,6,5,4,3,1,1,1,1] (.node [8,7,6,6,5,4,2,2,2,1] .empty .empty) (.node [8,7,6,6,5,4,3,2,1,1] .empty .empty)))) (.node [8,7,6,6,5,5,3,1,1,1] (.node [8,7,6,6,5,4,4,3] (.node [8,7,6,6,5,4,4,1,1,1] (.node [8,7,6,6,5,4,3,3,1] .empty .empty) (.node [8,7,6,6,5,4,4,2,1] .empty .empty)) (.node [8,7,6,6,5,5,2,2,1,1] (.node [8,7,6,6,5,5,2,1,1,1,1] .empty .empty) (.node [8,7,6,6,5,5,2,2,2] .empty .empty))) (.node [8,7,6,6,5,5,4,2] (.node [8,7,6,6,5,5,3,3] (.node [8,7,6,6,5,5,3,2,1] .empty .empty) (.node [8,7,6,6,5,5,4,1,1] .empty .empty)) (.node [8,7,6,6,6,1,1,1,1,1,1,1,1,1,1] (.node [8,7,6,6,5,5,5,1] .empty .empty) (.node [8,7,6,6,6,2,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_37 : RowTree := (.node [8,7,6,6,4,4,4,1,1,1,1] degreeTree43_35 degreeTree43_36) + +def degreeTree43_38 : RowTree := (.node [8,7,6,5,5,4,4,2,2] degreeTree43_34 degreeTree43_37) + +def degreeTree43_39 : RowTree := (.node [8,7,5,5,5,5,3,3,2] degreeTree43_29 degreeTree43_38) + +def degreeTree43_40 : RowTree := (.node [8,6,6,6,5,3,3,2,2,2] degreeTree43_20 degreeTree43_39) + +def degreeTree43_41 : RowTree := (.node [8,7,6,6,6,3,3,2,1,1] (.node [8,7,6,6,6,3,2,1,1,1,1,1] (.node [8,7,6,6,6,2,2,2,2,2] (.node [8,7,6,6,6,2,2,2,2,1,1] (.node [8,7,6,6,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [8,7,6,6,6,3,1,1,1,1,1,1,1] .empty .empty)) (.node [8,7,6,6,6,3,2,2,2,1] (.node [8,7,6,6,6,3,2,2,1,1,1] .empty .empty) (.node [8,7,6,6,6,3,3,1,1,1,1] .empty .empty))) (.node [8,7,6,6,6,4,2,1,1,1,1] (.node [8,7,6,6,6,3,3,3,1] (.node [8,7,6,6,6,3,3,2,2] .empty .empty) (.node [8,7,6,6,6,4,1,1,1,1,1,1] .empty .empty)) (.node [8,7,6,6,6,4,2,2,2] (.node [8,7,6,6,6,4,2,2,1,1] .empty .empty) (.node [8,7,6,6,6,4,3,1,1,1] .empty .empty)))) + +def degreeTree43_42 : RowTree := (.node [8,7,6,6,6,5,3,2] (.node [8,7,6,6,6,5,1,1,1,1,1] (.node [8,7,6,6,6,4,4,1,1] (.node [8,7,6,6,6,4,3,3] .empty .empty) (.node [8,7,6,6,6,4,4,2] .empty .empty)) (.node [8,7,6,6,6,5,2,2,1] (.node [8,7,6,6,6,5,2,1,1,1] .empty .empty) (.node [8,7,6,6,6,5,3,1,1] .empty .empty))) (.node [8,7,6,6,6,6,2,2] (.node [8,7,6,6,6,6,1,1,1,1] (.node [8,7,6,6,6,5,4,1] .empty .empty) (.node [8,7,6,6,6,6,2,1,1] .empty .empty)) (.node [8,7,7,3,3,3,3,3,2,2,2] (.node [8,7,6,6,6,6,3,1] .empty .empty) (.node [8,7,7,3,3,3,3,3,3,2,1] .empty .empty)))) + +def degreeTree43_43 : RowTree := (.node [8,7,6,6,6,4,3,2,1] degreeTree43_41 degreeTree43_42) + +def degreeTree43_44 : RowTree := (.node [8,7,7,4,4,4,4,2,1,1,1] (.node [8,7,7,4,4,3,3,3,2,2] (.node [8,7,7,4,3,3,3,3,3,2] (.node [8,7,7,4,3,3,3,3,2,2,1] (.node [8,7,7,4,3,3,3,2,2,2,2] .empty .empty) (.node [8,7,7,4,3,3,3,3,3,1,1] .empty .empty)) (.node [8,7,7,4,4,3,3,2,2,2,1] (.node [8,7,7,4,4,3,2,2,2,2,2] .empty .empty) (.node [8,7,7,4,4,3,3,3,2,1,1] .empty .empty))) (.node [8,7,7,4,4,4,3,2,2,2] (.node [8,7,7,4,4,4,2,2,2,2,1] (.node [8,7,7,4,4,3,3,3,3,1] .empty .empty) (.node [8,7,7,4,4,4,3,2,2,1,1] .empty .empty)) (.node [8,7,7,4,4,4,3,3,2,1] (.node [8,7,7,4,4,4,3,3,1,1,1] .empty .empty) (.node [8,7,7,4,4,4,3,3,3] .empty .empty)))) (.node [8,7,7,5,3,3,3,3,2,2] (.node [8,7,7,4,4,4,4,4,1] (.node [8,7,7,4,4,4,4,3,1,1] (.node [8,7,7,4,4,4,4,2,2,1] .empty .empty) (.node [8,7,7,4,4,4,4,3,2] .empty .empty)) (.node [8,7,7,5,3,3,3,2,2,2,1] (.node [8,7,7,5,3,3,2,2,2,2,2] .empty .empty) (.node [8,7,7,5,3,3,3,3,2,1,1] .empty .empty))) (.node [8,7,7,5,4,3,3,2,2,1,1] (.node [8,7,7,5,4,2,2,2,2,2,2] (.node [8,7,7,5,3,3,3,3,3,1] .empty .empty) (.node [8,7,7,5,4,3,2,2,2,2,1] .empty .empty)) (.node [8,7,7,5,4,3,3,3,1,1,1] (.node [8,7,7,5,4,3,3,2,2,2] .empty .empty) (.node [8,7,7,5,4,3,3,3,2,1] .empty .empty))))) + +def degreeTree43_45 : RowTree := (.node [8,7,7,3,3,3,3,3,3,3] degreeTree43_43 degreeTree43_44) + +def degreeTree43_46 : RowTree := (.node [8,7,7,5,5,3,3,2,2,1] (.node [8,7,7,5,4,4,4,2,1,1] (.node [8,7,7,5,4,4,3,2,2,1] (.node [8,7,7,5,4,4,2,2,2,2] (.node [8,7,7,5,4,4,2,2,2,1,1] .empty .empty) (.node [8,7,7,5,4,4,3,2,1,1,1] .empty .empty)) (.node [8,7,7,5,4,4,3,3,2] (.node [8,7,7,5,4,4,3,3,1,1] .empty .empty) (.node [8,7,7,5,4,4,4,1,1,1,1] .empty .empty))) (.node [8,7,7,5,5,2,2,2,2,2,1] (.node [8,7,7,5,4,4,4,3,1] (.node [8,7,7,5,4,4,4,2,2] .empty .empty) (.node [8,7,7,5,4,4,4,4] .empty .empty)) (.node [8,7,7,5,5,3,2,2,2,2] (.node [8,7,7,5,5,3,2,2,2,1,1] .empty .empty) (.node [8,7,7,5,5,3,3,2,1,1,1] .empty .empty)))) (.node [8,7,7,5,5,4,3,3,1] (.node [8,7,7,5,5,4,2,2,2,1] (.node [8,7,7,5,5,3,3,3,2] (.node [8,7,7,5,5,3,3,3,1,1] .empty .empty) (.node [8,7,7,5,5,4,2,2,1,1,1] .empty .empty)) (.node [8,7,7,5,5,4,3,2,1,1] (.node [8,7,7,5,5,4,3,1,1,1,1] .empty .empty) (.node [8,7,7,5,5,4,3,2,2] .empty .empty))) (.node [8,7,7,5,5,5,2,1,1,1,1] (.node [8,7,7,5,5,4,4,2,1] (.node [8,7,7,5,5,4,4,1,1,1] .empty .empty) (.node [8,7,7,5,5,4,4,3] .empty .empty)) (.node [8,7,7,5,5,5,2,2,2] (.node [8,7,7,5,5,5,2,2,1,1] .empty .empty) (.node [8,7,7,5,5,5,3,1,1,1] .empty .empty))))) + +def degreeTree43_47 : RowTree := (.node [8,7,7,6,3,2,2,2,1,1,1,1,1,1] (.node [8,7,7,6,2,2,2,1,1,1,1,1,1,1,1,1] (.node [8,7,7,5,5,5,5,1] (.node [8,7,7,5,5,5,4,1,1] (.node [8,7,7,5,5,5,3,3] .empty .empty) (.node [8,7,7,5,5,5,4,2] .empty .empty)) (.node [8,7,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,7,7,6,2,2,2,2,2,2,2,1] (.node [8,7,7,6,2,2,2,2,2,1,1,1,1,1] (.node [8,7,7,6,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [8,7,7,6,3,2,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,6,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,3,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,7,7,6,3,3,2,2,2,2,1] (.node [8,7,7,6,3,3,1,1,1,1,1,1,1,1,1] (.node [8,7,7,6,3,2,2,2,2,2,1,1] (.node [8,7,7,6,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [8,7,7,6,3,2,2,2,2,2,2] .empty .empty)) (.node [8,7,7,6,3,3,2,2,1,1,1,1,1] (.node [8,7,7,6,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,3,3,2,2,2,1,1,1] .empty .empty))) (.node [8,7,7,6,3,3,3,2,2,2] (.node [8,7,7,6,3,3,3,2,1,1,1,1] (.node [8,7,7,6,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,3,3,3,2,2,1,1] .empty .empty)) (.node [8,7,7,6,3,3,3,3,2,1] (.node [8,7,7,6,3,3,3,3,1,1,1] .empty .empty) (.node [8,7,7,6,3,3,3,3,3] .empty .empty))))) + +def degreeTree43_48 : RowTree := (.node [8,7,7,5,5,5,3,2,1] degreeTree43_46 degreeTree43_47) + +def degreeTree43_49 : RowTree := (.node [8,7,7,5,4,3,3,3,3] degreeTree43_45 degreeTree43_48) + +def degreeTree43_50 : RowTree := (.node [8,7,7,6,4,3,2,2,2,1,1] (.node [8,7,7,6,4,2,2,2,2,2,1] (.node [8,7,7,6,4,2,2,2,1,1,1,1,1] (.node [8,7,7,6,4,2,2,1,1,1,1,1,1,1] (.node [8,7,7,6,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,7,7,6,4,2,2,2,2,1,1,1] .empty .empty)) (.node [8,7,7,6,4,3,2,1,1,1,1,1,1] (.node [8,7,7,6,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,4,3,2,2,1,1,1,1] .empty .empty))) (.node [8,7,7,6,4,3,3,2,2,1] (.node [8,7,7,6,4,3,3,1,1,1,1,1] (.node [8,7,7,6,4,3,2,2,2,2] .empty .empty) (.node [8,7,7,6,4,3,3,2,1,1,1] .empty .empty)) (.node [8,7,7,6,4,3,3,3,2] (.node [8,7,7,6,4,3,3,3,1,1] .empty .empty) (.node [8,7,7,6,4,4,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_51 : RowTree := (.node [8,7,7,6,4,4,4,2,1] (.node [8,7,7,6,4,4,3,2,1,1] (.node [8,7,7,6,4,4,2,2,2,1] (.node [8,7,7,6,4,4,2,2,1,1,1] .empty .empty) (.node [8,7,7,6,4,4,3,1,1,1,1] .empty .empty)) (.node [8,7,7,6,4,4,3,3,1] (.node [8,7,7,6,4,4,3,2,2] .empty .empty) (.node [8,7,7,6,4,4,4,1,1,1] .empty .empty))) (.node [8,7,7,6,5,2,2,1,1,1,1,1,1] (.node [8,7,7,6,5,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,6,4,4,4,3] .empty .empty) (.node [8,7,7,6,5,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,7,7,6,5,2,2,2,2,1,1] (.node [8,7,7,6,5,2,2,2,1,1,1,1] .empty .empty) (.node [8,7,7,6,5,2,2,2,2,2] .empty .empty)))) + +def degreeTree43_52 : RowTree := (.node [8,7,7,6,4,4,2,1,1,1,1,1] degreeTree43_50 degreeTree43_51) + +def degreeTree43_53 : RowTree := (.node [8,7,7,6,5,4,4,2] (.node [8,7,7,6,5,4,1,1,1,1,1,1] (.node [8,7,7,6,5,3,3,1,1,1,1] (.node [8,7,7,6,5,3,2,2,1,1,1] (.node [8,7,7,6,5,3,2,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,5,3,2,2,2,1] .empty .empty)) (.node [8,7,7,6,5,3,3,2,2] (.node [8,7,7,6,5,3,3,2,1,1] .empty .empty) (.node [8,7,7,6,5,3,3,3,1] .empty .empty))) (.node [8,7,7,6,5,4,3,1,1,1] (.node [8,7,7,6,5,4,2,2,1,1] (.node [8,7,7,6,5,4,2,1,1,1,1] .empty .empty) (.node [8,7,7,6,5,4,2,2,2] .empty .empty)) (.node [8,7,7,6,5,4,3,3] (.node [8,7,7,6,5,4,3,2,1] .empty .empty) (.node [8,7,7,6,5,4,4,1,1] .empty .empty)))) (.node [8,7,7,6,6,2,1,1,1,1,1,1,1] (.node [8,7,7,6,5,5,3,1,1] (.node [8,7,7,6,5,5,2,1,1,1] (.node [8,7,7,6,5,5,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,5,5,2,2,1] .empty .empty)) (.node [8,7,7,6,5,5,4,1] (.node [8,7,7,6,5,5,3,2] .empty .empty) (.node [8,7,7,6,6,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,7,7,6,6,3,1,1,1,1,1,1] (.node [8,7,7,6,6,2,2,2,1,1,1] (.node [8,7,7,6,6,2,2,1,1,1,1,1] .empty .empty) (.node [8,7,7,6,6,2,2,2,2,1] .empty .empty)) (.node [8,7,7,6,6,3,2,2,1,1] (.node [8,7,7,6,6,3,2,1,1,1,1] .empty .empty) (.node [8,7,7,6,6,3,2,2,2] .empty .empty))))) + +def degreeTree43_54 : RowTree := (.node [8,7,7,6,5,3,1,1,1,1,1,1,1] degreeTree43_52 degreeTree43_53) + +def degreeTree43_55 : RowTree := (.node [8,7,7,7,2,2,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,6,6,4,4,1] (.node [8,7,7,6,6,4,2,1,1,1] (.node [8,7,7,6,6,3,3,3] (.node [8,7,7,6,6,3,3,2,1] .empty .empty) (.node [8,7,7,6,6,4,1,1,1,1,1] .empty .empty)) (.node [8,7,7,6,6,4,3,1,1] (.node [8,7,7,6,6,4,2,2,1] .empty .empty) (.node [8,7,7,6,6,4,3,2] .empty .empty))) (.node [8,7,7,6,6,5,3,1] (.node [8,7,7,6,6,5,2,1,1] (.node [8,7,7,6,6,5,1,1,1,1] .empty .empty) (.node [8,7,7,6,6,5,2,2] .empty .empty)) (.node [8,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,6,6,6,1,1,1] .empty .empty) (.node [8,7,7,7,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,7,7,7,3,2,2,1,1,1,1,1,1,1] (.node [8,7,7,7,2,2,2,2,2,2,1,1] (.node [8,7,7,7,2,2,2,2,1,1,1,1,1,1] (.node [8,7,7,7,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [8,7,7,7,3,1,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,7,2,2,2,2,2,2,2] .empty .empty) (.node [8,7,7,7,3,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,7,7,7,3,3,1,1,1,1,1,1,1,1] (.node [8,7,7,7,3,2,2,2,2,1,1,1] (.node [8,7,7,7,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,3,2,2,2,2,2,1] .empty .empty)) (.node [8,7,7,7,3,3,2,2,1,1,1,1] (.node [8,7,7,7,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,3,3,2,2,2,1,1] .empty .empty))))) + +def degreeTree43_56 : RowTree := (.node [8,7,7,7,4,3,3,1,1,1,1] (.node [8,7,7,7,4,2,2,1,1,1,1,1,1] (.node [8,7,7,7,3,3,3,3,1,1] (.node [8,7,7,7,3,3,3,2,1,1,1] (.node [8,7,7,7,3,3,3,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,3,3,3,2,2,1] .empty .empty)) (.node [8,7,7,7,4,1,1,1,1,1,1,1,1,1,1] (.node [8,7,7,7,3,3,3,3,2] .empty .empty) (.node [8,7,7,7,4,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,7,7,7,4,3,1,1,1,1,1,1,1] (.node [8,7,7,7,4,2,2,2,2,1,1] (.node [8,7,7,7,4,2,2,2,1,1,1,1] .empty .empty) (.node [8,7,7,7,4,2,2,2,2,2] .empty .empty)) (.node [8,7,7,7,4,3,2,2,1,1,1] (.node [8,7,7,7,4,3,2,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,4,3,2,2,2,1] .empty .empty)))) (.node [8,7,7,7,4,4,3,1,1,1] (.node [8,7,7,7,4,4,1,1,1,1,1,1] (.node [8,7,7,7,4,3,3,2,2] (.node [8,7,7,7,4,3,3,2,1,1] .empty .empty) (.node [8,7,7,7,4,3,3,3,1] .empty .empty)) (.node [8,7,7,7,4,4,2,2,1,1] (.node [8,7,7,7,4,4,2,1,1,1,1] .empty .empty) (.node [8,7,7,7,4,4,2,2,2] .empty .empty))) (.node [8,7,7,7,4,4,4,2] (.node [8,7,7,7,4,4,3,3] (.node [8,7,7,7,4,4,3,2,1] .empty .empty) (.node [8,7,7,7,4,4,4,1,1] .empty .empty)) (.node [8,7,7,7,5,2,1,1,1,1,1,1,1] (.node [8,7,7,7,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,5,2,2,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_57 : RowTree := (.node [8,7,7,7,3,3,2,2,2,2] degreeTree43_55 degreeTree43_56) + +def degreeTree43_58 : RowTree := (.node [8,7,7,6,6,3,3,1,1,1] degreeTree43_54 degreeTree43_57) + +def degreeTree43_59 : RowTree := (.node [8,7,7,6,4,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_49 degreeTree43_58) + +def degreeTree43_60 : RowTree := (.node [8,7,7,7,5,4,1,1,1,1,1] (.node [8,7,7,7,5,3,2,2,2] (.node [8,7,7,7,5,3,2,1,1,1,1] (.node [8,7,7,7,5,3,1,1,1,1,1,1] (.node [8,7,7,7,5,2,2,2,2,1] .empty .empty) .empty) (.node [8,7,7,7,5,3,2,2,1,1] .empty .empty)) (.node [8,7,7,7,5,3,3,2,1] (.node [8,7,7,7,5,3,3,1,1,1] .empty .empty) (.node [8,7,7,7,5,3,3,3] .empty .empty))) (.node [8,7,7,7,5,4,3,2] (.node [8,7,7,7,5,4,2,2,1] (.node [8,7,7,7,5,4,2,1,1,1] .empty .empty) (.node [8,7,7,7,5,4,3,1,1] .empty .empty)) (.node [8,7,7,7,5,5,1,1,1,1] (.node [8,7,7,7,5,4,4,1] .empty .empty) (.node [8,7,7,7,5,5,2,1,1] .empty .empty)))) + +def degreeTree43_61 : RowTree := (.node [8,7,7,7,6,3,2,2,1] (.node [8,7,7,7,6,2,2,2,1,1] (.node [8,7,7,7,6,2,1,1,1,1,1,1] (.node [8,7,7,7,6,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,7,7,7,6,2,2,1,1,1,1] .empty .empty)) (.node [8,7,7,7,6,3,1,1,1,1,1] (.node [8,7,7,7,6,2,2,2,2] .empty .empty) (.node [8,7,7,7,6,3,2,1,1,1] .empty .empty))) (.node [8,7,7,7,6,4,2,1,1] (.node [8,7,7,7,6,3,3,2] (.node [8,7,7,7,6,3,3,1,1] .empty .empty) (.node [8,7,7,7,6,4,1,1,1,1] .empty .empty)) (.node [8,7,7,7,6,5,1,1,1] (.node [8,7,7,7,6,4,2,2] .empty .empty) (.node [8,7,7,7,7,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_62 : RowTree := (.node [8,7,7,7,5,5,2,2] degreeTree43_60 degreeTree43_61) + +def degreeTree43_63 : RowTree := (.node [8,8,4,4,4,4,3,3,3,1,1] (.node [8,8,4,3,3,3,3,3,3,3,2] (.node [8,7,7,7,7,3,2,1,1] (.node [8,7,7,7,7,2,2,2,1] (.node [8,7,7,7,7,2,2,1,1,1] .empty .empty) (.node [8,7,7,7,7,3,1,1,1,1] .empty .empty)) (.node [8,7,7,7,7,4,1,1,1] (.node [8,7,7,7,7,3,2,2] .empty .empty) (.node [8,8,3,3,3,3,3,3,3,3,3] .empty .empty))) (.node [8,8,4,4,4,3,3,3,3,2,1] (.node [8,8,4,4,3,3,3,3,3,3,1] (.node [8,8,4,4,3,3,3,3,3,2,2] .empty .empty) (.node [8,8,4,4,4,3,3,3,2,2,2] .empty .empty)) (.node [8,8,4,4,4,4,3,2,2,2,2] (.node [8,8,4,4,4,3,3,3,3,3] .empty .empty) (.node [8,8,4,4,4,4,3,3,2,2,1] .empty .empty)))) (.node [8,8,4,4,4,4,4,4,3] (.node [8,8,4,4,4,4,4,3,2,2] (.node [8,8,4,4,4,4,4,2,2,2,1] (.node [8,8,4,4,4,4,3,3,3,2] .empty .empty) (.node [8,8,4,4,4,4,4,3,2,1,1] .empty .empty)) (.node [8,8,4,4,4,4,4,4,1,1,1] (.node [8,8,4,4,4,4,4,3,3,1] .empty .empty) (.node [8,8,4,4,4,4,4,4,2,1] .empty .empty))) (.node [8,8,5,4,3,3,3,3,3,2,1] (.node [8,8,5,3,3,3,3,3,3,3,1] (.node [8,8,5,3,3,3,3,3,3,2,2] .empty .empty) (.node [8,8,5,4,3,3,3,3,2,2,2] .empty .empty)) (.node [8,8,5,4,4,3,3,2,2,2,2] (.node [8,8,5,4,3,3,3,3,3,3] .empty .empty) (.node [8,8,5,4,4,3,3,3,2,2,1] .empty .empty))))) + +def degreeTree43_64 : RowTree := (.node [8,7,7,7,7,2,1,1,1,1,1] degreeTree43_62 degreeTree43_63) + +def degreeTree43_65 : RowTree := (.node [8,8,5,5,3,3,3,3,3,1,1] (.node [8,8,5,4,4,4,4,2,2,2] (.node [8,8,5,4,4,4,3,3,2,1,1] (.node [8,8,5,4,4,4,2,2,2,2,2] (.node [8,8,5,4,4,3,3,3,3,2] .empty .empty) (.node [8,8,5,4,4,4,3,2,2,2,1] .empty .empty)) (.node [8,8,5,4,4,4,3,3,3,1] (.node [8,8,5,4,4,4,3,3,2,2] .empty .empty) (.node [8,8,5,4,4,4,4,2,2,1,1] .empty .empty))) (.node [8,8,5,4,4,4,4,4,1,1] (.node [8,8,5,4,4,4,4,3,2,1] (.node [8,8,5,4,4,4,4,3,1,1,1] .empty .empty) (.node [8,8,5,4,4,4,4,3,3] .empty .empty)) (.node [8,8,5,5,3,3,3,2,2,2,2] (.node [8,8,5,4,4,4,4,4,2] .empty .empty) (.node [8,8,5,5,3,3,3,3,2,2,1] .empty .empty)))) (.node [8,8,5,5,4,4,3,2,2,1,1] (.node [8,8,5,5,4,3,3,3,2,1,1] (.node [8,8,5,5,4,3,2,2,2,2,2] (.node [8,8,5,5,3,3,3,3,3,2] .empty .empty) (.node [8,8,5,5,4,3,3,2,2,2,1] .empty .empty)) (.node [8,8,5,5,4,3,3,3,3,1] (.node [8,8,5,5,4,3,3,3,2,2] .empty .empty) (.node [8,8,5,5,4,4,2,2,2,2,1] .empty .empty))) (.node [8,8,5,5,4,4,3,3,3] (.node [8,8,5,5,4,4,3,3,1,1,1] (.node [8,8,5,5,4,4,3,2,2,2] .empty .empty) (.node [8,8,5,5,4,4,3,3,2,1] .empty .empty)) (.node [8,8,5,5,4,4,4,2,2,1] (.node [8,8,5,5,4,4,4,2,1,1,1] .empty .empty) (.node [8,8,5,5,4,4,4,3,1,1] .empty .empty))))) + +def degreeTree43_66 : RowTree := (.node [8,8,5,5,5,4,4,2,1,1] (.node [8,8,5,5,5,3,3,3,3] (.node [8,8,5,5,5,3,3,2,2,1,1] (.node [8,8,5,5,5,2,2,2,2,2,2] (.node [8,8,5,5,4,4,4,4,1] .empty .empty) (.node [8,8,5,5,5,3,2,2,2,2,1] .empty .empty)) (.node [8,8,5,5,5,3,3,3,1,1,1] (.node [8,8,5,5,5,3,3,2,2,2] .empty .empty) (.node [8,8,5,5,5,3,3,3,2,1] .empty .empty))) (.node [8,8,5,5,5,4,3,2,2,1] (.node [8,8,5,5,5,4,2,2,2,2] (.node [8,8,5,5,5,4,2,2,2,1,1] .empty .empty) (.node [8,8,5,5,5,4,3,2,1,1,1] .empty .empty)) (.node [8,8,5,5,5,4,3,3,2] (.node [8,8,5,5,5,4,3,3,1,1] .empty .empty) (.node [8,8,5,5,5,4,4,1,1,1,1] .empty .empty)))) (.node [8,8,5,5,5,5,3,2,2] (.node [8,8,5,5,5,5,2,2,1,1,1] (.node [8,8,5,5,5,4,4,3,1] (.node [8,8,5,5,5,4,4,2,2] .empty .empty) (.node [8,8,5,5,5,4,4,4] .empty .empty)) (.node [8,8,5,5,5,5,3,1,1,1,1] (.node [8,8,5,5,5,5,2,2,2,1] .empty .empty) (.node [8,8,5,5,5,5,3,2,1,1] .empty .empty))) (.node [8,8,5,5,5,5,4,3] (.node [8,8,5,5,5,5,4,1,1,1] (.node [8,8,5,5,5,5,3,3,1] .empty .empty) (.node [8,8,5,5,5,5,4,2,1] .empty .empty)) (.node [8,8,5,5,5,5,5,2] (.node [8,8,5,5,5,5,5,1,1] .empty .empty) (.node [8,8,6,3,3,3,3,3,2,2,2] .empty .empty))))) + +def degreeTree43_67 : RowTree := (.node [8,8,5,5,4,4,4,3,2] degreeTree43_65 degreeTree43_66) + +def degreeTree43_68 : RowTree := (.node [8,8,5,4,4,3,3,3,3,1,1] degreeTree43_64 degreeTree43_67) + +def degreeTree43_69 : RowTree := (.node [8,8,6,4,4,3,3,3,2,2] (.node [8,8,6,4,3,3,3,3,3,2] (.node [8,8,6,4,3,3,3,3,2,2,1] (.node [8,8,6,4,3,3,3,2,2,2,2] (.node [8,8,6,3,3,3,3,3,3,3] .empty .empty) .empty) (.node [8,8,6,4,3,3,3,3,3,1,1] .empty .empty)) (.node [8,8,6,4,4,3,3,2,2,2,1] (.node [8,8,6,4,4,3,2,2,2,2,2] .empty .empty) (.node [8,8,6,4,4,3,3,3,2,1,1] .empty .empty))) (.node [8,8,6,4,4,4,3,2,2,2] (.node [8,8,6,4,4,4,2,2,2,2,1] (.node [8,8,6,4,4,3,3,3,3,1] .empty .empty) (.node [8,8,6,4,4,4,3,2,2,1,1] .empty .empty)) (.node [8,8,6,4,4,4,3,3,2,1] (.node [8,8,6,4,4,4,3,3,1,1,1] .empty .empty) (.node [8,8,6,4,4,4,3,3,3] .empty .empty)))) + +def degreeTree43_70 : RowTree := (.node [8,8,6,5,3,3,3,3,2,2] (.node [8,8,6,4,4,4,4,4,1] (.node [8,8,6,4,4,4,4,3,1,1] (.node [8,8,6,4,4,4,4,2,2,1] .empty .empty) (.node [8,8,6,4,4,4,4,3,2] .empty .empty)) (.node [8,8,6,5,3,3,3,2,2,2,1] (.node [8,8,6,5,3,3,2,2,2,2,2] .empty .empty) (.node [8,8,6,5,3,3,3,3,2,1,1] .empty .empty))) (.node [8,8,6,5,4,3,3,2,2,1,1] (.node [8,8,6,5,4,2,2,2,2,2,2] (.node [8,8,6,5,3,3,3,3,3,1] .empty .empty) (.node [8,8,6,5,4,3,2,2,2,2,1] .empty .empty)) (.node [8,8,6,5,4,3,3,3,1,1,1] (.node [8,8,6,5,4,3,3,2,2,2] .empty .empty) (.node [8,8,6,5,4,3,3,3,2,1] .empty .empty)))) + +def degreeTree43_71 : RowTree := (.node [8,8,6,4,4,4,4,2,1,1,1] degreeTree43_69 degreeTree43_70) + +def degreeTree43_72 : RowTree := (.node [8,8,6,5,5,3,3,2,2,1] (.node [8,8,6,5,4,4,4,2,1,1] (.node [8,8,6,5,4,4,3,2,2,1] (.node [8,8,6,5,4,4,2,2,2,2] (.node [8,8,6,5,4,4,2,2,2,1,1] .empty .empty) (.node [8,8,6,5,4,4,3,2,1,1,1] .empty .empty)) (.node [8,8,6,5,4,4,3,3,2] (.node [8,8,6,5,4,4,3,3,1,1] .empty .empty) (.node [8,8,6,5,4,4,4,1,1,1,1] .empty .empty))) (.node [8,8,6,5,5,2,2,2,2,2,1] (.node [8,8,6,5,4,4,4,3,1] (.node [8,8,6,5,4,4,4,2,2] .empty .empty) (.node [8,8,6,5,4,4,4,4] .empty .empty)) (.node [8,8,6,5,5,3,2,2,2,2] (.node [8,8,6,5,5,3,2,2,2,1,1] .empty .empty) (.node [8,8,6,5,5,3,3,2,1,1,1] .empty .empty)))) (.node [8,8,6,5,5,4,3,3,1] (.node [8,8,6,5,5,4,2,2,2,1] (.node [8,8,6,5,5,3,3,3,2] (.node [8,8,6,5,5,3,3,3,1,1] .empty .empty) (.node [8,8,6,5,5,4,2,2,1,1,1] .empty .empty)) (.node [8,8,6,5,5,4,3,2,1,1] (.node [8,8,6,5,5,4,3,1,1,1,1] .empty .empty) (.node [8,8,6,5,5,4,3,2,2] .empty .empty))) (.node [8,8,6,5,5,5,2,1,1,1,1] (.node [8,8,6,5,5,4,4,2,1] (.node [8,8,6,5,5,4,4,1,1,1] .empty .empty) (.node [8,8,6,5,5,4,4,3] .empty .empty)) (.node [8,8,6,5,5,5,2,2,2] (.node [8,8,6,5,5,5,2,2,1,1] .empty .empty) (.node [8,8,6,5,5,5,3,1,1,1] .empty .empty))))) + +def degreeTree43_73 : RowTree := (.node [8,8,6,5,4,3,3,3,3] degreeTree43_71 degreeTree43_72) + +def degreeTree43_74 : RowTree := (.node [8,8,6,6,3,2,2,2,2,1,1,1,1] (.node [8,8,6,6,2,2,2,2,1,1,1,1,1,1,1] (.node [8,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,6,5,5,5,4,1,1] (.node [8,8,6,5,5,5,3,3] .empty .empty) (.node [8,8,6,5,5,5,4,2] .empty .empty)) (.node [8,8,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,6,6,2,2,2,2,2,2,1,1,1] (.node [8,8,6,6,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,2,2,2,2,2,2,2,1] .empty .empty)) (.node [8,8,6,6,3,2,2,1,1,1,1,1,1,1,1] (.node [8,8,6,6,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,3,2,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,6,6,3,3,3,1,1,1,1,1,1] (.node [8,8,6,6,3,3,2,1,1,1,1,1,1,1] (.node [8,8,6,6,3,2,2,2,2,2,2] (.node [8,8,6,6,3,2,2,2,2,2,1,1] .empty .empty) (.node [8,8,6,6,3,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,6,6,3,3,2,2,2,1,1,1] (.node [8,8,6,6,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,3,3,2,2,2,2,1] .empty .empty))) (.node [8,8,6,6,3,3,3,3,1,1,1] (.node [8,8,6,6,3,3,3,2,2,1,1] (.node [8,8,6,6,3,3,3,2,1,1,1,1] .empty .empty) (.node [8,8,6,6,3,3,3,2,2,2] .empty .empty)) (.node [8,8,6,6,3,3,3,3,3] (.node [8,8,6,6,3,3,3,3,2,1] .empty .empty) (.node [8,8,6,6,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_75 : RowTree := (.node [8,8,6,6,4,4,2,1,1,1,1,1] (.node [8,8,6,6,4,3,2,2,2,1,1] (.node [8,8,6,6,4,2,2,2,2,2,1] (.node [8,8,6,6,4,2,2,2,1,1,1,1,1] (.node [8,8,6,6,4,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,4,2,2,2,2,1,1,1] .empty .empty)) (.node [8,8,6,6,4,3,2,1,1,1,1,1,1] (.node [8,8,6,6,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,4,3,2,2,1,1,1,1] .empty .empty))) (.node [8,8,6,6,4,3,3,2,2,1] (.node [8,8,6,6,4,3,3,1,1,1,1,1] (.node [8,8,6,6,4,3,2,2,2,2] .empty .empty) (.node [8,8,6,6,4,3,3,2,1,1,1] .empty .empty)) (.node [8,8,6,6,4,3,3,3,2] (.node [8,8,6,6,4,3,3,3,1,1] .empty .empty) (.node [8,8,6,6,4,4,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,6,6,4,4,4,2,1] (.node [8,8,6,6,4,4,3,2,1,1] (.node [8,8,6,6,4,4,2,2,2,1] (.node [8,8,6,6,4,4,2,2,1,1,1] .empty .empty) (.node [8,8,6,6,4,4,3,1,1,1,1] .empty .empty)) (.node [8,8,6,6,4,4,3,3,1] (.node [8,8,6,6,4,4,3,2,2] .empty .empty) (.node [8,8,6,6,4,4,4,1,1,1] .empty .empty))) (.node [8,8,6,6,5,2,2,1,1,1,1,1,1] (.node [8,8,6,6,5,1,1,1,1,1,1,1,1,1,1] (.node [8,8,6,6,4,4,4,3] .empty .empty) (.node [8,8,6,6,5,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,6,6,5,2,2,2,2,1,1] (.node [8,8,6,6,5,2,2,2,1,1,1,1] .empty .empty) (.node [8,8,6,6,5,2,2,2,2,2] .empty .empty))))) + +def degreeTree43_76 : RowTree := (.node [8,8,6,6,4,2,1,1,1,1,1,1,1,1,1] degreeTree43_74 degreeTree43_75) + +def degreeTree43_77 : RowTree := (.node [8,8,6,5,5,5,3,2,1] degreeTree43_73 degreeTree43_76) + +def degreeTree43_78 : RowTree := (.node [8,8,6,3,3,3,3,3,3,2,1] degreeTree43_68 degreeTree43_77) + +def degreeTree43_79 : RowTree := (.node [8,7,7,7,5,2,2,2,1,1,1] degreeTree43_59 degreeTree43_78) + +def degreeTree43_80 : RowTree := (.node [8,7,6,6,6,2,2,1,1,1,1,1,1] degreeTree43_40 degreeTree43_79) + +def degreeTree43_81 : RowTree := (.node [8,8,6,6,5,4,2,1,1,1,1] (.node [8,8,6,6,5,3,3,2,1,1] (.node [8,8,6,6,5,3,2,2,2,1] (.node [8,8,6,6,5,3,2,2,1,1,1] (.node [8,8,6,6,5,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [8,8,6,6,5,3,3,1,1,1,1] .empty .empty)) (.node [8,8,6,6,5,3,3,3,1] (.node [8,8,6,6,5,3,3,2,2] .empty .empty) (.node [8,8,6,6,5,4,1,1,1,1,1,1] .empty .empty))) (.node [8,8,6,6,5,4,3,2,1] (.node [8,8,6,6,5,4,2,2,2] (.node [8,8,6,6,5,4,2,2,1,1] .empty .empty) (.node [8,8,6,6,5,4,3,1,1,1] .empty .empty)) (.node [8,8,6,6,5,4,4,1,1] (.node [8,8,6,6,5,4,3,3] .empty .empty) (.node [8,8,6,6,5,4,4,2] .empty .empty)))) + +def degreeTree43_82 : RowTree := (.node [8,8,6,6,6,2,2,2,1,1,1] (.node [8,8,6,6,5,5,3,2] (.node [8,8,6,6,5,5,2,2,1] (.node [8,8,6,6,5,5,2,1,1,1] .empty .empty) (.node [8,8,6,6,5,5,3,1,1] .empty .empty)) (.node [8,8,6,6,6,2,1,1,1,1,1,1,1] (.node [8,8,6,6,6,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,6,2,2,1,1,1,1,1] .empty .empty))) (.node [8,8,6,6,6,3,2,2,1,1] (.node [8,8,6,6,6,3,1,1,1,1,1,1] (.node [8,8,6,6,6,2,2,2,2,1] .empty .empty) (.node [8,8,6,6,6,3,2,1,1,1,1] .empty .empty)) (.node [8,8,6,6,6,3,3,1,1,1] (.node [8,8,6,6,6,3,2,2,2] .empty .empty) (.node [8,8,6,6,6,3,3,2,1] .empty .empty)))) + +def degreeTree43_83 : RowTree := (.node [8,8,6,6,5,5,1,1,1,1,1] degreeTree43_81 degreeTree43_82) + +def degreeTree43_84 : RowTree := (.node [8,8,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [8,8,6,6,6,5,2,2] (.node [8,8,6,6,6,4,3,1,1] (.node [8,8,6,6,6,4,2,1,1,1] (.node [8,8,6,6,6,4,1,1,1,1,1] .empty .empty) (.node [8,8,6,6,6,4,2,2,1] .empty .empty)) (.node [8,8,6,6,6,5,1,1,1,1] (.node [8,8,6,6,6,4,3,2] .empty .empty) (.node [8,8,6,6,6,5,2,1,1] .empty .empty))) (.node [8,8,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,6,6,6,6,1,1,1] .empty .empty) (.node [8,8,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,2,2,2,2,2,2,2,2,2,2] (.node [8,8,7,2,2,2,2,2,2,2,2,1,1,1,1] (.node [8,8,7,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [8,8,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,3,2,2,2,2,2,2,2,1,1,1] (.node [8,8,7,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [8,8,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [8,8,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,3,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [8,8,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_85 : RowTree := (.node [8,8,6,6,6,3,3,3] degreeTree43_83 degreeTree43_84) + +def degreeTree43_86 : RowTree := (.node [8,8,7,3,3,3,2,2,2,1,1,1,1,1] (.node [8,8,7,3,3,2,2,2,2,2,2,2] (.node [8,8,7,3,3,2,2,2,2,2,1,1,1,1] (.node [8,8,7,3,3,2,2,2,2,1,1,1,1,1,1] (.node [8,8,7,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [8,8,7,3,3,2,2,2,2,2,2,1,1] .empty .empty)) (.node [8,8,7,3,3,3,2,1,1,1,1,1,1,1,1,1] (.node [8,8,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,3,3,3,3,2,1,1,1,1,1,1] (.node [8,8,7,3,3,3,2,2,2,2,2,1] (.node [8,8,7,3,3,3,2,2,2,2,1,1,1] .empty .empty) (.node [8,8,7,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,3,3,3,3,2,2,2,1,1] (.node [8,8,7,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [8,8,7,3,3,3,3,2,2,2,2] .empty .empty)))) + +def degreeTree43_87 : RowTree := (.node [8,8,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,3,3,3,3,3,3,2] (.node [8,8,7,3,3,3,3,3,2,2,1] (.node [8,8,7,3,3,3,3,3,2,1,1,1] .empty .empty) (.node [8,8,7,3,3,3,3,3,3,1,1] .empty .empty)) (.node [8,8,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,4,2,2,2,2,2,2,2,1,1] (.node [8,8,7,4,2,2,2,2,2,1,1,1,1,1,1] (.node [8,8,7,4,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,4,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [8,8,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,4,2,2,2,2,2,2,2,2] .empty .empty) (.node [8,8,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_88 : RowTree := (.node [8,8,7,3,3,3,3,3,1,1,1,1,1] degreeTree43_86 degreeTree43_87) + +def degreeTree43_89 : RowTree := (.node [8,8,7,4,3,3,3,3,2,1,1] (.node [8,8,7,4,3,3,2,2,2,1,1,1,1] (.node [8,8,7,4,3,2,2,2,2,2,2,1] (.node [8,8,7,4,3,2,2,2,2,1,1,1,1,1] (.node [8,8,7,4,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,4,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [8,8,7,4,3,3,2,1,1,1,1,1,1,1,1] (.node [8,8,7,4,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,4,3,3,2,2,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,4,3,3,3,2,1,1,1,1,1] (.node [8,8,7,4,3,3,2,2,2,2,2] (.node [8,8,7,4,3,3,2,2,2,2,1,1] .empty .empty) (.node [8,8,7,4,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,4,3,3,3,2,2,2,1] (.node [8,8,7,4,3,3,3,2,2,1,1,1] .empty .empty) (.node [8,8,7,4,3,3,3,3,1,1,1,1] .empty .empty)))) (.node [8,8,7,4,4,2,2,2,2,2,1,1] (.node [8,8,7,4,4,2,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,4,3,3,3,3,3,1] (.node [8,8,7,4,3,3,3,3,2,2] .empty .empty) (.node [8,8,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,4,4,2,2,2,1,1,1,1,1,1] (.node [8,8,7,4,4,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,4,4,2,2,2,2,1,1,1,1] .empty .empty))) (.node [8,8,7,4,4,3,2,2,1,1,1,1,1] (.node [8,8,7,4,4,3,1,1,1,1,1,1,1,1,1] (.node [8,8,7,4,4,2,2,2,2,2,2] .empty .empty) (.node [8,8,7,4,4,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,4,4,3,2,2,2,2,1] (.node [8,8,7,4,4,3,2,2,2,1,1,1] .empty .empty) (.node [8,8,7,4,4,3,3,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_90 : RowTree := (.node [8,8,7,4,3,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_88 degreeTree43_89) + +def degreeTree43_91 : RowTree := (.node [8,8,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_85 degreeTree43_90) + +def degreeTree43_92 : RowTree := (.node [8,8,7,4,4,4,2,2,2,1,1] (.node [8,8,7,4,4,3,3,3,3] (.node [8,8,7,4,4,3,3,3,1,1,1] (.node [8,8,7,4,4,3,3,2,2,2] (.node [8,8,7,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [8,8,7,4,4,3,3,3,2,1] .empty .empty)) (.node [8,8,7,4,4,4,2,1,1,1,1,1,1] (.node [8,8,7,4,4,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,4,4,4,2,2,1,1,1,1] .empty .empty))) (.node [8,8,7,4,4,4,3,2,2,1] (.node [8,8,7,4,4,4,3,1,1,1,1,1] (.node [8,8,7,4,4,4,2,2,2,2] .empty .empty) (.node [8,8,7,4,4,4,3,2,1,1,1] .empty .empty)) (.node [8,8,7,4,4,4,3,3,2] (.node [8,8,7,4,4,4,3,3,1,1] .empty .empty) (.node [8,8,7,4,4,4,4,1,1,1,1] .empty .empty)))) + +def degreeTree43_93 : RowTree := (.node [8,8,7,5,2,2,2,2,1,1,1,1,1,1,1] (.node [8,8,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,4,4,4,4,3,1] (.node [8,8,7,4,4,4,4,2,2] .empty .empty) (.node [8,8,7,4,4,4,4,4] .empty .empty)) (.node [8,8,7,5,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,5,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,5,2,2,2,2,2,2,1,1,1] (.node [8,8,7,5,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,2,2,2,2,2,2,2,1] .empty .empty)) (.node [8,8,7,5,3,2,2,1,1,1,1,1,1,1,1] (.node [8,8,7,5,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,3,2,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_94 : RowTree := (.node [8,8,7,4,4,4,4,2,1,1] degreeTree43_92 degreeTree43_93) + +def degreeTree43_95 : RowTree := (.node [8,8,7,5,4,2,1,1,1,1,1,1,1,1,1] (.node [8,8,7,5,3,3,3,1,1,1,1,1,1] (.node [8,8,7,5,3,3,2,1,1,1,1,1,1,1] (.node [8,8,7,5,3,2,2,2,2,2,2] (.node [8,8,7,5,3,2,2,2,2,2,1,1] .empty .empty) (.node [8,8,7,5,3,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,5,3,3,2,2,2,1,1,1] (.node [8,8,7,5,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,3,3,2,2,2,2,1] .empty .empty))) (.node [8,8,7,5,3,3,3,3,1,1,1] (.node [8,8,7,5,3,3,3,2,2,1,1] (.node [8,8,7,5,3,3,3,2,1,1,1,1] .empty .empty) (.node [8,8,7,5,3,3,3,2,2,2] .empty .empty)) (.node [8,8,7,5,3,3,3,3,3] (.node [8,8,7,5,3,3,3,3,2,1] .empty .empty) (.node [8,8,7,5,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,7,5,4,3,2,2,2,1,1] (.node [8,8,7,5,4,2,2,2,2,2,1] (.node [8,8,7,5,4,2,2,2,1,1,1,1,1] (.node [8,8,7,5,4,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,4,2,2,2,2,1,1,1] .empty .empty)) (.node [8,8,7,5,4,3,2,1,1,1,1,1,1] (.node [8,8,7,5,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,4,3,2,2,1,1,1,1] .empty .empty))) (.node [8,8,7,5,4,3,3,2,2,1] (.node [8,8,7,5,4,3,3,1,1,1,1,1] (.node [8,8,7,5,4,3,2,2,2,2] .empty .empty) (.node [8,8,7,5,4,3,3,2,1,1,1] .empty .empty)) (.node [8,8,7,5,4,3,3,3,2] (.node [8,8,7,5,4,3,3,3,1,1] .empty .empty) (.node [8,8,7,5,4,4,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_96 : RowTree := (.node [8,8,7,5,3,2,2,2,2,1,1,1,1] degreeTree43_94 degreeTree43_95) + +def degreeTree43_97 : RowTree := (.node [8,8,7,5,5,3,1,1,1,1,1,1,1] (.node [8,8,7,5,4,4,4,2,1] (.node [8,8,7,5,4,4,3,2,1,1] (.node [8,8,7,5,4,4,2,2,2,1] (.node [8,8,7,5,4,4,2,2,1,1,1] .empty .empty) (.node [8,8,7,5,4,4,3,1,1,1,1] .empty .empty)) (.node [8,8,7,5,4,4,3,3,1] (.node [8,8,7,5,4,4,3,2,2] .empty .empty) (.node [8,8,7,5,4,4,4,1,1,1] .empty .empty))) (.node [8,8,7,5,5,2,2,1,1,1,1,1,1] (.node [8,8,7,5,5,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,5,4,4,4,3] .empty .empty) (.node [8,8,7,5,5,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,5,5,2,2,2,2,1,1] (.node [8,8,7,5,5,2,2,2,1,1,1,1] .empty .empty) (.node [8,8,7,5,5,2,2,2,2,2] .empty .empty)))) (.node [8,8,7,5,5,4,1,1,1,1,1,1] (.node [8,8,7,5,5,3,3,1,1,1,1] (.node [8,8,7,5,5,3,2,2,1,1,1] (.node [8,8,7,5,5,3,2,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,5,3,2,2,2,1] .empty .empty)) (.node [8,8,7,5,5,3,3,2,2] (.node [8,8,7,5,5,3,3,2,1,1] .empty .empty) (.node [8,8,7,5,5,3,3,3,1] .empty .empty))) (.node [8,8,7,5,5,4,3,1,1,1] (.node [8,8,7,5,5,4,2,2,1,1] (.node [8,8,7,5,5,4,2,1,1,1,1] .empty .empty) (.node [8,8,7,5,5,4,2,2,2] .empty .empty)) (.node [8,8,7,5,5,4,3,3] (.node [8,8,7,5,5,4,3,2,1] .empty .empty) (.node [8,8,7,5,5,4,4,1,1] .empty .empty))))) + +def degreeTree43_98 : RowTree := (.node [8,8,7,6,3,2,2,1,1,1,1,1,1,1] (.node [8,8,7,6,2,2,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,5,5,5,3,1,1] (.node [8,8,7,5,5,5,2,1,1,1] (.node [8,8,7,5,5,5,1,1,1,1,1] .empty .empty) (.node [8,8,7,5,5,5,2,2,1] .empty .empty)) (.node [8,8,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,5,5,5,3,2] .empty .empty) (.node [8,8,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,6,2,2,2,2,2,2,1,1] (.node [8,8,7,6,2,2,2,2,1,1,1,1,1,1] (.node [8,8,7,6,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [8,8,7,6,3,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,6,2,2,2,2,2,2,2] .empty .empty) (.node [8,8,7,6,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,7,6,3,3,2,2,2,2] (.node [8,8,7,6,3,3,1,1,1,1,1,1,1,1] (.node [8,8,7,6,3,2,2,2,2,1,1,1] (.node [8,8,7,6,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,3,2,2,2,2,2,1] .empty .empty)) (.node [8,8,7,6,3,3,2,2,1,1,1,1] (.node [8,8,7,6,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,3,3,2,2,2,1,1] .empty .empty))) (.node [8,8,7,6,3,3,3,3,1,1] (.node [8,8,7,6,3,3,3,2,1,1,1] (.node [8,8,7,6,3,3,3,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,3,3,3,2,2,1] .empty .empty)) (.node [8,8,7,6,4,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,6,3,3,3,3,2] .empty .empty) (.node [8,8,7,6,4,2,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_99 : RowTree := (.node [8,8,7,5,5,4,4,2] degreeTree43_97 degreeTree43_98) + +def degreeTree43_100 : RowTree := (.node [8,8,7,5,4,4,2,1,1,1,1,1] degreeTree43_96 degreeTree43_99) + +def degreeTree43_101 : RowTree := (.node [8,8,7,4,4,3,3,2,1,1,1,1] degreeTree43_91 degreeTree43_100) + +def degreeTree43_102 : RowTree := (.node [8,8,7,6,4,3,3,2,1,1] (.node [8,8,7,6,4,3,2,1,1,1,1,1] (.node [8,8,7,6,4,2,2,2,2,2] (.node [8,8,7,6,4,2,2,2,2,1,1] (.node [8,8,7,6,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [8,8,7,6,4,3,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,6,4,3,2,2,2,1] (.node [8,8,7,6,4,3,2,2,1,1,1] .empty .empty) (.node [8,8,7,6,4,3,3,1,1,1,1] .empty .empty))) (.node [8,8,7,6,4,4,2,1,1,1,1] (.node [8,8,7,6,4,3,3,3,1] (.node [8,8,7,6,4,3,3,2,2] .empty .empty) (.node [8,8,7,6,4,4,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,6,4,4,2,2,2] (.node [8,8,7,6,4,4,2,2,1,1] .empty .empty) (.node [8,8,7,6,4,4,3,1,1,1] .empty .empty)))) + +def degreeTree43_103 : RowTree := (.node [8,8,7,6,5,2,2,2,2,1] (.node [8,8,7,6,5,1,1,1,1,1,1,1,1,1] (.node [8,8,7,6,4,4,4,1,1] (.node [8,8,7,6,4,4,3,3] .empty .empty) (.node [8,8,7,6,4,4,4,2] .empty .empty)) (.node [8,8,7,6,5,2,2,1,1,1,1,1] (.node [8,8,7,6,5,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,5,2,2,2,1,1,1] .empty .empty))) (.node [8,8,7,6,5,3,2,2,2] (.node [8,8,7,6,5,3,2,1,1,1,1] (.node [8,8,7,6,5,3,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,6,5,3,2,2,1,1] .empty .empty)) (.node [8,8,7,6,5,3,3,2,1] (.node [8,8,7,6,5,3,3,1,1,1] .empty .empty) (.node [8,8,7,6,5,3,3,3] .empty .empty)))) + +def degreeTree43_104 : RowTree := (.node [8,8,7,6,4,4,3,2,1] degreeTree43_102 degreeTree43_103) + +def degreeTree43_105 : RowTree := (.node [8,8,7,6,6,4,1,1,1,1] (.node [8,8,7,6,6,2,1,1,1,1,1,1] (.node [8,8,7,6,5,4,3,2] (.node [8,8,7,6,5,4,2,2,1] (.node [8,8,7,6,5,4,2,1,1,1] .empty .empty) (.node [8,8,7,6,5,4,3,1,1] .empty .empty)) (.node [8,8,7,6,5,5,2,1,1] (.node [8,8,7,6,5,5,1,1,1,1] .empty .empty) (.node [8,8,7,6,6,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,7,6,6,3,1,1,1,1,1] (.node [8,8,7,6,6,2,2,2,1,1] (.node [8,8,7,6,6,2,2,1,1,1,1] .empty .empty) (.node [8,8,7,6,6,2,2,2,2] .empty .empty)) (.node [8,8,7,6,6,3,2,2,1] (.node [8,8,7,6,6,3,2,1,1,1] .empty .empty) (.node [8,8,7,6,6,3,3,1,1] .empty .empty)))) (.node [8,8,7,7,2,2,2,2,2,1,1,1] (.node [8,8,7,7,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,6,6,5,1,1,1] (.node [8,8,7,6,6,4,2,1,1] .empty .empty) (.node [8,8,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,7,2,2,2,1,1,1,1,1,1,1] (.node [8,8,7,7,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [8,8,7,7,3,2,2,1,1,1,1,1,1] (.node [8,8,7,7,3,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,7,2,2,2,2,2,2,1] .empty .empty) (.node [8,8,7,7,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,7,3,2,2,2,2,1,1] (.node [8,8,7,7,3,2,2,2,1,1,1,1] .empty .empty) (.node [8,8,7,7,3,2,2,2,2,2] .empty .empty))))) + +def degreeTree43_106 : RowTree := (.node [8,8,7,6,5,4,1,1,1,1,1] degreeTree43_104 degreeTree43_105) + +def degreeTree43_107 : RowTree := (.node [8,8,7,7,4,3,2,2,2] (.node [8,8,7,7,4,1,1,1,1,1,1,1,1,1] (.node [8,8,7,7,3,3,3,1,1,1,1] (.node [8,8,7,7,3,3,2,2,1,1,1] (.node [8,8,7,7,3,3,2,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,3,3,2,2,2,1] .empty .empty)) (.node [8,8,7,7,3,3,3,2,2] (.node [8,8,7,7,3,3,3,2,1,1] .empty .empty) (.node [8,8,7,7,3,3,3,3,1] .empty .empty))) (.node [8,8,7,7,4,2,2,2,2,1] (.node [8,8,7,7,4,2,2,1,1,1,1,1] (.node [8,8,7,7,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,4,2,2,2,1,1,1] .empty .empty)) (.node [8,8,7,7,4,3,2,1,1,1,1] (.node [8,8,7,7,4,3,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,4,3,2,2,1,1] .empty .empty)))) (.node [8,8,7,7,5,1,1,1,1,1,1,1,1] (.node [8,8,7,7,4,4,1,1,1,1,1] (.node [8,8,7,7,4,3,3,2,1] (.node [8,8,7,7,4,3,3,1,1,1] .empty .empty) (.node [8,8,7,7,4,3,3,3] .empty .empty)) (.node [8,8,7,7,4,4,2,2,1] (.node [8,8,7,7,4,4,2,1,1,1] .empty .empty) (.node [8,8,7,7,4,4,3,1,1] .empty .empty))) (.node [8,8,7,7,5,2,2,2,2] (.node [8,8,7,7,5,2,2,1,1,1,1] (.node [8,8,7,7,5,2,1,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,5,2,2,2,1,1] .empty .empty)) (.node [8,8,7,7,5,3,2,1,1,1] (.node [8,8,7,7,5,3,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,5,3,2,2,1] .empty .empty))))) + +def degreeTree43_108 : RowTree := (.node [8,8,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,7,7,6,3,1,1,1,1] (.node [8,8,7,7,6,1,1,1,1,1,1,1] (.node [8,8,7,7,5,4,2,1,1] (.node [8,8,7,7,5,4,1,1,1,1] .empty .empty) (.node [8,8,7,7,5,5,1,1,1] .empty .empty)) (.node [8,8,7,7,6,2,2,1,1,1] (.node [8,8,7,7,6,2,1,1,1,1,1] .empty .empty) (.node [8,8,7,7,6,2,2,2,1] .empty .empty))) (.node [8,8,7,7,7,2,1,1,1,1] (.node [8,8,7,7,6,4,1,1,1] (.node [8,8,7,7,6,3,2,1,1] .empty .empty) (.node [8,8,7,7,7,1,1,1,1,1,1] .empty .empty)) (.node [8,8,7,7,7,3,1,1,1] (.node [8,8,7,7,7,2,2,1,1] .empty .empty) (.node [8,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,8,2,2,2,2,2,2,2,2,2,1] (.node [8,8,8,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [8,8,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,2,2,2,2,2,2,2,1,1,1,1,1] (.node [8,8,8,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,2,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [8,8,8,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,3,2,2,2,2,2,1,1,1,1,1,1] (.node [8,8,8,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,3,2,2,2,2,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_109 : RowTree := (.node [8,8,7,7,5,3,3,1,1] degreeTree43_107 degreeTree43_108) + +def degreeTree43_110 : RowTree := (.node [8,8,7,7,3,3,1,1,1,1,1,1,1] degreeTree43_106 degreeTree43_109) + +def degreeTree43_111 : RowTree := (.node [8,8,8,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,3,2,2,2,1,1,1,1,1,1,1] (.node [8,8,8,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [8,8,8,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,3,3,2,2,2,2,2,1,1,1] (.node [8,8,8,3,3,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [8,8,8,3,3,2,2,2,2,2,2,1] .empty .empty))) (.node [8,8,8,3,3,3,2,2,2,2,1,1] (.node [8,8,8,3,3,3,2,2,1,1,1,1,1,1] (.node [8,8,8,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,3,3,3,2,2,2,1,1,1,1] .empty .empty)) (.node [8,8,8,3,3,3,3,1,1,1,1,1,1,1] (.node [8,8,8,3,3,3,2,2,2,2,2] .empty .empty) (.node [8,8,8,3,3,3,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_112 : RowTree := (.node [8,8,8,4,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,3,3,3,3,2,2] (.node [8,8,8,3,3,3,3,3,1,1,1,1] (.node [8,8,8,3,3,3,3,2,2,2,1] .empty .empty) (.node [8,8,8,3,3,3,3,3,2,1,1] .empty .empty)) (.node [8,8,8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,3,3,3,3,3,3,1] .empty .empty) (.node [8,8,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,8,4,2,2,2,2,2,2,1,1,1] (.node [8,8,8,4,2,2,2,2,1,1,1,1,1,1,1] (.node [8,8,8,4,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,4,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [8,8,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,4,2,2,2,2,2,2,2,1] .empty .empty) (.node [8,8,8,4,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_113 : RowTree := (.node [8,8,8,3,3,3,3,2,2,1,1,1] degreeTree43_111 degreeTree43_112) + +def degreeTree43_114 : RowTree := (.node [8,8,8,4,3,3,3,3,3] (.node [8,8,8,4,3,3,2,2,2,1,1,1] (.node [8,8,8,4,3,2,2,2,2,2,2] (.node [8,8,8,4,3,2,2,2,2,1,1,1,1] (.node [8,8,8,4,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,4,3,2,2,2,2,2,1,1] .empty .empty)) (.node [8,8,8,4,3,3,2,1,1,1,1,1,1,1] (.node [8,8,8,4,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,4,3,3,2,2,1,1,1,1,1] .empty .empty))) (.node [8,8,8,4,3,3,3,2,2,1,1] (.node [8,8,8,4,3,3,3,1,1,1,1,1,1] (.node [8,8,8,4,3,3,2,2,2,2,1] .empty .empty) (.node [8,8,8,4,3,3,3,2,1,1,1,1] .empty .empty)) (.node [8,8,8,4,3,3,3,3,1,1,1] (.node [8,8,8,4,3,3,3,2,2,2] .empty .empty) (.node [8,8,8,4,3,3,3,3,2,1] .empty .empty)))) (.node [8,8,8,4,4,3,2,1,1,1,1,1,1] (.node [8,8,8,4,4,2,2,2,1,1,1,1,1] (.node [8,8,8,4,4,2,1,1,1,1,1,1,1,1,1] (.node [8,8,8,4,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,4,4,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,4,4,2,2,2,2,2,1] (.node [8,8,8,4,4,2,2,2,2,1,1,1] .empty .empty) (.node [8,8,8,4,4,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [8,8,8,4,4,3,3,1,1,1,1,1] (.node [8,8,8,4,4,3,2,2,2,1,1] (.node [8,8,8,4,4,3,2,2,1,1,1,1] .empty .empty) (.node [8,8,8,4,4,3,2,2,2,2] .empty .empty)) (.node [8,8,8,4,4,3,3,2,2,1] (.node [8,8,8,4,4,3,3,2,1,1,1] .empty .empty) (.node [8,8,8,4,4,3,3,3,1,1] .empty .empty))))) + +def degreeTree43_115 : RowTree := (.node [8,8,8,4,3,2,2,1,1,1,1,1,1,1,1] degreeTree43_113 degreeTree43_114) + +def degreeTree43_116 : RowTree := (.node [8,8,8,5,2,2,2,2,1,1,1,1,1,1] (.node [8,8,8,4,4,4,3,3,1] (.node [8,8,8,4,4,4,2,2,2,1] (.node [8,8,8,4,4,4,2,1,1,1,1,1] (.node [8,8,8,4,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,4,4,4,2,2,1,1,1] .empty .empty)) (.node [8,8,8,4,4,4,3,2,1,1] (.node [8,8,8,4,4,4,3,1,1,1,1] .empty .empty) (.node [8,8,8,4,4,4,3,2,2] .empty .empty))) (.node [8,8,8,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,4,4,4,4,2,1] (.node [8,8,8,4,4,4,4,1,1,1] .empty .empty) (.node [8,8,8,4,4,4,4,3] .empty .empty)) (.node [8,8,8,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,8,5,3,2,2,2,2,1,1,1] (.node [8,8,8,5,3,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,5,2,2,2,2,2,2,1,1] (.node [8,8,8,5,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [8,8,8,5,2,2,2,2,2,2,2] .empty .empty)) (.node [8,8,8,5,3,2,2,1,1,1,1,1,1,1] (.node [8,8,8,5,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,5,3,2,2,2,1,1,1,1,1] .empty .empty))) (.node [8,8,8,5,3,3,2,2,1,1,1,1] (.node [8,8,8,5,3,3,1,1,1,1,1,1,1,1] (.node [8,8,8,5,3,2,2,2,2,2,1] .empty .empty) (.node [8,8,8,5,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,5,3,3,2,2,2,2] (.node [8,8,8,5,3,3,2,2,2,1,1] .empty .empty) (.node [8,8,8,5,3,3,3,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_117 : RowTree := (.node [8,8,8,5,4,3,3,2,2] (.node [8,8,8,5,4,2,2,2,2,1,1] (.node [8,8,8,5,4,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,5,3,3,3,3,1,1] (.node [8,8,8,5,3,3,3,2,2,1] .empty .empty) (.node [8,8,8,5,3,3,3,3,2] .empty .empty)) (.node [8,8,8,5,4,2,2,1,1,1,1,1,1] (.node [8,8,8,5,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,5,4,2,2,2,1,1,1,1] .empty .empty))) (.node [8,8,8,5,4,3,2,2,1,1,1] (.node [8,8,8,5,4,3,1,1,1,1,1,1,1] (.node [8,8,8,5,4,2,2,2,2,2] .empty .empty) (.node [8,8,8,5,4,3,2,1,1,1,1,1] .empty .empty)) (.node [8,8,8,5,4,3,3,1,1,1,1] (.node [8,8,8,5,4,3,2,2,2,1] .empty .empty) (.node [8,8,8,5,4,3,3,2,1,1] .empty .empty)))) (.node [8,8,8,5,4,4,3,3] (.node [8,8,8,5,4,4,2,2,1,1] (.node [8,8,8,5,4,4,1,1,1,1,1,1] (.node [8,8,8,5,4,3,3,3,1] .empty .empty) (.node [8,8,8,5,4,4,2,1,1,1,1] .empty .empty)) (.node [8,8,8,5,4,4,3,1,1,1] (.node [8,8,8,5,4,4,2,2,2] .empty .empty) (.node [8,8,8,5,4,4,3,2,1] .empty .empty))) (.node [8,8,8,5,5,2,2,1,1,1,1,1] (.node [8,8,8,5,5,1,1,1,1,1,1,1,1,1] (.node [8,8,8,5,4,4,4,1,1] .empty .empty) (.node [8,8,8,5,5,2,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,5,5,2,2,2,2,1] (.node [8,8,8,5,5,2,2,2,1,1,1] .empty .empty) (.node [8,8,8,5,5,3,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_118 : RowTree := (.node [8,8,8,5,3,3,3,2,1,1,1] degreeTree43_116 degreeTree43_117) + +def degreeTree43_119 : RowTree := (.node [8,8,8,4,4,3,3,3,2] degreeTree43_115 degreeTree43_118) + +def degreeTree43_120 : RowTree := (.node [8,8,8,3,2,2,2,2,2,2,2,1,1] degreeTree43_110 degreeTree43_119) + +def degreeTree43_121 : RowTree := (.node [8,8,7,6,4,2,2,1,1,1,1,1,1] degreeTree43_101 degreeTree43_120) + +def degreeTree43_122 : RowTree := (.node [8,8,8,5,5,4,3,1,1] (.node [8,8,8,5,5,3,3,3] (.node [8,8,8,5,5,3,3,1,1,1] (.node [8,8,8,5,5,3,2,2,2] (.node [8,8,8,5,5,3,2,2,1,1] .empty .empty) .empty) (.node [8,8,8,5,5,3,3,2,1] .empty .empty)) (.node [8,8,8,5,5,4,2,1,1,1] (.node [8,8,8,5,5,4,1,1,1,1,1] .empty .empty) (.node [8,8,8,5,5,4,2,2,1] .empty .empty))) (.node [8,8,8,6,2,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,5,5,5,2,1,1] (.node [8,8,8,5,5,5,1,1,1,1] .empty .empty) (.node [8,8,8,6,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,6,2,2,2,1,1,1,1,1,1,1] (.node [8,8,8,6,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,6,2,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_123 : RowTree := (.node [8,8,8,6,3,3,1,1,1,1,1,1,1] (.node [8,8,8,6,3,2,2,1,1,1,1,1,1] (.node [8,8,8,6,3,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,6,2,2,2,2,2,2,1] .empty .empty) (.node [8,8,8,6,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,6,3,2,2,2,2,1,1] (.node [8,8,8,6,3,2,2,2,1,1,1,1] .empty .empty) (.node [8,8,8,6,3,2,2,2,2,2] .empty .empty))) (.node [8,8,8,6,3,3,3,1,1,1,1] (.node [8,8,8,6,3,3,2,2,1,1,1] (.node [8,8,8,6,3,3,2,1,1,1,1,1] .empty .empty) (.node [8,8,8,6,3,3,2,2,2,1] .empty .empty)) (.node [8,8,8,6,3,3,3,2,2] (.node [8,8,8,6,3,3,3,2,1,1] .empty .empty) (.node [8,8,8,6,3,3,3,3,1] .empty .empty)))) + +def degreeTree43_124 : RowTree := (.node [8,8,8,6,2,2,2,2,2,1,1,1] degreeTree43_122 degreeTree43_123) + +def degreeTree43_125 : RowTree := (.node [8,8,8,6,5,2,1,1,1,1,1,1] (.node [8,8,8,6,4,3,2,2,2] (.node [8,8,8,6,4,2,2,2,2,1] (.node [8,8,8,6,4,2,2,1,1,1,1,1] (.node [8,8,8,6,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,6,4,2,2,2,1,1,1] .empty .empty)) (.node [8,8,8,6,4,3,2,1,1,1,1] (.node [8,8,8,6,4,3,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,6,4,3,2,2,1,1] .empty .empty))) (.node [8,8,8,6,4,4,2,1,1,1] (.node [8,8,8,6,4,3,3,2,1] (.node [8,8,8,6,4,3,3,1,1,1] .empty .empty) (.node [8,8,8,6,4,4,1,1,1,1,1] .empty .empty)) (.node [8,8,8,6,4,4,3,1,1] (.node [8,8,8,6,4,4,2,2,1] .empty .empty) (.node [8,8,8,6,5,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [8,8,8,6,5,4,1,1,1,1] (.node [8,8,8,6,5,3,1,1,1,1,1] (.node [8,8,8,6,5,2,2,2,1,1] (.node [8,8,8,6,5,2,2,1,1,1,1] .empty .empty) (.node [8,8,8,6,5,2,2,2,2] .empty .empty)) (.node [8,8,8,6,5,3,2,2,1] (.node [8,8,8,6,5,3,2,1,1,1] .empty .empty) (.node [8,8,8,6,5,3,3,1,1] .empty .empty))) (.node [8,8,8,6,6,2,1,1,1,1,1] (.node [8,8,8,6,5,5,1,1,1] (.node [8,8,8,6,5,4,2,1,1] .empty .empty) (.node [8,8,8,6,6,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,6,6,2,2,2,1] (.node [8,8,8,6,6,2,2,1,1,1] .empty .empty) (.node [8,8,8,6,6,3,1,1,1,1] .empty .empty))))) + +def degreeTree43_126 : RowTree := (.node [8,8,8,6,4,1,1,1,1,1,1,1,1,1] degreeTree43_124 degreeTree43_125) + +def degreeTree43_127 : RowTree := (.node [8,8,8,7,3,3,2,2,1,1] (.node [8,8,8,7,2,2,2,2,2,2] (.node [8,8,8,7,2,2,1,1,1,1,1,1,1,1] (.node [8,8,8,7,1,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,6,6,4,1,1,1] .empty .empty) (.node [8,8,8,7,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,7,2,2,2,2,1,1,1,1] (.node [8,8,8,7,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,7,2,2,2,2,2,1,1] .empty .empty))) (.node [8,8,8,7,3,2,2,2,1,1,1] (.node [8,8,8,7,3,2,1,1,1,1,1,1,1] (.node [8,8,8,7,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,7,3,2,2,1,1,1,1,1] .empty .empty)) (.node [8,8,8,7,3,3,1,1,1,1,1,1] (.node [8,8,8,7,3,2,2,2,2,1] .empty .empty) (.node [8,8,8,7,3,3,2,1,1,1,1] .empty .empty)))) (.node [8,8,8,7,4,2,2,2,2] (.node [8,8,8,7,4,1,1,1,1,1,1,1,1] (.node [8,8,8,7,3,3,3,1,1,1] (.node [8,8,8,7,3,3,2,2,2] .empty .empty) (.node [8,8,8,7,3,3,3,2,1] .empty .empty)) (.node [8,8,8,7,4,2,2,1,1,1,1] (.node [8,8,8,7,4,2,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,7,4,2,2,2,1,1] .empty .empty))) (.node [8,8,8,7,4,3,3,1,1] (.node [8,8,8,7,4,3,2,1,1,1] (.node [8,8,8,7,4,3,1,1,1,1,1] .empty .empty) (.node [8,8,8,7,4,3,2,2,1] .empty .empty)) (.node [8,8,8,7,4,4,2,1,1] (.node [8,8,8,7,4,4,1,1,1,1] .empty .empty) (.node [8,8,8,7,5,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_128 : RowTree := (.node [8,8,8,8,2,2,2,2,1,1,1] (.node [8,8,8,7,6,2,2,1,1] (.node [8,8,8,7,5,3,2,1,1] (.node [8,8,8,7,5,2,2,2,1] (.node [8,8,8,7,5,2,2,1,1,1] .empty .empty) (.node [8,8,8,7,5,3,1,1,1,1] .empty .empty)) (.node [8,8,8,7,6,1,1,1,1,1,1] (.node [8,8,8,7,5,4,1,1,1] .empty .empty) (.node [8,8,8,7,6,2,1,1,1,1] .empty .empty))) (.node [8,8,8,8,1,1,1,1,1,1,1,1,1,1,1] (.node [8,8,8,7,7,1,1,1,1,1] (.node [8,8,8,7,6,3,1,1,1] .empty .empty) (.node [8,8,8,7,7,2,1,1,1] .empty .empty)) (.node [8,8,8,8,2,2,1,1,1,1,1,1,1] (.node [8,8,8,8,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [8,8,8,8,2,2,2,1,1,1,1,1] .empty .empty)))) (.node [8,8,8,8,3,3,2,1,1,1] (.node [8,8,8,8,3,2,2,1,1,1,1] (.node [8,8,8,8,3,1,1,1,1,1,1,1,1] (.node [8,8,8,8,2,2,2,2,2,1] .empty .empty) (.node [8,8,8,8,3,2,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,8,3,2,2,2,2] (.node [8,8,8,8,3,2,2,2,1,1] .empty .empty) (.node [8,8,8,8,3,3,1,1,1,1,1] .empty .empty))) (.node [8,8,8,8,4,2,1,1,1,1,1] (.node [8,8,8,8,3,3,3,1,1] (.node [8,8,8,8,3,3,2,2,1] .empty .empty) (.node [8,8,8,8,4,1,1,1,1,1,1,1] .empty .empty)) (.node [8,8,8,8,4,2,2,2,1] (.node [8,8,8,8,4,2,2,1,1,1] .empty .empty) (.node [8,8,8,8,4,3,1,1,1,1] .empty .empty))))) + +def degreeTree43_129 : RowTree := (.node [8,8,8,7,5,2,1,1,1,1,1] degreeTree43_127 degreeTree43_128) + +def degreeTree43_130 : RowTree := (.node [8,8,8,6,6,3,2,1,1] degreeTree43_126 degreeTree43_129) + +def degreeTree43_131 : RowTree := (.node [9,4,4,4,4,3,3,3,3,3,3] (.node [8,8,8,8,5,3,1,1,1] (.node [8,8,8,8,5,2,1,1,1,1] (.node [8,8,8,8,5,1,1,1,1,1,1] (.node [8,8,8,8,4,4,1,1,1] .empty .empty) .empty) (.node [8,8,8,8,5,2,2,1,1] .empty .empty)) (.node [8,8,8,8,6,2,1,1,1] (.node [8,8,8,8,6,1,1,1,1,1] .empty .empty) (.node [8,8,8,8,7,1,1,1,1] .empty .empty))) (.node [9,4,4,4,4,4,4,4,2,2,2] (.node [9,4,4,4,4,4,4,3,3,2,2] (.node [9,4,4,4,4,4,3,3,3,3,2] .empty .empty) (.node [9,4,4,4,4,4,4,3,3,3,1] .empty .empty)) (.node [9,4,4,4,4,4,4,4,3,3] (.node [9,4,4,4,4,4,4,4,3,2,1] .empty .empty) (.node [9,4,4,4,4,4,4,4,4,1,1] .empty .empty)))) + +def degreeTree43_132 : RowTree := (.node [9,5,4,4,4,4,4,4,2,2,1] (.node [9,5,4,4,4,4,3,3,3,3,1] (.node [9,5,4,4,4,3,3,3,3,3,2] (.node [9,5,4,4,3,3,3,3,3,3,3] .empty .empty) (.node [9,5,4,4,4,4,3,3,3,2,2] .empty .empty)) (.node [9,5,4,4,4,4,4,3,3,2,1] (.node [9,5,4,4,4,4,4,3,2,2,2] .empty .empty) (.node [9,5,4,4,4,4,4,3,3,3] .empty .empty))) (.node [9,5,5,3,3,3,3,3,3,3,3] (.node [9,5,4,4,4,4,4,4,3,2] (.node [9,5,4,4,4,4,4,4,3,1,1] .empty .empty) (.node [9,5,4,4,4,4,4,4,4,1] .empty .empty)) (.node [9,5,5,4,4,3,3,3,3,2,2] (.node [9,5,5,4,3,3,3,3,3,3,2] .empty .empty) (.node [9,5,5,4,4,3,3,3,3,3,1] .empty .empty)))) + +def degreeTree43_133 : RowTree := (.node [9,4,4,4,4,4,4,4,4,2] degreeTree43_131 degreeTree43_132) + +def degreeTree43_134 : RowTree := (.node [9,5,5,5,4,4,3,2,2,2,2] (.node [9,5,5,4,4,4,4,4,2,2] (.node [9,5,5,4,4,4,4,3,2,2,1] (.node [9,5,5,4,4,4,3,3,3,3] (.node [9,5,5,4,4,4,3,3,3,2,1] .empty .empty) (.node [9,5,5,4,4,4,4,2,2,2,2] .empty .empty)) (.node [9,5,5,4,4,4,4,3,3,2] (.node [9,5,5,4,4,4,4,3,3,1,1] .empty .empty) (.node [9,5,5,4,4,4,4,4,2,1,1] .empty .empty))) (.node [9,5,5,5,3,3,3,3,3,3,1] (.node [9,5,5,4,4,4,4,4,4] (.node [9,5,5,4,4,4,4,4,3,1] .empty .empty) (.node [9,5,5,5,3,3,3,3,3,2,2] .empty .empty)) (.node [9,5,5,5,4,3,3,3,3,2,1] (.node [9,5,5,5,4,3,3,3,2,2,2] .empty .empty) (.node [9,5,5,5,4,3,3,3,3,3] .empty .empty)))) (.node [9,5,5,5,4,4,4,4,1,1,1] (.node [9,5,5,5,4,4,4,2,2,2,1] (.node [9,5,5,5,4,4,3,3,3,1,1] (.node [9,5,5,5,4,4,3,3,2,2,1] .empty .empty) (.node [9,5,5,5,4,4,3,3,3,2] .empty .empty)) (.node [9,5,5,5,4,4,4,3,2,2] (.node [9,5,5,5,4,4,4,3,2,1,1] .empty .empty) (.node [9,5,5,5,4,4,4,3,3,1] .empty .empty))) (.node [9,5,5,5,5,3,3,3,2,2,1] (.node [9,5,5,5,4,4,4,4,3] (.node [9,5,5,5,4,4,4,4,2,1] .empty .empty) (.node [9,5,5,5,5,3,3,2,2,2,2] .empty .empty)) (.node [9,5,5,5,5,3,3,3,3,2] (.node [9,5,5,5,5,3,3,3,3,1,1] .empty .empty) (.node [9,5,5,5,5,4,2,2,2,2,2] .empty .empty))))) + +def degreeTree43_135 : RowTree := (.node [9,5,5,4,4,4,3,3,2,2,2] degreeTree43_133 degreeTree43_134) + +def degreeTree43_136 : RowTree := (.node [9,5,5,5,5,5,3,3,3] (.node [9,5,5,5,5,4,4,3,3] (.node [9,5,5,5,5,4,4,2,2,1,1] (.node [9,5,5,5,5,4,3,3,2,2] (.node [9,5,5,5,5,4,3,3,2,1,1] .empty .empty) (.node [9,5,5,5,5,4,3,3,3,1] .empty .empty)) (.node [9,5,5,5,5,4,4,3,1,1,1] (.node [9,5,5,5,5,4,4,2,2,2] .empty .empty) (.node [9,5,5,5,5,4,4,3,2,1] .empty .empty))) (.node [9,5,5,5,5,5,3,2,2,1,1] (.node [9,5,5,5,5,4,4,4,2] (.node [9,5,5,5,5,4,4,4,1,1] .empty .empty) (.node [9,5,5,5,5,5,2,2,2,2,1] .empty .empty)) (.node [9,5,5,5,5,5,3,3,1,1,1] (.node [9,5,5,5,5,5,3,2,2,2] .empty .empty) (.node [9,5,5,5,5,5,3,3,2,1] .empty .empty)))) (.node [9,5,5,5,5,5,5,2,2] (.node [9,5,5,5,5,5,4,3,2] (.node [9,5,5,5,5,5,4,2,2,1] (.node [9,5,5,5,5,5,4,2,1,1,1] .empty .empty) (.node [9,5,5,5,5,5,4,3,1,1] .empty .empty)) (.node [9,5,5,5,5,5,5,1,1,1,1] (.node [9,5,5,5,5,5,4,4,1] .empty .empty) (.node [9,5,5,5,5,5,5,2,1,1] .empty .empty))) (.node [9,6,4,4,4,3,3,3,3,2,2] (.node [9,6,4,3,3,3,3,3,3,3,3] (.node [9,5,5,5,5,5,5,3,1] .empty .empty) (.node [9,6,4,4,3,3,3,3,3,3,2] .empty .empty)) (.node [9,6,4,4,4,4,3,3,2,2,2] (.node [9,6,4,4,4,3,3,3,3,3,1] .empty .empty) (.node [9,6,4,4,4,4,3,3,3,2,1] .empty .empty))))) + +def degreeTree43_137 : RowTree := (.node [9,6,5,4,4,4,3,3,2,2,1] (.node [9,6,4,4,4,4,4,4,4] (.node [9,6,4,4,4,4,4,3,3,2] (.node [9,6,4,4,4,4,4,3,2,2,1] (.node [9,6,4,4,4,4,4,2,2,2,2] .empty .empty) (.node [9,6,4,4,4,4,4,3,3,1,1] .empty .empty)) (.node [9,6,4,4,4,4,4,4,2,2] (.node [9,6,4,4,4,4,4,4,2,1,1] .empty .empty) (.node [9,6,4,4,4,4,4,4,3,1] .empty .empty))) (.node [9,6,5,4,4,3,3,3,2,2,2] (.node [9,6,5,4,3,3,3,3,3,2,2] (.node [9,6,5,3,3,3,3,3,3,3,2] .empty .empty) (.node [9,6,5,4,3,3,3,3,3,3,1] .empty .empty)) (.node [9,6,5,4,4,3,3,3,3,3] (.node [9,6,5,4,4,3,3,3,3,2,1] .empty .empty) (.node [9,6,5,4,4,4,3,2,2,2,2] .empty .empty)))) (.node [9,6,5,4,4,4,4,4,2,1] (.node [9,6,5,4,4,4,4,3,2,1,1] (.node [9,6,5,4,4,4,3,3,3,2] (.node [9,6,5,4,4,4,3,3,3,1,1] .empty .empty) (.node [9,6,5,4,4,4,4,2,2,2,1] .empty .empty)) (.node [9,6,5,4,4,4,4,3,3,1] (.node [9,6,5,4,4,4,4,3,2,2] .empty .empty) (.node [9,6,5,4,4,4,4,4,1,1,1] .empty .empty))) (.node [9,6,5,5,3,3,3,3,3,3] (.node [9,6,5,5,3,3,3,3,2,2,2] (.node [9,6,5,4,4,4,4,4,3] .empty .empty) (.node [9,6,5,5,3,3,3,3,3,2,1] .empty .empty)) (.node [9,6,5,5,4,3,3,3,2,2,1] (.node [9,6,5,5,4,3,3,2,2,2,2] .empty .empty) (.node [9,6,5,5,4,3,3,3,3,1,1] .empty .empty))))) + +def degreeTree43_138 : RowTree := (.node [9,6,4,4,4,4,3,3,3,3] degreeTree43_136 degreeTree43_137) + +def degreeTree43_139 : RowTree := (.node [9,5,5,5,5,4,3,2,2,2,1] degreeTree43_135 degreeTree43_138) + +def degreeTree43_140 : RowTree := (.node [8,8,8,8,4,3,2,1,1] degreeTree43_130 degreeTree43_139) + +def degreeTree43_141 : RowTree := (.node [9,6,5,5,4,4,4,3,2,1] (.node [9,6,5,5,4,4,3,3,3,1] (.node [9,6,5,5,4,4,3,3,2,1,1] (.node [9,6,5,5,4,4,3,2,2,2,1] (.node [9,6,5,5,4,4,2,2,2,2,2] .empty .empty) .empty) (.node [9,6,5,5,4,4,3,3,2,2] .empty .empty)) (.node [9,6,5,5,4,4,4,2,2,2] (.node [9,6,5,5,4,4,4,2,2,1,1] .empty .empty) (.node [9,6,5,5,4,4,4,3,1,1,1] .empty .empty))) (.node [9,6,5,5,5,3,2,2,2,2,2] (.node [9,6,5,5,4,4,4,4,1,1] (.node [9,6,5,5,4,4,4,3,3] .empty .empty) (.node [9,6,5,5,4,4,4,4,2] .empty .empty)) (.node [9,6,5,5,5,3,3,3,2,1,1] (.node [9,6,5,5,5,3,3,2,2,2,1] .empty .empty) (.node [9,6,5,5,5,3,3,3,2,2] .empty .empty)))) + +def degreeTree43_142 : RowTree := (.node [9,6,5,5,5,4,4,2,2,1] (.node [9,6,5,5,5,4,3,3,1,1,1] (.node [9,6,5,5,5,4,3,2,2,1,1] (.node [9,6,5,5,5,4,2,2,2,2,1] .empty .empty) (.node [9,6,5,5,5,4,3,2,2,2] .empty .empty)) (.node [9,6,5,5,5,4,3,3,3] (.node [9,6,5,5,5,4,3,3,2,1] .empty .empty) (.node [9,6,5,5,5,4,4,2,1,1,1] .empty .empty))) (.node [9,6,5,5,5,5,2,2,2,1,1] (.node [9,6,5,5,5,4,4,3,2] (.node [9,6,5,5,5,4,4,3,1,1] .empty .empty) (.node [9,6,5,5,5,4,4,4,1] .empty .empty)) (.node [9,6,5,5,5,5,3,2,1,1,1] (.node [9,6,5,5,5,5,2,2,2,2] .empty .empty) (.node [9,6,5,5,5,5,3,2,2,1] .empty .empty)))) + +def degreeTree43_143 : RowTree := (.node [9,6,5,5,5,3,3,3,3,1] degreeTree43_141 degreeTree43_142) + +def degreeTree43_144 : RowTree := (.node [9,6,6,4,4,3,3,3,3,2] (.node [9,6,6,3,3,3,3,3,3,2,2] (.node [9,6,5,5,5,5,4,2,2] (.node [9,6,5,5,5,5,4,1,1,1,1] (.node [9,6,5,5,5,5,3,3,2] .empty .empty) (.node [9,6,5,5,5,5,4,2,1,1] .empty .empty)) (.node [9,6,5,5,5,5,5,1,1,1] (.node [9,6,5,5,5,5,4,3,1] .empty .empty) (.node [9,6,5,5,5,5,5,2,1] .empty .empty))) (.node [9,6,6,4,3,3,3,3,3,3] (.node [9,6,6,4,3,3,3,3,2,2,2] (.node [9,6,6,3,3,3,3,3,3,3,1] .empty .empty) (.node [9,6,6,4,3,3,3,3,3,2,1] .empty .empty)) (.node [9,6,6,4,4,3,3,3,2,2,1] (.node [9,6,6,4,4,3,3,2,2,2,2] .empty .empty) (.node [9,6,6,4,4,3,3,3,3,1,1] .empty .empty)))) (.node [9,6,6,4,4,4,4,3,1,1,1] (.node [9,6,6,4,4,4,3,3,2,2] (.node [9,6,6,4,4,4,3,2,2,2,1] (.node [9,6,6,4,4,4,2,2,2,2,2] .empty .empty) (.node [9,6,6,4,4,4,3,3,2,1,1] .empty .empty)) (.node [9,6,6,4,4,4,4,2,2,1,1] (.node [9,6,6,4,4,4,3,3,3,1] .empty .empty) (.node [9,6,6,4,4,4,4,2,2,2] .empty .empty))) (.node [9,6,6,4,4,4,4,4,2] (.node [9,6,6,4,4,4,4,3,3] (.node [9,6,6,4,4,4,4,3,2,1] .empty .empty) (.node [9,6,6,4,4,4,4,4,1,1] .empty .empty)) (.node [9,6,6,5,3,3,3,3,2,2,1] (.node [9,6,6,5,3,3,3,2,2,2,2] .empty .empty) (.node [9,6,6,5,3,3,3,3,3,1,1] .empty .empty))))) + +def degreeTree43_145 : RowTree := (.node [9,6,5,5,5,5,3,3,1,1] degreeTree43_143 degreeTree43_144) + +def degreeTree43_146 : RowTree := (.node [9,6,6,5,4,4,4,4,1] (.node [9,6,6,5,4,4,3,2,2,2] (.node [9,6,6,5,4,3,3,3,2,2] (.node [9,6,6,5,4,3,3,2,2,2,1] (.node [9,6,6,5,4,3,2,2,2,2,2] .empty .empty) (.node [9,6,6,5,4,3,3,3,2,1,1] .empty .empty)) (.node [9,6,6,5,4,4,2,2,2,2,1] (.node [9,6,6,5,4,3,3,3,3,1] .empty .empty) (.node [9,6,6,5,4,4,3,2,2,1,1] .empty .empty))) (.node [9,6,6,5,4,4,4,2,1,1,1] (.node [9,6,6,5,4,4,3,3,2,1] (.node [9,6,6,5,4,4,3,3,1,1,1] .empty .empty) (.node [9,6,6,5,4,4,3,3,3] .empty .empty)) (.node [9,6,6,5,4,4,4,3,1,1] (.node [9,6,6,5,4,4,4,2,2,1] .empty .empty) (.node [9,6,6,5,4,4,4,3,2] .empty .empty)))) (.node [9,6,6,5,5,4,2,2,2,1,1] (.node [9,6,6,5,5,3,3,2,2,2] (.node [9,6,6,5,5,3,2,2,2,2,1] (.node [9,6,6,5,5,2,2,2,2,2,2] .empty .empty) (.node [9,6,6,5,5,3,3,2,2,1,1] .empty .empty)) (.node [9,6,6,5,5,3,3,3,2,1] (.node [9,6,6,5,5,3,3,3,1,1,1] .empty .empty) (.node [9,6,6,5,5,3,3,3,3] .empty .empty))) (.node [9,6,6,5,5,4,3,3,1,1] (.node [9,6,6,5,5,4,3,2,1,1,1] (.node [9,6,6,5,5,4,2,2,2,2] .empty .empty) (.node [9,6,6,5,5,4,3,2,2,1] .empty .empty)) (.node [9,6,6,5,5,4,4,1,1,1,1] (.node [9,6,6,5,5,4,3,3,2] .empty .empty) (.node [9,6,6,5,5,4,4,2,1,1] .empty .empty))))) + +def degreeTree43_147 : RowTree := (.node [9,6,6,6,4,2,2,2,2,2,2] (.node [9,6,6,5,5,5,4,1,1,1] (.node [9,6,6,5,5,5,3,1,1,1,1] (.node [9,6,6,5,5,5,2,2,1,1,1] (.node [9,6,6,5,5,4,4,3,1] .empty .empty) (.node [9,6,6,5,5,5,2,2,2,1] .empty .empty)) (.node [9,6,6,5,5,5,3,2,2] (.node [9,6,6,5,5,5,3,2,1,1] .empty .empty) (.node [9,6,6,5,5,5,3,3,1] .empty .empty))) (.node [9,6,6,6,3,3,3,2,2,2,1] (.node [9,6,6,5,5,5,5,1,1] (.node [9,6,6,5,5,5,4,2,1] .empty .empty) (.node [9,6,6,6,3,3,2,2,2,2,2] .empty .empty)) (.node [9,6,6,6,3,3,3,3,2,2] (.node [9,6,6,6,3,3,3,3,2,1,1] .empty .empty) (.node [9,6,6,6,3,3,3,3,3,1] .empty .empty)))) (.node [9,6,6,6,4,4,2,2,2,2] (.node [9,6,6,6,4,3,3,3,1,1,1] (.node [9,6,6,6,4,3,3,2,2,1,1] (.node [9,6,6,6,4,3,2,2,2,2,1] .empty .empty) (.node [9,6,6,6,4,3,3,2,2,2] .empty .empty)) (.node [9,6,6,6,4,3,3,3,3] (.node [9,6,6,6,4,3,3,3,2,1] .empty .empty) (.node [9,6,6,6,4,4,2,2,2,1,1] .empty .empty))) (.node [9,6,6,6,4,4,3,3,2] (.node [9,6,6,6,4,4,3,2,2,1] (.node [9,6,6,6,4,4,3,2,1,1,1] .empty .empty) (.node [9,6,6,6,4,4,3,3,1,1] .empty .empty)) (.node [9,6,6,6,4,4,4,2,1,1] (.node [9,6,6,6,4,4,4,1,1,1,1] .empty .empty) (.node [9,6,6,6,4,4,4,2,2] .empty .empty))))) + +def degreeTree43_148 : RowTree := (.node [9,6,6,5,5,4,4,2,2] degreeTree43_146 degreeTree43_147) + +def degreeTree43_149 : RowTree := (.node [9,6,6,5,3,3,3,3,3,2] degreeTree43_145 degreeTree43_148) + +def degreeTree43_150 : RowTree := (.node [9,6,6,6,5,4,2,2,2,1] (.node [9,6,6,6,5,3,3,2,2,1] (.node [9,6,6,6,5,3,2,2,2,2] (.node [9,6,6,6,5,3,2,2,2,1,1] (.node [9,6,6,6,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [9,6,6,6,5,3,3,2,1,1,1] .empty .empty)) (.node [9,6,6,6,5,3,3,3,2] (.node [9,6,6,6,5,3,3,3,1,1] .empty .empty) (.node [9,6,6,6,5,4,2,2,1,1,1] .empty .empty))) (.node [9,6,6,6,5,4,3,3,1] (.node [9,6,6,6,5,4,3,2,1,1] (.node [9,6,6,6,5,4,3,1,1,1,1] .empty .empty) (.node [9,6,6,6,5,4,3,2,2] .empty .empty)) (.node [9,6,6,6,5,4,4,2,1] (.node [9,6,6,6,5,4,4,1,1,1] .empty .empty) (.node [9,6,6,6,5,5,2,1,1,1,1] .empty .empty)))) + +def degreeTree43_151 : RowTree := (.node [9,6,6,6,6,2,2,2,1,1,1,1] (.node [9,6,6,6,5,5,4,1,1] (.node [9,6,6,6,5,5,3,1,1,1] (.node [9,6,6,6,5,5,2,2,2] .empty .empty) (.node [9,6,6,6,5,5,3,2,1] .empty .empty)) (.node [9,6,6,6,6,2,1,1,1,1,1,1,1,1] (.node [9,6,6,6,6,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,6,6,6,6,2,2,1,1,1,1,1,1] .empty .empty))) (.node [9,6,6,6,6,3,2,1,1,1,1,1] (.node [9,6,6,6,6,2,2,2,2,2] (.node [9,6,6,6,6,2,2,2,2,1,1] .empty .empty) (.node [9,6,6,6,6,3,1,1,1,1,1,1,1] .empty .empty)) (.node [9,6,6,6,6,3,2,2,2,1] (.node [9,6,6,6,6,3,2,2,1,1,1] .empty .empty) (.node [9,6,6,6,6,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree43_152 : RowTree := (.node [9,6,6,6,5,5,2,2,1,1] degreeTree43_150 degreeTree43_151) + +def degreeTree43_153 : RowTree := (.node [9,7,3,3,3,3,3,3,3,3,3] (.node [9,6,6,6,6,4,3,2,1] (.node [9,6,6,6,6,4,2,1,1,1,1] (.node [9,6,6,6,6,3,3,3,1] (.node [9,6,6,6,6,3,3,2,2] .empty .empty) (.node [9,6,6,6,6,4,1,1,1,1,1,1] .empty .empty)) (.node [9,6,6,6,6,4,2,2,2] (.node [9,6,6,6,6,4,2,2,1,1] .empty .empty) (.node [9,6,6,6,6,4,3,1,1,1] .empty .empty))) (.node [9,6,6,6,6,5,2,2,1] (.node [9,6,6,6,6,5,1,1,1,1,1] (.node [9,6,6,6,6,4,4,1,1] .empty .empty) (.node [9,6,6,6,6,5,2,1,1,1] .empty .empty)) (.node [9,6,6,6,6,6,1,1,1,1] (.node [9,6,6,6,6,5,3,1,1] .empty .empty) (.node [9,6,6,6,6,6,2,1,1] .empty .empty)))) (.node [9,7,4,4,4,4,3,3,2,2,1] (.node [9,7,4,4,4,3,3,3,2,2,2] (.node [9,7,4,4,3,3,3,3,3,2,2] (.node [9,7,4,3,3,3,3,3,3,3,2] .empty .empty) (.node [9,7,4,4,3,3,3,3,3,3,1] .empty .empty)) (.node [9,7,4,4,4,3,3,3,3,3] (.node [9,7,4,4,4,3,3,3,3,2,1] .empty .empty) (.node [9,7,4,4,4,4,3,2,2,2,2] .empty .empty))) (.node [9,7,4,4,4,4,4,3,2,1,1] (.node [9,7,4,4,4,4,3,3,3,2] (.node [9,7,4,4,4,4,3,3,3,1,1] .empty .empty) (.node [9,7,4,4,4,4,4,2,2,2,1] .empty .empty)) (.node [9,7,4,4,4,4,4,3,3,1] (.node [9,7,4,4,4,4,4,3,2,2] .empty .empty) (.node [9,7,4,4,4,4,4,4,1,1,1] .empty .empty))))) + +def degreeTree43_154 : RowTree := (.node [9,6,6,6,6,3,3,2,1,1] degreeTree43_152 degreeTree43_153) + +def degreeTree43_155 : RowTree := (.node [9,7,5,4,4,4,4,2,2,1,1] (.node [9,7,5,4,4,3,3,3,2,2,1] (.node [9,7,5,4,3,3,3,3,2,2,2] (.node [9,7,5,3,3,3,3,3,3,2,2] (.node [9,7,4,4,4,4,4,4,3] .empty .empty) (.node [9,7,5,3,3,3,3,3,3,3,1] .empty .empty)) (.node [9,7,5,4,3,3,3,3,3,3] (.node [9,7,5,4,3,3,3,3,3,2,1] .empty .empty) (.node [9,7,5,4,4,3,3,2,2,2,2] .empty .empty))) (.node [9,7,5,4,4,4,3,2,2,2,1] (.node [9,7,5,4,4,3,3,3,3,2] (.node [9,7,5,4,4,3,3,3,3,1,1] .empty .empty) (.node [9,7,5,4,4,4,2,2,2,2,2] .empty .empty)) (.node [9,7,5,4,4,4,3,3,2,2] (.node [9,7,5,4,4,4,3,3,2,1,1] .empty .empty) (.node [9,7,5,4,4,4,3,3,3,1] .empty .empty)))) (.node [9,7,5,5,3,3,3,3,2,2,1] (.node [9,7,5,4,4,4,4,3,3] (.node [9,7,5,4,4,4,4,3,1,1,1] (.node [9,7,5,4,4,4,4,2,2,2] .empty .empty) (.node [9,7,5,4,4,4,4,3,2,1] .empty .empty)) (.node [9,7,5,4,4,4,4,4,2] (.node [9,7,5,4,4,4,4,4,1,1] .empty .empty) (.node [9,7,5,5,3,3,3,2,2,2,2] .empty .empty))) (.node [9,7,5,5,4,3,3,2,2,2,1] (.node [9,7,5,5,3,3,3,3,3,2] (.node [9,7,5,5,3,3,3,3,3,1,1] .empty .empty) (.node [9,7,5,5,4,3,2,2,2,2,2] .empty .empty)) (.node [9,7,5,5,4,3,3,3,2,2] (.node [9,7,5,5,4,3,3,3,2,1,1] .empty .empty) (.node [9,7,5,5,4,3,3,3,3,1] .empty .empty))))) + +def degreeTree43_156 : RowTree := (.node [9,7,5,5,5,3,3,3,2,1] (.node [9,7,5,5,4,4,4,3,1,1] (.node [9,7,5,5,4,4,3,3,2,1] (.node [9,7,5,5,4,4,3,2,2,2] (.node [9,7,5,5,4,4,3,2,2,1,1] .empty .empty) (.node [9,7,5,5,4,4,3,3,1,1,1] .empty .empty)) (.node [9,7,5,5,4,4,4,2,1,1,1] (.node [9,7,5,5,4,4,3,3,3] .empty .empty) (.node [9,7,5,5,4,4,4,2,2,1] .empty .empty))) (.node [9,7,5,5,5,3,2,2,2,2,1] (.node [9,7,5,5,4,4,4,4,1] (.node [9,7,5,5,4,4,4,3,2] .empty .empty) (.node [9,7,5,5,5,2,2,2,2,2,2] .empty .empty)) (.node [9,7,5,5,5,3,3,2,2,2] (.node [9,7,5,5,5,3,3,2,2,1,1] .empty .empty) (.node [9,7,5,5,5,3,3,3,1,1,1] .empty .empty)))) (.node [9,7,5,5,5,4,4,1,1,1,1] (.node [9,7,5,5,5,4,3,2,1,1,1] (.node [9,7,5,5,5,4,2,2,2,1,1] (.node [9,7,5,5,5,3,3,3,3] .empty .empty) (.node [9,7,5,5,5,4,2,2,2,2] .empty .empty)) (.node [9,7,5,5,5,4,3,3,1,1] (.node [9,7,5,5,5,4,3,2,2,1] .empty .empty) (.node [9,7,5,5,5,4,3,3,2] .empty .empty))) (.node [9,7,5,5,5,5,2,2,1,1,1] (.node [9,7,5,5,5,4,4,2,2] (.node [9,7,5,5,5,4,4,2,1,1] .empty .empty) (.node [9,7,5,5,5,4,4,3,1] .empty .empty)) (.node [9,7,5,5,5,5,3,1,1,1,1] (.node [9,7,5,5,5,5,2,2,2,1] .empty .empty) (.node [9,7,5,5,5,5,3,2,1,1] .empty .empty))))) + +def degreeTree43_157 : RowTree := (.node [9,7,5,5,4,4,2,2,2,2,1] degreeTree43_155 degreeTree43_156) + +def degreeTree43_158 : RowTree := (.node [9,7,4,4,4,4,4,4,2,1] degreeTree43_154 degreeTree43_157) + +def degreeTree43_159 : RowTree := (.node [9,6,6,6,4,4,4,3,1] degreeTree43_149 degreeTree43_158) + +def degreeTree43_160 : RowTree := (.node [9,6,5,5,4,3,3,3,3,2] degreeTree43_140 degreeTree43_159) + +def degreeTree43_161 : RowTree := (.node [8,8,8,5,5,3,2,1,1,1,1] degreeTree43_121 degreeTree43_160) + +def degreeTree43_162 : RowTree := (.node [8,8,6,6,5,3,1,1,1,1,1,1,1] degreeTree43_80 degreeTree43_161) + +def degreeTree43_163 : RowTree := (.node [9,7,6,4,3,3,3,3,2,2,1] (.node [9,7,6,3,3,3,3,3,2,2,2] (.node [9,7,5,5,5,5,4,2,1] (.node [9,7,5,5,5,5,4,1,1,1] (.node [9,7,5,5,5,5,3,3,1] .empty .empty) .empty) (.node [9,7,5,5,5,5,5,1,1] .empty .empty)) (.node [9,7,6,3,3,3,3,3,3,3] (.node [9,7,6,3,3,3,3,3,3,2,1] .empty .empty) (.node [9,7,6,4,3,3,3,2,2,2,2] .empty .empty))) (.node [9,7,6,4,4,3,3,2,2,2,1] (.node [9,7,6,4,3,3,3,3,3,2] (.node [9,7,6,4,3,3,3,3,3,1,1] .empty .empty) (.node [9,7,6,4,4,3,2,2,2,2,2] .empty .empty)) (.node [9,7,6,4,4,3,3,3,2,2] (.node [9,7,6,4,4,3,3,3,2,1,1] .empty .empty) (.node [9,7,6,4,4,3,3,3,3,1] .empty .empty)))) + +def degreeTree43_164 : RowTree := (.node [9,7,6,4,4,4,4,3,1,1] (.node [9,7,6,4,4,4,3,3,2,1] (.node [9,7,6,4,4,4,3,2,2,2] (.node [9,7,6,4,4,4,3,2,2,1,1] .empty .empty) (.node [9,7,6,4,4,4,3,3,1,1,1] .empty .empty)) (.node [9,7,6,4,4,4,4,2,1,1,1] (.node [9,7,6,4,4,4,3,3,3] .empty .empty) (.node [9,7,6,4,4,4,4,2,2,1] .empty .empty))) (.node [9,7,6,5,3,3,3,2,2,2,1] (.node [9,7,6,4,4,4,4,4,1] (.node [9,7,6,4,4,4,4,3,2] .empty .empty) (.node [9,7,6,5,3,3,2,2,2,2,2] .empty .empty)) (.node [9,7,6,5,3,3,3,3,2,2] (.node [9,7,6,5,3,3,3,3,2,1,1] .empty .empty) (.node [9,7,6,5,3,3,3,3,3,1] .empty .empty)))) + +def degreeTree43_165 : RowTree := (.node [9,7,6,4,4,4,2,2,2,2,1] degreeTree43_163 degreeTree43_164) + +def degreeTree43_166 : RowTree := (.node [9,7,6,5,4,4,4,3,1] (.node [9,7,6,5,4,4,2,2,2,2] (.node [9,7,6,5,4,3,3,3,1,1,1] (.node [9,7,6,5,4,3,3,2,2,1,1] (.node [9,7,6,5,4,3,2,2,2,2,1] .empty .empty) (.node [9,7,6,5,4,3,3,2,2,2] .empty .empty)) (.node [9,7,6,5,4,3,3,3,3] (.node [9,7,6,5,4,3,3,3,2,1] .empty .empty) (.node [9,7,6,5,4,4,2,2,2,1,1] .empty .empty))) (.node [9,7,6,5,4,4,3,3,2] (.node [9,7,6,5,4,4,3,2,2,1] (.node [9,7,6,5,4,4,3,2,1,1,1] .empty .empty) (.node [9,7,6,5,4,4,3,3,1,1] .empty .empty)) (.node [9,7,6,5,4,4,4,2,1,1] (.node [9,7,6,5,4,4,4,1,1,1,1] .empty .empty) (.node [9,7,6,5,4,4,4,2,2] .empty .empty)))) (.node [9,7,6,5,5,4,2,2,1,1,1] (.node [9,7,6,5,5,3,3,2,1,1,1] (.node [9,7,6,5,5,3,2,2,2,1,1] (.node [9,7,6,5,5,2,2,2,2,2,1] .empty .empty) (.node [9,7,6,5,5,3,2,2,2,2] .empty .empty)) (.node [9,7,6,5,5,3,3,3,1,1] (.node [9,7,6,5,5,3,3,2,2,1] .empty .empty) (.node [9,7,6,5,5,3,3,3,2] .empty .empty))) (.node [9,7,6,5,5,4,3,2,2] (.node [9,7,6,5,5,4,3,1,1,1,1] (.node [9,7,6,5,5,4,2,2,2,1] .empty .empty) (.node [9,7,6,5,5,4,3,2,1,1] .empty .empty)) (.node [9,7,6,5,5,4,4,1,1,1] (.node [9,7,6,5,5,4,3,3,1] .empty .empty) (.node [9,7,6,5,5,4,4,2,1] .empty .empty))))) + +def degreeTree43_167 : RowTree := (.node [9,7,6,5,4,2,2,2,2,2,2] degreeTree43_165 degreeTree43_166) + +def degreeTree43_168 : RowTree := (.node [9,7,6,6,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,7,6,5,5,5,4,1,1] (.node [9,7,6,5,5,5,3,1,1,1] (.node [9,7,6,5,5,5,2,2,2] (.node [9,7,6,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [9,7,6,5,5,5,3,2,1] .empty .empty)) (.node [9,7,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,6,6,2,2,2,2,2,2,2,1] (.node [9,7,6,6,2,2,2,2,2,1,1,1,1,1] (.node [9,7,6,6,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,7,6,6,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,7,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,3,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_169 : RowTree := (.node [9,7,6,6,3,3,2,2,2,2,1] (.node [9,7,6,6,3,3,1,1,1,1,1,1,1,1,1] (.node [9,7,6,6,3,2,2,2,2,2,1,1] (.node [9,7,6,6,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,7,6,6,3,2,2,2,2,2,2] .empty .empty)) (.node [9,7,6,6,3,3,2,2,1,1,1,1,1] (.node [9,7,6,6,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,3,3,2,2,2,1,1,1] .empty .empty))) (.node [9,7,6,6,3,3,3,2,2,2] (.node [9,7,6,6,3,3,3,2,1,1,1,1] (.node [9,7,6,6,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,3,3,3,2,2,1,1] .empty .empty)) (.node [9,7,6,6,3,3,3,3,2,1] (.node [9,7,6,6,3,3,3,3,1,1,1] .empty .empty) (.node [9,7,6,6,3,3,3,3,3] .empty .empty)))) + +def degreeTree43_170 : RowTree := (.node [9,7,6,6,3,2,2,2,1,1,1,1,1,1] degreeTree43_168 degreeTree43_169) + +def degreeTree43_171 : RowTree := (.node [9,7,6,6,4,4,1,1,1,1,1,1,1] (.node [9,7,6,6,4,3,2,2,1,1,1,1] (.node [9,7,6,6,4,2,2,2,2,1,1,1] (.node [9,7,6,6,4,2,2,1,1,1,1,1,1,1] (.node [9,7,6,6,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,4,2,2,2,1,1,1,1,1] .empty .empty)) (.node [9,7,6,6,4,3,1,1,1,1,1,1,1,1] (.node [9,7,6,6,4,2,2,2,2,2,1] .empty .empty) (.node [9,7,6,6,4,3,2,1,1,1,1,1,1] .empty .empty))) (.node [9,7,6,6,4,3,3,2,1,1,1] (.node [9,7,6,6,4,3,2,2,2,2] (.node [9,7,6,6,4,3,2,2,2,1,1] .empty .empty) (.node [9,7,6,6,4,3,3,1,1,1,1,1] .empty .empty)) (.node [9,7,6,6,4,3,3,3,1,1] (.node [9,7,6,6,4,3,3,2,2,1] .empty .empty) (.node [9,7,6,6,4,3,3,3,2] .empty .empty)))) (.node [9,7,6,6,4,4,4,1,1,1] (.node [9,7,6,6,4,4,3,1,1,1,1] (.node [9,7,6,6,4,4,2,2,1,1,1] (.node [9,7,6,6,4,4,2,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,4,4,2,2,2,1] .empty .empty)) (.node [9,7,6,6,4,4,3,2,2] (.node [9,7,6,6,4,4,3,2,1,1] .empty .empty) (.node [9,7,6,6,4,4,3,3,1] .empty .empty))) (.node [9,7,6,6,5,2,2,1,1,1,1,1,1] (.node [9,7,6,6,5,1,1,1,1,1,1,1,1,1,1] (.node [9,7,6,6,4,4,4,2,1] .empty .empty) (.node [9,7,6,6,5,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,6,6,5,2,2,2,2,1,1] (.node [9,7,6,6,5,2,2,2,1,1,1,1] .empty .empty) (.node [9,7,6,6,5,2,2,2,2,2] .empty .empty))))) + +def degreeTree43_172 : RowTree := (.node [9,7,6,6,4,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_170 degreeTree43_171) + +def degreeTree43_173 : RowTree := (.node [9,7,6,5,5,5,2,1,1,1,1] degreeTree43_167 degreeTree43_172) + +def degreeTree43_174 : RowTree := (.node [9,7,6,6,5,4,2,1,1,1,1] (.node [9,7,6,6,5,3,3,2,1,1] (.node [9,7,6,6,5,3,2,2,2,1] (.node [9,7,6,6,5,3,2,2,1,1,1] (.node [9,7,6,6,5,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [9,7,6,6,5,3,3,1,1,1,1] .empty .empty)) (.node [9,7,6,6,5,3,3,3,1] (.node [9,7,6,6,5,3,3,2,2] .empty .empty) (.node [9,7,6,6,5,4,1,1,1,1,1,1] .empty .empty))) (.node [9,7,6,6,5,4,3,2,1] (.node [9,7,6,6,5,4,2,2,2] (.node [9,7,6,6,5,4,2,2,1,1] .empty .empty) (.node [9,7,6,6,5,4,3,1,1,1] .empty .empty)) (.node [9,7,6,6,5,5,1,1,1,1,1] (.node [9,7,6,6,5,4,4,1,1] .empty .empty) (.node [9,7,6,6,5,5,2,1,1,1] .empty .empty)))) + +def degreeTree43_175 : RowTree := (.node [9,7,6,6,6,3,2,1,1,1,1] (.node [9,7,6,6,6,2,2,1,1,1,1,1] (.node [9,7,6,6,6,1,1,1,1,1,1,1,1,1] (.node [9,7,6,6,5,5,3,1,1] .empty .empty) (.node [9,7,6,6,6,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,6,6,6,2,2,2,2,1] (.node [9,7,6,6,6,2,2,2,1,1,1] .empty .empty) (.node [9,7,6,6,6,3,1,1,1,1,1,1] .empty .empty))) (.node [9,7,6,6,6,3,3,2,1] (.node [9,7,6,6,6,3,2,2,2] (.node [9,7,6,6,6,3,2,2,1,1] .empty .empty) (.node [9,7,6,6,6,3,3,1,1,1] .empty .empty)) (.node [9,7,6,6,6,4,2,1,1,1] (.node [9,7,6,6,6,4,1,1,1,1,1] .empty .empty) (.node [9,7,6,6,6,4,2,2,1] .empty .empty)))) + +def degreeTree43_176 : RowTree := (.node [9,7,6,6,5,5,2,2,1] degreeTree43_174 degreeTree43_175) + +def degreeTree43_177 : RowTree := (.node [9,7,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,6,6,6,5,2,1,1] (.node [9,7,6,6,6,5,1,1,1,1] .empty .empty) (.node [9,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,7,2,2,2,2,2,2,2,2,2,1,1] (.node [9,7,7,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [9,7,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [9,7,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [9,7,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,7,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,3,2,2,2,2,2,2,1,1,1,1,1] (.node [9,7,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,7,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,3,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,3,2,2,2,2,2,2,2,2,1] (.node [9,7,7,3,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,7,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,7,3,3,2,2,2,2,2,1,1,1,1] (.node [9,7,7,3,3,2,2,2,1,1,1,1,1,1,1,1] (.node [9,7,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,3,3,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,3,3,2,2,2,2,2,2,2] (.node [9,7,7,3,3,2,2,2,2,2,2,1,1] .empty .empty) (.node [9,7,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_178 : RowTree := (.node [9,7,6,6,6,4,3,1,1] degreeTree43_176 degreeTree43_177) + +def degreeTree43_179 : RowTree := (.node [9,7,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,3,3,3,3,2,2,2,1,1] (.node [9,7,7,3,3,3,2,2,2,2,2,1] (.node [9,7,7,3,3,3,2,2,2,1,1,1,1,1] (.node [9,7,7,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,3,3,3,2,2,2,2,1,1,1] .empty .empty)) (.node [9,7,7,3,3,3,3,2,1,1,1,1,1,1] (.node [9,7,7,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,3,3,3,3,2,2,1,1,1,1] .empty .empty))) (.node [9,7,7,3,3,3,3,3,2,2,1] (.node [9,7,7,3,3,3,3,3,1,1,1,1,1] (.node [9,7,7,3,3,3,3,2,2,2,2] .empty .empty) (.node [9,7,7,3,3,3,3,3,2,1,1,1] .empty .empty)) (.node [9,7,7,3,3,3,3,3,3,2] (.node [9,7,7,3,3,3,3,3,3,1,1] .empty .empty) (.node [9,7,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,7,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,4,2,2,2,2,2,1,1,1,1,1,1] (.node [9,7,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,4,2,2,2,2,2,2,2,1,1] (.node [9,7,7,4,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,4,2,2,2,2,2,2,2,2] .empty .empty))) (.node [9,7,7,4,3,2,2,2,2,1,1,1,1,1] (.node [9,7,7,4,3,2,2,1,1,1,1,1,1,1,1,1] (.node [9,7,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,3,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,4,3,2,2,2,2,2,2,1] (.node [9,7,7,4,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,7,7,4,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_180 : RowTree := (.node [9,7,7,4,4,2,2,2,1,1,1,1,1,1] (.node [9,7,7,4,3,3,3,2,2,2,1] (.node [9,7,7,4,3,3,2,2,2,2,2] (.node [9,7,7,4,3,3,2,2,2,1,1,1,1] (.node [9,7,7,4,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,3,3,2,2,2,2,1,1] .empty .empty)) (.node [9,7,7,4,3,3,3,2,1,1,1,1,1] (.node [9,7,7,4,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,3,3,3,2,2,1,1,1] .empty .empty))) (.node [9,7,7,4,3,3,3,3,3,1] (.node [9,7,7,4,3,3,3,3,2,1,1] (.node [9,7,7,4,3,3,3,3,1,1,1,1] .empty .empty) (.node [9,7,7,4,3,3,3,3,2,2] .empty .empty)) (.node [9,7,7,4,4,2,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,4,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,7,7,4,4,3,2,2,2,2,1] (.node [9,7,7,4,4,3,1,1,1,1,1,1,1,1,1] (.node [9,7,7,4,4,2,2,2,2,2,1,1] (.node [9,7,7,4,4,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,4,4,2,2,2,2,2,2] .empty .empty)) (.node [9,7,7,4,4,3,2,2,1,1,1,1,1] (.node [9,7,7,4,4,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,4,3,2,2,2,1,1,1] .empty .empty))) (.node [9,7,7,4,4,3,3,2,2,2] (.node [9,7,7,4,4,3,3,2,1,1,1,1] (.node [9,7,7,4,4,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,4,4,3,3,2,2,1,1] .empty .empty)) (.node [9,7,7,4,4,3,3,3,2,1] (.node [9,7,7,4,4,3,3,3,1,1,1] .empty .empty) (.node [9,7,7,4,4,3,3,3,3] .empty .empty))))) + +def degreeTree43_181 : RowTree := (.node [9,7,7,4,3,3,2,1,1,1,1,1,1,1,1] degreeTree43_179 degreeTree43_180) + +def degreeTree43_182 : RowTree := (.node [9,7,7,3,3,3,2,1,1,1,1,1,1,1,1,1] degreeTree43_178 degreeTree43_181) + +def degreeTree43_183 : RowTree := (.node [9,7,6,6,5,3,1,1,1,1,1,1,1] degreeTree43_173 degreeTree43_182) + +def degreeTree43_184 : RowTree := (.node [9,7,7,4,4,4,3,3,2] (.node [9,7,7,4,4,4,3,1,1,1,1,1] (.node [9,7,7,4,4,4,2,2,2,1,1] (.node [9,7,7,4,4,4,2,2,1,1,1,1] (.node [9,7,7,4,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,7,7,4,4,4,2,2,2,2] .empty .empty)) (.node [9,7,7,4,4,4,3,2,2,1] (.node [9,7,7,4,4,4,3,2,1,1,1] .empty .empty) (.node [9,7,7,4,4,4,3,3,1,1] .empty .empty))) (.node [9,7,7,4,4,4,4,3,1] (.node [9,7,7,4,4,4,4,2,1,1] (.node [9,7,7,4,4,4,4,1,1,1,1] .empty .empty) (.node [9,7,7,4,4,4,4,2,2] .empty .empty)) (.node [9,7,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_185 : RowTree := (.node [9,7,7,5,3,2,2,2,1,1,1,1,1,1] (.node [9,7,7,5,2,2,2,2,2,2,2,1] (.node [9,7,7,5,2,2,2,2,2,1,1,1,1,1] (.node [9,7,7,5,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,7,7,5,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,5,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,3,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,7,5,3,3,1,1,1,1,1,1,1,1,1] (.node [9,7,7,5,3,2,2,2,2,2,1,1] (.node [9,7,7,5,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,5,3,2,2,2,2,2,2] .empty .empty)) (.node [9,7,7,5,3,3,2,2,1,1,1,1,1] (.node [9,7,7,5,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,3,3,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree43_186 : RowTree := (.node [9,7,7,5,2,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_184 degreeTree43_185) + +def degreeTree43_187 : RowTree := (.node [9,7,7,5,4,3,2,2,1,1,1,1] (.node [9,7,7,5,4,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,5,3,3,3,2,2,2] (.node [9,7,7,5,3,3,3,2,1,1,1,1] (.node [9,7,7,5,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,3,3,3,2,2,1,1] .empty .empty)) (.node [9,7,7,5,3,3,3,3,2,1] (.node [9,7,7,5,3,3,3,3,1,1,1] .empty .empty) (.node [9,7,7,5,3,3,3,3,3] .empty .empty))) (.node [9,7,7,5,4,2,2,2,2,1,1,1] (.node [9,7,7,5,4,2,2,1,1,1,1,1,1,1] (.node [9,7,7,5,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,4,2,2,2,1,1,1,1,1] .empty .empty)) (.node [9,7,7,5,4,3,1,1,1,1,1,1,1,1] (.node [9,7,7,5,4,2,2,2,2,2,1] .empty .empty) (.node [9,7,7,5,4,3,2,1,1,1,1,1,1] .empty .empty)))) (.node [9,7,7,5,4,4,1,1,1,1,1,1,1] (.node [9,7,7,5,4,3,3,2,1,1,1] (.node [9,7,7,5,4,3,2,2,2,2] (.node [9,7,7,5,4,3,2,2,2,1,1] .empty .empty) (.node [9,7,7,5,4,3,3,1,1,1,1,1] .empty .empty)) (.node [9,7,7,5,4,3,3,3,1,1] (.node [9,7,7,5,4,3,3,2,2,1] .empty .empty) (.node [9,7,7,5,4,3,3,3,2] .empty .empty))) (.node [9,7,7,5,4,4,3,1,1,1,1] (.node [9,7,7,5,4,4,2,2,1,1,1] (.node [9,7,7,5,4,4,2,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,4,4,2,2,2,1] .empty .empty)) (.node [9,7,7,5,4,4,3,2,2] (.node [9,7,7,5,4,4,3,2,1,1] .empty .empty) (.node [9,7,7,5,4,4,3,3,1] .empty .empty))))) + +def degreeTree43_188 : RowTree := (.node [9,7,7,5,3,3,2,2,2,2,1] degreeTree43_186 degreeTree43_187) + +def degreeTree43_189 : RowTree := (.node [9,7,7,5,5,4,1,1,1,1,1,1] (.node [9,7,7,5,5,3,1,1,1,1,1,1,1] (.node [9,7,7,5,5,2,2,1,1,1,1,1,1] (.node [9,7,7,5,5,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,5,4,4,4,2,1] .empty .empty) (.node [9,7,7,5,5,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,5,5,2,2,2,2,1,1] (.node [9,7,7,5,5,2,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,5,5,2,2,2,2,2] .empty .empty))) (.node [9,7,7,5,5,3,3,1,1,1,1] (.node [9,7,7,5,5,3,2,2,1,1,1] (.node [9,7,7,5,5,3,2,1,1,1,1,1] .empty .empty) (.node [9,7,7,5,5,3,2,2,2,1] .empty .empty)) (.node [9,7,7,5,5,3,3,2,2] (.node [9,7,7,5,5,3,3,2,1,1] .empty .empty) (.node [9,7,7,5,5,3,3,3,1] .empty .empty)))) (.node [9,7,7,5,5,5,2,1,1,1] (.node [9,7,7,5,5,4,3,1,1,1] (.node [9,7,7,5,5,4,2,2,1,1] (.node [9,7,7,5,5,4,2,1,1,1,1] .empty .empty) (.node [9,7,7,5,5,4,2,2,2] .empty .empty)) (.node [9,7,7,5,5,4,4,1,1] (.node [9,7,7,5,5,4,3,2,1] .empty .empty) (.node [9,7,7,5,5,5,1,1,1,1,1] .empty .empty))) (.node [9,7,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,7,7,5,5,5,3,1,1] (.node [9,7,7,5,5,5,2,2,1] .empty .empty) (.node [9,7,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,6,2,2,2,1,1,1,1,1,1,1,1] (.node [9,7,7,6,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,6,2,2,2,2,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_190 : RowTree := (.node [9,7,7,6,3,3,3,2,2,1] (.node [9,7,7,6,3,2,2,2,2,2,1] (.node [9,7,7,6,3,2,1,1,1,1,1,1,1,1,1] (.node [9,7,7,6,2,2,2,2,2,2,2] (.node [9,7,7,6,2,2,2,2,2,2,1,1] .empty .empty) (.node [9,7,7,6,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,6,3,2,2,2,1,1,1,1,1] (.node [9,7,7,6,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,6,3,2,2,2,2,1,1,1] .empty .empty))) (.node [9,7,7,6,3,3,2,2,2,1,1] (.node [9,7,7,6,3,3,2,1,1,1,1,1,1] (.node [9,7,7,6,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,6,3,3,2,2,1,1,1,1] .empty .empty)) (.node [9,7,7,6,3,3,3,1,1,1,1,1] (.node [9,7,7,6,3,3,2,2,2,2] .empty .empty) (.node [9,7,7,6,3,3,3,2,1,1,1] .empty .empty)))) (.node [9,7,7,6,4,2,2,2,2,2] (.node [9,7,7,6,4,2,1,1,1,1,1,1,1,1] (.node [9,7,7,6,3,3,3,3,2] (.node [9,7,7,6,3,3,3,3,1,1] .empty .empty) (.node [9,7,7,6,4,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,6,4,2,2,2,1,1,1,1] (.node [9,7,7,6,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,6,4,2,2,2,2,1,1] .empty .empty))) (.node [9,7,7,6,4,3,2,2,2,1] (.node [9,7,7,6,4,3,2,1,1,1,1,1] (.node [9,7,7,6,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,6,4,3,2,2,1,1,1] .empty .empty)) (.node [9,7,7,6,4,3,3,2,1,1] (.node [9,7,7,6,4,3,3,1,1,1,1] .empty .empty) (.node [9,7,7,6,4,3,3,2,2] .empty .empty))))) + +def degreeTree43_191 : RowTree := (.node [9,7,7,6,2,2,2,2,2,1,1,1,1] degreeTree43_189 degreeTree43_190) + +def degreeTree43_192 : RowTree := (.node [9,7,7,5,4,4,4,1,1,1] degreeTree43_188 degreeTree43_191) + +def degreeTree43_193 : RowTree := (.node [9,7,7,6,5,2,1,1,1,1,1,1,1] (.node [9,7,7,6,4,4,3,1,1,1] (.node [9,7,7,6,4,4,2,2,1,1] (.node [9,7,7,6,4,4,2,1,1,1,1] (.node [9,7,7,6,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,7,7,6,4,4,2,2,2] .empty .empty)) (.node [9,7,7,6,4,4,4,1,1] (.node [9,7,7,6,4,4,3,2,1] .empty .empty) (.node [9,7,7,6,5,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,7,6,5,3,1,1,1,1,1,1] (.node [9,7,7,6,5,2,2,2,1,1,1] (.node [9,7,7,6,5,2,2,1,1,1,1,1] .empty .empty) (.node [9,7,7,6,5,2,2,2,2,1] .empty .empty)) (.node [9,7,7,6,5,3,2,2,1,1] (.node [9,7,7,6,5,3,2,1,1,1,1] .empty .empty) (.node [9,7,7,6,5,3,2,2,2] .empty .empty)))) + +def degreeTree43_194 : RowTree := (.node [9,7,7,6,6,2,1,1,1,1,1,1] (.node [9,7,7,6,5,4,2,2,1] (.node [9,7,7,6,5,4,1,1,1,1,1] (.node [9,7,7,6,5,3,3,2,1] .empty .empty) (.node [9,7,7,6,5,4,2,1,1,1] .empty .empty)) (.node [9,7,7,6,5,5,1,1,1,1] (.node [9,7,7,6,5,4,3,1,1] .empty .empty) (.node [9,7,7,6,6,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,7,6,6,3,1,1,1,1,1] (.node [9,7,7,6,6,2,2,2,1,1] (.node [9,7,7,6,6,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,6,6,2,2,2,2] .empty .empty)) (.node [9,7,7,6,6,3,2,2,1] (.node [9,7,7,6,6,3,2,1,1,1] .empty .empty) (.node [9,7,7,6,6,4,1,1,1,1] .empty .empty)))) + +def degreeTree43_195 : RowTree := (.node [9,7,7,6,5,3,3,1,1,1] degreeTree43_193 degreeTree43_194) + +def degreeTree43_196 : RowTree := (.node [9,7,7,7,3,3,2,2,2,1] (.node [9,7,7,7,3,2,1,1,1,1,1,1,1,1] (.node [9,7,7,7,2,2,2,2,1,1,1,1,1] (.node [9,7,7,7,2,2,1,1,1,1,1,1,1,1,1] (.node [9,7,7,7,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,7,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,7,2,2,2,2,2,2,1] (.node [9,7,7,7,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,7,7,7,3,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,7,7,7,3,2,2,2,2,2] (.node [9,7,7,7,3,2,2,2,1,1,1,1] (.node [9,7,7,7,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,7,3,2,2,2,2,1,1] .empty .empty)) (.node [9,7,7,7,3,3,2,1,1,1,1,1] (.node [9,7,7,7,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,7,3,3,2,2,1,1,1] .empty .empty)))) (.node [9,7,7,7,4,2,2,2,1,1,1] (.node [9,7,7,7,3,3,3,3,1] (.node [9,7,7,7,3,3,3,2,1,1] (.node [9,7,7,7,3,3,3,1,1,1,1] .empty .empty) (.node [9,7,7,7,3,3,3,2,2] .empty .empty)) (.node [9,7,7,7,4,2,1,1,1,1,1,1,1] (.node [9,7,7,7,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,7,7,7,4,2,2,1,1,1,1,1] .empty .empty))) (.node [9,7,7,7,4,3,2,2,1,1] (.node [9,7,7,7,4,3,1,1,1,1,1,1] (.node [9,7,7,7,4,2,2,2,2,1] .empty .empty) (.node [9,7,7,7,4,3,2,1,1,1,1] .empty .empty)) (.node [9,7,7,7,4,3,3,1,1,1] (.node [9,7,7,7,4,3,2,2,2] .empty .empty) (.node [9,7,7,7,4,3,3,2,1] .empty .empty))))) + +def degreeTree43_197 : RowTree := (.node [9,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_195 degreeTree43_196) + +def degreeTree43_198 : RowTree := (.node [9,7,7,7,6,3,1,1,1,1] (.node [9,7,7,7,5,3,1,1,1,1,1] (.node [9,7,7,7,5,2,1,1,1,1,1,1] (.node [9,7,7,7,4,4,2,2,1] (.node [9,7,7,7,4,4,2,1,1,1] .empty .empty) (.node [9,7,7,7,5,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,7,7,7,5,2,2,2,1,1] (.node [9,7,7,7,5,2,2,1,1,1,1] .empty .empty) (.node [9,7,7,7,5,2,2,2,2] .empty .empty))) (.node [9,7,7,7,6,1,1,1,1,1,1,1] (.node [9,7,7,7,5,3,2,2,1] (.node [9,7,7,7,5,3,2,1,1,1] .empty .empty) (.node [9,7,7,7,5,4,1,1,1,1] .empty .empty)) (.node [9,7,7,7,6,2,2,1,1,1] (.node [9,7,7,7,6,2,1,1,1,1,1] .empty .empty) (.node [9,7,7,7,6,2,2,2,1] .empty .empty)))) (.node [9,8,4,4,3,3,3,3,3,3] (.node [9,8,4,3,3,3,3,3,3,2,2] (.node [9,7,7,7,7,2,1,1,1,1] (.node [9,7,7,7,7,1,1,1,1,1,1] .empty .empty) (.node [9,8,3,3,3,3,3,3,3,3,2] .empty .empty)) (.node [9,8,4,4,3,3,3,3,2,2,2] (.node [9,8,4,3,3,3,3,3,3,3,1] .empty .empty) (.node [9,8,4,4,3,3,3,3,3,2,1] .empty .empty))) (.node [9,8,4,4,4,3,3,3,3,2] (.node [9,8,4,4,4,3,3,3,2,2,1] (.node [9,8,4,4,4,3,3,2,2,2,2] .empty .empty) (.node [9,8,4,4,4,3,3,3,3,1,1] .empty .empty)) (.node [9,8,4,4,4,4,3,2,2,2,1] (.node [9,8,4,4,4,4,2,2,2,2,2] .empty .empty) (.node [9,8,4,4,4,4,3,3,2,1,1] .empty .empty))))) + +def degreeTree43_199 : RowTree := (.node [9,8,5,4,4,3,2,2,2,2,2] (.node [9,8,4,4,4,4,4,4,2] (.node [9,8,4,4,4,4,4,3,1,1,1] (.node [9,8,4,4,4,4,4,2,2,1,1] (.node [9,8,4,4,4,4,3,3,3,1] .empty .empty) (.node [9,8,4,4,4,4,4,2,2,2] .empty .empty)) (.node [9,8,4,4,4,4,4,3,3] (.node [9,8,4,4,4,4,4,3,2,1] .empty .empty) (.node [9,8,4,4,4,4,4,4,1,1] .empty .empty))) (.node [9,8,5,4,3,3,3,2,2,2,2] (.node [9,8,5,3,3,3,3,3,3,2,1] (.node [9,8,5,3,3,3,3,3,2,2,2] .empty .empty) (.node [9,8,5,3,3,3,3,3,3,3] .empty .empty)) (.node [9,8,5,4,3,3,3,3,3,1,1] (.node [9,8,5,4,3,3,3,3,2,2,1] .empty .empty) (.node [9,8,5,4,3,3,3,3,3,2] .empty .empty)))) (.node [9,8,5,4,4,4,3,3,1,1,1] (.node [9,8,5,4,4,3,3,3,3,1] (.node [9,8,5,4,4,3,3,3,2,1,1] (.node [9,8,5,4,4,3,3,2,2,2,1] .empty .empty) (.node [9,8,5,4,4,3,3,3,2,2] .empty .empty)) (.node [9,8,5,4,4,4,3,2,2,1,1] (.node [9,8,5,4,4,4,2,2,2,2,1] .empty .empty) (.node [9,8,5,4,4,4,3,2,2,2] .empty .empty))) (.node [9,8,5,4,4,4,4,2,2,1] (.node [9,8,5,4,4,4,3,3,3] (.node [9,8,5,4,4,4,3,3,2,1] .empty .empty) (.node [9,8,5,4,4,4,4,2,1,1,1] .empty .empty)) (.node [9,8,5,4,4,4,4,3,2] (.node [9,8,5,4,4,4,4,3,1,1] .empty .empty) (.node [9,8,5,4,4,4,4,4,1] .empty .empty))))) + +def degreeTree43_200 : RowTree := (.node [9,8,4,4,4,4,3,3,2,2] degreeTree43_198 degreeTree43_199) + +def degreeTree43_201 : RowTree := (.node [9,7,7,7,4,4,1,1,1,1,1] degreeTree43_197 degreeTree43_200) + +def degreeTree43_202 : RowTree := (.node [9,7,7,6,4,3,3,3,1] degreeTree43_192 degreeTree43_201) + +def degreeTree43_203 : RowTree := (.node [9,7,7,4,4,4,1,1,1,1,1,1,1,1] degreeTree43_183 degreeTree43_202) + +def degreeTree43_204 : RowTree := (.node [9,8,5,5,4,3,3,3,1,1,1] (.node [9,8,5,5,4,2,2,2,2,2,2] (.node [9,8,5,5,3,3,3,3,2,2] (.node [9,8,5,5,3,3,3,3,2,1,1] (.node [9,8,5,5,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [9,8,5,5,3,3,3,3,3,1] .empty .empty)) (.node [9,8,5,5,4,3,3,2,2,1,1] (.node [9,8,5,5,4,3,2,2,2,2,1] .empty .empty) (.node [9,8,5,5,4,3,3,2,2,2] .empty .empty))) (.node [9,8,5,5,4,4,2,2,2,2] (.node [9,8,5,5,4,3,3,3,3] (.node [9,8,5,5,4,3,3,3,2,1] .empty .empty) (.node [9,8,5,5,4,4,2,2,2,1,1] .empty .empty)) (.node [9,8,5,5,4,4,3,2,2,1] (.node [9,8,5,5,4,4,3,2,1,1,1] .empty .empty) (.node [9,8,5,5,4,4,3,3,1,1] .empty .empty)))) + +def degreeTree43_205 : RowTree := (.node [9,8,5,5,5,3,3,2,1,1,1] (.node [9,8,5,5,4,4,4,3,1] (.node [9,8,5,5,4,4,4,2,1,1] (.node [9,8,5,5,4,4,4,1,1,1,1] .empty .empty) (.node [9,8,5,5,4,4,4,2,2] .empty .empty)) (.node [9,8,5,5,5,3,2,2,2,1,1] (.node [9,8,5,5,5,2,2,2,2,2,1] .empty .empty) (.node [9,8,5,5,5,3,2,2,2,2] .empty .empty))) (.node [9,8,5,5,5,4,2,2,1,1,1] (.node [9,8,5,5,5,3,3,3,1,1] (.node [9,8,5,5,5,3,3,2,2,1] .empty .empty) (.node [9,8,5,5,5,3,3,3,2] .empty .empty)) (.node [9,8,5,5,5,4,3,1,1,1,1] (.node [9,8,5,5,5,4,2,2,2,1] .empty .empty) (.node [9,8,5,5,5,4,3,2,1,1] .empty .empty)))) + +def degreeTree43_206 : RowTree := (.node [9,8,5,5,4,4,3,3,2] degreeTree43_204 degreeTree43_205) + +def degreeTree43_207 : RowTree := (.node [9,8,6,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [9,8,5,5,5,5,3,2,1] (.node [9,8,5,5,5,5,2,1,1,1,1] (.node [9,8,5,5,5,4,4,1,1,1] (.node [9,8,5,5,5,4,3,3,1] .empty .empty) (.node [9,8,5,5,5,4,4,2,1] .empty .empty)) (.node [9,8,5,5,5,5,2,2,2] (.node [9,8,5,5,5,5,2,2,1,1] .empty .empty) (.node [9,8,5,5,5,5,3,1,1,1] .empty .empty))) (.node [9,8,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,8,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,8,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,2,2,2,2,2,2,2,2,2,1,1] (.node [9,8,6,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,6,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [9,8,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,3,2,2,2,2,2,2,2,2,1] (.node [9,8,6,3,2,2,2,2,2,2,1,1,1,1,1] (.node [9,8,6,3,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,3,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,8,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_208 : RowTree := (.node [9,8,5,5,5,4,3,2,2] degreeTree43_206 degreeTree43_207) + +def degreeTree43_209 : RowTree := (.node [9,8,6,3,3,3,3,3,1,1,1,1,1] (.node [9,8,6,3,3,3,2,2,2,1,1,1,1,1] (.node [9,8,6,3,3,2,2,2,2,2,2,2] (.node [9,8,6,3,3,2,2,2,2,2,1,1,1,1] (.node [9,8,6,3,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,3,3,2,2,2,2,2,2,1,1] .empty .empty)) (.node [9,8,6,3,3,3,2,1,1,1,1,1,1,1,1,1] (.node [9,8,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,3,3,3,3,2,1,1,1,1,1,1] (.node [9,8,6,3,3,3,2,2,2,2,2,1] (.node [9,8,6,3,3,3,2,2,2,2,1,1,1] .empty .empty) (.node [9,8,6,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,3,3,3,3,2,2,2,1,1] (.node [9,8,6,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [9,8,6,3,3,3,3,2,2,2,2] .empty .empty)))) (.node [9,8,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,3,3,3,3,3,3,2] (.node [9,8,6,3,3,3,3,3,2,2,1] (.node [9,8,6,3,3,3,3,3,2,1,1,1] .empty .empty) (.node [9,8,6,3,3,3,3,3,3,1,1] .empty .empty)) (.node [9,8,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,4,2,2,2,2,2,2,2,1,1] (.node [9,8,6,4,2,2,2,2,2,1,1,1,1,1,1] (.node [9,8,6,4,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,4,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [9,8,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,4,2,2,2,2,2,2,2,2] .empty .empty) (.node [9,8,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_210 : RowTree := (.node [9,8,6,4,3,3,3,3,2,1,1] (.node [9,8,6,4,3,3,2,2,2,1,1,1,1] (.node [9,8,6,4,3,2,2,2,2,2,2,1] (.node [9,8,6,4,3,2,2,2,2,1,1,1,1,1] (.node [9,8,6,4,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,4,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,8,6,4,3,3,2,1,1,1,1,1,1,1,1] (.node [9,8,6,4,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,4,3,3,2,2,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,4,3,3,3,2,1,1,1,1,1] (.node [9,8,6,4,3,3,2,2,2,2,2] (.node [9,8,6,4,3,3,2,2,2,2,1,1] .empty .empty) (.node [9,8,6,4,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,4,3,3,3,2,2,2,1] (.node [9,8,6,4,3,3,3,2,2,1,1,1] .empty .empty) (.node [9,8,6,4,3,3,3,3,1,1,1,1] .empty .empty)))) (.node [9,8,6,4,4,2,2,2,2,2,1,1] (.node [9,8,6,4,4,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,4,3,3,3,3,3,1] (.node [9,8,6,4,3,3,3,3,2,2] .empty .empty) (.node [9,8,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,4,4,2,2,2,1,1,1,1,1,1] (.node [9,8,6,4,4,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,4,4,2,2,2,2,1,1,1,1] .empty .empty))) (.node [9,8,6,4,4,3,2,2,1,1,1,1,1] (.node [9,8,6,4,4,3,1,1,1,1,1,1,1,1,1] (.node [9,8,6,4,4,2,2,2,2,2,2] .empty .empty) (.node [9,8,6,4,4,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,4,4,3,2,2,2,2,1] (.node [9,8,6,4,4,3,2,2,2,1,1,1] .empty .empty) (.node [9,8,6,4,4,3,3,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_211 : RowTree := (.node [9,8,6,4,3,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_209 degreeTree43_210) + +def degreeTree43_212 : RowTree := (.node [9,8,6,3,3,2,2,2,1,1,1,1,1,1,1,1] degreeTree43_208 degreeTree43_211) + +def degreeTree43_213 : RowTree := (.node [9,8,6,4,4,4,2,2,2,1,1] (.node [9,8,6,4,4,3,3,3,3] (.node [9,8,6,4,4,3,3,3,1,1,1] (.node [9,8,6,4,4,3,3,2,2,2] (.node [9,8,6,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [9,8,6,4,4,3,3,3,2,1] .empty .empty)) (.node [9,8,6,4,4,4,2,1,1,1,1,1,1] (.node [9,8,6,4,4,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,4,4,4,2,2,1,1,1,1] .empty .empty))) (.node [9,8,6,4,4,4,3,2,2,1] (.node [9,8,6,4,4,4,3,1,1,1,1,1] (.node [9,8,6,4,4,4,2,2,2,2] .empty .empty) (.node [9,8,6,4,4,4,3,2,1,1,1] .empty .empty)) (.node [9,8,6,4,4,4,3,3,2] (.node [9,8,6,4,4,4,3,3,1,1] .empty .empty) (.node [9,8,6,4,4,4,4,1,1,1,1] .empty .empty)))) + +def degreeTree43_214 : RowTree := (.node [9,8,6,5,2,2,2,2,2,1,1,1,1,1] (.node [9,8,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,4,4,4,4,3,1] (.node [9,8,6,4,4,4,4,2,2] .empty .empty) (.node [9,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,5,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,8,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,5,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,5,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,5,2,2,2,2,2,2,2,1] (.node [9,8,6,5,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,8,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,5,3,2,2,2,1,1,1,1,1,1] (.node [9,8,6,5,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,5,3,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree43_215 : RowTree := (.node [9,8,6,4,4,4,4,2,1,1] degreeTree43_213 degreeTree43_214) + +def degreeTree43_216 : RowTree := (.node [9,8,6,5,4,2,2,1,1,1,1,1,1,1] (.node [9,8,6,5,3,3,3,2,1,1,1,1] (.node [9,8,6,5,3,3,2,2,1,1,1,1,1] (.node [9,8,6,5,3,3,1,1,1,1,1,1,1,1,1] (.node [9,8,6,5,3,2,2,2,2,2,2] .empty .empty) (.node [9,8,6,5,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,5,3,3,2,2,2,2,1] (.node [9,8,6,5,3,3,2,2,2,1,1,1] .empty .empty) (.node [9,8,6,5,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,5,3,3,3,3,2,1] (.node [9,8,6,5,3,3,3,2,2,2] (.node [9,8,6,5,3,3,3,2,2,1,1] .empty .empty) (.node [9,8,6,5,3,3,3,3,1,1,1] .empty .empty)) (.node [9,8,6,5,4,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,5,3,3,3,3,3] .empty .empty) (.node [9,8,6,5,4,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,8,6,5,4,3,2,2,2,2] (.node [9,8,6,5,4,3,1,1,1,1,1,1,1,1] (.node [9,8,6,5,4,2,2,2,2,1,1,1] (.node [9,8,6,5,4,2,2,2,1,1,1,1,1] .empty .empty) (.node [9,8,6,5,4,2,2,2,2,2,1] .empty .empty)) (.node [9,8,6,5,4,3,2,2,1,1,1,1] (.node [9,8,6,5,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,5,4,3,2,2,2,1,1] .empty .empty))) (.node [9,8,6,5,4,3,3,3,1,1] (.node [9,8,6,5,4,3,3,2,1,1,1] (.node [9,8,6,5,4,3,3,1,1,1,1,1] .empty .empty) (.node [9,8,6,5,4,3,3,2,2,1] .empty .empty)) (.node [9,8,6,5,4,4,1,1,1,1,1,1,1] (.node [9,8,6,5,4,3,3,3,2] .empty .empty) (.node [9,8,6,5,4,4,2,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_217 : RowTree := (.node [9,8,6,5,3,2,2,2,2,2,1,1] degreeTree43_215 degreeTree43_216) + +def degreeTree43_218 : RowTree := (.node [9,8,6,5,5,3,2,2,1,1,1] (.node [9,8,6,5,5,1,1,1,1,1,1,1,1,1,1] (.node [9,8,6,5,4,4,3,2,2] (.node [9,8,6,5,4,4,3,1,1,1,1] (.node [9,8,6,5,4,4,2,2,2,1] .empty .empty) (.node [9,8,6,5,4,4,3,2,1,1] .empty .empty)) (.node [9,8,6,5,4,4,4,1,1,1] (.node [9,8,6,5,4,4,3,3,1] .empty .empty) (.node [9,8,6,5,4,4,4,2,1] .empty .empty))) (.node [9,8,6,5,5,2,2,2,2,1,1] (.node [9,8,6,5,5,2,2,1,1,1,1,1,1] (.node [9,8,6,5,5,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,5,5,2,2,2,1,1,1,1] .empty .empty)) (.node [9,8,6,5,5,3,1,1,1,1,1,1,1] (.node [9,8,6,5,5,2,2,2,2,2] .empty .empty) (.node [9,8,6,5,5,3,2,1,1,1,1,1] .empty .empty)))) (.node [9,8,6,5,5,4,2,2,1,1] (.node [9,8,6,5,5,3,3,2,2] (.node [9,8,6,5,5,3,3,1,1,1,1] (.node [9,8,6,5,5,3,2,2,2,1] .empty .empty) (.node [9,8,6,5,5,3,3,2,1,1] .empty .empty)) (.node [9,8,6,5,5,4,1,1,1,1,1,1] (.node [9,8,6,5,5,3,3,3,1] .empty .empty) (.node [9,8,6,5,5,4,2,1,1,1,1] .empty .empty))) (.node [9,8,6,5,5,5,1,1,1,1,1] (.node [9,8,6,5,5,4,3,1,1,1] (.node [9,8,6,5,5,4,2,2,2] .empty .empty) (.node [9,8,6,5,5,4,3,2,1] .empty .empty)) (.node [9,8,6,5,5,5,2,2,1] (.node [9,8,6,5,5,5,2,1,1,1] .empty .empty) (.node [9,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_219 : RowTree := (.node [9,8,6,6,3,3,2,2,2,1,1] (.node [9,8,6,6,3,2,1,1,1,1,1,1,1,1,1] (.node [9,8,6,6,2,2,2,2,2,1,1,1,1] (.node [9,8,6,6,2,2,2,1,1,1,1,1,1,1,1] (.node [9,8,6,6,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,6,2,2,2,2,2,2,2] (.node [9,8,6,6,2,2,2,2,2,2,1,1] .empty .empty) (.node [9,8,6,6,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,6,3,2,2,2,2,2,1] (.node [9,8,6,6,3,2,2,2,1,1,1,1,1] (.node [9,8,6,6,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,3,2,2,2,2,1,1,1] .empty .empty)) (.node [9,8,6,6,3,3,2,1,1,1,1,1,1] (.node [9,8,6,6,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,3,3,2,2,1,1,1,1] .empty .empty)))) (.node [9,8,6,6,4,2,1,1,1,1,1,1,1,1] (.node [9,8,6,6,3,3,3,2,2,1] (.node [9,8,6,6,3,3,3,1,1,1,1,1] (.node [9,8,6,6,3,3,2,2,2,2] .empty .empty) (.node [9,8,6,6,3,3,3,2,1,1,1] .empty .empty)) (.node [9,8,6,6,3,3,3,3,2] (.node [9,8,6,6,3,3,3,3,1,1] .empty .empty) (.node [9,8,6,6,4,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,6,6,4,2,2,2,2,2] (.node [9,8,6,6,4,2,2,2,1,1,1,1] (.node [9,8,6,6,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,4,2,2,2,2,1,1] .empty .empty)) (.node [9,8,6,6,4,3,2,1,1,1,1,1] (.node [9,8,6,6,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,4,3,2,2,1,1,1] .empty .empty))))) + +def degreeTree43_220 : RowTree := (.node [9,8,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_218 degreeTree43_219) + +def degreeTree43_221 : RowTree := (.node [9,8,6,5,4,4,2,2,1,1,1] degreeTree43_217 degreeTree43_220) + +def degreeTree43_222 : RowTree := (.node [9,8,6,4,4,3,3,2,1,1,1,1] degreeTree43_212 degreeTree43_221) + +def degreeTree43_223 : RowTree := (.node [9,8,6,6,4,4,3,1,1,1] (.node [9,8,6,6,4,4,1,1,1,1,1,1] (.node [9,8,6,6,4,3,3,2,2] (.node [9,8,6,6,4,3,3,2,1,1] (.node [9,8,6,6,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [9,8,6,6,4,3,3,3,1] .empty .empty)) (.node [9,8,6,6,4,4,2,2,1,1] (.node [9,8,6,6,4,4,2,1,1,1,1] .empty .empty) (.node [9,8,6,6,4,4,2,2,2] .empty .empty))) (.node [9,8,6,6,5,2,2,1,1,1,1,1] (.node [9,8,6,6,5,1,1,1,1,1,1,1,1,1] (.node [9,8,6,6,4,4,3,2,1] .empty .empty) (.node [9,8,6,6,5,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,6,6,5,2,2,2,2,1] (.node [9,8,6,6,5,2,2,2,1,1,1] .empty .empty) (.node [9,8,6,6,5,3,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_224 : RowTree := (.node [9,8,6,6,5,5,1,1,1,1] (.node [9,8,6,6,5,3,3,2,1] (.node [9,8,6,6,5,3,2,2,2] (.node [9,8,6,6,5,3,2,2,1,1] .empty .empty) (.node [9,8,6,6,5,3,3,1,1,1] .empty .empty)) (.node [9,8,6,6,5,4,2,1,1,1] (.node [9,8,6,6,5,4,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,5,4,2,2,1] .empty .empty))) (.node [9,8,6,6,6,2,2,2,1,1] (.node [9,8,6,6,6,2,1,1,1,1,1,1] (.node [9,8,6,6,6,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,6,6,6,2,2,1,1,1,1] .empty .empty)) (.node [9,8,6,6,6,3,1,1,1,1,1] (.node [9,8,6,6,6,2,2,2,2] .empty .empty) (.node [9,8,6,6,6,3,2,1,1,1] .empty .empty)))) + +def degreeTree43_225 : RowTree := (.node [9,8,6,6,5,3,2,1,1,1,1] degreeTree43_223 degreeTree43_224) + +def degreeTree43_226 : RowTree := (.node [9,8,7,3,2,2,2,2,2,1,1,1,1,1,1] (.node [9,8,7,2,2,2,2,2,2,2,1,1,1,1,1] (.node [9,8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,8,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,2,2,2,2,2,2,2,2,2,1] (.node [9,8,7,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,8,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,8,7,3,3,2,2,2,2,1,1,1,1,1] (.node [9,8,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,3,2,2,2,2,2,2,2,1,1] (.node [9,8,7,3,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,7,3,2,2,2,2,2,2,2,2] .empty .empty)) (.node [9,8,7,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [9,8,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,7,3,3,3,2,1,1,1,1,1,1,1,1] (.node [9,8,7,3,3,2,2,2,2,2,2,1] (.node [9,8,7,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,8,7,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,3,3,3,2,2,2,1,1,1,1] (.node [9,8,7,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,3,3,3,2,2,2,2,1,1] .empty .empty))))) + +def degreeTree43_227 : RowTree := (.node [9,8,6,6,6,4,1,1,1,1] degreeTree43_225 degreeTree43_226) + +def degreeTree43_228 : RowTree := (.node [9,8,7,4,2,2,2,2,2,2,2,1] (.node [9,8,7,3,3,3,3,3,3,1] (.node [9,8,7,3,3,3,3,2,2,2,1] (.node [9,8,7,3,3,3,3,2,1,1,1,1,1] (.node [9,8,7,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,3,3,3,3,2,2,1,1,1] .empty .empty)) (.node [9,8,7,3,3,3,3,3,2,1,1] (.node [9,8,7,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [9,8,7,3,3,3,3,3,2,2] .empty .empty))) (.node [9,8,7,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,8,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,4,2,2,2,2,2,1,1,1,1,1] (.node [9,8,7,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,2,2,2,2,2,2,1,1,1] .empty .empty)))) (.node [9,8,7,4,3,3,1,1,1,1,1,1,1,1,1] (.node [9,8,7,4,3,2,2,2,1,1,1,1,1,1] (.node [9,8,7,4,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,4,3,2,2,2,2,2,1,1] (.node [9,8,7,4,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,7,4,3,2,2,2,2,2,2] .empty .empty))) (.node [9,8,7,4,3,3,2,2,2,2,1] (.node [9,8,7,4,3,3,2,2,1,1,1,1,1] (.node [9,8,7,4,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,3,3,2,2,2,1,1,1] .empty .empty)) (.node [9,8,7,4,3,3,3,2,1,1,1,1] (.node [9,8,7,4,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,3,3,3,2,2,1,1] .empty .empty))))) + +def degreeTree43_229 : RowTree := (.node [9,8,7,4,4,3,3,2,1,1,1] (.node [9,8,7,4,4,2,2,2,2,1,1,1] (.node [9,8,7,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,4,3,3,3,3,2,1] (.node [9,8,7,4,3,3,3,3,1,1,1] .empty .empty) (.node [9,8,7,4,3,3,3,3,3] .empty .empty)) (.node [9,8,7,4,4,2,2,1,1,1,1,1,1,1] (.node [9,8,7,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,4,2,2,2,1,1,1,1,1] .empty .empty))) (.node [9,8,7,4,4,3,2,2,1,1,1,1] (.node [9,8,7,4,4,3,1,1,1,1,1,1,1,1] (.node [9,8,7,4,4,2,2,2,2,2,1] .empty .empty) (.node [9,8,7,4,4,3,2,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,4,4,3,2,2,2,2] (.node [9,8,7,4,4,3,2,2,2,1,1] .empty .empty) (.node [9,8,7,4,4,3,3,1,1,1,1,1] .empty .empty)))) (.node [9,8,7,4,4,4,3,1,1,1,1] (.node [9,8,7,4,4,4,1,1,1,1,1,1,1] (.node [9,8,7,4,4,3,3,3,1,1] (.node [9,8,7,4,4,3,3,2,2,1] .empty .empty) (.node [9,8,7,4,4,3,3,3,2] .empty .empty)) (.node [9,8,7,4,4,4,2,2,1,1,1] (.node [9,8,7,4,4,4,2,1,1,1,1,1] .empty .empty) (.node [9,8,7,4,4,4,2,2,2,1] .empty .empty))) (.node [9,8,7,4,4,4,4,1,1,1] (.node [9,8,7,4,4,4,3,2,2] (.node [9,8,7,4,4,4,3,2,1,1] .empty .empty) (.node [9,8,7,4,4,4,3,3,1] .empty .empty)) (.node [9,8,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,4,4,4,4,2,1] .empty .empty) (.node [9,8,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_230 : RowTree := (.node [9,8,7,4,3,3,3,2,2,2] degreeTree43_228 degreeTree43_229) + +def degreeTree43_231 : RowTree := (.node [9,8,7,3,3,3,2,2,2,2,2] degreeTree43_227 degreeTree43_230) + +def degreeTree43_232 : RowTree := (.node [9,8,7,5,3,2,2,2,1,1,1,1,1] (.node [9,8,7,5,2,2,2,2,2,2,2] (.node [9,8,7,5,2,2,2,2,2,1,1,1,1] (.node [9,8,7,5,2,2,2,2,1,1,1,1,1,1] (.node [9,8,7,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,8,7,5,2,2,2,2,2,2,1,1] .empty .empty)) (.node [9,8,7,5,3,2,1,1,1,1,1,1,1,1,1] (.node [9,8,7,5,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,5,3,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,7,5,3,3,2,1,1,1,1,1,1] (.node [9,8,7,5,3,2,2,2,2,2,1] (.node [9,8,7,5,3,2,2,2,2,1,1,1] .empty .empty) (.node [9,8,7,5,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,5,3,3,2,2,2,1,1] (.node [9,8,7,5,3,3,2,2,1,1,1,1] .empty .empty) (.node [9,8,7,5,3,3,2,2,2,2] .empty .empty)))) + +def degreeTree43_233 : RowTree := (.node [9,8,7,5,4,2,2,2,1,1,1,1] (.node [9,8,7,5,3,3,3,3,2] (.node [9,8,7,5,3,3,3,2,2,1] (.node [9,8,7,5,3,3,3,2,1,1,1] .empty .empty) (.node [9,8,7,5,3,3,3,3,1,1] .empty .empty)) (.node [9,8,7,5,4,2,1,1,1,1,1,1,1,1] (.node [9,8,7,5,4,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,5,4,2,2,1,1,1,1,1,1] .empty .empty))) (.node [9,8,7,5,4,3,2,1,1,1,1,1] (.node [9,8,7,5,4,2,2,2,2,2] (.node [9,8,7,5,4,2,2,2,2,1,1] .empty .empty) (.node [9,8,7,5,4,3,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,5,4,3,2,2,2,1] (.node [9,8,7,5,4,3,2,2,1,1,1] .empty .empty) (.node [9,8,7,5,4,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree43_234 : RowTree := (.node [9,8,7,5,3,3,3,1,1,1,1,1] degreeTree43_232 degreeTree43_233) + +def degreeTree43_235 : RowTree := (.node [9,8,7,5,5,3,2,2,1,1] (.node [9,8,7,5,4,4,3,2,1] (.node [9,8,7,5,4,4,2,1,1,1,1] (.node [9,8,7,5,4,3,3,3,1] (.node [9,8,7,5,4,3,3,2,2] .empty .empty) (.node [9,8,7,5,4,4,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,5,4,4,2,2,2] (.node [9,8,7,5,4,4,2,2,1,1] .empty .empty) (.node [9,8,7,5,4,4,3,1,1,1] .empty .empty))) (.node [9,8,7,5,5,2,2,2,1,1,1] (.node [9,8,7,5,5,2,1,1,1,1,1,1,1] (.node [9,8,7,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,5,5,2,2,1,1,1,1,1] .empty .empty)) (.node [9,8,7,5,5,3,1,1,1,1,1,1] (.node [9,8,7,5,5,2,2,2,2,1] .empty .empty) (.node [9,8,7,5,5,3,2,1,1,1,1] .empty .empty)))) (.node [9,8,7,6,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,5,5,4,1,1,1,1,1] (.node [9,8,7,5,5,3,3,1,1,1] (.node [9,8,7,5,5,3,2,2,2] .empty .empty) (.node [9,8,7,5,5,3,3,2,1] .empty .empty)) (.node [9,8,7,5,5,5,1,1,1,1] (.node [9,8,7,5,5,4,2,1,1,1] .empty .empty) (.node [9,8,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,7,6,2,2,2,2,2,1,1,1] (.node [9,8,7,6,2,2,2,1,1,1,1,1,1,1] (.node [9,8,7,6,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [9,8,7,6,3,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,6,2,2,2,2,2,2,1] .empty .empty) (.node [9,8,7,6,3,2,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_236 : RowTree := (.node [9,8,7,5,4,3,3,2,1,1] degreeTree43_234 degreeTree43_235) + +def degreeTree43_237 : RowTree := (.node [9,8,7,6,4,2,2,2,2,1] (.node [9,8,7,6,3,3,3,1,1,1,1] (.node [9,8,7,6,3,3,1,1,1,1,1,1,1] (.node [9,8,7,6,3,2,2,2,2,1,1] (.node [9,8,7,6,3,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,7,6,3,2,2,2,2,2] .empty .empty)) (.node [9,8,7,6,3,3,2,2,1,1,1] (.node [9,8,7,6,3,3,2,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,3,3,2,2,2,1] .empty .empty))) (.node [9,8,7,6,4,1,1,1,1,1,1,1,1,1] (.node [9,8,7,6,3,3,3,2,2] (.node [9,8,7,6,3,3,3,2,1,1] .empty .empty) (.node [9,8,7,6,3,3,3,3,1] .empty .empty)) (.node [9,8,7,6,4,2,2,1,1,1,1,1] (.node [9,8,7,6,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,4,2,2,2,1,1,1] .empty .empty)))) (.node [9,8,7,6,5,1,1,1,1,1,1,1,1] (.node [9,8,7,6,4,3,2,2,2] (.node [9,8,7,6,4,3,2,1,1,1,1] (.node [9,8,7,6,4,3,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,4,3,2,2,1,1] .empty .empty)) (.node [9,8,7,6,4,4,1,1,1,1,1] (.node [9,8,7,6,4,3,3,1,1,1] .empty .empty) (.node [9,8,7,6,4,4,2,1,1,1] .empty .empty))) (.node [9,8,7,6,5,2,2,2,2] (.node [9,8,7,6,5,2,2,1,1,1,1] (.node [9,8,7,6,5,2,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,5,2,2,2,1,1] .empty .empty)) (.node [9,8,7,6,5,3,2,1,1,1] (.node [9,8,7,6,5,3,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,5,4,1,1,1,1] .empty .empty))))) + +def degreeTree43_238 : RowTree := (.node [9,8,7,7,3,3,1,1,1,1,1,1] (.node [9,8,7,7,2,2,2,2,1,1,1,1] (.node [9,8,7,7,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,6,6,2,2,1,1,1] (.node [9,8,7,6,6,2,1,1,1,1,1] .empty .empty) (.node [9,8,7,6,6,3,1,1,1,1] .empty .empty)) (.node [9,8,7,7,2,2,1,1,1,1,1,1,1,1] (.node [9,8,7,7,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,7,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [9,8,7,7,3,2,1,1,1,1,1,1,1] (.node [9,8,7,7,2,2,2,2,2,2] (.node [9,8,7,7,2,2,2,2,2,1,1] .empty .empty) (.node [9,8,7,7,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,7,7,3,2,2,2,1,1,1] (.node [9,8,7,7,3,2,2,1,1,1,1,1] .empty .empty) (.node [9,8,7,7,3,2,2,2,2,1] .empty .empty)))) (.node [9,8,7,7,4,2,2,2,1,1] (.node [9,8,7,7,3,3,3,1,1,1] (.node [9,8,7,7,3,3,2,2,1,1] (.node [9,8,7,7,3,3,2,1,1,1,1] .empty .empty) (.node [9,8,7,7,3,3,2,2,2] .empty .empty)) (.node [9,8,7,7,4,2,1,1,1,1,1,1] (.node [9,8,7,7,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,7,4,2,2,1,1,1,1] .empty .empty))) (.node [9,8,7,7,4,4,1,1,1,1] (.node [9,8,7,7,4,3,1,1,1,1,1] (.node [9,8,7,7,4,2,2,2,2] .empty .empty) (.node [9,8,7,7,4,3,2,1,1,1] .empty .empty)) (.node [9,8,7,7,5,2,1,1,1,1,1] (.node [9,8,7,7,5,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,7,7,5,2,2,1,1,1] .empty .empty))))) + +def degreeTree43_239 : RowTree := (.node [9,8,7,6,6,1,1,1,1,1,1,1] degreeTree43_237 degreeTree43_238) + +def degreeTree43_240 : RowTree := (.node [9,8,7,6,3,2,2,1,1,1,1,1,1] degreeTree43_236 degreeTree43_239) + +def degreeTree43_241 : RowTree := (.node [9,8,7,5,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_231 degreeTree43_240) + +def degreeTree43_242 : RowTree := (.node [9,8,6,6,4,3,2,2,2,1] degreeTree43_222 degreeTree43_241) + +def degreeTree43_243 : RowTree := (.node [9,8,5,5,3,3,2,2,2,2,2] degreeTree43_203 degreeTree43_242) + +def degreeTree43_244 : RowTree := (.node [9,8,8,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [9,8,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,7,7,7,1,1,1,1,1] (.node [9,8,7,7,6,2,1,1,1,1] (.node [9,8,7,7,6,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,8,2,2,2,2,2,2,2,2,2] (.node [9,8,8,2,2,2,2,2,2,2,1,1,1,1] (.node [9,8,8,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [9,8,8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_245 : RowTree := (.node [9,8,8,3,3,2,2,2,1,1,1,1,1,1] (.node [9,8,8,3,2,2,2,2,2,2,2,1] (.node [9,8,8,3,2,2,2,2,2,1,1,1,1,1] (.node [9,8,8,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,3,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,8,8,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,8,3,3,3,1,1,1,1,1,1,1,1,1] (.node [9,8,8,3,3,2,2,2,2,2,1,1] (.node [9,8,8,3,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,3,3,2,2,2,2,2,2] .empty .empty)) (.node [9,8,8,3,3,3,2,2,1,1,1,1,1] (.node [9,8,8,3,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,3,3,3,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree43_246 : RowTree := (.node [9,8,8,3,2,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_244 degreeTree43_245) + +def degreeTree43_247 : RowTree := (.node [9,8,8,4,3,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,3,3,3,3,2,2,2] (.node [9,8,8,3,3,3,3,2,1,1,1,1] (.node [9,8,8,3,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,3,3,3,3,2,2,1,1] .empty .empty)) (.node [9,8,8,3,3,3,3,3,2,1] (.node [9,8,8,3,3,3,3,3,1,1,1] .empty .empty) (.node [9,8,8,3,3,3,3,3,3] .empty .empty))) (.node [9,8,8,4,2,2,2,2,1,1,1,1,1,1] (.node [9,8,8,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,4,2,2,2,2,2,2,1,1] (.node [9,8,8,4,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,4,2,2,2,2,2,2,2] .empty .empty)))) (.node [9,8,8,4,3,3,2,2,1,1,1,1] (.node [9,8,8,4,3,2,2,2,2,1,1,1] (.node [9,8,8,4,3,2,2,1,1,1,1,1,1,1] (.node [9,8,8,4,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,4,3,2,2,2,1,1,1,1,1] .empty .empty)) (.node [9,8,8,4,3,3,1,1,1,1,1,1,1,1] (.node [9,8,8,4,3,2,2,2,2,2,1] .empty .empty) (.node [9,8,8,4,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [9,8,8,4,3,3,3,2,1,1,1] (.node [9,8,8,4,3,3,2,2,2,2] (.node [9,8,8,4,3,3,2,2,2,1,1] .empty .empty) (.node [9,8,8,4,3,3,3,1,1,1,1,1] .empty .empty)) (.node [9,8,8,4,3,3,3,3,1,1] (.node [9,8,8,4,3,3,3,2,2,1] .empty .empty) (.node [9,8,8,4,3,3,3,3,2] .empty .empty))))) + +def degreeTree43_248 : RowTree := (.node [9,8,8,3,3,3,2,2,2,2,1] degreeTree43_246 degreeTree43_247) + +def degreeTree43_249 : RowTree := (.node [9,8,8,4,4,4,2,2,1,1] (.node [9,8,8,4,4,3,2,2,1,1,1] (.node [9,8,8,4,4,2,2,2,2,1,1] (.node [9,8,8,4,4,2,2,1,1,1,1,1,1] (.node [9,8,8,4,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,4,4,2,2,2,1,1,1,1] .empty .empty)) (.node [9,8,8,4,4,3,1,1,1,1,1,1,1] (.node [9,8,8,4,4,2,2,2,2,2] .empty .empty) (.node [9,8,8,4,4,3,2,1,1,1,1,1] .empty .empty))) (.node [9,8,8,4,4,3,3,2,2] (.node [9,8,8,4,4,3,3,1,1,1,1] (.node [9,8,8,4,4,3,2,2,2,1] .empty .empty) (.node [9,8,8,4,4,3,3,2,1,1] .empty .empty)) (.node [9,8,8,4,4,4,1,1,1,1,1,1] (.node [9,8,8,4,4,3,3,3,1] .empty .empty) (.node [9,8,8,4,4,4,2,1,1,1,1] .empty .empty)))) (.node [9,8,8,5,2,2,2,2,2,1,1,1] (.node [9,8,8,5,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,4,4,4,3,1,1,1] (.node [9,8,8,4,4,4,2,2,2] .empty .empty) (.node [9,8,8,5,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,5,2,2,2,1,1,1,1,1,1,1] (.node [9,8,8,5,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,5,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [9,8,8,5,3,2,2,1,1,1,1,1,1] (.node [9,8,8,5,3,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,5,2,2,2,2,2,2,1] .empty .empty) (.node [9,8,8,5,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,5,3,2,2,2,2,1,1] (.node [9,8,8,5,3,2,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,5,3,2,2,2,2,2] .empty .empty))))) + +def degreeTree43_250 : RowTree := (.node [9,8,8,5,4,3,3,1,1,1] (.node [9,8,8,5,4,2,1,1,1,1,1,1,1] (.node [9,8,8,5,3,3,3,1,1,1,1] (.node [9,8,8,5,3,3,2,2,1,1,1] (.node [9,8,8,5,3,3,2,1,1,1,1,1] .empty .empty) (.node [9,8,8,5,3,3,2,2,2,1] .empty .empty)) (.node [9,8,8,5,3,3,3,2,2] (.node [9,8,8,5,3,3,3,2,1,1] .empty .empty) (.node [9,8,8,5,4,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,8,8,5,4,3,1,1,1,1,1,1] (.node [9,8,8,5,4,2,2,2,1,1,1] (.node [9,8,8,5,4,2,2,1,1,1,1,1] .empty .empty) (.node [9,8,8,5,4,2,2,2,2,1] .empty .empty)) (.node [9,8,8,5,4,3,2,2,1,1] (.node [9,8,8,5,4,3,2,1,1,1,1] .empty .empty) (.node [9,8,8,5,4,3,2,2,2] .empty .empty)))) (.node [9,8,8,5,5,3,1,1,1,1,1] (.node [9,8,8,5,5,2,1,1,1,1,1,1] (.node [9,8,8,5,4,4,2,1,1,1] (.node [9,8,8,5,4,4,1,1,1,1,1] .empty .empty) (.node [9,8,8,5,5,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,5,5,2,2,2,1,1] (.node [9,8,8,5,5,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,5,5,2,2,2,2] .empty .empty))) (.node [9,8,8,6,2,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,5,5,4,1,1,1,1] (.node [9,8,8,5,5,3,2,1,1,1] .empty .empty) (.node [9,8,8,6,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,6,2,2,2,1,1,1,1,1,1] (.node [9,8,8,6,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,6,2,2,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_251 : RowTree := (.node [9,8,8,5,3,3,1,1,1,1,1,1,1] degreeTree43_249 degreeTree43_250) + +def degreeTree43_252 : RowTree := (.node [9,8,8,4,4,1,1,1,1,1,1,1,1,1,1] degreeTree43_248 degreeTree43_251) + +def degreeTree43_253 : RowTree := (.node [9,8,8,6,3,3,2,2,1,1] (.node [9,8,8,6,3,2,2,2,1,1,1] (.node [9,8,8,6,3,2,1,1,1,1,1,1,1] (.node [9,8,8,6,3,1,1,1,1,1,1,1,1,1] (.node [9,8,8,6,2,2,2,2,2,2] .empty .empty) .empty) (.node [9,8,8,6,3,2,2,1,1,1,1,1] .empty .empty)) (.node [9,8,8,6,3,3,1,1,1,1,1,1] (.node [9,8,8,6,3,2,2,2,2,1] .empty .empty) (.node [9,8,8,6,3,3,2,1,1,1,1] .empty .empty))) (.node [9,8,8,6,4,2,1,1,1,1,1,1] (.node [9,8,8,6,3,3,3,1,1,1] (.node [9,8,8,6,3,3,2,2,2] .empty .empty) (.node [9,8,8,6,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,6,4,2,2,2,1,1] (.node [9,8,8,6,4,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,6,4,2,2,2,2] .empty .empty)))) + +def degreeTree43_254 : RowTree := (.node [9,8,8,6,6,2,1,1,1,1] (.node [9,8,8,6,5,2,1,1,1,1,1] (.node [9,8,8,6,4,4,1,1,1,1] (.node [9,8,8,6,4,3,2,1,1,1] .empty .empty) (.node [9,8,8,6,5,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,6,5,3,1,1,1,1] (.node [9,8,8,6,5,2,2,1,1,1] .empty .empty) (.node [9,8,8,6,6,1,1,1,1,1,1] .empty .empty))) (.node [9,8,8,7,2,2,2,1,1,1,1,1] (.node [9,8,8,7,2,1,1,1,1,1,1,1,1,1] (.node [9,8,8,7,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,7,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,7,2,2,2,2,2,1] (.node [9,8,8,7,2,2,2,2,1,1,1] .empty .empty) (.node [9,8,8,7,3,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_255 : RowTree := (.node [9,8,8,6,4,3,1,1,1,1,1] degreeTree43_253 degreeTree43_254) + +def degreeTree43_256 : RowTree := (.node [9,8,8,8,2,2,2,1,1,1,1] (.node [9,8,8,7,4,2,2,1,1,1] (.node [9,8,8,7,3,3,1,1,1,1,1] (.node [9,8,8,7,3,2,2,2,1,1] (.node [9,8,8,7,3,2,2,1,1,1,1] .empty .empty) (.node [9,8,8,7,3,2,2,2,2] .empty .empty)) (.node [9,8,8,7,4,1,1,1,1,1,1,1] (.node [9,8,8,7,3,3,2,1,1,1] .empty .empty) (.node [9,8,8,7,4,2,1,1,1,1,1] .empty .empty))) (.node [9,8,8,7,6,1,1,1,1,1] (.node [9,8,8,7,5,1,1,1,1,1,1] (.node [9,8,8,7,4,3,1,1,1,1] .empty .empty) (.node [9,8,8,7,5,2,1,1,1,1] .empty .empty)) (.node [9,8,8,8,2,1,1,1,1,1,1,1,1] (.node [9,8,8,8,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,8,8,8,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [9,8,8,8,4,2,1,1,1,1] (.node [9,8,8,8,3,2,1,1,1,1,1] (.node [9,8,8,8,2,2,2,2,2] (.node [9,8,8,8,2,2,2,2,1,1] .empty .empty) (.node [9,8,8,8,3,1,1,1,1,1,1,1] .empty .empty)) (.node [9,8,8,8,3,3,1,1,1,1] (.node [9,8,8,8,3,2,2,1,1,1] .empty .empty) (.node [9,8,8,8,4,1,1,1,1,1,1] .empty .empty))) (.node [9,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,8,8,8,5,1,1,1,1,1] .empty .empty) (.node [9,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_257 : RowTree := (.node [9,8,8,7,3,2,1,1,1,1,1,1] degreeTree43_255 degreeTree43_256) + +def degreeTree43_258 : RowTree := (.node [9,9,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [9,9,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [9,9,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,3,2,2,2,2,2,2,2,2,2,2,2] (.node [9,9,3,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [9,9,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [9,9,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,9,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,3,3,2,2,2,2,2,2,2,1,1,1,1,1] (.node [9,9,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,3,3,2,2,2,2,2,2,2,2,2,1] (.node [9,9,3,3,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,3,3,3,2,2,2,2,2,1,1,1,1,1,1] (.node [9,9,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,3,3,3,2,2,2,2,2,2,2,1,1] (.node [9,9,3,3,3,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,9,3,3,3,2,2,2,2,2,2,2,2] .empty .empty))))) + +def degreeTree43_259 : RowTree := (.node [9,9,3,3,3,3,3,3,2,2,2,1] (.node [9,9,3,3,3,3,3,2,1,1,1,1,1,1,1,1] (.node [9,9,3,3,3,3,2,2,2,2,1,1,1,1,1] (.node [9,9,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,3,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,3,3,3,3,2,2,2,2,2,2,1] (.node [9,9,3,3,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,3,3,3,3,3,2,2,2,2,2] (.node [9,9,3,3,3,3,3,2,2,2,1,1,1,1] (.node [9,9,3,3,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,3,3,3,3,2,2,2,2,1,1] .empty .empty)) (.node [9,9,3,3,3,3,3,3,2,1,1,1,1,1] (.node [9,9,3,3,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,3,3,3,3,3,3,2,2,1,1,1] .empty .empty)))) (.node [9,9,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,3,3,3,3,3,3,3,3,1] (.node [9,9,3,3,3,3,3,3,3,2,1,1] (.node [9,9,3,3,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [9,9,3,3,3,3,3,3,3,2,2] .empty .empty)) (.node [9,9,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,4,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [9,9,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,2,2,2,2,2,2,2,2,2,2,1] (.node [9,9,4,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_260 : RowTree := (.node [9,9,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_258 degreeTree43_259) + +def degreeTree43_261 : RowTree := (.node [9,9,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] degreeTree43_257 degreeTree43_260) + +def degreeTree43_262 : RowTree := (.node [9,8,8,6,2,2,2,2,2,1,1] degreeTree43_252 degreeTree43_261) + +def degreeTree43_263 : RowTree := (.node [9,9,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [9,9,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,9,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,3,2,2,2,2,2,2,2,2,1,1] (.node [9,9,4,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,9,4,3,2,2,2,2,2,2,2,2,2] .empty .empty))) (.node [9,9,4,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [9,9,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,3,3,2,2,2,2,2,2,1,1,1] (.node [9,9,4,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [9,9,4,3,3,2,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree43_264 : RowTree := (.node [9,9,4,3,3,3,3,2,1,1,1,1,1,1,1] (.node [9,9,4,3,3,3,2,2,2,2,1,1,1,1] (.node [9,9,4,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [9,9,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,3,3,3,2,2,2,2,2,2] (.node [9,9,4,3,3,3,2,2,2,2,2,1,1] .empty .empty) (.node [9,9,4,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,4,3,3,3,3,3,1,1,1,1,1,1] (.node [9,9,4,3,3,3,3,2,2,2,1,1,1] (.node [9,9,4,3,3,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [9,9,4,3,3,3,3,2,2,2,2,1] .empty .empty)) (.node [9,9,4,3,3,3,3,3,2,2,1,1] (.node [9,9,4,3,3,3,3,3,2,1,1,1,1] .empty .empty) (.node [9,9,4,3,3,3,3,3,2,2,2] .empty .empty)))) + +def degreeTree43_265 : RowTree := (.node [9,9,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_263 degreeTree43_264) + +def degreeTree43_266 : RowTree := (.node [9,9,4,4,3,2,2,2,2,1,1,1,1,1,1] (.node [9,9,4,4,2,2,2,2,2,1,1,1,1,1,1,1] (.node [9,9,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,3,3,3,3,3,3,3] (.node [9,9,4,3,3,3,3,3,3,2,1] .empty .empty) (.node [9,9,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,2,2,2,2,2,2,2,1,1,1] (.node [9,9,4,4,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,2,2,2,2,2,2,2,2,1] .empty .empty)) (.node [9,9,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,9,4,4,3,3,2,2,2,2,1,1,1] (.node [9,9,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,3,2,2,2,2,2,2,1,1] (.node [9,9,4,4,3,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,9,4,4,3,2,2,2,2,2,2,2] .empty .empty)) (.node [9,9,4,4,3,3,2,2,1,1,1,1,1,1,1] (.node [9,9,4,4,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,3,3,2,2,2,1,1,1,1,1] .empty .empty))) (.node [9,9,4,4,3,3,3,2,2,1,1,1,1] (.node [9,9,4,4,3,3,3,1,1,1,1,1,1,1,1] (.node [9,9,4,4,3,3,2,2,2,2,2,1] .empty .empty) (.node [9,9,4,4,3,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,4,3,3,3,2,2,2,2] (.node [9,9,4,4,3,3,3,2,2,2,1,1] .empty .empty) (.node [9,9,4,4,3,3,3,3,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_267 : RowTree := (.node [9,9,4,3,3,3,3,3,3,1,1,1] degreeTree43_265 degreeTree43_266) + +def degreeTree43_268 : RowTree := (.node [9,9,4,4,4,3,2,2,2,2,2] (.node [9,9,4,4,4,2,2,2,2,1,1,1,1,1] (.node [9,9,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,3,3,3,3,3,1,1] (.node [9,9,4,4,3,3,3,3,2,2,1] .empty .empty) (.node [9,9,4,4,3,3,3,3,3,2] .empty .empty)) (.node [9,9,4,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,4,4,4,3,2,1,1,1,1,1,1,1,1] (.node [9,9,4,4,4,2,2,2,2,2,2,1] (.node [9,9,4,4,4,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,4,4,4,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,4,4,4,3,2,2,2,1,1,1,1] (.node [9,9,4,4,4,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,4,3,2,2,2,2,1,1] .empty .empty)))) (.node [9,9,4,4,4,3,3,3,3,1] (.node [9,9,4,4,4,3,3,2,2,2,1] (.node [9,9,4,4,4,3,3,2,1,1,1,1,1] (.node [9,9,4,4,4,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,4,3,3,2,2,1,1,1] .empty .empty)) (.node [9,9,4,4,4,3,3,3,2,1,1] (.node [9,9,4,4,4,3,3,3,1,1,1,1] .empty .empty) (.node [9,9,4,4,4,3,3,3,2,2] .empty .empty))) (.node [9,9,4,4,4,4,2,2,2,1,1,1] (.node [9,9,4,4,4,4,2,1,1,1,1,1,1,1] (.node [9,9,4,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,4,4,2,2,1,1,1,1,1] .empty .empty)) (.node [9,9,4,4,4,4,3,1,1,1,1,1,1] (.node [9,9,4,4,4,4,2,2,2,2,1] .empty .empty) (.node [9,9,4,4,4,4,3,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_269 : RowTree := (.node [9,9,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [9,9,4,4,4,4,4,3,1,1] (.node [9,9,4,4,4,4,3,3,3] (.node [9,9,4,4,4,4,3,3,1,1,1] (.node [9,9,4,4,4,4,3,2,2,2] .empty .empty) (.node [9,9,4,4,4,4,3,3,2,1] .empty .empty)) (.node [9,9,4,4,4,4,4,2,1,1,1] (.node [9,9,4,4,4,4,4,1,1,1,1,1] .empty .empty) (.node [9,9,4,4,4,4,4,2,2,1] .empty .empty))) (.node [9,9,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,4,4,4,4,4,3,2] .empty .empty) (.node [9,9,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,9,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,2,2,2,2,2,2,2,2,2,2] (.node [9,9,5,2,2,2,2,2,2,2,2,1,1,1,1] (.node [9,9,5,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [9,9,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,3,2,2,2,2,2,2,2,1,1,1] (.node [9,9,5,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [9,9,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [9,9,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,3,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [9,9,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_270 : RowTree := (.node [9,9,4,4,4,4,3,2,2,1,1] degreeTree43_268 degreeTree43_269) + +def degreeTree43_271 : RowTree := (.node [9,9,4,4,3,3,3,3,2,1,1,1] degreeTree43_267 degreeTree43_270) + +def degreeTree43_272 : RowTree := (.node [9,9,5,3,3,3,2,2,2,1,1,1,1,1] (.node [9,9,5,3,3,2,2,2,2,2,2,2] (.node [9,9,5,3,3,2,2,2,2,2,1,1,1,1] (.node [9,9,5,3,3,2,2,2,2,1,1,1,1,1,1] (.node [9,9,5,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,9,5,3,3,2,2,2,2,2,2,1,1] .empty .empty)) (.node [9,9,5,3,3,3,2,1,1,1,1,1,1,1,1,1] (.node [9,9,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,3,3,3,3,2,1,1,1,1,1,1] (.node [9,9,5,3,3,3,2,2,2,2,2,1] (.node [9,9,5,3,3,3,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,5,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,3,3,3,3,2,2,2,1,1] (.node [9,9,5,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [9,9,5,3,3,3,3,2,2,2,2] .empty .empty)))) + +def degreeTree43_273 : RowTree := (.node [9,9,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,3,3,3,3,3,3,2] (.node [9,9,5,3,3,3,3,3,2,2,1] (.node [9,9,5,3,3,3,3,3,2,1,1,1] .empty .empty) (.node [9,9,5,3,3,3,3,3,3,1,1] .empty .empty)) (.node [9,9,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,4,2,2,2,2,2,2,2,1,1] (.node [9,9,5,4,2,2,2,2,2,1,1,1,1,1,1] (.node [9,9,5,4,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,4,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [9,9,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,4,2,2,2,2,2,2,2,2] .empty .empty) (.node [9,9,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_274 : RowTree := (.node [9,9,5,3,3,3,3,3,1,1,1,1,1] degreeTree43_272 degreeTree43_273) + +def degreeTree43_275 : RowTree := (.node [9,9,5,4,3,3,3,3,2,1,1] (.node [9,9,5,4,3,3,2,2,2,1,1,1,1] (.node [9,9,5,4,3,2,2,2,2,2,2,1] (.node [9,9,5,4,3,2,2,2,2,1,1,1,1,1] (.node [9,9,5,4,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,4,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [9,9,5,4,3,3,2,1,1,1,1,1,1,1,1] (.node [9,9,5,4,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,4,3,3,2,2,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,4,3,3,3,2,1,1,1,1,1] (.node [9,9,5,4,3,3,2,2,2,2,2] (.node [9,9,5,4,3,3,2,2,2,2,1,1] .empty .empty) (.node [9,9,5,4,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,4,3,3,3,2,2,2,1] (.node [9,9,5,4,3,3,3,2,2,1,1,1] .empty .empty) (.node [9,9,5,4,3,3,3,3,1,1,1,1] .empty .empty)))) (.node [9,9,5,4,4,2,2,2,2,2,1,1] (.node [9,9,5,4,4,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,4,3,3,3,3,3,1] (.node [9,9,5,4,3,3,3,3,2,2] .empty .empty) (.node [9,9,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,4,4,2,2,2,1,1,1,1,1,1] (.node [9,9,5,4,4,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,4,4,2,2,2,2,1,1,1,1] .empty .empty))) (.node [9,9,5,4,4,3,2,2,1,1,1,1,1] (.node [9,9,5,4,4,3,1,1,1,1,1,1,1,1,1] (.node [9,9,5,4,4,2,2,2,2,2,2] .empty .empty) (.node [9,9,5,4,4,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,4,4,3,2,2,2,2,1] (.node [9,9,5,4,4,3,2,2,2,1,1,1] .empty .empty) (.node [9,9,5,4,4,3,3,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_276 : RowTree := (.node [9,9,5,4,3,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_274 degreeTree43_275) + +def degreeTree43_277 : RowTree := (.node [9,9,5,4,4,4,4,1,1,1,1] (.node [9,9,5,4,4,4,2,2,1,1,1,1] (.node [9,9,5,4,4,3,3,3,2,1] (.node [9,9,5,4,4,3,3,2,2,2] (.node [9,9,5,4,4,3,3,2,2,1,1] .empty .empty) (.node [9,9,5,4,4,3,3,3,1,1,1] .empty .empty)) (.node [9,9,5,4,4,4,1,1,1,1,1,1,1,1] (.node [9,9,5,4,4,3,3,3,3] .empty .empty) (.node [9,9,5,4,4,4,2,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,4,4,4,3,2,1,1,1] (.node [9,9,5,4,4,4,2,2,2,2] (.node [9,9,5,4,4,4,2,2,2,1,1] .empty .empty) (.node [9,9,5,4,4,4,3,1,1,1,1,1] .empty .empty)) (.node [9,9,5,4,4,4,3,3,1,1] (.node [9,9,5,4,4,4,3,2,2,1] .empty .empty) (.node [9,9,5,4,4,4,3,3,2] .empty .empty)))) (.node [9,9,5,5,2,2,2,2,2,1,1,1,1,1] (.node [9,9,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,4,4,4,4,2,2] (.node [9,9,5,4,4,4,4,2,1,1] .empty .empty) (.node [9,9,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,5,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,5,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,5,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,5,2,2,2,2,2,2,2,1] (.node [9,9,5,5,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,5,3,2,2,2,1,1,1,1,1,1] (.node [9,9,5,5,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,5,3,2,2,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_278 : RowTree := (.node [9,9,5,5,4,2,2,1,1,1,1,1,1,1] (.node [9,9,5,5,3,3,3,2,1,1,1,1] (.node [9,9,5,5,3,3,2,2,1,1,1,1,1] (.node [9,9,5,5,3,3,1,1,1,1,1,1,1,1,1] (.node [9,9,5,5,3,2,2,2,2,2,2] .empty .empty) (.node [9,9,5,5,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,5,3,3,2,2,2,2,1] (.node [9,9,5,5,3,3,2,2,2,1,1,1] .empty .empty) (.node [9,9,5,5,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,5,3,3,3,3,2,1] (.node [9,9,5,5,3,3,3,2,2,2] (.node [9,9,5,5,3,3,3,2,2,1,1] .empty .empty) (.node [9,9,5,5,3,3,3,3,1,1,1] .empty .empty)) (.node [9,9,5,5,4,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,5,5,3,3,3,3,3] .empty .empty) (.node [9,9,5,5,4,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,9,5,5,4,3,2,2,2,2] (.node [9,9,5,5,4,3,1,1,1,1,1,1,1,1] (.node [9,9,5,5,4,2,2,2,2,1,1,1] (.node [9,9,5,5,4,2,2,2,1,1,1,1,1] .empty .empty) (.node [9,9,5,5,4,2,2,2,2,2,1] .empty .empty)) (.node [9,9,5,5,4,3,2,2,1,1,1,1] (.node [9,9,5,5,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,5,4,3,2,2,2,1,1] .empty .empty))) (.node [9,9,5,5,4,3,3,3,1,1] (.node [9,9,5,5,4,3,3,2,1,1,1] (.node [9,9,5,5,4,3,3,1,1,1,1,1] .empty .empty) (.node [9,9,5,5,4,3,3,2,2,1] .empty .empty)) (.node [9,9,5,5,4,4,1,1,1,1,1,1,1] (.node [9,9,5,5,4,3,3,3,2] .empty .empty) (.node [9,9,5,5,4,4,2,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_279 : RowTree := (.node [9,9,5,5,3,2,2,2,2,2,1,1] degreeTree43_277 degreeTree43_278) + +def degreeTree43_280 : RowTree := (.node [9,9,5,4,4,3,3,2,1,1,1,1] degreeTree43_276 degreeTree43_279) + +def degreeTree43_281 : RowTree := (.node [9,9,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_271 degreeTree43_280) + +def degreeTree43_282 : RowTree := (.node [9,9,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_262 degreeTree43_281) + +def degreeTree43_283 : RowTree := (.node [9,9,5,5,5,2,2,2,1,1,1,1] (.node [9,9,5,5,4,4,4,1,1,1] (.node [9,9,5,5,4,4,3,2,1,1] (.node [9,9,5,5,4,4,3,1,1,1,1] (.node [9,9,5,5,4,4,2,2,2,1] .empty .empty) .empty) (.node [9,9,5,5,4,4,3,2,2] .empty .empty)) (.node [9,9,5,5,5,2,1,1,1,1,1,1,1,1] (.node [9,9,5,5,5,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,5,5,5,2,2,1,1,1,1,1,1] .empty .empty))) (.node [9,9,5,5,5,3,2,1,1,1,1,1] (.node [9,9,5,5,5,2,2,2,2,2] (.node [9,9,5,5,5,2,2,2,2,1,1] .empty .empty) (.node [9,9,5,5,5,3,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,5,5,5,3,2,2,2,1] (.node [9,9,5,5,5,3,2,2,1,1,1] .empty .empty) (.node [9,9,5,5,5,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree43_284 : RowTree := (.node [9,9,5,5,5,5,2,1,1,1] (.node [9,9,5,5,5,4,2,2,1,1] (.node [9,9,5,5,5,4,1,1,1,1,1,1] (.node [9,9,5,5,5,3,3,2,2] .empty .empty) (.node [9,9,5,5,5,4,2,1,1,1,1] .empty .empty)) (.node [9,9,5,5,5,4,3,1,1,1] (.node [9,9,5,5,5,4,2,2,2] .empty .empty) (.node [9,9,5,5,5,5,1,1,1,1,1] .empty .empty))) (.node [9,9,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_285 : RowTree := (.node [9,9,5,5,5,3,3,2,1,1] degreeTree43_283 degreeTree43_284) + +def degreeTree43_286 : RowTree := (.node [9,9,6,3,3,2,2,2,2,1,1,1,1,1] (.node [9,9,6,3,2,2,2,2,2,1,1,1,1,1,1] (.node [9,9,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,2,2,2,2,2,2,2,2,2,1] (.node [9,9,6,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,3,2,2,2,2,2,2,2,1,1] (.node [9,9,6,3,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,9,6,3,2,2,2,2,2,2,2,2] .empty .empty)) (.node [9,9,6,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [9,9,6,3,3,3,2,2,2,2,2] (.node [9,9,6,3,3,3,2,1,1,1,1,1,1,1,1] (.node [9,9,6,3,3,2,2,2,2,2,2,1] (.node [9,9,6,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [9,9,6,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,3,3,3,2,2,2,1,1,1,1] (.node [9,9,6,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,3,3,3,2,2,2,2,1,1] .empty .empty))) (.node [9,9,6,3,3,3,3,2,2,2,1] (.node [9,9,6,3,3,3,3,2,1,1,1,1,1] (.node [9,9,6,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,3,3,3,3,2,2,1,1,1] .empty .empty)) (.node [9,9,6,3,3,3,3,3,2,1,1] (.node [9,9,6,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [9,9,6,3,3,3,3,3,2,2] .empty .empty))))) + +def degreeTree43_287 : RowTree := (.node [9,9,6,2,2,2,2,2,2,2,1,1,1,1,1] degreeTree43_285 degreeTree43_286) + +def degreeTree43_288 : RowTree := (.node [9,9,6,4,3,3,1,1,1,1,1,1,1,1,1] (.node [9,9,6,4,2,2,2,2,2,2,2,1] (.node [9,9,6,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,4,2,2,2,2,2,1,1,1,1,1] (.node [9,9,6,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [9,9,6,4,3,2,2,2,1,1,1,1,1,1] (.node [9,9,6,4,3,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,4,3,2,2,2,2,2,1,1] (.node [9,9,6,4,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,9,6,4,3,2,2,2,2,2,2] .empty .empty)))) (.node [9,9,6,4,3,3,3,2,2,2] (.node [9,9,6,4,3,3,2,2,2,2,1] (.node [9,9,6,4,3,3,2,2,1,1,1,1,1] (.node [9,9,6,4,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,3,3,2,2,2,1,1,1] .empty .empty)) (.node [9,9,6,4,3,3,3,2,1,1,1,1] (.node [9,9,6,4,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,3,3,3,2,2,1,1] .empty .empty))) (.node [9,9,6,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,4,3,3,3,3,2,1] (.node [9,9,6,4,3,3,3,3,1,1,1] .empty .empty) (.node [9,9,6,4,3,3,3,3,3] .empty .empty)) (.node [9,9,6,4,4,2,2,1,1,1,1,1,1,1] (.node [9,9,6,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,4,2,2,2,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_289 : RowTree := (.node [9,9,6,4,4,4,3,1,1,1,1] (.node [9,9,6,4,4,3,3,2,1,1,1] (.node [9,9,6,4,4,3,2,2,1,1,1,1] (.node [9,9,6,4,4,3,1,1,1,1,1,1,1,1] (.node [9,9,6,4,4,2,2,2,2,2,1] .empty .empty) (.node [9,9,6,4,4,3,2,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,4,4,3,2,2,2,2] (.node [9,9,6,4,4,3,2,2,2,1,1] .empty .empty) (.node [9,9,6,4,4,3,3,1,1,1,1,1] .empty .empty))) (.node [9,9,6,4,4,4,1,1,1,1,1,1,1] (.node [9,9,6,4,4,3,3,3,1,1] (.node [9,9,6,4,4,3,3,2,2,1] .empty .empty) (.node [9,9,6,4,4,3,3,3,2] .empty .empty)) (.node [9,9,6,4,4,4,2,2,1,1,1] (.node [9,9,6,4,4,4,2,1,1,1,1,1] .empty .empty) (.node [9,9,6,4,4,4,2,2,2,1] .empty .empty)))) (.node [9,9,6,5,2,2,2,2,1,1,1,1,1,1] (.node [9,9,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,4,4,4,3,2,2] (.node [9,9,6,4,4,4,3,2,1,1] .empty .empty) (.node [9,9,6,4,4,4,4,1,1,1] .empty .empty)) (.node [9,9,6,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,6,5,3,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,5,2,2,2,2,2,2,1,1] (.node [9,9,6,5,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [9,9,6,5,2,2,2,2,2,2,2] .empty .empty)) (.node [9,9,6,5,3,2,2,1,1,1,1,1,1,1] (.node [9,9,6,5,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,5,3,2,2,2,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_290 : RowTree := (.node [9,9,6,4,4,2,2,2,2,1,1,1] degreeTree43_288 degreeTree43_289) + +def degreeTree43_291 : RowTree := (.node [9,9,6,3,3,3,3,3,3,1] degreeTree43_287 degreeTree43_290) + +def degreeTree43_292 : RowTree := (.node [9,9,6,5,3,3,3,2,2,1] (.node [9,9,6,5,3,3,2,2,2,1,1] (.node [9,9,6,5,3,3,2,1,1,1,1,1,1] (.node [9,9,6,5,3,3,1,1,1,1,1,1,1,1] (.node [9,9,6,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [9,9,6,5,3,3,2,2,1,1,1,1] .empty .empty)) (.node [9,9,6,5,3,3,3,1,1,1,1,1] (.node [9,9,6,5,3,3,2,2,2,2] .empty .empty) (.node [9,9,6,5,3,3,3,2,1,1,1] .empty .empty))) (.node [9,9,6,5,4,2,1,1,1,1,1,1,1,1] (.node [9,9,6,5,3,3,3,3,2] (.node [9,9,6,5,3,3,3,3,1,1] .empty .empty) (.node [9,9,6,5,4,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,5,4,2,2,2,1,1,1,1] (.node [9,9,6,5,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,5,4,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree43_293 : RowTree := (.node [9,9,6,5,4,4,1,1,1,1,1,1] (.node [9,9,6,5,4,3,2,2,2,1] (.node [9,9,6,5,4,3,2,1,1,1,1,1] (.node [9,9,6,5,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,5,4,3,2,2,1,1,1] .empty .empty)) (.node [9,9,6,5,4,3,3,2,1,1] (.node [9,9,6,5,4,3,3,1,1,1,1] .empty .empty) (.node [9,9,6,5,4,3,3,2,2] .empty .empty))) (.node [9,9,6,5,4,4,3,1,1,1] (.node [9,9,6,5,4,4,2,2,1,1] (.node [9,9,6,5,4,4,2,1,1,1,1] .empty .empty) (.node [9,9,6,5,4,4,2,2,2] .empty .empty)) (.node [9,9,6,5,5,2,1,1,1,1,1,1,1] (.node [9,9,6,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,5,5,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_294 : RowTree := (.node [9,9,6,5,4,2,2,2,2,2] degreeTree43_292 degreeTree43_293) + +def degreeTree43_295 : RowTree := (.node [9,9,6,6,2,2,2,2,2,2,1] (.node [9,9,6,5,5,4,2,1,1,1] (.node [9,9,6,5,5,3,2,2,1,1] (.node [9,9,6,5,5,3,1,1,1,1,1,1] (.node [9,9,6,5,5,2,2,2,2,1] .empty .empty) (.node [9,9,6,5,5,3,2,1,1,1,1] .empty .empty)) (.node [9,9,6,5,5,3,3,1,1,1] (.node [9,9,6,5,5,3,2,2,2] .empty .empty) (.node [9,9,6,5,5,4,1,1,1,1,1] .empty .empty))) (.node [9,9,6,6,2,2,1,1,1,1,1,1,1,1,1] (.node [9,9,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [9,9,6,5,5,5,1,1,1,1] .empty .empty) (.node [9,9,6,6,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,6,2,2,2,2,1,1,1,1,1] (.node [9,9,6,6,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,6,2,2,2,2,2,1,1,1] .empty .empty)))) (.node [9,9,6,6,3,3,2,1,1,1,1,1] (.node [9,9,6,6,3,2,2,2,1,1,1,1] (.node [9,9,6,6,3,2,1,1,1,1,1,1,1,1] (.node [9,9,6,6,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,6,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,6,3,2,2,2,2,2] (.node [9,9,6,6,3,2,2,2,2,1,1] .empty .empty) (.node [9,9,6,6,3,3,1,1,1,1,1,1,1] .empty .empty))) (.node [9,9,6,6,3,3,3,2,1,1] (.node [9,9,6,6,3,3,2,2,2,1] (.node [9,9,6,6,3,3,2,2,1,1,1] .empty .empty) (.node [9,9,6,6,3,3,3,1,1,1,1] .empty .empty)) (.node [9,9,6,6,4,1,1,1,1,1,1,1,1,1] (.node [9,9,6,6,3,3,3,2,2] .empty .empty) (.node [9,9,6,6,4,2,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_296 : RowTree := (.node [9,9,6,5,5,2,2,2,1,1,1] degreeTree43_294 degreeTree43_295) + +def degreeTree43_297 : RowTree := (.node [9,9,6,6,6,1,1,1,1,1,1,1] (.node [9,9,6,6,4,4,2,1,1,1] (.node [9,9,6,6,4,3,2,1,1,1,1] (.node [9,9,6,6,4,2,2,2,2,1] (.node [9,9,6,6,4,2,2,2,1,1,1] .empty .empty) (.node [9,9,6,6,4,3,1,1,1,1,1,1] .empty .empty)) (.node [9,9,6,6,4,3,3,1,1,1] (.node [9,9,6,6,4,3,2,2,1,1] .empty .empty) (.node [9,9,6,6,4,4,1,1,1,1,1] .empty .empty))) (.node [9,9,6,6,5,2,2,2,1,1] (.node [9,9,6,6,5,2,1,1,1,1,1,1] (.node [9,9,6,6,5,1,1,1,1,1,1,1,1] .empty .empty) (.node [9,9,6,6,5,2,2,1,1,1,1] .empty .empty)) (.node [9,9,6,6,5,3,2,1,1,1] (.node [9,9,6,6,5,3,1,1,1,1,1] .empty .empty) (.node [9,9,6,6,5,4,1,1,1,1] .empty .empty)))) (.node [9,9,7,4,3,3,3,2,2,1] (.node [9,9,7,3,3,3,3,2,2,2] (.node [9,9,6,6,6,2,2,1,1,1] (.node [9,9,6,6,6,2,1,1,1,1,1] .empty .empty) (.node [9,9,6,6,6,3,1,1,1,1] .empty .empty)) (.node [9,9,7,3,3,3,3,3,3] (.node [9,9,7,3,3,3,3,3,2,1] .empty .empty) (.node [9,9,7,4,3,3,2,2,2,2] .empty .empty))) (.node [9,9,7,4,4,3,2,2,2,1] (.node [9,9,7,4,3,3,3,3,2] (.node [9,9,7,4,3,3,3,3,1,1] .empty .empty) (.node [9,9,7,4,4,2,2,2,2,2] .empty .empty)) (.node [9,9,7,4,4,3,3,2,2] (.node [9,9,7,4,4,3,3,2,1,1] .empty .empty) (.node [9,9,7,4,4,4,2,2,1,1] .empty .empty))))) + +def degreeTree43_298 : RowTree := (.node [9,9,7,6,4,3,2,1,1,1] (.node [9,9,7,5,5,2,2,2,1,1] (.node [9,9,7,5,4,2,2,2,2,1] (.node [9,9,7,5,3,3,2,2,2,1] (.node [9,9,7,5,3,2,2,2,2,2] .empty .empty) (.node [9,9,7,5,3,3,3,2,1,1] .empty .empty)) (.node [9,9,7,5,4,3,3,1,1,1] (.node [9,9,7,5,4,3,2,2,1,1] .empty .empty) (.node [9,9,7,5,4,4,2,1,1,1] .empty .empty))) (.node [9,9,7,6,3,2,2,2,2,1] (.node [9,9,7,5,5,4,1,1,1,1] (.node [9,9,7,5,5,3,2,1,1,1] .empty .empty) (.node [9,9,7,6,2,2,2,2,2,2] .empty .empty)) (.node [9,9,7,6,3,3,3,1,1,1] (.node [9,9,7,6,3,3,2,2,1,1] .empty .empty) (.node [9,9,7,6,4,2,2,2,1,1] .empty .empty)))) (.node [9,9,7,7,4,2,2,1,1,1] (.node [9,9,7,6,6,2,1,1,1,1] (.node [9,9,7,6,5,2,2,1,1,1] (.node [9,9,7,6,4,4,1,1,1,1] .empty .empty) (.node [9,9,7,6,5,3,1,1,1,1] .empty .empty)) (.node [9,9,7,7,3,2,2,2,1,1] (.node [9,9,7,7,2,2,2,2,2,1] .empty .empty) (.node [9,9,7,7,3,3,2,1,1,1] .empty .empty))) (.node [9,9,8,3,3,3,2,2,2,2] (.node [9,9,7,7,5,2,1,1,1,1] (.node [9,9,7,7,4,3,1,1,1,1] .empty .empty) (.node [9,9,7,7,6,1,1,1,1,1] .empty .empty)) (.node [9,9,8,3,3,3,3,3,1,1] (.node [9,9,8,3,3,3,3,2,2,1] .empty .empty) (.node [9,9,8,3,3,3,3,3,2] .empty .empty))))) + +def degreeTree43_299 : RowTree := (.node [9,9,7,4,4,4,3,1,1,1] degreeTree43_297 degreeTree43_298) + +def degreeTree43_300 : RowTree := (.node [9,9,6,6,4,2,2,1,1,1,1,1] degreeTree43_296 degreeTree43_299) + +def degreeTree43_301 : RowTree := (.node [9,9,6,5,3,2,2,2,2,1,1,1] degreeTree43_291 degreeTree43_300) + +def degreeTree43_302 : RowTree := (.node [9,9,8,5,3,3,2,2,1,1] (.node [9,9,8,4,4,3,3,1,1,1] (.node [9,9,8,4,4,2,2,2,2,1] (.node [9,9,8,4,3,3,3,2,1,1] (.node [9,9,8,4,3,3,2,2,2,1] .empty .empty) .empty) (.node [9,9,8,4,4,3,2,2,1,1] .empty .empty)) (.node [9,9,8,5,2,2,2,2,2,2] (.node [9,9,8,4,4,4,2,1,1,1] .empty .empty) (.node [9,9,8,5,3,2,2,2,2,1] .empty .empty))) (.node [9,9,8,5,4,4,1,1,1,1] (.node [9,9,8,5,4,2,2,2,1,1] (.node [9,9,8,5,3,3,3,1,1,1] .empty .empty) (.node [9,9,8,5,4,3,2,1,1,1] .empty .empty)) (.node [9,9,8,5,5,3,1,1,1,1] (.node [9,9,8,5,5,2,2,1,1,1] .empty .empty) (.node [9,9,8,6,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree43_303 : RowTree := (.node [9,9,8,7,3,3,1,1,1,1] (.node [9,9,8,6,5,2,1,1,1,1] (.node [9,9,8,6,4,2,2,1,1,1] (.node [9,9,8,6,3,3,2,1,1,1] .empty .empty) (.node [9,9,8,6,4,3,1,1,1,1] .empty .empty)) (.node [9,9,8,7,2,2,2,2,1,1] (.node [9,9,8,6,6,1,1,1,1,1] .empty .empty) (.node [9,9,8,7,3,2,2,1,1,1] .empty .empty))) (.node [9,9,8,8,3,2,1,1,1,1] (.node [9,9,8,7,5,1,1,1,1,1] (.node [9,9,8,7,4,2,1,1,1,1] .empty .empty) (.node [9,9,8,8,2,2,2,1,1,1] .empty .empty)) (.node [9,9,9,3,3,2,2,2,2,2] (.node [9,9,8,8,4,1,1,1,1,1] .empty .empty) (.node [9,9,9,3,3,3,2,2,2,1] .empty .empty)))) + +def degreeTree43_304 : RowTree := (.node [9,9,8,6,3,2,2,2,1,1] degreeTree43_302 degreeTree43_303) + +def degreeTree43_305 : RowTree := (.node [9,9,9,6,3,3,1,1,1,1] (.node [9,9,9,5,2,2,2,2,2,1] (.node [9,9,9,4,3,3,3,1,1,1] (.node [9,9,9,4,3,2,2,2,2,1] (.node [9,9,9,4,2,2,2,2,2,2] .empty .empty) (.node [9,9,9,4,3,3,2,2,1,1] .empty .empty)) (.node [9,9,9,4,4,3,2,1,1,1] (.node [9,9,9,4,4,2,2,2,1,1] .empty .empty) (.node [9,9,9,4,4,4,1,1,1,1] .empty .empty))) (.node [9,9,9,5,4,3,1,1,1,1] (.node [9,9,9,5,3,3,2,1,1,1] (.node [9,9,9,5,3,2,2,2,1,1] .empty .empty) (.node [9,9,9,5,4,2,2,1,1,1] .empty .empty)) (.node [9,9,9,6,2,2,2,2,1,1] (.node [9,9,9,5,5,2,1,1,1,1] .empty .empty) (.node [9,9,9,6,3,2,2,1,1,1] .empty .empty)))) (.node [9,9,9,9,2,1,1,1,1,1] (.node [9,9,9,7,3,2,1,1,1,1] (.node [9,9,9,6,5,1,1,1,1,1] (.node [9,9,9,6,4,2,1,1,1,1] .empty .empty) (.node [9,9,9,7,2,2,2,1,1,1] .empty .empty)) (.node [9,9,9,8,2,2,1,1,1,1] (.node [9,9,9,7,4,1,1,1,1,1] .empty .empty) (.node [9,9,9,8,3,1,1,1,1,1] .empty .empty))) (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_306 : RowTree := (.node [9,9,9,3,3,3,3,2,1,1] degreeTree43_304 degreeTree43_305) + +def degreeTree43_307 : RowTree := (.node [10,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,3,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2] (.node [10,3,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,3,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,2,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,3,3,3,2,2,2,2,2,2,2,2,2,2,1] (.node [10,3,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,3,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_308 : RowTree := (.node [10,3,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,2,2,2,2,2,2,2,1,1] (.node [10,3,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,3,3,3,3,3,3,2,2,2,2,2,2,1,1,1] (.node [10,3,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,3,3,3,3,3,3,3,3,2,2,2,1,1,1] (.node [10,3,3,3,3,3,3,3,2,2,2,2,2,2] (.node [10,3,3,3,3,3,3,3,2,2,2,2,1,1,1,1] (.node [10,3,3,3,3,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,2,2,2,2,2,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,3,3,2,1,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,3,2,2,1,1,1,1,1] .empty .empty))) (.node [10,3,3,3,3,3,3,3,3,3,2,2,1,1] (.node [10,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1] (.node [10,3,3,3,3,3,3,3,3,2,2,2,2,1] .empty .empty) (.node [10,3,3,3,3,3,3,3,3,3,2,1,1,1,1] .empty .empty)) (.node [10,3,3,3,3,3,3,3,3,3,3,1,1,1] (.node [10,3,3,3,3,3,3,3,3,3,2,2,2] .empty .empty) (.node [10,3,3,3,3,3,3,3,3,3,3,2,1] .empty .empty))))) + +def degreeTree43_309 : RowTree := (.node [10,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_307 degreeTree43_308) + +def degreeTree43_310 : RowTree := (.node [10,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_306 degreeTree43_309) + +def degreeTree43_311 : RowTree := (.node [10,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,4,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,4,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,2,2,2,2,2,2,2,2,2,2,2,2,2] (.node [10,4,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_312 : RowTree := (.node [10,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,4,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,4,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,2,2,2,2,2,2,2,2,2,1,1] (.node [10,4,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,2,2,2,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree43_313 : RowTree := (.node [10,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_311 degreeTree43_312) + +def degreeTree43_314 : RowTree := (.node [10,4,3,3,3,3,3,2,2,2,2,2,2,2] (.node [10,4,3,3,3,3,2,2,2,2,2,2,2,2,1] (.node [10,4,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,4,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,3,3,2,2,2,2,2,1,1,1,1] (.node [10,4,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,2,2,2,2,2,2,1,1] .empty .empty)))) (.node [10,4,3,3,3,3,3,3,3,2,1,1,1,1,1,1] (.node [10,4,3,3,3,3,3,3,2,2,2,1,1,1,1,1] (.node [10,4,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] (.node [10,4,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,3,3,3,3,3,3,2,2,2,2,2,1] (.node [10,4,3,3,3,3,3,3,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,3,3,3,3,3,3,3,3,1,1,1,1,1] (.node [10,4,3,3,3,3,3,3,3,2,2,2,1,1] (.node [10,4,3,3,3,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,3,3,2,2,2,2] .empty .empty)) (.node [10,4,3,3,3,3,3,3,3,3,2,2,1] (.node [10,4,3,3,3,3,3,3,3,3,2,1,1,1] .empty .empty) (.node [10,4,3,3,3,3,3,3,3,3,3,1,1] .empty .empty))))) + +def degreeTree43_315 : RowTree := (.node [10,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_313 degreeTree43_314) + +def degreeTree43_316 : RowTree := (.node [10,4,4,3,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,4,4,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,4,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)))) (.node [10,4,4,3,3,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,2,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,2,2,2,2,2,2,2,2,2,1] (.node [10,4,4,3,3,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_317 : RowTree := (.node [10,4,4,3,3,3,3,3,2,2,2,2,2] (.node [10,4,4,3,3,3,3,2,2,2,2,1,1,1,1,1] (.node [10,4,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,2,2,2,2,2,2,2,1,1] (.node [10,4,4,3,3,3,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,4,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,3,3,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,4,4,3,3,3,3,2,2,2,2,2,2,1] (.node [10,4,4,3,3,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,3,3,3,3,3,2,2,2,1,1,1,1] (.node [10,4,4,3,3,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,3,3,2,2,2,2,1,1] .empty .empty)))) (.node [10,4,4,3,3,3,3,3,3,3,3,1] (.node [10,4,4,3,3,3,3,3,3,2,2,2,1] (.node [10,4,4,3,3,3,3,3,3,2,1,1,1,1,1] (.node [10,4,4,3,3,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,3,3,3,2,2,1,1,1] .empty .empty)) (.node [10,4,4,3,3,3,3,3,3,3,2,1,1] (.node [10,4,4,3,3,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [10,4,4,3,3,3,3,3,3,3,2,2] .empty .empty))) (.node [10,4,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_318 : RowTree := (.node [10,4,4,3,3,3,2,2,2,2,2,1,1,1,1,1,1] degreeTree43_316 degreeTree43_317) + +def degreeTree43_319 : RowTree := (.node [10,4,3,3,3,3,3,3,3,3,3,2] degreeTree43_315 degreeTree43_318) + +def degreeTree43_320 : RowTree := (.node [10,3,3,3,3,3,3,3,3,3,3,3] degreeTree43_310 degreeTree43_319) + +def degreeTree43_321 : RowTree := (.node [9,9,8,4,3,2,2,2,2,2] degreeTree43_301 degreeTree43_320) + +def degreeTree43_322 : RowTree := (.node [9,9,5,5,4,4,2,2,1,1,1] degreeTree43_282 degreeTree43_321) + +def degreeTree43_323 : RowTree := (.node [9,8,7,7,5,3,1,1,1,1] degreeTree43_243 degreeTree43_322) + +def degreeTree43_324 : RowTree := (.node [9,7,5,5,5,5,3,2,2] degreeTree43_162 degreeTree43_323) + +def degreeTree43_325 : RowTree := (.node [10,4,4,4,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,4,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,3,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,2,2,2,2,2,2,2,2,2] (.node [10,4,4,4,3,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,3,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_326 : RowTree := (.node [10,4,4,4,3,3,3,2,2,2,2,2,1,1] (.node [10,4,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,2,2,2,2,2,2,2,1] (.node [10,4,4,4,3,3,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,3,3,2,2,2,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,3,3,3,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,4,4,4,3,3,3,3,2,2,1,1,1,1,1] (.node [10,4,4,4,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,4,4,4,3,3,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,3,3,3,3,2,2,2,2,1] (.node [10,4,4,4,3,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,4,4,4,3,3,3,3,3,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_327 : RowTree := (.node [10,4,4,4,3,3,2,2,2,2,2,1,1,1,1,1] degreeTree43_325 degreeTree43_326) + +def degreeTree43_328 : RowTree := (.node [10,4,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,3,3,3,2,1] (.node [10,4,4,4,3,3,3,3,3,2,2,2] (.node [10,4,4,4,3,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,4,4,4,3,3,3,3,3,3,1,1,1] .empty .empty)) (.node [10,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,3,3,3,3,3,3,3] .empty .empty) (.node [10,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,4,4,2,2,2,2,2,2,1,1,1,1,1] (.node [10,4,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,2,2,2,2,2,2,2,2,1] (.node [10,4,4,4,4,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,4,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,4,4,4,4,3,3,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,3,2,2,2,2,2,1,1,1,1] (.node [10,4,4,4,4,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,3,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,3,2,2,2,2,2,2,2] (.node [10,4,4,4,4,3,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,4,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,4,4,3,3,2,2,2,2,2,1] (.node [10,4,4,4,4,3,3,2,2,2,1,1,1,1,1] (.node [10,4,4,4,4,3,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,3,3,2,2,2,2,1,1,1] .empty .empty)) (.node [10,4,4,4,4,3,3,3,2,1,1,1,1,1,1] (.node [10,4,4,4,4,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,3,3,3,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_329 : RowTree := (.node [10,4,4,4,3,3,3,3,3,2,1,1,1,1] degreeTree43_327 degreeTree43_328) + +def degreeTree43_330 : RowTree := (.node [10,4,4,4,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,3,3,3,3,3,1,1] (.node [10,4,4,4,4,3,3,3,3,2,1,1,1] (.node [10,4,4,4,4,3,3,3,3,1,1,1,1,1] (.node [10,4,4,4,4,3,3,3,2,2,2,2] .empty .empty) .empty) (.node [10,4,4,4,4,3,3,3,3,2,2,1] .empty .empty)) (.node [10,4,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,3,3,3,3,3,2] .empty .empty) (.node [10,4,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,4,4,4,4,4,2,2,2,2,2,2,1] (.node [10,4,4,4,4,4,2,2,2,2,1,1,1,1,1] (.node [10,4,4,4,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,4,4,4,4,4,3,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,4,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,3,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_331 : RowTree := (.node [10,4,4,4,4,4,3,3,3,2,1,1] (.node [10,4,4,4,4,4,3,3,2,1,1,1,1,1] (.node [10,4,4,4,4,4,3,2,2,2,2,2] (.node [10,4,4,4,4,4,3,2,2,2,2,1,1] .empty .empty) (.node [10,4,4,4,4,4,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,4,3,3,2,2,2,1] (.node [10,4,4,4,4,4,3,3,2,2,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,3,3,3,1,1,1,1] .empty .empty))) (.node [10,4,4,4,4,4,4,2,1,1,1,1,1,1,1] (.node [10,4,4,4,4,4,3,3,3,3,1] (.node [10,4,4,4,4,4,3,3,3,2,2] .empty .empty) (.node [10,4,4,4,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,4,4,4,4,4,4,2,2,2,1,1,1] (.node [10,4,4,4,4,4,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,4,2,2,2,2,1] .empty .empty)))) + +def degreeTree43_332 : RowTree := (.node [10,4,4,4,4,4,3,2,2,2,1,1,1,1] degreeTree43_330 degreeTree43_331) + +def degreeTree43_333 : RowTree := (.node [10,5,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,4,4,4,4,4,4,4,2,1,1,1] (.node [10,4,4,4,4,4,4,3,3,1,1,1] (.node [10,4,4,4,4,4,4,3,2,2,1,1] (.node [10,4,4,4,4,4,4,3,2,1,1,1,1] .empty .empty) (.node [10,4,4,4,4,4,4,3,2,2,2] .empty .empty)) (.node [10,4,4,4,4,4,4,3,3,3] (.node [10,4,4,4,4,4,4,3,3,2,1] .empty .empty) (.node [10,4,4,4,4,4,4,4,1,1,1,1,1] .empty .empty))) (.node [10,4,4,4,4,4,4,4,4,1] (.node [10,4,4,4,4,4,4,4,3,1,1] (.node [10,4,4,4,4,4,4,4,2,2,1] .empty .empty) (.node [10,4,4,4,4,4,4,4,3,2] .empty .empty)) (.node [10,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,2,2,2,2,2,2,2,2,2,2,2,2,2,2] (.node [10,5,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,3,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,5,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,5,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_334 : RowTree := (.node [10,4,4,4,4,4,4,3,1,1,1,1,1,1] degreeTree43_332 degreeTree43_333) + +def degreeTree43_335 : RowTree := (.node [10,4,4,4,4,3,3,3,2,2,2,1,1] degreeTree43_329 degreeTree43_334) + +def degreeTree43_336 : RowTree := (.node [10,5,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,2,2,2,2,2,2,2,2,2,2,2] (.node [10,5,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,5,3,3,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,3,3,3,2,2,2,2,2,2,2,2,1,1,1] (.node [10,5,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,5,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_337 : RowTree := (.node [10,5,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,2,2,2,2,2,2,1,1,1,1] (.node [10,5,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,3,3,3,3,2,2,2,2,2,2,2,2] (.node [10,5,3,3,3,3,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,3,3,3,3,3,2,2,2,2,2,1,1,1] (.node [10,5,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,5,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_338 : RowTree := (.node [10,5,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_336 degreeTree43_337) + +def degreeTree43_339 : RowTree := (.node [10,5,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,3,3,3,1,1,1,1] (.node [10,5,3,3,3,3,3,3,3,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,3,2,2,2,2,1,1] (.node [10,5,3,3,3,3,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,3,2,2,2,2,2] .empty .empty)) (.node [10,5,3,3,3,3,3,3,3,2,2,1,1,1] (.node [10,5,3,3,3,3,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,3,3,2,2,2,1] .empty .empty))) (.node [10,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,3,3,3,3,3,3,3,3,2,2] (.node [10,5,3,3,3,3,3,3,3,3,2,1,1] .empty .empty) (.node [10,5,3,3,3,3,3,3,3,3,3,1] .empty .empty)) (.node [10,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,2,2,2,2,2,2,2,2,2,2,2,2] (.node [10,5,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,2,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,3,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,5,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_340 : RowTree := (.node [10,5,3,3,3,3,3,3,2,2,1,1,1,1,1,1] degreeTree43_338 degreeTree43_339) + +def degreeTree43_341 : RowTree := (.node [10,5,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,3,2,2,2,2,2,2,2,2,1,1] (.node [10,5,4,3,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,2,2,2,2,2,2,2,2,2] .empty .empty))) (.node [10,5,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,3,3,2,2,2,2,2,2,1,1,1] (.node [10,5,4,3,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,2,2,2,2,2,2,2,1] .empty .empty)))) (.node [10,5,4,3,3,3,3,3,2,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,3,2,2,2,2,1,1,1,1] (.node [10,5,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,3,3,3,3,2,2,2,2,2,2] (.node [10,5,4,3,3,3,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,3,3,3,3,3,3,1,1,1,1,1,1] (.node [10,5,4,3,3,3,3,3,2,2,2,1,1,1] (.node [10,5,4,3,3,3,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,3,2,2,2,2,1] .empty .empty)) (.node [10,5,4,3,3,3,3,3,3,2,2,1,1] (.node [10,5,4,3,3,3,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,5,4,3,3,3,3,3,3,2,2,2] .empty .empty))))) + +def degreeTree43_342 : RowTree := (.node [10,5,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,3,3,3,3,3,3,3,3] (.node [10,5,4,3,3,3,3,3,3,3,2,1] .empty .empty) (.node [10,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,4,2,2,2,2,2,2,2,2,2,2] (.node [10,5,4,4,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,5,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,3,2,2,2,2,2,2,2,1,1,1] (.node [10,5,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,3,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,5,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,4,3,3,2,2,2,2,2,2,1,1] (.node [10,5,4,4,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,5,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,3,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,3,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,5,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_343 : RowTree := (.node [10,5,4,3,3,3,3,3,3,3,1,1,1] degreeTree43_341 degreeTree43_342) + +def degreeTree43_344 : RowTree := (.node [10,5,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_340 degreeTree43_343) + +def degreeTree43_345 : RowTree := (.node [10,5,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_335 degreeTree43_344) + +def degreeTree43_346 : RowTree := (.node [10,5,4,4,3,3,3,3,3,1,1,1,1,1] (.node [10,5,4,4,3,3,3,3,2,1,1,1,1,1,1] (.node [10,5,4,4,3,3,3,2,2,2,2,2,1] (.node [10,5,4,4,3,3,3,2,2,2,2,1,1,1] (.node [10,5,4,4,3,3,3,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,5,4,4,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,3,3,3,3,2,2,2,1,1] (.node [10,5,4,4,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,5,4,4,3,3,3,3,2,2,2,2] .empty .empty))) (.node [10,5,4,4,3,3,3,3,3,3,2] (.node [10,5,4,4,3,3,3,3,3,2,2,1] (.node [10,5,4,4,3,3,3,3,3,2,1,1,1] .empty .empty) (.node [10,5,4,4,3,3,3,3,3,3,1,1] .empty .empty)) (.node [10,5,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_347 : RowTree := (.node [10,5,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,2,2,2,2,2,2,2,1,1] (.node [10,5,4,4,4,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,4,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,5,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,4,4,3,2,2,2,2,2,2,1] (.node [10,5,4,4,4,3,2,2,2,2,1,1,1,1,1] (.node [10,5,4,4,4,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,4,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,5,4,4,4,3,3,2,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,4,3,3,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_348 : RowTree := (.node [10,5,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_346 degreeTree43_347) + +def degreeTree43_349 : RowTree := (.node [10,5,4,4,4,4,2,2,2,2,2,1,1] (.node [10,5,4,4,4,3,3,3,3,2,1,1] (.node [10,5,4,4,4,3,3,3,2,1,1,1,1,1] (.node [10,5,4,4,4,3,3,2,2,2,2,2] (.node [10,5,4,4,4,3,3,2,2,2,2,1,1] .empty .empty) (.node [10,5,4,4,4,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,3,3,3,2,2,2,1] (.node [10,5,4,4,4,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,5,4,4,4,3,3,3,3,1,1,1,1] .empty .empty))) (.node [10,5,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,3,3,3,3,3,1] (.node [10,5,4,4,4,3,3,3,3,2,2] .empty .empty) (.node [10,5,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,4,2,2,2,1,1,1,1,1,1] (.node [10,5,4,4,4,4,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,4,4,4,4,2,2,2,2,1,1,1,1] .empty .empty)))) (.node [10,5,4,4,4,4,3,3,2,1,1,1,1] (.node [10,5,4,4,4,4,3,2,2,1,1,1,1,1] (.node [10,5,4,4,4,4,3,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,4,2,2,2,2,2,2] .empty .empty) (.node [10,5,4,4,4,4,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,4,3,2,2,2,2,1] (.node [10,5,4,4,4,4,3,2,2,2,1,1,1] .empty .empty) (.node [10,5,4,4,4,4,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,5,4,4,4,4,3,3,3,2,1] (.node [10,5,4,4,4,4,3,3,2,2,2] (.node [10,5,4,4,4,4,3,3,2,2,1,1] .empty .empty) (.node [10,5,4,4,4,4,3,3,3,1,1,1] .empty .empty)) (.node [10,5,4,4,4,4,4,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,4,3,3,3,3] .empty .empty) (.node [10,5,4,4,4,4,4,2,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_350 : RowTree := (.node [10,5,4,4,4,3,3,2,2,2,1,1,1,1] degreeTree43_348 degreeTree43_349) + +def degreeTree43_351 : RowTree := (.node [10,5,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,4,4,4,1,1,1,1] (.node [10,5,4,4,4,4,4,3,2,1,1,1] (.node [10,5,4,4,4,4,4,2,2,2,2] (.node [10,5,4,4,4,4,4,2,2,2,1,1] .empty .empty) (.node [10,5,4,4,4,4,4,3,1,1,1,1,1] .empty .empty)) (.node [10,5,4,4,4,4,4,3,3,1,1] (.node [10,5,4,4,4,4,4,3,2,2,1] .empty .empty) (.node [10,5,4,4,4,4,4,3,3,2] .empty .empty))) (.node [10,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,4,4,4,4,4,4,2,2] (.node [10,5,4,4,4,4,4,4,2,1,1] .empty .empty) (.node [10,5,4,4,4,4,4,4,3,1] .empty .empty)) (.node [10,5,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,5,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,5,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,3,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,5,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,5,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,3,2,2,2,2,2,2,2,2,2,2] (.node [10,5,5,3,2,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_352 : RowTree := (.node [10,5,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,3,3,2,2,2,2,2,2,2,1,1,1] (.node [10,5,5,3,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,2,2,2,2,2,2,2,2,1] .empty .empty))) (.node [10,5,5,3,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,5,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,3,3,3,2,2,2,2,2,2,1,1] (.node [10,5,5,3,3,3,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,3,2,2,2,2,2,2,2] .empty .empty)))) (.node [10,5,5,3,3,3,3,3,2,2,1,1,1,1] (.node [10,5,5,3,3,3,3,2,2,2,2,1,1,1] (.node [10,5,5,3,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,5,5,3,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,3,3,3,3,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,3,3,3,3,3,1,1,1,1,1,1,1,1] (.node [10,5,5,3,3,3,3,2,2,2,2,2,1] .empty .empty) (.node [10,5,5,3,3,3,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,3,3,3,3,3,3,2,1,1,1] (.node [10,5,5,3,3,3,3,3,2,2,2,2] (.node [10,5,5,3,3,3,3,3,2,2,2,1,1] .empty .empty) (.node [10,5,5,3,3,3,3,3,3,1,1,1,1,1] .empty .empty)) (.node [10,5,5,3,3,3,3,3,3,3,1,1] (.node [10,5,5,3,3,3,3,3,3,2,2,1] .empty .empty) (.node [10,5,5,3,3,3,3,3,3,3,2] .empty .empty))))) + +def degreeTree43_353 : RowTree := (.node [10,5,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_351 degreeTree43_352) + +def degreeTree43_354 : RowTree := (.node [10,5,4,4,4,4,4,2,2,1,1,1,1] degreeTree43_350 degreeTree43_353) + +def degreeTree43_355 : RowTree := (.node [10,5,5,4,2,2,2,2,2,2,2,2,2,1] (.node [10,5,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,5,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,5,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,2,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,5,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,5,4,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,3,2,2,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree43_356 : RowTree := (.node [10,5,5,4,3,3,2,2,2,2,2,2,1] (.node [10,5,5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,5,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,3,2,2,2,2,1,1,1,1,1] (.node [10,5,5,4,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,3,3,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,5,5,4,3,3,3,2,2,2,1,1,1,1] (.node [10,5,5,4,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,3,3,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,3,3,2,2,2,2,2] (.node [10,5,5,4,3,3,3,2,2,2,2,1,1] .empty .empty) (.node [10,5,5,4,3,3,3,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_357 : RowTree := (.node [10,5,5,4,3,2,2,2,2,2,2,2,1,1] degreeTree43_355 degreeTree43_356) + +def degreeTree43_358 : RowTree := (.node [10,5,5,4,4,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,3,3,3,3,3,2,1,1] (.node [10,5,5,4,3,3,3,3,2,2,2,1] (.node [10,5,5,4,3,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,5,5,4,3,3,3,3,3,1,1,1,1] .empty .empty)) (.node [10,5,5,4,3,3,3,3,3,3,1] (.node [10,5,5,4,3,3,3,3,3,2,2] .empty .empty) (.node [10,5,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,4,4,2,2,2,2,2,1,1,1,1,1] (.node [10,5,5,4,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,2,2,2,2,2,2,2,1] (.node [10,5,5,4,4,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,5,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,5,4,4,3,3,2,2,1,1,1,1,1] (.node [10,5,5,4,4,3,2,2,2,2,2,1,1] (.node [10,5,5,4,4,3,2,2,2,1,1,1,1,1,1] (.node [10,5,5,4,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,4,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,3,3,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,3,2,2,2,2,2,2] .empty .empty) (.node [10,5,5,4,4,3,3,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,4,4,3,3,3,2,1,1,1,1] (.node [10,5,5,4,4,3,3,2,2,2,2,1] (.node [10,5,5,4,4,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,5,5,4,4,3,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,3,3,3,2,2,2] (.node [10,5,5,4,4,3,3,3,2,2,1,1] .empty .empty) (.node [10,5,5,4,4,3,3,3,3,1,1,1] .empty .empty))))) + +def degreeTree43_359 : RowTree := (.node [10,5,5,4,3,3,3,3,2,1,1,1,1,1] degreeTree43_357 degreeTree43_358) + +def degreeTree43_360 : RowTree := (.node [10,5,5,4,4,4,3,3,3,1,1] (.node [10,5,5,4,4,4,3,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,4,2,2,1,1,1,1,1,1,1] (.node [10,5,5,4,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,3,3,3,3,3] .empty .empty) (.node [10,5,5,4,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,4,2,2,2,2,1,1,1] (.node [10,5,5,4,4,4,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,4,4,2,2,2,2,2,1] .empty .empty))) (.node [10,5,5,4,4,4,3,2,2,2,2] (.node [10,5,5,4,4,4,3,2,2,1,1,1,1] (.node [10,5,5,4,4,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,4,4,3,2,2,2,1,1] .empty .empty)) (.node [10,5,5,4,4,4,3,3,2,1,1,1] (.node [10,5,5,4,4,4,3,3,1,1,1,1,1] .empty .empty) (.node [10,5,5,4,4,4,3,3,2,2,1] .empty .empty)))) (.node [10,5,5,4,4,4,4,3,2,2] (.node [10,5,5,4,4,4,4,2,2,1,1,1] (.node [10,5,5,4,4,4,4,1,1,1,1,1,1,1] (.node [10,5,5,4,4,4,3,3,3,2] .empty .empty) (.node [10,5,5,4,4,4,4,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,4,4,4,4,3,1,1,1,1] (.node [10,5,5,4,4,4,4,2,2,2,1] .empty .empty) (.node [10,5,5,4,4,4,4,3,2,1,1] .empty .empty))) (.node [10,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,4,4,4,4,4,1,1,1] (.node [10,5,5,4,4,4,4,3,3,1] .empty .empty) (.node [10,5,5,4,4,4,4,4,2,1] .empty .empty)) (.node [10,5,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_361 : RowTree := (.node [10,5,5,5,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,5,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,2,2,2,2,2,2,2,2,1,1] (.node [10,5,5,5,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,5,5,5,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,5,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,5,3,2,2,2,2,2,2,1,1,1] (.node [10,5,5,5,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,5,5,5,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,5,5,5,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,5,5,3,3,3,2,2,2,1,1,1] (.node [10,5,5,5,3,3,2,2,2,2,2,2] (.node [10,5,5,5,3,3,2,2,2,2,1,1,1,1] (.node [10,5,5,5,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,3,3,2,2,2,2,2,1,1] .empty .empty)) (.node [10,5,5,5,3,3,3,2,1,1,1,1,1,1,1] (.node [10,5,5,5,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,3,3,3,2,2,1,1,1,1,1] .empty .empty))) (.node [10,5,5,5,3,3,3,3,2,2,1,1] (.node [10,5,5,5,3,3,3,3,1,1,1,1,1,1] (.node [10,5,5,5,3,3,3,2,2,2,2,1] .empty .empty) (.node [10,5,5,5,3,3,3,3,2,1,1,1,1] .empty .empty)) (.node [10,5,5,5,3,3,3,3,3,1,1,1] (.node [10,5,5,5,3,3,3,3,2,2,2] .empty .empty) (.node [10,5,5,5,3,3,3,3,3,2,1] .empty .empty))))) + +def degreeTree43_362 : RowTree := (.node [10,5,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_360 degreeTree43_361) + +def degreeTree43_363 : RowTree := (.node [10,5,5,4,4,3,3,3,3,2,1] degreeTree43_359 degreeTree43_362) + +def degreeTree43_364 : RowTree := (.node [10,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_354 degreeTree43_363) + +def degreeTree43_365 : RowTree := (.node [10,5,4,4,3,3,3,2,2,1,1,1,1,1,1,1] degreeTree43_345 degreeTree43_364) + +def degreeTree43_366 : RowTree := (.node [10,5,5,5,4,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,4,2,2,2,2,1,1,1,1,1,1] (.node [10,5,5,5,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,5,5,5,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,4,2,2,2,2,2,2,1,1] (.node [10,5,5,5,4,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,5,5,5,4,2,2,2,2,2,2,2] .empty .empty))) (.node [10,5,5,5,4,3,2,2,2,2,1,1,1] (.node [10,5,5,5,4,3,2,2,1,1,1,1,1,1,1] (.node [10,5,5,5,4,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,4,3,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,4,3,3,1,1,1,1,1,1,1,1] (.node [10,5,5,5,4,3,2,2,2,2,2,1] .empty .empty) (.node [10,5,5,5,4,3,3,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_367 : RowTree := (.node [10,5,5,5,4,4,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,4,3,3,3,2,1,1,1] (.node [10,5,5,5,4,3,3,2,2,2,2] (.node [10,5,5,5,4,3,3,2,2,2,1,1] .empty .empty) (.node [10,5,5,5,4,3,3,3,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,4,3,3,3,3,1,1] (.node [10,5,5,5,4,3,3,3,2,2,1] .empty .empty) (.node [10,5,5,5,4,3,3,3,3,2] .empty .empty))) (.node [10,5,5,5,4,4,2,2,2,2,1,1] (.node [10,5,5,5,4,4,2,2,1,1,1,1,1,1] (.node [10,5,5,5,4,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,4,4,2,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,5,4,4,3,1,1,1,1,1,1,1] (.node [10,5,5,5,4,4,2,2,2,2,2] .empty .empty) (.node [10,5,5,5,4,4,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_368 : RowTree := (.node [10,5,5,5,4,3,3,2,2,1,1,1,1] degreeTree43_366 degreeTree43_367) + +def degreeTree43_369 : RowTree := (.node [10,5,5,5,5,2,2,2,1,1,1,1,1,1,1] (.node [10,5,5,5,4,4,4,2,2,1,1] (.node [10,5,5,5,4,4,3,3,2,2] (.node [10,5,5,5,4,4,3,3,1,1,1,1] (.node [10,5,5,5,4,4,3,2,2,2,1] .empty .empty) (.node [10,5,5,5,4,4,3,3,2,1,1] .empty .empty)) (.node [10,5,5,5,4,4,4,1,1,1,1,1,1] (.node [10,5,5,5,4,4,3,3,3,1] .empty .empty) (.node [10,5,5,5,4,4,4,2,1,1,1,1] .empty .empty))) (.node [10,5,5,5,4,4,4,4,1,1] (.node [10,5,5,5,4,4,4,3,1,1,1] (.node [10,5,5,5,4,4,4,2,2,2] .empty .empty) (.node [10,5,5,5,4,4,4,3,2,1] .empty .empty)) (.node [10,5,5,5,5,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,5,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,5,5,5,5,3,2,2,2,2,1,1] (.node [10,5,5,5,5,3,1,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,5,2,2,2,2,2,1,1,1] (.node [10,5,5,5,5,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,5,2,2,2,2,2,2,1] .empty .empty)) (.node [10,5,5,5,5,3,2,2,1,1,1,1,1,1] (.node [10,5,5,5,5,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,5,3,2,2,2,1,1,1,1] .empty .empty))) (.node [10,5,5,5,5,3,3,2,2,1,1,1] (.node [10,5,5,5,5,3,3,1,1,1,1,1,1,1] (.node [10,5,5,5,5,3,2,2,2,2,2] .empty .empty) (.node [10,5,5,5,5,3,3,2,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,5,3,3,3,1,1,1,1] (.node [10,5,5,5,5,3,3,2,2,2,1] .empty .empty) (.node [10,5,5,5,5,3,3,3,2,1,1] .empty .empty))))) + +def degreeTree43_370 : RowTree := (.node [10,5,5,5,4,4,3,2,2,1,1,1] degreeTree43_368 degreeTree43_369) + +def degreeTree43_371 : RowTree := (.node [10,5,5,5,5,4,4,3,1,1] (.node [10,5,5,5,5,4,3,2,1,1,1,1] (.node [10,5,5,5,5,4,2,2,1,1,1,1,1] (.node [10,5,5,5,5,4,1,1,1,1,1,1,1,1,1] (.node [10,5,5,5,5,3,3,3,3,1] .empty .empty) (.node [10,5,5,5,5,4,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,5,5,5,5,4,2,2,2,2,1] (.node [10,5,5,5,5,4,2,2,2,1,1,1] .empty .empty) (.node [10,5,5,5,5,4,3,1,1,1,1,1,1] .empty .empty))) (.node [10,5,5,5,5,4,3,3,2,1] (.node [10,5,5,5,5,4,3,2,2,2] (.node [10,5,5,5,5,4,3,2,2,1,1] .empty .empty) (.node [10,5,5,5,5,4,3,3,1,1,1] .empty .empty)) (.node [10,5,5,5,5,4,4,2,1,1,1] (.node [10,5,5,5,5,4,4,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,5,4,4,2,2,1] .empty .empty)))) (.node [10,5,5,5,5,5,3,2,2,1] (.node [10,5,5,5,5,5,2,2,2,1,1] (.node [10,5,5,5,5,5,2,1,1,1,1,1,1] (.node [10,5,5,5,5,5,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,5,5,5,5,5,2,2,1,1,1,1] .empty .empty)) (.node [10,5,5,5,5,5,3,1,1,1,1,1] (.node [10,5,5,5,5,5,2,2,2,2] .empty .empty) (.node [10,5,5,5,5,5,3,2,1,1,1] .empty .empty))) (.node [10,5,5,5,5,5,5,1,1,1] (.node [10,5,5,5,5,5,4,1,1,1,1] (.node [10,5,5,5,5,5,3,3,1,1] .empty .empty) (.node [10,5,5,5,5,5,4,2,1,1] .empty .empty)) (.node [10,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_372 : RowTree := (.node [10,6,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,2,2,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,3,2,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,6,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,2,2,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,2,2,2,2,2,2,2,2,2,2,1] (.node [10,6,3,3,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,6,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,2,2,2,2,2,2,2,2,1,1] .empty .empty))))) + +def degreeTree43_373 : RowTree := (.node [10,6,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_371 degreeTree43_372) + +def degreeTree43_374 : RowTree := (.node [10,5,5,5,5,3,3,3,2,2] degreeTree43_370 degreeTree43_373) + +def degreeTree43_375 : RowTree := (.node [10,6,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,6,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,3,3,2,2,2,2,2,2,1,1,1] (.node [10,6,3,3,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,3,2,2,2,2,2,2,2,1] .empty .empty))) (.node [10,6,3,3,3,3,3,2,2,2,2,1,1,1,1] (.node [10,6,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,3,3,3,3,3,2,2,2,2,2,2] (.node [10,6,3,3,3,3,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,6,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_376 : RowTree := (.node [10,6,3,3,3,3,3,3,3,3,1,1,1] (.node [10,6,3,3,3,3,3,3,3,1,1,1,1,1,1] (.node [10,6,3,3,3,3,3,3,2,2,2,1,1,1] (.node [10,6,3,3,3,3,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,3,3,3,2,2,2,2,1] .empty .empty)) (.node [10,6,3,3,3,3,3,3,3,2,2,1,1] (.node [10,6,3,3,3,3,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,6,3,3,3,3,3,3,3,2,2,2] .empty .empty))) (.node [10,6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,3,3,3,3,3,3,3,3,3] (.node [10,6,3,3,3,3,3,3,3,3,2,1] .empty .empty) (.node [10,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_377 : RowTree := (.node [10,6,3,3,3,3,3,3,2,1,1,1,1,1,1,1] degreeTree43_375 degreeTree43_376) + +def degreeTree43_378 : RowTree := (.node [10,6,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,2,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,6,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,4,2,2,2,2,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,6,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,4,3,2,2,2,2,2,2,2,2,2,1,1] (.node [10,6,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,6,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,3,3,2,2,2,2,2,2,2,2,1] (.node [10,6,4,3,3,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,4,3,3,3,2,2,2,2,2,1,1,1,1] (.node [10,6,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,3,3,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,3,3,3,2,2,2,2,2,2,2] (.node [10,6,4,3,3,3,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,6,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_379 : RowTree := (.node [10,6,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] degreeTree43_377 degreeTree43_378) + +def degreeTree43_380 : RowTree := (.node [10,6,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,3,3,3,3,3,2,2,2,1,1] (.node [10,6,4,3,3,3,3,2,2,2,2,2,1] (.node [10,6,4,3,3,3,3,2,2,2,1,1,1,1,1] (.node [10,6,4,3,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,3,3,3,2,2,2,2,1,1,1] .empty .empty)) (.node [10,6,4,3,3,3,3,3,2,1,1,1,1,1,1] (.node [10,6,4,3,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,3,3,3,3,3,2,2,1,1,1,1] .empty .empty))) (.node [10,6,4,3,3,3,3,3,3,2,2,1] (.node [10,6,4,3,3,3,3,3,3,1,1,1,1,1] (.node [10,6,4,3,3,3,3,3,2,2,2,2] .empty .empty) (.node [10,6,4,3,3,3,3,3,3,2,1,1,1] .empty .empty)) (.node [10,6,4,3,3,3,3,3,3,3,2] (.node [10,6,4,3,3,3,3,3,3,3,1,1] .empty .empty) (.node [10,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,4,4,2,2,2,2,2,2,2,2,2,1] (.node [10,6,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,2,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,6,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,3,2,2,2,2,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_381 : RowTree := (.node [10,6,4,4,3,3,3,3,2,1,1,1,1,1] (.node [10,6,4,4,3,3,2,2,2,2,2,2,1] (.node [10,6,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,3,3,2,2,2,2,1,1,1,1,1] (.node [10,6,4,4,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,3,3,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,6,4,4,3,3,3,2,2,2,1,1,1,1] (.node [10,6,4,4,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,3,3,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,3,3,3,2,2,2,2,2] (.node [10,6,4,4,3,3,3,2,2,2,2,1,1] .empty .empty) (.node [10,6,4,4,3,3,3,3,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,3,3,3,3,3,2,1,1] (.node [10,6,4,4,3,3,3,3,2,2,2,1] (.node [10,6,4,4,3,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,6,4,4,3,3,3,3,3,1,1,1,1] .empty .empty)) (.node [10,6,4,4,3,3,3,3,3,3,1] (.node [10,6,4,4,3,3,3,3,3,2,2] .empty .empty) (.node [10,6,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,4,4,4,2,2,2,2,2,1,1,1,1,1] (.node [10,6,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,4,2,2,2,2,2,2,2,1] (.node [10,6,4,4,4,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_382 : RowTree := (.node [10,6,4,4,3,2,2,2,2,2,2,2,1,1] degreeTree43_380 degreeTree43_381) + +def degreeTree43_383 : RowTree := (.node [10,6,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] degreeTree43_379 degreeTree43_382) + +def degreeTree43_384 : RowTree := (.node [10,6,3,3,3,2,2,2,2,2,2,2,2,2] degreeTree43_374 degreeTree43_383) + +def degreeTree43_385 : RowTree := (.node [10,6,4,4,4,3,3,2,2,2,1,1,1] (.node [10,6,4,4,4,3,2,2,2,2,2,2] (.node [10,6,4,4,4,3,2,2,2,2,1,1,1,1] (.node [10,6,4,4,4,3,2,2,2,1,1,1,1,1,1] (.node [10,6,4,4,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,6,4,4,4,3,2,2,2,2,2,1,1] .empty .empty)) (.node [10,6,4,4,4,3,3,2,1,1,1,1,1,1,1] (.node [10,6,4,4,4,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,3,3,2,2,1,1,1,1,1] .empty .empty))) (.node [10,6,4,4,4,3,3,3,2,2,1,1] (.node [10,6,4,4,4,3,3,3,1,1,1,1,1,1] (.node [10,6,4,4,4,3,3,2,2,2,2,1] .empty .empty) (.node [10,6,4,4,4,3,3,3,2,1,1,1,1] .empty .empty)) (.node [10,6,4,4,4,3,3,3,3,1,1,1] (.node [10,6,4,4,4,3,3,3,2,2,2] .empty .empty) (.node [10,6,4,4,4,3,3,3,3,2,1] .empty .empty)))) + +def degreeTree43_386 : RowTree := (.node [10,6,4,4,4,4,3,2,1,1,1,1,1,1] (.node [10,6,4,4,4,4,2,2,2,1,1,1,1,1] (.node [10,6,4,4,4,4,2,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,4,4,4,4,2,2,2,2,2,1] (.node [10,6,4,4,4,4,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,4,4,4,4,3,3,1,1,1,1,1] (.node [10,6,4,4,4,4,3,2,2,2,1,1] (.node [10,6,4,4,4,4,3,2,2,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,3,2,2,2,2] .empty .empty)) (.node [10,6,4,4,4,4,3,3,2,2,1] (.node [10,6,4,4,4,4,3,3,2,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,3,3,3,1,1] .empty .empty)))) + +def degreeTree43_387 : RowTree := (.node [10,6,4,4,4,3,3,3,3,3] degreeTree43_385 degreeTree43_386) + +def degreeTree43_388 : RowTree := (.node [10,6,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,4,4,4,4,4,3,3,1] (.node [10,6,4,4,4,4,4,2,2,2,1] (.node [10,6,4,4,4,4,4,2,1,1,1,1,1] (.node [10,6,4,4,4,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,4,2,2,1,1,1] .empty .empty)) (.node [10,6,4,4,4,4,4,3,2,1,1] (.node [10,6,4,4,4,4,4,3,1,1,1,1] .empty .empty) (.node [10,6,4,4,4,4,4,3,2,2] .empty .empty))) (.node [10,6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,4,4,4,4,4,4,2,1] (.node [10,6,4,4,4,4,4,4,1,1,1] .empty .empty) (.node [10,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,2,2,2,2,2,2,2,2,2,2,2] (.node [10,6,5,2,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,6,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,2,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,6,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,3,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,3,2,2,2,2,2,2,2,2,2,1] (.node [10,6,5,3,2,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_389 : RowTree := (.node [10,6,4,4,4,4,3,3,3,2] degreeTree43_387 degreeTree43_388) + +def degreeTree43_390 : RowTree := (.node [10,6,5,3,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,6,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,3,3,2,2,2,2,2,2,2,1,1] (.node [10,6,5,3,3,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,2,2,2,2,2,2,2,2] .empty .empty))) (.node [10,6,5,3,3,3,2,2,2,2,1,1,1,1,1] (.node [10,6,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,3,3,3,2,2,2,2,2,2,1] (.node [10,6,5,3,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,5,3,3,3,3,3,2,2,2,1] (.node [10,6,5,3,3,3,3,2,2,2,2,2] (.node [10,6,5,3,3,3,3,2,2,2,1,1,1,1] (.node [10,6,5,3,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,3,3,2,2,2,2,1,1] .empty .empty)) (.node [10,6,5,3,3,3,3,3,2,1,1,1,1,1] (.node [10,6,5,3,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,3,3,3,2,2,1,1,1] .empty .empty))) (.node [10,6,5,3,3,3,3,3,3,3,1] (.node [10,6,5,3,3,3,3,3,3,2,1,1] (.node [10,6,5,3,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [10,6,5,3,3,3,3,3,3,2,2] .empty .empty)) (.node [10,6,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_391 : RowTree := (.node [10,6,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,2,2,2,2,2,2,2,1,1,1,1] (.node [10,6,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,2,2,2,2,2,2,2,2,2] (.node [10,6,5,4,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,6,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,4,3,2,2,2,2,2,1,1,1,1,1] (.node [10,6,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,3,2,2,2,2,2,2,2,1] (.node [10,6,5,4,3,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,5,4,3,3,3,2,2,1,1,1,1,1] (.node [10,6,5,4,3,3,2,2,2,2,2,1,1] (.node [10,6,5,4,3,3,2,2,2,1,1,1,1,1,1] (.node [10,6,5,4,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,3,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,6,5,4,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,6,5,4,3,3,3,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,4,3,3,3,3,2,1,1,1,1] (.node [10,6,5,4,3,3,3,2,2,2,2,1] (.node [10,6,5,4,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,4,3,3,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,3,3,3,3,2,2,2] (.node [10,6,5,4,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,6,5,4,3,3,3,3,3,1,1,1] .empty .empty))))) + +def degreeTree43_392 : RowTree := (.node [10,6,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_390 degreeTree43_391) + +def degreeTree43_393 : RowTree := (.node [10,6,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_389 degreeTree43_392) + +def degreeTree43_394 : RowTree := (.node [10,6,5,4,4,2,2,2,2,2,2,2] (.node [10,6,5,4,4,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,3,3,3,3,3,3] .empty .empty) .empty) (.node [10,6,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,4,2,2,2,2,2,1,1,1,1] (.node [10,6,5,4,4,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,2,2,2,2,2,2,1,1] .empty .empty))) (.node [10,6,5,4,4,3,2,2,2,1,1,1,1,1] (.node [10,6,5,4,4,3,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,3,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,4,3,2,2,2,2,2,1] (.node [10,6,5,4,4,3,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,4,4,3,3,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_395 : RowTree := (.node [10,6,5,4,4,3,3,3,3,2] (.node [10,6,5,4,4,3,3,3,1,1,1,1,1] (.node [10,6,5,4,4,3,3,2,2,2,1,1] (.node [10,6,5,4,4,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,3,3,2,2,2,2] .empty .empty)) (.node [10,6,5,4,4,3,3,3,2,2,1] (.node [10,6,5,4,4,3,3,3,2,1,1,1] .empty .empty) (.node [10,6,5,4,4,3,3,3,3,1,1] .empty .empty))) (.node [10,6,5,4,4,4,2,2,2,1,1,1,1] (.node [10,6,5,4,4,4,2,1,1,1,1,1,1,1,1] (.node [10,6,5,4,4,4,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,4,4,4,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,4,4,4,2,2,2,2,2] (.node [10,6,5,4,4,4,2,2,2,2,1,1] .empty .empty) (.node [10,6,5,4,4,4,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_396 : RowTree := (.node [10,6,5,4,4,3,3,2,1,1,1,1,1,1] degreeTree43_394 degreeTree43_395) + +def degreeTree43_397 : RowTree := (.node [10,6,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,4,4,4,2,1,1,1,1] (.node [10,6,5,4,4,4,3,3,2,1,1] (.node [10,6,5,4,4,4,3,2,2,2,1] (.node [10,6,5,4,4,4,3,2,2,1,1,1] .empty .empty) (.node [10,6,5,4,4,4,3,3,1,1,1,1] .empty .empty)) (.node [10,6,5,4,4,4,3,3,3,1] (.node [10,6,5,4,4,4,3,3,2,2] .empty .empty) (.node [10,6,5,4,4,4,4,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,4,4,4,4,3,2,1] (.node [10,6,5,4,4,4,4,2,2,2] (.node [10,6,5,4,4,4,4,2,2,1,1] .empty .empty) (.node [10,6,5,4,4,4,4,3,1,1,1] .empty .empty)) (.node [10,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,4,4,4,4,4,1,1] .empty .empty) (.node [10,6,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,2,2,2,2,2,2,1,1,1,1,1] (.node [10,6,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,5,2,2,2,2,2,2,2,2,1] (.node [10,6,5,5,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,5,3,2,2,2,2,2,1,1,1,1] (.node [10,6,5,5,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,6,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,3,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,5,3,2,2,2,2,2,2,2] (.node [10,6,5,5,3,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,6,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_398 : RowTree := (.node [10,6,5,4,4,4,3,2,1,1,1,1,1] degreeTree43_396 degreeTree43_397) + +def degreeTree43_399 : RowTree := (.node [10,6,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,3,3,3,2,2,2,1,1] (.node [10,6,5,5,3,3,2,2,2,2,2,1] (.node [10,6,5,5,3,3,2,2,2,1,1,1,1,1] (.node [10,6,5,5,3,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,3,3,2,2,2,2,1,1,1] .empty .empty)) (.node [10,6,5,5,3,3,3,2,1,1,1,1,1,1] (.node [10,6,5,5,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,3,3,3,2,2,1,1,1,1] .empty .empty))) (.node [10,6,5,5,3,3,3,3,2,2,1] (.node [10,6,5,5,3,3,3,3,1,1,1,1,1] (.node [10,6,5,5,3,3,3,2,2,2,2] .empty .empty) (.node [10,6,5,5,3,3,3,3,2,1,1,1] .empty .empty)) (.node [10,6,5,5,3,3,3,3,3,2] (.node [10,6,5,5,3,3,3,3,3,1,1] .empty .empty) (.node [10,6,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,5,5,4,3,2,2,1,1,1,1,1,1] (.node [10,6,5,5,4,2,2,2,2,2,1,1,1] (.node [10,6,5,5,4,2,2,2,1,1,1,1,1,1,1] (.node [10,6,5,5,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,4,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,5,5,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,4,2,2,2,2,2,2,1] .empty .empty) (.node [10,6,5,5,4,3,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,5,5,4,3,3,1,1,1,1,1,1,1] (.node [10,6,5,5,4,3,2,2,2,2,1,1] (.node [10,6,5,5,4,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,6,5,5,4,3,2,2,2,2,2] .empty .empty)) (.node [10,6,5,5,4,3,3,2,2,1,1,1] (.node [10,6,5,5,4,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,4,3,3,2,2,2,1] .empty .empty))))) + +def degreeTree43_400 : RowTree := (.node [10,6,5,5,4,4,4,2,1,1,1] (.node [10,6,5,5,4,4,2,2,2,2,1] (.node [10,6,5,5,4,4,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,4,3,3,3,2,2] (.node [10,6,5,5,4,3,3,3,2,1,1] .empty .empty) (.node [10,6,5,5,4,3,3,3,3,1] .empty .empty)) (.node [10,6,5,5,4,4,2,2,1,1,1,1,1] (.node [10,6,5,5,4,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,4,4,2,2,2,1,1,1] .empty .empty))) (.node [10,6,5,5,4,4,3,2,2,2] (.node [10,6,5,5,4,4,3,2,1,1,1,1] (.node [10,6,5,5,4,4,3,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,4,4,3,2,2,1,1] .empty .empty)) (.node [10,6,5,5,4,4,3,3,2,1] (.node [10,6,5,5,4,4,3,3,1,1,1] .empty .empty) (.node [10,6,5,5,4,4,4,1,1,1,1,1] .empty .empty)))) (.node [10,6,5,5,5,2,2,2,2,2,1,1] (.node [10,6,5,5,5,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,4,4,4,3,1,1] (.node [10,6,5,5,4,4,4,2,2,1] .empty .empty) (.node [10,6,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,5,5,2,2,2,1,1,1,1,1,1] (.node [10,6,5,5,5,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,5,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,6,5,5,5,3,2,2,1,1,1,1,1] (.node [10,6,5,5,5,3,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,5,2,2,2,2,2,2] .empty .empty) (.node [10,6,5,5,5,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,5,5,5,3,2,2,2,2,1] (.node [10,6,5,5,5,3,2,2,2,1,1,1] .empty .empty) (.node [10,6,5,5,5,3,3,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_401 : RowTree := (.node [10,6,5,5,4,3,3,3,1,1,1,1] degreeTree43_399 degreeTree43_400) + +def degreeTree43_402 : RowTree := (.node [10,6,5,5,3,3,2,1,1,1,1,1,1,1,1,1] degreeTree43_398 degreeTree43_401) + +def degreeTree43_403 : RowTree := (.node [10,6,5,4,3,3,3,3,3,2,1] degreeTree43_393 degreeTree43_402) + +def degreeTree43_404 : RowTree := (.node [10,6,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_384 degreeTree43_403) + +def degreeTree43_405 : RowTree := (.node [10,5,5,5,3,3,3,3,3,3] degreeTree43_365 degreeTree43_404) + +def degreeTree43_406 : RowTree := (.node [10,6,5,5,5,4,2,2,2,2] (.node [10,6,5,5,5,4,1,1,1,1,1,1,1,1] (.node [10,6,5,5,5,3,3,3,1,1,1] (.node [10,6,5,5,5,3,3,2,2,2] (.node [10,6,5,5,5,3,3,2,2,1,1] .empty .empty) .empty) (.node [10,6,5,5,5,3,3,3,2,1] .empty .empty)) (.node [10,6,5,5,5,4,2,2,1,1,1,1] (.node [10,6,5,5,5,4,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,5,4,2,2,2,1,1] .empty .empty))) (.node [10,6,5,5,5,4,3,3,1,1] (.node [10,6,5,5,5,4,3,2,1,1,1] (.node [10,6,5,5,5,4,3,1,1,1,1,1] .empty .empty) (.node [10,6,5,5,5,4,3,2,2,1] .empty .empty)) (.node [10,6,5,5,5,4,4,2,1,1] (.node [10,6,5,5,5,4,4,1,1,1,1] .empty .empty) (.node [10,6,5,5,5,5,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_407 : RowTree := (.node [10,6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,5,5,3,2,1,1] (.node [10,6,5,5,5,5,2,2,2,1] (.node [10,6,5,5,5,5,2,2,1,1,1] .empty .empty) (.node [10,6,5,5,5,5,3,1,1,1,1] .empty .empty)) (.node [10,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,5,5,5,5,4,1,1,1] .empty .empty) (.node [10,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,6,6,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,6,2,2,2,2,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree43_408 : RowTree := (.node [10,6,5,5,5,5,2,1,1,1,1,1] degreeTree43_406 degreeTree43_407) + +def degreeTree43_409 : RowTree := (.node [10,6,6,3,3,2,2,2,2,2,2,1,1,1] (.node [10,6,6,3,2,2,2,2,2,2,2,2,1,1] (.node [10,6,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,6,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,6,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)))) (.node [10,6,6,3,3,3,2,2,2,2,2,2] (.node [10,6,6,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,6,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,6,6,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,3,3,3,2,2,2,2,1,1,1,1] (.node [10,6,6,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,3,3,2,2,2,2,2,1,1] .empty .empty))) (.node [10,6,6,3,3,3,3,2,2,2,1,1,1] (.node [10,6,6,3,3,3,3,2,1,1,1,1,1,1,1] (.node [10,6,6,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,3,3,3,3,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,6,3,3,3,3,3,1,1,1,1,1,1] (.node [10,6,6,3,3,3,3,2,2,2,2,1] .empty .empty) (.node [10,6,6,3,3,3,3,3,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_410 : RowTree := (.node [10,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_408 degreeTree43_409) + +def degreeTree43_411 : RowTree := (.node [10,6,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,3,3,3,3,3,3,3] (.node [10,6,6,3,3,3,3,3,3,1,1,1] (.node [10,6,6,3,3,3,3,3,2,2,2] .empty .empty) (.node [10,6,6,3,3,3,3,3,3,2,1] .empty .empty)) (.node [10,6,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,6,4,2,2,2,2,2,2,2,1,1,1] (.node [10,6,6,4,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,6,4,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,6,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,6,4,3,3,2,2,1,1,1,1,1,1,1] (.node [10,6,6,4,3,2,2,2,2,2,2,1,1] (.node [10,6,6,4,3,2,2,2,2,1,1,1,1,1,1] (.node [10,6,6,4,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,3,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,6,6,4,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,6,4,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,6,4,3,3,3,1,1,1,1,1,1,1,1] (.node [10,6,6,4,3,3,2,2,2,2,1,1,1] (.node [10,6,6,4,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,3,3,2,2,2,2,2,1] .empty .empty)) (.node [10,6,6,4,3,3,3,2,2,1,1,1,1] (.node [10,6,6,4,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,3,3,3,2,2,2,1,1] .empty .empty))))) + +def degreeTree43_412 : RowTree := (.node [10,6,6,4,4,3,2,2,2,1,1,1,1] (.node [10,6,6,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,3,3,3,3,3,1,1] (.node [10,6,6,4,3,3,3,3,2,1,1,1] (.node [10,6,6,4,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,3,3,3,3,2,2,1] .empty .empty)) (.node [10,6,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,4,3,3,3,3,3,2] .empty .empty) (.node [10,6,6,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,6,4,4,2,2,2,2,2,2,1] (.node [10,6,6,4,4,2,2,2,2,1,1,1,1,1] (.node [10,6,6,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,4,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,6,6,4,4,3,2,1,1,1,1,1,1,1,1] (.node [10,6,6,4,4,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,4,3,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,6,4,4,3,3,3,2,1,1] (.node [10,6,6,4,4,3,3,2,1,1,1,1,1] (.node [10,6,6,4,4,3,2,2,2,2,2] (.node [10,6,6,4,4,3,2,2,2,2,1,1] .empty .empty) (.node [10,6,6,4,4,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,4,4,3,3,2,2,2,1] (.node [10,6,6,4,4,3,3,2,2,1,1,1] .empty .empty) (.node [10,6,6,4,4,3,3,3,1,1,1,1] .empty .empty))) (.node [10,6,6,4,4,4,2,1,1,1,1,1,1,1] (.node [10,6,6,4,4,3,3,3,3,1] (.node [10,6,6,4,4,3,3,3,2,2] .empty .empty) (.node [10,6,6,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,4,4,4,2,2,2,1,1,1] (.node [10,6,6,4,4,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,4,4,2,2,2,2,1] .empty .empty))))) + +def degreeTree43_413 : RowTree := (.node [10,6,6,4,3,3,3,2,2,2,2] degreeTree43_411 degreeTree43_412) + +def degreeTree43_414 : RowTree := (.node [10,6,6,3,3,3,3,3,2,2,1,1] degreeTree43_410 degreeTree43_413) + +def degreeTree43_415 : RowTree := (.node [10,6,6,4,4,4,4,3,1,1] (.node [10,6,6,4,4,4,3,3,2,1] (.node [10,6,6,4,4,4,3,2,2,2] (.node [10,6,6,4,4,4,3,2,2,1,1] (.node [10,6,6,4,4,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,6,6,4,4,4,3,3,1,1,1] .empty .empty)) (.node [10,6,6,4,4,4,4,2,1,1,1] (.node [10,6,6,4,4,4,4,1,1,1,1,1] .empty .empty) (.node [10,6,6,4,4,4,4,2,2,1] .empty .empty))) (.node [10,6,6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,6,5,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,2,2,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree43_416 : RowTree := (.node [10,6,6,5,3,2,2,2,2,2,2,1] (.node [10,6,6,5,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,6,6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,3,2,2,2,2,1,1,1,1,1] (.node [10,6,6,5,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,3,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,6,6,5,3,3,2,2,2,1,1,1,1] (.node [10,6,6,5,3,3,2,1,1,1,1,1,1,1,1] (.node [10,6,6,5,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,3,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,3,3,2,2,2,2,2] (.node [10,6,6,5,3,3,2,2,2,2,1,1] .empty .empty) (.node [10,6,6,5,3,3,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_417 : RowTree := (.node [10,6,6,5,2,2,2,2,2,2,2,1,1] degreeTree43_415 degreeTree43_416) + +def degreeTree43_418 : RowTree := (.node [10,6,6,5,4,3,2,2,1,1,1,1,1] (.node [10,6,6,5,4,2,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,3,3,3,3,2,1,1] (.node [10,6,6,5,3,3,3,2,2,2,1] (.node [10,6,6,5,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,6,6,5,3,3,3,3,1,1,1,1] .empty .empty)) (.node [10,6,6,5,3,3,3,3,3,1] (.node [10,6,6,5,3,3,3,3,2,2] .empty .empty) (.node [10,6,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,6,5,4,2,2,2,2,2,1,1] (.node [10,6,6,5,4,2,2,2,1,1,1,1,1,1] (.node [10,6,6,5,4,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,4,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,6,6,5,4,3,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,4,2,2,2,2,2,2] .empty .empty) (.node [10,6,6,5,4,3,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,6,6,5,4,3,3,3,2,1] (.node [10,6,6,5,4,3,3,2,1,1,1,1] (.node [10,6,6,5,4,3,2,2,2,2,1] (.node [10,6,6,5,4,3,2,2,2,1,1,1] .empty .empty) (.node [10,6,6,5,4,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,4,3,3,2,2,2] (.node [10,6,6,5,4,3,3,2,2,1,1] .empty .empty) (.node [10,6,6,5,4,3,3,3,1,1,1] .empty .empty))) (.node [10,6,6,5,4,4,2,2,2,1,1] (.node [10,6,6,5,4,4,2,1,1,1,1,1,1] (.node [10,6,6,5,4,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,4,4,2,2,1,1,1,1] .empty .empty)) (.node [10,6,6,5,4,4,3,1,1,1,1,1] (.node [10,6,6,5,4,4,2,2,2,2] .empty .empty) (.node [10,6,6,5,4,4,3,2,1,1,1] .empty .empty))))) + +def degreeTree43_419 : RowTree := (.node [10,6,6,5,3,3,3,2,1,1,1,1,1] degreeTree43_417 degreeTree43_418) + +def degreeTree43_420 : RowTree := (.node [10,6,6,5,5,3,3,2,1,1,1] (.node [10,6,6,5,5,2,2,2,2,1,1,1] (.node [10,6,6,5,5,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,4,4,4,1,1,1,1] (.node [10,6,6,5,4,4,3,3,1,1] .empty .empty) (.node [10,6,6,5,4,4,4,2,1,1] .empty .empty)) (.node [10,6,6,5,5,2,2,1,1,1,1,1,1,1] (.node [10,6,6,5,5,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,5,5,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,6,6,5,5,3,2,2,1,1,1,1] (.node [10,6,6,5,5,3,1,1,1,1,1,1,1,1] (.node [10,6,6,5,5,2,2,2,2,2,1] .empty .empty) (.node [10,6,6,5,5,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,5,3,2,2,2,2] (.node [10,6,6,5,5,3,2,2,2,1,1] .empty .empty) (.node [10,6,6,5,5,3,3,1,1,1,1,1] .empty .empty)))) (.node [10,6,6,5,5,4,3,2,1,1] (.node [10,6,6,5,5,4,2,1,1,1,1,1] (.node [10,6,6,5,5,3,3,3,1,1] (.node [10,6,6,5,5,3,3,2,2,1] .empty .empty) (.node [10,6,6,5,5,4,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,5,5,4,2,2,2,1] (.node [10,6,6,5,5,4,2,2,1,1,1] .empty .empty) (.node [10,6,6,5,5,4,3,1,1,1,1] .empty .empty))) (.node [10,6,6,5,5,5,2,2,1,1] (.node [10,6,6,5,5,5,1,1,1,1,1,1] (.node [10,6,6,5,5,4,4,1,1,1] .empty .empty) (.node [10,6,6,5,5,5,2,1,1,1,1] .empty .empty)) (.node [10,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,5,5,5,3,1,1,1] .empty .empty) (.node [10,6,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_421 : RowTree := (.node [10,6,6,6,3,3,2,2,2,1,1,1] (.node [10,6,6,6,3,2,2,1,1,1,1,1,1,1,1] (.node [10,6,6,6,2,2,2,2,2,2,1,1,1] (.node [10,6,6,6,2,2,2,2,1,1,1,1,1,1,1] (.node [10,6,6,6,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,6,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,6,6,6,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,6,6,6,3,2,2,2,2,2,2] (.node [10,6,6,6,3,2,2,2,2,1,1,1,1] (.node [10,6,6,6,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,3,2,2,2,2,2,1,1] .empty .empty)) (.node [10,6,6,6,3,3,2,1,1,1,1,1,1,1] (.node [10,6,6,6,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,3,3,2,2,1,1,1,1,1] .empty .empty)))) (.node [10,6,6,6,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,6,3,3,3,2,2,1,1] (.node [10,6,6,6,3,3,3,1,1,1,1,1,1] (.node [10,6,6,6,3,3,2,2,2,2,1] .empty .empty) (.node [10,6,6,6,3,3,3,2,1,1,1,1] .empty .empty)) (.node [10,6,6,6,3,3,3,3,1,1,1] (.node [10,6,6,6,3,3,3,2,2,2] .empty .empty) (.node [10,6,6,6,3,3,3,3,2,1] .empty .empty))) (.node [10,6,6,6,4,2,2,2,2,1,1,1] (.node [10,6,6,6,4,2,2,1,1,1,1,1,1,1] (.node [10,6,6,6,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,4,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,6,6,6,4,3,1,1,1,1,1,1,1,1] (.node [10,6,6,6,4,2,2,2,2,2,1] .empty .empty) (.node [10,6,6,6,4,3,2,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_422 : RowTree := (.node [10,6,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_420 degreeTree43_421) + +def degreeTree43_423 : RowTree := (.node [10,6,6,5,4,4,3,2,2,1] degreeTree43_419 degreeTree43_422) + +def degreeTree43_424 : RowTree := (.node [10,6,6,4,4,4,3,1,1,1,1,1,1] degreeTree43_414 degreeTree43_423) + +def degreeTree43_425 : RowTree := (.node [10,6,6,6,4,4,2,2,1,1,1] (.node [10,6,6,6,4,3,3,2,2,1] (.node [10,6,6,6,4,3,3,1,1,1,1,1] (.node [10,6,6,6,4,3,2,2,2,2] (.node [10,6,6,6,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [10,6,6,6,4,3,3,2,1,1,1] .empty .empty)) (.node [10,6,6,6,4,4,1,1,1,1,1,1,1] (.node [10,6,6,6,4,3,3,3,1,1] .empty .empty) (.node [10,6,6,6,4,4,2,1,1,1,1,1] .empty .empty))) (.node [10,6,6,6,4,4,4,1,1,1] (.node [10,6,6,6,4,4,3,1,1,1,1] (.node [10,6,6,6,4,4,2,2,2,1] .empty .empty) (.node [10,6,6,6,4,4,3,2,1,1] .empty .empty)) (.node [10,6,6,6,5,2,1,1,1,1,1,1,1,1] (.node [10,6,6,6,5,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,5,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_426 : RowTree := (.node [10,6,6,6,5,3,3,2,1,1] (.node [10,6,6,6,5,3,2,1,1,1,1,1] (.node [10,6,6,6,5,2,2,2,2,2] (.node [10,6,6,6,5,2,2,2,2,1,1] .empty .empty) (.node [10,6,6,6,5,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,6,6,6,5,3,2,2,2,1] (.node [10,6,6,6,5,3,2,2,1,1,1] .empty .empty) (.node [10,6,6,6,5,3,3,1,1,1,1] .empty .empty))) (.node [10,6,6,6,5,4,3,1,1,1] (.node [10,6,6,6,5,4,2,1,1,1,1] (.node [10,6,6,6,5,4,1,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,5,4,2,2,1,1] .empty .empty)) (.node [10,6,6,6,5,5,2,1,1,1] (.node [10,6,6,6,5,5,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,6,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_427 : RowTree := (.node [10,6,6,6,5,2,2,2,1,1,1,1] degreeTree43_425 degreeTree43_426) + +def degreeTree43_428 : RowTree := (.node [10,7,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,6,6,6,6,4,1,1,1,1,1] (.node [10,6,6,6,6,3,1,1,1,1,1,1] (.node [10,6,6,6,6,2,2,2,1,1,1] (.node [10,6,6,6,6,2,2,1,1,1,1,1] .empty .empty) (.node [10,6,6,6,6,2,2,2,2,1] .empty .empty)) (.node [10,6,6,6,6,3,2,2,1,1] (.node [10,6,6,6,6,3,2,1,1,1,1] .empty .empty) (.node [10,6,6,6,6,3,3,1,1,1] .empty .empty))) (.node [10,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,6,6,6,6,5,1,1,1,1] (.node [10,6,6,6,6,4,2,1,1,1] .empty .empty) (.node [10,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,7,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,2,2,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,7,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,2,2,2,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,7,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,3,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,7,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,7,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_429 : RowTree := (.node [10,6,6,6,6,2,1,1,1,1,1,1,1] degreeTree43_427 degreeTree43_428) + +def degreeTree43_430 : RowTree := (.node [10,7,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,7,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,2,2,2,2,2,2,2,2,2,2] (.node [10,7,3,3,2,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,2,2,2,2,2,2,2,1,1,1] (.node [10,7,3,3,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,3,3,3,2,2,2,2,2,2,2,2,1] .empty .empty)))) (.node [10,7,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,7,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,3,2,2,2,2,2,2,1,1] (.node [10,7,3,3,3,3,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,3,3,3,3,2,2,2,2,2,2,2] .empty .empty))) (.node [10,7,3,3,3,3,3,2,2,2,2,1,1,1] (.node [10,7,3,3,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,3,3,3,3,3,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,3,3,3,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,3,2,2,2,2,2,1] .empty .empty) (.node [10,7,3,3,3,3,3,3,2,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_431 : RowTree := (.node [10,7,4,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,3,3,3,3,3,3,3,2,1,1,1] (.node [10,7,3,3,3,3,3,3,2,2,2,2] (.node [10,7,3,3,3,3,3,3,2,2,2,1,1] .empty .empty) (.node [10,7,3,3,3,3,3,3,3,1,1,1,1,1] .empty .empty)) (.node [10,7,3,3,3,3,3,3,3,3,1,1] (.node [10,7,3,3,3,3,3,3,3,2,2,1] .empty .empty) (.node [10,7,3,3,3,3,3,3,3,3,2] .empty .empty))) (.node [10,7,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,7,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty)))) (.node [10,7,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,2,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,2,2,2,2,2,2,2,2,1,1,1] (.node [10,7,4,3,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,2,2,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,7,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_432 : RowTree := (.node [10,7,3,3,3,3,3,3,2,2,1,1,1,1] degreeTree43_430 degreeTree43_431) + +def degreeTree43_433 : RowTree := (.node [10,7,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_429 degreeTree43_432) + +def degreeTree43_434 : RowTree := (.node [10,7,4,3,3,3,2,2,2,2,1,1,1,1,1] (.node [10,7,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,2,2,2,2,2,2,2,1,1] (.node [10,7,4,3,3,2,2,2,2,2,2,1,1,1,1] (.node [10,7,4,3,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,7,4,3,3,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,7,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,4,3,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,7,4,3,3,3,2,2,2,2,2,2,1] (.node [10,7,4,3,3,3,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,3,3,3,3,2,2,2,1,1,1,1] (.node [10,7,4,3,3,3,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,3,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree43_435 : RowTree := (.node [10,7,4,3,3,3,3,3,3,3,1] (.node [10,7,4,3,3,3,3,3,2,2,2,1] (.node [10,7,4,3,3,3,3,3,2,1,1,1,1,1] (.node [10,7,4,3,3,3,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,3,3,2,2,1,1,1] .empty .empty)) (.node [10,7,4,3,3,3,3,3,3,2,1,1] (.node [10,7,4,3,3,3,3,3,3,1,1,1,1] .empty .empty) (.node [10,7,4,3,3,3,3,3,3,2,2] .empty .empty))) (.node [10,7,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_436 : RowTree := (.node [10,7,4,3,3,3,3,2,2,2,2,2] degreeTree43_434 degreeTree43_435) + +def degreeTree43_437 : RowTree := (.node [10,7,4,4,3,3,2,2,2,2,2,1,1] (.node [10,7,4,4,3,2,2,2,2,2,1,1,1,1,1] (.node [10,7,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,2,2,2,2,2,2,2,2,2] (.node [10,7,4,4,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,3,2,2,2,2,2,2,2,1] (.node [10,7,4,4,3,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,7,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,3,3,2,2,2,1,1,1,1,1,1] (.node [10,7,4,4,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,3,3,2,2,2,2,1,1,1,1] .empty .empty)))) (.node [10,7,4,4,3,3,3,3,2,1,1,1,1] (.node [10,7,4,4,3,3,3,2,2,1,1,1,1,1] (.node [10,7,4,4,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,7,4,4,3,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,4,4,3,3,3,2,2,2,2,1] (.node [10,7,4,4,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,7,4,4,3,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,7,4,4,3,3,3,3,3,2,1] (.node [10,7,4,4,3,3,3,3,2,2,2] (.node [10,7,4,4,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,7,4,4,3,3,3,3,3,1,1,1] .empty .empty)) (.node [10,7,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,3,3,3,3,3,3] .empty .empty) (.node [10,7,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_438 : RowTree := (.node [10,7,4,4,2,2,2,2,2,2,2,1,1,1,1] degreeTree43_436 degreeTree43_437) + +def degreeTree43_439 : RowTree := (.node [10,7,4,4,4,3,3,2,2,2,2] (.node [10,7,4,4,4,3,2,2,1,1,1,1,1,1,1] (.node [10,7,4,4,4,2,2,2,2,2,2,1,1] (.node [10,7,4,4,4,2,2,2,2,1,1,1,1,1,1] (.node [10,7,4,4,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,7,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,4,2,2,2,2,2,2,2] .empty .empty) (.node [10,7,4,4,4,3,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,4,4,4,3,3,1,1,1,1,1,1,1,1] (.node [10,7,4,4,4,3,2,2,2,2,1,1,1] (.node [10,7,4,4,4,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,3,2,2,2,2,2,1] .empty .empty)) (.node [10,7,4,4,4,3,3,2,2,1,1,1,1] (.node [10,7,4,4,4,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,3,3,2,2,2,1,1] .empty .empty)))) (.node [10,7,4,4,4,4,2,2,1,1,1,1,1,1] (.node [10,7,4,4,4,3,3,3,3,1,1] (.node [10,7,4,4,4,3,3,3,2,1,1,1] (.node [10,7,4,4,4,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,3,3,3,2,2,1] .empty .empty)) (.node [10,7,4,4,4,4,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,4,3,3,3,3,2] .empty .empty) (.node [10,7,4,4,4,4,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,4,4,4,4,3,1,1,1,1,1,1,1] (.node [10,7,4,4,4,4,2,2,2,2,1,1] (.node [10,7,4,4,4,4,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,4,2,2,2,2,2] .empty .empty)) (.node [10,7,4,4,4,4,3,2,2,1,1,1] (.node [10,7,4,4,4,4,3,2,1,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,4,3,2,2,2,1] .empty .empty))))) + +def degreeTree43_440 : RowTree := (.node [10,7,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,4,4,4,3,1,1,1] (.node [10,7,4,4,4,4,4,1,1,1,1,1,1] (.node [10,7,4,4,4,4,3,3,2,2] (.node [10,7,4,4,4,4,3,3,2,1,1] .empty .empty) (.node [10,7,4,4,4,4,3,3,3,1] .empty .empty)) (.node [10,7,4,4,4,4,4,2,2,1,1] (.node [10,7,4,4,4,4,4,2,1,1,1,1] .empty .empty) (.node [10,7,4,4,4,4,4,2,2,2] .empty .empty))) (.node [10,7,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,4,4,4,4,4,4,1,1] (.node [10,7,4,4,4,4,4,3,2,1] .empty .empty) (.node [10,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,7,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,2,2,2,2,2,2,2,2,2,2,1] (.node [10,7,5,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,7,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,7,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,5,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,7,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,3,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,3,2,2,2,2,2,2,2,2,2] (.node [10,7,5,3,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_441 : RowTree := (.node [10,7,4,4,4,4,3,3,1,1,1,1] degreeTree43_439 degreeTree43_440) + +def degreeTree43_442 : RowTree := (.node [10,7,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_438 degreeTree43_441) + +def degreeTree43_443 : RowTree := (.node [10,7,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1] degreeTree43_433 degreeTree43_442) + +def degreeTree43_444 : RowTree := (.node [10,6,6,6,4,3,2,2,1,1,1,1] degreeTree43_424 degreeTree43_443) + +def degreeTree43_445 : RowTree := (.node [10,7,5,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,7,5,3,3,2,2,2,2,2,2,1,1,1] (.node [10,7,5,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,7,5,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,3,3,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,5,3,3,3,2,2,2,2,2,2] (.node [10,7,5,3,3,3,2,2,2,2,1,1,1,1] (.node [10,7,5,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,3,3,3,2,2,2,2,2,1,1] .empty .empty)) (.node [10,7,5,3,3,3,3,2,1,1,1,1,1,1,1] (.node [10,7,5,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,3,3,3,3,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_446 : RowTree := (.node [10,7,5,3,3,3,3,3,3,3] (.node [10,7,5,3,3,3,3,3,2,2,1,1] (.node [10,7,5,3,3,3,3,3,1,1,1,1,1,1] (.node [10,7,5,3,3,3,3,2,2,2,2,1] .empty .empty) (.node [10,7,5,3,3,3,3,3,2,1,1,1,1] .empty .empty)) (.node [10,7,5,3,3,3,3,3,3,1,1,1] (.node [10,7,5,3,3,3,3,3,2,2,2] .empty .empty) (.node [10,7,5,3,3,3,3,3,3,2,1] .empty .empty))) (.node [10,7,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,4,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_447 : RowTree := (.node [10,7,5,3,3,3,3,2,2,2,1,1,1] degreeTree43_445 degreeTree43_446) + +def degreeTree43_448 : RowTree := (.node [10,7,5,4,3,3,3,1,1,1,1,1,1,1,1] (.node [10,7,5,4,3,2,2,2,2,2,2,1,1] (.node [10,7,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,4,3,2,2,2,2,1,1,1,1,1,1] (.node [10,7,5,4,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,3,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,7,5,4,3,3,2,2,1,1,1,1,1,1,1] (.node [10,7,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,7,5,4,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,4,3,3,2,2,2,2,1,1,1] (.node [10,7,5,4,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,3,3,2,2,2,2,2,1] .empty .empty)))) (.node [10,7,5,4,3,3,3,3,3,1,1] (.node [10,7,5,4,3,3,3,2,2,2,2] (.node [10,7,5,4,3,3,3,2,2,1,1,1,1] (.node [10,7,5,4,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,7,5,4,3,3,3,3,2,1,1,1] (.node [10,7,5,4,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,3,3,3,3,2,2,1] .empty .empty))) (.node [10,7,5,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,3,3,3,3,3,2] .empty .empty) (.node [10,7,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,4,4,2,2,2,2,1,1,1,1,1] (.node [10,7,5,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,4,2,2,2,2,2,1,1,1] .empty .empty))))) + +def degreeTree43_449 : RowTree := (.node [10,7,5,4,2,2,2,2,2,2,2,1,1,1] degreeTree43_447 degreeTree43_448) + +def degreeTree43_450 : RowTree := (.node [10,7,5,4,4,4,2,1,1,1,1,1,1,1] (.node [10,7,5,4,4,3,3,2,1,1,1,1,1] (.node [10,7,5,4,4,3,2,2,2,1,1,1,1] (.node [10,7,5,4,4,3,2,1,1,1,1,1,1,1,1] (.node [10,7,5,4,4,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,4,3,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,4,4,3,2,2,2,2,2] (.node [10,7,5,4,4,3,2,2,2,2,1,1] .empty .empty) (.node [10,7,5,4,4,3,3,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,5,4,4,3,3,3,2,1,1] (.node [10,7,5,4,4,3,3,2,2,2,1] (.node [10,7,5,4,4,3,3,2,2,1,1,1] .empty .empty) (.node [10,7,5,4,4,3,3,3,1,1,1,1] .empty .empty)) (.node [10,7,5,4,4,3,3,3,3,1] (.node [10,7,5,4,4,3,3,3,2,2] .empty .empty) (.node [10,7,5,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,7,5,4,4,4,3,3,1,1,1] (.node [10,7,5,4,4,4,3,1,1,1,1,1,1] (.node [10,7,5,4,4,4,2,2,2,1,1,1] (.node [10,7,5,4,4,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,5,4,4,4,2,2,2,2,1] .empty .empty)) (.node [10,7,5,4,4,4,3,2,2,1,1] (.node [10,7,5,4,4,4,3,2,1,1,1,1] .empty .empty) (.node [10,7,5,4,4,4,3,2,2,2] .empty .empty))) (.node [10,7,5,4,4,4,4,2,2,1] (.node [10,7,5,4,4,4,4,1,1,1,1,1] (.node [10,7,5,4,4,4,3,3,2,1] .empty .empty) (.node [10,7,5,4,4,4,4,2,1,1,1] .empty .empty)) (.node [10,7,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,4,4,4,4,3,1,1] .empty .empty) (.node [10,7,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_451 : RowTree := (.node [10,7,5,5,3,3,2,2,1,1,1,1,1,1] (.node [10,7,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,5,2,2,2,2,2,2,1,1,1,1] (.node [10,7,5,5,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,5,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,5,2,2,2,2,2,2,2,2] (.node [10,7,5,5,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,5,5,3,2,2,2,2,2,1,1,1] (.node [10,7,5,5,3,2,2,2,1,1,1,1,1,1,1] (.node [10,7,5,5,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,5,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,5,5,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,5,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,5,5,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,7,5,5,3,3,3,3,1,1,1,1] (.node [10,7,5,5,3,3,3,1,1,1,1,1,1,1] (.node [10,7,5,5,3,3,2,2,2,2,1,1] (.node [10,7,5,5,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,5,5,3,3,2,2,2,2,2] .empty .empty)) (.node [10,7,5,5,3,3,3,2,2,1,1,1] (.node [10,7,5,5,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,7,5,5,3,3,3,2,2,2,1] .empty .empty))) (.node [10,7,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,5,3,3,3,3,2,2] (.node [10,7,5,5,3,3,3,3,2,1,1] .empty .empty) (.node [10,7,5,5,3,3,3,3,3,1] .empty .empty)) (.node [10,7,5,5,4,2,2,1,1,1,1,1,1,1,1] (.node [10,7,5,5,4,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,5,4,2,2,2,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_452 : RowTree := (.node [10,7,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_450 degreeTree43_451) + +def degreeTree43_453 : RowTree := (.node [10,7,5,4,4,2,2,2,2,2,2,1] degreeTree43_449 degreeTree43_452) + +def degreeTree43_454 : RowTree := (.node [10,7,5,5,4,3,3,2,1,1,1,1] (.node [10,7,5,5,4,3,2,2,1,1,1,1,1] (.node [10,7,5,5,4,3,1,1,1,1,1,1,1,1,1] (.node [10,7,5,5,4,2,2,2,2,2,2] (.node [10,7,5,5,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,7,5,5,4,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,5,5,4,3,2,2,2,2,1] (.node [10,7,5,5,4,3,2,2,2,1,1,1] .empty .empty) (.node [10,7,5,5,4,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,7,5,5,4,3,3,3,2,1] (.node [10,7,5,5,4,3,3,2,2,2] (.node [10,7,5,5,4,3,3,2,2,1,1] .empty .empty) (.node [10,7,5,5,4,3,3,3,1,1,1] .empty .empty)) (.node [10,7,5,5,4,4,2,1,1,1,1,1,1] (.node [10,7,5,5,4,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,5,4,4,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree43_455 : RowTree := (.node [10,7,5,5,5,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,5,4,4,3,2,2,1] (.node [10,7,5,5,4,4,3,1,1,1,1,1] (.node [10,7,5,5,4,4,2,2,2,2] .empty .empty) (.node [10,7,5,5,4,4,3,2,1,1,1] .empty .empty)) (.node [10,7,5,5,4,4,4,1,1,1,1] (.node [10,7,5,5,4,4,3,3,1,1] .empty .empty) (.node [10,7,5,5,4,4,4,2,1,1] .empty .empty))) (.node [10,7,5,5,5,2,2,2,2,1,1,1] (.node [10,7,5,5,5,2,2,1,1,1,1,1,1,1] (.node [10,7,5,5,5,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,5,5,5,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,5,5,5,3,1,1,1,1,1,1,1,1] (.node [10,7,5,5,5,2,2,2,2,2,1] .empty .empty) (.node [10,7,5,5,5,3,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_456 : RowTree := (.node [10,7,5,5,4,4,2,2,2,1,1] degreeTree43_454 degreeTree43_455) + +def degreeTree43_457 : RowTree := (.node [10,7,5,5,5,5,2,2,1,1] (.node [10,7,5,5,5,4,2,1,1,1,1,1] (.node [10,7,5,5,5,3,3,2,1,1,1] (.node [10,7,5,5,5,3,2,2,2,2] (.node [10,7,5,5,5,3,2,2,2,1,1] .empty .empty) (.node [10,7,5,5,5,3,3,1,1,1,1,1] .empty .empty)) (.node [10,7,5,5,5,3,3,3,1,1] (.node [10,7,5,5,5,3,3,2,2,1] .empty .empty) (.node [10,7,5,5,5,4,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,5,5,5,4,3,2,1,1] (.node [10,7,5,5,5,4,2,2,2,1] (.node [10,7,5,5,5,4,2,2,1,1,1] .empty .empty) (.node [10,7,5,5,5,4,3,1,1,1,1] .empty .empty)) (.node [10,7,5,5,5,5,1,1,1,1,1,1] (.node [10,7,5,5,5,4,4,1,1,1] .empty .empty) (.node [10,7,5,5,5,5,2,1,1,1,1] .empty .empty)))) (.node [10,7,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,5,5,5,5,3,1,1,1] .empty .empty) (.node [10,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,6,2,2,2,2,2,2,2,2,2,2] (.node [10,7,6,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,7,6,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,2,2,2,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,7,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_458 : RowTree := (.node [10,7,5,5,5,3,2,2,1,1,1,1] degreeTree43_456 degreeTree43_457) + +def degreeTree43_459 : RowTree := (.node [10,7,6,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,7,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,3,2,2,2,2,2,2,2,1,1,1] (.node [10,7,6,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,3,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,6,3,3,2,2,2,2,2,2,1,1] (.node [10,7,6,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,7,6,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,3,3,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,7,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,3,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,7,6,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,7,6,3,3,3,3,2,2,2,2] (.node [10,7,6,3,3,3,3,1,1,1,1,1,1,1,1] (.node [10,7,6,3,3,3,2,2,2,2,1,1,1] (.node [10,7,6,3,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,6,3,3,3,2,2,2,2,2,1] .empty .empty)) (.node [10,7,6,3,3,3,3,2,2,1,1,1,1] (.node [10,7,6,3,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,3,3,3,3,2,2,2,1,1] .empty .empty))) (.node [10,7,6,3,3,3,3,3,3,1,1] (.node [10,7,6,3,3,3,3,3,2,1,1,1] (.node [10,7,6,3,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,6,3,3,3,3,3,2,2,1] .empty .empty)) (.node [10,7,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,3,3,3,3,3,3,2] .empty .empty) (.node [10,7,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_460 : RowTree := (.node [10,7,6,4,3,3,2,2,1,1,1,1,1,1] (.node [10,7,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,4,2,2,2,2,2,2,1,1,1,1] (.node [10,7,6,4,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,4,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,4,2,2,2,2,2,2,2,2] (.node [10,7,6,4,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,6,4,3,2,2,2,2,2,1,1,1] (.node [10,7,6,4,3,2,2,2,1,1,1,1,1,1,1] (.node [10,7,6,4,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,4,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,6,4,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,4,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,6,4,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,7,6,4,3,3,3,3,1,1,1,1] (.node [10,7,6,4,3,3,3,1,1,1,1,1,1,1] (.node [10,7,6,4,3,3,2,2,2,2,1,1] (.node [10,7,6,4,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,6,4,3,3,2,2,2,2,2] .empty .empty)) (.node [10,7,6,4,3,3,3,2,2,1,1,1] (.node [10,7,6,4,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,7,6,4,3,3,3,2,2,2,1] .empty .empty))) (.node [10,7,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,4,3,3,3,3,2,2] (.node [10,7,6,4,3,3,3,3,2,1,1] .empty .empty) (.node [10,7,6,4,3,3,3,3,3,1] .empty .empty)) (.node [10,7,6,4,4,2,2,1,1,1,1,1,1,1,1] (.node [10,7,6,4,4,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,4,4,2,2,2,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_461 : RowTree := (.node [10,7,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_459 degreeTree43_460) + +def degreeTree43_462 : RowTree := (.node [10,7,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_458 degreeTree43_461) + +def degreeTree43_463 : RowTree := (.node [10,7,5,5,4,2,2,2,2,1,1,1,1] degreeTree43_453 degreeTree43_462) + +def degreeTree43_464 : RowTree := (.node [10,7,6,4,4,3,3,2,1,1,1,1] (.node [10,7,6,4,4,3,2,2,1,1,1,1,1] (.node [10,7,6,4,4,3,1,1,1,1,1,1,1,1,1] (.node [10,7,6,4,4,2,2,2,2,2,2] (.node [10,7,6,4,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,7,6,4,4,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,4,4,3,2,2,2,2,1] (.node [10,7,6,4,4,3,2,2,2,1,1,1] .empty .empty) (.node [10,7,6,4,4,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,7,6,4,4,3,3,3,2,1] (.node [10,7,6,4,4,3,3,2,2,2] (.node [10,7,6,4,4,3,3,2,2,1,1] .empty .empty) (.node [10,7,6,4,4,3,3,3,1,1,1] .empty .empty)) (.node [10,7,6,4,4,4,2,1,1,1,1,1,1] (.node [10,7,6,4,4,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,4,4,4,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree43_465 : RowTree := (.node [10,7,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,4,4,4,3,2,2,1] (.node [10,7,6,4,4,4,3,1,1,1,1,1] (.node [10,7,6,4,4,4,2,2,2,2] .empty .empty) (.node [10,7,6,4,4,4,3,2,1,1,1] .empty .empty)) (.node [10,7,6,4,4,4,4,1,1,1,1] (.node [10,7,6,4,4,4,3,3,1,1] .empty .empty) (.node [10,7,6,4,4,4,4,2,1,1] .empty .empty))) (.node [10,7,6,5,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,5,2,2,2,2,2,2,1,1,1] (.node [10,7,6,5,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,2,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree43_466 : RowTree := (.node [10,7,6,4,4,4,2,2,2,1,1] degreeTree43_464 degreeTree43_465) + +def degreeTree43_467 : RowTree := (.node [10,7,6,5,3,3,3,3,1,1,1] (.node [10,7,6,5,3,3,2,1,1,1,1,1,1,1] (.node [10,7,6,5,3,2,2,2,2,1,1,1,1] (.node [10,7,6,5,3,2,2,1,1,1,1,1,1,1,1] (.node [10,7,6,5,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,3,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,5,3,2,2,2,2,2,2] (.node [10,7,6,5,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,6,5,3,3,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,6,5,3,3,3,1,1,1,1,1,1] (.node [10,7,6,5,3,3,2,2,2,1,1,1] (.node [10,7,6,5,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,3,3,2,2,2,2,1] .empty .empty)) (.node [10,7,6,5,3,3,3,2,2,1,1] (.node [10,7,6,5,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,7,6,5,3,3,3,2,2,2] .empty .empty)))) (.node [10,7,6,5,4,3,1,1,1,1,1,1,1,1] (.node [10,7,6,5,4,2,2,1,1,1,1,1,1,1] (.node [10,7,6,5,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,5,3,3,3,3,2,1] .empty .empty) (.node [10,7,6,5,4,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,5,4,2,2,2,2,1,1,1] (.node [10,7,6,5,4,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,4,2,2,2,2,2,1] .empty .empty))) (.node [10,7,6,5,4,3,2,2,2,2] (.node [10,7,6,5,4,3,2,2,1,1,1,1] (.node [10,7,6,5,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,4,3,2,2,2,1,1] .empty .empty)) (.node [10,7,6,5,4,3,3,2,1,1,1] (.node [10,7,6,5,4,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,4,3,3,2,2,1] .empty .empty))))) + +def degreeTree43_468 : RowTree := (.node [10,7,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_466 degreeTree43_467) + +def degreeTree43_469 : RowTree := (.node [10,7,6,5,5,3,2,2,1,1,1] (.node [10,7,6,5,5,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,5,4,4,2,2,2,1] (.node [10,7,6,5,4,4,2,1,1,1,1,1] (.node [10,7,6,5,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,4,4,2,2,1,1,1] .empty .empty)) (.node [10,7,6,5,4,4,3,2,1,1] (.node [10,7,6,5,4,4,3,1,1,1,1] .empty .empty) (.node [10,7,6,5,4,4,4,1,1,1] .empty .empty))) (.node [10,7,6,5,5,2,2,2,2,1,1] (.node [10,7,6,5,5,2,2,1,1,1,1,1,1] (.node [10,7,6,5,5,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,5,5,2,2,2,1,1,1,1] .empty .empty)) (.node [10,7,6,5,5,3,1,1,1,1,1,1,1] (.node [10,7,6,5,5,2,2,2,2,2] .empty .empty) (.node [10,7,6,5,5,3,2,1,1,1,1,1] .empty .empty)))) (.node [10,7,6,5,5,5,1,1,1,1,1] (.node [10,7,6,5,5,4,1,1,1,1,1,1] (.node [10,7,6,5,5,3,3,1,1,1,1] (.node [10,7,6,5,5,3,2,2,2,1] .empty .empty) (.node [10,7,6,5,5,3,3,2,1,1] .empty .empty)) (.node [10,7,6,5,5,4,2,2,1,1] (.node [10,7,6,5,5,4,2,1,1,1,1] .empty .empty) (.node [10,7,6,5,5,4,3,1,1,1] .empty .empty))) (.node [10,7,6,6,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,5,5,5,2,1,1,1] .empty .empty) (.node [10,7,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,6,2,2,2,2,1,1,1,1,1,1] (.node [10,7,6,6,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,2,2,2,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_470 : RowTree := (.node [10,7,6,6,3,3,3,3,1,1] (.node [10,7,6,6,3,3,1,1,1,1,1,1,1,1] (.node [10,7,6,6,3,2,2,1,1,1,1,1,1,1] (.node [10,7,6,6,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,6,6,2,2,2,2,2,2,2] .empty .empty) (.node [10,7,6,6,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,6,3,2,2,2,2,1,1,1] (.node [10,7,6,6,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,3,2,2,2,2,2,1] .empty .empty))) (.node [10,7,6,6,3,3,2,2,2,2] (.node [10,7,6,6,3,3,2,2,1,1,1,1] (.node [10,7,6,6,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,3,3,2,2,2,1,1] .empty .empty)) (.node [10,7,6,6,3,3,3,2,1,1,1] (.node [10,7,6,6,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,3,3,3,2,2,1] .empty .empty)))) (.node [10,7,6,6,4,3,2,1,1,1,1,1] (.node [10,7,6,6,4,2,2,2,1,1,1,1] (.node [10,7,6,6,4,2,1,1,1,1,1,1,1,1] (.node [10,7,6,6,4,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,4,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,6,4,2,2,2,2,2] (.node [10,7,6,6,4,2,2,2,2,1,1] .empty .empty) (.node [10,7,6,6,4,3,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,6,6,4,3,3,2,1,1] (.node [10,7,6,6,4,3,2,2,2,1] (.node [10,7,6,6,4,3,2,2,1,1,1] .empty .empty) (.node [10,7,6,6,4,3,3,1,1,1,1] .empty .empty)) (.node [10,7,6,6,4,4,2,1,1,1,1] (.node [10,7,6,6,4,4,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,4,4,2,2,1,1] .empty .empty))))) + +def degreeTree43_471 : RowTree := (.node [10,7,6,6,2,2,2,2,2,2,1,1] degreeTree43_469 degreeTree43_470) + +def degreeTree43_472 : RowTree := (.node [10,7,6,5,4,3,3,3,1,1] degreeTree43_468 degreeTree43_471) + +def degreeTree43_473 : RowTree := (.node [10,7,6,6,5,3,3,1,1,1] (.node [10,7,6,6,5,2,2,2,2,1] (.node [10,7,6,6,5,2,2,1,1,1,1,1] (.node [10,7,6,6,5,2,1,1,1,1,1,1,1] (.node [10,7,6,6,5,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,7,6,6,5,2,2,2,1,1,1] .empty .empty)) (.node [10,7,6,6,5,3,2,1,1,1,1] (.node [10,7,6,6,5,3,1,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,5,3,2,2,1,1] .empty .empty))) (.node [10,7,6,6,6,2,1,1,1,1,1,1] (.node [10,7,6,6,5,4,2,1,1,1] (.node [10,7,6,6,5,4,1,1,1,1,1] .empty .empty) (.node [10,7,6,6,6,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,6,6,6,2,2,2,1,1] (.node [10,7,6,6,6,2,2,1,1,1,1] .empty .empty) (.node [10,7,6,6,6,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_474 : RowTree := (.node [10,7,7,2,2,2,2,2,2,2,2,1,1,1] (.node [10,7,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,7,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,7,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_475 : RowTree := (.node [10,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_473 degreeTree43_474) + +def degreeTree43_476 : RowTree := (.node [10,7,7,3,3,3,3,1,1,1,1,1,1,1] (.node [10,7,7,3,3,2,2,2,2,2,1,1,1] (.node [10,7,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,3,2,2,2,2,2,2,2,2] (.node [10,7,7,3,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,7,7,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,3,3,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,7,7,3,3,3,2,2,1,1,1,1,1,1] (.node [10,7,7,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,3,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,7,7,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,3,3,3,2,2,2,2,1,1] (.node [10,7,7,3,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,7,3,3,3,2,2,2,2,2] .empty .empty)))) (.node [10,7,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,3,3,3,3,3,1,1,1,1] (.node [10,7,7,3,3,3,3,2,2,1,1,1] (.node [10,7,7,3,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,7,7,3,3,3,3,2,2,2,1] .empty .empty)) (.node [10,7,7,3,3,3,3,3,2,2] (.node [10,7,7,3,3,3,3,3,2,1,1] .empty .empty) (.node [10,7,7,3,3,3,3,3,3,1] .empty .empty))) (.node [10,7,7,4,2,2,2,2,1,1,1,1,1,1,1] (.node [10,7,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,4,2,2,2,2,2,2,1,1,1] (.node [10,7,7,4,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,2,2,2,2,2,2,2,1] .empty .empty))))) + +def degreeTree43_477 : RowTree := (.node [10,7,7,3,2,2,2,2,2,2,1,1,1,1] degreeTree43_475 degreeTree43_476) + +def degreeTree43_478 : RowTree := (.node [10,7,7,4,3,3,3,3,1,1,1] (.node [10,7,7,4,3,3,2,1,1,1,1,1,1,1] (.node [10,7,7,4,3,2,2,2,2,1,1,1,1] (.node [10,7,7,4,3,2,2,1,1,1,1,1,1,1,1] (.node [10,7,7,4,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,3,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,4,3,2,2,2,2,2,2] (.node [10,7,7,4,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,7,7,4,3,3,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,7,7,4,3,3,3,1,1,1,1,1,1] (.node [10,7,7,4,3,3,2,2,2,1,1,1] (.node [10,7,7,4,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,3,3,2,2,2,2,1] .empty .empty)) (.node [10,7,7,4,3,3,3,2,2,1,1] (.node [10,7,7,4,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,7,7,4,3,3,3,2,2,2] .empty .empty)))) (.node [10,7,7,4,4,3,1,1,1,1,1,1,1,1] (.node [10,7,7,4,4,2,2,1,1,1,1,1,1,1] (.node [10,7,7,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,4,3,3,3,3,2,1] .empty .empty) (.node [10,7,7,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,4,4,2,2,2,2,1,1,1] (.node [10,7,7,4,4,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,4,2,2,2,2,2,1] .empty .empty))) (.node [10,7,7,4,4,3,2,2,2,2] (.node [10,7,7,4,4,3,2,2,1,1,1,1] (.node [10,7,7,4,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,4,3,2,2,2,1,1] .empty .empty)) (.node [10,7,7,4,4,3,3,2,1,1,1] (.node [10,7,7,4,4,3,3,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,4,3,3,2,2,1] .empty .empty))))) + +def degreeTree43_479 : RowTree := (.node [10,7,7,5,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,4,4,4,2,2,2,1] (.node [10,7,7,4,4,4,2,1,1,1,1,1] (.node [10,7,7,4,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,4,4,4,2,2,1,1,1] .empty .empty)) (.node [10,7,7,4,4,4,3,2,1,1] (.node [10,7,7,4,4,4,3,1,1,1,1] .empty .empty) (.node [10,7,7,4,4,4,4,1,1,1] .empty .empty))) (.node [10,7,7,5,2,2,2,2,1,1,1,1,1,1] (.node [10,7,7,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,5,2,2,2,2,2,2,1,1] (.node [10,7,7,5,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,7,7,5,2,2,2,2,2,2,2] .empty .empty)))) (.node [10,7,7,5,3,3,2,2,1,1,1,1] (.node [10,7,7,5,3,2,2,2,2,1,1,1] (.node [10,7,7,5,3,2,2,1,1,1,1,1,1,1] (.node [10,7,7,5,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,5,3,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,7,5,3,3,1,1,1,1,1,1,1,1] (.node [10,7,7,5,3,2,2,2,2,2,1] .empty .empty) (.node [10,7,7,5,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [10,7,7,5,3,3,3,2,1,1,1] (.node [10,7,7,5,3,3,2,2,2,2] (.node [10,7,7,5,3,3,2,2,2,1,1] .empty .empty) (.node [10,7,7,5,3,3,3,1,1,1,1,1] .empty .empty)) (.node [10,7,7,5,3,3,3,3,1,1] (.node [10,7,7,5,3,3,3,2,2,1] .empty .empty) (.node [10,7,7,5,4,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_480 : RowTree := (.node [10,7,7,4,4,3,3,3,1,1] degreeTree43_478 degreeTree43_479) + +def degreeTree43_481 : RowTree := (.node [10,7,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_477 degreeTree43_480) + +def degreeTree43_482 : RowTree := (.node [10,7,6,6,4,4,3,1,1,1] degreeTree43_472 degreeTree43_481) + +def degreeTree43_483 : RowTree := (.node [10,7,6,4,4,2,2,2,2,1,1,1,1] degreeTree43_463 degreeTree43_482) + +def degreeTree43_484 : RowTree := (.node [10,7,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_444 degreeTree43_483) + +def degreeTree43_485 : RowTree := (.node [10,6,5,5,5,3,3,2,1,1,1,1] degreeTree43_405 degreeTree43_484) + +def degreeTree43_486 : RowTree := (.node [10,7,7,5,4,3,3,1,1,1,1] (.node [10,7,7,5,4,3,1,1,1,1,1,1,1] (.node [10,7,7,5,4,2,2,2,2,1,1] (.node [10,7,7,5,4,2,2,2,1,1,1,1] (.node [10,7,7,5,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,7,7,5,4,2,2,2,2,2] .empty .empty)) (.node [10,7,7,5,4,3,2,2,1,1,1] (.node [10,7,7,5,4,3,2,1,1,1,1,1] .empty .empty) (.node [10,7,7,5,4,3,2,2,2,1] .empty .empty))) (.node [10,7,7,5,4,4,2,2,1,1] (.node [10,7,7,5,4,4,1,1,1,1,1,1] (.node [10,7,7,5,4,3,3,2,1,1] .empty .empty) (.node [10,7,7,5,4,4,2,1,1,1,1] .empty .empty)) (.node [10,7,7,5,5,1,1,1,1,1,1,1,1,1] (.node [10,7,7,5,4,4,3,1,1,1] .empty .empty) (.node [10,7,7,5,5,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_487 : RowTree := (.node [10,7,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,5,5,3,2,1,1,1,1] (.node [10,7,7,5,5,2,2,2,2,1] (.node [10,7,7,5,5,2,2,2,1,1,1] .empty .empty) (.node [10,7,7,5,5,3,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,5,5,3,3,1,1,1] (.node [10,7,7,5,5,3,2,2,1,1] .empty .empty) (.node [10,7,7,5,5,4,1,1,1,1,1] .empty .empty))) (.node [10,7,7,6,2,2,2,2,1,1,1,1,1] (.node [10,7,7,6,2,2,1,1,1,1,1,1,1,1,1] (.node [10,7,7,6,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,6,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,6,2,2,2,2,2,2,1] (.node [10,7,7,6,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,7,7,6,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_488 : RowTree := (.node [10,7,7,5,5,2,2,1,1,1,1,1] degreeTree43_486 degreeTree43_487) + +def degreeTree43_489 : RowTree := (.node [10,7,7,6,4,3,1,1,1,1,1,1] (.node [10,7,7,6,3,3,2,2,2,1] (.node [10,7,7,6,3,2,2,2,2,2] (.node [10,7,7,6,3,2,2,2,1,1,1,1] (.node [10,7,7,6,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,6,3,2,2,2,2,1,1] .empty .empty)) (.node [10,7,7,6,3,3,2,1,1,1,1,1] (.node [10,7,7,6,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,6,3,3,2,2,1,1,1] .empty .empty))) (.node [10,7,7,6,4,2,1,1,1,1,1,1,1] (.node [10,7,7,6,3,3,3,2,1,1] (.node [10,7,7,6,3,3,3,1,1,1,1] .empty .empty) (.node [10,7,7,6,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,6,4,2,2,2,1,1,1] (.node [10,7,7,6,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,7,7,6,4,2,2,2,2,1] .empty .empty)))) (.node [10,7,7,6,5,3,1,1,1,1,1] (.node [10,7,7,6,5,1,1,1,1,1,1,1,1] (.node [10,7,7,6,4,3,2,2,1,1] (.node [10,7,7,6,4,3,2,1,1,1,1] .empty .empty) (.node [10,7,7,6,4,4,1,1,1,1,1] .empty .empty)) (.node [10,7,7,6,5,2,2,1,1,1,1] (.node [10,7,7,6,5,2,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,6,5,2,2,2,1,1] .empty .empty))) (.node [10,7,7,7,2,1,1,1,1,1,1,1,1,1,1] (.node [10,7,7,6,6,2,1,1,1,1,1] (.node [10,7,7,6,6,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,7,7,7,2,2,2,1,1,1,1,1,1] (.node [10,7,7,7,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,7,2,2,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_490 : RowTree := (.node [10,7,7,6,3,2,1,1,1,1,1,1,1,1] degreeTree43_488 degreeTree43_489) + +def degreeTree43_491 : RowTree := (.node [10,7,7,7,3,3,2,2,1,1] (.node [10,7,7,7,3,2,2,2,1,1,1] (.node [10,7,7,7,3,2,1,1,1,1,1,1,1] (.node [10,7,7,7,3,1,1,1,1,1,1,1,1,1] (.node [10,7,7,7,2,2,2,2,2,2] .empty .empty) .empty) (.node [10,7,7,7,3,2,2,1,1,1,1,1] .empty .empty)) (.node [10,7,7,7,3,3,1,1,1,1,1,1] (.node [10,7,7,7,3,2,2,2,2,1] .empty .empty) (.node [10,7,7,7,3,3,2,1,1,1,1] .empty .empty))) (.node [10,7,7,7,4,2,2,2,1,1] (.node [10,7,7,7,4,2,1,1,1,1,1,1] (.node [10,7,7,7,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,7,7,7,4,2,2,1,1,1,1] .empty .empty)) (.node [10,7,7,7,5,1,1,1,1,1,1,1] (.node [10,7,7,7,4,3,1,1,1,1,1] .empty .empty) (.node [10,7,7,7,5,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_492 : RowTree := (.node [10,8,2,2,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,8,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,8,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,2,2,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_493 : RowTree := (.node [10,7,7,7,6,1,1,1,1,1,1] degreeTree43_491 degreeTree43_492) + +def degreeTree43_494 : RowTree := (.node [10,8,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,8,3,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,8,3,2,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,8,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,3,3,2,2,2,2,2,2,2,2,1,1,1] (.node [10,8,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,8,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,2,2,2,2,2,2,1,1,1,1] (.node [10,8,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,8,3,3,3,2,2,2,2,2,2,2,2] (.node [10,8,3,3,3,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,3,3,3,3,2,2,2,2,2,1,1,1] (.node [10,8,3,3,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,8,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,3,3,3,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,8,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,3,3,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_495 : RowTree := (.node [10,8,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] degreeTree43_493 degreeTree43_494) + +def degreeTree43_496 : RowTree := (.node [10,7,7,7,2,2,2,2,2,1,1] degreeTree43_490 degreeTree43_495) + +def degreeTree43_497 : RowTree := (.node [10,8,3,3,3,3,3,3,3,2,1,1] (.node [10,8,3,3,3,3,3,3,2,1,1,1,1,1] (.node [10,8,3,3,3,3,3,2,2,2,2,2] (.node [10,8,3,3,3,3,3,2,2,2,2,1,1] (.node [10,8,3,3,3,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,8,3,3,3,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,3,3,3,3,3,3,2,2,2,1] (.node [10,8,3,3,3,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,8,3,3,3,3,3,3,3,1,1,1,1] .empty .empty))) (.node [10,8,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,3,3,3,3,3,3,3,3,1] (.node [10,8,3,3,3,3,3,3,3,2,2] .empty .empty) (.node [10,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_498 : RowTree := (.node [10,8,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,2,2,2,2,2,2,2,2,2,2,1] (.node [10,8,4,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,8,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,8,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,4,3,2,2,2,2,2,2,2,1,1,1,1] (.node [10,8,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,3,2,2,2,2,2,2,2,2,2] (.node [10,8,4,3,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_499 : RowTree := (.node [10,8,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_497 degreeTree43_498) + +def degreeTree43_500 : RowTree := (.node [10,8,4,3,3,3,3,2,2,1,1,1,1,1] (.node [10,8,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,3,2,2,2,2,2,1,1,1,1,1] (.node [10,8,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,3,3,2,2,2,2,2,2,2,1] (.node [10,8,4,3,3,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,4,3,3,3,2,2,2,2,2,1,1] (.node [10,8,4,3,3,3,2,2,2,1,1,1,1,1,1] (.node [10,8,4,3,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,3,3,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,8,4,3,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,8,4,3,3,3,3,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,4,3,3,3,3,3,3,2,1] (.node [10,8,4,3,3,3,3,3,2,1,1,1,1] (.node [10,8,4,3,3,3,3,2,2,2,2,1] (.node [10,8,4,3,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,8,4,3,3,3,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,3,3,3,3,3,2,2,2] (.node [10,8,4,3,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,8,4,3,3,3,3,3,3,1,1,1] .empty .empty))) (.node [10,8,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,3,3,3,3,3,3,3] .empty .empty) (.node [10,8,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_501 : RowTree := (.node [10,8,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_499 degreeTree43_500) + +def degreeTree43_502 : RowTree := (.node [10,8,4,4,3,3,2,2,2,2,2,1] (.node [10,8,4,4,3,2,2,2,2,2,1,1,1,1] (.node [10,8,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,2,2,2,2,2,2,2,2,1] (.node [10,8,4,4,2,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,3,2,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,8,4,4,3,3,2,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,3,2,2,2,2,2,2,2] (.node [10,8,4,4,3,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,3,3,2,2,2,1,1,1,1,1] (.node [10,8,4,4,3,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,3,3,2,2,2,2,1,1,1] .empty .empty)))) (.node [10,8,4,4,3,3,3,3,2,2,1] (.node [10,8,4,4,3,3,3,2,2,2,1,1] (.node [10,8,4,4,3,3,3,2,1,1,1,1,1,1] (.node [10,8,4,4,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,3,3,3,2,2,1,1,1,1] .empty .empty)) (.node [10,8,4,4,3,3,3,3,1,1,1,1,1] (.node [10,8,4,4,3,3,3,2,2,2,2] .empty .empty) (.node [10,8,4,4,3,3,3,3,2,1,1,1] .empty .empty))) (.node [10,8,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,3,3,3,3,3,2] (.node [10,8,4,4,3,3,3,3,3,1,1] .empty .empty) (.node [10,8,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,4,2,2,2,1,1,1,1,1,1,1] (.node [10,8,4,4,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,2,2,2,2,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_503 : RowTree := (.node [10,8,4,4,4,4,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,4,3,3,1,1,1,1,1,1,1] (.node [10,8,4,4,4,3,2,2,1,1,1,1,1,1] (.node [10,8,4,4,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,8,4,4,4,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,4,4,4,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,4,3,2,2,2,2,1,1] (.node [10,8,4,4,4,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,3,2,2,2,2,2] .empty .empty))) (.node [10,8,4,4,4,3,3,3,1,1,1,1] (.node [10,8,4,4,4,3,3,2,2,1,1,1] (.node [10,8,4,4,4,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,3,3,2,2,2,1] .empty .empty)) (.node [10,8,4,4,4,3,3,3,2,2] (.node [10,8,4,4,4,3,3,3,2,1,1] .empty .empty) (.node [10,8,4,4,4,3,3,3,3,1] .empty .empty)))) (.node [10,8,4,4,4,4,3,2,2,2] (.node [10,8,4,4,4,4,2,2,2,2,1] (.node [10,8,4,4,4,4,2,2,1,1,1,1,1] (.node [10,8,4,4,4,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,4,2,2,2,1,1,1] .empty .empty)) (.node [10,8,4,4,4,4,3,2,1,1,1,1] (.node [10,8,4,4,4,4,3,1,1,1,1,1,1] .empty .empty) (.node [10,8,4,4,4,4,3,2,2,1,1] .empty .empty))) (.node [10,8,4,4,4,4,4,2,1,1,1] (.node [10,8,4,4,4,4,3,3,2,1] (.node [10,8,4,4,4,4,3,3,1,1,1] .empty .empty) (.node [10,8,4,4,4,4,4,1,1,1,1,1] .empty .empty)) (.node [10,8,4,4,4,4,4,3,1,1] (.node [10,8,4,4,4,4,4,2,2,1] .empty .empty) (.node [10,8,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_504 : RowTree := (.node [10,8,4,4,4,2,2,2,2,2,1,1,1] degreeTree43_502 degreeTree43_503) + +def degreeTree43_505 : RowTree := (.node [10,8,4,4,2,2,2,2,2,2,1,1,1,1,1] degreeTree43_501 degreeTree43_504) + +def degreeTree43_506 : RowTree := (.node [10,8,3,3,3,3,3,2,2,1,1,1,1,1,1] degreeTree43_496 degreeTree43_505) + +def degreeTree43_507 : RowTree := (.node [10,8,5,2,2,2,2,2,2,2,2,2,2] (.node [10,8,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,8,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,2,2,2,2,2,2,2,2,1,1,1,1] (.node [10,8,5,2,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,2,2,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [10,8,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,3,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,3,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_508 : RowTree := (.node [10,8,5,3,3,2,2,2,2,2,2,1,1] (.node [10,8,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,3,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,8,5,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,3,3,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,8,5,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,8,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,3,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,8,5,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,3,3,3,2,2,2,2,1,1,1] (.node [10,8,5,3,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,5,3,3,3,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree43_509 : RowTree := (.node [10,8,5,3,2,2,2,2,2,2,2,1,1,1] degreeTree43_507 degreeTree43_508) + +def degreeTree43_510 : RowTree := (.node [10,8,5,4,2,2,2,2,2,2,1,1,1,1] (.node [10,8,5,3,3,3,3,3,3,1,1] (.node [10,8,5,3,3,3,3,2,2,2,2] (.node [10,8,5,3,3,3,3,2,2,1,1,1,1] (.node [10,8,5,3,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,3,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,8,5,3,3,3,3,3,2,1,1,1] (.node [10,8,5,3,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,8,5,3,3,3,3,3,2,2,1] .empty .empty))) (.node [10,8,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,3,3,3,3,3,3,2] .empty .empty) (.node [10,8,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,4,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,4,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,5,4,3,2,2,2,2,2,1,1,1] (.node [10,8,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,4,2,2,2,2,2,2,2,2] (.node [10,8,5,4,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,4,3,2,2,2,1,1,1,1,1,1,1] (.node [10,8,5,4,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,4,3,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,8,5,4,3,3,2,2,1,1,1,1,1,1] (.node [10,8,5,4,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,4,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,5,4,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,4,3,3,2,2,2,2,1,1] (.node [10,8,5,4,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,8,5,4,3,3,2,2,2,2,2] .empty .empty))))) + +def degreeTree43_511 : RowTree := (.node [10,8,5,3,3,3,3,1,1,1,1,1,1,1,1] degreeTree43_509 degreeTree43_510) + +def degreeTree43_512 : RowTree := (.node [10,8,5,4,4,3,2,1,1,1,1,1,1,1] (.node [10,8,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,4,3,3,3,3,1,1,1,1] (.node [10,8,5,4,3,3,3,2,2,1,1,1] (.node [10,8,5,4,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,8,5,4,3,3,3,2,2,2,1] .empty .empty)) (.node [10,8,5,4,3,3,3,3,2,2] (.node [10,8,5,4,3,3,3,3,2,1,1] .empty .empty) (.node [10,8,5,4,3,3,3,3,3,1] .empty .empty))) (.node [10,8,5,4,4,2,2,2,2,1,1,1,1] (.node [10,8,5,4,4,2,2,1,1,1,1,1,1,1,1] (.node [10,8,5,4,4,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,4,4,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,4,4,2,2,2,2,2,2] (.node [10,8,5,4,4,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,5,4,4,3,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,5,4,4,3,3,3,1,1,1] (.node [10,8,5,4,4,3,3,1,1,1,1,1,1] (.node [10,8,5,4,4,3,2,2,2,1,1,1] (.node [10,8,5,4,4,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,5,4,4,3,2,2,2,2,1] .empty .empty)) (.node [10,8,5,4,4,3,3,2,2,1,1] (.node [10,8,5,4,4,3,3,2,1,1,1,1] .empty .empty) (.node [10,8,5,4,4,3,3,2,2,2] .empty .empty))) (.node [10,8,5,4,4,4,2,2,1,1,1,1] (.node [10,8,5,4,4,4,1,1,1,1,1,1,1,1] (.node [10,8,5,4,4,3,3,3,2,1] .empty .empty) (.node [10,8,5,4,4,4,2,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,4,4,4,2,2,2,2] (.node [10,8,5,4,4,4,2,2,2,1,1] .empty .empty) (.node [10,8,5,4,4,4,3,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_513 : RowTree := (.node [10,8,5,5,3,2,2,2,1,1,1,1,1,1] (.node [10,8,5,5,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,5,4,4,4,4,2,1,1] (.node [10,8,5,4,4,4,3,3,1,1] (.node [10,8,5,4,4,4,3,2,2,1] .empty .empty) (.node [10,8,5,4,4,4,4,1,1,1,1] .empty .empty)) (.node [10,8,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,5,5,2,2,2,2,2,2,2,1] (.node [10,8,5,5,2,2,2,2,2,1,1,1,1,1] (.node [10,8,5,5,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,8,5,5,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,3,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,5,5,3,3,2,2,2,2,1] (.node [10,8,5,5,3,3,1,1,1,1,1,1,1,1,1] (.node [10,8,5,5,3,2,2,2,2,2,1,1] (.node [10,8,5,5,3,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,8,5,5,3,2,2,2,2,2,2] .empty .empty)) (.node [10,8,5,5,3,3,2,2,1,1,1,1,1] (.node [10,8,5,5,3,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,3,3,2,2,2,1,1,1] .empty .empty))) (.node [10,8,5,5,3,3,3,2,2,2] (.node [10,8,5,5,3,3,3,2,1,1,1,1] (.node [10,8,5,5,3,3,3,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,3,3,3,2,2,1,1] .empty .empty)) (.node [10,8,5,5,3,3,3,3,2,1] (.node [10,8,5,5,3,3,3,3,1,1,1] .empty .empty) (.node [10,8,5,5,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_514 : RowTree := (.node [10,8,5,4,4,4,3,2,1,1,1] degreeTree43_512 degreeTree43_513) + +def degreeTree43_515 : RowTree := (.node [10,8,5,4,3,3,3,1,1,1,1,1,1,1] degreeTree43_511 degreeTree43_514) + +def degreeTree43_516 : RowTree := (.node [10,8,5,5,4,3,2,2,2,2] (.node [10,8,5,5,4,3,1,1,1,1,1,1,1,1] (.node [10,8,5,5,4,2,2,2,2,1,1,1] (.node [10,8,5,5,4,2,2,2,1,1,1,1,1] (.node [10,8,5,5,4,2,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,8,5,5,4,2,2,2,2,2,1] .empty .empty)) (.node [10,8,5,5,4,3,2,2,1,1,1,1] (.node [10,8,5,5,4,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,4,3,2,2,2,1,1] .empty .empty))) (.node [10,8,5,5,4,3,3,3,1,1] (.node [10,8,5,5,4,3,3,2,1,1,1] (.node [10,8,5,5,4,3,3,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,4,3,3,2,2,1] .empty .empty)) (.node [10,8,5,5,4,4,2,1,1,1,1,1] (.node [10,8,5,5,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,4,4,2,2,1,1,1] .empty .empty)))) + +def degreeTree43_517 : RowTree := (.node [10,8,5,5,5,2,2,2,2,2] (.node [10,8,5,5,5,2,1,1,1,1,1,1,1,1] (.node [10,8,5,5,4,4,3,2,1,1] (.node [10,8,5,5,4,4,3,1,1,1,1] .empty .empty) (.node [10,8,5,5,5,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,5,5,5,2,2,2,1,1,1,1] (.node [10,8,5,5,5,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,5,2,2,2,2,1,1] .empty .empty))) (.node [10,8,5,5,5,3,2,2,2,1] (.node [10,8,5,5,5,3,2,1,1,1,1,1] (.node [10,8,5,5,5,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,5,5,5,3,2,2,1,1,1] .empty .empty)) (.node [10,8,5,5,5,3,3,2,1,1] (.node [10,8,5,5,5,3,3,1,1,1,1] .empty .empty) (.node [10,8,5,5,5,4,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_518 : RowTree := (.node [10,8,5,5,4,4,2,2,2,1] degreeTree43_516 degreeTree43_517) + +def degreeTree43_519 : RowTree := (.node [10,8,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,5,5,5,5,1,1,1,1,1] (.node [10,8,5,5,5,4,2,2,1,1] .empty .empty) (.node [10,8,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,6,2,2,2,2,2,2,2,2,2,1] (.node [10,8,6,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,8,6,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,8,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,6,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,6,3,2,2,2,2,2,2,2,1,1] (.node [10,8,6,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,8,6,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,3,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,8,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,3,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,8,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,6,3,3,2,2,2,2,2,2,1] (.node [10,8,6,3,3,2,2,2,2,1,1,1,1,1] (.node [10,8,6,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,3,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,8,6,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,8,6,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,3,3,3,2,2,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_520 : RowTree := (.node [10,8,5,5,5,4,2,1,1,1,1] degreeTree43_518 degreeTree43_519) + +def degreeTree43_521 : RowTree := (.node [10,8,6,4,2,2,2,2,2,1,1,1,1,1] (.node [10,8,6,3,3,3,3,3,2,1,1] (.node [10,8,6,3,3,3,3,2,1,1,1,1,1] (.node [10,8,6,3,3,3,2,2,2,2,2] (.node [10,8,6,3,3,3,2,2,2,2,1,1] .empty .empty) (.node [10,8,6,3,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,3,3,3,3,2,2,2,1] (.node [10,8,6,3,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,8,6,3,3,3,3,3,1,1,1,1] .empty .empty))) (.node [10,8,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,3,3,3,3,3,3,1] (.node [10,8,6,3,3,3,3,3,2,2] .empty .empty) (.node [10,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,6,4,3,2,2,2,2,2,1,1] (.node [10,8,6,4,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,4,2,2,2,2,2,2,2,1] (.node [10,8,6,4,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,4,3,2,2,2,1,1,1,1,1,1] (.node [10,8,6,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,4,3,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,8,6,4,3,3,2,2,1,1,1,1,1] (.node [10,8,6,4,3,3,1,1,1,1,1,1,1,1,1] (.node [10,8,6,4,3,2,2,2,2,2,2] .empty .empty) (.node [10,8,6,4,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,4,3,3,2,2,2,2,1] (.node [10,8,6,4,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,8,6,4,3,3,3,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_522 : RowTree := (.node [10,8,6,4,4,3,3,1,1,1,1,1] (.node [10,8,6,4,4,2,2,2,1,1,1,1,1] (.node [10,8,6,4,3,3,3,3,2,1] (.node [10,8,6,4,3,3,3,2,2,2] (.node [10,8,6,4,3,3,3,2,2,1,1] .empty .empty) (.node [10,8,6,4,3,3,3,3,1,1,1] .empty .empty)) (.node [10,8,6,4,4,2,1,1,1,1,1,1,1,1,1] (.node [10,8,6,4,4,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,4,4,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,6,4,4,3,2,1,1,1,1,1,1] (.node [10,8,6,4,4,2,2,2,2,2,1] (.node [10,8,6,4,4,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,6,4,4,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,4,4,3,2,2,2,1,1] (.node [10,8,6,4,4,3,2,2,1,1,1,1] .empty .empty) (.node [10,8,6,4,4,3,2,2,2,2] .empty .empty)))) (.node [10,8,6,4,4,4,3,1,1,1,1] (.node [10,8,6,4,4,4,1,1,1,1,1,1,1] (.node [10,8,6,4,4,3,3,2,2,1] (.node [10,8,6,4,4,3,3,2,1,1,1] .empty .empty) (.node [10,8,6,4,4,3,3,3,1,1] .empty .empty)) (.node [10,8,6,4,4,4,2,2,1,1,1] (.node [10,8,6,4,4,4,2,1,1,1,1,1] .empty .empty) (.node [10,8,6,4,4,4,2,2,2,1] .empty .empty))) (.node [10,8,6,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,4,4,4,3,2,1,1] .empty .empty) (.node [10,8,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,5,2,2,2,2,1,1,1,1,1,1] (.node [10,8,6,5,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,5,2,2,2,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_523 : RowTree := (.node [10,8,6,4,3,3,3,2,1,1,1,1] degreeTree43_521 degreeTree43_522) + +def degreeTree43_524 : RowTree := (.node [10,8,6,3,3,3,2,2,2,1,1,1,1] degreeTree43_520 degreeTree43_523) + +def degreeTree43_525 : RowTree := (.node [10,8,5,5,4,2,1,1,1,1,1,1,1,1,1] degreeTree43_515 degreeTree43_524) + +def degreeTree43_526 : RowTree := (.node [10,8,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_506 degreeTree43_525) + +def degreeTree43_527 : RowTree := (.node [10,8,6,5,3,3,2,1,1,1,1,1,1] (.node [10,8,6,5,3,2,2,2,1,1,1,1,1] (.node [10,8,6,5,3,2,1,1,1,1,1,1,1,1,1] (.node [10,8,6,5,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [10,8,6,5,3,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,5,3,2,2,2,2,2,1] (.node [10,8,6,5,3,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,6,5,3,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,6,5,3,3,3,1,1,1,1,1] (.node [10,8,6,5,3,3,2,2,2,1,1] (.node [10,8,6,5,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,8,6,5,3,3,2,2,2,2] .empty .empty)) (.node [10,8,6,5,3,3,3,2,2,1] (.node [10,8,6,5,3,3,3,2,1,1,1] .empty .empty) (.node [10,8,6,5,3,3,3,3,1,1] .empty .empty)))) + +def degreeTree43_528 : RowTree := (.node [10,8,6,5,4,3,2,2,1,1,1] (.node [10,8,6,5,4,2,2,2,2,1,1] (.node [10,8,6,5,4,2,2,1,1,1,1,1,1] (.node [10,8,6,5,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,5,4,2,2,2,1,1,1,1] .empty .empty)) (.node [10,8,6,5,4,3,1,1,1,1,1,1,1] (.node [10,8,6,5,4,2,2,2,2,2] .empty .empty) (.node [10,8,6,5,4,3,2,1,1,1,1,1] .empty .empty))) (.node [10,8,6,5,4,4,1,1,1,1,1,1] (.node [10,8,6,5,4,3,3,1,1,1,1] (.node [10,8,6,5,4,3,2,2,2,1] .empty .empty) (.node [10,8,6,5,4,3,3,2,1,1] .empty .empty)) (.node [10,8,6,5,4,4,2,2,1,1] (.node [10,8,6,5,4,4,2,1,1,1,1] .empty .empty) (.node [10,8,6,5,5,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_529 : RowTree := (.node [10,8,6,5,4,1,1,1,1,1,1,1,1,1,1] degreeTree43_527 degreeTree43_528) + +def degreeTree43_530 : RowTree := (.node [10,8,6,6,3,2,1,1,1,1,1,1,1,1] (.node [10,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,6,5,5,3,1,1,1,1,1,1] (.node [10,8,6,5,5,2,2,2,1,1,1] (.node [10,8,6,5,5,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,6,5,5,2,2,2,2,1] .empty .empty)) (.node [10,8,6,5,5,3,2,2,1,1] (.node [10,8,6,5,5,3,2,1,1,1,1] .empty .empty) (.node [10,8,6,5,5,4,1,1,1,1,1] .empty .empty))) (.node [10,8,6,6,2,2,2,2,1,1,1,1,1] (.node [10,8,6,6,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,6,6,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,6,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,6,2,2,2,2,2,2,1] (.node [10,8,6,6,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,6,6,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,6,6,3,3,2,2,2,1] (.node [10,8,6,6,3,2,2,2,2,2] (.node [10,8,6,6,3,2,2,2,1,1,1,1] (.node [10,8,6,6,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,6,3,2,2,2,2,1,1] .empty .empty)) (.node [10,8,6,6,3,3,2,1,1,1,1,1] (.node [10,8,6,6,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,6,6,3,3,2,2,1,1,1] .empty .empty))) (.node [10,8,6,6,4,2,1,1,1,1,1,1,1] (.node [10,8,6,6,3,3,3,2,1,1] (.node [10,8,6,6,3,3,3,1,1,1,1] .empty .empty) (.node [10,8,6,6,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,6,4,2,2,2,1,1,1] (.node [10,8,6,6,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,6,6,4,2,2,2,2,1] .empty .empty))))) + +def degreeTree43_531 : RowTree := (.node [10,8,6,5,5,2,1,1,1,1,1,1,1] degreeTree43_529 degreeTree43_530) + +def degreeTree43_532 : RowTree := (.node [10,8,7,2,2,2,2,2,2,2,1,1,1,1] (.node [10,8,6,6,6,2,1,1,1,1,1] (.node [10,8,6,6,5,2,1,1,1,1,1,1] (.node [10,8,6,6,4,4,1,1,1,1,1] (.node [10,8,6,6,4,3,2,1,1,1,1] .empty .empty) (.node [10,8,6,6,5,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,6,6,5,3,1,1,1,1,1] (.node [10,8,6,6,5,2,2,1,1,1,1] .empty .empty) (.node [10,8,6,6,6,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,7,3,2,2,2,2,2,1,1,1,1,1] (.node [10,8,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,2,2,2,2,2,2,2,2,2] (.node [10,8,7,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,8,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,8,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,7,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,3,2,2,2,2,2,2,2,1] (.node [10,8,7,3,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,3,3,2,2,2,1,1,1,1,1,1] (.node [10,8,7,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,3,3,2,2,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_533 : RowTree := (.node [10,8,7,4,2,2,2,1,1,1,1,1,1,1,1] (.node [10,8,7,3,3,3,3,2,1,1,1,1] (.node [10,8,7,3,3,3,2,2,1,1,1,1,1] (.node [10,8,7,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,8,7,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,8,7,3,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,3,3,3,2,2,2,2,1] (.node [10,8,7,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,8,7,3,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,8,7,3,3,3,3,3,2,1] (.node [10,8,7,3,3,3,3,2,2,2] (.node [10,8,7,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,8,7,3,3,3,3,3,1,1,1] .empty .empty)) (.node [10,8,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,7,4,3,2,2,2,1,1,1,1,1] (.node [10,8,7,4,2,2,2,2,2,2,2] (.node [10,8,7,4,2,2,2,2,2,1,1,1,1] (.node [10,8,7,4,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,4,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,8,7,4,3,2,1,1,1,1,1,1,1,1,1] (.node [10,8,7,4,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,4,3,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,7,4,3,3,2,1,1,1,1,1,1] (.node [10,8,7,4,3,2,2,2,2,2,1] (.node [10,8,7,4,3,2,2,2,2,1,1,1] .empty .empty) (.node [10,8,7,4,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,4,3,3,2,2,2,1,1] (.node [10,8,7,4,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,8,7,4,3,3,2,2,2,2] .empty .empty))))) + +def degreeTree43_534 : RowTree := (.node [10,8,7,3,3,2,2,2,2,2,1,1] degreeTree43_532 degreeTree43_533) + +def degreeTree43_535 : RowTree := (.node [10,8,6,6,4,3,1,1,1,1,1,1] degreeTree43_531 degreeTree43_534) + +def degreeTree43_536 : RowTree := (.node [10,8,7,4,4,2,2,2,2,2] (.node [10,8,7,4,4,2,1,1,1,1,1,1,1,1] (.node [10,8,7,4,3,3,3,3,1,1] (.node [10,8,7,4,3,3,3,2,2,1] (.node [10,8,7,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [10,8,7,4,4,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,4,4,2,2,2,1,1,1,1] (.node [10,8,7,4,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,4,4,2,2,2,2,1,1] .empty .empty))) (.node [10,8,7,4,4,3,2,2,2,1] (.node [10,8,7,4,4,3,2,1,1,1,1,1] (.node [10,8,7,4,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,4,4,3,2,2,1,1,1] .empty .empty)) (.node [10,8,7,4,4,3,3,2,1,1] (.node [10,8,7,4,4,3,3,1,1,1,1] .empty .empty) (.node [10,8,7,4,4,4,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_537 : RowTree := (.node [10,8,7,5,3,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,5,2,2,2,1,1,1,1,1,1,1] (.node [10,8,7,5,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,5,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,5,2,2,2,2,2,1,1,1] (.node [10,8,7,5,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,7,5,2,2,2,2,2,2,1] .empty .empty))) (.node [10,8,7,5,3,2,2,2,2,1,1] (.node [10,8,7,5,3,2,2,1,1,1,1,1,1] (.node [10,8,7,5,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,5,3,2,2,2,1,1,1,1] .empty .empty)) (.node [10,8,7,5,3,3,1,1,1,1,1,1,1] (.node [10,8,7,5,3,2,2,2,2,2] .empty .empty) (.node [10,8,7,5,3,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_538 : RowTree := (.node [10,8,7,4,4,4,2,1,1,1,1] degreeTree43_536 degreeTree43_537) + +def degreeTree43_539 : RowTree := (.node [10,8,7,6,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,5,4,3,1,1,1,1,1,1] (.node [10,8,7,5,4,2,1,1,1,1,1,1,1] (.node [10,8,7,5,3,3,3,1,1,1,1] (.node [10,8,7,5,3,3,2,2,2,1] .empty .empty) (.node [10,8,7,5,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,5,4,2,2,2,1,1,1] (.node [10,8,7,5,4,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,7,5,4,2,2,2,2,1] .empty .empty))) (.node [10,8,7,5,5,2,1,1,1,1,1,1] (.node [10,8,7,5,4,4,1,1,1,1,1] (.node [10,8,7,5,4,3,2,1,1,1,1] .empty .empty) (.node [10,8,7,5,5,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,5,5,3,1,1,1,1,1] (.node [10,8,7,5,5,2,2,1,1,1,1] .empty .empty) (.node [10,8,7,6,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,8,7,6,3,2,2,1,1,1,1,1] (.node [10,8,7,6,2,2,2,2,2,1,1] (.node [10,8,7,6,2,2,2,1,1,1,1,1,1] (.node [10,8,7,6,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,6,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,8,7,6,3,1,1,1,1,1,1,1,1,1] (.node [10,8,7,6,2,2,2,2,2,2] .empty .empty) (.node [10,8,7,6,3,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,8,7,6,3,3,2,1,1,1,1] (.node [10,8,7,6,3,2,2,2,2,1] (.node [10,8,7,6,3,2,2,2,1,1,1] .empty .empty) (.node [10,8,7,6,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,6,4,2,1,1,1,1,1,1] (.node [10,8,7,6,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,6,4,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_540 : RowTree := (.node [10,8,7,5,3,3,2,2,1,1,1] degreeTree43_538 degreeTree43_539) + +def degreeTree43_541 : RowTree := (.node [10,8,7,7,5,1,1,1,1,1,1] (.node [10,8,7,7,2,2,2,2,1,1,1] (.node [10,8,7,7,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,7,6,5,2,1,1,1,1,1] (.node [10,8,7,6,5,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,6,6,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,7,2,2,1,1,1,1,1,1,1] (.node [10,8,7,7,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,7,7,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,8,7,7,3,2,2,1,1,1,1] (.node [10,8,7,7,3,1,1,1,1,1,1,1,1] (.node [10,8,7,7,2,2,2,2,2,1] .empty .empty) (.node [10,8,7,7,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,8,7,7,4,1,1,1,1,1,1,1] (.node [10,8,7,7,3,3,1,1,1,1,1] .empty .empty) (.node [10,8,7,7,4,2,1,1,1,1,1] .empty .empty)))) (.node [10,8,8,2,2,2,2,2,2,2,1,1,1] (.node [10,8,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,8,8,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,8,8,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,8,8,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,3,2,2,2,2,1,1,1,1,1,1] (.node [10,8,8,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,3,2,2,2,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_542 : RowTree := (.node [10,8,8,3,3,3,3,3,1,1] (.node [10,8,8,3,3,3,1,1,1,1,1,1,1,1] (.node [10,8,8,3,3,2,2,1,1,1,1,1,1,1] (.node [10,8,8,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,8,8,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,3,3,2,2,2,2,1,1,1] (.node [10,8,8,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,8,3,3,2,2,2,2,2,1] .empty .empty))) (.node [10,8,8,3,3,3,2,2,2,2] (.node [10,8,8,3,3,3,2,2,1,1,1,1] (.node [10,8,8,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,8,8,3,3,3,3,2,1,1,1] (.node [10,8,8,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,8,8,3,3,3,3,2,2,1] .empty .empty)))) (.node [10,8,8,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,4,2,2,2,1,1,1,1,1,1,1] (.node [10,8,8,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,4,2,2,2,2,2,1,1,1] (.node [10,8,8,4,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,8,4,2,2,2,2,2,2,1] .empty .empty))) (.node [10,8,8,4,3,2,2,2,2,1,1] (.node [10,8,8,4,3,2,2,1,1,1,1,1,1] (.node [10,8,8,4,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,4,3,2,2,2,1,1,1,1] .empty .empty)) (.node [10,8,8,4,3,3,1,1,1,1,1,1,1] (.node [10,8,8,4,3,2,2,2,2,2] .empty .empty) (.node [10,8,8,4,3,3,2,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_543 : RowTree := (.node [10,8,8,3,2,2,2,2,2,2,1,1] degreeTree43_541 degreeTree43_542) + +def degreeTree43_544 : RowTree := (.node [10,8,7,6,4,3,1,1,1,1,1] degreeTree43_540 degreeTree43_543) + +def degreeTree43_545 : RowTree := (.node [10,8,7,4,3,3,3,1,1,1,1,1] degreeTree43_535 degreeTree43_544) + +def degreeTree43_546 : RowTree := (.node [10,8,8,4,4,3,2,1,1,1,1] (.node [10,8,8,4,4,2,2,1,1,1,1,1] (.node [10,8,8,4,4,1,1,1,1,1,1,1,1,1] (.node [10,8,8,4,3,3,3,1,1,1,1] (.node [10,8,8,4,3,3,2,2,2,1] .empty .empty) .empty) (.node [10,8,8,4,4,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,4,4,2,2,2,2,1] (.node [10,8,8,4,4,2,2,2,1,1,1] .empty .empty) (.node [10,8,8,4,4,3,1,1,1,1,1,1] .empty .empty))) (.node [10,8,8,5,2,2,1,1,1,1,1,1,1,1] (.node [10,8,8,5,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,4,4,4,1,1,1,1,1] .empty .empty) (.node [10,8,8,5,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,5,2,2,2,2,1,1,1,1] (.node [10,8,8,5,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,5,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree43_547 : RowTree := (.node [10,8,8,5,4,1,1,1,1,1,1,1,1] (.node [10,8,8,5,3,2,2,2,1,1,1] (.node [10,8,8,5,3,2,1,1,1,1,1,1,1] (.node [10,8,8,5,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,5,3,2,2,1,1,1,1,1] .empty .empty)) (.node [10,8,8,5,3,3,1,1,1,1,1,1] (.node [10,8,8,5,3,2,2,2,2,1] .empty .empty) (.node [10,8,8,5,3,3,2,1,1,1,1] .empty .empty))) (.node [10,8,8,5,5,1,1,1,1,1,1,1] (.node [10,8,8,5,4,2,2,1,1,1,1] (.node [10,8,8,5,4,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,5,4,3,1,1,1,1,1] .empty .empty)) (.node [10,8,8,6,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,5,5,2,1,1,1,1,1] .empty .empty) (.node [10,8,8,6,2,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_548 : RowTree := (.node [10,8,8,5,2,2,2,2,2,2] degreeTree43_546 degreeTree43_547) + +def degreeTree43_549 : RowTree := (.node [10,8,8,7,3,2,1,1,1,1,1] (.node [10,8,8,6,4,1,1,1,1,1,1,1] (.node [10,8,8,6,3,1,1,1,1,1,1,1,1] (.node [10,8,8,6,2,2,2,2,1,1,1] (.node [10,8,8,6,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,8,8,6,2,2,2,2,2,1] .empty .empty)) (.node [10,8,8,6,3,2,2,1,1,1,1] (.node [10,8,8,6,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,6,3,3,1,1,1,1,1] .empty .empty))) (.node [10,8,8,7,2,1,1,1,1,1,1,1,1] (.node [10,8,8,6,5,1,1,1,1,1,1] (.node [10,8,8,6,4,2,1,1,1,1,1] .empty .empty) (.node [10,8,8,7,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,8,8,7,2,2,2,1,1,1,1] (.node [10,8,8,7,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,7,3,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,8,2,2,1,1,1,1,1] (.node [10,8,8,8,1,1,1,1,1,1,1,1,1] (.node [10,8,8,7,4,1,1,1,1,1,1] .empty .empty) (.node [10,8,8,8,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,8,8,8,3,1,1,1,1,1,1] .empty .empty) (.node [10,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,9,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,2,2,2,2,2,2,2,2,2,2,2,1,1] (.node [10,9,2,2,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,9,2,2,2,2,2,2,2,2,2,2,2,2] .empty .empty))))) + +def degreeTree43_550 : RowTree := (.node [10,8,8,6,2,2,1,1,1,1,1,1,1] degreeTree43_548 degreeTree43_549) + +def degreeTree43_551 : RowTree := (.node [10,9,3,3,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,9,3,2,2,2,2,2,2,2,2,2,1,1,1] (.node [10,9,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,9,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,3,2,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,9,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,2,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,9,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,9,3,3,3,2,2,2,2,1,1,1,1,1,1,1] (.node [10,9,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,3,2,2,2,2,2,2,2,2,1,1] (.node [10,9,3,3,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,9,3,3,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,9,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,3,3,2,2,2,2,2,2,1,1,1] (.node [10,9,3,3,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,3,3,3,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,9,3,3,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,9,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,3,3,3,3,2,2,2,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_552 : RowTree := (.node [10,9,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,3,3,3,3,3,3,1,1,1,1,1,1] (.node [10,9,3,3,3,3,3,2,1,1,1,1,1,1,1] (.node [10,9,3,3,3,3,2,2,2,2,2,2] (.node [10,9,3,3,3,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,9,3,3,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,3,3,3,3,3,2,2,2,1,1,1] (.node [10,9,3,3,3,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,3,3,3,3,3,2,2,2,2,1] .empty .empty))) (.node [10,9,3,3,3,3,3,3,3,1,1,1] (.node [10,9,3,3,3,3,3,3,2,2,1,1] (.node [10,9,3,3,3,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,9,3,3,3,3,3,3,2,2,2] .empty .empty)) (.node [10,9,3,3,3,3,3,3,3,3] (.node [10,9,3,3,3,3,3,3,3,2,1] .empty .empty) (.node [10,9,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,9,4,2,2,2,2,2,2,2,2,2,1,1] (.node [10,9,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,2,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,9,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,9,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,9,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,9,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,3,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_553 : RowTree := (.node [10,9,3,3,3,3,2,2,2,2,1,1,1,1] degreeTree43_551 degreeTree43_552) + +def degreeTree43_554 : RowTree := (.node [10,9,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_550 degreeTree43_553) + +def degreeTree43_555 : RowTree := (.node [10,9,4,3,3,2,2,2,2,2,2,1,1] (.node [10,9,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,3,2,2,2,2,2,2,2,2,1] (.node [10,9,4,3,2,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,9,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,3,3,2,2,2,2,1,1,1,1,1,1] (.node [10,9,4,3,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,3,3,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,9,4,3,3,3,2,2,1,1,1,1,1,1,1] (.node [10,9,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,3,3,2,2,2,2,2,2,2] .empty .empty) (.node [10,9,4,3,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,3,3,3,2,2,2,2,1,1,1] (.node [10,9,4,3,3,3,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,4,3,3,3,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree43_556 : RowTree := (.node [10,9,4,3,3,3,3,3,3,1,1] (.node [10,9,4,3,3,3,3,2,2,2,2] (.node [10,9,4,3,3,3,3,2,2,1,1,1,1] (.node [10,9,4,3,3,3,3,2,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,3,3,3,3,2,2,2,1,1] .empty .empty)) (.node [10,9,4,3,3,3,3,3,2,1,1,1] (.node [10,9,4,3,3,3,3,3,1,1,1,1,1] .empty .empty) (.node [10,9,4,3,3,3,3,3,2,2,1] .empty .empty))) (.node [10,9,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,3,3,3,3,3,3,2] .empty .empty) (.node [10,9,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,4,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,9,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,4,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_557 : RowTree := (.node [10,9,4,3,3,3,3,1,1,1,1,1,1,1,1] degreeTree43_555 degreeTree43_556) + +def degreeTree43_558 : RowTree := (.node [10,9,4,4,3,3,3,1,1,1,1,1,1,1] (.node [10,9,4,4,3,2,2,2,2,2,1,1,1] (.node [10,9,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,4,2,2,2,2,2,2,2,2] (.node [10,9,4,4,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,9,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,4,3,2,2,2,1,1,1,1,1,1,1] (.node [10,9,4,4,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,4,3,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,9,4,4,3,3,2,2,1,1,1,1,1,1] (.node [10,9,4,4,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,4,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,9,4,4,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,4,3,3,2,2,2,2,1,1] (.node [10,9,4,4,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,9,4,4,3,3,2,2,2,2,2] .empty .empty)))) (.node [10,9,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,4,3,3,3,3,1,1,1,1] (.node [10,9,4,4,3,3,3,2,2,1,1,1] (.node [10,9,4,4,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,9,4,4,3,3,3,2,2,2,1] .empty .empty)) (.node [10,9,4,4,3,3,3,3,2,2] (.node [10,9,4,4,3,3,3,3,2,1,1] .empty .empty) (.node [10,9,4,4,3,3,3,3,3,1] .empty .empty))) (.node [10,9,4,4,4,2,2,2,2,1,1,1,1] (.node [10,9,4,4,4,2,2,1,1,1,1,1,1,1,1] (.node [10,9,4,4,4,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,4,4,4,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,4,4,2,2,2,2,2,2] (.node [10,9,4,4,4,2,2,2,2,2,1,1] .empty .empty) (.node [10,9,4,4,4,3,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_559 : RowTree := (.node [10,9,4,4,2,2,2,2,2,2,1,1,1,1] degreeTree43_557 degreeTree43_558) + +def degreeTree43_560 : RowTree := (.node [10,9,4,4,4,4,3,2,1,1,1] (.node [10,9,4,4,4,3,3,3,1,1,1] (.node [10,9,4,4,4,3,3,1,1,1,1,1,1] (.node [10,9,4,4,4,3,2,2,2,1,1,1] (.node [10,9,4,4,4,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,4,4,4,3,2,2,2,2,1] .empty .empty)) (.node [10,9,4,4,4,3,3,2,2,1,1] (.node [10,9,4,4,4,3,3,2,1,1,1,1] .empty .empty) (.node [10,9,4,4,4,3,3,2,2,2] .empty .empty))) (.node [10,9,4,4,4,4,2,2,1,1,1,1] (.node [10,9,4,4,4,4,1,1,1,1,1,1,1,1] (.node [10,9,4,4,4,3,3,3,2,1] .empty .empty) (.node [10,9,4,4,4,4,2,1,1,1,1,1,1] .empty .empty)) (.node [10,9,4,4,4,4,2,2,2,2] (.node [10,9,4,4,4,4,2,2,2,1,1] .empty .empty) (.node [10,9,4,4,4,4,3,1,1,1,1,1] .empty .empty)))) (.node [10,9,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,9,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,4,4,4,4,4,1,1,1,1] (.node [10,9,4,4,4,4,3,2,2,1] .empty .empty) (.node [10,9,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,5,2,2,2,2,2,2,2,2,2,1] (.node [10,9,5,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,9,5,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,9,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_561 : RowTree := (.node [10,9,5,3,3,3,2,2,2,1,1,1,1] (.node [10,9,5,3,3,2,2,1,1,1,1,1,1,1,1,1] (.node [10,9,5,3,2,2,2,2,2,2,2,1,1] (.node [10,9,5,3,2,2,2,2,2,1,1,1,1,1,1] (.node [10,9,5,3,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,3,2,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,9,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,3,2,2,2,2,2,2,2,2] .empty .empty) (.node [10,9,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,5,3,3,2,2,2,2,2,2,1] (.node [10,9,5,3,3,2,2,2,2,1,1,1,1,1] (.node [10,9,5,3,3,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,3,3,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,9,5,3,3,3,2,1,1,1,1,1,1,1,1] (.node [10,9,5,3,3,3,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,3,3,3,2,2,1,1,1,1,1,1] .empty .empty)))) (.node [10,9,5,3,3,3,3,3,2,1,1] (.node [10,9,5,3,3,3,3,2,1,1,1,1,1] (.node [10,9,5,3,3,3,2,2,2,2,2] (.node [10,9,5,3,3,3,2,2,2,2,1,1] .empty .empty) (.node [10,9,5,3,3,3,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,3,3,3,3,2,2,2,1] (.node [10,9,5,3,3,3,3,2,2,1,1,1] .empty .empty) (.node [10,9,5,3,3,3,3,3,1,1,1,1] .empty .empty))) (.node [10,9,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,3,3,3,3,3,3,1] (.node [10,9,5,3,3,3,3,3,2,2] .empty .empty) (.node [10,9,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,9,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_562 : RowTree := (.node [10,9,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_560 degreeTree43_561) + +def degreeTree43_563 : RowTree := (.node [10,9,4,4,4,3,2,1,1,1,1,1,1,1] degreeTree43_559 degreeTree43_562) + +def degreeTree43_564 : RowTree := (.node [10,9,4,3,2,2,2,2,2,2,1,1,1,1,1] degreeTree43_554 degreeTree43_563) + +def degreeTree43_565 : RowTree := (.node [10,8,8,4,3,3,2,2,1,1,1] degreeTree43_545 degreeTree43_564) + +def degreeTree43_566 : RowTree := (.node [10,8,6,5,2,2,2,2,2,2,1,1] degreeTree43_526 degreeTree43_565) + +def degreeTree43_567 : RowTree := (.node [10,9,5,4,3,2,2,2,2,2,2] (.node [10,9,5,4,3,2,2,1,1,1,1,1,1,1,1] (.node [10,9,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,4,2,2,2,2,2,2,2,1] (.node [10,9,5,4,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,9,5,4,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,4,3,2,2,2,2,1,1,1,1] (.node [10,9,5,4,3,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,4,3,2,2,2,2,2,1,1] .empty .empty))) (.node [10,9,5,4,3,3,2,2,2,1,1,1] (.node [10,9,5,4,3,3,2,1,1,1,1,1,1,1] (.node [10,9,5,4,3,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,4,3,3,2,2,1,1,1,1,1] .empty .empty)) (.node [10,9,5,4,3,3,3,1,1,1,1,1,1] (.node [10,9,5,4,3,3,2,2,2,2,1] .empty .empty) (.node [10,9,5,4,3,3,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree43_568 : RowTree := (.node [10,9,5,4,4,2,2,2,2,1,1,1] (.node [10,9,5,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,4,3,3,3,3,1,1,1] (.node [10,9,5,4,3,3,3,2,2,2] .empty .empty) (.node [10,9,5,4,3,3,3,3,2,1] .empty .empty)) (.node [10,9,5,4,4,2,2,1,1,1,1,1,1,1] (.node [10,9,5,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,4,4,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,9,5,4,4,3,2,2,1,1,1,1] (.node [10,9,5,4,4,3,1,1,1,1,1,1,1,1] (.node [10,9,5,4,4,2,2,2,2,2,1] .empty .empty) (.node [10,9,5,4,4,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,4,4,3,2,2,2,2] (.node [10,9,5,4,4,3,2,2,2,1,1] .empty .empty) (.node [10,9,5,4,4,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_569 : RowTree := (.node [10,9,5,4,3,3,3,2,2,1,1] degreeTree43_567 degreeTree43_568) + +def degreeTree43_570 : RowTree := (.node [10,9,5,5,3,2,1,1,1,1,1,1,1,1,1] (.node [10,9,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,4,4,4,2,2,1,1,1] (.node [10,9,5,4,4,4,1,1,1,1,1,1,1] (.node [10,9,5,4,4,3,3,2,2,1] .empty .empty) (.node [10,9,5,4,4,4,2,1,1,1,1,1] .empty .empty)) (.node [10,9,5,4,4,4,3,1,1,1,1] (.node [10,9,5,4,4,4,2,2,2,1] .empty .empty) (.node [10,9,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,5,5,2,2,2,2,2,1,1,1,1] (.node [10,9,5,5,2,2,2,1,1,1,1,1,1,1,1] (.node [10,9,5,5,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,5,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,5,2,2,2,2,2,2,2] (.node [10,9,5,5,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,9,5,5,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,9,5,5,3,3,2,2,2,1,1] (.node [10,9,5,5,3,2,2,2,2,2,1] (.node [10,9,5,5,3,2,2,2,1,1,1,1,1] (.node [10,9,5,5,3,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,5,3,2,2,2,2,1,1,1] .empty .empty)) (.node [10,9,5,5,3,3,2,1,1,1,1,1,1] (.node [10,9,5,5,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,5,3,3,2,2,1,1,1,1] .empty .empty))) (.node [10,9,5,5,3,3,3,2,2,1] (.node [10,9,5,5,3,3,3,1,1,1,1,1] (.node [10,9,5,5,3,3,2,2,2,2] .empty .empty) (.node [10,9,5,5,3,3,3,2,1,1,1] .empty .empty)) (.node [10,9,5,5,4,2,1,1,1,1,1,1,1,1] (.node [10,9,5,5,4,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,5,5,4,2,2,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_571 : RowTree := (.node [10,9,5,4,4,3,3,2,1,1,1] degreeTree43_569 degreeTree43_570) + +def degreeTree43_572 : RowTree := (.node [10,9,5,5,5,3,2,1,1,1,1] (.node [10,9,5,5,4,4,1,1,1,1,1,1] (.node [10,9,5,5,4,3,2,1,1,1,1,1] (.node [10,9,5,5,4,2,2,2,2,2] (.node [10,9,5,5,4,2,2,2,2,1,1] .empty .empty) (.node [10,9,5,5,4,3,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,5,4,3,2,2,2,1] (.node [10,9,5,5,4,3,2,2,1,1,1] .empty .empty) (.node [10,9,5,5,4,3,3,1,1,1,1] .empty .empty))) (.node [10,9,5,5,5,2,2,1,1,1,1,1] (.node [10,9,5,5,5,1,1,1,1,1,1,1,1,1] (.node [10,9,5,5,4,4,2,1,1,1,1] .empty .empty) (.node [10,9,5,5,5,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,5,5,5,2,2,2,2,1] (.node [10,9,5,5,5,2,2,2,1,1,1] .empty .empty) (.node [10,9,5,5,5,3,1,1,1,1,1,1] .empty .empty)))) (.node [10,9,6,2,2,2,2,2,2,1,1,1,1,1,1] (.node [10,9,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,5,5,5,4,1,1,1,1,1] .empty .empty) (.node [10,9,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,2,2,2,2,2,2,2,2,1,1] (.node [10,9,6,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,9,6,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,9,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,3,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_573 : RowTree := (.node [10,9,6,3,3,3,3,1,1,1,1,1,1] (.node [10,9,6,3,3,2,2,2,2,1,1,1,1] (.node [10,9,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,3,2,2,2,2,2,2,1,1,1] (.node [10,9,6,3,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,6,3,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,9,6,3,3,2,2,1,1,1,1,1,1,1,1] (.node [10,9,6,3,3,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,3,3,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,9,6,3,3,3,2,1,1,1,1,1,1,1] (.node [10,9,6,3,3,2,2,2,2,2,2] (.node [10,9,6,3,3,2,2,2,2,2,1,1] .empty .empty) (.node [10,9,6,3,3,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,6,3,3,3,2,2,2,1,1,1] (.node [10,9,6,3,3,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,6,3,3,3,2,2,2,2,1] .empty .empty)))) (.node [10,9,6,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,3,3,3,3,3,1,1,1] (.node [10,9,6,3,3,3,3,2,2,1,1] (.node [10,9,6,3,3,3,3,2,1,1,1,1] .empty .empty) (.node [10,9,6,3,3,3,3,2,2,2] .empty .empty)) (.node [10,9,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,3,3,3,3,3,2,1] .empty .empty) (.node [10,9,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,9,6,4,2,2,2,2,2,2,1,1] (.node [10,9,6,4,2,2,2,2,1,1,1,1,1,1] (.node [10,9,6,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,4,2,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,9,6,4,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,4,2,2,2,2,2,2,2] .empty .empty) (.node [10,9,6,4,3,2,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_574 : RowTree := (.node [10,9,6,3,2,2,2,2,1,1,1,1,1,1,1] degreeTree43_572 degreeTree43_573) + +def degreeTree43_575 : RowTree := (.node [10,9,5,5,4,2,2,2,1,1,1,1] degreeTree43_571 degreeTree43_574) + +def degreeTree43_576 : RowTree := (.node [10,9,6,4,3,3,3,1,1,1,1,1] (.node [10,9,6,4,3,3,2,1,1,1,1,1,1] (.node [10,9,6,4,3,2,2,2,2,2,1] (.node [10,9,6,4,3,2,2,2,2,1,1,1] (.node [10,9,6,4,3,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,6,4,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,6,4,3,3,2,2,2,1,1] (.node [10,9,6,4,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,9,6,4,3,3,2,2,2,2] .empty .empty))) (.node [10,9,6,4,4,2,1,1,1,1,1,1,1,1] (.node [10,9,6,4,3,3,3,2,2,1] (.node [10,9,6,4,3,3,3,2,1,1,1] .empty .empty) (.node [10,9,6,4,4,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,6,4,4,2,2,2,1,1,1,1] (.node [10,9,6,4,4,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,4,4,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree43_577 : RowTree := (.node [10,9,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,4,4,3,2,2,2,1] (.node [10,9,6,4,4,3,2,1,1,1,1,1] (.node [10,9,6,4,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,4,4,3,2,2,1,1,1] .empty .empty)) (.node [10,9,6,4,4,4,1,1,1,1,1,1] (.node [10,9,6,4,4,3,3,1,1,1,1] .empty .empty) (.node [10,9,6,4,4,4,2,1,1,1,1] .empty .empty))) (.node [10,9,6,5,2,2,2,2,1,1,1,1,1] (.node [10,9,6,5,2,2,1,1,1,1,1,1,1,1,1] (.node [10,9,6,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,5,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,6,5,2,2,2,2,2,2,1] (.node [10,9,6,5,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,9,6,5,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_578 : RowTree := (.node [10,9,6,4,4,2,2,2,2,2] degreeTree43_576 degreeTree43_577) + +def degreeTree43_579 : RowTree := (.node [10,9,6,5,5,1,1,1,1,1,1,1,1] (.node [10,9,6,5,3,3,3,1,1,1,1] (.node [10,9,6,5,3,2,2,2,2,2] (.node [10,9,6,5,3,2,2,2,1,1,1,1] (.node [10,9,6,5,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,5,3,2,2,2,2,1,1] .empty .empty)) (.node [10,9,6,5,3,3,2,1,1,1,1,1] (.node [10,9,6,5,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,5,3,3,2,2,1,1,1] .empty .empty))) (.node [10,9,6,5,4,2,2,2,1,1,1] (.node [10,9,6,5,4,2,1,1,1,1,1,1,1] (.node [10,9,6,5,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,5,4,2,2,1,1,1,1,1] .empty .empty)) (.node [10,9,6,5,4,3,2,1,1,1,1] (.node [10,9,6,5,4,3,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,5,4,4,1,1,1,1,1] .empty .empty)))) (.node [10,9,6,6,2,2,2,2,1,1,1,1] (.node [10,9,6,6,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,6,5,5,2,2,1,1,1,1] (.node [10,9,6,5,5,2,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,5,5,3,1,1,1,1,1] .empty .empty)) (.node [10,9,6,6,2,2,1,1,1,1,1,1,1,1] (.node [10,9,6,6,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,6,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,9,6,6,3,2,1,1,1,1,1,1,1] (.node [10,9,6,6,2,2,2,2,2,2] (.node [10,9,6,6,2,2,2,2,2,1,1] .empty .empty) (.node [10,9,6,6,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,9,6,6,3,2,2,2,1,1,1] (.node [10,9,6,6,3,2,2,1,1,1,1,1] .empty .empty) (.node [10,9,6,6,3,3,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_580 : RowTree := (.node [10,9,6,5,3,2,1,1,1,1,1,1,1,1] degreeTree43_578 degreeTree43_579) + +def degreeTree43_581 : RowTree := (.node [10,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,9,7,3,3,3,2,2,2,2] (.node [10,9,6,6,4,3,1,1,1,1,1] (.node [10,9,6,6,4,2,1,1,1,1,1,1] (.node [10,9,6,6,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,6,4,2,2,1,1,1,1] .empty .empty)) (.node [10,9,6,6,5,2,1,1,1,1,1] (.node [10,9,6,6,5,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,6,6,6,1,1,1,1,1,1] .empty .empty))) (.node [10,9,8,3,3,2,2,2,2,2] (.node [10,9,7,4,3,2,2,2,2,2] (.node [10,9,7,3,3,3,3,2,2,1] .empty .empty) (.node [10,9,7,5,2,2,2,2,2,2] .empty .empty)) (.node [10,9,9,3,2,2,2,2,2,2] (.node [10,9,8,4,2,2,2,2,2,2] .empty .empty) (.node [10,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,10,2,2,2,2,2,2,2,2,2,2,2,1] (.node [10,10,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,2,2,2,2,2,2,2,2,2,1,1,1,1,1] (.node [10,10,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,2,2,2,2,2,2,2,2,2,2,1,1,1] .empty .empty))) (.node [10,10,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_582 : RowTree := (.node [10,10,3,3,3,2,2,2,1,1,1,1,1,1,1,1] (.node [10,10,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,2,2,2,2,2,2,2,2,2,1,1] (.node [10,10,3,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,10,3,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [10,10,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,3,3,2,2,2,2,2,2,2,2,1] (.node [10,10,3,3,2,2,2,2,2,2,1,1,1,1,1] (.node [10,10,3,3,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,3,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [10,10,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,10,3,3,3,3,2,2,2,1,1,1,1,1] (.node [10,10,3,3,3,2,2,2,2,2,2,2] (.node [10,10,3,3,3,2,2,2,2,2,1,1,1,1] (.node [10,10,3,3,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,3,3,2,2,2,2,2,2,1,1] .empty .empty)) (.node [10,10,3,3,3,3,2,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,3,3,3,3,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,3,3,3,3,3,2,1,1,1,1,1,1] (.node [10,10,3,3,3,3,2,2,2,2,2,1] (.node [10,10,3,3,3,3,2,2,2,2,1,1,1] .empty .empty) (.node [10,10,3,3,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,3,3,3,3,3,2,2,2,1,1] (.node [10,10,3,3,3,3,3,2,2,1,1,1,1] .empty .empty) (.node [10,10,3,3,3,3,3,2,2,2,2] .empty .empty))))) + +def degreeTree43_583 : RowTree := (.node [10,10,3,2,2,2,2,2,2,2,1,1,1,1,1,1] degreeTree43_581 degreeTree43_582) + +def degreeTree43_584 : RowTree := (.node [10,9,6,6,3,3,2,1,1,1,1] degreeTree43_580 degreeTree43_583) + +def degreeTree43_585 : RowTree := (.node [10,9,6,4,3,2,2,1,1,1,1,1,1,1] degreeTree43_575 degreeTree43_584) + +def degreeTree43_586 : RowTree := (.node [10,10,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,3,3,3,3,3,3,3,1,1] (.node [10,10,3,3,3,3,3,3,2,2,1] (.node [10,10,3,3,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [10,10,3,3,3,3,3,3,3,2] .empty .empty)) (.node [10,10,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,4,2,2,2,2,2,2,2,2,1,1,1] (.node [10,10,4,2,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,10,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,2,2,2,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,10,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,2,2,2,2,2,2,2,2,2,1] .empty .empty) (.node [10,10,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_587 : RowTree := (.node [10,10,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,3,2,2,2,2,2,2,1,1,1,1] (.node [10,10,4,3,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,10,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,3,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,3,2,2,2,2,2,2,2,2] (.node [10,10,4,3,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,10,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,4,3,3,2,2,2,2,2,1,1,1] (.node [10,10,4,3,3,2,2,2,1,1,1,1,1,1,1] (.node [10,10,4,3,3,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,3,3,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [10,10,4,3,3,3,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,3,3,2,2,2,2,2,2,1] .empty .empty) (.node [10,10,4,3,3,3,2,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_588 : RowTree := (.node [10,10,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_586 degreeTree43_587) + +def degreeTree43_589 : RowTree := (.node [10,10,4,4,2,2,2,2,2,1,1,1,1,1] (.node [10,10,4,3,3,3,3,3,1,1,1,1] (.node [10,10,4,3,3,3,3,1,1,1,1,1,1,1] (.node [10,10,4,3,3,3,2,2,2,2,1,1] (.node [10,10,4,3,3,3,2,2,2,1,1,1,1] .empty .empty) (.node [10,10,4,3,3,3,2,2,2,2,2] .empty .empty)) (.node [10,10,4,3,3,3,3,2,2,1,1,1] (.node [10,10,4,3,3,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,10,4,3,3,3,3,2,2,2,1] .empty .empty))) (.node [10,10,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,3,3,3,3,3,2,2] (.node [10,10,4,3,3,3,3,3,2,1,1] .empty .empty) (.node [10,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,4,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,10,4,4,3,2,2,2,2,2,1,1] (.node [10,10,4,4,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,2,2,2,2,2,2,2,1] (.node [10,10,4,4,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,10,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,4,3,2,2,2,1,1,1,1,1,1] (.node [10,10,4,4,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,3,2,2,2,2,1,1,1,1] .empty .empty))) (.node [10,10,4,4,3,3,2,2,1,1,1,1,1] (.node [10,10,4,4,3,3,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,3,2,2,2,2,2,2] .empty .empty) (.node [10,10,4,4,3,3,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,4,3,3,2,2,2,2,1] (.node [10,10,4,4,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,10,4,4,3,3,3,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_590 : RowTree := (.node [10,10,4,3,3,3,2,2,1,1,1,1,1,1] degreeTree43_588 degreeTree43_589) + +def degreeTree43_591 : RowTree := (.node [10,10,4,4,4,3,3,2,1,1,1] (.node [10,10,4,4,4,2,2,2,2,1,1,1] (.node [10,10,4,4,4,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,3,3,3,2,2,2] (.node [10,10,4,4,3,3,3,2,2,1,1] .empty .empty) (.node [10,10,4,4,3,3,3,3,1,1,1] .empty .empty)) (.node [10,10,4,4,4,2,2,1,1,1,1,1,1,1] (.node [10,10,4,4,4,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,4,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,10,4,4,4,3,2,2,1,1,1,1] (.node [10,10,4,4,4,3,1,1,1,1,1,1,1,1] (.node [10,10,4,4,4,2,2,2,2,2,1] .empty .empty) (.node [10,10,4,4,4,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,10,4,4,4,3,2,2,2,2] (.node [10,10,4,4,4,3,2,2,2,1,1] .empty .empty) (.node [10,10,4,4,4,3,3,1,1,1,1,1] .empty .empty)))) (.node [10,10,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,4,4,4,4,3,1,1,1,1] (.node [10,10,4,4,4,4,2,1,1,1,1,1] (.node [10,10,4,4,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,4,4,4,4,2,2,1,1,1] .empty .empty)) (.node [10,10,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,5,2,2,2,2,2,2,2,1,1,1,1] (.node [10,10,5,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [10,10,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,2,2,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,10,5,2,2,2,2,2,2,2,2,2] (.node [10,10,5,2,2,2,2,2,2,2,2,1,1] .empty .empty) (.node [10,10,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_592 : RowTree := (.node [10,10,5,3,3,3,2,2,1,1,1,1,1] (.node [10,10,5,3,3,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,3,2,2,2,2,2,1,1,1,1,1] (.node [10,10,5,3,2,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,3,2,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,5,3,2,2,2,2,2,2,2,1] (.node [10,10,5,3,2,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,10,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,5,3,3,2,2,2,2,2,1,1] (.node [10,10,5,3,3,2,2,2,1,1,1,1,1,1] (.node [10,10,5,3,3,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,3,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [10,10,5,3,3,3,1,1,1,1,1,1,1,1,1] (.node [10,10,5,3,3,2,2,2,2,2,2] .empty .empty) (.node [10,10,5,3,3,3,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,10,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,3,3,3,3,2,1,1,1,1] (.node [10,10,5,3,3,3,2,2,2,2,1] (.node [10,10,5,3,3,3,2,2,2,1,1,1] .empty .empty) (.node [10,10,5,3,3,3,3,1,1,1,1,1,1] .empty .empty)) (.node [10,10,5,3,3,3,3,2,2,2] (.node [10,10,5,3,3,3,3,2,2,1,1] .empty .empty) (.node [10,10,5,3,3,3,3,3,1,1,1] .empty .empty))) (.node [10,10,5,4,2,2,2,2,1,1,1,1,1,1] (.node [10,10,5,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,4,2,2,2,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,5,4,2,2,2,2,2,2,1,1] (.node [10,10,5,4,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,10,5,4,2,2,2,2,2,2,2] .empty .empty))))) + +def degreeTree43_593 : RowTree := (.node [10,10,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_591 degreeTree43_592) + +def degreeTree43_594 : RowTree := (.node [10,10,4,4,3,3,3,2,1,1,1,1] degreeTree43_590 degreeTree43_593) + +def degreeTree43_595 : RowTree := (.node [10,10,5,4,3,3,2,2,2,1,1] (.node [10,10,5,4,3,2,2,2,2,2,1] (.node [10,10,5,4,3,2,2,2,1,1,1,1,1] (.node [10,10,5,4,3,2,2,1,1,1,1,1,1,1] (.node [10,10,5,4,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,5,4,3,2,2,2,2,1,1,1] .empty .empty)) (.node [10,10,5,4,3,3,2,1,1,1,1,1,1] (.node [10,10,5,4,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,4,3,3,2,2,1,1,1,1] .empty .empty))) (.node [10,10,5,4,4,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,4,3,3,3,1,1,1,1,1] (.node [10,10,5,4,3,3,2,2,2,2] .empty .empty) (.node [10,10,5,4,3,3,3,2,1,1,1] .empty .empty)) (.node [10,10,5,4,4,2,2,1,1,1,1,1,1] (.node [10,10,5,4,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,4,4,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree43_596 : RowTree := (.node [10,10,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,4,4,3,2,2,1,1,1] (.node [10,10,5,4,4,3,1,1,1,1,1,1,1] (.node [10,10,5,4,4,2,2,2,2,2] .empty .empty) (.node [10,10,5,4,4,3,2,1,1,1,1,1] .empty .empty)) (.node [10,10,5,4,4,4,1,1,1,1,1,1] (.node [10,10,5,4,4,3,3,1,1,1,1] .empty .empty) (.node [10,10,5,4,4,4,2,1,1,1,1] .empty .empty))) (.node [10,10,5,5,2,2,2,2,1,1,1,1,1] (.node [10,10,5,5,2,2,1,1,1,1,1,1,1,1,1] (.node [10,10,5,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,5,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,5,5,2,2,2,2,2,2,1] (.node [10,10,5,5,2,2,2,2,2,1,1,1] .empty .empty) (.node [10,10,5,5,3,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_597 : RowTree := (.node [10,10,5,4,4,2,2,2,2,1,1] degreeTree43_595 degreeTree43_596) + +def degreeTree43_598 : RowTree := (.node [10,10,5,5,5,2,1,1,1,1,1,1] (.node [10,10,5,5,4,1,1,1,1,1,1,1,1,1] (.node [10,10,5,5,3,3,1,1,1,1,1,1,1] (.node [10,10,5,5,3,2,2,2,1,1,1,1] (.node [10,10,5,5,3,2,2,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,5,3,2,2,2,2,1,1] .empty .empty)) (.node [10,10,5,5,3,3,2,2,1,1,1] (.node [10,10,5,5,3,3,2,1,1,1,1,1] .empty .empty) (.node [10,10,5,5,3,3,3,1,1,1,1] .empty .empty))) (.node [10,10,5,5,4,3,1,1,1,1,1,1] (.node [10,10,5,5,4,2,2,1,1,1,1,1] (.node [10,10,5,5,4,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,5,5,4,2,2,2,1,1,1] .empty .empty)) (.node [10,10,5,5,4,4,1,1,1,1,1] (.node [10,10,5,5,4,3,2,1,1,1,1] .empty .empty) (.node [10,10,5,5,5,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,10,6,2,2,2,2,2,1,1,1,1,1,1,1] (.node [10,10,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,5,5,5,3,1,1,1,1,1] (.node [10,10,5,5,5,2,2,1,1,1,1] .empty .empty) (.node [10,10,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,2,2,2,2,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,2,2,2,2,2,2,2,1,1,1] (.node [10,10,6,2,2,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,10,6,2,2,2,2,2,2,2,2,1] .empty .empty)) (.node [10,10,6,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,3,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_599 : RowTree := (.node [10,10,5,5,3,2,1,1,1,1,1,1,1,1] degreeTree43_597 degreeTree43_598) + +def degreeTree43_600 : RowTree := (.node [10,10,6,3,3,3,3,2,1,1,1] (.node [10,10,6,3,3,2,2,2,2,1,1,1] (.node [10,10,6,3,3,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,3,2,2,2,2,2,2,1,1] (.node [10,10,6,3,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [10,10,6,3,2,2,2,2,2,2,2] .empty .empty)) (.node [10,10,6,3,3,2,2,1,1,1,1,1,1,1] (.node [10,10,6,3,3,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,3,3,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,10,6,3,3,3,2,2,1,1,1,1] (.node [10,10,6,3,3,3,1,1,1,1,1,1,1,1] (.node [10,10,6,3,3,2,2,2,2,2,1] .empty .empty) (.node [10,10,6,3,3,3,2,1,1,1,1,1,1] .empty .empty)) (.node [10,10,6,3,3,3,2,2,2,2] (.node [10,10,6,3,3,3,2,2,2,1,1] .empty .empty) (.node [10,10,6,3,3,3,3,1,1,1,1,1] .empty .empty)))) (.node [10,10,6,4,3,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,4,2,2,2,1,1,1,1,1,1,1] (.node [10,10,6,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,6,4,2,2,2,2,2,1,1,1] (.node [10,10,6,4,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,10,6,4,2,2,2,2,2,2,1] .empty .empty))) (.node [10,10,6,4,3,2,2,2,2,1,1] (.node [10,10,6,4,3,2,2,1,1,1,1,1,1] (.node [10,10,6,4,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,4,3,2,2,2,1,1,1,1] .empty .empty)) (.node [10,10,6,4,3,3,2,1,1,1,1,1] (.node [10,10,6,4,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,4,3,3,2,2,1,1,1] .empty .empty))))) + +def degreeTree43_601 : RowTree := (.node [10,10,6,5,3,2,2,1,1,1,1,1] (.node [10,10,6,5,1,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,4,4,2,2,2,1,1,1] (.node [10,10,6,4,4,2,1,1,1,1,1,1,1] (.node [10,10,6,4,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,4,4,2,2,1,1,1,1,1] .empty .empty)) (.node [10,10,6,4,4,3,2,1,1,1,1] (.node [10,10,6,4,4,3,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,4,4,4,1,1,1,1,1] .empty .empty))) (.node [10,10,6,5,2,2,2,2,1,1,1,1] (.node [10,10,6,5,2,2,1,1,1,1,1,1,1,1] (.node [10,10,6,5,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,5,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [10,10,6,5,3,1,1,1,1,1,1,1,1,1] (.node [10,10,6,5,2,2,2,2,2,1,1] .empty .empty) (.node [10,10,6,5,3,2,1,1,1,1,1,1,1] .empty .empty)))) (.node [10,10,6,5,5,1,1,1,1,1,1,1] (.node [10,10,6,5,4,1,1,1,1,1,1,1,1] (.node [10,10,6,5,3,3,1,1,1,1,1,1] (.node [10,10,6,5,3,2,2,2,1,1,1] .empty .empty) (.node [10,10,6,5,3,3,2,1,1,1,1] .empty .empty)) (.node [10,10,6,5,4,2,2,1,1,1,1] (.node [10,10,6,5,4,2,1,1,1,1,1,1] .empty .empty) (.node [10,10,6,5,4,3,1,1,1,1,1] .empty .empty))) (.node [10,10,6,6,2,2,1,1,1,1,1,1,1] (.node [10,10,6,6,1,1,1,1,1,1,1,1,1,1,1] (.node [10,10,6,5,5,2,1,1,1,1,1] .empty .empty) (.node [10,10,6,6,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [10,10,6,6,2,2,2,2,1,1,1] (.node [10,10,6,6,2,2,2,1,1,1,1,1] .empty .empty) (.node [10,10,6,6,3,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_602 : RowTree := (.node [10,10,6,4,3,3,3,1,1,1,1] degreeTree43_600 degreeTree43_601) + +def degreeTree43_603 : RowTree := (.node [10,10,6,3,2,2,2,2,1,1,1,1,1,1] degreeTree43_599 degreeTree43_602) + +def degreeTree43_604 : RowTree := (.node [10,10,5,4,3,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_594 degreeTree43_603) + +def degreeTree43_605 : RowTree := (.node [10,10,3,3,3,3,3,3,1,1,1,1,1] degreeTree43_585 degreeTree43_604) + +def degreeTree43_606 : RowTree := (.node [11,5,5,5,5,5,2,1,1,1,1,1] (.node [10,10,6,6,5,1,1,1,1,1,1] (.node [10,10,6,6,4,1,1,1,1,1,1,1] (.node [10,10,6,6,3,3,1,1,1,1,1] (.node [10,10,6,6,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,6,6,4,2,1,1,1,1,1] .empty .empty)) (.node [11,5,5,5,5,4,2,2,1,1,1,1] (.node [11,5,5,5,5,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,5,5,5,5,5,1,1,1,1,1,1,1] .empty .empty))) (.node [11,6,5,5,5,3,1,1,1,1,1,1,1,1] (.node [11,6,5,5,4,4,1,1,1,1,1,1,1,1] (.node [11,5,5,5,5,5,2,2,1,1,1] .empty .empty) (.node [11,6,5,5,4,4,2,2,1,1,1,1] .empty .empty)) (.node [11,6,5,5,5,4,1,1,1,1,1,1,1] (.node [11,6,5,5,5,3,2,2,1,1,1,1] .empty .empty) (.node [11,6,5,5,5,4,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_607 : RowTree := (.node [11,6,6,5,4,4,2,1,1,1,1,1] (.node [11,6,6,4,4,4,2,2,1,1,1,1] (.node [11,6,5,5,5,5,2,1,1,1,1] (.node [11,6,5,5,5,5,1,1,1,1,1,1] .empty .empty) (.node [11,6,6,4,4,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,6,6,5,4,3,2,2,1,1,1,1] (.node [11,6,6,5,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,6,6,5,4,4,1,1,1,1,1,1,1] .empty .empty))) (.node [11,6,6,5,5,3,1,1,1,1,1,1,1] (.node [11,6,6,5,5,2,1,1,1,1,1,1,1,1] (.node [11,6,6,5,4,4,2,2,1,1,1] .empty .empty) (.node [11,6,6,5,5,2,2,2,1,1,1,1] .empty .empty)) (.node [11,6,6,5,5,3,2,2,1,1,1] (.node [11,6,6,5,5,3,2,1,1,1,1,1] .empty .empty) (.node [11,6,6,5,5,4,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_608 : RowTree := (.node [11,6,5,5,5,4,2,2,1,1,1] degreeTree43_606 degreeTree43_607) + +def degreeTree43_609 : RowTree := (.node [11,6,6,6,5,2,1,1,1,1,1,1,1] (.node [11,6,6,6,4,2,1,1,1,1,1,1,1,1] (.node [11,6,6,6,2,2,2,2,1,1,1,1,1,1] (.node [11,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,6,6,5,5,5,1,1,1,1,1] .empty .empty) (.node [11,6,6,6,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,6,6,6,3,3,1,1,1,1,1,1,1,1] (.node [11,6,6,6,2,2,2,2,2,2,1,1] .empty .empty) (.node [11,6,6,6,3,3,2,2,1,1,1,1] .empty .empty))) (.node [11,6,6,6,4,3,2,2,1,1,1] (.node [11,6,6,6,4,3,1,1,1,1,1,1,1] (.node [11,6,6,6,4,2,2,2,1,1,1,1] .empty .empty) (.node [11,6,6,6,4,3,2,1,1,1,1,1] .empty .empty)) (.node [11,6,6,6,4,4,2,1,1,1,1] (.node [11,6,6,6,4,4,1,1,1,1,1,1] .empty .empty) (.node [11,6,6,6,5,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [11,6,6,6,6,2,2,1,1,1,1] (.node [11,6,6,6,5,3,2,1,1,1,1] (.node [11,6,6,6,5,2,2,2,1,1,1] (.node [11,6,6,6,5,2,2,1,1,1,1,1] .empty .empty) (.node [11,6,6,6,5,3,1,1,1,1,1,1] .empty .empty)) (.node [11,6,6,6,6,1,1,1,1,1,1,1,1] (.node [11,6,6,6,5,4,1,1,1,1,1] .empty .empty) (.node [11,6,6,6,6,2,1,1,1,1,1,1] .empty .empty))) (.node [11,7,5,5,4,3,2,2,1,1,1,1] (.node [11,7,5,4,4,4,2,2,1,1,1,1] (.node [11,7,5,4,4,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,7,5,5,4,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,7,5,5,4,4,2,1,1,1,1,1] (.node [11,7,5,5,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [11,7,5,5,4,4,2,2,1,1,1] .empty .empty))))) + +def degreeTree43_610 : RowTree := (.node [11,6,6,5,5,4,2,1,1,1,1] degreeTree43_608 degreeTree43_609) + +def degreeTree43_611 : RowTree := (.node [11,7,6,5,3,3,1,1,1,1,1,1,1,1] (.node [11,7,6,4,4,3,2,2,1,1,1,1] (.node [11,7,5,5,5,3,2,2,1,1,1] (.node [11,7,5,5,5,3,1,1,1,1,1,1,1] (.node [11,7,5,5,5,2,2,2,1,1,1,1] .empty .empty) (.node [11,7,5,5,5,3,2,1,1,1,1,1] .empty .empty)) (.node [11,7,5,5,5,4,2,1,1,1,1] (.node [11,7,5,5,5,4,1,1,1,1,1,1] .empty .empty) (.node [11,7,6,4,4,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [11,7,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,7,6,4,4,4,2,1,1,1,1,1] (.node [11,7,6,4,4,4,1,1,1,1,1,1,1] .empty .empty) (.node [11,7,6,4,4,4,2,2,1,1,1] .empty .empty)) (.node [11,7,6,5,2,2,2,2,1,1,1,1,1,1] (.node [11,7,6,5,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,7,6,5,2,2,2,2,2,2,1,1] .empty .empty)))) (.node [11,7,6,5,4,4,2,1,1,1,1] (.node [11,7,6,5,4,3,1,1,1,1,1,1,1] (.node [11,7,6,5,4,2,1,1,1,1,1,1,1,1] (.node [11,7,6,5,3,3,2,2,1,1,1,1] .empty .empty) (.node [11,7,6,5,4,2,2,2,1,1,1,1] .empty .empty)) (.node [11,7,6,5,4,3,2,2,1,1,1] (.node [11,7,6,5,4,3,2,1,1,1,1,1] .empty .empty) (.node [11,7,6,5,4,4,1,1,1,1,1,1] .empty .empty))) (.node [11,7,6,5,5,2,2,2,1,1,1] (.node [11,7,6,5,5,2,1,1,1,1,1,1,1] (.node [11,7,6,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,7,6,5,5,2,2,1,1,1,1,1] .empty .empty)) (.node [11,7,6,5,5,3,2,1,1,1,1] (.node [11,7,6,5,5,3,1,1,1,1,1,1] .empty .empty) (.node [11,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_612 : RowTree := (.node [11,7,6,6,5,1,1,1,1,1,1,1,1] (.node [11,7,6,6,3,3,1,1,1,1,1,1,1] (.node [11,7,6,6,2,2,2,2,2,1,1,1] (.node [11,7,6,6,2,2,2,1,1,1,1,1,1,1] (.node [11,7,6,6,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,7,6,6,2,2,2,2,1,1,1,1,1] .empty .empty)) (.node [11,7,6,6,3,2,1,1,1,1,1,1,1,1] (.node [11,7,6,6,2,2,2,2,2,2,1] .empty .empty) (.node [11,7,6,6,3,2,2,2,1,1,1,1] .empty .empty))) (.node [11,7,6,6,4,2,1,1,1,1,1,1,1] (.node [11,7,6,6,3,3,2,2,1,1,1] (.node [11,7,6,6,3,3,2,1,1,1,1,1] .empty .empty) (.node [11,7,6,6,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,7,6,6,4,2,2,2,1,1,1] (.node [11,7,6,6,4,2,2,1,1,1,1,1] .empty .empty) (.node [11,7,6,6,4,3,1,1,1,1,1,1] .empty .empty)))) (.node [11,8,5,4,4,4,2,1,1,1,1,1] (.node [11,8,4,4,4,4,2,2,1,1,1,1] (.node [11,7,6,6,6,1,1,1,1,1,1,1] (.node [11,7,6,6,5,2,1,1,1,1,1,1] .empty .empty) (.node [11,8,4,4,4,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,8,5,4,4,3,2,2,1,1,1,1] (.node [11,8,5,4,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,5,4,4,4,1,1,1,1,1,1,1] .empty .empty))) (.node [11,8,5,5,2,2,2,2,1,1,1,1,1,1] (.node [11,8,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,8,5,4,4,4,2,2,1,1,1] .empty .empty) (.node [11,8,5,5,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,8,5,5,3,3,1,1,1,1,1,1,1,1] (.node [11,8,5,5,2,2,2,2,2,2,1,1] .empty .empty) (.node [11,8,5,5,3,3,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_613 : RowTree := (.node [11,7,6,6,2,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_611 degreeTree43_612) + +def degreeTree43_614 : RowTree := (.node [11,7,5,5,5,2,1,1,1,1,1,1,1,1] degreeTree43_610 degreeTree43_613) + +def degreeTree43_615 : RowTree := (.node [11,8,5,5,5,2,2,2,1,1,1] (.node [11,8,5,5,4,4,1,1,1,1,1,1] (.node [11,8,5,5,4,3,2,1,1,1,1,1] (.node [11,8,5,5,4,3,1,1,1,1,1,1,1] (.node [11,8,5,5,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,8,5,5,4,3,2,2,1,1,1] .empty .empty)) (.node [11,8,5,5,5,2,1,1,1,1,1,1,1] (.node [11,8,5,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,5,5,5,2,2,1,1,1,1,1] .empty .empty))) (.node [11,8,6,4,2,2,2,2,1,1,1,1,1,1] (.node [11,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,8,5,5,5,3,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,8,6,4,3,3,1,1,1,1,1,1,1,1] (.node [11,8,6,4,2,2,2,2,2,2,1,1] .empty .empty) (.node [11,8,6,4,3,3,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree43_616 : RowTree := (.node [11,8,6,5,2,2,1,1,1,1,1,1,1,1,1] (.node [11,8,6,4,4,3,2,2,1,1,1] (.node [11,8,6,4,4,3,1,1,1,1,1,1,1] (.node [11,8,6,4,4,2,2,2,1,1,1,1] .empty .empty) (.node [11,8,6,4,4,3,2,1,1,1,1,1] .empty .empty)) (.node [11,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,8,6,4,4,4,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [11,8,6,5,2,2,2,2,2,2,1] (.node [11,8,6,5,2,2,2,2,1,1,1,1,1] (.node [11,8,6,5,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,5,2,2,2,2,2,1,1,1] .empty .empty)) (.node [11,8,6,5,3,2,2,2,1,1,1,1] (.node [11,8,6,5,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,5,3,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_617 : RowTree := (.node [11,8,6,4,4,2,1,1,1,1,1,1,1,1] degreeTree43_615 degreeTree43_616) + +def degreeTree43_618 : RowTree := (.node [11,8,6,6,3,3,1,1,1,1,1,1] (.node [11,8,6,6,2,1,1,1,1,1,1,1,1,1,1] (.node [11,8,6,5,4,3,1,1,1,1,1,1] (.node [11,8,6,5,4,2,1,1,1,1,1,1,1] (.node [11,8,6,5,4,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,5,4,2,2,1,1,1,1,1] .empty .empty)) (.node [11,8,6,5,5,2,1,1,1,1,1,1] (.node [11,8,6,5,5,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [11,8,6,6,2,2,2,2,2,1,1] (.node [11,8,6,6,2,2,2,1,1,1,1,1,1] (.node [11,8,6,6,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,6,2,2,2,2,1,1,1,1] .empty .empty)) (.node [11,8,6,6,3,2,1,1,1,1,1,1,1] (.node [11,8,6,6,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,6,3,2,2,1,1,1,1,1] .empty .empty)))) (.node [11,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [11,9,4,4,4,3,1,1,1,1,1,1,1,1] (.node [11,8,6,6,4,2,1,1,1,1,1,1] (.node [11,8,6,6,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,8,6,6,5,1,1,1,1,1,1,1] .empty .empty)) (.node [11,9,4,4,4,4,1,1,1,1,1,1,1] (.node [11,9,4,4,4,3,2,2,1,1,1,1] .empty .empty) (.node [11,9,4,4,4,4,2,1,1,1,1,1] .empty .empty))) (.node [11,10,4,4,3,3,1,1,1,1,1,1,1,1] (.node [11,10,4,4,2,2,2,2,1,1,1,1,1,1] (.node [11,10,4,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [11,10,4,4,2,2,2,2,2,2,1,1] .empty .empty)) (.node [11,10,4,4,4,2,1,1,1,1,1,1,1,1] (.node [11,10,4,4,3,3,2,2,1,1,1,1] .empty .empty) (.node [11,10,4,4,4,2,2,2,1,1,1,1] .empty .empty))))) + +def degreeTree43_619 : RowTree := (.node [11,8,6,5,3,3,2,1,1,1,1,1] degreeTree43_617 degreeTree43_618) + +def degreeTree43_620 : RowTree := (.node [12,6,5,5,5,2,1,1,1,1,1,1,1,1] (.node [12,5,5,5,5,4,2,1,1,1,1,1] (.node [12,5,5,5,4,4,2,2,1,1,1,1] (.node [11,10,4,4,4,4,1,1,1,1,1,1] (.node [11,10,4,4,4,3,2,1,1,1,1,1] .empty .empty) (.node [12,5,5,5,4,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,5,5,5,5,3,2,2,1,1,1,1] (.node [12,5,5,5,5,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,5,5,5,5,4,1,1,1,1,1,1,1] .empty .empty))) (.node [12,6,5,5,4,3,1,1,1,1,1,1,1,1] (.node [12,6,5,4,4,4,1,1,1,1,1,1,1,1] (.node [12,5,5,5,5,5,1,1,1,1,1,1] .empty .empty) (.node [12,6,5,4,4,4,2,2,1,1,1,1] .empty .empty)) (.node [12,6,5,5,4,4,1,1,1,1,1,1,1] (.node [12,6,5,5,4,3,2,2,1,1,1,1] .empty .empty) (.node [12,6,5,5,4,4,2,1,1,1,1,1] .empty .empty)))) (.node [12,6,6,4,4,4,2,1,1,1,1,1] (.node [12,6,5,5,5,4,1,1,1,1,1,1] (.node [12,6,5,5,5,3,1,1,1,1,1,1,1] (.node [12,6,5,5,5,2,2,2,1,1,1,1] .empty .empty) (.node [12,6,5,5,5,3,2,1,1,1,1,1] .empty .empty)) (.node [12,6,6,4,4,3,2,2,1,1,1,1] (.node [12,6,6,4,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,4,4,4,1,1,1,1,1,1,1] .empty .empty))) (.node [12,6,6,5,2,2,2,2,2,2,1,1] (.node [12,6,6,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [12,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,5,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [12,6,6,5,3,3,2,2,1,1,1,1] (.node [12,6,6,5,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,5,4,2,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_621 : RowTree := (.node [12,6,6,6,3,3,1,1,1,1,1,1,1] (.node [12,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,6,6,5,5,1,1,1,1,1,1,1,1,1] (.node [12,6,6,5,4,3,2,1,1,1,1,1] (.node [12,6,6,5,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,5,4,4,1,1,1,1,1,1] .empty .empty)) (.node [12,6,6,5,5,2,2,1,1,1,1,1] (.node [12,6,6,5,5,2,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,5,5,3,1,1,1,1,1,1] .empty .empty))) (.node [12,6,6,6,2,2,2,2,1,1,1,1,1] (.node [12,6,6,6,2,2,1,1,1,1,1,1,1,1,1] (.node [12,6,6,6,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,6,6,6,2,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [12,6,6,6,3,2,1,1,1,1,1,1,1,1] (.node [12,6,6,6,2,2,2,2,2,1,1,1] .empty .empty) (.node [12,6,6,6,3,2,2,2,1,1,1,1] .empty .empty)))) (.node [12,7,5,4,4,3,1,1,1,1,1,1,1,1] (.node [12,6,6,6,4,2,2,1,1,1,1,1] (.node [12,6,6,6,4,1,1,1,1,1,1,1,1,1] (.node [12,6,6,6,3,3,2,1,1,1,1,1] .empty .empty) (.node [12,6,6,6,4,2,1,1,1,1,1,1,1] .empty .empty)) (.node [12,7,4,4,4,4,1,1,1,1,1,1,1,1] (.node [12,6,6,6,5,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,7,4,4,4,4,2,2,1,1,1,1] .empty .empty))) (.node [12,7,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,7,5,4,4,4,1,1,1,1,1,1,1] (.node [12,7,5,4,4,3,2,2,1,1,1,1] .empty .empty) (.node [12,7,5,4,4,4,2,1,1,1,1,1] .empty .empty)) (.node [12,7,5,5,2,2,2,2,1,1,1,1,1,1] (.node [12,7,5,5,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,7,5,5,2,2,2,2,2,2,1,1] .empty .empty))))) + +def degreeTree43_622 : RowTree := (.node [12,6,6,5,4,2,2,2,1,1,1,1] degreeTree43_620 degreeTree43_621) + +def degreeTree43_623 : RowTree := (.node [11,10,4,4,4,3,1,1,1,1,1,1,1] degreeTree43_619 degreeTree43_622) + +def degreeTree43_624 : RowTree := (.node [11,8,5,5,4,2,1,1,1,1,1,1,1,1] degreeTree43_614 degreeTree43_623) + +def degreeTree43_625 : RowTree := (.node [12,7,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,7,5,5,4,3,2,1,1,1,1,1] (.node [12,7,5,5,4,2,2,2,1,1,1,1] (.node [12,7,5,5,4,2,1,1,1,1,1,1,1,1] (.node [12,7,5,5,3,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,7,5,5,4,3,1,1,1,1,1,1,1] .empty .empty)) (.node [12,7,5,5,5,2,1,1,1,1,1,1,1] (.node [12,7,5,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,7,5,5,5,2,2,1,1,1,1,1] .empty .empty))) (.node [12,7,6,4,3,3,1,1,1,1,1,1,1,1] (.node [12,7,6,4,2,2,2,2,1,1,1,1,1,1] (.node [12,7,6,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,7,6,4,2,2,2,2,2,2,1,1] .empty .empty)) (.node [12,7,6,4,4,2,1,1,1,1,1,1,1,1] (.node [12,7,6,4,3,3,2,2,1,1,1,1] .empty .empty) (.node [12,7,6,4,4,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree43_626 : RowTree := (.node [12,7,6,5,3,2,1,1,1,1,1,1,1,1] (.node [12,7,6,5,2,2,1,1,1,1,1,1,1,1,1] (.node [12,7,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,7,6,4,4,3,2,1,1,1,1,1] .empty .empty) (.node [12,7,6,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,7,6,5,2,2,2,2,1,1,1,1,1] (.node [12,7,6,5,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [12,7,6,5,2,2,2,2,2,1,1,1] .empty .empty))) (.node [12,7,6,5,4,2,1,1,1,1,1,1,1] (.node [12,7,6,5,3,3,1,1,1,1,1,1,1] (.node [12,7,6,5,3,2,2,2,1,1,1,1] .empty .empty) (.node [12,7,6,5,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,7,6,5,5,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,7,6,6,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_627 : RowTree := (.node [12,7,6,4,4,3,1,1,1,1,1,1,1] degreeTree43_625 degreeTree43_626) + +def degreeTree43_628 : RowTree := (.node [12,8,5,4,4,2,2,2,1,1,1,1] (.node [12,8,4,4,4,4,1,1,1,1,1,1,1] (.node [12,7,6,6,3,2,1,1,1,1,1,1,1] (.node [12,7,6,6,2,2,2,2,1,1,1,1] (.node [12,7,6,6,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [12,7,6,6,3,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,8,4,4,4,3,1,1,1,1,1,1,1,1] (.node [12,7,6,6,4,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,4,4,4,3,2,2,1,1,1,1] .empty .empty))) (.node [12,8,5,4,2,2,2,2,2,2,1,1] (.node [12,8,5,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [12,8,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,5,4,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [12,8,5,4,3,3,2,2,1,1,1,1] (.node [12,8,5,4,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,5,4,4,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [12,8,5,5,3,2,1,1,1,1,1,1,1,1] (.node [12,8,5,5,2,2,1,1,1,1,1,1,1,1,1] (.node [12,8,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,8,5,4,4,3,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,5,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,8,5,5,2,2,2,2,1,1,1,1,1] (.node [12,8,5,5,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,5,5,2,2,2,2,2,1,1,1] .empty .empty))) (.node [12,8,5,5,5,1,1,1,1,1,1,1,1] (.node [12,8,5,5,4,1,1,1,1,1,1,1,1,1] (.node [12,8,5,5,3,3,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,5,5,4,2,1,1,1,1,1,1,1] .empty .empty)) (.node [12,8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] (.node [12,8,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,3,2,2,2,2,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_629 : RowTree := (.node [12,7,6,6,2,2,1,1,1,1,1,1,1,1] degreeTree43_627 degreeTree43_628) + +def degreeTree43_630 : RowTree := (.node [12,8,6,5,2,2,2,1,1,1,1,1,1] (.node [12,8,6,4,2,2,2,2,2,1,1,1] (.node [12,8,6,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [12,8,6,3,3,3,2,2,1,1,1,1] (.node [12,8,6,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,8,6,4,2,2,2,1,1,1,1,1,1,1] (.node [12,8,6,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,4,2,2,2,2,1,1,1,1,1] .empty .empty))) (.node [12,8,6,4,4,2,1,1,1,1,1,1,1] (.node [12,8,6,4,3,3,1,1,1,1,1,1,1] (.node [12,8,6,4,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,4,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,8,6,5,2,1,1,1,1,1,1,1,1,1,1] (.node [12,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,5,2,2,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [12,9,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,8,6,6,1,1,1,1,1,1,1,1,1,1,1] (.node [12,8,6,5,3,2,1,1,1,1,1,1,1] (.node [12,8,6,5,3,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,5,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,8,6,6,2,2,1,1,1,1,1,1,1] (.node [12,8,6,6,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,8,6,6,3,1,1,1,1,1,1,1,1] .empty .empty))) (.node [12,9,4,4,3,3,1,1,1,1,1,1,1,1] (.node [12,9,4,4,2,2,2,2,1,1,1,1,1,1] (.node [12,9,4,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,9,4,4,2,2,2,2,2,2,1,1] .empty .empty)) (.node [12,9,4,4,4,3,1,1,1,1,1,1,1] (.node [12,9,4,4,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,10,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_631 : RowTree := (.node [12,11,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [12,10,4,4,2,2,2,2,1,1,1,1,1] (.node [12,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,10,4,3,2,2,2,2,2,2,1,1] (.node [12,10,4,3,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [12,10,4,3,3,3,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,10,4,4,2,2,1,1,1,1,1,1,1,1,1] (.node [12,10,4,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,10,4,4,2,2,2,1,1,1,1,1,1,1] .empty .empty))) (.node [12,10,4,4,4,2,1,1,1,1,1,1,1] (.node [12,10,4,4,3,3,1,1,1,1,1,1,1] (.node [12,10,4,4,3,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,10,4,4,4,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,11,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,11,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [12,12,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [12,12,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,11,2,2,2,2,2,2,2,2,2,2] (.node [12,11,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty) (.node [12,12,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [12,12,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [12,12,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [12,12,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [13,5,5,4,4,4,1,1,1,1,1,1,1,1] (.node [12,12,2,2,2,2,2,2,2,1,1,1,1,1] (.node [12,12,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [12,12,2,2,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [13,5,5,5,4,4,1,1,1,1,1,1,1] (.node [13,5,5,5,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,5,5,5,5,2,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_632 : RowTree := (.node [12,10,4,3,2,2,1,1,1,1,1,1,1,1,1,1] degreeTree43_630 degreeTree43_631) + +def degreeTree43_633 : RowTree := (.node [12,8,6,3,2,2,2,2,2,2,1,1] degreeTree43_629 degreeTree43_632) + +def degreeTree43_634 : RowTree := (.node [13,6,5,5,4,3,1,1,1,1,1,1,1] (.node [13,6,5,5,2,2,1,1,1,1,1,1,1,1,1,1] (.node [13,6,5,4,4,4,1,1,1,1,1,1,1] (.node [13,6,5,4,4,3,1,1,1,1,1,1,1,1] (.node [13,6,4,4,4,4,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [13,6,5,5,3,3,1,1,1,1,1,1,1,1] (.node [13,6,5,5,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [13,6,5,5,4,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [13,6,6,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [13,6,5,5,5,2,1,1,1,1,1,1,1] (.node [13,6,5,5,5,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [13,6,6,4,3,3,1,1,1,1,1,1,1,1] (.node [13,6,6,4,2,2,2,2,1,1,1,1,1,1] .empty .empty) (.node [13,6,6,4,4,2,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_635 : RowTree := (.node [13,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1] (.node [13,6,6,5,2,2,2,1,1,1,1,1,1,1] (.node [13,6,6,5,2,1,1,1,1,1,1,1,1,1,1,1] (.node [13,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,6,6,5,2,2,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [13,6,6,5,3,2,1,1,1,1,1,1,1,1] (.node [13,6,6,5,2,2,2,2,1,1,1,1,1] .empty .empty) (.node [13,6,6,5,4,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [13,6,6,6,3,1,1,1,1,1,1,1,1,1] (.node [13,6,6,6,2,2,1,1,1,1,1,1,1,1] (.node [13,6,6,6,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,6,6,6,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [13,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [13,7,4,4,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,8,4,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree43_636 : RowTree := (.node [13,6,6,4,4,3,1,1,1,1,1,1,1] degreeTree43_634 degreeTree43_635) + +def degreeTree43_637 : RowTree := (.node [14,6,4,4,4,3,1,1,1,1,1,1,1,1] (.node [14,5,4,4,4,4,1,1,1,1,1,1,1,1] (.node [13,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [13,8,4,4,4,2,1,1,1,1,1,1,1,1] (.node [13,8,4,4,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [13,10,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [13,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [13,10,2,2,2,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [14,5,5,5,2,2,2,2,1,1,1,1,1,1] (.node [14,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,5,5,4,4,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,5,5,5,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [14,5,5,5,4,2,1,1,1,1,1,1,1,1] (.node [14,5,5,5,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,5,5,5,5,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [14,6,5,5,2,2,1,1,1,1,1,1,1,1,1] (.node [14,6,5,4,3,3,1,1,1,1,1,1,1,1] (.node [14,6,5,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [14,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,6,5,4,2,2,2,2,1,1,1,1,1,1] .empty .empty)) (.node [14,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,6,5,4,4,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,6,5,5,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [14,6,6,3,2,2,2,2,1,1,1,1,1,1] (.node [14,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,6,5,5,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [14,6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [14,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,6,6,3,3,3,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,6,6,4,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_638 : RowTree := (.node [13,8,4,4,2,2,2,2,1,1,1,1,1,1] degreeTree43_636 degreeTree43_637) + +def degreeTree43_639 : RowTree := (.node [14,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,6,6,6,1,1,1,1,1,1,1,1,1,1,1] (.node [14,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,6,6,4,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [14,6,6,5,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [14,7,4,4,2,2,1,1,1,1,1,1,1,1,1,1] (.node [14,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,7,4,4,2,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [14,8,4,4,2,1,1,1,1,1,1,1,1,1,1,1] (.node [14,8,4,3,2,2,2,2,1,1,1,1,1,1] (.node [14,8,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [14,9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,8,4,4,2,2,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,9,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [14,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1] (.node [14,10,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,9,2,2,2,2,2,2,2,2,1,1,1,1] (.node [14,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [14,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [14,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [15,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [15,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [14,10,2,2,2,2,2,2,1,1,1,1,1,1,1] .empty .empty) (.node [15,6,4,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [15,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] (.node [15,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [15,8,2,2,2,2,2,2,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_640 : RowTree := (.node [17,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1] (.node [16,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [16,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [16,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [16,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [16,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [16,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [17,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [16,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [17,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)))) (.node [18,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [18,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [18,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [17,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [18,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [18,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [18,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [18,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))) (.node [20,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [19,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [19,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [20,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty)) (.node [21,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] (.node [20,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty) (.node [22,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] .empty .empty))))) + +def degreeTree43_641 : RowTree := (.node [16,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] degreeTree43_639 degreeTree43_640) + +def degreeTree43_642 : RowTree := (.node [14,6,6,4,2,2,1,1,1,1,1,1,1,1,1] degreeTree43_638 degreeTree43_641) + +def degreeTree43_643 : RowTree := (.node [13,5,5,5,5,3,1,1,1,1,1,1,1] degreeTree43_633 degreeTree43_642) + +def degreeTree43_644 : RowTree := (.node [12,7,5,5,3,3,1,1,1,1,1,1,1,1] degreeTree43_624 degreeTree43_643) + +def degreeTree43_645 : RowTree := (.node [10,10,6,6,3,2,1,1,1,1,1,1] degreeTree43_605 degreeTree43_644) + +def degreeTree43_646 : RowTree := (.node [10,9,5,4,2,2,2,2,2,1,1,1,1,1] degreeTree43_566 degreeTree43_645) + +def degreeTree43_647 : RowTree := (.node [10,7,7,5,4,2,1,1,1,1,1,1,1,1] degreeTree43_485 degreeTree43_646) + +def degreeTree43_648 : RowTree := (.node [10,4,4,4,2,2,2,2,2,2,2,2,2,1,1,1] degreeTree43_324 degreeTree43_647) + +def degreeTree43 : RowTree := degreeTree43_648 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData58.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData58.lean index 3191a716b96623b547e304838374194e697fde85..a65f2397acfd8b5f2c7f0560ae7a67b98cc1dbe7 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData58.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData58.lean @@ -1,27 +1,27 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 58. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree58_0 : RowTree := (.node [10,9,9,9,9,4,2,1,1,1,1,1,1] (.node [10,9,9,9,9,2,2,2,2,2,1,1] (.node [10,9,9,9,8,7,1,1,1,1,1,1] (.node [9,9,9,9,9,7,1,1,1,1,1,1] (.node [9,9,9,9,8,8,1,1,1,1,1,1] .empty .empty) (.node [10,9,9,8,8,8,1,1,1,1,1,1] .empty .empty)) (.node [10,9,9,9,9,2,2,2,2,1,1,1,1] (.node [10,9,9,9,9,2,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,9,3,3,1,1,1,1,1,1] (.node [10,9,9,9,9,3,2,2,1,1,1,1,1] (.node [10,9,9,9,9,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,9,9,9,3,2,2,2,1,1,1] .empty .empty)) (.node [10,9,9,9,9,4,1,1,1,1,1,1,1,1] (.node [10,9,9,9,9,3,3,2,1,1,1,1] .empty .empty) .empty))) (.node [11,9,9,8,8,7,1,1,1,1,1,1] (.node [10,9,9,9,9,5,2,1,1,1,1,1] (.node [10,9,9,9,9,4,3,1,1,1,1,1] (.node [10,9,9,9,9,4,2,2,1,1,1,1] .empty .empty) (.node [10,9,9,9,9,5,1,1,1,1,1,1,1] .empty .empty)) (.node [11,9,8,8,8,8,1,1,1,1,1,1] (.node [10,9,9,9,9,6,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,8,2,2,2,2,2,1,1] (.node [11,9,9,9,8,2,2,2,1,1,1,1,1,1] (.node [11,9,9,9,7,7,1,1,1,1,1,1] .empty .empty) (.node [11,9,9,9,8,2,2,2,2,1,1,1,1] .empty .empty)) (.node [11,9,9,9,8,3,2,2,1,1,1,1,1] (.node [11,9,9,9,8,3,2,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree58_1 : RowTree := (.node [11,9,9,9,9,3,2,1,1,1,1,1,1] (.node [11,9,9,9,8,5,1,1,1,1,1,1,1] (.node [11,9,9,9,8,4,2,1,1,1,1,1,1] (.node [11,9,9,9,8,3,3,2,1,1,1,1] (.node [11,9,9,9,8,3,3,1,1,1,1,1,1] .empty .empty) (.node [11,9,9,9,8,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,9,9,9,8,4,3,1,1,1,1,1] (.node [11,9,9,9,8,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,9,2,2,2,1,1,1,1,1] (.node [11,9,9,9,8,6,1,1,1,1,1,1] (.node [11,9,9,9,8,5,2,1,1,1,1,1] .empty .empty) (.node [11,9,9,9,9,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [11,9,9,9,9,3,1,1,1,1,1,1,1,1] (.node [11,9,9,9,9,2,2,2,2,1,1,1] .empty .empty) .empty))) (.node [13,8,7,7,7,7,2,1,1,1,1,1,1,1] (.node [11,9,9,9,9,4,2,1,1,1,1,1] (.node [11,9,9,9,9,3,3,1,1,1,1,1] (.node [11,9,9,9,9,3,2,2,1,1,1,1] .empty .empty) (.node [11,9,9,9,9,4,1,1,1,1,1,1,1] .empty .empty)) (.node [12,9,7,7,7,7,2,1,1,1,1,1,1,1] (.node [11,9,9,9,9,5,1,1,1,1,1,1] .empty .empty) .empty)) (.node [14,7,7,6,6,6,5,1,1,1,1,1,1,1] (.node [13,9,7,7,7,7,1,1,1,1,1,1,1,1] (.node [13,9,7,7,7,6,2,1,1,1,1,1,1,1] .empty .empty) (.node [14,7,6,6,6,6,6,1,1,1,1,1,1,1] .empty .empty)) (.node [14,7,7,7,6,6,4,1,1,1,1,1,1,1] (.node [14,7,7,7,6,5,5,1,1,1,1,1,1,1] .empty .empty) .empty)))) - -def degreeTree58_2 : RowTree := (.node [11,9,9,9,8,3,2,2,2,1,1,1] degreeTree58_0 degreeTree58_1) - -def degreeTree58 : RowTree := degreeTree58_2 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 58. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree58_0 : RowTree := (.node [10,9,9,9,9,4,2,1,1,1,1,1,1] (.node [10,9,9,9,9,2,2,2,2,2,1,1] (.node [10,9,9,9,8,7,1,1,1,1,1,1] (.node [9,9,9,9,9,7,1,1,1,1,1,1] (.node [9,9,9,9,8,8,1,1,1,1,1,1] .empty .empty) (.node [10,9,9,8,8,8,1,1,1,1,1,1] .empty .empty)) (.node [10,9,9,9,9,2,2,2,2,1,1,1,1] (.node [10,9,9,9,9,2,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,9,3,3,1,1,1,1,1,1] (.node [10,9,9,9,9,3,2,2,1,1,1,1,1] (.node [10,9,9,9,9,3,2,1,1,1,1,1,1,1] .empty .empty) (.node [10,9,9,9,9,3,2,2,2,1,1,1] .empty .empty)) (.node [10,9,9,9,9,4,1,1,1,1,1,1,1,1] (.node [10,9,9,9,9,3,3,2,1,1,1,1] .empty .empty) .empty))) (.node [11,9,9,8,8,7,1,1,1,1,1,1] (.node [10,9,9,9,9,5,2,1,1,1,1,1] (.node [10,9,9,9,9,4,3,1,1,1,1,1] (.node [10,9,9,9,9,4,2,2,1,1,1,1] .empty .empty) (.node [10,9,9,9,9,5,1,1,1,1,1,1,1] .empty .empty)) (.node [11,9,8,8,8,8,1,1,1,1,1,1] (.node [10,9,9,9,9,6,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,8,2,2,2,2,2,1,1] (.node [11,9,9,9,8,2,2,2,1,1,1,1,1,1] (.node [11,9,9,9,7,7,1,1,1,1,1,1] .empty .empty) (.node [11,9,9,9,8,2,2,2,2,1,1,1,1] .empty .empty)) (.node [11,9,9,9,8,3,2,2,1,1,1,1,1] (.node [11,9,9,9,8,3,2,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree58_1 : RowTree := (.node [11,9,9,9,9,3,2,1,1,1,1,1,1] (.node [11,9,9,9,8,5,1,1,1,1,1,1,1] (.node [11,9,9,9,8,4,2,1,1,1,1,1,1] (.node [11,9,9,9,8,3,3,2,1,1,1,1] (.node [11,9,9,9,8,3,3,1,1,1,1,1,1] .empty .empty) (.node [11,9,9,9,8,4,1,1,1,1,1,1,1,1] .empty .empty)) (.node [11,9,9,9,8,4,3,1,1,1,1,1] (.node [11,9,9,9,8,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,9,2,2,2,1,1,1,1,1] (.node [11,9,9,9,8,6,1,1,1,1,1,1] (.node [11,9,9,9,8,5,2,1,1,1,1,1] .empty .empty) (.node [11,9,9,9,9,2,2,1,1,1,1,1,1,1] .empty .empty)) (.node [11,9,9,9,9,3,1,1,1,1,1,1,1,1] (.node [11,9,9,9,9,2,2,2,2,1,1,1] .empty .empty) .empty))) (.node [13,8,7,7,7,7,2,1,1,1,1,1,1,1] (.node [11,9,9,9,9,4,2,1,1,1,1,1] (.node [11,9,9,9,9,3,3,1,1,1,1,1] (.node [11,9,9,9,9,3,2,2,1,1,1,1] .empty .empty) (.node [11,9,9,9,9,4,1,1,1,1,1,1,1] .empty .empty)) (.node [12,9,7,7,7,7,2,1,1,1,1,1,1,1] (.node [11,9,9,9,9,5,1,1,1,1,1,1] .empty .empty) .empty)) (.node [14,7,7,6,6,6,5,1,1,1,1,1,1,1] (.node [13,9,7,7,7,7,1,1,1,1,1,1,1,1] (.node [13,9,7,7,7,6,2,1,1,1,1,1,1,1] .empty .empty) (.node [14,7,6,6,6,6,6,1,1,1,1,1,1,1] .empty .empty)) (.node [14,7,7,7,6,6,4,1,1,1,1,1,1,1] (.node [14,7,7,7,6,5,5,1,1,1,1,1,1,1] .empty .empty) .empty)))) + +def degreeTree58_2 : RowTree := (.node [11,9,9,9,8,3,2,2,2,1,1,1] degreeTree58_0 degreeTree58_1) + +def degreeTree58 : RowTree := degreeTree58_2 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData62.lean index 4f52f5a4006fae5f5857f0974e3853c06f6dbe26..8ba4413798186cb5f04fc947a8cdb48701fac980 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData62.lean @@ -1,2067 +1,2067 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 62. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree62_0 : RowTree := (.node [9,9,9,9,8,8,5,1,1,1,1,1] (.node [9,9,9,9,8,8,3,2,1,1,1,1,1] (.node [9,9,9,9,8,8,2,2,2,1,1,1,1] (.node [9,9,9,9,8,8,2,2,1,1,1,1,1,1] (.node [8,8,8,8,8,8,7,7] .empty .empty) .empty) (.node [9,9,9,9,8,8,3,1,1,1,1,1,1,1] (.node [9,9,9,9,8,8,2,2,2,2,1,1] .empty .empty) .empty)) (.node [9,9,9,9,8,8,4,1,1,1,1,1,1] (.node [9,9,9,9,8,8,3,3,1,1,1,1] (.node [9,9,9,9,8,8,3,2,2,1,1,1] .empty .empty) .empty) (.node [9,9,9,9,8,8,4,2,1,1,1,1] .empty .empty))) (.node [9,9,9,9,9,7,3,2,2,1,1,1] (.node [9,9,9,9,9,7,2,2,2,2,1,1] (.node [9,9,9,9,9,7,2,2,2,1,1,1,1] (.node [9,9,9,9,9,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,9,9,9,9,7,3,2,1,1,1,1,1] (.node [9,9,9,9,9,7,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [9,9,9,9,9,7,4,2,1,1,1,1] (.node [9,9,9,9,9,7,4,1,1,1,1,1,1] (.node [9,9,9,9,9,7,3,3,1,1,1,1] .empty .empty) .empty) (.node [9,9,9,9,9,7,5,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_1 : RowTree := (.node [10,9,9,8,8,8,2,2,2,1,1,1,1] (.node [9,9,9,9,9,9,1,1,1,1,1,1,1,1] (.node [9,9,9,9,9,8,3,1,1,1,1,1,1] (.node [9,9,9,9,9,8,2,2,2,1,1,1] (.node [9,9,9,9,9,8,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [9,9,9,9,9,8,4,1,1,1,1,1] (.node [9,9,9,9,9,8,3,2,1,1,1,1] .empty .empty) .empty)) (.node [9,9,9,9,9,9,3,1,1,1,1,1] (.node [9,9,9,9,9,9,2,2,1,1,1,1] (.node [9,9,9,9,9,9,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,8,8,8,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,9,9,8,8,8,4,1,1,1,1,1,1] (.node [10,9,9,8,8,8,3,2,1,1,1,1,1] (.node [10,9,9,8,8,8,3,1,1,1,1,1,1,1] (.node [10,9,9,8,8,8,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,9,9,8,8,8,3,3,1,1,1,1] (.node [10,9,9,8,8,8,3,2,2,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,8,7,2,2,1,1,1,1,1,1] (.node [10,9,9,8,8,8,5,1,1,1,1,1] (.node [10,9,9,8,8,8,4,2,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,8,7,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_2 : RowTree := (.node [9,9,9,9,9,8,2,1,1,1,1,1,1,1] degreeTree62_0 degreeTree62_1) - -def degreeTree62_3 : RowTree := (.node [10,9,9,9,8,8,3,1,1,1,1,1,1] (.node [10,9,9,9,8,7,4,2,1,1,1,1] (.node [10,9,9,9,8,7,3,2,2,1,1,1] (.node [10,9,9,9,8,7,3,2,1,1,1,1,1] (.node [10,9,9,9,8,7,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,8,7,4,1,1,1,1,1,1] (.node [10,9,9,9,8,7,3,3,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,8,8,2,2,1,1,1,1,1] (.node [10,9,9,9,8,8,2,1,1,1,1,1,1,1] (.node [10,9,9,9,8,7,5,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,8,8,2,2,2,1,1,1] .empty .empty))) (.node [10,9,9,9,9,3,2,2,2,2,2,2,1] (.node [10,9,9,9,9,2,2,2,2,2,2,2,1,1] (.node [10,9,9,9,8,8,4,1,1,1,1,1] (.node [10,9,9,9,8,8,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,3,2,2,2,2,2,1,1,1] (.node [10,9,9,9,9,2,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [10,9,9,9,9,3,3,2,2,2,2,2] (.node [10,9,9,9,9,3,3,2,2,2,2,1,1] (.node [10,9,9,9,9,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,3,3,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_4 : RowTree := (.node [10,9,9,9,9,4,3,3,2,1,1,1,1] (.node [10,9,9,9,9,4,2,2,2,2,2,2] (.node [10,9,9,9,9,3,3,3,3,2,1,1] (.node [10,9,9,9,9,3,3,3,3,1,1,1,1] (.node [10,9,9,9,9,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [10,9,9,9,9,4,2,2,2,2,2,1,1] (.node [10,9,9,9,9,4,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,9,4,3,2,2,2,2,1] (.node [10,9,9,9,9,4,3,2,2,2,1,1,1] (.node [10,9,9,9,9,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,4,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,9,9,9,9,4,4,3,1,1,1,1,1] (.node [10,9,9,9,9,4,4,2,1,1,1,1,1,1] (.node [10,9,9,9,9,4,3,3,3,1,1,1] (.node [10,9,9,9,9,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,4,4,2,2,2,1,1] (.node [10,9,9,9,9,4,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,9,5,2,2,2,1,1,1,1,1] (.node [10,9,9,9,9,4,4,4,1,1,1,1] (.node [10,9,9,9,9,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,5,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_5 : RowTree := (.node [10,9,9,9,9,3,3,3,2,2,1,1,1] degreeTree62_3 degreeTree62_4) - -def degreeTree62_6 : RowTree := (.node [10,9,9,9,8,7,2,2,2,2,1,1] degreeTree62_2 degreeTree62_5) - -def degreeTree62_7 : RowTree := (.node [10,9,9,9,9,5,5,2,1,1,1,1] (.node [10,9,9,9,9,5,4,1,1,1,1,1,1,1] (.node [10,9,9,9,9,5,3,2,2,2,1,1] (.node [10,9,9,9,9,5,3,2,2,1,1,1,1] (.node [10,9,9,9,9,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,5,3,3,2,1,1,1] (.node [10,9,9,9,9,5,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,9,5,4,3,1,1,1,1] (.node [10,9,9,9,9,5,4,2,2,1,1,1] (.node [10,9,9,9,9,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,5,5,1,1,1,1,1,1] .empty .empty))) (.node [10,9,9,9,9,6,3,2,2,1,1,1] (.node [10,9,9,9,9,6,2,2,2,2,1,1] (.node [10,9,9,9,9,6,2,2,2,1,1,1,1] (.node [10,9,9,9,9,6,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,6,3,2,1,1,1,1,1] (.node [10,9,9,9,9,6,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,9,6,4,2,1,1,1,1] (.node [10,9,9,9,9,6,4,1,1,1,1,1,1] (.node [10,9,9,9,9,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,6,5,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_8 : RowTree := (.node [10,9,9,9,9,9,2,1,1,1,1,1] (.node [10,9,9,9,9,8,1,1,1,1,1,1,1,1] (.node [10,9,9,9,9,7,3,1,1,1,1,1,1] (.node [10,9,9,9,9,7,2,2,2,1,1,1] (.node [10,9,9,9,9,7,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,7,4,1,1,1,1,1] (.node [10,9,9,9,9,7,3,2,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,9,8,3,1,1,1,1,1] (.node [10,9,9,9,9,8,2,2,1,1,1,1] (.node [10,9,9,9,9,8,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,9,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,8,8,8,8,3,2,2,1,1,1] (.node [10,10,8,8,8,8,2,2,2,2,1,1] (.node [10,10,8,8,8,8,2,2,2,1,1,1,1] (.node [10,10,8,8,8,8,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,8,8,8,8,3,2,1,1,1,1,1] (.node [10,10,8,8,8,8,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,8,8,8,8,4,2,1,1,1,1] (.node [10,10,8,8,8,8,4,1,1,1,1,1,1] (.node [10,10,8,8,8,8,3,3,1,1,1,1] .empty .empty) .empty) (.node [10,10,8,8,8,8,5,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_9 : RowTree := (.node [10,9,9,9,9,7,2,1,1,1,1,1,1,1] degreeTree62_7 degreeTree62_8) - -def degreeTree62_10 : RowTree := (.node [10,10,9,8,8,8,2,2,1,1,1,1,1] (.node [10,10,9,8,8,7,3,3,1,1,1,1] (.node [10,10,9,8,8,7,3,1,1,1,1,1,1,1] (.node [10,10,9,8,8,7,2,2,2,2,1,1] (.node [10,10,9,8,8,7,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,8,8,7,3,2,2,1,1,1] (.node [10,10,9,8,8,7,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,9,8,8,7,5,1,1,1,1,1] (.node [10,10,9,8,8,7,4,2,1,1,1,1] (.node [10,10,9,8,8,7,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,8,8,8,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,9,9,7,7,2,2,2,1,1,1,1] (.node [10,10,9,8,8,8,3,2,1,1,1,1] (.node [10,10,9,8,8,8,3,1,1,1,1,1,1] (.node [10,10,9,8,8,8,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,7,7,2,2,1,1,1,1,1,1] (.node [10,10,9,8,8,8,4,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,9,9,7,7,3,2,1,1,1,1,1] (.node [10,10,9,9,7,7,3,1,1,1,1,1,1,1] (.node [10,10,9,9,7,7,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,9,9,7,7,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_11 : RowTree := (.node [10,10,9,9,8,3,3,3,2,1,1,1,1,1] (.node [10,10,9,9,8,3,2,2,2,2,2,1,1,1] (.node [10,10,9,9,7,7,5,1,1,1,1,1] (.node [10,10,9,9,7,7,4,2,1,1,1,1] (.node [10,10,9,9,7,7,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,2,2,2,2,2,2,2,2] (.node [10,10,9,9,8,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,9,9,8,3,3,2,2,2,2,1,1] (.node [10,10,9,9,8,3,3,2,2,2,1,1,1,1] (.node [10,10,9,9,8,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,9,9,8,3,3,2,2,2,2,2] .empty .empty))) (.node [10,10,9,9,8,4,2,2,2,2,2,1,1] (.node [10,10,9,9,8,3,3,3,3,1,1,1,1] (.node [10,10,9,9,8,3,3,3,2,2,2,1] (.node [10,10,9,9,8,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,4,2,2,2,2,1,1,1,1] (.node [10,10,9,9,8,3,3,3,3,2,1,1] .empty .empty) .empty)) (.node [10,10,9,9,8,4,3,2,2,2,1,1,1] (.node [10,10,9,9,8,4,3,2,2,1,1,1,1,1] (.node [10,10,9,9,8,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [10,10,9,9,8,4,3,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_12 : RowTree := (.node [10,10,9,9,7,7,3,3,1,1,1,1] degreeTree62_10 degreeTree62_11) - -def degreeTree62_13 : RowTree := (.node [10,10,9,8,8,7,2,2,1,1,1,1,1,1] degreeTree62_9 degreeTree62_12) - -def degreeTree62_14 : RowTree := (.node [10,9,9,9,9,5,2,2,2,2,2,1] degreeTree62_6 degreeTree62_13) - -def degreeTree62_15 : RowTree := (.node [10,10,9,9,8,5,2,2,2,2,1,1,1] (.node [10,10,9,9,8,4,4,2,2,2,1,1] (.node [10,10,9,9,8,4,3,3,3,1,1,1] (.node [10,10,9,9,8,4,3,3,2,2,1,1] (.node [10,10,9,9,8,4,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,4,4,2,2,1,1,1,1] (.node [10,10,9,9,8,4,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,9,9,8,4,4,4,1,1,1,1] (.node [10,10,9,9,8,4,4,3,2,1,1,1] (.node [10,10,9,9,8,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,5,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,10,9,9,8,5,3,3,2,1,1,1] (.node [10,10,9,9,8,5,3,2,2,1,1,1,1] (.node [10,10,9,9,8,5,3,2,1,1,1,1,1,1] (.node [10,10,9,9,8,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,9,9,8,5,3,3,1,1,1,1,1] (.node [10,10,9,9,8,5,3,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,9,9,8,5,4,2,2,1,1,1] (.node [10,10,9,9,8,5,4,2,1,1,1,1,1] (.node [10,10,9,9,8,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,5,4,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_16 : RowTree := (.node [10,10,9,9,8,6,5,1,1,1,1,1] (.node [10,10,9,9,8,6,3,2,1,1,1,1,1] (.node [10,10,9,9,8,6,2,2,2,1,1,1,1] (.node [10,10,9,9,8,6,2,2,1,1,1,1,1,1] (.node [10,10,9,9,8,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,6,3,1,1,1,1,1,1,1] (.node [10,10,9,9,8,6,2,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,9,9,8,6,4,1,1,1,1,1,1] (.node [10,10,9,9,8,6,3,3,1,1,1,1] (.node [10,10,9,9,8,6,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,6,4,2,1,1,1,1] .empty .empty))) (.node [10,10,9,9,8,7,4,1,1,1,1,1] (.node [10,10,9,9,8,7,2,2,2,1,1,1] (.node [10,10,9,9,8,7,2,2,1,1,1,1,1] (.node [10,10,9,9,8,7,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,7,3,2,1,1,1,1] (.node [10,10,9,9,8,7,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,9,9,8,8,2,2,1,1,1,1] (.node [10,10,9,9,8,8,2,1,1,1,1,1,1] (.node [10,10,9,9,8,8,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,8,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_17 : RowTree := (.node [10,10,9,9,8,5,5,1,1,1,1,1,1] degreeTree62_15 degreeTree62_16) - -def degreeTree62_18 : RowTree := (.node [10,10,9,9,9,3,3,3,3,1,1,1] (.node [10,10,9,9,9,3,3,2,2,2,1,1,1] (.node [10,10,9,9,9,3,2,2,2,2,2,1,1] (.node [10,10,9,9,9,3,2,2,2,2,1,1,1,1] (.node [10,10,9,9,9,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,9,9,9,3,3,2,2,1,1,1,1,1] (.node [10,10,9,9,9,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [10,10,9,9,9,3,3,3,2,1,1,1,1] (.node [10,10,9,9,9,3,3,3,1,1,1,1,1,1] (.node [10,10,9,9,9,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,9,9,9,3,3,3,2,2,1,1] .empty .empty))) (.node [10,10,9,9,9,4,3,2,2,2,1,1] (.node [10,10,9,9,9,4,2,2,2,2,2,1] (.node [10,10,9,9,9,4,2,2,2,2,1,1,1] (.node [10,10,9,9,9,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,9,4,3,2,2,1,1,1,1] (.node [10,10,9,9,9,4,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,9,9,9,4,4,1,1,1,1,1,1,1] (.node [10,10,9,9,9,4,3,3,2,1,1,1] (.node [10,10,9,9,9,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,9,4,4,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_19 : RowTree := (.node [10,10,9,9,9,5,5,1,1,1,1,1] (.node [10,10,9,9,9,5,3,2,1,1,1,1,1] (.node [10,10,9,9,9,5,2,2,2,1,1,1,1] (.node [10,10,9,9,9,5,2,2,1,1,1,1,1,1] (.node [10,10,9,9,9,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,9,5,3,1,1,1,1,1,1,1] (.node [10,10,9,9,9,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,9,9,9,5,4,1,1,1,1,1,1] (.node [10,10,9,9,9,5,3,3,1,1,1,1] (.node [10,10,9,9,9,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,9,5,4,2,1,1,1,1] .empty .empty))) (.node [10,10,9,9,9,6,4,1,1,1,1,1] (.node [10,10,9,9,9,6,2,2,2,1,1,1] (.node [10,10,9,9,9,6,2,2,1,1,1,1,1] (.node [10,10,9,9,9,6,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,9,6,3,2,1,1,1,1] (.node [10,10,9,9,9,6,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,9,9,9,7,2,2,1,1,1,1] (.node [10,10,9,9,9,7,2,1,1,1,1,1,1] (.node [10,10,9,9,9,7,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,9,7,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_20 : RowTree := (.node [10,10,9,9,9,4,4,2,2,1,1,1] degreeTree62_18 degreeTree62_19) - -def degreeTree62_21 : RowTree := (.node [10,10,9,9,9,2,2,2,2,2,2,1,1,1] degreeTree62_17 degreeTree62_20) - -def degreeTree62_22 : RowTree := (.node [10,10,10,8,7,7,4,2,1,1,1,1] (.node [10,10,10,8,7,7,3,1,1,1,1,1,1,1] (.node [10,10,10,8,7,7,2,2,1,1,1,1,1,1] (.node [10,10,9,9,9,9,1,1,1,1,1,1] (.node [10,10,9,9,9,8,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,7,7,2,2,2,2,1,1] (.node [10,10,10,8,7,7,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,8,7,7,3,3,1,1,1,1] (.node [10,10,10,8,7,7,3,2,2,1,1,1] (.node [10,10,10,8,7,7,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,7,7,4,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,8,8,3,3,2,2,2,1,1,1,1] (.node [10,10,10,8,8,2,2,2,2,2,2,2,2] (.node [10,10,10,8,8,2,2,2,2,2,2,2,1,1] (.node [10,10,10,8,7,7,5,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,3,2,2,2,2,2,2,1] (.node [10,10,10,8,8,3,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,8,8,3,3,3,2,1,1,1,1,1] (.node [10,10,10,8,8,3,3,2,2,2,2,2] (.node [10,10,10,8,8,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,3,3,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_23 : RowTree := (.node [10,10,10,8,8,4,3,3,2,2,1,1] (.node [10,10,10,8,8,4,3,2,2,1,1,1,1,1] (.node [10,10,10,8,8,4,2,2,2,2,1,1,1,1] (.node [10,10,10,8,8,3,3,3,3,2,1,1] (.node [10,10,10,8,8,3,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,4,2,2,2,2,2,2] (.node [10,10,10,8,8,4,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,10,8,8,4,3,3,1,1,1,1,1,1] (.node [10,10,10,8,8,4,3,2,2,2,2,1] (.node [10,10,10,8,8,4,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,4,3,3,2,1,1,1,1] .empty .empty))) (.node [10,10,10,8,8,4,4,3,2,1,1,1] (.node [10,10,10,8,8,4,4,2,2,1,1,1,1] (.node [10,10,10,8,8,4,4,2,1,1,1,1,1,1] (.node [10,10,10,8,8,4,3,3,3,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,4,4,3,1,1,1,1,1] (.node [10,10,10,8,8,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,10,8,8,5,2,2,2,2,1,1,1] (.node [10,10,10,8,8,5,2,2,2,1,1,1,1,1] (.node [10,10,10,8,8,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,5,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_24 : RowTree := (.node [10,10,10,8,8,3,3,3,2,2,2,1] degreeTree62_22 degreeTree62_23) - -def degreeTree62_25 : RowTree := (.node [10,10,10,8,8,6,2,2,1,1,1,1,1,1] (.node [10,10,10,8,8,5,4,2,1,1,1,1,1] (.node [10,10,10,8,8,5,3,3,1,1,1,1,1] (.node [10,10,10,8,8,5,3,2,2,2,1,1] (.node [10,10,10,8,8,5,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,5,4,1,1,1,1,1,1,1] (.node [10,10,10,8,8,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,8,8,5,5,1,1,1,1,1,1] (.node [10,10,10,8,8,5,4,3,1,1,1,1] (.node [10,10,10,8,8,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,5,5,2,1,1,1,1] .empty .empty))) (.node [10,10,10,8,8,6,3,3,1,1,1,1] (.node [10,10,10,8,8,6,3,1,1,1,1,1,1,1] (.node [10,10,10,8,8,6,2,2,2,2,1,1] (.node [10,10,10,8,8,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,6,3,2,2,1,1,1] (.node [10,10,10,8,8,6,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,8,8,6,5,1,1,1,1,1] (.node [10,10,10,8,8,6,4,2,1,1,1,1] (.node [10,10,10,8,8,6,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,7,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_26 : RowTree := (.node [10,10,10,9,7,3,2,2,2,2,2,1,1,1] (.node [10,10,10,8,8,8,2,1,1,1,1,1,1] (.node [10,10,10,8,8,7,3,2,1,1,1,1] (.node [10,10,10,8,8,7,3,1,1,1,1,1,1] (.node [10,10,10,8,8,7,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,8,1,1,1,1,1,1,1,1] (.node [10,10,10,8,8,7,4,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,7,2,2,2,2,2,2,2,1,1] (.node [10,10,10,8,8,8,3,1,1,1,1,1] (.node [10,10,10,8,8,8,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,2,2,2,2,2,2,2,2] .empty .empty))) (.node [10,10,10,9,7,3,3,3,2,1,1,1,1,1] (.node [10,10,10,9,7,3,3,2,2,2,2,1,1] (.node [10,10,10,9,7,3,3,2,2,2,1,1,1,1] (.node [10,10,10,9,7,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,10,9,7,3,3,2,2,2,2,2] .empty .empty)) (.node [10,10,10,9,7,3,3,3,3,1,1,1,1] (.node [10,10,10,9,7,3,3,3,2,2,2,1] (.node [10,10,10,9,7,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,3,3,3,3,2,1,1] .empty .empty)))) - -def degreeTree62_27 : RowTree := (.node [10,10,10,8,8,7,2,2,1,1,1,1,1] degreeTree62_25 degreeTree62_26) - -def degreeTree62_28 : RowTree := (.node [10,10,10,8,8,5,3,2,1,1,1,1,1,1] degreeTree62_24 degreeTree62_27) - -def degreeTree62_29 : RowTree := (.node [10,10,9,9,9,8,1,1,1,1,1,1,1] degreeTree62_21 degreeTree62_28) - -def degreeTree62_30 : RowTree := (.node [10,10,9,9,8,4,3,3,1,1,1,1,1,1] degreeTree62_14 degreeTree62_29) - -def degreeTree62_31 : RowTree := (.node [10,10,10,9,7,4,4,2,2,1,1,1,1] (.node [10,10,10,9,7,4,3,3,1,1,1,1,1,1] (.node [10,10,10,9,7,4,3,2,2,1,1,1,1,1] (.node [10,10,10,9,7,4,2,2,2,2,2,2] (.node [10,10,10,9,7,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,4,3,2,2,2,2,1] (.node [10,10,10,9,7,4,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,7,4,3,3,3,1,1,1] (.node [10,10,10,9,7,4,3,3,2,2,1,1] (.node [10,10,10,9,7,4,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,4,4,2,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,9,7,5,2,2,2,2,1,1,1] (.node [10,10,10,9,7,4,4,3,2,1,1,1] (.node [10,10,10,9,7,4,4,3,1,1,1,1,1] (.node [10,10,10,9,7,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,5,2,2,2,1,1,1,1,1] (.node [10,10,10,9,7,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,7,5,3,2,2,1,1,1,1] (.node [10,10,10,9,7,5,3,2,1,1,1,1,1,1] (.node [10,10,10,9,7,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,10,9,7,5,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_32 : RowTree := (.node [10,10,10,9,7,6,3,1,1,1,1,1,1,1] (.node [10,10,10,9,7,5,5,1,1,1,1,1,1] (.node [10,10,10,9,7,5,4,2,1,1,1,1,1] (.node [10,10,10,9,7,5,4,1,1,1,1,1,1,1] (.node [10,10,10,9,7,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,5,4,3,1,1,1,1] (.node [10,10,10,9,7,5,4,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,7,6,2,2,2,1,1,1,1] (.node [10,10,10,9,7,6,2,2,1,1,1,1,1,1] (.node [10,10,10,9,7,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,6,2,2,2,2,1,1] .empty .empty))) (.node [10,10,10,9,7,6,5,1,1,1,1,1] (.node [10,10,10,9,7,6,3,3,1,1,1,1] (.node [10,10,10,9,7,6,3,2,2,1,1,1] (.node [10,10,10,9,7,6,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,6,4,2,1,1,1,1] (.node [10,10,10,9,7,6,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,7,7,2,2,2,1,1,1] (.node [10,10,10,9,7,7,2,2,1,1,1,1,1] (.node [10,10,10,9,7,7,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,7,3,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_33 : RowTree := (.node [10,10,10,9,7,5,3,3,1,1,1,1,1] degreeTree62_31 degreeTree62_32) - -def degreeTree62_34 : RowTree := (.node [10,10,10,9,8,3,3,3,2,1,1,1,1] (.node [10,10,10,9,8,3,2,2,2,2,2,2] (.node [10,10,10,9,8,2,2,2,2,2,2,2,1] (.node [10,10,10,9,8,2,2,2,2,2,2,1,1,1] (.node [10,10,10,9,7,7,4,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,3,2,2,2,2,2,1,1] (.node [10,10,10,9,8,3,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,8,3,3,2,2,2,2,1] (.node [10,10,10,9,8,3,3,2,2,2,1,1,1] (.node [10,10,10,9,8,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,9,8,4,3,2,1,1,1,1,1,1] (.node [10,10,10,9,8,4,2,2,2,1,1,1,1,1] (.node [10,10,10,9,8,3,3,3,3,1,1,1] (.node [10,10,10,9,8,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,4,2,2,2,2,2,1] (.node [10,10,10,9,8,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,8,4,3,3,1,1,1,1,1] (.node [10,10,10,9,8,4,3,2,2,2,1,1] (.node [10,10,10,9,8,4,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,4,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_35 : RowTree := (.node [10,10,10,9,8,5,4,1,1,1,1,1,1] (.node [10,10,10,9,8,5,2,2,2,2,1,1] (.node [10,10,10,9,8,4,4,3,1,1,1,1] (.node [10,10,10,9,8,4,4,2,2,1,1,1] (.node [10,10,10,9,8,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,5,2,2,2,1,1,1,1] (.node [10,10,10,9,8,5,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,8,5,3,2,2,1,1,1] (.node [10,10,10,9,8,5,3,2,1,1,1,1,1] (.node [10,10,10,9,8,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,5,3,3,1,1,1,1] .empty .empty))) (.node [10,10,10,9,8,6,3,1,1,1,1,1,1] (.node [10,10,10,9,8,6,2,1,1,1,1,1,1,1] (.node [10,10,10,9,8,5,5,1,1,1,1,1] (.node [10,10,10,9,8,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,6,2,2,2,1,1,1] (.node [10,10,10,9,8,6,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,8,7,1,1,1,1,1,1,1,1] (.node [10,10,10,9,8,6,4,1,1,1,1,1] (.node [10,10,10,9,8,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,7,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_36 : RowTree := (.node [10,10,10,9,8,4,4,1,1,1,1,1,1,1] degreeTree62_34 degreeTree62_35) - -def degreeTree62_37 : RowTree := (.node [10,10,10,9,7,7,3,2,1,1,1,1] degreeTree62_33 degreeTree62_36) - -def degreeTree62_38 : RowTree := (.node [10,10,10,9,9,3,3,2,2,1,1,1,1] (.node [10,10,10,9,9,2,2,2,2,2,2,2] (.node [10,10,10,9,8,8,2,1,1,1,1,1] (.node [10,10,10,9,8,8,1,1,1,1,1,1,1] (.node [10,10,10,9,8,7,3,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,9,2,2,2,2,2,2,1,1] (.node [10,10,10,9,9,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,9,3,2,2,2,2,2,1] (.node [10,10,10,9,9,3,2,2,2,2,1,1,1] (.node [10,10,10,9,9,3,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,9,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,9,9,4,2,2,2,2,1,1] (.node [10,10,10,9,9,3,3,3,2,1,1,1] (.node [10,10,10,9,9,3,3,3,1,1,1,1,1] (.node [10,10,10,9,9,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,9,9,4,2,2,2,1,1,1,1] (.node [10,10,10,9,9,4,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,9,4,3,2,2,1,1,1] (.node [10,10,10,9,9,4,3,2,1,1,1,1,1] (.node [10,10,10,9,9,4,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,9,4,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_39 : RowTree := (.node [10,10,10,9,9,6,3,1,1,1,1,1] (.node [10,10,10,9,9,5,3,2,1,1,1,1] (.node [10,10,10,9,9,5,2,2,1,1,1,1,1] (.node [10,10,10,9,9,5,2,1,1,1,1,1,1,1] (.node [10,10,10,9,9,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,9,5,3,1,1,1,1,1,1] (.node [10,10,10,9,9,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,9,6,2,1,1,1,1,1,1] (.node [10,10,10,9,9,6,1,1,1,1,1,1,1,1] (.node [10,10,10,9,9,5,4,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,9,6,2,2,1,1,1,1] .empty .empty))) (.node [10,10,10,10,4,3,3,3,3,3,3] (.node [10,10,10,9,9,8,1,1,1,1,1,1] (.node [10,10,10,9,9,7,2,1,1,1,1,1] (.node [10,10,10,9,9,7,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,4,3,3,3,3,2,2,1,1] (.node [10,10,10,10,4,3,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [10,10,10,10,4,4,3,2,2,2,2,2,1] (.node [10,10,10,10,4,4,3,2,2,2,2,1,1,1] (.node [10,10,10,10,4,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [10,10,10,10,4,4,3,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_40 : RowTree := (.node [10,10,10,9,9,4,4,1,1,1,1,1,1] degreeTree62_38 degreeTree62_39) - -def degreeTree62_41 : RowTree := (.node [10,10,10,10,4,4,4,4,1,1,1,1,1,1] (.node [10,10,10,10,4,4,4,3,2,1,1,1,1,1] (.node [10,10,10,10,4,4,4,2,2,2,1,1,1,1] (.node [10,10,10,10,4,4,3,3,3,2,2,1] (.node [10,10,10,10,4,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,4,4,4,2,2,2,2,2] (.node [10,10,10,10,4,4,4,2,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,10,10,4,4,4,3,3,1,1,1,1] (.node [10,10,10,10,4,4,4,3,2,2,2,1] (.node [10,10,10,10,4,4,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,4,4,4,3,3,2,1,1] .empty .empty))) (.node [10,10,10,10,5,3,3,2,2,2,2,1,1,1] (.node [10,10,10,10,4,4,4,4,3,1,1,1] (.node [10,10,10,10,4,4,4,4,2,2,1,1] (.node [10,10,10,10,4,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,3,2,2,2,2,2,2,2] (.node [10,10,10,10,5,2,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [10,10,10,10,5,3,3,3,3,1,1,1,1,1] (.node [10,10,10,10,5,3,3,3,2,2,2,1,1] (.node [10,10,10,10,5,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,10,10,5,3,3,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_42 : RowTree := (.node [10,10,10,10,5,4,4,2,2,1,1,1,1,1] (.node [10,10,10,10,5,4,3,3,2,1,1,1,1,1] (.node [10,10,10,10,5,4,3,2,2,2,1,1,1,1] (.node [10,10,10,10,5,4,2,2,2,2,2,2,1] (.node [10,10,10,10,5,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,4,3,2,2,2,2,2] (.node [10,10,10,10,5,4,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,10,10,5,4,3,3,3,1,1,1,1] (.node [10,10,10,10,5,4,3,3,2,2,2,1] (.node [10,10,10,10,5,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,4,3,3,3,2,1,1] .empty .empty))) (.node [10,10,10,10,5,4,4,3,3,1,1,1] (.node [10,10,10,10,5,4,4,3,1,1,1,1,1,1] (.node [10,10,10,10,5,4,4,2,2,2,2,1] (.node [10,10,10,10,5,4,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,4,4,3,2,2,1,1] (.node [10,10,10,10,5,4,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,5,5,2,2,2,2,1,1,1,1] (.node [10,10,10,10,5,4,4,4,2,1,1,1] (.node [10,10,10,10,5,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,5,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_43 : RowTree := (.node [10,10,10,10,5,3,3,3,3,2,2,1] degreeTree62_41 degreeTree62_42) - -def degreeTree62_44 : RowTree := (.node [10,10,10,10,4,4,3,3,3,1,1,1,1,1] degreeTree62_40 degreeTree62_43) - -def degreeTree62_45 : RowTree := (.node [10,10,10,9,8,7,2,2,1,1,1,1] degreeTree62_37 degreeTree62_44) - -def degreeTree62_46 : RowTree := (.node [10,10,10,10,5,5,4,3,1,1,1,1,1] (.node [10,10,10,10,5,5,3,3,2,2,1,1] (.node [10,10,10,10,5,5,3,2,2,2,2,1] (.node [10,10,10,10,5,5,3,2,2,2,1,1,1] (.node [10,10,10,10,5,5,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,5,3,3,2,1,1,1,1] (.node [10,10,10,10,5,5,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,5,5,4,2,2,1,1,1,1] (.node [10,10,10,10,5,5,4,2,1,1,1,1,1,1] (.node [10,10,10,10,5,5,3,3,3,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,5,4,2,2,2,1,1] .empty .empty))) (.node [10,10,10,10,5,5,5,3,1,1,1,1] (.node [10,10,10,10,5,5,5,1,1,1,1,1,1,1] (.node [10,10,10,10,5,5,4,4,1,1,1,1] (.node [10,10,10,10,5,5,4,3,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,5,5,2,2,1,1,1] (.node [10,10,10,10,5,5,5,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,6,3,2,2,2,2,2,1,1,1] (.node [10,10,10,10,6,2,2,2,2,2,2,2,2] (.node [10,10,10,10,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,3,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_47 : RowTree := (.node [10,10,10,10,6,4,3,2,2,1,1,1,1,1] (.node [10,10,10,10,6,3,3,3,3,1,1,1,1] (.node [10,10,10,10,6,3,3,3,2,1,1,1,1,1] (.node [10,10,10,10,6,3,3,2,2,2,2,2] (.node [10,10,10,10,6,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,3,3,3,2,2,2,1] (.node [10,10,10,10,6,3,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,6,4,2,2,2,2,2,1,1] (.node [10,10,10,10,6,4,2,2,2,2,1,1,1,1] (.node [10,10,10,10,6,3,3,3,3,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,4,2,2,2,2,2,2] .empty .empty))) (.node [10,10,10,10,6,4,3,3,3,1,1,1] (.node [10,10,10,10,6,4,3,3,1,1,1,1,1,1] (.node [10,10,10,10,6,4,3,2,2,2,2,1] (.node [10,10,10,10,6,4,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,4,3,3,2,2,1,1] (.node [10,10,10,10,6,4,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,6,4,4,2,2,2,1,1] (.node [10,10,10,10,6,4,4,2,2,1,1,1,1] (.node [10,10,10,10,6,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,4,4,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_48 : RowTree := (.node [10,10,10,10,6,3,3,2,2,2,1,1,1,1] degreeTree62_46 degreeTree62_47) - -def degreeTree62_49 : RowTree := (.node [10,10,10,10,6,5,4,2,1,1,1,1,1] (.node [10,10,10,10,6,5,3,2,2,1,1,1,1] (.node [10,10,10,10,6,5,2,2,2,2,1,1,1] (.node [10,10,10,10,6,5,2,2,2,1,1,1,1,1] (.node [10,10,10,10,6,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,5,3,2,1,1,1,1,1,1] (.node [10,10,10,10,6,5,2,2,2,2,2,1] .empty .empty) .empty)) (.node [10,10,10,10,6,5,3,3,2,1,1,1] (.node [10,10,10,10,6,5,3,3,1,1,1,1,1] (.node [10,10,10,10,6,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,5,4,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,10,6,6,2,2,2,1,1,1,1] (.node [10,10,10,10,6,5,5,1,1,1,1,1,1] (.node [10,10,10,10,6,5,4,3,1,1,1,1] (.node [10,10,10,10,6,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,6,2,2,1,1,1,1,1,1] (.node [10,10,10,10,6,5,5,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,6,6,3,2,1,1,1,1,1] (.node [10,10,10,10,6,6,3,1,1,1,1,1,1,1] (.node [10,10,10,10,6,6,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,6,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_50 : RowTree := (.node [10,10,10,10,7,3,3,2,2,2,2,1] (.node [10,10,10,10,7,3,2,2,2,2,1,1,1,1] (.node [10,10,10,10,6,6,5,1,1,1,1,1] (.node [10,10,10,10,6,6,4,2,1,1,1,1] (.node [10,10,10,10,6,6,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,2,2,2,2,2,2,2,1] (.node [10,10,10,10,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,7,3,3,2,2,1,1,1,1,1] (.node [10,10,10,10,7,3,2,2,2,2,2,2] (.node [10,10,10,10,7,3,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,3,3,2,2,2,1,1,1] .empty .empty))) (.node [10,10,10,10,7,4,2,2,2,2,1,1,1] (.node [10,10,10,10,7,3,3,3,2,2,1,1] (.node [10,10,10,10,7,3,3,3,2,1,1,1,1] (.node [10,10,10,10,7,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,4,2,2,2,1,1,1,1,1] (.node [10,10,10,10,7,3,3,3,3,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,7,4,3,2,2,1,1,1,1] (.node [10,10,10,10,7,4,3,2,1,1,1,1,1,1] (.node [10,10,10,10,7,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,10,10,7,4,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_51 : RowTree := (.node [10,10,10,10,6,6,3,3,1,1,1,1] degreeTree62_49 degreeTree62_50) - -def degreeTree62_52 : RowTree := (.node [10,10,10,10,6,4,4,3,2,1,1,1] degreeTree62_48 degreeTree62_51) - -def degreeTree62_53 : RowTree := (.node [10,10,10,10,7,5,3,2,2,1,1,1] (.node [10,10,10,10,7,5,2,2,1,1,1,1,1,1] (.node [10,10,10,10,7,4,4,2,1,1,1,1,1] (.node [10,10,10,10,7,4,4,1,1,1,1,1,1,1] (.node [10,10,10,10,7,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,4,4,3,1,1,1,1] (.node [10,10,10,10,7,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,7,5,3,1,1,1,1,1,1,1] (.node [10,10,10,10,7,5,2,2,2,2,1,1] (.node [10,10,10,10,7,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,5,3,2,1,1,1,1,1] .empty .empty))) (.node [10,10,10,10,7,6,2,2,1,1,1,1,1] (.node [10,10,10,10,7,5,4,2,1,1,1,1] (.node [10,10,10,10,7,5,4,1,1,1,1,1,1] (.node [10,10,10,10,7,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,6,2,1,1,1,1,1,1,1] (.node [10,10,10,10,7,5,5,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,7,6,3,2,1,1,1,1] (.node [10,10,10,10,7,6,3,1,1,1,1,1,1] (.node [10,10,10,10,7,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,6,4,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_54 : RowTree := (.node [10,10,10,10,8,3,3,2,2,1,1,1,1] (.node [10,10,10,10,8,2,2,2,2,2,2,2] (.node [10,10,10,10,7,7,3,1,1,1,1,1] (.node [10,10,10,10,7,7,2,2,1,1,1,1] (.node [10,10,10,10,7,7,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,8,2,2,2,2,2,2,1,1] (.node [10,10,10,10,8,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,8,3,2,2,2,2,2,1] (.node [10,10,10,10,8,3,2,2,2,2,1,1,1] (.node [10,10,10,10,8,3,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,8,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,10,8,4,2,2,2,2,1,1] (.node [10,10,10,10,8,3,3,3,2,1,1,1] (.node [10,10,10,10,8,3,3,3,1,1,1,1,1] (.node [10,10,10,10,8,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,8,4,2,2,2,1,1,1,1] (.node [10,10,10,10,8,4,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,8,4,3,2,2,1,1,1] (.node [10,10,10,10,8,4,3,2,1,1,1,1,1] (.node [10,10,10,10,8,4,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,8,4,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_55 : RowTree := (.node [10,10,10,10,7,7,1,1,1,1,1,1,1,1] degreeTree62_53 degreeTree62_54) - -def degreeTree62_56 : RowTree := (.node [10,10,10,10,8,6,3,1,1,1,1,1] (.node [10,10,10,10,8,5,3,2,1,1,1,1] (.node [10,10,10,10,8,5,2,2,1,1,1,1,1] (.node [10,10,10,10,8,5,2,1,1,1,1,1,1,1] (.node [10,10,10,10,8,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,8,5,3,1,1,1,1,1,1] (.node [10,10,10,10,8,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,8,6,2,1,1,1,1,1,1] (.node [10,10,10,10,8,6,1,1,1,1,1,1,1,1] (.node [10,10,10,10,8,5,4,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,8,6,2,2,1,1,1,1] .empty .empty))) (.node [10,10,10,10,9,2,2,2,2,2,2,1] (.node [10,10,10,10,8,8,1,1,1,1,1,1] (.node [10,10,10,10,8,7,2,1,1,1,1,1] (.node [10,10,10,10,8,7,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,9,2,2,2,2,2,1,1,1] (.node [10,10,10,10,9,2,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,9,3,2,2,2,2,1,1] (.node [10,10,10,10,9,3,2,2,2,1,1,1,1] (.node [10,10,10,10,9,3,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,9,3,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_57 : RowTree := (.node [10,10,10,10,9,5,2,2,1,1,1,1] (.node [10,10,10,10,9,4,3,1,1,1,1,1,1] (.node [10,10,10,10,9,4,2,1,1,1,1,1,1,1] (.node [10,10,10,10,9,3,3,3,1,1,1,1] (.node [10,10,10,10,9,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,9,4,2,2,2,1,1,1] (.node [10,10,10,10,9,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,9,5,1,1,1,1,1,1,1,1] (.node [10,10,10,10,9,4,4,1,1,1,1,1] (.node [10,10,10,10,9,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,9,5,2,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,10,10,2,2,2,1,1,1,1,1,1] (.node [10,10,10,10,9,6,2,1,1,1,1,1] (.node [10,10,10,10,9,6,1,1,1,1,1,1,1] (.node [10,10,10,10,9,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,9,7,1,1,1,1,1,1] .empty .empty)) (.node [10,10,10,10,10,3,2,1,1,1,1,1,1,1] (.node [10,10,10,10,10,2,2,2,2,2,1,1] (.node [10,10,10,10,10,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,10,3,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_58 : RowTree := (.node [10,10,10,10,9,3,3,2,1,1,1,1,1] degreeTree62_56 degreeTree62_57) - -def degreeTree62_59 : RowTree := (.node [10,10,10,10,8,4,4,1,1,1,1,1,1] degreeTree62_55 degreeTree62_58) - -def degreeTree62_60 : RowTree := (.node [10,10,10,10,7,4,3,3,1,1,1,1,1] degreeTree62_52 degreeTree62_59) - -def degreeTree62_61 : RowTree := (.node [10,10,10,10,5,5,2,2,2,2,2,2] degreeTree62_45 degreeTree62_60) - -def degreeTree62_62 : RowTree := (.node [10,10,10,9,7,4,2,2,2,2,1,1,1,1] degreeTree62_30 degreeTree62_61) - -def degreeTree62_63 : RowTree := (.node [11,9,8,8,8,8,2,2,2,1,1,1,1] (.node [10,10,10,10,10,4,3,1,1,1,1,1] (.node [10,10,10,10,10,4,1,1,1,1,1,1,1,1] (.node [10,10,10,10,10,3,3,2,1,1,1,1] (.node [10,10,10,10,10,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,10,4,2,2,1,1,1,1] (.node [10,10,10,10,10,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,10,6,1,1,1,1,1,1] (.node [10,10,10,10,10,5,2,1,1,1,1,1] (.node [10,10,10,10,10,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,8,8,8,8,2,2,1,1,1,1,1,1] .empty .empty))) (.node [11,9,8,8,8,8,4,1,1,1,1,1,1] (.node [11,9,8,8,8,8,3,2,1,1,1,1,1] (.node [11,9,8,8,8,8,3,1,1,1,1,1,1,1] (.node [11,9,8,8,8,8,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,9,8,8,8,8,3,3,1,1,1,1] (.node [11,9,8,8,8,8,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,9,9,8,8,7,2,2,1,1,1,1,1,1] (.node [11,9,8,8,8,8,5,1,1,1,1,1] (.node [11,9,8,8,8,8,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,8,8,7,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_64 : RowTree := (.node [11,9,9,8,8,8,3,1,1,1,1,1,1] (.node [11,9,9,8,8,7,4,2,1,1,1,1] (.node [11,9,9,8,8,7,3,2,2,1,1,1] (.node [11,9,9,8,8,7,3,2,1,1,1,1,1] (.node [11,9,9,8,8,7,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,8,8,7,4,1,1,1,1,1,1] (.node [11,9,9,8,8,7,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,8,8,8,2,2,1,1,1,1,1] (.node [11,9,9,8,8,8,2,1,1,1,1,1,1,1] (.node [11,9,9,8,8,7,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,8,8,8,2,2,2,1,1,1] .empty .empty))) (.node [11,9,9,9,7,7,3,1,1,1,1,1,1,1] (.node [11,9,9,9,7,7,2,2,1,1,1,1,1,1] (.node [11,9,9,8,8,8,4,1,1,1,1,1] (.node [11,9,9,8,8,8,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,7,7,2,2,2,2,1,1] (.node [11,9,9,9,7,7,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,7,7,3,3,1,1,1,1] (.node [11,9,9,9,7,7,3,2,2,1,1,1] (.node [11,9,9,9,7,7,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,7,7,4,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_65 : RowTree := (.node [11,9,9,8,8,7,2,2,2,2,1,1] degreeTree62_63 degreeTree62_64) - -def degreeTree62_66 : RowTree := (.node [11,9,9,9,8,3,3,3,2,2,2,1] (.node [11,9,9,9,8,3,3,2,2,2,1,1,1,1] (.node [11,9,9,9,8,2,2,2,2,2,2,2,2] (.node [11,9,9,9,8,2,2,2,2,2,2,2,1,1] (.node [11,9,9,9,7,7,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,3,2,2,2,2,2,2,1] (.node [11,9,9,9,8,3,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,8,3,3,3,2,1,1,1,1,1] (.node [11,9,9,9,8,3,3,2,2,2,2,2] (.node [11,9,9,9,8,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,3,3,3,2,2,1,1,1] .empty .empty))) (.node [11,9,9,9,8,4,3,2,2,1,1,1,1,1] (.node [11,9,9,9,8,4,2,2,2,2,1,1,1,1] (.node [11,9,9,9,8,3,3,3,3,2,1,1] (.node [11,9,9,9,8,3,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,4,2,2,2,2,2,2] (.node [11,9,9,9,8,4,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,9,9,9,8,4,3,3,1,1,1,1,1,1] (.node [11,9,9,9,8,4,3,2,2,2,2,1] (.node [11,9,9,9,8,4,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,4,3,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_67 : RowTree := (.node [11,9,9,9,8,5,3,2,1,1,1,1,1,1] (.node [11,9,9,9,8,4,4,3,2,1,1,1] (.node [11,9,9,9,8,4,4,2,2,1,1,1,1] (.node [11,9,9,9,8,4,4,2,1,1,1,1,1,1] (.node [11,9,9,9,8,4,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,4,4,3,1,1,1,1,1] (.node [11,9,9,9,8,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [11,9,9,9,8,5,2,2,2,2,1,1,1] (.node [11,9,9,9,8,5,2,2,2,1,1,1,1,1] (.node [11,9,9,9,8,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,5,2,2,2,2,2,1] .empty .empty))) (.node [11,9,9,9,8,5,4,2,1,1,1,1,1] (.node [11,9,9,9,8,5,3,3,1,1,1,1,1] (.node [11,9,9,9,8,5,3,2,2,2,1,1] (.node [11,9,9,9,8,5,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,5,4,1,1,1,1,1,1,1] (.node [11,9,9,9,8,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,8,5,5,1,1,1,1,1,1] (.node [11,9,9,9,8,5,4,3,1,1,1,1] (.node [11,9,9,9,8,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,5,5,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_68 : RowTree := (.node [11,9,9,9,8,4,3,3,2,2,1,1] degreeTree62_66 degreeTree62_67) - -def degreeTree62_69 : RowTree := (.node [11,9,9,9,7,7,4,2,1,1,1,1] degreeTree62_65 degreeTree62_68) - -def degreeTree62_70 : RowTree := (.node [11,9,9,9,8,7,2,2,1,1,1,1,1] (.node [11,9,9,9,8,6,3,3,1,1,1,1] (.node [11,9,9,9,8,6,3,1,1,1,1,1,1,1] (.node [11,9,9,9,8,6,2,2,2,2,1,1] (.node [11,9,9,9,8,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,6,3,2,2,1,1,1] (.node [11,9,9,9,8,6,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,8,6,5,1,1,1,1,1] (.node [11,9,9,9,8,6,4,2,1,1,1,1] (.node [11,9,9,9,8,6,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,7,2,1,1,1,1,1,1,1] .empty .empty))) (.node [11,9,9,9,8,8,2,1,1,1,1,1,1] (.node [11,9,9,9,8,7,3,2,1,1,1,1] (.node [11,9,9,9,8,7,3,1,1,1,1,1,1] (.node [11,9,9,9,8,7,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,8,1,1,1,1,1,1,1,1] (.node [11,9,9,9,8,7,4,1,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,9,2,2,2,2,2,2,1,1,1] (.node [11,9,9,9,8,8,3,1,1,1,1,1] (.node [11,9,9,9,8,8,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,2,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_71 : RowTree := (.node [11,9,9,9,9,4,2,2,2,2,1,1,1] (.node [11,9,9,9,9,3,3,3,1,1,1,1,1,1] (.node [11,9,9,9,9,3,3,2,2,1,1,1,1,1] (.node [11,9,9,9,9,3,2,2,2,2,2,2] (.node [11,9,9,9,9,3,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,3,3,2,2,2,2,1] (.node [11,9,9,9,9,3,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,9,3,3,3,3,1,1,1] (.node [11,9,9,9,9,3,3,3,2,2,1,1] (.node [11,9,9,9,9,3,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,4,2,2,2,1,1,1,1,1] .empty .empty))) (.node [11,9,9,9,9,4,3,3,2,1,1,1] (.node [11,9,9,9,9,4,3,2,2,1,1,1,1] (.node [11,9,9,9,9,4,3,2,1,1,1,1,1,1] (.node [11,9,9,9,9,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,9,9,9,9,4,3,3,1,1,1,1,1] (.node [11,9,9,9,9,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [11,9,9,9,9,4,4,2,2,1,1,1] (.node [11,9,9,9,9,4,4,2,1,1,1,1,1] (.node [11,9,9,9,9,4,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,4,4,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_72 : RowTree := (.node [11,9,9,9,9,3,2,2,2,2,1,1,1,1] degreeTree62_70 degreeTree62_71) - -def degreeTree62_73 : RowTree := (.node [11,9,9,9,9,6,2,2,1,1,1,1,1] (.node [11,9,9,9,9,5,3,3,1,1,1,1] (.node [11,9,9,9,9,5,3,1,1,1,1,1,1,1] (.node [11,9,9,9,9,5,2,2,2,2,1,1] (.node [11,9,9,9,9,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,5,3,2,2,1,1,1] (.node [11,9,9,9,9,5,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,9,5,5,1,1,1,1,1] (.node [11,9,9,9,9,5,4,2,1,1,1,1] (.node [11,9,9,9,9,5,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,6,2,1,1,1,1,1,1,1] .empty .empty))) (.node [11,9,9,9,9,7,2,1,1,1,1,1,1] (.node [11,9,9,9,9,6,3,2,1,1,1,1] (.node [11,9,9,9,9,6,3,1,1,1,1,1,1] (.node [11,9,9,9,9,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,7,1,1,1,1,1,1,1,1] (.node [11,9,9,9,9,6,4,1,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,9,8,1,1,1,1,1,1,1] (.node [11,9,9,9,9,7,3,1,1,1,1,1] (.node [11,9,9,9,9,7,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,8,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_74 : RowTree := (.node [11,10,8,8,8,8,2,1,1,1,1,1,1,1] (.node [11,10,8,8,8,7,3,2,2,1,1,1] (.node [11,10,8,8,8,7,2,2,2,2,1,1] (.node [11,10,8,8,8,7,2,2,2,1,1,1,1] (.node [11,10,8,8,8,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,8,8,8,7,3,2,1,1,1,1,1] (.node [11,10,8,8,8,7,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,8,8,8,7,4,2,1,1,1,1] (.node [11,10,8,8,8,7,4,1,1,1,1,1,1] (.node [11,10,8,8,8,7,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,8,8,8,7,5,1,1,1,1,1] .empty .empty))) (.node [11,10,9,8,7,7,2,2,1,1,1,1,1,1] (.node [11,10,8,8,8,8,3,1,1,1,1,1,1] (.node [11,10,8,8,8,8,2,2,2,1,1,1] (.node [11,10,8,8,8,8,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,8,8,8,8,4,1,1,1,1,1] (.node [11,10,8,8,8,8,3,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,7,7,3,1,1,1,1,1,1,1] (.node [11,10,9,8,7,7,2,2,2,2,1,1] (.node [11,10,9,8,7,7,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,7,7,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_75 : RowTree := (.node [11,9,9,9,9,9,1,1,1,1,1,1] degreeTree62_73 degreeTree62_74) - -def degreeTree62_76 : RowTree := (.node [11,9,9,9,9,5,2,2,1,1,1,1,1,1] degreeTree62_72 degreeTree62_75) - -def degreeTree62_77 : RowTree := (.node [11,9,9,9,8,6,2,2,1,1,1,1,1,1] degreeTree62_69 degreeTree62_76) - -def degreeTree62_78 : RowTree := (.node [11,10,9,8,8,3,3,2,2,2,2,2] (.node [11,10,9,8,8,2,2,2,2,2,2,2,2] (.node [11,10,9,8,7,7,4,2,1,1,1,1] (.node [11,10,9,8,7,7,4,1,1,1,1,1,1] (.node [11,10,9,8,7,7,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,2,2,2,2,2,2,2,1,1] (.node [11,10,9,8,7,7,5,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,8,3,3,2,2,2,1,1,1,1] (.node [11,10,9,8,8,3,2,2,2,2,2,2,1] (.node [11,10,9,8,8,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,3,3,2,2,2,2,1,1] .empty .empty))) (.node [11,10,9,8,8,4,2,2,2,2,1,1,1,1] (.node [11,10,9,8,8,3,3,3,2,2,2,1] (.node [11,10,9,8,8,3,3,3,2,2,1,1,1] (.node [11,10,9,8,8,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,3,3,3,3,2,1,1] (.node [11,10,9,8,8,3,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,8,4,3,2,2,1,1,1,1,1] (.node [11,10,9,8,8,4,2,2,2,2,2,2] (.node [11,10,9,8,8,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,4,3,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_79 : RowTree := (.node [11,10,9,8,8,5,2,2,2,1,1,1,1,1] (.node [11,10,9,8,8,4,4,2,2,1,1,1,1] (.node [11,10,9,8,8,4,3,3,2,2,1,1] (.node [11,10,9,8,8,4,3,3,2,1,1,1,1] (.node [11,10,9,8,8,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,4,4,2,1,1,1,1,1,1] (.node [11,10,9,8,8,4,3,3,3,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,8,4,4,3,2,1,1,1] (.node [11,10,9,8,8,4,4,3,1,1,1,1,1] (.node [11,10,9,8,8,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,4,4,4,1,1,1,1] .empty .empty))) (.node [11,10,9,8,8,5,3,3,1,1,1,1,1] (.node [11,10,9,8,8,5,3,2,1,1,1,1,1,1] (.node [11,10,9,8,8,5,2,2,2,2,2,1] (.node [11,10,9,8,8,5,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,5,3,2,2,2,1,1] (.node [11,10,9,8,8,5,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,8,5,4,2,1,1,1,1,1] (.node [11,10,9,8,8,5,4,1,1,1,1,1,1,1] (.node [11,10,9,8,8,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,5,4,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_80 : RowTree := (.node [11,10,9,8,8,4,3,2,2,2,2,1] degreeTree62_78 degreeTree62_79) - -def degreeTree62_81 : RowTree := (.node [11,10,9,8,8,6,4,2,1,1,1,1] (.node [11,10,9,8,8,6,3,1,1,1,1,1,1,1] (.node [11,10,9,8,8,6,2,2,1,1,1,1,1,1] (.node [11,10,9,8,8,5,5,2,1,1,1,1] (.node [11,10,9,8,8,5,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,6,2,2,2,2,1,1] (.node [11,10,9,8,8,6,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,8,6,3,3,1,1,1,1] (.node [11,10,9,8,8,6,3,2,2,1,1,1] (.node [11,10,9,8,8,6,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,6,4,1,1,1,1,1,1] .empty .empty))) (.node [11,10,9,8,8,7,3,2,1,1,1,1] (.node [11,10,9,8,8,7,2,2,1,1,1,1,1] (.node [11,10,9,8,8,7,2,1,1,1,1,1,1,1] (.node [11,10,9,8,8,6,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,7,3,1,1,1,1,1,1] (.node [11,10,9,8,8,7,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,8,8,2,1,1,1,1,1,1] (.node [11,10,9,8,8,8,1,1,1,1,1,1,1,1] (.node [11,10,9,8,8,7,4,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,8,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_82 : RowTree := (.node [11,10,9,9,7,3,3,3,3,1,1,1,1] (.node [11,10,9,9,7,3,3,2,2,2,2,1,1] (.node [11,10,9,9,7,3,2,2,2,2,2,1,1,1] (.node [11,10,9,9,7,2,2,2,2,2,2,2,2] (.node [11,10,9,9,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,3,3,2,2,2,1,1,1,1] (.node [11,10,9,9,7,3,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,10,9,9,7,3,3,3,2,2,1,1,1] (.node [11,10,9,9,7,3,3,3,2,1,1,1,1,1] (.node [11,10,9,9,7,3,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,9,9,7,3,3,3,2,2,2,1] .empty .empty))) (.node [11,10,9,9,7,4,3,2,2,2,1,1,1] (.node [11,10,9,9,7,4,2,2,2,2,2,1,1] (.node [11,10,9,9,7,4,2,2,2,2,1,1,1,1] (.node [11,10,9,9,7,3,3,3,3,2,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,4,3,2,2,1,1,1,1,1] (.node [11,10,9,9,7,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,10,9,9,7,4,3,3,2,1,1,1,1] (.node [11,10,9,9,7,4,3,3,1,1,1,1,1,1] (.node [11,10,9,9,7,4,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,9,9,7,4,3,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_83 : RowTree := (.node [11,10,9,8,8,8,3,1,1,1,1,1] degreeTree62_81 degreeTree62_82) - -def degreeTree62_84 : RowTree := (.node [11,10,9,8,8,5,4,3,1,1,1,1] degreeTree62_80 degreeTree62_83) - -def degreeTree62_85 : RowTree := (.node [11,10,9,9,7,5,3,2,2,1,1,1,1] (.node [11,10,9,9,7,4,4,4,1,1,1,1] (.node [11,10,9,9,7,4,4,2,2,2,1,1] (.node [11,10,9,9,7,4,4,2,2,1,1,1,1] (.node [11,10,9,9,7,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,4,4,3,2,1,1,1] (.node [11,10,9,9,7,4,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,7,5,2,2,2,2,2,1] (.node [11,10,9,9,7,5,2,2,2,2,1,1,1] (.node [11,10,9,9,7,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,5,3,2,1,1,1,1,1,1] .empty .empty))) (.node [11,10,9,9,7,5,4,2,2,1,1,1] (.node [11,10,9,9,7,5,3,3,2,1,1,1] (.node [11,10,9,9,7,5,3,3,1,1,1,1,1] (.node [11,10,9,9,7,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,5,4,2,1,1,1,1,1] (.node [11,10,9,9,7,5,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,7,5,5,2,1,1,1,1] (.node [11,10,9,9,7,5,5,1,1,1,1,1,1] (.node [11,10,9,9,7,5,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,6,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_86 : RowTree := (.node [11,10,9,9,7,7,2,2,2,1,1,1] (.node [11,10,9,9,7,6,4,1,1,1,1,1,1] (.node [11,10,9,9,7,6,3,2,1,1,1,1,1] (.node [11,10,9,9,7,6,3,1,1,1,1,1,1,1] (.node [11,10,9,9,7,6,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,6,3,3,1,1,1,1] (.node [11,10,9,9,7,6,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,7,7,2,1,1,1,1,1,1,1] (.node [11,10,9,9,7,6,5,1,1,1,1,1] (.node [11,10,9,9,7,6,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,7,2,2,1,1,1,1,1] .empty .empty))) (.node [11,10,9,9,8,3,2,2,2,2,1,1,1,1] (.node [11,10,9,9,7,7,4,1,1,1,1,1] (.node [11,10,9,9,7,7,3,2,1,1,1,1] (.node [11,10,9,9,7,7,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,2,2,2,2,2,2,2,1] (.node [11,10,9,9,8,2,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,8,3,3,2,2,1,1,1,1,1] (.node [11,10,9,9,8,3,2,2,2,2,2,2] (.node [11,10,9,9,8,3,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,3,3,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_87 : RowTree := (.node [11,10,9,9,7,6,2,2,2,1,1,1,1] degreeTree62_85 degreeTree62_86) - -def degreeTree62_88 : RowTree := (.node [11,10,9,9,8,4,3,3,1,1,1,1,1] (.node [11,10,9,9,8,4,2,2,2,2,1,1,1] (.node [11,10,9,9,8,3,3,3,2,2,1,1] (.node [11,10,9,9,8,3,3,3,2,1,1,1,1] (.node [11,10,9,9,8,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,4,2,2,2,1,1,1,1,1] (.node [11,10,9,9,8,3,3,3,3,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,8,4,3,2,2,1,1,1,1] (.node [11,10,9,9,8,4,3,2,1,1,1,1,1,1] (.node [11,10,9,9,8,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,9,9,8,4,3,2,2,2,1,1] .empty .empty))) (.node [11,10,9,9,8,5,2,2,1,1,1,1,1,1] (.node [11,10,9,9,8,4,4,2,1,1,1,1,1] (.node [11,10,9,9,8,4,4,1,1,1,1,1,1,1] (.node [11,10,9,9,8,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,4,4,3,1,1,1,1] (.node [11,10,9,9,8,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,8,5,3,1,1,1,1,1,1,1] (.node [11,10,9,9,8,5,2,2,2,2,1,1] (.node [11,10,9,9,8,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,5,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_89 : RowTree := (.node [11,10,9,9,8,7,1,1,1,1,1,1,1,1] (.node [11,10,9,9,8,6,2,2,1,1,1,1,1] (.node [11,10,9,9,8,5,4,2,1,1,1,1] (.node [11,10,9,9,8,5,4,1,1,1,1,1,1] (.node [11,10,9,9,8,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,6,2,1,1,1,1,1,1,1] (.node [11,10,9,9,8,5,5,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,8,6,3,2,1,1,1,1] (.node [11,10,9,9,8,6,3,1,1,1,1,1,1] (.node [11,10,9,9,8,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,6,4,1,1,1,1,1] .empty .empty))) (.node [11,10,9,9,8,8,2,1,1,1,1,1] (.node [11,10,9,9,8,7,3,1,1,1,1,1] (.node [11,10,9,9,8,7,2,2,1,1,1,1] (.node [11,10,9,9,8,7,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,8,1,1,1,1,1,1,1] .empty .empty)) (.node [11,10,9,9,9,2,2,2,2,2,2,2] (.node [11,10,9,9,9,2,2,2,2,2,2,1,1] (.node [11,10,9,9,9,2,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,9,3,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_90 : RowTree := (.node [11,10,9,9,8,5,3,2,2,1,1,1] degreeTree62_88 degreeTree62_89) - -def degreeTree62_91 : RowTree := (.node [11,10,9,9,8,3,3,2,2,2,2,1] degreeTree62_87 degreeTree62_90) - -def degreeTree62_92 : RowTree := (.node [11,10,9,9,7,4,3,3,3,1,1,1] degreeTree62_84 degreeTree62_91) - -def degreeTree62_93 : RowTree := (.node [11,10,9,8,7,7,3,2,2,1,1,1] degreeTree62_77 degreeTree62_92) - -def degreeTree62_94 : RowTree := (.node [11,10,9,9,9,4,3,2,1,1,1,1,1] (.node [11,10,9,9,9,3,3,3,2,1,1,1] (.node [11,10,9,9,9,3,3,2,2,1,1,1,1] (.node [11,10,9,9,9,3,3,2,1,1,1,1,1,1] (.node [11,10,9,9,9,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,9,9,9,3,3,3,1,1,1,1,1] (.node [11,10,9,9,9,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [11,10,9,9,9,4,2,2,2,2,1,1] (.node [11,10,9,9,9,4,2,2,2,1,1,1,1] (.node [11,10,9,9,9,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,9,4,3,1,1,1,1,1,1,1] .empty .empty))) (.node [11,10,9,9,9,5,2,2,1,1,1,1,1] (.node [11,10,9,9,9,4,4,1,1,1,1,1,1] (.node [11,10,9,9,9,4,3,3,1,1,1,1] (.node [11,10,9,9,9,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,9,5,2,1,1,1,1,1,1,1] (.node [11,10,9,9,9,4,4,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,9,5,3,2,1,1,1,1] (.node [11,10,9,9,9,5,3,1,1,1,1,1,1] (.node [11,10,9,9,9,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,9,5,4,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_95 : RowTree := (.node [11,10,10,7,7,7,3,2,1,1,1,1,1] (.node [11,10,9,9,9,8,1,1,1,1,1,1] (.node [11,10,9,9,9,6,3,1,1,1,1,1] (.node [11,10,9,9,9,6,2,2,1,1,1,1] (.node [11,10,9,9,9,6,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,9,7,2,1,1,1,1,1] (.node [11,10,9,9,9,7,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,7,7,7,2,2,2,2,1,1] (.node [11,10,10,7,7,7,2,2,2,1,1,1,1] (.node [11,10,10,7,7,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,7,7,7,3,1,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,8,7,2,2,2,2,2,2,2,1,1] (.node [11,10,10,7,7,7,4,1,1,1,1,1,1] (.node [11,10,10,7,7,7,3,3,1,1,1,1] (.node [11,10,10,7,7,7,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,7,7,7,5,1,1,1,1,1] (.node [11,10,10,7,7,7,4,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,7,3,2,2,2,2,2,2,1] (.node [11,10,10,8,7,3,2,2,2,2,2,1,1,1] (.node [11,10,10,8,7,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,8,7,3,3,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_96 : RowTree := (.node [11,10,9,9,9,6,1,1,1,1,1,1,1,1] degreeTree62_94 degreeTree62_95) - -def degreeTree62_97 : RowTree := (.node [11,10,10,8,7,4,3,2,2,2,1,1,1] (.node [11,10,10,8,7,3,3,3,3,2,1,1] (.node [11,10,10,8,7,3,3,3,2,2,1,1,1] (.node [11,10,10,8,7,3,3,3,2,1,1,1,1,1] (.node [11,10,10,8,7,3,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,8,7,3,3,3,3,1,1,1,1] (.node [11,10,10,8,7,3,3,3,2,2,2,1] .empty .empty) .empty)) (.node [11,10,10,8,7,4,2,2,2,2,2,2] (.node [11,10,10,8,7,4,2,2,2,2,2,1,1] (.node [11,10,10,8,7,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,4,3,2,2,1,1,1,1,1] .empty .empty))) (.node [11,10,10,8,7,4,4,2,1,1,1,1,1,1] (.node [11,10,10,8,7,4,3,3,2,1,1,1,1] (.node [11,10,10,8,7,4,3,3,1,1,1,1,1,1] (.node [11,10,10,8,7,4,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,10,8,7,4,3,3,3,1,1,1] (.node [11,10,10,8,7,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [11,10,10,8,7,4,4,3,1,1,1,1,1] (.node [11,10,10,8,7,4,4,2,2,2,1,1] (.node [11,10,10,8,7,4,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,4,4,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_98 : RowTree := (.node [11,10,10,8,7,5,4,2,2,1,1,1] (.node [11,10,10,8,7,5,3,2,2,2,1,1] (.node [11,10,10,8,7,5,2,2,2,2,2,1] (.node [11,10,10,8,7,5,2,2,2,2,1,1,1] (.node [11,10,10,8,7,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,5,3,2,2,1,1,1,1] (.node [11,10,10,8,7,5,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,7,5,4,1,1,1,1,1,1,1] (.node [11,10,10,8,7,5,3,3,2,1,1,1] (.node [11,10,10,8,7,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,5,4,2,1,1,1,1,1] .empty .empty))) (.node [11,10,10,8,7,6,2,2,2,2,1,1] (.node [11,10,10,8,7,5,5,2,1,1,1,1] (.node [11,10,10,8,7,5,5,1,1,1,1,1,1] (.node [11,10,10,8,7,5,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,6,2,2,2,1,1,1,1] (.node [11,10,10,8,7,6,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,7,6,3,2,2,1,1,1] (.node [11,10,10,8,7,6,3,2,1,1,1,1,1] (.node [11,10,10,8,7,6,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,6,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_99 : RowTree := (.node [11,10,10,8,7,4,4,4,1,1,1,1] degreeTree62_97 degreeTree62_98) - -def degreeTree62_100 : RowTree := (.node [11,10,10,8,7,3,3,2,2,2,2,1,1] degreeTree62_96 degreeTree62_99) - -def degreeTree62_101 : RowTree := (.node [11,10,10,8,8,3,2,2,2,2,1,1,1,1] (.node [11,10,10,8,7,7,3,1,1,1,1,1,1] (.node [11,10,10,8,7,7,2,1,1,1,1,1,1,1] (.node [11,10,10,8,7,6,5,1,1,1,1,1] (.node [11,10,10,8,7,6,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,7,2,2,2,1,1,1] (.node [11,10,10,8,7,7,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,8,2,2,2,2,2,2,1,1,1] (.node [11,10,10,8,7,7,4,1,1,1,1,1] (.node [11,10,10,8,7,7,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,2,2,2,2,2,2,2,1] .empty .empty))) (.node [11,10,10,8,8,3,3,3,1,1,1,1,1,1] (.node [11,10,10,8,8,3,3,2,2,1,1,1,1,1] (.node [11,10,10,8,8,3,2,2,2,2,2,2] (.node [11,10,10,8,8,3,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,3,3,2,2,2,2,1] (.node [11,10,10,8,8,3,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,8,3,3,3,3,1,1,1] (.node [11,10,10,8,8,3,3,3,2,2,1,1] (.node [11,10,10,8,8,3,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,4,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_102 : RowTree := (.node [11,10,10,8,8,5,2,2,1,1,1,1,1,1] (.node [11,10,10,8,8,4,3,3,2,1,1,1] (.node [11,10,10,8,8,4,3,2,2,1,1,1,1] (.node [11,10,10,8,8,4,3,2,1,1,1,1,1,1] (.node [11,10,10,8,8,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,10,8,8,4,3,3,1,1,1,1,1] (.node [11,10,10,8,8,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [11,10,10,8,8,4,4,2,2,1,1,1] (.node [11,10,10,8,8,4,4,2,1,1,1,1,1] (.node [11,10,10,8,8,4,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,4,4,3,1,1,1,1] .empty .empty))) (.node [11,10,10,8,8,5,3,3,1,1,1,1] (.node [11,10,10,8,8,5,3,1,1,1,1,1,1,1] (.node [11,10,10,8,8,5,2,2,2,2,1,1] (.node [11,10,10,8,8,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,5,3,2,2,1,1,1] (.node [11,10,10,8,8,5,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,8,5,5,1,1,1,1,1] (.node [11,10,10,8,8,5,4,2,1,1,1,1] (.node [11,10,10,8,8,5,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,6,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_103 : RowTree := (.node [11,10,10,8,8,4,2,2,2,2,1,1,1] degreeTree62_101 degreeTree62_102) - -def degreeTree62_104 : RowTree := (.node [11,10,10,9,4,3,3,2,2,2,2,2,2] (.node [11,10,10,8,8,7,2,1,1,1,1,1,1] (.node [11,10,10,8,8,6,3,2,1,1,1,1] (.node [11,10,10,8,8,6,3,1,1,1,1,1,1] (.node [11,10,10,8,8,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,7,1,1,1,1,1,1,1,1] (.node [11,10,10,8,8,6,4,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,8,8,1,1,1,1,1,1,1] (.node [11,10,10,8,8,7,3,1,1,1,1,1] (.node [11,10,10,8,8,7,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,8,2,1,1,1,1,1] .empty .empty))) (.node [11,10,10,9,4,4,3,3,2,2,2,1,1] (.node [11,10,10,9,4,4,2,2,2,2,2,2,2] (.node [11,10,10,9,4,3,3,3,3,3,3] (.node [11,10,10,9,4,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,9,4,4,3,2,2,2,2,2,1] (.node [11,10,10,9,4,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,4,4,3,3,3,2,2,1] (.node [11,10,10,9,4,4,3,3,3,2,1,1,1] (.node [11,10,10,9,4,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,4,4,4,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_105 : RowTree := (.node [11,10,10,9,5,2,2,2,2,2,2,2,2,1] (.node [11,10,10,9,4,4,4,3,3,2,1,1] (.node [11,10,10,9,4,4,4,3,2,2,1,1,1] (.node [11,10,10,9,4,4,4,3,2,1,1,1,1,1] (.node [11,10,10,9,4,4,4,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,9,4,4,4,3,3,1,1,1,1] (.node [11,10,10,9,4,4,4,3,2,2,2,1] .empty .empty) .empty)) (.node [11,10,10,9,4,4,4,4,2,2,1,1] (.node [11,10,10,9,4,4,4,4,2,1,1,1,1] (.node [11,10,10,9,4,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,4,4,4,4,3,1,1,1] .empty .empty))) (.node [11,10,10,9,5,3,3,3,3,2,1,1,1] (.node [11,10,10,9,5,3,3,2,2,2,2,2,1] (.node [11,10,10,9,5,3,3,2,2,2,2,1,1,1] (.node [11,10,10,9,5,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,9,5,3,3,3,3,1,1,1,1,1] (.node [11,10,10,9,5,3,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [11,10,10,9,5,4,2,2,2,2,2,2,1] (.node [11,10,10,9,5,4,2,2,2,2,2,1,1,1] (.node [11,10,10,9,5,3,3,3,3,2,2,1] .empty .empty) .empty) (.node [11,10,10,9,5,4,3,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_106 : RowTree := (.node [11,10,10,9,4,4,4,2,2,2,2,1,1] degreeTree62_104 degreeTree62_105) - -def degreeTree62_107 : RowTree := (.node [11,10,10,8,8,6,2,2,1,1,1,1,1] degreeTree62_103 degreeTree62_106) - -def degreeTree62_108 : RowTree := (.node [11,10,10,8,7,6,4,1,1,1,1,1,1] degreeTree62_100 degreeTree62_107) - -def degreeTree62_109 : RowTree := (.node [11,10,10,9,5,4,4,3,2,1,1,1,1] (.node [11,10,10,9,5,4,3,3,3,2,1,1] (.node [11,10,10,9,5,4,3,3,2,2,1,1,1] (.node [11,10,10,9,5,4,3,3,2,1,1,1,1,1] (.node [11,10,10,9,5,4,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,9,5,4,3,3,3,1,1,1,1] (.node [11,10,10,9,5,4,3,3,2,2,2,1] .empty .empty) .empty)) (.node [11,10,10,9,5,4,4,2,2,2,2,1] (.node [11,10,10,9,5,4,4,2,2,2,1,1,1] (.node [11,10,10,9,5,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,5,4,4,3,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,9,5,5,2,2,2,2,2,1,1] (.node [11,10,10,9,5,4,4,4,1,1,1,1,1] (.node [11,10,10,9,5,4,4,3,3,1,1,1] (.node [11,10,10,9,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,9,5,5,2,2,2,2,1,1,1,1] (.node [11,10,10,9,5,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,5,5,3,2,2,2,1,1,1] (.node [11,10,10,9,5,5,3,2,2,1,1,1,1,1] (.node [11,10,10,9,5,5,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,9,5,5,3,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_110 : RowTree := (.node [11,10,10,9,5,5,5,2,1,1,1,1,1] (.node [11,10,10,9,5,5,4,2,2,2,1,1] (.node [11,10,10,9,5,5,3,3,3,1,1,1] (.node [11,10,10,9,5,5,3,3,2,2,1,1] (.node [11,10,10,9,5,5,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,5,5,4,2,2,1,1,1,1] (.node [11,10,10,9,5,5,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,5,5,4,4,1,1,1,1] (.node [11,10,10,9,5,5,4,3,2,1,1,1] (.node [11,10,10,9,5,5,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,5,5,5,1,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,9,6,3,2,2,2,2,2,2,1] (.node [11,10,10,9,6,2,2,2,2,2,2,2,1,1] (.node [11,10,10,9,5,5,5,3,1,1,1,1] (.node [11,10,10,9,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,3,2,2,2,2,2,1,1,1] (.node [11,10,10,9,6,2,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,10,10,9,6,3,3,2,2,2,2,2] (.node [11,10,10,9,6,3,3,2,2,2,2,1,1] (.node [11,10,10,9,6,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,3,3,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_111 : RowTree := (.node [11,10,10,9,5,5,3,3,1,1,1,1,1,1] degreeTree62_109 degreeTree62_110) - -def degreeTree62_112 : RowTree := (.node [11,10,10,9,6,4,3,3,2,1,1,1,1] (.node [11,10,10,9,6,4,2,2,2,2,2,2] (.node [11,10,10,9,6,3,3,3,3,2,1,1] (.node [11,10,10,9,6,3,3,3,3,1,1,1,1] (.node [11,10,10,9,6,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [11,10,10,9,6,4,2,2,2,2,2,1,1] (.node [11,10,10,9,6,4,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,6,4,3,2,2,2,2,1] (.node [11,10,10,9,6,4,3,2,2,2,1,1,1] (.node [11,10,10,9,6,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,4,3,3,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,9,6,4,4,3,1,1,1,1,1] (.node [11,10,10,9,6,4,4,2,1,1,1,1,1,1] (.node [11,10,10,9,6,4,3,3,3,1,1,1] (.node [11,10,10,9,6,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,4,4,2,2,2,1,1] (.node [11,10,10,9,6,4,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,6,5,2,2,2,1,1,1,1,1] (.node [11,10,10,9,6,4,4,4,1,1,1,1] (.node [11,10,10,9,6,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,5,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_113 : RowTree := (.node [11,10,10,9,6,5,5,2,1,1,1,1] (.node [11,10,10,9,6,5,4,1,1,1,1,1,1,1] (.node [11,10,10,9,6,5,3,2,2,2,1,1] (.node [11,10,10,9,6,5,3,2,2,1,1,1,1] (.node [11,10,10,9,6,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,5,3,3,2,1,1,1] (.node [11,10,10,9,6,5,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,6,5,4,3,1,1,1,1] (.node [11,10,10,9,6,5,4,2,2,1,1,1] (.node [11,10,10,9,6,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,5,5,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,9,6,6,3,2,2,1,1,1] (.node [11,10,10,9,6,6,2,2,2,2,1,1] (.node [11,10,10,9,6,6,2,2,2,1,1,1,1] (.node [11,10,10,9,6,6,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,6,3,2,1,1,1,1,1] (.node [11,10,10,9,6,6,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,6,6,4,2,1,1,1,1] (.node [11,10,10,9,6,6,4,1,1,1,1,1,1] (.node [11,10,10,9,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,6,5,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_114 : RowTree := (.node [11,10,10,9,6,5,2,2,2,2,2,1] degreeTree62_112 degreeTree62_113) - -def degreeTree62_115 : RowTree := (.node [11,10,10,9,6,3,3,3,2,2,1,1,1] degreeTree62_111 degreeTree62_114) - -def degreeTree62_116 : RowTree := (.node [11,10,10,9,7,3,3,3,3,1,1,1] (.node [11,10,10,9,7,3,3,2,2,2,1,1,1] (.node [11,10,10,9,7,3,2,2,2,2,2,1,1] (.node [11,10,10,9,7,3,2,2,2,2,1,1,1,1] (.node [11,10,10,9,7,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,10,9,7,3,3,2,2,1,1,1,1,1] (.node [11,10,10,9,7,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,10,10,9,7,3,3,3,2,1,1,1,1] (.node [11,10,10,9,7,3,3,3,1,1,1,1,1,1] (.node [11,10,10,9,7,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,10,9,7,3,3,3,2,2,1,1] .empty .empty))) (.node [11,10,10,9,7,4,3,2,2,2,1,1] (.node [11,10,10,9,7,4,2,2,2,2,2,1] (.node [11,10,10,9,7,4,2,2,2,2,1,1,1] (.node [11,10,10,9,7,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,7,4,3,2,2,1,1,1,1] (.node [11,10,10,9,7,4,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,7,4,4,1,1,1,1,1,1,1] (.node [11,10,10,9,7,4,3,3,2,1,1,1] (.node [11,10,10,9,7,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,7,4,4,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_117 : RowTree := (.node [11,10,10,9,7,5,5,1,1,1,1,1] (.node [11,10,10,9,7,5,3,2,1,1,1,1,1] (.node [11,10,10,9,7,5,2,2,2,1,1,1,1] (.node [11,10,10,9,7,5,2,2,1,1,1,1,1,1] (.node [11,10,10,9,7,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,7,5,3,1,1,1,1,1,1,1] (.node [11,10,10,9,7,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,10,10,9,7,5,4,1,1,1,1,1,1] (.node [11,10,10,9,7,5,3,3,1,1,1,1] (.node [11,10,10,9,7,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,7,5,4,2,1,1,1,1] .empty .empty))) (.node [11,10,10,9,7,6,4,1,1,1,1,1] (.node [11,10,10,9,7,6,2,2,2,1,1,1] (.node [11,10,10,9,7,6,2,2,1,1,1,1,1] (.node [11,10,10,9,7,6,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,7,6,3,2,1,1,1,1] (.node [11,10,10,9,7,6,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,7,7,2,2,1,1,1,1] (.node [11,10,10,9,7,7,2,1,1,1,1,1,1] (.node [11,10,10,9,7,7,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,7,7,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_118 : RowTree := (.node [11,10,10,9,7,4,4,2,2,1,1,1] degreeTree62_116 degreeTree62_117) - -def degreeTree62_119 : RowTree := (.node [11,10,10,9,8,4,2,2,1,1,1,1,1,1] (.node [11,10,10,9,8,3,3,2,1,1,1,1,1,1] (.node [11,10,10,9,8,3,2,2,2,1,1,1,1,1] (.node [11,10,10,9,8,2,2,2,2,2,2,2] (.node [11,10,10,9,8,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,9,8,3,2,2,2,2,2,1] (.node [11,10,10,9,8,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,8,3,3,3,1,1,1,1,1] (.node [11,10,10,9,8,3,3,2,2,2,1,1] (.node [11,10,10,9,8,3,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,8,3,3,3,2,1,1,1] .empty .empty))) (.node [11,10,10,9,8,4,3,3,1,1,1,1] (.node [11,10,10,9,8,4,3,1,1,1,1,1,1,1] (.node [11,10,10,9,8,4,2,2,2,2,1,1] (.node [11,10,10,9,8,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,8,4,3,2,2,1,1,1] (.node [11,10,10,9,8,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,8,5,2,1,1,1,1,1,1,1] (.node [11,10,10,9,8,4,4,2,1,1,1,1] (.node [11,10,10,9,8,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,8,5,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_120 : RowTree := (.node [11,10,10,9,9,2,2,2,2,1,1,1,1,1] (.node [11,10,10,9,8,6,2,2,1,1,1,1] (.node [11,10,10,9,8,5,4,1,1,1,1,1] (.node [11,10,10,9,8,5,3,2,1,1,1,1] (.node [11,10,10,9,8,5,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,8,6,2,1,1,1,1,1,1] (.node [11,10,10,9,8,6,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,8,7,2,1,1,1,1,1] (.node [11,10,10,9,8,7,1,1,1,1,1,1,1] (.node [11,10,10,9,8,6,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,8,8,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,9,9,3,2,2,2,2,1,1] (.node [11,10,10,9,9,3,2,2,1,1,1,1,1,1] (.node [11,10,10,9,9,2,2,2,2,2,2,1] (.node [11,10,10,9,9,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,9,3,2,2,2,1,1,1,1] .empty .empty)) (.node [11,10,10,9,9,3,3,2,2,1,1,1] (.node [11,10,10,9,9,3,3,2,1,1,1,1,1] (.node [11,10,10,9,9,3,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,9,3,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_121 : RowTree := (.node [11,10,10,9,8,5,2,2,2,1,1,1] degreeTree62_119 degreeTree62_120) - -def degreeTree62_122 : RowTree := (.node [11,10,10,9,8,2,2,2,2,2,1,1,1,1] degreeTree62_118 degreeTree62_121) - -def degreeTree62_123 : RowTree := (.node [11,10,10,9,7,2,2,2,2,2,2,1,1,1] degreeTree62_115 degreeTree62_122) - -def degreeTree62_124 : RowTree := (.node [11,10,10,9,5,4,3,2,2,2,2,1,1] degreeTree62_108 degreeTree62_123) - -def degreeTree62_125 : RowTree := (.node [11,10,9,9,9,3,2,2,2,2,1,1,1] degreeTree62_93 degreeTree62_124) - -def degreeTree62_126 : RowTree := (.node [10,10,10,10,10,3,2,2,2,1,1,1] degreeTree62_62 degreeTree62_125) - -def degreeTree62_127 : RowTree := (.node [11,10,10,9,9,6,2,1,1,1,1,1] (.node [11,10,10,9,9,5,1,1,1,1,1,1,1,1] (.node [11,10,10,9,9,4,3,1,1,1,1,1,1] (.node [11,10,10,9,9,4,2,2,2,1,1,1] (.node [11,10,10,9,9,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,9,4,4,1,1,1,1,1] (.node [11,10,10,9,9,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,9,5,3,1,1,1,1,1] (.node [11,10,10,9,9,5,2,2,1,1,1,1] (.node [11,10,10,9,9,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,9,6,1,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,10,4,3,2,2,2,2,2,2,2] (.node [11,10,10,10,3,3,3,3,3,2,2,1,1] (.node [11,10,10,10,3,3,3,2,2,2,2,2,2] (.node [11,10,10,9,9,7,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,4,2,2,2,2,2,2,2,2,1] (.node [11,10,10,10,3,3,3,3,3,3,3] .empty .empty) .empty)) (.node [11,10,10,10,4,3,3,3,2,2,2,1,1] (.node [11,10,10,10,4,3,3,2,2,2,2,2,1] (.node [11,10,10,10,4,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,4,3,3,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_128 : RowTree := (.node [11,10,10,10,4,4,3,3,3,2,1,1] (.node [11,10,10,10,4,4,3,2,2,2,2,2] (.node [11,10,10,10,4,4,2,2,2,2,2,2,1] (.node [11,10,10,10,4,4,2,2,2,2,2,1,1,1] (.node [11,10,10,10,4,3,3,3,3,2,2,1] .empty .empty) .empty) (.node [11,10,10,10,4,4,3,2,2,2,2,1,1] (.node [11,10,10,10,4,4,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,4,4,3,3,2,2,2,1] (.node [11,10,10,10,4,4,3,3,2,2,1,1,1] (.node [11,10,10,10,4,4,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,4,4,3,3,3,1,1,1,1] .empty .empty))) (.node [11,10,10,10,4,4,4,3,2,2,1,1] (.node [11,10,10,10,4,4,4,2,2,2,2,1] (.node [11,10,10,10,4,4,4,2,2,2,1,1,1] (.node [11,10,10,10,4,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,4,4,4,3,2,1,1,1,1] (.node [11,10,10,10,4,4,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,4,4,4,4,2,1,1,1] (.node [11,10,10,10,4,4,4,4,1,1,1,1,1] (.node [11,10,10,10,4,4,4,3,3,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,2,2,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_129 : RowTree := (.node [11,10,10,10,4,3,3,3,3,2,1,1,1] degreeTree62_127 degreeTree62_128) - -def degreeTree62_130 : RowTree := (.node [11,10,10,10,5,4,2,2,2,2,1,1,1,1] (.node [11,10,10,10,5,3,3,3,2,1,1,1,1,1] (.node [11,10,10,10,5,3,3,2,2,2,1,1,1,1] (.node [11,10,10,10,5,3,2,2,2,2,2,2,1] (.node [11,10,10,10,5,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,3,3,2,2,2,2,2] (.node [11,10,10,10,5,3,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,10,10,10,5,3,3,3,3,1,1,1,1] (.node [11,10,10,10,5,3,3,3,2,2,2,1] (.node [11,10,10,10,5,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,3,3,3,3,2,1,1] .empty .empty))) (.node [11,10,10,10,5,4,3,3,1,1,1,1,1,1] (.node [11,10,10,10,5,4,3,2,2,1,1,1,1,1] (.node [11,10,10,10,5,4,2,2,2,2,2,2] (.node [11,10,10,10,5,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,4,3,2,2,2,2,1] (.node [11,10,10,10,5,4,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,5,4,3,3,3,1,1,1] (.node [11,10,10,10,5,4,3,3,2,2,1,1] (.node [11,10,10,10,5,4,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,4,4,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_131 : RowTree := (.node [11,10,10,10,5,5,3,3,1,1,1,1,1] (.node [11,10,10,10,5,5,2,2,2,2,1,1,1] (.node [11,10,10,10,5,4,4,3,2,1,1,1] (.node [11,10,10,10,5,4,4,3,1,1,1,1,1] (.node [11,10,10,10,5,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,5,2,2,2,1,1,1,1,1] (.node [11,10,10,10,5,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,5,5,3,2,2,1,1,1,1] (.node [11,10,10,10,5,5,3,2,1,1,1,1,1,1] (.node [11,10,10,10,5,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,10,10,5,5,3,2,2,2,1,1] .empty .empty))) (.node [11,10,10,10,5,5,5,1,1,1,1,1,1] (.node [11,10,10,10,5,5,4,2,1,1,1,1,1] (.node [11,10,10,10,5,5,4,1,1,1,1,1,1,1] (.node [11,10,10,10,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,5,4,3,1,1,1,1] (.node [11,10,10,10,5,5,4,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,6,2,2,2,2,2,2,2,1] (.node [11,10,10,10,6,2,2,2,2,2,2,1,1,1] (.node [11,10,10,10,5,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,6,3,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_132 : RowTree := (.node [11,10,10,10,5,4,4,2,2,1,1,1,1] degreeTree62_130 degreeTree62_131) - -def degreeTree62_133 : RowTree := (.node [11,10,10,10,5,2,2,2,2,2,2,2,2] degreeTree62_129 degreeTree62_132) - -def degreeTree62_134 : RowTree := (.node [11,10,10,10,6,4,2,2,2,2,2,1] (.node [11,10,10,10,6,3,3,3,2,1,1,1,1] (.node [11,10,10,10,6,3,3,2,2,2,1,1,1] (.node [11,10,10,10,6,3,3,2,2,1,1,1,1,1] (.node [11,10,10,10,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,10,6,3,3,3,1,1,1,1,1,1] (.node [11,10,10,10,6,3,3,2,2,2,2,1] .empty .empty) .empty)) (.node [11,10,10,10,6,4,2,2,2,1,1,1,1,1] (.node [11,10,10,10,6,3,3,3,3,1,1,1] (.node [11,10,10,10,6,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,10,6,4,2,2,2,2,1,1,1] .empty .empty))) (.node [11,10,10,10,6,4,4,1,1,1,1,1,1,1] (.node [11,10,10,10,6,4,3,2,2,2,1,1] (.node [11,10,10,10,6,4,3,2,2,1,1,1,1] (.node [11,10,10,10,6,4,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,6,4,3,3,2,1,1,1] (.node [11,10,10,10,6,4,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,6,4,4,3,1,1,1,1] (.node [11,10,10,10,6,4,4,2,2,1,1,1] (.node [11,10,10,10,6,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,6,5,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_135 : RowTree := (.node [11,10,10,10,6,6,2,2,2,1,1,1] (.node [11,10,10,10,6,5,4,1,1,1,1,1,1] (.node [11,10,10,10,6,5,3,2,1,1,1,1,1] (.node [11,10,10,10,6,5,3,1,1,1,1,1,1,1] (.node [11,10,10,10,6,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,10,6,5,3,3,1,1,1,1] (.node [11,10,10,10,6,5,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,6,6,2,1,1,1,1,1,1,1] (.node [11,10,10,10,6,5,5,1,1,1,1,1] (.node [11,10,10,10,6,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,6,6,2,2,1,1,1,1,1] .empty .empty))) (.node [11,10,10,10,7,2,2,2,2,2,2,2] (.node [11,10,10,10,6,6,4,1,1,1,1,1] (.node [11,10,10,10,6,6,3,2,1,1,1,1] (.node [11,10,10,10,6,6,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,7,2,2,2,2,2,2,1,1] (.node [11,10,10,10,7,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,7,3,2,2,2,2,2,1] (.node [11,10,10,10,7,3,2,2,2,2,1,1,1] (.node [11,10,10,10,7,3,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,7,3,3,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_136 : RowTree := (.node [11,10,10,10,6,5,2,2,2,1,1,1,1] degreeTree62_134 degreeTree62_135) - -def degreeTree62_137 : RowTree := (.node [11,10,10,10,7,4,4,1,1,1,1,1,1] (.node [11,10,10,10,7,4,2,2,2,2,1,1] (.node [11,10,10,10,7,3,3,3,2,1,1,1] (.node [11,10,10,10,7,3,3,3,1,1,1,1,1] (.node [11,10,10,10,7,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,10,7,4,2,2,2,1,1,1,1] (.node [11,10,10,10,7,4,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,7,4,3,2,2,1,1,1] (.node [11,10,10,10,7,4,3,2,1,1,1,1,1] (.node [11,10,10,10,7,4,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,7,4,3,3,1,1,1,1] .empty .empty))) (.node [11,10,10,10,7,5,3,2,1,1,1,1] (.node [11,10,10,10,7,5,2,2,1,1,1,1,1] (.node [11,10,10,10,7,5,2,1,1,1,1,1,1,1] (.node [11,10,10,10,7,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,7,5,3,1,1,1,1,1,1] (.node [11,10,10,10,7,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,7,6,2,1,1,1,1,1,1] (.node [11,10,10,10,7,6,1,1,1,1,1,1,1,1] (.node [11,10,10,10,7,5,4,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,7,6,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_138 : RowTree := (.node [11,10,10,10,8,3,3,2,2,1,1,1] (.node [11,10,10,10,8,3,2,2,1,1,1,1,1,1] (.node [11,10,10,10,8,2,2,2,2,1,1,1,1,1] (.node [11,10,10,10,7,7,2,1,1,1,1,1] (.node [11,10,10,10,7,7,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,8,2,2,2,2,2,2,1] (.node [11,10,10,10,8,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,8,3,3,1,1,1,1,1,1,1] (.node [11,10,10,10,8,3,2,2,2,2,1,1] (.node [11,10,10,10,8,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,8,3,3,2,1,1,1,1,1] .empty .empty))) (.node [11,10,10,10,8,4,3,2,1,1,1,1] (.node [11,10,10,10,8,4,2,2,1,1,1,1,1] (.node [11,10,10,10,8,4,2,1,1,1,1,1,1,1] (.node [11,10,10,10,8,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,8,4,3,1,1,1,1,1,1] (.node [11,10,10,10,8,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,8,5,2,1,1,1,1,1,1] (.node [11,10,10,10,8,5,1,1,1,1,1,1,1,1] (.node [11,10,10,10,8,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,8,5,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_139 : RowTree := (.node [11,10,10,10,7,6,3,1,1,1,1,1] degreeTree62_137 degreeTree62_138) - -def degreeTree62_140 : RowTree := (.node [11,10,10,10,7,3,3,2,2,1,1,1,1] degreeTree62_136 degreeTree62_139) - -def degreeTree62_141 : RowTree := (.node [11,10,10,10,6,3,2,2,2,2,2,1,1] degreeTree62_133 degreeTree62_140) - -def degreeTree62_142 : RowTree := (.node [11,10,10,10,9,3,3,2,1,1,1,1] (.node [11,10,10,10,9,2,2,2,2,2,1,1] (.node [11,10,10,10,8,7,1,1,1,1,1,1] (.node [11,10,10,10,8,6,2,1,1,1,1,1] (.node [11,10,10,10,8,6,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,9,2,2,2,2,1,1,1,1] (.node [11,10,10,10,9,2,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,9,3,2,2,2,1,1,1] (.node [11,10,10,10,9,3,2,2,1,1,1,1,1] (.node [11,10,10,10,9,3,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,9,3,3,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,10,9,5,2,1,1,1,1,1] (.node [11,10,10,10,9,4,2,2,1,1,1,1] (.node [11,10,10,10,9,4,2,1,1,1,1,1,1] (.node [11,10,10,10,9,4,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,9,5,1,1,1,1,1,1,1] (.node [11,10,10,10,9,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,10,2,2,2,1,1,1,1,1] (.node [11,10,10,10,10,2,2,1,1,1,1,1,1,1] (.node [11,10,10,10,9,6,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,10,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_143 : RowTree := (.node [11,11,8,8,7,7,3,2,1,1,1,1,1] (.node [11,10,10,10,10,5,1,1,1,1,1,1] (.node [11,10,10,10,10,3,3,1,1,1,1,1] (.node [11,10,10,10,10,3,2,2,1,1,1,1] (.node [11,10,10,10,10,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,10,4,2,1,1,1,1,1] (.node [11,10,10,10,10,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,8,8,7,7,2,2,2,2,1,1] (.node [11,11,8,8,7,7,2,2,2,1,1,1,1] (.node [11,11,8,8,7,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,7,7,3,1,1,1,1,1,1,1] .empty .empty))) (.node [11,11,8,8,8,2,2,2,2,2,2,2,1,1] (.node [11,11,8,8,7,7,4,1,1,1,1,1,1] (.node [11,11,8,8,7,7,3,3,1,1,1,1] (.node [11,11,8,8,7,7,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,7,7,5,1,1,1,1,1] (.node [11,11,8,8,7,7,4,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,8,8,8,3,2,2,2,2,2,2,1] (.node [11,11,8,8,8,3,2,2,2,2,2,1,1,1] (.node [11,11,8,8,8,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,8,8,8,3,3,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_144 : RowTree := (.node [11,10,10,10,10,3,1,1,1,1,1,1,1,1] degreeTree62_142 degreeTree62_143) - -def degreeTree62_145 : RowTree := (.node [11,11,8,8,8,4,3,2,2,2,1,1,1] (.node [11,11,8,8,8,3,3,3,3,2,1,1] (.node [11,11,8,8,8,3,3,3,2,2,1,1,1] (.node [11,11,8,8,8,3,3,3,2,1,1,1,1,1] (.node [11,11,8,8,8,3,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,8,8,8,3,3,3,3,1,1,1,1] (.node [11,11,8,8,8,3,3,3,2,2,2,1] .empty .empty) .empty)) (.node [11,11,8,8,8,4,2,2,2,2,2,2] (.node [11,11,8,8,8,4,2,2,2,2,2,1,1] (.node [11,11,8,8,8,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,4,3,2,2,1,1,1,1,1] .empty .empty))) (.node [11,11,8,8,8,4,4,2,1,1,1,1,1,1] (.node [11,11,8,8,8,4,3,3,2,1,1,1,1] (.node [11,11,8,8,8,4,3,3,1,1,1,1,1,1] (.node [11,11,8,8,8,4,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,8,8,8,4,3,3,3,1,1,1] (.node [11,11,8,8,8,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [11,11,8,8,8,4,4,3,1,1,1,1,1] (.node [11,11,8,8,8,4,4,2,2,2,1,1] (.node [11,11,8,8,8,4,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,4,4,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_146 : RowTree := (.node [11,11,8,8,8,5,4,2,2,1,1,1] (.node [11,11,8,8,8,5,3,2,2,2,1,1] (.node [11,11,8,8,8,5,2,2,2,2,2,1] (.node [11,11,8,8,8,5,2,2,2,2,1,1,1] (.node [11,11,8,8,8,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,5,3,2,2,1,1,1,1] (.node [11,11,8,8,8,5,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,8,8,8,5,4,1,1,1,1,1,1,1] (.node [11,11,8,8,8,5,3,3,2,1,1,1] (.node [11,11,8,8,8,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,5,4,2,1,1,1,1,1] .empty .empty))) (.node [11,11,8,8,8,6,2,2,2,2,1,1] (.node [11,11,8,8,8,5,5,2,1,1,1,1] (.node [11,11,8,8,8,5,5,1,1,1,1,1,1] (.node [11,11,8,8,8,5,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,6,2,2,2,1,1,1,1] (.node [11,11,8,8,8,6,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,8,8,8,6,3,2,2,1,1,1] (.node [11,11,8,8,8,6,3,2,1,1,1,1,1] (.node [11,11,8,8,8,6,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,6,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_147 : RowTree := (.node [11,11,8,8,8,4,4,4,1,1,1,1] degreeTree62_145 degreeTree62_146) - -def degreeTree62_148 : RowTree := (.node [11,11,8,8,8,3,3,2,2,2,2,1,1] degreeTree62_144 degreeTree62_147) - -def degreeTree62_149 : RowTree := (.node [11,11,8,8,8,8,2,2,1,1,1,1] (.node [11,11,8,8,8,7,3,1,1,1,1,1,1] (.node [11,11,8,8,8,7,2,1,1,1,1,1,1,1] (.node [11,11,8,8,8,6,5,1,1,1,1,1] (.node [11,11,8,8,8,6,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,7,2,2,2,1,1,1] (.node [11,11,8,8,8,7,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,8,8,8,8,1,1,1,1,1,1,1,1] (.node [11,11,8,8,8,7,4,1,1,1,1,1] (.node [11,11,8,8,8,7,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,8,2,1,1,1,1,1,1] .empty .empty))) (.node [11,11,9,7,7,7,3,2,1,1,1,1,1] (.node [11,11,9,7,7,7,2,2,2,1,1,1,1] (.node [11,11,9,7,7,7,2,2,1,1,1,1,1,1] (.node [11,11,8,8,8,8,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,7,7,7,3,1,1,1,1,1,1,1] (.node [11,11,9,7,7,7,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,9,7,7,7,4,1,1,1,1,1,1] (.node [11,11,9,7,7,7,3,3,1,1,1,1] (.node [11,11,9,7,7,7,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,7,7,7,4,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_150 : RowTree := (.node [11,11,9,8,7,3,3,3,3,1,1,1,1] (.node [11,11,9,8,7,3,3,2,2,2,2,1,1] (.node [11,11,9,8,7,3,2,2,2,2,2,1,1,1] (.node [11,11,9,8,7,2,2,2,2,2,2,2,2] (.node [11,11,9,8,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,3,3,2,2,2,1,1,1,1] (.node [11,11,9,8,7,3,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,9,8,7,3,3,3,2,2,1,1,1] (.node [11,11,9,8,7,3,3,3,2,1,1,1,1,1] (.node [11,11,9,8,7,3,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,9,8,7,3,3,3,2,2,2,1] .empty .empty))) (.node [11,11,9,8,7,4,3,2,2,2,1,1,1] (.node [11,11,9,8,7,4,2,2,2,2,2,1,1] (.node [11,11,9,8,7,4,2,2,2,2,1,1,1,1] (.node [11,11,9,8,7,3,3,3,3,2,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,4,3,2,2,1,1,1,1,1] (.node [11,11,9,8,7,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,9,8,7,4,3,3,2,1,1,1,1] (.node [11,11,9,8,7,4,3,3,1,1,1,1,1,1] (.node [11,11,9,8,7,4,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,9,8,7,4,3,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_151 : RowTree := (.node [11,11,9,7,7,7,5,1,1,1,1,1] degreeTree62_149 degreeTree62_150) - -def degreeTree62_152 : RowTree := (.node [11,11,9,8,7,5,3,2,2,1,1,1,1] (.node [11,11,9,8,7,4,4,4,1,1,1,1] (.node [11,11,9,8,7,4,4,2,2,2,1,1] (.node [11,11,9,8,7,4,4,2,2,1,1,1,1] (.node [11,11,9,8,7,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,4,4,3,2,1,1,1] (.node [11,11,9,8,7,4,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,8,7,5,2,2,2,2,2,1] (.node [11,11,9,8,7,5,2,2,2,2,1,1,1] (.node [11,11,9,8,7,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,5,3,2,1,1,1,1,1,1] .empty .empty))) (.node [11,11,9,8,7,5,4,2,2,1,1,1] (.node [11,11,9,8,7,5,3,3,2,1,1,1] (.node [11,11,9,8,7,5,3,3,1,1,1,1,1] (.node [11,11,9,8,7,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,5,4,2,1,1,1,1,1] (.node [11,11,9,8,7,5,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,8,7,5,5,2,1,1,1,1] (.node [11,11,9,8,7,5,5,1,1,1,1,1,1] (.node [11,11,9,8,7,5,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,6,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_153 : RowTree := (.node [11,11,9,8,7,7,2,2,2,1,1,1] (.node [11,11,9,8,7,6,4,1,1,1,1,1,1] (.node [11,11,9,8,7,6,3,2,1,1,1,1,1] (.node [11,11,9,8,7,6,3,1,1,1,1,1,1,1] (.node [11,11,9,8,7,6,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,6,3,3,1,1,1,1] (.node [11,11,9,8,7,6,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,8,7,7,2,1,1,1,1,1,1,1] (.node [11,11,9,8,7,6,5,1,1,1,1,1] (.node [11,11,9,8,7,6,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,7,2,2,1,1,1,1,1] .empty .empty))) (.node [11,11,9,8,8,2,2,2,2,2,2,2,1] (.node [11,11,9,8,7,7,4,1,1,1,1,1] (.node [11,11,9,8,7,7,3,2,1,1,1,1] (.node [11,11,9,8,7,7,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [11,11,9,8,8,3,2,2,2,2,2,2] (.node [11,11,9,8,8,3,2,2,2,2,2,1,1] (.node [11,11,9,8,8,3,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,3,3,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_154 : RowTree := (.node [11,11,9,8,7,6,2,2,2,1,1,1,1] degreeTree62_152 degreeTree62_153) - -def degreeTree62_155 : RowTree := (.node [11,11,9,8,7,4,3,3,3,1,1,1] degreeTree62_151 degreeTree62_154) - -def degreeTree62_156 : RowTree := (.node [11,11,8,8,8,6,4,1,1,1,1,1,1] degreeTree62_148 degreeTree62_155) - -def degreeTree62_157 : RowTree := (.node [11,10,10,10,8,5,3,1,1,1,1,1] degreeTree62_141 degreeTree62_156) - -def degreeTree62_158 : RowTree := (.node [11,11,9,8,8,4,3,2,2,2,1,1] (.node [11,11,9,8,8,4,2,2,2,1,1,1,1,1] (.node [11,11,9,8,8,3,3,3,2,1,1,1,1] (.node [11,11,9,8,8,3,3,3,1,1,1,1,1,1] (.node [11,11,9,8,8,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,9,8,8,3,3,3,3,1,1,1] (.node [11,11,9,8,8,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [11,11,9,8,8,4,3,2,1,1,1,1,1,1] (.node [11,11,9,8,8,4,2,2,2,2,2,1] (.node [11,11,9,8,8,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,4,3,2,2,1,1,1,1] .empty .empty))) (.node [11,11,9,8,8,4,4,3,1,1,1,1] (.node [11,11,9,8,8,4,4,1,1,1,1,1,1,1] (.node [11,11,9,8,8,4,3,3,2,1,1,1] (.node [11,11,9,8,8,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,4,4,2,2,1,1,1] (.node [11,11,9,8,8,4,4,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,8,8,5,2,2,2,2,1,1] (.node [11,11,9,8,8,5,2,2,2,1,1,1,1] (.node [11,11,9,8,8,5,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,5,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_159 : RowTree := (.node [11,11,9,8,8,6,4,1,1,1,1,1] (.node [11,11,9,8,8,6,2,1,1,1,1,1,1,1] (.node [11,11,9,8,8,5,4,1,1,1,1,1,1] (.node [11,11,9,8,8,5,3,3,1,1,1,1] (.node [11,11,9,8,8,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,5,5,1,1,1,1,1] (.node [11,11,9,8,8,5,4,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,8,8,6,3,1,1,1,1,1,1] (.node [11,11,9,8,8,6,2,2,2,1,1,1] (.node [11,11,9,8,8,6,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,6,3,2,1,1,1,1] .empty .empty))) (.node [11,11,9,8,8,8,2,1,1,1,1,1] (.node [11,11,9,8,8,7,2,2,1,1,1,1] (.node [11,11,9,8,8,7,2,1,1,1,1,1,1] (.node [11,11,9,8,8,7,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,8,1,1,1,1,1,1,1] (.node [11,11,9,8,8,7,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,4,3,3,3,3,3,3] (.node [11,11,9,9,4,3,3,3,3,2,2,1,1] (.node [11,11,9,9,4,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,9,9,4,4,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_160 : RowTree := (.node [11,11,9,8,8,5,3,2,1,1,1,1,1] degreeTree62_158 degreeTree62_159) - -def degreeTree62_161 : RowTree := (.node [11,11,9,9,4,4,4,3,2,2,2,1] (.node [11,11,9,9,4,4,4,2,2,2,1,1,1,1] (.node [11,11,9,9,4,4,3,3,3,1,1,1,1,1] (.node [11,11,9,9,4,4,3,3,2,2,2,1,1] (.node [11,11,9,9,4,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,9,9,4,4,3,3,3,2,2,1] (.node [11,11,9,9,4,4,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,4,4,4,3,2,1,1,1,1,1] (.node [11,11,9,9,4,4,4,2,2,2,2,2] (.node [11,11,9,9,4,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,9,4,4,4,3,2,2,1,1,1] .empty .empty))) (.node [11,11,9,9,4,4,4,4,3,1,1,1] (.node [11,11,9,9,4,4,4,4,1,1,1,1,1,1] (.node [11,11,9,9,4,4,4,3,3,2,1,1] (.node [11,11,9,9,4,4,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,4,4,4,4,2,2,1,1] (.node [11,11,9,9,4,4,4,4,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,5,3,3,2,2,2,2,1,1,1] (.node [11,11,9,9,5,3,2,2,2,2,2,2,2] (.node [11,11,9,9,5,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,9,9,5,3,3,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_162 : RowTree := (.node [11,11,9,9,5,4,3,3,2,2,2,1] (.node [11,11,9,9,5,4,3,2,2,2,1,1,1,1] (.node [11,11,9,9,5,3,3,3,3,2,2,1] (.node [11,11,9,9,5,3,3,3,3,2,1,1,1] (.node [11,11,9,9,5,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,4,2,2,2,2,2,2,1] (.node [11,11,9,9,5,4,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,5,4,3,3,2,1,1,1,1,1] (.node [11,11,9,9,5,4,3,2,2,2,2,2] (.node [11,11,9,9,5,4,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,4,3,3,2,2,1,1,1] .empty .empty))) (.node [11,11,9,9,5,4,4,3,1,1,1,1,1,1] (.node [11,11,9,9,5,4,4,2,2,1,1,1,1,1] (.node [11,11,9,9,5,4,3,3,3,2,1,1] (.node [11,11,9,9,5,4,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,4,4,2,2,2,2,1] (.node [11,11,9,9,5,4,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,5,4,4,3,3,1,1,1] (.node [11,11,9,9,5,4,4,3,2,2,1,1] (.node [11,11,9,9,5,4,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,4,4,4,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_163 : RowTree := (.node [11,11,9,9,5,3,3,3,2,2,2,1,1] degreeTree62_161 degreeTree62_162) - -def degreeTree62_164 : RowTree := (.node [11,11,9,9,4,4,3,2,2,2,2,1,1,1] degreeTree62_160 degreeTree62_163) - -def degreeTree62_165 : RowTree := (.node [11,11,9,9,5,5,4,2,1,1,1,1,1,1] (.node [11,11,9,9,5,5,3,2,2,2,2,1] (.node [11,11,9,9,5,5,2,2,2,2,2,2] (.node [11,11,9,9,5,5,2,2,2,2,2,1,1] (.node [11,11,9,9,5,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,5,3,2,2,2,1,1,1] (.node [11,11,9,9,5,5,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,5,5,3,3,2,2,1,1] (.node [11,11,9,9,5,5,3,3,2,1,1,1,1] (.node [11,11,9,9,5,5,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,5,3,3,3,1,1,1] .empty .empty))) (.node [11,11,9,9,5,5,5,1,1,1,1,1,1,1] (.node [11,11,9,9,5,5,4,3,1,1,1,1,1] (.node [11,11,9,9,5,5,4,2,2,2,1,1] (.node [11,11,9,9,5,5,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,5,4,4,1,1,1,1] (.node [11,11,9,9,5,5,4,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,5,5,5,3,1,1,1,1] (.node [11,11,9,9,5,5,5,2,2,1,1,1] (.node [11,11,9,9,5,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,2,2,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_166 : RowTree := (.node [11,11,9,9,6,4,2,2,2,2,1,1,1,1] (.node [11,11,9,9,6,3,3,3,2,1,1,1,1,1] (.node [11,11,9,9,6,3,3,2,2,2,1,1,1,1] (.node [11,11,9,9,6,3,2,2,2,2,2,2,1] (.node [11,11,9,9,6,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,3,3,2,2,2,2,2] (.node [11,11,9,9,6,3,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,9,9,6,3,3,3,3,1,1,1,1] (.node [11,11,9,9,6,3,3,3,2,2,2,1] (.node [11,11,9,9,6,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,3,3,3,3,2,1,1] .empty .empty))) (.node [11,11,9,9,6,4,3,3,1,1,1,1,1,1] (.node [11,11,9,9,6,4,3,2,2,1,1,1,1,1] (.node [11,11,9,9,6,4,2,2,2,2,2,2] (.node [11,11,9,9,6,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,4,3,2,2,2,2,1] (.node [11,11,9,9,6,4,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,6,4,3,3,3,1,1,1] (.node [11,11,9,9,6,4,3,3,2,2,1,1] (.node [11,11,9,9,6,4,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,4,4,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_167 : RowTree := (.node [11,11,9,9,6,2,2,2,2,2,2,2,2] degreeTree62_165 degreeTree62_166) - -def degreeTree62_168 : RowTree := (.node [11,11,9,9,6,5,3,3,1,1,1,1,1] (.node [11,11,9,9,6,5,2,2,2,2,1,1,1] (.node [11,11,9,9,6,4,4,3,2,1,1,1] (.node [11,11,9,9,6,4,4,3,1,1,1,1,1] (.node [11,11,9,9,6,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,5,2,2,2,1,1,1,1,1] (.node [11,11,9,9,6,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,6,5,3,2,2,1,1,1,1] (.node [11,11,9,9,6,5,3,2,1,1,1,1,1,1] (.node [11,11,9,9,6,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,9,9,6,5,3,2,2,2,1,1] .empty .empty))) (.node [11,11,9,9,6,5,5,1,1,1,1,1,1] (.node [11,11,9,9,6,5,4,2,1,1,1,1,1] (.node [11,11,9,9,6,5,4,1,1,1,1,1,1,1] (.node [11,11,9,9,6,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,5,4,3,1,1,1,1] (.node [11,11,9,9,6,5,4,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,6,6,2,2,2,1,1,1,1] (.node [11,11,9,9,6,6,2,2,1,1,1,1,1,1] (.node [11,11,9,9,6,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,6,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_169 : RowTree := (.node [11,11,9,9,7,3,2,2,2,2,2,2] (.node [11,11,9,9,6,6,5,1,1,1,1,1] (.node [11,11,9,9,6,6,3,3,1,1,1,1] (.node [11,11,9,9,6,6,3,2,2,1,1,1] (.node [11,11,9,9,6,6,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,6,4,2,1,1,1,1] (.node [11,11,9,9,6,6,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,7,3,2,2,2,2,1,1,1,1] (.node [11,11,9,9,7,2,2,2,2,2,2,2,1] (.node [11,11,9,9,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,3,2,2,2,2,2,1,1] .empty .empty))) (.node [11,11,9,9,7,3,3,3,2,2,1,1] (.node [11,11,9,9,7,3,3,2,2,2,2,1] (.node [11,11,9,9,7,3,3,2,2,2,1,1,1] (.node [11,11,9,9,7,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,3,3,3,2,1,1,1,1] (.node [11,11,9,9,7,3,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,7,4,2,2,2,2,1,1,1] (.node [11,11,9,9,7,4,2,2,2,1,1,1,1,1] (.node [11,11,9,9,7,3,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,4,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_170 : RowTree := (.node [11,11,9,9,6,6,3,1,1,1,1,1,1,1] degreeTree62_168 degreeTree62_169) - -def degreeTree62_171 : RowTree := (.node [11,11,9,9,6,4,4,2,2,1,1,1,1] degreeTree62_167 degreeTree62_170) - -def degreeTree62_172 : RowTree := (.node [11,11,9,9,5,4,4,4,2,1,1,1] degreeTree62_164 degreeTree62_171) - -def degreeTree62_173 : RowTree := (.node [11,11,9,9,7,5,2,2,2,2,1,1] (.node [11,11,9,9,7,4,4,2,1,1,1,1,1] (.node [11,11,9,9,7,4,3,3,1,1,1,1,1] (.node [11,11,9,9,7,4,3,2,2,2,1,1] (.node [11,11,9,9,7,4,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,4,4,1,1,1,1,1,1,1] (.node [11,11,9,9,7,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,7,5,2,2,1,1,1,1,1,1] (.node [11,11,9,9,7,4,4,3,1,1,1,1] (.node [11,11,9,9,7,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,5,2,2,2,1,1,1,1] .empty .empty))) (.node [11,11,9,9,7,5,4,2,1,1,1,1] (.node [11,11,9,9,7,5,3,2,2,1,1,1] (.node [11,11,9,9,7,5,3,2,1,1,1,1,1] (.node [11,11,9,9,7,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,5,4,1,1,1,1,1,1] (.node [11,11,9,9,7,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,7,6,2,2,1,1,1,1,1] (.node [11,11,9,9,7,6,2,1,1,1,1,1,1,1] (.node [11,11,9,9,7,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,6,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_174 : RowTree := (.node [11,11,9,9,8,3,2,2,2,2,1,1,1] (.node [11,11,9,9,7,7,3,1,1,1,1,1] (.node [11,11,9,9,7,7,1,1,1,1,1,1,1,1] (.node [11,11,9,9,7,6,4,1,1,1,1,1] (.node [11,11,9,9,7,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,7,2,2,1,1,1,1] (.node [11,11,9,9,7,7,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,8,2,2,2,2,2,2,2] (.node [11,11,9,9,8,2,2,2,2,2,2,1,1] (.node [11,11,9,9,8,2,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,8,3,2,2,2,1,1,1,1,1] .empty .empty))) (.node [11,11,9,9,8,3,3,3,2,1,1,1] (.node [11,11,9,9,8,3,3,2,2,1,1,1,1] (.node [11,11,9,9,8,3,3,2,1,1,1,1,1,1] (.node [11,11,9,9,8,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,9,9,8,3,3,3,1,1,1,1,1] (.node [11,11,9,9,8,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,9,9,8,4,2,2,2,2,1,1] (.node [11,11,9,9,8,4,2,2,2,1,1,1,1] (.node [11,11,9,9,8,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,8,4,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_175 : RowTree := (.node [11,11,9,9,7,6,3,1,1,1,1,1,1] degreeTree62_173 degreeTree62_174) - -def degreeTree62_176 : RowTree := (.node [11,11,9,9,8,6,1,1,1,1,1,1,1,1] (.node [11,11,9,9,8,5,2,2,1,1,1,1,1] (.node [11,11,9,9,8,4,4,1,1,1,1,1,1] (.node [11,11,9,9,8,4,3,3,1,1,1,1] (.node [11,11,9,9,8,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,8,5,2,1,1,1,1,1,1,1] (.node [11,11,9,9,8,4,4,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,8,5,3,2,1,1,1,1] (.node [11,11,9,9,8,5,3,1,1,1,1,1,1] (.node [11,11,9,9,8,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,8,5,4,1,1,1,1,1] .empty .empty))) (.node [11,11,9,9,8,8,1,1,1,1,1,1] (.node [11,11,9,9,8,6,3,1,1,1,1,1] (.node [11,11,9,9,8,6,2,2,1,1,1,1] (.node [11,11,9,9,8,6,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,8,7,2,1,1,1,1,1] (.node [11,11,9,9,8,7,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,9,2,2,2,2,2,2,1] (.node [11,11,9,9,9,2,2,2,2,2,1,1,1] (.node [11,11,9,9,9,2,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,9,3,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_177 : RowTree := (.node [11,11,9,9,9,4,4,1,1,1,1,1] (.node [11,11,9,9,9,4,2,1,1,1,1,1,1,1] (.node [11,11,9,9,9,3,3,2,1,1,1,1,1] (.node [11,11,9,9,9,3,3,1,1,1,1,1,1,1] (.node [11,11,9,9,9,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,9,9,3,3,3,1,1,1,1] (.node [11,11,9,9,9,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,9,4,3,1,1,1,1,1,1] (.node [11,11,9,9,9,4,2,2,2,1,1,1] (.node [11,11,9,9,9,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,9,4,3,2,1,1,1,1] .empty .empty))) (.node [11,11,9,9,9,6,2,1,1,1,1,1] (.node [11,11,9,9,9,5,2,2,1,1,1,1] (.node [11,11,9,9,9,5,2,1,1,1,1,1,1] (.node [11,11,9,9,9,5,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,9,6,1,1,1,1,1,1,1] (.node [11,11,9,9,9,5,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,7,7,2,2,2,2,2,2,2,2] (.node [11,11,10,7,7,2,2,2,2,2,2,2,1,1] (.node [11,11,9,9,9,7,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,3,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_178 : RowTree := (.node [11,11,9,9,9,3,2,2,2,1,1,1,1] degreeTree62_176 degreeTree62_177) - -def degreeTree62_179 : RowTree := (.node [11,11,9,9,8,4,3,2,1,1,1,1,1] degreeTree62_175 degreeTree62_178) - -def degreeTree62_180 : RowTree := (.node [11,11,10,7,7,4,2,2,2,2,2,2] (.node [11,11,10,7,7,3,3,3,2,2,2,1] (.node [11,11,10,7,7,3,3,2,2,2,2,2] (.node [11,11,10,7,7,3,3,2,2,2,2,1,1] (.node [11,11,10,7,7,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,3,3,3,2,2,1,1,1] (.node [11,11,10,7,7,3,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,7,7,4,2,2,2,2,1,1,1,1] (.node [11,11,10,7,7,3,3,3,3,2,1,1] (.node [11,11,10,7,7,3,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,4,2,2,2,2,2,1,1] .empty .empty))) (.node [11,11,10,7,7,4,3,3,2,2,1,1] (.node [11,11,10,7,7,4,3,2,2,2,2,1] (.node [11,11,10,7,7,4,3,2,2,2,1,1,1] (.node [11,11,10,7,7,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,4,3,3,2,1,1,1,1] (.node [11,11,10,7,7,4,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,7,7,4,4,2,2,1,1,1,1] (.node [11,11,10,7,7,4,4,2,1,1,1,1,1,1] (.node [11,11,10,7,7,4,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,4,4,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_181 : RowTree := (.node [11,11,10,7,7,5,4,1,1,1,1,1,1,1] (.node [11,11,10,7,7,5,3,2,1,1,1,1,1,1] (.node [11,11,10,7,7,5,2,2,2,1,1,1,1,1] (.node [11,11,10,7,7,4,4,4,1,1,1,1] (.node [11,11,10,7,7,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,5,2,2,2,2,2,1] (.node [11,11,10,7,7,5,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,10,7,7,5,3,3,1,1,1,1,1] (.node [11,11,10,7,7,5,3,2,2,2,1,1] (.node [11,11,10,7,7,5,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,5,3,3,2,1,1,1] .empty .empty))) (.node [11,11,10,7,7,6,2,2,1,1,1,1,1,1] (.node [11,11,10,7,7,5,4,3,1,1,1,1] (.node [11,11,10,7,7,5,4,2,2,1,1,1] (.node [11,11,10,7,7,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,5,5,2,1,1,1,1] (.node [11,11,10,7,7,5,5,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,7,7,6,3,1,1,1,1,1,1,1] (.node [11,11,10,7,7,6,2,2,2,2,1,1] (.node [11,11,10,7,7,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,6,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_182 : RowTree := (.node [11,11,10,7,7,4,4,3,1,1,1,1,1] degreeTree62_180 degreeTree62_181) - -def degreeTree62_183 : RowTree := (.node [11,11,10,8,4,3,3,2,2,2,2,2,2] (.node [11,11,10,7,7,7,2,2,1,1,1,1,1] (.node [11,11,10,7,7,6,4,2,1,1,1,1] (.node [11,11,10,7,7,6,4,1,1,1,1,1,1] (.node [11,11,10,7,7,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,7,2,1,1,1,1,1,1,1] (.node [11,11,10,7,7,6,5,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,7,7,7,3,2,1,1,1,1] (.node [11,11,10,7,7,7,3,1,1,1,1,1,1] (.node [11,11,10,7,7,7,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,7,4,1,1,1,1,1] .empty .empty))) (.node [11,11,10,8,4,4,3,3,2,2,2,1,1] (.node [11,11,10,8,4,4,2,2,2,2,2,2,2] (.node [11,11,10,8,4,3,3,3,3,3,3] (.node [11,11,10,8,4,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,8,4,4,3,2,2,2,2,2,1] (.node [11,11,10,8,4,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,4,4,3,3,3,2,2,1] (.node [11,11,10,8,4,4,3,3,3,2,1,1,1] (.node [11,11,10,8,4,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,4,4,4,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_184 : RowTree := (.node [11,11,10,8,5,2,2,2,2,2,2,2,2,1] (.node [11,11,10,8,4,4,4,3,3,2,1,1] (.node [11,11,10,8,4,4,4,3,2,2,1,1,1] (.node [11,11,10,8,4,4,4,3,2,1,1,1,1,1] (.node [11,11,10,8,4,4,4,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,10,8,4,4,4,3,3,1,1,1,1] (.node [11,11,10,8,4,4,4,3,2,2,2,1] .empty .empty) .empty)) (.node [11,11,10,8,4,4,4,4,2,2,1,1] (.node [11,11,10,8,4,4,4,4,2,1,1,1,1] (.node [11,11,10,8,4,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,4,4,4,4,3,1,1,1] .empty .empty))) (.node [11,11,10,8,5,3,3,3,3,1,1,1,1,1] (.node [11,11,10,8,5,3,3,2,2,2,2,2,1] (.node [11,11,10,8,5,3,3,2,2,2,2,1,1,1] (.node [11,11,10,8,5,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,10,8,5,3,3,3,2,2,2,1,1] .empty .empty)) (.node [11,11,10,8,5,4,2,2,2,2,2,1,1,1] (.node [11,11,10,8,5,3,3,3,3,2,2,1] (.node [11,11,10,8,5,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,4,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_185 : RowTree := (.node [11,11,10,8,4,4,4,2,2,2,2,1,1] degreeTree62_183 degreeTree62_184) - -def degreeTree62_186 : RowTree := (.node [11,11,10,7,7,6,3,2,2,1,1,1] degreeTree62_182 degreeTree62_185) - -def degreeTree62_187 : RowTree := (.node [11,11,10,7,7,3,2,2,2,2,2,2,1] degreeTree62_179 degreeTree62_186) - -def degreeTree62_188 : RowTree := (.node [11,11,9,9,7,4,3,2,1,1,1,1,1,1] degreeTree62_172 degreeTree62_187) - -def degreeTree62_189 : RowTree := (.node [11,11,9,8,8,3,3,2,2,2,1,1,1] degreeTree62_157 degreeTree62_188) - -def degreeTree62_190 : RowTree := (.node [11,11,10,8,5,4,4,3,1,1,1,1,1,1] (.node [11,11,10,8,5,4,3,3,3,1,1,1,1] (.node [11,11,10,8,5,4,3,3,2,1,1,1,1,1] (.node [11,11,10,8,5,4,3,2,2,2,2,2] (.node [11,11,10,8,5,4,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,4,3,3,2,2,2,1] (.node [11,11,10,8,5,4,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,5,4,4,2,2,2,1,1,1] (.node [11,11,10,8,5,4,4,2,2,1,1,1,1,1] (.node [11,11,10,8,5,4,3,3,3,2,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,4,4,2,2,2,2,1] .empty .empty))) (.node [11,11,10,8,5,5,2,2,2,2,1,1,1,1] (.node [11,11,10,8,5,4,4,3,3,1,1,1] (.node [11,11,10,8,5,4,4,3,2,2,1,1] (.node [11,11,10,8,5,4,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,4,4,4,2,1,1,1] (.node [11,11,10,8,5,4,4,4,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,5,5,3,2,2,1,1,1,1,1] (.node [11,11,10,8,5,5,2,2,2,2,2,2] (.node [11,11,10,8,5,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,5,3,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_191 : RowTree := (.node [11,11,10,8,5,5,5,1,1,1,1,1,1,1] (.node [11,11,10,8,5,5,4,2,2,1,1,1,1] (.node [11,11,10,8,5,5,3,3,2,2,1,1] (.node [11,11,10,8,5,5,3,3,2,1,1,1,1] (.node [11,11,10,8,5,5,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,5,4,2,1,1,1,1,1,1] (.node [11,11,10,8,5,5,3,3,3,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,5,5,4,3,2,1,1,1] (.node [11,11,10,8,5,5,4,3,1,1,1,1,1] (.node [11,11,10,8,5,5,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,5,4,4,1,1,1,1] .empty .empty))) (.node [11,11,10,8,6,3,2,2,2,2,2,1,1,1] (.node [11,11,10,8,5,5,5,3,1,1,1,1] (.node [11,11,10,8,5,5,5,2,2,1,1,1] (.node [11,11,10,8,5,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,2,2,2,2,2,2,2,2] (.node [11,11,10,8,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,8,6,3,3,2,2,2,2,1,1] (.node [11,11,10,8,6,3,3,2,2,2,1,1,1,1] (.node [11,11,10,8,6,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,8,6,3,3,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_192 : RowTree := (.node [11,11,10,8,5,5,3,2,2,2,2,1] degreeTree62_190 degreeTree62_191) - -def degreeTree62_193 : RowTree := (.node [11,11,10,8,6,4,3,3,1,1,1,1,1,1] (.node [11,11,10,8,6,4,2,2,2,2,2,1,1] (.node [11,11,10,8,6,3,3,3,3,1,1,1,1] (.node [11,11,10,8,6,3,3,3,2,2,2,1] (.node [11,11,10,8,6,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,4,2,2,2,2,1,1,1,1] (.node [11,11,10,8,6,3,3,3,3,2,1,1] .empty .empty) .empty)) (.node [11,11,10,8,6,4,3,2,2,2,1,1,1] (.node [11,11,10,8,6,4,3,2,2,1,1,1,1,1] (.node [11,11,10,8,6,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,10,8,6,4,3,2,2,2,2,1] .empty .empty))) (.node [11,11,10,8,6,4,4,2,2,2,1,1] (.node [11,11,10,8,6,4,3,3,3,1,1,1] (.node [11,11,10,8,6,4,3,3,2,2,1,1] (.node [11,11,10,8,6,4,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,4,4,2,2,1,1,1,1] (.node [11,11,10,8,6,4,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,6,4,4,4,1,1,1,1] (.node [11,11,10,8,6,4,4,3,2,1,1,1] (.node [11,11,10,8,6,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,5,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_194 : RowTree := (.node [11,11,10,8,6,5,5,1,1,1,1,1,1] (.node [11,11,10,8,6,5,3,3,2,1,1,1] (.node [11,11,10,8,6,5,3,2,2,1,1,1,1] (.node [11,11,10,8,6,5,3,2,1,1,1,1,1,1] (.node [11,11,10,8,6,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,8,6,5,3,3,1,1,1,1,1] (.node [11,11,10,8,6,5,3,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,8,6,5,4,2,2,1,1,1] (.node [11,11,10,8,6,5,4,2,1,1,1,1,1] (.node [11,11,10,8,6,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,5,4,3,1,1,1,1] .empty .empty))) (.node [11,11,10,8,6,6,3,2,1,1,1,1,1] (.node [11,11,10,8,6,6,2,2,2,1,1,1,1] (.node [11,11,10,8,6,6,2,2,1,1,1,1,1,1] (.node [11,11,10,8,6,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,6,3,1,1,1,1,1,1,1] (.node [11,11,10,8,6,6,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,8,6,6,4,1,1,1,1,1,1] (.node [11,11,10,8,6,6,3,3,1,1,1,1] (.node [11,11,10,8,6,6,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,6,4,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_195 : RowTree := (.node [11,11,10,8,6,5,2,2,2,2,1,1,1] degreeTree62_193 degreeTree62_194) - -def degreeTree62_196 : RowTree := (.node [11,11,10,8,6,3,3,3,2,1,1,1,1,1] degreeTree62_192 degreeTree62_195) - -def degreeTree62_197 : RowTree := (.node [11,11,10,8,7,3,3,3,2,2,1,1] (.node [11,11,10,8,7,3,3,2,2,1,1,1,1,1] (.node [11,11,10,8,7,3,2,2,2,2,1,1,1,1] (.node [11,11,10,8,7,2,2,2,2,2,2,2,1] (.node [11,11,10,8,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,3,2,2,2,2,2,2] (.node [11,11,10,8,7,3,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,8,7,3,3,3,1,1,1,1,1,1] (.node [11,11,10,8,7,3,3,2,2,2,2,1] (.node [11,11,10,8,7,3,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,3,3,3,2,1,1,1,1] .empty .empty))) (.node [11,11,10,8,7,4,3,2,2,1,1,1,1] (.node [11,11,10,8,7,4,2,2,2,2,1,1,1] (.node [11,11,10,8,7,4,2,2,2,1,1,1,1,1] (.node [11,11,10,8,7,3,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,4,3,2,1,1,1,1,1,1] (.node [11,11,10,8,7,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,10,8,7,4,3,3,2,1,1,1] (.node [11,11,10,8,7,4,3,3,1,1,1,1,1] (.node [11,11,10,8,7,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,4,4,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_198 : RowTree := (.node [11,11,10,8,7,5,4,2,1,1,1,1] (.node [11,11,10,8,7,5,3,1,1,1,1,1,1,1] (.node [11,11,10,8,7,5,2,2,1,1,1,1,1,1] (.node [11,11,10,8,7,4,4,3,1,1,1,1] (.node [11,11,10,8,7,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,5,2,2,2,2,1,1] (.node [11,11,10,8,7,5,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,7,5,3,3,1,1,1,1] (.node [11,11,10,8,7,5,3,2,2,1,1,1] (.node [11,11,10,8,7,5,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,5,4,1,1,1,1,1,1] .empty .empty))) (.node [11,11,10,8,7,6,3,2,1,1,1,1] (.node [11,11,10,8,7,6,2,2,1,1,1,1,1] (.node [11,11,10,8,7,6,2,1,1,1,1,1,1,1] (.node [11,11,10,8,7,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,6,3,1,1,1,1,1,1] (.node [11,11,10,8,7,6,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,7,7,2,1,1,1,1,1,1] (.node [11,11,10,8,7,7,1,1,1,1,1,1,1,1] (.node [11,11,10,8,7,6,4,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,7,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_199 : RowTree := (.node [11,11,10,8,7,4,4,2,1,1,1,1,1] degreeTree62_197 degreeTree62_198) - -def degreeTree62_200 : RowTree := (.node [11,11,10,8,8,3,3,3,2,1,1,1] (.node [11,11,10,8,8,3,2,2,2,2,2,1] (.node [11,11,10,8,8,2,2,2,2,2,2,2] (.node [11,11,10,8,8,2,2,2,2,2,2,1,1] (.node [11,11,10,8,8,2,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,8,3,2,2,2,2,1,1,1] (.node [11,11,10,8,8,3,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,8,3,3,2,2,2,1,1] (.node [11,11,10,8,8,3,3,2,2,1,1,1,1] (.node [11,11,10,8,8,3,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,8,3,3,3,1,1,1,1,1] .empty .empty))) (.node [11,11,10,8,8,4,3,2,2,1,1,1] (.node [11,11,10,8,8,4,2,2,2,2,1,1] (.node [11,11,10,8,8,4,2,2,2,1,1,1,1] (.node [11,11,10,8,8,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,8,4,3,2,1,1,1,1,1] (.node [11,11,10,8,8,4,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,8,4,4,2,1,1,1,1] (.node [11,11,10,8,8,4,4,1,1,1,1,1,1] (.node [11,11,10,8,8,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,8,5,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_201 : RowTree := (.node [11,11,10,8,8,8,1,1,1,1,1,1] (.node [11,11,10,8,8,6,2,1,1,1,1,1,1] (.node [11,11,10,8,8,5,3,2,1,1,1,1] (.node [11,11,10,8,8,5,3,1,1,1,1,1,1] (.node [11,11,10,8,8,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,8,6,1,1,1,1,1,1,1,1] (.node [11,11,10,8,8,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,8,7,1,1,1,1,1,1,1] (.node [11,11,10,8,8,6,3,1,1,1,1,1] (.node [11,11,10,8,8,6,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,8,7,2,1,1,1,1,1] .empty .empty))) (.node [11,11,10,9,4,3,3,2,2,2,2,1,1,1] (.node [11,11,10,9,3,3,3,3,3,3,3] (.node [11,11,10,9,3,3,3,3,3,2,2,1,1] (.node [11,11,10,9,3,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,10,9,4,3,2,2,2,2,2,2,2] (.node [11,11,10,9,4,2,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,10,9,4,3,3,3,3,1,1,1,1,1] (.node [11,11,10,9,4,3,3,3,2,2,2,1,1] (.node [11,11,10,9,4,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,9,4,3,3,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_202 : RowTree := (.node [11,11,10,8,8,5,2,2,1,1,1,1,1] degreeTree62_200 degreeTree62_201) - -def degreeTree62_203 : RowTree := (.node [11,11,10,8,7,7,3,1,1,1,1,1] degreeTree62_199 degreeTree62_202) - -def degreeTree62_204 : RowTree := (.node [11,11,10,8,6,6,5,1,1,1,1,1] degreeTree62_196 degreeTree62_203) - -def degreeTree62_205 : RowTree := (.node [11,11,10,9,4,4,4,2,2,1,1,1,1,1] (.node [11,11,10,9,4,4,3,3,2,1,1,1,1,1] (.node [11,11,10,9,4,4,3,2,2,2,1,1,1,1] (.node [11,11,10,9,4,4,2,2,2,2,2,2,1] (.node [11,11,10,9,4,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,4,4,3,2,2,2,2,2] (.node [11,11,10,9,4,4,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,9,4,4,3,3,3,1,1,1,1] (.node [11,11,10,9,4,4,3,3,2,2,2,1] (.node [11,11,10,9,4,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,4,4,3,3,3,2,1,1] .empty .empty))) (.node [11,11,10,9,4,4,4,3,3,1,1,1] (.node [11,11,10,9,4,4,4,3,1,1,1,1,1,1] (.node [11,11,10,9,4,4,4,2,2,2,2,1] (.node [11,11,10,9,4,4,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,4,4,4,3,2,2,1,1] (.node [11,11,10,9,4,4,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,5,2,2,2,2,2,2,2,1,1] (.node [11,11,10,9,4,4,4,4,2,1,1,1] (.node [11,11,10,9,4,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,5,2,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_206 : RowTree := (.node [11,11,10,9,5,4,2,2,2,2,2,1,1] (.node [11,11,10,9,5,3,3,3,2,2,1,1,1] (.node [11,11,10,9,5,3,3,2,2,2,2,1,1] (.node [11,11,10,9,5,3,3,2,2,2,1,1,1,1] (.node [11,11,10,9,5,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,9,5,3,3,3,2,1,1,1,1,1] (.node [11,11,10,9,5,3,3,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,10,9,5,3,3,3,3,2,1,1] (.node [11,11,10,9,5,3,3,3,3,1,1,1,1] (.node [11,11,10,9,5,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,9,5,4,2,2,2,2,1,1,1,1] .empty .empty))) (.node [11,11,10,9,5,4,3,3,2,1,1,1,1] (.node [11,11,10,9,5,4,3,2,2,2,1,1,1] (.node [11,11,10,9,5,4,3,2,2,1,1,1,1,1] (.node [11,11,10,9,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,10,9,5,4,3,3,1,1,1,1,1,1] (.node [11,11,10,9,5,4,3,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,10,9,5,4,4,2,1,1,1,1,1,1] (.node [11,11,10,9,5,4,3,3,3,1,1,1] (.node [11,11,10,9,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,9,5,4,4,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_207 : RowTree := (.node [11,11,10,9,5,3,2,2,2,2,2,1,1,1] degreeTree62_205 degreeTree62_206) - -def degreeTree62_208 : RowTree := (.node [11,11,10,9,5,5,3,3,2,1,1,1] (.node [11,11,10,9,5,5,2,2,2,2,2,1] (.node [11,11,10,9,5,4,4,4,1,1,1,1] (.node [11,11,10,9,5,4,4,3,2,1,1,1] (.node [11,11,10,9,5,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,5,5,2,2,2,2,1,1,1] (.node [11,11,10,9,5,5,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,5,5,3,2,2,2,1,1] (.node [11,11,10,9,5,5,3,2,2,1,1,1,1] (.node [11,11,10,9,5,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,5,5,3,3,1,1,1,1,1] .empty .empty))) (.node [11,11,10,9,5,5,5,2,1,1,1,1] (.node [11,11,10,9,5,5,4,2,2,1,1,1] (.node [11,11,10,9,5,5,4,2,1,1,1,1,1] (.node [11,11,10,9,5,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,5,5,5,1,1,1,1,1,1] (.node [11,11,10,9,5,5,4,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,6,3,2,2,2,2,1,1,1,1] (.node [11,11,10,9,6,2,2,2,2,2,2,2,1] (.node [11,11,10,9,6,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,3,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_209 : RowTree := (.node [11,11,10,9,6,4,3,2,1,1,1,1,1,1] (.node [11,11,10,9,6,3,3,3,2,2,1,1] (.node [11,11,10,9,6,3,3,2,2,2,2,1] (.node [11,11,10,9,6,3,3,2,2,2,1,1,1] (.node [11,11,10,9,6,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,3,3,3,2,1,1,1,1] (.node [11,11,10,9,6,3,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,6,4,2,2,2,2,1,1,1] (.node [11,11,10,9,6,4,2,2,2,1,1,1,1,1] (.node [11,11,10,9,6,3,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,4,2,2,2,2,2,1] .empty .empty))) (.node [11,11,10,9,6,4,4,2,1,1,1,1,1] (.node [11,11,10,9,6,4,3,3,1,1,1,1,1] (.node [11,11,10,9,6,4,3,2,2,2,1,1] (.node [11,11,10,9,6,4,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,4,4,1,1,1,1,1,1,1] (.node [11,11,10,9,6,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,6,5,2,2,1,1,1,1,1,1] (.node [11,11,10,9,6,4,4,3,1,1,1,1] (.node [11,11,10,9,6,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,5,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_210 : RowTree := (.node [11,11,10,9,6,3,2,2,2,2,2,2] degreeTree62_208 degreeTree62_209) - -def degreeTree62_211 : RowTree := (.node [11,11,10,9,5,4,4,2,2,2,1,1] degreeTree62_207 degreeTree62_210) - -def degreeTree62_212 : RowTree := (.node [11,11,10,9,6,6,3,1,1,1,1,1,1] (.node [11,11,10,9,6,5,4,2,1,1,1,1] (.node [11,11,10,9,6,5,3,2,2,1,1,1] (.node [11,11,10,9,6,5,3,2,1,1,1,1,1] (.node [11,11,10,9,6,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,5,4,1,1,1,1,1,1] (.node [11,11,10,9,6,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,6,6,2,2,1,1,1,1,1] (.node [11,11,10,9,6,6,2,1,1,1,1,1,1,1] (.node [11,11,10,9,6,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,6,2,2,2,1,1,1] .empty .empty))) (.node [11,11,10,9,7,3,2,2,2,1,1,1,1,1] (.node [11,11,10,9,7,2,2,2,2,2,1,1,1,1] (.node [11,11,10,9,6,6,4,1,1,1,1,1] (.node [11,11,10,9,6,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,7,2,2,2,2,2,2,2] (.node [11,11,10,9,7,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,9,7,3,3,2,1,1,1,1,1,1] (.node [11,11,10,9,7,3,2,2,2,2,2,1] (.node [11,11,10,9,7,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,7,3,3,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_213 : RowTree := (.node [11,11,10,9,7,4,4,2,1,1,1,1] (.node [11,11,10,9,7,4,3,1,1,1,1,1,1,1] (.node [11,11,10,9,7,4,2,2,1,1,1,1,1,1] (.node [11,11,10,9,7,3,3,3,2,1,1,1] (.node [11,11,10,9,7,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,7,4,2,2,2,2,1,1] (.node [11,11,10,9,7,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,7,4,3,3,1,1,1,1] (.node [11,11,10,9,7,4,3,2,2,1,1,1] (.node [11,11,10,9,7,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,7,4,4,1,1,1,1,1,1] .empty .empty))) (.node [11,11,10,9,7,5,4,1,1,1,1,1] (.node [11,11,10,9,7,5,2,2,2,1,1,1] (.node [11,11,10,9,7,5,2,2,1,1,1,1,1] (.node [11,11,10,9,7,5,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,7,5,3,2,1,1,1,1] (.node [11,11,10,9,7,5,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,7,6,2,2,1,1,1,1] (.node [11,11,10,9,7,6,2,1,1,1,1,1,1] (.node [11,11,10,9,7,6,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,7,6,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_214 : RowTree := (.node [11,11,10,9,7,3,3,2,2,2,1,1] degreeTree62_212 degreeTree62_213) - -def degreeTree62_215 : RowTree := (.node [11,11,10,9,8,3,3,3,1,1,1,1] (.node [11,11,10,9,8,3,2,2,2,1,1,1,1] (.node [11,11,10,9,8,2,2,2,2,2,1,1,1] (.node [11,11,10,9,8,2,2,2,2,1,1,1,1,1] (.node [11,11,10,9,7,7,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,8,3,2,2,1,1,1,1,1,1] (.node [11,11,10,9,8,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,10,9,8,3,3,2,1,1,1,1,1] (.node [11,11,10,9,8,3,3,1,1,1,1,1,1,1] (.node [11,11,10,9,8,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,9,8,3,3,2,2,1,1,1] .empty .empty))) (.node [11,11,10,9,8,4,4,1,1,1,1,1] (.node [11,11,10,9,8,4,2,2,2,1,1,1] (.node [11,11,10,9,8,4,2,2,1,1,1,1,1] (.node [11,11,10,9,8,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,8,4,3,2,1,1,1,1] (.node [11,11,10,9,8,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,8,5,2,2,1,1,1,1] (.node [11,11,10,9,8,5,2,1,1,1,1,1,1] (.node [11,11,10,9,8,5,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,8,5,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_216 : RowTree := (.node [11,11,10,9,9,4,1,1,1,1,1,1,1,1] (.node [11,11,10,9,9,3,2,1,1,1,1,1,1,1] (.node [11,11,10,9,9,2,2,2,1,1,1,1,1,1] (.node [11,11,10,9,8,7,1,1,1,1,1,1] (.node [11,11,10,9,8,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,9,2,2,2,2,2,1,1] (.node [11,11,10,9,9,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,9,3,3,1,1,1,1,1,1] (.node [11,11,10,9,9,3,2,2,2,1,1,1] (.node [11,11,10,9,9,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,9,3,3,2,1,1,1,1] .empty .empty))) (.node [11,11,10,9,9,5,2,1,1,1,1,1] (.node [11,11,10,9,9,4,3,1,1,1,1,1] (.node [11,11,10,9,9,4,2,2,1,1,1,1] (.node [11,11,10,9,9,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,9,5,1,1,1,1,1,1,1] .empty .empty)) (.node [11,11,10,10,3,3,2,2,2,2,2,2,2] (.node [11,11,10,10,3,2,2,2,2,2,2,2,2,1] (.node [11,11,10,9,9,6,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,3,3,3,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_217 : RowTree := (.node [11,11,10,9,8,6,1,1,1,1,1,1,1] degreeTree62_215 degreeTree62_216) - -def degreeTree62_218 : RowTree := (.node [11,11,10,9,7,7,1,1,1,1,1,1,1] degreeTree62_214 degreeTree62_217) - -def degreeTree62_219 : RowTree := (.node [11,11,10,9,6,5,2,2,2,2,1,1] degreeTree62_211 degreeTree62_218) - -def degreeTree62_220 : RowTree := (.node [11,11,10,9,4,3,3,3,3,2,2,1] degreeTree62_204 degreeTree62_219) - -def degreeTree62_221 : RowTree := (.node [11,11,10,10,4,3,3,2,2,2,2,2] (.node [11,11,10,10,4,2,2,2,2,2,2,2,2] (.node [11,11,10,10,3,3,3,3,3,2,1,1,1] (.node [11,11,10,10,3,3,3,3,3,1,1,1,1,1] (.node [11,11,10,10,3,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,10,4,2,2,2,2,2,2,2,1,1] (.node [11,11,10,10,3,3,3,3,3,2,2,1] .empty .empty) .empty)) (.node [11,11,10,10,4,3,3,2,2,2,1,1,1,1] (.node [11,11,10,10,4,3,2,2,2,2,2,2,1] (.node [11,11,10,10,4,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,4,3,3,2,2,2,2,1,1] .empty .empty))) (.node [11,11,10,10,4,4,2,2,2,2,1,1,1,1] (.node [11,11,10,10,4,3,3,3,2,2,2,1] (.node [11,11,10,10,4,3,3,3,2,2,1,1,1] (.node [11,11,10,10,4,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,4,3,3,3,3,2,1,1] (.node [11,11,10,10,4,3,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,4,4,3,2,2,1,1,1,1,1] (.node [11,11,10,10,4,4,2,2,2,2,2,2] (.node [11,11,10,10,4,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,10,4,4,3,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_222 : RowTree := (.node [11,11,10,10,5,2,2,2,2,2,2,1,1,1] (.node [11,11,10,10,4,4,4,2,2,1,1,1,1] (.node [11,11,10,10,4,4,3,3,2,2,1,1] (.node [11,11,10,10,4,4,3,3,2,1,1,1,1] (.node [11,11,10,10,4,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,4,4,4,2,1,1,1,1,1,1] (.node [11,11,10,10,4,4,3,3,3,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,4,4,4,3,2,1,1,1] (.node [11,11,10,10,4,4,4,3,1,1,1,1,1] (.node [11,11,10,10,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,10,4,4,4,4,1,1,1,1] .empty .empty))) (.node [11,11,10,10,5,3,3,2,2,2,1,1,1] (.node [11,11,10,10,5,3,2,2,2,2,2,1,1] (.node [11,11,10,10,5,3,2,2,2,2,1,1,1,1] (.node [11,11,10,10,5,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,10,5,3,3,2,2,1,1,1,1,1] (.node [11,11,10,10,5,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,10,10,5,3,3,3,2,1,1,1,1] (.node [11,11,10,10,5,3,3,3,1,1,1,1,1,1] (.node [11,11,10,10,5,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,10,5,3,3,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_223 : RowTree := (.node [11,11,10,10,4,4,3,2,2,2,2,1] degreeTree62_221 degreeTree62_222) - -def degreeTree62_224 : RowTree := (.node [11,11,10,10,5,4,4,2,2,1,1,1] (.node [11,11,10,10,5,4,3,2,2,2,1,1] (.node [11,11,10,10,5,4,2,2,2,2,2,1] (.node [11,11,10,10,5,4,2,2,2,2,1,1,1] (.node [11,11,10,10,5,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,5,4,3,2,2,1,1,1,1] (.node [11,11,10,10,5,4,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,5,4,4,1,1,1,1,1,1,1] (.node [11,11,10,10,5,4,3,3,2,1,1,1] (.node [11,11,10,10,5,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,5,4,4,2,1,1,1,1,1] .empty .empty))) (.node [11,11,10,10,5,5,3,2,1,1,1,1,1] (.node [11,11,10,10,5,5,2,2,2,1,1,1,1] (.node [11,11,10,10,5,5,2,2,1,1,1,1,1,1] (.node [11,11,10,10,5,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,5,5,3,1,1,1,1,1,1,1] (.node [11,11,10,10,5,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,10,5,5,4,1,1,1,1,1,1] (.node [11,11,10,10,5,5,3,3,1,1,1,1] (.node [11,11,10,10,5,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,5,5,4,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_225 : RowTree := (.node [11,11,10,10,6,3,3,3,2,1,1,1] (.node [11,11,10,10,6,3,2,2,2,2,2,1] (.node [11,11,10,10,6,2,2,2,2,2,2,2] (.node [11,11,10,10,6,2,2,2,2,2,2,1,1] (.node [11,11,10,10,6,2,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,6,3,2,2,2,2,1,1,1] (.node [11,11,10,10,6,3,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,6,3,3,2,2,2,1,1] (.node [11,11,10,10,6,3,3,2,2,1,1,1,1] (.node [11,11,10,10,6,3,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,6,3,3,3,1,1,1,1,1] .empty .empty))) (.node [11,11,10,10,6,4,3,2,2,1,1,1] (.node [11,11,10,10,6,4,2,2,2,2,1,1] (.node [11,11,10,10,6,4,2,2,2,1,1,1,1] (.node [11,11,10,10,6,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,6,4,3,2,1,1,1,1,1] (.node [11,11,10,10,6,4,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,6,4,4,2,1,1,1,1] (.node [11,11,10,10,6,4,4,1,1,1,1,1,1] (.node [11,11,10,10,6,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,6,5,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_226 : RowTree := (.node [11,11,10,10,5,5,5,1,1,1,1,1] degreeTree62_224 degreeTree62_225) - -def degreeTree62_227 : RowTree := (.node [11,11,10,10,5,3,3,3,3,1,1,1] degreeTree62_223 degreeTree62_226) - -def degreeTree62_228 : RowTree := (.node [11,11,10,10,7,2,2,2,2,2,2,1] (.node [11,11,10,10,6,6,2,1,1,1,1,1,1] (.node [11,11,10,10,6,5,3,2,1,1,1,1] (.node [11,11,10,10,6,5,3,1,1,1,1,1,1] (.node [11,11,10,10,6,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,6,6,1,1,1,1,1,1,1,1] (.node [11,11,10,10,6,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,7,2,2,2,2,1,1,1,1,1] (.node [11,11,10,10,6,6,3,1,1,1,1,1] (.node [11,11,10,10,6,6,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,7,2,2,2,2,2,1,1,1] .empty .empty))) (.node [11,11,10,10,7,3,3,2,2,1,1,1] (.node [11,11,10,10,7,3,2,2,2,2,1,1] (.node [11,11,10,10,7,3,2,2,2,1,1,1,1] (.node [11,11,10,10,7,3,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,7,3,3,2,1,1,1,1,1] (.node [11,11,10,10,7,3,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,7,4,2,2,1,1,1,1,1] (.node [11,11,10,10,7,4,2,1,1,1,1,1,1,1] (.node [11,11,10,10,7,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,7,4,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_229 : RowTree := (.node [11,11,10,10,8,2,2,2,2,1,1,1,1] (.node [11,11,10,10,7,5,3,1,1,1,1,1] (.node [11,11,10,10,7,5,1,1,1,1,1,1,1,1] (.node [11,11,10,10,7,4,4,1,1,1,1,1] (.node [11,11,10,10,7,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,7,5,2,2,1,1,1,1] (.node [11,11,10,10,7,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,7,7,1,1,1,1,1,1] (.node [11,11,10,10,7,6,2,1,1,1,1,1] (.node [11,11,10,10,7,6,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,8,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [11,11,10,10,8,3,3,2,1,1,1,1] (.node [11,11,10,10,8,3,2,2,1,1,1,1,1] (.node [11,11,10,10,8,3,2,1,1,1,1,1,1,1] (.node [11,11,10,10,8,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,10,8,3,3,1,1,1,1,1,1] (.node [11,11,10,10,8,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,8,4,2,2,1,1,1,1] (.node [11,11,10,10,8,4,2,1,1,1,1,1,1] (.node [11,11,10,10,8,4,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,8,4,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_230 : RowTree := (.node [11,11,10,10,7,4,3,1,1,1,1,1,1] degreeTree62_228 degreeTree62_229) - -def degreeTree62_231 : RowTree := (.node [11,11,10,10,9,4,2,1,1,1,1,1] (.node [11,11,10,10,9,3,1,1,1,1,1,1,1,1] (.node [11,11,10,10,9,2,2,1,1,1,1,1,1,1] (.node [11,11,10,10,8,6,1,1,1,1,1,1] (.node [11,11,10,10,8,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,9,2,2,2,2,1,1,1] (.node [11,11,10,10,9,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,9,3,3,1,1,1,1,1] (.node [11,11,10,10,9,3,2,2,1,1,1,1] (.node [11,11,10,10,9,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,9,4,1,1,1,1,1,1,1] .empty .empty))) (.node [11,11,10,10,10,3,2,1,1,1,1,1] (.node [11,11,10,10,10,2,2,1,1,1,1,1,1] (.node [11,11,10,10,10,2,1,1,1,1,1,1,1,1] (.node [11,11,10,10,9,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,10,3,1,1,1,1,1,1,1] (.node [11,11,10,10,10,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,4,4,4,4,4,3,3,3] (.node [11,11,11,4,4,4,4,4,3,2,2,1,1] (.node [11,11,10,10,10,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,4,4,4,4,4,4,2,1,1,1] .empty .empty)))) - -def degreeTree62_232 : RowTree := (.node [11,11,11,5,5,4,3,3,3,3,3] (.node [11,11,11,5,4,4,4,4,3,2,2,1] (.node [11,11,11,5,4,4,4,3,3,3,3] (.node [11,11,11,5,4,4,4,3,3,2,2,1,1] (.node [11,11,11,5,4,4,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,11,5,4,4,4,4,3,2,1,1,1] (.node [11,11,11,5,4,4,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,11,5,5,4,3,2,2,2,2,2,2] (.node [11,11,11,5,4,4,4,4,4,2,1,1] (.node [11,11,11,5,4,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,5,5,4,3,3,3,2,2,1,1] .empty .empty))) (.node [11,11,11,5,5,4,4,4,2,2,1,1,1] (.node [11,11,11,5,5,4,4,3,3,2,1,1,1] (.node [11,11,11,5,5,4,4,3,2,2,2,1,1] (.node [11,11,11,5,5,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,5,5,4,4,3,3,2,2,1] .empty .empty)) (.node [11,11,11,5,5,4,4,4,3,2,1,1] (.node [11,11,11,5,5,4,4,4,3,1,1,1,1] (.node [11,11,11,5,5,4,4,4,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,5,5,4,4,4,4,1,1,1] .empty .empty)))) - -def degreeTree62_233 : RowTree := (.node [11,11,11,4,4,4,4,4,4,2,2,1] degreeTree62_231 degreeTree62_232) - -def degreeTree62_234 : RowTree := (.node [11,11,10,10,8,5,1,1,1,1,1,1,1] degreeTree62_230 degreeTree62_233) - -def degreeTree62_235 : RowTree := (.node [11,11,10,10,6,5,2,2,1,1,1,1,1] degreeTree62_227 degreeTree62_234) - -def degreeTree62_236 : RowTree := (.node [11,11,11,5,5,5,4,4,2,1,1,1,1] (.node [11,11,11,5,5,5,4,2,2,2,2,2] (.node [11,11,11,5,5,5,3,3,3,2,1,1,1] (.node [11,11,11,5,5,5,3,3,2,2,2,1,1] (.node [11,11,11,5,5,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,5,5,5,4,2,2,2,2,1,1] (.node [11,11,11,5,5,5,3,3,3,2,2,1] .empty .empty) .empty)) (.node [11,11,11,5,5,5,4,3,3,1,1,1,1] (.node [11,11,11,5,5,5,4,3,2,2,2,1] (.node [11,11,11,5,5,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,5,5,5,4,3,3,2,1,1] .empty .empty))) (.node [11,11,11,5,5,5,5,3,2,2,1,1] (.node [11,11,11,5,5,5,5,2,2,2,1,1,1] (.node [11,11,11,5,5,5,4,4,3,1,1,1] (.node [11,11,11,5,5,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,5,5,5,5,3,2,1,1,1,1] (.node [11,11,11,5,5,5,5,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,5,5,5,5,4,2,1,1,1] (.node [11,11,11,5,5,5,5,4,1,1,1,1,1] (.node [11,11,11,5,5,5,5,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,11,5,5,5,5,5,1,1,1,1] .empty .empty)))) - -def degreeTree62_237 : RowTree := (.node [11,11,11,6,4,4,4,4,2,2,2,1] (.node [11,11,11,6,4,4,4,3,3,1,1,1,1,1] (.node [11,11,11,6,4,4,4,2,2,2,2,1,1,1] (.node [11,11,11,6,4,4,3,3,3,3,3] (.node [11,11,11,6,4,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,4,4,4,3,2,2,2,1,1] (.node [11,11,11,6,4,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,6,4,4,4,4,2,1,1,1,1,1] (.node [11,11,11,6,4,4,4,3,3,2,2,1] (.node [11,11,11,6,4,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,4,4,4,4,2,2,1,1,1] .empty .empty))) (.node [11,11,11,6,5,4,2,2,2,2,2,2,2] (.node [11,11,11,6,4,4,4,4,4,1,1,1] (.node [11,11,11,6,4,4,4,4,3,2,1,1] (.node [11,11,11,6,4,4,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,5,3,3,3,3,2,2,1,1] (.node [11,11,11,6,5,3,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,6,5,4,3,3,2,2,2,1,1] (.node [11,11,11,6,5,4,3,2,2,2,2,2,1] (.node [11,11,11,6,5,4,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,5,4,3,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_238 : RowTree := (.node [11,11,11,6,4,4,3,2,2,2,2,2,2] degreeTree62_236 degreeTree62_237) - -def degreeTree62_239 : RowTree := (.node [11,11,11,6,5,4,4,4,2,1,1,1,1] (.node [11,11,11,6,5,4,4,3,2,2,1,1,1] (.node [11,11,11,6,5,4,4,2,2,2,2,1,1] (.node [11,11,11,6,5,4,4,2,2,2,1,1,1,1] (.node [11,11,11,6,5,4,3,3,3,2,2,1] .empty .empty) .empty) (.node [11,11,11,6,5,4,4,3,2,1,1,1,1,1] (.node [11,11,11,6,5,4,4,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,6,5,4,4,3,3,2,1,1] (.node [11,11,11,6,5,4,4,3,3,1,1,1,1] (.node [11,11,11,6,5,4,4,3,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,6,5,4,4,4,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,6,5,5,3,2,2,2,2,1,1] (.node [11,11,11,6,5,5,2,2,2,2,2,1,1,1] (.node [11,11,11,6,5,4,4,4,3,1,1,1] (.node [11,11,11,6,5,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,5,5,3,2,2,2,1,1,1,1] (.node [11,11,11,6,5,5,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,6,5,5,3,3,2,2,1,1,1] (.node [11,11,11,6,5,5,3,3,2,1,1,1,1,1] (.node [11,11,11,6,5,5,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,11,6,5,5,3,3,2,2,2,1] .empty .empty)))) - -def degreeTree62_240 : RowTree := (.node [11,11,11,6,5,5,5,2,1,1,1,1,1,1] (.node [11,11,11,6,5,5,4,3,2,1,1,1,1] (.node [11,11,11,6,5,5,4,2,2,2,1,1,1] (.node [11,11,11,6,5,5,4,2,2,1,1,1,1,1] (.node [11,11,11,6,5,5,3,3,3,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,5,5,4,3,1,1,1,1,1,1] (.node [11,11,11,6,5,5,4,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,6,5,5,4,4,1,1,1,1,1] (.node [11,11,11,6,5,5,4,3,3,1,1,1] (.node [11,11,11,6,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,5,5,4,4,2,1,1,1] .empty .empty))) (.node [11,11,11,6,6,2,2,2,2,2,2,2,2,1] (.node [11,11,11,6,5,5,5,3,1,1,1,1,1] (.node [11,11,11,6,5,5,5,2,2,2,1,1] (.node [11,11,11,6,5,5,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,5,5,5,4,1,1,1,1] (.node [11,11,11,6,5,5,5,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,6,6,3,3,2,2,2,2,2,1] (.node [11,11,11,6,6,3,3,2,2,2,2,1,1,1] (.node [11,11,11,6,6,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,11,6,6,3,3,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_241 : RowTree := (.node [11,11,11,6,5,5,3,3,3,1,1,1,1] degreeTree62_239 degreeTree62_240) - -def degreeTree62_242 : RowTree := (.node [11,11,11,6,5,4,3,3,3,2,1,1,1] degreeTree62_238 degreeTree62_241) - -def degreeTree62_243 : RowTree := (.node [11,11,11,6,6,4,3,3,3,1,1,1,1] (.node [11,11,11,6,6,4,3,2,2,2,2,1,1] (.node [11,11,11,6,6,4,2,2,2,2,2,1,1,1] (.node [11,11,11,6,6,3,3,3,3,2,2,1] (.node [11,11,11,6,6,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,4,3,2,2,2,1,1,1,1] (.node [11,11,11,6,6,4,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,6,6,4,3,3,2,2,1,1,1] (.node [11,11,11,6,6,4,3,3,2,1,1,1,1,1] (.node [11,11,11,6,6,4,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,11,6,6,4,3,3,2,2,2,1] .empty .empty))) (.node [11,11,11,6,6,4,4,3,2,1,1,1,1] (.node [11,11,11,6,6,4,4,2,2,2,1,1,1] (.node [11,11,11,6,6,4,4,2,2,1,1,1,1,1] (.node [11,11,11,6,6,4,3,3,3,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,4,4,3,1,1,1,1,1,1] (.node [11,11,11,6,6,4,4,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,6,6,4,4,4,1,1,1,1,1] (.node [11,11,11,6,6,4,4,3,3,1,1,1] (.node [11,11,11,6,6,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,4,4,4,2,1,1,1] .empty .empty)))) - -def degreeTree62_244 : RowTree := (.node [11,11,11,6,6,5,4,2,2,1,1,1,1] (.node [11,11,11,6,6,5,3,3,1,1,1,1,1,1] (.node [11,11,11,6,6,5,3,2,2,1,1,1,1,1] (.node [11,11,11,6,6,5,2,2,2,2,2,2] (.node [11,11,11,6,6,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,5,3,2,2,2,2,1] (.node [11,11,11,6,6,5,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,6,6,5,3,3,3,1,1,1] (.node [11,11,11,6,6,5,3,3,2,2,1,1] (.node [11,11,11,6,6,5,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,5,4,2,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,6,6,5,5,2,1,1,1,1,1] (.node [11,11,11,6,6,5,4,3,2,1,1,1] (.node [11,11,11,6,6,5,4,3,1,1,1,1,1] (.node [11,11,11,6,6,5,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,5,5,1,1,1,1,1,1,1] (.node [11,11,11,6,6,5,4,4,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,6,6,6,2,2,2,1,1,1,1,1] (.node [11,11,11,6,6,5,5,3,1,1,1,1] (.node [11,11,11,6,6,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,6,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_245 : RowTree := (.node [11,11,11,6,6,5,2,2,2,2,1,1,1,1] degreeTree62_243 degreeTree62_244) - -def degreeTree62_246 : RowTree := (.node [11,11,11,6,6,6,5,2,1,1,1,1] (.node [11,11,11,6,6,6,4,1,1,1,1,1,1,1] (.node [11,11,11,6,6,6,3,2,2,2,1,1] (.node [11,11,11,6,6,6,3,2,2,1,1,1,1] (.node [11,11,11,6,6,6,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,6,3,3,2,1,1,1] (.node [11,11,11,6,6,6,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,6,6,6,4,3,1,1,1,1] (.node [11,11,11,6,6,6,4,2,2,1,1,1] (.node [11,11,11,6,6,6,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,6,5,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,7,4,4,3,2,2,2,2,2,1] (.node [11,11,11,7,4,3,3,3,3,2,2,1,1] (.node [11,11,11,7,4,3,3,2,2,2,2,2,2] (.node [11,11,11,6,6,6,6,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,4,4,3,2,2,2,2,1,1,1] (.node [11,11,11,7,4,4,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,7,4,4,3,3,3,2,1,1,1] (.node [11,11,11,7,4,4,3,3,3,1,1,1,1,1] (.node [11,11,11,7,4,4,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,7,4,4,3,3,3,2,2,1] .empty .empty)))) - -def degreeTree62_247 : RowTree := (.node [11,11,11,7,4,4,4,4,3,1,1,1] (.node [11,11,11,7,4,4,4,3,3,1,1,1,1] (.node [11,11,11,7,4,4,4,3,2,1,1,1,1,1] (.node [11,11,11,7,4,4,4,2,2,2,2,2] (.node [11,11,11,7,4,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,7,4,4,4,3,2,2,2,1] (.node [11,11,11,7,4,4,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,4,4,4,4,2,1,1,1,1] (.node [11,11,11,7,4,4,4,4,1,1,1,1,1,1] (.node [11,11,11,7,4,4,4,3,3,2,1,1] .empty .empty) .empty) (.node [11,11,11,7,4,4,4,4,2,2,1,1] .empty .empty))) (.node [11,11,11,7,5,3,3,3,2,2,2,1,1] (.node [11,11,11,7,5,3,3,2,2,2,2,1,1,1] (.node [11,11,11,7,5,3,2,2,2,2,2,2,2] (.node [11,11,11,7,5,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,7,5,3,3,2,2,2,2,2,1] .empty .empty)) (.node [11,11,11,7,5,3,3,3,3,2,2,1] (.node [11,11,11,7,5,3,3,3,3,2,1,1,1] (.node [11,11,11,7,5,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,5,4,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_248 : RowTree := (.node [11,11,11,7,4,4,4,2,2,2,1,1,1,1] degreeTree62_246 degreeTree62_247) - -def degreeTree62_249 : RowTree := (.node [11,11,11,6,6,6,2,2,2,2,2,1] degreeTree62_245 degreeTree62_248) - -def degreeTree62_250 : RowTree := (.node [11,11,11,6,6,3,3,3,3,1,1,1,1,1] degreeTree62_242 degreeTree62_249) - -def degreeTree62_251 : RowTree := (.node [11,11,11,5,5,5,2,2,2,2,2,2,2] degreeTree62_235 degreeTree62_250) - -def degreeTree62_252 : RowTree := (.node [11,11,10,10,3,3,3,2,2,2,2,2,1] degreeTree62_220 degreeTree62_251) - -def degreeTree62_253 : RowTree := (.node [11,11,10,8,5,4,3,2,2,2,1,1,1,1] degreeTree62_189 degreeTree62_252) - -def degreeTree62_254 : RowTree := (.node [11,10,10,9,9,4,2,1,1,1,1,1,1,1] degreeTree62_126 degreeTree62_253) - -def degreeTree62_255 : RowTree := (.node [11,11,11,7,5,4,4,2,2,2,2,1] (.node [11,11,11,7,5,4,3,3,2,2,2,1] (.node [11,11,11,7,5,4,3,2,2,2,2,2] (.node [11,11,11,7,5,4,3,2,2,2,2,1,1] (.node [11,11,11,7,5,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,5,4,3,3,2,2,1,1,1] (.node [11,11,11,7,5,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,5,4,4,2,2,1,1,1,1,1] (.node [11,11,11,7,5,4,3,3,3,2,1,1] (.node [11,11,11,7,5,4,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,5,4,4,2,2,2,1,1,1] .empty .empty))) (.node [11,11,11,7,5,4,4,4,2,1,1,1] (.node [11,11,11,7,5,4,4,3,2,2,1,1] (.node [11,11,11,7,5,4,4,3,2,1,1,1,1] (.node [11,11,11,7,5,4,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,5,4,4,4,1,1,1,1,1] (.node [11,11,11,7,5,4,4,3,3,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,5,5,2,2,2,2,2,2] (.node [11,11,11,7,5,5,2,2,2,2,2,1,1] (.node [11,11,11,7,5,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,5,5,3,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_256 : RowTree := (.node [11,11,11,7,5,5,4,4,1,1,1,1] (.node [11,11,11,7,5,5,4,2,1,1,1,1,1,1] (.node [11,11,11,7,5,5,3,3,2,1,1,1,1] (.node [11,11,11,7,5,5,3,3,1,1,1,1,1,1] (.node [11,11,11,7,5,5,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,7,5,5,3,3,3,1,1,1] (.node [11,11,11,7,5,5,3,3,2,2,1,1] .empty .empty) .empty)) (.node [11,11,11,7,5,5,4,3,1,1,1,1,1] (.node [11,11,11,7,5,5,4,2,2,2,1,1] (.node [11,11,11,7,5,5,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,5,5,4,3,2,1,1,1] .empty .empty))) (.node [11,11,11,7,6,2,2,2,2,2,2,2,2] (.node [11,11,11,7,5,5,5,2,2,1,1,1] (.node [11,11,11,7,5,5,5,2,1,1,1,1,1] (.node [11,11,11,7,5,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,2,2,2,2,2,2,2,1,1] (.node [11,11,11,7,5,5,5,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,6,3,3,2,2,2,1,1,1,1] (.node [11,11,11,7,6,3,2,2,2,2,2,2,1] (.node [11,11,11,7,6,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,3,3,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_257 : RowTree := (.node [11,11,11,7,5,5,3,2,2,2,1,1,1] degreeTree62_255 degreeTree62_256) - -def degreeTree62_258 : RowTree := (.node [11,11,11,7,6,4,3,2,2,2,2,1] (.node [11,11,11,7,6,4,2,2,2,2,1,1,1,1] (.node [11,11,11,7,6,3,3,3,2,2,2,1] (.node [11,11,11,7,6,3,3,3,2,2,1,1,1] (.node [11,11,11,7,6,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,3,3,3,3,2,1,1] (.node [11,11,11,7,6,3,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,6,4,3,2,2,1,1,1,1,1] (.node [11,11,11,7,6,4,2,2,2,2,2,2] (.node [11,11,11,7,6,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,4,3,2,2,2,1,1,1] .empty .empty))) (.node [11,11,11,7,6,4,4,2,2,1,1,1,1] (.node [11,11,11,7,6,4,3,3,2,2,1,1] (.node [11,11,11,7,6,4,3,3,2,1,1,1,1] (.node [11,11,11,7,6,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,4,4,2,1,1,1,1,1,1] (.node [11,11,11,7,6,4,3,3,3,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,6,4,4,3,2,1,1,1] (.node [11,11,11,7,6,4,4,3,1,1,1,1,1] (.node [11,11,11,7,6,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,4,4,4,1,1,1,1] .empty .empty)))) - -def degreeTree62_259 : RowTree := (.node [11,11,11,7,6,5,4,3,1,1,1,1] (.node [11,11,11,7,6,5,3,3,1,1,1,1,1] (.node [11,11,11,7,6,5,3,2,1,1,1,1,1,1] (.node [11,11,11,7,6,5,2,2,2,2,2,1] (.node [11,11,11,7,6,5,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,5,3,2,2,2,1,1] (.node [11,11,11,7,6,5,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,6,5,4,2,1,1,1,1,1] (.node [11,11,11,7,6,5,4,1,1,1,1,1,1,1] (.node [11,11,11,7,6,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,5,4,2,2,1,1,1] .empty .empty))) (.node [11,11,11,7,6,6,3,1,1,1,1,1,1,1] (.node [11,11,11,7,6,6,2,2,1,1,1,1,1,1] (.node [11,11,11,7,6,5,5,2,1,1,1,1] (.node [11,11,11,7,6,5,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,6,2,2,2,2,1,1] (.node [11,11,11,7,6,6,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,6,6,3,3,1,1,1,1] (.node [11,11,11,7,6,6,3,2,2,1,1,1] (.node [11,11,11,7,6,6,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,6,4,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_260 : RowTree := (.node [11,11,11,7,6,5,2,2,2,1,1,1,1,1] degreeTree62_258 degreeTree62_259) - -def degreeTree62_261 : RowTree := (.node [11,11,11,7,6,3,3,2,2,2,2,2] degreeTree62_257 degreeTree62_260) - -def degreeTree62_262 : RowTree := (.node [11,11,11,7,7,3,3,3,2,1,1,1,1] (.node [11,11,11,7,7,3,2,2,2,2,2,2] (.node [11,11,11,7,7,2,2,2,2,2,2,2,1] (.node [11,11,11,7,7,2,2,2,2,2,2,1,1,1] (.node [11,11,11,7,6,6,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,3,2,2,2,2,2,1,1] (.node [11,11,11,7,7,3,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,7,3,3,2,2,2,2,1] (.node [11,11,11,7,7,3,3,2,2,2,1,1,1] (.node [11,11,11,7,7,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,7,7,4,3,2,1,1,1,1,1,1] (.node [11,11,11,7,7,4,2,2,2,1,1,1,1,1] (.node [11,11,11,7,7,3,3,3,3,1,1,1] (.node [11,11,11,7,7,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,4,2,2,2,2,2,1] (.node [11,11,11,7,7,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,7,4,3,3,1,1,1,1,1] (.node [11,11,11,7,7,4,3,2,2,2,1,1] (.node [11,11,11,7,7,4,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,4,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_263 : RowTree := (.node [11,11,11,7,7,5,4,1,1,1,1,1,1] (.node [11,11,11,7,7,5,2,2,2,2,1,1] (.node [11,11,11,7,7,4,4,3,1,1,1,1] (.node [11,11,11,7,7,4,4,2,2,1,1,1] (.node [11,11,11,7,7,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,5,2,2,2,1,1,1,1] (.node [11,11,11,7,7,5,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,7,5,3,2,2,1,1,1] (.node [11,11,11,7,7,5,3,2,1,1,1,1,1] (.node [11,11,11,7,7,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,5,3,3,1,1,1,1] .empty .empty))) (.node [11,11,11,7,7,6,3,1,1,1,1,1,1] (.node [11,11,11,7,7,6,2,1,1,1,1,1,1,1] (.node [11,11,11,7,7,5,5,1,1,1,1,1] (.node [11,11,11,7,7,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,6,2,2,2,1,1,1] (.node [11,11,11,7,7,6,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,7,7,1,1,1,1,1,1,1,1] (.node [11,11,11,7,7,6,4,1,1,1,1,1] (.node [11,11,11,7,7,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,7,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_264 : RowTree := (.node [11,11,11,7,7,4,4,1,1,1,1,1,1,1] degreeTree62_262 degreeTree62_263) - -def degreeTree62_265 : RowTree := (.node [11,11,11,8,4,3,3,3,3,2,2,1] (.node [11,11,11,8,4,3,3,2,2,2,2,1,1,1] (.node [11,11,11,8,3,3,3,3,3,2,2,1,1] (.node [11,11,11,8,3,3,3,2,2,2,2,2,2] (.node [11,11,11,7,7,7,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,4,3,2,2,2,2,2,2,2] (.node [11,11,11,8,4,2,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,8,4,3,3,3,3,1,1,1,1,1] (.node [11,11,11,8,4,3,3,3,2,2,2,1,1] (.node [11,11,11,8,4,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,8,4,3,3,3,3,2,1,1,1] .empty .empty))) (.node [11,11,11,8,4,4,3,3,2,1,1,1,1,1] (.node [11,11,11,8,4,4,3,2,2,2,1,1,1,1] (.node [11,11,11,8,4,4,2,2,2,2,2,2,1] (.node [11,11,11,8,4,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,4,4,3,2,2,2,2,2] (.node [11,11,11,8,4,4,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,11,8,4,4,3,3,3,1,1,1,1] (.node [11,11,11,8,4,4,3,3,2,2,2,1] (.node [11,11,11,8,4,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,4,4,3,3,3,2,1,1] .empty .empty)))) - -def degreeTree62_266 : RowTree := (.node [11,11,11,8,5,3,2,2,2,2,2,1,1,1] (.node [11,11,11,8,4,4,4,3,3,1,1,1] (.node [11,11,11,8,4,4,4,3,1,1,1,1,1,1] (.node [11,11,11,8,4,4,4,2,2,2,2,1] (.node [11,11,11,8,4,4,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,4,4,4,3,2,2,1,1] (.node [11,11,11,8,4,4,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,5,2,2,2,2,2,2,2,1,1] (.node [11,11,11,8,4,4,4,4,2,1,1,1] (.node [11,11,11,8,4,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,5,2,2,2,2,2,2,2,2] .empty .empty))) (.node [11,11,11,8,5,3,3,3,2,2,1,1,1] (.node [11,11,11,8,5,3,3,2,2,2,2,1,1] (.node [11,11,11,8,5,3,3,2,2,2,1,1,1,1] (.node [11,11,11,8,5,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,8,5,3,3,3,2,1,1,1,1,1] (.node [11,11,11,8,5,3,3,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,8,5,3,3,3,3,2,1,1] (.node [11,11,11,8,5,3,3,3,3,1,1,1,1] (.node [11,11,11,8,5,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,8,5,4,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_267 : RowTree := (.node [11,11,11,8,4,4,4,2,2,1,1,1,1,1] degreeTree62_265 degreeTree62_266) - -def degreeTree62_268 : RowTree := (.node [11,11,11,7,7,7,2,2,1,1,1,1] degreeTree62_264 degreeTree62_267) - -def degreeTree62_269 : RowTree := (.node [11,11,11,7,6,6,4,2,1,1,1,1] degreeTree62_261 degreeTree62_268) - -def degreeTree62_270 : RowTree := (.node [11,11,11,8,5,4,4,2,2,2,1,1] (.node [11,11,11,8,5,4,3,3,2,1,1,1,1] (.node [11,11,11,8,5,4,3,2,2,2,1,1,1] (.node [11,11,11,8,5,4,3,2,2,1,1,1,1,1] (.node [11,11,11,8,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,11,8,5,4,3,3,1,1,1,1,1,1] (.node [11,11,11,8,5,4,3,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,8,5,4,4,2,1,1,1,1,1,1] (.node [11,11,11,8,5,4,3,3,3,1,1,1] (.node [11,11,11,8,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,8,5,4,4,2,2,1,1,1,1] .empty .empty))) (.node [11,11,11,8,5,5,2,2,2,2,2,1] (.node [11,11,11,8,5,4,4,4,1,1,1,1] (.node [11,11,11,8,5,4,4,3,2,1,1,1] (.node [11,11,11,8,5,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,5,5,2,2,2,2,1,1,1] (.node [11,11,11,8,5,5,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,5,5,3,2,2,2,1,1] (.node [11,11,11,8,5,5,3,2,2,1,1,1,1] (.node [11,11,11,8,5,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,5,5,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_271 : RowTree := (.node [11,11,11,8,6,3,2,2,2,2,2,2] (.node [11,11,11,8,5,5,5,2,1,1,1,1] (.node [11,11,11,8,5,5,4,2,2,1,1,1] (.node [11,11,11,8,5,5,4,2,1,1,1,1,1] (.node [11,11,11,8,5,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,5,5,5,1,1,1,1,1,1] (.node [11,11,11,8,5,5,4,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,6,3,2,2,2,2,1,1,1,1] (.node [11,11,11,8,6,2,2,2,2,2,2,2,1] (.node [11,11,11,8,6,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,3,2,2,2,2,2,1,1] .empty .empty))) (.node [11,11,11,8,6,3,3,3,2,2,1,1] (.node [11,11,11,8,6,3,3,2,2,2,2,1] (.node [11,11,11,8,6,3,3,2,2,2,1,1,1] (.node [11,11,11,8,6,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,3,3,3,2,1,1,1,1] (.node [11,11,11,8,6,3,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,6,4,2,2,2,2,1,1,1] (.node [11,11,11,8,6,4,2,2,2,1,1,1,1,1] (.node [11,11,11,8,6,3,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,4,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_272 : RowTree := (.node [11,11,11,8,5,5,3,3,2,1,1,1] degreeTree62_270 degreeTree62_271) - -def degreeTree62_273 : RowTree := (.node [11,11,11,8,6,5,2,2,2,2,1,1] (.node [11,11,11,8,6,4,4,2,1,1,1,1,1] (.node [11,11,11,8,6,4,3,3,1,1,1,1,1] (.node [11,11,11,8,6,4,3,2,2,2,1,1] (.node [11,11,11,8,6,4,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,4,4,1,1,1,1,1,1,1] (.node [11,11,11,8,6,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,6,5,2,2,1,1,1,1,1,1] (.node [11,11,11,8,6,4,4,3,1,1,1,1] (.node [11,11,11,8,6,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,5,2,2,2,1,1,1,1] .empty .empty))) (.node [11,11,11,8,6,5,4,2,1,1,1,1] (.node [11,11,11,8,6,5,3,2,2,1,1,1] (.node [11,11,11,8,6,5,3,2,1,1,1,1,1] (.node [11,11,11,8,6,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,5,4,1,1,1,1,1,1] (.node [11,11,11,8,6,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,6,6,2,2,1,1,1,1,1] (.node [11,11,11,8,6,6,2,1,1,1,1,1,1,1] (.node [11,11,11,8,6,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,6,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_274 : RowTree := (.node [11,11,11,8,7,3,3,2,2,2,1,1] (.node [11,11,11,8,7,3,2,2,2,1,1,1,1,1] (.node [11,11,11,8,7,2,2,2,2,2,1,1,1,1] (.node [11,11,11,8,6,6,4,1,1,1,1,1] (.node [11,11,11,8,6,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,7,2,2,2,2,2,2,2] (.node [11,11,11,8,7,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,11,8,7,3,3,2,1,1,1,1,1,1] (.node [11,11,11,8,7,3,2,2,2,2,2,1] (.node [11,11,11,8,7,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,7,3,3,2,2,1,1,1,1] .empty .empty))) (.node [11,11,11,8,7,4,3,1,1,1,1,1,1,1] (.node [11,11,11,8,7,4,2,2,1,1,1,1,1,1] (.node [11,11,11,8,7,3,3,3,2,1,1,1] (.node [11,11,11,8,7,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,7,4,2,2,2,2,1,1] (.node [11,11,11,8,7,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,7,4,3,3,1,1,1,1] (.node [11,11,11,8,7,4,3,2,2,1,1,1] (.node [11,11,11,8,7,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,7,4,4,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_275 : RowTree := (.node [11,11,11,8,6,6,3,1,1,1,1,1,1] degreeTree62_273 degreeTree62_274) - -def degreeTree62_276 : RowTree := (.node [11,11,11,8,6,4,3,2,1,1,1,1,1,1] degreeTree62_272 degreeTree62_275) - -def degreeTree62_277 : RowTree := (.node [11,11,11,8,7,7,1,1,1,1,1,1,1] (.node [11,11,11,8,7,5,4,1,1,1,1,1] (.node [11,11,11,8,7,5,2,2,2,1,1,1] (.node [11,11,11,8,7,5,2,2,1,1,1,1,1] (.node [11,11,11,8,7,5,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,7,5,3,2,1,1,1,1] (.node [11,11,11,8,7,5,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,7,6,2,2,1,1,1,1] (.node [11,11,11,8,7,6,2,1,1,1,1,1,1] (.node [11,11,11,8,7,6,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,7,6,3,1,1,1,1,1] .empty .empty))) (.node [11,11,11,8,8,3,2,2,2,1,1,1,1] (.node [11,11,11,8,8,2,2,2,2,2,1,1,1] (.node [11,11,11,8,8,2,2,2,2,1,1,1,1,1] (.node [11,11,11,8,7,7,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,8,3,2,2,1,1,1,1,1,1] (.node [11,11,11,8,8,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,8,8,3,3,2,1,1,1,1,1] (.node [11,11,11,8,8,3,3,1,1,1,1,1,1,1] (.node [11,11,11,8,8,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,8,8,3,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_278 : RowTree := (.node [11,11,11,8,8,6,1,1,1,1,1,1,1] (.node [11,11,11,8,8,4,4,1,1,1,1,1] (.node [11,11,11,8,8,4,2,2,2,1,1,1] (.node [11,11,11,8,8,4,2,2,1,1,1,1,1] (.node [11,11,11,8,8,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,8,4,3,2,1,1,1,1] (.node [11,11,11,8,8,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,8,5,2,2,1,1,1,1] (.node [11,11,11,8,8,5,2,1,1,1,1,1,1] (.node [11,11,11,8,8,5,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,8,5,3,1,1,1,1,1] .empty .empty))) (.node [11,11,11,9,3,3,3,2,2,2,2,2,1] (.node [11,11,11,9,3,2,2,2,2,2,2,2,2,1] (.node [11,11,11,8,8,7,1,1,1,1,1,1] (.node [11,11,11,8,8,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,3,3,3,2,2,2,2,1,1,1] (.node [11,11,11,9,3,3,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,9,3,3,3,3,3,2,1,1,1] (.node [11,11,11,9,3,3,3,3,3,1,1,1,1,1] (.node [11,11,11,9,3,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,9,3,3,3,3,3,2,2,1] .empty .empty)))) - -def degreeTree62_279 : RowTree := (.node [11,11,11,8,8,3,3,3,1,1,1,1] degreeTree62_277 degreeTree62_278) - -def degreeTree62_280 : RowTree := (.node [11,11,11,9,4,3,3,3,3,2,1,1] (.node [11,11,11,9,4,3,3,2,2,2,2,2] (.node [11,11,11,9,4,3,2,2,2,2,2,2,1] (.node [11,11,11,9,4,3,2,2,2,2,2,1,1,1] (.node [11,11,11,9,4,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,11,9,4,3,3,2,2,2,2,1,1] (.node [11,11,11,9,4,3,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,4,3,3,3,2,2,2,1] (.node [11,11,11,9,4,3,3,3,2,2,1,1,1] (.node [11,11,11,9,4,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,4,3,3,3,3,1,1,1,1] .empty .empty))) (.node [11,11,11,9,4,4,3,2,2,2,2,1] (.node [11,11,11,9,4,4,2,2,2,2,2,2] (.node [11,11,11,9,4,4,2,2,2,2,2,1,1] (.node [11,11,11,9,4,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,4,4,3,2,2,2,1,1,1] (.node [11,11,11,9,4,4,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,4,4,3,3,2,2,1,1] (.node [11,11,11,9,4,4,3,3,2,1,1,1,1] (.node [11,11,11,9,4,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,4,4,3,3,3,1,1,1] .empty .empty)))) - -def degreeTree62_281 : RowTree := (.node [11,11,11,9,5,3,3,2,2,1,1,1,1,1] (.node [11,11,11,9,5,2,2,2,2,2,2,1,1,1] (.node [11,11,11,9,4,4,4,3,1,1,1,1,1] (.node [11,11,11,9,4,4,4,2,2,2,1,1] (.node [11,11,11,9,4,4,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,4,4,4,4,1,1,1,1] (.node [11,11,11,9,4,4,4,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,5,3,2,2,2,2,2,1,1] (.node [11,11,11,9,5,3,2,2,2,2,1,1,1,1] (.node [11,11,11,9,5,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,9,5,3,2,2,2,2,2,2] .empty .empty))) (.node [11,11,11,9,5,3,3,3,2,2,1,1] (.node [11,11,11,9,5,3,3,3,1,1,1,1,1,1] (.node [11,11,11,9,5,3,3,2,2,2,2,1] (.node [11,11,11,9,5,3,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,5,3,3,3,2,1,1,1,1] .empty .empty)) (.node [11,11,11,9,5,4,2,2,2,2,1,1,1] (.node [11,11,11,9,5,4,2,2,2,1,1,1,1,1] (.node [11,11,11,9,5,3,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,5,4,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_282 : RowTree := (.node [11,11,11,9,4,4,4,2,1,1,1,1,1,1] degreeTree62_280 degreeTree62_281) - -def degreeTree62_283 : RowTree := (.node [11,11,11,9,4,2,2,2,2,2,2,2,1,1] degreeTree62_279 degreeTree62_282) - -def degreeTree62_284 : RowTree := (.node [11,11,11,8,7,4,4,2,1,1,1,1] degreeTree62_276 degreeTree62_283) - -def degreeTree62_285 : RowTree := (.node [11,11,11,8,5,4,2,2,2,2,2,1,1] degreeTree62_269 degreeTree62_284) - -def degreeTree62_286 : RowTree := (.node [11,11,11,9,5,5,2,2,2,2,1,1] (.node [11,11,11,9,5,4,4,2,1,1,1,1,1] (.node [11,11,11,9,5,4,3,3,1,1,1,1,1] (.node [11,11,11,9,5,4,3,2,2,2,1,1] (.node [11,11,11,9,5,4,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,5,4,4,1,1,1,1,1,1,1] (.node [11,11,11,9,5,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,5,5,2,2,1,1,1,1,1,1] (.node [11,11,11,9,5,4,4,3,1,1,1,1] (.node [11,11,11,9,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,5,5,2,2,2,1,1,1,1] .empty .empty))) (.node [11,11,11,9,5,5,4,2,1,1,1,1] (.node [11,11,11,9,5,5,3,2,2,1,1,1] (.node [11,11,11,9,5,5,3,2,1,1,1,1,1] (.node [11,11,11,9,5,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,5,5,4,1,1,1,1,1,1] (.node [11,11,11,9,5,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,6,2,2,2,2,2,2,1,1] (.node [11,11,11,9,6,2,2,2,2,2,1,1,1,1] (.node [11,11,11,9,5,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,6,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_287 : RowTree := (.node [11,11,11,9,6,4,3,1,1,1,1,1,1,1] (.node [11,11,11,9,6,3,3,3,1,1,1,1,1] (.node [11,11,11,9,6,3,3,2,1,1,1,1,1,1] (.node [11,11,11,9,6,3,2,2,2,2,2,1] (.node [11,11,11,9,6,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,6,3,3,2,2,2,1,1] (.node [11,11,11,9,6,3,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,6,4,2,2,2,1,1,1,1] (.node [11,11,11,9,6,4,2,2,1,1,1,1,1,1] (.node [11,11,11,9,6,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,6,4,2,2,2,2,1,1] .empty .empty))) (.node [11,11,11,9,6,5,2,1,1,1,1,1,1,1] (.node [11,11,11,9,6,4,3,3,1,1,1,1] (.node [11,11,11,9,6,4,3,2,2,1,1,1] (.node [11,11,11,9,6,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,6,4,4,2,1,1,1,1] (.node [11,11,11,9,6,4,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,6,5,3,1,1,1,1,1,1] (.node [11,11,11,9,6,5,2,2,2,1,1,1] (.node [11,11,11,9,6,5,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,6,5,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_288 : RowTree := (.node [11,11,11,9,6,3,2,2,2,1,1,1,1,1] degreeTree62_286 degreeTree62_287) - -def degreeTree62_289 : RowTree := (.node [11,11,11,9,7,3,3,1,1,1,1,1,1,1] (.node [11,11,11,9,7,2,2,2,2,2,1,1,1] (.node [11,11,11,9,6,6,2,2,1,1,1,1] (.node [11,11,11,9,6,6,2,1,1,1,1,1,1] (.node [11,11,11,9,6,6,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,7,2,2,2,2,1,1,1,1,1] (.node [11,11,11,9,6,6,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,7,3,2,2,2,1,1,1,1] (.node [11,11,11,9,7,3,2,2,1,1,1,1,1,1] (.node [11,11,11,9,7,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,9,7,3,2,2,2,2,1,1] .empty .empty))) (.node [11,11,11,9,7,4,2,2,2,1,1,1] (.node [11,11,11,9,7,3,3,3,1,1,1,1] (.node [11,11,11,9,7,3,3,2,2,1,1,1] (.node [11,11,11,9,7,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,7,4,2,2,1,1,1,1,1] (.node [11,11,11,9,7,4,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,7,4,4,1,1,1,1,1] (.node [11,11,11,9,7,4,3,2,1,1,1,1] (.node [11,11,11,9,7,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,7,5,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_290 : RowTree := (.node [11,11,11,9,8,3,2,2,2,1,1,1] (.node [11,11,11,9,8,2,2,2,1,1,1,1,1,1] (.node [11,11,11,9,7,6,1,1,1,1,1,1,1] (.node [11,11,11,9,7,5,3,1,1,1,1,1] (.node [11,11,11,9,7,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,7,7,1,1,1,1,1,1] (.node [11,11,11,9,7,6,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,8,3,2,1,1,1,1,1,1,1] (.node [11,11,11,9,8,2,2,2,2,2,1,1] (.node [11,11,11,9,8,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,8,3,2,2,1,1,1,1,1] .empty .empty))) (.node [11,11,11,9,8,4,3,1,1,1,1,1] (.node [11,11,11,9,8,4,1,1,1,1,1,1,1,1] (.node [11,11,11,9,8,3,3,2,1,1,1,1] (.node [11,11,11,9,8,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,8,4,2,2,1,1,1,1] (.node [11,11,11,9,8,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,8,6,1,1,1,1,1,1] (.node [11,11,11,9,8,5,2,1,1,1,1,1] (.node [11,11,11,9,8,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,9,2,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_291 : RowTree := (.node [11,11,11,9,7,5,2,1,1,1,1,1,1] degreeTree62_289 degreeTree62_290) - -def degreeTree62_292 : RowTree := (.node [11,11,11,9,6,5,4,1,1,1,1,1] degreeTree62_288 degreeTree62_291) - -def degreeTree62_293 : RowTree := (.node [11,11,11,10,3,2,2,2,2,2,2,2,2] (.node [11,11,11,9,9,4,1,1,1,1,1,1,1] (.node [11,11,11,9,9,3,2,1,1,1,1,1,1] (.node [11,11,11,9,9,3,1,1,1,1,1,1,1,1] (.node [11,11,11,9,9,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,9,3,3,1,1,1,1,1] (.node [11,11,11,9,9,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,2,2,2,2,2,2,2,2,2,1] (.node [11,11,11,9,9,5,1,1,1,1,1,1] (.node [11,11,11,9,9,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,3,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [11,11,11,10,3,3,3,3,2,1,1,1,1,1] (.node [11,11,11,10,3,3,3,2,2,2,1,1,1,1] (.node [11,11,11,10,3,3,2,2,2,2,2,2,1] (.node [11,11,11,10,3,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,3,3,3,2,2,2,2,2] (.node [11,11,11,10,3,3,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,11,10,3,3,3,3,3,1,1,1,1] (.node [11,11,11,10,3,3,3,3,2,2,2,1] (.node [11,11,11,10,3,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,3,3,3,3,3,2,1,1] .empty .empty)))) - -def degreeTree62_294 : RowTree := (.node [11,11,11,10,4,3,3,3,3,1,1,1] (.node [11,11,11,10,4,3,3,2,2,2,1,1,1] (.node [11,11,11,10,4,3,2,2,2,2,2,1,1] (.node [11,11,11,10,4,3,2,2,2,2,1,1,1,1] (.node [11,11,11,10,4,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,10,4,3,3,2,2,1,1,1,1,1] (.node [11,11,11,10,4,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,10,4,3,3,3,2,1,1,1,1] (.node [11,11,11,10,4,3,3,3,1,1,1,1,1,1] (.node [11,11,11,10,4,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,10,4,3,3,3,2,2,1,1] .empty .empty))) (.node [11,11,11,10,4,4,3,2,2,2,1,1] (.node [11,11,11,10,4,4,2,2,2,2,2,1] (.node [11,11,11,10,4,4,2,2,2,2,1,1,1] (.node [11,11,11,10,4,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,4,4,3,2,2,1,1,1,1] (.node [11,11,11,10,4,4,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,4,4,4,1,1,1,1,1,1,1] (.node [11,11,11,10,4,4,3,3,2,1,1,1] (.node [11,11,11,10,4,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,4,4,4,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_295 : RowTree := (.node [11,11,11,10,4,2,2,2,2,2,2,1,1,1] degreeTree62_293 degreeTree62_294) - -def degreeTree62_296 : RowTree := (.node [11,11,11,10,5,3,3,3,1,1,1,1,1] (.node [11,11,11,10,5,3,2,2,2,2,1,1,1] (.node [11,11,11,10,5,2,2,2,2,2,2,1,1] (.node [11,11,11,10,5,2,2,2,2,2,1,1,1,1] (.node [11,11,11,10,4,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,5,3,2,2,2,1,1,1,1,1] (.node [11,11,11,10,5,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,10,5,3,3,2,2,1,1,1,1] (.node [11,11,11,10,5,3,3,2,1,1,1,1,1,1] (.node [11,11,11,10,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,10,5,3,3,2,2,2,1,1] .empty .empty))) (.node [11,11,11,10,5,4,3,2,1,1,1,1,1] (.node [11,11,11,10,5,4,2,2,2,1,1,1,1] (.node [11,11,11,10,5,4,2,2,1,1,1,1,1,1] (.node [11,11,11,10,5,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,5,4,3,1,1,1,1,1,1,1] (.node [11,11,11,10,5,4,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,11,10,5,4,4,1,1,1,1,1,1] (.node [11,11,11,10,5,4,3,3,1,1,1,1] (.node [11,11,11,10,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,5,4,4,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_297 : RowTree := (.node [11,11,11,10,6,3,2,2,2,2,1,1] (.node [11,11,11,10,6,2,2,2,2,1,1,1,1,1] (.node [11,11,11,10,5,5,3,1,1,1,1,1,1] (.node [11,11,11,10,5,5,2,2,2,1,1,1] (.node [11,11,11,10,5,5,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,5,5,4,1,1,1,1,1] (.node [11,11,11,10,5,5,3,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,6,3,2,2,1,1,1,1,1,1] (.node [11,11,11,10,6,2,2,2,2,2,2,1] (.node [11,11,11,10,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,6,3,2,2,2,1,1,1,1] .empty .empty))) (.node [11,11,11,10,6,4,2,2,1,1,1,1,1] (.node [11,11,11,10,6,3,3,2,2,1,1,1] (.node [11,11,11,10,6,3,3,2,1,1,1,1,1] (.node [11,11,11,10,6,3,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,6,4,2,1,1,1,1,1,1,1] (.node [11,11,11,10,6,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,6,4,3,2,1,1,1,1] (.node [11,11,11,10,6,4,3,1,1,1,1,1,1] (.node [11,11,11,10,6,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,6,4,4,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_298 : RowTree := (.node [11,11,11,10,5,5,2,1,1,1,1,1,1,1] degreeTree62_296 degreeTree62_297) - -def degreeTree62_299 : RowTree := (.node [11,11,11,10,4,4,4,2,2,1,1,1] degreeTree62_295 degreeTree62_298) - -def degreeTree62_300 : RowTree := (.node [11,11,11,9,9,2,2,2,1,1,1,1,1] degreeTree62_292 degreeTree62_299) - -def degreeTree62_301 : RowTree := (.node [11,11,11,10,7,3,2,2,2,1,1,1] (.node [11,11,11,10,7,2,2,2,1,1,1,1,1,1] (.node [11,11,11,10,6,5,3,1,1,1,1,1] (.node [11,11,11,10,6,5,2,2,1,1,1,1] (.node [11,11,11,10,6,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,6,6,2,1,1,1,1,1] (.node [11,11,11,10,6,6,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,7,3,2,1,1,1,1,1,1,1] (.node [11,11,11,10,7,2,2,2,2,2,1,1] (.node [11,11,11,10,7,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,7,3,2,2,1,1,1,1,1] .empty .empty))) (.node [11,11,11,10,7,4,3,1,1,1,1,1] (.node [11,11,11,10,7,4,1,1,1,1,1,1,1,1] (.node [11,11,11,10,7,3,3,2,1,1,1,1] (.node [11,11,11,10,7,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,7,4,2,2,1,1,1,1] (.node [11,11,11,10,7,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,7,6,1,1,1,1,1,1] (.node [11,11,11,10,7,5,2,1,1,1,1,1] (.node [11,11,11,10,7,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,8,2,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_302 : RowTree := (.node [11,11,11,10,9,2,2,2,1,1,1,1] (.node [11,11,11,10,8,4,1,1,1,1,1,1,1] (.node [11,11,11,10,8,3,2,1,1,1,1,1,1] (.node [11,11,11,10,8,3,1,1,1,1,1,1,1,1] (.node [11,11,11,10,8,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,8,3,3,1,1,1,1,1] (.node [11,11,11,10,8,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,9,2,1,1,1,1,1,1,1,1] (.node [11,11,11,10,8,5,1,1,1,1,1,1] (.node [11,11,11,10,8,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,9,2,2,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,10,10,2,2,1,1,1,1,1] (.node [11,11,11,10,9,4,1,1,1,1,1,1] (.node [11,11,11,10,9,3,2,1,1,1,1,1] (.node [11,11,11,10,9,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,10,2,1,1,1,1,1,1,1] (.node [11,11,11,10,10,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,2,2,2,2,2,2,2,2,2] (.node [11,11,11,11,2,2,2,2,2,2,2,2,1,1] (.node [11,11,11,10,10,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,3,2,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_303 : RowTree := (.node [11,11,11,10,8,2,2,2,1,1,1,1,1] degreeTree62_301 degreeTree62_302) - -def degreeTree62_304 : RowTree := (.node [11,11,11,11,4,2,2,2,2,2,1,1,1,1] (.node [11,11,11,11,3,3,3,2,2,2,2,1] (.node [11,11,11,11,3,3,2,2,2,2,2,2] (.node [11,11,11,11,3,3,2,2,2,2,2,1,1] (.node [11,11,11,11,3,3,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,3,3,3,2,2,2,1,1,1] (.node [11,11,11,11,3,3,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,3,3,3,3,2,2,1,1] (.node [11,11,11,11,3,3,3,3,2,1,1,1,1] (.node [11,11,11,11,3,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,3,3,3,3,3,1,1,1] .empty .empty))) (.node [11,11,11,11,4,3,3,2,1,1,1,1,1,1] (.node [11,11,11,11,4,3,2,2,2,1,1,1,1,1] (.node [11,11,11,11,4,2,2,2,2,2,2,2] (.node [11,11,11,11,4,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,11,4,3,2,2,2,2,2,1] (.node [11,11,11,11,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,4,3,3,3,1,1,1,1,1] (.node [11,11,11,11,4,3,3,2,2,2,1,1] (.node [11,11,11,11,4,3,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,4,3,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_305 : RowTree := (.node [11,11,11,11,5,2,2,2,2,2,2,1] (.node [11,11,11,11,4,4,3,3,1,1,1,1] (.node [11,11,11,11,4,4,3,1,1,1,1,1,1,1] (.node [11,11,11,11,4,4,2,2,2,2,1,1] (.node [11,11,11,11,4,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,4,4,3,2,2,1,1,1] (.node [11,11,11,11,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,5,2,2,2,2,1,1,1,1,1] (.node [11,11,11,11,4,4,4,2,1,1,1,1] (.node [11,11,11,11,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,5,2,2,2,2,2,1,1,1] .empty .empty))) (.node [11,11,11,11,5,3,3,2,2,1,1,1] (.node [11,11,11,11,5,3,2,2,2,2,1,1] (.node [11,11,11,11,5,3,2,2,2,1,1,1,1] (.node [11,11,11,11,5,3,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,5,3,3,2,1,1,1,1,1] (.node [11,11,11,11,5,3,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,5,4,2,2,1,1,1,1,1] (.node [11,11,11,11,5,4,2,1,1,1,1,1,1,1] (.node [11,11,11,11,5,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,5,4,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_306 : RowTree := (.node [11,11,11,11,4,4,2,2,1,1,1,1,1,1] degreeTree62_304 degreeTree62_305) - -def degreeTree62_307 : RowTree := (.node [11,11,11,11,3,2,2,2,2,2,2,2,1] degreeTree62_303 degreeTree62_306) - -def degreeTree62_308 : RowTree := (.node [11,11,11,11,6,3,2,2,1,1,1,1,1] (.node [11,11,11,11,5,5,3,1,1,1,1,1] (.node [11,11,11,11,5,5,1,1,1,1,1,1,1,1] (.node [11,11,11,11,5,4,4,1,1,1,1,1] (.node [11,11,11,11,5,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,5,5,2,2,1,1,1,1] (.node [11,11,11,11,5,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,6,2,2,2,2,2,1,1] (.node [11,11,11,11,6,2,2,2,2,1,1,1,1] (.node [11,11,11,11,6,2,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,6,3,2,1,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,11,6,4,2,2,1,1,1,1] (.node [11,11,11,11,6,3,3,2,1,1,1,1] (.node [11,11,11,11,6,3,3,1,1,1,1,1,1] (.node [11,11,11,11,6,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,6,4,2,1,1,1,1,1,1] (.node [11,11,11,11,6,4,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,6,5,2,1,1,1,1,1] (.node [11,11,11,11,6,5,1,1,1,1,1,1,1] (.node [11,11,11,11,6,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,6,6,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_309 : RowTree := (.node [11,11,11,11,8,2,2,1,1,1,1,1,1] (.node [11,11,11,11,7,3,3,1,1,1,1,1] (.node [11,11,11,11,7,3,1,1,1,1,1,1,1,1] (.node [11,11,11,11,7,2,2,2,2,1,1,1] (.node [11,11,11,11,7,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,7,3,2,2,1,1,1,1] (.node [11,11,11,11,7,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,7,5,1,1,1,1,1,1] (.node [11,11,11,11,7,4,2,1,1,1,1,1] (.node [11,11,11,11,7,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,8,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,11,9,2,1,1,1,1,1,1,1] (.node [11,11,11,11,8,3,2,1,1,1,1,1] (.node [11,11,11,11,8,3,1,1,1,1,1,1,1] (.node [11,11,11,11,8,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,9,1,1,1,1,1,1,1,1,1] (.node [11,11,11,11,8,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,10,1,1,1,1,1,1,1,1] (.node [11,11,11,11,9,3,1,1,1,1,1,1] (.node [11,11,11,11,9,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,10,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_310 : RowTree := (.node [11,11,11,11,7,2,2,1,1,1,1,1,1,1] degreeTree62_308 degreeTree62_309) - -def degreeTree62_311 : RowTree := (.node [12,6,6,6,6,6,6,6,2,2,2,1,1] (.node [12,6,6,6,6,6,6,5,3,2,2,1,1] (.node [12,6,6,6,6,6,5,5,5,2,1,1,1] (.node [12,6,6,6,6,6,5,5,4,2,2,1,1] (.node [12,6,6,6,6,5,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,6,6,6,6,6,6,4,4,2,2,1,1] (.node [12,6,6,6,6,6,5,5,5,2,2,1] .empty .empty) .empty)) (.node [12,6,6,6,6,6,6,5,5,1,1,1,1] (.node [12,6,6,6,6,6,6,5,4,2,2,1] (.node [12,6,6,6,6,6,6,5,4,2,1,1,1] .empty .empty) .empty) (.node [12,6,6,6,6,6,6,5,5,2,1,1] .empty .empty))) (.node [12,7,6,6,5,5,5,5,5,2,2,1,1] (.node [12,6,6,6,6,6,6,6,4,1,1,1,1] (.node [12,6,6,6,6,6,6,6,3,2,2,1] (.node [12,6,6,6,6,6,6,6,3,2,1,1,1] .empty .empty) .empty) (.node [12,6,6,6,6,6,6,6,5,1,1,1] (.node [12,6,6,6,6,6,6,6,4,2,1,1] .empty .empty) .empty)) (.node [12,7,6,6,6,5,5,5,5,2,2,1] (.node [12,7,6,6,6,5,5,5,5,2,1,1,1] (.node [12,7,6,6,6,5,5,5,4,2,2,1,1] .empty .empty) .empty) (.node [12,7,6,6,6,6,5,4,4,2,2,1,1] .empty .empty)))) - -def degreeTree62_312 : RowTree := (.node [12,7,6,6,6,6,6,5,4,1,1,1,1] (.node [12,7,6,6,6,6,6,4,4,2,1,1,1] (.node [12,7,6,6,6,6,5,5,5,1,1,1,1] (.node [12,7,6,6,6,6,5,5,4,2,2,1] (.node [12,7,6,6,6,6,5,5,4,2,1,1,1] .empty .empty) .empty) (.node [12,7,6,6,6,6,6,4,3,2,2,1,1] (.node [12,7,6,6,6,6,5,5,5,2,1,1] .empty .empty) .empty)) (.node [12,7,6,6,6,6,6,5,3,2,1,1,1] (.node [12,7,6,6,6,6,6,5,2,2,2,1,1] (.node [12,7,6,6,6,6,6,4,4,2,2,1] .empty .empty) .empty) (.node [12,7,6,6,6,6,6,5,3,2,2,1] .empty .empty))) (.node [12,7,6,6,6,6,6,6,3,1,1,1,1] (.node [12,7,6,6,6,6,6,6,2,2,1,1,1] (.node [12,7,6,6,6,6,6,5,5,1,1,1] (.node [12,7,6,6,6,6,6,5,4,2,1,1] .empty .empty) .empty) (.node [12,7,6,6,6,6,6,6,2,2,2,1] .empty .empty)) (.node [12,7,7,5,5,5,5,5,5,2,2,1,1] (.node [12,7,6,6,6,6,6,6,4,1,1,1] (.node [12,7,6,6,6,6,6,6,3,2,1,1] .empty .empty) .empty) (.node [12,7,7,6,5,5,5,5,4,2,2,1,1] .empty .empty)))) - -def degreeTree62_313 : RowTree := (.node [12,7,6,6,6,6,5,5,3,2,2,1,1] degreeTree62_311 degreeTree62_312) - -def degreeTree62_314 : RowTree := (.node [11,11,11,11,11,1,1,1,1,1,1,1] degreeTree62_310 degreeTree62_313) - -def degreeTree62_315 : RowTree := (.node [11,11,11,11,5,4,3,1,1,1,1,1,1] degreeTree62_307 degreeTree62_314) - -def degreeTree62_316 : RowTree := (.node [11,11,11,10,6,5,1,1,1,1,1,1,1,1] degreeTree62_300 degreeTree62_315) - -def degreeTree62_317 : RowTree := (.node [11,11,11,9,5,4,3,2,1,1,1,1,1,1] degreeTree62_285 degreeTree62_316) - -def degreeTree62_318 : RowTree := (.node [12,7,7,6,6,6,5,4,4,2,2,1] (.node [12,7,7,6,6,5,5,5,5,1,1,1,1] (.node [12,7,7,6,6,5,5,5,3,2,2,1,1] (.node [12,7,7,6,6,5,5,4,4,2,2,1,1] (.node [12,7,7,6,5,5,5,5,5,2,2,1] .empty .empty) .empty) (.node [12,7,7,6,6,5,5,5,4,2,2,1] (.node [12,7,7,6,6,5,5,5,4,2,1,1,1] .empty .empty) .empty)) (.node [12,7,7,6,6,6,5,4,3,2,2,1,1] (.node [12,7,7,6,6,6,4,4,4,2,2,1,1] (.node [12,7,7,6,6,5,5,5,5,2,1,1] .empty .empty) .empty) (.node [12,7,7,6,6,6,5,4,4,2,1,1,1] .empty .empty))) (.node [12,7,7,6,6,6,5,5,5,1,1,1] (.node [12,7,7,6,6,6,5,5,3,2,2,1] (.node [12,7,7,6,6,6,5,5,3,2,1,1,1] (.node [12,7,7,6,6,6,5,5,2,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,6,6,6,5,5,4,2,1,1] (.node [12,7,7,6,6,6,5,5,4,1,1,1,1] .empty .empty) .empty)) (.node [12,7,7,6,6,6,6,4,2,2,2,1,1] (.node [12,7,7,6,6,6,6,3,3,2,2,1,1] (.node [12,7,7,6,6,6,6,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,7,7,6,6,6,6,4,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_319 : RowTree := (.node [12,7,7,7,5,5,5,4,4,2,2,1,1] (.node [12,7,7,6,6,6,6,5,3,2,1,1] (.node [12,7,7,6,6,6,6,5,2,2,1,1,1] (.node [12,7,7,6,6,6,6,4,4,2,1,1] (.node [12,7,7,6,6,6,6,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,7,7,6,6,6,6,5,3,1,1,1,1] (.node [12,7,7,6,6,6,6,5,2,2,2,1] .empty .empty) .empty)) (.node [12,7,7,6,6,6,6,6,2,2,1,1] (.node [12,7,7,6,6,6,6,6,2,1,1,1,1] (.node [12,7,7,6,6,6,6,5,4,1,1,1] .empty .empty) .empty) (.node [12,7,7,6,6,6,6,6,3,1,1,1] .empty .empty))) (.node [12,7,7,7,6,5,4,4,4,2,2,1,1] (.node [12,7,7,7,5,5,5,5,4,2,2,1] (.node [12,7,7,7,5,5,5,5,4,2,1,1,1] (.node [12,7,7,7,5,5,5,5,3,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,5,5,5,5,5,2,1,1] (.node [12,7,7,7,5,5,5,5,5,1,1,1,1] .empty .empty) .empty)) (.node [12,7,7,7,6,5,5,4,4,2,2,1] (.node [12,7,7,7,6,5,5,4,4,2,1,1,1] (.node [12,7,7,7,6,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,6,5,5,5,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_320 : RowTree := (.node [12,7,7,6,6,6,6,4,3,2,2,1] degreeTree62_318 degreeTree62_319) - -def degreeTree62_321 : RowTree := (.node [12,7,7,7,6,6,5,4,3,2,1,1,1] (.node [12,7,7,7,6,6,4,4,4,2,1,1,1] (.node [12,7,7,7,6,5,5,5,4,2,1,1] (.node [12,7,7,7,6,5,5,5,4,1,1,1,1] (.node [12,7,7,7,6,5,5,5,3,2,2,1] .empty .empty) .empty) (.node [12,7,7,7,6,6,4,4,3,2,2,1,1] (.node [12,7,7,7,6,5,5,5,5,1,1,1] .empty .empty) .empty)) (.node [12,7,7,7,6,6,5,3,3,2,2,1,1] (.node [12,7,7,7,6,6,5,2,2,2,2,2,2] (.node [12,7,7,7,6,6,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,7,7,7,6,6,5,4,2,2,2,1,1] .empty .empty))) (.node [12,7,7,7,6,6,5,5,3,1,1,1,1] (.node [12,7,7,7,6,6,5,4,4,2,1,1] (.node [12,7,7,7,6,6,5,4,4,1,1,1,1] (.node [12,7,7,7,6,6,5,4,3,2,2,1] .empty .empty) .empty) (.node [12,7,7,7,6,6,5,5,2,2,2,1] (.node [12,7,7,7,6,6,5,5,2,2,1,1,1] .empty .empty) .empty)) (.node [12,7,7,7,6,6,6,2,2,2,2,2,1] (.node [12,7,7,7,6,6,5,5,4,1,1,1] (.node [12,7,7,7,6,6,5,5,3,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,6,6,6,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_322 : RowTree := (.node [12,7,7,7,6,6,6,6,2,1,1,1] (.node [12,7,7,7,6,6,6,4,4,1,1,1] (.node [12,7,7,7,6,6,6,4,2,2,2,1] (.node [12,7,7,7,6,6,6,4,2,2,1,1,1] (.node [12,7,7,7,6,6,6,3,3,2,2,1] .empty .empty) .empty) (.node [12,7,7,7,6,6,6,4,3,2,1,1] (.node [12,7,7,7,6,6,6,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,7,7,7,6,6,6,5,3,1,1,1] (.node [12,7,7,7,6,6,6,5,2,2,1,1] (.node [12,7,7,7,6,6,6,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,6,6,6,6,1,1,1,1,1] .empty .empty))) (.node [12,7,7,7,7,5,5,3,3,2,2,1,1] (.node [12,7,7,7,7,5,4,4,4,2,1,1,1] (.node [12,7,7,7,7,5,4,4,3,2,2,1,1] (.node [12,7,7,7,7,4,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,5,5,2,2,2,2,2,2] (.node [12,7,7,7,7,5,4,4,4,2,2,1] .empty .empty) .empty)) (.node [12,7,7,7,7,5,5,4,3,2,2,1] (.node [12,7,7,7,7,5,5,4,3,2,1,1,1] (.node [12,7,7,7,7,5,5,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,5,5,4,4,1,1,1,1] .empty .empty)))) - -def degreeTree62_323 : RowTree := (.node [12,7,7,7,6,6,6,3,3,2,1,1,1] degreeTree62_321 degreeTree62_322) - -def degreeTree62_324 : RowTree := (.node [12,7,7,7,6,5,5,5,3,2,1,1,1] degreeTree62_320 degreeTree62_323) - -def degreeTree62_325 : RowTree := (.node [12,7,7,7,7,6,4,4,4,1,1,1,1] (.node [12,7,7,7,7,6,4,2,2,2,2,2,2] (.node [12,7,7,7,7,5,5,5,3,1,1,1,1] (.node [12,7,7,7,7,5,5,5,2,2,2,1] (.node [12,7,7,7,7,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,5,5,5,4,1,1,1] (.node [12,7,7,7,7,5,5,5,3,2,1,1] .empty .empty) .empty)) (.node [12,7,7,7,7,6,4,4,3,2,1,1,1] (.node [12,7,7,7,7,6,4,4,2,2,2,1,1] (.node [12,7,7,7,7,6,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,6,4,4,3,2,2,1] .empty .empty))) (.node [12,7,7,7,7,6,5,4,2,2,1,1,1] (.node [12,7,7,7,7,6,5,3,2,2,2,1,1] (.node [12,7,7,7,7,6,5,2,2,2,2,2,1] (.node [12,7,7,7,7,6,4,4,4,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,6,5,3,3,2,2,1] (.node [12,7,7,7,7,6,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,7,7,7,7,6,5,4,3,2,1,1] (.node [12,7,7,7,7,6,5,4,3,1,1,1,1] (.node [12,7,7,7,7,6,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,7,7,7,7,6,5,4,4,1,1,1] .empty .empty)))) - -def degreeTree62_326 : RowTree := (.node [12,7,7,7,7,6,6,4,3,1,1,1] (.node [12,7,7,7,7,6,6,3,2,2,2,1] (.node [12,7,7,7,7,6,6,2,2,2,2,1,1] (.node [12,7,7,7,7,6,5,5,3,1,1,1] (.node [12,7,7,7,7,6,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,6,6,3,2,2,1,1,1] (.node [12,7,7,7,7,6,6,2,2,2,2,2] .empty .empty) .empty)) (.node [12,7,7,7,7,6,6,4,2,1,1,1,1] (.node [12,7,7,7,7,6,6,3,3,2,1,1] (.node [12,7,7,7,7,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,6,6,4,2,2,1,1] .empty .empty))) (.node [12,7,7,7,7,7,4,2,2,2,2,2,1] (.node [12,7,7,7,7,6,6,6,1,1,1,1] (.node [12,7,7,7,7,6,6,5,2,1,1,1] (.node [12,7,7,7,7,6,6,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,3,3,3,2,2,1,1] (.node [12,7,7,7,7,7,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,7,7,7,7,7,4,3,3,2,2,1] (.node [12,7,7,7,7,7,4,3,3,2,1,1,1] (.node [12,7,7,7,7,7,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,4,4,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_327 : RowTree := (.node [12,7,7,7,7,6,5,5,2,1,1,1,1] degreeTree62_325 degreeTree62_326) - -def degreeTree62_328 : RowTree := (.node [12,7,7,7,7,7,5,4,2,2,1,1] (.node [12,7,7,7,7,7,5,3,2,2,1,1,1] (.node [12,7,7,7,7,7,4,4,4,1,1,1] (.node [12,7,7,7,7,7,4,4,3,2,1,1] (.node [12,7,7,7,7,7,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,5,2,2,2,2,2] (.node [12,7,7,7,7,7,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,7,7,7,7,7,5,3,3,2,1,1] (.node [12,7,7,7,7,7,5,3,3,1,1,1,1] (.node [12,7,7,7,7,7,5,3,2,2,2,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,5,4,2,1,1,1,1] .empty .empty))) (.node [12,7,7,7,7,7,6,3,2,1,1,1,1] (.node [12,7,7,7,7,7,5,5,2,1,1,1] (.node [12,7,7,7,7,7,5,5,1,1,1,1,1] (.node [12,7,7,7,7,7,5,4,3,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,6,2,2,2,2,1] (.node [12,7,7,7,7,7,6,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,7,7,7,7,7,6,4,1,1,1,1,1] (.node [12,7,7,7,7,7,6,3,3,1,1,1] (.node [12,7,7,7,7,7,6,3,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,6,4,2,1,1,1] .empty .empty)))) - -def degreeTree62_329 : RowTree := (.node [12,8,6,6,6,5,5,4,4,2,2,1,1] (.node [12,7,7,7,7,7,7,4,1,1,1,1] (.node [12,7,7,7,7,7,7,2,2,2,1,1] (.node [12,7,7,7,7,7,7,2,2,1,1,1,1] (.node [12,7,7,7,7,7,7,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,7,3,2,1,1,1] (.node [12,7,7,7,7,7,7,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,6,6,5,5,5,5,5,2,1,1,1] (.node [12,8,6,6,5,5,5,5,4,2,2,1,1] (.node [12,8,6,5,5,5,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,8,6,6,5,5,5,5,5,2,2,1] .empty .empty))) (.node [12,8,6,6,6,6,4,4,4,2,2,1,1] (.node [12,8,6,6,6,5,5,5,4,2,2,1] (.node [12,8,6,6,6,5,5,5,4,2,1,1,1] (.node [12,8,6,6,6,5,5,5,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,6,6,6,5,5,5,5,2,1,1] (.node [12,8,6,6,6,5,5,5,5,1,1,1,1] .empty .empty) .empty)) (.node [12,8,6,6,6,6,5,4,4,2,2,1] (.node [12,8,6,6,6,6,5,4,4,2,1,1,1] (.node [12,8,6,6,6,6,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,6,6,6,6,5,5,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_330 : RowTree := (.node [12,7,7,7,7,7,6,5,1,1,1,1] degreeTree62_328 degreeTree62_329) - -def degreeTree62_331 : RowTree := (.node [12,7,7,7,7,7,4,4,2,2,2,1] degreeTree62_327 degreeTree62_330) - -def degreeTree62_332 : RowTree := (.node [12,7,7,7,7,5,5,4,4,2,1,1] degreeTree62_324 degreeTree62_331) - -def degreeTree62_333 : RowTree := (.node [12,8,6,6,6,6,6,4,4,2,1,1] (.node [12,8,6,6,6,6,6,3,3,2,2,1,1] (.node [12,8,6,6,6,6,5,5,4,2,1,1] (.node [12,8,6,6,6,6,5,5,4,1,1,1,1] (.node [12,8,6,6,6,6,5,5,3,2,2,1] .empty .empty) .empty) (.node [12,8,6,6,6,6,6,2,2,2,2,2,2] (.node [12,8,6,6,6,6,5,5,5,1,1,1] .empty .empty) .empty)) (.node [12,8,6,6,6,6,6,4,3,2,2,1] (.node [12,8,6,6,6,6,6,4,3,2,1,1,1] (.node [12,8,6,6,6,6,6,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,6,6,6,6,6,4,4,1,1,1,1] .empty .empty))) (.node [12,8,6,6,6,6,6,6,2,1,1,1,1] (.node [12,8,6,6,6,6,6,5,3,1,1,1,1] (.node [12,8,6,6,6,6,6,5,2,2,2,1] (.node [12,8,6,6,6,6,6,5,2,2,1,1,1] .empty .empty) .empty) (.node [12,8,6,6,6,6,6,5,4,1,1,1] (.node [12,8,6,6,6,6,6,5,3,2,1,1] .empty .empty) .empty)) (.node [12,8,7,5,5,5,5,5,4,2,2,1,1] (.node [12,8,6,6,6,6,6,6,3,1,1,1] (.node [12,8,6,6,6,6,6,6,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,5,5,5,5,5,5,2,1,1,1] .empty .empty)))) - -def degreeTree62_334 : RowTree := (.node [12,8,7,6,6,5,5,5,2,2,2,1,1] (.node [12,8,7,6,5,5,5,5,5,2,1,1] (.node [12,8,7,6,5,5,5,5,4,2,1,1,1] (.node [12,8,7,6,5,5,5,5,3,2,2,1,1] (.node [12,8,7,6,5,5,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,6,5,5,5,5,5,1,1,1,1] (.node [12,8,7,6,5,5,5,5,4,2,2,1] .empty .empty) .empty)) (.node [12,8,7,6,6,5,5,4,4,2,1,1,1] (.node [12,8,7,6,6,5,5,4,3,2,2,1,1] (.node [12,8,7,6,6,5,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,5,5,4,4,2,2,1] .empty .empty))) (.node [12,8,7,6,6,6,4,4,3,2,2,1,1] (.node [12,8,7,6,6,5,5,5,4,1,1,1,1] (.node [12,8,7,6,6,5,5,5,3,2,2,1] (.node [12,8,7,6,6,5,5,5,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,5,5,5,5,1,1,1] (.node [12,8,7,6,6,5,5,5,4,2,1,1] .empty .empty) .empty)) (.node [12,8,7,6,6,6,5,2,2,2,2,2,2] (.node [12,8,7,6,6,6,4,4,4,2,2,1] (.node [12,8,7,6,6,6,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,6,5,3,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_335 : RowTree := (.node [12,8,7,5,5,5,5,5,5,2,2,1] degreeTree62_333 degreeTree62_334) - -def degreeTree62_336 : RowTree := (.node [12,8,7,6,6,6,6,3,2,2,2,1,1] (.node [12,8,7,6,6,6,5,5,2,2,2,1] (.node [12,8,7,6,6,6,5,4,4,1,1,1,1] (.node [12,8,7,6,6,6,5,4,3,2,2,1] (.node [12,8,7,6,6,6,5,4,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,6,5,5,2,2,1,1,1] (.node [12,8,7,6,6,6,5,4,4,2,1,1] .empty .empty) .empty)) (.node [12,8,7,6,6,6,5,5,4,1,1,1] (.node [12,8,7,6,6,6,5,5,3,2,1,1] (.node [12,8,7,6,6,6,5,5,3,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,6,6,2,2,2,2,2,1] .empty .empty))) (.node [12,8,7,6,6,6,6,4,3,2,1,1] (.node [12,8,7,6,6,6,6,4,2,2,1,1,1] (.node [12,8,7,6,6,6,6,3,3,2,2,1] (.node [12,8,7,6,6,6,6,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,6,6,4,3,1,1,1,1] (.node [12,8,7,6,6,6,6,4,2,2,2,1] .empty .empty) .empty)) (.node [12,8,7,6,6,6,6,5,2,2,1,1] (.node [12,8,7,6,6,6,6,5,2,1,1,1,1] (.node [12,8,7,6,6,6,6,4,4,1,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,6,6,5,3,1,1,1] .empty .empty)))) - -def degreeTree62_337 : RowTree := (.node [12,8,7,7,5,5,5,5,5,1,1,1] (.node [12,8,7,7,5,5,5,5,2,2,2,1,1] (.node [12,8,7,7,5,5,5,4,3,2,2,1,1] (.node [12,8,7,7,5,5,4,4,4,2,2,1,1] (.node [12,8,7,6,6,6,6,6,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,5,5,5,4,4,2,2,1] (.node [12,8,7,7,5,5,5,4,4,2,1,1,1] .empty .empty) .empty)) (.node [12,8,7,7,5,5,5,5,4,1,1,1,1] (.node [12,8,7,7,5,5,5,5,3,2,2,1] (.node [12,8,7,7,5,5,5,5,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,5,5,5,5,4,2,1,1] .empty .empty))) (.node [12,8,7,7,6,5,5,3,3,2,2,1,1] (.node [12,8,7,7,6,5,4,4,4,2,1,1,1] (.node [12,8,7,7,6,5,4,4,3,2,2,1,1] (.node [12,8,7,7,6,4,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,5,5,2,2,2,2,2,2] (.node [12,8,7,7,6,5,4,4,4,2,2,1] .empty .empty) .empty)) (.node [12,8,7,7,6,5,5,4,3,2,2,1] (.node [12,8,7,7,6,5,5,4,3,2,1,1,1] (.node [12,8,7,7,6,5,5,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,5,5,4,4,1,1,1,1] .empty .empty)))) - -def degreeTree62_338 : RowTree := (.node [12,8,7,6,6,6,6,6,1,1,1,1,1] degreeTree62_336 degreeTree62_337) - -def degreeTree62_339 : RowTree := (.node [12,8,7,6,6,6,5,4,2,2,2,1,1] degreeTree62_335 degreeTree62_338) - -def degreeTree62_340 : RowTree := (.node [12,8,7,7,6,6,4,4,4,1,1,1,1] (.node [12,8,7,7,6,6,4,2,2,2,2,2,2] (.node [12,8,7,7,6,5,5,5,3,1,1,1,1] (.node [12,8,7,7,6,5,5,5,2,2,2,1] (.node [12,8,7,7,6,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,5,5,5,4,1,1,1] (.node [12,8,7,7,6,5,5,5,3,2,1,1] .empty .empty) .empty)) (.node [12,8,7,7,6,6,4,4,3,2,1,1,1] (.node [12,8,7,7,6,6,4,4,2,2,2,1,1] (.node [12,8,7,7,6,6,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,6,4,4,3,2,2,1] .empty .empty))) (.node [12,8,7,7,6,6,5,4,2,2,1,1,1] (.node [12,8,7,7,6,6,5,3,2,2,2,1,1] (.node [12,8,7,7,6,6,5,2,2,2,2,2,1] (.node [12,8,7,7,6,6,4,4,4,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,6,5,3,3,2,2,1] (.node [12,8,7,7,6,6,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,8,7,7,6,6,5,4,3,2,1,1] (.node [12,8,7,7,6,6,5,4,3,1,1,1,1] (.node [12,8,7,7,6,6,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,8,7,7,6,6,5,4,4,1,1,1] .empty .empty)))) - -def degreeTree62_341 : RowTree := (.node [12,8,7,7,6,6,6,4,3,1,1,1] (.node [12,8,7,7,6,6,6,3,2,2,2,1] (.node [12,8,7,7,6,6,6,2,2,2,2,1,1] (.node [12,8,7,7,6,6,5,5,3,1,1,1] (.node [12,8,7,7,6,6,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,6,6,3,2,2,1,1,1] (.node [12,8,7,7,6,6,6,2,2,2,2,2] .empty .empty) .empty)) (.node [12,8,7,7,6,6,6,4,2,1,1,1,1] (.node [12,8,7,7,6,6,6,3,3,2,1,1] (.node [12,8,7,7,6,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,6,6,4,2,2,1,1] .empty .empty))) (.node [12,8,7,7,7,4,4,4,4,2,2,1] (.node [12,8,7,7,6,6,6,6,1,1,1,1] (.node [12,8,7,7,6,6,6,5,2,1,1,1] (.node [12,8,7,7,6,6,6,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,4,4,4,4,2,1,1,1] (.node [12,8,7,7,7,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [12,8,7,7,7,5,4,4,2,2,2,1,1] (.node [12,8,7,7,7,5,4,3,3,2,2,1,1] (.node [12,8,7,7,7,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,8,7,7,7,5,4,4,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_342 : RowTree := (.node [12,8,7,7,6,6,5,5,2,1,1,1,1] degreeTree62_340 degreeTree62_341) - -def degreeTree62_343 : RowTree := (.node [12,8,7,7,7,5,5,4,4,1,1,1] (.node [12,8,7,7,7,5,5,3,3,2,2,1] (.node [12,8,7,7,7,5,5,2,2,2,2,2,1] (.node [12,8,7,7,7,5,4,4,4,2,1,1] (.node [12,8,7,7,7,5,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,5,5,3,3,2,1,1,1] (.node [12,8,7,7,7,5,5,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,8,7,7,7,5,5,4,3,1,1,1,1] (.node [12,8,7,7,7,5,5,4,2,2,2,1] (.node [12,8,7,7,7,5,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,5,5,4,3,2,1,1] .empty .empty))) (.node [12,8,7,7,7,6,4,2,2,2,2,2,1] (.node [12,8,7,7,7,5,5,5,3,1,1,1] (.node [12,8,7,7,7,5,5,5,2,2,1,1] (.node [12,8,7,7,7,5,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,6,3,3,3,2,2,1,1] (.node [12,8,7,7,7,6,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,8,7,7,7,6,4,3,3,2,2,1] (.node [12,8,7,7,7,6,4,3,3,2,1,1,1] (.node [12,8,7,7,7,6,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,6,4,4,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_344 : RowTree := (.node [12,8,7,7,7,6,5,4,2,2,1,1] (.node [12,8,7,7,7,6,5,3,2,2,1,1,1] (.node [12,8,7,7,7,6,4,4,4,1,1,1] (.node [12,8,7,7,7,6,4,4,3,2,1,1] (.node [12,8,7,7,7,6,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,6,5,2,2,2,2,2] (.node [12,8,7,7,7,6,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,8,7,7,7,6,5,3,3,2,1,1] (.node [12,8,7,7,7,6,5,3,3,1,1,1,1] (.node [12,8,7,7,7,6,5,3,2,2,2,1] .empty .empty) .empty) (.node [12,8,7,7,7,6,5,4,2,1,1,1,1] .empty .empty))) (.node [12,8,7,7,7,6,6,2,2,2,2,1] (.node [12,8,7,7,7,6,5,5,2,1,1,1] (.node [12,8,7,7,7,6,5,5,1,1,1,1,1] (.node [12,8,7,7,7,6,5,4,3,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,6,6,2,2,2,1,1,1] .empty .empty)) (.node [12,8,7,7,7,6,6,3,3,1,1,1] (.node [12,8,7,7,7,6,6,3,2,2,1,1] (.node [12,8,7,7,7,6,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,6,6,4,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_345 : RowTree := (.node [12,8,7,7,7,6,4,4,2,2,2,1] degreeTree62_343 degreeTree62_344) - -def degreeTree62_346 : RowTree := (.node [12,8,7,7,7,5,4,4,3,2,2,1] degreeTree62_342 degreeTree62_345) - -def degreeTree62_347 : RowTree := (.node [12,8,7,7,6,5,5,4,4,2,1,1] degreeTree62_339 degreeTree62_346) - -def degreeTree62_348 : RowTree := (.node [12,8,6,6,6,6,5,5,3,2,1,1,1] degreeTree62_332 degreeTree62_347) - -def degreeTree62_349 : RowTree := (.node [12,8,7,7,7,7,4,3,3,1,1,1,1] (.node [12,8,7,7,7,7,3,3,3,2,2,1] (.node [12,8,7,7,7,7,3,2,2,2,2,2,1] (.node [12,8,7,7,7,7,2,2,2,2,2,2,2] (.node [12,8,7,7,7,6,6,5,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,7,3,3,3,2,1,1,1] (.node [12,8,7,7,7,7,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,8,7,7,7,7,4,3,2,2,1,1,1] (.node [12,8,7,7,7,7,4,2,2,2,2,2] (.node [12,8,7,7,7,7,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,7,4,3,2,2,2,1] .empty .empty))) (.node [12,8,7,7,7,7,5,2,2,2,2,1] (.node [12,8,7,7,7,7,4,4,2,2,1,1] (.node [12,8,7,7,7,7,4,4,2,1,1,1,1] (.node [12,8,7,7,7,7,4,3,3,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,7,5,2,2,2,1,1,1] (.node [12,8,7,7,7,7,4,4,3,1,1,1] .empty .empty) .empty)) (.node [12,8,7,7,7,7,5,3,3,1,1,1] (.node [12,8,7,7,7,7,5,3,2,2,1,1] (.node [12,8,7,7,7,7,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,7,5,4,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_350 : RowTree := (.node [12,8,7,7,7,7,7,3,1,1,1,1] (.node [12,8,7,7,7,7,6,3,2,1,1,1] (.node [12,8,7,7,7,7,6,2,2,1,1,1,1] (.node [12,8,7,7,7,7,6,2,1,1,1,1,1,1] (.node [12,8,7,7,7,7,5,5,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,7,6,3,1,1,1,1,1] (.node [12,8,7,7,7,7,6,2,2,2,1,1] .empty .empty) .empty)) (.node [12,8,7,7,7,7,7,2,1,1,1,1,1] (.node [12,8,7,7,7,7,7,1,1,1,1,1,1,1] (.node [12,8,7,7,7,7,6,4,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,7,7,2,2,1,1,1] .empty .empty))) (.node [12,8,8,5,5,5,5,5,5,2,1,1] (.node [12,8,8,5,5,5,5,5,4,2,1,1,1] (.node [12,8,8,5,5,5,5,5,3,2,2,1,1] (.node [12,8,8,5,5,5,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,5,5,5,5,5,5,1,1,1,1] (.node [12,8,8,5,5,5,5,5,4,2,2,1] .empty .empty) .empty)) (.node [12,8,8,6,5,5,5,4,4,2,1,1,1] (.node [12,8,8,6,5,5,5,4,3,2,2,1,1] (.node [12,8,8,6,5,5,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,6,5,5,5,4,4,2,2,1] .empty .empty)))) - -def degreeTree62_351 : RowTree := (.node [12,8,7,7,7,7,5,4,2,1,1,1] degreeTree62_349 degreeTree62_350) - -def degreeTree62_352 : RowTree := (.node [12,8,8,6,6,5,5,3,3,2,2,1,1] (.node [12,8,8,6,6,4,4,4,4,2,2,1,1] (.node [12,8,8,6,5,5,5,5,4,1,1,1,1] (.node [12,8,8,6,5,5,5,5,3,2,2,1] (.node [12,8,8,6,5,5,5,5,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,6,5,5,5,5,5,1,1,1] (.node [12,8,8,6,5,5,5,5,4,2,1,1] .empty .empty) .empty)) (.node [12,8,8,6,6,5,4,4,4,2,2,1] (.node [12,8,8,6,6,5,4,4,4,2,1,1,1] (.node [12,8,8,6,6,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,6,6,5,5,2,2,2,2,2,2] .empty .empty))) (.node [12,8,8,6,6,5,5,5,2,2,1,1,1] (.node [12,8,8,6,6,5,5,4,3,2,2,1] (.node [12,8,8,6,6,5,5,4,3,2,1,1,1] (.node [12,8,8,6,6,5,5,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,6,6,5,5,4,4,2,1,1] (.node [12,8,8,6,6,5,5,4,4,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,6,6,5,5,5,3,2,1,1] (.node [12,8,8,6,6,5,5,5,3,1,1,1,1] (.node [12,8,8,6,6,5,5,5,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,6,6,5,5,5,4,1,1,1] .empty .empty)))) - -def degreeTree62_353 : RowTree := (.node [12,8,8,6,6,6,5,4,2,2,1,1,1] (.node [12,8,8,6,6,6,4,4,4,2,1,1] (.node [12,8,8,6,6,6,4,4,3,2,1,1,1] (.node [12,8,8,6,6,6,4,4,2,2,2,1,1] (.node [12,8,8,6,6,6,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,6,6,6,4,4,4,1,1,1,1] (.node [12,8,8,6,6,6,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,8,8,6,6,6,5,3,3,2,1,1,1] (.node [12,8,8,6,6,6,5,3,2,2,2,1,1] (.node [12,8,8,6,6,6,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,6,6,6,5,3,3,2,2,1] .empty .empty))) (.node [12,8,8,6,6,6,5,5,2,2,1,1] (.node [12,8,8,6,6,6,5,4,3,2,1,1] (.node [12,8,8,6,6,6,5,4,3,1,1,1,1] (.node [12,8,8,6,6,6,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,6,6,6,5,5,2,1,1,1,1] (.node [12,8,8,6,6,6,5,4,4,1,1,1] .empty .empty) .empty)) (.node [12,8,8,6,6,6,6,2,2,2,2,2] (.node [12,8,8,6,6,6,6,2,2,2,2,1,1] (.node [12,8,8,6,6,6,5,5,3,1,1,1] .empty .empty) .empty) (.node [12,8,8,6,6,6,6,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_354 : RowTree := (.node [12,8,8,6,6,6,4,2,2,2,2,2,2] degreeTree62_352 degreeTree62_353) - -def degreeTree62_355 : RowTree := (.node [12,8,8,6,5,5,5,5,2,2,2,1,1] degreeTree62_351 degreeTree62_354) - -def degreeTree62_356 : RowTree := (.node [12,8,8,7,5,5,4,4,4,2,1,1,1] (.node [12,8,8,6,6,6,6,5,1,1,1,1,1] (.node [12,8,8,6,6,6,6,4,2,1,1,1,1] (.node [12,8,8,6,6,6,6,3,3,2,1,1] (.node [12,8,8,6,6,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,6,6,6,6,4,3,1,1,1] (.node [12,8,8,6,6,6,6,4,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,7,5,4,4,4,4,2,2,1,1] (.node [12,8,8,6,6,6,6,6,1,1,1,1] (.node [12,8,8,6,6,6,6,5,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,5,5,4,4,3,2,2,1,1] .empty .empty))) (.node [12,8,8,7,5,5,5,4,3,2,2,1] (.node [12,8,8,7,5,5,5,3,3,2,2,1,1] (.node [12,8,8,7,5,5,5,2,2,2,2,2,2] (.node [12,8,8,7,5,5,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,8,8,7,5,5,5,4,3,2,1,1,1] (.node [12,8,8,7,5,5,5,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,7,5,5,5,5,2,2,1,1,1] (.node [12,8,8,7,5,5,5,4,4,2,1,1] (.node [12,8,8,7,5,5,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,5,5,5,5,2,2,2,1] .empty .empty)))) - -def degreeTree62_357 : RowTree := (.node [12,8,8,7,6,5,4,4,4,1,1,1,1] (.node [12,8,8,7,6,5,4,2,2,2,2,2,2] (.node [12,8,8,7,6,4,4,4,3,2,2,1,1] (.node [12,8,8,7,5,5,5,5,4,1,1,1] (.node [12,8,8,7,5,5,5,5,3,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,4,4,4,4,2,2,1] (.node [12,8,8,7,6,4,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,6,5,4,4,3,2,1,1,1] (.node [12,8,8,7,6,5,4,4,2,2,2,1,1] (.node [12,8,8,7,6,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,5,4,4,3,2,2,1] .empty .empty))) (.node [12,8,8,7,6,5,5,4,2,2,1,1,1] (.node [12,8,8,7,6,5,5,3,2,2,2,1,1] (.node [12,8,8,7,6,5,5,2,2,2,2,2,1] (.node [12,8,8,7,6,5,4,4,4,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,5,5,3,3,2,2,1] (.node [12,8,8,7,6,5,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,6,5,5,4,3,2,1,1] (.node [12,8,8,7,6,5,5,4,3,1,1,1,1] (.node [12,8,8,7,6,5,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,7,6,5,5,4,4,1,1,1] .empty .empty)))) - -def degreeTree62_358 : RowTree := (.node [12,8,8,7,5,5,5,5,3,1,1,1,1] degreeTree62_356 degreeTree62_357) - -def degreeTree62_359 : RowTree := (.node [12,8,8,7,6,6,4,4,3,1,1,1,1] (.node [12,8,8,7,6,6,4,3,2,2,2,1,1] (.node [12,8,8,7,6,6,3,2,2,2,2,2,2] (.node [12,8,8,7,6,5,5,5,3,1,1,1] (.node [12,8,8,7,6,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,6,4,2,2,2,2,2,1] (.node [12,8,8,7,6,6,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,7,6,6,4,4,2,2,1,1,1] (.node [12,8,8,7,6,6,4,3,3,2,2,1] (.node [12,8,8,7,6,6,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,6,4,4,2,2,2,1] .empty .empty))) (.node [12,8,8,7,6,6,5,3,2,2,2,1] (.node [12,8,8,7,6,6,5,2,2,2,2,1,1] (.node [12,8,8,7,6,6,4,4,4,1,1,1] (.node [12,8,8,7,6,6,4,4,3,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,6,5,3,2,2,1,1,1] (.node [12,8,8,7,6,6,5,2,2,2,2,2] .empty .empty) .empty)) (.node [12,8,8,7,6,6,5,4,2,1,1,1,1] (.node [12,8,8,7,6,6,5,3,3,2,1,1] (.node [12,8,8,7,6,6,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,6,5,4,2,2,1,1] .empty .empty)))) - -def degreeTree62_360 : RowTree := (.node [12,8,8,7,7,4,4,2,2,2,2,2,2] (.node [12,8,8,7,6,6,6,3,2,2,1,1] (.node [12,8,8,7,6,6,6,2,2,2,1,1,1] (.node [12,8,8,7,6,6,5,5,2,1,1,1] (.node [12,8,8,7,6,6,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,6,6,3,2,1,1,1,1] (.node [12,8,8,7,6,6,6,2,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,7,6,6,6,4,2,1,1,1] (.node [12,8,8,7,6,6,6,4,1,1,1,1,1] (.node [12,8,8,7,6,6,6,3,3,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,6,6,5,1,1,1,1] .empty .empty))) (.node [12,8,8,7,7,4,4,4,4,2,1,1] (.node [12,8,8,7,7,4,4,4,3,2,1,1,1] (.node [12,8,8,7,7,4,4,4,2,2,2,1,1] (.node [12,8,8,7,7,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,4,4,4,4,1,1,1,1] (.node [12,8,8,7,7,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,8,8,7,7,5,4,2,2,2,2,2,1] (.node [12,8,8,7,7,5,3,3,3,2,2,1,1] (.node [12,8,8,7,7,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,8,8,7,7,5,4,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_361 : RowTree := (.node [12,8,8,7,6,6,5,4,3,1,1,1] degreeTree62_359 degreeTree62_360) - -def degreeTree62_362 : RowTree := (.node [12,8,8,7,6,5,5,5,2,1,1,1,1] degreeTree62_358 degreeTree62_361) - -def degreeTree62_363 : RowTree := (.node [12,8,8,6,6,6,6,3,2,2,2,1] degreeTree62_355 degreeTree62_362) - -def degreeTree62_364 : RowTree := (.node [12,8,8,7,7,5,5,3,3,1,1,1,1] (.node [12,8,8,7,7,5,4,4,4,1,1,1] (.node [12,8,8,7,7,5,4,4,2,2,2,1] (.node [12,8,8,7,7,5,4,4,2,2,1,1,1] (.node [12,8,8,7,7,5,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,8,8,7,7,5,4,4,3,2,1,1] (.node [12,8,8,7,7,5,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,7,5,5,3,2,2,1,1,1] (.node [12,8,8,7,7,5,5,2,2,2,2,2] (.node [12,8,8,7,7,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,5,5,3,2,2,2,1] .empty .empty))) (.node [12,8,8,7,7,5,5,5,2,1,1,1] (.node [12,8,8,7,7,5,5,4,2,2,1,1] (.node [12,8,8,7,7,5,5,4,2,1,1,1,1] (.node [12,8,8,7,7,5,5,3,3,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,5,5,5,1,1,1,1,1] (.node [12,8,8,7,7,5,5,4,3,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,7,6,3,3,2,2,2,1,1] (.node [12,8,8,7,7,6,3,2,2,2,2,2,1] (.node [12,8,8,7,7,6,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,8,8,7,7,6,3,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_365 : RowTree := (.node [12,8,8,7,7,6,5,2,2,2,2,1] (.node [12,8,8,7,7,6,4,3,3,2,1,1] (.node [12,8,8,7,7,6,4,3,2,2,1,1,1] (.node [12,8,8,7,7,6,4,2,2,2,2,2] (.node [12,8,8,7,7,6,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,6,4,3,3,1,1,1,1] (.node [12,8,8,7,7,6,4,3,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,7,7,6,4,4,3,1,1,1] (.node [12,8,8,7,7,6,4,4,2,2,1,1] (.node [12,8,8,7,7,6,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,6,5,2,2,2,1,1,1] .empty .empty))) (.node [12,8,8,7,7,6,5,5,1,1,1,1] (.node [12,8,8,7,7,6,5,3,3,1,1,1] (.node [12,8,8,7,7,6,5,3,2,2,1,1] (.node [12,8,8,7,7,6,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,6,5,4,2,1,1,1] (.node [12,8,8,7,7,6,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,7,6,6,2,2,2,1,1] (.node [12,8,8,7,7,6,6,2,2,1,1,1,1] (.node [12,8,8,7,7,6,6,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,6,6,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_366 : RowTree := (.node [12,8,8,7,7,6,3,3,3,2,2,1] degreeTree62_364 degreeTree62_365) - -def degreeTree62_367 : RowTree := (.node [12,8,8,7,7,7,3,3,3,2,1,1] (.node [12,8,8,7,7,7,3,2,2,2,2,2] (.node [12,8,8,7,7,7,2,2,2,2,2,2,1] (.node [12,8,8,7,7,7,2,2,2,2,2,1,1,1] (.node [12,8,8,7,7,6,6,4,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,7,3,2,2,2,2,1,1] (.node [12,8,8,7,7,7,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,7,7,3,3,2,2,2,1] (.node [12,8,8,7,7,7,3,3,2,2,1,1,1] (.node [12,8,8,7,7,7,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,7,3,3,3,1,1,1,1] .empty .empty))) (.node [12,8,8,7,7,7,4,3,2,2,1,1] (.node [12,8,8,7,7,7,4,2,2,2,2,1] (.node [12,8,8,7,7,7,4,2,2,2,1,1,1] (.node [12,8,8,7,7,7,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,7,4,3,2,1,1,1,1] (.node [12,8,8,7,7,7,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,7,7,4,4,2,1,1,1] (.node [12,8,8,7,7,7,4,4,1,1,1,1,1] (.node [12,8,8,7,7,7,4,3,3,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,7,5,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_368 : RowTree := (.node [12,8,8,8,5,4,4,4,3,2,2,1,1] (.node [12,8,8,7,7,7,6,2,1,1,1,1,1] (.node [12,8,8,7,7,7,5,3,2,1,1,1] (.node [12,8,8,7,7,7,5,3,1,1,1,1,1] (.node [12,8,8,7,7,7,5,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,7,6,1,1,1,1,1,1,1] (.node [12,8,8,7,7,7,5,4,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,7,7,7,1,1,1,1,1,1] (.node [12,8,8,7,7,7,6,3,1,1,1,1] (.node [12,8,8,7,7,7,6,2,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,4,4,4,4,4,2,2,1,1] .empty .empty))) (.node [12,8,8,8,5,5,4,4,3,2,1,1,1] (.node [12,8,8,8,5,5,4,2,2,2,2,2,2] (.node [12,8,8,8,5,4,4,4,4,2,2,1] (.node [12,8,8,8,5,4,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,5,5,4,4,2,2,2,1,1] (.node [12,8,8,8,5,5,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,8,5,5,4,4,4,2,1,1] (.node [12,8,8,8,5,5,4,4,4,1,1,1,1] (.node [12,8,8,8,5,5,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,5,5,5,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_369 : RowTree := (.node [12,8,8,7,7,7,5,2,2,1,1,1,1] degreeTree62_367 degreeTree62_368) - -def degreeTree62_370 : RowTree := (.node [12,8,8,7,7,6,6,3,2,1,1,1] degreeTree62_366 degreeTree62_369) - -def degreeTree62_371 : RowTree := (.node [12,8,8,8,6,4,4,2,2,2,2,2,2] (.node [12,8,8,8,5,5,5,4,3,2,1,1] (.node [12,8,8,8,5,5,5,4,2,2,1,1,1] (.node [12,8,8,8,5,5,5,3,3,2,2,1] (.node [12,8,8,8,5,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,5,5,5,4,3,1,1,1,1] (.node [12,8,8,8,5,5,5,4,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,8,5,5,5,5,2,2,1,1] (.node [12,8,8,8,5,5,5,5,2,1,1,1,1] (.node [12,8,8,8,5,5,5,4,4,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,5,5,5,5,3,1,1,1] .empty .empty))) (.node [12,8,8,8,6,4,4,4,4,2,1,1] (.node [12,8,8,8,6,4,4,4,3,2,1,1,1] (.node [12,8,8,8,6,4,4,4,2,2,2,1,1] (.node [12,8,8,8,6,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,4,4,4,4,1,1,1,1] (.node [12,8,8,8,6,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,8,8,8,6,5,4,2,2,2,2,2,1] (.node [12,8,8,8,6,5,3,3,3,2,2,1,1] (.node [12,8,8,8,6,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,8,8,8,6,5,4,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_372 : RowTree := (.node [12,8,8,8,6,5,5,3,3,1,1,1,1] (.node [12,8,8,8,6,5,4,4,4,1,1,1] (.node [12,8,8,8,6,5,4,4,2,2,2,1] (.node [12,8,8,8,6,5,4,4,2,2,1,1,1] (.node [12,8,8,8,6,5,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,6,5,4,4,3,2,1,1] (.node [12,8,8,8,6,5,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,6,5,5,3,2,2,1,1,1] (.node [12,8,8,8,6,5,5,2,2,2,2,2] (.node [12,8,8,8,6,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,5,5,3,2,2,2,1] .empty .empty))) (.node [12,8,8,8,6,5,5,5,2,1,1,1] (.node [12,8,8,8,6,5,5,4,2,2,1,1] (.node [12,8,8,8,6,5,5,4,2,1,1,1,1] (.node [12,8,8,8,6,5,5,3,3,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,5,5,5,1,1,1,1,1] (.node [12,8,8,8,6,5,5,4,3,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,6,6,3,3,2,2,2,1,1] (.node [12,8,8,8,6,6,3,2,2,2,2,2,1] (.node [12,8,8,8,6,6,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,8,8,8,6,6,3,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_373 : RowTree := (.node [12,8,8,8,6,5,4,3,3,2,1,1,1] degreeTree62_371 degreeTree62_372) - -def degreeTree62_374 : RowTree := (.node [12,8,8,8,6,6,5,2,2,2,2,1] (.node [12,8,8,8,6,6,4,3,3,2,1,1] (.node [12,8,8,8,6,6,4,3,2,2,1,1,1] (.node [12,8,8,8,6,6,4,2,2,2,2,2] (.node [12,8,8,8,6,6,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,6,4,3,3,1,1,1,1] (.node [12,8,8,8,6,6,4,3,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,8,6,6,4,4,3,1,1,1] (.node [12,8,8,8,6,6,4,4,2,2,1,1] (.node [12,8,8,8,6,6,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,6,5,2,2,2,1,1,1] .empty .empty))) (.node [12,8,8,8,6,6,5,5,1,1,1,1] (.node [12,8,8,8,6,6,5,3,3,1,1,1] (.node [12,8,8,8,6,6,5,3,2,2,1,1] (.node [12,8,8,8,6,6,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,6,5,4,2,1,1,1] (.node [12,8,8,8,6,6,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,6,6,6,2,2,2,1,1] (.node [12,8,8,8,6,6,6,2,2,1,1,1,1] (.node [12,8,8,8,6,6,6,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,6,6,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_375 : RowTree := (.node [12,8,8,8,7,4,4,4,3,2,1,1] (.node [12,8,8,8,7,4,4,3,3,2,1,1,1] (.node [12,8,8,8,7,4,3,3,3,2,2,1,1] (.node [12,8,8,8,7,4,3,2,2,2,2,2,2] (.node [12,8,8,8,6,6,6,4,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,4,4,3,2,2,2,1,1] (.node [12,8,8,8,7,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,8,7,4,4,4,2,2,2,1] (.node [12,8,8,8,7,4,4,4,2,2,1,1,1] (.node [12,8,8,8,7,4,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,7,4,4,4,3,1,1,1,1] .empty .empty))) (.node [12,8,8,8,7,5,3,3,3,2,1,1,1] (.node [12,8,8,8,7,5,3,2,2,2,2,2,1] (.node [12,8,8,8,7,5,2,2,2,2,2,2,2] (.node [12,8,8,8,7,4,4,4,4,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,5,3,3,2,2,2,1,1] .empty .empty)) (.node [12,8,8,8,7,5,4,2,2,2,2,2] (.node [12,8,8,8,7,5,4,2,2,2,2,1,1] (.node [12,8,8,8,7,5,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,7,5,4,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_376 : RowTree := (.node [12,8,8,8,6,6,6,3,2,1,1,1] degreeTree62_374 degreeTree62_375) - -def degreeTree62_377 : RowTree := (.node [12,8,8,8,6,6,3,3,3,2,2,1] degreeTree62_373 degreeTree62_376) - -def degreeTree62_378 : RowTree := (.node [12,8,8,8,5,5,5,3,2,2,2,1,1] degreeTree62_370 degreeTree62_377) - -def degreeTree62_379 : RowTree := (.node [12,8,8,7,7,5,4,3,3,2,1,1,1] degreeTree62_363 degreeTree62_378) - -def degreeTree62_380 : RowTree := (.node [12,8,7,7,7,6,6,4,2,1,1,1] degreeTree62_348 degreeTree62_379) - -def degreeTree62_381 : RowTree := (.node [12,7,7,6,5,5,5,5,5,2,1,1,1] degreeTree62_317 degreeTree62_380) - -def degreeTree62_382 : RowTree := (.node [12,8,8,8,7,5,5,4,1,1,1,1,1] (.node [12,8,8,8,7,5,5,2,2,2,1,1,1] (.node [12,8,8,8,7,5,4,4,2,1,1,1,1] (.node [12,8,8,8,7,5,4,3,3,2,1,1] (.node [12,8,8,8,7,5,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,5,4,4,3,1,1,1] (.node [12,8,8,8,7,5,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,8,7,5,5,3,2,2,1,1] (.node [12,8,8,8,7,5,5,3,2,1,1,1,1] (.node [12,8,8,8,7,5,5,2,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,7,5,5,3,3,1,1,1] .empty .empty))) (.node [12,8,8,8,7,6,3,2,2,2,2,1,1] (.node [12,8,8,8,7,6,2,2,2,2,2,1,1,1] (.node [12,8,8,8,7,5,5,5,1,1,1,1] (.node [12,8,8,8,7,5,5,4,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,6,3,2,2,2,1,1,1,1] (.node [12,8,8,8,7,6,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,8,7,6,3,3,2,2,1,1,1] (.node [12,8,8,8,7,6,3,3,2,1,1,1,1,1] (.node [12,8,8,8,7,6,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,8,8,8,7,6,3,3,2,2,2,1] .empty .empty)))) - -def degreeTree62_383 : RowTree := (.node [12,8,8,8,7,6,5,2,1,1,1,1,1,1] (.node [12,8,8,8,7,6,4,3,2,1,1,1,1] (.node [12,8,8,8,7,6,4,2,2,2,1,1,1] (.node [12,8,8,8,7,6,4,2,2,1,1,1,1,1] (.node [12,8,8,8,7,6,3,3,3,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,6,4,3,1,1,1,1,1,1] (.node [12,8,8,8,7,6,4,2,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,8,7,6,4,4,1,1,1,1,1] (.node [12,8,8,8,7,6,4,3,3,1,1,1] (.node [12,8,8,8,7,6,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,6,4,4,2,1,1,1] .empty .empty))) (.node [12,8,8,8,7,6,6,1,1,1,1,1,1,1] (.node [12,8,8,8,7,6,5,3,1,1,1,1,1] (.node [12,8,8,8,7,6,5,2,2,2,1,1] (.node [12,8,8,8,7,6,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,6,5,4,1,1,1,1] (.node [12,8,8,8,7,6,5,3,2,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,7,7,2,2,2,2,1,1,1,1] (.node [12,8,8,8,7,6,6,2,2,1,1,1] (.node [12,8,8,8,7,6,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,7,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_384 : RowTree := (.node [12,8,8,8,7,6,3,3,3,1,1,1,1] degreeTree62_382 degreeTree62_383) - -def degreeTree62_385 : RowTree := (.node [12,8,8,8,7,7,4,3,1,1,1,1,1] (.node [12,8,8,8,7,7,3,3,2,2,1,1] (.node [12,8,8,8,7,7,3,2,2,2,2,1] (.node [12,8,8,8,7,7,3,2,2,2,1,1,1] (.node [12,8,8,8,7,7,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,7,3,3,2,1,1,1,1] (.node [12,8,8,8,7,7,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,7,7,4,2,2,1,1,1,1] (.node [12,8,8,8,7,7,4,2,1,1,1,1,1,1] (.node [12,8,8,8,7,7,3,3,3,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,7,4,2,2,2,1,1] .empty .empty))) (.node [12,8,8,8,8,3,3,2,2,2,2,2,2] (.node [12,8,8,8,7,7,5,2,1,1,1,1,1] (.node [12,8,8,8,7,7,5,1,1,1,1,1,1,1] (.node [12,8,8,8,7,7,4,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,7,6,1,1,1,1,1,1] (.node [12,8,8,8,7,7,5,2,2,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,4,3,2,2,2,2,1,1,1] (.node [12,8,8,8,8,4,2,2,2,2,2,2,2] (.node [12,8,8,8,8,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,4,3,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_386 : RowTree := (.node [12,8,8,8,8,4,4,3,3,2,1,1] (.node [12,8,8,8,8,4,4,2,2,2,2,2] (.node [12,8,8,8,8,4,3,3,3,2,2,1] (.node [12,8,8,8,8,4,3,3,3,2,1,1,1] (.node [12,8,8,8,8,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,4,4,2,2,2,2,1,1] (.node [12,8,8,8,8,4,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,4,4,3,2,2,2,1] (.node [12,8,8,8,8,4,4,3,2,2,1,1,1] (.node [12,8,8,8,8,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,4,4,3,3,1,1,1,1] .empty .empty))) (.node [12,8,8,8,8,5,2,2,2,2,2,2,1] (.node [12,8,8,8,8,4,4,4,2,2,1,1] (.node [12,8,8,8,8,4,4,4,2,1,1,1,1] (.node [12,8,8,8,8,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,5,2,2,2,2,2,1,1,1] (.node [12,8,8,8,8,4,4,4,3,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,5,3,2,2,2,2,2] (.node [12,8,8,8,8,5,3,2,2,2,2,1,1] (.node [12,8,8,8,8,5,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,5,3,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_387 : RowTree := (.node [12,8,8,8,8,4,3,3,2,2,2,1,1] degreeTree62_385 degreeTree62_386) - -def degreeTree62_388 : RowTree := (.node [12,8,8,8,7,7,2,2,2,2,2,2] degreeTree62_384 degreeTree62_387) - -def degreeTree62_389 : RowTree := (.node [12,8,8,8,8,5,4,4,1,1,1,1,1] (.node [12,8,8,8,8,5,4,2,2,2,2,1] (.node [12,8,8,8,8,5,3,3,3,2,1,1] (.node [12,8,8,8,8,5,3,3,3,1,1,1,1] (.node [12,8,8,8,8,5,3,3,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,8,5,4,2,2,2,1,1,1] (.node [12,8,8,8,8,5,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,5,4,3,2,2,1,1] (.node [12,8,8,8,8,5,4,3,2,1,1,1,1] (.node [12,8,8,8,8,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,5,4,3,3,1,1,1] .empty .empty))) (.node [12,8,8,8,8,5,5,3,2,1,1,1] (.node [12,8,8,8,8,5,5,2,2,1,1,1,1] (.node [12,8,8,8,8,5,5,2,1,1,1,1,1,1] (.node [12,8,8,8,8,5,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,5,5,3,1,1,1,1,1] (.node [12,8,8,8,8,5,5,2,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,6,2,2,2,2,2,2] (.node [12,8,8,8,8,6,2,2,2,2,2,1,1] (.node [12,8,8,8,8,6,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,6,3,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_390 : RowTree := (.node [12,8,8,8,8,6,5,1,1,1,1,1,1,1] (.node [12,8,8,8,8,6,4,2,1,1,1,1,1,1] (.node [12,8,8,8,8,6,3,3,2,1,1,1,1] (.node [12,8,8,8,8,6,3,3,1,1,1,1,1,1] (.node [12,8,8,8,8,6,3,2,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,8,6,3,3,3,1,1,1] (.node [12,8,8,8,8,6,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,6,4,3,1,1,1,1,1] (.node [12,8,8,8,8,6,4,2,2,2,1,1] (.node [12,8,8,8,8,6,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,6,4,3,2,1,1,1] .empty .empty))) (.node [12,8,8,8,8,7,2,2,2,2,2,1] (.node [12,8,8,8,8,6,6,1,1,1,1,1,1] (.node [12,8,8,8,8,6,5,2,2,1,1,1] (.node [12,8,8,8,8,6,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,7,2,2,2,2,1,1,1] (.node [12,8,8,8,8,7,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,7,3,2,2,2,1,1] (.node [12,8,8,8,8,7,3,2,2,1,1,1,1] (.node [12,8,8,8,8,7,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,7,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_391 : RowTree := (.node [12,8,8,8,8,6,3,2,2,2,1,1,1] degreeTree62_389 degreeTree62_390) - -def degreeTree62_392 : RowTree := (.node [12,8,8,8,8,8,4,1,1,1,1,1,1] (.node [12,8,8,8,8,8,2,2,2,1,1,1,1] (.node [12,8,8,8,8,7,4,2,2,1,1,1] (.node [12,8,8,8,8,7,4,2,1,1,1,1,1] (.node [12,8,8,8,8,7,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,8,2,2,1,1,1,1,1,1] (.node [12,8,8,8,8,7,5,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,8,3,2,1,1,1,1,1] (.node [12,8,8,8,8,8,3,1,1,1,1,1,1,1] (.node [12,8,8,8,8,8,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,8,3,2,2,1,1,1] .empty .empty))) (.node [12,9,6,6,5,5,5,5,3,2,2,1,1] (.node [12,9,6,5,5,5,5,5,5,2,1,1,1] (.node [12,9,6,5,5,5,5,5,4,2,2,1,1] (.node [12,9,5,5,5,5,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,9,6,6,5,5,5,4,4,2,2,1,1] (.node [12,9,6,5,5,5,5,5,5,2,2,1] .empty .empty) .empty)) (.node [12,9,6,6,5,5,5,5,5,1,1,1,1] (.node [12,9,6,6,5,5,5,5,4,2,2,1] (.node [12,9,6,6,5,5,5,5,4,2,1,1,1] .empty .empty) .empty) (.node [12,9,6,6,5,5,5,5,5,2,1,1] .empty .empty)))) - -def degreeTree62_393 : RowTree := (.node [12,9,6,6,6,6,4,4,4,2,1,1,1] (.node [12,9,6,6,6,5,5,5,3,2,2,1] (.node [12,9,6,6,6,5,5,4,4,2,2,1] (.node [12,9,6,6,6,5,5,4,4,2,1,1,1] (.node [12,9,6,6,6,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,6,6,6,5,5,5,3,2,1,1,1] (.node [12,9,6,6,6,5,5,5,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,6,6,6,5,5,5,5,1,1,1] (.node [12,9,6,6,6,5,5,5,4,2,1,1] (.node [12,9,6,6,6,5,5,5,4,1,1,1,1] .empty .empty) .empty) (.node [12,9,6,6,6,6,4,4,3,2,2,1,1] .empty .empty))) (.node [12,9,6,6,6,6,5,4,3,2,2,1] (.node [12,9,6,6,6,6,5,3,3,2,2,1,1] (.node [12,9,6,6,6,6,5,2,2,2,2,2,2] (.node [12,9,6,6,6,6,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,9,6,6,6,6,5,4,3,2,1,1,1] (.node [12,9,6,6,6,6,5,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,6,6,6,6,5,5,2,2,1,1,1] (.node [12,9,6,6,6,6,5,4,4,2,1,1] (.node [12,9,6,6,6,6,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,9,6,6,6,6,5,5,2,2,2,1] .empty .empty)))) - -def degreeTree62_394 : RowTree := (.node [12,9,6,6,6,5,4,4,4,2,2,1,1] degreeTree62_392 degreeTree62_393) - -def degreeTree62_395 : RowTree := (.node [12,8,8,8,8,7,3,3,2,1,1,1] degreeTree62_391 degreeTree62_394) - -def degreeTree62_396 : RowTree := (.node [12,8,8,8,8,5,3,3,2,2,1,1,1] degreeTree62_388 degreeTree62_395) - -def degreeTree62_397 : RowTree := (.node [12,9,6,6,6,6,6,4,4,1,1,1] (.node [12,9,6,6,6,6,6,3,3,2,2,1] (.node [12,9,6,6,6,6,6,2,2,2,2,2,1] (.node [12,9,6,6,6,6,5,5,4,1,1,1] (.node [12,9,6,6,6,6,5,5,3,2,1,1] .empty .empty) .empty) (.node [12,9,6,6,6,6,6,3,3,2,1,1,1] (.node [12,9,6,6,6,6,6,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,6,6,6,6,6,4,3,1,1,1,1] (.node [12,9,6,6,6,6,6,4,2,2,2,1] (.node [12,9,6,6,6,6,6,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,6,6,6,6,6,4,3,2,1,1] .empty .empty))) (.node [12,9,7,5,5,5,5,4,4,2,2,1,1] (.node [12,9,6,6,6,6,6,5,3,1,1,1] (.node [12,9,6,6,6,6,6,5,2,2,1,1] (.node [12,9,6,6,6,6,6,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,6,6,6,6,6,6,2,1,1,1] (.node [12,9,6,6,6,6,6,6,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,7,5,5,5,5,5,4,2,2,1] (.node [12,9,7,5,5,5,5,5,4,2,1,1,1] (.node [12,9,7,5,5,5,5,5,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,5,5,5,5,5,5,1,1,1,1] .empty .empty)))) - -def degreeTree62_398 : RowTree := (.node [12,9,7,6,6,4,4,4,4,2,2,1,1] (.node [12,9,7,6,5,5,5,5,3,2,1,1,1] (.node [12,9,7,6,5,5,5,4,4,2,1,1,1] (.node [12,9,7,6,5,5,5,4,3,2,2,1,1] (.node [12,9,7,6,5,5,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,6,5,5,5,5,2,2,2,1,1] (.node [12,9,7,6,5,5,5,4,4,2,2,1] .empty .empty) .empty)) (.node [12,9,7,6,5,5,5,5,4,2,1,1] (.node [12,9,7,6,5,5,5,5,4,1,1,1,1] (.node [12,9,7,6,5,5,5,5,3,2,2,1] .empty .empty) .empty) (.node [12,9,7,6,5,5,5,5,5,1,1,1] .empty .empty))) (.node [12,9,7,6,6,5,5,4,2,2,2,1,1] (.node [12,9,7,6,6,5,4,4,4,2,2,1] (.node [12,9,7,6,6,5,4,4,4,2,1,1,1] (.node [12,9,7,6,6,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,6,6,5,5,3,3,2,2,1,1] (.node [12,9,7,6,6,5,5,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,9,7,6,6,5,5,4,4,1,1,1,1] (.node [12,9,7,6,6,5,5,4,3,2,2,1] (.node [12,9,7,6,6,5,5,4,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,7,6,6,5,5,4,4,2,1,1] .empty .empty)))) - -def degreeTree62_399 : RowTree := (.node [12,9,7,5,5,5,5,5,5,2,1,1] degreeTree62_397 degreeTree62_398) - -def degreeTree62_400 : RowTree := (.node [12,9,7,6,6,6,4,4,4,2,1,1] (.node [12,9,7,6,6,6,4,3,3,2,2,1,1] (.node [12,9,7,6,6,5,5,5,3,2,1,1] (.node [12,9,7,6,6,5,5,5,3,1,1,1,1] (.node [12,9,7,6,6,5,5,5,2,2,2,1] .empty .empty) .empty) (.node [12,9,7,6,6,6,4,2,2,2,2,2,2] (.node [12,9,7,6,6,5,5,5,4,1,1,1] .empty .empty) .empty)) (.node [12,9,7,6,6,6,4,4,3,2,2,1] (.node [12,9,7,6,6,6,4,4,3,2,1,1,1] (.node [12,9,7,6,6,6,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,6,6,6,4,4,4,1,1,1,1] .empty .empty))) (.node [12,9,7,6,6,6,5,4,2,2,2,1] (.node [12,9,7,6,6,6,5,3,3,2,1,1,1] (.node [12,9,7,6,6,6,5,3,2,2,2,1,1] (.node [12,9,7,6,6,6,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,7,6,6,6,5,4,2,2,1,1,1] (.node [12,9,7,6,6,6,5,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,7,6,6,6,5,4,4,1,1,1] (.node [12,9,7,6,6,6,5,4,3,2,1,1] (.node [12,9,7,6,6,6,5,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,6,6,6,5,5,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_401 : RowTree := (.node [12,9,7,6,6,6,6,5,1,1,1,1,1] (.node [12,9,7,6,6,6,6,3,3,1,1,1,1] (.node [12,9,7,6,6,6,6,2,2,2,2,2] (.node [12,9,7,6,6,6,6,2,2,2,2,1,1] (.node [12,9,7,6,6,6,5,5,3,1,1,1] .empty .empty) .empty) (.node [12,9,7,6,6,6,6,3,2,2,2,1] (.node [12,9,7,6,6,6,6,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,7,6,6,6,6,4,2,2,1,1] (.node [12,9,7,6,6,6,6,4,2,1,1,1,1] (.node [12,9,7,6,6,6,6,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,7,6,6,6,6,4,3,1,1,1] .empty .empty))) (.node [12,9,7,7,5,5,5,2,2,2,2,2,2] (.node [12,9,7,7,5,5,4,4,3,2,2,1,1] (.node [12,9,7,7,5,4,4,4,4,2,2,1,1] (.node [12,9,7,6,6,6,6,5,2,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,5,5,4,4,4,2,2,1] (.node [12,9,7,7,5,5,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,5,5,5,4,3,2,1,1,1] (.node [12,9,7,7,5,5,5,4,2,2,2,1,1] (.node [12,9,7,7,5,5,5,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,5,5,5,4,3,2,2,1] .empty .empty)))) - -def degreeTree62_402 : RowTree := (.node [12,9,7,6,6,6,5,5,2,2,1,1] degreeTree62_400 degreeTree62_401) - -def degreeTree62_403 : RowTree := (.node [12,9,7,6,6,5,5,5,2,2,1,1,1] degreeTree62_399 degreeTree62_402) - -def degreeTree62_404 : RowTree := (.node [12,9,7,7,6,5,4,3,3,2,2,1,1] (.node [12,9,7,7,5,5,5,5,4,1,1,1] (.node [12,9,7,7,5,5,5,5,2,2,2,1] (.node [12,9,7,7,5,5,5,5,2,2,1,1,1] (.node [12,9,7,7,5,5,5,4,4,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,5,5,5,5,3,2,1,1] (.node [12,9,7,7,5,5,5,5,3,1,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,6,4,4,4,4,2,2,1] (.node [12,9,7,7,6,4,4,4,4,2,1,1,1] (.node [12,9,7,7,6,4,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,5,4,2,2,2,2,2,2] .empty .empty))) (.node [12,9,7,7,6,5,5,2,2,2,2,2,1] (.node [12,9,7,7,6,5,4,4,3,2,2,1] (.node [12,9,7,7,6,5,4,4,3,2,1,1,1] (.node [12,9,7,7,6,5,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,5,4,4,4,2,1,1] (.node [12,9,7,7,6,5,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,6,5,5,3,3,2,2,1] (.node [12,9,7,7,6,5,5,3,3,2,1,1,1] (.node [12,9,7,7,6,5,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,5,5,4,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_405 : RowTree := (.node [12,9,7,7,6,6,4,3,3,2,1,1,1] (.node [12,9,7,7,6,5,5,5,3,1,1,1] (.node [12,9,7,7,6,5,5,4,4,1,1,1] (.node [12,9,7,7,6,5,5,4,3,2,1,1] (.node [12,9,7,7,6,5,5,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,5,5,5,2,2,1,1] (.node [12,9,7,7,6,5,5,5,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,6,6,4,2,2,2,2,2,1] (.node [12,9,7,7,6,6,3,3,3,2,2,1,1] (.node [12,9,7,7,6,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,7,7,6,6,4,3,2,2,2,1,1] .empty .empty))) (.node [12,9,7,7,6,6,4,4,4,1,1,1] (.node [12,9,7,7,6,6,4,4,2,2,2,1] (.node [12,9,7,7,6,6,4,4,2,2,1,1,1] (.node [12,9,7,7,6,6,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,9,7,7,6,6,4,4,3,2,1,1] (.node [12,9,7,7,6,6,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,6,6,5,3,2,2,1,1,1] (.node [12,9,7,7,6,6,5,2,2,2,2,2] (.node [12,9,7,7,6,6,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,6,5,3,2,2,2,1] .empty .empty)))) - -def degreeTree62_406 : RowTree := (.node [12,9,7,7,6,5,5,4,2,2,2,1] degreeTree62_404 degreeTree62_405) - -def degreeTree62_407 : RowTree := (.node [12,9,7,7,6,6,6,3,3,1,1,1] (.node [12,9,7,7,6,6,5,5,2,1,1,1] (.node [12,9,7,7,6,6,5,4,2,2,1,1] (.node [12,9,7,7,6,6,5,4,2,1,1,1,1] (.node [12,9,7,7,6,6,5,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,6,5,5,1,1,1,1,1] (.node [12,9,7,7,6,6,5,4,3,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,6,6,6,3,2,1,1,1,1] (.node [12,9,7,7,6,6,6,2,2,2,2,1] (.node [12,9,7,7,6,6,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,6,6,3,2,2,1,1] .empty .empty))) (.node [12,9,7,7,7,4,4,4,3,2,1,1,1] (.node [12,9,7,7,7,4,4,2,2,2,2,2,2] (.node [12,9,7,7,6,6,6,4,2,1,1,1] (.node [12,9,7,7,6,6,6,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,4,4,4,2,2,2,1,1] (.node [12,9,7,7,7,4,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,9,7,7,7,4,4,4,4,2,1,1] (.node [12,9,7,7,7,4,4,4,4,1,1,1,1] (.node [12,9,7,7,7,4,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,9,7,7,7,5,3,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_408 : RowTree := (.node [12,9,7,7,7,5,5,2,2,2,2,2] (.node [12,9,7,7,7,5,4,4,2,2,2,1] (.node [12,9,7,7,7,5,4,3,3,2,1,1,1] (.node [12,9,7,7,7,5,4,3,2,2,2,1,1] (.node [12,9,7,7,7,5,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,7,7,7,5,4,4,2,2,1,1,1] (.node [12,9,7,7,7,5,4,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,7,7,7,5,4,4,4,1,1,1] (.node [12,9,7,7,7,5,4,4,3,2,1,1] (.node [12,9,7,7,7,5,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,5,5,2,2,2,2,1,1] .empty .empty))) (.node [12,9,7,7,7,5,5,4,2,1,1,1,1] (.node [12,9,7,7,7,5,5,3,3,1,1,1,1] (.node [12,9,7,7,7,5,5,3,2,2,2,1] (.node [12,9,7,7,7,5,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,5,5,3,3,2,1,1] .empty .empty)) (.node [12,9,7,7,7,5,5,5,1,1,1,1,1] (.node [12,9,7,7,7,5,5,4,3,1,1,1] (.node [12,9,7,7,7,5,5,4,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,5,5,5,2,1,1,1] .empty .empty)))) - -def degreeTree62_409 : RowTree := (.node [12,9,7,7,7,5,3,3,3,2,2,1,1] degreeTree62_407 degreeTree62_408) - -def degreeTree62_410 : RowTree := (.node [12,9,7,7,6,6,5,3,3,1,1,1,1] degreeTree62_406 degreeTree62_409) - -def degreeTree62_411 : RowTree := (.node [12,9,7,7,5,5,5,4,4,1,1,1,1] degreeTree62_403 degreeTree62_410) - -def degreeTree62_412 : RowTree := (.node [12,9,6,6,6,6,5,5,3,1,1,1,1] degreeTree62_396 degreeTree62_411) - -def degreeTree62_413 : RowTree := (.node [12,9,7,7,7,6,4,4,2,1,1,1,1] (.node [12,9,7,7,7,6,4,2,2,2,2,2] (.node [12,9,7,7,7,6,3,3,3,2,1,1,1] (.node [12,9,7,7,7,6,3,3,2,2,2,1,1] (.node [12,9,7,7,7,6,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,7,7,7,6,4,2,2,2,2,1,1] (.node [12,9,7,7,7,6,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,7,7,7,6,4,3,3,1,1,1,1] (.node [12,9,7,7,7,6,4,3,2,2,2,1] (.node [12,9,7,7,7,6,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,6,4,3,3,2,1,1] .empty .empty))) (.node [12,9,7,7,7,6,5,3,2,2,1,1] (.node [12,9,7,7,7,6,5,2,2,2,1,1,1] (.node [12,9,7,7,7,6,4,4,3,1,1,1] (.node [12,9,7,7,7,6,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,6,5,3,2,1,1,1,1] (.node [12,9,7,7,7,6,5,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,7,7,7,6,5,4,2,1,1,1] (.node [12,9,7,7,7,6,5,4,1,1,1,1,1] (.node [12,9,7,7,7,6,5,3,3,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,6,6,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_414 : RowTree := (.node [12,9,7,7,7,7,3,3,2,2,2,1] (.node [12,9,7,7,7,7,3,2,2,2,1,1,1,1] (.node [12,9,7,7,7,6,6,3,2,1,1,1] (.node [12,9,7,7,7,6,6,3,1,1,1,1,1] (.node [12,9,7,7,7,6,6,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,7,2,2,2,2,2,2,1] (.node [12,9,7,7,7,7,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,7,7,3,3,2,1,1,1,1,1] (.node [12,9,7,7,7,7,3,2,2,2,2,2] (.node [12,9,7,7,7,7,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,7,3,3,2,2,1,1,1] .empty .empty))) (.node [12,9,7,7,7,7,4,3,1,1,1,1,1,1] (.node [12,9,7,7,7,7,4,2,2,1,1,1,1,1] (.node [12,9,7,7,7,7,3,3,3,2,1,1] (.node [12,9,7,7,7,7,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,7,4,2,2,2,2,1] (.node [12,9,7,7,7,7,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,7,7,4,3,3,1,1,1] (.node [12,9,7,7,7,7,4,3,2,2,1,1] (.node [12,9,7,7,7,7,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,7,4,4,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_415 : RowTree := (.node [12,9,7,7,7,6,6,2,2,1,1,1,1] degreeTree62_413 degreeTree62_414) - -def degreeTree62_416 : RowTree := (.node [12,9,8,5,5,5,5,4,3,2,2,1,1] (.node [12,9,7,7,7,7,6,1,1,1,1,1,1,1] (.node [12,9,7,7,7,7,5,2,2,2,1,1] (.node [12,9,7,7,7,7,5,2,2,1,1,1,1] (.node [12,9,7,7,7,7,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,7,5,3,2,1,1,1] (.node [12,9,7,7,7,7,5,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,7,7,7,1,1,1,1,1,1] (.node [12,9,7,7,7,7,6,2,2,1,1,1] (.node [12,9,7,7,7,7,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,5,5,5,4,4,4,2,2,1,1] .empty .empty))) (.node [12,9,8,5,5,5,5,5,4,1,1,1,1] (.node [12,9,8,5,5,5,5,5,2,2,2,1,1] (.node [12,9,8,5,5,5,5,4,4,2,2,1] (.node [12,9,8,5,5,5,5,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,5,5,5,5,5,3,2,2,1] (.node [12,9,8,5,5,5,5,5,3,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,6,5,4,4,4,4,2,2,1,1] (.node [12,9,8,5,5,5,5,5,5,1,1,1] (.node [12,9,8,5,5,5,5,5,4,2,1,1] .empty .empty) .empty) (.node [12,9,8,6,5,5,4,4,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_417 : RowTree := (.node [12,9,8,6,5,5,5,5,3,1,1,1,1] (.node [12,9,8,6,5,5,5,4,3,2,2,1] (.node [12,9,8,6,5,5,5,3,3,2,2,1,1] (.node [12,9,8,6,5,5,5,2,2,2,2,2,2] (.node [12,9,8,6,5,5,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,9,8,6,5,5,5,4,3,2,1,1,1] (.node [12,9,8,6,5,5,5,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,6,5,5,5,5,2,2,1,1,1] (.node [12,9,8,6,5,5,5,4,4,2,1,1] (.node [12,9,8,6,5,5,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,6,5,5,5,5,2,2,2,1] .empty .empty))) (.node [12,9,8,6,6,5,4,2,2,2,2,2,2] (.node [12,9,8,6,6,4,4,4,3,2,2,1,1] (.node [12,9,8,6,5,5,5,5,4,1,1,1] (.node [12,9,8,6,5,5,5,5,3,2,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,4,4,4,4,2,2,1] (.node [12,9,8,6,6,4,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,6,6,5,4,4,3,2,1,1,1] (.node [12,9,8,6,6,5,4,4,2,2,2,1,1] (.node [12,9,8,6,6,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,5,4,4,3,2,2,1] .empty .empty)))) - -def degreeTree62_418 : RowTree := (.node [12,9,8,6,5,5,4,4,4,2,1,1,1] degreeTree62_416 degreeTree62_417) - -def degreeTree62_419 : RowTree := (.node [12,9,7,7,7,7,4,4,2,1,1,1] degreeTree62_415 degreeTree62_418) - -def degreeTree62_420 : RowTree := (.node [12,9,8,6,6,5,5,5,2,1,1,1,1] (.node [12,9,8,6,6,5,5,4,2,2,1,1,1] (.node [12,9,8,6,6,5,5,3,2,2,2,1,1] (.node [12,9,8,6,6,5,5,2,2,2,2,2,1] (.node [12,9,8,6,6,5,4,4,4,2,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,5,5,3,3,2,2,1] (.node [12,9,8,6,6,5,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,6,6,5,5,4,3,2,1,1] (.node [12,9,8,6,6,5,5,4,3,1,1,1,1] (.node [12,9,8,6,6,5,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,9,8,6,6,5,5,4,4,1,1,1] .empty .empty))) (.node [12,9,8,6,6,6,4,3,2,2,2,1,1] (.node [12,9,8,6,6,6,3,2,2,2,2,2,2] (.node [12,9,8,6,6,5,5,5,3,1,1,1] (.node [12,9,8,6,6,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,6,4,2,2,2,2,2,1] (.node [12,9,8,6,6,6,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,6,6,6,4,4,2,2,1,1,1] (.node [12,9,8,6,6,6,4,3,3,2,2,1] (.node [12,9,8,6,6,6,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,6,4,4,2,2,2,1] .empty .empty)))) - -def degreeTree62_421 : RowTree := (.node [12,9,8,6,6,6,5,4,3,1,1,1] (.node [12,9,8,6,6,6,5,3,2,2,2,1] (.node [12,9,8,6,6,6,5,2,2,2,2,1,1] (.node [12,9,8,6,6,6,4,4,4,1,1,1] (.node [12,9,8,6,6,6,4,4,3,2,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,6,5,3,2,2,1,1,1] (.node [12,9,8,6,6,6,5,2,2,2,2,2] .empty .empty) .empty)) (.node [12,9,8,6,6,6,5,4,2,1,1,1,1] (.node [12,9,8,6,6,6,5,3,3,2,1,1] (.node [12,9,8,6,6,6,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,6,5,4,2,2,1,1] .empty .empty))) (.node [12,9,8,6,6,6,6,3,2,2,1,1] (.node [12,9,8,6,6,6,6,2,2,2,1,1,1] (.node [12,9,8,6,6,6,5,5,2,1,1,1] (.node [12,9,8,6,6,6,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,6,6,3,2,1,1,1,1] (.node [12,9,8,6,6,6,6,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,6,6,6,6,4,2,1,1,1] (.node [12,9,8,6,6,6,6,4,1,1,1,1,1] (.node [12,9,8,6,6,6,6,3,3,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,4,4,4,4,4,2,2,1,1] .empty .empty)))) - -def degreeTree62_422 : RowTree := (.node [12,9,8,6,6,6,4,4,3,1,1,1,1] degreeTree62_420 degreeTree62_421) - -def degreeTree62_423 : RowTree := (.node [12,9,8,7,5,5,5,3,2,2,2,1,1] (.node [12,9,8,7,5,5,4,4,3,2,1,1,1] (.node [12,9,8,7,5,5,4,2,2,2,2,2,2] (.node [12,9,8,7,5,4,4,4,4,2,2,1] (.node [12,9,8,7,5,4,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,5,5,4,4,2,2,2,1,1] (.node [12,9,8,7,5,5,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,7,5,5,4,4,4,2,1,1] (.node [12,9,8,7,5,5,4,4,4,1,1,1,1] (.node [12,9,8,7,5,5,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,9,8,7,5,5,5,2,2,2,2,2,1] .empty .empty))) (.node [12,9,8,7,5,5,5,4,3,2,1,1] (.node [12,9,8,7,5,5,5,4,2,2,1,1,1] (.node [12,9,8,7,5,5,5,3,3,2,2,1] (.node [12,9,8,7,5,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,5,5,5,4,3,1,1,1,1] (.node [12,9,8,7,5,5,5,4,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,7,5,5,5,5,2,2,1,1] (.node [12,9,8,7,5,5,5,5,2,1,1,1,1] (.node [12,9,8,7,5,5,5,4,4,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,5,5,5,5,3,1,1,1] .empty .empty)))) - -def degreeTree62_424 : RowTree := (.node [12,9,8,7,6,5,4,3,3,2,1,1,1] (.node [12,9,8,7,6,4,4,4,4,2,1,1] (.node [12,9,8,7,6,4,4,4,3,2,1,1,1] (.node [12,9,8,7,6,4,4,4,2,2,2,1,1] (.node [12,9,8,7,6,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,4,4,4,4,1,1,1,1] (.node [12,9,8,7,6,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,9,8,7,6,5,4,2,2,2,2,2,1] (.node [12,9,8,7,6,5,3,3,3,2,2,1,1] (.node [12,9,8,7,6,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,8,7,6,5,4,3,2,2,2,1,1] .empty .empty))) (.node [12,9,8,7,6,5,4,4,4,1,1,1] (.node [12,9,8,7,6,5,4,4,2,2,2,1] (.node [12,9,8,7,6,5,4,4,2,2,1,1,1] (.node [12,9,8,7,6,5,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,9,8,7,6,5,4,4,3,2,1,1] (.node [12,9,8,7,6,5,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,7,6,5,5,3,2,2,1,1,1] (.node [12,9,8,7,6,5,5,2,2,2,2,2] (.node [12,9,8,7,6,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,5,5,3,2,2,2,1] .empty .empty)))) - -def degreeTree62_425 : RowTree := (.node [12,9,8,7,6,4,4,2,2,2,2,2,2] degreeTree62_423 degreeTree62_424) - -def degreeTree62_426 : RowTree := (.node [12,9,8,7,5,4,4,4,3,2,2,1,1] degreeTree62_422 degreeTree62_425) - -def degreeTree62_427 : RowTree := (.node [12,9,8,6,6,5,4,4,4,1,1,1,1] degreeTree62_419 degreeTree62_426) - -def degreeTree62_428 : RowTree := (.node [12,9,8,7,6,6,3,3,3,2,2,1] (.node [12,9,8,7,6,5,5,5,2,1,1,1] (.node [12,9,8,7,6,5,5,4,2,2,1,1] (.node [12,9,8,7,6,5,5,4,2,1,1,1,1] (.node [12,9,8,7,6,5,5,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,5,5,5,1,1,1,1,1] (.node [12,9,8,7,6,5,5,4,3,1,1,1] .empty .empty) .empty)) (.node [12,9,8,7,6,6,3,3,2,2,2,1,1] (.node [12,9,8,7,6,6,3,2,2,2,2,2,1] (.node [12,9,8,7,6,6,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,8,7,6,6,3,3,3,2,1,1,1] .empty .empty))) (.node [12,9,8,7,6,6,4,3,3,2,1,1] (.node [12,9,8,7,6,6,4,3,2,2,1,1,1] (.node [12,9,8,7,6,6,4,2,2,2,2,2] (.node [12,9,8,7,6,6,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,6,4,3,3,1,1,1,1] (.node [12,9,8,7,6,6,4,3,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,7,6,6,4,4,3,1,1,1] (.node [12,9,8,7,6,6,4,4,2,2,1,1] (.node [12,9,8,7,6,6,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,6,5,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_429 : RowTree := (.node [12,9,8,7,7,4,3,2,2,2,2,2,2] (.node [12,9,8,7,6,6,6,2,1,1,1,1,1,1] (.node [12,9,8,7,6,6,5,3,3,1,1,1] (.node [12,9,8,7,6,6,5,3,2,2,1,1] (.node [12,9,8,7,6,6,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,6,5,4,2,1,1,1] (.node [12,9,8,7,6,6,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,7,6,6,6,3,1,1,1,1,1] (.node [12,9,8,7,6,6,6,2,2,2,1,1] (.node [12,9,8,7,6,6,6,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,6,6,3,2,1,1,1] .empty .empty))) (.node [12,9,8,7,7,4,4,4,2,2,1,1,1] (.node [12,9,8,7,7,4,4,3,2,2,2,1,1] (.node [12,9,8,7,7,4,4,2,2,2,2,2,1] (.node [12,9,8,7,7,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,4,4,3,3,2,2,1] (.node [12,9,8,7,7,4,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,7,7,4,4,4,3,2,1,1] (.node [12,9,8,7,7,4,4,4,3,1,1,1,1] (.node [12,9,8,7,7,4,4,4,2,2,2,1] .empty .empty) .empty) (.node [12,9,8,7,7,4,4,4,4,1,1,1] .empty .empty)))) - -def degreeTree62_430 : RowTree := (.node [12,9,8,7,6,6,5,2,2,2,2,1] degreeTree62_428 degreeTree62_429) - -def degreeTree62_431 : RowTree := (.node [12,9,8,7,7,5,4,4,2,1,1,1,1] (.node [12,9,8,7,7,5,4,2,2,2,2,2] (.node [12,9,8,7,7,5,3,3,3,2,1,1,1] (.node [12,9,8,7,7,5,3,3,2,2,2,1,1] (.node [12,9,8,7,7,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,8,7,7,5,4,2,2,2,2,1,1] (.node [12,9,8,7,7,5,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,8,7,7,5,4,3,3,1,1,1,1] (.node [12,9,8,7,7,5,4,3,2,2,2,1] (.node [12,9,8,7,7,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,5,4,3,3,2,1,1] .empty .empty))) (.node [12,9,8,7,7,5,5,3,2,2,1,1] (.node [12,9,8,7,7,5,5,2,2,2,1,1,1] (.node [12,9,8,7,7,5,4,4,3,1,1,1] (.node [12,9,8,7,7,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,5,5,3,2,1,1,1,1] (.node [12,9,8,7,7,5,5,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,7,7,5,5,4,2,1,1,1] (.node [12,9,8,7,7,5,5,4,1,1,1,1,1] (.node [12,9,8,7,7,5,5,3,3,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,6,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_432 : RowTree := (.node [12,9,8,7,7,6,4,2,2,2,2,1] (.node [12,9,8,7,7,6,3,3,2,2,2,1] (.node [12,9,8,7,7,6,3,2,2,2,2,2] (.node [12,9,8,7,7,6,3,2,2,2,2,1,1] (.node [12,9,8,7,7,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,6,3,3,2,2,1,1,1] (.node [12,9,8,7,7,6,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,7,7,6,4,2,2,1,1,1,1,1] (.node [12,9,8,7,7,6,3,3,3,2,1,1] (.node [12,9,8,7,7,6,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,6,4,2,2,2,1,1,1] .empty .empty))) (.node [12,9,8,7,7,6,4,4,2,1,1,1] (.node [12,9,8,7,7,6,4,3,2,2,1,1] (.node [12,9,8,7,7,6,4,3,2,1,1,1,1] (.node [12,9,8,7,7,6,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,6,4,4,1,1,1,1,1] (.node [12,9,8,7,7,6,4,3,3,1,1,1] .empty .empty) .empty)) (.node [12,9,8,7,7,6,5,2,2,2,1,1] (.node [12,9,8,7,7,6,5,2,2,1,1,1,1] (.node [12,9,8,7,7,6,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,6,5,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_433 : RowTree := (.node [12,9,8,7,7,6,2,2,2,2,2,2,1] degreeTree62_431 degreeTree62_432) - -def degreeTree62_434 : RowTree := (.node [12,9,8,7,7,5,2,2,2,2,2,2,2] degreeTree62_430 degreeTree62_433) - -def degreeTree62_435 : RowTree := (.node [12,9,8,7,7,7,3,3,2,2,1,1] (.node [12,9,8,7,7,7,3,2,2,1,1,1,1,1] (.node [12,9,8,7,7,7,2,2,2,2,1,1,1,1] (.node [12,9,8,7,7,6,6,2,1,1,1,1,1] (.node [12,9,8,7,7,6,6,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,7,2,2,2,2,2,2] (.node [12,9,8,7,7,7,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,7,7,7,3,3,1,1,1,1,1,1] (.node [12,9,8,7,7,7,3,2,2,2,2,1] (.node [12,9,8,7,7,7,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,7,3,3,2,1,1,1,1] .empty .empty))) (.node [12,9,8,7,7,7,5,1,1,1,1,1,1,1] (.node [12,9,8,7,7,7,4,2,2,1,1,1,1] (.node [12,9,8,7,7,7,4,2,1,1,1,1,1,1] (.node [12,9,8,7,7,7,3,3,3,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,7,4,3,1,1,1,1,1] (.node [12,9,8,7,7,7,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,8,4,4,4,4,3,2,2,1,1] (.node [12,9,8,7,7,7,6,1,1,1,1,1,1] (.node [12,9,8,7,7,7,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,4,4,4,4,4,2,1,1,1] .empty .empty)))) - -def degreeTree62_436 : RowTree := (.node [12,9,8,8,5,5,4,3,2,2,2,1,1] (.node [12,9,8,8,5,4,4,4,4,1,1,1,1] (.node [12,9,8,8,5,4,4,4,2,2,2,1,1] (.node [12,9,8,8,5,4,4,3,3,2,2,1,1] (.node [12,9,8,8,5,4,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,8,8,5,4,4,4,3,2,2,1] (.node [12,9,8,8,5,4,4,4,3,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,5,5,3,3,3,2,2,1,1] (.node [12,9,8,8,5,5,3,2,2,2,2,2,2] (.node [12,9,8,8,5,4,4,4,4,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,5,5,4,2,2,2,2,2,1] .empty .empty))) (.node [12,9,8,8,5,5,4,4,3,2,1,1] (.node [12,9,8,8,5,5,4,4,2,2,1,1,1] (.node [12,9,8,8,5,5,4,3,3,2,2,1] (.node [12,9,8,8,5,5,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,5,5,4,4,3,1,1,1,1] (.node [12,9,8,8,5,5,4,4,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,5,5,5,2,2,2,2,2] (.node [12,9,8,8,5,5,5,2,2,2,2,1,1] (.node [12,9,8,8,5,5,4,4,4,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,5,5,5,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_437 : RowTree := (.node [12,9,8,8,4,4,4,4,4,2,2,1] degreeTree62_435 degreeTree62_436) - -def degreeTree62_438 : RowTree := (.node [12,9,8,8,6,4,4,3,2,2,2,1,1] (.node [12,9,8,8,5,5,5,5,1,1,1,1,1] (.node [12,9,8,8,5,5,5,4,2,1,1,1,1] (.node [12,9,8,8,5,5,5,3,3,2,1,1] (.node [12,9,8,8,5,5,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,5,5,5,4,3,1,1,1] (.node [12,9,8,8,5,5,5,4,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,8,6,4,3,3,3,2,2,1,1] (.node [12,9,8,8,6,4,3,2,2,2,2,2,2] (.node [12,9,8,8,5,5,5,5,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,4,4,2,2,2,2,2,1] .empty .empty))) (.node [12,9,8,8,6,4,4,4,3,2,1,1] (.node [12,9,8,8,6,4,4,4,2,2,1,1,1] (.node [12,9,8,8,6,4,4,3,3,2,2,1] (.node [12,9,8,8,6,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,4,4,4,3,1,1,1,1] (.node [12,9,8,8,6,4,4,4,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,6,5,3,2,2,2,2,2,1] (.node [12,9,8,8,6,5,2,2,2,2,2,2,2] (.node [12,9,8,8,6,4,4,4,4,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,5,3,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_439 : RowTree := (.node [12,9,8,8,6,5,5,2,2,2,1,1,1] (.node [12,9,8,8,6,5,4,3,3,1,1,1,1] (.node [12,9,8,8,6,5,4,2,2,2,2,2] (.node [12,9,8,8,6,5,4,2,2,2,2,1,1] (.node [12,9,8,8,6,5,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,9,8,8,6,5,4,3,2,2,2,1] (.node [12,9,8,8,6,5,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,6,5,4,4,2,2,1,1] (.node [12,9,8,8,6,5,4,4,2,1,1,1,1] (.node [12,9,8,8,6,5,4,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,5,4,4,3,1,1,1] .empty .empty))) (.node [12,9,8,8,6,5,5,4,1,1,1,1,1] (.node [12,9,8,8,6,5,5,3,2,2,1,1] (.node [12,9,8,8,6,5,5,3,2,1,1,1,1] (.node [12,9,8,8,6,5,5,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,8,8,6,5,5,3,3,1,1,1] .empty .empty)) (.node [12,9,8,8,6,6,2,2,2,2,2,2,1] (.node [12,9,8,8,6,6,2,2,2,2,2,1,1,1] (.node [12,9,8,8,6,5,5,4,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,6,3,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_440 : RowTree := (.node [12,9,8,8,6,5,3,3,3,2,1,1,1] degreeTree62_438 degreeTree62_439) - -def degreeTree62_441 : RowTree := (.node [12,9,8,8,5,5,5,3,2,2,2,1] degreeTree62_437 degreeTree62_440) - -def degreeTree62_442 : RowTree := (.node [12,9,8,7,7,6,5,3,2,1,1,1] degreeTree62_434 degreeTree62_441) - -def degreeTree62_443 : RowTree := (.node [12,9,8,7,6,5,5,3,3,1,1,1,1] degreeTree62_427 degreeTree62_442) - -def degreeTree62_444 : RowTree := (.node [12,9,7,7,7,6,2,2,2,2,2,2,2] degreeTree62_412 degreeTree62_443) - -def degreeTree62_445 : RowTree := (.node [12,9,8,8,6,6,4,3,2,1,1,1,1] (.node [12,9,8,8,6,6,3,3,3,2,1,1] (.node [12,9,8,8,6,6,3,3,2,2,1,1,1] (.node [12,9,8,8,6,6,3,3,2,1,1,1,1,1] (.node [12,9,8,8,6,6,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,8,8,6,6,3,3,3,1,1,1,1] (.node [12,9,8,8,6,6,3,3,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,6,6,4,2,2,2,2,1] (.node [12,9,8,8,6,6,4,2,2,2,1,1,1] (.node [12,9,8,8,6,6,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,6,4,3,1,1,1,1,1,1] .empty .empty))) (.node [12,9,8,8,6,6,5,2,2,1,1,1,1] (.node [12,9,8,8,6,6,4,4,1,1,1,1,1] (.node [12,9,8,8,6,6,4,3,3,1,1,1] (.node [12,9,8,8,6,6,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,6,5,2,1,1,1,1,1,1] (.node [12,9,8,8,6,6,4,4,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,6,6,6,1,1,1,1,1,1,1] (.node [12,9,8,8,6,6,5,3,1,1,1,1,1] (.node [12,9,8,8,6,6,5,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,6,6,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_446 : RowTree := (.node [12,9,8,8,7,4,4,2,2,2,2,2] (.node [12,9,8,8,7,4,3,3,3,1,1,1,1,1] (.node [12,9,8,8,7,4,3,2,2,2,2,1,1,1] (.node [12,9,8,8,7,4,2,2,2,2,2,2,2] (.node [12,9,8,8,7,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,4,3,3,2,2,2,1,1] (.node [12,9,8,8,7,4,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,7,4,4,2,2,2,1,1,1,1] (.node [12,9,8,8,7,4,3,3,3,2,2,1] (.node [12,9,8,8,7,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,4,4,2,2,2,2,1,1] .empty .empty))) (.node [12,9,8,8,7,4,4,4,1,1,1,1,1,1] (.node [12,9,8,8,7,4,4,3,2,2,2,1] (.node [12,9,8,8,7,4,4,3,2,2,1,1,1] (.node [12,9,8,8,7,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,4,4,3,3,2,1,1] (.node [12,9,8,8,7,4,4,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,7,4,4,4,3,1,1,1] (.node [12,9,8,8,7,4,4,4,2,2,1,1] (.node [12,9,8,8,7,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,5,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_447 : RowTree := (.node [12,9,8,8,7,3,3,2,2,2,2,2,2] degreeTree62_445 degreeTree62_446) - -def degreeTree62_448 : RowTree := (.node [12,9,8,8,7,5,4,2,2,2,2,1] (.node [12,9,8,8,7,5,3,3,2,2,2,1] (.node [12,9,8,8,7,5,3,2,2,2,2,2] (.node [12,9,8,8,7,5,3,2,2,2,2,1,1] (.node [12,9,8,8,7,5,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,5,3,3,2,2,1,1,1] (.node [12,9,8,8,7,5,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,7,5,4,2,2,1,1,1,1,1] (.node [12,9,8,8,7,5,3,3,3,2,1,1] (.node [12,9,8,8,7,5,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,5,4,2,2,2,1,1,1] .empty .empty))) (.node [12,9,8,8,7,5,5,2,1,1,1,1,1,1] (.node [12,9,8,8,7,5,4,3,2,2,1,1] (.node [12,9,8,8,7,5,4,3,2,1,1,1,1] (.node [12,9,8,8,7,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,5,4,4,1,1,1,1,1] (.node [12,9,8,8,7,5,4,3,3,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,7,5,5,3,1,1,1,1,1] (.node [12,9,8,8,7,5,5,2,2,2,1,1] (.node [12,9,8,8,7,5,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,6,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_449 : RowTree := (.node [12,9,8,8,7,6,4,2,2,2,1,1] (.node [12,9,8,8,7,6,3,3,2,1,1,1,1] (.node [12,9,8,8,7,6,3,2,2,2,1,1,1] (.node [12,9,8,8,7,6,3,2,2,1,1,1,1,1] (.node [12,9,8,8,7,6,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,8,8,7,6,3,3,1,1,1,1,1,1] (.node [12,9,8,8,7,6,3,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,7,6,4,2,1,1,1,1,1,1] (.node [12,9,8,8,7,6,3,3,3,1,1,1] (.node [12,9,8,8,7,6,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,6,4,2,2,1,1,1,1] .empty .empty))) (.node [12,9,8,8,7,7,2,2,2,2,1,1,1] (.node [12,9,8,8,7,6,5,2,1,1,1,1,1] (.node [12,9,8,8,7,6,5,1,1,1,1,1,1,1] (.node [12,9,8,8,7,6,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,7,2,2,2,1,1,1,1,1] (.node [12,9,8,8,7,6,6,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,7,7,3,2,2,1,1,1,1] (.node [12,9,8,8,7,7,3,2,1,1,1,1,1,1] (.node [12,9,8,8,7,7,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,8,8,7,7,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_450 : RowTree := (.node [12,9,8,8,7,6,2,2,2,2,2,1,1] degreeTree62_448 degreeTree62_449) - -def degreeTree62_451 : RowTree := (.node [12,9,8,8,7,5,2,2,2,2,2,2,1] degreeTree62_447 degreeTree62_450) - -def degreeTree62_452 : RowTree := (.node [12,9,8,8,8,3,3,3,3,2,2,1] (.node [12,9,8,8,8,3,3,2,2,2,2,1,1,1] (.node [12,9,8,8,7,7,5,1,1,1,1,1,1] (.node [12,9,8,8,7,7,4,2,1,1,1,1,1] (.node [12,9,8,8,7,7,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,3,2,2,2,2,2,2,2] (.node [12,9,8,8,8,2,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,8,3,3,3,3,1,1,1,1,1] (.node [12,9,8,8,8,3,3,3,2,2,2,1,1] (.node [12,9,8,8,8,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,8,8,8,3,3,3,3,2,1,1,1] .empty .empty))) (.node [12,9,8,8,8,4,3,3,2,1,1,1,1,1] (.node [12,9,8,8,8,4,3,2,2,2,1,1,1,1] (.node [12,9,8,8,8,4,2,2,2,2,2,2,1] (.node [12,9,8,8,8,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,4,3,2,2,2,2,2] (.node [12,9,8,8,8,4,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,8,8,4,3,3,3,1,1,1,1] (.node [12,9,8,8,8,4,3,3,2,2,2,1] (.node [12,9,8,8,8,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,4,3,3,3,2,1,1] .empty .empty)))) - -def degreeTree62_453 : RowTree := (.node [12,9,8,8,8,5,3,2,2,1,1,1,1,1] (.node [12,9,8,8,8,4,4,3,3,1,1,1] (.node [12,9,8,8,8,4,4,3,1,1,1,1,1,1] (.node [12,9,8,8,8,4,4,2,2,2,2,1] (.node [12,9,8,8,8,4,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,4,4,3,2,2,1,1] (.node [12,9,8,8,8,4,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,8,5,2,2,2,2,2,1,1] (.node [12,9,8,8,8,5,2,2,2,2,1,1,1,1] (.node [12,9,8,8,8,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,5,2,2,2,2,2,2] .empty .empty))) (.node [12,9,8,8,8,5,3,3,3,1,1,1] (.node [12,9,8,8,8,5,3,3,1,1,1,1,1,1] (.node [12,9,8,8,8,5,3,2,2,2,2,1] (.node [12,9,8,8,8,5,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,5,3,3,2,2,1,1] (.node [12,9,8,8,8,5,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,8,5,4,2,2,2,1,1] (.node [12,9,8,8,8,5,4,2,2,1,1,1,1] (.node [12,9,8,8,8,5,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,5,4,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_454 : RowTree := (.node [12,9,8,8,8,4,4,2,2,1,1,1,1,1] degreeTree62_452 degreeTree62_453) - -def degreeTree62_455 : RowTree := (.node [12,9,8,8,8,6,5,1,1,1,1,1,1] (.node [12,9,8,8,8,6,3,2,2,1,1,1,1] (.node [12,9,8,8,8,6,2,2,2,2,1,1,1] (.node [12,9,8,8,8,6,2,2,2,1,1,1,1,1] (.node [12,9,8,8,8,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,6,3,2,1,1,1,1,1,1] (.node [12,9,8,8,8,6,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,8,6,4,1,1,1,1,1,1,1] (.node [12,9,8,8,8,6,3,3,1,1,1,1,1] (.node [12,9,8,8,8,6,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,6,4,2,1,1,1,1,1] .empty .empty))) (.node [12,9,8,8,8,7,4,1,1,1,1,1,1] (.node [12,9,8,8,8,7,2,2,2,2,1,1] (.node [12,9,8,8,8,7,2,2,2,1,1,1,1] (.node [12,9,8,8,8,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,7,3,2,1,1,1,1,1] (.node [12,9,8,8,8,7,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,8,8,3,1,1,1,1,1,1] (.node [12,9,8,8,8,8,2,2,1,1,1,1,1] (.node [12,9,8,8,8,8,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,5,5,4,4,4,4,2,2,1,1] .empty .empty)))) - -def degreeTree62_456 : RowTree := (.node [12,9,9,5,5,5,5,5,2,2,2,1] (.node [12,9,9,5,5,5,5,4,3,2,1,1,1] (.node [12,9,9,5,5,5,5,2,2,2,2,2,2] (.node [12,9,9,5,5,5,4,4,4,2,2,1] (.node [12,9,9,5,5,5,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,5,5,5,5,4,2,2,2,1,1] (.node [12,9,9,5,5,5,5,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,5,5,5,5,4,4,2,1,1] (.node [12,9,9,5,5,5,5,4,4,1,1,1,1] (.node [12,9,9,5,5,5,5,4,3,2,2,1] .empty .empty) .empty) (.node [12,9,9,5,5,5,5,5,2,2,1,1,1] .empty .empty))) (.node [12,9,9,6,5,4,4,4,4,2,1,1,1] (.node [12,9,9,5,5,5,5,5,4,1,1,1] (.node [12,9,9,5,5,5,5,5,3,2,1,1] (.node [12,9,9,5,5,5,5,5,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,6,5,4,4,4,3,2,2,1,1] (.node [12,9,9,6,4,4,4,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,6,5,5,4,3,3,2,2,1,1] (.node [12,9,9,6,5,5,4,2,2,2,2,2,2] (.node [12,9,9,6,5,4,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,9,9,6,5,5,4,4,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_457 : RowTree := (.node [12,9,9,5,5,5,4,4,3,2,2,1,1] degreeTree62_455 degreeTree62_456) - -def degreeTree62_458 : RowTree := (.node [12,9,8,8,8,5,5,1,1,1,1,1,1,1] degreeTree62_454 degreeTree62_457) - -def degreeTree62_459 : RowTree := (.node [12,9,8,8,7,7,3,3,1,1,1,1,1] degreeTree62_451 degreeTree62_458) - -def degreeTree62_460 : RowTree := (.node [12,9,9,6,5,5,5,4,3,2,1,1] (.node [12,9,9,6,5,5,5,3,3,2,1,1,1] (.node [12,9,9,6,5,5,4,4,4,2,1,1] (.node [12,9,9,6,5,5,4,4,4,1,1,1,1] (.node [12,9,9,6,5,5,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,9,9,6,5,5,5,3,2,2,2,1,1] (.node [12,9,9,6,5,5,5,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,6,5,5,5,4,2,2,2,1] (.node [12,9,9,6,5,5,5,4,2,2,1,1,1] (.node [12,9,9,6,5,5,5,3,3,2,2,1] .empty .empty) .empty) (.node [12,9,9,6,5,5,5,4,3,1,1,1,1] .empty .empty))) (.node [12,9,9,6,6,4,4,3,3,2,2,1,1] (.node [12,9,9,6,5,5,5,5,2,2,1,1] (.node [12,9,9,6,5,5,5,5,2,1,1,1,1] (.node [12,9,9,6,5,5,5,4,4,1,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,4,4,2,2,2,2,2,2] (.node [12,9,9,6,5,5,5,5,3,1,1,1] .empty .empty) .empty)) (.node [12,9,9,6,6,4,4,4,3,2,2,1] (.node [12,9,9,6,6,4,4,4,3,2,1,1,1] (.node [12,9,9,6,6,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,4,4,4,4,1,1,1,1] .empty .empty)))) - -def degreeTree62_461 : RowTree := (.node [12,9,9,6,6,5,4,4,4,1,1,1] (.node [12,9,9,6,6,5,4,3,3,2,2,1] (.node [12,9,9,6,6,5,4,2,2,2,2,2,1] (.node [12,9,9,6,6,5,3,3,3,2,2,1,1] (.node [12,9,9,6,6,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,6,6,5,4,3,3,2,1,1,1] (.node [12,9,9,6,6,5,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,6,6,5,4,4,3,1,1,1,1] (.node [12,9,9,6,6,5,4,4,2,2,2,1] (.node [12,9,9,6,6,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,5,4,4,3,2,1,1] .empty .empty))) (.node [12,9,9,6,6,5,5,3,3,2,1,1] (.node [12,9,9,6,6,5,5,3,2,2,1,1,1] (.node [12,9,9,6,6,5,5,2,2,2,2,2] (.node [12,9,9,6,6,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,5,5,3,3,1,1,1,1] (.node [12,9,9,6,6,5,5,3,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,6,6,5,5,4,3,1,1,1] (.node [12,9,9,6,6,5,5,4,2,2,1,1] (.node [12,9,9,6,6,5,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,5,5,5,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_462 : RowTree := (.node [12,9,9,6,6,4,4,4,4,2,1,1] degreeTree62_460 degreeTree62_461) - -def degreeTree62_463 : RowTree := (.node [12,9,9,6,6,6,4,4,2,1,1,1,1] (.node [12,9,9,6,6,6,4,2,2,2,2,2] (.node [12,9,9,6,6,6,3,3,3,2,1,1,1] (.node [12,9,9,6,6,6,3,3,2,2,2,1,1] (.node [12,9,9,6,6,6,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,6,6,6,4,2,2,2,2,1,1] (.node [12,9,9,6,6,6,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,9,6,6,6,4,3,3,1,1,1,1] (.node [12,9,9,6,6,6,4,3,2,2,2,1] (.node [12,9,9,6,6,6,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,6,4,3,3,2,1,1] .empty .empty))) (.node [12,9,9,6,6,6,5,3,2,2,1,1] (.node [12,9,9,6,6,6,5,2,2,2,1,1,1] (.node [12,9,9,6,6,6,4,4,3,1,1,1] (.node [12,9,9,6,6,6,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,6,5,3,2,1,1,1,1] (.node [12,9,9,6,6,6,5,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,6,6,6,6,2,1,1,1,1,1,1] (.node [12,9,9,6,6,6,5,4,1,1,1,1,1] (.node [12,9,9,6,6,6,5,3,3,1,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,6,6,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_464 : RowTree := (.node [12,9,9,7,5,4,4,4,4,2,1,1] (.node [12,9,9,7,5,4,4,3,3,2,2,1,1] (.node [12,9,9,7,4,4,4,4,4,2,1,1,1] (.node [12,9,9,7,4,4,4,4,3,2,2,1,1] (.node [12,9,9,6,6,6,6,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,5,4,4,2,2,2,2,2,2] (.node [12,9,9,7,4,4,4,4,4,2,2,1] .empty .empty) .empty)) (.node [12,9,9,7,5,4,4,4,3,2,2,1] (.node [12,9,9,7,5,4,4,4,3,2,1,1,1] (.node [12,9,9,7,5,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,5,4,4,4,4,1,1,1,1] .empty .empty))) (.node [12,9,9,7,5,5,4,3,3,2,2,1] (.node [12,9,9,7,5,5,4,2,2,2,2,2,1] (.node [12,9,9,7,5,5,3,3,3,2,2,1,1] (.node [12,9,9,7,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,7,5,5,4,3,3,2,1,1,1] (.node [12,9,9,7,5,5,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,7,5,5,4,4,3,1,1,1,1] (.node [12,9,9,7,5,5,4,4,2,2,2,1] (.node [12,9,9,7,5,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,5,5,4,4,3,2,1,1] .empty .empty)))) - -def degreeTree62_465 : RowTree := (.node [12,9,9,6,6,6,6,2,2,2,1,1] degreeTree62_463 degreeTree62_464) - -def degreeTree62_466 : RowTree := (.node [12,9,9,6,6,6,2,2,2,2,2,2,2] degreeTree62_462 degreeTree62_465) - -def degreeTree62_467 : RowTree := (.node [12,9,9,7,6,4,3,2,2,2,2,2,2] (.node [12,9,9,7,5,5,5,3,3,2,1,1] (.node [12,9,9,7,5,5,5,3,2,2,1,1,1] (.node [12,9,9,7,5,5,5,2,2,2,2,2] (.node [12,9,9,7,5,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,5,5,5,3,3,1,1,1,1] (.node [12,9,9,7,5,5,5,3,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,7,5,5,5,4,3,1,1,1] (.node [12,9,9,7,5,5,5,4,2,2,1,1] (.node [12,9,9,7,5,5,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,5,5,5,5,1,1,1,1,1] .empty .empty))) (.node [12,9,9,7,6,4,4,4,2,2,1,1,1] (.node [12,9,9,7,6,4,4,3,2,2,2,1,1] (.node [12,9,9,7,6,4,4,2,2,2,2,2,1] (.node [12,9,9,7,6,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,4,4,3,3,2,2,1] (.node [12,9,9,7,6,4,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,7,6,4,4,4,3,2,1,1] (.node [12,9,9,7,6,4,4,4,3,1,1,1,1] (.node [12,9,9,7,6,4,4,4,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,7,6,4,4,4,4,1,1,1] .empty .empty)))) - -def degreeTree62_468 : RowTree := (.node [12,9,9,7,6,5,4,4,2,1,1,1,1] (.node [12,9,9,7,6,5,4,2,2,2,2,2] (.node [12,9,9,7,6,5,3,3,3,2,1,1,1] (.node [12,9,9,7,6,5,3,3,2,2,2,1,1] (.node [12,9,9,7,6,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,7,6,5,4,2,2,2,2,1,1] (.node [12,9,9,7,6,5,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,9,7,6,5,4,3,3,1,1,1,1] (.node [12,9,9,7,6,5,4,3,2,2,2,1] (.node [12,9,9,7,6,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,5,4,3,3,2,1,1] .empty .empty))) (.node [12,9,9,7,6,5,5,3,2,2,1,1] (.node [12,9,9,7,6,5,5,2,2,2,1,1,1] (.node [12,9,9,7,6,5,4,4,3,1,1,1] (.node [12,9,9,7,6,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,5,5,3,2,1,1,1,1] (.node [12,9,9,7,6,5,5,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,7,6,6,2,2,2,2,2,1,1,1] (.node [12,9,9,7,6,5,5,4,1,1,1,1,1] (.node [12,9,9,7,6,5,5,3,3,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,6,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_469 : RowTree := (.node [12,9,9,7,6,5,2,2,2,2,2,2,2] degreeTree62_467 degreeTree62_468) - -def degreeTree62_470 : RowTree := (.node [12,9,9,7,6,6,4,3,1,1,1,1,1,1] (.node [12,9,9,7,6,6,3,3,3,1,1,1,1] (.node [12,9,9,7,6,6,3,3,2,1,1,1,1,1] (.node [12,9,9,7,6,6,3,2,2,2,2,2] (.node [12,9,9,7,6,6,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,6,3,3,2,2,2,1] (.node [12,9,9,7,6,6,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,7,6,6,4,2,2,2,1,1,1] (.node [12,9,9,7,6,6,4,2,2,1,1,1,1,1] (.node [12,9,9,7,6,6,3,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,6,4,2,2,2,2,1] .empty .empty))) (.node [12,9,9,7,6,6,5,2,2,1,1,1,1] (.node [12,9,9,7,6,6,4,3,3,1,1,1] (.node [12,9,9,7,6,6,4,3,2,2,1,1] (.node [12,9,9,7,6,6,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,6,5,2,1,1,1,1,1,1] (.node [12,9,9,7,6,6,4,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,7,6,6,6,1,1,1,1,1,1,1] (.node [12,9,9,7,6,6,5,3,1,1,1,1,1] (.node [12,9,9,7,6,6,5,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,6,6,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_471 : RowTree := (.node [12,9,9,7,7,4,4,2,2,2,2,2] (.node [12,9,9,7,7,4,3,3,3,1,1,1,1,1] (.node [12,9,9,7,7,4,3,2,2,2,2,1,1,1] (.node [12,9,9,7,7,4,2,2,2,2,2,2,2] (.node [12,9,9,7,7,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,4,3,3,2,2,2,1,1] (.node [12,9,9,7,7,4,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,7,7,4,4,2,2,2,1,1,1,1] (.node [12,9,9,7,7,4,3,3,3,2,2,1] (.node [12,9,9,7,7,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,4,4,2,2,2,2,1,1] .empty .empty))) (.node [12,9,9,7,7,4,4,3,3,2,1,1] (.node [12,9,9,7,7,4,4,3,2,2,2,1] (.node [12,9,9,7,7,4,4,3,2,2,1,1,1] (.node [12,9,9,7,7,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,4,4,3,3,1,1,1,1] .empty .empty)) (.node [12,9,9,7,7,4,4,4,2,2,1,1] (.node [12,9,9,7,7,4,4,4,2,1,1,1,1] (.node [12,9,9,7,7,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,4,4,4,3,1,1,1] .empty .empty)))) - -def degreeTree62_472 : RowTree := (.node [12,9,9,7,7,3,3,2,2,2,2,2,2] degreeTree62_470 degreeTree62_471) - -def degreeTree62_473 : RowTree := (.node [12,9,9,7,6,6,3,2,2,2,1,1,1,1] degreeTree62_469 degreeTree62_472) - -def degreeTree62_474 : RowTree := (.node [12,9,9,7,5,5,4,4,4,1,1,1] degreeTree62_466 degreeTree62_473) - -def degreeTree62_475 : RowTree := (.node [12,9,9,6,5,5,4,4,3,2,1,1,1] degreeTree62_459 degreeTree62_474) - -def degreeTree62_476 : RowTree := (.node [12,9,9,7,7,5,4,2,2,2,1,1,1] (.node [12,9,9,7,7,5,3,3,2,2,1,1,1] (.node [12,9,9,7,7,5,3,2,2,2,2,1,1] (.node [12,9,9,7,7,5,3,2,2,2,1,1,1,1] (.node [12,9,9,7,7,5,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,7,7,5,3,3,2,1,1,1,1,1] (.node [12,9,9,7,7,5,3,2,2,2,2,2] .empty .empty) .empty)) (.node [12,9,9,7,7,5,3,3,3,2,1,1] (.node [12,9,9,7,7,5,3,3,3,1,1,1,1] (.node [12,9,9,7,7,5,3,3,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,7,7,5,4,2,2,1,1,1,1,1] .empty .empty))) (.node [12,9,9,7,7,5,5,2,1,1,1,1,1,1] (.node [12,9,9,7,7,5,4,3,2,1,1,1,1] (.node [12,9,9,7,7,5,4,3,1,1,1,1,1,1] (.node [12,9,9,7,7,5,4,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,7,7,5,4,4,1,1,1,1,1] (.node [12,9,9,7,7,5,4,3,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,7,7,5,5,3,1,1,1,1,1] (.node [12,9,9,7,7,5,5,2,2,2,1,1] (.node [12,9,9,7,7,5,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,6,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_477 : RowTree := (.node [12,9,9,7,7,6,4,3,1,1,1,1,1] (.node [12,9,9,7,7,6,3,3,2,1,1,1,1] (.node [12,9,9,7,7,6,3,2,2,2,1,1,1] (.node [12,9,9,7,7,6,3,2,2,1,1,1,1,1] (.node [12,9,9,7,7,6,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,7,7,6,3,3,1,1,1,1,1,1] (.node [12,9,9,7,7,6,3,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,7,7,6,4,2,2,1,1,1,1] (.node [12,9,9,7,7,6,4,2,1,1,1,1,1,1] (.node [12,9,9,7,7,6,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,6,4,2,2,2,1,1] .empty .empty))) (.node [12,9,9,7,7,7,2,2,2,2,2,1] (.node [12,9,9,7,7,6,6,1,1,1,1,1,1] (.node [12,9,9,7,7,6,5,2,1,1,1,1,1] (.node [12,9,9,7,7,6,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,7,2,2,2,2,1,1,1] (.node [12,9,9,7,7,7,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,7,7,7,3,2,2,2,1,1] (.node [12,9,9,7,7,7,3,2,2,1,1,1,1] (.node [12,9,9,7,7,7,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,7,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_478 : RowTree := (.node [12,9,9,7,7,6,2,2,2,2,2,1,1] degreeTree62_476 degreeTree62_477) - -def degreeTree62_479 : RowTree := (.node [12,9,9,8,5,4,3,3,3,2,2,1,1] (.node [12,9,9,8,4,4,4,4,3,2,1,1,1] (.node [12,9,9,8,4,4,4,2,2,2,2,2,2] (.node [12,9,9,7,7,7,5,1,1,1,1,1,1] (.node [12,9,9,7,7,7,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,4,4,4,4,2,2,2,1,1] (.node [12,9,9,8,4,4,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,8,4,4,4,4,4,2,1,1] (.node [12,9,9,8,4,4,4,4,4,1,1,1,1] (.node [12,9,9,8,4,4,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,5,4,3,2,2,2,2,2,2] .empty .empty))) (.node [12,9,9,8,5,4,4,4,2,2,2,1] (.node [12,9,9,8,5,4,4,3,3,2,1,1,1] (.node [12,9,9,8,5,4,4,3,2,2,2,1,1] (.node [12,9,9,8,5,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,5,4,4,4,2,2,1,1,1] (.node [12,9,9,8,5,4,4,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,9,8,5,4,4,4,4,1,1,1] (.node [12,9,9,8,5,4,4,4,3,2,1,1] (.node [12,9,9,8,5,4,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,5,5,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_480 : RowTree := (.node [12,9,9,8,5,5,4,4,2,2,1,1] (.node [12,9,9,8,5,5,4,3,2,2,1,1,1] (.node [12,9,9,8,5,5,3,3,3,2,2,1] (.node [12,9,9,8,5,5,3,3,3,2,1,1,1] (.node [12,9,9,8,5,5,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,8,5,5,4,2,2,2,2,2] (.node [12,9,9,8,5,5,4,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,8,5,5,4,3,3,2,1,1] (.node [12,9,9,8,5,5,4,3,3,1,1,1,1] (.node [12,9,9,8,5,5,4,3,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,5,5,4,4,2,1,1,1,1] .empty .empty))) (.node [12,9,9,8,5,5,5,4,1,1,1,1,1] (.node [12,9,9,8,5,5,5,2,2,2,2,1] (.node [12,9,9,8,5,5,5,2,2,2,1,1,1] (.node [12,9,9,8,5,5,4,4,3,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,5,5,5,3,2,2,1,1] (.node [12,9,9,8,5,5,5,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,6,4,2,2,2,2,2,2,2] (.node [12,9,9,8,6,3,3,3,3,2,2,1,1] (.node [12,9,9,8,6,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,8,6,4,3,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_481 : RowTree := (.node [12,9,9,8,5,5,3,2,2,2,2,2,1] degreeTree62_479 degreeTree62_480) - -def degreeTree62_482 : RowTree := (.node [12,9,9,7,7,7,4,1,1,1,1,1,1,1] degreeTree62_478 degreeTree62_481) - -def degreeTree62_483 : RowTree := (.node [12,9,9,8,6,4,4,3,3,1,1,1,1] (.node [12,9,9,8,6,4,4,2,2,2,2,1,1] (.node [12,9,9,8,6,4,3,3,3,2,1,1,1] (.node [12,9,9,8,6,4,3,3,3,1,1,1,1,1] (.node [12,9,9,8,6,4,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,4,4,2,2,2,1,1,1,1] (.node [12,9,9,8,6,4,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,9,8,6,4,4,3,2,2,1,1,1] (.node [12,9,9,8,6,4,4,3,2,1,1,1,1,1] (.node [12,9,9,8,6,4,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,8,6,4,4,3,2,2,2,1] .empty .empty))) (.node [12,9,9,8,6,5,2,2,2,2,2,2,1] (.node [12,9,9,8,6,4,4,4,2,1,1,1,1] (.node [12,9,9,8,6,4,4,4,1,1,1,1,1,1] (.node [12,9,9,8,6,4,4,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,5,2,2,2,2,2,1,1,1] (.node [12,9,9,8,6,4,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,8,6,5,3,2,2,2,2,2] (.node [12,9,9,8,6,5,3,2,2,2,2,1,1] (.node [12,9,9,8,6,5,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,5,3,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_484 : RowTree := (.node [12,9,9,8,6,5,5,2,1,1,1,1,1,1] (.node [12,9,9,8,6,5,4,2,2,2,2,1] (.node [12,9,9,8,6,5,3,3,3,2,1,1] (.node [12,9,9,8,6,5,3,3,3,1,1,1,1] (.node [12,9,9,8,6,5,3,3,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,6,5,4,2,2,2,1,1,1] (.node [12,9,9,8,6,5,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,6,5,4,3,2,2,1,1] (.node [12,9,9,8,6,5,4,3,2,1,1,1,1] (.node [12,9,9,8,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,5,4,4,1,1,1,1,1] .empty .empty))) (.node [12,9,9,8,6,6,2,2,2,2,2,2] (.node [12,9,9,8,6,5,5,3,1,1,1,1,1] (.node [12,9,9,8,6,5,5,2,2,2,1,1] (.node [12,9,9,8,6,5,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,6,2,2,2,2,2,1,1] (.node [12,9,9,8,6,6,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,6,6,3,2,2,2,2,1] (.node [12,9,9,8,6,6,3,2,2,2,1,1,1] (.node [12,9,9,8,6,6,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,6,3,3,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_485 : RowTree := (.node [12,9,9,8,6,5,3,3,2,2,1,1,1] degreeTree62_483 degreeTree62_484) - -def degreeTree62_486 : RowTree := (.node [12,9,9,8,7,3,3,2,2,2,2,1,1,1] (.node [12,9,9,8,6,6,5,1,1,1,1,1,1,1] (.node [12,9,9,8,6,6,4,2,2,1,1,1,1] (.node [12,9,9,8,6,6,4,2,1,1,1,1,1,1] (.node [12,9,9,8,6,6,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,6,4,3,1,1,1,1,1] (.node [12,9,9,8,6,6,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,8,7,2,2,2,2,2,2,2,2,1] (.node [12,9,9,8,6,6,6,1,1,1,1,1,1] (.node [12,9,9,8,6,6,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,3,2,2,2,2,2,2,2] .empty .empty))) (.node [12,9,9,8,7,4,2,2,2,2,2,1,1,1] (.node [12,9,9,8,7,3,3,3,3,1,1,1,1,1] (.node [12,9,9,8,7,3,3,3,2,2,2,1,1] (.node [12,9,9,8,7,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,7,3,3,3,3,2,2,1] (.node [12,9,9,8,7,3,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,7,4,3,2,2,2,2,1,1] (.node [12,9,9,8,7,4,3,2,2,2,1,1,1,1] (.node [12,9,9,8,7,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,7,4,3,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_487 : RowTree := (.node [12,9,9,8,7,4,4,4,1,1,1,1,1] (.node [12,9,9,8,7,4,4,2,2,2,1,1,1] (.node [12,9,9,8,7,4,3,3,3,1,1,1,1] (.node [12,9,9,8,7,4,3,3,2,2,2,1] (.node [12,9,9,8,7,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,4,4,2,2,1,1,1,1,1] (.node [12,9,9,8,7,4,3,3,3,2,1,1] .empty .empty) .empty)) (.node [12,9,9,8,7,4,4,3,2,1,1,1,1] (.node [12,9,9,8,7,4,4,3,1,1,1,1,1,1] (.node [12,9,9,8,7,4,4,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,7,4,4,3,2,2,1,1] .empty .empty))) (.node [12,9,9,8,7,5,3,2,2,2,1,1,1] (.node [12,9,9,8,7,5,2,2,2,2,2,2] (.node [12,9,9,8,7,5,2,2,2,2,2,1,1] (.node [12,9,9,8,7,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,5,3,2,2,1,1,1,1,1] .empty .empty)) (.node [12,9,9,8,7,5,3,3,2,1,1,1,1] (.node [12,9,9,8,7,5,3,3,1,1,1,1,1,1] (.node [12,9,9,8,7,5,3,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,7,5,3,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_488 : RowTree := (.node [12,9,9,8,7,4,3,3,2,1,1,1,1,1] degreeTree62_486 degreeTree62_487) - -def degreeTree62_489 : RowTree := (.node [12,9,9,8,6,6,3,3,2,1,1,1,1] degreeTree62_485 degreeTree62_488) - -def degreeTree62_490 : RowTree := (.node [12,9,9,8,6,4,3,2,2,2,2,2,1] degreeTree62_482 degreeTree62_489) - -def degreeTree62_491 : RowTree := (.node [12,9,9,8,7,6,3,2,2,2,1,1] (.node [12,9,9,8,7,6,2,2,2,1,1,1,1,1] (.node [12,9,9,8,7,5,4,3,1,1,1,1,1] (.node [12,9,9,8,7,5,4,2,2,2,1,1] (.node [12,9,9,8,7,5,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,5,5,2,1,1,1,1,1] (.node [12,9,9,8,7,5,5,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,7,6,3,2,1,1,1,1,1,1] (.node [12,9,9,8,7,6,2,2,2,2,2,1] (.node [12,9,9,8,7,6,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,6,3,2,2,1,1,1,1] .empty .empty))) (.node [12,9,9,8,7,7,2,2,2,1,1,1,1] (.node [12,9,9,8,7,6,4,2,1,1,1,1,1] (.node [12,9,9,8,7,6,4,1,1,1,1,1,1,1] (.node [12,9,9,8,7,6,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,7,2,2,1,1,1,1,1,1] (.node [12,9,9,8,7,6,5,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,7,7,3,2,1,1,1,1,1] (.node [12,9,9,8,7,7,3,1,1,1,1,1,1,1] (.node [12,9,9,8,7,7,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,7,4,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_492 : RowTree := (.node [12,9,9,8,8,3,3,3,3,2,1,1] (.node [12,9,9,8,8,3,3,2,2,2,2,2] (.node [12,9,9,8,8,3,2,2,2,2,2,2,1] (.node [12,9,9,8,8,3,2,2,2,2,2,1,1,1] (.node [12,9,9,8,8,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,8,8,3,3,2,2,2,2,1,1] (.node [12,9,9,8,8,3,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,8,3,3,3,2,2,2,1] (.node [12,9,9,8,8,3,3,3,2,2,1,1,1] (.node [12,9,9,8,8,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,3,3,3,3,1,1,1,1] .empty .empty))) (.node [12,9,9,8,8,4,3,2,2,2,2,1] (.node [12,9,9,8,8,4,2,2,2,2,2,2] (.node [12,9,9,8,8,4,2,2,2,2,2,1,1] (.node [12,9,9,8,8,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,4,3,2,2,2,1,1,1] (.node [12,9,9,8,8,4,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,8,4,3,3,2,2,1,1] (.node [12,9,9,8,8,4,3,3,2,1,1,1,1] (.node [12,9,9,8,8,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,4,4,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_493 : RowTree := (.node [12,9,9,8,8,2,2,2,2,2,2,2,1,1] degreeTree62_491 degreeTree62_492) - -def degreeTree62_494 : RowTree := (.node [12,9,9,8,8,5,4,2,1,1,1,1,1] (.node [12,9,9,8,8,5,3,2,1,1,1,1,1,1] (.node [12,9,9,8,8,5,2,2,2,1,1,1,1,1] (.node [12,9,9,8,8,4,4,3,1,1,1,1,1] (.node [12,9,9,8,8,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,5,2,2,2,2,2,1] (.node [12,9,9,8,8,5,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,8,5,3,3,1,1,1,1,1] (.node [12,9,9,8,8,5,3,2,2,2,1,1] (.node [12,9,9,8,8,5,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,5,4,1,1,1,1,1,1,1] .empty .empty))) (.node [12,9,9,8,8,6,3,2,1,1,1,1,1] (.node [12,9,9,8,8,6,2,2,2,1,1,1,1] (.node [12,9,9,8,8,6,2,2,1,1,1,1,1,1] (.node [12,9,9,8,8,5,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,6,3,1,1,1,1,1,1,1] (.node [12,9,9,8,8,6,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,8,8,7,2,2,1,1,1,1,1] (.node [12,9,9,8,8,7,2,1,1,1,1,1,1,1] (.node [12,9,9,8,8,6,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,7,3,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_495 : RowTree := (.node [12,9,9,9,4,4,4,4,2,2,1,1,1] (.node [12,9,9,9,4,4,4,3,2,2,2,1,1] (.node [12,9,9,9,4,4,3,3,3,2,2,1,1] (.node [12,9,9,9,4,4,3,2,2,2,2,2,2] (.node [12,9,9,8,8,8,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,4,4,4,2,2,2,2,2,1] (.node [12,9,9,9,4,4,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,4,4,4,3,3,2,2,1] (.node [12,9,9,9,4,4,4,3,3,2,1,1,1] (.node [12,9,9,9,4,4,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,4,4,4,4,2,1,1,1,1,1] .empty .empty))) (.node [12,9,9,9,5,3,3,3,3,2,2,1,1] (.node [12,9,9,9,4,4,4,4,3,2,1,1] (.node [12,9,9,9,4,4,4,4,3,1,1,1,1] (.node [12,9,9,9,4,4,4,4,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,9,5,3,3,2,2,2,2,2,2] (.node [12,9,9,9,4,4,4,4,4,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,5,4,3,2,2,2,2,2,1] (.node [12,9,9,9,5,4,3,2,2,2,2,1,1,1] (.node [12,9,9,9,5,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,9,5,4,3,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_496 : RowTree := (.node [12,9,9,8,8,8,1,1,1,1,1,1,1,1] degreeTree62_494 degreeTree62_495) - -def degreeTree62_497 : RowTree := (.node [12,9,9,8,8,4,4,2,2,1,1,1,1] degreeTree62_493 degreeTree62_496) - -def degreeTree62_498 : RowTree := (.node [12,9,9,9,5,4,4,4,1,1,1,1,1,1] (.node [12,9,9,9,5,4,4,3,2,1,1,1,1,1] (.node [12,9,9,9,5,4,4,2,2,2,1,1,1,1] (.node [12,9,9,9,5,4,3,3,3,2,2,1] (.node [12,9,9,9,5,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,5,4,4,2,2,2,2,2] (.node [12,9,9,9,5,4,4,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,9,5,4,4,3,3,1,1,1,1] (.node [12,9,9,9,5,4,4,3,2,2,2,1] (.node [12,9,9,9,5,4,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,5,4,4,3,3,2,1,1] .empty .empty))) (.node [12,9,9,9,5,5,3,2,2,2,2,1,1] (.node [12,9,9,9,5,5,2,2,2,2,2,1,1,1] (.node [12,9,9,9,5,4,4,4,2,2,1,1] (.node [12,9,9,9,5,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,5,5,3,2,2,2,1,1,1,1] (.node [12,9,9,9,5,5,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,9,5,5,3,3,2,2,1,1,1] (.node [12,9,9,9,5,5,3,3,2,1,1,1,1,1] (.node [12,9,9,9,5,5,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,9,5,5,3,3,2,2,2,1] .empty .empty)))) - -def degreeTree62_499 : RowTree := (.node [12,9,9,9,5,5,5,2,2,2,1,1] (.node [12,9,9,9,5,5,4,3,2,1,1,1,1] (.node [12,9,9,9,5,5,4,2,2,2,1,1,1] (.node [12,9,9,9,5,5,4,2,2,1,1,1,1,1] (.node [12,9,9,9,5,5,3,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,9,9,5,5,4,3,1,1,1,1,1,1] (.node [12,9,9,9,5,5,4,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,9,5,5,5,2,1,1,1,1,1,1] (.node [12,9,9,9,5,5,4,4,1,1,1,1,1] (.node [12,9,9,9,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,9,5,5,5,2,2,1,1,1,1] .empty .empty))) (.node [12,9,9,9,6,3,3,3,2,2,2,1,1] (.node [12,9,9,9,6,3,2,2,2,2,2,2,2] (.node [12,9,9,9,6,2,2,2,2,2,2,2,2,1] (.node [12,9,9,9,5,5,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,3,3,2,2,2,2,2,1] (.node [12,9,9,9,6,3,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,6,3,3,3,3,2,2,1] (.node [12,9,9,9,6,3,3,3,3,2,1,1,1] (.node [12,9,9,9,6,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,4,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_500 : RowTree := (.node [12,9,9,9,5,5,3,3,3,1,1,1,1] degreeTree62_498 degreeTree62_499) - -def degreeTree62_501 : RowTree := (.node [12,9,9,9,6,4,4,2,2,2,2,1] (.node [12,9,9,9,6,4,3,3,2,2,2,1] (.node [12,9,9,9,6,4,3,2,2,2,2,2] (.node [12,9,9,9,6,4,3,2,2,2,2,1,1] (.node [12,9,9,9,6,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,4,3,3,2,2,1,1,1] (.node [12,9,9,9,6,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,6,4,4,2,2,1,1,1,1,1] (.node [12,9,9,9,6,4,3,3,3,2,1,1] (.node [12,9,9,9,6,4,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,4,4,2,2,2,1,1,1] .empty .empty))) (.node [12,9,9,9,6,5,2,2,2,2,2,1,1] (.node [12,9,9,9,6,4,4,3,2,2,1,1] (.node [12,9,9,9,6,4,4,3,2,1,1,1,1] (.node [12,9,9,9,6,4,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,5,2,2,2,2,1,1,1,1] (.node [12,9,9,9,6,4,4,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,6,5,3,2,2,2,1,1,1] (.node [12,9,9,9,6,5,3,2,2,1,1,1,1,1] (.node [12,9,9,9,6,5,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,9,6,5,3,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_502 : RowTree := (.node [12,9,9,9,6,6,2,2,2,2,2,1] (.node [12,9,9,9,6,5,4,3,1,1,1,1,1] (.node [12,9,9,9,6,5,4,2,1,1,1,1,1,1] (.node [12,9,9,9,6,5,3,3,2,2,1,1] (.node [12,9,9,9,6,5,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,5,4,2,2,2,1,1] (.node [12,9,9,9,6,5,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,6,6,2,2,2,1,1,1,1,1] (.node [12,9,9,9,6,5,5,2,1,1,1,1,1] (.node [12,9,9,9,6,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,6,2,2,2,2,1,1,1] .empty .empty))) (.node [12,9,9,9,6,6,4,1,1,1,1,1,1,1] (.node [12,9,9,9,6,6,3,2,2,2,1,1] (.node [12,9,9,9,6,6,3,2,2,1,1,1,1] (.node [12,9,9,9,6,6,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,6,3,3,1,1,1,1,1] .empty .empty)) (.node [12,9,9,9,7,2,2,2,2,2,2,2,1,1] (.node [12,9,9,9,6,6,5,1,1,1,1,1,1] (.node [12,9,9,9,6,6,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,7,2,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_503 : RowTree := (.node [12,9,9,9,6,5,3,3,1,1,1,1,1,1] degreeTree62_501 degreeTree62_502) - -def degreeTree62_504 : RowTree := (.node [12,9,9,9,6,4,2,2,2,2,2,2,1] degreeTree62_500 degreeTree62_503) - -def degreeTree62_505 : RowTree := (.node [12,9,9,9,5,4,3,3,3,1,1,1,1,1] degreeTree62_497 degreeTree62_504) - -def degreeTree62_506 : RowTree := (.node [12,9,9,8,7,5,4,2,1,1,1,1,1,1] degreeTree62_490 degreeTree62_505) - -def degreeTree62_507 : RowTree := (.node [12,9,9,7,7,5,2,2,2,2,2,1,1,1] degreeTree62_475 degreeTree62_506) - -def degreeTree62_508 : RowTree := (.node [12,9,8,8,6,6,3,2,2,2,2,1,1] degreeTree62_444 degreeTree62_507) - -def degreeTree62_509 : RowTree := (.node [12,8,8,8,7,5,4,3,2,2,2,1] degreeTree62_381 degreeTree62_508) - -def degreeTree62_510 : RowTree := (.node [11,11,11,7,5,4,2,2,2,2,2,2,1] degreeTree62_254 degreeTree62_509) - -def degreeTree62_511 : RowTree := (.node [12,9,9,9,7,4,2,2,2,2,2,1,1] (.node [12,9,9,9,7,3,3,3,2,2,1,1,1] (.node [12,9,9,9,7,3,3,2,2,2,2,1,1] (.node [12,9,9,9,7,3,3,2,2,2,1,1,1,1] (.node [12,9,9,9,7,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,9,7,3,3,3,2,1,1,1,1,1] (.node [12,9,9,9,7,3,3,2,2,2,2,2] .empty .empty) .empty)) (.node [12,9,9,9,7,3,3,3,3,2,1,1] (.node [12,9,9,9,7,3,3,3,3,1,1,1,1] (.node [12,9,9,9,7,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,9,7,4,2,2,2,2,1,1,1,1] .empty .empty))) (.node [12,9,9,9,7,4,3,3,2,1,1,1,1] (.node [12,9,9,9,7,4,3,2,2,2,1,1,1] (.node [12,9,9,9,7,4,3,2,2,1,1,1,1,1] (.node [12,9,9,9,7,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,9,7,4,3,3,1,1,1,1,1,1] (.node [12,9,9,9,7,4,3,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,9,7,4,4,2,2,1,1,1,1] (.node [12,9,9,9,7,4,4,2,1,1,1,1,1,1] (.node [12,9,9,9,7,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,9,7,4,4,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_512 : RowTree := (.node [12,9,9,9,7,6,2,2,1,1,1,1,1,1] (.node [12,9,9,9,7,5,3,2,2,2,1,1] (.node [12,9,9,9,7,5,2,2,2,2,2,1] (.node [12,9,9,9,7,5,2,2,2,2,1,1,1] (.node [12,9,9,9,7,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,7,5,3,2,2,1,1,1,1] (.node [12,9,9,9,7,5,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,7,5,4,2,1,1,1,1,1] (.node [12,9,9,9,7,5,4,1,1,1,1,1,1,1] (.node [12,9,9,9,7,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,7,5,5,1,1,1,1,1,1] .empty .empty))) (.node [12,9,9,9,7,7,2,1,1,1,1,1,1,1] (.node [12,9,9,9,7,6,3,1,1,1,1,1,1,1] (.node [12,9,9,9,7,6,2,2,2,2,1,1] (.node [12,9,9,9,7,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,7,6,4,1,1,1,1,1,1] (.node [12,9,9,9,7,6,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,8,2,2,2,2,2,2,1,1,1] (.node [12,9,9,9,7,7,3,1,1,1,1,1,1] (.node [12,9,9,9,7,7,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,8,2,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_513 : RowTree := (.node [12,9,9,9,7,4,4,3,1,1,1,1,1] degreeTree62_511 degreeTree62_512) - -def degreeTree62_514 : RowTree := (.node [12,9,9,9,8,4,2,2,2,2,2,1] (.node [12,9,9,9,8,3,3,3,1,1,1,1,1,1] (.node [12,9,9,9,8,3,3,2,2,1,1,1,1,1] (.node [12,9,9,9,8,3,2,2,2,2,2,2] (.node [12,9,9,9,8,3,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,9,8,3,3,2,2,2,2,1] (.node [12,9,9,9,8,3,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,8,4,2,2,2,1,1,1,1,1] (.node [12,9,9,9,8,3,3,3,2,2,1,1] (.node [12,9,9,9,8,3,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,8,4,2,2,2,2,1,1,1] .empty .empty))) (.node [12,9,9,9,8,4,4,2,1,1,1,1,1] (.node [12,9,9,9,8,4,3,2,2,2,1,1] (.node [12,9,9,9,8,4,3,2,2,1,1,1,1] (.node [12,9,9,9,8,4,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,8,4,4,1,1,1,1,1,1,1] (.node [12,9,9,9,8,4,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,8,5,2,2,2,2,1,1] (.node [12,9,9,9,8,5,2,2,2,1,1,1,1] (.node [12,9,9,9,8,5,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,8,5,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_515 : RowTree := (.node [12,9,9,9,9,3,2,2,2,1,1,1,1,1] (.node [12,9,9,9,8,7,2,1,1,1,1,1,1] (.node [12,9,9,9,8,6,2,2,1,1,1,1,1] (.node [12,9,9,9,8,6,2,1,1,1,1,1,1,1] (.node [12,9,9,9,8,5,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,8,7,1,1,1,1,1,1,1,1] (.node [12,9,9,9,8,6,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,9,2,2,2,2,2,2,1,1] (.node [12,9,9,9,9,2,2,2,2,2,1,1,1,1] (.node [12,9,9,9,8,8,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,9,2,2,2,2,2,2,2] .empty .empty))) (.node [12,9,9,9,9,3,3,3,1,1,1,1,1] (.node [12,9,9,9,9,3,3,2,1,1,1,1,1,1] (.node [12,9,9,9,9,3,2,2,2,2,2,1] (.node [12,9,9,9,9,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,9,3,3,2,2,2,1,1] (.node [12,9,9,9,9,3,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,9,4,2,2,2,2,1,1] (.node [12,9,9,9,9,4,2,2,2,1,1,1,1] (.node [12,9,9,9,9,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,9,4,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_516 : RowTree := (.node [12,9,9,9,8,5,3,2,1,1,1,1,1] degreeTree62_514 degreeTree62_515) - -def degreeTree62_517 : RowTree := (.node [12,9,9,9,8,3,2,2,2,2,1,1,1,1] degreeTree62_513 degreeTree62_516) - -def degreeTree62_518 : RowTree := (.node [12,10,6,5,5,5,5,4,4,2,2,1,1] (.node [12,9,9,9,9,6,2,1,1,1,1,1,1] (.node [12,9,9,9,9,5,2,2,1,1,1,1,1] (.node [12,9,9,9,9,5,2,1,1,1,1,1,1,1] (.node [12,9,9,9,9,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,9,6,1,1,1,1,1,1,1,1] (.node [12,9,9,9,9,5,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,5,5,5,5,5,5,5,2,1,1,1] (.node [12,10,5,5,5,5,5,5,4,2,2,1,1] (.node [12,9,9,9,9,7,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,5,5,5,5,5,5,5,2,2,1] .empty .empty))) (.node [12,10,6,6,5,5,4,4,4,2,2,1,1] (.node [12,10,6,5,5,5,5,5,4,2,2,1] (.node [12,10,6,5,5,5,5,5,4,2,1,1,1] (.node [12,10,6,5,5,5,5,5,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,6,5,5,5,5,5,5,2,1,1] (.node [12,10,6,5,5,5,5,5,5,1,1,1,1] .empty .empty) .empty)) (.node [12,10,6,6,5,5,5,4,4,2,2,1] (.node [12,10,6,6,5,5,5,4,4,2,1,1,1] (.node [12,10,6,6,5,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,6,6,5,5,5,5,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_519 : RowTree := (.node [12,10,6,6,6,5,5,4,3,2,1,1,1] (.node [12,10,6,6,6,5,4,4,4,2,1,1,1] (.node [12,10,6,6,5,5,5,5,4,2,1,1] (.node [12,10,6,6,5,5,5,5,4,1,1,1,1] (.node [12,10,6,6,5,5,5,5,3,2,2,1] .empty .empty) .empty) (.node [12,10,6,6,6,5,4,4,3,2,2,1,1] (.node [12,10,6,6,6,4,4,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,10,6,6,6,5,5,3,3,2,2,1,1] (.node [12,10,6,6,6,5,5,2,2,2,2,2,2] (.node [12,10,6,6,6,5,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,10,6,6,6,5,5,4,2,2,2,1,1] .empty .empty))) (.node [12,10,6,6,6,5,5,5,3,1,1,1,1] (.node [12,10,6,6,6,5,5,4,4,2,1,1] (.node [12,10,6,6,6,5,5,4,4,1,1,1,1] (.node [12,10,6,6,6,5,5,4,3,2,2,1] .empty .empty) .empty) (.node [12,10,6,6,6,5,5,5,2,2,2,1] (.node [12,10,6,6,6,5,5,5,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,6,6,6,6,4,3,3,2,2,1,1] (.node [12,10,6,6,6,6,4,2,2,2,2,2,2] (.node [12,10,6,6,6,5,5,5,3,2,1,1] .empty .empty) .empty) (.node [12,10,6,6,6,6,4,4,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_520 : RowTree := (.node [12,10,6,6,5,5,5,5,3,2,1,1,1] degreeTree62_518 degreeTree62_519) - -def degreeTree62_521 : RowTree := (.node [12,10,6,6,6,6,5,4,3,2,1,1] (.node [12,10,6,6,6,6,5,3,3,2,1,1,1] (.node [12,10,6,6,6,6,4,4,4,2,1,1] (.node [12,10,6,6,6,6,4,4,4,1,1,1,1] (.node [12,10,6,6,6,6,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,10,6,6,6,6,5,3,2,2,2,1,1] (.node [12,10,6,6,6,6,5,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,6,6,6,6,5,4,2,2,2,1] (.node [12,10,6,6,6,6,5,4,2,2,1,1,1] (.node [12,10,6,6,6,6,5,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,6,6,6,6,5,4,3,1,1,1,1] .empty .empty))) (.node [12,10,6,6,6,6,6,3,2,2,2,1] (.node [12,10,6,6,6,6,6,2,2,2,2,1,1] (.node [12,10,6,6,6,6,5,5,2,2,1,1] (.node [12,10,6,6,6,6,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,6,6,6,6,6,3,2,2,1,1,1] (.node [12,10,6,6,6,6,6,2,2,2,2,2] .empty .empty) .empty)) (.node [12,10,6,6,6,6,6,4,2,1,1,1,1] (.node [12,10,6,6,6,6,6,3,3,2,1,1] (.node [12,10,6,6,6,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,6,6,6,6,6,4,2,2,1,1] .empty .empty)))) - -def degreeTree62_522 : RowTree := (.node [12,10,7,6,5,5,4,4,3,2,2,1,1] (.node [12,10,7,5,5,5,5,5,3,2,1,1,1] (.node [12,10,7,5,5,5,5,4,4,2,1,1,1] (.node [12,10,7,5,5,5,5,4,3,2,2,1,1] (.node [12,10,7,5,5,5,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,5,5,5,5,5,2,2,2,1,1] (.node [12,10,7,5,5,5,5,4,4,2,2,1] .empty .empty) .empty)) (.node [12,10,7,5,5,5,5,5,4,2,1,1] (.node [12,10,7,5,5,5,5,5,4,1,1,1,1] (.node [12,10,7,5,5,5,5,5,3,2,2,1] .empty .empty) .empty) (.node [12,10,7,6,5,4,4,4,4,2,2,1,1] .empty .empty))) (.node [12,10,7,6,5,5,5,4,3,2,1,1,1] (.node [12,10,7,6,5,5,5,2,2,2,2,2,2] (.node [12,10,7,6,5,5,4,4,4,2,2,1] (.node [12,10,7,6,5,5,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,6,5,5,5,4,2,2,2,1,1] (.node [12,10,7,6,5,5,5,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,6,5,5,5,4,4,2,1,1] (.node [12,10,7,6,5,5,5,4,4,1,1,1,1] (.node [12,10,7,6,5,5,5,4,3,2,2,1] .empty .empty) .empty) (.node [12,10,7,6,5,5,5,5,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_523 : RowTree := (.node [12,10,6,6,6,6,6,5,1,1,1,1,1] degreeTree62_521 degreeTree62_522) - -def degreeTree62_524 : RowTree := (.node [12,10,6,6,6,6,4,4,3,2,1,1,1] degreeTree62_520 degreeTree62_523) - -def degreeTree62_525 : RowTree := (.node [12,9,9,9,9,4,3,2,1,1,1,1,1] degreeTree62_517 degreeTree62_524) - -def degreeTree62_526 : RowTree := (.node [12,10,7,6,6,5,4,4,4,1,1,1,1] (.node [12,10,7,6,6,5,4,2,2,2,2,2,2] (.node [12,10,7,6,6,4,4,4,3,2,2,1,1] (.node [12,10,7,6,5,5,5,5,3,2,1,1] (.node [12,10,7,6,5,5,5,5,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,6,6,4,4,4,4,2,2,1] (.node [12,10,7,6,6,4,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [12,10,7,6,6,5,4,4,3,2,1,1,1] (.node [12,10,7,6,6,5,4,4,2,2,2,1,1] (.node [12,10,7,6,6,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,6,6,5,4,4,3,2,2,1] .empty .empty))) (.node [12,10,7,6,6,5,5,4,2,2,1,1,1] (.node [12,10,7,6,6,5,5,3,2,2,2,1,1] (.node [12,10,7,6,6,5,5,2,2,2,2,2,1] (.node [12,10,7,6,6,5,4,4,4,2,1,1] .empty .empty) .empty) (.node [12,10,7,6,6,5,5,3,3,2,2,1] (.node [12,10,7,6,6,5,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,10,7,6,6,5,5,4,3,2,1,1] (.node [12,10,7,6,6,5,5,4,3,1,1,1,1] (.node [12,10,7,6,6,5,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,10,7,6,6,5,5,5,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_527 : RowTree := (.node [12,10,7,6,6,6,5,2,2,2,2,1,1] (.node [12,10,7,6,6,6,4,3,3,2,2,1] (.node [12,10,7,6,6,6,4,2,2,2,2,2,1] (.node [12,10,7,6,6,6,3,3,3,2,2,1,1] (.node [12,10,7,6,6,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,7,6,6,6,4,3,3,2,1,1,1] (.node [12,10,7,6,6,6,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,6,6,6,4,4,3,1,1,1,1] (.node [12,10,7,6,6,6,4,4,2,2,2,1] (.node [12,10,7,6,6,6,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,6,6,6,4,4,3,2,1,1] .empty .empty))) (.node [12,10,7,6,6,6,5,4,2,1,1,1,1] (.node [12,10,7,6,6,6,5,3,2,2,2,1] (.node [12,10,7,6,6,6,5,3,2,2,1,1,1] (.node [12,10,7,6,6,6,5,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,7,6,6,6,5,3,3,2,1,1] (.node [12,10,7,6,6,6,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,7,6,6,6,6,2,2,2,1,1,1] (.node [12,10,7,6,6,6,5,5,1,1,1,1,1] (.node [12,10,7,6,6,6,5,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,6,6,6,6,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_528 : RowTree := (.node [12,10,7,6,6,5,5,5,2,2,1,1] degreeTree62_526 degreeTree62_527) - -def degreeTree62_529 : RowTree := (.node [12,10,7,7,5,5,4,4,3,2,2,1] (.node [12,10,7,7,5,4,4,4,4,2,2,1] (.node [12,10,7,7,4,4,4,4,4,2,2,1,1] (.node [12,10,7,6,6,6,6,4,1,1,1,1,1] (.node [12,10,7,6,6,6,6,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,5,4,4,4,4,2,1,1,1] (.node [12,10,7,7,5,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,5,5,4,4,2,2,2,1,1] (.node [12,10,7,7,5,5,4,3,3,2,2,1,1] (.node [12,10,7,7,5,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,7,7,5,5,4,4,3,2,1,1,1] .empty .empty))) (.node [12,10,7,7,5,5,5,3,3,2,2,1] (.node [12,10,7,7,5,5,5,2,2,2,2,2,1] (.node [12,10,7,7,5,5,4,4,4,2,1,1] (.node [12,10,7,7,5,5,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,5,5,5,3,3,2,1,1,1] (.node [12,10,7,7,5,5,5,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,5,5,5,4,3,1,1,1,1] (.node [12,10,7,7,5,5,5,4,2,2,2,1] (.node [12,10,7,7,5,5,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,5,5,5,4,3,2,1,1] .empty .empty)))) - -def degreeTree62_530 : RowTree := (.node [12,10,7,7,6,5,4,2,2,2,2,2,1] (.node [12,10,7,7,6,4,4,4,3,2,2,1] (.node [12,10,7,7,6,4,4,3,3,2,2,1,1] (.node [12,10,7,7,6,4,4,2,2,2,2,2,2] (.node [12,10,7,7,5,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,4,4,4,3,2,1,1,1] (.node [12,10,7,7,6,4,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,6,5,3,2,2,2,2,2,2] (.node [12,10,7,7,6,4,4,4,4,2,1,1] (.node [12,10,7,7,6,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,5,3,3,3,2,2,1,1] .empty .empty))) (.node [12,10,7,7,6,5,4,4,3,1,1,1,1] (.node [12,10,7,7,6,5,4,3,3,2,2,1] (.node [12,10,7,7,6,5,4,3,3,2,1,1,1] (.node [12,10,7,7,6,5,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,5,4,4,2,2,2,1] (.node [12,10,7,7,6,5,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,7,7,6,5,5,2,2,2,2,2] (.node [12,10,7,7,6,5,5,2,2,2,2,1,1] (.node [12,10,7,7,6,5,4,4,3,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,5,5,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_531 : RowTree := (.node [12,10,7,7,5,5,5,5,2,1,1,1,1] degreeTree62_529 degreeTree62_530) - -def degreeTree62_532 : RowTree := (.node [12,10,7,6,6,6,6,3,2,1,1,1,1] degreeTree62_528 degreeTree62_531) - -def degreeTree62_533 : RowTree := (.node [12,10,7,7,6,6,4,2,2,2,2,1,1] (.node [12,10,7,7,6,6,2,2,2,2,2,2,2] (.node [12,10,7,7,6,5,5,4,2,1,1,1,1] (.node [12,10,7,7,6,5,5,3,3,2,1,1] (.node [12,10,7,7,6,5,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,5,5,5,1,1,1,1,1] (.node [12,10,7,7,6,5,5,4,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,6,6,3,3,3,2,1,1,1] (.node [12,10,7,7,6,6,3,3,2,2,2,1,1] (.node [12,10,7,7,6,6,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,7,7,6,6,3,3,3,2,2,1] .empty .empty))) (.node [12,10,7,7,6,6,4,4,2,1,1,1,1] (.node [12,10,7,7,6,6,4,3,2,2,2,1] (.node [12,10,7,7,6,6,4,3,2,2,1,1,1] (.node [12,10,7,7,6,6,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,7,7,6,6,4,3,3,2,1,1] (.node [12,10,7,7,6,6,4,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,7,7,6,6,5,2,2,2,2,1] (.node [12,10,7,7,6,6,5,2,2,2,1,1,1] (.node [12,10,7,7,6,6,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,6,5,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_534 : RowTree := (.node [12,10,7,7,7,4,4,3,3,2,2,1] (.node [12,10,7,7,7,4,3,2,2,2,2,2,2] (.node [12,10,7,7,6,6,6,2,2,1,1,1,1] (.node [12,10,7,7,6,6,6,2,1,1,1,1,1,1] (.node [12,10,7,7,6,6,5,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,6,6,3,1,1,1,1,1] (.node [12,10,7,7,6,6,6,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,7,4,4,3,2,2,2,1,1] (.node [12,10,7,7,7,4,4,2,2,2,2,2,1] (.node [12,10,7,7,7,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,4,4,3,3,2,1,1,1] .empty .empty))) (.node [12,10,7,7,7,5,3,2,2,2,2,2,1] (.node [12,10,7,7,7,4,4,4,3,1,1,1,1] (.node [12,10,7,7,7,4,4,4,2,2,2,1] (.node [12,10,7,7,7,4,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,5,2,2,2,2,2,2,2] (.node [12,10,7,7,7,4,4,4,3,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,7,5,3,3,3,2,2,1] (.node [12,10,7,7,7,5,3,3,3,2,1,1,1] (.node [12,10,7,7,7,5,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,5,4,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_535 : RowTree := (.node [12,10,7,7,6,6,5,3,2,2,1,1] degreeTree62_533 degreeTree62_534) - -def degreeTree62_536 : RowTree := (.node [12,10,7,7,7,5,5,4,1,1,1,1,1] (.node [12,10,7,7,7,5,4,4,2,2,1,1] (.node [12,10,7,7,7,5,4,3,3,1,1,1,1] (.node [12,10,7,7,7,5,4,3,2,2,2,1] (.node [12,10,7,7,7,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,5,4,4,2,1,1,1,1] (.node [12,10,7,7,7,5,4,3,3,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,7,5,5,3,2,1,1,1,1] (.node [12,10,7,7,7,5,5,2,2,2,2,1] (.node [12,10,7,7,7,5,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,5,5,3,2,2,1,1] .empty .empty))) (.node [12,10,7,7,7,6,3,3,2,1,1,1,1,1] (.node [12,10,7,7,7,6,3,2,2,2,1,1,1,1] (.node [12,10,7,7,7,6,2,2,2,2,2,2,1] (.node [12,10,7,7,7,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,6,3,2,2,2,2,2] (.node [12,10,7,7,7,6,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,7,6,3,3,3,1,1,1,1] (.node [12,10,7,7,7,6,3,3,2,2,2,1] (.node [12,10,7,7,7,6,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,6,3,3,3,2,1,1] .empty .empty)))) - -def degreeTree62_537 : RowTree := (.node [12,10,7,7,7,6,6,1,1,1,1,1,1,1] (.node [12,10,7,7,7,6,4,4,1,1,1,1,1] (.node [12,10,7,7,7,6,4,3,1,1,1,1,1,1] (.node [12,10,7,7,7,6,4,2,2,2,2,1] (.node [12,10,7,7,7,6,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,6,4,3,2,2,1,1] (.node [12,10,7,7,7,6,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,7,7,7,6,5,2,2,2,1,1] (.node [12,10,7,7,7,6,5,2,2,1,1,1,1] (.node [12,10,7,7,7,6,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,6,5,3,1,1,1,1,1] .empty .empty))) (.node [12,10,7,7,7,7,3,2,2,1,1,1,1,1] (.node [12,10,7,7,7,7,2,2,2,2,2,1,1] (.node [12,10,7,7,7,7,2,2,2,2,1,1,1,1] (.node [12,10,7,7,7,6,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,7,2,2,2,2,2,2] .empty .empty)) (.node [12,10,7,7,7,7,3,3,1,1,1,1,1,1] (.node [12,10,7,7,7,7,3,2,2,2,2,1] (.node [12,10,7,7,7,7,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,7,3,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_538 : RowTree := (.node [12,10,7,7,7,6,4,2,2,1,1,1,1,1] degreeTree62_536 degreeTree62_537) - -def degreeTree62_539 : RowTree := (.node [12,10,7,7,7,5,4,2,2,2,2,2] degreeTree62_535 degreeTree62_538) - -def degreeTree62_540 : RowTree := (.node [12,10,7,7,6,5,5,3,2,2,2,1] degreeTree62_532 degreeTree62_539) - -def degreeTree62_541 : RowTree := (.node [12,10,7,6,5,5,5,5,2,2,2,1] degreeTree62_525 degreeTree62_540) - -def degreeTree62_542 : RowTree := (.node [12,10,8,5,5,5,5,2,2,2,2,2,2] (.node [12,10,7,7,7,7,6,1,1,1,1,1,1] (.node [12,10,7,7,7,7,4,3,1,1,1,1,1] (.node [12,10,7,7,7,7,4,2,2,1,1,1,1] (.node [12,10,7,7,7,7,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,7,5,2,1,1,1,1,1] (.node [12,10,7,7,7,7,5,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,5,5,5,4,4,4,2,1,1,1] (.node [12,10,8,5,5,5,4,4,3,2,2,1,1] (.node [12,10,8,5,5,4,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,5,5,5,4,4,4,2,2,1] .empty .empty))) (.node [12,10,8,5,5,5,5,4,4,2,1,1] (.node [12,10,8,5,5,5,5,4,3,2,1,1,1] (.node [12,10,8,5,5,5,5,4,2,2,2,1,1] (.node [12,10,8,5,5,5,5,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,5,5,5,5,4,4,1,1,1,1] (.node [12,10,8,5,5,5,5,4,3,2,2,1] .empty .empty) .empty)) (.node [12,10,8,5,5,5,5,5,3,1,1,1,1] (.node [12,10,8,5,5,5,5,5,2,2,2,1] (.node [12,10,8,5,5,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,5,5,5,5,5,3,2,1,1] .empty .empty)))) - -def degreeTree62_543 : RowTree := (.node [12,10,8,6,5,5,5,2,2,2,2,2,1] (.node [12,10,8,6,5,5,4,4,2,2,2,1,1] (.node [12,10,8,6,5,4,4,4,4,2,2,1] (.node [12,10,8,6,5,4,4,4,4,2,1,1,1] (.node [12,10,8,6,5,4,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,6,5,5,4,3,3,2,2,1,1] (.node [12,10,8,6,5,5,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,10,8,6,5,5,4,4,4,1,1,1,1] (.node [12,10,8,6,5,5,4,4,3,2,2,1] (.node [12,10,8,6,5,5,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,6,5,5,4,4,4,2,1,1] .empty .empty))) (.node [12,10,8,6,5,5,5,4,3,1,1,1,1] (.node [12,10,8,6,5,5,5,3,3,2,2,1] (.node [12,10,8,6,5,5,5,3,3,2,1,1,1] (.node [12,10,8,6,5,5,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,6,5,5,5,4,2,2,2,1] (.node [12,10,8,6,5,5,5,4,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,6,5,5,5,5,2,2,1,1] (.node [12,10,8,6,5,5,5,5,2,1,1,1,1] (.node [12,10,8,6,5,5,5,4,3,2,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,4,4,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_544 : RowTree := (.node [12,10,8,6,4,4,4,4,4,2,2,1,1] degreeTree62_542 degreeTree62_543) - -def degreeTree62_545 : RowTree := (.node [12,10,8,6,6,5,4,3,3,2,2,1] (.node [12,10,8,6,6,5,3,2,2,2,2,2,2] (.node [12,10,8,6,6,4,4,4,3,2,2,1] (.node [12,10,8,6,6,4,4,4,3,2,1,1,1] (.node [12,10,8,6,6,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,4,4,4,4,2,1,1] (.node [12,10,8,6,6,4,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,6,6,5,4,3,2,2,2,1,1] (.node [12,10,8,6,6,5,4,2,2,2,2,2,1] (.node [12,10,8,6,6,5,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,5,4,3,3,2,1,1,1] .empty .empty))) (.node [12,10,8,6,6,5,5,2,2,2,2,2] (.node [12,10,8,6,6,5,4,4,3,1,1,1,1] (.node [12,10,8,6,6,5,4,4,2,2,2,1] (.node [12,10,8,6,6,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,5,5,2,2,2,2,1,1] (.node [12,10,8,6,6,5,4,4,3,2,1,1] .empty .empty) .empty)) (.node [12,10,8,6,6,5,5,3,3,1,1,1,1] (.node [12,10,8,6,6,5,5,3,2,2,2,1] (.node [12,10,8,6,6,5,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,5,5,3,3,2,1,1] .empty .empty)))) - -def degreeTree62_546 : RowTree := (.node [12,10,8,6,6,6,4,3,2,2,2,1] (.node [12,10,8,6,6,6,3,3,3,2,1,1,1] (.node [12,10,8,6,6,6,2,2,2,2,2,2,2] (.node [12,10,8,6,6,5,5,5,1,1,1,1,1] (.node [12,10,8,6,6,5,5,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,6,3,3,2,2,2,1,1] (.node [12,10,8,6,6,6,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,8,6,6,6,4,2,2,2,2,2] (.node [12,10,8,6,6,6,4,2,2,2,2,1,1] (.node [12,10,8,6,6,6,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,8,6,6,6,4,3,2,2,1,1,1] .empty .empty))) (.node [12,10,8,6,6,6,5,2,2,2,2,1] (.node [12,10,8,6,6,6,4,4,2,1,1,1,1] (.node [12,10,8,6,6,6,4,3,3,2,1,1] (.node [12,10,8,6,6,6,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,6,5,2,2,2,1,1,1] (.node [12,10,8,6,6,6,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,10,8,6,6,6,5,4,1,1,1,1,1] (.node [12,10,8,6,6,6,5,3,2,2,1,1] (.node [12,10,8,6,6,6,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,6,6,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_547 : RowTree := (.node [12,10,8,6,6,5,5,4,2,1,1,1,1] degreeTree62_545 degreeTree62_546) - -def degreeTree62_548 : RowTree := (.node [12,10,8,6,6,4,4,3,3,2,2,1,1] degreeTree62_544 degreeTree62_547) - -def degreeTree62_549 : RowTree := (.node [12,10,8,7,5,4,4,4,4,2,1,1] (.node [12,10,8,7,5,4,4,3,3,2,2,1,1] (.node [12,10,8,7,4,4,4,4,4,2,1,1,1] (.node [12,10,8,7,4,4,4,4,3,2,2,1,1] (.node [12,10,8,6,6,6,6,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,5,4,4,2,2,2,2,2,2] (.node [12,10,8,7,4,4,4,4,4,2,2,1] .empty .empty) .empty)) (.node [12,10,8,7,5,4,4,4,3,2,2,1] (.node [12,10,8,7,5,4,4,4,3,2,1,1,1] (.node [12,10,8,7,5,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,5,4,4,4,4,1,1,1,1] .empty .empty))) (.node [12,10,8,7,5,5,4,3,3,2,2,1] (.node [12,10,8,7,5,5,4,2,2,2,2,2,1] (.node [12,10,8,7,5,5,3,3,3,2,2,1,1] (.node [12,10,8,7,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,7,5,5,4,3,3,2,1,1,1] (.node [12,10,8,7,5,5,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,8,7,5,5,4,4,3,1,1,1,1] (.node [12,10,8,7,5,5,4,4,2,2,2,1] (.node [12,10,8,7,5,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,5,5,4,4,3,2,1,1] .empty .empty)))) - -def degreeTree62_550 : RowTree := (.node [12,10,8,7,6,4,4,2,2,2,2,2,1] (.node [12,10,8,7,5,5,5,4,2,1,1,1,1] (.node [12,10,8,7,5,5,5,3,2,2,2,1] (.node [12,10,8,7,5,5,5,3,2,2,1,1,1] (.node [12,10,8,7,5,5,5,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,7,5,5,5,3,3,2,1,1] (.node [12,10,8,7,5,5,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,6,4,3,2,2,2,2,2,2] (.node [12,10,8,7,5,5,5,5,1,1,1,1,1] (.node [12,10,8,7,5,5,5,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,4,3,3,3,2,2,1,1] .empty .empty))) (.node [12,10,8,7,6,4,4,4,3,1,1,1,1] (.node [12,10,8,7,6,4,4,3,3,2,2,1] (.node [12,10,8,7,6,4,4,3,3,2,1,1,1] (.node [12,10,8,7,6,4,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,4,4,4,2,2,2,1] (.node [12,10,8,7,6,4,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,6,5,3,2,2,2,2,2,1] (.node [12,10,8,7,6,5,2,2,2,2,2,2,2] (.node [12,10,8,7,6,4,4,4,3,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,5,3,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_551 : RowTree := (.node [12,10,8,7,5,5,5,2,2,2,2,1,1] degreeTree62_549 degreeTree62_550) - -def degreeTree62_552 : RowTree := (.node [12,10,8,7,6,5,5,2,2,2,2,1] (.node [12,10,8,7,6,5,4,3,3,1,1,1,1] (.node [12,10,8,7,6,5,4,2,2,2,2,2] (.node [12,10,8,7,6,5,4,2,2,2,2,1,1] (.node [12,10,8,7,6,5,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,8,7,6,5,4,3,2,2,2,1] (.node [12,10,8,7,6,5,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,6,5,4,4,2,2,1,1] (.node [12,10,8,7,6,5,4,4,2,1,1,1,1] (.node [12,10,8,7,6,5,4,3,3,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,5,5,2,2,2,1,1,1] .empty .empty))) (.node [12,10,8,7,6,6,3,2,2,2,1,1,1,1] (.node [12,10,8,7,6,5,5,4,1,1,1,1,1] (.node [12,10,8,7,6,5,5,3,2,2,1,1] (.node [12,10,8,7,6,5,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,6,2,2,2,2,2,2,1] (.node [12,10,8,7,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,6,6,3,3,2,1,1,1,1,1] (.node [12,10,8,7,6,6,3,2,2,2,2,2] (.node [12,10,8,7,6,6,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,6,3,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_553 : RowTree := (.node [12,10,8,7,6,6,5,2,2,1,1,1,1] (.node [12,10,8,7,6,6,4,3,1,1,1,1,1,1] (.node [12,10,8,7,6,6,4,2,2,1,1,1,1,1] (.node [12,10,8,7,6,6,3,3,3,2,1,1] (.node [12,10,8,7,6,6,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,6,4,2,2,2,2,1] (.node [12,10,8,7,6,6,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,6,6,4,4,1,1,1,1,1] (.node [12,10,8,7,6,6,4,3,2,2,1,1] (.node [12,10,8,7,6,6,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,6,5,2,1,1,1,1,1,1] .empty .empty))) (.node [12,10,8,7,7,4,2,2,2,2,2,2,2] (.node [12,10,8,7,6,6,6,2,1,1,1,1,1] (.node [12,10,8,7,6,6,6,1,1,1,1,1,1,1] (.node [12,10,8,7,6,6,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,3,3,3,3,2,2,1,1] (.node [12,10,8,7,7,3,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,10,8,7,7,4,3,3,2,2,2,1,1] (.node [12,10,8,7,7,4,3,2,2,2,2,2,1] (.node [12,10,8,7,7,4,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,4,3,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_554 : RowTree := (.node [12,10,8,7,6,6,3,3,2,2,2,1] degreeTree62_552 degreeTree62_553) - -def degreeTree62_555 : RowTree := (.node [12,10,8,7,6,5,3,3,3,2,1,1,1] degreeTree62_551 degreeTree62_554) - -def degreeTree62_556 : RowTree := (.node [12,10,8,6,6,6,6,2,2,1,1,1,1] degreeTree62_548 degreeTree62_555) - -def degreeTree62_557 : RowTree := (.node [12,10,8,7,7,4,4,4,2,1,1,1,1] (.node [12,10,8,7,7,4,4,3,2,2,1,1,1] (.node [12,10,8,7,7,4,4,2,2,2,2,1,1] (.node [12,10,8,7,7,4,4,2,2,2,1,1,1,1] (.node [12,10,8,7,7,4,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,8,7,7,4,4,3,2,1,1,1,1,1] (.node [12,10,8,7,7,4,4,2,2,2,2,2] .empty .empty) .empty)) (.node [12,10,8,7,7,4,4,3,3,2,1,1] (.node [12,10,8,7,7,4,4,3,3,1,1,1,1] (.node [12,10,8,7,7,4,4,3,2,2,2,1] .empty .empty) .empty) (.node [12,10,8,7,7,4,4,4,1,1,1,1,1,1] .empty .empty))) (.node [12,10,8,7,7,5,3,2,2,2,2,2] (.node [12,10,8,7,7,5,2,2,2,2,2,2,1] (.node [12,10,8,7,7,5,2,2,2,2,2,1,1,1] (.node [12,10,8,7,7,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,5,3,2,2,2,2,1,1] (.node [12,10,8,7,7,5,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,7,5,3,3,2,2,2,1] (.node [12,10,8,7,7,5,3,3,2,2,1,1,1] (.node [12,10,8,7,7,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,5,3,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_558 : RowTree := (.node [12,10,8,7,7,6,2,2,2,2,2,1,1] (.node [12,10,8,7,7,5,4,4,1,1,1,1,1] (.node [12,10,8,7,7,5,4,2,2,2,2,1] (.node [12,10,8,7,7,5,4,2,2,2,1,1,1] (.node [12,10,8,7,7,5,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,5,4,3,2,1,1,1,1] (.node [12,10,8,7,7,5,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,7,5,5,3,1,1,1,1,1] (.node [12,10,8,7,7,5,5,2,2,1,1,1,1] (.node [12,10,8,7,7,5,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,6,2,2,2,2,1,1,1,1] .empty .empty))) (.node [12,10,8,7,7,6,3,3,2,1,1,1,1] (.node [12,10,8,7,7,6,3,2,2,2,1,1,1] (.node [12,10,8,7,7,6,3,2,2,1,1,1,1,1] (.node [12,10,8,7,7,6,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,7,7,6,3,3,1,1,1,1,1,1] (.node [12,10,8,7,7,6,3,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,8,7,7,6,4,3,1,1,1,1,1] (.node [12,10,8,7,7,6,4,2,2,1,1,1,1] (.node [12,10,8,7,7,6,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,6,5,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_559 : RowTree := (.node [12,10,8,7,7,5,3,3,3,2,1,1] degreeTree62_557 degreeTree62_558) - -def degreeTree62_560 : RowTree := (.node [12,10,8,8,4,4,4,2,2,2,2,2,2] (.node [12,10,8,7,7,7,3,2,2,1,1,1,1] (.node [12,10,8,7,7,7,2,2,2,2,1,1,1] (.node [12,10,8,7,7,7,2,2,2,1,1,1,1,1] (.node [12,10,8,7,7,6,6,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,7,3,2,1,1,1,1,1,1] (.node [12,10,8,7,7,7,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,8,7,7,7,4,2,1,1,1,1,1] (.node [12,10,8,7,7,7,4,1,1,1,1,1,1,1] (.node [12,10,8,7,7,7,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,7,5,1,1,1,1,1,1] .empty .empty))) (.node [12,10,8,8,4,4,4,4,4,2,1,1] (.node [12,10,8,8,4,4,4,4,3,2,1,1,1] (.node [12,10,8,8,4,4,4,4,2,2,2,1,1] (.node [12,10,8,8,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,8,4,4,4,4,4,1,1,1,1] (.node [12,10,8,8,4,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,10,8,8,5,4,4,2,2,2,2,2,1] (.node [12,10,8,8,5,4,3,3,3,2,2,1,1] (.node [12,10,8,8,5,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,8,5,4,4,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_561 : RowTree := (.node [12,10,8,8,5,5,4,2,2,2,2,1,1] (.node [12,10,8,8,5,5,2,2,2,2,2,2,2] (.node [12,10,8,8,5,4,4,4,2,2,2,1] (.node [12,10,8,8,5,4,4,4,2,2,1,1,1] (.node [12,10,8,8,5,4,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,8,8,5,4,4,4,3,2,1,1] (.node [12,10,8,8,5,4,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,5,5,3,3,3,2,1,1,1] (.node [12,10,8,8,5,5,3,3,2,2,2,1,1] (.node [12,10,8,8,5,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,8,8,5,5,3,3,3,2,2,1] .empty .empty))) (.node [12,10,8,8,5,5,4,4,2,1,1,1,1] (.node [12,10,8,8,5,5,4,3,2,2,2,1] (.node [12,10,8,8,5,5,4,3,2,2,1,1,1] (.node [12,10,8,8,5,5,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,8,5,5,4,3,3,2,1,1] (.node [12,10,8,8,5,5,4,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,5,5,5,2,2,2,2,1] (.node [12,10,8,8,5,5,5,2,2,2,1,1,1] (.node [12,10,8,8,5,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,8,5,5,5,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_562 : RowTree := (.node [12,10,8,8,5,4,4,3,3,2,1,1,1] degreeTree62_560 degreeTree62_561) - -def degreeTree62_563 : RowTree := (.node [12,10,8,7,7,6,5,2,1,1,1,1,1] degreeTree62_559 degreeTree62_562) - -def degreeTree62_564 : RowTree := (.node [12,10,8,8,6,4,4,2,2,2,2,1,1] (.node [12,10,8,8,6,4,3,3,2,2,2,1,1] (.node [12,10,8,8,6,4,2,2,2,2,2,2,2] (.node [12,10,8,8,6,3,3,3,3,2,2,1,1] (.node [12,10,8,8,6,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,8,6,4,3,2,2,2,2,2,1] (.node [12,10,8,8,6,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,6,4,3,3,3,2,2,1] (.node [12,10,8,8,6,4,3,3,3,2,1,1,1] (.node [12,10,8,8,6,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,4,4,2,2,2,1,1,1,1] .empty .empty))) (.node [12,10,8,8,6,4,4,3,3,2,1,1] (.node [12,10,8,8,6,4,4,3,2,2,1,1,1] (.node [12,10,8,8,6,4,4,3,2,1,1,1,1,1] (.node [12,10,8,8,6,4,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,8,6,4,4,3,3,1,1,1,1] (.node [12,10,8,8,6,4,4,3,2,2,2,1] .empty .empty) .empty)) (.node [12,10,8,8,6,5,2,2,2,2,2,1,1,1] (.node [12,10,8,8,6,4,4,4,2,1,1,1,1] (.node [12,10,8,8,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,5,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_565 : RowTree := (.node [12,10,8,8,6,5,4,3,1,1,1,1,1,1] (.node [12,10,8,8,6,5,3,3,3,1,1,1,1] (.node [12,10,8,8,6,5,3,3,2,1,1,1,1,1] (.node [12,10,8,8,6,5,3,2,2,2,2,2] (.node [12,10,8,8,6,5,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,5,3,3,2,2,2,1] (.node [12,10,8,8,6,5,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,6,5,4,2,2,2,1,1,1] (.node [12,10,8,8,6,5,4,2,2,1,1,1,1,1] (.node [12,10,8,8,6,5,3,3,3,2,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,5,4,2,2,2,2,1] .empty .empty))) (.node [12,10,8,8,6,6,2,2,2,2,1,1,1,1] (.node [12,10,8,8,6,5,5,2,1,1,1,1,1,1] (.node [12,10,8,8,6,5,4,4,1,1,1,1,1] (.node [12,10,8,8,6,5,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,5,5,3,1,1,1,1,1] (.node [12,10,8,8,6,5,5,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,6,6,3,2,2,1,1,1,1,1] (.node [12,10,8,8,6,6,2,2,2,2,2,2] (.node [12,10,8,8,6,6,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,6,3,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_566 : RowTree := (.node [12,10,8,8,6,5,3,2,2,2,1,1,1,1] degreeTree62_564 degreeTree62_565) - -def degreeTree62_567 : RowTree := (.node [12,10,8,8,7,3,3,2,2,2,2,1,1,1] (.node [12,10,8,8,6,6,5,1,1,1,1,1,1,1] (.node [12,10,8,8,6,6,4,2,1,1,1,1,1,1] (.node [12,10,8,8,6,6,3,3,2,1,1,1,1] (.node [12,10,8,8,6,6,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,6,4,3,1,1,1,1,1] (.node [12,10,8,8,6,6,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,7,2,2,2,2,2,2,2,2,1] (.node [12,10,8,8,6,6,6,1,1,1,1,1,1] (.node [12,10,8,8,6,6,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,3,2,2,2,2,2,2,2] .empty .empty))) (.node [12,10,8,8,7,4,2,2,2,2,2,1,1,1] (.node [12,10,8,8,7,3,3,3,3,1,1,1,1,1] (.node [12,10,8,8,7,3,3,3,2,2,2,1,1] (.node [12,10,8,8,7,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,8,8,7,3,3,3,3,2,2,1] (.node [12,10,8,8,7,3,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,7,4,3,2,2,2,2,1,1] (.node [12,10,8,8,7,4,3,2,2,2,1,1,1,1] (.node [12,10,8,8,7,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,8,8,7,4,3,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_568 : RowTree := (.node [12,10,8,8,7,5,2,2,2,2,1,1,1,1] (.node [12,10,8,8,7,4,4,2,2,2,1,1,1] (.node [12,10,8,8,7,4,3,3,3,1,1,1,1] (.node [12,10,8,8,7,4,3,3,2,2,2,1] (.node [12,10,8,8,7,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,4,4,2,2,1,1,1,1,1] (.node [12,10,8,8,7,4,3,3,3,2,1,1] .empty .empty) .empty)) (.node [12,10,8,8,7,4,4,3,2,1,1,1,1] (.node [12,10,8,8,7,4,4,3,1,1,1,1,1,1] (.node [12,10,8,8,7,4,4,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,8,8,7,4,4,4,1,1,1,1,1] .empty .empty))) (.node [12,10,8,8,7,5,3,2,2,2,2,1] (.node [12,10,8,8,7,5,3,2,2,1,1,1,1,1] (.node [12,10,8,8,7,5,2,2,2,2,2,2] (.node [12,10,8,8,7,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,5,3,2,2,2,1,1,1] .empty .empty)) (.node [12,10,8,8,7,5,4,2,1,1,1,1,1,1] (.node [12,10,8,8,7,5,3,3,2,1,1,1,1] (.node [12,10,8,8,7,5,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,5,4,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_569 : RowTree := (.node [12,10,8,8,7,4,3,3,2,1,1,1,1,1] degreeTree62_567 degreeTree62_568) - -def degreeTree62_570 : RowTree := (.node [12,10,8,8,6,6,3,2,2,2,2,1] degreeTree62_566 degreeTree62_569) - -def degreeTree62_571 : RowTree := (.node [12,10,8,8,5,5,5,4,1,1,1,1,1] degreeTree62_563 degreeTree62_570) - -def degreeTree62_572 : RowTree := (.node [12,10,8,7,7,4,3,3,3,2,1,1,1] degreeTree62_556 degreeTree62_571) - -def degreeTree62_573 : RowTree := (.node [12,10,7,7,7,7,3,3,2,2,1,1] degreeTree62_541 degreeTree62_572) - -def degreeTree62_574 : RowTree := (.node [12,10,8,8,7,6,5,1,1,1,1,1,1] (.node [12,10,8,8,7,6,3,2,1,1,1,1,1,1] (.node [12,10,8,8,7,6,2,2,2,1,1,1,1,1] (.node [12,10,8,8,7,5,5,2,1,1,1,1,1] (.node [12,10,8,8,7,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,6,2,2,2,2,2,1] (.node [12,10,8,8,7,6,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,7,6,4,1,1,1,1,1,1,1] (.node [12,10,8,8,7,6,3,3,1,1,1,1,1] (.node [12,10,8,8,7,6,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,6,4,2,1,1,1,1,1] .empty .empty))) (.node [12,10,8,8,8,2,2,2,2,2,2,2,1,1] (.node [12,10,8,8,7,7,3,1,1,1,1,1,1,1] (.node [12,10,8,8,7,7,2,2,2,1,1,1,1] (.node [12,10,8,8,7,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,7,4,1,1,1,1,1,1] (.node [12,10,8,8,7,7,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,8,3,2,2,2,2,2,2,1] (.node [12,10,8,8,8,3,2,2,2,2,2,1,1,1] (.node [12,10,8,8,8,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,8,8,3,3,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_575 : RowTree := (.node [12,10,8,8,8,4,3,2,2,2,1,1,1] (.node [12,10,8,8,8,3,3,3,3,2,1,1] (.node [12,10,8,8,8,3,3,3,2,2,1,1,1] (.node [12,10,8,8,8,3,3,3,2,1,1,1,1,1] (.node [12,10,8,8,8,3,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,8,8,3,3,3,3,1,1,1,1] (.node [12,10,8,8,8,3,3,3,2,2,2,1] .empty .empty) .empty)) (.node [12,10,8,8,8,4,2,2,2,2,2,2] (.node [12,10,8,8,8,4,2,2,2,2,2,1,1] (.node [12,10,8,8,8,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,8,4,3,2,2,1,1,1,1,1] .empty .empty))) (.node [12,10,8,8,8,4,4,3,1,1,1,1,1] (.node [12,10,8,8,8,4,3,3,2,1,1,1,1] (.node [12,10,8,8,8,4,3,3,1,1,1,1,1,1] (.node [12,10,8,8,8,4,3,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,8,8,8,4,4,2,2,1,1,1,1] (.node [12,10,8,8,8,4,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,8,5,2,2,2,2,2,1] (.node [12,10,8,8,8,5,2,2,2,2,1,1,1] (.node [12,10,8,8,8,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,8,5,3,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_576 : RowTree := (.node [12,10,8,8,8,3,3,2,2,2,2,1,1] degreeTree62_574 degreeTree62_575) - -def degreeTree62_577 : RowTree := (.node [12,10,8,8,8,7,2,2,1,1,1,1,1] (.node [12,10,8,8,8,6,2,2,2,1,1,1,1] (.node [12,10,8,8,8,5,4,2,1,1,1,1,1] (.node [12,10,8,8,8,5,4,1,1,1,1,1,1,1] (.node [12,10,8,8,8,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,8,6,2,2,1,1,1,1,1,1] (.node [12,10,8,8,8,5,5,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,8,6,4,1,1,1,1,1,1] (.node [12,10,8,8,8,6,3,2,1,1,1,1,1] (.node [12,10,8,8,8,6,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,8,7,2,1,1,1,1,1,1,1] .empty .empty))) (.node [12,10,9,5,5,4,4,4,4,2,1,1,1] (.node [12,10,8,8,8,8,2,1,1,1,1,1,1] (.node [12,10,8,8,8,8,1,1,1,1,1,1,1,1] (.node [12,10,8,8,8,7,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,5,5,4,4,4,3,2,2,1,1] (.node [12,10,9,5,4,4,4,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,5,5,5,4,3,3,2,2,1,1] (.node [12,10,9,5,5,5,4,2,2,2,2,2,2] (.node [12,10,9,5,5,4,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,10,9,5,5,5,4,4,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_578 : RowTree := (.node [12,10,9,5,5,5,5,4,3,2,1,1] (.node [12,10,9,5,5,5,5,3,3,2,1,1,1] (.node [12,10,9,5,5,5,4,4,4,2,1,1] (.node [12,10,9,5,5,5,4,4,4,1,1,1,1] (.node [12,10,9,5,5,5,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,10,9,5,5,5,5,3,2,2,2,1,1] (.node [12,10,9,5,5,5,5,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,5,5,5,5,4,2,2,2,1] (.node [12,10,9,5,5,5,5,4,2,2,1,1,1] (.node [12,10,9,5,5,5,5,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,9,5,5,5,5,4,3,1,1,1,1] .empty .empty))) (.node [12,10,9,6,5,4,4,3,3,2,2,1,1] (.node [12,10,9,6,4,4,4,4,4,2,1,1,1] (.node [12,10,9,6,4,4,4,4,3,2,2,1,1] (.node [12,10,9,5,5,5,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,5,4,4,2,2,2,2,2,2] (.node [12,10,9,6,4,4,4,4,4,2,2,1] .empty .empty) .empty)) (.node [12,10,9,6,5,4,4,4,3,2,2,1] (.node [12,10,9,6,5,4,4,4,3,2,1,1,1] (.node [12,10,9,6,5,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,9,6,5,4,4,4,4,1,1,1,1] .empty .empty)))) - -def degreeTree62_579 : RowTree := (.node [12,10,9,5,5,5,4,4,3,2,1,1,1] degreeTree62_577 degreeTree62_578) - -def degreeTree62_580 : RowTree := (.node [12,10,8,8,8,5,3,2,2,1,1,1,1] degreeTree62_576 degreeTree62_579) - -def degreeTree62_581 : RowTree := (.node [12,10,9,6,5,5,5,2,2,2,2,1,1] (.node [12,10,9,6,5,5,4,3,3,2,2,1] (.node [12,10,9,6,5,5,4,2,2,2,2,2,1] (.node [12,10,9,6,5,5,3,3,3,2,2,1,1] (.node [12,10,9,6,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,6,5,5,4,3,3,2,1,1,1] (.node [12,10,9,6,5,5,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,6,5,5,4,4,3,1,1,1,1] (.node [12,10,9,6,5,5,4,4,2,2,2,1] (.node [12,10,9,6,5,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,5,5,4,4,3,2,1,1] .empty .empty))) (.node [12,10,9,6,5,5,5,4,2,1,1,1,1] (.node [12,10,9,6,5,5,5,3,2,2,2,1] (.node [12,10,9,6,5,5,5,3,2,2,1,1,1] (.node [12,10,9,6,5,5,5,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,6,5,5,5,3,3,2,1,1] (.node [12,10,9,6,5,5,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,6,6,4,3,3,3,2,2,1,1] (.node [12,10,9,6,6,4,3,2,2,2,2,2,2] (.node [12,10,9,6,5,5,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,4,4,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_582 : RowTree := (.node [12,10,9,6,6,5,3,3,3,2,2,1] (.node [12,10,9,6,6,4,4,4,3,2,1,1] (.node [12,10,9,6,6,4,4,4,2,2,1,1,1] (.node [12,10,9,6,6,4,4,3,3,2,2,1] (.node [12,10,9,6,6,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,4,4,4,3,1,1,1,1] (.node [12,10,9,6,6,4,4,4,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,6,6,5,3,3,2,2,2,1,1] (.node [12,10,9,6,6,5,3,2,2,2,2,2,1] (.node [12,10,9,6,6,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,6,6,5,3,3,3,2,1,1,1] .empty .empty))) (.node [12,10,9,6,6,5,4,3,3,2,1,1] (.node [12,10,9,6,6,5,4,3,2,2,1,1,1] (.node [12,10,9,6,6,5,4,2,2,2,2,2] (.node [12,10,9,6,6,5,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,5,4,3,3,1,1,1,1] (.node [12,10,9,6,6,5,4,3,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,6,6,5,5,2,2,2,2,1] (.node [12,10,9,6,6,5,5,2,2,2,1,1,1] (.node [12,10,9,6,6,5,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,5,5,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_583 : RowTree := (.node [12,10,9,6,6,4,4,3,2,2,2,1,1] degreeTree62_581 degreeTree62_582) - -def degreeTree62_584 : RowTree := (.node [12,10,9,6,6,6,4,2,2,1,1,1,1,1] (.node [12,10,9,6,6,6,3,3,2,1,1,1,1,1] (.node [12,10,9,6,6,6,3,2,2,2,1,1,1,1] (.node [12,10,9,6,6,6,2,2,2,2,2,2,1] (.node [12,10,9,6,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,6,3,2,2,2,2,2] (.node [12,10,9,6,6,6,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,6,6,6,3,3,3,1,1,1,1] (.node [12,10,9,6,6,6,3,3,2,2,2,1] (.node [12,10,9,6,6,6,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,6,3,3,3,2,1,1] .empty .empty))) (.node [12,10,9,6,6,6,5,2,1,1,1,1,1,1] (.node [12,10,9,6,6,6,4,3,1,1,1,1,1,1] (.node [12,10,9,6,6,6,4,2,2,2,2,1] (.node [12,10,9,6,6,6,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,6,4,4,1,1,1,1,1] (.node [12,10,9,6,6,6,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,6,6,6,6,1,1,1,1,1,1,1] (.node [12,10,9,6,6,6,5,3,1,1,1,1,1] (.node [12,10,9,6,6,6,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,6,6,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_585 : RowTree := (.node [12,10,9,7,5,4,4,3,3,2,1,1,1] (.node [12,10,9,7,4,4,4,4,4,2,1,1] (.node [12,10,9,7,4,4,4,4,3,2,1,1,1] (.node [12,10,9,7,4,4,4,4,2,2,2,1,1] (.node [12,10,9,7,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,9,7,4,4,4,4,4,1,1,1,1] (.node [12,10,9,7,4,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,10,9,7,5,4,4,2,2,2,2,2,1] (.node [12,10,9,7,5,4,3,3,3,2,2,1,1] (.node [12,10,9,7,5,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,7,5,4,4,3,2,2,2,1,1] .empty .empty))) (.node [12,10,9,7,5,5,2,2,2,2,2,2,2] (.node [12,10,9,7,5,4,4,4,2,2,2,1] (.node [12,10,9,7,5,4,4,4,2,2,1,1,1] (.node [12,10,9,7,5,4,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,9,7,5,4,4,4,3,2,1,1] (.node [12,10,9,7,5,4,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,5,5,3,3,3,2,1,1,1] (.node [12,10,9,7,5,5,3,3,2,2,2,1,1] (.node [12,10,9,7,5,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,7,5,5,3,3,3,2,2,1] .empty .empty)))) - -def degreeTree62_586 : RowTree := (.node [12,10,9,7,4,4,4,2,2,2,2,2,2] degreeTree62_584 degreeTree62_585) - -def degreeTree62_587 : RowTree := (.node [12,10,9,6,6,5,5,4,1,1,1,1,1] degreeTree62_583 degreeTree62_586) - -def degreeTree62_588 : RowTree := (.node [12,10,9,6,5,4,4,4,4,2,1,1] degreeTree62_580 degreeTree62_587) - -def degreeTree62_589 : RowTree := (.node [12,10,9,7,6,3,3,2,2,2,2,2,2] (.node [12,10,9,7,5,5,4,4,2,1,1,1,1] (.node [12,10,9,7,5,5,4,3,2,2,2,1] (.node [12,10,9,7,5,5,4,3,2,2,1,1,1] (.node [12,10,9,7,5,5,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,7,5,5,4,3,3,2,1,1] (.node [12,10,9,7,5,5,4,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,5,5,5,3,2,1,1,1,1] (.node [12,10,9,7,5,5,5,2,2,2,2,1] (.node [12,10,9,7,5,5,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,5,5,5,4,1,1,1,1,1] .empty .empty))) (.node [12,10,9,7,6,4,3,3,3,1,1,1,1,1] (.node [12,10,9,7,6,4,3,2,2,2,2,1,1,1] (.node [12,10,9,7,6,4,2,2,2,2,2,2,2] (.node [12,10,9,7,6,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,4,3,3,2,2,2,1,1] (.node [12,10,9,7,6,4,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,7,6,4,4,2,2,2,1,1,1,1] (.node [12,10,9,7,6,4,3,3,3,2,2,1] (.node [12,10,9,7,6,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,4,4,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_590 : RowTree := (.node [12,10,9,7,6,5,3,2,2,2,2,2] (.node [12,10,9,7,6,4,4,4,2,1,1,1,1] (.node [12,10,9,7,6,4,4,3,2,2,2,1] (.node [12,10,9,7,6,4,4,3,2,2,1,1,1] (.node [12,10,9,7,6,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,4,4,4,1,1,1,1,1,1] (.node [12,10,9,7,6,4,4,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,6,5,3,2,2,2,1,1,1,1] (.node [12,10,9,7,6,5,2,2,2,2,2,2,1] (.node [12,10,9,7,6,5,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,5,3,2,2,2,2,1,1] .empty .empty))) (.node [12,10,9,7,6,5,4,2,2,2,1,1,1] (.node [12,10,9,7,6,5,3,3,2,2,2,1] (.node [12,10,9,7,6,5,3,3,2,2,1,1,1] (.node [12,10,9,7,6,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,5,4,2,2,1,1,1,1,1] (.node [12,10,9,7,6,5,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,6,5,4,3,2,1,1,1,1] (.node [12,10,9,7,6,5,4,3,1,1,1,1,1,1] (.node [12,10,9,7,6,5,4,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,7,6,5,4,4,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_591 : RowTree := (.node [12,10,9,7,6,4,4,2,2,2,2,2] degreeTree62_589 degreeTree62_590) - -def degreeTree62_592 : RowTree := (.node [12,10,9,7,6,6,4,2,1,1,1,1,1,1] (.node [12,10,9,7,6,6,3,2,2,1,1,1,1,1] (.node [12,10,9,7,6,6,2,2,2,2,1,1,1,1] (.node [12,10,9,7,6,5,5,3,1,1,1,1,1] (.node [12,10,9,7,6,5,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,6,2,2,2,2,2,2] (.node [12,10,9,7,6,6,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,7,6,6,3,3,1,1,1,1,1,1] (.node [12,10,9,7,6,6,3,2,2,2,2,1] (.node [12,10,9,7,6,6,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,6,3,3,2,1,1,1,1] .empty .empty))) (.node [12,10,9,7,7,2,2,2,2,2,2,2,2,1] (.node [12,10,9,7,6,6,5,1,1,1,1,1,1,1] (.node [12,10,9,7,6,6,4,3,1,1,1,1,1] (.node [12,10,9,7,6,6,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,6,6,1,1,1,1,1,1] (.node [12,10,9,7,6,6,5,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,7,3,3,2,2,2,2,2,1] (.node [12,10,9,7,7,3,3,2,2,2,2,1,1,1] (.node [12,10,9,7,7,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,7,7,3,3,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_593 : RowTree := (.node [12,10,9,7,7,4,3,3,3,1,1,1,1] (.node [12,10,9,7,7,4,3,2,2,2,2,1,1] (.node [12,10,9,7,7,4,2,2,2,2,2,1,1,1] (.node [12,10,9,7,7,3,3,3,3,2,2,1] (.node [12,10,9,7,7,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,7,4,3,2,2,2,1,1,1,1] (.node [12,10,9,7,7,4,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,7,7,4,3,3,2,2,1,1,1] (.node [12,10,9,7,7,4,3,3,2,1,1,1,1,1] (.node [12,10,9,7,7,4,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,7,7,4,3,3,2,2,2,1] .empty .empty))) (.node [12,10,9,7,7,4,4,4,1,1,1,1,1] (.node [12,10,9,7,7,4,4,2,2,2,2,1] (.node [12,10,9,7,7,4,4,2,2,2,1,1,1] (.node [12,10,9,7,7,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,7,4,4,3,2,1,1,1,1] (.node [12,10,9,7,7,4,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,7,5,2,2,2,2,2,2] (.node [12,10,9,7,7,5,2,2,2,2,2,1,1] (.node [12,10,9,7,7,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,7,5,3,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_594 : RowTree := (.node [12,10,9,7,7,3,3,3,3,1,1,1,1,1] degreeTree62_592 degreeTree62_593) - -def degreeTree62_595 : RowTree := (.node [12,10,9,7,6,5,5,2,1,1,1,1,1,1] degreeTree62_591 degreeTree62_594) - -def degreeTree62_596 : RowTree := (.node [12,10,9,7,7,6,2,2,2,2,2,1] (.node [12,10,9,7,7,5,4,3,1,1,1,1,1] (.node [12,10,9,7,7,5,3,3,2,1,1,1,1] (.node [12,10,9,7,7,5,3,3,1,1,1,1,1,1] (.node [12,10,9,7,7,5,3,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,7,7,5,4,2,2,1,1,1,1] (.node [12,10,9,7,7,5,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,7,6,2,2,2,1,1,1,1,1] (.node [12,10,9,7,7,5,5,2,1,1,1,1,1] (.node [12,10,9,7,7,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,7,6,2,2,2,2,1,1,1] .empty .empty))) (.node [12,10,9,7,7,6,5,1,1,1,1,1,1] (.node [12,10,9,7,7,6,3,3,1,1,1,1,1] (.node [12,10,9,7,7,6,3,2,2,1,1,1,1] (.node [12,10,9,7,7,6,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,7,6,4,2,1,1,1,1,1] (.node [12,10,9,7,7,6,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,7,7,3,1,1,1,1,1,1,1] (.node [12,10,9,7,7,7,2,2,2,1,1,1,1] (.node [12,10,9,7,7,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,7,7,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_597 : RowTree := (.node [12,10,9,8,4,4,4,4,2,2,2,1] (.node [12,10,9,8,4,4,4,3,3,1,1,1,1,1] (.node [12,10,9,8,4,4,4,2,2,2,2,1,1,1] (.node [12,10,9,8,4,4,3,3,3,2,2,1,1] (.node [12,10,9,8,4,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,8,4,4,4,3,2,2,2,1,1] (.node [12,10,9,8,4,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,8,4,4,4,4,2,1,1,1,1,1] (.node [12,10,9,8,4,4,4,3,3,2,2,1] (.node [12,10,9,8,4,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,4,4,4,4,2,2,1,1,1] .empty .empty))) (.node [12,10,9,8,5,4,3,2,2,2,2,1,1,1] (.node [12,10,9,8,5,3,3,2,2,2,2,2,2] (.node [12,10,9,8,4,4,4,4,3,2,1,1] (.node [12,10,9,8,4,4,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,5,4,2,2,2,2,2,2,2] (.node [12,10,9,8,5,3,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,8,5,4,3,3,3,1,1,1,1,1] (.node [12,10,9,8,5,4,3,3,2,2,2,1,1] (.node [12,10,9,8,5,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,8,5,4,3,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_598 : RowTree := (.node [12,10,9,7,7,7,4,1,1,1,1,1,1] degreeTree62_596 degreeTree62_597) - -def degreeTree62_599 : RowTree := (.node [12,10,9,8,5,5,2,2,2,2,2,2,1] (.node [12,10,9,8,5,4,4,3,2,2,2,1] (.node [12,10,9,8,5,4,4,2,2,2,2,2] (.node [12,10,9,8,5,4,4,2,2,2,2,1,1] (.node [12,10,9,8,5,4,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,5,4,4,3,2,2,1,1,1] (.node [12,10,9,8,5,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,5,4,4,4,2,1,1,1,1] (.node [12,10,9,8,5,4,4,4,1,1,1,1,1,1] (.node [12,10,9,8,5,4,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,5,5,2,2,2,2,2,1,1,1] .empty .empty))) (.node [12,10,9,8,5,5,3,3,2,2,2,1] (.node [12,10,9,8,5,5,3,2,2,2,2,2] (.node [12,10,9,8,5,5,3,2,2,2,2,1,1] (.node [12,10,9,8,5,5,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,5,5,3,3,2,2,1,1,1] (.node [12,10,9,8,5,5,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,5,5,4,2,2,2,1,1,1] (.node [12,10,9,8,5,5,4,2,2,1,1,1,1,1] (.node [12,10,9,8,5,5,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,5,5,4,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_600 : RowTree := (.node [12,10,9,8,6,3,3,3,3,1,1,1,1,1] (.node [12,10,9,8,6,2,2,2,2,2,2,2,2,1] (.node [12,10,9,8,5,5,5,2,1,1,1,1,1,1] (.node [12,10,9,8,5,5,4,4,1,1,1,1,1] (.node [12,10,9,8,5,5,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,5,5,5,3,1,1,1,1,1] (.node [12,10,9,8,5,5,5,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,6,3,3,2,2,2,2,2,1] (.node [12,10,9,8,6,3,3,2,2,2,2,1,1,1] (.node [12,10,9,8,6,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,8,6,3,3,3,2,2,2,1,1] .empty .empty))) (.node [12,10,9,8,6,4,3,2,2,2,1,1,1,1] (.node [12,10,9,8,6,4,2,2,2,2,2,1,1,1] (.node [12,10,9,8,6,3,3,3,3,2,2,1] (.node [12,10,9,8,6,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,6,4,2,2,2,2,2,2,1] .empty .empty)) (.node [12,10,9,8,6,4,3,3,2,1,1,1,1,1] (.node [12,10,9,8,6,4,3,2,2,2,2,2] (.node [12,10,9,8,6,4,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,9,8,6,4,3,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_601 : RowTree := (.node [12,10,9,8,5,5,4,3,1,1,1,1,1,1] degreeTree62_599 degreeTree62_600) - -def degreeTree62_602 : RowTree := (.node [12,10,9,8,5,4,3,3,3,2,2,1] degreeTree62_598 degreeTree62_601) - -def degreeTree62_603 : RowTree := (.node [12,10,9,7,7,5,3,2,2,2,1,1,1] degreeTree62_595 degreeTree62_602) - -def degreeTree62_604 : RowTree := (.node [12,10,9,7,5,5,4,2,2,2,2,1,1] degreeTree62_588 degreeTree62_603) - -def degreeTree62_605 : RowTree := (.node [12,10,9,8,6,5,3,2,2,1,1,1,1,1] (.node [12,10,9,8,6,4,4,3,2,1,1,1,1] (.node [12,10,9,8,6,4,4,2,2,2,1,1,1] (.node [12,10,9,8,6,4,4,2,2,1,1,1,1,1] (.node [12,10,9,8,6,4,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,6,4,4,3,1,1,1,1,1,1] (.node [12,10,9,8,6,4,4,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,8,6,5,2,2,2,2,2,1,1] (.node [12,10,9,8,6,5,2,2,2,2,1,1,1,1] (.node [12,10,9,8,6,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,6,5,2,2,2,2,2,2] .empty .empty))) (.node [12,10,9,8,6,5,4,2,2,1,1,1,1] (.node [12,10,9,8,6,5,3,3,1,1,1,1,1,1] (.node [12,10,9,8,6,5,3,2,2,2,2,1] (.node [12,10,9,8,6,5,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,6,5,4,2,1,1,1,1,1,1] (.node [12,10,9,8,6,5,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,6,5,5,2,1,1,1,1,1] (.node [12,10,9,8,6,5,5,1,1,1,1,1,1,1] (.node [12,10,9,8,6,5,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,6,6,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_606 : RowTree := (.node [12,10,9,8,7,3,2,2,2,2,2,2,1] (.node [12,10,9,8,6,6,4,2,1,1,1,1,1] (.node [12,10,9,8,6,6,3,2,2,1,1,1,1] (.node [12,10,9,8,6,6,3,2,1,1,1,1,1,1] (.node [12,10,9,8,6,6,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,8,6,6,4,1,1,1,1,1,1,1] (.node [12,10,9,8,6,6,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,7,2,2,2,2,2,2,2,2] (.node [12,10,9,8,7,2,2,2,2,2,2,2,1,1] (.node [12,10,9,8,6,6,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,3,2,2,2,2,2,1,1,1] .empty .empty))) (.node [12,10,9,8,7,3,3,3,2,2,2,1] (.node [12,10,9,8,7,3,3,2,2,2,2,2] (.node [12,10,9,8,7,3,3,2,2,2,2,1,1] (.node [12,10,9,8,7,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,3,3,3,2,2,1,1,1] (.node [12,10,9,8,7,3,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,7,4,2,2,2,2,2,1,1] (.node [12,10,9,8,7,4,2,2,2,2,1,1,1,1] (.node [12,10,9,8,7,3,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,4,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_607 : RowTree := (.node [12,10,9,8,6,6,2,2,2,2,1,1,1] degreeTree62_605 degreeTree62_606) - -def degreeTree62_608 : RowTree := (.node [12,10,9,8,7,5,3,2,1,1,1,1,1,1] (.node [12,10,9,8,7,4,4,2,2,1,1,1,1] (.node [12,10,9,8,7,4,3,3,1,1,1,1,1,1] (.node [12,10,9,8,7,4,3,2,2,2,2,1] (.node [12,10,9,8,7,4,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,4,4,2,1,1,1,1,1,1] (.node [12,10,9,8,7,4,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,7,5,2,2,2,2,1,1,1] (.node [12,10,9,8,7,5,2,2,2,1,1,1,1,1] (.node [12,10,9,8,7,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,5,2,2,2,2,2,1] .empty .empty))) (.node [12,10,9,8,7,6,2,2,1,1,1,1,1,1] (.node [12,10,9,8,7,5,4,1,1,1,1,1,1,1] (.node [12,10,9,8,7,5,3,3,1,1,1,1,1] (.node [12,10,9,8,7,5,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,5,5,1,1,1,1,1,1] (.node [12,10,9,8,7,5,4,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,7,6,3,2,1,1,1,1,1] (.node [12,10,9,8,7,6,3,1,1,1,1,1,1,1] (.node [12,10,9,8,7,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,6,4,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_609 : RowTree := (.node [12,10,9,8,8,3,3,3,1,1,1,1,1,1] (.node [12,10,9,8,8,3,2,2,2,2,2,1,1] (.node [12,10,9,8,8,2,2,2,2,2,2,1,1,1] (.node [12,10,9,8,7,7,3,1,1,1,1,1,1] (.node [12,10,9,8,7,7,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,8,3,2,2,2,2,1,1,1,1] (.node [12,10,9,8,8,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,8,8,3,3,2,2,2,1,1,1] (.node [12,10,9,8,8,3,3,2,2,1,1,1,1,1] (.node [12,10,9,8,8,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,8,8,3,3,2,2,2,2,1] .empty .empty))) (.node [12,10,9,8,8,4,3,2,2,1,1,1,1] (.node [12,10,9,8,8,4,2,2,2,2,1,1,1] (.node [12,10,9,8,8,4,2,2,2,1,1,1,1,1] (.node [12,10,9,8,8,3,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,8,4,3,2,1,1,1,1,1,1] (.node [12,10,9,8,8,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,8,8,4,4,2,1,1,1,1,1] (.node [12,10,9,8,8,4,4,1,1,1,1,1,1,1] (.node [12,10,9,8,8,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,8,5,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_610 : RowTree := (.node [12,10,9,8,7,7,2,1,1,1,1,1,1,1] degreeTree62_608 degreeTree62_609) - -def degreeTree62_611 : RowTree := (.node [12,10,9,8,7,4,3,2,2,1,1,1,1,1] degreeTree62_607 degreeTree62_610) - -def degreeTree62_612 : RowTree := (.node [12,10,9,9,4,3,3,3,3,2,2,1,1] (.node [12,10,9,8,8,6,3,1,1,1,1,1,1] (.node [12,10,9,8,8,5,4,1,1,1,1,1,1] (.node [12,10,9,8,8,5,3,2,1,1,1,1,1] (.node [12,10,9,8,8,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,8,6,2,2,1,1,1,1,1] (.node [12,10,9,8,8,6,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,8,8,1,1,1,1,1,1,1] (.node [12,10,9,8,8,7,2,1,1,1,1,1,1] (.node [12,10,9,8,8,7,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,4,3,3,2,2,2,2,2,2] .empty .empty))) (.node [12,10,9,9,4,4,3,3,3,2,1,1,1] (.node [12,10,9,9,4,4,3,2,2,2,2,2,1] (.node [12,10,9,9,4,4,3,2,2,2,2,1,1,1] (.node [12,10,9,9,4,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,9,4,4,3,3,3,1,1,1,1,1] (.node [12,10,9,9,4,4,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,9,4,4,4,2,2,2,2,1,1] (.node [12,10,9,9,4,4,4,2,2,2,1,1,1,1] (.node [12,10,9,9,4,4,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,9,9,4,4,4,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_613 : RowTree := (.node [12,10,9,9,5,3,3,3,3,1,1,1,1,1] (.node [12,10,9,9,5,2,2,2,2,2,2,2,2,1] (.node [12,10,9,9,4,4,4,3,3,1,1,1,1] (.node [12,10,9,9,4,4,4,3,2,2,2,1] (.node [12,10,9,9,4,4,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,4,4,4,4,2,1,1,1,1] (.node [12,10,9,9,4,4,4,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,5,3,3,2,2,2,2,2,1] (.node [12,10,9,9,5,3,3,2,2,2,2,1,1,1] (.node [12,10,9,9,5,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,9,5,3,3,3,2,2,2,1,1] .empty .empty))) (.node [12,10,9,9,5,4,3,2,2,2,2,1,1] (.node [12,10,9,9,5,4,2,2,2,2,2,1,1,1] (.node [12,10,9,9,5,3,3,3,3,2,2,1] (.node [12,10,9,9,5,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,5,4,3,2,2,2,1,1,1,1] (.node [12,10,9,9,5,4,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,9,5,4,3,3,2,2,1,1,1] (.node [12,10,9,9,5,4,3,3,2,1,1,1,1,1] (.node [12,10,9,9,5,4,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,9,5,4,3,3,2,2,2,1] .empty .empty)))) - -def degreeTree62_614 : RowTree := (.node [12,10,9,9,4,4,4,3,2,1,1,1,1,1] degreeTree62_612 degreeTree62_613) - -def degreeTree62_615 : RowTree := (.node [12,10,9,9,5,5,3,2,2,2,1,1,1] (.node [12,10,9,9,5,4,4,4,1,1,1,1,1] (.node [12,10,9,9,5,4,4,2,2,2,2,1] (.node [12,10,9,9,5,4,4,2,2,2,1,1,1] (.node [12,10,9,9,5,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,5,4,4,3,2,1,1,1,1] (.node [12,10,9,9,5,4,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,5,5,2,2,2,2,2,2] (.node [12,10,9,9,5,5,2,2,2,2,2,1,1] (.node [12,10,9,9,5,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,5,5,3,2,2,1,1,1,1,1] .empty .empty))) (.node [12,10,9,9,5,5,4,3,1,1,1,1,1] (.node [12,10,9,9,5,5,3,3,2,1,1,1,1] (.node [12,10,9,9,5,5,3,3,1,1,1,1,1,1] (.node [12,10,9,9,5,5,3,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,9,5,5,4,2,2,1,1,1,1] (.node [12,10,9,9,5,5,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,6,2,2,2,2,2,2,2,1,1] (.node [12,10,9,9,5,5,5,2,1,1,1,1,1] (.node [12,10,9,9,5,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,6,2,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_616 : RowTree := (.node [12,10,9,9,6,4,2,2,2,2,2,2] (.node [12,10,9,9,6,3,3,3,2,2,1,1,1] (.node [12,10,9,9,6,3,3,2,2,2,2,1,1] (.node [12,10,9,9,6,3,3,2,2,2,1,1,1,1] (.node [12,10,9,9,6,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,9,6,3,3,3,2,1,1,1,1,1] (.node [12,10,9,9,6,3,3,2,2,2,2,2] .empty .empty) .empty)) (.node [12,10,9,9,6,4,2,2,2,2,1,1,1,1] (.node [12,10,9,9,6,3,3,3,3,1,1,1,1] (.node [12,10,9,9,6,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,9,6,4,2,2,2,2,2,1,1] .empty .empty))) (.node [12,10,9,9,6,4,4,2,1,1,1,1,1,1] (.node [12,10,9,9,6,4,3,2,2,2,2,1] (.node [12,10,9,9,6,4,3,2,2,2,1,1,1] (.node [12,10,9,9,6,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,6,4,3,3,2,1,1,1,1] (.node [12,10,9,9,6,4,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,6,5,2,2,2,1,1,1,1,1] (.node [12,10,9,9,6,4,4,3,1,1,1,1,1] (.node [12,10,9,9,6,4,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,6,5,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_617 : RowTree := (.node [12,10,9,9,6,3,2,2,2,2,2,1,1,1] degreeTree62_615 degreeTree62_616) - -def degreeTree62_618 : RowTree := (.node [12,10,9,9,5,4,3,3,3,1,1,1,1] degreeTree62_614 degreeTree62_617) - -def degreeTree62_619 : RowTree := (.node [12,10,9,8,8,5,2,2,2,1,1,1,1] degreeTree62_611 degreeTree62_618) - -def degreeTree62_620 : RowTree := (.node [12,10,9,9,6,6,4,1,1,1,1,1,1] (.node [12,10,9,9,6,5,5,1,1,1,1,1,1] (.node [12,10,9,9,6,5,3,3,1,1,1,1,1] (.node [12,10,9,9,6,5,3,2,2,1,1,1,1] (.node [12,10,9,9,6,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,6,5,4,2,1,1,1,1,1] (.node [12,10,9,9,6,5,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,6,6,3,1,1,1,1,1,1,1] (.node [12,10,9,9,6,6,2,2,2,1,1,1,1] (.node [12,10,9,9,6,6,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,6,6,3,2,1,1,1,1,1] .empty .empty))) (.node [12,10,9,9,7,3,3,2,2,1,1,1,1,1] (.node [12,10,9,9,7,3,2,2,2,2,1,1,1,1] (.node [12,10,9,9,7,2,2,2,2,2,2,2,1] (.node [12,10,9,9,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,7,3,2,2,2,2,2,2] (.node [12,10,9,9,7,3,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,9,7,3,3,3,1,1,1,1,1,1] (.node [12,10,9,9,7,3,3,2,2,2,2,1] (.node [12,10,9,9,7,3,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,7,3,3,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_621 : RowTree := (.node [12,10,9,9,7,5,3,2,1,1,1,1,1] (.node [12,10,9,9,7,4,4,1,1,1,1,1,1,1] (.node [12,10,9,9,7,4,3,2,1,1,1,1,1,1] (.node [12,10,9,9,7,4,2,2,2,2,2,1] (.node [12,10,9,9,7,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,7,4,3,3,1,1,1,1,1] (.node [12,10,9,9,7,4,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,7,5,2,2,2,1,1,1,1] (.node [12,10,9,9,7,5,2,2,1,1,1,1,1,1] (.node [12,10,9,9,7,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,7,5,3,1,1,1,1,1,1,1] .empty .empty))) (.node [12,10,9,9,7,7,2,1,1,1,1,1,1] (.node [12,10,9,9,7,6,2,2,1,1,1,1,1] (.node [12,10,9,9,7,6,2,1,1,1,1,1,1,1] (.node [12,10,9,9,7,5,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,7,7,1,1,1,1,1,1,1,1] (.node [12,10,9,9,7,6,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,8,2,2,2,2,2,2,2] (.node [12,10,9,9,8,2,2,2,2,2,2,1,1] (.node [12,10,9,9,8,2,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,8,3,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_622 : RowTree := (.node [12,10,9,9,7,4,2,2,2,1,1,1,1,1] degreeTree62_620 degreeTree62_621) - -def degreeTree62_623 : RowTree := (.node [12,10,9,9,8,5,2,2,1,1,1,1,1] (.node [12,10,9,9,8,4,2,2,2,1,1,1,1] (.node [12,10,9,9,8,3,3,2,2,1,1,1,1] (.node [12,10,9,9,8,3,3,2,1,1,1,1,1,1] (.node [12,10,9,9,8,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,9,8,4,2,2,1,1,1,1,1,1] (.node [12,10,9,9,8,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,8,4,4,1,1,1,1,1,1] (.node [12,10,9,9,8,4,3,2,1,1,1,1,1] (.node [12,10,9,9,8,4,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,8,5,2,1,1,1,1,1,1,1] .empty .empty))) (.node [12,10,9,9,9,2,2,2,2,2,1,1,1] (.node [12,10,9,9,8,6,2,1,1,1,1,1,1] (.node [12,10,9,9,8,6,1,1,1,1,1,1,1,1] (.node [12,10,9,9,8,5,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,9,2,2,2,2,1,1,1,1,1] (.node [12,10,9,9,8,7,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,9,3,2,2,2,1,1,1,1] (.node [12,10,9,9,9,3,2,2,1,1,1,1,1,1] (.node [12,10,9,9,9,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,9,9,3,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_624 : RowTree := (.node [12,11,5,5,5,5,5,5,5,1,1,1,1] (.node [12,10,9,9,9,6,1,1,1,1,1,1,1] (.node [12,10,9,9,9,4,3,1,1,1,1,1,1] (.node [12,10,9,9,9,4,2,2,1,1,1,1,1] (.node [12,10,9,9,9,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,9,5,2,1,1,1,1,1,1] (.node [12,10,9,9,9,5,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,5,5,5,5,5,5,4,2,1,1,1] (.node [12,11,5,5,5,5,5,5,3,2,2,1,1] (.node [12,11,5,5,5,5,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,11,5,5,5,5,5,5,4,2,2,1] .empty .empty))) (.node [12,11,6,5,5,5,5,5,3,2,1,1,1] (.node [12,11,6,5,5,5,5,4,4,2,1,1,1] (.node [12,11,6,5,5,5,5,4,3,2,2,1,1] (.node [12,11,6,5,5,5,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,11,6,5,5,5,5,5,2,2,2,1,1] (.node [12,11,6,5,5,5,5,4,4,2,2,1] .empty .empty) .empty)) (.node [12,11,6,6,5,4,4,4,4,2,2,1,1] (.node [12,11,6,5,5,5,5,5,4,1,1,1,1] (.node [12,11,6,5,5,5,5,5,3,2,2,1] .empty .empty) .empty) (.node [12,11,6,6,5,5,4,4,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_625 : RowTree := (.node [12,10,9,9,9,3,3,2,1,1,1,1,1] degreeTree62_623 degreeTree62_624) - -def degreeTree62_626 : RowTree := (.node [12,10,9,9,8,3,2,2,2,2,1,1,1] degreeTree62_622 degreeTree62_625) - -def degreeTree62_627 : RowTree := (.node [12,11,6,6,6,4,4,4,3,2,2,1,1] (.node [12,11,6,6,5,5,5,4,3,2,2,1] (.node [12,11,6,6,5,5,5,3,3,2,2,1,1] (.node [12,11,6,6,5,5,5,2,2,2,2,2,2] (.node [12,11,6,6,5,5,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,11,6,6,5,5,5,4,3,2,1,1,1] (.node [12,11,6,6,5,5,5,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,11,6,6,5,5,5,5,2,2,2,1] (.node [12,11,6,6,5,5,5,5,2,2,1,1,1] (.node [12,11,6,6,5,5,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,11,6,6,5,5,5,5,3,1,1,1,1] .empty .empty))) (.node [12,11,6,6,6,5,4,4,3,2,1,1,1] (.node [12,11,6,6,6,5,4,2,2,2,2,2,2] (.node [12,11,6,6,6,4,4,4,4,2,2,1] (.node [12,11,6,6,6,4,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,11,6,6,6,5,4,4,2,2,2,1,1] (.node [12,11,6,6,6,5,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,11,6,6,6,5,5,2,2,2,2,2,1] (.node [12,11,6,6,6,5,4,4,4,1,1,1,1] (.node [12,11,6,6,6,5,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,11,6,6,6,5,5,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_628 : RowTree := (.node [12,11,6,6,6,6,4,3,3,2,2,1] (.node [12,11,6,6,6,6,3,2,2,2,2,2,2] (.node [12,11,6,6,6,5,5,4,2,2,2,1] (.node [12,11,6,6,6,5,5,4,2,2,1,1,1] (.node [12,11,6,6,6,5,5,3,3,2,2,1] .empty .empty) .empty) (.node [12,11,6,6,6,5,5,5,2,1,1,1,1] (.node [12,11,6,6,6,5,5,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,11,6,6,6,6,4,3,2,2,2,1,1] (.node [12,11,6,6,6,6,4,2,2,2,2,2,1] (.node [12,11,6,6,6,6,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,11,6,6,6,6,4,3,3,2,1,1,1] .empty .empty))) (.node [12,11,6,6,6,6,5,3,2,2,1,1,1] (.node [12,11,6,6,6,6,4,4,3,1,1,1,1] (.node [12,11,6,6,6,6,4,4,2,2,2,1] (.node [12,11,6,6,6,6,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,6,6,6,6,5,2,2,2,2,2] (.node [12,11,6,6,6,6,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,11,6,6,6,6,5,4,2,1,1,1,1] (.node [12,11,6,6,6,6,5,3,3,1,1,1,1] (.node [12,11,6,6,6,6,5,3,2,2,2,1] .empty .empty) .empty) (.node [12,11,6,6,6,6,5,5,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_629 : RowTree := (.node [12,11,6,6,6,5,5,3,3,2,1,1,1] degreeTree62_627 degreeTree62_628) - -def degreeTree62_630 : RowTree := (.node [12,11,7,5,5,5,5,4,3,2,1,1,1] (.node [12,11,7,5,5,5,4,4,4,2,1,1,1] (.node [12,11,6,6,6,6,6,4,1,1,1,1,1] (.node [12,11,6,6,6,6,6,3,2,1,1,1,1] (.node [12,11,6,6,6,6,6,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,7,5,5,5,4,4,3,2,2,1,1] (.node [12,11,7,5,5,4,4,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,11,7,5,5,5,5,3,3,2,2,1,1] (.node [12,11,7,5,5,5,5,2,2,2,2,2,2] (.node [12,11,7,5,5,5,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,11,7,5,5,5,5,4,2,2,2,1,1] .empty .empty))) (.node [12,11,7,6,4,4,4,4,4,2,2,1,1] (.node [12,11,7,5,5,5,5,5,2,2,1,1,1] (.node [12,11,7,5,5,5,5,4,4,1,1,1,1] (.node [12,11,7,5,5,5,5,4,3,2,2,1] .empty .empty) .empty) (.node [12,11,7,5,5,5,5,5,3,1,1,1,1] (.node [12,11,7,5,5,5,5,5,2,2,2,1] .empty .empty) .empty)) (.node [12,11,7,6,5,4,4,4,4,2,2,1] (.node [12,11,7,6,5,4,4,4,4,2,1,1,1] (.node [12,11,7,6,5,4,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,6,5,5,4,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_631 : RowTree := (.node [12,11,7,6,5,5,5,4,3,1,1,1,1] (.node [12,11,7,6,5,5,5,3,2,2,2,1,1] (.node [12,11,7,6,5,5,4,4,3,2,2,1] (.node [12,11,7,6,5,5,4,4,3,2,1,1,1] (.node [12,11,7,6,5,5,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,6,5,5,5,2,2,2,2,2,1] (.node [12,11,7,6,5,5,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [12,11,7,6,5,5,5,4,2,2,1,1,1] (.node [12,11,7,6,5,5,5,3,3,2,2,1] (.node [12,11,7,6,5,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,11,7,6,5,5,5,4,2,2,2,1] .empty .empty))) (.node [12,11,7,6,6,4,4,4,3,2,1,1,1] (.node [12,11,7,6,6,4,4,3,3,2,2,1,1] (.node [12,11,7,6,6,4,4,2,2,2,2,2,2] (.node [12,11,7,6,5,5,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,6,6,4,4,4,2,2,2,1,1] .empty .empty)) (.node [12,11,7,6,6,5,3,2,2,2,2,2,2] (.node [12,11,7,6,6,4,4,4,4,1,1,1,1] (.node [12,11,7,6,6,4,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,11,7,6,6,5,3,3,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_632 : RowTree := (.node [12,11,7,6,5,5,4,3,3,2,2,1,1] degreeTree62_630 degreeTree62_631) - -def degreeTree62_633 : RowTree := (.node [12,11,6,6,6,6,6,2,2,2,1,1,1] degreeTree62_629 degreeTree62_632) - -def degreeTree62_634 : RowTree := (.node [12,11,6,6,5,5,4,4,4,2,1,1,1] degreeTree62_626 degreeTree62_633) - -def degreeTree62_635 : RowTree := (.node [12,10,9,9,6,5,2,2,2,2,2,1] degreeTree62_619 degreeTree62_634) - -def degreeTree62_636 : RowTree := (.node [12,10,9,8,6,4,3,3,2,2,2,1] degreeTree62_604 degreeTree62_635) - -def degreeTree62_637 : RowTree := (.node [12,10,8,8,7,5,4,3,1,1,1,1,1] degreeTree62_573 degreeTree62_636) - -def degreeTree62_638 : RowTree := (.node [12,11,7,6,6,5,5,3,3,1,1,1,1] (.node [12,11,7,6,6,5,4,4,3,1,1,1,1] (.node [12,11,7,6,6,5,4,3,3,2,2,1] (.node [12,11,7,6,6,5,4,3,3,2,1,1,1] (.node [12,11,7,6,6,5,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,6,6,5,4,4,2,2,2,1] (.node [12,11,7,6,6,5,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,7,6,6,5,5,3,2,2,1,1,1] (.node [12,11,7,6,6,5,5,2,2,2,2,2] (.node [12,11,7,6,6,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,6,6,5,5,3,2,2,2,1] .empty .empty))) (.node [12,11,7,6,6,6,3,3,3,2,1,1,1] (.node [12,11,7,6,6,6,2,2,2,2,2,2,2] (.node [12,11,7,6,6,5,5,5,1,1,1,1,1] (.node [12,11,7,6,6,5,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,6,6,6,3,3,2,2,2,1,1] (.node [12,11,7,6,6,6,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,7,6,6,6,4,2,2,2,2,2] (.node [12,11,7,6,6,6,4,2,2,2,2,1,1] (.node [12,11,7,6,6,6,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,11,7,6,6,6,4,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_639 : RowTree := (.node [12,11,7,7,4,4,4,4,4,2,1,1,1] (.node [12,11,7,6,6,6,5,4,1,1,1,1,1] (.node [12,11,7,6,6,6,5,2,2,2,1,1,1] (.node [12,11,7,6,6,6,4,4,2,1,1,1,1] (.node [12,11,7,6,6,6,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,6,6,6,5,3,2,1,1,1,1] (.node [12,11,7,6,6,6,5,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,7,6,6,6,6,3,1,1,1,1,1] (.node [12,11,7,6,6,6,6,2,2,1,1,1,1] (.node [12,11,7,6,6,6,6,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,4,4,4,4,3,2,2,1,1] .empty .empty))) (.node [12,11,7,7,5,4,4,4,3,2,2,1] (.node [12,11,7,7,5,4,4,3,3,2,2,1,1] (.node [12,11,7,7,5,4,4,2,2,2,2,2,2] (.node [12,11,7,7,4,4,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,11,7,7,5,4,4,4,3,2,1,1,1] (.node [12,11,7,7,5,4,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,11,7,7,5,5,3,3,3,2,2,1,1] (.node [12,11,7,7,5,5,3,2,2,2,2,2,2] (.node [12,11,7,7,5,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,5,5,4,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_640 : RowTree := (.node [12,11,7,6,6,6,4,3,2,2,2,1] degreeTree62_638 degreeTree62_639) - -def degreeTree62_641 : RowTree := (.node [12,11,7,7,5,5,5,4,2,1,1,1,1] (.node [12,11,7,7,5,5,5,2,2,2,2,1,1] (.node [12,11,7,7,5,5,4,4,2,2,1,1,1] (.node [12,11,7,7,5,5,4,3,3,2,2,1] (.node [12,11,7,7,5,5,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,5,5,4,4,3,1,1,1,1] (.node [12,11,7,7,5,5,4,4,2,2,2,1] .empty .empty) .empty)) (.node [12,11,7,7,5,5,5,3,2,2,2,1] (.node [12,11,7,7,5,5,5,3,2,2,1,1,1] (.node [12,11,7,7,5,5,5,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,7,7,5,5,5,3,3,1,1,1,1] .empty .empty))) (.node [12,11,7,7,6,4,4,3,3,2,1,1,1] (.node [12,11,7,7,6,4,3,3,3,2,2,1,1] (.node [12,11,7,7,6,4,3,2,2,2,2,2,2] (.node [12,11,7,7,5,5,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,6,4,4,3,2,2,2,1,1] (.node [12,11,7,7,6,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,7,7,6,4,4,4,2,2,2,1] (.node [12,11,7,7,6,4,4,4,2,2,1,1,1] (.node [12,11,7,7,6,4,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,11,7,7,6,4,4,4,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_642 : RowTree := (.node [12,11,7,7,6,5,5,2,2,2,1,1,1] (.node [12,11,7,7,6,5,4,2,2,2,2,2] (.node [12,11,7,7,6,5,3,3,3,2,1,1,1] (.node [12,11,7,7,6,5,3,3,2,2,2,1,1] (.node [12,11,7,7,6,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,7,7,6,5,4,2,2,2,2,1,1] (.node [12,11,7,7,6,5,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,11,7,7,6,5,4,3,3,1,1,1,1] (.node [12,11,7,7,6,5,4,3,2,2,2,1] (.node [12,11,7,7,6,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,6,5,4,4,2,1,1,1,1] .empty .empty))) (.node [12,11,7,7,6,6,3,2,2,2,1,1,1,1] (.node [12,11,7,7,6,5,5,4,1,1,1,1,1] (.node [12,11,7,7,6,5,5,3,2,1,1,1,1] (.node [12,11,7,7,6,5,5,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,7,7,6,6,2,2,2,2,2,2,1] (.node [12,11,7,7,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,7,7,6,6,3,3,2,1,1,1,1,1] (.node [12,11,7,7,6,6,3,2,2,2,2,2] (.node [12,11,7,7,6,6,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,7,6,6,3,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_643 : RowTree := (.node [12,11,7,7,6,5,2,2,2,2,2,2,2] degreeTree62_641 degreeTree62_642) - -def degreeTree62_644 : RowTree := (.node [12,11,7,7,5,5,4,3,2,2,2,1,1] degreeTree62_640 degreeTree62_643) - -def degreeTree62_645 : RowTree := (.node [12,11,7,7,6,6,6,1,1,1,1,1,1,1] (.node [12,11,7,7,6,6,4,3,2,1,1,1,1] (.node [12,11,7,7,6,6,4,2,2,2,1,1,1] (.node [12,11,7,7,6,6,4,2,2,1,1,1,1,1] (.node [12,11,7,7,6,6,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,6,6,4,3,1,1,1,1,1,1] (.node [12,11,7,7,6,6,4,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,7,7,6,6,5,2,2,1,1,1,1] (.node [12,11,7,7,6,6,5,2,1,1,1,1,1,1] (.node [12,11,7,7,6,6,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,6,6,5,3,1,1,1,1,1] .empty .empty))) (.node [12,11,7,7,7,4,3,2,2,2,2,2,1] (.node [12,11,7,7,7,3,3,3,3,2,2,1,1] (.node [12,11,7,7,7,3,3,2,2,2,2,2,2] (.node [12,11,7,7,6,6,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,4,3,2,2,2,2,1,1,1] (.node [12,11,7,7,7,4,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,7,7,7,4,3,3,3,2,1,1,1] (.node [12,11,7,7,7,4,3,3,3,1,1,1,1,1] (.node [12,11,7,7,7,4,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,4,3,3,3,2,2,1] .empty .empty)))) - -def degreeTree62_646 : RowTree := (.node [12,11,7,7,7,5,3,2,2,2,1,1,1,1] (.node [12,11,7,7,7,4,4,3,3,1,1,1,1] (.node [12,11,7,7,7,4,4,3,2,1,1,1,1,1] (.node [12,11,7,7,7,4,4,2,2,2,2,2] (.node [12,11,7,7,7,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,4,4,3,2,2,2,1] (.node [12,11,7,7,7,4,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,7,7,7,5,2,2,2,2,2,1,1,1] (.node [12,11,7,7,7,4,4,4,2,1,1,1,1] (.node [12,11,7,7,7,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,5,2,2,2,2,2,2,1] .empty .empty))) (.node [12,11,7,7,7,5,3,3,3,1,1,1,1] (.node [12,11,7,7,7,5,3,3,2,1,1,1,1,1] (.node [12,11,7,7,7,5,3,2,2,2,2,2] (.node [12,11,7,7,7,5,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,5,3,3,2,2,2,1] (.node [12,11,7,7,7,5,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,7,7,7,5,4,3,1,1,1,1,1,1] (.node [12,11,7,7,7,5,4,2,2,2,1,1,1] (.node [12,11,7,7,7,5,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,5,4,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_647 : RowTree := (.node [12,11,7,7,7,4,4,2,2,2,1,1,1,1] degreeTree62_645 degreeTree62_646) - -def degreeTree62_648 : RowTree := (.node [12,11,7,7,7,6,4,2,1,1,1,1,1,1] (.node [12,11,7,7,7,6,2,2,2,2,2,2] (.node [12,11,7,7,7,5,5,3,1,1,1,1,1] (.node [12,11,7,7,7,5,5,2,2,1,1,1,1] (.node [12,11,7,7,7,5,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,6,2,2,2,2,2,1,1] (.node [12,11,7,7,7,6,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,7,7,7,6,3,3,1,1,1,1,1,1] (.node [12,11,7,7,7,6,3,2,2,2,1,1,1] (.node [12,11,7,7,7,6,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,6,3,3,2,1,1,1,1] .empty .empty))) (.node [12,11,7,7,7,7,2,2,2,1,1,1,1,1] (.node [12,11,7,7,7,6,5,1,1,1,1,1,1,1] (.node [12,11,7,7,7,6,4,3,1,1,1,1,1] (.node [12,11,7,7,7,6,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,6,6,1,1,1,1,1,1] (.node [12,11,7,7,7,6,5,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,7,7,7,7,3,2,2,1,1,1,1] (.node [12,11,7,7,7,7,3,2,1,1,1,1,1,1] (.node [12,11,7,7,7,7,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,7,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_649 : RowTree := (.node [12,11,8,5,5,5,4,4,3,2,2,1] (.node [12,11,8,5,5,4,4,4,4,2,2,1] (.node [12,11,8,5,4,4,4,4,4,2,2,1,1] (.node [12,11,7,7,7,7,5,1,1,1,1,1,1] (.node [12,11,7,7,7,7,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,5,5,4,4,4,4,2,1,1,1] (.node [12,11,8,5,5,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [12,11,8,5,5,5,4,4,2,2,2,1,1] (.node [12,11,8,5,5,5,4,3,3,2,2,1,1] (.node [12,11,8,5,5,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,5,5,5,4,4,3,2,1,1,1] .empty .empty))) (.node [12,11,8,5,5,5,5,4,2,2,1,1,1] (.node [12,11,8,5,5,5,5,3,2,2,2,1,1] (.node [12,11,8,5,5,5,5,2,2,2,2,2,1] (.node [12,11,8,5,5,5,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,5,5,5,5,3,3,2,2,1] (.node [12,11,8,5,5,5,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,11,8,5,5,5,5,5,2,1,1,1,1] (.node [12,11,8,5,5,5,5,4,3,1,1,1,1] (.node [12,11,8,5,5,5,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,11,8,6,4,4,4,4,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_650 : RowTree := (.node [12,11,7,7,7,7,4,1,1,1,1,1,1,1] degreeTree62_648 degreeTree62_649) - -def degreeTree62_651 : RowTree := (.node [12,11,7,7,7,5,4,4,1,1,1,1,1] degreeTree62_647 degreeTree62_650) - -def degreeTree62_652 : RowTree := (.node [12,11,7,7,6,6,3,3,2,2,2,1] degreeTree62_644 degreeTree62_651) - -def degreeTree62_653 : RowTree := (.node [12,11,8,6,5,5,4,3,2,2,2,1,1] (.node [12,11,8,6,5,4,4,4,3,2,2,1] (.node [12,11,8,6,5,4,4,3,3,2,2,1,1] (.node [12,11,8,6,5,4,4,2,2,2,2,2,2] (.node [12,11,8,6,4,4,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,11,8,6,5,4,4,4,3,2,1,1,1] (.node [12,11,8,6,5,4,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,11,8,6,5,5,3,3,3,2,2,1,1] (.node [12,11,8,6,5,5,3,2,2,2,2,2,2] (.node [12,11,8,6,5,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,5,5,4,2,2,2,2,2,1] .empty .empty))) (.node [12,11,8,6,5,5,5,2,2,2,2,1,1] (.node [12,11,8,6,5,5,4,4,2,2,1,1,1] (.node [12,11,8,6,5,5,4,3,3,2,2,1] (.node [12,11,8,6,5,5,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,5,5,4,4,3,1,1,1,1] (.node [12,11,8,6,5,5,4,4,2,2,2,1] .empty .empty) .empty)) (.node [12,11,8,6,5,5,5,3,2,2,2,1] (.node [12,11,8,6,5,5,5,3,2,2,1,1,1] (.node [12,11,8,6,5,5,5,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,6,5,5,5,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_654 : RowTree := (.node [12,11,8,6,6,5,2,2,2,2,2,2,2] (.node [12,11,8,6,6,4,4,3,3,2,1,1,1] (.node [12,11,8,6,6,4,3,3,3,2,2,1,1] (.node [12,11,8,6,6,4,3,2,2,2,2,2,2] (.node [12,11,8,6,5,5,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,6,4,4,3,2,2,2,1,1] (.node [12,11,8,6,6,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,8,6,6,4,4,4,2,2,2,1] (.node [12,11,8,6,6,4,4,4,2,2,1,1,1] (.node [12,11,8,6,6,4,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,11,8,6,6,4,4,4,3,1,1,1,1] .empty .empty))) (.node [12,11,8,6,6,5,4,2,2,2,2,2] (.node [12,11,8,6,6,5,3,3,3,2,1,1,1] (.node [12,11,8,6,6,5,3,3,2,2,2,1,1] (.node [12,11,8,6,6,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,8,6,6,5,4,2,2,2,2,1,1] (.node [12,11,8,6,6,5,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,11,8,6,6,5,4,3,3,1,1,1,1] (.node [12,11,8,6,6,5,4,3,2,2,2,1] (.node [12,11,8,6,6,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,6,5,4,4,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_655 : RowTree := (.node [12,11,8,6,5,5,5,4,2,1,1,1,1] degreeTree62_653 degreeTree62_654) - -def degreeTree62_656 : RowTree := (.node [12,11,8,6,6,6,3,3,3,1,1,1,1] (.node [12,11,8,6,6,6,3,2,2,2,2,1,1] (.node [12,11,8,6,6,6,2,2,2,2,2,1,1,1] (.node [12,11,8,6,6,5,5,4,1,1,1,1,1] (.node [12,11,8,6,6,5,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,6,6,3,2,2,2,1,1,1,1] (.node [12,11,8,6,6,6,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,8,6,6,6,3,3,2,2,1,1,1] (.node [12,11,8,6,6,6,3,3,2,1,1,1,1,1] (.node [12,11,8,6,6,6,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,6,6,6,3,3,2,2,2,1] .empty .empty))) (.node [12,11,8,6,6,6,5,2,1,1,1,1,1,1] (.node [12,11,8,6,6,6,4,3,1,1,1,1,1,1] (.node [12,11,8,6,6,6,4,2,2,2,1,1,1] (.node [12,11,8,6,6,6,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,6,6,4,4,1,1,1,1,1] (.node [12,11,8,6,6,6,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,6,6,6,6,1,1,1,1,1,1,1] (.node [12,11,8,6,6,6,5,3,1,1,1,1,1] (.node [12,11,8,6,6,6,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,6,6,6,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_657 : RowTree := (.node [12,11,8,7,5,4,4,3,3,2,2,1] (.node [12,11,8,7,5,4,3,2,2,2,2,2,2] (.node [12,11,8,7,4,4,4,4,3,2,1,1,1] (.node [12,11,8,7,4,4,4,4,2,2,2,1,1] (.node [12,11,8,7,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,11,8,7,4,4,4,4,4,1,1,1,1] (.node [12,11,8,7,4,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,11,8,7,5,4,4,3,2,2,2,1,1] (.node [12,11,8,7,5,4,4,2,2,2,2,2,1] (.node [12,11,8,7,5,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,11,8,7,5,4,4,3,3,2,1,1,1] .empty .empty))) (.node [12,11,8,7,5,5,3,3,2,2,2,1,1] (.node [12,11,8,7,5,4,4,4,3,1,1,1,1] (.node [12,11,8,7,5,4,4,4,2,2,2,1] (.node [12,11,8,7,5,4,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,5,5,3,2,2,2,2,2,1] (.node [12,11,8,7,5,5,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,8,7,5,5,4,2,2,2,2,1,1] (.node [12,11,8,7,5,5,3,3,3,2,2,1] (.node [12,11,8,7,5,5,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,5,5,4,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_658 : RowTree := (.node [12,11,8,7,4,4,4,2,2,2,2,2,2] degreeTree62_656 degreeTree62_657) - -def degreeTree62_659 : RowTree := (.node [12,11,8,6,6,5,5,2,2,2,1,1,1] degreeTree62_655 degreeTree62_658) - -def degreeTree62_660 : RowTree := (.node [12,11,8,7,6,4,3,2,2,2,2,2,1] (.node [12,11,8,7,5,5,5,4,1,1,1,1,1] (.node [12,11,8,7,5,5,4,4,2,1,1,1,1] (.node [12,11,8,7,5,5,4,3,3,1,1,1,1] (.node [12,11,8,7,5,5,4,3,2,2,2,1] .empty .empty) .empty) (.node [12,11,8,7,5,5,5,3,2,1,1,1,1] (.node [12,11,8,7,5,5,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,6,4,2,2,2,2,2,2,2] (.node [12,11,8,7,6,3,3,3,3,2,2,1,1] (.node [12,11,8,7,6,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,7,6,4,3,2,2,2,2,1,1,1] .empty .empty))) (.node [12,11,8,7,6,4,4,2,2,2,2,1,1] (.node [12,11,8,7,6,4,3,3,3,2,1,1,1] (.node [12,11,8,7,6,4,3,3,3,1,1,1,1,1] (.node [12,11,8,7,6,4,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,8,7,6,4,4,2,2,2,1,1,1,1] (.node [12,11,8,7,6,4,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,11,8,7,6,4,4,3,2,2,1,1,1] (.node [12,11,8,7,6,4,4,3,2,1,1,1,1,1] (.node [12,11,8,7,6,4,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,7,6,4,4,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_661 : RowTree := (.node [12,11,8,7,6,5,4,2,2,2,1,1,1] (.node [12,11,8,7,6,5,3,2,2,2,2,2] (.node [12,11,8,7,6,5,2,2,2,2,2,2,1] (.node [12,11,8,7,6,5,2,2,2,2,2,1,1,1] (.node [12,11,8,7,6,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,6,5,3,2,2,2,2,1,1] (.node [12,11,8,7,6,5,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,6,5,3,3,3,1,1,1,1] (.node [12,11,8,7,6,5,3,3,2,2,1,1,1] (.node [12,11,8,7,6,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,6,5,4,2,2,1,1,1,1,1] .empty .empty))) (.node [12,11,8,7,6,5,5,3,1,1,1,1,1] (.node [12,11,8,7,6,5,4,4,1,1,1,1,1] (.node [12,11,8,7,6,5,4,3,2,1,1,1,1] (.node [12,11,8,7,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,6,5,5,2,2,1,1,1,1] (.node [12,11,8,7,6,5,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,6,6,2,2,2,2,2,2] (.node [12,11,8,7,6,6,2,2,2,2,2,1,1] (.node [12,11,8,7,6,6,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,6,6,3,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_662 : RowTree := (.node [12,11,8,7,6,4,4,4,1,1,1,1,1,1] degreeTree62_660 degreeTree62_661) - -def degreeTree62_663 : RowTree := (.node [12,11,8,7,7,3,3,2,2,2,2,1,1,1] (.node [12,11,8,7,6,6,5,1,1,1,1,1,1,1] (.node [12,11,8,7,6,6,4,2,1,1,1,1,1,1] (.node [12,11,8,7,6,6,3,3,2,1,1,1,1] (.node [12,11,8,7,6,6,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,6,6,4,3,1,1,1,1,1] (.node [12,11,8,7,6,6,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,7,2,2,2,2,2,2,2,2,1] (.node [12,11,8,7,6,6,6,1,1,1,1,1,1] (.node [12,11,8,7,6,6,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,3,2,2,2,2,2,2,2] .empty .empty))) (.node [12,11,8,7,7,4,2,2,2,2,2,1,1,1] (.node [12,11,8,7,7,3,3,3,3,1,1,1,1,1] (.node [12,11,8,7,7,3,3,3,2,2,2,1,1] (.node [12,11,8,7,7,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,8,7,7,3,3,3,3,2,2,1] (.node [12,11,8,7,7,3,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,7,4,3,2,2,2,2,1,1] (.node [12,11,8,7,7,4,3,2,2,2,1,1,1,1] (.node [12,11,8,7,7,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,8,7,7,4,3,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_664 : RowTree := (.node [12,11,8,7,7,5,3,2,2,1,1,1,1,1] (.node [12,11,8,7,7,4,4,3,2,1,1,1,1] (.node [12,11,8,7,7,4,4,2,2,1,1,1,1,1] (.node [12,11,8,7,7,4,3,3,3,1,1,1,1] (.node [12,11,8,7,7,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,4,4,3,1,1,1,1,1,1] (.node [12,11,8,7,7,4,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,7,5,2,2,2,2,2,1,1] (.node [12,11,8,7,7,5,2,2,2,2,1,1,1,1] (.node [12,11,8,7,7,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,5,2,2,2,2,2,2] .empty .empty))) (.node [12,11,8,7,7,5,4,2,2,1,1,1,1] (.node [12,11,8,7,7,5,3,3,2,1,1,1,1] (.node [12,11,8,7,7,5,3,3,1,1,1,1,1,1] (.node [12,11,8,7,7,5,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,5,4,2,1,1,1,1,1,1] .empty .empty)) (.node [12,11,8,7,7,5,5,2,1,1,1,1,1] (.node [12,11,8,7,7,5,5,1,1,1,1,1,1,1] (.node [12,11,8,7,7,5,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,6,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_665 : RowTree := (.node [12,11,8,7,7,4,3,3,2,1,1,1,1,1] degreeTree62_663 degreeTree62_664) - -def degreeTree62_666 : RowTree := (.node [12,11,8,7,6,6,3,2,2,2,1,1,1] degreeTree62_662 degreeTree62_665) - -def degreeTree62_667 : RowTree := (.node [12,11,8,7,5,5,4,3,2,2,1,1,1] degreeTree62_659 degreeTree62_666) - -def degreeTree62_668 : RowTree := (.node [12,11,8,6,4,4,4,4,4,2,1,1,1] degreeTree62_652 degreeTree62_667) - -def degreeTree62_669 : RowTree := (.node [12,11,8,7,7,7,4,1,1,1,1,1,1] (.node [12,11,8,7,7,6,5,1,1,1,1,1,1] (.node [12,11,8,7,7,6,3,3,1,1,1,1,1] (.node [12,11,8,7,7,6,3,2,2,1,1,1,1] (.node [12,11,8,7,7,6,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,6,4,2,1,1,1,1,1] (.node [12,11,8,7,7,6,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,7,7,3,1,1,1,1,1,1,1] (.node [12,11,8,7,7,7,2,2,2,1,1,1,1] (.node [12,11,8,7,7,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,7,3,2,1,1,1,1,1] .empty .empty))) (.node [12,11,8,8,4,4,4,3,3,1,1,1,1,1] (.node [12,11,8,8,4,4,4,2,2,2,2,1,1,1] (.node [12,11,8,8,4,4,3,3,3,2,2,1,1] (.node [12,11,8,8,4,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,8,4,4,4,3,2,2,2,1,1] (.node [12,11,8,8,4,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,8,8,4,4,4,4,2,1,1,1,1,1] (.node [12,11,8,8,4,4,4,3,3,2,2,1] (.node [12,11,8,8,4,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,4,4,4,4,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_670 : RowTree := (.node [12,11,8,8,5,4,4,2,2,2,1,1,1,1] (.node [12,11,8,8,5,4,3,2,2,2,2,2,1] (.node [12,11,8,8,5,3,3,3,3,2,2,1,1] (.node [12,11,8,8,5,3,3,2,2,2,2,2,2] (.node [12,11,8,8,4,4,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,5,4,3,2,2,2,2,1,1,1] (.node [12,11,8,8,5,4,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,8,8,5,4,3,3,3,2,1,1,1] (.node [12,11,8,8,5,4,3,3,3,1,1,1,1,1] (.node [12,11,8,8,5,4,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,8,8,5,4,3,3,3,2,2,1] .empty .empty))) (.node [12,11,8,8,5,4,4,4,1,1,1,1,1,1] (.node [12,11,8,8,5,4,4,3,2,1,1,1,1,1] (.node [12,11,8,8,5,4,4,2,2,2,2,2] (.node [12,11,8,8,5,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,8,8,5,4,4,3,3,1,1,1,1] (.node [12,11,8,8,5,4,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,5,5,2,2,2,2,2,2,1] (.node [12,11,8,8,5,5,2,2,2,2,2,1,1,1] (.node [12,11,8,8,5,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,5,5,3,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_671 : RowTree := (.node [12,11,8,8,4,4,4,4,2,2,2,1] degreeTree62_669 degreeTree62_670) - -def degreeTree62_672 : RowTree := (.node [12,11,8,8,5,5,5,2,2,1,1,1,1] (.node [12,11,8,8,5,5,4,2,2,2,1,1,1] (.node [12,11,8,8,5,5,3,3,2,2,1,1,1] (.node [12,11,8,8,5,5,3,3,2,1,1,1,1,1] (.node [12,11,8,8,5,5,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,8,5,5,4,2,2,1,1,1,1,1] (.node [12,11,8,8,5,5,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,5,5,4,4,1,1,1,1,1] (.node [12,11,8,8,5,5,4,3,2,1,1,1,1] (.node [12,11,8,8,5,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,5,5,5,2,1,1,1,1,1,1] .empty .empty))) (.node [12,11,8,8,6,3,3,3,2,2,2,1,1] (.node [12,11,8,8,6,3,2,2,2,2,2,2,2] (.node [12,11,8,8,6,2,2,2,2,2,2,2,2,1] (.node [12,11,8,8,5,5,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,3,3,2,2,2,2,2,1] (.node [12,11,8,8,6,3,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,6,3,3,3,3,2,2,1] (.node [12,11,8,8,6,3,3,3,3,2,1,1,1] (.node [12,11,8,8,6,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,4,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_673 : RowTree := (.node [12,11,8,8,6,4,4,4,1,1,1,1,1] (.node [12,11,8,8,6,4,3,3,3,1,1,1,1] (.node [12,11,8,8,6,4,3,2,2,2,2,2] (.node [12,11,8,8,6,4,3,2,2,2,2,1,1] (.node [12,11,8,8,6,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,4,3,3,2,2,1,1,1] (.node [12,11,8,8,6,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,6,4,4,3,1,1,1,1,1,1] (.node [12,11,8,8,6,4,4,2,2,2,1,1,1] (.node [12,11,8,8,6,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,4,4,3,2,1,1,1,1] .empty .empty))) (.node [12,11,8,8,6,5,3,3,1,1,1,1,1,1] (.node [12,11,8,8,6,5,2,2,2,2,2,2] (.node [12,11,8,8,6,5,2,2,2,2,2,1,1] (.node [12,11,8,8,6,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,5,3,2,2,2,1,1,1] (.node [12,11,8,8,6,5,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,6,5,4,2,2,1,1,1,1] (.node [12,11,8,8,6,5,4,2,1,1,1,1,1,1] (.node [12,11,8,8,6,5,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,5,4,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_674 : RowTree := (.node [12,11,8,8,6,4,2,2,2,2,2,2,1] degreeTree62_672 degreeTree62_673) - -def degreeTree62_675 : RowTree := (.node [12,11,8,8,5,5,3,2,2,2,2,1,1] degreeTree62_671 degreeTree62_674) - -def degreeTree62_676 : RowTree := (.node [12,11,8,8,7,2,2,2,2,2,2,2,2] (.node [12,11,8,8,6,6,3,3,1,1,1,1,1] (.node [12,11,8,8,6,6,2,2,2,2,1,1,1] (.node [12,11,8,8,6,6,2,2,2,1,1,1,1,1] (.node [12,11,8,8,6,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,6,3,2,2,1,1,1,1] (.node [12,11,8,8,6,6,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,6,6,5,1,1,1,1,1,1] (.node [12,11,8,8,6,6,4,2,1,1,1,1,1] (.node [12,11,8,8,6,6,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [12,11,8,8,7,3,3,3,2,1,1,1,1,1] (.node [12,11,8,8,7,3,3,2,2,2,1,1,1,1] (.node [12,11,8,8,7,3,2,2,2,2,2,2,1] (.node [12,11,8,8,7,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,3,3,2,2,2,2,2] (.node [12,11,8,8,7,3,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,11,8,8,7,4,2,2,2,2,1,1,1,1] (.node [12,11,8,8,7,3,3,3,3,1,1,1,1] (.node [12,11,8,8,7,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,4,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_677 : RowTree := (.node [12,11,8,8,7,5,3,2,2,1,1,1,1] (.node [12,11,8,8,7,4,4,2,2,1,1,1,1] (.node [12,11,8,8,7,4,3,3,1,1,1,1,1,1] (.node [12,11,8,8,7,4,3,2,2,2,1,1,1] (.node [12,11,8,8,7,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,4,4,2,1,1,1,1,1,1] (.node [12,11,8,8,7,4,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,7,5,2,2,2,2,1,1,1] (.node [12,11,8,8,7,5,2,2,2,1,1,1,1,1] (.node [12,11,8,8,7,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,5,3,2,1,1,1,1,1,1] .empty .empty))) (.node [12,11,8,8,7,6,2,2,2,1,1,1,1] (.node [12,11,8,8,7,5,4,2,1,1,1,1,1] (.node [12,11,8,8,7,5,4,1,1,1,1,1,1,1] (.node [12,11,8,8,7,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,6,2,2,1,1,1,1,1,1] (.node [12,11,8,8,7,5,5,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,7,6,4,1,1,1,1,1,1] (.node [12,11,8,8,7,6,3,2,1,1,1,1,1] (.node [12,11,8,8,7,6,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,7,2,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_678 : RowTree := (.node [12,11,8,8,7,4,2,2,2,2,2,2] degreeTree62_676 degreeTree62_677) - -def degreeTree62_679 : RowTree := (.node [12,11,8,8,8,4,2,2,2,1,1,1,1,1] (.node [12,11,8,8,8,3,2,2,2,2,2,2] (.node [12,11,8,8,8,2,2,2,2,2,2,2,1] (.node [12,11,8,8,8,2,2,2,2,2,2,1,1,1] (.node [12,11,8,8,7,7,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,8,3,2,2,2,2,2,1,1] (.node [12,11,8,8,8,3,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,8,3,3,3,1,1,1,1,1,1] (.node [12,11,8,8,8,3,3,2,2,2,1,1,1] (.node [12,11,8,8,8,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,8,3,3,3,2,1,1,1,1] .empty .empty))) (.node [12,11,8,8,8,4,4,2,1,1,1,1,1] (.node [12,11,8,8,8,4,3,2,2,1,1,1,1] (.node [12,11,8,8,8,4,3,2,1,1,1,1,1,1] (.node [12,11,8,8,8,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,8,4,4,1,1,1,1,1,1,1] (.node [12,11,8,8,8,4,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,8,5,3,1,1,1,1,1,1,1] (.node [12,11,8,8,8,5,2,2,2,1,1,1,1] (.node [12,11,8,8,8,5,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,8,5,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_680 : RowTree := (.node [12,11,9,5,5,4,4,2,2,2,2,2,2] (.node [12,11,8,8,8,8,1,1,1,1,1,1,1] (.node [12,11,8,8,8,6,3,1,1,1,1,1,1] (.node [12,11,8,8,8,6,2,2,1,1,1,1,1] (.node [12,11,8,8,8,6,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,8,7,2,1,1,1,1,1,1] (.node [12,11,8,8,8,7,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,5,4,4,4,4,4,2,1,1,1] (.node [12,11,9,5,4,4,4,4,3,2,2,1,1] (.node [12,11,9,4,4,4,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,5,4,4,4,4,4,2,2,1] .empty .empty))) (.node [12,11,9,5,5,5,3,2,2,2,2,2,2] (.node [12,11,9,5,5,4,4,4,3,2,1,1,1] (.node [12,11,9,5,5,4,4,4,2,2,2,1,1] (.node [12,11,9,5,5,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,5,5,4,4,4,4,1,1,1,1] (.node [12,11,9,5,5,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,11,9,5,5,5,4,3,2,2,2,1,1] (.node [12,11,9,5,5,5,4,2,2,2,2,2,1] (.node [12,11,9,5,5,5,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,5,5,5,4,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_681 : RowTree := (.node [12,11,8,8,8,5,4,1,1,1,1,1,1] degreeTree62_679 degreeTree62_680) - -def degreeTree62_682 : RowTree := (.node [12,11,8,8,7,7,2,2,1,1,1,1,1] degreeTree62_678 degreeTree62_681) - -def degreeTree62_683 : RowTree := (.node [12,11,8,8,6,5,5,1,1,1,1,1,1,1] degreeTree62_675 degreeTree62_682) - -def degreeTree62_684 : RowTree := (.node [12,11,9,6,4,4,4,4,2,2,2,1,1] (.node [12,11,9,5,5,5,5,3,3,1,1,1,1] (.node [12,11,9,5,5,5,5,2,2,2,2,1,1] (.node [12,11,9,5,5,5,4,4,3,1,1,1,1] (.node [12,11,9,5,5,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,5,5,5,5,3,2,2,1,1,1] (.node [12,11,9,5,5,5,5,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,9,6,4,4,4,2,2,2,2,2,2] (.node [12,11,9,5,5,5,5,5,1,1,1,1,1] (.node [12,11,9,5,5,5,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,4,4,4,3,3,2,2,1,1] .empty .empty))) (.node [12,11,9,6,5,4,4,2,2,2,2,2,1] (.node [12,11,9,6,4,4,4,4,4,1,1,1,1] (.node [12,11,9,6,4,4,4,4,3,2,2,1] (.node [12,11,9,6,4,4,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,5,4,3,3,3,2,2,1,1] (.node [12,11,9,6,5,4,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,9,6,5,4,4,3,3,2,2,1] (.node [12,11,9,6,5,4,4,3,3,2,1,1,1] (.node [12,11,9,6,5,4,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,6,5,4,4,4,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_685 : RowTree := (.node [12,11,9,6,5,5,5,2,2,2,1,1,1] (.node [12,11,9,6,5,5,4,2,2,2,2,1,1] (.node [12,11,9,6,5,5,3,3,2,2,2,1,1] (.node [12,11,9,6,5,5,3,2,2,2,2,2,1] (.node [12,11,9,6,5,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,9,6,5,5,3,3,3,2,2,1] (.node [12,11,9,6,5,5,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,6,5,5,4,3,3,1,1,1,1] (.node [12,11,9,6,5,5,4,3,2,2,1,1,1] (.node [12,11,9,6,5,5,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,9,6,5,5,4,4,2,1,1,1,1] .empty .empty))) (.node [12,11,9,6,6,4,3,2,2,2,2,1,1,1] (.node [12,11,9,6,6,3,3,2,2,2,2,2,2] (.node [12,11,9,6,5,5,5,4,1,1,1,1,1] (.node [12,11,9,6,5,5,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,6,4,2,2,2,2,2,2,2] (.node [12,11,9,6,6,3,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,11,9,6,6,4,3,3,3,1,1,1,1,1] (.node [12,11,9,6,6,4,3,3,2,2,2,1,1] (.node [12,11,9,6,6,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,9,6,6,4,3,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_686 : RowTree := (.node [12,11,9,6,5,4,4,4,3,1,1,1,1] degreeTree62_684 degreeTree62_685) - -def degreeTree62_687 : RowTree := (.node [12,11,9,6,6,5,3,2,2,2,2,1,1] (.node [12,11,9,6,6,4,4,4,1,1,1,1,1,1] (.node [12,11,9,6,6,4,4,3,2,1,1,1,1,1] (.node [12,11,9,6,6,4,4,2,2,2,2,2] (.node [12,11,9,6,6,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,6,6,4,4,3,3,1,1,1,1] (.node [12,11,9,6,6,4,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,6,6,5,2,2,2,2,2,2,1] (.node [12,11,9,6,6,5,2,2,2,2,2,1,1,1] (.node [12,11,9,6,6,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,6,5,3,2,2,2,1,1,1,1] .empty .empty))) (.node [12,11,9,6,6,5,4,2,2,2,1,1,1] (.node [12,11,9,6,6,5,3,3,2,2,1,1,1] (.node [12,11,9,6,6,5,3,3,2,1,1,1,1,1] (.node [12,11,9,6,6,5,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,9,6,6,5,4,2,2,1,1,1,1,1] (.node [12,11,9,6,6,5,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,6,6,5,4,4,1,1,1,1,1] (.node [12,11,9,6,6,5,4,3,2,1,1,1,1] (.node [12,11,9,6,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,6,5,5,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_688 : RowTree := (.node [12,11,9,6,6,6,4,3,1,1,1,1,1] (.node [12,11,9,6,6,6,3,2,2,2,1,1,1] (.node [12,11,9,6,6,6,2,2,2,2,2,1,1] (.node [12,11,9,6,6,6,2,2,2,2,1,1,1,1] (.node [12,11,9,6,6,5,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,6,6,3,2,2,1,1,1,1,1] (.node [12,11,9,6,6,6,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,9,6,6,6,4,2,1,1,1,1,1,1] (.node [12,11,9,6,6,6,3,3,2,1,1,1,1] (.node [12,11,9,6,6,6,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,6,6,4,2,2,1,1,1,1] .empty .empty))) (.node [12,11,9,7,4,4,4,2,2,2,2,1,1,1] (.node [12,11,9,6,6,6,6,1,1,1,1,1,1] (.node [12,11,9,6,6,6,5,2,1,1,1,1,1] (.node [12,11,9,6,6,6,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,4,4,3,3,3,2,2,1,1] (.node [12,11,9,7,4,4,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,9,7,4,4,4,3,3,1,1,1,1,1] (.node [12,11,9,7,4,4,4,3,2,2,2,1,1] (.node [12,11,9,7,4,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,9,7,4,4,4,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_689 : RowTree := (.node [12,11,9,6,6,5,5,2,2,1,1,1,1] degreeTree62_687 degreeTree62_688) - -def degreeTree62_690 : RowTree := (.node [12,11,9,6,6,4,4,2,2,2,1,1,1,1] degreeTree62_686 degreeTree62_689) - -def degreeTree62_691 : RowTree := (.node [12,11,9,7,5,4,3,3,3,2,1,1,1] (.node [12,11,9,7,5,4,2,2,2,2,2,2,2] (.node [12,11,9,7,4,4,4,4,3,1,1,1,1] (.node [12,11,9,7,4,4,4,4,2,2,1,1,1] (.node [12,11,9,7,4,4,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,5,3,3,3,3,2,2,1,1] (.node [12,11,9,7,5,3,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,9,7,5,4,3,3,2,2,2,1,1] (.node [12,11,9,7,5,4,3,2,2,2,2,2,1] (.node [12,11,9,7,5,4,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,5,4,3,3,3,1,1,1,1,1] .empty .empty))) (.node [12,11,9,7,5,4,4,3,3,1,1,1,1] (.node [12,11,9,7,5,4,4,2,2,2,2,2] (.node [12,11,9,7,5,4,4,2,2,2,2,1,1] (.node [12,11,9,7,5,4,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,5,4,4,3,2,2,1,1,1] (.node [12,11,9,7,5,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,5,5,2,2,2,2,2,1,1,1] (.node [12,11,9,7,5,4,4,4,2,1,1,1,1] (.node [12,11,9,7,5,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,5,5,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_692 : RowTree := (.node [12,11,9,7,5,5,5,2,1,1,1,1,1,1] (.node [12,11,9,7,5,5,4,2,2,1,1,1,1,1] (.node [12,11,9,7,5,5,3,3,2,1,1,1,1,1] (.node [12,11,9,7,5,5,3,2,2,2,2,2] (.node [12,11,9,7,5,5,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,7,5,5,3,3,3,1,1,1,1] (.node [12,11,9,7,5,5,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,5,5,4,3,2,1,1,1,1] (.node [12,11,9,7,5,5,4,3,1,1,1,1,1,1] (.node [12,11,9,7,5,5,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,5,5,4,4,1,1,1,1,1] .empty .empty))) (.node [12,11,9,7,6,3,3,2,2,2,2,2,1] (.node [12,11,9,7,6,2,2,2,2,2,2,2,2,1] (.node [12,11,9,7,5,5,5,3,1,1,1,1,1] (.node [12,11,9,7,5,5,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,3,3,2,2,2,2,1,1,1] (.node [12,11,9,7,6,3,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,9,7,6,3,3,3,3,2,1,1,1] (.node [12,11,9,7,6,3,3,3,3,1,1,1,1,1] (.node [12,11,9,7,6,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,4,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_693 : RowTree := (.node [12,11,9,7,5,5,3,2,2,2,1,1,1,1] degreeTree62_691 degreeTree62_692) - -def degreeTree62_694 : RowTree := (.node [12,11,9,7,6,4,4,4,1,1,1,1,1] (.node [12,11,9,7,6,4,3,3,3,1,1,1,1] (.node [12,11,9,7,6,4,3,2,2,2,2,2] (.node [12,11,9,7,6,4,3,2,2,2,2,1,1] (.node [12,11,9,7,6,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,4,3,3,2,2,1,1,1] (.node [12,11,9,7,6,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,6,4,4,3,1,1,1,1,1,1] (.node [12,11,9,7,6,4,4,2,2,2,1,1,1] (.node [12,11,9,7,6,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,4,4,3,2,1,1,1,1] .empty .empty))) (.node [12,11,9,7,6,5,3,3,1,1,1,1,1,1] (.node [12,11,9,7,6,5,2,2,2,2,2,2] (.node [12,11,9,7,6,5,2,2,2,2,2,1,1] (.node [12,11,9,7,6,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,5,3,2,2,2,1,1,1] (.node [12,11,9,7,6,5,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,6,5,4,2,2,1,1,1,1] (.node [12,11,9,7,6,5,4,2,1,1,1,1,1,1] (.node [12,11,9,7,6,5,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,5,4,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_695 : RowTree := (.node [12,11,9,7,7,2,2,2,2,2,2,2,2] (.node [12,11,9,7,6,6,3,3,1,1,1,1,1] (.node [12,11,9,7,6,6,2,2,2,2,1,1,1] (.node [12,11,9,7,6,6,2,2,2,1,1,1,1,1] (.node [12,11,9,7,6,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,6,3,2,2,1,1,1,1] (.node [12,11,9,7,6,6,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,6,6,5,1,1,1,1,1,1] (.node [12,11,9,7,6,6,4,2,1,1,1,1,1] (.node [12,11,9,7,6,6,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,7,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [12,11,9,7,7,3,3,2,2,2,2,2] (.node [12,11,9,7,7,3,3,2,2,2,1,1,1,1] (.node [12,11,9,7,7,3,2,2,2,2,2,2,1] (.node [12,11,9,7,7,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,7,3,3,2,2,2,2,1,1] .empty .empty)) (.node [12,11,9,7,7,3,3,3,3,1,1,1,1] (.node [12,11,9,7,7,3,3,3,2,2,1,1,1] (.node [12,11,9,7,7,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,7,4,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_696 : RowTree := (.node [12,11,9,7,6,5,5,1,1,1,1,1,1,1] degreeTree62_694 degreeTree62_695) - -def degreeTree62_697 : RowTree := (.node [12,11,9,7,6,4,2,2,2,2,2,2,1] degreeTree62_693 degreeTree62_696) - -def degreeTree62_698 : RowTree := (.node [12,11,9,7,4,4,4,3,3,2,2,1] degreeTree62_690 degreeTree62_697) - -def degreeTree62_699 : RowTree := (.node [12,11,9,5,5,5,4,3,3,2,2,1] degreeTree62_683 degreeTree62_698) - -def degreeTree62_700 : RowTree := (.node [12,11,8,7,7,6,2,2,2,2,1,1,1] degreeTree62_668 degreeTree62_699) - -def degreeTree62_701 : RowTree := (.node [12,11,9,7,7,5,3,2,1,1,1,1,1,1] (.node [12,11,9,7,7,4,4,2,1,1,1,1,1,1] (.node [12,11,9,7,7,4,3,2,2,2,1,1,1] (.node [12,11,9,7,7,4,3,2,2,1,1,1,1,1] (.node [12,11,9,7,7,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,9,7,7,4,3,3,2,1,1,1,1] (.node [12,11,9,7,7,4,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,7,5,2,2,2,1,1,1,1,1] (.node [12,11,9,7,7,4,4,3,1,1,1,1,1] (.node [12,11,9,7,7,4,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,7,5,2,2,2,2,1,1,1] .empty .empty))) (.node [12,11,9,7,7,6,2,2,1,1,1,1,1,1] (.node [12,11,9,7,7,5,4,1,1,1,1,1,1,1] (.node [12,11,9,7,7,5,3,3,1,1,1,1,1] (.node [12,11,9,7,7,5,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,7,5,5,1,1,1,1,1,1] (.node [12,11,9,7,7,5,4,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,7,6,3,2,1,1,1,1,1] (.node [12,11,9,7,7,6,3,1,1,1,1,1,1,1] (.node [12,11,9,7,7,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,7,6,4,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_702 : RowTree := (.node [12,11,9,8,4,4,4,2,2,2,1,1,1,1] (.node [12,11,9,8,4,4,3,2,2,2,2,1,1,1] (.node [12,11,9,8,4,3,3,2,2,2,2,2,2] (.node [12,11,9,7,7,7,3,1,1,1,1,1,1] (.node [12,11,9,7,7,7,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,4,4,2,2,2,2,2,2,2] (.node [12,11,9,8,4,3,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,11,9,8,4,4,3,3,3,1,1,1,1,1] (.node [12,11,9,8,4,4,3,3,2,2,2,1,1] (.node [12,11,9,8,4,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,9,8,4,4,3,3,3,2,1,1,1] .empty .empty))) (.node [12,11,9,8,4,4,4,4,1,1,1,1,1,1] (.node [12,11,9,8,4,4,4,3,2,1,1,1,1,1] (.node [12,11,9,8,4,4,4,2,2,2,2,2] (.node [12,11,9,8,4,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,4,4,4,3,3,1,1,1,1] (.node [12,11,9,8,4,4,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,5,3,2,2,2,2,2,2,2] (.node [12,11,9,8,5,2,2,2,2,2,2,2,2,1] (.node [12,11,9,8,4,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,5,3,3,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_703 : RowTree := (.node [12,11,9,7,7,7,2,1,1,1,1,1,1,1] degreeTree62_701 degreeTree62_702) - -def degreeTree62_704 : RowTree := (.node [12,11,9,8,5,4,3,3,3,1,1,1,1] (.node [12,11,9,8,5,4,3,2,2,2,1,1,1,1] (.node [12,11,9,8,5,3,3,3,3,2,1,1,1] (.node [12,11,9,8,5,3,3,3,3,1,1,1,1,1] (.node [12,11,9,8,5,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,5,4,2,2,2,2,2,2,1] (.node [12,11,9,8,5,4,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,5,4,3,3,2,1,1,1,1,1] (.node [12,11,9,8,5,4,3,2,2,2,2,2] (.node [12,11,9,8,5,4,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,5,4,3,3,2,2,1,1,1] .empty .empty))) (.node [12,11,9,8,5,5,2,2,2,2,1,1,1,1] (.node [12,11,9,8,5,4,4,3,1,1,1,1,1,1] (.node [12,11,9,8,5,4,4,2,2,2,1,1,1] (.node [12,11,9,8,5,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,5,4,4,4,1,1,1,1,1] (.node [12,11,9,8,5,4,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,5,5,3,2,2,1,1,1,1,1] (.node [12,11,9,8,5,5,2,2,2,2,2,2] (.node [12,11,9,8,5,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,5,5,3,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_705 : RowTree := (.node [12,11,9,8,6,3,3,2,2,2,1,1,1,1] (.node [12,11,9,8,5,5,5,2,1,1,1,1,1] (.node [12,11,9,8,5,5,4,2,2,1,1,1,1] (.node [12,11,9,8,5,5,4,2,1,1,1,1,1,1] (.node [12,11,9,8,5,5,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,5,5,5,1,1,1,1,1,1,1] (.node [12,11,9,8,5,5,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,6,3,2,2,2,2,2,1,1,1] (.node [12,11,9,8,6,2,2,2,2,2,2,2,2] (.node [12,11,9,8,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,6,3,2,2,2,2,2,2,1] .empty .empty))) (.node [12,11,9,8,6,4,2,2,2,2,1,1,1,1] (.node [12,11,9,8,6,3,3,3,2,1,1,1,1,1] (.node [12,11,9,8,6,3,3,2,2,2,2,2] (.node [12,11,9,8,6,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,6,3,3,3,3,1,1,1,1] (.node [12,11,9,8,6,3,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,6,4,3,2,2,1,1,1,1,1] (.node [12,11,9,8,6,4,2,2,2,2,2,2] (.node [12,11,9,8,6,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,6,4,3,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_706 : RowTree := (.node [12,11,9,8,5,5,3,3,1,1,1,1,1,1] degreeTree62_704 degreeTree62_705) - -def degreeTree62_707 : RowTree := (.node [12,11,9,8,5,3,3,2,2,2,2,2,1] degreeTree62_703 degreeTree62_706) - -def degreeTree62_708 : RowTree := (.node [12,11,9,8,6,5,4,2,1,1,1,1,1] (.node [12,11,9,8,6,5,2,2,2,2,1,1,1] (.node [12,11,9,8,6,4,4,2,2,1,1,1,1] (.node [12,11,9,8,6,4,4,2,1,1,1,1,1,1] (.node [12,11,9,8,6,4,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,6,5,2,2,2,1,1,1,1,1] (.node [12,11,9,8,6,4,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,6,5,3,3,1,1,1,1,1] (.node [12,11,9,8,6,5,3,2,2,1,1,1,1] (.node [12,11,9,8,6,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,6,5,4,1,1,1,1,1,1,1] .empty .empty))) (.node [12,11,9,8,6,6,4,1,1,1,1,1,1] (.node [12,11,9,8,6,6,2,2,2,1,1,1,1] (.node [12,11,9,8,6,6,2,2,1,1,1,1,1,1] (.node [12,11,9,8,6,5,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,6,6,3,2,1,1,1,1,1] (.node [12,11,9,8,6,6,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,7,3,2,2,2,2,1,1,1,1] (.node [12,11,9,8,7,2,2,2,2,2,2,2,1] (.node [12,11,9,8,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,7,3,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_709 : RowTree := (.node [12,11,9,8,7,4,4,2,1,1,1,1,1] (.node [12,11,9,8,7,4,2,2,2,2,1,1,1] (.node [12,11,9,8,7,3,3,3,1,1,1,1,1,1] (.node [12,11,9,8,7,3,3,2,2,2,1,1,1] (.node [12,11,9,8,7,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,7,4,2,2,2,1,1,1,1,1] (.node [12,11,9,8,7,3,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,7,4,3,3,1,1,1,1,1] (.node [12,11,9,8,7,4,3,2,2,1,1,1,1] (.node [12,11,9,8,7,4,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,7,4,4,1,1,1,1,1,1,1] .empty .empty))) (.node [12,11,9,8,7,6,2,1,1,1,1,1,1,1] (.node [12,11,9,8,7,5,3,1,1,1,1,1,1,1] (.node [12,11,9,8,7,5,2,2,2,1,1,1,1] (.node [12,11,9,8,7,5,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,7,5,4,1,1,1,1,1,1] (.node [12,11,9,8,7,5,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,7,7,1,1,1,1,1,1,1,1] (.node [12,11,9,8,7,6,3,1,1,1,1,1,1] (.node [12,11,9,8,7,6,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,7,7,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_710 : RowTree := (.node [12,11,9,8,7,3,2,2,2,2,2,2] degreeTree62_708 degreeTree62_709) - -def degreeTree62_711 : RowTree := (.node [12,11,9,8,8,4,3,2,1,1,1,1,1] (.node [12,11,9,8,8,3,3,2,2,1,1,1,1] (.node [12,11,9,8,8,3,2,2,2,1,1,1,1,1] (.node [12,11,9,8,8,2,2,2,2,2,2,2] (.node [12,11,9,8,8,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,8,3,3,2,1,1,1,1,1,1] (.node [12,11,9,8,8,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,8,4,2,2,2,1,1,1,1] (.node [12,11,9,8,8,4,2,2,1,1,1,1,1,1] (.node [12,11,9,8,8,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,8,4,3,1,1,1,1,1,1,1] .empty .empty))) (.node [12,11,9,8,8,6,2,1,1,1,1,1,1] (.node [12,11,9,8,8,5,2,2,1,1,1,1,1] (.node [12,11,9,8,8,5,2,1,1,1,1,1,1,1] (.node [12,11,9,8,8,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,8,6,1,1,1,1,1,1,1,1] (.node [12,11,9,8,8,5,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,3,3,3,3,3,2,2,1,1] (.node [12,11,9,9,3,3,3,2,2,2,2,2,2] (.node [12,11,9,8,8,7,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,4,2,2,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_712 : RowTree := (.node [12,11,9,9,4,4,3,3,2,1,1,1,1,1] (.node [12,11,9,9,4,4,2,2,2,2,2,1,1,1] (.node [12,11,9,9,4,3,3,3,2,2,2,1,1] (.node [12,11,9,9,4,3,3,2,2,2,2,2,1] (.node [12,11,9,9,4,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,4,3,3,3,3,2,1,1,1] (.node [12,11,9,9,4,3,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,4,4,3,2,2,2,2,1,1] (.node [12,11,9,9,4,4,3,2,2,2,1,1,1,1] (.node [12,11,9,9,4,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,9,9,4,4,3,2,2,2,2,2] .empty .empty))) (.node [12,11,9,9,4,4,4,3,2,1,1,1,1] (.node [12,11,9,9,4,4,4,2,2,1,1,1,1,1] (.node [12,11,9,9,4,4,3,3,3,1,1,1,1] (.node [12,11,9,9,4,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,4,4,4,3,1,1,1,1,1,1] (.node [12,11,9,9,4,4,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,5,2,2,2,2,2,2,2,2] (.node [12,11,9,9,5,2,2,2,2,2,2,2,1,1] (.node [12,11,9,9,4,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,5,3,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_713 : RowTree := (.node [12,11,9,9,4,3,2,2,2,2,2,2,2] degreeTree62_711 degreeTree62_712) - -def degreeTree62_714 : RowTree := (.node [12,11,9,8,8,2,2,2,2,2,1,1,1,1] degreeTree62_710 degreeTree62_713) - -def degreeTree62_715 : RowTree := (.node [12,11,9,8,6,4,3,3,1,1,1,1,1,1] degreeTree62_707 degreeTree62_714) - -def degreeTree62_716 : RowTree := (.node [12,11,9,9,5,4,3,2,2,2,1,1,1] (.node [12,11,9,9,5,3,3,3,3,1,1,1,1] (.node [12,11,9,9,5,3,3,2,2,2,2,2] (.node [12,11,9,9,5,3,3,2,2,2,2,1,1] (.node [12,11,9,9,5,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,5,3,3,3,2,2,1,1,1] (.node [12,11,9,9,5,3,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,5,4,2,2,2,2,2,2] (.node [12,11,9,9,5,4,2,2,2,2,2,1,1] (.node [12,11,9,9,5,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,5,4,3,2,2,1,1,1,1,1] .empty .empty))) (.node [12,11,9,9,5,5,2,2,2,1,1,1,1,1] (.node [12,11,9,9,5,4,4,2,1,1,1,1,1,1] (.node [12,11,9,9,5,4,3,3,2,1,1,1,1] (.node [12,11,9,9,5,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,5,4,4,3,1,1,1,1,1] (.node [12,11,9,9,5,4,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,5,5,3,2,2,1,1,1,1] (.node [12,11,9,9,5,5,3,2,1,1,1,1,1,1] (.node [12,11,9,9,5,5,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,5,5,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_717 : RowTree := (.node [12,11,9,9,6,3,3,3,2,1,1,1,1] (.node [12,11,9,9,6,3,2,2,2,2,2,1,1] (.node [12,11,9,9,6,2,2,2,2,2,2,1,1,1] (.node [12,11,9,9,5,5,5,1,1,1,1,1,1] (.node [12,11,9,9,5,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,6,3,2,2,2,2,1,1,1,1] (.node [12,11,9,9,6,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,9,9,6,3,3,2,2,2,1,1,1] (.node [12,11,9,9,6,3,3,2,2,1,1,1,1,1] (.node [12,11,9,9,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,9,9,6,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [12,11,9,9,6,4,4,1,1,1,1,1,1,1] (.node [12,11,9,9,6,4,3,2,1,1,1,1,1,1] (.node [12,11,9,9,6,4,2,2,2,2,1,1,1] (.node [12,11,9,9,6,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,6,4,3,3,1,1,1,1,1] (.node [12,11,9,9,6,4,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,6,5,2,2,2,1,1,1,1] (.node [12,11,9,9,6,5,2,2,1,1,1,1,1,1] (.node [12,11,9,9,6,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,6,5,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_718 : RowTree := (.node [12,11,9,9,5,5,4,1,1,1,1,1,1,1] degreeTree62_716 degreeTree62_717) - -def degreeTree62_719 : RowTree := (.node [12,11,9,9,7,3,3,2,2,1,1,1,1] (.node [12,11,9,9,7,2,2,2,2,2,2,1,1] (.node [12,11,9,9,6,6,2,2,1,1,1,1,1] (.node [12,11,9,9,6,6,2,1,1,1,1,1,1,1] (.node [12,11,9,9,6,5,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,7,2,2,2,2,2,1,1,1,1] (.node [12,11,9,9,6,6,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,7,3,2,2,2,2,1,1,1] (.node [12,11,9,9,7,3,2,2,2,1,1,1,1,1] (.node [12,11,9,9,7,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,9,9,7,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [12,11,9,9,7,4,4,1,1,1,1,1,1] (.node [12,11,9,9,7,4,2,2,2,1,1,1,1] (.node [12,11,9,9,7,4,2,2,1,1,1,1,1,1] (.node [12,11,9,9,7,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,7,4,3,2,1,1,1,1,1] (.node [12,11,9,9,7,4,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,7,5,3,1,1,1,1,1,1] (.node [12,11,9,9,7,5,2,2,1,1,1,1,1] (.node [12,11,9,9,7,5,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,7,6,1,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_720 : RowTree := (.node [12,11,9,9,8,5,1,1,1,1,1,1,1,1] (.node [12,11,9,9,8,3,3,1,1,1,1,1,1,1] (.node [12,11,9,9,8,2,2,2,2,2,1,1,1] (.node [12,11,9,9,8,2,2,2,2,1,1,1,1,1] (.node [12,11,9,9,7,7,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,8,3,2,2,2,1,1,1,1] (.node [12,11,9,9,8,3,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,8,4,2,2,1,1,1,1,1] (.node [12,11,9,9,8,4,2,1,1,1,1,1,1,1] (.node [12,11,9,9,8,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,8,4,3,1,1,1,1,1,1] .empty .empty))) (.node [12,11,9,9,9,3,2,2,1,1,1,1,1] (.node [12,11,9,9,9,2,2,2,1,1,1,1,1,1] (.node [12,11,9,9,8,6,1,1,1,1,1,1,1] (.node [12,11,9,9,8,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,9,3,2,1,1,1,1,1,1,1] (.node [12,11,9,9,9,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,9,4,2,1,1,1,1,1,1] (.node [12,11,9,9,9,4,1,1,1,1,1,1,1,1] (.node [12,11,9,9,9,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,9,5,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_721 : RowTree := (.node [12,11,9,9,7,6,2,1,1,1,1,1,1] degreeTree62_719 degreeTree62_720) - -def degreeTree62_722 : RowTree := (.node [12,11,9,9,6,5,3,2,1,1,1,1,1] degreeTree62_718 degreeTree62_721) - -def degreeTree62_723 : RowTree := (.node [12,12,6,5,5,5,5,4,2,2,2,1,1] (.node [12,12,6,5,5,4,4,4,4,2,2,1,1] (.node [12,12,5,5,5,5,5,5,2,2,2,1,1] (.node [12,12,5,5,5,5,5,4,4,2,1,1,1] (.node [12,12,5,5,5,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,12,5,5,5,5,5,5,4,1,1,1,1] (.node [12,12,5,5,5,5,5,5,3,2,1,1,1] .empty .empty) .empty)) (.node [12,12,6,5,5,5,5,2,2,2,2,2,2] (.node [12,12,6,5,5,5,4,4,4,2,1,1,1] (.node [12,12,6,5,5,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,12,6,5,5,5,5,3,3,2,2,1,1] .empty .empty))) (.node [12,12,6,6,5,4,4,4,3,2,2,1,1] (.node [12,12,6,5,5,5,5,5,2,2,1,1,1] (.node [12,12,6,5,5,5,5,4,4,1,1,1,1] (.node [12,12,6,5,5,5,5,4,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,4,4,4,4,4,2,2,1,1] (.node [12,12,6,5,5,5,5,5,3,1,1,1,1] .empty .empty) .empty)) (.node [12,12,6,6,5,5,4,3,3,2,2,1,1] (.node [12,12,6,6,5,5,4,2,2,2,2,2,2] (.node [12,12,6,6,5,4,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,5,5,4,4,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_724 : RowTree := (.node [12,12,6,6,6,4,4,4,3,2,1,1,1] (.node [12,12,6,6,5,5,5,4,3,1,1,1,1] (.node [12,12,6,6,5,5,5,3,2,2,2,1,1] (.node [12,12,6,6,5,5,5,2,2,2,2,2,1] (.node [12,12,6,6,5,5,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,5,5,5,4,2,2,1,1,1] (.node [12,12,6,6,5,5,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,12,6,6,6,4,4,3,3,2,2,1,1] (.node [12,12,6,6,6,4,4,2,2,2,2,2,2] (.node [12,12,6,6,5,5,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,6,4,4,4,2,2,2,1,1] .empty .empty))) (.node [12,12,6,6,6,5,4,3,3,2,1,1,1] (.node [12,12,6,6,6,5,3,3,3,2,2,1,1] (.node [12,12,6,6,6,5,3,2,2,2,2,2,2] (.node [12,12,6,6,6,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,6,5,4,3,2,2,2,1,1] (.node [12,12,6,6,6,5,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,12,6,6,6,5,5,2,2,2,2,1,1] (.node [12,12,6,6,6,5,4,4,3,1,1,1,1] (.node [12,12,6,6,6,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,6,5,5,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_725 : RowTree := (.node [12,12,6,6,5,5,4,4,3,2,1,1,1] degreeTree62_723 degreeTree62_724) - -def degreeTree62_726 : RowTree := (.node [12,12,6,6,6,6,4,3,3,1,1,1,1] (.node [12,12,6,6,6,6,3,3,2,2,2,1,1] (.node [12,12,6,6,6,5,5,5,1,1,1,1,1] (.node [12,12,6,6,6,5,5,4,2,1,1,1,1] (.node [12,12,6,6,6,5,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,6,6,3,2,2,2,2,2,1] (.node [12,12,6,6,6,6,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,12,6,6,6,6,4,2,2,2,2,2] (.node [12,12,6,6,6,6,4,2,2,2,2,1,1] (.node [12,12,6,6,6,6,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,6,6,4,3,2,2,1,1,1] .empty .empty))) (.node [12,12,6,6,6,6,6,2,2,1,1,1,1] (.node [12,12,6,6,6,6,5,3,2,1,1,1,1] (.node [12,12,6,6,6,6,5,2,2,2,1,1,1] (.node [12,12,6,6,6,6,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,6,6,6,2,1,1,1,1,1,1] (.node [12,12,6,6,6,6,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,5,5,4,4,4,3,2,2,1,1] (.node [12,12,7,5,4,4,4,4,4,2,2,1,1] (.node [12,12,6,6,6,6,6,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,5,5,4,4,4,4,2,1,1,1] .empty .empty)))) - -def degreeTree62_727 : RowTree := (.node [12,12,7,6,4,4,4,4,3,2,2,1,1] (.node [12,12,7,5,5,5,5,3,2,2,2,1,1] (.node [12,12,7,5,5,5,4,4,3,2,1,1,1] (.node [12,12,7,5,5,5,4,4,2,2,2,1,1] (.node [12,12,7,5,5,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,12,7,5,5,5,5,2,2,2,2,2,1] (.node [12,12,7,5,5,5,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,5,5,5,5,4,3,1,1,1,1] (.node [12,12,7,5,5,5,5,4,2,2,1,1,1] (.node [12,12,7,5,5,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,5,5,5,5,5,2,1,1,1,1] .empty .empty))) (.node [12,12,7,6,5,4,4,4,3,2,1,1,1] (.node [12,12,7,6,5,4,4,3,3,2,2,1,1] (.node [12,12,7,6,5,4,4,2,2,2,2,2,2] (.node [12,12,7,6,4,4,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,5,4,4,4,2,2,2,1,1] .empty .empty)) (.node [12,12,7,6,5,5,3,3,3,2,2,1,1] (.node [12,12,7,6,5,5,3,2,2,2,2,2,2] (.node [12,12,7,6,5,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,5,5,4,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_728 : RowTree := (.node [12,12,7,5,5,5,4,2,2,2,2,2,2] degreeTree62_726 degreeTree62_727) - -def degreeTree62_729 : RowTree := (.node [12,12,6,6,6,5,5,3,2,2,1,1,1] degreeTree62_725 degreeTree62_728) - -def degreeTree62_730 : RowTree := (.node [12,12,5,5,5,5,4,4,4,2,2,1,1] degreeTree62_722 degreeTree62_729) - -def degreeTree62_731 : RowTree := (.node [12,11,9,9,5,3,2,2,2,2,2,2,1] degreeTree62_715 degreeTree62_730) - -def degreeTree62_732 : RowTree := (.node [12,12,7,6,6,4,3,3,3,2,2,1,1] (.node [12,12,7,6,5,5,5,3,2,2,1,1,1] (.node [12,12,7,6,5,5,4,4,3,1,1,1,1] (.node [12,12,7,6,5,5,4,4,2,2,1,1,1] (.node [12,12,7,6,5,5,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,5,5,5,2,2,2,2,2] (.node [12,12,7,6,5,5,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,12,7,6,5,5,5,5,1,1,1,1,1] (.node [12,12,7,6,5,5,5,4,2,1,1,1,1] (.node [12,12,7,6,5,5,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,6,4,3,2,2,2,2,2,2] .empty .empty))) (.node [12,12,7,6,6,5,2,2,2,2,2,2,2] (.node [12,12,7,6,6,4,4,3,3,2,1,1,1] (.node [12,12,7,6,6,4,4,3,2,2,2,1,1] (.node [12,12,7,6,6,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,12,7,6,6,4,4,4,3,1,1,1,1] (.node [12,12,7,6,6,4,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [12,12,7,6,6,5,3,3,3,2,1,1,1] (.node [12,12,7,6,6,5,3,3,2,2,2,1,1] (.node [12,12,7,6,6,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,12,7,6,6,5,4,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_733 : RowTree := (.node [12,12,7,6,6,6,3,2,2,2,2,2] (.node [12,12,7,6,6,5,5,4,1,1,1,1,1] (.node [12,12,7,6,6,5,4,4,2,1,1,1,1] (.node [12,12,7,6,6,5,4,3,3,1,1,1,1] (.node [12,12,7,6,6,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,6,5,5,3,2,1,1,1,1] (.node [12,12,7,6,6,5,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,12,7,6,6,6,3,2,2,2,1,1,1,1] (.node [12,12,7,6,6,6,2,2,2,2,2,2,1] (.node [12,12,7,6,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,6,6,3,2,2,2,2,1,1] .empty .empty))) (.node [12,12,7,6,6,6,4,3,1,1,1,1,1,1] (.node [12,12,7,6,6,6,3,3,3,1,1,1,1] (.node [12,12,7,6,6,6,3,3,2,2,1,1,1] (.node [12,12,7,6,6,6,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,6,6,4,2,2,2,1,1,1] (.node [12,12,7,6,6,6,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,6,6,6,5,2,1,1,1,1,1,1] (.node [12,12,7,6,6,6,4,4,1,1,1,1,1] (.node [12,12,7,6,6,6,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,6,6,5,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_734 : RowTree := (.node [12,12,7,6,6,5,4,2,2,2,2,2] degreeTree62_732 degreeTree62_733) - -def degreeTree62_735 : RowTree := (.node [12,12,7,7,5,4,4,3,2,2,2,1,1] (.node [12,12,7,7,4,4,4,4,3,2,1,1,1] (.node [12,12,7,7,4,4,4,2,2,2,2,2,2] (.node [12,12,7,6,6,6,6,2,1,1,1,1,1] (.node [12,12,7,6,6,6,6,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,4,4,4,4,2,2,2,1,1] (.node [12,12,7,7,4,4,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,12,7,7,5,4,3,3,3,2,2,1,1] (.node [12,12,7,7,5,4,3,2,2,2,2,2,2] (.node [12,12,7,7,4,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,5,4,4,2,2,2,2,2,1] .empty .empty))) (.node [12,12,7,7,5,5,3,3,2,2,2,1,1] (.node [12,12,7,7,5,4,4,4,3,1,1,1,1] (.node [12,12,7,7,5,4,4,4,2,2,1,1,1] (.node [12,12,7,7,5,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,5,5,3,2,2,2,2,2,1] (.node [12,12,7,7,5,5,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,12,7,7,5,5,4,2,2,2,2,2] (.node [12,12,7,7,5,5,4,2,2,2,2,1,1] (.node [12,12,7,7,5,5,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,5,5,4,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_736 : RowTree := (.node [12,12,7,7,6,4,3,3,3,1,1,1,1,1] (.node [12,12,7,7,6,3,3,3,3,2,2,1,1] (.node [12,12,7,7,5,5,5,3,2,1,1,1,1] (.node [12,12,7,7,5,5,5,2,2,2,1,1,1] (.node [12,12,7,7,5,5,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,3,3,2,2,2,2,2,2] (.node [12,12,7,7,5,5,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,6,4,3,2,2,2,2,2,1] (.node [12,12,7,7,6,4,3,2,2,2,2,1,1,1] (.node [12,12,7,7,6,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,12,7,7,6,4,3,3,2,2,2,1,1] .empty .empty))) (.node [12,12,7,7,6,4,4,3,3,1,1,1,1] (.node [12,12,7,7,6,4,4,2,2,2,2,1,1] (.node [12,12,7,7,6,4,4,2,2,2,1,1,1,1] (.node [12,12,7,7,6,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,4,4,3,2,2,1,1,1] (.node [12,12,7,7,6,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,6,5,2,2,2,2,2,1,1,1] (.node [12,12,7,7,6,4,4,4,2,1,1,1,1] (.node [12,12,7,7,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,5,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_737 : RowTree := (.node [12,12,7,7,5,5,4,3,3,1,1,1,1] degreeTree62_735 degreeTree62_736) - -def degreeTree62_738 : RowTree := (.node [12,12,7,6,6,6,5,3,1,1,1,1,1] degreeTree62_734 degreeTree62_737) - -def degreeTree62_739 : RowTree := (.node [12,12,7,7,6,5,5,2,2,1,1,1,1] (.node [12,12,7,7,6,5,4,2,2,2,1,1,1] (.node [12,12,7,7,6,5,3,3,2,2,1,1,1] (.node [12,12,7,7,6,5,3,3,2,1,1,1,1,1] (.node [12,12,7,7,6,5,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,5,4,2,2,1,1,1,1,1] (.node [12,12,7,7,6,5,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,6,5,4,4,1,1,1,1,1] (.node [12,12,7,7,6,5,4,3,2,1,1,1,1] (.node [12,12,7,7,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,5,5,2,1,1,1,1,1,1] .empty .empty))) (.node [12,12,7,7,6,6,3,3,1,1,1,1,1,1] (.node [12,12,7,7,6,6,2,2,2,2,2,1,1] (.node [12,12,7,7,6,6,2,2,2,2,1,1,1,1] (.node [12,12,7,7,6,5,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,6,3,2,2,2,1,1,1] (.node [12,12,7,7,6,6,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,6,6,4,2,2,1,1,1,1] (.node [12,12,7,7,6,6,4,2,1,1,1,1,1,1] (.node [12,12,7,7,6,6,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,6,4,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_740 : RowTree := (.node [12,12,7,7,7,4,2,2,2,2,2,2,1] (.node [12,12,7,7,7,3,3,2,2,2,2,2,1] (.node [12,12,7,7,7,2,2,2,2,2,2,2,2,1] (.node [12,12,7,7,6,6,6,1,1,1,1,1,1] (.node [12,12,7,7,6,6,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,3,3,2,2,2,2,1,1,1] (.node [12,12,7,7,7,3,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,12,7,7,7,3,3,3,3,2,1,1,1] (.node [12,12,7,7,7,3,3,3,3,1,1,1,1,1] (.node [12,12,7,7,7,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,4,2,2,2,2,2,1,1,1] .empty .empty))) (.node [12,12,7,7,7,4,4,2,2,1,1,1,1,1] (.node [12,12,7,7,7,4,3,3,2,1,1,1,1,1] (.node [12,12,7,7,7,4,3,2,2,2,2,1,1] (.node [12,12,7,7,7,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,4,3,3,3,1,1,1,1] (.node [12,12,7,7,7,4,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,7,4,4,3,2,1,1,1,1] (.node [12,12,7,7,7,4,4,3,1,1,1,1,1,1] (.node [12,12,7,7,7,4,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,4,4,4,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_741 : RowTree := (.node [12,12,7,7,6,6,5,1,1,1,1,1,1,1] degreeTree62_739 degreeTree62_740) - -def degreeTree62_742 : RowTree := (.node [12,12,7,7,7,6,2,2,2,1,1,1,1,1] (.node [12,12,7,7,7,5,4,2,1,1,1,1,1,1] (.node [12,12,7,7,7,5,3,2,2,2,1,1,1] (.node [12,12,7,7,7,5,3,2,2,1,1,1,1,1] (.node [12,12,7,7,7,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,5,3,3,2,1,1,1,1] (.node [12,12,7,7,7,5,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,7,5,5,1,1,1,1,1,1,1] (.node [12,12,7,7,7,5,4,3,1,1,1,1,1] (.node [12,12,7,7,7,5,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,5,5,2,1,1,1,1,1] .empty .empty))) (.node [12,12,7,7,7,6,4,2,1,1,1,1,1] (.node [12,12,7,7,7,6,3,2,2,1,1,1,1] (.node [12,12,7,7,7,6,3,2,1,1,1,1,1,1] (.node [12,12,7,7,7,6,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,6,4,1,1,1,1,1,1,1] (.node [12,12,7,7,7,6,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,7,7,2,2,2,1,1,1,1] (.node [12,12,7,7,7,7,2,2,1,1,1,1,1,1] (.node [12,12,7,7,7,6,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,7,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_743 : RowTree := (.node [13,6,6,6,6,6,6,5,2,2,2,1,1] (.node [13,6,6,6,6,6,5,5,3,2,2,1,1] (.node [13,6,6,6,6,5,5,5,4,2,2,1,1] (.node [13,6,6,6,5,5,5,5,5,2,2,1,1] (.node [12,12,7,7,7,7,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,6,6,6,6,6,5,4,4,2,2,1,1] (.node [13,6,6,6,6,5,5,5,5,2,1,1,1] .empty .empty) .empty)) (.node [13,6,6,6,6,6,6,4,3,2,2,1,1] (.node [13,6,6,6,6,6,5,5,5,1,1,1,1] (.node [13,6,6,6,6,6,5,5,4,2,1,1,1] .empty .empty) .empty) (.node [13,6,6,6,6,6,6,4,4,2,1,1,1] .empty .empty))) (.node [13,7,6,5,5,5,5,5,5,2,2,1,1] (.node [13,6,6,6,6,6,6,6,2,2,1,1,1] (.node [13,6,6,6,6,6,6,5,4,1,1,1,1] (.node [13,6,6,6,6,6,6,5,3,2,1,1,1] .empty .empty) .empty) (.node [13,6,6,6,6,6,6,6,3,1,1,1,1] .empty .empty)) (.node [13,7,6,6,6,5,5,4,4,2,2,1,1] (.node [13,7,6,6,5,5,5,5,5,2,1,1,1] (.node [13,7,6,6,5,5,5,5,4,2,2,1,1] .empty .empty) .empty) (.node [13,7,6,6,6,5,5,5,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_744 : RowTree := (.node [12,12,7,7,7,7,3,2,1,1,1,1,1] degreeTree62_742 degreeTree62_743) - -def degreeTree62_745 : RowTree := (.node [12,12,7,7,7,5,2,2,2,2,1,1,1,1] degreeTree62_741 degreeTree62_744) - -def degreeTree62_746 : RowTree := (.node [12,12,7,7,6,5,3,2,2,2,1,1,1,1] degreeTree62_738 degreeTree62_745) - -def degreeTree62_747 : RowTree := (.node [13,7,6,6,6,6,6,4,3,2,1,1,1] (.node [13,7,6,6,6,6,5,5,3,2,1,1,1] (.node [13,7,6,6,6,6,5,4,3,2,2,1,1] (.node [13,7,6,6,6,6,4,4,4,2,2,1,1] (.node [13,7,6,6,6,5,5,5,5,1,1,1,1] .empty .empty) .empty) (.node [13,7,6,6,6,6,5,5,2,2,2,1,1] (.node [13,7,6,6,6,6,5,4,4,2,1,1,1] .empty .empty) .empty)) (.node [13,7,6,6,6,6,6,3,3,2,2,1,1] (.node [13,7,6,6,6,6,6,2,2,2,2,2,2] (.node [13,7,6,6,6,6,5,5,4,1,1,1,1] .empty .empty) .empty) (.node [13,7,6,6,6,6,6,4,2,2,2,1,1] .empty .empty))) (.node [13,7,7,5,5,5,5,5,5,2,1,1,1] (.node [13,7,6,6,6,6,6,5,3,1,1,1,1] (.node [13,7,6,6,6,6,6,5,2,2,1,1,1] (.node [13,7,6,6,6,6,6,4,4,1,1,1,1] .empty .empty) .empty) (.node [13,7,7,5,5,5,5,5,4,2,2,1,1] (.node [13,7,6,6,6,6,6,6,2,1,1,1,1] .empty .empty) .empty)) (.node [13,7,7,6,5,5,5,5,4,2,1,1,1] (.node [13,7,7,6,5,5,5,5,3,2,2,1,1] (.node [13,7,7,6,5,5,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,6,5,5,5,5,5,1,1,1,1] .empty .empty)))) - -def degreeTree62_748 : RowTree := (.node [13,7,7,6,6,6,5,4,3,2,1,1,1] (.node [13,7,7,6,6,6,4,4,3,2,2,1,1] (.node [13,7,7,6,6,5,5,5,2,2,2,1,1] (.node [13,7,7,6,6,5,5,4,4,2,1,1,1] (.node [13,7,7,6,6,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,6,6,5,5,5,4,1,1,1,1] (.node [13,7,7,6,6,5,5,5,3,2,1,1,1] .empty .empty) .empty)) (.node [13,7,7,6,6,6,5,3,3,2,2,1,1] (.node [13,7,7,6,6,6,5,2,2,2,2,2,2] (.node [13,7,7,6,6,6,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [13,7,7,6,6,6,5,4,2,2,2,1,1] .empty .empty))) (.node [13,7,7,6,6,6,6,3,3,2,1,1,1] (.node [13,7,7,6,6,6,5,5,3,1,1,1,1] (.node [13,7,7,6,6,6,5,5,2,2,1,1,1] (.node [13,7,7,6,6,6,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [13,7,7,6,6,6,6,3,2,2,2,1,1] (.node [13,7,7,6,6,6,6,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,7,7,6,6,6,6,5,2,1,1,1,1] (.node [13,7,7,6,6,6,6,4,3,1,1,1,1] (.node [13,7,7,6,6,6,6,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,7,7,6,6,6,6,6,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_749 : RowTree := (.node [13,7,7,6,6,5,4,4,4,2,2,1,1] degreeTree62_747 degreeTree62_748) - -def degreeTree62_750 : RowTree := (.node [13,7,7,7,6,5,5,4,2,2,2,1,1] (.node [13,7,7,7,6,4,4,4,4,2,2,1,1] (.node [13,7,7,7,5,5,5,5,2,2,2,1,1] (.node [13,7,7,7,5,5,5,4,4,2,1,1,1] (.node [13,7,7,7,5,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,7,5,5,5,5,4,1,1,1,1] (.node [13,7,7,7,5,5,5,5,3,2,1,1,1] .empty .empty) .empty)) (.node [13,7,7,7,6,5,5,2,2,2,2,2,2] (.node [13,7,7,7,6,5,4,4,4,2,1,1,1] (.node [13,7,7,7,6,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,7,6,5,5,3,3,2,2,1,1] .empty .empty))) (.node [13,7,7,7,6,6,4,3,3,2,2,1,1] (.node [13,7,7,7,6,5,5,5,2,2,1,1,1] (.node [13,7,7,7,6,5,5,4,4,1,1,1,1] (.node [13,7,7,7,6,5,5,4,3,2,1,1,1] .empty .empty) .empty) (.node [13,7,7,7,6,6,4,2,2,2,2,2,2] (.node [13,7,7,7,6,5,5,5,3,1,1,1,1] .empty .empty) .empty)) (.node [13,7,7,7,6,6,4,4,4,1,1,1,1] (.node [13,7,7,7,6,6,4,4,3,2,1,1,1] (.node [13,7,7,7,6,6,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,7,6,6,5,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_751 : RowTree := (.node [13,7,7,7,7,4,4,4,4,2,1,1,1] (.node [13,7,7,7,6,6,6,3,2,2,1,1,1] (.node [13,7,7,7,6,6,5,4,3,1,1,1,1] (.node [13,7,7,7,6,6,5,4,2,2,1,1,1] (.node [13,7,7,7,6,6,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,7,7,7,6,6,6,2,2,2,2,1,1] (.node [13,7,7,7,6,6,5,5,2,1,1,1,1] .empty .empty) .empty)) (.node [13,7,7,7,6,6,6,5,1,1,1,1,1] (.node [13,7,7,7,6,6,6,4,2,1,1,1,1] (.node [13,7,7,7,6,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,7,7,7,7,4,4,4,3,2,2,1,1] .empty .empty))) (.node [13,7,7,7,7,5,5,2,2,2,2,2,1] (.node [13,7,7,7,7,5,4,4,2,2,2,1,1] (.node [13,7,7,7,7,5,4,3,3,2,2,1,1] (.node [13,7,7,7,7,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,7,7,7,7,5,4,4,4,1,1,1,1] (.node [13,7,7,7,7,5,4,4,3,2,1,1,1] .empty .empty) .empty)) (.node [13,7,7,7,7,5,5,4,2,2,1,1,1] (.node [13,7,7,7,7,5,5,3,3,2,1,1,1] (.node [13,7,7,7,7,5,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,7,7,5,5,4,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_752 : RowTree := (.node [13,7,7,7,6,6,5,3,2,2,2,1,1] degreeTree62_750 degreeTree62_751) - -def degreeTree62_753 : RowTree := (.node [13,7,7,7,5,5,4,4,4,2,2,1,1] degreeTree62_749 degreeTree62_752) - -def degreeTree62_754 : RowTree := (.node [13,7,7,7,7,6,5,4,2,1,1,1,1] (.node [13,7,7,7,7,6,4,4,2,2,1,1,1] (.node [13,7,7,7,7,6,4,2,2,2,2,2,1] (.node [13,7,7,7,7,6,3,3,3,2,2,1,1] (.node [13,7,7,7,7,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,7,7,7,7,6,4,3,3,2,1,1,1] (.node [13,7,7,7,7,6,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [13,7,7,7,7,6,5,3,2,2,1,1,1] (.node [13,7,7,7,7,6,5,2,2,2,2,1,1] (.node [13,7,7,7,7,6,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [13,7,7,7,7,6,5,3,3,1,1,1,1] .empty .empty))) (.node [13,7,7,7,7,7,3,2,2,2,2,2,1] (.node [13,7,7,7,7,6,6,3,2,1,1,1,1] (.node [13,7,7,7,7,6,6,2,2,2,1,1,1] (.node [13,7,7,7,7,6,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [13,7,7,7,7,7,2,2,2,2,2,2,2] (.node [13,7,7,7,7,6,6,4,1,1,1,1,1] .empty .empty) .empty)) (.node [13,7,7,7,7,7,4,2,2,2,2,1,1] (.node [13,7,7,7,7,7,3,3,3,2,1,1,1] (.node [13,7,7,7,7,7,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,7,7,7,4,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_755 : RowTree := (.node [13,8,6,5,5,5,5,5,4,2,2,1,1] (.node [13,7,7,7,7,7,6,2,2,1,1,1,1] (.node [13,7,7,7,7,7,5,3,2,1,1,1,1] (.node [13,7,7,7,7,7,5,2,2,2,1,1,1] (.node [13,7,7,7,7,7,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [13,7,7,7,7,7,6,2,1,1,1,1,1,1] (.node [13,7,7,7,7,7,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [13,7,7,7,7,7,7,2,1,1,1,1,1] (.node [13,7,7,7,7,7,7,1,1,1,1,1,1,1] (.node [13,7,7,7,7,7,6,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,5,5,5,5,5,5,5,2,2,1,1] .empty .empty))) (.node [13,8,6,6,6,5,4,4,4,2,2,1,1] (.node [13,8,6,6,5,5,5,5,3,2,2,1,1] (.node [13,8,6,6,5,5,5,4,4,2,2,1,1] (.node [13,8,6,5,5,5,5,5,5,2,1,1,1] .empty .empty) .empty) (.node [13,8,6,6,5,5,5,5,5,1,1,1,1] (.node [13,8,6,6,5,5,5,5,4,2,1,1,1] .empty .empty) .empty)) (.node [13,8,6,6,6,5,5,5,2,2,2,1,1] (.node [13,8,6,6,6,5,5,4,4,2,1,1,1] (.node [13,8,6,6,6,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,6,6,6,5,5,5,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_756 : RowTree := (.node [13,7,7,7,7,7,4,3,3,1,1,1,1] degreeTree62_754 degreeTree62_755) - -def degreeTree62_757 : RowTree := (.node [13,8,6,6,6,6,6,3,2,2,2,1,1] (.node [13,8,6,6,6,6,5,4,3,2,1,1,1] (.node [13,8,6,6,6,6,5,2,2,2,2,2,2] (.node [13,8,6,6,6,6,4,4,4,2,1,1,1] (.node [13,8,6,6,6,6,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,6,6,6,6,5,4,2,2,2,1,1] (.node [13,8,6,6,6,6,5,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,8,6,6,6,6,5,5,3,1,1,1,1] (.node [13,8,6,6,6,6,5,5,2,2,1,1,1] (.node [13,8,6,6,6,6,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [13,8,6,6,6,6,6,2,2,2,2,2,1] .empty .empty))) (.node [13,8,7,5,5,5,5,4,4,2,2,1,1] (.node [13,8,6,6,6,6,6,4,3,1,1,1,1] (.node [13,8,6,6,6,6,6,4,2,2,1,1,1] (.node [13,8,6,6,6,6,6,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,6,6,6,6,6,6,1,1,1,1,1] (.node [13,8,6,6,6,6,6,5,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,7,5,5,5,5,5,5,1,1,1,1] (.node [13,8,7,5,5,5,5,5,4,2,1,1,1] (.node [13,8,7,5,5,5,5,5,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,6,5,5,4,4,4,2,2,1,1] .empty .empty)))) - -def degreeTree62_758 : RowTree := (.node [13,8,7,6,6,5,5,4,3,2,1,1,1] (.node [13,8,7,6,6,5,4,4,3,2,2,1,1] (.node [13,8,7,6,5,5,5,5,3,2,1,1,1] (.node [13,8,7,6,5,5,5,5,2,2,2,1,1] (.node [13,8,7,6,5,5,5,4,4,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,6,6,4,4,4,4,2,2,1,1] (.node [13,8,7,6,5,5,5,5,4,1,1,1,1] .empty .empty) .empty)) (.node [13,8,7,6,6,5,5,3,3,2,2,1,1] (.node [13,8,7,6,6,5,5,2,2,2,2,2,2] (.node [13,8,7,6,6,5,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,6,6,5,5,4,2,2,2,1,1] .empty .empty))) (.node [13,8,7,6,6,6,4,3,3,2,2,1,1] (.node [13,8,7,6,6,5,5,5,3,1,1,1,1] (.node [13,8,7,6,6,5,5,5,2,2,1,1,1] (.node [13,8,7,6,6,5,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [13,8,7,6,6,6,4,2,2,2,2,2,2] .empty .empty)) (.node [13,8,7,6,6,6,4,4,4,1,1,1,1] (.node [13,8,7,6,6,6,4,4,3,2,1,1,1] (.node [13,8,7,6,6,6,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,6,6,6,5,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_759 : RowTree := (.node [13,8,7,6,5,5,5,4,3,2,2,1,1] degreeTree62_757 degreeTree62_758) - -def degreeTree62_760 : RowTree := (.node [13,8,6,6,6,5,5,5,4,1,1,1,1] degreeTree62_756 degreeTree62_759) - -def degreeTree62_761 : RowTree := (.node [13,7,7,7,7,5,5,5,2,1,1,1,1] degreeTree62_753 degreeTree62_760) - -def degreeTree62_762 : RowTree := (.node [13,7,6,6,6,5,5,5,4,2,1,1,1] degreeTree62_746 degreeTree62_761) - -def degreeTree62_763 : RowTree := (.node [12,12,7,6,5,5,4,3,2,2,2,1,1] degreeTree62_731 degreeTree62_762) - -def degreeTree62_764 : RowTree := (.node [12,11,9,7,7,4,2,2,2,2,2,1,1] degreeTree62_700 degreeTree62_763) - -def degreeTree62_765 : RowTree := (.node [12,11,7,6,6,5,4,2,2,2,2,2,1] degreeTree62_637 degreeTree62_764) - -def degreeTree62_766 : RowTree := (.node [13,8,7,7,5,5,4,4,3,2,2,1,1] (.node [13,8,7,6,6,6,6,3,2,2,1,1,1] (.node [13,8,7,6,6,6,5,4,3,1,1,1,1] (.node [13,8,7,6,6,6,5,4,2,2,1,1,1] (.node [13,8,7,6,6,6,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,6,6,6,6,2,2,2,2,1,1] (.node [13,8,7,6,6,6,5,5,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,7,6,6,6,6,5,1,1,1,1,1] (.node [13,8,7,6,6,6,6,4,2,1,1,1,1] (.node [13,8,7,6,6,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,5,4,4,4,4,2,2,1,1] .empty .empty))) (.node [13,8,7,7,5,5,5,4,4,1,1,1,1] (.node [13,8,7,7,5,5,5,3,3,2,2,1,1] (.node [13,8,7,7,5,5,5,2,2,2,2,2,2] (.node [13,8,7,7,5,5,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,5,5,5,4,3,2,1,1,1] (.node [13,8,7,7,5,5,5,4,2,2,2,1,1] .empty .empty) .empty)) (.node [13,8,7,7,6,4,4,4,3,2,2,1,1] (.node [13,8,7,7,5,5,5,5,3,1,1,1,1] (.node [13,8,7,7,5,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,6,4,4,4,4,2,1,1,1] .empty .empty)))) - -def degreeTree62_767 : RowTree := (.node [13,8,7,7,6,6,3,2,2,2,2,2,2] (.node [13,8,7,7,6,5,5,3,2,2,2,1,1] (.node [13,8,7,7,6,5,4,4,3,2,1,1,1] (.node [13,8,7,7,6,5,4,4,2,2,2,1,1] (.node [13,8,7,7,6,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,7,6,5,5,2,2,2,2,2,1] (.node [13,8,7,7,6,5,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [13,8,7,7,6,5,5,4,3,1,1,1,1] (.node [13,8,7,7,6,5,5,4,2,2,1,1,1] (.node [13,8,7,7,6,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,6,5,5,5,2,1,1,1,1] .empty .empty))) (.node [13,8,7,7,6,6,4,4,3,1,1,1,1] (.node [13,8,7,7,6,6,4,3,2,2,2,1,1] (.node [13,8,7,7,6,6,4,2,2,2,2,2,1] (.node [13,8,7,7,6,6,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,7,6,6,4,4,2,2,1,1,1] (.node [13,8,7,7,6,6,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [13,8,7,7,6,6,5,3,3,1,1,1,1] (.node [13,8,7,7,6,6,5,3,2,2,1,1,1] (.node [13,8,7,7,6,6,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,7,6,6,5,4,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_768 : RowTree := (.node [13,8,7,7,6,5,4,2,2,2,2,2,2] degreeTree62_766 degreeTree62_767) - -def degreeTree62_769 : RowTree := (.node [13,8,7,7,7,5,4,2,2,2,2,2,1] (.node [13,8,7,7,7,4,4,4,2,2,2,1,1] (.node [13,8,7,7,6,6,6,4,1,1,1,1,1] (.node [13,8,7,7,6,6,6,3,2,1,1,1,1] (.node [13,8,7,7,6,6,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,4,4,3,3,2,2,1,1] (.node [13,8,7,7,7,4,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,8,7,7,7,5,3,2,2,2,2,2,2] (.node [13,8,7,7,7,4,4,4,4,1,1,1,1] (.node [13,8,7,7,7,4,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,5,3,3,3,2,2,1,1] .empty .empty))) (.node [13,8,7,7,7,5,5,3,2,2,1,1,1] (.node [13,8,7,7,7,5,4,4,2,2,1,1,1] (.node [13,8,7,7,7,5,4,3,3,2,1,1,1] (.node [13,8,7,7,7,5,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,5,5,2,2,2,2,1,1] (.node [13,8,7,7,7,5,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [13,8,7,7,7,5,5,5,1,1,1,1,1] (.node [13,8,7,7,7,5,5,4,2,1,1,1,1] (.node [13,8,7,7,7,5,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,6,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_770 : RowTree := (.node [13,8,7,7,7,6,6,2,2,1,1,1,1] (.node [13,8,7,7,7,6,4,4,2,1,1,1,1] (.node [13,8,7,7,7,6,4,2,2,2,2,1,1] (.node [13,8,7,7,7,6,3,3,3,2,1,1,1] (.node [13,8,7,7,7,6,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,6,4,3,3,1,1,1,1] (.node [13,8,7,7,7,6,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [13,8,7,7,7,6,5,4,1,1,1,1,1] (.node [13,8,7,7,7,6,5,3,2,1,1,1,1] (.node [13,8,7,7,7,6,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,6,6,2,1,1,1,1,1,1] .empty .empty))) (.node [13,8,7,7,7,7,3,3,2,1,1,1,1,1] (.node [13,8,7,7,7,7,2,2,2,2,2,2,1] (.node [13,8,7,7,7,7,2,2,2,2,2,1,1,1] (.node [13,8,7,7,7,6,6,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,7,3,2,2,2,2,1,1] (.node [13,8,7,7,7,7,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,7,7,7,7,4,2,2,1,1,1,1,1] (.node [13,8,7,7,7,7,3,3,3,1,1,1,1] (.node [13,8,7,7,7,7,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,7,4,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_771 : RowTree := (.node [13,8,7,7,7,6,3,2,2,2,2,2,1] degreeTree62_769 degreeTree62_770) - -def degreeTree62_772 : RowTree := (.node [13,8,7,7,6,6,5,5,1,1,1,1,1] degreeTree62_768 degreeTree62_771) - -def degreeTree62_773 : RowTree := (.node [13,8,8,5,5,5,5,5,2,2,2,1,1] (.node [13,8,7,7,7,7,6,1,1,1,1,1,1,1] (.node [13,8,7,7,7,7,5,2,1,1,1,1,1,1] (.node [13,8,7,7,7,7,4,4,1,1,1,1,1] (.node [13,8,7,7,7,7,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,7,5,3,1,1,1,1,1] (.node [13,8,7,7,7,7,5,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,5,5,5,5,4,3,2,2,1,1] (.node [13,8,8,5,5,5,4,4,4,2,2,1,1] (.node [13,8,7,7,7,7,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,5,5,5,5,4,4,2,1,1,1] .empty .empty))) (.node [13,8,8,6,5,5,5,2,2,2,2,2,2] (.node [13,8,8,6,5,4,4,4,4,2,2,1,1] (.node [13,8,8,5,5,5,5,5,4,1,1,1,1] (.node [13,8,8,5,5,5,5,5,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,6,5,5,4,4,4,2,1,1,1] (.node [13,8,8,6,5,5,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [13,8,8,6,5,5,5,4,3,2,1,1,1] (.node [13,8,8,6,5,5,5,4,2,2,2,1,1] (.node [13,8,8,6,5,5,5,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,6,5,5,5,4,4,1,1,1,1] .empty .empty)))) - -def degreeTree62_774 : RowTree := (.node [13,8,8,6,6,5,5,3,3,2,1,1,1] (.node [13,8,8,6,6,5,4,4,2,2,2,1,1] (.node [13,8,8,6,6,4,4,4,4,2,1,1,1] (.node [13,8,8,6,6,4,4,4,3,2,2,1,1] (.node [13,8,8,6,5,5,5,5,3,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,6,6,5,4,3,3,2,2,1,1] (.node [13,8,8,6,6,5,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,8,8,6,6,5,5,2,2,2,2,2,1] (.node [13,8,8,6,6,5,4,4,4,1,1,1,1] (.node [13,8,8,6,6,5,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,6,6,5,5,3,2,2,2,1,1] .empty .empty))) (.node [13,8,8,6,6,6,4,2,2,2,2,2,1] (.node [13,8,8,6,6,5,5,5,2,1,1,1,1] (.node [13,8,8,6,6,5,5,4,3,1,1,1,1] (.node [13,8,8,6,6,5,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,6,6,6,3,3,3,2,2,1,1] (.node [13,8,8,6,6,6,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,8,8,6,6,6,4,4,2,2,1,1,1] (.node [13,8,8,6,6,6,4,3,3,2,1,1,1] (.node [13,8,8,6,6,6,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,6,6,6,4,4,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_775 : RowTree := (.node [13,8,8,6,5,5,5,5,2,2,1,1,1] degreeTree62_773 degreeTree62_774) - -def degreeTree62_776 : RowTree := (.node [13,8,8,7,5,5,4,2,2,2,2,2,2] (.node [13,8,8,6,6,6,6,3,2,1,1,1,1] (.node [13,8,8,6,6,6,5,4,2,1,1,1,1] (.node [13,8,8,6,6,6,5,3,3,1,1,1,1] (.node [13,8,8,6,6,6,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,6,6,6,6,2,2,2,1,1,1] (.node [13,8,8,6,6,6,5,5,1,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,5,4,4,4,3,2,2,1,1] (.node [13,8,8,7,4,4,4,4,4,2,2,1,1] (.node [13,8,8,6,6,6,6,4,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,5,4,4,4,4,2,1,1,1] .empty .empty))) (.node [13,8,8,7,5,5,5,3,2,2,2,1,1] (.node [13,8,8,7,5,5,4,4,3,2,1,1,1] (.node [13,8,8,7,5,5,4,4,2,2,2,1,1] (.node [13,8,8,7,5,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,7,5,5,5,2,2,2,2,2,1] (.node [13,8,8,7,5,5,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,5,5,5,4,3,1,1,1,1] (.node [13,8,8,7,5,5,5,4,2,2,1,1,1] (.node [13,8,8,7,5,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,5,5,5,5,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_777 : RowTree := (.node [13,8,8,7,6,5,4,4,3,1,1,1,1] (.node [13,8,8,7,6,5,3,3,3,2,2,1,1] (.node [13,8,8,7,6,4,4,4,3,2,1,1,1] (.node [13,8,8,7,6,4,4,4,2,2,2,1,1] (.node [13,8,8,7,6,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,7,6,5,3,2,2,2,2,2,2] (.node [13,8,8,7,6,4,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,6,5,4,3,3,2,1,1,1] (.node [13,8,8,7,6,5,4,3,2,2,2,1,1] (.node [13,8,8,7,6,5,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,8,8,7,6,5,4,4,2,2,1,1,1] .empty .empty))) (.node [13,8,8,7,6,6,2,2,2,2,2,2,2] (.node [13,8,8,7,6,5,5,3,3,1,1,1,1] (.node [13,8,8,7,6,5,5,3,2,2,1,1,1] (.node [13,8,8,7,6,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,7,6,5,5,5,1,1,1,1,1] (.node [13,8,8,7,6,5,5,4,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,6,6,3,3,3,2,1,1,1] (.node [13,8,8,7,6,6,3,3,2,2,2,1,1] (.node [13,8,8,7,6,6,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,8,8,7,6,6,4,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_778 : RowTree := (.node [13,8,8,7,6,4,4,2,2,2,2,2,2] degreeTree62_776 degreeTree62_777) - -def degreeTree62_779 : RowTree := (.node [13,8,8,6,6,6,5,2,2,2,2,1,1] degreeTree62_775 degreeTree62_778) - -def degreeTree62_780 : RowTree := (.node [13,8,7,7,7,7,4,3,1,1,1,1,1,1] degreeTree62_772 degreeTree62_779) - -def degreeTree62_781 : RowTree := (.node [13,8,8,7,7,4,4,2,2,2,2,2,1] (.node [13,8,8,7,6,6,6,2,1,1,1,1,1,1] (.node [13,8,8,7,6,6,5,2,2,2,1,1,1] (.node [13,8,8,7,6,6,4,4,2,1,1,1,1] (.node [13,8,8,7,6,6,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,6,6,5,4,1,1,1,1,1] (.node [13,8,8,7,6,6,5,3,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,7,4,3,2,2,2,2,2,2] (.node [13,8,8,7,6,6,6,3,1,1,1,1,1] (.node [13,8,8,7,6,6,6,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,4,3,3,3,2,2,1,1] .empty .empty))) (.node [13,8,8,7,7,5,3,2,2,2,2,2,1] (.node [13,8,8,7,7,4,4,4,2,2,1,1,1] (.node [13,8,8,7,7,4,4,3,3,2,1,1,1] (.node [13,8,8,7,7,4,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,5,2,2,2,2,2,2,2] (.node [13,8,8,7,7,4,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,7,5,4,2,2,2,2,1,1] (.node [13,8,8,7,7,5,3,3,3,2,1,1,1] (.node [13,8,8,7,7,5,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,5,4,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_782 : RowTree := (.node [13,8,8,7,7,6,3,3,3,1,1,1,1] (.node [13,8,8,7,7,6,2,2,2,2,2,2,1] (.node [13,8,8,7,7,5,5,3,2,1,1,1,1] (.node [13,8,8,7,7,5,5,2,2,2,1,1,1] (.node [13,8,8,7,7,5,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,6,2,2,2,2,2,1,1,1] (.node [13,8,8,7,7,5,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,7,6,3,3,2,1,1,1,1,1] (.node [13,8,8,7,7,6,3,2,2,2,2,1,1] (.node [13,8,8,7,7,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,6,3,3,2,2,1,1,1] .empty .empty))) (.node [13,8,8,7,7,6,5,2,1,1,1,1,1,1] (.node [13,8,8,7,7,6,4,3,1,1,1,1,1,1] (.node [13,8,8,7,7,6,4,2,2,2,1,1,1] (.node [13,8,8,7,7,6,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,6,4,4,1,1,1,1,1] (.node [13,8,8,7,7,6,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,7,6,6,1,1,1,1,1,1,1] (.node [13,8,8,7,7,6,5,3,1,1,1,1,1] (.node [13,8,8,7,7,6,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,7,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_783 : RowTree := (.node [13,8,8,7,7,5,4,3,3,1,1,1,1] degreeTree62_781 degreeTree62_782) - -def degreeTree62_784 : RowTree := (.node [13,8,8,8,5,4,4,3,3,2,2,1,1] (.node [13,8,8,7,7,7,4,2,2,1,1,1,1] (.node [13,8,8,7,7,7,3,3,1,1,1,1,1,1] (.node [13,8,8,7,7,7,3,2,2,2,1,1,1] (.node [13,8,8,7,7,7,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,7,4,2,1,1,1,1,1,1] (.node [13,8,8,7,7,7,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,4,4,4,4,4,2,1,1,1] (.node [13,8,8,8,4,4,4,4,3,2,2,1,1] (.node [13,8,8,7,7,7,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,5,4,4,2,2,2,2,2,2] .empty .empty))) (.node [13,8,8,8,5,5,4,2,2,2,2,2,1] (.node [13,8,8,8,5,4,4,4,4,1,1,1,1] (.node [13,8,8,8,5,4,4,4,3,2,1,1,1] (.node [13,8,8,8,5,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,8,5,5,3,3,3,2,2,1,1] (.node [13,8,8,8,5,5,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,8,8,8,5,5,4,4,2,2,1,1,1] (.node [13,8,8,8,5,5,4,3,3,2,1,1,1] (.node [13,8,8,8,5,5,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,8,5,5,4,4,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_785 : RowTree := (.node [13,8,8,8,6,4,4,4,3,1,1,1,1] (.node [13,8,8,8,6,4,3,3,3,2,2,1,1] (.node [13,8,8,8,5,5,5,4,2,1,1,1,1] (.node [13,8,8,8,5,5,5,3,3,1,1,1,1] (.node [13,8,8,8,5,5,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,6,4,3,2,2,2,2,2,2] (.node [13,8,8,8,5,5,5,5,1,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,6,4,4,3,3,2,1,1,1] (.node [13,8,8,8,6,4,4,3,2,2,2,1,1] (.node [13,8,8,8,6,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,8,8,8,6,4,4,4,2,2,1,1,1] .empty .empty))) (.node [13,8,8,8,6,5,4,3,2,2,1,1,1] (.node [13,8,8,8,6,5,3,3,2,2,2,1,1] (.node [13,8,8,8,6,5,3,2,2,2,2,2,1] (.node [13,8,8,8,6,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,8,8,8,6,5,4,2,2,2,2,1,1] (.node [13,8,8,8,6,5,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,6,5,5,2,2,2,1,1,1] (.node [13,8,8,8,6,5,4,4,2,1,1,1,1] (.node [13,8,8,8,6,5,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,6,5,5,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_786 : RowTree := (.node [13,8,8,8,5,5,5,2,2,2,2,1,1] degreeTree62_784 degreeTree62_785) - -def degreeTree62_787 : RowTree := (.node [13,8,8,7,7,7,2,2,2,2,2,1,1] degreeTree62_783 degreeTree62_786) - -def degreeTree62_788 : RowTree := (.node [13,8,8,8,6,6,4,3,2,1,1,1,1] (.node [13,8,8,8,6,6,3,3,2,2,1,1,1] (.node [13,8,8,8,6,6,3,2,2,2,1,1,1,1] (.node [13,8,8,8,6,6,2,2,2,2,2,2,1] (.node [13,8,8,8,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,6,6,3,3,2,1,1,1,1,1] (.node [13,8,8,8,6,6,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,8,8,8,6,6,4,2,2,2,1,1,1] (.node [13,8,8,8,6,6,4,2,2,1,1,1,1,1] (.node [13,8,8,8,6,6,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,6,6,4,3,1,1,1,1,1,1] .empty .empty))) (.node [13,8,8,8,7,3,3,3,3,2,2,1,1] (.node [13,8,8,8,6,6,5,2,2,1,1,1,1] (.node [13,8,8,8,6,6,5,2,1,1,1,1,1,1] (.node [13,8,8,8,6,6,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,3,3,2,2,2,2,2,2] (.node [13,8,8,8,6,6,6,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,7,4,3,2,2,2,2,2,1] (.node [13,8,8,8,7,4,3,2,2,2,2,1,1,1] (.node [13,8,8,8,7,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,8,8,8,7,4,3,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_789 : RowTree := (.node [13,8,8,8,7,5,3,2,2,2,1,1,1,1] (.node [13,8,8,8,7,4,4,3,3,1,1,1,1] (.node [13,8,8,8,7,4,4,2,2,2,2,1,1] (.node [13,8,8,8,7,4,4,2,2,2,1,1,1,1] (.node [13,8,8,8,7,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,4,4,3,2,2,1,1,1] (.node [13,8,8,8,7,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,7,5,2,2,2,2,2,1,1,1] (.node [13,8,8,8,7,4,4,4,2,1,1,1,1] (.node [13,8,8,8,7,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,5,2,2,2,2,2,2,1] .empty .empty))) (.node [13,8,8,8,7,5,4,2,2,2,1,1,1] (.node [13,8,8,8,7,5,3,3,2,2,1,1,1] (.node [13,8,8,8,7,5,3,3,2,1,1,1,1,1] (.node [13,8,8,8,7,5,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,5,4,2,2,1,1,1,1,1] (.node [13,8,8,8,7,5,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,7,5,5,2,1,1,1,1,1,1] (.node [13,8,8,8,7,5,4,3,2,1,1,1,1] (.node [13,8,8,8,7,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,5,5,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_790 : RowTree := (.node [13,8,8,8,7,4,3,3,3,1,1,1,1,1] degreeTree62_788 degreeTree62_789) - -def degreeTree62_791 : RowTree := (.node [13,8,8,8,7,7,3,2,1,1,1,1,1,1] (.node [13,8,8,8,7,6,4,2,1,1,1,1,1,1] (.node [13,8,8,8,7,6,3,2,2,2,1,1,1] (.node [13,8,8,8,7,6,3,2,2,1,1,1,1,1] (.node [13,8,8,8,7,6,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,6,3,3,2,1,1,1,1] (.node [13,8,8,8,7,6,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,7,7,2,2,2,1,1,1,1,1] (.node [13,8,8,8,7,6,5,1,1,1,1,1,1,1] (.node [13,8,8,8,7,6,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,7,2,2,2,2,1,1,1] .empty .empty))) (.node [13,8,8,8,8,3,3,2,2,2,2,2,1] (.node [13,8,8,8,8,2,2,2,2,2,2,2,2,1] (.node [13,8,8,8,7,7,4,1,1,1,1,1,1,1] (.node [13,8,8,8,7,7,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,3,3,2,2,2,2,1,1,1] (.node [13,8,8,8,8,3,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,8,8,8,8,3,3,3,3,2,1,1,1] (.node [13,8,8,8,8,3,3,3,3,1,1,1,1,1] (.node [13,8,8,8,8,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,4,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_792 : RowTree := (.node [13,8,8,8,8,5,2,2,2,2,2,1,1] (.node [13,8,8,8,8,4,4,2,2,1,1,1,1,1] (.node [13,8,8,8,8,4,3,3,2,1,1,1,1,1] (.node [13,8,8,8,8,4,3,2,2,2,2,1,1] (.node [13,8,8,8,8,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,4,3,3,3,1,1,1,1] (.node [13,8,8,8,8,4,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,8,4,4,3,2,1,1,1,1] (.node [13,8,8,8,8,4,4,3,1,1,1,1,1,1] (.node [13,8,8,8,8,4,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,5,2,2,2,2,1,1,1,1] .empty .empty))) (.node [13,8,8,8,8,5,4,2,1,1,1,1,1,1] (.node [13,8,8,8,8,5,3,3,1,1,1,1,1,1] (.node [13,8,8,8,8,5,3,2,2,2,1,1,1] (.node [13,8,8,8,8,5,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,5,3,3,2,1,1,1,1] .empty .empty)) (.node [13,8,8,8,8,6,2,2,2,1,1,1,1,1] (.node [13,8,8,8,8,5,5,1,1,1,1,1,1,1] (.node [13,8,8,8,8,5,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,6,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_793 : RowTree := (.node [13,8,8,8,8,4,2,2,2,2,2,2,1] degreeTree62_791 degreeTree62_792) - -def degreeTree62_794 : RowTree := (.node [13,8,8,8,7,6,2,2,2,2,1,1,1,1] degreeTree62_790 degreeTree62_793) - -def degreeTree62_795 : RowTree := (.node [13,8,8,8,6,5,5,4,1,1,1,1,1] degreeTree62_787 degreeTree62_794) - -def degreeTree62_796 : RowTree := (.node [13,8,8,7,6,6,4,3,2,2,1,1,1] degreeTree62_780 degreeTree62_795) - -def degreeTree62_797 : RowTree := (.node [13,9,6,5,5,5,5,5,4,2,1,1,1] (.node [13,8,8,8,8,8,2,1,1,1,1,1,1,1] (.node [13,8,8,8,8,7,2,2,1,1,1,1,1,1] (.node [13,8,8,8,8,6,4,1,1,1,1,1,1,1] (.node [13,8,8,8,8,6,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,7,3,1,1,1,1,1,1,1] (.node [13,8,8,8,8,7,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,6,5,5,5,5,4,4,2,2,1,1] (.node [13,9,5,5,5,5,5,5,5,2,1,1,1] (.node [13,9,5,5,5,5,5,5,4,2,2,1,1] .empty .empty) .empty) (.node [13,9,6,5,5,5,5,5,3,2,2,1,1] .empty .empty))) (.node [13,9,6,6,5,5,5,5,3,2,1,1,1] (.node [13,9,6,6,5,5,5,4,3,2,2,1,1] (.node [13,9,6,6,5,5,4,4,4,2,2,1,1] (.node [13,9,6,5,5,5,5,5,5,1,1,1,1] .empty .empty) .empty) (.node [13,9,6,6,5,5,5,5,2,2,2,1,1] (.node [13,9,6,6,5,5,5,4,4,2,1,1,1] .empty .empty) .empty)) (.node [13,9,6,6,6,5,4,4,3,2,2,1,1] (.node [13,9,6,6,6,4,4,4,4,2,2,1,1] (.node [13,9,6,6,5,5,5,5,4,1,1,1,1] .empty .empty) .empty) (.node [13,9,6,6,6,5,4,4,4,2,1,1,1] .empty .empty)))) - -def degreeTree62_798 : RowTree := (.node [13,9,6,6,6,6,4,4,4,1,1,1,1] (.node [13,9,6,6,6,5,5,5,3,1,1,1,1] (.node [13,9,6,6,6,5,5,4,3,2,1,1,1] (.node [13,9,6,6,6,5,5,4,2,2,2,1,1] (.node [13,9,6,6,6,5,5,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,6,6,6,5,5,5,2,2,1,1,1] (.node [13,9,6,6,6,5,5,4,4,1,1,1,1] .empty .empty) .empty)) (.node [13,9,6,6,6,6,4,4,2,2,2,1,1] (.node [13,9,6,6,6,6,4,3,3,2,2,1,1] (.node [13,9,6,6,6,6,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,6,6,6,6,4,4,3,2,1,1,1] .empty .empty))) (.node [13,9,6,6,6,6,5,5,2,1,1,1,1] (.node [13,9,6,6,6,6,5,3,3,2,1,1,1] (.node [13,9,6,6,6,6,5,3,2,2,2,1,1] (.node [13,9,6,6,6,6,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,6,6,6,6,5,4,3,1,1,1,1] (.node [13,9,6,6,6,6,5,4,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,6,6,6,6,6,3,3,1,1,1,1] (.node [13,9,6,6,6,6,6,3,2,2,1,1,1] (.node [13,9,6,6,6,6,6,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,6,6,6,6,6,4,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_799 : RowTree := (.node [13,9,6,6,6,5,5,2,2,2,2,2,2] degreeTree62_797 degreeTree62_798) - -def degreeTree62_800 : RowTree := (.node [13,9,7,6,5,5,5,4,2,2,2,1,1] (.node [13,9,7,6,5,4,4,4,4,2,2,1,1] (.node [13,9,7,5,5,5,5,5,2,2,2,1,1] (.node [13,9,7,5,5,5,5,4,4,2,1,1,1] (.node [13,9,7,5,5,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,7,5,5,5,5,5,4,1,1,1,1] (.node [13,9,7,5,5,5,5,5,3,2,1,1,1] .empty .empty) .empty)) (.node [13,9,7,6,5,5,5,2,2,2,2,2,2] (.node [13,9,7,6,5,5,4,4,4,2,1,1,1] (.node [13,9,7,6,5,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,7,6,5,5,5,3,3,2,2,1,1] .empty .empty))) (.node [13,9,7,6,6,4,4,4,4,2,1,1,1] (.node [13,9,7,6,5,5,5,5,2,2,1,1,1] (.node [13,9,7,6,5,5,5,4,4,1,1,1,1] (.node [13,9,7,6,5,5,5,4,3,2,1,1,1] .empty .empty) .empty) (.node [13,9,7,6,6,4,4,4,3,2,2,1,1] (.node [13,9,7,6,5,5,5,5,3,1,1,1,1] .empty .empty) .empty)) (.node [13,9,7,6,6,5,4,4,2,2,2,1,1] (.node [13,9,7,6,6,5,4,3,3,2,2,1,1] (.node [13,9,7,6,6,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,7,6,6,5,4,4,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_801 : RowTree := (.node [13,9,7,6,6,6,4,3,3,2,1,1,1] (.node [13,9,7,6,6,5,5,5,2,1,1,1,1] (.node [13,9,7,6,6,5,5,3,3,2,1,1,1] (.node [13,9,7,6,6,5,5,3,2,2,2,1,1] (.node [13,9,7,6,6,5,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,7,6,6,5,5,4,3,1,1,1,1] (.node [13,9,7,6,6,5,5,4,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,7,6,6,6,4,2,2,2,2,2,1] (.node [13,9,7,6,6,6,3,3,3,2,2,1,1] (.node [13,9,7,6,6,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,7,6,6,6,4,3,2,2,2,1,1] .empty .empty))) (.node [13,9,7,6,6,6,5,4,2,1,1,1,1] (.node [13,9,7,6,6,6,5,2,2,2,2,1,1] (.node [13,9,7,6,6,6,4,4,3,1,1,1,1] (.node [13,9,7,6,6,6,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,7,6,6,6,5,3,3,1,1,1,1] (.node [13,9,7,6,6,6,5,3,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,4,4,4,4,4,2,2,1,1] (.node [13,9,7,6,6,6,6,3,2,1,1,1,1] (.node [13,9,7,6,6,6,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,5,4,4,4,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_802 : RowTree := (.node [13,9,7,6,6,5,4,4,4,1,1,1,1] degreeTree62_800 degreeTree62_801) - -def degreeTree62_803 : RowTree := (.node [13,9,7,5,5,5,4,4,4,2,2,1,1] degreeTree62_799 degreeTree62_802) - -def degreeTree62_804 : RowTree := (.node [13,9,7,7,5,5,5,5,2,1,1,1,1] (.node [13,9,7,7,5,5,5,2,2,2,2,2,1] (.node [13,9,7,7,5,5,4,4,2,2,2,1,1] (.node [13,9,7,7,5,5,4,3,3,2,2,1,1] (.node [13,9,7,7,5,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,7,7,5,5,4,4,4,1,1,1,1] (.node [13,9,7,7,5,5,4,4,3,2,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,5,5,5,4,2,2,1,1,1] (.node [13,9,7,7,5,5,5,3,3,2,1,1,1] (.node [13,9,7,7,5,5,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,7,7,5,5,5,4,3,1,1,1,1] .empty .empty))) (.node [13,9,7,7,6,5,3,2,2,2,2,2,2] (.node [13,9,7,7,6,4,4,4,2,2,2,1,1] (.node [13,9,7,7,6,4,4,3,3,2,2,1,1] (.node [13,9,7,7,6,4,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,7,7,6,4,4,4,4,1,1,1,1] (.node [13,9,7,7,6,4,4,4,3,2,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,6,5,4,3,2,2,2,1,1] (.node [13,9,7,7,6,5,4,2,2,2,2,2,1] (.node [13,9,7,7,6,5,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,7,7,6,5,4,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_805 : RowTree := (.node [13,9,7,7,6,6,4,3,2,2,1,1,1] (.node [13,9,7,7,6,6,2,2,2,2,2,2,2] (.node [13,9,7,7,6,5,5,3,2,2,1,1,1] (.node [13,9,7,7,6,5,5,2,2,2,2,1,1] (.node [13,9,7,7,6,5,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,6,5,5,4,2,1,1,1,1] (.node [13,9,7,7,6,5,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,6,6,3,3,3,2,1,1,1] (.node [13,9,7,7,6,6,3,3,2,2,2,1,1] (.node [13,9,7,7,6,6,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,7,7,6,6,4,2,2,2,2,1,1] .empty .empty))) (.node [13,9,7,7,6,6,6,2,2,1,1,1,1] (.node [13,9,7,7,6,6,5,2,2,2,1,1,1] (.node [13,9,7,7,6,6,4,4,2,1,1,1,1] (.node [13,9,7,7,6,6,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,6,6,6,2,1,1,1,1,1,1] (.node [13,9,7,7,6,6,5,3,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,7,4,4,2,2,2,2,2,1] (.node [13,9,7,7,7,4,3,3,3,2,2,1,1] (.node [13,9,7,7,7,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,7,7,7,4,4,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_806 : RowTree := (.node [13,9,7,7,6,5,4,4,2,2,1,1,1] degreeTree62_804 degreeTree62_805) - -def degreeTree62_807 : RowTree := (.node [13,9,7,7,7,5,5,2,2,2,1,1,1] (.node [13,9,7,7,7,5,3,3,3,2,1,1,1] (.node [13,9,7,7,7,5,2,2,2,2,2,2,2] (.node [13,9,7,7,7,4,4,4,3,1,1,1,1] (.node [13,9,7,7,7,4,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,7,5,3,3,2,2,2,1,1] (.node [13,9,7,7,7,5,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,9,7,7,7,5,4,3,3,1,1,1,1] (.node [13,9,7,7,7,5,4,3,2,2,1,1,1] (.node [13,9,7,7,7,5,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,7,7,7,5,4,4,2,1,1,1,1] .empty .empty))) (.node [13,9,7,7,7,6,3,3,2,1,1,1,1,1] (.node [13,9,7,7,7,6,2,2,2,2,2,2,1] (.node [13,9,7,7,7,6,2,2,2,2,2,1,1,1] (.node [13,9,7,7,7,5,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,7,6,3,2,2,2,2,1,1] (.node [13,9,7,7,7,6,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,7,6,4,2,2,1,1,1,1,1] (.node [13,9,7,7,7,6,3,3,3,1,1,1,1] (.node [13,9,7,7,7,6,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,7,6,4,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_808 : RowTree := (.node [13,9,7,7,7,7,4,2,1,1,1,1,1,1] (.node [13,9,7,7,7,7,2,2,2,2,2,1,1] (.node [13,9,7,7,7,6,5,2,2,1,1,1,1] (.node [13,9,7,7,7,6,5,2,1,1,1,1,1,1] (.node [13,9,7,7,7,6,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,7,7,2,2,2,2,1,1,1,1] (.node [13,9,7,7,7,6,6,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,7,7,3,3,1,1,1,1,1,1] (.node [13,9,7,7,7,7,3,2,2,2,1,1,1] (.node [13,9,7,7,7,7,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,7,7,3,3,2,1,1,1,1] .empty .empty))) (.node [13,9,8,5,5,5,5,3,3,2,2,1,1] (.node [13,9,8,5,5,5,4,4,3,2,2,1,1] (.node [13,9,8,5,5,4,4,4,4,2,2,1,1] (.node [13,9,7,7,7,7,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,5,5,5,5,2,2,2,2,2,2] (.node [13,9,8,5,5,5,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [13,9,8,5,5,5,5,4,4,1,1,1,1] (.node [13,9,8,5,5,5,5,4,3,2,1,1,1] (.node [13,9,8,5,5,5,5,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,5,5,5,5,5,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_809 : RowTree := (.node [13,9,7,7,7,6,4,3,1,1,1,1,1,1] degreeTree62_807 degreeTree62_808) - -def degreeTree62_810 : RowTree := (.node [13,9,7,7,7,4,4,3,3,2,1,1,1] degreeTree62_806 degreeTree62_809) - -def degreeTree62_811 : RowTree := (.node [13,9,7,7,5,4,4,4,4,2,1,1,1] degreeTree62_803 degreeTree62_810) - -def degreeTree62_812 : RowTree := (.node [13,9,8,6,5,5,5,3,3,2,1,1,1] (.node [13,9,8,6,5,5,4,4,2,2,2,1,1] (.node [13,9,8,6,5,4,4,4,4,2,1,1,1] (.node [13,9,8,6,5,4,4,4,3,2,2,1,1] (.node [13,9,8,6,4,4,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,6,5,5,4,3,3,2,2,1,1] (.node [13,9,8,6,5,5,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,9,8,6,5,5,5,2,2,2,2,2,1] (.node [13,9,8,6,5,5,4,4,4,1,1,1,1] (.node [13,9,8,6,5,5,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,6,5,5,5,3,2,2,2,1,1] .empty .empty))) (.node [13,9,8,6,6,4,4,4,2,2,2,1,1] (.node [13,9,8,6,5,5,5,5,2,1,1,1,1] (.node [13,9,8,6,5,5,5,4,3,1,1,1,1] (.node [13,9,8,6,5,5,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,6,6,4,4,3,3,2,2,1,1] (.node [13,9,8,6,6,4,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,9,8,6,6,5,3,2,2,2,2,2,2] (.node [13,9,8,6,6,4,4,4,4,1,1,1,1] (.node [13,9,8,6,6,4,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,6,6,5,3,3,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_813 : RowTree := (.node [13,9,8,6,6,6,3,3,2,2,2,1,1] (.node [13,9,8,6,6,5,5,3,2,2,1,1,1] (.node [13,9,8,6,6,5,4,4,2,2,1,1,1] (.node [13,9,8,6,6,5,4,3,3,2,1,1,1] (.node [13,9,8,6,6,5,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,6,6,5,5,2,2,2,2,1,1] (.node [13,9,8,6,6,5,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,6,6,6,2,2,2,2,2,2,2] (.node [13,9,8,6,6,5,5,4,2,1,1,1,1] (.node [13,9,8,6,6,5,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,6,6,6,3,2,2,2,2,2,1] .empty .empty))) (.node [13,9,8,6,6,6,5,2,2,2,1,1,1] (.node [13,9,8,6,6,6,4,3,2,2,1,1,1] (.node [13,9,8,6,6,6,4,2,2,2,2,1,1] (.node [13,9,8,6,6,6,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,6,6,6,4,4,2,1,1,1,1] (.node [13,9,8,6,6,6,4,3,3,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,4,4,4,4,3,2,2,1,1] (.node [13,9,8,6,6,6,6,2,1,1,1,1,1,1] (.node [13,9,8,6,6,6,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,4,4,4,4,4,2,1,1,1] .empty .empty)))) - -def degreeTree62_814 : RowTree := (.node [13,9,8,6,6,5,4,2,2,2,2,2,1] degreeTree62_812 degreeTree62_813) - -def degreeTree62_815 : RowTree := (.node [13,9,8,7,5,5,4,4,3,1,1,1,1] (.node [13,9,8,7,5,5,3,3,3,2,2,1,1] (.node [13,9,8,7,5,4,4,4,3,2,1,1,1] (.node [13,9,8,7,5,4,4,4,2,2,2,1,1] (.node [13,9,8,7,5,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,7,5,5,3,2,2,2,2,2,2] (.node [13,9,8,7,5,4,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,5,5,4,3,3,2,1,1,1] (.node [13,9,8,7,5,5,4,3,2,2,2,1,1] (.node [13,9,8,7,5,5,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,8,7,5,5,4,4,2,2,1,1,1] .empty .empty))) (.node [13,9,8,7,6,4,3,3,3,2,2,1,1] (.node [13,9,8,7,5,5,5,3,3,1,1,1,1] (.node [13,9,8,7,5,5,5,3,2,2,1,1,1] (.node [13,9,8,7,5,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,7,6,4,3,2,2,2,2,2,2] (.node [13,9,8,7,5,5,5,4,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,6,4,4,3,3,2,1,1,1] (.node [13,9,8,7,6,4,4,3,2,2,2,1,1] (.node [13,9,8,7,6,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,8,7,6,4,4,4,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_816 : RowTree := (.node [13,9,8,7,6,6,2,2,2,2,2,1,1,1] (.node [13,9,8,7,6,5,4,3,2,2,1,1,1] (.node [13,9,8,7,6,5,3,3,2,2,2,1,1] (.node [13,9,8,7,6,5,3,2,2,2,2,2,1] (.node [13,9,8,7,6,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,8,7,6,5,4,2,2,2,2,1,1] (.node [13,9,8,7,6,5,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,6,5,5,2,2,2,1,1,1] (.node [13,9,8,7,6,5,4,4,2,1,1,1,1] (.node [13,9,8,7,6,5,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,6,5,5,3,2,1,1,1,1] .empty .empty))) (.node [13,9,8,7,6,6,3,3,3,1,1,1,1] (.node [13,9,8,7,6,6,3,2,2,2,2,1,1] (.node [13,9,8,7,6,6,3,2,2,2,1,1,1,1] (.node [13,9,8,7,6,6,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,8,7,6,6,3,3,2,2,1,1,1] (.node [13,9,8,7,6,6,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,6,6,4,3,1,1,1,1,1,1] (.node [13,9,8,7,6,6,4,2,2,2,1,1,1] (.node [13,9,8,7,6,6,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,6,6,4,3,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_817 : RowTree := (.node [13,9,8,7,6,4,4,4,3,1,1,1,1] degreeTree62_815 degreeTree62_816) - -def degreeTree62_818 : RowTree := (.node [13,9,8,7,5,4,4,2,2,2,2,2,2] degreeTree62_814 degreeTree62_817) - -def degreeTree62_819 : RowTree := (.node [13,9,8,7,7,4,4,2,2,2,2,1,1] (.node [13,9,8,7,7,4,3,2,2,2,2,2,1] (.node [13,9,8,7,7,3,3,3,3,2,2,1,1] (.node [13,9,8,7,7,3,3,2,2,2,2,2,2] (.node [13,9,8,7,6,6,6,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,7,4,3,2,2,2,2,1,1,1] (.node [13,9,8,7,7,4,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,9,8,7,7,4,3,3,3,2,1,1,1] (.node [13,9,8,7,7,4,3,3,3,1,1,1,1,1] (.node [13,9,8,7,7,4,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,7,7,4,4,2,2,2,1,1,1,1] .empty .empty))) (.node [13,9,8,7,7,5,2,2,2,2,2,1,1,1] (.node [13,9,8,7,7,4,4,3,3,1,1,1,1] (.node [13,9,8,7,7,4,4,3,2,2,1,1,1] (.node [13,9,8,7,7,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,7,4,4,4,2,1,1,1,1] (.node [13,9,8,7,7,4,4,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,7,5,3,2,2,2,2,1,1] (.node [13,9,8,7,7,5,3,2,2,2,1,1,1,1] (.node [13,9,8,7,7,5,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,8,7,7,5,3,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_820 : RowTree := (.node [13,9,8,7,7,6,4,2,1,1,1,1,1,1] (.node [13,9,8,7,7,6,2,2,2,2,1,1,1,1] (.node [13,9,8,7,7,5,4,2,2,2,1,1,1] (.node [13,9,8,7,7,5,4,2,2,1,1,1,1,1] (.node [13,9,8,7,7,5,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,7,5,5,2,1,1,1,1,1,1] (.node [13,9,8,7,7,5,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,7,6,3,2,2,2,1,1,1] (.node [13,9,8,7,7,6,3,2,2,1,1,1,1,1] (.node [13,9,8,7,7,6,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,7,7,6,3,3,1,1,1,1,1,1] .empty .empty))) (.node [13,9,8,8,4,4,4,2,2,2,2,2,2] (.node [13,9,8,7,7,7,2,2,2,2,1,1,1] (.node [13,9,8,7,7,7,2,2,2,1,1,1,1,1] (.node [13,9,8,7,7,6,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,7,7,4,1,1,1,1,1,1,1] (.node [13,9,8,7,7,7,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,4,4,4,4,3,2,1,1,1] (.node [13,9,8,8,4,4,4,4,2,2,2,1,1] (.node [13,9,8,8,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,8,4,4,4,4,4,1,1,1,1] .empty .empty)))) - -def degreeTree62_821 : RowTree := (.node [13,9,8,7,7,5,3,3,2,2,1,1,1] degreeTree62_819 degreeTree62_820) - -def degreeTree62_822 : RowTree := (.node [13,9,8,8,5,5,4,2,2,2,2,1,1] (.node [13,9,8,8,5,4,4,4,3,1,1,1,1] (.node [13,9,8,8,5,4,4,3,2,2,2,1,1] (.node [13,9,8,8,5,4,4,2,2,2,2,2,1] (.node [13,9,8,8,5,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,8,5,4,4,4,2,2,1,1,1] (.node [13,9,8,8,5,4,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,5,5,3,3,2,2,2,1,1] (.node [13,9,8,8,5,5,3,2,2,2,2,2,1] (.node [13,9,8,8,5,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,8,8,5,5,3,3,3,2,1,1,1] .empty .empty))) (.node [13,9,8,8,6,3,3,3,3,2,2,1,1] (.node [13,9,8,8,5,5,4,4,2,1,1,1,1] (.node [13,9,8,8,5,5,4,3,3,1,1,1,1] (.node [13,9,8,8,5,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,6,3,3,2,2,2,2,2,2] (.node [13,9,8,8,5,5,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,6,4,3,2,2,2,2,2,1] (.node [13,9,8,8,6,4,3,2,2,2,2,1,1,1] (.node [13,9,8,8,6,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,8,8,6,4,3,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_823 : RowTree := (.node [13,9,8,8,6,5,3,2,2,2,2,1,1] (.node [13,9,8,8,6,4,4,3,3,1,1,1,1] (.node [13,9,8,8,6,4,4,2,2,2,2,1,1] (.node [13,9,8,8,6,4,4,2,2,2,1,1,1,1] (.node [13,9,8,8,6,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,6,4,4,3,2,2,1,1,1] (.node [13,9,8,8,6,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,6,5,2,2,2,2,2,2,1] (.node [13,9,8,8,6,5,2,2,2,2,2,1,1,1] (.node [13,9,8,8,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,6,5,3,2,2,2,1,1,1,1] .empty .empty))) (.node [13,9,8,8,6,5,4,2,2,2,1,1,1] (.node [13,9,8,8,6,5,3,3,3,1,1,1,1] (.node [13,9,8,8,6,5,3,3,2,2,1,1,1] (.node [13,9,8,8,6,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,6,5,4,2,2,1,1,1,1,1] .empty .empty)) (.node [13,9,8,8,6,6,2,2,2,2,1,1,1,1] (.node [13,9,8,8,6,5,5,2,1,1,1,1,1,1] (.node [13,9,8,8,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,6,6,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_824 : RowTree := (.node [13,9,8,8,6,4,3,3,3,1,1,1,1,1] degreeTree62_822 degreeTree62_823) - -def degreeTree62_825 : RowTree := (.node [13,9,8,8,5,4,3,2,2,2,2,2,2] degreeTree62_821 degreeTree62_824) - -def degreeTree62_826 : RowTree := (.node [13,9,8,7,6,6,5,2,1,1,1,1,1,1] degreeTree62_818 degreeTree62_825) - -def degreeTree62_827 : RowTree := (.node [13,9,8,5,5,5,5,5,3,1,1,1,1] degreeTree62_811 degreeTree62_826) - -def degreeTree62_828 : RowTree := (.node [13,8,8,8,8,6,3,2,1,1,1,1,1,1] degreeTree62_796 degreeTree62_827) - -def degreeTree62_829 : RowTree := (.node [13,9,8,8,7,3,3,3,3,2,1,1,1] (.node [13,9,8,8,7,3,2,2,2,2,2,2,2] (.node [13,9,8,8,6,6,4,2,1,1,1,1,1,1] (.node [13,9,8,8,6,6,3,3,1,1,1,1,1,1] (.node [13,9,8,8,6,6,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,7,2,2,2,2,2,2,2,2,1] (.node [13,9,8,8,6,6,5,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,7,3,3,3,2,2,2,1,1] (.node [13,9,8,8,7,3,3,2,2,2,2,2,1] (.node [13,9,8,8,7,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,7,3,3,3,3,1,1,1,1,1] .empty .empty))) (.node [13,9,8,8,7,4,3,3,2,2,1,1,1] (.node [13,9,8,8,7,4,3,2,2,2,1,1,1,1] (.node [13,9,8,8,7,4,2,2,2,2,2,2,1] (.node [13,9,8,8,7,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,7,4,3,3,2,1,1,1,1,1] (.node [13,9,8,8,7,4,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,9,8,8,7,4,4,2,2,2,1,1,1] (.node [13,9,8,8,7,4,4,2,2,1,1,1,1,1] (.node [13,9,8,8,7,4,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,7,4,4,3,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_830 : RowTree := (.node [13,9,8,8,7,7,2,2,1,1,1,1,1,1] (.node [13,9,8,8,7,5,5,1,1,1,1,1,1,1] (.node [13,9,8,8,7,5,3,2,2,2,1,1,1] (.node [13,9,8,8,7,5,3,2,2,1,1,1,1,1] (.node [13,9,8,8,7,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,8,7,5,4,2,1,1,1,1,1,1] (.node [13,9,8,8,7,5,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,7,6,3,2,1,1,1,1,1,1] (.node [13,9,8,8,7,6,2,2,2,2,1,1,1] (.node [13,9,8,8,7,6,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,7,6,4,1,1,1,1,1,1,1] .empty .empty))) (.node [13,9,8,8,8,3,3,2,2,2,1,1,1,1] (.node [13,9,8,8,8,2,2,2,2,2,2,2,2] (.node [13,9,8,8,8,2,2,2,2,2,2,2,1,1] (.node [13,9,8,8,7,7,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,8,3,2,2,2,2,2,2,1] (.node [13,9,8,8,8,3,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,8,3,3,3,2,2,1,1,1] (.node [13,9,8,8,8,3,3,3,2,1,1,1,1,1] (.node [13,9,8,8,8,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,8,8,3,3,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_831 : RowTree := (.node [13,9,8,8,7,5,2,2,2,2,1,1,1,1] degreeTree62_829 degreeTree62_830) - -def degreeTree62_832 : RowTree := (.node [13,9,8,8,8,6,3,1,1,1,1,1,1,1] (.node [13,9,8,8,8,5,2,2,2,1,1,1,1,1] (.node [13,9,8,8,8,4,3,2,2,2,1,1,1] (.node [13,9,8,8,8,4,3,2,2,1,1,1,1,1] (.node [13,9,8,8,8,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,8,8,4,4,2,1,1,1,1,1,1] (.node [13,9,8,8,8,4,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,8,5,4,1,1,1,1,1,1,1] (.node [13,9,8,8,8,5,3,2,1,1,1,1,1,1] (.node [13,9,8,8,8,5,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,8,6,2,2,1,1,1,1,1,1] .empty .empty))) (.node [13,9,9,5,5,5,4,2,2,2,2,2,2] (.node [13,9,9,5,4,4,4,4,4,2,2,1,1] (.node [13,9,8,8,8,8,1,1,1,1,1,1,1,1] (.node [13,9,8,8,8,7,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,5,5,4,4,4,4,2,1,1,1] (.node [13,9,9,5,5,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [13,9,9,5,5,5,4,4,3,2,1,1,1] (.node [13,9,9,5,5,5,4,4,2,2,2,1,1] (.node [13,9,9,5,5,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,5,5,5,4,4,4,1,1,1,1] .empty .empty)))) - -def degreeTree62_833 : RowTree := (.node [13,9,9,6,5,4,4,4,4,1,1,1,1] (.node [13,9,9,6,4,4,4,4,4,2,1,1,1] (.node [13,9,9,5,5,5,5,4,2,2,1,1,1] (.node [13,9,9,5,5,5,5,3,3,2,1,1,1] (.node [13,9,9,5,5,5,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,6,4,4,4,4,3,2,2,1,1] (.node [13,9,9,5,5,5,5,4,3,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,6,5,4,4,4,2,2,2,1,1] (.node [13,9,9,6,5,4,4,3,3,2,2,1,1] (.node [13,9,9,6,5,4,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,9,6,5,4,4,4,3,2,1,1,1] .empty .empty))) (.node [13,9,9,6,5,5,4,4,2,2,1,1,1] (.node [13,9,9,6,5,5,4,2,2,2,2,2,1] (.node [13,9,9,6,5,5,3,3,3,2,2,1,1] (.node [13,9,9,6,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,9,6,5,5,4,3,3,2,1,1,1] (.node [13,9,9,6,5,5,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [13,9,9,6,5,5,5,3,2,2,1,1,1] (.node [13,9,9,6,5,5,5,2,2,2,2,1,1] (.node [13,9,9,6,5,5,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,6,5,5,5,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_834 : RowTree := (.node [13,9,9,5,5,5,5,2,2,2,2,2,1] degreeTree62_832 degreeTree62_833) - -def degreeTree62_835 : RowTree := (.node [13,9,8,8,8,4,2,2,2,2,1,1,1,1] degreeTree62_831 degreeTree62_834) - -def degreeTree62_836 : RowTree := (.node [13,9,9,6,6,5,4,2,2,2,2,1,1] (.node [13,9,9,6,6,4,4,4,3,1,1,1,1] (.node [13,9,9,6,6,4,4,3,2,2,2,1,1] (.node [13,9,9,6,6,4,4,2,2,2,2,2,1] (.node [13,9,9,6,6,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,6,6,4,4,4,2,2,1,1,1] (.node [13,9,9,6,6,4,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,6,6,5,3,3,2,2,2,1,1] (.node [13,9,9,6,6,5,3,2,2,2,2,2,1] (.node [13,9,9,6,6,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,9,6,6,5,3,3,3,2,1,1,1] .empty .empty))) (.node [13,9,9,6,6,6,3,2,2,2,1,1,1,1] (.node [13,9,9,6,6,5,5,2,2,2,1,1,1] (.node [13,9,9,6,6,5,4,3,3,1,1,1,1] (.node [13,9,9,6,6,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,6,6,6,2,2,2,2,2,2,1] (.node [13,9,9,6,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,6,6,6,3,3,2,2,1,1,1] (.node [13,9,9,6,6,6,3,3,2,1,1,1,1,1] (.node [13,9,9,6,6,6,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,6,6,6,3,3,3,1,1,1,1] .empty .empty)))) - -def degreeTree62_837 : RowTree := (.node [13,9,9,7,5,4,3,3,3,2,2,1,1] (.node [13,9,9,7,4,4,4,3,3,2,2,1,1] (.node [13,9,9,6,6,6,5,2,1,1,1,1,1,1] (.node [13,9,9,6,6,6,4,3,1,1,1,1,1,1] (.node [13,9,9,6,6,6,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,4,4,4,2,2,2,2,2,2] (.node [13,9,9,6,6,6,6,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,7,4,4,4,4,4,1,1,1,1] (.node [13,9,9,7,4,4,4,4,3,2,1,1,1] (.node [13,9,9,7,4,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,7,5,4,3,2,2,2,2,2,2] .empty .empty))) (.node [13,9,9,7,5,5,2,2,2,2,2,2,2] (.node [13,9,9,7,5,4,4,3,3,2,1,1,1] (.node [13,9,9,7,5,4,4,3,2,2,2,1,1] (.node [13,9,9,7,5,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,9,7,5,4,4,4,3,1,1,1,1] (.node [13,9,9,7,5,4,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,7,5,5,3,3,3,2,1,1,1] (.node [13,9,9,7,5,5,3,3,2,2,2,1,1] (.node [13,9,9,7,5,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,9,7,5,5,4,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_838 : RowTree := (.node [13,9,9,6,6,6,4,2,2,1,1,1,1,1] degreeTree62_836 degreeTree62_837) - -def degreeTree62_839 : RowTree := (.node [13,9,9,7,6,4,4,2,2,2,1,1,1,1] (.node [13,9,9,7,6,4,3,2,2,2,2,1,1,1] (.node [13,9,9,7,6,3,3,2,2,2,2,2,2] (.node [13,9,9,7,5,5,5,2,2,2,1,1,1] (.node [13,9,9,7,5,5,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,6,4,2,2,2,2,2,2,2] (.node [13,9,9,7,6,3,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,9,9,7,6,4,3,3,3,1,1,1,1,1] (.node [13,9,9,7,6,4,3,3,2,2,2,1,1] (.node [13,9,9,7,6,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,9,7,6,4,3,3,3,2,1,1,1] .empty .empty))) (.node [13,9,9,7,6,5,2,2,2,2,2,2,1] (.node [13,9,9,7,6,4,4,3,2,2,1,1,1] (.node [13,9,9,7,6,4,4,3,2,1,1,1,1,1] (.node [13,9,9,7,6,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,7,6,5,2,2,2,2,2,1,1,1] (.node [13,9,9,7,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,7,6,5,3,3,2,1,1,1,1,1] (.node [13,9,9,7,6,5,3,2,2,2,2,1,1] (.node [13,9,9,7,6,5,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,6,5,3,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_840 : RowTree := (.node [13,9,9,7,7,2,2,2,2,2,2,2,2,1] (.node [13,9,9,7,6,6,3,2,2,1,1,1,1,1] (.node [13,9,9,7,6,5,5,2,1,1,1,1,1,1] (.node [13,9,9,7,6,5,4,3,1,1,1,1,1,1] (.node [13,9,9,7,6,5,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,6,6,2,2,2,2,2,1,1] (.node [13,9,9,7,6,6,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,7,6,6,4,2,1,1,1,1,1,1] (.node [13,9,9,7,6,6,3,3,1,1,1,1,1,1] (.node [13,9,9,7,6,6,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,6,6,5,1,1,1,1,1,1,1] .empty .empty))) (.node [13,9,9,7,7,3,3,3,3,2,1,1,1] (.node [13,9,9,7,7,3,3,2,2,2,2,2,1] (.node [13,9,9,7,7,3,3,2,2,2,2,1,1,1] (.node [13,9,9,7,7,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,9,7,7,3,3,3,3,1,1,1,1,1] (.node [13,9,9,7,7,3,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [13,9,9,7,7,4,3,2,2,2,1,1,1,1] (.node [13,9,9,7,7,4,2,2,2,2,2,2,1] (.node [13,9,9,7,7,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,7,4,3,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_841 : RowTree := (.node [13,9,9,7,6,5,4,2,2,1,1,1,1,1] degreeTree62_839 degreeTree62_840) - -def degreeTree62_842 : RowTree := (.node [13,9,9,7,5,5,4,3,2,2,1,1,1] degreeTree62_838 degreeTree62_841) - -def degreeTree62_843 : RowTree := (.node [13,9,9,6,6,4,3,2,2,2,2,2,2] degreeTree62_835 degreeTree62_842) - -def degreeTree62_844 : RowTree := (.node [13,9,9,7,7,5,5,1,1,1,1,1,1,1] (.node [13,9,9,7,7,5,2,2,2,2,2,1,1] (.node [13,9,9,7,7,4,4,2,2,2,1,1,1] (.node [13,9,9,7,7,4,4,2,2,1,1,1,1,1] (.node [13,9,9,7,7,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,7,5,2,2,2,2,1,1,1,1] (.node [13,9,9,7,7,4,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,7,7,5,3,3,1,1,1,1,1,1] (.node [13,9,9,7,7,5,3,2,2,2,1,1,1] (.node [13,9,9,7,7,5,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,7,5,4,2,1,1,1,1,1,1] .empty .empty))) (.node [13,9,9,7,7,7,3,1,1,1,1,1,1,1] (.node [13,9,9,7,7,6,3,2,1,1,1,1,1,1] (.node [13,9,9,7,7,6,2,2,2,2,1,1,1] (.node [13,9,9,7,7,6,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,7,7,2,2,1,1,1,1,1,1] (.node [13,9,9,7,7,6,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,8,4,4,4,2,2,2,2,1,1,1] (.node [13,9,9,8,4,4,3,3,3,2,2,1,1] (.node [13,9,9,8,4,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,9,8,4,4,4,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_845 : RowTree := (.node [13,9,9,8,5,4,3,3,2,2,2,1,1] (.node [13,9,9,8,5,3,3,2,2,2,2,2,2] (.node [13,9,9,8,4,4,4,4,2,1,1,1,1,1] (.node [13,9,9,8,4,4,4,3,3,2,1,1,1] (.node [13,9,9,8,4,4,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,4,4,4,4,3,1,1,1,1] (.node [13,9,9,8,4,4,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,8,5,4,3,2,2,2,2,1,1,1] (.node [13,9,9,8,5,4,2,2,2,2,2,2,2] (.node [13,9,9,8,5,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,8,5,4,3,2,2,2,2,2,1] .empty .empty))) (.node [13,9,9,8,5,4,4,3,2,2,1,1,1] (.node [13,9,9,8,5,4,4,2,2,2,1,1,1,1] (.node [13,9,9,8,5,4,3,3,3,2,1,1,1] (.node [13,9,9,8,5,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,5,4,4,3,2,1,1,1,1,1] (.node [13,9,9,8,5,4,4,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,9,9,8,5,5,2,2,2,2,2,2,1] (.node [13,9,9,8,5,5,2,2,2,2,2,1,1,1] (.node [13,9,9,8,5,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,5,5,3,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_846 : RowTree := (.node [13,9,9,8,4,4,4,3,2,2,2,1,1] degreeTree62_844 degreeTree62_845) - -def degreeTree62_847 : RowTree := (.node [13,9,9,8,6,3,3,3,2,2,2,1,1] (.node [13,9,9,8,5,5,5,2,1,1,1,1,1,1] (.node [13,9,9,8,5,5,4,2,2,1,1,1,1,1] (.node [13,9,9,8,5,5,3,3,2,2,1,1,1] (.node [13,9,9,8,5,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,5,5,4,3,1,1,1,1,1,1] (.node [13,9,9,8,5,5,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,8,6,3,3,2,2,2,2,1,1,1] (.node [13,9,9,8,6,3,2,2,2,2,2,2,2] (.node [13,9,9,8,6,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,9,8,6,3,3,2,2,2,2,2,1] .empty .empty))) (.node [13,9,9,8,6,4,3,2,2,2,2,1,1] (.node [13,9,9,8,6,4,2,2,2,2,2,1,1,1] (.node [13,9,9,8,6,3,3,3,3,2,1,1,1] (.node [13,9,9,8,6,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,6,4,3,2,2,2,1,1,1,1] (.node [13,9,9,8,6,4,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,9,9,8,6,4,4,2,2,1,1,1,1,1] (.node [13,9,9,8,6,4,3,3,2,2,1,1,1] (.node [13,9,9,8,6,4,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,6,4,4,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_848 : RowTree := (.node [13,9,9,8,6,6,4,1,1,1,1,1,1,1] (.node [13,9,9,8,6,5,4,2,1,1,1,1,1,1] (.node [13,9,9,8,6,5,3,2,2,1,1,1,1,1] (.node [13,9,9,8,6,5,2,2,2,2,2,1,1] (.node [13,9,9,8,6,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,6,5,3,3,1,1,1,1,1,1] (.node [13,9,9,8,6,5,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,8,6,6,2,2,2,2,1,1,1] (.node [13,9,9,8,6,6,2,2,2,1,1,1,1,1] (.node [13,9,9,8,6,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,6,6,3,2,1,1,1,1,1,1] .empty .empty))) (.node [13,9,9,8,7,3,3,2,2,2,2,1,1] (.node [13,9,9,8,7,3,2,2,2,2,2,1,1,1] (.node [13,9,9,8,7,2,2,2,2,2,2,2,2] (.node [13,9,9,8,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,8,7,3,3,2,2,2,1,1,1,1] (.node [13,9,9,8,7,3,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,9,9,8,7,4,2,2,2,2,1,1,1,1] (.node [13,9,9,8,7,3,3,3,2,2,1,1,1] (.node [13,9,9,8,7,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,7,4,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_849 : RowTree := (.node [13,9,9,8,6,4,4,3,1,1,1,1,1,1] degreeTree62_847 degreeTree62_848) - -def degreeTree62_850 : RowTree := (.node [13,9,9,8,5,5,3,2,2,2,2,1,1] degreeTree62_846 degreeTree62_849) - -def degreeTree62_851 : RowTree := (.node [13,9,9,8,8,2,2,2,2,2,2,1,1,1] (.node [13,9,9,8,7,5,3,2,1,1,1,1,1,1] (.node [13,9,9,8,7,4,4,2,1,1,1,1,1,1] (.node [13,9,9,8,7,4,3,3,1,1,1,1,1,1] (.node [13,9,9,8,7,4,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,7,5,2,2,2,2,1,1,1] (.node [13,9,9,8,7,5,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,8,7,6,3,1,1,1,1,1,1,1] (.node [13,9,9,8,7,6,2,2,1,1,1,1,1,1] (.node [13,9,9,8,7,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,7,7,2,1,1,1,1,1,1,1] .empty .empty))) (.node [13,9,9,8,8,3,3,3,1,1,1,1,1,1] (.node [13,9,9,8,8,3,2,2,2,2,2,1,1] (.node [13,9,9,8,8,3,2,2,2,2,1,1,1,1] (.node [13,9,9,8,8,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,9,8,8,3,3,2,2,2,1,1,1] (.node [13,9,9,8,8,3,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,8,8,4,3,2,1,1,1,1,1,1] (.node [13,9,9,8,8,4,2,2,2,2,1,1,1] (.node [13,9,9,8,8,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,8,4,4,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_852 : RowTree := (.node [13,9,9,9,4,4,3,3,3,2,1,1,1] (.node [13,9,9,9,4,4,2,2,2,2,2,2,2] (.node [13,9,9,8,8,7,1,1,1,1,1,1,1,1] (.node [13,9,9,8,8,6,2,1,1,1,1,1,1,1] (.node [13,9,9,8,8,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,4,3,3,3,3,2,2,1,1] (.node [13,9,9,9,4,3,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,9,9,9,4,4,3,3,2,2,2,1,1] (.node [13,9,9,9,4,4,3,2,2,2,2,2,1] (.node [13,9,9,9,4,4,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,4,4,3,3,3,1,1,1,1,1] .empty .empty))) (.node [13,9,9,9,5,2,2,2,2,2,2,2,2,1] (.node [13,9,9,9,4,4,4,3,2,1,1,1,1,1] (.node [13,9,9,9,4,4,4,2,2,2,2,1,1] (.node [13,9,9,9,4,4,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,4,4,4,4,1,1,1,1,1,1] (.node [13,9,9,9,4,4,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,9,5,3,3,2,2,2,2,2,1] (.node [13,9,9,9,5,3,3,2,2,2,2,1,1,1] (.node [13,9,9,9,5,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,9,9,5,3,3,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_853 : RowTree := (.node [13,9,9,8,8,5,2,2,1,1,1,1,1,1] degreeTree62_851 degreeTree62_852) - -def degreeTree62_854 : RowTree := (.node [13,9,9,9,5,5,2,2,2,2,1,1,1,1] (.node [13,9,9,9,5,4,3,3,2,1,1,1,1,1] (.node [13,9,9,9,5,4,2,2,2,2,2,2,1] (.node [13,9,9,9,5,4,2,2,2,2,2,1,1,1] (.node [13,9,9,9,5,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,5,4,3,2,2,2,2,1,1] (.node [13,9,9,9,5,4,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,9,5,4,4,2,2,2,1,1,1] (.node [13,9,9,9,5,4,4,2,2,1,1,1,1,1] (.node [13,9,9,9,5,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,5,4,4,3,1,1,1,1,1,1] .empty .empty))) (.node [13,9,9,9,5,5,5,1,1,1,1,1,1,1] (.node [13,9,9,9,5,5,3,2,2,2,1,1,1] (.node [13,9,9,9,5,5,3,2,2,1,1,1,1,1] (.node [13,9,9,9,5,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,9,5,5,4,2,1,1,1,1,1,1] (.node [13,9,9,9,5,5,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,9,6,3,2,2,2,2,2,1,1,1] (.node [13,9,9,9,6,2,2,2,2,2,2,2,2] (.node [13,9,9,9,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,9,6,3,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_855 : RowTree := (.node [13,9,9,9,6,5,2,2,2,2,1,1,1] (.node [13,9,9,9,6,4,3,2,2,1,1,1,1,1] (.node [13,9,9,9,6,3,3,3,2,2,1,1,1] (.node [13,9,9,9,6,3,3,3,2,1,1,1,1,1] (.node [13,9,9,9,6,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,9,6,4,2,2,2,2,2,1,1] (.node [13,9,9,9,6,4,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,9,6,4,4,2,1,1,1,1,1,1] (.node [13,9,9,9,6,4,3,3,1,1,1,1,1,1] (.node [13,9,9,9,6,4,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,6,5,2,2,2,1,1,1,1,1] .empty .empty))) (.node [13,9,9,9,7,2,2,2,2,2,2,1,1,1] (.node [13,9,9,9,6,6,2,2,1,1,1,1,1,1] (.node [13,9,9,9,6,5,4,1,1,1,1,1,1,1] (.node [13,9,9,9,6,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,6,6,3,1,1,1,1,1,1,1] .empty .empty)) (.node [13,9,9,9,7,3,2,2,2,2,2,1,1] (.node [13,9,9,9,7,3,2,2,2,2,1,1,1,1] (.node [13,9,9,9,7,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,9,9,7,3,3,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_856 : RowTree := (.node [13,9,9,9,6,3,3,2,2,2,1,1,1,1] degreeTree62_854 degreeTree62_855) - -def degreeTree62_857 : RowTree := (.node [13,9,9,9,5,3,3,3,3,1,1,1,1,1] degreeTree62_853 degreeTree62_856) - -def degreeTree62_858 : RowTree := (.node [13,9,9,8,7,4,3,2,2,1,1,1,1,1] degreeTree62_850 degreeTree62_857) - -def degreeTree62_859 : RowTree := (.node [13,9,9,7,7,4,3,3,2,1,1,1,1,1] degreeTree62_843 degreeTree62_858) - -def degreeTree62_860 : RowTree := (.node [13,9,9,9,8,2,2,2,2,2,2,1,1] (.node [13,9,9,9,7,5,2,2,1,1,1,1,1,1] (.node [13,9,9,9,7,4,2,2,2,2,1,1,1] (.node [13,9,9,9,7,4,2,2,2,1,1,1,1,1] (.node [13,9,9,9,7,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,7,4,4,1,1,1,1,1,1,1] (.node [13,9,9,9,7,4,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,9,7,7,1,1,1,1,1,1,1,1] (.node [13,9,9,9,7,6,2,1,1,1,1,1,1,1] (.node [13,9,9,9,7,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,8,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [13,9,9,9,8,5,2,1,1,1,1,1,1,1] (.node [13,9,9,9,8,3,3,2,1,1,1,1,1,1] (.node [13,9,9,9,8,3,2,2,2,2,1,1,1] (.node [13,9,9,9,8,3,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,8,4,3,1,1,1,1,1,1,1] (.node [13,9,9,9,8,4,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,9,9,2,2,2,2,2,1,1,1] (.node [13,9,9,9,9,2,2,2,2,1,1,1,1,1] (.node [13,9,9,9,8,6,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,9,3,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_861 : RowTree := (.node [13,10,6,6,5,4,4,4,4,2,2,1,1] (.node [13,10,6,5,5,5,4,4,4,2,2,1,1] (.node [13,10,5,5,5,5,5,4,4,2,2,1,1] (.node [13,9,9,9,9,5,1,1,1,1,1,1,1,1] (.node [13,9,9,9,9,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,5,5,5,5,5,5,4,2,1,1,1] (.node [13,10,5,5,5,5,5,5,3,2,2,1,1] .empty .empty) .empty)) (.node [13,10,6,5,5,5,5,5,2,2,2,1,1] (.node [13,10,6,5,5,5,5,4,4,2,1,1,1] (.node [13,10,6,5,5,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,6,5,5,5,5,5,3,2,1,1,1] .empty .empty))) (.node [13,10,6,6,5,5,5,4,3,2,1,1,1] (.node [13,10,6,6,5,5,5,2,2,2,2,2,2] (.node [13,10,6,6,5,5,4,4,4,2,1,1,1] (.node [13,10,6,6,5,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,6,6,5,5,5,4,2,2,2,1,1] (.node [13,10,6,6,5,5,5,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,10,6,6,6,4,4,4,4,2,1,1,1] (.node [13,10,6,6,6,4,4,4,3,2,2,1,1] (.node [13,10,6,6,5,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,6,6,6,5,4,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_862 : RowTree := (.node [13,9,9,9,9,3,3,1,1,1,1,1,1,1] degreeTree62_860 degreeTree62_861) - -def degreeTree62_863 : RowTree := (.node [13,10,6,6,6,6,4,3,3,2,1,1,1] (.node [13,10,6,6,6,5,5,4,2,2,1,1,1] (.node [13,10,6,6,6,5,5,2,2,2,2,2,1] (.node [13,10,6,6,6,5,4,4,3,2,1,1,1] (.node [13,10,6,6,6,5,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,6,6,6,5,5,3,3,2,1,1,1] (.node [13,10,6,6,6,5,5,3,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,6,6,6,6,4,2,2,2,2,2,1] (.node [13,10,6,6,6,6,3,3,3,2,2,1,1] (.node [13,10,6,6,6,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,10,6,6,6,6,4,3,2,2,2,1,1] .empty .empty))) (.node [13,10,7,5,5,5,4,4,3,2,2,1,1] (.node [13,10,6,6,6,6,5,3,2,2,1,1,1] (.node [13,10,6,6,6,6,5,2,2,2,2,1,1] (.node [13,10,6,6,6,6,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,5,5,4,4,4,4,2,2,1,1] (.node [13,10,6,6,6,6,6,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,10,7,5,5,5,5,3,3,2,2,1,1] (.node [13,10,7,5,5,5,5,2,2,2,2,2,2] (.node [13,10,7,5,5,5,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,5,5,5,5,4,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_864 : RowTree := (.node [13,10,7,6,5,5,5,3,3,2,1,1,1] (.node [13,10,7,6,5,5,4,3,3,2,2,1,1] (.node [13,10,7,6,5,4,4,4,3,2,2,1,1] (.node [13,10,7,6,4,4,4,4,4,2,2,1,1] (.node [13,10,7,5,5,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,6,5,5,4,2,2,2,2,2,2] (.node [13,10,7,6,5,4,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [13,10,7,6,5,5,5,2,2,2,2,2,1] (.node [13,10,7,6,5,5,4,4,3,2,1,1,1] (.node [13,10,7,6,5,5,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,7,6,5,5,5,3,2,2,2,1,1] .empty .empty))) (.node [13,10,7,6,6,5,3,2,2,2,2,2,2] (.node [13,10,7,6,6,4,4,3,3,2,2,1,1] (.node [13,10,7,6,6,4,4,2,2,2,2,2,2] (.node [13,10,7,6,5,5,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,6,6,4,4,4,3,2,1,1,1] (.node [13,10,7,6,6,4,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,7,6,6,5,4,3,2,2,2,1,1] (.node [13,10,7,6,6,5,4,2,2,2,2,2,1] (.node [13,10,7,6,6,5,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,7,6,6,5,4,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_865 : RowTree := (.node [13,10,7,5,5,5,5,4,3,2,1,1,1] degreeTree62_863 degreeTree62_864) - -def degreeTree62_866 : RowTree := (.node [13,10,6,6,6,5,4,3,3,2,2,1,1] degreeTree62_862 degreeTree62_865) - -def degreeTree62_867 : RowTree := (.node [13,10,7,7,4,4,4,4,3,2,2,1,1] (.node [13,10,7,6,6,6,3,3,3,2,1,1,1] (.node [13,10,7,6,6,6,2,2,2,2,2,2,2] (.node [13,10,7,6,6,5,5,3,2,2,1,1,1] (.node [13,10,7,6,6,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,7,6,6,6,3,3,2,2,2,1,1] (.node [13,10,7,6,6,6,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,10,7,6,6,6,5,2,2,2,1,1,1] (.node [13,10,7,6,6,6,4,3,2,2,1,1,1] (.node [13,10,7,6,6,6,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,7,6,6,6,6,2,1,1,1,1,1,1] .empty .empty))) (.node [13,10,7,7,5,5,3,2,2,2,2,2,2] (.node [13,10,7,7,5,4,4,3,3,2,2,1,1] (.node [13,10,7,7,5,4,4,2,2,2,2,2,2] (.node [13,10,7,7,4,4,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,5,4,4,4,3,2,1,1,1] (.node [13,10,7,7,5,4,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,7,7,5,5,4,3,2,2,2,1,1] (.node [13,10,7,7,5,5,4,2,2,2,2,2,1] (.node [13,10,7,7,5,5,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,7,7,5,5,4,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_868 : RowTree := (.node [13,10,7,7,6,5,3,3,2,2,2,1,1] (.node [13,10,7,7,6,4,4,3,2,2,2,1,1] (.node [13,10,7,7,6,4,3,2,2,2,2,2,2] (.node [13,10,7,7,5,5,5,3,2,2,1,1,1] (.node [13,10,7,7,5,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,7,7,6,4,4,2,2,2,2,2,1] (.node [13,10,7,7,6,4,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,10,7,7,6,5,2,2,2,2,2,2,2] (.node [13,10,7,7,6,4,4,4,2,2,1,1,1] (.node [13,10,7,7,6,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,6,5,3,2,2,2,2,2,1] .empty .empty))) (.node [13,10,7,7,6,6,2,2,2,2,2,2,1] (.node [13,10,7,7,6,5,4,3,2,2,1,1,1] (.node [13,10,7,7,6,5,4,2,2,2,2,1,1] (.node [13,10,7,7,6,5,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,6,6,2,2,2,2,2,1,1,1] (.node [13,10,7,7,6,5,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,10,7,7,6,6,3,3,2,1,1,1,1,1] (.node [13,10,7,7,6,6,3,2,2,2,2,1,1] (.node [13,10,7,7,6,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,6,6,3,3,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_869 : RowTree := (.node [13,10,7,7,5,5,4,4,2,2,1,1,1] degreeTree62_867 degreeTree62_868) - -def degreeTree62_870 : RowTree := (.node [13,10,7,7,7,4,3,3,3,1,1,1,1,1] (.node [13,10,7,7,7,3,3,3,3,2,2,1,1] (.node [13,10,7,7,6,6,5,2,1,1,1,1,1,1] (.node [13,10,7,7,6,6,4,3,1,1,1,1,1,1] (.node [13,10,7,7,6,6,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,7,3,3,2,2,2,2,2,2] (.node [13,10,7,7,6,6,6,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,7,7,7,4,3,2,2,2,2,2,1] (.node [13,10,7,7,7,4,3,2,2,2,2,1,1,1] (.node [13,10,7,7,7,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,10,7,7,7,4,3,3,2,2,2,1,1] .empty .empty))) (.node [13,10,7,7,7,4,4,4,1,1,1,1,1,1] (.node [13,10,7,7,7,4,4,2,2,2,2,1,1] (.node [13,10,7,7,7,4,4,2,2,2,1,1,1,1] (.node [13,10,7,7,7,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,7,4,4,3,2,2,1,1,1] (.node [13,10,7,7,7,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,7,7,7,5,3,2,2,2,1,1,1,1] (.node [13,10,7,7,7,5,2,2,2,2,2,2,1] (.node [13,10,7,7,7,5,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,7,5,3,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_871 : RowTree := (.node [13,10,7,7,7,7,2,2,2,1,1,1,1,1] (.node [13,10,7,7,7,6,2,2,2,2,2,1,1] (.node [13,10,7,7,7,5,4,3,1,1,1,1,1,1] (.node [13,10,7,7,7,5,4,2,2,1,1,1,1,1] (.node [13,10,7,7,7,5,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,7,6,2,2,2,2,1,1,1,1] (.node [13,10,7,7,7,5,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,7,7,7,6,4,2,1,1,1,1,1,1] (.node [13,10,7,7,7,6,3,3,1,1,1,1,1,1] (.node [13,10,7,7,7,6,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,7,6,5,1,1,1,1,1,1,1] .empty .empty))) (.node [13,10,8,5,5,5,4,2,2,2,2,2,2] (.node [13,10,8,5,4,4,4,4,4,2,2,1,1] (.node [13,10,7,7,7,7,4,1,1,1,1,1,1,1] (.node [13,10,7,7,7,7,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,5,5,4,4,4,4,2,1,1,1] (.node [13,10,8,5,5,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [13,10,8,5,5,5,4,4,3,2,1,1,1] (.node [13,10,8,5,5,5,4,4,2,2,2,1,1] (.node [13,10,8,5,5,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,5,5,5,5,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_872 : RowTree := (.node [13,10,7,7,7,5,3,3,2,1,1,1,1,1] degreeTree62_870 degreeTree62_871) - -def degreeTree62_873 : RowTree := (.node [13,10,7,7,6,6,4,2,2,1,1,1,1,1] degreeTree62_869 degreeTree62_872) - -def degreeTree62_874 : RowTree := (.node [13,10,7,6,6,5,4,4,2,2,1,1,1] degreeTree62_866 degreeTree62_873) - -def degreeTree62_875 : RowTree := (.node [13,10,8,6,5,5,4,2,2,2,2,2,1] (.node [13,10,8,6,5,4,4,3,3,2,2,1,1] (.node [13,10,8,6,4,4,4,4,3,2,2,1,1] (.node [13,10,8,5,5,5,5,4,2,2,1,1,1] (.node [13,10,8,5,5,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,6,5,4,4,2,2,2,2,2,2] (.node [13,10,8,6,4,4,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [13,10,8,6,5,5,3,2,2,2,2,2,2] (.node [13,10,8,6,5,4,4,4,3,2,1,1,1] (.node [13,10,8,6,5,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,6,5,5,3,3,3,2,2,1,1] .empty .empty))) (.node [13,10,8,6,6,4,3,2,2,2,2,2,2] (.node [13,10,8,6,5,5,4,4,2,2,1,1,1] (.node [13,10,8,6,5,5,4,3,3,2,1,1,1] (.node [13,10,8,6,5,5,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,6,5,5,5,3,2,2,1,1,1] (.node [13,10,8,6,5,5,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,8,6,6,4,4,3,2,2,2,1,1] (.node [13,10,8,6,6,4,4,2,2,2,2,2,1] (.node [13,10,8,6,6,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,6,6,4,4,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_876 : RowTree := (.node [13,10,8,6,6,6,3,3,2,1,1,1,1,1] (.node [13,10,8,6,6,5,4,3,2,2,1,1,1] (.node [13,10,8,6,6,5,3,3,2,2,2,1,1] (.node [13,10,8,6,6,5,3,2,2,2,2,2,1] (.node [13,10,8,6,6,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,10,8,6,6,5,4,2,2,2,2,1,1] (.node [13,10,8,6,6,5,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [13,10,8,6,6,6,3,2,2,2,1,1,1,1] (.node [13,10,8,6,6,6,2,2,2,2,2,2,1] (.node [13,10,8,6,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,6,6,6,3,2,2,2,2,1,1] .empty .empty))) (.node [13,10,8,7,4,4,4,2,2,2,2,2,2] (.node [13,10,8,6,6,6,4,3,1,1,1,1,1,1] (.node [13,10,8,6,6,6,4,2,2,1,1,1,1,1] (.node [13,10,8,6,6,6,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,6,6,6,6,1,1,1,1,1,1,1] (.node [13,10,8,6,6,6,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,8,7,4,4,4,4,3,2,1,1,1] (.node [13,10,8,7,4,4,4,4,2,2,2,1,1] (.node [13,10,8,7,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,7,5,4,3,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_877 : RowTree := (.node [13,10,8,6,6,4,4,4,2,2,1,1,1] degreeTree62_875 degreeTree62_876) - -def degreeTree62_878 : RowTree := (.node [13,10,8,7,6,3,3,2,2,2,2,2,2] (.node [13,10,8,7,5,5,3,2,2,2,2,2,1] (.node [13,10,8,7,5,4,4,3,3,2,1,1,1] (.node [13,10,8,7,5,4,4,3,2,2,2,1,1] (.node [13,10,8,7,5,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,8,7,5,5,2,2,2,2,2,2,2] (.node [13,10,8,7,5,4,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [13,10,8,7,5,5,4,2,2,2,2,1,1] (.node [13,10,8,7,5,5,3,3,3,2,1,1,1] (.node [13,10,8,7,5,5,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,7,5,5,4,3,2,2,1,1,1] .empty .empty))) (.node [13,10,8,7,6,4,3,3,3,1,1,1,1,1] (.node [13,10,8,7,6,4,3,2,2,2,2,1,1,1] (.node [13,10,8,7,6,4,2,2,2,2,2,2,2] (.node [13,10,8,7,6,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,7,6,4,3,3,2,2,2,1,1] (.node [13,10,8,7,6,4,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,10,8,7,6,4,4,2,2,2,2,1,1] (.node [13,10,8,7,6,4,4,2,2,2,1,1,1,1] (.node [13,10,8,7,6,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,7,6,4,4,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_879 : RowTree := (.node [13,10,8,7,6,6,3,2,2,1,1,1,1,1] (.node [13,10,8,7,6,5,4,2,2,1,1,1,1,1] (.node [13,10,8,7,6,5,3,2,2,2,1,1,1,1] (.node [13,10,8,7,6,5,2,2,2,2,2,2,1] (.node [13,10,8,7,6,5,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,7,6,5,3,3,2,1,1,1,1,1] (.node [13,10,8,7,6,5,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,8,7,6,6,2,2,2,2,1,1,1,1] (.node [13,10,8,7,6,5,5,2,1,1,1,1,1,1] (.node [13,10,8,7,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,7,6,6,2,2,2,2,2,1,1] .empty .empty))) (.node [13,10,8,7,7,3,3,2,2,2,2,1,1,1] (.node [13,10,8,7,6,6,5,1,1,1,1,1,1,1] (.node [13,10,8,7,6,6,4,2,1,1,1,1,1,1] (.node [13,10,8,7,6,6,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,7,7,3,2,2,2,2,2,2,2] (.node [13,10,8,7,7,2,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,10,8,7,7,3,3,3,3,1,1,1,1,1] (.node [13,10,8,7,7,3,3,3,2,2,2,1,1] (.node [13,10,8,7,7,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,8,7,7,3,3,3,3,2,1,1,1] .empty .empty)))) - -def degreeTree62_880 : RowTree := (.node [13,10,8,7,6,4,4,4,1,1,1,1,1,1] degreeTree62_878 degreeTree62_879) - -def degreeTree62_881 : RowTree := (.node [13,10,8,7,5,4,3,3,3,2,2,1,1] degreeTree62_877 degreeTree62_880) - -def degreeTree62_882 : RowTree := (.node [13,10,8,7,7,5,4,2,1,1,1,1,1,1] (.node [13,10,8,7,7,4,4,3,1,1,1,1,1,1] (.node [13,10,8,7,7,4,3,2,2,2,2,1,1] (.node [13,10,8,7,7,4,3,2,2,2,1,1,1,1] (.node [13,10,8,7,7,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,8,7,7,4,4,2,2,1,1,1,1,1] (.node [13,10,8,7,7,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,8,7,7,5,3,2,2,1,1,1,1,1] (.node [13,10,8,7,7,5,2,2,2,2,2,1,1] (.node [13,10,8,7,7,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,7,7,5,3,3,1,1,1,1,1,1] .empty .empty))) (.node [13,10,8,7,7,7,3,1,1,1,1,1,1,1] (.node [13,10,8,7,7,6,3,2,1,1,1,1,1,1] (.node [13,10,8,7,7,6,2,2,2,1,1,1,1,1] (.node [13,10,8,7,7,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,7,7,7,2,2,1,1,1,1,1,1] (.node [13,10,8,7,7,6,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,8,8,4,4,4,2,2,2,2,1,1,1] (.node [13,10,8,8,4,4,3,3,3,2,2,1,1] (.node [13,10,8,8,4,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,10,8,8,4,4,4,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_883 : RowTree := (.node [13,10,8,8,5,4,3,3,3,1,1,1,1,1] (.node [13,10,8,8,5,3,3,3,3,2,2,1,1] (.node [13,10,8,8,4,4,4,4,2,1,1,1,1,1] (.node [13,10,8,8,4,4,4,3,3,2,1,1,1] (.node [13,10,8,8,4,4,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,5,3,3,2,2,2,2,2,2] (.node [13,10,8,8,4,4,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [13,10,8,8,5,4,3,2,2,2,2,2,1] (.node [13,10,8,8,5,4,3,2,2,2,2,1,1,1] (.node [13,10,8,8,5,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,10,8,8,5,4,3,3,2,2,2,1,1] .empty .empty))) (.node [13,10,8,8,5,5,2,2,2,2,2,1,1,1] (.node [13,10,8,8,5,4,4,2,2,2,2,1,1] (.node [13,10,8,8,5,4,4,2,2,2,1,1,1,1] (.node [13,10,8,8,5,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,5,4,4,4,1,1,1,1,1,1] (.node [13,10,8,8,5,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,8,8,5,5,3,2,2,2,2,1,1] (.node [13,10,8,8,5,5,3,2,2,2,1,1,1,1] (.node [13,10,8,8,5,5,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,8,8,5,5,3,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_884 : RowTree := (.node [13,10,8,8,4,4,4,3,2,2,2,1,1] degreeTree62_882 degreeTree62_883) - -def degreeTree62_885 : RowTree := (.node [13,10,8,8,6,4,2,2,2,2,2,2,1] (.node [13,10,8,8,6,3,3,2,2,2,2,2,1] (.node [13,10,8,8,6,2,2,2,2,2,2,2,2,1] (.node [13,10,8,8,5,5,5,2,1,1,1,1,1,1] (.node [13,10,8,8,5,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,6,3,3,2,2,2,2,1,1,1] (.node [13,10,8,8,6,3,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,10,8,8,6,3,3,3,3,2,1,1,1] (.node [13,10,8,8,6,3,3,3,3,1,1,1,1,1] (.node [13,10,8,8,6,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,8,6,4,2,2,2,2,2,1,1,1] .empty .empty))) (.node [13,10,8,8,6,5,2,2,2,2,1,1,1,1] (.node [13,10,8,8,6,4,3,3,2,1,1,1,1,1] (.node [13,10,8,8,6,4,3,2,2,2,2,1,1] (.node [13,10,8,8,6,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,6,4,4,3,1,1,1,1,1,1] (.node [13,10,8,8,6,4,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,8,8,6,5,3,3,1,1,1,1,1,1] (.node [13,10,8,8,6,5,3,2,2,1,1,1,1,1] (.node [13,10,8,8,6,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,8,6,5,4,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_886 : RowTree := (.node [13,10,8,8,7,4,2,2,2,2,1,1,1,1] (.node [13,10,8,8,7,3,2,2,2,2,2,1,1,1] (.node [13,10,8,8,6,6,4,1,1,1,1,1,1,1] (.node [13,10,8,8,6,6,3,2,1,1,1,1,1,1] (.node [13,10,8,8,6,6,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,7,2,2,2,2,2,2,2,2] (.node [13,10,8,8,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,8,8,7,3,3,2,2,2,2,1,1] (.node [13,10,8,8,7,3,3,2,2,2,1,1,1,1] (.node [13,10,8,8,7,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,8,8,7,3,3,3,2,1,1,1,1,1] .empty .empty))) (.node [13,10,8,8,7,5,2,2,2,1,1,1,1,1] (.node [13,10,8,8,7,4,3,3,1,1,1,1,1,1] (.node [13,10,8,8,7,4,3,2,2,1,1,1,1,1] (.node [13,10,8,8,7,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,8,7,4,4,2,1,1,1,1,1,1] .empty .empty)) (.node [13,10,8,8,7,6,2,2,1,1,1,1,1,1] (.node [13,10,8,8,7,5,4,1,1,1,1,1,1,1] (.node [13,10,8,8,7,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,7,6,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_887 : RowTree := (.node [13,10,8,8,6,5,5,1,1,1,1,1,1,1] degreeTree62_885 degreeTree62_886) - -def degreeTree62_888 : RowTree := (.node [13,10,8,8,5,5,4,2,2,1,1,1,1,1] degreeTree62_884 degreeTree62_887) - -def degreeTree62_889 : RowTree := (.node [13,10,8,7,7,4,2,2,2,2,2,1,1,1] degreeTree62_881 degreeTree62_888) - -def degreeTree62_890 : RowTree := (.node [13,10,8,5,5,5,5,3,2,2,2,1,1] degreeTree62_874 degreeTree62_889) - -def degreeTree62_891 : RowTree := (.node [13,9,9,9,7,3,3,2,2,2,1,1,1] degreeTree62_859 degreeTree62_890) - -def degreeTree62_892 : RowTree := (.node [13,9,8,8,6,6,3,2,2,1,1,1,1,1] degreeTree62_828 degreeTree62_891) - -def degreeTree62_893 : RowTree := (.node [13,10,8,8,8,5,3,1,1,1,1,1,1,1] (.node [13,10,8,8,8,3,3,3,1,1,1,1,1,1] (.node [13,10,8,8,8,3,2,2,2,2,1,1,1,1] (.node [13,10,8,8,8,2,2,2,2,2,2,2,1] (.node [13,10,8,8,8,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,8,3,3,2,2,1,1,1,1,1] (.node [13,10,8,8,8,3,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,8,8,8,4,4,1,1,1,1,1,1,1] (.node [13,10,8,8,8,4,3,2,1,1,1,1,1,1] (.node [13,10,8,8,8,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,8,5,2,2,1,1,1,1,1,1] .empty .empty))) (.node [13,10,9,5,5,4,4,2,2,2,2,2,2] (.node [13,10,9,4,4,4,4,4,4,2,2,1,1] (.node [13,10,8,8,8,7,1,1,1,1,1,1,1,1] (.node [13,10,8,8,8,6,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,5,4,4,4,4,4,2,1,1,1] (.node [13,10,9,5,4,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [13,10,9,5,5,4,4,4,3,2,1,1,1] (.node [13,10,9,5,5,4,4,4,2,2,2,1,1] (.node [13,10,9,5,5,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,5,5,5,3,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_894 : RowTree := (.node [13,10,9,6,5,4,4,2,2,2,2,2,1] (.node [13,10,9,6,4,4,4,3,3,2,2,1,1] (.node [13,10,9,5,5,5,4,3,3,2,1,1,1] (.node [13,10,9,5,5,5,4,3,2,2,2,1,1] (.node [13,10,9,5,5,5,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,6,4,4,4,2,2,2,2,2,2] (.node [13,10,9,5,5,5,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,9,6,5,4,3,2,2,2,2,2,2] (.node [13,10,9,6,4,4,4,4,3,2,1,1,1] (.node [13,10,9,6,4,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,6,5,4,3,3,3,2,2,1,1] .empty .empty))) (.node [13,10,9,6,5,5,3,3,3,2,1,1,1] (.node [13,10,9,6,5,5,2,2,2,2,2,2,2] (.node [13,10,9,6,5,4,4,3,3,2,1,1,1] (.node [13,10,9,6,5,4,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,6,5,5,3,3,2,2,2,1,1] (.node [13,10,9,6,5,5,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,10,9,6,6,3,3,3,3,2,2,1,1] (.node [13,10,9,6,6,3,3,2,2,2,2,2,2] (.node [13,10,9,6,5,5,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,6,6,4,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_895 : RowTree := (.node [13,10,9,5,5,5,3,3,3,2,2,1,1] degreeTree62_893 degreeTree62_894) - -def degreeTree62_896 : RowTree := (.node [13,10,9,6,6,5,3,2,2,2,2,1,1] (.node [13,10,9,6,6,4,4,3,2,1,1,1,1,1] (.node [13,10,9,6,6,4,3,3,3,1,1,1,1,1] (.node [13,10,9,6,6,4,3,3,2,2,2,1,1] (.node [13,10,9,6,6,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,6,6,4,4,2,2,2,2,1,1] (.node [13,10,9,6,6,4,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,6,6,5,2,2,2,2,2,2,1] (.node [13,10,9,6,6,5,2,2,2,2,2,1,1,1] (.node [13,10,9,6,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,6,6,5,3,2,2,2,1,1,1,1] .empty .empty))) (.node [13,10,9,6,6,6,2,2,2,2,2,1,1] (.node [13,10,9,6,6,5,4,3,1,1,1,1,1,1] (.node [13,10,9,6,6,5,4,2,2,1,1,1,1,1] (.node [13,10,9,6,6,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,6,6,6,2,2,2,2,1,1,1,1] (.node [13,10,9,6,6,5,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,6,6,6,4,2,1,1,1,1,1,1] (.node [13,10,9,6,6,6,3,3,1,1,1,1,1,1] (.node [13,10,9,6,6,6,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,6,6,6,5,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_897 : RowTree := (.node [13,10,9,7,5,4,3,2,2,2,2,1,1,1] (.node [13,10,9,7,4,4,4,3,3,2,1,1,1] (.node [13,10,9,7,4,4,4,2,2,2,2,2,1] (.node [13,10,9,7,4,4,4,2,2,2,2,1,1,1] (.node [13,10,9,7,4,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,7,4,4,4,3,3,1,1,1,1,1] (.node [13,10,9,7,4,4,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,9,7,5,3,3,3,3,2,2,1,1] (.node [13,10,9,7,5,3,3,2,2,2,2,2,2] (.node [13,10,9,7,4,4,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,5,4,2,2,2,2,2,2,2] .empty .empty))) (.node [13,10,9,7,5,4,4,3,2,1,1,1,1,1] (.node [13,10,9,7,5,4,3,3,3,1,1,1,1,1] (.node [13,10,9,7,5,4,3,3,2,2,2,1,1] (.node [13,10,9,7,5,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,7,5,4,4,2,2,2,2,1,1] (.node [13,10,9,7,5,4,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,7,5,5,2,2,2,2,2,2,1] (.node [13,10,9,7,5,5,2,2,2,2,2,1,1,1] (.node [13,10,9,7,5,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,5,5,3,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_898 : RowTree := (.node [13,10,9,7,4,4,3,2,2,2,2,2,2] degreeTree62_896 degreeTree62_897) - -def degreeTree62_899 : RowTree := (.node [13,10,9,6,6,4,3,2,2,2,2,1,1,1] degreeTree62_895 degreeTree62_898) - -def degreeTree62_900 : RowTree := (.node [13,10,9,7,6,4,2,2,2,2,2,1,1,1] (.node [13,10,9,7,6,3,2,2,2,2,2,2,2] (.node [13,10,9,7,5,5,4,3,1,1,1,1,1,1] (.node [13,10,9,7,5,5,4,2,2,1,1,1,1,1] (.node [13,10,9,7,5,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,6,2,2,2,2,2,2,2,2,1] (.node [13,10,9,7,5,5,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,7,6,3,3,3,2,2,2,1,1] (.node [13,10,9,7,6,3,3,2,2,2,2,2,1] (.node [13,10,9,7,6,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,6,3,3,3,3,1,1,1,1,1] .empty .empty))) (.node [13,10,9,7,6,4,4,3,1,1,1,1,1,1] (.node [13,10,9,7,6,4,3,2,2,2,2,1,1] (.node [13,10,9,7,6,4,3,2,2,2,1,1,1,1] (.node [13,10,9,7,6,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,7,6,4,4,2,2,1,1,1,1,1] (.node [13,10,9,7,6,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,7,6,5,3,2,2,1,1,1,1,1] (.node [13,10,9,7,6,5,2,2,2,2,2,1,1] (.node [13,10,9,7,6,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,6,5,3,3,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_901 : RowTree := (.node [13,10,9,7,7,3,3,3,2,1,1,1,1,1] (.node [13,10,9,7,7,2,2,2,2,2,2,2,2] (.node [13,10,9,7,6,6,3,2,1,1,1,1,1,1] (.node [13,10,9,7,6,6,2,2,2,1,1,1,1,1] (.node [13,10,9,7,6,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,7,2,2,2,2,2,2,2,1,1] (.node [13,10,9,7,6,6,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,7,7,3,3,2,2,2,1,1,1,1] (.node [13,10,9,7,7,3,2,2,2,2,2,2,1] (.node [13,10,9,7,7,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,7,3,3,2,2,2,2,1,1] .empty .empty))) (.node [13,10,9,7,7,5,2,2,2,1,1,1,1,1] (.node [13,10,9,7,7,4,3,2,2,1,1,1,1,1] (.node [13,10,9,7,7,4,2,2,2,2,2,1,1] (.node [13,10,9,7,7,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,7,4,4,2,1,1,1,1,1,1] (.node [13,10,9,7,7,4,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,7,7,6,2,2,1,1,1,1,1,1] (.node [13,10,9,7,7,5,4,1,1,1,1,1,1,1] (.node [13,10,9,7,7,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,7,6,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_902 : RowTree := (.node [13,10,9,7,6,5,4,2,1,1,1,1,1,1] degreeTree62_900 degreeTree62_901) - -def degreeTree62_903 : RowTree := (.node [13,10,9,8,4,4,4,4,1,1,1,1,1,1] (.node [13,10,9,8,4,4,3,3,2,2,2,1,1] (.node [13,10,9,8,4,4,2,2,2,2,2,2,2] (.node [13,10,9,8,4,3,3,3,3,2,2,1,1] (.node [13,10,9,8,4,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,10,9,8,4,4,3,2,2,2,2,2,1] (.node [13,10,9,8,4,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,10,9,8,4,4,4,2,2,2,2,1,1] (.node [13,10,9,8,4,4,4,2,2,2,1,1,1,1] (.node [13,10,9,8,4,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,4,4,4,3,2,1,1,1,1,1] .empty .empty))) (.node [13,10,9,8,5,3,3,3,3,1,1,1,1,1] (.node [13,10,9,8,5,3,3,2,2,2,2,1,1,1] (.node [13,10,9,8,5,3,2,2,2,2,2,2,2] (.node [13,10,9,8,5,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,8,5,3,3,3,2,2,2,1,1] (.node [13,10,9,8,5,3,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,10,9,8,5,4,3,2,2,2,1,1,1,1] (.node [13,10,9,8,5,4,2,2,2,2,2,2,1] (.node [13,10,9,8,5,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,5,4,3,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_904 : RowTree := (.node [13,10,9,8,6,3,2,2,2,2,2,1,1,1] (.node [13,10,9,8,5,5,3,3,1,1,1,1,1,1] (.node [13,10,9,8,5,5,2,2,2,2,1,1,1,1] (.node [13,10,9,8,5,4,4,3,1,1,1,1,1,1] (.node [13,10,9,8,5,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,5,5,3,2,2,1,1,1,1,1] (.node [13,10,9,8,5,5,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,9,8,6,2,2,2,2,2,2,2,1,1] (.node [13,10,9,8,5,5,5,1,1,1,1,1,1,1] (.node [13,10,9,8,5,5,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,6,2,2,2,2,2,2,2,2] .empty .empty))) (.node [13,10,9,8,6,4,2,2,2,2,2,1,1] (.node [13,10,9,8,6,3,3,2,2,2,2,1,1] (.node [13,10,9,8,6,3,3,2,2,2,1,1,1,1] (.node [13,10,9,8,6,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,8,6,4,2,2,2,2,1,1,1,1] (.node [13,10,9,8,6,3,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,8,6,4,4,2,1,1,1,1,1,1] (.node [13,10,9,8,6,4,3,3,1,1,1,1,1,1] (.node [13,10,9,8,6,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,6,5,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_905 : RowTree := (.node [13,10,9,8,5,4,3,3,2,1,1,1,1,1] degreeTree62_903 degreeTree62_904) - -def degreeTree62_906 : RowTree := (.node [13,10,9,7,7,7,2,1,1,1,1,1,1,1] degreeTree62_902 degreeTree62_905) - -def degreeTree62_907 : RowTree := (.node [13,10,9,7,5,5,3,2,2,2,2,1,1] degreeTree62_899 degreeTree62_906) - -def degreeTree62_908 : RowTree := (.node [13,10,9,8,7,4,3,2,1,1,1,1,1,1] (.node [13,10,9,8,7,3,2,2,2,2,1,1,1,1] (.node [13,10,9,8,6,6,3,1,1,1,1,1,1,1] (.node [13,10,9,8,6,6,2,2,1,1,1,1,1,1] (.node [13,10,9,8,6,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,7,2,2,2,2,2,2,2,1] (.node [13,10,9,8,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,10,9,8,7,3,3,3,1,1,1,1,1,1] (.node [13,10,9,8,7,3,3,2,2,1,1,1,1,1] (.node [13,10,9,8,7,3,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,8,7,4,2,2,2,1,1,1,1,1] .empty .empty))) (.node [13,10,9,8,8,2,2,2,2,2,1,1,1,1] (.node [13,10,9,8,7,5,3,1,1,1,1,1,1,1] (.node [13,10,9,8,7,5,2,2,1,1,1,1,1,1] (.node [13,10,9,8,7,4,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,7,7,1,1,1,1,1,1,1,1] (.node [13,10,9,8,7,6,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,8,8,3,3,2,1,1,1,1,1,1] (.node [13,10,9,8,8,3,2,2,2,1,1,1,1,1] (.node [13,10,9,8,8,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,8,8,4,2,2,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_909 : RowTree := (.node [13,10,9,9,4,4,2,2,2,2,2,1,1,1] (.node [13,10,9,9,4,3,2,2,2,2,2,2,2] (.node [13,10,9,9,3,3,3,2,2,2,2,2,2] (.node [13,10,9,8,8,6,1,1,1,1,1,1,1,1] (.node [13,10,9,8,8,5,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,4,2,2,2,2,2,2,2,2,1] (.node [13,10,9,9,3,3,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,10,9,9,4,3,3,3,2,2,2,1,1] (.node [13,10,9,9,4,3,3,2,2,2,2,2,1] (.node [13,10,9,9,4,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,4,3,3,3,3,1,1,1,1,1] .empty .empty))) (.node [13,10,9,9,4,4,4,3,1,1,1,1,1,1] (.node [13,10,9,9,4,4,3,2,2,2,2,1,1] (.node [13,10,9,9,4,4,3,2,2,2,1,1,1,1] (.node [13,10,9,9,4,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,9,4,4,4,2,2,1,1,1,1,1] (.node [13,10,9,9,4,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,9,5,3,2,2,2,2,2,1,1,1] (.node [13,10,9,9,5,2,2,2,2,2,2,2,2] (.node [13,10,9,9,5,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,9,5,3,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_910 : RowTree := (.node [13,10,9,8,8,4,3,1,1,1,1,1,1,1] degreeTree62_908 degreeTree62_909) - -def degreeTree62_911 : RowTree := (.node [13,10,9,9,6,2,2,2,2,2,2,1,1,1] (.node [13,10,9,9,5,4,3,3,1,1,1,1,1,1] (.node [13,10,9,9,5,4,2,2,2,2,1,1,1,1] (.node [13,10,9,9,5,3,3,3,2,1,1,1,1,1] (.node [13,10,9,9,5,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,9,5,4,3,2,2,1,1,1,1,1] (.node [13,10,9,9,5,4,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,9,9,5,5,3,2,1,1,1,1,1,1] (.node [13,10,9,9,5,5,2,2,2,1,1,1,1,1] (.node [13,10,9,9,5,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,5,5,4,1,1,1,1,1,1,1] .empty .empty))) (.node [13,10,9,9,6,4,2,2,2,1,1,1,1,1] (.node [13,10,9,9,6,3,2,2,2,2,2,1,1] (.node [13,10,9,9,6,3,2,2,2,2,1,1,1,1] (.node [13,10,9,9,6,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,9,6,3,3,3,1,1,1,1,1,1] (.node [13,10,9,9,6,3,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,9,6,5,2,2,1,1,1,1,1,1] (.node [13,10,9,9,6,4,4,1,1,1,1,1,1,1] (.node [13,10,9,9,6,4,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,6,5,3,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_912 : RowTree := (.node [13,10,9,9,8,3,3,1,1,1,1,1,1,1] (.node [13,10,9,9,7,4,3,1,1,1,1,1,1,1] (.node [13,10,9,9,7,3,2,2,2,1,1,1,1,1] (.node [13,10,9,9,7,2,2,2,2,2,2,1,1] (.node [13,10,9,9,7,2,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,7,4,2,2,1,1,1,1,1,1] (.node [13,10,9,9,7,3,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,9,8,2,2,2,2,1,1,1,1,1] (.node [13,10,9,9,7,6,1,1,1,1,1,1,1,1] (.node [13,10,9,9,7,5,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,8,3,2,2,1,1,1,1,1,1] .empty .empty))) (.node [13,11,5,5,5,5,4,4,4,2,2,1,1] (.node [13,10,9,9,9,2,2,2,1,1,1,1,1,1] (.node [13,10,9,9,8,5,1,1,1,1,1,1,1,1] (.node [13,10,9,9,8,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,9,4,1,1,1,1,1,1,1,1] (.node [13,10,9,9,9,3,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,6,5,5,4,4,4,4,2,2,1,1] (.node [13,11,5,5,5,5,5,5,2,2,2,1,1] (.node [13,11,5,5,5,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,11,6,5,5,5,4,4,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_913 : RowTree := (.node [13,10,9,9,6,6,2,1,1,1,1,1,1,1] degreeTree62_911 degreeTree62_912) - -def degreeTree62_914 : RowTree := (.node [13,10,9,9,5,3,3,2,2,2,1,1,1,1] degreeTree62_910 degreeTree62_913) - -def degreeTree62_915 : RowTree := (.node [13,11,6,6,6,4,4,3,3,2,2,1,1] (.node [13,11,6,6,5,5,4,3,3,2,2,1,1] (.node [13,11,6,6,4,4,4,4,4,2,2,1,1] (.node [13,11,6,5,5,5,5,4,2,2,2,1,1] (.node [13,11,6,5,5,5,5,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,11,6,6,5,5,4,2,2,2,2,2,2] (.node [13,11,6,6,5,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [13,11,6,6,5,5,5,3,2,2,2,1,1] (.node [13,11,6,6,5,5,5,2,2,2,2,2,1] (.node [13,11,6,6,5,5,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,11,6,6,6,4,4,2,2,2,2,2,2] .empty .empty))) (.node [13,11,6,6,6,5,5,2,2,2,2,1,1] (.node [13,11,6,6,6,5,3,3,3,2,2,1,1] (.node [13,11,6,6,6,5,3,2,2,2,2,2,2] (.node [13,11,6,6,6,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,11,6,6,6,5,4,3,2,2,2,1,1] (.node [13,11,6,6,6,5,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,11,6,6,6,6,3,3,2,2,2,1,1] (.node [13,11,6,6,6,6,3,2,2,2,2,2,1] (.node [13,11,6,6,6,6,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,6,6,6,6,4,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_916 : RowTree := (.node [13,11,7,6,5,4,4,4,2,2,2,1,1] (.node [13,11,7,5,5,5,5,2,2,2,2,2,1] (.node [13,11,7,5,5,5,4,2,2,2,2,2,2] (.node [13,11,7,5,5,4,4,4,3,2,2,1,1] (.node [13,11,7,5,4,4,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [13,11,7,5,5,5,4,4,2,2,2,1,1] (.node [13,11,7,5,5,5,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,11,7,6,5,4,4,2,2,2,2,2,2] (.node [13,11,7,6,4,4,4,4,3,2,2,1,1] (.node [13,11,7,5,5,5,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,11,7,6,5,4,4,3,3,2,2,1,1] .empty .empty))) (.node [13,11,7,6,6,4,3,2,2,2,2,2,2] (.node [13,11,7,6,5,5,4,2,2,2,2,2,1] (.node [13,11,7,6,5,5,3,3,3,2,2,1,1] (.node [13,11,7,6,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,7,6,5,5,5,2,2,2,2,1,1] (.node [13,11,7,6,5,5,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [13,11,7,6,6,4,4,3,2,2,2,1,1] (.node [13,11,7,6,6,4,4,2,2,2,2,2,1] (.node [13,11,7,6,6,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,11,7,6,6,5,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_917 : RowTree := (.node [13,11,6,6,6,6,6,2,1,1,1,1,1,1] degreeTree62_915 degreeTree62_916) - -def degreeTree62_918 : RowTree := (.node [13,11,7,6,6,6,6,1,1,1,1,1,1,1] (.node [13,11,7,6,6,6,3,2,2,2,2,1,1] (.node [13,11,7,6,6,6,2,2,2,2,2,1,1,1] (.node [13,11,7,6,6,5,4,2,2,2,2,1,1] (.node [13,11,7,6,6,5,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,11,7,6,6,6,3,2,2,2,1,1,1,1] (.node [13,11,7,6,6,6,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,11,7,6,6,6,4,3,1,1,1,1,1,1] (.node [13,11,7,6,6,6,4,2,2,1,1,1,1,1] (.node [13,11,7,6,6,6,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,6,6,6,5,2,1,1,1,1,1,1] .empty .empty))) (.node [13,11,7,7,5,4,4,2,2,2,2,2,1] (.node [13,11,7,7,4,4,4,4,2,2,2,1,1] (.node [13,11,7,7,4,4,4,3,3,2,2,1,1] (.node [13,11,7,7,4,4,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,7,7,5,4,3,3,3,2,2,1,1] (.node [13,11,7,7,5,4,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,11,7,7,5,5,3,2,2,2,2,2,1] (.node [13,11,7,7,5,5,2,2,2,2,2,2,2] (.node [13,11,7,7,5,4,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,11,7,7,5,5,3,3,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_919 : RowTree := (.node [13,11,7,7,6,5,2,2,2,2,2,1,1,1] (.node [13,11,7,7,6,4,3,3,2,2,2,1,1] (.node [13,11,7,7,6,4,2,2,2,2,2,2,2] (.node [13,11,7,7,6,3,3,3,3,2,2,1,1] (.node [13,11,7,7,6,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,7,7,6,4,3,2,2,2,2,2,1] (.node [13,11,7,7,6,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,7,7,6,4,4,3,2,1,1,1,1,1] (.node [13,11,7,7,6,4,4,2,2,2,1,1,1,1] (.node [13,11,7,7,6,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,7,6,4,4,4,1,1,1,1,1,1] .empty .empty))) (.node [13,11,7,7,6,5,4,3,1,1,1,1,1,1] (.node [13,11,7,7,6,5,3,3,2,1,1,1,1,1] (.node [13,11,7,7,6,5,3,2,2,2,1,1,1,1] (.node [13,11,7,7,6,5,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,7,7,6,5,4,2,2,1,1,1,1,1] .empty .empty)) (.node [13,11,7,7,6,6,3,2,2,1,1,1,1,1] (.node [13,11,7,7,6,6,2,2,2,2,1,1,1,1] (.node [13,11,7,7,6,5,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,7,6,6,3,3,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_920 : RowTree := (.node [13,11,7,7,5,5,4,2,2,2,2,1,1] degreeTree62_918 degreeTree62_919) - -def degreeTree62_921 : RowTree := (.node [13,11,7,6,6,5,3,2,2,2,2,2,1] degreeTree62_917 degreeTree62_920) - -def degreeTree62_922 : RowTree := (.node [13,11,6,5,5,5,5,2,2,2,2,2,2] degreeTree62_914 degreeTree62_921) - -def degreeTree62_923 : RowTree := (.node [13,10,9,8,6,5,3,2,1,1,1,1,1,1] degreeTree62_907 degreeTree62_922) - -def degreeTree62_924 : RowTree := (.node [13,11,7,7,7,4,3,3,2,1,1,1,1,1] (.node [13,11,7,7,7,3,3,3,2,2,2,1,1] (.node [13,11,7,7,7,3,2,2,2,2,2,2,2] (.node [13,11,7,7,7,2,2,2,2,2,2,2,2,1] (.node [13,11,7,7,6,6,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,7,7,3,3,2,2,2,2,2,1] (.node [13,11,7,7,7,3,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,7,7,7,4,2,2,2,2,2,2,1] (.node [13,11,7,7,7,4,2,2,2,2,2,1,1,1] (.node [13,11,7,7,7,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,7,7,4,3,2,2,2,1,1,1,1] .empty .empty))) (.node [13,11,7,7,7,5,4,2,1,1,1,1,1,1] (.node [13,11,7,7,7,5,2,2,2,2,1,1,1,1] (.node [13,11,7,7,7,4,4,3,1,1,1,1,1,1] (.node [13,11,7,7,7,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,7,7,5,3,3,1,1,1,1,1,1] (.node [13,11,7,7,7,5,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,7,7,7,6,3,2,1,1,1,1,1,1] (.node [13,11,7,7,7,6,2,2,2,1,1,1,1,1] (.node [13,11,7,7,7,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,7,7,6,4,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_925 : RowTree := (.node [13,11,8,6,4,4,4,2,2,2,2,2,2] (.node [13,11,8,5,5,4,4,4,2,2,2,1,1] (.node [13,11,8,5,4,4,4,4,3,2,2,1,1] (.node [13,11,8,4,4,4,4,4,4,2,2,1,1] (.node [13,11,7,7,7,7,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,5,5,4,4,3,3,2,2,1,1] (.node [13,11,8,5,5,4,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,11,8,5,5,5,4,2,2,2,2,2,1] (.node [13,11,8,5,5,5,3,3,3,2,2,1,1] (.node [13,11,8,5,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,8,5,5,5,4,3,2,2,2,1,1] .empty .empty))) (.node [13,11,8,6,5,4,4,3,2,2,2,1,1] (.node [13,11,8,6,5,4,3,2,2,2,2,2,2] (.node [13,11,8,6,4,4,4,4,2,2,2,1,1] (.node [13,11,8,6,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,11,8,6,5,4,4,2,2,2,2,2,1] (.node [13,11,8,6,5,4,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,11,8,6,5,5,3,3,2,2,2,1,1] (.node [13,11,8,6,5,5,3,2,2,2,2,2,1] (.node [13,11,8,6,5,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,8,6,6,3,3,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_926 : RowTree := (.node [13,11,7,7,7,7,2,2,1,1,1,1,1,1] degreeTree62_924 degreeTree62_925) - -def degreeTree62_927 : RowTree := (.node [13,11,8,6,6,5,3,3,2,1,1,1,1,1] (.node [13,11,8,6,6,4,4,3,2,1,1,1,1,1] (.node [13,11,8,6,6,4,3,2,2,2,2,2,1] (.node [13,11,8,6,6,4,3,2,2,2,2,1,1,1] (.node [13,11,8,6,6,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,8,6,6,4,4,2,2,2,1,1,1,1] (.node [13,11,8,6,6,4,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,6,6,5,2,2,2,2,2,2,1] (.node [13,11,8,6,6,5,2,2,2,2,2,1,1,1] (.node [13,11,8,6,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,6,6,5,3,2,2,2,1,1,1,1] .empty .empty))) (.node [13,11,8,6,6,6,3,3,1,1,1,1,1,1] (.node [13,11,8,6,6,5,5,2,1,1,1,1,1,1] (.node [13,11,8,6,6,5,4,3,1,1,1,1,1,1] (.node [13,11,8,6,6,5,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,6,6,6,3,2,2,1,1,1,1,1] (.node [13,11,8,6,6,6,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,7,4,4,3,2,2,2,2,2,2] (.node [13,11,8,6,6,6,5,1,1,1,1,1,1,1] (.node [13,11,8,6,6,6,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,4,4,3,3,3,2,2,1,1] .empty .empty)))) - -def degreeTree62_928 : RowTree := (.node [13,11,8,7,5,4,4,2,2,2,1,1,1,1] (.node [13,11,8,7,5,3,3,3,3,2,2,1,1] (.node [13,11,8,7,4,4,4,3,3,1,1,1,1,1] (.node [13,11,8,7,4,4,4,3,2,2,2,1,1] (.node [13,11,8,7,4,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,8,7,5,3,3,2,2,2,2,2,2] (.node [13,11,8,7,4,4,4,4,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,7,5,4,3,2,2,2,2,2,1] (.node [13,11,8,7,5,4,3,2,2,2,2,1,1,1] (.node [13,11,8,7,5,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,8,7,5,4,3,3,3,1,1,1,1,1] .empty .empty))) (.node [13,11,8,7,5,5,3,3,2,1,1,1,1,1] (.node [13,11,8,7,5,5,2,2,2,2,2,1,1,1] (.node [13,11,8,7,5,4,4,4,1,1,1,1,1,1] (.node [13,11,8,7,5,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,5,5,3,2,2,2,1,1,1,1] (.node [13,11,8,7,5,5,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,11,8,7,5,5,5,2,1,1,1,1,1,1] (.node [13,11,8,7,5,5,4,3,1,1,1,1,1,1] (.node [13,11,8,7,5,5,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,6,2,2,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_929 : RowTree := (.node [13,11,8,7,4,4,4,2,2,2,2,1,1,1] degreeTree62_927 degreeTree62_928) - -def degreeTree62_930 : RowTree := (.node [13,11,8,6,6,3,3,3,3,2,2,1,1] degreeTree62_926 degreeTree62_929) - -def degreeTree62_931 : RowTree := (.node [13,11,8,7,6,5,3,2,2,1,1,1,1,1] (.node [13,11,8,7,6,4,3,2,2,2,1,1,1,1] (.node [13,11,8,7,6,3,3,3,3,1,1,1,1,1] (.node [13,11,8,7,6,3,3,2,2,2,2,2,1] (.node [13,11,8,7,6,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,6,4,2,2,2,2,2,2,1] (.node [13,11,8,7,6,4,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,8,7,6,4,4,3,1,1,1,1,1,1] (.node [13,11,8,7,6,4,4,2,2,1,1,1,1,1] (.node [13,11,8,7,6,4,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,6,5,2,2,2,2,1,1,1,1] .empty .empty))) (.node [13,11,8,7,6,6,4,1,1,1,1,1,1,1] (.node [13,11,8,7,6,5,5,1,1,1,1,1,1,1] (.node [13,11,8,7,6,5,4,2,1,1,1,1,1,1] (.node [13,11,8,7,6,5,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,6,6,3,2,1,1,1,1,1,1] (.node [13,11,8,7,6,6,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,7,7,3,2,2,2,2,2,1,1,1] (.node [13,11,8,7,7,2,2,2,2,2,2,2,2] (.node [13,11,8,7,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,11,8,7,7,3,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_932 : RowTree := (.node [13,11,8,7,7,7,2,1,1,1,1,1,1,1] (.node [13,11,8,7,7,5,2,2,2,1,1,1,1,1] (.node [13,11,8,7,7,4,3,2,2,1,1,1,1,1] (.node [13,11,8,7,7,4,2,2,2,2,1,1,1,1] (.node [13,11,8,7,7,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,7,4,4,2,1,1,1,1,1,1] (.node [13,11,8,7,7,4,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,7,7,6,2,2,1,1,1,1,1,1] (.node [13,11,8,7,7,5,4,1,1,1,1,1,1,1] (.node [13,11,8,7,7,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,7,6,3,1,1,1,1,1,1,1] .empty .empty))) (.node [13,11,8,8,4,4,3,3,3,1,1,1,1,1] (.node [13,11,8,8,4,4,2,2,2,2,2,2,2] (.node [13,11,8,8,4,3,3,3,3,2,2,1,1] (.node [13,11,8,8,4,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,8,8,4,4,3,2,2,2,2,2,1] (.node [13,11,8,8,4,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,8,8,4,4,4,4,1,1,1,1,1,1] (.node [13,11,8,8,4,4,4,3,2,1,1,1,1,1] (.node [13,11,8,8,4,4,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,5,2,2,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_933 : RowTree := (.node [13,11,8,7,7,3,3,2,2,2,1,1,1,1] degreeTree62_931 degreeTree62_932) - -def degreeTree62_934 : RowTree := (.node [13,11,8,8,5,5,3,2,2,1,1,1,1,1] (.node [13,11,8,8,5,4,3,2,2,2,1,1,1,1] (.node [13,11,8,8,5,3,3,3,3,1,1,1,1,1] (.node [13,11,8,8,5,3,3,2,2,2,2,2,1] (.node [13,11,8,8,5,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,5,4,2,2,2,2,2,2,1] (.node [13,11,8,8,5,4,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,8,8,5,4,4,3,1,1,1,1,1,1] (.node [13,11,8,8,5,4,4,2,2,1,1,1,1,1] (.node [13,11,8,8,5,4,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,5,5,2,2,2,2,1,1,1,1] .empty .empty))) (.node [13,11,8,8,6,3,2,2,2,2,2,1,1,1] (.node [13,11,8,8,5,5,5,1,1,1,1,1,1,1] (.node [13,11,8,8,5,5,4,2,1,1,1,1,1,1] (.node [13,11,8,8,5,5,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,6,2,2,2,2,2,2,2,2] (.node [13,11,8,8,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,11,8,8,6,3,3,3,2,1,1,1,1,1] (.node [13,11,8,8,6,3,3,2,2,2,1,1,1,1] (.node [13,11,8,8,6,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,8,8,6,4,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_935 : RowTree := (.node [13,11,8,8,7,3,3,2,2,1,1,1,1,1] (.node [13,11,8,8,6,6,2,2,1,1,1,1,1,1] (.node [13,11,8,8,6,5,2,2,2,1,1,1,1,1] (.node [13,11,8,8,6,4,4,2,1,1,1,1,1,1] (.node [13,11,8,8,6,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,6,5,4,1,1,1,1,1,1,1] (.node [13,11,8,8,6,5,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,8,7,2,2,2,2,2,2,2,1] (.node [13,11,8,8,7,2,2,2,2,2,2,1,1,1] (.node [13,11,8,8,6,6,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,7,3,2,2,2,2,1,1,1,1] .empty .empty))) (.node [13,11,8,8,7,5,3,1,1,1,1,1,1,1] (.node [13,11,8,8,7,4,3,2,1,1,1,1,1,1] (.node [13,11,8,8,7,4,2,2,2,1,1,1,1,1] (.node [13,11,8,8,7,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,7,5,2,2,1,1,1,1,1,1] (.node [13,11,8,8,7,4,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,8,8,2,2,2,2,2,1,1,1,1] (.node [13,11,8,8,7,7,1,1,1,1,1,1,1,1] (.node [13,11,8,8,7,6,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,8,3,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_936 : RowTree := (.node [13,11,8,8,6,4,3,2,2,1,1,1,1,1] degreeTree62_934 degreeTree62_935) - -def degreeTree62_937 : RowTree := (.node [13,11,8,8,5,3,2,2,2,2,2,2,2] degreeTree62_933 degreeTree62_936) - -def degreeTree62_938 : RowTree := (.node [13,11,8,7,6,3,2,2,2,2,2,2,2] degreeTree62_930 degreeTree62_937) - -def degreeTree62_939 : RowTree := (.node [13,11,9,5,5,5,2,2,2,2,2,2,2] (.node [13,11,9,5,4,4,4,2,2,2,2,2,2] (.node [13,11,8,8,8,5,2,1,1,1,1,1,1,1] (.node [13,11,8,8,8,4,3,1,1,1,1,1,1,1] (.node [13,11,8,8,8,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,4,4,4,4,4,3,2,2,1,1] (.node [13,11,8,8,8,6,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,5,5,4,3,3,3,2,2,1,1] (.node [13,11,9,5,5,4,3,2,2,2,2,2,2] (.node [13,11,9,5,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,11,9,5,5,4,4,2,2,2,2,2,1] .empty .empty))) (.node [13,11,9,6,4,4,4,3,3,1,1,1,1,1] (.node [13,11,9,6,4,4,3,3,3,2,2,1,1] (.node [13,11,9,6,4,4,3,2,2,2,2,2,2] (.node [13,11,9,5,5,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,6,4,4,4,2,2,2,2,2,1] (.node [13,11,9,6,4,4,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,9,6,5,4,2,2,2,2,2,2,2] (.node [13,11,9,6,5,3,3,2,2,2,2,2,2] (.node [13,11,9,6,4,4,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,6,5,4,3,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_940 : RowTree := (.node [13,11,9,6,5,5,5,2,1,1,1,1,1,1] (.node [13,11,9,6,5,5,2,2,2,2,2,2,1] (.node [13,11,9,6,5,4,4,3,2,1,1,1,1,1] (.node [13,11,9,6,5,4,4,2,2,2,1,1,1,1] (.node [13,11,9,6,5,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,6,5,5,2,2,2,2,2,1,1,1] (.node [13,11,9,6,5,4,4,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,6,5,5,4,2,2,1,1,1,1,1] (.node [13,11,9,6,5,5,3,3,2,1,1,1,1,1] (.node [13,11,9,6,5,5,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,6,5,5,4,3,1,1,1,1,1,1] .empty .empty))) (.node [13,11,9,6,6,4,2,2,2,2,2,1,1,1] (.node [13,11,9,6,6,3,3,2,2,2,2,1,1,1] (.node [13,11,9,6,6,3,2,2,2,2,2,2,2] (.node [13,11,9,6,6,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,6,6,3,3,3,3,1,1,1,1,1] (.node [13,11,9,6,6,3,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,11,9,6,6,4,3,3,2,1,1,1,1,1] (.node [13,11,9,6,6,4,3,2,2,2,1,1,1,1] (.node [13,11,9,6,6,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,6,6,4,4,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_941 : RowTree := (.node [13,11,9,6,5,4,3,2,2,2,2,2,1] degreeTree62_939 degreeTree62_940) - -def degreeTree62_942 : RowTree := (.node [13,11,9,7,4,4,3,2,2,2,2,1,1,1] (.node [13,11,9,6,6,6,2,2,2,1,1,1,1,1] (.node [13,11,9,6,6,5,3,3,1,1,1,1,1,1] (.node [13,11,9,6,6,5,3,2,2,1,1,1,1,1] (.node [13,11,9,6,6,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,6,6,5,5,1,1,1,1,1,1,1] (.node [13,11,9,6,6,5,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,7,4,3,3,2,2,2,2,2,2] (.node [13,11,9,6,6,6,4,1,1,1,1,1,1,1] (.node [13,11,9,6,6,6,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,7,4,4,2,2,2,2,2,2,2] .empty .empty))) (.node [13,11,9,7,5,2,2,2,2,2,2,2,2,1] (.node [13,11,9,7,4,4,4,2,2,2,1,1,1,1] (.node [13,11,9,7,4,4,3,3,3,1,1,1,1,1] (.node [13,11,9,7,4,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,7,4,4,4,4,1,1,1,1,1,1] (.node [13,11,9,7,4,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,7,5,3,3,2,2,2,2,2,1] (.node [13,11,9,7,5,3,3,2,2,2,2,1,1,1] (.node [13,11,9,7,5,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,9,7,5,3,3,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_943 : RowTree := (.node [13,11,9,7,6,2,2,2,2,2,2,2,1,1] (.node [13,11,9,7,5,5,2,2,2,2,1,1,1,1] (.node [13,11,9,7,5,4,3,3,2,1,1,1,1,1] (.node [13,11,9,7,5,4,3,2,2,2,1,1,1,1] (.node [13,11,9,7,5,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,7,5,4,4,3,1,1,1,1,1,1] (.node [13,11,9,7,5,4,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,7,5,5,4,2,1,1,1,1,1,1] (.node [13,11,9,7,5,5,3,3,1,1,1,1,1,1] (.node [13,11,9,7,5,5,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,7,5,5,5,1,1,1,1,1,1,1] .empty .empty))) (.node [13,11,9,7,6,4,2,2,2,2,1,1,1,1] (.node [13,11,9,7,6,3,2,2,2,2,2,2,1] (.node [13,11,9,7,6,3,2,2,2,2,2,1,1,1] (.node [13,11,9,7,6,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,9,7,6,3,3,3,2,1,1,1,1,1] (.node [13,11,9,7,6,3,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,7,6,4,4,2,1,1,1,1,1,1] (.node [13,11,9,7,6,4,3,3,1,1,1,1,1,1] (.node [13,11,9,7,6,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,7,6,5,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_944 : RowTree := (.node [13,11,9,7,5,4,2,2,2,2,2,1,1,1] degreeTree62_942 degreeTree62_943) - -def degreeTree62_945 : RowTree := (.node [13,11,9,6,6,4,4,3,1,1,1,1,1,1] degreeTree62_941 degreeTree62_944) - -def degreeTree62_946 : RowTree := (.node [13,11,9,7,7,4,4,1,1,1,1,1,1,1] (.node [13,11,9,7,7,3,2,2,2,2,1,1,1,1] (.node [13,11,9,7,6,6,3,1,1,1,1,1,1,1] (.node [13,11,9,7,6,6,2,2,1,1,1,1,1,1] (.node [13,11,9,7,6,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,7,7,2,2,2,2,2,2,2,1] (.node [13,11,9,7,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,9,7,7,4,2,2,2,1,1,1,1,1] (.node [13,11,9,7,7,3,3,3,1,1,1,1,1,1] (.node [13,11,9,7,7,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,7,7,4,3,2,1,1,1,1,1,1] .empty .empty))) (.node [13,11,9,8,4,2,2,2,2,2,2,2,2,1] (.node [13,11,9,7,7,6,2,1,1,1,1,1,1,1] (.node [13,11,9,7,7,5,3,1,1,1,1,1,1,1] (.node [13,11,9,7,7,5,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,8,3,3,3,2,2,2,2,2,2] (.node [13,11,9,7,7,7,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,8,4,3,3,2,2,2,2,2,1] (.node [13,11,9,8,4,3,3,2,2,2,2,1,1,1] (.node [13,11,9,8,4,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,9,8,4,3,3,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_947 : RowTree := (.node [13,11,9,8,5,3,3,3,2,1,1,1,1,1] (.node [13,11,9,8,5,2,2,2,2,2,2,2,1,1] (.node [13,11,9,8,4,4,3,3,2,1,1,1,1,1] (.node [13,11,9,8,4,4,3,2,2,2,1,1,1,1] (.node [13,11,9,8,4,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,8,4,4,4,3,1,1,1,1,1,1] (.node [13,11,9,8,4,4,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,8,5,3,2,2,2,2,2,2,1] (.node [13,11,9,8,5,3,2,2,2,2,2,1,1,1] (.node [13,11,9,8,5,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,9,8,5,3,3,2,2,2,1,1,1,1] .empty .empty))) (.node [13,11,9,8,5,5,3,2,1,1,1,1,1,1] (.node [13,11,9,8,5,4,3,3,1,1,1,1,1,1] (.node [13,11,9,8,5,4,3,2,2,1,1,1,1,1] (.node [13,11,9,8,5,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,8,5,5,2,2,2,1,1,1,1,1] (.node [13,11,9,8,5,4,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,8,6,2,2,2,2,2,2,2,1] (.node [13,11,9,8,6,2,2,2,2,2,2,1,1,1] (.node [13,11,9,8,5,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,8,6,3,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_948 : RowTree := (.node [13,11,9,8,4,4,2,2,2,2,2,1,1,1] degreeTree62_946 degreeTree62_947) - -def degreeTree62_949 : RowTree := (.node [13,11,9,8,7,4,2,2,1,1,1,1,1,1] (.node [13,11,9,8,6,5,3,1,1,1,1,1,1,1] (.node [13,11,9,8,6,4,3,2,1,1,1,1,1,1] (.node [13,11,9,8,6,4,2,2,2,1,1,1,1,1] (.node [13,11,9,8,6,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,8,6,5,2,2,1,1,1,1,1,1] (.node [13,11,9,8,6,4,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,8,7,3,2,2,2,1,1,1,1,1] (.node [13,11,9,8,7,2,2,2,2,2,1,1,1,1] (.node [13,11,9,8,6,6,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,8,7,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [13,11,9,8,8,3,3,1,1,1,1,1,1,1] (.node [13,11,9,8,7,6,1,1,1,1,1,1,1,1] (.node [13,11,9,8,7,5,2,1,1,1,1,1,1,1] (.node [13,11,9,8,7,4,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,8,8,3,2,2,1,1,1,1,1,1] (.node [13,11,9,8,8,2,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,9,3,2,2,2,2,2,2,2,2,1] (.node [13,11,9,8,8,5,1,1,1,1,1,1,1,1] (.node [13,11,9,8,8,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,3,3,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_950 : RowTree := (.node [13,11,9,9,4,4,3,3,1,1,1,1,1,1] (.node [13,11,9,9,4,3,2,2,2,2,2,2,1] (.node [13,11,9,9,4,2,2,2,2,2,2,2,1,1] (.node [13,11,9,9,3,3,3,3,3,1,1,1,1,1] (.node [13,11,9,9,3,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,9,4,3,2,2,2,2,2,1,1,1] (.node [13,11,9,9,4,2,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,11,9,9,4,4,2,2,2,2,1,1,1,1] (.node [13,11,9,9,4,3,3,3,2,1,1,1,1,1] (.node [13,11,9,9,4,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,4,4,3,2,2,1,1,1,1,1] .empty .empty))) (.node [13,11,9,9,5,3,3,2,2,1,1,1,1,1] (.node [13,11,9,9,5,2,2,2,2,2,2,2,1] (.node [13,11,9,9,5,2,2,2,2,2,2,1,1,1] (.node [13,11,9,9,4,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,5,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [13,11,9,9,5,4,3,2,1,1,1,1,1,1] (.node [13,11,9,9,5,4,2,2,2,1,1,1,1,1] (.node [13,11,9,9,5,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,5,4,4,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_951 : RowTree := (.node [13,11,9,9,3,3,3,2,2,2,2,1,1,1] degreeTree62_949 degreeTree62_950) - -def degreeTree62_952 : RowTree := (.node [13,11,9,8,6,3,3,2,2,1,1,1,1,1] degreeTree62_948 degreeTree62_951) - -def degreeTree62_953 : RowTree := (.node [13,11,9,7,6,5,3,2,1,1,1,1,1,1] degreeTree62_945 degreeTree62_952) - -def degreeTree62_954 : RowTree := (.node [13,11,8,8,8,3,3,2,1,1,1,1,1,1] degreeTree62_938 degreeTree62_953) - -def degreeTree62_955 : RowTree := (.node [13,11,7,7,6,6,4,2,1,1,1,1,1,1] degreeTree62_923 degreeTree62_954) - -def degreeTree62_956 : RowTree := (.node [13,11,9,9,7,3,3,1,1,1,1,1,1,1] (.node [13,11,9,9,6,4,3,1,1,1,1,1,1,1] (.node [13,11,9,9,6,3,2,2,2,1,1,1,1,1] (.node [13,11,9,9,6,2,2,2,2,2,1,1,1,1] (.node [13,11,9,9,5,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,6,4,2,2,1,1,1,1,1,1] (.node [13,11,9,9,6,3,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,9,7,2,2,2,2,1,1,1,1,1] (.node [13,11,9,9,6,6,1,1,1,1,1,1,1,1] (.node [13,11,9,9,6,5,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,7,3,2,2,1,1,1,1,1,1] .empty .empty))) (.node [13,11,9,9,9,2,2,1,1,1,1,1,1,1] (.node [13,11,9,9,8,2,2,2,1,1,1,1,1,1] (.node [13,11,9,9,7,5,1,1,1,1,1,1,1,1] (.node [13,11,9,9,7,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,8,4,1,1,1,1,1,1,1,1] (.node [13,11,9,9,8,3,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,12,6,5,5,5,4,2,2,2,2,2,2] (.node [13,12,5,5,5,5,5,2,2,2,2,2,2] (.node [13,11,9,9,9,3,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,6,5,5,5,5,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_957 : RowTree := (.node [13,12,6,6,6,6,4,2,2,1,1,1,1,1] (.node [13,12,6,6,6,5,3,2,2,2,2,2,1] (.node [13,12,6,6,6,4,3,2,2,2,2,2,2] (.node [13,12,6,6,5,5,4,2,2,2,2,2,1] (.node [13,12,6,6,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,12,6,6,6,5,2,2,2,2,2,2,2] (.node [13,12,6,6,6,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,12,6,6,6,6,3,2,2,2,1,1,1,1] (.node [13,12,6,6,6,6,2,2,2,2,2,2,1] (.node [13,12,6,6,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,12,6,6,6,6,3,3,2,1,1,1,1,1] .empty .empty))) (.node [13,12,7,5,5,5,4,2,2,2,2,2,1] (.node [13,12,6,6,6,6,6,1,1,1,1,1,1,1] (.node [13,12,6,6,6,6,5,2,1,1,1,1,1,1] (.node [13,12,6,6,6,6,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,5,5,5,3,2,2,2,2,2,2] (.node [13,12,7,5,5,4,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,12,7,6,5,4,4,2,2,2,2,2,1] (.node [13,12,7,6,5,4,3,2,2,2,2,2,2] (.node [13,12,7,6,4,4,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,12,7,6,5,5,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_958 : RowTree := (.node [13,12,6,6,5,4,4,2,2,2,2,2,2] degreeTree62_956 degreeTree62_957) - -def degreeTree62_959 : RowTree := (.node [13,12,7,6,6,5,4,2,2,1,1,1,1,1] (.node [13,12,7,6,6,4,4,3,2,1,1,1,1,1] (.node [13,12,7,6,6,4,3,2,2,2,2,1,1,1] (.node [13,12,7,6,6,4,2,2,2,2,2,2,2] (.node [13,12,7,6,6,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,12,7,6,6,4,4,2,2,2,1,1,1,1] (.node [13,12,7,6,6,4,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [13,12,7,6,6,5,3,2,2,2,1,1,1,1] (.node [13,12,7,6,6,5,2,2,2,2,2,1,1,1] (.node [13,12,7,6,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,6,6,5,3,3,2,1,1,1,1,1] .empty .empty))) (.node [13,12,7,6,6,6,4,2,1,1,1,1,1,1] (.node [13,12,7,6,6,6,2,2,2,2,1,1,1,1] (.node [13,12,7,6,6,5,5,2,1,1,1,1,1,1] (.node [13,12,7,6,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,6,6,6,3,3,1,1,1,1,1,1] (.node [13,12,7,6,6,6,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,12,7,7,4,4,4,2,2,2,2,1,1,1] (.node [13,12,7,7,4,4,3,2,2,2,2,2,2] (.node [13,12,7,6,6,6,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,4,4,4,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_960 : RowTree := (.node [13,12,7,7,5,5,3,3,2,1,1,1,1,1] (.node [13,12,7,7,5,4,4,2,2,2,1,1,1,1] (.node [13,12,7,7,5,4,2,2,2,2,2,2,2] (.node [13,12,7,7,5,3,3,2,2,2,2,2,2] (.node [13,12,7,7,4,4,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,5,4,3,3,3,1,1,1,1,1] (.node [13,12,7,7,5,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,12,7,7,5,5,2,2,2,2,2,1,1,1] (.node [13,12,7,7,5,4,4,4,1,1,1,1,1,1] (.node [13,12,7,7,5,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,5,5,3,2,2,2,1,1,1,1] .empty .empty))) (.node [13,12,7,7,6,3,3,2,2,2,2,1,1,1] (.node [13,12,7,7,5,5,5,2,1,1,1,1,1,1] (.node [13,12,7,7,5,5,4,3,1,1,1,1,1,1] (.node [13,12,7,7,5,5,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,6,3,2,2,2,2,2,2,2] (.node [13,12,7,7,6,2,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,12,7,7,6,4,3,2,2,2,1,1,1,1] (.node [13,12,7,7,6,4,2,2,2,2,2,1,1,1] (.node [13,12,7,7,6,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,6,4,3,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_961 : RowTree := (.node [13,12,7,7,4,4,4,3,3,1,1,1,1,1] degreeTree62_959 degreeTree62_960) - -def degreeTree62_962 : RowTree := (.node [13,12,7,6,5,5,3,2,2,2,2,2,1] degreeTree62_958 degreeTree62_961) - -def degreeTree62_963 : RowTree := (.node [13,12,7,7,7,2,2,2,2,2,2,2,2] (.node [13,12,7,7,6,5,5,1,1,1,1,1,1,1] (.node [13,12,7,7,6,5,3,2,2,1,1,1,1,1] (.node [13,12,7,7,6,5,2,2,2,2,1,1,1,1] (.node [13,12,7,7,6,4,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,6,5,4,2,1,1,1,1,1,1] (.node [13,12,7,7,6,5,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,12,7,7,6,6,4,1,1,1,1,1,1,1] (.node [13,12,7,7,6,6,3,2,1,1,1,1,1,1] (.node [13,12,7,7,6,6,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,7,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [13,12,7,7,7,4,3,3,1,1,1,1,1,1] (.node [13,12,7,7,7,3,3,3,2,1,1,1,1,1] (.node [13,12,7,7,7,3,3,2,2,2,1,1,1,1] (.node [13,12,7,7,7,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,7,4,3,2,2,1,1,1,1,1] (.node [13,12,7,7,7,4,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,12,7,7,7,5,3,2,1,1,1,1,1,1] (.node [13,12,7,7,7,5,2,2,2,1,1,1,1,1] (.node [13,12,7,7,7,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,7,5,4,1,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_964 : RowTree := (.node [13,13,6,5,5,4,4,2,2,2,2,2,2] (.node [13,13,5,5,5,5,5,2,2,2,2,1,1,1] (.node [13,13,5,5,5,4,4,4,4,1,1,1,1,1] (.node [13,12,7,7,7,7,2,1,1,1,1,1,1,1] (.node [13,12,7,7,7,6,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,5,5,5,5,4,4,3,1,1,1,1,1] (.node [13,13,5,5,5,5,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,13,5,5,5,5,5,5,1,1,1,1,1,1] (.node [13,13,5,5,5,5,5,4,2,1,1,1,1,1] (.node [13,13,5,5,5,5,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,6,5,4,4,4,4,4,1,1,1,1,1] .empty .empty))) (.node [13,13,6,5,5,5,5,2,2,2,1,1,1,1] (.node [13,13,6,5,5,5,4,2,2,2,2,1,1,1] (.node [13,13,6,5,5,5,3,2,2,2,2,2,2] (.node [13,13,6,5,5,4,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,6,5,5,5,4,4,2,1,1,1,1,1] (.node [13,13,6,5,5,5,4,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,6,6,4,4,4,2,2,2,2,2,2] (.node [13,13,6,5,5,5,5,4,1,1,1,1,1,1] (.node [13,13,6,5,5,5,5,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,6,6,4,4,4,4,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_965 : RowTree := (.node [13,12,7,7,7,6,2,2,1,1,1,1,1,1] degreeTree62_963 degreeTree62_964) - -def degreeTree62_966 : RowTree := (.node [13,13,6,6,5,5,5,3,1,1,1,1,1,1] (.node [13,13,6,6,5,5,3,3,3,1,1,1,1,1] (.node [13,13,6,6,5,4,4,4,2,1,1,1,1,1] (.node [13,13,6,6,5,4,4,3,3,1,1,1,1,1] (.node [13,13,6,6,5,4,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,13,6,6,5,5,3,2,2,2,2,1,1,1] (.node [13,13,6,6,5,5,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,13,6,6,5,5,4,4,1,1,1,1,1,1] (.node [13,13,6,6,5,5,4,3,2,1,1,1,1,1] (.node [13,13,6,6,5,5,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,13,6,6,5,5,5,2,2,1,1,1,1,1] .empty .empty))) (.node [13,13,6,6,6,4,4,4,1,1,1,1,1,1] (.node [13,13,6,6,6,4,3,3,3,1,1,1,1,1] (.node [13,13,6,6,6,4,3,2,2,2,2,1,1,1] (.node [13,13,6,6,6,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,13,6,6,6,4,4,3,2,1,1,1,1,1] (.node [13,13,6,6,6,4,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,13,6,6,6,5,3,3,2,1,1,1,1,1] (.node [13,13,6,6,6,5,3,2,2,2,1,1,1,1] (.node [13,13,6,6,6,5,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,13,6,6,6,5,4,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_967 : RowTree := (.node [13,13,7,5,5,4,4,2,2,2,2,1,1,1] (.node [13,13,6,6,6,6,5,1,1,1,1,1,1,1] (.node [13,13,6,6,6,6,3,2,2,1,1,1,1,1] (.node [13,13,6,6,6,6,2,2,2,2,1,1,1,1] (.node [13,13,6,6,6,5,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,6,6,6,6,4,2,1,1,1,1,1,1] (.node [13,13,6,6,6,6,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,7,5,4,4,4,4,3,1,1,1,1,1] (.node [13,13,7,5,4,4,4,2,2,2,2,2,2] (.node [13,13,7,4,4,4,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,5,5,4,3,2,2,2,2,2,2] .empty .empty))) (.node [13,13,7,5,5,5,4,3,2,1,1,1,1,1] (.node [13,13,7,5,5,5,3,2,2,2,2,1,1,1] (.node [13,13,7,5,5,4,4,4,2,1,1,1,1,1] (.node [13,13,7,5,5,4,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,5,5,5,4,2,2,2,1,1,1,1] (.node [13,13,7,5,5,5,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,7,5,5,5,5,3,1,1,1,1,1,1] (.node [13,13,7,5,5,5,5,2,2,1,1,1,1,1] (.node [13,13,7,5,5,5,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,6,4,4,3,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree62_968 : RowTree := (.node [13,13,6,6,6,5,4,3,1,1,1,1,1,1] degreeTree62_966 degreeTree62_967) - -def degreeTree62_969 : RowTree := (.node [13,13,6,6,5,4,3,2,2,2,2,2,2] degreeTree62_965 degreeTree62_968) - -def degreeTree62_970 : RowTree := (.node [13,12,7,7,6,4,4,2,2,1,1,1,1,1] degreeTree62_962 degreeTree62_969) - -def degreeTree62_971 : RowTree := (.node [13,13,7,6,5,5,4,2,2,1,1,1,1,1] (.node [13,13,7,6,5,4,4,3,2,1,1,1,1,1] (.node [13,13,7,6,5,4,3,2,2,2,2,1,1,1] (.node [13,13,7,6,4,4,4,4,2,1,1,1,1,1] (.node [13,13,7,6,4,4,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,6,5,4,4,2,2,2,1,1,1,1] (.node [13,13,7,6,5,4,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,7,6,5,5,3,2,2,2,1,1,1,1] (.node [13,13,7,6,5,5,2,2,2,2,2,1,1,1] (.node [13,13,7,6,5,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,6,5,5,3,3,2,1,1,1,1,1] .empty .empty))) (.node [13,13,7,6,6,4,2,2,2,2,2,1,1,1] (.node [13,13,7,6,6,2,2,2,2,2,2,2,2,1] (.node [13,13,7,6,5,5,5,2,1,1,1,1,1,1] (.node [13,13,7,6,5,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,6,6,3,3,3,3,1,1,1,1,1] (.node [13,13,7,6,6,3,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,13,7,6,6,4,4,2,2,1,1,1,1,1] (.node [13,13,7,6,6,4,3,3,2,1,1,1,1,1] (.node [13,13,7,6,6,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,6,6,4,4,3,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_972 : RowTree := (.node [13,13,7,7,4,4,4,3,2,1,1,1,1,1] (.node [13,13,7,6,6,6,3,2,1,1,1,1,1,1] (.node [13,13,7,6,6,5,4,2,1,1,1,1,1,1] (.node [13,13,7,6,6,5,3,3,1,1,1,1,1,1] (.node [13,13,7,6,6,5,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,6,6,6,2,2,2,1,1,1,1,1] (.node [13,13,7,6,6,5,5,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,7,7,4,4,3,3,3,1,1,1,1,1] (.node [13,13,7,7,4,4,3,2,2,2,2,1,1,1] (.node [13,13,7,6,6,6,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,4,4,4,2,2,2,1,1,1,1] .empty .empty))) (.node [13,13,7,7,5,4,3,2,2,2,1,1,1,1] (.node [13,13,7,7,5,3,3,2,2,2,2,1,1,1] (.node [13,13,7,7,5,2,2,2,2,2,2,2,2,1] (.node [13,13,7,7,4,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,5,4,2,2,2,2,2,1,1,1] (.node [13,13,7,7,5,3,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,7,7,5,4,4,3,1,1,1,1,1,1] (.node [13,13,7,7,5,4,4,2,2,1,1,1,1,1] (.node [13,13,7,7,5,4,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,5,5,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_973 : RowTree := (.node [13,13,7,6,6,5,2,2,2,2,1,1,1,1] degreeTree62_971 degreeTree62_972) - -def degreeTree62_974 : RowTree := (.node [13,13,7,7,6,4,4,2,1,1,1,1,1,1] (.node [13,13,7,7,6,3,3,2,2,2,1,1,1,1] (.node [13,13,7,7,5,5,5,1,1,1,1,1,1,1] (.node [13,13,7,7,5,5,4,2,1,1,1,1,1,1] (.node [13,13,7,7,5,5,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,6,3,2,2,2,2,2,1,1,1] (.node [13,13,7,7,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,13,7,7,6,4,3,2,2,1,1,1,1,1] (.node [13,13,7,7,6,4,2,2,2,2,1,1,1,1] (.node [13,13,7,7,6,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,6,4,3,3,1,1,1,1,1,1] .empty .empty))) (.node [13,13,7,7,7,2,2,2,2,2,2,1,1,1] (.node [13,13,7,7,6,5,4,1,1,1,1,1,1,1] (.node [13,13,7,7,6,5,3,2,1,1,1,1,1,1] (.node [13,13,7,7,6,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,6,6,3,1,1,1,1,1,1,1] (.node [13,13,7,7,6,6,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,7,7,7,3,3,3,1,1,1,1,1,1] (.node [13,13,7,7,7,3,3,2,2,1,1,1,1,1] (.node [13,13,7,7,7,3,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,7,4,2,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_975 : RowTree := (.node [14,6,6,6,6,6,6,5,2,1,1,1,1,1] (.node [14,6,6,6,5,5,5,5,5,1,1,1,1,1] (.node [13,13,7,7,7,5,3,1,1,1,1,1,1,1] (.node [13,13,7,7,7,5,2,2,1,1,1,1,1,1] (.node [13,13,7,7,7,4,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,7,7,1,1,1,1,1,1,1,1] (.node [13,13,7,7,7,6,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [14,6,6,6,6,6,5,5,3,1,1,1,1,1] (.node [14,6,6,6,6,6,5,4,4,1,1,1,1,1] (.node [14,6,6,6,6,5,5,5,4,1,1,1,1,1] .empty .empty) .empty) (.node [14,6,6,6,6,6,6,4,3,1,1,1,1,1] .empty .empty))) (.node [14,7,6,6,6,6,4,4,4,1,1,1,1,1] (.node [14,7,6,6,5,5,5,5,4,1,1,1,1,1] (.node [14,7,6,5,5,5,5,5,5,1,1,1,1,1] (.node [14,6,6,6,6,6,6,6,1,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,6,6,6,5,5,5,3,1,1,1,1,1] (.node [14,7,6,6,6,5,5,4,4,1,1,1,1,1] .empty .empty) .empty)) (.node [14,7,6,6,6,6,6,2,2,2,2,1,1,1] (.node [14,7,6,6,6,6,5,5,2,1,1,1,1,1] (.node [14,7,6,6,6,6,5,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,6,6,6,6,6,3,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_976 : RowTree := (.node [13,13,7,7,7,4,3,2,1,1,1,1,1,1] degreeTree62_974 degreeTree62_975) - -def degreeTree62_977 : RowTree := (.node [13,13,7,7,5,5,3,2,2,1,1,1,1,1] degreeTree62_973 degreeTree62_976) - -def degreeTree62_978 : RowTree := (.node [14,7,7,6,6,6,5,4,2,1,1,1,1,1] (.node [14,7,7,6,6,5,5,4,3,1,1,1,1,1] (.node [14,7,7,6,5,5,5,4,4,1,1,1,1,1] (.node [14,7,7,5,5,5,5,5,4,1,1,1,1,1] (.node [14,7,6,6,6,6,6,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,6,6,5,4,4,4,1,1,1,1,1] (.node [14,7,7,6,5,5,5,5,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,7,7,6,6,6,5,2,2,2,2,1,1,1] (.node [14,7,7,6,6,6,4,4,3,1,1,1,1,1] (.node [14,7,7,6,6,5,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,6,6,6,5,3,3,1,1,1,1,1] .empty .empty))) (.node [14,7,7,7,5,5,5,4,3,1,1,1,1,1] (.node [14,7,7,6,6,6,6,3,2,1,1,1,1,1] (.node [14,7,7,6,6,6,6,2,2,2,1,1,1,1] (.node [14,7,7,6,6,6,5,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,5,5,4,4,4,1,1,1,1,1] (.node [14,7,7,6,6,6,6,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [14,7,7,7,6,5,4,4,3,1,1,1,1,1] (.node [14,7,7,7,6,4,4,4,4,1,1,1,1,1] (.node [14,7,7,7,5,5,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,6,5,5,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_979 : RowTree := (.node [14,7,7,7,7,4,4,4,3,1,1,1,1,1] (.node [14,7,7,7,6,6,5,2,2,2,1,1,1,1] (.node [14,7,7,7,6,6,4,2,2,2,2,1,1,1] (.node [14,7,7,7,6,5,5,5,1,1,1,1,1,1] (.node [14,7,7,7,6,5,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,6,6,4,4,2,1,1,1,1,1] (.node [14,7,7,7,6,6,4,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,7,7,7,6,6,6,2,2,1,1,1,1,1] (.node [14,7,7,7,6,6,5,4,1,1,1,1,1,1] (.node [14,7,7,7,6,6,5,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,6,6,6,3,1,1,1,1,1,1] .empty .empty))) (.node [14,7,7,7,7,5,5,4,1,1,1,1,1,1] (.node [14,7,7,7,7,5,4,4,2,1,1,1,1,1] (.node [14,7,7,7,7,5,4,3,3,1,1,1,1,1] (.node [14,7,7,7,7,5,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,7,5,5,3,2,1,1,1,1,1] (.node [14,7,7,7,7,5,5,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [14,7,7,7,7,6,4,2,2,2,1,1,1,1] (.node [14,7,7,7,7,6,3,3,3,1,1,1,1,1] (.node [14,7,7,7,7,6,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,7,6,4,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_980 : RowTree := (.node [14,7,7,7,6,5,5,3,3,1,1,1,1,1] degreeTree62_978 degreeTree62_979) - -def degreeTree62_981 : RowTree := (.node [14,8,5,5,5,5,5,5,5,1,1,1,1,1] (.node [14,7,7,7,7,7,3,3,2,1,1,1,1,1] (.node [14,7,7,7,7,6,6,2,1,1,1,1,1,1] (.node [14,7,7,7,7,6,5,3,1,1,1,1,1,1] (.node [14,7,7,7,7,6,5,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,7,7,3,2,2,2,1,1,1,1] (.node [14,7,7,7,7,7,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,7,7,7,7,7,5,2,1,1,1,1,1,1] (.node [14,7,7,7,7,7,4,3,1,1,1,1,1,1] (.node [14,7,7,7,7,7,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,7,7,6,1,1,1,1,1,1,1] .empty .empty))) (.node [14,8,6,6,6,5,5,5,2,1,1,1,1,1] (.node [14,8,6,6,5,5,5,5,3,1,1,1,1,1] (.node [14,8,6,6,5,5,5,4,4,1,1,1,1,1] (.node [14,8,6,5,5,5,5,5,4,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,6,6,6,5,5,4,3,1,1,1,1,1] (.node [14,8,6,6,6,5,4,4,4,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,6,6,6,6,5,3,3,1,1,1,1,1] (.node [14,8,6,6,6,6,5,2,2,2,2,1,1,1] (.node [14,8,6,6,6,6,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,6,6,6,6,5,4,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_982 : RowTree := (.node [14,8,7,6,6,5,5,2,2,2,2,1,1,1] (.node [14,8,7,6,5,5,4,4,4,1,1,1,1,1] (.node [14,8,6,6,6,6,6,4,1,1,1,1,1,1] (.node [14,8,6,6,6,6,6,3,2,1,1,1,1,1] (.node [14,8,6,6,6,6,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,5,5,5,5,5,3,1,1,1,1,1] (.node [14,8,7,5,5,5,5,4,4,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,7,6,6,4,4,4,4,1,1,1,1,1] (.node [14,8,7,6,5,5,5,5,2,1,1,1,1,1] (.node [14,8,7,6,5,5,5,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,6,6,5,4,4,3,1,1,1,1,1] .empty .empty))) (.node [14,8,7,6,6,6,4,3,3,1,1,1,1,1] (.node [14,8,7,6,6,5,5,5,1,1,1,1,1,1] (.node [14,8,7,6,6,5,5,4,2,1,1,1,1,1] (.node [14,8,7,6,6,5,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,6,6,6,4,2,2,2,2,1,1,1] .empty .empty)) (.node [14,8,7,6,6,6,5,3,2,1,1,1,1,1] (.node [14,8,7,6,6,6,5,2,2,2,1,1,1,1] (.node [14,8,7,6,6,6,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,6,6,6,5,4,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_983 : RowTree := (.node [14,8,6,6,6,6,5,5,1,1,1,1,1,1] degreeTree62_981 degreeTree62_982) - -def degreeTree62_984 : RowTree := (.node [14,7,7,7,7,6,4,4,1,1,1,1,1,1] degreeTree62_980 degreeTree62_983) - -def degreeTree62_985 : RowTree := (.node [14,7,6,6,6,6,6,4,2,1,1,1,1,1] degreeTree62_977 degreeTree62_984) - -def degreeTree62_986 : RowTree := (.node [13,13,7,6,4,4,4,2,2,2,2,1,1,1] degreeTree62_970 degreeTree62_985) - -def degreeTree62_987 : RowTree := (.node [14,8,7,7,6,5,4,4,2,1,1,1,1,1] (.node [14,8,7,7,5,5,5,4,2,1,1,1,1,1] (.node [14,8,7,7,5,5,4,4,3,1,1,1,1,1] (.node [14,8,7,7,5,4,4,4,4,1,1,1,1,1] (.node [14,8,7,6,6,6,6,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,5,5,5,3,3,1,1,1,1,1] (.node [14,8,7,7,5,5,5,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,8,7,7,6,5,4,2,2,2,2,1,1,1] (.node [14,8,7,7,6,4,4,4,3,1,1,1,1,1] (.node [14,8,7,7,5,5,5,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,6,5,4,3,3,1,1,1,1,1] .empty .empty))) (.node [14,8,7,7,6,6,4,2,2,2,1,1,1,1] (.node [14,8,7,7,6,5,5,4,1,1,1,1,1,1] (.node [14,8,7,7,6,5,5,3,2,1,1,1,1,1] (.node [14,8,7,7,6,5,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,6,6,3,3,3,1,1,1,1,1] (.node [14,8,7,7,6,6,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,8,7,7,6,6,5,2,2,1,1,1,1,1] (.node [14,8,7,7,6,6,4,4,1,1,1,1,1,1] (.node [14,8,7,7,6,6,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,6,6,5,3,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_988 : RowTree := (.node [14,8,7,7,7,6,2,2,2,2,2,1,1,1] (.node [14,8,7,7,7,5,4,2,2,2,1,1,1,1] (.node [14,8,7,7,7,4,4,4,2,1,1,1,1,1] (.node [14,8,7,7,7,4,4,3,3,1,1,1,1,1] (.node [14,8,7,7,7,4,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,7,5,3,3,3,1,1,1,1,1] (.node [14,8,7,7,7,5,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,8,7,7,7,5,5,2,2,1,1,1,1,1] (.node [14,8,7,7,7,5,4,4,1,1,1,1,1,1] (.node [14,8,7,7,7,5,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,7,5,5,3,1,1,1,1,1,1] .empty .empty))) (.node [14,8,7,7,7,7,2,2,2,2,1,1,1,1] (.node [14,8,7,7,7,6,4,2,2,1,1,1,1,1] (.node [14,8,7,7,7,6,3,3,2,1,1,1,1,1] (.node [14,8,7,7,7,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,7,6,5,2,1,1,1,1,1,1] (.node [14,8,7,7,7,6,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,5,5,5,4,4,4,1,1,1,1,1] (.node [14,8,7,7,7,7,3,3,1,1,1,1,1,1] (.node [14,8,7,7,7,7,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,5,5,5,5,4,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_989 : RowTree := (.node [14,8,7,7,6,6,6,2,1,1,1,1,1,1] degreeTree62_987 degreeTree62_988) - -def degreeTree62_990 : RowTree := (.node [14,8,8,6,6,5,5,2,2,2,1,1,1,1] (.node [14,8,8,6,5,5,5,5,1,1,1,1,1,1] (.node [14,8,8,6,5,5,5,2,2,2,2,1,1,1] (.node [14,8,8,6,5,5,4,4,3,1,1,1,1,1] (.node [14,8,8,6,5,4,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,6,5,5,5,4,2,1,1,1,1,1] (.node [14,8,8,6,5,5,5,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,6,6,5,4,3,3,1,1,1,1,1] (.node [14,8,8,6,6,5,4,2,2,2,2,1,1,1] (.node [14,8,8,6,6,4,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,6,6,5,4,4,2,1,1,1,1,1] .empty .empty))) (.node [14,8,8,6,6,6,4,3,2,1,1,1,1,1] (.node [14,8,8,6,6,6,3,2,2,2,2,1,1,1] (.node [14,8,8,6,6,5,5,4,1,1,1,1,1,1] (.node [14,8,8,6,6,5,5,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,6,6,6,4,2,2,2,1,1,1,1] (.node [14,8,8,6,6,6,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,6,6,6,5,3,1,1,1,1,1,1] (.node [14,8,8,6,6,6,5,2,2,1,1,1,1,1] (.node [14,8,8,6,6,6,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,4,4,4,4,4,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_991 : RowTree := (.node [14,8,8,7,6,5,3,3,3,1,1,1,1,1] (.node [14,8,8,7,5,5,5,4,1,1,1,1,1,1] (.node [14,8,8,7,5,5,4,4,2,1,1,1,1,1] (.node [14,8,8,7,5,5,4,3,3,1,1,1,1,1] (.node [14,8,8,7,5,5,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,5,5,5,3,2,1,1,1,1,1] (.node [14,8,8,7,5,5,5,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,7,6,4,4,4,2,1,1,1,1,1] (.node [14,8,8,7,6,4,4,3,3,1,1,1,1,1] (.node [14,8,8,7,6,4,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,6,5,3,2,2,2,2,1,1,1] .empty .empty))) (.node [14,8,8,7,6,6,2,2,2,2,2,1,1,1] (.node [14,8,8,7,6,5,4,4,1,1,1,1,1,1] (.node [14,8,8,7,6,5,4,3,2,1,1,1,1,1] (.node [14,8,8,7,6,5,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,6,5,5,3,1,1,1,1,1,1] (.node [14,8,8,7,6,5,5,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,7,6,6,4,2,2,1,1,1,1,1] (.node [14,8,8,7,6,6,3,3,2,1,1,1,1,1] (.node [14,8,8,7,6,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,6,6,4,3,1,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_992 : RowTree := (.node [14,8,8,7,5,4,4,4,3,1,1,1,1,1] degreeTree62_990 degreeTree62_991) - -def degreeTree62_993 : RowTree := (.node [14,8,8,5,5,5,5,5,2,1,1,1,1,1] degreeTree62_989 degreeTree62_992) - -def degreeTree62_994 : RowTree := (.node [14,8,8,7,7,7,2,2,2,1,1,1,1,1] (.node [14,8,8,7,7,5,3,2,2,2,1,1,1,1] (.node [14,8,8,7,7,4,4,3,2,1,1,1,1,1] (.node [14,8,8,7,7,4,4,2,2,2,1,1,1,1] (.node [14,8,8,7,7,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,7,5,2,2,2,2,2,1,1,1] (.node [14,8,8,7,7,4,4,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,7,7,6,2,2,2,2,1,1,1,1] (.node [14,8,8,7,7,5,4,2,2,1,1,1,1,1] (.node [14,8,8,7,7,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,7,6,3,2,2,1,1,1,1,1] .empty .empty))) (.node [14,8,8,8,5,5,3,3,3,1,1,1,1,1] (.node [14,8,8,8,5,4,4,3,3,1,1,1,1,1] (.node [14,8,8,8,5,4,4,2,2,2,2,1,1,1] (.node [14,8,8,8,4,4,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,8,5,5,3,2,2,2,2,1,1,1] (.node [14,8,8,8,5,4,4,4,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,8,5,5,4,4,1,1,1,1,1,1] (.node [14,8,8,8,5,5,4,3,2,1,1,1,1,1] (.node [14,8,8,8,5,5,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,8,5,5,5,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_995 : RowTree := (.node [14,8,8,8,7,3,3,2,2,2,2,1,1,1] (.node [14,8,8,8,6,5,3,3,2,1,1,1,1,1] (.node [14,8,8,8,6,4,4,3,2,1,1,1,1,1] (.node [14,8,8,8,6,4,4,2,2,2,1,1,1,1] (.node [14,8,8,8,6,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,8,6,5,3,2,2,2,1,1,1,1] (.node [14,8,8,8,6,5,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,8,8,8,6,6,3,2,2,1,1,1,1,1] (.node [14,8,8,8,6,6,2,2,2,2,1,1,1,1] (.node [14,8,8,8,6,5,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,8,7,2,2,2,2,2,2,2,2,1] .empty .empty))) (.node [14,8,8,8,7,5,2,2,2,2,1,1,1,1] (.node [14,8,8,8,7,4,3,2,2,2,1,1,1,1] (.node [14,8,8,8,7,4,2,2,2,2,2,1,1,1] (.node [14,8,8,8,7,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,8,7,4,4,2,2,1,1,1,1,1] (.node [14,8,8,8,7,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,8,8,2,2,2,2,2,2,2,1,1] (.node [14,8,8,8,7,6,2,2,2,1,1,1,1,1] (.node [14,8,8,8,7,5,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,8,8,3,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_996 : RowTree := (.node [14,8,8,8,6,4,3,2,2,2,2,1,1,1] degreeTree62_994 degreeTree62_995) - -def degreeTree62_997 : RowTree := (.node [14,9,6,6,6,4,4,4,4,1,1,1,1,1] (.node [14,9,6,5,5,5,5,4,4,1,1,1,1,1] (.node [14,8,8,8,8,4,3,2,2,1,1,1,1,1] (.node [14,8,8,8,8,4,2,2,2,2,1,1,1,1] (.node [14,8,8,8,8,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,5,5,5,5,5,5,4,1,1,1,1,1] (.node [14,8,8,8,8,5,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,6,6,5,5,5,4,3,1,1,1,1,1] (.node [14,9,6,6,5,5,4,4,4,1,1,1,1,1] (.node [14,9,6,5,5,5,5,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,6,6,5,5,5,5,2,1,1,1,1,1] .empty .empty))) (.node [14,9,6,6,6,6,4,3,3,1,1,1,1,1] (.node [14,9,6,6,6,5,5,3,3,1,1,1,1,1] (.node [14,9,6,6,6,5,5,2,2,2,2,1,1,1] (.node [14,9,6,6,6,5,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,6,6,6,6,4,2,2,2,2,1,1,1] (.node [14,9,6,6,6,5,5,4,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,6,6,6,6,5,3,2,1,1,1,1,1] (.node [14,9,6,6,6,6,5,2,2,2,1,1,1,1] (.node [14,9,6,6,6,6,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,6,6,6,6,6,2,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_998 : RowTree := (.node [14,9,7,6,6,5,4,4,2,1,1,1,1,1] (.node [14,9,7,6,5,5,5,3,3,1,1,1,1,1] (.node [14,9,7,6,5,4,4,4,4,1,1,1,1,1] (.node [14,9,7,5,5,5,5,5,2,1,1,1,1,1] (.node [14,9,7,5,5,5,5,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,6,5,5,5,2,2,2,2,1,1,1] (.node [14,9,7,6,5,5,4,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,7,6,6,5,4,2,2,2,2,1,1,1] (.node [14,9,7,6,6,4,4,4,3,1,1,1,1,1] (.node [14,9,7,6,5,5,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,6,6,5,4,3,3,1,1,1,1,1] .empty .empty))) (.node [14,9,7,6,6,6,4,2,2,2,1,1,1,1] (.node [14,9,7,6,6,6,3,2,2,2,2,1,1,1] (.node [14,9,7,6,6,5,5,3,2,1,1,1,1,1] (.node [14,9,7,6,6,5,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,6,6,6,3,3,3,1,1,1,1,1] .empty .empty)) (.node [14,9,7,7,4,4,4,4,4,1,1,1,1,1] (.node [14,9,7,6,6,6,5,2,2,1,1,1,1,1] (.node [14,9,7,6,6,6,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,7,5,4,4,4,3,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_999 : RowTree := (.node [14,9,7,5,5,5,4,4,4,1,1,1,1,1] degreeTree62_997 degreeTree62_998) - -def degreeTree62_1000 : RowTree := (.node [14,8,8,8,8,3,3,2,2,2,1,1,1,1] degreeTree62_996 degreeTree62_999) - -def degreeTree62_1001 : RowTree := (.node [14,8,8,7,7,4,3,2,2,2,2,1,1,1] degreeTree62_993 degreeTree62_1000) - -def degreeTree62_1002 : RowTree := (.node [14,9,7,7,6,5,4,3,2,1,1,1,1,1] (.node [14,9,7,7,6,4,4,3,3,1,1,1,1,1] (.node [14,9,7,7,5,5,5,2,2,2,1,1,1,1] (.node [14,9,7,7,5,5,4,4,2,1,1,1,1,1] (.node [14,9,7,7,5,5,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,7,6,4,4,2,2,2,2,1,1,1] (.node [14,9,7,7,5,5,5,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,7,7,6,5,3,3,3,1,1,1,1,1] (.node [14,9,7,7,6,5,3,2,2,2,2,1,1,1] (.node [14,9,7,7,6,4,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,7,6,5,4,2,2,2,1,1,1,1] .empty .empty))) (.node [14,9,7,7,7,4,3,2,2,2,2,1,1,1] (.node [14,9,7,7,6,6,3,2,2,2,1,1,1,1] (.node [14,9,7,7,6,6,2,2,2,2,2,1,1,1] (.node [14,9,7,7,6,5,5,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,7,6,6,4,2,2,1,1,1,1,1] (.node [14,9,7,7,6,6,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,7,7,7,4,4,3,2,1,1,1,1,1] (.node [14,9,7,7,7,4,4,2,2,2,1,1,1,1] (.node [14,9,7,7,7,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,7,7,5,2,2,2,2,2,1,1,1] .empty .empty)))) - -def degreeTree62_1003 : RowTree := (.node [14,9,8,6,5,5,4,3,3,1,1,1,1,1] (.node [14,9,8,5,5,5,5,3,3,1,1,1,1,1] (.node [14,9,8,5,5,4,4,4,4,1,1,1,1,1] (.node [14,9,7,7,7,6,2,2,2,2,1,1,1,1] (.node [14,9,7,7,7,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,8,5,5,5,5,2,2,2,2,1,1,1] (.node [14,9,8,5,5,5,4,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,8,6,5,4,4,4,3,1,1,1,1,1] (.node [14,9,8,6,4,4,4,4,4,1,1,1,1,1] (.node [14,9,8,5,5,5,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,8,6,5,5,4,2,2,2,2,1,1,1] .empty .empty))) (.node [14,9,8,6,6,4,4,4,2,1,1,1,1,1] (.node [14,9,8,6,5,5,5,3,2,1,1,1,1,1] (.node [14,9,8,6,5,5,5,2,2,2,1,1,1,1] (.node [14,9,8,6,5,5,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,8,6,6,4,4,3,3,1,1,1,1,1] (.node [14,9,8,6,6,4,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,9,8,6,6,5,4,2,2,2,1,1,1,1] (.node [14,9,8,6,6,5,3,3,3,1,1,1,1,1] (.node [14,9,8,6,6,5,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,8,6,6,5,4,3,2,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_1004 : RowTree := (.node [14,9,7,7,7,5,3,2,2,2,1,1,1,1] degreeTree62_1002 degreeTree62_1003) - -def degreeTree62_1005 : RowTree := (.node [14,9,8,7,6,4,3,2,2,2,2,1,1,1] (.node [14,9,8,7,5,4,4,4,2,1,1,1,1,1] (.node [14,9,8,7,4,4,4,4,3,1,1,1,1,1] (.node [14,9,8,6,6,6,3,3,2,1,1,1,1,1] (.node [14,9,8,6,6,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,8,7,5,4,4,3,3,1,1,1,1,1] (.node [14,9,8,7,5,4,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,9,8,7,5,5,4,2,2,2,1,1,1,1] (.node [14,9,8,7,5,5,3,3,3,1,1,1,1,1] (.node [14,9,8,7,5,5,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,8,7,5,5,4,3,2,1,1,1,1,1] .empty .empty))) (.node [14,9,8,7,7,2,2,2,2,2,2,2,2,1] (.node [14,9,8,7,6,5,2,2,2,2,2,1,1,1] (.node [14,9,8,7,6,4,4,2,2,2,1,1,1,1] (.node [14,9,8,7,6,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,8,7,6,6,2,2,2,2,1,1,1,1] (.node [14,9,8,7,6,5,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [14,9,8,7,7,4,2,2,2,2,2,1,1,1] (.node [14,9,8,7,7,3,3,3,3,1,1,1,1,1] (.node [14,9,8,7,7,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,8,7,7,4,3,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_1006 : RowTree := (.node [14,9,8,8,6,3,3,3,3,1,1,1,1,1] (.node [14,9,8,8,5,4,4,2,2,2,1,1,1,1] (.node [14,9,8,8,4,4,4,4,2,1,1,1,1,1] (.node [14,9,8,8,4,4,4,3,3,1,1,1,1,1] (.node [14,9,8,8,4,4,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,8,8,5,4,3,3,3,1,1,1,1,1] (.node [14,9,8,8,5,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,9,8,8,6,2,2,2,2,2,2,2,2,1] (.node [14,9,8,8,5,5,3,2,2,2,1,1,1,1] (.node [14,9,8,8,5,5,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,8,8,6,3,3,2,2,2,2,1,1,1] .empty .empty))) (.node [14,9,8,8,7,3,3,2,2,2,1,1,1,1] (.node [14,9,8,8,6,5,2,2,2,2,1,1,1,1] (.node [14,9,8,8,6,4,3,2,2,2,1,1,1,1] (.node [14,9,8,8,6,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,8,8,7,3,2,2,2,2,2,1,1,1] (.node [14,9,8,8,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [14,9,8,8,8,3,2,2,2,2,1,1,1,1] (.node [14,9,8,8,8,2,2,2,2,2,2,1,1,1] (.node [14,9,8,8,7,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,9,5,4,4,4,4,4,1,1,1,1,1] .empty .empty)))) - -def degreeTree62_1007 : RowTree := (.node [14,9,8,7,7,5,2,2,2,2,1,1,1,1] degreeTree62_1005 degreeTree62_1006) - -def degreeTree62_1008 : RowTree := (.node [14,9,8,6,6,6,2,2,2,2,2,1,1,1] degreeTree62_1004 degreeTree62_1007) - -def degreeTree62_1009 : RowTree := (.node [14,9,9,6,6,4,4,2,2,2,1,1,1,1] (.node [14,9,9,6,5,4,4,3,3,1,1,1,1,1] (.node [14,9,9,5,5,5,5,2,2,2,1,1,1,1] (.node [14,9,9,5,5,5,4,3,3,1,1,1,1,1] (.node [14,9,9,5,5,5,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,9,6,5,4,4,2,2,2,2,1,1,1] (.node [14,9,9,6,4,4,4,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,9,6,5,5,4,2,2,2,1,1,1,1] (.node [14,9,9,6,5,5,3,3,3,1,1,1,1,1] (.node [14,9,9,6,5,5,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,9,6,6,4,3,2,2,2,2,1,1,1] .empty .empty))) (.node [14,9,9,7,5,4,3,2,2,2,2,1,1,1] (.node [14,9,9,6,6,6,2,2,2,2,1,1,1,1] (.node [14,9,9,6,6,5,3,2,2,2,1,1,1,1] (.node [14,9,9,6,6,5,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,9,7,4,4,4,3,3,1,1,1,1,1] (.node [14,9,9,7,4,4,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,9,9,7,5,5,3,2,2,2,1,1,1,1] (.node [14,9,9,7,5,5,2,2,2,2,2,1,1,1] (.node [14,9,9,7,5,4,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,9,7,6,2,2,2,2,2,2,2,2,1] .empty .empty)))) - -def degreeTree62_1010 : RowTree := (.node [14,9,9,8,5,3,3,2,2,2,2,1,1,1] (.node [14,9,9,7,7,3,3,2,2,2,1,1,1,1] (.node [14,9,9,7,6,5,2,2,2,2,1,1,1,1] (.node [14,9,9,7,6,4,3,2,2,2,1,1,1,1] (.node [14,9,9,7,6,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,9,7,7,3,2,2,2,2,2,1,1,1] (.node [14,9,9,7,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [14,9,9,8,4,4,4,2,2,2,1,1,1,1] (.node [14,9,9,8,4,4,3,2,2,2,2,1,1,1] (.node [14,9,9,7,7,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,9,8,5,2,2,2,2,2,2,2,2,1] .empty .empty))) (.node [14,9,9,8,6,3,3,2,2,2,1,1,1,1] (.node [14,9,9,8,5,5,2,2,2,2,1,1,1,1] (.node [14,9,9,8,5,4,3,2,2,2,1,1,1,1] (.node [14,9,9,8,5,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,9,8,6,3,2,2,2,2,2,1,1,1] (.node [14,9,9,8,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [14,9,9,8,7,3,2,2,2,2,1,1,1,1] (.node [14,9,9,8,7,2,2,2,2,2,2,1,1,1] (.node [14,9,9,8,6,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,9,8,8,2,2,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_1011 : RowTree := (.node [14,9,9,7,6,3,3,2,2,2,2,1,1,1] degreeTree62_1009 degreeTree62_1010) - -def degreeTree62_1012 : RowTree := (.node [14,10,6,6,5,5,5,2,2,2,2,1,1,1] (.node [14,9,9,9,5,3,3,2,2,2,1,1,1,1] (.node [14,9,9,9,4,4,3,2,2,2,1,1,1,1] (.node [14,9,9,9,4,4,2,2,2,2,2,1,1,1] (.node [14,9,9,9,4,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,9,9,5,3,2,2,2,2,2,1,1,1] (.node [14,9,9,9,5,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [14,9,9,9,6,3,2,2,2,2,1,1,1,1] (.node [14,9,9,9,6,2,2,2,2,2,2,1,1,1] (.node [14,9,9,9,5,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,9,9,7,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [14,10,7,6,5,5,4,2,2,2,2,1,1,1] (.node [14,10,6,6,6,6,3,2,2,2,2,1,1,1] (.node [14,10,6,6,6,5,5,2,2,2,1,1,1,1] (.node [14,10,6,6,6,5,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,10,7,5,5,5,5,2,2,2,2,1,1,1] (.node [14,10,6,6,6,6,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [14,10,7,6,6,5,3,2,2,2,2,1,1,1] (.node [14,10,7,6,6,4,4,2,2,2,2,1,1,1] (.node [14,10,7,6,5,5,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,10,7,6,6,5,4,2,2,2,1,1,1,1] .empty .empty)))) - -def degreeTree62_1013 : RowTree := (.node [14,11,6,6,5,5,4,2,2,2,2,1,1,1] (.node [14,10,7,7,6,5,2,2,2,2,2,1,1,1] (.node [14,10,7,7,5,5,3,2,2,2,2,1,1,1] (.node [14,10,7,7,5,4,4,2,2,2,2,1,1,1] (.node [14,10,7,6,6,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,10,7,7,6,4,3,2,2,2,2,1,1,1] (.node [14,10,7,7,5,5,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [14,10,7,7,7,4,2,2,2,2,2,1,1,1] (.node [14,10,7,7,7,3,3,2,2,2,2,1,1,1] (.node [14,10,7,7,7,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [14,11,6,5,5,5,5,2,2,2,2,1,1,1] .empty .empty))) (.node [14,11,7,6,5,4,4,2,2,2,2,1,1,1] (.node [14,11,6,6,6,6,2,2,2,2,2,1,1,1] (.node [14,11,6,6,6,5,3,2,2,2,2,1,1,1] (.node [14,11,6,6,6,4,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,11,7,5,5,5,4,2,2,2,2,1,1,1] .empty .empty)) (.node [14,11,7,7,6,2,2,2,2,2,2,2,2,1] (.node [14,11,7,7,4,4,4,2,2,2,2,1,1,1] (.node [14,11,7,6,5,5,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,11,7,7,7,2,2,2,2,2,2,2,1,1] .empty .empty)))) - -def degreeTree62_1014 : RowTree := (.node [14,10,7,6,6,6,2,2,2,2,2,1,1,1] degreeTree62_1012 degreeTree62_1013) - -def degreeTree62_1015 : RowTree := (.node [14,9,9,9,4,2,2,2,2,2,2,2,2,1] degreeTree62_1011 degreeTree62_1014) - -def degreeTree62_1016 : RowTree := (.node [14,9,9,5,5,4,4,4,3,1,1,1,1,1] degreeTree62_1008 degreeTree62_1015) - -def degreeTree62_1017 : RowTree := (.node [14,9,7,7,5,5,4,2,2,2,2,1,1,1] degreeTree62_1001 degreeTree62_1016) - -def degreeTree62_1018 : RowTree := (.node [14,8,7,6,6,6,6,2,2,1,1,1,1,1] degreeTree62_986 degreeTree62_1017) - -def degreeTree62_1019 : RowTree := (.node [13,11,9,9,5,5,2,2,1,1,1,1,1,1] degreeTree62_955 degreeTree62_1018) - -def degreeTree62_1020 : RowTree := (.node [13,10,8,8,7,7,2,1,1,1,1,1,1,1] degreeTree62_892 degreeTree62_1019) - -def degreeTree62_1021 : RowTree := (.node [13,8,7,6,6,6,5,3,2,2,2,1,1] degreeTree62_765 degreeTree62_1020) - -def degreeTree62_1022 : RowTree := (.node [12,9,9,9,7,3,2,2,2,2,2,1,1,1] degreeTree62_510 degreeTree62_1021) - -def degreeTree62 : RowTree := degreeTree62_1022 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 62. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree62_0 : RowTree := (.node [9,9,9,9,8,8,5,1,1,1,1,1] (.node [9,9,9,9,8,8,3,2,1,1,1,1,1] (.node [9,9,9,9,8,8,2,2,2,1,1,1,1] (.node [9,9,9,9,8,8,2,2,1,1,1,1,1,1] (.node [8,8,8,8,8,8,7,7] .empty .empty) .empty) (.node [9,9,9,9,8,8,3,1,1,1,1,1,1,1] (.node [9,9,9,9,8,8,2,2,2,2,1,1] .empty .empty) .empty)) (.node [9,9,9,9,8,8,4,1,1,1,1,1,1] (.node [9,9,9,9,8,8,3,3,1,1,1,1] (.node [9,9,9,9,8,8,3,2,2,1,1,1] .empty .empty) .empty) (.node [9,9,9,9,8,8,4,2,1,1,1,1] .empty .empty))) (.node [9,9,9,9,9,7,3,2,2,1,1,1] (.node [9,9,9,9,9,7,2,2,2,2,1,1] (.node [9,9,9,9,9,7,2,2,2,1,1,1,1] (.node [9,9,9,9,9,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [9,9,9,9,9,7,3,2,1,1,1,1,1] (.node [9,9,9,9,9,7,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [9,9,9,9,9,7,4,2,1,1,1,1] (.node [9,9,9,9,9,7,4,1,1,1,1,1,1] (.node [9,9,9,9,9,7,3,3,1,1,1,1] .empty .empty) .empty) (.node [9,9,9,9,9,7,5,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_1 : RowTree := (.node [10,9,9,8,8,8,2,2,2,1,1,1,1] (.node [9,9,9,9,9,9,1,1,1,1,1,1,1,1] (.node [9,9,9,9,9,8,3,1,1,1,1,1,1] (.node [9,9,9,9,9,8,2,2,2,1,1,1] (.node [9,9,9,9,9,8,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [9,9,9,9,9,8,4,1,1,1,1,1] (.node [9,9,9,9,9,8,3,2,1,1,1,1] .empty .empty) .empty)) (.node [9,9,9,9,9,9,3,1,1,1,1,1] (.node [9,9,9,9,9,9,2,2,1,1,1,1] (.node [9,9,9,9,9,9,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,8,8,8,2,2,1,1,1,1,1,1] .empty .empty))) (.node [10,9,9,8,8,8,4,1,1,1,1,1,1] (.node [10,9,9,8,8,8,3,2,1,1,1,1,1] (.node [10,9,9,8,8,8,3,1,1,1,1,1,1,1] (.node [10,9,9,8,8,8,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,9,9,8,8,8,3,3,1,1,1,1] (.node [10,9,9,8,8,8,3,2,2,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,8,7,2,2,1,1,1,1,1,1] (.node [10,9,9,8,8,8,5,1,1,1,1,1] (.node [10,9,9,8,8,8,4,2,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,8,7,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_2 : RowTree := (.node [9,9,9,9,9,8,2,1,1,1,1,1,1,1] degreeTree62_0 degreeTree62_1) + +def degreeTree62_3 : RowTree := (.node [10,9,9,9,8,8,3,1,1,1,1,1,1] (.node [10,9,9,9,8,7,4,2,1,1,1,1] (.node [10,9,9,9,8,7,3,2,2,1,1,1] (.node [10,9,9,9,8,7,3,2,1,1,1,1,1] (.node [10,9,9,9,8,7,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,8,7,4,1,1,1,1,1,1] (.node [10,9,9,9,8,7,3,3,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,8,8,2,2,1,1,1,1,1] (.node [10,9,9,9,8,8,2,1,1,1,1,1,1,1] (.node [10,9,9,9,8,7,5,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,8,8,2,2,2,1,1,1] .empty .empty))) (.node [10,9,9,9,9,3,2,2,2,2,2,2,1] (.node [10,9,9,9,9,2,2,2,2,2,2,2,1,1] (.node [10,9,9,9,8,8,4,1,1,1,1,1] (.node [10,9,9,9,8,8,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,3,2,2,2,2,2,1,1,1] (.node [10,9,9,9,9,2,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [10,9,9,9,9,3,3,2,2,2,2,2] (.node [10,9,9,9,9,3,3,2,2,2,2,1,1] (.node [10,9,9,9,9,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,3,3,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_4 : RowTree := (.node [10,9,9,9,9,4,3,3,2,1,1,1,1] (.node [10,9,9,9,9,4,2,2,2,2,2,2] (.node [10,9,9,9,9,3,3,3,3,2,1,1] (.node [10,9,9,9,9,3,3,3,3,1,1,1,1] (.node [10,9,9,9,9,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [10,9,9,9,9,4,2,2,2,2,2,1,1] (.node [10,9,9,9,9,4,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,9,4,3,2,2,2,2,1] (.node [10,9,9,9,9,4,3,2,2,2,1,1,1] (.node [10,9,9,9,9,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,4,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,9,9,9,9,4,4,3,1,1,1,1,1] (.node [10,9,9,9,9,4,4,2,1,1,1,1,1,1] (.node [10,9,9,9,9,4,3,3,3,1,1,1] (.node [10,9,9,9,9,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,4,4,2,2,2,1,1] (.node [10,9,9,9,9,4,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,9,5,2,2,2,1,1,1,1,1] (.node [10,9,9,9,9,4,4,4,1,1,1,1] (.node [10,9,9,9,9,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,5,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_5 : RowTree := (.node [10,9,9,9,9,3,3,3,2,2,1,1,1] degreeTree62_3 degreeTree62_4) + +def degreeTree62_6 : RowTree := (.node [10,9,9,9,8,7,2,2,2,2,1,1] degreeTree62_2 degreeTree62_5) + +def degreeTree62_7 : RowTree := (.node [10,9,9,9,9,5,5,2,1,1,1,1] (.node [10,9,9,9,9,5,4,1,1,1,1,1,1,1] (.node [10,9,9,9,9,5,3,2,2,2,1,1] (.node [10,9,9,9,9,5,3,2,2,1,1,1,1] (.node [10,9,9,9,9,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,5,3,3,2,1,1,1] (.node [10,9,9,9,9,5,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,9,5,4,3,1,1,1,1] (.node [10,9,9,9,9,5,4,2,2,1,1,1] (.node [10,9,9,9,9,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,5,5,1,1,1,1,1,1] .empty .empty))) (.node [10,9,9,9,9,6,3,2,2,1,1,1] (.node [10,9,9,9,9,6,2,2,2,2,1,1] (.node [10,9,9,9,9,6,2,2,2,1,1,1,1] (.node [10,9,9,9,9,6,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,6,3,2,1,1,1,1,1] (.node [10,9,9,9,9,6,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,9,6,4,2,1,1,1,1] (.node [10,9,9,9,9,6,4,1,1,1,1,1,1] (.node [10,9,9,9,9,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,6,5,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_8 : RowTree := (.node [10,9,9,9,9,9,2,1,1,1,1,1] (.node [10,9,9,9,9,8,1,1,1,1,1,1,1,1] (.node [10,9,9,9,9,7,3,1,1,1,1,1,1] (.node [10,9,9,9,9,7,2,2,2,1,1,1] (.node [10,9,9,9,9,7,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,7,4,1,1,1,1,1] (.node [10,9,9,9,9,7,3,2,1,1,1,1] .empty .empty) .empty)) (.node [10,9,9,9,9,8,3,1,1,1,1,1] (.node [10,9,9,9,9,8,2,2,1,1,1,1] (.node [10,9,9,9,9,8,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,9,9,9,9,9,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,8,8,8,8,3,2,2,1,1,1] (.node [10,10,8,8,8,8,2,2,2,2,1,1] (.node [10,10,8,8,8,8,2,2,2,1,1,1,1] (.node [10,10,8,8,8,8,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,8,8,8,8,3,2,1,1,1,1,1] (.node [10,10,8,8,8,8,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,8,8,8,8,4,2,1,1,1,1] (.node [10,10,8,8,8,8,4,1,1,1,1,1,1] (.node [10,10,8,8,8,8,3,3,1,1,1,1] .empty .empty) .empty) (.node [10,10,8,8,8,8,5,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_9 : RowTree := (.node [10,9,9,9,9,7,2,1,1,1,1,1,1,1] degreeTree62_7 degreeTree62_8) + +def degreeTree62_10 : RowTree := (.node [10,10,9,8,8,8,2,2,1,1,1,1,1] (.node [10,10,9,8,8,7,3,3,1,1,1,1] (.node [10,10,9,8,8,7,3,1,1,1,1,1,1,1] (.node [10,10,9,8,8,7,2,2,2,2,1,1] (.node [10,10,9,8,8,7,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,8,8,7,3,2,2,1,1,1] (.node [10,10,9,8,8,7,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,9,8,8,7,5,1,1,1,1,1] (.node [10,10,9,8,8,7,4,2,1,1,1,1] (.node [10,10,9,8,8,7,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,8,8,8,2,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,9,9,7,7,2,2,2,1,1,1,1] (.node [10,10,9,8,8,8,3,2,1,1,1,1] (.node [10,10,9,8,8,8,3,1,1,1,1,1,1] (.node [10,10,9,8,8,8,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,7,7,2,2,1,1,1,1,1,1] (.node [10,10,9,8,8,8,4,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,9,9,7,7,3,2,1,1,1,1,1] (.node [10,10,9,9,7,7,3,1,1,1,1,1,1,1] (.node [10,10,9,9,7,7,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,9,9,7,7,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_11 : RowTree := (.node [10,10,9,9,8,3,3,3,2,1,1,1,1,1] (.node [10,10,9,9,8,3,2,2,2,2,2,1,1,1] (.node [10,10,9,9,7,7,5,1,1,1,1,1] (.node [10,10,9,9,7,7,4,2,1,1,1,1] (.node [10,10,9,9,7,7,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,2,2,2,2,2,2,2,2] (.node [10,10,9,9,8,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,9,9,8,3,3,2,2,2,2,1,1] (.node [10,10,9,9,8,3,3,2,2,2,1,1,1,1] (.node [10,10,9,9,8,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,9,9,8,3,3,2,2,2,2,2] .empty .empty))) (.node [10,10,9,9,8,4,2,2,2,2,2,1,1] (.node [10,10,9,9,8,3,3,3,3,1,1,1,1] (.node [10,10,9,9,8,3,3,3,2,2,2,1] (.node [10,10,9,9,8,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,4,2,2,2,2,1,1,1,1] (.node [10,10,9,9,8,3,3,3,3,2,1,1] .empty .empty) .empty)) (.node [10,10,9,9,8,4,3,2,2,2,1,1,1] (.node [10,10,9,9,8,4,3,2,2,1,1,1,1,1] (.node [10,10,9,9,8,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [10,10,9,9,8,4,3,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_12 : RowTree := (.node [10,10,9,9,7,7,3,3,1,1,1,1] degreeTree62_10 degreeTree62_11) + +def degreeTree62_13 : RowTree := (.node [10,10,9,8,8,7,2,2,1,1,1,1,1,1] degreeTree62_9 degreeTree62_12) + +def degreeTree62_14 : RowTree := (.node [10,9,9,9,9,5,2,2,2,2,2,1] degreeTree62_6 degreeTree62_13) + +def degreeTree62_15 : RowTree := (.node [10,10,9,9,8,5,2,2,2,2,1,1,1] (.node [10,10,9,9,8,4,4,2,2,2,1,1] (.node [10,10,9,9,8,4,3,3,3,1,1,1] (.node [10,10,9,9,8,4,3,3,2,2,1,1] (.node [10,10,9,9,8,4,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,4,4,2,2,1,1,1,1] (.node [10,10,9,9,8,4,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,9,9,8,4,4,4,1,1,1,1] (.node [10,10,9,9,8,4,4,3,2,1,1,1] (.node [10,10,9,9,8,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,5,2,2,2,1,1,1,1,1] .empty .empty))) (.node [10,10,9,9,8,5,3,3,2,1,1,1] (.node [10,10,9,9,8,5,3,2,2,1,1,1,1] (.node [10,10,9,9,8,5,3,2,1,1,1,1,1,1] (.node [10,10,9,9,8,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,9,9,8,5,3,3,1,1,1,1,1] (.node [10,10,9,9,8,5,3,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,9,9,8,5,4,2,2,1,1,1] (.node [10,10,9,9,8,5,4,2,1,1,1,1,1] (.node [10,10,9,9,8,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,5,4,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_16 : RowTree := (.node [10,10,9,9,8,6,5,1,1,1,1,1] (.node [10,10,9,9,8,6,3,2,1,1,1,1,1] (.node [10,10,9,9,8,6,2,2,2,1,1,1,1] (.node [10,10,9,9,8,6,2,2,1,1,1,1,1,1] (.node [10,10,9,9,8,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,6,3,1,1,1,1,1,1,1] (.node [10,10,9,9,8,6,2,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,9,9,8,6,4,1,1,1,1,1,1] (.node [10,10,9,9,8,6,3,3,1,1,1,1] (.node [10,10,9,9,8,6,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,6,4,2,1,1,1,1] .empty .empty))) (.node [10,10,9,9,8,7,4,1,1,1,1,1] (.node [10,10,9,9,8,7,2,2,2,1,1,1] (.node [10,10,9,9,8,7,2,2,1,1,1,1,1] (.node [10,10,9,9,8,7,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,7,3,2,1,1,1,1] (.node [10,10,9,9,8,7,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,9,9,8,8,2,2,1,1,1,1] (.node [10,10,9,9,8,8,2,1,1,1,1,1,1] (.node [10,10,9,9,8,8,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,8,8,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_17 : RowTree := (.node [10,10,9,9,8,5,5,1,1,1,1,1,1] degreeTree62_15 degreeTree62_16) + +def degreeTree62_18 : RowTree := (.node [10,10,9,9,9,3,3,3,3,1,1,1] (.node [10,10,9,9,9,3,3,2,2,2,1,1,1] (.node [10,10,9,9,9,3,2,2,2,2,2,1,1] (.node [10,10,9,9,9,3,2,2,2,2,1,1,1,1] (.node [10,10,9,9,9,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,9,9,9,3,3,2,2,1,1,1,1,1] (.node [10,10,9,9,9,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [10,10,9,9,9,3,3,3,2,1,1,1,1] (.node [10,10,9,9,9,3,3,3,1,1,1,1,1,1] (.node [10,10,9,9,9,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,9,9,9,3,3,3,2,2,1,1] .empty .empty))) (.node [10,10,9,9,9,4,3,2,2,2,1,1] (.node [10,10,9,9,9,4,2,2,2,2,2,1] (.node [10,10,9,9,9,4,2,2,2,2,1,1,1] (.node [10,10,9,9,9,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,9,4,3,2,2,1,1,1,1] (.node [10,10,9,9,9,4,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,9,9,9,4,4,1,1,1,1,1,1,1] (.node [10,10,9,9,9,4,3,3,2,1,1,1] (.node [10,10,9,9,9,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,9,4,4,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_19 : RowTree := (.node [10,10,9,9,9,5,5,1,1,1,1,1] (.node [10,10,9,9,9,5,3,2,1,1,1,1,1] (.node [10,10,9,9,9,5,2,2,2,1,1,1,1] (.node [10,10,9,9,9,5,2,2,1,1,1,1,1,1] (.node [10,10,9,9,9,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,9,5,3,1,1,1,1,1,1,1] (.node [10,10,9,9,9,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,9,9,9,5,4,1,1,1,1,1,1] (.node [10,10,9,9,9,5,3,3,1,1,1,1] (.node [10,10,9,9,9,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,9,5,4,2,1,1,1,1] .empty .empty))) (.node [10,10,9,9,9,6,4,1,1,1,1,1] (.node [10,10,9,9,9,6,2,2,2,1,1,1] (.node [10,10,9,9,9,6,2,2,1,1,1,1,1] (.node [10,10,9,9,9,6,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,9,6,3,2,1,1,1,1] (.node [10,10,9,9,9,6,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,9,9,9,7,2,2,1,1,1,1] (.node [10,10,9,9,9,7,2,1,1,1,1,1,1] (.node [10,10,9,9,9,7,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,9,9,9,7,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_20 : RowTree := (.node [10,10,9,9,9,4,4,2,2,1,1,1] degreeTree62_18 degreeTree62_19) + +def degreeTree62_21 : RowTree := (.node [10,10,9,9,9,2,2,2,2,2,2,1,1,1] degreeTree62_17 degreeTree62_20) + +def degreeTree62_22 : RowTree := (.node [10,10,10,8,7,7,4,2,1,1,1,1] (.node [10,10,10,8,7,7,3,1,1,1,1,1,1,1] (.node [10,10,10,8,7,7,2,2,1,1,1,1,1,1] (.node [10,10,9,9,9,9,1,1,1,1,1,1] (.node [10,10,9,9,9,8,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,7,7,2,2,2,2,1,1] (.node [10,10,10,8,7,7,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,8,7,7,3,3,1,1,1,1] (.node [10,10,10,8,7,7,3,2,2,1,1,1] (.node [10,10,10,8,7,7,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,7,7,4,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,8,8,3,3,2,2,2,1,1,1,1] (.node [10,10,10,8,8,2,2,2,2,2,2,2,2] (.node [10,10,10,8,8,2,2,2,2,2,2,2,1,1] (.node [10,10,10,8,7,7,5,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,3,2,2,2,2,2,2,1] (.node [10,10,10,8,8,3,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,8,8,3,3,3,2,1,1,1,1,1] (.node [10,10,10,8,8,3,3,2,2,2,2,2] (.node [10,10,10,8,8,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,3,3,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_23 : RowTree := (.node [10,10,10,8,8,4,3,3,2,2,1,1] (.node [10,10,10,8,8,4,3,2,2,1,1,1,1,1] (.node [10,10,10,8,8,4,2,2,2,2,1,1,1,1] (.node [10,10,10,8,8,3,3,3,3,2,1,1] (.node [10,10,10,8,8,3,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,4,2,2,2,2,2,2] (.node [10,10,10,8,8,4,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,10,8,8,4,3,3,1,1,1,1,1,1] (.node [10,10,10,8,8,4,3,2,2,2,2,1] (.node [10,10,10,8,8,4,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,4,3,3,2,1,1,1,1] .empty .empty))) (.node [10,10,10,8,8,4,4,3,2,1,1,1] (.node [10,10,10,8,8,4,4,2,2,1,1,1,1] (.node [10,10,10,8,8,4,4,2,1,1,1,1,1,1] (.node [10,10,10,8,8,4,3,3,3,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,4,4,3,1,1,1,1,1] (.node [10,10,10,8,8,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,10,8,8,5,2,2,2,2,1,1,1] (.node [10,10,10,8,8,5,2,2,2,1,1,1,1,1] (.node [10,10,10,8,8,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,5,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_24 : RowTree := (.node [10,10,10,8,8,3,3,3,2,2,2,1] degreeTree62_22 degreeTree62_23) + +def degreeTree62_25 : RowTree := (.node [10,10,10,8,8,6,2,2,1,1,1,1,1,1] (.node [10,10,10,8,8,5,4,2,1,1,1,1,1] (.node [10,10,10,8,8,5,3,3,1,1,1,1,1] (.node [10,10,10,8,8,5,3,2,2,2,1,1] (.node [10,10,10,8,8,5,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,5,4,1,1,1,1,1,1,1] (.node [10,10,10,8,8,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,8,8,5,5,1,1,1,1,1,1] (.node [10,10,10,8,8,5,4,3,1,1,1,1] (.node [10,10,10,8,8,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,5,5,2,1,1,1,1] .empty .empty))) (.node [10,10,10,8,8,6,3,3,1,1,1,1] (.node [10,10,10,8,8,6,3,1,1,1,1,1,1,1] (.node [10,10,10,8,8,6,2,2,2,2,1,1] (.node [10,10,10,8,8,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,6,3,2,2,1,1,1] (.node [10,10,10,8,8,6,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,8,8,6,5,1,1,1,1,1] (.node [10,10,10,8,8,6,4,2,1,1,1,1] (.node [10,10,10,8,8,6,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,7,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_26 : RowTree := (.node [10,10,10,9,7,3,2,2,2,2,2,1,1,1] (.node [10,10,10,8,8,8,2,1,1,1,1,1,1] (.node [10,10,10,8,8,7,3,2,1,1,1,1] (.node [10,10,10,8,8,7,3,1,1,1,1,1,1] (.node [10,10,10,8,8,7,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,8,8,8,1,1,1,1,1,1,1,1] (.node [10,10,10,8,8,7,4,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,7,2,2,2,2,2,2,2,1,1] (.node [10,10,10,8,8,8,3,1,1,1,1,1] (.node [10,10,10,8,8,8,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,2,2,2,2,2,2,2,2] .empty .empty))) (.node [10,10,10,9,7,3,3,3,2,1,1,1,1,1] (.node [10,10,10,9,7,3,3,2,2,2,2,1,1] (.node [10,10,10,9,7,3,3,2,2,2,1,1,1,1] (.node [10,10,10,9,7,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,10,9,7,3,3,2,2,2,2,2] .empty .empty)) (.node [10,10,10,9,7,3,3,3,3,1,1,1,1] (.node [10,10,10,9,7,3,3,3,2,2,2,1] (.node [10,10,10,9,7,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,3,3,3,3,2,1,1] .empty .empty)))) + +def degreeTree62_27 : RowTree := (.node [10,10,10,8,8,7,2,2,1,1,1,1,1] degreeTree62_25 degreeTree62_26) + +def degreeTree62_28 : RowTree := (.node [10,10,10,8,8,5,3,2,1,1,1,1,1,1] degreeTree62_24 degreeTree62_27) + +def degreeTree62_29 : RowTree := (.node [10,10,9,9,9,8,1,1,1,1,1,1,1] degreeTree62_21 degreeTree62_28) + +def degreeTree62_30 : RowTree := (.node [10,10,9,9,8,4,3,3,1,1,1,1,1,1] degreeTree62_14 degreeTree62_29) + +def degreeTree62_31 : RowTree := (.node [10,10,10,9,7,4,4,2,2,1,1,1,1] (.node [10,10,10,9,7,4,3,3,1,1,1,1,1,1] (.node [10,10,10,9,7,4,3,2,2,1,1,1,1,1] (.node [10,10,10,9,7,4,2,2,2,2,2,2] (.node [10,10,10,9,7,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,4,3,2,2,2,2,1] (.node [10,10,10,9,7,4,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,7,4,3,3,3,1,1,1] (.node [10,10,10,9,7,4,3,3,2,2,1,1] (.node [10,10,10,9,7,4,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,4,4,2,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,9,7,5,2,2,2,2,1,1,1] (.node [10,10,10,9,7,4,4,3,2,1,1,1] (.node [10,10,10,9,7,4,4,3,1,1,1,1,1] (.node [10,10,10,9,7,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,5,2,2,2,1,1,1,1,1] (.node [10,10,10,9,7,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,7,5,3,2,2,1,1,1,1] (.node [10,10,10,9,7,5,3,2,1,1,1,1,1,1] (.node [10,10,10,9,7,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,10,9,7,5,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_32 : RowTree := (.node [10,10,10,9,7,6,3,1,1,1,1,1,1,1] (.node [10,10,10,9,7,5,5,1,1,1,1,1,1] (.node [10,10,10,9,7,5,4,2,1,1,1,1,1] (.node [10,10,10,9,7,5,4,1,1,1,1,1,1,1] (.node [10,10,10,9,7,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,5,4,3,1,1,1,1] (.node [10,10,10,9,7,5,4,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,7,6,2,2,2,1,1,1,1] (.node [10,10,10,9,7,6,2,2,1,1,1,1,1,1] (.node [10,10,10,9,7,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,6,2,2,2,2,1,1] .empty .empty))) (.node [10,10,10,9,7,6,5,1,1,1,1,1] (.node [10,10,10,9,7,6,3,3,1,1,1,1] (.node [10,10,10,9,7,6,3,2,2,1,1,1] (.node [10,10,10,9,7,6,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,6,4,2,1,1,1,1] (.node [10,10,10,9,7,6,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,7,7,2,2,2,1,1,1] (.node [10,10,10,9,7,7,2,2,1,1,1,1,1] (.node [10,10,10,9,7,7,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,7,7,3,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_33 : RowTree := (.node [10,10,10,9,7,5,3,3,1,1,1,1,1] degreeTree62_31 degreeTree62_32) + +def degreeTree62_34 : RowTree := (.node [10,10,10,9,8,3,3,3,2,1,1,1,1] (.node [10,10,10,9,8,3,2,2,2,2,2,2] (.node [10,10,10,9,8,2,2,2,2,2,2,2,1] (.node [10,10,10,9,8,2,2,2,2,2,2,1,1,1] (.node [10,10,10,9,7,7,4,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,3,2,2,2,2,2,1,1] (.node [10,10,10,9,8,3,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,8,3,3,2,2,2,2,1] (.node [10,10,10,9,8,3,3,2,2,2,1,1,1] (.node [10,10,10,9,8,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,9,8,4,3,2,1,1,1,1,1,1] (.node [10,10,10,9,8,4,2,2,2,1,1,1,1,1] (.node [10,10,10,9,8,3,3,3,3,1,1,1] (.node [10,10,10,9,8,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,4,2,2,2,2,2,1] (.node [10,10,10,9,8,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,8,4,3,3,1,1,1,1,1] (.node [10,10,10,9,8,4,3,2,2,2,1,1] (.node [10,10,10,9,8,4,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,4,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_35 : RowTree := (.node [10,10,10,9,8,5,4,1,1,1,1,1,1] (.node [10,10,10,9,8,5,2,2,2,2,1,1] (.node [10,10,10,9,8,4,4,3,1,1,1,1] (.node [10,10,10,9,8,4,4,2,2,1,1,1] (.node [10,10,10,9,8,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,5,2,2,2,1,1,1,1] (.node [10,10,10,9,8,5,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,8,5,3,2,2,1,1,1] (.node [10,10,10,9,8,5,3,2,1,1,1,1,1] (.node [10,10,10,9,8,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,5,3,3,1,1,1,1] .empty .empty))) (.node [10,10,10,9,8,6,3,1,1,1,1,1,1] (.node [10,10,10,9,8,6,2,1,1,1,1,1,1,1] (.node [10,10,10,9,8,5,5,1,1,1,1,1] (.node [10,10,10,9,8,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,6,2,2,2,1,1,1] (.node [10,10,10,9,8,6,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,8,7,1,1,1,1,1,1,1,1] (.node [10,10,10,9,8,6,4,1,1,1,1,1] (.node [10,10,10,9,8,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,8,7,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_36 : RowTree := (.node [10,10,10,9,8,4,4,1,1,1,1,1,1,1] degreeTree62_34 degreeTree62_35) + +def degreeTree62_37 : RowTree := (.node [10,10,10,9,7,7,3,2,1,1,1,1] degreeTree62_33 degreeTree62_36) + +def degreeTree62_38 : RowTree := (.node [10,10,10,9,9,3,3,2,2,1,1,1,1] (.node [10,10,10,9,9,2,2,2,2,2,2,2] (.node [10,10,10,9,8,8,2,1,1,1,1,1] (.node [10,10,10,9,8,8,1,1,1,1,1,1,1] (.node [10,10,10,9,8,7,3,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,9,2,2,2,2,2,2,1,1] (.node [10,10,10,9,9,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,9,3,2,2,2,2,2,1] (.node [10,10,10,9,9,3,2,2,2,2,1,1,1] (.node [10,10,10,9,9,3,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,9,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,9,9,4,2,2,2,2,1,1] (.node [10,10,10,9,9,3,3,3,2,1,1,1] (.node [10,10,10,9,9,3,3,3,1,1,1,1,1] (.node [10,10,10,9,9,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,9,9,4,2,2,2,1,1,1,1] (.node [10,10,10,9,9,4,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,9,4,3,2,2,1,1,1] (.node [10,10,10,9,9,4,3,2,1,1,1,1,1] (.node [10,10,10,9,9,4,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,9,4,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_39 : RowTree := (.node [10,10,10,9,9,6,3,1,1,1,1,1] (.node [10,10,10,9,9,5,3,2,1,1,1,1] (.node [10,10,10,9,9,5,2,2,1,1,1,1,1] (.node [10,10,10,9,9,5,2,1,1,1,1,1,1,1] (.node [10,10,10,9,9,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,9,5,3,1,1,1,1,1,1] (.node [10,10,10,9,9,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,9,9,6,2,1,1,1,1,1,1] (.node [10,10,10,9,9,6,1,1,1,1,1,1,1,1] (.node [10,10,10,9,9,5,4,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,9,9,6,2,2,1,1,1,1] .empty .empty))) (.node [10,10,10,10,4,3,3,3,3,3,3] (.node [10,10,10,9,9,8,1,1,1,1,1,1] (.node [10,10,10,9,9,7,2,1,1,1,1,1] (.node [10,10,10,9,9,7,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,4,3,3,3,3,2,2,1,1] (.node [10,10,10,10,4,3,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [10,10,10,10,4,4,3,2,2,2,2,2,1] (.node [10,10,10,10,4,4,3,2,2,2,2,1,1,1] (.node [10,10,10,10,4,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [10,10,10,10,4,4,3,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_40 : RowTree := (.node [10,10,10,9,9,4,4,1,1,1,1,1,1] degreeTree62_38 degreeTree62_39) + +def degreeTree62_41 : RowTree := (.node [10,10,10,10,4,4,4,4,1,1,1,1,1,1] (.node [10,10,10,10,4,4,4,3,2,1,1,1,1,1] (.node [10,10,10,10,4,4,4,2,2,2,1,1,1,1] (.node [10,10,10,10,4,4,3,3,3,2,2,1] (.node [10,10,10,10,4,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,4,4,4,2,2,2,2,2] (.node [10,10,10,10,4,4,4,2,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,10,10,4,4,4,3,3,1,1,1,1] (.node [10,10,10,10,4,4,4,3,2,2,2,1] (.node [10,10,10,10,4,4,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,4,4,4,3,3,2,1,1] .empty .empty))) (.node [10,10,10,10,5,3,3,2,2,2,2,1,1,1] (.node [10,10,10,10,4,4,4,4,3,1,1,1] (.node [10,10,10,10,4,4,4,4,2,2,1,1] (.node [10,10,10,10,4,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,3,2,2,2,2,2,2,2] (.node [10,10,10,10,5,2,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [10,10,10,10,5,3,3,3,3,1,1,1,1,1] (.node [10,10,10,10,5,3,3,3,2,2,2,1,1] (.node [10,10,10,10,5,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,10,10,5,3,3,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_42 : RowTree := (.node [10,10,10,10,5,4,4,2,2,1,1,1,1,1] (.node [10,10,10,10,5,4,3,3,2,1,1,1,1,1] (.node [10,10,10,10,5,4,3,2,2,2,1,1,1,1] (.node [10,10,10,10,5,4,2,2,2,2,2,2,1] (.node [10,10,10,10,5,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,4,3,2,2,2,2,2] (.node [10,10,10,10,5,4,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [10,10,10,10,5,4,3,3,3,1,1,1,1] (.node [10,10,10,10,5,4,3,3,2,2,2,1] (.node [10,10,10,10,5,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,4,3,3,3,2,1,1] .empty .empty))) (.node [10,10,10,10,5,4,4,3,3,1,1,1] (.node [10,10,10,10,5,4,4,3,1,1,1,1,1,1] (.node [10,10,10,10,5,4,4,2,2,2,2,1] (.node [10,10,10,10,5,4,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,4,4,3,2,2,1,1] (.node [10,10,10,10,5,4,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,5,5,2,2,2,2,1,1,1,1] (.node [10,10,10,10,5,4,4,4,2,1,1,1] (.node [10,10,10,10,5,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,5,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_43 : RowTree := (.node [10,10,10,10,5,3,3,3,3,2,2,1] degreeTree62_41 degreeTree62_42) + +def degreeTree62_44 : RowTree := (.node [10,10,10,10,4,4,3,3,3,1,1,1,1,1] degreeTree62_40 degreeTree62_43) + +def degreeTree62_45 : RowTree := (.node [10,10,10,9,8,7,2,2,1,1,1,1] degreeTree62_37 degreeTree62_44) + +def degreeTree62_46 : RowTree := (.node [10,10,10,10,5,5,4,3,1,1,1,1,1] (.node [10,10,10,10,5,5,3,3,2,2,1,1] (.node [10,10,10,10,5,5,3,2,2,2,2,1] (.node [10,10,10,10,5,5,3,2,2,2,1,1,1] (.node [10,10,10,10,5,5,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,5,3,3,2,1,1,1,1] (.node [10,10,10,10,5,5,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,5,5,4,2,2,1,1,1,1] (.node [10,10,10,10,5,5,4,2,1,1,1,1,1,1] (.node [10,10,10,10,5,5,3,3,3,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,5,4,2,2,2,1,1] .empty .empty))) (.node [10,10,10,10,5,5,5,3,1,1,1,1] (.node [10,10,10,10,5,5,5,1,1,1,1,1,1,1] (.node [10,10,10,10,5,5,4,4,1,1,1,1] (.node [10,10,10,10,5,5,4,3,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,5,5,5,2,2,1,1,1] (.node [10,10,10,10,5,5,5,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,6,3,2,2,2,2,2,1,1,1] (.node [10,10,10,10,6,2,2,2,2,2,2,2,2] (.node [10,10,10,10,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,3,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_47 : RowTree := (.node [10,10,10,10,6,4,3,2,2,1,1,1,1,1] (.node [10,10,10,10,6,3,3,3,3,1,1,1,1] (.node [10,10,10,10,6,3,3,3,2,1,1,1,1,1] (.node [10,10,10,10,6,3,3,2,2,2,2,2] (.node [10,10,10,10,6,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,3,3,3,2,2,2,1] (.node [10,10,10,10,6,3,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,6,4,2,2,2,2,2,1,1] (.node [10,10,10,10,6,4,2,2,2,2,1,1,1,1] (.node [10,10,10,10,6,3,3,3,3,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,4,2,2,2,2,2,2] .empty .empty))) (.node [10,10,10,10,6,4,3,3,3,1,1,1] (.node [10,10,10,10,6,4,3,3,1,1,1,1,1,1] (.node [10,10,10,10,6,4,3,2,2,2,2,1] (.node [10,10,10,10,6,4,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,4,3,3,2,2,1,1] (.node [10,10,10,10,6,4,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,6,4,4,2,2,2,1,1] (.node [10,10,10,10,6,4,4,2,2,1,1,1,1] (.node [10,10,10,10,6,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,4,4,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_48 : RowTree := (.node [10,10,10,10,6,3,3,2,2,2,1,1,1,1] degreeTree62_46 degreeTree62_47) + +def degreeTree62_49 : RowTree := (.node [10,10,10,10,6,5,4,2,1,1,1,1,1] (.node [10,10,10,10,6,5,3,2,2,1,1,1,1] (.node [10,10,10,10,6,5,2,2,2,2,1,1,1] (.node [10,10,10,10,6,5,2,2,2,1,1,1,1,1] (.node [10,10,10,10,6,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,5,3,2,1,1,1,1,1,1] (.node [10,10,10,10,6,5,2,2,2,2,2,1] .empty .empty) .empty)) (.node [10,10,10,10,6,5,3,3,2,1,1,1] (.node [10,10,10,10,6,5,3,3,1,1,1,1,1] (.node [10,10,10,10,6,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,5,4,1,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,10,6,6,2,2,2,1,1,1,1] (.node [10,10,10,10,6,5,5,1,1,1,1,1,1] (.node [10,10,10,10,6,5,4,3,1,1,1,1] (.node [10,10,10,10,6,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,6,2,2,1,1,1,1,1,1] (.node [10,10,10,10,6,5,5,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,6,6,3,2,1,1,1,1,1] (.node [10,10,10,10,6,6,3,1,1,1,1,1,1,1] (.node [10,10,10,10,6,6,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,6,6,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_50 : RowTree := (.node [10,10,10,10,7,3,3,2,2,2,2,1] (.node [10,10,10,10,7,3,2,2,2,2,1,1,1,1] (.node [10,10,10,10,6,6,5,1,1,1,1,1] (.node [10,10,10,10,6,6,4,2,1,1,1,1] (.node [10,10,10,10,6,6,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,2,2,2,2,2,2,2,1] (.node [10,10,10,10,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,7,3,3,2,2,1,1,1,1,1] (.node [10,10,10,10,7,3,2,2,2,2,2,2] (.node [10,10,10,10,7,3,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,3,3,2,2,2,1,1,1] .empty .empty))) (.node [10,10,10,10,7,4,2,2,2,2,1,1,1] (.node [10,10,10,10,7,3,3,3,2,2,1,1] (.node [10,10,10,10,7,3,3,3,2,1,1,1,1] (.node [10,10,10,10,7,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,4,2,2,2,1,1,1,1,1] (.node [10,10,10,10,7,3,3,3,3,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,7,4,3,2,2,1,1,1,1] (.node [10,10,10,10,7,4,3,2,1,1,1,1,1,1] (.node [10,10,10,10,7,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [10,10,10,10,7,4,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_51 : RowTree := (.node [10,10,10,10,6,6,3,3,1,1,1,1] degreeTree62_49 degreeTree62_50) + +def degreeTree62_52 : RowTree := (.node [10,10,10,10,6,4,4,3,2,1,1,1] degreeTree62_48 degreeTree62_51) + +def degreeTree62_53 : RowTree := (.node [10,10,10,10,7,5,3,2,2,1,1,1] (.node [10,10,10,10,7,5,2,2,1,1,1,1,1,1] (.node [10,10,10,10,7,4,4,2,1,1,1,1,1] (.node [10,10,10,10,7,4,4,1,1,1,1,1,1,1] (.node [10,10,10,10,7,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,4,4,3,1,1,1,1] (.node [10,10,10,10,7,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,7,5,3,1,1,1,1,1,1,1] (.node [10,10,10,10,7,5,2,2,2,2,1,1] (.node [10,10,10,10,7,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,5,3,2,1,1,1,1,1] .empty .empty))) (.node [10,10,10,10,7,6,2,2,1,1,1,1,1] (.node [10,10,10,10,7,5,4,2,1,1,1,1] (.node [10,10,10,10,7,5,4,1,1,1,1,1,1] (.node [10,10,10,10,7,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,6,2,1,1,1,1,1,1,1] (.node [10,10,10,10,7,5,5,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,7,6,3,2,1,1,1,1] (.node [10,10,10,10,7,6,3,1,1,1,1,1,1] (.node [10,10,10,10,7,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,7,6,4,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_54 : RowTree := (.node [10,10,10,10,8,3,3,2,2,1,1,1,1] (.node [10,10,10,10,8,2,2,2,2,2,2,2] (.node [10,10,10,10,7,7,3,1,1,1,1,1] (.node [10,10,10,10,7,7,2,2,1,1,1,1] (.node [10,10,10,10,7,7,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,8,2,2,2,2,2,2,1,1] (.node [10,10,10,10,8,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,8,3,2,2,2,2,2,1] (.node [10,10,10,10,8,3,2,2,2,2,1,1,1] (.node [10,10,10,10,8,3,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,8,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,10,8,4,2,2,2,2,1,1] (.node [10,10,10,10,8,3,3,3,2,1,1,1] (.node [10,10,10,10,8,3,3,3,1,1,1,1,1] (.node [10,10,10,10,8,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [10,10,10,10,8,4,2,2,2,1,1,1,1] (.node [10,10,10,10,8,4,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,8,4,3,2,2,1,1,1] (.node [10,10,10,10,8,4,3,2,1,1,1,1,1] (.node [10,10,10,10,8,4,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,8,4,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_55 : RowTree := (.node [10,10,10,10,7,7,1,1,1,1,1,1,1,1] degreeTree62_53 degreeTree62_54) + +def degreeTree62_56 : RowTree := (.node [10,10,10,10,8,6,3,1,1,1,1,1] (.node [10,10,10,10,8,5,3,2,1,1,1,1] (.node [10,10,10,10,8,5,2,2,1,1,1,1,1] (.node [10,10,10,10,8,5,2,1,1,1,1,1,1,1] (.node [10,10,10,10,8,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,8,5,3,1,1,1,1,1,1] (.node [10,10,10,10,8,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,8,6,2,1,1,1,1,1,1] (.node [10,10,10,10,8,6,1,1,1,1,1,1,1,1] (.node [10,10,10,10,8,5,4,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,8,6,2,2,1,1,1,1] .empty .empty))) (.node [10,10,10,10,9,2,2,2,2,2,2,1] (.node [10,10,10,10,8,8,1,1,1,1,1,1] (.node [10,10,10,10,8,7,2,1,1,1,1,1] (.node [10,10,10,10,8,7,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,9,2,2,2,2,2,1,1,1] (.node [10,10,10,10,9,2,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,9,3,2,2,2,2,1,1] (.node [10,10,10,10,9,3,2,2,2,1,1,1,1] (.node [10,10,10,10,9,3,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,9,3,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_57 : RowTree := (.node [10,10,10,10,9,5,2,2,1,1,1,1] (.node [10,10,10,10,9,4,3,1,1,1,1,1,1] (.node [10,10,10,10,9,4,2,1,1,1,1,1,1,1] (.node [10,10,10,10,9,3,3,3,1,1,1,1] (.node [10,10,10,10,9,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,9,4,2,2,2,1,1,1] (.node [10,10,10,10,9,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,9,5,1,1,1,1,1,1,1,1] (.node [10,10,10,10,9,4,4,1,1,1,1,1] (.node [10,10,10,10,9,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,9,5,2,1,1,1,1,1,1] .empty .empty))) (.node [10,10,10,10,10,2,2,2,1,1,1,1,1,1] (.node [10,10,10,10,9,6,2,1,1,1,1,1] (.node [10,10,10,10,9,6,1,1,1,1,1,1,1] (.node [10,10,10,10,9,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,9,7,1,1,1,1,1,1] .empty .empty)) (.node [10,10,10,10,10,3,2,1,1,1,1,1,1,1] (.node [10,10,10,10,10,2,2,2,2,2,1,1] (.node [10,10,10,10,10,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,10,3,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_58 : RowTree := (.node [10,10,10,10,9,3,3,2,1,1,1,1,1] degreeTree62_56 degreeTree62_57) + +def degreeTree62_59 : RowTree := (.node [10,10,10,10,8,4,4,1,1,1,1,1,1] degreeTree62_55 degreeTree62_58) + +def degreeTree62_60 : RowTree := (.node [10,10,10,10,7,4,3,3,1,1,1,1,1] degreeTree62_52 degreeTree62_59) + +def degreeTree62_61 : RowTree := (.node [10,10,10,10,5,5,2,2,2,2,2,2] degreeTree62_45 degreeTree62_60) + +def degreeTree62_62 : RowTree := (.node [10,10,10,9,7,4,2,2,2,2,1,1,1,1] degreeTree62_30 degreeTree62_61) + +def degreeTree62_63 : RowTree := (.node [11,9,8,8,8,8,2,2,2,1,1,1,1] (.node [10,10,10,10,10,4,3,1,1,1,1,1] (.node [10,10,10,10,10,4,1,1,1,1,1,1,1,1] (.node [10,10,10,10,10,3,3,2,1,1,1,1] (.node [10,10,10,10,10,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [10,10,10,10,10,4,2,2,1,1,1,1] (.node [10,10,10,10,10,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [10,10,10,10,10,6,1,1,1,1,1,1] (.node [10,10,10,10,10,5,2,1,1,1,1,1] (.node [10,10,10,10,10,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,8,8,8,8,2,2,1,1,1,1,1,1] .empty .empty))) (.node [11,9,8,8,8,8,4,1,1,1,1,1,1] (.node [11,9,8,8,8,8,3,2,1,1,1,1,1] (.node [11,9,8,8,8,8,3,1,1,1,1,1,1,1] (.node [11,9,8,8,8,8,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,9,8,8,8,8,3,3,1,1,1,1] (.node [11,9,8,8,8,8,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,9,9,8,8,7,2,2,1,1,1,1,1,1] (.node [11,9,8,8,8,8,5,1,1,1,1,1] (.node [11,9,8,8,8,8,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,8,8,7,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_64 : RowTree := (.node [11,9,9,8,8,8,3,1,1,1,1,1,1] (.node [11,9,9,8,8,7,4,2,1,1,1,1] (.node [11,9,9,8,8,7,3,2,2,1,1,1] (.node [11,9,9,8,8,7,3,2,1,1,1,1,1] (.node [11,9,9,8,8,7,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,8,8,7,4,1,1,1,1,1,1] (.node [11,9,9,8,8,7,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,8,8,8,2,2,1,1,1,1,1] (.node [11,9,9,8,8,8,2,1,1,1,1,1,1,1] (.node [11,9,9,8,8,7,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,8,8,8,2,2,2,1,1,1] .empty .empty))) (.node [11,9,9,9,7,7,3,1,1,1,1,1,1,1] (.node [11,9,9,9,7,7,2,2,1,1,1,1,1,1] (.node [11,9,9,8,8,8,4,1,1,1,1,1] (.node [11,9,9,8,8,8,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,7,7,2,2,2,2,1,1] (.node [11,9,9,9,7,7,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,7,7,3,3,1,1,1,1] (.node [11,9,9,9,7,7,3,2,2,1,1,1] (.node [11,9,9,9,7,7,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,7,7,4,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_65 : RowTree := (.node [11,9,9,8,8,7,2,2,2,2,1,1] degreeTree62_63 degreeTree62_64) + +def degreeTree62_66 : RowTree := (.node [11,9,9,9,8,3,3,3,2,2,2,1] (.node [11,9,9,9,8,3,3,2,2,2,1,1,1,1] (.node [11,9,9,9,8,2,2,2,2,2,2,2,2] (.node [11,9,9,9,8,2,2,2,2,2,2,2,1,1] (.node [11,9,9,9,7,7,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,3,2,2,2,2,2,2,1] (.node [11,9,9,9,8,3,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,8,3,3,3,2,1,1,1,1,1] (.node [11,9,9,9,8,3,3,2,2,2,2,2] (.node [11,9,9,9,8,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,3,3,3,2,2,1,1,1] .empty .empty))) (.node [11,9,9,9,8,4,3,2,2,1,1,1,1,1] (.node [11,9,9,9,8,4,2,2,2,2,1,1,1,1] (.node [11,9,9,9,8,3,3,3,3,2,1,1] (.node [11,9,9,9,8,3,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,4,2,2,2,2,2,2] (.node [11,9,9,9,8,4,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,9,9,9,8,4,3,3,1,1,1,1,1,1] (.node [11,9,9,9,8,4,3,2,2,2,2,1] (.node [11,9,9,9,8,4,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,4,3,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_67 : RowTree := (.node [11,9,9,9,8,5,3,2,1,1,1,1,1,1] (.node [11,9,9,9,8,4,4,3,2,1,1,1] (.node [11,9,9,9,8,4,4,2,2,1,1,1,1] (.node [11,9,9,9,8,4,4,2,1,1,1,1,1,1] (.node [11,9,9,9,8,4,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,4,4,3,1,1,1,1,1] (.node [11,9,9,9,8,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [11,9,9,9,8,5,2,2,2,2,1,1,1] (.node [11,9,9,9,8,5,2,2,2,1,1,1,1,1] (.node [11,9,9,9,8,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,5,2,2,2,2,2,1] .empty .empty))) (.node [11,9,9,9,8,5,4,2,1,1,1,1,1] (.node [11,9,9,9,8,5,3,3,1,1,1,1,1] (.node [11,9,9,9,8,5,3,2,2,2,1,1] (.node [11,9,9,9,8,5,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,5,4,1,1,1,1,1,1,1] (.node [11,9,9,9,8,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,8,5,5,1,1,1,1,1,1] (.node [11,9,9,9,8,5,4,3,1,1,1,1] (.node [11,9,9,9,8,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,5,5,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_68 : RowTree := (.node [11,9,9,9,8,4,3,3,2,2,1,1] degreeTree62_66 degreeTree62_67) + +def degreeTree62_69 : RowTree := (.node [11,9,9,9,7,7,4,2,1,1,1,1] degreeTree62_65 degreeTree62_68) + +def degreeTree62_70 : RowTree := (.node [11,9,9,9,8,7,2,2,1,1,1,1,1] (.node [11,9,9,9,8,6,3,3,1,1,1,1] (.node [11,9,9,9,8,6,3,1,1,1,1,1,1,1] (.node [11,9,9,9,8,6,2,2,2,2,1,1] (.node [11,9,9,9,8,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,6,3,2,2,1,1,1] (.node [11,9,9,9,8,6,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,8,6,5,1,1,1,1,1] (.node [11,9,9,9,8,6,4,2,1,1,1,1] (.node [11,9,9,9,8,6,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,7,2,1,1,1,1,1,1,1] .empty .empty))) (.node [11,9,9,9,8,8,2,1,1,1,1,1,1] (.node [11,9,9,9,8,7,3,2,1,1,1,1] (.node [11,9,9,9,8,7,3,1,1,1,1,1,1] (.node [11,9,9,9,8,7,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,8,8,1,1,1,1,1,1,1,1] (.node [11,9,9,9,8,7,4,1,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,9,2,2,2,2,2,2,1,1,1] (.node [11,9,9,9,8,8,3,1,1,1,1,1] (.node [11,9,9,9,8,8,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,2,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_71 : RowTree := (.node [11,9,9,9,9,4,2,2,2,2,1,1,1] (.node [11,9,9,9,9,3,3,3,1,1,1,1,1,1] (.node [11,9,9,9,9,3,3,2,2,1,1,1,1,1] (.node [11,9,9,9,9,3,2,2,2,2,2,2] (.node [11,9,9,9,9,3,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,3,3,2,2,2,2,1] (.node [11,9,9,9,9,3,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,9,3,3,3,3,1,1,1] (.node [11,9,9,9,9,3,3,3,2,2,1,1] (.node [11,9,9,9,9,3,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,4,2,2,2,1,1,1,1,1] .empty .empty))) (.node [11,9,9,9,9,4,3,3,2,1,1,1] (.node [11,9,9,9,9,4,3,2,2,1,1,1,1] (.node [11,9,9,9,9,4,3,2,1,1,1,1,1,1] (.node [11,9,9,9,9,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,9,9,9,9,4,3,3,1,1,1,1,1] (.node [11,9,9,9,9,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [11,9,9,9,9,4,4,2,2,1,1,1] (.node [11,9,9,9,9,4,4,2,1,1,1,1,1] (.node [11,9,9,9,9,4,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,4,4,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_72 : RowTree := (.node [11,9,9,9,9,3,2,2,2,2,1,1,1,1] degreeTree62_70 degreeTree62_71) + +def degreeTree62_73 : RowTree := (.node [11,9,9,9,9,6,2,2,1,1,1,1,1] (.node [11,9,9,9,9,5,3,3,1,1,1,1] (.node [11,9,9,9,9,5,3,1,1,1,1,1,1,1] (.node [11,9,9,9,9,5,2,2,2,2,1,1] (.node [11,9,9,9,9,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,5,3,2,2,1,1,1] (.node [11,9,9,9,9,5,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,9,5,5,1,1,1,1,1] (.node [11,9,9,9,9,5,4,2,1,1,1,1] (.node [11,9,9,9,9,5,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,6,2,1,1,1,1,1,1,1] .empty .empty))) (.node [11,9,9,9,9,7,2,1,1,1,1,1,1] (.node [11,9,9,9,9,6,3,2,1,1,1,1] (.node [11,9,9,9,9,6,3,1,1,1,1,1,1] (.node [11,9,9,9,9,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,7,1,1,1,1,1,1,1,1] (.node [11,9,9,9,9,6,4,1,1,1,1,1] .empty .empty) .empty)) (.node [11,9,9,9,9,8,1,1,1,1,1,1,1] (.node [11,9,9,9,9,7,3,1,1,1,1,1] (.node [11,9,9,9,9,7,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,9,9,9,9,8,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_74 : RowTree := (.node [11,10,8,8,8,8,2,1,1,1,1,1,1,1] (.node [11,10,8,8,8,7,3,2,2,1,1,1] (.node [11,10,8,8,8,7,2,2,2,2,1,1] (.node [11,10,8,8,8,7,2,2,2,1,1,1,1] (.node [11,10,8,8,8,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,8,8,8,7,3,2,1,1,1,1,1] (.node [11,10,8,8,8,7,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,8,8,8,7,4,2,1,1,1,1] (.node [11,10,8,8,8,7,4,1,1,1,1,1,1] (.node [11,10,8,8,8,7,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,8,8,8,7,5,1,1,1,1,1] .empty .empty))) (.node [11,10,9,8,7,7,2,2,1,1,1,1,1,1] (.node [11,10,8,8,8,8,3,1,1,1,1,1,1] (.node [11,10,8,8,8,8,2,2,2,1,1,1] (.node [11,10,8,8,8,8,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,8,8,8,8,4,1,1,1,1,1] (.node [11,10,8,8,8,8,3,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,7,7,3,1,1,1,1,1,1,1] (.node [11,10,9,8,7,7,2,2,2,2,1,1] (.node [11,10,9,8,7,7,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,7,7,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_75 : RowTree := (.node [11,9,9,9,9,9,1,1,1,1,1,1] degreeTree62_73 degreeTree62_74) + +def degreeTree62_76 : RowTree := (.node [11,9,9,9,9,5,2,2,1,1,1,1,1,1] degreeTree62_72 degreeTree62_75) + +def degreeTree62_77 : RowTree := (.node [11,9,9,9,8,6,2,2,1,1,1,1,1,1] degreeTree62_69 degreeTree62_76) + +def degreeTree62_78 : RowTree := (.node [11,10,9,8,8,3,3,2,2,2,2,2] (.node [11,10,9,8,8,2,2,2,2,2,2,2,2] (.node [11,10,9,8,7,7,4,2,1,1,1,1] (.node [11,10,9,8,7,7,4,1,1,1,1,1,1] (.node [11,10,9,8,7,7,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,2,2,2,2,2,2,2,1,1] (.node [11,10,9,8,7,7,5,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,8,3,3,2,2,2,1,1,1,1] (.node [11,10,9,8,8,3,2,2,2,2,2,2,1] (.node [11,10,9,8,8,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,3,3,2,2,2,2,1,1] .empty .empty))) (.node [11,10,9,8,8,4,2,2,2,2,1,1,1,1] (.node [11,10,9,8,8,3,3,3,2,2,2,1] (.node [11,10,9,8,8,3,3,3,2,2,1,1,1] (.node [11,10,9,8,8,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,3,3,3,3,2,1,1] (.node [11,10,9,8,8,3,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,8,4,3,2,2,1,1,1,1,1] (.node [11,10,9,8,8,4,2,2,2,2,2,2] (.node [11,10,9,8,8,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,4,3,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_79 : RowTree := (.node [11,10,9,8,8,5,2,2,2,1,1,1,1,1] (.node [11,10,9,8,8,4,4,2,2,1,1,1,1] (.node [11,10,9,8,8,4,3,3,2,2,1,1] (.node [11,10,9,8,8,4,3,3,2,1,1,1,1] (.node [11,10,9,8,8,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,4,4,2,1,1,1,1,1,1] (.node [11,10,9,8,8,4,3,3,3,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,8,4,4,3,2,1,1,1] (.node [11,10,9,8,8,4,4,3,1,1,1,1,1] (.node [11,10,9,8,8,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,4,4,4,1,1,1,1] .empty .empty))) (.node [11,10,9,8,8,5,3,3,1,1,1,1,1] (.node [11,10,9,8,8,5,3,2,1,1,1,1,1,1] (.node [11,10,9,8,8,5,2,2,2,2,2,1] (.node [11,10,9,8,8,5,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,5,3,2,2,2,1,1] (.node [11,10,9,8,8,5,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,8,5,4,2,1,1,1,1,1] (.node [11,10,9,8,8,5,4,1,1,1,1,1,1,1] (.node [11,10,9,8,8,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,5,4,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_80 : RowTree := (.node [11,10,9,8,8,4,3,2,2,2,2,1] degreeTree62_78 degreeTree62_79) + +def degreeTree62_81 : RowTree := (.node [11,10,9,8,8,6,4,2,1,1,1,1] (.node [11,10,9,8,8,6,3,1,1,1,1,1,1,1] (.node [11,10,9,8,8,6,2,2,1,1,1,1,1,1] (.node [11,10,9,8,8,5,5,2,1,1,1,1] (.node [11,10,9,8,8,5,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,6,2,2,2,2,1,1] (.node [11,10,9,8,8,6,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,8,6,3,3,1,1,1,1] (.node [11,10,9,8,8,6,3,2,2,1,1,1] (.node [11,10,9,8,8,6,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,6,4,1,1,1,1,1,1] .empty .empty))) (.node [11,10,9,8,8,7,3,2,1,1,1,1] (.node [11,10,9,8,8,7,2,2,1,1,1,1,1] (.node [11,10,9,8,8,7,2,1,1,1,1,1,1,1] (.node [11,10,9,8,8,6,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,7,3,1,1,1,1,1,1] (.node [11,10,9,8,8,7,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,9,8,8,8,2,1,1,1,1,1,1] (.node [11,10,9,8,8,8,1,1,1,1,1,1,1,1] (.node [11,10,9,8,8,7,4,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,8,8,8,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_82 : RowTree := (.node [11,10,9,9,7,3,3,3,3,1,1,1,1] (.node [11,10,9,9,7,3,3,2,2,2,2,1,1] (.node [11,10,9,9,7,3,2,2,2,2,2,1,1,1] (.node [11,10,9,9,7,2,2,2,2,2,2,2,2] (.node [11,10,9,9,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,3,3,2,2,2,1,1,1,1] (.node [11,10,9,9,7,3,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,10,9,9,7,3,3,3,2,2,1,1,1] (.node [11,10,9,9,7,3,3,3,2,1,1,1,1,1] (.node [11,10,9,9,7,3,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,9,9,7,3,3,3,2,2,2,1] .empty .empty))) (.node [11,10,9,9,7,4,3,2,2,2,1,1,1] (.node [11,10,9,9,7,4,2,2,2,2,2,1,1] (.node [11,10,9,9,7,4,2,2,2,2,1,1,1,1] (.node [11,10,9,9,7,3,3,3,3,2,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,4,3,2,2,1,1,1,1,1] (.node [11,10,9,9,7,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,10,9,9,7,4,3,3,2,1,1,1,1] (.node [11,10,9,9,7,4,3,3,1,1,1,1,1,1] (.node [11,10,9,9,7,4,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,9,9,7,4,3,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_83 : RowTree := (.node [11,10,9,8,8,8,3,1,1,1,1,1] degreeTree62_81 degreeTree62_82) + +def degreeTree62_84 : RowTree := (.node [11,10,9,8,8,5,4,3,1,1,1,1] degreeTree62_80 degreeTree62_83) + +def degreeTree62_85 : RowTree := (.node [11,10,9,9,7,5,3,2,2,1,1,1,1] (.node [11,10,9,9,7,4,4,4,1,1,1,1] (.node [11,10,9,9,7,4,4,2,2,2,1,1] (.node [11,10,9,9,7,4,4,2,2,1,1,1,1] (.node [11,10,9,9,7,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,4,4,3,2,1,1,1] (.node [11,10,9,9,7,4,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,7,5,2,2,2,2,2,1] (.node [11,10,9,9,7,5,2,2,2,2,1,1,1] (.node [11,10,9,9,7,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,5,3,2,1,1,1,1,1,1] .empty .empty))) (.node [11,10,9,9,7,5,4,2,2,1,1,1] (.node [11,10,9,9,7,5,3,3,2,1,1,1] (.node [11,10,9,9,7,5,3,3,1,1,1,1,1] (.node [11,10,9,9,7,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,5,4,2,1,1,1,1,1] (.node [11,10,9,9,7,5,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,7,5,5,2,1,1,1,1] (.node [11,10,9,9,7,5,5,1,1,1,1,1,1] (.node [11,10,9,9,7,5,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,6,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_86 : RowTree := (.node [11,10,9,9,7,7,2,2,2,1,1,1] (.node [11,10,9,9,7,6,4,1,1,1,1,1,1] (.node [11,10,9,9,7,6,3,2,1,1,1,1,1] (.node [11,10,9,9,7,6,3,1,1,1,1,1,1,1] (.node [11,10,9,9,7,6,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,6,3,3,1,1,1,1] (.node [11,10,9,9,7,6,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,7,7,2,1,1,1,1,1,1,1] (.node [11,10,9,9,7,6,5,1,1,1,1,1] (.node [11,10,9,9,7,6,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,7,7,2,2,1,1,1,1,1] .empty .empty))) (.node [11,10,9,9,8,3,2,2,2,2,1,1,1,1] (.node [11,10,9,9,7,7,4,1,1,1,1,1] (.node [11,10,9,9,7,7,3,2,1,1,1,1] (.node [11,10,9,9,7,7,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,2,2,2,2,2,2,2,1] (.node [11,10,9,9,8,2,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,8,3,3,2,2,1,1,1,1,1] (.node [11,10,9,9,8,3,2,2,2,2,2,2] (.node [11,10,9,9,8,3,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,3,3,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_87 : RowTree := (.node [11,10,9,9,7,6,2,2,2,1,1,1,1] degreeTree62_85 degreeTree62_86) + +def degreeTree62_88 : RowTree := (.node [11,10,9,9,8,4,3,3,1,1,1,1,1] (.node [11,10,9,9,8,4,2,2,2,2,1,1,1] (.node [11,10,9,9,8,3,3,3,2,2,1,1] (.node [11,10,9,9,8,3,3,3,2,1,1,1,1] (.node [11,10,9,9,8,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,4,2,2,2,1,1,1,1,1] (.node [11,10,9,9,8,3,3,3,3,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,8,4,3,2,2,1,1,1,1] (.node [11,10,9,9,8,4,3,2,1,1,1,1,1,1] (.node [11,10,9,9,8,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,9,9,8,4,3,2,2,2,1,1] .empty .empty))) (.node [11,10,9,9,8,5,2,2,1,1,1,1,1,1] (.node [11,10,9,9,8,4,4,2,1,1,1,1,1] (.node [11,10,9,9,8,4,4,1,1,1,1,1,1,1] (.node [11,10,9,9,8,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,4,4,3,1,1,1,1] (.node [11,10,9,9,8,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,8,5,3,1,1,1,1,1,1,1] (.node [11,10,9,9,8,5,2,2,2,2,1,1] (.node [11,10,9,9,8,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,5,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_89 : RowTree := (.node [11,10,9,9,8,7,1,1,1,1,1,1,1,1] (.node [11,10,9,9,8,6,2,2,1,1,1,1,1] (.node [11,10,9,9,8,5,4,2,1,1,1,1] (.node [11,10,9,9,8,5,4,1,1,1,1,1,1] (.node [11,10,9,9,8,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,6,2,1,1,1,1,1,1,1] (.node [11,10,9,9,8,5,5,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,8,6,3,2,1,1,1,1] (.node [11,10,9,9,8,6,3,1,1,1,1,1,1] (.node [11,10,9,9,8,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,6,4,1,1,1,1,1] .empty .empty))) (.node [11,10,9,9,8,8,2,1,1,1,1,1] (.node [11,10,9,9,8,7,3,1,1,1,1,1] (.node [11,10,9,9,8,7,2,2,1,1,1,1] (.node [11,10,9,9,8,7,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,8,8,1,1,1,1,1,1,1] .empty .empty)) (.node [11,10,9,9,9,2,2,2,2,2,2,2] (.node [11,10,9,9,9,2,2,2,2,2,2,1,1] (.node [11,10,9,9,9,2,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,9,3,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_90 : RowTree := (.node [11,10,9,9,8,5,3,2,2,1,1,1] degreeTree62_88 degreeTree62_89) + +def degreeTree62_91 : RowTree := (.node [11,10,9,9,8,3,3,2,2,2,2,1] degreeTree62_87 degreeTree62_90) + +def degreeTree62_92 : RowTree := (.node [11,10,9,9,7,4,3,3,3,1,1,1] degreeTree62_84 degreeTree62_91) + +def degreeTree62_93 : RowTree := (.node [11,10,9,8,7,7,3,2,2,1,1,1] degreeTree62_77 degreeTree62_92) + +def degreeTree62_94 : RowTree := (.node [11,10,9,9,9,4,3,2,1,1,1,1,1] (.node [11,10,9,9,9,3,3,3,2,1,1,1] (.node [11,10,9,9,9,3,3,2,2,1,1,1,1] (.node [11,10,9,9,9,3,3,2,1,1,1,1,1,1] (.node [11,10,9,9,9,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,9,9,9,3,3,3,1,1,1,1,1] (.node [11,10,9,9,9,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [11,10,9,9,9,4,2,2,2,2,1,1] (.node [11,10,9,9,9,4,2,2,2,1,1,1,1] (.node [11,10,9,9,9,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,9,4,3,1,1,1,1,1,1,1] .empty .empty))) (.node [11,10,9,9,9,5,2,2,1,1,1,1,1] (.node [11,10,9,9,9,4,4,1,1,1,1,1,1] (.node [11,10,9,9,9,4,3,3,1,1,1,1] (.node [11,10,9,9,9,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,9,5,2,1,1,1,1,1,1,1] (.node [11,10,9,9,9,4,4,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,9,9,9,5,3,2,1,1,1,1] (.node [11,10,9,9,9,5,3,1,1,1,1,1,1] (.node [11,10,9,9,9,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,9,5,4,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_95 : RowTree := (.node [11,10,10,7,7,7,3,2,1,1,1,1,1] (.node [11,10,9,9,9,8,1,1,1,1,1,1] (.node [11,10,9,9,9,6,3,1,1,1,1,1] (.node [11,10,9,9,9,6,2,2,1,1,1,1] (.node [11,10,9,9,9,6,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,9,9,9,7,2,1,1,1,1,1] (.node [11,10,9,9,9,7,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,7,7,7,2,2,2,2,1,1] (.node [11,10,10,7,7,7,2,2,2,1,1,1,1] (.node [11,10,10,7,7,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,7,7,7,3,1,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,8,7,2,2,2,2,2,2,2,1,1] (.node [11,10,10,7,7,7,4,1,1,1,1,1,1] (.node [11,10,10,7,7,7,3,3,1,1,1,1] (.node [11,10,10,7,7,7,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,7,7,7,5,1,1,1,1,1] (.node [11,10,10,7,7,7,4,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,7,3,2,2,2,2,2,2,1] (.node [11,10,10,8,7,3,2,2,2,2,2,1,1,1] (.node [11,10,10,8,7,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,8,7,3,3,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_96 : RowTree := (.node [11,10,9,9,9,6,1,1,1,1,1,1,1,1] degreeTree62_94 degreeTree62_95) + +def degreeTree62_97 : RowTree := (.node [11,10,10,8,7,4,3,2,2,2,1,1,1] (.node [11,10,10,8,7,3,3,3,3,2,1,1] (.node [11,10,10,8,7,3,3,3,2,2,1,1,1] (.node [11,10,10,8,7,3,3,3,2,1,1,1,1,1] (.node [11,10,10,8,7,3,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,8,7,3,3,3,3,1,1,1,1] (.node [11,10,10,8,7,3,3,3,2,2,2,1] .empty .empty) .empty)) (.node [11,10,10,8,7,4,2,2,2,2,2,2] (.node [11,10,10,8,7,4,2,2,2,2,2,1,1] (.node [11,10,10,8,7,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,4,3,2,2,1,1,1,1,1] .empty .empty))) (.node [11,10,10,8,7,4,4,2,1,1,1,1,1,1] (.node [11,10,10,8,7,4,3,3,2,1,1,1,1] (.node [11,10,10,8,7,4,3,3,1,1,1,1,1,1] (.node [11,10,10,8,7,4,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,10,8,7,4,3,3,3,1,1,1] (.node [11,10,10,8,7,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [11,10,10,8,7,4,4,3,1,1,1,1,1] (.node [11,10,10,8,7,4,4,2,2,2,1,1] (.node [11,10,10,8,7,4,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,4,4,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_98 : RowTree := (.node [11,10,10,8,7,5,4,2,2,1,1,1] (.node [11,10,10,8,7,5,3,2,2,2,1,1] (.node [11,10,10,8,7,5,2,2,2,2,2,1] (.node [11,10,10,8,7,5,2,2,2,2,1,1,1] (.node [11,10,10,8,7,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,5,3,2,2,1,1,1,1] (.node [11,10,10,8,7,5,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,7,5,4,1,1,1,1,1,1,1] (.node [11,10,10,8,7,5,3,3,2,1,1,1] (.node [11,10,10,8,7,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,5,4,2,1,1,1,1,1] .empty .empty))) (.node [11,10,10,8,7,6,2,2,2,2,1,1] (.node [11,10,10,8,7,5,5,2,1,1,1,1] (.node [11,10,10,8,7,5,5,1,1,1,1,1,1] (.node [11,10,10,8,7,5,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,6,2,2,2,1,1,1,1] (.node [11,10,10,8,7,6,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,7,6,3,2,2,1,1,1] (.node [11,10,10,8,7,6,3,2,1,1,1,1,1] (.node [11,10,10,8,7,6,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,6,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_99 : RowTree := (.node [11,10,10,8,7,4,4,4,1,1,1,1] degreeTree62_97 degreeTree62_98) + +def degreeTree62_100 : RowTree := (.node [11,10,10,8,7,3,3,2,2,2,2,1,1] degreeTree62_96 degreeTree62_99) + +def degreeTree62_101 : RowTree := (.node [11,10,10,8,8,3,2,2,2,2,1,1,1,1] (.node [11,10,10,8,7,7,3,1,1,1,1,1,1] (.node [11,10,10,8,7,7,2,1,1,1,1,1,1,1] (.node [11,10,10,8,7,6,5,1,1,1,1,1] (.node [11,10,10,8,7,6,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,7,7,2,2,2,1,1,1] (.node [11,10,10,8,7,7,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,8,2,2,2,2,2,2,1,1,1] (.node [11,10,10,8,7,7,4,1,1,1,1,1] (.node [11,10,10,8,7,7,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,2,2,2,2,2,2,2,1] .empty .empty))) (.node [11,10,10,8,8,3,3,3,1,1,1,1,1,1] (.node [11,10,10,8,8,3,3,2,2,1,1,1,1,1] (.node [11,10,10,8,8,3,2,2,2,2,2,2] (.node [11,10,10,8,8,3,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,3,3,2,2,2,2,1] (.node [11,10,10,8,8,3,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,8,3,3,3,3,1,1,1] (.node [11,10,10,8,8,3,3,3,2,2,1,1] (.node [11,10,10,8,8,3,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,4,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_102 : RowTree := (.node [11,10,10,8,8,5,2,2,1,1,1,1,1,1] (.node [11,10,10,8,8,4,3,3,2,1,1,1] (.node [11,10,10,8,8,4,3,2,2,1,1,1,1] (.node [11,10,10,8,8,4,3,2,1,1,1,1,1,1] (.node [11,10,10,8,8,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,10,8,8,4,3,3,1,1,1,1,1] (.node [11,10,10,8,8,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [11,10,10,8,8,4,4,2,2,1,1,1] (.node [11,10,10,8,8,4,4,2,1,1,1,1,1] (.node [11,10,10,8,8,4,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,4,4,3,1,1,1,1] .empty .empty))) (.node [11,10,10,8,8,5,3,3,1,1,1,1] (.node [11,10,10,8,8,5,3,1,1,1,1,1,1,1] (.node [11,10,10,8,8,5,2,2,2,2,1,1] (.node [11,10,10,8,8,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,5,3,2,2,1,1,1] (.node [11,10,10,8,8,5,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,8,5,5,1,1,1,1,1] (.node [11,10,10,8,8,5,4,2,1,1,1,1] (.node [11,10,10,8,8,5,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,6,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_103 : RowTree := (.node [11,10,10,8,8,4,2,2,2,2,1,1,1] degreeTree62_101 degreeTree62_102) + +def degreeTree62_104 : RowTree := (.node [11,10,10,9,4,3,3,2,2,2,2,2,2] (.node [11,10,10,8,8,7,2,1,1,1,1,1,1] (.node [11,10,10,8,8,6,3,2,1,1,1,1] (.node [11,10,10,8,8,6,3,1,1,1,1,1,1] (.node [11,10,10,8,8,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,7,1,1,1,1,1,1,1,1] (.node [11,10,10,8,8,6,4,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,8,8,8,1,1,1,1,1,1,1] (.node [11,10,10,8,8,7,3,1,1,1,1,1] (.node [11,10,10,8,8,7,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,8,8,8,2,1,1,1,1,1] .empty .empty))) (.node [11,10,10,9,4,4,3,3,2,2,2,1,1] (.node [11,10,10,9,4,4,2,2,2,2,2,2,2] (.node [11,10,10,9,4,3,3,3,3,3,3] (.node [11,10,10,9,4,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,9,4,4,3,2,2,2,2,2,1] (.node [11,10,10,9,4,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,4,4,3,3,3,2,2,1] (.node [11,10,10,9,4,4,3,3,3,2,1,1,1] (.node [11,10,10,9,4,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,4,4,4,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_105 : RowTree := (.node [11,10,10,9,5,2,2,2,2,2,2,2,2,1] (.node [11,10,10,9,4,4,4,3,3,2,1,1] (.node [11,10,10,9,4,4,4,3,2,2,1,1,1] (.node [11,10,10,9,4,4,4,3,2,1,1,1,1,1] (.node [11,10,10,9,4,4,4,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,9,4,4,4,3,3,1,1,1,1] (.node [11,10,10,9,4,4,4,3,2,2,2,1] .empty .empty) .empty)) (.node [11,10,10,9,4,4,4,4,2,2,1,1] (.node [11,10,10,9,4,4,4,4,2,1,1,1,1] (.node [11,10,10,9,4,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,4,4,4,4,3,1,1,1] .empty .empty))) (.node [11,10,10,9,5,3,3,3,3,2,1,1,1] (.node [11,10,10,9,5,3,3,2,2,2,2,2,1] (.node [11,10,10,9,5,3,3,2,2,2,2,1,1,1] (.node [11,10,10,9,5,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,9,5,3,3,3,3,1,1,1,1,1] (.node [11,10,10,9,5,3,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [11,10,10,9,5,4,2,2,2,2,2,2,1] (.node [11,10,10,9,5,4,2,2,2,2,2,1,1,1] (.node [11,10,10,9,5,3,3,3,3,2,2,1] .empty .empty) .empty) (.node [11,10,10,9,5,4,3,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_106 : RowTree := (.node [11,10,10,9,4,4,4,2,2,2,2,1,1] degreeTree62_104 degreeTree62_105) + +def degreeTree62_107 : RowTree := (.node [11,10,10,8,8,6,2,2,1,1,1,1,1] degreeTree62_103 degreeTree62_106) + +def degreeTree62_108 : RowTree := (.node [11,10,10,8,7,6,4,1,1,1,1,1,1] degreeTree62_100 degreeTree62_107) + +def degreeTree62_109 : RowTree := (.node [11,10,10,9,5,4,4,3,2,1,1,1,1] (.node [11,10,10,9,5,4,3,3,3,2,1,1] (.node [11,10,10,9,5,4,3,3,2,2,1,1,1] (.node [11,10,10,9,5,4,3,3,2,1,1,1,1,1] (.node [11,10,10,9,5,4,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,9,5,4,3,3,3,1,1,1,1] (.node [11,10,10,9,5,4,3,3,2,2,2,1] .empty .empty) .empty)) (.node [11,10,10,9,5,4,4,2,2,2,2,1] (.node [11,10,10,9,5,4,4,2,2,2,1,1,1] (.node [11,10,10,9,5,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,5,4,4,3,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,9,5,5,2,2,2,2,2,1,1] (.node [11,10,10,9,5,4,4,4,1,1,1,1,1] (.node [11,10,10,9,5,4,4,3,3,1,1,1] (.node [11,10,10,9,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,9,5,5,2,2,2,2,1,1,1,1] (.node [11,10,10,9,5,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,5,5,3,2,2,2,1,1,1] (.node [11,10,10,9,5,5,3,2,2,1,1,1,1,1] (.node [11,10,10,9,5,5,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,9,5,5,3,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_110 : RowTree := (.node [11,10,10,9,5,5,5,2,1,1,1,1,1] (.node [11,10,10,9,5,5,4,2,2,2,1,1] (.node [11,10,10,9,5,5,3,3,3,1,1,1] (.node [11,10,10,9,5,5,3,3,2,2,1,1] (.node [11,10,10,9,5,5,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,5,5,4,2,2,1,1,1,1] (.node [11,10,10,9,5,5,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,5,5,4,4,1,1,1,1] (.node [11,10,10,9,5,5,4,3,2,1,1,1] (.node [11,10,10,9,5,5,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,5,5,5,1,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,9,6,3,2,2,2,2,2,2,1] (.node [11,10,10,9,6,2,2,2,2,2,2,2,1,1] (.node [11,10,10,9,5,5,5,3,1,1,1,1] (.node [11,10,10,9,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,3,2,2,2,2,2,1,1,1] (.node [11,10,10,9,6,2,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,10,10,9,6,3,3,2,2,2,2,2] (.node [11,10,10,9,6,3,3,2,2,2,2,1,1] (.node [11,10,10,9,6,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,3,3,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_111 : RowTree := (.node [11,10,10,9,5,5,3,3,1,1,1,1,1,1] degreeTree62_109 degreeTree62_110) + +def degreeTree62_112 : RowTree := (.node [11,10,10,9,6,4,3,3,2,1,1,1,1] (.node [11,10,10,9,6,4,2,2,2,2,2,2] (.node [11,10,10,9,6,3,3,3,3,2,1,1] (.node [11,10,10,9,6,3,3,3,3,1,1,1,1] (.node [11,10,10,9,6,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [11,10,10,9,6,4,2,2,2,2,2,1,1] (.node [11,10,10,9,6,4,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,6,4,3,2,2,2,2,1] (.node [11,10,10,9,6,4,3,2,2,2,1,1,1] (.node [11,10,10,9,6,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,4,3,3,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,9,6,4,4,3,1,1,1,1,1] (.node [11,10,10,9,6,4,4,2,1,1,1,1,1,1] (.node [11,10,10,9,6,4,3,3,3,1,1,1] (.node [11,10,10,9,6,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,4,4,2,2,2,1,1] (.node [11,10,10,9,6,4,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,6,5,2,2,2,1,1,1,1,1] (.node [11,10,10,9,6,4,4,4,1,1,1,1] (.node [11,10,10,9,6,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,5,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_113 : RowTree := (.node [11,10,10,9,6,5,5,2,1,1,1,1] (.node [11,10,10,9,6,5,4,1,1,1,1,1,1,1] (.node [11,10,10,9,6,5,3,2,2,2,1,1] (.node [11,10,10,9,6,5,3,2,2,1,1,1,1] (.node [11,10,10,9,6,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,5,3,3,2,1,1,1] (.node [11,10,10,9,6,5,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,6,5,4,3,1,1,1,1] (.node [11,10,10,9,6,5,4,2,2,1,1,1] (.node [11,10,10,9,6,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,5,5,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,9,6,6,3,2,2,1,1,1] (.node [11,10,10,9,6,6,2,2,2,2,1,1] (.node [11,10,10,9,6,6,2,2,2,1,1,1,1] (.node [11,10,10,9,6,6,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,6,3,2,1,1,1,1,1] (.node [11,10,10,9,6,6,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,6,6,4,2,1,1,1,1] (.node [11,10,10,9,6,6,4,1,1,1,1,1,1] (.node [11,10,10,9,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,6,6,5,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_114 : RowTree := (.node [11,10,10,9,6,5,2,2,2,2,2,1] degreeTree62_112 degreeTree62_113) + +def degreeTree62_115 : RowTree := (.node [11,10,10,9,6,3,3,3,2,2,1,1,1] degreeTree62_111 degreeTree62_114) + +def degreeTree62_116 : RowTree := (.node [11,10,10,9,7,3,3,3,3,1,1,1] (.node [11,10,10,9,7,3,3,2,2,2,1,1,1] (.node [11,10,10,9,7,3,2,2,2,2,2,1,1] (.node [11,10,10,9,7,3,2,2,2,2,1,1,1,1] (.node [11,10,10,9,7,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,10,9,7,3,3,2,2,1,1,1,1,1] (.node [11,10,10,9,7,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,10,10,9,7,3,3,3,2,1,1,1,1] (.node [11,10,10,9,7,3,3,3,1,1,1,1,1,1] (.node [11,10,10,9,7,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,10,9,7,3,3,3,2,2,1,1] .empty .empty))) (.node [11,10,10,9,7,4,3,2,2,2,1,1] (.node [11,10,10,9,7,4,2,2,2,2,2,1] (.node [11,10,10,9,7,4,2,2,2,2,1,1,1] (.node [11,10,10,9,7,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,7,4,3,2,2,1,1,1,1] (.node [11,10,10,9,7,4,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,7,4,4,1,1,1,1,1,1,1] (.node [11,10,10,9,7,4,3,3,2,1,1,1] (.node [11,10,10,9,7,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,7,4,4,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_117 : RowTree := (.node [11,10,10,9,7,5,5,1,1,1,1,1] (.node [11,10,10,9,7,5,3,2,1,1,1,1,1] (.node [11,10,10,9,7,5,2,2,2,1,1,1,1] (.node [11,10,10,9,7,5,2,2,1,1,1,1,1,1] (.node [11,10,10,9,7,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,7,5,3,1,1,1,1,1,1,1] (.node [11,10,10,9,7,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,10,10,9,7,5,4,1,1,1,1,1,1] (.node [11,10,10,9,7,5,3,3,1,1,1,1] (.node [11,10,10,9,7,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,7,5,4,2,1,1,1,1] .empty .empty))) (.node [11,10,10,9,7,6,4,1,1,1,1,1] (.node [11,10,10,9,7,6,2,2,2,1,1,1] (.node [11,10,10,9,7,6,2,2,1,1,1,1,1] (.node [11,10,10,9,7,6,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,7,6,3,2,1,1,1,1] (.node [11,10,10,9,7,6,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,7,7,2,2,1,1,1,1] (.node [11,10,10,9,7,7,2,1,1,1,1,1,1] (.node [11,10,10,9,7,7,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,7,7,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_118 : RowTree := (.node [11,10,10,9,7,4,4,2,2,1,1,1] degreeTree62_116 degreeTree62_117) + +def degreeTree62_119 : RowTree := (.node [11,10,10,9,8,4,2,2,1,1,1,1,1,1] (.node [11,10,10,9,8,3,3,2,1,1,1,1,1,1] (.node [11,10,10,9,8,3,2,2,2,1,1,1,1,1] (.node [11,10,10,9,8,2,2,2,2,2,2,2] (.node [11,10,10,9,8,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,9,8,3,2,2,2,2,2,1] (.node [11,10,10,9,8,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,8,3,3,3,1,1,1,1,1] (.node [11,10,10,9,8,3,3,2,2,2,1,1] (.node [11,10,10,9,8,3,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,8,3,3,3,2,1,1,1] .empty .empty))) (.node [11,10,10,9,8,4,3,3,1,1,1,1] (.node [11,10,10,9,8,4,3,1,1,1,1,1,1,1] (.node [11,10,10,9,8,4,2,2,2,2,1,1] (.node [11,10,10,9,8,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,8,4,3,2,2,1,1,1] (.node [11,10,10,9,8,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,8,5,2,1,1,1,1,1,1,1] (.node [11,10,10,9,8,4,4,2,1,1,1,1] (.node [11,10,10,9,8,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,8,5,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_120 : RowTree := (.node [11,10,10,9,9,2,2,2,2,1,1,1,1,1] (.node [11,10,10,9,8,6,2,2,1,1,1,1] (.node [11,10,10,9,8,5,4,1,1,1,1,1] (.node [11,10,10,9,8,5,3,2,1,1,1,1] (.node [11,10,10,9,8,5,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,8,6,2,1,1,1,1,1,1] (.node [11,10,10,9,8,6,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,8,7,2,1,1,1,1,1] (.node [11,10,10,9,8,7,1,1,1,1,1,1,1] (.node [11,10,10,9,8,6,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,8,8,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,9,9,3,2,2,2,2,1,1] (.node [11,10,10,9,9,3,2,2,1,1,1,1,1,1] (.node [11,10,10,9,9,2,2,2,2,2,2,1] (.node [11,10,10,9,9,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,9,3,2,2,2,1,1,1,1] .empty .empty)) (.node [11,10,10,9,9,3,3,2,2,1,1,1] (.node [11,10,10,9,9,3,3,2,1,1,1,1,1] (.node [11,10,10,9,9,3,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,9,3,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_121 : RowTree := (.node [11,10,10,9,8,5,2,2,2,1,1,1] degreeTree62_119 degreeTree62_120) + +def degreeTree62_122 : RowTree := (.node [11,10,10,9,8,2,2,2,2,2,1,1,1,1] degreeTree62_118 degreeTree62_121) + +def degreeTree62_123 : RowTree := (.node [11,10,10,9,7,2,2,2,2,2,2,1,1,1] degreeTree62_115 degreeTree62_122) + +def degreeTree62_124 : RowTree := (.node [11,10,10,9,5,4,3,2,2,2,2,1,1] degreeTree62_108 degreeTree62_123) + +def degreeTree62_125 : RowTree := (.node [11,10,9,9,9,3,2,2,2,2,1,1,1] degreeTree62_93 degreeTree62_124) + +def degreeTree62_126 : RowTree := (.node [10,10,10,10,10,3,2,2,2,1,1,1] degreeTree62_62 degreeTree62_125) + +def degreeTree62_127 : RowTree := (.node [11,10,10,9,9,6,2,1,1,1,1,1] (.node [11,10,10,9,9,5,1,1,1,1,1,1,1,1] (.node [11,10,10,9,9,4,3,1,1,1,1,1,1] (.node [11,10,10,9,9,4,2,2,2,1,1,1] (.node [11,10,10,9,9,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,9,4,4,1,1,1,1,1] (.node [11,10,10,9,9,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,9,9,5,3,1,1,1,1,1] (.node [11,10,10,9,9,5,2,2,1,1,1,1] (.node [11,10,10,9,9,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,9,9,6,1,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,10,4,3,2,2,2,2,2,2,2] (.node [11,10,10,10,3,3,3,3,3,2,2,1,1] (.node [11,10,10,10,3,3,3,2,2,2,2,2,2] (.node [11,10,10,9,9,7,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,4,2,2,2,2,2,2,2,2,1] (.node [11,10,10,10,3,3,3,3,3,3,3] .empty .empty) .empty)) (.node [11,10,10,10,4,3,3,3,2,2,2,1,1] (.node [11,10,10,10,4,3,3,2,2,2,2,2,1] (.node [11,10,10,10,4,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,4,3,3,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_128 : RowTree := (.node [11,10,10,10,4,4,3,3,3,2,1,1] (.node [11,10,10,10,4,4,3,2,2,2,2,2] (.node [11,10,10,10,4,4,2,2,2,2,2,2,1] (.node [11,10,10,10,4,4,2,2,2,2,2,1,1,1] (.node [11,10,10,10,4,3,3,3,3,2,2,1] .empty .empty) .empty) (.node [11,10,10,10,4,4,3,2,2,2,2,1,1] (.node [11,10,10,10,4,4,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,4,4,3,3,2,2,2,1] (.node [11,10,10,10,4,4,3,3,2,2,1,1,1] (.node [11,10,10,10,4,4,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,4,4,3,3,3,1,1,1,1] .empty .empty))) (.node [11,10,10,10,4,4,4,3,2,2,1,1] (.node [11,10,10,10,4,4,4,2,2,2,2,1] (.node [11,10,10,10,4,4,4,2,2,2,1,1,1] (.node [11,10,10,10,4,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,4,4,4,3,2,1,1,1,1] (.node [11,10,10,10,4,4,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,4,4,4,4,2,1,1,1] (.node [11,10,10,10,4,4,4,4,1,1,1,1,1] (.node [11,10,10,10,4,4,4,3,3,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,2,2,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_129 : RowTree := (.node [11,10,10,10,4,3,3,3,3,2,1,1,1] degreeTree62_127 degreeTree62_128) + +def degreeTree62_130 : RowTree := (.node [11,10,10,10,5,4,2,2,2,2,1,1,1,1] (.node [11,10,10,10,5,3,3,3,2,1,1,1,1,1] (.node [11,10,10,10,5,3,3,2,2,2,1,1,1,1] (.node [11,10,10,10,5,3,2,2,2,2,2,2,1] (.node [11,10,10,10,5,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,3,3,2,2,2,2,2] (.node [11,10,10,10,5,3,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,10,10,10,5,3,3,3,3,1,1,1,1] (.node [11,10,10,10,5,3,3,3,2,2,2,1] (.node [11,10,10,10,5,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,3,3,3,3,2,1,1] .empty .empty))) (.node [11,10,10,10,5,4,3,3,1,1,1,1,1,1] (.node [11,10,10,10,5,4,3,2,2,1,1,1,1,1] (.node [11,10,10,10,5,4,2,2,2,2,2,2] (.node [11,10,10,10,5,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,4,3,2,2,2,2,1] (.node [11,10,10,10,5,4,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,5,4,3,3,3,1,1,1] (.node [11,10,10,10,5,4,3,3,2,2,1,1] (.node [11,10,10,10,5,4,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,4,4,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_131 : RowTree := (.node [11,10,10,10,5,5,3,3,1,1,1,1,1] (.node [11,10,10,10,5,5,2,2,2,2,1,1,1] (.node [11,10,10,10,5,4,4,3,2,1,1,1] (.node [11,10,10,10,5,4,4,3,1,1,1,1,1] (.node [11,10,10,10,5,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,5,2,2,2,1,1,1,1,1] (.node [11,10,10,10,5,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,5,5,3,2,2,1,1,1,1] (.node [11,10,10,10,5,5,3,2,1,1,1,1,1,1] (.node [11,10,10,10,5,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,10,10,10,5,5,3,2,2,2,1,1] .empty .empty))) (.node [11,10,10,10,5,5,5,1,1,1,1,1,1] (.node [11,10,10,10,5,5,4,2,1,1,1,1,1] (.node [11,10,10,10,5,5,4,1,1,1,1,1,1,1] (.node [11,10,10,10,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,5,5,4,3,1,1,1,1] (.node [11,10,10,10,5,5,4,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,6,2,2,2,2,2,2,2,1] (.node [11,10,10,10,6,2,2,2,2,2,2,1,1,1] (.node [11,10,10,10,5,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,6,3,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_132 : RowTree := (.node [11,10,10,10,5,4,4,2,2,1,1,1,1] degreeTree62_130 degreeTree62_131) + +def degreeTree62_133 : RowTree := (.node [11,10,10,10,5,2,2,2,2,2,2,2,2] degreeTree62_129 degreeTree62_132) + +def degreeTree62_134 : RowTree := (.node [11,10,10,10,6,4,2,2,2,2,2,1] (.node [11,10,10,10,6,3,3,3,2,1,1,1,1] (.node [11,10,10,10,6,3,3,2,2,2,1,1,1] (.node [11,10,10,10,6,3,3,2,2,1,1,1,1,1] (.node [11,10,10,10,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,10,10,10,6,3,3,3,1,1,1,1,1,1] (.node [11,10,10,10,6,3,3,2,2,2,2,1] .empty .empty) .empty)) (.node [11,10,10,10,6,4,2,2,2,1,1,1,1,1] (.node [11,10,10,10,6,3,3,3,3,1,1,1] (.node [11,10,10,10,6,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,10,6,4,2,2,2,2,1,1,1] .empty .empty))) (.node [11,10,10,10,6,4,4,1,1,1,1,1,1,1] (.node [11,10,10,10,6,4,3,2,2,2,1,1] (.node [11,10,10,10,6,4,3,2,2,1,1,1,1] (.node [11,10,10,10,6,4,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,6,4,3,3,2,1,1,1] (.node [11,10,10,10,6,4,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,6,4,4,3,1,1,1,1] (.node [11,10,10,10,6,4,4,2,2,1,1,1] (.node [11,10,10,10,6,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,6,5,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_135 : RowTree := (.node [11,10,10,10,6,6,2,2,2,1,1,1] (.node [11,10,10,10,6,5,4,1,1,1,1,1,1] (.node [11,10,10,10,6,5,3,2,1,1,1,1,1] (.node [11,10,10,10,6,5,3,1,1,1,1,1,1,1] (.node [11,10,10,10,6,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,10,6,5,3,3,1,1,1,1] (.node [11,10,10,10,6,5,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,6,6,2,1,1,1,1,1,1,1] (.node [11,10,10,10,6,5,5,1,1,1,1,1] (.node [11,10,10,10,6,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,6,6,2,2,1,1,1,1,1] .empty .empty))) (.node [11,10,10,10,7,2,2,2,2,2,2,2] (.node [11,10,10,10,6,6,4,1,1,1,1,1] (.node [11,10,10,10,6,6,3,2,1,1,1,1] (.node [11,10,10,10,6,6,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,7,2,2,2,2,2,2,1,1] (.node [11,10,10,10,7,2,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,7,3,2,2,2,2,2,1] (.node [11,10,10,10,7,3,2,2,2,2,1,1,1] (.node [11,10,10,10,7,3,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,7,3,3,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_136 : RowTree := (.node [11,10,10,10,6,5,2,2,2,1,1,1,1] degreeTree62_134 degreeTree62_135) + +def degreeTree62_137 : RowTree := (.node [11,10,10,10,7,4,4,1,1,1,1,1,1] (.node [11,10,10,10,7,4,2,2,2,2,1,1] (.node [11,10,10,10,7,3,3,3,2,1,1,1] (.node [11,10,10,10,7,3,3,3,1,1,1,1,1] (.node [11,10,10,10,7,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,10,10,10,7,4,2,2,2,1,1,1,1] (.node [11,10,10,10,7,4,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,7,4,3,2,2,1,1,1] (.node [11,10,10,10,7,4,3,2,1,1,1,1,1] (.node [11,10,10,10,7,4,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,7,4,3,3,1,1,1,1] .empty .empty))) (.node [11,10,10,10,7,5,3,2,1,1,1,1] (.node [11,10,10,10,7,5,2,2,1,1,1,1,1] (.node [11,10,10,10,7,5,2,1,1,1,1,1,1,1] (.node [11,10,10,10,7,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,7,5,3,1,1,1,1,1,1] (.node [11,10,10,10,7,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,7,6,2,1,1,1,1,1,1] (.node [11,10,10,10,7,6,1,1,1,1,1,1,1,1] (.node [11,10,10,10,7,5,4,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,7,6,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_138 : RowTree := (.node [11,10,10,10,8,3,3,2,2,1,1,1] (.node [11,10,10,10,8,3,2,2,1,1,1,1,1,1] (.node [11,10,10,10,8,2,2,2,2,1,1,1,1,1] (.node [11,10,10,10,7,7,2,1,1,1,1,1] (.node [11,10,10,10,7,7,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,8,2,2,2,2,2,2,1] (.node [11,10,10,10,8,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,8,3,3,1,1,1,1,1,1,1] (.node [11,10,10,10,8,3,2,2,2,2,1,1] (.node [11,10,10,10,8,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,8,3,3,2,1,1,1,1,1] .empty .empty))) (.node [11,10,10,10,8,4,3,2,1,1,1,1] (.node [11,10,10,10,8,4,2,2,1,1,1,1,1] (.node [11,10,10,10,8,4,2,1,1,1,1,1,1,1] (.node [11,10,10,10,8,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,8,4,3,1,1,1,1,1,1] (.node [11,10,10,10,8,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,8,5,2,1,1,1,1,1,1] (.node [11,10,10,10,8,5,1,1,1,1,1,1,1,1] (.node [11,10,10,10,8,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,8,5,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_139 : RowTree := (.node [11,10,10,10,7,6,3,1,1,1,1,1] degreeTree62_137 degreeTree62_138) + +def degreeTree62_140 : RowTree := (.node [11,10,10,10,7,3,3,2,2,1,1,1,1] degreeTree62_136 degreeTree62_139) + +def degreeTree62_141 : RowTree := (.node [11,10,10,10,6,3,2,2,2,2,2,1,1] degreeTree62_133 degreeTree62_140) + +def degreeTree62_142 : RowTree := (.node [11,10,10,10,9,3,3,2,1,1,1,1] (.node [11,10,10,10,9,2,2,2,2,2,1,1] (.node [11,10,10,10,8,7,1,1,1,1,1,1] (.node [11,10,10,10,8,6,2,1,1,1,1,1] (.node [11,10,10,10,8,6,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,9,2,2,2,2,1,1,1,1] (.node [11,10,10,10,9,2,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,9,3,2,2,2,1,1,1] (.node [11,10,10,10,9,3,2,2,1,1,1,1,1] (.node [11,10,10,10,9,3,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,9,3,3,1,1,1,1,1,1] .empty .empty))) (.node [11,10,10,10,9,5,2,1,1,1,1,1] (.node [11,10,10,10,9,4,2,2,1,1,1,1] (.node [11,10,10,10,9,4,2,1,1,1,1,1,1] (.node [11,10,10,10,9,4,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,9,5,1,1,1,1,1,1,1] (.node [11,10,10,10,9,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,10,10,10,10,2,2,2,1,1,1,1,1] (.node [11,10,10,10,10,2,2,1,1,1,1,1,1,1] (.node [11,10,10,10,9,6,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,10,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_143 : RowTree := (.node [11,11,8,8,7,7,3,2,1,1,1,1,1] (.node [11,10,10,10,10,5,1,1,1,1,1,1] (.node [11,10,10,10,10,3,3,1,1,1,1,1] (.node [11,10,10,10,10,3,2,2,1,1,1,1] (.node [11,10,10,10,10,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,10,10,10,10,4,2,1,1,1,1,1] (.node [11,10,10,10,10,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,8,8,7,7,2,2,2,2,1,1] (.node [11,11,8,8,7,7,2,2,2,1,1,1,1] (.node [11,11,8,8,7,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,7,7,3,1,1,1,1,1,1,1] .empty .empty))) (.node [11,11,8,8,8,2,2,2,2,2,2,2,1,1] (.node [11,11,8,8,7,7,4,1,1,1,1,1,1] (.node [11,11,8,8,7,7,3,3,1,1,1,1] (.node [11,11,8,8,7,7,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,7,7,5,1,1,1,1,1] (.node [11,11,8,8,7,7,4,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,8,8,8,3,2,2,2,2,2,2,1] (.node [11,11,8,8,8,3,2,2,2,2,2,1,1,1] (.node [11,11,8,8,8,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,8,8,8,3,3,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_144 : RowTree := (.node [11,10,10,10,10,3,1,1,1,1,1,1,1,1] degreeTree62_142 degreeTree62_143) + +def degreeTree62_145 : RowTree := (.node [11,11,8,8,8,4,3,2,2,2,1,1,1] (.node [11,11,8,8,8,3,3,3,3,2,1,1] (.node [11,11,8,8,8,3,3,3,2,2,1,1,1] (.node [11,11,8,8,8,3,3,3,2,1,1,1,1,1] (.node [11,11,8,8,8,3,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,8,8,8,3,3,3,3,1,1,1,1] (.node [11,11,8,8,8,3,3,3,2,2,2,1] .empty .empty) .empty)) (.node [11,11,8,8,8,4,2,2,2,2,2,2] (.node [11,11,8,8,8,4,2,2,2,2,2,1,1] (.node [11,11,8,8,8,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,4,3,2,2,1,1,1,1,1] .empty .empty))) (.node [11,11,8,8,8,4,4,2,1,1,1,1,1,1] (.node [11,11,8,8,8,4,3,3,2,1,1,1,1] (.node [11,11,8,8,8,4,3,3,1,1,1,1,1,1] (.node [11,11,8,8,8,4,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,8,8,8,4,3,3,3,1,1,1] (.node [11,11,8,8,8,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [11,11,8,8,8,4,4,3,1,1,1,1,1] (.node [11,11,8,8,8,4,4,2,2,2,1,1] (.node [11,11,8,8,8,4,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,4,4,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_146 : RowTree := (.node [11,11,8,8,8,5,4,2,2,1,1,1] (.node [11,11,8,8,8,5,3,2,2,2,1,1] (.node [11,11,8,8,8,5,2,2,2,2,2,1] (.node [11,11,8,8,8,5,2,2,2,2,1,1,1] (.node [11,11,8,8,8,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,5,3,2,2,1,1,1,1] (.node [11,11,8,8,8,5,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,8,8,8,5,4,1,1,1,1,1,1,1] (.node [11,11,8,8,8,5,3,3,2,1,1,1] (.node [11,11,8,8,8,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,5,4,2,1,1,1,1,1] .empty .empty))) (.node [11,11,8,8,8,6,2,2,2,2,1,1] (.node [11,11,8,8,8,5,5,2,1,1,1,1] (.node [11,11,8,8,8,5,5,1,1,1,1,1,1] (.node [11,11,8,8,8,5,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,6,2,2,2,1,1,1,1] (.node [11,11,8,8,8,6,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,8,8,8,6,3,2,2,1,1,1] (.node [11,11,8,8,8,6,3,2,1,1,1,1,1] (.node [11,11,8,8,8,6,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,6,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_147 : RowTree := (.node [11,11,8,8,8,4,4,4,1,1,1,1] degreeTree62_145 degreeTree62_146) + +def degreeTree62_148 : RowTree := (.node [11,11,8,8,8,3,3,2,2,2,2,1,1] degreeTree62_144 degreeTree62_147) + +def degreeTree62_149 : RowTree := (.node [11,11,8,8,8,8,2,2,1,1,1,1] (.node [11,11,8,8,8,7,3,1,1,1,1,1,1] (.node [11,11,8,8,8,7,2,1,1,1,1,1,1,1] (.node [11,11,8,8,8,6,5,1,1,1,1,1] (.node [11,11,8,8,8,6,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,7,2,2,2,1,1,1] (.node [11,11,8,8,8,7,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,8,8,8,8,1,1,1,1,1,1,1,1] (.node [11,11,8,8,8,7,4,1,1,1,1,1] (.node [11,11,8,8,8,7,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,8,8,8,8,2,1,1,1,1,1,1] .empty .empty))) (.node [11,11,9,7,7,7,3,2,1,1,1,1,1] (.node [11,11,9,7,7,7,2,2,2,1,1,1,1] (.node [11,11,9,7,7,7,2,2,1,1,1,1,1,1] (.node [11,11,8,8,8,8,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,7,7,7,3,1,1,1,1,1,1,1] (.node [11,11,9,7,7,7,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,9,7,7,7,4,1,1,1,1,1,1] (.node [11,11,9,7,7,7,3,3,1,1,1,1] (.node [11,11,9,7,7,7,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,7,7,7,4,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_150 : RowTree := (.node [11,11,9,8,7,3,3,3,3,1,1,1,1] (.node [11,11,9,8,7,3,3,2,2,2,2,1,1] (.node [11,11,9,8,7,3,2,2,2,2,2,1,1,1] (.node [11,11,9,8,7,2,2,2,2,2,2,2,2] (.node [11,11,9,8,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,3,3,2,2,2,1,1,1,1] (.node [11,11,9,8,7,3,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,9,8,7,3,3,3,2,2,1,1,1] (.node [11,11,9,8,7,3,3,3,2,1,1,1,1,1] (.node [11,11,9,8,7,3,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,9,8,7,3,3,3,2,2,2,1] .empty .empty))) (.node [11,11,9,8,7,4,3,2,2,2,1,1,1] (.node [11,11,9,8,7,4,2,2,2,2,2,1,1] (.node [11,11,9,8,7,4,2,2,2,2,1,1,1,1] (.node [11,11,9,8,7,3,3,3,3,2,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,4,3,2,2,1,1,1,1,1] (.node [11,11,9,8,7,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,9,8,7,4,3,3,2,1,1,1,1] (.node [11,11,9,8,7,4,3,3,1,1,1,1,1,1] (.node [11,11,9,8,7,4,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,9,8,7,4,3,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_151 : RowTree := (.node [11,11,9,7,7,7,5,1,1,1,1,1] degreeTree62_149 degreeTree62_150) + +def degreeTree62_152 : RowTree := (.node [11,11,9,8,7,5,3,2,2,1,1,1,1] (.node [11,11,9,8,7,4,4,4,1,1,1,1] (.node [11,11,9,8,7,4,4,2,2,2,1,1] (.node [11,11,9,8,7,4,4,2,2,1,1,1,1] (.node [11,11,9,8,7,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,4,4,3,2,1,1,1] (.node [11,11,9,8,7,4,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,8,7,5,2,2,2,2,2,1] (.node [11,11,9,8,7,5,2,2,2,2,1,1,1] (.node [11,11,9,8,7,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,5,3,2,1,1,1,1,1,1] .empty .empty))) (.node [11,11,9,8,7,5,4,2,2,1,1,1] (.node [11,11,9,8,7,5,3,3,2,1,1,1] (.node [11,11,9,8,7,5,3,3,1,1,1,1,1] (.node [11,11,9,8,7,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,5,4,2,1,1,1,1,1] (.node [11,11,9,8,7,5,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,8,7,5,5,2,1,1,1,1] (.node [11,11,9,8,7,5,5,1,1,1,1,1,1] (.node [11,11,9,8,7,5,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,6,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_153 : RowTree := (.node [11,11,9,8,7,7,2,2,2,1,1,1] (.node [11,11,9,8,7,6,4,1,1,1,1,1,1] (.node [11,11,9,8,7,6,3,2,1,1,1,1,1] (.node [11,11,9,8,7,6,3,1,1,1,1,1,1,1] (.node [11,11,9,8,7,6,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,6,3,3,1,1,1,1] (.node [11,11,9,8,7,6,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,8,7,7,2,1,1,1,1,1,1,1] (.node [11,11,9,8,7,6,5,1,1,1,1,1] (.node [11,11,9,8,7,6,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,7,7,2,2,1,1,1,1,1] .empty .empty))) (.node [11,11,9,8,8,2,2,2,2,2,2,2,1] (.node [11,11,9,8,7,7,4,1,1,1,1,1] (.node [11,11,9,8,7,7,3,2,1,1,1,1] (.node [11,11,9,8,7,7,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,2,2,2,2,2,2,1,1,1] .empty .empty)) (.node [11,11,9,8,8,3,2,2,2,2,2,2] (.node [11,11,9,8,8,3,2,2,2,2,2,1,1] (.node [11,11,9,8,8,3,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,3,3,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_154 : RowTree := (.node [11,11,9,8,7,6,2,2,2,1,1,1,1] degreeTree62_152 degreeTree62_153) + +def degreeTree62_155 : RowTree := (.node [11,11,9,8,7,4,3,3,3,1,1,1] degreeTree62_151 degreeTree62_154) + +def degreeTree62_156 : RowTree := (.node [11,11,8,8,8,6,4,1,1,1,1,1,1] degreeTree62_148 degreeTree62_155) + +def degreeTree62_157 : RowTree := (.node [11,10,10,10,8,5,3,1,1,1,1,1] degreeTree62_141 degreeTree62_156) + +def degreeTree62_158 : RowTree := (.node [11,11,9,8,8,4,3,2,2,2,1,1] (.node [11,11,9,8,8,4,2,2,2,1,1,1,1,1] (.node [11,11,9,8,8,3,3,3,2,1,1,1,1] (.node [11,11,9,8,8,3,3,3,1,1,1,1,1,1] (.node [11,11,9,8,8,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,9,8,8,3,3,3,3,1,1,1] (.node [11,11,9,8,8,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [11,11,9,8,8,4,3,2,1,1,1,1,1,1] (.node [11,11,9,8,8,4,2,2,2,2,2,1] (.node [11,11,9,8,8,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,4,3,2,2,1,1,1,1] .empty .empty))) (.node [11,11,9,8,8,4,4,3,1,1,1,1] (.node [11,11,9,8,8,4,4,1,1,1,1,1,1,1] (.node [11,11,9,8,8,4,3,3,2,1,1,1] (.node [11,11,9,8,8,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,4,4,2,2,1,1,1] (.node [11,11,9,8,8,4,4,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,8,8,5,2,2,2,2,1,1] (.node [11,11,9,8,8,5,2,2,2,1,1,1,1] (.node [11,11,9,8,8,5,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,5,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_159 : RowTree := (.node [11,11,9,8,8,6,4,1,1,1,1,1] (.node [11,11,9,8,8,6,2,1,1,1,1,1,1,1] (.node [11,11,9,8,8,5,4,1,1,1,1,1,1] (.node [11,11,9,8,8,5,3,3,1,1,1,1] (.node [11,11,9,8,8,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,5,5,1,1,1,1,1] (.node [11,11,9,8,8,5,4,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,8,8,6,3,1,1,1,1,1,1] (.node [11,11,9,8,8,6,2,2,2,1,1,1] (.node [11,11,9,8,8,6,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,6,3,2,1,1,1,1] .empty .empty))) (.node [11,11,9,8,8,8,2,1,1,1,1,1] (.node [11,11,9,8,8,7,2,2,1,1,1,1] (.node [11,11,9,8,8,7,2,1,1,1,1,1,1] (.node [11,11,9,8,8,7,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,8,8,8,1,1,1,1,1,1,1] (.node [11,11,9,8,8,7,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,4,3,3,3,3,3,3] (.node [11,11,9,9,4,3,3,3,3,2,2,1,1] (.node [11,11,9,9,4,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,9,9,4,4,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_160 : RowTree := (.node [11,11,9,8,8,5,3,2,1,1,1,1,1] degreeTree62_158 degreeTree62_159) + +def degreeTree62_161 : RowTree := (.node [11,11,9,9,4,4,4,3,2,2,2,1] (.node [11,11,9,9,4,4,4,2,2,2,1,1,1,1] (.node [11,11,9,9,4,4,3,3,3,1,1,1,1,1] (.node [11,11,9,9,4,4,3,3,2,2,2,1,1] (.node [11,11,9,9,4,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,9,9,4,4,3,3,3,2,2,1] (.node [11,11,9,9,4,4,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,4,4,4,3,2,1,1,1,1,1] (.node [11,11,9,9,4,4,4,2,2,2,2,2] (.node [11,11,9,9,4,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,9,4,4,4,3,2,2,1,1,1] .empty .empty))) (.node [11,11,9,9,4,4,4,4,3,1,1,1] (.node [11,11,9,9,4,4,4,4,1,1,1,1,1,1] (.node [11,11,9,9,4,4,4,3,3,2,1,1] (.node [11,11,9,9,4,4,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,4,4,4,4,2,2,1,1] (.node [11,11,9,9,4,4,4,4,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,5,3,3,2,2,2,2,1,1,1] (.node [11,11,9,9,5,3,2,2,2,2,2,2,2] (.node [11,11,9,9,5,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,9,9,5,3,3,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_162 : RowTree := (.node [11,11,9,9,5,4,3,3,2,2,2,1] (.node [11,11,9,9,5,4,3,2,2,2,1,1,1,1] (.node [11,11,9,9,5,3,3,3,3,2,2,1] (.node [11,11,9,9,5,3,3,3,3,2,1,1,1] (.node [11,11,9,9,5,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,4,2,2,2,2,2,2,1] (.node [11,11,9,9,5,4,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,5,4,3,3,2,1,1,1,1,1] (.node [11,11,9,9,5,4,3,2,2,2,2,2] (.node [11,11,9,9,5,4,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,4,3,3,2,2,1,1,1] .empty .empty))) (.node [11,11,9,9,5,4,4,3,1,1,1,1,1,1] (.node [11,11,9,9,5,4,4,2,2,1,1,1,1,1] (.node [11,11,9,9,5,4,3,3,3,2,1,1] (.node [11,11,9,9,5,4,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,4,4,2,2,2,2,1] (.node [11,11,9,9,5,4,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,5,4,4,3,3,1,1,1] (.node [11,11,9,9,5,4,4,3,2,2,1,1] (.node [11,11,9,9,5,4,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,4,4,4,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_163 : RowTree := (.node [11,11,9,9,5,3,3,3,2,2,2,1,1] degreeTree62_161 degreeTree62_162) + +def degreeTree62_164 : RowTree := (.node [11,11,9,9,4,4,3,2,2,2,2,1,1,1] degreeTree62_160 degreeTree62_163) + +def degreeTree62_165 : RowTree := (.node [11,11,9,9,5,5,4,2,1,1,1,1,1,1] (.node [11,11,9,9,5,5,3,2,2,2,2,1] (.node [11,11,9,9,5,5,2,2,2,2,2,2] (.node [11,11,9,9,5,5,2,2,2,2,2,1,1] (.node [11,11,9,9,5,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,5,3,2,2,2,1,1,1] (.node [11,11,9,9,5,5,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,5,5,3,3,2,2,1,1] (.node [11,11,9,9,5,5,3,3,2,1,1,1,1] (.node [11,11,9,9,5,5,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,5,3,3,3,1,1,1] .empty .empty))) (.node [11,11,9,9,5,5,5,1,1,1,1,1,1,1] (.node [11,11,9,9,5,5,4,3,1,1,1,1,1] (.node [11,11,9,9,5,5,4,2,2,2,1,1] (.node [11,11,9,9,5,5,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,5,5,4,4,1,1,1,1] (.node [11,11,9,9,5,5,4,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,5,5,5,3,1,1,1,1] (.node [11,11,9,9,5,5,5,2,2,1,1,1] (.node [11,11,9,9,5,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,2,2,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_166 : RowTree := (.node [11,11,9,9,6,4,2,2,2,2,1,1,1,1] (.node [11,11,9,9,6,3,3,3,2,1,1,1,1,1] (.node [11,11,9,9,6,3,3,2,2,2,1,1,1,1] (.node [11,11,9,9,6,3,2,2,2,2,2,2,1] (.node [11,11,9,9,6,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,3,3,2,2,2,2,2] (.node [11,11,9,9,6,3,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,9,9,6,3,3,3,3,1,1,1,1] (.node [11,11,9,9,6,3,3,3,2,2,2,1] (.node [11,11,9,9,6,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,3,3,3,3,2,1,1] .empty .empty))) (.node [11,11,9,9,6,4,3,3,1,1,1,1,1,1] (.node [11,11,9,9,6,4,3,2,2,1,1,1,1,1] (.node [11,11,9,9,6,4,2,2,2,2,2,2] (.node [11,11,9,9,6,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,4,3,2,2,2,2,1] (.node [11,11,9,9,6,4,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,6,4,3,3,3,1,1,1] (.node [11,11,9,9,6,4,3,3,2,2,1,1] (.node [11,11,9,9,6,4,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,4,4,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_167 : RowTree := (.node [11,11,9,9,6,2,2,2,2,2,2,2,2] degreeTree62_165 degreeTree62_166) + +def degreeTree62_168 : RowTree := (.node [11,11,9,9,6,5,3,3,1,1,1,1,1] (.node [11,11,9,9,6,5,2,2,2,2,1,1,1] (.node [11,11,9,9,6,4,4,3,2,1,1,1] (.node [11,11,9,9,6,4,4,3,1,1,1,1,1] (.node [11,11,9,9,6,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,5,2,2,2,1,1,1,1,1] (.node [11,11,9,9,6,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,6,5,3,2,2,1,1,1,1] (.node [11,11,9,9,6,5,3,2,1,1,1,1,1,1] (.node [11,11,9,9,6,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,9,9,6,5,3,2,2,2,1,1] .empty .empty))) (.node [11,11,9,9,6,5,5,1,1,1,1,1,1] (.node [11,11,9,9,6,5,4,2,1,1,1,1,1] (.node [11,11,9,9,6,5,4,1,1,1,1,1,1,1] (.node [11,11,9,9,6,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,5,4,3,1,1,1,1] (.node [11,11,9,9,6,5,4,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,6,6,2,2,2,1,1,1,1] (.node [11,11,9,9,6,6,2,2,1,1,1,1,1,1] (.node [11,11,9,9,6,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,6,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_169 : RowTree := (.node [11,11,9,9,7,3,2,2,2,2,2,2] (.node [11,11,9,9,6,6,5,1,1,1,1,1] (.node [11,11,9,9,6,6,3,3,1,1,1,1] (.node [11,11,9,9,6,6,3,2,2,1,1,1] (.node [11,11,9,9,6,6,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,6,6,4,2,1,1,1,1] (.node [11,11,9,9,6,6,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,7,3,2,2,2,2,1,1,1,1] (.node [11,11,9,9,7,2,2,2,2,2,2,2,1] (.node [11,11,9,9,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,3,2,2,2,2,2,1,1] .empty .empty))) (.node [11,11,9,9,7,3,3,3,2,2,1,1] (.node [11,11,9,9,7,3,3,2,2,2,2,1] (.node [11,11,9,9,7,3,3,2,2,2,1,1,1] (.node [11,11,9,9,7,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,3,3,3,2,1,1,1,1] (.node [11,11,9,9,7,3,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,7,4,2,2,2,2,1,1,1] (.node [11,11,9,9,7,4,2,2,2,1,1,1,1,1] (.node [11,11,9,9,7,3,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,4,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_170 : RowTree := (.node [11,11,9,9,6,6,3,1,1,1,1,1,1,1] degreeTree62_168 degreeTree62_169) + +def degreeTree62_171 : RowTree := (.node [11,11,9,9,6,4,4,2,2,1,1,1,1] degreeTree62_167 degreeTree62_170) + +def degreeTree62_172 : RowTree := (.node [11,11,9,9,5,4,4,4,2,1,1,1] degreeTree62_164 degreeTree62_171) + +def degreeTree62_173 : RowTree := (.node [11,11,9,9,7,5,2,2,2,2,1,1] (.node [11,11,9,9,7,4,4,2,1,1,1,1,1] (.node [11,11,9,9,7,4,3,3,1,1,1,1,1] (.node [11,11,9,9,7,4,3,2,2,2,1,1] (.node [11,11,9,9,7,4,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,4,4,1,1,1,1,1,1,1] (.node [11,11,9,9,7,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,7,5,2,2,1,1,1,1,1,1] (.node [11,11,9,9,7,4,4,3,1,1,1,1] (.node [11,11,9,9,7,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,5,2,2,2,1,1,1,1] .empty .empty))) (.node [11,11,9,9,7,5,4,2,1,1,1,1] (.node [11,11,9,9,7,5,3,2,2,1,1,1] (.node [11,11,9,9,7,5,3,2,1,1,1,1,1] (.node [11,11,9,9,7,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,5,4,1,1,1,1,1,1] (.node [11,11,9,9,7,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,7,6,2,2,1,1,1,1,1] (.node [11,11,9,9,7,6,2,1,1,1,1,1,1,1] (.node [11,11,9,9,7,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,6,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_174 : RowTree := (.node [11,11,9,9,8,3,2,2,2,2,1,1,1] (.node [11,11,9,9,7,7,3,1,1,1,1,1] (.node [11,11,9,9,7,7,1,1,1,1,1,1,1,1] (.node [11,11,9,9,7,6,4,1,1,1,1,1] (.node [11,11,9,9,7,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,7,7,2,2,1,1,1,1] (.node [11,11,9,9,7,7,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,8,2,2,2,2,2,2,2] (.node [11,11,9,9,8,2,2,2,2,2,2,1,1] (.node [11,11,9,9,8,2,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,8,3,2,2,2,1,1,1,1,1] .empty .empty))) (.node [11,11,9,9,8,3,3,3,2,1,1,1] (.node [11,11,9,9,8,3,3,2,2,1,1,1,1] (.node [11,11,9,9,8,3,3,2,1,1,1,1,1,1] (.node [11,11,9,9,8,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,9,9,8,3,3,3,1,1,1,1,1] (.node [11,11,9,9,8,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,9,9,8,4,2,2,2,2,1,1] (.node [11,11,9,9,8,4,2,2,2,1,1,1,1] (.node [11,11,9,9,8,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,8,4,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_175 : RowTree := (.node [11,11,9,9,7,6,3,1,1,1,1,1,1] degreeTree62_173 degreeTree62_174) + +def degreeTree62_176 : RowTree := (.node [11,11,9,9,8,6,1,1,1,1,1,1,1,1] (.node [11,11,9,9,8,5,2,2,1,1,1,1,1] (.node [11,11,9,9,8,4,4,1,1,1,1,1,1] (.node [11,11,9,9,8,4,3,3,1,1,1,1] (.node [11,11,9,9,8,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,8,5,2,1,1,1,1,1,1,1] (.node [11,11,9,9,8,4,4,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,8,5,3,2,1,1,1,1] (.node [11,11,9,9,8,5,3,1,1,1,1,1,1] (.node [11,11,9,9,8,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,8,5,4,1,1,1,1,1] .empty .empty))) (.node [11,11,9,9,8,8,1,1,1,1,1,1] (.node [11,11,9,9,8,6,3,1,1,1,1,1] (.node [11,11,9,9,8,6,2,2,1,1,1,1] (.node [11,11,9,9,8,6,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,8,7,2,1,1,1,1,1] (.node [11,11,9,9,8,7,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,9,2,2,2,2,2,2,1] (.node [11,11,9,9,9,2,2,2,2,2,1,1,1] (.node [11,11,9,9,9,2,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,9,3,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_177 : RowTree := (.node [11,11,9,9,9,4,4,1,1,1,1,1] (.node [11,11,9,9,9,4,2,1,1,1,1,1,1,1] (.node [11,11,9,9,9,3,3,2,1,1,1,1,1] (.node [11,11,9,9,9,3,3,1,1,1,1,1,1,1] (.node [11,11,9,9,9,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,9,9,9,3,3,3,1,1,1,1] (.node [11,11,9,9,9,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,9,9,9,4,3,1,1,1,1,1,1] (.node [11,11,9,9,9,4,2,2,2,1,1,1] (.node [11,11,9,9,9,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,9,4,3,2,1,1,1,1] .empty .empty))) (.node [11,11,9,9,9,6,2,1,1,1,1,1] (.node [11,11,9,9,9,5,2,2,1,1,1,1] (.node [11,11,9,9,9,5,2,1,1,1,1,1,1] (.node [11,11,9,9,9,5,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,9,9,9,6,1,1,1,1,1,1,1] (.node [11,11,9,9,9,5,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,7,7,2,2,2,2,2,2,2,2] (.node [11,11,10,7,7,2,2,2,2,2,2,2,1,1] (.node [11,11,9,9,9,7,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,3,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_178 : RowTree := (.node [11,11,9,9,9,3,2,2,2,1,1,1,1] degreeTree62_176 degreeTree62_177) + +def degreeTree62_179 : RowTree := (.node [11,11,9,9,8,4,3,2,1,1,1,1,1] degreeTree62_175 degreeTree62_178) + +def degreeTree62_180 : RowTree := (.node [11,11,10,7,7,4,2,2,2,2,2,2] (.node [11,11,10,7,7,3,3,3,2,2,2,1] (.node [11,11,10,7,7,3,3,2,2,2,2,2] (.node [11,11,10,7,7,3,3,2,2,2,2,1,1] (.node [11,11,10,7,7,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,3,3,3,2,2,1,1,1] (.node [11,11,10,7,7,3,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,7,7,4,2,2,2,2,1,1,1,1] (.node [11,11,10,7,7,3,3,3,3,2,1,1] (.node [11,11,10,7,7,3,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,4,2,2,2,2,2,1,1] .empty .empty))) (.node [11,11,10,7,7,4,3,3,2,2,1,1] (.node [11,11,10,7,7,4,3,2,2,2,2,1] (.node [11,11,10,7,7,4,3,2,2,2,1,1,1] (.node [11,11,10,7,7,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,4,3,3,2,1,1,1,1] (.node [11,11,10,7,7,4,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,7,7,4,4,2,2,1,1,1,1] (.node [11,11,10,7,7,4,4,2,1,1,1,1,1,1] (.node [11,11,10,7,7,4,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,4,4,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_181 : RowTree := (.node [11,11,10,7,7,5,4,1,1,1,1,1,1,1] (.node [11,11,10,7,7,5,3,2,1,1,1,1,1,1] (.node [11,11,10,7,7,5,2,2,2,1,1,1,1,1] (.node [11,11,10,7,7,4,4,4,1,1,1,1] (.node [11,11,10,7,7,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,5,2,2,2,2,2,1] (.node [11,11,10,7,7,5,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,10,7,7,5,3,3,1,1,1,1,1] (.node [11,11,10,7,7,5,3,2,2,2,1,1] (.node [11,11,10,7,7,5,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,5,3,3,2,1,1,1] .empty .empty))) (.node [11,11,10,7,7,6,2,2,1,1,1,1,1,1] (.node [11,11,10,7,7,5,4,3,1,1,1,1] (.node [11,11,10,7,7,5,4,2,2,1,1,1] (.node [11,11,10,7,7,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,5,5,2,1,1,1,1] (.node [11,11,10,7,7,5,5,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,7,7,6,3,1,1,1,1,1,1,1] (.node [11,11,10,7,7,6,2,2,2,2,1,1] (.node [11,11,10,7,7,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,6,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_182 : RowTree := (.node [11,11,10,7,7,4,4,3,1,1,1,1,1] degreeTree62_180 degreeTree62_181) + +def degreeTree62_183 : RowTree := (.node [11,11,10,8,4,3,3,2,2,2,2,2,2] (.node [11,11,10,7,7,7,2,2,1,1,1,1,1] (.node [11,11,10,7,7,6,4,2,1,1,1,1] (.node [11,11,10,7,7,6,4,1,1,1,1,1,1] (.node [11,11,10,7,7,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,7,2,1,1,1,1,1,1,1] (.node [11,11,10,7,7,6,5,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,7,7,7,3,2,1,1,1,1] (.node [11,11,10,7,7,7,3,1,1,1,1,1,1] (.node [11,11,10,7,7,7,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,7,7,7,4,1,1,1,1,1] .empty .empty))) (.node [11,11,10,8,4,4,3,3,2,2,2,1,1] (.node [11,11,10,8,4,4,2,2,2,2,2,2,2] (.node [11,11,10,8,4,3,3,3,3,3,3] (.node [11,11,10,8,4,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,8,4,4,3,2,2,2,2,2,1] (.node [11,11,10,8,4,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,4,4,3,3,3,2,2,1] (.node [11,11,10,8,4,4,3,3,3,2,1,1,1] (.node [11,11,10,8,4,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,4,4,4,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_184 : RowTree := (.node [11,11,10,8,5,2,2,2,2,2,2,2,2,1] (.node [11,11,10,8,4,4,4,3,3,2,1,1] (.node [11,11,10,8,4,4,4,3,2,2,1,1,1] (.node [11,11,10,8,4,4,4,3,2,1,1,1,1,1] (.node [11,11,10,8,4,4,4,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,10,8,4,4,4,3,3,1,1,1,1] (.node [11,11,10,8,4,4,4,3,2,2,2,1] .empty .empty) .empty)) (.node [11,11,10,8,4,4,4,4,2,2,1,1] (.node [11,11,10,8,4,4,4,4,2,1,1,1,1] (.node [11,11,10,8,4,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,4,4,4,4,3,1,1,1] .empty .empty))) (.node [11,11,10,8,5,3,3,3,3,1,1,1,1,1] (.node [11,11,10,8,5,3,3,2,2,2,2,2,1] (.node [11,11,10,8,5,3,3,2,2,2,2,1,1,1] (.node [11,11,10,8,5,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,10,8,5,3,3,3,2,2,2,1,1] .empty .empty)) (.node [11,11,10,8,5,4,2,2,2,2,2,1,1,1] (.node [11,11,10,8,5,3,3,3,3,2,2,1] (.node [11,11,10,8,5,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,4,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_185 : RowTree := (.node [11,11,10,8,4,4,4,2,2,2,2,1,1] degreeTree62_183 degreeTree62_184) + +def degreeTree62_186 : RowTree := (.node [11,11,10,7,7,6,3,2,2,1,1,1] degreeTree62_182 degreeTree62_185) + +def degreeTree62_187 : RowTree := (.node [11,11,10,7,7,3,2,2,2,2,2,2,1] degreeTree62_179 degreeTree62_186) + +def degreeTree62_188 : RowTree := (.node [11,11,9,9,7,4,3,2,1,1,1,1,1,1] degreeTree62_172 degreeTree62_187) + +def degreeTree62_189 : RowTree := (.node [11,11,9,8,8,3,3,2,2,2,1,1,1] degreeTree62_157 degreeTree62_188) + +def degreeTree62_190 : RowTree := (.node [11,11,10,8,5,4,4,3,1,1,1,1,1,1] (.node [11,11,10,8,5,4,3,3,3,1,1,1,1] (.node [11,11,10,8,5,4,3,3,2,1,1,1,1,1] (.node [11,11,10,8,5,4,3,2,2,2,2,2] (.node [11,11,10,8,5,4,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,4,3,3,2,2,2,1] (.node [11,11,10,8,5,4,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,5,4,4,2,2,2,1,1,1] (.node [11,11,10,8,5,4,4,2,2,1,1,1,1,1] (.node [11,11,10,8,5,4,3,3,3,2,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,4,4,2,2,2,2,1] .empty .empty))) (.node [11,11,10,8,5,5,2,2,2,2,1,1,1,1] (.node [11,11,10,8,5,4,4,3,3,1,1,1] (.node [11,11,10,8,5,4,4,3,2,2,1,1] (.node [11,11,10,8,5,4,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,4,4,4,2,1,1,1] (.node [11,11,10,8,5,4,4,4,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,5,5,3,2,2,1,1,1,1,1] (.node [11,11,10,8,5,5,2,2,2,2,2,2] (.node [11,11,10,8,5,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,5,3,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_191 : RowTree := (.node [11,11,10,8,5,5,5,1,1,1,1,1,1,1] (.node [11,11,10,8,5,5,4,2,2,1,1,1,1] (.node [11,11,10,8,5,5,3,3,2,2,1,1] (.node [11,11,10,8,5,5,3,3,2,1,1,1,1] (.node [11,11,10,8,5,5,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,5,4,2,1,1,1,1,1,1] (.node [11,11,10,8,5,5,3,3,3,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,5,5,4,3,2,1,1,1] (.node [11,11,10,8,5,5,4,3,1,1,1,1,1] (.node [11,11,10,8,5,5,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,8,5,5,4,4,1,1,1,1] .empty .empty))) (.node [11,11,10,8,6,3,2,2,2,2,2,1,1,1] (.node [11,11,10,8,5,5,5,3,1,1,1,1] (.node [11,11,10,8,5,5,5,2,2,1,1,1] (.node [11,11,10,8,5,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,2,2,2,2,2,2,2,2] (.node [11,11,10,8,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,8,6,3,3,2,2,2,2,1,1] (.node [11,11,10,8,6,3,3,2,2,2,1,1,1,1] (.node [11,11,10,8,6,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,8,6,3,3,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_192 : RowTree := (.node [11,11,10,8,5,5,3,2,2,2,2,1] degreeTree62_190 degreeTree62_191) + +def degreeTree62_193 : RowTree := (.node [11,11,10,8,6,4,3,3,1,1,1,1,1,1] (.node [11,11,10,8,6,4,2,2,2,2,2,1,1] (.node [11,11,10,8,6,3,3,3,3,1,1,1,1] (.node [11,11,10,8,6,3,3,3,2,2,2,1] (.node [11,11,10,8,6,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,4,2,2,2,2,1,1,1,1] (.node [11,11,10,8,6,3,3,3,3,2,1,1] .empty .empty) .empty)) (.node [11,11,10,8,6,4,3,2,2,2,1,1,1] (.node [11,11,10,8,6,4,3,2,2,1,1,1,1,1] (.node [11,11,10,8,6,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,10,8,6,4,3,2,2,2,2,1] .empty .empty))) (.node [11,11,10,8,6,4,4,2,2,2,1,1] (.node [11,11,10,8,6,4,3,3,3,1,1,1] (.node [11,11,10,8,6,4,3,3,2,2,1,1] (.node [11,11,10,8,6,4,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,4,4,2,2,1,1,1,1] (.node [11,11,10,8,6,4,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,6,4,4,4,1,1,1,1] (.node [11,11,10,8,6,4,4,3,2,1,1,1] (.node [11,11,10,8,6,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,5,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_194 : RowTree := (.node [11,11,10,8,6,5,5,1,1,1,1,1,1] (.node [11,11,10,8,6,5,3,3,2,1,1,1] (.node [11,11,10,8,6,5,3,2,2,1,1,1,1] (.node [11,11,10,8,6,5,3,2,1,1,1,1,1,1] (.node [11,11,10,8,6,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,8,6,5,3,3,1,1,1,1,1] (.node [11,11,10,8,6,5,3,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,8,6,5,4,2,2,1,1,1] (.node [11,11,10,8,6,5,4,2,1,1,1,1,1] (.node [11,11,10,8,6,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,5,4,3,1,1,1,1] .empty .empty))) (.node [11,11,10,8,6,6,3,2,1,1,1,1,1] (.node [11,11,10,8,6,6,2,2,2,1,1,1,1] (.node [11,11,10,8,6,6,2,2,1,1,1,1,1,1] (.node [11,11,10,8,6,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,6,3,1,1,1,1,1,1,1] (.node [11,11,10,8,6,6,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,8,6,6,4,1,1,1,1,1,1] (.node [11,11,10,8,6,6,3,3,1,1,1,1] (.node [11,11,10,8,6,6,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,6,6,4,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_195 : RowTree := (.node [11,11,10,8,6,5,2,2,2,2,1,1,1] degreeTree62_193 degreeTree62_194) + +def degreeTree62_196 : RowTree := (.node [11,11,10,8,6,3,3,3,2,1,1,1,1,1] degreeTree62_192 degreeTree62_195) + +def degreeTree62_197 : RowTree := (.node [11,11,10,8,7,3,3,3,2,2,1,1] (.node [11,11,10,8,7,3,3,2,2,1,1,1,1,1] (.node [11,11,10,8,7,3,2,2,2,2,1,1,1,1] (.node [11,11,10,8,7,2,2,2,2,2,2,2,1] (.node [11,11,10,8,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,3,2,2,2,2,2,2] (.node [11,11,10,8,7,3,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,8,7,3,3,3,1,1,1,1,1,1] (.node [11,11,10,8,7,3,3,2,2,2,2,1] (.node [11,11,10,8,7,3,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,3,3,3,2,1,1,1,1] .empty .empty))) (.node [11,11,10,8,7,4,3,2,2,1,1,1,1] (.node [11,11,10,8,7,4,2,2,2,2,1,1,1] (.node [11,11,10,8,7,4,2,2,2,1,1,1,1,1] (.node [11,11,10,8,7,3,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,4,3,2,1,1,1,1,1,1] (.node [11,11,10,8,7,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,10,8,7,4,3,3,2,1,1,1] (.node [11,11,10,8,7,4,3,3,1,1,1,1,1] (.node [11,11,10,8,7,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,4,4,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_198 : RowTree := (.node [11,11,10,8,7,5,4,2,1,1,1,1] (.node [11,11,10,8,7,5,3,1,1,1,1,1,1,1] (.node [11,11,10,8,7,5,2,2,1,1,1,1,1,1] (.node [11,11,10,8,7,4,4,3,1,1,1,1] (.node [11,11,10,8,7,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,5,2,2,2,2,1,1] (.node [11,11,10,8,7,5,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,7,5,3,3,1,1,1,1] (.node [11,11,10,8,7,5,3,2,2,1,1,1] (.node [11,11,10,8,7,5,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,5,4,1,1,1,1,1,1] .empty .empty))) (.node [11,11,10,8,7,6,3,2,1,1,1,1] (.node [11,11,10,8,7,6,2,2,1,1,1,1,1] (.node [11,11,10,8,7,6,2,1,1,1,1,1,1,1] (.node [11,11,10,8,7,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,6,3,1,1,1,1,1,1] (.node [11,11,10,8,7,6,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,7,7,2,1,1,1,1,1,1] (.node [11,11,10,8,7,7,1,1,1,1,1,1,1,1] (.node [11,11,10,8,7,6,4,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,7,7,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_199 : RowTree := (.node [11,11,10,8,7,4,4,2,1,1,1,1,1] degreeTree62_197 degreeTree62_198) + +def degreeTree62_200 : RowTree := (.node [11,11,10,8,8,3,3,3,2,1,1,1] (.node [11,11,10,8,8,3,2,2,2,2,2,1] (.node [11,11,10,8,8,2,2,2,2,2,2,2] (.node [11,11,10,8,8,2,2,2,2,2,2,1,1] (.node [11,11,10,8,8,2,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,8,3,2,2,2,2,1,1,1] (.node [11,11,10,8,8,3,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,8,3,3,2,2,2,1,1] (.node [11,11,10,8,8,3,3,2,2,1,1,1,1] (.node [11,11,10,8,8,3,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,8,3,3,3,1,1,1,1,1] .empty .empty))) (.node [11,11,10,8,8,4,3,2,2,1,1,1] (.node [11,11,10,8,8,4,2,2,2,2,1,1] (.node [11,11,10,8,8,4,2,2,2,1,1,1,1] (.node [11,11,10,8,8,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,8,4,3,2,1,1,1,1,1] (.node [11,11,10,8,8,4,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,8,4,4,2,1,1,1,1] (.node [11,11,10,8,8,4,4,1,1,1,1,1,1] (.node [11,11,10,8,8,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,8,5,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_201 : RowTree := (.node [11,11,10,8,8,8,1,1,1,1,1,1] (.node [11,11,10,8,8,6,2,1,1,1,1,1,1] (.node [11,11,10,8,8,5,3,2,1,1,1,1] (.node [11,11,10,8,8,5,3,1,1,1,1,1,1] (.node [11,11,10,8,8,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,8,6,1,1,1,1,1,1,1,1] (.node [11,11,10,8,8,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,8,8,7,1,1,1,1,1,1,1] (.node [11,11,10,8,8,6,3,1,1,1,1,1] (.node [11,11,10,8,8,6,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,8,8,7,2,1,1,1,1,1] .empty .empty))) (.node [11,11,10,9,4,3,3,2,2,2,2,1,1,1] (.node [11,11,10,9,3,3,3,3,3,3,3] (.node [11,11,10,9,3,3,3,3,3,2,2,1,1] (.node [11,11,10,9,3,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,10,9,4,3,2,2,2,2,2,2,2] (.node [11,11,10,9,4,2,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,10,9,4,3,3,3,3,1,1,1,1,1] (.node [11,11,10,9,4,3,3,3,2,2,2,1,1] (.node [11,11,10,9,4,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,9,4,3,3,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_202 : RowTree := (.node [11,11,10,8,8,5,2,2,1,1,1,1,1] degreeTree62_200 degreeTree62_201) + +def degreeTree62_203 : RowTree := (.node [11,11,10,8,7,7,3,1,1,1,1,1] degreeTree62_199 degreeTree62_202) + +def degreeTree62_204 : RowTree := (.node [11,11,10,8,6,6,5,1,1,1,1,1] degreeTree62_196 degreeTree62_203) + +def degreeTree62_205 : RowTree := (.node [11,11,10,9,4,4,4,2,2,1,1,1,1,1] (.node [11,11,10,9,4,4,3,3,2,1,1,1,1,1] (.node [11,11,10,9,4,4,3,2,2,2,1,1,1,1] (.node [11,11,10,9,4,4,2,2,2,2,2,2,1] (.node [11,11,10,9,4,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,4,4,3,2,2,2,2,2] (.node [11,11,10,9,4,4,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,9,4,4,3,3,3,1,1,1,1] (.node [11,11,10,9,4,4,3,3,2,2,2,1] (.node [11,11,10,9,4,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,4,4,3,3,3,2,1,1] .empty .empty))) (.node [11,11,10,9,4,4,4,3,3,1,1,1] (.node [11,11,10,9,4,4,4,3,1,1,1,1,1,1] (.node [11,11,10,9,4,4,4,2,2,2,2,1] (.node [11,11,10,9,4,4,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,4,4,4,3,2,2,1,1] (.node [11,11,10,9,4,4,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,5,2,2,2,2,2,2,2,1,1] (.node [11,11,10,9,4,4,4,4,2,1,1,1] (.node [11,11,10,9,4,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,5,2,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_206 : RowTree := (.node [11,11,10,9,5,4,2,2,2,2,2,1,1] (.node [11,11,10,9,5,3,3,3,2,2,1,1,1] (.node [11,11,10,9,5,3,3,2,2,2,2,1,1] (.node [11,11,10,9,5,3,3,2,2,2,1,1,1,1] (.node [11,11,10,9,5,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,9,5,3,3,3,2,1,1,1,1,1] (.node [11,11,10,9,5,3,3,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,10,9,5,3,3,3,3,2,1,1] (.node [11,11,10,9,5,3,3,3,3,1,1,1,1] (.node [11,11,10,9,5,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,9,5,4,2,2,2,2,1,1,1,1] .empty .empty))) (.node [11,11,10,9,5,4,3,3,2,1,1,1,1] (.node [11,11,10,9,5,4,3,2,2,2,1,1,1] (.node [11,11,10,9,5,4,3,2,2,1,1,1,1,1] (.node [11,11,10,9,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,10,9,5,4,3,3,1,1,1,1,1,1] (.node [11,11,10,9,5,4,3,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,10,9,5,4,4,2,1,1,1,1,1,1] (.node [11,11,10,9,5,4,3,3,3,1,1,1] (.node [11,11,10,9,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,9,5,4,4,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_207 : RowTree := (.node [11,11,10,9,5,3,2,2,2,2,2,1,1,1] degreeTree62_205 degreeTree62_206) + +def degreeTree62_208 : RowTree := (.node [11,11,10,9,5,5,3,3,2,1,1,1] (.node [11,11,10,9,5,5,2,2,2,2,2,1] (.node [11,11,10,9,5,4,4,4,1,1,1,1] (.node [11,11,10,9,5,4,4,3,2,1,1,1] (.node [11,11,10,9,5,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,5,5,2,2,2,2,1,1,1] (.node [11,11,10,9,5,5,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,5,5,3,2,2,2,1,1] (.node [11,11,10,9,5,5,3,2,2,1,1,1,1] (.node [11,11,10,9,5,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,5,5,3,3,1,1,1,1,1] .empty .empty))) (.node [11,11,10,9,5,5,5,2,1,1,1,1] (.node [11,11,10,9,5,5,4,2,2,1,1,1] (.node [11,11,10,9,5,5,4,2,1,1,1,1,1] (.node [11,11,10,9,5,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,5,5,5,1,1,1,1,1,1] (.node [11,11,10,9,5,5,4,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,6,3,2,2,2,2,1,1,1,1] (.node [11,11,10,9,6,2,2,2,2,2,2,2,1] (.node [11,11,10,9,6,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,3,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_209 : RowTree := (.node [11,11,10,9,6,4,3,2,1,1,1,1,1,1] (.node [11,11,10,9,6,3,3,3,2,2,1,1] (.node [11,11,10,9,6,3,3,2,2,2,2,1] (.node [11,11,10,9,6,3,3,2,2,2,1,1,1] (.node [11,11,10,9,6,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,3,3,3,2,1,1,1,1] (.node [11,11,10,9,6,3,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,6,4,2,2,2,2,1,1,1] (.node [11,11,10,9,6,4,2,2,2,1,1,1,1,1] (.node [11,11,10,9,6,3,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,4,2,2,2,2,2,1] .empty .empty))) (.node [11,11,10,9,6,4,4,2,1,1,1,1,1] (.node [11,11,10,9,6,4,3,3,1,1,1,1,1] (.node [11,11,10,9,6,4,3,2,2,2,1,1] (.node [11,11,10,9,6,4,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,4,4,1,1,1,1,1,1,1] (.node [11,11,10,9,6,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,6,5,2,2,1,1,1,1,1,1] (.node [11,11,10,9,6,4,4,3,1,1,1,1] (.node [11,11,10,9,6,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,5,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_210 : RowTree := (.node [11,11,10,9,6,3,2,2,2,2,2,2] degreeTree62_208 degreeTree62_209) + +def degreeTree62_211 : RowTree := (.node [11,11,10,9,5,4,4,2,2,2,1,1] degreeTree62_207 degreeTree62_210) + +def degreeTree62_212 : RowTree := (.node [11,11,10,9,6,6,3,1,1,1,1,1,1] (.node [11,11,10,9,6,5,4,2,1,1,1,1] (.node [11,11,10,9,6,5,3,2,2,1,1,1] (.node [11,11,10,9,6,5,3,2,1,1,1,1,1] (.node [11,11,10,9,6,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,5,4,1,1,1,1,1,1] (.node [11,11,10,9,6,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,6,6,2,2,1,1,1,1,1] (.node [11,11,10,9,6,6,2,1,1,1,1,1,1,1] (.node [11,11,10,9,6,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,6,6,2,2,2,1,1,1] .empty .empty))) (.node [11,11,10,9,7,3,2,2,2,1,1,1,1,1] (.node [11,11,10,9,7,2,2,2,2,2,1,1,1,1] (.node [11,11,10,9,6,6,4,1,1,1,1,1] (.node [11,11,10,9,6,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,7,2,2,2,2,2,2,2] (.node [11,11,10,9,7,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,9,7,3,3,2,1,1,1,1,1,1] (.node [11,11,10,9,7,3,2,2,2,2,2,1] (.node [11,11,10,9,7,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,7,3,3,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_213 : RowTree := (.node [11,11,10,9,7,4,4,2,1,1,1,1] (.node [11,11,10,9,7,4,3,1,1,1,1,1,1,1] (.node [11,11,10,9,7,4,2,2,1,1,1,1,1,1] (.node [11,11,10,9,7,3,3,3,2,1,1,1] (.node [11,11,10,9,7,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,7,4,2,2,2,2,1,1] (.node [11,11,10,9,7,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,7,4,3,3,1,1,1,1] (.node [11,11,10,9,7,4,3,2,2,1,1,1] (.node [11,11,10,9,7,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,7,4,4,1,1,1,1,1,1] .empty .empty))) (.node [11,11,10,9,7,5,4,1,1,1,1,1] (.node [11,11,10,9,7,5,2,2,2,1,1,1] (.node [11,11,10,9,7,5,2,2,1,1,1,1,1] (.node [11,11,10,9,7,5,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,7,5,3,2,1,1,1,1] (.node [11,11,10,9,7,5,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,7,6,2,2,1,1,1,1] (.node [11,11,10,9,7,6,2,1,1,1,1,1,1] (.node [11,11,10,9,7,6,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,7,6,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_214 : RowTree := (.node [11,11,10,9,7,3,3,2,2,2,1,1] degreeTree62_212 degreeTree62_213) + +def degreeTree62_215 : RowTree := (.node [11,11,10,9,8,3,3,3,1,1,1,1] (.node [11,11,10,9,8,3,2,2,2,1,1,1,1] (.node [11,11,10,9,8,2,2,2,2,2,1,1,1] (.node [11,11,10,9,8,2,2,2,2,1,1,1,1,1] (.node [11,11,10,9,7,7,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,8,3,2,2,1,1,1,1,1,1] (.node [11,11,10,9,8,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,10,9,8,3,3,2,1,1,1,1,1] (.node [11,11,10,9,8,3,3,1,1,1,1,1,1,1] (.node [11,11,10,9,8,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,9,8,3,3,2,2,1,1,1] .empty .empty))) (.node [11,11,10,9,8,4,4,1,1,1,1,1] (.node [11,11,10,9,8,4,2,2,2,1,1,1] (.node [11,11,10,9,8,4,2,2,1,1,1,1,1] (.node [11,11,10,9,8,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,8,4,3,2,1,1,1,1] (.node [11,11,10,9,8,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,8,5,2,2,1,1,1,1] (.node [11,11,10,9,8,5,2,1,1,1,1,1,1] (.node [11,11,10,9,8,5,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,8,5,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_216 : RowTree := (.node [11,11,10,9,9,4,1,1,1,1,1,1,1,1] (.node [11,11,10,9,9,3,2,1,1,1,1,1,1,1] (.node [11,11,10,9,9,2,2,2,1,1,1,1,1,1] (.node [11,11,10,9,8,7,1,1,1,1,1,1] (.node [11,11,10,9,8,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,9,2,2,2,2,2,1,1] (.node [11,11,10,9,9,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,9,9,3,3,1,1,1,1,1,1] (.node [11,11,10,9,9,3,2,2,2,1,1,1] (.node [11,11,10,9,9,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,9,3,3,2,1,1,1,1] .empty .empty))) (.node [11,11,10,9,9,5,2,1,1,1,1,1] (.node [11,11,10,9,9,4,3,1,1,1,1,1] (.node [11,11,10,9,9,4,2,2,1,1,1,1] (.node [11,11,10,9,9,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,9,9,5,1,1,1,1,1,1,1] .empty .empty)) (.node [11,11,10,10,3,3,2,2,2,2,2,2,2] (.node [11,11,10,10,3,2,2,2,2,2,2,2,2,1] (.node [11,11,10,9,9,6,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,3,3,3,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_217 : RowTree := (.node [11,11,10,9,8,6,1,1,1,1,1,1,1] degreeTree62_215 degreeTree62_216) + +def degreeTree62_218 : RowTree := (.node [11,11,10,9,7,7,1,1,1,1,1,1,1] degreeTree62_214 degreeTree62_217) + +def degreeTree62_219 : RowTree := (.node [11,11,10,9,6,5,2,2,2,2,1,1] degreeTree62_211 degreeTree62_218) + +def degreeTree62_220 : RowTree := (.node [11,11,10,9,4,3,3,3,3,2,2,1] degreeTree62_204 degreeTree62_219) + +def degreeTree62_221 : RowTree := (.node [11,11,10,10,4,3,3,2,2,2,2,2] (.node [11,11,10,10,4,2,2,2,2,2,2,2,2] (.node [11,11,10,10,3,3,3,3,3,2,1,1,1] (.node [11,11,10,10,3,3,3,3,3,1,1,1,1,1] (.node [11,11,10,10,3,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,10,4,2,2,2,2,2,2,2,1,1] (.node [11,11,10,10,3,3,3,3,3,2,2,1] .empty .empty) .empty)) (.node [11,11,10,10,4,3,3,2,2,2,1,1,1,1] (.node [11,11,10,10,4,3,2,2,2,2,2,2,1] (.node [11,11,10,10,4,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,4,3,3,2,2,2,2,1,1] .empty .empty))) (.node [11,11,10,10,4,4,2,2,2,2,1,1,1,1] (.node [11,11,10,10,4,3,3,3,2,2,2,1] (.node [11,11,10,10,4,3,3,3,2,2,1,1,1] (.node [11,11,10,10,4,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,4,3,3,3,3,2,1,1] (.node [11,11,10,10,4,3,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,4,4,3,2,2,1,1,1,1,1] (.node [11,11,10,10,4,4,2,2,2,2,2,2] (.node [11,11,10,10,4,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,10,4,4,3,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_222 : RowTree := (.node [11,11,10,10,5,2,2,2,2,2,2,1,1,1] (.node [11,11,10,10,4,4,4,2,2,1,1,1,1] (.node [11,11,10,10,4,4,3,3,2,2,1,1] (.node [11,11,10,10,4,4,3,3,2,1,1,1,1] (.node [11,11,10,10,4,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,4,4,4,2,1,1,1,1,1,1] (.node [11,11,10,10,4,4,3,3,3,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,4,4,4,3,2,1,1,1] (.node [11,11,10,10,4,4,4,3,1,1,1,1,1] (.node [11,11,10,10,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,10,4,4,4,4,1,1,1,1] .empty .empty))) (.node [11,11,10,10,5,3,3,2,2,2,1,1,1] (.node [11,11,10,10,5,3,2,2,2,2,2,1,1] (.node [11,11,10,10,5,3,2,2,2,2,1,1,1,1] (.node [11,11,10,10,5,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,10,5,3,3,2,2,1,1,1,1,1] (.node [11,11,10,10,5,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,10,10,5,3,3,3,2,1,1,1,1] (.node [11,11,10,10,5,3,3,3,1,1,1,1,1,1] (.node [11,11,10,10,5,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,10,10,5,3,3,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_223 : RowTree := (.node [11,11,10,10,4,4,3,2,2,2,2,1] degreeTree62_221 degreeTree62_222) + +def degreeTree62_224 : RowTree := (.node [11,11,10,10,5,4,4,2,2,1,1,1] (.node [11,11,10,10,5,4,3,2,2,2,1,1] (.node [11,11,10,10,5,4,2,2,2,2,2,1] (.node [11,11,10,10,5,4,2,2,2,2,1,1,1] (.node [11,11,10,10,5,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,5,4,3,2,2,1,1,1,1] (.node [11,11,10,10,5,4,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,5,4,4,1,1,1,1,1,1,1] (.node [11,11,10,10,5,4,3,3,2,1,1,1] (.node [11,11,10,10,5,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,5,4,4,2,1,1,1,1,1] .empty .empty))) (.node [11,11,10,10,5,5,3,2,1,1,1,1,1] (.node [11,11,10,10,5,5,2,2,2,1,1,1,1] (.node [11,11,10,10,5,5,2,2,1,1,1,1,1,1] (.node [11,11,10,10,5,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,5,5,3,1,1,1,1,1,1,1] (.node [11,11,10,10,5,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,10,10,5,5,4,1,1,1,1,1,1] (.node [11,11,10,10,5,5,3,3,1,1,1,1] (.node [11,11,10,10,5,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,5,5,4,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_225 : RowTree := (.node [11,11,10,10,6,3,3,3,2,1,1,1] (.node [11,11,10,10,6,3,2,2,2,2,2,1] (.node [11,11,10,10,6,2,2,2,2,2,2,2] (.node [11,11,10,10,6,2,2,2,2,2,2,1,1] (.node [11,11,10,10,6,2,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,6,3,2,2,2,2,1,1,1] (.node [11,11,10,10,6,3,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,6,3,3,2,2,2,1,1] (.node [11,11,10,10,6,3,3,2,2,1,1,1,1] (.node [11,11,10,10,6,3,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,6,3,3,3,1,1,1,1,1] .empty .empty))) (.node [11,11,10,10,6,4,3,2,2,1,1,1] (.node [11,11,10,10,6,4,2,2,2,2,1,1] (.node [11,11,10,10,6,4,2,2,2,1,1,1,1] (.node [11,11,10,10,6,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,6,4,3,2,1,1,1,1,1] (.node [11,11,10,10,6,4,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,6,4,4,2,1,1,1,1] (.node [11,11,10,10,6,4,4,1,1,1,1,1,1] (.node [11,11,10,10,6,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,6,5,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_226 : RowTree := (.node [11,11,10,10,5,5,5,1,1,1,1,1] degreeTree62_224 degreeTree62_225) + +def degreeTree62_227 : RowTree := (.node [11,11,10,10,5,3,3,3,3,1,1,1] degreeTree62_223 degreeTree62_226) + +def degreeTree62_228 : RowTree := (.node [11,11,10,10,7,2,2,2,2,2,2,1] (.node [11,11,10,10,6,6,2,1,1,1,1,1,1] (.node [11,11,10,10,6,5,3,2,1,1,1,1] (.node [11,11,10,10,6,5,3,1,1,1,1,1,1] (.node [11,11,10,10,6,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,6,6,1,1,1,1,1,1,1,1] (.node [11,11,10,10,6,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,7,2,2,2,2,1,1,1,1,1] (.node [11,11,10,10,6,6,3,1,1,1,1,1] (.node [11,11,10,10,6,6,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,7,2,2,2,2,2,1,1,1] .empty .empty))) (.node [11,11,10,10,7,3,3,2,2,1,1,1] (.node [11,11,10,10,7,3,2,2,2,2,1,1] (.node [11,11,10,10,7,3,2,2,2,1,1,1,1] (.node [11,11,10,10,7,3,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,7,3,3,2,1,1,1,1,1] (.node [11,11,10,10,7,3,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,7,4,2,2,1,1,1,1,1] (.node [11,11,10,10,7,4,2,1,1,1,1,1,1,1] (.node [11,11,10,10,7,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,7,4,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_229 : RowTree := (.node [11,11,10,10,8,2,2,2,2,1,1,1,1] (.node [11,11,10,10,7,5,3,1,1,1,1,1] (.node [11,11,10,10,7,5,1,1,1,1,1,1,1,1] (.node [11,11,10,10,7,4,4,1,1,1,1,1] (.node [11,11,10,10,7,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,7,5,2,2,1,1,1,1] (.node [11,11,10,10,7,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,7,7,1,1,1,1,1,1] (.node [11,11,10,10,7,6,2,1,1,1,1,1] (.node [11,11,10,10,7,6,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,8,2,2,2,1,1,1,1,1,1] .empty .empty))) (.node [11,11,10,10,8,3,3,2,1,1,1,1] (.node [11,11,10,10,8,3,2,2,1,1,1,1,1] (.node [11,11,10,10,8,3,2,1,1,1,1,1,1,1] (.node [11,11,10,10,8,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,10,10,8,3,3,1,1,1,1,1,1] (.node [11,11,10,10,8,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,8,4,2,2,1,1,1,1] (.node [11,11,10,10,8,4,2,1,1,1,1,1,1] (.node [11,11,10,10,8,4,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,8,4,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_230 : RowTree := (.node [11,11,10,10,7,4,3,1,1,1,1,1,1] degreeTree62_228 degreeTree62_229) + +def degreeTree62_231 : RowTree := (.node [11,11,10,10,9,4,2,1,1,1,1,1] (.node [11,11,10,10,9,3,1,1,1,1,1,1,1,1] (.node [11,11,10,10,9,2,2,1,1,1,1,1,1,1] (.node [11,11,10,10,8,6,1,1,1,1,1,1] (.node [11,11,10,10,8,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,9,2,2,2,2,1,1,1] (.node [11,11,10,10,9,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,10,10,9,3,3,1,1,1,1,1] (.node [11,11,10,10,9,3,2,2,1,1,1,1] (.node [11,11,10,10,9,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,9,4,1,1,1,1,1,1,1] .empty .empty))) (.node [11,11,10,10,10,3,2,1,1,1,1,1] (.node [11,11,10,10,10,2,2,1,1,1,1,1,1] (.node [11,11,10,10,10,2,1,1,1,1,1,1,1,1] (.node [11,11,10,10,9,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,10,10,10,3,1,1,1,1,1,1,1] (.node [11,11,10,10,10,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,4,4,4,4,4,3,3,3] (.node [11,11,11,4,4,4,4,4,3,2,2,1,1] (.node [11,11,10,10,10,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,4,4,4,4,4,4,2,1,1,1] .empty .empty)))) + +def degreeTree62_232 : RowTree := (.node [11,11,11,5,5,4,3,3,3,3,3] (.node [11,11,11,5,4,4,4,4,3,2,2,1] (.node [11,11,11,5,4,4,4,3,3,3,3] (.node [11,11,11,5,4,4,4,3,3,2,2,1,1] (.node [11,11,11,5,4,4,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,11,5,4,4,4,4,3,2,1,1,1] (.node [11,11,11,5,4,4,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,11,5,5,4,3,2,2,2,2,2,2] (.node [11,11,11,5,4,4,4,4,4,2,1,1] (.node [11,11,11,5,4,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,5,5,4,3,3,3,2,2,1,1] .empty .empty))) (.node [11,11,11,5,5,4,4,4,2,2,1,1,1] (.node [11,11,11,5,5,4,4,3,3,2,1,1,1] (.node [11,11,11,5,5,4,4,3,2,2,2,1,1] (.node [11,11,11,5,5,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,5,5,4,4,3,3,2,2,1] .empty .empty)) (.node [11,11,11,5,5,4,4,4,3,2,1,1] (.node [11,11,11,5,5,4,4,4,3,1,1,1,1] (.node [11,11,11,5,5,4,4,4,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,5,5,4,4,4,4,1,1,1] .empty .empty)))) + +def degreeTree62_233 : RowTree := (.node [11,11,11,4,4,4,4,4,4,2,2,1] degreeTree62_231 degreeTree62_232) + +def degreeTree62_234 : RowTree := (.node [11,11,10,10,8,5,1,1,1,1,1,1,1] degreeTree62_230 degreeTree62_233) + +def degreeTree62_235 : RowTree := (.node [11,11,10,10,6,5,2,2,1,1,1,1,1] degreeTree62_227 degreeTree62_234) + +def degreeTree62_236 : RowTree := (.node [11,11,11,5,5,5,4,4,2,1,1,1,1] (.node [11,11,11,5,5,5,4,2,2,2,2,2] (.node [11,11,11,5,5,5,3,3,3,2,1,1,1] (.node [11,11,11,5,5,5,3,3,2,2,2,1,1] (.node [11,11,11,5,5,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,5,5,5,4,2,2,2,2,1,1] (.node [11,11,11,5,5,5,3,3,3,2,2,1] .empty .empty) .empty)) (.node [11,11,11,5,5,5,4,3,3,1,1,1,1] (.node [11,11,11,5,5,5,4,3,2,2,2,1] (.node [11,11,11,5,5,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,5,5,5,4,3,3,2,1,1] .empty .empty))) (.node [11,11,11,5,5,5,5,3,2,2,1,1] (.node [11,11,11,5,5,5,5,2,2,2,1,1,1] (.node [11,11,11,5,5,5,4,4,3,1,1,1] (.node [11,11,11,5,5,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,5,5,5,5,3,2,1,1,1,1] (.node [11,11,11,5,5,5,5,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,5,5,5,5,4,2,1,1,1] (.node [11,11,11,5,5,5,5,4,1,1,1,1,1] (.node [11,11,11,5,5,5,5,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,11,5,5,5,5,5,1,1,1,1] .empty .empty)))) + +def degreeTree62_237 : RowTree := (.node [11,11,11,6,4,4,4,4,2,2,2,1] (.node [11,11,11,6,4,4,4,3,3,1,1,1,1,1] (.node [11,11,11,6,4,4,4,2,2,2,2,1,1,1] (.node [11,11,11,6,4,4,3,3,3,3,3] (.node [11,11,11,6,4,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,4,4,4,3,2,2,2,1,1] (.node [11,11,11,6,4,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,6,4,4,4,4,2,1,1,1,1,1] (.node [11,11,11,6,4,4,4,3,3,2,2,1] (.node [11,11,11,6,4,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,4,4,4,4,2,2,1,1,1] .empty .empty))) (.node [11,11,11,6,5,4,2,2,2,2,2,2,2] (.node [11,11,11,6,4,4,4,4,4,1,1,1] (.node [11,11,11,6,4,4,4,4,3,2,1,1] (.node [11,11,11,6,4,4,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,5,3,3,3,3,2,2,1,1] (.node [11,11,11,6,5,3,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,6,5,4,3,3,2,2,2,1,1] (.node [11,11,11,6,5,4,3,2,2,2,2,2,1] (.node [11,11,11,6,5,4,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,5,4,3,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_238 : RowTree := (.node [11,11,11,6,4,4,3,2,2,2,2,2,2] degreeTree62_236 degreeTree62_237) + +def degreeTree62_239 : RowTree := (.node [11,11,11,6,5,4,4,4,2,1,1,1,1] (.node [11,11,11,6,5,4,4,3,2,2,1,1,1] (.node [11,11,11,6,5,4,4,2,2,2,2,1,1] (.node [11,11,11,6,5,4,4,2,2,2,1,1,1,1] (.node [11,11,11,6,5,4,3,3,3,2,2,1] .empty .empty) .empty) (.node [11,11,11,6,5,4,4,3,2,1,1,1,1,1] (.node [11,11,11,6,5,4,4,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,6,5,4,4,3,3,2,1,1] (.node [11,11,11,6,5,4,4,3,3,1,1,1,1] (.node [11,11,11,6,5,4,4,3,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,6,5,4,4,4,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,6,5,5,3,2,2,2,2,1,1] (.node [11,11,11,6,5,5,2,2,2,2,2,1,1,1] (.node [11,11,11,6,5,4,4,4,3,1,1,1] (.node [11,11,11,6,5,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,5,5,3,2,2,2,1,1,1,1] (.node [11,11,11,6,5,5,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,6,5,5,3,3,2,2,1,1,1] (.node [11,11,11,6,5,5,3,3,2,1,1,1,1,1] (.node [11,11,11,6,5,5,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,11,6,5,5,3,3,2,2,2,1] .empty .empty)))) + +def degreeTree62_240 : RowTree := (.node [11,11,11,6,5,5,5,2,1,1,1,1,1,1] (.node [11,11,11,6,5,5,4,3,2,1,1,1,1] (.node [11,11,11,6,5,5,4,2,2,2,1,1,1] (.node [11,11,11,6,5,5,4,2,2,1,1,1,1,1] (.node [11,11,11,6,5,5,3,3,3,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,5,5,4,3,1,1,1,1,1,1] (.node [11,11,11,6,5,5,4,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,6,5,5,4,4,1,1,1,1,1] (.node [11,11,11,6,5,5,4,3,3,1,1,1] (.node [11,11,11,6,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,5,5,4,4,2,1,1,1] .empty .empty))) (.node [11,11,11,6,6,2,2,2,2,2,2,2,2,1] (.node [11,11,11,6,5,5,5,3,1,1,1,1,1] (.node [11,11,11,6,5,5,5,2,2,2,1,1] (.node [11,11,11,6,5,5,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,5,5,5,4,1,1,1,1] (.node [11,11,11,6,5,5,5,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,6,6,3,3,2,2,2,2,2,1] (.node [11,11,11,6,6,3,3,2,2,2,2,1,1,1] (.node [11,11,11,6,6,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,11,6,6,3,3,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_241 : RowTree := (.node [11,11,11,6,5,5,3,3,3,1,1,1,1] degreeTree62_239 degreeTree62_240) + +def degreeTree62_242 : RowTree := (.node [11,11,11,6,5,4,3,3,3,2,1,1,1] degreeTree62_238 degreeTree62_241) + +def degreeTree62_243 : RowTree := (.node [11,11,11,6,6,4,3,3,3,1,1,1,1] (.node [11,11,11,6,6,4,3,2,2,2,2,1,1] (.node [11,11,11,6,6,4,2,2,2,2,2,1,1,1] (.node [11,11,11,6,6,3,3,3,3,2,2,1] (.node [11,11,11,6,6,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,4,3,2,2,2,1,1,1,1] (.node [11,11,11,6,6,4,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,6,6,4,3,3,2,2,1,1,1] (.node [11,11,11,6,6,4,3,3,2,1,1,1,1,1] (.node [11,11,11,6,6,4,3,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,11,6,6,4,3,3,2,2,2,1] .empty .empty))) (.node [11,11,11,6,6,4,4,3,2,1,1,1,1] (.node [11,11,11,6,6,4,4,2,2,2,1,1,1] (.node [11,11,11,6,6,4,4,2,2,1,1,1,1,1] (.node [11,11,11,6,6,4,3,3,3,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,4,4,3,1,1,1,1,1,1] (.node [11,11,11,6,6,4,4,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,6,6,4,4,4,1,1,1,1,1] (.node [11,11,11,6,6,4,4,3,3,1,1,1] (.node [11,11,11,6,6,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,4,4,4,2,1,1,1] .empty .empty)))) + +def degreeTree62_244 : RowTree := (.node [11,11,11,6,6,5,4,2,2,1,1,1,1] (.node [11,11,11,6,6,5,3,3,1,1,1,1,1,1] (.node [11,11,11,6,6,5,3,2,2,1,1,1,1,1] (.node [11,11,11,6,6,5,2,2,2,2,2,2] (.node [11,11,11,6,6,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,5,3,2,2,2,2,1] (.node [11,11,11,6,6,5,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,6,6,5,3,3,3,1,1,1] (.node [11,11,11,6,6,5,3,3,2,2,1,1] (.node [11,11,11,6,6,5,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,5,4,2,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,6,6,5,5,2,1,1,1,1,1] (.node [11,11,11,6,6,5,4,3,2,1,1,1] (.node [11,11,11,6,6,5,4,3,1,1,1,1,1] (.node [11,11,11,6,6,5,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,5,5,1,1,1,1,1,1,1] (.node [11,11,11,6,6,5,4,4,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,6,6,6,2,2,2,1,1,1,1,1] (.node [11,11,11,6,6,5,5,3,1,1,1,1] (.node [11,11,11,6,6,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,6,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_245 : RowTree := (.node [11,11,11,6,6,5,2,2,2,2,1,1,1,1] degreeTree62_243 degreeTree62_244) + +def degreeTree62_246 : RowTree := (.node [11,11,11,6,6,6,5,2,1,1,1,1] (.node [11,11,11,6,6,6,4,1,1,1,1,1,1,1] (.node [11,11,11,6,6,6,3,2,2,2,1,1] (.node [11,11,11,6,6,6,3,2,2,1,1,1,1] (.node [11,11,11,6,6,6,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,6,3,3,2,1,1,1] (.node [11,11,11,6,6,6,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,6,6,6,4,3,1,1,1,1] (.node [11,11,11,6,6,6,4,2,2,1,1,1] (.node [11,11,11,6,6,6,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,6,6,6,5,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,7,4,4,3,2,2,2,2,2,1] (.node [11,11,11,7,4,3,3,3,3,2,2,1,1] (.node [11,11,11,7,4,3,3,2,2,2,2,2,2] (.node [11,11,11,6,6,6,6,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,4,4,3,2,2,2,2,1,1,1] (.node [11,11,11,7,4,4,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,7,4,4,3,3,3,2,1,1,1] (.node [11,11,11,7,4,4,3,3,3,1,1,1,1,1] (.node [11,11,11,7,4,4,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,7,4,4,3,3,3,2,2,1] .empty .empty)))) + +def degreeTree62_247 : RowTree := (.node [11,11,11,7,4,4,4,4,3,1,1,1] (.node [11,11,11,7,4,4,4,3,3,1,1,1,1] (.node [11,11,11,7,4,4,4,3,2,1,1,1,1,1] (.node [11,11,11,7,4,4,4,2,2,2,2,2] (.node [11,11,11,7,4,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,7,4,4,4,3,2,2,2,1] (.node [11,11,11,7,4,4,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,4,4,4,4,2,1,1,1,1] (.node [11,11,11,7,4,4,4,4,1,1,1,1,1,1] (.node [11,11,11,7,4,4,4,3,3,2,1,1] .empty .empty) .empty) (.node [11,11,11,7,4,4,4,4,2,2,1,1] .empty .empty))) (.node [11,11,11,7,5,3,3,3,2,2,2,1,1] (.node [11,11,11,7,5,3,3,2,2,2,2,1,1,1] (.node [11,11,11,7,5,3,2,2,2,2,2,2,2] (.node [11,11,11,7,5,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,7,5,3,3,2,2,2,2,2,1] .empty .empty)) (.node [11,11,11,7,5,3,3,3,3,2,2,1] (.node [11,11,11,7,5,3,3,3,3,2,1,1,1] (.node [11,11,11,7,5,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,5,4,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_248 : RowTree := (.node [11,11,11,7,4,4,4,2,2,2,1,1,1,1] degreeTree62_246 degreeTree62_247) + +def degreeTree62_249 : RowTree := (.node [11,11,11,6,6,6,2,2,2,2,2,1] degreeTree62_245 degreeTree62_248) + +def degreeTree62_250 : RowTree := (.node [11,11,11,6,6,3,3,3,3,1,1,1,1,1] degreeTree62_242 degreeTree62_249) + +def degreeTree62_251 : RowTree := (.node [11,11,11,5,5,5,2,2,2,2,2,2,2] degreeTree62_235 degreeTree62_250) + +def degreeTree62_252 : RowTree := (.node [11,11,10,10,3,3,3,2,2,2,2,2,1] degreeTree62_220 degreeTree62_251) + +def degreeTree62_253 : RowTree := (.node [11,11,10,8,5,4,3,2,2,2,1,1,1,1] degreeTree62_189 degreeTree62_252) + +def degreeTree62_254 : RowTree := (.node [11,10,10,9,9,4,2,1,1,1,1,1,1,1] degreeTree62_126 degreeTree62_253) + +def degreeTree62_255 : RowTree := (.node [11,11,11,7,5,4,4,2,2,2,2,1] (.node [11,11,11,7,5,4,3,3,2,2,2,1] (.node [11,11,11,7,5,4,3,2,2,2,2,2] (.node [11,11,11,7,5,4,3,2,2,2,2,1,1] (.node [11,11,11,7,5,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,5,4,3,3,2,2,1,1,1] (.node [11,11,11,7,5,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,5,4,4,2,2,1,1,1,1,1] (.node [11,11,11,7,5,4,3,3,3,2,1,1] (.node [11,11,11,7,5,4,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,5,4,4,2,2,2,1,1,1] .empty .empty))) (.node [11,11,11,7,5,4,4,4,2,1,1,1] (.node [11,11,11,7,5,4,4,3,2,2,1,1] (.node [11,11,11,7,5,4,4,3,2,1,1,1,1] (.node [11,11,11,7,5,4,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,5,4,4,4,1,1,1,1,1] (.node [11,11,11,7,5,4,4,3,3,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,5,5,2,2,2,2,2,2] (.node [11,11,11,7,5,5,2,2,2,2,2,1,1] (.node [11,11,11,7,5,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,5,5,3,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_256 : RowTree := (.node [11,11,11,7,5,5,4,4,1,1,1,1] (.node [11,11,11,7,5,5,4,2,1,1,1,1,1,1] (.node [11,11,11,7,5,5,3,3,2,1,1,1,1] (.node [11,11,11,7,5,5,3,3,1,1,1,1,1,1] (.node [11,11,11,7,5,5,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,7,5,5,3,3,3,1,1,1] (.node [11,11,11,7,5,5,3,3,2,2,1,1] .empty .empty) .empty)) (.node [11,11,11,7,5,5,4,3,1,1,1,1,1] (.node [11,11,11,7,5,5,4,2,2,2,1,1] (.node [11,11,11,7,5,5,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,5,5,4,3,2,1,1,1] .empty .empty))) (.node [11,11,11,7,6,2,2,2,2,2,2,2,2] (.node [11,11,11,7,5,5,5,2,2,1,1,1] (.node [11,11,11,7,5,5,5,2,1,1,1,1,1] (.node [11,11,11,7,5,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,2,2,2,2,2,2,2,1,1] (.node [11,11,11,7,5,5,5,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,6,3,3,2,2,2,1,1,1,1] (.node [11,11,11,7,6,3,2,2,2,2,2,2,1] (.node [11,11,11,7,6,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,3,3,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_257 : RowTree := (.node [11,11,11,7,5,5,3,2,2,2,1,1,1] degreeTree62_255 degreeTree62_256) + +def degreeTree62_258 : RowTree := (.node [11,11,11,7,6,4,3,2,2,2,2,1] (.node [11,11,11,7,6,4,2,2,2,2,1,1,1,1] (.node [11,11,11,7,6,3,3,3,2,2,2,1] (.node [11,11,11,7,6,3,3,3,2,2,1,1,1] (.node [11,11,11,7,6,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,3,3,3,3,2,1,1] (.node [11,11,11,7,6,3,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,6,4,3,2,2,1,1,1,1,1] (.node [11,11,11,7,6,4,2,2,2,2,2,2] (.node [11,11,11,7,6,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,4,3,2,2,2,1,1,1] .empty .empty))) (.node [11,11,11,7,6,4,4,2,2,1,1,1,1] (.node [11,11,11,7,6,4,3,3,2,2,1,1] (.node [11,11,11,7,6,4,3,3,2,1,1,1,1] (.node [11,11,11,7,6,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,4,4,2,1,1,1,1,1,1] (.node [11,11,11,7,6,4,3,3,3,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,6,4,4,3,2,1,1,1] (.node [11,11,11,7,6,4,4,3,1,1,1,1,1] (.node [11,11,11,7,6,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,4,4,4,1,1,1,1] .empty .empty)))) + +def degreeTree62_259 : RowTree := (.node [11,11,11,7,6,5,4,3,1,1,1,1] (.node [11,11,11,7,6,5,3,3,1,1,1,1,1] (.node [11,11,11,7,6,5,3,2,1,1,1,1,1,1] (.node [11,11,11,7,6,5,2,2,2,2,2,1] (.node [11,11,11,7,6,5,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,5,3,2,2,2,1,1] (.node [11,11,11,7,6,5,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,6,5,4,2,1,1,1,1,1] (.node [11,11,11,7,6,5,4,1,1,1,1,1,1,1] (.node [11,11,11,7,6,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,5,4,2,2,1,1,1] .empty .empty))) (.node [11,11,11,7,6,6,3,1,1,1,1,1,1,1] (.node [11,11,11,7,6,6,2,2,1,1,1,1,1,1] (.node [11,11,11,7,6,5,5,2,1,1,1,1] (.node [11,11,11,7,6,5,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,6,2,2,2,2,1,1] (.node [11,11,11,7,6,6,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,6,6,3,3,1,1,1,1] (.node [11,11,11,7,6,6,3,2,2,1,1,1] (.node [11,11,11,7,6,6,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,6,6,4,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_260 : RowTree := (.node [11,11,11,7,6,5,2,2,2,1,1,1,1,1] degreeTree62_258 degreeTree62_259) + +def degreeTree62_261 : RowTree := (.node [11,11,11,7,6,3,3,2,2,2,2,2] degreeTree62_257 degreeTree62_260) + +def degreeTree62_262 : RowTree := (.node [11,11,11,7,7,3,3,3,2,1,1,1,1] (.node [11,11,11,7,7,3,2,2,2,2,2,2] (.node [11,11,11,7,7,2,2,2,2,2,2,2,1] (.node [11,11,11,7,7,2,2,2,2,2,2,1,1,1] (.node [11,11,11,7,6,6,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,3,2,2,2,2,2,1,1] (.node [11,11,11,7,7,3,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,7,3,3,2,2,2,2,1] (.node [11,11,11,7,7,3,3,2,2,2,1,1,1] (.node [11,11,11,7,7,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,7,7,4,3,2,1,1,1,1,1,1] (.node [11,11,11,7,7,4,2,2,2,1,1,1,1,1] (.node [11,11,11,7,7,3,3,3,3,1,1,1] (.node [11,11,11,7,7,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,4,2,2,2,2,2,1] (.node [11,11,11,7,7,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,7,4,3,3,1,1,1,1,1] (.node [11,11,11,7,7,4,3,2,2,2,1,1] (.node [11,11,11,7,7,4,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,4,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_263 : RowTree := (.node [11,11,11,7,7,5,4,1,1,1,1,1,1] (.node [11,11,11,7,7,5,2,2,2,2,1,1] (.node [11,11,11,7,7,4,4,3,1,1,1,1] (.node [11,11,11,7,7,4,4,2,2,1,1,1] (.node [11,11,11,7,7,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,5,2,2,2,1,1,1,1] (.node [11,11,11,7,7,5,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,7,5,3,2,2,1,1,1] (.node [11,11,11,7,7,5,3,2,1,1,1,1,1] (.node [11,11,11,7,7,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,5,3,3,1,1,1,1] .empty .empty))) (.node [11,11,11,7,7,6,3,1,1,1,1,1,1] (.node [11,11,11,7,7,6,2,1,1,1,1,1,1,1] (.node [11,11,11,7,7,5,5,1,1,1,1,1] (.node [11,11,11,7,7,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,6,2,2,2,1,1,1] (.node [11,11,11,7,7,6,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,7,7,7,1,1,1,1,1,1,1,1] (.node [11,11,11,7,7,6,4,1,1,1,1,1] (.node [11,11,11,7,7,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,7,7,7,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_264 : RowTree := (.node [11,11,11,7,7,4,4,1,1,1,1,1,1,1] degreeTree62_262 degreeTree62_263) + +def degreeTree62_265 : RowTree := (.node [11,11,11,8,4,3,3,3,3,2,2,1] (.node [11,11,11,8,4,3,3,2,2,2,2,1,1,1] (.node [11,11,11,8,3,3,3,3,3,2,2,1,1] (.node [11,11,11,8,3,3,3,2,2,2,2,2,2] (.node [11,11,11,7,7,7,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,4,3,2,2,2,2,2,2,2] (.node [11,11,11,8,4,2,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,8,4,3,3,3,3,1,1,1,1,1] (.node [11,11,11,8,4,3,3,3,2,2,2,1,1] (.node [11,11,11,8,4,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,8,4,3,3,3,3,2,1,1,1] .empty .empty))) (.node [11,11,11,8,4,4,3,3,2,1,1,1,1,1] (.node [11,11,11,8,4,4,3,2,2,2,1,1,1,1] (.node [11,11,11,8,4,4,2,2,2,2,2,2,1] (.node [11,11,11,8,4,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,4,4,3,2,2,2,2,2] (.node [11,11,11,8,4,4,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,11,8,4,4,3,3,3,1,1,1,1] (.node [11,11,11,8,4,4,3,3,2,2,2,1] (.node [11,11,11,8,4,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,4,4,3,3,3,2,1,1] .empty .empty)))) + +def degreeTree62_266 : RowTree := (.node [11,11,11,8,5,3,2,2,2,2,2,1,1,1] (.node [11,11,11,8,4,4,4,3,3,1,1,1] (.node [11,11,11,8,4,4,4,3,1,1,1,1,1,1] (.node [11,11,11,8,4,4,4,2,2,2,2,1] (.node [11,11,11,8,4,4,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,4,4,4,3,2,2,1,1] (.node [11,11,11,8,4,4,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,5,2,2,2,2,2,2,2,1,1] (.node [11,11,11,8,4,4,4,4,2,1,1,1] (.node [11,11,11,8,4,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,5,2,2,2,2,2,2,2,2] .empty .empty))) (.node [11,11,11,8,5,3,3,3,2,2,1,1,1] (.node [11,11,11,8,5,3,3,2,2,2,2,1,1] (.node [11,11,11,8,5,3,3,2,2,2,1,1,1,1] (.node [11,11,11,8,5,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,8,5,3,3,3,2,1,1,1,1,1] (.node [11,11,11,8,5,3,3,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,8,5,3,3,3,3,2,1,1] (.node [11,11,11,8,5,3,3,3,3,1,1,1,1] (.node [11,11,11,8,5,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,8,5,4,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_267 : RowTree := (.node [11,11,11,8,4,4,4,2,2,1,1,1,1,1] degreeTree62_265 degreeTree62_266) + +def degreeTree62_268 : RowTree := (.node [11,11,11,7,7,7,2,2,1,1,1,1] degreeTree62_264 degreeTree62_267) + +def degreeTree62_269 : RowTree := (.node [11,11,11,7,6,6,4,2,1,1,1,1] degreeTree62_261 degreeTree62_268) + +def degreeTree62_270 : RowTree := (.node [11,11,11,8,5,4,4,2,2,2,1,1] (.node [11,11,11,8,5,4,3,3,2,1,1,1,1] (.node [11,11,11,8,5,4,3,2,2,2,1,1,1] (.node [11,11,11,8,5,4,3,2,2,1,1,1,1,1] (.node [11,11,11,8,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,11,8,5,4,3,3,1,1,1,1,1,1] (.node [11,11,11,8,5,4,3,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,8,5,4,4,2,1,1,1,1,1,1] (.node [11,11,11,8,5,4,3,3,3,1,1,1] (.node [11,11,11,8,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,8,5,4,4,2,2,1,1,1,1] .empty .empty))) (.node [11,11,11,8,5,5,2,2,2,2,2,1] (.node [11,11,11,8,5,4,4,4,1,1,1,1] (.node [11,11,11,8,5,4,4,3,2,1,1,1] (.node [11,11,11,8,5,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,5,5,2,2,2,2,1,1,1] (.node [11,11,11,8,5,5,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,5,5,3,2,2,2,1,1] (.node [11,11,11,8,5,5,3,2,2,1,1,1,1] (.node [11,11,11,8,5,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,5,5,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_271 : RowTree := (.node [11,11,11,8,6,3,2,2,2,2,2,2] (.node [11,11,11,8,5,5,5,2,1,1,1,1] (.node [11,11,11,8,5,5,4,2,2,1,1,1] (.node [11,11,11,8,5,5,4,2,1,1,1,1,1] (.node [11,11,11,8,5,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,5,5,5,1,1,1,1,1,1] (.node [11,11,11,8,5,5,4,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,6,3,2,2,2,2,1,1,1,1] (.node [11,11,11,8,6,2,2,2,2,2,2,2,1] (.node [11,11,11,8,6,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,3,2,2,2,2,2,1,1] .empty .empty))) (.node [11,11,11,8,6,3,3,3,2,2,1,1] (.node [11,11,11,8,6,3,3,2,2,2,2,1] (.node [11,11,11,8,6,3,3,2,2,2,1,1,1] (.node [11,11,11,8,6,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,3,3,3,2,1,1,1,1] (.node [11,11,11,8,6,3,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,6,4,2,2,2,2,1,1,1] (.node [11,11,11,8,6,4,2,2,2,1,1,1,1,1] (.node [11,11,11,8,6,3,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,4,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_272 : RowTree := (.node [11,11,11,8,5,5,3,3,2,1,1,1] degreeTree62_270 degreeTree62_271) + +def degreeTree62_273 : RowTree := (.node [11,11,11,8,6,5,2,2,2,2,1,1] (.node [11,11,11,8,6,4,4,2,1,1,1,1,1] (.node [11,11,11,8,6,4,3,3,1,1,1,1,1] (.node [11,11,11,8,6,4,3,2,2,2,1,1] (.node [11,11,11,8,6,4,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,4,4,1,1,1,1,1,1,1] (.node [11,11,11,8,6,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,6,5,2,2,1,1,1,1,1,1] (.node [11,11,11,8,6,4,4,3,1,1,1,1] (.node [11,11,11,8,6,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,5,2,2,2,1,1,1,1] .empty .empty))) (.node [11,11,11,8,6,5,4,2,1,1,1,1] (.node [11,11,11,8,6,5,3,2,2,1,1,1] (.node [11,11,11,8,6,5,3,2,1,1,1,1,1] (.node [11,11,11,8,6,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,5,4,1,1,1,1,1,1] (.node [11,11,11,8,6,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,6,6,2,2,1,1,1,1,1] (.node [11,11,11,8,6,6,2,1,1,1,1,1,1,1] (.node [11,11,11,8,6,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,6,6,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_274 : RowTree := (.node [11,11,11,8,7,3,3,2,2,2,1,1] (.node [11,11,11,8,7,3,2,2,2,1,1,1,1,1] (.node [11,11,11,8,7,2,2,2,2,2,1,1,1,1] (.node [11,11,11,8,6,6,4,1,1,1,1,1] (.node [11,11,11,8,6,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,7,2,2,2,2,2,2,2] (.node [11,11,11,8,7,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,11,8,7,3,3,2,1,1,1,1,1,1] (.node [11,11,11,8,7,3,2,2,2,2,2,1] (.node [11,11,11,8,7,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,7,3,3,2,2,1,1,1,1] .empty .empty))) (.node [11,11,11,8,7,4,3,1,1,1,1,1,1,1] (.node [11,11,11,8,7,4,2,2,1,1,1,1,1,1] (.node [11,11,11,8,7,3,3,3,2,1,1,1] (.node [11,11,11,8,7,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,7,4,2,2,2,2,1,1] (.node [11,11,11,8,7,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,7,4,3,3,1,1,1,1] (.node [11,11,11,8,7,4,3,2,2,1,1,1] (.node [11,11,11,8,7,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,7,4,4,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_275 : RowTree := (.node [11,11,11,8,6,6,3,1,1,1,1,1,1] degreeTree62_273 degreeTree62_274) + +def degreeTree62_276 : RowTree := (.node [11,11,11,8,6,4,3,2,1,1,1,1,1,1] degreeTree62_272 degreeTree62_275) + +def degreeTree62_277 : RowTree := (.node [11,11,11,8,7,7,1,1,1,1,1,1,1] (.node [11,11,11,8,7,5,4,1,1,1,1,1] (.node [11,11,11,8,7,5,2,2,2,1,1,1] (.node [11,11,11,8,7,5,2,2,1,1,1,1,1] (.node [11,11,11,8,7,5,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,7,5,3,2,1,1,1,1] (.node [11,11,11,8,7,5,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,7,6,2,2,1,1,1,1] (.node [11,11,11,8,7,6,2,1,1,1,1,1,1] (.node [11,11,11,8,7,6,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,7,6,3,1,1,1,1,1] .empty .empty))) (.node [11,11,11,8,8,3,2,2,2,1,1,1,1] (.node [11,11,11,8,8,2,2,2,2,2,1,1,1] (.node [11,11,11,8,8,2,2,2,2,1,1,1,1,1] (.node [11,11,11,8,7,7,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,8,3,2,2,1,1,1,1,1,1] (.node [11,11,11,8,8,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [11,11,11,8,8,3,3,2,1,1,1,1,1] (.node [11,11,11,8,8,3,3,1,1,1,1,1,1,1] (.node [11,11,11,8,8,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,8,8,3,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_278 : RowTree := (.node [11,11,11,8,8,6,1,1,1,1,1,1,1] (.node [11,11,11,8,8,4,4,1,1,1,1,1] (.node [11,11,11,8,8,4,2,2,2,1,1,1] (.node [11,11,11,8,8,4,2,2,1,1,1,1,1] (.node [11,11,11,8,8,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,8,4,3,2,1,1,1,1] (.node [11,11,11,8,8,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,8,8,5,2,2,1,1,1,1] (.node [11,11,11,8,8,5,2,1,1,1,1,1,1] (.node [11,11,11,8,8,5,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,8,8,5,3,1,1,1,1,1] .empty .empty))) (.node [11,11,11,9,3,3,3,2,2,2,2,2,1] (.node [11,11,11,9,3,2,2,2,2,2,2,2,2,1] (.node [11,11,11,8,8,7,1,1,1,1,1,1] (.node [11,11,11,8,8,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,3,3,3,2,2,2,2,1,1,1] (.node [11,11,11,9,3,3,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,9,3,3,3,3,3,2,1,1,1] (.node [11,11,11,9,3,3,3,3,3,1,1,1,1,1] (.node [11,11,11,9,3,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,9,3,3,3,3,3,2,2,1] .empty .empty)))) + +def degreeTree62_279 : RowTree := (.node [11,11,11,8,8,3,3,3,1,1,1,1] degreeTree62_277 degreeTree62_278) + +def degreeTree62_280 : RowTree := (.node [11,11,11,9,4,3,3,3,3,2,1,1] (.node [11,11,11,9,4,3,3,2,2,2,2,2] (.node [11,11,11,9,4,3,2,2,2,2,2,2,1] (.node [11,11,11,9,4,3,2,2,2,2,2,1,1,1] (.node [11,11,11,9,4,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [11,11,11,9,4,3,3,2,2,2,2,1,1] (.node [11,11,11,9,4,3,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,4,3,3,3,2,2,2,1] (.node [11,11,11,9,4,3,3,3,2,2,1,1,1] (.node [11,11,11,9,4,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,4,3,3,3,3,1,1,1,1] .empty .empty))) (.node [11,11,11,9,4,4,3,2,2,2,2,1] (.node [11,11,11,9,4,4,2,2,2,2,2,2] (.node [11,11,11,9,4,4,2,2,2,2,2,1,1] (.node [11,11,11,9,4,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,4,4,3,2,2,2,1,1,1] (.node [11,11,11,9,4,4,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,4,4,3,3,2,2,1,1] (.node [11,11,11,9,4,4,3,3,2,1,1,1,1] (.node [11,11,11,9,4,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,4,4,3,3,3,1,1,1] .empty .empty)))) + +def degreeTree62_281 : RowTree := (.node [11,11,11,9,5,3,3,2,2,1,1,1,1,1] (.node [11,11,11,9,5,2,2,2,2,2,2,1,1,1] (.node [11,11,11,9,4,4,4,3,1,1,1,1,1] (.node [11,11,11,9,4,4,4,2,2,2,1,1] (.node [11,11,11,9,4,4,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,4,4,4,4,1,1,1,1] (.node [11,11,11,9,4,4,4,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,5,3,2,2,2,2,2,1,1] (.node [11,11,11,9,5,3,2,2,2,2,1,1,1,1] (.node [11,11,11,9,5,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,9,5,3,2,2,2,2,2,2] .empty .empty))) (.node [11,11,11,9,5,3,3,3,2,2,1,1] (.node [11,11,11,9,5,3,3,3,1,1,1,1,1,1] (.node [11,11,11,9,5,3,3,2,2,2,2,1] (.node [11,11,11,9,5,3,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,5,3,3,3,2,1,1,1,1] .empty .empty)) (.node [11,11,11,9,5,4,2,2,2,2,1,1,1] (.node [11,11,11,9,5,4,2,2,2,1,1,1,1,1] (.node [11,11,11,9,5,3,3,3,3,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,5,4,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_282 : RowTree := (.node [11,11,11,9,4,4,4,2,1,1,1,1,1,1] degreeTree62_280 degreeTree62_281) + +def degreeTree62_283 : RowTree := (.node [11,11,11,9,4,2,2,2,2,2,2,2,1,1] degreeTree62_279 degreeTree62_282) + +def degreeTree62_284 : RowTree := (.node [11,11,11,8,7,4,4,2,1,1,1,1] degreeTree62_276 degreeTree62_283) + +def degreeTree62_285 : RowTree := (.node [11,11,11,8,5,4,2,2,2,2,2,1,1] degreeTree62_269 degreeTree62_284) + +def degreeTree62_286 : RowTree := (.node [11,11,11,9,5,5,2,2,2,2,1,1] (.node [11,11,11,9,5,4,4,2,1,1,1,1,1] (.node [11,11,11,9,5,4,3,3,1,1,1,1,1] (.node [11,11,11,9,5,4,3,2,2,2,1,1] (.node [11,11,11,9,5,4,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,5,4,4,1,1,1,1,1,1,1] (.node [11,11,11,9,5,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,5,5,2,2,1,1,1,1,1,1] (.node [11,11,11,9,5,4,4,3,1,1,1,1] (.node [11,11,11,9,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,5,5,2,2,2,1,1,1,1] .empty .empty))) (.node [11,11,11,9,5,5,4,2,1,1,1,1] (.node [11,11,11,9,5,5,3,2,2,1,1,1] (.node [11,11,11,9,5,5,3,2,1,1,1,1,1] (.node [11,11,11,9,5,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,5,5,4,1,1,1,1,1,1] (.node [11,11,11,9,5,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,6,2,2,2,2,2,2,1,1] (.node [11,11,11,9,6,2,2,2,2,2,1,1,1,1] (.node [11,11,11,9,5,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,6,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_287 : RowTree := (.node [11,11,11,9,6,4,3,1,1,1,1,1,1,1] (.node [11,11,11,9,6,3,3,3,1,1,1,1,1] (.node [11,11,11,9,6,3,3,2,1,1,1,1,1,1] (.node [11,11,11,9,6,3,2,2,2,2,2,1] (.node [11,11,11,9,6,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,6,3,3,2,2,2,1,1] (.node [11,11,11,9,6,3,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,6,4,2,2,2,1,1,1,1] (.node [11,11,11,9,6,4,2,2,1,1,1,1,1,1] (.node [11,11,11,9,6,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,6,4,2,2,2,2,1,1] .empty .empty))) (.node [11,11,11,9,6,5,2,1,1,1,1,1,1,1] (.node [11,11,11,9,6,4,3,3,1,1,1,1] (.node [11,11,11,9,6,4,3,2,2,1,1,1] (.node [11,11,11,9,6,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,6,4,4,2,1,1,1,1] (.node [11,11,11,9,6,4,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,6,5,3,1,1,1,1,1,1] (.node [11,11,11,9,6,5,2,2,2,1,1,1] (.node [11,11,11,9,6,5,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,6,5,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_288 : RowTree := (.node [11,11,11,9,6,3,2,2,2,1,1,1,1,1] degreeTree62_286 degreeTree62_287) + +def degreeTree62_289 : RowTree := (.node [11,11,11,9,7,3,3,1,1,1,1,1,1,1] (.node [11,11,11,9,7,2,2,2,2,2,1,1,1] (.node [11,11,11,9,6,6,2,2,1,1,1,1] (.node [11,11,11,9,6,6,2,1,1,1,1,1,1] (.node [11,11,11,9,6,6,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,7,2,2,2,2,1,1,1,1,1] (.node [11,11,11,9,6,6,3,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,7,3,2,2,2,1,1,1,1] (.node [11,11,11,9,7,3,2,2,1,1,1,1,1,1] (.node [11,11,11,9,7,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,9,7,3,2,2,2,2,1,1] .empty .empty))) (.node [11,11,11,9,7,4,2,2,2,1,1,1] (.node [11,11,11,9,7,3,3,3,1,1,1,1] (.node [11,11,11,9,7,3,3,2,2,1,1,1] (.node [11,11,11,9,7,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,7,4,2,2,1,1,1,1,1] (.node [11,11,11,9,7,4,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,7,4,4,1,1,1,1,1] (.node [11,11,11,9,7,4,3,2,1,1,1,1] (.node [11,11,11,9,7,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,7,5,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_290 : RowTree := (.node [11,11,11,9,8,3,2,2,2,1,1,1] (.node [11,11,11,9,8,2,2,2,1,1,1,1,1,1] (.node [11,11,11,9,7,6,1,1,1,1,1,1,1] (.node [11,11,11,9,7,5,3,1,1,1,1,1] (.node [11,11,11,9,7,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,7,7,1,1,1,1,1,1] (.node [11,11,11,9,7,6,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,8,3,2,1,1,1,1,1,1,1] (.node [11,11,11,9,8,2,2,2,2,2,1,1] (.node [11,11,11,9,8,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,8,3,2,2,1,1,1,1,1] .empty .empty))) (.node [11,11,11,9,8,4,3,1,1,1,1,1] (.node [11,11,11,9,8,4,1,1,1,1,1,1,1,1] (.node [11,11,11,9,8,3,3,2,1,1,1,1] (.node [11,11,11,9,8,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,8,4,2,2,1,1,1,1] (.node [11,11,11,9,8,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,9,8,6,1,1,1,1,1,1] (.node [11,11,11,9,8,5,2,1,1,1,1,1] (.node [11,11,11,9,8,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,9,2,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_291 : RowTree := (.node [11,11,11,9,7,5,2,1,1,1,1,1,1] degreeTree62_289 degreeTree62_290) + +def degreeTree62_292 : RowTree := (.node [11,11,11,9,6,5,4,1,1,1,1,1] degreeTree62_288 degreeTree62_291) + +def degreeTree62_293 : RowTree := (.node [11,11,11,10,3,2,2,2,2,2,2,2,2] (.node [11,11,11,9,9,4,1,1,1,1,1,1,1] (.node [11,11,11,9,9,3,2,1,1,1,1,1,1] (.node [11,11,11,9,9,3,1,1,1,1,1,1,1,1] (.node [11,11,11,9,9,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,9,9,3,3,1,1,1,1,1] (.node [11,11,11,9,9,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,2,2,2,2,2,2,2,2,2,1] (.node [11,11,11,9,9,5,1,1,1,1,1,1] (.node [11,11,11,9,9,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,3,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [11,11,11,10,3,3,3,3,2,1,1,1,1,1] (.node [11,11,11,10,3,3,3,2,2,2,1,1,1,1] (.node [11,11,11,10,3,3,2,2,2,2,2,2,1] (.node [11,11,11,10,3,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,3,3,3,2,2,2,2,2] (.node [11,11,11,10,3,3,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,11,10,3,3,3,3,3,1,1,1,1] (.node [11,11,11,10,3,3,3,3,2,2,2,1] (.node [11,11,11,10,3,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,3,3,3,3,3,2,1,1] .empty .empty)))) + +def degreeTree62_294 : RowTree := (.node [11,11,11,10,4,3,3,3,3,1,1,1] (.node [11,11,11,10,4,3,3,2,2,2,1,1,1] (.node [11,11,11,10,4,3,2,2,2,2,2,1,1] (.node [11,11,11,10,4,3,2,2,2,2,1,1,1,1] (.node [11,11,11,10,4,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,10,4,3,3,2,2,1,1,1,1,1] (.node [11,11,11,10,4,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,10,4,3,3,3,2,1,1,1,1] (.node [11,11,11,10,4,3,3,3,1,1,1,1,1,1] (.node [11,11,11,10,4,3,3,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,10,4,3,3,3,2,2,1,1] .empty .empty))) (.node [11,11,11,10,4,4,3,2,2,2,1,1] (.node [11,11,11,10,4,4,2,2,2,2,2,1] (.node [11,11,11,10,4,4,2,2,2,2,1,1,1] (.node [11,11,11,10,4,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,4,4,3,2,2,1,1,1,1] (.node [11,11,11,10,4,4,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,4,4,4,1,1,1,1,1,1,1] (.node [11,11,11,10,4,4,3,3,2,1,1,1] (.node [11,11,11,10,4,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,4,4,4,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_295 : RowTree := (.node [11,11,11,10,4,2,2,2,2,2,2,1,1,1] degreeTree62_293 degreeTree62_294) + +def degreeTree62_296 : RowTree := (.node [11,11,11,10,5,3,3,3,1,1,1,1,1] (.node [11,11,11,10,5,3,2,2,2,2,1,1,1] (.node [11,11,11,10,5,2,2,2,2,2,2,1,1] (.node [11,11,11,10,5,2,2,2,2,2,1,1,1,1] (.node [11,11,11,10,4,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,5,3,2,2,2,1,1,1,1,1] (.node [11,11,11,10,5,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [11,11,11,10,5,3,3,2,2,1,1,1,1] (.node [11,11,11,10,5,3,3,2,1,1,1,1,1,1] (.node [11,11,11,10,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [11,11,11,10,5,3,3,2,2,2,1,1] .empty .empty))) (.node [11,11,11,10,5,4,3,2,1,1,1,1,1] (.node [11,11,11,10,5,4,2,2,2,1,1,1,1] (.node [11,11,11,10,5,4,2,2,1,1,1,1,1,1] (.node [11,11,11,10,5,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,5,4,3,1,1,1,1,1,1,1] (.node [11,11,11,10,5,4,2,2,2,2,1,1] .empty .empty) .empty)) (.node [11,11,11,10,5,4,4,1,1,1,1,1,1] (.node [11,11,11,10,5,4,3,3,1,1,1,1] (.node [11,11,11,10,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,5,4,4,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_297 : RowTree := (.node [11,11,11,10,6,3,2,2,2,2,1,1] (.node [11,11,11,10,6,2,2,2,2,1,1,1,1,1] (.node [11,11,11,10,5,5,3,1,1,1,1,1,1] (.node [11,11,11,10,5,5,2,2,2,1,1,1] (.node [11,11,11,10,5,5,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,5,5,4,1,1,1,1,1] (.node [11,11,11,10,5,5,3,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,6,3,2,2,1,1,1,1,1,1] (.node [11,11,11,10,6,2,2,2,2,2,2,1] (.node [11,11,11,10,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,6,3,2,2,2,1,1,1,1] .empty .empty))) (.node [11,11,11,10,6,4,2,2,1,1,1,1,1] (.node [11,11,11,10,6,3,3,2,2,1,1,1] (.node [11,11,11,10,6,3,3,2,1,1,1,1,1] (.node [11,11,11,10,6,3,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,6,4,2,1,1,1,1,1,1,1] (.node [11,11,11,10,6,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,6,4,3,2,1,1,1,1] (.node [11,11,11,10,6,4,3,1,1,1,1,1,1] (.node [11,11,11,10,6,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,6,4,4,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_298 : RowTree := (.node [11,11,11,10,5,5,2,1,1,1,1,1,1,1] degreeTree62_296 degreeTree62_297) + +def degreeTree62_299 : RowTree := (.node [11,11,11,10,4,4,4,2,2,1,1,1] degreeTree62_295 degreeTree62_298) + +def degreeTree62_300 : RowTree := (.node [11,11,11,9,9,2,2,2,1,1,1,1,1] degreeTree62_292 degreeTree62_299) + +def degreeTree62_301 : RowTree := (.node [11,11,11,10,7,3,2,2,2,1,1,1] (.node [11,11,11,10,7,2,2,2,1,1,1,1,1,1] (.node [11,11,11,10,6,5,3,1,1,1,1,1] (.node [11,11,11,10,6,5,2,2,1,1,1,1] (.node [11,11,11,10,6,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,6,6,2,1,1,1,1,1] (.node [11,11,11,10,6,6,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,7,3,2,1,1,1,1,1,1,1] (.node [11,11,11,10,7,2,2,2,2,2,1,1] (.node [11,11,11,10,7,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,7,3,2,2,1,1,1,1,1] .empty .empty))) (.node [11,11,11,10,7,4,3,1,1,1,1,1] (.node [11,11,11,10,7,4,1,1,1,1,1,1,1,1] (.node [11,11,11,10,7,3,3,2,1,1,1,1] (.node [11,11,11,10,7,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,7,4,2,2,1,1,1,1] (.node [11,11,11,10,7,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,7,6,1,1,1,1,1,1] (.node [11,11,11,10,7,5,2,1,1,1,1,1] (.node [11,11,11,10,7,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,8,2,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_302 : RowTree := (.node [11,11,11,10,9,2,2,2,1,1,1,1] (.node [11,11,11,10,8,4,1,1,1,1,1,1,1] (.node [11,11,11,10,8,3,2,1,1,1,1,1,1] (.node [11,11,11,10,8,3,1,1,1,1,1,1,1,1] (.node [11,11,11,10,8,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,8,3,3,1,1,1,1,1] (.node [11,11,11,10,8,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,10,9,2,1,1,1,1,1,1,1,1] (.node [11,11,11,10,8,5,1,1,1,1,1,1] (.node [11,11,11,10,8,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,9,2,2,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,10,10,2,2,1,1,1,1,1] (.node [11,11,11,10,9,4,1,1,1,1,1,1] (.node [11,11,11,10,9,3,2,1,1,1,1,1] (.node [11,11,11,10,9,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,10,10,2,1,1,1,1,1,1,1] (.node [11,11,11,10,10,1,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,2,2,2,2,2,2,2,2,2] (.node [11,11,11,11,2,2,2,2,2,2,2,2,1,1] (.node [11,11,11,10,10,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,3,2,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_303 : RowTree := (.node [11,11,11,10,8,2,2,2,1,1,1,1,1] degreeTree62_301 degreeTree62_302) + +def degreeTree62_304 : RowTree := (.node [11,11,11,11,4,2,2,2,2,2,1,1,1,1] (.node [11,11,11,11,3,3,3,2,2,2,2,1] (.node [11,11,11,11,3,3,2,2,2,2,2,2] (.node [11,11,11,11,3,3,2,2,2,2,2,1,1] (.node [11,11,11,11,3,3,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,3,3,3,2,2,2,1,1,1] (.node [11,11,11,11,3,3,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,3,3,3,3,2,2,1,1] (.node [11,11,11,11,3,3,3,3,2,1,1,1,1] (.node [11,11,11,11,3,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,3,3,3,3,3,1,1,1] .empty .empty))) (.node [11,11,11,11,4,3,3,2,1,1,1,1,1,1] (.node [11,11,11,11,4,3,2,2,2,1,1,1,1,1] (.node [11,11,11,11,4,2,2,2,2,2,2,2] (.node [11,11,11,11,4,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [11,11,11,11,4,3,2,2,2,2,2,1] (.node [11,11,11,11,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,4,3,3,3,1,1,1,1,1] (.node [11,11,11,11,4,3,3,2,2,2,1,1] (.node [11,11,11,11,4,3,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,4,3,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_305 : RowTree := (.node [11,11,11,11,5,2,2,2,2,2,2,1] (.node [11,11,11,11,4,4,3,3,1,1,1,1] (.node [11,11,11,11,4,4,3,1,1,1,1,1,1,1] (.node [11,11,11,11,4,4,2,2,2,2,1,1] (.node [11,11,11,11,4,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,4,4,3,2,2,1,1,1] (.node [11,11,11,11,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,5,2,2,2,2,1,1,1,1,1] (.node [11,11,11,11,4,4,4,2,1,1,1,1] (.node [11,11,11,11,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,5,2,2,2,2,2,1,1,1] .empty .empty))) (.node [11,11,11,11,5,3,3,2,2,1,1,1] (.node [11,11,11,11,5,3,2,2,2,2,1,1] (.node [11,11,11,11,5,3,2,2,2,1,1,1,1] (.node [11,11,11,11,5,3,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,5,3,3,2,1,1,1,1,1] (.node [11,11,11,11,5,3,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,5,4,2,2,1,1,1,1,1] (.node [11,11,11,11,5,4,2,1,1,1,1,1,1,1] (.node [11,11,11,11,5,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,5,4,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_306 : RowTree := (.node [11,11,11,11,4,4,2,2,1,1,1,1,1,1] degreeTree62_304 degreeTree62_305) + +def degreeTree62_307 : RowTree := (.node [11,11,11,11,3,2,2,2,2,2,2,2,1] degreeTree62_303 degreeTree62_306) + +def degreeTree62_308 : RowTree := (.node [11,11,11,11,6,3,2,2,1,1,1,1,1] (.node [11,11,11,11,5,5,3,1,1,1,1,1] (.node [11,11,11,11,5,5,1,1,1,1,1,1,1,1] (.node [11,11,11,11,5,4,4,1,1,1,1,1] (.node [11,11,11,11,5,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,5,5,2,2,1,1,1,1] (.node [11,11,11,11,5,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,6,2,2,2,2,2,1,1] (.node [11,11,11,11,6,2,2,2,2,1,1,1,1] (.node [11,11,11,11,6,2,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,6,3,2,1,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,11,6,4,2,2,1,1,1,1] (.node [11,11,11,11,6,3,3,2,1,1,1,1] (.node [11,11,11,11,6,3,3,1,1,1,1,1,1] (.node [11,11,11,11,6,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,6,4,2,1,1,1,1,1,1] (.node [11,11,11,11,6,4,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,6,5,2,1,1,1,1,1] (.node [11,11,11,11,6,5,1,1,1,1,1,1,1] (.node [11,11,11,11,6,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,6,6,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_309 : RowTree := (.node [11,11,11,11,8,2,2,1,1,1,1,1,1] (.node [11,11,11,11,7,3,3,1,1,1,1,1] (.node [11,11,11,11,7,3,1,1,1,1,1,1,1,1] (.node [11,11,11,11,7,2,2,2,2,1,1,1] (.node [11,11,11,11,7,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,7,3,2,2,1,1,1,1] (.node [11,11,11,11,7,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,7,5,1,1,1,1,1,1] (.node [11,11,11,11,7,4,2,1,1,1,1,1] (.node [11,11,11,11,7,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,8,2,1,1,1,1,1,1,1,1] .empty .empty))) (.node [11,11,11,11,9,2,1,1,1,1,1,1,1] (.node [11,11,11,11,8,3,2,1,1,1,1,1] (.node [11,11,11,11,8,3,1,1,1,1,1,1,1] (.node [11,11,11,11,8,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,9,1,1,1,1,1,1,1,1,1] (.node [11,11,11,11,8,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [11,11,11,11,10,1,1,1,1,1,1,1,1] (.node [11,11,11,11,9,3,1,1,1,1,1,1] (.node [11,11,11,11,9,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [11,11,11,11,10,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_310 : RowTree := (.node [11,11,11,11,7,2,2,1,1,1,1,1,1,1] degreeTree62_308 degreeTree62_309) + +def degreeTree62_311 : RowTree := (.node [12,6,6,6,6,6,6,6,2,2,2,1,1] (.node [12,6,6,6,6,6,6,5,3,2,2,1,1] (.node [12,6,6,6,6,6,5,5,5,2,1,1,1] (.node [12,6,6,6,6,6,5,5,4,2,2,1,1] (.node [12,6,6,6,6,5,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,6,6,6,6,6,6,4,4,2,2,1,1] (.node [12,6,6,6,6,6,5,5,5,2,2,1] .empty .empty) .empty)) (.node [12,6,6,6,6,6,6,5,5,1,1,1,1] (.node [12,6,6,6,6,6,6,5,4,2,2,1] (.node [12,6,6,6,6,6,6,5,4,2,1,1,1] .empty .empty) .empty) (.node [12,6,6,6,6,6,6,5,5,2,1,1] .empty .empty))) (.node [12,7,6,6,5,5,5,5,5,2,2,1,1] (.node [12,6,6,6,6,6,6,6,4,1,1,1,1] (.node [12,6,6,6,6,6,6,6,3,2,2,1] (.node [12,6,6,6,6,6,6,6,3,2,1,1,1] .empty .empty) .empty) (.node [12,6,6,6,6,6,6,6,5,1,1,1] (.node [12,6,6,6,6,6,6,6,4,2,1,1] .empty .empty) .empty)) (.node [12,7,6,6,6,5,5,5,5,2,2,1] (.node [12,7,6,6,6,5,5,5,5,2,1,1,1] (.node [12,7,6,6,6,5,5,5,4,2,2,1,1] .empty .empty) .empty) (.node [12,7,6,6,6,6,5,4,4,2,2,1,1] .empty .empty)))) + +def degreeTree62_312 : RowTree := (.node [12,7,6,6,6,6,6,5,4,1,1,1,1] (.node [12,7,6,6,6,6,6,4,4,2,1,1,1] (.node [12,7,6,6,6,6,5,5,5,1,1,1,1] (.node [12,7,6,6,6,6,5,5,4,2,2,1] (.node [12,7,6,6,6,6,5,5,4,2,1,1,1] .empty .empty) .empty) (.node [12,7,6,6,6,6,6,4,3,2,2,1,1] (.node [12,7,6,6,6,6,5,5,5,2,1,1] .empty .empty) .empty)) (.node [12,7,6,6,6,6,6,5,3,2,1,1,1] (.node [12,7,6,6,6,6,6,5,2,2,2,1,1] (.node [12,7,6,6,6,6,6,4,4,2,2,1] .empty .empty) .empty) (.node [12,7,6,6,6,6,6,5,3,2,2,1] .empty .empty))) (.node [12,7,6,6,6,6,6,6,3,1,1,1,1] (.node [12,7,6,6,6,6,6,6,2,2,1,1,1] (.node [12,7,6,6,6,6,6,5,5,1,1,1] (.node [12,7,6,6,6,6,6,5,4,2,1,1] .empty .empty) .empty) (.node [12,7,6,6,6,6,6,6,2,2,2,1] .empty .empty)) (.node [12,7,7,5,5,5,5,5,5,2,2,1,1] (.node [12,7,6,6,6,6,6,6,4,1,1,1] (.node [12,7,6,6,6,6,6,6,3,2,1,1] .empty .empty) .empty) (.node [12,7,7,6,5,5,5,5,4,2,2,1,1] .empty .empty)))) + +def degreeTree62_313 : RowTree := (.node [12,7,6,6,6,6,5,5,3,2,2,1,1] degreeTree62_311 degreeTree62_312) + +def degreeTree62_314 : RowTree := (.node [11,11,11,11,11,1,1,1,1,1,1,1] degreeTree62_310 degreeTree62_313) + +def degreeTree62_315 : RowTree := (.node [11,11,11,11,5,4,3,1,1,1,1,1,1] degreeTree62_307 degreeTree62_314) + +def degreeTree62_316 : RowTree := (.node [11,11,11,10,6,5,1,1,1,1,1,1,1,1] degreeTree62_300 degreeTree62_315) + +def degreeTree62_317 : RowTree := (.node [11,11,11,9,5,4,3,2,1,1,1,1,1,1] degreeTree62_285 degreeTree62_316) + +def degreeTree62_318 : RowTree := (.node [12,7,7,6,6,6,5,4,4,2,2,1] (.node [12,7,7,6,6,5,5,5,5,1,1,1,1] (.node [12,7,7,6,6,5,5,5,3,2,2,1,1] (.node [12,7,7,6,6,5,5,4,4,2,2,1,1] (.node [12,7,7,6,5,5,5,5,5,2,2,1] .empty .empty) .empty) (.node [12,7,7,6,6,5,5,5,4,2,2,1] (.node [12,7,7,6,6,5,5,5,4,2,1,1,1] .empty .empty) .empty)) (.node [12,7,7,6,6,6,5,4,3,2,2,1,1] (.node [12,7,7,6,6,6,4,4,4,2,2,1,1] (.node [12,7,7,6,6,5,5,5,5,2,1,1] .empty .empty) .empty) (.node [12,7,7,6,6,6,5,4,4,2,1,1,1] .empty .empty))) (.node [12,7,7,6,6,6,5,5,5,1,1,1] (.node [12,7,7,6,6,6,5,5,3,2,2,1] (.node [12,7,7,6,6,6,5,5,3,2,1,1,1] (.node [12,7,7,6,6,6,5,5,2,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,6,6,6,5,5,4,2,1,1] (.node [12,7,7,6,6,6,5,5,4,1,1,1,1] .empty .empty) .empty)) (.node [12,7,7,6,6,6,6,4,2,2,2,1,1] (.node [12,7,7,6,6,6,6,3,3,2,2,1,1] (.node [12,7,7,6,6,6,6,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,7,7,6,6,6,6,4,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_319 : RowTree := (.node [12,7,7,7,5,5,5,4,4,2,2,1,1] (.node [12,7,7,6,6,6,6,5,3,2,1,1] (.node [12,7,7,6,6,6,6,5,2,2,1,1,1] (.node [12,7,7,6,6,6,6,4,4,2,1,1] (.node [12,7,7,6,6,6,6,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,7,7,6,6,6,6,5,3,1,1,1,1] (.node [12,7,7,6,6,6,6,5,2,2,2,1] .empty .empty) .empty)) (.node [12,7,7,6,6,6,6,6,2,2,1,1] (.node [12,7,7,6,6,6,6,6,2,1,1,1,1] (.node [12,7,7,6,6,6,6,5,4,1,1,1] .empty .empty) .empty) (.node [12,7,7,6,6,6,6,6,3,1,1,1] .empty .empty))) (.node [12,7,7,7,6,5,4,4,4,2,2,1,1] (.node [12,7,7,7,5,5,5,5,4,2,2,1] (.node [12,7,7,7,5,5,5,5,4,2,1,1,1] (.node [12,7,7,7,5,5,5,5,3,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,5,5,5,5,5,2,1,1] (.node [12,7,7,7,5,5,5,5,5,1,1,1,1] .empty .empty) .empty)) (.node [12,7,7,7,6,5,5,4,4,2,2,1] (.node [12,7,7,7,6,5,5,4,4,2,1,1,1] (.node [12,7,7,7,6,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,6,5,5,5,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_320 : RowTree := (.node [12,7,7,6,6,6,6,4,3,2,2,1] degreeTree62_318 degreeTree62_319) + +def degreeTree62_321 : RowTree := (.node [12,7,7,7,6,6,5,4,3,2,1,1,1] (.node [12,7,7,7,6,6,4,4,4,2,1,1,1] (.node [12,7,7,7,6,5,5,5,4,2,1,1] (.node [12,7,7,7,6,5,5,5,4,1,1,1,1] (.node [12,7,7,7,6,5,5,5,3,2,2,1] .empty .empty) .empty) (.node [12,7,7,7,6,6,4,4,3,2,2,1,1] (.node [12,7,7,7,6,5,5,5,5,1,1,1] .empty .empty) .empty)) (.node [12,7,7,7,6,6,5,3,3,2,2,1,1] (.node [12,7,7,7,6,6,5,2,2,2,2,2,2] (.node [12,7,7,7,6,6,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,7,7,7,6,6,5,4,2,2,2,1,1] .empty .empty))) (.node [12,7,7,7,6,6,5,5,3,1,1,1,1] (.node [12,7,7,7,6,6,5,4,4,2,1,1] (.node [12,7,7,7,6,6,5,4,4,1,1,1,1] (.node [12,7,7,7,6,6,5,4,3,2,2,1] .empty .empty) .empty) (.node [12,7,7,7,6,6,5,5,2,2,2,1] (.node [12,7,7,7,6,6,5,5,2,2,1,1,1] .empty .empty) .empty)) (.node [12,7,7,7,6,6,6,2,2,2,2,2,1] (.node [12,7,7,7,6,6,5,5,4,1,1,1] (.node [12,7,7,7,6,6,5,5,3,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,6,6,6,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_322 : RowTree := (.node [12,7,7,7,6,6,6,6,2,1,1,1] (.node [12,7,7,7,6,6,6,4,4,1,1,1] (.node [12,7,7,7,6,6,6,4,2,2,2,1] (.node [12,7,7,7,6,6,6,4,2,2,1,1,1] (.node [12,7,7,7,6,6,6,3,3,2,2,1] .empty .empty) .empty) (.node [12,7,7,7,6,6,6,4,3,2,1,1] (.node [12,7,7,7,6,6,6,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,7,7,7,6,6,6,5,3,1,1,1] (.node [12,7,7,7,6,6,6,5,2,2,1,1] (.node [12,7,7,7,6,6,6,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,6,6,6,6,1,1,1,1,1] .empty .empty))) (.node [12,7,7,7,7,5,5,3,3,2,2,1,1] (.node [12,7,7,7,7,5,4,4,4,2,1,1,1] (.node [12,7,7,7,7,5,4,4,3,2,2,1,1] (.node [12,7,7,7,7,4,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,5,5,2,2,2,2,2,2] (.node [12,7,7,7,7,5,4,4,4,2,2,1] .empty .empty) .empty)) (.node [12,7,7,7,7,5,5,4,3,2,2,1] (.node [12,7,7,7,7,5,5,4,3,2,1,1,1] (.node [12,7,7,7,7,5,5,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,5,5,4,4,1,1,1,1] .empty .empty)))) + +def degreeTree62_323 : RowTree := (.node [12,7,7,7,6,6,6,3,3,2,1,1,1] degreeTree62_321 degreeTree62_322) + +def degreeTree62_324 : RowTree := (.node [12,7,7,7,6,5,5,5,3,2,1,1,1] degreeTree62_320 degreeTree62_323) + +def degreeTree62_325 : RowTree := (.node [12,7,7,7,7,6,4,4,4,1,1,1,1] (.node [12,7,7,7,7,6,4,2,2,2,2,2,2] (.node [12,7,7,7,7,5,5,5,3,1,1,1,1] (.node [12,7,7,7,7,5,5,5,2,2,2,1] (.node [12,7,7,7,7,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,5,5,5,4,1,1,1] (.node [12,7,7,7,7,5,5,5,3,2,1,1] .empty .empty) .empty)) (.node [12,7,7,7,7,6,4,4,3,2,1,1,1] (.node [12,7,7,7,7,6,4,4,2,2,2,1,1] (.node [12,7,7,7,7,6,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,6,4,4,3,2,2,1] .empty .empty))) (.node [12,7,7,7,7,6,5,4,2,2,1,1,1] (.node [12,7,7,7,7,6,5,3,2,2,2,1,1] (.node [12,7,7,7,7,6,5,2,2,2,2,2,1] (.node [12,7,7,7,7,6,4,4,4,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,6,5,3,3,2,2,1] (.node [12,7,7,7,7,6,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,7,7,7,7,6,5,4,3,2,1,1] (.node [12,7,7,7,7,6,5,4,3,1,1,1,1] (.node [12,7,7,7,7,6,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,7,7,7,7,6,5,4,4,1,1,1] .empty .empty)))) + +def degreeTree62_326 : RowTree := (.node [12,7,7,7,7,6,6,4,3,1,1,1] (.node [12,7,7,7,7,6,6,3,2,2,2,1] (.node [12,7,7,7,7,6,6,2,2,2,2,1,1] (.node [12,7,7,7,7,6,5,5,3,1,1,1] (.node [12,7,7,7,7,6,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,6,6,3,2,2,1,1,1] (.node [12,7,7,7,7,6,6,2,2,2,2,2] .empty .empty) .empty)) (.node [12,7,7,7,7,6,6,4,2,1,1,1,1] (.node [12,7,7,7,7,6,6,3,3,2,1,1] (.node [12,7,7,7,7,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,6,6,4,2,2,1,1] .empty .empty))) (.node [12,7,7,7,7,7,4,2,2,2,2,2,1] (.node [12,7,7,7,7,6,6,6,1,1,1,1] (.node [12,7,7,7,7,6,6,5,2,1,1,1] (.node [12,7,7,7,7,6,6,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,3,3,3,2,2,1,1] (.node [12,7,7,7,7,7,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,7,7,7,7,7,4,3,3,2,2,1] (.node [12,7,7,7,7,7,4,3,3,2,1,1,1] (.node [12,7,7,7,7,7,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,4,4,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_327 : RowTree := (.node [12,7,7,7,7,6,5,5,2,1,1,1,1] degreeTree62_325 degreeTree62_326) + +def degreeTree62_328 : RowTree := (.node [12,7,7,7,7,7,5,4,2,2,1,1] (.node [12,7,7,7,7,7,5,3,2,2,1,1,1] (.node [12,7,7,7,7,7,4,4,4,1,1,1] (.node [12,7,7,7,7,7,4,4,3,2,1,1] (.node [12,7,7,7,7,7,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,5,2,2,2,2,2] (.node [12,7,7,7,7,7,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,7,7,7,7,7,5,3,3,2,1,1] (.node [12,7,7,7,7,7,5,3,3,1,1,1,1] (.node [12,7,7,7,7,7,5,3,2,2,2,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,5,4,2,1,1,1,1] .empty .empty))) (.node [12,7,7,7,7,7,6,3,2,1,1,1,1] (.node [12,7,7,7,7,7,5,5,2,1,1,1] (.node [12,7,7,7,7,7,5,5,1,1,1,1,1] (.node [12,7,7,7,7,7,5,4,3,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,6,2,2,2,2,1] (.node [12,7,7,7,7,7,6,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,7,7,7,7,7,6,4,1,1,1,1,1] (.node [12,7,7,7,7,7,6,3,3,1,1,1] (.node [12,7,7,7,7,7,6,3,2,2,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,6,4,2,1,1,1] .empty .empty)))) + +def degreeTree62_329 : RowTree := (.node [12,8,6,6,6,5,5,4,4,2,2,1,1] (.node [12,7,7,7,7,7,7,4,1,1,1,1] (.node [12,7,7,7,7,7,7,2,2,2,1,1] (.node [12,7,7,7,7,7,7,2,2,1,1,1,1] (.node [12,7,7,7,7,7,7,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,7,7,7,7,7,7,3,2,1,1,1] (.node [12,7,7,7,7,7,7,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,6,6,5,5,5,5,5,2,1,1,1] (.node [12,8,6,6,5,5,5,5,4,2,2,1,1] (.node [12,8,6,5,5,5,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,8,6,6,5,5,5,5,5,2,2,1] .empty .empty))) (.node [12,8,6,6,6,6,4,4,4,2,2,1,1] (.node [12,8,6,6,6,5,5,5,4,2,2,1] (.node [12,8,6,6,6,5,5,5,4,2,1,1,1] (.node [12,8,6,6,6,5,5,5,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,6,6,6,5,5,5,5,2,1,1] (.node [12,8,6,6,6,5,5,5,5,1,1,1,1] .empty .empty) .empty)) (.node [12,8,6,6,6,6,5,4,4,2,2,1] (.node [12,8,6,6,6,6,5,4,4,2,1,1,1] (.node [12,8,6,6,6,6,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,6,6,6,6,5,5,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_330 : RowTree := (.node [12,7,7,7,7,7,6,5,1,1,1,1] degreeTree62_328 degreeTree62_329) + +def degreeTree62_331 : RowTree := (.node [12,7,7,7,7,7,4,4,2,2,2,1] degreeTree62_327 degreeTree62_330) + +def degreeTree62_332 : RowTree := (.node [12,7,7,7,7,5,5,4,4,2,1,1] degreeTree62_324 degreeTree62_331) + +def degreeTree62_333 : RowTree := (.node [12,8,6,6,6,6,6,4,4,2,1,1] (.node [12,8,6,6,6,6,6,3,3,2,2,1,1] (.node [12,8,6,6,6,6,5,5,4,2,1,1] (.node [12,8,6,6,6,6,5,5,4,1,1,1,1] (.node [12,8,6,6,6,6,5,5,3,2,2,1] .empty .empty) .empty) (.node [12,8,6,6,6,6,6,2,2,2,2,2,2] (.node [12,8,6,6,6,6,5,5,5,1,1,1] .empty .empty) .empty)) (.node [12,8,6,6,6,6,6,4,3,2,2,1] (.node [12,8,6,6,6,6,6,4,3,2,1,1,1] (.node [12,8,6,6,6,6,6,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,6,6,6,6,6,4,4,1,1,1,1] .empty .empty))) (.node [12,8,6,6,6,6,6,6,2,1,1,1,1] (.node [12,8,6,6,6,6,6,5,3,1,1,1,1] (.node [12,8,6,6,6,6,6,5,2,2,2,1] (.node [12,8,6,6,6,6,6,5,2,2,1,1,1] .empty .empty) .empty) (.node [12,8,6,6,6,6,6,5,4,1,1,1] (.node [12,8,6,6,6,6,6,5,3,2,1,1] .empty .empty) .empty)) (.node [12,8,7,5,5,5,5,5,4,2,2,1,1] (.node [12,8,6,6,6,6,6,6,3,1,1,1] (.node [12,8,6,6,6,6,6,6,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,5,5,5,5,5,5,2,1,1,1] .empty .empty)))) + +def degreeTree62_334 : RowTree := (.node [12,8,7,6,6,5,5,5,2,2,2,1,1] (.node [12,8,7,6,5,5,5,5,5,2,1,1] (.node [12,8,7,6,5,5,5,5,4,2,1,1,1] (.node [12,8,7,6,5,5,5,5,3,2,2,1,1] (.node [12,8,7,6,5,5,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,6,5,5,5,5,5,1,1,1,1] (.node [12,8,7,6,5,5,5,5,4,2,2,1] .empty .empty) .empty)) (.node [12,8,7,6,6,5,5,4,4,2,1,1,1] (.node [12,8,7,6,6,5,5,4,3,2,2,1,1] (.node [12,8,7,6,6,5,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,5,5,4,4,2,2,1] .empty .empty))) (.node [12,8,7,6,6,6,4,4,3,2,2,1,1] (.node [12,8,7,6,6,5,5,5,4,1,1,1,1] (.node [12,8,7,6,6,5,5,5,3,2,2,1] (.node [12,8,7,6,6,5,5,5,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,5,5,5,5,1,1,1] (.node [12,8,7,6,6,5,5,5,4,2,1,1] .empty .empty) .empty)) (.node [12,8,7,6,6,6,5,2,2,2,2,2,2] (.node [12,8,7,6,6,6,4,4,4,2,2,1] (.node [12,8,7,6,6,6,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,6,5,3,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_335 : RowTree := (.node [12,8,7,5,5,5,5,5,5,2,2,1] degreeTree62_333 degreeTree62_334) + +def degreeTree62_336 : RowTree := (.node [12,8,7,6,6,6,6,3,2,2,2,1,1] (.node [12,8,7,6,6,6,5,5,2,2,2,1] (.node [12,8,7,6,6,6,5,4,4,1,1,1,1] (.node [12,8,7,6,6,6,5,4,3,2,2,1] (.node [12,8,7,6,6,6,5,4,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,6,5,5,2,2,1,1,1] (.node [12,8,7,6,6,6,5,4,4,2,1,1] .empty .empty) .empty)) (.node [12,8,7,6,6,6,5,5,4,1,1,1] (.node [12,8,7,6,6,6,5,5,3,2,1,1] (.node [12,8,7,6,6,6,5,5,3,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,6,6,2,2,2,2,2,1] .empty .empty))) (.node [12,8,7,6,6,6,6,4,3,2,1,1] (.node [12,8,7,6,6,6,6,4,2,2,1,1,1] (.node [12,8,7,6,6,6,6,3,3,2,2,1] (.node [12,8,7,6,6,6,6,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,6,6,4,3,1,1,1,1] (.node [12,8,7,6,6,6,6,4,2,2,2,1] .empty .empty) .empty)) (.node [12,8,7,6,6,6,6,5,2,2,1,1] (.node [12,8,7,6,6,6,6,5,2,1,1,1,1] (.node [12,8,7,6,6,6,6,4,4,1,1,1] .empty .empty) .empty) (.node [12,8,7,6,6,6,6,5,3,1,1,1] .empty .empty)))) + +def degreeTree62_337 : RowTree := (.node [12,8,7,7,5,5,5,5,5,1,1,1] (.node [12,8,7,7,5,5,5,5,2,2,2,1,1] (.node [12,8,7,7,5,5,5,4,3,2,2,1,1] (.node [12,8,7,7,5,5,4,4,4,2,2,1,1] (.node [12,8,7,6,6,6,6,6,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,5,5,5,4,4,2,2,1] (.node [12,8,7,7,5,5,5,4,4,2,1,1,1] .empty .empty) .empty)) (.node [12,8,7,7,5,5,5,5,4,1,1,1,1] (.node [12,8,7,7,5,5,5,5,3,2,2,1] (.node [12,8,7,7,5,5,5,5,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,5,5,5,5,4,2,1,1] .empty .empty))) (.node [12,8,7,7,6,5,5,3,3,2,2,1,1] (.node [12,8,7,7,6,5,4,4,4,2,1,1,1] (.node [12,8,7,7,6,5,4,4,3,2,2,1,1] (.node [12,8,7,7,6,4,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,5,5,2,2,2,2,2,2] (.node [12,8,7,7,6,5,4,4,4,2,2,1] .empty .empty) .empty)) (.node [12,8,7,7,6,5,5,4,3,2,2,1] (.node [12,8,7,7,6,5,5,4,3,2,1,1,1] (.node [12,8,7,7,6,5,5,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,5,5,4,4,1,1,1,1] .empty .empty)))) + +def degreeTree62_338 : RowTree := (.node [12,8,7,6,6,6,6,6,1,1,1,1,1] degreeTree62_336 degreeTree62_337) + +def degreeTree62_339 : RowTree := (.node [12,8,7,6,6,6,5,4,2,2,2,1,1] degreeTree62_335 degreeTree62_338) + +def degreeTree62_340 : RowTree := (.node [12,8,7,7,6,6,4,4,4,1,1,1,1] (.node [12,8,7,7,6,6,4,2,2,2,2,2,2] (.node [12,8,7,7,6,5,5,5,3,1,1,1,1] (.node [12,8,7,7,6,5,5,5,2,2,2,1] (.node [12,8,7,7,6,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,5,5,5,4,1,1,1] (.node [12,8,7,7,6,5,5,5,3,2,1,1] .empty .empty) .empty)) (.node [12,8,7,7,6,6,4,4,3,2,1,1,1] (.node [12,8,7,7,6,6,4,4,2,2,2,1,1] (.node [12,8,7,7,6,6,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,6,4,4,3,2,2,1] .empty .empty))) (.node [12,8,7,7,6,6,5,4,2,2,1,1,1] (.node [12,8,7,7,6,6,5,3,2,2,2,1,1] (.node [12,8,7,7,6,6,5,2,2,2,2,2,1] (.node [12,8,7,7,6,6,4,4,4,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,6,5,3,3,2,2,1] (.node [12,8,7,7,6,6,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,8,7,7,6,6,5,4,3,2,1,1] (.node [12,8,7,7,6,6,5,4,3,1,1,1,1] (.node [12,8,7,7,6,6,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,8,7,7,6,6,5,4,4,1,1,1] .empty .empty)))) + +def degreeTree62_341 : RowTree := (.node [12,8,7,7,6,6,6,4,3,1,1,1] (.node [12,8,7,7,6,6,6,3,2,2,2,1] (.node [12,8,7,7,6,6,6,2,2,2,2,1,1] (.node [12,8,7,7,6,6,5,5,3,1,1,1] (.node [12,8,7,7,6,6,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,6,6,3,2,2,1,1,1] (.node [12,8,7,7,6,6,6,2,2,2,2,2] .empty .empty) .empty)) (.node [12,8,7,7,6,6,6,4,2,1,1,1,1] (.node [12,8,7,7,6,6,6,3,3,2,1,1] (.node [12,8,7,7,6,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,6,6,6,4,2,2,1,1] .empty .empty))) (.node [12,8,7,7,7,4,4,4,4,2,2,1] (.node [12,8,7,7,6,6,6,6,1,1,1,1] (.node [12,8,7,7,6,6,6,5,2,1,1,1] (.node [12,8,7,7,6,6,6,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,4,4,4,4,2,1,1,1] (.node [12,8,7,7,7,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [12,8,7,7,7,5,4,4,2,2,2,1,1] (.node [12,8,7,7,7,5,4,3,3,2,2,1,1] (.node [12,8,7,7,7,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,8,7,7,7,5,4,4,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_342 : RowTree := (.node [12,8,7,7,6,6,5,5,2,1,1,1,1] degreeTree62_340 degreeTree62_341) + +def degreeTree62_343 : RowTree := (.node [12,8,7,7,7,5,5,4,4,1,1,1] (.node [12,8,7,7,7,5,5,3,3,2,2,1] (.node [12,8,7,7,7,5,5,2,2,2,2,2,1] (.node [12,8,7,7,7,5,4,4,4,2,1,1] (.node [12,8,7,7,7,5,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,5,5,3,3,2,1,1,1] (.node [12,8,7,7,7,5,5,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,8,7,7,7,5,5,4,3,1,1,1,1] (.node [12,8,7,7,7,5,5,4,2,2,2,1] (.node [12,8,7,7,7,5,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,5,5,4,3,2,1,1] .empty .empty))) (.node [12,8,7,7,7,6,4,2,2,2,2,2,1] (.node [12,8,7,7,7,5,5,5,3,1,1,1] (.node [12,8,7,7,7,5,5,5,2,2,1,1] (.node [12,8,7,7,7,5,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,6,3,3,3,2,2,1,1] (.node [12,8,7,7,7,6,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,8,7,7,7,6,4,3,3,2,2,1] (.node [12,8,7,7,7,6,4,3,3,2,1,1,1] (.node [12,8,7,7,7,6,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,6,4,4,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_344 : RowTree := (.node [12,8,7,7,7,6,5,4,2,2,1,1] (.node [12,8,7,7,7,6,5,3,2,2,1,1,1] (.node [12,8,7,7,7,6,4,4,4,1,1,1] (.node [12,8,7,7,7,6,4,4,3,2,1,1] (.node [12,8,7,7,7,6,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,6,5,2,2,2,2,2] (.node [12,8,7,7,7,6,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,8,7,7,7,6,5,3,3,2,1,1] (.node [12,8,7,7,7,6,5,3,3,1,1,1,1] (.node [12,8,7,7,7,6,5,3,2,2,2,1] .empty .empty) .empty) (.node [12,8,7,7,7,6,5,4,2,1,1,1,1] .empty .empty))) (.node [12,8,7,7,7,6,6,2,2,2,2,1] (.node [12,8,7,7,7,6,5,5,2,1,1,1] (.node [12,8,7,7,7,6,5,5,1,1,1,1,1] (.node [12,8,7,7,7,6,5,4,3,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,6,6,2,2,2,1,1,1] .empty .empty)) (.node [12,8,7,7,7,6,6,3,3,1,1,1] (.node [12,8,7,7,7,6,6,3,2,2,1,1] (.node [12,8,7,7,7,6,6,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,6,6,4,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_345 : RowTree := (.node [12,8,7,7,7,6,4,4,2,2,2,1] degreeTree62_343 degreeTree62_344) + +def degreeTree62_346 : RowTree := (.node [12,8,7,7,7,5,4,4,3,2,2,1] degreeTree62_342 degreeTree62_345) + +def degreeTree62_347 : RowTree := (.node [12,8,7,7,6,5,5,4,4,2,1,1] degreeTree62_339 degreeTree62_346) + +def degreeTree62_348 : RowTree := (.node [12,8,6,6,6,6,5,5,3,2,1,1,1] degreeTree62_332 degreeTree62_347) + +def degreeTree62_349 : RowTree := (.node [12,8,7,7,7,7,4,3,3,1,1,1,1] (.node [12,8,7,7,7,7,3,3,3,2,2,1] (.node [12,8,7,7,7,7,3,2,2,2,2,2,1] (.node [12,8,7,7,7,7,2,2,2,2,2,2,2] (.node [12,8,7,7,7,6,6,5,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,7,3,3,3,2,1,1,1] (.node [12,8,7,7,7,7,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,8,7,7,7,7,4,3,2,2,1,1,1] (.node [12,8,7,7,7,7,4,2,2,2,2,2] (.node [12,8,7,7,7,7,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,7,4,3,2,2,2,1] .empty .empty))) (.node [12,8,7,7,7,7,5,2,2,2,2,1] (.node [12,8,7,7,7,7,4,4,2,2,1,1] (.node [12,8,7,7,7,7,4,4,2,1,1,1,1] (.node [12,8,7,7,7,7,4,3,3,2,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,7,5,2,2,2,1,1,1] (.node [12,8,7,7,7,7,4,4,3,1,1,1] .empty .empty) .empty)) (.node [12,8,7,7,7,7,5,3,3,1,1,1] (.node [12,8,7,7,7,7,5,3,2,2,1,1] (.node [12,8,7,7,7,7,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,7,5,4,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_350 : RowTree := (.node [12,8,7,7,7,7,7,3,1,1,1,1] (.node [12,8,7,7,7,7,6,3,2,1,1,1] (.node [12,8,7,7,7,7,6,2,2,1,1,1,1] (.node [12,8,7,7,7,7,6,2,1,1,1,1,1,1] (.node [12,8,7,7,7,7,5,5,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,7,6,3,1,1,1,1,1] (.node [12,8,7,7,7,7,6,2,2,2,1,1] .empty .empty) .empty)) (.node [12,8,7,7,7,7,7,2,1,1,1,1,1] (.node [12,8,7,7,7,7,7,1,1,1,1,1,1,1] (.node [12,8,7,7,7,7,6,4,1,1,1,1] .empty .empty) .empty) (.node [12,8,7,7,7,7,7,2,2,1,1,1] .empty .empty))) (.node [12,8,8,5,5,5,5,5,5,2,1,1] (.node [12,8,8,5,5,5,5,5,4,2,1,1,1] (.node [12,8,8,5,5,5,5,5,3,2,2,1,1] (.node [12,8,8,5,5,5,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,5,5,5,5,5,5,1,1,1,1] (.node [12,8,8,5,5,5,5,5,4,2,2,1] .empty .empty) .empty)) (.node [12,8,8,6,5,5,5,4,4,2,1,1,1] (.node [12,8,8,6,5,5,5,4,3,2,2,1,1] (.node [12,8,8,6,5,5,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,6,5,5,5,4,4,2,2,1] .empty .empty)))) + +def degreeTree62_351 : RowTree := (.node [12,8,7,7,7,7,5,4,2,1,1,1] degreeTree62_349 degreeTree62_350) + +def degreeTree62_352 : RowTree := (.node [12,8,8,6,6,5,5,3,3,2,2,1,1] (.node [12,8,8,6,6,4,4,4,4,2,2,1,1] (.node [12,8,8,6,5,5,5,5,4,1,1,1,1] (.node [12,8,8,6,5,5,5,5,3,2,2,1] (.node [12,8,8,6,5,5,5,5,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,6,5,5,5,5,5,1,1,1] (.node [12,8,8,6,5,5,5,5,4,2,1,1] .empty .empty) .empty)) (.node [12,8,8,6,6,5,4,4,4,2,2,1] (.node [12,8,8,6,6,5,4,4,4,2,1,1,1] (.node [12,8,8,6,6,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,6,6,5,5,2,2,2,2,2,2] .empty .empty))) (.node [12,8,8,6,6,5,5,5,2,2,1,1,1] (.node [12,8,8,6,6,5,5,4,3,2,2,1] (.node [12,8,8,6,6,5,5,4,3,2,1,1,1] (.node [12,8,8,6,6,5,5,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,6,6,5,5,4,4,2,1,1] (.node [12,8,8,6,6,5,5,4,4,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,6,6,5,5,5,3,2,1,1] (.node [12,8,8,6,6,5,5,5,3,1,1,1,1] (.node [12,8,8,6,6,5,5,5,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,6,6,5,5,5,4,1,1,1] .empty .empty)))) + +def degreeTree62_353 : RowTree := (.node [12,8,8,6,6,6,5,4,2,2,1,1,1] (.node [12,8,8,6,6,6,4,4,4,2,1,1] (.node [12,8,8,6,6,6,4,4,3,2,1,1,1] (.node [12,8,8,6,6,6,4,4,2,2,2,1,1] (.node [12,8,8,6,6,6,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,6,6,6,4,4,4,1,1,1,1] (.node [12,8,8,6,6,6,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,8,8,6,6,6,5,3,3,2,1,1,1] (.node [12,8,8,6,6,6,5,3,2,2,2,1,1] (.node [12,8,8,6,6,6,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,6,6,6,5,3,3,2,2,1] .empty .empty))) (.node [12,8,8,6,6,6,5,5,2,2,1,1] (.node [12,8,8,6,6,6,5,4,3,2,1,1] (.node [12,8,8,6,6,6,5,4,3,1,1,1,1] (.node [12,8,8,6,6,6,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,6,6,6,5,5,2,1,1,1,1] (.node [12,8,8,6,6,6,5,4,4,1,1,1] .empty .empty) .empty)) (.node [12,8,8,6,6,6,6,2,2,2,2,2] (.node [12,8,8,6,6,6,6,2,2,2,2,1,1] (.node [12,8,8,6,6,6,5,5,3,1,1,1] .empty .empty) .empty) (.node [12,8,8,6,6,6,6,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_354 : RowTree := (.node [12,8,8,6,6,6,4,2,2,2,2,2,2] degreeTree62_352 degreeTree62_353) + +def degreeTree62_355 : RowTree := (.node [12,8,8,6,5,5,5,5,2,2,2,1,1] degreeTree62_351 degreeTree62_354) + +def degreeTree62_356 : RowTree := (.node [12,8,8,7,5,5,4,4,4,2,1,1,1] (.node [12,8,8,6,6,6,6,5,1,1,1,1,1] (.node [12,8,8,6,6,6,6,4,2,1,1,1,1] (.node [12,8,8,6,6,6,6,3,3,2,1,1] (.node [12,8,8,6,6,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,6,6,6,6,4,3,1,1,1] (.node [12,8,8,6,6,6,6,4,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,7,5,4,4,4,4,2,2,1,1] (.node [12,8,8,6,6,6,6,6,1,1,1,1] (.node [12,8,8,6,6,6,6,5,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,5,5,4,4,3,2,2,1,1] .empty .empty))) (.node [12,8,8,7,5,5,5,4,3,2,2,1] (.node [12,8,8,7,5,5,5,3,3,2,2,1,1] (.node [12,8,8,7,5,5,5,2,2,2,2,2,2] (.node [12,8,8,7,5,5,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,8,8,7,5,5,5,4,3,2,1,1,1] (.node [12,8,8,7,5,5,5,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,7,5,5,5,5,2,2,1,1,1] (.node [12,8,8,7,5,5,5,4,4,2,1,1] (.node [12,8,8,7,5,5,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,5,5,5,5,2,2,2,1] .empty .empty)))) + +def degreeTree62_357 : RowTree := (.node [12,8,8,7,6,5,4,4,4,1,1,1,1] (.node [12,8,8,7,6,5,4,2,2,2,2,2,2] (.node [12,8,8,7,6,4,4,4,3,2,2,1,1] (.node [12,8,8,7,5,5,5,5,4,1,1,1] (.node [12,8,8,7,5,5,5,5,3,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,4,4,4,4,2,2,1] (.node [12,8,8,7,6,4,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,6,5,4,4,3,2,1,1,1] (.node [12,8,8,7,6,5,4,4,2,2,2,1,1] (.node [12,8,8,7,6,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,5,4,4,3,2,2,1] .empty .empty))) (.node [12,8,8,7,6,5,5,4,2,2,1,1,1] (.node [12,8,8,7,6,5,5,3,2,2,2,1,1] (.node [12,8,8,7,6,5,5,2,2,2,2,2,1] (.node [12,8,8,7,6,5,4,4,4,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,5,5,3,3,2,2,1] (.node [12,8,8,7,6,5,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,6,5,5,4,3,2,1,1] (.node [12,8,8,7,6,5,5,4,3,1,1,1,1] (.node [12,8,8,7,6,5,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,7,6,5,5,4,4,1,1,1] .empty .empty)))) + +def degreeTree62_358 : RowTree := (.node [12,8,8,7,5,5,5,5,3,1,1,1,1] degreeTree62_356 degreeTree62_357) + +def degreeTree62_359 : RowTree := (.node [12,8,8,7,6,6,4,4,3,1,1,1,1] (.node [12,8,8,7,6,6,4,3,2,2,2,1,1] (.node [12,8,8,7,6,6,3,2,2,2,2,2,2] (.node [12,8,8,7,6,5,5,5,3,1,1,1] (.node [12,8,8,7,6,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,6,4,2,2,2,2,2,1] (.node [12,8,8,7,6,6,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,7,6,6,4,4,2,2,1,1,1] (.node [12,8,8,7,6,6,4,3,3,2,2,1] (.node [12,8,8,7,6,6,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,6,4,4,2,2,2,1] .empty .empty))) (.node [12,8,8,7,6,6,5,3,2,2,2,1] (.node [12,8,8,7,6,6,5,2,2,2,2,1,1] (.node [12,8,8,7,6,6,4,4,4,1,1,1] (.node [12,8,8,7,6,6,4,4,3,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,6,5,3,2,2,1,1,1] (.node [12,8,8,7,6,6,5,2,2,2,2,2] .empty .empty) .empty)) (.node [12,8,8,7,6,6,5,4,2,1,1,1,1] (.node [12,8,8,7,6,6,5,3,3,2,1,1] (.node [12,8,8,7,6,6,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,6,5,4,2,2,1,1] .empty .empty)))) + +def degreeTree62_360 : RowTree := (.node [12,8,8,7,7,4,4,2,2,2,2,2,2] (.node [12,8,8,7,6,6,6,3,2,2,1,1] (.node [12,8,8,7,6,6,6,2,2,2,1,1,1] (.node [12,8,8,7,6,6,5,5,2,1,1,1] (.node [12,8,8,7,6,6,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,6,6,3,2,1,1,1,1] (.node [12,8,8,7,6,6,6,2,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,7,6,6,6,4,2,1,1,1] (.node [12,8,8,7,6,6,6,4,1,1,1,1,1] (.node [12,8,8,7,6,6,6,3,3,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,6,6,6,5,1,1,1,1] .empty .empty))) (.node [12,8,8,7,7,4,4,4,4,2,1,1] (.node [12,8,8,7,7,4,4,4,3,2,1,1,1] (.node [12,8,8,7,7,4,4,4,2,2,2,1,1] (.node [12,8,8,7,7,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,4,4,4,4,1,1,1,1] (.node [12,8,8,7,7,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,8,8,7,7,5,4,2,2,2,2,2,1] (.node [12,8,8,7,7,5,3,3,3,2,2,1,1] (.node [12,8,8,7,7,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,8,8,7,7,5,4,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_361 : RowTree := (.node [12,8,8,7,6,6,5,4,3,1,1,1] degreeTree62_359 degreeTree62_360) + +def degreeTree62_362 : RowTree := (.node [12,8,8,7,6,5,5,5,2,1,1,1,1] degreeTree62_358 degreeTree62_361) + +def degreeTree62_363 : RowTree := (.node [12,8,8,6,6,6,6,3,2,2,2,1] degreeTree62_355 degreeTree62_362) + +def degreeTree62_364 : RowTree := (.node [12,8,8,7,7,5,5,3,3,1,1,1,1] (.node [12,8,8,7,7,5,4,4,4,1,1,1] (.node [12,8,8,7,7,5,4,4,2,2,2,1] (.node [12,8,8,7,7,5,4,4,2,2,1,1,1] (.node [12,8,8,7,7,5,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,8,8,7,7,5,4,4,3,2,1,1] (.node [12,8,8,7,7,5,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,7,5,5,3,2,2,1,1,1] (.node [12,8,8,7,7,5,5,2,2,2,2,2] (.node [12,8,8,7,7,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,5,5,3,2,2,2,1] .empty .empty))) (.node [12,8,8,7,7,5,5,5,2,1,1,1] (.node [12,8,8,7,7,5,5,4,2,2,1,1] (.node [12,8,8,7,7,5,5,4,2,1,1,1,1] (.node [12,8,8,7,7,5,5,3,3,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,5,5,5,1,1,1,1,1] (.node [12,8,8,7,7,5,5,4,3,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,7,6,3,3,2,2,2,1,1] (.node [12,8,8,7,7,6,3,2,2,2,2,2,1] (.node [12,8,8,7,7,6,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,8,8,7,7,6,3,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_365 : RowTree := (.node [12,8,8,7,7,6,5,2,2,2,2,1] (.node [12,8,8,7,7,6,4,3,3,2,1,1] (.node [12,8,8,7,7,6,4,3,2,2,1,1,1] (.node [12,8,8,7,7,6,4,2,2,2,2,2] (.node [12,8,8,7,7,6,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,6,4,3,3,1,1,1,1] (.node [12,8,8,7,7,6,4,3,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,7,7,6,4,4,3,1,1,1] (.node [12,8,8,7,7,6,4,4,2,2,1,1] (.node [12,8,8,7,7,6,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,6,5,2,2,2,1,1,1] .empty .empty))) (.node [12,8,8,7,7,6,5,5,1,1,1,1] (.node [12,8,8,7,7,6,5,3,3,1,1,1] (.node [12,8,8,7,7,6,5,3,2,2,1,1] (.node [12,8,8,7,7,6,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,6,5,4,2,1,1,1] (.node [12,8,8,7,7,6,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,7,6,6,2,2,2,1,1] (.node [12,8,8,7,7,6,6,2,2,1,1,1,1] (.node [12,8,8,7,7,6,6,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,6,6,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_366 : RowTree := (.node [12,8,8,7,7,6,3,3,3,2,2,1] degreeTree62_364 degreeTree62_365) + +def degreeTree62_367 : RowTree := (.node [12,8,8,7,7,7,3,3,3,2,1,1] (.node [12,8,8,7,7,7,3,2,2,2,2,2] (.node [12,8,8,7,7,7,2,2,2,2,2,2,1] (.node [12,8,8,7,7,7,2,2,2,2,2,1,1,1] (.node [12,8,8,7,7,6,6,4,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,7,3,2,2,2,2,1,1] (.node [12,8,8,7,7,7,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,7,7,3,3,2,2,2,1] (.node [12,8,8,7,7,7,3,3,2,2,1,1,1] (.node [12,8,8,7,7,7,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,7,3,3,3,1,1,1,1] .empty .empty))) (.node [12,8,8,7,7,7,4,3,2,2,1,1] (.node [12,8,8,7,7,7,4,2,2,2,2,1] (.node [12,8,8,7,7,7,4,2,2,2,1,1,1] (.node [12,8,8,7,7,7,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,7,4,3,2,1,1,1,1] (.node [12,8,8,7,7,7,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,7,7,4,4,2,1,1,1] (.node [12,8,8,7,7,7,4,4,1,1,1,1,1] (.node [12,8,8,7,7,7,4,3,3,1,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,7,5,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_368 : RowTree := (.node [12,8,8,8,5,4,4,4,3,2,2,1,1] (.node [12,8,8,7,7,7,6,2,1,1,1,1,1] (.node [12,8,8,7,7,7,5,3,2,1,1,1] (.node [12,8,8,7,7,7,5,3,1,1,1,1,1] (.node [12,8,8,7,7,7,5,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,7,7,7,6,1,1,1,1,1,1,1] (.node [12,8,8,7,7,7,5,4,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,7,7,7,7,1,1,1,1,1,1] (.node [12,8,8,7,7,7,6,3,1,1,1,1] (.node [12,8,8,7,7,7,6,2,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,4,4,4,4,4,2,2,1,1] .empty .empty))) (.node [12,8,8,8,5,5,4,4,3,2,1,1,1] (.node [12,8,8,8,5,5,4,2,2,2,2,2,2] (.node [12,8,8,8,5,4,4,4,4,2,2,1] (.node [12,8,8,8,5,4,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,5,5,4,4,2,2,2,1,1] (.node [12,8,8,8,5,5,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,8,5,5,4,4,4,2,1,1] (.node [12,8,8,8,5,5,4,4,4,1,1,1,1] (.node [12,8,8,8,5,5,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,5,5,5,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_369 : RowTree := (.node [12,8,8,7,7,7,5,2,2,1,1,1,1] degreeTree62_367 degreeTree62_368) + +def degreeTree62_370 : RowTree := (.node [12,8,8,7,7,6,6,3,2,1,1,1] degreeTree62_366 degreeTree62_369) + +def degreeTree62_371 : RowTree := (.node [12,8,8,8,6,4,4,2,2,2,2,2,2] (.node [12,8,8,8,5,5,5,4,3,2,1,1] (.node [12,8,8,8,5,5,5,4,2,2,1,1,1] (.node [12,8,8,8,5,5,5,3,3,2,2,1] (.node [12,8,8,8,5,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,5,5,5,4,3,1,1,1,1] (.node [12,8,8,8,5,5,5,4,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,8,5,5,5,5,2,2,1,1] (.node [12,8,8,8,5,5,5,5,2,1,1,1,1] (.node [12,8,8,8,5,5,5,4,4,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,5,5,5,5,3,1,1,1] .empty .empty))) (.node [12,8,8,8,6,4,4,4,4,2,1,1] (.node [12,8,8,8,6,4,4,4,3,2,1,1,1] (.node [12,8,8,8,6,4,4,4,2,2,2,1,1] (.node [12,8,8,8,6,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,4,4,4,4,1,1,1,1] (.node [12,8,8,8,6,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,8,8,8,6,5,4,2,2,2,2,2,1] (.node [12,8,8,8,6,5,3,3,3,2,2,1,1] (.node [12,8,8,8,6,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,8,8,8,6,5,4,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_372 : RowTree := (.node [12,8,8,8,6,5,5,3,3,1,1,1,1] (.node [12,8,8,8,6,5,4,4,4,1,1,1] (.node [12,8,8,8,6,5,4,4,2,2,2,1] (.node [12,8,8,8,6,5,4,4,2,2,1,1,1] (.node [12,8,8,8,6,5,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,6,5,4,4,3,2,1,1] (.node [12,8,8,8,6,5,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,6,5,5,3,2,2,1,1,1] (.node [12,8,8,8,6,5,5,2,2,2,2,2] (.node [12,8,8,8,6,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,5,5,3,2,2,2,1] .empty .empty))) (.node [12,8,8,8,6,5,5,5,2,1,1,1] (.node [12,8,8,8,6,5,5,4,2,2,1,1] (.node [12,8,8,8,6,5,5,4,2,1,1,1,1] (.node [12,8,8,8,6,5,5,3,3,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,5,5,5,1,1,1,1,1] (.node [12,8,8,8,6,5,5,4,3,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,6,6,3,3,2,2,2,1,1] (.node [12,8,8,8,6,6,3,2,2,2,2,2,1] (.node [12,8,8,8,6,6,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,8,8,8,6,6,3,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_373 : RowTree := (.node [12,8,8,8,6,5,4,3,3,2,1,1,1] degreeTree62_371 degreeTree62_372) + +def degreeTree62_374 : RowTree := (.node [12,8,8,8,6,6,5,2,2,2,2,1] (.node [12,8,8,8,6,6,4,3,3,2,1,1] (.node [12,8,8,8,6,6,4,3,2,2,1,1,1] (.node [12,8,8,8,6,6,4,2,2,2,2,2] (.node [12,8,8,8,6,6,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,6,4,3,3,1,1,1,1] (.node [12,8,8,8,6,6,4,3,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,8,6,6,4,4,3,1,1,1] (.node [12,8,8,8,6,6,4,4,2,2,1,1] (.node [12,8,8,8,6,6,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,6,5,2,2,2,1,1,1] .empty .empty))) (.node [12,8,8,8,6,6,5,5,1,1,1,1] (.node [12,8,8,8,6,6,5,3,3,1,1,1] (.node [12,8,8,8,6,6,5,3,2,2,1,1] (.node [12,8,8,8,6,6,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,6,5,4,2,1,1,1] (.node [12,8,8,8,6,6,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,6,6,6,2,2,2,1,1] (.node [12,8,8,8,6,6,6,2,2,1,1,1,1] (.node [12,8,8,8,6,6,6,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,6,6,6,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_375 : RowTree := (.node [12,8,8,8,7,4,4,4,3,2,1,1] (.node [12,8,8,8,7,4,4,3,3,2,1,1,1] (.node [12,8,8,8,7,4,3,3,3,2,2,1,1] (.node [12,8,8,8,7,4,3,2,2,2,2,2,2] (.node [12,8,8,8,6,6,6,4,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,4,4,3,2,2,2,1,1] (.node [12,8,8,8,7,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,8,7,4,4,4,2,2,2,1] (.node [12,8,8,8,7,4,4,4,2,2,1,1,1] (.node [12,8,8,8,7,4,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,7,4,4,4,3,1,1,1,1] .empty .empty))) (.node [12,8,8,8,7,5,3,3,3,2,1,1,1] (.node [12,8,8,8,7,5,3,2,2,2,2,2,1] (.node [12,8,8,8,7,5,2,2,2,2,2,2,2] (.node [12,8,8,8,7,4,4,4,4,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,5,3,3,2,2,2,1,1] .empty .empty)) (.node [12,8,8,8,7,5,4,2,2,2,2,2] (.node [12,8,8,8,7,5,4,2,2,2,2,1,1] (.node [12,8,8,8,7,5,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,7,5,4,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_376 : RowTree := (.node [12,8,8,8,6,6,6,3,2,1,1,1] degreeTree62_374 degreeTree62_375) + +def degreeTree62_377 : RowTree := (.node [12,8,8,8,6,6,3,3,3,2,2,1] degreeTree62_373 degreeTree62_376) + +def degreeTree62_378 : RowTree := (.node [12,8,8,8,5,5,5,3,2,2,2,1,1] degreeTree62_370 degreeTree62_377) + +def degreeTree62_379 : RowTree := (.node [12,8,8,7,7,5,4,3,3,2,1,1,1] degreeTree62_363 degreeTree62_378) + +def degreeTree62_380 : RowTree := (.node [12,8,7,7,7,6,6,4,2,1,1,1] degreeTree62_348 degreeTree62_379) + +def degreeTree62_381 : RowTree := (.node [12,7,7,6,5,5,5,5,5,2,1,1,1] degreeTree62_317 degreeTree62_380) + +def degreeTree62_382 : RowTree := (.node [12,8,8,8,7,5,5,4,1,1,1,1,1] (.node [12,8,8,8,7,5,5,2,2,2,1,1,1] (.node [12,8,8,8,7,5,4,4,2,1,1,1,1] (.node [12,8,8,8,7,5,4,3,3,2,1,1] (.node [12,8,8,8,7,5,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,5,4,4,3,1,1,1] (.node [12,8,8,8,7,5,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,8,7,5,5,3,2,2,1,1] (.node [12,8,8,8,7,5,5,3,2,1,1,1,1] (.node [12,8,8,8,7,5,5,2,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,7,5,5,3,3,1,1,1] .empty .empty))) (.node [12,8,8,8,7,6,3,2,2,2,2,1,1] (.node [12,8,8,8,7,6,2,2,2,2,2,1,1,1] (.node [12,8,8,8,7,5,5,5,1,1,1,1] (.node [12,8,8,8,7,5,5,4,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,6,3,2,2,2,1,1,1,1] (.node [12,8,8,8,7,6,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,8,7,6,3,3,2,2,1,1,1] (.node [12,8,8,8,7,6,3,3,2,1,1,1,1,1] (.node [12,8,8,8,7,6,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,8,8,8,7,6,3,3,2,2,2,1] .empty .empty)))) + +def degreeTree62_383 : RowTree := (.node [12,8,8,8,7,6,5,2,1,1,1,1,1,1] (.node [12,8,8,8,7,6,4,3,2,1,1,1,1] (.node [12,8,8,8,7,6,4,2,2,2,1,1,1] (.node [12,8,8,8,7,6,4,2,2,1,1,1,1,1] (.node [12,8,8,8,7,6,3,3,3,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,6,4,3,1,1,1,1,1,1] (.node [12,8,8,8,7,6,4,2,2,2,2,1] .empty .empty) .empty)) (.node [12,8,8,8,7,6,4,4,1,1,1,1,1] (.node [12,8,8,8,7,6,4,3,3,1,1,1] (.node [12,8,8,8,7,6,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,6,4,4,2,1,1,1] .empty .empty))) (.node [12,8,8,8,7,6,6,1,1,1,1,1,1,1] (.node [12,8,8,8,7,6,5,3,1,1,1,1,1] (.node [12,8,8,8,7,6,5,2,2,2,1,1] (.node [12,8,8,8,7,6,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,6,5,4,1,1,1,1] (.node [12,8,8,8,7,6,5,3,2,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,7,7,2,2,2,2,1,1,1,1] (.node [12,8,8,8,7,6,6,2,2,1,1,1] (.node [12,8,8,8,7,6,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,7,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_384 : RowTree := (.node [12,8,8,8,7,6,3,3,3,1,1,1,1] degreeTree62_382 degreeTree62_383) + +def degreeTree62_385 : RowTree := (.node [12,8,8,8,7,7,4,3,1,1,1,1,1] (.node [12,8,8,8,7,7,3,3,2,2,1,1] (.node [12,8,8,8,7,7,3,2,2,2,2,1] (.node [12,8,8,8,7,7,3,2,2,2,1,1,1] (.node [12,8,8,8,7,7,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,7,3,3,2,1,1,1,1] (.node [12,8,8,8,7,7,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,7,7,4,2,2,1,1,1,1] (.node [12,8,8,8,7,7,4,2,1,1,1,1,1,1] (.node [12,8,8,8,7,7,3,3,3,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,7,4,2,2,2,1,1] .empty .empty))) (.node [12,8,8,8,8,3,3,2,2,2,2,2,2] (.node [12,8,8,8,7,7,5,2,1,1,1,1,1] (.node [12,8,8,8,7,7,5,1,1,1,1,1,1,1] (.node [12,8,8,8,7,7,4,3,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,7,7,6,1,1,1,1,1,1] (.node [12,8,8,8,7,7,5,2,2,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,4,3,2,2,2,2,1,1,1] (.node [12,8,8,8,8,4,2,2,2,2,2,2,2] (.node [12,8,8,8,8,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,4,3,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_386 : RowTree := (.node [12,8,8,8,8,4,4,3,3,2,1,1] (.node [12,8,8,8,8,4,4,2,2,2,2,2] (.node [12,8,8,8,8,4,3,3,3,2,2,1] (.node [12,8,8,8,8,4,3,3,3,2,1,1,1] (.node [12,8,8,8,8,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,4,4,2,2,2,2,1,1] (.node [12,8,8,8,8,4,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,4,4,3,2,2,2,1] (.node [12,8,8,8,8,4,4,3,2,2,1,1,1] (.node [12,8,8,8,8,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,4,4,3,3,1,1,1,1] .empty .empty))) (.node [12,8,8,8,8,5,2,2,2,2,2,2,1] (.node [12,8,8,8,8,4,4,4,2,2,1,1] (.node [12,8,8,8,8,4,4,4,2,1,1,1,1] (.node [12,8,8,8,8,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,5,2,2,2,2,2,1,1,1] (.node [12,8,8,8,8,4,4,4,3,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,5,3,2,2,2,2,2] (.node [12,8,8,8,8,5,3,2,2,2,2,1,1] (.node [12,8,8,8,8,5,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,5,3,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_387 : RowTree := (.node [12,8,8,8,8,4,3,3,2,2,2,1,1] degreeTree62_385 degreeTree62_386) + +def degreeTree62_388 : RowTree := (.node [12,8,8,8,7,7,2,2,2,2,2,2] degreeTree62_384 degreeTree62_387) + +def degreeTree62_389 : RowTree := (.node [12,8,8,8,8,5,4,4,1,1,1,1,1] (.node [12,8,8,8,8,5,4,2,2,2,2,1] (.node [12,8,8,8,8,5,3,3,3,2,1,1] (.node [12,8,8,8,8,5,3,3,3,1,1,1,1] (.node [12,8,8,8,8,5,3,3,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,8,5,4,2,2,2,1,1,1] (.node [12,8,8,8,8,5,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,5,4,3,2,2,1,1] (.node [12,8,8,8,8,5,4,3,2,1,1,1,1] (.node [12,8,8,8,8,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,5,4,3,3,1,1,1] .empty .empty))) (.node [12,8,8,8,8,5,5,3,2,1,1,1] (.node [12,8,8,8,8,5,5,2,2,1,1,1,1] (.node [12,8,8,8,8,5,5,2,1,1,1,1,1,1] (.node [12,8,8,8,8,5,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,5,5,3,1,1,1,1,1] (.node [12,8,8,8,8,5,5,2,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,6,2,2,2,2,2,2] (.node [12,8,8,8,8,6,2,2,2,2,2,1,1] (.node [12,8,8,8,8,6,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,6,3,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_390 : RowTree := (.node [12,8,8,8,8,6,5,1,1,1,1,1,1,1] (.node [12,8,8,8,8,6,4,2,1,1,1,1,1,1] (.node [12,8,8,8,8,6,3,3,2,1,1,1,1] (.node [12,8,8,8,8,6,3,3,1,1,1,1,1,1] (.node [12,8,8,8,8,6,3,2,2,2,2,1] .empty .empty) .empty) (.node [12,8,8,8,8,6,3,3,3,1,1,1] (.node [12,8,8,8,8,6,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,6,4,3,1,1,1,1,1] (.node [12,8,8,8,8,6,4,2,2,2,1,1] (.node [12,8,8,8,8,6,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,6,4,3,2,1,1,1] .empty .empty))) (.node [12,8,8,8,8,7,2,2,2,2,2,1] (.node [12,8,8,8,8,6,6,1,1,1,1,1,1] (.node [12,8,8,8,8,6,5,2,2,1,1,1] (.node [12,8,8,8,8,6,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,7,2,2,2,2,1,1,1] (.node [12,8,8,8,8,7,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,7,3,2,2,2,1,1] (.node [12,8,8,8,8,7,3,2,2,1,1,1,1] (.node [12,8,8,8,8,7,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,7,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_391 : RowTree := (.node [12,8,8,8,8,6,3,2,2,2,1,1,1] degreeTree62_389 degreeTree62_390) + +def degreeTree62_392 : RowTree := (.node [12,8,8,8,8,8,4,1,1,1,1,1,1] (.node [12,8,8,8,8,8,2,2,2,1,1,1,1] (.node [12,8,8,8,8,7,4,2,2,1,1,1] (.node [12,8,8,8,8,7,4,2,1,1,1,1,1] (.node [12,8,8,8,8,7,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,8,2,2,1,1,1,1,1,1] (.node [12,8,8,8,8,7,5,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,8,8,8,8,8,3,2,1,1,1,1,1] (.node [12,8,8,8,8,8,3,1,1,1,1,1,1,1] (.node [12,8,8,8,8,8,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,8,8,8,8,8,3,2,2,1,1,1] .empty .empty))) (.node [12,9,6,6,5,5,5,5,3,2,2,1,1] (.node [12,9,6,5,5,5,5,5,5,2,1,1,1] (.node [12,9,6,5,5,5,5,5,4,2,2,1,1] (.node [12,9,5,5,5,5,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,9,6,6,5,5,5,4,4,2,2,1,1] (.node [12,9,6,5,5,5,5,5,5,2,2,1] .empty .empty) .empty)) (.node [12,9,6,6,5,5,5,5,5,1,1,1,1] (.node [12,9,6,6,5,5,5,5,4,2,2,1] (.node [12,9,6,6,5,5,5,5,4,2,1,1,1] .empty .empty) .empty) (.node [12,9,6,6,5,5,5,5,5,2,1,1] .empty .empty)))) + +def degreeTree62_393 : RowTree := (.node [12,9,6,6,6,6,4,4,4,2,1,1,1] (.node [12,9,6,6,6,5,5,5,3,2,2,1] (.node [12,9,6,6,6,5,5,4,4,2,2,1] (.node [12,9,6,6,6,5,5,4,4,2,1,1,1] (.node [12,9,6,6,6,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,6,6,6,5,5,5,3,2,1,1,1] (.node [12,9,6,6,6,5,5,5,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,6,6,6,5,5,5,5,1,1,1] (.node [12,9,6,6,6,5,5,5,4,2,1,1] (.node [12,9,6,6,6,5,5,5,4,1,1,1,1] .empty .empty) .empty) (.node [12,9,6,6,6,6,4,4,3,2,2,1,1] .empty .empty))) (.node [12,9,6,6,6,6,5,4,3,2,2,1] (.node [12,9,6,6,6,6,5,3,3,2,2,1,1] (.node [12,9,6,6,6,6,5,2,2,2,2,2,2] (.node [12,9,6,6,6,6,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,9,6,6,6,6,5,4,3,2,1,1,1] (.node [12,9,6,6,6,6,5,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,6,6,6,6,5,5,2,2,1,1,1] (.node [12,9,6,6,6,6,5,4,4,2,1,1] (.node [12,9,6,6,6,6,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,9,6,6,6,6,5,5,2,2,2,1] .empty .empty)))) + +def degreeTree62_394 : RowTree := (.node [12,9,6,6,6,5,4,4,4,2,2,1,1] degreeTree62_392 degreeTree62_393) + +def degreeTree62_395 : RowTree := (.node [12,8,8,8,8,7,3,3,2,1,1,1] degreeTree62_391 degreeTree62_394) + +def degreeTree62_396 : RowTree := (.node [12,8,8,8,8,5,3,3,2,2,1,1,1] degreeTree62_388 degreeTree62_395) + +def degreeTree62_397 : RowTree := (.node [12,9,6,6,6,6,6,4,4,1,1,1] (.node [12,9,6,6,6,6,6,3,3,2,2,1] (.node [12,9,6,6,6,6,6,2,2,2,2,2,1] (.node [12,9,6,6,6,6,5,5,4,1,1,1] (.node [12,9,6,6,6,6,5,5,3,2,1,1] .empty .empty) .empty) (.node [12,9,6,6,6,6,6,3,3,2,1,1,1] (.node [12,9,6,6,6,6,6,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,6,6,6,6,6,4,3,1,1,1,1] (.node [12,9,6,6,6,6,6,4,2,2,2,1] (.node [12,9,6,6,6,6,6,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,6,6,6,6,6,4,3,2,1,1] .empty .empty))) (.node [12,9,7,5,5,5,5,4,4,2,2,1,1] (.node [12,9,6,6,6,6,6,5,3,1,1,1] (.node [12,9,6,6,6,6,6,5,2,2,1,1] (.node [12,9,6,6,6,6,6,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,6,6,6,6,6,6,2,1,1,1] (.node [12,9,6,6,6,6,6,6,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,7,5,5,5,5,5,4,2,2,1] (.node [12,9,7,5,5,5,5,5,4,2,1,1,1] (.node [12,9,7,5,5,5,5,5,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,5,5,5,5,5,5,1,1,1,1] .empty .empty)))) + +def degreeTree62_398 : RowTree := (.node [12,9,7,6,6,4,4,4,4,2,2,1,1] (.node [12,9,7,6,5,5,5,5,3,2,1,1,1] (.node [12,9,7,6,5,5,5,4,4,2,1,1,1] (.node [12,9,7,6,5,5,5,4,3,2,2,1,1] (.node [12,9,7,6,5,5,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,6,5,5,5,5,2,2,2,1,1] (.node [12,9,7,6,5,5,5,4,4,2,2,1] .empty .empty) .empty)) (.node [12,9,7,6,5,5,5,5,4,2,1,1] (.node [12,9,7,6,5,5,5,5,4,1,1,1,1] (.node [12,9,7,6,5,5,5,5,3,2,2,1] .empty .empty) .empty) (.node [12,9,7,6,5,5,5,5,5,1,1,1] .empty .empty))) (.node [12,9,7,6,6,5,5,4,2,2,2,1,1] (.node [12,9,7,6,6,5,4,4,4,2,2,1] (.node [12,9,7,6,6,5,4,4,4,2,1,1,1] (.node [12,9,7,6,6,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,6,6,5,5,3,3,2,2,1,1] (.node [12,9,7,6,6,5,5,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,9,7,6,6,5,5,4,4,1,1,1,1] (.node [12,9,7,6,6,5,5,4,3,2,2,1] (.node [12,9,7,6,6,5,5,4,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,7,6,6,5,5,4,4,2,1,1] .empty .empty)))) + +def degreeTree62_399 : RowTree := (.node [12,9,7,5,5,5,5,5,5,2,1,1] degreeTree62_397 degreeTree62_398) + +def degreeTree62_400 : RowTree := (.node [12,9,7,6,6,6,4,4,4,2,1,1] (.node [12,9,7,6,6,6,4,3,3,2,2,1,1] (.node [12,9,7,6,6,5,5,5,3,2,1,1] (.node [12,9,7,6,6,5,5,5,3,1,1,1,1] (.node [12,9,7,6,6,5,5,5,2,2,2,1] .empty .empty) .empty) (.node [12,9,7,6,6,6,4,2,2,2,2,2,2] (.node [12,9,7,6,6,5,5,5,4,1,1,1] .empty .empty) .empty)) (.node [12,9,7,6,6,6,4,4,3,2,2,1] (.node [12,9,7,6,6,6,4,4,3,2,1,1,1] (.node [12,9,7,6,6,6,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,6,6,6,4,4,4,1,1,1,1] .empty .empty))) (.node [12,9,7,6,6,6,5,4,2,2,2,1] (.node [12,9,7,6,6,6,5,3,3,2,1,1,1] (.node [12,9,7,6,6,6,5,3,2,2,2,1,1] (.node [12,9,7,6,6,6,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,7,6,6,6,5,4,2,2,1,1,1] (.node [12,9,7,6,6,6,5,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,7,6,6,6,5,4,4,1,1,1] (.node [12,9,7,6,6,6,5,4,3,2,1,1] (.node [12,9,7,6,6,6,5,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,6,6,6,5,5,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_401 : RowTree := (.node [12,9,7,6,6,6,6,5,1,1,1,1,1] (.node [12,9,7,6,6,6,6,3,3,1,1,1,1] (.node [12,9,7,6,6,6,6,2,2,2,2,2] (.node [12,9,7,6,6,6,6,2,2,2,2,1,1] (.node [12,9,7,6,6,6,5,5,3,1,1,1] .empty .empty) .empty) (.node [12,9,7,6,6,6,6,3,2,2,2,1] (.node [12,9,7,6,6,6,6,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,7,6,6,6,6,4,2,2,1,1] (.node [12,9,7,6,6,6,6,4,2,1,1,1,1] (.node [12,9,7,6,6,6,6,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,7,6,6,6,6,4,3,1,1,1] .empty .empty))) (.node [12,9,7,7,5,5,5,2,2,2,2,2,2] (.node [12,9,7,7,5,5,4,4,3,2,2,1,1] (.node [12,9,7,7,5,4,4,4,4,2,2,1,1] (.node [12,9,7,6,6,6,6,5,2,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,5,5,4,4,4,2,2,1] (.node [12,9,7,7,5,5,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,5,5,5,4,3,2,1,1,1] (.node [12,9,7,7,5,5,5,4,2,2,2,1,1] (.node [12,9,7,7,5,5,5,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,5,5,5,4,3,2,2,1] .empty .empty)))) + +def degreeTree62_402 : RowTree := (.node [12,9,7,6,6,6,5,5,2,2,1,1] degreeTree62_400 degreeTree62_401) + +def degreeTree62_403 : RowTree := (.node [12,9,7,6,6,5,5,5,2,2,1,1,1] degreeTree62_399 degreeTree62_402) + +def degreeTree62_404 : RowTree := (.node [12,9,7,7,6,5,4,3,3,2,2,1,1] (.node [12,9,7,7,5,5,5,5,4,1,1,1] (.node [12,9,7,7,5,5,5,5,2,2,2,1] (.node [12,9,7,7,5,5,5,5,2,2,1,1,1] (.node [12,9,7,7,5,5,5,4,4,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,5,5,5,5,3,2,1,1] (.node [12,9,7,7,5,5,5,5,3,1,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,6,4,4,4,4,2,2,1] (.node [12,9,7,7,6,4,4,4,4,2,1,1,1] (.node [12,9,7,7,6,4,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,5,4,2,2,2,2,2,2] .empty .empty))) (.node [12,9,7,7,6,5,5,2,2,2,2,2,1] (.node [12,9,7,7,6,5,4,4,3,2,2,1] (.node [12,9,7,7,6,5,4,4,3,2,1,1,1] (.node [12,9,7,7,6,5,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,5,4,4,4,2,1,1] (.node [12,9,7,7,6,5,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,6,5,5,3,3,2,2,1] (.node [12,9,7,7,6,5,5,3,3,2,1,1,1] (.node [12,9,7,7,6,5,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,5,5,4,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_405 : RowTree := (.node [12,9,7,7,6,6,4,3,3,2,1,1,1] (.node [12,9,7,7,6,5,5,5,3,1,1,1] (.node [12,9,7,7,6,5,5,4,4,1,1,1] (.node [12,9,7,7,6,5,5,4,3,2,1,1] (.node [12,9,7,7,6,5,5,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,5,5,5,2,2,1,1] (.node [12,9,7,7,6,5,5,5,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,6,6,4,2,2,2,2,2,1] (.node [12,9,7,7,6,6,3,3,3,2,2,1,1] (.node [12,9,7,7,6,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,7,7,6,6,4,3,2,2,2,1,1] .empty .empty))) (.node [12,9,7,7,6,6,4,4,4,1,1,1] (.node [12,9,7,7,6,6,4,4,2,2,2,1] (.node [12,9,7,7,6,6,4,4,2,2,1,1,1] (.node [12,9,7,7,6,6,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,9,7,7,6,6,4,4,3,2,1,1] (.node [12,9,7,7,6,6,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,6,6,5,3,2,2,1,1,1] (.node [12,9,7,7,6,6,5,2,2,2,2,2] (.node [12,9,7,7,6,6,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,6,5,3,2,2,2,1] .empty .empty)))) + +def degreeTree62_406 : RowTree := (.node [12,9,7,7,6,5,5,4,2,2,2,1] degreeTree62_404 degreeTree62_405) + +def degreeTree62_407 : RowTree := (.node [12,9,7,7,6,6,6,3,3,1,1,1] (.node [12,9,7,7,6,6,5,5,2,1,1,1] (.node [12,9,7,7,6,6,5,4,2,2,1,1] (.node [12,9,7,7,6,6,5,4,2,1,1,1,1] (.node [12,9,7,7,6,6,5,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,6,5,5,1,1,1,1,1] (.node [12,9,7,7,6,6,5,4,3,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,6,6,6,3,2,1,1,1,1] (.node [12,9,7,7,6,6,6,2,2,2,2,1] (.node [12,9,7,7,6,6,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,6,6,6,3,2,2,1,1] .empty .empty))) (.node [12,9,7,7,7,4,4,4,3,2,1,1,1] (.node [12,9,7,7,7,4,4,2,2,2,2,2,2] (.node [12,9,7,7,6,6,6,4,2,1,1,1] (.node [12,9,7,7,6,6,6,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,4,4,4,2,2,2,1,1] (.node [12,9,7,7,7,4,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,9,7,7,7,4,4,4,4,2,1,1] (.node [12,9,7,7,7,4,4,4,4,1,1,1,1] (.node [12,9,7,7,7,4,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,9,7,7,7,5,3,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_408 : RowTree := (.node [12,9,7,7,7,5,5,2,2,2,2,2] (.node [12,9,7,7,7,5,4,4,2,2,2,1] (.node [12,9,7,7,7,5,4,3,3,2,1,1,1] (.node [12,9,7,7,7,5,4,3,2,2,2,1,1] (.node [12,9,7,7,7,5,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,7,7,7,5,4,4,2,2,1,1,1] (.node [12,9,7,7,7,5,4,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,7,7,7,5,4,4,4,1,1,1] (.node [12,9,7,7,7,5,4,4,3,2,1,1] (.node [12,9,7,7,7,5,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,5,5,2,2,2,2,1,1] .empty .empty))) (.node [12,9,7,7,7,5,5,4,2,1,1,1,1] (.node [12,9,7,7,7,5,5,3,3,1,1,1,1] (.node [12,9,7,7,7,5,5,3,2,2,2,1] (.node [12,9,7,7,7,5,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,5,5,3,3,2,1,1] .empty .empty)) (.node [12,9,7,7,7,5,5,5,1,1,1,1,1] (.node [12,9,7,7,7,5,5,4,3,1,1,1] (.node [12,9,7,7,7,5,5,4,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,5,5,5,2,1,1,1] .empty .empty)))) + +def degreeTree62_409 : RowTree := (.node [12,9,7,7,7,5,3,3,3,2,2,1,1] degreeTree62_407 degreeTree62_408) + +def degreeTree62_410 : RowTree := (.node [12,9,7,7,6,6,5,3,3,1,1,1,1] degreeTree62_406 degreeTree62_409) + +def degreeTree62_411 : RowTree := (.node [12,9,7,7,5,5,5,4,4,1,1,1,1] degreeTree62_403 degreeTree62_410) + +def degreeTree62_412 : RowTree := (.node [12,9,6,6,6,6,5,5,3,1,1,1,1] degreeTree62_396 degreeTree62_411) + +def degreeTree62_413 : RowTree := (.node [12,9,7,7,7,6,4,4,2,1,1,1,1] (.node [12,9,7,7,7,6,4,2,2,2,2,2] (.node [12,9,7,7,7,6,3,3,3,2,1,1,1] (.node [12,9,7,7,7,6,3,3,2,2,2,1,1] (.node [12,9,7,7,7,6,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,7,7,7,6,4,2,2,2,2,1,1] (.node [12,9,7,7,7,6,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,7,7,7,6,4,3,3,1,1,1,1] (.node [12,9,7,7,7,6,4,3,2,2,2,1] (.node [12,9,7,7,7,6,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,6,4,3,3,2,1,1] .empty .empty))) (.node [12,9,7,7,7,6,5,3,2,2,1,1] (.node [12,9,7,7,7,6,5,2,2,2,1,1,1] (.node [12,9,7,7,7,6,4,4,3,1,1,1] (.node [12,9,7,7,7,6,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,6,5,3,2,1,1,1,1] (.node [12,9,7,7,7,6,5,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,7,7,7,6,5,4,2,1,1,1] (.node [12,9,7,7,7,6,5,4,1,1,1,1,1] (.node [12,9,7,7,7,6,5,3,3,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,6,6,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_414 : RowTree := (.node [12,9,7,7,7,7,3,3,2,2,2,1] (.node [12,9,7,7,7,7,3,2,2,2,1,1,1,1] (.node [12,9,7,7,7,6,6,3,2,1,1,1] (.node [12,9,7,7,7,6,6,3,1,1,1,1,1] (.node [12,9,7,7,7,6,6,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,7,2,2,2,2,2,2,1] (.node [12,9,7,7,7,7,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,7,7,3,3,2,1,1,1,1,1] (.node [12,9,7,7,7,7,3,2,2,2,2,2] (.node [12,9,7,7,7,7,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,7,3,3,2,2,1,1,1] .empty .empty))) (.node [12,9,7,7,7,7,4,3,1,1,1,1,1,1] (.node [12,9,7,7,7,7,4,2,2,1,1,1,1,1] (.node [12,9,7,7,7,7,3,3,3,2,1,1] (.node [12,9,7,7,7,7,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,7,4,2,2,2,2,1] (.node [12,9,7,7,7,7,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,7,7,4,3,3,1,1,1] (.node [12,9,7,7,7,7,4,3,2,2,1,1] (.node [12,9,7,7,7,7,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,7,4,4,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_415 : RowTree := (.node [12,9,7,7,7,6,6,2,2,1,1,1,1] degreeTree62_413 degreeTree62_414) + +def degreeTree62_416 : RowTree := (.node [12,9,8,5,5,5,5,4,3,2,2,1,1] (.node [12,9,7,7,7,7,6,1,1,1,1,1,1,1] (.node [12,9,7,7,7,7,5,2,2,2,1,1] (.node [12,9,7,7,7,7,5,2,2,1,1,1,1] (.node [12,9,7,7,7,7,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,7,7,7,7,5,3,2,1,1,1] (.node [12,9,7,7,7,7,5,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,7,7,7,7,7,1,1,1,1,1,1] (.node [12,9,7,7,7,7,6,2,2,1,1,1] (.node [12,9,7,7,7,7,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,5,5,5,4,4,4,2,2,1,1] .empty .empty))) (.node [12,9,8,5,5,5,5,5,4,1,1,1,1] (.node [12,9,8,5,5,5,5,5,2,2,2,1,1] (.node [12,9,8,5,5,5,5,4,4,2,2,1] (.node [12,9,8,5,5,5,5,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,5,5,5,5,5,3,2,2,1] (.node [12,9,8,5,5,5,5,5,3,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,6,5,4,4,4,4,2,2,1,1] (.node [12,9,8,5,5,5,5,5,5,1,1,1] (.node [12,9,8,5,5,5,5,5,4,2,1,1] .empty .empty) .empty) (.node [12,9,8,6,5,5,4,4,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_417 : RowTree := (.node [12,9,8,6,5,5,5,5,3,1,1,1,1] (.node [12,9,8,6,5,5,5,4,3,2,2,1] (.node [12,9,8,6,5,5,5,3,3,2,2,1,1] (.node [12,9,8,6,5,5,5,2,2,2,2,2,2] (.node [12,9,8,6,5,5,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,9,8,6,5,5,5,4,3,2,1,1,1] (.node [12,9,8,6,5,5,5,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,6,5,5,5,5,2,2,1,1,1] (.node [12,9,8,6,5,5,5,4,4,2,1,1] (.node [12,9,8,6,5,5,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,6,5,5,5,5,2,2,2,1] .empty .empty))) (.node [12,9,8,6,6,5,4,2,2,2,2,2,2] (.node [12,9,8,6,6,4,4,4,3,2,2,1,1] (.node [12,9,8,6,5,5,5,5,4,1,1,1] (.node [12,9,8,6,5,5,5,5,3,2,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,4,4,4,4,2,2,1] (.node [12,9,8,6,6,4,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,6,6,5,4,4,3,2,1,1,1] (.node [12,9,8,6,6,5,4,4,2,2,2,1,1] (.node [12,9,8,6,6,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,5,4,4,3,2,2,1] .empty .empty)))) + +def degreeTree62_418 : RowTree := (.node [12,9,8,6,5,5,4,4,4,2,1,1,1] degreeTree62_416 degreeTree62_417) + +def degreeTree62_419 : RowTree := (.node [12,9,7,7,7,7,4,4,2,1,1,1] degreeTree62_415 degreeTree62_418) + +def degreeTree62_420 : RowTree := (.node [12,9,8,6,6,5,5,5,2,1,1,1,1] (.node [12,9,8,6,6,5,5,4,2,2,1,1,1] (.node [12,9,8,6,6,5,5,3,2,2,2,1,1] (.node [12,9,8,6,6,5,5,2,2,2,2,2,1] (.node [12,9,8,6,6,5,4,4,4,2,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,5,5,3,3,2,2,1] (.node [12,9,8,6,6,5,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,6,6,5,5,4,3,2,1,1] (.node [12,9,8,6,6,5,5,4,3,1,1,1,1] (.node [12,9,8,6,6,5,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,9,8,6,6,5,5,4,4,1,1,1] .empty .empty))) (.node [12,9,8,6,6,6,4,3,2,2,2,1,1] (.node [12,9,8,6,6,6,3,2,2,2,2,2,2] (.node [12,9,8,6,6,5,5,5,3,1,1,1] (.node [12,9,8,6,6,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,6,4,2,2,2,2,2,1] (.node [12,9,8,6,6,6,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,6,6,6,4,4,2,2,1,1,1] (.node [12,9,8,6,6,6,4,3,3,2,2,1] (.node [12,9,8,6,6,6,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,6,4,4,2,2,2,1] .empty .empty)))) + +def degreeTree62_421 : RowTree := (.node [12,9,8,6,6,6,5,4,3,1,1,1] (.node [12,9,8,6,6,6,5,3,2,2,2,1] (.node [12,9,8,6,6,6,5,2,2,2,2,1,1] (.node [12,9,8,6,6,6,4,4,4,1,1,1] (.node [12,9,8,6,6,6,4,4,3,2,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,6,5,3,2,2,1,1,1] (.node [12,9,8,6,6,6,5,2,2,2,2,2] .empty .empty) .empty)) (.node [12,9,8,6,6,6,5,4,2,1,1,1,1] (.node [12,9,8,6,6,6,5,3,3,2,1,1] (.node [12,9,8,6,6,6,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,6,5,4,2,2,1,1] .empty .empty))) (.node [12,9,8,6,6,6,6,3,2,2,1,1] (.node [12,9,8,6,6,6,6,2,2,2,1,1,1] (.node [12,9,8,6,6,6,5,5,2,1,1,1] (.node [12,9,8,6,6,6,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,6,6,6,6,3,2,1,1,1,1] (.node [12,9,8,6,6,6,6,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,6,6,6,6,4,2,1,1,1] (.node [12,9,8,6,6,6,6,4,1,1,1,1,1] (.node [12,9,8,6,6,6,6,3,3,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,4,4,4,4,4,2,2,1,1] .empty .empty)))) + +def degreeTree62_422 : RowTree := (.node [12,9,8,6,6,6,4,4,3,1,1,1,1] degreeTree62_420 degreeTree62_421) + +def degreeTree62_423 : RowTree := (.node [12,9,8,7,5,5,5,3,2,2,2,1,1] (.node [12,9,8,7,5,5,4,4,3,2,1,1,1] (.node [12,9,8,7,5,5,4,2,2,2,2,2,2] (.node [12,9,8,7,5,4,4,4,4,2,2,1] (.node [12,9,8,7,5,4,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,5,5,4,4,2,2,2,1,1] (.node [12,9,8,7,5,5,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,7,5,5,4,4,4,2,1,1] (.node [12,9,8,7,5,5,4,4,4,1,1,1,1] (.node [12,9,8,7,5,5,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,9,8,7,5,5,5,2,2,2,2,2,1] .empty .empty))) (.node [12,9,8,7,5,5,5,4,3,2,1,1] (.node [12,9,8,7,5,5,5,4,2,2,1,1,1] (.node [12,9,8,7,5,5,5,3,3,2,2,1] (.node [12,9,8,7,5,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,5,5,5,4,3,1,1,1,1] (.node [12,9,8,7,5,5,5,4,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,7,5,5,5,5,2,2,1,1] (.node [12,9,8,7,5,5,5,5,2,1,1,1,1] (.node [12,9,8,7,5,5,5,4,4,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,5,5,5,5,3,1,1,1] .empty .empty)))) + +def degreeTree62_424 : RowTree := (.node [12,9,8,7,6,5,4,3,3,2,1,1,1] (.node [12,9,8,7,6,4,4,4,4,2,1,1] (.node [12,9,8,7,6,4,4,4,3,2,1,1,1] (.node [12,9,8,7,6,4,4,4,2,2,2,1,1] (.node [12,9,8,7,6,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,4,4,4,4,1,1,1,1] (.node [12,9,8,7,6,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,9,8,7,6,5,4,2,2,2,2,2,1] (.node [12,9,8,7,6,5,3,3,3,2,2,1,1] (.node [12,9,8,7,6,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,8,7,6,5,4,3,2,2,2,1,1] .empty .empty))) (.node [12,9,8,7,6,5,4,4,4,1,1,1] (.node [12,9,8,7,6,5,4,4,2,2,2,1] (.node [12,9,8,7,6,5,4,4,2,2,1,1,1] (.node [12,9,8,7,6,5,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,9,8,7,6,5,4,4,3,2,1,1] (.node [12,9,8,7,6,5,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,7,6,5,5,3,2,2,1,1,1] (.node [12,9,8,7,6,5,5,2,2,2,2,2] (.node [12,9,8,7,6,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,5,5,3,2,2,2,1] .empty .empty)))) + +def degreeTree62_425 : RowTree := (.node [12,9,8,7,6,4,4,2,2,2,2,2,2] degreeTree62_423 degreeTree62_424) + +def degreeTree62_426 : RowTree := (.node [12,9,8,7,5,4,4,4,3,2,2,1,1] degreeTree62_422 degreeTree62_425) + +def degreeTree62_427 : RowTree := (.node [12,9,8,6,6,5,4,4,4,1,1,1,1] degreeTree62_419 degreeTree62_426) + +def degreeTree62_428 : RowTree := (.node [12,9,8,7,6,6,3,3,3,2,2,1] (.node [12,9,8,7,6,5,5,5,2,1,1,1] (.node [12,9,8,7,6,5,5,4,2,2,1,1] (.node [12,9,8,7,6,5,5,4,2,1,1,1,1] (.node [12,9,8,7,6,5,5,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,5,5,5,1,1,1,1,1] (.node [12,9,8,7,6,5,5,4,3,1,1,1] .empty .empty) .empty)) (.node [12,9,8,7,6,6,3,3,2,2,2,1,1] (.node [12,9,8,7,6,6,3,2,2,2,2,2,1] (.node [12,9,8,7,6,6,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,8,7,6,6,3,3,3,2,1,1,1] .empty .empty))) (.node [12,9,8,7,6,6,4,3,3,2,1,1] (.node [12,9,8,7,6,6,4,3,2,2,1,1,1] (.node [12,9,8,7,6,6,4,2,2,2,2,2] (.node [12,9,8,7,6,6,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,6,4,3,3,1,1,1,1] (.node [12,9,8,7,6,6,4,3,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,7,6,6,4,4,3,1,1,1] (.node [12,9,8,7,6,6,4,4,2,2,1,1] (.node [12,9,8,7,6,6,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,6,5,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_429 : RowTree := (.node [12,9,8,7,7,4,3,2,2,2,2,2,2] (.node [12,9,8,7,6,6,6,2,1,1,1,1,1,1] (.node [12,9,8,7,6,6,5,3,3,1,1,1] (.node [12,9,8,7,6,6,5,3,2,2,1,1] (.node [12,9,8,7,6,6,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,6,5,4,2,1,1,1] (.node [12,9,8,7,6,6,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,7,6,6,6,3,1,1,1,1,1] (.node [12,9,8,7,6,6,6,2,2,2,1,1] (.node [12,9,8,7,6,6,6,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,6,6,6,3,2,1,1,1] .empty .empty))) (.node [12,9,8,7,7,4,4,4,2,2,1,1,1] (.node [12,9,8,7,7,4,4,3,2,2,2,1,1] (.node [12,9,8,7,7,4,4,2,2,2,2,2,1] (.node [12,9,8,7,7,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,4,4,3,3,2,2,1] (.node [12,9,8,7,7,4,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,7,7,4,4,4,3,2,1,1] (.node [12,9,8,7,7,4,4,4,3,1,1,1,1] (.node [12,9,8,7,7,4,4,4,2,2,2,1] .empty .empty) .empty) (.node [12,9,8,7,7,4,4,4,4,1,1,1] .empty .empty)))) + +def degreeTree62_430 : RowTree := (.node [12,9,8,7,6,6,5,2,2,2,2,1] degreeTree62_428 degreeTree62_429) + +def degreeTree62_431 : RowTree := (.node [12,9,8,7,7,5,4,4,2,1,1,1,1] (.node [12,9,8,7,7,5,4,2,2,2,2,2] (.node [12,9,8,7,7,5,3,3,3,2,1,1,1] (.node [12,9,8,7,7,5,3,3,2,2,2,1,1] (.node [12,9,8,7,7,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,8,7,7,5,4,2,2,2,2,1,1] (.node [12,9,8,7,7,5,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,8,7,7,5,4,3,3,1,1,1,1] (.node [12,9,8,7,7,5,4,3,2,2,2,1] (.node [12,9,8,7,7,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,5,4,3,3,2,1,1] .empty .empty))) (.node [12,9,8,7,7,5,5,3,2,2,1,1] (.node [12,9,8,7,7,5,5,2,2,2,1,1,1] (.node [12,9,8,7,7,5,4,4,3,1,1,1] (.node [12,9,8,7,7,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,5,5,3,2,1,1,1,1] (.node [12,9,8,7,7,5,5,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,7,7,5,5,4,2,1,1,1] (.node [12,9,8,7,7,5,5,4,1,1,1,1,1] (.node [12,9,8,7,7,5,5,3,3,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,6,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_432 : RowTree := (.node [12,9,8,7,7,6,4,2,2,2,2,1] (.node [12,9,8,7,7,6,3,3,2,2,2,1] (.node [12,9,8,7,7,6,3,2,2,2,2,2] (.node [12,9,8,7,7,6,3,2,2,2,2,1,1] (.node [12,9,8,7,7,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,6,3,3,2,2,1,1,1] (.node [12,9,8,7,7,6,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,7,7,6,4,2,2,1,1,1,1,1] (.node [12,9,8,7,7,6,3,3,3,2,1,1] (.node [12,9,8,7,7,6,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,6,4,2,2,2,1,1,1] .empty .empty))) (.node [12,9,8,7,7,6,4,4,2,1,1,1] (.node [12,9,8,7,7,6,4,3,2,2,1,1] (.node [12,9,8,7,7,6,4,3,2,1,1,1,1] (.node [12,9,8,7,7,6,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,6,4,4,1,1,1,1,1] (.node [12,9,8,7,7,6,4,3,3,1,1,1] .empty .empty) .empty)) (.node [12,9,8,7,7,6,5,2,2,2,1,1] (.node [12,9,8,7,7,6,5,2,2,1,1,1,1] (.node [12,9,8,7,7,6,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,6,5,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_433 : RowTree := (.node [12,9,8,7,7,6,2,2,2,2,2,2,1] degreeTree62_431 degreeTree62_432) + +def degreeTree62_434 : RowTree := (.node [12,9,8,7,7,5,2,2,2,2,2,2,2] degreeTree62_430 degreeTree62_433) + +def degreeTree62_435 : RowTree := (.node [12,9,8,7,7,7,3,3,2,2,1,1] (.node [12,9,8,7,7,7,3,2,2,1,1,1,1,1] (.node [12,9,8,7,7,7,2,2,2,2,1,1,1,1] (.node [12,9,8,7,7,6,6,2,1,1,1,1,1] (.node [12,9,8,7,7,6,6,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,7,2,2,2,2,2,2] (.node [12,9,8,7,7,7,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,7,7,7,3,3,1,1,1,1,1,1] (.node [12,9,8,7,7,7,3,2,2,2,2,1] (.node [12,9,8,7,7,7,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,7,3,3,2,1,1,1,1] .empty .empty))) (.node [12,9,8,7,7,7,5,1,1,1,1,1,1,1] (.node [12,9,8,7,7,7,4,2,2,1,1,1,1] (.node [12,9,8,7,7,7,4,2,1,1,1,1,1,1] (.node [12,9,8,7,7,7,3,3,3,1,1,1] .empty .empty) .empty) (.node [12,9,8,7,7,7,4,3,1,1,1,1,1] (.node [12,9,8,7,7,7,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,8,4,4,4,4,3,2,2,1,1] (.node [12,9,8,7,7,7,6,1,1,1,1,1,1] (.node [12,9,8,7,7,7,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,4,4,4,4,4,2,1,1,1] .empty .empty)))) + +def degreeTree62_436 : RowTree := (.node [12,9,8,8,5,5,4,3,2,2,2,1,1] (.node [12,9,8,8,5,4,4,4,4,1,1,1,1] (.node [12,9,8,8,5,4,4,4,2,2,2,1,1] (.node [12,9,8,8,5,4,4,3,3,2,2,1,1] (.node [12,9,8,8,5,4,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,8,8,5,4,4,4,3,2,2,1] (.node [12,9,8,8,5,4,4,4,3,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,5,5,3,3,3,2,2,1,1] (.node [12,9,8,8,5,5,3,2,2,2,2,2,2] (.node [12,9,8,8,5,4,4,4,4,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,5,5,4,2,2,2,2,2,1] .empty .empty))) (.node [12,9,8,8,5,5,4,4,3,2,1,1] (.node [12,9,8,8,5,5,4,4,2,2,1,1,1] (.node [12,9,8,8,5,5,4,3,3,2,2,1] (.node [12,9,8,8,5,5,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,5,5,4,4,3,1,1,1,1] (.node [12,9,8,8,5,5,4,4,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,5,5,5,2,2,2,2,2] (.node [12,9,8,8,5,5,5,2,2,2,2,1,1] (.node [12,9,8,8,5,5,4,4,4,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,5,5,5,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_437 : RowTree := (.node [12,9,8,8,4,4,4,4,4,2,2,1] degreeTree62_435 degreeTree62_436) + +def degreeTree62_438 : RowTree := (.node [12,9,8,8,6,4,4,3,2,2,2,1,1] (.node [12,9,8,8,5,5,5,5,1,1,1,1,1] (.node [12,9,8,8,5,5,5,4,2,1,1,1,1] (.node [12,9,8,8,5,5,5,3,3,2,1,1] (.node [12,9,8,8,5,5,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,5,5,5,4,3,1,1,1] (.node [12,9,8,8,5,5,5,4,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,8,6,4,3,3,3,2,2,1,1] (.node [12,9,8,8,6,4,3,2,2,2,2,2,2] (.node [12,9,8,8,5,5,5,5,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,4,4,2,2,2,2,2,1] .empty .empty))) (.node [12,9,8,8,6,4,4,4,3,2,1,1] (.node [12,9,8,8,6,4,4,4,2,2,1,1,1] (.node [12,9,8,8,6,4,4,3,3,2,2,1] (.node [12,9,8,8,6,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,4,4,4,3,1,1,1,1] (.node [12,9,8,8,6,4,4,4,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,6,5,3,2,2,2,2,2,1] (.node [12,9,8,8,6,5,2,2,2,2,2,2,2] (.node [12,9,8,8,6,4,4,4,4,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,5,3,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_439 : RowTree := (.node [12,9,8,8,6,5,5,2,2,2,1,1,1] (.node [12,9,8,8,6,5,4,3,3,1,1,1,1] (.node [12,9,8,8,6,5,4,2,2,2,2,2] (.node [12,9,8,8,6,5,4,2,2,2,2,1,1] (.node [12,9,8,8,6,5,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,9,8,8,6,5,4,3,2,2,2,1] (.node [12,9,8,8,6,5,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,6,5,4,4,2,2,1,1] (.node [12,9,8,8,6,5,4,4,2,1,1,1,1] (.node [12,9,8,8,6,5,4,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,5,4,4,3,1,1,1] .empty .empty))) (.node [12,9,8,8,6,5,5,4,1,1,1,1,1] (.node [12,9,8,8,6,5,5,3,2,2,1,1] (.node [12,9,8,8,6,5,5,3,2,1,1,1,1] (.node [12,9,8,8,6,5,5,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,8,8,6,5,5,3,3,1,1,1] .empty .empty)) (.node [12,9,8,8,6,6,2,2,2,2,2,2,1] (.node [12,9,8,8,6,6,2,2,2,2,2,1,1,1] (.node [12,9,8,8,6,5,5,4,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,6,3,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_440 : RowTree := (.node [12,9,8,8,6,5,3,3,3,2,1,1,1] degreeTree62_438 degreeTree62_439) + +def degreeTree62_441 : RowTree := (.node [12,9,8,8,5,5,5,3,2,2,2,1] degreeTree62_437 degreeTree62_440) + +def degreeTree62_442 : RowTree := (.node [12,9,8,7,7,6,5,3,2,1,1,1] degreeTree62_434 degreeTree62_441) + +def degreeTree62_443 : RowTree := (.node [12,9,8,7,6,5,5,3,3,1,1,1,1] degreeTree62_427 degreeTree62_442) + +def degreeTree62_444 : RowTree := (.node [12,9,7,7,7,6,2,2,2,2,2,2,2] degreeTree62_412 degreeTree62_443) + +def degreeTree62_445 : RowTree := (.node [12,9,8,8,6,6,4,3,2,1,1,1,1] (.node [12,9,8,8,6,6,3,3,3,2,1,1] (.node [12,9,8,8,6,6,3,3,2,2,1,1,1] (.node [12,9,8,8,6,6,3,3,2,1,1,1,1,1] (.node [12,9,8,8,6,6,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,8,8,6,6,3,3,3,1,1,1,1] (.node [12,9,8,8,6,6,3,3,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,6,6,4,2,2,2,2,1] (.node [12,9,8,8,6,6,4,2,2,2,1,1,1] (.node [12,9,8,8,6,6,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,6,4,3,1,1,1,1,1,1] .empty .empty))) (.node [12,9,8,8,6,6,5,2,2,1,1,1,1] (.node [12,9,8,8,6,6,4,4,1,1,1,1,1] (.node [12,9,8,8,6,6,4,3,3,1,1,1] (.node [12,9,8,8,6,6,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,6,5,2,1,1,1,1,1,1] (.node [12,9,8,8,6,6,4,4,2,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,6,6,6,1,1,1,1,1,1,1] (.node [12,9,8,8,6,6,5,3,1,1,1,1,1] (.node [12,9,8,8,6,6,5,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,6,6,6,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_446 : RowTree := (.node [12,9,8,8,7,4,4,2,2,2,2,2] (.node [12,9,8,8,7,4,3,3,3,1,1,1,1,1] (.node [12,9,8,8,7,4,3,2,2,2,2,1,1,1] (.node [12,9,8,8,7,4,2,2,2,2,2,2,2] (.node [12,9,8,8,7,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,4,3,3,2,2,2,1,1] (.node [12,9,8,8,7,4,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,7,4,4,2,2,2,1,1,1,1] (.node [12,9,8,8,7,4,3,3,3,2,2,1] (.node [12,9,8,8,7,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,4,4,2,2,2,2,1,1] .empty .empty))) (.node [12,9,8,8,7,4,4,4,1,1,1,1,1,1] (.node [12,9,8,8,7,4,4,3,2,2,2,1] (.node [12,9,8,8,7,4,4,3,2,2,1,1,1] (.node [12,9,8,8,7,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,4,4,3,3,2,1,1] (.node [12,9,8,8,7,4,4,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,7,4,4,4,3,1,1,1] (.node [12,9,8,8,7,4,4,4,2,2,1,1] (.node [12,9,8,8,7,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,5,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_447 : RowTree := (.node [12,9,8,8,7,3,3,2,2,2,2,2,2] degreeTree62_445 degreeTree62_446) + +def degreeTree62_448 : RowTree := (.node [12,9,8,8,7,5,4,2,2,2,2,1] (.node [12,9,8,8,7,5,3,3,2,2,2,1] (.node [12,9,8,8,7,5,3,2,2,2,2,2] (.node [12,9,8,8,7,5,3,2,2,2,2,1,1] (.node [12,9,8,8,7,5,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,5,3,3,2,2,1,1,1] (.node [12,9,8,8,7,5,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,7,5,4,2,2,1,1,1,1,1] (.node [12,9,8,8,7,5,3,3,3,2,1,1] (.node [12,9,8,8,7,5,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,5,4,2,2,2,1,1,1] .empty .empty))) (.node [12,9,8,8,7,5,5,2,1,1,1,1,1,1] (.node [12,9,8,8,7,5,4,3,2,2,1,1] (.node [12,9,8,8,7,5,4,3,2,1,1,1,1] (.node [12,9,8,8,7,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,5,4,4,1,1,1,1,1] (.node [12,9,8,8,7,5,4,3,3,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,7,5,5,3,1,1,1,1,1] (.node [12,9,8,8,7,5,5,2,2,2,1,1] (.node [12,9,8,8,7,5,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,6,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_449 : RowTree := (.node [12,9,8,8,7,6,4,2,2,2,1,1] (.node [12,9,8,8,7,6,3,3,2,1,1,1,1] (.node [12,9,8,8,7,6,3,2,2,2,1,1,1] (.node [12,9,8,8,7,6,3,2,2,1,1,1,1,1] (.node [12,9,8,8,7,6,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,8,8,7,6,3,3,1,1,1,1,1,1] (.node [12,9,8,8,7,6,3,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,7,6,4,2,1,1,1,1,1,1] (.node [12,9,8,8,7,6,3,3,3,1,1,1] (.node [12,9,8,8,7,6,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,6,4,2,2,1,1,1,1] .empty .empty))) (.node [12,9,8,8,7,7,2,2,2,2,1,1,1] (.node [12,9,8,8,7,6,5,2,1,1,1,1,1] (.node [12,9,8,8,7,6,5,1,1,1,1,1,1,1] (.node [12,9,8,8,7,6,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,7,7,2,2,2,1,1,1,1,1] (.node [12,9,8,8,7,6,6,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,7,7,3,2,2,1,1,1,1] (.node [12,9,8,8,7,7,3,2,1,1,1,1,1,1] (.node [12,9,8,8,7,7,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,8,8,7,7,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_450 : RowTree := (.node [12,9,8,8,7,6,2,2,2,2,2,1,1] degreeTree62_448 degreeTree62_449) + +def degreeTree62_451 : RowTree := (.node [12,9,8,8,7,5,2,2,2,2,2,2,1] degreeTree62_447 degreeTree62_450) + +def degreeTree62_452 : RowTree := (.node [12,9,8,8,8,3,3,3,3,2,2,1] (.node [12,9,8,8,8,3,3,2,2,2,2,1,1,1] (.node [12,9,8,8,7,7,5,1,1,1,1,1,1] (.node [12,9,8,8,7,7,4,2,1,1,1,1,1] (.node [12,9,8,8,7,7,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,3,2,2,2,2,2,2,2] (.node [12,9,8,8,8,2,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,8,3,3,3,3,1,1,1,1,1] (.node [12,9,8,8,8,3,3,3,2,2,2,1,1] (.node [12,9,8,8,8,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,8,8,8,3,3,3,3,2,1,1,1] .empty .empty))) (.node [12,9,8,8,8,4,3,3,2,1,1,1,1,1] (.node [12,9,8,8,8,4,3,2,2,2,1,1,1,1] (.node [12,9,8,8,8,4,2,2,2,2,2,2,1] (.node [12,9,8,8,8,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,4,3,2,2,2,2,2] (.node [12,9,8,8,8,4,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,8,8,8,4,3,3,3,1,1,1,1] (.node [12,9,8,8,8,4,3,3,2,2,2,1] (.node [12,9,8,8,8,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,4,3,3,3,2,1,1] .empty .empty)))) + +def degreeTree62_453 : RowTree := (.node [12,9,8,8,8,5,3,2,2,1,1,1,1,1] (.node [12,9,8,8,8,4,4,3,3,1,1,1] (.node [12,9,8,8,8,4,4,3,1,1,1,1,1,1] (.node [12,9,8,8,8,4,4,2,2,2,2,1] (.node [12,9,8,8,8,4,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,4,4,3,2,2,1,1] (.node [12,9,8,8,8,4,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,8,5,2,2,2,2,2,1,1] (.node [12,9,8,8,8,5,2,2,2,2,1,1,1,1] (.node [12,9,8,8,8,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,5,2,2,2,2,2,2] .empty .empty))) (.node [12,9,8,8,8,5,3,3,3,1,1,1] (.node [12,9,8,8,8,5,3,3,1,1,1,1,1,1] (.node [12,9,8,8,8,5,3,2,2,2,2,1] (.node [12,9,8,8,8,5,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,5,3,3,2,2,1,1] (.node [12,9,8,8,8,5,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,8,5,4,2,2,2,1,1] (.node [12,9,8,8,8,5,4,2,2,1,1,1,1] (.node [12,9,8,8,8,5,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,5,4,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_454 : RowTree := (.node [12,9,8,8,8,4,4,2,2,1,1,1,1,1] degreeTree62_452 degreeTree62_453) + +def degreeTree62_455 : RowTree := (.node [12,9,8,8,8,6,5,1,1,1,1,1,1] (.node [12,9,8,8,8,6,3,2,2,1,1,1,1] (.node [12,9,8,8,8,6,2,2,2,2,1,1,1] (.node [12,9,8,8,8,6,2,2,2,1,1,1,1,1] (.node [12,9,8,8,8,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,6,3,2,1,1,1,1,1,1] (.node [12,9,8,8,8,6,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,8,8,8,6,4,1,1,1,1,1,1,1] (.node [12,9,8,8,8,6,3,3,1,1,1,1,1] (.node [12,9,8,8,8,6,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,6,4,2,1,1,1,1,1] .empty .empty))) (.node [12,9,8,8,8,7,4,1,1,1,1,1,1] (.node [12,9,8,8,8,7,2,2,2,2,1,1] (.node [12,9,8,8,8,7,2,2,2,1,1,1,1] (.node [12,9,8,8,8,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,8,8,8,7,3,2,1,1,1,1,1] (.node [12,9,8,8,8,7,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,8,8,8,8,3,1,1,1,1,1,1] (.node [12,9,8,8,8,8,2,2,1,1,1,1,1] (.node [12,9,8,8,8,8,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,5,5,4,4,4,4,2,2,1,1] .empty .empty)))) + +def degreeTree62_456 : RowTree := (.node [12,9,9,5,5,5,5,5,2,2,2,1] (.node [12,9,9,5,5,5,5,4,3,2,1,1,1] (.node [12,9,9,5,5,5,5,2,2,2,2,2,2] (.node [12,9,9,5,5,5,4,4,4,2,2,1] (.node [12,9,9,5,5,5,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,5,5,5,5,4,2,2,2,1,1] (.node [12,9,9,5,5,5,5,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,5,5,5,5,4,4,2,1,1] (.node [12,9,9,5,5,5,5,4,4,1,1,1,1] (.node [12,9,9,5,5,5,5,4,3,2,2,1] .empty .empty) .empty) (.node [12,9,9,5,5,5,5,5,2,2,1,1,1] .empty .empty))) (.node [12,9,9,6,5,4,4,4,4,2,1,1,1] (.node [12,9,9,5,5,5,5,5,4,1,1,1] (.node [12,9,9,5,5,5,5,5,3,2,1,1] (.node [12,9,9,5,5,5,5,5,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,6,5,4,4,4,3,2,2,1,1] (.node [12,9,9,6,4,4,4,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,6,5,5,4,3,3,2,2,1,1] (.node [12,9,9,6,5,5,4,2,2,2,2,2,2] (.node [12,9,9,6,5,4,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,9,9,6,5,5,4,4,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_457 : RowTree := (.node [12,9,9,5,5,5,4,4,3,2,2,1,1] degreeTree62_455 degreeTree62_456) + +def degreeTree62_458 : RowTree := (.node [12,9,8,8,8,5,5,1,1,1,1,1,1,1] degreeTree62_454 degreeTree62_457) + +def degreeTree62_459 : RowTree := (.node [12,9,8,8,7,7,3,3,1,1,1,1,1] degreeTree62_451 degreeTree62_458) + +def degreeTree62_460 : RowTree := (.node [12,9,9,6,5,5,5,4,3,2,1,1] (.node [12,9,9,6,5,5,5,3,3,2,1,1,1] (.node [12,9,9,6,5,5,4,4,4,2,1,1] (.node [12,9,9,6,5,5,4,4,4,1,1,1,1] (.node [12,9,9,6,5,5,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,9,9,6,5,5,5,3,2,2,2,1,1] (.node [12,9,9,6,5,5,5,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,6,5,5,5,4,2,2,2,1] (.node [12,9,9,6,5,5,5,4,2,2,1,1,1] (.node [12,9,9,6,5,5,5,3,3,2,2,1] .empty .empty) .empty) (.node [12,9,9,6,5,5,5,4,3,1,1,1,1] .empty .empty))) (.node [12,9,9,6,6,4,4,3,3,2,2,1,1] (.node [12,9,9,6,5,5,5,5,2,2,1,1] (.node [12,9,9,6,5,5,5,5,2,1,1,1,1] (.node [12,9,9,6,5,5,5,4,4,1,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,4,4,2,2,2,2,2,2] (.node [12,9,9,6,5,5,5,5,3,1,1,1] .empty .empty) .empty)) (.node [12,9,9,6,6,4,4,4,3,2,2,1] (.node [12,9,9,6,6,4,4,4,3,2,1,1,1] (.node [12,9,9,6,6,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,4,4,4,4,1,1,1,1] .empty .empty)))) + +def degreeTree62_461 : RowTree := (.node [12,9,9,6,6,5,4,4,4,1,1,1] (.node [12,9,9,6,6,5,4,3,3,2,2,1] (.node [12,9,9,6,6,5,4,2,2,2,2,2,1] (.node [12,9,9,6,6,5,3,3,3,2,2,1,1] (.node [12,9,9,6,6,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,6,6,5,4,3,3,2,1,1,1] (.node [12,9,9,6,6,5,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,6,6,5,4,4,3,1,1,1,1] (.node [12,9,9,6,6,5,4,4,2,2,2,1] (.node [12,9,9,6,6,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,5,4,4,3,2,1,1] .empty .empty))) (.node [12,9,9,6,6,5,5,3,3,2,1,1] (.node [12,9,9,6,6,5,5,3,2,2,1,1,1] (.node [12,9,9,6,6,5,5,2,2,2,2,2] (.node [12,9,9,6,6,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,5,5,3,3,1,1,1,1] (.node [12,9,9,6,6,5,5,3,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,6,6,5,5,4,3,1,1,1] (.node [12,9,9,6,6,5,5,4,2,2,1,1] (.node [12,9,9,6,6,5,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,5,5,5,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_462 : RowTree := (.node [12,9,9,6,6,4,4,4,4,2,1,1] degreeTree62_460 degreeTree62_461) + +def degreeTree62_463 : RowTree := (.node [12,9,9,6,6,6,4,4,2,1,1,1,1] (.node [12,9,9,6,6,6,4,2,2,2,2,2] (.node [12,9,9,6,6,6,3,3,3,2,1,1,1] (.node [12,9,9,6,6,6,3,3,2,2,2,1,1] (.node [12,9,9,6,6,6,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,6,6,6,4,2,2,2,2,1,1] (.node [12,9,9,6,6,6,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,9,6,6,6,4,3,3,1,1,1,1] (.node [12,9,9,6,6,6,4,3,2,2,2,1] (.node [12,9,9,6,6,6,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,6,4,3,3,2,1,1] .empty .empty))) (.node [12,9,9,6,6,6,5,3,2,2,1,1] (.node [12,9,9,6,6,6,5,2,2,2,1,1,1] (.node [12,9,9,6,6,6,4,4,3,1,1,1] (.node [12,9,9,6,6,6,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,6,5,3,2,1,1,1,1] (.node [12,9,9,6,6,6,5,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,6,6,6,6,2,1,1,1,1,1,1] (.node [12,9,9,6,6,6,5,4,1,1,1,1,1] (.node [12,9,9,6,6,6,5,3,3,1,1,1] .empty .empty) .empty) (.node [12,9,9,6,6,6,6,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_464 : RowTree := (.node [12,9,9,7,5,4,4,4,4,2,1,1] (.node [12,9,9,7,5,4,4,3,3,2,2,1,1] (.node [12,9,9,7,4,4,4,4,4,2,1,1,1] (.node [12,9,9,7,4,4,4,4,3,2,2,1,1] (.node [12,9,9,6,6,6,6,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,5,4,4,2,2,2,2,2,2] (.node [12,9,9,7,4,4,4,4,4,2,2,1] .empty .empty) .empty)) (.node [12,9,9,7,5,4,4,4,3,2,2,1] (.node [12,9,9,7,5,4,4,4,3,2,1,1,1] (.node [12,9,9,7,5,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,5,4,4,4,4,1,1,1,1] .empty .empty))) (.node [12,9,9,7,5,5,4,3,3,2,2,1] (.node [12,9,9,7,5,5,4,2,2,2,2,2,1] (.node [12,9,9,7,5,5,3,3,3,2,2,1,1] (.node [12,9,9,7,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,7,5,5,4,3,3,2,1,1,1] (.node [12,9,9,7,5,5,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,7,5,5,4,4,3,1,1,1,1] (.node [12,9,9,7,5,5,4,4,2,2,2,1] (.node [12,9,9,7,5,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,5,5,4,4,3,2,1,1] .empty .empty)))) + +def degreeTree62_465 : RowTree := (.node [12,9,9,6,6,6,6,2,2,2,1,1] degreeTree62_463 degreeTree62_464) + +def degreeTree62_466 : RowTree := (.node [12,9,9,6,6,6,2,2,2,2,2,2,2] degreeTree62_462 degreeTree62_465) + +def degreeTree62_467 : RowTree := (.node [12,9,9,7,6,4,3,2,2,2,2,2,2] (.node [12,9,9,7,5,5,5,3,3,2,1,1] (.node [12,9,9,7,5,5,5,3,2,2,1,1,1] (.node [12,9,9,7,5,5,5,2,2,2,2,2] (.node [12,9,9,7,5,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,5,5,5,3,3,1,1,1,1] (.node [12,9,9,7,5,5,5,3,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,7,5,5,5,4,3,1,1,1] (.node [12,9,9,7,5,5,5,4,2,2,1,1] (.node [12,9,9,7,5,5,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,5,5,5,5,1,1,1,1,1] .empty .empty))) (.node [12,9,9,7,6,4,4,4,2,2,1,1,1] (.node [12,9,9,7,6,4,4,3,2,2,2,1,1] (.node [12,9,9,7,6,4,4,2,2,2,2,2,1] (.node [12,9,9,7,6,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,4,4,3,3,2,2,1] (.node [12,9,9,7,6,4,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,7,6,4,4,4,3,2,1,1] (.node [12,9,9,7,6,4,4,4,3,1,1,1,1] (.node [12,9,9,7,6,4,4,4,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,7,6,4,4,4,4,1,1,1] .empty .empty)))) + +def degreeTree62_468 : RowTree := (.node [12,9,9,7,6,5,4,4,2,1,1,1,1] (.node [12,9,9,7,6,5,4,2,2,2,2,2] (.node [12,9,9,7,6,5,3,3,3,2,1,1,1] (.node [12,9,9,7,6,5,3,3,2,2,2,1,1] (.node [12,9,9,7,6,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,7,6,5,4,2,2,2,2,1,1] (.node [12,9,9,7,6,5,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,9,7,6,5,4,3,3,1,1,1,1] (.node [12,9,9,7,6,5,4,3,2,2,2,1] (.node [12,9,9,7,6,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,5,4,3,3,2,1,1] .empty .empty))) (.node [12,9,9,7,6,5,5,3,2,2,1,1] (.node [12,9,9,7,6,5,5,2,2,2,1,1,1] (.node [12,9,9,7,6,5,4,4,3,1,1,1] (.node [12,9,9,7,6,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,5,5,3,2,1,1,1,1] (.node [12,9,9,7,6,5,5,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,7,6,6,2,2,2,2,2,1,1,1] (.node [12,9,9,7,6,5,5,4,1,1,1,1,1] (.node [12,9,9,7,6,5,5,3,3,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,6,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_469 : RowTree := (.node [12,9,9,7,6,5,2,2,2,2,2,2,2] degreeTree62_467 degreeTree62_468) + +def degreeTree62_470 : RowTree := (.node [12,9,9,7,6,6,4,3,1,1,1,1,1,1] (.node [12,9,9,7,6,6,3,3,3,1,1,1,1] (.node [12,9,9,7,6,6,3,3,2,1,1,1,1,1] (.node [12,9,9,7,6,6,3,2,2,2,2,2] (.node [12,9,9,7,6,6,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,6,3,3,2,2,2,1] (.node [12,9,9,7,6,6,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,7,6,6,4,2,2,2,1,1,1] (.node [12,9,9,7,6,6,4,2,2,1,1,1,1,1] (.node [12,9,9,7,6,6,3,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,6,4,2,2,2,2,1] .empty .empty))) (.node [12,9,9,7,6,6,5,2,2,1,1,1,1] (.node [12,9,9,7,6,6,4,3,3,1,1,1] (.node [12,9,9,7,6,6,4,3,2,2,1,1] (.node [12,9,9,7,6,6,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,6,5,2,1,1,1,1,1,1] (.node [12,9,9,7,6,6,4,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,7,6,6,6,1,1,1,1,1,1,1] (.node [12,9,9,7,6,6,5,3,1,1,1,1,1] (.node [12,9,9,7,6,6,5,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,6,6,6,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_471 : RowTree := (.node [12,9,9,7,7,4,4,2,2,2,2,2] (.node [12,9,9,7,7,4,3,3,3,1,1,1,1,1] (.node [12,9,9,7,7,4,3,2,2,2,2,1,1,1] (.node [12,9,9,7,7,4,2,2,2,2,2,2,2] (.node [12,9,9,7,7,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,4,3,3,2,2,2,1,1] (.node [12,9,9,7,7,4,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,7,7,4,4,2,2,2,1,1,1,1] (.node [12,9,9,7,7,4,3,3,3,2,2,1] (.node [12,9,9,7,7,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,4,4,2,2,2,2,1,1] .empty .empty))) (.node [12,9,9,7,7,4,4,3,3,2,1,1] (.node [12,9,9,7,7,4,4,3,2,2,2,1] (.node [12,9,9,7,7,4,4,3,2,2,1,1,1] (.node [12,9,9,7,7,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,4,4,3,3,1,1,1,1] .empty .empty)) (.node [12,9,9,7,7,4,4,4,2,2,1,1] (.node [12,9,9,7,7,4,4,4,2,1,1,1,1] (.node [12,9,9,7,7,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,4,4,4,3,1,1,1] .empty .empty)))) + +def degreeTree62_472 : RowTree := (.node [12,9,9,7,7,3,3,2,2,2,2,2,2] degreeTree62_470 degreeTree62_471) + +def degreeTree62_473 : RowTree := (.node [12,9,9,7,6,6,3,2,2,2,1,1,1,1] degreeTree62_469 degreeTree62_472) + +def degreeTree62_474 : RowTree := (.node [12,9,9,7,5,5,4,4,4,1,1,1] degreeTree62_466 degreeTree62_473) + +def degreeTree62_475 : RowTree := (.node [12,9,9,6,5,5,4,4,3,2,1,1,1] degreeTree62_459 degreeTree62_474) + +def degreeTree62_476 : RowTree := (.node [12,9,9,7,7,5,4,2,2,2,1,1,1] (.node [12,9,9,7,7,5,3,3,2,2,1,1,1] (.node [12,9,9,7,7,5,3,2,2,2,2,1,1] (.node [12,9,9,7,7,5,3,2,2,2,1,1,1,1] (.node [12,9,9,7,7,5,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,7,7,5,3,3,2,1,1,1,1,1] (.node [12,9,9,7,7,5,3,2,2,2,2,2] .empty .empty) .empty)) (.node [12,9,9,7,7,5,3,3,3,2,1,1] (.node [12,9,9,7,7,5,3,3,3,1,1,1,1] (.node [12,9,9,7,7,5,3,3,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,7,7,5,4,2,2,1,1,1,1,1] .empty .empty))) (.node [12,9,9,7,7,5,5,2,1,1,1,1,1,1] (.node [12,9,9,7,7,5,4,3,2,1,1,1,1] (.node [12,9,9,7,7,5,4,3,1,1,1,1,1,1] (.node [12,9,9,7,7,5,4,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,7,7,5,4,4,1,1,1,1,1] (.node [12,9,9,7,7,5,4,3,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,7,7,5,5,3,1,1,1,1,1] (.node [12,9,9,7,7,5,5,2,2,2,1,1] (.node [12,9,9,7,7,5,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,6,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_477 : RowTree := (.node [12,9,9,7,7,6,4,3,1,1,1,1,1] (.node [12,9,9,7,7,6,3,3,2,1,1,1,1] (.node [12,9,9,7,7,6,3,2,2,2,1,1,1] (.node [12,9,9,7,7,6,3,2,2,1,1,1,1,1] (.node [12,9,9,7,7,6,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,7,7,6,3,3,1,1,1,1,1,1] (.node [12,9,9,7,7,6,3,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,7,7,6,4,2,2,1,1,1,1] (.node [12,9,9,7,7,6,4,2,1,1,1,1,1,1] (.node [12,9,9,7,7,6,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,6,4,2,2,2,1,1] .empty .empty))) (.node [12,9,9,7,7,7,2,2,2,2,2,1] (.node [12,9,9,7,7,6,6,1,1,1,1,1,1] (.node [12,9,9,7,7,6,5,2,1,1,1,1,1] (.node [12,9,9,7,7,6,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,7,2,2,2,2,1,1,1] (.node [12,9,9,7,7,7,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,7,7,7,3,2,2,2,1,1] (.node [12,9,9,7,7,7,3,2,2,1,1,1,1] (.node [12,9,9,7,7,7,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,7,7,7,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_478 : RowTree := (.node [12,9,9,7,7,6,2,2,2,2,2,1,1] degreeTree62_476 degreeTree62_477) + +def degreeTree62_479 : RowTree := (.node [12,9,9,8,5,4,3,3,3,2,2,1,1] (.node [12,9,9,8,4,4,4,4,3,2,1,1,1] (.node [12,9,9,8,4,4,4,2,2,2,2,2,2] (.node [12,9,9,7,7,7,5,1,1,1,1,1,1] (.node [12,9,9,7,7,7,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,4,4,4,4,2,2,2,1,1] (.node [12,9,9,8,4,4,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,8,4,4,4,4,4,2,1,1] (.node [12,9,9,8,4,4,4,4,4,1,1,1,1] (.node [12,9,9,8,4,4,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,5,4,3,2,2,2,2,2,2] .empty .empty))) (.node [12,9,9,8,5,4,4,4,2,2,2,1] (.node [12,9,9,8,5,4,4,3,3,2,1,1,1] (.node [12,9,9,8,5,4,4,3,2,2,2,1,1] (.node [12,9,9,8,5,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,5,4,4,4,2,2,1,1,1] (.node [12,9,9,8,5,4,4,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,9,8,5,4,4,4,4,1,1,1] (.node [12,9,9,8,5,4,4,4,3,2,1,1] (.node [12,9,9,8,5,4,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,5,5,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_480 : RowTree := (.node [12,9,9,8,5,5,4,4,2,2,1,1] (.node [12,9,9,8,5,5,4,3,2,2,1,1,1] (.node [12,9,9,8,5,5,3,3,3,2,2,1] (.node [12,9,9,8,5,5,3,3,3,2,1,1,1] (.node [12,9,9,8,5,5,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,8,5,5,4,2,2,2,2,2] (.node [12,9,9,8,5,5,4,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,8,5,5,4,3,3,2,1,1] (.node [12,9,9,8,5,5,4,3,3,1,1,1,1] (.node [12,9,9,8,5,5,4,3,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,5,5,4,4,2,1,1,1,1] .empty .empty))) (.node [12,9,9,8,5,5,5,4,1,1,1,1,1] (.node [12,9,9,8,5,5,5,2,2,2,2,1] (.node [12,9,9,8,5,5,5,2,2,2,1,1,1] (.node [12,9,9,8,5,5,4,4,3,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,5,5,5,3,2,2,1,1] (.node [12,9,9,8,5,5,5,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,6,4,2,2,2,2,2,2,2] (.node [12,9,9,8,6,3,3,3,3,2,2,1,1] (.node [12,9,9,8,6,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,8,6,4,3,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_481 : RowTree := (.node [12,9,9,8,5,5,3,2,2,2,2,2,1] degreeTree62_479 degreeTree62_480) + +def degreeTree62_482 : RowTree := (.node [12,9,9,7,7,7,4,1,1,1,1,1,1,1] degreeTree62_478 degreeTree62_481) + +def degreeTree62_483 : RowTree := (.node [12,9,9,8,6,4,4,3,3,1,1,1,1] (.node [12,9,9,8,6,4,4,2,2,2,2,1,1] (.node [12,9,9,8,6,4,3,3,3,2,1,1,1] (.node [12,9,9,8,6,4,3,3,3,1,1,1,1,1] (.node [12,9,9,8,6,4,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,4,4,2,2,2,1,1,1,1] (.node [12,9,9,8,6,4,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,9,9,8,6,4,4,3,2,2,1,1,1] (.node [12,9,9,8,6,4,4,3,2,1,1,1,1,1] (.node [12,9,9,8,6,4,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,8,6,4,4,3,2,2,2,1] .empty .empty))) (.node [12,9,9,8,6,5,2,2,2,2,2,2,1] (.node [12,9,9,8,6,4,4,4,2,1,1,1,1] (.node [12,9,9,8,6,4,4,4,1,1,1,1,1,1] (.node [12,9,9,8,6,4,4,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,5,2,2,2,2,2,1,1,1] (.node [12,9,9,8,6,4,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,8,6,5,3,2,2,2,2,2] (.node [12,9,9,8,6,5,3,2,2,2,2,1,1] (.node [12,9,9,8,6,5,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,5,3,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_484 : RowTree := (.node [12,9,9,8,6,5,5,2,1,1,1,1,1,1] (.node [12,9,9,8,6,5,4,2,2,2,2,1] (.node [12,9,9,8,6,5,3,3,3,2,1,1] (.node [12,9,9,8,6,5,3,3,3,1,1,1,1] (.node [12,9,9,8,6,5,3,3,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,6,5,4,2,2,2,1,1,1] (.node [12,9,9,8,6,5,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,6,5,4,3,2,2,1,1] (.node [12,9,9,8,6,5,4,3,2,1,1,1,1] (.node [12,9,9,8,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,5,4,4,1,1,1,1,1] .empty .empty))) (.node [12,9,9,8,6,6,2,2,2,2,2,2] (.node [12,9,9,8,6,5,5,3,1,1,1,1,1] (.node [12,9,9,8,6,5,5,2,2,2,1,1] (.node [12,9,9,8,6,5,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,6,2,2,2,2,2,1,1] (.node [12,9,9,8,6,6,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,6,6,3,2,2,2,2,1] (.node [12,9,9,8,6,6,3,2,2,2,1,1,1] (.node [12,9,9,8,6,6,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,6,3,3,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_485 : RowTree := (.node [12,9,9,8,6,5,3,3,2,2,1,1,1] degreeTree62_483 degreeTree62_484) + +def degreeTree62_486 : RowTree := (.node [12,9,9,8,7,3,3,2,2,2,2,1,1,1] (.node [12,9,9,8,6,6,5,1,1,1,1,1,1,1] (.node [12,9,9,8,6,6,4,2,2,1,1,1,1] (.node [12,9,9,8,6,6,4,2,1,1,1,1,1,1] (.node [12,9,9,8,6,6,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,8,6,6,4,3,1,1,1,1,1] (.node [12,9,9,8,6,6,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,8,7,2,2,2,2,2,2,2,2,1] (.node [12,9,9,8,6,6,6,1,1,1,1,1,1] (.node [12,9,9,8,6,6,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,3,2,2,2,2,2,2,2] .empty .empty))) (.node [12,9,9,8,7,4,2,2,2,2,2,1,1,1] (.node [12,9,9,8,7,3,3,3,3,1,1,1,1,1] (.node [12,9,9,8,7,3,3,3,2,2,2,1,1] (.node [12,9,9,8,7,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,7,3,3,3,3,2,2,1] (.node [12,9,9,8,7,3,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,7,4,3,2,2,2,2,1,1] (.node [12,9,9,8,7,4,3,2,2,2,1,1,1,1] (.node [12,9,9,8,7,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,7,4,3,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_487 : RowTree := (.node [12,9,9,8,7,4,4,4,1,1,1,1,1] (.node [12,9,9,8,7,4,4,2,2,2,1,1,1] (.node [12,9,9,8,7,4,3,3,3,1,1,1,1] (.node [12,9,9,8,7,4,3,3,2,2,2,1] (.node [12,9,9,8,7,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,4,4,2,2,1,1,1,1,1] (.node [12,9,9,8,7,4,3,3,3,2,1,1] .empty .empty) .empty)) (.node [12,9,9,8,7,4,4,3,2,1,1,1,1] (.node [12,9,9,8,7,4,4,3,1,1,1,1,1,1] (.node [12,9,9,8,7,4,4,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,7,4,4,3,2,2,1,1] .empty .empty))) (.node [12,9,9,8,7,5,3,2,2,2,1,1,1] (.node [12,9,9,8,7,5,2,2,2,2,2,2] (.node [12,9,9,8,7,5,2,2,2,2,2,1,1] (.node [12,9,9,8,7,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,5,3,2,2,1,1,1,1,1] .empty .empty)) (.node [12,9,9,8,7,5,3,3,2,1,1,1,1] (.node [12,9,9,8,7,5,3,3,1,1,1,1,1,1] (.node [12,9,9,8,7,5,3,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,8,7,5,3,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_488 : RowTree := (.node [12,9,9,8,7,4,3,3,2,1,1,1,1,1] degreeTree62_486 degreeTree62_487) + +def degreeTree62_489 : RowTree := (.node [12,9,9,8,6,6,3,3,2,1,1,1,1] degreeTree62_485 degreeTree62_488) + +def degreeTree62_490 : RowTree := (.node [12,9,9,8,6,4,3,2,2,2,2,2,1] degreeTree62_482 degreeTree62_489) + +def degreeTree62_491 : RowTree := (.node [12,9,9,8,7,6,3,2,2,2,1,1] (.node [12,9,9,8,7,6,2,2,2,1,1,1,1,1] (.node [12,9,9,8,7,5,4,3,1,1,1,1,1] (.node [12,9,9,8,7,5,4,2,2,2,1,1] (.node [12,9,9,8,7,5,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,5,5,2,1,1,1,1,1] (.node [12,9,9,8,7,5,5,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,7,6,3,2,1,1,1,1,1,1] (.node [12,9,9,8,7,6,2,2,2,2,2,1] (.node [12,9,9,8,7,6,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,6,3,2,2,1,1,1,1] .empty .empty))) (.node [12,9,9,8,7,7,2,2,2,1,1,1,1] (.node [12,9,9,8,7,6,4,2,1,1,1,1,1] (.node [12,9,9,8,7,6,4,1,1,1,1,1,1,1] (.node [12,9,9,8,7,6,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,7,2,2,1,1,1,1,1,1] (.node [12,9,9,8,7,6,5,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,7,7,3,2,1,1,1,1,1] (.node [12,9,9,8,7,7,3,1,1,1,1,1,1,1] (.node [12,9,9,8,7,7,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,8,7,7,4,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_492 : RowTree := (.node [12,9,9,8,8,3,3,3,3,2,1,1] (.node [12,9,9,8,8,3,3,2,2,2,2,2] (.node [12,9,9,8,8,3,2,2,2,2,2,2,1] (.node [12,9,9,8,8,3,2,2,2,2,2,1,1,1] (.node [12,9,9,8,8,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,8,8,3,3,2,2,2,2,1,1] (.node [12,9,9,8,8,3,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,8,3,3,3,2,2,2,1] (.node [12,9,9,8,8,3,3,3,2,2,1,1,1] (.node [12,9,9,8,8,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,3,3,3,3,1,1,1,1] .empty .empty))) (.node [12,9,9,8,8,4,3,2,2,2,2,1] (.node [12,9,9,8,8,4,2,2,2,2,2,2] (.node [12,9,9,8,8,4,2,2,2,2,2,1,1] (.node [12,9,9,8,8,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,4,3,2,2,2,1,1,1] (.node [12,9,9,8,8,4,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,8,4,3,3,2,2,1,1] (.node [12,9,9,8,8,4,3,3,2,1,1,1,1] (.node [12,9,9,8,8,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,4,4,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_493 : RowTree := (.node [12,9,9,8,8,2,2,2,2,2,2,2,1,1] degreeTree62_491 degreeTree62_492) + +def degreeTree62_494 : RowTree := (.node [12,9,9,8,8,5,4,2,1,1,1,1,1] (.node [12,9,9,8,8,5,3,2,1,1,1,1,1,1] (.node [12,9,9,8,8,5,2,2,2,1,1,1,1,1] (.node [12,9,9,8,8,4,4,3,1,1,1,1,1] (.node [12,9,9,8,8,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,5,2,2,2,2,2,1] (.node [12,9,9,8,8,5,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,8,8,5,3,3,1,1,1,1,1] (.node [12,9,9,8,8,5,3,2,2,2,1,1] (.node [12,9,9,8,8,5,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,5,4,1,1,1,1,1,1,1] .empty .empty))) (.node [12,9,9,8,8,6,3,2,1,1,1,1,1] (.node [12,9,9,8,8,6,2,2,2,1,1,1,1] (.node [12,9,9,8,8,6,2,2,1,1,1,1,1,1] (.node [12,9,9,8,8,5,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,6,3,1,1,1,1,1,1,1] (.node [12,9,9,8,8,6,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,8,8,7,2,2,1,1,1,1,1] (.node [12,9,9,8,8,7,2,1,1,1,1,1,1,1] (.node [12,9,9,8,8,6,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,8,8,7,3,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_495 : RowTree := (.node [12,9,9,9,4,4,4,4,2,2,1,1,1] (.node [12,9,9,9,4,4,4,3,2,2,2,1,1] (.node [12,9,9,9,4,4,3,3,3,2,2,1,1] (.node [12,9,9,9,4,4,3,2,2,2,2,2,2] (.node [12,9,9,8,8,8,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,4,4,4,2,2,2,2,2,1] (.node [12,9,9,9,4,4,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,4,4,4,3,3,2,2,1] (.node [12,9,9,9,4,4,4,3,3,2,1,1,1] (.node [12,9,9,9,4,4,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,4,4,4,4,2,1,1,1,1,1] .empty .empty))) (.node [12,9,9,9,5,3,3,3,3,2,2,1,1] (.node [12,9,9,9,4,4,4,4,3,2,1,1] (.node [12,9,9,9,4,4,4,4,3,1,1,1,1] (.node [12,9,9,9,4,4,4,4,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,9,5,3,3,2,2,2,2,2,2] (.node [12,9,9,9,4,4,4,4,4,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,5,4,3,2,2,2,2,2,1] (.node [12,9,9,9,5,4,3,2,2,2,2,1,1,1] (.node [12,9,9,9,5,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,9,5,4,3,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_496 : RowTree := (.node [12,9,9,8,8,8,1,1,1,1,1,1,1,1] degreeTree62_494 degreeTree62_495) + +def degreeTree62_497 : RowTree := (.node [12,9,9,8,8,4,4,2,2,1,1,1,1] degreeTree62_493 degreeTree62_496) + +def degreeTree62_498 : RowTree := (.node [12,9,9,9,5,4,4,4,1,1,1,1,1,1] (.node [12,9,9,9,5,4,4,3,2,1,1,1,1,1] (.node [12,9,9,9,5,4,4,2,2,2,1,1,1,1] (.node [12,9,9,9,5,4,3,3,3,2,2,1] (.node [12,9,9,9,5,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,5,4,4,2,2,2,2,2] (.node [12,9,9,9,5,4,4,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,9,9,9,5,4,4,3,3,1,1,1,1] (.node [12,9,9,9,5,4,4,3,2,2,2,1] (.node [12,9,9,9,5,4,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,5,4,4,3,3,2,1,1] .empty .empty))) (.node [12,9,9,9,5,5,3,2,2,2,2,1,1] (.node [12,9,9,9,5,5,2,2,2,2,2,1,1,1] (.node [12,9,9,9,5,4,4,4,2,2,1,1] (.node [12,9,9,9,5,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,5,5,3,2,2,2,1,1,1,1] (.node [12,9,9,9,5,5,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,9,5,5,3,3,2,2,1,1,1] (.node [12,9,9,9,5,5,3,3,2,1,1,1,1,1] (.node [12,9,9,9,5,5,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,9,5,5,3,3,2,2,2,1] .empty .empty)))) + +def degreeTree62_499 : RowTree := (.node [12,9,9,9,5,5,5,2,2,2,1,1] (.node [12,9,9,9,5,5,4,3,2,1,1,1,1] (.node [12,9,9,9,5,5,4,2,2,2,1,1,1] (.node [12,9,9,9,5,5,4,2,2,1,1,1,1,1] (.node [12,9,9,9,5,5,3,3,3,2,1,1] .empty .empty) .empty) (.node [12,9,9,9,5,5,4,3,1,1,1,1,1,1] (.node [12,9,9,9,5,5,4,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,9,5,5,5,2,1,1,1,1,1,1] (.node [12,9,9,9,5,5,4,4,1,1,1,1,1] (.node [12,9,9,9,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,9,5,5,5,2,2,1,1,1,1] .empty .empty))) (.node [12,9,9,9,6,3,3,3,2,2,2,1,1] (.node [12,9,9,9,6,3,2,2,2,2,2,2,2] (.node [12,9,9,9,6,2,2,2,2,2,2,2,2,1] (.node [12,9,9,9,5,5,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,3,3,2,2,2,2,2,1] (.node [12,9,9,9,6,3,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,6,3,3,3,3,2,2,1] (.node [12,9,9,9,6,3,3,3,3,2,1,1,1] (.node [12,9,9,9,6,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,4,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_500 : RowTree := (.node [12,9,9,9,5,5,3,3,3,1,1,1,1] degreeTree62_498 degreeTree62_499) + +def degreeTree62_501 : RowTree := (.node [12,9,9,9,6,4,4,2,2,2,2,1] (.node [12,9,9,9,6,4,3,3,2,2,2,1] (.node [12,9,9,9,6,4,3,2,2,2,2,2] (.node [12,9,9,9,6,4,3,2,2,2,2,1,1] (.node [12,9,9,9,6,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,4,3,3,2,2,1,1,1] (.node [12,9,9,9,6,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,6,4,4,2,2,1,1,1,1,1] (.node [12,9,9,9,6,4,3,3,3,2,1,1] (.node [12,9,9,9,6,4,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,4,4,2,2,2,1,1,1] .empty .empty))) (.node [12,9,9,9,6,5,2,2,2,2,2,1,1] (.node [12,9,9,9,6,4,4,3,2,2,1,1] (.node [12,9,9,9,6,4,4,3,2,1,1,1,1] (.node [12,9,9,9,6,4,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,5,2,2,2,2,1,1,1,1] (.node [12,9,9,9,6,4,4,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,6,5,3,2,2,2,1,1,1] (.node [12,9,9,9,6,5,3,2,2,1,1,1,1,1] (.node [12,9,9,9,6,5,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,9,6,5,3,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_502 : RowTree := (.node [12,9,9,9,6,6,2,2,2,2,2,1] (.node [12,9,9,9,6,5,4,3,1,1,1,1,1] (.node [12,9,9,9,6,5,4,2,1,1,1,1,1,1] (.node [12,9,9,9,6,5,3,3,2,2,1,1] (.node [12,9,9,9,6,5,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,5,4,2,2,2,1,1] (.node [12,9,9,9,6,5,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,6,6,2,2,2,1,1,1,1,1] (.node [12,9,9,9,6,5,5,2,1,1,1,1,1] (.node [12,9,9,9,6,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,6,2,2,2,2,1,1,1] .empty .empty))) (.node [12,9,9,9,6,6,4,1,1,1,1,1,1,1] (.node [12,9,9,9,6,6,3,2,2,2,1,1] (.node [12,9,9,9,6,6,3,2,2,1,1,1,1] (.node [12,9,9,9,6,6,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,6,6,3,3,1,1,1,1,1] .empty .empty)) (.node [12,9,9,9,7,2,2,2,2,2,2,2,1,1] (.node [12,9,9,9,6,6,5,1,1,1,1,1,1] (.node [12,9,9,9,6,6,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,7,2,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_503 : RowTree := (.node [12,9,9,9,6,5,3,3,1,1,1,1,1,1] degreeTree62_501 degreeTree62_502) + +def degreeTree62_504 : RowTree := (.node [12,9,9,9,6,4,2,2,2,2,2,2,1] degreeTree62_500 degreeTree62_503) + +def degreeTree62_505 : RowTree := (.node [12,9,9,9,5,4,3,3,3,1,1,1,1,1] degreeTree62_497 degreeTree62_504) + +def degreeTree62_506 : RowTree := (.node [12,9,9,8,7,5,4,2,1,1,1,1,1,1] degreeTree62_490 degreeTree62_505) + +def degreeTree62_507 : RowTree := (.node [12,9,9,7,7,5,2,2,2,2,2,1,1,1] degreeTree62_475 degreeTree62_506) + +def degreeTree62_508 : RowTree := (.node [12,9,8,8,6,6,3,2,2,2,2,1,1] degreeTree62_444 degreeTree62_507) + +def degreeTree62_509 : RowTree := (.node [12,8,8,8,7,5,4,3,2,2,2,1] degreeTree62_381 degreeTree62_508) + +def degreeTree62_510 : RowTree := (.node [11,11,11,7,5,4,2,2,2,2,2,2,1] degreeTree62_254 degreeTree62_509) + +def degreeTree62_511 : RowTree := (.node [12,9,9,9,7,4,2,2,2,2,2,1,1] (.node [12,9,9,9,7,3,3,3,2,2,1,1,1] (.node [12,9,9,9,7,3,3,2,2,2,2,1,1] (.node [12,9,9,9,7,3,3,2,2,2,1,1,1,1] (.node [12,9,9,9,7,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,9,7,3,3,3,2,1,1,1,1,1] (.node [12,9,9,9,7,3,3,2,2,2,2,2] .empty .empty) .empty)) (.node [12,9,9,9,7,3,3,3,3,2,1,1] (.node [12,9,9,9,7,3,3,3,3,1,1,1,1] (.node [12,9,9,9,7,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [12,9,9,9,7,4,2,2,2,2,1,1,1,1] .empty .empty))) (.node [12,9,9,9,7,4,3,3,2,1,1,1,1] (.node [12,9,9,9,7,4,3,2,2,2,1,1,1] (.node [12,9,9,9,7,4,3,2,2,1,1,1,1,1] (.node [12,9,9,9,7,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,9,9,9,7,4,3,3,1,1,1,1,1,1] (.node [12,9,9,9,7,4,3,2,2,2,2,1] .empty .empty) .empty)) (.node [12,9,9,9,7,4,4,2,2,1,1,1,1] (.node [12,9,9,9,7,4,4,2,1,1,1,1,1,1] (.node [12,9,9,9,7,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,9,7,4,4,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_512 : RowTree := (.node [12,9,9,9,7,6,2,2,1,1,1,1,1,1] (.node [12,9,9,9,7,5,3,2,2,2,1,1] (.node [12,9,9,9,7,5,2,2,2,2,2,1] (.node [12,9,9,9,7,5,2,2,2,2,1,1,1] (.node [12,9,9,9,7,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,7,5,3,2,2,1,1,1,1] (.node [12,9,9,9,7,5,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,7,5,4,2,1,1,1,1,1] (.node [12,9,9,9,7,5,4,1,1,1,1,1,1,1] (.node [12,9,9,9,7,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,7,5,5,1,1,1,1,1,1] .empty .empty))) (.node [12,9,9,9,7,7,2,1,1,1,1,1,1,1] (.node [12,9,9,9,7,6,3,1,1,1,1,1,1,1] (.node [12,9,9,9,7,6,2,2,2,2,1,1] (.node [12,9,9,9,7,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,7,6,4,1,1,1,1,1,1] (.node [12,9,9,9,7,6,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,8,2,2,2,2,2,2,1,1,1] (.node [12,9,9,9,7,7,3,1,1,1,1,1,1] (.node [12,9,9,9,7,7,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,8,2,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_513 : RowTree := (.node [12,9,9,9,7,4,4,3,1,1,1,1,1] degreeTree62_511 degreeTree62_512) + +def degreeTree62_514 : RowTree := (.node [12,9,9,9,8,4,2,2,2,2,2,1] (.node [12,9,9,9,8,3,3,3,1,1,1,1,1,1] (.node [12,9,9,9,8,3,3,2,2,1,1,1,1,1] (.node [12,9,9,9,8,3,2,2,2,2,2,2] (.node [12,9,9,9,8,3,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,9,9,9,8,3,3,2,2,2,2,1] (.node [12,9,9,9,8,3,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,8,4,2,2,2,1,1,1,1,1] (.node [12,9,9,9,8,3,3,3,2,2,1,1] (.node [12,9,9,9,8,3,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,8,4,2,2,2,2,1,1,1] .empty .empty))) (.node [12,9,9,9,8,4,4,2,1,1,1,1,1] (.node [12,9,9,9,8,4,3,2,2,2,1,1] (.node [12,9,9,9,8,4,3,2,2,1,1,1,1] (.node [12,9,9,9,8,4,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,8,4,4,1,1,1,1,1,1,1] (.node [12,9,9,9,8,4,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,8,5,2,2,2,2,1,1] (.node [12,9,9,9,8,5,2,2,2,1,1,1,1] (.node [12,9,9,9,8,5,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,8,5,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_515 : RowTree := (.node [12,9,9,9,9,3,2,2,2,1,1,1,1,1] (.node [12,9,9,9,8,7,2,1,1,1,1,1,1] (.node [12,9,9,9,8,6,2,2,1,1,1,1,1] (.node [12,9,9,9,8,6,2,1,1,1,1,1,1,1] (.node [12,9,9,9,8,5,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,8,7,1,1,1,1,1,1,1,1] (.node [12,9,9,9,8,6,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,9,2,2,2,2,2,2,1,1] (.node [12,9,9,9,9,2,2,2,2,2,1,1,1,1] (.node [12,9,9,9,8,8,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,9,2,2,2,2,2,2,2] .empty .empty))) (.node [12,9,9,9,9,3,3,3,1,1,1,1,1] (.node [12,9,9,9,9,3,3,2,1,1,1,1,1,1] (.node [12,9,9,9,9,3,2,2,2,2,2,1] (.node [12,9,9,9,9,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,9,3,3,2,2,2,1,1] (.node [12,9,9,9,9,3,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,9,9,9,9,4,2,2,2,2,1,1] (.node [12,9,9,9,9,4,2,2,2,1,1,1,1] (.node [12,9,9,9,9,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,9,4,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_516 : RowTree := (.node [12,9,9,9,8,5,3,2,1,1,1,1,1] degreeTree62_514 degreeTree62_515) + +def degreeTree62_517 : RowTree := (.node [12,9,9,9,8,3,2,2,2,2,1,1,1,1] degreeTree62_513 degreeTree62_516) + +def degreeTree62_518 : RowTree := (.node [12,10,6,5,5,5,5,4,4,2,2,1,1] (.node [12,9,9,9,9,6,2,1,1,1,1,1,1] (.node [12,9,9,9,9,5,2,2,1,1,1,1,1] (.node [12,9,9,9,9,5,2,1,1,1,1,1,1,1] (.node [12,9,9,9,9,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,9,9,9,9,6,1,1,1,1,1,1,1,1] (.node [12,9,9,9,9,5,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,5,5,5,5,5,5,5,2,1,1,1] (.node [12,10,5,5,5,5,5,5,4,2,2,1,1] (.node [12,9,9,9,9,7,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,5,5,5,5,5,5,5,2,2,1] .empty .empty))) (.node [12,10,6,6,5,5,4,4,4,2,2,1,1] (.node [12,10,6,5,5,5,5,5,4,2,2,1] (.node [12,10,6,5,5,5,5,5,4,2,1,1,1] (.node [12,10,6,5,5,5,5,5,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,6,5,5,5,5,5,5,2,1,1] (.node [12,10,6,5,5,5,5,5,5,1,1,1,1] .empty .empty) .empty)) (.node [12,10,6,6,5,5,5,4,4,2,2,1] (.node [12,10,6,6,5,5,5,4,4,2,1,1,1] (.node [12,10,6,6,5,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,6,6,5,5,5,5,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_519 : RowTree := (.node [12,10,6,6,6,5,5,4,3,2,1,1,1] (.node [12,10,6,6,6,5,4,4,4,2,1,1,1] (.node [12,10,6,6,5,5,5,5,4,2,1,1] (.node [12,10,6,6,5,5,5,5,4,1,1,1,1] (.node [12,10,6,6,5,5,5,5,3,2,2,1] .empty .empty) .empty) (.node [12,10,6,6,6,5,4,4,3,2,2,1,1] (.node [12,10,6,6,6,4,4,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,10,6,6,6,5,5,3,3,2,2,1,1] (.node [12,10,6,6,6,5,5,2,2,2,2,2,2] (.node [12,10,6,6,6,5,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,10,6,6,6,5,5,4,2,2,2,1,1] .empty .empty))) (.node [12,10,6,6,6,5,5,5,3,1,1,1,1] (.node [12,10,6,6,6,5,5,4,4,2,1,1] (.node [12,10,6,6,6,5,5,4,4,1,1,1,1] (.node [12,10,6,6,6,5,5,4,3,2,2,1] .empty .empty) .empty) (.node [12,10,6,6,6,5,5,5,2,2,2,1] (.node [12,10,6,6,6,5,5,5,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,6,6,6,6,4,3,3,2,2,1,1] (.node [12,10,6,6,6,6,4,2,2,2,2,2,2] (.node [12,10,6,6,6,5,5,5,3,2,1,1] .empty .empty) .empty) (.node [12,10,6,6,6,6,4,4,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_520 : RowTree := (.node [12,10,6,6,5,5,5,5,3,2,1,1,1] degreeTree62_518 degreeTree62_519) + +def degreeTree62_521 : RowTree := (.node [12,10,6,6,6,6,5,4,3,2,1,1] (.node [12,10,6,6,6,6,5,3,3,2,1,1,1] (.node [12,10,6,6,6,6,4,4,4,2,1,1] (.node [12,10,6,6,6,6,4,4,4,1,1,1,1] (.node [12,10,6,6,6,6,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,10,6,6,6,6,5,3,2,2,2,1,1] (.node [12,10,6,6,6,6,5,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,6,6,6,6,5,4,2,2,2,1] (.node [12,10,6,6,6,6,5,4,2,2,1,1,1] (.node [12,10,6,6,6,6,5,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,6,6,6,6,5,4,3,1,1,1,1] .empty .empty))) (.node [12,10,6,6,6,6,6,3,2,2,2,1] (.node [12,10,6,6,6,6,6,2,2,2,2,1,1] (.node [12,10,6,6,6,6,5,5,2,2,1,1] (.node [12,10,6,6,6,6,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,6,6,6,6,6,3,2,2,1,1,1] (.node [12,10,6,6,6,6,6,2,2,2,2,2] .empty .empty) .empty)) (.node [12,10,6,6,6,6,6,4,2,1,1,1,1] (.node [12,10,6,6,6,6,6,3,3,2,1,1] (.node [12,10,6,6,6,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,6,6,6,6,6,4,2,2,1,1] .empty .empty)))) + +def degreeTree62_522 : RowTree := (.node [12,10,7,6,5,5,4,4,3,2,2,1,1] (.node [12,10,7,5,5,5,5,5,3,2,1,1,1] (.node [12,10,7,5,5,5,5,4,4,2,1,1,1] (.node [12,10,7,5,5,5,5,4,3,2,2,1,1] (.node [12,10,7,5,5,5,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,5,5,5,5,5,2,2,2,1,1] (.node [12,10,7,5,5,5,5,4,4,2,2,1] .empty .empty) .empty)) (.node [12,10,7,5,5,5,5,5,4,2,1,1] (.node [12,10,7,5,5,5,5,5,4,1,1,1,1] (.node [12,10,7,5,5,5,5,5,3,2,2,1] .empty .empty) .empty) (.node [12,10,7,6,5,4,4,4,4,2,2,1,1] .empty .empty))) (.node [12,10,7,6,5,5,5,4,3,2,1,1,1] (.node [12,10,7,6,5,5,5,2,2,2,2,2,2] (.node [12,10,7,6,5,5,4,4,4,2,2,1] (.node [12,10,7,6,5,5,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,6,5,5,5,4,2,2,2,1,1] (.node [12,10,7,6,5,5,5,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,6,5,5,5,4,4,2,1,1] (.node [12,10,7,6,5,5,5,4,4,1,1,1,1] (.node [12,10,7,6,5,5,5,4,3,2,2,1] .empty .empty) .empty) (.node [12,10,7,6,5,5,5,5,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_523 : RowTree := (.node [12,10,6,6,6,6,6,5,1,1,1,1,1] degreeTree62_521 degreeTree62_522) + +def degreeTree62_524 : RowTree := (.node [12,10,6,6,6,6,4,4,3,2,1,1,1] degreeTree62_520 degreeTree62_523) + +def degreeTree62_525 : RowTree := (.node [12,9,9,9,9,4,3,2,1,1,1,1,1] degreeTree62_517 degreeTree62_524) + +def degreeTree62_526 : RowTree := (.node [12,10,7,6,6,5,4,4,4,1,1,1,1] (.node [12,10,7,6,6,5,4,2,2,2,2,2,2] (.node [12,10,7,6,6,4,4,4,3,2,2,1,1] (.node [12,10,7,6,5,5,5,5,3,2,1,1] (.node [12,10,7,6,5,5,5,5,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,6,6,4,4,4,4,2,2,1] (.node [12,10,7,6,6,4,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [12,10,7,6,6,5,4,4,3,2,1,1,1] (.node [12,10,7,6,6,5,4,4,2,2,2,1,1] (.node [12,10,7,6,6,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,6,6,5,4,4,3,2,2,1] .empty .empty))) (.node [12,10,7,6,6,5,5,4,2,2,1,1,1] (.node [12,10,7,6,6,5,5,3,2,2,2,1,1] (.node [12,10,7,6,6,5,5,2,2,2,2,2,1] (.node [12,10,7,6,6,5,4,4,4,2,1,1] .empty .empty) .empty) (.node [12,10,7,6,6,5,5,3,3,2,2,1] (.node [12,10,7,6,6,5,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,10,7,6,6,5,5,4,3,2,1,1] (.node [12,10,7,6,6,5,5,4,3,1,1,1,1] (.node [12,10,7,6,6,5,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,10,7,6,6,5,5,5,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_527 : RowTree := (.node [12,10,7,6,6,6,5,2,2,2,2,1,1] (.node [12,10,7,6,6,6,4,3,3,2,2,1] (.node [12,10,7,6,6,6,4,2,2,2,2,2,1] (.node [12,10,7,6,6,6,3,3,3,2,2,1,1] (.node [12,10,7,6,6,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,7,6,6,6,4,3,3,2,1,1,1] (.node [12,10,7,6,6,6,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,6,6,6,4,4,3,1,1,1,1] (.node [12,10,7,6,6,6,4,4,2,2,2,1] (.node [12,10,7,6,6,6,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,6,6,6,4,4,3,2,1,1] .empty .empty))) (.node [12,10,7,6,6,6,5,4,2,1,1,1,1] (.node [12,10,7,6,6,6,5,3,2,2,2,1] (.node [12,10,7,6,6,6,5,3,2,2,1,1,1] (.node [12,10,7,6,6,6,5,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,7,6,6,6,5,3,3,2,1,1] (.node [12,10,7,6,6,6,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,7,6,6,6,6,2,2,2,1,1,1] (.node [12,10,7,6,6,6,5,5,1,1,1,1,1] (.node [12,10,7,6,6,6,5,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,6,6,6,6,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_528 : RowTree := (.node [12,10,7,6,6,5,5,5,2,2,1,1] degreeTree62_526 degreeTree62_527) + +def degreeTree62_529 : RowTree := (.node [12,10,7,7,5,5,4,4,3,2,2,1] (.node [12,10,7,7,5,4,4,4,4,2,2,1] (.node [12,10,7,7,4,4,4,4,4,2,2,1,1] (.node [12,10,7,6,6,6,6,4,1,1,1,1,1] (.node [12,10,7,6,6,6,6,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,5,4,4,4,4,2,1,1,1] (.node [12,10,7,7,5,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,5,5,4,4,2,2,2,1,1] (.node [12,10,7,7,5,5,4,3,3,2,2,1,1] (.node [12,10,7,7,5,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,7,7,5,5,4,4,3,2,1,1,1] .empty .empty))) (.node [12,10,7,7,5,5,5,3,3,2,2,1] (.node [12,10,7,7,5,5,5,2,2,2,2,2,1] (.node [12,10,7,7,5,5,4,4,4,2,1,1] (.node [12,10,7,7,5,5,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,5,5,5,3,3,2,1,1,1] (.node [12,10,7,7,5,5,5,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,5,5,5,4,3,1,1,1,1] (.node [12,10,7,7,5,5,5,4,2,2,2,1] (.node [12,10,7,7,5,5,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,5,5,5,4,3,2,1,1] .empty .empty)))) + +def degreeTree62_530 : RowTree := (.node [12,10,7,7,6,5,4,2,2,2,2,2,1] (.node [12,10,7,7,6,4,4,4,3,2,2,1] (.node [12,10,7,7,6,4,4,3,3,2,2,1,1] (.node [12,10,7,7,6,4,4,2,2,2,2,2,2] (.node [12,10,7,7,5,5,5,5,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,4,4,4,3,2,1,1,1] (.node [12,10,7,7,6,4,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,6,5,3,2,2,2,2,2,2] (.node [12,10,7,7,6,4,4,4,4,2,1,1] (.node [12,10,7,7,6,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,5,3,3,3,2,2,1,1] .empty .empty))) (.node [12,10,7,7,6,5,4,4,3,1,1,1,1] (.node [12,10,7,7,6,5,4,3,3,2,2,1] (.node [12,10,7,7,6,5,4,3,3,2,1,1,1] (.node [12,10,7,7,6,5,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,5,4,4,2,2,2,1] (.node [12,10,7,7,6,5,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,7,7,6,5,5,2,2,2,2,2] (.node [12,10,7,7,6,5,5,2,2,2,2,1,1] (.node [12,10,7,7,6,5,4,4,3,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,5,5,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_531 : RowTree := (.node [12,10,7,7,5,5,5,5,2,1,1,1,1] degreeTree62_529 degreeTree62_530) + +def degreeTree62_532 : RowTree := (.node [12,10,7,6,6,6,6,3,2,1,1,1,1] degreeTree62_528 degreeTree62_531) + +def degreeTree62_533 : RowTree := (.node [12,10,7,7,6,6,4,2,2,2,2,1,1] (.node [12,10,7,7,6,6,2,2,2,2,2,2,2] (.node [12,10,7,7,6,5,5,4,2,1,1,1,1] (.node [12,10,7,7,6,5,5,3,3,2,1,1] (.node [12,10,7,7,6,5,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,5,5,5,1,1,1,1,1] (.node [12,10,7,7,6,5,5,4,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,6,6,3,3,3,2,1,1,1] (.node [12,10,7,7,6,6,3,3,2,2,2,1,1] (.node [12,10,7,7,6,6,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,7,7,6,6,3,3,3,2,2,1] .empty .empty))) (.node [12,10,7,7,6,6,4,4,2,1,1,1,1] (.node [12,10,7,7,6,6,4,3,2,2,2,1] (.node [12,10,7,7,6,6,4,3,2,2,1,1,1] (.node [12,10,7,7,6,6,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,7,7,6,6,4,3,3,2,1,1] (.node [12,10,7,7,6,6,4,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,7,7,6,6,5,2,2,2,2,1] (.node [12,10,7,7,6,6,5,2,2,2,1,1,1] (.node [12,10,7,7,6,6,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,6,5,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_534 : RowTree := (.node [12,10,7,7,7,4,4,3,3,2,2,1] (.node [12,10,7,7,7,4,3,2,2,2,2,2,2] (.node [12,10,7,7,6,6,6,2,2,1,1,1,1] (.node [12,10,7,7,6,6,6,2,1,1,1,1,1,1] (.node [12,10,7,7,6,6,5,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,6,6,6,3,1,1,1,1,1] (.node [12,10,7,7,6,6,6,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,7,4,4,3,2,2,2,1,1] (.node [12,10,7,7,7,4,4,2,2,2,2,2,1] (.node [12,10,7,7,7,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,4,4,3,3,2,1,1,1] .empty .empty))) (.node [12,10,7,7,7,5,3,2,2,2,2,2,1] (.node [12,10,7,7,7,4,4,4,3,1,1,1,1] (.node [12,10,7,7,7,4,4,4,2,2,2,1] (.node [12,10,7,7,7,4,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,5,2,2,2,2,2,2,2] (.node [12,10,7,7,7,4,4,4,3,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,7,5,3,3,3,2,2,1] (.node [12,10,7,7,7,5,3,3,3,2,1,1,1] (.node [12,10,7,7,7,5,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,5,4,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_535 : RowTree := (.node [12,10,7,7,6,6,5,3,2,2,1,1] degreeTree62_533 degreeTree62_534) + +def degreeTree62_536 : RowTree := (.node [12,10,7,7,7,5,5,4,1,1,1,1,1] (.node [12,10,7,7,7,5,4,4,2,2,1,1] (.node [12,10,7,7,7,5,4,3,3,1,1,1,1] (.node [12,10,7,7,7,5,4,3,2,2,2,1] (.node [12,10,7,7,7,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,5,4,4,2,1,1,1,1] (.node [12,10,7,7,7,5,4,3,3,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,7,5,5,3,2,1,1,1,1] (.node [12,10,7,7,7,5,5,2,2,2,2,1] (.node [12,10,7,7,7,5,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,5,5,3,2,2,1,1] .empty .empty))) (.node [12,10,7,7,7,6,3,3,2,1,1,1,1,1] (.node [12,10,7,7,7,6,3,2,2,2,1,1,1,1] (.node [12,10,7,7,7,6,2,2,2,2,2,2,1] (.node [12,10,7,7,7,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,6,3,2,2,2,2,2] (.node [12,10,7,7,7,6,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,7,7,7,6,3,3,3,1,1,1,1] (.node [12,10,7,7,7,6,3,3,2,2,2,1] (.node [12,10,7,7,7,6,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,6,3,3,3,2,1,1] .empty .empty)))) + +def degreeTree62_537 : RowTree := (.node [12,10,7,7,7,6,6,1,1,1,1,1,1,1] (.node [12,10,7,7,7,6,4,4,1,1,1,1,1] (.node [12,10,7,7,7,6,4,3,1,1,1,1,1,1] (.node [12,10,7,7,7,6,4,2,2,2,2,1] (.node [12,10,7,7,7,6,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,6,4,3,2,2,1,1] (.node [12,10,7,7,7,6,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,7,7,7,6,5,2,2,2,1,1] (.node [12,10,7,7,7,6,5,2,2,1,1,1,1] (.node [12,10,7,7,7,6,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,6,5,3,1,1,1,1,1] .empty .empty))) (.node [12,10,7,7,7,7,3,2,2,1,1,1,1,1] (.node [12,10,7,7,7,7,2,2,2,2,2,1,1] (.node [12,10,7,7,7,7,2,2,2,2,1,1,1,1] (.node [12,10,7,7,7,6,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,7,2,2,2,2,2,2] .empty .empty)) (.node [12,10,7,7,7,7,3,3,1,1,1,1,1,1] (.node [12,10,7,7,7,7,3,2,2,2,2,1] (.node [12,10,7,7,7,7,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,7,3,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_538 : RowTree := (.node [12,10,7,7,7,6,4,2,2,1,1,1,1,1] degreeTree62_536 degreeTree62_537) + +def degreeTree62_539 : RowTree := (.node [12,10,7,7,7,5,4,2,2,2,2,2] degreeTree62_535 degreeTree62_538) + +def degreeTree62_540 : RowTree := (.node [12,10,7,7,6,5,5,3,2,2,2,1] degreeTree62_532 degreeTree62_539) + +def degreeTree62_541 : RowTree := (.node [12,10,7,6,5,5,5,5,2,2,2,1] degreeTree62_525 degreeTree62_540) + +def degreeTree62_542 : RowTree := (.node [12,10,8,5,5,5,5,2,2,2,2,2,2] (.node [12,10,7,7,7,7,6,1,1,1,1,1,1] (.node [12,10,7,7,7,7,4,3,1,1,1,1,1] (.node [12,10,7,7,7,7,4,2,2,1,1,1,1] (.node [12,10,7,7,7,7,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,7,7,7,7,5,2,1,1,1,1,1] (.node [12,10,7,7,7,7,5,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,5,5,5,4,4,4,2,1,1,1] (.node [12,10,8,5,5,5,4,4,3,2,2,1,1] (.node [12,10,8,5,5,4,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,5,5,5,4,4,4,2,2,1] .empty .empty))) (.node [12,10,8,5,5,5,5,4,4,2,1,1] (.node [12,10,8,5,5,5,5,4,3,2,1,1,1] (.node [12,10,8,5,5,5,5,4,2,2,2,1,1] (.node [12,10,8,5,5,5,5,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,5,5,5,5,4,4,1,1,1,1] (.node [12,10,8,5,5,5,5,4,3,2,2,1] .empty .empty) .empty)) (.node [12,10,8,5,5,5,5,5,3,1,1,1,1] (.node [12,10,8,5,5,5,5,5,2,2,2,1] (.node [12,10,8,5,5,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,5,5,5,5,5,3,2,1,1] .empty .empty)))) + +def degreeTree62_543 : RowTree := (.node [12,10,8,6,5,5,5,2,2,2,2,2,1] (.node [12,10,8,6,5,5,4,4,2,2,2,1,1] (.node [12,10,8,6,5,4,4,4,4,2,2,1] (.node [12,10,8,6,5,4,4,4,4,2,1,1,1] (.node [12,10,8,6,5,4,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,6,5,5,4,3,3,2,2,1,1] (.node [12,10,8,6,5,5,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,10,8,6,5,5,4,4,4,1,1,1,1] (.node [12,10,8,6,5,5,4,4,3,2,2,1] (.node [12,10,8,6,5,5,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,6,5,5,4,4,4,2,1,1] .empty .empty))) (.node [12,10,8,6,5,5,5,4,3,1,1,1,1] (.node [12,10,8,6,5,5,5,3,3,2,2,1] (.node [12,10,8,6,5,5,5,3,3,2,1,1,1] (.node [12,10,8,6,5,5,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,6,5,5,5,4,2,2,2,1] (.node [12,10,8,6,5,5,5,4,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,6,5,5,5,5,2,2,1,1] (.node [12,10,8,6,5,5,5,5,2,1,1,1,1] (.node [12,10,8,6,5,5,5,4,3,2,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,4,4,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_544 : RowTree := (.node [12,10,8,6,4,4,4,4,4,2,2,1,1] degreeTree62_542 degreeTree62_543) + +def degreeTree62_545 : RowTree := (.node [12,10,8,6,6,5,4,3,3,2,2,1] (.node [12,10,8,6,6,5,3,2,2,2,2,2,2] (.node [12,10,8,6,6,4,4,4,3,2,2,1] (.node [12,10,8,6,6,4,4,4,3,2,1,1,1] (.node [12,10,8,6,6,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,4,4,4,4,2,1,1] (.node [12,10,8,6,6,4,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,6,6,5,4,3,2,2,2,1,1] (.node [12,10,8,6,6,5,4,2,2,2,2,2,1] (.node [12,10,8,6,6,5,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,5,4,3,3,2,1,1,1] .empty .empty))) (.node [12,10,8,6,6,5,5,2,2,2,2,2] (.node [12,10,8,6,6,5,4,4,3,1,1,1,1] (.node [12,10,8,6,6,5,4,4,2,2,2,1] (.node [12,10,8,6,6,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,5,5,2,2,2,2,1,1] (.node [12,10,8,6,6,5,4,4,3,2,1,1] .empty .empty) .empty)) (.node [12,10,8,6,6,5,5,3,3,1,1,1,1] (.node [12,10,8,6,6,5,5,3,2,2,2,1] (.node [12,10,8,6,6,5,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,5,5,3,3,2,1,1] .empty .empty)))) + +def degreeTree62_546 : RowTree := (.node [12,10,8,6,6,6,4,3,2,2,2,1] (.node [12,10,8,6,6,6,3,3,3,2,1,1,1] (.node [12,10,8,6,6,6,2,2,2,2,2,2,2] (.node [12,10,8,6,6,5,5,5,1,1,1,1,1] (.node [12,10,8,6,6,5,5,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,6,3,3,2,2,2,1,1] (.node [12,10,8,6,6,6,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,8,6,6,6,4,2,2,2,2,2] (.node [12,10,8,6,6,6,4,2,2,2,2,1,1] (.node [12,10,8,6,6,6,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,8,6,6,6,4,3,2,2,1,1,1] .empty .empty))) (.node [12,10,8,6,6,6,5,2,2,2,2,1] (.node [12,10,8,6,6,6,4,4,2,1,1,1,1] (.node [12,10,8,6,6,6,4,3,3,2,1,1] (.node [12,10,8,6,6,6,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,6,5,2,2,2,1,1,1] (.node [12,10,8,6,6,6,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,10,8,6,6,6,5,4,1,1,1,1,1] (.node [12,10,8,6,6,6,5,3,2,2,1,1] (.node [12,10,8,6,6,6,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,6,6,6,6,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_547 : RowTree := (.node [12,10,8,6,6,5,5,4,2,1,1,1,1] degreeTree62_545 degreeTree62_546) + +def degreeTree62_548 : RowTree := (.node [12,10,8,6,6,4,4,3,3,2,2,1,1] degreeTree62_544 degreeTree62_547) + +def degreeTree62_549 : RowTree := (.node [12,10,8,7,5,4,4,4,4,2,1,1] (.node [12,10,8,7,5,4,4,3,3,2,2,1,1] (.node [12,10,8,7,4,4,4,4,4,2,1,1,1] (.node [12,10,8,7,4,4,4,4,3,2,2,1,1] (.node [12,10,8,6,6,6,6,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,5,4,4,2,2,2,2,2,2] (.node [12,10,8,7,4,4,4,4,4,2,2,1] .empty .empty) .empty)) (.node [12,10,8,7,5,4,4,4,3,2,2,1] (.node [12,10,8,7,5,4,4,4,3,2,1,1,1] (.node [12,10,8,7,5,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,5,4,4,4,4,1,1,1,1] .empty .empty))) (.node [12,10,8,7,5,5,4,3,3,2,2,1] (.node [12,10,8,7,5,5,4,2,2,2,2,2,1] (.node [12,10,8,7,5,5,3,3,3,2,2,1,1] (.node [12,10,8,7,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,7,5,5,4,3,3,2,1,1,1] (.node [12,10,8,7,5,5,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,8,7,5,5,4,4,3,1,1,1,1] (.node [12,10,8,7,5,5,4,4,2,2,2,1] (.node [12,10,8,7,5,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,5,5,4,4,3,2,1,1] .empty .empty)))) + +def degreeTree62_550 : RowTree := (.node [12,10,8,7,6,4,4,2,2,2,2,2,1] (.node [12,10,8,7,5,5,5,4,2,1,1,1,1] (.node [12,10,8,7,5,5,5,3,2,2,2,1] (.node [12,10,8,7,5,5,5,3,2,2,1,1,1] (.node [12,10,8,7,5,5,5,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,7,5,5,5,3,3,2,1,1] (.node [12,10,8,7,5,5,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,6,4,3,2,2,2,2,2,2] (.node [12,10,8,7,5,5,5,5,1,1,1,1,1] (.node [12,10,8,7,5,5,5,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,4,3,3,3,2,2,1,1] .empty .empty))) (.node [12,10,8,7,6,4,4,4,3,1,1,1,1] (.node [12,10,8,7,6,4,4,3,3,2,2,1] (.node [12,10,8,7,6,4,4,3,3,2,1,1,1] (.node [12,10,8,7,6,4,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,4,4,4,2,2,2,1] (.node [12,10,8,7,6,4,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,6,5,3,2,2,2,2,2,1] (.node [12,10,8,7,6,5,2,2,2,2,2,2,2] (.node [12,10,8,7,6,4,4,4,3,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,5,3,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_551 : RowTree := (.node [12,10,8,7,5,5,5,2,2,2,2,1,1] degreeTree62_549 degreeTree62_550) + +def degreeTree62_552 : RowTree := (.node [12,10,8,7,6,5,5,2,2,2,2,1] (.node [12,10,8,7,6,5,4,3,3,1,1,1,1] (.node [12,10,8,7,6,5,4,2,2,2,2,2] (.node [12,10,8,7,6,5,4,2,2,2,2,1,1] (.node [12,10,8,7,6,5,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,8,7,6,5,4,3,2,2,2,1] (.node [12,10,8,7,6,5,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,6,5,4,4,2,2,1,1] (.node [12,10,8,7,6,5,4,4,2,1,1,1,1] (.node [12,10,8,7,6,5,4,3,3,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,5,5,2,2,2,1,1,1] .empty .empty))) (.node [12,10,8,7,6,6,3,2,2,2,1,1,1,1] (.node [12,10,8,7,6,5,5,4,1,1,1,1,1] (.node [12,10,8,7,6,5,5,3,2,2,1,1] (.node [12,10,8,7,6,5,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,6,2,2,2,2,2,2,1] (.node [12,10,8,7,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,6,6,3,3,2,1,1,1,1,1] (.node [12,10,8,7,6,6,3,2,2,2,2,2] (.node [12,10,8,7,6,6,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,6,3,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_553 : RowTree := (.node [12,10,8,7,6,6,5,2,2,1,1,1,1] (.node [12,10,8,7,6,6,4,3,1,1,1,1,1,1] (.node [12,10,8,7,6,6,4,2,2,1,1,1,1,1] (.node [12,10,8,7,6,6,3,3,3,2,1,1] (.node [12,10,8,7,6,6,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,6,4,2,2,2,2,1] (.node [12,10,8,7,6,6,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,6,6,4,4,1,1,1,1,1] (.node [12,10,8,7,6,6,4,3,2,2,1,1] (.node [12,10,8,7,6,6,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,6,6,5,2,1,1,1,1,1,1] .empty .empty))) (.node [12,10,8,7,7,4,2,2,2,2,2,2,2] (.node [12,10,8,7,6,6,6,2,1,1,1,1,1] (.node [12,10,8,7,6,6,6,1,1,1,1,1,1,1] (.node [12,10,8,7,6,6,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,3,3,3,3,2,2,1,1] (.node [12,10,8,7,7,3,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,10,8,7,7,4,3,3,2,2,2,1,1] (.node [12,10,8,7,7,4,3,2,2,2,2,2,1] (.node [12,10,8,7,7,4,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,4,3,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_554 : RowTree := (.node [12,10,8,7,6,6,3,3,2,2,2,1] degreeTree62_552 degreeTree62_553) + +def degreeTree62_555 : RowTree := (.node [12,10,8,7,6,5,3,3,3,2,1,1,1] degreeTree62_551 degreeTree62_554) + +def degreeTree62_556 : RowTree := (.node [12,10,8,6,6,6,6,2,2,1,1,1,1] degreeTree62_548 degreeTree62_555) + +def degreeTree62_557 : RowTree := (.node [12,10,8,7,7,4,4,4,2,1,1,1,1] (.node [12,10,8,7,7,4,4,3,2,2,1,1,1] (.node [12,10,8,7,7,4,4,2,2,2,2,1,1] (.node [12,10,8,7,7,4,4,2,2,2,1,1,1,1] (.node [12,10,8,7,7,4,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,8,7,7,4,4,3,2,1,1,1,1,1] (.node [12,10,8,7,7,4,4,2,2,2,2,2] .empty .empty) .empty)) (.node [12,10,8,7,7,4,4,3,3,2,1,1] (.node [12,10,8,7,7,4,4,3,3,1,1,1,1] (.node [12,10,8,7,7,4,4,3,2,2,2,1] .empty .empty) .empty) (.node [12,10,8,7,7,4,4,4,1,1,1,1,1,1] .empty .empty))) (.node [12,10,8,7,7,5,3,2,2,2,2,2] (.node [12,10,8,7,7,5,2,2,2,2,2,2,1] (.node [12,10,8,7,7,5,2,2,2,2,2,1,1,1] (.node [12,10,8,7,7,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,5,3,2,2,2,2,1,1] (.node [12,10,8,7,7,5,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,7,5,3,3,2,2,2,1] (.node [12,10,8,7,7,5,3,3,2,2,1,1,1] (.node [12,10,8,7,7,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,5,3,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_558 : RowTree := (.node [12,10,8,7,7,6,2,2,2,2,2,1,1] (.node [12,10,8,7,7,5,4,4,1,1,1,1,1] (.node [12,10,8,7,7,5,4,2,2,2,2,1] (.node [12,10,8,7,7,5,4,2,2,2,1,1,1] (.node [12,10,8,7,7,5,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,5,4,3,2,1,1,1,1] (.node [12,10,8,7,7,5,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,7,7,5,5,3,1,1,1,1,1] (.node [12,10,8,7,7,5,5,2,2,1,1,1,1] (.node [12,10,8,7,7,5,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,6,2,2,2,2,1,1,1,1] .empty .empty))) (.node [12,10,8,7,7,6,3,3,2,1,1,1,1] (.node [12,10,8,7,7,6,3,2,2,2,1,1,1] (.node [12,10,8,7,7,6,3,2,2,1,1,1,1,1] (.node [12,10,8,7,7,6,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,7,7,6,3,3,1,1,1,1,1,1] (.node [12,10,8,7,7,6,3,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,8,7,7,6,4,3,1,1,1,1,1] (.node [12,10,8,7,7,6,4,2,2,1,1,1,1] (.node [12,10,8,7,7,6,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,6,5,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_559 : RowTree := (.node [12,10,8,7,7,5,3,3,3,2,1,1] degreeTree62_557 degreeTree62_558) + +def degreeTree62_560 : RowTree := (.node [12,10,8,8,4,4,4,2,2,2,2,2,2] (.node [12,10,8,7,7,7,3,2,2,1,1,1,1] (.node [12,10,8,7,7,7,2,2,2,2,1,1,1] (.node [12,10,8,7,7,7,2,2,2,1,1,1,1,1] (.node [12,10,8,7,7,6,6,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,7,3,2,1,1,1,1,1,1] (.node [12,10,8,7,7,7,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,8,7,7,7,4,2,1,1,1,1,1] (.node [12,10,8,7,7,7,4,1,1,1,1,1,1,1] (.node [12,10,8,7,7,7,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,7,7,7,5,1,1,1,1,1,1] .empty .empty))) (.node [12,10,8,8,4,4,4,4,4,2,1,1] (.node [12,10,8,8,4,4,4,4,3,2,1,1,1] (.node [12,10,8,8,4,4,4,4,2,2,2,1,1] (.node [12,10,8,8,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,8,4,4,4,4,4,1,1,1,1] (.node [12,10,8,8,4,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,10,8,8,5,4,4,2,2,2,2,2,1] (.node [12,10,8,8,5,4,3,3,3,2,2,1,1] (.node [12,10,8,8,5,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,8,5,4,4,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_561 : RowTree := (.node [12,10,8,8,5,5,4,2,2,2,2,1,1] (.node [12,10,8,8,5,5,2,2,2,2,2,2,2] (.node [12,10,8,8,5,4,4,4,2,2,2,1] (.node [12,10,8,8,5,4,4,4,2,2,1,1,1] (.node [12,10,8,8,5,4,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,8,8,5,4,4,4,3,2,1,1] (.node [12,10,8,8,5,4,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,5,5,3,3,3,2,1,1,1] (.node [12,10,8,8,5,5,3,3,2,2,2,1,1] (.node [12,10,8,8,5,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,8,8,5,5,3,3,3,2,2,1] .empty .empty))) (.node [12,10,8,8,5,5,4,4,2,1,1,1,1] (.node [12,10,8,8,5,5,4,3,2,2,2,1] (.node [12,10,8,8,5,5,4,3,2,2,1,1,1] (.node [12,10,8,8,5,5,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,8,5,5,4,3,3,2,1,1] (.node [12,10,8,8,5,5,4,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,5,5,5,2,2,2,2,1] (.node [12,10,8,8,5,5,5,2,2,2,1,1,1] (.node [12,10,8,8,5,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,8,5,5,5,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_562 : RowTree := (.node [12,10,8,8,5,4,4,3,3,2,1,1,1] degreeTree62_560 degreeTree62_561) + +def degreeTree62_563 : RowTree := (.node [12,10,8,7,7,6,5,2,1,1,1,1,1] degreeTree62_559 degreeTree62_562) + +def degreeTree62_564 : RowTree := (.node [12,10,8,8,6,4,4,2,2,2,2,1,1] (.node [12,10,8,8,6,4,3,3,2,2,2,1,1] (.node [12,10,8,8,6,4,2,2,2,2,2,2,2] (.node [12,10,8,8,6,3,3,3,3,2,2,1,1] (.node [12,10,8,8,6,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,8,6,4,3,2,2,2,2,2,1] (.node [12,10,8,8,6,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,6,4,3,3,3,2,2,1] (.node [12,10,8,8,6,4,3,3,3,2,1,1,1] (.node [12,10,8,8,6,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,4,4,2,2,2,1,1,1,1] .empty .empty))) (.node [12,10,8,8,6,4,4,3,3,2,1,1] (.node [12,10,8,8,6,4,4,3,2,2,1,1,1] (.node [12,10,8,8,6,4,4,3,2,1,1,1,1,1] (.node [12,10,8,8,6,4,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,8,6,4,4,3,3,1,1,1,1] (.node [12,10,8,8,6,4,4,3,2,2,2,1] .empty .empty) .empty)) (.node [12,10,8,8,6,5,2,2,2,2,2,1,1,1] (.node [12,10,8,8,6,4,4,4,2,1,1,1,1] (.node [12,10,8,8,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,5,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_565 : RowTree := (.node [12,10,8,8,6,5,4,3,1,1,1,1,1,1] (.node [12,10,8,8,6,5,3,3,3,1,1,1,1] (.node [12,10,8,8,6,5,3,3,2,1,1,1,1,1] (.node [12,10,8,8,6,5,3,2,2,2,2,2] (.node [12,10,8,8,6,5,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,5,3,3,2,2,2,1] (.node [12,10,8,8,6,5,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,6,5,4,2,2,2,1,1,1] (.node [12,10,8,8,6,5,4,2,2,1,1,1,1,1] (.node [12,10,8,8,6,5,3,3,3,2,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,5,4,2,2,2,2,1] .empty .empty))) (.node [12,10,8,8,6,6,2,2,2,2,1,1,1,1] (.node [12,10,8,8,6,5,5,2,1,1,1,1,1,1] (.node [12,10,8,8,6,5,4,4,1,1,1,1,1] (.node [12,10,8,8,6,5,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,5,5,3,1,1,1,1,1] (.node [12,10,8,8,6,5,5,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,6,6,3,2,2,1,1,1,1,1] (.node [12,10,8,8,6,6,2,2,2,2,2,2] (.node [12,10,8,8,6,6,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,6,3,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_566 : RowTree := (.node [12,10,8,8,6,5,3,2,2,2,1,1,1,1] degreeTree62_564 degreeTree62_565) + +def degreeTree62_567 : RowTree := (.node [12,10,8,8,7,3,3,2,2,2,2,1,1,1] (.node [12,10,8,8,6,6,5,1,1,1,1,1,1,1] (.node [12,10,8,8,6,6,4,2,1,1,1,1,1,1] (.node [12,10,8,8,6,6,3,3,2,1,1,1,1] (.node [12,10,8,8,6,6,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,6,6,4,3,1,1,1,1,1] (.node [12,10,8,8,6,6,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,7,2,2,2,2,2,2,2,2,1] (.node [12,10,8,8,6,6,6,1,1,1,1,1,1] (.node [12,10,8,8,6,6,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,3,2,2,2,2,2,2,2] .empty .empty))) (.node [12,10,8,8,7,4,2,2,2,2,2,1,1,1] (.node [12,10,8,8,7,3,3,3,3,1,1,1,1,1] (.node [12,10,8,8,7,3,3,3,2,2,2,1,1] (.node [12,10,8,8,7,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,8,8,7,3,3,3,3,2,2,1] (.node [12,10,8,8,7,3,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,7,4,3,2,2,2,2,1,1] (.node [12,10,8,8,7,4,3,2,2,2,1,1,1,1] (.node [12,10,8,8,7,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,8,8,7,4,3,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_568 : RowTree := (.node [12,10,8,8,7,5,2,2,2,2,1,1,1,1] (.node [12,10,8,8,7,4,4,2,2,2,1,1,1] (.node [12,10,8,8,7,4,3,3,3,1,1,1,1] (.node [12,10,8,8,7,4,3,3,2,2,2,1] (.node [12,10,8,8,7,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,4,4,2,2,1,1,1,1,1] (.node [12,10,8,8,7,4,3,3,3,2,1,1] .empty .empty) .empty)) (.node [12,10,8,8,7,4,4,3,2,1,1,1,1] (.node [12,10,8,8,7,4,4,3,1,1,1,1,1,1] (.node [12,10,8,8,7,4,4,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,8,8,7,4,4,4,1,1,1,1,1] .empty .empty))) (.node [12,10,8,8,7,5,3,2,2,2,2,1] (.node [12,10,8,8,7,5,3,2,2,1,1,1,1,1] (.node [12,10,8,8,7,5,2,2,2,2,2,2] (.node [12,10,8,8,7,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,5,3,2,2,2,1,1,1] .empty .empty)) (.node [12,10,8,8,7,5,4,2,1,1,1,1,1,1] (.node [12,10,8,8,7,5,3,3,2,1,1,1,1] (.node [12,10,8,8,7,5,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,5,4,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_569 : RowTree := (.node [12,10,8,8,7,4,3,3,2,1,1,1,1,1] degreeTree62_567 degreeTree62_568) + +def degreeTree62_570 : RowTree := (.node [12,10,8,8,6,6,3,2,2,2,2,1] degreeTree62_566 degreeTree62_569) + +def degreeTree62_571 : RowTree := (.node [12,10,8,8,5,5,5,4,1,1,1,1,1] degreeTree62_563 degreeTree62_570) + +def degreeTree62_572 : RowTree := (.node [12,10,8,7,7,4,3,3,3,2,1,1,1] degreeTree62_556 degreeTree62_571) + +def degreeTree62_573 : RowTree := (.node [12,10,7,7,7,7,3,3,2,2,1,1] degreeTree62_541 degreeTree62_572) + +def degreeTree62_574 : RowTree := (.node [12,10,8,8,7,6,5,1,1,1,1,1,1] (.node [12,10,8,8,7,6,3,2,1,1,1,1,1,1] (.node [12,10,8,8,7,6,2,2,2,1,1,1,1,1] (.node [12,10,8,8,7,5,5,2,1,1,1,1,1] (.node [12,10,8,8,7,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,6,2,2,2,2,2,1] (.node [12,10,8,8,7,6,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,7,6,4,1,1,1,1,1,1,1] (.node [12,10,8,8,7,6,3,3,1,1,1,1,1] (.node [12,10,8,8,7,6,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,6,4,2,1,1,1,1,1] .empty .empty))) (.node [12,10,8,8,8,2,2,2,2,2,2,2,1,1] (.node [12,10,8,8,7,7,3,1,1,1,1,1,1,1] (.node [12,10,8,8,7,7,2,2,2,1,1,1,1] (.node [12,10,8,8,7,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,7,7,4,1,1,1,1,1,1] (.node [12,10,8,8,7,7,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,8,3,2,2,2,2,2,2,1] (.node [12,10,8,8,8,3,2,2,2,2,2,1,1,1] (.node [12,10,8,8,8,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,8,8,3,3,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_575 : RowTree := (.node [12,10,8,8,8,4,3,2,2,2,1,1,1] (.node [12,10,8,8,8,3,3,3,3,2,1,1] (.node [12,10,8,8,8,3,3,3,2,2,1,1,1] (.node [12,10,8,8,8,3,3,3,2,1,1,1,1,1] (.node [12,10,8,8,8,3,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,8,8,8,3,3,3,3,1,1,1,1] (.node [12,10,8,8,8,3,3,3,2,2,2,1] .empty .empty) .empty)) (.node [12,10,8,8,8,4,2,2,2,2,2,2] (.node [12,10,8,8,8,4,2,2,2,2,2,1,1] (.node [12,10,8,8,8,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,8,4,3,2,2,1,1,1,1,1] .empty .empty))) (.node [12,10,8,8,8,4,4,3,1,1,1,1,1] (.node [12,10,8,8,8,4,3,3,2,1,1,1,1] (.node [12,10,8,8,8,4,3,3,1,1,1,1,1,1] (.node [12,10,8,8,8,4,3,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,8,8,8,4,4,2,2,1,1,1,1] (.node [12,10,8,8,8,4,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,8,5,2,2,2,2,2,1] (.node [12,10,8,8,8,5,2,2,2,2,1,1,1] (.node [12,10,8,8,8,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,8,5,3,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_576 : RowTree := (.node [12,10,8,8,8,3,3,2,2,2,2,1,1] degreeTree62_574 degreeTree62_575) + +def degreeTree62_577 : RowTree := (.node [12,10,8,8,8,7,2,2,1,1,1,1,1] (.node [12,10,8,8,8,6,2,2,2,1,1,1,1] (.node [12,10,8,8,8,5,4,2,1,1,1,1,1] (.node [12,10,8,8,8,5,4,1,1,1,1,1,1,1] (.node [12,10,8,8,8,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,8,6,2,2,1,1,1,1,1,1] (.node [12,10,8,8,8,5,5,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,8,8,8,6,4,1,1,1,1,1,1] (.node [12,10,8,8,8,6,3,2,1,1,1,1,1] (.node [12,10,8,8,8,6,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,8,8,8,7,2,1,1,1,1,1,1,1] .empty .empty))) (.node [12,10,9,5,5,4,4,4,4,2,1,1,1] (.node [12,10,8,8,8,8,2,1,1,1,1,1,1] (.node [12,10,8,8,8,8,1,1,1,1,1,1,1,1] (.node [12,10,8,8,8,7,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,5,5,4,4,4,3,2,2,1,1] (.node [12,10,9,5,4,4,4,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,5,5,5,4,3,3,2,2,1,1] (.node [12,10,9,5,5,5,4,2,2,2,2,2,2] (.node [12,10,9,5,5,4,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,10,9,5,5,5,4,4,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_578 : RowTree := (.node [12,10,9,5,5,5,5,4,3,2,1,1] (.node [12,10,9,5,5,5,5,3,3,2,1,1,1] (.node [12,10,9,5,5,5,4,4,4,2,1,1] (.node [12,10,9,5,5,5,4,4,4,1,1,1,1] (.node [12,10,9,5,5,5,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,10,9,5,5,5,5,3,2,2,2,1,1] (.node [12,10,9,5,5,5,5,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,5,5,5,5,4,2,2,2,1] (.node [12,10,9,5,5,5,5,4,2,2,1,1,1] (.node [12,10,9,5,5,5,5,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,9,5,5,5,5,4,3,1,1,1,1] .empty .empty))) (.node [12,10,9,6,5,4,4,3,3,2,2,1,1] (.node [12,10,9,6,4,4,4,4,4,2,1,1,1] (.node [12,10,9,6,4,4,4,4,3,2,2,1,1] (.node [12,10,9,5,5,5,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,5,4,4,2,2,2,2,2,2] (.node [12,10,9,6,4,4,4,4,4,2,2,1] .empty .empty) .empty)) (.node [12,10,9,6,5,4,4,4,3,2,2,1] (.node [12,10,9,6,5,4,4,4,3,2,1,1,1] (.node [12,10,9,6,5,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,9,6,5,4,4,4,4,1,1,1,1] .empty .empty)))) + +def degreeTree62_579 : RowTree := (.node [12,10,9,5,5,5,4,4,3,2,1,1,1] degreeTree62_577 degreeTree62_578) + +def degreeTree62_580 : RowTree := (.node [12,10,8,8,8,5,3,2,2,1,1,1,1] degreeTree62_576 degreeTree62_579) + +def degreeTree62_581 : RowTree := (.node [12,10,9,6,5,5,5,2,2,2,2,1,1] (.node [12,10,9,6,5,5,4,3,3,2,2,1] (.node [12,10,9,6,5,5,4,2,2,2,2,2,1] (.node [12,10,9,6,5,5,3,3,3,2,2,1,1] (.node [12,10,9,6,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,6,5,5,4,3,3,2,1,1,1] (.node [12,10,9,6,5,5,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,6,5,5,4,4,3,1,1,1,1] (.node [12,10,9,6,5,5,4,4,2,2,2,1] (.node [12,10,9,6,5,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,5,5,4,4,3,2,1,1] .empty .empty))) (.node [12,10,9,6,5,5,5,4,2,1,1,1,1] (.node [12,10,9,6,5,5,5,3,2,2,2,1] (.node [12,10,9,6,5,5,5,3,2,2,1,1,1] (.node [12,10,9,6,5,5,5,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,6,5,5,5,3,3,2,1,1] (.node [12,10,9,6,5,5,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,6,6,4,3,3,3,2,2,1,1] (.node [12,10,9,6,6,4,3,2,2,2,2,2,2] (.node [12,10,9,6,5,5,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,4,4,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_582 : RowTree := (.node [12,10,9,6,6,5,3,3,3,2,2,1] (.node [12,10,9,6,6,4,4,4,3,2,1,1] (.node [12,10,9,6,6,4,4,4,2,2,1,1,1] (.node [12,10,9,6,6,4,4,3,3,2,2,1] (.node [12,10,9,6,6,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,4,4,4,3,1,1,1,1] (.node [12,10,9,6,6,4,4,4,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,6,6,5,3,3,2,2,2,1,1] (.node [12,10,9,6,6,5,3,2,2,2,2,2,1] (.node [12,10,9,6,6,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,6,6,5,3,3,3,2,1,1,1] .empty .empty))) (.node [12,10,9,6,6,5,4,3,3,2,1,1] (.node [12,10,9,6,6,5,4,3,2,2,1,1,1] (.node [12,10,9,6,6,5,4,2,2,2,2,2] (.node [12,10,9,6,6,5,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,5,4,3,3,1,1,1,1] (.node [12,10,9,6,6,5,4,3,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,6,6,5,5,2,2,2,2,1] (.node [12,10,9,6,6,5,5,2,2,2,1,1,1] (.node [12,10,9,6,6,5,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,5,5,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_583 : RowTree := (.node [12,10,9,6,6,4,4,3,2,2,2,1,1] degreeTree62_581 degreeTree62_582) + +def degreeTree62_584 : RowTree := (.node [12,10,9,6,6,6,4,2,2,1,1,1,1,1] (.node [12,10,9,6,6,6,3,3,2,1,1,1,1,1] (.node [12,10,9,6,6,6,3,2,2,2,1,1,1,1] (.node [12,10,9,6,6,6,2,2,2,2,2,2,1] (.node [12,10,9,6,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,6,3,2,2,2,2,2] (.node [12,10,9,6,6,6,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,6,6,6,3,3,3,1,1,1,1] (.node [12,10,9,6,6,6,3,3,2,2,2,1] (.node [12,10,9,6,6,6,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,6,3,3,3,2,1,1] .empty .empty))) (.node [12,10,9,6,6,6,5,2,1,1,1,1,1,1] (.node [12,10,9,6,6,6,4,3,1,1,1,1,1,1] (.node [12,10,9,6,6,6,4,2,2,2,2,1] (.node [12,10,9,6,6,6,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,6,4,4,1,1,1,1,1] (.node [12,10,9,6,6,6,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,6,6,6,6,1,1,1,1,1,1,1] (.node [12,10,9,6,6,6,5,3,1,1,1,1,1] (.node [12,10,9,6,6,6,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,6,6,6,6,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_585 : RowTree := (.node [12,10,9,7,5,4,4,3,3,2,1,1,1] (.node [12,10,9,7,4,4,4,4,4,2,1,1] (.node [12,10,9,7,4,4,4,4,3,2,1,1,1] (.node [12,10,9,7,4,4,4,4,2,2,2,1,1] (.node [12,10,9,7,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,9,7,4,4,4,4,4,1,1,1,1] (.node [12,10,9,7,4,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,10,9,7,5,4,4,2,2,2,2,2,1] (.node [12,10,9,7,5,4,3,3,3,2,2,1,1] (.node [12,10,9,7,5,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,7,5,4,4,3,2,2,2,1,1] .empty .empty))) (.node [12,10,9,7,5,5,2,2,2,2,2,2,2] (.node [12,10,9,7,5,4,4,4,2,2,2,1] (.node [12,10,9,7,5,4,4,4,2,2,1,1,1] (.node [12,10,9,7,5,4,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,9,7,5,4,4,4,3,2,1,1] (.node [12,10,9,7,5,4,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,5,5,3,3,3,2,1,1,1] (.node [12,10,9,7,5,5,3,3,2,2,2,1,1] (.node [12,10,9,7,5,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,7,5,5,3,3,3,2,2,1] .empty .empty)))) + +def degreeTree62_586 : RowTree := (.node [12,10,9,7,4,4,4,2,2,2,2,2,2] degreeTree62_584 degreeTree62_585) + +def degreeTree62_587 : RowTree := (.node [12,10,9,6,6,5,5,4,1,1,1,1,1] degreeTree62_583 degreeTree62_586) + +def degreeTree62_588 : RowTree := (.node [12,10,9,6,5,4,4,4,4,2,1,1] degreeTree62_580 degreeTree62_587) + +def degreeTree62_589 : RowTree := (.node [12,10,9,7,6,3,3,2,2,2,2,2,2] (.node [12,10,9,7,5,5,4,4,2,1,1,1,1] (.node [12,10,9,7,5,5,4,3,2,2,2,1] (.node [12,10,9,7,5,5,4,3,2,2,1,1,1] (.node [12,10,9,7,5,5,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,7,5,5,4,3,3,2,1,1] (.node [12,10,9,7,5,5,4,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,5,5,5,3,2,1,1,1,1] (.node [12,10,9,7,5,5,5,2,2,2,2,1] (.node [12,10,9,7,5,5,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,5,5,5,4,1,1,1,1,1] .empty .empty))) (.node [12,10,9,7,6,4,3,3,3,1,1,1,1,1] (.node [12,10,9,7,6,4,3,2,2,2,2,1,1,1] (.node [12,10,9,7,6,4,2,2,2,2,2,2,2] (.node [12,10,9,7,6,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,4,3,3,2,2,2,1,1] (.node [12,10,9,7,6,4,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,7,6,4,4,2,2,2,1,1,1,1] (.node [12,10,9,7,6,4,3,3,3,2,2,1] (.node [12,10,9,7,6,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,4,4,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_590 : RowTree := (.node [12,10,9,7,6,5,3,2,2,2,2,2] (.node [12,10,9,7,6,4,4,4,2,1,1,1,1] (.node [12,10,9,7,6,4,4,3,2,2,2,1] (.node [12,10,9,7,6,4,4,3,2,2,1,1,1] (.node [12,10,9,7,6,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,4,4,4,1,1,1,1,1,1] (.node [12,10,9,7,6,4,4,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,6,5,3,2,2,2,1,1,1,1] (.node [12,10,9,7,6,5,2,2,2,2,2,2,1] (.node [12,10,9,7,6,5,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,5,3,2,2,2,2,1,1] .empty .empty))) (.node [12,10,9,7,6,5,4,2,2,2,1,1,1] (.node [12,10,9,7,6,5,3,3,2,2,2,1] (.node [12,10,9,7,6,5,3,3,2,2,1,1,1] (.node [12,10,9,7,6,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,5,4,2,2,1,1,1,1,1] (.node [12,10,9,7,6,5,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,6,5,4,3,2,1,1,1,1] (.node [12,10,9,7,6,5,4,3,1,1,1,1,1,1] (.node [12,10,9,7,6,5,4,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,7,6,5,4,4,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_591 : RowTree := (.node [12,10,9,7,6,4,4,2,2,2,2,2] degreeTree62_589 degreeTree62_590) + +def degreeTree62_592 : RowTree := (.node [12,10,9,7,6,6,4,2,1,1,1,1,1,1] (.node [12,10,9,7,6,6,3,2,2,1,1,1,1,1] (.node [12,10,9,7,6,6,2,2,2,2,1,1,1,1] (.node [12,10,9,7,6,5,5,3,1,1,1,1,1] (.node [12,10,9,7,6,5,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,6,2,2,2,2,2,2] (.node [12,10,9,7,6,6,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,7,6,6,3,3,1,1,1,1,1,1] (.node [12,10,9,7,6,6,3,2,2,2,2,1] (.node [12,10,9,7,6,6,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,6,3,3,2,1,1,1,1] .empty .empty))) (.node [12,10,9,7,7,2,2,2,2,2,2,2,2,1] (.node [12,10,9,7,6,6,5,1,1,1,1,1,1,1] (.node [12,10,9,7,6,6,4,3,1,1,1,1,1] (.node [12,10,9,7,6,6,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,6,6,6,1,1,1,1,1,1] (.node [12,10,9,7,6,6,5,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,7,3,3,2,2,2,2,2,1] (.node [12,10,9,7,7,3,3,2,2,2,2,1,1,1] (.node [12,10,9,7,7,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,7,7,3,3,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_593 : RowTree := (.node [12,10,9,7,7,4,3,3,3,1,1,1,1] (.node [12,10,9,7,7,4,3,2,2,2,2,1,1] (.node [12,10,9,7,7,4,2,2,2,2,2,1,1,1] (.node [12,10,9,7,7,3,3,3,3,2,2,1] (.node [12,10,9,7,7,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,7,4,3,2,2,2,1,1,1,1] (.node [12,10,9,7,7,4,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,7,7,4,3,3,2,2,1,1,1] (.node [12,10,9,7,7,4,3,3,2,1,1,1,1,1] (.node [12,10,9,7,7,4,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,7,7,4,3,3,2,2,2,1] .empty .empty))) (.node [12,10,9,7,7,4,4,4,1,1,1,1,1] (.node [12,10,9,7,7,4,4,2,2,2,2,1] (.node [12,10,9,7,7,4,4,2,2,2,1,1,1] (.node [12,10,9,7,7,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,7,4,4,3,2,1,1,1,1] (.node [12,10,9,7,7,4,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,7,5,2,2,2,2,2,2] (.node [12,10,9,7,7,5,2,2,2,2,2,1,1] (.node [12,10,9,7,7,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,7,5,3,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_594 : RowTree := (.node [12,10,9,7,7,3,3,3,3,1,1,1,1,1] degreeTree62_592 degreeTree62_593) + +def degreeTree62_595 : RowTree := (.node [12,10,9,7,6,5,5,2,1,1,1,1,1,1] degreeTree62_591 degreeTree62_594) + +def degreeTree62_596 : RowTree := (.node [12,10,9,7,7,6,2,2,2,2,2,1] (.node [12,10,9,7,7,5,4,3,1,1,1,1,1] (.node [12,10,9,7,7,5,3,3,2,1,1,1,1] (.node [12,10,9,7,7,5,3,3,1,1,1,1,1,1] (.node [12,10,9,7,7,5,3,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,7,7,5,4,2,2,1,1,1,1] (.node [12,10,9,7,7,5,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,7,6,2,2,2,1,1,1,1,1] (.node [12,10,9,7,7,5,5,2,1,1,1,1,1] (.node [12,10,9,7,7,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,7,6,2,2,2,2,1,1,1] .empty .empty))) (.node [12,10,9,7,7,6,5,1,1,1,1,1,1] (.node [12,10,9,7,7,6,3,3,1,1,1,1,1] (.node [12,10,9,7,7,6,3,2,2,1,1,1,1] (.node [12,10,9,7,7,6,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,7,6,4,2,1,1,1,1,1] (.node [12,10,9,7,7,6,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,7,7,7,3,1,1,1,1,1,1,1] (.node [12,10,9,7,7,7,2,2,2,1,1,1,1] (.node [12,10,9,7,7,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,7,7,7,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_597 : RowTree := (.node [12,10,9,8,4,4,4,4,2,2,2,1] (.node [12,10,9,8,4,4,4,3,3,1,1,1,1,1] (.node [12,10,9,8,4,4,4,2,2,2,2,1,1,1] (.node [12,10,9,8,4,4,3,3,3,2,2,1,1] (.node [12,10,9,8,4,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,8,4,4,4,3,2,2,2,1,1] (.node [12,10,9,8,4,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,8,4,4,4,4,2,1,1,1,1,1] (.node [12,10,9,8,4,4,4,3,3,2,2,1] (.node [12,10,9,8,4,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,4,4,4,4,2,2,1,1,1] .empty .empty))) (.node [12,10,9,8,5,4,3,2,2,2,2,1,1,1] (.node [12,10,9,8,5,3,3,2,2,2,2,2,2] (.node [12,10,9,8,4,4,4,4,3,2,1,1] (.node [12,10,9,8,4,4,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,5,4,2,2,2,2,2,2,2] (.node [12,10,9,8,5,3,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,8,5,4,3,3,3,1,1,1,1,1] (.node [12,10,9,8,5,4,3,3,2,2,2,1,1] (.node [12,10,9,8,5,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,8,5,4,3,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_598 : RowTree := (.node [12,10,9,7,7,7,4,1,1,1,1,1,1] degreeTree62_596 degreeTree62_597) + +def degreeTree62_599 : RowTree := (.node [12,10,9,8,5,5,2,2,2,2,2,2,1] (.node [12,10,9,8,5,4,4,3,2,2,2,1] (.node [12,10,9,8,5,4,4,2,2,2,2,2] (.node [12,10,9,8,5,4,4,2,2,2,2,1,1] (.node [12,10,9,8,5,4,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,5,4,4,3,2,2,1,1,1] (.node [12,10,9,8,5,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,5,4,4,4,2,1,1,1,1] (.node [12,10,9,8,5,4,4,4,1,1,1,1,1,1] (.node [12,10,9,8,5,4,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,5,5,2,2,2,2,2,1,1,1] .empty .empty))) (.node [12,10,9,8,5,5,3,3,2,2,2,1] (.node [12,10,9,8,5,5,3,2,2,2,2,2] (.node [12,10,9,8,5,5,3,2,2,2,2,1,1] (.node [12,10,9,8,5,5,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,5,5,3,3,2,2,1,1,1] (.node [12,10,9,8,5,5,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,5,5,4,2,2,2,1,1,1] (.node [12,10,9,8,5,5,4,2,2,1,1,1,1,1] (.node [12,10,9,8,5,5,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,5,5,4,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_600 : RowTree := (.node [12,10,9,8,6,3,3,3,3,1,1,1,1,1] (.node [12,10,9,8,6,2,2,2,2,2,2,2,2,1] (.node [12,10,9,8,5,5,5,2,1,1,1,1,1,1] (.node [12,10,9,8,5,5,4,4,1,1,1,1,1] (.node [12,10,9,8,5,5,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,5,5,5,3,1,1,1,1,1] (.node [12,10,9,8,5,5,5,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,6,3,3,2,2,2,2,2,1] (.node [12,10,9,8,6,3,3,2,2,2,2,1,1,1] (.node [12,10,9,8,6,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,8,6,3,3,3,2,2,2,1,1] .empty .empty))) (.node [12,10,9,8,6,4,3,2,2,2,1,1,1,1] (.node [12,10,9,8,6,4,2,2,2,2,2,1,1,1] (.node [12,10,9,8,6,3,3,3,3,2,2,1] (.node [12,10,9,8,6,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,6,4,2,2,2,2,2,2,1] .empty .empty)) (.node [12,10,9,8,6,4,3,3,2,1,1,1,1,1] (.node [12,10,9,8,6,4,3,2,2,2,2,2] (.node [12,10,9,8,6,4,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,10,9,8,6,4,3,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_601 : RowTree := (.node [12,10,9,8,5,5,4,3,1,1,1,1,1,1] degreeTree62_599 degreeTree62_600) + +def degreeTree62_602 : RowTree := (.node [12,10,9,8,5,4,3,3,3,2,2,1] degreeTree62_598 degreeTree62_601) + +def degreeTree62_603 : RowTree := (.node [12,10,9,7,7,5,3,2,2,2,1,1,1] degreeTree62_595 degreeTree62_602) + +def degreeTree62_604 : RowTree := (.node [12,10,9,7,5,5,4,2,2,2,2,1,1] degreeTree62_588 degreeTree62_603) + +def degreeTree62_605 : RowTree := (.node [12,10,9,8,6,5,3,2,2,1,1,1,1,1] (.node [12,10,9,8,6,4,4,3,2,1,1,1,1] (.node [12,10,9,8,6,4,4,2,2,2,1,1,1] (.node [12,10,9,8,6,4,4,2,2,1,1,1,1,1] (.node [12,10,9,8,6,4,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,6,4,4,3,1,1,1,1,1,1] (.node [12,10,9,8,6,4,4,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,8,6,5,2,2,2,2,2,1,1] (.node [12,10,9,8,6,5,2,2,2,2,1,1,1,1] (.node [12,10,9,8,6,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,6,5,2,2,2,2,2,2] .empty .empty))) (.node [12,10,9,8,6,5,4,2,2,1,1,1,1] (.node [12,10,9,8,6,5,3,3,1,1,1,1,1,1] (.node [12,10,9,8,6,5,3,2,2,2,2,1] (.node [12,10,9,8,6,5,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,6,5,4,2,1,1,1,1,1,1] (.node [12,10,9,8,6,5,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,6,5,5,2,1,1,1,1,1] (.node [12,10,9,8,6,5,5,1,1,1,1,1,1,1] (.node [12,10,9,8,6,5,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,6,6,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_606 : RowTree := (.node [12,10,9,8,7,3,2,2,2,2,2,2,1] (.node [12,10,9,8,6,6,4,2,1,1,1,1,1] (.node [12,10,9,8,6,6,3,2,2,1,1,1,1] (.node [12,10,9,8,6,6,3,2,1,1,1,1,1,1] (.node [12,10,9,8,6,6,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,8,6,6,4,1,1,1,1,1,1,1] (.node [12,10,9,8,6,6,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,7,2,2,2,2,2,2,2,2] (.node [12,10,9,8,7,2,2,2,2,2,2,2,1,1] (.node [12,10,9,8,6,6,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,3,2,2,2,2,2,1,1,1] .empty .empty))) (.node [12,10,9,8,7,3,3,3,2,2,2,1] (.node [12,10,9,8,7,3,3,2,2,2,2,2] (.node [12,10,9,8,7,3,3,2,2,2,2,1,1] (.node [12,10,9,8,7,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,3,3,3,2,2,1,1,1] (.node [12,10,9,8,7,3,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,7,4,2,2,2,2,2,1,1] (.node [12,10,9,8,7,4,2,2,2,2,1,1,1,1] (.node [12,10,9,8,7,3,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,4,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_607 : RowTree := (.node [12,10,9,8,6,6,2,2,2,2,1,1,1] degreeTree62_605 degreeTree62_606) + +def degreeTree62_608 : RowTree := (.node [12,10,9,8,7,5,3,2,1,1,1,1,1,1] (.node [12,10,9,8,7,4,4,2,2,1,1,1,1] (.node [12,10,9,8,7,4,3,3,1,1,1,1,1,1] (.node [12,10,9,8,7,4,3,2,2,2,2,1] (.node [12,10,9,8,7,4,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,4,4,2,1,1,1,1,1,1] (.node [12,10,9,8,7,4,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,7,5,2,2,2,2,1,1,1] (.node [12,10,9,8,7,5,2,2,2,1,1,1,1,1] (.node [12,10,9,8,7,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,5,2,2,2,2,2,1] .empty .empty))) (.node [12,10,9,8,7,6,2,2,1,1,1,1,1,1] (.node [12,10,9,8,7,5,4,1,1,1,1,1,1,1] (.node [12,10,9,8,7,5,3,3,1,1,1,1,1] (.node [12,10,9,8,7,5,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,5,5,1,1,1,1,1,1] (.node [12,10,9,8,7,5,4,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,7,6,3,2,1,1,1,1,1] (.node [12,10,9,8,7,6,3,1,1,1,1,1,1,1] (.node [12,10,9,8,7,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,7,6,4,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_609 : RowTree := (.node [12,10,9,8,8,3,3,3,1,1,1,1,1,1] (.node [12,10,9,8,8,3,2,2,2,2,2,1,1] (.node [12,10,9,8,8,2,2,2,2,2,2,1,1,1] (.node [12,10,9,8,7,7,3,1,1,1,1,1,1] (.node [12,10,9,8,7,7,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,8,3,2,2,2,2,1,1,1,1] (.node [12,10,9,8,8,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,8,8,3,3,2,2,2,1,1,1] (.node [12,10,9,8,8,3,3,2,2,1,1,1,1,1] (.node [12,10,9,8,8,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,8,8,3,3,2,2,2,2,1] .empty .empty))) (.node [12,10,9,8,8,4,3,2,2,1,1,1,1] (.node [12,10,9,8,8,4,2,2,2,2,1,1,1] (.node [12,10,9,8,8,4,2,2,2,1,1,1,1,1] (.node [12,10,9,8,8,3,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,8,4,3,2,1,1,1,1,1,1] (.node [12,10,9,8,8,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,8,8,4,4,2,1,1,1,1,1] (.node [12,10,9,8,8,4,4,1,1,1,1,1,1,1] (.node [12,10,9,8,8,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,8,5,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_610 : RowTree := (.node [12,10,9,8,7,7,2,1,1,1,1,1,1,1] degreeTree62_608 degreeTree62_609) + +def degreeTree62_611 : RowTree := (.node [12,10,9,8,7,4,3,2,2,1,1,1,1,1] degreeTree62_607 degreeTree62_610) + +def degreeTree62_612 : RowTree := (.node [12,10,9,9,4,3,3,3,3,2,2,1,1] (.node [12,10,9,8,8,6,3,1,1,1,1,1,1] (.node [12,10,9,8,8,5,4,1,1,1,1,1,1] (.node [12,10,9,8,8,5,3,2,1,1,1,1,1] (.node [12,10,9,8,8,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,8,8,6,2,2,1,1,1,1,1] (.node [12,10,9,8,8,6,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,8,8,8,1,1,1,1,1,1,1] (.node [12,10,9,8,8,7,2,1,1,1,1,1,1] (.node [12,10,9,8,8,7,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,4,3,3,2,2,2,2,2,2] .empty .empty))) (.node [12,10,9,9,4,4,3,3,3,2,1,1,1] (.node [12,10,9,9,4,4,3,2,2,2,2,2,1] (.node [12,10,9,9,4,4,3,2,2,2,2,1,1,1] (.node [12,10,9,9,4,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,9,4,4,3,3,3,1,1,1,1,1] (.node [12,10,9,9,4,4,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,9,4,4,4,2,2,2,2,1,1] (.node [12,10,9,9,4,4,4,2,2,2,1,1,1,1] (.node [12,10,9,9,4,4,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,10,9,9,4,4,4,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_613 : RowTree := (.node [12,10,9,9,5,3,3,3,3,1,1,1,1,1] (.node [12,10,9,9,5,2,2,2,2,2,2,2,2,1] (.node [12,10,9,9,4,4,4,3,3,1,1,1,1] (.node [12,10,9,9,4,4,4,3,2,2,2,1] (.node [12,10,9,9,4,4,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,4,4,4,4,2,1,1,1,1] (.node [12,10,9,9,4,4,4,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,5,3,3,2,2,2,2,2,1] (.node [12,10,9,9,5,3,3,2,2,2,2,1,1,1] (.node [12,10,9,9,5,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,9,5,3,3,3,2,2,2,1,1] .empty .empty))) (.node [12,10,9,9,5,4,3,2,2,2,2,1,1] (.node [12,10,9,9,5,4,2,2,2,2,2,1,1,1] (.node [12,10,9,9,5,3,3,3,3,2,2,1] (.node [12,10,9,9,5,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,5,4,3,2,2,2,1,1,1,1] (.node [12,10,9,9,5,4,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,10,9,9,5,4,3,3,2,2,1,1,1] (.node [12,10,9,9,5,4,3,3,2,1,1,1,1,1] (.node [12,10,9,9,5,4,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,10,9,9,5,4,3,3,2,2,2,1] .empty .empty)))) + +def degreeTree62_614 : RowTree := (.node [12,10,9,9,4,4,4,3,2,1,1,1,1,1] degreeTree62_612 degreeTree62_613) + +def degreeTree62_615 : RowTree := (.node [12,10,9,9,5,5,3,2,2,2,1,1,1] (.node [12,10,9,9,5,4,4,4,1,1,1,1,1] (.node [12,10,9,9,5,4,4,2,2,2,2,1] (.node [12,10,9,9,5,4,4,2,2,2,1,1,1] (.node [12,10,9,9,5,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,5,4,4,3,2,1,1,1,1] (.node [12,10,9,9,5,4,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,5,5,2,2,2,2,2,2] (.node [12,10,9,9,5,5,2,2,2,2,2,1,1] (.node [12,10,9,9,5,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,5,5,3,2,2,1,1,1,1,1] .empty .empty))) (.node [12,10,9,9,5,5,4,3,1,1,1,1,1] (.node [12,10,9,9,5,5,3,3,2,1,1,1,1] (.node [12,10,9,9,5,5,3,3,1,1,1,1,1,1] (.node [12,10,9,9,5,5,3,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,9,5,5,4,2,2,1,1,1,1] (.node [12,10,9,9,5,5,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,6,2,2,2,2,2,2,2,1,1] (.node [12,10,9,9,5,5,5,2,1,1,1,1,1] (.node [12,10,9,9,5,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,6,2,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_616 : RowTree := (.node [12,10,9,9,6,4,2,2,2,2,2,2] (.node [12,10,9,9,6,3,3,3,2,2,1,1,1] (.node [12,10,9,9,6,3,3,2,2,2,2,1,1] (.node [12,10,9,9,6,3,3,2,2,2,1,1,1,1] (.node [12,10,9,9,6,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,9,6,3,3,3,2,1,1,1,1,1] (.node [12,10,9,9,6,3,3,2,2,2,2,2] .empty .empty) .empty)) (.node [12,10,9,9,6,4,2,2,2,2,1,1,1,1] (.node [12,10,9,9,6,3,3,3,3,1,1,1,1] (.node [12,10,9,9,6,3,3,3,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,9,6,4,2,2,2,2,2,1,1] .empty .empty))) (.node [12,10,9,9,6,4,4,2,1,1,1,1,1,1] (.node [12,10,9,9,6,4,3,2,2,2,2,1] (.node [12,10,9,9,6,4,3,2,2,2,1,1,1] (.node [12,10,9,9,6,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,6,4,3,3,2,1,1,1,1] (.node [12,10,9,9,6,4,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,6,5,2,2,2,1,1,1,1,1] (.node [12,10,9,9,6,4,4,3,1,1,1,1,1] (.node [12,10,9,9,6,4,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,6,5,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_617 : RowTree := (.node [12,10,9,9,6,3,2,2,2,2,2,1,1,1] degreeTree62_615 degreeTree62_616) + +def degreeTree62_618 : RowTree := (.node [12,10,9,9,5,4,3,3,3,1,1,1,1] degreeTree62_614 degreeTree62_617) + +def degreeTree62_619 : RowTree := (.node [12,10,9,8,8,5,2,2,2,1,1,1,1] degreeTree62_611 degreeTree62_618) + +def degreeTree62_620 : RowTree := (.node [12,10,9,9,6,6,4,1,1,1,1,1,1] (.node [12,10,9,9,6,5,5,1,1,1,1,1,1] (.node [12,10,9,9,6,5,3,3,1,1,1,1,1] (.node [12,10,9,9,6,5,3,2,2,1,1,1,1] (.node [12,10,9,9,6,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,6,5,4,2,1,1,1,1,1] (.node [12,10,9,9,6,5,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,6,6,3,1,1,1,1,1,1,1] (.node [12,10,9,9,6,6,2,2,2,1,1,1,1] (.node [12,10,9,9,6,6,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,6,6,3,2,1,1,1,1,1] .empty .empty))) (.node [12,10,9,9,7,3,3,2,2,1,1,1,1,1] (.node [12,10,9,9,7,3,2,2,2,2,1,1,1,1] (.node [12,10,9,9,7,2,2,2,2,2,2,2,1] (.node [12,10,9,9,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,7,3,2,2,2,2,2,2] (.node [12,10,9,9,7,3,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,10,9,9,7,3,3,3,1,1,1,1,1,1] (.node [12,10,9,9,7,3,3,2,2,2,2,1] (.node [12,10,9,9,7,3,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,7,3,3,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_621 : RowTree := (.node [12,10,9,9,7,5,3,2,1,1,1,1,1] (.node [12,10,9,9,7,4,4,1,1,1,1,1,1,1] (.node [12,10,9,9,7,4,3,2,1,1,1,1,1,1] (.node [12,10,9,9,7,4,2,2,2,2,2,1] (.node [12,10,9,9,7,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,7,4,3,3,1,1,1,1,1] (.node [12,10,9,9,7,4,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,7,5,2,2,2,1,1,1,1] (.node [12,10,9,9,7,5,2,2,1,1,1,1,1,1] (.node [12,10,9,9,7,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,7,5,3,1,1,1,1,1,1,1] .empty .empty))) (.node [12,10,9,9,7,7,2,1,1,1,1,1,1] (.node [12,10,9,9,7,6,2,2,1,1,1,1,1] (.node [12,10,9,9,7,6,2,1,1,1,1,1,1,1] (.node [12,10,9,9,7,5,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,7,7,1,1,1,1,1,1,1,1] (.node [12,10,9,9,7,6,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,8,2,2,2,2,2,2,2] (.node [12,10,9,9,8,2,2,2,2,2,2,1,1] (.node [12,10,9,9,8,2,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,8,3,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_622 : RowTree := (.node [12,10,9,9,7,4,2,2,2,1,1,1,1,1] degreeTree62_620 degreeTree62_621) + +def degreeTree62_623 : RowTree := (.node [12,10,9,9,8,5,2,2,1,1,1,1,1] (.node [12,10,9,9,8,4,2,2,2,1,1,1,1] (.node [12,10,9,9,8,3,3,2,2,1,1,1,1] (.node [12,10,9,9,8,3,3,2,1,1,1,1,1,1] (.node [12,10,9,9,8,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,9,8,4,2,2,1,1,1,1,1,1] (.node [12,10,9,9,8,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,8,4,4,1,1,1,1,1,1] (.node [12,10,9,9,8,4,3,2,1,1,1,1,1] (.node [12,10,9,9,8,4,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,8,5,2,1,1,1,1,1,1,1] .empty .empty))) (.node [12,10,9,9,9,2,2,2,2,2,1,1,1] (.node [12,10,9,9,8,6,2,1,1,1,1,1,1] (.node [12,10,9,9,8,6,1,1,1,1,1,1,1,1] (.node [12,10,9,9,8,5,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,9,2,2,2,2,1,1,1,1,1] (.node [12,10,9,9,8,7,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,10,9,9,9,3,2,2,2,1,1,1,1] (.node [12,10,9,9,9,3,2,2,1,1,1,1,1,1] (.node [12,10,9,9,9,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,10,9,9,9,3,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_624 : RowTree := (.node [12,11,5,5,5,5,5,5,5,1,1,1,1] (.node [12,10,9,9,9,6,1,1,1,1,1,1,1] (.node [12,10,9,9,9,4,3,1,1,1,1,1,1] (.node [12,10,9,9,9,4,2,2,1,1,1,1,1] (.node [12,10,9,9,9,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,10,9,9,9,5,2,1,1,1,1,1,1] (.node [12,10,9,9,9,5,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,5,5,5,5,5,5,4,2,1,1,1] (.node [12,11,5,5,5,5,5,5,3,2,2,1,1] (.node [12,11,5,5,5,5,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,11,5,5,5,5,5,5,4,2,2,1] .empty .empty))) (.node [12,11,6,5,5,5,5,5,3,2,1,1,1] (.node [12,11,6,5,5,5,5,4,4,2,1,1,1] (.node [12,11,6,5,5,5,5,4,3,2,2,1,1] (.node [12,11,6,5,5,5,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,11,6,5,5,5,5,5,2,2,2,1,1] (.node [12,11,6,5,5,5,5,4,4,2,2,1] .empty .empty) .empty)) (.node [12,11,6,6,5,4,4,4,4,2,2,1,1] (.node [12,11,6,5,5,5,5,5,4,1,1,1,1] (.node [12,11,6,5,5,5,5,5,3,2,2,1] .empty .empty) .empty) (.node [12,11,6,6,5,5,4,4,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_625 : RowTree := (.node [12,10,9,9,9,3,3,2,1,1,1,1,1] degreeTree62_623 degreeTree62_624) + +def degreeTree62_626 : RowTree := (.node [12,10,9,9,8,3,2,2,2,2,1,1,1] degreeTree62_622 degreeTree62_625) + +def degreeTree62_627 : RowTree := (.node [12,11,6,6,6,4,4,4,3,2,2,1,1] (.node [12,11,6,6,5,5,5,4,3,2,2,1] (.node [12,11,6,6,5,5,5,3,3,2,2,1,1] (.node [12,11,6,6,5,5,5,2,2,2,2,2,2] (.node [12,11,6,6,5,5,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,11,6,6,5,5,5,4,3,2,1,1,1] (.node [12,11,6,6,5,5,5,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,11,6,6,5,5,5,5,2,2,2,1] (.node [12,11,6,6,5,5,5,5,2,2,1,1,1] (.node [12,11,6,6,5,5,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,11,6,6,5,5,5,5,3,1,1,1,1] .empty .empty))) (.node [12,11,6,6,6,5,4,4,3,2,1,1,1] (.node [12,11,6,6,6,5,4,2,2,2,2,2,2] (.node [12,11,6,6,6,4,4,4,4,2,2,1] (.node [12,11,6,6,6,4,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,11,6,6,6,5,4,4,2,2,2,1,1] (.node [12,11,6,6,6,5,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,11,6,6,6,5,5,2,2,2,2,2,1] (.node [12,11,6,6,6,5,4,4,4,1,1,1,1] (.node [12,11,6,6,6,5,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,11,6,6,6,5,5,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_628 : RowTree := (.node [12,11,6,6,6,6,4,3,3,2,2,1] (.node [12,11,6,6,6,6,3,2,2,2,2,2,2] (.node [12,11,6,6,6,5,5,4,2,2,2,1] (.node [12,11,6,6,6,5,5,4,2,2,1,1,1] (.node [12,11,6,6,6,5,5,3,3,2,2,1] .empty .empty) .empty) (.node [12,11,6,6,6,5,5,5,2,1,1,1,1] (.node [12,11,6,6,6,5,5,4,3,1,1,1,1] .empty .empty) .empty)) (.node [12,11,6,6,6,6,4,3,2,2,2,1,1] (.node [12,11,6,6,6,6,4,2,2,2,2,2,1] (.node [12,11,6,6,6,6,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,11,6,6,6,6,4,3,3,2,1,1,1] .empty .empty))) (.node [12,11,6,6,6,6,5,3,2,2,1,1,1] (.node [12,11,6,6,6,6,4,4,3,1,1,1,1] (.node [12,11,6,6,6,6,4,4,2,2,2,1] (.node [12,11,6,6,6,6,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,6,6,6,6,5,2,2,2,2,2] (.node [12,11,6,6,6,6,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,11,6,6,6,6,5,4,2,1,1,1,1] (.node [12,11,6,6,6,6,5,3,3,1,1,1,1] (.node [12,11,6,6,6,6,5,3,2,2,2,1] .empty .empty) .empty) (.node [12,11,6,6,6,6,5,5,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_629 : RowTree := (.node [12,11,6,6,6,5,5,3,3,2,1,1,1] degreeTree62_627 degreeTree62_628) + +def degreeTree62_630 : RowTree := (.node [12,11,7,5,5,5,5,4,3,2,1,1,1] (.node [12,11,7,5,5,5,4,4,4,2,1,1,1] (.node [12,11,6,6,6,6,6,4,1,1,1,1,1] (.node [12,11,6,6,6,6,6,3,2,1,1,1,1] (.node [12,11,6,6,6,6,6,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,7,5,5,5,4,4,3,2,2,1,1] (.node [12,11,7,5,5,4,4,4,4,2,2,1,1] .empty .empty) .empty)) (.node [12,11,7,5,5,5,5,3,3,2,2,1,1] (.node [12,11,7,5,5,5,5,2,2,2,2,2,2] (.node [12,11,7,5,5,5,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,11,7,5,5,5,5,4,2,2,2,1,1] .empty .empty))) (.node [12,11,7,6,4,4,4,4,4,2,2,1,1] (.node [12,11,7,5,5,5,5,5,2,2,1,1,1] (.node [12,11,7,5,5,5,5,4,4,1,1,1,1] (.node [12,11,7,5,5,5,5,4,3,2,2,1] .empty .empty) .empty) (.node [12,11,7,5,5,5,5,5,3,1,1,1,1] (.node [12,11,7,5,5,5,5,5,2,2,2,1] .empty .empty) .empty)) (.node [12,11,7,6,5,4,4,4,4,2,2,1] (.node [12,11,7,6,5,4,4,4,4,2,1,1,1] (.node [12,11,7,6,5,4,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,6,5,5,4,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_631 : RowTree := (.node [12,11,7,6,5,5,5,4,3,1,1,1,1] (.node [12,11,7,6,5,5,5,3,2,2,2,1,1] (.node [12,11,7,6,5,5,4,4,3,2,2,1] (.node [12,11,7,6,5,5,4,4,3,2,1,1,1] (.node [12,11,7,6,5,5,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,6,5,5,5,2,2,2,2,2,1] (.node [12,11,7,6,5,5,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [12,11,7,6,5,5,5,4,2,2,1,1,1] (.node [12,11,7,6,5,5,5,3,3,2,2,1] (.node [12,11,7,6,5,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,11,7,6,5,5,5,4,2,2,2,1] .empty .empty))) (.node [12,11,7,6,6,4,4,4,3,2,1,1,1] (.node [12,11,7,6,6,4,4,3,3,2,2,1,1] (.node [12,11,7,6,6,4,4,2,2,2,2,2,2] (.node [12,11,7,6,5,5,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,6,6,4,4,4,2,2,2,1,1] .empty .empty)) (.node [12,11,7,6,6,5,3,2,2,2,2,2,2] (.node [12,11,7,6,6,4,4,4,4,1,1,1,1] (.node [12,11,7,6,6,4,4,4,3,2,2,1] .empty .empty) .empty) (.node [12,11,7,6,6,5,3,3,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_632 : RowTree := (.node [12,11,7,6,5,5,4,3,3,2,2,1,1] degreeTree62_630 degreeTree62_631) + +def degreeTree62_633 : RowTree := (.node [12,11,6,6,6,6,6,2,2,2,1,1,1] degreeTree62_629 degreeTree62_632) + +def degreeTree62_634 : RowTree := (.node [12,11,6,6,5,5,4,4,4,2,1,1,1] degreeTree62_626 degreeTree62_633) + +def degreeTree62_635 : RowTree := (.node [12,10,9,9,6,5,2,2,2,2,2,1] degreeTree62_619 degreeTree62_634) + +def degreeTree62_636 : RowTree := (.node [12,10,9,8,6,4,3,3,2,2,2,1] degreeTree62_604 degreeTree62_635) + +def degreeTree62_637 : RowTree := (.node [12,10,8,8,7,5,4,3,1,1,1,1,1] degreeTree62_573 degreeTree62_636) + +def degreeTree62_638 : RowTree := (.node [12,11,7,6,6,5,5,3,3,1,1,1,1] (.node [12,11,7,6,6,5,4,4,3,1,1,1,1] (.node [12,11,7,6,6,5,4,3,3,2,2,1] (.node [12,11,7,6,6,5,4,3,3,2,1,1,1] (.node [12,11,7,6,6,5,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,6,6,5,4,4,2,2,2,1] (.node [12,11,7,6,6,5,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,7,6,6,5,5,3,2,2,1,1,1] (.node [12,11,7,6,6,5,5,2,2,2,2,2] (.node [12,11,7,6,6,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,6,6,5,5,3,2,2,2,1] .empty .empty))) (.node [12,11,7,6,6,6,3,3,3,2,1,1,1] (.node [12,11,7,6,6,6,2,2,2,2,2,2,2] (.node [12,11,7,6,6,5,5,5,1,1,1,1,1] (.node [12,11,7,6,6,5,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,6,6,6,3,3,2,2,2,1,1] (.node [12,11,7,6,6,6,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,7,6,6,6,4,2,2,2,2,2] (.node [12,11,7,6,6,6,4,2,2,2,2,1,1] (.node [12,11,7,6,6,6,3,3,3,2,2,1] .empty .empty) .empty) (.node [12,11,7,6,6,6,4,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_639 : RowTree := (.node [12,11,7,7,4,4,4,4,4,2,1,1,1] (.node [12,11,7,6,6,6,5,4,1,1,1,1,1] (.node [12,11,7,6,6,6,5,2,2,2,1,1,1] (.node [12,11,7,6,6,6,4,4,2,1,1,1,1] (.node [12,11,7,6,6,6,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,6,6,6,5,3,2,1,1,1,1] (.node [12,11,7,6,6,6,5,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,7,6,6,6,6,3,1,1,1,1,1] (.node [12,11,7,6,6,6,6,2,2,1,1,1,1] (.node [12,11,7,6,6,6,6,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,4,4,4,4,3,2,2,1,1] .empty .empty))) (.node [12,11,7,7,5,4,4,4,3,2,2,1] (.node [12,11,7,7,5,4,4,3,3,2,2,1,1] (.node [12,11,7,7,5,4,4,2,2,2,2,2,2] (.node [12,11,7,7,4,4,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,11,7,7,5,4,4,4,3,2,1,1,1] (.node [12,11,7,7,5,4,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,11,7,7,5,5,3,3,3,2,2,1,1] (.node [12,11,7,7,5,5,3,2,2,2,2,2,2] (.node [12,11,7,7,5,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,5,5,4,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_640 : RowTree := (.node [12,11,7,6,6,6,4,3,2,2,2,1] degreeTree62_638 degreeTree62_639) + +def degreeTree62_641 : RowTree := (.node [12,11,7,7,5,5,5,4,2,1,1,1,1] (.node [12,11,7,7,5,5,5,2,2,2,2,1,1] (.node [12,11,7,7,5,5,4,4,2,2,1,1,1] (.node [12,11,7,7,5,5,4,3,3,2,2,1] (.node [12,11,7,7,5,5,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,5,5,4,4,3,1,1,1,1] (.node [12,11,7,7,5,5,4,4,2,2,2,1] .empty .empty) .empty)) (.node [12,11,7,7,5,5,5,3,2,2,2,1] (.node [12,11,7,7,5,5,5,3,2,2,1,1,1] (.node [12,11,7,7,5,5,5,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,7,7,5,5,5,3,3,1,1,1,1] .empty .empty))) (.node [12,11,7,7,6,4,4,3,3,2,1,1,1] (.node [12,11,7,7,6,4,3,3,3,2,2,1,1] (.node [12,11,7,7,6,4,3,2,2,2,2,2,2] (.node [12,11,7,7,5,5,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,6,4,4,3,2,2,2,1,1] (.node [12,11,7,7,6,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,7,7,6,4,4,4,2,2,2,1] (.node [12,11,7,7,6,4,4,4,2,2,1,1,1] (.node [12,11,7,7,6,4,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,11,7,7,6,4,4,4,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_642 : RowTree := (.node [12,11,7,7,6,5,5,2,2,2,1,1,1] (.node [12,11,7,7,6,5,4,2,2,2,2,2] (.node [12,11,7,7,6,5,3,3,3,2,1,1,1] (.node [12,11,7,7,6,5,3,3,2,2,2,1,1] (.node [12,11,7,7,6,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,7,7,6,5,4,2,2,2,2,1,1] (.node [12,11,7,7,6,5,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,11,7,7,6,5,4,3,3,1,1,1,1] (.node [12,11,7,7,6,5,4,3,2,2,2,1] (.node [12,11,7,7,6,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,6,5,4,4,2,1,1,1,1] .empty .empty))) (.node [12,11,7,7,6,6,3,2,2,2,1,1,1,1] (.node [12,11,7,7,6,5,5,4,1,1,1,1,1] (.node [12,11,7,7,6,5,5,3,2,1,1,1,1] (.node [12,11,7,7,6,5,5,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,7,7,6,6,2,2,2,2,2,2,1] (.node [12,11,7,7,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,7,7,6,6,3,3,2,1,1,1,1,1] (.node [12,11,7,7,6,6,3,2,2,2,2,2] (.node [12,11,7,7,6,6,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,7,6,6,3,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_643 : RowTree := (.node [12,11,7,7,6,5,2,2,2,2,2,2,2] degreeTree62_641 degreeTree62_642) + +def degreeTree62_644 : RowTree := (.node [12,11,7,7,5,5,4,3,2,2,2,1,1] degreeTree62_640 degreeTree62_643) + +def degreeTree62_645 : RowTree := (.node [12,11,7,7,6,6,6,1,1,1,1,1,1,1] (.node [12,11,7,7,6,6,4,3,2,1,1,1,1] (.node [12,11,7,7,6,6,4,2,2,2,1,1,1] (.node [12,11,7,7,6,6,4,2,2,1,1,1,1,1] (.node [12,11,7,7,6,6,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,6,6,4,3,1,1,1,1,1,1] (.node [12,11,7,7,6,6,4,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,7,7,6,6,5,2,2,1,1,1,1] (.node [12,11,7,7,6,6,5,2,1,1,1,1,1,1] (.node [12,11,7,7,6,6,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,6,6,5,3,1,1,1,1,1] .empty .empty))) (.node [12,11,7,7,7,4,3,2,2,2,2,2,1] (.node [12,11,7,7,7,3,3,3,3,2,2,1,1] (.node [12,11,7,7,7,3,3,2,2,2,2,2,2] (.node [12,11,7,7,6,6,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,4,3,2,2,2,2,1,1,1] (.node [12,11,7,7,7,4,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,7,7,7,4,3,3,3,2,1,1,1] (.node [12,11,7,7,7,4,3,3,3,1,1,1,1,1] (.node [12,11,7,7,7,4,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,4,3,3,3,2,2,1] .empty .empty)))) + +def degreeTree62_646 : RowTree := (.node [12,11,7,7,7,5,3,2,2,2,1,1,1,1] (.node [12,11,7,7,7,4,4,3,3,1,1,1,1] (.node [12,11,7,7,7,4,4,3,2,1,1,1,1,1] (.node [12,11,7,7,7,4,4,2,2,2,2,2] (.node [12,11,7,7,7,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,4,4,3,2,2,2,1] (.node [12,11,7,7,7,4,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,7,7,7,5,2,2,2,2,2,1,1,1] (.node [12,11,7,7,7,4,4,4,2,1,1,1,1] (.node [12,11,7,7,7,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,5,2,2,2,2,2,2,1] .empty .empty))) (.node [12,11,7,7,7,5,3,3,3,1,1,1,1] (.node [12,11,7,7,7,5,3,3,2,1,1,1,1,1] (.node [12,11,7,7,7,5,3,2,2,2,2,2] (.node [12,11,7,7,7,5,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,5,3,3,2,2,2,1] (.node [12,11,7,7,7,5,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,7,7,7,5,4,3,1,1,1,1,1,1] (.node [12,11,7,7,7,5,4,2,2,2,1,1,1] (.node [12,11,7,7,7,5,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,5,4,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_647 : RowTree := (.node [12,11,7,7,7,4,4,2,2,2,1,1,1,1] degreeTree62_645 degreeTree62_646) + +def degreeTree62_648 : RowTree := (.node [12,11,7,7,7,6,4,2,1,1,1,1,1,1] (.node [12,11,7,7,7,6,2,2,2,2,2,2] (.node [12,11,7,7,7,5,5,3,1,1,1,1,1] (.node [12,11,7,7,7,5,5,2,2,1,1,1,1] (.node [12,11,7,7,7,5,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,6,2,2,2,2,2,1,1] (.node [12,11,7,7,7,6,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,7,7,7,6,3,3,1,1,1,1,1,1] (.node [12,11,7,7,7,6,3,2,2,2,1,1,1] (.node [12,11,7,7,7,6,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,6,3,3,2,1,1,1,1] .empty .empty))) (.node [12,11,7,7,7,7,2,2,2,1,1,1,1,1] (.node [12,11,7,7,7,6,5,1,1,1,1,1,1,1] (.node [12,11,7,7,7,6,4,3,1,1,1,1,1] (.node [12,11,7,7,7,6,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,6,6,1,1,1,1,1,1] (.node [12,11,7,7,7,6,5,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,7,7,7,7,3,2,2,1,1,1,1] (.node [12,11,7,7,7,7,3,2,1,1,1,1,1,1] (.node [12,11,7,7,7,7,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,7,7,7,7,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_649 : RowTree := (.node [12,11,8,5,5,5,4,4,3,2,2,1] (.node [12,11,8,5,5,4,4,4,4,2,2,1] (.node [12,11,8,5,4,4,4,4,4,2,2,1,1] (.node [12,11,7,7,7,7,5,1,1,1,1,1,1] (.node [12,11,7,7,7,7,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,5,5,4,4,4,4,2,1,1,1] (.node [12,11,8,5,5,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [12,11,8,5,5,5,4,4,2,2,2,1,1] (.node [12,11,8,5,5,5,4,3,3,2,2,1,1] (.node [12,11,8,5,5,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,5,5,5,4,4,3,2,1,1,1] .empty .empty))) (.node [12,11,8,5,5,5,5,4,2,2,1,1,1] (.node [12,11,8,5,5,5,5,3,2,2,2,1,1] (.node [12,11,8,5,5,5,5,2,2,2,2,2,1] (.node [12,11,8,5,5,5,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,5,5,5,5,3,3,2,2,1] (.node [12,11,8,5,5,5,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,11,8,5,5,5,5,5,2,1,1,1,1] (.node [12,11,8,5,5,5,5,4,3,1,1,1,1] (.node [12,11,8,5,5,5,5,4,2,2,2,1] .empty .empty) .empty) (.node [12,11,8,6,4,4,4,4,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_650 : RowTree := (.node [12,11,7,7,7,7,4,1,1,1,1,1,1,1] degreeTree62_648 degreeTree62_649) + +def degreeTree62_651 : RowTree := (.node [12,11,7,7,7,5,4,4,1,1,1,1,1] degreeTree62_647 degreeTree62_650) + +def degreeTree62_652 : RowTree := (.node [12,11,7,7,6,6,3,3,2,2,2,1] degreeTree62_644 degreeTree62_651) + +def degreeTree62_653 : RowTree := (.node [12,11,8,6,5,5,4,3,2,2,2,1,1] (.node [12,11,8,6,5,4,4,4,3,2,2,1] (.node [12,11,8,6,5,4,4,3,3,2,2,1,1] (.node [12,11,8,6,5,4,4,2,2,2,2,2,2] (.node [12,11,8,6,4,4,4,4,4,2,2,1] .empty .empty) .empty) (.node [12,11,8,6,5,4,4,4,3,2,1,1,1] (.node [12,11,8,6,5,4,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [12,11,8,6,5,5,3,3,3,2,2,1,1] (.node [12,11,8,6,5,5,3,2,2,2,2,2,2] (.node [12,11,8,6,5,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,5,5,4,2,2,2,2,2,1] .empty .empty))) (.node [12,11,8,6,5,5,5,2,2,2,2,1,1] (.node [12,11,8,6,5,5,4,4,2,2,1,1,1] (.node [12,11,8,6,5,5,4,3,3,2,2,1] (.node [12,11,8,6,5,5,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,5,5,4,4,3,1,1,1,1] (.node [12,11,8,6,5,5,4,4,2,2,2,1] .empty .empty) .empty)) (.node [12,11,8,6,5,5,5,3,2,2,2,1] (.node [12,11,8,6,5,5,5,3,2,2,1,1,1] (.node [12,11,8,6,5,5,5,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,6,5,5,5,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_654 : RowTree := (.node [12,11,8,6,6,5,2,2,2,2,2,2,2] (.node [12,11,8,6,6,4,4,3,3,2,1,1,1] (.node [12,11,8,6,6,4,3,3,3,2,2,1,1] (.node [12,11,8,6,6,4,3,2,2,2,2,2,2] (.node [12,11,8,6,5,5,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,6,4,4,3,2,2,2,1,1] (.node [12,11,8,6,6,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,8,6,6,4,4,4,2,2,2,1] (.node [12,11,8,6,6,4,4,4,2,2,1,1,1] (.node [12,11,8,6,6,4,4,3,3,2,2,1] .empty .empty) .empty) (.node [12,11,8,6,6,4,4,4,3,1,1,1,1] .empty .empty))) (.node [12,11,8,6,6,5,4,2,2,2,2,2] (.node [12,11,8,6,6,5,3,3,3,2,1,1,1] (.node [12,11,8,6,6,5,3,3,2,2,2,1,1] (.node [12,11,8,6,6,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,8,6,6,5,4,2,2,2,2,1,1] (.node [12,11,8,6,6,5,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,11,8,6,6,5,4,3,3,1,1,1,1] (.node [12,11,8,6,6,5,4,3,2,2,2,1] (.node [12,11,8,6,6,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,6,5,4,4,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_655 : RowTree := (.node [12,11,8,6,5,5,5,4,2,1,1,1,1] degreeTree62_653 degreeTree62_654) + +def degreeTree62_656 : RowTree := (.node [12,11,8,6,6,6,3,3,3,1,1,1,1] (.node [12,11,8,6,6,6,3,2,2,2,2,1,1] (.node [12,11,8,6,6,6,2,2,2,2,2,1,1,1] (.node [12,11,8,6,6,5,5,4,1,1,1,1,1] (.node [12,11,8,6,6,5,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,6,6,3,2,2,2,1,1,1,1] (.node [12,11,8,6,6,6,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,8,6,6,6,3,3,2,2,1,1,1] (.node [12,11,8,6,6,6,3,3,2,1,1,1,1,1] (.node [12,11,8,6,6,6,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,6,6,6,3,3,2,2,2,1] .empty .empty))) (.node [12,11,8,6,6,6,5,2,1,1,1,1,1,1] (.node [12,11,8,6,6,6,4,3,1,1,1,1,1,1] (.node [12,11,8,6,6,6,4,2,2,2,1,1,1] (.node [12,11,8,6,6,6,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,6,6,4,4,1,1,1,1,1] (.node [12,11,8,6,6,6,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,6,6,6,6,1,1,1,1,1,1,1] (.node [12,11,8,6,6,6,5,3,1,1,1,1,1] (.node [12,11,8,6,6,6,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,6,6,6,6,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_657 : RowTree := (.node [12,11,8,7,5,4,4,3,3,2,2,1] (.node [12,11,8,7,5,4,3,2,2,2,2,2,2] (.node [12,11,8,7,4,4,4,4,3,2,1,1,1] (.node [12,11,8,7,4,4,4,4,2,2,2,1,1] (.node [12,11,8,7,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,11,8,7,4,4,4,4,4,1,1,1,1] (.node [12,11,8,7,4,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,11,8,7,5,4,4,3,2,2,2,1,1] (.node [12,11,8,7,5,4,4,2,2,2,2,2,1] (.node [12,11,8,7,5,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,11,8,7,5,4,4,3,3,2,1,1,1] .empty .empty))) (.node [12,11,8,7,5,5,3,3,2,2,2,1,1] (.node [12,11,8,7,5,4,4,4,3,1,1,1,1] (.node [12,11,8,7,5,4,4,4,2,2,2,1] (.node [12,11,8,7,5,4,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,5,5,3,2,2,2,2,2,1] (.node [12,11,8,7,5,5,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,8,7,5,5,4,2,2,2,2,1,1] (.node [12,11,8,7,5,5,3,3,3,2,2,1] (.node [12,11,8,7,5,5,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,5,5,4,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_658 : RowTree := (.node [12,11,8,7,4,4,4,2,2,2,2,2,2] degreeTree62_656 degreeTree62_657) + +def degreeTree62_659 : RowTree := (.node [12,11,8,6,6,5,5,2,2,2,1,1,1] degreeTree62_655 degreeTree62_658) + +def degreeTree62_660 : RowTree := (.node [12,11,8,7,6,4,3,2,2,2,2,2,1] (.node [12,11,8,7,5,5,5,4,1,1,1,1,1] (.node [12,11,8,7,5,5,4,4,2,1,1,1,1] (.node [12,11,8,7,5,5,4,3,3,1,1,1,1] (.node [12,11,8,7,5,5,4,3,2,2,2,1] .empty .empty) .empty) (.node [12,11,8,7,5,5,5,3,2,1,1,1,1] (.node [12,11,8,7,5,5,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,6,4,2,2,2,2,2,2,2] (.node [12,11,8,7,6,3,3,3,3,2,2,1,1] (.node [12,11,8,7,6,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,7,6,4,3,2,2,2,2,1,1,1] .empty .empty))) (.node [12,11,8,7,6,4,4,2,2,2,2,1,1] (.node [12,11,8,7,6,4,3,3,3,2,1,1,1] (.node [12,11,8,7,6,4,3,3,3,1,1,1,1,1] (.node [12,11,8,7,6,4,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,8,7,6,4,4,2,2,2,1,1,1,1] (.node [12,11,8,7,6,4,3,3,3,2,2,1] .empty .empty) .empty)) (.node [12,11,8,7,6,4,4,3,2,2,1,1,1] (.node [12,11,8,7,6,4,4,3,2,1,1,1,1,1] (.node [12,11,8,7,6,4,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,7,6,4,4,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_661 : RowTree := (.node [12,11,8,7,6,5,4,2,2,2,1,1,1] (.node [12,11,8,7,6,5,3,2,2,2,2,2] (.node [12,11,8,7,6,5,2,2,2,2,2,2,1] (.node [12,11,8,7,6,5,2,2,2,2,2,1,1,1] (.node [12,11,8,7,6,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,6,5,3,2,2,2,2,1,1] (.node [12,11,8,7,6,5,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,6,5,3,3,3,1,1,1,1] (.node [12,11,8,7,6,5,3,3,2,2,1,1,1] (.node [12,11,8,7,6,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,6,5,4,2,2,1,1,1,1,1] .empty .empty))) (.node [12,11,8,7,6,5,5,3,1,1,1,1,1] (.node [12,11,8,7,6,5,4,4,1,1,1,1,1] (.node [12,11,8,7,6,5,4,3,2,1,1,1,1] (.node [12,11,8,7,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,6,5,5,2,2,1,1,1,1] (.node [12,11,8,7,6,5,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,6,6,2,2,2,2,2,2] (.node [12,11,8,7,6,6,2,2,2,2,2,1,1] (.node [12,11,8,7,6,6,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,6,6,3,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_662 : RowTree := (.node [12,11,8,7,6,4,4,4,1,1,1,1,1,1] degreeTree62_660 degreeTree62_661) + +def degreeTree62_663 : RowTree := (.node [12,11,8,7,7,3,3,2,2,2,2,1,1,1] (.node [12,11,8,7,6,6,5,1,1,1,1,1,1,1] (.node [12,11,8,7,6,6,4,2,1,1,1,1,1,1] (.node [12,11,8,7,6,6,3,3,2,1,1,1,1] (.node [12,11,8,7,6,6,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,6,6,4,3,1,1,1,1,1] (.node [12,11,8,7,6,6,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,7,2,2,2,2,2,2,2,2,1] (.node [12,11,8,7,6,6,6,1,1,1,1,1,1] (.node [12,11,8,7,6,6,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,3,2,2,2,2,2,2,2] .empty .empty))) (.node [12,11,8,7,7,4,2,2,2,2,2,1,1,1] (.node [12,11,8,7,7,3,3,3,3,1,1,1,1,1] (.node [12,11,8,7,7,3,3,3,2,2,2,1,1] (.node [12,11,8,7,7,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,8,7,7,3,3,3,3,2,2,1] (.node [12,11,8,7,7,3,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,7,4,3,2,2,2,2,1,1] (.node [12,11,8,7,7,4,3,2,2,2,1,1,1,1] (.node [12,11,8,7,7,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,8,7,7,4,3,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_664 : RowTree := (.node [12,11,8,7,7,5,3,2,2,1,1,1,1,1] (.node [12,11,8,7,7,4,4,3,2,1,1,1,1] (.node [12,11,8,7,7,4,4,2,2,1,1,1,1,1] (.node [12,11,8,7,7,4,3,3,3,1,1,1,1] (.node [12,11,8,7,7,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,4,4,3,1,1,1,1,1,1] (.node [12,11,8,7,7,4,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,7,5,2,2,2,2,2,1,1] (.node [12,11,8,7,7,5,2,2,2,2,1,1,1,1] (.node [12,11,8,7,7,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,5,2,2,2,2,2,2] .empty .empty))) (.node [12,11,8,7,7,5,4,2,2,1,1,1,1] (.node [12,11,8,7,7,5,3,3,2,1,1,1,1] (.node [12,11,8,7,7,5,3,3,1,1,1,1,1,1] (.node [12,11,8,7,7,5,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,5,4,2,1,1,1,1,1,1] .empty .empty)) (.node [12,11,8,7,7,5,5,2,1,1,1,1,1] (.node [12,11,8,7,7,5,5,1,1,1,1,1,1,1] (.node [12,11,8,7,7,5,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,6,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_665 : RowTree := (.node [12,11,8,7,7,4,3,3,2,1,1,1,1,1] degreeTree62_663 degreeTree62_664) + +def degreeTree62_666 : RowTree := (.node [12,11,8,7,6,6,3,2,2,2,1,1,1] degreeTree62_662 degreeTree62_665) + +def degreeTree62_667 : RowTree := (.node [12,11,8,7,5,5,4,3,2,2,1,1,1] degreeTree62_659 degreeTree62_666) + +def degreeTree62_668 : RowTree := (.node [12,11,8,6,4,4,4,4,4,2,1,1,1] degreeTree62_652 degreeTree62_667) + +def degreeTree62_669 : RowTree := (.node [12,11,8,7,7,7,4,1,1,1,1,1,1] (.node [12,11,8,7,7,6,5,1,1,1,1,1,1] (.node [12,11,8,7,7,6,3,3,1,1,1,1,1] (.node [12,11,8,7,7,6,3,2,2,1,1,1,1] (.node [12,11,8,7,7,6,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,6,4,2,1,1,1,1,1] (.node [12,11,8,7,7,6,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,7,7,7,3,1,1,1,1,1,1,1] (.node [12,11,8,7,7,7,2,2,2,1,1,1,1] (.node [12,11,8,7,7,7,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,7,7,7,3,2,1,1,1,1,1] .empty .empty))) (.node [12,11,8,8,4,4,4,3,3,1,1,1,1,1] (.node [12,11,8,8,4,4,4,2,2,2,2,1,1,1] (.node [12,11,8,8,4,4,3,3,3,2,2,1,1] (.node [12,11,8,8,4,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,8,4,4,4,3,2,2,2,1,1] (.node [12,11,8,8,4,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,8,8,4,4,4,4,2,1,1,1,1,1] (.node [12,11,8,8,4,4,4,3,3,2,2,1] (.node [12,11,8,8,4,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,4,4,4,4,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_670 : RowTree := (.node [12,11,8,8,5,4,4,2,2,2,1,1,1,1] (.node [12,11,8,8,5,4,3,2,2,2,2,2,1] (.node [12,11,8,8,5,3,3,3,3,2,2,1,1] (.node [12,11,8,8,5,3,3,2,2,2,2,2,2] (.node [12,11,8,8,4,4,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,5,4,3,2,2,2,2,1,1,1] (.node [12,11,8,8,5,4,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,8,8,5,4,3,3,3,2,1,1,1] (.node [12,11,8,8,5,4,3,3,3,1,1,1,1,1] (.node [12,11,8,8,5,4,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,8,8,5,4,3,3,3,2,2,1] .empty .empty))) (.node [12,11,8,8,5,4,4,4,1,1,1,1,1,1] (.node [12,11,8,8,5,4,4,3,2,1,1,1,1,1] (.node [12,11,8,8,5,4,4,2,2,2,2,2] (.node [12,11,8,8,5,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,8,8,5,4,4,3,3,1,1,1,1] (.node [12,11,8,8,5,4,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,5,5,2,2,2,2,2,2,1] (.node [12,11,8,8,5,5,2,2,2,2,2,1,1,1] (.node [12,11,8,8,5,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,5,5,3,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_671 : RowTree := (.node [12,11,8,8,4,4,4,4,2,2,2,1] degreeTree62_669 degreeTree62_670) + +def degreeTree62_672 : RowTree := (.node [12,11,8,8,5,5,5,2,2,1,1,1,1] (.node [12,11,8,8,5,5,4,2,2,2,1,1,1] (.node [12,11,8,8,5,5,3,3,2,2,1,1,1] (.node [12,11,8,8,5,5,3,3,2,1,1,1,1,1] (.node [12,11,8,8,5,5,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,8,8,5,5,4,2,2,1,1,1,1,1] (.node [12,11,8,8,5,5,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,5,5,4,4,1,1,1,1,1] (.node [12,11,8,8,5,5,4,3,2,1,1,1,1] (.node [12,11,8,8,5,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,5,5,5,2,1,1,1,1,1,1] .empty .empty))) (.node [12,11,8,8,6,3,3,3,2,2,2,1,1] (.node [12,11,8,8,6,3,2,2,2,2,2,2,2] (.node [12,11,8,8,6,2,2,2,2,2,2,2,2,1] (.node [12,11,8,8,5,5,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,3,3,2,2,2,2,2,1] (.node [12,11,8,8,6,3,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,6,3,3,3,3,2,2,1] (.node [12,11,8,8,6,3,3,3,3,2,1,1,1] (.node [12,11,8,8,6,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,4,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_673 : RowTree := (.node [12,11,8,8,6,4,4,4,1,1,1,1,1] (.node [12,11,8,8,6,4,3,3,3,1,1,1,1] (.node [12,11,8,8,6,4,3,2,2,2,2,2] (.node [12,11,8,8,6,4,3,2,2,2,2,1,1] (.node [12,11,8,8,6,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,4,3,3,2,2,1,1,1] (.node [12,11,8,8,6,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,6,4,4,3,1,1,1,1,1,1] (.node [12,11,8,8,6,4,4,2,2,2,1,1,1] (.node [12,11,8,8,6,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,4,4,3,2,1,1,1,1] .empty .empty))) (.node [12,11,8,8,6,5,3,3,1,1,1,1,1,1] (.node [12,11,8,8,6,5,2,2,2,2,2,2] (.node [12,11,8,8,6,5,2,2,2,2,2,1,1] (.node [12,11,8,8,6,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,5,3,2,2,2,1,1,1] (.node [12,11,8,8,6,5,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,6,5,4,2,2,1,1,1,1] (.node [12,11,8,8,6,5,4,2,1,1,1,1,1,1] (.node [12,11,8,8,6,5,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,5,4,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_674 : RowTree := (.node [12,11,8,8,6,4,2,2,2,2,2,2,1] degreeTree62_672 degreeTree62_673) + +def degreeTree62_675 : RowTree := (.node [12,11,8,8,5,5,3,2,2,2,2,1,1] degreeTree62_671 degreeTree62_674) + +def degreeTree62_676 : RowTree := (.node [12,11,8,8,7,2,2,2,2,2,2,2,2] (.node [12,11,8,8,6,6,3,3,1,1,1,1,1] (.node [12,11,8,8,6,6,2,2,2,2,1,1,1] (.node [12,11,8,8,6,6,2,2,2,1,1,1,1,1] (.node [12,11,8,8,6,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,6,6,3,2,2,1,1,1,1] (.node [12,11,8,8,6,6,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,6,6,5,1,1,1,1,1,1] (.node [12,11,8,8,6,6,4,2,1,1,1,1,1] (.node [12,11,8,8,6,6,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [12,11,8,8,7,3,3,3,2,1,1,1,1,1] (.node [12,11,8,8,7,3,3,2,2,2,1,1,1,1] (.node [12,11,8,8,7,3,2,2,2,2,2,2,1] (.node [12,11,8,8,7,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,3,3,2,2,2,2,2] (.node [12,11,8,8,7,3,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,11,8,8,7,4,2,2,2,2,1,1,1,1] (.node [12,11,8,8,7,3,3,3,3,1,1,1,1] (.node [12,11,8,8,7,3,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,4,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_677 : RowTree := (.node [12,11,8,8,7,5,3,2,2,1,1,1,1] (.node [12,11,8,8,7,4,4,2,2,1,1,1,1] (.node [12,11,8,8,7,4,3,3,1,1,1,1,1,1] (.node [12,11,8,8,7,4,3,2,2,2,1,1,1] (.node [12,11,8,8,7,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,4,4,2,1,1,1,1,1,1] (.node [12,11,8,8,7,4,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,7,5,2,2,2,2,1,1,1] (.node [12,11,8,8,7,5,2,2,2,1,1,1,1,1] (.node [12,11,8,8,7,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,5,3,2,1,1,1,1,1,1] .empty .empty))) (.node [12,11,8,8,7,6,2,2,2,1,1,1,1] (.node [12,11,8,8,7,5,4,2,1,1,1,1,1] (.node [12,11,8,8,7,5,4,1,1,1,1,1,1,1] (.node [12,11,8,8,7,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,6,2,2,1,1,1,1,1,1] (.node [12,11,8,8,7,5,5,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,7,6,4,1,1,1,1,1,1] (.node [12,11,8,8,7,6,3,2,1,1,1,1,1] (.node [12,11,8,8,7,6,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,7,7,2,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_678 : RowTree := (.node [12,11,8,8,7,4,2,2,2,2,2,2] degreeTree62_676 degreeTree62_677) + +def degreeTree62_679 : RowTree := (.node [12,11,8,8,8,4,2,2,2,1,1,1,1,1] (.node [12,11,8,8,8,3,2,2,2,2,2,2] (.node [12,11,8,8,8,2,2,2,2,2,2,2,1] (.node [12,11,8,8,8,2,2,2,2,2,2,1,1,1] (.node [12,11,8,8,7,7,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,8,3,2,2,2,2,2,1,1] (.node [12,11,8,8,8,3,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,8,3,3,3,1,1,1,1,1,1] (.node [12,11,8,8,8,3,3,2,2,2,1,1,1] (.node [12,11,8,8,8,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,8,3,3,3,2,1,1,1,1] .empty .empty))) (.node [12,11,8,8,8,4,4,2,1,1,1,1,1] (.node [12,11,8,8,8,4,3,2,2,1,1,1,1] (.node [12,11,8,8,8,4,3,2,1,1,1,1,1,1] (.node [12,11,8,8,8,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,8,4,4,1,1,1,1,1,1,1] (.node [12,11,8,8,8,4,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,8,8,8,5,3,1,1,1,1,1,1,1] (.node [12,11,8,8,8,5,2,2,2,1,1,1,1] (.node [12,11,8,8,8,5,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,8,5,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_680 : RowTree := (.node [12,11,9,5,5,4,4,2,2,2,2,2,2] (.node [12,11,8,8,8,8,1,1,1,1,1,1,1] (.node [12,11,8,8,8,6,3,1,1,1,1,1,1] (.node [12,11,8,8,8,6,2,2,1,1,1,1,1] (.node [12,11,8,8,8,6,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,8,8,8,7,2,1,1,1,1,1,1] (.node [12,11,8,8,8,7,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,5,4,4,4,4,4,2,1,1,1] (.node [12,11,9,5,4,4,4,4,3,2,2,1,1] (.node [12,11,9,4,4,4,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,5,4,4,4,4,4,2,2,1] .empty .empty))) (.node [12,11,9,5,5,5,3,2,2,2,2,2,2] (.node [12,11,9,5,5,4,4,4,3,2,1,1,1] (.node [12,11,9,5,5,4,4,4,2,2,2,1,1] (.node [12,11,9,5,5,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,5,5,4,4,4,4,1,1,1,1] (.node [12,11,9,5,5,4,4,4,3,2,2,1] .empty .empty) .empty)) (.node [12,11,9,5,5,5,4,3,2,2,2,1,1] (.node [12,11,9,5,5,5,4,2,2,2,2,2,1] (.node [12,11,9,5,5,5,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,5,5,5,4,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_681 : RowTree := (.node [12,11,8,8,8,5,4,1,1,1,1,1,1] degreeTree62_679 degreeTree62_680) + +def degreeTree62_682 : RowTree := (.node [12,11,8,8,7,7,2,2,1,1,1,1,1] degreeTree62_678 degreeTree62_681) + +def degreeTree62_683 : RowTree := (.node [12,11,8,8,6,5,5,1,1,1,1,1,1,1] degreeTree62_675 degreeTree62_682) + +def degreeTree62_684 : RowTree := (.node [12,11,9,6,4,4,4,4,2,2,2,1,1] (.node [12,11,9,5,5,5,5,3,3,1,1,1,1] (.node [12,11,9,5,5,5,5,2,2,2,2,1,1] (.node [12,11,9,5,5,5,4,4,3,1,1,1,1] (.node [12,11,9,5,5,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,5,5,5,5,3,2,2,1,1,1] (.node [12,11,9,5,5,5,5,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,9,6,4,4,4,2,2,2,2,2,2] (.node [12,11,9,5,5,5,5,5,1,1,1,1,1] (.node [12,11,9,5,5,5,5,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,4,4,4,3,3,2,2,1,1] .empty .empty))) (.node [12,11,9,6,5,4,4,2,2,2,2,2,1] (.node [12,11,9,6,4,4,4,4,4,1,1,1,1] (.node [12,11,9,6,4,4,4,4,3,2,2,1] (.node [12,11,9,6,4,4,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,5,4,3,3,3,2,2,1,1] (.node [12,11,9,6,5,4,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,9,6,5,4,4,3,3,2,2,1] (.node [12,11,9,6,5,4,4,3,3,2,1,1,1] (.node [12,11,9,6,5,4,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,6,5,4,4,4,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_685 : RowTree := (.node [12,11,9,6,5,5,5,2,2,2,1,1,1] (.node [12,11,9,6,5,5,4,2,2,2,2,1,1] (.node [12,11,9,6,5,5,3,3,2,2,2,1,1] (.node [12,11,9,6,5,5,3,2,2,2,2,2,1] (.node [12,11,9,6,5,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,9,6,5,5,3,3,3,2,2,1] (.node [12,11,9,6,5,5,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,6,5,5,4,3,3,1,1,1,1] (.node [12,11,9,6,5,5,4,3,2,2,1,1,1] (.node [12,11,9,6,5,5,4,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,9,6,5,5,4,4,2,1,1,1,1] .empty .empty))) (.node [12,11,9,6,6,4,3,2,2,2,2,1,1,1] (.node [12,11,9,6,6,3,3,2,2,2,2,2,2] (.node [12,11,9,6,5,5,5,4,1,1,1,1,1] (.node [12,11,9,6,5,5,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,6,4,2,2,2,2,2,2,2] (.node [12,11,9,6,6,3,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,11,9,6,6,4,3,3,3,1,1,1,1,1] (.node [12,11,9,6,6,4,3,3,2,2,2,1,1] (.node [12,11,9,6,6,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,9,6,6,4,3,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_686 : RowTree := (.node [12,11,9,6,5,4,4,4,3,1,1,1,1] degreeTree62_684 degreeTree62_685) + +def degreeTree62_687 : RowTree := (.node [12,11,9,6,6,5,3,2,2,2,2,1,1] (.node [12,11,9,6,6,4,4,4,1,1,1,1,1,1] (.node [12,11,9,6,6,4,4,3,2,1,1,1,1,1] (.node [12,11,9,6,6,4,4,2,2,2,2,2] (.node [12,11,9,6,6,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,6,6,4,4,3,3,1,1,1,1] (.node [12,11,9,6,6,4,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,6,6,5,2,2,2,2,2,2,1] (.node [12,11,9,6,6,5,2,2,2,2,2,1,1,1] (.node [12,11,9,6,6,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,6,5,3,2,2,2,1,1,1,1] .empty .empty))) (.node [12,11,9,6,6,5,4,2,2,2,1,1,1] (.node [12,11,9,6,6,5,3,3,2,2,1,1,1] (.node [12,11,9,6,6,5,3,3,2,1,1,1,1,1] (.node [12,11,9,6,6,5,3,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,9,6,6,5,4,2,2,1,1,1,1,1] (.node [12,11,9,6,6,5,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,6,6,5,4,4,1,1,1,1,1] (.node [12,11,9,6,6,5,4,3,2,1,1,1,1] (.node [12,11,9,6,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,6,5,5,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_688 : RowTree := (.node [12,11,9,6,6,6,4,3,1,1,1,1,1] (.node [12,11,9,6,6,6,3,2,2,2,1,1,1] (.node [12,11,9,6,6,6,2,2,2,2,2,1,1] (.node [12,11,9,6,6,6,2,2,2,2,1,1,1,1] (.node [12,11,9,6,6,5,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,6,6,3,2,2,1,1,1,1,1] (.node [12,11,9,6,6,6,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,9,6,6,6,4,2,1,1,1,1,1,1] (.node [12,11,9,6,6,6,3,3,2,1,1,1,1] (.node [12,11,9,6,6,6,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,6,6,6,4,2,2,1,1,1,1] .empty .empty))) (.node [12,11,9,7,4,4,4,2,2,2,2,1,1,1] (.node [12,11,9,6,6,6,6,1,1,1,1,1,1] (.node [12,11,9,6,6,6,5,2,1,1,1,1,1] (.node [12,11,9,6,6,6,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,4,4,3,3,3,2,2,1,1] (.node [12,11,9,7,4,4,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,9,7,4,4,4,3,3,1,1,1,1,1] (.node [12,11,9,7,4,4,4,3,2,2,2,1,1] (.node [12,11,9,7,4,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,9,7,4,4,4,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_689 : RowTree := (.node [12,11,9,6,6,5,5,2,2,1,1,1,1] degreeTree62_687 degreeTree62_688) + +def degreeTree62_690 : RowTree := (.node [12,11,9,6,6,4,4,2,2,2,1,1,1,1] degreeTree62_686 degreeTree62_689) + +def degreeTree62_691 : RowTree := (.node [12,11,9,7,5,4,3,3,3,2,1,1,1] (.node [12,11,9,7,5,4,2,2,2,2,2,2,2] (.node [12,11,9,7,4,4,4,4,3,1,1,1,1] (.node [12,11,9,7,4,4,4,4,2,2,1,1,1] (.node [12,11,9,7,4,4,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,5,3,3,3,3,2,2,1,1] (.node [12,11,9,7,5,3,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,9,7,5,4,3,3,2,2,2,1,1] (.node [12,11,9,7,5,4,3,2,2,2,2,2,1] (.node [12,11,9,7,5,4,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,5,4,3,3,3,1,1,1,1,1] .empty .empty))) (.node [12,11,9,7,5,4,4,3,3,1,1,1,1] (.node [12,11,9,7,5,4,4,2,2,2,2,2] (.node [12,11,9,7,5,4,4,2,2,2,2,1,1] (.node [12,11,9,7,5,4,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,5,4,4,3,2,2,1,1,1] (.node [12,11,9,7,5,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,5,5,2,2,2,2,2,1,1,1] (.node [12,11,9,7,5,4,4,4,2,1,1,1,1] (.node [12,11,9,7,5,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,5,5,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_692 : RowTree := (.node [12,11,9,7,5,5,5,2,1,1,1,1,1,1] (.node [12,11,9,7,5,5,4,2,2,1,1,1,1,1] (.node [12,11,9,7,5,5,3,3,2,1,1,1,1,1] (.node [12,11,9,7,5,5,3,2,2,2,2,2] (.node [12,11,9,7,5,5,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,7,5,5,3,3,3,1,1,1,1] (.node [12,11,9,7,5,5,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,5,5,4,3,2,1,1,1,1] (.node [12,11,9,7,5,5,4,3,1,1,1,1,1,1] (.node [12,11,9,7,5,5,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,5,5,4,4,1,1,1,1,1] .empty .empty))) (.node [12,11,9,7,6,3,3,2,2,2,2,2,1] (.node [12,11,9,7,6,2,2,2,2,2,2,2,2,1] (.node [12,11,9,7,5,5,5,3,1,1,1,1,1] (.node [12,11,9,7,5,5,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,3,3,2,2,2,2,1,1,1] (.node [12,11,9,7,6,3,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,11,9,7,6,3,3,3,3,2,1,1,1] (.node [12,11,9,7,6,3,3,3,3,1,1,1,1,1] (.node [12,11,9,7,6,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,4,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_693 : RowTree := (.node [12,11,9,7,5,5,3,2,2,2,1,1,1,1] degreeTree62_691 degreeTree62_692) + +def degreeTree62_694 : RowTree := (.node [12,11,9,7,6,4,4,4,1,1,1,1,1] (.node [12,11,9,7,6,4,3,3,3,1,1,1,1] (.node [12,11,9,7,6,4,3,2,2,2,2,2] (.node [12,11,9,7,6,4,3,2,2,2,2,1,1] (.node [12,11,9,7,6,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,4,3,3,2,2,1,1,1] (.node [12,11,9,7,6,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,6,4,4,3,1,1,1,1,1,1] (.node [12,11,9,7,6,4,4,2,2,2,1,1,1] (.node [12,11,9,7,6,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,4,4,3,2,1,1,1,1] .empty .empty))) (.node [12,11,9,7,6,5,3,3,1,1,1,1,1,1] (.node [12,11,9,7,6,5,2,2,2,2,2,2] (.node [12,11,9,7,6,5,2,2,2,2,2,1,1] (.node [12,11,9,7,6,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,5,3,2,2,2,1,1,1] (.node [12,11,9,7,6,5,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,6,5,4,2,2,1,1,1,1] (.node [12,11,9,7,6,5,4,2,1,1,1,1,1,1] (.node [12,11,9,7,6,5,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,5,4,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_695 : RowTree := (.node [12,11,9,7,7,2,2,2,2,2,2,2,2] (.node [12,11,9,7,6,6,3,3,1,1,1,1,1] (.node [12,11,9,7,6,6,2,2,2,2,1,1,1] (.node [12,11,9,7,6,6,2,2,2,1,1,1,1,1] (.node [12,11,9,7,6,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,6,6,3,2,2,1,1,1,1] (.node [12,11,9,7,6,6,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,6,6,5,1,1,1,1,1,1] (.node [12,11,9,7,6,6,4,2,1,1,1,1,1] (.node [12,11,9,7,6,6,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,7,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [12,11,9,7,7,3,3,2,2,2,2,2] (.node [12,11,9,7,7,3,3,2,2,2,1,1,1,1] (.node [12,11,9,7,7,3,2,2,2,2,2,2,1] (.node [12,11,9,7,7,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,7,3,3,2,2,2,2,1,1] .empty .empty)) (.node [12,11,9,7,7,3,3,3,3,1,1,1,1] (.node [12,11,9,7,7,3,3,3,2,2,1,1,1] (.node [12,11,9,7,7,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,7,4,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_696 : RowTree := (.node [12,11,9,7,6,5,5,1,1,1,1,1,1,1] degreeTree62_694 degreeTree62_695) + +def degreeTree62_697 : RowTree := (.node [12,11,9,7,6,4,2,2,2,2,2,2,1] degreeTree62_693 degreeTree62_696) + +def degreeTree62_698 : RowTree := (.node [12,11,9,7,4,4,4,3,3,2,2,1] degreeTree62_690 degreeTree62_697) + +def degreeTree62_699 : RowTree := (.node [12,11,9,5,5,5,4,3,3,2,2,1] degreeTree62_683 degreeTree62_698) + +def degreeTree62_700 : RowTree := (.node [12,11,8,7,7,6,2,2,2,2,1,1,1] degreeTree62_668 degreeTree62_699) + +def degreeTree62_701 : RowTree := (.node [12,11,9,7,7,5,3,2,1,1,1,1,1,1] (.node [12,11,9,7,7,4,4,2,1,1,1,1,1,1] (.node [12,11,9,7,7,4,3,2,2,2,1,1,1] (.node [12,11,9,7,7,4,3,2,2,1,1,1,1,1] (.node [12,11,9,7,7,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,9,7,7,4,3,3,2,1,1,1,1] (.node [12,11,9,7,7,4,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,7,5,2,2,2,1,1,1,1,1] (.node [12,11,9,7,7,4,4,3,1,1,1,1,1] (.node [12,11,9,7,7,4,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,7,5,2,2,2,2,1,1,1] .empty .empty))) (.node [12,11,9,7,7,6,2,2,1,1,1,1,1,1] (.node [12,11,9,7,7,5,4,1,1,1,1,1,1,1] (.node [12,11,9,7,7,5,3,3,1,1,1,1,1] (.node [12,11,9,7,7,5,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,7,5,5,1,1,1,1,1,1] (.node [12,11,9,7,7,5,4,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,7,7,6,3,2,1,1,1,1,1] (.node [12,11,9,7,7,6,3,1,1,1,1,1,1,1] (.node [12,11,9,7,7,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,7,7,6,4,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_702 : RowTree := (.node [12,11,9,8,4,4,4,2,2,2,1,1,1,1] (.node [12,11,9,8,4,4,3,2,2,2,2,1,1,1] (.node [12,11,9,8,4,3,3,2,2,2,2,2,2] (.node [12,11,9,7,7,7,3,1,1,1,1,1,1] (.node [12,11,9,7,7,7,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,4,4,2,2,2,2,2,2,2] (.node [12,11,9,8,4,3,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,11,9,8,4,4,3,3,3,1,1,1,1,1] (.node [12,11,9,8,4,4,3,3,2,2,2,1,1] (.node [12,11,9,8,4,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,9,8,4,4,3,3,3,2,1,1,1] .empty .empty))) (.node [12,11,9,8,4,4,4,4,1,1,1,1,1,1] (.node [12,11,9,8,4,4,4,3,2,1,1,1,1,1] (.node [12,11,9,8,4,4,4,2,2,2,2,2] (.node [12,11,9,8,4,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,4,4,4,3,3,1,1,1,1] (.node [12,11,9,8,4,4,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,5,3,2,2,2,2,2,2,2] (.node [12,11,9,8,5,2,2,2,2,2,2,2,2,1] (.node [12,11,9,8,4,4,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,5,3,3,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_703 : RowTree := (.node [12,11,9,7,7,7,2,1,1,1,1,1,1,1] degreeTree62_701 degreeTree62_702) + +def degreeTree62_704 : RowTree := (.node [12,11,9,8,5,4,3,3,3,1,1,1,1] (.node [12,11,9,8,5,4,3,2,2,2,1,1,1,1] (.node [12,11,9,8,5,3,3,3,3,2,1,1,1] (.node [12,11,9,8,5,3,3,3,3,1,1,1,1,1] (.node [12,11,9,8,5,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,5,4,2,2,2,2,2,2,1] (.node [12,11,9,8,5,4,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,5,4,3,3,2,1,1,1,1,1] (.node [12,11,9,8,5,4,3,2,2,2,2,2] (.node [12,11,9,8,5,4,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,5,4,3,3,2,2,1,1,1] .empty .empty))) (.node [12,11,9,8,5,5,2,2,2,2,1,1,1,1] (.node [12,11,9,8,5,4,4,3,1,1,1,1,1,1] (.node [12,11,9,8,5,4,4,2,2,2,1,1,1] (.node [12,11,9,8,5,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,5,4,4,4,1,1,1,1,1] (.node [12,11,9,8,5,4,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,5,5,3,2,2,1,1,1,1,1] (.node [12,11,9,8,5,5,2,2,2,2,2,2] (.node [12,11,9,8,5,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,5,5,3,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_705 : RowTree := (.node [12,11,9,8,6,3,3,2,2,2,1,1,1,1] (.node [12,11,9,8,5,5,5,2,1,1,1,1,1] (.node [12,11,9,8,5,5,4,2,2,1,1,1,1] (.node [12,11,9,8,5,5,4,2,1,1,1,1,1,1] (.node [12,11,9,8,5,5,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,5,5,5,1,1,1,1,1,1,1] (.node [12,11,9,8,5,5,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,6,3,2,2,2,2,2,1,1,1] (.node [12,11,9,8,6,2,2,2,2,2,2,2,2] (.node [12,11,9,8,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,6,3,2,2,2,2,2,2,1] .empty .empty))) (.node [12,11,9,8,6,4,2,2,2,2,1,1,1,1] (.node [12,11,9,8,6,3,3,3,2,1,1,1,1,1] (.node [12,11,9,8,6,3,3,2,2,2,2,2] (.node [12,11,9,8,6,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,6,3,3,3,3,1,1,1,1] (.node [12,11,9,8,6,3,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,6,4,3,2,2,1,1,1,1,1] (.node [12,11,9,8,6,4,2,2,2,2,2,2] (.node [12,11,9,8,6,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,6,4,3,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_706 : RowTree := (.node [12,11,9,8,5,5,3,3,1,1,1,1,1,1] degreeTree62_704 degreeTree62_705) + +def degreeTree62_707 : RowTree := (.node [12,11,9,8,5,3,3,2,2,2,2,2,1] degreeTree62_703 degreeTree62_706) + +def degreeTree62_708 : RowTree := (.node [12,11,9,8,6,5,4,2,1,1,1,1,1] (.node [12,11,9,8,6,5,2,2,2,2,1,1,1] (.node [12,11,9,8,6,4,4,2,2,1,1,1,1] (.node [12,11,9,8,6,4,4,2,1,1,1,1,1,1] (.node [12,11,9,8,6,4,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,6,5,2,2,2,1,1,1,1,1] (.node [12,11,9,8,6,4,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,6,5,3,3,1,1,1,1,1] (.node [12,11,9,8,6,5,3,2,2,1,1,1,1] (.node [12,11,9,8,6,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,6,5,4,1,1,1,1,1,1,1] .empty .empty))) (.node [12,11,9,8,6,6,4,1,1,1,1,1,1] (.node [12,11,9,8,6,6,2,2,2,1,1,1,1] (.node [12,11,9,8,6,6,2,2,1,1,1,1,1,1] (.node [12,11,9,8,6,5,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,6,6,3,2,1,1,1,1,1] (.node [12,11,9,8,6,6,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,7,3,2,2,2,2,1,1,1,1] (.node [12,11,9,8,7,2,2,2,2,2,2,2,1] (.node [12,11,9,8,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,7,3,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_709 : RowTree := (.node [12,11,9,8,7,4,4,2,1,1,1,1,1] (.node [12,11,9,8,7,4,2,2,2,2,1,1,1] (.node [12,11,9,8,7,3,3,3,1,1,1,1,1,1] (.node [12,11,9,8,7,3,3,2,2,2,1,1,1] (.node [12,11,9,8,7,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,7,4,2,2,2,1,1,1,1,1] (.node [12,11,9,8,7,3,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,7,4,3,3,1,1,1,1,1] (.node [12,11,9,8,7,4,3,2,2,1,1,1,1] (.node [12,11,9,8,7,4,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,7,4,4,1,1,1,1,1,1,1] .empty .empty))) (.node [12,11,9,8,7,6,2,1,1,1,1,1,1,1] (.node [12,11,9,8,7,5,3,1,1,1,1,1,1,1] (.node [12,11,9,8,7,5,2,2,2,1,1,1,1] (.node [12,11,9,8,7,5,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,7,5,4,1,1,1,1,1,1] (.node [12,11,9,8,7,5,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,7,7,1,1,1,1,1,1,1,1] (.node [12,11,9,8,7,6,3,1,1,1,1,1,1] (.node [12,11,9,8,7,6,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,7,7,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_710 : RowTree := (.node [12,11,9,8,7,3,2,2,2,2,2,2] degreeTree62_708 degreeTree62_709) + +def degreeTree62_711 : RowTree := (.node [12,11,9,8,8,4,3,2,1,1,1,1,1] (.node [12,11,9,8,8,3,3,2,2,1,1,1,1] (.node [12,11,9,8,8,3,2,2,2,1,1,1,1,1] (.node [12,11,9,8,8,2,2,2,2,2,2,2] (.node [12,11,9,8,8,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,11,9,8,8,3,3,2,1,1,1,1,1,1] (.node [12,11,9,8,8,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,8,8,4,2,2,2,1,1,1,1] (.node [12,11,9,8,8,4,2,2,1,1,1,1,1,1] (.node [12,11,9,8,8,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,8,4,3,1,1,1,1,1,1,1] .empty .empty))) (.node [12,11,9,8,8,6,2,1,1,1,1,1,1] (.node [12,11,9,8,8,5,2,2,1,1,1,1,1] (.node [12,11,9,8,8,5,2,1,1,1,1,1,1,1] (.node [12,11,9,8,8,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,8,8,6,1,1,1,1,1,1,1,1] (.node [12,11,9,8,8,5,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,3,3,3,3,3,2,2,1,1] (.node [12,11,9,9,3,3,3,2,2,2,2,2,2] (.node [12,11,9,8,8,7,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,4,2,2,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_712 : RowTree := (.node [12,11,9,9,4,4,3,3,2,1,1,1,1,1] (.node [12,11,9,9,4,4,2,2,2,2,2,1,1,1] (.node [12,11,9,9,4,3,3,3,2,2,2,1,1] (.node [12,11,9,9,4,3,3,2,2,2,2,2,1] (.node [12,11,9,9,4,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,4,3,3,3,3,2,1,1,1] (.node [12,11,9,9,4,3,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,4,4,3,2,2,2,2,1,1] (.node [12,11,9,9,4,4,3,2,2,2,1,1,1,1] (.node [12,11,9,9,4,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,11,9,9,4,4,3,2,2,2,2,2] .empty .empty))) (.node [12,11,9,9,4,4,4,3,2,1,1,1,1] (.node [12,11,9,9,4,4,4,2,2,1,1,1,1,1] (.node [12,11,9,9,4,4,3,3,3,1,1,1,1] (.node [12,11,9,9,4,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,4,4,4,3,1,1,1,1,1,1] (.node [12,11,9,9,4,4,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,5,2,2,2,2,2,2,2,2] (.node [12,11,9,9,5,2,2,2,2,2,2,2,1,1] (.node [12,11,9,9,4,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,5,3,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_713 : RowTree := (.node [12,11,9,9,4,3,2,2,2,2,2,2,2] degreeTree62_711 degreeTree62_712) + +def degreeTree62_714 : RowTree := (.node [12,11,9,8,8,2,2,2,2,2,1,1,1,1] degreeTree62_710 degreeTree62_713) + +def degreeTree62_715 : RowTree := (.node [12,11,9,8,6,4,3,3,1,1,1,1,1,1] degreeTree62_707 degreeTree62_714) + +def degreeTree62_716 : RowTree := (.node [12,11,9,9,5,4,3,2,2,2,1,1,1] (.node [12,11,9,9,5,3,3,3,3,1,1,1,1] (.node [12,11,9,9,5,3,3,2,2,2,2,2] (.node [12,11,9,9,5,3,3,2,2,2,2,1,1] (.node [12,11,9,9,5,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,5,3,3,3,2,2,1,1,1] (.node [12,11,9,9,5,3,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,5,4,2,2,2,2,2,2] (.node [12,11,9,9,5,4,2,2,2,2,2,1,1] (.node [12,11,9,9,5,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,5,4,3,2,2,1,1,1,1,1] .empty .empty))) (.node [12,11,9,9,5,5,2,2,2,1,1,1,1,1] (.node [12,11,9,9,5,4,4,2,1,1,1,1,1,1] (.node [12,11,9,9,5,4,3,3,2,1,1,1,1] (.node [12,11,9,9,5,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,5,4,4,3,1,1,1,1,1] (.node [12,11,9,9,5,4,4,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,5,5,3,2,2,1,1,1,1] (.node [12,11,9,9,5,5,3,2,1,1,1,1,1,1] (.node [12,11,9,9,5,5,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,5,5,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_717 : RowTree := (.node [12,11,9,9,6,3,3,3,2,1,1,1,1] (.node [12,11,9,9,6,3,2,2,2,2,2,1,1] (.node [12,11,9,9,6,2,2,2,2,2,2,1,1,1] (.node [12,11,9,9,5,5,5,1,1,1,1,1,1] (.node [12,11,9,9,5,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,6,3,2,2,2,2,1,1,1,1] (.node [12,11,9,9,6,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,11,9,9,6,3,3,2,2,2,1,1,1] (.node [12,11,9,9,6,3,3,2,2,1,1,1,1,1] (.node [12,11,9,9,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,9,9,6,3,3,3,1,1,1,1,1,1] .empty .empty))) (.node [12,11,9,9,6,4,4,1,1,1,1,1,1,1] (.node [12,11,9,9,6,4,3,2,1,1,1,1,1,1] (.node [12,11,9,9,6,4,2,2,2,2,1,1,1] (.node [12,11,9,9,6,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,6,4,3,3,1,1,1,1,1] (.node [12,11,9,9,6,4,3,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,6,5,2,2,2,1,1,1,1] (.node [12,11,9,9,6,5,2,2,1,1,1,1,1,1] (.node [12,11,9,9,6,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,6,5,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_718 : RowTree := (.node [12,11,9,9,5,5,4,1,1,1,1,1,1,1] degreeTree62_716 degreeTree62_717) + +def degreeTree62_719 : RowTree := (.node [12,11,9,9,7,3,3,2,2,1,1,1,1] (.node [12,11,9,9,7,2,2,2,2,2,2,1,1] (.node [12,11,9,9,6,6,2,2,1,1,1,1,1] (.node [12,11,9,9,6,6,2,1,1,1,1,1,1,1] (.node [12,11,9,9,6,5,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,7,2,2,2,2,2,1,1,1,1] (.node [12,11,9,9,6,6,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,7,3,2,2,2,2,1,1,1] (.node [12,11,9,9,7,3,2,2,2,1,1,1,1,1] (.node [12,11,9,9,7,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,11,9,9,7,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [12,11,9,9,7,4,4,1,1,1,1,1,1] (.node [12,11,9,9,7,4,2,2,2,1,1,1,1] (.node [12,11,9,9,7,4,2,2,1,1,1,1,1,1] (.node [12,11,9,9,7,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,7,4,3,2,1,1,1,1,1] (.node [12,11,9,9,7,4,3,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,7,5,3,1,1,1,1,1,1] (.node [12,11,9,9,7,5,2,2,1,1,1,1,1] (.node [12,11,9,9,7,5,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,7,6,1,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_720 : RowTree := (.node [12,11,9,9,8,5,1,1,1,1,1,1,1,1] (.node [12,11,9,9,8,3,3,1,1,1,1,1,1,1] (.node [12,11,9,9,8,2,2,2,2,2,1,1,1] (.node [12,11,9,9,8,2,2,2,2,1,1,1,1,1] (.node [12,11,9,9,7,7,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,8,3,2,2,2,1,1,1,1] (.node [12,11,9,9,8,3,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,8,4,2,2,1,1,1,1,1] (.node [12,11,9,9,8,4,2,1,1,1,1,1,1,1] (.node [12,11,9,9,8,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,8,4,3,1,1,1,1,1,1] .empty .empty))) (.node [12,11,9,9,9,3,2,2,1,1,1,1,1] (.node [12,11,9,9,9,2,2,2,1,1,1,1,1,1] (.node [12,11,9,9,8,6,1,1,1,1,1,1,1] (.node [12,11,9,9,8,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,9,3,2,1,1,1,1,1,1,1] (.node [12,11,9,9,9,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [12,11,9,9,9,4,2,1,1,1,1,1,1] (.node [12,11,9,9,9,4,1,1,1,1,1,1,1,1] (.node [12,11,9,9,9,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,11,9,9,9,5,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_721 : RowTree := (.node [12,11,9,9,7,6,2,1,1,1,1,1,1] degreeTree62_719 degreeTree62_720) + +def degreeTree62_722 : RowTree := (.node [12,11,9,9,6,5,3,2,1,1,1,1,1] degreeTree62_718 degreeTree62_721) + +def degreeTree62_723 : RowTree := (.node [12,12,6,5,5,5,5,4,2,2,2,1,1] (.node [12,12,6,5,5,4,4,4,4,2,2,1,1] (.node [12,12,5,5,5,5,5,5,2,2,2,1,1] (.node [12,12,5,5,5,5,5,4,4,2,1,1,1] (.node [12,12,5,5,5,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,12,5,5,5,5,5,5,4,1,1,1,1] (.node [12,12,5,5,5,5,5,5,3,2,1,1,1] .empty .empty) .empty)) (.node [12,12,6,5,5,5,5,2,2,2,2,2,2] (.node [12,12,6,5,5,5,4,4,4,2,1,1,1] (.node [12,12,6,5,5,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [12,12,6,5,5,5,5,3,3,2,2,1,1] .empty .empty))) (.node [12,12,6,6,5,4,4,4,3,2,2,1,1] (.node [12,12,6,5,5,5,5,5,2,2,1,1,1] (.node [12,12,6,5,5,5,5,4,4,1,1,1,1] (.node [12,12,6,5,5,5,5,4,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,4,4,4,4,4,2,2,1,1] (.node [12,12,6,5,5,5,5,5,3,1,1,1,1] .empty .empty) .empty)) (.node [12,12,6,6,5,5,4,3,3,2,2,1,1] (.node [12,12,6,6,5,5,4,2,2,2,2,2,2] (.node [12,12,6,6,5,4,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,5,5,4,4,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_724 : RowTree := (.node [12,12,6,6,6,4,4,4,3,2,1,1,1] (.node [12,12,6,6,5,5,5,4,3,1,1,1,1] (.node [12,12,6,6,5,5,5,3,2,2,2,1,1] (.node [12,12,6,6,5,5,5,2,2,2,2,2,1] (.node [12,12,6,6,5,5,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,5,5,5,4,2,2,1,1,1] (.node [12,12,6,6,5,5,5,3,3,2,1,1,1] .empty .empty) .empty)) (.node [12,12,6,6,6,4,4,3,3,2,2,1,1] (.node [12,12,6,6,6,4,4,2,2,2,2,2,2] (.node [12,12,6,6,5,5,5,5,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,6,4,4,4,2,2,2,1,1] .empty .empty))) (.node [12,12,6,6,6,5,4,3,3,2,1,1,1] (.node [12,12,6,6,6,5,3,3,3,2,2,1,1] (.node [12,12,6,6,6,5,3,2,2,2,2,2,2] (.node [12,12,6,6,6,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,6,5,4,3,2,2,2,1,1] (.node [12,12,6,6,6,5,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [12,12,6,6,6,5,5,2,2,2,2,1,1] (.node [12,12,6,6,6,5,4,4,3,1,1,1,1] (.node [12,12,6,6,6,5,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,6,5,5,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_725 : RowTree := (.node [12,12,6,6,5,5,4,4,3,2,1,1,1] degreeTree62_723 degreeTree62_724) + +def degreeTree62_726 : RowTree := (.node [12,12,6,6,6,6,4,3,3,1,1,1,1] (.node [12,12,6,6,6,6,3,3,2,2,2,1,1] (.node [12,12,6,6,6,5,5,5,1,1,1,1,1] (.node [12,12,6,6,6,5,5,4,2,1,1,1,1] (.node [12,12,6,6,6,5,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,6,6,3,2,2,2,2,2,1] (.node [12,12,6,6,6,6,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,12,6,6,6,6,4,2,2,2,2,2] (.node [12,12,6,6,6,6,4,2,2,2,2,1,1] (.node [12,12,6,6,6,6,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,6,6,4,3,2,2,1,1,1] .empty .empty))) (.node [12,12,6,6,6,6,6,2,2,1,1,1,1] (.node [12,12,6,6,6,6,5,3,2,1,1,1,1] (.node [12,12,6,6,6,6,5,2,2,2,1,1,1] (.node [12,12,6,6,6,6,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,6,6,6,6,6,2,1,1,1,1,1,1] (.node [12,12,6,6,6,6,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,5,5,4,4,4,3,2,2,1,1] (.node [12,12,7,5,4,4,4,4,4,2,2,1,1] (.node [12,12,6,6,6,6,6,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,5,5,4,4,4,4,2,1,1,1] .empty .empty)))) + +def degreeTree62_727 : RowTree := (.node [12,12,7,6,4,4,4,4,3,2,2,1,1] (.node [12,12,7,5,5,5,5,3,2,2,2,1,1] (.node [12,12,7,5,5,5,4,4,3,2,1,1,1] (.node [12,12,7,5,5,5,4,4,2,2,2,1,1] (.node [12,12,7,5,5,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [12,12,7,5,5,5,5,2,2,2,2,2,1] (.node [12,12,7,5,5,5,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,5,5,5,5,4,3,1,1,1,1] (.node [12,12,7,5,5,5,5,4,2,2,1,1,1] (.node [12,12,7,5,5,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,5,5,5,5,5,2,1,1,1,1] .empty .empty))) (.node [12,12,7,6,5,4,4,4,3,2,1,1,1] (.node [12,12,7,6,5,4,4,3,3,2,2,1,1] (.node [12,12,7,6,5,4,4,2,2,2,2,2,2] (.node [12,12,7,6,4,4,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,5,4,4,4,2,2,2,1,1] .empty .empty)) (.node [12,12,7,6,5,5,3,3,3,2,2,1,1] (.node [12,12,7,6,5,5,3,2,2,2,2,2,2] (.node [12,12,7,6,5,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,5,5,4,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_728 : RowTree := (.node [12,12,7,5,5,5,4,2,2,2,2,2,2] degreeTree62_726 degreeTree62_727) + +def degreeTree62_729 : RowTree := (.node [12,12,6,6,6,5,5,3,2,2,1,1,1] degreeTree62_725 degreeTree62_728) + +def degreeTree62_730 : RowTree := (.node [12,12,5,5,5,5,4,4,4,2,2,1,1] degreeTree62_722 degreeTree62_729) + +def degreeTree62_731 : RowTree := (.node [12,11,9,9,5,3,2,2,2,2,2,2,1] degreeTree62_715 degreeTree62_730) + +def degreeTree62_732 : RowTree := (.node [12,12,7,6,6,4,3,3,3,2,2,1,1] (.node [12,12,7,6,5,5,5,3,2,2,1,1,1] (.node [12,12,7,6,5,5,4,4,3,1,1,1,1] (.node [12,12,7,6,5,5,4,4,2,2,1,1,1] (.node [12,12,7,6,5,5,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,5,5,5,2,2,2,2,2] (.node [12,12,7,6,5,5,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [12,12,7,6,5,5,5,5,1,1,1,1,1] (.node [12,12,7,6,5,5,5,4,2,1,1,1,1] (.node [12,12,7,6,5,5,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,6,4,3,2,2,2,2,2,2] .empty .empty))) (.node [12,12,7,6,6,5,2,2,2,2,2,2,2] (.node [12,12,7,6,6,4,4,3,3,2,1,1,1] (.node [12,12,7,6,6,4,4,3,2,2,2,1,1] (.node [12,12,7,6,6,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,12,7,6,6,4,4,4,3,1,1,1,1] (.node [12,12,7,6,6,4,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [12,12,7,6,6,5,3,3,3,2,1,1,1] (.node [12,12,7,6,6,5,3,3,2,2,2,1,1] (.node [12,12,7,6,6,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [12,12,7,6,6,5,4,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_733 : RowTree := (.node [12,12,7,6,6,6,3,2,2,2,2,2] (.node [12,12,7,6,6,5,5,4,1,1,1,1,1] (.node [12,12,7,6,6,5,4,4,2,1,1,1,1] (.node [12,12,7,6,6,5,4,3,3,1,1,1,1] (.node [12,12,7,6,6,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,6,5,5,3,2,1,1,1,1] (.node [12,12,7,6,6,5,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [12,12,7,6,6,6,3,2,2,2,1,1,1,1] (.node [12,12,7,6,6,6,2,2,2,2,2,2,1] (.node [12,12,7,6,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,6,6,3,2,2,2,2,1,1] .empty .empty))) (.node [12,12,7,6,6,6,4,3,1,1,1,1,1,1] (.node [12,12,7,6,6,6,3,3,3,1,1,1,1] (.node [12,12,7,6,6,6,3,3,2,2,1,1,1] (.node [12,12,7,6,6,6,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,6,6,4,2,2,2,1,1,1] (.node [12,12,7,6,6,6,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,6,6,6,5,2,1,1,1,1,1,1] (.node [12,12,7,6,6,6,4,4,1,1,1,1,1] (.node [12,12,7,6,6,6,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,6,6,6,5,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_734 : RowTree := (.node [12,12,7,6,6,5,4,2,2,2,2,2] degreeTree62_732 degreeTree62_733) + +def degreeTree62_735 : RowTree := (.node [12,12,7,7,5,4,4,3,2,2,2,1,1] (.node [12,12,7,7,4,4,4,4,3,2,1,1,1] (.node [12,12,7,7,4,4,4,2,2,2,2,2,2] (.node [12,12,7,6,6,6,6,2,1,1,1,1,1] (.node [12,12,7,6,6,6,6,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,4,4,4,4,2,2,2,1,1] (.node [12,12,7,7,4,4,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [12,12,7,7,5,4,3,3,3,2,2,1,1] (.node [12,12,7,7,5,4,3,2,2,2,2,2,2] (.node [12,12,7,7,4,4,4,4,4,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,5,4,4,2,2,2,2,2,1] .empty .empty))) (.node [12,12,7,7,5,5,3,3,2,2,2,1,1] (.node [12,12,7,7,5,4,4,4,3,1,1,1,1] (.node [12,12,7,7,5,4,4,4,2,2,1,1,1] (.node [12,12,7,7,5,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,5,5,3,2,2,2,2,2,1] (.node [12,12,7,7,5,5,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,12,7,7,5,5,4,2,2,2,2,2] (.node [12,12,7,7,5,5,4,2,2,2,2,1,1] (.node [12,12,7,7,5,5,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,5,5,4,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_736 : RowTree := (.node [12,12,7,7,6,4,3,3,3,1,1,1,1,1] (.node [12,12,7,7,6,3,3,3,3,2,2,1,1] (.node [12,12,7,7,5,5,5,3,2,1,1,1,1] (.node [12,12,7,7,5,5,5,2,2,2,1,1,1] (.node [12,12,7,7,5,5,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,3,3,2,2,2,2,2,2] (.node [12,12,7,7,5,5,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,6,4,3,2,2,2,2,2,1] (.node [12,12,7,7,6,4,3,2,2,2,2,1,1,1] (.node [12,12,7,7,6,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [12,12,7,7,6,4,3,3,2,2,2,1,1] .empty .empty))) (.node [12,12,7,7,6,4,4,3,3,1,1,1,1] (.node [12,12,7,7,6,4,4,2,2,2,2,1,1] (.node [12,12,7,7,6,4,4,2,2,2,1,1,1,1] (.node [12,12,7,7,6,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,4,4,3,2,2,1,1,1] (.node [12,12,7,7,6,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,6,5,2,2,2,2,2,1,1,1] (.node [12,12,7,7,6,4,4,4,2,1,1,1,1] (.node [12,12,7,7,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,5,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_737 : RowTree := (.node [12,12,7,7,5,5,4,3,3,1,1,1,1] degreeTree62_735 degreeTree62_736) + +def degreeTree62_738 : RowTree := (.node [12,12,7,6,6,6,5,3,1,1,1,1,1] degreeTree62_734 degreeTree62_737) + +def degreeTree62_739 : RowTree := (.node [12,12,7,7,6,5,5,2,2,1,1,1,1] (.node [12,12,7,7,6,5,4,2,2,2,1,1,1] (.node [12,12,7,7,6,5,3,3,2,2,1,1,1] (.node [12,12,7,7,6,5,3,3,2,1,1,1,1,1] (.node [12,12,7,7,6,5,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,5,4,2,2,1,1,1,1,1] (.node [12,12,7,7,6,5,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,6,5,4,4,1,1,1,1,1] (.node [12,12,7,7,6,5,4,3,2,1,1,1,1] (.node [12,12,7,7,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,5,5,2,1,1,1,1,1,1] .empty .empty))) (.node [12,12,7,7,6,6,3,3,1,1,1,1,1,1] (.node [12,12,7,7,6,6,2,2,2,2,2,1,1] (.node [12,12,7,7,6,6,2,2,2,2,1,1,1,1] (.node [12,12,7,7,6,5,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,6,3,2,2,2,1,1,1] (.node [12,12,7,7,6,6,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,6,6,4,2,2,1,1,1,1] (.node [12,12,7,7,6,6,4,2,1,1,1,1,1,1] (.node [12,12,7,7,6,6,3,3,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,6,6,4,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_740 : RowTree := (.node [12,12,7,7,7,4,2,2,2,2,2,2,1] (.node [12,12,7,7,7,3,3,2,2,2,2,2,1] (.node [12,12,7,7,7,2,2,2,2,2,2,2,2,1] (.node [12,12,7,7,6,6,6,1,1,1,1,1,1] (.node [12,12,7,7,6,6,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,3,3,2,2,2,2,1,1,1] (.node [12,12,7,7,7,3,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [12,12,7,7,7,3,3,3,3,2,1,1,1] (.node [12,12,7,7,7,3,3,3,3,1,1,1,1,1] (.node [12,12,7,7,7,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,4,2,2,2,2,2,1,1,1] .empty .empty))) (.node [12,12,7,7,7,4,4,2,2,1,1,1,1,1] (.node [12,12,7,7,7,4,3,3,2,1,1,1,1,1] (.node [12,12,7,7,7,4,3,2,2,2,2,1,1] (.node [12,12,7,7,7,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,4,3,3,3,1,1,1,1] (.node [12,12,7,7,7,4,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,7,4,4,3,2,1,1,1,1] (.node [12,12,7,7,7,4,4,3,1,1,1,1,1,1] (.node [12,12,7,7,7,4,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,4,4,4,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_741 : RowTree := (.node [12,12,7,7,6,6,5,1,1,1,1,1,1,1] degreeTree62_739 degreeTree62_740) + +def degreeTree62_742 : RowTree := (.node [12,12,7,7,7,6,2,2,2,1,1,1,1,1] (.node [12,12,7,7,7,5,4,2,1,1,1,1,1,1] (.node [12,12,7,7,7,5,3,2,2,2,1,1,1] (.node [12,12,7,7,7,5,3,2,2,1,1,1,1,1] (.node [12,12,7,7,7,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,5,3,3,2,1,1,1,1] (.node [12,12,7,7,7,5,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,7,5,5,1,1,1,1,1,1,1] (.node [12,12,7,7,7,5,4,3,1,1,1,1,1] (.node [12,12,7,7,7,5,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,5,5,2,1,1,1,1,1] .empty .empty))) (.node [12,12,7,7,7,6,4,2,1,1,1,1,1] (.node [12,12,7,7,7,6,3,2,2,1,1,1,1] (.node [12,12,7,7,7,6,3,2,1,1,1,1,1,1] (.node [12,12,7,7,7,6,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,6,4,1,1,1,1,1,1,1] (.node [12,12,7,7,7,6,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [12,12,7,7,7,7,2,2,2,1,1,1,1] (.node [12,12,7,7,7,7,2,2,1,1,1,1,1,1] (.node [12,12,7,7,7,6,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [12,12,7,7,7,7,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_743 : RowTree := (.node [13,6,6,6,6,6,6,5,2,2,2,1,1] (.node [13,6,6,6,6,6,5,5,3,2,2,1,1] (.node [13,6,6,6,6,5,5,5,4,2,2,1,1] (.node [13,6,6,6,5,5,5,5,5,2,2,1,1] (.node [12,12,7,7,7,7,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,6,6,6,6,6,5,4,4,2,2,1,1] (.node [13,6,6,6,6,5,5,5,5,2,1,1,1] .empty .empty) .empty)) (.node [13,6,6,6,6,6,6,4,3,2,2,1,1] (.node [13,6,6,6,6,6,5,5,5,1,1,1,1] (.node [13,6,6,6,6,6,5,5,4,2,1,1,1] .empty .empty) .empty) (.node [13,6,6,6,6,6,6,4,4,2,1,1,1] .empty .empty))) (.node [13,7,6,5,5,5,5,5,5,2,2,1,1] (.node [13,6,6,6,6,6,6,6,2,2,1,1,1] (.node [13,6,6,6,6,6,6,5,4,1,1,1,1] (.node [13,6,6,6,6,6,6,5,3,2,1,1,1] .empty .empty) .empty) (.node [13,6,6,6,6,6,6,6,3,1,1,1,1] .empty .empty)) (.node [13,7,6,6,6,5,5,4,4,2,2,1,1] (.node [13,7,6,6,5,5,5,5,5,2,1,1,1] (.node [13,7,6,6,5,5,5,5,4,2,2,1,1] .empty .empty) .empty) (.node [13,7,6,6,6,5,5,5,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_744 : RowTree := (.node [12,12,7,7,7,7,3,2,1,1,1,1,1] degreeTree62_742 degreeTree62_743) + +def degreeTree62_745 : RowTree := (.node [12,12,7,7,7,5,2,2,2,2,1,1,1,1] degreeTree62_741 degreeTree62_744) + +def degreeTree62_746 : RowTree := (.node [12,12,7,7,6,5,3,2,2,2,1,1,1,1] degreeTree62_738 degreeTree62_745) + +def degreeTree62_747 : RowTree := (.node [13,7,6,6,6,6,6,4,3,2,1,1,1] (.node [13,7,6,6,6,6,5,5,3,2,1,1,1] (.node [13,7,6,6,6,6,5,4,3,2,2,1,1] (.node [13,7,6,6,6,6,4,4,4,2,2,1,1] (.node [13,7,6,6,6,5,5,5,5,1,1,1,1] .empty .empty) .empty) (.node [13,7,6,6,6,6,5,5,2,2,2,1,1] (.node [13,7,6,6,6,6,5,4,4,2,1,1,1] .empty .empty) .empty)) (.node [13,7,6,6,6,6,6,3,3,2,2,1,1] (.node [13,7,6,6,6,6,6,2,2,2,2,2,2] (.node [13,7,6,6,6,6,5,5,4,1,1,1,1] .empty .empty) .empty) (.node [13,7,6,6,6,6,6,4,2,2,2,1,1] .empty .empty))) (.node [13,7,7,5,5,5,5,5,5,2,1,1,1] (.node [13,7,6,6,6,6,6,5,3,1,1,1,1] (.node [13,7,6,6,6,6,6,5,2,2,1,1,1] (.node [13,7,6,6,6,6,6,4,4,1,1,1,1] .empty .empty) .empty) (.node [13,7,7,5,5,5,5,5,4,2,2,1,1] (.node [13,7,6,6,6,6,6,6,2,1,1,1,1] .empty .empty) .empty)) (.node [13,7,7,6,5,5,5,5,4,2,1,1,1] (.node [13,7,7,6,5,5,5,5,3,2,2,1,1] (.node [13,7,7,6,5,5,5,4,4,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,6,5,5,5,5,5,1,1,1,1] .empty .empty)))) + +def degreeTree62_748 : RowTree := (.node [13,7,7,6,6,6,5,4,3,2,1,1,1] (.node [13,7,7,6,6,6,4,4,3,2,2,1,1] (.node [13,7,7,6,6,5,5,5,2,2,2,1,1] (.node [13,7,7,6,6,5,5,4,4,2,1,1,1] (.node [13,7,7,6,6,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,6,6,5,5,5,4,1,1,1,1] (.node [13,7,7,6,6,5,5,5,3,2,1,1,1] .empty .empty) .empty)) (.node [13,7,7,6,6,6,5,3,3,2,2,1,1] (.node [13,7,7,6,6,6,5,2,2,2,2,2,2] (.node [13,7,7,6,6,6,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [13,7,7,6,6,6,5,4,2,2,2,1,1] .empty .empty))) (.node [13,7,7,6,6,6,6,3,3,2,1,1,1] (.node [13,7,7,6,6,6,5,5,3,1,1,1,1] (.node [13,7,7,6,6,6,5,5,2,2,1,1,1] (.node [13,7,7,6,6,6,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [13,7,7,6,6,6,6,3,2,2,2,1,1] (.node [13,7,7,6,6,6,6,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,7,7,6,6,6,6,5,2,1,1,1,1] (.node [13,7,7,6,6,6,6,4,3,1,1,1,1] (.node [13,7,7,6,6,6,6,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,7,7,6,6,6,6,6,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_749 : RowTree := (.node [13,7,7,6,6,5,4,4,4,2,2,1,1] degreeTree62_747 degreeTree62_748) + +def degreeTree62_750 : RowTree := (.node [13,7,7,7,6,5,5,4,2,2,2,1,1] (.node [13,7,7,7,6,4,4,4,4,2,2,1,1] (.node [13,7,7,7,5,5,5,5,2,2,2,1,1] (.node [13,7,7,7,5,5,5,4,4,2,1,1,1] (.node [13,7,7,7,5,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,7,5,5,5,5,4,1,1,1,1] (.node [13,7,7,7,5,5,5,5,3,2,1,1,1] .empty .empty) .empty)) (.node [13,7,7,7,6,5,5,2,2,2,2,2,2] (.node [13,7,7,7,6,5,4,4,4,2,1,1,1] (.node [13,7,7,7,6,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,7,6,5,5,3,3,2,2,1,1] .empty .empty))) (.node [13,7,7,7,6,6,4,3,3,2,2,1,1] (.node [13,7,7,7,6,5,5,5,2,2,1,1,1] (.node [13,7,7,7,6,5,5,4,4,1,1,1,1] (.node [13,7,7,7,6,5,5,4,3,2,1,1,1] .empty .empty) .empty) (.node [13,7,7,7,6,6,4,2,2,2,2,2,2] (.node [13,7,7,7,6,5,5,5,3,1,1,1,1] .empty .empty) .empty)) (.node [13,7,7,7,6,6,4,4,4,1,1,1,1] (.node [13,7,7,7,6,6,4,4,3,2,1,1,1] (.node [13,7,7,7,6,6,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,7,6,6,5,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_751 : RowTree := (.node [13,7,7,7,7,4,4,4,4,2,1,1,1] (.node [13,7,7,7,6,6,6,3,2,2,1,1,1] (.node [13,7,7,7,6,6,5,4,3,1,1,1,1] (.node [13,7,7,7,6,6,5,4,2,2,1,1,1] (.node [13,7,7,7,6,6,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,7,7,7,6,6,6,2,2,2,2,1,1] (.node [13,7,7,7,6,6,5,5,2,1,1,1,1] .empty .empty) .empty)) (.node [13,7,7,7,6,6,6,5,1,1,1,1,1] (.node [13,7,7,7,6,6,6,4,2,1,1,1,1] (.node [13,7,7,7,6,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,7,7,7,7,4,4,4,3,2,2,1,1] .empty .empty))) (.node [13,7,7,7,7,5,5,2,2,2,2,2,1] (.node [13,7,7,7,7,5,4,4,2,2,2,1,1] (.node [13,7,7,7,7,5,4,3,3,2,2,1,1] (.node [13,7,7,7,7,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,7,7,7,7,5,4,4,4,1,1,1,1] (.node [13,7,7,7,7,5,4,4,3,2,1,1,1] .empty .empty) .empty)) (.node [13,7,7,7,7,5,5,4,2,2,1,1,1] (.node [13,7,7,7,7,5,5,3,3,2,1,1,1] (.node [13,7,7,7,7,5,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,7,7,5,5,4,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_752 : RowTree := (.node [13,7,7,7,6,6,5,3,2,2,2,1,1] degreeTree62_750 degreeTree62_751) + +def degreeTree62_753 : RowTree := (.node [13,7,7,7,5,5,4,4,4,2,2,1,1] degreeTree62_749 degreeTree62_752) + +def degreeTree62_754 : RowTree := (.node [13,7,7,7,7,6,5,4,2,1,1,1,1] (.node [13,7,7,7,7,6,4,4,2,2,1,1,1] (.node [13,7,7,7,7,6,4,2,2,2,2,2,1] (.node [13,7,7,7,7,6,3,3,3,2,2,1,1] (.node [13,7,7,7,7,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,7,7,7,7,6,4,3,3,2,1,1,1] (.node [13,7,7,7,7,6,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [13,7,7,7,7,6,5,3,2,2,1,1,1] (.node [13,7,7,7,7,6,5,2,2,2,2,1,1] (.node [13,7,7,7,7,6,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [13,7,7,7,7,6,5,3,3,1,1,1,1] .empty .empty))) (.node [13,7,7,7,7,7,3,2,2,2,2,2,1] (.node [13,7,7,7,7,6,6,3,2,1,1,1,1] (.node [13,7,7,7,7,6,6,2,2,2,1,1,1] (.node [13,7,7,7,7,6,5,5,1,1,1,1,1] .empty .empty) .empty) (.node [13,7,7,7,7,7,2,2,2,2,2,2,2] (.node [13,7,7,7,7,6,6,4,1,1,1,1,1] .empty .empty) .empty)) (.node [13,7,7,7,7,7,4,2,2,2,2,1,1] (.node [13,7,7,7,7,7,3,3,3,2,1,1,1] (.node [13,7,7,7,7,7,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,7,7,7,7,7,4,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_755 : RowTree := (.node [13,8,6,5,5,5,5,5,4,2,2,1,1] (.node [13,7,7,7,7,7,6,2,2,1,1,1,1] (.node [13,7,7,7,7,7,5,3,2,1,1,1,1] (.node [13,7,7,7,7,7,5,2,2,2,1,1,1] (.node [13,7,7,7,7,7,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [13,7,7,7,7,7,6,2,1,1,1,1,1,1] (.node [13,7,7,7,7,7,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [13,7,7,7,7,7,7,2,1,1,1,1,1] (.node [13,7,7,7,7,7,7,1,1,1,1,1,1,1] (.node [13,7,7,7,7,7,6,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,5,5,5,5,5,5,5,2,2,1,1] .empty .empty))) (.node [13,8,6,6,6,5,4,4,4,2,2,1,1] (.node [13,8,6,6,5,5,5,5,3,2,2,1,1] (.node [13,8,6,6,5,5,5,4,4,2,2,1,1] (.node [13,8,6,5,5,5,5,5,5,2,1,1,1] .empty .empty) .empty) (.node [13,8,6,6,5,5,5,5,5,1,1,1,1] (.node [13,8,6,6,5,5,5,5,4,2,1,1,1] .empty .empty) .empty)) (.node [13,8,6,6,6,5,5,5,2,2,2,1,1] (.node [13,8,6,6,6,5,5,4,4,2,1,1,1] (.node [13,8,6,6,6,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,6,6,6,5,5,5,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_756 : RowTree := (.node [13,7,7,7,7,7,4,3,3,1,1,1,1] degreeTree62_754 degreeTree62_755) + +def degreeTree62_757 : RowTree := (.node [13,8,6,6,6,6,6,3,2,2,2,1,1] (.node [13,8,6,6,6,6,5,4,3,2,1,1,1] (.node [13,8,6,6,6,6,5,2,2,2,2,2,2] (.node [13,8,6,6,6,6,4,4,4,2,1,1,1] (.node [13,8,6,6,6,6,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,6,6,6,6,5,4,2,2,2,1,1] (.node [13,8,6,6,6,6,5,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,8,6,6,6,6,5,5,3,1,1,1,1] (.node [13,8,6,6,6,6,5,5,2,2,1,1,1] (.node [13,8,6,6,6,6,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [13,8,6,6,6,6,6,2,2,2,2,2,1] .empty .empty))) (.node [13,8,7,5,5,5,5,4,4,2,2,1,1] (.node [13,8,6,6,6,6,6,4,3,1,1,1,1] (.node [13,8,6,6,6,6,6,4,2,2,1,1,1] (.node [13,8,6,6,6,6,6,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,6,6,6,6,6,6,1,1,1,1,1] (.node [13,8,6,6,6,6,6,5,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,7,5,5,5,5,5,5,1,1,1,1] (.node [13,8,7,5,5,5,5,5,4,2,1,1,1] (.node [13,8,7,5,5,5,5,5,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,6,5,5,4,4,4,2,2,1,1] .empty .empty)))) + +def degreeTree62_758 : RowTree := (.node [13,8,7,6,6,5,5,4,3,2,1,1,1] (.node [13,8,7,6,6,5,4,4,3,2,2,1,1] (.node [13,8,7,6,5,5,5,5,3,2,1,1,1] (.node [13,8,7,6,5,5,5,5,2,2,2,1,1] (.node [13,8,7,6,5,5,5,4,4,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,6,6,4,4,4,4,2,2,1,1] (.node [13,8,7,6,5,5,5,5,4,1,1,1,1] .empty .empty) .empty)) (.node [13,8,7,6,6,5,5,3,3,2,2,1,1] (.node [13,8,7,6,6,5,5,2,2,2,2,2,2] (.node [13,8,7,6,6,5,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,6,6,5,5,4,2,2,2,1,1] .empty .empty))) (.node [13,8,7,6,6,6,4,3,3,2,2,1,1] (.node [13,8,7,6,6,5,5,5,3,1,1,1,1] (.node [13,8,7,6,6,5,5,5,2,2,1,1,1] (.node [13,8,7,6,6,5,5,4,4,1,1,1,1] .empty .empty) .empty) (.node [13,8,7,6,6,6,4,2,2,2,2,2,2] .empty .empty)) (.node [13,8,7,6,6,6,4,4,4,1,1,1,1] (.node [13,8,7,6,6,6,4,4,3,2,1,1,1] (.node [13,8,7,6,6,6,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,6,6,6,5,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_759 : RowTree := (.node [13,8,7,6,5,5,5,4,3,2,2,1,1] degreeTree62_757 degreeTree62_758) + +def degreeTree62_760 : RowTree := (.node [13,8,6,6,6,5,5,5,4,1,1,1,1] degreeTree62_756 degreeTree62_759) + +def degreeTree62_761 : RowTree := (.node [13,7,7,7,7,5,5,5,2,1,1,1,1] degreeTree62_753 degreeTree62_760) + +def degreeTree62_762 : RowTree := (.node [13,7,6,6,6,5,5,5,4,2,1,1,1] degreeTree62_746 degreeTree62_761) + +def degreeTree62_763 : RowTree := (.node [12,12,7,6,5,5,4,3,2,2,2,1,1] degreeTree62_731 degreeTree62_762) + +def degreeTree62_764 : RowTree := (.node [12,11,9,7,7,4,2,2,2,2,2,1,1] degreeTree62_700 degreeTree62_763) + +def degreeTree62_765 : RowTree := (.node [12,11,7,6,6,5,4,2,2,2,2,2,1] degreeTree62_637 degreeTree62_764) + +def degreeTree62_766 : RowTree := (.node [13,8,7,7,5,5,4,4,3,2,2,1,1] (.node [13,8,7,6,6,6,6,3,2,2,1,1,1] (.node [13,8,7,6,6,6,5,4,3,1,1,1,1] (.node [13,8,7,6,6,6,5,4,2,2,1,1,1] (.node [13,8,7,6,6,6,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,6,6,6,6,2,2,2,2,1,1] (.node [13,8,7,6,6,6,5,5,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,7,6,6,6,6,5,1,1,1,1,1] (.node [13,8,7,6,6,6,6,4,2,1,1,1,1] (.node [13,8,7,6,6,6,6,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,5,4,4,4,4,2,2,1,1] .empty .empty))) (.node [13,8,7,7,5,5,5,4,4,1,1,1,1] (.node [13,8,7,7,5,5,5,3,3,2,2,1,1] (.node [13,8,7,7,5,5,5,2,2,2,2,2,2] (.node [13,8,7,7,5,5,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,5,5,5,4,3,2,1,1,1] (.node [13,8,7,7,5,5,5,4,2,2,2,1,1] .empty .empty) .empty)) (.node [13,8,7,7,6,4,4,4,3,2,2,1,1] (.node [13,8,7,7,5,5,5,5,3,1,1,1,1] (.node [13,8,7,7,5,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,6,4,4,4,4,2,1,1,1] .empty .empty)))) + +def degreeTree62_767 : RowTree := (.node [13,8,7,7,6,6,3,2,2,2,2,2,2] (.node [13,8,7,7,6,5,5,3,2,2,2,1,1] (.node [13,8,7,7,6,5,4,4,3,2,1,1,1] (.node [13,8,7,7,6,5,4,4,2,2,2,1,1] (.node [13,8,7,7,6,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,7,6,5,5,2,2,2,2,2,1] (.node [13,8,7,7,6,5,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [13,8,7,7,6,5,5,4,3,1,1,1,1] (.node [13,8,7,7,6,5,5,4,2,2,1,1,1] (.node [13,8,7,7,6,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,6,5,5,5,2,1,1,1,1] .empty .empty))) (.node [13,8,7,7,6,6,4,4,3,1,1,1,1] (.node [13,8,7,7,6,6,4,3,2,2,2,1,1] (.node [13,8,7,7,6,6,4,2,2,2,2,2,1] (.node [13,8,7,7,6,6,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,7,6,6,4,4,2,2,1,1,1] (.node [13,8,7,7,6,6,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [13,8,7,7,6,6,5,3,3,1,1,1,1] (.node [13,8,7,7,6,6,5,3,2,2,1,1,1] (.node [13,8,7,7,6,6,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,7,6,6,5,4,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_768 : RowTree := (.node [13,8,7,7,6,5,4,2,2,2,2,2,2] degreeTree62_766 degreeTree62_767) + +def degreeTree62_769 : RowTree := (.node [13,8,7,7,7,5,4,2,2,2,2,2,1] (.node [13,8,7,7,7,4,4,4,2,2,2,1,1] (.node [13,8,7,7,6,6,6,4,1,1,1,1,1] (.node [13,8,7,7,6,6,6,3,2,1,1,1,1] (.node [13,8,7,7,6,6,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,4,4,3,3,2,2,1,1] (.node [13,8,7,7,7,4,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,8,7,7,7,5,3,2,2,2,2,2,2] (.node [13,8,7,7,7,4,4,4,4,1,1,1,1] (.node [13,8,7,7,7,4,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,5,3,3,3,2,2,1,1] .empty .empty))) (.node [13,8,7,7,7,5,5,3,2,2,1,1,1] (.node [13,8,7,7,7,5,4,4,2,2,1,1,1] (.node [13,8,7,7,7,5,4,3,3,2,1,1,1] (.node [13,8,7,7,7,5,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,5,5,2,2,2,2,1,1] (.node [13,8,7,7,7,5,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [13,8,7,7,7,5,5,5,1,1,1,1,1] (.node [13,8,7,7,7,5,5,4,2,1,1,1,1] (.node [13,8,7,7,7,5,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,6,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_770 : RowTree := (.node [13,8,7,7,7,6,6,2,2,1,1,1,1] (.node [13,8,7,7,7,6,4,4,2,1,1,1,1] (.node [13,8,7,7,7,6,4,2,2,2,2,1,1] (.node [13,8,7,7,7,6,3,3,3,2,1,1,1] (.node [13,8,7,7,7,6,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,6,4,3,3,1,1,1,1] (.node [13,8,7,7,7,6,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [13,8,7,7,7,6,5,4,1,1,1,1,1] (.node [13,8,7,7,7,6,5,3,2,1,1,1,1] (.node [13,8,7,7,7,6,5,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,6,6,2,1,1,1,1,1,1] .empty .empty))) (.node [13,8,7,7,7,7,3,3,2,1,1,1,1,1] (.node [13,8,7,7,7,7,2,2,2,2,2,2,1] (.node [13,8,7,7,7,7,2,2,2,2,2,1,1,1] (.node [13,8,7,7,7,6,6,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,7,3,2,2,2,2,1,1] (.node [13,8,7,7,7,7,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,7,7,7,7,4,2,2,1,1,1,1,1] (.node [13,8,7,7,7,7,3,3,3,1,1,1,1] (.node [13,8,7,7,7,7,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,7,4,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_771 : RowTree := (.node [13,8,7,7,7,6,3,2,2,2,2,2,1] degreeTree62_769 degreeTree62_770) + +def degreeTree62_772 : RowTree := (.node [13,8,7,7,6,6,5,5,1,1,1,1,1] degreeTree62_768 degreeTree62_771) + +def degreeTree62_773 : RowTree := (.node [13,8,8,5,5,5,5,5,2,2,2,1,1] (.node [13,8,7,7,7,7,6,1,1,1,1,1,1,1] (.node [13,8,7,7,7,7,5,2,1,1,1,1,1,1] (.node [13,8,7,7,7,7,4,4,1,1,1,1,1] (.node [13,8,7,7,7,7,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,7,7,7,7,5,3,1,1,1,1,1] (.node [13,8,7,7,7,7,5,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,5,5,5,5,4,3,2,2,1,1] (.node [13,8,8,5,5,5,4,4,4,2,2,1,1] (.node [13,8,7,7,7,7,6,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,5,5,5,5,4,4,2,1,1,1] .empty .empty))) (.node [13,8,8,6,5,5,5,2,2,2,2,2,2] (.node [13,8,8,6,5,4,4,4,4,2,2,1,1] (.node [13,8,8,5,5,5,5,5,4,1,1,1,1] (.node [13,8,8,5,5,5,5,5,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,6,5,5,4,4,4,2,1,1,1] (.node [13,8,8,6,5,5,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [13,8,8,6,5,5,5,4,3,2,1,1,1] (.node [13,8,8,6,5,5,5,4,2,2,2,1,1] (.node [13,8,8,6,5,5,5,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,6,5,5,5,4,4,1,1,1,1] .empty .empty)))) + +def degreeTree62_774 : RowTree := (.node [13,8,8,6,6,5,5,3,3,2,1,1,1] (.node [13,8,8,6,6,5,4,4,2,2,2,1,1] (.node [13,8,8,6,6,4,4,4,4,2,1,1,1] (.node [13,8,8,6,6,4,4,4,3,2,2,1,1] (.node [13,8,8,6,5,5,5,5,3,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,6,6,5,4,3,3,2,2,1,1] (.node [13,8,8,6,6,5,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,8,8,6,6,5,5,2,2,2,2,2,1] (.node [13,8,8,6,6,5,4,4,4,1,1,1,1] (.node [13,8,8,6,6,5,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,6,6,5,5,3,2,2,2,1,1] .empty .empty))) (.node [13,8,8,6,6,6,4,2,2,2,2,2,1] (.node [13,8,8,6,6,5,5,5,2,1,1,1,1] (.node [13,8,8,6,6,5,5,4,3,1,1,1,1] (.node [13,8,8,6,6,5,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,6,6,6,3,3,3,2,2,1,1] (.node [13,8,8,6,6,6,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,8,8,6,6,6,4,4,2,2,1,1,1] (.node [13,8,8,6,6,6,4,3,3,2,1,1,1] (.node [13,8,8,6,6,6,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,6,6,6,4,4,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_775 : RowTree := (.node [13,8,8,6,5,5,5,5,2,2,1,1,1] degreeTree62_773 degreeTree62_774) + +def degreeTree62_776 : RowTree := (.node [13,8,8,7,5,5,4,2,2,2,2,2,2] (.node [13,8,8,6,6,6,6,3,2,1,1,1,1] (.node [13,8,8,6,6,6,5,4,2,1,1,1,1] (.node [13,8,8,6,6,6,5,3,3,1,1,1,1] (.node [13,8,8,6,6,6,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,6,6,6,6,2,2,2,1,1,1] (.node [13,8,8,6,6,6,5,5,1,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,5,4,4,4,3,2,2,1,1] (.node [13,8,8,7,4,4,4,4,4,2,2,1,1] (.node [13,8,8,6,6,6,6,4,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,5,4,4,4,4,2,1,1,1] .empty .empty))) (.node [13,8,8,7,5,5,5,3,2,2,2,1,1] (.node [13,8,8,7,5,5,4,4,3,2,1,1,1] (.node [13,8,8,7,5,5,4,4,2,2,2,1,1] (.node [13,8,8,7,5,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,7,5,5,5,2,2,2,2,2,1] (.node [13,8,8,7,5,5,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,5,5,5,4,3,1,1,1,1] (.node [13,8,8,7,5,5,5,4,2,2,1,1,1] (.node [13,8,8,7,5,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,5,5,5,5,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_777 : RowTree := (.node [13,8,8,7,6,5,4,4,3,1,1,1,1] (.node [13,8,8,7,6,5,3,3,3,2,2,1,1] (.node [13,8,8,7,6,4,4,4,3,2,1,1,1] (.node [13,8,8,7,6,4,4,4,2,2,2,1,1] (.node [13,8,8,7,6,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,7,6,5,3,2,2,2,2,2,2] (.node [13,8,8,7,6,4,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,6,5,4,3,3,2,1,1,1] (.node [13,8,8,7,6,5,4,3,2,2,2,1,1] (.node [13,8,8,7,6,5,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,8,8,7,6,5,4,4,2,2,1,1,1] .empty .empty))) (.node [13,8,8,7,6,6,2,2,2,2,2,2,2] (.node [13,8,8,7,6,5,5,3,3,1,1,1,1] (.node [13,8,8,7,6,5,5,3,2,2,1,1,1] (.node [13,8,8,7,6,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,7,6,5,5,5,1,1,1,1,1] (.node [13,8,8,7,6,5,5,4,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,6,6,3,3,3,2,1,1,1] (.node [13,8,8,7,6,6,3,3,2,2,2,1,1] (.node [13,8,8,7,6,6,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,8,8,7,6,6,4,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_778 : RowTree := (.node [13,8,8,7,6,4,4,2,2,2,2,2,2] degreeTree62_776 degreeTree62_777) + +def degreeTree62_779 : RowTree := (.node [13,8,8,6,6,6,5,2,2,2,2,1,1] degreeTree62_775 degreeTree62_778) + +def degreeTree62_780 : RowTree := (.node [13,8,7,7,7,7,4,3,1,1,1,1,1,1] degreeTree62_772 degreeTree62_779) + +def degreeTree62_781 : RowTree := (.node [13,8,8,7,7,4,4,2,2,2,2,2,1] (.node [13,8,8,7,6,6,6,2,1,1,1,1,1,1] (.node [13,8,8,7,6,6,5,2,2,2,1,1,1] (.node [13,8,8,7,6,6,4,4,2,1,1,1,1] (.node [13,8,8,7,6,6,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,6,6,5,4,1,1,1,1,1] (.node [13,8,8,7,6,6,5,3,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,7,4,3,2,2,2,2,2,2] (.node [13,8,8,7,6,6,6,3,1,1,1,1,1] (.node [13,8,8,7,6,6,6,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,4,3,3,3,2,2,1,1] .empty .empty))) (.node [13,8,8,7,7,5,3,2,2,2,2,2,1] (.node [13,8,8,7,7,4,4,4,2,2,1,1,1] (.node [13,8,8,7,7,4,4,3,3,2,1,1,1] (.node [13,8,8,7,7,4,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,5,2,2,2,2,2,2,2] (.node [13,8,8,7,7,4,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,7,5,4,2,2,2,2,1,1] (.node [13,8,8,7,7,5,3,3,3,2,1,1,1] (.node [13,8,8,7,7,5,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,5,4,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_782 : RowTree := (.node [13,8,8,7,7,6,3,3,3,1,1,1,1] (.node [13,8,8,7,7,6,2,2,2,2,2,2,1] (.node [13,8,8,7,7,5,5,3,2,1,1,1,1] (.node [13,8,8,7,7,5,5,2,2,2,1,1,1] (.node [13,8,8,7,7,5,4,4,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,6,2,2,2,2,2,1,1,1] (.node [13,8,8,7,7,5,5,4,1,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,7,6,3,3,2,1,1,1,1,1] (.node [13,8,8,7,7,6,3,2,2,2,2,1,1] (.node [13,8,8,7,7,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,6,3,3,2,2,1,1,1] .empty .empty))) (.node [13,8,8,7,7,6,5,2,1,1,1,1,1,1] (.node [13,8,8,7,7,6,4,3,1,1,1,1,1,1] (.node [13,8,8,7,7,6,4,2,2,2,1,1,1] (.node [13,8,8,7,7,6,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,6,4,4,1,1,1,1,1] (.node [13,8,8,7,7,6,4,3,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,7,7,6,6,1,1,1,1,1,1,1] (.node [13,8,8,7,7,6,5,3,1,1,1,1,1] (.node [13,8,8,7,7,6,5,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,7,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_783 : RowTree := (.node [13,8,8,7,7,5,4,3,3,1,1,1,1] degreeTree62_781 degreeTree62_782) + +def degreeTree62_784 : RowTree := (.node [13,8,8,8,5,4,4,3,3,2,2,1,1] (.node [13,8,8,7,7,7,4,2,2,1,1,1,1] (.node [13,8,8,7,7,7,3,3,1,1,1,1,1,1] (.node [13,8,8,7,7,7,3,2,2,2,1,1,1] (.node [13,8,8,7,7,7,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,7,7,7,4,2,1,1,1,1,1,1] (.node [13,8,8,7,7,7,3,3,2,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,4,4,4,4,4,2,1,1,1] (.node [13,8,8,8,4,4,4,4,3,2,2,1,1] (.node [13,8,8,7,7,7,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,5,4,4,2,2,2,2,2,2] .empty .empty))) (.node [13,8,8,8,5,5,4,2,2,2,2,2,1] (.node [13,8,8,8,5,4,4,4,4,1,1,1,1] (.node [13,8,8,8,5,4,4,4,3,2,1,1,1] (.node [13,8,8,8,5,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,8,5,5,3,3,3,2,2,1,1] (.node [13,8,8,8,5,5,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,8,8,8,5,5,4,4,2,2,1,1,1] (.node [13,8,8,8,5,5,4,3,3,2,1,1,1] (.node [13,8,8,8,5,5,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,8,5,5,4,4,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_785 : RowTree := (.node [13,8,8,8,6,4,4,4,3,1,1,1,1] (.node [13,8,8,8,6,4,3,3,3,2,2,1,1] (.node [13,8,8,8,5,5,5,4,2,1,1,1,1] (.node [13,8,8,8,5,5,5,3,3,1,1,1,1] (.node [13,8,8,8,5,5,5,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,6,4,3,2,2,2,2,2,2] (.node [13,8,8,8,5,5,5,5,1,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,6,4,4,3,3,2,1,1,1] (.node [13,8,8,8,6,4,4,3,2,2,2,1,1] (.node [13,8,8,8,6,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,8,8,8,6,4,4,4,2,2,1,1,1] .empty .empty))) (.node [13,8,8,8,6,5,4,3,2,2,1,1,1] (.node [13,8,8,8,6,5,3,3,2,2,2,1,1] (.node [13,8,8,8,6,5,3,2,2,2,2,2,1] (.node [13,8,8,8,6,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,8,8,8,6,5,4,2,2,2,2,1,1] (.node [13,8,8,8,6,5,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,6,5,5,2,2,2,1,1,1] (.node [13,8,8,8,6,5,4,4,2,1,1,1,1] (.node [13,8,8,8,6,5,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,6,5,5,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_786 : RowTree := (.node [13,8,8,8,5,5,5,2,2,2,2,1,1] degreeTree62_784 degreeTree62_785) + +def degreeTree62_787 : RowTree := (.node [13,8,8,7,7,7,2,2,2,2,2,1,1] degreeTree62_783 degreeTree62_786) + +def degreeTree62_788 : RowTree := (.node [13,8,8,8,6,6,4,3,2,1,1,1,1] (.node [13,8,8,8,6,6,3,3,2,2,1,1,1] (.node [13,8,8,8,6,6,3,2,2,2,1,1,1,1] (.node [13,8,8,8,6,6,2,2,2,2,2,2,1] (.node [13,8,8,8,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,6,6,3,3,2,1,1,1,1,1] (.node [13,8,8,8,6,6,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,8,8,8,6,6,4,2,2,2,1,1,1] (.node [13,8,8,8,6,6,4,2,2,1,1,1,1,1] (.node [13,8,8,8,6,6,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,6,6,4,3,1,1,1,1,1,1] .empty .empty))) (.node [13,8,8,8,7,3,3,3,3,2,2,1,1] (.node [13,8,8,8,6,6,5,2,2,1,1,1,1] (.node [13,8,8,8,6,6,5,2,1,1,1,1,1,1] (.node [13,8,8,8,6,6,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,3,3,2,2,2,2,2,2] (.node [13,8,8,8,6,6,6,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,7,4,3,2,2,2,2,2,1] (.node [13,8,8,8,7,4,3,2,2,2,2,1,1,1] (.node [13,8,8,8,7,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,8,8,8,7,4,3,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_789 : RowTree := (.node [13,8,8,8,7,5,3,2,2,2,1,1,1,1] (.node [13,8,8,8,7,4,4,3,3,1,1,1,1] (.node [13,8,8,8,7,4,4,2,2,2,2,1,1] (.node [13,8,8,8,7,4,4,2,2,2,1,1,1,1] (.node [13,8,8,8,7,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,4,4,3,2,2,1,1,1] (.node [13,8,8,8,7,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,7,5,2,2,2,2,2,1,1,1] (.node [13,8,8,8,7,4,4,4,2,1,1,1,1] (.node [13,8,8,8,7,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,5,2,2,2,2,2,2,1] .empty .empty))) (.node [13,8,8,8,7,5,4,2,2,2,1,1,1] (.node [13,8,8,8,7,5,3,3,2,2,1,1,1] (.node [13,8,8,8,7,5,3,3,2,1,1,1,1,1] (.node [13,8,8,8,7,5,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,5,4,2,2,1,1,1,1,1] (.node [13,8,8,8,7,5,3,3,3,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,7,5,5,2,1,1,1,1,1,1] (.node [13,8,8,8,7,5,4,3,2,1,1,1,1] (.node [13,8,8,8,7,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,5,5,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_790 : RowTree := (.node [13,8,8,8,7,4,3,3,3,1,1,1,1,1] degreeTree62_788 degreeTree62_789) + +def degreeTree62_791 : RowTree := (.node [13,8,8,8,7,7,3,2,1,1,1,1,1,1] (.node [13,8,8,8,7,6,4,2,1,1,1,1,1,1] (.node [13,8,8,8,7,6,3,2,2,2,1,1,1] (.node [13,8,8,8,7,6,3,2,2,1,1,1,1,1] (.node [13,8,8,8,7,6,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,6,3,3,2,1,1,1,1] (.node [13,8,8,8,7,6,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,7,7,2,2,2,1,1,1,1,1] (.node [13,8,8,8,7,6,5,1,1,1,1,1,1,1] (.node [13,8,8,8,7,6,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,7,7,2,2,2,2,1,1,1] .empty .empty))) (.node [13,8,8,8,8,3,3,2,2,2,2,2,1] (.node [13,8,8,8,8,2,2,2,2,2,2,2,2,1] (.node [13,8,8,8,7,7,4,1,1,1,1,1,1,1] (.node [13,8,8,8,7,7,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,3,3,2,2,2,2,1,1,1] (.node [13,8,8,8,8,3,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,8,8,8,8,3,3,3,3,2,1,1,1] (.node [13,8,8,8,8,3,3,3,3,1,1,1,1,1] (.node [13,8,8,8,8,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,4,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_792 : RowTree := (.node [13,8,8,8,8,5,2,2,2,2,2,1,1] (.node [13,8,8,8,8,4,4,2,2,1,1,1,1,1] (.node [13,8,8,8,8,4,3,3,2,1,1,1,1,1] (.node [13,8,8,8,8,4,3,2,2,2,2,1,1] (.node [13,8,8,8,8,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,4,3,3,3,1,1,1,1] (.node [13,8,8,8,8,4,3,3,2,2,1,1,1] .empty .empty) .empty)) (.node [13,8,8,8,8,4,4,3,2,1,1,1,1] (.node [13,8,8,8,8,4,4,3,1,1,1,1,1,1] (.node [13,8,8,8,8,4,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,5,2,2,2,2,1,1,1,1] .empty .empty))) (.node [13,8,8,8,8,5,4,2,1,1,1,1,1,1] (.node [13,8,8,8,8,5,3,3,1,1,1,1,1,1] (.node [13,8,8,8,8,5,3,2,2,2,1,1,1] (.node [13,8,8,8,8,5,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,5,3,3,2,1,1,1,1] .empty .empty)) (.node [13,8,8,8,8,6,2,2,2,1,1,1,1,1] (.node [13,8,8,8,8,5,5,1,1,1,1,1,1,1] (.node [13,8,8,8,8,5,4,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,6,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_793 : RowTree := (.node [13,8,8,8,8,4,2,2,2,2,2,2,1] degreeTree62_791 degreeTree62_792) + +def degreeTree62_794 : RowTree := (.node [13,8,8,8,7,6,2,2,2,2,1,1,1,1] degreeTree62_790 degreeTree62_793) + +def degreeTree62_795 : RowTree := (.node [13,8,8,8,6,5,5,4,1,1,1,1,1] degreeTree62_787 degreeTree62_794) + +def degreeTree62_796 : RowTree := (.node [13,8,8,7,6,6,4,3,2,2,1,1,1] degreeTree62_780 degreeTree62_795) + +def degreeTree62_797 : RowTree := (.node [13,9,6,5,5,5,5,5,4,2,1,1,1] (.node [13,8,8,8,8,8,2,1,1,1,1,1,1,1] (.node [13,8,8,8,8,7,2,2,1,1,1,1,1,1] (.node [13,8,8,8,8,6,4,1,1,1,1,1,1,1] (.node [13,8,8,8,8,6,3,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,8,8,8,8,7,3,1,1,1,1,1,1,1] (.node [13,8,8,8,8,7,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,6,5,5,5,5,4,4,2,2,1,1] (.node [13,9,5,5,5,5,5,5,5,2,1,1,1] (.node [13,9,5,5,5,5,5,5,4,2,2,1,1] .empty .empty) .empty) (.node [13,9,6,5,5,5,5,5,3,2,2,1,1] .empty .empty))) (.node [13,9,6,6,5,5,5,5,3,2,1,1,1] (.node [13,9,6,6,5,5,5,4,3,2,2,1,1] (.node [13,9,6,6,5,5,4,4,4,2,2,1,1] (.node [13,9,6,5,5,5,5,5,5,1,1,1,1] .empty .empty) .empty) (.node [13,9,6,6,5,5,5,5,2,2,2,1,1] (.node [13,9,6,6,5,5,5,4,4,2,1,1,1] .empty .empty) .empty)) (.node [13,9,6,6,6,5,4,4,3,2,2,1,1] (.node [13,9,6,6,6,4,4,4,4,2,2,1,1] (.node [13,9,6,6,5,5,5,5,4,1,1,1,1] .empty .empty) .empty) (.node [13,9,6,6,6,5,4,4,4,2,1,1,1] .empty .empty)))) + +def degreeTree62_798 : RowTree := (.node [13,9,6,6,6,6,4,4,4,1,1,1,1] (.node [13,9,6,6,6,5,5,5,3,1,1,1,1] (.node [13,9,6,6,6,5,5,4,3,2,1,1,1] (.node [13,9,6,6,6,5,5,4,2,2,2,1,1] (.node [13,9,6,6,6,5,5,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,6,6,6,5,5,5,2,2,1,1,1] (.node [13,9,6,6,6,5,5,4,4,1,1,1,1] .empty .empty) .empty)) (.node [13,9,6,6,6,6,4,4,2,2,2,1,1] (.node [13,9,6,6,6,6,4,3,3,2,2,1,1] (.node [13,9,6,6,6,6,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,6,6,6,6,4,4,3,2,1,1,1] .empty .empty))) (.node [13,9,6,6,6,6,5,5,2,1,1,1,1] (.node [13,9,6,6,6,6,5,3,3,2,1,1,1] (.node [13,9,6,6,6,6,5,3,2,2,2,1,1] (.node [13,9,6,6,6,6,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,6,6,6,6,5,4,3,1,1,1,1] (.node [13,9,6,6,6,6,5,4,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,6,6,6,6,6,3,3,1,1,1,1] (.node [13,9,6,6,6,6,6,3,2,2,1,1,1] (.node [13,9,6,6,6,6,6,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,6,6,6,6,6,4,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_799 : RowTree := (.node [13,9,6,6,6,5,5,2,2,2,2,2,2] degreeTree62_797 degreeTree62_798) + +def degreeTree62_800 : RowTree := (.node [13,9,7,6,5,5,5,4,2,2,2,1,1] (.node [13,9,7,6,5,4,4,4,4,2,2,1,1] (.node [13,9,7,5,5,5,5,5,2,2,2,1,1] (.node [13,9,7,5,5,5,5,4,4,2,1,1,1] (.node [13,9,7,5,5,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,7,5,5,5,5,5,4,1,1,1,1] (.node [13,9,7,5,5,5,5,5,3,2,1,1,1] .empty .empty) .empty)) (.node [13,9,7,6,5,5,5,2,2,2,2,2,2] (.node [13,9,7,6,5,5,4,4,4,2,1,1,1] (.node [13,9,7,6,5,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,7,6,5,5,5,3,3,2,2,1,1] .empty .empty))) (.node [13,9,7,6,6,4,4,4,4,2,1,1,1] (.node [13,9,7,6,5,5,5,5,2,2,1,1,1] (.node [13,9,7,6,5,5,5,4,4,1,1,1,1] (.node [13,9,7,6,5,5,5,4,3,2,1,1,1] .empty .empty) .empty) (.node [13,9,7,6,6,4,4,4,3,2,2,1,1] (.node [13,9,7,6,5,5,5,5,3,1,1,1,1] .empty .empty) .empty)) (.node [13,9,7,6,6,5,4,4,2,2,2,1,1] (.node [13,9,7,6,6,5,4,3,3,2,2,1,1] (.node [13,9,7,6,6,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,7,6,6,5,4,4,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_801 : RowTree := (.node [13,9,7,6,6,6,4,3,3,2,1,1,1] (.node [13,9,7,6,6,5,5,5,2,1,1,1,1] (.node [13,9,7,6,6,5,5,3,3,2,1,1,1] (.node [13,9,7,6,6,5,5,3,2,2,2,1,1] (.node [13,9,7,6,6,5,5,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,7,6,6,5,5,4,3,1,1,1,1] (.node [13,9,7,6,6,5,5,4,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,7,6,6,6,4,2,2,2,2,2,1] (.node [13,9,7,6,6,6,3,3,3,2,2,1,1] (.node [13,9,7,6,6,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,7,6,6,6,4,3,2,2,2,1,1] .empty .empty))) (.node [13,9,7,6,6,6,5,4,2,1,1,1,1] (.node [13,9,7,6,6,6,5,2,2,2,2,1,1] (.node [13,9,7,6,6,6,4,4,3,1,1,1,1] (.node [13,9,7,6,6,6,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,7,6,6,6,5,3,3,1,1,1,1] (.node [13,9,7,6,6,6,5,3,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,4,4,4,4,4,2,2,1,1] (.node [13,9,7,6,6,6,6,3,2,1,1,1,1] (.node [13,9,7,6,6,6,6,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,5,4,4,4,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_802 : RowTree := (.node [13,9,7,6,6,5,4,4,4,1,1,1,1] degreeTree62_800 degreeTree62_801) + +def degreeTree62_803 : RowTree := (.node [13,9,7,5,5,5,4,4,4,2,2,1,1] degreeTree62_799 degreeTree62_802) + +def degreeTree62_804 : RowTree := (.node [13,9,7,7,5,5,5,5,2,1,1,1,1] (.node [13,9,7,7,5,5,5,2,2,2,2,2,1] (.node [13,9,7,7,5,5,4,4,2,2,2,1,1] (.node [13,9,7,7,5,5,4,3,3,2,2,1,1] (.node [13,9,7,7,5,5,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,7,7,5,5,4,4,4,1,1,1,1] (.node [13,9,7,7,5,5,4,4,3,2,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,5,5,5,4,2,2,1,1,1] (.node [13,9,7,7,5,5,5,3,3,2,1,1,1] (.node [13,9,7,7,5,5,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,7,7,5,5,5,4,3,1,1,1,1] .empty .empty))) (.node [13,9,7,7,6,5,3,2,2,2,2,2,2] (.node [13,9,7,7,6,4,4,4,2,2,2,1,1] (.node [13,9,7,7,6,4,4,3,3,2,2,1,1] (.node [13,9,7,7,6,4,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,7,7,6,4,4,4,4,1,1,1,1] (.node [13,9,7,7,6,4,4,4,3,2,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,6,5,4,3,2,2,2,1,1] (.node [13,9,7,7,6,5,4,2,2,2,2,2,1] (.node [13,9,7,7,6,5,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,7,7,6,5,4,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_805 : RowTree := (.node [13,9,7,7,6,6,4,3,2,2,1,1,1] (.node [13,9,7,7,6,6,2,2,2,2,2,2,2] (.node [13,9,7,7,6,5,5,3,2,2,1,1,1] (.node [13,9,7,7,6,5,5,2,2,2,2,1,1] (.node [13,9,7,7,6,5,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,6,5,5,4,2,1,1,1,1] (.node [13,9,7,7,6,5,5,3,3,1,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,6,6,3,3,3,2,1,1,1] (.node [13,9,7,7,6,6,3,3,2,2,2,1,1] (.node [13,9,7,7,6,6,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,7,7,6,6,4,2,2,2,2,1,1] .empty .empty))) (.node [13,9,7,7,6,6,6,2,2,1,1,1,1] (.node [13,9,7,7,6,6,5,2,2,2,1,1,1] (.node [13,9,7,7,6,6,4,4,2,1,1,1,1] (.node [13,9,7,7,6,6,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,6,6,6,2,1,1,1,1,1,1] (.node [13,9,7,7,6,6,5,3,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,7,4,4,2,2,2,2,2,1] (.node [13,9,7,7,7,4,3,3,3,2,2,1,1] (.node [13,9,7,7,7,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,7,7,7,4,4,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_806 : RowTree := (.node [13,9,7,7,6,5,4,4,2,2,1,1,1] degreeTree62_804 degreeTree62_805) + +def degreeTree62_807 : RowTree := (.node [13,9,7,7,7,5,5,2,2,2,1,1,1] (.node [13,9,7,7,7,5,3,3,3,2,1,1,1] (.node [13,9,7,7,7,5,2,2,2,2,2,2,2] (.node [13,9,7,7,7,4,4,4,3,1,1,1,1] (.node [13,9,7,7,7,4,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,7,5,3,3,2,2,2,1,1] (.node [13,9,7,7,7,5,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,9,7,7,7,5,4,3,3,1,1,1,1] (.node [13,9,7,7,7,5,4,3,2,2,1,1,1] (.node [13,9,7,7,7,5,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,7,7,7,5,4,4,2,1,1,1,1] .empty .empty))) (.node [13,9,7,7,7,6,3,3,2,1,1,1,1,1] (.node [13,9,7,7,7,6,2,2,2,2,2,2,1] (.node [13,9,7,7,7,6,2,2,2,2,2,1,1,1] (.node [13,9,7,7,7,5,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,7,6,3,2,2,2,2,1,1] (.node [13,9,7,7,7,6,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,7,6,4,2,2,1,1,1,1,1] (.node [13,9,7,7,7,6,3,3,3,1,1,1,1] (.node [13,9,7,7,7,6,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,7,6,4,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_808 : RowTree := (.node [13,9,7,7,7,7,4,2,1,1,1,1,1,1] (.node [13,9,7,7,7,7,2,2,2,2,2,1,1] (.node [13,9,7,7,7,6,5,2,2,1,1,1,1] (.node [13,9,7,7,7,6,5,2,1,1,1,1,1,1] (.node [13,9,7,7,7,6,4,3,2,1,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,7,7,2,2,2,2,1,1,1,1] (.node [13,9,7,7,7,6,6,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,7,7,7,7,3,3,1,1,1,1,1,1] (.node [13,9,7,7,7,7,3,2,2,2,1,1,1] (.node [13,9,7,7,7,7,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,7,7,7,7,3,3,2,1,1,1,1] .empty .empty))) (.node [13,9,8,5,5,5,5,3,3,2,2,1,1] (.node [13,9,8,5,5,5,4,4,3,2,2,1,1] (.node [13,9,8,5,5,4,4,4,4,2,2,1,1] (.node [13,9,7,7,7,7,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,5,5,5,5,2,2,2,2,2,2] (.node [13,9,8,5,5,5,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [13,9,8,5,5,5,5,4,4,1,1,1,1] (.node [13,9,8,5,5,5,5,4,3,2,1,1,1] (.node [13,9,8,5,5,5,5,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,5,5,5,5,5,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_809 : RowTree := (.node [13,9,7,7,7,6,4,3,1,1,1,1,1,1] degreeTree62_807 degreeTree62_808) + +def degreeTree62_810 : RowTree := (.node [13,9,7,7,7,4,4,3,3,2,1,1,1] degreeTree62_806 degreeTree62_809) + +def degreeTree62_811 : RowTree := (.node [13,9,7,7,5,4,4,4,4,2,1,1,1] degreeTree62_803 degreeTree62_810) + +def degreeTree62_812 : RowTree := (.node [13,9,8,6,5,5,5,3,3,2,1,1,1] (.node [13,9,8,6,5,5,4,4,2,2,2,1,1] (.node [13,9,8,6,5,4,4,4,4,2,1,1,1] (.node [13,9,8,6,5,4,4,4,3,2,2,1,1] (.node [13,9,8,6,4,4,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,6,5,5,4,3,3,2,2,1,1] (.node [13,9,8,6,5,5,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,9,8,6,5,5,5,2,2,2,2,2,1] (.node [13,9,8,6,5,5,4,4,4,1,1,1,1] (.node [13,9,8,6,5,5,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,6,5,5,5,3,2,2,2,1,1] .empty .empty))) (.node [13,9,8,6,6,4,4,4,2,2,2,1,1] (.node [13,9,8,6,5,5,5,5,2,1,1,1,1] (.node [13,9,8,6,5,5,5,4,3,1,1,1,1] (.node [13,9,8,6,5,5,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,6,6,4,4,3,3,2,2,1,1] (.node [13,9,8,6,6,4,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,9,8,6,6,5,3,2,2,2,2,2,2] (.node [13,9,8,6,6,4,4,4,4,1,1,1,1] (.node [13,9,8,6,6,4,4,4,3,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,6,6,5,3,3,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_813 : RowTree := (.node [13,9,8,6,6,6,3,3,2,2,2,1,1] (.node [13,9,8,6,6,5,5,3,2,2,1,1,1] (.node [13,9,8,6,6,5,4,4,2,2,1,1,1] (.node [13,9,8,6,6,5,4,3,3,2,1,1,1] (.node [13,9,8,6,6,5,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,6,6,5,5,2,2,2,2,1,1] (.node [13,9,8,6,6,5,4,4,3,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,6,6,6,2,2,2,2,2,2,2] (.node [13,9,8,6,6,5,5,4,2,1,1,1,1] (.node [13,9,8,6,6,5,5,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,6,6,6,3,2,2,2,2,2,1] .empty .empty))) (.node [13,9,8,6,6,6,5,2,2,2,1,1,1] (.node [13,9,8,6,6,6,4,3,2,2,1,1,1] (.node [13,9,8,6,6,6,4,2,2,2,2,1,1] (.node [13,9,8,6,6,6,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,6,6,6,4,4,2,1,1,1,1] (.node [13,9,8,6,6,6,4,3,3,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,4,4,4,4,3,2,2,1,1] (.node [13,9,8,6,6,6,6,2,1,1,1,1,1,1] (.node [13,9,8,6,6,6,5,3,2,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,4,4,4,4,4,2,1,1,1] .empty .empty)))) + +def degreeTree62_814 : RowTree := (.node [13,9,8,6,6,5,4,2,2,2,2,2,1] degreeTree62_812 degreeTree62_813) + +def degreeTree62_815 : RowTree := (.node [13,9,8,7,5,5,4,4,3,1,1,1,1] (.node [13,9,8,7,5,5,3,3,3,2,2,1,1] (.node [13,9,8,7,5,4,4,4,3,2,1,1,1] (.node [13,9,8,7,5,4,4,4,2,2,2,1,1] (.node [13,9,8,7,5,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,7,5,5,3,2,2,2,2,2,2] (.node [13,9,8,7,5,4,4,4,4,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,5,5,4,3,3,2,1,1,1] (.node [13,9,8,7,5,5,4,3,2,2,2,1,1] (.node [13,9,8,7,5,5,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,8,7,5,5,4,4,2,2,1,1,1] .empty .empty))) (.node [13,9,8,7,6,4,3,3,3,2,2,1,1] (.node [13,9,8,7,5,5,5,3,3,1,1,1,1] (.node [13,9,8,7,5,5,5,3,2,2,1,1,1] (.node [13,9,8,7,5,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,7,6,4,3,2,2,2,2,2,2] (.node [13,9,8,7,5,5,5,4,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,6,4,4,3,3,2,1,1,1] (.node [13,9,8,7,6,4,4,3,2,2,2,1,1] (.node [13,9,8,7,6,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,8,7,6,4,4,4,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_816 : RowTree := (.node [13,9,8,7,6,6,2,2,2,2,2,1,1,1] (.node [13,9,8,7,6,5,4,3,2,2,1,1,1] (.node [13,9,8,7,6,5,3,3,2,2,2,1,1] (.node [13,9,8,7,6,5,3,2,2,2,2,2,1] (.node [13,9,8,7,6,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,8,7,6,5,4,2,2,2,2,1,1] (.node [13,9,8,7,6,5,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,6,5,5,2,2,2,1,1,1] (.node [13,9,8,7,6,5,4,4,2,1,1,1,1] (.node [13,9,8,7,6,5,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,6,5,5,3,2,1,1,1,1] .empty .empty))) (.node [13,9,8,7,6,6,3,3,3,1,1,1,1] (.node [13,9,8,7,6,6,3,2,2,2,2,1,1] (.node [13,9,8,7,6,6,3,2,2,2,1,1,1,1] (.node [13,9,8,7,6,6,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,8,7,6,6,3,3,2,2,1,1,1] (.node [13,9,8,7,6,6,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,6,6,4,3,1,1,1,1,1,1] (.node [13,9,8,7,6,6,4,2,2,2,1,1,1] (.node [13,9,8,7,6,6,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,6,6,4,3,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_817 : RowTree := (.node [13,9,8,7,6,4,4,4,3,1,1,1,1] degreeTree62_815 degreeTree62_816) + +def degreeTree62_818 : RowTree := (.node [13,9,8,7,5,4,4,2,2,2,2,2,2] degreeTree62_814 degreeTree62_817) + +def degreeTree62_819 : RowTree := (.node [13,9,8,7,7,4,4,2,2,2,2,1,1] (.node [13,9,8,7,7,4,3,2,2,2,2,2,1] (.node [13,9,8,7,7,3,3,3,3,2,2,1,1] (.node [13,9,8,7,7,3,3,2,2,2,2,2,2] (.node [13,9,8,7,6,6,6,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,7,4,3,2,2,2,2,1,1,1] (.node [13,9,8,7,7,4,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,9,8,7,7,4,3,3,3,2,1,1,1] (.node [13,9,8,7,7,4,3,3,3,1,1,1,1,1] (.node [13,9,8,7,7,4,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,7,7,4,4,2,2,2,1,1,1,1] .empty .empty))) (.node [13,9,8,7,7,5,2,2,2,2,2,1,1,1] (.node [13,9,8,7,7,4,4,3,3,1,1,1,1] (.node [13,9,8,7,7,4,4,3,2,2,1,1,1] (.node [13,9,8,7,7,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,7,4,4,4,2,1,1,1,1] (.node [13,9,8,7,7,4,4,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,7,5,3,2,2,2,2,1,1] (.node [13,9,8,7,7,5,3,2,2,2,1,1,1,1] (.node [13,9,8,7,7,5,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,8,7,7,5,3,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_820 : RowTree := (.node [13,9,8,7,7,6,4,2,1,1,1,1,1,1] (.node [13,9,8,7,7,6,2,2,2,2,1,1,1,1] (.node [13,9,8,7,7,5,4,2,2,2,1,1,1] (.node [13,9,8,7,7,5,4,2,2,1,1,1,1,1] (.node [13,9,8,7,7,5,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,7,5,5,2,1,1,1,1,1,1] (.node [13,9,8,7,7,5,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,7,7,6,3,2,2,2,1,1,1] (.node [13,9,8,7,7,6,3,2,2,1,1,1,1,1] (.node [13,9,8,7,7,6,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,7,7,6,3,3,1,1,1,1,1,1] .empty .empty))) (.node [13,9,8,8,4,4,4,2,2,2,2,2,2] (.node [13,9,8,7,7,7,2,2,2,2,1,1,1] (.node [13,9,8,7,7,7,2,2,2,1,1,1,1,1] (.node [13,9,8,7,7,6,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,7,7,7,4,1,1,1,1,1,1,1] (.node [13,9,8,7,7,7,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,4,4,4,4,3,2,1,1,1] (.node [13,9,8,8,4,4,4,4,2,2,2,1,1] (.node [13,9,8,8,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,8,4,4,4,4,4,1,1,1,1] .empty .empty)))) + +def degreeTree62_821 : RowTree := (.node [13,9,8,7,7,5,3,3,2,2,1,1,1] degreeTree62_819 degreeTree62_820) + +def degreeTree62_822 : RowTree := (.node [13,9,8,8,5,5,4,2,2,2,2,1,1] (.node [13,9,8,8,5,4,4,4,3,1,1,1,1] (.node [13,9,8,8,5,4,4,3,2,2,2,1,1] (.node [13,9,8,8,5,4,4,2,2,2,2,2,1] (.node [13,9,8,8,5,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,8,5,4,4,4,2,2,1,1,1] (.node [13,9,8,8,5,4,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,5,5,3,3,2,2,2,1,1] (.node [13,9,8,8,5,5,3,2,2,2,2,2,1] (.node [13,9,8,8,5,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,8,8,5,5,3,3,3,2,1,1,1] .empty .empty))) (.node [13,9,8,8,6,3,3,3,3,2,2,1,1] (.node [13,9,8,8,5,5,4,4,2,1,1,1,1] (.node [13,9,8,8,5,5,4,3,3,1,1,1,1] (.node [13,9,8,8,5,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,6,3,3,2,2,2,2,2,2] (.node [13,9,8,8,5,5,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,6,4,3,2,2,2,2,2,1] (.node [13,9,8,8,6,4,3,2,2,2,2,1,1,1] (.node [13,9,8,8,6,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,8,8,6,4,3,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_823 : RowTree := (.node [13,9,8,8,6,5,3,2,2,2,2,1,1] (.node [13,9,8,8,6,4,4,3,3,1,1,1,1] (.node [13,9,8,8,6,4,4,2,2,2,2,1,1] (.node [13,9,8,8,6,4,4,2,2,2,1,1,1,1] (.node [13,9,8,8,6,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,6,4,4,3,2,2,1,1,1] (.node [13,9,8,8,6,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,6,5,2,2,2,2,2,2,1] (.node [13,9,8,8,6,5,2,2,2,2,2,1,1,1] (.node [13,9,8,8,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,6,5,3,2,2,2,1,1,1,1] .empty .empty))) (.node [13,9,8,8,6,5,4,2,2,2,1,1,1] (.node [13,9,8,8,6,5,3,3,3,1,1,1,1] (.node [13,9,8,8,6,5,3,3,2,2,1,1,1] (.node [13,9,8,8,6,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,6,5,4,2,2,1,1,1,1,1] .empty .empty)) (.node [13,9,8,8,6,6,2,2,2,2,1,1,1,1] (.node [13,9,8,8,6,5,5,2,1,1,1,1,1,1] (.node [13,9,8,8,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,6,6,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_824 : RowTree := (.node [13,9,8,8,6,4,3,3,3,1,1,1,1,1] degreeTree62_822 degreeTree62_823) + +def degreeTree62_825 : RowTree := (.node [13,9,8,8,5,4,3,2,2,2,2,2,2] degreeTree62_821 degreeTree62_824) + +def degreeTree62_826 : RowTree := (.node [13,9,8,7,6,6,5,2,1,1,1,1,1,1] degreeTree62_818 degreeTree62_825) + +def degreeTree62_827 : RowTree := (.node [13,9,8,5,5,5,5,5,3,1,1,1,1] degreeTree62_811 degreeTree62_826) + +def degreeTree62_828 : RowTree := (.node [13,8,8,8,8,6,3,2,1,1,1,1,1,1] degreeTree62_796 degreeTree62_827) + +def degreeTree62_829 : RowTree := (.node [13,9,8,8,7,3,3,3,3,2,1,1,1] (.node [13,9,8,8,7,3,2,2,2,2,2,2,2] (.node [13,9,8,8,6,6,4,2,1,1,1,1,1,1] (.node [13,9,8,8,6,6,3,3,1,1,1,1,1,1] (.node [13,9,8,8,6,6,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,7,2,2,2,2,2,2,2,2,1] (.node [13,9,8,8,6,6,5,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,7,3,3,3,2,2,2,1,1] (.node [13,9,8,8,7,3,3,2,2,2,2,2,1] (.node [13,9,8,8,7,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,7,3,3,3,3,1,1,1,1,1] .empty .empty))) (.node [13,9,8,8,7,4,3,3,2,2,1,1,1] (.node [13,9,8,8,7,4,3,2,2,2,1,1,1,1] (.node [13,9,8,8,7,4,2,2,2,2,2,2,1] (.node [13,9,8,8,7,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,7,4,3,3,2,1,1,1,1,1] (.node [13,9,8,8,7,4,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,9,8,8,7,4,4,2,2,2,1,1,1] (.node [13,9,8,8,7,4,4,2,2,1,1,1,1,1] (.node [13,9,8,8,7,4,3,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,7,4,4,3,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_830 : RowTree := (.node [13,9,8,8,7,7,2,2,1,1,1,1,1,1] (.node [13,9,8,8,7,5,5,1,1,1,1,1,1,1] (.node [13,9,8,8,7,5,3,2,2,2,1,1,1] (.node [13,9,8,8,7,5,3,2,2,1,1,1,1,1] (.node [13,9,8,8,7,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,8,7,5,4,2,1,1,1,1,1,1] (.node [13,9,8,8,7,5,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,7,6,3,2,1,1,1,1,1,1] (.node [13,9,8,8,7,6,2,2,2,2,1,1,1] (.node [13,9,8,8,7,6,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,7,6,4,1,1,1,1,1,1,1] .empty .empty))) (.node [13,9,8,8,8,3,3,2,2,2,1,1,1,1] (.node [13,9,8,8,8,2,2,2,2,2,2,2,2] (.node [13,9,8,8,8,2,2,2,2,2,2,2,1,1] (.node [13,9,8,8,7,7,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,8,3,2,2,2,2,2,2,1] (.node [13,9,8,8,8,3,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,8,3,3,3,2,2,1,1,1] (.node [13,9,8,8,8,3,3,3,2,1,1,1,1,1] (.node [13,9,8,8,8,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,8,8,3,3,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_831 : RowTree := (.node [13,9,8,8,7,5,2,2,2,2,1,1,1,1] degreeTree62_829 degreeTree62_830) + +def degreeTree62_832 : RowTree := (.node [13,9,8,8,8,6,3,1,1,1,1,1,1,1] (.node [13,9,8,8,8,5,2,2,2,1,1,1,1,1] (.node [13,9,8,8,8,4,3,2,2,2,1,1,1] (.node [13,9,8,8,8,4,3,2,2,1,1,1,1,1] (.node [13,9,8,8,8,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,8,8,8,4,4,2,1,1,1,1,1,1] (.node [13,9,8,8,8,4,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,8,8,8,5,4,1,1,1,1,1,1,1] (.node [13,9,8,8,8,5,3,2,1,1,1,1,1,1] (.node [13,9,8,8,8,5,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,8,8,8,6,2,2,1,1,1,1,1,1] .empty .empty))) (.node [13,9,9,5,5,5,4,2,2,2,2,2,2] (.node [13,9,9,5,4,4,4,4,4,2,2,1,1] (.node [13,9,8,8,8,8,1,1,1,1,1,1,1,1] (.node [13,9,8,8,8,7,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,5,5,4,4,4,4,2,1,1,1] (.node [13,9,9,5,5,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [13,9,9,5,5,5,4,4,3,2,1,1,1] (.node [13,9,9,5,5,5,4,4,2,2,2,1,1] (.node [13,9,9,5,5,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,5,5,5,4,4,4,1,1,1,1] .empty .empty)))) + +def degreeTree62_833 : RowTree := (.node [13,9,9,6,5,4,4,4,4,1,1,1,1] (.node [13,9,9,6,4,4,4,4,4,2,1,1,1] (.node [13,9,9,5,5,5,5,4,2,2,1,1,1] (.node [13,9,9,5,5,5,5,3,3,2,1,1,1] (.node [13,9,9,5,5,5,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,6,4,4,4,4,3,2,2,1,1] (.node [13,9,9,5,5,5,5,4,3,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,6,5,4,4,4,2,2,2,1,1] (.node [13,9,9,6,5,4,4,3,3,2,2,1,1] (.node [13,9,9,6,5,4,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,9,6,5,4,4,4,3,2,1,1,1] .empty .empty))) (.node [13,9,9,6,5,5,4,4,2,2,1,1,1] (.node [13,9,9,6,5,5,4,2,2,2,2,2,1] (.node [13,9,9,6,5,5,3,3,3,2,2,1,1] (.node [13,9,9,6,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,9,6,5,5,4,3,3,2,1,1,1] (.node [13,9,9,6,5,5,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [13,9,9,6,5,5,5,3,2,2,1,1,1] (.node [13,9,9,6,5,5,5,2,2,2,2,1,1] (.node [13,9,9,6,5,5,4,4,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,6,5,5,5,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_834 : RowTree := (.node [13,9,9,5,5,5,5,2,2,2,2,2,1] degreeTree62_832 degreeTree62_833) + +def degreeTree62_835 : RowTree := (.node [13,9,8,8,8,4,2,2,2,2,1,1,1,1] degreeTree62_831 degreeTree62_834) + +def degreeTree62_836 : RowTree := (.node [13,9,9,6,6,5,4,2,2,2,2,1,1] (.node [13,9,9,6,6,4,4,4,3,1,1,1,1] (.node [13,9,9,6,6,4,4,3,2,2,2,1,1] (.node [13,9,9,6,6,4,4,2,2,2,2,2,1] (.node [13,9,9,6,6,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,6,6,4,4,4,2,2,1,1,1] (.node [13,9,9,6,6,4,4,3,3,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,6,6,5,3,3,2,2,2,1,1] (.node [13,9,9,6,6,5,3,2,2,2,2,2,1] (.node [13,9,9,6,6,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,9,6,6,5,3,3,3,2,1,1,1] .empty .empty))) (.node [13,9,9,6,6,6,3,2,2,2,1,1,1,1] (.node [13,9,9,6,6,5,5,2,2,2,1,1,1] (.node [13,9,9,6,6,5,4,3,3,1,1,1,1] (.node [13,9,9,6,6,5,4,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,6,6,6,2,2,2,2,2,2,1] (.node [13,9,9,6,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,6,6,6,3,3,2,2,1,1,1] (.node [13,9,9,6,6,6,3,3,2,1,1,1,1,1] (.node [13,9,9,6,6,6,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,6,6,6,3,3,3,1,1,1,1] .empty .empty)))) + +def degreeTree62_837 : RowTree := (.node [13,9,9,7,5,4,3,3,3,2,2,1,1] (.node [13,9,9,7,4,4,4,3,3,2,2,1,1] (.node [13,9,9,6,6,6,5,2,1,1,1,1,1,1] (.node [13,9,9,6,6,6,4,3,1,1,1,1,1,1] (.node [13,9,9,6,6,6,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,4,4,4,2,2,2,2,2,2] (.node [13,9,9,6,6,6,6,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,7,4,4,4,4,4,1,1,1,1] (.node [13,9,9,7,4,4,4,4,3,2,1,1,1] (.node [13,9,9,7,4,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,7,5,4,3,2,2,2,2,2,2] .empty .empty))) (.node [13,9,9,7,5,5,2,2,2,2,2,2,2] (.node [13,9,9,7,5,4,4,3,3,2,1,1,1] (.node [13,9,9,7,5,4,4,3,2,2,2,1,1] (.node [13,9,9,7,5,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,9,7,5,4,4,4,3,1,1,1,1] (.node [13,9,9,7,5,4,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,7,5,5,3,3,3,2,1,1,1] (.node [13,9,9,7,5,5,3,3,2,2,2,1,1] (.node [13,9,9,7,5,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,9,7,5,5,4,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_838 : RowTree := (.node [13,9,9,6,6,6,4,2,2,1,1,1,1,1] degreeTree62_836 degreeTree62_837) + +def degreeTree62_839 : RowTree := (.node [13,9,9,7,6,4,4,2,2,2,1,1,1,1] (.node [13,9,9,7,6,4,3,2,2,2,2,1,1,1] (.node [13,9,9,7,6,3,3,2,2,2,2,2,2] (.node [13,9,9,7,5,5,5,2,2,2,1,1,1] (.node [13,9,9,7,5,5,4,3,3,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,6,4,2,2,2,2,2,2,2] (.node [13,9,9,7,6,3,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,9,9,7,6,4,3,3,3,1,1,1,1,1] (.node [13,9,9,7,6,4,3,3,2,2,2,1,1] (.node [13,9,9,7,6,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,9,7,6,4,3,3,3,2,1,1,1] .empty .empty))) (.node [13,9,9,7,6,5,2,2,2,2,2,2,1] (.node [13,9,9,7,6,4,4,3,2,2,1,1,1] (.node [13,9,9,7,6,4,4,3,2,1,1,1,1,1] (.node [13,9,9,7,6,4,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,7,6,5,2,2,2,2,2,1,1,1] (.node [13,9,9,7,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,7,6,5,3,3,2,1,1,1,1,1] (.node [13,9,9,7,6,5,3,2,2,2,2,1,1] (.node [13,9,9,7,6,5,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,6,5,3,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_840 : RowTree := (.node [13,9,9,7,7,2,2,2,2,2,2,2,2,1] (.node [13,9,9,7,6,6,3,2,2,1,1,1,1,1] (.node [13,9,9,7,6,5,5,2,1,1,1,1,1,1] (.node [13,9,9,7,6,5,4,3,1,1,1,1,1,1] (.node [13,9,9,7,6,5,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,6,6,2,2,2,2,2,1,1] (.node [13,9,9,7,6,6,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,7,6,6,4,2,1,1,1,1,1,1] (.node [13,9,9,7,6,6,3,3,1,1,1,1,1,1] (.node [13,9,9,7,6,6,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,6,6,5,1,1,1,1,1,1,1] .empty .empty))) (.node [13,9,9,7,7,3,3,3,3,2,1,1,1] (.node [13,9,9,7,7,3,3,2,2,2,2,2,1] (.node [13,9,9,7,7,3,3,2,2,2,2,1,1,1] (.node [13,9,9,7,7,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,9,7,7,3,3,3,3,1,1,1,1,1] (.node [13,9,9,7,7,3,3,3,2,2,2,1,1] .empty .empty) .empty)) (.node [13,9,9,7,7,4,3,2,2,2,1,1,1,1] (.node [13,9,9,7,7,4,2,2,2,2,2,2,1] (.node [13,9,9,7,7,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,7,4,3,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_841 : RowTree := (.node [13,9,9,7,6,5,4,2,2,1,1,1,1,1] degreeTree62_839 degreeTree62_840) + +def degreeTree62_842 : RowTree := (.node [13,9,9,7,5,5,4,3,2,2,1,1,1] degreeTree62_838 degreeTree62_841) + +def degreeTree62_843 : RowTree := (.node [13,9,9,6,6,4,3,2,2,2,2,2,2] degreeTree62_835 degreeTree62_842) + +def degreeTree62_844 : RowTree := (.node [13,9,9,7,7,5,5,1,1,1,1,1,1,1] (.node [13,9,9,7,7,5,2,2,2,2,2,1,1] (.node [13,9,9,7,7,4,4,2,2,2,1,1,1] (.node [13,9,9,7,7,4,4,2,2,1,1,1,1,1] (.node [13,9,9,7,7,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,7,5,2,2,2,2,1,1,1,1] (.node [13,9,9,7,7,4,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,7,7,5,3,3,1,1,1,1,1,1] (.node [13,9,9,7,7,5,3,2,2,2,1,1,1] (.node [13,9,9,7,7,5,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,7,5,4,2,1,1,1,1,1,1] .empty .empty))) (.node [13,9,9,7,7,7,3,1,1,1,1,1,1,1] (.node [13,9,9,7,7,6,3,2,1,1,1,1,1,1] (.node [13,9,9,7,7,6,2,2,2,2,1,1,1] (.node [13,9,9,7,7,6,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,7,7,7,2,2,1,1,1,1,1,1] (.node [13,9,9,7,7,6,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,8,4,4,4,2,2,2,2,1,1,1] (.node [13,9,9,8,4,4,3,3,3,2,2,1,1] (.node [13,9,9,8,4,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,9,8,4,4,4,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_845 : RowTree := (.node [13,9,9,8,5,4,3,3,2,2,2,1,1] (.node [13,9,9,8,5,3,3,2,2,2,2,2,2] (.node [13,9,9,8,4,4,4,4,2,1,1,1,1,1] (.node [13,9,9,8,4,4,4,3,3,2,1,1,1] (.node [13,9,9,8,4,4,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,4,4,4,4,3,1,1,1,1] (.node [13,9,9,8,4,4,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,8,5,4,3,2,2,2,2,1,1,1] (.node [13,9,9,8,5,4,2,2,2,2,2,2,2] (.node [13,9,9,8,5,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,8,5,4,3,2,2,2,2,2,1] .empty .empty))) (.node [13,9,9,8,5,4,4,3,2,2,1,1,1] (.node [13,9,9,8,5,4,4,2,2,2,1,1,1,1] (.node [13,9,9,8,5,4,3,3,3,2,1,1,1] (.node [13,9,9,8,5,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,5,4,4,3,2,1,1,1,1,1] (.node [13,9,9,8,5,4,4,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,9,9,8,5,5,2,2,2,2,2,2,1] (.node [13,9,9,8,5,5,2,2,2,2,2,1,1,1] (.node [13,9,9,8,5,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,5,5,3,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_846 : RowTree := (.node [13,9,9,8,4,4,4,3,2,2,2,1,1] degreeTree62_844 degreeTree62_845) + +def degreeTree62_847 : RowTree := (.node [13,9,9,8,6,3,3,3,2,2,2,1,1] (.node [13,9,9,8,5,5,5,2,1,1,1,1,1,1] (.node [13,9,9,8,5,5,4,2,2,1,1,1,1,1] (.node [13,9,9,8,5,5,3,3,2,2,1,1,1] (.node [13,9,9,8,5,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,5,5,4,3,1,1,1,1,1,1] (.node [13,9,9,8,5,5,4,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,8,6,3,3,2,2,2,2,1,1,1] (.node [13,9,9,8,6,3,2,2,2,2,2,2,2] (.node [13,9,9,8,6,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,9,8,6,3,3,2,2,2,2,2,1] .empty .empty))) (.node [13,9,9,8,6,4,3,2,2,2,2,1,1] (.node [13,9,9,8,6,4,2,2,2,2,2,1,1,1] (.node [13,9,9,8,6,3,3,3,3,2,1,1,1] (.node [13,9,9,8,6,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,6,4,3,2,2,2,1,1,1,1] (.node [13,9,9,8,6,4,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,9,9,8,6,4,4,2,2,1,1,1,1,1] (.node [13,9,9,8,6,4,3,3,2,2,1,1,1] (.node [13,9,9,8,6,4,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,6,4,4,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_848 : RowTree := (.node [13,9,9,8,6,6,4,1,1,1,1,1,1,1] (.node [13,9,9,8,6,5,4,2,1,1,1,1,1,1] (.node [13,9,9,8,6,5,3,2,2,1,1,1,1,1] (.node [13,9,9,8,6,5,2,2,2,2,2,1,1] (.node [13,9,9,8,6,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,6,5,3,3,1,1,1,1,1,1] (.node [13,9,9,8,6,5,3,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,8,6,6,2,2,2,2,1,1,1] (.node [13,9,9,8,6,6,2,2,2,1,1,1,1,1] (.node [13,9,9,8,6,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,6,6,3,2,1,1,1,1,1,1] .empty .empty))) (.node [13,9,9,8,7,3,3,2,2,2,2,1,1] (.node [13,9,9,8,7,3,2,2,2,2,2,1,1,1] (.node [13,9,9,8,7,2,2,2,2,2,2,2,2] (.node [13,9,9,8,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,8,7,3,3,2,2,2,1,1,1,1] (.node [13,9,9,8,7,3,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,9,9,8,7,4,2,2,2,2,1,1,1,1] (.node [13,9,9,8,7,3,3,3,2,2,1,1,1] (.node [13,9,9,8,7,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,7,4,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_849 : RowTree := (.node [13,9,9,8,6,4,4,3,1,1,1,1,1,1] degreeTree62_847 degreeTree62_848) + +def degreeTree62_850 : RowTree := (.node [13,9,9,8,5,5,3,2,2,2,2,1,1] degreeTree62_846 degreeTree62_849) + +def degreeTree62_851 : RowTree := (.node [13,9,9,8,8,2,2,2,2,2,2,1,1,1] (.node [13,9,9,8,7,5,3,2,1,1,1,1,1,1] (.node [13,9,9,8,7,4,4,2,1,1,1,1,1,1] (.node [13,9,9,8,7,4,3,3,1,1,1,1,1,1] (.node [13,9,9,8,7,4,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,7,5,2,2,2,2,1,1,1] (.node [13,9,9,8,7,5,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,8,7,6,3,1,1,1,1,1,1,1] (.node [13,9,9,8,7,6,2,2,1,1,1,1,1,1] (.node [13,9,9,8,7,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,7,7,2,1,1,1,1,1,1,1] .empty .empty))) (.node [13,9,9,8,8,3,3,3,1,1,1,1,1,1] (.node [13,9,9,8,8,3,2,2,2,2,2,1,1] (.node [13,9,9,8,8,3,2,2,2,2,1,1,1,1] (.node [13,9,9,8,8,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,9,8,8,3,3,2,2,2,1,1,1] (.node [13,9,9,8,8,3,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,8,8,4,3,2,1,1,1,1,1,1] (.node [13,9,9,8,8,4,2,2,2,2,1,1,1] (.node [13,9,9,8,8,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,8,8,4,4,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_852 : RowTree := (.node [13,9,9,9,4,4,3,3,3,2,1,1,1] (.node [13,9,9,9,4,4,2,2,2,2,2,2,2] (.node [13,9,9,8,8,7,1,1,1,1,1,1,1,1] (.node [13,9,9,8,8,6,2,1,1,1,1,1,1,1] (.node [13,9,9,8,8,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,4,3,3,3,3,2,2,1,1] (.node [13,9,9,9,4,3,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,9,9,9,4,4,3,3,2,2,2,1,1] (.node [13,9,9,9,4,4,3,2,2,2,2,2,1] (.node [13,9,9,9,4,4,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,4,4,3,3,3,1,1,1,1,1] .empty .empty))) (.node [13,9,9,9,5,2,2,2,2,2,2,2,2,1] (.node [13,9,9,9,4,4,4,3,2,1,1,1,1,1] (.node [13,9,9,9,4,4,4,2,2,2,2,1,1] (.node [13,9,9,9,4,4,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,4,4,4,4,1,1,1,1,1,1] (.node [13,9,9,9,4,4,4,3,2,2,1,1,1] .empty .empty) .empty)) (.node [13,9,9,9,5,3,3,2,2,2,2,2,1] (.node [13,9,9,9,5,3,3,2,2,2,2,1,1,1] (.node [13,9,9,9,5,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,9,9,9,5,3,3,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_853 : RowTree := (.node [13,9,9,8,8,5,2,2,1,1,1,1,1,1] degreeTree62_851 degreeTree62_852) + +def degreeTree62_854 : RowTree := (.node [13,9,9,9,5,5,2,2,2,2,1,1,1,1] (.node [13,9,9,9,5,4,3,3,2,1,1,1,1,1] (.node [13,9,9,9,5,4,2,2,2,2,2,2,1] (.node [13,9,9,9,5,4,2,2,2,2,2,1,1,1] (.node [13,9,9,9,5,3,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,5,4,3,2,2,2,2,1,1] (.node [13,9,9,9,5,4,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,9,5,4,4,2,2,2,1,1,1] (.node [13,9,9,9,5,4,4,2,2,1,1,1,1,1] (.node [13,9,9,9,5,4,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,5,4,4,3,1,1,1,1,1,1] .empty .empty))) (.node [13,9,9,9,5,5,5,1,1,1,1,1,1,1] (.node [13,9,9,9,5,5,3,2,2,2,1,1,1] (.node [13,9,9,9,5,5,3,2,2,1,1,1,1,1] (.node [13,9,9,9,5,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,9,5,5,4,2,1,1,1,1,1,1] (.node [13,9,9,9,5,5,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,9,6,3,2,2,2,2,2,1,1,1] (.node [13,9,9,9,6,2,2,2,2,2,2,2,2] (.node [13,9,9,9,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,9,6,3,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_855 : RowTree := (.node [13,9,9,9,6,5,2,2,2,2,1,1,1] (.node [13,9,9,9,6,4,3,2,2,1,1,1,1,1] (.node [13,9,9,9,6,3,3,3,2,2,1,1,1] (.node [13,9,9,9,6,3,3,3,2,1,1,1,1,1] (.node [13,9,9,9,6,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,9,9,9,6,4,2,2,2,2,2,1,1] (.node [13,9,9,9,6,4,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,9,6,4,4,2,1,1,1,1,1,1] (.node [13,9,9,9,6,4,3,3,1,1,1,1,1,1] (.node [13,9,9,9,6,4,3,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,6,5,2,2,2,1,1,1,1,1] .empty .empty))) (.node [13,9,9,9,7,2,2,2,2,2,2,1,1,1] (.node [13,9,9,9,6,6,2,2,1,1,1,1,1,1] (.node [13,9,9,9,6,5,4,1,1,1,1,1,1,1] (.node [13,9,9,9,6,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,6,6,3,1,1,1,1,1,1,1] .empty .empty)) (.node [13,9,9,9,7,3,2,2,2,2,2,1,1] (.node [13,9,9,9,7,3,2,2,2,2,1,1,1,1] (.node [13,9,9,9,7,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,9,9,9,7,3,3,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_856 : RowTree := (.node [13,9,9,9,6,3,3,2,2,2,1,1,1,1] degreeTree62_854 degreeTree62_855) + +def degreeTree62_857 : RowTree := (.node [13,9,9,9,5,3,3,3,3,1,1,1,1,1] degreeTree62_853 degreeTree62_856) + +def degreeTree62_858 : RowTree := (.node [13,9,9,8,7,4,3,2,2,1,1,1,1,1] degreeTree62_850 degreeTree62_857) + +def degreeTree62_859 : RowTree := (.node [13,9,9,7,7,4,3,3,2,1,1,1,1,1] degreeTree62_843 degreeTree62_858) + +def degreeTree62_860 : RowTree := (.node [13,9,9,9,8,2,2,2,2,2,2,1,1] (.node [13,9,9,9,7,5,2,2,1,1,1,1,1,1] (.node [13,9,9,9,7,4,2,2,2,2,1,1,1] (.node [13,9,9,9,7,4,2,2,2,1,1,1,1,1] (.node [13,9,9,9,7,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,7,4,4,1,1,1,1,1,1,1] (.node [13,9,9,9,7,4,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,9,7,7,1,1,1,1,1,1,1,1] (.node [13,9,9,9,7,6,2,1,1,1,1,1,1,1] (.node [13,9,9,9,7,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,8,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [13,9,9,9,8,5,2,1,1,1,1,1,1,1] (.node [13,9,9,9,8,3,3,2,1,1,1,1,1,1] (.node [13,9,9,9,8,3,2,2,2,2,1,1,1] (.node [13,9,9,9,8,3,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,8,4,3,1,1,1,1,1,1,1] (.node [13,9,9,9,8,4,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,9,9,9,9,2,2,2,2,2,1,1,1] (.node [13,9,9,9,9,2,2,2,2,1,1,1,1,1] (.node [13,9,9,9,8,6,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,9,9,9,9,3,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_861 : RowTree := (.node [13,10,6,6,5,4,4,4,4,2,2,1,1] (.node [13,10,6,5,5,5,4,4,4,2,2,1,1] (.node [13,10,5,5,5,5,5,4,4,2,2,1,1] (.node [13,9,9,9,9,5,1,1,1,1,1,1,1,1] (.node [13,9,9,9,9,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,5,5,5,5,5,5,4,2,1,1,1] (.node [13,10,5,5,5,5,5,5,3,2,2,1,1] .empty .empty) .empty)) (.node [13,10,6,5,5,5,5,5,2,2,2,1,1] (.node [13,10,6,5,5,5,5,4,4,2,1,1,1] (.node [13,10,6,5,5,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,6,5,5,5,5,5,3,2,1,1,1] .empty .empty))) (.node [13,10,6,6,5,5,5,4,3,2,1,1,1] (.node [13,10,6,6,5,5,5,2,2,2,2,2,2] (.node [13,10,6,6,5,5,4,4,4,2,1,1,1] (.node [13,10,6,6,5,5,4,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,6,6,5,5,5,4,2,2,2,1,1] (.node [13,10,6,6,5,5,5,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,10,6,6,6,4,4,4,4,2,1,1,1] (.node [13,10,6,6,6,4,4,4,3,2,2,1,1] (.node [13,10,6,6,5,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,6,6,6,5,4,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_862 : RowTree := (.node [13,9,9,9,9,3,3,1,1,1,1,1,1,1] degreeTree62_860 degreeTree62_861) + +def degreeTree62_863 : RowTree := (.node [13,10,6,6,6,6,4,3,3,2,1,1,1] (.node [13,10,6,6,6,5,5,4,2,2,1,1,1] (.node [13,10,6,6,6,5,5,2,2,2,2,2,1] (.node [13,10,6,6,6,5,4,4,3,2,1,1,1] (.node [13,10,6,6,6,5,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,6,6,6,5,5,3,3,2,1,1,1] (.node [13,10,6,6,6,5,5,3,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,6,6,6,6,4,2,2,2,2,2,1] (.node [13,10,6,6,6,6,3,3,3,2,2,1,1] (.node [13,10,6,6,6,6,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,10,6,6,6,6,4,3,2,2,2,1,1] .empty .empty))) (.node [13,10,7,5,5,5,4,4,3,2,2,1,1] (.node [13,10,6,6,6,6,5,3,2,2,1,1,1] (.node [13,10,6,6,6,6,5,2,2,2,2,1,1] (.node [13,10,6,6,6,6,4,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,5,5,4,4,4,4,2,2,1,1] (.node [13,10,6,6,6,6,6,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,10,7,5,5,5,5,3,3,2,2,1,1] (.node [13,10,7,5,5,5,5,2,2,2,2,2,2] (.node [13,10,7,5,5,5,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,5,5,5,5,4,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_864 : RowTree := (.node [13,10,7,6,5,5,5,3,3,2,1,1,1] (.node [13,10,7,6,5,5,4,3,3,2,2,1,1] (.node [13,10,7,6,5,4,4,4,3,2,2,1,1] (.node [13,10,7,6,4,4,4,4,4,2,2,1,1] (.node [13,10,7,5,5,5,5,5,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,6,5,5,4,2,2,2,2,2,2] (.node [13,10,7,6,5,4,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [13,10,7,6,5,5,5,2,2,2,2,2,1] (.node [13,10,7,6,5,5,4,4,3,2,1,1,1] (.node [13,10,7,6,5,5,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,7,6,5,5,5,3,2,2,2,1,1] .empty .empty))) (.node [13,10,7,6,6,5,3,2,2,2,2,2,2] (.node [13,10,7,6,6,4,4,3,3,2,2,1,1] (.node [13,10,7,6,6,4,4,2,2,2,2,2,2] (.node [13,10,7,6,5,5,5,4,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,6,6,4,4,4,3,2,1,1,1] (.node [13,10,7,6,6,4,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,7,6,6,5,4,3,2,2,2,1,1] (.node [13,10,7,6,6,5,4,2,2,2,2,2,1] (.node [13,10,7,6,6,5,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,7,6,6,5,4,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_865 : RowTree := (.node [13,10,7,5,5,5,5,4,3,2,1,1,1] degreeTree62_863 degreeTree62_864) + +def degreeTree62_866 : RowTree := (.node [13,10,6,6,6,5,4,3,3,2,2,1,1] degreeTree62_862 degreeTree62_865) + +def degreeTree62_867 : RowTree := (.node [13,10,7,7,4,4,4,4,3,2,2,1,1] (.node [13,10,7,6,6,6,3,3,3,2,1,1,1] (.node [13,10,7,6,6,6,2,2,2,2,2,2,2] (.node [13,10,7,6,6,5,5,3,2,2,1,1,1] (.node [13,10,7,6,6,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,7,6,6,6,3,3,2,2,2,1,1] (.node [13,10,7,6,6,6,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,10,7,6,6,6,5,2,2,2,1,1,1] (.node [13,10,7,6,6,6,4,3,2,2,1,1,1] (.node [13,10,7,6,6,6,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,7,6,6,6,6,2,1,1,1,1,1,1] .empty .empty))) (.node [13,10,7,7,5,5,3,2,2,2,2,2,2] (.node [13,10,7,7,5,4,4,3,3,2,2,1,1] (.node [13,10,7,7,5,4,4,2,2,2,2,2,2] (.node [13,10,7,7,4,4,4,4,4,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,5,4,4,4,3,2,1,1,1] (.node [13,10,7,7,5,4,4,4,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,7,7,5,5,4,3,2,2,2,1,1] (.node [13,10,7,7,5,5,4,2,2,2,2,2,1] (.node [13,10,7,7,5,5,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,7,7,5,5,4,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_868 : RowTree := (.node [13,10,7,7,6,5,3,3,2,2,2,1,1] (.node [13,10,7,7,6,4,4,3,2,2,2,1,1] (.node [13,10,7,7,6,4,3,2,2,2,2,2,2] (.node [13,10,7,7,5,5,5,3,2,2,1,1,1] (.node [13,10,7,7,5,5,5,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,7,7,6,4,4,2,2,2,2,2,1] (.node [13,10,7,7,6,4,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,10,7,7,6,5,2,2,2,2,2,2,2] (.node [13,10,7,7,6,4,4,4,2,2,1,1,1] (.node [13,10,7,7,6,4,4,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,6,5,3,2,2,2,2,2,1] .empty .empty))) (.node [13,10,7,7,6,6,2,2,2,2,2,2,1] (.node [13,10,7,7,6,5,4,3,2,2,1,1,1] (.node [13,10,7,7,6,5,4,2,2,2,2,1,1] (.node [13,10,7,7,6,5,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,6,6,2,2,2,2,2,1,1,1] (.node [13,10,7,7,6,5,5,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,10,7,7,6,6,3,3,2,1,1,1,1,1] (.node [13,10,7,7,6,6,3,2,2,2,2,1,1] (.node [13,10,7,7,6,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,6,6,3,3,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_869 : RowTree := (.node [13,10,7,7,5,5,4,4,2,2,1,1,1] degreeTree62_867 degreeTree62_868) + +def degreeTree62_870 : RowTree := (.node [13,10,7,7,7,4,3,3,3,1,1,1,1,1] (.node [13,10,7,7,7,3,3,3,3,2,2,1,1] (.node [13,10,7,7,6,6,5,2,1,1,1,1,1,1] (.node [13,10,7,7,6,6,4,3,1,1,1,1,1,1] (.node [13,10,7,7,6,6,4,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,7,3,3,2,2,2,2,2,2] (.node [13,10,7,7,6,6,6,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,7,7,7,4,3,2,2,2,2,2,1] (.node [13,10,7,7,7,4,3,2,2,2,2,1,1,1] (.node [13,10,7,7,7,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,10,7,7,7,4,3,3,2,2,2,1,1] .empty .empty))) (.node [13,10,7,7,7,4,4,4,1,1,1,1,1,1] (.node [13,10,7,7,7,4,4,2,2,2,2,1,1] (.node [13,10,7,7,7,4,4,2,2,2,1,1,1,1] (.node [13,10,7,7,7,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,7,4,4,3,2,2,1,1,1] (.node [13,10,7,7,7,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,7,7,7,5,3,2,2,2,1,1,1,1] (.node [13,10,7,7,7,5,2,2,2,2,2,2,1] (.node [13,10,7,7,7,5,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,7,5,3,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_871 : RowTree := (.node [13,10,7,7,7,7,2,2,2,1,1,1,1,1] (.node [13,10,7,7,7,6,2,2,2,2,2,1,1] (.node [13,10,7,7,7,5,4,3,1,1,1,1,1,1] (.node [13,10,7,7,7,5,4,2,2,1,1,1,1,1] (.node [13,10,7,7,7,5,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,7,6,2,2,2,2,1,1,1,1] (.node [13,10,7,7,7,5,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,7,7,7,6,4,2,1,1,1,1,1,1] (.node [13,10,7,7,7,6,3,3,1,1,1,1,1,1] (.node [13,10,7,7,7,6,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,7,7,7,6,5,1,1,1,1,1,1,1] .empty .empty))) (.node [13,10,8,5,5,5,4,2,2,2,2,2,2] (.node [13,10,8,5,4,4,4,4,4,2,2,1,1] (.node [13,10,7,7,7,7,4,1,1,1,1,1,1,1] (.node [13,10,7,7,7,7,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,5,5,4,4,4,4,2,1,1,1] (.node [13,10,8,5,5,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [13,10,8,5,5,5,4,4,3,2,1,1,1] (.node [13,10,8,5,5,5,4,4,2,2,2,1,1] (.node [13,10,8,5,5,5,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,5,5,5,5,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_872 : RowTree := (.node [13,10,7,7,7,5,3,3,2,1,1,1,1,1] degreeTree62_870 degreeTree62_871) + +def degreeTree62_873 : RowTree := (.node [13,10,7,7,6,6,4,2,2,1,1,1,1,1] degreeTree62_869 degreeTree62_872) + +def degreeTree62_874 : RowTree := (.node [13,10,7,6,6,5,4,4,2,2,1,1,1] degreeTree62_866 degreeTree62_873) + +def degreeTree62_875 : RowTree := (.node [13,10,8,6,5,5,4,2,2,2,2,2,1] (.node [13,10,8,6,5,4,4,3,3,2,2,1,1] (.node [13,10,8,6,4,4,4,4,3,2,2,1,1] (.node [13,10,8,5,5,5,5,4,2,2,1,1,1] (.node [13,10,8,5,5,5,5,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,6,5,4,4,2,2,2,2,2,2] (.node [13,10,8,6,4,4,4,4,4,2,1,1,1] .empty .empty) .empty)) (.node [13,10,8,6,5,5,3,2,2,2,2,2,2] (.node [13,10,8,6,5,4,4,4,3,2,1,1,1] (.node [13,10,8,6,5,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,6,5,5,3,3,3,2,2,1,1] .empty .empty))) (.node [13,10,8,6,6,4,3,2,2,2,2,2,2] (.node [13,10,8,6,5,5,4,4,2,2,1,1,1] (.node [13,10,8,6,5,5,4,3,3,2,1,1,1] (.node [13,10,8,6,5,5,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,6,5,5,5,3,2,2,1,1,1] (.node [13,10,8,6,5,5,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,8,6,6,4,4,3,2,2,2,1,1] (.node [13,10,8,6,6,4,4,2,2,2,2,2,1] (.node [13,10,8,6,6,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,6,6,4,4,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_876 : RowTree := (.node [13,10,8,6,6,6,3,3,2,1,1,1,1,1] (.node [13,10,8,6,6,5,4,3,2,2,1,1,1] (.node [13,10,8,6,6,5,3,3,2,2,2,1,1] (.node [13,10,8,6,6,5,3,2,2,2,2,2,1] (.node [13,10,8,6,6,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,10,8,6,6,5,4,2,2,2,2,1,1] (.node [13,10,8,6,6,5,3,3,3,2,1,1,1] .empty .empty) .empty)) (.node [13,10,8,6,6,6,3,2,2,2,1,1,1,1] (.node [13,10,8,6,6,6,2,2,2,2,2,2,1] (.node [13,10,8,6,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,6,6,6,3,2,2,2,2,1,1] .empty .empty))) (.node [13,10,8,7,4,4,4,2,2,2,2,2,2] (.node [13,10,8,6,6,6,4,3,1,1,1,1,1,1] (.node [13,10,8,6,6,6,4,2,2,1,1,1,1,1] (.node [13,10,8,6,6,6,3,3,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,6,6,6,6,1,1,1,1,1,1,1] (.node [13,10,8,6,6,6,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,8,7,4,4,4,4,3,2,1,1,1] (.node [13,10,8,7,4,4,4,4,2,2,2,1,1] (.node [13,10,8,7,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,7,5,4,3,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_877 : RowTree := (.node [13,10,8,6,6,4,4,4,2,2,1,1,1] degreeTree62_875 degreeTree62_876) + +def degreeTree62_878 : RowTree := (.node [13,10,8,7,6,3,3,2,2,2,2,2,2] (.node [13,10,8,7,5,5,3,2,2,2,2,2,1] (.node [13,10,8,7,5,4,4,3,3,2,1,1,1] (.node [13,10,8,7,5,4,4,3,2,2,2,1,1] (.node [13,10,8,7,5,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,8,7,5,5,2,2,2,2,2,2,2] (.node [13,10,8,7,5,4,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [13,10,8,7,5,5,4,2,2,2,2,1,1] (.node [13,10,8,7,5,5,3,3,3,2,1,1,1] (.node [13,10,8,7,5,5,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,7,5,5,4,3,2,2,1,1,1] .empty .empty))) (.node [13,10,8,7,6,4,3,3,3,1,1,1,1,1] (.node [13,10,8,7,6,4,3,2,2,2,2,1,1,1] (.node [13,10,8,7,6,4,2,2,2,2,2,2,2] (.node [13,10,8,7,6,3,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,7,6,4,3,3,2,2,2,1,1] (.node [13,10,8,7,6,4,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,10,8,7,6,4,4,2,2,2,2,1,1] (.node [13,10,8,7,6,4,4,2,2,2,1,1,1,1] (.node [13,10,8,7,6,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,7,6,4,4,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_879 : RowTree := (.node [13,10,8,7,6,6,3,2,2,1,1,1,1,1] (.node [13,10,8,7,6,5,4,2,2,1,1,1,1,1] (.node [13,10,8,7,6,5,3,2,2,2,1,1,1,1] (.node [13,10,8,7,6,5,2,2,2,2,2,2,1] (.node [13,10,8,7,6,5,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,7,6,5,3,3,2,1,1,1,1,1] (.node [13,10,8,7,6,5,3,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,8,7,6,6,2,2,2,2,1,1,1,1] (.node [13,10,8,7,6,5,5,2,1,1,1,1,1,1] (.node [13,10,8,7,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,7,6,6,2,2,2,2,2,1,1] .empty .empty))) (.node [13,10,8,7,7,3,3,2,2,2,2,1,1,1] (.node [13,10,8,7,6,6,5,1,1,1,1,1,1,1] (.node [13,10,8,7,6,6,4,2,1,1,1,1,1,1] (.node [13,10,8,7,6,6,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,7,7,3,2,2,2,2,2,2,2] (.node [13,10,8,7,7,2,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,10,8,7,7,3,3,3,3,1,1,1,1,1] (.node [13,10,8,7,7,3,3,3,2,2,2,1,1] (.node [13,10,8,7,7,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,8,7,7,3,3,3,3,2,1,1,1] .empty .empty)))) + +def degreeTree62_880 : RowTree := (.node [13,10,8,7,6,4,4,4,1,1,1,1,1,1] degreeTree62_878 degreeTree62_879) + +def degreeTree62_881 : RowTree := (.node [13,10,8,7,5,4,3,3,3,2,2,1,1] degreeTree62_877 degreeTree62_880) + +def degreeTree62_882 : RowTree := (.node [13,10,8,7,7,5,4,2,1,1,1,1,1,1] (.node [13,10,8,7,7,4,4,3,1,1,1,1,1,1] (.node [13,10,8,7,7,4,3,2,2,2,2,1,1] (.node [13,10,8,7,7,4,3,2,2,2,1,1,1,1] (.node [13,10,8,7,7,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,8,7,7,4,4,2,2,1,1,1,1,1] (.node [13,10,8,7,7,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,8,7,7,5,3,2,2,1,1,1,1,1] (.node [13,10,8,7,7,5,2,2,2,2,2,1,1] (.node [13,10,8,7,7,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,7,7,5,3,3,1,1,1,1,1,1] .empty .empty))) (.node [13,10,8,7,7,7,3,1,1,1,1,1,1,1] (.node [13,10,8,7,7,6,3,2,1,1,1,1,1,1] (.node [13,10,8,7,7,6,2,2,2,1,1,1,1,1] (.node [13,10,8,7,7,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,7,7,7,2,2,1,1,1,1,1,1] (.node [13,10,8,7,7,6,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,8,8,4,4,4,2,2,2,2,1,1,1] (.node [13,10,8,8,4,4,3,3,3,2,2,1,1] (.node [13,10,8,8,4,4,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,10,8,8,4,4,4,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_883 : RowTree := (.node [13,10,8,8,5,4,3,3,3,1,1,1,1,1] (.node [13,10,8,8,5,3,3,3,3,2,2,1,1] (.node [13,10,8,8,4,4,4,4,2,1,1,1,1,1] (.node [13,10,8,8,4,4,4,3,3,2,1,1,1] (.node [13,10,8,8,4,4,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,5,3,3,2,2,2,2,2,2] (.node [13,10,8,8,4,4,4,4,2,2,1,1,1] .empty .empty) .empty)) (.node [13,10,8,8,5,4,3,2,2,2,2,2,1] (.node [13,10,8,8,5,4,3,2,2,2,2,1,1,1] (.node [13,10,8,8,5,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,10,8,8,5,4,3,3,2,2,2,1,1] .empty .empty))) (.node [13,10,8,8,5,5,2,2,2,2,2,1,1,1] (.node [13,10,8,8,5,4,4,2,2,2,2,1,1] (.node [13,10,8,8,5,4,4,2,2,2,1,1,1,1] (.node [13,10,8,8,5,4,3,3,3,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,5,4,4,4,1,1,1,1,1,1] (.node [13,10,8,8,5,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,8,8,5,5,3,2,2,2,2,1,1] (.node [13,10,8,8,5,5,3,2,2,2,1,1,1,1] (.node [13,10,8,8,5,5,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,8,8,5,5,3,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_884 : RowTree := (.node [13,10,8,8,4,4,4,3,2,2,2,1,1] degreeTree62_882 degreeTree62_883) + +def degreeTree62_885 : RowTree := (.node [13,10,8,8,6,4,2,2,2,2,2,2,1] (.node [13,10,8,8,6,3,3,2,2,2,2,2,1] (.node [13,10,8,8,6,2,2,2,2,2,2,2,2,1] (.node [13,10,8,8,5,5,5,2,1,1,1,1,1,1] (.node [13,10,8,8,5,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,6,3,3,2,2,2,2,1,1,1] (.node [13,10,8,8,6,3,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,10,8,8,6,3,3,3,3,2,1,1,1] (.node [13,10,8,8,6,3,3,3,3,1,1,1,1,1] (.node [13,10,8,8,6,3,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,8,6,4,2,2,2,2,2,1,1,1] .empty .empty))) (.node [13,10,8,8,6,5,2,2,2,2,1,1,1,1] (.node [13,10,8,8,6,4,3,3,2,1,1,1,1,1] (.node [13,10,8,8,6,4,3,2,2,2,2,1,1] (.node [13,10,8,8,6,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,6,4,4,3,1,1,1,1,1,1] (.node [13,10,8,8,6,4,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,8,8,6,5,3,3,1,1,1,1,1,1] (.node [13,10,8,8,6,5,3,2,2,1,1,1,1,1] (.node [13,10,8,8,6,5,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,8,6,5,4,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_886 : RowTree := (.node [13,10,8,8,7,4,2,2,2,2,1,1,1,1] (.node [13,10,8,8,7,3,2,2,2,2,2,1,1,1] (.node [13,10,8,8,6,6,4,1,1,1,1,1,1,1] (.node [13,10,8,8,6,6,3,2,1,1,1,1,1,1] (.node [13,10,8,8,6,6,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,7,2,2,2,2,2,2,2,2] (.node [13,10,8,8,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,8,8,7,3,3,2,2,2,2,1,1] (.node [13,10,8,8,7,3,3,2,2,2,1,1,1,1] (.node [13,10,8,8,7,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,8,8,7,3,3,3,2,1,1,1,1,1] .empty .empty))) (.node [13,10,8,8,7,5,2,2,2,1,1,1,1,1] (.node [13,10,8,8,7,4,3,3,1,1,1,1,1,1] (.node [13,10,8,8,7,4,3,2,2,1,1,1,1,1] (.node [13,10,8,8,7,4,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,8,8,7,4,4,2,1,1,1,1,1,1] .empty .empty)) (.node [13,10,8,8,7,6,2,2,1,1,1,1,1,1] (.node [13,10,8,8,7,5,4,1,1,1,1,1,1,1] (.node [13,10,8,8,7,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,7,6,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_887 : RowTree := (.node [13,10,8,8,6,5,5,1,1,1,1,1,1,1] degreeTree62_885 degreeTree62_886) + +def degreeTree62_888 : RowTree := (.node [13,10,8,8,5,5,4,2,2,1,1,1,1,1] degreeTree62_884 degreeTree62_887) + +def degreeTree62_889 : RowTree := (.node [13,10,8,7,7,4,2,2,2,2,2,1,1,1] degreeTree62_881 degreeTree62_888) + +def degreeTree62_890 : RowTree := (.node [13,10,8,5,5,5,5,3,2,2,2,1,1] degreeTree62_874 degreeTree62_889) + +def degreeTree62_891 : RowTree := (.node [13,9,9,9,7,3,3,2,2,2,1,1,1] degreeTree62_859 degreeTree62_890) + +def degreeTree62_892 : RowTree := (.node [13,9,8,8,6,6,3,2,2,1,1,1,1,1] degreeTree62_828 degreeTree62_891) + +def degreeTree62_893 : RowTree := (.node [13,10,8,8,8,5,3,1,1,1,1,1,1,1] (.node [13,10,8,8,8,3,3,3,1,1,1,1,1,1] (.node [13,10,8,8,8,3,2,2,2,2,1,1,1,1] (.node [13,10,8,8,8,2,2,2,2,2,2,2,1] (.node [13,10,8,8,8,2,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,8,3,3,2,2,1,1,1,1,1] (.node [13,10,8,8,8,3,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,8,8,8,4,4,1,1,1,1,1,1,1] (.node [13,10,8,8,8,4,3,2,1,1,1,1,1,1] (.node [13,10,8,8,8,4,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,8,8,8,5,2,2,1,1,1,1,1,1] .empty .empty))) (.node [13,10,9,5,5,4,4,2,2,2,2,2,2] (.node [13,10,9,4,4,4,4,4,4,2,2,1,1] (.node [13,10,8,8,8,7,1,1,1,1,1,1,1,1] (.node [13,10,8,8,8,6,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,5,4,4,4,4,4,2,1,1,1] (.node [13,10,9,5,4,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [13,10,9,5,5,4,4,4,3,2,1,1,1] (.node [13,10,9,5,5,4,4,4,2,2,2,1,1] (.node [13,10,9,5,5,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,5,5,5,3,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_894 : RowTree := (.node [13,10,9,6,5,4,4,2,2,2,2,2,1] (.node [13,10,9,6,4,4,4,3,3,2,2,1,1] (.node [13,10,9,5,5,5,4,3,3,2,1,1,1] (.node [13,10,9,5,5,5,4,3,2,2,2,1,1] (.node [13,10,9,5,5,5,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,6,4,4,4,2,2,2,2,2,2] (.node [13,10,9,5,5,5,5,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,9,6,5,4,3,2,2,2,2,2,2] (.node [13,10,9,6,4,4,4,4,3,2,1,1,1] (.node [13,10,9,6,4,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,6,5,4,3,3,3,2,2,1,1] .empty .empty))) (.node [13,10,9,6,5,5,3,3,3,2,1,1,1] (.node [13,10,9,6,5,5,2,2,2,2,2,2,2] (.node [13,10,9,6,5,4,4,3,3,2,1,1,1] (.node [13,10,9,6,5,4,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,6,5,5,3,3,2,2,2,1,1] (.node [13,10,9,6,5,5,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,10,9,6,6,3,3,3,3,2,2,1,1] (.node [13,10,9,6,6,3,3,2,2,2,2,2,2] (.node [13,10,9,6,5,5,4,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,6,6,4,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_895 : RowTree := (.node [13,10,9,5,5,5,3,3,3,2,2,1,1] degreeTree62_893 degreeTree62_894) + +def degreeTree62_896 : RowTree := (.node [13,10,9,6,6,5,3,2,2,2,2,1,1] (.node [13,10,9,6,6,4,4,3,2,1,1,1,1,1] (.node [13,10,9,6,6,4,3,3,3,1,1,1,1,1] (.node [13,10,9,6,6,4,3,3,2,2,2,1,1] (.node [13,10,9,6,6,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,6,6,4,4,2,2,2,2,1,1] (.node [13,10,9,6,6,4,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,6,6,5,2,2,2,2,2,2,1] (.node [13,10,9,6,6,5,2,2,2,2,2,1,1,1] (.node [13,10,9,6,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,6,6,5,3,2,2,2,1,1,1,1] .empty .empty))) (.node [13,10,9,6,6,6,2,2,2,2,2,1,1] (.node [13,10,9,6,6,5,4,3,1,1,1,1,1,1] (.node [13,10,9,6,6,5,4,2,2,1,1,1,1,1] (.node [13,10,9,6,6,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,6,6,6,2,2,2,2,1,1,1,1] (.node [13,10,9,6,6,5,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,6,6,6,4,2,1,1,1,1,1,1] (.node [13,10,9,6,6,6,3,3,1,1,1,1,1,1] (.node [13,10,9,6,6,6,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,6,6,6,5,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_897 : RowTree := (.node [13,10,9,7,5,4,3,2,2,2,2,1,1,1] (.node [13,10,9,7,4,4,4,3,3,2,1,1,1] (.node [13,10,9,7,4,4,4,2,2,2,2,2,1] (.node [13,10,9,7,4,4,4,2,2,2,2,1,1,1] (.node [13,10,9,7,4,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,7,4,4,4,3,3,1,1,1,1,1] (.node [13,10,9,7,4,4,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,9,7,5,3,3,3,3,2,2,1,1] (.node [13,10,9,7,5,3,3,2,2,2,2,2,2] (.node [13,10,9,7,4,4,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,5,4,2,2,2,2,2,2,2] .empty .empty))) (.node [13,10,9,7,5,4,4,3,2,1,1,1,1,1] (.node [13,10,9,7,5,4,3,3,3,1,1,1,1,1] (.node [13,10,9,7,5,4,3,3,2,2,2,1,1] (.node [13,10,9,7,5,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,7,5,4,4,2,2,2,2,1,1] (.node [13,10,9,7,5,4,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,7,5,5,2,2,2,2,2,2,1] (.node [13,10,9,7,5,5,2,2,2,2,2,1,1,1] (.node [13,10,9,7,5,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,5,5,3,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_898 : RowTree := (.node [13,10,9,7,4,4,3,2,2,2,2,2,2] degreeTree62_896 degreeTree62_897) + +def degreeTree62_899 : RowTree := (.node [13,10,9,6,6,4,3,2,2,2,2,1,1,1] degreeTree62_895 degreeTree62_898) + +def degreeTree62_900 : RowTree := (.node [13,10,9,7,6,4,2,2,2,2,2,1,1,1] (.node [13,10,9,7,6,3,2,2,2,2,2,2,2] (.node [13,10,9,7,5,5,4,3,1,1,1,1,1,1] (.node [13,10,9,7,5,5,4,2,2,1,1,1,1,1] (.node [13,10,9,7,5,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,6,2,2,2,2,2,2,2,2,1] (.node [13,10,9,7,5,5,5,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,7,6,3,3,3,2,2,2,1,1] (.node [13,10,9,7,6,3,3,2,2,2,2,2,1] (.node [13,10,9,7,6,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,6,3,3,3,3,1,1,1,1,1] .empty .empty))) (.node [13,10,9,7,6,4,4,3,1,1,1,1,1,1] (.node [13,10,9,7,6,4,3,2,2,2,2,1,1] (.node [13,10,9,7,6,4,3,2,2,2,1,1,1,1] (.node [13,10,9,7,6,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,7,6,4,4,2,2,1,1,1,1,1] (.node [13,10,9,7,6,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,7,6,5,3,2,2,1,1,1,1,1] (.node [13,10,9,7,6,5,2,2,2,2,2,1,1] (.node [13,10,9,7,6,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,6,5,3,3,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_901 : RowTree := (.node [13,10,9,7,7,3,3,3,2,1,1,1,1,1] (.node [13,10,9,7,7,2,2,2,2,2,2,2,2] (.node [13,10,9,7,6,6,3,2,1,1,1,1,1,1] (.node [13,10,9,7,6,6,2,2,2,1,1,1,1,1] (.node [13,10,9,7,6,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,7,2,2,2,2,2,2,2,1,1] (.node [13,10,9,7,6,6,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,7,7,3,3,2,2,2,1,1,1,1] (.node [13,10,9,7,7,3,2,2,2,2,2,2,1] (.node [13,10,9,7,7,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,7,3,3,2,2,2,2,1,1] .empty .empty))) (.node [13,10,9,7,7,5,2,2,2,1,1,1,1,1] (.node [13,10,9,7,7,4,3,2,2,1,1,1,1,1] (.node [13,10,9,7,7,4,2,2,2,2,2,1,1] (.node [13,10,9,7,7,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,7,4,4,2,1,1,1,1,1,1] (.node [13,10,9,7,7,4,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,7,7,6,2,2,1,1,1,1,1,1] (.node [13,10,9,7,7,5,4,1,1,1,1,1,1,1] (.node [13,10,9,7,7,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,7,7,6,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_902 : RowTree := (.node [13,10,9,7,6,5,4,2,1,1,1,1,1,1] degreeTree62_900 degreeTree62_901) + +def degreeTree62_903 : RowTree := (.node [13,10,9,8,4,4,4,4,1,1,1,1,1,1] (.node [13,10,9,8,4,4,3,3,2,2,2,1,1] (.node [13,10,9,8,4,4,2,2,2,2,2,2,2] (.node [13,10,9,8,4,3,3,3,3,2,2,1,1] (.node [13,10,9,8,4,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,10,9,8,4,4,3,2,2,2,2,2,1] (.node [13,10,9,8,4,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,10,9,8,4,4,4,2,2,2,2,1,1] (.node [13,10,9,8,4,4,4,2,2,2,1,1,1,1] (.node [13,10,9,8,4,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,4,4,4,3,2,1,1,1,1,1] .empty .empty))) (.node [13,10,9,8,5,3,3,3,3,1,1,1,1,1] (.node [13,10,9,8,5,3,3,2,2,2,2,1,1,1] (.node [13,10,9,8,5,3,2,2,2,2,2,2,2] (.node [13,10,9,8,5,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,8,5,3,3,3,2,2,2,1,1] (.node [13,10,9,8,5,3,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,10,9,8,5,4,3,2,2,2,1,1,1,1] (.node [13,10,9,8,5,4,2,2,2,2,2,2,1] (.node [13,10,9,8,5,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,5,4,3,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_904 : RowTree := (.node [13,10,9,8,6,3,2,2,2,2,2,1,1,1] (.node [13,10,9,8,5,5,3,3,1,1,1,1,1,1] (.node [13,10,9,8,5,5,2,2,2,2,1,1,1,1] (.node [13,10,9,8,5,4,4,3,1,1,1,1,1,1] (.node [13,10,9,8,5,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,5,5,3,2,2,1,1,1,1,1] (.node [13,10,9,8,5,5,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,9,8,6,2,2,2,2,2,2,2,1,1] (.node [13,10,9,8,5,5,5,1,1,1,1,1,1,1] (.node [13,10,9,8,5,5,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,6,2,2,2,2,2,2,2,2] .empty .empty))) (.node [13,10,9,8,6,4,2,2,2,2,2,1,1] (.node [13,10,9,8,6,3,3,2,2,2,2,1,1] (.node [13,10,9,8,6,3,3,2,2,2,1,1,1,1] (.node [13,10,9,8,6,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,8,6,4,2,2,2,2,1,1,1,1] (.node [13,10,9,8,6,3,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,8,6,4,4,2,1,1,1,1,1,1] (.node [13,10,9,8,6,4,3,3,1,1,1,1,1,1] (.node [13,10,9,8,6,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,6,5,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_905 : RowTree := (.node [13,10,9,8,5,4,3,3,2,1,1,1,1,1] degreeTree62_903 degreeTree62_904) + +def degreeTree62_906 : RowTree := (.node [13,10,9,7,7,7,2,1,1,1,1,1,1,1] degreeTree62_902 degreeTree62_905) + +def degreeTree62_907 : RowTree := (.node [13,10,9,7,5,5,3,2,2,2,2,1,1] degreeTree62_899 degreeTree62_906) + +def degreeTree62_908 : RowTree := (.node [13,10,9,8,7,4,3,2,1,1,1,1,1,1] (.node [13,10,9,8,7,3,2,2,2,2,1,1,1,1] (.node [13,10,9,8,6,6,3,1,1,1,1,1,1,1] (.node [13,10,9,8,6,6,2,2,1,1,1,1,1,1] (.node [13,10,9,8,6,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,7,2,2,2,2,2,2,2,1] (.node [13,10,9,8,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,10,9,8,7,3,3,3,1,1,1,1,1,1] (.node [13,10,9,8,7,3,3,2,2,1,1,1,1,1] (.node [13,10,9,8,7,3,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,8,7,4,2,2,2,1,1,1,1,1] .empty .empty))) (.node [13,10,9,8,8,2,2,2,2,2,1,1,1,1] (.node [13,10,9,8,7,5,3,1,1,1,1,1,1,1] (.node [13,10,9,8,7,5,2,2,1,1,1,1,1,1] (.node [13,10,9,8,7,4,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,8,7,7,1,1,1,1,1,1,1,1] (.node [13,10,9,8,7,6,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,8,8,3,3,2,1,1,1,1,1,1] (.node [13,10,9,8,8,3,2,2,2,1,1,1,1,1] (.node [13,10,9,8,8,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,8,8,4,2,2,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_909 : RowTree := (.node [13,10,9,9,4,4,2,2,2,2,2,1,1,1] (.node [13,10,9,9,4,3,2,2,2,2,2,2,2] (.node [13,10,9,9,3,3,3,2,2,2,2,2,2] (.node [13,10,9,8,8,6,1,1,1,1,1,1,1,1] (.node [13,10,9,8,8,5,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,4,2,2,2,2,2,2,2,2,1] (.node [13,10,9,9,3,3,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,10,9,9,4,3,3,3,2,2,2,1,1] (.node [13,10,9,9,4,3,3,2,2,2,2,2,1] (.node [13,10,9,9,4,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,4,3,3,3,3,1,1,1,1,1] .empty .empty))) (.node [13,10,9,9,4,4,4,3,1,1,1,1,1,1] (.node [13,10,9,9,4,4,3,2,2,2,2,1,1] (.node [13,10,9,9,4,4,3,2,2,2,1,1,1,1] (.node [13,10,9,9,4,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,9,4,4,4,2,2,1,1,1,1,1] (.node [13,10,9,9,4,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,9,5,3,2,2,2,2,2,1,1,1] (.node [13,10,9,9,5,2,2,2,2,2,2,2,2] (.node [13,10,9,9,5,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,9,5,3,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_910 : RowTree := (.node [13,10,9,8,8,4,3,1,1,1,1,1,1,1] degreeTree62_908 degreeTree62_909) + +def degreeTree62_911 : RowTree := (.node [13,10,9,9,6,2,2,2,2,2,2,1,1,1] (.node [13,10,9,9,5,4,3,3,1,1,1,1,1,1] (.node [13,10,9,9,5,4,2,2,2,2,1,1,1,1] (.node [13,10,9,9,5,3,3,3,2,1,1,1,1,1] (.node [13,10,9,9,5,3,3,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,10,9,9,5,4,3,2,2,1,1,1,1,1] (.node [13,10,9,9,5,4,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,10,9,9,5,5,3,2,1,1,1,1,1,1] (.node [13,10,9,9,5,5,2,2,2,1,1,1,1,1] (.node [13,10,9,9,5,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,5,5,4,1,1,1,1,1,1,1] .empty .empty))) (.node [13,10,9,9,6,4,2,2,2,1,1,1,1,1] (.node [13,10,9,9,6,3,2,2,2,2,2,1,1] (.node [13,10,9,9,6,3,2,2,2,2,1,1,1,1] (.node [13,10,9,9,6,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,10,9,9,6,3,3,3,1,1,1,1,1,1] (.node [13,10,9,9,6,3,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,9,6,5,2,2,1,1,1,1,1,1] (.node [13,10,9,9,6,4,4,1,1,1,1,1,1,1] (.node [13,10,9,9,6,4,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,6,5,3,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_912 : RowTree := (.node [13,10,9,9,8,3,3,1,1,1,1,1,1,1] (.node [13,10,9,9,7,4,3,1,1,1,1,1,1,1] (.node [13,10,9,9,7,3,2,2,2,1,1,1,1,1] (.node [13,10,9,9,7,2,2,2,2,2,2,1,1] (.node [13,10,9,9,7,2,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,7,4,2,2,1,1,1,1,1,1] (.node [13,10,9,9,7,3,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,10,9,9,8,2,2,2,2,1,1,1,1,1] (.node [13,10,9,9,7,6,1,1,1,1,1,1,1,1] (.node [13,10,9,9,7,5,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,8,3,2,2,1,1,1,1,1,1] .empty .empty))) (.node [13,11,5,5,5,5,4,4,4,2,2,1,1] (.node [13,10,9,9,9,2,2,2,1,1,1,1,1,1] (.node [13,10,9,9,8,5,1,1,1,1,1,1,1,1] (.node [13,10,9,9,8,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,10,9,9,9,4,1,1,1,1,1,1,1,1] (.node [13,10,9,9,9,3,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,6,5,5,4,4,4,4,2,2,1,1] (.node [13,11,5,5,5,5,5,5,2,2,2,1,1] (.node [13,11,5,5,5,5,5,4,3,2,2,1,1] .empty .empty) .empty) (.node [13,11,6,5,5,5,4,4,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_913 : RowTree := (.node [13,10,9,9,6,6,2,1,1,1,1,1,1,1] degreeTree62_911 degreeTree62_912) + +def degreeTree62_914 : RowTree := (.node [13,10,9,9,5,3,3,2,2,2,1,1,1,1] degreeTree62_910 degreeTree62_913) + +def degreeTree62_915 : RowTree := (.node [13,11,6,6,6,4,4,3,3,2,2,1,1] (.node [13,11,6,6,5,5,4,3,3,2,2,1,1] (.node [13,11,6,6,4,4,4,4,4,2,2,1,1] (.node [13,11,6,5,5,5,5,4,2,2,2,1,1] (.node [13,11,6,5,5,5,5,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,11,6,6,5,5,4,2,2,2,2,2,2] (.node [13,11,6,6,5,4,4,4,3,2,2,1,1] .empty .empty) .empty)) (.node [13,11,6,6,5,5,5,3,2,2,2,1,1] (.node [13,11,6,6,5,5,5,2,2,2,2,2,1] (.node [13,11,6,6,5,5,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,11,6,6,6,4,4,2,2,2,2,2,2] .empty .empty))) (.node [13,11,6,6,6,5,5,2,2,2,2,1,1] (.node [13,11,6,6,6,5,3,3,3,2,2,1,1] (.node [13,11,6,6,6,5,3,2,2,2,2,2,2] (.node [13,11,6,6,6,4,4,4,2,2,2,1,1] .empty .empty) .empty) (.node [13,11,6,6,6,5,4,3,2,2,2,1,1] (.node [13,11,6,6,6,5,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,11,6,6,6,6,3,3,2,2,2,1,1] (.node [13,11,6,6,6,6,3,2,2,2,2,2,1] (.node [13,11,6,6,6,6,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,6,6,6,6,4,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_916 : RowTree := (.node [13,11,7,6,5,4,4,4,2,2,2,1,1] (.node [13,11,7,5,5,5,5,2,2,2,2,2,1] (.node [13,11,7,5,5,5,4,2,2,2,2,2,2] (.node [13,11,7,5,5,4,4,4,3,2,2,1,1] (.node [13,11,7,5,4,4,4,4,4,2,2,1,1] .empty .empty) .empty) (.node [13,11,7,5,5,5,4,4,2,2,2,1,1] (.node [13,11,7,5,5,5,4,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,11,7,6,5,4,4,2,2,2,2,2,2] (.node [13,11,7,6,4,4,4,4,3,2,2,1,1] (.node [13,11,7,5,5,5,5,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,11,7,6,5,4,4,3,3,2,2,1,1] .empty .empty))) (.node [13,11,7,6,6,4,3,2,2,2,2,2,2] (.node [13,11,7,6,5,5,4,2,2,2,2,2,1] (.node [13,11,7,6,5,5,3,3,3,2,2,1,1] (.node [13,11,7,6,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,7,6,5,5,5,2,2,2,2,1,1] (.node [13,11,7,6,5,5,4,3,2,2,2,1,1] .empty .empty) .empty)) (.node [13,11,7,6,6,4,4,3,2,2,2,1,1] (.node [13,11,7,6,6,4,4,2,2,2,2,2,1] (.node [13,11,7,6,6,4,3,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,11,7,6,6,5,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_917 : RowTree := (.node [13,11,6,6,6,6,6,2,1,1,1,1,1,1] degreeTree62_915 degreeTree62_916) + +def degreeTree62_918 : RowTree := (.node [13,11,7,6,6,6,6,1,1,1,1,1,1,1] (.node [13,11,7,6,6,6,3,2,2,2,2,1,1] (.node [13,11,7,6,6,6,2,2,2,2,2,1,1,1] (.node [13,11,7,6,6,5,4,2,2,2,2,1,1] (.node [13,11,7,6,6,5,3,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,11,7,6,6,6,3,2,2,2,1,1,1,1] (.node [13,11,7,6,6,6,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,11,7,6,6,6,4,3,1,1,1,1,1,1] (.node [13,11,7,6,6,6,4,2,2,1,1,1,1,1] (.node [13,11,7,6,6,6,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,6,6,6,5,2,1,1,1,1,1,1] .empty .empty))) (.node [13,11,7,7,5,4,4,2,2,2,2,2,1] (.node [13,11,7,7,4,4,4,4,2,2,2,1,1] (.node [13,11,7,7,4,4,4,3,3,2,2,1,1] (.node [13,11,7,7,4,4,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,7,7,5,4,3,3,3,2,2,1,1] (.node [13,11,7,7,5,4,3,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,11,7,7,5,5,3,2,2,2,2,2,1] (.node [13,11,7,7,5,5,2,2,2,2,2,2,2] (.node [13,11,7,7,5,4,4,3,2,2,2,1,1] .empty .empty) .empty) (.node [13,11,7,7,5,5,3,3,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_919 : RowTree := (.node [13,11,7,7,6,5,2,2,2,2,2,1,1,1] (.node [13,11,7,7,6,4,3,3,2,2,2,1,1] (.node [13,11,7,7,6,4,2,2,2,2,2,2,2] (.node [13,11,7,7,6,3,3,3,3,2,2,1,1] (.node [13,11,7,7,6,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,7,7,6,4,3,2,2,2,2,2,1] (.node [13,11,7,7,6,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,7,7,6,4,4,3,2,1,1,1,1,1] (.node [13,11,7,7,6,4,4,2,2,2,1,1,1,1] (.node [13,11,7,7,6,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,7,6,4,4,4,1,1,1,1,1,1] .empty .empty))) (.node [13,11,7,7,6,5,4,3,1,1,1,1,1,1] (.node [13,11,7,7,6,5,3,3,2,1,1,1,1,1] (.node [13,11,7,7,6,5,3,2,2,2,1,1,1,1] (.node [13,11,7,7,6,5,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,7,7,6,5,4,2,2,1,1,1,1,1] .empty .empty)) (.node [13,11,7,7,6,6,3,2,2,1,1,1,1,1] (.node [13,11,7,7,6,6,2,2,2,2,1,1,1,1] (.node [13,11,7,7,6,5,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,7,6,6,3,3,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_920 : RowTree := (.node [13,11,7,7,5,5,4,2,2,2,2,1,1] degreeTree62_918 degreeTree62_919) + +def degreeTree62_921 : RowTree := (.node [13,11,7,6,6,5,3,2,2,2,2,2,1] degreeTree62_917 degreeTree62_920) + +def degreeTree62_922 : RowTree := (.node [13,11,6,5,5,5,5,2,2,2,2,2,2] degreeTree62_914 degreeTree62_921) + +def degreeTree62_923 : RowTree := (.node [13,10,9,8,6,5,3,2,1,1,1,1,1,1] degreeTree62_907 degreeTree62_922) + +def degreeTree62_924 : RowTree := (.node [13,11,7,7,7,4,3,3,2,1,1,1,1,1] (.node [13,11,7,7,7,3,3,3,2,2,2,1,1] (.node [13,11,7,7,7,3,2,2,2,2,2,2,2] (.node [13,11,7,7,7,2,2,2,2,2,2,2,2,1] (.node [13,11,7,7,6,6,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,7,7,3,3,2,2,2,2,2,1] (.node [13,11,7,7,7,3,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,7,7,7,4,2,2,2,2,2,2,1] (.node [13,11,7,7,7,4,2,2,2,2,2,1,1,1] (.node [13,11,7,7,7,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,7,7,4,3,2,2,2,1,1,1,1] .empty .empty))) (.node [13,11,7,7,7,5,4,2,1,1,1,1,1,1] (.node [13,11,7,7,7,5,2,2,2,2,1,1,1,1] (.node [13,11,7,7,7,4,4,3,1,1,1,1,1,1] (.node [13,11,7,7,7,4,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,7,7,5,3,3,1,1,1,1,1,1] (.node [13,11,7,7,7,5,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,7,7,7,6,3,2,1,1,1,1,1,1] (.node [13,11,7,7,7,6,2,2,2,1,1,1,1,1] (.node [13,11,7,7,7,5,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,7,7,7,6,4,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_925 : RowTree := (.node [13,11,8,6,4,4,4,2,2,2,2,2,2] (.node [13,11,8,5,5,4,4,4,2,2,2,1,1] (.node [13,11,8,5,4,4,4,4,3,2,2,1,1] (.node [13,11,8,4,4,4,4,4,4,2,2,1,1] (.node [13,11,7,7,7,7,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,5,5,4,4,3,3,2,2,1,1] (.node [13,11,8,5,5,4,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,11,8,5,5,5,4,2,2,2,2,2,1] (.node [13,11,8,5,5,5,3,3,3,2,2,1,1] (.node [13,11,8,5,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,8,5,5,5,4,3,2,2,2,1,1] .empty .empty))) (.node [13,11,8,6,5,4,4,3,2,2,2,1,1] (.node [13,11,8,6,5,4,3,2,2,2,2,2,2] (.node [13,11,8,6,4,4,4,4,2,2,2,1,1] (.node [13,11,8,6,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,11,8,6,5,4,4,2,2,2,2,2,1] (.node [13,11,8,6,5,4,3,3,3,2,2,1,1] .empty .empty) .empty)) (.node [13,11,8,6,5,5,3,3,2,2,2,1,1] (.node [13,11,8,6,5,5,3,2,2,2,2,2,1] (.node [13,11,8,6,5,5,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,8,6,6,3,3,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_926 : RowTree := (.node [13,11,7,7,7,7,2,2,1,1,1,1,1,1] degreeTree62_924 degreeTree62_925) + +def degreeTree62_927 : RowTree := (.node [13,11,8,6,6,5,3,3,2,1,1,1,1,1] (.node [13,11,8,6,6,4,4,3,2,1,1,1,1,1] (.node [13,11,8,6,6,4,3,2,2,2,2,2,1] (.node [13,11,8,6,6,4,3,2,2,2,2,1,1,1] (.node [13,11,8,6,6,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,8,6,6,4,4,2,2,2,1,1,1,1] (.node [13,11,8,6,6,4,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,6,6,5,2,2,2,2,2,2,1] (.node [13,11,8,6,6,5,2,2,2,2,2,1,1,1] (.node [13,11,8,6,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,6,6,5,3,2,2,2,1,1,1,1] .empty .empty))) (.node [13,11,8,6,6,6,3,3,1,1,1,1,1,1] (.node [13,11,8,6,6,5,5,2,1,1,1,1,1,1] (.node [13,11,8,6,6,5,4,3,1,1,1,1,1,1] (.node [13,11,8,6,6,5,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,6,6,6,3,2,2,1,1,1,1,1] (.node [13,11,8,6,6,6,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,7,4,4,3,2,2,2,2,2,2] (.node [13,11,8,6,6,6,5,1,1,1,1,1,1,1] (.node [13,11,8,6,6,6,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,4,4,3,3,3,2,2,1,1] .empty .empty)))) + +def degreeTree62_928 : RowTree := (.node [13,11,8,7,5,4,4,2,2,2,1,1,1,1] (.node [13,11,8,7,5,3,3,3,3,2,2,1,1] (.node [13,11,8,7,4,4,4,3,3,1,1,1,1,1] (.node [13,11,8,7,4,4,4,3,2,2,2,1,1] (.node [13,11,8,7,4,4,4,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,8,7,5,3,3,2,2,2,2,2,2] (.node [13,11,8,7,4,4,4,4,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,7,5,4,3,2,2,2,2,2,1] (.node [13,11,8,7,5,4,3,2,2,2,2,1,1,1] (.node [13,11,8,7,5,4,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,8,7,5,4,3,3,3,1,1,1,1,1] .empty .empty))) (.node [13,11,8,7,5,5,3,3,2,1,1,1,1,1] (.node [13,11,8,7,5,5,2,2,2,2,2,1,1,1] (.node [13,11,8,7,5,4,4,4,1,1,1,1,1,1] (.node [13,11,8,7,5,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,5,5,3,2,2,2,1,1,1,1] (.node [13,11,8,7,5,5,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,11,8,7,5,5,5,2,1,1,1,1,1,1] (.node [13,11,8,7,5,5,4,3,1,1,1,1,1,1] (.node [13,11,8,7,5,5,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,6,2,2,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_929 : RowTree := (.node [13,11,8,7,4,4,4,2,2,2,2,1,1,1] degreeTree62_927 degreeTree62_928) + +def degreeTree62_930 : RowTree := (.node [13,11,8,6,6,3,3,3,3,2,2,1,1] degreeTree62_926 degreeTree62_929) + +def degreeTree62_931 : RowTree := (.node [13,11,8,7,6,5,3,2,2,1,1,1,1,1] (.node [13,11,8,7,6,4,3,2,2,2,1,1,1,1] (.node [13,11,8,7,6,3,3,3,3,1,1,1,1,1] (.node [13,11,8,7,6,3,3,2,2,2,2,2,1] (.node [13,11,8,7,6,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,6,4,2,2,2,2,2,2,1] (.node [13,11,8,7,6,4,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,8,7,6,4,4,3,1,1,1,1,1,1] (.node [13,11,8,7,6,4,4,2,2,1,1,1,1,1] (.node [13,11,8,7,6,4,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,6,5,2,2,2,2,1,1,1,1] .empty .empty))) (.node [13,11,8,7,6,6,4,1,1,1,1,1,1,1] (.node [13,11,8,7,6,5,5,1,1,1,1,1,1,1] (.node [13,11,8,7,6,5,4,2,1,1,1,1,1,1] (.node [13,11,8,7,6,5,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,6,6,3,2,1,1,1,1,1,1] (.node [13,11,8,7,6,6,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,7,7,3,2,2,2,2,2,1,1,1] (.node [13,11,8,7,7,2,2,2,2,2,2,2,2] (.node [13,11,8,7,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty) (.node [13,11,8,7,7,3,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_932 : RowTree := (.node [13,11,8,7,7,7,2,1,1,1,1,1,1,1] (.node [13,11,8,7,7,5,2,2,2,1,1,1,1,1] (.node [13,11,8,7,7,4,3,2,2,1,1,1,1,1] (.node [13,11,8,7,7,4,2,2,2,2,1,1,1,1] (.node [13,11,8,7,7,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,7,4,4,2,1,1,1,1,1,1] (.node [13,11,8,7,7,4,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,7,7,6,2,2,1,1,1,1,1,1] (.node [13,11,8,7,7,5,4,1,1,1,1,1,1,1] (.node [13,11,8,7,7,5,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,7,7,6,3,1,1,1,1,1,1,1] .empty .empty))) (.node [13,11,8,8,4,4,3,3,3,1,1,1,1,1] (.node [13,11,8,8,4,4,2,2,2,2,2,2,2] (.node [13,11,8,8,4,3,3,3,3,2,2,1,1] (.node [13,11,8,8,4,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,8,8,4,4,3,2,2,2,2,2,1] (.node [13,11,8,8,4,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,8,8,4,4,4,4,1,1,1,1,1,1] (.node [13,11,8,8,4,4,4,3,2,1,1,1,1,1] (.node [13,11,8,8,4,4,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,5,2,2,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_933 : RowTree := (.node [13,11,8,7,7,3,3,2,2,2,1,1,1,1] degreeTree62_931 degreeTree62_932) + +def degreeTree62_934 : RowTree := (.node [13,11,8,8,5,5,3,2,2,1,1,1,1,1] (.node [13,11,8,8,5,4,3,2,2,2,1,1,1,1] (.node [13,11,8,8,5,3,3,3,3,1,1,1,1,1] (.node [13,11,8,8,5,3,3,2,2,2,2,2,1] (.node [13,11,8,8,5,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,5,4,2,2,2,2,2,2,1] (.node [13,11,8,8,5,4,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,8,8,5,4,4,3,1,1,1,1,1,1] (.node [13,11,8,8,5,4,4,2,2,1,1,1,1,1] (.node [13,11,8,8,5,4,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,5,5,2,2,2,2,1,1,1,1] .empty .empty))) (.node [13,11,8,8,6,3,2,2,2,2,2,1,1,1] (.node [13,11,8,8,5,5,5,1,1,1,1,1,1,1] (.node [13,11,8,8,5,5,4,2,1,1,1,1,1,1] (.node [13,11,8,8,5,5,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,6,2,2,2,2,2,2,2,2] (.node [13,11,8,8,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,11,8,8,6,3,3,3,2,1,1,1,1,1] (.node [13,11,8,8,6,3,3,2,2,2,1,1,1,1] (.node [13,11,8,8,6,3,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,8,8,6,4,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_935 : RowTree := (.node [13,11,8,8,7,3,3,2,2,1,1,1,1,1] (.node [13,11,8,8,6,6,2,2,1,1,1,1,1,1] (.node [13,11,8,8,6,5,2,2,2,1,1,1,1,1] (.node [13,11,8,8,6,4,4,2,1,1,1,1,1,1] (.node [13,11,8,8,6,4,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,6,5,4,1,1,1,1,1,1,1] (.node [13,11,8,8,6,5,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,8,7,2,2,2,2,2,2,2,1] (.node [13,11,8,8,7,2,2,2,2,2,2,1,1,1] (.node [13,11,8,8,6,6,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,7,3,2,2,2,2,1,1,1,1] .empty .empty))) (.node [13,11,8,8,7,5,3,1,1,1,1,1,1,1] (.node [13,11,8,8,7,4,3,2,1,1,1,1,1,1] (.node [13,11,8,8,7,4,2,2,2,1,1,1,1,1] (.node [13,11,8,8,7,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,7,5,2,2,1,1,1,1,1,1] (.node [13,11,8,8,7,4,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,8,8,8,2,2,2,2,2,1,1,1,1] (.node [13,11,8,8,7,7,1,1,1,1,1,1,1,1] (.node [13,11,8,8,7,6,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,8,8,8,3,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_936 : RowTree := (.node [13,11,8,8,6,4,3,2,2,1,1,1,1,1] degreeTree62_934 degreeTree62_935) + +def degreeTree62_937 : RowTree := (.node [13,11,8,8,5,3,2,2,2,2,2,2,2] degreeTree62_933 degreeTree62_936) + +def degreeTree62_938 : RowTree := (.node [13,11,8,7,6,3,2,2,2,2,2,2,2] degreeTree62_930 degreeTree62_937) + +def degreeTree62_939 : RowTree := (.node [13,11,9,5,5,5,2,2,2,2,2,2,2] (.node [13,11,9,5,4,4,4,2,2,2,2,2,2] (.node [13,11,8,8,8,5,2,1,1,1,1,1,1,1] (.node [13,11,8,8,8,4,3,1,1,1,1,1,1,1] (.node [13,11,8,8,8,4,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,4,4,4,4,4,3,2,2,1,1] (.node [13,11,8,8,8,6,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,5,5,4,3,3,3,2,2,1,1] (.node [13,11,9,5,5,4,3,2,2,2,2,2,2] (.node [13,11,9,5,4,4,4,3,3,2,2,1,1] .empty .empty) .empty) (.node [13,11,9,5,5,4,4,2,2,2,2,2,1] .empty .empty))) (.node [13,11,9,6,4,4,4,3,3,1,1,1,1,1] (.node [13,11,9,6,4,4,3,3,3,2,2,1,1] (.node [13,11,9,6,4,4,3,2,2,2,2,2,2] (.node [13,11,9,5,5,5,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,6,4,4,4,2,2,2,2,2,1] (.node [13,11,9,6,4,4,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,9,6,5,4,2,2,2,2,2,2,2] (.node [13,11,9,6,5,3,3,2,2,2,2,2,2] (.node [13,11,9,6,4,4,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,6,5,4,3,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_940 : RowTree := (.node [13,11,9,6,5,5,5,2,1,1,1,1,1,1] (.node [13,11,9,6,5,5,2,2,2,2,2,2,1] (.node [13,11,9,6,5,4,4,3,2,1,1,1,1,1] (.node [13,11,9,6,5,4,4,2,2,2,1,1,1,1] (.node [13,11,9,6,5,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,6,5,5,2,2,2,2,2,1,1,1] (.node [13,11,9,6,5,4,4,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,6,5,5,4,2,2,1,1,1,1,1] (.node [13,11,9,6,5,5,3,3,2,1,1,1,1,1] (.node [13,11,9,6,5,5,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,6,5,5,4,3,1,1,1,1,1,1] .empty .empty))) (.node [13,11,9,6,6,4,2,2,2,2,2,1,1,1] (.node [13,11,9,6,6,3,3,2,2,2,2,1,1,1] (.node [13,11,9,6,6,3,2,2,2,2,2,2,2] (.node [13,11,9,6,6,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,6,6,3,3,3,3,1,1,1,1,1] (.node [13,11,9,6,6,3,3,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,11,9,6,6,4,3,3,2,1,1,1,1,1] (.node [13,11,9,6,6,4,3,2,2,2,1,1,1,1] (.node [13,11,9,6,6,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,6,6,4,4,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_941 : RowTree := (.node [13,11,9,6,5,4,3,2,2,2,2,2,1] degreeTree62_939 degreeTree62_940) + +def degreeTree62_942 : RowTree := (.node [13,11,9,7,4,4,3,2,2,2,2,1,1,1] (.node [13,11,9,6,6,6,2,2,2,1,1,1,1,1] (.node [13,11,9,6,6,5,3,3,1,1,1,1,1,1] (.node [13,11,9,6,6,5,3,2,2,1,1,1,1,1] (.node [13,11,9,6,6,5,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,6,6,5,5,1,1,1,1,1,1,1] (.node [13,11,9,6,6,5,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,7,4,3,3,2,2,2,2,2,2] (.node [13,11,9,6,6,6,4,1,1,1,1,1,1,1] (.node [13,11,9,6,6,6,3,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,7,4,4,2,2,2,2,2,2,2] .empty .empty))) (.node [13,11,9,7,5,2,2,2,2,2,2,2,2,1] (.node [13,11,9,7,4,4,4,2,2,2,1,1,1,1] (.node [13,11,9,7,4,4,3,3,3,1,1,1,1,1] (.node [13,11,9,7,4,4,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,7,4,4,4,4,1,1,1,1,1,1] (.node [13,11,9,7,4,4,4,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,7,5,3,3,2,2,2,2,2,1] (.node [13,11,9,7,5,3,3,2,2,2,2,1,1,1] (.node [13,11,9,7,5,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,9,7,5,3,3,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_943 : RowTree := (.node [13,11,9,7,6,2,2,2,2,2,2,2,1,1] (.node [13,11,9,7,5,5,2,2,2,2,1,1,1,1] (.node [13,11,9,7,5,4,3,3,2,1,1,1,1,1] (.node [13,11,9,7,5,4,3,2,2,2,1,1,1,1] (.node [13,11,9,7,5,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,7,5,4,4,3,1,1,1,1,1,1] (.node [13,11,9,7,5,4,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,7,5,5,4,2,1,1,1,1,1,1] (.node [13,11,9,7,5,5,3,3,1,1,1,1,1,1] (.node [13,11,9,7,5,5,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,7,5,5,5,1,1,1,1,1,1,1] .empty .empty))) (.node [13,11,9,7,6,4,2,2,2,2,1,1,1,1] (.node [13,11,9,7,6,3,2,2,2,2,2,2,1] (.node [13,11,9,7,6,3,2,2,2,2,2,1,1,1] (.node [13,11,9,7,6,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,9,7,6,3,3,3,2,1,1,1,1,1] (.node [13,11,9,7,6,3,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,7,6,4,4,2,1,1,1,1,1,1] (.node [13,11,9,7,6,4,3,3,1,1,1,1,1,1] (.node [13,11,9,7,6,4,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,7,6,5,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_944 : RowTree := (.node [13,11,9,7,5,4,2,2,2,2,2,1,1,1] degreeTree62_942 degreeTree62_943) + +def degreeTree62_945 : RowTree := (.node [13,11,9,6,6,4,4,3,1,1,1,1,1,1] degreeTree62_941 degreeTree62_944) + +def degreeTree62_946 : RowTree := (.node [13,11,9,7,7,4,4,1,1,1,1,1,1,1] (.node [13,11,9,7,7,3,2,2,2,2,1,1,1,1] (.node [13,11,9,7,6,6,3,1,1,1,1,1,1,1] (.node [13,11,9,7,6,6,2,2,1,1,1,1,1,1] (.node [13,11,9,7,6,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,7,7,2,2,2,2,2,2,2,1] (.node [13,11,9,7,7,2,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,11,9,7,7,4,2,2,2,1,1,1,1,1] (.node [13,11,9,7,7,3,3,3,1,1,1,1,1,1] (.node [13,11,9,7,7,3,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,7,7,4,3,2,1,1,1,1,1,1] .empty .empty))) (.node [13,11,9,8,4,2,2,2,2,2,2,2,2,1] (.node [13,11,9,7,7,6,2,1,1,1,1,1,1,1] (.node [13,11,9,7,7,5,3,1,1,1,1,1,1,1] (.node [13,11,9,7,7,5,2,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,8,3,3,3,2,2,2,2,2,2] (.node [13,11,9,7,7,7,1,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,8,4,3,3,2,2,2,2,2,1] (.node [13,11,9,8,4,3,3,2,2,2,2,1,1,1] (.node [13,11,9,8,4,3,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,9,8,4,3,3,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_947 : RowTree := (.node [13,11,9,8,5,3,3,3,2,1,1,1,1,1] (.node [13,11,9,8,5,2,2,2,2,2,2,2,1,1] (.node [13,11,9,8,4,4,3,3,2,1,1,1,1,1] (.node [13,11,9,8,4,4,3,2,2,2,1,1,1,1] (.node [13,11,9,8,4,4,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,8,4,4,4,3,1,1,1,1,1,1] (.node [13,11,9,8,4,4,4,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,8,5,3,2,2,2,2,2,2,1] (.node [13,11,9,8,5,3,2,2,2,2,2,1,1,1] (.node [13,11,9,8,5,2,2,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,11,9,8,5,3,3,2,2,2,1,1,1,1] .empty .empty))) (.node [13,11,9,8,5,5,3,2,1,1,1,1,1,1] (.node [13,11,9,8,5,4,3,3,1,1,1,1,1,1] (.node [13,11,9,8,5,4,3,2,2,1,1,1,1,1] (.node [13,11,9,8,5,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,8,5,5,2,2,2,1,1,1,1,1] (.node [13,11,9,8,5,4,4,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,8,6,2,2,2,2,2,2,2,1] (.node [13,11,9,8,6,2,2,2,2,2,2,1,1,1] (.node [13,11,9,8,5,5,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,8,6,3,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_948 : RowTree := (.node [13,11,9,8,4,4,2,2,2,2,2,1,1,1] degreeTree62_946 degreeTree62_947) + +def degreeTree62_949 : RowTree := (.node [13,11,9,8,7,4,2,2,1,1,1,1,1,1] (.node [13,11,9,8,6,5,3,1,1,1,1,1,1,1] (.node [13,11,9,8,6,4,3,2,1,1,1,1,1,1] (.node [13,11,9,8,6,4,2,2,2,1,1,1,1,1] (.node [13,11,9,8,6,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,8,6,5,2,2,1,1,1,1,1,1] (.node [13,11,9,8,6,4,4,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,8,7,3,2,2,2,1,1,1,1,1] (.node [13,11,9,8,7,2,2,2,2,2,1,1,1,1] (.node [13,11,9,8,6,6,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,8,7,3,3,2,1,1,1,1,1,1] .empty .empty))) (.node [13,11,9,8,8,3,3,1,1,1,1,1,1,1] (.node [13,11,9,8,7,6,1,1,1,1,1,1,1,1] (.node [13,11,9,8,7,5,2,1,1,1,1,1,1,1] (.node [13,11,9,8,7,4,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,8,8,3,2,2,1,1,1,1,1,1] (.node [13,11,9,8,8,2,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,9,3,2,2,2,2,2,2,2,2,1] (.node [13,11,9,8,8,5,1,1,1,1,1,1,1,1] (.node [13,11,9,8,8,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,3,3,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_950 : RowTree := (.node [13,11,9,9,4,4,3,3,1,1,1,1,1,1] (.node [13,11,9,9,4,3,2,2,2,2,2,2,1] (.node [13,11,9,9,4,2,2,2,2,2,2,2,1,1] (.node [13,11,9,9,3,3,3,3,3,1,1,1,1,1] (.node [13,11,9,9,3,3,3,2,2,2,2,2,1] .empty .empty) .empty) (.node [13,11,9,9,4,3,2,2,2,2,2,1,1,1] (.node [13,11,9,9,4,2,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,11,9,9,4,4,2,2,2,2,1,1,1,1] (.node [13,11,9,9,4,3,3,3,2,1,1,1,1,1] (.node [13,11,9,9,4,3,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,4,4,3,2,2,1,1,1,1,1] .empty .empty))) (.node [13,11,9,9,5,3,3,2,2,1,1,1,1,1] (.node [13,11,9,9,5,2,2,2,2,2,2,2,1] (.node [13,11,9,9,5,2,2,2,2,2,2,1,1,1] (.node [13,11,9,9,4,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,5,3,2,2,2,2,1,1,1,1] .empty .empty)) (.node [13,11,9,9,5,4,3,2,1,1,1,1,1,1] (.node [13,11,9,9,5,4,2,2,2,1,1,1,1,1] (.node [13,11,9,9,5,3,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,5,4,4,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_951 : RowTree := (.node [13,11,9,9,3,3,3,2,2,2,2,1,1,1] degreeTree62_949 degreeTree62_950) + +def degreeTree62_952 : RowTree := (.node [13,11,9,8,6,3,3,2,2,1,1,1,1,1] degreeTree62_948 degreeTree62_951) + +def degreeTree62_953 : RowTree := (.node [13,11,9,7,6,5,3,2,1,1,1,1,1,1] degreeTree62_945 degreeTree62_952) + +def degreeTree62_954 : RowTree := (.node [13,11,8,8,8,3,3,2,1,1,1,1,1,1] degreeTree62_938 degreeTree62_953) + +def degreeTree62_955 : RowTree := (.node [13,11,7,7,6,6,4,2,1,1,1,1,1,1] degreeTree62_923 degreeTree62_954) + +def degreeTree62_956 : RowTree := (.node [13,11,9,9,7,3,3,1,1,1,1,1,1,1] (.node [13,11,9,9,6,4,3,1,1,1,1,1,1,1] (.node [13,11,9,9,6,3,2,2,2,1,1,1,1,1] (.node [13,11,9,9,6,2,2,2,2,2,1,1,1,1] (.node [13,11,9,9,5,5,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,6,4,2,2,1,1,1,1,1,1] (.node [13,11,9,9,6,3,3,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,11,9,9,7,2,2,2,2,1,1,1,1,1] (.node [13,11,9,9,6,6,1,1,1,1,1,1,1,1] (.node [13,11,9,9,6,5,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,7,3,2,2,1,1,1,1,1,1] .empty .empty))) (.node [13,11,9,9,9,2,2,1,1,1,1,1,1,1] (.node [13,11,9,9,8,2,2,2,1,1,1,1,1,1] (.node [13,11,9,9,7,5,1,1,1,1,1,1,1,1] (.node [13,11,9,9,7,4,2,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,11,9,9,8,4,1,1,1,1,1,1,1,1] (.node [13,11,9,9,8,3,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,12,6,5,5,5,4,2,2,2,2,2,2] (.node [13,12,5,5,5,5,5,2,2,2,2,2,2] (.node [13,11,9,9,9,3,1,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,6,5,5,5,5,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_957 : RowTree := (.node [13,12,6,6,6,6,4,2,2,1,1,1,1,1] (.node [13,12,6,6,6,5,3,2,2,2,2,2,1] (.node [13,12,6,6,6,4,3,2,2,2,2,2,2] (.node [13,12,6,6,5,5,4,2,2,2,2,2,1] (.node [13,12,6,6,5,5,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,12,6,6,6,5,2,2,2,2,2,2,2] (.node [13,12,6,6,6,4,4,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,12,6,6,6,6,3,2,2,2,1,1,1,1] (.node [13,12,6,6,6,6,2,2,2,2,2,2,1] (.node [13,12,6,6,6,6,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,12,6,6,6,6,3,3,2,1,1,1,1,1] .empty .empty))) (.node [13,12,7,5,5,5,4,2,2,2,2,2,1] (.node [13,12,6,6,6,6,6,1,1,1,1,1,1,1] (.node [13,12,6,6,6,6,5,2,1,1,1,1,1,1] (.node [13,12,6,6,6,6,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,5,5,5,3,2,2,2,2,2,2] (.node [13,12,7,5,5,4,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,12,7,6,5,4,4,2,2,2,2,2,1] (.node [13,12,7,6,5,4,3,2,2,2,2,2,2] (.node [13,12,7,6,4,4,4,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,12,7,6,5,5,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_958 : RowTree := (.node [13,12,6,6,5,4,4,2,2,2,2,2,2] degreeTree62_956 degreeTree62_957) + +def degreeTree62_959 : RowTree := (.node [13,12,7,6,6,5,4,2,2,1,1,1,1,1] (.node [13,12,7,6,6,4,4,3,2,1,1,1,1,1] (.node [13,12,7,6,6,4,3,2,2,2,2,1,1,1] (.node [13,12,7,6,6,4,2,2,2,2,2,2,2] (.node [13,12,7,6,6,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,12,7,6,6,4,4,2,2,2,1,1,1,1] (.node [13,12,7,6,6,4,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [13,12,7,6,6,5,3,2,2,2,1,1,1,1] (.node [13,12,7,6,6,5,2,2,2,2,2,1,1,1] (.node [13,12,7,6,6,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,6,6,5,3,3,2,1,1,1,1,1] .empty .empty))) (.node [13,12,7,6,6,6,4,2,1,1,1,1,1,1] (.node [13,12,7,6,6,6,2,2,2,2,1,1,1,1] (.node [13,12,7,6,6,5,5,2,1,1,1,1,1,1] (.node [13,12,7,6,6,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,6,6,6,3,3,1,1,1,1,1,1] (.node [13,12,7,6,6,6,3,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [13,12,7,7,4,4,4,2,2,2,2,1,1,1] (.node [13,12,7,7,4,4,3,2,2,2,2,2,2] (.node [13,12,7,6,6,6,5,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,4,4,4,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_960 : RowTree := (.node [13,12,7,7,5,5,3,3,2,1,1,1,1,1] (.node [13,12,7,7,5,4,4,2,2,2,1,1,1,1] (.node [13,12,7,7,5,4,2,2,2,2,2,2,2] (.node [13,12,7,7,5,3,3,2,2,2,2,2,2] (.node [13,12,7,7,4,4,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,5,4,3,3,3,1,1,1,1,1] (.node [13,12,7,7,5,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,12,7,7,5,5,2,2,2,2,2,1,1,1] (.node [13,12,7,7,5,4,4,4,1,1,1,1,1,1] (.node [13,12,7,7,5,4,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,5,5,3,2,2,2,1,1,1,1] .empty .empty))) (.node [13,12,7,7,6,3,3,2,2,2,2,1,1,1] (.node [13,12,7,7,5,5,5,2,1,1,1,1,1,1] (.node [13,12,7,7,5,5,4,3,1,1,1,1,1,1] (.node [13,12,7,7,5,5,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,6,3,2,2,2,2,2,2,2] (.node [13,12,7,7,6,2,2,2,2,2,2,2,2,1] .empty .empty) .empty)) (.node [13,12,7,7,6,4,3,2,2,2,1,1,1,1] (.node [13,12,7,7,6,4,2,2,2,2,2,1,1,1] (.node [13,12,7,7,6,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,6,4,3,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_961 : RowTree := (.node [13,12,7,7,4,4,4,3,3,1,1,1,1,1] degreeTree62_959 degreeTree62_960) + +def degreeTree62_962 : RowTree := (.node [13,12,7,6,5,5,3,2,2,2,2,2,1] degreeTree62_958 degreeTree62_961) + +def degreeTree62_963 : RowTree := (.node [13,12,7,7,7,2,2,2,2,2,2,2,2] (.node [13,12,7,7,6,5,5,1,1,1,1,1,1,1] (.node [13,12,7,7,6,5,3,2,2,1,1,1,1,1] (.node [13,12,7,7,6,5,2,2,2,2,1,1,1,1] (.node [13,12,7,7,6,4,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,6,5,4,2,1,1,1,1,1,1] (.node [13,12,7,7,6,5,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,12,7,7,6,6,4,1,1,1,1,1,1,1] (.node [13,12,7,7,6,6,3,2,1,1,1,1,1,1] (.node [13,12,7,7,6,6,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,7,2,2,2,2,2,2,2,1,1] .empty .empty))) (.node [13,12,7,7,7,4,3,3,1,1,1,1,1,1] (.node [13,12,7,7,7,3,3,3,2,1,1,1,1,1] (.node [13,12,7,7,7,3,3,2,2,2,1,1,1,1] (.node [13,12,7,7,7,3,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,7,4,3,2,2,1,1,1,1,1] (.node [13,12,7,7,7,4,2,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,12,7,7,7,5,3,2,1,1,1,1,1,1] (.node [13,12,7,7,7,5,2,2,2,1,1,1,1,1] (.node [13,12,7,7,7,4,4,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,12,7,7,7,5,4,1,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_964 : RowTree := (.node [13,13,6,5,5,4,4,2,2,2,2,2,2] (.node [13,13,5,5,5,5,5,2,2,2,2,1,1,1] (.node [13,13,5,5,5,4,4,4,4,1,1,1,1,1] (.node [13,12,7,7,7,7,2,1,1,1,1,1,1,1] (.node [13,12,7,7,7,6,3,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,5,5,5,5,4,4,3,1,1,1,1,1] (.node [13,13,5,5,5,5,4,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,13,5,5,5,5,5,5,1,1,1,1,1,1] (.node [13,13,5,5,5,5,5,4,2,1,1,1,1,1] (.node [13,13,5,5,5,5,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,6,5,4,4,4,4,4,1,1,1,1,1] .empty .empty))) (.node [13,13,6,5,5,5,5,2,2,2,1,1,1,1] (.node [13,13,6,5,5,5,4,2,2,2,2,1,1,1] (.node [13,13,6,5,5,5,3,2,2,2,2,2,2] (.node [13,13,6,5,5,4,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,6,5,5,5,4,4,2,1,1,1,1,1] (.node [13,13,6,5,5,5,4,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,6,6,4,4,4,2,2,2,2,2,2] (.node [13,13,6,5,5,5,5,4,1,1,1,1,1,1] (.node [13,13,6,5,5,5,5,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,6,6,4,4,4,4,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_965 : RowTree := (.node [13,12,7,7,7,6,2,2,1,1,1,1,1,1] degreeTree62_963 degreeTree62_964) + +def degreeTree62_966 : RowTree := (.node [13,13,6,6,5,5,5,3,1,1,1,1,1,1] (.node [13,13,6,6,5,5,3,3,3,1,1,1,1,1] (.node [13,13,6,6,5,4,4,4,2,1,1,1,1,1] (.node [13,13,6,6,5,4,4,3,3,1,1,1,1,1] (.node [13,13,6,6,5,4,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,13,6,6,5,5,3,2,2,2,2,1,1,1] (.node [13,13,6,6,5,5,2,2,2,2,2,2,2] .empty .empty) .empty)) (.node [13,13,6,6,5,5,4,4,1,1,1,1,1,1] (.node [13,13,6,6,5,5,4,3,2,1,1,1,1,1] (.node [13,13,6,6,5,5,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,13,6,6,5,5,5,2,2,1,1,1,1,1] .empty .empty))) (.node [13,13,6,6,6,4,4,4,1,1,1,1,1,1] (.node [13,13,6,6,6,4,3,3,3,1,1,1,1,1] (.node [13,13,6,6,6,4,3,2,2,2,2,1,1,1] (.node [13,13,6,6,6,3,3,2,2,2,2,2,2] .empty .empty) .empty) (.node [13,13,6,6,6,4,4,3,2,1,1,1,1,1] (.node [13,13,6,6,6,4,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [13,13,6,6,6,5,3,3,2,1,1,1,1,1] (.node [13,13,6,6,6,5,3,2,2,2,1,1,1,1] (.node [13,13,6,6,6,5,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [13,13,6,6,6,5,4,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_967 : RowTree := (.node [13,13,7,5,5,4,4,2,2,2,2,1,1,1] (.node [13,13,6,6,6,6,5,1,1,1,1,1,1,1] (.node [13,13,6,6,6,6,3,2,2,1,1,1,1,1] (.node [13,13,6,6,6,6,2,2,2,2,1,1,1,1] (.node [13,13,6,6,6,5,5,2,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,6,6,6,6,4,2,1,1,1,1,1,1] (.node [13,13,6,6,6,6,3,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,7,5,4,4,4,4,3,1,1,1,1,1] (.node [13,13,7,5,4,4,4,2,2,2,2,2,2] (.node [13,13,7,4,4,4,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,5,5,4,3,2,2,2,2,2,2] .empty .empty))) (.node [13,13,7,5,5,5,4,3,2,1,1,1,1,1] (.node [13,13,7,5,5,5,3,2,2,2,2,1,1,1] (.node [13,13,7,5,5,4,4,4,2,1,1,1,1,1] (.node [13,13,7,5,5,4,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,5,5,5,4,2,2,2,1,1,1,1] (.node [13,13,7,5,5,5,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,7,5,5,5,5,3,1,1,1,1,1,1] (.node [13,13,7,5,5,5,5,2,2,1,1,1,1,1] (.node [13,13,7,5,5,5,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,6,4,4,3,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree62_968 : RowTree := (.node [13,13,6,6,6,5,4,3,1,1,1,1,1,1] degreeTree62_966 degreeTree62_967) + +def degreeTree62_969 : RowTree := (.node [13,13,6,6,5,4,3,2,2,2,2,2,2] degreeTree62_965 degreeTree62_968) + +def degreeTree62_970 : RowTree := (.node [13,12,7,7,6,4,4,2,2,1,1,1,1,1] degreeTree62_962 degreeTree62_969) + +def degreeTree62_971 : RowTree := (.node [13,13,7,6,5,5,4,2,2,1,1,1,1,1] (.node [13,13,7,6,5,4,4,3,2,1,1,1,1,1] (.node [13,13,7,6,5,4,3,2,2,2,2,1,1,1] (.node [13,13,7,6,4,4,4,4,2,1,1,1,1,1] (.node [13,13,7,6,4,4,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,6,5,4,4,2,2,2,1,1,1,1] (.node [13,13,7,6,5,4,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,7,6,5,5,3,2,2,2,1,1,1,1] (.node [13,13,7,6,5,5,2,2,2,2,2,1,1,1] (.node [13,13,7,6,5,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,6,5,5,3,3,2,1,1,1,1,1] .empty .empty))) (.node [13,13,7,6,6,4,2,2,2,2,2,1,1,1] (.node [13,13,7,6,6,2,2,2,2,2,2,2,2,1] (.node [13,13,7,6,5,5,5,2,1,1,1,1,1,1] (.node [13,13,7,6,5,5,4,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,6,6,3,3,3,3,1,1,1,1,1] (.node [13,13,7,6,6,3,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [13,13,7,6,6,4,4,2,2,1,1,1,1,1] (.node [13,13,7,6,6,4,3,3,2,1,1,1,1,1] (.node [13,13,7,6,6,4,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,6,6,4,4,3,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_972 : RowTree := (.node [13,13,7,7,4,4,4,3,2,1,1,1,1,1] (.node [13,13,7,6,6,6,3,2,1,1,1,1,1,1] (.node [13,13,7,6,6,5,4,2,1,1,1,1,1,1] (.node [13,13,7,6,6,5,3,3,1,1,1,1,1,1] (.node [13,13,7,6,6,5,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,6,6,6,2,2,2,1,1,1,1,1] (.node [13,13,7,6,6,5,5,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,7,7,4,4,3,3,3,1,1,1,1,1] (.node [13,13,7,7,4,4,3,2,2,2,2,1,1,1] (.node [13,13,7,6,6,6,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,4,4,4,2,2,2,1,1,1,1] .empty .empty))) (.node [13,13,7,7,5,4,3,2,2,2,1,1,1,1] (.node [13,13,7,7,5,3,3,2,2,2,2,1,1,1] (.node [13,13,7,7,5,2,2,2,2,2,2,2,2,1] (.node [13,13,7,7,4,4,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,5,4,2,2,2,2,2,1,1,1] (.node [13,13,7,7,5,3,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,7,7,5,4,4,3,1,1,1,1,1,1] (.node [13,13,7,7,5,4,4,2,2,1,1,1,1,1] (.node [13,13,7,7,5,4,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,5,5,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_973 : RowTree := (.node [13,13,7,6,6,5,2,2,2,2,1,1,1,1] degreeTree62_971 degreeTree62_972) + +def degreeTree62_974 : RowTree := (.node [13,13,7,7,6,4,4,2,1,1,1,1,1,1] (.node [13,13,7,7,6,3,3,2,2,2,1,1,1,1] (.node [13,13,7,7,5,5,5,1,1,1,1,1,1,1] (.node [13,13,7,7,5,5,4,2,1,1,1,1,1,1] (.node [13,13,7,7,5,5,3,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,6,3,2,2,2,2,2,1,1,1] (.node [13,13,7,7,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [13,13,7,7,6,4,3,2,2,1,1,1,1,1] (.node [13,13,7,7,6,4,2,2,2,2,1,1,1,1] (.node [13,13,7,7,6,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,6,4,3,3,1,1,1,1,1,1] .empty .empty))) (.node [13,13,7,7,7,2,2,2,2,2,2,1,1,1] (.node [13,13,7,7,6,5,4,1,1,1,1,1,1,1] (.node [13,13,7,7,6,5,3,2,1,1,1,1,1,1] (.node [13,13,7,7,6,5,2,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,6,6,3,1,1,1,1,1,1,1] (.node [13,13,7,7,6,6,2,2,1,1,1,1,1,1] .empty .empty) .empty)) (.node [13,13,7,7,7,3,3,3,1,1,1,1,1,1] (.node [13,13,7,7,7,3,3,2,2,1,1,1,1,1] (.node [13,13,7,7,7,3,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,7,4,2,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_975 : RowTree := (.node [14,6,6,6,6,6,6,5,2,1,1,1,1,1] (.node [14,6,6,6,5,5,5,5,5,1,1,1,1,1] (.node [13,13,7,7,7,5,3,1,1,1,1,1,1,1] (.node [13,13,7,7,7,5,2,2,1,1,1,1,1,1] (.node [13,13,7,7,7,4,4,1,1,1,1,1,1,1] .empty .empty) .empty) (.node [13,13,7,7,7,7,1,1,1,1,1,1,1,1] (.node [13,13,7,7,7,6,2,1,1,1,1,1,1,1] .empty .empty) .empty)) (.node [14,6,6,6,6,6,5,5,3,1,1,1,1,1] (.node [14,6,6,6,6,6,5,4,4,1,1,1,1,1] (.node [14,6,6,6,6,5,5,5,4,1,1,1,1,1] .empty .empty) .empty) (.node [14,6,6,6,6,6,6,4,3,1,1,1,1,1] .empty .empty))) (.node [14,7,6,6,6,6,4,4,4,1,1,1,1,1] (.node [14,7,6,6,5,5,5,5,4,1,1,1,1,1] (.node [14,7,6,5,5,5,5,5,5,1,1,1,1,1] (.node [14,6,6,6,6,6,6,6,1,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,6,6,6,5,5,5,3,1,1,1,1,1] (.node [14,7,6,6,6,5,5,4,4,1,1,1,1,1] .empty .empty) .empty)) (.node [14,7,6,6,6,6,6,2,2,2,2,1,1,1] (.node [14,7,6,6,6,6,5,5,2,1,1,1,1,1] (.node [14,7,6,6,6,6,5,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,6,6,6,6,6,3,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_976 : RowTree := (.node [13,13,7,7,7,4,3,2,1,1,1,1,1,1] degreeTree62_974 degreeTree62_975) + +def degreeTree62_977 : RowTree := (.node [13,13,7,7,5,5,3,2,2,1,1,1,1,1] degreeTree62_973 degreeTree62_976) + +def degreeTree62_978 : RowTree := (.node [14,7,7,6,6,6,5,4,2,1,1,1,1,1] (.node [14,7,7,6,6,5,5,4,3,1,1,1,1,1] (.node [14,7,7,6,5,5,5,4,4,1,1,1,1,1] (.node [14,7,7,5,5,5,5,5,4,1,1,1,1,1] (.node [14,7,6,6,6,6,6,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,6,6,5,4,4,4,1,1,1,1,1] (.node [14,7,7,6,5,5,5,5,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,7,7,6,6,6,5,2,2,2,2,1,1,1] (.node [14,7,7,6,6,6,4,4,3,1,1,1,1,1] (.node [14,7,7,6,6,5,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,6,6,6,5,3,3,1,1,1,1,1] .empty .empty))) (.node [14,7,7,7,5,5,5,4,3,1,1,1,1,1] (.node [14,7,7,6,6,6,6,3,2,1,1,1,1,1] (.node [14,7,7,6,6,6,6,2,2,2,1,1,1,1] (.node [14,7,7,6,6,6,5,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,5,5,4,4,4,1,1,1,1,1] (.node [14,7,7,6,6,6,6,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [14,7,7,7,6,5,4,4,3,1,1,1,1,1] (.node [14,7,7,7,6,4,4,4,4,1,1,1,1,1] (.node [14,7,7,7,5,5,5,5,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,6,5,5,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_979 : RowTree := (.node [14,7,7,7,7,4,4,4,3,1,1,1,1,1] (.node [14,7,7,7,6,6,5,2,2,2,1,1,1,1] (.node [14,7,7,7,6,6,4,2,2,2,2,1,1,1] (.node [14,7,7,7,6,5,5,5,1,1,1,1,1,1] (.node [14,7,7,7,6,5,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,6,6,4,4,2,1,1,1,1,1] (.node [14,7,7,7,6,6,4,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,7,7,7,6,6,6,2,2,1,1,1,1,1] (.node [14,7,7,7,6,6,5,4,1,1,1,1,1,1] (.node [14,7,7,7,6,6,5,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,6,6,6,3,1,1,1,1,1,1] .empty .empty))) (.node [14,7,7,7,7,5,5,4,1,1,1,1,1,1] (.node [14,7,7,7,7,5,4,4,2,1,1,1,1,1] (.node [14,7,7,7,7,5,4,3,3,1,1,1,1,1] (.node [14,7,7,7,7,5,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,7,5,5,3,2,1,1,1,1,1] (.node [14,7,7,7,7,5,5,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [14,7,7,7,7,6,4,2,2,2,1,1,1,1] (.node [14,7,7,7,7,6,3,3,3,1,1,1,1,1] (.node [14,7,7,7,7,6,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,7,6,4,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_980 : RowTree := (.node [14,7,7,7,6,5,5,3,3,1,1,1,1,1] degreeTree62_978 degreeTree62_979) + +def degreeTree62_981 : RowTree := (.node [14,8,5,5,5,5,5,5,5,1,1,1,1,1] (.node [14,7,7,7,7,7,3,3,2,1,1,1,1,1] (.node [14,7,7,7,7,6,6,2,1,1,1,1,1,1] (.node [14,7,7,7,7,6,5,3,1,1,1,1,1,1] (.node [14,7,7,7,7,6,5,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,7,7,3,2,2,2,1,1,1,1] (.node [14,7,7,7,7,7,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,7,7,7,7,7,5,2,1,1,1,1,1,1] (.node [14,7,7,7,7,7,4,3,1,1,1,1,1,1] (.node [14,7,7,7,7,7,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,7,7,7,7,7,6,1,1,1,1,1,1,1] .empty .empty))) (.node [14,8,6,6,6,5,5,5,2,1,1,1,1,1] (.node [14,8,6,6,5,5,5,5,3,1,1,1,1,1] (.node [14,8,6,6,5,5,5,4,4,1,1,1,1,1] (.node [14,8,6,5,5,5,5,5,4,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,6,6,6,5,5,4,3,1,1,1,1,1] (.node [14,8,6,6,6,5,4,4,4,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,6,6,6,6,5,3,3,1,1,1,1,1] (.node [14,8,6,6,6,6,5,2,2,2,2,1,1,1] (.node [14,8,6,6,6,6,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,6,6,6,6,5,4,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_982 : RowTree := (.node [14,8,7,6,6,5,5,2,2,2,2,1,1,1] (.node [14,8,7,6,5,5,4,4,4,1,1,1,1,1] (.node [14,8,6,6,6,6,6,4,1,1,1,1,1,1] (.node [14,8,6,6,6,6,6,3,2,1,1,1,1,1] (.node [14,8,6,6,6,6,6,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,5,5,5,5,5,3,1,1,1,1,1] (.node [14,8,7,5,5,5,5,4,4,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,7,6,6,4,4,4,4,1,1,1,1,1] (.node [14,8,7,6,5,5,5,5,2,1,1,1,1,1] (.node [14,8,7,6,5,5,5,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,6,6,5,4,4,3,1,1,1,1,1] .empty .empty))) (.node [14,8,7,6,6,6,4,3,3,1,1,1,1,1] (.node [14,8,7,6,6,5,5,5,1,1,1,1,1,1] (.node [14,8,7,6,6,5,5,4,2,1,1,1,1,1] (.node [14,8,7,6,6,5,5,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,6,6,6,4,2,2,2,2,1,1,1] .empty .empty)) (.node [14,8,7,6,6,6,5,3,2,1,1,1,1,1] (.node [14,8,7,6,6,6,5,2,2,2,1,1,1,1] (.node [14,8,7,6,6,6,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,6,6,6,5,4,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_983 : RowTree := (.node [14,8,6,6,6,6,5,5,1,1,1,1,1,1] degreeTree62_981 degreeTree62_982) + +def degreeTree62_984 : RowTree := (.node [14,7,7,7,7,6,4,4,1,1,1,1,1,1] degreeTree62_980 degreeTree62_983) + +def degreeTree62_985 : RowTree := (.node [14,7,6,6,6,6,6,4,2,1,1,1,1,1] degreeTree62_977 degreeTree62_984) + +def degreeTree62_986 : RowTree := (.node [13,13,7,6,4,4,4,2,2,2,2,1,1,1] degreeTree62_970 degreeTree62_985) + +def degreeTree62_987 : RowTree := (.node [14,8,7,7,6,5,4,4,2,1,1,1,1,1] (.node [14,8,7,7,5,5,5,4,2,1,1,1,1,1] (.node [14,8,7,7,5,5,4,4,3,1,1,1,1,1] (.node [14,8,7,7,5,4,4,4,4,1,1,1,1,1] (.node [14,8,7,6,6,6,6,3,1,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,5,5,5,3,3,1,1,1,1,1] (.node [14,8,7,7,5,5,5,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,8,7,7,6,5,4,2,2,2,2,1,1,1] (.node [14,8,7,7,6,4,4,4,3,1,1,1,1,1] (.node [14,8,7,7,5,5,5,5,1,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,6,5,4,3,3,1,1,1,1,1] .empty .empty))) (.node [14,8,7,7,6,6,4,2,2,2,1,1,1,1] (.node [14,8,7,7,6,5,5,4,1,1,1,1,1,1] (.node [14,8,7,7,6,5,5,3,2,1,1,1,1,1] (.node [14,8,7,7,6,5,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,6,6,3,3,3,1,1,1,1,1] (.node [14,8,7,7,6,6,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,8,7,7,6,6,5,2,2,1,1,1,1,1] (.node [14,8,7,7,6,6,4,4,1,1,1,1,1,1] (.node [14,8,7,7,6,6,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,6,6,5,3,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_988 : RowTree := (.node [14,8,7,7,7,6,2,2,2,2,2,1,1,1] (.node [14,8,7,7,7,5,4,2,2,2,1,1,1,1] (.node [14,8,7,7,7,4,4,4,2,1,1,1,1,1] (.node [14,8,7,7,7,4,4,3,3,1,1,1,1,1] (.node [14,8,7,7,7,4,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,7,5,3,3,3,1,1,1,1,1] (.node [14,8,7,7,7,5,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,8,7,7,7,5,5,2,2,1,1,1,1,1] (.node [14,8,7,7,7,5,4,4,1,1,1,1,1,1] (.node [14,8,7,7,7,5,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,7,5,5,3,1,1,1,1,1,1] .empty .empty))) (.node [14,8,7,7,7,7,2,2,2,2,1,1,1,1] (.node [14,8,7,7,7,6,4,2,2,1,1,1,1,1] (.node [14,8,7,7,7,6,3,3,2,1,1,1,1,1] (.node [14,8,7,7,7,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,8,7,7,7,6,5,2,1,1,1,1,1,1] (.node [14,8,7,7,7,6,4,3,1,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,5,5,5,4,4,4,1,1,1,1,1] (.node [14,8,7,7,7,7,3,3,1,1,1,1,1,1] (.node [14,8,7,7,7,7,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,5,5,5,5,4,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_989 : RowTree := (.node [14,8,7,7,6,6,6,2,1,1,1,1,1,1] degreeTree62_987 degreeTree62_988) + +def degreeTree62_990 : RowTree := (.node [14,8,8,6,6,5,5,2,2,2,1,1,1,1] (.node [14,8,8,6,5,5,5,5,1,1,1,1,1,1] (.node [14,8,8,6,5,5,5,2,2,2,2,1,1,1] (.node [14,8,8,6,5,5,4,4,3,1,1,1,1,1] (.node [14,8,8,6,5,4,4,4,4,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,6,5,5,5,4,2,1,1,1,1,1] (.node [14,8,8,6,5,5,5,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,6,6,5,4,3,3,1,1,1,1,1] (.node [14,8,8,6,6,5,4,2,2,2,2,1,1,1] (.node [14,8,8,6,6,4,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,6,6,5,4,4,2,1,1,1,1,1] .empty .empty))) (.node [14,8,8,6,6,6,4,3,2,1,1,1,1,1] (.node [14,8,8,6,6,6,3,2,2,2,2,1,1,1] (.node [14,8,8,6,6,5,5,4,1,1,1,1,1,1] (.node [14,8,8,6,6,5,5,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,6,6,6,4,2,2,2,1,1,1,1] (.node [14,8,8,6,6,6,3,3,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,6,6,6,5,3,1,1,1,1,1,1] (.node [14,8,8,6,6,6,5,2,2,1,1,1,1,1] (.node [14,8,8,6,6,6,4,4,1,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,4,4,4,4,4,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_991 : RowTree := (.node [14,8,8,7,6,5,3,3,3,1,1,1,1,1] (.node [14,8,8,7,5,5,5,4,1,1,1,1,1,1] (.node [14,8,8,7,5,5,4,4,2,1,1,1,1,1] (.node [14,8,8,7,5,5,4,3,3,1,1,1,1,1] (.node [14,8,8,7,5,5,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,5,5,5,3,2,1,1,1,1,1] (.node [14,8,8,7,5,5,5,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,7,6,4,4,4,2,1,1,1,1,1] (.node [14,8,8,7,6,4,4,3,3,1,1,1,1,1] (.node [14,8,8,7,6,4,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,6,5,3,2,2,2,2,1,1,1] .empty .empty))) (.node [14,8,8,7,6,6,2,2,2,2,2,1,1,1] (.node [14,8,8,7,6,5,4,4,1,1,1,1,1,1] (.node [14,8,8,7,6,5,4,3,2,1,1,1,1,1] (.node [14,8,8,7,6,5,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,6,5,5,3,1,1,1,1,1,1] (.node [14,8,8,7,6,5,5,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,7,6,6,4,2,2,1,1,1,1,1] (.node [14,8,8,7,6,6,3,3,2,1,1,1,1,1] (.node [14,8,8,7,6,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,6,6,4,3,1,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_992 : RowTree := (.node [14,8,8,7,5,4,4,4,3,1,1,1,1,1] degreeTree62_990 degreeTree62_991) + +def degreeTree62_993 : RowTree := (.node [14,8,8,5,5,5,5,5,2,1,1,1,1,1] degreeTree62_989 degreeTree62_992) + +def degreeTree62_994 : RowTree := (.node [14,8,8,7,7,7,2,2,2,1,1,1,1,1] (.node [14,8,8,7,7,5,3,2,2,2,1,1,1,1] (.node [14,8,8,7,7,4,4,3,2,1,1,1,1,1] (.node [14,8,8,7,7,4,4,2,2,2,1,1,1,1] (.node [14,8,8,7,7,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,7,5,2,2,2,2,2,1,1,1] (.node [14,8,8,7,7,4,4,4,1,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,7,7,6,2,2,2,2,1,1,1,1] (.node [14,8,8,7,7,5,4,2,2,1,1,1,1,1] (.node [14,8,8,7,7,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,7,7,6,3,2,2,1,1,1,1,1] .empty .empty))) (.node [14,8,8,8,5,5,3,3,3,1,1,1,1,1] (.node [14,8,8,8,5,4,4,3,3,1,1,1,1,1] (.node [14,8,8,8,5,4,4,2,2,2,2,1,1,1] (.node [14,8,8,8,4,4,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,8,5,5,3,2,2,2,2,1,1,1] (.node [14,8,8,8,5,4,4,4,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,8,5,5,4,4,1,1,1,1,1,1] (.node [14,8,8,8,5,5,4,3,2,1,1,1,1,1] (.node [14,8,8,8,5,5,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,8,5,5,5,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_995 : RowTree := (.node [14,8,8,8,7,3,3,2,2,2,2,1,1,1] (.node [14,8,8,8,6,5,3,3,2,1,1,1,1,1] (.node [14,8,8,8,6,4,4,3,2,1,1,1,1,1] (.node [14,8,8,8,6,4,4,2,2,2,1,1,1,1] (.node [14,8,8,8,6,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,8,6,5,3,2,2,2,1,1,1,1] (.node [14,8,8,8,6,5,2,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,8,8,8,6,6,3,2,2,1,1,1,1,1] (.node [14,8,8,8,6,6,2,2,2,2,1,1,1,1] (.node [14,8,8,8,6,5,4,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,8,7,2,2,2,2,2,2,2,2,1] .empty .empty))) (.node [14,8,8,8,7,5,2,2,2,2,1,1,1,1] (.node [14,8,8,8,7,4,3,2,2,2,1,1,1,1] (.node [14,8,8,8,7,4,2,2,2,2,2,1,1,1] (.node [14,8,8,8,7,3,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,8,7,4,4,2,2,1,1,1,1,1] (.node [14,8,8,8,7,4,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,8,8,8,8,2,2,2,2,2,2,2,1,1] (.node [14,8,8,8,7,6,2,2,2,1,1,1,1,1] (.node [14,8,8,8,7,5,3,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,8,8,8,8,3,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_996 : RowTree := (.node [14,8,8,8,6,4,3,2,2,2,2,1,1,1] degreeTree62_994 degreeTree62_995) + +def degreeTree62_997 : RowTree := (.node [14,9,6,6,6,4,4,4,4,1,1,1,1,1] (.node [14,9,6,5,5,5,5,4,4,1,1,1,1,1] (.node [14,8,8,8,8,4,3,2,2,1,1,1,1,1] (.node [14,8,8,8,8,4,2,2,2,2,1,1,1,1] (.node [14,8,8,8,8,3,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,5,5,5,5,5,5,4,1,1,1,1,1] (.node [14,8,8,8,8,5,2,2,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,6,6,5,5,5,4,3,1,1,1,1,1] (.node [14,9,6,6,5,5,4,4,4,1,1,1,1,1] (.node [14,9,6,5,5,5,5,5,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,6,6,5,5,5,5,2,1,1,1,1,1] .empty .empty))) (.node [14,9,6,6,6,6,4,3,3,1,1,1,1,1] (.node [14,9,6,6,6,5,5,3,3,1,1,1,1,1] (.node [14,9,6,6,6,5,5,2,2,2,2,1,1,1] (.node [14,9,6,6,6,5,4,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,6,6,6,6,4,2,2,2,2,1,1,1] (.node [14,9,6,6,6,5,5,4,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,6,6,6,6,5,3,2,1,1,1,1,1] (.node [14,9,6,6,6,6,5,2,2,2,1,1,1,1] (.node [14,9,6,6,6,6,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,6,6,6,6,6,2,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_998 : RowTree := (.node [14,9,7,6,6,5,4,4,2,1,1,1,1,1] (.node [14,9,7,6,5,5,5,3,3,1,1,1,1,1] (.node [14,9,7,6,5,4,4,4,4,1,1,1,1,1] (.node [14,9,7,5,5,5,5,5,2,1,1,1,1,1] (.node [14,9,7,5,5,5,5,4,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,6,5,5,5,2,2,2,2,1,1,1] (.node [14,9,7,6,5,5,4,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,7,6,6,5,4,2,2,2,2,1,1,1] (.node [14,9,7,6,6,4,4,4,3,1,1,1,1,1] (.node [14,9,7,6,5,5,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,6,6,5,4,3,3,1,1,1,1,1] .empty .empty))) (.node [14,9,7,6,6,6,4,2,2,2,1,1,1,1] (.node [14,9,7,6,6,6,3,2,2,2,2,1,1,1] (.node [14,9,7,6,6,5,5,3,2,1,1,1,1,1] (.node [14,9,7,6,6,5,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,6,6,6,3,3,3,1,1,1,1,1] .empty .empty)) (.node [14,9,7,7,4,4,4,4,4,1,1,1,1,1] (.node [14,9,7,6,6,6,5,2,2,1,1,1,1,1] (.node [14,9,7,6,6,6,4,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,7,5,4,4,4,3,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_999 : RowTree := (.node [14,9,7,5,5,5,4,4,4,1,1,1,1,1] degreeTree62_997 degreeTree62_998) + +def degreeTree62_1000 : RowTree := (.node [14,8,8,8,8,3,3,2,2,2,1,1,1,1] degreeTree62_996 degreeTree62_999) + +def degreeTree62_1001 : RowTree := (.node [14,8,8,7,7,4,3,2,2,2,2,1,1,1] degreeTree62_993 degreeTree62_1000) + +def degreeTree62_1002 : RowTree := (.node [14,9,7,7,6,5,4,3,2,1,1,1,1,1] (.node [14,9,7,7,6,4,4,3,3,1,1,1,1,1] (.node [14,9,7,7,5,5,5,2,2,2,1,1,1,1] (.node [14,9,7,7,5,5,4,4,2,1,1,1,1,1] (.node [14,9,7,7,5,5,4,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,7,6,4,4,2,2,2,2,1,1,1] (.node [14,9,7,7,5,5,5,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,7,7,6,5,3,3,3,1,1,1,1,1] (.node [14,9,7,7,6,5,3,2,2,2,2,1,1,1] (.node [14,9,7,7,6,4,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,7,6,5,4,2,2,2,1,1,1,1] .empty .empty))) (.node [14,9,7,7,7,4,3,2,2,2,2,1,1,1] (.node [14,9,7,7,6,6,3,2,2,2,1,1,1,1] (.node [14,9,7,7,6,6,2,2,2,2,2,1,1,1] (.node [14,9,7,7,6,5,5,2,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,7,6,6,4,2,2,1,1,1,1,1] (.node [14,9,7,7,6,6,3,3,2,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,7,7,7,4,4,3,2,1,1,1,1,1] (.node [14,9,7,7,7,4,4,2,2,2,1,1,1,1] (.node [14,9,7,7,7,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,7,7,7,5,2,2,2,2,2,1,1,1] .empty .empty)))) + +def degreeTree62_1003 : RowTree := (.node [14,9,8,6,5,5,4,3,3,1,1,1,1,1] (.node [14,9,8,5,5,5,5,3,3,1,1,1,1,1] (.node [14,9,8,5,5,4,4,4,4,1,1,1,1,1] (.node [14,9,7,7,7,6,2,2,2,2,1,1,1,1] (.node [14,9,7,7,7,5,3,3,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,8,5,5,5,5,2,2,2,2,1,1,1] (.node [14,9,8,5,5,5,4,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,8,6,5,4,4,4,3,1,1,1,1,1] (.node [14,9,8,6,4,4,4,4,4,1,1,1,1,1] (.node [14,9,8,5,5,5,5,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,8,6,5,5,4,2,2,2,2,1,1,1] .empty .empty))) (.node [14,9,8,6,6,4,4,4,2,1,1,1,1,1] (.node [14,9,8,6,5,5,5,3,2,1,1,1,1,1] (.node [14,9,8,6,5,5,5,2,2,2,1,1,1,1] (.node [14,9,8,6,5,5,4,4,2,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,8,6,6,4,4,3,3,1,1,1,1,1] (.node [14,9,8,6,6,4,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,9,8,6,6,5,4,2,2,2,1,1,1,1] (.node [14,9,8,6,6,5,3,3,3,1,1,1,1,1] (.node [14,9,8,6,6,5,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,8,6,6,5,4,3,2,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_1004 : RowTree := (.node [14,9,7,7,7,5,3,2,2,2,1,1,1,1] degreeTree62_1002 degreeTree62_1003) + +def degreeTree62_1005 : RowTree := (.node [14,9,8,7,6,4,3,2,2,2,2,1,1,1] (.node [14,9,8,7,5,4,4,4,2,1,1,1,1,1] (.node [14,9,8,7,4,4,4,4,3,1,1,1,1,1] (.node [14,9,8,6,6,6,3,3,2,1,1,1,1,1] (.node [14,9,8,6,6,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,8,7,5,4,4,3,3,1,1,1,1,1] (.node [14,9,8,7,5,4,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,9,8,7,5,5,4,2,2,2,1,1,1,1] (.node [14,9,8,7,5,5,3,3,3,1,1,1,1,1] (.node [14,9,8,7,5,5,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,8,7,5,5,4,3,2,1,1,1,1,1] .empty .empty))) (.node [14,9,8,7,7,2,2,2,2,2,2,2,2,1] (.node [14,9,8,7,6,5,2,2,2,2,2,1,1,1] (.node [14,9,8,7,6,4,4,2,2,2,1,1,1,1] (.node [14,9,8,7,6,4,3,3,3,1,1,1,1,1] .empty .empty) .empty) (.node [14,9,8,7,6,6,2,2,2,2,1,1,1,1] (.node [14,9,8,7,6,5,3,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [14,9,8,7,7,4,2,2,2,2,2,1,1,1] (.node [14,9,8,7,7,3,3,3,3,1,1,1,1,1] (.node [14,9,8,7,7,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,8,7,7,4,3,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_1006 : RowTree := (.node [14,9,8,8,6,3,3,3,3,1,1,1,1,1] (.node [14,9,8,8,5,4,4,2,2,2,1,1,1,1] (.node [14,9,8,8,4,4,4,4,2,1,1,1,1,1] (.node [14,9,8,8,4,4,4,3,3,1,1,1,1,1] (.node [14,9,8,8,4,4,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,8,8,5,4,3,3,3,1,1,1,1,1] (.node [14,9,8,8,5,4,3,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,9,8,8,6,2,2,2,2,2,2,2,2,1] (.node [14,9,8,8,5,5,3,2,2,2,1,1,1,1] (.node [14,9,8,8,5,5,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,8,8,6,3,3,2,2,2,2,1,1,1] .empty .empty))) (.node [14,9,8,8,7,3,3,2,2,2,1,1,1,1] (.node [14,9,8,8,6,5,2,2,2,2,1,1,1,1] (.node [14,9,8,8,6,4,3,2,2,2,1,1,1,1] (.node [14,9,8,8,6,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,8,8,7,3,2,2,2,2,2,1,1,1] (.node [14,9,8,8,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [14,9,8,8,8,3,2,2,2,2,1,1,1,1] (.node [14,9,8,8,8,2,2,2,2,2,2,1,1,1] (.node [14,9,8,8,7,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,9,5,4,4,4,4,4,1,1,1,1,1] .empty .empty)))) + +def degreeTree62_1007 : RowTree := (.node [14,9,8,7,7,5,2,2,2,2,1,1,1,1] degreeTree62_1005 degreeTree62_1006) + +def degreeTree62_1008 : RowTree := (.node [14,9,8,6,6,6,2,2,2,2,2,1,1,1] degreeTree62_1004 degreeTree62_1007) + +def degreeTree62_1009 : RowTree := (.node [14,9,9,6,6,4,4,2,2,2,1,1,1,1] (.node [14,9,9,6,5,4,4,3,3,1,1,1,1,1] (.node [14,9,9,5,5,5,5,2,2,2,1,1,1,1] (.node [14,9,9,5,5,5,4,3,3,1,1,1,1,1] (.node [14,9,9,5,5,5,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,9,6,5,4,4,2,2,2,2,1,1,1] (.node [14,9,9,6,4,4,4,4,3,1,1,1,1,1] .empty .empty) .empty)) (.node [14,9,9,6,5,5,4,2,2,2,1,1,1,1] (.node [14,9,9,6,5,5,3,3,3,1,1,1,1,1] (.node [14,9,9,6,5,5,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,9,6,6,4,3,2,2,2,2,1,1,1] .empty .empty))) (.node [14,9,9,7,5,4,3,2,2,2,2,1,1,1] (.node [14,9,9,6,6,6,2,2,2,2,1,1,1,1] (.node [14,9,9,6,6,5,3,2,2,2,1,1,1,1] (.node [14,9,9,6,6,5,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,9,7,4,4,4,3,3,1,1,1,1,1] (.node [14,9,9,7,4,4,4,2,2,2,2,1,1,1] .empty .empty) .empty)) (.node [14,9,9,7,5,5,3,2,2,2,1,1,1,1] (.node [14,9,9,7,5,5,2,2,2,2,2,1,1,1] (.node [14,9,9,7,5,4,4,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,9,7,6,2,2,2,2,2,2,2,2,1] .empty .empty)))) + +def degreeTree62_1010 : RowTree := (.node [14,9,9,8,5,3,3,2,2,2,2,1,1,1] (.node [14,9,9,7,7,3,3,2,2,2,1,1,1,1] (.node [14,9,9,7,6,5,2,2,2,2,1,1,1,1] (.node [14,9,9,7,6,4,3,2,2,2,1,1,1,1] (.node [14,9,9,7,6,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,9,7,7,3,2,2,2,2,2,1,1,1] (.node [14,9,9,7,7,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [14,9,9,8,4,4,4,2,2,2,1,1,1,1] (.node [14,9,9,8,4,4,3,2,2,2,2,1,1,1] (.node [14,9,9,7,7,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,9,8,5,2,2,2,2,2,2,2,2,1] .empty .empty))) (.node [14,9,9,8,6,3,3,2,2,2,1,1,1,1] (.node [14,9,9,8,5,5,2,2,2,2,1,1,1,1] (.node [14,9,9,8,5,4,3,2,2,2,1,1,1,1] (.node [14,9,9,8,5,4,2,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,9,8,6,3,2,2,2,2,2,1,1,1] (.node [14,9,9,8,6,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [14,9,9,8,7,3,2,2,2,2,1,1,1,1] (.node [14,9,9,8,7,2,2,2,2,2,2,1,1,1] (.node [14,9,9,8,6,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,9,8,8,2,2,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_1011 : RowTree := (.node [14,9,9,7,6,3,3,2,2,2,2,1,1,1] degreeTree62_1009 degreeTree62_1010) + +def degreeTree62_1012 : RowTree := (.node [14,10,6,6,5,5,5,2,2,2,2,1,1,1] (.node [14,9,9,9,5,3,3,2,2,2,1,1,1,1] (.node [14,9,9,9,4,4,3,2,2,2,1,1,1,1] (.node [14,9,9,9,4,4,2,2,2,2,2,1,1,1] (.node [14,9,9,9,4,3,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,9,9,9,5,3,2,2,2,2,2,1,1,1] (.node [14,9,9,9,5,2,2,2,2,2,2,2,1,1] .empty .empty) .empty)) (.node [14,9,9,9,6,3,2,2,2,2,1,1,1,1] (.node [14,9,9,9,6,2,2,2,2,2,2,1,1,1] (.node [14,9,9,9,5,4,2,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,9,9,9,7,2,2,2,2,2,1,1,1,1] .empty .empty))) (.node [14,10,7,6,5,5,4,2,2,2,2,1,1,1] (.node [14,10,6,6,6,6,3,2,2,2,2,1,1,1] (.node [14,10,6,6,6,5,5,2,2,2,1,1,1,1] (.node [14,10,6,6,6,5,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,10,7,5,5,5,5,2,2,2,2,1,1,1] (.node [14,10,6,6,6,6,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [14,10,7,6,6,5,3,2,2,2,2,1,1,1] (.node [14,10,7,6,6,4,4,2,2,2,2,1,1,1] (.node [14,10,7,6,5,5,5,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,10,7,6,6,5,4,2,2,2,1,1,1,1] .empty .empty)))) + +def degreeTree62_1013 : RowTree := (.node [14,11,6,6,5,5,4,2,2,2,2,1,1,1] (.node [14,10,7,7,6,5,2,2,2,2,2,1,1,1] (.node [14,10,7,7,5,5,3,2,2,2,2,1,1,1] (.node [14,10,7,7,5,4,4,2,2,2,2,1,1,1] (.node [14,10,7,6,6,6,3,2,2,2,1,1,1,1] .empty .empty) .empty) (.node [14,10,7,7,6,4,3,2,2,2,2,1,1,1] (.node [14,10,7,7,5,5,4,2,2,2,1,1,1,1] .empty .empty) .empty)) (.node [14,10,7,7,7,4,2,2,2,2,2,1,1,1] (.node [14,10,7,7,7,3,3,2,2,2,2,1,1,1] (.node [14,10,7,7,7,2,2,2,2,2,2,2,2,1] .empty .empty) .empty) (.node [14,11,6,5,5,5,5,2,2,2,2,1,1,1] .empty .empty))) (.node [14,11,7,6,5,4,4,2,2,2,2,1,1,1] (.node [14,11,6,6,6,6,2,2,2,2,2,1,1,1] (.node [14,11,6,6,6,5,3,2,2,2,2,1,1,1] (.node [14,11,6,6,6,4,4,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,11,7,5,5,5,4,2,2,2,2,1,1,1] .empty .empty)) (.node [14,11,7,7,6,2,2,2,2,2,2,2,2,1] (.node [14,11,7,7,4,4,4,2,2,2,2,1,1,1] (.node [14,11,7,6,5,5,3,2,2,2,2,1,1,1] .empty .empty) .empty) (.node [14,11,7,7,7,2,2,2,2,2,2,2,1,1] .empty .empty)))) + +def degreeTree62_1014 : RowTree := (.node [14,10,7,6,6,6,2,2,2,2,2,1,1,1] degreeTree62_1012 degreeTree62_1013) + +def degreeTree62_1015 : RowTree := (.node [14,9,9,9,4,2,2,2,2,2,2,2,2,1] degreeTree62_1011 degreeTree62_1014) + +def degreeTree62_1016 : RowTree := (.node [14,9,9,5,5,4,4,4,3,1,1,1,1,1] degreeTree62_1008 degreeTree62_1015) + +def degreeTree62_1017 : RowTree := (.node [14,9,7,7,5,5,4,2,2,2,2,1,1,1] degreeTree62_1001 degreeTree62_1016) + +def degreeTree62_1018 : RowTree := (.node [14,8,7,6,6,6,6,2,2,1,1,1,1,1] degreeTree62_986 degreeTree62_1017) + +def degreeTree62_1019 : RowTree := (.node [13,11,9,9,5,5,2,2,1,1,1,1,1,1] degreeTree62_955 degreeTree62_1018) + +def degreeTree62_1020 : RowTree := (.node [13,10,8,8,7,7,2,1,1,1,1,1,1,1] degreeTree62_892 degreeTree62_1019) + +def degreeTree62_1021 : RowTree := (.node [13,8,7,6,6,6,5,3,2,2,2,1,1] degreeTree62_765 degreeTree62_1020) + +def degreeTree62_1022 : RowTree := (.node [12,9,9,9,7,3,2,2,2,2,2,1,1,1] degreeTree62_510 degreeTree62_1021) + +def degreeTree62 : RowTree := degreeTree62_1022 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData64.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData64.lean index bd8c6b6ec6d508325364a6d6c975ba092f97835a..4613bb94f8743f7b6bc9eb10e943e14b45cd00ed 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData64.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData64.lean @@ -1,23 +1,23 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 64. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree64_0 : RowTree := (.node [13,11,10,9,3,2,2,2,2,2,2,2,2,2] (.node [12,11,10,10,3,2,2,2,2,2,2,2,2,2] (.node [11,11,11,10,3,2,2,2,2,2,2,2,2,2] (.node [8,8,8,8,8,8,8,8] .empty .empty) (.node [11,11,11,11,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [12,11,11,10,2,2,2,2,2,2,2,2,2,2] (.node [12,11,11,9,3,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [13,10,10,10,3,2,2,2,2,2,2,2,2,2] .empty .empty))) (.node [13,12,9,9,3,2,2,2,2,2,2,2,2,2] (.node [13,11,11,8,3,2,2,2,2,2,2,2,2,2] (.node [13,11,10,10,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [13,11,11,9,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [13,13,9,9,2,2,2,2,2,2,2,2,2,2] (.node [13,13,9,8,3,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [14,11,9,9,3,2,2,2,2,2,2,2,2,2] .empty .empty)))) - -def degreeTree64 : RowTree := degreeTree64_0 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 64. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree64_0 : RowTree := (.node [13,11,10,9,3,2,2,2,2,2,2,2,2,2] (.node [12,11,10,10,3,2,2,2,2,2,2,2,2,2] (.node [11,11,11,10,3,2,2,2,2,2,2,2,2,2] (.node [8,8,8,8,8,8,8,8] .empty .empty) (.node [11,11,11,11,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [12,11,11,10,2,2,2,2,2,2,2,2,2,2] (.node [12,11,11,9,3,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [13,10,10,10,3,2,2,2,2,2,2,2,2,2] .empty .empty))) (.node [13,12,9,9,3,2,2,2,2,2,2,2,2,2] (.node [13,11,11,8,3,2,2,2,2,2,2,2,2,2] (.node [13,11,10,10,2,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [13,11,11,9,2,2,2,2,2,2,2,2,2,2] .empty .empty)) (.node [13,13,9,9,2,2,2,2,2,2,2,2,2,2] (.node [13,13,9,8,3,2,2,2,2,2,2,2,2,2] .empty .empty) (.node [14,11,9,9,3,2,2,2,2,2,2,2,2,2] .empty .empty)))) + +def degreeTree64 : RowTree := degreeTree64_0 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData89.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData89.lean index 40290f68fc10fcff75ffd4a3520bc2d194057193..9c8f7610a5aec9b590da4d660220bc2c949dbd5d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData89.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeData89.lean @@ -1,23 +1,23 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Degree Tree Data 89. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -def degreeTree89_0 : RowTree := (.node [10,10,10,10,10,10,10,10,9] .empty .empty) - -def degreeTree89 : RowTree := degreeTree89_0 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Degree Tree Data 89. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +def degreeTree89_0 : RowTree := (.node [10,10,10,10,10,10,10,10,9] .empty .empty) + +def degreeTree89 : RowTree := degreeTree89_0 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof116.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof116.lean index f39fef51478625f48128c80e032d23233227c967..f7ea308112f106c9e223135c650003aa058fe56c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof116.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof116.lean @@ -1,29 +1,29 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData116 -import OAI.RepresentationTheory.UniversalSquare.Finite.PieriRows116 - -namespace OAI - -/-! Degree Tree Proof 116. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree116_0All : degreeTree116_0.All (RowSquare [22,20,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,1,1]) := by - exact ⟨pieriSquare116_2,⟨pieriSquare116_1,⟨pieriSquare116_0,True.intro,True.intro⟩,True.intro⟩,⟨pieriSquare116_3,True.intro,True.intro⟩⟩ - -lemma degreeTreeAll116 : degreeTree116.All - (fun rs => SquareOccurs (candidate 12 9 1) (rowDiagram rs)) := by - have hp : rowDiagram [22,20,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,1,1] = candidate 12 9 1 := rowDiagram_candidate (M := 12) (b := 9) (δ := 1) (by decide) - rw [← hp] - exact degreeTree116_0All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData116 +import OAI.RepresentationTheory.UniversalSquare.Finite.PieriRows116 + +namespace OAI + +/-! Degree Tree Proof 116. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree116_0All : degreeTree116_0.All (RowSquare [22,20,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,1,1]) := by + exact ⟨pieriSquare116_2,⟨pieriSquare116_1,⟨pieriSquare116_0,True.intro,True.intro⟩,True.intro⟩,⟨pieriSquare116_3,True.intro,True.intro⟩⟩ + +lemma degreeTreeAll116 : degreeTree116.All + (fun rs => SquareOccurs (candidate 12 9 1) (rowDiagram rs)) := by + have hp : rowDiagram [22,20,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,1,1] = candidate 12 9 1 := rowDiagram_candidate (M := 12) (b := 9) (δ := 1) (by decide) + rw [← hp] + exact degreeTree116_0All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof118.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof118.lean index f8553200f43745c51a8da03b92283a1d7de9d83a..34e252b44e4feed8af480718c39be4e3b1dad097 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof118.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof118.lean @@ -1,29 +1,29 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData118 -import OAI.RepresentationTheory.UniversalSquare.Finite.PieriRows118 - -namespace OAI - -/-! Degree Tree Proof 118. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree118_0All : degreeTree118_0.All (RowSquare [22,21,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,2,1]) := by - exact ⟨pieriSquare118_1,⟨pieriSquare118_0,True.intro,True.intro⟩,True.intro⟩ - -lemma degreeTreeAll118 : degreeTree118.All - (fun rs => SquareOccurs (candidate 12 10 0) (rowDiagram rs)) := by - have hp : rowDiagram [22,21,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,2,1] = candidate 12 10 0 := rowDiagram_candidate (M := 12) (b := 10) (δ := 0) (by decide) - rw [← hp] - exact degreeTree118_0All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData118 +import OAI.RepresentationTheory.UniversalSquare.Finite.PieriRows118 + +namespace OAI + +/-! Degree Tree Proof 118. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree118_0All : degreeTree118_0.All (RowSquare [22,21,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,2,1]) := by + exact ⟨pieriSquare118_1,⟨pieriSquare118_0,True.intro,True.intro⟩,True.intro⟩ + +lemma degreeTreeAll118 : degreeTree118.All + (fun rs => SquareOccurs (candidate 12 10 0) (rowDiagram rs)) := by + have hp : rowDiagram [22,21,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,2,1] = candidate 12 10 0 := rowDiagram_candidate (M := 12) (b := 10) (δ := 0) (by decide) + rw [← hp] + exact degreeTree118_0All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof14.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof14.lean index 823afbfe69774e332b67c950a334bb5764ae0293..c8d7ddf63d9d224ee71e364278f44a1bb5aa88d8 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof14.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof14.lean @@ -1,29 +1,29 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData14 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes5 - -namespace OAI - -/-! Degree Tree Proof 14. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree14_0All : degreeTree14_0.All (RowSquare [5,4,2,2,1]) := by - exact ⟨sg2613,⟨sg2612,True.intro,True.intro⟩,True.intro⟩ - -lemma degreeTreeAll14 : degreeTree14.All - (fun rs => SquareOccurs (candidate 4 1 0) (rowDiagram rs)) := by - have hp : rowDiagram [5,4,2,2,1] = candidate 4 1 0 := rowDiagram_candidate (M := 4) (b := 1) (δ := 0) (by decide) - rw [← hp] - exact degreeTree14_0All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData14 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes5 + +namespace OAI + +/-! Degree Tree Proof 14. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree14_0All : degreeTree14_0.All (RowSquare [5,4,2,2,1]) := by + exact ⟨sg2613,⟨sg2612,True.intro,True.intro⟩,True.intro⟩ + +lemma degreeTreeAll14 : degreeTree14.All + (fun rs => SquareOccurs (candidate 4 1 0) (rowDiagram rs)) := by + have hp : rowDiagram [5,4,2,2,1] = candidate 4 1 0 := rowDiagram_candidate (M := 4) (b := 1) (δ := 0) (by decide) + rw [← hp] + exact degreeTree14_0All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof16.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof16.lean index 67d620cb2393722df3ebbbb57cccc90605b5cc78..fb76faebb3f02a40551c5dba723f67f4c1b226b1 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof16.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof16.lean @@ -1,29 +1,29 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData16 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes8 - -namespace OAI - -/-! Degree Tree Proof 16. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree16_0All : degreeTree16_0.All (RowSquare [6,4,2,2,1,1]) := by - exact ⟨sg4098,⟨sg4092,⟨sg4089,⟨sg4087,⟨sg4086,True.intro,True.intro⟩,⟨sg4088,True.intro,True.intro⟩⟩,⟨sg4091,⟨sg4090,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg4095,⟨sg4094,⟨sg4093,True.intro,True.intro⟩,True.intro⟩,⟨sg4097,⟨sg4096,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg4105,⟨sg4101,⟨sg4100,⟨sg4099,True.intro,True.intro⟩,True.intro⟩,⟨sg4104,⟨sg4103,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg4108,⟨sg4107,⟨sg4106,True.intro,True.intro⟩,True.intro⟩,⟨sg4110,⟨sg4109,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTreeAll16 : degreeTree16.All - (fun rs => SquareOccurs (candidate 4 1 1) (rowDiagram rs)) := by - have hp : rowDiagram [6,4,2,2,1,1] = candidate 4 1 1 := rowDiagram_candidate (M := 4) (b := 1) (δ := 1) (by decide) - rw [← hp] - exact degreeTree16_0All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData16 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes8 + +namespace OAI + +/-! Degree Tree Proof 16. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree16_0All : degreeTree16_0.All (RowSquare [6,4,2,2,1,1]) := by + exact ⟨sg4098,⟨sg4092,⟨sg4089,⟨sg4087,⟨sg4086,True.intro,True.intro⟩,⟨sg4088,True.intro,True.intro⟩⟩,⟨sg4091,⟨sg4090,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg4095,⟨sg4094,⟨sg4093,True.intro,True.intro⟩,True.intro⟩,⟨sg4097,⟨sg4096,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg4105,⟨sg4101,⟨sg4100,⟨sg4099,True.intro,True.intro⟩,True.intro⟩,⟨sg4104,⟨sg4103,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg4108,⟨sg4107,⟨sg4106,True.intro,True.intro⟩,True.intro⟩,⟨sg4110,⟨sg4109,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTreeAll16 : degreeTree16.All + (fun rs => SquareOccurs (candidate 4 1 1) (rowDiagram rs)) := by + have hp : rowDiagram [6,4,2,2,1,1] = candidate 4 1 1 := rowDiagram_candidate (M := 4) (b := 1) (δ := 1) (by decide) + rw [← hp] + exact degreeTree16_0All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof18.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof18.lean index c373761cf715945dc760b0836e388e9fa3850e0f..853220425c20c1408899cc6120839f43e3ec65ee 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof18.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof18.lean @@ -1,30 +1,30 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData18 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes12 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes13 - -namespace OAI - -/-! Degree Tree Proof 18. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree18_0All : degreeTree18_0.All (RowSquare [6,5,2,2,2,1]) := by - exact ⟨sg5719,⟨sg5713,⟨sg5710,⟨sg5708,⟨sg5707,True.intro,True.intro⟩,⟨sg5709,True.intro,True.intro⟩⟩,⟨sg5712,⟨sg5711,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg5716,⟨sg5715,⟨sg5714,True.intro,True.intro⟩,True.intro⟩,⟨sg5718,⟨sg5717,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg5725,⟨sg5722,⟨sg5721,⟨sg5720,True.intro,True.intro⟩,True.intro⟩,⟨sg5724,⟨sg5723,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg5728,⟨sg5727,⟨sg5726,True.intro,True.intro⟩,True.intro⟩,⟨sg5730,⟨sg5729,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTreeAll18 : degreeTree18.All - (fun rs => SquareOccurs (candidate 4 2 0) (rowDiagram rs)) := by - have hp : rowDiagram [6,5,2,2,2,1] = candidate 4 2 0 := rowDiagram_candidate (M := 4) (b := 2) (δ := 0) (by decide) - rw [← hp] - exact degreeTree18_0All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData18 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes12 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes13 + +namespace OAI + +/-! Degree Tree Proof 18. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree18_0All : degreeTree18_0.All (RowSquare [6,5,2,2,2,1]) := by + exact ⟨sg5719,⟨sg5713,⟨sg5710,⟨sg5708,⟨sg5707,True.intro,True.intro⟩,⟨sg5709,True.intro,True.intro⟩⟩,⟨sg5712,⟨sg5711,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg5716,⟨sg5715,⟨sg5714,True.intro,True.intro⟩,True.intro⟩,⟨sg5718,⟨sg5717,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg5725,⟨sg5722,⟨sg5721,⟨sg5720,True.intro,True.intro⟩,True.intro⟩,⟨sg5724,⟨sg5723,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg5728,⟨sg5727,⟨sg5726,True.intro,True.intro⟩,True.intro⟩,⟨sg5730,⟨sg5729,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTreeAll18 : degreeTree18.All + (fun rs => SquareOccurs (candidate 4 2 0) (rowDiagram rs)) := by + have hp : rowDiagram [6,5,2,2,2,1] = candidate 4 2 0 := rowDiagram_candidate (M := 4) (b := 2) (δ := 0) (by decide) + rw [← hp] + exact degreeTree18_0All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof19.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof19.lean index 2e5055c0f111db00690201f20c8c7763ebcad09a..352eba6c36f827a05464fbebe502cfc6101d1ca3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof19.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof19.lean @@ -1,29 +1,29 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData19 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes14 - -namespace OAI - -/-! Degree Tree Proof 19. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree19_0All : degreeTree19_0.All (RowSquare [6,5,3,2,2,1]) := by - exact ⟨sg6462,⟨sg6461,True.intro,True.intro⟩,⟨sg6463,True.intro,True.intro⟩⟩ - -lemma degreeTreeAll19 : degreeTree19.All - (fun rs => SquareOccurs (candidate 5 1 0) (rowDiagram rs)) := by - have hp : rowDiagram [6,5,3,2,2,1] = candidate 5 1 0 := rowDiagram_candidate (M := 5) (b := 1) (δ := 0) (by decide) - rw [← hp] - exact degreeTree19_0All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData19 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes14 + +namespace OAI + +/-! Degree Tree Proof 19. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree19_0All : degreeTree19_0.All (RowSquare [6,5,3,2,2,1]) := by + exact ⟨sg6462,⟨sg6461,True.intro,True.intro⟩,⟨sg6463,True.intro,True.intro⟩⟩ + +lemma degreeTreeAll19 : degreeTree19.All + (fun rs => SquareOccurs (candidate 5 1 0) (rowDiagram rs)) := by + have hp : rowDiagram [6,5,3,2,2,1] = candidate 5 1 0 := rowDiagram_candidate (M := 5) (b := 1) (δ := 0) (by decide) + rw [← hp] + exact degreeTree19_0All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof20.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof20.lean index ccc90f81e5341bbe91c15ef1aab3cea4fe3fb192..ccc4de9a4d9ceaa20284ab7f88ae4ee3f4711d09 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof20.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof20.lean @@ -1,71 +1,71 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData20 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes18 - -namespace OAI - -/-! Degree Tree Proof 20. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree20_0All : degreeTree20_0.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7869,⟨sg7865,⟨sg7863,⟨sg7862,⟨sg7861,True.intro,True.intro⟩,True.intro⟩,⟨sg7864,True.intro,True.intro⟩⟩,⟨sg7867,⟨sg7866,True.intro,True.intro⟩,⟨sg7868,True.intro,True.intro⟩⟩⟩,⟨sg7873,⟨sg7871,⟨sg7870,True.intro,True.intro⟩,⟨sg7872,True.intro,True.intro⟩⟩,⟨sg7875,⟨sg7874,True.intro,True.intro⟩,⟨sg7876,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree20_1All : degreeTree20_1.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7886,⟨sg7882,⟨sg7880,⟨sg7879,⟨sg7878,True.intro,True.intro⟩,True.intro⟩,⟨sg7881,True.intro,True.intro⟩⟩,⟨sg7884,⟨sg7883,True.intro,True.intro⟩,⟨sg7885,True.intro,True.intro⟩⟩⟩,⟨sg7890,⟨sg7888,⟨sg7887,True.intro,True.intro⟩,⟨sg7889,True.intro,True.intro⟩⟩,⟨sg7892,⟨sg7891,True.intro,True.intro⟩,⟨sg7893,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree20_2All : degreeTree20_2.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7877,degreeTree20_0All,degreeTree20_1All⟩ - -lemma degreeTree20_3All : degreeTree20_3.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7903,⟨sg7899,⟨sg7897,⟨sg7896,⟨sg7895,True.intro,True.intro⟩,True.intro⟩,⟨sg7898,True.intro,True.intro⟩⟩,⟨sg7901,⟨sg7900,True.intro,True.intro⟩,⟨sg7902,True.intro,True.intro⟩⟩⟩,⟨sg7907,⟨sg7905,⟨sg7904,True.intro,True.intro⟩,⟨sg7906,True.intro,True.intro⟩⟩,⟨sg7909,⟨sg7908,True.intro,True.intro⟩,⟨sg7910,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree20_4All : degreeTree20_4.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7919,⟨sg7915,⟨sg7913,⟨sg7912,True.intro,True.intro⟩,⟨sg7914,True.intro,True.intro⟩⟩,⟨sg7917,⟨sg7916,True.intro,True.intro⟩,⟨sg7918,True.intro,True.intro⟩⟩⟩,⟨sg7923,⟨sg7921,⟨sg7920,True.intro,True.intro⟩,⟨sg7922,True.intro,True.intro⟩⟩,⟨sg7925,⟨sg7924,True.intro,True.intro⟩,⟨sg7926,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree20_5All : degreeTree20_5.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7911,degreeTree20_3All,degreeTree20_4All⟩ - -lemma degreeTree20_6All : degreeTree20_6.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7894,degreeTree20_2All,degreeTree20_5All⟩ - -lemma degreeTree20_7All : degreeTree20_7.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7936,⟨sg7932,⟨sg7930,⟨sg7929,⟨sg7928,True.intro,True.intro⟩,True.intro⟩,⟨sg7931,True.intro,True.intro⟩⟩,⟨sg7934,⟨sg7933,True.intro,True.intro⟩,⟨sg7935,True.intro,True.intro⟩⟩⟩,⟨sg7940,⟨sg7938,⟨sg7937,True.intro,True.intro⟩,⟨sg7939,True.intro,True.intro⟩⟩,⟨sg7942,⟨sg7941,True.intro,True.intro⟩,⟨sg7943,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree20_8All : degreeTree20_8.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7952,⟨sg7948,⟨sg7946,⟨sg7945,True.intro,True.intro⟩,⟨sg7947,True.intro,True.intro⟩⟩,⟨sg7950,⟨sg7949,True.intro,True.intro⟩,⟨sg7951,True.intro,True.intro⟩⟩⟩,⟨sg7956,⟨sg7954,⟨sg7953,True.intro,True.intro⟩,⟨sg7955,True.intro,True.intro⟩⟩,⟨sg7958,⟨sg7957,True.intro,True.intro⟩,⟨sg7959,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree20_9All : degreeTree20_9.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7944,degreeTree20_7All,degreeTree20_8All⟩ - -lemma degreeTree20_10All : degreeTree20_10.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7969,⟨sg7965,⟨sg7963,⟨sg7962,⟨sg7961,True.intro,True.intro⟩,True.intro⟩,⟨sg7964,True.intro,True.intro⟩⟩,⟨sg7967,⟨sg7966,True.intro,True.intro⟩,⟨sg7968,True.intro,True.intro⟩⟩⟩,⟨sg7973,⟨sg7971,⟨sg7970,True.intro,True.intro⟩,⟨sg7972,True.intro,True.intro⟩⟩,⟨sg7975,⟨sg7974,True.intro,True.intro⟩,⟨sg7976,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree20_11All : degreeTree20_11.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7985,⟨sg7981,⟨sg7979,⟨sg7978,True.intro,True.intro⟩,⟨sg7980,True.intro,True.intro⟩⟩,⟨sg7983,⟨sg7982,True.intro,True.intro⟩,⟨sg7984,True.intro,True.intro⟩⟩⟩,⟨sg7989,⟨sg7987,⟨sg7986,True.intro,True.intro⟩,⟨sg7988,True.intro,True.intro⟩⟩,⟨sg7991,⟨sg7990,True.intro,True.intro⟩,⟨sg7992,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree20_12All : degreeTree20_12.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7977,degreeTree20_10All,degreeTree20_11All⟩ - -lemma degreeTree20_13All : degreeTree20_13.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7960,degreeTree20_9All,degreeTree20_12All⟩ - -lemma degreeTree20_14All : degreeTree20_14.All (RowSquare [7,5,2,2,2,1,1]) := by - exact ⟨sg7927,degreeTree20_6All,degreeTree20_13All⟩ - -lemma degreeTreeAll20 : degreeTree20.All - (fun rs => SquareOccurs (candidate 4 2 1) (rowDiagram rs)) := by - have hp : rowDiagram [7,5,2,2,2,1,1] = candidate 4 2 1 := rowDiagram_candidate (M := 4) (b := 2) (δ := 1) (by decide) - rw [← hp] - exact degreeTree20_14All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData20 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes18 + +namespace OAI + +/-! Degree Tree Proof 20. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree20_0All : degreeTree20_0.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7869,⟨sg7865,⟨sg7863,⟨sg7862,⟨sg7861,True.intro,True.intro⟩,True.intro⟩,⟨sg7864,True.intro,True.intro⟩⟩,⟨sg7867,⟨sg7866,True.intro,True.intro⟩,⟨sg7868,True.intro,True.intro⟩⟩⟩,⟨sg7873,⟨sg7871,⟨sg7870,True.intro,True.intro⟩,⟨sg7872,True.intro,True.intro⟩⟩,⟨sg7875,⟨sg7874,True.intro,True.intro⟩,⟨sg7876,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree20_1All : degreeTree20_1.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7886,⟨sg7882,⟨sg7880,⟨sg7879,⟨sg7878,True.intro,True.intro⟩,True.intro⟩,⟨sg7881,True.intro,True.intro⟩⟩,⟨sg7884,⟨sg7883,True.intro,True.intro⟩,⟨sg7885,True.intro,True.intro⟩⟩⟩,⟨sg7890,⟨sg7888,⟨sg7887,True.intro,True.intro⟩,⟨sg7889,True.intro,True.intro⟩⟩,⟨sg7892,⟨sg7891,True.intro,True.intro⟩,⟨sg7893,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree20_2All : degreeTree20_2.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7877,degreeTree20_0All,degreeTree20_1All⟩ + +lemma degreeTree20_3All : degreeTree20_3.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7903,⟨sg7899,⟨sg7897,⟨sg7896,⟨sg7895,True.intro,True.intro⟩,True.intro⟩,⟨sg7898,True.intro,True.intro⟩⟩,⟨sg7901,⟨sg7900,True.intro,True.intro⟩,⟨sg7902,True.intro,True.intro⟩⟩⟩,⟨sg7907,⟨sg7905,⟨sg7904,True.intro,True.intro⟩,⟨sg7906,True.intro,True.intro⟩⟩,⟨sg7909,⟨sg7908,True.intro,True.intro⟩,⟨sg7910,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree20_4All : degreeTree20_4.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7919,⟨sg7915,⟨sg7913,⟨sg7912,True.intro,True.intro⟩,⟨sg7914,True.intro,True.intro⟩⟩,⟨sg7917,⟨sg7916,True.intro,True.intro⟩,⟨sg7918,True.intro,True.intro⟩⟩⟩,⟨sg7923,⟨sg7921,⟨sg7920,True.intro,True.intro⟩,⟨sg7922,True.intro,True.intro⟩⟩,⟨sg7925,⟨sg7924,True.intro,True.intro⟩,⟨sg7926,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree20_5All : degreeTree20_5.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7911,degreeTree20_3All,degreeTree20_4All⟩ + +lemma degreeTree20_6All : degreeTree20_6.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7894,degreeTree20_2All,degreeTree20_5All⟩ + +lemma degreeTree20_7All : degreeTree20_7.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7936,⟨sg7932,⟨sg7930,⟨sg7929,⟨sg7928,True.intro,True.intro⟩,True.intro⟩,⟨sg7931,True.intro,True.intro⟩⟩,⟨sg7934,⟨sg7933,True.intro,True.intro⟩,⟨sg7935,True.intro,True.intro⟩⟩⟩,⟨sg7940,⟨sg7938,⟨sg7937,True.intro,True.intro⟩,⟨sg7939,True.intro,True.intro⟩⟩,⟨sg7942,⟨sg7941,True.intro,True.intro⟩,⟨sg7943,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree20_8All : degreeTree20_8.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7952,⟨sg7948,⟨sg7946,⟨sg7945,True.intro,True.intro⟩,⟨sg7947,True.intro,True.intro⟩⟩,⟨sg7950,⟨sg7949,True.intro,True.intro⟩,⟨sg7951,True.intro,True.intro⟩⟩⟩,⟨sg7956,⟨sg7954,⟨sg7953,True.intro,True.intro⟩,⟨sg7955,True.intro,True.intro⟩⟩,⟨sg7958,⟨sg7957,True.intro,True.intro⟩,⟨sg7959,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree20_9All : degreeTree20_9.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7944,degreeTree20_7All,degreeTree20_8All⟩ + +lemma degreeTree20_10All : degreeTree20_10.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7969,⟨sg7965,⟨sg7963,⟨sg7962,⟨sg7961,True.intro,True.intro⟩,True.intro⟩,⟨sg7964,True.intro,True.intro⟩⟩,⟨sg7967,⟨sg7966,True.intro,True.intro⟩,⟨sg7968,True.intro,True.intro⟩⟩⟩,⟨sg7973,⟨sg7971,⟨sg7970,True.intro,True.intro⟩,⟨sg7972,True.intro,True.intro⟩⟩,⟨sg7975,⟨sg7974,True.intro,True.intro⟩,⟨sg7976,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree20_11All : degreeTree20_11.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7985,⟨sg7981,⟨sg7979,⟨sg7978,True.intro,True.intro⟩,⟨sg7980,True.intro,True.intro⟩⟩,⟨sg7983,⟨sg7982,True.intro,True.intro⟩,⟨sg7984,True.intro,True.intro⟩⟩⟩,⟨sg7989,⟨sg7987,⟨sg7986,True.intro,True.intro⟩,⟨sg7988,True.intro,True.intro⟩⟩,⟨sg7991,⟨sg7990,True.intro,True.intro⟩,⟨sg7992,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree20_12All : degreeTree20_12.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7977,degreeTree20_10All,degreeTree20_11All⟩ + +lemma degreeTree20_13All : degreeTree20_13.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7960,degreeTree20_9All,degreeTree20_12All⟩ + +lemma degreeTree20_14All : degreeTree20_14.All (RowSquare [7,5,2,2,2,1,1]) := by + exact ⟨sg7927,degreeTree20_6All,degreeTree20_13All⟩ + +lemma degreeTreeAll20 : degreeTree20.All + (fun rs => SquareOccurs (candidate 4 2 1) (rowDiagram rs)) := by + have hp : rowDiagram [7,5,2,2,2,1,1] = candidate 4 2 1 := rowDiagram_candidate (M := 4) (b := 2) (δ := 1) (by decide) + rw [← hp] + exact degreeTree20_14All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof22.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof22.lean index bd2453a6f10225c31f9b80759502830b6ec40680..f8274f8a8f0918545cdd5ed3a42e38dd1d795448 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof22.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof22.lean @@ -1,72 +1,72 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData22 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes25 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes26 - -namespace OAI - -/-! Degree Tree Proof 22. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree22_0All : degreeTree22_0.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg10919,⟨sg10915,⟨sg10913,⟨sg10912,⟨sg10911,True.intro,True.intro⟩,True.intro⟩,⟨sg10914,True.intro,True.intro⟩⟩,⟨sg10917,⟨sg10916,True.intro,True.intro⟩,⟨sg10918,True.intro,True.intro⟩⟩⟩,⟨sg10924,⟨sg10922,⟨sg10921,⟨sg10920,True.intro,True.intro⟩,True.intro⟩,⟨sg10923,True.intro,True.intro⟩⟩,⟨sg10926,⟨sg10925,True.intro,True.intro⟩,⟨sg10927,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree22_1All : degreeTree22_1.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg10937,⟨sg10933,⟨sg10931,⟨sg10930,⟨sg10929,True.intro,True.intro⟩,True.intro⟩,⟨sg10932,True.intro,True.intro⟩⟩,⟨sg10935,⟨sg10934,True.intro,True.intro⟩,⟨sg10936,True.intro,True.intro⟩⟩⟩,⟨sg10941,⟨sg10939,⟨sg10938,True.intro,True.intro⟩,⟨sg10940,True.intro,True.intro⟩⟩,⟨sg10943,⟨sg10942,True.intro,True.intro⟩,⟨sg10944,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree22_2All : degreeTree22_2.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg10928,degreeTree22_0All,degreeTree22_1All⟩ - -lemma degreeTree22_3All : degreeTree22_3.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg10954,⟨sg10950,⟨sg10948,⟨sg10947,⟨sg10946,True.intro,True.intro⟩,True.intro⟩,⟨sg10949,True.intro,True.intro⟩⟩,⟨sg10952,⟨sg10951,True.intro,True.intro⟩,⟨sg10953,True.intro,True.intro⟩⟩⟩,⟨sg10958,⟨sg10956,⟨sg10955,True.intro,True.intro⟩,⟨sg10957,True.intro,True.intro⟩⟩,⟨sg10960,⟨sg10959,True.intro,True.intro⟩,⟨sg10961,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree22_4All : degreeTree22_4.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg10971,⟨sg10967,⟨sg10965,⟨sg10964,⟨sg10963,True.intro,True.intro⟩,True.intro⟩,⟨sg10966,True.intro,True.intro⟩⟩,⟨sg10969,⟨sg10968,True.intro,True.intro⟩,⟨sg10970,True.intro,True.intro⟩⟩⟩,⟨sg10975,⟨sg10973,⟨sg10972,True.intro,True.intro⟩,⟨sg10974,True.intro,True.intro⟩⟩,⟨sg10977,⟨sg10976,True.intro,True.intro⟩,⟨sg10978,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree22_5All : degreeTree22_5.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg10962,degreeTree22_3All,degreeTree22_4All⟩ - -lemma degreeTree22_6All : degreeTree22_6.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg10945,degreeTree22_2All,degreeTree22_5All⟩ - -lemma degreeTree22_7All : degreeTree22_7.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg10988,⟨sg10984,⟨sg10982,⟨sg10981,⟨sg10980,True.intro,True.intro⟩,True.intro⟩,⟨sg10983,True.intro,True.intro⟩⟩,⟨sg10986,⟨sg10985,True.intro,True.intro⟩,⟨sg10987,True.intro,True.intro⟩⟩⟩,⟨sg10993,⟨sg10991,⟨sg10990,⟨sg10989,True.intro,True.intro⟩,True.intro⟩,⟨sg10992,True.intro,True.intro⟩⟩,⟨sg10995,⟨sg10994,True.intro,True.intro⟩,⟨sg10996,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree22_8All : degreeTree22_8.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg11006,⟨sg11002,⟨sg11000,⟨sg10999,⟨sg10998,True.intro,True.intro⟩,True.intro⟩,⟨sg11001,True.intro,True.intro⟩⟩,⟨sg11004,⟨sg11003,True.intro,True.intro⟩,⟨sg11005,True.intro,True.intro⟩⟩⟩,⟨sg11010,⟨sg11008,⟨sg11007,True.intro,True.intro⟩,⟨sg11009,True.intro,True.intro⟩⟩,⟨sg11012,⟨sg11011,True.intro,True.intro⟩,⟨sg11013,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree22_9All : degreeTree22_9.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg10997,degreeTree22_7All,degreeTree22_8All⟩ - -lemma degreeTree22_10All : degreeTree22_10.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg11023,⟨sg11019,⟨sg11017,⟨sg11016,⟨sg11015,True.intro,True.intro⟩,True.intro⟩,⟨sg11018,True.intro,True.intro⟩⟩,⟨sg11021,⟨sg11020,True.intro,True.intro⟩,⟨sg11022,True.intro,True.intro⟩⟩⟩,⟨sg11027,⟨sg11025,⟨sg11024,True.intro,True.intro⟩,⟨sg11026,True.intro,True.intro⟩⟩,⟨sg11029,⟨sg11028,True.intro,True.intro⟩,⟨sg11030,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree22_11All : degreeTree22_11.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg11040,⟨sg11036,⟨sg11034,⟨sg11033,⟨sg11032,True.intro,True.intro⟩,True.intro⟩,⟨sg11035,True.intro,True.intro⟩⟩,⟨sg11038,⟨sg11037,True.intro,True.intro⟩,⟨sg11039,True.intro,True.intro⟩⟩⟩,⟨sg11044,⟨sg11042,⟨sg11041,True.intro,True.intro⟩,⟨sg11043,True.intro,True.intro⟩⟩,⟨sg11046,⟨sg11045,True.intro,True.intro⟩,⟨sg11047,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree22_12All : degreeTree22_12.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg11031,degreeTree22_10All,degreeTree22_11All⟩ - -lemma degreeTree22_13All : degreeTree22_13.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg11014,degreeTree22_9All,degreeTree22_12All⟩ - -lemma degreeTree22_14All : degreeTree22_14.All (RowSquare [7,6,2,2,2,2,1]) := by - exact ⟨sg10979,degreeTree22_6All,degreeTree22_13All⟩ - -lemma degreeTreeAll22 : degreeTree22.All - (fun rs => SquareOccurs (candidate 4 3 0) (rowDiagram rs)) := by - have hp : rowDiagram [7,6,2,2,2,2,1] = candidate 4 3 0 := rowDiagram_candidate (M := 4) (b := 3) (δ := 0) (by decide) - rw [← hp] - exact degreeTree22_14All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData22 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes25 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes26 + +namespace OAI + +/-! Degree Tree Proof 22. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree22_0All : degreeTree22_0.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg10919,⟨sg10915,⟨sg10913,⟨sg10912,⟨sg10911,True.intro,True.intro⟩,True.intro⟩,⟨sg10914,True.intro,True.intro⟩⟩,⟨sg10917,⟨sg10916,True.intro,True.intro⟩,⟨sg10918,True.intro,True.intro⟩⟩⟩,⟨sg10924,⟨sg10922,⟨sg10921,⟨sg10920,True.intro,True.intro⟩,True.intro⟩,⟨sg10923,True.intro,True.intro⟩⟩,⟨sg10926,⟨sg10925,True.intro,True.intro⟩,⟨sg10927,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree22_1All : degreeTree22_1.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg10937,⟨sg10933,⟨sg10931,⟨sg10930,⟨sg10929,True.intro,True.intro⟩,True.intro⟩,⟨sg10932,True.intro,True.intro⟩⟩,⟨sg10935,⟨sg10934,True.intro,True.intro⟩,⟨sg10936,True.intro,True.intro⟩⟩⟩,⟨sg10941,⟨sg10939,⟨sg10938,True.intro,True.intro⟩,⟨sg10940,True.intro,True.intro⟩⟩,⟨sg10943,⟨sg10942,True.intro,True.intro⟩,⟨sg10944,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree22_2All : degreeTree22_2.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg10928,degreeTree22_0All,degreeTree22_1All⟩ + +lemma degreeTree22_3All : degreeTree22_3.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg10954,⟨sg10950,⟨sg10948,⟨sg10947,⟨sg10946,True.intro,True.intro⟩,True.intro⟩,⟨sg10949,True.intro,True.intro⟩⟩,⟨sg10952,⟨sg10951,True.intro,True.intro⟩,⟨sg10953,True.intro,True.intro⟩⟩⟩,⟨sg10958,⟨sg10956,⟨sg10955,True.intro,True.intro⟩,⟨sg10957,True.intro,True.intro⟩⟩,⟨sg10960,⟨sg10959,True.intro,True.intro⟩,⟨sg10961,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree22_4All : degreeTree22_4.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg10971,⟨sg10967,⟨sg10965,⟨sg10964,⟨sg10963,True.intro,True.intro⟩,True.intro⟩,⟨sg10966,True.intro,True.intro⟩⟩,⟨sg10969,⟨sg10968,True.intro,True.intro⟩,⟨sg10970,True.intro,True.intro⟩⟩⟩,⟨sg10975,⟨sg10973,⟨sg10972,True.intro,True.intro⟩,⟨sg10974,True.intro,True.intro⟩⟩,⟨sg10977,⟨sg10976,True.intro,True.intro⟩,⟨sg10978,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree22_5All : degreeTree22_5.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg10962,degreeTree22_3All,degreeTree22_4All⟩ + +lemma degreeTree22_6All : degreeTree22_6.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg10945,degreeTree22_2All,degreeTree22_5All⟩ + +lemma degreeTree22_7All : degreeTree22_7.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg10988,⟨sg10984,⟨sg10982,⟨sg10981,⟨sg10980,True.intro,True.intro⟩,True.intro⟩,⟨sg10983,True.intro,True.intro⟩⟩,⟨sg10986,⟨sg10985,True.intro,True.intro⟩,⟨sg10987,True.intro,True.intro⟩⟩⟩,⟨sg10993,⟨sg10991,⟨sg10990,⟨sg10989,True.intro,True.intro⟩,True.intro⟩,⟨sg10992,True.intro,True.intro⟩⟩,⟨sg10995,⟨sg10994,True.intro,True.intro⟩,⟨sg10996,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree22_8All : degreeTree22_8.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg11006,⟨sg11002,⟨sg11000,⟨sg10999,⟨sg10998,True.intro,True.intro⟩,True.intro⟩,⟨sg11001,True.intro,True.intro⟩⟩,⟨sg11004,⟨sg11003,True.intro,True.intro⟩,⟨sg11005,True.intro,True.intro⟩⟩⟩,⟨sg11010,⟨sg11008,⟨sg11007,True.intro,True.intro⟩,⟨sg11009,True.intro,True.intro⟩⟩,⟨sg11012,⟨sg11011,True.intro,True.intro⟩,⟨sg11013,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree22_9All : degreeTree22_9.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg10997,degreeTree22_7All,degreeTree22_8All⟩ + +lemma degreeTree22_10All : degreeTree22_10.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg11023,⟨sg11019,⟨sg11017,⟨sg11016,⟨sg11015,True.intro,True.intro⟩,True.intro⟩,⟨sg11018,True.intro,True.intro⟩⟩,⟨sg11021,⟨sg11020,True.intro,True.intro⟩,⟨sg11022,True.intro,True.intro⟩⟩⟩,⟨sg11027,⟨sg11025,⟨sg11024,True.intro,True.intro⟩,⟨sg11026,True.intro,True.intro⟩⟩,⟨sg11029,⟨sg11028,True.intro,True.intro⟩,⟨sg11030,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree22_11All : degreeTree22_11.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg11040,⟨sg11036,⟨sg11034,⟨sg11033,⟨sg11032,True.intro,True.intro⟩,True.intro⟩,⟨sg11035,True.intro,True.intro⟩⟩,⟨sg11038,⟨sg11037,True.intro,True.intro⟩,⟨sg11039,True.intro,True.intro⟩⟩⟩,⟨sg11044,⟨sg11042,⟨sg11041,True.intro,True.intro⟩,⟨sg11043,True.intro,True.intro⟩⟩,⟨sg11046,⟨sg11045,True.intro,True.intro⟩,⟨sg11047,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree22_12All : degreeTree22_12.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg11031,degreeTree22_10All,degreeTree22_11All⟩ + +lemma degreeTree22_13All : degreeTree22_13.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg11014,degreeTree22_9All,degreeTree22_12All⟩ + +lemma degreeTree22_14All : degreeTree22_14.All (RowSquare [7,6,2,2,2,2,1]) := by + exact ⟨sg10979,degreeTree22_6All,degreeTree22_13All⟩ + +lemma degreeTreeAll22 : degreeTree22.All + (fun rs => SquareOccurs (candidate 4 3 0) (rowDiagram rs)) := by + have hp : rowDiagram [7,6,2,2,2,2,1] = candidate 4 3 0 := rowDiagram_candidate (M := 4) (b := 3) (δ := 0) (by decide) + rw [← hp] + exact degreeTree22_14All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof24.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof24.lean index 09d041745cbda2ea02a83fbeafced31e8a65a0bd..f63ed36af8497cd9fe473d71eaf4c3fe56538ec3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof24.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof24.lean @@ -1,120 +1,120 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes28 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes29 - -namespace OAI - -/-! Degree Tree Proof 24. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree24_0All : degreeTree24_0.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg11856,⟨sg11848,⟨sg11844,⟨sg11842,⟨sg11841,True.intro,True.intro⟩,⟨sg11843,True.intro,True.intro⟩⟩,⟨sg11846,⟨sg11845,True.intro,True.intro⟩,⟨sg11847,True.intro,True.intro⟩⟩⟩,⟨sg11852,⟨sg11850,⟨sg11849,True.intro,True.intro⟩,⟨sg11851,True.intro,True.intro⟩⟩,⟨sg11854,⟨sg11853,True.intro,True.intro⟩,⟨sg11855,True.intro,True.intro⟩⟩⟩⟩,⟨sg11864,⟨sg11860,⟨sg11858,⟨sg11857,True.intro,True.intro⟩,⟨sg11859,True.intro,True.intro⟩⟩,⟨sg11862,⟨sg11861,True.intro,True.intro⟩,⟨sg11863,True.intro,True.intro⟩⟩⟩,⟨sg11868,⟨sg11866,⟨sg11865,True.intro,True.intro⟩,⟨sg11867,True.intro,True.intro⟩⟩,⟨sg11870,⟨sg11869,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_1All : degreeTree24_1.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg11887,⟨sg11879,⟨sg11875,⟨sg11873,⟨sg11872,True.intro,True.intro⟩,⟨sg11874,True.intro,True.intro⟩⟩,⟨sg11877,⟨sg11876,True.intro,True.intro⟩,⟨sg11878,True.intro,True.intro⟩⟩⟩,⟨sg11883,⟨sg11881,⟨sg11880,True.intro,True.intro⟩,⟨sg11882,True.intro,True.intro⟩⟩,⟨sg11885,⟨sg11884,True.intro,True.intro⟩,⟨sg11886,True.intro,True.intro⟩⟩⟩⟩,⟨sg11895,⟨sg11891,⟨sg11889,⟨sg11888,True.intro,True.intro⟩,⟨sg11890,True.intro,True.intro⟩⟩,⟨sg11893,⟨sg11892,True.intro,True.intro⟩,⟨sg11894,True.intro,True.intro⟩⟩⟩,⟨sg11899,⟨sg11897,⟨sg11896,True.intro,True.intro⟩,⟨sg11898,True.intro,True.intro⟩⟩,⟨sg11901,⟨sg11900,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_2All : degreeTree24_2.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg11871,degreeTree24_0All,degreeTree24_1All⟩ - -lemma degreeTree24_3All : degreeTree24_3.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg11918,⟨sg11910,⟨sg11906,⟨sg11904,⟨sg11903,True.intro,True.intro⟩,⟨sg11905,True.intro,True.intro⟩⟩,⟨sg11908,⟨sg11907,True.intro,True.intro⟩,⟨sg11909,True.intro,True.intro⟩⟩⟩,⟨sg11914,⟨sg11912,⟨sg11911,True.intro,True.intro⟩,⟨sg11913,True.intro,True.intro⟩⟩,⟨sg11916,⟨sg11915,True.intro,True.intro⟩,⟨sg11917,True.intro,True.intro⟩⟩⟩⟩,⟨sg11926,⟨sg11922,⟨sg11920,⟨sg11919,True.intro,True.intro⟩,⟨sg11921,True.intro,True.intro⟩⟩,⟨sg11924,⟨sg11923,True.intro,True.intro⟩,⟨sg11925,True.intro,True.intro⟩⟩⟩,⟨sg11930,⟨sg11928,⟨sg11927,True.intro,True.intro⟩,⟨sg11929,True.intro,True.intro⟩⟩,⟨sg11932,⟨sg11931,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_4All : degreeTree24_4.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg11948,⟨sg11941,⟨sg11937,⟨sg11935,⟨sg11934,True.intro,True.intro⟩,⟨sg11936,True.intro,True.intro⟩⟩,⟨sg11939,⟨sg11938,True.intro,True.intro⟩,⟨sg11940,True.intro,True.intro⟩⟩⟩,⟨sg11945,⟨sg11943,⟨sg11942,True.intro,True.intro⟩,⟨sg11944,True.intro,True.intro⟩⟩,⟨sg11947,⟨sg11946,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg11956,⟨sg11952,⟨sg11950,⟨sg11949,True.intro,True.intro⟩,⟨sg11951,True.intro,True.intro⟩⟩,⟨sg11954,⟨sg11953,True.intro,True.intro⟩,⟨sg11955,True.intro,True.intro⟩⟩⟩,⟨sg11960,⟨sg11958,⟨sg11957,True.intro,True.intro⟩,⟨sg11959,True.intro,True.intro⟩⟩,⟨sg11962,⟨sg11961,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_5All : degreeTree24_5.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg11933,degreeTree24_3All,degreeTree24_4All⟩ - -lemma degreeTree24_6All : degreeTree24_6.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg11902,degreeTree24_2All,degreeTree24_5All⟩ - -lemma degreeTree24_7All : degreeTree24_7.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg11979,⟨sg11971,⟨sg11967,⟨sg11965,⟨sg11964,True.intro,True.intro⟩,⟨sg11966,True.intro,True.intro⟩⟩,⟨sg11969,⟨sg11968,True.intro,True.intro⟩,⟨sg11970,True.intro,True.intro⟩⟩⟩,⟨sg11975,⟨sg11973,⟨sg11972,True.intro,True.intro⟩,⟨sg11974,True.intro,True.intro⟩⟩,⟨sg11977,⟨sg11976,True.intro,True.intro⟩,⟨sg11978,True.intro,True.intro⟩⟩⟩⟩,⟨sg11987,⟨sg11983,⟨sg11981,⟨sg11980,True.intro,True.intro⟩,⟨sg11982,True.intro,True.intro⟩⟩,⟨sg11985,⟨sg11984,True.intro,True.intro⟩,⟨sg11986,True.intro,True.intro⟩⟩⟩,⟨sg11991,⟨sg11989,⟨sg11988,True.intro,True.intro⟩,⟨sg11990,True.intro,True.intro⟩⟩,⟨sg11993,⟨sg11992,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_8All : degreeTree24_8.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12010,⟨sg12002,⟨sg11998,⟨sg11996,⟨sg11995,True.intro,True.intro⟩,⟨sg11997,True.intro,True.intro⟩⟩,⟨sg12000,⟨sg11999,True.intro,True.intro⟩,⟨sg12001,True.intro,True.intro⟩⟩⟩,⟨sg12006,⟨sg12004,⟨sg12003,True.intro,True.intro⟩,⟨sg12005,True.intro,True.intro⟩⟩,⟨sg12008,⟨sg12007,True.intro,True.intro⟩,⟨sg12009,True.intro,True.intro⟩⟩⟩⟩,⟨sg12018,⟨sg12014,⟨sg12012,⟨sg12011,True.intro,True.intro⟩,⟨sg12013,True.intro,True.intro⟩⟩,⟨sg12016,⟨sg12015,True.intro,True.intro⟩,⟨sg12017,True.intro,True.intro⟩⟩⟩,⟨sg12022,⟨sg12020,⟨sg12019,True.intro,True.intro⟩,⟨sg12021,True.intro,True.intro⟩⟩,⟨sg12024,⟨sg12023,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_9All : degreeTree24_9.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg11994,degreeTree24_7All,degreeTree24_8All⟩ - -lemma degreeTree24_10All : degreeTree24_10.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12041,⟨sg12033,⟨sg12029,⟨sg12027,⟨sg12026,True.intro,True.intro⟩,⟨sg12028,True.intro,True.intro⟩⟩,⟨sg12031,⟨sg12030,True.intro,True.intro⟩,⟨sg12032,True.intro,True.intro⟩⟩⟩,⟨sg12037,⟨sg12035,⟨sg12034,True.intro,True.intro⟩,⟨sg12036,True.intro,True.intro⟩⟩,⟨sg12039,⟨sg12038,True.intro,True.intro⟩,⟨sg12040,True.intro,True.intro⟩⟩⟩⟩,⟨sg12049,⟨sg12045,⟨sg12043,⟨sg12042,True.intro,True.intro⟩,⟨sg12044,True.intro,True.intro⟩⟩,⟨sg12047,⟨sg12046,True.intro,True.intro⟩,⟨sg12048,True.intro,True.intro⟩⟩⟩,⟨sg12053,⟨sg12051,⟨sg12050,True.intro,True.intro⟩,⟨sg12052,True.intro,True.intro⟩⟩,⟨sg12055,⟨sg12054,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_11All : degreeTree24_11.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12071,⟨sg12064,⟨sg12060,⟨sg12058,⟨sg12057,True.intro,True.intro⟩,⟨sg12059,True.intro,True.intro⟩⟩,⟨sg12062,⟨sg12061,True.intro,True.intro⟩,⟨sg12063,True.intro,True.intro⟩⟩⟩,⟨sg12068,⟨sg12066,⟨sg12065,True.intro,True.intro⟩,⟨sg12067,True.intro,True.intro⟩⟩,⟨sg12070,⟨sg12069,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg12079,⟨sg12075,⟨sg12073,⟨sg12072,True.intro,True.intro⟩,⟨sg12074,True.intro,True.intro⟩⟩,⟨sg12077,⟨sg12076,True.intro,True.intro⟩,⟨sg12078,True.intro,True.intro⟩⟩⟩,⟨sg12083,⟨sg12081,⟨sg12080,True.intro,True.intro⟩,⟨sg12082,True.intro,True.intro⟩⟩,⟨sg12085,⟨sg12084,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_12All : degreeTree24_12.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12056,degreeTree24_10All,degreeTree24_11All⟩ - -lemma degreeTree24_13All : degreeTree24_13.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12025,degreeTree24_9All,degreeTree24_12All⟩ - -lemma degreeTree24_14All : degreeTree24_14.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg11963,degreeTree24_6All,degreeTree24_13All⟩ - -lemma degreeTree24_15All : degreeTree24_15.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12102,⟨sg12094,⟨sg12090,⟨sg12088,⟨sg12087,True.intro,True.intro⟩,⟨sg12089,True.intro,True.intro⟩⟩,⟨sg12092,⟨sg12091,True.intro,True.intro⟩,⟨sg12093,True.intro,True.intro⟩⟩⟩,⟨sg12098,⟨sg12096,⟨sg12095,True.intro,True.intro⟩,⟨sg12097,True.intro,True.intro⟩⟩,⟨sg12100,⟨sg12099,True.intro,True.intro⟩,⟨sg12101,True.intro,True.intro⟩⟩⟩⟩,⟨sg12110,⟨sg12106,⟨sg12104,⟨sg12103,True.intro,True.intro⟩,⟨sg12105,True.intro,True.intro⟩⟩,⟨sg12108,⟨sg12107,True.intro,True.intro⟩,⟨sg12109,True.intro,True.intro⟩⟩⟩,⟨sg12114,⟨sg12112,⟨sg12111,True.intro,True.intro⟩,⟨sg12113,True.intro,True.intro⟩⟩,⟨sg12116,⟨sg12115,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_16All : degreeTree24_16.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12133,⟨sg12125,⟨sg12121,⟨sg12119,⟨sg12118,True.intro,True.intro⟩,⟨sg12120,True.intro,True.intro⟩⟩,⟨sg12123,⟨sg12122,True.intro,True.intro⟩,⟨sg12124,True.intro,True.intro⟩⟩⟩,⟨sg12129,⟨sg12127,⟨sg12126,True.intro,True.intro⟩,⟨sg12128,True.intro,True.intro⟩⟩,⟨sg12131,⟨sg12130,True.intro,True.intro⟩,⟨sg12132,True.intro,True.intro⟩⟩⟩⟩,⟨sg12141,⟨sg12137,⟨sg12135,⟨sg12134,True.intro,True.intro⟩,⟨sg12136,True.intro,True.intro⟩⟩,⟨sg12139,⟨sg12138,True.intro,True.intro⟩,⟨sg12140,True.intro,True.intro⟩⟩⟩,⟨sg12145,⟨sg12143,⟨sg12142,True.intro,True.intro⟩,⟨sg12144,True.intro,True.intro⟩⟩,⟨sg12147,⟨sg12146,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_17All : degreeTree24_17.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12117,degreeTree24_15All,degreeTree24_16All⟩ - -lemma degreeTree24_18All : degreeTree24_18.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12164,⟨sg12156,⟨sg12152,⟨sg12150,⟨sg12149,True.intro,True.intro⟩,⟨sg12151,True.intro,True.intro⟩⟩,⟨sg12154,⟨sg12153,True.intro,True.intro⟩,⟨sg12155,True.intro,True.intro⟩⟩⟩,⟨sg12160,⟨sg12158,⟨sg12157,True.intro,True.intro⟩,⟨sg12159,True.intro,True.intro⟩⟩,⟨sg12162,⟨sg12161,True.intro,True.intro⟩,⟨sg12163,True.intro,True.intro⟩⟩⟩⟩,⟨sg12172,⟨sg12168,⟨sg12166,⟨sg12165,True.intro,True.intro⟩,⟨sg12167,True.intro,True.intro⟩⟩,⟨sg12170,⟨sg12169,True.intro,True.intro⟩,⟨sg12171,True.intro,True.intro⟩⟩⟩,⟨sg12176,⟨sg12174,⟨sg12173,True.intro,True.intro⟩,⟨sg12175,True.intro,True.intro⟩⟩,⟨sg12178,⟨sg12177,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_19All : degreeTree24_19.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12194,⟨sg12187,⟨sg12183,⟨sg12181,⟨sg12180,True.intro,True.intro⟩,⟨sg12182,True.intro,True.intro⟩⟩,⟨sg12185,⟨sg12184,True.intro,True.intro⟩,⟨sg12186,True.intro,True.intro⟩⟩⟩,⟨sg12191,⟨sg12189,⟨sg12188,True.intro,True.intro⟩,⟨sg12190,True.intro,True.intro⟩⟩,⟨sg12193,⟨sg12192,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg12202,⟨sg12198,⟨sg12196,⟨sg12195,True.intro,True.intro⟩,⟨sg12197,True.intro,True.intro⟩⟩,⟨sg12200,⟨sg12199,True.intro,True.intro⟩,⟨sg12201,True.intro,True.intro⟩⟩⟩,⟨sg12206,⟨sg12204,⟨sg12203,True.intro,True.intro⟩,⟨sg12205,True.intro,True.intro⟩⟩,⟨sg12208,⟨sg12207,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_20All : degreeTree24_20.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12179,degreeTree24_18All,degreeTree24_19All⟩ - -lemma degreeTree24_21All : degreeTree24_21.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12148,degreeTree24_17All,degreeTree24_20All⟩ - -lemma degreeTree24_22All : degreeTree24_22.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12225,⟨sg12217,⟨sg12213,⟨sg12211,⟨sg12210,True.intro,True.intro⟩,⟨sg12212,True.intro,True.intro⟩⟩,⟨sg12215,⟨sg12214,True.intro,True.intro⟩,⟨sg12216,True.intro,True.intro⟩⟩⟩,⟨sg12221,⟨sg12219,⟨sg12218,True.intro,True.intro⟩,⟨sg12220,True.intro,True.intro⟩⟩,⟨sg12223,⟨sg12222,True.intro,True.intro⟩,⟨sg12224,True.intro,True.intro⟩⟩⟩⟩,⟨sg12233,⟨sg12229,⟨sg12227,⟨sg12226,True.intro,True.intro⟩,⟨sg12228,True.intro,True.intro⟩⟩,⟨sg12231,⟨sg12230,True.intro,True.intro⟩,⟨sg12232,True.intro,True.intro⟩⟩⟩,⟨sg12237,⟨sg12235,⟨sg12234,True.intro,True.intro⟩,⟨sg12236,True.intro,True.intro⟩⟩,⟨sg12239,⟨sg12238,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_23All : degreeTree24_23.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12255,⟨sg12248,⟨sg12244,⟨sg12242,⟨sg12241,True.intro,True.intro⟩,⟨sg12243,True.intro,True.intro⟩⟩,⟨sg12246,⟨sg12245,True.intro,True.intro⟩,⟨sg12247,True.intro,True.intro⟩⟩⟩,⟨sg12252,⟨sg12250,⟨sg12249,True.intro,True.intro⟩,⟨sg12251,True.intro,True.intro⟩⟩,⟨sg12254,⟨sg12253,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg12263,⟨sg12259,⟨sg12257,⟨sg12256,True.intro,True.intro⟩,⟨sg12258,True.intro,True.intro⟩⟩,⟨sg12261,⟨sg12260,True.intro,True.intro⟩,⟨sg12262,True.intro,True.intro⟩⟩⟩,⟨sg12267,⟨sg12265,⟨sg12264,True.intro,True.intro⟩,⟨sg12266,True.intro,True.intro⟩⟩,⟨sg12269,⟨sg12268,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_24All : degreeTree24_24.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12240,degreeTree24_22All,degreeTree24_23All⟩ - -lemma degreeTree24_25All : degreeTree24_25.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12286,⟨sg12278,⟨sg12274,⟨sg12272,⟨sg12271,True.intro,True.intro⟩,⟨sg12273,True.intro,True.intro⟩⟩,⟨sg12276,⟨sg12275,True.intro,True.intro⟩,⟨sg12277,True.intro,True.intro⟩⟩⟩,⟨sg12282,⟨sg12280,⟨sg12279,True.intro,True.intro⟩,⟨sg12281,True.intro,True.intro⟩⟩,⟨sg12284,⟨sg12283,True.intro,True.intro⟩,⟨sg12285,True.intro,True.intro⟩⟩⟩⟩,⟨sg12294,⟨sg12290,⟨sg12288,⟨sg12287,True.intro,True.intro⟩,⟨sg12289,True.intro,True.intro⟩⟩,⟨sg12292,⟨sg12291,True.intro,True.intro⟩,⟨sg12293,True.intro,True.intro⟩⟩⟩,⟨sg12298,⟨sg12296,⟨sg12295,True.intro,True.intro⟩,⟨sg12297,True.intro,True.intro⟩⟩,⟨sg12300,⟨sg12299,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_26All : degreeTree24_26.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12316,⟨sg12309,⟨sg12305,⟨sg12303,⟨sg12302,True.intro,True.intro⟩,⟨sg12304,True.intro,True.intro⟩⟩,⟨sg12307,⟨sg12306,True.intro,True.intro⟩,⟨sg12308,True.intro,True.intro⟩⟩⟩,⟨sg12313,⟨sg12311,⟨sg12310,True.intro,True.intro⟩,⟨sg12312,True.intro,True.intro⟩⟩,⟨sg12315,⟨sg12314,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg12324,⟨sg12320,⟨sg12318,⟨sg12317,True.intro,True.intro⟩,⟨sg12319,True.intro,True.intro⟩⟩,⟨sg12322,⟨sg12321,True.intro,True.intro⟩,⟨sg12323,True.intro,True.intro⟩⟩⟩,⟨sg12328,⟨sg12326,⟨sg12325,True.intro,True.intro⟩,⟨sg12327,True.intro,True.intro⟩⟩,⟨sg12330,⟨sg12329,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree24_27All : degreeTree24_27.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12301,degreeTree24_25All,degreeTree24_26All⟩ - -lemma degreeTree24_28All : degreeTree24_28.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12270,degreeTree24_24All,degreeTree24_27All⟩ - -lemma degreeTree24_29All : degreeTree24_29.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12209,degreeTree24_21All,degreeTree24_28All⟩ - -lemma degreeTree24_30All : degreeTree24_30.All (RowSquare [8,6,2,2,2,2,1,1]) := by - exact ⟨sg12086,degreeTree24_14All,degreeTree24_29All⟩ - -lemma degreeTreeAll24 : degreeTree24.All - (fun rs => SquareOccurs (candidate 4 3 1) (rowDiagram rs)) := by - have hp : rowDiagram [8,6,2,2,2,2,1,1] = candidate 4 3 1 := rowDiagram_candidate (M := 4) (b := 3) (δ := 1) (by decide) - rw [← hp] - exact degreeTree24_30All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes28 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes29 + +namespace OAI + +/-! Degree Tree Proof 24. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree24_0All : degreeTree24_0.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg11856,⟨sg11848,⟨sg11844,⟨sg11842,⟨sg11841,True.intro,True.intro⟩,⟨sg11843,True.intro,True.intro⟩⟩,⟨sg11846,⟨sg11845,True.intro,True.intro⟩,⟨sg11847,True.intro,True.intro⟩⟩⟩,⟨sg11852,⟨sg11850,⟨sg11849,True.intro,True.intro⟩,⟨sg11851,True.intro,True.intro⟩⟩,⟨sg11854,⟨sg11853,True.intro,True.intro⟩,⟨sg11855,True.intro,True.intro⟩⟩⟩⟩,⟨sg11864,⟨sg11860,⟨sg11858,⟨sg11857,True.intro,True.intro⟩,⟨sg11859,True.intro,True.intro⟩⟩,⟨sg11862,⟨sg11861,True.intro,True.intro⟩,⟨sg11863,True.intro,True.intro⟩⟩⟩,⟨sg11868,⟨sg11866,⟨sg11865,True.intro,True.intro⟩,⟨sg11867,True.intro,True.intro⟩⟩,⟨sg11870,⟨sg11869,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_1All : degreeTree24_1.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg11887,⟨sg11879,⟨sg11875,⟨sg11873,⟨sg11872,True.intro,True.intro⟩,⟨sg11874,True.intro,True.intro⟩⟩,⟨sg11877,⟨sg11876,True.intro,True.intro⟩,⟨sg11878,True.intro,True.intro⟩⟩⟩,⟨sg11883,⟨sg11881,⟨sg11880,True.intro,True.intro⟩,⟨sg11882,True.intro,True.intro⟩⟩,⟨sg11885,⟨sg11884,True.intro,True.intro⟩,⟨sg11886,True.intro,True.intro⟩⟩⟩⟩,⟨sg11895,⟨sg11891,⟨sg11889,⟨sg11888,True.intro,True.intro⟩,⟨sg11890,True.intro,True.intro⟩⟩,⟨sg11893,⟨sg11892,True.intro,True.intro⟩,⟨sg11894,True.intro,True.intro⟩⟩⟩,⟨sg11899,⟨sg11897,⟨sg11896,True.intro,True.intro⟩,⟨sg11898,True.intro,True.intro⟩⟩,⟨sg11901,⟨sg11900,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_2All : degreeTree24_2.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg11871,degreeTree24_0All,degreeTree24_1All⟩ + +lemma degreeTree24_3All : degreeTree24_3.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg11918,⟨sg11910,⟨sg11906,⟨sg11904,⟨sg11903,True.intro,True.intro⟩,⟨sg11905,True.intro,True.intro⟩⟩,⟨sg11908,⟨sg11907,True.intro,True.intro⟩,⟨sg11909,True.intro,True.intro⟩⟩⟩,⟨sg11914,⟨sg11912,⟨sg11911,True.intro,True.intro⟩,⟨sg11913,True.intro,True.intro⟩⟩,⟨sg11916,⟨sg11915,True.intro,True.intro⟩,⟨sg11917,True.intro,True.intro⟩⟩⟩⟩,⟨sg11926,⟨sg11922,⟨sg11920,⟨sg11919,True.intro,True.intro⟩,⟨sg11921,True.intro,True.intro⟩⟩,⟨sg11924,⟨sg11923,True.intro,True.intro⟩,⟨sg11925,True.intro,True.intro⟩⟩⟩,⟨sg11930,⟨sg11928,⟨sg11927,True.intro,True.intro⟩,⟨sg11929,True.intro,True.intro⟩⟩,⟨sg11932,⟨sg11931,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_4All : degreeTree24_4.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg11948,⟨sg11941,⟨sg11937,⟨sg11935,⟨sg11934,True.intro,True.intro⟩,⟨sg11936,True.intro,True.intro⟩⟩,⟨sg11939,⟨sg11938,True.intro,True.intro⟩,⟨sg11940,True.intro,True.intro⟩⟩⟩,⟨sg11945,⟨sg11943,⟨sg11942,True.intro,True.intro⟩,⟨sg11944,True.intro,True.intro⟩⟩,⟨sg11947,⟨sg11946,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg11956,⟨sg11952,⟨sg11950,⟨sg11949,True.intro,True.intro⟩,⟨sg11951,True.intro,True.intro⟩⟩,⟨sg11954,⟨sg11953,True.intro,True.intro⟩,⟨sg11955,True.intro,True.intro⟩⟩⟩,⟨sg11960,⟨sg11958,⟨sg11957,True.intro,True.intro⟩,⟨sg11959,True.intro,True.intro⟩⟩,⟨sg11962,⟨sg11961,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_5All : degreeTree24_5.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg11933,degreeTree24_3All,degreeTree24_4All⟩ + +lemma degreeTree24_6All : degreeTree24_6.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg11902,degreeTree24_2All,degreeTree24_5All⟩ + +lemma degreeTree24_7All : degreeTree24_7.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg11979,⟨sg11971,⟨sg11967,⟨sg11965,⟨sg11964,True.intro,True.intro⟩,⟨sg11966,True.intro,True.intro⟩⟩,⟨sg11969,⟨sg11968,True.intro,True.intro⟩,⟨sg11970,True.intro,True.intro⟩⟩⟩,⟨sg11975,⟨sg11973,⟨sg11972,True.intro,True.intro⟩,⟨sg11974,True.intro,True.intro⟩⟩,⟨sg11977,⟨sg11976,True.intro,True.intro⟩,⟨sg11978,True.intro,True.intro⟩⟩⟩⟩,⟨sg11987,⟨sg11983,⟨sg11981,⟨sg11980,True.intro,True.intro⟩,⟨sg11982,True.intro,True.intro⟩⟩,⟨sg11985,⟨sg11984,True.intro,True.intro⟩,⟨sg11986,True.intro,True.intro⟩⟩⟩,⟨sg11991,⟨sg11989,⟨sg11988,True.intro,True.intro⟩,⟨sg11990,True.intro,True.intro⟩⟩,⟨sg11993,⟨sg11992,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_8All : degreeTree24_8.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12010,⟨sg12002,⟨sg11998,⟨sg11996,⟨sg11995,True.intro,True.intro⟩,⟨sg11997,True.intro,True.intro⟩⟩,⟨sg12000,⟨sg11999,True.intro,True.intro⟩,⟨sg12001,True.intro,True.intro⟩⟩⟩,⟨sg12006,⟨sg12004,⟨sg12003,True.intro,True.intro⟩,⟨sg12005,True.intro,True.intro⟩⟩,⟨sg12008,⟨sg12007,True.intro,True.intro⟩,⟨sg12009,True.intro,True.intro⟩⟩⟩⟩,⟨sg12018,⟨sg12014,⟨sg12012,⟨sg12011,True.intro,True.intro⟩,⟨sg12013,True.intro,True.intro⟩⟩,⟨sg12016,⟨sg12015,True.intro,True.intro⟩,⟨sg12017,True.intro,True.intro⟩⟩⟩,⟨sg12022,⟨sg12020,⟨sg12019,True.intro,True.intro⟩,⟨sg12021,True.intro,True.intro⟩⟩,⟨sg12024,⟨sg12023,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_9All : degreeTree24_9.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg11994,degreeTree24_7All,degreeTree24_8All⟩ + +lemma degreeTree24_10All : degreeTree24_10.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12041,⟨sg12033,⟨sg12029,⟨sg12027,⟨sg12026,True.intro,True.intro⟩,⟨sg12028,True.intro,True.intro⟩⟩,⟨sg12031,⟨sg12030,True.intro,True.intro⟩,⟨sg12032,True.intro,True.intro⟩⟩⟩,⟨sg12037,⟨sg12035,⟨sg12034,True.intro,True.intro⟩,⟨sg12036,True.intro,True.intro⟩⟩,⟨sg12039,⟨sg12038,True.intro,True.intro⟩,⟨sg12040,True.intro,True.intro⟩⟩⟩⟩,⟨sg12049,⟨sg12045,⟨sg12043,⟨sg12042,True.intro,True.intro⟩,⟨sg12044,True.intro,True.intro⟩⟩,⟨sg12047,⟨sg12046,True.intro,True.intro⟩,⟨sg12048,True.intro,True.intro⟩⟩⟩,⟨sg12053,⟨sg12051,⟨sg12050,True.intro,True.intro⟩,⟨sg12052,True.intro,True.intro⟩⟩,⟨sg12055,⟨sg12054,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_11All : degreeTree24_11.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12071,⟨sg12064,⟨sg12060,⟨sg12058,⟨sg12057,True.intro,True.intro⟩,⟨sg12059,True.intro,True.intro⟩⟩,⟨sg12062,⟨sg12061,True.intro,True.intro⟩,⟨sg12063,True.intro,True.intro⟩⟩⟩,⟨sg12068,⟨sg12066,⟨sg12065,True.intro,True.intro⟩,⟨sg12067,True.intro,True.intro⟩⟩,⟨sg12070,⟨sg12069,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg12079,⟨sg12075,⟨sg12073,⟨sg12072,True.intro,True.intro⟩,⟨sg12074,True.intro,True.intro⟩⟩,⟨sg12077,⟨sg12076,True.intro,True.intro⟩,⟨sg12078,True.intro,True.intro⟩⟩⟩,⟨sg12083,⟨sg12081,⟨sg12080,True.intro,True.intro⟩,⟨sg12082,True.intro,True.intro⟩⟩,⟨sg12085,⟨sg12084,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_12All : degreeTree24_12.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12056,degreeTree24_10All,degreeTree24_11All⟩ + +lemma degreeTree24_13All : degreeTree24_13.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12025,degreeTree24_9All,degreeTree24_12All⟩ + +lemma degreeTree24_14All : degreeTree24_14.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg11963,degreeTree24_6All,degreeTree24_13All⟩ + +lemma degreeTree24_15All : degreeTree24_15.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12102,⟨sg12094,⟨sg12090,⟨sg12088,⟨sg12087,True.intro,True.intro⟩,⟨sg12089,True.intro,True.intro⟩⟩,⟨sg12092,⟨sg12091,True.intro,True.intro⟩,⟨sg12093,True.intro,True.intro⟩⟩⟩,⟨sg12098,⟨sg12096,⟨sg12095,True.intro,True.intro⟩,⟨sg12097,True.intro,True.intro⟩⟩,⟨sg12100,⟨sg12099,True.intro,True.intro⟩,⟨sg12101,True.intro,True.intro⟩⟩⟩⟩,⟨sg12110,⟨sg12106,⟨sg12104,⟨sg12103,True.intro,True.intro⟩,⟨sg12105,True.intro,True.intro⟩⟩,⟨sg12108,⟨sg12107,True.intro,True.intro⟩,⟨sg12109,True.intro,True.intro⟩⟩⟩,⟨sg12114,⟨sg12112,⟨sg12111,True.intro,True.intro⟩,⟨sg12113,True.intro,True.intro⟩⟩,⟨sg12116,⟨sg12115,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_16All : degreeTree24_16.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12133,⟨sg12125,⟨sg12121,⟨sg12119,⟨sg12118,True.intro,True.intro⟩,⟨sg12120,True.intro,True.intro⟩⟩,⟨sg12123,⟨sg12122,True.intro,True.intro⟩,⟨sg12124,True.intro,True.intro⟩⟩⟩,⟨sg12129,⟨sg12127,⟨sg12126,True.intro,True.intro⟩,⟨sg12128,True.intro,True.intro⟩⟩,⟨sg12131,⟨sg12130,True.intro,True.intro⟩,⟨sg12132,True.intro,True.intro⟩⟩⟩⟩,⟨sg12141,⟨sg12137,⟨sg12135,⟨sg12134,True.intro,True.intro⟩,⟨sg12136,True.intro,True.intro⟩⟩,⟨sg12139,⟨sg12138,True.intro,True.intro⟩,⟨sg12140,True.intro,True.intro⟩⟩⟩,⟨sg12145,⟨sg12143,⟨sg12142,True.intro,True.intro⟩,⟨sg12144,True.intro,True.intro⟩⟩,⟨sg12147,⟨sg12146,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_17All : degreeTree24_17.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12117,degreeTree24_15All,degreeTree24_16All⟩ + +lemma degreeTree24_18All : degreeTree24_18.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12164,⟨sg12156,⟨sg12152,⟨sg12150,⟨sg12149,True.intro,True.intro⟩,⟨sg12151,True.intro,True.intro⟩⟩,⟨sg12154,⟨sg12153,True.intro,True.intro⟩,⟨sg12155,True.intro,True.intro⟩⟩⟩,⟨sg12160,⟨sg12158,⟨sg12157,True.intro,True.intro⟩,⟨sg12159,True.intro,True.intro⟩⟩,⟨sg12162,⟨sg12161,True.intro,True.intro⟩,⟨sg12163,True.intro,True.intro⟩⟩⟩⟩,⟨sg12172,⟨sg12168,⟨sg12166,⟨sg12165,True.intro,True.intro⟩,⟨sg12167,True.intro,True.intro⟩⟩,⟨sg12170,⟨sg12169,True.intro,True.intro⟩,⟨sg12171,True.intro,True.intro⟩⟩⟩,⟨sg12176,⟨sg12174,⟨sg12173,True.intro,True.intro⟩,⟨sg12175,True.intro,True.intro⟩⟩,⟨sg12178,⟨sg12177,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_19All : degreeTree24_19.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12194,⟨sg12187,⟨sg12183,⟨sg12181,⟨sg12180,True.intro,True.intro⟩,⟨sg12182,True.intro,True.intro⟩⟩,⟨sg12185,⟨sg12184,True.intro,True.intro⟩,⟨sg12186,True.intro,True.intro⟩⟩⟩,⟨sg12191,⟨sg12189,⟨sg12188,True.intro,True.intro⟩,⟨sg12190,True.intro,True.intro⟩⟩,⟨sg12193,⟨sg12192,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg12202,⟨sg12198,⟨sg12196,⟨sg12195,True.intro,True.intro⟩,⟨sg12197,True.intro,True.intro⟩⟩,⟨sg12200,⟨sg12199,True.intro,True.intro⟩,⟨sg12201,True.intro,True.intro⟩⟩⟩,⟨sg12206,⟨sg12204,⟨sg12203,True.intro,True.intro⟩,⟨sg12205,True.intro,True.intro⟩⟩,⟨sg12208,⟨sg12207,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_20All : degreeTree24_20.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12179,degreeTree24_18All,degreeTree24_19All⟩ + +lemma degreeTree24_21All : degreeTree24_21.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12148,degreeTree24_17All,degreeTree24_20All⟩ + +lemma degreeTree24_22All : degreeTree24_22.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12225,⟨sg12217,⟨sg12213,⟨sg12211,⟨sg12210,True.intro,True.intro⟩,⟨sg12212,True.intro,True.intro⟩⟩,⟨sg12215,⟨sg12214,True.intro,True.intro⟩,⟨sg12216,True.intro,True.intro⟩⟩⟩,⟨sg12221,⟨sg12219,⟨sg12218,True.intro,True.intro⟩,⟨sg12220,True.intro,True.intro⟩⟩,⟨sg12223,⟨sg12222,True.intro,True.intro⟩,⟨sg12224,True.intro,True.intro⟩⟩⟩⟩,⟨sg12233,⟨sg12229,⟨sg12227,⟨sg12226,True.intro,True.intro⟩,⟨sg12228,True.intro,True.intro⟩⟩,⟨sg12231,⟨sg12230,True.intro,True.intro⟩,⟨sg12232,True.intro,True.intro⟩⟩⟩,⟨sg12237,⟨sg12235,⟨sg12234,True.intro,True.intro⟩,⟨sg12236,True.intro,True.intro⟩⟩,⟨sg12239,⟨sg12238,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_23All : degreeTree24_23.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12255,⟨sg12248,⟨sg12244,⟨sg12242,⟨sg12241,True.intro,True.intro⟩,⟨sg12243,True.intro,True.intro⟩⟩,⟨sg12246,⟨sg12245,True.intro,True.intro⟩,⟨sg12247,True.intro,True.intro⟩⟩⟩,⟨sg12252,⟨sg12250,⟨sg12249,True.intro,True.intro⟩,⟨sg12251,True.intro,True.intro⟩⟩,⟨sg12254,⟨sg12253,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg12263,⟨sg12259,⟨sg12257,⟨sg12256,True.intro,True.intro⟩,⟨sg12258,True.intro,True.intro⟩⟩,⟨sg12261,⟨sg12260,True.intro,True.intro⟩,⟨sg12262,True.intro,True.intro⟩⟩⟩,⟨sg12267,⟨sg12265,⟨sg12264,True.intro,True.intro⟩,⟨sg12266,True.intro,True.intro⟩⟩,⟨sg12269,⟨sg12268,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_24All : degreeTree24_24.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12240,degreeTree24_22All,degreeTree24_23All⟩ + +lemma degreeTree24_25All : degreeTree24_25.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12286,⟨sg12278,⟨sg12274,⟨sg12272,⟨sg12271,True.intro,True.intro⟩,⟨sg12273,True.intro,True.intro⟩⟩,⟨sg12276,⟨sg12275,True.intro,True.intro⟩,⟨sg12277,True.intro,True.intro⟩⟩⟩,⟨sg12282,⟨sg12280,⟨sg12279,True.intro,True.intro⟩,⟨sg12281,True.intro,True.intro⟩⟩,⟨sg12284,⟨sg12283,True.intro,True.intro⟩,⟨sg12285,True.intro,True.intro⟩⟩⟩⟩,⟨sg12294,⟨sg12290,⟨sg12288,⟨sg12287,True.intro,True.intro⟩,⟨sg12289,True.intro,True.intro⟩⟩,⟨sg12292,⟨sg12291,True.intro,True.intro⟩,⟨sg12293,True.intro,True.intro⟩⟩⟩,⟨sg12298,⟨sg12296,⟨sg12295,True.intro,True.intro⟩,⟨sg12297,True.intro,True.intro⟩⟩,⟨sg12300,⟨sg12299,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_26All : degreeTree24_26.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12316,⟨sg12309,⟨sg12305,⟨sg12303,⟨sg12302,True.intro,True.intro⟩,⟨sg12304,True.intro,True.intro⟩⟩,⟨sg12307,⟨sg12306,True.intro,True.intro⟩,⟨sg12308,True.intro,True.intro⟩⟩⟩,⟨sg12313,⟨sg12311,⟨sg12310,True.intro,True.intro⟩,⟨sg12312,True.intro,True.intro⟩⟩,⟨sg12315,⟨sg12314,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg12324,⟨sg12320,⟨sg12318,⟨sg12317,True.intro,True.intro⟩,⟨sg12319,True.intro,True.intro⟩⟩,⟨sg12322,⟨sg12321,True.intro,True.intro⟩,⟨sg12323,True.intro,True.intro⟩⟩⟩,⟨sg12328,⟨sg12326,⟨sg12325,True.intro,True.intro⟩,⟨sg12327,True.intro,True.intro⟩⟩,⟨sg12330,⟨sg12329,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree24_27All : degreeTree24_27.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12301,degreeTree24_25All,degreeTree24_26All⟩ + +lemma degreeTree24_28All : degreeTree24_28.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12270,degreeTree24_24All,degreeTree24_27All⟩ + +lemma degreeTree24_29All : degreeTree24_29.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12209,degreeTree24_21All,degreeTree24_28All⟩ + +lemma degreeTree24_30All : degreeTree24_30.All (RowSquare [8,6,2,2,2,2,1,1]) := by + exact ⟨sg12086,degreeTree24_14All,degreeTree24_29All⟩ + +lemma degreeTreeAll24 : degreeTree24.All + (fun rs => SquareOccurs (candidate 4 3 1) (rowDiagram rs)) := by + have hp : rowDiagram [8,6,2,2,2,2,1,1] = candidate 4 3 1 := rowDiagram_candidate (M := 4) (b := 3) (δ := 1) (by decide) + rw [← hp] + exact degreeTree24_30All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof26.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof26.lean index bfabbc7701d15b91a23350226a0f9f35e94164e8..d92db8db0d33a7034d614c826a9e77a581e4f0a5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof26.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof26.lean @@ -1,216 +1,216 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData26 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes31 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 - -namespace OAI - -/-! Degree Tree Proof 26. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree26_0All : degreeTree26_0.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg12979,⟨sg12975,⟨sg12973,⟨sg12972,⟨sg12971,True.intro,True.intro⟩,True.intro⟩,⟨sg12974,True.intro,True.intro⟩⟩,⟨sg12977,⟨sg12976,True.intro,True.intro⟩,⟨sg12978,True.intro,True.intro⟩⟩⟩,⟨sg12983,⟨sg12981,⟨sg12980,True.intro,True.intro⟩,⟨sg12982,True.intro,True.intro⟩⟩,⟨sg12985,⟨sg12984,True.intro,True.intro⟩,⟨sg12986,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_1All : degreeTree26_1.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg12996,⟨sg12992,⟨sg12990,⟨sg12989,⟨sg12988,True.intro,True.intro⟩,True.intro⟩,⟨sg12991,True.intro,True.intro⟩⟩,⟨sg12994,⟨sg12993,True.intro,True.intro⟩,⟨sg12995,True.intro,True.intro⟩⟩⟩,⟨sg13000,⟨sg12998,⟨sg12997,True.intro,True.intro⟩,⟨sg12999,True.intro,True.intro⟩⟩,⟨sg13002,⟨sg13001,True.intro,True.intro⟩,⟨sg13003,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_2All : degreeTree26_2.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg12987,degreeTree26_0All,degreeTree26_1All⟩ - -lemma degreeTree26_3All : degreeTree26_3.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13013,⟨sg13009,⟨sg13007,⟨sg13006,⟨sg13005,True.intro,True.intro⟩,True.intro⟩,⟨sg13008,True.intro,True.intro⟩⟩,⟨sg13011,⟨sg13010,True.intro,True.intro⟩,⟨sg13012,True.intro,True.intro⟩⟩⟩,⟨sg13017,⟨sg13015,⟨sg13014,True.intro,True.intro⟩,⟨sg13016,True.intro,True.intro⟩⟩,⟨sg13019,⟨sg13018,True.intro,True.intro⟩,⟨sg13020,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_4All : degreeTree26_4.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13029,⟨sg13025,⟨sg13023,⟨sg13022,True.intro,True.intro⟩,⟨sg13024,True.intro,True.intro⟩⟩,⟨sg13027,⟨sg13026,True.intro,True.intro⟩,⟨sg13028,True.intro,True.intro⟩⟩⟩,⟨sg13033,⟨sg13031,⟨sg13030,True.intro,True.intro⟩,⟨sg13032,True.intro,True.intro⟩⟩,⟨sg13035,⟨sg13034,True.intro,True.intro⟩,⟨sg13036,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_5All : degreeTree26_5.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13021,degreeTree26_3All,degreeTree26_4All⟩ - -lemma degreeTree26_6All : degreeTree26_6.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13004,degreeTree26_2All,degreeTree26_5All⟩ - -lemma degreeTree26_7All : degreeTree26_7.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13046,⟨sg13042,⟨sg13040,⟨sg13039,⟨sg13038,True.intro,True.intro⟩,True.intro⟩,⟨sg13041,True.intro,True.intro⟩⟩,⟨sg13044,⟨sg13043,True.intro,True.intro⟩,⟨sg13045,True.intro,True.intro⟩⟩⟩,⟨sg13050,⟨sg13048,⟨sg13047,True.intro,True.intro⟩,⟨sg13049,True.intro,True.intro⟩⟩,⟨sg13052,⟨sg13051,True.intro,True.intro⟩,⟨sg13053,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_8All : degreeTree26_8.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13062,⟨sg13058,⟨sg13056,⟨sg13055,True.intro,True.intro⟩,⟨sg13057,True.intro,True.intro⟩⟩,⟨sg13060,⟨sg13059,True.intro,True.intro⟩,⟨sg13061,True.intro,True.intro⟩⟩⟩,⟨sg13066,⟨sg13064,⟨sg13063,True.intro,True.intro⟩,⟨sg13065,True.intro,True.intro⟩⟩,⟨sg13068,⟨sg13067,True.intro,True.intro⟩,⟨sg13069,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_9All : degreeTree26_9.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13054,degreeTree26_7All,degreeTree26_8All⟩ - -lemma degreeTree26_10All : degreeTree26_10.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13079,⟨sg13075,⟨sg13073,⟨sg13072,⟨sg13071,True.intro,True.intro⟩,True.intro⟩,⟨sg13074,True.intro,True.intro⟩⟩,⟨sg13077,⟨sg13076,True.intro,True.intro⟩,⟨sg13078,True.intro,True.intro⟩⟩⟩,⟨sg13083,⟨sg13081,⟨sg13080,True.intro,True.intro⟩,⟨sg13082,True.intro,True.intro⟩⟩,⟨sg13085,⟨sg13084,True.intro,True.intro⟩,⟨sg13086,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_11All : degreeTree26_11.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13095,⟨sg13091,⟨sg13089,⟨sg13088,True.intro,True.intro⟩,⟨sg13090,True.intro,True.intro⟩⟩,⟨sg13093,⟨sg13092,True.intro,True.intro⟩,⟨sg13094,True.intro,True.intro⟩⟩⟩,⟨sg13099,⟨sg13097,⟨sg13096,True.intro,True.intro⟩,⟨sg13098,True.intro,True.intro⟩⟩,⟨sg13101,⟨sg13100,True.intro,True.intro⟩,⟨sg13102,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_12All : degreeTree26_12.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13087,degreeTree26_10All,degreeTree26_11All⟩ - -lemma degreeTree26_13All : degreeTree26_13.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13070,degreeTree26_9All,degreeTree26_12All⟩ - -lemma degreeTree26_14All : degreeTree26_14.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13037,degreeTree26_6All,degreeTree26_13All⟩ - -lemma degreeTree26_15All : degreeTree26_15.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13112,⟨sg13108,⟨sg13106,⟨sg13105,⟨sg13104,True.intro,True.intro⟩,True.intro⟩,⟨sg13107,True.intro,True.intro⟩⟩,⟨sg13110,⟨sg13109,True.intro,True.intro⟩,⟨sg13111,True.intro,True.intro⟩⟩⟩,⟨sg13116,⟨sg13114,⟨sg13113,True.intro,True.intro⟩,⟨sg13115,True.intro,True.intro⟩⟩,⟨sg13118,⟨sg13117,True.intro,True.intro⟩,⟨sg13119,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_16All : degreeTree26_16.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13128,⟨sg13124,⟨sg13122,⟨sg13121,True.intro,True.intro⟩,⟨sg13123,True.intro,True.intro⟩⟩,⟨sg13126,⟨sg13125,True.intro,True.intro⟩,⟨sg13127,True.intro,True.intro⟩⟩⟩,⟨sg13132,⟨sg13130,⟨sg13129,True.intro,True.intro⟩,⟨sg13131,True.intro,True.intro⟩⟩,⟨sg13134,⟨sg13133,True.intro,True.intro⟩,⟨sg13135,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_17All : degreeTree26_17.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13120,degreeTree26_15All,degreeTree26_16All⟩ - -lemma degreeTree26_18All : degreeTree26_18.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13145,⟨sg13141,⟨sg13139,⟨sg13138,⟨sg13137,True.intro,True.intro⟩,True.intro⟩,⟨sg13140,True.intro,True.intro⟩⟩,⟨sg13143,⟨sg13142,True.intro,True.intro⟩,⟨sg13144,True.intro,True.intro⟩⟩⟩,⟨sg13149,⟨sg13147,⟨sg13146,True.intro,True.intro⟩,⟨sg13148,True.intro,True.intro⟩⟩,⟨sg13151,⟨sg13150,True.intro,True.intro⟩,⟨sg13152,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_19All : degreeTree26_19.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13161,⟨sg13157,⟨sg13155,⟨sg13154,True.intro,True.intro⟩,⟨sg13156,True.intro,True.intro⟩⟩,⟨sg13159,⟨sg13158,True.intro,True.intro⟩,⟨sg13160,True.intro,True.intro⟩⟩⟩,⟨sg13165,⟨sg13163,⟨sg13162,True.intro,True.intro⟩,⟨sg13164,True.intro,True.intro⟩⟩,⟨sg13167,⟨sg13166,True.intro,True.intro⟩,⟨sg13168,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_20All : degreeTree26_20.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13153,degreeTree26_18All,degreeTree26_19All⟩ - -lemma degreeTree26_21All : degreeTree26_21.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13136,degreeTree26_17All,degreeTree26_20All⟩ - -lemma degreeTree26_22All : degreeTree26_22.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13178,⟨sg13174,⟨sg13172,⟨sg13171,⟨sg13170,True.intro,True.intro⟩,True.intro⟩,⟨sg13173,True.intro,True.intro⟩⟩,⟨sg13176,⟨sg13175,True.intro,True.intro⟩,⟨sg13177,True.intro,True.intro⟩⟩⟩,⟨sg13182,⟨sg13180,⟨sg13179,True.intro,True.intro⟩,⟨sg13181,True.intro,True.intro⟩⟩,⟨sg13184,⟨sg13183,True.intro,True.intro⟩,⟨sg13185,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_23All : degreeTree26_23.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13194,⟨sg13190,⟨sg13188,⟨sg13187,True.intro,True.intro⟩,⟨sg13189,True.intro,True.intro⟩⟩,⟨sg13192,⟨sg13191,True.intro,True.intro⟩,⟨sg13193,True.intro,True.intro⟩⟩⟩,⟨sg13198,⟨sg13196,⟨sg13195,True.intro,True.intro⟩,⟨sg13197,True.intro,True.intro⟩⟩,⟨sg13200,⟨sg13199,True.intro,True.intro⟩,⟨sg13201,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_24All : degreeTree26_24.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13186,degreeTree26_22All,degreeTree26_23All⟩ - -lemma degreeTree26_25All : degreeTree26_25.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13211,⟨sg13207,⟨sg13205,⟨sg13204,⟨sg13203,True.intro,True.intro⟩,True.intro⟩,⟨sg13206,True.intro,True.intro⟩⟩,⟨sg13209,⟨sg13208,True.intro,True.intro⟩,⟨sg13210,True.intro,True.intro⟩⟩⟩,⟨sg13215,⟨sg13213,⟨sg13212,True.intro,True.intro⟩,⟨sg13214,True.intro,True.intro⟩⟩,⟨sg13217,⟨sg13216,True.intro,True.intro⟩,⟨sg13218,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_26All : degreeTree26_26.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13227,⟨sg13223,⟨sg13221,⟨sg13220,True.intro,True.intro⟩,⟨sg13222,True.intro,True.intro⟩⟩,⟨sg13225,⟨sg13224,True.intro,True.intro⟩,⟨sg13226,True.intro,True.intro⟩⟩⟩,⟨sg13231,⟨sg13229,⟨sg13228,True.intro,True.intro⟩,⟨sg13230,True.intro,True.intro⟩⟩,⟨sg13233,⟨sg13232,True.intro,True.intro⟩,⟨sg13234,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_27All : degreeTree26_27.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13219,degreeTree26_25All,degreeTree26_26All⟩ - -lemma degreeTree26_28All : degreeTree26_28.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13202,degreeTree26_24All,degreeTree26_27All⟩ - -lemma degreeTree26_29All : degreeTree26_29.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13169,degreeTree26_21All,degreeTree26_28All⟩ - -lemma degreeTree26_30All : degreeTree26_30.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13103,degreeTree26_14All,degreeTree26_29All⟩ - -lemma degreeTree26_31All : degreeTree26_31.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13244,⟨sg13240,⟨sg13238,⟨sg13237,⟨sg13236,True.intro,True.intro⟩,True.intro⟩,⟨sg13239,True.intro,True.intro⟩⟩,⟨sg13242,⟨sg13241,True.intro,True.intro⟩,⟨sg13243,True.intro,True.intro⟩⟩⟩,⟨sg13248,⟨sg13246,⟨sg13245,True.intro,True.intro⟩,⟨sg13247,True.intro,True.intro⟩⟩,⟨sg13250,⟨sg13249,True.intro,True.intro⟩,⟨sg13251,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_32All : degreeTree26_32.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13260,⟨sg13256,⟨sg13254,⟨sg13253,True.intro,True.intro⟩,⟨sg13255,True.intro,True.intro⟩⟩,⟨sg13258,⟨sg13257,True.intro,True.intro⟩,⟨sg13259,True.intro,True.intro⟩⟩⟩,⟨sg13264,⟨sg13262,⟨sg13261,True.intro,True.intro⟩,⟨sg13263,True.intro,True.intro⟩⟩,⟨sg13266,⟨sg13265,True.intro,True.intro⟩,⟨sg13267,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_33All : degreeTree26_33.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13252,degreeTree26_31All,degreeTree26_32All⟩ - -lemma degreeTree26_34All : degreeTree26_34.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13277,⟨sg13273,⟨sg13271,⟨sg13270,⟨sg13269,True.intro,True.intro⟩,True.intro⟩,⟨sg13272,True.intro,True.intro⟩⟩,⟨sg13275,⟨sg13274,True.intro,True.intro⟩,⟨sg13276,True.intro,True.intro⟩⟩⟩,⟨sg13281,⟨sg13279,⟨sg13278,True.intro,True.intro⟩,⟨sg13280,True.intro,True.intro⟩⟩,⟨sg13283,⟨sg13282,True.intro,True.intro⟩,⟨sg13284,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_35All : degreeTree26_35.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13293,⟨sg13289,⟨sg13287,⟨sg13286,True.intro,True.intro⟩,⟨sg13288,True.intro,True.intro⟩⟩,⟨sg13291,⟨sg13290,True.intro,True.intro⟩,⟨sg13292,True.intro,True.intro⟩⟩⟩,⟨sg13297,⟨sg13295,⟨sg13294,True.intro,True.intro⟩,⟨sg13296,True.intro,True.intro⟩⟩,⟨sg13299,⟨sg13298,True.intro,True.intro⟩,⟨sg13300,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_36All : degreeTree26_36.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13285,degreeTree26_34All,degreeTree26_35All⟩ - -lemma degreeTree26_37All : degreeTree26_37.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13268,degreeTree26_33All,degreeTree26_36All⟩ - -lemma degreeTree26_38All : degreeTree26_38.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13310,⟨sg13306,⟨sg13304,⟨sg13303,⟨sg13302,True.intro,True.intro⟩,True.intro⟩,⟨sg13305,True.intro,True.intro⟩⟩,⟨sg13308,⟨sg13307,True.intro,True.intro⟩,⟨sg13309,True.intro,True.intro⟩⟩⟩,⟨sg13314,⟨sg13312,⟨sg13311,True.intro,True.intro⟩,⟨sg13313,True.intro,True.intro⟩⟩,⟨sg13316,⟨sg13315,True.intro,True.intro⟩,⟨sg13317,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_39All : degreeTree26_39.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13326,⟨sg13322,⟨sg13320,⟨sg13319,True.intro,True.intro⟩,⟨sg13321,True.intro,True.intro⟩⟩,⟨sg13324,⟨sg13323,True.intro,True.intro⟩,⟨sg13325,True.intro,True.intro⟩⟩⟩,⟨sg13330,⟨sg13328,⟨sg13327,True.intro,True.intro⟩,⟨sg13329,True.intro,True.intro⟩⟩,⟨sg13332,⟨sg13331,True.intro,True.intro⟩,⟨sg13333,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_40All : degreeTree26_40.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13318,degreeTree26_38All,degreeTree26_39All⟩ - -lemma degreeTree26_41All : degreeTree26_41.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13343,⟨sg13339,⟨sg13337,⟨sg13336,⟨sg13335,True.intro,True.intro⟩,True.intro⟩,⟨sg13338,True.intro,True.intro⟩⟩,⟨sg13341,⟨sg13340,True.intro,True.intro⟩,⟨sg13342,True.intro,True.intro⟩⟩⟩,⟨sg13347,⟨sg13345,⟨sg13344,True.intro,True.intro⟩,⟨sg13346,True.intro,True.intro⟩⟩,⟨sg13349,⟨sg13348,True.intro,True.intro⟩,⟨sg13350,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_42All : degreeTree26_42.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13359,⟨sg13355,⟨sg13353,⟨sg13352,True.intro,True.intro⟩,⟨sg13354,True.intro,True.intro⟩⟩,⟨sg13357,⟨sg13356,True.intro,True.intro⟩,⟨sg13358,True.intro,True.intro⟩⟩⟩,⟨sg13363,⟨sg13361,⟨sg13360,True.intro,True.intro⟩,⟨sg13362,True.intro,True.intro⟩⟩,⟨sg13365,⟨sg13364,True.intro,True.intro⟩,⟨sg13366,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_43All : degreeTree26_43.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13351,degreeTree26_41All,degreeTree26_42All⟩ - -lemma degreeTree26_44All : degreeTree26_44.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13334,degreeTree26_40All,degreeTree26_43All⟩ - -lemma degreeTree26_45All : degreeTree26_45.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13301,degreeTree26_37All,degreeTree26_44All⟩ - -lemma degreeTree26_46All : degreeTree26_46.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13376,⟨sg13372,⟨sg13370,⟨sg13369,⟨sg13368,True.intro,True.intro⟩,True.intro⟩,⟨sg13371,True.intro,True.intro⟩⟩,⟨sg13374,⟨sg13373,True.intro,True.intro⟩,⟨sg13375,True.intro,True.intro⟩⟩⟩,⟨sg13380,⟨sg13378,⟨sg13377,True.intro,True.intro⟩,⟨sg13379,True.intro,True.intro⟩⟩,⟨sg13382,⟨sg13381,True.intro,True.intro⟩,⟨sg13383,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_47All : degreeTree26_47.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13392,⟨sg13388,⟨sg13386,⟨sg13385,True.intro,True.intro⟩,⟨sg13387,True.intro,True.intro⟩⟩,⟨sg13390,⟨sg13389,True.intro,True.intro⟩,⟨sg13391,True.intro,True.intro⟩⟩⟩,⟨sg13396,⟨sg13394,⟨sg13393,True.intro,True.intro⟩,⟨sg13395,True.intro,True.intro⟩⟩,⟨sg13398,⟨sg13397,True.intro,True.intro⟩,⟨sg13399,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_48All : degreeTree26_48.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13384,degreeTree26_46All,degreeTree26_47All⟩ - -lemma degreeTree26_49All : degreeTree26_49.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13409,⟨sg13405,⟨sg13403,⟨sg13402,⟨sg13401,True.intro,True.intro⟩,True.intro⟩,⟨sg13404,True.intro,True.intro⟩⟩,⟨sg13407,⟨sg13406,True.intro,True.intro⟩,⟨sg13408,True.intro,True.intro⟩⟩⟩,⟨sg13413,⟨sg13411,⟨sg13410,True.intro,True.intro⟩,⟨sg13412,True.intro,True.intro⟩⟩,⟨sg13415,⟨sg13414,True.intro,True.intro⟩,⟨sg13416,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_50All : degreeTree26_50.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13425,⟨sg13421,⟨sg13419,⟨sg13418,True.intro,True.intro⟩,⟨sg13420,True.intro,True.intro⟩⟩,⟨sg13423,⟨sg13422,True.intro,True.intro⟩,⟨sg13424,True.intro,True.intro⟩⟩⟩,⟨sg13429,⟨sg13427,⟨sg13426,True.intro,True.intro⟩,⟨sg13428,True.intro,True.intro⟩⟩,⟨sg13431,⟨sg13430,True.intro,True.intro⟩,⟨sg13432,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_51All : degreeTree26_51.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13417,degreeTree26_49All,degreeTree26_50All⟩ - -lemma degreeTree26_52All : degreeTree26_52.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13400,degreeTree26_48All,degreeTree26_51All⟩ - -lemma degreeTree26_53All : degreeTree26_53.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13442,⟨sg13438,⟨sg13436,⟨sg13435,⟨sg13434,True.intro,True.intro⟩,True.intro⟩,⟨sg13437,True.intro,True.intro⟩⟩,⟨sg13440,⟨sg13439,True.intro,True.intro⟩,⟨sg13441,True.intro,True.intro⟩⟩⟩,⟨sg13446,⟨sg13444,⟨sg13443,True.intro,True.intro⟩,⟨sg13445,True.intro,True.intro⟩⟩,⟨sg13448,⟨sg13447,True.intro,True.intro⟩,⟨sg13449,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_54All : degreeTree26_54.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13458,⟨sg13454,⟨sg13452,⟨sg13451,True.intro,True.intro⟩,⟨sg13453,True.intro,True.intro⟩⟩,⟨sg13456,⟨sg13455,True.intro,True.intro⟩,⟨sg13457,True.intro,True.intro⟩⟩⟩,⟨sg13462,⟨sg13460,⟨sg13459,True.intro,True.intro⟩,⟨sg13461,True.intro,True.intro⟩⟩,⟨sg13464,⟨sg13463,True.intro,True.intro⟩,⟨sg13465,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_55All : degreeTree26_55.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13450,degreeTree26_53All,degreeTree26_54All⟩ - -lemma degreeTree26_56All : degreeTree26_56.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13475,⟨sg13471,⟨sg13469,⟨sg13468,⟨sg13467,True.intro,True.intro⟩,True.intro⟩,⟨sg13470,True.intro,True.intro⟩⟩,⟨sg13473,⟨sg13472,True.intro,True.intro⟩,⟨sg13474,True.intro,True.intro⟩⟩⟩,⟨sg13479,⟨sg13477,⟨sg13476,True.intro,True.intro⟩,⟨sg13478,True.intro,True.intro⟩⟩,⟨sg13481,⟨sg13480,True.intro,True.intro⟩,⟨sg13482,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_57All : degreeTree26_57.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13491,⟨sg13487,⟨sg13485,⟨sg13484,True.intro,True.intro⟩,⟨sg13486,True.intro,True.intro⟩⟩,⟨sg13489,⟨sg13488,True.intro,True.intro⟩,⟨sg13490,True.intro,True.intro⟩⟩⟩,⟨sg13495,⟨sg13493,⟨sg13492,True.intro,True.intro⟩,⟨sg13494,True.intro,True.intro⟩⟩,⟨sg13497,⟨sg13496,True.intro,True.intro⟩,⟨sg13498,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree26_58All : degreeTree26_58.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13483,degreeTree26_56All,degreeTree26_57All⟩ - -lemma degreeTree26_59All : degreeTree26_59.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13466,degreeTree26_55All,degreeTree26_58All⟩ - -lemma degreeTree26_60All : degreeTree26_60.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13433,degreeTree26_52All,degreeTree26_59All⟩ - -lemma degreeTree26_61All : degreeTree26_61.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13367,degreeTree26_45All,degreeTree26_60All⟩ - -lemma degreeTree26_62All : degreeTree26_62.All (RowSquare [8,7,2,2,2,2,2,1]) := by - exact ⟨sg13235,degreeTree26_30All,degreeTree26_61All⟩ - -lemma degreeTreeAll26 : degreeTree26.All - (fun rs => SquareOccurs (candidate 4 4 0) (rowDiagram rs)) := by - have hp : rowDiagram [8,7,2,2,2,2,2,1] = candidate 4 4 0 := rowDiagram_candidate (M := 4) (b := 4) (δ := 0) (by decide) - rw [← hp] - exact degreeTree26_62All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData26 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes31 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 + +namespace OAI + +/-! Degree Tree Proof 26. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree26_0All : degreeTree26_0.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg12979,⟨sg12975,⟨sg12973,⟨sg12972,⟨sg12971,True.intro,True.intro⟩,True.intro⟩,⟨sg12974,True.intro,True.intro⟩⟩,⟨sg12977,⟨sg12976,True.intro,True.intro⟩,⟨sg12978,True.intro,True.intro⟩⟩⟩,⟨sg12983,⟨sg12981,⟨sg12980,True.intro,True.intro⟩,⟨sg12982,True.intro,True.intro⟩⟩,⟨sg12985,⟨sg12984,True.intro,True.intro⟩,⟨sg12986,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_1All : degreeTree26_1.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg12996,⟨sg12992,⟨sg12990,⟨sg12989,⟨sg12988,True.intro,True.intro⟩,True.intro⟩,⟨sg12991,True.intro,True.intro⟩⟩,⟨sg12994,⟨sg12993,True.intro,True.intro⟩,⟨sg12995,True.intro,True.intro⟩⟩⟩,⟨sg13000,⟨sg12998,⟨sg12997,True.intro,True.intro⟩,⟨sg12999,True.intro,True.intro⟩⟩,⟨sg13002,⟨sg13001,True.intro,True.intro⟩,⟨sg13003,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_2All : degreeTree26_2.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg12987,degreeTree26_0All,degreeTree26_1All⟩ + +lemma degreeTree26_3All : degreeTree26_3.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13013,⟨sg13009,⟨sg13007,⟨sg13006,⟨sg13005,True.intro,True.intro⟩,True.intro⟩,⟨sg13008,True.intro,True.intro⟩⟩,⟨sg13011,⟨sg13010,True.intro,True.intro⟩,⟨sg13012,True.intro,True.intro⟩⟩⟩,⟨sg13017,⟨sg13015,⟨sg13014,True.intro,True.intro⟩,⟨sg13016,True.intro,True.intro⟩⟩,⟨sg13019,⟨sg13018,True.intro,True.intro⟩,⟨sg13020,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_4All : degreeTree26_4.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13029,⟨sg13025,⟨sg13023,⟨sg13022,True.intro,True.intro⟩,⟨sg13024,True.intro,True.intro⟩⟩,⟨sg13027,⟨sg13026,True.intro,True.intro⟩,⟨sg13028,True.intro,True.intro⟩⟩⟩,⟨sg13033,⟨sg13031,⟨sg13030,True.intro,True.intro⟩,⟨sg13032,True.intro,True.intro⟩⟩,⟨sg13035,⟨sg13034,True.intro,True.intro⟩,⟨sg13036,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_5All : degreeTree26_5.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13021,degreeTree26_3All,degreeTree26_4All⟩ + +lemma degreeTree26_6All : degreeTree26_6.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13004,degreeTree26_2All,degreeTree26_5All⟩ + +lemma degreeTree26_7All : degreeTree26_7.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13046,⟨sg13042,⟨sg13040,⟨sg13039,⟨sg13038,True.intro,True.intro⟩,True.intro⟩,⟨sg13041,True.intro,True.intro⟩⟩,⟨sg13044,⟨sg13043,True.intro,True.intro⟩,⟨sg13045,True.intro,True.intro⟩⟩⟩,⟨sg13050,⟨sg13048,⟨sg13047,True.intro,True.intro⟩,⟨sg13049,True.intro,True.intro⟩⟩,⟨sg13052,⟨sg13051,True.intro,True.intro⟩,⟨sg13053,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_8All : degreeTree26_8.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13062,⟨sg13058,⟨sg13056,⟨sg13055,True.intro,True.intro⟩,⟨sg13057,True.intro,True.intro⟩⟩,⟨sg13060,⟨sg13059,True.intro,True.intro⟩,⟨sg13061,True.intro,True.intro⟩⟩⟩,⟨sg13066,⟨sg13064,⟨sg13063,True.intro,True.intro⟩,⟨sg13065,True.intro,True.intro⟩⟩,⟨sg13068,⟨sg13067,True.intro,True.intro⟩,⟨sg13069,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_9All : degreeTree26_9.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13054,degreeTree26_7All,degreeTree26_8All⟩ + +lemma degreeTree26_10All : degreeTree26_10.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13079,⟨sg13075,⟨sg13073,⟨sg13072,⟨sg13071,True.intro,True.intro⟩,True.intro⟩,⟨sg13074,True.intro,True.intro⟩⟩,⟨sg13077,⟨sg13076,True.intro,True.intro⟩,⟨sg13078,True.intro,True.intro⟩⟩⟩,⟨sg13083,⟨sg13081,⟨sg13080,True.intro,True.intro⟩,⟨sg13082,True.intro,True.intro⟩⟩,⟨sg13085,⟨sg13084,True.intro,True.intro⟩,⟨sg13086,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_11All : degreeTree26_11.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13095,⟨sg13091,⟨sg13089,⟨sg13088,True.intro,True.intro⟩,⟨sg13090,True.intro,True.intro⟩⟩,⟨sg13093,⟨sg13092,True.intro,True.intro⟩,⟨sg13094,True.intro,True.intro⟩⟩⟩,⟨sg13099,⟨sg13097,⟨sg13096,True.intro,True.intro⟩,⟨sg13098,True.intro,True.intro⟩⟩,⟨sg13101,⟨sg13100,True.intro,True.intro⟩,⟨sg13102,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_12All : degreeTree26_12.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13087,degreeTree26_10All,degreeTree26_11All⟩ + +lemma degreeTree26_13All : degreeTree26_13.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13070,degreeTree26_9All,degreeTree26_12All⟩ + +lemma degreeTree26_14All : degreeTree26_14.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13037,degreeTree26_6All,degreeTree26_13All⟩ + +lemma degreeTree26_15All : degreeTree26_15.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13112,⟨sg13108,⟨sg13106,⟨sg13105,⟨sg13104,True.intro,True.intro⟩,True.intro⟩,⟨sg13107,True.intro,True.intro⟩⟩,⟨sg13110,⟨sg13109,True.intro,True.intro⟩,⟨sg13111,True.intro,True.intro⟩⟩⟩,⟨sg13116,⟨sg13114,⟨sg13113,True.intro,True.intro⟩,⟨sg13115,True.intro,True.intro⟩⟩,⟨sg13118,⟨sg13117,True.intro,True.intro⟩,⟨sg13119,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_16All : degreeTree26_16.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13128,⟨sg13124,⟨sg13122,⟨sg13121,True.intro,True.intro⟩,⟨sg13123,True.intro,True.intro⟩⟩,⟨sg13126,⟨sg13125,True.intro,True.intro⟩,⟨sg13127,True.intro,True.intro⟩⟩⟩,⟨sg13132,⟨sg13130,⟨sg13129,True.intro,True.intro⟩,⟨sg13131,True.intro,True.intro⟩⟩,⟨sg13134,⟨sg13133,True.intro,True.intro⟩,⟨sg13135,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_17All : degreeTree26_17.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13120,degreeTree26_15All,degreeTree26_16All⟩ + +lemma degreeTree26_18All : degreeTree26_18.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13145,⟨sg13141,⟨sg13139,⟨sg13138,⟨sg13137,True.intro,True.intro⟩,True.intro⟩,⟨sg13140,True.intro,True.intro⟩⟩,⟨sg13143,⟨sg13142,True.intro,True.intro⟩,⟨sg13144,True.intro,True.intro⟩⟩⟩,⟨sg13149,⟨sg13147,⟨sg13146,True.intro,True.intro⟩,⟨sg13148,True.intro,True.intro⟩⟩,⟨sg13151,⟨sg13150,True.intro,True.intro⟩,⟨sg13152,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_19All : degreeTree26_19.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13161,⟨sg13157,⟨sg13155,⟨sg13154,True.intro,True.intro⟩,⟨sg13156,True.intro,True.intro⟩⟩,⟨sg13159,⟨sg13158,True.intro,True.intro⟩,⟨sg13160,True.intro,True.intro⟩⟩⟩,⟨sg13165,⟨sg13163,⟨sg13162,True.intro,True.intro⟩,⟨sg13164,True.intro,True.intro⟩⟩,⟨sg13167,⟨sg13166,True.intro,True.intro⟩,⟨sg13168,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_20All : degreeTree26_20.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13153,degreeTree26_18All,degreeTree26_19All⟩ + +lemma degreeTree26_21All : degreeTree26_21.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13136,degreeTree26_17All,degreeTree26_20All⟩ + +lemma degreeTree26_22All : degreeTree26_22.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13178,⟨sg13174,⟨sg13172,⟨sg13171,⟨sg13170,True.intro,True.intro⟩,True.intro⟩,⟨sg13173,True.intro,True.intro⟩⟩,⟨sg13176,⟨sg13175,True.intro,True.intro⟩,⟨sg13177,True.intro,True.intro⟩⟩⟩,⟨sg13182,⟨sg13180,⟨sg13179,True.intro,True.intro⟩,⟨sg13181,True.intro,True.intro⟩⟩,⟨sg13184,⟨sg13183,True.intro,True.intro⟩,⟨sg13185,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_23All : degreeTree26_23.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13194,⟨sg13190,⟨sg13188,⟨sg13187,True.intro,True.intro⟩,⟨sg13189,True.intro,True.intro⟩⟩,⟨sg13192,⟨sg13191,True.intro,True.intro⟩,⟨sg13193,True.intro,True.intro⟩⟩⟩,⟨sg13198,⟨sg13196,⟨sg13195,True.intro,True.intro⟩,⟨sg13197,True.intro,True.intro⟩⟩,⟨sg13200,⟨sg13199,True.intro,True.intro⟩,⟨sg13201,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_24All : degreeTree26_24.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13186,degreeTree26_22All,degreeTree26_23All⟩ + +lemma degreeTree26_25All : degreeTree26_25.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13211,⟨sg13207,⟨sg13205,⟨sg13204,⟨sg13203,True.intro,True.intro⟩,True.intro⟩,⟨sg13206,True.intro,True.intro⟩⟩,⟨sg13209,⟨sg13208,True.intro,True.intro⟩,⟨sg13210,True.intro,True.intro⟩⟩⟩,⟨sg13215,⟨sg13213,⟨sg13212,True.intro,True.intro⟩,⟨sg13214,True.intro,True.intro⟩⟩,⟨sg13217,⟨sg13216,True.intro,True.intro⟩,⟨sg13218,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_26All : degreeTree26_26.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13227,⟨sg13223,⟨sg13221,⟨sg13220,True.intro,True.intro⟩,⟨sg13222,True.intro,True.intro⟩⟩,⟨sg13225,⟨sg13224,True.intro,True.intro⟩,⟨sg13226,True.intro,True.intro⟩⟩⟩,⟨sg13231,⟨sg13229,⟨sg13228,True.intro,True.intro⟩,⟨sg13230,True.intro,True.intro⟩⟩,⟨sg13233,⟨sg13232,True.intro,True.intro⟩,⟨sg13234,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_27All : degreeTree26_27.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13219,degreeTree26_25All,degreeTree26_26All⟩ + +lemma degreeTree26_28All : degreeTree26_28.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13202,degreeTree26_24All,degreeTree26_27All⟩ + +lemma degreeTree26_29All : degreeTree26_29.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13169,degreeTree26_21All,degreeTree26_28All⟩ + +lemma degreeTree26_30All : degreeTree26_30.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13103,degreeTree26_14All,degreeTree26_29All⟩ + +lemma degreeTree26_31All : degreeTree26_31.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13244,⟨sg13240,⟨sg13238,⟨sg13237,⟨sg13236,True.intro,True.intro⟩,True.intro⟩,⟨sg13239,True.intro,True.intro⟩⟩,⟨sg13242,⟨sg13241,True.intro,True.intro⟩,⟨sg13243,True.intro,True.intro⟩⟩⟩,⟨sg13248,⟨sg13246,⟨sg13245,True.intro,True.intro⟩,⟨sg13247,True.intro,True.intro⟩⟩,⟨sg13250,⟨sg13249,True.intro,True.intro⟩,⟨sg13251,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_32All : degreeTree26_32.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13260,⟨sg13256,⟨sg13254,⟨sg13253,True.intro,True.intro⟩,⟨sg13255,True.intro,True.intro⟩⟩,⟨sg13258,⟨sg13257,True.intro,True.intro⟩,⟨sg13259,True.intro,True.intro⟩⟩⟩,⟨sg13264,⟨sg13262,⟨sg13261,True.intro,True.intro⟩,⟨sg13263,True.intro,True.intro⟩⟩,⟨sg13266,⟨sg13265,True.intro,True.intro⟩,⟨sg13267,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_33All : degreeTree26_33.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13252,degreeTree26_31All,degreeTree26_32All⟩ + +lemma degreeTree26_34All : degreeTree26_34.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13277,⟨sg13273,⟨sg13271,⟨sg13270,⟨sg13269,True.intro,True.intro⟩,True.intro⟩,⟨sg13272,True.intro,True.intro⟩⟩,⟨sg13275,⟨sg13274,True.intro,True.intro⟩,⟨sg13276,True.intro,True.intro⟩⟩⟩,⟨sg13281,⟨sg13279,⟨sg13278,True.intro,True.intro⟩,⟨sg13280,True.intro,True.intro⟩⟩,⟨sg13283,⟨sg13282,True.intro,True.intro⟩,⟨sg13284,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_35All : degreeTree26_35.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13293,⟨sg13289,⟨sg13287,⟨sg13286,True.intro,True.intro⟩,⟨sg13288,True.intro,True.intro⟩⟩,⟨sg13291,⟨sg13290,True.intro,True.intro⟩,⟨sg13292,True.intro,True.intro⟩⟩⟩,⟨sg13297,⟨sg13295,⟨sg13294,True.intro,True.intro⟩,⟨sg13296,True.intro,True.intro⟩⟩,⟨sg13299,⟨sg13298,True.intro,True.intro⟩,⟨sg13300,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_36All : degreeTree26_36.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13285,degreeTree26_34All,degreeTree26_35All⟩ + +lemma degreeTree26_37All : degreeTree26_37.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13268,degreeTree26_33All,degreeTree26_36All⟩ + +lemma degreeTree26_38All : degreeTree26_38.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13310,⟨sg13306,⟨sg13304,⟨sg13303,⟨sg13302,True.intro,True.intro⟩,True.intro⟩,⟨sg13305,True.intro,True.intro⟩⟩,⟨sg13308,⟨sg13307,True.intro,True.intro⟩,⟨sg13309,True.intro,True.intro⟩⟩⟩,⟨sg13314,⟨sg13312,⟨sg13311,True.intro,True.intro⟩,⟨sg13313,True.intro,True.intro⟩⟩,⟨sg13316,⟨sg13315,True.intro,True.intro⟩,⟨sg13317,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_39All : degreeTree26_39.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13326,⟨sg13322,⟨sg13320,⟨sg13319,True.intro,True.intro⟩,⟨sg13321,True.intro,True.intro⟩⟩,⟨sg13324,⟨sg13323,True.intro,True.intro⟩,⟨sg13325,True.intro,True.intro⟩⟩⟩,⟨sg13330,⟨sg13328,⟨sg13327,True.intro,True.intro⟩,⟨sg13329,True.intro,True.intro⟩⟩,⟨sg13332,⟨sg13331,True.intro,True.intro⟩,⟨sg13333,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_40All : degreeTree26_40.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13318,degreeTree26_38All,degreeTree26_39All⟩ + +lemma degreeTree26_41All : degreeTree26_41.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13343,⟨sg13339,⟨sg13337,⟨sg13336,⟨sg13335,True.intro,True.intro⟩,True.intro⟩,⟨sg13338,True.intro,True.intro⟩⟩,⟨sg13341,⟨sg13340,True.intro,True.intro⟩,⟨sg13342,True.intro,True.intro⟩⟩⟩,⟨sg13347,⟨sg13345,⟨sg13344,True.intro,True.intro⟩,⟨sg13346,True.intro,True.intro⟩⟩,⟨sg13349,⟨sg13348,True.intro,True.intro⟩,⟨sg13350,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_42All : degreeTree26_42.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13359,⟨sg13355,⟨sg13353,⟨sg13352,True.intro,True.intro⟩,⟨sg13354,True.intro,True.intro⟩⟩,⟨sg13357,⟨sg13356,True.intro,True.intro⟩,⟨sg13358,True.intro,True.intro⟩⟩⟩,⟨sg13363,⟨sg13361,⟨sg13360,True.intro,True.intro⟩,⟨sg13362,True.intro,True.intro⟩⟩,⟨sg13365,⟨sg13364,True.intro,True.intro⟩,⟨sg13366,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_43All : degreeTree26_43.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13351,degreeTree26_41All,degreeTree26_42All⟩ + +lemma degreeTree26_44All : degreeTree26_44.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13334,degreeTree26_40All,degreeTree26_43All⟩ + +lemma degreeTree26_45All : degreeTree26_45.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13301,degreeTree26_37All,degreeTree26_44All⟩ + +lemma degreeTree26_46All : degreeTree26_46.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13376,⟨sg13372,⟨sg13370,⟨sg13369,⟨sg13368,True.intro,True.intro⟩,True.intro⟩,⟨sg13371,True.intro,True.intro⟩⟩,⟨sg13374,⟨sg13373,True.intro,True.intro⟩,⟨sg13375,True.intro,True.intro⟩⟩⟩,⟨sg13380,⟨sg13378,⟨sg13377,True.intro,True.intro⟩,⟨sg13379,True.intro,True.intro⟩⟩,⟨sg13382,⟨sg13381,True.intro,True.intro⟩,⟨sg13383,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_47All : degreeTree26_47.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13392,⟨sg13388,⟨sg13386,⟨sg13385,True.intro,True.intro⟩,⟨sg13387,True.intro,True.intro⟩⟩,⟨sg13390,⟨sg13389,True.intro,True.intro⟩,⟨sg13391,True.intro,True.intro⟩⟩⟩,⟨sg13396,⟨sg13394,⟨sg13393,True.intro,True.intro⟩,⟨sg13395,True.intro,True.intro⟩⟩,⟨sg13398,⟨sg13397,True.intro,True.intro⟩,⟨sg13399,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_48All : degreeTree26_48.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13384,degreeTree26_46All,degreeTree26_47All⟩ + +lemma degreeTree26_49All : degreeTree26_49.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13409,⟨sg13405,⟨sg13403,⟨sg13402,⟨sg13401,True.intro,True.intro⟩,True.intro⟩,⟨sg13404,True.intro,True.intro⟩⟩,⟨sg13407,⟨sg13406,True.intro,True.intro⟩,⟨sg13408,True.intro,True.intro⟩⟩⟩,⟨sg13413,⟨sg13411,⟨sg13410,True.intro,True.intro⟩,⟨sg13412,True.intro,True.intro⟩⟩,⟨sg13415,⟨sg13414,True.intro,True.intro⟩,⟨sg13416,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_50All : degreeTree26_50.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13425,⟨sg13421,⟨sg13419,⟨sg13418,True.intro,True.intro⟩,⟨sg13420,True.intro,True.intro⟩⟩,⟨sg13423,⟨sg13422,True.intro,True.intro⟩,⟨sg13424,True.intro,True.intro⟩⟩⟩,⟨sg13429,⟨sg13427,⟨sg13426,True.intro,True.intro⟩,⟨sg13428,True.intro,True.intro⟩⟩,⟨sg13431,⟨sg13430,True.intro,True.intro⟩,⟨sg13432,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_51All : degreeTree26_51.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13417,degreeTree26_49All,degreeTree26_50All⟩ + +lemma degreeTree26_52All : degreeTree26_52.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13400,degreeTree26_48All,degreeTree26_51All⟩ + +lemma degreeTree26_53All : degreeTree26_53.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13442,⟨sg13438,⟨sg13436,⟨sg13435,⟨sg13434,True.intro,True.intro⟩,True.intro⟩,⟨sg13437,True.intro,True.intro⟩⟩,⟨sg13440,⟨sg13439,True.intro,True.intro⟩,⟨sg13441,True.intro,True.intro⟩⟩⟩,⟨sg13446,⟨sg13444,⟨sg13443,True.intro,True.intro⟩,⟨sg13445,True.intro,True.intro⟩⟩,⟨sg13448,⟨sg13447,True.intro,True.intro⟩,⟨sg13449,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_54All : degreeTree26_54.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13458,⟨sg13454,⟨sg13452,⟨sg13451,True.intro,True.intro⟩,⟨sg13453,True.intro,True.intro⟩⟩,⟨sg13456,⟨sg13455,True.intro,True.intro⟩,⟨sg13457,True.intro,True.intro⟩⟩⟩,⟨sg13462,⟨sg13460,⟨sg13459,True.intro,True.intro⟩,⟨sg13461,True.intro,True.intro⟩⟩,⟨sg13464,⟨sg13463,True.intro,True.intro⟩,⟨sg13465,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_55All : degreeTree26_55.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13450,degreeTree26_53All,degreeTree26_54All⟩ + +lemma degreeTree26_56All : degreeTree26_56.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13475,⟨sg13471,⟨sg13469,⟨sg13468,⟨sg13467,True.intro,True.intro⟩,True.intro⟩,⟨sg13470,True.intro,True.intro⟩⟩,⟨sg13473,⟨sg13472,True.intro,True.intro⟩,⟨sg13474,True.intro,True.intro⟩⟩⟩,⟨sg13479,⟨sg13477,⟨sg13476,True.intro,True.intro⟩,⟨sg13478,True.intro,True.intro⟩⟩,⟨sg13481,⟨sg13480,True.intro,True.intro⟩,⟨sg13482,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_57All : degreeTree26_57.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13491,⟨sg13487,⟨sg13485,⟨sg13484,True.intro,True.intro⟩,⟨sg13486,True.intro,True.intro⟩⟩,⟨sg13489,⟨sg13488,True.intro,True.intro⟩,⟨sg13490,True.intro,True.intro⟩⟩⟩,⟨sg13495,⟨sg13493,⟨sg13492,True.intro,True.intro⟩,⟨sg13494,True.intro,True.intro⟩⟩,⟨sg13497,⟨sg13496,True.intro,True.intro⟩,⟨sg13498,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree26_58All : degreeTree26_58.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13483,degreeTree26_56All,degreeTree26_57All⟩ + +lemma degreeTree26_59All : degreeTree26_59.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13466,degreeTree26_55All,degreeTree26_58All⟩ + +lemma degreeTree26_60All : degreeTree26_60.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13433,degreeTree26_52All,degreeTree26_59All⟩ + +lemma degreeTree26_61All : degreeTree26_61.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13367,degreeTree26_45All,degreeTree26_60All⟩ + +lemma degreeTree26_62All : degreeTree26_62.All (RowSquare [8,7,2,2,2,2,2,1]) := by + exact ⟨sg13235,degreeTree26_30All,degreeTree26_61All⟩ + +lemma degreeTreeAll26 : degreeTree26.All + (fun rs => SquareOccurs (candidate 4 4 0) (rowDiagram rs)) := by + have hp : rowDiagram [8,7,2,2,2,2,2,1] = candidate 4 4 0 := rowDiagram_candidate (M := 4) (b := 4) (δ := 0) (by decide) + rw [← hp] + exact degreeTree26_62All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof31.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof31.lean index 615ff454e3143cf0dbadaa3339858dcf62dfe4e8..d0b7055af473fbaa42fd825bd61a2d76144250dd 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof31.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof31.lean @@ -1,35 +1,35 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData31 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes50 - -namespace OAI - -/-! Degree Tree Proof 31. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree31_0All : degreeTree31_0.All (RowSquare [9,7,4,3,2,2,2,1,1]) := by - exact ⟨sg20595,⟨sg20589,⟨sg20586,⟨sg20584,⟨sg20583,True.intro,True.intro⟩,⟨sg20585,True.intro,True.intro⟩⟩,⟨sg20588,⟨sg20587,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg20592,⟨sg20591,⟨sg20590,True.intro,True.intro⟩,True.intro⟩,⟨sg20594,⟨sg20593,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg20601,⟨sg20598,⟨sg20597,⟨sg20596,True.intro,True.intro⟩,True.intro⟩,⟨sg20600,⟨sg20599,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg20604,⟨sg20603,⟨sg20602,True.intro,True.intro⟩,True.intro⟩,⟨sg20606,⟨sg20605,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree31_1All : degreeTree31_1.All (RowSquare [9,7,4,3,2,2,2,1,1]) := by - exact ⟨sg20619,⟨sg20613,⟨sg20610,⟨sg20609,⟨sg20608,True.intro,True.intro⟩,True.intro⟩,⟨sg20612,⟨sg20611,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg20616,⟨sg20615,⟨sg20614,True.intro,True.intro⟩,True.intro⟩,⟨sg20618,⟨sg20617,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg20625,⟨sg20622,⟨sg20621,⟨sg20620,True.intro,True.intro⟩,True.intro⟩,⟨sg20624,⟨sg20623,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg20628,⟨sg20627,⟨sg20626,True.intro,True.intro⟩,True.intro⟩,⟨sg20630,⟨sg20629,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree31_2All : degreeTree31_2.All (RowSquare [9,7,4,3,2,2,2,1,1]) := by - exact ⟨sg20607,degreeTree31_0All,degreeTree31_1All⟩ - -lemma degreeTreeAll31 : degreeTree31.All - (fun rs => SquareOccurs (candidate 6 2 1) (rowDiagram rs)) := by - have hp : rowDiagram [9,7,4,3,2,2,2,1,1] = candidate 6 2 1 := rowDiagram_candidate (M := 6) (b := 2) (δ := 1) (by decide) - rw [← hp] - exact degreeTree31_2All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData31 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes50 + +namespace OAI + +/-! Degree Tree Proof 31. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree31_0All : degreeTree31_0.All (RowSquare [9,7,4,3,2,2,2,1,1]) := by + exact ⟨sg20595,⟨sg20589,⟨sg20586,⟨sg20584,⟨sg20583,True.intro,True.intro⟩,⟨sg20585,True.intro,True.intro⟩⟩,⟨sg20588,⟨sg20587,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg20592,⟨sg20591,⟨sg20590,True.intro,True.intro⟩,True.intro⟩,⟨sg20594,⟨sg20593,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg20601,⟨sg20598,⟨sg20597,⟨sg20596,True.intro,True.intro⟩,True.intro⟩,⟨sg20600,⟨sg20599,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg20604,⟨sg20603,⟨sg20602,True.intro,True.intro⟩,True.intro⟩,⟨sg20606,⟨sg20605,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree31_1All : degreeTree31_1.All (RowSquare [9,7,4,3,2,2,2,1,1]) := by + exact ⟨sg20619,⟨sg20613,⟨sg20610,⟨sg20609,⟨sg20608,True.intro,True.intro⟩,True.intro⟩,⟨sg20612,⟨sg20611,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg20616,⟨sg20615,⟨sg20614,True.intro,True.intro⟩,True.intro⟩,⟨sg20618,⟨sg20617,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg20625,⟨sg20622,⟨sg20621,⟨sg20620,True.intro,True.intro⟩,True.intro⟩,⟨sg20624,⟨sg20623,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg20628,⟨sg20627,⟨sg20626,True.intro,True.intro⟩,True.intro⟩,⟨sg20630,⟨sg20629,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree31_2All : degreeTree31_2.All (RowSquare [9,7,4,3,2,2,2,1,1]) := by + exact ⟨sg20607,degreeTree31_0All,degreeTree31_1All⟩ + +lemma degreeTreeAll31 : degreeTree31.All + (fun rs => SquareOccurs (candidate 6 2 1) (rowDiagram rs)) := by + have hp : rowDiagram [9,7,4,3,2,2,2,1,1] = candidate 6 2 1 := rowDiagram_candidate (M := 6) (b := 2) (δ := 1) (by decide) + rw [← hp] + exact degreeTree31_2All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof35.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof35.lean index bfa4342084ce997904953cc3b5e8c4a0ba89548e..9a7359f2e580b9e800a352403ec22b8f36b30cb1 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof35.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof35.lean @@ -1,101 +1,101 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData35 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 - -namespace OAI - -/-! Degree Tree Proof 35. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree35_0All : degreeTree35_0.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21357,⟨sg21353,⟨sg21351,⟨sg21350,⟨sg21349,True.intro,True.intro⟩,True.intro⟩,⟨sg21352,True.intro,True.intro⟩⟩,⟨sg21355,⟨sg21354,True.intro,True.intro⟩,⟨sg21356,True.intro,True.intro⟩⟩⟩,⟨sg21361,⟨sg21359,⟨sg21358,True.intro,True.intro⟩,⟨sg21360,True.intro,True.intro⟩⟩,⟨sg21363,⟨sg21362,True.intro,True.intro⟩,⟨sg21364,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree35_1All : degreeTree35_1.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21373,⟨sg21369,⟨sg21367,⟨sg21366,True.intro,True.intro⟩,⟨sg21368,True.intro,True.intro⟩⟩,⟨sg21371,⟨sg21370,True.intro,True.intro⟩,⟨sg21372,True.intro,True.intro⟩⟩⟩,⟨sg21377,⟨sg21375,⟨sg21374,True.intro,True.intro⟩,⟨sg21376,True.intro,True.intro⟩⟩,⟨sg21379,⟨sg21378,True.intro,True.intro⟩,⟨sg21380,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree35_2All : degreeTree35_2.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21365,degreeTree35_0All,degreeTree35_1All⟩ - -lemma degreeTree35_3All : degreeTree35_3.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21390,⟨sg21386,⟨sg21384,⟨sg21383,⟨sg21382,True.intro,True.intro⟩,True.intro⟩,⟨sg21385,True.intro,True.intro⟩⟩,⟨sg21388,⟨sg21387,True.intro,True.intro⟩,⟨sg21389,True.intro,True.intro⟩⟩⟩,⟨sg21394,⟨sg21392,⟨sg21391,True.intro,True.intro⟩,⟨sg21393,True.intro,True.intro⟩⟩,⟨sg21396,⟨sg21395,True.intro,True.intro⟩,⟨sg21397,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree35_4All : degreeTree35_4.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21406,⟨sg21402,⟨sg21400,⟨sg21399,True.intro,True.intro⟩,⟨sg21401,True.intro,True.intro⟩⟩,⟨sg21404,⟨sg21403,True.intro,True.intro⟩,⟨sg21405,True.intro,True.intro⟩⟩⟩,⟨sg21410,⟨sg21408,⟨sg21407,True.intro,True.intro⟩,⟨sg21409,True.intro,True.intro⟩⟩,⟨sg21412,⟨sg21411,True.intro,True.intro⟩,⟨sg21413,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree35_5All : degreeTree35_5.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21398,degreeTree35_3All,degreeTree35_4All⟩ - -lemma degreeTree35_6All : degreeTree35_6.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21381,degreeTree35_2All,degreeTree35_5All⟩ - -lemma degreeTree35_7All : degreeTree35_7.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21423,⟨sg21419,⟨sg21417,⟨sg21416,⟨sg21415,True.intro,True.intro⟩,True.intro⟩,⟨sg21418,True.intro,True.intro⟩⟩,⟨sg21421,⟨sg21420,True.intro,True.intro⟩,⟨sg21422,True.intro,True.intro⟩⟩⟩,⟨sg21427,⟨sg21425,⟨sg21424,True.intro,True.intro⟩,⟨sg21426,True.intro,True.intro⟩⟩,⟨sg21429,⟨sg21428,True.intro,True.intro⟩,⟨sg21430,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree35_8All : degreeTree35_8.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21439,⟨sg21435,⟨sg21433,⟨sg21432,True.intro,True.intro⟩,⟨sg21434,True.intro,True.intro⟩⟩,⟨sg21437,⟨sg21436,True.intro,True.intro⟩,⟨sg21438,True.intro,True.intro⟩⟩⟩,⟨sg21443,⟨sg21441,⟨sg21440,True.intro,True.intro⟩,⟨sg21442,True.intro,True.intro⟩⟩,⟨sg21445,⟨sg21444,True.intro,True.intro⟩,⟨sg21446,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree35_9All : degreeTree35_9.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21431,degreeTree35_7All,degreeTree35_8All⟩ - -lemma degreeTree35_10All : degreeTree35_10.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21463,⟨sg21455,⟨sg21451,⟨sg21449,⟨sg21448,True.intro,True.intro⟩,⟨sg21450,True.intro,True.intro⟩⟩,⟨sg21453,⟨sg21452,True.intro,True.intro⟩,⟨sg21454,True.intro,True.intro⟩⟩⟩,⟨sg21459,⟨sg21457,⟨sg21456,True.intro,True.intro⟩,⟨sg21458,True.intro,True.intro⟩⟩,⟨sg21461,⟨sg21460,True.intro,True.intro⟩,⟨sg21462,True.intro,True.intro⟩⟩⟩⟩,⟨sg21471,⟨sg21467,⟨sg21465,⟨sg21464,True.intro,True.intro⟩,⟨sg21466,True.intro,True.intro⟩⟩,⟨sg21469,⟨sg21468,True.intro,True.intro⟩,⟨sg21470,True.intro,True.intro⟩⟩⟩,⟨sg21475,⟨sg21473,⟨sg21472,True.intro,True.intro⟩,⟨sg21474,True.intro,True.intro⟩⟩,⟨sg21477,⟨sg21476,True.intro,True.intro⟩,⟨sg21478,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree35_11All : degreeTree35_11.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21447,degreeTree35_9All,degreeTree35_10All⟩ - -lemma degreeTree35_12All : degreeTree35_12.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21414,degreeTree35_6All,degreeTree35_11All⟩ - -lemma degreeTree35_13All : degreeTree35_13.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21488,⟨sg21484,⟨sg21482,⟨sg21481,⟨sg21480,True.intro,True.intro⟩,True.intro⟩,⟨sg21483,True.intro,True.intro⟩⟩,⟨sg21486,⟨sg21485,True.intro,True.intro⟩,⟨sg21487,True.intro,True.intro⟩⟩⟩,⟨sg21492,⟨sg21490,⟨sg21489,True.intro,True.intro⟩,⟨sg21491,True.intro,True.intro⟩⟩,⟨sg21494,⟨sg21493,True.intro,True.intro⟩,⟨sg21495,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree35_14All : degreeTree35_14.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21504,⟨sg21500,⟨sg21498,⟨sg21497,True.intro,True.intro⟩,⟨sg21499,True.intro,True.intro⟩⟩,⟨sg21502,⟨sg21501,True.intro,True.intro⟩,⟨sg21503,True.intro,True.intro⟩⟩⟩,⟨sg21508,⟨sg21506,⟨sg21505,True.intro,True.intro⟩,⟨sg21507,True.intro,True.intro⟩⟩,⟨sg21510,⟨sg21509,True.intro,True.intro⟩,⟨sg21511,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree35_15All : degreeTree35_15.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21496,degreeTree35_13All,degreeTree35_14All⟩ - -lemma degreeTree35_16All : degreeTree35_16.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21528,⟨sg21520,⟨sg21516,⟨sg21514,⟨sg21513,True.intro,True.intro⟩,⟨sg21515,True.intro,True.intro⟩⟩,⟨sg21518,⟨sg21517,True.intro,True.intro⟩,⟨sg21519,True.intro,True.intro⟩⟩⟩,⟨sg21524,⟨sg21522,⟨sg21521,True.intro,True.intro⟩,⟨sg21523,True.intro,True.intro⟩⟩,⟨sg21526,⟨sg21525,True.intro,True.intro⟩,⟨sg21527,True.intro,True.intro⟩⟩⟩⟩,⟨sg21536,⟨sg21532,⟨sg21530,⟨sg21529,True.intro,True.intro⟩,⟨sg21531,True.intro,True.intro⟩⟩,⟨sg21534,⟨sg21533,True.intro,True.intro⟩,⟨sg21535,True.intro,True.intro⟩⟩⟩,⟨sg21540,⟨sg21538,⟨sg21537,True.intro,True.intro⟩,⟨sg21539,True.intro,True.intro⟩⟩,⟨sg21542,⟨sg21541,True.intro,True.intro⟩,⟨sg21543,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree35_17All : degreeTree35_17.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21512,degreeTree35_15All,degreeTree35_16All⟩ - -lemma degreeTree35_18All : degreeTree35_18.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21553,⟨sg21549,⟨sg21547,⟨sg21546,⟨sg21545,True.intro,True.intro⟩,True.intro⟩,⟨sg21548,True.intro,True.intro⟩⟩,⟨sg21551,⟨sg21550,True.intro,True.intro⟩,⟨sg21552,True.intro,True.intro⟩⟩⟩,⟨sg21557,⟨sg21555,⟨sg21554,True.intro,True.intro⟩,⟨sg21556,True.intro,True.intro⟩⟩,⟨sg21559,⟨sg21558,True.intro,True.intro⟩,⟨sg21560,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree35_19All : degreeTree35_19.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21569,⟨sg21565,⟨sg21563,⟨sg21562,True.intro,True.intro⟩,⟨sg21564,True.intro,True.intro⟩⟩,⟨sg21567,⟨sg21566,True.intro,True.intro⟩,⟨sg21568,True.intro,True.intro⟩⟩⟩,⟨sg21573,⟨sg21571,⟨sg21570,True.intro,True.intro⟩,⟨sg21572,True.intro,True.intro⟩⟩,⟨sg21575,⟨sg21574,True.intro,True.intro⟩,⟨sg21576,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree35_20All : degreeTree35_20.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21561,degreeTree35_18All,degreeTree35_19All⟩ - -lemma degreeTree35_21All : degreeTree35_21.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21593,⟨sg21585,⟨sg21581,⟨sg21579,⟨sg21578,True.intro,True.intro⟩,⟨sg21580,True.intro,True.intro⟩⟩,⟨sg21583,⟨sg21582,True.intro,True.intro⟩,⟨sg21584,True.intro,True.intro⟩⟩⟩,⟨sg21589,⟨sg21587,⟨sg21586,True.intro,True.intro⟩,⟨sg21588,True.intro,True.intro⟩⟩,⟨sg21591,⟨sg21590,True.intro,True.intro⟩,⟨sg21592,True.intro,True.intro⟩⟩⟩⟩,⟨sg21601,⟨sg21597,⟨sg21595,⟨sg21594,True.intro,True.intro⟩,⟨sg21596,True.intro,True.intro⟩⟩,⟨sg21599,⟨sg21598,True.intro,True.intro⟩,⟨sg21600,True.intro,True.intro⟩⟩⟩,⟨sg21605,⟨sg21603,⟨sg21602,True.intro,True.intro⟩,⟨sg21604,True.intro,True.intro⟩⟩,⟨sg21607,⟨sg21606,True.intro,True.intro⟩,⟨sg21608,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree35_22All : degreeTree35_22.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21577,degreeTree35_20All,degreeTree35_21All⟩ - -lemma degreeTree35_23All : degreeTree35_23.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21544,degreeTree35_17All,degreeTree35_22All⟩ - -lemma degreeTree35_24All : degreeTree35_24.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by - exact ⟨sg21479,degreeTree35_12All,degreeTree35_23All⟩ - -lemma degreeTreeAll35 : degreeTree35.All - (fun rs => SquareOccurs (candidate 6 3 1) (rowDiagram rs)) := by - have hp : rowDiagram [10,8,4,3,2,2,2,2,1,1] = candidate 6 3 1 := rowDiagram_candidate (M := 6) (b := 3) (δ := 1) (by decide) - rw [← hp] - exact degreeTree35_24All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData35 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 + +namespace OAI + +/-! Degree Tree Proof 35. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree35_0All : degreeTree35_0.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21357,⟨sg21353,⟨sg21351,⟨sg21350,⟨sg21349,True.intro,True.intro⟩,True.intro⟩,⟨sg21352,True.intro,True.intro⟩⟩,⟨sg21355,⟨sg21354,True.intro,True.intro⟩,⟨sg21356,True.intro,True.intro⟩⟩⟩,⟨sg21361,⟨sg21359,⟨sg21358,True.intro,True.intro⟩,⟨sg21360,True.intro,True.intro⟩⟩,⟨sg21363,⟨sg21362,True.intro,True.intro⟩,⟨sg21364,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree35_1All : degreeTree35_1.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21373,⟨sg21369,⟨sg21367,⟨sg21366,True.intro,True.intro⟩,⟨sg21368,True.intro,True.intro⟩⟩,⟨sg21371,⟨sg21370,True.intro,True.intro⟩,⟨sg21372,True.intro,True.intro⟩⟩⟩,⟨sg21377,⟨sg21375,⟨sg21374,True.intro,True.intro⟩,⟨sg21376,True.intro,True.intro⟩⟩,⟨sg21379,⟨sg21378,True.intro,True.intro⟩,⟨sg21380,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree35_2All : degreeTree35_2.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21365,degreeTree35_0All,degreeTree35_1All⟩ + +lemma degreeTree35_3All : degreeTree35_3.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21390,⟨sg21386,⟨sg21384,⟨sg21383,⟨sg21382,True.intro,True.intro⟩,True.intro⟩,⟨sg21385,True.intro,True.intro⟩⟩,⟨sg21388,⟨sg21387,True.intro,True.intro⟩,⟨sg21389,True.intro,True.intro⟩⟩⟩,⟨sg21394,⟨sg21392,⟨sg21391,True.intro,True.intro⟩,⟨sg21393,True.intro,True.intro⟩⟩,⟨sg21396,⟨sg21395,True.intro,True.intro⟩,⟨sg21397,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree35_4All : degreeTree35_4.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21406,⟨sg21402,⟨sg21400,⟨sg21399,True.intro,True.intro⟩,⟨sg21401,True.intro,True.intro⟩⟩,⟨sg21404,⟨sg21403,True.intro,True.intro⟩,⟨sg21405,True.intro,True.intro⟩⟩⟩,⟨sg21410,⟨sg21408,⟨sg21407,True.intro,True.intro⟩,⟨sg21409,True.intro,True.intro⟩⟩,⟨sg21412,⟨sg21411,True.intro,True.intro⟩,⟨sg21413,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree35_5All : degreeTree35_5.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21398,degreeTree35_3All,degreeTree35_4All⟩ + +lemma degreeTree35_6All : degreeTree35_6.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21381,degreeTree35_2All,degreeTree35_5All⟩ + +lemma degreeTree35_7All : degreeTree35_7.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21423,⟨sg21419,⟨sg21417,⟨sg21416,⟨sg21415,True.intro,True.intro⟩,True.intro⟩,⟨sg21418,True.intro,True.intro⟩⟩,⟨sg21421,⟨sg21420,True.intro,True.intro⟩,⟨sg21422,True.intro,True.intro⟩⟩⟩,⟨sg21427,⟨sg21425,⟨sg21424,True.intro,True.intro⟩,⟨sg21426,True.intro,True.intro⟩⟩,⟨sg21429,⟨sg21428,True.intro,True.intro⟩,⟨sg21430,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree35_8All : degreeTree35_8.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21439,⟨sg21435,⟨sg21433,⟨sg21432,True.intro,True.intro⟩,⟨sg21434,True.intro,True.intro⟩⟩,⟨sg21437,⟨sg21436,True.intro,True.intro⟩,⟨sg21438,True.intro,True.intro⟩⟩⟩,⟨sg21443,⟨sg21441,⟨sg21440,True.intro,True.intro⟩,⟨sg21442,True.intro,True.intro⟩⟩,⟨sg21445,⟨sg21444,True.intro,True.intro⟩,⟨sg21446,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree35_9All : degreeTree35_9.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21431,degreeTree35_7All,degreeTree35_8All⟩ + +lemma degreeTree35_10All : degreeTree35_10.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21463,⟨sg21455,⟨sg21451,⟨sg21449,⟨sg21448,True.intro,True.intro⟩,⟨sg21450,True.intro,True.intro⟩⟩,⟨sg21453,⟨sg21452,True.intro,True.intro⟩,⟨sg21454,True.intro,True.intro⟩⟩⟩,⟨sg21459,⟨sg21457,⟨sg21456,True.intro,True.intro⟩,⟨sg21458,True.intro,True.intro⟩⟩,⟨sg21461,⟨sg21460,True.intro,True.intro⟩,⟨sg21462,True.intro,True.intro⟩⟩⟩⟩,⟨sg21471,⟨sg21467,⟨sg21465,⟨sg21464,True.intro,True.intro⟩,⟨sg21466,True.intro,True.intro⟩⟩,⟨sg21469,⟨sg21468,True.intro,True.intro⟩,⟨sg21470,True.intro,True.intro⟩⟩⟩,⟨sg21475,⟨sg21473,⟨sg21472,True.intro,True.intro⟩,⟨sg21474,True.intro,True.intro⟩⟩,⟨sg21477,⟨sg21476,True.intro,True.intro⟩,⟨sg21478,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree35_11All : degreeTree35_11.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21447,degreeTree35_9All,degreeTree35_10All⟩ + +lemma degreeTree35_12All : degreeTree35_12.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21414,degreeTree35_6All,degreeTree35_11All⟩ + +lemma degreeTree35_13All : degreeTree35_13.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21488,⟨sg21484,⟨sg21482,⟨sg21481,⟨sg21480,True.intro,True.intro⟩,True.intro⟩,⟨sg21483,True.intro,True.intro⟩⟩,⟨sg21486,⟨sg21485,True.intro,True.intro⟩,⟨sg21487,True.intro,True.intro⟩⟩⟩,⟨sg21492,⟨sg21490,⟨sg21489,True.intro,True.intro⟩,⟨sg21491,True.intro,True.intro⟩⟩,⟨sg21494,⟨sg21493,True.intro,True.intro⟩,⟨sg21495,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree35_14All : degreeTree35_14.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21504,⟨sg21500,⟨sg21498,⟨sg21497,True.intro,True.intro⟩,⟨sg21499,True.intro,True.intro⟩⟩,⟨sg21502,⟨sg21501,True.intro,True.intro⟩,⟨sg21503,True.intro,True.intro⟩⟩⟩,⟨sg21508,⟨sg21506,⟨sg21505,True.intro,True.intro⟩,⟨sg21507,True.intro,True.intro⟩⟩,⟨sg21510,⟨sg21509,True.intro,True.intro⟩,⟨sg21511,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree35_15All : degreeTree35_15.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21496,degreeTree35_13All,degreeTree35_14All⟩ + +lemma degreeTree35_16All : degreeTree35_16.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21528,⟨sg21520,⟨sg21516,⟨sg21514,⟨sg21513,True.intro,True.intro⟩,⟨sg21515,True.intro,True.intro⟩⟩,⟨sg21518,⟨sg21517,True.intro,True.intro⟩,⟨sg21519,True.intro,True.intro⟩⟩⟩,⟨sg21524,⟨sg21522,⟨sg21521,True.intro,True.intro⟩,⟨sg21523,True.intro,True.intro⟩⟩,⟨sg21526,⟨sg21525,True.intro,True.intro⟩,⟨sg21527,True.intro,True.intro⟩⟩⟩⟩,⟨sg21536,⟨sg21532,⟨sg21530,⟨sg21529,True.intro,True.intro⟩,⟨sg21531,True.intro,True.intro⟩⟩,⟨sg21534,⟨sg21533,True.intro,True.intro⟩,⟨sg21535,True.intro,True.intro⟩⟩⟩,⟨sg21540,⟨sg21538,⟨sg21537,True.intro,True.intro⟩,⟨sg21539,True.intro,True.intro⟩⟩,⟨sg21542,⟨sg21541,True.intro,True.intro⟩,⟨sg21543,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree35_17All : degreeTree35_17.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21512,degreeTree35_15All,degreeTree35_16All⟩ + +lemma degreeTree35_18All : degreeTree35_18.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21553,⟨sg21549,⟨sg21547,⟨sg21546,⟨sg21545,True.intro,True.intro⟩,True.intro⟩,⟨sg21548,True.intro,True.intro⟩⟩,⟨sg21551,⟨sg21550,True.intro,True.intro⟩,⟨sg21552,True.intro,True.intro⟩⟩⟩,⟨sg21557,⟨sg21555,⟨sg21554,True.intro,True.intro⟩,⟨sg21556,True.intro,True.intro⟩⟩,⟨sg21559,⟨sg21558,True.intro,True.intro⟩,⟨sg21560,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree35_19All : degreeTree35_19.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21569,⟨sg21565,⟨sg21563,⟨sg21562,True.intro,True.intro⟩,⟨sg21564,True.intro,True.intro⟩⟩,⟨sg21567,⟨sg21566,True.intro,True.intro⟩,⟨sg21568,True.intro,True.intro⟩⟩⟩,⟨sg21573,⟨sg21571,⟨sg21570,True.intro,True.intro⟩,⟨sg21572,True.intro,True.intro⟩⟩,⟨sg21575,⟨sg21574,True.intro,True.intro⟩,⟨sg21576,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree35_20All : degreeTree35_20.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21561,degreeTree35_18All,degreeTree35_19All⟩ + +lemma degreeTree35_21All : degreeTree35_21.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21593,⟨sg21585,⟨sg21581,⟨sg21579,⟨sg21578,True.intro,True.intro⟩,⟨sg21580,True.intro,True.intro⟩⟩,⟨sg21583,⟨sg21582,True.intro,True.intro⟩,⟨sg21584,True.intro,True.intro⟩⟩⟩,⟨sg21589,⟨sg21587,⟨sg21586,True.intro,True.intro⟩,⟨sg21588,True.intro,True.intro⟩⟩,⟨sg21591,⟨sg21590,True.intro,True.intro⟩,⟨sg21592,True.intro,True.intro⟩⟩⟩⟩,⟨sg21601,⟨sg21597,⟨sg21595,⟨sg21594,True.intro,True.intro⟩,⟨sg21596,True.intro,True.intro⟩⟩,⟨sg21599,⟨sg21598,True.intro,True.intro⟩,⟨sg21600,True.intro,True.intro⟩⟩⟩,⟨sg21605,⟨sg21603,⟨sg21602,True.intro,True.intro⟩,⟨sg21604,True.intro,True.intro⟩⟩,⟨sg21607,⟨sg21606,True.intro,True.intro⟩,⟨sg21608,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree35_22All : degreeTree35_22.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21577,degreeTree35_20All,degreeTree35_21All⟩ + +lemma degreeTree35_23All : degreeTree35_23.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21544,degreeTree35_17All,degreeTree35_22All⟩ + +lemma degreeTree35_24All : degreeTree35_24.All (RowSquare [10,8,4,3,2,2,2,2,1,1]) := by + exact ⟨sg21479,degreeTree35_12All,degreeTree35_23All⟩ + +lemma degreeTreeAll35 : degreeTree35.All + (fun rs => SquareOccurs (candidate 6 3 1) (rowDiagram rs)) := by + have hp : rowDiagram [10,8,4,3,2,2,2,2,1,1] = candidate 6 3 1 := rowDiagram_candidate (M := 6) (b := 3) (δ := 1) (by decide) + rw [← hp] + exact degreeTree35_24All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof37.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof37.lean index d2ebec828813560361372d95b8f8d02308aedcca..70c393c0a736e58762ecce899912cee855b41768 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof37.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof37.lean @@ -1,29 +1,29 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData37 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 - -namespace OAI - -/-! Degree Tree Proof 37. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree37_0All : degreeTree37_0.All (RowSquare [10,9,4,3,2,2,2,2,2,1]) := by - exact ⟨sg21656,True.intro,True.intro⟩ - -lemma degreeTreeAll37 : degreeTree37.All - (fun rs => SquareOccurs (candidate 6 4 0) (rowDiagram rs)) := by - have hp : rowDiagram [10,9,4,3,2,2,2,2,2,1] = candidate 6 4 0 := rowDiagram_candidate (M := 6) (b := 4) (δ := 0) (by decide) - rw [← hp] - exact degreeTree37_0All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData37 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 + +namespace OAI + +/-! Degree Tree Proof 37. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree37_0All : degreeTree37_0.All (RowSquare [10,9,4,3,2,2,2,2,2,1]) := by + exact ⟨sg21656,True.intro,True.intro⟩ + +lemma degreeTreeAll37 : degreeTree37.All + (fun rs => SquareOccurs (candidate 6 4 0) (rowDiagram rs)) := by + have hp : rowDiagram [10,9,4,3,2,2,2,2,2,1] = candidate 6 4 0 := rowDiagram_candidate (M := 6) (b := 4) (δ := 0) (by decide) + rw [← hp] + exact degreeTree37_0All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof39.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof39.lean index 0108931cd662c6e10cdae4f806dc244eec28ab8c..2e8ca6a8268bf9d6c7f9c3076440e1203ea33997 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof39.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof39.lean @@ -1,411 +1,411 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes53 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes54 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes55 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes56 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes57 - -namespace OAI - -/-! Degree Tree Proof 39. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree39_0All : degreeTree39_0.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21685,⟨sg21678,⟨sg21674,⟨sg21672,⟨sg21671,True.intro,True.intro⟩,⟨sg21673,True.intro,True.intro⟩⟩,⟨sg21676,⟨sg21675,True.intro,True.intro⟩,⟨sg21677,True.intro,True.intro⟩⟩⟩,⟨sg21682,⟨sg21680,⟨sg21679,True.intro,True.intro⟩,⟨sg21681,True.intro,True.intro⟩⟩,⟨sg21684,⟨sg21683,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21693,⟨sg21689,⟨sg21687,⟨sg21686,True.intro,True.intro⟩,⟨sg21688,True.intro,True.intro⟩⟩,⟨sg21691,⟨sg21690,True.intro,True.intro⟩,⟨sg21692,True.intro,True.intro⟩⟩⟩,⟨sg21697,⟨sg21695,⟨sg21694,True.intro,True.intro⟩,⟨sg21696,True.intro,True.intro⟩⟩,⟨sg21699,⟨sg21698,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_1All : degreeTree39_1.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21715,⟨sg21708,⟨sg21704,⟨sg21702,⟨sg21701,True.intro,True.intro⟩,⟨sg21703,True.intro,True.intro⟩⟩,⟨sg21706,⟨sg21705,True.intro,True.intro⟩,⟨sg21707,True.intro,True.intro⟩⟩⟩,⟨sg21712,⟨sg21710,⟨sg21709,True.intro,True.intro⟩,⟨sg21711,True.intro,True.intro⟩⟩,⟨sg21714,⟨sg21713,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21722,⟨sg21719,⟨sg21717,⟨sg21716,True.intro,True.intro⟩,⟨sg21718,True.intro,True.intro⟩⟩,⟨sg21721,⟨sg21720,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21726,⟨sg21724,⟨sg21723,True.intro,True.intro⟩,⟨sg21725,True.intro,True.intro⟩⟩,⟨sg21728,⟨sg21727,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_2All : degreeTree39_2.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21700,degreeTree39_0All,degreeTree39_1All⟩ - -lemma degreeTree39_3All : degreeTree39_3.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21744,⟨sg21737,⟨sg21733,⟨sg21731,⟨sg21730,True.intro,True.intro⟩,⟨sg21732,True.intro,True.intro⟩⟩,⟨sg21735,⟨sg21734,True.intro,True.intro⟩,⟨sg21736,True.intro,True.intro⟩⟩⟩,⟨sg21741,⟨sg21739,⟨sg21738,True.intro,True.intro⟩,⟨sg21740,True.intro,True.intro⟩⟩,⟨sg21743,⟨sg21742,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21751,⟨sg21748,⟨sg21746,⟨sg21745,True.intro,True.intro⟩,⟨sg21747,True.intro,True.intro⟩⟩,⟨sg21750,⟨sg21749,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21755,⟨sg21753,⟨sg21752,True.intro,True.intro⟩,⟨sg21754,True.intro,True.intro⟩⟩,⟨sg21757,⟨sg21756,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_4All : degreeTree39_4.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21773,⟨sg21766,⟨sg21762,⟨sg21760,⟨sg21759,True.intro,True.intro⟩,⟨sg21761,True.intro,True.intro⟩⟩,⟨sg21764,⟨sg21763,True.intro,True.intro⟩,⟨sg21765,True.intro,True.intro⟩⟩⟩,⟨sg21770,⟨sg21768,⟨sg21767,True.intro,True.intro⟩,⟨sg21769,True.intro,True.intro⟩⟩,⟨sg21772,⟨sg21771,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21780,⟨sg21777,⟨sg21775,⟨sg21774,True.intro,True.intro⟩,⟨sg21776,True.intro,True.intro⟩⟩,⟨sg21779,⟨sg21778,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21784,⟨sg21782,⟨sg21781,True.intro,True.intro⟩,⟨sg21783,True.intro,True.intro⟩⟩,⟨sg21786,⟨sg21785,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_5All : degreeTree39_5.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21758,degreeTree39_3All,degreeTree39_4All⟩ - -lemma degreeTree39_6All : degreeTree39_6.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21729,degreeTree39_2All,degreeTree39_5All⟩ - -lemma degreeTree39_7All : degreeTree39_7.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21802,⟨sg21795,⟨sg21791,⟨sg21789,⟨sg21788,True.intro,True.intro⟩,⟨sg21790,True.intro,True.intro⟩⟩,⟨sg21793,⟨sg21792,True.intro,True.intro⟩,⟨sg21794,True.intro,True.intro⟩⟩⟩,⟨sg21799,⟨sg21797,⟨sg21796,True.intro,True.intro⟩,⟨sg21798,True.intro,True.intro⟩⟩,⟨sg21801,⟨sg21800,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21809,⟨sg21806,⟨sg21804,⟨sg21803,True.intro,True.intro⟩,⟨sg21805,True.intro,True.intro⟩⟩,⟨sg21808,⟨sg21807,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21813,⟨sg21811,⟨sg21810,True.intro,True.intro⟩,⟨sg21812,True.intro,True.intro⟩⟩,⟨sg21815,⟨sg21814,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_8All : degreeTree39_8.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21831,⟨sg21824,⟨sg21820,⟨sg21818,⟨sg21817,True.intro,True.intro⟩,⟨sg21819,True.intro,True.intro⟩⟩,⟨sg21822,⟨sg21821,True.intro,True.intro⟩,⟨sg21823,True.intro,True.intro⟩⟩⟩,⟨sg21828,⟨sg21826,⟨sg21825,True.intro,True.intro⟩,⟨sg21827,True.intro,True.intro⟩⟩,⟨sg21830,⟨sg21829,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21838,⟨sg21835,⟨sg21833,⟨sg21832,True.intro,True.intro⟩,⟨sg21834,True.intro,True.intro⟩⟩,⟨sg21837,⟨sg21836,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21842,⟨sg21840,⟨sg21839,True.intro,True.intro⟩,⟨sg21841,True.intro,True.intro⟩⟩,⟨sg21844,⟨sg21843,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_9All : degreeTree39_9.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21816,degreeTree39_7All,degreeTree39_8All⟩ - -lemma degreeTree39_10All : degreeTree39_10.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21860,⟨sg21853,⟨sg21849,⟨sg21847,⟨sg21846,True.intro,True.intro⟩,⟨sg21848,True.intro,True.intro⟩⟩,⟨sg21851,⟨sg21850,True.intro,True.intro⟩,⟨sg21852,True.intro,True.intro⟩⟩⟩,⟨sg21857,⟨sg21855,⟨sg21854,True.intro,True.intro⟩,⟨sg21856,True.intro,True.intro⟩⟩,⟨sg21859,⟨sg21858,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21867,⟨sg21864,⟨sg21862,⟨sg21861,True.intro,True.intro⟩,⟨sg21863,True.intro,True.intro⟩⟩,⟨sg21866,⟨sg21865,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21871,⟨sg21869,⟨sg21868,True.intro,True.intro⟩,⟨sg21870,True.intro,True.intro⟩⟩,⟨sg21873,⟨sg21872,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_11All : degreeTree39_11.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21889,⟨sg21882,⟨sg21878,⟨sg21876,⟨sg21875,True.intro,True.intro⟩,⟨sg21877,True.intro,True.intro⟩⟩,⟨sg21880,⟨sg21879,True.intro,True.intro⟩,⟨sg21881,True.intro,True.intro⟩⟩⟩,⟨sg21886,⟨sg21884,⟨sg21883,True.intro,True.intro⟩,⟨sg21885,True.intro,True.intro⟩⟩,⟨sg21888,⟨sg21887,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21896,⟨sg21893,⟨sg21891,⟨sg21890,True.intro,True.intro⟩,⟨sg21892,True.intro,True.intro⟩⟩,⟨sg21895,⟨sg21894,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21900,⟨sg21898,⟨sg21897,True.intro,True.intro⟩,⟨sg21899,True.intro,True.intro⟩⟩,⟨sg21902,⟨sg21901,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_12All : degreeTree39_12.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21874,degreeTree39_10All,degreeTree39_11All⟩ - -lemma degreeTree39_13All : degreeTree39_13.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21845,degreeTree39_9All,degreeTree39_12All⟩ - -lemma degreeTree39_14All : degreeTree39_14.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21787,degreeTree39_6All,degreeTree39_13All⟩ - -lemma degreeTree39_15All : degreeTree39_15.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21918,⟨sg21911,⟨sg21907,⟨sg21905,⟨sg21904,True.intro,True.intro⟩,⟨sg21906,True.intro,True.intro⟩⟩,⟨sg21909,⟨sg21908,True.intro,True.intro⟩,⟨sg21910,True.intro,True.intro⟩⟩⟩,⟨sg21915,⟨sg21913,⟨sg21912,True.intro,True.intro⟩,⟨sg21914,True.intro,True.intro⟩⟩,⟨sg21917,⟨sg21916,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21925,⟨sg21922,⟨sg21920,⟨sg21919,True.intro,True.intro⟩,⟨sg21921,True.intro,True.intro⟩⟩,⟨sg21924,⟨sg21923,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21929,⟨sg21927,⟨sg21926,True.intro,True.intro⟩,⟨sg21928,True.intro,True.intro⟩⟩,⟨sg21931,⟨sg21930,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_16All : degreeTree39_16.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21947,⟨sg21940,⟨sg21936,⟨sg21934,⟨sg21933,True.intro,True.intro⟩,⟨sg21935,True.intro,True.intro⟩⟩,⟨sg21938,⟨sg21937,True.intro,True.intro⟩,⟨sg21939,True.intro,True.intro⟩⟩⟩,⟨sg21944,⟨sg21942,⟨sg21941,True.intro,True.intro⟩,⟨sg21943,True.intro,True.intro⟩⟩,⟨sg21946,⟨sg21945,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21954,⟨sg21951,⟨sg21949,⟨sg21948,True.intro,True.intro⟩,⟨sg21950,True.intro,True.intro⟩⟩,⟨sg21953,⟨sg21952,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21958,⟨sg21956,⟨sg21955,True.intro,True.intro⟩,⟨sg21957,True.intro,True.intro⟩⟩,⟨sg21960,⟨sg21959,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_17All : degreeTree39_17.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21932,degreeTree39_15All,degreeTree39_16All⟩ - -lemma degreeTree39_18All : degreeTree39_18.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21976,⟨sg21969,⟨sg21965,⟨sg21963,⟨sg21962,True.intro,True.intro⟩,⟨sg21964,True.intro,True.intro⟩⟩,⟨sg21967,⟨sg21966,True.intro,True.intro⟩,⟨sg21968,True.intro,True.intro⟩⟩⟩,⟨sg21973,⟨sg21971,⟨sg21970,True.intro,True.intro⟩,⟨sg21972,True.intro,True.intro⟩⟩,⟨sg21975,⟨sg21974,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21983,⟨sg21980,⟨sg21978,⟨sg21977,True.intro,True.intro⟩,⟨sg21979,True.intro,True.intro⟩⟩,⟨sg21982,⟨sg21981,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21987,⟨sg21985,⟨sg21984,True.intro,True.intro⟩,⟨sg21986,True.intro,True.intro⟩⟩,⟨sg21989,⟨sg21988,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_19All : degreeTree39_19.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22005,⟨sg21998,⟨sg21994,⟨sg21992,⟨sg21991,True.intro,True.intro⟩,⟨sg21993,True.intro,True.intro⟩⟩,⟨sg21996,⟨sg21995,True.intro,True.intro⟩,⟨sg21997,True.intro,True.intro⟩⟩⟩,⟨sg22002,⟨sg22000,⟨sg21999,True.intro,True.intro⟩,⟨sg22001,True.intro,True.intro⟩⟩,⟨sg22004,⟨sg22003,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22012,⟨sg22009,⟨sg22007,⟨sg22006,True.intro,True.intro⟩,⟨sg22008,True.intro,True.intro⟩⟩,⟨sg22011,⟨sg22010,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22016,⟨sg22014,⟨sg22013,True.intro,True.intro⟩,⟨sg22015,True.intro,True.intro⟩⟩,⟨sg22018,⟨sg22017,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_20All : degreeTree39_20.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21990,degreeTree39_18All,degreeTree39_19All⟩ - -lemma degreeTree39_21All : degreeTree39_21.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21961,degreeTree39_17All,degreeTree39_20All⟩ - -lemma degreeTree39_22All : degreeTree39_22.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22034,⟨sg22027,⟨sg22023,⟨sg22021,⟨sg22020,True.intro,True.intro⟩,⟨sg22022,True.intro,True.intro⟩⟩,⟨sg22025,⟨sg22024,True.intro,True.intro⟩,⟨sg22026,True.intro,True.intro⟩⟩⟩,⟨sg22031,⟨sg22029,⟨sg22028,True.intro,True.intro⟩,⟨sg22030,True.intro,True.intro⟩⟩,⟨sg22033,⟨sg22032,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22041,⟨sg22038,⟨sg22036,⟨sg22035,True.intro,True.intro⟩,⟨sg22037,True.intro,True.intro⟩⟩,⟨sg22040,⟨sg22039,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22045,⟨sg22043,⟨sg22042,True.intro,True.intro⟩,⟨sg22044,True.intro,True.intro⟩⟩,⟨sg22047,⟨sg22046,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_23All : degreeTree39_23.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22063,⟨sg22056,⟨sg22052,⟨sg22050,⟨sg22049,True.intro,True.intro⟩,⟨sg22051,True.intro,True.intro⟩⟩,⟨sg22054,⟨sg22053,True.intro,True.intro⟩,⟨sg22055,True.intro,True.intro⟩⟩⟩,⟨sg22060,⟨sg22058,⟨sg22057,True.intro,True.intro⟩,⟨sg22059,True.intro,True.intro⟩⟩,⟨sg22062,⟨sg22061,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22070,⟨sg22067,⟨sg22065,⟨sg22064,True.intro,True.intro⟩,⟨sg22066,True.intro,True.intro⟩⟩,⟨sg22069,⟨sg22068,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22074,⟨sg22072,⟨sg22071,True.intro,True.intro⟩,⟨sg22073,True.intro,True.intro⟩⟩,⟨sg22076,⟨sg22075,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_24All : degreeTree39_24.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22048,degreeTree39_22All,degreeTree39_23All⟩ - -lemma degreeTree39_25All : degreeTree39_25.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22092,⟨sg22085,⟨sg22081,⟨sg22079,⟨sg22078,True.intro,True.intro⟩,⟨sg22080,True.intro,True.intro⟩⟩,⟨sg22083,⟨sg22082,True.intro,True.intro⟩,⟨sg22084,True.intro,True.intro⟩⟩⟩,⟨sg22089,⟨sg22087,⟨sg22086,True.intro,True.intro⟩,⟨sg22088,True.intro,True.intro⟩⟩,⟨sg22091,⟨sg22090,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22099,⟨sg22096,⟨sg22094,⟨sg22093,True.intro,True.intro⟩,⟨sg22095,True.intro,True.intro⟩⟩,⟨sg22098,⟨sg22097,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22103,⟨sg22101,⟨sg22100,True.intro,True.intro⟩,⟨sg22102,True.intro,True.intro⟩⟩,⟨sg22105,⟨sg22104,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_26All : degreeTree39_26.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22121,⟨sg22114,⟨sg22110,⟨sg22108,⟨sg22107,True.intro,True.intro⟩,⟨sg22109,True.intro,True.intro⟩⟩,⟨sg22112,⟨sg22111,True.intro,True.intro⟩,⟨sg22113,True.intro,True.intro⟩⟩⟩,⟨sg22118,⟨sg22116,⟨sg22115,True.intro,True.intro⟩,⟨sg22117,True.intro,True.intro⟩⟩,⟨sg22120,⟨sg22119,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22128,⟨sg22125,⟨sg22123,⟨sg22122,True.intro,True.intro⟩,⟨sg22124,True.intro,True.intro⟩⟩,⟨sg22127,⟨sg22126,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22132,⟨sg22130,⟨sg22129,True.intro,True.intro⟩,⟨sg22131,True.intro,True.intro⟩⟩,⟨sg22134,⟨sg22133,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_27All : degreeTree39_27.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22106,degreeTree39_25All,degreeTree39_26All⟩ - -lemma degreeTree39_28All : degreeTree39_28.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22077,degreeTree39_24All,degreeTree39_27All⟩ - -lemma degreeTree39_29All : degreeTree39_29.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22019,degreeTree39_21All,degreeTree39_28All⟩ - -lemma degreeTree39_30All : degreeTree39_30.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg21903,degreeTree39_14All,degreeTree39_29All⟩ - -lemma degreeTree39_31All : degreeTree39_31.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22150,⟨sg22143,⟨sg22139,⟨sg22137,⟨sg22136,True.intro,True.intro⟩,⟨sg22138,True.intro,True.intro⟩⟩,⟨sg22141,⟨sg22140,True.intro,True.intro⟩,⟨sg22142,True.intro,True.intro⟩⟩⟩,⟨sg22147,⟨sg22145,⟨sg22144,True.intro,True.intro⟩,⟨sg22146,True.intro,True.intro⟩⟩,⟨sg22149,⟨sg22148,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22158,⟨sg22154,⟨sg22152,⟨sg22151,True.intro,True.intro⟩,⟨sg22153,True.intro,True.intro⟩⟩,⟨sg22156,⟨sg22155,True.intro,True.intro⟩,⟨sg22157,True.intro,True.intro⟩⟩⟩,⟨sg22162,⟨sg22160,⟨sg22159,True.intro,True.intro⟩,⟨sg22161,True.intro,True.intro⟩⟩,⟨sg22164,⟨sg22163,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_32All : degreeTree39_32.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22180,⟨sg22173,⟨sg22169,⟨sg22167,⟨sg22166,True.intro,True.intro⟩,⟨sg22168,True.intro,True.intro⟩⟩,⟨sg22171,⟨sg22170,True.intro,True.intro⟩,⟨sg22172,True.intro,True.intro⟩⟩⟩,⟨sg22177,⟨sg22175,⟨sg22174,True.intro,True.intro⟩,⟨sg22176,True.intro,True.intro⟩⟩,⟨sg22179,⟨sg22178,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22187,⟨sg22184,⟨sg22182,⟨sg22181,True.intro,True.intro⟩,⟨sg22183,True.intro,True.intro⟩⟩,⟨sg22186,⟨sg22185,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22191,⟨sg22189,⟨sg22188,True.intro,True.intro⟩,⟨sg22190,True.intro,True.intro⟩⟩,⟨sg22193,⟨sg22192,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_33All : degreeTree39_33.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22165,degreeTree39_31All,degreeTree39_32All⟩ - -lemma degreeTree39_34All : degreeTree39_34.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22209,⟨sg22202,⟨sg22198,⟨sg22196,⟨sg22195,True.intro,True.intro⟩,⟨sg22197,True.intro,True.intro⟩⟩,⟨sg22200,⟨sg22199,True.intro,True.intro⟩,⟨sg22201,True.intro,True.intro⟩⟩⟩,⟨sg22206,⟨sg22204,⟨sg22203,True.intro,True.intro⟩,⟨sg22205,True.intro,True.intro⟩⟩,⟨sg22208,⟨sg22207,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22216,⟨sg22213,⟨sg22211,⟨sg22210,True.intro,True.intro⟩,⟨sg22212,True.intro,True.intro⟩⟩,⟨sg22215,⟨sg22214,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22220,⟨sg22218,⟨sg22217,True.intro,True.intro⟩,⟨sg22219,True.intro,True.intro⟩⟩,⟨sg22222,⟨sg22221,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_35All : degreeTree39_35.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22238,⟨sg22231,⟨sg22227,⟨sg22225,⟨sg22224,True.intro,True.intro⟩,⟨sg22226,True.intro,True.intro⟩⟩,⟨sg22229,⟨sg22228,True.intro,True.intro⟩,⟨sg22230,True.intro,True.intro⟩⟩⟩,⟨sg22235,⟨sg22233,⟨sg22232,True.intro,True.intro⟩,⟨sg22234,True.intro,True.intro⟩⟩,⟨sg22237,⟨sg22236,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22245,⟨sg22242,⟨sg22240,⟨sg22239,True.intro,True.intro⟩,⟨sg22241,True.intro,True.intro⟩⟩,⟨sg22244,⟨sg22243,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22249,⟨sg22247,⟨sg22246,True.intro,True.intro⟩,⟨sg22248,True.intro,True.intro⟩⟩,⟨sg22251,⟨sg22250,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_36All : degreeTree39_36.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22223,degreeTree39_34All,degreeTree39_35All⟩ - -lemma degreeTree39_37All : degreeTree39_37.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22194,degreeTree39_33All,degreeTree39_36All⟩ - -lemma degreeTree39_38All : degreeTree39_38.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22267,⟨sg22260,⟨sg22256,⟨sg22254,⟨sg22253,True.intro,True.intro⟩,⟨sg22255,True.intro,True.intro⟩⟩,⟨sg22258,⟨sg22257,True.intro,True.intro⟩,⟨sg22259,True.intro,True.intro⟩⟩⟩,⟨sg22264,⟨sg22262,⟨sg22261,True.intro,True.intro⟩,⟨sg22263,True.intro,True.intro⟩⟩,⟨sg22266,⟨sg22265,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22274,⟨sg22271,⟨sg22269,⟨sg22268,True.intro,True.intro⟩,⟨sg22270,True.intro,True.intro⟩⟩,⟨sg22273,⟨sg22272,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22278,⟨sg22276,⟨sg22275,True.intro,True.intro⟩,⟨sg22277,True.intro,True.intro⟩⟩,⟨sg22280,⟨sg22279,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_39All : degreeTree39_39.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22296,⟨sg22289,⟨sg22285,⟨sg22283,⟨sg22282,True.intro,True.intro⟩,⟨sg22284,True.intro,True.intro⟩⟩,⟨sg22287,⟨sg22286,True.intro,True.intro⟩,⟨sg22288,True.intro,True.intro⟩⟩⟩,⟨sg22293,⟨sg22291,⟨sg22290,True.intro,True.intro⟩,⟨sg22292,True.intro,True.intro⟩⟩,⟨sg22295,⟨sg22294,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22303,⟨sg22300,⟨sg22298,⟨sg22297,True.intro,True.intro⟩,⟨sg22299,True.intro,True.intro⟩⟩,⟨sg22302,⟨sg22301,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22307,⟨sg22305,⟨sg22304,True.intro,True.intro⟩,⟨sg22306,True.intro,True.intro⟩⟩,⟨sg22309,⟨sg22308,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_40All : degreeTree39_40.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22281,degreeTree39_38All,degreeTree39_39All⟩ - -lemma degreeTree39_41All : degreeTree39_41.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22325,⟨sg22318,⟨sg22314,⟨sg22312,⟨sg22311,True.intro,True.intro⟩,⟨sg22313,True.intro,True.intro⟩⟩,⟨sg22316,⟨sg22315,True.intro,True.intro⟩,⟨sg22317,True.intro,True.intro⟩⟩⟩,⟨sg22322,⟨sg22320,⟨sg22319,True.intro,True.intro⟩,⟨sg22321,True.intro,True.intro⟩⟩,⟨sg22324,⟨sg22323,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22332,⟨sg22329,⟨sg22327,⟨sg22326,True.intro,True.intro⟩,⟨sg22328,True.intro,True.intro⟩⟩,⟨sg22331,⟨sg22330,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22336,⟨sg22334,⟨sg22333,True.intro,True.intro⟩,⟨sg22335,True.intro,True.intro⟩⟩,⟨sg22338,⟨sg22337,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_42All : degreeTree39_42.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22354,⟨sg22347,⟨sg22343,⟨sg22341,⟨sg22340,True.intro,True.intro⟩,⟨sg22342,True.intro,True.intro⟩⟩,⟨sg22345,⟨sg22344,True.intro,True.intro⟩,⟨sg22346,True.intro,True.intro⟩⟩⟩,⟨sg22351,⟨sg22349,⟨sg22348,True.intro,True.intro⟩,⟨sg22350,True.intro,True.intro⟩⟩,⟨sg22353,⟨sg22352,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22361,⟨sg22358,⟨sg22356,⟨sg22355,True.intro,True.intro⟩,⟨sg22357,True.intro,True.intro⟩⟩,⟨sg22360,⟨sg22359,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22365,⟨sg22363,⟨sg22362,True.intro,True.intro⟩,⟨sg22364,True.intro,True.intro⟩⟩,⟨sg22367,⟨sg22366,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_43All : degreeTree39_43.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22339,degreeTree39_41All,degreeTree39_42All⟩ - -lemma degreeTree39_44All : degreeTree39_44.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22310,degreeTree39_40All,degreeTree39_43All⟩ - -lemma degreeTree39_45All : degreeTree39_45.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22252,degreeTree39_37All,degreeTree39_44All⟩ - -lemma degreeTree39_46All : degreeTree39_46.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22383,⟨sg22376,⟨sg22372,⟨sg22370,⟨sg22369,True.intro,True.intro⟩,⟨sg22371,True.intro,True.intro⟩⟩,⟨sg22374,⟨sg22373,True.intro,True.intro⟩,⟨sg22375,True.intro,True.intro⟩⟩⟩,⟨sg22380,⟨sg22378,⟨sg22377,True.intro,True.intro⟩,⟨sg22379,True.intro,True.intro⟩⟩,⟨sg22382,⟨sg22381,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22390,⟨sg22387,⟨sg22385,⟨sg22384,True.intro,True.intro⟩,⟨sg22386,True.intro,True.intro⟩⟩,⟨sg22389,⟨sg22388,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22394,⟨sg22392,⟨sg22391,True.intro,True.intro⟩,⟨sg22393,True.intro,True.intro⟩⟩,⟨sg22396,⟨sg22395,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_47All : degreeTree39_47.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22412,⟨sg22405,⟨sg22401,⟨sg22399,⟨sg22398,True.intro,True.intro⟩,⟨sg22400,True.intro,True.intro⟩⟩,⟨sg22403,⟨sg22402,True.intro,True.intro⟩,⟨sg22404,True.intro,True.intro⟩⟩⟩,⟨sg22409,⟨sg22407,⟨sg22406,True.intro,True.intro⟩,⟨sg22408,True.intro,True.intro⟩⟩,⟨sg22411,⟨sg22410,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22419,⟨sg22416,⟨sg22414,⟨sg22413,True.intro,True.intro⟩,⟨sg22415,True.intro,True.intro⟩⟩,⟨sg22418,⟨sg22417,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22423,⟨sg22421,⟨sg22420,True.intro,True.intro⟩,⟨sg22422,True.intro,True.intro⟩⟩,⟨sg22425,⟨sg22424,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_48All : degreeTree39_48.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22397,degreeTree39_46All,degreeTree39_47All⟩ - -lemma degreeTree39_49All : degreeTree39_49.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22441,⟨sg22434,⟨sg22430,⟨sg22428,⟨sg22427,True.intro,True.intro⟩,⟨sg22429,True.intro,True.intro⟩⟩,⟨sg22432,⟨sg22431,True.intro,True.intro⟩,⟨sg22433,True.intro,True.intro⟩⟩⟩,⟨sg22438,⟨sg22436,⟨sg22435,True.intro,True.intro⟩,⟨sg22437,True.intro,True.intro⟩⟩,⟨sg22440,⟨sg22439,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22448,⟨sg22445,⟨sg22443,⟨sg22442,True.intro,True.intro⟩,⟨sg22444,True.intro,True.intro⟩⟩,⟨sg22447,⟨sg22446,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22452,⟨sg22450,⟨sg22449,True.intro,True.intro⟩,⟨sg22451,True.intro,True.intro⟩⟩,⟨sg22454,⟨sg22453,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_50All : degreeTree39_50.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22470,⟨sg22463,⟨sg22459,⟨sg22457,⟨sg22456,True.intro,True.intro⟩,⟨sg22458,True.intro,True.intro⟩⟩,⟨sg22461,⟨sg22460,True.intro,True.intro⟩,⟨sg22462,True.intro,True.intro⟩⟩⟩,⟨sg22467,⟨sg22465,⟨sg22464,True.intro,True.intro⟩,⟨sg22466,True.intro,True.intro⟩⟩,⟨sg22469,⟨sg22468,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22477,⟨sg22474,⟨sg22472,⟨sg22471,True.intro,True.intro⟩,⟨sg22473,True.intro,True.intro⟩⟩,⟨sg22476,⟨sg22475,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22481,⟨sg22479,⟨sg22478,True.intro,True.intro⟩,⟨sg22480,True.intro,True.intro⟩⟩,⟨sg22483,⟨sg22482,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_51All : degreeTree39_51.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22455,degreeTree39_49All,degreeTree39_50All⟩ - -lemma degreeTree39_52All : degreeTree39_52.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22426,degreeTree39_48All,degreeTree39_51All⟩ - -lemma degreeTree39_53All : degreeTree39_53.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22499,⟨sg22492,⟨sg22488,⟨sg22486,⟨sg22485,True.intro,True.intro⟩,⟨sg22487,True.intro,True.intro⟩⟩,⟨sg22490,⟨sg22489,True.intro,True.intro⟩,⟨sg22491,True.intro,True.intro⟩⟩⟩,⟨sg22496,⟨sg22494,⟨sg22493,True.intro,True.intro⟩,⟨sg22495,True.intro,True.intro⟩⟩,⟨sg22498,⟨sg22497,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22506,⟨sg22503,⟨sg22501,⟨sg22500,True.intro,True.intro⟩,⟨sg22502,True.intro,True.intro⟩⟩,⟨sg22505,⟨sg22504,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22510,⟨sg22508,⟨sg22507,True.intro,True.intro⟩,⟨sg22509,True.intro,True.intro⟩⟩,⟨sg22512,⟨sg22511,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_54All : degreeTree39_54.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22528,⟨sg22521,⟨sg22517,⟨sg22515,⟨sg22514,True.intro,True.intro⟩,⟨sg22516,True.intro,True.intro⟩⟩,⟨sg22519,⟨sg22518,True.intro,True.intro⟩,⟨sg22520,True.intro,True.intro⟩⟩⟩,⟨sg22525,⟨sg22523,⟨sg22522,True.intro,True.intro⟩,⟨sg22524,True.intro,True.intro⟩⟩,⟨sg22527,⟨sg22526,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22535,⟨sg22532,⟨sg22530,⟨sg22529,True.intro,True.intro⟩,⟨sg22531,True.intro,True.intro⟩⟩,⟨sg22534,⟨sg22533,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22539,⟨sg22537,⟨sg22536,True.intro,True.intro⟩,⟨sg22538,True.intro,True.intro⟩⟩,⟨sg22541,⟨sg22540,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_55All : degreeTree39_55.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22513,degreeTree39_53All,degreeTree39_54All⟩ - -lemma degreeTree39_56All : degreeTree39_56.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22557,⟨sg22550,⟨sg22546,⟨sg22544,⟨sg22543,True.intro,True.intro⟩,⟨sg22545,True.intro,True.intro⟩⟩,⟨sg22548,⟨sg22547,True.intro,True.intro⟩,⟨sg22549,True.intro,True.intro⟩⟩⟩,⟨sg22554,⟨sg22552,⟨sg22551,True.intro,True.intro⟩,⟨sg22553,True.intro,True.intro⟩⟩,⟨sg22556,⟨sg22555,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22564,⟨sg22561,⟨sg22559,⟨sg22558,True.intro,True.intro⟩,⟨sg22560,True.intro,True.intro⟩⟩,⟨sg22563,⟨sg22562,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22568,⟨sg22566,⟨sg22565,True.intro,True.intro⟩,⟨sg22567,True.intro,True.intro⟩⟩,⟨sg22570,⟨sg22569,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_57All : degreeTree39_57.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22586,⟨sg22579,⟨sg22575,⟨sg22573,⟨sg22572,True.intro,True.intro⟩,⟨sg22574,True.intro,True.intro⟩⟩,⟨sg22577,⟨sg22576,True.intro,True.intro⟩,⟨sg22578,True.intro,True.intro⟩⟩⟩,⟨sg22583,⟨sg22581,⟨sg22580,True.intro,True.intro⟩,⟨sg22582,True.intro,True.intro⟩⟩,⟨sg22585,⟨sg22584,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22593,⟨sg22590,⟨sg22588,⟨sg22587,True.intro,True.intro⟩,⟨sg22589,True.intro,True.intro⟩⟩,⟨sg22592,⟨sg22591,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22597,⟨sg22595,⟨sg22594,True.intro,True.intro⟩,⟨sg22596,True.intro,True.intro⟩⟩,⟨sg22599,⟨sg22598,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_58All : degreeTree39_58.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22571,degreeTree39_56All,degreeTree39_57All⟩ - -lemma degreeTree39_59All : degreeTree39_59.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22542,degreeTree39_55All,degreeTree39_58All⟩ - -lemma degreeTree39_60All : degreeTree39_60.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22484,degreeTree39_52All,degreeTree39_59All⟩ - -lemma degreeTree39_61All : degreeTree39_61.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22368,degreeTree39_45All,degreeTree39_60All⟩ - -lemma degreeTree39_62All : degreeTree39_62.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22135,degreeTree39_30All,degreeTree39_61All⟩ - -lemma degreeTree39_63All : degreeTree39_63.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22615,⟨sg22608,⟨sg22604,⟨sg22602,⟨sg22601,True.intro,True.intro⟩,⟨sg22603,True.intro,True.intro⟩⟩,⟨sg22606,⟨sg22605,True.intro,True.intro⟩,⟨sg22607,True.intro,True.intro⟩⟩⟩,⟨sg22612,⟨sg22610,⟨sg22609,True.intro,True.intro⟩,⟨sg22611,True.intro,True.intro⟩⟩,⟨sg22614,⟨sg22613,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22623,⟨sg22619,⟨sg22617,⟨sg22616,True.intro,True.intro⟩,⟨sg22618,True.intro,True.intro⟩⟩,⟨sg22621,⟨sg22620,True.intro,True.intro⟩,⟨sg22622,True.intro,True.intro⟩⟩⟩,⟨sg22627,⟨sg22625,⟨sg22624,True.intro,True.intro⟩,⟨sg22626,True.intro,True.intro⟩⟩,⟨sg22629,⟨sg22628,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_64All : degreeTree39_64.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22645,⟨sg22638,⟨sg22634,⟨sg22632,⟨sg22631,True.intro,True.intro⟩,⟨sg22633,True.intro,True.intro⟩⟩,⟨sg22636,⟨sg22635,True.intro,True.intro⟩,⟨sg22637,True.intro,True.intro⟩⟩⟩,⟨sg22642,⟨sg22640,⟨sg22639,True.intro,True.intro⟩,⟨sg22641,True.intro,True.intro⟩⟩,⟨sg22644,⟨sg22643,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22652,⟨sg22649,⟨sg22647,⟨sg22646,True.intro,True.intro⟩,⟨sg22648,True.intro,True.intro⟩⟩,⟨sg22651,⟨sg22650,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22656,⟨sg22654,⟨sg22653,True.intro,True.intro⟩,⟨sg22655,True.intro,True.intro⟩⟩,⟨sg22658,⟨sg22657,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_65All : degreeTree39_65.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22630,degreeTree39_63All,degreeTree39_64All⟩ - -lemma degreeTree39_66All : degreeTree39_66.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22674,⟨sg22667,⟨sg22663,⟨sg22661,⟨sg22660,True.intro,True.intro⟩,⟨sg22662,True.intro,True.intro⟩⟩,⟨sg22665,⟨sg22664,True.intro,True.intro⟩,⟨sg22666,True.intro,True.intro⟩⟩⟩,⟨sg22671,⟨sg22669,⟨sg22668,True.intro,True.intro⟩,⟨sg22670,True.intro,True.intro⟩⟩,⟨sg22673,⟨sg22672,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22681,⟨sg22678,⟨sg22676,⟨sg22675,True.intro,True.intro⟩,⟨sg22677,True.intro,True.intro⟩⟩,⟨sg22680,⟨sg22679,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22685,⟨sg22683,⟨sg22682,True.intro,True.intro⟩,⟨sg22684,True.intro,True.intro⟩⟩,⟨sg22687,⟨sg22686,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_67All : degreeTree39_67.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22703,⟨sg22696,⟨sg22692,⟨sg22690,⟨sg22689,True.intro,True.intro⟩,⟨sg22691,True.intro,True.intro⟩⟩,⟨sg22694,⟨sg22693,True.intro,True.intro⟩,⟨sg22695,True.intro,True.intro⟩⟩⟩,⟨sg22700,⟨sg22698,⟨sg22697,True.intro,True.intro⟩,⟨sg22699,True.intro,True.intro⟩⟩,⟨sg22702,⟨sg22701,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22710,⟨sg22707,⟨sg22705,⟨sg22704,True.intro,True.intro⟩,⟨sg22706,True.intro,True.intro⟩⟩,⟨sg22709,⟨sg22708,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22714,⟨sg22712,⟨sg22711,True.intro,True.intro⟩,⟨sg22713,True.intro,True.intro⟩⟩,⟨sg22716,⟨sg22715,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_68All : degreeTree39_68.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22688,degreeTree39_66All,degreeTree39_67All⟩ - -lemma degreeTree39_69All : degreeTree39_69.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22659,degreeTree39_65All,degreeTree39_68All⟩ - -lemma degreeTree39_70All : degreeTree39_70.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22732,⟨sg22725,⟨sg22721,⟨sg22719,⟨sg22718,True.intro,True.intro⟩,⟨sg22720,True.intro,True.intro⟩⟩,⟨sg22723,⟨sg22722,True.intro,True.intro⟩,⟨sg22724,True.intro,True.intro⟩⟩⟩,⟨sg22729,⟨sg22727,⟨sg22726,True.intro,True.intro⟩,⟨sg22728,True.intro,True.intro⟩⟩,⟨sg22731,⟨sg22730,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22739,⟨sg22736,⟨sg22734,⟨sg22733,True.intro,True.intro⟩,⟨sg22735,True.intro,True.intro⟩⟩,⟨sg22738,⟨sg22737,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22743,⟨sg22741,⟨sg22740,True.intro,True.intro⟩,⟨sg22742,True.intro,True.intro⟩⟩,⟨sg22745,⟨sg22744,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_71All : degreeTree39_71.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22761,⟨sg22754,⟨sg22750,⟨sg22748,⟨sg22747,True.intro,True.intro⟩,⟨sg22749,True.intro,True.intro⟩⟩,⟨sg22752,⟨sg22751,True.intro,True.intro⟩,⟨sg22753,True.intro,True.intro⟩⟩⟩,⟨sg22758,⟨sg22756,⟨sg22755,True.intro,True.intro⟩,⟨sg22757,True.intro,True.intro⟩⟩,⟨sg22760,⟨sg22759,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22768,⟨sg22765,⟨sg22763,⟨sg22762,True.intro,True.intro⟩,⟨sg22764,True.intro,True.intro⟩⟩,⟨sg22767,⟨sg22766,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22772,⟨sg22770,⟨sg22769,True.intro,True.intro⟩,⟨sg22771,True.intro,True.intro⟩⟩,⟨sg22774,⟨sg22773,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_72All : degreeTree39_72.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22746,degreeTree39_70All,degreeTree39_71All⟩ - -lemma degreeTree39_73All : degreeTree39_73.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22790,⟨sg22783,⟨sg22779,⟨sg22777,⟨sg22776,True.intro,True.intro⟩,⟨sg22778,True.intro,True.intro⟩⟩,⟨sg22781,⟨sg22780,True.intro,True.intro⟩,⟨sg22782,True.intro,True.intro⟩⟩⟩,⟨sg22787,⟨sg22785,⟨sg22784,True.intro,True.intro⟩,⟨sg22786,True.intro,True.intro⟩⟩,⟨sg22789,⟨sg22788,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22797,⟨sg22794,⟨sg22792,⟨sg22791,True.intro,True.intro⟩,⟨sg22793,True.intro,True.intro⟩⟩,⟨sg22796,⟨sg22795,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22801,⟨sg22799,⟨sg22798,True.intro,True.intro⟩,⟨sg22800,True.intro,True.intro⟩⟩,⟨sg22803,⟨sg22802,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_74All : degreeTree39_74.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22819,⟨sg22812,⟨sg22808,⟨sg22806,⟨sg22805,True.intro,True.intro⟩,⟨sg22807,True.intro,True.intro⟩⟩,⟨sg22810,⟨sg22809,True.intro,True.intro⟩,⟨sg22811,True.intro,True.intro⟩⟩⟩,⟨sg22816,⟨sg22814,⟨sg22813,True.intro,True.intro⟩,⟨sg22815,True.intro,True.intro⟩⟩,⟨sg22818,⟨sg22817,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22826,⟨sg22823,⟨sg22821,⟨sg22820,True.intro,True.intro⟩,⟨sg22822,True.intro,True.intro⟩⟩,⟨sg22825,⟨sg22824,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22830,⟨sg22828,⟨sg22827,True.intro,True.intro⟩,⟨sg22829,True.intro,True.intro⟩⟩,⟨sg22832,⟨sg22831,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_75All : degreeTree39_75.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22804,degreeTree39_73All,degreeTree39_74All⟩ - -lemma degreeTree39_76All : degreeTree39_76.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22775,degreeTree39_72All,degreeTree39_75All⟩ - -lemma degreeTree39_77All : degreeTree39_77.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22717,degreeTree39_69All,degreeTree39_76All⟩ - -lemma degreeTree39_78All : degreeTree39_78.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22848,⟨sg22841,⟨sg22837,⟨sg22835,⟨sg22834,True.intro,True.intro⟩,⟨sg22836,True.intro,True.intro⟩⟩,⟨sg22839,⟨sg22838,True.intro,True.intro⟩,⟨sg22840,True.intro,True.intro⟩⟩⟩,⟨sg22845,⟨sg22843,⟨sg22842,True.intro,True.intro⟩,⟨sg22844,True.intro,True.intro⟩⟩,⟨sg22847,⟨sg22846,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22855,⟨sg22852,⟨sg22850,⟨sg22849,True.intro,True.intro⟩,⟨sg22851,True.intro,True.intro⟩⟩,⟨sg22854,⟨sg22853,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22859,⟨sg22857,⟨sg22856,True.intro,True.intro⟩,⟨sg22858,True.intro,True.intro⟩⟩,⟨sg22861,⟨sg22860,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_79All : degreeTree39_79.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22877,⟨sg22870,⟨sg22866,⟨sg22864,⟨sg22863,True.intro,True.intro⟩,⟨sg22865,True.intro,True.intro⟩⟩,⟨sg22868,⟨sg22867,True.intro,True.intro⟩,⟨sg22869,True.intro,True.intro⟩⟩⟩,⟨sg22874,⟨sg22872,⟨sg22871,True.intro,True.intro⟩,⟨sg22873,True.intro,True.intro⟩⟩,⟨sg22876,⟨sg22875,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22884,⟨sg22881,⟨sg22879,⟨sg22878,True.intro,True.intro⟩,⟨sg22880,True.intro,True.intro⟩⟩,⟨sg22883,⟨sg22882,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22888,⟨sg22886,⟨sg22885,True.intro,True.intro⟩,⟨sg22887,True.intro,True.intro⟩⟩,⟨sg22890,⟨sg22889,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_80All : degreeTree39_80.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22862,degreeTree39_78All,degreeTree39_79All⟩ - -lemma degreeTree39_81All : degreeTree39_81.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22906,⟨sg22899,⟨sg22895,⟨sg22893,⟨sg22892,True.intro,True.intro⟩,⟨sg22894,True.intro,True.intro⟩⟩,⟨sg22897,⟨sg22896,True.intro,True.intro⟩,⟨sg22898,True.intro,True.intro⟩⟩⟩,⟨sg22903,⟨sg22901,⟨sg22900,True.intro,True.intro⟩,⟨sg22902,True.intro,True.intro⟩⟩,⟨sg22905,⟨sg22904,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22913,⟨sg22910,⟨sg22908,⟨sg22907,True.intro,True.intro⟩,⟨sg22909,True.intro,True.intro⟩⟩,⟨sg22912,⟨sg22911,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22917,⟨sg22915,⟨sg22914,True.intro,True.intro⟩,⟨sg22916,True.intro,True.intro⟩⟩,⟨sg22919,⟨sg22918,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_82All : degreeTree39_82.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22935,⟨sg22928,⟨sg22924,⟨sg22922,⟨sg22921,True.intro,True.intro⟩,⟨sg22923,True.intro,True.intro⟩⟩,⟨sg22926,⟨sg22925,True.intro,True.intro⟩,⟨sg22927,True.intro,True.intro⟩⟩⟩,⟨sg22932,⟨sg22930,⟨sg22929,True.intro,True.intro⟩,⟨sg22931,True.intro,True.intro⟩⟩,⟨sg22934,⟨sg22933,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22942,⟨sg22939,⟨sg22937,⟨sg22936,True.intro,True.intro⟩,⟨sg22938,True.intro,True.intro⟩⟩,⟨sg22941,⟨sg22940,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22946,⟨sg22944,⟨sg22943,True.intro,True.intro⟩,⟨sg22945,True.intro,True.intro⟩⟩,⟨sg22948,⟨sg22947,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_83All : degreeTree39_83.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22920,degreeTree39_81All,degreeTree39_82All⟩ - -lemma degreeTree39_84All : degreeTree39_84.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22891,degreeTree39_80All,degreeTree39_83All⟩ - -lemma degreeTree39_85All : degreeTree39_85.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22964,⟨sg22957,⟨sg22953,⟨sg22951,⟨sg22950,True.intro,True.intro⟩,⟨sg22952,True.intro,True.intro⟩⟩,⟨sg22955,⟨sg22954,True.intro,True.intro⟩,⟨sg22956,True.intro,True.intro⟩⟩⟩,⟨sg22961,⟨sg22959,⟨sg22958,True.intro,True.intro⟩,⟨sg22960,True.intro,True.intro⟩⟩,⟨sg22963,⟨sg22962,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22971,⟨sg22968,⟨sg22966,⟨sg22965,True.intro,True.intro⟩,⟨sg22967,True.intro,True.intro⟩⟩,⟨sg22970,⟨sg22969,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22975,⟨sg22973,⟨sg22972,True.intro,True.intro⟩,⟨sg22974,True.intro,True.intro⟩⟩,⟨sg22977,⟨sg22976,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_86All : degreeTree39_86.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22993,⟨sg22986,⟨sg22982,⟨sg22980,⟨sg22979,True.intro,True.intro⟩,⟨sg22981,True.intro,True.intro⟩⟩,⟨sg22984,⟨sg22983,True.intro,True.intro⟩,⟨sg22985,True.intro,True.intro⟩⟩⟩,⟨sg22990,⟨sg22988,⟨sg22987,True.intro,True.intro⟩,⟨sg22989,True.intro,True.intro⟩⟩,⟨sg22992,⟨sg22991,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23000,⟨sg22997,⟨sg22995,⟨sg22994,True.intro,True.intro⟩,⟨sg22996,True.intro,True.intro⟩⟩,⟨sg22999,⟨sg22998,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23004,⟨sg23002,⟨sg23001,True.intro,True.intro⟩,⟨sg23003,True.intro,True.intro⟩⟩,⟨sg23006,⟨sg23005,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_87All : degreeTree39_87.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22978,degreeTree39_85All,degreeTree39_86All⟩ - -lemma degreeTree39_88All : degreeTree39_88.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23022,⟨sg23015,⟨sg23011,⟨sg23009,⟨sg23008,True.intro,True.intro⟩,⟨sg23010,True.intro,True.intro⟩⟩,⟨sg23013,⟨sg23012,True.intro,True.intro⟩,⟨sg23014,True.intro,True.intro⟩⟩⟩,⟨sg23019,⟨sg23017,⟨sg23016,True.intro,True.intro⟩,⟨sg23018,True.intro,True.intro⟩⟩,⟨sg23021,⟨sg23020,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23029,⟨sg23026,⟨sg23024,⟨sg23023,True.intro,True.intro⟩,⟨sg23025,True.intro,True.intro⟩⟩,⟨sg23028,⟨sg23027,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23033,⟨sg23031,⟨sg23030,True.intro,True.intro⟩,⟨sg23032,True.intro,True.intro⟩⟩,⟨sg23035,⟨sg23034,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_89All : degreeTree39_89.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23051,⟨sg23044,⟨sg23040,⟨sg23038,⟨sg23037,True.intro,True.intro⟩,⟨sg23039,True.intro,True.intro⟩⟩,⟨sg23042,⟨sg23041,True.intro,True.intro⟩,⟨sg23043,True.intro,True.intro⟩⟩⟩,⟨sg23048,⟨sg23046,⟨sg23045,True.intro,True.intro⟩,⟨sg23047,True.intro,True.intro⟩⟩,⟨sg23050,⟨sg23049,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23058,⟨sg23055,⟨sg23053,⟨sg23052,True.intro,True.intro⟩,⟨sg23054,True.intro,True.intro⟩⟩,⟨sg23057,⟨sg23056,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23062,⟨sg23060,⟨sg23059,True.intro,True.intro⟩,⟨sg23061,True.intro,True.intro⟩⟩,⟨sg23064,⟨sg23063,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_90All : degreeTree39_90.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23036,degreeTree39_88All,degreeTree39_89All⟩ - -lemma degreeTree39_91All : degreeTree39_91.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23007,degreeTree39_87All,degreeTree39_90All⟩ - -lemma degreeTree39_92All : degreeTree39_92.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22949,degreeTree39_84All,degreeTree39_91All⟩ - -lemma degreeTree39_93All : degreeTree39_93.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22833,degreeTree39_77All,degreeTree39_92All⟩ - -lemma degreeTree39_94All : degreeTree39_94.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23080,⟨sg23073,⟨sg23069,⟨sg23067,⟨sg23066,True.intro,True.intro⟩,⟨sg23068,True.intro,True.intro⟩⟩,⟨sg23071,⟨sg23070,True.intro,True.intro⟩,⟨sg23072,True.intro,True.intro⟩⟩⟩,⟨sg23077,⟨sg23075,⟨sg23074,True.intro,True.intro⟩,⟨sg23076,True.intro,True.intro⟩⟩,⟨sg23079,⟨sg23078,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23088,⟨sg23084,⟨sg23082,⟨sg23081,True.intro,True.intro⟩,⟨sg23083,True.intro,True.intro⟩⟩,⟨sg23086,⟨sg23085,True.intro,True.intro⟩,⟨sg23087,True.intro,True.intro⟩⟩⟩,⟨sg23092,⟨sg23090,⟨sg23089,True.intro,True.intro⟩,⟨sg23091,True.intro,True.intro⟩⟩,⟨sg23094,⟨sg23093,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_95All : degreeTree39_95.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23110,⟨sg23103,⟨sg23099,⟨sg23097,⟨sg23096,True.intro,True.intro⟩,⟨sg23098,True.intro,True.intro⟩⟩,⟨sg23101,⟨sg23100,True.intro,True.intro⟩,⟨sg23102,True.intro,True.intro⟩⟩⟩,⟨sg23107,⟨sg23105,⟨sg23104,True.intro,True.intro⟩,⟨sg23106,True.intro,True.intro⟩⟩,⟨sg23109,⟨sg23108,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23117,⟨sg23114,⟨sg23112,⟨sg23111,True.intro,True.intro⟩,⟨sg23113,True.intro,True.intro⟩⟩,⟨sg23116,⟨sg23115,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23121,⟨sg23119,⟨sg23118,True.intro,True.intro⟩,⟨sg23120,True.intro,True.intro⟩⟩,⟨sg23123,⟨sg23122,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_96All : degreeTree39_96.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23095,degreeTree39_94All,degreeTree39_95All⟩ - -lemma degreeTree39_97All : degreeTree39_97.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23139,⟨sg23132,⟨sg23128,⟨sg23126,⟨sg23125,True.intro,True.intro⟩,⟨sg23127,True.intro,True.intro⟩⟩,⟨sg23130,⟨sg23129,True.intro,True.intro⟩,⟨sg23131,True.intro,True.intro⟩⟩⟩,⟨sg23136,⟨sg23134,⟨sg23133,True.intro,True.intro⟩,⟨sg23135,True.intro,True.intro⟩⟩,⟨sg23138,⟨sg23137,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23146,⟨sg23143,⟨sg23141,⟨sg23140,True.intro,True.intro⟩,⟨sg23142,True.intro,True.intro⟩⟩,⟨sg23145,⟨sg23144,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23150,⟨sg23148,⟨sg23147,True.intro,True.intro⟩,⟨sg23149,True.intro,True.intro⟩⟩,⟨sg23152,⟨sg23151,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_98All : degreeTree39_98.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23168,⟨sg23161,⟨sg23157,⟨sg23155,⟨sg23154,True.intro,True.intro⟩,⟨sg23156,True.intro,True.intro⟩⟩,⟨sg23159,⟨sg23158,True.intro,True.intro⟩,⟨sg23160,True.intro,True.intro⟩⟩⟩,⟨sg23165,⟨sg23163,⟨sg23162,True.intro,True.intro⟩,⟨sg23164,True.intro,True.intro⟩⟩,⟨sg23167,⟨sg23166,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23175,⟨sg23172,⟨sg23170,⟨sg23169,True.intro,True.intro⟩,⟨sg23171,True.intro,True.intro⟩⟩,⟨sg23174,⟨sg23173,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23179,⟨sg23177,⟨sg23176,True.intro,True.intro⟩,⟨sg23178,True.intro,True.intro⟩⟩,⟨sg23181,⟨sg23180,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_99All : degreeTree39_99.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23153,degreeTree39_97All,degreeTree39_98All⟩ - -lemma degreeTree39_100All : degreeTree39_100.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23124,degreeTree39_96All,degreeTree39_99All⟩ - -lemma degreeTree39_101All : degreeTree39_101.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23197,⟨sg23190,⟨sg23186,⟨sg23184,⟨sg23183,True.intro,True.intro⟩,⟨sg23185,True.intro,True.intro⟩⟩,⟨sg23188,⟨sg23187,True.intro,True.intro⟩,⟨sg23189,True.intro,True.intro⟩⟩⟩,⟨sg23194,⟨sg23192,⟨sg23191,True.intro,True.intro⟩,⟨sg23193,True.intro,True.intro⟩⟩,⟨sg23196,⟨sg23195,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23204,⟨sg23201,⟨sg23199,⟨sg23198,True.intro,True.intro⟩,⟨sg23200,True.intro,True.intro⟩⟩,⟨sg23203,⟨sg23202,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23208,⟨sg23206,⟨sg23205,True.intro,True.intro⟩,⟨sg23207,True.intro,True.intro⟩⟩,⟨sg23210,⟨sg23209,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_102All : degreeTree39_102.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23226,⟨sg23219,⟨sg23215,⟨sg23213,⟨sg23212,True.intro,True.intro⟩,⟨sg23214,True.intro,True.intro⟩⟩,⟨sg23217,⟨sg23216,True.intro,True.intro⟩,⟨sg23218,True.intro,True.intro⟩⟩⟩,⟨sg23223,⟨sg23221,⟨sg23220,True.intro,True.intro⟩,⟨sg23222,True.intro,True.intro⟩⟩,⟨sg23225,⟨sg23224,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23233,⟨sg23230,⟨sg23228,⟨sg23227,True.intro,True.intro⟩,⟨sg23229,True.intro,True.intro⟩⟩,⟨sg23232,⟨sg23231,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23237,⟨sg23235,⟨sg23234,True.intro,True.intro⟩,⟨sg23236,True.intro,True.intro⟩⟩,⟨sg23239,⟨sg23238,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_103All : degreeTree39_103.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23211,degreeTree39_101All,degreeTree39_102All⟩ - -lemma degreeTree39_104All : degreeTree39_104.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23255,⟨sg23248,⟨sg23244,⟨sg23242,⟨sg23241,True.intro,True.intro⟩,⟨sg23243,True.intro,True.intro⟩⟩,⟨sg23246,⟨sg23245,True.intro,True.intro⟩,⟨sg23247,True.intro,True.intro⟩⟩⟩,⟨sg23252,⟨sg23250,⟨sg23249,True.intro,True.intro⟩,⟨sg23251,True.intro,True.intro⟩⟩,⟨sg23254,⟨sg23253,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23262,⟨sg23259,⟨sg23257,⟨sg23256,True.intro,True.intro⟩,⟨sg23258,True.intro,True.intro⟩⟩,⟨sg23261,⟨sg23260,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23266,⟨sg23264,⟨sg23263,True.intro,True.intro⟩,⟨sg23265,True.intro,True.intro⟩⟩,⟨sg23268,⟨sg23267,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_105All : degreeTree39_105.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23284,⟨sg23277,⟨sg23273,⟨sg23271,⟨sg23270,True.intro,True.intro⟩,⟨sg23272,True.intro,True.intro⟩⟩,⟨sg23275,⟨sg23274,True.intro,True.intro⟩,⟨sg23276,True.intro,True.intro⟩⟩⟩,⟨sg23281,⟨sg23279,⟨sg23278,True.intro,True.intro⟩,⟨sg23280,True.intro,True.intro⟩⟩,⟨sg23283,⟨sg23282,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23291,⟨sg23288,⟨sg23286,⟨sg23285,True.intro,True.intro⟩,⟨sg23287,True.intro,True.intro⟩⟩,⟨sg23290,⟨sg23289,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23295,⟨sg23293,⟨sg23292,True.intro,True.intro⟩,⟨sg23294,True.intro,True.intro⟩⟩,⟨sg23297,⟨sg23296,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_106All : degreeTree39_106.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23269,degreeTree39_104All,degreeTree39_105All⟩ - -lemma degreeTree39_107All : degreeTree39_107.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23240,degreeTree39_103All,degreeTree39_106All⟩ - -lemma degreeTree39_108All : degreeTree39_108.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23182,degreeTree39_100All,degreeTree39_107All⟩ - -lemma degreeTree39_109All : degreeTree39_109.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23313,⟨sg23306,⟨sg23302,⟨sg23300,⟨sg23299,True.intro,True.intro⟩,⟨sg23301,True.intro,True.intro⟩⟩,⟨sg23304,⟨sg23303,True.intro,True.intro⟩,⟨sg23305,True.intro,True.intro⟩⟩⟩,⟨sg23310,⟨sg23308,⟨sg23307,True.intro,True.intro⟩,⟨sg23309,True.intro,True.intro⟩⟩,⟨sg23312,⟨sg23311,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23320,⟨sg23317,⟨sg23315,⟨sg23314,True.intro,True.intro⟩,⟨sg23316,True.intro,True.intro⟩⟩,⟨sg23319,⟨sg23318,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23324,⟨sg23322,⟨sg23321,True.intro,True.intro⟩,⟨sg23323,True.intro,True.intro⟩⟩,⟨sg23326,⟨sg23325,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_110All : degreeTree39_110.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23342,⟨sg23335,⟨sg23331,⟨sg23329,⟨sg23328,True.intro,True.intro⟩,⟨sg23330,True.intro,True.intro⟩⟩,⟨sg23333,⟨sg23332,True.intro,True.intro⟩,⟨sg23334,True.intro,True.intro⟩⟩⟩,⟨sg23339,⟨sg23337,⟨sg23336,True.intro,True.intro⟩,⟨sg23338,True.intro,True.intro⟩⟩,⟨sg23341,⟨sg23340,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23349,⟨sg23346,⟨sg23344,⟨sg23343,True.intro,True.intro⟩,⟨sg23345,True.intro,True.intro⟩⟩,⟨sg23348,⟨sg23347,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23353,⟨sg23351,⟨sg23350,True.intro,True.intro⟩,⟨sg23352,True.intro,True.intro⟩⟩,⟨sg23355,⟨sg23354,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_111All : degreeTree39_111.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23327,degreeTree39_109All,degreeTree39_110All⟩ - -lemma degreeTree39_112All : degreeTree39_112.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23371,⟨sg23364,⟨sg23360,⟨sg23358,⟨sg23357,True.intro,True.intro⟩,⟨sg23359,True.intro,True.intro⟩⟩,⟨sg23362,⟨sg23361,True.intro,True.intro⟩,⟨sg23363,True.intro,True.intro⟩⟩⟩,⟨sg23368,⟨sg23366,⟨sg23365,True.intro,True.intro⟩,⟨sg23367,True.intro,True.intro⟩⟩,⟨sg23370,⟨sg23369,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23378,⟨sg23375,⟨sg23373,⟨sg23372,True.intro,True.intro⟩,⟨sg23374,True.intro,True.intro⟩⟩,⟨sg23377,⟨sg23376,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23382,⟨sg23380,⟨sg23379,True.intro,True.intro⟩,⟨sg23381,True.intro,True.intro⟩⟩,⟨sg23384,⟨sg23383,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_113All : degreeTree39_113.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23400,⟨sg23393,⟨sg23389,⟨sg23387,⟨sg23386,True.intro,True.intro⟩,⟨sg23388,True.intro,True.intro⟩⟩,⟨sg23391,⟨sg23390,True.intro,True.intro⟩,⟨sg23392,True.intro,True.intro⟩⟩⟩,⟨sg23397,⟨sg23395,⟨sg23394,True.intro,True.intro⟩,⟨sg23396,True.intro,True.intro⟩⟩,⟨sg23399,⟨sg23398,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23407,⟨sg23404,⟨sg23402,⟨sg23401,True.intro,True.intro⟩,⟨sg23403,True.intro,True.intro⟩⟩,⟨sg23406,⟨sg23405,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23411,⟨sg23409,⟨sg23408,True.intro,True.intro⟩,⟨sg23410,True.intro,True.intro⟩⟩,⟨sg23413,⟨sg23412,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_114All : degreeTree39_114.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23385,degreeTree39_112All,degreeTree39_113All⟩ - -lemma degreeTree39_115All : degreeTree39_115.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23356,degreeTree39_111All,degreeTree39_114All⟩ - -lemma degreeTree39_116All : degreeTree39_116.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23429,⟨sg23422,⟨sg23418,⟨sg23416,⟨sg23415,True.intro,True.intro⟩,⟨sg23417,True.intro,True.intro⟩⟩,⟨sg23420,⟨sg23419,True.intro,True.intro⟩,⟨sg23421,True.intro,True.intro⟩⟩⟩,⟨sg23426,⟨sg23424,⟨sg23423,True.intro,True.intro⟩,⟨sg23425,True.intro,True.intro⟩⟩,⟨sg23428,⟨sg23427,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23436,⟨sg23433,⟨sg23431,⟨sg23430,True.intro,True.intro⟩,⟨sg23432,True.intro,True.intro⟩⟩,⟨sg23435,⟨sg23434,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23440,⟨sg23438,⟨sg23437,True.intro,True.intro⟩,⟨sg23439,True.intro,True.intro⟩⟩,⟨sg23442,⟨sg23441,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_117All : degreeTree39_117.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23458,⟨sg23451,⟨sg23447,⟨sg23445,⟨sg23444,True.intro,True.intro⟩,⟨sg23446,True.intro,True.intro⟩⟩,⟨sg23449,⟨sg23448,True.intro,True.intro⟩,⟨sg23450,True.intro,True.intro⟩⟩⟩,⟨sg23455,⟨sg23453,⟨sg23452,True.intro,True.intro⟩,⟨sg23454,True.intro,True.intro⟩⟩,⟨sg23457,⟨sg23456,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23465,⟨sg23462,⟨sg23460,⟨sg23459,True.intro,True.intro⟩,⟨sg23461,True.intro,True.intro⟩⟩,⟨sg23464,⟨sg23463,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23469,⟨sg23467,⟨sg23466,True.intro,True.intro⟩,⟨sg23468,True.intro,True.intro⟩⟩,⟨sg23471,⟨sg23470,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_118All : degreeTree39_118.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23443,degreeTree39_116All,degreeTree39_117All⟩ - -lemma degreeTree39_119All : degreeTree39_119.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23487,⟨sg23480,⟨sg23476,⟨sg23474,⟨sg23473,True.intro,True.intro⟩,⟨sg23475,True.intro,True.intro⟩⟩,⟨sg23478,⟨sg23477,True.intro,True.intro⟩,⟨sg23479,True.intro,True.intro⟩⟩⟩,⟨sg23484,⟨sg23482,⟨sg23481,True.intro,True.intro⟩,⟨sg23483,True.intro,True.intro⟩⟩,⟨sg23486,⟨sg23485,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23494,⟨sg23491,⟨sg23489,⟨sg23488,True.intro,True.intro⟩,⟨sg23490,True.intro,True.intro⟩⟩,⟨sg23493,⟨sg23492,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23498,⟨sg23496,⟨sg23495,True.intro,True.intro⟩,⟨sg23497,True.intro,True.intro⟩⟩,⟨sg23500,⟨sg23499,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_120All : degreeTree39_120.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23516,⟨sg23509,⟨sg23505,⟨sg23503,⟨sg23502,True.intro,True.intro⟩,⟨sg23504,True.intro,True.intro⟩⟩,⟨sg23507,⟨sg23506,True.intro,True.intro⟩,⟨sg23508,True.intro,True.intro⟩⟩⟩,⟨sg23513,⟨sg23511,⟨sg23510,True.intro,True.intro⟩,⟨sg23512,True.intro,True.intro⟩⟩,⟨sg23515,⟨sg23514,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23523,⟨sg23520,⟨sg23518,⟨sg23517,True.intro,True.intro⟩,⟨sg23519,True.intro,True.intro⟩⟩,⟨sg23522,⟨sg23521,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23527,⟨sg23525,⟨sg23524,True.intro,True.intro⟩,⟨sg23526,True.intro,True.intro⟩⟩,⟨sg23529,⟨sg23528,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree39_121All : degreeTree39_121.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23501,degreeTree39_119All,degreeTree39_120All⟩ - -lemma degreeTree39_122All : degreeTree39_122.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23472,degreeTree39_118All,degreeTree39_121All⟩ - -lemma degreeTree39_123All : degreeTree39_123.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23414,degreeTree39_115All,degreeTree39_122All⟩ - -lemma degreeTree39_124All : degreeTree39_124.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23298,degreeTree39_108All,degreeTree39_123All⟩ - -lemma degreeTree39_125All : degreeTree39_125.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg23065,degreeTree39_93All,degreeTree39_124All⟩ - -lemma degreeTree39_126All : degreeTree39_126.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by - exact ⟨sg22600,degreeTree39_62All,degreeTree39_125All⟩ - -lemma degreeTreeAll39 : degreeTree39.All - (fun rs => SquareOccurs (candidate 6 4 1) (rowDiagram rs)) := by - have hp : rowDiagram [11,9,4,3,2,2,2,2,2,1,1] = candidate 6 4 1 := rowDiagram_candidate (M := 6) (b := 4) (δ := 1) (by decide) - rw [← hp] - exact degreeTree39_126All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes53 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes54 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes55 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes56 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes57 + +namespace OAI + +/-! Degree Tree Proof 39. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree39_0All : degreeTree39_0.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21685,⟨sg21678,⟨sg21674,⟨sg21672,⟨sg21671,True.intro,True.intro⟩,⟨sg21673,True.intro,True.intro⟩⟩,⟨sg21676,⟨sg21675,True.intro,True.intro⟩,⟨sg21677,True.intro,True.intro⟩⟩⟩,⟨sg21682,⟨sg21680,⟨sg21679,True.intro,True.intro⟩,⟨sg21681,True.intro,True.intro⟩⟩,⟨sg21684,⟨sg21683,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21693,⟨sg21689,⟨sg21687,⟨sg21686,True.intro,True.intro⟩,⟨sg21688,True.intro,True.intro⟩⟩,⟨sg21691,⟨sg21690,True.intro,True.intro⟩,⟨sg21692,True.intro,True.intro⟩⟩⟩,⟨sg21697,⟨sg21695,⟨sg21694,True.intro,True.intro⟩,⟨sg21696,True.intro,True.intro⟩⟩,⟨sg21699,⟨sg21698,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_1All : degreeTree39_1.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21715,⟨sg21708,⟨sg21704,⟨sg21702,⟨sg21701,True.intro,True.intro⟩,⟨sg21703,True.intro,True.intro⟩⟩,⟨sg21706,⟨sg21705,True.intro,True.intro⟩,⟨sg21707,True.intro,True.intro⟩⟩⟩,⟨sg21712,⟨sg21710,⟨sg21709,True.intro,True.intro⟩,⟨sg21711,True.intro,True.intro⟩⟩,⟨sg21714,⟨sg21713,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21722,⟨sg21719,⟨sg21717,⟨sg21716,True.intro,True.intro⟩,⟨sg21718,True.intro,True.intro⟩⟩,⟨sg21721,⟨sg21720,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21726,⟨sg21724,⟨sg21723,True.intro,True.intro⟩,⟨sg21725,True.intro,True.intro⟩⟩,⟨sg21728,⟨sg21727,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_2All : degreeTree39_2.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21700,degreeTree39_0All,degreeTree39_1All⟩ + +lemma degreeTree39_3All : degreeTree39_3.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21744,⟨sg21737,⟨sg21733,⟨sg21731,⟨sg21730,True.intro,True.intro⟩,⟨sg21732,True.intro,True.intro⟩⟩,⟨sg21735,⟨sg21734,True.intro,True.intro⟩,⟨sg21736,True.intro,True.intro⟩⟩⟩,⟨sg21741,⟨sg21739,⟨sg21738,True.intro,True.intro⟩,⟨sg21740,True.intro,True.intro⟩⟩,⟨sg21743,⟨sg21742,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21751,⟨sg21748,⟨sg21746,⟨sg21745,True.intro,True.intro⟩,⟨sg21747,True.intro,True.intro⟩⟩,⟨sg21750,⟨sg21749,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21755,⟨sg21753,⟨sg21752,True.intro,True.intro⟩,⟨sg21754,True.intro,True.intro⟩⟩,⟨sg21757,⟨sg21756,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_4All : degreeTree39_4.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21773,⟨sg21766,⟨sg21762,⟨sg21760,⟨sg21759,True.intro,True.intro⟩,⟨sg21761,True.intro,True.intro⟩⟩,⟨sg21764,⟨sg21763,True.intro,True.intro⟩,⟨sg21765,True.intro,True.intro⟩⟩⟩,⟨sg21770,⟨sg21768,⟨sg21767,True.intro,True.intro⟩,⟨sg21769,True.intro,True.intro⟩⟩,⟨sg21772,⟨sg21771,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21780,⟨sg21777,⟨sg21775,⟨sg21774,True.intro,True.intro⟩,⟨sg21776,True.intro,True.intro⟩⟩,⟨sg21779,⟨sg21778,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21784,⟨sg21782,⟨sg21781,True.intro,True.intro⟩,⟨sg21783,True.intro,True.intro⟩⟩,⟨sg21786,⟨sg21785,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_5All : degreeTree39_5.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21758,degreeTree39_3All,degreeTree39_4All⟩ + +lemma degreeTree39_6All : degreeTree39_6.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21729,degreeTree39_2All,degreeTree39_5All⟩ + +lemma degreeTree39_7All : degreeTree39_7.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21802,⟨sg21795,⟨sg21791,⟨sg21789,⟨sg21788,True.intro,True.intro⟩,⟨sg21790,True.intro,True.intro⟩⟩,⟨sg21793,⟨sg21792,True.intro,True.intro⟩,⟨sg21794,True.intro,True.intro⟩⟩⟩,⟨sg21799,⟨sg21797,⟨sg21796,True.intro,True.intro⟩,⟨sg21798,True.intro,True.intro⟩⟩,⟨sg21801,⟨sg21800,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21809,⟨sg21806,⟨sg21804,⟨sg21803,True.intro,True.intro⟩,⟨sg21805,True.intro,True.intro⟩⟩,⟨sg21808,⟨sg21807,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21813,⟨sg21811,⟨sg21810,True.intro,True.intro⟩,⟨sg21812,True.intro,True.intro⟩⟩,⟨sg21815,⟨sg21814,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_8All : degreeTree39_8.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21831,⟨sg21824,⟨sg21820,⟨sg21818,⟨sg21817,True.intro,True.intro⟩,⟨sg21819,True.intro,True.intro⟩⟩,⟨sg21822,⟨sg21821,True.intro,True.intro⟩,⟨sg21823,True.intro,True.intro⟩⟩⟩,⟨sg21828,⟨sg21826,⟨sg21825,True.intro,True.intro⟩,⟨sg21827,True.intro,True.intro⟩⟩,⟨sg21830,⟨sg21829,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21838,⟨sg21835,⟨sg21833,⟨sg21832,True.intro,True.intro⟩,⟨sg21834,True.intro,True.intro⟩⟩,⟨sg21837,⟨sg21836,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21842,⟨sg21840,⟨sg21839,True.intro,True.intro⟩,⟨sg21841,True.intro,True.intro⟩⟩,⟨sg21844,⟨sg21843,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_9All : degreeTree39_9.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21816,degreeTree39_7All,degreeTree39_8All⟩ + +lemma degreeTree39_10All : degreeTree39_10.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21860,⟨sg21853,⟨sg21849,⟨sg21847,⟨sg21846,True.intro,True.intro⟩,⟨sg21848,True.intro,True.intro⟩⟩,⟨sg21851,⟨sg21850,True.intro,True.intro⟩,⟨sg21852,True.intro,True.intro⟩⟩⟩,⟨sg21857,⟨sg21855,⟨sg21854,True.intro,True.intro⟩,⟨sg21856,True.intro,True.intro⟩⟩,⟨sg21859,⟨sg21858,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21867,⟨sg21864,⟨sg21862,⟨sg21861,True.intro,True.intro⟩,⟨sg21863,True.intro,True.intro⟩⟩,⟨sg21866,⟨sg21865,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21871,⟨sg21869,⟨sg21868,True.intro,True.intro⟩,⟨sg21870,True.intro,True.intro⟩⟩,⟨sg21873,⟨sg21872,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_11All : degreeTree39_11.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21889,⟨sg21882,⟨sg21878,⟨sg21876,⟨sg21875,True.intro,True.intro⟩,⟨sg21877,True.intro,True.intro⟩⟩,⟨sg21880,⟨sg21879,True.intro,True.intro⟩,⟨sg21881,True.intro,True.intro⟩⟩⟩,⟨sg21886,⟨sg21884,⟨sg21883,True.intro,True.intro⟩,⟨sg21885,True.intro,True.intro⟩⟩,⟨sg21888,⟨sg21887,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21896,⟨sg21893,⟨sg21891,⟨sg21890,True.intro,True.intro⟩,⟨sg21892,True.intro,True.intro⟩⟩,⟨sg21895,⟨sg21894,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21900,⟨sg21898,⟨sg21897,True.intro,True.intro⟩,⟨sg21899,True.intro,True.intro⟩⟩,⟨sg21902,⟨sg21901,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_12All : degreeTree39_12.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21874,degreeTree39_10All,degreeTree39_11All⟩ + +lemma degreeTree39_13All : degreeTree39_13.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21845,degreeTree39_9All,degreeTree39_12All⟩ + +lemma degreeTree39_14All : degreeTree39_14.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21787,degreeTree39_6All,degreeTree39_13All⟩ + +lemma degreeTree39_15All : degreeTree39_15.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21918,⟨sg21911,⟨sg21907,⟨sg21905,⟨sg21904,True.intro,True.intro⟩,⟨sg21906,True.intro,True.intro⟩⟩,⟨sg21909,⟨sg21908,True.intro,True.intro⟩,⟨sg21910,True.intro,True.intro⟩⟩⟩,⟨sg21915,⟨sg21913,⟨sg21912,True.intro,True.intro⟩,⟨sg21914,True.intro,True.intro⟩⟩,⟨sg21917,⟨sg21916,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21925,⟨sg21922,⟨sg21920,⟨sg21919,True.intro,True.intro⟩,⟨sg21921,True.intro,True.intro⟩⟩,⟨sg21924,⟨sg21923,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21929,⟨sg21927,⟨sg21926,True.intro,True.intro⟩,⟨sg21928,True.intro,True.intro⟩⟩,⟨sg21931,⟨sg21930,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_16All : degreeTree39_16.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21947,⟨sg21940,⟨sg21936,⟨sg21934,⟨sg21933,True.intro,True.intro⟩,⟨sg21935,True.intro,True.intro⟩⟩,⟨sg21938,⟨sg21937,True.intro,True.intro⟩,⟨sg21939,True.intro,True.intro⟩⟩⟩,⟨sg21944,⟨sg21942,⟨sg21941,True.intro,True.intro⟩,⟨sg21943,True.intro,True.intro⟩⟩,⟨sg21946,⟨sg21945,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21954,⟨sg21951,⟨sg21949,⟨sg21948,True.intro,True.intro⟩,⟨sg21950,True.intro,True.intro⟩⟩,⟨sg21953,⟨sg21952,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21958,⟨sg21956,⟨sg21955,True.intro,True.intro⟩,⟨sg21957,True.intro,True.intro⟩⟩,⟨sg21960,⟨sg21959,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_17All : degreeTree39_17.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21932,degreeTree39_15All,degreeTree39_16All⟩ + +lemma degreeTree39_18All : degreeTree39_18.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21976,⟨sg21969,⟨sg21965,⟨sg21963,⟨sg21962,True.intro,True.intro⟩,⟨sg21964,True.intro,True.intro⟩⟩,⟨sg21967,⟨sg21966,True.intro,True.intro⟩,⟨sg21968,True.intro,True.intro⟩⟩⟩,⟨sg21973,⟨sg21971,⟨sg21970,True.intro,True.intro⟩,⟨sg21972,True.intro,True.intro⟩⟩,⟨sg21975,⟨sg21974,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg21983,⟨sg21980,⟨sg21978,⟨sg21977,True.intro,True.intro⟩,⟨sg21979,True.intro,True.intro⟩⟩,⟨sg21982,⟨sg21981,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg21987,⟨sg21985,⟨sg21984,True.intro,True.intro⟩,⟨sg21986,True.intro,True.intro⟩⟩,⟨sg21989,⟨sg21988,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_19All : degreeTree39_19.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22005,⟨sg21998,⟨sg21994,⟨sg21992,⟨sg21991,True.intro,True.intro⟩,⟨sg21993,True.intro,True.intro⟩⟩,⟨sg21996,⟨sg21995,True.intro,True.intro⟩,⟨sg21997,True.intro,True.intro⟩⟩⟩,⟨sg22002,⟨sg22000,⟨sg21999,True.intro,True.intro⟩,⟨sg22001,True.intro,True.intro⟩⟩,⟨sg22004,⟨sg22003,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22012,⟨sg22009,⟨sg22007,⟨sg22006,True.intro,True.intro⟩,⟨sg22008,True.intro,True.intro⟩⟩,⟨sg22011,⟨sg22010,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22016,⟨sg22014,⟨sg22013,True.intro,True.intro⟩,⟨sg22015,True.intro,True.intro⟩⟩,⟨sg22018,⟨sg22017,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_20All : degreeTree39_20.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21990,degreeTree39_18All,degreeTree39_19All⟩ + +lemma degreeTree39_21All : degreeTree39_21.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21961,degreeTree39_17All,degreeTree39_20All⟩ + +lemma degreeTree39_22All : degreeTree39_22.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22034,⟨sg22027,⟨sg22023,⟨sg22021,⟨sg22020,True.intro,True.intro⟩,⟨sg22022,True.intro,True.intro⟩⟩,⟨sg22025,⟨sg22024,True.intro,True.intro⟩,⟨sg22026,True.intro,True.intro⟩⟩⟩,⟨sg22031,⟨sg22029,⟨sg22028,True.intro,True.intro⟩,⟨sg22030,True.intro,True.intro⟩⟩,⟨sg22033,⟨sg22032,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22041,⟨sg22038,⟨sg22036,⟨sg22035,True.intro,True.intro⟩,⟨sg22037,True.intro,True.intro⟩⟩,⟨sg22040,⟨sg22039,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22045,⟨sg22043,⟨sg22042,True.intro,True.intro⟩,⟨sg22044,True.intro,True.intro⟩⟩,⟨sg22047,⟨sg22046,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_23All : degreeTree39_23.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22063,⟨sg22056,⟨sg22052,⟨sg22050,⟨sg22049,True.intro,True.intro⟩,⟨sg22051,True.intro,True.intro⟩⟩,⟨sg22054,⟨sg22053,True.intro,True.intro⟩,⟨sg22055,True.intro,True.intro⟩⟩⟩,⟨sg22060,⟨sg22058,⟨sg22057,True.intro,True.intro⟩,⟨sg22059,True.intro,True.intro⟩⟩,⟨sg22062,⟨sg22061,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22070,⟨sg22067,⟨sg22065,⟨sg22064,True.intro,True.intro⟩,⟨sg22066,True.intro,True.intro⟩⟩,⟨sg22069,⟨sg22068,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22074,⟨sg22072,⟨sg22071,True.intro,True.intro⟩,⟨sg22073,True.intro,True.intro⟩⟩,⟨sg22076,⟨sg22075,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_24All : degreeTree39_24.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22048,degreeTree39_22All,degreeTree39_23All⟩ + +lemma degreeTree39_25All : degreeTree39_25.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22092,⟨sg22085,⟨sg22081,⟨sg22079,⟨sg22078,True.intro,True.intro⟩,⟨sg22080,True.intro,True.intro⟩⟩,⟨sg22083,⟨sg22082,True.intro,True.intro⟩,⟨sg22084,True.intro,True.intro⟩⟩⟩,⟨sg22089,⟨sg22087,⟨sg22086,True.intro,True.intro⟩,⟨sg22088,True.intro,True.intro⟩⟩,⟨sg22091,⟨sg22090,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22099,⟨sg22096,⟨sg22094,⟨sg22093,True.intro,True.intro⟩,⟨sg22095,True.intro,True.intro⟩⟩,⟨sg22098,⟨sg22097,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22103,⟨sg22101,⟨sg22100,True.intro,True.intro⟩,⟨sg22102,True.intro,True.intro⟩⟩,⟨sg22105,⟨sg22104,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_26All : degreeTree39_26.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22121,⟨sg22114,⟨sg22110,⟨sg22108,⟨sg22107,True.intro,True.intro⟩,⟨sg22109,True.intro,True.intro⟩⟩,⟨sg22112,⟨sg22111,True.intro,True.intro⟩,⟨sg22113,True.intro,True.intro⟩⟩⟩,⟨sg22118,⟨sg22116,⟨sg22115,True.intro,True.intro⟩,⟨sg22117,True.intro,True.intro⟩⟩,⟨sg22120,⟨sg22119,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22128,⟨sg22125,⟨sg22123,⟨sg22122,True.intro,True.intro⟩,⟨sg22124,True.intro,True.intro⟩⟩,⟨sg22127,⟨sg22126,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22132,⟨sg22130,⟨sg22129,True.intro,True.intro⟩,⟨sg22131,True.intro,True.intro⟩⟩,⟨sg22134,⟨sg22133,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_27All : degreeTree39_27.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22106,degreeTree39_25All,degreeTree39_26All⟩ + +lemma degreeTree39_28All : degreeTree39_28.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22077,degreeTree39_24All,degreeTree39_27All⟩ + +lemma degreeTree39_29All : degreeTree39_29.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22019,degreeTree39_21All,degreeTree39_28All⟩ + +lemma degreeTree39_30All : degreeTree39_30.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg21903,degreeTree39_14All,degreeTree39_29All⟩ + +lemma degreeTree39_31All : degreeTree39_31.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22150,⟨sg22143,⟨sg22139,⟨sg22137,⟨sg22136,True.intro,True.intro⟩,⟨sg22138,True.intro,True.intro⟩⟩,⟨sg22141,⟨sg22140,True.intro,True.intro⟩,⟨sg22142,True.intro,True.intro⟩⟩⟩,⟨sg22147,⟨sg22145,⟨sg22144,True.intro,True.intro⟩,⟨sg22146,True.intro,True.intro⟩⟩,⟨sg22149,⟨sg22148,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22158,⟨sg22154,⟨sg22152,⟨sg22151,True.intro,True.intro⟩,⟨sg22153,True.intro,True.intro⟩⟩,⟨sg22156,⟨sg22155,True.intro,True.intro⟩,⟨sg22157,True.intro,True.intro⟩⟩⟩,⟨sg22162,⟨sg22160,⟨sg22159,True.intro,True.intro⟩,⟨sg22161,True.intro,True.intro⟩⟩,⟨sg22164,⟨sg22163,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_32All : degreeTree39_32.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22180,⟨sg22173,⟨sg22169,⟨sg22167,⟨sg22166,True.intro,True.intro⟩,⟨sg22168,True.intro,True.intro⟩⟩,⟨sg22171,⟨sg22170,True.intro,True.intro⟩,⟨sg22172,True.intro,True.intro⟩⟩⟩,⟨sg22177,⟨sg22175,⟨sg22174,True.intro,True.intro⟩,⟨sg22176,True.intro,True.intro⟩⟩,⟨sg22179,⟨sg22178,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22187,⟨sg22184,⟨sg22182,⟨sg22181,True.intro,True.intro⟩,⟨sg22183,True.intro,True.intro⟩⟩,⟨sg22186,⟨sg22185,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22191,⟨sg22189,⟨sg22188,True.intro,True.intro⟩,⟨sg22190,True.intro,True.intro⟩⟩,⟨sg22193,⟨sg22192,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_33All : degreeTree39_33.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22165,degreeTree39_31All,degreeTree39_32All⟩ + +lemma degreeTree39_34All : degreeTree39_34.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22209,⟨sg22202,⟨sg22198,⟨sg22196,⟨sg22195,True.intro,True.intro⟩,⟨sg22197,True.intro,True.intro⟩⟩,⟨sg22200,⟨sg22199,True.intro,True.intro⟩,⟨sg22201,True.intro,True.intro⟩⟩⟩,⟨sg22206,⟨sg22204,⟨sg22203,True.intro,True.intro⟩,⟨sg22205,True.intro,True.intro⟩⟩,⟨sg22208,⟨sg22207,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22216,⟨sg22213,⟨sg22211,⟨sg22210,True.intro,True.intro⟩,⟨sg22212,True.intro,True.intro⟩⟩,⟨sg22215,⟨sg22214,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22220,⟨sg22218,⟨sg22217,True.intro,True.intro⟩,⟨sg22219,True.intro,True.intro⟩⟩,⟨sg22222,⟨sg22221,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_35All : degreeTree39_35.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22238,⟨sg22231,⟨sg22227,⟨sg22225,⟨sg22224,True.intro,True.intro⟩,⟨sg22226,True.intro,True.intro⟩⟩,⟨sg22229,⟨sg22228,True.intro,True.intro⟩,⟨sg22230,True.intro,True.intro⟩⟩⟩,⟨sg22235,⟨sg22233,⟨sg22232,True.intro,True.intro⟩,⟨sg22234,True.intro,True.intro⟩⟩,⟨sg22237,⟨sg22236,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22245,⟨sg22242,⟨sg22240,⟨sg22239,True.intro,True.intro⟩,⟨sg22241,True.intro,True.intro⟩⟩,⟨sg22244,⟨sg22243,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22249,⟨sg22247,⟨sg22246,True.intro,True.intro⟩,⟨sg22248,True.intro,True.intro⟩⟩,⟨sg22251,⟨sg22250,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_36All : degreeTree39_36.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22223,degreeTree39_34All,degreeTree39_35All⟩ + +lemma degreeTree39_37All : degreeTree39_37.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22194,degreeTree39_33All,degreeTree39_36All⟩ + +lemma degreeTree39_38All : degreeTree39_38.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22267,⟨sg22260,⟨sg22256,⟨sg22254,⟨sg22253,True.intro,True.intro⟩,⟨sg22255,True.intro,True.intro⟩⟩,⟨sg22258,⟨sg22257,True.intro,True.intro⟩,⟨sg22259,True.intro,True.intro⟩⟩⟩,⟨sg22264,⟨sg22262,⟨sg22261,True.intro,True.intro⟩,⟨sg22263,True.intro,True.intro⟩⟩,⟨sg22266,⟨sg22265,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22274,⟨sg22271,⟨sg22269,⟨sg22268,True.intro,True.intro⟩,⟨sg22270,True.intro,True.intro⟩⟩,⟨sg22273,⟨sg22272,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22278,⟨sg22276,⟨sg22275,True.intro,True.intro⟩,⟨sg22277,True.intro,True.intro⟩⟩,⟨sg22280,⟨sg22279,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_39All : degreeTree39_39.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22296,⟨sg22289,⟨sg22285,⟨sg22283,⟨sg22282,True.intro,True.intro⟩,⟨sg22284,True.intro,True.intro⟩⟩,⟨sg22287,⟨sg22286,True.intro,True.intro⟩,⟨sg22288,True.intro,True.intro⟩⟩⟩,⟨sg22293,⟨sg22291,⟨sg22290,True.intro,True.intro⟩,⟨sg22292,True.intro,True.intro⟩⟩,⟨sg22295,⟨sg22294,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22303,⟨sg22300,⟨sg22298,⟨sg22297,True.intro,True.intro⟩,⟨sg22299,True.intro,True.intro⟩⟩,⟨sg22302,⟨sg22301,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22307,⟨sg22305,⟨sg22304,True.intro,True.intro⟩,⟨sg22306,True.intro,True.intro⟩⟩,⟨sg22309,⟨sg22308,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_40All : degreeTree39_40.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22281,degreeTree39_38All,degreeTree39_39All⟩ + +lemma degreeTree39_41All : degreeTree39_41.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22325,⟨sg22318,⟨sg22314,⟨sg22312,⟨sg22311,True.intro,True.intro⟩,⟨sg22313,True.intro,True.intro⟩⟩,⟨sg22316,⟨sg22315,True.intro,True.intro⟩,⟨sg22317,True.intro,True.intro⟩⟩⟩,⟨sg22322,⟨sg22320,⟨sg22319,True.intro,True.intro⟩,⟨sg22321,True.intro,True.intro⟩⟩,⟨sg22324,⟨sg22323,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22332,⟨sg22329,⟨sg22327,⟨sg22326,True.intro,True.intro⟩,⟨sg22328,True.intro,True.intro⟩⟩,⟨sg22331,⟨sg22330,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22336,⟨sg22334,⟨sg22333,True.intro,True.intro⟩,⟨sg22335,True.intro,True.intro⟩⟩,⟨sg22338,⟨sg22337,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_42All : degreeTree39_42.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22354,⟨sg22347,⟨sg22343,⟨sg22341,⟨sg22340,True.intro,True.intro⟩,⟨sg22342,True.intro,True.intro⟩⟩,⟨sg22345,⟨sg22344,True.intro,True.intro⟩,⟨sg22346,True.intro,True.intro⟩⟩⟩,⟨sg22351,⟨sg22349,⟨sg22348,True.intro,True.intro⟩,⟨sg22350,True.intro,True.intro⟩⟩,⟨sg22353,⟨sg22352,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22361,⟨sg22358,⟨sg22356,⟨sg22355,True.intro,True.intro⟩,⟨sg22357,True.intro,True.intro⟩⟩,⟨sg22360,⟨sg22359,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22365,⟨sg22363,⟨sg22362,True.intro,True.intro⟩,⟨sg22364,True.intro,True.intro⟩⟩,⟨sg22367,⟨sg22366,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_43All : degreeTree39_43.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22339,degreeTree39_41All,degreeTree39_42All⟩ + +lemma degreeTree39_44All : degreeTree39_44.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22310,degreeTree39_40All,degreeTree39_43All⟩ + +lemma degreeTree39_45All : degreeTree39_45.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22252,degreeTree39_37All,degreeTree39_44All⟩ + +lemma degreeTree39_46All : degreeTree39_46.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22383,⟨sg22376,⟨sg22372,⟨sg22370,⟨sg22369,True.intro,True.intro⟩,⟨sg22371,True.intro,True.intro⟩⟩,⟨sg22374,⟨sg22373,True.intro,True.intro⟩,⟨sg22375,True.intro,True.intro⟩⟩⟩,⟨sg22380,⟨sg22378,⟨sg22377,True.intro,True.intro⟩,⟨sg22379,True.intro,True.intro⟩⟩,⟨sg22382,⟨sg22381,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22390,⟨sg22387,⟨sg22385,⟨sg22384,True.intro,True.intro⟩,⟨sg22386,True.intro,True.intro⟩⟩,⟨sg22389,⟨sg22388,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22394,⟨sg22392,⟨sg22391,True.intro,True.intro⟩,⟨sg22393,True.intro,True.intro⟩⟩,⟨sg22396,⟨sg22395,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_47All : degreeTree39_47.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22412,⟨sg22405,⟨sg22401,⟨sg22399,⟨sg22398,True.intro,True.intro⟩,⟨sg22400,True.intro,True.intro⟩⟩,⟨sg22403,⟨sg22402,True.intro,True.intro⟩,⟨sg22404,True.intro,True.intro⟩⟩⟩,⟨sg22409,⟨sg22407,⟨sg22406,True.intro,True.intro⟩,⟨sg22408,True.intro,True.intro⟩⟩,⟨sg22411,⟨sg22410,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22419,⟨sg22416,⟨sg22414,⟨sg22413,True.intro,True.intro⟩,⟨sg22415,True.intro,True.intro⟩⟩,⟨sg22418,⟨sg22417,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22423,⟨sg22421,⟨sg22420,True.intro,True.intro⟩,⟨sg22422,True.intro,True.intro⟩⟩,⟨sg22425,⟨sg22424,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_48All : degreeTree39_48.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22397,degreeTree39_46All,degreeTree39_47All⟩ + +lemma degreeTree39_49All : degreeTree39_49.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22441,⟨sg22434,⟨sg22430,⟨sg22428,⟨sg22427,True.intro,True.intro⟩,⟨sg22429,True.intro,True.intro⟩⟩,⟨sg22432,⟨sg22431,True.intro,True.intro⟩,⟨sg22433,True.intro,True.intro⟩⟩⟩,⟨sg22438,⟨sg22436,⟨sg22435,True.intro,True.intro⟩,⟨sg22437,True.intro,True.intro⟩⟩,⟨sg22440,⟨sg22439,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22448,⟨sg22445,⟨sg22443,⟨sg22442,True.intro,True.intro⟩,⟨sg22444,True.intro,True.intro⟩⟩,⟨sg22447,⟨sg22446,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22452,⟨sg22450,⟨sg22449,True.intro,True.intro⟩,⟨sg22451,True.intro,True.intro⟩⟩,⟨sg22454,⟨sg22453,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_50All : degreeTree39_50.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22470,⟨sg22463,⟨sg22459,⟨sg22457,⟨sg22456,True.intro,True.intro⟩,⟨sg22458,True.intro,True.intro⟩⟩,⟨sg22461,⟨sg22460,True.intro,True.intro⟩,⟨sg22462,True.intro,True.intro⟩⟩⟩,⟨sg22467,⟨sg22465,⟨sg22464,True.intro,True.intro⟩,⟨sg22466,True.intro,True.intro⟩⟩,⟨sg22469,⟨sg22468,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22477,⟨sg22474,⟨sg22472,⟨sg22471,True.intro,True.intro⟩,⟨sg22473,True.intro,True.intro⟩⟩,⟨sg22476,⟨sg22475,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22481,⟨sg22479,⟨sg22478,True.intro,True.intro⟩,⟨sg22480,True.intro,True.intro⟩⟩,⟨sg22483,⟨sg22482,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_51All : degreeTree39_51.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22455,degreeTree39_49All,degreeTree39_50All⟩ + +lemma degreeTree39_52All : degreeTree39_52.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22426,degreeTree39_48All,degreeTree39_51All⟩ + +lemma degreeTree39_53All : degreeTree39_53.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22499,⟨sg22492,⟨sg22488,⟨sg22486,⟨sg22485,True.intro,True.intro⟩,⟨sg22487,True.intro,True.intro⟩⟩,⟨sg22490,⟨sg22489,True.intro,True.intro⟩,⟨sg22491,True.intro,True.intro⟩⟩⟩,⟨sg22496,⟨sg22494,⟨sg22493,True.intro,True.intro⟩,⟨sg22495,True.intro,True.intro⟩⟩,⟨sg22498,⟨sg22497,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22506,⟨sg22503,⟨sg22501,⟨sg22500,True.intro,True.intro⟩,⟨sg22502,True.intro,True.intro⟩⟩,⟨sg22505,⟨sg22504,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22510,⟨sg22508,⟨sg22507,True.intro,True.intro⟩,⟨sg22509,True.intro,True.intro⟩⟩,⟨sg22512,⟨sg22511,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_54All : degreeTree39_54.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22528,⟨sg22521,⟨sg22517,⟨sg22515,⟨sg22514,True.intro,True.intro⟩,⟨sg22516,True.intro,True.intro⟩⟩,⟨sg22519,⟨sg22518,True.intro,True.intro⟩,⟨sg22520,True.intro,True.intro⟩⟩⟩,⟨sg22525,⟨sg22523,⟨sg22522,True.intro,True.intro⟩,⟨sg22524,True.intro,True.intro⟩⟩,⟨sg22527,⟨sg22526,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22535,⟨sg22532,⟨sg22530,⟨sg22529,True.intro,True.intro⟩,⟨sg22531,True.intro,True.intro⟩⟩,⟨sg22534,⟨sg22533,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22539,⟨sg22537,⟨sg22536,True.intro,True.intro⟩,⟨sg22538,True.intro,True.intro⟩⟩,⟨sg22541,⟨sg22540,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_55All : degreeTree39_55.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22513,degreeTree39_53All,degreeTree39_54All⟩ + +lemma degreeTree39_56All : degreeTree39_56.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22557,⟨sg22550,⟨sg22546,⟨sg22544,⟨sg22543,True.intro,True.intro⟩,⟨sg22545,True.intro,True.intro⟩⟩,⟨sg22548,⟨sg22547,True.intro,True.intro⟩,⟨sg22549,True.intro,True.intro⟩⟩⟩,⟨sg22554,⟨sg22552,⟨sg22551,True.intro,True.intro⟩,⟨sg22553,True.intro,True.intro⟩⟩,⟨sg22556,⟨sg22555,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22564,⟨sg22561,⟨sg22559,⟨sg22558,True.intro,True.intro⟩,⟨sg22560,True.intro,True.intro⟩⟩,⟨sg22563,⟨sg22562,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22568,⟨sg22566,⟨sg22565,True.intro,True.intro⟩,⟨sg22567,True.intro,True.intro⟩⟩,⟨sg22570,⟨sg22569,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_57All : degreeTree39_57.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22586,⟨sg22579,⟨sg22575,⟨sg22573,⟨sg22572,True.intro,True.intro⟩,⟨sg22574,True.intro,True.intro⟩⟩,⟨sg22577,⟨sg22576,True.intro,True.intro⟩,⟨sg22578,True.intro,True.intro⟩⟩⟩,⟨sg22583,⟨sg22581,⟨sg22580,True.intro,True.intro⟩,⟨sg22582,True.intro,True.intro⟩⟩,⟨sg22585,⟨sg22584,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22593,⟨sg22590,⟨sg22588,⟨sg22587,True.intro,True.intro⟩,⟨sg22589,True.intro,True.intro⟩⟩,⟨sg22592,⟨sg22591,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22597,⟨sg22595,⟨sg22594,True.intro,True.intro⟩,⟨sg22596,True.intro,True.intro⟩⟩,⟨sg22599,⟨sg22598,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_58All : degreeTree39_58.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22571,degreeTree39_56All,degreeTree39_57All⟩ + +lemma degreeTree39_59All : degreeTree39_59.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22542,degreeTree39_55All,degreeTree39_58All⟩ + +lemma degreeTree39_60All : degreeTree39_60.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22484,degreeTree39_52All,degreeTree39_59All⟩ + +lemma degreeTree39_61All : degreeTree39_61.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22368,degreeTree39_45All,degreeTree39_60All⟩ + +lemma degreeTree39_62All : degreeTree39_62.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22135,degreeTree39_30All,degreeTree39_61All⟩ + +lemma degreeTree39_63All : degreeTree39_63.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22615,⟨sg22608,⟨sg22604,⟨sg22602,⟨sg22601,True.intro,True.intro⟩,⟨sg22603,True.intro,True.intro⟩⟩,⟨sg22606,⟨sg22605,True.intro,True.intro⟩,⟨sg22607,True.intro,True.intro⟩⟩⟩,⟨sg22612,⟨sg22610,⟨sg22609,True.intro,True.intro⟩,⟨sg22611,True.intro,True.intro⟩⟩,⟨sg22614,⟨sg22613,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22623,⟨sg22619,⟨sg22617,⟨sg22616,True.intro,True.intro⟩,⟨sg22618,True.intro,True.intro⟩⟩,⟨sg22621,⟨sg22620,True.intro,True.intro⟩,⟨sg22622,True.intro,True.intro⟩⟩⟩,⟨sg22627,⟨sg22625,⟨sg22624,True.intro,True.intro⟩,⟨sg22626,True.intro,True.intro⟩⟩,⟨sg22629,⟨sg22628,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_64All : degreeTree39_64.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22645,⟨sg22638,⟨sg22634,⟨sg22632,⟨sg22631,True.intro,True.intro⟩,⟨sg22633,True.intro,True.intro⟩⟩,⟨sg22636,⟨sg22635,True.intro,True.intro⟩,⟨sg22637,True.intro,True.intro⟩⟩⟩,⟨sg22642,⟨sg22640,⟨sg22639,True.intro,True.intro⟩,⟨sg22641,True.intro,True.intro⟩⟩,⟨sg22644,⟨sg22643,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22652,⟨sg22649,⟨sg22647,⟨sg22646,True.intro,True.intro⟩,⟨sg22648,True.intro,True.intro⟩⟩,⟨sg22651,⟨sg22650,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22656,⟨sg22654,⟨sg22653,True.intro,True.intro⟩,⟨sg22655,True.intro,True.intro⟩⟩,⟨sg22658,⟨sg22657,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_65All : degreeTree39_65.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22630,degreeTree39_63All,degreeTree39_64All⟩ + +lemma degreeTree39_66All : degreeTree39_66.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22674,⟨sg22667,⟨sg22663,⟨sg22661,⟨sg22660,True.intro,True.intro⟩,⟨sg22662,True.intro,True.intro⟩⟩,⟨sg22665,⟨sg22664,True.intro,True.intro⟩,⟨sg22666,True.intro,True.intro⟩⟩⟩,⟨sg22671,⟨sg22669,⟨sg22668,True.intro,True.intro⟩,⟨sg22670,True.intro,True.intro⟩⟩,⟨sg22673,⟨sg22672,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22681,⟨sg22678,⟨sg22676,⟨sg22675,True.intro,True.intro⟩,⟨sg22677,True.intro,True.intro⟩⟩,⟨sg22680,⟨sg22679,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22685,⟨sg22683,⟨sg22682,True.intro,True.intro⟩,⟨sg22684,True.intro,True.intro⟩⟩,⟨sg22687,⟨sg22686,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_67All : degreeTree39_67.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22703,⟨sg22696,⟨sg22692,⟨sg22690,⟨sg22689,True.intro,True.intro⟩,⟨sg22691,True.intro,True.intro⟩⟩,⟨sg22694,⟨sg22693,True.intro,True.intro⟩,⟨sg22695,True.intro,True.intro⟩⟩⟩,⟨sg22700,⟨sg22698,⟨sg22697,True.intro,True.intro⟩,⟨sg22699,True.intro,True.intro⟩⟩,⟨sg22702,⟨sg22701,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22710,⟨sg22707,⟨sg22705,⟨sg22704,True.intro,True.intro⟩,⟨sg22706,True.intro,True.intro⟩⟩,⟨sg22709,⟨sg22708,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22714,⟨sg22712,⟨sg22711,True.intro,True.intro⟩,⟨sg22713,True.intro,True.intro⟩⟩,⟨sg22716,⟨sg22715,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_68All : degreeTree39_68.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22688,degreeTree39_66All,degreeTree39_67All⟩ + +lemma degreeTree39_69All : degreeTree39_69.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22659,degreeTree39_65All,degreeTree39_68All⟩ + +lemma degreeTree39_70All : degreeTree39_70.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22732,⟨sg22725,⟨sg22721,⟨sg22719,⟨sg22718,True.intro,True.intro⟩,⟨sg22720,True.intro,True.intro⟩⟩,⟨sg22723,⟨sg22722,True.intro,True.intro⟩,⟨sg22724,True.intro,True.intro⟩⟩⟩,⟨sg22729,⟨sg22727,⟨sg22726,True.intro,True.intro⟩,⟨sg22728,True.intro,True.intro⟩⟩,⟨sg22731,⟨sg22730,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22739,⟨sg22736,⟨sg22734,⟨sg22733,True.intro,True.intro⟩,⟨sg22735,True.intro,True.intro⟩⟩,⟨sg22738,⟨sg22737,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22743,⟨sg22741,⟨sg22740,True.intro,True.intro⟩,⟨sg22742,True.intro,True.intro⟩⟩,⟨sg22745,⟨sg22744,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_71All : degreeTree39_71.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22761,⟨sg22754,⟨sg22750,⟨sg22748,⟨sg22747,True.intro,True.intro⟩,⟨sg22749,True.intro,True.intro⟩⟩,⟨sg22752,⟨sg22751,True.intro,True.intro⟩,⟨sg22753,True.intro,True.intro⟩⟩⟩,⟨sg22758,⟨sg22756,⟨sg22755,True.intro,True.intro⟩,⟨sg22757,True.intro,True.intro⟩⟩,⟨sg22760,⟨sg22759,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22768,⟨sg22765,⟨sg22763,⟨sg22762,True.intro,True.intro⟩,⟨sg22764,True.intro,True.intro⟩⟩,⟨sg22767,⟨sg22766,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22772,⟨sg22770,⟨sg22769,True.intro,True.intro⟩,⟨sg22771,True.intro,True.intro⟩⟩,⟨sg22774,⟨sg22773,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_72All : degreeTree39_72.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22746,degreeTree39_70All,degreeTree39_71All⟩ + +lemma degreeTree39_73All : degreeTree39_73.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22790,⟨sg22783,⟨sg22779,⟨sg22777,⟨sg22776,True.intro,True.intro⟩,⟨sg22778,True.intro,True.intro⟩⟩,⟨sg22781,⟨sg22780,True.intro,True.intro⟩,⟨sg22782,True.intro,True.intro⟩⟩⟩,⟨sg22787,⟨sg22785,⟨sg22784,True.intro,True.intro⟩,⟨sg22786,True.intro,True.intro⟩⟩,⟨sg22789,⟨sg22788,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22797,⟨sg22794,⟨sg22792,⟨sg22791,True.intro,True.intro⟩,⟨sg22793,True.intro,True.intro⟩⟩,⟨sg22796,⟨sg22795,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22801,⟨sg22799,⟨sg22798,True.intro,True.intro⟩,⟨sg22800,True.intro,True.intro⟩⟩,⟨sg22803,⟨sg22802,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_74All : degreeTree39_74.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22819,⟨sg22812,⟨sg22808,⟨sg22806,⟨sg22805,True.intro,True.intro⟩,⟨sg22807,True.intro,True.intro⟩⟩,⟨sg22810,⟨sg22809,True.intro,True.intro⟩,⟨sg22811,True.intro,True.intro⟩⟩⟩,⟨sg22816,⟨sg22814,⟨sg22813,True.intro,True.intro⟩,⟨sg22815,True.intro,True.intro⟩⟩,⟨sg22818,⟨sg22817,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22826,⟨sg22823,⟨sg22821,⟨sg22820,True.intro,True.intro⟩,⟨sg22822,True.intro,True.intro⟩⟩,⟨sg22825,⟨sg22824,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22830,⟨sg22828,⟨sg22827,True.intro,True.intro⟩,⟨sg22829,True.intro,True.intro⟩⟩,⟨sg22832,⟨sg22831,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_75All : degreeTree39_75.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22804,degreeTree39_73All,degreeTree39_74All⟩ + +lemma degreeTree39_76All : degreeTree39_76.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22775,degreeTree39_72All,degreeTree39_75All⟩ + +lemma degreeTree39_77All : degreeTree39_77.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22717,degreeTree39_69All,degreeTree39_76All⟩ + +lemma degreeTree39_78All : degreeTree39_78.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22848,⟨sg22841,⟨sg22837,⟨sg22835,⟨sg22834,True.intro,True.intro⟩,⟨sg22836,True.intro,True.intro⟩⟩,⟨sg22839,⟨sg22838,True.intro,True.intro⟩,⟨sg22840,True.intro,True.intro⟩⟩⟩,⟨sg22845,⟨sg22843,⟨sg22842,True.intro,True.intro⟩,⟨sg22844,True.intro,True.intro⟩⟩,⟨sg22847,⟨sg22846,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22855,⟨sg22852,⟨sg22850,⟨sg22849,True.intro,True.intro⟩,⟨sg22851,True.intro,True.intro⟩⟩,⟨sg22854,⟨sg22853,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22859,⟨sg22857,⟨sg22856,True.intro,True.intro⟩,⟨sg22858,True.intro,True.intro⟩⟩,⟨sg22861,⟨sg22860,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_79All : degreeTree39_79.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22877,⟨sg22870,⟨sg22866,⟨sg22864,⟨sg22863,True.intro,True.intro⟩,⟨sg22865,True.intro,True.intro⟩⟩,⟨sg22868,⟨sg22867,True.intro,True.intro⟩,⟨sg22869,True.intro,True.intro⟩⟩⟩,⟨sg22874,⟨sg22872,⟨sg22871,True.intro,True.intro⟩,⟨sg22873,True.intro,True.intro⟩⟩,⟨sg22876,⟨sg22875,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22884,⟨sg22881,⟨sg22879,⟨sg22878,True.intro,True.intro⟩,⟨sg22880,True.intro,True.intro⟩⟩,⟨sg22883,⟨sg22882,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22888,⟨sg22886,⟨sg22885,True.intro,True.intro⟩,⟨sg22887,True.intro,True.intro⟩⟩,⟨sg22890,⟨sg22889,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_80All : degreeTree39_80.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22862,degreeTree39_78All,degreeTree39_79All⟩ + +lemma degreeTree39_81All : degreeTree39_81.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22906,⟨sg22899,⟨sg22895,⟨sg22893,⟨sg22892,True.intro,True.intro⟩,⟨sg22894,True.intro,True.intro⟩⟩,⟨sg22897,⟨sg22896,True.intro,True.intro⟩,⟨sg22898,True.intro,True.intro⟩⟩⟩,⟨sg22903,⟨sg22901,⟨sg22900,True.intro,True.intro⟩,⟨sg22902,True.intro,True.intro⟩⟩,⟨sg22905,⟨sg22904,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22913,⟨sg22910,⟨sg22908,⟨sg22907,True.intro,True.intro⟩,⟨sg22909,True.intro,True.intro⟩⟩,⟨sg22912,⟨sg22911,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22917,⟨sg22915,⟨sg22914,True.intro,True.intro⟩,⟨sg22916,True.intro,True.intro⟩⟩,⟨sg22919,⟨sg22918,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_82All : degreeTree39_82.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22935,⟨sg22928,⟨sg22924,⟨sg22922,⟨sg22921,True.intro,True.intro⟩,⟨sg22923,True.intro,True.intro⟩⟩,⟨sg22926,⟨sg22925,True.intro,True.intro⟩,⟨sg22927,True.intro,True.intro⟩⟩⟩,⟨sg22932,⟨sg22930,⟨sg22929,True.intro,True.intro⟩,⟨sg22931,True.intro,True.intro⟩⟩,⟨sg22934,⟨sg22933,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22942,⟨sg22939,⟨sg22937,⟨sg22936,True.intro,True.intro⟩,⟨sg22938,True.intro,True.intro⟩⟩,⟨sg22941,⟨sg22940,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22946,⟨sg22944,⟨sg22943,True.intro,True.intro⟩,⟨sg22945,True.intro,True.intro⟩⟩,⟨sg22948,⟨sg22947,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_83All : degreeTree39_83.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22920,degreeTree39_81All,degreeTree39_82All⟩ + +lemma degreeTree39_84All : degreeTree39_84.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22891,degreeTree39_80All,degreeTree39_83All⟩ + +lemma degreeTree39_85All : degreeTree39_85.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22964,⟨sg22957,⟨sg22953,⟨sg22951,⟨sg22950,True.intro,True.intro⟩,⟨sg22952,True.intro,True.intro⟩⟩,⟨sg22955,⟨sg22954,True.intro,True.intro⟩,⟨sg22956,True.intro,True.intro⟩⟩⟩,⟨sg22961,⟨sg22959,⟨sg22958,True.intro,True.intro⟩,⟨sg22960,True.intro,True.intro⟩⟩,⟨sg22963,⟨sg22962,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg22971,⟨sg22968,⟨sg22966,⟨sg22965,True.intro,True.intro⟩,⟨sg22967,True.intro,True.intro⟩⟩,⟨sg22970,⟨sg22969,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg22975,⟨sg22973,⟨sg22972,True.intro,True.intro⟩,⟨sg22974,True.intro,True.intro⟩⟩,⟨sg22977,⟨sg22976,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_86All : degreeTree39_86.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22993,⟨sg22986,⟨sg22982,⟨sg22980,⟨sg22979,True.intro,True.intro⟩,⟨sg22981,True.intro,True.intro⟩⟩,⟨sg22984,⟨sg22983,True.intro,True.intro⟩,⟨sg22985,True.intro,True.intro⟩⟩⟩,⟨sg22990,⟨sg22988,⟨sg22987,True.intro,True.intro⟩,⟨sg22989,True.intro,True.intro⟩⟩,⟨sg22992,⟨sg22991,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23000,⟨sg22997,⟨sg22995,⟨sg22994,True.intro,True.intro⟩,⟨sg22996,True.intro,True.intro⟩⟩,⟨sg22999,⟨sg22998,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23004,⟨sg23002,⟨sg23001,True.intro,True.intro⟩,⟨sg23003,True.intro,True.intro⟩⟩,⟨sg23006,⟨sg23005,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_87All : degreeTree39_87.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22978,degreeTree39_85All,degreeTree39_86All⟩ + +lemma degreeTree39_88All : degreeTree39_88.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23022,⟨sg23015,⟨sg23011,⟨sg23009,⟨sg23008,True.intro,True.intro⟩,⟨sg23010,True.intro,True.intro⟩⟩,⟨sg23013,⟨sg23012,True.intro,True.intro⟩,⟨sg23014,True.intro,True.intro⟩⟩⟩,⟨sg23019,⟨sg23017,⟨sg23016,True.intro,True.intro⟩,⟨sg23018,True.intro,True.intro⟩⟩,⟨sg23021,⟨sg23020,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23029,⟨sg23026,⟨sg23024,⟨sg23023,True.intro,True.intro⟩,⟨sg23025,True.intro,True.intro⟩⟩,⟨sg23028,⟨sg23027,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23033,⟨sg23031,⟨sg23030,True.intro,True.intro⟩,⟨sg23032,True.intro,True.intro⟩⟩,⟨sg23035,⟨sg23034,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_89All : degreeTree39_89.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23051,⟨sg23044,⟨sg23040,⟨sg23038,⟨sg23037,True.intro,True.intro⟩,⟨sg23039,True.intro,True.intro⟩⟩,⟨sg23042,⟨sg23041,True.intro,True.intro⟩,⟨sg23043,True.intro,True.intro⟩⟩⟩,⟨sg23048,⟨sg23046,⟨sg23045,True.intro,True.intro⟩,⟨sg23047,True.intro,True.intro⟩⟩,⟨sg23050,⟨sg23049,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23058,⟨sg23055,⟨sg23053,⟨sg23052,True.intro,True.intro⟩,⟨sg23054,True.intro,True.intro⟩⟩,⟨sg23057,⟨sg23056,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23062,⟨sg23060,⟨sg23059,True.intro,True.intro⟩,⟨sg23061,True.intro,True.intro⟩⟩,⟨sg23064,⟨sg23063,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_90All : degreeTree39_90.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23036,degreeTree39_88All,degreeTree39_89All⟩ + +lemma degreeTree39_91All : degreeTree39_91.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23007,degreeTree39_87All,degreeTree39_90All⟩ + +lemma degreeTree39_92All : degreeTree39_92.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22949,degreeTree39_84All,degreeTree39_91All⟩ + +lemma degreeTree39_93All : degreeTree39_93.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22833,degreeTree39_77All,degreeTree39_92All⟩ + +lemma degreeTree39_94All : degreeTree39_94.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23080,⟨sg23073,⟨sg23069,⟨sg23067,⟨sg23066,True.intro,True.intro⟩,⟨sg23068,True.intro,True.intro⟩⟩,⟨sg23071,⟨sg23070,True.intro,True.intro⟩,⟨sg23072,True.intro,True.intro⟩⟩⟩,⟨sg23077,⟨sg23075,⟨sg23074,True.intro,True.intro⟩,⟨sg23076,True.intro,True.intro⟩⟩,⟨sg23079,⟨sg23078,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23088,⟨sg23084,⟨sg23082,⟨sg23081,True.intro,True.intro⟩,⟨sg23083,True.intro,True.intro⟩⟩,⟨sg23086,⟨sg23085,True.intro,True.intro⟩,⟨sg23087,True.intro,True.intro⟩⟩⟩,⟨sg23092,⟨sg23090,⟨sg23089,True.intro,True.intro⟩,⟨sg23091,True.intro,True.intro⟩⟩,⟨sg23094,⟨sg23093,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_95All : degreeTree39_95.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23110,⟨sg23103,⟨sg23099,⟨sg23097,⟨sg23096,True.intro,True.intro⟩,⟨sg23098,True.intro,True.intro⟩⟩,⟨sg23101,⟨sg23100,True.intro,True.intro⟩,⟨sg23102,True.intro,True.intro⟩⟩⟩,⟨sg23107,⟨sg23105,⟨sg23104,True.intro,True.intro⟩,⟨sg23106,True.intro,True.intro⟩⟩,⟨sg23109,⟨sg23108,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23117,⟨sg23114,⟨sg23112,⟨sg23111,True.intro,True.intro⟩,⟨sg23113,True.intro,True.intro⟩⟩,⟨sg23116,⟨sg23115,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23121,⟨sg23119,⟨sg23118,True.intro,True.intro⟩,⟨sg23120,True.intro,True.intro⟩⟩,⟨sg23123,⟨sg23122,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_96All : degreeTree39_96.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23095,degreeTree39_94All,degreeTree39_95All⟩ + +lemma degreeTree39_97All : degreeTree39_97.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23139,⟨sg23132,⟨sg23128,⟨sg23126,⟨sg23125,True.intro,True.intro⟩,⟨sg23127,True.intro,True.intro⟩⟩,⟨sg23130,⟨sg23129,True.intro,True.intro⟩,⟨sg23131,True.intro,True.intro⟩⟩⟩,⟨sg23136,⟨sg23134,⟨sg23133,True.intro,True.intro⟩,⟨sg23135,True.intro,True.intro⟩⟩,⟨sg23138,⟨sg23137,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23146,⟨sg23143,⟨sg23141,⟨sg23140,True.intro,True.intro⟩,⟨sg23142,True.intro,True.intro⟩⟩,⟨sg23145,⟨sg23144,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23150,⟨sg23148,⟨sg23147,True.intro,True.intro⟩,⟨sg23149,True.intro,True.intro⟩⟩,⟨sg23152,⟨sg23151,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_98All : degreeTree39_98.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23168,⟨sg23161,⟨sg23157,⟨sg23155,⟨sg23154,True.intro,True.intro⟩,⟨sg23156,True.intro,True.intro⟩⟩,⟨sg23159,⟨sg23158,True.intro,True.intro⟩,⟨sg23160,True.intro,True.intro⟩⟩⟩,⟨sg23165,⟨sg23163,⟨sg23162,True.intro,True.intro⟩,⟨sg23164,True.intro,True.intro⟩⟩,⟨sg23167,⟨sg23166,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23175,⟨sg23172,⟨sg23170,⟨sg23169,True.intro,True.intro⟩,⟨sg23171,True.intro,True.intro⟩⟩,⟨sg23174,⟨sg23173,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23179,⟨sg23177,⟨sg23176,True.intro,True.intro⟩,⟨sg23178,True.intro,True.intro⟩⟩,⟨sg23181,⟨sg23180,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_99All : degreeTree39_99.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23153,degreeTree39_97All,degreeTree39_98All⟩ + +lemma degreeTree39_100All : degreeTree39_100.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23124,degreeTree39_96All,degreeTree39_99All⟩ + +lemma degreeTree39_101All : degreeTree39_101.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23197,⟨sg23190,⟨sg23186,⟨sg23184,⟨sg23183,True.intro,True.intro⟩,⟨sg23185,True.intro,True.intro⟩⟩,⟨sg23188,⟨sg23187,True.intro,True.intro⟩,⟨sg23189,True.intro,True.intro⟩⟩⟩,⟨sg23194,⟨sg23192,⟨sg23191,True.intro,True.intro⟩,⟨sg23193,True.intro,True.intro⟩⟩,⟨sg23196,⟨sg23195,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23204,⟨sg23201,⟨sg23199,⟨sg23198,True.intro,True.intro⟩,⟨sg23200,True.intro,True.intro⟩⟩,⟨sg23203,⟨sg23202,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23208,⟨sg23206,⟨sg23205,True.intro,True.intro⟩,⟨sg23207,True.intro,True.intro⟩⟩,⟨sg23210,⟨sg23209,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_102All : degreeTree39_102.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23226,⟨sg23219,⟨sg23215,⟨sg23213,⟨sg23212,True.intro,True.intro⟩,⟨sg23214,True.intro,True.intro⟩⟩,⟨sg23217,⟨sg23216,True.intro,True.intro⟩,⟨sg23218,True.intro,True.intro⟩⟩⟩,⟨sg23223,⟨sg23221,⟨sg23220,True.intro,True.intro⟩,⟨sg23222,True.intro,True.intro⟩⟩,⟨sg23225,⟨sg23224,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23233,⟨sg23230,⟨sg23228,⟨sg23227,True.intro,True.intro⟩,⟨sg23229,True.intro,True.intro⟩⟩,⟨sg23232,⟨sg23231,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23237,⟨sg23235,⟨sg23234,True.intro,True.intro⟩,⟨sg23236,True.intro,True.intro⟩⟩,⟨sg23239,⟨sg23238,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_103All : degreeTree39_103.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23211,degreeTree39_101All,degreeTree39_102All⟩ + +lemma degreeTree39_104All : degreeTree39_104.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23255,⟨sg23248,⟨sg23244,⟨sg23242,⟨sg23241,True.intro,True.intro⟩,⟨sg23243,True.intro,True.intro⟩⟩,⟨sg23246,⟨sg23245,True.intro,True.intro⟩,⟨sg23247,True.intro,True.intro⟩⟩⟩,⟨sg23252,⟨sg23250,⟨sg23249,True.intro,True.intro⟩,⟨sg23251,True.intro,True.intro⟩⟩,⟨sg23254,⟨sg23253,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23262,⟨sg23259,⟨sg23257,⟨sg23256,True.intro,True.intro⟩,⟨sg23258,True.intro,True.intro⟩⟩,⟨sg23261,⟨sg23260,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23266,⟨sg23264,⟨sg23263,True.intro,True.intro⟩,⟨sg23265,True.intro,True.intro⟩⟩,⟨sg23268,⟨sg23267,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_105All : degreeTree39_105.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23284,⟨sg23277,⟨sg23273,⟨sg23271,⟨sg23270,True.intro,True.intro⟩,⟨sg23272,True.intro,True.intro⟩⟩,⟨sg23275,⟨sg23274,True.intro,True.intro⟩,⟨sg23276,True.intro,True.intro⟩⟩⟩,⟨sg23281,⟨sg23279,⟨sg23278,True.intro,True.intro⟩,⟨sg23280,True.intro,True.intro⟩⟩,⟨sg23283,⟨sg23282,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23291,⟨sg23288,⟨sg23286,⟨sg23285,True.intro,True.intro⟩,⟨sg23287,True.intro,True.intro⟩⟩,⟨sg23290,⟨sg23289,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23295,⟨sg23293,⟨sg23292,True.intro,True.intro⟩,⟨sg23294,True.intro,True.intro⟩⟩,⟨sg23297,⟨sg23296,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_106All : degreeTree39_106.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23269,degreeTree39_104All,degreeTree39_105All⟩ + +lemma degreeTree39_107All : degreeTree39_107.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23240,degreeTree39_103All,degreeTree39_106All⟩ + +lemma degreeTree39_108All : degreeTree39_108.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23182,degreeTree39_100All,degreeTree39_107All⟩ + +lemma degreeTree39_109All : degreeTree39_109.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23313,⟨sg23306,⟨sg23302,⟨sg23300,⟨sg23299,True.intro,True.intro⟩,⟨sg23301,True.intro,True.intro⟩⟩,⟨sg23304,⟨sg23303,True.intro,True.intro⟩,⟨sg23305,True.intro,True.intro⟩⟩⟩,⟨sg23310,⟨sg23308,⟨sg23307,True.intro,True.intro⟩,⟨sg23309,True.intro,True.intro⟩⟩,⟨sg23312,⟨sg23311,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23320,⟨sg23317,⟨sg23315,⟨sg23314,True.intro,True.intro⟩,⟨sg23316,True.intro,True.intro⟩⟩,⟨sg23319,⟨sg23318,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23324,⟨sg23322,⟨sg23321,True.intro,True.intro⟩,⟨sg23323,True.intro,True.intro⟩⟩,⟨sg23326,⟨sg23325,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_110All : degreeTree39_110.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23342,⟨sg23335,⟨sg23331,⟨sg23329,⟨sg23328,True.intro,True.intro⟩,⟨sg23330,True.intro,True.intro⟩⟩,⟨sg23333,⟨sg23332,True.intro,True.intro⟩,⟨sg23334,True.intro,True.intro⟩⟩⟩,⟨sg23339,⟨sg23337,⟨sg23336,True.intro,True.intro⟩,⟨sg23338,True.intro,True.intro⟩⟩,⟨sg23341,⟨sg23340,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23349,⟨sg23346,⟨sg23344,⟨sg23343,True.intro,True.intro⟩,⟨sg23345,True.intro,True.intro⟩⟩,⟨sg23348,⟨sg23347,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23353,⟨sg23351,⟨sg23350,True.intro,True.intro⟩,⟨sg23352,True.intro,True.intro⟩⟩,⟨sg23355,⟨sg23354,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_111All : degreeTree39_111.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23327,degreeTree39_109All,degreeTree39_110All⟩ + +lemma degreeTree39_112All : degreeTree39_112.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23371,⟨sg23364,⟨sg23360,⟨sg23358,⟨sg23357,True.intro,True.intro⟩,⟨sg23359,True.intro,True.intro⟩⟩,⟨sg23362,⟨sg23361,True.intro,True.intro⟩,⟨sg23363,True.intro,True.intro⟩⟩⟩,⟨sg23368,⟨sg23366,⟨sg23365,True.intro,True.intro⟩,⟨sg23367,True.intro,True.intro⟩⟩,⟨sg23370,⟨sg23369,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23378,⟨sg23375,⟨sg23373,⟨sg23372,True.intro,True.intro⟩,⟨sg23374,True.intro,True.intro⟩⟩,⟨sg23377,⟨sg23376,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23382,⟨sg23380,⟨sg23379,True.intro,True.intro⟩,⟨sg23381,True.intro,True.intro⟩⟩,⟨sg23384,⟨sg23383,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_113All : degreeTree39_113.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23400,⟨sg23393,⟨sg23389,⟨sg23387,⟨sg23386,True.intro,True.intro⟩,⟨sg23388,True.intro,True.intro⟩⟩,⟨sg23391,⟨sg23390,True.intro,True.intro⟩,⟨sg23392,True.intro,True.intro⟩⟩⟩,⟨sg23397,⟨sg23395,⟨sg23394,True.intro,True.intro⟩,⟨sg23396,True.intro,True.intro⟩⟩,⟨sg23399,⟨sg23398,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23407,⟨sg23404,⟨sg23402,⟨sg23401,True.intro,True.intro⟩,⟨sg23403,True.intro,True.intro⟩⟩,⟨sg23406,⟨sg23405,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23411,⟨sg23409,⟨sg23408,True.intro,True.intro⟩,⟨sg23410,True.intro,True.intro⟩⟩,⟨sg23413,⟨sg23412,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_114All : degreeTree39_114.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23385,degreeTree39_112All,degreeTree39_113All⟩ + +lemma degreeTree39_115All : degreeTree39_115.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23356,degreeTree39_111All,degreeTree39_114All⟩ + +lemma degreeTree39_116All : degreeTree39_116.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23429,⟨sg23422,⟨sg23418,⟨sg23416,⟨sg23415,True.intro,True.intro⟩,⟨sg23417,True.intro,True.intro⟩⟩,⟨sg23420,⟨sg23419,True.intro,True.intro⟩,⟨sg23421,True.intro,True.intro⟩⟩⟩,⟨sg23426,⟨sg23424,⟨sg23423,True.intro,True.intro⟩,⟨sg23425,True.intro,True.intro⟩⟩,⟨sg23428,⟨sg23427,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23436,⟨sg23433,⟨sg23431,⟨sg23430,True.intro,True.intro⟩,⟨sg23432,True.intro,True.intro⟩⟩,⟨sg23435,⟨sg23434,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23440,⟨sg23438,⟨sg23437,True.intro,True.intro⟩,⟨sg23439,True.intro,True.intro⟩⟩,⟨sg23442,⟨sg23441,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_117All : degreeTree39_117.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23458,⟨sg23451,⟨sg23447,⟨sg23445,⟨sg23444,True.intro,True.intro⟩,⟨sg23446,True.intro,True.intro⟩⟩,⟨sg23449,⟨sg23448,True.intro,True.intro⟩,⟨sg23450,True.intro,True.intro⟩⟩⟩,⟨sg23455,⟨sg23453,⟨sg23452,True.intro,True.intro⟩,⟨sg23454,True.intro,True.intro⟩⟩,⟨sg23457,⟨sg23456,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23465,⟨sg23462,⟨sg23460,⟨sg23459,True.intro,True.intro⟩,⟨sg23461,True.intro,True.intro⟩⟩,⟨sg23464,⟨sg23463,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23469,⟨sg23467,⟨sg23466,True.intro,True.intro⟩,⟨sg23468,True.intro,True.intro⟩⟩,⟨sg23471,⟨sg23470,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_118All : degreeTree39_118.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23443,degreeTree39_116All,degreeTree39_117All⟩ + +lemma degreeTree39_119All : degreeTree39_119.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23487,⟨sg23480,⟨sg23476,⟨sg23474,⟨sg23473,True.intro,True.intro⟩,⟨sg23475,True.intro,True.intro⟩⟩,⟨sg23478,⟨sg23477,True.intro,True.intro⟩,⟨sg23479,True.intro,True.intro⟩⟩⟩,⟨sg23484,⟨sg23482,⟨sg23481,True.intro,True.intro⟩,⟨sg23483,True.intro,True.intro⟩⟩,⟨sg23486,⟨sg23485,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23494,⟨sg23491,⟨sg23489,⟨sg23488,True.intro,True.intro⟩,⟨sg23490,True.intro,True.intro⟩⟩,⟨sg23493,⟨sg23492,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23498,⟨sg23496,⟨sg23495,True.intro,True.intro⟩,⟨sg23497,True.intro,True.intro⟩⟩,⟨sg23500,⟨sg23499,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_120All : degreeTree39_120.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23516,⟨sg23509,⟨sg23505,⟨sg23503,⟨sg23502,True.intro,True.intro⟩,⟨sg23504,True.intro,True.intro⟩⟩,⟨sg23507,⟨sg23506,True.intro,True.intro⟩,⟨sg23508,True.intro,True.intro⟩⟩⟩,⟨sg23513,⟨sg23511,⟨sg23510,True.intro,True.intro⟩,⟨sg23512,True.intro,True.intro⟩⟩,⟨sg23515,⟨sg23514,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg23523,⟨sg23520,⟨sg23518,⟨sg23517,True.intro,True.intro⟩,⟨sg23519,True.intro,True.intro⟩⟩,⟨sg23522,⟨sg23521,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg23527,⟨sg23525,⟨sg23524,True.intro,True.intro⟩,⟨sg23526,True.intro,True.intro⟩⟩,⟨sg23529,⟨sg23528,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree39_121All : degreeTree39_121.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23501,degreeTree39_119All,degreeTree39_120All⟩ + +lemma degreeTree39_122All : degreeTree39_122.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23472,degreeTree39_118All,degreeTree39_121All⟩ + +lemma degreeTree39_123All : degreeTree39_123.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23414,degreeTree39_115All,degreeTree39_122All⟩ + +lemma degreeTree39_124All : degreeTree39_124.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23298,degreeTree39_108All,degreeTree39_123All⟩ + +lemma degreeTree39_125All : degreeTree39_125.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg23065,degreeTree39_93All,degreeTree39_124All⟩ + +lemma degreeTree39_126All : degreeTree39_126.All (RowSquare [11,9,4,3,2,2,2,2,2,1,1]) := by + exact ⟨sg22600,degreeTree39_62All,degreeTree39_125All⟩ + +lemma degreeTreeAll39 : degreeTree39.All + (fun rs => SquareOccurs (candidate 6 4 1) (rowDiagram rs)) := by + have hp : rowDiagram [11,9,4,3,2,2,2,2,2,1,1] = candidate 6 4 1 := rowDiagram_candidate (M := 6) (b := 4) (δ := 1) (by decide) + rw [← hp] + exact degreeTree39_126All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof41.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof41.lean index 0454b2eb1f9eaca9ced1f2577f94c3e876b94d9b..0b535577c30c91d98b1d67030673be0df01a07c4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof41.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof41.lean @@ -1,71 +1,71 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData41 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes57 - -namespace OAI - -/-! Degree Tree Proof 41. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree41_0All : degreeTree41_0.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23542,⟨sg23538,⟨sg23536,⟨sg23535,⟨sg23534,True.intro,True.intro⟩,True.intro⟩,⟨sg23537,True.intro,True.intro⟩⟩,⟨sg23540,⟨sg23539,True.intro,True.intro⟩,⟨sg23541,True.intro,True.intro⟩⟩⟩,⟨sg23547,⟨sg23545,⟨sg23544,⟨sg23543,True.intro,True.intro⟩,True.intro⟩,⟨sg23546,True.intro,True.intro⟩⟩,⟨sg23549,⟨sg23548,True.intro,True.intro⟩,⟨sg23550,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree41_1All : degreeTree41_1.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23560,⟨sg23556,⟨sg23554,⟨sg23553,⟨sg23552,True.intro,True.intro⟩,True.intro⟩,⟨sg23555,True.intro,True.intro⟩⟩,⟨sg23558,⟨sg23557,True.intro,True.intro⟩,⟨sg23559,True.intro,True.intro⟩⟩⟩,⟨sg23564,⟨sg23562,⟨sg23561,True.intro,True.intro⟩,⟨sg23563,True.intro,True.intro⟩⟩,⟨sg23566,⟨sg23565,True.intro,True.intro⟩,⟨sg23567,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree41_2All : degreeTree41_2.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23551,degreeTree41_0All,degreeTree41_1All⟩ - -lemma degreeTree41_3All : degreeTree41_3.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23577,⟨sg23573,⟨sg23571,⟨sg23570,⟨sg23569,True.intro,True.intro⟩,True.intro⟩,⟨sg23572,True.intro,True.intro⟩⟩,⟨sg23575,⟨sg23574,True.intro,True.intro⟩,⟨sg23576,True.intro,True.intro⟩⟩⟩,⟨sg23582,⟨sg23580,⟨sg23579,⟨sg23578,True.intro,True.intro⟩,True.intro⟩,⟨sg23581,True.intro,True.intro⟩⟩,⟨sg23584,⟨sg23583,True.intro,True.intro⟩,⟨sg23585,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree41_4All : degreeTree41_4.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23595,⟨sg23591,⟨sg23589,⟨sg23588,⟨sg23587,True.intro,True.intro⟩,True.intro⟩,⟨sg23590,True.intro,True.intro⟩⟩,⟨sg23593,⟨sg23592,True.intro,True.intro⟩,⟨sg23594,True.intro,True.intro⟩⟩⟩,⟨sg23599,⟨sg23597,⟨sg23596,True.intro,True.intro⟩,⟨sg23598,True.intro,True.intro⟩⟩,⟨sg23601,⟨sg23600,True.intro,True.intro⟩,⟨sg23602,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree41_5All : degreeTree41_5.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23586,degreeTree41_3All,degreeTree41_4All⟩ - -lemma degreeTree41_6All : degreeTree41_6.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23568,degreeTree41_2All,degreeTree41_5All⟩ - -lemma degreeTree41_7All : degreeTree41_7.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23612,⟨sg23608,⟨sg23606,⟨sg23605,⟨sg23604,True.intro,True.intro⟩,True.intro⟩,⟨sg23607,True.intro,True.intro⟩⟩,⟨sg23610,⟨sg23609,True.intro,True.intro⟩,⟨sg23611,True.intro,True.intro⟩⟩⟩,⟨sg23617,⟨sg23615,⟨sg23614,⟨sg23613,True.intro,True.intro⟩,True.intro⟩,⟨sg23616,True.intro,True.intro⟩⟩,⟨sg23619,⟨sg23618,True.intro,True.intro⟩,⟨sg23620,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree41_8All : degreeTree41_8.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23630,⟨sg23626,⟨sg23624,⟨sg23623,⟨sg23622,True.intro,True.intro⟩,True.intro⟩,⟨sg23625,True.intro,True.intro⟩⟩,⟨sg23628,⟨sg23627,True.intro,True.intro⟩,⟨sg23629,True.intro,True.intro⟩⟩⟩,⟨sg23634,⟨sg23632,⟨sg23631,True.intro,True.intro⟩,⟨sg23633,True.intro,True.intro⟩⟩,⟨sg23636,⟨sg23635,True.intro,True.intro⟩,⟨sg23637,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree41_9All : degreeTree41_9.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23621,degreeTree41_7All,degreeTree41_8All⟩ - -lemma degreeTree41_10All : degreeTree41_10.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23647,⟨sg23643,⟨sg23641,⟨sg23640,⟨sg23639,True.intro,True.intro⟩,True.intro⟩,⟨sg23642,True.intro,True.intro⟩⟩,⟨sg23645,⟨sg23644,True.intro,True.intro⟩,⟨sg23646,True.intro,True.intro⟩⟩⟩,⟨sg23651,⟨sg23649,⟨sg23648,True.intro,True.intro⟩,⟨sg23650,True.intro,True.intro⟩⟩,⟨sg23653,⟨sg23652,True.intro,True.intro⟩,⟨sg23654,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree41_11All : degreeTree41_11.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23664,⟨sg23660,⟨sg23658,⟨sg23657,⟨sg23656,True.intro,True.intro⟩,True.intro⟩,⟨sg23659,True.intro,True.intro⟩⟩,⟨sg23662,⟨sg23661,True.intro,True.intro⟩,⟨sg23663,True.intro,True.intro⟩⟩⟩,⟨sg23668,⟨sg23666,⟨sg23665,True.intro,True.intro⟩,⟨sg23667,True.intro,True.intro⟩⟩,⟨sg23670,⟨sg23669,True.intro,True.intro⟩,⟨sg23671,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree41_12All : degreeTree41_12.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23655,degreeTree41_10All,degreeTree41_11All⟩ - -lemma degreeTree41_13All : degreeTree41_13.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23638,degreeTree41_9All,degreeTree41_12All⟩ - -lemma degreeTree41_14All : degreeTree41_14.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by - exact ⟨sg23603,degreeTree41_6All,degreeTree41_13All⟩ - -lemma degreeTreeAll41 : degreeTree41.All - (fun rs => SquareOccurs (candidate 6 5 0) (rowDiagram rs)) := by - have hp : rowDiagram [11,10,4,3,2,2,2,2,2,2,1] = candidate 6 5 0 := rowDiagram_candidate (M := 6) (b := 5) (δ := 0) (by decide) - rw [← hp] - exact degreeTree41_14All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData41 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes57 + +namespace OAI + +/-! Degree Tree Proof 41. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree41_0All : degreeTree41_0.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23542,⟨sg23538,⟨sg23536,⟨sg23535,⟨sg23534,True.intro,True.intro⟩,True.intro⟩,⟨sg23537,True.intro,True.intro⟩⟩,⟨sg23540,⟨sg23539,True.intro,True.intro⟩,⟨sg23541,True.intro,True.intro⟩⟩⟩,⟨sg23547,⟨sg23545,⟨sg23544,⟨sg23543,True.intro,True.intro⟩,True.intro⟩,⟨sg23546,True.intro,True.intro⟩⟩,⟨sg23549,⟨sg23548,True.intro,True.intro⟩,⟨sg23550,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree41_1All : degreeTree41_1.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23560,⟨sg23556,⟨sg23554,⟨sg23553,⟨sg23552,True.intro,True.intro⟩,True.intro⟩,⟨sg23555,True.intro,True.intro⟩⟩,⟨sg23558,⟨sg23557,True.intro,True.intro⟩,⟨sg23559,True.intro,True.intro⟩⟩⟩,⟨sg23564,⟨sg23562,⟨sg23561,True.intro,True.intro⟩,⟨sg23563,True.intro,True.intro⟩⟩,⟨sg23566,⟨sg23565,True.intro,True.intro⟩,⟨sg23567,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree41_2All : degreeTree41_2.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23551,degreeTree41_0All,degreeTree41_1All⟩ + +lemma degreeTree41_3All : degreeTree41_3.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23577,⟨sg23573,⟨sg23571,⟨sg23570,⟨sg23569,True.intro,True.intro⟩,True.intro⟩,⟨sg23572,True.intro,True.intro⟩⟩,⟨sg23575,⟨sg23574,True.intro,True.intro⟩,⟨sg23576,True.intro,True.intro⟩⟩⟩,⟨sg23582,⟨sg23580,⟨sg23579,⟨sg23578,True.intro,True.intro⟩,True.intro⟩,⟨sg23581,True.intro,True.intro⟩⟩,⟨sg23584,⟨sg23583,True.intro,True.intro⟩,⟨sg23585,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree41_4All : degreeTree41_4.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23595,⟨sg23591,⟨sg23589,⟨sg23588,⟨sg23587,True.intro,True.intro⟩,True.intro⟩,⟨sg23590,True.intro,True.intro⟩⟩,⟨sg23593,⟨sg23592,True.intro,True.intro⟩,⟨sg23594,True.intro,True.intro⟩⟩⟩,⟨sg23599,⟨sg23597,⟨sg23596,True.intro,True.intro⟩,⟨sg23598,True.intro,True.intro⟩⟩,⟨sg23601,⟨sg23600,True.intro,True.intro⟩,⟨sg23602,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree41_5All : degreeTree41_5.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23586,degreeTree41_3All,degreeTree41_4All⟩ + +lemma degreeTree41_6All : degreeTree41_6.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23568,degreeTree41_2All,degreeTree41_5All⟩ + +lemma degreeTree41_7All : degreeTree41_7.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23612,⟨sg23608,⟨sg23606,⟨sg23605,⟨sg23604,True.intro,True.intro⟩,True.intro⟩,⟨sg23607,True.intro,True.intro⟩⟩,⟨sg23610,⟨sg23609,True.intro,True.intro⟩,⟨sg23611,True.intro,True.intro⟩⟩⟩,⟨sg23617,⟨sg23615,⟨sg23614,⟨sg23613,True.intro,True.intro⟩,True.intro⟩,⟨sg23616,True.intro,True.intro⟩⟩,⟨sg23619,⟨sg23618,True.intro,True.intro⟩,⟨sg23620,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree41_8All : degreeTree41_8.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23630,⟨sg23626,⟨sg23624,⟨sg23623,⟨sg23622,True.intro,True.intro⟩,True.intro⟩,⟨sg23625,True.intro,True.intro⟩⟩,⟨sg23628,⟨sg23627,True.intro,True.intro⟩,⟨sg23629,True.intro,True.intro⟩⟩⟩,⟨sg23634,⟨sg23632,⟨sg23631,True.intro,True.intro⟩,⟨sg23633,True.intro,True.intro⟩⟩,⟨sg23636,⟨sg23635,True.intro,True.intro⟩,⟨sg23637,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree41_9All : degreeTree41_9.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23621,degreeTree41_7All,degreeTree41_8All⟩ + +lemma degreeTree41_10All : degreeTree41_10.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23647,⟨sg23643,⟨sg23641,⟨sg23640,⟨sg23639,True.intro,True.intro⟩,True.intro⟩,⟨sg23642,True.intro,True.intro⟩⟩,⟨sg23645,⟨sg23644,True.intro,True.intro⟩,⟨sg23646,True.intro,True.intro⟩⟩⟩,⟨sg23651,⟨sg23649,⟨sg23648,True.intro,True.intro⟩,⟨sg23650,True.intro,True.intro⟩⟩,⟨sg23653,⟨sg23652,True.intro,True.intro⟩,⟨sg23654,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree41_11All : degreeTree41_11.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23664,⟨sg23660,⟨sg23658,⟨sg23657,⟨sg23656,True.intro,True.intro⟩,True.intro⟩,⟨sg23659,True.intro,True.intro⟩⟩,⟨sg23662,⟨sg23661,True.intro,True.intro⟩,⟨sg23663,True.intro,True.intro⟩⟩⟩,⟨sg23668,⟨sg23666,⟨sg23665,True.intro,True.intro⟩,⟨sg23667,True.intro,True.intro⟩⟩,⟨sg23670,⟨sg23669,True.intro,True.intro⟩,⟨sg23671,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree41_12All : degreeTree41_12.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23655,degreeTree41_10All,degreeTree41_11All⟩ + +lemma degreeTree41_13All : degreeTree41_13.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23638,degreeTree41_9All,degreeTree41_12All⟩ + +lemma degreeTree41_14All : degreeTree41_14.All (RowSquare [11,10,4,3,2,2,2,2,2,2,1]) := by + exact ⟨sg23603,degreeTree41_6All,degreeTree41_13All⟩ + +lemma degreeTreeAll41 : degreeTree41.All + (fun rs => SquareOccurs (candidate 6 5 0) (rowDiagram rs)) := by + have hp : rowDiagram [11,10,4,3,2,2,2,2,2,2,1] = candidate 6 5 0 := rowDiagram_candidate (M := 6) (b := 5) (δ := 0) (by decide) + rw [← hp] + exact degreeTree41_14All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof43.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof43.lean index e9c55923328b684e5ec7f3e7edc4696053ca9dbf..d8ff61d9cc1eeb0700eb1387cf38bbead94d3cf4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof43.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof43.lean @@ -1,1993 +1,1993 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData43 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes58 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes59 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes60 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes61 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes62 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes63 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes64 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes65 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes66 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes67 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes68 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes69 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes70 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes71 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes72 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes73 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes74 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes75 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes76 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes77 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes78 - -namespace OAI - -/-! Degree Tree Proof 43. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree43_0All : degreeTree43_0.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23683,⟨sg23679,⟨sg23677,⟨sg23676,⟨sg23675,True.intro,True.intro⟩,True.intro⟩,⟨sg23678,True.intro,True.intro⟩⟩,⟨sg23681,⟨sg23680,True.intro,True.intro⟩,⟨sg23682,True.intro,True.intro⟩⟩⟩,⟨sg23687,⟨sg23685,⟨sg23684,True.intro,True.intro⟩,⟨sg23686,True.intro,True.intro⟩⟩,⟨sg23689,⟨sg23688,True.intro,True.intro⟩,⟨sg23690,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_1All : degreeTree43_1.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23699,⟨sg23695,⟨sg23693,⟨sg23692,True.intro,True.intro⟩,⟨sg23694,True.intro,True.intro⟩⟩,⟨sg23697,⟨sg23696,True.intro,True.intro⟩,⟨sg23698,True.intro,True.intro⟩⟩⟩,⟨sg23703,⟨sg23701,⟨sg23700,True.intro,True.intro⟩,⟨sg23702,True.intro,True.intro⟩⟩,⟨sg23705,⟨sg23704,True.intro,True.intro⟩,⟨sg23706,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_2All : degreeTree43_2.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23691,degreeTree43_0All,degreeTree43_1All⟩ - -lemma degreeTree43_3All : degreeTree43_3.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23723,⟨sg23715,⟨sg23711,⟨sg23709,⟨sg23708,True.intro,True.intro⟩,⟨sg23710,True.intro,True.intro⟩⟩,⟨sg23713,⟨sg23712,True.intro,True.intro⟩,⟨sg23714,True.intro,True.intro⟩⟩⟩,⟨sg23719,⟨sg23717,⟨sg23716,True.intro,True.intro⟩,⟨sg23718,True.intro,True.intro⟩⟩,⟨sg23721,⟨sg23720,True.intro,True.intro⟩,⟨sg23722,True.intro,True.intro⟩⟩⟩⟩,⟨sg23731,⟨sg23727,⟨sg23725,⟨sg23724,True.intro,True.intro⟩,⟨sg23726,True.intro,True.intro⟩⟩,⟨sg23729,⟨sg23728,True.intro,True.intro⟩,⟨sg23730,True.intro,True.intro⟩⟩⟩,⟨sg23735,⟨sg23733,⟨sg23732,True.intro,True.intro⟩,⟨sg23734,True.intro,True.intro⟩⟩,⟨sg23737,⟨sg23736,True.intro,True.intro⟩,⟨sg23738,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_4All : degreeTree43_4.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23707,degreeTree43_2All,degreeTree43_3All⟩ - -lemma degreeTree43_5All : degreeTree43_5.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23748,⟨sg23744,⟨sg23742,⟨sg23741,⟨sg23740,True.intro,True.intro⟩,True.intro⟩,⟨sg23743,True.intro,True.intro⟩⟩,⟨sg23746,⟨sg23745,True.intro,True.intro⟩,⟨sg23747,True.intro,True.intro⟩⟩⟩,⟨sg23752,⟨sg23750,⟨sg23749,True.intro,True.intro⟩,⟨sg23751,True.intro,True.intro⟩⟩,⟨sg23754,⟨sg23753,True.intro,True.intro⟩,⟨sg23755,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_6All : degreeTree43_6.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23764,⟨sg23760,⟨sg23758,⟨sg23757,True.intro,True.intro⟩,⟨sg23759,True.intro,True.intro⟩⟩,⟨sg23762,⟨sg23761,True.intro,True.intro⟩,⟨sg23763,True.intro,True.intro⟩⟩⟩,⟨sg23768,⟨sg23766,⟨sg23765,True.intro,True.intro⟩,⟨sg23767,True.intro,True.intro⟩⟩,⟨sg23770,⟨sg23769,True.intro,True.intro⟩,⟨sg23771,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_7All : degreeTree43_7.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23756,degreeTree43_5All,degreeTree43_6All⟩ - -lemma degreeTree43_8All : degreeTree43_8.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23788,⟨sg23780,⟨sg23776,⟨sg23774,⟨sg23773,True.intro,True.intro⟩,⟨sg23775,True.intro,True.intro⟩⟩,⟨sg23778,⟨sg23777,True.intro,True.intro⟩,⟨sg23779,True.intro,True.intro⟩⟩⟩,⟨sg23784,⟨sg23782,⟨sg23781,True.intro,True.intro⟩,⟨sg23783,True.intro,True.intro⟩⟩,⟨sg23786,⟨sg23785,True.intro,True.intro⟩,⟨sg23787,True.intro,True.intro⟩⟩⟩⟩,⟨sg23796,⟨sg23792,⟨sg23790,⟨sg23789,True.intro,True.intro⟩,⟨sg23791,True.intro,True.intro⟩⟩,⟨sg23794,⟨sg23793,True.intro,True.intro⟩,⟨sg23795,True.intro,True.intro⟩⟩⟩,⟨sg23800,⟨sg23798,⟨sg23797,True.intro,True.intro⟩,⟨sg23799,True.intro,True.intro⟩⟩,⟨sg23802,⟨sg23801,True.intro,True.intro⟩,⟨sg23803,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_9All : degreeTree43_9.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23772,degreeTree43_7All,degreeTree43_8All⟩ - -lemma degreeTree43_10All : degreeTree43_10.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23739,degreeTree43_4All,degreeTree43_9All⟩ - -lemma degreeTree43_11All : degreeTree43_11.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23813,⟨sg23809,⟨sg23807,⟨sg23806,⟨sg23805,True.intro,True.intro⟩,True.intro⟩,⟨sg23808,True.intro,True.intro⟩⟩,⟨sg23811,⟨sg23810,True.intro,True.intro⟩,⟨sg23812,True.intro,True.intro⟩⟩⟩,⟨sg23817,⟨sg23815,⟨sg23814,True.intro,True.intro⟩,⟨sg23816,True.intro,True.intro⟩⟩,⟨sg23819,⟨sg23818,True.intro,True.intro⟩,⟨sg23820,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_12All : degreeTree43_12.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23829,⟨sg23825,⟨sg23823,⟨sg23822,True.intro,True.intro⟩,⟨sg23824,True.intro,True.intro⟩⟩,⟨sg23827,⟨sg23826,True.intro,True.intro⟩,⟨sg23828,True.intro,True.intro⟩⟩⟩,⟨sg23833,⟨sg23831,⟨sg23830,True.intro,True.intro⟩,⟨sg23832,True.intro,True.intro⟩⟩,⟨sg23835,⟨sg23834,True.intro,True.intro⟩,⟨sg23836,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_13All : degreeTree43_13.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23821,degreeTree43_11All,degreeTree43_12All⟩ - -lemma degreeTree43_14All : degreeTree43_14.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23853,⟨sg23845,⟨sg23841,⟨sg23839,⟨sg23838,True.intro,True.intro⟩,⟨sg23840,True.intro,True.intro⟩⟩,⟨sg23843,⟨sg23842,True.intro,True.intro⟩,⟨sg23844,True.intro,True.intro⟩⟩⟩,⟨sg23849,⟨sg23847,⟨sg23846,True.intro,True.intro⟩,⟨sg23848,True.intro,True.intro⟩⟩,⟨sg23851,⟨sg23850,True.intro,True.intro⟩,⟨sg23852,True.intro,True.intro⟩⟩⟩⟩,⟨sg23861,⟨sg23857,⟨sg23855,⟨sg23854,True.intro,True.intro⟩,⟨sg23856,True.intro,True.intro⟩⟩,⟨sg23859,⟨sg23858,True.intro,True.intro⟩,⟨sg23860,True.intro,True.intro⟩⟩⟩,⟨sg23865,⟨sg23863,⟨sg23862,True.intro,True.intro⟩,⟨sg23864,True.intro,True.intro⟩⟩,⟨sg23867,⟨sg23866,True.intro,True.intro⟩,⟨sg23868,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_15All : degreeTree43_15.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23837,degreeTree43_13All,degreeTree43_14All⟩ - -lemma degreeTree43_16All : degreeTree43_16.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23885,⟨sg23877,⟨sg23873,⟨sg23871,⟨sg23870,True.intro,True.intro⟩,⟨sg23872,True.intro,True.intro⟩⟩,⟨sg23875,⟨sg23874,True.intro,True.intro⟩,⟨sg23876,True.intro,True.intro⟩⟩⟩,⟨sg23881,⟨sg23879,⟨sg23878,True.intro,True.intro⟩,⟨sg23880,True.intro,True.intro⟩⟩,⟨sg23883,⟨sg23882,True.intro,True.intro⟩,⟨sg23884,True.intro,True.intro⟩⟩⟩⟩,⟨sg23893,⟨sg23889,⟨sg23887,⟨sg23886,True.intro,True.intro⟩,⟨sg23888,True.intro,True.intro⟩⟩,⟨sg23891,⟨sg23890,True.intro,True.intro⟩,⟨sg23892,True.intro,True.intro⟩⟩⟩,⟨sg23897,⟨sg23895,⟨sg23894,True.intro,True.intro⟩,⟨sg23896,True.intro,True.intro⟩⟩,⟨sg23899,⟨sg23898,True.intro,True.intro⟩,⟨sg23900,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_17All : degreeTree43_17.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23917,⟨sg23909,⟨sg23905,⟨sg23903,⟨sg23902,True.intro,True.intro⟩,⟨sg23904,True.intro,True.intro⟩⟩,⟨sg23907,⟨sg23906,True.intro,True.intro⟩,⟨sg23908,True.intro,True.intro⟩⟩⟩,⟨sg23913,⟨sg23911,⟨sg23910,True.intro,True.intro⟩,⟨sg23912,True.intro,True.intro⟩⟩,⟨sg23915,⟨sg23914,True.intro,True.intro⟩,⟨sg23916,True.intro,True.intro⟩⟩⟩⟩,⟨sg23925,⟨sg23921,⟨sg23919,⟨sg23918,True.intro,True.intro⟩,⟨sg23920,True.intro,True.intro⟩⟩,⟨sg23923,⟨sg23922,True.intro,True.intro⟩,⟨sg23924,True.intro,True.intro⟩⟩⟩,⟨sg23929,⟨sg23927,⟨sg23926,True.intro,True.intro⟩,⟨sg23928,True.intro,True.intro⟩⟩,⟨sg23931,⟨sg23930,True.intro,True.intro⟩,⟨sg23932,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_18All : degreeTree43_18.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23901,degreeTree43_16All,degreeTree43_17All⟩ - -lemma degreeTree43_19All : degreeTree43_19.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23869,degreeTree43_15All,degreeTree43_18All⟩ - -lemma degreeTree43_20All : degreeTree43_20.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23804,degreeTree43_10All,degreeTree43_19All⟩ - -lemma degreeTree43_21All : degreeTree43_21.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23942,⟨sg23938,⟨sg23936,⟨sg23935,⟨sg23934,True.intro,True.intro⟩,True.intro⟩,⟨sg23937,True.intro,True.intro⟩⟩,⟨sg23940,⟨sg23939,True.intro,True.intro⟩,⟨sg23941,True.intro,True.intro⟩⟩⟩,⟨sg23946,⟨sg23944,⟨sg23943,True.intro,True.intro⟩,⟨sg23945,True.intro,True.intro⟩⟩,⟨sg23948,⟨sg23947,True.intro,True.intro⟩,⟨sg23949,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_22All : degreeTree43_22.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23958,⟨sg23954,⟨sg23952,⟨sg23951,True.intro,True.intro⟩,⟨sg23953,True.intro,True.intro⟩⟩,⟨sg23956,⟨sg23955,True.intro,True.intro⟩,⟨sg23957,True.intro,True.intro⟩⟩⟩,⟨sg23962,⟨sg23960,⟨sg23959,True.intro,True.intro⟩,⟨sg23961,True.intro,True.intro⟩⟩,⟨sg23964,⟨sg23963,True.intro,True.intro⟩,⟨sg23965,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_23All : degreeTree43_23.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23950,degreeTree43_21All,degreeTree43_22All⟩ - -lemma degreeTree43_24All : degreeTree43_24.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23982,⟨sg23974,⟨sg23970,⟨sg23968,⟨sg23967,True.intro,True.intro⟩,⟨sg23969,True.intro,True.intro⟩⟩,⟨sg23972,⟨sg23971,True.intro,True.intro⟩,⟨sg23973,True.intro,True.intro⟩⟩⟩,⟨sg23978,⟨sg23976,⟨sg23975,True.intro,True.intro⟩,⟨sg23977,True.intro,True.intro⟩⟩,⟨sg23980,⟨sg23979,True.intro,True.intro⟩,⟨sg23981,True.intro,True.intro⟩⟩⟩⟩,⟨sg23990,⟨sg23986,⟨sg23984,⟨sg23983,True.intro,True.intro⟩,⟨sg23985,True.intro,True.intro⟩⟩,⟨sg23988,⟨sg23987,True.intro,True.intro⟩,⟨sg23989,True.intro,True.intro⟩⟩⟩,⟨sg23994,⟨sg23992,⟨sg23991,True.intro,True.intro⟩,⟨sg23993,True.intro,True.intro⟩⟩,⟨sg23996,⟨sg23995,True.intro,True.intro⟩,⟨sg23997,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_25All : degreeTree43_25.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23966,degreeTree43_23All,degreeTree43_24All⟩ - -lemma degreeTree43_26All : degreeTree43_26.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24014,⟨sg24006,⟨sg24002,⟨sg24000,⟨sg23999,True.intro,True.intro⟩,⟨sg24001,True.intro,True.intro⟩⟩,⟨sg24004,⟨sg24003,True.intro,True.intro⟩,⟨sg24005,True.intro,True.intro⟩⟩⟩,⟨sg24010,⟨sg24008,⟨sg24007,True.intro,True.intro⟩,⟨sg24009,True.intro,True.intro⟩⟩,⟨sg24012,⟨sg24011,True.intro,True.intro⟩,⟨sg24013,True.intro,True.intro⟩⟩⟩⟩,⟨sg24022,⟨sg24018,⟨sg24016,⟨sg24015,True.intro,True.intro⟩,⟨sg24017,True.intro,True.intro⟩⟩,⟨sg24020,⟨sg24019,True.intro,True.intro⟩,⟨sg24021,True.intro,True.intro⟩⟩⟩,⟨sg24026,⟨sg24024,⟨sg24023,True.intro,True.intro⟩,⟨sg24025,True.intro,True.intro⟩⟩,⟨sg24028,⟨sg24027,True.intro,True.intro⟩,⟨sg24029,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_27All : degreeTree43_27.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24046,⟨sg24038,⟨sg24034,⟨sg24032,⟨sg24031,True.intro,True.intro⟩,⟨sg24033,True.intro,True.intro⟩⟩,⟨sg24036,⟨sg24035,True.intro,True.intro⟩,⟨sg24037,True.intro,True.intro⟩⟩⟩,⟨sg24042,⟨sg24040,⟨sg24039,True.intro,True.intro⟩,⟨sg24041,True.intro,True.intro⟩⟩,⟨sg24044,⟨sg24043,True.intro,True.intro⟩,⟨sg24045,True.intro,True.intro⟩⟩⟩⟩,⟨sg24054,⟨sg24050,⟨sg24048,⟨sg24047,True.intro,True.intro⟩,⟨sg24049,True.intro,True.intro⟩⟩,⟨sg24052,⟨sg24051,True.intro,True.intro⟩,⟨sg24053,True.intro,True.intro⟩⟩⟩,⟨sg24058,⟨sg24056,⟨sg24055,True.intro,True.intro⟩,⟨sg24057,True.intro,True.intro⟩⟩,⟨sg24060,⟨sg24059,True.intro,True.intro⟩,⟨sg24061,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_28All : degreeTree43_28.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24030,degreeTree43_26All,degreeTree43_27All⟩ - -lemma degreeTree43_29All : degreeTree43_29.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23998,degreeTree43_25All,degreeTree43_28All⟩ - -lemma degreeTree43_30All : degreeTree43_30.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24071,⟨sg24067,⟨sg24065,⟨sg24064,⟨sg24063,True.intro,True.intro⟩,True.intro⟩,⟨sg24066,True.intro,True.intro⟩⟩,⟨sg24069,⟨sg24068,True.intro,True.intro⟩,⟨sg24070,True.intro,True.intro⟩⟩⟩,⟨sg24075,⟨sg24073,⟨sg24072,True.intro,True.intro⟩,⟨sg24074,True.intro,True.intro⟩⟩,⟨sg24077,⟨sg24076,True.intro,True.intro⟩,⟨sg24078,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_31All : degreeTree43_31.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24087,⟨sg24083,⟨sg24081,⟨sg24080,True.intro,True.intro⟩,⟨sg24082,True.intro,True.intro⟩⟩,⟨sg24085,⟨sg24084,True.intro,True.intro⟩,⟨sg24086,True.intro,True.intro⟩⟩⟩,⟨sg24091,⟨sg24089,⟨sg24088,True.intro,True.intro⟩,⟨sg24090,True.intro,True.intro⟩⟩,⟨sg24093,⟨sg24092,True.intro,True.intro⟩,⟨sg24094,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_32All : degreeTree43_32.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24079,degreeTree43_30All,degreeTree43_31All⟩ - -lemma degreeTree43_33All : degreeTree43_33.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24111,⟨sg24103,⟨sg24099,⟨sg24097,⟨sg24096,True.intro,True.intro⟩,⟨sg24098,True.intro,True.intro⟩⟩,⟨sg24101,⟨sg24100,True.intro,True.intro⟩,⟨sg24102,True.intro,True.intro⟩⟩⟩,⟨sg24107,⟨sg24105,⟨sg24104,True.intro,True.intro⟩,⟨sg24106,True.intro,True.intro⟩⟩,⟨sg24109,⟨sg24108,True.intro,True.intro⟩,⟨sg24110,True.intro,True.intro⟩⟩⟩⟩,⟨sg24119,⟨sg24115,⟨sg24113,⟨sg24112,True.intro,True.intro⟩,⟨sg24114,True.intro,True.intro⟩⟩,⟨sg24117,⟨sg24116,True.intro,True.intro⟩,⟨sg24118,True.intro,True.intro⟩⟩⟩,⟨sg24123,⟨sg24121,⟨sg24120,True.intro,True.intro⟩,⟨sg24122,True.intro,True.intro⟩⟩,⟨sg24125,⟨sg24124,True.intro,True.intro⟩,⟨sg24126,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_34All : degreeTree43_34.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24095,degreeTree43_32All,degreeTree43_33All⟩ - -lemma degreeTree43_35All : degreeTree43_35.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24143,⟨sg24135,⟨sg24131,⟨sg24129,⟨sg24128,True.intro,True.intro⟩,⟨sg24130,True.intro,True.intro⟩⟩,⟨sg24133,⟨sg24132,True.intro,True.intro⟩,⟨sg24134,True.intro,True.intro⟩⟩⟩,⟨sg24139,⟨sg24137,⟨sg24136,True.intro,True.intro⟩,⟨sg24138,True.intro,True.intro⟩⟩,⟨sg24141,⟨sg24140,True.intro,True.intro⟩,⟨sg24142,True.intro,True.intro⟩⟩⟩⟩,⟨sg24151,⟨sg24147,⟨sg24145,⟨sg24144,True.intro,True.intro⟩,⟨sg24146,True.intro,True.intro⟩⟩,⟨sg24149,⟨sg24148,True.intro,True.intro⟩,⟨sg24150,True.intro,True.intro⟩⟩⟩,⟨sg24155,⟨sg24153,⟨sg24152,True.intro,True.intro⟩,⟨sg24154,True.intro,True.intro⟩⟩,⟨sg24157,⟨sg24156,True.intro,True.intro⟩,⟨sg24158,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_36All : degreeTree43_36.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24175,⟨sg24167,⟨sg24163,⟨sg24161,⟨sg24160,True.intro,True.intro⟩,⟨sg24162,True.intro,True.intro⟩⟩,⟨sg24165,⟨sg24164,True.intro,True.intro⟩,⟨sg24166,True.intro,True.intro⟩⟩⟩,⟨sg24171,⟨sg24169,⟨sg24168,True.intro,True.intro⟩,⟨sg24170,True.intro,True.intro⟩⟩,⟨sg24173,⟨sg24172,True.intro,True.intro⟩,⟨sg24174,True.intro,True.intro⟩⟩⟩⟩,⟨sg24183,⟨sg24179,⟨sg24177,⟨sg24176,True.intro,True.intro⟩,⟨sg24178,True.intro,True.intro⟩⟩,⟨sg24181,⟨sg24180,True.intro,True.intro⟩,⟨sg24182,True.intro,True.intro⟩⟩⟩,⟨sg24187,⟨sg24185,⟨sg24184,True.intro,True.intro⟩,⟨sg24186,True.intro,True.intro⟩⟩,⟨sg24189,⟨sg24188,True.intro,True.intro⟩,⟨sg24190,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_37All : degreeTree43_37.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24159,degreeTree43_35All,degreeTree43_36All⟩ - -lemma degreeTree43_38All : degreeTree43_38.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24127,degreeTree43_34All,degreeTree43_37All⟩ - -lemma degreeTree43_39All : degreeTree43_39.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24062,degreeTree43_29All,degreeTree43_38All⟩ - -lemma degreeTree43_40All : degreeTree43_40.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg23933,degreeTree43_20All,degreeTree43_39All⟩ - -lemma degreeTree43_41All : degreeTree43_41.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24200,⟨sg24196,⟨sg24194,⟨sg24193,⟨sg24192,True.intro,True.intro⟩,True.intro⟩,⟨sg24195,True.intro,True.intro⟩⟩,⟨sg24198,⟨sg24197,True.intro,True.intro⟩,⟨sg24199,True.intro,True.intro⟩⟩⟩,⟨sg24204,⟨sg24202,⟨sg24201,True.intro,True.intro⟩,⟨sg24203,True.intro,True.intro⟩⟩,⟨sg24206,⟨sg24205,True.intro,True.intro⟩,⟨sg24207,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_42All : degreeTree43_42.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24216,⟨sg24212,⟨sg24210,⟨sg24209,True.intro,True.intro⟩,⟨sg24211,True.intro,True.intro⟩⟩,⟨sg24214,⟨sg24213,True.intro,True.intro⟩,⟨sg24215,True.intro,True.intro⟩⟩⟩,⟨sg24220,⟨sg24218,⟨sg24217,True.intro,True.intro⟩,⟨sg24219,True.intro,True.intro⟩⟩,⟨sg24222,⟨sg24221,True.intro,True.intro⟩,⟨sg24223,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_43All : degreeTree43_43.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24208,degreeTree43_41All,degreeTree43_42All⟩ - -lemma degreeTree43_44All : degreeTree43_44.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24240,⟨sg24232,⟨sg24228,⟨sg24226,⟨sg24225,True.intro,True.intro⟩,⟨sg24227,True.intro,True.intro⟩⟩,⟨sg24230,⟨sg24229,True.intro,True.intro⟩,⟨sg24231,True.intro,True.intro⟩⟩⟩,⟨sg24236,⟨sg24234,⟨sg24233,True.intro,True.intro⟩,⟨sg24235,True.intro,True.intro⟩⟩,⟨sg24238,⟨sg24237,True.intro,True.intro⟩,⟨sg24239,True.intro,True.intro⟩⟩⟩⟩,⟨sg24248,⟨sg24244,⟨sg24242,⟨sg24241,True.intro,True.intro⟩,⟨sg24243,True.intro,True.intro⟩⟩,⟨sg24246,⟨sg24245,True.intro,True.intro⟩,⟨sg24247,True.intro,True.intro⟩⟩⟩,⟨sg24252,⟨sg24250,⟨sg24249,True.intro,True.intro⟩,⟨sg24251,True.intro,True.intro⟩⟩,⟨sg24254,⟨sg24253,True.intro,True.intro⟩,⟨sg24255,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_45All : degreeTree43_45.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24224,degreeTree43_43All,degreeTree43_44All⟩ - -lemma degreeTree43_46All : degreeTree43_46.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24272,⟨sg24264,⟨sg24260,⟨sg24258,⟨sg24257,True.intro,True.intro⟩,⟨sg24259,True.intro,True.intro⟩⟩,⟨sg24262,⟨sg24261,True.intro,True.intro⟩,⟨sg24263,True.intro,True.intro⟩⟩⟩,⟨sg24268,⟨sg24266,⟨sg24265,True.intro,True.intro⟩,⟨sg24267,True.intro,True.intro⟩⟩,⟨sg24270,⟨sg24269,True.intro,True.intro⟩,⟨sg24271,True.intro,True.intro⟩⟩⟩⟩,⟨sg24280,⟨sg24276,⟨sg24274,⟨sg24273,True.intro,True.intro⟩,⟨sg24275,True.intro,True.intro⟩⟩,⟨sg24278,⟨sg24277,True.intro,True.intro⟩,⟨sg24279,True.intro,True.intro⟩⟩⟩,⟨sg24284,⟨sg24282,⟨sg24281,True.intro,True.intro⟩,⟨sg24283,True.intro,True.intro⟩⟩,⟨sg24286,⟨sg24285,True.intro,True.intro⟩,⟨sg24287,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_47All : degreeTree43_47.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24304,⟨sg24296,⟨sg24292,⟨sg24290,⟨sg24289,True.intro,True.intro⟩,⟨sg24291,True.intro,True.intro⟩⟩,⟨sg24294,⟨sg24293,True.intro,True.intro⟩,⟨sg24295,True.intro,True.intro⟩⟩⟩,⟨sg24300,⟨sg24298,⟨sg24297,True.intro,True.intro⟩,⟨sg24299,True.intro,True.intro⟩⟩,⟨sg24302,⟨sg24301,True.intro,True.intro⟩,⟨sg24303,True.intro,True.intro⟩⟩⟩⟩,⟨sg24312,⟨sg24308,⟨sg24306,⟨sg24305,True.intro,True.intro⟩,⟨sg24307,True.intro,True.intro⟩⟩,⟨sg24310,⟨sg24309,True.intro,True.intro⟩,⟨sg24311,True.intro,True.intro⟩⟩⟩,⟨sg24316,⟨sg24314,⟨sg24313,True.intro,True.intro⟩,⟨sg24315,True.intro,True.intro⟩⟩,⟨sg24318,⟨sg24317,True.intro,True.intro⟩,⟨sg24319,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_48All : degreeTree43_48.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24288,degreeTree43_46All,degreeTree43_47All⟩ - -lemma degreeTree43_49All : degreeTree43_49.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24256,degreeTree43_45All,degreeTree43_48All⟩ - -lemma degreeTree43_50All : degreeTree43_50.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24329,⟨sg24325,⟨sg24323,⟨sg24322,⟨sg24321,True.intro,True.intro⟩,True.intro⟩,⟨sg24324,True.intro,True.intro⟩⟩,⟨sg24327,⟨sg24326,True.intro,True.intro⟩,⟨sg24328,True.intro,True.intro⟩⟩⟩,⟨sg24333,⟨sg24331,⟨sg24330,True.intro,True.intro⟩,⟨sg24332,True.intro,True.intro⟩⟩,⟨sg24335,⟨sg24334,True.intro,True.intro⟩,⟨sg24336,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_51All : degreeTree43_51.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24345,⟨sg24341,⟨sg24339,⟨sg24338,True.intro,True.intro⟩,⟨sg24340,True.intro,True.intro⟩⟩,⟨sg24343,⟨sg24342,True.intro,True.intro⟩,⟨sg24344,True.intro,True.intro⟩⟩⟩,⟨sg24349,⟨sg24347,⟨sg24346,True.intro,True.intro⟩,⟨sg24348,True.intro,True.intro⟩⟩,⟨sg24351,⟨sg24350,True.intro,True.intro⟩,⟨sg24352,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_52All : degreeTree43_52.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24337,degreeTree43_50All,degreeTree43_51All⟩ - -lemma degreeTree43_53All : degreeTree43_53.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24369,⟨sg24361,⟨sg24357,⟨sg24355,⟨sg24354,True.intro,True.intro⟩,⟨sg24356,True.intro,True.intro⟩⟩,⟨sg24359,⟨sg24358,True.intro,True.intro⟩,⟨sg24360,True.intro,True.intro⟩⟩⟩,⟨sg24365,⟨sg24363,⟨sg24362,True.intro,True.intro⟩,⟨sg24364,True.intro,True.intro⟩⟩,⟨sg24367,⟨sg24366,True.intro,True.intro⟩,⟨sg24368,True.intro,True.intro⟩⟩⟩⟩,⟨sg24377,⟨sg24373,⟨sg24371,⟨sg24370,True.intro,True.intro⟩,⟨sg24372,True.intro,True.intro⟩⟩,⟨sg24375,⟨sg24374,True.intro,True.intro⟩,⟨sg24376,True.intro,True.intro⟩⟩⟩,⟨sg24381,⟨sg24379,⟨sg24378,True.intro,True.intro⟩,⟨sg24380,True.intro,True.intro⟩⟩,⟨sg24383,⟨sg24382,True.intro,True.intro⟩,⟨sg24384,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_54All : degreeTree43_54.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24353,degreeTree43_52All,degreeTree43_53All⟩ - -lemma degreeTree43_55All : degreeTree43_55.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24401,⟨sg24393,⟨sg24389,⟨sg24387,⟨sg24386,True.intro,True.intro⟩,⟨sg24388,True.intro,True.intro⟩⟩,⟨sg24391,⟨sg24390,True.intro,True.intro⟩,⟨sg24392,True.intro,True.intro⟩⟩⟩,⟨sg24397,⟨sg24395,⟨sg24394,True.intro,True.intro⟩,⟨sg24396,True.intro,True.intro⟩⟩,⟨sg24399,⟨sg24398,True.intro,True.intro⟩,⟨sg24400,True.intro,True.intro⟩⟩⟩⟩,⟨sg24409,⟨sg24405,⟨sg24403,⟨sg24402,True.intro,True.intro⟩,⟨sg24404,True.intro,True.intro⟩⟩,⟨sg24407,⟨sg24406,True.intro,True.intro⟩,⟨sg24408,True.intro,True.intro⟩⟩⟩,⟨sg24413,⟨sg24411,⟨sg24410,True.intro,True.intro⟩,⟨sg24412,True.intro,True.intro⟩⟩,⟨sg24415,⟨sg24414,True.intro,True.intro⟩,⟨sg24416,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_56All : degreeTree43_56.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24433,⟨sg24425,⟨sg24421,⟨sg24419,⟨sg24418,True.intro,True.intro⟩,⟨sg24420,True.intro,True.intro⟩⟩,⟨sg24423,⟨sg24422,True.intro,True.intro⟩,⟨sg24424,True.intro,True.intro⟩⟩⟩,⟨sg24429,⟨sg24427,⟨sg24426,True.intro,True.intro⟩,⟨sg24428,True.intro,True.intro⟩⟩,⟨sg24431,⟨sg24430,True.intro,True.intro⟩,⟨sg24432,True.intro,True.intro⟩⟩⟩⟩,⟨sg24441,⟨sg24437,⟨sg24435,⟨sg24434,True.intro,True.intro⟩,⟨sg24436,True.intro,True.intro⟩⟩,⟨sg24439,⟨sg24438,True.intro,True.intro⟩,⟨sg24440,True.intro,True.intro⟩⟩⟩,⟨sg24445,⟨sg24443,⟨sg24442,True.intro,True.intro⟩,⟨sg24444,True.intro,True.intro⟩⟩,⟨sg24447,⟨sg24446,True.intro,True.intro⟩,⟨sg24448,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_57All : degreeTree43_57.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24417,degreeTree43_55All,degreeTree43_56All⟩ - -lemma degreeTree43_58All : degreeTree43_58.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24385,degreeTree43_54All,degreeTree43_57All⟩ - -lemma degreeTree43_59All : degreeTree43_59.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24320,degreeTree43_49All,degreeTree43_58All⟩ - -lemma degreeTree43_60All : degreeTree43_60.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24458,⟨sg24454,⟨sg24452,⟨sg24451,⟨sg24450,True.intro,True.intro⟩,True.intro⟩,⟨sg24453,True.intro,True.intro⟩⟩,⟨sg24456,⟨sg24455,True.intro,True.intro⟩,⟨sg24457,True.intro,True.intro⟩⟩⟩,⟨sg24462,⟨sg24460,⟨sg24459,True.intro,True.intro⟩,⟨sg24461,True.intro,True.intro⟩⟩,⟨sg24464,⟨sg24463,True.intro,True.intro⟩,⟨sg24465,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_61All : degreeTree43_61.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24474,⟨sg24470,⟨sg24468,⟨sg24467,True.intro,True.intro⟩,⟨sg24469,True.intro,True.intro⟩⟩,⟨sg24472,⟨sg24471,True.intro,True.intro⟩,⟨sg24473,True.intro,True.intro⟩⟩⟩,⟨sg24478,⟨sg24476,⟨sg24475,True.intro,True.intro⟩,⟨sg24477,True.intro,True.intro⟩⟩,⟨sg24480,⟨sg24479,True.intro,True.intro⟩,⟨sg24481,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_62All : degreeTree43_62.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24466,degreeTree43_60All,degreeTree43_61All⟩ - -lemma degreeTree43_63All : degreeTree43_63.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24498,⟨sg24490,⟨sg24486,⟨sg24484,⟨sg24483,True.intro,True.intro⟩,⟨sg24485,True.intro,True.intro⟩⟩,⟨sg24488,⟨sg24487,True.intro,True.intro⟩,⟨sg24489,True.intro,True.intro⟩⟩⟩,⟨sg24494,⟨sg24492,⟨sg24491,True.intro,True.intro⟩,⟨sg24493,True.intro,True.intro⟩⟩,⟨sg24496,⟨sg24495,True.intro,True.intro⟩,⟨sg24497,True.intro,True.intro⟩⟩⟩⟩,⟨sg24506,⟨sg24502,⟨sg24500,⟨sg24499,True.intro,True.intro⟩,⟨sg24501,True.intro,True.intro⟩⟩,⟨sg24504,⟨sg24503,True.intro,True.intro⟩,⟨sg24505,True.intro,True.intro⟩⟩⟩,⟨sg24510,⟨sg24508,⟨sg24507,True.intro,True.intro⟩,⟨sg24509,True.intro,True.intro⟩⟩,⟨sg24512,⟨sg24511,True.intro,True.intro⟩,⟨sg24513,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_64All : degreeTree43_64.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24482,degreeTree43_62All,degreeTree43_63All⟩ - -lemma degreeTree43_65All : degreeTree43_65.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24530,⟨sg24522,⟨sg24518,⟨sg24516,⟨sg24515,True.intro,True.intro⟩,⟨sg24517,True.intro,True.intro⟩⟩,⟨sg24520,⟨sg24519,True.intro,True.intro⟩,⟨sg24521,True.intro,True.intro⟩⟩⟩,⟨sg24526,⟨sg24524,⟨sg24523,True.intro,True.intro⟩,⟨sg24525,True.intro,True.intro⟩⟩,⟨sg24528,⟨sg24527,True.intro,True.intro⟩,⟨sg24529,True.intro,True.intro⟩⟩⟩⟩,⟨sg24538,⟨sg24534,⟨sg24532,⟨sg24531,True.intro,True.intro⟩,⟨sg24533,True.intro,True.intro⟩⟩,⟨sg24536,⟨sg24535,True.intro,True.intro⟩,⟨sg24537,True.intro,True.intro⟩⟩⟩,⟨sg24542,⟨sg24540,⟨sg24539,True.intro,True.intro⟩,⟨sg24541,True.intro,True.intro⟩⟩,⟨sg24544,⟨sg24543,True.intro,True.intro⟩,⟨sg24545,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_66All : degreeTree43_66.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24562,⟨sg24554,⟨sg24550,⟨sg24548,⟨sg24547,True.intro,True.intro⟩,⟨sg24549,True.intro,True.intro⟩⟩,⟨sg24552,⟨sg24551,True.intro,True.intro⟩,⟨sg24553,True.intro,True.intro⟩⟩⟩,⟨sg24558,⟨sg24556,⟨sg24555,True.intro,True.intro⟩,⟨sg24557,True.intro,True.intro⟩⟩,⟨sg24560,⟨sg24559,True.intro,True.intro⟩,⟨sg24561,True.intro,True.intro⟩⟩⟩⟩,⟨sg24570,⟨sg24566,⟨sg24564,⟨sg24563,True.intro,True.intro⟩,⟨sg24565,True.intro,True.intro⟩⟩,⟨sg24568,⟨sg24567,True.intro,True.intro⟩,⟨sg24569,True.intro,True.intro⟩⟩⟩,⟨sg24574,⟨sg24572,⟨sg24571,True.intro,True.intro⟩,⟨sg24573,True.intro,True.intro⟩⟩,⟨sg24576,⟨sg24575,True.intro,True.intro⟩,⟨sg24577,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_67All : degreeTree43_67.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24546,degreeTree43_65All,degreeTree43_66All⟩ - -lemma degreeTree43_68All : degreeTree43_68.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24514,degreeTree43_64All,degreeTree43_67All⟩ - -lemma degreeTree43_69All : degreeTree43_69.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24587,⟨sg24583,⟨sg24581,⟨sg24580,⟨sg24579,True.intro,True.intro⟩,True.intro⟩,⟨sg24582,True.intro,True.intro⟩⟩,⟨sg24585,⟨sg24584,True.intro,True.intro⟩,⟨sg24586,True.intro,True.intro⟩⟩⟩,⟨sg24591,⟨sg24589,⟨sg24588,True.intro,True.intro⟩,⟨sg24590,True.intro,True.intro⟩⟩,⟨sg24593,⟨sg24592,True.intro,True.intro⟩,⟨sg24594,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_70All : degreeTree43_70.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24603,⟨sg24599,⟨sg24597,⟨sg24596,True.intro,True.intro⟩,⟨sg24598,True.intro,True.intro⟩⟩,⟨sg24601,⟨sg24600,True.intro,True.intro⟩,⟨sg24602,True.intro,True.intro⟩⟩⟩,⟨sg24607,⟨sg24605,⟨sg24604,True.intro,True.intro⟩,⟨sg24606,True.intro,True.intro⟩⟩,⟨sg24609,⟨sg24608,True.intro,True.intro⟩,⟨sg24610,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_71All : degreeTree43_71.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24595,degreeTree43_69All,degreeTree43_70All⟩ - -lemma degreeTree43_72All : degreeTree43_72.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24627,⟨sg24619,⟨sg24615,⟨sg24613,⟨sg24612,True.intro,True.intro⟩,⟨sg24614,True.intro,True.intro⟩⟩,⟨sg24617,⟨sg24616,True.intro,True.intro⟩,⟨sg24618,True.intro,True.intro⟩⟩⟩,⟨sg24623,⟨sg24621,⟨sg24620,True.intro,True.intro⟩,⟨sg24622,True.intro,True.intro⟩⟩,⟨sg24625,⟨sg24624,True.intro,True.intro⟩,⟨sg24626,True.intro,True.intro⟩⟩⟩⟩,⟨sg24635,⟨sg24631,⟨sg24629,⟨sg24628,True.intro,True.intro⟩,⟨sg24630,True.intro,True.intro⟩⟩,⟨sg24633,⟨sg24632,True.intro,True.intro⟩,⟨sg24634,True.intro,True.intro⟩⟩⟩,⟨sg24639,⟨sg24637,⟨sg24636,True.intro,True.intro⟩,⟨sg24638,True.intro,True.intro⟩⟩,⟨sg24641,⟨sg24640,True.intro,True.intro⟩,⟨sg24642,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_73All : degreeTree43_73.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24611,degreeTree43_71All,degreeTree43_72All⟩ - -lemma degreeTree43_74All : degreeTree43_74.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24659,⟨sg24651,⟨sg24647,⟨sg24645,⟨sg24644,True.intro,True.intro⟩,⟨sg24646,True.intro,True.intro⟩⟩,⟨sg24649,⟨sg24648,True.intro,True.intro⟩,⟨sg24650,True.intro,True.intro⟩⟩⟩,⟨sg24655,⟨sg24653,⟨sg24652,True.intro,True.intro⟩,⟨sg24654,True.intro,True.intro⟩⟩,⟨sg24657,⟨sg24656,True.intro,True.intro⟩,⟨sg24658,True.intro,True.intro⟩⟩⟩⟩,⟨sg24667,⟨sg24663,⟨sg24661,⟨sg24660,True.intro,True.intro⟩,⟨sg24662,True.intro,True.intro⟩⟩,⟨sg24665,⟨sg24664,True.intro,True.intro⟩,⟨sg24666,True.intro,True.intro⟩⟩⟩,⟨sg24671,⟨sg24669,⟨sg24668,True.intro,True.intro⟩,⟨sg24670,True.intro,True.intro⟩⟩,⟨sg24673,⟨sg24672,True.intro,True.intro⟩,⟨sg24674,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_75All : degreeTree43_75.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24691,⟨sg24683,⟨sg24679,⟨sg24677,⟨sg24676,True.intro,True.intro⟩,⟨sg24678,True.intro,True.intro⟩⟩,⟨sg24681,⟨sg24680,True.intro,True.intro⟩,⟨sg24682,True.intro,True.intro⟩⟩⟩,⟨sg24687,⟨sg24685,⟨sg24684,True.intro,True.intro⟩,⟨sg24686,True.intro,True.intro⟩⟩,⟨sg24689,⟨sg24688,True.intro,True.intro⟩,⟨sg24690,True.intro,True.intro⟩⟩⟩⟩,⟨sg24699,⟨sg24695,⟨sg24693,⟨sg24692,True.intro,True.intro⟩,⟨sg24694,True.intro,True.intro⟩⟩,⟨sg24697,⟨sg24696,True.intro,True.intro⟩,⟨sg24698,True.intro,True.intro⟩⟩⟩,⟨sg24703,⟨sg24701,⟨sg24700,True.intro,True.intro⟩,⟨sg24702,True.intro,True.intro⟩⟩,⟨sg24705,⟨sg24704,True.intro,True.intro⟩,⟨sg24706,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_76All : degreeTree43_76.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24675,degreeTree43_74All,degreeTree43_75All⟩ - -lemma degreeTree43_77All : degreeTree43_77.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24643,degreeTree43_73All,degreeTree43_76All⟩ - -lemma degreeTree43_78All : degreeTree43_78.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24578,degreeTree43_68All,degreeTree43_77All⟩ - -lemma degreeTree43_79All : degreeTree43_79.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24449,degreeTree43_59All,degreeTree43_78All⟩ - -lemma degreeTree43_80All : degreeTree43_80.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24191,degreeTree43_40All,degreeTree43_79All⟩ - -lemma degreeTree43_81All : degreeTree43_81.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24716,⟨sg24712,⟨sg24710,⟨sg24709,⟨sg24708,True.intro,True.intro⟩,True.intro⟩,⟨sg24711,True.intro,True.intro⟩⟩,⟨sg24714,⟨sg24713,True.intro,True.intro⟩,⟨sg24715,True.intro,True.intro⟩⟩⟩,⟨sg24720,⟨sg24718,⟨sg24717,True.intro,True.intro⟩,⟨sg24719,True.intro,True.intro⟩⟩,⟨sg24722,⟨sg24721,True.intro,True.intro⟩,⟨sg24723,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_82All : degreeTree43_82.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24732,⟨sg24728,⟨sg24726,⟨sg24725,True.intro,True.intro⟩,⟨sg24727,True.intro,True.intro⟩⟩,⟨sg24730,⟨sg24729,True.intro,True.intro⟩,⟨sg24731,True.intro,True.intro⟩⟩⟩,⟨sg24736,⟨sg24734,⟨sg24733,True.intro,True.intro⟩,⟨sg24735,True.intro,True.intro⟩⟩,⟨sg24738,⟨sg24737,True.intro,True.intro⟩,⟨sg24739,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_83All : degreeTree43_83.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24724,degreeTree43_81All,degreeTree43_82All⟩ - -lemma degreeTree43_84All : degreeTree43_84.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24756,⟨sg24748,⟨sg24744,⟨sg24742,⟨sg24741,True.intro,True.intro⟩,⟨sg24743,True.intro,True.intro⟩⟩,⟨sg24746,⟨sg24745,True.intro,True.intro⟩,⟨sg24747,True.intro,True.intro⟩⟩⟩,⟨sg24752,⟨sg24750,⟨sg24749,True.intro,True.intro⟩,⟨sg24751,True.intro,True.intro⟩⟩,⟨sg24754,⟨sg24753,True.intro,True.intro⟩,⟨sg24755,True.intro,True.intro⟩⟩⟩⟩,⟨sg24764,⟨sg24760,⟨sg24758,⟨sg24757,True.intro,True.intro⟩,⟨sg24759,True.intro,True.intro⟩⟩,⟨sg24762,⟨sg24761,True.intro,True.intro⟩,⟨sg24763,True.intro,True.intro⟩⟩⟩,⟨sg24768,⟨sg24766,⟨sg24765,True.intro,True.intro⟩,⟨sg24767,True.intro,True.intro⟩⟩,⟨sg24770,⟨sg24769,True.intro,True.intro⟩,⟨sg24771,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_85All : degreeTree43_85.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24740,degreeTree43_83All,degreeTree43_84All⟩ - -lemma degreeTree43_86All : degreeTree43_86.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24781,⟨sg24777,⟨sg24775,⟨sg24774,⟨sg24773,True.intro,True.intro⟩,True.intro⟩,⟨sg24776,True.intro,True.intro⟩⟩,⟨sg24779,⟨sg24778,True.intro,True.intro⟩,⟨sg24780,True.intro,True.intro⟩⟩⟩,⟨sg24785,⟨sg24783,⟨sg24782,True.intro,True.intro⟩,⟨sg24784,True.intro,True.intro⟩⟩,⟨sg24787,⟨sg24786,True.intro,True.intro⟩,⟨sg24788,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_87All : degreeTree43_87.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24797,⟨sg24793,⟨sg24791,⟨sg24790,True.intro,True.intro⟩,⟨sg24792,True.intro,True.intro⟩⟩,⟨sg24795,⟨sg24794,True.intro,True.intro⟩,⟨sg24796,True.intro,True.intro⟩⟩⟩,⟨sg24801,⟨sg24799,⟨sg24798,True.intro,True.intro⟩,⟨sg24800,True.intro,True.intro⟩⟩,⟨sg24803,⟨sg24802,True.intro,True.intro⟩,⟨sg24804,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_88All : degreeTree43_88.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24789,degreeTree43_86All,degreeTree43_87All⟩ - -lemma degreeTree43_89All : degreeTree43_89.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24821,⟨sg24813,⟨sg24809,⟨sg24807,⟨sg24806,True.intro,True.intro⟩,⟨sg24808,True.intro,True.intro⟩⟩,⟨sg24811,⟨sg24810,True.intro,True.intro⟩,⟨sg24812,True.intro,True.intro⟩⟩⟩,⟨sg24817,⟨sg24815,⟨sg24814,True.intro,True.intro⟩,⟨sg24816,True.intro,True.intro⟩⟩,⟨sg24819,⟨sg24818,True.intro,True.intro⟩,⟨sg24820,True.intro,True.intro⟩⟩⟩⟩,⟨sg24829,⟨sg24825,⟨sg24823,⟨sg24822,True.intro,True.intro⟩,⟨sg24824,True.intro,True.intro⟩⟩,⟨sg24827,⟨sg24826,True.intro,True.intro⟩,⟨sg24828,True.intro,True.intro⟩⟩⟩,⟨sg24833,⟨sg24831,⟨sg24830,True.intro,True.intro⟩,⟨sg24832,True.intro,True.intro⟩⟩,⟨sg24835,⟨sg24834,True.intro,True.intro⟩,⟨sg24836,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_90All : degreeTree43_90.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24805,degreeTree43_88All,degreeTree43_89All⟩ - -lemma degreeTree43_91All : degreeTree43_91.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24772,degreeTree43_85All,degreeTree43_90All⟩ - -lemma degreeTree43_92All : degreeTree43_92.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24846,⟨sg24842,⟨sg24840,⟨sg24839,⟨sg24838,True.intro,True.intro⟩,True.intro⟩,⟨sg24841,True.intro,True.intro⟩⟩,⟨sg24844,⟨sg24843,True.intro,True.intro⟩,⟨sg24845,True.intro,True.intro⟩⟩⟩,⟨sg24850,⟨sg24848,⟨sg24847,True.intro,True.intro⟩,⟨sg24849,True.intro,True.intro⟩⟩,⟨sg24852,⟨sg24851,True.intro,True.intro⟩,⟨sg24853,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_93All : degreeTree43_93.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24862,⟨sg24858,⟨sg24856,⟨sg24855,True.intro,True.intro⟩,⟨sg24857,True.intro,True.intro⟩⟩,⟨sg24860,⟨sg24859,True.intro,True.intro⟩,⟨sg24861,True.intro,True.intro⟩⟩⟩,⟨sg24866,⟨sg24864,⟨sg24863,True.intro,True.intro⟩,⟨sg24865,True.intro,True.intro⟩⟩,⟨sg24868,⟨sg24867,True.intro,True.intro⟩,⟨sg24869,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_94All : degreeTree43_94.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24854,degreeTree43_92All,degreeTree43_93All⟩ - -lemma degreeTree43_95All : degreeTree43_95.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24886,⟨sg24878,⟨sg24874,⟨sg24872,⟨sg24871,True.intro,True.intro⟩,⟨sg24873,True.intro,True.intro⟩⟩,⟨sg24876,⟨sg24875,True.intro,True.intro⟩,⟨sg24877,True.intro,True.intro⟩⟩⟩,⟨sg24882,⟨sg24880,⟨sg24879,True.intro,True.intro⟩,⟨sg24881,True.intro,True.intro⟩⟩,⟨sg24884,⟨sg24883,True.intro,True.intro⟩,⟨sg24885,True.intro,True.intro⟩⟩⟩⟩,⟨sg24894,⟨sg24890,⟨sg24888,⟨sg24887,True.intro,True.intro⟩,⟨sg24889,True.intro,True.intro⟩⟩,⟨sg24892,⟨sg24891,True.intro,True.intro⟩,⟨sg24893,True.intro,True.intro⟩⟩⟩,⟨sg24898,⟨sg24896,⟨sg24895,True.intro,True.intro⟩,⟨sg24897,True.intro,True.intro⟩⟩,⟨sg24900,⟨sg24899,True.intro,True.intro⟩,⟨sg24901,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_96All : degreeTree43_96.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24870,degreeTree43_94All,degreeTree43_95All⟩ - -lemma degreeTree43_97All : degreeTree43_97.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24918,⟨sg24910,⟨sg24906,⟨sg24904,⟨sg24903,True.intro,True.intro⟩,⟨sg24905,True.intro,True.intro⟩⟩,⟨sg24908,⟨sg24907,True.intro,True.intro⟩,⟨sg24909,True.intro,True.intro⟩⟩⟩,⟨sg24914,⟨sg24912,⟨sg24911,True.intro,True.intro⟩,⟨sg24913,True.intro,True.intro⟩⟩,⟨sg24916,⟨sg24915,True.intro,True.intro⟩,⟨sg24917,True.intro,True.intro⟩⟩⟩⟩,⟨sg24926,⟨sg24922,⟨sg24920,⟨sg24919,True.intro,True.intro⟩,⟨sg24921,True.intro,True.intro⟩⟩,⟨sg24924,⟨sg24923,True.intro,True.intro⟩,⟨sg24925,True.intro,True.intro⟩⟩⟩,⟨sg24930,⟨sg24928,⟨sg24927,True.intro,True.intro⟩,⟨sg24929,True.intro,True.intro⟩⟩,⟨sg24932,⟨sg24931,True.intro,True.intro⟩,⟨sg24933,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_98All : degreeTree43_98.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24950,⟨sg24942,⟨sg24938,⟨sg24936,⟨sg24935,True.intro,True.intro⟩,⟨sg24937,True.intro,True.intro⟩⟩,⟨sg24940,⟨sg24939,True.intro,True.intro⟩,⟨sg24941,True.intro,True.intro⟩⟩⟩,⟨sg24946,⟨sg24944,⟨sg24943,True.intro,True.intro⟩,⟨sg24945,True.intro,True.intro⟩⟩,⟨sg24948,⟨sg24947,True.intro,True.intro⟩,⟨sg24949,True.intro,True.intro⟩⟩⟩⟩,⟨sg24958,⟨sg24954,⟨sg24952,⟨sg24951,True.intro,True.intro⟩,⟨sg24953,True.intro,True.intro⟩⟩,⟨sg24956,⟨sg24955,True.intro,True.intro⟩,⟨sg24957,True.intro,True.intro⟩⟩⟩,⟨sg24962,⟨sg24960,⟨sg24959,True.intro,True.intro⟩,⟨sg24961,True.intro,True.intro⟩⟩,⟨sg24964,⟨sg24963,True.intro,True.intro⟩,⟨sg24965,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_99All : degreeTree43_99.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24934,degreeTree43_97All,degreeTree43_98All⟩ - -lemma degreeTree43_100All : degreeTree43_100.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24902,degreeTree43_96All,degreeTree43_99All⟩ - -lemma degreeTree43_101All : degreeTree43_101.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24837,degreeTree43_91All,degreeTree43_100All⟩ - -lemma degreeTree43_102All : degreeTree43_102.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24975,⟨sg24971,⟨sg24969,⟨sg24968,⟨sg24967,True.intro,True.intro⟩,True.intro⟩,⟨sg24970,True.intro,True.intro⟩⟩,⟨sg24973,⟨sg24972,True.intro,True.intro⟩,⟨sg24974,True.intro,True.intro⟩⟩⟩,⟨sg24979,⟨sg24977,⟨sg24976,True.intro,True.intro⟩,⟨sg24978,True.intro,True.intro⟩⟩,⟨sg24981,⟨sg24980,True.intro,True.intro⟩,⟨sg24982,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_103All : degreeTree43_103.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24991,⟨sg24987,⟨sg24985,⟨sg24984,True.intro,True.intro⟩,⟨sg24986,True.intro,True.intro⟩⟩,⟨sg24989,⟨sg24988,True.intro,True.intro⟩,⟨sg24990,True.intro,True.intro⟩⟩⟩,⟨sg24995,⟨sg24993,⟨sg24992,True.intro,True.intro⟩,⟨sg24994,True.intro,True.intro⟩⟩,⟨sg24997,⟨sg24996,True.intro,True.intro⟩,⟨sg24998,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_104All : degreeTree43_104.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24983,degreeTree43_102All,degreeTree43_103All⟩ - -lemma degreeTree43_105All : degreeTree43_105.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25015,⟨sg25007,⟨sg25003,⟨sg25001,⟨sg25000,True.intro,True.intro⟩,⟨sg25002,True.intro,True.intro⟩⟩,⟨sg25005,⟨sg25004,True.intro,True.intro⟩,⟨sg25006,True.intro,True.intro⟩⟩⟩,⟨sg25011,⟨sg25009,⟨sg25008,True.intro,True.intro⟩,⟨sg25010,True.intro,True.intro⟩⟩,⟨sg25013,⟨sg25012,True.intro,True.intro⟩,⟨sg25014,True.intro,True.intro⟩⟩⟩⟩,⟨sg25023,⟨sg25019,⟨sg25017,⟨sg25016,True.intro,True.intro⟩,⟨sg25018,True.intro,True.intro⟩⟩,⟨sg25021,⟨sg25020,True.intro,True.intro⟩,⟨sg25022,True.intro,True.intro⟩⟩⟩,⟨sg25027,⟨sg25025,⟨sg25024,True.intro,True.intro⟩,⟨sg25026,True.intro,True.intro⟩⟩,⟨sg25029,⟨sg25028,True.intro,True.intro⟩,⟨sg25030,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_106All : degreeTree43_106.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24999,degreeTree43_104All,degreeTree43_105All⟩ - -lemma degreeTree43_107All : degreeTree43_107.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25047,⟨sg25039,⟨sg25035,⟨sg25033,⟨sg25032,True.intro,True.intro⟩,⟨sg25034,True.intro,True.intro⟩⟩,⟨sg25037,⟨sg25036,True.intro,True.intro⟩,⟨sg25038,True.intro,True.intro⟩⟩⟩,⟨sg25043,⟨sg25041,⟨sg25040,True.intro,True.intro⟩,⟨sg25042,True.intro,True.intro⟩⟩,⟨sg25045,⟨sg25044,True.intro,True.intro⟩,⟨sg25046,True.intro,True.intro⟩⟩⟩⟩,⟨sg25055,⟨sg25051,⟨sg25049,⟨sg25048,True.intro,True.intro⟩,⟨sg25050,True.intro,True.intro⟩⟩,⟨sg25053,⟨sg25052,True.intro,True.intro⟩,⟨sg25054,True.intro,True.intro⟩⟩⟩,⟨sg25059,⟨sg25057,⟨sg25056,True.intro,True.intro⟩,⟨sg25058,True.intro,True.intro⟩⟩,⟨sg25061,⟨sg25060,True.intro,True.intro⟩,⟨sg25062,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_108All : degreeTree43_108.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25079,⟨sg25071,⟨sg25067,⟨sg25065,⟨sg25064,True.intro,True.intro⟩,⟨sg25066,True.intro,True.intro⟩⟩,⟨sg25069,⟨sg25068,True.intro,True.intro⟩,⟨sg25070,True.intro,True.intro⟩⟩⟩,⟨sg25075,⟨sg25073,⟨sg25072,True.intro,True.intro⟩,⟨sg25074,True.intro,True.intro⟩⟩,⟨sg25077,⟨sg25076,True.intro,True.intro⟩,⟨sg25078,True.intro,True.intro⟩⟩⟩⟩,⟨sg25087,⟨sg25083,⟨sg25081,⟨sg25080,True.intro,True.intro⟩,⟨sg25082,True.intro,True.intro⟩⟩,⟨sg25085,⟨sg25084,True.intro,True.intro⟩,⟨sg25086,True.intro,True.intro⟩⟩⟩,⟨sg25091,⟨sg25089,⟨sg25088,True.intro,True.intro⟩,⟨sg25090,True.intro,True.intro⟩⟩,⟨sg25093,⟨sg25092,True.intro,True.intro⟩,⟨sg25094,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_109All : degreeTree43_109.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25063,degreeTree43_107All,degreeTree43_108All⟩ - -lemma degreeTree43_110All : degreeTree43_110.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25031,degreeTree43_106All,degreeTree43_109All⟩ - -lemma degreeTree43_111All : degreeTree43_111.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25104,⟨sg25100,⟨sg25098,⟨sg25097,⟨sg25096,True.intro,True.intro⟩,True.intro⟩,⟨sg25099,True.intro,True.intro⟩⟩,⟨sg25102,⟨sg25101,True.intro,True.intro⟩,⟨sg25103,True.intro,True.intro⟩⟩⟩,⟨sg25108,⟨sg25106,⟨sg25105,True.intro,True.intro⟩,⟨sg25107,True.intro,True.intro⟩⟩,⟨sg25110,⟨sg25109,True.intro,True.intro⟩,⟨sg25111,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_112All : degreeTree43_112.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25120,⟨sg25116,⟨sg25114,⟨sg25113,True.intro,True.intro⟩,⟨sg25115,True.intro,True.intro⟩⟩,⟨sg25118,⟨sg25117,True.intro,True.intro⟩,⟨sg25119,True.intro,True.intro⟩⟩⟩,⟨sg25124,⟨sg25122,⟨sg25121,True.intro,True.intro⟩,⟨sg25123,True.intro,True.intro⟩⟩,⟨sg25126,⟨sg25125,True.intro,True.intro⟩,⟨sg25127,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_113All : degreeTree43_113.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25112,degreeTree43_111All,degreeTree43_112All⟩ - -lemma degreeTree43_114All : degreeTree43_114.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25144,⟨sg25136,⟨sg25132,⟨sg25130,⟨sg25129,True.intro,True.intro⟩,⟨sg25131,True.intro,True.intro⟩⟩,⟨sg25134,⟨sg25133,True.intro,True.intro⟩,⟨sg25135,True.intro,True.intro⟩⟩⟩,⟨sg25140,⟨sg25138,⟨sg25137,True.intro,True.intro⟩,⟨sg25139,True.intro,True.intro⟩⟩,⟨sg25142,⟨sg25141,True.intro,True.intro⟩,⟨sg25143,True.intro,True.intro⟩⟩⟩⟩,⟨sg25152,⟨sg25148,⟨sg25146,⟨sg25145,True.intro,True.intro⟩,⟨sg25147,True.intro,True.intro⟩⟩,⟨sg25150,⟨sg25149,True.intro,True.intro⟩,⟨sg25151,True.intro,True.intro⟩⟩⟩,⟨sg25156,⟨sg25154,⟨sg25153,True.intro,True.intro⟩,⟨sg25155,True.intro,True.intro⟩⟩,⟨sg25158,⟨sg25157,True.intro,True.intro⟩,⟨sg25159,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_115All : degreeTree43_115.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25128,degreeTree43_113All,degreeTree43_114All⟩ - -lemma degreeTree43_116All : degreeTree43_116.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25176,⟨sg25168,⟨sg25164,⟨sg25162,⟨sg25161,True.intro,True.intro⟩,⟨sg25163,True.intro,True.intro⟩⟩,⟨sg25166,⟨sg25165,True.intro,True.intro⟩,⟨sg25167,True.intro,True.intro⟩⟩⟩,⟨sg25172,⟨sg25170,⟨sg25169,True.intro,True.intro⟩,⟨sg25171,True.intro,True.intro⟩⟩,⟨sg25174,⟨sg25173,True.intro,True.intro⟩,⟨sg25175,True.intro,True.intro⟩⟩⟩⟩,⟨sg25184,⟨sg25180,⟨sg25178,⟨sg25177,True.intro,True.intro⟩,⟨sg25179,True.intro,True.intro⟩⟩,⟨sg25182,⟨sg25181,True.intro,True.intro⟩,⟨sg25183,True.intro,True.intro⟩⟩⟩,⟨sg25188,⟨sg25186,⟨sg25185,True.intro,True.intro⟩,⟨sg25187,True.intro,True.intro⟩⟩,⟨sg25190,⟨sg25189,True.intro,True.intro⟩,⟨sg25191,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_117All : degreeTree43_117.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25208,⟨sg25200,⟨sg25196,⟨sg25194,⟨sg25193,True.intro,True.intro⟩,⟨sg25195,True.intro,True.intro⟩⟩,⟨sg25198,⟨sg25197,True.intro,True.intro⟩,⟨sg25199,True.intro,True.intro⟩⟩⟩,⟨sg25204,⟨sg25202,⟨sg25201,True.intro,True.intro⟩,⟨sg25203,True.intro,True.intro⟩⟩,⟨sg25206,⟨sg25205,True.intro,True.intro⟩,⟨sg25207,True.intro,True.intro⟩⟩⟩⟩,⟨sg25216,⟨sg25212,⟨sg25210,⟨sg25209,True.intro,True.intro⟩,⟨sg25211,True.intro,True.intro⟩⟩,⟨sg25214,⟨sg25213,True.intro,True.intro⟩,⟨sg25215,True.intro,True.intro⟩⟩⟩,⟨sg25220,⟨sg25218,⟨sg25217,True.intro,True.intro⟩,⟨sg25219,True.intro,True.intro⟩⟩,⟨sg25222,⟨sg25221,True.intro,True.intro⟩,⟨sg25223,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_118All : degreeTree43_118.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25192,degreeTree43_116All,degreeTree43_117All⟩ - -lemma degreeTree43_119All : degreeTree43_119.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25160,degreeTree43_115All,degreeTree43_118All⟩ - -lemma degreeTree43_120All : degreeTree43_120.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25095,degreeTree43_110All,degreeTree43_119All⟩ - -lemma degreeTree43_121All : degreeTree43_121.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24966,degreeTree43_101All,degreeTree43_120All⟩ - -lemma degreeTree43_122All : degreeTree43_122.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25233,⟨sg25229,⟨sg25227,⟨sg25226,⟨sg25225,True.intro,True.intro⟩,True.intro⟩,⟨sg25228,True.intro,True.intro⟩⟩,⟨sg25231,⟨sg25230,True.intro,True.intro⟩,⟨sg25232,True.intro,True.intro⟩⟩⟩,⟨sg25237,⟨sg25235,⟨sg25234,True.intro,True.intro⟩,⟨sg25236,True.intro,True.intro⟩⟩,⟨sg25239,⟨sg25238,True.intro,True.intro⟩,⟨sg25240,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_123All : degreeTree43_123.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25249,⟨sg25245,⟨sg25243,⟨sg25242,True.intro,True.intro⟩,⟨sg25244,True.intro,True.intro⟩⟩,⟨sg25247,⟨sg25246,True.intro,True.intro⟩,⟨sg25248,True.intro,True.intro⟩⟩⟩,⟨sg25253,⟨sg25251,⟨sg25250,True.intro,True.intro⟩,⟨sg25252,True.intro,True.intro⟩⟩,⟨sg25255,⟨sg25254,True.intro,True.intro⟩,⟨sg25256,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_124All : degreeTree43_124.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25241,degreeTree43_122All,degreeTree43_123All⟩ - -lemma degreeTree43_125All : degreeTree43_125.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25273,⟨sg25265,⟨sg25261,⟨sg25259,⟨sg25258,True.intro,True.intro⟩,⟨sg25260,True.intro,True.intro⟩⟩,⟨sg25263,⟨sg25262,True.intro,True.intro⟩,⟨sg25264,True.intro,True.intro⟩⟩⟩,⟨sg25269,⟨sg25267,⟨sg25266,True.intro,True.intro⟩,⟨sg25268,True.intro,True.intro⟩⟩,⟨sg25271,⟨sg25270,True.intro,True.intro⟩,⟨sg25272,True.intro,True.intro⟩⟩⟩⟩,⟨sg25281,⟨sg25277,⟨sg25275,⟨sg25274,True.intro,True.intro⟩,⟨sg25276,True.intro,True.intro⟩⟩,⟨sg25279,⟨sg25278,True.intro,True.intro⟩,⟨sg25280,True.intro,True.intro⟩⟩⟩,⟨sg25285,⟨sg25283,⟨sg25282,True.intro,True.intro⟩,⟨sg25284,True.intro,True.intro⟩⟩,⟨sg25287,⟨sg25286,True.intro,True.intro⟩,⟨sg25288,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_126All : degreeTree43_126.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25257,degreeTree43_124All,degreeTree43_125All⟩ - -lemma degreeTree43_127All : degreeTree43_127.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25305,⟨sg25297,⟨sg25293,⟨sg25291,⟨sg25290,True.intro,True.intro⟩,⟨sg25292,True.intro,True.intro⟩⟩,⟨sg25295,⟨sg25294,True.intro,True.intro⟩,⟨sg25296,True.intro,True.intro⟩⟩⟩,⟨sg25301,⟨sg25299,⟨sg25298,True.intro,True.intro⟩,⟨sg25300,True.intro,True.intro⟩⟩,⟨sg25303,⟨sg25302,True.intro,True.intro⟩,⟨sg25304,True.intro,True.intro⟩⟩⟩⟩,⟨sg25313,⟨sg25309,⟨sg25307,⟨sg25306,True.intro,True.intro⟩,⟨sg25308,True.intro,True.intro⟩⟩,⟨sg25311,⟨sg25310,True.intro,True.intro⟩,⟨sg25312,True.intro,True.intro⟩⟩⟩,⟨sg25317,⟨sg25315,⟨sg25314,True.intro,True.intro⟩,⟨sg25316,True.intro,True.intro⟩⟩,⟨sg25319,⟨sg25318,True.intro,True.intro⟩,⟨sg25320,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_128All : degreeTree43_128.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25337,⟨sg25329,⟨sg25325,⟨sg25323,⟨sg25322,True.intro,True.intro⟩,⟨sg25324,True.intro,True.intro⟩⟩,⟨sg25327,⟨sg25326,True.intro,True.intro⟩,⟨sg25328,True.intro,True.intro⟩⟩⟩,⟨sg25333,⟨sg25331,⟨sg25330,True.intro,True.intro⟩,⟨sg25332,True.intro,True.intro⟩⟩,⟨sg25335,⟨sg25334,True.intro,True.intro⟩,⟨sg25336,True.intro,True.intro⟩⟩⟩⟩,⟨sg25345,⟨sg25341,⟨sg25339,⟨sg25338,True.intro,True.intro⟩,⟨sg25340,True.intro,True.intro⟩⟩,⟨sg25343,⟨sg25342,True.intro,True.intro⟩,⟨sg25344,True.intro,True.intro⟩⟩⟩,⟨sg25349,⟨sg25347,⟨sg25346,True.intro,True.intro⟩,⟨sg25348,True.intro,True.intro⟩⟩,⟨sg25351,⟨sg25350,True.intro,True.intro⟩,⟨sg25352,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_129All : degreeTree43_129.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25321,degreeTree43_127All,degreeTree43_128All⟩ - -lemma degreeTree43_130All : degreeTree43_130.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25289,degreeTree43_126All,degreeTree43_129All⟩ - -lemma degreeTree43_131All : degreeTree43_131.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25362,⟨sg25358,⟨sg25356,⟨sg25355,⟨sg25354,True.intro,True.intro⟩,True.intro⟩,⟨sg25357,True.intro,True.intro⟩⟩,⟨sg25360,⟨sg25359,True.intro,True.intro⟩,⟨sg25361,True.intro,True.intro⟩⟩⟩,⟨sg25366,⟨sg25364,⟨sg25363,True.intro,True.intro⟩,⟨sg25365,True.intro,True.intro⟩⟩,⟨sg25368,⟨sg25367,True.intro,True.intro⟩,⟨sg25369,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_132All : degreeTree43_132.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25378,⟨sg25374,⟨sg25372,⟨sg25371,True.intro,True.intro⟩,⟨sg25373,True.intro,True.intro⟩⟩,⟨sg25376,⟨sg25375,True.intro,True.intro⟩,⟨sg25377,True.intro,True.intro⟩⟩⟩,⟨sg25382,⟨sg25380,⟨sg25379,True.intro,True.intro⟩,⟨sg25381,True.intro,True.intro⟩⟩,⟨sg25384,⟨sg25383,True.intro,True.intro⟩,⟨sg25385,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_133All : degreeTree43_133.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25370,degreeTree43_131All,degreeTree43_132All⟩ - -lemma degreeTree43_134All : degreeTree43_134.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25402,⟨sg25394,⟨sg25390,⟨sg25388,⟨sg25387,True.intro,True.intro⟩,⟨sg25389,True.intro,True.intro⟩⟩,⟨sg25392,⟨sg25391,True.intro,True.intro⟩,⟨sg25393,True.intro,True.intro⟩⟩⟩,⟨sg25398,⟨sg25396,⟨sg25395,True.intro,True.intro⟩,⟨sg25397,True.intro,True.intro⟩⟩,⟨sg25400,⟨sg25399,True.intro,True.intro⟩,⟨sg25401,True.intro,True.intro⟩⟩⟩⟩,⟨sg25410,⟨sg25406,⟨sg25404,⟨sg25403,True.intro,True.intro⟩,⟨sg25405,True.intro,True.intro⟩⟩,⟨sg25408,⟨sg25407,True.intro,True.intro⟩,⟨sg25409,True.intro,True.intro⟩⟩⟩,⟨sg25414,⟨sg25412,⟨sg25411,True.intro,True.intro⟩,⟨sg25413,True.intro,True.intro⟩⟩,⟨sg25416,⟨sg25415,True.intro,True.intro⟩,⟨sg25417,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_135All : degreeTree43_135.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25386,degreeTree43_133All,degreeTree43_134All⟩ - -lemma degreeTree43_136All : degreeTree43_136.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25434,⟨sg25426,⟨sg25422,⟨sg25420,⟨sg25419,True.intro,True.intro⟩,⟨sg25421,True.intro,True.intro⟩⟩,⟨sg25424,⟨sg25423,True.intro,True.intro⟩,⟨sg25425,True.intro,True.intro⟩⟩⟩,⟨sg25430,⟨sg25428,⟨sg25427,True.intro,True.intro⟩,⟨sg25429,True.intro,True.intro⟩⟩,⟨sg25432,⟨sg25431,True.intro,True.intro⟩,⟨sg25433,True.intro,True.intro⟩⟩⟩⟩,⟨sg25442,⟨sg25438,⟨sg25436,⟨sg25435,True.intro,True.intro⟩,⟨sg25437,True.intro,True.intro⟩⟩,⟨sg25440,⟨sg25439,True.intro,True.intro⟩,⟨sg25441,True.intro,True.intro⟩⟩⟩,⟨sg25446,⟨sg25444,⟨sg25443,True.intro,True.intro⟩,⟨sg25445,True.intro,True.intro⟩⟩,⟨sg25448,⟨sg25447,True.intro,True.intro⟩,⟨sg25449,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_137All : degreeTree43_137.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25466,⟨sg25458,⟨sg25454,⟨sg25452,⟨sg25451,True.intro,True.intro⟩,⟨sg25453,True.intro,True.intro⟩⟩,⟨sg25456,⟨sg25455,True.intro,True.intro⟩,⟨sg25457,True.intro,True.intro⟩⟩⟩,⟨sg25462,⟨sg25460,⟨sg25459,True.intro,True.intro⟩,⟨sg25461,True.intro,True.intro⟩⟩,⟨sg25464,⟨sg25463,True.intro,True.intro⟩,⟨sg25465,True.intro,True.intro⟩⟩⟩⟩,⟨sg25474,⟨sg25470,⟨sg25468,⟨sg25467,True.intro,True.intro⟩,⟨sg25469,True.intro,True.intro⟩⟩,⟨sg25472,⟨sg25471,True.intro,True.intro⟩,⟨sg25473,True.intro,True.intro⟩⟩⟩,⟨sg25478,⟨sg25476,⟨sg25475,True.intro,True.intro⟩,⟨sg25477,True.intro,True.intro⟩⟩,⟨sg25480,⟨sg25479,True.intro,True.intro⟩,⟨sg25481,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_138All : degreeTree43_138.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25450,degreeTree43_136All,degreeTree43_137All⟩ - -lemma degreeTree43_139All : degreeTree43_139.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25418,degreeTree43_135All,degreeTree43_138All⟩ - -lemma degreeTree43_140All : degreeTree43_140.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25353,degreeTree43_130All,degreeTree43_139All⟩ - -lemma degreeTree43_141All : degreeTree43_141.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25491,⟨sg25487,⟨sg25485,⟨sg25484,⟨sg25483,True.intro,True.intro⟩,True.intro⟩,⟨sg25486,True.intro,True.intro⟩⟩,⟨sg25489,⟨sg25488,True.intro,True.intro⟩,⟨sg25490,True.intro,True.intro⟩⟩⟩,⟨sg25495,⟨sg25493,⟨sg25492,True.intro,True.intro⟩,⟨sg25494,True.intro,True.intro⟩⟩,⟨sg25497,⟨sg25496,True.intro,True.intro⟩,⟨sg25498,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_142All : degreeTree43_142.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25507,⟨sg25503,⟨sg25501,⟨sg25500,True.intro,True.intro⟩,⟨sg25502,True.intro,True.intro⟩⟩,⟨sg25505,⟨sg25504,True.intro,True.intro⟩,⟨sg25506,True.intro,True.intro⟩⟩⟩,⟨sg25511,⟨sg25509,⟨sg25508,True.intro,True.intro⟩,⟨sg25510,True.intro,True.intro⟩⟩,⟨sg25513,⟨sg25512,True.intro,True.intro⟩,⟨sg25514,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_143All : degreeTree43_143.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25499,degreeTree43_141All,degreeTree43_142All⟩ - -lemma degreeTree43_144All : degreeTree43_144.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25531,⟨sg25523,⟨sg25519,⟨sg25517,⟨sg25516,True.intro,True.intro⟩,⟨sg25518,True.intro,True.intro⟩⟩,⟨sg25521,⟨sg25520,True.intro,True.intro⟩,⟨sg25522,True.intro,True.intro⟩⟩⟩,⟨sg25527,⟨sg25525,⟨sg25524,True.intro,True.intro⟩,⟨sg25526,True.intro,True.intro⟩⟩,⟨sg25529,⟨sg25528,True.intro,True.intro⟩,⟨sg25530,True.intro,True.intro⟩⟩⟩⟩,⟨sg25539,⟨sg25535,⟨sg25533,⟨sg25532,True.intro,True.intro⟩,⟨sg25534,True.intro,True.intro⟩⟩,⟨sg25537,⟨sg25536,True.intro,True.intro⟩,⟨sg25538,True.intro,True.intro⟩⟩⟩,⟨sg25543,⟨sg25541,⟨sg25540,True.intro,True.intro⟩,⟨sg25542,True.intro,True.intro⟩⟩,⟨sg25545,⟨sg25544,True.intro,True.intro⟩,⟨sg25546,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_145All : degreeTree43_145.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25515,degreeTree43_143All,degreeTree43_144All⟩ - -lemma degreeTree43_146All : degreeTree43_146.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25563,⟨sg25555,⟨sg25551,⟨sg25549,⟨sg25548,True.intro,True.intro⟩,⟨sg25550,True.intro,True.intro⟩⟩,⟨sg25553,⟨sg25552,True.intro,True.intro⟩,⟨sg25554,True.intro,True.intro⟩⟩⟩,⟨sg25559,⟨sg25557,⟨sg25556,True.intro,True.intro⟩,⟨sg25558,True.intro,True.intro⟩⟩,⟨sg25561,⟨sg25560,True.intro,True.intro⟩,⟨sg25562,True.intro,True.intro⟩⟩⟩⟩,⟨sg25571,⟨sg25567,⟨sg25565,⟨sg25564,True.intro,True.intro⟩,⟨sg25566,True.intro,True.intro⟩⟩,⟨sg25569,⟨sg25568,True.intro,True.intro⟩,⟨sg25570,True.intro,True.intro⟩⟩⟩,⟨sg25575,⟨sg25573,⟨sg25572,True.intro,True.intro⟩,⟨sg25574,True.intro,True.intro⟩⟩,⟨sg25577,⟨sg25576,True.intro,True.intro⟩,⟨sg25578,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_147All : degreeTree43_147.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25595,⟨sg25587,⟨sg25583,⟨sg25581,⟨sg25580,True.intro,True.intro⟩,⟨sg25582,True.intro,True.intro⟩⟩,⟨sg25585,⟨sg25584,True.intro,True.intro⟩,⟨sg25586,True.intro,True.intro⟩⟩⟩,⟨sg25591,⟨sg25589,⟨sg25588,True.intro,True.intro⟩,⟨sg25590,True.intro,True.intro⟩⟩,⟨sg25593,⟨sg25592,True.intro,True.intro⟩,⟨sg25594,True.intro,True.intro⟩⟩⟩⟩,⟨sg25603,⟨sg25599,⟨sg25597,⟨sg25596,True.intro,True.intro⟩,⟨sg25598,True.intro,True.intro⟩⟩,⟨sg25601,⟨sg25600,True.intro,True.intro⟩,⟨sg25602,True.intro,True.intro⟩⟩⟩,⟨sg25607,⟨sg25605,⟨sg25604,True.intro,True.intro⟩,⟨sg25606,True.intro,True.intro⟩⟩,⟨sg25609,⟨sg25608,True.intro,True.intro⟩,⟨sg25610,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_148All : degreeTree43_148.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25579,degreeTree43_146All,degreeTree43_147All⟩ - -lemma degreeTree43_149All : degreeTree43_149.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25547,degreeTree43_145All,degreeTree43_148All⟩ - -lemma degreeTree43_150All : degreeTree43_150.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25620,⟨sg25616,⟨sg25614,⟨sg25613,⟨sg25612,True.intro,True.intro⟩,True.intro⟩,⟨sg25615,True.intro,True.intro⟩⟩,⟨sg25618,⟨sg25617,True.intro,True.intro⟩,⟨sg25619,True.intro,True.intro⟩⟩⟩,⟨sg25624,⟨sg25622,⟨sg25621,True.intro,True.intro⟩,⟨sg25623,True.intro,True.intro⟩⟩,⟨sg25626,⟨sg25625,True.intro,True.intro⟩,⟨sg25627,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_151All : degreeTree43_151.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25636,⟨sg25632,⟨sg25630,⟨sg25629,True.intro,True.intro⟩,⟨sg25631,True.intro,True.intro⟩⟩,⟨sg25634,⟨sg25633,True.intro,True.intro⟩,⟨sg25635,True.intro,True.intro⟩⟩⟩,⟨sg25640,⟨sg25638,⟨sg25637,True.intro,True.intro⟩,⟨sg25639,True.intro,True.intro⟩⟩,⟨sg25642,⟨sg25641,True.intro,True.intro⟩,⟨sg25643,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_152All : degreeTree43_152.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25628,degreeTree43_150All,degreeTree43_151All⟩ - -lemma degreeTree43_153All : degreeTree43_153.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25660,⟨sg25652,⟨sg25648,⟨sg25646,⟨sg25645,True.intro,True.intro⟩,⟨sg25647,True.intro,True.intro⟩⟩,⟨sg25650,⟨sg25649,True.intro,True.intro⟩,⟨sg25651,True.intro,True.intro⟩⟩⟩,⟨sg25656,⟨sg25654,⟨sg25653,True.intro,True.intro⟩,⟨sg25655,True.intro,True.intro⟩⟩,⟨sg25658,⟨sg25657,True.intro,True.intro⟩,⟨sg25659,True.intro,True.intro⟩⟩⟩⟩,⟨sg25668,⟨sg25664,⟨sg25662,⟨sg25661,True.intro,True.intro⟩,⟨sg25663,True.intro,True.intro⟩⟩,⟨sg25666,⟨sg25665,True.intro,True.intro⟩,⟨sg25667,True.intro,True.intro⟩⟩⟩,⟨sg25672,⟨sg25670,⟨sg25669,True.intro,True.intro⟩,⟨sg25671,True.intro,True.intro⟩⟩,⟨sg25674,⟨sg25673,True.intro,True.intro⟩,⟨sg25675,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_154All : degreeTree43_154.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25644,degreeTree43_152All,degreeTree43_153All⟩ - -lemma degreeTree43_155All : degreeTree43_155.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25692,⟨sg25684,⟨sg25680,⟨sg25678,⟨sg25677,True.intro,True.intro⟩,⟨sg25679,True.intro,True.intro⟩⟩,⟨sg25682,⟨sg25681,True.intro,True.intro⟩,⟨sg25683,True.intro,True.intro⟩⟩⟩,⟨sg25688,⟨sg25686,⟨sg25685,True.intro,True.intro⟩,⟨sg25687,True.intro,True.intro⟩⟩,⟨sg25690,⟨sg25689,True.intro,True.intro⟩,⟨sg25691,True.intro,True.intro⟩⟩⟩⟩,⟨sg25700,⟨sg25696,⟨sg25694,⟨sg25693,True.intro,True.intro⟩,⟨sg25695,True.intro,True.intro⟩⟩,⟨sg25698,⟨sg25697,True.intro,True.intro⟩,⟨sg25699,True.intro,True.intro⟩⟩⟩,⟨sg25704,⟨sg25702,⟨sg25701,True.intro,True.intro⟩,⟨sg25703,True.intro,True.intro⟩⟩,⟨sg25706,⟨sg25705,True.intro,True.intro⟩,⟨sg25707,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_156All : degreeTree43_156.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25724,⟨sg25716,⟨sg25712,⟨sg25710,⟨sg25709,True.intro,True.intro⟩,⟨sg25711,True.intro,True.intro⟩⟩,⟨sg25714,⟨sg25713,True.intro,True.intro⟩,⟨sg25715,True.intro,True.intro⟩⟩⟩,⟨sg25720,⟨sg25718,⟨sg25717,True.intro,True.intro⟩,⟨sg25719,True.intro,True.intro⟩⟩,⟨sg25722,⟨sg25721,True.intro,True.intro⟩,⟨sg25723,True.intro,True.intro⟩⟩⟩⟩,⟨sg25732,⟨sg25728,⟨sg25726,⟨sg25725,True.intro,True.intro⟩,⟨sg25727,True.intro,True.intro⟩⟩,⟨sg25730,⟨sg25729,True.intro,True.intro⟩,⟨sg25731,True.intro,True.intro⟩⟩⟩,⟨sg25736,⟨sg25734,⟨sg25733,True.intro,True.intro⟩,⟨sg25735,True.intro,True.intro⟩⟩,⟨sg25738,⟨sg25737,True.intro,True.intro⟩,⟨sg25739,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_157All : degreeTree43_157.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25708,degreeTree43_155All,degreeTree43_156All⟩ - -lemma degreeTree43_158All : degreeTree43_158.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25676,degreeTree43_154All,degreeTree43_157All⟩ - -lemma degreeTree43_159All : degreeTree43_159.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25611,degreeTree43_149All,degreeTree43_158All⟩ - -lemma degreeTree43_160All : degreeTree43_160.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25482,degreeTree43_140All,degreeTree43_159All⟩ - -lemma degreeTree43_161All : degreeTree43_161.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25224,degreeTree43_121All,degreeTree43_160All⟩ - -lemma degreeTree43_162All : degreeTree43_162.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg24707,degreeTree43_80All,degreeTree43_161All⟩ - -lemma degreeTree43_163All : degreeTree43_163.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25749,⟨sg25745,⟨sg25743,⟨sg25742,⟨sg25741,True.intro,True.intro⟩,True.intro⟩,⟨sg25744,True.intro,True.intro⟩⟩,⟨sg25747,⟨sg25746,True.intro,True.intro⟩,⟨sg25748,True.intro,True.intro⟩⟩⟩,⟨sg25753,⟨sg25751,⟨sg25750,True.intro,True.intro⟩,⟨sg25752,True.intro,True.intro⟩⟩,⟨sg25755,⟨sg25754,True.intro,True.intro⟩,⟨sg25756,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_164All : degreeTree43_164.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25765,⟨sg25761,⟨sg25759,⟨sg25758,True.intro,True.intro⟩,⟨sg25760,True.intro,True.intro⟩⟩,⟨sg25763,⟨sg25762,True.intro,True.intro⟩,⟨sg25764,True.intro,True.intro⟩⟩⟩,⟨sg25769,⟨sg25767,⟨sg25766,True.intro,True.intro⟩,⟨sg25768,True.intro,True.intro⟩⟩,⟨sg25771,⟨sg25770,True.intro,True.intro⟩,⟨sg25772,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_165All : degreeTree43_165.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25757,degreeTree43_163All,degreeTree43_164All⟩ - -lemma degreeTree43_166All : degreeTree43_166.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25789,⟨sg25781,⟨sg25777,⟨sg25775,⟨sg25774,True.intro,True.intro⟩,⟨sg25776,True.intro,True.intro⟩⟩,⟨sg25779,⟨sg25778,True.intro,True.intro⟩,⟨sg25780,True.intro,True.intro⟩⟩⟩,⟨sg25785,⟨sg25783,⟨sg25782,True.intro,True.intro⟩,⟨sg25784,True.intro,True.intro⟩⟩,⟨sg25787,⟨sg25786,True.intro,True.intro⟩,⟨sg25788,True.intro,True.intro⟩⟩⟩⟩,⟨sg25797,⟨sg25793,⟨sg25791,⟨sg25790,True.intro,True.intro⟩,⟨sg25792,True.intro,True.intro⟩⟩,⟨sg25795,⟨sg25794,True.intro,True.intro⟩,⟨sg25796,True.intro,True.intro⟩⟩⟩,⟨sg25801,⟨sg25799,⟨sg25798,True.intro,True.intro⟩,⟨sg25800,True.intro,True.intro⟩⟩,⟨sg25803,⟨sg25802,True.intro,True.intro⟩,⟨sg25804,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_167All : degreeTree43_167.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25773,degreeTree43_165All,degreeTree43_166All⟩ - -lemma degreeTree43_168All : degreeTree43_168.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25814,⟨sg25810,⟨sg25808,⟨sg25807,⟨sg25806,True.intro,True.intro⟩,True.intro⟩,⟨sg25809,True.intro,True.intro⟩⟩,⟨sg25812,⟨sg25811,True.intro,True.intro⟩,⟨sg25813,True.intro,True.intro⟩⟩⟩,⟨sg25818,⟨sg25816,⟨sg25815,True.intro,True.intro⟩,⟨sg25817,True.intro,True.intro⟩⟩,⟨sg25820,⟨sg25819,True.intro,True.intro⟩,⟨sg25821,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_169All : degreeTree43_169.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25830,⟨sg25826,⟨sg25824,⟨sg25823,True.intro,True.intro⟩,⟨sg25825,True.intro,True.intro⟩⟩,⟨sg25828,⟨sg25827,True.intro,True.intro⟩,⟨sg25829,True.intro,True.intro⟩⟩⟩,⟨sg25834,⟨sg25832,⟨sg25831,True.intro,True.intro⟩,⟨sg25833,True.intro,True.intro⟩⟩,⟨sg25836,⟨sg25835,True.intro,True.intro⟩,⟨sg25837,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_170All : degreeTree43_170.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25822,degreeTree43_168All,degreeTree43_169All⟩ - -lemma degreeTree43_171All : degreeTree43_171.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25854,⟨sg25846,⟨sg25842,⟨sg25840,⟨sg25839,True.intro,True.intro⟩,⟨sg25841,True.intro,True.intro⟩⟩,⟨sg25844,⟨sg25843,True.intro,True.intro⟩,⟨sg25845,True.intro,True.intro⟩⟩⟩,⟨sg25850,⟨sg25848,⟨sg25847,True.intro,True.intro⟩,⟨sg25849,True.intro,True.intro⟩⟩,⟨sg25852,⟨sg25851,True.intro,True.intro⟩,⟨sg25853,True.intro,True.intro⟩⟩⟩⟩,⟨sg25862,⟨sg25858,⟨sg25856,⟨sg25855,True.intro,True.intro⟩,⟨sg25857,True.intro,True.intro⟩⟩,⟨sg25860,⟨sg25859,True.intro,True.intro⟩,⟨sg25861,True.intro,True.intro⟩⟩⟩,⟨sg25866,⟨sg25864,⟨sg25863,True.intro,True.intro⟩,⟨sg25865,True.intro,True.intro⟩⟩,⟨sg25868,⟨sg25867,True.intro,True.intro⟩,⟨sg25869,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_172All : degreeTree43_172.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25838,degreeTree43_170All,degreeTree43_171All⟩ - -lemma degreeTree43_173All : degreeTree43_173.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25805,degreeTree43_167All,degreeTree43_172All⟩ - -lemma degreeTree43_174All : degreeTree43_174.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25879,⟨sg25875,⟨sg25873,⟨sg25872,⟨sg25871,True.intro,True.intro⟩,True.intro⟩,⟨sg25874,True.intro,True.intro⟩⟩,⟨sg25877,⟨sg25876,True.intro,True.intro⟩,⟨sg25878,True.intro,True.intro⟩⟩⟩,⟨sg25883,⟨sg25881,⟨sg25880,True.intro,True.intro⟩,⟨sg25882,True.intro,True.intro⟩⟩,⟨sg25885,⟨sg25884,True.intro,True.intro⟩,⟨sg25886,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_175All : degreeTree43_175.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25895,⟨sg25891,⟨sg25889,⟨sg25888,True.intro,True.intro⟩,⟨sg25890,True.intro,True.intro⟩⟩,⟨sg25893,⟨sg25892,True.intro,True.intro⟩,⟨sg25894,True.intro,True.intro⟩⟩⟩,⟨sg25899,⟨sg25897,⟨sg25896,True.intro,True.intro⟩,⟨sg25898,True.intro,True.intro⟩⟩,⟨sg25901,⟨sg25900,True.intro,True.intro⟩,⟨sg25902,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_176All : degreeTree43_176.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25887,degreeTree43_174All,degreeTree43_175All⟩ - -lemma degreeTree43_177All : degreeTree43_177.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25919,⟨sg25911,⟨sg25907,⟨sg25905,⟨sg25904,True.intro,True.intro⟩,⟨sg25906,True.intro,True.intro⟩⟩,⟨sg25909,⟨sg25908,True.intro,True.intro⟩,⟨sg25910,True.intro,True.intro⟩⟩⟩,⟨sg25915,⟨sg25913,⟨sg25912,True.intro,True.intro⟩,⟨sg25914,True.intro,True.intro⟩⟩,⟨sg25917,⟨sg25916,True.intro,True.intro⟩,⟨sg25918,True.intro,True.intro⟩⟩⟩⟩,⟨sg25927,⟨sg25923,⟨sg25921,⟨sg25920,True.intro,True.intro⟩,⟨sg25922,True.intro,True.intro⟩⟩,⟨sg25925,⟨sg25924,True.intro,True.intro⟩,⟨sg25926,True.intro,True.intro⟩⟩⟩,⟨sg25931,⟨sg25929,⟨sg25928,True.intro,True.intro⟩,⟨sg25930,True.intro,True.intro⟩⟩,⟨sg25933,⟨sg25932,True.intro,True.intro⟩,⟨sg25934,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_178All : degreeTree43_178.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25903,degreeTree43_176All,degreeTree43_177All⟩ - -lemma degreeTree43_179All : degreeTree43_179.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25951,⟨sg25943,⟨sg25939,⟨sg25937,⟨sg25936,True.intro,True.intro⟩,⟨sg25938,True.intro,True.intro⟩⟩,⟨sg25941,⟨sg25940,True.intro,True.intro⟩,⟨sg25942,True.intro,True.intro⟩⟩⟩,⟨sg25947,⟨sg25945,⟨sg25944,True.intro,True.intro⟩,⟨sg25946,True.intro,True.intro⟩⟩,⟨sg25949,⟨sg25948,True.intro,True.intro⟩,⟨sg25950,True.intro,True.intro⟩⟩⟩⟩,⟨sg25959,⟨sg25955,⟨sg25953,⟨sg25952,True.intro,True.intro⟩,⟨sg25954,True.intro,True.intro⟩⟩,⟨sg25957,⟨sg25956,True.intro,True.intro⟩,⟨sg25958,True.intro,True.intro⟩⟩⟩,⟨sg25963,⟨sg25961,⟨sg25960,True.intro,True.intro⟩,⟨sg25962,True.intro,True.intro⟩⟩,⟨sg25965,⟨sg25964,True.intro,True.intro⟩,⟨sg25966,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_180All : degreeTree43_180.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25983,⟨sg25975,⟨sg25971,⟨sg25969,⟨sg25968,True.intro,True.intro⟩,⟨sg25970,True.intro,True.intro⟩⟩,⟨sg25973,⟨sg25972,True.intro,True.intro⟩,⟨sg25974,True.intro,True.intro⟩⟩⟩,⟨sg25979,⟨sg25977,⟨sg25976,True.intro,True.intro⟩,⟨sg25978,True.intro,True.intro⟩⟩,⟨sg25981,⟨sg25980,True.intro,True.intro⟩,⟨sg25982,True.intro,True.intro⟩⟩⟩⟩,⟨sg25991,⟨sg25987,⟨sg25985,⟨sg25984,True.intro,True.intro⟩,⟨sg25986,True.intro,True.intro⟩⟩,⟨sg25989,⟨sg25988,True.intro,True.intro⟩,⟨sg25990,True.intro,True.intro⟩⟩⟩,⟨sg25995,⟨sg25993,⟨sg25992,True.intro,True.intro⟩,⟨sg25994,True.intro,True.intro⟩⟩,⟨sg25997,⟨sg25996,True.intro,True.intro⟩,⟨sg25998,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_181All : degreeTree43_181.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25967,degreeTree43_179All,degreeTree43_180All⟩ - -lemma degreeTree43_182All : degreeTree43_182.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25935,degreeTree43_178All,degreeTree43_181All⟩ - -lemma degreeTree43_183All : degreeTree43_183.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25870,degreeTree43_173All,degreeTree43_182All⟩ - -lemma degreeTree43_184All : degreeTree43_184.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26008,⟨sg26004,⟨sg26002,⟨sg26001,⟨sg26000,True.intro,True.intro⟩,True.intro⟩,⟨sg26003,True.intro,True.intro⟩⟩,⟨sg26006,⟨sg26005,True.intro,True.intro⟩,⟨sg26007,True.intro,True.intro⟩⟩⟩,⟨sg26012,⟨sg26010,⟨sg26009,True.intro,True.intro⟩,⟨sg26011,True.intro,True.intro⟩⟩,⟨sg26014,⟨sg26013,True.intro,True.intro⟩,⟨sg26015,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_185All : degreeTree43_185.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26024,⟨sg26020,⟨sg26018,⟨sg26017,True.intro,True.intro⟩,⟨sg26019,True.intro,True.intro⟩⟩,⟨sg26022,⟨sg26021,True.intro,True.intro⟩,⟨sg26023,True.intro,True.intro⟩⟩⟩,⟨sg26028,⟨sg26026,⟨sg26025,True.intro,True.intro⟩,⟨sg26027,True.intro,True.intro⟩⟩,⟨sg26030,⟨sg26029,True.intro,True.intro⟩,⟨sg26031,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_186All : degreeTree43_186.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26016,degreeTree43_184All,degreeTree43_185All⟩ - -lemma degreeTree43_187All : degreeTree43_187.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26048,⟨sg26040,⟨sg26036,⟨sg26034,⟨sg26033,True.intro,True.intro⟩,⟨sg26035,True.intro,True.intro⟩⟩,⟨sg26038,⟨sg26037,True.intro,True.intro⟩,⟨sg26039,True.intro,True.intro⟩⟩⟩,⟨sg26044,⟨sg26042,⟨sg26041,True.intro,True.intro⟩,⟨sg26043,True.intro,True.intro⟩⟩,⟨sg26046,⟨sg26045,True.intro,True.intro⟩,⟨sg26047,True.intro,True.intro⟩⟩⟩⟩,⟨sg26056,⟨sg26052,⟨sg26050,⟨sg26049,True.intro,True.intro⟩,⟨sg26051,True.intro,True.intro⟩⟩,⟨sg26054,⟨sg26053,True.intro,True.intro⟩,⟨sg26055,True.intro,True.intro⟩⟩⟩,⟨sg26060,⟨sg26058,⟨sg26057,True.intro,True.intro⟩,⟨sg26059,True.intro,True.intro⟩⟩,⟨sg26062,⟨sg26061,True.intro,True.intro⟩,⟨sg26063,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_188All : degreeTree43_188.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26032,degreeTree43_186All,degreeTree43_187All⟩ - -lemma degreeTree43_189All : degreeTree43_189.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26080,⟨sg26072,⟨sg26068,⟨sg26066,⟨sg26065,True.intro,True.intro⟩,⟨sg26067,True.intro,True.intro⟩⟩,⟨sg26070,⟨sg26069,True.intro,True.intro⟩,⟨sg26071,True.intro,True.intro⟩⟩⟩,⟨sg26076,⟨sg26074,⟨sg26073,True.intro,True.intro⟩,⟨sg26075,True.intro,True.intro⟩⟩,⟨sg26078,⟨sg26077,True.intro,True.intro⟩,⟨sg26079,True.intro,True.intro⟩⟩⟩⟩,⟨sg26088,⟨sg26084,⟨sg26082,⟨sg26081,True.intro,True.intro⟩,⟨sg26083,True.intro,True.intro⟩⟩,⟨sg26086,⟨sg26085,True.intro,True.intro⟩,⟨sg26087,True.intro,True.intro⟩⟩⟩,⟨sg26092,⟨sg26090,⟨sg26089,True.intro,True.intro⟩,⟨sg26091,True.intro,True.intro⟩⟩,⟨sg26094,⟨sg26093,True.intro,True.intro⟩,⟨sg26095,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_190All : degreeTree43_190.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26112,⟨sg26104,⟨sg26100,⟨sg26098,⟨sg26097,True.intro,True.intro⟩,⟨sg26099,True.intro,True.intro⟩⟩,⟨sg26102,⟨sg26101,True.intro,True.intro⟩,⟨sg26103,True.intro,True.intro⟩⟩⟩,⟨sg26108,⟨sg26106,⟨sg26105,True.intro,True.intro⟩,⟨sg26107,True.intro,True.intro⟩⟩,⟨sg26110,⟨sg26109,True.intro,True.intro⟩,⟨sg26111,True.intro,True.intro⟩⟩⟩⟩,⟨sg26120,⟨sg26116,⟨sg26114,⟨sg26113,True.intro,True.intro⟩,⟨sg26115,True.intro,True.intro⟩⟩,⟨sg26118,⟨sg26117,True.intro,True.intro⟩,⟨sg26119,True.intro,True.intro⟩⟩⟩,⟨sg26124,⟨sg26122,⟨sg26121,True.intro,True.intro⟩,⟨sg26123,True.intro,True.intro⟩⟩,⟨sg26126,⟨sg26125,True.intro,True.intro⟩,⟨sg26127,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_191All : degreeTree43_191.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26096,degreeTree43_189All,degreeTree43_190All⟩ - -lemma degreeTree43_192All : degreeTree43_192.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26064,degreeTree43_188All,degreeTree43_191All⟩ - -lemma degreeTree43_193All : degreeTree43_193.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26137,⟨sg26133,⟨sg26131,⟨sg26130,⟨sg26129,True.intro,True.intro⟩,True.intro⟩,⟨sg26132,True.intro,True.intro⟩⟩,⟨sg26135,⟨sg26134,True.intro,True.intro⟩,⟨sg26136,True.intro,True.intro⟩⟩⟩,⟨sg26141,⟨sg26139,⟨sg26138,True.intro,True.intro⟩,⟨sg26140,True.intro,True.intro⟩⟩,⟨sg26143,⟨sg26142,True.intro,True.intro⟩,⟨sg26144,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_194All : degreeTree43_194.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26153,⟨sg26149,⟨sg26147,⟨sg26146,True.intro,True.intro⟩,⟨sg26148,True.intro,True.intro⟩⟩,⟨sg26151,⟨sg26150,True.intro,True.intro⟩,⟨sg26152,True.intro,True.intro⟩⟩⟩,⟨sg26157,⟨sg26155,⟨sg26154,True.intro,True.intro⟩,⟨sg26156,True.intro,True.intro⟩⟩,⟨sg26159,⟨sg26158,True.intro,True.intro⟩,⟨sg26160,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_195All : degreeTree43_195.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26145,degreeTree43_193All,degreeTree43_194All⟩ - -lemma degreeTree43_196All : degreeTree43_196.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26177,⟨sg26169,⟨sg26165,⟨sg26163,⟨sg26162,True.intro,True.intro⟩,⟨sg26164,True.intro,True.intro⟩⟩,⟨sg26167,⟨sg26166,True.intro,True.intro⟩,⟨sg26168,True.intro,True.intro⟩⟩⟩,⟨sg26173,⟨sg26171,⟨sg26170,True.intro,True.intro⟩,⟨sg26172,True.intro,True.intro⟩⟩,⟨sg26175,⟨sg26174,True.intro,True.intro⟩,⟨sg26176,True.intro,True.intro⟩⟩⟩⟩,⟨sg26185,⟨sg26181,⟨sg26179,⟨sg26178,True.intro,True.intro⟩,⟨sg26180,True.intro,True.intro⟩⟩,⟨sg26183,⟨sg26182,True.intro,True.intro⟩,⟨sg26184,True.intro,True.intro⟩⟩⟩,⟨sg26189,⟨sg26187,⟨sg26186,True.intro,True.intro⟩,⟨sg26188,True.intro,True.intro⟩⟩,⟨sg26191,⟨sg26190,True.intro,True.intro⟩,⟨sg26192,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_197All : degreeTree43_197.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26161,degreeTree43_195All,degreeTree43_196All⟩ - -lemma degreeTree43_198All : degreeTree43_198.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26209,⟨sg26201,⟨sg26197,⟨sg26195,⟨sg26194,True.intro,True.intro⟩,⟨sg26196,True.intro,True.intro⟩⟩,⟨sg26199,⟨sg26198,True.intro,True.intro⟩,⟨sg26200,True.intro,True.intro⟩⟩⟩,⟨sg26205,⟨sg26203,⟨sg26202,True.intro,True.intro⟩,⟨sg26204,True.intro,True.intro⟩⟩,⟨sg26207,⟨sg26206,True.intro,True.intro⟩,⟨sg26208,True.intro,True.intro⟩⟩⟩⟩,⟨sg26217,⟨sg26213,⟨sg26211,⟨sg26210,True.intro,True.intro⟩,⟨sg26212,True.intro,True.intro⟩⟩,⟨sg26215,⟨sg26214,True.intro,True.intro⟩,⟨sg26216,True.intro,True.intro⟩⟩⟩,⟨sg26221,⟨sg26219,⟨sg26218,True.intro,True.intro⟩,⟨sg26220,True.intro,True.intro⟩⟩,⟨sg26223,⟨sg26222,True.intro,True.intro⟩,⟨sg26224,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_199All : degreeTree43_199.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26241,⟨sg26233,⟨sg26229,⟨sg26227,⟨sg26226,True.intro,True.intro⟩,⟨sg26228,True.intro,True.intro⟩⟩,⟨sg26231,⟨sg26230,True.intro,True.intro⟩,⟨sg26232,True.intro,True.intro⟩⟩⟩,⟨sg26237,⟨sg26235,⟨sg26234,True.intro,True.intro⟩,⟨sg26236,True.intro,True.intro⟩⟩,⟨sg26239,⟨sg26238,True.intro,True.intro⟩,⟨sg26240,True.intro,True.intro⟩⟩⟩⟩,⟨sg26249,⟨sg26245,⟨sg26243,⟨sg26242,True.intro,True.intro⟩,⟨sg26244,True.intro,True.intro⟩⟩,⟨sg26247,⟨sg26246,True.intro,True.intro⟩,⟨sg26248,True.intro,True.intro⟩⟩⟩,⟨sg26253,⟨sg26251,⟨sg26250,True.intro,True.intro⟩,⟨sg26252,True.intro,True.intro⟩⟩,⟨sg26255,⟨sg26254,True.intro,True.intro⟩,⟨sg26256,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_200All : degreeTree43_200.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26225,degreeTree43_198All,degreeTree43_199All⟩ - -lemma degreeTree43_201All : degreeTree43_201.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26193,degreeTree43_197All,degreeTree43_200All⟩ - -lemma degreeTree43_202All : degreeTree43_202.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26128,degreeTree43_192All,degreeTree43_201All⟩ - -lemma degreeTree43_203All : degreeTree43_203.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25999,degreeTree43_183All,degreeTree43_202All⟩ - -lemma degreeTree43_204All : degreeTree43_204.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26266,⟨sg26262,⟨sg26260,⟨sg26259,⟨sg26258,True.intro,True.intro⟩,True.intro⟩,⟨sg26261,True.intro,True.intro⟩⟩,⟨sg26264,⟨sg26263,True.intro,True.intro⟩,⟨sg26265,True.intro,True.intro⟩⟩⟩,⟨sg26270,⟨sg26268,⟨sg26267,True.intro,True.intro⟩,⟨sg26269,True.intro,True.intro⟩⟩,⟨sg26272,⟨sg26271,True.intro,True.intro⟩,⟨sg26273,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_205All : degreeTree43_205.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26282,⟨sg26278,⟨sg26276,⟨sg26275,True.intro,True.intro⟩,⟨sg26277,True.intro,True.intro⟩⟩,⟨sg26280,⟨sg26279,True.intro,True.intro⟩,⟨sg26281,True.intro,True.intro⟩⟩⟩,⟨sg26286,⟨sg26284,⟨sg26283,True.intro,True.intro⟩,⟨sg26285,True.intro,True.intro⟩⟩,⟨sg26288,⟨sg26287,True.intro,True.intro⟩,⟨sg26289,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_206All : degreeTree43_206.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26274,degreeTree43_204All,degreeTree43_205All⟩ - -lemma degreeTree43_207All : degreeTree43_207.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26306,⟨sg26298,⟨sg26294,⟨sg26292,⟨sg26291,True.intro,True.intro⟩,⟨sg26293,True.intro,True.intro⟩⟩,⟨sg26296,⟨sg26295,True.intro,True.intro⟩,⟨sg26297,True.intro,True.intro⟩⟩⟩,⟨sg26302,⟨sg26300,⟨sg26299,True.intro,True.intro⟩,⟨sg26301,True.intro,True.intro⟩⟩,⟨sg26304,⟨sg26303,True.intro,True.intro⟩,⟨sg26305,True.intro,True.intro⟩⟩⟩⟩,⟨sg26314,⟨sg26310,⟨sg26308,⟨sg26307,True.intro,True.intro⟩,⟨sg26309,True.intro,True.intro⟩⟩,⟨sg26312,⟨sg26311,True.intro,True.intro⟩,⟨sg26313,True.intro,True.intro⟩⟩⟩,⟨sg26318,⟨sg26316,⟨sg26315,True.intro,True.intro⟩,⟨sg26317,True.intro,True.intro⟩⟩,⟨sg26320,⟨sg26319,True.intro,True.intro⟩,⟨sg26321,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_208All : degreeTree43_208.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26290,degreeTree43_206All,degreeTree43_207All⟩ - -lemma degreeTree43_209All : degreeTree43_209.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26338,⟨sg26330,⟨sg26326,⟨sg26324,⟨sg26323,True.intro,True.intro⟩,⟨sg26325,True.intro,True.intro⟩⟩,⟨sg26328,⟨sg26327,True.intro,True.intro⟩,⟨sg26329,True.intro,True.intro⟩⟩⟩,⟨sg26334,⟨sg26332,⟨sg26331,True.intro,True.intro⟩,⟨sg26333,True.intro,True.intro⟩⟩,⟨sg26336,⟨sg26335,True.intro,True.intro⟩,⟨sg26337,True.intro,True.intro⟩⟩⟩⟩,⟨sg26346,⟨sg26342,⟨sg26340,⟨sg26339,True.intro,True.intro⟩,⟨sg26341,True.intro,True.intro⟩⟩,⟨sg26344,⟨sg26343,True.intro,True.intro⟩,⟨sg26345,True.intro,True.intro⟩⟩⟩,⟨sg26350,⟨sg26348,⟨sg26347,True.intro,True.intro⟩,⟨sg26349,True.intro,True.intro⟩⟩,⟨sg26352,⟨sg26351,True.intro,True.intro⟩,⟨sg26353,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_210All : degreeTree43_210.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26370,⟨sg26362,⟨sg26358,⟨sg26356,⟨sg26355,True.intro,True.intro⟩,⟨sg26357,True.intro,True.intro⟩⟩,⟨sg26360,⟨sg26359,True.intro,True.intro⟩,⟨sg26361,True.intro,True.intro⟩⟩⟩,⟨sg26366,⟨sg26364,⟨sg26363,True.intro,True.intro⟩,⟨sg26365,True.intro,True.intro⟩⟩,⟨sg26368,⟨sg26367,True.intro,True.intro⟩,⟨sg26369,True.intro,True.intro⟩⟩⟩⟩,⟨sg26378,⟨sg26374,⟨sg26372,⟨sg26371,True.intro,True.intro⟩,⟨sg26373,True.intro,True.intro⟩⟩,⟨sg26376,⟨sg26375,True.intro,True.intro⟩,⟨sg26377,True.intro,True.intro⟩⟩⟩,⟨sg26382,⟨sg26380,⟨sg26379,True.intro,True.intro⟩,⟨sg26381,True.intro,True.intro⟩⟩,⟨sg26384,⟨sg26383,True.intro,True.intro⟩,⟨sg26385,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_211All : degreeTree43_211.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26354,degreeTree43_209All,degreeTree43_210All⟩ - -lemma degreeTree43_212All : degreeTree43_212.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26322,degreeTree43_208All,degreeTree43_211All⟩ - -lemma degreeTree43_213All : degreeTree43_213.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26395,⟨sg26391,⟨sg26389,⟨sg26388,⟨sg26387,True.intro,True.intro⟩,True.intro⟩,⟨sg26390,True.intro,True.intro⟩⟩,⟨sg26393,⟨sg26392,True.intro,True.intro⟩,⟨sg26394,True.intro,True.intro⟩⟩⟩,⟨sg26399,⟨sg26397,⟨sg26396,True.intro,True.intro⟩,⟨sg26398,True.intro,True.intro⟩⟩,⟨sg26401,⟨sg26400,True.intro,True.intro⟩,⟨sg26402,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_214All : degreeTree43_214.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26411,⟨sg26407,⟨sg26405,⟨sg26404,True.intro,True.intro⟩,⟨sg26406,True.intro,True.intro⟩⟩,⟨sg26409,⟨sg26408,True.intro,True.intro⟩,⟨sg26410,True.intro,True.intro⟩⟩⟩,⟨sg26415,⟨sg26413,⟨sg26412,True.intro,True.intro⟩,⟨sg26414,True.intro,True.intro⟩⟩,⟨sg26417,⟨sg26416,True.intro,True.intro⟩,⟨sg26418,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_215All : degreeTree43_215.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26403,degreeTree43_213All,degreeTree43_214All⟩ - -lemma degreeTree43_216All : degreeTree43_216.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26435,⟨sg26427,⟨sg26423,⟨sg26421,⟨sg26420,True.intro,True.intro⟩,⟨sg26422,True.intro,True.intro⟩⟩,⟨sg26425,⟨sg26424,True.intro,True.intro⟩,⟨sg26426,True.intro,True.intro⟩⟩⟩,⟨sg26431,⟨sg26429,⟨sg26428,True.intro,True.intro⟩,⟨sg26430,True.intro,True.intro⟩⟩,⟨sg26433,⟨sg26432,True.intro,True.intro⟩,⟨sg26434,True.intro,True.intro⟩⟩⟩⟩,⟨sg26443,⟨sg26439,⟨sg26437,⟨sg26436,True.intro,True.intro⟩,⟨sg26438,True.intro,True.intro⟩⟩,⟨sg26441,⟨sg26440,True.intro,True.intro⟩,⟨sg26442,True.intro,True.intro⟩⟩⟩,⟨sg26447,⟨sg26445,⟨sg26444,True.intro,True.intro⟩,⟨sg26446,True.intro,True.intro⟩⟩,⟨sg26449,⟨sg26448,True.intro,True.intro⟩,⟨sg26450,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_217All : degreeTree43_217.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26419,degreeTree43_215All,degreeTree43_216All⟩ - -lemma degreeTree43_218All : degreeTree43_218.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26467,⟨sg26459,⟨sg26455,⟨sg26453,⟨sg26452,True.intro,True.intro⟩,⟨sg26454,True.intro,True.intro⟩⟩,⟨sg26457,⟨sg26456,True.intro,True.intro⟩,⟨sg26458,True.intro,True.intro⟩⟩⟩,⟨sg26463,⟨sg26461,⟨sg26460,True.intro,True.intro⟩,⟨sg26462,True.intro,True.intro⟩⟩,⟨sg26465,⟨sg26464,True.intro,True.intro⟩,⟨sg26466,True.intro,True.intro⟩⟩⟩⟩,⟨sg26475,⟨sg26471,⟨sg26469,⟨sg26468,True.intro,True.intro⟩,⟨sg26470,True.intro,True.intro⟩⟩,⟨sg26473,⟨sg26472,True.intro,True.intro⟩,⟨sg26474,True.intro,True.intro⟩⟩⟩,⟨sg26479,⟨sg26477,⟨sg26476,True.intro,True.intro⟩,⟨sg26478,True.intro,True.intro⟩⟩,⟨sg26481,⟨sg26480,True.intro,True.intro⟩,⟨sg26482,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_219All : degreeTree43_219.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26499,⟨sg26491,⟨sg26487,⟨sg26485,⟨sg26484,True.intro,True.intro⟩,⟨sg26486,True.intro,True.intro⟩⟩,⟨sg26489,⟨sg26488,True.intro,True.intro⟩,⟨sg26490,True.intro,True.intro⟩⟩⟩,⟨sg26495,⟨sg26493,⟨sg26492,True.intro,True.intro⟩,⟨sg26494,True.intro,True.intro⟩⟩,⟨sg26497,⟨sg26496,True.intro,True.intro⟩,⟨sg26498,True.intro,True.intro⟩⟩⟩⟩,⟨sg26507,⟨sg26503,⟨sg26501,⟨sg26500,True.intro,True.intro⟩,⟨sg26502,True.intro,True.intro⟩⟩,⟨sg26505,⟨sg26504,True.intro,True.intro⟩,⟨sg26506,True.intro,True.intro⟩⟩⟩,⟨sg26511,⟨sg26509,⟨sg26508,True.intro,True.intro⟩,⟨sg26510,True.intro,True.intro⟩⟩,⟨sg26513,⟨sg26512,True.intro,True.intro⟩,⟨sg26514,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_220All : degreeTree43_220.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26483,degreeTree43_218All,degreeTree43_219All⟩ - -lemma degreeTree43_221All : degreeTree43_221.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26451,degreeTree43_217All,degreeTree43_220All⟩ - -lemma degreeTree43_222All : degreeTree43_222.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26386,degreeTree43_212All,degreeTree43_221All⟩ - -lemma degreeTree43_223All : degreeTree43_223.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26524,⟨sg26520,⟨sg26518,⟨sg26517,⟨sg26516,True.intro,True.intro⟩,True.intro⟩,⟨sg26519,True.intro,True.intro⟩⟩,⟨sg26522,⟨sg26521,True.intro,True.intro⟩,⟨sg26523,True.intro,True.intro⟩⟩⟩,⟨sg26528,⟨sg26526,⟨sg26525,True.intro,True.intro⟩,⟨sg26527,True.intro,True.intro⟩⟩,⟨sg26530,⟨sg26529,True.intro,True.intro⟩,⟨sg26531,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_224All : degreeTree43_224.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26540,⟨sg26536,⟨sg26534,⟨sg26533,True.intro,True.intro⟩,⟨sg26535,True.intro,True.intro⟩⟩,⟨sg26538,⟨sg26537,True.intro,True.intro⟩,⟨sg26539,True.intro,True.intro⟩⟩⟩,⟨sg26544,⟨sg26542,⟨sg26541,True.intro,True.intro⟩,⟨sg26543,True.intro,True.intro⟩⟩,⟨sg26546,⟨sg26545,True.intro,True.intro⟩,⟨sg26547,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_225All : degreeTree43_225.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26532,degreeTree43_223All,degreeTree43_224All⟩ - -lemma degreeTree43_226All : degreeTree43_226.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26564,⟨sg26556,⟨sg26552,⟨sg26550,⟨sg26549,True.intro,True.intro⟩,⟨sg26551,True.intro,True.intro⟩⟩,⟨sg26554,⟨sg26553,True.intro,True.intro⟩,⟨sg26555,True.intro,True.intro⟩⟩⟩,⟨sg26560,⟨sg26558,⟨sg26557,True.intro,True.intro⟩,⟨sg26559,True.intro,True.intro⟩⟩,⟨sg26562,⟨sg26561,True.intro,True.intro⟩,⟨sg26563,True.intro,True.intro⟩⟩⟩⟩,⟨sg26572,⟨sg26568,⟨sg26566,⟨sg26565,True.intro,True.intro⟩,⟨sg26567,True.intro,True.intro⟩⟩,⟨sg26570,⟨sg26569,True.intro,True.intro⟩,⟨sg26571,True.intro,True.intro⟩⟩⟩,⟨sg26576,⟨sg26574,⟨sg26573,True.intro,True.intro⟩,⟨sg26575,True.intro,True.intro⟩⟩,⟨sg26578,⟨sg26577,True.intro,True.intro⟩,⟨sg26579,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_227All : degreeTree43_227.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26548,degreeTree43_225All,degreeTree43_226All⟩ - -lemma degreeTree43_228All : degreeTree43_228.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26596,⟨sg26588,⟨sg26584,⟨sg26582,⟨sg26581,True.intro,True.intro⟩,⟨sg26583,True.intro,True.intro⟩⟩,⟨sg26586,⟨sg26585,True.intro,True.intro⟩,⟨sg26587,True.intro,True.intro⟩⟩⟩,⟨sg26592,⟨sg26590,⟨sg26589,True.intro,True.intro⟩,⟨sg26591,True.intro,True.intro⟩⟩,⟨sg26594,⟨sg26593,True.intro,True.intro⟩,⟨sg26595,True.intro,True.intro⟩⟩⟩⟩,⟨sg26604,⟨sg26600,⟨sg26598,⟨sg26597,True.intro,True.intro⟩,⟨sg26599,True.intro,True.intro⟩⟩,⟨sg26602,⟨sg26601,True.intro,True.intro⟩,⟨sg26603,True.intro,True.intro⟩⟩⟩,⟨sg26608,⟨sg26606,⟨sg26605,True.intro,True.intro⟩,⟨sg26607,True.intro,True.intro⟩⟩,⟨sg26610,⟨sg26609,True.intro,True.intro⟩,⟨sg26611,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_229All : degreeTree43_229.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26628,⟨sg26620,⟨sg26616,⟨sg26614,⟨sg26613,True.intro,True.intro⟩,⟨sg26615,True.intro,True.intro⟩⟩,⟨sg26618,⟨sg26617,True.intro,True.intro⟩,⟨sg26619,True.intro,True.intro⟩⟩⟩,⟨sg26624,⟨sg26622,⟨sg26621,True.intro,True.intro⟩,⟨sg26623,True.intro,True.intro⟩⟩,⟨sg26626,⟨sg26625,True.intro,True.intro⟩,⟨sg26627,True.intro,True.intro⟩⟩⟩⟩,⟨sg26636,⟨sg26632,⟨sg26630,⟨sg26629,True.intro,True.intro⟩,⟨sg26631,True.intro,True.intro⟩⟩,⟨sg26634,⟨sg26633,True.intro,True.intro⟩,⟨sg26635,True.intro,True.intro⟩⟩⟩,⟨sg26640,⟨sg26638,⟨sg26637,True.intro,True.intro⟩,⟨sg26639,True.intro,True.intro⟩⟩,⟨sg26642,⟨sg26641,True.intro,True.intro⟩,⟨sg26643,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_230All : degreeTree43_230.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26612,degreeTree43_228All,degreeTree43_229All⟩ - -lemma degreeTree43_231All : degreeTree43_231.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26580,degreeTree43_227All,degreeTree43_230All⟩ - -lemma degreeTree43_232All : degreeTree43_232.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26653,⟨sg26649,⟨sg26647,⟨sg26646,⟨sg26645,True.intro,True.intro⟩,True.intro⟩,⟨sg26648,True.intro,True.intro⟩⟩,⟨sg26651,⟨sg26650,True.intro,True.intro⟩,⟨sg26652,True.intro,True.intro⟩⟩⟩,⟨sg26657,⟨sg26655,⟨sg26654,True.intro,True.intro⟩,⟨sg26656,True.intro,True.intro⟩⟩,⟨sg26659,⟨sg26658,True.intro,True.intro⟩,⟨sg26660,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_233All : degreeTree43_233.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26669,⟨sg26665,⟨sg26663,⟨sg26662,True.intro,True.intro⟩,⟨sg26664,True.intro,True.intro⟩⟩,⟨sg26667,⟨sg26666,True.intro,True.intro⟩,⟨sg26668,True.intro,True.intro⟩⟩⟩,⟨sg26673,⟨sg26671,⟨sg26670,True.intro,True.intro⟩,⟨sg26672,True.intro,True.intro⟩⟩,⟨sg26675,⟨sg26674,True.intro,True.intro⟩,⟨sg26676,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_234All : degreeTree43_234.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26661,degreeTree43_232All,degreeTree43_233All⟩ - -lemma degreeTree43_235All : degreeTree43_235.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26693,⟨sg26685,⟨sg26681,⟨sg26679,⟨sg26678,True.intro,True.intro⟩,⟨sg26680,True.intro,True.intro⟩⟩,⟨sg26683,⟨sg26682,True.intro,True.intro⟩,⟨sg26684,True.intro,True.intro⟩⟩⟩,⟨sg26689,⟨sg26687,⟨sg26686,True.intro,True.intro⟩,⟨sg26688,True.intro,True.intro⟩⟩,⟨sg26691,⟨sg26690,True.intro,True.intro⟩,⟨sg26692,True.intro,True.intro⟩⟩⟩⟩,⟨sg26701,⟨sg26697,⟨sg26695,⟨sg26694,True.intro,True.intro⟩,⟨sg26696,True.intro,True.intro⟩⟩,⟨sg26699,⟨sg26698,True.intro,True.intro⟩,⟨sg26700,True.intro,True.intro⟩⟩⟩,⟨sg26705,⟨sg26703,⟨sg26702,True.intro,True.intro⟩,⟨sg26704,True.intro,True.intro⟩⟩,⟨sg26707,⟨sg26706,True.intro,True.intro⟩,⟨sg26708,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_236All : degreeTree43_236.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26677,degreeTree43_234All,degreeTree43_235All⟩ - -lemma degreeTree43_237All : degreeTree43_237.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26725,⟨sg26717,⟨sg26713,⟨sg26711,⟨sg26710,True.intro,True.intro⟩,⟨sg26712,True.intro,True.intro⟩⟩,⟨sg26715,⟨sg26714,True.intro,True.intro⟩,⟨sg26716,True.intro,True.intro⟩⟩⟩,⟨sg26721,⟨sg26719,⟨sg26718,True.intro,True.intro⟩,⟨sg26720,True.intro,True.intro⟩⟩,⟨sg26723,⟨sg26722,True.intro,True.intro⟩,⟨sg26724,True.intro,True.intro⟩⟩⟩⟩,⟨sg26733,⟨sg26729,⟨sg26727,⟨sg26726,True.intro,True.intro⟩,⟨sg26728,True.intro,True.intro⟩⟩,⟨sg26731,⟨sg26730,True.intro,True.intro⟩,⟨sg26732,True.intro,True.intro⟩⟩⟩,⟨sg26737,⟨sg26735,⟨sg26734,True.intro,True.intro⟩,⟨sg26736,True.intro,True.intro⟩⟩,⟨sg26739,⟨sg26738,True.intro,True.intro⟩,⟨sg26740,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_238All : degreeTree43_238.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26757,⟨sg26749,⟨sg26745,⟨sg26743,⟨sg26742,True.intro,True.intro⟩,⟨sg26744,True.intro,True.intro⟩⟩,⟨sg26747,⟨sg26746,True.intro,True.intro⟩,⟨sg26748,True.intro,True.intro⟩⟩⟩,⟨sg26753,⟨sg26751,⟨sg26750,True.intro,True.intro⟩,⟨sg26752,True.intro,True.intro⟩⟩,⟨sg26755,⟨sg26754,True.intro,True.intro⟩,⟨sg26756,True.intro,True.intro⟩⟩⟩⟩,⟨sg26765,⟨sg26761,⟨sg26759,⟨sg26758,True.intro,True.intro⟩,⟨sg26760,True.intro,True.intro⟩⟩,⟨sg26763,⟨sg26762,True.intro,True.intro⟩,⟨sg26764,True.intro,True.intro⟩⟩⟩,⟨sg26769,⟨sg26767,⟨sg26766,True.intro,True.intro⟩,⟨sg26768,True.intro,True.intro⟩⟩,⟨sg26771,⟨sg26770,True.intro,True.intro⟩,⟨sg26772,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_239All : degreeTree43_239.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26741,degreeTree43_237All,degreeTree43_238All⟩ - -lemma degreeTree43_240All : degreeTree43_240.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26709,degreeTree43_236All,degreeTree43_239All⟩ - -lemma degreeTree43_241All : degreeTree43_241.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26644,degreeTree43_231All,degreeTree43_240All⟩ - -lemma degreeTree43_242All : degreeTree43_242.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26515,degreeTree43_222All,degreeTree43_241All⟩ - -lemma degreeTree43_243All : degreeTree43_243.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26257,degreeTree43_203All,degreeTree43_242All⟩ - -lemma degreeTree43_244All : degreeTree43_244.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26782,⟨sg26778,⟨sg26776,⟨sg26775,⟨sg26774,True.intro,True.intro⟩,True.intro⟩,⟨sg26777,True.intro,True.intro⟩⟩,⟨sg26780,⟨sg26779,True.intro,True.intro⟩,⟨sg26781,True.intro,True.intro⟩⟩⟩,⟨sg26786,⟨sg26784,⟨sg26783,True.intro,True.intro⟩,⟨sg26785,True.intro,True.intro⟩⟩,⟨sg26788,⟨sg26787,True.intro,True.intro⟩,⟨sg26789,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_245All : degreeTree43_245.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26798,⟨sg26794,⟨sg26792,⟨sg26791,True.intro,True.intro⟩,⟨sg26793,True.intro,True.intro⟩⟩,⟨sg26796,⟨sg26795,True.intro,True.intro⟩,⟨sg26797,True.intro,True.intro⟩⟩⟩,⟨sg26802,⟨sg26800,⟨sg26799,True.intro,True.intro⟩,⟨sg26801,True.intro,True.intro⟩⟩,⟨sg26804,⟨sg26803,True.intro,True.intro⟩,⟨sg26805,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_246All : degreeTree43_246.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26790,degreeTree43_244All,degreeTree43_245All⟩ - -lemma degreeTree43_247All : degreeTree43_247.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26822,⟨sg26814,⟨sg26810,⟨sg26808,⟨sg26807,True.intro,True.intro⟩,⟨sg26809,True.intro,True.intro⟩⟩,⟨sg26812,⟨sg26811,True.intro,True.intro⟩,⟨sg26813,True.intro,True.intro⟩⟩⟩,⟨sg26818,⟨sg26816,⟨sg26815,True.intro,True.intro⟩,⟨sg26817,True.intro,True.intro⟩⟩,⟨sg26820,⟨sg26819,True.intro,True.intro⟩,⟨sg26821,True.intro,True.intro⟩⟩⟩⟩,⟨sg26830,⟨sg26826,⟨sg26824,⟨sg26823,True.intro,True.intro⟩,⟨sg26825,True.intro,True.intro⟩⟩,⟨sg26828,⟨sg26827,True.intro,True.intro⟩,⟨sg26829,True.intro,True.intro⟩⟩⟩,⟨sg26834,⟨sg26832,⟨sg26831,True.intro,True.intro⟩,⟨sg26833,True.intro,True.intro⟩⟩,⟨sg26836,⟨sg26835,True.intro,True.intro⟩,⟨sg26837,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_248All : degreeTree43_248.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26806,degreeTree43_246All,degreeTree43_247All⟩ - -lemma degreeTree43_249All : degreeTree43_249.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26854,⟨sg26846,⟨sg26842,⟨sg26840,⟨sg26839,True.intro,True.intro⟩,⟨sg26841,True.intro,True.intro⟩⟩,⟨sg26844,⟨sg26843,True.intro,True.intro⟩,⟨sg26845,True.intro,True.intro⟩⟩⟩,⟨sg26850,⟨sg26848,⟨sg26847,True.intro,True.intro⟩,⟨sg26849,True.intro,True.intro⟩⟩,⟨sg26852,⟨sg26851,True.intro,True.intro⟩,⟨sg26853,True.intro,True.intro⟩⟩⟩⟩,⟨sg26862,⟨sg26858,⟨sg26856,⟨sg26855,True.intro,True.intro⟩,⟨sg26857,True.intro,True.intro⟩⟩,⟨sg26860,⟨sg26859,True.intro,True.intro⟩,⟨sg26861,True.intro,True.intro⟩⟩⟩,⟨sg26866,⟨sg26864,⟨sg26863,True.intro,True.intro⟩,⟨sg26865,True.intro,True.intro⟩⟩,⟨sg26868,⟨sg26867,True.intro,True.intro⟩,⟨sg26869,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_250All : degreeTree43_250.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26886,⟨sg26878,⟨sg26874,⟨sg26872,⟨sg26871,True.intro,True.intro⟩,⟨sg26873,True.intro,True.intro⟩⟩,⟨sg26876,⟨sg26875,True.intro,True.intro⟩,⟨sg26877,True.intro,True.intro⟩⟩⟩,⟨sg26882,⟨sg26880,⟨sg26879,True.intro,True.intro⟩,⟨sg26881,True.intro,True.intro⟩⟩,⟨sg26884,⟨sg26883,True.intro,True.intro⟩,⟨sg26885,True.intro,True.intro⟩⟩⟩⟩,⟨sg26894,⟨sg26890,⟨sg26888,⟨sg26887,True.intro,True.intro⟩,⟨sg26889,True.intro,True.intro⟩⟩,⟨sg26892,⟨sg26891,True.intro,True.intro⟩,⟨sg26893,True.intro,True.intro⟩⟩⟩,⟨sg26898,⟨sg26896,⟨sg26895,True.intro,True.intro⟩,⟨sg26897,True.intro,True.intro⟩⟩,⟨sg26900,⟨sg26899,True.intro,True.intro⟩,⟨sg26901,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_251All : degreeTree43_251.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26870,degreeTree43_249All,degreeTree43_250All⟩ - -lemma degreeTree43_252All : degreeTree43_252.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26838,degreeTree43_248All,degreeTree43_251All⟩ - -lemma degreeTree43_253All : degreeTree43_253.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26911,⟨sg26907,⟨sg26905,⟨sg26904,⟨sg26903,True.intro,True.intro⟩,True.intro⟩,⟨sg26906,True.intro,True.intro⟩⟩,⟨sg26909,⟨sg26908,True.intro,True.intro⟩,⟨sg26910,True.intro,True.intro⟩⟩⟩,⟨sg26915,⟨sg26913,⟨sg26912,True.intro,True.intro⟩,⟨sg26914,True.intro,True.intro⟩⟩,⟨sg26917,⟨sg26916,True.intro,True.intro⟩,⟨sg26918,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_254All : degreeTree43_254.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26927,⟨sg26923,⟨sg26921,⟨sg26920,True.intro,True.intro⟩,⟨sg26922,True.intro,True.intro⟩⟩,⟨sg26925,⟨sg26924,True.intro,True.intro⟩,⟨sg26926,True.intro,True.intro⟩⟩⟩,⟨sg26931,⟨sg26929,⟨sg26928,True.intro,True.intro⟩,⟨sg26930,True.intro,True.intro⟩⟩,⟨sg26933,⟨sg26932,True.intro,True.intro⟩,⟨sg26934,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_255All : degreeTree43_255.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26919,degreeTree43_253All,degreeTree43_254All⟩ - -lemma degreeTree43_256All : degreeTree43_256.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26951,⟨sg26943,⟨sg26939,⟨sg26937,⟨sg26936,True.intro,True.intro⟩,⟨sg26938,True.intro,True.intro⟩⟩,⟨sg26941,⟨sg26940,True.intro,True.intro⟩,⟨sg26942,True.intro,True.intro⟩⟩⟩,⟨sg26947,⟨sg26945,⟨sg26944,True.intro,True.intro⟩,⟨sg26946,True.intro,True.intro⟩⟩,⟨sg26949,⟨sg26948,True.intro,True.intro⟩,⟨sg26950,True.intro,True.intro⟩⟩⟩⟩,⟨sg26959,⟨sg26955,⟨sg26953,⟨sg26952,True.intro,True.intro⟩,⟨sg26954,True.intro,True.intro⟩⟩,⟨sg26957,⟨sg26956,True.intro,True.intro⟩,⟨sg26958,True.intro,True.intro⟩⟩⟩,⟨sg26963,⟨sg26961,⟨sg26960,True.intro,True.intro⟩,⟨sg26962,True.intro,True.intro⟩⟩,⟨sg26965,⟨sg26964,True.intro,True.intro⟩,⟨sg26966,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_257All : degreeTree43_257.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26935,degreeTree43_255All,degreeTree43_256All⟩ - -lemma degreeTree43_258All : degreeTree43_258.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26983,⟨sg26975,⟨sg26971,⟨sg26969,⟨sg26968,True.intro,True.intro⟩,⟨sg26970,True.intro,True.intro⟩⟩,⟨sg26973,⟨sg26972,True.intro,True.intro⟩,⟨sg26974,True.intro,True.intro⟩⟩⟩,⟨sg26979,⟨sg26977,⟨sg26976,True.intro,True.intro⟩,⟨sg26978,True.intro,True.intro⟩⟩,⟨sg26981,⟨sg26980,True.intro,True.intro⟩,⟨sg26982,True.intro,True.intro⟩⟩⟩⟩,⟨sg26991,⟨sg26987,⟨sg26985,⟨sg26984,True.intro,True.intro⟩,⟨sg26986,True.intro,True.intro⟩⟩,⟨sg26989,⟨sg26988,True.intro,True.intro⟩,⟨sg26990,True.intro,True.intro⟩⟩⟩,⟨sg26995,⟨sg26993,⟨sg26992,True.intro,True.intro⟩,⟨sg26994,True.intro,True.intro⟩⟩,⟨sg26997,⟨sg26996,True.intro,True.intro⟩,⟨sg26998,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_259All : degreeTree43_259.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27015,⟨sg27007,⟨sg27003,⟨sg27001,⟨sg27000,True.intro,True.intro⟩,⟨sg27002,True.intro,True.intro⟩⟩,⟨sg27005,⟨sg27004,True.intro,True.intro⟩,⟨sg27006,True.intro,True.intro⟩⟩⟩,⟨sg27011,⟨sg27009,⟨sg27008,True.intro,True.intro⟩,⟨sg27010,True.intro,True.intro⟩⟩,⟨sg27013,⟨sg27012,True.intro,True.intro⟩,⟨sg27014,True.intro,True.intro⟩⟩⟩⟩,⟨sg27023,⟨sg27019,⟨sg27017,⟨sg27016,True.intro,True.intro⟩,⟨sg27018,True.intro,True.intro⟩⟩,⟨sg27021,⟨sg27020,True.intro,True.intro⟩,⟨sg27022,True.intro,True.intro⟩⟩⟩,⟨sg27027,⟨sg27025,⟨sg27024,True.intro,True.intro⟩,⟨sg27026,True.intro,True.intro⟩⟩,⟨sg27029,⟨sg27028,True.intro,True.intro⟩,⟨sg27030,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_260All : degreeTree43_260.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26999,degreeTree43_258All,degreeTree43_259All⟩ - -lemma degreeTree43_261All : degreeTree43_261.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26967,degreeTree43_257All,degreeTree43_260All⟩ - -lemma degreeTree43_262All : degreeTree43_262.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26902,degreeTree43_252All,degreeTree43_261All⟩ - -lemma degreeTree43_263All : degreeTree43_263.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27040,⟨sg27036,⟨sg27034,⟨sg27033,⟨sg27032,True.intro,True.intro⟩,True.intro⟩,⟨sg27035,True.intro,True.intro⟩⟩,⟨sg27038,⟨sg27037,True.intro,True.intro⟩,⟨sg27039,True.intro,True.intro⟩⟩⟩,⟨sg27044,⟨sg27042,⟨sg27041,True.intro,True.intro⟩,⟨sg27043,True.intro,True.intro⟩⟩,⟨sg27046,⟨sg27045,True.intro,True.intro⟩,⟨sg27047,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_264All : degreeTree43_264.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27056,⟨sg27052,⟨sg27050,⟨sg27049,True.intro,True.intro⟩,⟨sg27051,True.intro,True.intro⟩⟩,⟨sg27054,⟨sg27053,True.intro,True.intro⟩,⟨sg27055,True.intro,True.intro⟩⟩⟩,⟨sg27060,⟨sg27058,⟨sg27057,True.intro,True.intro⟩,⟨sg27059,True.intro,True.intro⟩⟩,⟨sg27062,⟨sg27061,True.intro,True.intro⟩,⟨sg27063,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_265All : degreeTree43_265.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27048,degreeTree43_263All,degreeTree43_264All⟩ - -lemma degreeTree43_266All : degreeTree43_266.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27080,⟨sg27072,⟨sg27068,⟨sg27066,⟨sg27065,True.intro,True.intro⟩,⟨sg27067,True.intro,True.intro⟩⟩,⟨sg27070,⟨sg27069,True.intro,True.intro⟩,⟨sg27071,True.intro,True.intro⟩⟩⟩,⟨sg27076,⟨sg27074,⟨sg27073,True.intro,True.intro⟩,⟨sg27075,True.intro,True.intro⟩⟩,⟨sg27078,⟨sg27077,True.intro,True.intro⟩,⟨sg27079,True.intro,True.intro⟩⟩⟩⟩,⟨sg27088,⟨sg27084,⟨sg27082,⟨sg27081,True.intro,True.intro⟩,⟨sg27083,True.intro,True.intro⟩⟩,⟨sg27086,⟨sg27085,True.intro,True.intro⟩,⟨sg27087,True.intro,True.intro⟩⟩⟩,⟨sg27092,⟨sg27090,⟨sg27089,True.intro,True.intro⟩,⟨sg27091,True.intro,True.intro⟩⟩,⟨sg27094,⟨sg27093,True.intro,True.intro⟩,⟨sg27095,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_267All : degreeTree43_267.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27064,degreeTree43_265All,degreeTree43_266All⟩ - -lemma degreeTree43_268All : degreeTree43_268.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27112,⟨sg27104,⟨sg27100,⟨sg27098,⟨sg27097,True.intro,True.intro⟩,⟨sg27099,True.intro,True.intro⟩⟩,⟨sg27102,⟨sg27101,True.intro,True.intro⟩,⟨sg27103,True.intro,True.intro⟩⟩⟩,⟨sg27108,⟨sg27106,⟨sg27105,True.intro,True.intro⟩,⟨sg27107,True.intro,True.intro⟩⟩,⟨sg27110,⟨sg27109,True.intro,True.intro⟩,⟨sg27111,True.intro,True.intro⟩⟩⟩⟩,⟨sg27120,⟨sg27116,⟨sg27114,⟨sg27113,True.intro,True.intro⟩,⟨sg27115,True.intro,True.intro⟩⟩,⟨sg27118,⟨sg27117,True.intro,True.intro⟩,⟨sg27119,True.intro,True.intro⟩⟩⟩,⟨sg27124,⟨sg27122,⟨sg27121,True.intro,True.intro⟩,⟨sg27123,True.intro,True.intro⟩⟩,⟨sg27126,⟨sg27125,True.intro,True.intro⟩,⟨sg27127,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_269All : degreeTree43_269.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27144,⟨sg27136,⟨sg27132,⟨sg27130,⟨sg27129,True.intro,True.intro⟩,⟨sg27131,True.intro,True.intro⟩⟩,⟨sg27134,⟨sg27133,True.intro,True.intro⟩,⟨sg27135,True.intro,True.intro⟩⟩⟩,⟨sg27140,⟨sg27138,⟨sg27137,True.intro,True.intro⟩,⟨sg27139,True.intro,True.intro⟩⟩,⟨sg27142,⟨sg27141,True.intro,True.intro⟩,⟨sg27143,True.intro,True.intro⟩⟩⟩⟩,⟨sg27152,⟨sg27148,⟨sg27146,⟨sg27145,True.intro,True.intro⟩,⟨sg27147,True.intro,True.intro⟩⟩,⟨sg27150,⟨sg27149,True.intro,True.intro⟩,⟨sg27151,True.intro,True.intro⟩⟩⟩,⟨sg27156,⟨sg27154,⟨sg27153,True.intro,True.intro⟩,⟨sg27155,True.intro,True.intro⟩⟩,⟨sg27158,⟨sg27157,True.intro,True.intro⟩,⟨sg27159,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_270All : degreeTree43_270.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27128,degreeTree43_268All,degreeTree43_269All⟩ - -lemma degreeTree43_271All : degreeTree43_271.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27096,degreeTree43_267All,degreeTree43_270All⟩ - -lemma degreeTree43_272All : degreeTree43_272.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27169,⟨sg27165,⟨sg27163,⟨sg27162,⟨sg27161,True.intro,True.intro⟩,True.intro⟩,⟨sg27164,True.intro,True.intro⟩⟩,⟨sg27167,⟨sg27166,True.intro,True.intro⟩,⟨sg27168,True.intro,True.intro⟩⟩⟩,⟨sg27173,⟨sg27171,⟨sg27170,True.intro,True.intro⟩,⟨sg27172,True.intro,True.intro⟩⟩,⟨sg27175,⟨sg27174,True.intro,True.intro⟩,⟨sg27176,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_273All : degreeTree43_273.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27185,⟨sg27181,⟨sg27179,⟨sg27178,True.intro,True.intro⟩,⟨sg27180,True.intro,True.intro⟩⟩,⟨sg27183,⟨sg27182,True.intro,True.intro⟩,⟨sg27184,True.intro,True.intro⟩⟩⟩,⟨sg27189,⟨sg27187,⟨sg27186,True.intro,True.intro⟩,⟨sg27188,True.intro,True.intro⟩⟩,⟨sg27191,⟨sg27190,True.intro,True.intro⟩,⟨sg27192,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_274All : degreeTree43_274.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27177,degreeTree43_272All,degreeTree43_273All⟩ - -lemma degreeTree43_275All : degreeTree43_275.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27209,⟨sg27201,⟨sg27197,⟨sg27195,⟨sg27194,True.intro,True.intro⟩,⟨sg27196,True.intro,True.intro⟩⟩,⟨sg27199,⟨sg27198,True.intro,True.intro⟩,⟨sg27200,True.intro,True.intro⟩⟩⟩,⟨sg27205,⟨sg27203,⟨sg27202,True.intro,True.intro⟩,⟨sg27204,True.intro,True.intro⟩⟩,⟨sg27207,⟨sg27206,True.intro,True.intro⟩,⟨sg27208,True.intro,True.intro⟩⟩⟩⟩,⟨sg27217,⟨sg27213,⟨sg27211,⟨sg27210,True.intro,True.intro⟩,⟨sg27212,True.intro,True.intro⟩⟩,⟨sg27215,⟨sg27214,True.intro,True.intro⟩,⟨sg27216,True.intro,True.intro⟩⟩⟩,⟨sg27221,⟨sg27219,⟨sg27218,True.intro,True.intro⟩,⟨sg27220,True.intro,True.intro⟩⟩,⟨sg27223,⟨sg27222,True.intro,True.intro⟩,⟨sg27224,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_276All : degreeTree43_276.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27193,degreeTree43_274All,degreeTree43_275All⟩ - -lemma degreeTree43_277All : degreeTree43_277.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27241,⟨sg27233,⟨sg27229,⟨sg27227,⟨sg27226,True.intro,True.intro⟩,⟨sg27228,True.intro,True.intro⟩⟩,⟨sg27231,⟨sg27230,True.intro,True.intro⟩,⟨sg27232,True.intro,True.intro⟩⟩⟩,⟨sg27237,⟨sg27235,⟨sg27234,True.intro,True.intro⟩,⟨sg27236,True.intro,True.intro⟩⟩,⟨sg27239,⟨sg27238,True.intro,True.intro⟩,⟨sg27240,True.intro,True.intro⟩⟩⟩⟩,⟨sg27249,⟨sg27245,⟨sg27243,⟨sg27242,True.intro,True.intro⟩,⟨sg27244,True.intro,True.intro⟩⟩,⟨sg27247,⟨sg27246,True.intro,True.intro⟩,⟨sg27248,True.intro,True.intro⟩⟩⟩,⟨sg27253,⟨sg27251,⟨sg27250,True.intro,True.intro⟩,⟨sg27252,True.intro,True.intro⟩⟩,⟨sg27255,⟨sg27254,True.intro,True.intro⟩,⟨sg27256,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_278All : degreeTree43_278.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27273,⟨sg27265,⟨sg27261,⟨sg27259,⟨sg27258,True.intro,True.intro⟩,⟨sg27260,True.intro,True.intro⟩⟩,⟨sg27263,⟨sg27262,True.intro,True.intro⟩,⟨sg27264,True.intro,True.intro⟩⟩⟩,⟨sg27269,⟨sg27267,⟨sg27266,True.intro,True.intro⟩,⟨sg27268,True.intro,True.intro⟩⟩,⟨sg27271,⟨sg27270,True.intro,True.intro⟩,⟨sg27272,True.intro,True.intro⟩⟩⟩⟩,⟨sg27281,⟨sg27277,⟨sg27275,⟨sg27274,True.intro,True.intro⟩,⟨sg27276,True.intro,True.intro⟩⟩,⟨sg27279,⟨sg27278,True.intro,True.intro⟩,⟨sg27280,True.intro,True.intro⟩⟩⟩,⟨sg27285,⟨sg27283,⟨sg27282,True.intro,True.intro⟩,⟨sg27284,True.intro,True.intro⟩⟩,⟨sg27287,⟨sg27286,True.intro,True.intro⟩,⟨sg27288,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_279All : degreeTree43_279.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27257,degreeTree43_277All,degreeTree43_278All⟩ - -lemma degreeTree43_280All : degreeTree43_280.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27225,degreeTree43_276All,degreeTree43_279All⟩ - -lemma degreeTree43_281All : degreeTree43_281.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27160,degreeTree43_271All,degreeTree43_280All⟩ - -lemma degreeTree43_282All : degreeTree43_282.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27031,degreeTree43_262All,degreeTree43_281All⟩ - -lemma degreeTree43_283All : degreeTree43_283.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27298,⟨sg27294,⟨sg27292,⟨sg27291,⟨sg27290,True.intro,True.intro⟩,True.intro⟩,⟨sg27293,True.intro,True.intro⟩⟩,⟨sg27296,⟨sg27295,True.intro,True.intro⟩,⟨sg27297,True.intro,True.intro⟩⟩⟩,⟨sg27302,⟨sg27300,⟨sg27299,True.intro,True.intro⟩,⟨sg27301,True.intro,True.intro⟩⟩,⟨sg27304,⟨sg27303,True.intro,True.intro⟩,⟨sg27305,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_284All : degreeTree43_284.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27314,⟨sg27310,⟨sg27308,⟨sg27307,True.intro,True.intro⟩,⟨sg27309,True.intro,True.intro⟩⟩,⟨sg27312,⟨sg27311,True.intro,True.intro⟩,⟨sg27313,True.intro,True.intro⟩⟩⟩,⟨sg27318,⟨sg27316,⟨sg27315,True.intro,True.intro⟩,⟨sg27317,True.intro,True.intro⟩⟩,⟨sg27320,⟨sg27319,True.intro,True.intro⟩,⟨sg27321,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_285All : degreeTree43_285.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27306,degreeTree43_283All,degreeTree43_284All⟩ - -lemma degreeTree43_286All : degreeTree43_286.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27338,⟨sg27330,⟨sg27326,⟨sg27324,⟨sg27323,True.intro,True.intro⟩,⟨sg27325,True.intro,True.intro⟩⟩,⟨sg27328,⟨sg27327,True.intro,True.intro⟩,⟨sg27329,True.intro,True.intro⟩⟩⟩,⟨sg27334,⟨sg27332,⟨sg27331,True.intro,True.intro⟩,⟨sg27333,True.intro,True.intro⟩⟩,⟨sg27336,⟨sg27335,True.intro,True.intro⟩,⟨sg27337,True.intro,True.intro⟩⟩⟩⟩,⟨sg27346,⟨sg27342,⟨sg27340,⟨sg27339,True.intro,True.intro⟩,⟨sg27341,True.intro,True.intro⟩⟩,⟨sg27344,⟨sg27343,True.intro,True.intro⟩,⟨sg27345,True.intro,True.intro⟩⟩⟩,⟨sg27350,⟨sg27348,⟨sg27347,True.intro,True.intro⟩,⟨sg27349,True.intro,True.intro⟩⟩,⟨sg27352,⟨sg27351,True.intro,True.intro⟩,⟨sg27353,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_287All : degreeTree43_287.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27322,degreeTree43_285All,degreeTree43_286All⟩ - -lemma degreeTree43_288All : degreeTree43_288.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27370,⟨sg27362,⟨sg27358,⟨sg27356,⟨sg27355,True.intro,True.intro⟩,⟨sg27357,True.intro,True.intro⟩⟩,⟨sg27360,⟨sg27359,True.intro,True.intro⟩,⟨sg27361,True.intro,True.intro⟩⟩⟩,⟨sg27366,⟨sg27364,⟨sg27363,True.intro,True.intro⟩,⟨sg27365,True.intro,True.intro⟩⟩,⟨sg27368,⟨sg27367,True.intro,True.intro⟩,⟨sg27369,True.intro,True.intro⟩⟩⟩⟩,⟨sg27378,⟨sg27374,⟨sg27372,⟨sg27371,True.intro,True.intro⟩,⟨sg27373,True.intro,True.intro⟩⟩,⟨sg27376,⟨sg27375,True.intro,True.intro⟩,⟨sg27377,True.intro,True.intro⟩⟩⟩,⟨sg27382,⟨sg27380,⟨sg27379,True.intro,True.intro⟩,⟨sg27381,True.intro,True.intro⟩⟩,⟨sg27384,⟨sg27383,True.intro,True.intro⟩,⟨sg27385,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_289All : degreeTree43_289.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27402,⟨sg27394,⟨sg27390,⟨sg27388,⟨sg27387,True.intro,True.intro⟩,⟨sg27389,True.intro,True.intro⟩⟩,⟨sg27392,⟨sg27391,True.intro,True.intro⟩,⟨sg27393,True.intro,True.intro⟩⟩⟩,⟨sg27398,⟨sg27396,⟨sg27395,True.intro,True.intro⟩,⟨sg27397,True.intro,True.intro⟩⟩,⟨sg27400,⟨sg27399,True.intro,True.intro⟩,⟨sg27401,True.intro,True.intro⟩⟩⟩⟩,⟨sg27410,⟨sg27406,⟨sg27404,⟨sg27403,True.intro,True.intro⟩,⟨sg27405,True.intro,True.intro⟩⟩,⟨sg27408,⟨sg27407,True.intro,True.intro⟩,⟨sg27409,True.intro,True.intro⟩⟩⟩,⟨sg27414,⟨sg27412,⟨sg27411,True.intro,True.intro⟩,⟨sg27413,True.intro,True.intro⟩⟩,⟨sg27416,⟨sg27415,True.intro,True.intro⟩,⟨sg27417,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_290All : degreeTree43_290.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27386,degreeTree43_288All,degreeTree43_289All⟩ - -lemma degreeTree43_291All : degreeTree43_291.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27354,degreeTree43_287All,degreeTree43_290All⟩ - -lemma degreeTree43_292All : degreeTree43_292.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27427,⟨sg27423,⟨sg27421,⟨sg27420,⟨sg27419,True.intro,True.intro⟩,True.intro⟩,⟨sg27422,True.intro,True.intro⟩⟩,⟨sg27425,⟨sg27424,True.intro,True.intro⟩,⟨sg27426,True.intro,True.intro⟩⟩⟩,⟨sg27431,⟨sg27429,⟨sg27428,True.intro,True.intro⟩,⟨sg27430,True.intro,True.intro⟩⟩,⟨sg27433,⟨sg27432,True.intro,True.intro⟩,⟨sg27434,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_293All : degreeTree43_293.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27443,⟨sg27439,⟨sg27437,⟨sg27436,True.intro,True.intro⟩,⟨sg27438,True.intro,True.intro⟩⟩,⟨sg27441,⟨sg27440,True.intro,True.intro⟩,⟨sg27442,True.intro,True.intro⟩⟩⟩,⟨sg27447,⟨sg27445,⟨sg27444,True.intro,True.intro⟩,⟨sg27446,True.intro,True.intro⟩⟩,⟨sg27449,⟨sg27448,True.intro,True.intro⟩,⟨sg27450,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_294All : degreeTree43_294.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27435,degreeTree43_292All,degreeTree43_293All⟩ - -lemma degreeTree43_295All : degreeTree43_295.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27467,⟨sg27459,⟨sg27455,⟨sg27453,⟨sg27452,True.intro,True.intro⟩,⟨sg27454,True.intro,True.intro⟩⟩,⟨sg27457,⟨sg27456,True.intro,True.intro⟩,⟨sg27458,True.intro,True.intro⟩⟩⟩,⟨sg27463,⟨sg27461,⟨sg27460,True.intro,True.intro⟩,⟨sg27462,True.intro,True.intro⟩⟩,⟨sg27465,⟨sg27464,True.intro,True.intro⟩,⟨sg27466,True.intro,True.intro⟩⟩⟩⟩,⟨sg27475,⟨sg27471,⟨sg27469,⟨sg27468,True.intro,True.intro⟩,⟨sg27470,True.intro,True.intro⟩⟩,⟨sg27473,⟨sg27472,True.intro,True.intro⟩,⟨sg27474,True.intro,True.intro⟩⟩⟩,⟨sg27479,⟨sg27477,⟨sg27476,True.intro,True.intro⟩,⟨sg27478,True.intro,True.intro⟩⟩,⟨sg27481,⟨sg27480,True.intro,True.intro⟩,⟨sg27482,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_296All : degreeTree43_296.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27451,degreeTree43_294All,degreeTree43_295All⟩ - -lemma degreeTree43_297All : degreeTree43_297.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27499,⟨sg27491,⟨sg27487,⟨sg27485,⟨sg27484,True.intro,True.intro⟩,⟨sg27486,True.intro,True.intro⟩⟩,⟨sg27489,⟨sg27488,True.intro,True.intro⟩,⟨sg27490,True.intro,True.intro⟩⟩⟩,⟨sg27495,⟨sg27493,⟨sg27492,True.intro,True.intro⟩,⟨sg27494,True.intro,True.intro⟩⟩,⟨sg27497,⟨sg27496,True.intro,True.intro⟩,⟨sg27498,True.intro,True.intro⟩⟩⟩⟩,⟨sg27507,⟨sg27503,⟨sg27501,⟨sg27500,True.intro,True.intro⟩,⟨sg27502,True.intro,True.intro⟩⟩,⟨sg27505,⟨sg27504,True.intro,True.intro⟩,⟨sg27506,True.intro,True.intro⟩⟩⟩,⟨sg27511,⟨sg27509,⟨sg27508,True.intro,True.intro⟩,⟨sg27510,True.intro,True.intro⟩⟩,⟨sg27513,⟨sg27512,True.intro,True.intro⟩,⟨sg27514,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_298All : degreeTree43_298.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27531,⟨sg27523,⟨sg27519,⟨sg27517,⟨sg27516,True.intro,True.intro⟩,⟨sg27518,True.intro,True.intro⟩⟩,⟨sg27521,⟨sg27520,True.intro,True.intro⟩,⟨sg27522,True.intro,True.intro⟩⟩⟩,⟨sg27527,⟨sg27525,⟨sg27524,True.intro,True.intro⟩,⟨sg27526,True.intro,True.intro⟩⟩,⟨sg27529,⟨sg27528,True.intro,True.intro⟩,⟨sg27530,True.intro,True.intro⟩⟩⟩⟩,⟨sg27539,⟨sg27535,⟨sg27533,⟨sg27532,True.intro,True.intro⟩,⟨sg27534,True.intro,True.intro⟩⟩,⟨sg27537,⟨sg27536,True.intro,True.intro⟩,⟨sg27538,True.intro,True.intro⟩⟩⟩,⟨sg27543,⟨sg27541,⟨sg27540,True.intro,True.intro⟩,⟨sg27542,True.intro,True.intro⟩⟩,⟨sg27545,⟨sg27544,True.intro,True.intro⟩,⟨sg27546,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_299All : degreeTree43_299.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27515,degreeTree43_297All,degreeTree43_298All⟩ - -lemma degreeTree43_300All : degreeTree43_300.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27483,degreeTree43_296All,degreeTree43_299All⟩ - -lemma degreeTree43_301All : degreeTree43_301.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27418,degreeTree43_291All,degreeTree43_300All⟩ - -lemma degreeTree43_302All : degreeTree43_302.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27556,⟨sg27552,⟨sg27550,⟨sg27549,⟨sg27548,True.intro,True.intro⟩,True.intro⟩,⟨sg27551,True.intro,True.intro⟩⟩,⟨sg27554,⟨sg27553,True.intro,True.intro⟩,⟨sg27555,True.intro,True.intro⟩⟩⟩,⟨sg27560,⟨sg27558,⟨sg27557,True.intro,True.intro⟩,⟨sg27559,True.intro,True.intro⟩⟩,⟨sg27562,⟨sg27561,True.intro,True.intro⟩,⟨sg27563,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_303All : degreeTree43_303.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27572,⟨sg27568,⟨sg27566,⟨sg27565,True.intro,True.intro⟩,⟨sg27567,True.intro,True.intro⟩⟩,⟨sg27570,⟨sg27569,True.intro,True.intro⟩,⟨sg27571,True.intro,True.intro⟩⟩⟩,⟨sg27576,⟨sg27574,⟨sg27573,True.intro,True.intro⟩,⟨sg27575,True.intro,True.intro⟩⟩,⟨sg27578,⟨sg27577,True.intro,True.intro⟩,⟨sg27579,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_304All : degreeTree43_304.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27564,degreeTree43_302All,degreeTree43_303All⟩ - -lemma degreeTree43_305All : degreeTree43_305.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27596,⟨sg27588,⟨sg27584,⟨sg27582,⟨sg27581,True.intro,True.intro⟩,⟨sg27583,True.intro,True.intro⟩⟩,⟨sg27586,⟨sg27585,True.intro,True.intro⟩,⟨sg27587,True.intro,True.intro⟩⟩⟩,⟨sg27592,⟨sg27590,⟨sg27589,True.intro,True.intro⟩,⟨sg27591,True.intro,True.intro⟩⟩,⟨sg27594,⟨sg27593,True.intro,True.intro⟩,⟨sg27595,True.intro,True.intro⟩⟩⟩⟩,⟨sg27604,⟨sg27600,⟨sg27598,⟨sg27597,True.intro,True.intro⟩,⟨sg27599,True.intro,True.intro⟩⟩,⟨sg27602,⟨sg27601,True.intro,True.intro⟩,⟨sg27603,True.intro,True.intro⟩⟩⟩,⟨sg27608,⟨sg27606,⟨sg27605,True.intro,True.intro⟩,⟨sg27607,True.intro,True.intro⟩⟩,⟨sg27610,⟨sg27609,True.intro,True.intro⟩,⟨sg27611,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_306All : degreeTree43_306.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27580,degreeTree43_304All,degreeTree43_305All⟩ - -lemma degreeTree43_307All : degreeTree43_307.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27628,⟨sg27620,⟨sg27616,⟨sg27614,⟨sg27613,True.intro,True.intro⟩,⟨sg27615,True.intro,True.intro⟩⟩,⟨sg27618,⟨sg27617,True.intro,True.intro⟩,⟨sg27619,True.intro,True.intro⟩⟩⟩,⟨sg27624,⟨sg27622,⟨sg27621,True.intro,True.intro⟩,⟨sg27623,True.intro,True.intro⟩⟩,⟨sg27626,⟨sg27625,True.intro,True.intro⟩,⟨sg27627,True.intro,True.intro⟩⟩⟩⟩,⟨sg27636,⟨sg27632,⟨sg27630,⟨sg27629,True.intro,True.intro⟩,⟨sg27631,True.intro,True.intro⟩⟩,⟨sg27634,⟨sg27633,True.intro,True.intro⟩,⟨sg27635,True.intro,True.intro⟩⟩⟩,⟨sg27640,⟨sg27638,⟨sg27637,True.intro,True.intro⟩,⟨sg27639,True.intro,True.intro⟩⟩,⟨sg27642,⟨sg27641,True.intro,True.intro⟩,⟨sg27643,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_308All : degreeTree43_308.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27660,⟨sg27652,⟨sg27648,⟨sg27646,⟨sg27645,True.intro,True.intro⟩,⟨sg27647,True.intro,True.intro⟩⟩,⟨sg27650,⟨sg27649,True.intro,True.intro⟩,⟨sg27651,True.intro,True.intro⟩⟩⟩,⟨sg27656,⟨sg27654,⟨sg27653,True.intro,True.intro⟩,⟨sg27655,True.intro,True.intro⟩⟩,⟨sg27658,⟨sg27657,True.intro,True.intro⟩,⟨sg27659,True.intro,True.intro⟩⟩⟩⟩,⟨sg27668,⟨sg27664,⟨sg27662,⟨sg27661,True.intro,True.intro⟩,⟨sg27663,True.intro,True.intro⟩⟩,⟨sg27666,⟨sg27665,True.intro,True.intro⟩,⟨sg27667,True.intro,True.intro⟩⟩⟩,⟨sg27672,⟨sg27670,⟨sg27669,True.intro,True.intro⟩,⟨sg27671,True.intro,True.intro⟩⟩,⟨sg27674,⟨sg27673,True.intro,True.intro⟩,⟨sg27675,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_309All : degreeTree43_309.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27644,degreeTree43_307All,degreeTree43_308All⟩ - -lemma degreeTree43_310All : degreeTree43_310.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27612,degreeTree43_306All,degreeTree43_309All⟩ - -lemma degreeTree43_311All : degreeTree43_311.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27685,⟨sg27681,⟨sg27679,⟨sg27678,⟨sg27677,True.intro,True.intro⟩,True.intro⟩,⟨sg27680,True.intro,True.intro⟩⟩,⟨sg27683,⟨sg27682,True.intro,True.intro⟩,⟨sg27684,True.intro,True.intro⟩⟩⟩,⟨sg27689,⟨sg27687,⟨sg27686,True.intro,True.intro⟩,⟨sg27688,True.intro,True.intro⟩⟩,⟨sg27691,⟨sg27690,True.intro,True.intro⟩,⟨sg27692,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_312All : degreeTree43_312.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27701,⟨sg27697,⟨sg27695,⟨sg27694,True.intro,True.intro⟩,⟨sg27696,True.intro,True.intro⟩⟩,⟨sg27699,⟨sg27698,True.intro,True.intro⟩,⟨sg27700,True.intro,True.intro⟩⟩⟩,⟨sg27705,⟨sg27703,⟨sg27702,True.intro,True.intro⟩,⟨sg27704,True.intro,True.intro⟩⟩,⟨sg27707,⟨sg27706,True.intro,True.intro⟩,⟨sg27708,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_313All : degreeTree43_313.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27693,degreeTree43_311All,degreeTree43_312All⟩ - -lemma degreeTree43_314All : degreeTree43_314.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27725,⟨sg27717,⟨sg27713,⟨sg27711,⟨sg27710,True.intro,True.intro⟩,⟨sg27712,True.intro,True.intro⟩⟩,⟨sg27715,⟨sg27714,True.intro,True.intro⟩,⟨sg27716,True.intro,True.intro⟩⟩⟩,⟨sg27721,⟨sg27719,⟨sg27718,True.intro,True.intro⟩,⟨sg27720,True.intro,True.intro⟩⟩,⟨sg27723,⟨sg27722,True.intro,True.intro⟩,⟨sg27724,True.intro,True.intro⟩⟩⟩⟩,⟨sg27733,⟨sg27729,⟨sg27727,⟨sg27726,True.intro,True.intro⟩,⟨sg27728,True.intro,True.intro⟩⟩,⟨sg27731,⟨sg27730,True.intro,True.intro⟩,⟨sg27732,True.intro,True.intro⟩⟩⟩,⟨sg27737,⟨sg27735,⟨sg27734,True.intro,True.intro⟩,⟨sg27736,True.intro,True.intro⟩⟩,⟨sg27739,⟨sg27738,True.intro,True.intro⟩,⟨sg27740,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_315All : degreeTree43_315.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27709,degreeTree43_313All,degreeTree43_314All⟩ - -lemma degreeTree43_316All : degreeTree43_316.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27757,⟨sg27749,⟨sg27745,⟨sg27743,⟨sg27742,True.intro,True.intro⟩,⟨sg27744,True.intro,True.intro⟩⟩,⟨sg27747,⟨sg27746,True.intro,True.intro⟩,⟨sg27748,True.intro,True.intro⟩⟩⟩,⟨sg27753,⟨sg27751,⟨sg27750,True.intro,True.intro⟩,⟨sg27752,True.intro,True.intro⟩⟩,⟨sg27755,⟨sg27754,True.intro,True.intro⟩,⟨sg27756,True.intro,True.intro⟩⟩⟩⟩,⟨sg27765,⟨sg27761,⟨sg27759,⟨sg27758,True.intro,True.intro⟩,⟨sg27760,True.intro,True.intro⟩⟩,⟨sg27763,⟨sg27762,True.intro,True.intro⟩,⟨sg27764,True.intro,True.intro⟩⟩⟩,⟨sg27769,⟨sg27767,⟨sg27766,True.intro,True.intro⟩,⟨sg27768,True.intro,True.intro⟩⟩,⟨sg27771,⟨sg27770,True.intro,True.intro⟩,⟨sg27772,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_317All : degreeTree43_317.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27789,⟨sg27781,⟨sg27777,⟨sg27775,⟨sg27774,True.intro,True.intro⟩,⟨sg27776,True.intro,True.intro⟩⟩,⟨sg27779,⟨sg27778,True.intro,True.intro⟩,⟨sg27780,True.intro,True.intro⟩⟩⟩,⟨sg27785,⟨sg27783,⟨sg27782,True.intro,True.intro⟩,⟨sg27784,True.intro,True.intro⟩⟩,⟨sg27787,⟨sg27786,True.intro,True.intro⟩,⟨sg27788,True.intro,True.intro⟩⟩⟩⟩,⟨sg27797,⟨sg27793,⟨sg27791,⟨sg27790,True.intro,True.intro⟩,⟨sg27792,True.intro,True.intro⟩⟩,⟨sg27795,⟨sg27794,True.intro,True.intro⟩,⟨sg27796,True.intro,True.intro⟩⟩⟩,⟨sg27801,⟨sg27799,⟨sg27798,True.intro,True.intro⟩,⟨sg27800,True.intro,True.intro⟩⟩,⟨sg27803,⟨sg27802,True.intro,True.intro⟩,⟨sg27804,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_318All : degreeTree43_318.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27773,degreeTree43_316All,degreeTree43_317All⟩ - -lemma degreeTree43_319All : degreeTree43_319.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27741,degreeTree43_315All,degreeTree43_318All⟩ - -lemma degreeTree43_320All : degreeTree43_320.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27676,degreeTree43_310All,degreeTree43_319All⟩ - -lemma degreeTree43_321All : degreeTree43_321.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27547,degreeTree43_301All,degreeTree43_320All⟩ - -lemma degreeTree43_322All : degreeTree43_322.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27289,degreeTree43_282All,degreeTree43_321All⟩ - -lemma degreeTree43_323All : degreeTree43_323.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg26773,degreeTree43_243All,degreeTree43_322All⟩ - -lemma degreeTree43_324All : degreeTree43_324.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg25740,degreeTree43_162All,degreeTree43_323All⟩ - -lemma degreeTree43_325All : degreeTree43_325.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27814,⟨sg27810,⟨sg27808,⟨sg27807,⟨sg27806,True.intro,True.intro⟩,True.intro⟩,⟨sg27809,True.intro,True.intro⟩⟩,⟨sg27812,⟨sg27811,True.intro,True.intro⟩,⟨sg27813,True.intro,True.intro⟩⟩⟩,⟨sg27818,⟨sg27816,⟨sg27815,True.intro,True.intro⟩,⟨sg27817,True.intro,True.intro⟩⟩,⟨sg27820,⟨sg27819,True.intro,True.intro⟩,⟨sg27821,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_326All : degreeTree43_326.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27830,⟨sg27826,⟨sg27824,⟨sg27823,True.intro,True.intro⟩,⟨sg27825,True.intro,True.intro⟩⟩,⟨sg27828,⟨sg27827,True.intro,True.intro⟩,⟨sg27829,True.intro,True.intro⟩⟩⟩,⟨sg27834,⟨sg27832,⟨sg27831,True.intro,True.intro⟩,⟨sg27833,True.intro,True.intro⟩⟩,⟨sg27836,⟨sg27835,True.intro,True.intro⟩,⟨sg27837,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_327All : degreeTree43_327.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27822,degreeTree43_325All,degreeTree43_326All⟩ - -lemma degreeTree43_328All : degreeTree43_328.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27854,⟨sg27846,⟨sg27842,⟨sg27840,⟨sg27839,True.intro,True.intro⟩,⟨sg27841,True.intro,True.intro⟩⟩,⟨sg27844,⟨sg27843,True.intro,True.intro⟩,⟨sg27845,True.intro,True.intro⟩⟩⟩,⟨sg27850,⟨sg27848,⟨sg27847,True.intro,True.intro⟩,⟨sg27849,True.intro,True.intro⟩⟩,⟨sg27852,⟨sg27851,True.intro,True.intro⟩,⟨sg27853,True.intro,True.intro⟩⟩⟩⟩,⟨sg27862,⟨sg27858,⟨sg27856,⟨sg27855,True.intro,True.intro⟩,⟨sg27857,True.intro,True.intro⟩⟩,⟨sg27860,⟨sg27859,True.intro,True.intro⟩,⟨sg27861,True.intro,True.intro⟩⟩⟩,⟨sg27866,⟨sg27864,⟨sg27863,True.intro,True.intro⟩,⟨sg27865,True.intro,True.intro⟩⟩,⟨sg27868,⟨sg27867,True.intro,True.intro⟩,⟨sg27869,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_329All : degreeTree43_329.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27838,degreeTree43_327All,degreeTree43_328All⟩ - -lemma degreeTree43_330All : degreeTree43_330.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27879,⟨sg27875,⟨sg27873,⟨sg27872,⟨sg27871,True.intro,True.intro⟩,True.intro⟩,⟨sg27874,True.intro,True.intro⟩⟩,⟨sg27877,⟨sg27876,True.intro,True.intro⟩,⟨sg27878,True.intro,True.intro⟩⟩⟩,⟨sg27883,⟨sg27881,⟨sg27880,True.intro,True.intro⟩,⟨sg27882,True.intro,True.intro⟩⟩,⟨sg27885,⟨sg27884,True.intro,True.intro⟩,⟨sg27886,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_331All : degreeTree43_331.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27895,⟨sg27891,⟨sg27889,⟨sg27888,True.intro,True.intro⟩,⟨sg27890,True.intro,True.intro⟩⟩,⟨sg27893,⟨sg27892,True.intro,True.intro⟩,⟨sg27894,True.intro,True.intro⟩⟩⟩,⟨sg27899,⟨sg27897,⟨sg27896,True.intro,True.intro⟩,⟨sg27898,True.intro,True.intro⟩⟩,⟨sg27901,⟨sg27900,True.intro,True.intro⟩,⟨sg27902,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_332All : degreeTree43_332.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27887,degreeTree43_330All,degreeTree43_331All⟩ - -lemma degreeTree43_333All : degreeTree43_333.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27919,⟨sg27911,⟨sg27907,⟨sg27905,⟨sg27904,True.intro,True.intro⟩,⟨sg27906,True.intro,True.intro⟩⟩,⟨sg27909,⟨sg27908,True.intro,True.intro⟩,⟨sg27910,True.intro,True.intro⟩⟩⟩,⟨sg27915,⟨sg27913,⟨sg27912,True.intro,True.intro⟩,⟨sg27914,True.intro,True.intro⟩⟩,⟨sg27917,⟨sg27916,True.intro,True.intro⟩,⟨sg27918,True.intro,True.intro⟩⟩⟩⟩,⟨sg27927,⟨sg27923,⟨sg27921,⟨sg27920,True.intro,True.intro⟩,⟨sg27922,True.intro,True.intro⟩⟩,⟨sg27925,⟨sg27924,True.intro,True.intro⟩,⟨sg27926,True.intro,True.intro⟩⟩⟩,⟨sg27931,⟨sg27929,⟨sg27928,True.intro,True.intro⟩,⟨sg27930,True.intro,True.intro⟩⟩,⟨sg27933,⟨sg27932,True.intro,True.intro⟩,⟨sg27934,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_334All : degreeTree43_334.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27903,degreeTree43_332All,degreeTree43_333All⟩ - -lemma degreeTree43_335All : degreeTree43_335.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27870,degreeTree43_329All,degreeTree43_334All⟩ - -lemma degreeTree43_336All : degreeTree43_336.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27944,⟨sg27940,⟨sg27938,⟨sg27937,⟨sg27936,True.intro,True.intro⟩,True.intro⟩,⟨sg27939,True.intro,True.intro⟩⟩,⟨sg27942,⟨sg27941,True.intro,True.intro⟩,⟨sg27943,True.intro,True.intro⟩⟩⟩,⟨sg27948,⟨sg27946,⟨sg27945,True.intro,True.intro⟩,⟨sg27947,True.intro,True.intro⟩⟩,⟨sg27950,⟨sg27949,True.intro,True.intro⟩,⟨sg27951,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_337All : degreeTree43_337.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27960,⟨sg27956,⟨sg27954,⟨sg27953,True.intro,True.intro⟩,⟨sg27955,True.intro,True.intro⟩⟩,⟨sg27958,⟨sg27957,True.intro,True.intro⟩,⟨sg27959,True.intro,True.intro⟩⟩⟩,⟨sg27964,⟨sg27962,⟨sg27961,True.intro,True.intro⟩,⟨sg27963,True.intro,True.intro⟩⟩,⟨sg27966,⟨sg27965,True.intro,True.intro⟩,⟨sg27967,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_338All : degreeTree43_338.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27952,degreeTree43_336All,degreeTree43_337All⟩ - -lemma degreeTree43_339All : degreeTree43_339.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27984,⟨sg27976,⟨sg27972,⟨sg27970,⟨sg27969,True.intro,True.intro⟩,⟨sg27971,True.intro,True.intro⟩⟩,⟨sg27974,⟨sg27973,True.intro,True.intro⟩,⟨sg27975,True.intro,True.intro⟩⟩⟩,⟨sg27980,⟨sg27978,⟨sg27977,True.intro,True.intro⟩,⟨sg27979,True.intro,True.intro⟩⟩,⟨sg27982,⟨sg27981,True.intro,True.intro⟩,⟨sg27983,True.intro,True.intro⟩⟩⟩⟩,⟨sg27992,⟨sg27988,⟨sg27986,⟨sg27985,True.intro,True.intro⟩,⟨sg27987,True.intro,True.intro⟩⟩,⟨sg27990,⟨sg27989,True.intro,True.intro⟩,⟨sg27991,True.intro,True.intro⟩⟩⟩,⟨sg27996,⟨sg27994,⟨sg27993,True.intro,True.intro⟩,⟨sg27995,True.intro,True.intro⟩⟩,⟨sg27998,⟨sg27997,True.intro,True.intro⟩,⟨sg27999,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_340All : degreeTree43_340.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27968,degreeTree43_338All,degreeTree43_339All⟩ - -lemma degreeTree43_341All : degreeTree43_341.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28016,⟨sg28008,⟨sg28004,⟨sg28002,⟨sg28001,True.intro,True.intro⟩,⟨sg28003,True.intro,True.intro⟩⟩,⟨sg28006,⟨sg28005,True.intro,True.intro⟩,⟨sg28007,True.intro,True.intro⟩⟩⟩,⟨sg28012,⟨sg28010,⟨sg28009,True.intro,True.intro⟩,⟨sg28011,True.intro,True.intro⟩⟩,⟨sg28014,⟨sg28013,True.intro,True.intro⟩,⟨sg28015,True.intro,True.intro⟩⟩⟩⟩,⟨sg28024,⟨sg28020,⟨sg28018,⟨sg28017,True.intro,True.intro⟩,⟨sg28019,True.intro,True.intro⟩⟩,⟨sg28022,⟨sg28021,True.intro,True.intro⟩,⟨sg28023,True.intro,True.intro⟩⟩⟩,⟨sg28028,⟨sg28026,⟨sg28025,True.intro,True.intro⟩,⟨sg28027,True.intro,True.intro⟩⟩,⟨sg28030,⟨sg28029,True.intro,True.intro⟩,⟨sg28031,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_342All : degreeTree43_342.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28048,⟨sg28040,⟨sg28036,⟨sg28034,⟨sg28033,True.intro,True.intro⟩,⟨sg28035,True.intro,True.intro⟩⟩,⟨sg28038,⟨sg28037,True.intro,True.intro⟩,⟨sg28039,True.intro,True.intro⟩⟩⟩,⟨sg28044,⟨sg28042,⟨sg28041,True.intro,True.intro⟩,⟨sg28043,True.intro,True.intro⟩⟩,⟨sg28046,⟨sg28045,True.intro,True.intro⟩,⟨sg28047,True.intro,True.intro⟩⟩⟩⟩,⟨sg28056,⟨sg28052,⟨sg28050,⟨sg28049,True.intro,True.intro⟩,⟨sg28051,True.intro,True.intro⟩⟩,⟨sg28054,⟨sg28053,True.intro,True.intro⟩,⟨sg28055,True.intro,True.intro⟩⟩⟩,⟨sg28060,⟨sg28058,⟨sg28057,True.intro,True.intro⟩,⟨sg28059,True.intro,True.intro⟩⟩,⟨sg28062,⟨sg28061,True.intro,True.intro⟩,⟨sg28063,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_343All : degreeTree43_343.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28032,degreeTree43_341All,degreeTree43_342All⟩ - -lemma degreeTree43_344All : degreeTree43_344.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28000,degreeTree43_340All,degreeTree43_343All⟩ - -lemma degreeTree43_345All : degreeTree43_345.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27935,degreeTree43_335All,degreeTree43_344All⟩ - -lemma degreeTree43_346All : degreeTree43_346.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28073,⟨sg28069,⟨sg28067,⟨sg28066,⟨sg28065,True.intro,True.intro⟩,True.intro⟩,⟨sg28068,True.intro,True.intro⟩⟩,⟨sg28071,⟨sg28070,True.intro,True.intro⟩,⟨sg28072,True.intro,True.intro⟩⟩⟩,⟨sg28077,⟨sg28075,⟨sg28074,True.intro,True.intro⟩,⟨sg28076,True.intro,True.intro⟩⟩,⟨sg28079,⟨sg28078,True.intro,True.intro⟩,⟨sg28080,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_347All : degreeTree43_347.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28089,⟨sg28085,⟨sg28083,⟨sg28082,True.intro,True.intro⟩,⟨sg28084,True.intro,True.intro⟩⟩,⟨sg28087,⟨sg28086,True.intro,True.intro⟩,⟨sg28088,True.intro,True.intro⟩⟩⟩,⟨sg28093,⟨sg28091,⟨sg28090,True.intro,True.intro⟩,⟨sg28092,True.intro,True.intro⟩⟩,⟨sg28095,⟨sg28094,True.intro,True.intro⟩,⟨sg28096,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_348All : degreeTree43_348.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28081,degreeTree43_346All,degreeTree43_347All⟩ - -lemma degreeTree43_349All : degreeTree43_349.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28113,⟨sg28105,⟨sg28101,⟨sg28099,⟨sg28098,True.intro,True.intro⟩,⟨sg28100,True.intro,True.intro⟩⟩,⟨sg28103,⟨sg28102,True.intro,True.intro⟩,⟨sg28104,True.intro,True.intro⟩⟩⟩,⟨sg28109,⟨sg28107,⟨sg28106,True.intro,True.intro⟩,⟨sg28108,True.intro,True.intro⟩⟩,⟨sg28111,⟨sg28110,True.intro,True.intro⟩,⟨sg28112,True.intro,True.intro⟩⟩⟩⟩,⟨sg28121,⟨sg28117,⟨sg28115,⟨sg28114,True.intro,True.intro⟩,⟨sg28116,True.intro,True.intro⟩⟩,⟨sg28119,⟨sg28118,True.intro,True.intro⟩,⟨sg28120,True.intro,True.intro⟩⟩⟩,⟨sg28125,⟨sg28123,⟨sg28122,True.intro,True.intro⟩,⟨sg28124,True.intro,True.intro⟩⟩,⟨sg28127,⟨sg28126,True.intro,True.intro⟩,⟨sg28128,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_350All : degreeTree43_350.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28097,degreeTree43_348All,degreeTree43_349All⟩ - -lemma degreeTree43_351All : degreeTree43_351.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28145,⟨sg28137,⟨sg28133,⟨sg28131,⟨sg28130,True.intro,True.intro⟩,⟨sg28132,True.intro,True.intro⟩⟩,⟨sg28135,⟨sg28134,True.intro,True.intro⟩,⟨sg28136,True.intro,True.intro⟩⟩⟩,⟨sg28141,⟨sg28139,⟨sg28138,True.intro,True.intro⟩,⟨sg28140,True.intro,True.intro⟩⟩,⟨sg28143,⟨sg28142,True.intro,True.intro⟩,⟨sg28144,True.intro,True.intro⟩⟩⟩⟩,⟨sg28153,⟨sg28149,⟨sg28147,⟨sg28146,True.intro,True.intro⟩,⟨sg28148,True.intro,True.intro⟩⟩,⟨sg28151,⟨sg28150,True.intro,True.intro⟩,⟨sg28152,True.intro,True.intro⟩⟩⟩,⟨sg28157,⟨sg28155,⟨sg28154,True.intro,True.intro⟩,⟨sg28156,True.intro,True.intro⟩⟩,⟨sg28159,⟨sg28158,True.intro,True.intro⟩,⟨sg28160,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_352All : degreeTree43_352.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28177,⟨sg28169,⟨sg28165,⟨sg28163,⟨sg28162,True.intro,True.intro⟩,⟨sg28164,True.intro,True.intro⟩⟩,⟨sg28167,⟨sg28166,True.intro,True.intro⟩,⟨sg28168,True.intro,True.intro⟩⟩⟩,⟨sg28173,⟨sg28171,⟨sg28170,True.intro,True.intro⟩,⟨sg28172,True.intro,True.intro⟩⟩,⟨sg28175,⟨sg28174,True.intro,True.intro⟩,⟨sg28176,True.intro,True.intro⟩⟩⟩⟩,⟨sg28185,⟨sg28181,⟨sg28179,⟨sg28178,True.intro,True.intro⟩,⟨sg28180,True.intro,True.intro⟩⟩,⟨sg28183,⟨sg28182,True.intro,True.intro⟩,⟨sg28184,True.intro,True.intro⟩⟩⟩,⟨sg28189,⟨sg28187,⟨sg28186,True.intro,True.intro⟩,⟨sg28188,True.intro,True.intro⟩⟩,⟨sg28191,⟨sg28190,True.intro,True.intro⟩,⟨sg28192,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_353All : degreeTree43_353.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28161,degreeTree43_351All,degreeTree43_352All⟩ - -lemma degreeTree43_354All : degreeTree43_354.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28129,degreeTree43_350All,degreeTree43_353All⟩ - -lemma degreeTree43_355All : degreeTree43_355.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28202,⟨sg28198,⟨sg28196,⟨sg28195,⟨sg28194,True.intro,True.intro⟩,True.intro⟩,⟨sg28197,True.intro,True.intro⟩⟩,⟨sg28200,⟨sg28199,True.intro,True.intro⟩,⟨sg28201,True.intro,True.intro⟩⟩⟩,⟨sg28206,⟨sg28204,⟨sg28203,True.intro,True.intro⟩,⟨sg28205,True.intro,True.intro⟩⟩,⟨sg28208,⟨sg28207,True.intro,True.intro⟩,⟨sg28209,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_356All : degreeTree43_356.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28218,⟨sg28214,⟨sg28212,⟨sg28211,True.intro,True.intro⟩,⟨sg28213,True.intro,True.intro⟩⟩,⟨sg28216,⟨sg28215,True.intro,True.intro⟩,⟨sg28217,True.intro,True.intro⟩⟩⟩,⟨sg28222,⟨sg28220,⟨sg28219,True.intro,True.intro⟩,⟨sg28221,True.intro,True.intro⟩⟩,⟨sg28224,⟨sg28223,True.intro,True.intro⟩,⟨sg28225,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_357All : degreeTree43_357.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28210,degreeTree43_355All,degreeTree43_356All⟩ - -lemma degreeTree43_358All : degreeTree43_358.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28242,⟨sg28234,⟨sg28230,⟨sg28228,⟨sg28227,True.intro,True.intro⟩,⟨sg28229,True.intro,True.intro⟩⟩,⟨sg28232,⟨sg28231,True.intro,True.intro⟩,⟨sg28233,True.intro,True.intro⟩⟩⟩,⟨sg28238,⟨sg28236,⟨sg28235,True.intro,True.intro⟩,⟨sg28237,True.intro,True.intro⟩⟩,⟨sg28240,⟨sg28239,True.intro,True.intro⟩,⟨sg28241,True.intro,True.intro⟩⟩⟩⟩,⟨sg28250,⟨sg28246,⟨sg28244,⟨sg28243,True.intro,True.intro⟩,⟨sg28245,True.intro,True.intro⟩⟩,⟨sg28248,⟨sg28247,True.intro,True.intro⟩,⟨sg28249,True.intro,True.intro⟩⟩⟩,⟨sg28254,⟨sg28252,⟨sg28251,True.intro,True.intro⟩,⟨sg28253,True.intro,True.intro⟩⟩,⟨sg28256,⟨sg28255,True.intro,True.intro⟩,⟨sg28257,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_359All : degreeTree43_359.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28226,degreeTree43_357All,degreeTree43_358All⟩ - -lemma degreeTree43_360All : degreeTree43_360.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28274,⟨sg28266,⟨sg28262,⟨sg28260,⟨sg28259,True.intro,True.intro⟩,⟨sg28261,True.intro,True.intro⟩⟩,⟨sg28264,⟨sg28263,True.intro,True.intro⟩,⟨sg28265,True.intro,True.intro⟩⟩⟩,⟨sg28270,⟨sg28268,⟨sg28267,True.intro,True.intro⟩,⟨sg28269,True.intro,True.intro⟩⟩,⟨sg28272,⟨sg28271,True.intro,True.intro⟩,⟨sg28273,True.intro,True.intro⟩⟩⟩⟩,⟨sg28282,⟨sg28278,⟨sg28276,⟨sg28275,True.intro,True.intro⟩,⟨sg28277,True.intro,True.intro⟩⟩,⟨sg28280,⟨sg28279,True.intro,True.intro⟩,⟨sg28281,True.intro,True.intro⟩⟩⟩,⟨sg28286,⟨sg28284,⟨sg28283,True.intro,True.intro⟩,⟨sg28285,True.intro,True.intro⟩⟩,⟨sg28288,⟨sg28287,True.intro,True.intro⟩,⟨sg28289,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_361All : degreeTree43_361.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28306,⟨sg28298,⟨sg28294,⟨sg28292,⟨sg28291,True.intro,True.intro⟩,⟨sg28293,True.intro,True.intro⟩⟩,⟨sg28296,⟨sg28295,True.intro,True.intro⟩,⟨sg28297,True.intro,True.intro⟩⟩⟩,⟨sg28302,⟨sg28300,⟨sg28299,True.intro,True.intro⟩,⟨sg28301,True.intro,True.intro⟩⟩,⟨sg28304,⟨sg28303,True.intro,True.intro⟩,⟨sg28305,True.intro,True.intro⟩⟩⟩⟩,⟨sg28314,⟨sg28310,⟨sg28308,⟨sg28307,True.intro,True.intro⟩,⟨sg28309,True.intro,True.intro⟩⟩,⟨sg28312,⟨sg28311,True.intro,True.intro⟩,⟨sg28313,True.intro,True.intro⟩⟩⟩,⟨sg28318,⟨sg28316,⟨sg28315,True.intro,True.intro⟩,⟨sg28317,True.intro,True.intro⟩⟩,⟨sg28320,⟨sg28319,True.intro,True.intro⟩,⟨sg28321,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_362All : degreeTree43_362.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28290,degreeTree43_360All,degreeTree43_361All⟩ - -lemma degreeTree43_363All : degreeTree43_363.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28258,degreeTree43_359All,degreeTree43_362All⟩ - -lemma degreeTree43_364All : degreeTree43_364.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28193,degreeTree43_354All,degreeTree43_363All⟩ - -lemma degreeTree43_365All : degreeTree43_365.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28064,degreeTree43_345All,degreeTree43_364All⟩ - -lemma degreeTree43_366All : degreeTree43_366.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28331,⟨sg28327,⟨sg28325,⟨sg28324,⟨sg28323,True.intro,True.intro⟩,True.intro⟩,⟨sg28326,True.intro,True.intro⟩⟩,⟨sg28329,⟨sg28328,True.intro,True.intro⟩,⟨sg28330,True.intro,True.intro⟩⟩⟩,⟨sg28335,⟨sg28333,⟨sg28332,True.intro,True.intro⟩,⟨sg28334,True.intro,True.intro⟩⟩,⟨sg28337,⟨sg28336,True.intro,True.intro⟩,⟨sg28338,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_367All : degreeTree43_367.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28347,⟨sg28343,⟨sg28341,⟨sg28340,True.intro,True.intro⟩,⟨sg28342,True.intro,True.intro⟩⟩,⟨sg28345,⟨sg28344,True.intro,True.intro⟩,⟨sg28346,True.intro,True.intro⟩⟩⟩,⟨sg28351,⟨sg28349,⟨sg28348,True.intro,True.intro⟩,⟨sg28350,True.intro,True.intro⟩⟩,⟨sg28353,⟨sg28352,True.intro,True.intro⟩,⟨sg28354,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_368All : degreeTree43_368.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28339,degreeTree43_366All,degreeTree43_367All⟩ - -lemma degreeTree43_369All : degreeTree43_369.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28371,⟨sg28363,⟨sg28359,⟨sg28357,⟨sg28356,True.intro,True.intro⟩,⟨sg28358,True.intro,True.intro⟩⟩,⟨sg28361,⟨sg28360,True.intro,True.intro⟩,⟨sg28362,True.intro,True.intro⟩⟩⟩,⟨sg28367,⟨sg28365,⟨sg28364,True.intro,True.intro⟩,⟨sg28366,True.intro,True.intro⟩⟩,⟨sg28369,⟨sg28368,True.intro,True.intro⟩,⟨sg28370,True.intro,True.intro⟩⟩⟩⟩,⟨sg28379,⟨sg28375,⟨sg28373,⟨sg28372,True.intro,True.intro⟩,⟨sg28374,True.intro,True.intro⟩⟩,⟨sg28377,⟨sg28376,True.intro,True.intro⟩,⟨sg28378,True.intro,True.intro⟩⟩⟩,⟨sg28383,⟨sg28381,⟨sg28380,True.intro,True.intro⟩,⟨sg28382,True.intro,True.intro⟩⟩,⟨sg28385,⟨sg28384,True.intro,True.intro⟩,⟨sg28386,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_370All : degreeTree43_370.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28355,degreeTree43_368All,degreeTree43_369All⟩ - -lemma degreeTree43_371All : degreeTree43_371.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28403,⟨sg28395,⟨sg28391,⟨sg28389,⟨sg28388,True.intro,True.intro⟩,⟨sg28390,True.intro,True.intro⟩⟩,⟨sg28393,⟨sg28392,True.intro,True.intro⟩,⟨sg28394,True.intro,True.intro⟩⟩⟩,⟨sg28399,⟨sg28397,⟨sg28396,True.intro,True.intro⟩,⟨sg28398,True.intro,True.intro⟩⟩,⟨sg28401,⟨sg28400,True.intro,True.intro⟩,⟨sg28402,True.intro,True.intro⟩⟩⟩⟩,⟨sg28411,⟨sg28407,⟨sg28405,⟨sg28404,True.intro,True.intro⟩,⟨sg28406,True.intro,True.intro⟩⟩,⟨sg28409,⟨sg28408,True.intro,True.intro⟩,⟨sg28410,True.intro,True.intro⟩⟩⟩,⟨sg28415,⟨sg28413,⟨sg28412,True.intro,True.intro⟩,⟨sg28414,True.intro,True.intro⟩⟩,⟨sg28417,⟨sg28416,True.intro,True.intro⟩,⟨sg28418,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_372All : degreeTree43_372.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28435,⟨sg28427,⟨sg28423,⟨sg28421,⟨sg28420,True.intro,True.intro⟩,⟨sg28422,True.intro,True.intro⟩⟩,⟨sg28425,⟨sg28424,True.intro,True.intro⟩,⟨sg28426,True.intro,True.intro⟩⟩⟩,⟨sg28431,⟨sg28429,⟨sg28428,True.intro,True.intro⟩,⟨sg28430,True.intro,True.intro⟩⟩,⟨sg28433,⟨sg28432,True.intro,True.intro⟩,⟨sg28434,True.intro,True.intro⟩⟩⟩⟩,⟨sg28443,⟨sg28439,⟨sg28437,⟨sg28436,True.intro,True.intro⟩,⟨sg28438,True.intro,True.intro⟩⟩,⟨sg28441,⟨sg28440,True.intro,True.intro⟩,⟨sg28442,True.intro,True.intro⟩⟩⟩,⟨sg28447,⟨sg28445,⟨sg28444,True.intro,True.intro⟩,⟨sg28446,True.intro,True.intro⟩⟩,⟨sg28449,⟨sg28448,True.intro,True.intro⟩,⟨sg28450,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_373All : degreeTree43_373.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28419,degreeTree43_371All,degreeTree43_372All⟩ - -lemma degreeTree43_374All : degreeTree43_374.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28387,degreeTree43_370All,degreeTree43_373All⟩ - -lemma degreeTree43_375All : degreeTree43_375.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28460,⟨sg28456,⟨sg28454,⟨sg28453,⟨sg28452,True.intro,True.intro⟩,True.intro⟩,⟨sg28455,True.intro,True.intro⟩⟩,⟨sg28458,⟨sg28457,True.intro,True.intro⟩,⟨sg28459,True.intro,True.intro⟩⟩⟩,⟨sg28464,⟨sg28462,⟨sg28461,True.intro,True.intro⟩,⟨sg28463,True.intro,True.intro⟩⟩,⟨sg28466,⟨sg28465,True.intro,True.intro⟩,⟨sg28467,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_376All : degreeTree43_376.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28476,⟨sg28472,⟨sg28470,⟨sg28469,True.intro,True.intro⟩,⟨sg28471,True.intro,True.intro⟩⟩,⟨sg28474,⟨sg28473,True.intro,True.intro⟩,⟨sg28475,True.intro,True.intro⟩⟩⟩,⟨sg28480,⟨sg28478,⟨sg28477,True.intro,True.intro⟩,⟨sg28479,True.intro,True.intro⟩⟩,⟨sg28482,⟨sg28481,True.intro,True.intro⟩,⟨sg28483,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_377All : degreeTree43_377.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28468,degreeTree43_375All,degreeTree43_376All⟩ - -lemma degreeTree43_378All : degreeTree43_378.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28500,⟨sg28492,⟨sg28488,⟨sg28486,⟨sg28485,True.intro,True.intro⟩,⟨sg28487,True.intro,True.intro⟩⟩,⟨sg28490,⟨sg28489,True.intro,True.intro⟩,⟨sg28491,True.intro,True.intro⟩⟩⟩,⟨sg28496,⟨sg28494,⟨sg28493,True.intro,True.intro⟩,⟨sg28495,True.intro,True.intro⟩⟩,⟨sg28498,⟨sg28497,True.intro,True.intro⟩,⟨sg28499,True.intro,True.intro⟩⟩⟩⟩,⟨sg28508,⟨sg28504,⟨sg28502,⟨sg28501,True.intro,True.intro⟩,⟨sg28503,True.intro,True.intro⟩⟩,⟨sg28506,⟨sg28505,True.intro,True.intro⟩,⟨sg28507,True.intro,True.intro⟩⟩⟩,⟨sg28512,⟨sg28510,⟨sg28509,True.intro,True.intro⟩,⟨sg28511,True.intro,True.intro⟩⟩,⟨sg28514,⟨sg28513,True.intro,True.intro⟩,⟨sg28515,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_379All : degreeTree43_379.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28484,degreeTree43_377All,degreeTree43_378All⟩ - -lemma degreeTree43_380All : degreeTree43_380.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28532,⟨sg28524,⟨sg28520,⟨sg28518,⟨sg28517,True.intro,True.intro⟩,⟨sg28519,True.intro,True.intro⟩⟩,⟨sg28522,⟨sg28521,True.intro,True.intro⟩,⟨sg28523,True.intro,True.intro⟩⟩⟩,⟨sg28528,⟨sg28526,⟨sg28525,True.intro,True.intro⟩,⟨sg28527,True.intro,True.intro⟩⟩,⟨sg28530,⟨sg28529,True.intro,True.intro⟩,⟨sg28531,True.intro,True.intro⟩⟩⟩⟩,⟨sg28540,⟨sg28536,⟨sg28534,⟨sg28533,True.intro,True.intro⟩,⟨sg28535,True.intro,True.intro⟩⟩,⟨sg28538,⟨sg28537,True.intro,True.intro⟩,⟨sg28539,True.intro,True.intro⟩⟩⟩,⟨sg28544,⟨sg28542,⟨sg28541,True.intro,True.intro⟩,⟨sg28543,True.intro,True.intro⟩⟩,⟨sg28546,⟨sg28545,True.intro,True.intro⟩,⟨sg28547,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_381All : degreeTree43_381.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28564,⟨sg28556,⟨sg28552,⟨sg28550,⟨sg28549,True.intro,True.intro⟩,⟨sg28551,True.intro,True.intro⟩⟩,⟨sg28554,⟨sg28553,True.intro,True.intro⟩,⟨sg28555,True.intro,True.intro⟩⟩⟩,⟨sg28560,⟨sg28558,⟨sg28557,True.intro,True.intro⟩,⟨sg28559,True.intro,True.intro⟩⟩,⟨sg28562,⟨sg28561,True.intro,True.intro⟩,⟨sg28563,True.intro,True.intro⟩⟩⟩⟩,⟨sg28572,⟨sg28568,⟨sg28566,⟨sg28565,True.intro,True.intro⟩,⟨sg28567,True.intro,True.intro⟩⟩,⟨sg28570,⟨sg28569,True.intro,True.intro⟩,⟨sg28571,True.intro,True.intro⟩⟩⟩,⟨sg28576,⟨sg28574,⟨sg28573,True.intro,True.intro⟩,⟨sg28575,True.intro,True.intro⟩⟩,⟨sg28578,⟨sg28577,True.intro,True.intro⟩,⟨sg28579,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_382All : degreeTree43_382.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28548,degreeTree43_380All,degreeTree43_381All⟩ - -lemma degreeTree43_383All : degreeTree43_383.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28516,degreeTree43_379All,degreeTree43_382All⟩ - -lemma degreeTree43_384All : degreeTree43_384.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28451,degreeTree43_374All,degreeTree43_383All⟩ - -lemma degreeTree43_385All : degreeTree43_385.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28589,⟨sg28585,⟨sg28583,⟨sg28582,⟨sg28581,True.intro,True.intro⟩,True.intro⟩,⟨sg28584,True.intro,True.intro⟩⟩,⟨sg28587,⟨sg28586,True.intro,True.intro⟩,⟨sg28588,True.intro,True.intro⟩⟩⟩,⟨sg28593,⟨sg28591,⟨sg28590,True.intro,True.intro⟩,⟨sg28592,True.intro,True.intro⟩⟩,⟨sg28595,⟨sg28594,True.intro,True.intro⟩,⟨sg28596,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_386All : degreeTree43_386.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28605,⟨sg28601,⟨sg28599,⟨sg28598,True.intro,True.intro⟩,⟨sg28600,True.intro,True.intro⟩⟩,⟨sg28603,⟨sg28602,True.intro,True.intro⟩,⟨sg28604,True.intro,True.intro⟩⟩⟩,⟨sg28609,⟨sg28607,⟨sg28606,True.intro,True.intro⟩,⟨sg28608,True.intro,True.intro⟩⟩,⟨sg28611,⟨sg28610,True.intro,True.intro⟩,⟨sg28612,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_387All : degreeTree43_387.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28597,degreeTree43_385All,degreeTree43_386All⟩ - -lemma degreeTree43_388All : degreeTree43_388.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28629,⟨sg28621,⟨sg28617,⟨sg28615,⟨sg28614,True.intro,True.intro⟩,⟨sg28616,True.intro,True.intro⟩⟩,⟨sg28619,⟨sg28618,True.intro,True.intro⟩,⟨sg28620,True.intro,True.intro⟩⟩⟩,⟨sg28625,⟨sg28623,⟨sg28622,True.intro,True.intro⟩,⟨sg28624,True.intro,True.intro⟩⟩,⟨sg28627,⟨sg28626,True.intro,True.intro⟩,⟨sg28628,True.intro,True.intro⟩⟩⟩⟩,⟨sg28637,⟨sg28633,⟨sg28631,⟨sg28630,True.intro,True.intro⟩,⟨sg28632,True.intro,True.intro⟩⟩,⟨sg28635,⟨sg28634,True.intro,True.intro⟩,⟨sg28636,True.intro,True.intro⟩⟩⟩,⟨sg28641,⟨sg28639,⟨sg28638,True.intro,True.intro⟩,⟨sg28640,True.intro,True.intro⟩⟩,⟨sg28643,⟨sg28642,True.intro,True.intro⟩,⟨sg28644,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_389All : degreeTree43_389.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28613,degreeTree43_387All,degreeTree43_388All⟩ - -lemma degreeTree43_390All : degreeTree43_390.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28661,⟨sg28653,⟨sg28649,⟨sg28647,⟨sg28646,True.intro,True.intro⟩,⟨sg28648,True.intro,True.intro⟩⟩,⟨sg28651,⟨sg28650,True.intro,True.intro⟩,⟨sg28652,True.intro,True.intro⟩⟩⟩,⟨sg28657,⟨sg28655,⟨sg28654,True.intro,True.intro⟩,⟨sg28656,True.intro,True.intro⟩⟩,⟨sg28659,⟨sg28658,True.intro,True.intro⟩,⟨sg28660,True.intro,True.intro⟩⟩⟩⟩,⟨sg28669,⟨sg28665,⟨sg28663,⟨sg28662,True.intro,True.intro⟩,⟨sg28664,True.intro,True.intro⟩⟩,⟨sg28667,⟨sg28666,True.intro,True.intro⟩,⟨sg28668,True.intro,True.intro⟩⟩⟩,⟨sg28673,⟨sg28671,⟨sg28670,True.intro,True.intro⟩,⟨sg28672,True.intro,True.intro⟩⟩,⟨sg28675,⟨sg28674,True.intro,True.intro⟩,⟨sg28676,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_391All : degreeTree43_391.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28693,⟨sg28685,⟨sg28681,⟨sg28679,⟨sg28678,True.intro,True.intro⟩,⟨sg28680,True.intro,True.intro⟩⟩,⟨sg28683,⟨sg28682,True.intro,True.intro⟩,⟨sg28684,True.intro,True.intro⟩⟩⟩,⟨sg28689,⟨sg28687,⟨sg28686,True.intro,True.intro⟩,⟨sg28688,True.intro,True.intro⟩⟩,⟨sg28691,⟨sg28690,True.intro,True.intro⟩,⟨sg28692,True.intro,True.intro⟩⟩⟩⟩,⟨sg28701,⟨sg28697,⟨sg28695,⟨sg28694,True.intro,True.intro⟩,⟨sg28696,True.intro,True.intro⟩⟩,⟨sg28699,⟨sg28698,True.intro,True.intro⟩,⟨sg28700,True.intro,True.intro⟩⟩⟩,⟨sg28705,⟨sg28703,⟨sg28702,True.intro,True.intro⟩,⟨sg28704,True.intro,True.intro⟩⟩,⟨sg28707,⟨sg28706,True.intro,True.intro⟩,⟨sg28708,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_392All : degreeTree43_392.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28677,degreeTree43_390All,degreeTree43_391All⟩ - -lemma degreeTree43_393All : degreeTree43_393.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28645,degreeTree43_389All,degreeTree43_392All⟩ - -lemma degreeTree43_394All : degreeTree43_394.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28718,⟨sg28714,⟨sg28712,⟨sg28711,⟨sg28710,True.intro,True.intro⟩,True.intro⟩,⟨sg28713,True.intro,True.intro⟩⟩,⟨sg28716,⟨sg28715,True.intro,True.intro⟩,⟨sg28717,True.intro,True.intro⟩⟩⟩,⟨sg28722,⟨sg28720,⟨sg28719,True.intro,True.intro⟩,⟨sg28721,True.intro,True.intro⟩⟩,⟨sg28724,⟨sg28723,True.intro,True.intro⟩,⟨sg28725,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_395All : degreeTree43_395.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28734,⟨sg28730,⟨sg28728,⟨sg28727,True.intro,True.intro⟩,⟨sg28729,True.intro,True.intro⟩⟩,⟨sg28732,⟨sg28731,True.intro,True.intro⟩,⟨sg28733,True.intro,True.intro⟩⟩⟩,⟨sg28738,⟨sg28736,⟨sg28735,True.intro,True.intro⟩,⟨sg28737,True.intro,True.intro⟩⟩,⟨sg28740,⟨sg28739,True.intro,True.intro⟩,⟨sg28741,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_396All : degreeTree43_396.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28726,degreeTree43_394All,degreeTree43_395All⟩ - -lemma degreeTree43_397All : degreeTree43_397.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28758,⟨sg28750,⟨sg28746,⟨sg28744,⟨sg28743,True.intro,True.intro⟩,⟨sg28745,True.intro,True.intro⟩⟩,⟨sg28748,⟨sg28747,True.intro,True.intro⟩,⟨sg28749,True.intro,True.intro⟩⟩⟩,⟨sg28754,⟨sg28752,⟨sg28751,True.intro,True.intro⟩,⟨sg28753,True.intro,True.intro⟩⟩,⟨sg28756,⟨sg28755,True.intro,True.intro⟩,⟨sg28757,True.intro,True.intro⟩⟩⟩⟩,⟨sg28766,⟨sg28762,⟨sg28760,⟨sg28759,True.intro,True.intro⟩,⟨sg28761,True.intro,True.intro⟩⟩,⟨sg28764,⟨sg28763,True.intro,True.intro⟩,⟨sg28765,True.intro,True.intro⟩⟩⟩,⟨sg28770,⟨sg28768,⟨sg28767,True.intro,True.intro⟩,⟨sg28769,True.intro,True.intro⟩⟩,⟨sg28772,⟨sg28771,True.intro,True.intro⟩,⟨sg28773,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_398All : degreeTree43_398.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28742,degreeTree43_396All,degreeTree43_397All⟩ - -lemma degreeTree43_399All : degreeTree43_399.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28790,⟨sg28782,⟨sg28778,⟨sg28776,⟨sg28775,True.intro,True.intro⟩,⟨sg28777,True.intro,True.intro⟩⟩,⟨sg28780,⟨sg28779,True.intro,True.intro⟩,⟨sg28781,True.intro,True.intro⟩⟩⟩,⟨sg28786,⟨sg28784,⟨sg28783,True.intro,True.intro⟩,⟨sg28785,True.intro,True.intro⟩⟩,⟨sg28788,⟨sg28787,True.intro,True.intro⟩,⟨sg28789,True.intro,True.intro⟩⟩⟩⟩,⟨sg28798,⟨sg28794,⟨sg28792,⟨sg28791,True.intro,True.intro⟩,⟨sg28793,True.intro,True.intro⟩⟩,⟨sg28796,⟨sg28795,True.intro,True.intro⟩,⟨sg28797,True.intro,True.intro⟩⟩⟩,⟨sg28802,⟨sg28800,⟨sg28799,True.intro,True.intro⟩,⟨sg28801,True.intro,True.intro⟩⟩,⟨sg28804,⟨sg28803,True.intro,True.intro⟩,⟨sg28805,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_400All : degreeTree43_400.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28822,⟨sg28814,⟨sg28810,⟨sg28808,⟨sg28807,True.intro,True.intro⟩,⟨sg28809,True.intro,True.intro⟩⟩,⟨sg28812,⟨sg28811,True.intro,True.intro⟩,⟨sg28813,True.intro,True.intro⟩⟩⟩,⟨sg28818,⟨sg28816,⟨sg28815,True.intro,True.intro⟩,⟨sg28817,True.intro,True.intro⟩⟩,⟨sg28820,⟨sg28819,True.intro,True.intro⟩,⟨sg28821,True.intro,True.intro⟩⟩⟩⟩,⟨sg28830,⟨sg28826,⟨sg28824,⟨sg28823,True.intro,True.intro⟩,⟨sg28825,True.intro,True.intro⟩⟩,⟨sg28828,⟨sg28827,True.intro,True.intro⟩,⟨sg28829,True.intro,True.intro⟩⟩⟩,⟨sg28834,⟨sg28832,⟨sg28831,True.intro,True.intro⟩,⟨sg28833,True.intro,True.intro⟩⟩,⟨sg28836,⟨sg28835,True.intro,True.intro⟩,⟨sg28837,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_401All : degreeTree43_401.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28806,degreeTree43_399All,degreeTree43_400All⟩ - -lemma degreeTree43_402All : degreeTree43_402.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28774,degreeTree43_398All,degreeTree43_401All⟩ - -lemma degreeTree43_403All : degreeTree43_403.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28709,degreeTree43_393All,degreeTree43_402All⟩ - -lemma degreeTree43_404All : degreeTree43_404.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28580,degreeTree43_384All,degreeTree43_403All⟩ - -lemma degreeTree43_405All : degreeTree43_405.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28322,degreeTree43_365All,degreeTree43_404All⟩ - -lemma degreeTree43_406All : degreeTree43_406.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28847,⟨sg28843,⟨sg28841,⟨sg28840,⟨sg28839,True.intro,True.intro⟩,True.intro⟩,⟨sg28842,True.intro,True.intro⟩⟩,⟨sg28845,⟨sg28844,True.intro,True.intro⟩,⟨sg28846,True.intro,True.intro⟩⟩⟩,⟨sg28851,⟨sg28849,⟨sg28848,True.intro,True.intro⟩,⟨sg28850,True.intro,True.intro⟩⟩,⟨sg28853,⟨sg28852,True.intro,True.intro⟩,⟨sg28854,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_407All : degreeTree43_407.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28863,⟨sg28859,⟨sg28857,⟨sg28856,True.intro,True.intro⟩,⟨sg28858,True.intro,True.intro⟩⟩,⟨sg28861,⟨sg28860,True.intro,True.intro⟩,⟨sg28862,True.intro,True.intro⟩⟩⟩,⟨sg28867,⟨sg28865,⟨sg28864,True.intro,True.intro⟩,⟨sg28866,True.intro,True.intro⟩⟩,⟨sg28869,⟨sg28868,True.intro,True.intro⟩,⟨sg28870,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_408All : degreeTree43_408.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28855,degreeTree43_406All,degreeTree43_407All⟩ - -lemma degreeTree43_409All : degreeTree43_409.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28887,⟨sg28879,⟨sg28875,⟨sg28873,⟨sg28872,True.intro,True.intro⟩,⟨sg28874,True.intro,True.intro⟩⟩,⟨sg28877,⟨sg28876,True.intro,True.intro⟩,⟨sg28878,True.intro,True.intro⟩⟩⟩,⟨sg28883,⟨sg28881,⟨sg28880,True.intro,True.intro⟩,⟨sg28882,True.intro,True.intro⟩⟩,⟨sg28885,⟨sg28884,True.intro,True.intro⟩,⟨sg28886,True.intro,True.intro⟩⟩⟩⟩,⟨sg28895,⟨sg28891,⟨sg28889,⟨sg28888,True.intro,True.intro⟩,⟨sg28890,True.intro,True.intro⟩⟩,⟨sg28893,⟨sg28892,True.intro,True.intro⟩,⟨sg28894,True.intro,True.intro⟩⟩⟩,⟨sg28899,⟨sg28897,⟨sg28896,True.intro,True.intro⟩,⟨sg28898,True.intro,True.intro⟩⟩,⟨sg28901,⟨sg28900,True.intro,True.intro⟩,⟨sg28902,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_410All : degreeTree43_410.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28871,degreeTree43_408All,degreeTree43_409All⟩ - -lemma degreeTree43_411All : degreeTree43_411.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28919,⟨sg28911,⟨sg28907,⟨sg28905,⟨sg28904,True.intro,True.intro⟩,⟨sg28906,True.intro,True.intro⟩⟩,⟨sg28909,⟨sg28908,True.intro,True.intro⟩,⟨sg28910,True.intro,True.intro⟩⟩⟩,⟨sg28915,⟨sg28913,⟨sg28912,True.intro,True.intro⟩,⟨sg28914,True.intro,True.intro⟩⟩,⟨sg28917,⟨sg28916,True.intro,True.intro⟩,⟨sg28918,True.intro,True.intro⟩⟩⟩⟩,⟨sg28927,⟨sg28923,⟨sg28921,⟨sg28920,True.intro,True.intro⟩,⟨sg28922,True.intro,True.intro⟩⟩,⟨sg28925,⟨sg28924,True.intro,True.intro⟩,⟨sg28926,True.intro,True.intro⟩⟩⟩,⟨sg28931,⟨sg28929,⟨sg28928,True.intro,True.intro⟩,⟨sg28930,True.intro,True.intro⟩⟩,⟨sg28933,⟨sg28932,True.intro,True.intro⟩,⟨sg28934,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_412All : degreeTree43_412.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28951,⟨sg28943,⟨sg28939,⟨sg28937,⟨sg28936,True.intro,True.intro⟩,⟨sg28938,True.intro,True.intro⟩⟩,⟨sg28941,⟨sg28940,True.intro,True.intro⟩,⟨sg28942,True.intro,True.intro⟩⟩⟩,⟨sg28947,⟨sg28945,⟨sg28944,True.intro,True.intro⟩,⟨sg28946,True.intro,True.intro⟩⟩,⟨sg28949,⟨sg28948,True.intro,True.intro⟩,⟨sg28950,True.intro,True.intro⟩⟩⟩⟩,⟨sg28959,⟨sg28955,⟨sg28953,⟨sg28952,True.intro,True.intro⟩,⟨sg28954,True.intro,True.intro⟩⟩,⟨sg28957,⟨sg28956,True.intro,True.intro⟩,⟨sg28958,True.intro,True.intro⟩⟩⟩,⟨sg28963,⟨sg28961,⟨sg28960,True.intro,True.intro⟩,⟨sg28962,True.intro,True.intro⟩⟩,⟨sg28965,⟨sg28964,True.intro,True.intro⟩,⟨sg28966,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_413All : degreeTree43_413.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28935,degreeTree43_411All,degreeTree43_412All⟩ - -lemma degreeTree43_414All : degreeTree43_414.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28903,degreeTree43_410All,degreeTree43_413All⟩ - -lemma degreeTree43_415All : degreeTree43_415.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28976,⟨sg28972,⟨sg28970,⟨sg28969,⟨sg28968,True.intro,True.intro⟩,True.intro⟩,⟨sg28971,True.intro,True.intro⟩⟩,⟨sg28974,⟨sg28973,True.intro,True.intro⟩,⟨sg28975,True.intro,True.intro⟩⟩⟩,⟨sg28980,⟨sg28978,⟨sg28977,True.intro,True.intro⟩,⟨sg28979,True.intro,True.intro⟩⟩,⟨sg28982,⟨sg28981,True.intro,True.intro⟩,⟨sg28983,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_416All : degreeTree43_416.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28992,⟨sg28988,⟨sg28986,⟨sg28985,True.intro,True.intro⟩,⟨sg28987,True.intro,True.intro⟩⟩,⟨sg28990,⟨sg28989,True.intro,True.intro⟩,⟨sg28991,True.intro,True.intro⟩⟩⟩,⟨sg28996,⟨sg28994,⟨sg28993,True.intro,True.intro⟩,⟨sg28995,True.intro,True.intro⟩⟩,⟨sg28998,⟨sg28997,True.intro,True.intro⟩,⟨sg28999,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_417All : degreeTree43_417.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28984,degreeTree43_415All,degreeTree43_416All⟩ - -lemma degreeTree43_418All : degreeTree43_418.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29016,⟨sg29008,⟨sg29004,⟨sg29002,⟨sg29001,True.intro,True.intro⟩,⟨sg29003,True.intro,True.intro⟩⟩,⟨sg29006,⟨sg29005,True.intro,True.intro⟩,⟨sg29007,True.intro,True.intro⟩⟩⟩,⟨sg29012,⟨sg29010,⟨sg29009,True.intro,True.intro⟩,⟨sg29011,True.intro,True.intro⟩⟩,⟨sg29014,⟨sg29013,True.intro,True.intro⟩,⟨sg29015,True.intro,True.intro⟩⟩⟩⟩,⟨sg29024,⟨sg29020,⟨sg29018,⟨sg29017,True.intro,True.intro⟩,⟨sg29019,True.intro,True.intro⟩⟩,⟨sg29022,⟨sg29021,True.intro,True.intro⟩,⟨sg29023,True.intro,True.intro⟩⟩⟩,⟨sg29028,⟨sg29026,⟨sg29025,True.intro,True.intro⟩,⟨sg29027,True.intro,True.intro⟩⟩,⟨sg29030,⟨sg29029,True.intro,True.intro⟩,⟨sg29031,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_419All : degreeTree43_419.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29000,degreeTree43_417All,degreeTree43_418All⟩ - -lemma degreeTree43_420All : degreeTree43_420.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29048,⟨sg29040,⟨sg29036,⟨sg29034,⟨sg29033,True.intro,True.intro⟩,⟨sg29035,True.intro,True.intro⟩⟩,⟨sg29038,⟨sg29037,True.intro,True.intro⟩,⟨sg29039,True.intro,True.intro⟩⟩⟩,⟨sg29044,⟨sg29042,⟨sg29041,True.intro,True.intro⟩,⟨sg29043,True.intro,True.intro⟩⟩,⟨sg29046,⟨sg29045,True.intro,True.intro⟩,⟨sg29047,True.intro,True.intro⟩⟩⟩⟩,⟨sg29056,⟨sg29052,⟨sg29050,⟨sg29049,True.intro,True.intro⟩,⟨sg29051,True.intro,True.intro⟩⟩,⟨sg29054,⟨sg29053,True.intro,True.intro⟩,⟨sg29055,True.intro,True.intro⟩⟩⟩,⟨sg29060,⟨sg29058,⟨sg29057,True.intro,True.intro⟩,⟨sg29059,True.intro,True.intro⟩⟩,⟨sg29062,⟨sg29061,True.intro,True.intro⟩,⟨sg29063,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_421All : degreeTree43_421.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29080,⟨sg29072,⟨sg29068,⟨sg29066,⟨sg29065,True.intro,True.intro⟩,⟨sg29067,True.intro,True.intro⟩⟩,⟨sg29070,⟨sg29069,True.intro,True.intro⟩,⟨sg29071,True.intro,True.intro⟩⟩⟩,⟨sg29076,⟨sg29074,⟨sg29073,True.intro,True.intro⟩,⟨sg29075,True.intro,True.intro⟩⟩,⟨sg29078,⟨sg29077,True.intro,True.intro⟩,⟨sg29079,True.intro,True.intro⟩⟩⟩⟩,⟨sg29088,⟨sg29084,⟨sg29082,⟨sg29081,True.intro,True.intro⟩,⟨sg29083,True.intro,True.intro⟩⟩,⟨sg29086,⟨sg29085,True.intro,True.intro⟩,⟨sg29087,True.intro,True.intro⟩⟩⟩,⟨sg29092,⟨sg29090,⟨sg29089,True.intro,True.intro⟩,⟨sg29091,True.intro,True.intro⟩⟩,⟨sg29094,⟨sg29093,True.intro,True.intro⟩,⟨sg29095,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_422All : degreeTree43_422.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29064,degreeTree43_420All,degreeTree43_421All⟩ - -lemma degreeTree43_423All : degreeTree43_423.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29032,degreeTree43_419All,degreeTree43_422All⟩ - -lemma degreeTree43_424All : degreeTree43_424.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28967,degreeTree43_414All,degreeTree43_423All⟩ - -lemma degreeTree43_425All : degreeTree43_425.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29105,⟨sg29101,⟨sg29099,⟨sg29098,⟨sg29097,True.intro,True.intro⟩,True.intro⟩,⟨sg29100,True.intro,True.intro⟩⟩,⟨sg29103,⟨sg29102,True.intro,True.intro⟩,⟨sg29104,True.intro,True.intro⟩⟩⟩,⟨sg29109,⟨sg29107,⟨sg29106,True.intro,True.intro⟩,⟨sg29108,True.intro,True.intro⟩⟩,⟨sg29111,⟨sg29110,True.intro,True.intro⟩,⟨sg29112,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_426All : degreeTree43_426.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29121,⟨sg29117,⟨sg29115,⟨sg29114,True.intro,True.intro⟩,⟨sg29116,True.intro,True.intro⟩⟩,⟨sg29119,⟨sg29118,True.intro,True.intro⟩,⟨sg29120,True.intro,True.intro⟩⟩⟩,⟨sg29125,⟨sg29123,⟨sg29122,True.intro,True.intro⟩,⟨sg29124,True.intro,True.intro⟩⟩,⟨sg29127,⟨sg29126,True.intro,True.intro⟩,⟨sg29128,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_427All : degreeTree43_427.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29113,degreeTree43_425All,degreeTree43_426All⟩ - -lemma degreeTree43_428All : degreeTree43_428.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29145,⟨sg29137,⟨sg29133,⟨sg29131,⟨sg29130,True.intro,True.intro⟩,⟨sg29132,True.intro,True.intro⟩⟩,⟨sg29135,⟨sg29134,True.intro,True.intro⟩,⟨sg29136,True.intro,True.intro⟩⟩⟩,⟨sg29141,⟨sg29139,⟨sg29138,True.intro,True.intro⟩,⟨sg29140,True.intro,True.intro⟩⟩,⟨sg29143,⟨sg29142,True.intro,True.intro⟩,⟨sg29144,True.intro,True.intro⟩⟩⟩⟩,⟨sg29153,⟨sg29149,⟨sg29147,⟨sg29146,True.intro,True.intro⟩,⟨sg29148,True.intro,True.intro⟩⟩,⟨sg29151,⟨sg29150,True.intro,True.intro⟩,⟨sg29152,True.intro,True.intro⟩⟩⟩,⟨sg29157,⟨sg29155,⟨sg29154,True.intro,True.intro⟩,⟨sg29156,True.intro,True.intro⟩⟩,⟨sg29159,⟨sg29158,True.intro,True.intro⟩,⟨sg29160,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_429All : degreeTree43_429.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29129,degreeTree43_427All,degreeTree43_428All⟩ - -lemma degreeTree43_430All : degreeTree43_430.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29177,⟨sg29169,⟨sg29165,⟨sg29163,⟨sg29162,True.intro,True.intro⟩,⟨sg29164,True.intro,True.intro⟩⟩,⟨sg29167,⟨sg29166,True.intro,True.intro⟩,⟨sg29168,True.intro,True.intro⟩⟩⟩,⟨sg29173,⟨sg29171,⟨sg29170,True.intro,True.intro⟩,⟨sg29172,True.intro,True.intro⟩⟩,⟨sg29175,⟨sg29174,True.intro,True.intro⟩,⟨sg29176,True.intro,True.intro⟩⟩⟩⟩,⟨sg29185,⟨sg29181,⟨sg29179,⟨sg29178,True.intro,True.intro⟩,⟨sg29180,True.intro,True.intro⟩⟩,⟨sg29183,⟨sg29182,True.intro,True.intro⟩,⟨sg29184,True.intro,True.intro⟩⟩⟩,⟨sg29189,⟨sg29187,⟨sg29186,True.intro,True.intro⟩,⟨sg29188,True.intro,True.intro⟩⟩,⟨sg29191,⟨sg29190,True.intro,True.intro⟩,⟨sg29192,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_431All : degreeTree43_431.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29209,⟨sg29201,⟨sg29197,⟨sg29195,⟨sg29194,True.intro,True.intro⟩,⟨sg29196,True.intro,True.intro⟩⟩,⟨sg29199,⟨sg29198,True.intro,True.intro⟩,⟨sg29200,True.intro,True.intro⟩⟩⟩,⟨sg29205,⟨sg29203,⟨sg29202,True.intro,True.intro⟩,⟨sg29204,True.intro,True.intro⟩⟩,⟨sg29207,⟨sg29206,True.intro,True.intro⟩,⟨sg29208,True.intro,True.intro⟩⟩⟩⟩,⟨sg29217,⟨sg29213,⟨sg29211,⟨sg29210,True.intro,True.intro⟩,⟨sg29212,True.intro,True.intro⟩⟩,⟨sg29215,⟨sg29214,True.intro,True.intro⟩,⟨sg29216,True.intro,True.intro⟩⟩⟩,⟨sg29221,⟨sg29219,⟨sg29218,True.intro,True.intro⟩,⟨sg29220,True.intro,True.intro⟩⟩,⟨sg29223,⟨sg29222,True.intro,True.intro⟩,⟨sg29224,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_432All : degreeTree43_432.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29193,degreeTree43_430All,degreeTree43_431All⟩ - -lemma degreeTree43_433All : degreeTree43_433.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29161,degreeTree43_429All,degreeTree43_432All⟩ - -lemma degreeTree43_434All : degreeTree43_434.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29234,⟨sg29230,⟨sg29228,⟨sg29227,⟨sg29226,True.intro,True.intro⟩,True.intro⟩,⟨sg29229,True.intro,True.intro⟩⟩,⟨sg29232,⟨sg29231,True.intro,True.intro⟩,⟨sg29233,True.intro,True.intro⟩⟩⟩,⟨sg29238,⟨sg29236,⟨sg29235,True.intro,True.intro⟩,⟨sg29237,True.intro,True.intro⟩⟩,⟨sg29240,⟨sg29239,True.intro,True.intro⟩,⟨sg29241,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_435All : degreeTree43_435.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29250,⟨sg29246,⟨sg29244,⟨sg29243,True.intro,True.intro⟩,⟨sg29245,True.intro,True.intro⟩⟩,⟨sg29248,⟨sg29247,True.intro,True.intro⟩,⟨sg29249,True.intro,True.intro⟩⟩⟩,⟨sg29254,⟨sg29252,⟨sg29251,True.intro,True.intro⟩,⟨sg29253,True.intro,True.intro⟩⟩,⟨sg29256,⟨sg29255,True.intro,True.intro⟩,⟨sg29257,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_436All : degreeTree43_436.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29242,degreeTree43_434All,degreeTree43_435All⟩ - -lemma degreeTree43_437All : degreeTree43_437.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29274,⟨sg29266,⟨sg29262,⟨sg29260,⟨sg29259,True.intro,True.intro⟩,⟨sg29261,True.intro,True.intro⟩⟩,⟨sg29264,⟨sg29263,True.intro,True.intro⟩,⟨sg29265,True.intro,True.intro⟩⟩⟩,⟨sg29270,⟨sg29268,⟨sg29267,True.intro,True.intro⟩,⟨sg29269,True.intro,True.intro⟩⟩,⟨sg29272,⟨sg29271,True.intro,True.intro⟩,⟨sg29273,True.intro,True.intro⟩⟩⟩⟩,⟨sg29282,⟨sg29278,⟨sg29276,⟨sg29275,True.intro,True.intro⟩,⟨sg29277,True.intro,True.intro⟩⟩,⟨sg29280,⟨sg29279,True.intro,True.intro⟩,⟨sg29281,True.intro,True.intro⟩⟩⟩,⟨sg29286,⟨sg29284,⟨sg29283,True.intro,True.intro⟩,⟨sg29285,True.intro,True.intro⟩⟩,⟨sg29288,⟨sg29287,True.intro,True.intro⟩,⟨sg29289,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_438All : degreeTree43_438.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29258,degreeTree43_436All,degreeTree43_437All⟩ - -lemma degreeTree43_439All : degreeTree43_439.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29306,⟨sg29298,⟨sg29294,⟨sg29292,⟨sg29291,True.intro,True.intro⟩,⟨sg29293,True.intro,True.intro⟩⟩,⟨sg29296,⟨sg29295,True.intro,True.intro⟩,⟨sg29297,True.intro,True.intro⟩⟩⟩,⟨sg29302,⟨sg29300,⟨sg29299,True.intro,True.intro⟩,⟨sg29301,True.intro,True.intro⟩⟩,⟨sg29304,⟨sg29303,True.intro,True.intro⟩,⟨sg29305,True.intro,True.intro⟩⟩⟩⟩,⟨sg29314,⟨sg29310,⟨sg29308,⟨sg29307,True.intro,True.intro⟩,⟨sg29309,True.intro,True.intro⟩⟩,⟨sg29312,⟨sg29311,True.intro,True.intro⟩,⟨sg29313,True.intro,True.intro⟩⟩⟩,⟨sg29318,⟨sg29316,⟨sg29315,True.intro,True.intro⟩,⟨sg29317,True.intro,True.intro⟩⟩,⟨sg29320,⟨sg29319,True.intro,True.intro⟩,⟨sg29321,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_440All : degreeTree43_440.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29338,⟨sg29330,⟨sg29326,⟨sg29324,⟨sg29323,True.intro,True.intro⟩,⟨sg29325,True.intro,True.intro⟩⟩,⟨sg29328,⟨sg29327,True.intro,True.intro⟩,⟨sg29329,True.intro,True.intro⟩⟩⟩,⟨sg29334,⟨sg29332,⟨sg29331,True.intro,True.intro⟩,⟨sg29333,True.intro,True.intro⟩⟩,⟨sg29336,⟨sg29335,True.intro,True.intro⟩,⟨sg29337,True.intro,True.intro⟩⟩⟩⟩,⟨sg29346,⟨sg29342,⟨sg29340,⟨sg29339,True.intro,True.intro⟩,⟨sg29341,True.intro,True.intro⟩⟩,⟨sg29344,⟨sg29343,True.intro,True.intro⟩,⟨sg29345,True.intro,True.intro⟩⟩⟩,⟨sg29350,⟨sg29348,⟨sg29347,True.intro,True.intro⟩,⟨sg29349,True.intro,True.intro⟩⟩,⟨sg29352,⟨sg29351,True.intro,True.intro⟩,⟨sg29353,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_441All : degreeTree43_441.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29322,degreeTree43_439All,degreeTree43_440All⟩ - -lemma degreeTree43_442All : degreeTree43_442.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29290,degreeTree43_438All,degreeTree43_441All⟩ - -lemma degreeTree43_443All : degreeTree43_443.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29225,degreeTree43_433All,degreeTree43_442All⟩ - -lemma degreeTree43_444All : degreeTree43_444.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29096,degreeTree43_424All,degreeTree43_443All⟩ - -lemma degreeTree43_445All : degreeTree43_445.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29363,⟨sg29359,⟨sg29357,⟨sg29356,⟨sg29355,True.intro,True.intro⟩,True.intro⟩,⟨sg29358,True.intro,True.intro⟩⟩,⟨sg29361,⟨sg29360,True.intro,True.intro⟩,⟨sg29362,True.intro,True.intro⟩⟩⟩,⟨sg29367,⟨sg29365,⟨sg29364,True.intro,True.intro⟩,⟨sg29366,True.intro,True.intro⟩⟩,⟨sg29369,⟨sg29368,True.intro,True.intro⟩,⟨sg29370,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_446All : degreeTree43_446.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29379,⟨sg29375,⟨sg29373,⟨sg29372,True.intro,True.intro⟩,⟨sg29374,True.intro,True.intro⟩⟩,⟨sg29377,⟨sg29376,True.intro,True.intro⟩,⟨sg29378,True.intro,True.intro⟩⟩⟩,⟨sg29383,⟨sg29381,⟨sg29380,True.intro,True.intro⟩,⟨sg29382,True.intro,True.intro⟩⟩,⟨sg29385,⟨sg29384,True.intro,True.intro⟩,⟨sg29386,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_447All : degreeTree43_447.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29371,degreeTree43_445All,degreeTree43_446All⟩ - -lemma degreeTree43_448All : degreeTree43_448.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29403,⟨sg29395,⟨sg29391,⟨sg29389,⟨sg29388,True.intro,True.intro⟩,⟨sg29390,True.intro,True.intro⟩⟩,⟨sg29393,⟨sg29392,True.intro,True.intro⟩,⟨sg29394,True.intro,True.intro⟩⟩⟩,⟨sg29399,⟨sg29397,⟨sg29396,True.intro,True.intro⟩,⟨sg29398,True.intro,True.intro⟩⟩,⟨sg29401,⟨sg29400,True.intro,True.intro⟩,⟨sg29402,True.intro,True.intro⟩⟩⟩⟩,⟨sg29411,⟨sg29407,⟨sg29405,⟨sg29404,True.intro,True.intro⟩,⟨sg29406,True.intro,True.intro⟩⟩,⟨sg29409,⟨sg29408,True.intro,True.intro⟩,⟨sg29410,True.intro,True.intro⟩⟩⟩,⟨sg29415,⟨sg29413,⟨sg29412,True.intro,True.intro⟩,⟨sg29414,True.intro,True.intro⟩⟩,⟨sg29417,⟨sg29416,True.intro,True.intro⟩,⟨sg29418,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_449All : degreeTree43_449.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29387,degreeTree43_447All,degreeTree43_448All⟩ - -lemma degreeTree43_450All : degreeTree43_450.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29435,⟨sg29427,⟨sg29423,⟨sg29421,⟨sg29420,True.intro,True.intro⟩,⟨sg29422,True.intro,True.intro⟩⟩,⟨sg29425,⟨sg29424,True.intro,True.intro⟩,⟨sg29426,True.intro,True.intro⟩⟩⟩,⟨sg29431,⟨sg29429,⟨sg29428,True.intro,True.intro⟩,⟨sg29430,True.intro,True.intro⟩⟩,⟨sg29433,⟨sg29432,True.intro,True.intro⟩,⟨sg29434,True.intro,True.intro⟩⟩⟩⟩,⟨sg29443,⟨sg29439,⟨sg29437,⟨sg29436,True.intro,True.intro⟩,⟨sg29438,True.intro,True.intro⟩⟩,⟨sg29441,⟨sg29440,True.intro,True.intro⟩,⟨sg29442,True.intro,True.intro⟩⟩⟩,⟨sg29447,⟨sg29445,⟨sg29444,True.intro,True.intro⟩,⟨sg29446,True.intro,True.intro⟩⟩,⟨sg29449,⟨sg29448,True.intro,True.intro⟩,⟨sg29450,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_451All : degreeTree43_451.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29467,⟨sg29459,⟨sg29455,⟨sg29453,⟨sg29452,True.intro,True.intro⟩,⟨sg29454,True.intro,True.intro⟩⟩,⟨sg29457,⟨sg29456,True.intro,True.intro⟩,⟨sg29458,True.intro,True.intro⟩⟩⟩,⟨sg29463,⟨sg29461,⟨sg29460,True.intro,True.intro⟩,⟨sg29462,True.intro,True.intro⟩⟩,⟨sg29465,⟨sg29464,True.intro,True.intro⟩,⟨sg29466,True.intro,True.intro⟩⟩⟩⟩,⟨sg29475,⟨sg29471,⟨sg29469,⟨sg29468,True.intro,True.intro⟩,⟨sg29470,True.intro,True.intro⟩⟩,⟨sg29473,⟨sg29472,True.intro,True.intro⟩,⟨sg29474,True.intro,True.intro⟩⟩⟩,⟨sg29479,⟨sg29477,⟨sg29476,True.intro,True.intro⟩,⟨sg29478,True.intro,True.intro⟩⟩,⟨sg29481,⟨sg29480,True.intro,True.intro⟩,⟨sg29482,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_452All : degreeTree43_452.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29451,degreeTree43_450All,degreeTree43_451All⟩ - -lemma degreeTree43_453All : degreeTree43_453.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29419,degreeTree43_449All,degreeTree43_452All⟩ - -lemma degreeTree43_454All : degreeTree43_454.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29492,⟨sg29488,⟨sg29486,⟨sg29485,⟨sg29484,True.intro,True.intro⟩,True.intro⟩,⟨sg29487,True.intro,True.intro⟩⟩,⟨sg29490,⟨sg29489,True.intro,True.intro⟩,⟨sg29491,True.intro,True.intro⟩⟩⟩,⟨sg29496,⟨sg29494,⟨sg29493,True.intro,True.intro⟩,⟨sg29495,True.intro,True.intro⟩⟩,⟨sg29498,⟨sg29497,True.intro,True.intro⟩,⟨sg29499,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_455All : degreeTree43_455.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29508,⟨sg29504,⟨sg29502,⟨sg29501,True.intro,True.intro⟩,⟨sg29503,True.intro,True.intro⟩⟩,⟨sg29506,⟨sg29505,True.intro,True.intro⟩,⟨sg29507,True.intro,True.intro⟩⟩⟩,⟨sg29512,⟨sg29510,⟨sg29509,True.intro,True.intro⟩,⟨sg29511,True.intro,True.intro⟩⟩,⟨sg29514,⟨sg29513,True.intro,True.intro⟩,⟨sg29515,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_456All : degreeTree43_456.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29500,degreeTree43_454All,degreeTree43_455All⟩ - -lemma degreeTree43_457All : degreeTree43_457.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29532,⟨sg29524,⟨sg29520,⟨sg29518,⟨sg29517,True.intro,True.intro⟩,⟨sg29519,True.intro,True.intro⟩⟩,⟨sg29522,⟨sg29521,True.intro,True.intro⟩,⟨sg29523,True.intro,True.intro⟩⟩⟩,⟨sg29528,⟨sg29526,⟨sg29525,True.intro,True.intro⟩,⟨sg29527,True.intro,True.intro⟩⟩,⟨sg29530,⟨sg29529,True.intro,True.intro⟩,⟨sg29531,True.intro,True.intro⟩⟩⟩⟩,⟨sg29540,⟨sg29536,⟨sg29534,⟨sg29533,True.intro,True.intro⟩,⟨sg29535,True.intro,True.intro⟩⟩,⟨sg29538,⟨sg29537,True.intro,True.intro⟩,⟨sg29539,True.intro,True.intro⟩⟩⟩,⟨sg29544,⟨sg29542,⟨sg29541,True.intro,True.intro⟩,⟨sg29543,True.intro,True.intro⟩⟩,⟨sg29546,⟨sg29545,True.intro,True.intro⟩,⟨sg29547,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_458All : degreeTree43_458.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29516,degreeTree43_456All,degreeTree43_457All⟩ - -lemma degreeTree43_459All : degreeTree43_459.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29564,⟨sg29556,⟨sg29552,⟨sg29550,⟨sg29549,True.intro,True.intro⟩,⟨sg29551,True.intro,True.intro⟩⟩,⟨sg29554,⟨sg29553,True.intro,True.intro⟩,⟨sg29555,True.intro,True.intro⟩⟩⟩,⟨sg29560,⟨sg29558,⟨sg29557,True.intro,True.intro⟩,⟨sg29559,True.intro,True.intro⟩⟩,⟨sg29562,⟨sg29561,True.intro,True.intro⟩,⟨sg29563,True.intro,True.intro⟩⟩⟩⟩,⟨sg29572,⟨sg29568,⟨sg29566,⟨sg29565,True.intro,True.intro⟩,⟨sg29567,True.intro,True.intro⟩⟩,⟨sg29570,⟨sg29569,True.intro,True.intro⟩,⟨sg29571,True.intro,True.intro⟩⟩⟩,⟨sg29576,⟨sg29574,⟨sg29573,True.intro,True.intro⟩,⟨sg29575,True.intro,True.intro⟩⟩,⟨sg29578,⟨sg29577,True.intro,True.intro⟩,⟨sg29579,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_460All : degreeTree43_460.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29596,⟨sg29588,⟨sg29584,⟨sg29582,⟨sg29581,True.intro,True.intro⟩,⟨sg29583,True.intro,True.intro⟩⟩,⟨sg29586,⟨sg29585,True.intro,True.intro⟩,⟨sg29587,True.intro,True.intro⟩⟩⟩,⟨sg29592,⟨sg29590,⟨sg29589,True.intro,True.intro⟩,⟨sg29591,True.intro,True.intro⟩⟩,⟨sg29594,⟨sg29593,True.intro,True.intro⟩,⟨sg29595,True.intro,True.intro⟩⟩⟩⟩,⟨sg29604,⟨sg29600,⟨sg29598,⟨sg29597,True.intro,True.intro⟩,⟨sg29599,True.intro,True.intro⟩⟩,⟨sg29602,⟨sg29601,True.intro,True.intro⟩,⟨sg29603,True.intro,True.intro⟩⟩⟩,⟨sg29608,⟨sg29606,⟨sg29605,True.intro,True.intro⟩,⟨sg29607,True.intro,True.intro⟩⟩,⟨sg29610,⟨sg29609,True.intro,True.intro⟩,⟨sg29611,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_461All : degreeTree43_461.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29580,degreeTree43_459All,degreeTree43_460All⟩ - -lemma degreeTree43_462All : degreeTree43_462.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29548,degreeTree43_458All,degreeTree43_461All⟩ - -lemma degreeTree43_463All : degreeTree43_463.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29483,degreeTree43_453All,degreeTree43_462All⟩ - -lemma degreeTree43_464All : degreeTree43_464.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29621,⟨sg29617,⟨sg29615,⟨sg29614,⟨sg29613,True.intro,True.intro⟩,True.intro⟩,⟨sg29616,True.intro,True.intro⟩⟩,⟨sg29619,⟨sg29618,True.intro,True.intro⟩,⟨sg29620,True.intro,True.intro⟩⟩⟩,⟨sg29625,⟨sg29623,⟨sg29622,True.intro,True.intro⟩,⟨sg29624,True.intro,True.intro⟩⟩,⟨sg29627,⟨sg29626,True.intro,True.intro⟩,⟨sg29628,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_465All : degreeTree43_465.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29637,⟨sg29633,⟨sg29631,⟨sg29630,True.intro,True.intro⟩,⟨sg29632,True.intro,True.intro⟩⟩,⟨sg29635,⟨sg29634,True.intro,True.intro⟩,⟨sg29636,True.intro,True.intro⟩⟩⟩,⟨sg29641,⟨sg29639,⟨sg29638,True.intro,True.intro⟩,⟨sg29640,True.intro,True.intro⟩⟩,⟨sg29643,⟨sg29642,True.intro,True.intro⟩,⟨sg29644,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_466All : degreeTree43_466.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29629,degreeTree43_464All,degreeTree43_465All⟩ - -lemma degreeTree43_467All : degreeTree43_467.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29661,⟨sg29653,⟨sg29649,⟨sg29647,⟨sg29646,True.intro,True.intro⟩,⟨sg29648,True.intro,True.intro⟩⟩,⟨sg29651,⟨sg29650,True.intro,True.intro⟩,⟨sg29652,True.intro,True.intro⟩⟩⟩,⟨sg29657,⟨sg29655,⟨sg29654,True.intro,True.intro⟩,⟨sg29656,True.intro,True.intro⟩⟩,⟨sg29659,⟨sg29658,True.intro,True.intro⟩,⟨sg29660,True.intro,True.intro⟩⟩⟩⟩,⟨sg29669,⟨sg29665,⟨sg29663,⟨sg29662,True.intro,True.intro⟩,⟨sg29664,True.intro,True.intro⟩⟩,⟨sg29667,⟨sg29666,True.intro,True.intro⟩,⟨sg29668,True.intro,True.intro⟩⟩⟩,⟨sg29673,⟨sg29671,⟨sg29670,True.intro,True.intro⟩,⟨sg29672,True.intro,True.intro⟩⟩,⟨sg29675,⟨sg29674,True.intro,True.intro⟩,⟨sg29676,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_468All : degreeTree43_468.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29645,degreeTree43_466All,degreeTree43_467All⟩ - -lemma degreeTree43_469All : degreeTree43_469.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29693,⟨sg29685,⟨sg29681,⟨sg29679,⟨sg29678,True.intro,True.intro⟩,⟨sg29680,True.intro,True.intro⟩⟩,⟨sg29683,⟨sg29682,True.intro,True.intro⟩,⟨sg29684,True.intro,True.intro⟩⟩⟩,⟨sg29689,⟨sg29687,⟨sg29686,True.intro,True.intro⟩,⟨sg29688,True.intro,True.intro⟩⟩,⟨sg29691,⟨sg29690,True.intro,True.intro⟩,⟨sg29692,True.intro,True.intro⟩⟩⟩⟩,⟨sg29701,⟨sg29697,⟨sg29695,⟨sg29694,True.intro,True.intro⟩,⟨sg29696,True.intro,True.intro⟩⟩,⟨sg29699,⟨sg29698,True.intro,True.intro⟩,⟨sg29700,True.intro,True.intro⟩⟩⟩,⟨sg29705,⟨sg29703,⟨sg29702,True.intro,True.intro⟩,⟨sg29704,True.intro,True.intro⟩⟩,⟨sg29707,⟨sg29706,True.intro,True.intro⟩,⟨sg29708,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_470All : degreeTree43_470.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29725,⟨sg29717,⟨sg29713,⟨sg29711,⟨sg29710,True.intro,True.intro⟩,⟨sg29712,True.intro,True.intro⟩⟩,⟨sg29715,⟨sg29714,True.intro,True.intro⟩,⟨sg29716,True.intro,True.intro⟩⟩⟩,⟨sg29721,⟨sg29719,⟨sg29718,True.intro,True.intro⟩,⟨sg29720,True.intro,True.intro⟩⟩,⟨sg29723,⟨sg29722,True.intro,True.intro⟩,⟨sg29724,True.intro,True.intro⟩⟩⟩⟩,⟨sg29733,⟨sg29729,⟨sg29727,⟨sg29726,True.intro,True.intro⟩,⟨sg29728,True.intro,True.intro⟩⟩,⟨sg29731,⟨sg29730,True.intro,True.intro⟩,⟨sg29732,True.intro,True.intro⟩⟩⟩,⟨sg29737,⟨sg29735,⟨sg29734,True.intro,True.intro⟩,⟨sg29736,True.intro,True.intro⟩⟩,⟨sg29739,⟨sg29738,True.intro,True.intro⟩,⟨sg29740,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_471All : degreeTree43_471.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29709,degreeTree43_469All,degreeTree43_470All⟩ - -lemma degreeTree43_472All : degreeTree43_472.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29677,degreeTree43_468All,degreeTree43_471All⟩ - -lemma degreeTree43_473All : degreeTree43_473.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29750,⟨sg29746,⟨sg29744,⟨sg29743,⟨sg29742,True.intro,True.intro⟩,True.intro⟩,⟨sg29745,True.intro,True.intro⟩⟩,⟨sg29748,⟨sg29747,True.intro,True.intro⟩,⟨sg29749,True.intro,True.intro⟩⟩⟩,⟨sg29754,⟨sg29752,⟨sg29751,True.intro,True.intro⟩,⟨sg29753,True.intro,True.intro⟩⟩,⟨sg29756,⟨sg29755,True.intro,True.intro⟩,⟨sg29757,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_474All : degreeTree43_474.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29766,⟨sg29762,⟨sg29760,⟨sg29759,True.intro,True.intro⟩,⟨sg29761,True.intro,True.intro⟩⟩,⟨sg29764,⟨sg29763,True.intro,True.intro⟩,⟨sg29765,True.intro,True.intro⟩⟩⟩,⟨sg29770,⟨sg29768,⟨sg29767,True.intro,True.intro⟩,⟨sg29769,True.intro,True.intro⟩⟩,⟨sg29772,⟨sg29771,True.intro,True.intro⟩,⟨sg29773,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_475All : degreeTree43_475.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29758,degreeTree43_473All,degreeTree43_474All⟩ - -lemma degreeTree43_476All : degreeTree43_476.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29790,⟨sg29782,⟨sg29778,⟨sg29776,⟨sg29775,True.intro,True.intro⟩,⟨sg29777,True.intro,True.intro⟩⟩,⟨sg29780,⟨sg29779,True.intro,True.intro⟩,⟨sg29781,True.intro,True.intro⟩⟩⟩,⟨sg29786,⟨sg29784,⟨sg29783,True.intro,True.intro⟩,⟨sg29785,True.intro,True.intro⟩⟩,⟨sg29788,⟨sg29787,True.intro,True.intro⟩,⟨sg29789,True.intro,True.intro⟩⟩⟩⟩,⟨sg29798,⟨sg29794,⟨sg29792,⟨sg29791,True.intro,True.intro⟩,⟨sg29793,True.intro,True.intro⟩⟩,⟨sg29796,⟨sg29795,True.intro,True.intro⟩,⟨sg29797,True.intro,True.intro⟩⟩⟩,⟨sg29802,⟨sg29800,⟨sg29799,True.intro,True.intro⟩,⟨sg29801,True.intro,True.intro⟩⟩,⟨sg29804,⟨sg29803,True.intro,True.intro⟩,⟨sg29805,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_477All : degreeTree43_477.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29774,degreeTree43_475All,degreeTree43_476All⟩ - -lemma degreeTree43_478All : degreeTree43_478.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29822,⟨sg29814,⟨sg29810,⟨sg29808,⟨sg29807,True.intro,True.intro⟩,⟨sg29809,True.intro,True.intro⟩⟩,⟨sg29812,⟨sg29811,True.intro,True.intro⟩,⟨sg29813,True.intro,True.intro⟩⟩⟩,⟨sg29818,⟨sg29816,⟨sg29815,True.intro,True.intro⟩,⟨sg29817,True.intro,True.intro⟩⟩,⟨sg29820,⟨sg29819,True.intro,True.intro⟩,⟨sg29821,True.intro,True.intro⟩⟩⟩⟩,⟨sg29830,⟨sg29826,⟨sg29824,⟨sg29823,True.intro,True.intro⟩,⟨sg29825,True.intro,True.intro⟩⟩,⟨sg29828,⟨sg29827,True.intro,True.intro⟩,⟨sg29829,True.intro,True.intro⟩⟩⟩,⟨sg29834,⟨sg29832,⟨sg29831,True.intro,True.intro⟩,⟨sg29833,True.intro,True.intro⟩⟩,⟨sg29836,⟨sg29835,True.intro,True.intro⟩,⟨sg29837,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_479All : degreeTree43_479.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29854,⟨sg29846,⟨sg29842,⟨sg29840,⟨sg29839,True.intro,True.intro⟩,⟨sg29841,True.intro,True.intro⟩⟩,⟨sg29844,⟨sg29843,True.intro,True.intro⟩,⟨sg29845,True.intro,True.intro⟩⟩⟩,⟨sg29850,⟨sg29848,⟨sg29847,True.intro,True.intro⟩,⟨sg29849,True.intro,True.intro⟩⟩,⟨sg29852,⟨sg29851,True.intro,True.intro⟩,⟨sg29853,True.intro,True.intro⟩⟩⟩⟩,⟨sg29862,⟨sg29858,⟨sg29856,⟨sg29855,True.intro,True.intro⟩,⟨sg29857,True.intro,True.intro⟩⟩,⟨sg29860,⟨sg29859,True.intro,True.intro⟩,⟨sg29861,True.intro,True.intro⟩⟩⟩,⟨sg29866,⟨sg29864,⟨sg29863,True.intro,True.intro⟩,⟨sg29865,True.intro,True.intro⟩⟩,⟨sg29868,⟨sg29867,True.intro,True.intro⟩,⟨sg29869,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_480All : degreeTree43_480.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29838,degreeTree43_478All,degreeTree43_479All⟩ - -lemma degreeTree43_481All : degreeTree43_481.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29806,degreeTree43_477All,degreeTree43_480All⟩ - -lemma degreeTree43_482All : degreeTree43_482.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29741,degreeTree43_472All,degreeTree43_481All⟩ - -lemma degreeTree43_483All : degreeTree43_483.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29612,degreeTree43_463All,degreeTree43_482All⟩ - -lemma degreeTree43_484All : degreeTree43_484.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29354,degreeTree43_444All,degreeTree43_483All⟩ - -lemma degreeTree43_485All : degreeTree43_485.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg28838,degreeTree43_405All,degreeTree43_484All⟩ - -lemma degreeTree43_486All : degreeTree43_486.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29879,⟨sg29875,⟨sg29873,⟨sg29872,⟨sg29871,True.intro,True.intro⟩,True.intro⟩,⟨sg29874,True.intro,True.intro⟩⟩,⟨sg29877,⟨sg29876,True.intro,True.intro⟩,⟨sg29878,True.intro,True.intro⟩⟩⟩,⟨sg29883,⟨sg29881,⟨sg29880,True.intro,True.intro⟩,⟨sg29882,True.intro,True.intro⟩⟩,⟨sg29885,⟨sg29884,True.intro,True.intro⟩,⟨sg29886,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_487All : degreeTree43_487.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29895,⟨sg29891,⟨sg29889,⟨sg29888,True.intro,True.intro⟩,⟨sg29890,True.intro,True.intro⟩⟩,⟨sg29893,⟨sg29892,True.intro,True.intro⟩,⟨sg29894,True.intro,True.intro⟩⟩⟩,⟨sg29899,⟨sg29897,⟨sg29896,True.intro,True.intro⟩,⟨sg29898,True.intro,True.intro⟩⟩,⟨sg29901,⟨sg29900,True.intro,True.intro⟩,⟨sg29902,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_488All : degreeTree43_488.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29887,degreeTree43_486All,degreeTree43_487All⟩ - -lemma degreeTree43_489All : degreeTree43_489.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29919,⟨sg29911,⟨sg29907,⟨sg29905,⟨sg29904,True.intro,True.intro⟩,⟨sg29906,True.intro,True.intro⟩⟩,⟨sg29909,⟨sg29908,True.intro,True.intro⟩,⟨sg29910,True.intro,True.intro⟩⟩⟩,⟨sg29915,⟨sg29913,⟨sg29912,True.intro,True.intro⟩,⟨sg29914,True.intro,True.intro⟩⟩,⟨sg29917,⟨sg29916,True.intro,True.intro⟩,⟨sg29918,True.intro,True.intro⟩⟩⟩⟩,⟨sg29927,⟨sg29923,⟨sg29921,⟨sg29920,True.intro,True.intro⟩,⟨sg29922,True.intro,True.intro⟩⟩,⟨sg29925,⟨sg29924,True.intro,True.intro⟩,⟨sg29926,True.intro,True.intro⟩⟩⟩,⟨sg29931,⟨sg29929,⟨sg29928,True.intro,True.intro⟩,⟨sg29930,True.intro,True.intro⟩⟩,⟨sg29933,⟨sg29932,True.intro,True.intro⟩,⟨sg29934,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_490All : degreeTree43_490.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29903,degreeTree43_488All,degreeTree43_489All⟩ - -lemma degreeTree43_491All : degreeTree43_491.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29944,⟨sg29940,⟨sg29938,⟨sg29937,⟨sg29936,True.intro,True.intro⟩,True.intro⟩,⟨sg29939,True.intro,True.intro⟩⟩,⟨sg29942,⟨sg29941,True.intro,True.intro⟩,⟨sg29943,True.intro,True.intro⟩⟩⟩,⟨sg29948,⟨sg29946,⟨sg29945,True.intro,True.intro⟩,⟨sg29947,True.intro,True.intro⟩⟩,⟨sg29950,⟨sg29949,True.intro,True.intro⟩,⟨sg29951,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_492All : degreeTree43_492.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29960,⟨sg29956,⟨sg29954,⟨sg29953,True.intro,True.intro⟩,⟨sg29955,True.intro,True.intro⟩⟩,⟨sg29958,⟨sg29957,True.intro,True.intro⟩,⟨sg29959,True.intro,True.intro⟩⟩⟩,⟨sg29964,⟨sg29962,⟨sg29961,True.intro,True.intro⟩,⟨sg29963,True.intro,True.intro⟩⟩,⟨sg29966,⟨sg29965,True.intro,True.intro⟩,⟨sg29967,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_493All : degreeTree43_493.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29952,degreeTree43_491All,degreeTree43_492All⟩ - -lemma degreeTree43_494All : degreeTree43_494.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29984,⟨sg29976,⟨sg29972,⟨sg29970,⟨sg29969,True.intro,True.intro⟩,⟨sg29971,True.intro,True.intro⟩⟩,⟨sg29974,⟨sg29973,True.intro,True.intro⟩,⟨sg29975,True.intro,True.intro⟩⟩⟩,⟨sg29980,⟨sg29978,⟨sg29977,True.intro,True.intro⟩,⟨sg29979,True.intro,True.intro⟩⟩,⟨sg29982,⟨sg29981,True.intro,True.intro⟩,⟨sg29983,True.intro,True.intro⟩⟩⟩⟩,⟨sg29992,⟨sg29988,⟨sg29986,⟨sg29985,True.intro,True.intro⟩,⟨sg29987,True.intro,True.intro⟩⟩,⟨sg29990,⟨sg29989,True.intro,True.intro⟩,⟨sg29991,True.intro,True.intro⟩⟩⟩,⟨sg29996,⟨sg29994,⟨sg29993,True.intro,True.intro⟩,⟨sg29995,True.intro,True.intro⟩⟩,⟨sg29998,⟨sg29997,True.intro,True.intro⟩,⟨sg29999,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_495All : degreeTree43_495.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29968,degreeTree43_493All,degreeTree43_494All⟩ - -lemma degreeTree43_496All : degreeTree43_496.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29935,degreeTree43_490All,degreeTree43_495All⟩ - -lemma degreeTree43_497All : degreeTree43_497.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30009,⟨sg30005,⟨sg30003,⟨sg30002,⟨sg30001,True.intro,True.intro⟩,True.intro⟩,⟨sg30004,True.intro,True.intro⟩⟩,⟨sg30007,⟨sg30006,True.intro,True.intro⟩,⟨sg30008,True.intro,True.intro⟩⟩⟩,⟨sg30013,⟨sg30011,⟨sg30010,True.intro,True.intro⟩,⟨sg30012,True.intro,True.intro⟩⟩,⟨sg30015,⟨sg30014,True.intro,True.intro⟩,⟨sg30016,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_498All : degreeTree43_498.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30025,⟨sg30021,⟨sg30019,⟨sg30018,True.intro,True.intro⟩,⟨sg30020,True.intro,True.intro⟩⟩,⟨sg30023,⟨sg30022,True.intro,True.intro⟩,⟨sg30024,True.intro,True.intro⟩⟩⟩,⟨sg30029,⟨sg30027,⟨sg30026,True.intro,True.intro⟩,⟨sg30028,True.intro,True.intro⟩⟩,⟨sg30031,⟨sg30030,True.intro,True.intro⟩,⟨sg30032,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_499All : degreeTree43_499.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30017,degreeTree43_497All,degreeTree43_498All⟩ - -lemma degreeTree43_500All : degreeTree43_500.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30049,⟨sg30041,⟨sg30037,⟨sg30035,⟨sg30034,True.intro,True.intro⟩,⟨sg30036,True.intro,True.intro⟩⟩,⟨sg30039,⟨sg30038,True.intro,True.intro⟩,⟨sg30040,True.intro,True.intro⟩⟩⟩,⟨sg30045,⟨sg30043,⟨sg30042,True.intro,True.intro⟩,⟨sg30044,True.intro,True.intro⟩⟩,⟨sg30047,⟨sg30046,True.intro,True.intro⟩,⟨sg30048,True.intro,True.intro⟩⟩⟩⟩,⟨sg30057,⟨sg30053,⟨sg30051,⟨sg30050,True.intro,True.intro⟩,⟨sg30052,True.intro,True.intro⟩⟩,⟨sg30055,⟨sg30054,True.intro,True.intro⟩,⟨sg30056,True.intro,True.intro⟩⟩⟩,⟨sg30061,⟨sg30059,⟨sg30058,True.intro,True.intro⟩,⟨sg30060,True.intro,True.intro⟩⟩,⟨sg30063,⟨sg30062,True.intro,True.intro⟩,⟨sg30064,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_501All : degreeTree43_501.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30033,degreeTree43_499All,degreeTree43_500All⟩ - -lemma degreeTree43_502All : degreeTree43_502.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30081,⟨sg30073,⟨sg30069,⟨sg30067,⟨sg30066,True.intro,True.intro⟩,⟨sg30068,True.intro,True.intro⟩⟩,⟨sg30071,⟨sg30070,True.intro,True.intro⟩,⟨sg30072,True.intro,True.intro⟩⟩⟩,⟨sg30077,⟨sg30075,⟨sg30074,True.intro,True.intro⟩,⟨sg30076,True.intro,True.intro⟩⟩,⟨sg30079,⟨sg30078,True.intro,True.intro⟩,⟨sg30080,True.intro,True.intro⟩⟩⟩⟩,⟨sg30089,⟨sg30085,⟨sg30083,⟨sg30082,True.intro,True.intro⟩,⟨sg30084,True.intro,True.intro⟩⟩,⟨sg30087,⟨sg30086,True.intro,True.intro⟩,⟨sg30088,True.intro,True.intro⟩⟩⟩,⟨sg30093,⟨sg30091,⟨sg30090,True.intro,True.intro⟩,⟨sg30092,True.intro,True.intro⟩⟩,⟨sg30095,⟨sg30094,True.intro,True.intro⟩,⟨sg30096,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_503All : degreeTree43_503.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30113,⟨sg30105,⟨sg30101,⟨sg30099,⟨sg30098,True.intro,True.intro⟩,⟨sg30100,True.intro,True.intro⟩⟩,⟨sg30103,⟨sg30102,True.intro,True.intro⟩,⟨sg30104,True.intro,True.intro⟩⟩⟩,⟨sg30109,⟨sg30107,⟨sg30106,True.intro,True.intro⟩,⟨sg30108,True.intro,True.intro⟩⟩,⟨sg30111,⟨sg30110,True.intro,True.intro⟩,⟨sg30112,True.intro,True.intro⟩⟩⟩⟩,⟨sg30121,⟨sg30117,⟨sg30115,⟨sg30114,True.intro,True.intro⟩,⟨sg30116,True.intro,True.intro⟩⟩,⟨sg30119,⟨sg30118,True.intro,True.intro⟩,⟨sg30120,True.intro,True.intro⟩⟩⟩,⟨sg30125,⟨sg30123,⟨sg30122,True.intro,True.intro⟩,⟨sg30124,True.intro,True.intro⟩⟩,⟨sg30127,⟨sg30126,True.intro,True.intro⟩,⟨sg30128,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_504All : degreeTree43_504.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30097,degreeTree43_502All,degreeTree43_503All⟩ - -lemma degreeTree43_505All : degreeTree43_505.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30065,degreeTree43_501All,degreeTree43_504All⟩ - -lemma degreeTree43_506All : degreeTree43_506.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30000,degreeTree43_496All,degreeTree43_505All⟩ - -lemma degreeTree43_507All : degreeTree43_507.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30138,⟨sg30134,⟨sg30132,⟨sg30131,⟨sg30130,True.intro,True.intro⟩,True.intro⟩,⟨sg30133,True.intro,True.intro⟩⟩,⟨sg30136,⟨sg30135,True.intro,True.intro⟩,⟨sg30137,True.intro,True.intro⟩⟩⟩,⟨sg30142,⟨sg30140,⟨sg30139,True.intro,True.intro⟩,⟨sg30141,True.intro,True.intro⟩⟩,⟨sg30144,⟨sg30143,True.intro,True.intro⟩,⟨sg30145,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_508All : degreeTree43_508.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30154,⟨sg30150,⟨sg30148,⟨sg30147,True.intro,True.intro⟩,⟨sg30149,True.intro,True.intro⟩⟩,⟨sg30152,⟨sg30151,True.intro,True.intro⟩,⟨sg30153,True.intro,True.intro⟩⟩⟩,⟨sg30158,⟨sg30156,⟨sg30155,True.intro,True.intro⟩,⟨sg30157,True.intro,True.intro⟩⟩,⟨sg30160,⟨sg30159,True.intro,True.intro⟩,⟨sg30161,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_509All : degreeTree43_509.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30146,degreeTree43_507All,degreeTree43_508All⟩ - -lemma degreeTree43_510All : degreeTree43_510.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30178,⟨sg30170,⟨sg30166,⟨sg30164,⟨sg30163,True.intro,True.intro⟩,⟨sg30165,True.intro,True.intro⟩⟩,⟨sg30168,⟨sg30167,True.intro,True.intro⟩,⟨sg30169,True.intro,True.intro⟩⟩⟩,⟨sg30174,⟨sg30172,⟨sg30171,True.intro,True.intro⟩,⟨sg30173,True.intro,True.intro⟩⟩,⟨sg30176,⟨sg30175,True.intro,True.intro⟩,⟨sg30177,True.intro,True.intro⟩⟩⟩⟩,⟨sg30186,⟨sg30182,⟨sg30180,⟨sg30179,True.intro,True.intro⟩,⟨sg30181,True.intro,True.intro⟩⟩,⟨sg30184,⟨sg30183,True.intro,True.intro⟩,⟨sg30185,True.intro,True.intro⟩⟩⟩,⟨sg30190,⟨sg30188,⟨sg30187,True.intro,True.intro⟩,⟨sg30189,True.intro,True.intro⟩⟩,⟨sg30192,⟨sg30191,True.intro,True.intro⟩,⟨sg30193,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_511All : degreeTree43_511.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30162,degreeTree43_509All,degreeTree43_510All⟩ - -lemma degreeTree43_512All : degreeTree43_512.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30210,⟨sg30202,⟨sg30198,⟨sg30196,⟨sg30195,True.intro,True.intro⟩,⟨sg30197,True.intro,True.intro⟩⟩,⟨sg30200,⟨sg30199,True.intro,True.intro⟩,⟨sg30201,True.intro,True.intro⟩⟩⟩,⟨sg30206,⟨sg30204,⟨sg30203,True.intro,True.intro⟩,⟨sg30205,True.intro,True.intro⟩⟩,⟨sg30208,⟨sg30207,True.intro,True.intro⟩,⟨sg30209,True.intro,True.intro⟩⟩⟩⟩,⟨sg30218,⟨sg30214,⟨sg30212,⟨sg30211,True.intro,True.intro⟩,⟨sg30213,True.intro,True.intro⟩⟩,⟨sg30216,⟨sg30215,True.intro,True.intro⟩,⟨sg30217,True.intro,True.intro⟩⟩⟩,⟨sg30222,⟨sg30220,⟨sg30219,True.intro,True.intro⟩,⟨sg30221,True.intro,True.intro⟩⟩,⟨sg30224,⟨sg30223,True.intro,True.intro⟩,⟨sg30225,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_513All : degreeTree43_513.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30242,⟨sg30234,⟨sg30230,⟨sg30228,⟨sg30227,True.intro,True.intro⟩,⟨sg30229,True.intro,True.intro⟩⟩,⟨sg30232,⟨sg30231,True.intro,True.intro⟩,⟨sg30233,True.intro,True.intro⟩⟩⟩,⟨sg30238,⟨sg30236,⟨sg30235,True.intro,True.intro⟩,⟨sg30237,True.intro,True.intro⟩⟩,⟨sg30240,⟨sg30239,True.intro,True.intro⟩,⟨sg30241,True.intro,True.intro⟩⟩⟩⟩,⟨sg30250,⟨sg30246,⟨sg30244,⟨sg30243,True.intro,True.intro⟩,⟨sg30245,True.intro,True.intro⟩⟩,⟨sg30248,⟨sg30247,True.intro,True.intro⟩,⟨sg30249,True.intro,True.intro⟩⟩⟩,⟨sg30254,⟨sg30252,⟨sg30251,True.intro,True.intro⟩,⟨sg30253,True.intro,True.intro⟩⟩,⟨sg30256,⟨sg30255,True.intro,True.intro⟩,⟨sg30257,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_514All : degreeTree43_514.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30226,degreeTree43_512All,degreeTree43_513All⟩ - -lemma degreeTree43_515All : degreeTree43_515.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30194,degreeTree43_511All,degreeTree43_514All⟩ - -lemma degreeTree43_516All : degreeTree43_516.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30267,⟨sg30263,⟨sg30261,⟨sg30260,⟨sg30259,True.intro,True.intro⟩,True.intro⟩,⟨sg30262,True.intro,True.intro⟩⟩,⟨sg30265,⟨sg30264,True.intro,True.intro⟩,⟨sg30266,True.intro,True.intro⟩⟩⟩,⟨sg30271,⟨sg30269,⟨sg30268,True.intro,True.intro⟩,⟨sg30270,True.intro,True.intro⟩⟩,⟨sg30273,⟨sg30272,True.intro,True.intro⟩,⟨sg30274,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_517All : degreeTree43_517.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30283,⟨sg30279,⟨sg30277,⟨sg30276,True.intro,True.intro⟩,⟨sg30278,True.intro,True.intro⟩⟩,⟨sg30281,⟨sg30280,True.intro,True.intro⟩,⟨sg30282,True.intro,True.intro⟩⟩⟩,⟨sg30287,⟨sg30285,⟨sg30284,True.intro,True.intro⟩,⟨sg30286,True.intro,True.intro⟩⟩,⟨sg30289,⟨sg30288,True.intro,True.intro⟩,⟨sg30290,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_518All : degreeTree43_518.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30275,degreeTree43_516All,degreeTree43_517All⟩ - -lemma degreeTree43_519All : degreeTree43_519.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30307,⟨sg30299,⟨sg30295,⟨sg30293,⟨sg30292,True.intro,True.intro⟩,⟨sg30294,True.intro,True.intro⟩⟩,⟨sg30297,⟨sg30296,True.intro,True.intro⟩,⟨sg30298,True.intro,True.intro⟩⟩⟩,⟨sg30303,⟨sg30301,⟨sg30300,True.intro,True.intro⟩,⟨sg30302,True.intro,True.intro⟩⟩,⟨sg30305,⟨sg30304,True.intro,True.intro⟩,⟨sg30306,True.intro,True.intro⟩⟩⟩⟩,⟨sg30315,⟨sg30311,⟨sg30309,⟨sg30308,True.intro,True.intro⟩,⟨sg30310,True.intro,True.intro⟩⟩,⟨sg30313,⟨sg30312,True.intro,True.intro⟩,⟨sg30314,True.intro,True.intro⟩⟩⟩,⟨sg30319,⟨sg30317,⟨sg30316,True.intro,True.intro⟩,⟨sg30318,True.intro,True.intro⟩⟩,⟨sg30321,⟨sg30320,True.intro,True.intro⟩,⟨sg30322,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_520All : degreeTree43_520.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30291,degreeTree43_518All,degreeTree43_519All⟩ - -lemma degreeTree43_521All : degreeTree43_521.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30339,⟨sg30331,⟨sg30327,⟨sg30325,⟨sg30324,True.intro,True.intro⟩,⟨sg30326,True.intro,True.intro⟩⟩,⟨sg30329,⟨sg30328,True.intro,True.intro⟩,⟨sg30330,True.intro,True.intro⟩⟩⟩,⟨sg30335,⟨sg30333,⟨sg30332,True.intro,True.intro⟩,⟨sg30334,True.intro,True.intro⟩⟩,⟨sg30337,⟨sg30336,True.intro,True.intro⟩,⟨sg30338,True.intro,True.intro⟩⟩⟩⟩,⟨sg30347,⟨sg30343,⟨sg30341,⟨sg30340,True.intro,True.intro⟩,⟨sg30342,True.intro,True.intro⟩⟩,⟨sg30345,⟨sg30344,True.intro,True.intro⟩,⟨sg30346,True.intro,True.intro⟩⟩⟩,⟨sg30351,⟨sg30349,⟨sg30348,True.intro,True.intro⟩,⟨sg30350,True.intro,True.intro⟩⟩,⟨sg30353,⟨sg30352,True.intro,True.intro⟩,⟨sg30354,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_522All : degreeTree43_522.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30371,⟨sg30363,⟨sg30359,⟨sg30357,⟨sg30356,True.intro,True.intro⟩,⟨sg30358,True.intro,True.intro⟩⟩,⟨sg30361,⟨sg30360,True.intro,True.intro⟩,⟨sg30362,True.intro,True.intro⟩⟩⟩,⟨sg30367,⟨sg30365,⟨sg30364,True.intro,True.intro⟩,⟨sg30366,True.intro,True.intro⟩⟩,⟨sg30369,⟨sg30368,True.intro,True.intro⟩,⟨sg30370,True.intro,True.intro⟩⟩⟩⟩,⟨sg30379,⟨sg30375,⟨sg30373,⟨sg30372,True.intro,True.intro⟩,⟨sg30374,True.intro,True.intro⟩⟩,⟨sg30377,⟨sg30376,True.intro,True.intro⟩,⟨sg30378,True.intro,True.intro⟩⟩⟩,⟨sg30383,⟨sg30381,⟨sg30380,True.intro,True.intro⟩,⟨sg30382,True.intro,True.intro⟩⟩,⟨sg30385,⟨sg30384,True.intro,True.intro⟩,⟨sg30386,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_523All : degreeTree43_523.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30355,degreeTree43_521All,degreeTree43_522All⟩ - -lemma degreeTree43_524All : degreeTree43_524.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30323,degreeTree43_520All,degreeTree43_523All⟩ - -lemma degreeTree43_525All : degreeTree43_525.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30258,degreeTree43_515All,degreeTree43_524All⟩ - -lemma degreeTree43_526All : degreeTree43_526.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30129,degreeTree43_506All,degreeTree43_525All⟩ - -lemma degreeTree43_527All : degreeTree43_527.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30396,⟨sg30392,⟨sg30390,⟨sg30389,⟨sg30388,True.intro,True.intro⟩,True.intro⟩,⟨sg30391,True.intro,True.intro⟩⟩,⟨sg30394,⟨sg30393,True.intro,True.intro⟩,⟨sg30395,True.intro,True.intro⟩⟩⟩,⟨sg30400,⟨sg30398,⟨sg30397,True.intro,True.intro⟩,⟨sg30399,True.intro,True.intro⟩⟩,⟨sg30402,⟨sg30401,True.intro,True.intro⟩,⟨sg30403,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_528All : degreeTree43_528.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30412,⟨sg30408,⟨sg30406,⟨sg30405,True.intro,True.intro⟩,⟨sg30407,True.intro,True.intro⟩⟩,⟨sg30410,⟨sg30409,True.intro,True.intro⟩,⟨sg30411,True.intro,True.intro⟩⟩⟩,⟨sg30416,⟨sg30414,⟨sg30413,True.intro,True.intro⟩,⟨sg30415,True.intro,True.intro⟩⟩,⟨sg30418,⟨sg30417,True.intro,True.intro⟩,⟨sg30419,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_529All : degreeTree43_529.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30404,degreeTree43_527All,degreeTree43_528All⟩ - -lemma degreeTree43_530All : degreeTree43_530.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30436,⟨sg30428,⟨sg30424,⟨sg30422,⟨sg30421,True.intro,True.intro⟩,⟨sg30423,True.intro,True.intro⟩⟩,⟨sg30426,⟨sg30425,True.intro,True.intro⟩,⟨sg30427,True.intro,True.intro⟩⟩⟩,⟨sg30432,⟨sg30430,⟨sg30429,True.intro,True.intro⟩,⟨sg30431,True.intro,True.intro⟩⟩,⟨sg30434,⟨sg30433,True.intro,True.intro⟩,⟨sg30435,True.intro,True.intro⟩⟩⟩⟩,⟨sg30444,⟨sg30440,⟨sg30438,⟨sg30437,True.intro,True.intro⟩,⟨sg30439,True.intro,True.intro⟩⟩,⟨sg30442,⟨sg30441,True.intro,True.intro⟩,⟨sg30443,True.intro,True.intro⟩⟩⟩,⟨sg30448,⟨sg30446,⟨sg30445,True.intro,True.intro⟩,⟨sg30447,True.intro,True.intro⟩⟩,⟨sg30450,⟨sg30449,True.intro,True.intro⟩,⟨sg30451,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_531All : degreeTree43_531.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30420,degreeTree43_529All,degreeTree43_530All⟩ - -lemma degreeTree43_532All : degreeTree43_532.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30468,⟨sg30460,⟨sg30456,⟨sg30454,⟨sg30453,True.intro,True.intro⟩,⟨sg30455,True.intro,True.intro⟩⟩,⟨sg30458,⟨sg30457,True.intro,True.intro⟩,⟨sg30459,True.intro,True.intro⟩⟩⟩,⟨sg30464,⟨sg30462,⟨sg30461,True.intro,True.intro⟩,⟨sg30463,True.intro,True.intro⟩⟩,⟨sg30466,⟨sg30465,True.intro,True.intro⟩,⟨sg30467,True.intro,True.intro⟩⟩⟩⟩,⟨sg30476,⟨sg30472,⟨sg30470,⟨sg30469,True.intro,True.intro⟩,⟨sg30471,True.intro,True.intro⟩⟩,⟨sg30474,⟨sg30473,True.intro,True.intro⟩,⟨sg30475,True.intro,True.intro⟩⟩⟩,⟨sg30480,⟨sg30478,⟨sg30477,True.intro,True.intro⟩,⟨sg30479,True.intro,True.intro⟩⟩,⟨sg30482,⟨sg30481,True.intro,True.intro⟩,⟨sg30483,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_533All : degreeTree43_533.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30500,⟨sg30492,⟨sg30488,⟨sg30486,⟨sg30485,True.intro,True.intro⟩,⟨sg30487,True.intro,True.intro⟩⟩,⟨sg30490,⟨sg30489,True.intro,True.intro⟩,⟨sg30491,True.intro,True.intro⟩⟩⟩,⟨sg30496,⟨sg30494,⟨sg30493,True.intro,True.intro⟩,⟨sg30495,True.intro,True.intro⟩⟩,⟨sg30498,⟨sg30497,True.intro,True.intro⟩,⟨sg30499,True.intro,True.intro⟩⟩⟩⟩,⟨sg30508,⟨sg30504,⟨sg30502,⟨sg30501,True.intro,True.intro⟩,⟨sg30503,True.intro,True.intro⟩⟩,⟨sg30506,⟨sg30505,True.intro,True.intro⟩,⟨sg30507,True.intro,True.intro⟩⟩⟩,⟨sg30512,⟨sg30510,⟨sg30509,True.intro,True.intro⟩,⟨sg30511,True.intro,True.intro⟩⟩,⟨sg30514,⟨sg30513,True.intro,True.intro⟩,⟨sg30515,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_534All : degreeTree43_534.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30484,degreeTree43_532All,degreeTree43_533All⟩ - -lemma degreeTree43_535All : degreeTree43_535.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30452,degreeTree43_531All,degreeTree43_534All⟩ - -lemma degreeTree43_536All : degreeTree43_536.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30525,⟨sg30521,⟨sg30519,⟨sg30518,⟨sg30517,True.intro,True.intro⟩,True.intro⟩,⟨sg30520,True.intro,True.intro⟩⟩,⟨sg30523,⟨sg30522,True.intro,True.intro⟩,⟨sg30524,True.intro,True.intro⟩⟩⟩,⟨sg30529,⟨sg30527,⟨sg30526,True.intro,True.intro⟩,⟨sg30528,True.intro,True.intro⟩⟩,⟨sg30531,⟨sg30530,True.intro,True.intro⟩,⟨sg30532,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_537All : degreeTree43_537.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30541,⟨sg30537,⟨sg30535,⟨sg30534,True.intro,True.intro⟩,⟨sg30536,True.intro,True.intro⟩⟩,⟨sg30539,⟨sg30538,True.intro,True.intro⟩,⟨sg30540,True.intro,True.intro⟩⟩⟩,⟨sg30545,⟨sg30543,⟨sg30542,True.intro,True.intro⟩,⟨sg30544,True.intro,True.intro⟩⟩,⟨sg30547,⟨sg30546,True.intro,True.intro⟩,⟨sg30548,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_538All : degreeTree43_538.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30533,degreeTree43_536All,degreeTree43_537All⟩ - -lemma degreeTree43_539All : degreeTree43_539.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30565,⟨sg30557,⟨sg30553,⟨sg30551,⟨sg30550,True.intro,True.intro⟩,⟨sg30552,True.intro,True.intro⟩⟩,⟨sg30555,⟨sg30554,True.intro,True.intro⟩,⟨sg30556,True.intro,True.intro⟩⟩⟩,⟨sg30561,⟨sg30559,⟨sg30558,True.intro,True.intro⟩,⟨sg30560,True.intro,True.intro⟩⟩,⟨sg30563,⟨sg30562,True.intro,True.intro⟩,⟨sg30564,True.intro,True.intro⟩⟩⟩⟩,⟨sg30573,⟨sg30569,⟨sg30567,⟨sg30566,True.intro,True.intro⟩,⟨sg30568,True.intro,True.intro⟩⟩,⟨sg30571,⟨sg30570,True.intro,True.intro⟩,⟨sg30572,True.intro,True.intro⟩⟩⟩,⟨sg30577,⟨sg30575,⟨sg30574,True.intro,True.intro⟩,⟨sg30576,True.intro,True.intro⟩⟩,⟨sg30579,⟨sg30578,True.intro,True.intro⟩,⟨sg30580,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_540All : degreeTree43_540.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30549,degreeTree43_538All,degreeTree43_539All⟩ - -lemma degreeTree43_541All : degreeTree43_541.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30597,⟨sg30589,⟨sg30585,⟨sg30583,⟨sg30582,True.intro,True.intro⟩,⟨sg30584,True.intro,True.intro⟩⟩,⟨sg30587,⟨sg30586,True.intro,True.intro⟩,⟨sg30588,True.intro,True.intro⟩⟩⟩,⟨sg30593,⟨sg30591,⟨sg30590,True.intro,True.intro⟩,⟨sg30592,True.intro,True.intro⟩⟩,⟨sg30595,⟨sg30594,True.intro,True.intro⟩,⟨sg30596,True.intro,True.intro⟩⟩⟩⟩,⟨sg30605,⟨sg30601,⟨sg30599,⟨sg30598,True.intro,True.intro⟩,⟨sg30600,True.intro,True.intro⟩⟩,⟨sg30603,⟨sg30602,True.intro,True.intro⟩,⟨sg30604,True.intro,True.intro⟩⟩⟩,⟨sg30609,⟨sg30607,⟨sg30606,True.intro,True.intro⟩,⟨sg30608,True.intro,True.intro⟩⟩,⟨sg30611,⟨sg30610,True.intro,True.intro⟩,⟨sg30612,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_542All : degreeTree43_542.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30629,⟨sg30621,⟨sg30617,⟨sg30615,⟨sg30614,True.intro,True.intro⟩,⟨sg30616,True.intro,True.intro⟩⟩,⟨sg30619,⟨sg30618,True.intro,True.intro⟩,⟨sg30620,True.intro,True.intro⟩⟩⟩,⟨sg30625,⟨sg30623,⟨sg30622,True.intro,True.intro⟩,⟨sg30624,True.intro,True.intro⟩⟩,⟨sg30627,⟨sg30626,True.intro,True.intro⟩,⟨sg30628,True.intro,True.intro⟩⟩⟩⟩,⟨sg30637,⟨sg30633,⟨sg30631,⟨sg30630,True.intro,True.intro⟩,⟨sg30632,True.intro,True.intro⟩⟩,⟨sg30635,⟨sg30634,True.intro,True.intro⟩,⟨sg30636,True.intro,True.intro⟩⟩⟩,⟨sg30641,⟨sg30639,⟨sg30638,True.intro,True.intro⟩,⟨sg30640,True.intro,True.intro⟩⟩,⟨sg30643,⟨sg30642,True.intro,True.intro⟩,⟨sg30644,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_543All : degreeTree43_543.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30613,degreeTree43_541All,degreeTree43_542All⟩ - -lemma degreeTree43_544All : degreeTree43_544.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30581,degreeTree43_540All,degreeTree43_543All⟩ - -lemma degreeTree43_545All : degreeTree43_545.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30516,degreeTree43_535All,degreeTree43_544All⟩ - -lemma degreeTree43_546All : degreeTree43_546.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30654,⟨sg30650,⟨sg30648,⟨sg30647,⟨sg30646,True.intro,True.intro⟩,True.intro⟩,⟨sg30649,True.intro,True.intro⟩⟩,⟨sg30652,⟨sg30651,True.intro,True.intro⟩,⟨sg30653,True.intro,True.intro⟩⟩⟩,⟨sg30658,⟨sg30656,⟨sg30655,True.intro,True.intro⟩,⟨sg30657,True.intro,True.intro⟩⟩,⟨sg30660,⟨sg30659,True.intro,True.intro⟩,⟨sg30661,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_547All : degreeTree43_547.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30670,⟨sg30666,⟨sg30664,⟨sg30663,True.intro,True.intro⟩,⟨sg30665,True.intro,True.intro⟩⟩,⟨sg30668,⟨sg30667,True.intro,True.intro⟩,⟨sg30669,True.intro,True.intro⟩⟩⟩,⟨sg30674,⟨sg30672,⟨sg30671,True.intro,True.intro⟩,⟨sg30673,True.intro,True.intro⟩⟩,⟨sg30676,⟨sg30675,True.intro,True.intro⟩,⟨sg30677,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_548All : degreeTree43_548.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30662,degreeTree43_546All,degreeTree43_547All⟩ - -lemma degreeTree43_549All : degreeTree43_549.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30694,⟨sg30686,⟨sg30682,⟨sg30680,⟨sg30679,True.intro,True.intro⟩,⟨sg30681,True.intro,True.intro⟩⟩,⟨sg30684,⟨sg30683,True.intro,True.intro⟩,⟨sg30685,True.intro,True.intro⟩⟩⟩,⟨sg30690,⟨sg30688,⟨sg30687,True.intro,True.intro⟩,⟨sg30689,True.intro,True.intro⟩⟩,⟨sg30692,⟨sg30691,True.intro,True.intro⟩,⟨sg30693,True.intro,True.intro⟩⟩⟩⟩,⟨sg30702,⟨sg30698,⟨sg30696,⟨sg30695,True.intro,True.intro⟩,⟨sg30697,True.intro,True.intro⟩⟩,⟨sg30700,⟨sg30699,True.intro,True.intro⟩,⟨sg30701,True.intro,True.intro⟩⟩⟩,⟨sg30706,⟨sg30704,⟨sg30703,True.intro,True.intro⟩,⟨sg30705,True.intro,True.intro⟩⟩,⟨sg30708,⟨sg30707,True.intro,True.intro⟩,⟨sg30709,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_550All : degreeTree43_550.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30678,degreeTree43_548All,degreeTree43_549All⟩ - -lemma degreeTree43_551All : degreeTree43_551.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30726,⟨sg30718,⟨sg30714,⟨sg30712,⟨sg30711,True.intro,True.intro⟩,⟨sg30713,True.intro,True.intro⟩⟩,⟨sg30716,⟨sg30715,True.intro,True.intro⟩,⟨sg30717,True.intro,True.intro⟩⟩⟩,⟨sg30722,⟨sg30720,⟨sg30719,True.intro,True.intro⟩,⟨sg30721,True.intro,True.intro⟩⟩,⟨sg30724,⟨sg30723,True.intro,True.intro⟩,⟨sg30725,True.intro,True.intro⟩⟩⟩⟩,⟨sg30734,⟨sg30730,⟨sg30728,⟨sg30727,True.intro,True.intro⟩,⟨sg30729,True.intro,True.intro⟩⟩,⟨sg30732,⟨sg30731,True.intro,True.intro⟩,⟨sg30733,True.intro,True.intro⟩⟩⟩,⟨sg30738,⟨sg30736,⟨sg30735,True.intro,True.intro⟩,⟨sg30737,True.intro,True.intro⟩⟩,⟨sg30740,⟨sg30739,True.intro,True.intro⟩,⟨sg30741,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_552All : degreeTree43_552.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30758,⟨sg30750,⟨sg30746,⟨sg30744,⟨sg30743,True.intro,True.intro⟩,⟨sg30745,True.intro,True.intro⟩⟩,⟨sg30748,⟨sg30747,True.intro,True.intro⟩,⟨sg30749,True.intro,True.intro⟩⟩⟩,⟨sg30754,⟨sg30752,⟨sg30751,True.intro,True.intro⟩,⟨sg30753,True.intro,True.intro⟩⟩,⟨sg30756,⟨sg30755,True.intro,True.intro⟩,⟨sg30757,True.intro,True.intro⟩⟩⟩⟩,⟨sg30766,⟨sg30762,⟨sg30760,⟨sg30759,True.intro,True.intro⟩,⟨sg30761,True.intro,True.intro⟩⟩,⟨sg30764,⟨sg30763,True.intro,True.intro⟩,⟨sg30765,True.intro,True.intro⟩⟩⟩,⟨sg30770,⟨sg30768,⟨sg30767,True.intro,True.intro⟩,⟨sg30769,True.intro,True.intro⟩⟩,⟨sg30772,⟨sg30771,True.intro,True.intro⟩,⟨sg30773,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_553All : degreeTree43_553.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30742,degreeTree43_551All,degreeTree43_552All⟩ - -lemma degreeTree43_554All : degreeTree43_554.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30710,degreeTree43_550All,degreeTree43_553All⟩ - -lemma degreeTree43_555All : degreeTree43_555.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30783,⟨sg30779,⟨sg30777,⟨sg30776,⟨sg30775,True.intro,True.intro⟩,True.intro⟩,⟨sg30778,True.intro,True.intro⟩⟩,⟨sg30781,⟨sg30780,True.intro,True.intro⟩,⟨sg30782,True.intro,True.intro⟩⟩⟩,⟨sg30787,⟨sg30785,⟨sg30784,True.intro,True.intro⟩,⟨sg30786,True.intro,True.intro⟩⟩,⟨sg30789,⟨sg30788,True.intro,True.intro⟩,⟨sg30790,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_556All : degreeTree43_556.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30799,⟨sg30795,⟨sg30793,⟨sg30792,True.intro,True.intro⟩,⟨sg30794,True.intro,True.intro⟩⟩,⟨sg30797,⟨sg30796,True.intro,True.intro⟩,⟨sg30798,True.intro,True.intro⟩⟩⟩,⟨sg30803,⟨sg30801,⟨sg30800,True.intro,True.intro⟩,⟨sg30802,True.intro,True.intro⟩⟩,⟨sg30805,⟨sg30804,True.intro,True.intro⟩,⟨sg30806,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_557All : degreeTree43_557.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30791,degreeTree43_555All,degreeTree43_556All⟩ - -lemma degreeTree43_558All : degreeTree43_558.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30823,⟨sg30815,⟨sg30811,⟨sg30809,⟨sg30808,True.intro,True.intro⟩,⟨sg30810,True.intro,True.intro⟩⟩,⟨sg30813,⟨sg30812,True.intro,True.intro⟩,⟨sg30814,True.intro,True.intro⟩⟩⟩,⟨sg30819,⟨sg30817,⟨sg30816,True.intro,True.intro⟩,⟨sg30818,True.intro,True.intro⟩⟩,⟨sg30821,⟨sg30820,True.intro,True.intro⟩,⟨sg30822,True.intro,True.intro⟩⟩⟩⟩,⟨sg30831,⟨sg30827,⟨sg30825,⟨sg30824,True.intro,True.intro⟩,⟨sg30826,True.intro,True.intro⟩⟩,⟨sg30829,⟨sg30828,True.intro,True.intro⟩,⟨sg30830,True.intro,True.intro⟩⟩⟩,⟨sg30835,⟨sg30833,⟨sg30832,True.intro,True.intro⟩,⟨sg30834,True.intro,True.intro⟩⟩,⟨sg30837,⟨sg30836,True.intro,True.intro⟩,⟨sg30838,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_559All : degreeTree43_559.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30807,degreeTree43_557All,degreeTree43_558All⟩ - -lemma degreeTree43_560All : degreeTree43_560.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30855,⟨sg30847,⟨sg30843,⟨sg30841,⟨sg30840,True.intro,True.intro⟩,⟨sg30842,True.intro,True.intro⟩⟩,⟨sg30845,⟨sg30844,True.intro,True.intro⟩,⟨sg30846,True.intro,True.intro⟩⟩⟩,⟨sg30851,⟨sg30849,⟨sg30848,True.intro,True.intro⟩,⟨sg30850,True.intro,True.intro⟩⟩,⟨sg30853,⟨sg30852,True.intro,True.intro⟩,⟨sg30854,True.intro,True.intro⟩⟩⟩⟩,⟨sg30863,⟨sg30859,⟨sg30857,⟨sg30856,True.intro,True.intro⟩,⟨sg30858,True.intro,True.intro⟩⟩,⟨sg30861,⟨sg30860,True.intro,True.intro⟩,⟨sg30862,True.intro,True.intro⟩⟩⟩,⟨sg30867,⟨sg30865,⟨sg30864,True.intro,True.intro⟩,⟨sg30866,True.intro,True.intro⟩⟩,⟨sg30869,⟨sg30868,True.intro,True.intro⟩,⟨sg30870,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_561All : degreeTree43_561.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30887,⟨sg30879,⟨sg30875,⟨sg30873,⟨sg30872,True.intro,True.intro⟩,⟨sg30874,True.intro,True.intro⟩⟩,⟨sg30877,⟨sg30876,True.intro,True.intro⟩,⟨sg30878,True.intro,True.intro⟩⟩⟩,⟨sg30883,⟨sg30881,⟨sg30880,True.intro,True.intro⟩,⟨sg30882,True.intro,True.intro⟩⟩,⟨sg30885,⟨sg30884,True.intro,True.intro⟩,⟨sg30886,True.intro,True.intro⟩⟩⟩⟩,⟨sg30895,⟨sg30891,⟨sg30889,⟨sg30888,True.intro,True.intro⟩,⟨sg30890,True.intro,True.intro⟩⟩,⟨sg30893,⟨sg30892,True.intro,True.intro⟩,⟨sg30894,True.intro,True.intro⟩⟩⟩,⟨sg30899,⟨sg30897,⟨sg30896,True.intro,True.intro⟩,⟨sg30898,True.intro,True.intro⟩⟩,⟨sg30901,⟨sg30900,True.intro,True.intro⟩,⟨sg30902,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_562All : degreeTree43_562.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30871,degreeTree43_560All,degreeTree43_561All⟩ - -lemma degreeTree43_563All : degreeTree43_563.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30839,degreeTree43_559All,degreeTree43_562All⟩ - -lemma degreeTree43_564All : degreeTree43_564.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30774,degreeTree43_554All,degreeTree43_563All⟩ - -lemma degreeTree43_565All : degreeTree43_565.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30645,degreeTree43_545All,degreeTree43_564All⟩ - -lemma degreeTree43_566All : degreeTree43_566.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30387,degreeTree43_526All,degreeTree43_565All⟩ - -lemma degreeTree43_567All : degreeTree43_567.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30912,⟨sg30908,⟨sg30906,⟨sg30905,⟨sg30904,True.intro,True.intro⟩,True.intro⟩,⟨sg30907,True.intro,True.intro⟩⟩,⟨sg30910,⟨sg30909,True.intro,True.intro⟩,⟨sg30911,True.intro,True.intro⟩⟩⟩,⟨sg30916,⟨sg30914,⟨sg30913,True.intro,True.intro⟩,⟨sg30915,True.intro,True.intro⟩⟩,⟨sg30918,⟨sg30917,True.intro,True.intro⟩,⟨sg30919,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_568All : degreeTree43_568.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30928,⟨sg30924,⟨sg30922,⟨sg30921,True.intro,True.intro⟩,⟨sg30923,True.intro,True.intro⟩⟩,⟨sg30926,⟨sg30925,True.intro,True.intro⟩,⟨sg30927,True.intro,True.intro⟩⟩⟩,⟨sg30932,⟨sg30930,⟨sg30929,True.intro,True.intro⟩,⟨sg30931,True.intro,True.intro⟩⟩,⟨sg30934,⟨sg30933,True.intro,True.intro⟩,⟨sg30935,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_569All : degreeTree43_569.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30920,degreeTree43_567All,degreeTree43_568All⟩ - -lemma degreeTree43_570All : degreeTree43_570.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30952,⟨sg30944,⟨sg30940,⟨sg30938,⟨sg30937,True.intro,True.intro⟩,⟨sg30939,True.intro,True.intro⟩⟩,⟨sg30942,⟨sg30941,True.intro,True.intro⟩,⟨sg30943,True.intro,True.intro⟩⟩⟩,⟨sg30948,⟨sg30946,⟨sg30945,True.intro,True.intro⟩,⟨sg30947,True.intro,True.intro⟩⟩,⟨sg30950,⟨sg30949,True.intro,True.intro⟩,⟨sg30951,True.intro,True.intro⟩⟩⟩⟩,⟨sg30960,⟨sg30956,⟨sg30954,⟨sg30953,True.intro,True.intro⟩,⟨sg30955,True.intro,True.intro⟩⟩,⟨sg30958,⟨sg30957,True.intro,True.intro⟩,⟨sg30959,True.intro,True.intro⟩⟩⟩,⟨sg30964,⟨sg30962,⟨sg30961,True.intro,True.intro⟩,⟨sg30963,True.intro,True.intro⟩⟩,⟨sg30966,⟨sg30965,True.intro,True.intro⟩,⟨sg30967,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_571All : degreeTree43_571.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30936,degreeTree43_569All,degreeTree43_570All⟩ - -lemma degreeTree43_572All : degreeTree43_572.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30984,⟨sg30976,⟨sg30972,⟨sg30970,⟨sg30969,True.intro,True.intro⟩,⟨sg30971,True.intro,True.intro⟩⟩,⟨sg30974,⟨sg30973,True.intro,True.intro⟩,⟨sg30975,True.intro,True.intro⟩⟩⟩,⟨sg30980,⟨sg30978,⟨sg30977,True.intro,True.intro⟩,⟨sg30979,True.intro,True.intro⟩⟩,⟨sg30982,⟨sg30981,True.intro,True.intro⟩,⟨sg30983,True.intro,True.intro⟩⟩⟩⟩,⟨sg30992,⟨sg30988,⟨sg30986,⟨sg30985,True.intro,True.intro⟩,⟨sg30987,True.intro,True.intro⟩⟩,⟨sg30990,⟨sg30989,True.intro,True.intro⟩,⟨sg30991,True.intro,True.intro⟩⟩⟩,⟨sg30996,⟨sg30994,⟨sg30993,True.intro,True.intro⟩,⟨sg30995,True.intro,True.intro⟩⟩,⟨sg30998,⟨sg30997,True.intro,True.intro⟩,⟨sg30999,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_573All : degreeTree43_573.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31016,⟨sg31008,⟨sg31004,⟨sg31002,⟨sg31001,True.intro,True.intro⟩,⟨sg31003,True.intro,True.intro⟩⟩,⟨sg31006,⟨sg31005,True.intro,True.intro⟩,⟨sg31007,True.intro,True.intro⟩⟩⟩,⟨sg31012,⟨sg31010,⟨sg31009,True.intro,True.intro⟩,⟨sg31011,True.intro,True.intro⟩⟩,⟨sg31014,⟨sg31013,True.intro,True.intro⟩,⟨sg31015,True.intro,True.intro⟩⟩⟩⟩,⟨sg31024,⟨sg31020,⟨sg31018,⟨sg31017,True.intro,True.intro⟩,⟨sg31019,True.intro,True.intro⟩⟩,⟨sg31022,⟨sg31021,True.intro,True.intro⟩,⟨sg31023,True.intro,True.intro⟩⟩⟩,⟨sg31028,⟨sg31026,⟨sg31025,True.intro,True.intro⟩,⟨sg31027,True.intro,True.intro⟩⟩,⟨sg31030,⟨sg31029,True.intro,True.intro⟩,⟨sg31031,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_574All : degreeTree43_574.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31000,degreeTree43_572All,degreeTree43_573All⟩ - -lemma degreeTree43_575All : degreeTree43_575.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30968,degreeTree43_571All,degreeTree43_574All⟩ - -lemma degreeTree43_576All : degreeTree43_576.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31041,⟨sg31037,⟨sg31035,⟨sg31034,⟨sg31033,True.intro,True.intro⟩,True.intro⟩,⟨sg31036,True.intro,True.intro⟩⟩,⟨sg31039,⟨sg31038,True.intro,True.intro⟩,⟨sg31040,True.intro,True.intro⟩⟩⟩,⟨sg31045,⟨sg31043,⟨sg31042,True.intro,True.intro⟩,⟨sg31044,True.intro,True.intro⟩⟩,⟨sg31047,⟨sg31046,True.intro,True.intro⟩,⟨sg31048,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_577All : degreeTree43_577.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31057,⟨sg31053,⟨sg31051,⟨sg31050,True.intro,True.intro⟩,⟨sg31052,True.intro,True.intro⟩⟩,⟨sg31055,⟨sg31054,True.intro,True.intro⟩,⟨sg31056,True.intro,True.intro⟩⟩⟩,⟨sg31061,⟨sg31059,⟨sg31058,True.intro,True.intro⟩,⟨sg31060,True.intro,True.intro⟩⟩,⟨sg31063,⟨sg31062,True.intro,True.intro⟩,⟨sg31064,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_578All : degreeTree43_578.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31049,degreeTree43_576All,degreeTree43_577All⟩ - -lemma degreeTree43_579All : degreeTree43_579.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31081,⟨sg31073,⟨sg31069,⟨sg31067,⟨sg31066,True.intro,True.intro⟩,⟨sg31068,True.intro,True.intro⟩⟩,⟨sg31071,⟨sg31070,True.intro,True.intro⟩,⟨sg31072,True.intro,True.intro⟩⟩⟩,⟨sg31077,⟨sg31075,⟨sg31074,True.intro,True.intro⟩,⟨sg31076,True.intro,True.intro⟩⟩,⟨sg31079,⟨sg31078,True.intro,True.intro⟩,⟨sg31080,True.intro,True.intro⟩⟩⟩⟩,⟨sg31089,⟨sg31085,⟨sg31083,⟨sg31082,True.intro,True.intro⟩,⟨sg31084,True.intro,True.intro⟩⟩,⟨sg31087,⟨sg31086,True.intro,True.intro⟩,⟨sg31088,True.intro,True.intro⟩⟩⟩,⟨sg31093,⟨sg31091,⟨sg31090,True.intro,True.intro⟩,⟨sg31092,True.intro,True.intro⟩⟩,⟨sg31095,⟨sg31094,True.intro,True.intro⟩,⟨sg31096,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_580All : degreeTree43_580.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31065,degreeTree43_578All,degreeTree43_579All⟩ - -lemma degreeTree43_581All : degreeTree43_581.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31113,⟨sg31105,⟨sg31101,⟨sg31099,⟨sg31098,True.intro,True.intro⟩,⟨sg31100,True.intro,True.intro⟩⟩,⟨sg31103,⟨sg31102,True.intro,True.intro⟩,⟨sg31104,True.intro,True.intro⟩⟩⟩,⟨sg31109,⟨sg31107,⟨sg31106,True.intro,True.intro⟩,⟨sg31108,True.intro,True.intro⟩⟩,⟨sg31111,⟨sg31110,True.intro,True.intro⟩,⟨sg31112,True.intro,True.intro⟩⟩⟩⟩,⟨sg31121,⟨sg31117,⟨sg31115,⟨sg31114,True.intro,True.intro⟩,⟨sg31116,True.intro,True.intro⟩⟩,⟨sg31119,⟨sg31118,True.intro,True.intro⟩,⟨sg31120,True.intro,True.intro⟩⟩⟩,⟨sg31125,⟨sg31123,⟨sg31122,True.intro,True.intro⟩,⟨sg31124,True.intro,True.intro⟩⟩,⟨sg31127,⟨sg31126,True.intro,True.intro⟩,⟨sg31128,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_582All : degreeTree43_582.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31145,⟨sg31137,⟨sg31133,⟨sg31131,⟨sg31130,True.intro,True.intro⟩,⟨sg31132,True.intro,True.intro⟩⟩,⟨sg31135,⟨sg31134,True.intro,True.intro⟩,⟨sg31136,True.intro,True.intro⟩⟩⟩,⟨sg31141,⟨sg31139,⟨sg31138,True.intro,True.intro⟩,⟨sg31140,True.intro,True.intro⟩⟩,⟨sg31143,⟨sg31142,True.intro,True.intro⟩,⟨sg31144,True.intro,True.intro⟩⟩⟩⟩,⟨sg31153,⟨sg31149,⟨sg31147,⟨sg31146,True.intro,True.intro⟩,⟨sg31148,True.intro,True.intro⟩⟩,⟨sg31151,⟨sg31150,True.intro,True.intro⟩,⟨sg31152,True.intro,True.intro⟩⟩⟩,⟨sg31157,⟨sg31155,⟨sg31154,True.intro,True.intro⟩,⟨sg31156,True.intro,True.intro⟩⟩,⟨sg31159,⟨sg31158,True.intro,True.intro⟩,⟨sg31160,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_583All : degreeTree43_583.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31129,degreeTree43_581All,degreeTree43_582All⟩ - -lemma degreeTree43_584All : degreeTree43_584.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31097,degreeTree43_580All,degreeTree43_583All⟩ - -lemma degreeTree43_585All : degreeTree43_585.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31032,degreeTree43_575All,degreeTree43_584All⟩ - -lemma degreeTree43_586All : degreeTree43_586.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31170,⟨sg31166,⟨sg31164,⟨sg31163,⟨sg31162,True.intro,True.intro⟩,True.intro⟩,⟨sg31165,True.intro,True.intro⟩⟩,⟨sg31168,⟨sg31167,True.intro,True.intro⟩,⟨sg31169,True.intro,True.intro⟩⟩⟩,⟨sg31174,⟨sg31172,⟨sg31171,True.intro,True.intro⟩,⟨sg31173,True.intro,True.intro⟩⟩,⟨sg31176,⟨sg31175,True.intro,True.intro⟩,⟨sg31177,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_587All : degreeTree43_587.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31186,⟨sg31182,⟨sg31180,⟨sg31179,True.intro,True.intro⟩,⟨sg31181,True.intro,True.intro⟩⟩,⟨sg31184,⟨sg31183,True.intro,True.intro⟩,⟨sg31185,True.intro,True.intro⟩⟩⟩,⟨sg31190,⟨sg31188,⟨sg31187,True.intro,True.intro⟩,⟨sg31189,True.intro,True.intro⟩⟩,⟨sg31192,⟨sg31191,True.intro,True.intro⟩,⟨sg31193,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_588All : degreeTree43_588.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31178,degreeTree43_586All,degreeTree43_587All⟩ - -lemma degreeTree43_589All : degreeTree43_589.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31210,⟨sg31202,⟨sg31198,⟨sg31196,⟨sg31195,True.intro,True.intro⟩,⟨sg31197,True.intro,True.intro⟩⟩,⟨sg31200,⟨sg31199,True.intro,True.intro⟩,⟨sg31201,True.intro,True.intro⟩⟩⟩,⟨sg31206,⟨sg31204,⟨sg31203,True.intro,True.intro⟩,⟨sg31205,True.intro,True.intro⟩⟩,⟨sg31208,⟨sg31207,True.intro,True.intro⟩,⟨sg31209,True.intro,True.intro⟩⟩⟩⟩,⟨sg31218,⟨sg31214,⟨sg31212,⟨sg31211,True.intro,True.intro⟩,⟨sg31213,True.intro,True.intro⟩⟩,⟨sg31216,⟨sg31215,True.intro,True.intro⟩,⟨sg31217,True.intro,True.intro⟩⟩⟩,⟨sg31222,⟨sg31220,⟨sg31219,True.intro,True.intro⟩,⟨sg31221,True.intro,True.intro⟩⟩,⟨sg31224,⟨sg31223,True.intro,True.intro⟩,⟨sg31225,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_590All : degreeTree43_590.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31194,degreeTree43_588All,degreeTree43_589All⟩ - -lemma degreeTree43_591All : degreeTree43_591.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31242,⟨sg31234,⟨sg31230,⟨sg31228,⟨sg31227,True.intro,True.intro⟩,⟨sg31229,True.intro,True.intro⟩⟩,⟨sg31232,⟨sg31231,True.intro,True.intro⟩,⟨sg31233,True.intro,True.intro⟩⟩⟩,⟨sg31238,⟨sg31236,⟨sg31235,True.intro,True.intro⟩,⟨sg31237,True.intro,True.intro⟩⟩,⟨sg31240,⟨sg31239,True.intro,True.intro⟩,⟨sg31241,True.intro,True.intro⟩⟩⟩⟩,⟨sg31250,⟨sg31246,⟨sg31244,⟨sg31243,True.intro,True.intro⟩,⟨sg31245,True.intro,True.intro⟩⟩,⟨sg31248,⟨sg31247,True.intro,True.intro⟩,⟨sg31249,True.intro,True.intro⟩⟩⟩,⟨sg31254,⟨sg31252,⟨sg31251,True.intro,True.intro⟩,⟨sg31253,True.intro,True.intro⟩⟩,⟨sg31256,⟨sg31255,True.intro,True.intro⟩,⟨sg31257,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_592All : degreeTree43_592.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31274,⟨sg31266,⟨sg31262,⟨sg31260,⟨sg31259,True.intro,True.intro⟩,⟨sg31261,True.intro,True.intro⟩⟩,⟨sg31264,⟨sg31263,True.intro,True.intro⟩,⟨sg31265,True.intro,True.intro⟩⟩⟩,⟨sg31270,⟨sg31268,⟨sg31267,True.intro,True.intro⟩,⟨sg31269,True.intro,True.intro⟩⟩,⟨sg31272,⟨sg31271,True.intro,True.intro⟩,⟨sg31273,True.intro,True.intro⟩⟩⟩⟩,⟨sg31282,⟨sg31278,⟨sg31276,⟨sg31275,True.intro,True.intro⟩,⟨sg31277,True.intro,True.intro⟩⟩,⟨sg31280,⟨sg31279,True.intro,True.intro⟩,⟨sg31281,True.intro,True.intro⟩⟩⟩,⟨sg31286,⟨sg31284,⟨sg31283,True.intro,True.intro⟩,⟨sg31285,True.intro,True.intro⟩⟩,⟨sg31288,⟨sg31287,True.intro,True.intro⟩,⟨sg31289,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_593All : degreeTree43_593.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31258,degreeTree43_591All,degreeTree43_592All⟩ - -lemma degreeTree43_594All : degreeTree43_594.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31226,degreeTree43_590All,degreeTree43_593All⟩ - -lemma degreeTree43_595All : degreeTree43_595.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31299,⟨sg31295,⟨sg31293,⟨sg31292,⟨sg31291,True.intro,True.intro⟩,True.intro⟩,⟨sg31294,True.intro,True.intro⟩⟩,⟨sg31297,⟨sg31296,True.intro,True.intro⟩,⟨sg31298,True.intro,True.intro⟩⟩⟩,⟨sg31303,⟨sg31301,⟨sg31300,True.intro,True.intro⟩,⟨sg31302,True.intro,True.intro⟩⟩,⟨sg31305,⟨sg31304,True.intro,True.intro⟩,⟨sg31306,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_596All : degreeTree43_596.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31315,⟨sg31311,⟨sg31309,⟨sg31308,True.intro,True.intro⟩,⟨sg31310,True.intro,True.intro⟩⟩,⟨sg31313,⟨sg31312,True.intro,True.intro⟩,⟨sg31314,True.intro,True.intro⟩⟩⟩,⟨sg31319,⟨sg31317,⟨sg31316,True.intro,True.intro⟩,⟨sg31318,True.intro,True.intro⟩⟩,⟨sg31321,⟨sg31320,True.intro,True.intro⟩,⟨sg31322,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_597All : degreeTree43_597.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31307,degreeTree43_595All,degreeTree43_596All⟩ - -lemma degreeTree43_598All : degreeTree43_598.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31339,⟨sg31331,⟨sg31327,⟨sg31325,⟨sg31324,True.intro,True.intro⟩,⟨sg31326,True.intro,True.intro⟩⟩,⟨sg31329,⟨sg31328,True.intro,True.intro⟩,⟨sg31330,True.intro,True.intro⟩⟩⟩,⟨sg31335,⟨sg31333,⟨sg31332,True.intro,True.intro⟩,⟨sg31334,True.intro,True.intro⟩⟩,⟨sg31337,⟨sg31336,True.intro,True.intro⟩,⟨sg31338,True.intro,True.intro⟩⟩⟩⟩,⟨sg31347,⟨sg31343,⟨sg31341,⟨sg31340,True.intro,True.intro⟩,⟨sg31342,True.intro,True.intro⟩⟩,⟨sg31345,⟨sg31344,True.intro,True.intro⟩,⟨sg31346,True.intro,True.intro⟩⟩⟩,⟨sg31351,⟨sg31349,⟨sg31348,True.intro,True.intro⟩,⟨sg31350,True.intro,True.intro⟩⟩,⟨sg31353,⟨sg31352,True.intro,True.intro⟩,⟨sg31354,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_599All : degreeTree43_599.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31323,degreeTree43_597All,degreeTree43_598All⟩ - -lemma degreeTree43_600All : degreeTree43_600.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31371,⟨sg31363,⟨sg31359,⟨sg31357,⟨sg31356,True.intro,True.intro⟩,⟨sg31358,True.intro,True.intro⟩⟩,⟨sg31361,⟨sg31360,True.intro,True.intro⟩,⟨sg31362,True.intro,True.intro⟩⟩⟩,⟨sg31367,⟨sg31365,⟨sg31364,True.intro,True.intro⟩,⟨sg31366,True.intro,True.intro⟩⟩,⟨sg31369,⟨sg31368,True.intro,True.intro⟩,⟨sg31370,True.intro,True.intro⟩⟩⟩⟩,⟨sg31379,⟨sg31375,⟨sg31373,⟨sg31372,True.intro,True.intro⟩,⟨sg31374,True.intro,True.intro⟩⟩,⟨sg31377,⟨sg31376,True.intro,True.intro⟩,⟨sg31378,True.intro,True.intro⟩⟩⟩,⟨sg31383,⟨sg31381,⟨sg31380,True.intro,True.intro⟩,⟨sg31382,True.intro,True.intro⟩⟩,⟨sg31385,⟨sg31384,True.intro,True.intro⟩,⟨sg31386,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_601All : degreeTree43_601.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31403,⟨sg31395,⟨sg31391,⟨sg31389,⟨sg31388,True.intro,True.intro⟩,⟨sg31390,True.intro,True.intro⟩⟩,⟨sg31393,⟨sg31392,True.intro,True.intro⟩,⟨sg31394,True.intro,True.intro⟩⟩⟩,⟨sg31399,⟨sg31397,⟨sg31396,True.intro,True.intro⟩,⟨sg31398,True.intro,True.intro⟩⟩,⟨sg31401,⟨sg31400,True.intro,True.intro⟩,⟨sg31402,True.intro,True.intro⟩⟩⟩⟩,⟨sg31411,⟨sg31407,⟨sg31405,⟨sg31404,True.intro,True.intro⟩,⟨sg31406,True.intro,True.intro⟩⟩,⟨sg31409,⟨sg31408,True.intro,True.intro⟩,⟨sg31410,True.intro,True.intro⟩⟩⟩,⟨sg31415,⟨sg31413,⟨sg31412,True.intro,True.intro⟩,⟨sg31414,True.intro,True.intro⟩⟩,⟨sg31417,⟨sg31416,True.intro,True.intro⟩,⟨sg31418,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_602All : degreeTree43_602.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31387,degreeTree43_600All,degreeTree43_601All⟩ - -lemma degreeTree43_603All : degreeTree43_603.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31355,degreeTree43_599All,degreeTree43_602All⟩ - -lemma degreeTree43_604All : degreeTree43_604.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31290,degreeTree43_594All,degreeTree43_603All⟩ - -lemma degreeTree43_605All : degreeTree43_605.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31161,degreeTree43_585All,degreeTree43_604All⟩ - -lemma degreeTree43_606All : degreeTree43_606.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31428,⟨sg31424,⟨sg31422,⟨sg31421,⟨sg31420,True.intro,True.intro⟩,True.intro⟩,⟨sg31423,True.intro,True.intro⟩⟩,⟨sg31426,⟨sg31425,True.intro,True.intro⟩,⟨sg31427,True.intro,True.intro⟩⟩⟩,⟨sg31432,⟨sg31430,⟨sg31429,True.intro,True.intro⟩,⟨sg31431,True.intro,True.intro⟩⟩,⟨sg31434,⟨sg31433,True.intro,True.intro⟩,⟨sg31435,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_607All : degreeTree43_607.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31444,⟨sg31440,⟨sg31438,⟨sg31437,True.intro,True.intro⟩,⟨sg31439,True.intro,True.intro⟩⟩,⟨sg31442,⟨sg31441,True.intro,True.intro⟩,⟨sg31443,True.intro,True.intro⟩⟩⟩,⟨sg31448,⟨sg31446,⟨sg31445,True.intro,True.intro⟩,⟨sg31447,True.intro,True.intro⟩⟩,⟨sg31450,⟨sg31449,True.intro,True.intro⟩,⟨sg31451,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_608All : degreeTree43_608.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31436,degreeTree43_606All,degreeTree43_607All⟩ - -lemma degreeTree43_609All : degreeTree43_609.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31468,⟨sg31460,⟨sg31456,⟨sg31454,⟨sg31453,True.intro,True.intro⟩,⟨sg31455,True.intro,True.intro⟩⟩,⟨sg31458,⟨sg31457,True.intro,True.intro⟩,⟨sg31459,True.intro,True.intro⟩⟩⟩,⟨sg31464,⟨sg31462,⟨sg31461,True.intro,True.intro⟩,⟨sg31463,True.intro,True.intro⟩⟩,⟨sg31466,⟨sg31465,True.intro,True.intro⟩,⟨sg31467,True.intro,True.intro⟩⟩⟩⟩,⟨sg31476,⟨sg31472,⟨sg31470,⟨sg31469,True.intro,True.intro⟩,⟨sg31471,True.intro,True.intro⟩⟩,⟨sg31474,⟨sg31473,True.intro,True.intro⟩,⟨sg31475,True.intro,True.intro⟩⟩⟩,⟨sg31480,⟨sg31478,⟨sg31477,True.intro,True.intro⟩,⟨sg31479,True.intro,True.intro⟩⟩,⟨sg31482,⟨sg31481,True.intro,True.intro⟩,⟨sg31483,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_610All : degreeTree43_610.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31452,degreeTree43_608All,degreeTree43_609All⟩ - -lemma degreeTree43_611All : degreeTree43_611.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31500,⟨sg31492,⟨sg31488,⟨sg31486,⟨sg31485,True.intro,True.intro⟩,⟨sg31487,True.intro,True.intro⟩⟩,⟨sg31490,⟨sg31489,True.intro,True.intro⟩,⟨sg31491,True.intro,True.intro⟩⟩⟩,⟨sg31496,⟨sg31494,⟨sg31493,True.intro,True.intro⟩,⟨sg31495,True.intro,True.intro⟩⟩,⟨sg31498,⟨sg31497,True.intro,True.intro⟩,⟨sg31499,True.intro,True.intro⟩⟩⟩⟩,⟨sg31508,⟨sg31504,⟨sg31502,⟨sg31501,True.intro,True.intro⟩,⟨sg31503,True.intro,True.intro⟩⟩,⟨sg31506,⟨sg31505,True.intro,True.intro⟩,⟨sg31507,True.intro,True.intro⟩⟩⟩,⟨sg31512,⟨sg31510,⟨sg31509,True.intro,True.intro⟩,⟨sg31511,True.intro,True.intro⟩⟩,⟨sg31514,⟨sg31513,True.intro,True.intro⟩,⟨sg31515,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_612All : degreeTree43_612.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31532,⟨sg31524,⟨sg31520,⟨sg31518,⟨sg31517,True.intro,True.intro⟩,⟨sg31519,True.intro,True.intro⟩⟩,⟨sg31522,⟨sg31521,True.intro,True.intro⟩,⟨sg31523,True.intro,True.intro⟩⟩⟩,⟨sg31528,⟨sg31526,⟨sg31525,True.intro,True.intro⟩,⟨sg31527,True.intro,True.intro⟩⟩,⟨sg31530,⟨sg31529,True.intro,True.intro⟩,⟨sg31531,True.intro,True.intro⟩⟩⟩⟩,⟨sg31540,⟨sg31536,⟨sg31534,⟨sg31533,True.intro,True.intro⟩,⟨sg31535,True.intro,True.intro⟩⟩,⟨sg31538,⟨sg31537,True.intro,True.intro⟩,⟨sg31539,True.intro,True.intro⟩⟩⟩,⟨sg31544,⟨sg31542,⟨sg31541,True.intro,True.intro⟩,⟨sg31543,True.intro,True.intro⟩⟩,⟨sg31546,⟨sg31545,True.intro,True.intro⟩,⟨sg31547,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_613All : degreeTree43_613.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31516,degreeTree43_611All,degreeTree43_612All⟩ - -lemma degreeTree43_614All : degreeTree43_614.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31484,degreeTree43_610All,degreeTree43_613All⟩ - -lemma degreeTree43_615All : degreeTree43_615.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31557,⟨sg31553,⟨sg31551,⟨sg31550,⟨sg31549,True.intro,True.intro⟩,True.intro⟩,⟨sg31552,True.intro,True.intro⟩⟩,⟨sg31555,⟨sg31554,True.intro,True.intro⟩,⟨sg31556,True.intro,True.intro⟩⟩⟩,⟨sg31561,⟨sg31559,⟨sg31558,True.intro,True.intro⟩,⟨sg31560,True.intro,True.intro⟩⟩,⟨sg31563,⟨sg31562,True.intro,True.intro⟩,⟨sg31564,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_616All : degreeTree43_616.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31573,⟨sg31569,⟨sg31567,⟨sg31566,True.intro,True.intro⟩,⟨sg31568,True.intro,True.intro⟩⟩,⟨sg31571,⟨sg31570,True.intro,True.intro⟩,⟨sg31572,True.intro,True.intro⟩⟩⟩,⟨sg31577,⟨sg31575,⟨sg31574,True.intro,True.intro⟩,⟨sg31576,True.intro,True.intro⟩⟩,⟨sg31579,⟨sg31578,True.intro,True.intro⟩,⟨sg31580,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_617All : degreeTree43_617.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31565,degreeTree43_615All,degreeTree43_616All⟩ - -lemma degreeTree43_618All : degreeTree43_618.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31597,⟨sg31589,⟨sg31585,⟨sg31583,⟨sg31582,True.intro,True.intro⟩,⟨sg31584,True.intro,True.intro⟩⟩,⟨sg31587,⟨sg31586,True.intro,True.intro⟩,⟨sg31588,True.intro,True.intro⟩⟩⟩,⟨sg31593,⟨sg31591,⟨sg31590,True.intro,True.intro⟩,⟨sg31592,True.intro,True.intro⟩⟩,⟨sg31595,⟨sg31594,True.intro,True.intro⟩,⟨sg31596,True.intro,True.intro⟩⟩⟩⟩,⟨sg31605,⟨sg31601,⟨sg31599,⟨sg31598,True.intro,True.intro⟩,⟨sg31600,True.intro,True.intro⟩⟩,⟨sg31603,⟨sg31602,True.intro,True.intro⟩,⟨sg31604,True.intro,True.intro⟩⟩⟩,⟨sg31609,⟨sg31607,⟨sg31606,True.intro,True.intro⟩,⟨sg31608,True.intro,True.intro⟩⟩,⟨sg31611,⟨sg31610,True.intro,True.intro⟩,⟨sg31612,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_619All : degreeTree43_619.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31581,degreeTree43_617All,degreeTree43_618All⟩ - -lemma degreeTree43_620All : degreeTree43_620.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31629,⟨sg31621,⟨sg31617,⟨sg31615,⟨sg31614,True.intro,True.intro⟩,⟨sg31616,True.intro,True.intro⟩⟩,⟨sg31619,⟨sg31618,True.intro,True.intro⟩,⟨sg31620,True.intro,True.intro⟩⟩⟩,⟨sg31625,⟨sg31623,⟨sg31622,True.intro,True.intro⟩,⟨sg31624,True.intro,True.intro⟩⟩,⟨sg31627,⟨sg31626,True.intro,True.intro⟩,⟨sg31628,True.intro,True.intro⟩⟩⟩⟩,⟨sg31637,⟨sg31633,⟨sg31631,⟨sg31630,True.intro,True.intro⟩,⟨sg31632,True.intro,True.intro⟩⟩,⟨sg31635,⟨sg31634,True.intro,True.intro⟩,⟨sg31636,True.intro,True.intro⟩⟩⟩,⟨sg31641,⟨sg31639,⟨sg31638,True.intro,True.intro⟩,⟨sg31640,True.intro,True.intro⟩⟩,⟨sg31643,⟨sg31642,True.intro,True.intro⟩,⟨sg31644,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_621All : degreeTree43_621.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31661,⟨sg31653,⟨sg31649,⟨sg31647,⟨sg31646,True.intro,True.intro⟩,⟨sg31648,True.intro,True.intro⟩⟩,⟨sg31651,⟨sg31650,True.intro,True.intro⟩,⟨sg31652,True.intro,True.intro⟩⟩⟩,⟨sg31657,⟨sg31655,⟨sg31654,True.intro,True.intro⟩,⟨sg31656,True.intro,True.intro⟩⟩,⟨sg31659,⟨sg31658,True.intro,True.intro⟩,⟨sg31660,True.intro,True.intro⟩⟩⟩⟩,⟨sg31669,⟨sg31665,⟨sg31663,⟨sg31662,True.intro,True.intro⟩,⟨sg31664,True.intro,True.intro⟩⟩,⟨sg31667,⟨sg31666,True.intro,True.intro⟩,⟨sg31668,True.intro,True.intro⟩⟩⟩,⟨sg31673,⟨sg31671,⟨sg31670,True.intro,True.intro⟩,⟨sg31672,True.intro,True.intro⟩⟩,⟨sg31675,⟨sg31674,True.intro,True.intro⟩,⟨sg31676,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_622All : degreeTree43_622.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31645,degreeTree43_620All,degreeTree43_621All⟩ - -lemma degreeTree43_623All : degreeTree43_623.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31613,degreeTree43_619All,degreeTree43_622All⟩ - -lemma degreeTree43_624All : degreeTree43_624.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31548,degreeTree43_614All,degreeTree43_623All⟩ - -lemma degreeTree43_625All : degreeTree43_625.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31686,⟨sg31682,⟨sg31680,⟨sg31679,⟨sg31678,True.intro,True.intro⟩,True.intro⟩,⟨sg31681,True.intro,True.intro⟩⟩,⟨sg31684,⟨sg31683,True.intro,True.intro⟩,⟨sg31685,True.intro,True.intro⟩⟩⟩,⟨sg31690,⟨sg31688,⟨sg31687,True.intro,True.intro⟩,⟨sg31689,True.intro,True.intro⟩⟩,⟨sg31692,⟨sg31691,True.intro,True.intro⟩,⟨sg31693,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_626All : degreeTree43_626.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31702,⟨sg31698,⟨sg31696,⟨sg31695,True.intro,True.intro⟩,⟨sg31697,True.intro,True.intro⟩⟩,⟨sg31700,⟨sg31699,True.intro,True.intro⟩,⟨sg31701,True.intro,True.intro⟩⟩⟩,⟨sg31706,⟨sg31704,⟨sg31703,True.intro,True.intro⟩,⟨sg31705,True.intro,True.intro⟩⟩,⟨sg31708,⟨sg31707,True.intro,True.intro⟩,⟨sg31709,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_627All : degreeTree43_627.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31694,degreeTree43_625All,degreeTree43_626All⟩ - -lemma degreeTree43_628All : degreeTree43_628.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31726,⟨sg31718,⟨sg31714,⟨sg31712,⟨sg31711,True.intro,True.intro⟩,⟨sg31713,True.intro,True.intro⟩⟩,⟨sg31716,⟨sg31715,True.intro,True.intro⟩,⟨sg31717,True.intro,True.intro⟩⟩⟩,⟨sg31722,⟨sg31720,⟨sg31719,True.intro,True.intro⟩,⟨sg31721,True.intro,True.intro⟩⟩,⟨sg31724,⟨sg31723,True.intro,True.intro⟩,⟨sg31725,True.intro,True.intro⟩⟩⟩⟩,⟨sg31734,⟨sg31730,⟨sg31728,⟨sg31727,True.intro,True.intro⟩,⟨sg31729,True.intro,True.intro⟩⟩,⟨sg31732,⟨sg31731,True.intro,True.intro⟩,⟨sg31733,True.intro,True.intro⟩⟩⟩,⟨sg31738,⟨sg31736,⟨sg31735,True.intro,True.intro⟩,⟨sg31737,True.intro,True.intro⟩⟩,⟨sg31740,⟨sg31739,True.intro,True.intro⟩,⟨sg31741,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_629All : degreeTree43_629.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31710,degreeTree43_627All,degreeTree43_628All⟩ - -lemma degreeTree43_630All : degreeTree43_630.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31758,⟨sg31750,⟨sg31746,⟨sg31744,⟨sg31743,True.intro,True.intro⟩,⟨sg31745,True.intro,True.intro⟩⟩,⟨sg31748,⟨sg31747,True.intro,True.intro⟩,⟨sg31749,True.intro,True.intro⟩⟩⟩,⟨sg31754,⟨sg31752,⟨sg31751,True.intro,True.intro⟩,⟨sg31753,True.intro,True.intro⟩⟩,⟨sg31756,⟨sg31755,True.intro,True.intro⟩,⟨sg31757,True.intro,True.intro⟩⟩⟩⟩,⟨sg31766,⟨sg31762,⟨sg31760,⟨sg31759,True.intro,True.intro⟩,⟨sg31761,True.intro,True.intro⟩⟩,⟨sg31764,⟨sg31763,True.intro,True.intro⟩,⟨sg31765,True.intro,True.intro⟩⟩⟩,⟨sg31770,⟨sg31768,⟨sg31767,True.intro,True.intro⟩,⟨sg31769,True.intro,True.intro⟩⟩,⟨sg31772,⟨sg31771,True.intro,True.intro⟩,⟨sg31773,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_631All : degreeTree43_631.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31790,⟨sg31782,⟨sg31778,⟨sg31776,⟨sg31775,True.intro,True.intro⟩,⟨sg31777,True.intro,True.intro⟩⟩,⟨sg31780,⟨sg31779,True.intro,True.intro⟩,⟨sg31781,True.intro,True.intro⟩⟩⟩,⟨sg31786,⟨sg31784,⟨sg31783,True.intro,True.intro⟩,⟨sg31785,True.intro,True.intro⟩⟩,⟨sg31788,⟨sg31787,True.intro,True.intro⟩,⟨sg31789,True.intro,True.intro⟩⟩⟩⟩,⟨sg31798,⟨sg31794,⟨sg31792,⟨sg31791,True.intro,True.intro⟩,⟨sg31793,True.intro,True.intro⟩⟩,⟨sg31796,⟨sg31795,True.intro,True.intro⟩,⟨sg31797,True.intro,True.intro⟩⟩⟩,⟨sg31802,⟨sg31800,⟨sg31799,True.intro,True.intro⟩,⟨sg31801,True.intro,True.intro⟩⟩,⟨sg31804,⟨sg31803,True.intro,True.intro⟩,⟨sg31805,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_632All : degreeTree43_632.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31774,degreeTree43_630All,degreeTree43_631All⟩ - -lemma degreeTree43_633All : degreeTree43_633.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31742,degreeTree43_629All,degreeTree43_632All⟩ - -lemma degreeTree43_634All : degreeTree43_634.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31815,⟨sg31811,⟨sg31809,⟨sg31808,⟨sg31807,True.intro,True.intro⟩,True.intro⟩,⟨sg31810,True.intro,True.intro⟩⟩,⟨sg31813,⟨sg31812,True.intro,True.intro⟩,⟨sg31814,True.intro,True.intro⟩⟩⟩,⟨sg31819,⟨sg31817,⟨sg31816,True.intro,True.intro⟩,⟨sg31818,True.intro,True.intro⟩⟩,⟨sg31821,⟨sg31820,True.intro,True.intro⟩,⟨sg31822,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_635All : degreeTree43_635.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31831,⟨sg31827,⟨sg31825,⟨sg31824,True.intro,True.intro⟩,⟨sg31826,True.intro,True.intro⟩⟩,⟨sg31829,⟨sg31828,True.intro,True.intro⟩,⟨sg31830,True.intro,True.intro⟩⟩⟩,⟨sg31835,⟨sg31833,⟨sg31832,True.intro,True.intro⟩,⟨sg31834,True.intro,True.intro⟩⟩,⟨sg31837,⟨sg31836,True.intro,True.intro⟩,⟨sg31838,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree43_636All : degreeTree43_636.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31823,degreeTree43_634All,degreeTree43_635All⟩ - -lemma degreeTree43_637All : degreeTree43_637.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31855,⟨sg31847,⟨sg31843,⟨sg31841,⟨sg31840,True.intro,True.intro⟩,⟨sg31842,True.intro,True.intro⟩⟩,⟨sg31845,⟨sg31844,True.intro,True.intro⟩,⟨sg31846,True.intro,True.intro⟩⟩⟩,⟨sg31851,⟨sg31849,⟨sg31848,True.intro,True.intro⟩,⟨sg31850,True.intro,True.intro⟩⟩,⟨sg31853,⟨sg31852,True.intro,True.intro⟩,⟨sg31854,True.intro,True.intro⟩⟩⟩⟩,⟨sg31863,⟨sg31859,⟨sg31857,⟨sg31856,True.intro,True.intro⟩,⟨sg31858,True.intro,True.intro⟩⟩,⟨sg31861,⟨sg31860,True.intro,True.intro⟩,⟨sg31862,True.intro,True.intro⟩⟩⟩,⟨sg31867,⟨sg31865,⟨sg31864,True.intro,True.intro⟩,⟨sg31866,True.intro,True.intro⟩⟩,⟨sg31869,⟨sg31868,True.intro,True.intro⟩,⟨sg31870,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_638All : degreeTree43_638.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31839,degreeTree43_636All,degreeTree43_637All⟩ - -lemma degreeTree43_639All : degreeTree43_639.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31887,⟨sg31879,⟨sg31875,⟨sg31873,⟨sg31872,True.intro,True.intro⟩,⟨sg31874,True.intro,True.intro⟩⟩,⟨sg31877,⟨sg31876,True.intro,True.intro⟩,⟨sg31878,True.intro,True.intro⟩⟩⟩,⟨sg31883,⟨sg31881,⟨sg31880,True.intro,True.intro⟩,⟨sg31882,True.intro,True.intro⟩⟩,⟨sg31885,⟨sg31884,True.intro,True.intro⟩,⟨sg31886,True.intro,True.intro⟩⟩⟩⟩,⟨sg31895,⟨sg31891,⟨sg31889,⟨sg31888,True.intro,True.intro⟩,⟨sg31890,True.intro,True.intro⟩⟩,⟨sg31893,⟨sg31892,True.intro,True.intro⟩,⟨sg31894,True.intro,True.intro⟩⟩⟩,⟨sg31899,⟨sg31897,⟨sg31896,True.intro,True.intro⟩,⟨sg31898,True.intro,True.intro⟩⟩,⟨sg31901,⟨sg31900,True.intro,True.intro⟩,⟨sg31902,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_640All : degreeTree43_640.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31919,⟨sg31911,⟨sg31907,⟨sg31905,⟨sg31904,True.intro,True.intro⟩,⟨sg31906,True.intro,True.intro⟩⟩,⟨sg31909,⟨sg31908,True.intro,True.intro⟩,⟨sg31910,True.intro,True.intro⟩⟩⟩,⟨sg31915,⟨sg31913,⟨sg31912,True.intro,True.intro⟩,⟨sg31914,True.intro,True.intro⟩⟩,⟨sg31917,⟨sg31916,True.intro,True.intro⟩,⟨sg31918,True.intro,True.intro⟩⟩⟩⟩,⟨sg31927,⟨sg31923,⟨sg31921,⟨sg31920,True.intro,True.intro⟩,⟨sg31922,True.intro,True.intro⟩⟩,⟨sg31925,⟨sg31924,True.intro,True.intro⟩,⟨sg31926,True.intro,True.intro⟩⟩⟩,⟨sg31931,⟨sg31929,⟨sg31928,True.intro,True.intro⟩,⟨sg31930,True.intro,True.intro⟩⟩,⟨sg31933,⟨sg31932,True.intro,True.intro⟩,⟨sg31934,True.intro,True.intro⟩⟩⟩⟩⟩ - -lemma degreeTree43_641All : degreeTree43_641.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31903,degreeTree43_639All,degreeTree43_640All⟩ - -lemma degreeTree43_642All : degreeTree43_642.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31871,degreeTree43_638All,degreeTree43_641All⟩ - -lemma degreeTree43_643All : degreeTree43_643.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31806,degreeTree43_633All,degreeTree43_642All⟩ - -lemma degreeTree43_644All : degreeTree43_644.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31677,degreeTree43_624All,degreeTree43_643All⟩ - -lemma degreeTree43_645All : degreeTree43_645.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31419,degreeTree43_605All,degreeTree43_644All⟩ - -lemma degreeTree43_646All : degreeTree43_646.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg30903,degreeTree43_566All,degreeTree43_645All⟩ - -lemma degreeTree43_647All : degreeTree43_647.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg29870,degreeTree43_485All,degreeTree43_646All⟩ - -lemma degreeTree43_648All : degreeTree43_648.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg27805,degreeTree43_324All,degreeTree43_647All⟩ - -lemma degreeTreeAll43 : degreeTree43.All - (fun rs => SquareOccurs (candidate 6 5 1) (rowDiagram rs)) := by - have hp : rowDiagram [12,10,4,3,2,2,2,2,2,2,1,1] = candidate 6 5 1 := rowDiagram_candidate (M := 6) (b := 5) (δ := 1) (by decide) - rw [← hp] - exact degreeTree43_648All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData43 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes58 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes59 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes60 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes61 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes62 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes63 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes64 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes65 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes66 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes67 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes68 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes69 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes70 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes71 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes72 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes73 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes74 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes75 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes76 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes77 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes78 + +namespace OAI + +/-! Degree Tree Proof 43. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree43_0All : degreeTree43_0.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23683,⟨sg23679,⟨sg23677,⟨sg23676,⟨sg23675,True.intro,True.intro⟩,True.intro⟩,⟨sg23678,True.intro,True.intro⟩⟩,⟨sg23681,⟨sg23680,True.intro,True.intro⟩,⟨sg23682,True.intro,True.intro⟩⟩⟩,⟨sg23687,⟨sg23685,⟨sg23684,True.intro,True.intro⟩,⟨sg23686,True.intro,True.intro⟩⟩,⟨sg23689,⟨sg23688,True.intro,True.intro⟩,⟨sg23690,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_1All : degreeTree43_1.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23699,⟨sg23695,⟨sg23693,⟨sg23692,True.intro,True.intro⟩,⟨sg23694,True.intro,True.intro⟩⟩,⟨sg23697,⟨sg23696,True.intro,True.intro⟩,⟨sg23698,True.intro,True.intro⟩⟩⟩,⟨sg23703,⟨sg23701,⟨sg23700,True.intro,True.intro⟩,⟨sg23702,True.intro,True.intro⟩⟩,⟨sg23705,⟨sg23704,True.intro,True.intro⟩,⟨sg23706,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_2All : degreeTree43_2.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23691,degreeTree43_0All,degreeTree43_1All⟩ + +lemma degreeTree43_3All : degreeTree43_3.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23723,⟨sg23715,⟨sg23711,⟨sg23709,⟨sg23708,True.intro,True.intro⟩,⟨sg23710,True.intro,True.intro⟩⟩,⟨sg23713,⟨sg23712,True.intro,True.intro⟩,⟨sg23714,True.intro,True.intro⟩⟩⟩,⟨sg23719,⟨sg23717,⟨sg23716,True.intro,True.intro⟩,⟨sg23718,True.intro,True.intro⟩⟩,⟨sg23721,⟨sg23720,True.intro,True.intro⟩,⟨sg23722,True.intro,True.intro⟩⟩⟩⟩,⟨sg23731,⟨sg23727,⟨sg23725,⟨sg23724,True.intro,True.intro⟩,⟨sg23726,True.intro,True.intro⟩⟩,⟨sg23729,⟨sg23728,True.intro,True.intro⟩,⟨sg23730,True.intro,True.intro⟩⟩⟩,⟨sg23735,⟨sg23733,⟨sg23732,True.intro,True.intro⟩,⟨sg23734,True.intro,True.intro⟩⟩,⟨sg23737,⟨sg23736,True.intro,True.intro⟩,⟨sg23738,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_4All : degreeTree43_4.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23707,degreeTree43_2All,degreeTree43_3All⟩ + +lemma degreeTree43_5All : degreeTree43_5.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23748,⟨sg23744,⟨sg23742,⟨sg23741,⟨sg23740,True.intro,True.intro⟩,True.intro⟩,⟨sg23743,True.intro,True.intro⟩⟩,⟨sg23746,⟨sg23745,True.intro,True.intro⟩,⟨sg23747,True.intro,True.intro⟩⟩⟩,⟨sg23752,⟨sg23750,⟨sg23749,True.intro,True.intro⟩,⟨sg23751,True.intro,True.intro⟩⟩,⟨sg23754,⟨sg23753,True.intro,True.intro⟩,⟨sg23755,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_6All : degreeTree43_6.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23764,⟨sg23760,⟨sg23758,⟨sg23757,True.intro,True.intro⟩,⟨sg23759,True.intro,True.intro⟩⟩,⟨sg23762,⟨sg23761,True.intro,True.intro⟩,⟨sg23763,True.intro,True.intro⟩⟩⟩,⟨sg23768,⟨sg23766,⟨sg23765,True.intro,True.intro⟩,⟨sg23767,True.intro,True.intro⟩⟩,⟨sg23770,⟨sg23769,True.intro,True.intro⟩,⟨sg23771,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_7All : degreeTree43_7.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23756,degreeTree43_5All,degreeTree43_6All⟩ + +lemma degreeTree43_8All : degreeTree43_8.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23788,⟨sg23780,⟨sg23776,⟨sg23774,⟨sg23773,True.intro,True.intro⟩,⟨sg23775,True.intro,True.intro⟩⟩,⟨sg23778,⟨sg23777,True.intro,True.intro⟩,⟨sg23779,True.intro,True.intro⟩⟩⟩,⟨sg23784,⟨sg23782,⟨sg23781,True.intro,True.intro⟩,⟨sg23783,True.intro,True.intro⟩⟩,⟨sg23786,⟨sg23785,True.intro,True.intro⟩,⟨sg23787,True.intro,True.intro⟩⟩⟩⟩,⟨sg23796,⟨sg23792,⟨sg23790,⟨sg23789,True.intro,True.intro⟩,⟨sg23791,True.intro,True.intro⟩⟩,⟨sg23794,⟨sg23793,True.intro,True.intro⟩,⟨sg23795,True.intro,True.intro⟩⟩⟩,⟨sg23800,⟨sg23798,⟨sg23797,True.intro,True.intro⟩,⟨sg23799,True.intro,True.intro⟩⟩,⟨sg23802,⟨sg23801,True.intro,True.intro⟩,⟨sg23803,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_9All : degreeTree43_9.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23772,degreeTree43_7All,degreeTree43_8All⟩ + +lemma degreeTree43_10All : degreeTree43_10.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23739,degreeTree43_4All,degreeTree43_9All⟩ + +lemma degreeTree43_11All : degreeTree43_11.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23813,⟨sg23809,⟨sg23807,⟨sg23806,⟨sg23805,True.intro,True.intro⟩,True.intro⟩,⟨sg23808,True.intro,True.intro⟩⟩,⟨sg23811,⟨sg23810,True.intro,True.intro⟩,⟨sg23812,True.intro,True.intro⟩⟩⟩,⟨sg23817,⟨sg23815,⟨sg23814,True.intro,True.intro⟩,⟨sg23816,True.intro,True.intro⟩⟩,⟨sg23819,⟨sg23818,True.intro,True.intro⟩,⟨sg23820,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_12All : degreeTree43_12.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23829,⟨sg23825,⟨sg23823,⟨sg23822,True.intro,True.intro⟩,⟨sg23824,True.intro,True.intro⟩⟩,⟨sg23827,⟨sg23826,True.intro,True.intro⟩,⟨sg23828,True.intro,True.intro⟩⟩⟩,⟨sg23833,⟨sg23831,⟨sg23830,True.intro,True.intro⟩,⟨sg23832,True.intro,True.intro⟩⟩,⟨sg23835,⟨sg23834,True.intro,True.intro⟩,⟨sg23836,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_13All : degreeTree43_13.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23821,degreeTree43_11All,degreeTree43_12All⟩ + +lemma degreeTree43_14All : degreeTree43_14.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23853,⟨sg23845,⟨sg23841,⟨sg23839,⟨sg23838,True.intro,True.intro⟩,⟨sg23840,True.intro,True.intro⟩⟩,⟨sg23843,⟨sg23842,True.intro,True.intro⟩,⟨sg23844,True.intro,True.intro⟩⟩⟩,⟨sg23849,⟨sg23847,⟨sg23846,True.intro,True.intro⟩,⟨sg23848,True.intro,True.intro⟩⟩,⟨sg23851,⟨sg23850,True.intro,True.intro⟩,⟨sg23852,True.intro,True.intro⟩⟩⟩⟩,⟨sg23861,⟨sg23857,⟨sg23855,⟨sg23854,True.intro,True.intro⟩,⟨sg23856,True.intro,True.intro⟩⟩,⟨sg23859,⟨sg23858,True.intro,True.intro⟩,⟨sg23860,True.intro,True.intro⟩⟩⟩,⟨sg23865,⟨sg23863,⟨sg23862,True.intro,True.intro⟩,⟨sg23864,True.intro,True.intro⟩⟩,⟨sg23867,⟨sg23866,True.intro,True.intro⟩,⟨sg23868,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_15All : degreeTree43_15.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23837,degreeTree43_13All,degreeTree43_14All⟩ + +lemma degreeTree43_16All : degreeTree43_16.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23885,⟨sg23877,⟨sg23873,⟨sg23871,⟨sg23870,True.intro,True.intro⟩,⟨sg23872,True.intro,True.intro⟩⟩,⟨sg23875,⟨sg23874,True.intro,True.intro⟩,⟨sg23876,True.intro,True.intro⟩⟩⟩,⟨sg23881,⟨sg23879,⟨sg23878,True.intro,True.intro⟩,⟨sg23880,True.intro,True.intro⟩⟩,⟨sg23883,⟨sg23882,True.intro,True.intro⟩,⟨sg23884,True.intro,True.intro⟩⟩⟩⟩,⟨sg23893,⟨sg23889,⟨sg23887,⟨sg23886,True.intro,True.intro⟩,⟨sg23888,True.intro,True.intro⟩⟩,⟨sg23891,⟨sg23890,True.intro,True.intro⟩,⟨sg23892,True.intro,True.intro⟩⟩⟩,⟨sg23897,⟨sg23895,⟨sg23894,True.intro,True.intro⟩,⟨sg23896,True.intro,True.intro⟩⟩,⟨sg23899,⟨sg23898,True.intro,True.intro⟩,⟨sg23900,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_17All : degreeTree43_17.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23917,⟨sg23909,⟨sg23905,⟨sg23903,⟨sg23902,True.intro,True.intro⟩,⟨sg23904,True.intro,True.intro⟩⟩,⟨sg23907,⟨sg23906,True.intro,True.intro⟩,⟨sg23908,True.intro,True.intro⟩⟩⟩,⟨sg23913,⟨sg23911,⟨sg23910,True.intro,True.intro⟩,⟨sg23912,True.intro,True.intro⟩⟩,⟨sg23915,⟨sg23914,True.intro,True.intro⟩,⟨sg23916,True.intro,True.intro⟩⟩⟩⟩,⟨sg23925,⟨sg23921,⟨sg23919,⟨sg23918,True.intro,True.intro⟩,⟨sg23920,True.intro,True.intro⟩⟩,⟨sg23923,⟨sg23922,True.intro,True.intro⟩,⟨sg23924,True.intro,True.intro⟩⟩⟩,⟨sg23929,⟨sg23927,⟨sg23926,True.intro,True.intro⟩,⟨sg23928,True.intro,True.intro⟩⟩,⟨sg23931,⟨sg23930,True.intro,True.intro⟩,⟨sg23932,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_18All : degreeTree43_18.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23901,degreeTree43_16All,degreeTree43_17All⟩ + +lemma degreeTree43_19All : degreeTree43_19.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23869,degreeTree43_15All,degreeTree43_18All⟩ + +lemma degreeTree43_20All : degreeTree43_20.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23804,degreeTree43_10All,degreeTree43_19All⟩ + +lemma degreeTree43_21All : degreeTree43_21.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23942,⟨sg23938,⟨sg23936,⟨sg23935,⟨sg23934,True.intro,True.intro⟩,True.intro⟩,⟨sg23937,True.intro,True.intro⟩⟩,⟨sg23940,⟨sg23939,True.intro,True.intro⟩,⟨sg23941,True.intro,True.intro⟩⟩⟩,⟨sg23946,⟨sg23944,⟨sg23943,True.intro,True.intro⟩,⟨sg23945,True.intro,True.intro⟩⟩,⟨sg23948,⟨sg23947,True.intro,True.intro⟩,⟨sg23949,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_22All : degreeTree43_22.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23958,⟨sg23954,⟨sg23952,⟨sg23951,True.intro,True.intro⟩,⟨sg23953,True.intro,True.intro⟩⟩,⟨sg23956,⟨sg23955,True.intro,True.intro⟩,⟨sg23957,True.intro,True.intro⟩⟩⟩,⟨sg23962,⟨sg23960,⟨sg23959,True.intro,True.intro⟩,⟨sg23961,True.intro,True.intro⟩⟩,⟨sg23964,⟨sg23963,True.intro,True.intro⟩,⟨sg23965,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_23All : degreeTree43_23.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23950,degreeTree43_21All,degreeTree43_22All⟩ + +lemma degreeTree43_24All : degreeTree43_24.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23982,⟨sg23974,⟨sg23970,⟨sg23968,⟨sg23967,True.intro,True.intro⟩,⟨sg23969,True.intro,True.intro⟩⟩,⟨sg23972,⟨sg23971,True.intro,True.intro⟩,⟨sg23973,True.intro,True.intro⟩⟩⟩,⟨sg23978,⟨sg23976,⟨sg23975,True.intro,True.intro⟩,⟨sg23977,True.intro,True.intro⟩⟩,⟨sg23980,⟨sg23979,True.intro,True.intro⟩,⟨sg23981,True.intro,True.intro⟩⟩⟩⟩,⟨sg23990,⟨sg23986,⟨sg23984,⟨sg23983,True.intro,True.intro⟩,⟨sg23985,True.intro,True.intro⟩⟩,⟨sg23988,⟨sg23987,True.intro,True.intro⟩,⟨sg23989,True.intro,True.intro⟩⟩⟩,⟨sg23994,⟨sg23992,⟨sg23991,True.intro,True.intro⟩,⟨sg23993,True.intro,True.intro⟩⟩,⟨sg23996,⟨sg23995,True.intro,True.intro⟩,⟨sg23997,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_25All : degreeTree43_25.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23966,degreeTree43_23All,degreeTree43_24All⟩ + +lemma degreeTree43_26All : degreeTree43_26.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24014,⟨sg24006,⟨sg24002,⟨sg24000,⟨sg23999,True.intro,True.intro⟩,⟨sg24001,True.intro,True.intro⟩⟩,⟨sg24004,⟨sg24003,True.intro,True.intro⟩,⟨sg24005,True.intro,True.intro⟩⟩⟩,⟨sg24010,⟨sg24008,⟨sg24007,True.intro,True.intro⟩,⟨sg24009,True.intro,True.intro⟩⟩,⟨sg24012,⟨sg24011,True.intro,True.intro⟩,⟨sg24013,True.intro,True.intro⟩⟩⟩⟩,⟨sg24022,⟨sg24018,⟨sg24016,⟨sg24015,True.intro,True.intro⟩,⟨sg24017,True.intro,True.intro⟩⟩,⟨sg24020,⟨sg24019,True.intro,True.intro⟩,⟨sg24021,True.intro,True.intro⟩⟩⟩,⟨sg24026,⟨sg24024,⟨sg24023,True.intro,True.intro⟩,⟨sg24025,True.intro,True.intro⟩⟩,⟨sg24028,⟨sg24027,True.intro,True.intro⟩,⟨sg24029,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_27All : degreeTree43_27.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24046,⟨sg24038,⟨sg24034,⟨sg24032,⟨sg24031,True.intro,True.intro⟩,⟨sg24033,True.intro,True.intro⟩⟩,⟨sg24036,⟨sg24035,True.intro,True.intro⟩,⟨sg24037,True.intro,True.intro⟩⟩⟩,⟨sg24042,⟨sg24040,⟨sg24039,True.intro,True.intro⟩,⟨sg24041,True.intro,True.intro⟩⟩,⟨sg24044,⟨sg24043,True.intro,True.intro⟩,⟨sg24045,True.intro,True.intro⟩⟩⟩⟩,⟨sg24054,⟨sg24050,⟨sg24048,⟨sg24047,True.intro,True.intro⟩,⟨sg24049,True.intro,True.intro⟩⟩,⟨sg24052,⟨sg24051,True.intro,True.intro⟩,⟨sg24053,True.intro,True.intro⟩⟩⟩,⟨sg24058,⟨sg24056,⟨sg24055,True.intro,True.intro⟩,⟨sg24057,True.intro,True.intro⟩⟩,⟨sg24060,⟨sg24059,True.intro,True.intro⟩,⟨sg24061,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_28All : degreeTree43_28.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24030,degreeTree43_26All,degreeTree43_27All⟩ + +lemma degreeTree43_29All : degreeTree43_29.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23998,degreeTree43_25All,degreeTree43_28All⟩ + +lemma degreeTree43_30All : degreeTree43_30.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24071,⟨sg24067,⟨sg24065,⟨sg24064,⟨sg24063,True.intro,True.intro⟩,True.intro⟩,⟨sg24066,True.intro,True.intro⟩⟩,⟨sg24069,⟨sg24068,True.intro,True.intro⟩,⟨sg24070,True.intro,True.intro⟩⟩⟩,⟨sg24075,⟨sg24073,⟨sg24072,True.intro,True.intro⟩,⟨sg24074,True.intro,True.intro⟩⟩,⟨sg24077,⟨sg24076,True.intro,True.intro⟩,⟨sg24078,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_31All : degreeTree43_31.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24087,⟨sg24083,⟨sg24081,⟨sg24080,True.intro,True.intro⟩,⟨sg24082,True.intro,True.intro⟩⟩,⟨sg24085,⟨sg24084,True.intro,True.intro⟩,⟨sg24086,True.intro,True.intro⟩⟩⟩,⟨sg24091,⟨sg24089,⟨sg24088,True.intro,True.intro⟩,⟨sg24090,True.intro,True.intro⟩⟩,⟨sg24093,⟨sg24092,True.intro,True.intro⟩,⟨sg24094,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_32All : degreeTree43_32.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24079,degreeTree43_30All,degreeTree43_31All⟩ + +lemma degreeTree43_33All : degreeTree43_33.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24111,⟨sg24103,⟨sg24099,⟨sg24097,⟨sg24096,True.intro,True.intro⟩,⟨sg24098,True.intro,True.intro⟩⟩,⟨sg24101,⟨sg24100,True.intro,True.intro⟩,⟨sg24102,True.intro,True.intro⟩⟩⟩,⟨sg24107,⟨sg24105,⟨sg24104,True.intro,True.intro⟩,⟨sg24106,True.intro,True.intro⟩⟩,⟨sg24109,⟨sg24108,True.intro,True.intro⟩,⟨sg24110,True.intro,True.intro⟩⟩⟩⟩,⟨sg24119,⟨sg24115,⟨sg24113,⟨sg24112,True.intro,True.intro⟩,⟨sg24114,True.intro,True.intro⟩⟩,⟨sg24117,⟨sg24116,True.intro,True.intro⟩,⟨sg24118,True.intro,True.intro⟩⟩⟩,⟨sg24123,⟨sg24121,⟨sg24120,True.intro,True.intro⟩,⟨sg24122,True.intro,True.intro⟩⟩,⟨sg24125,⟨sg24124,True.intro,True.intro⟩,⟨sg24126,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_34All : degreeTree43_34.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24095,degreeTree43_32All,degreeTree43_33All⟩ + +lemma degreeTree43_35All : degreeTree43_35.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24143,⟨sg24135,⟨sg24131,⟨sg24129,⟨sg24128,True.intro,True.intro⟩,⟨sg24130,True.intro,True.intro⟩⟩,⟨sg24133,⟨sg24132,True.intro,True.intro⟩,⟨sg24134,True.intro,True.intro⟩⟩⟩,⟨sg24139,⟨sg24137,⟨sg24136,True.intro,True.intro⟩,⟨sg24138,True.intro,True.intro⟩⟩,⟨sg24141,⟨sg24140,True.intro,True.intro⟩,⟨sg24142,True.intro,True.intro⟩⟩⟩⟩,⟨sg24151,⟨sg24147,⟨sg24145,⟨sg24144,True.intro,True.intro⟩,⟨sg24146,True.intro,True.intro⟩⟩,⟨sg24149,⟨sg24148,True.intro,True.intro⟩,⟨sg24150,True.intro,True.intro⟩⟩⟩,⟨sg24155,⟨sg24153,⟨sg24152,True.intro,True.intro⟩,⟨sg24154,True.intro,True.intro⟩⟩,⟨sg24157,⟨sg24156,True.intro,True.intro⟩,⟨sg24158,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_36All : degreeTree43_36.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24175,⟨sg24167,⟨sg24163,⟨sg24161,⟨sg24160,True.intro,True.intro⟩,⟨sg24162,True.intro,True.intro⟩⟩,⟨sg24165,⟨sg24164,True.intro,True.intro⟩,⟨sg24166,True.intro,True.intro⟩⟩⟩,⟨sg24171,⟨sg24169,⟨sg24168,True.intro,True.intro⟩,⟨sg24170,True.intro,True.intro⟩⟩,⟨sg24173,⟨sg24172,True.intro,True.intro⟩,⟨sg24174,True.intro,True.intro⟩⟩⟩⟩,⟨sg24183,⟨sg24179,⟨sg24177,⟨sg24176,True.intro,True.intro⟩,⟨sg24178,True.intro,True.intro⟩⟩,⟨sg24181,⟨sg24180,True.intro,True.intro⟩,⟨sg24182,True.intro,True.intro⟩⟩⟩,⟨sg24187,⟨sg24185,⟨sg24184,True.intro,True.intro⟩,⟨sg24186,True.intro,True.intro⟩⟩,⟨sg24189,⟨sg24188,True.intro,True.intro⟩,⟨sg24190,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_37All : degreeTree43_37.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24159,degreeTree43_35All,degreeTree43_36All⟩ + +lemma degreeTree43_38All : degreeTree43_38.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24127,degreeTree43_34All,degreeTree43_37All⟩ + +lemma degreeTree43_39All : degreeTree43_39.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24062,degreeTree43_29All,degreeTree43_38All⟩ + +lemma degreeTree43_40All : degreeTree43_40.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg23933,degreeTree43_20All,degreeTree43_39All⟩ + +lemma degreeTree43_41All : degreeTree43_41.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24200,⟨sg24196,⟨sg24194,⟨sg24193,⟨sg24192,True.intro,True.intro⟩,True.intro⟩,⟨sg24195,True.intro,True.intro⟩⟩,⟨sg24198,⟨sg24197,True.intro,True.intro⟩,⟨sg24199,True.intro,True.intro⟩⟩⟩,⟨sg24204,⟨sg24202,⟨sg24201,True.intro,True.intro⟩,⟨sg24203,True.intro,True.intro⟩⟩,⟨sg24206,⟨sg24205,True.intro,True.intro⟩,⟨sg24207,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_42All : degreeTree43_42.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24216,⟨sg24212,⟨sg24210,⟨sg24209,True.intro,True.intro⟩,⟨sg24211,True.intro,True.intro⟩⟩,⟨sg24214,⟨sg24213,True.intro,True.intro⟩,⟨sg24215,True.intro,True.intro⟩⟩⟩,⟨sg24220,⟨sg24218,⟨sg24217,True.intro,True.intro⟩,⟨sg24219,True.intro,True.intro⟩⟩,⟨sg24222,⟨sg24221,True.intro,True.intro⟩,⟨sg24223,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_43All : degreeTree43_43.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24208,degreeTree43_41All,degreeTree43_42All⟩ + +lemma degreeTree43_44All : degreeTree43_44.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24240,⟨sg24232,⟨sg24228,⟨sg24226,⟨sg24225,True.intro,True.intro⟩,⟨sg24227,True.intro,True.intro⟩⟩,⟨sg24230,⟨sg24229,True.intro,True.intro⟩,⟨sg24231,True.intro,True.intro⟩⟩⟩,⟨sg24236,⟨sg24234,⟨sg24233,True.intro,True.intro⟩,⟨sg24235,True.intro,True.intro⟩⟩,⟨sg24238,⟨sg24237,True.intro,True.intro⟩,⟨sg24239,True.intro,True.intro⟩⟩⟩⟩,⟨sg24248,⟨sg24244,⟨sg24242,⟨sg24241,True.intro,True.intro⟩,⟨sg24243,True.intro,True.intro⟩⟩,⟨sg24246,⟨sg24245,True.intro,True.intro⟩,⟨sg24247,True.intro,True.intro⟩⟩⟩,⟨sg24252,⟨sg24250,⟨sg24249,True.intro,True.intro⟩,⟨sg24251,True.intro,True.intro⟩⟩,⟨sg24254,⟨sg24253,True.intro,True.intro⟩,⟨sg24255,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_45All : degreeTree43_45.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24224,degreeTree43_43All,degreeTree43_44All⟩ + +lemma degreeTree43_46All : degreeTree43_46.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24272,⟨sg24264,⟨sg24260,⟨sg24258,⟨sg24257,True.intro,True.intro⟩,⟨sg24259,True.intro,True.intro⟩⟩,⟨sg24262,⟨sg24261,True.intro,True.intro⟩,⟨sg24263,True.intro,True.intro⟩⟩⟩,⟨sg24268,⟨sg24266,⟨sg24265,True.intro,True.intro⟩,⟨sg24267,True.intro,True.intro⟩⟩,⟨sg24270,⟨sg24269,True.intro,True.intro⟩,⟨sg24271,True.intro,True.intro⟩⟩⟩⟩,⟨sg24280,⟨sg24276,⟨sg24274,⟨sg24273,True.intro,True.intro⟩,⟨sg24275,True.intro,True.intro⟩⟩,⟨sg24278,⟨sg24277,True.intro,True.intro⟩,⟨sg24279,True.intro,True.intro⟩⟩⟩,⟨sg24284,⟨sg24282,⟨sg24281,True.intro,True.intro⟩,⟨sg24283,True.intro,True.intro⟩⟩,⟨sg24286,⟨sg24285,True.intro,True.intro⟩,⟨sg24287,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_47All : degreeTree43_47.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24304,⟨sg24296,⟨sg24292,⟨sg24290,⟨sg24289,True.intro,True.intro⟩,⟨sg24291,True.intro,True.intro⟩⟩,⟨sg24294,⟨sg24293,True.intro,True.intro⟩,⟨sg24295,True.intro,True.intro⟩⟩⟩,⟨sg24300,⟨sg24298,⟨sg24297,True.intro,True.intro⟩,⟨sg24299,True.intro,True.intro⟩⟩,⟨sg24302,⟨sg24301,True.intro,True.intro⟩,⟨sg24303,True.intro,True.intro⟩⟩⟩⟩,⟨sg24312,⟨sg24308,⟨sg24306,⟨sg24305,True.intro,True.intro⟩,⟨sg24307,True.intro,True.intro⟩⟩,⟨sg24310,⟨sg24309,True.intro,True.intro⟩,⟨sg24311,True.intro,True.intro⟩⟩⟩,⟨sg24316,⟨sg24314,⟨sg24313,True.intro,True.intro⟩,⟨sg24315,True.intro,True.intro⟩⟩,⟨sg24318,⟨sg24317,True.intro,True.intro⟩,⟨sg24319,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_48All : degreeTree43_48.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24288,degreeTree43_46All,degreeTree43_47All⟩ + +lemma degreeTree43_49All : degreeTree43_49.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24256,degreeTree43_45All,degreeTree43_48All⟩ + +lemma degreeTree43_50All : degreeTree43_50.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24329,⟨sg24325,⟨sg24323,⟨sg24322,⟨sg24321,True.intro,True.intro⟩,True.intro⟩,⟨sg24324,True.intro,True.intro⟩⟩,⟨sg24327,⟨sg24326,True.intro,True.intro⟩,⟨sg24328,True.intro,True.intro⟩⟩⟩,⟨sg24333,⟨sg24331,⟨sg24330,True.intro,True.intro⟩,⟨sg24332,True.intro,True.intro⟩⟩,⟨sg24335,⟨sg24334,True.intro,True.intro⟩,⟨sg24336,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_51All : degreeTree43_51.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24345,⟨sg24341,⟨sg24339,⟨sg24338,True.intro,True.intro⟩,⟨sg24340,True.intro,True.intro⟩⟩,⟨sg24343,⟨sg24342,True.intro,True.intro⟩,⟨sg24344,True.intro,True.intro⟩⟩⟩,⟨sg24349,⟨sg24347,⟨sg24346,True.intro,True.intro⟩,⟨sg24348,True.intro,True.intro⟩⟩,⟨sg24351,⟨sg24350,True.intro,True.intro⟩,⟨sg24352,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_52All : degreeTree43_52.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24337,degreeTree43_50All,degreeTree43_51All⟩ + +lemma degreeTree43_53All : degreeTree43_53.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24369,⟨sg24361,⟨sg24357,⟨sg24355,⟨sg24354,True.intro,True.intro⟩,⟨sg24356,True.intro,True.intro⟩⟩,⟨sg24359,⟨sg24358,True.intro,True.intro⟩,⟨sg24360,True.intro,True.intro⟩⟩⟩,⟨sg24365,⟨sg24363,⟨sg24362,True.intro,True.intro⟩,⟨sg24364,True.intro,True.intro⟩⟩,⟨sg24367,⟨sg24366,True.intro,True.intro⟩,⟨sg24368,True.intro,True.intro⟩⟩⟩⟩,⟨sg24377,⟨sg24373,⟨sg24371,⟨sg24370,True.intro,True.intro⟩,⟨sg24372,True.intro,True.intro⟩⟩,⟨sg24375,⟨sg24374,True.intro,True.intro⟩,⟨sg24376,True.intro,True.intro⟩⟩⟩,⟨sg24381,⟨sg24379,⟨sg24378,True.intro,True.intro⟩,⟨sg24380,True.intro,True.intro⟩⟩,⟨sg24383,⟨sg24382,True.intro,True.intro⟩,⟨sg24384,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_54All : degreeTree43_54.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24353,degreeTree43_52All,degreeTree43_53All⟩ + +lemma degreeTree43_55All : degreeTree43_55.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24401,⟨sg24393,⟨sg24389,⟨sg24387,⟨sg24386,True.intro,True.intro⟩,⟨sg24388,True.intro,True.intro⟩⟩,⟨sg24391,⟨sg24390,True.intro,True.intro⟩,⟨sg24392,True.intro,True.intro⟩⟩⟩,⟨sg24397,⟨sg24395,⟨sg24394,True.intro,True.intro⟩,⟨sg24396,True.intro,True.intro⟩⟩,⟨sg24399,⟨sg24398,True.intro,True.intro⟩,⟨sg24400,True.intro,True.intro⟩⟩⟩⟩,⟨sg24409,⟨sg24405,⟨sg24403,⟨sg24402,True.intro,True.intro⟩,⟨sg24404,True.intro,True.intro⟩⟩,⟨sg24407,⟨sg24406,True.intro,True.intro⟩,⟨sg24408,True.intro,True.intro⟩⟩⟩,⟨sg24413,⟨sg24411,⟨sg24410,True.intro,True.intro⟩,⟨sg24412,True.intro,True.intro⟩⟩,⟨sg24415,⟨sg24414,True.intro,True.intro⟩,⟨sg24416,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_56All : degreeTree43_56.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24433,⟨sg24425,⟨sg24421,⟨sg24419,⟨sg24418,True.intro,True.intro⟩,⟨sg24420,True.intro,True.intro⟩⟩,⟨sg24423,⟨sg24422,True.intro,True.intro⟩,⟨sg24424,True.intro,True.intro⟩⟩⟩,⟨sg24429,⟨sg24427,⟨sg24426,True.intro,True.intro⟩,⟨sg24428,True.intro,True.intro⟩⟩,⟨sg24431,⟨sg24430,True.intro,True.intro⟩,⟨sg24432,True.intro,True.intro⟩⟩⟩⟩,⟨sg24441,⟨sg24437,⟨sg24435,⟨sg24434,True.intro,True.intro⟩,⟨sg24436,True.intro,True.intro⟩⟩,⟨sg24439,⟨sg24438,True.intro,True.intro⟩,⟨sg24440,True.intro,True.intro⟩⟩⟩,⟨sg24445,⟨sg24443,⟨sg24442,True.intro,True.intro⟩,⟨sg24444,True.intro,True.intro⟩⟩,⟨sg24447,⟨sg24446,True.intro,True.intro⟩,⟨sg24448,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_57All : degreeTree43_57.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24417,degreeTree43_55All,degreeTree43_56All⟩ + +lemma degreeTree43_58All : degreeTree43_58.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24385,degreeTree43_54All,degreeTree43_57All⟩ + +lemma degreeTree43_59All : degreeTree43_59.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24320,degreeTree43_49All,degreeTree43_58All⟩ + +lemma degreeTree43_60All : degreeTree43_60.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24458,⟨sg24454,⟨sg24452,⟨sg24451,⟨sg24450,True.intro,True.intro⟩,True.intro⟩,⟨sg24453,True.intro,True.intro⟩⟩,⟨sg24456,⟨sg24455,True.intro,True.intro⟩,⟨sg24457,True.intro,True.intro⟩⟩⟩,⟨sg24462,⟨sg24460,⟨sg24459,True.intro,True.intro⟩,⟨sg24461,True.intro,True.intro⟩⟩,⟨sg24464,⟨sg24463,True.intro,True.intro⟩,⟨sg24465,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_61All : degreeTree43_61.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24474,⟨sg24470,⟨sg24468,⟨sg24467,True.intro,True.intro⟩,⟨sg24469,True.intro,True.intro⟩⟩,⟨sg24472,⟨sg24471,True.intro,True.intro⟩,⟨sg24473,True.intro,True.intro⟩⟩⟩,⟨sg24478,⟨sg24476,⟨sg24475,True.intro,True.intro⟩,⟨sg24477,True.intro,True.intro⟩⟩,⟨sg24480,⟨sg24479,True.intro,True.intro⟩,⟨sg24481,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_62All : degreeTree43_62.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24466,degreeTree43_60All,degreeTree43_61All⟩ + +lemma degreeTree43_63All : degreeTree43_63.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24498,⟨sg24490,⟨sg24486,⟨sg24484,⟨sg24483,True.intro,True.intro⟩,⟨sg24485,True.intro,True.intro⟩⟩,⟨sg24488,⟨sg24487,True.intro,True.intro⟩,⟨sg24489,True.intro,True.intro⟩⟩⟩,⟨sg24494,⟨sg24492,⟨sg24491,True.intro,True.intro⟩,⟨sg24493,True.intro,True.intro⟩⟩,⟨sg24496,⟨sg24495,True.intro,True.intro⟩,⟨sg24497,True.intro,True.intro⟩⟩⟩⟩,⟨sg24506,⟨sg24502,⟨sg24500,⟨sg24499,True.intro,True.intro⟩,⟨sg24501,True.intro,True.intro⟩⟩,⟨sg24504,⟨sg24503,True.intro,True.intro⟩,⟨sg24505,True.intro,True.intro⟩⟩⟩,⟨sg24510,⟨sg24508,⟨sg24507,True.intro,True.intro⟩,⟨sg24509,True.intro,True.intro⟩⟩,⟨sg24512,⟨sg24511,True.intro,True.intro⟩,⟨sg24513,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_64All : degreeTree43_64.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24482,degreeTree43_62All,degreeTree43_63All⟩ + +lemma degreeTree43_65All : degreeTree43_65.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24530,⟨sg24522,⟨sg24518,⟨sg24516,⟨sg24515,True.intro,True.intro⟩,⟨sg24517,True.intro,True.intro⟩⟩,⟨sg24520,⟨sg24519,True.intro,True.intro⟩,⟨sg24521,True.intro,True.intro⟩⟩⟩,⟨sg24526,⟨sg24524,⟨sg24523,True.intro,True.intro⟩,⟨sg24525,True.intro,True.intro⟩⟩,⟨sg24528,⟨sg24527,True.intro,True.intro⟩,⟨sg24529,True.intro,True.intro⟩⟩⟩⟩,⟨sg24538,⟨sg24534,⟨sg24532,⟨sg24531,True.intro,True.intro⟩,⟨sg24533,True.intro,True.intro⟩⟩,⟨sg24536,⟨sg24535,True.intro,True.intro⟩,⟨sg24537,True.intro,True.intro⟩⟩⟩,⟨sg24542,⟨sg24540,⟨sg24539,True.intro,True.intro⟩,⟨sg24541,True.intro,True.intro⟩⟩,⟨sg24544,⟨sg24543,True.intro,True.intro⟩,⟨sg24545,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_66All : degreeTree43_66.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24562,⟨sg24554,⟨sg24550,⟨sg24548,⟨sg24547,True.intro,True.intro⟩,⟨sg24549,True.intro,True.intro⟩⟩,⟨sg24552,⟨sg24551,True.intro,True.intro⟩,⟨sg24553,True.intro,True.intro⟩⟩⟩,⟨sg24558,⟨sg24556,⟨sg24555,True.intro,True.intro⟩,⟨sg24557,True.intro,True.intro⟩⟩,⟨sg24560,⟨sg24559,True.intro,True.intro⟩,⟨sg24561,True.intro,True.intro⟩⟩⟩⟩,⟨sg24570,⟨sg24566,⟨sg24564,⟨sg24563,True.intro,True.intro⟩,⟨sg24565,True.intro,True.intro⟩⟩,⟨sg24568,⟨sg24567,True.intro,True.intro⟩,⟨sg24569,True.intro,True.intro⟩⟩⟩,⟨sg24574,⟨sg24572,⟨sg24571,True.intro,True.intro⟩,⟨sg24573,True.intro,True.intro⟩⟩,⟨sg24576,⟨sg24575,True.intro,True.intro⟩,⟨sg24577,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_67All : degreeTree43_67.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24546,degreeTree43_65All,degreeTree43_66All⟩ + +lemma degreeTree43_68All : degreeTree43_68.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24514,degreeTree43_64All,degreeTree43_67All⟩ + +lemma degreeTree43_69All : degreeTree43_69.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24587,⟨sg24583,⟨sg24581,⟨sg24580,⟨sg24579,True.intro,True.intro⟩,True.intro⟩,⟨sg24582,True.intro,True.intro⟩⟩,⟨sg24585,⟨sg24584,True.intro,True.intro⟩,⟨sg24586,True.intro,True.intro⟩⟩⟩,⟨sg24591,⟨sg24589,⟨sg24588,True.intro,True.intro⟩,⟨sg24590,True.intro,True.intro⟩⟩,⟨sg24593,⟨sg24592,True.intro,True.intro⟩,⟨sg24594,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_70All : degreeTree43_70.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24603,⟨sg24599,⟨sg24597,⟨sg24596,True.intro,True.intro⟩,⟨sg24598,True.intro,True.intro⟩⟩,⟨sg24601,⟨sg24600,True.intro,True.intro⟩,⟨sg24602,True.intro,True.intro⟩⟩⟩,⟨sg24607,⟨sg24605,⟨sg24604,True.intro,True.intro⟩,⟨sg24606,True.intro,True.intro⟩⟩,⟨sg24609,⟨sg24608,True.intro,True.intro⟩,⟨sg24610,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_71All : degreeTree43_71.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24595,degreeTree43_69All,degreeTree43_70All⟩ + +lemma degreeTree43_72All : degreeTree43_72.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24627,⟨sg24619,⟨sg24615,⟨sg24613,⟨sg24612,True.intro,True.intro⟩,⟨sg24614,True.intro,True.intro⟩⟩,⟨sg24617,⟨sg24616,True.intro,True.intro⟩,⟨sg24618,True.intro,True.intro⟩⟩⟩,⟨sg24623,⟨sg24621,⟨sg24620,True.intro,True.intro⟩,⟨sg24622,True.intro,True.intro⟩⟩,⟨sg24625,⟨sg24624,True.intro,True.intro⟩,⟨sg24626,True.intro,True.intro⟩⟩⟩⟩,⟨sg24635,⟨sg24631,⟨sg24629,⟨sg24628,True.intro,True.intro⟩,⟨sg24630,True.intro,True.intro⟩⟩,⟨sg24633,⟨sg24632,True.intro,True.intro⟩,⟨sg24634,True.intro,True.intro⟩⟩⟩,⟨sg24639,⟨sg24637,⟨sg24636,True.intro,True.intro⟩,⟨sg24638,True.intro,True.intro⟩⟩,⟨sg24641,⟨sg24640,True.intro,True.intro⟩,⟨sg24642,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_73All : degreeTree43_73.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24611,degreeTree43_71All,degreeTree43_72All⟩ + +lemma degreeTree43_74All : degreeTree43_74.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24659,⟨sg24651,⟨sg24647,⟨sg24645,⟨sg24644,True.intro,True.intro⟩,⟨sg24646,True.intro,True.intro⟩⟩,⟨sg24649,⟨sg24648,True.intro,True.intro⟩,⟨sg24650,True.intro,True.intro⟩⟩⟩,⟨sg24655,⟨sg24653,⟨sg24652,True.intro,True.intro⟩,⟨sg24654,True.intro,True.intro⟩⟩,⟨sg24657,⟨sg24656,True.intro,True.intro⟩,⟨sg24658,True.intro,True.intro⟩⟩⟩⟩,⟨sg24667,⟨sg24663,⟨sg24661,⟨sg24660,True.intro,True.intro⟩,⟨sg24662,True.intro,True.intro⟩⟩,⟨sg24665,⟨sg24664,True.intro,True.intro⟩,⟨sg24666,True.intro,True.intro⟩⟩⟩,⟨sg24671,⟨sg24669,⟨sg24668,True.intro,True.intro⟩,⟨sg24670,True.intro,True.intro⟩⟩,⟨sg24673,⟨sg24672,True.intro,True.intro⟩,⟨sg24674,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_75All : degreeTree43_75.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24691,⟨sg24683,⟨sg24679,⟨sg24677,⟨sg24676,True.intro,True.intro⟩,⟨sg24678,True.intro,True.intro⟩⟩,⟨sg24681,⟨sg24680,True.intro,True.intro⟩,⟨sg24682,True.intro,True.intro⟩⟩⟩,⟨sg24687,⟨sg24685,⟨sg24684,True.intro,True.intro⟩,⟨sg24686,True.intro,True.intro⟩⟩,⟨sg24689,⟨sg24688,True.intro,True.intro⟩,⟨sg24690,True.intro,True.intro⟩⟩⟩⟩,⟨sg24699,⟨sg24695,⟨sg24693,⟨sg24692,True.intro,True.intro⟩,⟨sg24694,True.intro,True.intro⟩⟩,⟨sg24697,⟨sg24696,True.intro,True.intro⟩,⟨sg24698,True.intro,True.intro⟩⟩⟩,⟨sg24703,⟨sg24701,⟨sg24700,True.intro,True.intro⟩,⟨sg24702,True.intro,True.intro⟩⟩,⟨sg24705,⟨sg24704,True.intro,True.intro⟩,⟨sg24706,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_76All : degreeTree43_76.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24675,degreeTree43_74All,degreeTree43_75All⟩ + +lemma degreeTree43_77All : degreeTree43_77.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24643,degreeTree43_73All,degreeTree43_76All⟩ + +lemma degreeTree43_78All : degreeTree43_78.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24578,degreeTree43_68All,degreeTree43_77All⟩ + +lemma degreeTree43_79All : degreeTree43_79.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24449,degreeTree43_59All,degreeTree43_78All⟩ + +lemma degreeTree43_80All : degreeTree43_80.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24191,degreeTree43_40All,degreeTree43_79All⟩ + +lemma degreeTree43_81All : degreeTree43_81.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24716,⟨sg24712,⟨sg24710,⟨sg24709,⟨sg24708,True.intro,True.intro⟩,True.intro⟩,⟨sg24711,True.intro,True.intro⟩⟩,⟨sg24714,⟨sg24713,True.intro,True.intro⟩,⟨sg24715,True.intro,True.intro⟩⟩⟩,⟨sg24720,⟨sg24718,⟨sg24717,True.intro,True.intro⟩,⟨sg24719,True.intro,True.intro⟩⟩,⟨sg24722,⟨sg24721,True.intro,True.intro⟩,⟨sg24723,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_82All : degreeTree43_82.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24732,⟨sg24728,⟨sg24726,⟨sg24725,True.intro,True.intro⟩,⟨sg24727,True.intro,True.intro⟩⟩,⟨sg24730,⟨sg24729,True.intro,True.intro⟩,⟨sg24731,True.intro,True.intro⟩⟩⟩,⟨sg24736,⟨sg24734,⟨sg24733,True.intro,True.intro⟩,⟨sg24735,True.intro,True.intro⟩⟩,⟨sg24738,⟨sg24737,True.intro,True.intro⟩,⟨sg24739,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_83All : degreeTree43_83.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24724,degreeTree43_81All,degreeTree43_82All⟩ + +lemma degreeTree43_84All : degreeTree43_84.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24756,⟨sg24748,⟨sg24744,⟨sg24742,⟨sg24741,True.intro,True.intro⟩,⟨sg24743,True.intro,True.intro⟩⟩,⟨sg24746,⟨sg24745,True.intro,True.intro⟩,⟨sg24747,True.intro,True.intro⟩⟩⟩,⟨sg24752,⟨sg24750,⟨sg24749,True.intro,True.intro⟩,⟨sg24751,True.intro,True.intro⟩⟩,⟨sg24754,⟨sg24753,True.intro,True.intro⟩,⟨sg24755,True.intro,True.intro⟩⟩⟩⟩,⟨sg24764,⟨sg24760,⟨sg24758,⟨sg24757,True.intro,True.intro⟩,⟨sg24759,True.intro,True.intro⟩⟩,⟨sg24762,⟨sg24761,True.intro,True.intro⟩,⟨sg24763,True.intro,True.intro⟩⟩⟩,⟨sg24768,⟨sg24766,⟨sg24765,True.intro,True.intro⟩,⟨sg24767,True.intro,True.intro⟩⟩,⟨sg24770,⟨sg24769,True.intro,True.intro⟩,⟨sg24771,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_85All : degreeTree43_85.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24740,degreeTree43_83All,degreeTree43_84All⟩ + +lemma degreeTree43_86All : degreeTree43_86.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24781,⟨sg24777,⟨sg24775,⟨sg24774,⟨sg24773,True.intro,True.intro⟩,True.intro⟩,⟨sg24776,True.intro,True.intro⟩⟩,⟨sg24779,⟨sg24778,True.intro,True.intro⟩,⟨sg24780,True.intro,True.intro⟩⟩⟩,⟨sg24785,⟨sg24783,⟨sg24782,True.intro,True.intro⟩,⟨sg24784,True.intro,True.intro⟩⟩,⟨sg24787,⟨sg24786,True.intro,True.intro⟩,⟨sg24788,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_87All : degreeTree43_87.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24797,⟨sg24793,⟨sg24791,⟨sg24790,True.intro,True.intro⟩,⟨sg24792,True.intro,True.intro⟩⟩,⟨sg24795,⟨sg24794,True.intro,True.intro⟩,⟨sg24796,True.intro,True.intro⟩⟩⟩,⟨sg24801,⟨sg24799,⟨sg24798,True.intro,True.intro⟩,⟨sg24800,True.intro,True.intro⟩⟩,⟨sg24803,⟨sg24802,True.intro,True.intro⟩,⟨sg24804,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_88All : degreeTree43_88.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24789,degreeTree43_86All,degreeTree43_87All⟩ + +lemma degreeTree43_89All : degreeTree43_89.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24821,⟨sg24813,⟨sg24809,⟨sg24807,⟨sg24806,True.intro,True.intro⟩,⟨sg24808,True.intro,True.intro⟩⟩,⟨sg24811,⟨sg24810,True.intro,True.intro⟩,⟨sg24812,True.intro,True.intro⟩⟩⟩,⟨sg24817,⟨sg24815,⟨sg24814,True.intro,True.intro⟩,⟨sg24816,True.intro,True.intro⟩⟩,⟨sg24819,⟨sg24818,True.intro,True.intro⟩,⟨sg24820,True.intro,True.intro⟩⟩⟩⟩,⟨sg24829,⟨sg24825,⟨sg24823,⟨sg24822,True.intro,True.intro⟩,⟨sg24824,True.intro,True.intro⟩⟩,⟨sg24827,⟨sg24826,True.intro,True.intro⟩,⟨sg24828,True.intro,True.intro⟩⟩⟩,⟨sg24833,⟨sg24831,⟨sg24830,True.intro,True.intro⟩,⟨sg24832,True.intro,True.intro⟩⟩,⟨sg24835,⟨sg24834,True.intro,True.intro⟩,⟨sg24836,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_90All : degreeTree43_90.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24805,degreeTree43_88All,degreeTree43_89All⟩ + +lemma degreeTree43_91All : degreeTree43_91.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24772,degreeTree43_85All,degreeTree43_90All⟩ + +lemma degreeTree43_92All : degreeTree43_92.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24846,⟨sg24842,⟨sg24840,⟨sg24839,⟨sg24838,True.intro,True.intro⟩,True.intro⟩,⟨sg24841,True.intro,True.intro⟩⟩,⟨sg24844,⟨sg24843,True.intro,True.intro⟩,⟨sg24845,True.intro,True.intro⟩⟩⟩,⟨sg24850,⟨sg24848,⟨sg24847,True.intro,True.intro⟩,⟨sg24849,True.intro,True.intro⟩⟩,⟨sg24852,⟨sg24851,True.intro,True.intro⟩,⟨sg24853,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_93All : degreeTree43_93.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24862,⟨sg24858,⟨sg24856,⟨sg24855,True.intro,True.intro⟩,⟨sg24857,True.intro,True.intro⟩⟩,⟨sg24860,⟨sg24859,True.intro,True.intro⟩,⟨sg24861,True.intro,True.intro⟩⟩⟩,⟨sg24866,⟨sg24864,⟨sg24863,True.intro,True.intro⟩,⟨sg24865,True.intro,True.intro⟩⟩,⟨sg24868,⟨sg24867,True.intro,True.intro⟩,⟨sg24869,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_94All : degreeTree43_94.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24854,degreeTree43_92All,degreeTree43_93All⟩ + +lemma degreeTree43_95All : degreeTree43_95.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24886,⟨sg24878,⟨sg24874,⟨sg24872,⟨sg24871,True.intro,True.intro⟩,⟨sg24873,True.intro,True.intro⟩⟩,⟨sg24876,⟨sg24875,True.intro,True.intro⟩,⟨sg24877,True.intro,True.intro⟩⟩⟩,⟨sg24882,⟨sg24880,⟨sg24879,True.intro,True.intro⟩,⟨sg24881,True.intro,True.intro⟩⟩,⟨sg24884,⟨sg24883,True.intro,True.intro⟩,⟨sg24885,True.intro,True.intro⟩⟩⟩⟩,⟨sg24894,⟨sg24890,⟨sg24888,⟨sg24887,True.intro,True.intro⟩,⟨sg24889,True.intro,True.intro⟩⟩,⟨sg24892,⟨sg24891,True.intro,True.intro⟩,⟨sg24893,True.intro,True.intro⟩⟩⟩,⟨sg24898,⟨sg24896,⟨sg24895,True.intro,True.intro⟩,⟨sg24897,True.intro,True.intro⟩⟩,⟨sg24900,⟨sg24899,True.intro,True.intro⟩,⟨sg24901,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_96All : degreeTree43_96.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24870,degreeTree43_94All,degreeTree43_95All⟩ + +lemma degreeTree43_97All : degreeTree43_97.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24918,⟨sg24910,⟨sg24906,⟨sg24904,⟨sg24903,True.intro,True.intro⟩,⟨sg24905,True.intro,True.intro⟩⟩,⟨sg24908,⟨sg24907,True.intro,True.intro⟩,⟨sg24909,True.intro,True.intro⟩⟩⟩,⟨sg24914,⟨sg24912,⟨sg24911,True.intro,True.intro⟩,⟨sg24913,True.intro,True.intro⟩⟩,⟨sg24916,⟨sg24915,True.intro,True.intro⟩,⟨sg24917,True.intro,True.intro⟩⟩⟩⟩,⟨sg24926,⟨sg24922,⟨sg24920,⟨sg24919,True.intro,True.intro⟩,⟨sg24921,True.intro,True.intro⟩⟩,⟨sg24924,⟨sg24923,True.intro,True.intro⟩,⟨sg24925,True.intro,True.intro⟩⟩⟩,⟨sg24930,⟨sg24928,⟨sg24927,True.intro,True.intro⟩,⟨sg24929,True.intro,True.intro⟩⟩,⟨sg24932,⟨sg24931,True.intro,True.intro⟩,⟨sg24933,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_98All : degreeTree43_98.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24950,⟨sg24942,⟨sg24938,⟨sg24936,⟨sg24935,True.intro,True.intro⟩,⟨sg24937,True.intro,True.intro⟩⟩,⟨sg24940,⟨sg24939,True.intro,True.intro⟩,⟨sg24941,True.intro,True.intro⟩⟩⟩,⟨sg24946,⟨sg24944,⟨sg24943,True.intro,True.intro⟩,⟨sg24945,True.intro,True.intro⟩⟩,⟨sg24948,⟨sg24947,True.intro,True.intro⟩,⟨sg24949,True.intro,True.intro⟩⟩⟩⟩,⟨sg24958,⟨sg24954,⟨sg24952,⟨sg24951,True.intro,True.intro⟩,⟨sg24953,True.intro,True.intro⟩⟩,⟨sg24956,⟨sg24955,True.intro,True.intro⟩,⟨sg24957,True.intro,True.intro⟩⟩⟩,⟨sg24962,⟨sg24960,⟨sg24959,True.intro,True.intro⟩,⟨sg24961,True.intro,True.intro⟩⟩,⟨sg24964,⟨sg24963,True.intro,True.intro⟩,⟨sg24965,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_99All : degreeTree43_99.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24934,degreeTree43_97All,degreeTree43_98All⟩ + +lemma degreeTree43_100All : degreeTree43_100.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24902,degreeTree43_96All,degreeTree43_99All⟩ + +lemma degreeTree43_101All : degreeTree43_101.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24837,degreeTree43_91All,degreeTree43_100All⟩ + +lemma degreeTree43_102All : degreeTree43_102.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24975,⟨sg24971,⟨sg24969,⟨sg24968,⟨sg24967,True.intro,True.intro⟩,True.intro⟩,⟨sg24970,True.intro,True.intro⟩⟩,⟨sg24973,⟨sg24972,True.intro,True.intro⟩,⟨sg24974,True.intro,True.intro⟩⟩⟩,⟨sg24979,⟨sg24977,⟨sg24976,True.intro,True.intro⟩,⟨sg24978,True.intro,True.intro⟩⟩,⟨sg24981,⟨sg24980,True.intro,True.intro⟩,⟨sg24982,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_103All : degreeTree43_103.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24991,⟨sg24987,⟨sg24985,⟨sg24984,True.intro,True.intro⟩,⟨sg24986,True.intro,True.intro⟩⟩,⟨sg24989,⟨sg24988,True.intro,True.intro⟩,⟨sg24990,True.intro,True.intro⟩⟩⟩,⟨sg24995,⟨sg24993,⟨sg24992,True.intro,True.intro⟩,⟨sg24994,True.intro,True.intro⟩⟩,⟨sg24997,⟨sg24996,True.intro,True.intro⟩,⟨sg24998,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_104All : degreeTree43_104.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24983,degreeTree43_102All,degreeTree43_103All⟩ + +lemma degreeTree43_105All : degreeTree43_105.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25015,⟨sg25007,⟨sg25003,⟨sg25001,⟨sg25000,True.intro,True.intro⟩,⟨sg25002,True.intro,True.intro⟩⟩,⟨sg25005,⟨sg25004,True.intro,True.intro⟩,⟨sg25006,True.intro,True.intro⟩⟩⟩,⟨sg25011,⟨sg25009,⟨sg25008,True.intro,True.intro⟩,⟨sg25010,True.intro,True.intro⟩⟩,⟨sg25013,⟨sg25012,True.intro,True.intro⟩,⟨sg25014,True.intro,True.intro⟩⟩⟩⟩,⟨sg25023,⟨sg25019,⟨sg25017,⟨sg25016,True.intro,True.intro⟩,⟨sg25018,True.intro,True.intro⟩⟩,⟨sg25021,⟨sg25020,True.intro,True.intro⟩,⟨sg25022,True.intro,True.intro⟩⟩⟩,⟨sg25027,⟨sg25025,⟨sg25024,True.intro,True.intro⟩,⟨sg25026,True.intro,True.intro⟩⟩,⟨sg25029,⟨sg25028,True.intro,True.intro⟩,⟨sg25030,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_106All : degreeTree43_106.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24999,degreeTree43_104All,degreeTree43_105All⟩ + +lemma degreeTree43_107All : degreeTree43_107.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25047,⟨sg25039,⟨sg25035,⟨sg25033,⟨sg25032,True.intro,True.intro⟩,⟨sg25034,True.intro,True.intro⟩⟩,⟨sg25037,⟨sg25036,True.intro,True.intro⟩,⟨sg25038,True.intro,True.intro⟩⟩⟩,⟨sg25043,⟨sg25041,⟨sg25040,True.intro,True.intro⟩,⟨sg25042,True.intro,True.intro⟩⟩,⟨sg25045,⟨sg25044,True.intro,True.intro⟩,⟨sg25046,True.intro,True.intro⟩⟩⟩⟩,⟨sg25055,⟨sg25051,⟨sg25049,⟨sg25048,True.intro,True.intro⟩,⟨sg25050,True.intro,True.intro⟩⟩,⟨sg25053,⟨sg25052,True.intro,True.intro⟩,⟨sg25054,True.intro,True.intro⟩⟩⟩,⟨sg25059,⟨sg25057,⟨sg25056,True.intro,True.intro⟩,⟨sg25058,True.intro,True.intro⟩⟩,⟨sg25061,⟨sg25060,True.intro,True.intro⟩,⟨sg25062,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_108All : degreeTree43_108.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25079,⟨sg25071,⟨sg25067,⟨sg25065,⟨sg25064,True.intro,True.intro⟩,⟨sg25066,True.intro,True.intro⟩⟩,⟨sg25069,⟨sg25068,True.intro,True.intro⟩,⟨sg25070,True.intro,True.intro⟩⟩⟩,⟨sg25075,⟨sg25073,⟨sg25072,True.intro,True.intro⟩,⟨sg25074,True.intro,True.intro⟩⟩,⟨sg25077,⟨sg25076,True.intro,True.intro⟩,⟨sg25078,True.intro,True.intro⟩⟩⟩⟩,⟨sg25087,⟨sg25083,⟨sg25081,⟨sg25080,True.intro,True.intro⟩,⟨sg25082,True.intro,True.intro⟩⟩,⟨sg25085,⟨sg25084,True.intro,True.intro⟩,⟨sg25086,True.intro,True.intro⟩⟩⟩,⟨sg25091,⟨sg25089,⟨sg25088,True.intro,True.intro⟩,⟨sg25090,True.intro,True.intro⟩⟩,⟨sg25093,⟨sg25092,True.intro,True.intro⟩,⟨sg25094,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_109All : degreeTree43_109.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25063,degreeTree43_107All,degreeTree43_108All⟩ + +lemma degreeTree43_110All : degreeTree43_110.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25031,degreeTree43_106All,degreeTree43_109All⟩ + +lemma degreeTree43_111All : degreeTree43_111.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25104,⟨sg25100,⟨sg25098,⟨sg25097,⟨sg25096,True.intro,True.intro⟩,True.intro⟩,⟨sg25099,True.intro,True.intro⟩⟩,⟨sg25102,⟨sg25101,True.intro,True.intro⟩,⟨sg25103,True.intro,True.intro⟩⟩⟩,⟨sg25108,⟨sg25106,⟨sg25105,True.intro,True.intro⟩,⟨sg25107,True.intro,True.intro⟩⟩,⟨sg25110,⟨sg25109,True.intro,True.intro⟩,⟨sg25111,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_112All : degreeTree43_112.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25120,⟨sg25116,⟨sg25114,⟨sg25113,True.intro,True.intro⟩,⟨sg25115,True.intro,True.intro⟩⟩,⟨sg25118,⟨sg25117,True.intro,True.intro⟩,⟨sg25119,True.intro,True.intro⟩⟩⟩,⟨sg25124,⟨sg25122,⟨sg25121,True.intro,True.intro⟩,⟨sg25123,True.intro,True.intro⟩⟩,⟨sg25126,⟨sg25125,True.intro,True.intro⟩,⟨sg25127,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_113All : degreeTree43_113.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25112,degreeTree43_111All,degreeTree43_112All⟩ + +lemma degreeTree43_114All : degreeTree43_114.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25144,⟨sg25136,⟨sg25132,⟨sg25130,⟨sg25129,True.intro,True.intro⟩,⟨sg25131,True.intro,True.intro⟩⟩,⟨sg25134,⟨sg25133,True.intro,True.intro⟩,⟨sg25135,True.intro,True.intro⟩⟩⟩,⟨sg25140,⟨sg25138,⟨sg25137,True.intro,True.intro⟩,⟨sg25139,True.intro,True.intro⟩⟩,⟨sg25142,⟨sg25141,True.intro,True.intro⟩,⟨sg25143,True.intro,True.intro⟩⟩⟩⟩,⟨sg25152,⟨sg25148,⟨sg25146,⟨sg25145,True.intro,True.intro⟩,⟨sg25147,True.intro,True.intro⟩⟩,⟨sg25150,⟨sg25149,True.intro,True.intro⟩,⟨sg25151,True.intro,True.intro⟩⟩⟩,⟨sg25156,⟨sg25154,⟨sg25153,True.intro,True.intro⟩,⟨sg25155,True.intro,True.intro⟩⟩,⟨sg25158,⟨sg25157,True.intro,True.intro⟩,⟨sg25159,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_115All : degreeTree43_115.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25128,degreeTree43_113All,degreeTree43_114All⟩ + +lemma degreeTree43_116All : degreeTree43_116.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25176,⟨sg25168,⟨sg25164,⟨sg25162,⟨sg25161,True.intro,True.intro⟩,⟨sg25163,True.intro,True.intro⟩⟩,⟨sg25166,⟨sg25165,True.intro,True.intro⟩,⟨sg25167,True.intro,True.intro⟩⟩⟩,⟨sg25172,⟨sg25170,⟨sg25169,True.intro,True.intro⟩,⟨sg25171,True.intro,True.intro⟩⟩,⟨sg25174,⟨sg25173,True.intro,True.intro⟩,⟨sg25175,True.intro,True.intro⟩⟩⟩⟩,⟨sg25184,⟨sg25180,⟨sg25178,⟨sg25177,True.intro,True.intro⟩,⟨sg25179,True.intro,True.intro⟩⟩,⟨sg25182,⟨sg25181,True.intro,True.intro⟩,⟨sg25183,True.intro,True.intro⟩⟩⟩,⟨sg25188,⟨sg25186,⟨sg25185,True.intro,True.intro⟩,⟨sg25187,True.intro,True.intro⟩⟩,⟨sg25190,⟨sg25189,True.intro,True.intro⟩,⟨sg25191,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_117All : degreeTree43_117.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25208,⟨sg25200,⟨sg25196,⟨sg25194,⟨sg25193,True.intro,True.intro⟩,⟨sg25195,True.intro,True.intro⟩⟩,⟨sg25198,⟨sg25197,True.intro,True.intro⟩,⟨sg25199,True.intro,True.intro⟩⟩⟩,⟨sg25204,⟨sg25202,⟨sg25201,True.intro,True.intro⟩,⟨sg25203,True.intro,True.intro⟩⟩,⟨sg25206,⟨sg25205,True.intro,True.intro⟩,⟨sg25207,True.intro,True.intro⟩⟩⟩⟩,⟨sg25216,⟨sg25212,⟨sg25210,⟨sg25209,True.intro,True.intro⟩,⟨sg25211,True.intro,True.intro⟩⟩,⟨sg25214,⟨sg25213,True.intro,True.intro⟩,⟨sg25215,True.intro,True.intro⟩⟩⟩,⟨sg25220,⟨sg25218,⟨sg25217,True.intro,True.intro⟩,⟨sg25219,True.intro,True.intro⟩⟩,⟨sg25222,⟨sg25221,True.intro,True.intro⟩,⟨sg25223,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_118All : degreeTree43_118.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25192,degreeTree43_116All,degreeTree43_117All⟩ + +lemma degreeTree43_119All : degreeTree43_119.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25160,degreeTree43_115All,degreeTree43_118All⟩ + +lemma degreeTree43_120All : degreeTree43_120.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25095,degreeTree43_110All,degreeTree43_119All⟩ + +lemma degreeTree43_121All : degreeTree43_121.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24966,degreeTree43_101All,degreeTree43_120All⟩ + +lemma degreeTree43_122All : degreeTree43_122.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25233,⟨sg25229,⟨sg25227,⟨sg25226,⟨sg25225,True.intro,True.intro⟩,True.intro⟩,⟨sg25228,True.intro,True.intro⟩⟩,⟨sg25231,⟨sg25230,True.intro,True.intro⟩,⟨sg25232,True.intro,True.intro⟩⟩⟩,⟨sg25237,⟨sg25235,⟨sg25234,True.intro,True.intro⟩,⟨sg25236,True.intro,True.intro⟩⟩,⟨sg25239,⟨sg25238,True.intro,True.intro⟩,⟨sg25240,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_123All : degreeTree43_123.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25249,⟨sg25245,⟨sg25243,⟨sg25242,True.intro,True.intro⟩,⟨sg25244,True.intro,True.intro⟩⟩,⟨sg25247,⟨sg25246,True.intro,True.intro⟩,⟨sg25248,True.intro,True.intro⟩⟩⟩,⟨sg25253,⟨sg25251,⟨sg25250,True.intro,True.intro⟩,⟨sg25252,True.intro,True.intro⟩⟩,⟨sg25255,⟨sg25254,True.intro,True.intro⟩,⟨sg25256,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_124All : degreeTree43_124.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25241,degreeTree43_122All,degreeTree43_123All⟩ + +lemma degreeTree43_125All : degreeTree43_125.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25273,⟨sg25265,⟨sg25261,⟨sg25259,⟨sg25258,True.intro,True.intro⟩,⟨sg25260,True.intro,True.intro⟩⟩,⟨sg25263,⟨sg25262,True.intro,True.intro⟩,⟨sg25264,True.intro,True.intro⟩⟩⟩,⟨sg25269,⟨sg25267,⟨sg25266,True.intro,True.intro⟩,⟨sg25268,True.intro,True.intro⟩⟩,⟨sg25271,⟨sg25270,True.intro,True.intro⟩,⟨sg25272,True.intro,True.intro⟩⟩⟩⟩,⟨sg25281,⟨sg25277,⟨sg25275,⟨sg25274,True.intro,True.intro⟩,⟨sg25276,True.intro,True.intro⟩⟩,⟨sg25279,⟨sg25278,True.intro,True.intro⟩,⟨sg25280,True.intro,True.intro⟩⟩⟩,⟨sg25285,⟨sg25283,⟨sg25282,True.intro,True.intro⟩,⟨sg25284,True.intro,True.intro⟩⟩,⟨sg25287,⟨sg25286,True.intro,True.intro⟩,⟨sg25288,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_126All : degreeTree43_126.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25257,degreeTree43_124All,degreeTree43_125All⟩ + +lemma degreeTree43_127All : degreeTree43_127.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25305,⟨sg25297,⟨sg25293,⟨sg25291,⟨sg25290,True.intro,True.intro⟩,⟨sg25292,True.intro,True.intro⟩⟩,⟨sg25295,⟨sg25294,True.intro,True.intro⟩,⟨sg25296,True.intro,True.intro⟩⟩⟩,⟨sg25301,⟨sg25299,⟨sg25298,True.intro,True.intro⟩,⟨sg25300,True.intro,True.intro⟩⟩,⟨sg25303,⟨sg25302,True.intro,True.intro⟩,⟨sg25304,True.intro,True.intro⟩⟩⟩⟩,⟨sg25313,⟨sg25309,⟨sg25307,⟨sg25306,True.intro,True.intro⟩,⟨sg25308,True.intro,True.intro⟩⟩,⟨sg25311,⟨sg25310,True.intro,True.intro⟩,⟨sg25312,True.intro,True.intro⟩⟩⟩,⟨sg25317,⟨sg25315,⟨sg25314,True.intro,True.intro⟩,⟨sg25316,True.intro,True.intro⟩⟩,⟨sg25319,⟨sg25318,True.intro,True.intro⟩,⟨sg25320,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_128All : degreeTree43_128.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25337,⟨sg25329,⟨sg25325,⟨sg25323,⟨sg25322,True.intro,True.intro⟩,⟨sg25324,True.intro,True.intro⟩⟩,⟨sg25327,⟨sg25326,True.intro,True.intro⟩,⟨sg25328,True.intro,True.intro⟩⟩⟩,⟨sg25333,⟨sg25331,⟨sg25330,True.intro,True.intro⟩,⟨sg25332,True.intro,True.intro⟩⟩,⟨sg25335,⟨sg25334,True.intro,True.intro⟩,⟨sg25336,True.intro,True.intro⟩⟩⟩⟩,⟨sg25345,⟨sg25341,⟨sg25339,⟨sg25338,True.intro,True.intro⟩,⟨sg25340,True.intro,True.intro⟩⟩,⟨sg25343,⟨sg25342,True.intro,True.intro⟩,⟨sg25344,True.intro,True.intro⟩⟩⟩,⟨sg25349,⟨sg25347,⟨sg25346,True.intro,True.intro⟩,⟨sg25348,True.intro,True.intro⟩⟩,⟨sg25351,⟨sg25350,True.intro,True.intro⟩,⟨sg25352,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_129All : degreeTree43_129.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25321,degreeTree43_127All,degreeTree43_128All⟩ + +lemma degreeTree43_130All : degreeTree43_130.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25289,degreeTree43_126All,degreeTree43_129All⟩ + +lemma degreeTree43_131All : degreeTree43_131.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25362,⟨sg25358,⟨sg25356,⟨sg25355,⟨sg25354,True.intro,True.intro⟩,True.intro⟩,⟨sg25357,True.intro,True.intro⟩⟩,⟨sg25360,⟨sg25359,True.intro,True.intro⟩,⟨sg25361,True.intro,True.intro⟩⟩⟩,⟨sg25366,⟨sg25364,⟨sg25363,True.intro,True.intro⟩,⟨sg25365,True.intro,True.intro⟩⟩,⟨sg25368,⟨sg25367,True.intro,True.intro⟩,⟨sg25369,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_132All : degreeTree43_132.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25378,⟨sg25374,⟨sg25372,⟨sg25371,True.intro,True.intro⟩,⟨sg25373,True.intro,True.intro⟩⟩,⟨sg25376,⟨sg25375,True.intro,True.intro⟩,⟨sg25377,True.intro,True.intro⟩⟩⟩,⟨sg25382,⟨sg25380,⟨sg25379,True.intro,True.intro⟩,⟨sg25381,True.intro,True.intro⟩⟩,⟨sg25384,⟨sg25383,True.intro,True.intro⟩,⟨sg25385,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_133All : degreeTree43_133.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25370,degreeTree43_131All,degreeTree43_132All⟩ + +lemma degreeTree43_134All : degreeTree43_134.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25402,⟨sg25394,⟨sg25390,⟨sg25388,⟨sg25387,True.intro,True.intro⟩,⟨sg25389,True.intro,True.intro⟩⟩,⟨sg25392,⟨sg25391,True.intro,True.intro⟩,⟨sg25393,True.intro,True.intro⟩⟩⟩,⟨sg25398,⟨sg25396,⟨sg25395,True.intro,True.intro⟩,⟨sg25397,True.intro,True.intro⟩⟩,⟨sg25400,⟨sg25399,True.intro,True.intro⟩,⟨sg25401,True.intro,True.intro⟩⟩⟩⟩,⟨sg25410,⟨sg25406,⟨sg25404,⟨sg25403,True.intro,True.intro⟩,⟨sg25405,True.intro,True.intro⟩⟩,⟨sg25408,⟨sg25407,True.intro,True.intro⟩,⟨sg25409,True.intro,True.intro⟩⟩⟩,⟨sg25414,⟨sg25412,⟨sg25411,True.intro,True.intro⟩,⟨sg25413,True.intro,True.intro⟩⟩,⟨sg25416,⟨sg25415,True.intro,True.intro⟩,⟨sg25417,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_135All : degreeTree43_135.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25386,degreeTree43_133All,degreeTree43_134All⟩ + +lemma degreeTree43_136All : degreeTree43_136.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25434,⟨sg25426,⟨sg25422,⟨sg25420,⟨sg25419,True.intro,True.intro⟩,⟨sg25421,True.intro,True.intro⟩⟩,⟨sg25424,⟨sg25423,True.intro,True.intro⟩,⟨sg25425,True.intro,True.intro⟩⟩⟩,⟨sg25430,⟨sg25428,⟨sg25427,True.intro,True.intro⟩,⟨sg25429,True.intro,True.intro⟩⟩,⟨sg25432,⟨sg25431,True.intro,True.intro⟩,⟨sg25433,True.intro,True.intro⟩⟩⟩⟩,⟨sg25442,⟨sg25438,⟨sg25436,⟨sg25435,True.intro,True.intro⟩,⟨sg25437,True.intro,True.intro⟩⟩,⟨sg25440,⟨sg25439,True.intro,True.intro⟩,⟨sg25441,True.intro,True.intro⟩⟩⟩,⟨sg25446,⟨sg25444,⟨sg25443,True.intro,True.intro⟩,⟨sg25445,True.intro,True.intro⟩⟩,⟨sg25448,⟨sg25447,True.intro,True.intro⟩,⟨sg25449,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_137All : degreeTree43_137.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25466,⟨sg25458,⟨sg25454,⟨sg25452,⟨sg25451,True.intro,True.intro⟩,⟨sg25453,True.intro,True.intro⟩⟩,⟨sg25456,⟨sg25455,True.intro,True.intro⟩,⟨sg25457,True.intro,True.intro⟩⟩⟩,⟨sg25462,⟨sg25460,⟨sg25459,True.intro,True.intro⟩,⟨sg25461,True.intro,True.intro⟩⟩,⟨sg25464,⟨sg25463,True.intro,True.intro⟩,⟨sg25465,True.intro,True.intro⟩⟩⟩⟩,⟨sg25474,⟨sg25470,⟨sg25468,⟨sg25467,True.intro,True.intro⟩,⟨sg25469,True.intro,True.intro⟩⟩,⟨sg25472,⟨sg25471,True.intro,True.intro⟩,⟨sg25473,True.intro,True.intro⟩⟩⟩,⟨sg25478,⟨sg25476,⟨sg25475,True.intro,True.intro⟩,⟨sg25477,True.intro,True.intro⟩⟩,⟨sg25480,⟨sg25479,True.intro,True.intro⟩,⟨sg25481,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_138All : degreeTree43_138.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25450,degreeTree43_136All,degreeTree43_137All⟩ + +lemma degreeTree43_139All : degreeTree43_139.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25418,degreeTree43_135All,degreeTree43_138All⟩ + +lemma degreeTree43_140All : degreeTree43_140.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25353,degreeTree43_130All,degreeTree43_139All⟩ + +lemma degreeTree43_141All : degreeTree43_141.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25491,⟨sg25487,⟨sg25485,⟨sg25484,⟨sg25483,True.intro,True.intro⟩,True.intro⟩,⟨sg25486,True.intro,True.intro⟩⟩,⟨sg25489,⟨sg25488,True.intro,True.intro⟩,⟨sg25490,True.intro,True.intro⟩⟩⟩,⟨sg25495,⟨sg25493,⟨sg25492,True.intro,True.intro⟩,⟨sg25494,True.intro,True.intro⟩⟩,⟨sg25497,⟨sg25496,True.intro,True.intro⟩,⟨sg25498,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_142All : degreeTree43_142.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25507,⟨sg25503,⟨sg25501,⟨sg25500,True.intro,True.intro⟩,⟨sg25502,True.intro,True.intro⟩⟩,⟨sg25505,⟨sg25504,True.intro,True.intro⟩,⟨sg25506,True.intro,True.intro⟩⟩⟩,⟨sg25511,⟨sg25509,⟨sg25508,True.intro,True.intro⟩,⟨sg25510,True.intro,True.intro⟩⟩,⟨sg25513,⟨sg25512,True.intro,True.intro⟩,⟨sg25514,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_143All : degreeTree43_143.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25499,degreeTree43_141All,degreeTree43_142All⟩ + +lemma degreeTree43_144All : degreeTree43_144.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25531,⟨sg25523,⟨sg25519,⟨sg25517,⟨sg25516,True.intro,True.intro⟩,⟨sg25518,True.intro,True.intro⟩⟩,⟨sg25521,⟨sg25520,True.intro,True.intro⟩,⟨sg25522,True.intro,True.intro⟩⟩⟩,⟨sg25527,⟨sg25525,⟨sg25524,True.intro,True.intro⟩,⟨sg25526,True.intro,True.intro⟩⟩,⟨sg25529,⟨sg25528,True.intro,True.intro⟩,⟨sg25530,True.intro,True.intro⟩⟩⟩⟩,⟨sg25539,⟨sg25535,⟨sg25533,⟨sg25532,True.intro,True.intro⟩,⟨sg25534,True.intro,True.intro⟩⟩,⟨sg25537,⟨sg25536,True.intro,True.intro⟩,⟨sg25538,True.intro,True.intro⟩⟩⟩,⟨sg25543,⟨sg25541,⟨sg25540,True.intro,True.intro⟩,⟨sg25542,True.intro,True.intro⟩⟩,⟨sg25545,⟨sg25544,True.intro,True.intro⟩,⟨sg25546,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_145All : degreeTree43_145.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25515,degreeTree43_143All,degreeTree43_144All⟩ + +lemma degreeTree43_146All : degreeTree43_146.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25563,⟨sg25555,⟨sg25551,⟨sg25549,⟨sg25548,True.intro,True.intro⟩,⟨sg25550,True.intro,True.intro⟩⟩,⟨sg25553,⟨sg25552,True.intro,True.intro⟩,⟨sg25554,True.intro,True.intro⟩⟩⟩,⟨sg25559,⟨sg25557,⟨sg25556,True.intro,True.intro⟩,⟨sg25558,True.intro,True.intro⟩⟩,⟨sg25561,⟨sg25560,True.intro,True.intro⟩,⟨sg25562,True.intro,True.intro⟩⟩⟩⟩,⟨sg25571,⟨sg25567,⟨sg25565,⟨sg25564,True.intro,True.intro⟩,⟨sg25566,True.intro,True.intro⟩⟩,⟨sg25569,⟨sg25568,True.intro,True.intro⟩,⟨sg25570,True.intro,True.intro⟩⟩⟩,⟨sg25575,⟨sg25573,⟨sg25572,True.intro,True.intro⟩,⟨sg25574,True.intro,True.intro⟩⟩,⟨sg25577,⟨sg25576,True.intro,True.intro⟩,⟨sg25578,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_147All : degreeTree43_147.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25595,⟨sg25587,⟨sg25583,⟨sg25581,⟨sg25580,True.intro,True.intro⟩,⟨sg25582,True.intro,True.intro⟩⟩,⟨sg25585,⟨sg25584,True.intro,True.intro⟩,⟨sg25586,True.intro,True.intro⟩⟩⟩,⟨sg25591,⟨sg25589,⟨sg25588,True.intro,True.intro⟩,⟨sg25590,True.intro,True.intro⟩⟩,⟨sg25593,⟨sg25592,True.intro,True.intro⟩,⟨sg25594,True.intro,True.intro⟩⟩⟩⟩,⟨sg25603,⟨sg25599,⟨sg25597,⟨sg25596,True.intro,True.intro⟩,⟨sg25598,True.intro,True.intro⟩⟩,⟨sg25601,⟨sg25600,True.intro,True.intro⟩,⟨sg25602,True.intro,True.intro⟩⟩⟩,⟨sg25607,⟨sg25605,⟨sg25604,True.intro,True.intro⟩,⟨sg25606,True.intro,True.intro⟩⟩,⟨sg25609,⟨sg25608,True.intro,True.intro⟩,⟨sg25610,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_148All : degreeTree43_148.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25579,degreeTree43_146All,degreeTree43_147All⟩ + +lemma degreeTree43_149All : degreeTree43_149.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25547,degreeTree43_145All,degreeTree43_148All⟩ + +lemma degreeTree43_150All : degreeTree43_150.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25620,⟨sg25616,⟨sg25614,⟨sg25613,⟨sg25612,True.intro,True.intro⟩,True.intro⟩,⟨sg25615,True.intro,True.intro⟩⟩,⟨sg25618,⟨sg25617,True.intro,True.intro⟩,⟨sg25619,True.intro,True.intro⟩⟩⟩,⟨sg25624,⟨sg25622,⟨sg25621,True.intro,True.intro⟩,⟨sg25623,True.intro,True.intro⟩⟩,⟨sg25626,⟨sg25625,True.intro,True.intro⟩,⟨sg25627,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_151All : degreeTree43_151.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25636,⟨sg25632,⟨sg25630,⟨sg25629,True.intro,True.intro⟩,⟨sg25631,True.intro,True.intro⟩⟩,⟨sg25634,⟨sg25633,True.intro,True.intro⟩,⟨sg25635,True.intro,True.intro⟩⟩⟩,⟨sg25640,⟨sg25638,⟨sg25637,True.intro,True.intro⟩,⟨sg25639,True.intro,True.intro⟩⟩,⟨sg25642,⟨sg25641,True.intro,True.intro⟩,⟨sg25643,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_152All : degreeTree43_152.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25628,degreeTree43_150All,degreeTree43_151All⟩ + +lemma degreeTree43_153All : degreeTree43_153.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25660,⟨sg25652,⟨sg25648,⟨sg25646,⟨sg25645,True.intro,True.intro⟩,⟨sg25647,True.intro,True.intro⟩⟩,⟨sg25650,⟨sg25649,True.intro,True.intro⟩,⟨sg25651,True.intro,True.intro⟩⟩⟩,⟨sg25656,⟨sg25654,⟨sg25653,True.intro,True.intro⟩,⟨sg25655,True.intro,True.intro⟩⟩,⟨sg25658,⟨sg25657,True.intro,True.intro⟩,⟨sg25659,True.intro,True.intro⟩⟩⟩⟩,⟨sg25668,⟨sg25664,⟨sg25662,⟨sg25661,True.intro,True.intro⟩,⟨sg25663,True.intro,True.intro⟩⟩,⟨sg25666,⟨sg25665,True.intro,True.intro⟩,⟨sg25667,True.intro,True.intro⟩⟩⟩,⟨sg25672,⟨sg25670,⟨sg25669,True.intro,True.intro⟩,⟨sg25671,True.intro,True.intro⟩⟩,⟨sg25674,⟨sg25673,True.intro,True.intro⟩,⟨sg25675,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_154All : degreeTree43_154.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25644,degreeTree43_152All,degreeTree43_153All⟩ + +lemma degreeTree43_155All : degreeTree43_155.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25692,⟨sg25684,⟨sg25680,⟨sg25678,⟨sg25677,True.intro,True.intro⟩,⟨sg25679,True.intro,True.intro⟩⟩,⟨sg25682,⟨sg25681,True.intro,True.intro⟩,⟨sg25683,True.intro,True.intro⟩⟩⟩,⟨sg25688,⟨sg25686,⟨sg25685,True.intro,True.intro⟩,⟨sg25687,True.intro,True.intro⟩⟩,⟨sg25690,⟨sg25689,True.intro,True.intro⟩,⟨sg25691,True.intro,True.intro⟩⟩⟩⟩,⟨sg25700,⟨sg25696,⟨sg25694,⟨sg25693,True.intro,True.intro⟩,⟨sg25695,True.intro,True.intro⟩⟩,⟨sg25698,⟨sg25697,True.intro,True.intro⟩,⟨sg25699,True.intro,True.intro⟩⟩⟩,⟨sg25704,⟨sg25702,⟨sg25701,True.intro,True.intro⟩,⟨sg25703,True.intro,True.intro⟩⟩,⟨sg25706,⟨sg25705,True.intro,True.intro⟩,⟨sg25707,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_156All : degreeTree43_156.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25724,⟨sg25716,⟨sg25712,⟨sg25710,⟨sg25709,True.intro,True.intro⟩,⟨sg25711,True.intro,True.intro⟩⟩,⟨sg25714,⟨sg25713,True.intro,True.intro⟩,⟨sg25715,True.intro,True.intro⟩⟩⟩,⟨sg25720,⟨sg25718,⟨sg25717,True.intro,True.intro⟩,⟨sg25719,True.intro,True.intro⟩⟩,⟨sg25722,⟨sg25721,True.intro,True.intro⟩,⟨sg25723,True.intro,True.intro⟩⟩⟩⟩,⟨sg25732,⟨sg25728,⟨sg25726,⟨sg25725,True.intro,True.intro⟩,⟨sg25727,True.intro,True.intro⟩⟩,⟨sg25730,⟨sg25729,True.intro,True.intro⟩,⟨sg25731,True.intro,True.intro⟩⟩⟩,⟨sg25736,⟨sg25734,⟨sg25733,True.intro,True.intro⟩,⟨sg25735,True.intro,True.intro⟩⟩,⟨sg25738,⟨sg25737,True.intro,True.intro⟩,⟨sg25739,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_157All : degreeTree43_157.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25708,degreeTree43_155All,degreeTree43_156All⟩ + +lemma degreeTree43_158All : degreeTree43_158.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25676,degreeTree43_154All,degreeTree43_157All⟩ + +lemma degreeTree43_159All : degreeTree43_159.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25611,degreeTree43_149All,degreeTree43_158All⟩ + +lemma degreeTree43_160All : degreeTree43_160.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25482,degreeTree43_140All,degreeTree43_159All⟩ + +lemma degreeTree43_161All : degreeTree43_161.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25224,degreeTree43_121All,degreeTree43_160All⟩ + +lemma degreeTree43_162All : degreeTree43_162.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg24707,degreeTree43_80All,degreeTree43_161All⟩ + +lemma degreeTree43_163All : degreeTree43_163.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25749,⟨sg25745,⟨sg25743,⟨sg25742,⟨sg25741,True.intro,True.intro⟩,True.intro⟩,⟨sg25744,True.intro,True.intro⟩⟩,⟨sg25747,⟨sg25746,True.intro,True.intro⟩,⟨sg25748,True.intro,True.intro⟩⟩⟩,⟨sg25753,⟨sg25751,⟨sg25750,True.intro,True.intro⟩,⟨sg25752,True.intro,True.intro⟩⟩,⟨sg25755,⟨sg25754,True.intro,True.intro⟩,⟨sg25756,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_164All : degreeTree43_164.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25765,⟨sg25761,⟨sg25759,⟨sg25758,True.intro,True.intro⟩,⟨sg25760,True.intro,True.intro⟩⟩,⟨sg25763,⟨sg25762,True.intro,True.intro⟩,⟨sg25764,True.intro,True.intro⟩⟩⟩,⟨sg25769,⟨sg25767,⟨sg25766,True.intro,True.intro⟩,⟨sg25768,True.intro,True.intro⟩⟩,⟨sg25771,⟨sg25770,True.intro,True.intro⟩,⟨sg25772,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_165All : degreeTree43_165.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25757,degreeTree43_163All,degreeTree43_164All⟩ + +lemma degreeTree43_166All : degreeTree43_166.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25789,⟨sg25781,⟨sg25777,⟨sg25775,⟨sg25774,True.intro,True.intro⟩,⟨sg25776,True.intro,True.intro⟩⟩,⟨sg25779,⟨sg25778,True.intro,True.intro⟩,⟨sg25780,True.intro,True.intro⟩⟩⟩,⟨sg25785,⟨sg25783,⟨sg25782,True.intro,True.intro⟩,⟨sg25784,True.intro,True.intro⟩⟩,⟨sg25787,⟨sg25786,True.intro,True.intro⟩,⟨sg25788,True.intro,True.intro⟩⟩⟩⟩,⟨sg25797,⟨sg25793,⟨sg25791,⟨sg25790,True.intro,True.intro⟩,⟨sg25792,True.intro,True.intro⟩⟩,⟨sg25795,⟨sg25794,True.intro,True.intro⟩,⟨sg25796,True.intro,True.intro⟩⟩⟩,⟨sg25801,⟨sg25799,⟨sg25798,True.intro,True.intro⟩,⟨sg25800,True.intro,True.intro⟩⟩,⟨sg25803,⟨sg25802,True.intro,True.intro⟩,⟨sg25804,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_167All : degreeTree43_167.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25773,degreeTree43_165All,degreeTree43_166All⟩ + +lemma degreeTree43_168All : degreeTree43_168.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25814,⟨sg25810,⟨sg25808,⟨sg25807,⟨sg25806,True.intro,True.intro⟩,True.intro⟩,⟨sg25809,True.intro,True.intro⟩⟩,⟨sg25812,⟨sg25811,True.intro,True.intro⟩,⟨sg25813,True.intro,True.intro⟩⟩⟩,⟨sg25818,⟨sg25816,⟨sg25815,True.intro,True.intro⟩,⟨sg25817,True.intro,True.intro⟩⟩,⟨sg25820,⟨sg25819,True.intro,True.intro⟩,⟨sg25821,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_169All : degreeTree43_169.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25830,⟨sg25826,⟨sg25824,⟨sg25823,True.intro,True.intro⟩,⟨sg25825,True.intro,True.intro⟩⟩,⟨sg25828,⟨sg25827,True.intro,True.intro⟩,⟨sg25829,True.intro,True.intro⟩⟩⟩,⟨sg25834,⟨sg25832,⟨sg25831,True.intro,True.intro⟩,⟨sg25833,True.intro,True.intro⟩⟩,⟨sg25836,⟨sg25835,True.intro,True.intro⟩,⟨sg25837,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_170All : degreeTree43_170.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25822,degreeTree43_168All,degreeTree43_169All⟩ + +lemma degreeTree43_171All : degreeTree43_171.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25854,⟨sg25846,⟨sg25842,⟨sg25840,⟨sg25839,True.intro,True.intro⟩,⟨sg25841,True.intro,True.intro⟩⟩,⟨sg25844,⟨sg25843,True.intro,True.intro⟩,⟨sg25845,True.intro,True.intro⟩⟩⟩,⟨sg25850,⟨sg25848,⟨sg25847,True.intro,True.intro⟩,⟨sg25849,True.intro,True.intro⟩⟩,⟨sg25852,⟨sg25851,True.intro,True.intro⟩,⟨sg25853,True.intro,True.intro⟩⟩⟩⟩,⟨sg25862,⟨sg25858,⟨sg25856,⟨sg25855,True.intro,True.intro⟩,⟨sg25857,True.intro,True.intro⟩⟩,⟨sg25860,⟨sg25859,True.intro,True.intro⟩,⟨sg25861,True.intro,True.intro⟩⟩⟩,⟨sg25866,⟨sg25864,⟨sg25863,True.intro,True.intro⟩,⟨sg25865,True.intro,True.intro⟩⟩,⟨sg25868,⟨sg25867,True.intro,True.intro⟩,⟨sg25869,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_172All : degreeTree43_172.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25838,degreeTree43_170All,degreeTree43_171All⟩ + +lemma degreeTree43_173All : degreeTree43_173.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25805,degreeTree43_167All,degreeTree43_172All⟩ + +lemma degreeTree43_174All : degreeTree43_174.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25879,⟨sg25875,⟨sg25873,⟨sg25872,⟨sg25871,True.intro,True.intro⟩,True.intro⟩,⟨sg25874,True.intro,True.intro⟩⟩,⟨sg25877,⟨sg25876,True.intro,True.intro⟩,⟨sg25878,True.intro,True.intro⟩⟩⟩,⟨sg25883,⟨sg25881,⟨sg25880,True.intro,True.intro⟩,⟨sg25882,True.intro,True.intro⟩⟩,⟨sg25885,⟨sg25884,True.intro,True.intro⟩,⟨sg25886,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_175All : degreeTree43_175.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25895,⟨sg25891,⟨sg25889,⟨sg25888,True.intro,True.intro⟩,⟨sg25890,True.intro,True.intro⟩⟩,⟨sg25893,⟨sg25892,True.intro,True.intro⟩,⟨sg25894,True.intro,True.intro⟩⟩⟩,⟨sg25899,⟨sg25897,⟨sg25896,True.intro,True.intro⟩,⟨sg25898,True.intro,True.intro⟩⟩,⟨sg25901,⟨sg25900,True.intro,True.intro⟩,⟨sg25902,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_176All : degreeTree43_176.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25887,degreeTree43_174All,degreeTree43_175All⟩ + +lemma degreeTree43_177All : degreeTree43_177.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25919,⟨sg25911,⟨sg25907,⟨sg25905,⟨sg25904,True.intro,True.intro⟩,⟨sg25906,True.intro,True.intro⟩⟩,⟨sg25909,⟨sg25908,True.intro,True.intro⟩,⟨sg25910,True.intro,True.intro⟩⟩⟩,⟨sg25915,⟨sg25913,⟨sg25912,True.intro,True.intro⟩,⟨sg25914,True.intro,True.intro⟩⟩,⟨sg25917,⟨sg25916,True.intro,True.intro⟩,⟨sg25918,True.intro,True.intro⟩⟩⟩⟩,⟨sg25927,⟨sg25923,⟨sg25921,⟨sg25920,True.intro,True.intro⟩,⟨sg25922,True.intro,True.intro⟩⟩,⟨sg25925,⟨sg25924,True.intro,True.intro⟩,⟨sg25926,True.intro,True.intro⟩⟩⟩,⟨sg25931,⟨sg25929,⟨sg25928,True.intro,True.intro⟩,⟨sg25930,True.intro,True.intro⟩⟩,⟨sg25933,⟨sg25932,True.intro,True.intro⟩,⟨sg25934,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_178All : degreeTree43_178.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25903,degreeTree43_176All,degreeTree43_177All⟩ + +lemma degreeTree43_179All : degreeTree43_179.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25951,⟨sg25943,⟨sg25939,⟨sg25937,⟨sg25936,True.intro,True.intro⟩,⟨sg25938,True.intro,True.intro⟩⟩,⟨sg25941,⟨sg25940,True.intro,True.intro⟩,⟨sg25942,True.intro,True.intro⟩⟩⟩,⟨sg25947,⟨sg25945,⟨sg25944,True.intro,True.intro⟩,⟨sg25946,True.intro,True.intro⟩⟩,⟨sg25949,⟨sg25948,True.intro,True.intro⟩,⟨sg25950,True.intro,True.intro⟩⟩⟩⟩,⟨sg25959,⟨sg25955,⟨sg25953,⟨sg25952,True.intro,True.intro⟩,⟨sg25954,True.intro,True.intro⟩⟩,⟨sg25957,⟨sg25956,True.intro,True.intro⟩,⟨sg25958,True.intro,True.intro⟩⟩⟩,⟨sg25963,⟨sg25961,⟨sg25960,True.intro,True.intro⟩,⟨sg25962,True.intro,True.intro⟩⟩,⟨sg25965,⟨sg25964,True.intro,True.intro⟩,⟨sg25966,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_180All : degreeTree43_180.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25983,⟨sg25975,⟨sg25971,⟨sg25969,⟨sg25968,True.intro,True.intro⟩,⟨sg25970,True.intro,True.intro⟩⟩,⟨sg25973,⟨sg25972,True.intro,True.intro⟩,⟨sg25974,True.intro,True.intro⟩⟩⟩,⟨sg25979,⟨sg25977,⟨sg25976,True.intro,True.intro⟩,⟨sg25978,True.intro,True.intro⟩⟩,⟨sg25981,⟨sg25980,True.intro,True.intro⟩,⟨sg25982,True.intro,True.intro⟩⟩⟩⟩,⟨sg25991,⟨sg25987,⟨sg25985,⟨sg25984,True.intro,True.intro⟩,⟨sg25986,True.intro,True.intro⟩⟩,⟨sg25989,⟨sg25988,True.intro,True.intro⟩,⟨sg25990,True.intro,True.intro⟩⟩⟩,⟨sg25995,⟨sg25993,⟨sg25992,True.intro,True.intro⟩,⟨sg25994,True.intro,True.intro⟩⟩,⟨sg25997,⟨sg25996,True.intro,True.intro⟩,⟨sg25998,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_181All : degreeTree43_181.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25967,degreeTree43_179All,degreeTree43_180All⟩ + +lemma degreeTree43_182All : degreeTree43_182.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25935,degreeTree43_178All,degreeTree43_181All⟩ + +lemma degreeTree43_183All : degreeTree43_183.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25870,degreeTree43_173All,degreeTree43_182All⟩ + +lemma degreeTree43_184All : degreeTree43_184.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26008,⟨sg26004,⟨sg26002,⟨sg26001,⟨sg26000,True.intro,True.intro⟩,True.intro⟩,⟨sg26003,True.intro,True.intro⟩⟩,⟨sg26006,⟨sg26005,True.intro,True.intro⟩,⟨sg26007,True.intro,True.intro⟩⟩⟩,⟨sg26012,⟨sg26010,⟨sg26009,True.intro,True.intro⟩,⟨sg26011,True.intro,True.intro⟩⟩,⟨sg26014,⟨sg26013,True.intro,True.intro⟩,⟨sg26015,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_185All : degreeTree43_185.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26024,⟨sg26020,⟨sg26018,⟨sg26017,True.intro,True.intro⟩,⟨sg26019,True.intro,True.intro⟩⟩,⟨sg26022,⟨sg26021,True.intro,True.intro⟩,⟨sg26023,True.intro,True.intro⟩⟩⟩,⟨sg26028,⟨sg26026,⟨sg26025,True.intro,True.intro⟩,⟨sg26027,True.intro,True.intro⟩⟩,⟨sg26030,⟨sg26029,True.intro,True.intro⟩,⟨sg26031,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_186All : degreeTree43_186.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26016,degreeTree43_184All,degreeTree43_185All⟩ + +lemma degreeTree43_187All : degreeTree43_187.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26048,⟨sg26040,⟨sg26036,⟨sg26034,⟨sg26033,True.intro,True.intro⟩,⟨sg26035,True.intro,True.intro⟩⟩,⟨sg26038,⟨sg26037,True.intro,True.intro⟩,⟨sg26039,True.intro,True.intro⟩⟩⟩,⟨sg26044,⟨sg26042,⟨sg26041,True.intro,True.intro⟩,⟨sg26043,True.intro,True.intro⟩⟩,⟨sg26046,⟨sg26045,True.intro,True.intro⟩,⟨sg26047,True.intro,True.intro⟩⟩⟩⟩,⟨sg26056,⟨sg26052,⟨sg26050,⟨sg26049,True.intro,True.intro⟩,⟨sg26051,True.intro,True.intro⟩⟩,⟨sg26054,⟨sg26053,True.intro,True.intro⟩,⟨sg26055,True.intro,True.intro⟩⟩⟩,⟨sg26060,⟨sg26058,⟨sg26057,True.intro,True.intro⟩,⟨sg26059,True.intro,True.intro⟩⟩,⟨sg26062,⟨sg26061,True.intro,True.intro⟩,⟨sg26063,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_188All : degreeTree43_188.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26032,degreeTree43_186All,degreeTree43_187All⟩ + +lemma degreeTree43_189All : degreeTree43_189.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26080,⟨sg26072,⟨sg26068,⟨sg26066,⟨sg26065,True.intro,True.intro⟩,⟨sg26067,True.intro,True.intro⟩⟩,⟨sg26070,⟨sg26069,True.intro,True.intro⟩,⟨sg26071,True.intro,True.intro⟩⟩⟩,⟨sg26076,⟨sg26074,⟨sg26073,True.intro,True.intro⟩,⟨sg26075,True.intro,True.intro⟩⟩,⟨sg26078,⟨sg26077,True.intro,True.intro⟩,⟨sg26079,True.intro,True.intro⟩⟩⟩⟩,⟨sg26088,⟨sg26084,⟨sg26082,⟨sg26081,True.intro,True.intro⟩,⟨sg26083,True.intro,True.intro⟩⟩,⟨sg26086,⟨sg26085,True.intro,True.intro⟩,⟨sg26087,True.intro,True.intro⟩⟩⟩,⟨sg26092,⟨sg26090,⟨sg26089,True.intro,True.intro⟩,⟨sg26091,True.intro,True.intro⟩⟩,⟨sg26094,⟨sg26093,True.intro,True.intro⟩,⟨sg26095,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_190All : degreeTree43_190.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26112,⟨sg26104,⟨sg26100,⟨sg26098,⟨sg26097,True.intro,True.intro⟩,⟨sg26099,True.intro,True.intro⟩⟩,⟨sg26102,⟨sg26101,True.intro,True.intro⟩,⟨sg26103,True.intro,True.intro⟩⟩⟩,⟨sg26108,⟨sg26106,⟨sg26105,True.intro,True.intro⟩,⟨sg26107,True.intro,True.intro⟩⟩,⟨sg26110,⟨sg26109,True.intro,True.intro⟩,⟨sg26111,True.intro,True.intro⟩⟩⟩⟩,⟨sg26120,⟨sg26116,⟨sg26114,⟨sg26113,True.intro,True.intro⟩,⟨sg26115,True.intro,True.intro⟩⟩,⟨sg26118,⟨sg26117,True.intro,True.intro⟩,⟨sg26119,True.intro,True.intro⟩⟩⟩,⟨sg26124,⟨sg26122,⟨sg26121,True.intro,True.intro⟩,⟨sg26123,True.intro,True.intro⟩⟩,⟨sg26126,⟨sg26125,True.intro,True.intro⟩,⟨sg26127,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_191All : degreeTree43_191.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26096,degreeTree43_189All,degreeTree43_190All⟩ + +lemma degreeTree43_192All : degreeTree43_192.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26064,degreeTree43_188All,degreeTree43_191All⟩ + +lemma degreeTree43_193All : degreeTree43_193.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26137,⟨sg26133,⟨sg26131,⟨sg26130,⟨sg26129,True.intro,True.intro⟩,True.intro⟩,⟨sg26132,True.intro,True.intro⟩⟩,⟨sg26135,⟨sg26134,True.intro,True.intro⟩,⟨sg26136,True.intro,True.intro⟩⟩⟩,⟨sg26141,⟨sg26139,⟨sg26138,True.intro,True.intro⟩,⟨sg26140,True.intro,True.intro⟩⟩,⟨sg26143,⟨sg26142,True.intro,True.intro⟩,⟨sg26144,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_194All : degreeTree43_194.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26153,⟨sg26149,⟨sg26147,⟨sg26146,True.intro,True.intro⟩,⟨sg26148,True.intro,True.intro⟩⟩,⟨sg26151,⟨sg26150,True.intro,True.intro⟩,⟨sg26152,True.intro,True.intro⟩⟩⟩,⟨sg26157,⟨sg26155,⟨sg26154,True.intro,True.intro⟩,⟨sg26156,True.intro,True.intro⟩⟩,⟨sg26159,⟨sg26158,True.intro,True.intro⟩,⟨sg26160,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_195All : degreeTree43_195.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26145,degreeTree43_193All,degreeTree43_194All⟩ + +lemma degreeTree43_196All : degreeTree43_196.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26177,⟨sg26169,⟨sg26165,⟨sg26163,⟨sg26162,True.intro,True.intro⟩,⟨sg26164,True.intro,True.intro⟩⟩,⟨sg26167,⟨sg26166,True.intro,True.intro⟩,⟨sg26168,True.intro,True.intro⟩⟩⟩,⟨sg26173,⟨sg26171,⟨sg26170,True.intro,True.intro⟩,⟨sg26172,True.intro,True.intro⟩⟩,⟨sg26175,⟨sg26174,True.intro,True.intro⟩,⟨sg26176,True.intro,True.intro⟩⟩⟩⟩,⟨sg26185,⟨sg26181,⟨sg26179,⟨sg26178,True.intro,True.intro⟩,⟨sg26180,True.intro,True.intro⟩⟩,⟨sg26183,⟨sg26182,True.intro,True.intro⟩,⟨sg26184,True.intro,True.intro⟩⟩⟩,⟨sg26189,⟨sg26187,⟨sg26186,True.intro,True.intro⟩,⟨sg26188,True.intro,True.intro⟩⟩,⟨sg26191,⟨sg26190,True.intro,True.intro⟩,⟨sg26192,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_197All : degreeTree43_197.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26161,degreeTree43_195All,degreeTree43_196All⟩ + +lemma degreeTree43_198All : degreeTree43_198.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26209,⟨sg26201,⟨sg26197,⟨sg26195,⟨sg26194,True.intro,True.intro⟩,⟨sg26196,True.intro,True.intro⟩⟩,⟨sg26199,⟨sg26198,True.intro,True.intro⟩,⟨sg26200,True.intro,True.intro⟩⟩⟩,⟨sg26205,⟨sg26203,⟨sg26202,True.intro,True.intro⟩,⟨sg26204,True.intro,True.intro⟩⟩,⟨sg26207,⟨sg26206,True.intro,True.intro⟩,⟨sg26208,True.intro,True.intro⟩⟩⟩⟩,⟨sg26217,⟨sg26213,⟨sg26211,⟨sg26210,True.intro,True.intro⟩,⟨sg26212,True.intro,True.intro⟩⟩,⟨sg26215,⟨sg26214,True.intro,True.intro⟩,⟨sg26216,True.intro,True.intro⟩⟩⟩,⟨sg26221,⟨sg26219,⟨sg26218,True.intro,True.intro⟩,⟨sg26220,True.intro,True.intro⟩⟩,⟨sg26223,⟨sg26222,True.intro,True.intro⟩,⟨sg26224,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_199All : degreeTree43_199.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26241,⟨sg26233,⟨sg26229,⟨sg26227,⟨sg26226,True.intro,True.intro⟩,⟨sg26228,True.intro,True.intro⟩⟩,⟨sg26231,⟨sg26230,True.intro,True.intro⟩,⟨sg26232,True.intro,True.intro⟩⟩⟩,⟨sg26237,⟨sg26235,⟨sg26234,True.intro,True.intro⟩,⟨sg26236,True.intro,True.intro⟩⟩,⟨sg26239,⟨sg26238,True.intro,True.intro⟩,⟨sg26240,True.intro,True.intro⟩⟩⟩⟩,⟨sg26249,⟨sg26245,⟨sg26243,⟨sg26242,True.intro,True.intro⟩,⟨sg26244,True.intro,True.intro⟩⟩,⟨sg26247,⟨sg26246,True.intro,True.intro⟩,⟨sg26248,True.intro,True.intro⟩⟩⟩,⟨sg26253,⟨sg26251,⟨sg26250,True.intro,True.intro⟩,⟨sg26252,True.intro,True.intro⟩⟩,⟨sg26255,⟨sg26254,True.intro,True.intro⟩,⟨sg26256,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_200All : degreeTree43_200.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26225,degreeTree43_198All,degreeTree43_199All⟩ + +lemma degreeTree43_201All : degreeTree43_201.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26193,degreeTree43_197All,degreeTree43_200All⟩ + +lemma degreeTree43_202All : degreeTree43_202.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26128,degreeTree43_192All,degreeTree43_201All⟩ + +lemma degreeTree43_203All : degreeTree43_203.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25999,degreeTree43_183All,degreeTree43_202All⟩ + +lemma degreeTree43_204All : degreeTree43_204.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26266,⟨sg26262,⟨sg26260,⟨sg26259,⟨sg26258,True.intro,True.intro⟩,True.intro⟩,⟨sg26261,True.intro,True.intro⟩⟩,⟨sg26264,⟨sg26263,True.intro,True.intro⟩,⟨sg26265,True.intro,True.intro⟩⟩⟩,⟨sg26270,⟨sg26268,⟨sg26267,True.intro,True.intro⟩,⟨sg26269,True.intro,True.intro⟩⟩,⟨sg26272,⟨sg26271,True.intro,True.intro⟩,⟨sg26273,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_205All : degreeTree43_205.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26282,⟨sg26278,⟨sg26276,⟨sg26275,True.intro,True.intro⟩,⟨sg26277,True.intro,True.intro⟩⟩,⟨sg26280,⟨sg26279,True.intro,True.intro⟩,⟨sg26281,True.intro,True.intro⟩⟩⟩,⟨sg26286,⟨sg26284,⟨sg26283,True.intro,True.intro⟩,⟨sg26285,True.intro,True.intro⟩⟩,⟨sg26288,⟨sg26287,True.intro,True.intro⟩,⟨sg26289,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_206All : degreeTree43_206.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26274,degreeTree43_204All,degreeTree43_205All⟩ + +lemma degreeTree43_207All : degreeTree43_207.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26306,⟨sg26298,⟨sg26294,⟨sg26292,⟨sg26291,True.intro,True.intro⟩,⟨sg26293,True.intro,True.intro⟩⟩,⟨sg26296,⟨sg26295,True.intro,True.intro⟩,⟨sg26297,True.intro,True.intro⟩⟩⟩,⟨sg26302,⟨sg26300,⟨sg26299,True.intro,True.intro⟩,⟨sg26301,True.intro,True.intro⟩⟩,⟨sg26304,⟨sg26303,True.intro,True.intro⟩,⟨sg26305,True.intro,True.intro⟩⟩⟩⟩,⟨sg26314,⟨sg26310,⟨sg26308,⟨sg26307,True.intro,True.intro⟩,⟨sg26309,True.intro,True.intro⟩⟩,⟨sg26312,⟨sg26311,True.intro,True.intro⟩,⟨sg26313,True.intro,True.intro⟩⟩⟩,⟨sg26318,⟨sg26316,⟨sg26315,True.intro,True.intro⟩,⟨sg26317,True.intro,True.intro⟩⟩,⟨sg26320,⟨sg26319,True.intro,True.intro⟩,⟨sg26321,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_208All : degreeTree43_208.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26290,degreeTree43_206All,degreeTree43_207All⟩ + +lemma degreeTree43_209All : degreeTree43_209.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26338,⟨sg26330,⟨sg26326,⟨sg26324,⟨sg26323,True.intro,True.intro⟩,⟨sg26325,True.intro,True.intro⟩⟩,⟨sg26328,⟨sg26327,True.intro,True.intro⟩,⟨sg26329,True.intro,True.intro⟩⟩⟩,⟨sg26334,⟨sg26332,⟨sg26331,True.intro,True.intro⟩,⟨sg26333,True.intro,True.intro⟩⟩,⟨sg26336,⟨sg26335,True.intro,True.intro⟩,⟨sg26337,True.intro,True.intro⟩⟩⟩⟩,⟨sg26346,⟨sg26342,⟨sg26340,⟨sg26339,True.intro,True.intro⟩,⟨sg26341,True.intro,True.intro⟩⟩,⟨sg26344,⟨sg26343,True.intro,True.intro⟩,⟨sg26345,True.intro,True.intro⟩⟩⟩,⟨sg26350,⟨sg26348,⟨sg26347,True.intro,True.intro⟩,⟨sg26349,True.intro,True.intro⟩⟩,⟨sg26352,⟨sg26351,True.intro,True.intro⟩,⟨sg26353,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_210All : degreeTree43_210.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26370,⟨sg26362,⟨sg26358,⟨sg26356,⟨sg26355,True.intro,True.intro⟩,⟨sg26357,True.intro,True.intro⟩⟩,⟨sg26360,⟨sg26359,True.intro,True.intro⟩,⟨sg26361,True.intro,True.intro⟩⟩⟩,⟨sg26366,⟨sg26364,⟨sg26363,True.intro,True.intro⟩,⟨sg26365,True.intro,True.intro⟩⟩,⟨sg26368,⟨sg26367,True.intro,True.intro⟩,⟨sg26369,True.intro,True.intro⟩⟩⟩⟩,⟨sg26378,⟨sg26374,⟨sg26372,⟨sg26371,True.intro,True.intro⟩,⟨sg26373,True.intro,True.intro⟩⟩,⟨sg26376,⟨sg26375,True.intro,True.intro⟩,⟨sg26377,True.intro,True.intro⟩⟩⟩,⟨sg26382,⟨sg26380,⟨sg26379,True.intro,True.intro⟩,⟨sg26381,True.intro,True.intro⟩⟩,⟨sg26384,⟨sg26383,True.intro,True.intro⟩,⟨sg26385,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_211All : degreeTree43_211.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26354,degreeTree43_209All,degreeTree43_210All⟩ + +lemma degreeTree43_212All : degreeTree43_212.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26322,degreeTree43_208All,degreeTree43_211All⟩ + +lemma degreeTree43_213All : degreeTree43_213.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26395,⟨sg26391,⟨sg26389,⟨sg26388,⟨sg26387,True.intro,True.intro⟩,True.intro⟩,⟨sg26390,True.intro,True.intro⟩⟩,⟨sg26393,⟨sg26392,True.intro,True.intro⟩,⟨sg26394,True.intro,True.intro⟩⟩⟩,⟨sg26399,⟨sg26397,⟨sg26396,True.intro,True.intro⟩,⟨sg26398,True.intro,True.intro⟩⟩,⟨sg26401,⟨sg26400,True.intro,True.intro⟩,⟨sg26402,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_214All : degreeTree43_214.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26411,⟨sg26407,⟨sg26405,⟨sg26404,True.intro,True.intro⟩,⟨sg26406,True.intro,True.intro⟩⟩,⟨sg26409,⟨sg26408,True.intro,True.intro⟩,⟨sg26410,True.intro,True.intro⟩⟩⟩,⟨sg26415,⟨sg26413,⟨sg26412,True.intro,True.intro⟩,⟨sg26414,True.intro,True.intro⟩⟩,⟨sg26417,⟨sg26416,True.intro,True.intro⟩,⟨sg26418,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_215All : degreeTree43_215.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26403,degreeTree43_213All,degreeTree43_214All⟩ + +lemma degreeTree43_216All : degreeTree43_216.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26435,⟨sg26427,⟨sg26423,⟨sg26421,⟨sg26420,True.intro,True.intro⟩,⟨sg26422,True.intro,True.intro⟩⟩,⟨sg26425,⟨sg26424,True.intro,True.intro⟩,⟨sg26426,True.intro,True.intro⟩⟩⟩,⟨sg26431,⟨sg26429,⟨sg26428,True.intro,True.intro⟩,⟨sg26430,True.intro,True.intro⟩⟩,⟨sg26433,⟨sg26432,True.intro,True.intro⟩,⟨sg26434,True.intro,True.intro⟩⟩⟩⟩,⟨sg26443,⟨sg26439,⟨sg26437,⟨sg26436,True.intro,True.intro⟩,⟨sg26438,True.intro,True.intro⟩⟩,⟨sg26441,⟨sg26440,True.intro,True.intro⟩,⟨sg26442,True.intro,True.intro⟩⟩⟩,⟨sg26447,⟨sg26445,⟨sg26444,True.intro,True.intro⟩,⟨sg26446,True.intro,True.intro⟩⟩,⟨sg26449,⟨sg26448,True.intro,True.intro⟩,⟨sg26450,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_217All : degreeTree43_217.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26419,degreeTree43_215All,degreeTree43_216All⟩ + +lemma degreeTree43_218All : degreeTree43_218.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26467,⟨sg26459,⟨sg26455,⟨sg26453,⟨sg26452,True.intro,True.intro⟩,⟨sg26454,True.intro,True.intro⟩⟩,⟨sg26457,⟨sg26456,True.intro,True.intro⟩,⟨sg26458,True.intro,True.intro⟩⟩⟩,⟨sg26463,⟨sg26461,⟨sg26460,True.intro,True.intro⟩,⟨sg26462,True.intro,True.intro⟩⟩,⟨sg26465,⟨sg26464,True.intro,True.intro⟩,⟨sg26466,True.intro,True.intro⟩⟩⟩⟩,⟨sg26475,⟨sg26471,⟨sg26469,⟨sg26468,True.intro,True.intro⟩,⟨sg26470,True.intro,True.intro⟩⟩,⟨sg26473,⟨sg26472,True.intro,True.intro⟩,⟨sg26474,True.intro,True.intro⟩⟩⟩,⟨sg26479,⟨sg26477,⟨sg26476,True.intro,True.intro⟩,⟨sg26478,True.intro,True.intro⟩⟩,⟨sg26481,⟨sg26480,True.intro,True.intro⟩,⟨sg26482,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_219All : degreeTree43_219.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26499,⟨sg26491,⟨sg26487,⟨sg26485,⟨sg26484,True.intro,True.intro⟩,⟨sg26486,True.intro,True.intro⟩⟩,⟨sg26489,⟨sg26488,True.intro,True.intro⟩,⟨sg26490,True.intro,True.intro⟩⟩⟩,⟨sg26495,⟨sg26493,⟨sg26492,True.intro,True.intro⟩,⟨sg26494,True.intro,True.intro⟩⟩,⟨sg26497,⟨sg26496,True.intro,True.intro⟩,⟨sg26498,True.intro,True.intro⟩⟩⟩⟩,⟨sg26507,⟨sg26503,⟨sg26501,⟨sg26500,True.intro,True.intro⟩,⟨sg26502,True.intro,True.intro⟩⟩,⟨sg26505,⟨sg26504,True.intro,True.intro⟩,⟨sg26506,True.intro,True.intro⟩⟩⟩,⟨sg26511,⟨sg26509,⟨sg26508,True.intro,True.intro⟩,⟨sg26510,True.intro,True.intro⟩⟩,⟨sg26513,⟨sg26512,True.intro,True.intro⟩,⟨sg26514,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_220All : degreeTree43_220.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26483,degreeTree43_218All,degreeTree43_219All⟩ + +lemma degreeTree43_221All : degreeTree43_221.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26451,degreeTree43_217All,degreeTree43_220All⟩ + +lemma degreeTree43_222All : degreeTree43_222.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26386,degreeTree43_212All,degreeTree43_221All⟩ + +lemma degreeTree43_223All : degreeTree43_223.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26524,⟨sg26520,⟨sg26518,⟨sg26517,⟨sg26516,True.intro,True.intro⟩,True.intro⟩,⟨sg26519,True.intro,True.intro⟩⟩,⟨sg26522,⟨sg26521,True.intro,True.intro⟩,⟨sg26523,True.intro,True.intro⟩⟩⟩,⟨sg26528,⟨sg26526,⟨sg26525,True.intro,True.intro⟩,⟨sg26527,True.intro,True.intro⟩⟩,⟨sg26530,⟨sg26529,True.intro,True.intro⟩,⟨sg26531,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_224All : degreeTree43_224.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26540,⟨sg26536,⟨sg26534,⟨sg26533,True.intro,True.intro⟩,⟨sg26535,True.intro,True.intro⟩⟩,⟨sg26538,⟨sg26537,True.intro,True.intro⟩,⟨sg26539,True.intro,True.intro⟩⟩⟩,⟨sg26544,⟨sg26542,⟨sg26541,True.intro,True.intro⟩,⟨sg26543,True.intro,True.intro⟩⟩,⟨sg26546,⟨sg26545,True.intro,True.intro⟩,⟨sg26547,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_225All : degreeTree43_225.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26532,degreeTree43_223All,degreeTree43_224All⟩ + +lemma degreeTree43_226All : degreeTree43_226.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26564,⟨sg26556,⟨sg26552,⟨sg26550,⟨sg26549,True.intro,True.intro⟩,⟨sg26551,True.intro,True.intro⟩⟩,⟨sg26554,⟨sg26553,True.intro,True.intro⟩,⟨sg26555,True.intro,True.intro⟩⟩⟩,⟨sg26560,⟨sg26558,⟨sg26557,True.intro,True.intro⟩,⟨sg26559,True.intro,True.intro⟩⟩,⟨sg26562,⟨sg26561,True.intro,True.intro⟩,⟨sg26563,True.intro,True.intro⟩⟩⟩⟩,⟨sg26572,⟨sg26568,⟨sg26566,⟨sg26565,True.intro,True.intro⟩,⟨sg26567,True.intro,True.intro⟩⟩,⟨sg26570,⟨sg26569,True.intro,True.intro⟩,⟨sg26571,True.intro,True.intro⟩⟩⟩,⟨sg26576,⟨sg26574,⟨sg26573,True.intro,True.intro⟩,⟨sg26575,True.intro,True.intro⟩⟩,⟨sg26578,⟨sg26577,True.intro,True.intro⟩,⟨sg26579,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_227All : degreeTree43_227.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26548,degreeTree43_225All,degreeTree43_226All⟩ + +lemma degreeTree43_228All : degreeTree43_228.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26596,⟨sg26588,⟨sg26584,⟨sg26582,⟨sg26581,True.intro,True.intro⟩,⟨sg26583,True.intro,True.intro⟩⟩,⟨sg26586,⟨sg26585,True.intro,True.intro⟩,⟨sg26587,True.intro,True.intro⟩⟩⟩,⟨sg26592,⟨sg26590,⟨sg26589,True.intro,True.intro⟩,⟨sg26591,True.intro,True.intro⟩⟩,⟨sg26594,⟨sg26593,True.intro,True.intro⟩,⟨sg26595,True.intro,True.intro⟩⟩⟩⟩,⟨sg26604,⟨sg26600,⟨sg26598,⟨sg26597,True.intro,True.intro⟩,⟨sg26599,True.intro,True.intro⟩⟩,⟨sg26602,⟨sg26601,True.intro,True.intro⟩,⟨sg26603,True.intro,True.intro⟩⟩⟩,⟨sg26608,⟨sg26606,⟨sg26605,True.intro,True.intro⟩,⟨sg26607,True.intro,True.intro⟩⟩,⟨sg26610,⟨sg26609,True.intro,True.intro⟩,⟨sg26611,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_229All : degreeTree43_229.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26628,⟨sg26620,⟨sg26616,⟨sg26614,⟨sg26613,True.intro,True.intro⟩,⟨sg26615,True.intro,True.intro⟩⟩,⟨sg26618,⟨sg26617,True.intro,True.intro⟩,⟨sg26619,True.intro,True.intro⟩⟩⟩,⟨sg26624,⟨sg26622,⟨sg26621,True.intro,True.intro⟩,⟨sg26623,True.intro,True.intro⟩⟩,⟨sg26626,⟨sg26625,True.intro,True.intro⟩,⟨sg26627,True.intro,True.intro⟩⟩⟩⟩,⟨sg26636,⟨sg26632,⟨sg26630,⟨sg26629,True.intro,True.intro⟩,⟨sg26631,True.intro,True.intro⟩⟩,⟨sg26634,⟨sg26633,True.intro,True.intro⟩,⟨sg26635,True.intro,True.intro⟩⟩⟩,⟨sg26640,⟨sg26638,⟨sg26637,True.intro,True.intro⟩,⟨sg26639,True.intro,True.intro⟩⟩,⟨sg26642,⟨sg26641,True.intro,True.intro⟩,⟨sg26643,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_230All : degreeTree43_230.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26612,degreeTree43_228All,degreeTree43_229All⟩ + +lemma degreeTree43_231All : degreeTree43_231.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26580,degreeTree43_227All,degreeTree43_230All⟩ + +lemma degreeTree43_232All : degreeTree43_232.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26653,⟨sg26649,⟨sg26647,⟨sg26646,⟨sg26645,True.intro,True.intro⟩,True.intro⟩,⟨sg26648,True.intro,True.intro⟩⟩,⟨sg26651,⟨sg26650,True.intro,True.intro⟩,⟨sg26652,True.intro,True.intro⟩⟩⟩,⟨sg26657,⟨sg26655,⟨sg26654,True.intro,True.intro⟩,⟨sg26656,True.intro,True.intro⟩⟩,⟨sg26659,⟨sg26658,True.intro,True.intro⟩,⟨sg26660,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_233All : degreeTree43_233.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26669,⟨sg26665,⟨sg26663,⟨sg26662,True.intro,True.intro⟩,⟨sg26664,True.intro,True.intro⟩⟩,⟨sg26667,⟨sg26666,True.intro,True.intro⟩,⟨sg26668,True.intro,True.intro⟩⟩⟩,⟨sg26673,⟨sg26671,⟨sg26670,True.intro,True.intro⟩,⟨sg26672,True.intro,True.intro⟩⟩,⟨sg26675,⟨sg26674,True.intro,True.intro⟩,⟨sg26676,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_234All : degreeTree43_234.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26661,degreeTree43_232All,degreeTree43_233All⟩ + +lemma degreeTree43_235All : degreeTree43_235.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26693,⟨sg26685,⟨sg26681,⟨sg26679,⟨sg26678,True.intro,True.intro⟩,⟨sg26680,True.intro,True.intro⟩⟩,⟨sg26683,⟨sg26682,True.intro,True.intro⟩,⟨sg26684,True.intro,True.intro⟩⟩⟩,⟨sg26689,⟨sg26687,⟨sg26686,True.intro,True.intro⟩,⟨sg26688,True.intro,True.intro⟩⟩,⟨sg26691,⟨sg26690,True.intro,True.intro⟩,⟨sg26692,True.intro,True.intro⟩⟩⟩⟩,⟨sg26701,⟨sg26697,⟨sg26695,⟨sg26694,True.intro,True.intro⟩,⟨sg26696,True.intro,True.intro⟩⟩,⟨sg26699,⟨sg26698,True.intro,True.intro⟩,⟨sg26700,True.intro,True.intro⟩⟩⟩,⟨sg26705,⟨sg26703,⟨sg26702,True.intro,True.intro⟩,⟨sg26704,True.intro,True.intro⟩⟩,⟨sg26707,⟨sg26706,True.intro,True.intro⟩,⟨sg26708,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_236All : degreeTree43_236.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26677,degreeTree43_234All,degreeTree43_235All⟩ + +lemma degreeTree43_237All : degreeTree43_237.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26725,⟨sg26717,⟨sg26713,⟨sg26711,⟨sg26710,True.intro,True.intro⟩,⟨sg26712,True.intro,True.intro⟩⟩,⟨sg26715,⟨sg26714,True.intro,True.intro⟩,⟨sg26716,True.intro,True.intro⟩⟩⟩,⟨sg26721,⟨sg26719,⟨sg26718,True.intro,True.intro⟩,⟨sg26720,True.intro,True.intro⟩⟩,⟨sg26723,⟨sg26722,True.intro,True.intro⟩,⟨sg26724,True.intro,True.intro⟩⟩⟩⟩,⟨sg26733,⟨sg26729,⟨sg26727,⟨sg26726,True.intro,True.intro⟩,⟨sg26728,True.intro,True.intro⟩⟩,⟨sg26731,⟨sg26730,True.intro,True.intro⟩,⟨sg26732,True.intro,True.intro⟩⟩⟩,⟨sg26737,⟨sg26735,⟨sg26734,True.intro,True.intro⟩,⟨sg26736,True.intro,True.intro⟩⟩,⟨sg26739,⟨sg26738,True.intro,True.intro⟩,⟨sg26740,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_238All : degreeTree43_238.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26757,⟨sg26749,⟨sg26745,⟨sg26743,⟨sg26742,True.intro,True.intro⟩,⟨sg26744,True.intro,True.intro⟩⟩,⟨sg26747,⟨sg26746,True.intro,True.intro⟩,⟨sg26748,True.intro,True.intro⟩⟩⟩,⟨sg26753,⟨sg26751,⟨sg26750,True.intro,True.intro⟩,⟨sg26752,True.intro,True.intro⟩⟩,⟨sg26755,⟨sg26754,True.intro,True.intro⟩,⟨sg26756,True.intro,True.intro⟩⟩⟩⟩,⟨sg26765,⟨sg26761,⟨sg26759,⟨sg26758,True.intro,True.intro⟩,⟨sg26760,True.intro,True.intro⟩⟩,⟨sg26763,⟨sg26762,True.intro,True.intro⟩,⟨sg26764,True.intro,True.intro⟩⟩⟩,⟨sg26769,⟨sg26767,⟨sg26766,True.intro,True.intro⟩,⟨sg26768,True.intro,True.intro⟩⟩,⟨sg26771,⟨sg26770,True.intro,True.intro⟩,⟨sg26772,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_239All : degreeTree43_239.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26741,degreeTree43_237All,degreeTree43_238All⟩ + +lemma degreeTree43_240All : degreeTree43_240.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26709,degreeTree43_236All,degreeTree43_239All⟩ + +lemma degreeTree43_241All : degreeTree43_241.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26644,degreeTree43_231All,degreeTree43_240All⟩ + +lemma degreeTree43_242All : degreeTree43_242.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26515,degreeTree43_222All,degreeTree43_241All⟩ + +lemma degreeTree43_243All : degreeTree43_243.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26257,degreeTree43_203All,degreeTree43_242All⟩ + +lemma degreeTree43_244All : degreeTree43_244.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26782,⟨sg26778,⟨sg26776,⟨sg26775,⟨sg26774,True.intro,True.intro⟩,True.intro⟩,⟨sg26777,True.intro,True.intro⟩⟩,⟨sg26780,⟨sg26779,True.intro,True.intro⟩,⟨sg26781,True.intro,True.intro⟩⟩⟩,⟨sg26786,⟨sg26784,⟨sg26783,True.intro,True.intro⟩,⟨sg26785,True.intro,True.intro⟩⟩,⟨sg26788,⟨sg26787,True.intro,True.intro⟩,⟨sg26789,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_245All : degreeTree43_245.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26798,⟨sg26794,⟨sg26792,⟨sg26791,True.intro,True.intro⟩,⟨sg26793,True.intro,True.intro⟩⟩,⟨sg26796,⟨sg26795,True.intro,True.intro⟩,⟨sg26797,True.intro,True.intro⟩⟩⟩,⟨sg26802,⟨sg26800,⟨sg26799,True.intro,True.intro⟩,⟨sg26801,True.intro,True.intro⟩⟩,⟨sg26804,⟨sg26803,True.intro,True.intro⟩,⟨sg26805,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_246All : degreeTree43_246.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26790,degreeTree43_244All,degreeTree43_245All⟩ + +lemma degreeTree43_247All : degreeTree43_247.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26822,⟨sg26814,⟨sg26810,⟨sg26808,⟨sg26807,True.intro,True.intro⟩,⟨sg26809,True.intro,True.intro⟩⟩,⟨sg26812,⟨sg26811,True.intro,True.intro⟩,⟨sg26813,True.intro,True.intro⟩⟩⟩,⟨sg26818,⟨sg26816,⟨sg26815,True.intro,True.intro⟩,⟨sg26817,True.intro,True.intro⟩⟩,⟨sg26820,⟨sg26819,True.intro,True.intro⟩,⟨sg26821,True.intro,True.intro⟩⟩⟩⟩,⟨sg26830,⟨sg26826,⟨sg26824,⟨sg26823,True.intro,True.intro⟩,⟨sg26825,True.intro,True.intro⟩⟩,⟨sg26828,⟨sg26827,True.intro,True.intro⟩,⟨sg26829,True.intro,True.intro⟩⟩⟩,⟨sg26834,⟨sg26832,⟨sg26831,True.intro,True.intro⟩,⟨sg26833,True.intro,True.intro⟩⟩,⟨sg26836,⟨sg26835,True.intro,True.intro⟩,⟨sg26837,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_248All : degreeTree43_248.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26806,degreeTree43_246All,degreeTree43_247All⟩ + +lemma degreeTree43_249All : degreeTree43_249.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26854,⟨sg26846,⟨sg26842,⟨sg26840,⟨sg26839,True.intro,True.intro⟩,⟨sg26841,True.intro,True.intro⟩⟩,⟨sg26844,⟨sg26843,True.intro,True.intro⟩,⟨sg26845,True.intro,True.intro⟩⟩⟩,⟨sg26850,⟨sg26848,⟨sg26847,True.intro,True.intro⟩,⟨sg26849,True.intro,True.intro⟩⟩,⟨sg26852,⟨sg26851,True.intro,True.intro⟩,⟨sg26853,True.intro,True.intro⟩⟩⟩⟩,⟨sg26862,⟨sg26858,⟨sg26856,⟨sg26855,True.intro,True.intro⟩,⟨sg26857,True.intro,True.intro⟩⟩,⟨sg26860,⟨sg26859,True.intro,True.intro⟩,⟨sg26861,True.intro,True.intro⟩⟩⟩,⟨sg26866,⟨sg26864,⟨sg26863,True.intro,True.intro⟩,⟨sg26865,True.intro,True.intro⟩⟩,⟨sg26868,⟨sg26867,True.intro,True.intro⟩,⟨sg26869,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_250All : degreeTree43_250.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26886,⟨sg26878,⟨sg26874,⟨sg26872,⟨sg26871,True.intro,True.intro⟩,⟨sg26873,True.intro,True.intro⟩⟩,⟨sg26876,⟨sg26875,True.intro,True.intro⟩,⟨sg26877,True.intro,True.intro⟩⟩⟩,⟨sg26882,⟨sg26880,⟨sg26879,True.intro,True.intro⟩,⟨sg26881,True.intro,True.intro⟩⟩,⟨sg26884,⟨sg26883,True.intro,True.intro⟩,⟨sg26885,True.intro,True.intro⟩⟩⟩⟩,⟨sg26894,⟨sg26890,⟨sg26888,⟨sg26887,True.intro,True.intro⟩,⟨sg26889,True.intro,True.intro⟩⟩,⟨sg26892,⟨sg26891,True.intro,True.intro⟩,⟨sg26893,True.intro,True.intro⟩⟩⟩,⟨sg26898,⟨sg26896,⟨sg26895,True.intro,True.intro⟩,⟨sg26897,True.intro,True.intro⟩⟩,⟨sg26900,⟨sg26899,True.intro,True.intro⟩,⟨sg26901,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_251All : degreeTree43_251.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26870,degreeTree43_249All,degreeTree43_250All⟩ + +lemma degreeTree43_252All : degreeTree43_252.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26838,degreeTree43_248All,degreeTree43_251All⟩ + +lemma degreeTree43_253All : degreeTree43_253.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26911,⟨sg26907,⟨sg26905,⟨sg26904,⟨sg26903,True.intro,True.intro⟩,True.intro⟩,⟨sg26906,True.intro,True.intro⟩⟩,⟨sg26909,⟨sg26908,True.intro,True.intro⟩,⟨sg26910,True.intro,True.intro⟩⟩⟩,⟨sg26915,⟨sg26913,⟨sg26912,True.intro,True.intro⟩,⟨sg26914,True.intro,True.intro⟩⟩,⟨sg26917,⟨sg26916,True.intro,True.intro⟩,⟨sg26918,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_254All : degreeTree43_254.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26927,⟨sg26923,⟨sg26921,⟨sg26920,True.intro,True.intro⟩,⟨sg26922,True.intro,True.intro⟩⟩,⟨sg26925,⟨sg26924,True.intro,True.intro⟩,⟨sg26926,True.intro,True.intro⟩⟩⟩,⟨sg26931,⟨sg26929,⟨sg26928,True.intro,True.intro⟩,⟨sg26930,True.intro,True.intro⟩⟩,⟨sg26933,⟨sg26932,True.intro,True.intro⟩,⟨sg26934,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_255All : degreeTree43_255.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26919,degreeTree43_253All,degreeTree43_254All⟩ + +lemma degreeTree43_256All : degreeTree43_256.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26951,⟨sg26943,⟨sg26939,⟨sg26937,⟨sg26936,True.intro,True.intro⟩,⟨sg26938,True.intro,True.intro⟩⟩,⟨sg26941,⟨sg26940,True.intro,True.intro⟩,⟨sg26942,True.intro,True.intro⟩⟩⟩,⟨sg26947,⟨sg26945,⟨sg26944,True.intro,True.intro⟩,⟨sg26946,True.intro,True.intro⟩⟩,⟨sg26949,⟨sg26948,True.intro,True.intro⟩,⟨sg26950,True.intro,True.intro⟩⟩⟩⟩,⟨sg26959,⟨sg26955,⟨sg26953,⟨sg26952,True.intro,True.intro⟩,⟨sg26954,True.intro,True.intro⟩⟩,⟨sg26957,⟨sg26956,True.intro,True.intro⟩,⟨sg26958,True.intro,True.intro⟩⟩⟩,⟨sg26963,⟨sg26961,⟨sg26960,True.intro,True.intro⟩,⟨sg26962,True.intro,True.intro⟩⟩,⟨sg26965,⟨sg26964,True.intro,True.intro⟩,⟨sg26966,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_257All : degreeTree43_257.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26935,degreeTree43_255All,degreeTree43_256All⟩ + +lemma degreeTree43_258All : degreeTree43_258.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26983,⟨sg26975,⟨sg26971,⟨sg26969,⟨sg26968,True.intro,True.intro⟩,⟨sg26970,True.intro,True.intro⟩⟩,⟨sg26973,⟨sg26972,True.intro,True.intro⟩,⟨sg26974,True.intro,True.intro⟩⟩⟩,⟨sg26979,⟨sg26977,⟨sg26976,True.intro,True.intro⟩,⟨sg26978,True.intro,True.intro⟩⟩,⟨sg26981,⟨sg26980,True.intro,True.intro⟩,⟨sg26982,True.intro,True.intro⟩⟩⟩⟩,⟨sg26991,⟨sg26987,⟨sg26985,⟨sg26984,True.intro,True.intro⟩,⟨sg26986,True.intro,True.intro⟩⟩,⟨sg26989,⟨sg26988,True.intro,True.intro⟩,⟨sg26990,True.intro,True.intro⟩⟩⟩,⟨sg26995,⟨sg26993,⟨sg26992,True.intro,True.intro⟩,⟨sg26994,True.intro,True.intro⟩⟩,⟨sg26997,⟨sg26996,True.intro,True.intro⟩,⟨sg26998,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_259All : degreeTree43_259.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27015,⟨sg27007,⟨sg27003,⟨sg27001,⟨sg27000,True.intro,True.intro⟩,⟨sg27002,True.intro,True.intro⟩⟩,⟨sg27005,⟨sg27004,True.intro,True.intro⟩,⟨sg27006,True.intro,True.intro⟩⟩⟩,⟨sg27011,⟨sg27009,⟨sg27008,True.intro,True.intro⟩,⟨sg27010,True.intro,True.intro⟩⟩,⟨sg27013,⟨sg27012,True.intro,True.intro⟩,⟨sg27014,True.intro,True.intro⟩⟩⟩⟩,⟨sg27023,⟨sg27019,⟨sg27017,⟨sg27016,True.intro,True.intro⟩,⟨sg27018,True.intro,True.intro⟩⟩,⟨sg27021,⟨sg27020,True.intro,True.intro⟩,⟨sg27022,True.intro,True.intro⟩⟩⟩,⟨sg27027,⟨sg27025,⟨sg27024,True.intro,True.intro⟩,⟨sg27026,True.intro,True.intro⟩⟩,⟨sg27029,⟨sg27028,True.intro,True.intro⟩,⟨sg27030,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_260All : degreeTree43_260.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26999,degreeTree43_258All,degreeTree43_259All⟩ + +lemma degreeTree43_261All : degreeTree43_261.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26967,degreeTree43_257All,degreeTree43_260All⟩ + +lemma degreeTree43_262All : degreeTree43_262.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26902,degreeTree43_252All,degreeTree43_261All⟩ + +lemma degreeTree43_263All : degreeTree43_263.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27040,⟨sg27036,⟨sg27034,⟨sg27033,⟨sg27032,True.intro,True.intro⟩,True.intro⟩,⟨sg27035,True.intro,True.intro⟩⟩,⟨sg27038,⟨sg27037,True.intro,True.intro⟩,⟨sg27039,True.intro,True.intro⟩⟩⟩,⟨sg27044,⟨sg27042,⟨sg27041,True.intro,True.intro⟩,⟨sg27043,True.intro,True.intro⟩⟩,⟨sg27046,⟨sg27045,True.intro,True.intro⟩,⟨sg27047,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_264All : degreeTree43_264.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27056,⟨sg27052,⟨sg27050,⟨sg27049,True.intro,True.intro⟩,⟨sg27051,True.intro,True.intro⟩⟩,⟨sg27054,⟨sg27053,True.intro,True.intro⟩,⟨sg27055,True.intro,True.intro⟩⟩⟩,⟨sg27060,⟨sg27058,⟨sg27057,True.intro,True.intro⟩,⟨sg27059,True.intro,True.intro⟩⟩,⟨sg27062,⟨sg27061,True.intro,True.intro⟩,⟨sg27063,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_265All : degreeTree43_265.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27048,degreeTree43_263All,degreeTree43_264All⟩ + +lemma degreeTree43_266All : degreeTree43_266.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27080,⟨sg27072,⟨sg27068,⟨sg27066,⟨sg27065,True.intro,True.intro⟩,⟨sg27067,True.intro,True.intro⟩⟩,⟨sg27070,⟨sg27069,True.intro,True.intro⟩,⟨sg27071,True.intro,True.intro⟩⟩⟩,⟨sg27076,⟨sg27074,⟨sg27073,True.intro,True.intro⟩,⟨sg27075,True.intro,True.intro⟩⟩,⟨sg27078,⟨sg27077,True.intro,True.intro⟩,⟨sg27079,True.intro,True.intro⟩⟩⟩⟩,⟨sg27088,⟨sg27084,⟨sg27082,⟨sg27081,True.intro,True.intro⟩,⟨sg27083,True.intro,True.intro⟩⟩,⟨sg27086,⟨sg27085,True.intro,True.intro⟩,⟨sg27087,True.intro,True.intro⟩⟩⟩,⟨sg27092,⟨sg27090,⟨sg27089,True.intro,True.intro⟩,⟨sg27091,True.intro,True.intro⟩⟩,⟨sg27094,⟨sg27093,True.intro,True.intro⟩,⟨sg27095,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_267All : degreeTree43_267.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27064,degreeTree43_265All,degreeTree43_266All⟩ + +lemma degreeTree43_268All : degreeTree43_268.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27112,⟨sg27104,⟨sg27100,⟨sg27098,⟨sg27097,True.intro,True.intro⟩,⟨sg27099,True.intro,True.intro⟩⟩,⟨sg27102,⟨sg27101,True.intro,True.intro⟩,⟨sg27103,True.intro,True.intro⟩⟩⟩,⟨sg27108,⟨sg27106,⟨sg27105,True.intro,True.intro⟩,⟨sg27107,True.intro,True.intro⟩⟩,⟨sg27110,⟨sg27109,True.intro,True.intro⟩,⟨sg27111,True.intro,True.intro⟩⟩⟩⟩,⟨sg27120,⟨sg27116,⟨sg27114,⟨sg27113,True.intro,True.intro⟩,⟨sg27115,True.intro,True.intro⟩⟩,⟨sg27118,⟨sg27117,True.intro,True.intro⟩,⟨sg27119,True.intro,True.intro⟩⟩⟩,⟨sg27124,⟨sg27122,⟨sg27121,True.intro,True.intro⟩,⟨sg27123,True.intro,True.intro⟩⟩,⟨sg27126,⟨sg27125,True.intro,True.intro⟩,⟨sg27127,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_269All : degreeTree43_269.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27144,⟨sg27136,⟨sg27132,⟨sg27130,⟨sg27129,True.intro,True.intro⟩,⟨sg27131,True.intro,True.intro⟩⟩,⟨sg27134,⟨sg27133,True.intro,True.intro⟩,⟨sg27135,True.intro,True.intro⟩⟩⟩,⟨sg27140,⟨sg27138,⟨sg27137,True.intro,True.intro⟩,⟨sg27139,True.intro,True.intro⟩⟩,⟨sg27142,⟨sg27141,True.intro,True.intro⟩,⟨sg27143,True.intro,True.intro⟩⟩⟩⟩,⟨sg27152,⟨sg27148,⟨sg27146,⟨sg27145,True.intro,True.intro⟩,⟨sg27147,True.intro,True.intro⟩⟩,⟨sg27150,⟨sg27149,True.intro,True.intro⟩,⟨sg27151,True.intro,True.intro⟩⟩⟩,⟨sg27156,⟨sg27154,⟨sg27153,True.intro,True.intro⟩,⟨sg27155,True.intro,True.intro⟩⟩,⟨sg27158,⟨sg27157,True.intro,True.intro⟩,⟨sg27159,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_270All : degreeTree43_270.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27128,degreeTree43_268All,degreeTree43_269All⟩ + +lemma degreeTree43_271All : degreeTree43_271.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27096,degreeTree43_267All,degreeTree43_270All⟩ + +lemma degreeTree43_272All : degreeTree43_272.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27169,⟨sg27165,⟨sg27163,⟨sg27162,⟨sg27161,True.intro,True.intro⟩,True.intro⟩,⟨sg27164,True.intro,True.intro⟩⟩,⟨sg27167,⟨sg27166,True.intro,True.intro⟩,⟨sg27168,True.intro,True.intro⟩⟩⟩,⟨sg27173,⟨sg27171,⟨sg27170,True.intro,True.intro⟩,⟨sg27172,True.intro,True.intro⟩⟩,⟨sg27175,⟨sg27174,True.intro,True.intro⟩,⟨sg27176,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_273All : degreeTree43_273.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27185,⟨sg27181,⟨sg27179,⟨sg27178,True.intro,True.intro⟩,⟨sg27180,True.intro,True.intro⟩⟩,⟨sg27183,⟨sg27182,True.intro,True.intro⟩,⟨sg27184,True.intro,True.intro⟩⟩⟩,⟨sg27189,⟨sg27187,⟨sg27186,True.intro,True.intro⟩,⟨sg27188,True.intro,True.intro⟩⟩,⟨sg27191,⟨sg27190,True.intro,True.intro⟩,⟨sg27192,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_274All : degreeTree43_274.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27177,degreeTree43_272All,degreeTree43_273All⟩ + +lemma degreeTree43_275All : degreeTree43_275.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27209,⟨sg27201,⟨sg27197,⟨sg27195,⟨sg27194,True.intro,True.intro⟩,⟨sg27196,True.intro,True.intro⟩⟩,⟨sg27199,⟨sg27198,True.intro,True.intro⟩,⟨sg27200,True.intro,True.intro⟩⟩⟩,⟨sg27205,⟨sg27203,⟨sg27202,True.intro,True.intro⟩,⟨sg27204,True.intro,True.intro⟩⟩,⟨sg27207,⟨sg27206,True.intro,True.intro⟩,⟨sg27208,True.intro,True.intro⟩⟩⟩⟩,⟨sg27217,⟨sg27213,⟨sg27211,⟨sg27210,True.intro,True.intro⟩,⟨sg27212,True.intro,True.intro⟩⟩,⟨sg27215,⟨sg27214,True.intro,True.intro⟩,⟨sg27216,True.intro,True.intro⟩⟩⟩,⟨sg27221,⟨sg27219,⟨sg27218,True.intro,True.intro⟩,⟨sg27220,True.intro,True.intro⟩⟩,⟨sg27223,⟨sg27222,True.intro,True.intro⟩,⟨sg27224,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_276All : degreeTree43_276.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27193,degreeTree43_274All,degreeTree43_275All⟩ + +lemma degreeTree43_277All : degreeTree43_277.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27241,⟨sg27233,⟨sg27229,⟨sg27227,⟨sg27226,True.intro,True.intro⟩,⟨sg27228,True.intro,True.intro⟩⟩,⟨sg27231,⟨sg27230,True.intro,True.intro⟩,⟨sg27232,True.intro,True.intro⟩⟩⟩,⟨sg27237,⟨sg27235,⟨sg27234,True.intro,True.intro⟩,⟨sg27236,True.intro,True.intro⟩⟩,⟨sg27239,⟨sg27238,True.intro,True.intro⟩,⟨sg27240,True.intro,True.intro⟩⟩⟩⟩,⟨sg27249,⟨sg27245,⟨sg27243,⟨sg27242,True.intro,True.intro⟩,⟨sg27244,True.intro,True.intro⟩⟩,⟨sg27247,⟨sg27246,True.intro,True.intro⟩,⟨sg27248,True.intro,True.intro⟩⟩⟩,⟨sg27253,⟨sg27251,⟨sg27250,True.intro,True.intro⟩,⟨sg27252,True.intro,True.intro⟩⟩,⟨sg27255,⟨sg27254,True.intro,True.intro⟩,⟨sg27256,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_278All : degreeTree43_278.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27273,⟨sg27265,⟨sg27261,⟨sg27259,⟨sg27258,True.intro,True.intro⟩,⟨sg27260,True.intro,True.intro⟩⟩,⟨sg27263,⟨sg27262,True.intro,True.intro⟩,⟨sg27264,True.intro,True.intro⟩⟩⟩,⟨sg27269,⟨sg27267,⟨sg27266,True.intro,True.intro⟩,⟨sg27268,True.intro,True.intro⟩⟩,⟨sg27271,⟨sg27270,True.intro,True.intro⟩,⟨sg27272,True.intro,True.intro⟩⟩⟩⟩,⟨sg27281,⟨sg27277,⟨sg27275,⟨sg27274,True.intro,True.intro⟩,⟨sg27276,True.intro,True.intro⟩⟩,⟨sg27279,⟨sg27278,True.intro,True.intro⟩,⟨sg27280,True.intro,True.intro⟩⟩⟩,⟨sg27285,⟨sg27283,⟨sg27282,True.intro,True.intro⟩,⟨sg27284,True.intro,True.intro⟩⟩,⟨sg27287,⟨sg27286,True.intro,True.intro⟩,⟨sg27288,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_279All : degreeTree43_279.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27257,degreeTree43_277All,degreeTree43_278All⟩ + +lemma degreeTree43_280All : degreeTree43_280.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27225,degreeTree43_276All,degreeTree43_279All⟩ + +lemma degreeTree43_281All : degreeTree43_281.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27160,degreeTree43_271All,degreeTree43_280All⟩ + +lemma degreeTree43_282All : degreeTree43_282.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27031,degreeTree43_262All,degreeTree43_281All⟩ + +lemma degreeTree43_283All : degreeTree43_283.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27298,⟨sg27294,⟨sg27292,⟨sg27291,⟨sg27290,True.intro,True.intro⟩,True.intro⟩,⟨sg27293,True.intro,True.intro⟩⟩,⟨sg27296,⟨sg27295,True.intro,True.intro⟩,⟨sg27297,True.intro,True.intro⟩⟩⟩,⟨sg27302,⟨sg27300,⟨sg27299,True.intro,True.intro⟩,⟨sg27301,True.intro,True.intro⟩⟩,⟨sg27304,⟨sg27303,True.intro,True.intro⟩,⟨sg27305,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_284All : degreeTree43_284.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27314,⟨sg27310,⟨sg27308,⟨sg27307,True.intro,True.intro⟩,⟨sg27309,True.intro,True.intro⟩⟩,⟨sg27312,⟨sg27311,True.intro,True.intro⟩,⟨sg27313,True.intro,True.intro⟩⟩⟩,⟨sg27318,⟨sg27316,⟨sg27315,True.intro,True.intro⟩,⟨sg27317,True.intro,True.intro⟩⟩,⟨sg27320,⟨sg27319,True.intro,True.intro⟩,⟨sg27321,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_285All : degreeTree43_285.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27306,degreeTree43_283All,degreeTree43_284All⟩ + +lemma degreeTree43_286All : degreeTree43_286.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27338,⟨sg27330,⟨sg27326,⟨sg27324,⟨sg27323,True.intro,True.intro⟩,⟨sg27325,True.intro,True.intro⟩⟩,⟨sg27328,⟨sg27327,True.intro,True.intro⟩,⟨sg27329,True.intro,True.intro⟩⟩⟩,⟨sg27334,⟨sg27332,⟨sg27331,True.intro,True.intro⟩,⟨sg27333,True.intro,True.intro⟩⟩,⟨sg27336,⟨sg27335,True.intro,True.intro⟩,⟨sg27337,True.intro,True.intro⟩⟩⟩⟩,⟨sg27346,⟨sg27342,⟨sg27340,⟨sg27339,True.intro,True.intro⟩,⟨sg27341,True.intro,True.intro⟩⟩,⟨sg27344,⟨sg27343,True.intro,True.intro⟩,⟨sg27345,True.intro,True.intro⟩⟩⟩,⟨sg27350,⟨sg27348,⟨sg27347,True.intro,True.intro⟩,⟨sg27349,True.intro,True.intro⟩⟩,⟨sg27352,⟨sg27351,True.intro,True.intro⟩,⟨sg27353,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_287All : degreeTree43_287.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27322,degreeTree43_285All,degreeTree43_286All⟩ + +lemma degreeTree43_288All : degreeTree43_288.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27370,⟨sg27362,⟨sg27358,⟨sg27356,⟨sg27355,True.intro,True.intro⟩,⟨sg27357,True.intro,True.intro⟩⟩,⟨sg27360,⟨sg27359,True.intro,True.intro⟩,⟨sg27361,True.intro,True.intro⟩⟩⟩,⟨sg27366,⟨sg27364,⟨sg27363,True.intro,True.intro⟩,⟨sg27365,True.intro,True.intro⟩⟩,⟨sg27368,⟨sg27367,True.intro,True.intro⟩,⟨sg27369,True.intro,True.intro⟩⟩⟩⟩,⟨sg27378,⟨sg27374,⟨sg27372,⟨sg27371,True.intro,True.intro⟩,⟨sg27373,True.intro,True.intro⟩⟩,⟨sg27376,⟨sg27375,True.intro,True.intro⟩,⟨sg27377,True.intro,True.intro⟩⟩⟩,⟨sg27382,⟨sg27380,⟨sg27379,True.intro,True.intro⟩,⟨sg27381,True.intro,True.intro⟩⟩,⟨sg27384,⟨sg27383,True.intro,True.intro⟩,⟨sg27385,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_289All : degreeTree43_289.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27402,⟨sg27394,⟨sg27390,⟨sg27388,⟨sg27387,True.intro,True.intro⟩,⟨sg27389,True.intro,True.intro⟩⟩,⟨sg27392,⟨sg27391,True.intro,True.intro⟩,⟨sg27393,True.intro,True.intro⟩⟩⟩,⟨sg27398,⟨sg27396,⟨sg27395,True.intro,True.intro⟩,⟨sg27397,True.intro,True.intro⟩⟩,⟨sg27400,⟨sg27399,True.intro,True.intro⟩,⟨sg27401,True.intro,True.intro⟩⟩⟩⟩,⟨sg27410,⟨sg27406,⟨sg27404,⟨sg27403,True.intro,True.intro⟩,⟨sg27405,True.intro,True.intro⟩⟩,⟨sg27408,⟨sg27407,True.intro,True.intro⟩,⟨sg27409,True.intro,True.intro⟩⟩⟩,⟨sg27414,⟨sg27412,⟨sg27411,True.intro,True.intro⟩,⟨sg27413,True.intro,True.intro⟩⟩,⟨sg27416,⟨sg27415,True.intro,True.intro⟩,⟨sg27417,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_290All : degreeTree43_290.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27386,degreeTree43_288All,degreeTree43_289All⟩ + +lemma degreeTree43_291All : degreeTree43_291.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27354,degreeTree43_287All,degreeTree43_290All⟩ + +lemma degreeTree43_292All : degreeTree43_292.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27427,⟨sg27423,⟨sg27421,⟨sg27420,⟨sg27419,True.intro,True.intro⟩,True.intro⟩,⟨sg27422,True.intro,True.intro⟩⟩,⟨sg27425,⟨sg27424,True.intro,True.intro⟩,⟨sg27426,True.intro,True.intro⟩⟩⟩,⟨sg27431,⟨sg27429,⟨sg27428,True.intro,True.intro⟩,⟨sg27430,True.intro,True.intro⟩⟩,⟨sg27433,⟨sg27432,True.intro,True.intro⟩,⟨sg27434,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_293All : degreeTree43_293.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27443,⟨sg27439,⟨sg27437,⟨sg27436,True.intro,True.intro⟩,⟨sg27438,True.intro,True.intro⟩⟩,⟨sg27441,⟨sg27440,True.intro,True.intro⟩,⟨sg27442,True.intro,True.intro⟩⟩⟩,⟨sg27447,⟨sg27445,⟨sg27444,True.intro,True.intro⟩,⟨sg27446,True.intro,True.intro⟩⟩,⟨sg27449,⟨sg27448,True.intro,True.intro⟩,⟨sg27450,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_294All : degreeTree43_294.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27435,degreeTree43_292All,degreeTree43_293All⟩ + +lemma degreeTree43_295All : degreeTree43_295.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27467,⟨sg27459,⟨sg27455,⟨sg27453,⟨sg27452,True.intro,True.intro⟩,⟨sg27454,True.intro,True.intro⟩⟩,⟨sg27457,⟨sg27456,True.intro,True.intro⟩,⟨sg27458,True.intro,True.intro⟩⟩⟩,⟨sg27463,⟨sg27461,⟨sg27460,True.intro,True.intro⟩,⟨sg27462,True.intro,True.intro⟩⟩,⟨sg27465,⟨sg27464,True.intro,True.intro⟩,⟨sg27466,True.intro,True.intro⟩⟩⟩⟩,⟨sg27475,⟨sg27471,⟨sg27469,⟨sg27468,True.intro,True.intro⟩,⟨sg27470,True.intro,True.intro⟩⟩,⟨sg27473,⟨sg27472,True.intro,True.intro⟩,⟨sg27474,True.intro,True.intro⟩⟩⟩,⟨sg27479,⟨sg27477,⟨sg27476,True.intro,True.intro⟩,⟨sg27478,True.intro,True.intro⟩⟩,⟨sg27481,⟨sg27480,True.intro,True.intro⟩,⟨sg27482,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_296All : degreeTree43_296.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27451,degreeTree43_294All,degreeTree43_295All⟩ + +lemma degreeTree43_297All : degreeTree43_297.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27499,⟨sg27491,⟨sg27487,⟨sg27485,⟨sg27484,True.intro,True.intro⟩,⟨sg27486,True.intro,True.intro⟩⟩,⟨sg27489,⟨sg27488,True.intro,True.intro⟩,⟨sg27490,True.intro,True.intro⟩⟩⟩,⟨sg27495,⟨sg27493,⟨sg27492,True.intro,True.intro⟩,⟨sg27494,True.intro,True.intro⟩⟩,⟨sg27497,⟨sg27496,True.intro,True.intro⟩,⟨sg27498,True.intro,True.intro⟩⟩⟩⟩,⟨sg27507,⟨sg27503,⟨sg27501,⟨sg27500,True.intro,True.intro⟩,⟨sg27502,True.intro,True.intro⟩⟩,⟨sg27505,⟨sg27504,True.intro,True.intro⟩,⟨sg27506,True.intro,True.intro⟩⟩⟩,⟨sg27511,⟨sg27509,⟨sg27508,True.intro,True.intro⟩,⟨sg27510,True.intro,True.intro⟩⟩,⟨sg27513,⟨sg27512,True.intro,True.intro⟩,⟨sg27514,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_298All : degreeTree43_298.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27531,⟨sg27523,⟨sg27519,⟨sg27517,⟨sg27516,True.intro,True.intro⟩,⟨sg27518,True.intro,True.intro⟩⟩,⟨sg27521,⟨sg27520,True.intro,True.intro⟩,⟨sg27522,True.intro,True.intro⟩⟩⟩,⟨sg27527,⟨sg27525,⟨sg27524,True.intro,True.intro⟩,⟨sg27526,True.intro,True.intro⟩⟩,⟨sg27529,⟨sg27528,True.intro,True.intro⟩,⟨sg27530,True.intro,True.intro⟩⟩⟩⟩,⟨sg27539,⟨sg27535,⟨sg27533,⟨sg27532,True.intro,True.intro⟩,⟨sg27534,True.intro,True.intro⟩⟩,⟨sg27537,⟨sg27536,True.intro,True.intro⟩,⟨sg27538,True.intro,True.intro⟩⟩⟩,⟨sg27543,⟨sg27541,⟨sg27540,True.intro,True.intro⟩,⟨sg27542,True.intro,True.intro⟩⟩,⟨sg27545,⟨sg27544,True.intro,True.intro⟩,⟨sg27546,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_299All : degreeTree43_299.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27515,degreeTree43_297All,degreeTree43_298All⟩ + +lemma degreeTree43_300All : degreeTree43_300.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27483,degreeTree43_296All,degreeTree43_299All⟩ + +lemma degreeTree43_301All : degreeTree43_301.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27418,degreeTree43_291All,degreeTree43_300All⟩ + +lemma degreeTree43_302All : degreeTree43_302.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27556,⟨sg27552,⟨sg27550,⟨sg27549,⟨sg27548,True.intro,True.intro⟩,True.intro⟩,⟨sg27551,True.intro,True.intro⟩⟩,⟨sg27554,⟨sg27553,True.intro,True.intro⟩,⟨sg27555,True.intro,True.intro⟩⟩⟩,⟨sg27560,⟨sg27558,⟨sg27557,True.intro,True.intro⟩,⟨sg27559,True.intro,True.intro⟩⟩,⟨sg27562,⟨sg27561,True.intro,True.intro⟩,⟨sg27563,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_303All : degreeTree43_303.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27572,⟨sg27568,⟨sg27566,⟨sg27565,True.intro,True.intro⟩,⟨sg27567,True.intro,True.intro⟩⟩,⟨sg27570,⟨sg27569,True.intro,True.intro⟩,⟨sg27571,True.intro,True.intro⟩⟩⟩,⟨sg27576,⟨sg27574,⟨sg27573,True.intro,True.intro⟩,⟨sg27575,True.intro,True.intro⟩⟩,⟨sg27578,⟨sg27577,True.intro,True.intro⟩,⟨sg27579,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_304All : degreeTree43_304.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27564,degreeTree43_302All,degreeTree43_303All⟩ + +lemma degreeTree43_305All : degreeTree43_305.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27596,⟨sg27588,⟨sg27584,⟨sg27582,⟨sg27581,True.intro,True.intro⟩,⟨sg27583,True.intro,True.intro⟩⟩,⟨sg27586,⟨sg27585,True.intro,True.intro⟩,⟨sg27587,True.intro,True.intro⟩⟩⟩,⟨sg27592,⟨sg27590,⟨sg27589,True.intro,True.intro⟩,⟨sg27591,True.intro,True.intro⟩⟩,⟨sg27594,⟨sg27593,True.intro,True.intro⟩,⟨sg27595,True.intro,True.intro⟩⟩⟩⟩,⟨sg27604,⟨sg27600,⟨sg27598,⟨sg27597,True.intro,True.intro⟩,⟨sg27599,True.intro,True.intro⟩⟩,⟨sg27602,⟨sg27601,True.intro,True.intro⟩,⟨sg27603,True.intro,True.intro⟩⟩⟩,⟨sg27608,⟨sg27606,⟨sg27605,True.intro,True.intro⟩,⟨sg27607,True.intro,True.intro⟩⟩,⟨sg27610,⟨sg27609,True.intro,True.intro⟩,⟨sg27611,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_306All : degreeTree43_306.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27580,degreeTree43_304All,degreeTree43_305All⟩ + +lemma degreeTree43_307All : degreeTree43_307.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27628,⟨sg27620,⟨sg27616,⟨sg27614,⟨sg27613,True.intro,True.intro⟩,⟨sg27615,True.intro,True.intro⟩⟩,⟨sg27618,⟨sg27617,True.intro,True.intro⟩,⟨sg27619,True.intro,True.intro⟩⟩⟩,⟨sg27624,⟨sg27622,⟨sg27621,True.intro,True.intro⟩,⟨sg27623,True.intro,True.intro⟩⟩,⟨sg27626,⟨sg27625,True.intro,True.intro⟩,⟨sg27627,True.intro,True.intro⟩⟩⟩⟩,⟨sg27636,⟨sg27632,⟨sg27630,⟨sg27629,True.intro,True.intro⟩,⟨sg27631,True.intro,True.intro⟩⟩,⟨sg27634,⟨sg27633,True.intro,True.intro⟩,⟨sg27635,True.intro,True.intro⟩⟩⟩,⟨sg27640,⟨sg27638,⟨sg27637,True.intro,True.intro⟩,⟨sg27639,True.intro,True.intro⟩⟩,⟨sg27642,⟨sg27641,True.intro,True.intro⟩,⟨sg27643,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_308All : degreeTree43_308.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27660,⟨sg27652,⟨sg27648,⟨sg27646,⟨sg27645,True.intro,True.intro⟩,⟨sg27647,True.intro,True.intro⟩⟩,⟨sg27650,⟨sg27649,True.intro,True.intro⟩,⟨sg27651,True.intro,True.intro⟩⟩⟩,⟨sg27656,⟨sg27654,⟨sg27653,True.intro,True.intro⟩,⟨sg27655,True.intro,True.intro⟩⟩,⟨sg27658,⟨sg27657,True.intro,True.intro⟩,⟨sg27659,True.intro,True.intro⟩⟩⟩⟩,⟨sg27668,⟨sg27664,⟨sg27662,⟨sg27661,True.intro,True.intro⟩,⟨sg27663,True.intro,True.intro⟩⟩,⟨sg27666,⟨sg27665,True.intro,True.intro⟩,⟨sg27667,True.intro,True.intro⟩⟩⟩,⟨sg27672,⟨sg27670,⟨sg27669,True.intro,True.intro⟩,⟨sg27671,True.intro,True.intro⟩⟩,⟨sg27674,⟨sg27673,True.intro,True.intro⟩,⟨sg27675,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_309All : degreeTree43_309.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27644,degreeTree43_307All,degreeTree43_308All⟩ + +lemma degreeTree43_310All : degreeTree43_310.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27612,degreeTree43_306All,degreeTree43_309All⟩ + +lemma degreeTree43_311All : degreeTree43_311.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27685,⟨sg27681,⟨sg27679,⟨sg27678,⟨sg27677,True.intro,True.intro⟩,True.intro⟩,⟨sg27680,True.intro,True.intro⟩⟩,⟨sg27683,⟨sg27682,True.intro,True.intro⟩,⟨sg27684,True.intro,True.intro⟩⟩⟩,⟨sg27689,⟨sg27687,⟨sg27686,True.intro,True.intro⟩,⟨sg27688,True.intro,True.intro⟩⟩,⟨sg27691,⟨sg27690,True.intro,True.intro⟩,⟨sg27692,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_312All : degreeTree43_312.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27701,⟨sg27697,⟨sg27695,⟨sg27694,True.intro,True.intro⟩,⟨sg27696,True.intro,True.intro⟩⟩,⟨sg27699,⟨sg27698,True.intro,True.intro⟩,⟨sg27700,True.intro,True.intro⟩⟩⟩,⟨sg27705,⟨sg27703,⟨sg27702,True.intro,True.intro⟩,⟨sg27704,True.intro,True.intro⟩⟩,⟨sg27707,⟨sg27706,True.intro,True.intro⟩,⟨sg27708,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_313All : degreeTree43_313.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27693,degreeTree43_311All,degreeTree43_312All⟩ + +lemma degreeTree43_314All : degreeTree43_314.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27725,⟨sg27717,⟨sg27713,⟨sg27711,⟨sg27710,True.intro,True.intro⟩,⟨sg27712,True.intro,True.intro⟩⟩,⟨sg27715,⟨sg27714,True.intro,True.intro⟩,⟨sg27716,True.intro,True.intro⟩⟩⟩,⟨sg27721,⟨sg27719,⟨sg27718,True.intro,True.intro⟩,⟨sg27720,True.intro,True.intro⟩⟩,⟨sg27723,⟨sg27722,True.intro,True.intro⟩,⟨sg27724,True.intro,True.intro⟩⟩⟩⟩,⟨sg27733,⟨sg27729,⟨sg27727,⟨sg27726,True.intro,True.intro⟩,⟨sg27728,True.intro,True.intro⟩⟩,⟨sg27731,⟨sg27730,True.intro,True.intro⟩,⟨sg27732,True.intro,True.intro⟩⟩⟩,⟨sg27737,⟨sg27735,⟨sg27734,True.intro,True.intro⟩,⟨sg27736,True.intro,True.intro⟩⟩,⟨sg27739,⟨sg27738,True.intro,True.intro⟩,⟨sg27740,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_315All : degreeTree43_315.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27709,degreeTree43_313All,degreeTree43_314All⟩ + +lemma degreeTree43_316All : degreeTree43_316.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27757,⟨sg27749,⟨sg27745,⟨sg27743,⟨sg27742,True.intro,True.intro⟩,⟨sg27744,True.intro,True.intro⟩⟩,⟨sg27747,⟨sg27746,True.intro,True.intro⟩,⟨sg27748,True.intro,True.intro⟩⟩⟩,⟨sg27753,⟨sg27751,⟨sg27750,True.intro,True.intro⟩,⟨sg27752,True.intro,True.intro⟩⟩,⟨sg27755,⟨sg27754,True.intro,True.intro⟩,⟨sg27756,True.intro,True.intro⟩⟩⟩⟩,⟨sg27765,⟨sg27761,⟨sg27759,⟨sg27758,True.intro,True.intro⟩,⟨sg27760,True.intro,True.intro⟩⟩,⟨sg27763,⟨sg27762,True.intro,True.intro⟩,⟨sg27764,True.intro,True.intro⟩⟩⟩,⟨sg27769,⟨sg27767,⟨sg27766,True.intro,True.intro⟩,⟨sg27768,True.intro,True.intro⟩⟩,⟨sg27771,⟨sg27770,True.intro,True.intro⟩,⟨sg27772,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_317All : degreeTree43_317.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27789,⟨sg27781,⟨sg27777,⟨sg27775,⟨sg27774,True.intro,True.intro⟩,⟨sg27776,True.intro,True.intro⟩⟩,⟨sg27779,⟨sg27778,True.intro,True.intro⟩,⟨sg27780,True.intro,True.intro⟩⟩⟩,⟨sg27785,⟨sg27783,⟨sg27782,True.intro,True.intro⟩,⟨sg27784,True.intro,True.intro⟩⟩,⟨sg27787,⟨sg27786,True.intro,True.intro⟩,⟨sg27788,True.intro,True.intro⟩⟩⟩⟩,⟨sg27797,⟨sg27793,⟨sg27791,⟨sg27790,True.intro,True.intro⟩,⟨sg27792,True.intro,True.intro⟩⟩,⟨sg27795,⟨sg27794,True.intro,True.intro⟩,⟨sg27796,True.intro,True.intro⟩⟩⟩,⟨sg27801,⟨sg27799,⟨sg27798,True.intro,True.intro⟩,⟨sg27800,True.intro,True.intro⟩⟩,⟨sg27803,⟨sg27802,True.intro,True.intro⟩,⟨sg27804,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_318All : degreeTree43_318.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27773,degreeTree43_316All,degreeTree43_317All⟩ + +lemma degreeTree43_319All : degreeTree43_319.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27741,degreeTree43_315All,degreeTree43_318All⟩ + +lemma degreeTree43_320All : degreeTree43_320.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27676,degreeTree43_310All,degreeTree43_319All⟩ + +lemma degreeTree43_321All : degreeTree43_321.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27547,degreeTree43_301All,degreeTree43_320All⟩ + +lemma degreeTree43_322All : degreeTree43_322.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27289,degreeTree43_282All,degreeTree43_321All⟩ + +lemma degreeTree43_323All : degreeTree43_323.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg26773,degreeTree43_243All,degreeTree43_322All⟩ + +lemma degreeTree43_324All : degreeTree43_324.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg25740,degreeTree43_162All,degreeTree43_323All⟩ + +lemma degreeTree43_325All : degreeTree43_325.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27814,⟨sg27810,⟨sg27808,⟨sg27807,⟨sg27806,True.intro,True.intro⟩,True.intro⟩,⟨sg27809,True.intro,True.intro⟩⟩,⟨sg27812,⟨sg27811,True.intro,True.intro⟩,⟨sg27813,True.intro,True.intro⟩⟩⟩,⟨sg27818,⟨sg27816,⟨sg27815,True.intro,True.intro⟩,⟨sg27817,True.intro,True.intro⟩⟩,⟨sg27820,⟨sg27819,True.intro,True.intro⟩,⟨sg27821,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_326All : degreeTree43_326.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27830,⟨sg27826,⟨sg27824,⟨sg27823,True.intro,True.intro⟩,⟨sg27825,True.intro,True.intro⟩⟩,⟨sg27828,⟨sg27827,True.intro,True.intro⟩,⟨sg27829,True.intro,True.intro⟩⟩⟩,⟨sg27834,⟨sg27832,⟨sg27831,True.intro,True.intro⟩,⟨sg27833,True.intro,True.intro⟩⟩,⟨sg27836,⟨sg27835,True.intro,True.intro⟩,⟨sg27837,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_327All : degreeTree43_327.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27822,degreeTree43_325All,degreeTree43_326All⟩ + +lemma degreeTree43_328All : degreeTree43_328.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27854,⟨sg27846,⟨sg27842,⟨sg27840,⟨sg27839,True.intro,True.intro⟩,⟨sg27841,True.intro,True.intro⟩⟩,⟨sg27844,⟨sg27843,True.intro,True.intro⟩,⟨sg27845,True.intro,True.intro⟩⟩⟩,⟨sg27850,⟨sg27848,⟨sg27847,True.intro,True.intro⟩,⟨sg27849,True.intro,True.intro⟩⟩,⟨sg27852,⟨sg27851,True.intro,True.intro⟩,⟨sg27853,True.intro,True.intro⟩⟩⟩⟩,⟨sg27862,⟨sg27858,⟨sg27856,⟨sg27855,True.intro,True.intro⟩,⟨sg27857,True.intro,True.intro⟩⟩,⟨sg27860,⟨sg27859,True.intro,True.intro⟩,⟨sg27861,True.intro,True.intro⟩⟩⟩,⟨sg27866,⟨sg27864,⟨sg27863,True.intro,True.intro⟩,⟨sg27865,True.intro,True.intro⟩⟩,⟨sg27868,⟨sg27867,True.intro,True.intro⟩,⟨sg27869,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_329All : degreeTree43_329.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27838,degreeTree43_327All,degreeTree43_328All⟩ + +lemma degreeTree43_330All : degreeTree43_330.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27879,⟨sg27875,⟨sg27873,⟨sg27872,⟨sg27871,True.intro,True.intro⟩,True.intro⟩,⟨sg27874,True.intro,True.intro⟩⟩,⟨sg27877,⟨sg27876,True.intro,True.intro⟩,⟨sg27878,True.intro,True.intro⟩⟩⟩,⟨sg27883,⟨sg27881,⟨sg27880,True.intro,True.intro⟩,⟨sg27882,True.intro,True.intro⟩⟩,⟨sg27885,⟨sg27884,True.intro,True.intro⟩,⟨sg27886,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_331All : degreeTree43_331.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27895,⟨sg27891,⟨sg27889,⟨sg27888,True.intro,True.intro⟩,⟨sg27890,True.intro,True.intro⟩⟩,⟨sg27893,⟨sg27892,True.intro,True.intro⟩,⟨sg27894,True.intro,True.intro⟩⟩⟩,⟨sg27899,⟨sg27897,⟨sg27896,True.intro,True.intro⟩,⟨sg27898,True.intro,True.intro⟩⟩,⟨sg27901,⟨sg27900,True.intro,True.intro⟩,⟨sg27902,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_332All : degreeTree43_332.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27887,degreeTree43_330All,degreeTree43_331All⟩ + +lemma degreeTree43_333All : degreeTree43_333.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27919,⟨sg27911,⟨sg27907,⟨sg27905,⟨sg27904,True.intro,True.intro⟩,⟨sg27906,True.intro,True.intro⟩⟩,⟨sg27909,⟨sg27908,True.intro,True.intro⟩,⟨sg27910,True.intro,True.intro⟩⟩⟩,⟨sg27915,⟨sg27913,⟨sg27912,True.intro,True.intro⟩,⟨sg27914,True.intro,True.intro⟩⟩,⟨sg27917,⟨sg27916,True.intro,True.intro⟩,⟨sg27918,True.intro,True.intro⟩⟩⟩⟩,⟨sg27927,⟨sg27923,⟨sg27921,⟨sg27920,True.intro,True.intro⟩,⟨sg27922,True.intro,True.intro⟩⟩,⟨sg27925,⟨sg27924,True.intro,True.intro⟩,⟨sg27926,True.intro,True.intro⟩⟩⟩,⟨sg27931,⟨sg27929,⟨sg27928,True.intro,True.intro⟩,⟨sg27930,True.intro,True.intro⟩⟩,⟨sg27933,⟨sg27932,True.intro,True.intro⟩,⟨sg27934,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_334All : degreeTree43_334.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27903,degreeTree43_332All,degreeTree43_333All⟩ + +lemma degreeTree43_335All : degreeTree43_335.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27870,degreeTree43_329All,degreeTree43_334All⟩ + +lemma degreeTree43_336All : degreeTree43_336.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27944,⟨sg27940,⟨sg27938,⟨sg27937,⟨sg27936,True.intro,True.intro⟩,True.intro⟩,⟨sg27939,True.intro,True.intro⟩⟩,⟨sg27942,⟨sg27941,True.intro,True.intro⟩,⟨sg27943,True.intro,True.intro⟩⟩⟩,⟨sg27948,⟨sg27946,⟨sg27945,True.intro,True.intro⟩,⟨sg27947,True.intro,True.intro⟩⟩,⟨sg27950,⟨sg27949,True.intro,True.intro⟩,⟨sg27951,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_337All : degreeTree43_337.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27960,⟨sg27956,⟨sg27954,⟨sg27953,True.intro,True.intro⟩,⟨sg27955,True.intro,True.intro⟩⟩,⟨sg27958,⟨sg27957,True.intro,True.intro⟩,⟨sg27959,True.intro,True.intro⟩⟩⟩,⟨sg27964,⟨sg27962,⟨sg27961,True.intro,True.intro⟩,⟨sg27963,True.intro,True.intro⟩⟩,⟨sg27966,⟨sg27965,True.intro,True.intro⟩,⟨sg27967,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_338All : degreeTree43_338.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27952,degreeTree43_336All,degreeTree43_337All⟩ + +lemma degreeTree43_339All : degreeTree43_339.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27984,⟨sg27976,⟨sg27972,⟨sg27970,⟨sg27969,True.intro,True.intro⟩,⟨sg27971,True.intro,True.intro⟩⟩,⟨sg27974,⟨sg27973,True.intro,True.intro⟩,⟨sg27975,True.intro,True.intro⟩⟩⟩,⟨sg27980,⟨sg27978,⟨sg27977,True.intro,True.intro⟩,⟨sg27979,True.intro,True.intro⟩⟩,⟨sg27982,⟨sg27981,True.intro,True.intro⟩,⟨sg27983,True.intro,True.intro⟩⟩⟩⟩,⟨sg27992,⟨sg27988,⟨sg27986,⟨sg27985,True.intro,True.intro⟩,⟨sg27987,True.intro,True.intro⟩⟩,⟨sg27990,⟨sg27989,True.intro,True.intro⟩,⟨sg27991,True.intro,True.intro⟩⟩⟩,⟨sg27996,⟨sg27994,⟨sg27993,True.intro,True.intro⟩,⟨sg27995,True.intro,True.intro⟩⟩,⟨sg27998,⟨sg27997,True.intro,True.intro⟩,⟨sg27999,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_340All : degreeTree43_340.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27968,degreeTree43_338All,degreeTree43_339All⟩ + +lemma degreeTree43_341All : degreeTree43_341.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28016,⟨sg28008,⟨sg28004,⟨sg28002,⟨sg28001,True.intro,True.intro⟩,⟨sg28003,True.intro,True.intro⟩⟩,⟨sg28006,⟨sg28005,True.intro,True.intro⟩,⟨sg28007,True.intro,True.intro⟩⟩⟩,⟨sg28012,⟨sg28010,⟨sg28009,True.intro,True.intro⟩,⟨sg28011,True.intro,True.intro⟩⟩,⟨sg28014,⟨sg28013,True.intro,True.intro⟩,⟨sg28015,True.intro,True.intro⟩⟩⟩⟩,⟨sg28024,⟨sg28020,⟨sg28018,⟨sg28017,True.intro,True.intro⟩,⟨sg28019,True.intro,True.intro⟩⟩,⟨sg28022,⟨sg28021,True.intro,True.intro⟩,⟨sg28023,True.intro,True.intro⟩⟩⟩,⟨sg28028,⟨sg28026,⟨sg28025,True.intro,True.intro⟩,⟨sg28027,True.intro,True.intro⟩⟩,⟨sg28030,⟨sg28029,True.intro,True.intro⟩,⟨sg28031,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_342All : degreeTree43_342.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28048,⟨sg28040,⟨sg28036,⟨sg28034,⟨sg28033,True.intro,True.intro⟩,⟨sg28035,True.intro,True.intro⟩⟩,⟨sg28038,⟨sg28037,True.intro,True.intro⟩,⟨sg28039,True.intro,True.intro⟩⟩⟩,⟨sg28044,⟨sg28042,⟨sg28041,True.intro,True.intro⟩,⟨sg28043,True.intro,True.intro⟩⟩,⟨sg28046,⟨sg28045,True.intro,True.intro⟩,⟨sg28047,True.intro,True.intro⟩⟩⟩⟩,⟨sg28056,⟨sg28052,⟨sg28050,⟨sg28049,True.intro,True.intro⟩,⟨sg28051,True.intro,True.intro⟩⟩,⟨sg28054,⟨sg28053,True.intro,True.intro⟩,⟨sg28055,True.intro,True.intro⟩⟩⟩,⟨sg28060,⟨sg28058,⟨sg28057,True.intro,True.intro⟩,⟨sg28059,True.intro,True.intro⟩⟩,⟨sg28062,⟨sg28061,True.intro,True.intro⟩,⟨sg28063,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_343All : degreeTree43_343.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28032,degreeTree43_341All,degreeTree43_342All⟩ + +lemma degreeTree43_344All : degreeTree43_344.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28000,degreeTree43_340All,degreeTree43_343All⟩ + +lemma degreeTree43_345All : degreeTree43_345.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27935,degreeTree43_335All,degreeTree43_344All⟩ + +lemma degreeTree43_346All : degreeTree43_346.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28073,⟨sg28069,⟨sg28067,⟨sg28066,⟨sg28065,True.intro,True.intro⟩,True.intro⟩,⟨sg28068,True.intro,True.intro⟩⟩,⟨sg28071,⟨sg28070,True.intro,True.intro⟩,⟨sg28072,True.intro,True.intro⟩⟩⟩,⟨sg28077,⟨sg28075,⟨sg28074,True.intro,True.intro⟩,⟨sg28076,True.intro,True.intro⟩⟩,⟨sg28079,⟨sg28078,True.intro,True.intro⟩,⟨sg28080,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_347All : degreeTree43_347.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28089,⟨sg28085,⟨sg28083,⟨sg28082,True.intro,True.intro⟩,⟨sg28084,True.intro,True.intro⟩⟩,⟨sg28087,⟨sg28086,True.intro,True.intro⟩,⟨sg28088,True.intro,True.intro⟩⟩⟩,⟨sg28093,⟨sg28091,⟨sg28090,True.intro,True.intro⟩,⟨sg28092,True.intro,True.intro⟩⟩,⟨sg28095,⟨sg28094,True.intro,True.intro⟩,⟨sg28096,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_348All : degreeTree43_348.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28081,degreeTree43_346All,degreeTree43_347All⟩ + +lemma degreeTree43_349All : degreeTree43_349.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28113,⟨sg28105,⟨sg28101,⟨sg28099,⟨sg28098,True.intro,True.intro⟩,⟨sg28100,True.intro,True.intro⟩⟩,⟨sg28103,⟨sg28102,True.intro,True.intro⟩,⟨sg28104,True.intro,True.intro⟩⟩⟩,⟨sg28109,⟨sg28107,⟨sg28106,True.intro,True.intro⟩,⟨sg28108,True.intro,True.intro⟩⟩,⟨sg28111,⟨sg28110,True.intro,True.intro⟩,⟨sg28112,True.intro,True.intro⟩⟩⟩⟩,⟨sg28121,⟨sg28117,⟨sg28115,⟨sg28114,True.intro,True.intro⟩,⟨sg28116,True.intro,True.intro⟩⟩,⟨sg28119,⟨sg28118,True.intro,True.intro⟩,⟨sg28120,True.intro,True.intro⟩⟩⟩,⟨sg28125,⟨sg28123,⟨sg28122,True.intro,True.intro⟩,⟨sg28124,True.intro,True.intro⟩⟩,⟨sg28127,⟨sg28126,True.intro,True.intro⟩,⟨sg28128,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_350All : degreeTree43_350.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28097,degreeTree43_348All,degreeTree43_349All⟩ + +lemma degreeTree43_351All : degreeTree43_351.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28145,⟨sg28137,⟨sg28133,⟨sg28131,⟨sg28130,True.intro,True.intro⟩,⟨sg28132,True.intro,True.intro⟩⟩,⟨sg28135,⟨sg28134,True.intro,True.intro⟩,⟨sg28136,True.intro,True.intro⟩⟩⟩,⟨sg28141,⟨sg28139,⟨sg28138,True.intro,True.intro⟩,⟨sg28140,True.intro,True.intro⟩⟩,⟨sg28143,⟨sg28142,True.intro,True.intro⟩,⟨sg28144,True.intro,True.intro⟩⟩⟩⟩,⟨sg28153,⟨sg28149,⟨sg28147,⟨sg28146,True.intro,True.intro⟩,⟨sg28148,True.intro,True.intro⟩⟩,⟨sg28151,⟨sg28150,True.intro,True.intro⟩,⟨sg28152,True.intro,True.intro⟩⟩⟩,⟨sg28157,⟨sg28155,⟨sg28154,True.intro,True.intro⟩,⟨sg28156,True.intro,True.intro⟩⟩,⟨sg28159,⟨sg28158,True.intro,True.intro⟩,⟨sg28160,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_352All : degreeTree43_352.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28177,⟨sg28169,⟨sg28165,⟨sg28163,⟨sg28162,True.intro,True.intro⟩,⟨sg28164,True.intro,True.intro⟩⟩,⟨sg28167,⟨sg28166,True.intro,True.intro⟩,⟨sg28168,True.intro,True.intro⟩⟩⟩,⟨sg28173,⟨sg28171,⟨sg28170,True.intro,True.intro⟩,⟨sg28172,True.intro,True.intro⟩⟩,⟨sg28175,⟨sg28174,True.intro,True.intro⟩,⟨sg28176,True.intro,True.intro⟩⟩⟩⟩,⟨sg28185,⟨sg28181,⟨sg28179,⟨sg28178,True.intro,True.intro⟩,⟨sg28180,True.intro,True.intro⟩⟩,⟨sg28183,⟨sg28182,True.intro,True.intro⟩,⟨sg28184,True.intro,True.intro⟩⟩⟩,⟨sg28189,⟨sg28187,⟨sg28186,True.intro,True.intro⟩,⟨sg28188,True.intro,True.intro⟩⟩,⟨sg28191,⟨sg28190,True.intro,True.intro⟩,⟨sg28192,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_353All : degreeTree43_353.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28161,degreeTree43_351All,degreeTree43_352All⟩ + +lemma degreeTree43_354All : degreeTree43_354.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28129,degreeTree43_350All,degreeTree43_353All⟩ + +lemma degreeTree43_355All : degreeTree43_355.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28202,⟨sg28198,⟨sg28196,⟨sg28195,⟨sg28194,True.intro,True.intro⟩,True.intro⟩,⟨sg28197,True.intro,True.intro⟩⟩,⟨sg28200,⟨sg28199,True.intro,True.intro⟩,⟨sg28201,True.intro,True.intro⟩⟩⟩,⟨sg28206,⟨sg28204,⟨sg28203,True.intro,True.intro⟩,⟨sg28205,True.intro,True.intro⟩⟩,⟨sg28208,⟨sg28207,True.intro,True.intro⟩,⟨sg28209,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_356All : degreeTree43_356.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28218,⟨sg28214,⟨sg28212,⟨sg28211,True.intro,True.intro⟩,⟨sg28213,True.intro,True.intro⟩⟩,⟨sg28216,⟨sg28215,True.intro,True.intro⟩,⟨sg28217,True.intro,True.intro⟩⟩⟩,⟨sg28222,⟨sg28220,⟨sg28219,True.intro,True.intro⟩,⟨sg28221,True.intro,True.intro⟩⟩,⟨sg28224,⟨sg28223,True.intro,True.intro⟩,⟨sg28225,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_357All : degreeTree43_357.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28210,degreeTree43_355All,degreeTree43_356All⟩ + +lemma degreeTree43_358All : degreeTree43_358.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28242,⟨sg28234,⟨sg28230,⟨sg28228,⟨sg28227,True.intro,True.intro⟩,⟨sg28229,True.intro,True.intro⟩⟩,⟨sg28232,⟨sg28231,True.intro,True.intro⟩,⟨sg28233,True.intro,True.intro⟩⟩⟩,⟨sg28238,⟨sg28236,⟨sg28235,True.intro,True.intro⟩,⟨sg28237,True.intro,True.intro⟩⟩,⟨sg28240,⟨sg28239,True.intro,True.intro⟩,⟨sg28241,True.intro,True.intro⟩⟩⟩⟩,⟨sg28250,⟨sg28246,⟨sg28244,⟨sg28243,True.intro,True.intro⟩,⟨sg28245,True.intro,True.intro⟩⟩,⟨sg28248,⟨sg28247,True.intro,True.intro⟩,⟨sg28249,True.intro,True.intro⟩⟩⟩,⟨sg28254,⟨sg28252,⟨sg28251,True.intro,True.intro⟩,⟨sg28253,True.intro,True.intro⟩⟩,⟨sg28256,⟨sg28255,True.intro,True.intro⟩,⟨sg28257,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_359All : degreeTree43_359.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28226,degreeTree43_357All,degreeTree43_358All⟩ + +lemma degreeTree43_360All : degreeTree43_360.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28274,⟨sg28266,⟨sg28262,⟨sg28260,⟨sg28259,True.intro,True.intro⟩,⟨sg28261,True.intro,True.intro⟩⟩,⟨sg28264,⟨sg28263,True.intro,True.intro⟩,⟨sg28265,True.intro,True.intro⟩⟩⟩,⟨sg28270,⟨sg28268,⟨sg28267,True.intro,True.intro⟩,⟨sg28269,True.intro,True.intro⟩⟩,⟨sg28272,⟨sg28271,True.intro,True.intro⟩,⟨sg28273,True.intro,True.intro⟩⟩⟩⟩,⟨sg28282,⟨sg28278,⟨sg28276,⟨sg28275,True.intro,True.intro⟩,⟨sg28277,True.intro,True.intro⟩⟩,⟨sg28280,⟨sg28279,True.intro,True.intro⟩,⟨sg28281,True.intro,True.intro⟩⟩⟩,⟨sg28286,⟨sg28284,⟨sg28283,True.intro,True.intro⟩,⟨sg28285,True.intro,True.intro⟩⟩,⟨sg28288,⟨sg28287,True.intro,True.intro⟩,⟨sg28289,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_361All : degreeTree43_361.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28306,⟨sg28298,⟨sg28294,⟨sg28292,⟨sg28291,True.intro,True.intro⟩,⟨sg28293,True.intro,True.intro⟩⟩,⟨sg28296,⟨sg28295,True.intro,True.intro⟩,⟨sg28297,True.intro,True.intro⟩⟩⟩,⟨sg28302,⟨sg28300,⟨sg28299,True.intro,True.intro⟩,⟨sg28301,True.intro,True.intro⟩⟩,⟨sg28304,⟨sg28303,True.intro,True.intro⟩,⟨sg28305,True.intro,True.intro⟩⟩⟩⟩,⟨sg28314,⟨sg28310,⟨sg28308,⟨sg28307,True.intro,True.intro⟩,⟨sg28309,True.intro,True.intro⟩⟩,⟨sg28312,⟨sg28311,True.intro,True.intro⟩,⟨sg28313,True.intro,True.intro⟩⟩⟩,⟨sg28318,⟨sg28316,⟨sg28315,True.intro,True.intro⟩,⟨sg28317,True.intro,True.intro⟩⟩,⟨sg28320,⟨sg28319,True.intro,True.intro⟩,⟨sg28321,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_362All : degreeTree43_362.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28290,degreeTree43_360All,degreeTree43_361All⟩ + +lemma degreeTree43_363All : degreeTree43_363.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28258,degreeTree43_359All,degreeTree43_362All⟩ + +lemma degreeTree43_364All : degreeTree43_364.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28193,degreeTree43_354All,degreeTree43_363All⟩ + +lemma degreeTree43_365All : degreeTree43_365.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28064,degreeTree43_345All,degreeTree43_364All⟩ + +lemma degreeTree43_366All : degreeTree43_366.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28331,⟨sg28327,⟨sg28325,⟨sg28324,⟨sg28323,True.intro,True.intro⟩,True.intro⟩,⟨sg28326,True.intro,True.intro⟩⟩,⟨sg28329,⟨sg28328,True.intro,True.intro⟩,⟨sg28330,True.intro,True.intro⟩⟩⟩,⟨sg28335,⟨sg28333,⟨sg28332,True.intro,True.intro⟩,⟨sg28334,True.intro,True.intro⟩⟩,⟨sg28337,⟨sg28336,True.intro,True.intro⟩,⟨sg28338,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_367All : degreeTree43_367.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28347,⟨sg28343,⟨sg28341,⟨sg28340,True.intro,True.intro⟩,⟨sg28342,True.intro,True.intro⟩⟩,⟨sg28345,⟨sg28344,True.intro,True.intro⟩,⟨sg28346,True.intro,True.intro⟩⟩⟩,⟨sg28351,⟨sg28349,⟨sg28348,True.intro,True.intro⟩,⟨sg28350,True.intro,True.intro⟩⟩,⟨sg28353,⟨sg28352,True.intro,True.intro⟩,⟨sg28354,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_368All : degreeTree43_368.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28339,degreeTree43_366All,degreeTree43_367All⟩ + +lemma degreeTree43_369All : degreeTree43_369.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28371,⟨sg28363,⟨sg28359,⟨sg28357,⟨sg28356,True.intro,True.intro⟩,⟨sg28358,True.intro,True.intro⟩⟩,⟨sg28361,⟨sg28360,True.intro,True.intro⟩,⟨sg28362,True.intro,True.intro⟩⟩⟩,⟨sg28367,⟨sg28365,⟨sg28364,True.intro,True.intro⟩,⟨sg28366,True.intro,True.intro⟩⟩,⟨sg28369,⟨sg28368,True.intro,True.intro⟩,⟨sg28370,True.intro,True.intro⟩⟩⟩⟩,⟨sg28379,⟨sg28375,⟨sg28373,⟨sg28372,True.intro,True.intro⟩,⟨sg28374,True.intro,True.intro⟩⟩,⟨sg28377,⟨sg28376,True.intro,True.intro⟩,⟨sg28378,True.intro,True.intro⟩⟩⟩,⟨sg28383,⟨sg28381,⟨sg28380,True.intro,True.intro⟩,⟨sg28382,True.intro,True.intro⟩⟩,⟨sg28385,⟨sg28384,True.intro,True.intro⟩,⟨sg28386,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_370All : degreeTree43_370.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28355,degreeTree43_368All,degreeTree43_369All⟩ + +lemma degreeTree43_371All : degreeTree43_371.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28403,⟨sg28395,⟨sg28391,⟨sg28389,⟨sg28388,True.intro,True.intro⟩,⟨sg28390,True.intro,True.intro⟩⟩,⟨sg28393,⟨sg28392,True.intro,True.intro⟩,⟨sg28394,True.intro,True.intro⟩⟩⟩,⟨sg28399,⟨sg28397,⟨sg28396,True.intro,True.intro⟩,⟨sg28398,True.intro,True.intro⟩⟩,⟨sg28401,⟨sg28400,True.intro,True.intro⟩,⟨sg28402,True.intro,True.intro⟩⟩⟩⟩,⟨sg28411,⟨sg28407,⟨sg28405,⟨sg28404,True.intro,True.intro⟩,⟨sg28406,True.intro,True.intro⟩⟩,⟨sg28409,⟨sg28408,True.intro,True.intro⟩,⟨sg28410,True.intro,True.intro⟩⟩⟩,⟨sg28415,⟨sg28413,⟨sg28412,True.intro,True.intro⟩,⟨sg28414,True.intro,True.intro⟩⟩,⟨sg28417,⟨sg28416,True.intro,True.intro⟩,⟨sg28418,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_372All : degreeTree43_372.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28435,⟨sg28427,⟨sg28423,⟨sg28421,⟨sg28420,True.intro,True.intro⟩,⟨sg28422,True.intro,True.intro⟩⟩,⟨sg28425,⟨sg28424,True.intro,True.intro⟩,⟨sg28426,True.intro,True.intro⟩⟩⟩,⟨sg28431,⟨sg28429,⟨sg28428,True.intro,True.intro⟩,⟨sg28430,True.intro,True.intro⟩⟩,⟨sg28433,⟨sg28432,True.intro,True.intro⟩,⟨sg28434,True.intro,True.intro⟩⟩⟩⟩,⟨sg28443,⟨sg28439,⟨sg28437,⟨sg28436,True.intro,True.intro⟩,⟨sg28438,True.intro,True.intro⟩⟩,⟨sg28441,⟨sg28440,True.intro,True.intro⟩,⟨sg28442,True.intro,True.intro⟩⟩⟩,⟨sg28447,⟨sg28445,⟨sg28444,True.intro,True.intro⟩,⟨sg28446,True.intro,True.intro⟩⟩,⟨sg28449,⟨sg28448,True.intro,True.intro⟩,⟨sg28450,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_373All : degreeTree43_373.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28419,degreeTree43_371All,degreeTree43_372All⟩ + +lemma degreeTree43_374All : degreeTree43_374.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28387,degreeTree43_370All,degreeTree43_373All⟩ + +lemma degreeTree43_375All : degreeTree43_375.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28460,⟨sg28456,⟨sg28454,⟨sg28453,⟨sg28452,True.intro,True.intro⟩,True.intro⟩,⟨sg28455,True.intro,True.intro⟩⟩,⟨sg28458,⟨sg28457,True.intro,True.intro⟩,⟨sg28459,True.intro,True.intro⟩⟩⟩,⟨sg28464,⟨sg28462,⟨sg28461,True.intro,True.intro⟩,⟨sg28463,True.intro,True.intro⟩⟩,⟨sg28466,⟨sg28465,True.intro,True.intro⟩,⟨sg28467,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_376All : degreeTree43_376.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28476,⟨sg28472,⟨sg28470,⟨sg28469,True.intro,True.intro⟩,⟨sg28471,True.intro,True.intro⟩⟩,⟨sg28474,⟨sg28473,True.intro,True.intro⟩,⟨sg28475,True.intro,True.intro⟩⟩⟩,⟨sg28480,⟨sg28478,⟨sg28477,True.intro,True.intro⟩,⟨sg28479,True.intro,True.intro⟩⟩,⟨sg28482,⟨sg28481,True.intro,True.intro⟩,⟨sg28483,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_377All : degreeTree43_377.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28468,degreeTree43_375All,degreeTree43_376All⟩ + +lemma degreeTree43_378All : degreeTree43_378.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28500,⟨sg28492,⟨sg28488,⟨sg28486,⟨sg28485,True.intro,True.intro⟩,⟨sg28487,True.intro,True.intro⟩⟩,⟨sg28490,⟨sg28489,True.intro,True.intro⟩,⟨sg28491,True.intro,True.intro⟩⟩⟩,⟨sg28496,⟨sg28494,⟨sg28493,True.intro,True.intro⟩,⟨sg28495,True.intro,True.intro⟩⟩,⟨sg28498,⟨sg28497,True.intro,True.intro⟩,⟨sg28499,True.intro,True.intro⟩⟩⟩⟩,⟨sg28508,⟨sg28504,⟨sg28502,⟨sg28501,True.intro,True.intro⟩,⟨sg28503,True.intro,True.intro⟩⟩,⟨sg28506,⟨sg28505,True.intro,True.intro⟩,⟨sg28507,True.intro,True.intro⟩⟩⟩,⟨sg28512,⟨sg28510,⟨sg28509,True.intro,True.intro⟩,⟨sg28511,True.intro,True.intro⟩⟩,⟨sg28514,⟨sg28513,True.intro,True.intro⟩,⟨sg28515,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_379All : degreeTree43_379.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28484,degreeTree43_377All,degreeTree43_378All⟩ + +lemma degreeTree43_380All : degreeTree43_380.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28532,⟨sg28524,⟨sg28520,⟨sg28518,⟨sg28517,True.intro,True.intro⟩,⟨sg28519,True.intro,True.intro⟩⟩,⟨sg28522,⟨sg28521,True.intro,True.intro⟩,⟨sg28523,True.intro,True.intro⟩⟩⟩,⟨sg28528,⟨sg28526,⟨sg28525,True.intro,True.intro⟩,⟨sg28527,True.intro,True.intro⟩⟩,⟨sg28530,⟨sg28529,True.intro,True.intro⟩,⟨sg28531,True.intro,True.intro⟩⟩⟩⟩,⟨sg28540,⟨sg28536,⟨sg28534,⟨sg28533,True.intro,True.intro⟩,⟨sg28535,True.intro,True.intro⟩⟩,⟨sg28538,⟨sg28537,True.intro,True.intro⟩,⟨sg28539,True.intro,True.intro⟩⟩⟩,⟨sg28544,⟨sg28542,⟨sg28541,True.intro,True.intro⟩,⟨sg28543,True.intro,True.intro⟩⟩,⟨sg28546,⟨sg28545,True.intro,True.intro⟩,⟨sg28547,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_381All : degreeTree43_381.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28564,⟨sg28556,⟨sg28552,⟨sg28550,⟨sg28549,True.intro,True.intro⟩,⟨sg28551,True.intro,True.intro⟩⟩,⟨sg28554,⟨sg28553,True.intro,True.intro⟩,⟨sg28555,True.intro,True.intro⟩⟩⟩,⟨sg28560,⟨sg28558,⟨sg28557,True.intro,True.intro⟩,⟨sg28559,True.intro,True.intro⟩⟩,⟨sg28562,⟨sg28561,True.intro,True.intro⟩,⟨sg28563,True.intro,True.intro⟩⟩⟩⟩,⟨sg28572,⟨sg28568,⟨sg28566,⟨sg28565,True.intro,True.intro⟩,⟨sg28567,True.intro,True.intro⟩⟩,⟨sg28570,⟨sg28569,True.intro,True.intro⟩,⟨sg28571,True.intro,True.intro⟩⟩⟩,⟨sg28576,⟨sg28574,⟨sg28573,True.intro,True.intro⟩,⟨sg28575,True.intro,True.intro⟩⟩,⟨sg28578,⟨sg28577,True.intro,True.intro⟩,⟨sg28579,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_382All : degreeTree43_382.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28548,degreeTree43_380All,degreeTree43_381All⟩ + +lemma degreeTree43_383All : degreeTree43_383.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28516,degreeTree43_379All,degreeTree43_382All⟩ + +lemma degreeTree43_384All : degreeTree43_384.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28451,degreeTree43_374All,degreeTree43_383All⟩ + +lemma degreeTree43_385All : degreeTree43_385.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28589,⟨sg28585,⟨sg28583,⟨sg28582,⟨sg28581,True.intro,True.intro⟩,True.intro⟩,⟨sg28584,True.intro,True.intro⟩⟩,⟨sg28587,⟨sg28586,True.intro,True.intro⟩,⟨sg28588,True.intro,True.intro⟩⟩⟩,⟨sg28593,⟨sg28591,⟨sg28590,True.intro,True.intro⟩,⟨sg28592,True.intro,True.intro⟩⟩,⟨sg28595,⟨sg28594,True.intro,True.intro⟩,⟨sg28596,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_386All : degreeTree43_386.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28605,⟨sg28601,⟨sg28599,⟨sg28598,True.intro,True.intro⟩,⟨sg28600,True.intro,True.intro⟩⟩,⟨sg28603,⟨sg28602,True.intro,True.intro⟩,⟨sg28604,True.intro,True.intro⟩⟩⟩,⟨sg28609,⟨sg28607,⟨sg28606,True.intro,True.intro⟩,⟨sg28608,True.intro,True.intro⟩⟩,⟨sg28611,⟨sg28610,True.intro,True.intro⟩,⟨sg28612,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_387All : degreeTree43_387.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28597,degreeTree43_385All,degreeTree43_386All⟩ + +lemma degreeTree43_388All : degreeTree43_388.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28629,⟨sg28621,⟨sg28617,⟨sg28615,⟨sg28614,True.intro,True.intro⟩,⟨sg28616,True.intro,True.intro⟩⟩,⟨sg28619,⟨sg28618,True.intro,True.intro⟩,⟨sg28620,True.intro,True.intro⟩⟩⟩,⟨sg28625,⟨sg28623,⟨sg28622,True.intro,True.intro⟩,⟨sg28624,True.intro,True.intro⟩⟩,⟨sg28627,⟨sg28626,True.intro,True.intro⟩,⟨sg28628,True.intro,True.intro⟩⟩⟩⟩,⟨sg28637,⟨sg28633,⟨sg28631,⟨sg28630,True.intro,True.intro⟩,⟨sg28632,True.intro,True.intro⟩⟩,⟨sg28635,⟨sg28634,True.intro,True.intro⟩,⟨sg28636,True.intro,True.intro⟩⟩⟩,⟨sg28641,⟨sg28639,⟨sg28638,True.intro,True.intro⟩,⟨sg28640,True.intro,True.intro⟩⟩,⟨sg28643,⟨sg28642,True.intro,True.intro⟩,⟨sg28644,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_389All : degreeTree43_389.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28613,degreeTree43_387All,degreeTree43_388All⟩ + +lemma degreeTree43_390All : degreeTree43_390.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28661,⟨sg28653,⟨sg28649,⟨sg28647,⟨sg28646,True.intro,True.intro⟩,⟨sg28648,True.intro,True.intro⟩⟩,⟨sg28651,⟨sg28650,True.intro,True.intro⟩,⟨sg28652,True.intro,True.intro⟩⟩⟩,⟨sg28657,⟨sg28655,⟨sg28654,True.intro,True.intro⟩,⟨sg28656,True.intro,True.intro⟩⟩,⟨sg28659,⟨sg28658,True.intro,True.intro⟩,⟨sg28660,True.intro,True.intro⟩⟩⟩⟩,⟨sg28669,⟨sg28665,⟨sg28663,⟨sg28662,True.intro,True.intro⟩,⟨sg28664,True.intro,True.intro⟩⟩,⟨sg28667,⟨sg28666,True.intro,True.intro⟩,⟨sg28668,True.intro,True.intro⟩⟩⟩,⟨sg28673,⟨sg28671,⟨sg28670,True.intro,True.intro⟩,⟨sg28672,True.intro,True.intro⟩⟩,⟨sg28675,⟨sg28674,True.intro,True.intro⟩,⟨sg28676,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_391All : degreeTree43_391.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28693,⟨sg28685,⟨sg28681,⟨sg28679,⟨sg28678,True.intro,True.intro⟩,⟨sg28680,True.intro,True.intro⟩⟩,⟨sg28683,⟨sg28682,True.intro,True.intro⟩,⟨sg28684,True.intro,True.intro⟩⟩⟩,⟨sg28689,⟨sg28687,⟨sg28686,True.intro,True.intro⟩,⟨sg28688,True.intro,True.intro⟩⟩,⟨sg28691,⟨sg28690,True.intro,True.intro⟩,⟨sg28692,True.intro,True.intro⟩⟩⟩⟩,⟨sg28701,⟨sg28697,⟨sg28695,⟨sg28694,True.intro,True.intro⟩,⟨sg28696,True.intro,True.intro⟩⟩,⟨sg28699,⟨sg28698,True.intro,True.intro⟩,⟨sg28700,True.intro,True.intro⟩⟩⟩,⟨sg28705,⟨sg28703,⟨sg28702,True.intro,True.intro⟩,⟨sg28704,True.intro,True.intro⟩⟩,⟨sg28707,⟨sg28706,True.intro,True.intro⟩,⟨sg28708,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_392All : degreeTree43_392.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28677,degreeTree43_390All,degreeTree43_391All⟩ + +lemma degreeTree43_393All : degreeTree43_393.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28645,degreeTree43_389All,degreeTree43_392All⟩ + +lemma degreeTree43_394All : degreeTree43_394.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28718,⟨sg28714,⟨sg28712,⟨sg28711,⟨sg28710,True.intro,True.intro⟩,True.intro⟩,⟨sg28713,True.intro,True.intro⟩⟩,⟨sg28716,⟨sg28715,True.intro,True.intro⟩,⟨sg28717,True.intro,True.intro⟩⟩⟩,⟨sg28722,⟨sg28720,⟨sg28719,True.intro,True.intro⟩,⟨sg28721,True.intro,True.intro⟩⟩,⟨sg28724,⟨sg28723,True.intro,True.intro⟩,⟨sg28725,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_395All : degreeTree43_395.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28734,⟨sg28730,⟨sg28728,⟨sg28727,True.intro,True.intro⟩,⟨sg28729,True.intro,True.intro⟩⟩,⟨sg28732,⟨sg28731,True.intro,True.intro⟩,⟨sg28733,True.intro,True.intro⟩⟩⟩,⟨sg28738,⟨sg28736,⟨sg28735,True.intro,True.intro⟩,⟨sg28737,True.intro,True.intro⟩⟩,⟨sg28740,⟨sg28739,True.intro,True.intro⟩,⟨sg28741,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_396All : degreeTree43_396.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28726,degreeTree43_394All,degreeTree43_395All⟩ + +lemma degreeTree43_397All : degreeTree43_397.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28758,⟨sg28750,⟨sg28746,⟨sg28744,⟨sg28743,True.intro,True.intro⟩,⟨sg28745,True.intro,True.intro⟩⟩,⟨sg28748,⟨sg28747,True.intro,True.intro⟩,⟨sg28749,True.intro,True.intro⟩⟩⟩,⟨sg28754,⟨sg28752,⟨sg28751,True.intro,True.intro⟩,⟨sg28753,True.intro,True.intro⟩⟩,⟨sg28756,⟨sg28755,True.intro,True.intro⟩,⟨sg28757,True.intro,True.intro⟩⟩⟩⟩,⟨sg28766,⟨sg28762,⟨sg28760,⟨sg28759,True.intro,True.intro⟩,⟨sg28761,True.intro,True.intro⟩⟩,⟨sg28764,⟨sg28763,True.intro,True.intro⟩,⟨sg28765,True.intro,True.intro⟩⟩⟩,⟨sg28770,⟨sg28768,⟨sg28767,True.intro,True.intro⟩,⟨sg28769,True.intro,True.intro⟩⟩,⟨sg28772,⟨sg28771,True.intro,True.intro⟩,⟨sg28773,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_398All : degreeTree43_398.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28742,degreeTree43_396All,degreeTree43_397All⟩ + +lemma degreeTree43_399All : degreeTree43_399.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28790,⟨sg28782,⟨sg28778,⟨sg28776,⟨sg28775,True.intro,True.intro⟩,⟨sg28777,True.intro,True.intro⟩⟩,⟨sg28780,⟨sg28779,True.intro,True.intro⟩,⟨sg28781,True.intro,True.intro⟩⟩⟩,⟨sg28786,⟨sg28784,⟨sg28783,True.intro,True.intro⟩,⟨sg28785,True.intro,True.intro⟩⟩,⟨sg28788,⟨sg28787,True.intro,True.intro⟩,⟨sg28789,True.intro,True.intro⟩⟩⟩⟩,⟨sg28798,⟨sg28794,⟨sg28792,⟨sg28791,True.intro,True.intro⟩,⟨sg28793,True.intro,True.intro⟩⟩,⟨sg28796,⟨sg28795,True.intro,True.intro⟩,⟨sg28797,True.intro,True.intro⟩⟩⟩,⟨sg28802,⟨sg28800,⟨sg28799,True.intro,True.intro⟩,⟨sg28801,True.intro,True.intro⟩⟩,⟨sg28804,⟨sg28803,True.intro,True.intro⟩,⟨sg28805,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_400All : degreeTree43_400.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28822,⟨sg28814,⟨sg28810,⟨sg28808,⟨sg28807,True.intro,True.intro⟩,⟨sg28809,True.intro,True.intro⟩⟩,⟨sg28812,⟨sg28811,True.intro,True.intro⟩,⟨sg28813,True.intro,True.intro⟩⟩⟩,⟨sg28818,⟨sg28816,⟨sg28815,True.intro,True.intro⟩,⟨sg28817,True.intro,True.intro⟩⟩,⟨sg28820,⟨sg28819,True.intro,True.intro⟩,⟨sg28821,True.intro,True.intro⟩⟩⟩⟩,⟨sg28830,⟨sg28826,⟨sg28824,⟨sg28823,True.intro,True.intro⟩,⟨sg28825,True.intro,True.intro⟩⟩,⟨sg28828,⟨sg28827,True.intro,True.intro⟩,⟨sg28829,True.intro,True.intro⟩⟩⟩,⟨sg28834,⟨sg28832,⟨sg28831,True.intro,True.intro⟩,⟨sg28833,True.intro,True.intro⟩⟩,⟨sg28836,⟨sg28835,True.intro,True.intro⟩,⟨sg28837,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_401All : degreeTree43_401.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28806,degreeTree43_399All,degreeTree43_400All⟩ + +lemma degreeTree43_402All : degreeTree43_402.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28774,degreeTree43_398All,degreeTree43_401All⟩ + +lemma degreeTree43_403All : degreeTree43_403.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28709,degreeTree43_393All,degreeTree43_402All⟩ + +lemma degreeTree43_404All : degreeTree43_404.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28580,degreeTree43_384All,degreeTree43_403All⟩ + +lemma degreeTree43_405All : degreeTree43_405.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28322,degreeTree43_365All,degreeTree43_404All⟩ + +lemma degreeTree43_406All : degreeTree43_406.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28847,⟨sg28843,⟨sg28841,⟨sg28840,⟨sg28839,True.intro,True.intro⟩,True.intro⟩,⟨sg28842,True.intro,True.intro⟩⟩,⟨sg28845,⟨sg28844,True.intro,True.intro⟩,⟨sg28846,True.intro,True.intro⟩⟩⟩,⟨sg28851,⟨sg28849,⟨sg28848,True.intro,True.intro⟩,⟨sg28850,True.intro,True.intro⟩⟩,⟨sg28853,⟨sg28852,True.intro,True.intro⟩,⟨sg28854,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_407All : degreeTree43_407.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28863,⟨sg28859,⟨sg28857,⟨sg28856,True.intro,True.intro⟩,⟨sg28858,True.intro,True.intro⟩⟩,⟨sg28861,⟨sg28860,True.intro,True.intro⟩,⟨sg28862,True.intro,True.intro⟩⟩⟩,⟨sg28867,⟨sg28865,⟨sg28864,True.intro,True.intro⟩,⟨sg28866,True.intro,True.intro⟩⟩,⟨sg28869,⟨sg28868,True.intro,True.intro⟩,⟨sg28870,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_408All : degreeTree43_408.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28855,degreeTree43_406All,degreeTree43_407All⟩ + +lemma degreeTree43_409All : degreeTree43_409.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28887,⟨sg28879,⟨sg28875,⟨sg28873,⟨sg28872,True.intro,True.intro⟩,⟨sg28874,True.intro,True.intro⟩⟩,⟨sg28877,⟨sg28876,True.intro,True.intro⟩,⟨sg28878,True.intro,True.intro⟩⟩⟩,⟨sg28883,⟨sg28881,⟨sg28880,True.intro,True.intro⟩,⟨sg28882,True.intro,True.intro⟩⟩,⟨sg28885,⟨sg28884,True.intro,True.intro⟩,⟨sg28886,True.intro,True.intro⟩⟩⟩⟩,⟨sg28895,⟨sg28891,⟨sg28889,⟨sg28888,True.intro,True.intro⟩,⟨sg28890,True.intro,True.intro⟩⟩,⟨sg28893,⟨sg28892,True.intro,True.intro⟩,⟨sg28894,True.intro,True.intro⟩⟩⟩,⟨sg28899,⟨sg28897,⟨sg28896,True.intro,True.intro⟩,⟨sg28898,True.intro,True.intro⟩⟩,⟨sg28901,⟨sg28900,True.intro,True.intro⟩,⟨sg28902,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_410All : degreeTree43_410.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28871,degreeTree43_408All,degreeTree43_409All⟩ + +lemma degreeTree43_411All : degreeTree43_411.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28919,⟨sg28911,⟨sg28907,⟨sg28905,⟨sg28904,True.intro,True.intro⟩,⟨sg28906,True.intro,True.intro⟩⟩,⟨sg28909,⟨sg28908,True.intro,True.intro⟩,⟨sg28910,True.intro,True.intro⟩⟩⟩,⟨sg28915,⟨sg28913,⟨sg28912,True.intro,True.intro⟩,⟨sg28914,True.intro,True.intro⟩⟩,⟨sg28917,⟨sg28916,True.intro,True.intro⟩,⟨sg28918,True.intro,True.intro⟩⟩⟩⟩,⟨sg28927,⟨sg28923,⟨sg28921,⟨sg28920,True.intro,True.intro⟩,⟨sg28922,True.intro,True.intro⟩⟩,⟨sg28925,⟨sg28924,True.intro,True.intro⟩,⟨sg28926,True.intro,True.intro⟩⟩⟩,⟨sg28931,⟨sg28929,⟨sg28928,True.intro,True.intro⟩,⟨sg28930,True.intro,True.intro⟩⟩,⟨sg28933,⟨sg28932,True.intro,True.intro⟩,⟨sg28934,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_412All : degreeTree43_412.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28951,⟨sg28943,⟨sg28939,⟨sg28937,⟨sg28936,True.intro,True.intro⟩,⟨sg28938,True.intro,True.intro⟩⟩,⟨sg28941,⟨sg28940,True.intro,True.intro⟩,⟨sg28942,True.intro,True.intro⟩⟩⟩,⟨sg28947,⟨sg28945,⟨sg28944,True.intro,True.intro⟩,⟨sg28946,True.intro,True.intro⟩⟩,⟨sg28949,⟨sg28948,True.intro,True.intro⟩,⟨sg28950,True.intro,True.intro⟩⟩⟩⟩,⟨sg28959,⟨sg28955,⟨sg28953,⟨sg28952,True.intro,True.intro⟩,⟨sg28954,True.intro,True.intro⟩⟩,⟨sg28957,⟨sg28956,True.intro,True.intro⟩,⟨sg28958,True.intro,True.intro⟩⟩⟩,⟨sg28963,⟨sg28961,⟨sg28960,True.intro,True.intro⟩,⟨sg28962,True.intro,True.intro⟩⟩,⟨sg28965,⟨sg28964,True.intro,True.intro⟩,⟨sg28966,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_413All : degreeTree43_413.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28935,degreeTree43_411All,degreeTree43_412All⟩ + +lemma degreeTree43_414All : degreeTree43_414.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28903,degreeTree43_410All,degreeTree43_413All⟩ + +lemma degreeTree43_415All : degreeTree43_415.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28976,⟨sg28972,⟨sg28970,⟨sg28969,⟨sg28968,True.intro,True.intro⟩,True.intro⟩,⟨sg28971,True.intro,True.intro⟩⟩,⟨sg28974,⟨sg28973,True.intro,True.intro⟩,⟨sg28975,True.intro,True.intro⟩⟩⟩,⟨sg28980,⟨sg28978,⟨sg28977,True.intro,True.intro⟩,⟨sg28979,True.intro,True.intro⟩⟩,⟨sg28982,⟨sg28981,True.intro,True.intro⟩,⟨sg28983,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_416All : degreeTree43_416.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28992,⟨sg28988,⟨sg28986,⟨sg28985,True.intro,True.intro⟩,⟨sg28987,True.intro,True.intro⟩⟩,⟨sg28990,⟨sg28989,True.intro,True.intro⟩,⟨sg28991,True.intro,True.intro⟩⟩⟩,⟨sg28996,⟨sg28994,⟨sg28993,True.intro,True.intro⟩,⟨sg28995,True.intro,True.intro⟩⟩,⟨sg28998,⟨sg28997,True.intro,True.intro⟩,⟨sg28999,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_417All : degreeTree43_417.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28984,degreeTree43_415All,degreeTree43_416All⟩ + +lemma degreeTree43_418All : degreeTree43_418.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29016,⟨sg29008,⟨sg29004,⟨sg29002,⟨sg29001,True.intro,True.intro⟩,⟨sg29003,True.intro,True.intro⟩⟩,⟨sg29006,⟨sg29005,True.intro,True.intro⟩,⟨sg29007,True.intro,True.intro⟩⟩⟩,⟨sg29012,⟨sg29010,⟨sg29009,True.intro,True.intro⟩,⟨sg29011,True.intro,True.intro⟩⟩,⟨sg29014,⟨sg29013,True.intro,True.intro⟩,⟨sg29015,True.intro,True.intro⟩⟩⟩⟩,⟨sg29024,⟨sg29020,⟨sg29018,⟨sg29017,True.intro,True.intro⟩,⟨sg29019,True.intro,True.intro⟩⟩,⟨sg29022,⟨sg29021,True.intro,True.intro⟩,⟨sg29023,True.intro,True.intro⟩⟩⟩,⟨sg29028,⟨sg29026,⟨sg29025,True.intro,True.intro⟩,⟨sg29027,True.intro,True.intro⟩⟩,⟨sg29030,⟨sg29029,True.intro,True.intro⟩,⟨sg29031,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_419All : degreeTree43_419.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29000,degreeTree43_417All,degreeTree43_418All⟩ + +lemma degreeTree43_420All : degreeTree43_420.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29048,⟨sg29040,⟨sg29036,⟨sg29034,⟨sg29033,True.intro,True.intro⟩,⟨sg29035,True.intro,True.intro⟩⟩,⟨sg29038,⟨sg29037,True.intro,True.intro⟩,⟨sg29039,True.intro,True.intro⟩⟩⟩,⟨sg29044,⟨sg29042,⟨sg29041,True.intro,True.intro⟩,⟨sg29043,True.intro,True.intro⟩⟩,⟨sg29046,⟨sg29045,True.intro,True.intro⟩,⟨sg29047,True.intro,True.intro⟩⟩⟩⟩,⟨sg29056,⟨sg29052,⟨sg29050,⟨sg29049,True.intro,True.intro⟩,⟨sg29051,True.intro,True.intro⟩⟩,⟨sg29054,⟨sg29053,True.intro,True.intro⟩,⟨sg29055,True.intro,True.intro⟩⟩⟩,⟨sg29060,⟨sg29058,⟨sg29057,True.intro,True.intro⟩,⟨sg29059,True.intro,True.intro⟩⟩,⟨sg29062,⟨sg29061,True.intro,True.intro⟩,⟨sg29063,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_421All : degreeTree43_421.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29080,⟨sg29072,⟨sg29068,⟨sg29066,⟨sg29065,True.intro,True.intro⟩,⟨sg29067,True.intro,True.intro⟩⟩,⟨sg29070,⟨sg29069,True.intro,True.intro⟩,⟨sg29071,True.intro,True.intro⟩⟩⟩,⟨sg29076,⟨sg29074,⟨sg29073,True.intro,True.intro⟩,⟨sg29075,True.intro,True.intro⟩⟩,⟨sg29078,⟨sg29077,True.intro,True.intro⟩,⟨sg29079,True.intro,True.intro⟩⟩⟩⟩,⟨sg29088,⟨sg29084,⟨sg29082,⟨sg29081,True.intro,True.intro⟩,⟨sg29083,True.intro,True.intro⟩⟩,⟨sg29086,⟨sg29085,True.intro,True.intro⟩,⟨sg29087,True.intro,True.intro⟩⟩⟩,⟨sg29092,⟨sg29090,⟨sg29089,True.intro,True.intro⟩,⟨sg29091,True.intro,True.intro⟩⟩,⟨sg29094,⟨sg29093,True.intro,True.intro⟩,⟨sg29095,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_422All : degreeTree43_422.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29064,degreeTree43_420All,degreeTree43_421All⟩ + +lemma degreeTree43_423All : degreeTree43_423.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29032,degreeTree43_419All,degreeTree43_422All⟩ + +lemma degreeTree43_424All : degreeTree43_424.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28967,degreeTree43_414All,degreeTree43_423All⟩ + +lemma degreeTree43_425All : degreeTree43_425.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29105,⟨sg29101,⟨sg29099,⟨sg29098,⟨sg29097,True.intro,True.intro⟩,True.intro⟩,⟨sg29100,True.intro,True.intro⟩⟩,⟨sg29103,⟨sg29102,True.intro,True.intro⟩,⟨sg29104,True.intro,True.intro⟩⟩⟩,⟨sg29109,⟨sg29107,⟨sg29106,True.intro,True.intro⟩,⟨sg29108,True.intro,True.intro⟩⟩,⟨sg29111,⟨sg29110,True.intro,True.intro⟩,⟨sg29112,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_426All : degreeTree43_426.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29121,⟨sg29117,⟨sg29115,⟨sg29114,True.intro,True.intro⟩,⟨sg29116,True.intro,True.intro⟩⟩,⟨sg29119,⟨sg29118,True.intro,True.intro⟩,⟨sg29120,True.intro,True.intro⟩⟩⟩,⟨sg29125,⟨sg29123,⟨sg29122,True.intro,True.intro⟩,⟨sg29124,True.intro,True.intro⟩⟩,⟨sg29127,⟨sg29126,True.intro,True.intro⟩,⟨sg29128,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_427All : degreeTree43_427.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29113,degreeTree43_425All,degreeTree43_426All⟩ + +lemma degreeTree43_428All : degreeTree43_428.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29145,⟨sg29137,⟨sg29133,⟨sg29131,⟨sg29130,True.intro,True.intro⟩,⟨sg29132,True.intro,True.intro⟩⟩,⟨sg29135,⟨sg29134,True.intro,True.intro⟩,⟨sg29136,True.intro,True.intro⟩⟩⟩,⟨sg29141,⟨sg29139,⟨sg29138,True.intro,True.intro⟩,⟨sg29140,True.intro,True.intro⟩⟩,⟨sg29143,⟨sg29142,True.intro,True.intro⟩,⟨sg29144,True.intro,True.intro⟩⟩⟩⟩,⟨sg29153,⟨sg29149,⟨sg29147,⟨sg29146,True.intro,True.intro⟩,⟨sg29148,True.intro,True.intro⟩⟩,⟨sg29151,⟨sg29150,True.intro,True.intro⟩,⟨sg29152,True.intro,True.intro⟩⟩⟩,⟨sg29157,⟨sg29155,⟨sg29154,True.intro,True.intro⟩,⟨sg29156,True.intro,True.intro⟩⟩,⟨sg29159,⟨sg29158,True.intro,True.intro⟩,⟨sg29160,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_429All : degreeTree43_429.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29129,degreeTree43_427All,degreeTree43_428All⟩ + +lemma degreeTree43_430All : degreeTree43_430.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29177,⟨sg29169,⟨sg29165,⟨sg29163,⟨sg29162,True.intro,True.intro⟩,⟨sg29164,True.intro,True.intro⟩⟩,⟨sg29167,⟨sg29166,True.intro,True.intro⟩,⟨sg29168,True.intro,True.intro⟩⟩⟩,⟨sg29173,⟨sg29171,⟨sg29170,True.intro,True.intro⟩,⟨sg29172,True.intro,True.intro⟩⟩,⟨sg29175,⟨sg29174,True.intro,True.intro⟩,⟨sg29176,True.intro,True.intro⟩⟩⟩⟩,⟨sg29185,⟨sg29181,⟨sg29179,⟨sg29178,True.intro,True.intro⟩,⟨sg29180,True.intro,True.intro⟩⟩,⟨sg29183,⟨sg29182,True.intro,True.intro⟩,⟨sg29184,True.intro,True.intro⟩⟩⟩,⟨sg29189,⟨sg29187,⟨sg29186,True.intro,True.intro⟩,⟨sg29188,True.intro,True.intro⟩⟩,⟨sg29191,⟨sg29190,True.intro,True.intro⟩,⟨sg29192,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_431All : degreeTree43_431.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29209,⟨sg29201,⟨sg29197,⟨sg29195,⟨sg29194,True.intro,True.intro⟩,⟨sg29196,True.intro,True.intro⟩⟩,⟨sg29199,⟨sg29198,True.intro,True.intro⟩,⟨sg29200,True.intro,True.intro⟩⟩⟩,⟨sg29205,⟨sg29203,⟨sg29202,True.intro,True.intro⟩,⟨sg29204,True.intro,True.intro⟩⟩,⟨sg29207,⟨sg29206,True.intro,True.intro⟩,⟨sg29208,True.intro,True.intro⟩⟩⟩⟩,⟨sg29217,⟨sg29213,⟨sg29211,⟨sg29210,True.intro,True.intro⟩,⟨sg29212,True.intro,True.intro⟩⟩,⟨sg29215,⟨sg29214,True.intro,True.intro⟩,⟨sg29216,True.intro,True.intro⟩⟩⟩,⟨sg29221,⟨sg29219,⟨sg29218,True.intro,True.intro⟩,⟨sg29220,True.intro,True.intro⟩⟩,⟨sg29223,⟨sg29222,True.intro,True.intro⟩,⟨sg29224,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_432All : degreeTree43_432.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29193,degreeTree43_430All,degreeTree43_431All⟩ + +lemma degreeTree43_433All : degreeTree43_433.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29161,degreeTree43_429All,degreeTree43_432All⟩ + +lemma degreeTree43_434All : degreeTree43_434.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29234,⟨sg29230,⟨sg29228,⟨sg29227,⟨sg29226,True.intro,True.intro⟩,True.intro⟩,⟨sg29229,True.intro,True.intro⟩⟩,⟨sg29232,⟨sg29231,True.intro,True.intro⟩,⟨sg29233,True.intro,True.intro⟩⟩⟩,⟨sg29238,⟨sg29236,⟨sg29235,True.intro,True.intro⟩,⟨sg29237,True.intro,True.intro⟩⟩,⟨sg29240,⟨sg29239,True.intro,True.intro⟩,⟨sg29241,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_435All : degreeTree43_435.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29250,⟨sg29246,⟨sg29244,⟨sg29243,True.intro,True.intro⟩,⟨sg29245,True.intro,True.intro⟩⟩,⟨sg29248,⟨sg29247,True.intro,True.intro⟩,⟨sg29249,True.intro,True.intro⟩⟩⟩,⟨sg29254,⟨sg29252,⟨sg29251,True.intro,True.intro⟩,⟨sg29253,True.intro,True.intro⟩⟩,⟨sg29256,⟨sg29255,True.intro,True.intro⟩,⟨sg29257,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_436All : degreeTree43_436.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29242,degreeTree43_434All,degreeTree43_435All⟩ + +lemma degreeTree43_437All : degreeTree43_437.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29274,⟨sg29266,⟨sg29262,⟨sg29260,⟨sg29259,True.intro,True.intro⟩,⟨sg29261,True.intro,True.intro⟩⟩,⟨sg29264,⟨sg29263,True.intro,True.intro⟩,⟨sg29265,True.intro,True.intro⟩⟩⟩,⟨sg29270,⟨sg29268,⟨sg29267,True.intro,True.intro⟩,⟨sg29269,True.intro,True.intro⟩⟩,⟨sg29272,⟨sg29271,True.intro,True.intro⟩,⟨sg29273,True.intro,True.intro⟩⟩⟩⟩,⟨sg29282,⟨sg29278,⟨sg29276,⟨sg29275,True.intro,True.intro⟩,⟨sg29277,True.intro,True.intro⟩⟩,⟨sg29280,⟨sg29279,True.intro,True.intro⟩,⟨sg29281,True.intro,True.intro⟩⟩⟩,⟨sg29286,⟨sg29284,⟨sg29283,True.intro,True.intro⟩,⟨sg29285,True.intro,True.intro⟩⟩,⟨sg29288,⟨sg29287,True.intro,True.intro⟩,⟨sg29289,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_438All : degreeTree43_438.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29258,degreeTree43_436All,degreeTree43_437All⟩ + +lemma degreeTree43_439All : degreeTree43_439.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29306,⟨sg29298,⟨sg29294,⟨sg29292,⟨sg29291,True.intro,True.intro⟩,⟨sg29293,True.intro,True.intro⟩⟩,⟨sg29296,⟨sg29295,True.intro,True.intro⟩,⟨sg29297,True.intro,True.intro⟩⟩⟩,⟨sg29302,⟨sg29300,⟨sg29299,True.intro,True.intro⟩,⟨sg29301,True.intro,True.intro⟩⟩,⟨sg29304,⟨sg29303,True.intro,True.intro⟩,⟨sg29305,True.intro,True.intro⟩⟩⟩⟩,⟨sg29314,⟨sg29310,⟨sg29308,⟨sg29307,True.intro,True.intro⟩,⟨sg29309,True.intro,True.intro⟩⟩,⟨sg29312,⟨sg29311,True.intro,True.intro⟩,⟨sg29313,True.intro,True.intro⟩⟩⟩,⟨sg29318,⟨sg29316,⟨sg29315,True.intro,True.intro⟩,⟨sg29317,True.intro,True.intro⟩⟩,⟨sg29320,⟨sg29319,True.intro,True.intro⟩,⟨sg29321,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_440All : degreeTree43_440.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29338,⟨sg29330,⟨sg29326,⟨sg29324,⟨sg29323,True.intro,True.intro⟩,⟨sg29325,True.intro,True.intro⟩⟩,⟨sg29328,⟨sg29327,True.intro,True.intro⟩,⟨sg29329,True.intro,True.intro⟩⟩⟩,⟨sg29334,⟨sg29332,⟨sg29331,True.intro,True.intro⟩,⟨sg29333,True.intro,True.intro⟩⟩,⟨sg29336,⟨sg29335,True.intro,True.intro⟩,⟨sg29337,True.intro,True.intro⟩⟩⟩⟩,⟨sg29346,⟨sg29342,⟨sg29340,⟨sg29339,True.intro,True.intro⟩,⟨sg29341,True.intro,True.intro⟩⟩,⟨sg29344,⟨sg29343,True.intro,True.intro⟩,⟨sg29345,True.intro,True.intro⟩⟩⟩,⟨sg29350,⟨sg29348,⟨sg29347,True.intro,True.intro⟩,⟨sg29349,True.intro,True.intro⟩⟩,⟨sg29352,⟨sg29351,True.intro,True.intro⟩,⟨sg29353,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_441All : degreeTree43_441.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29322,degreeTree43_439All,degreeTree43_440All⟩ + +lemma degreeTree43_442All : degreeTree43_442.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29290,degreeTree43_438All,degreeTree43_441All⟩ + +lemma degreeTree43_443All : degreeTree43_443.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29225,degreeTree43_433All,degreeTree43_442All⟩ + +lemma degreeTree43_444All : degreeTree43_444.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29096,degreeTree43_424All,degreeTree43_443All⟩ + +lemma degreeTree43_445All : degreeTree43_445.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29363,⟨sg29359,⟨sg29357,⟨sg29356,⟨sg29355,True.intro,True.intro⟩,True.intro⟩,⟨sg29358,True.intro,True.intro⟩⟩,⟨sg29361,⟨sg29360,True.intro,True.intro⟩,⟨sg29362,True.intro,True.intro⟩⟩⟩,⟨sg29367,⟨sg29365,⟨sg29364,True.intro,True.intro⟩,⟨sg29366,True.intro,True.intro⟩⟩,⟨sg29369,⟨sg29368,True.intro,True.intro⟩,⟨sg29370,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_446All : degreeTree43_446.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29379,⟨sg29375,⟨sg29373,⟨sg29372,True.intro,True.intro⟩,⟨sg29374,True.intro,True.intro⟩⟩,⟨sg29377,⟨sg29376,True.intro,True.intro⟩,⟨sg29378,True.intro,True.intro⟩⟩⟩,⟨sg29383,⟨sg29381,⟨sg29380,True.intro,True.intro⟩,⟨sg29382,True.intro,True.intro⟩⟩,⟨sg29385,⟨sg29384,True.intro,True.intro⟩,⟨sg29386,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_447All : degreeTree43_447.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29371,degreeTree43_445All,degreeTree43_446All⟩ + +lemma degreeTree43_448All : degreeTree43_448.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29403,⟨sg29395,⟨sg29391,⟨sg29389,⟨sg29388,True.intro,True.intro⟩,⟨sg29390,True.intro,True.intro⟩⟩,⟨sg29393,⟨sg29392,True.intro,True.intro⟩,⟨sg29394,True.intro,True.intro⟩⟩⟩,⟨sg29399,⟨sg29397,⟨sg29396,True.intro,True.intro⟩,⟨sg29398,True.intro,True.intro⟩⟩,⟨sg29401,⟨sg29400,True.intro,True.intro⟩,⟨sg29402,True.intro,True.intro⟩⟩⟩⟩,⟨sg29411,⟨sg29407,⟨sg29405,⟨sg29404,True.intro,True.intro⟩,⟨sg29406,True.intro,True.intro⟩⟩,⟨sg29409,⟨sg29408,True.intro,True.intro⟩,⟨sg29410,True.intro,True.intro⟩⟩⟩,⟨sg29415,⟨sg29413,⟨sg29412,True.intro,True.intro⟩,⟨sg29414,True.intro,True.intro⟩⟩,⟨sg29417,⟨sg29416,True.intro,True.intro⟩,⟨sg29418,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_449All : degreeTree43_449.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29387,degreeTree43_447All,degreeTree43_448All⟩ + +lemma degreeTree43_450All : degreeTree43_450.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29435,⟨sg29427,⟨sg29423,⟨sg29421,⟨sg29420,True.intro,True.intro⟩,⟨sg29422,True.intro,True.intro⟩⟩,⟨sg29425,⟨sg29424,True.intro,True.intro⟩,⟨sg29426,True.intro,True.intro⟩⟩⟩,⟨sg29431,⟨sg29429,⟨sg29428,True.intro,True.intro⟩,⟨sg29430,True.intro,True.intro⟩⟩,⟨sg29433,⟨sg29432,True.intro,True.intro⟩,⟨sg29434,True.intro,True.intro⟩⟩⟩⟩,⟨sg29443,⟨sg29439,⟨sg29437,⟨sg29436,True.intro,True.intro⟩,⟨sg29438,True.intro,True.intro⟩⟩,⟨sg29441,⟨sg29440,True.intro,True.intro⟩,⟨sg29442,True.intro,True.intro⟩⟩⟩,⟨sg29447,⟨sg29445,⟨sg29444,True.intro,True.intro⟩,⟨sg29446,True.intro,True.intro⟩⟩,⟨sg29449,⟨sg29448,True.intro,True.intro⟩,⟨sg29450,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_451All : degreeTree43_451.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29467,⟨sg29459,⟨sg29455,⟨sg29453,⟨sg29452,True.intro,True.intro⟩,⟨sg29454,True.intro,True.intro⟩⟩,⟨sg29457,⟨sg29456,True.intro,True.intro⟩,⟨sg29458,True.intro,True.intro⟩⟩⟩,⟨sg29463,⟨sg29461,⟨sg29460,True.intro,True.intro⟩,⟨sg29462,True.intro,True.intro⟩⟩,⟨sg29465,⟨sg29464,True.intro,True.intro⟩,⟨sg29466,True.intro,True.intro⟩⟩⟩⟩,⟨sg29475,⟨sg29471,⟨sg29469,⟨sg29468,True.intro,True.intro⟩,⟨sg29470,True.intro,True.intro⟩⟩,⟨sg29473,⟨sg29472,True.intro,True.intro⟩,⟨sg29474,True.intro,True.intro⟩⟩⟩,⟨sg29479,⟨sg29477,⟨sg29476,True.intro,True.intro⟩,⟨sg29478,True.intro,True.intro⟩⟩,⟨sg29481,⟨sg29480,True.intro,True.intro⟩,⟨sg29482,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_452All : degreeTree43_452.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29451,degreeTree43_450All,degreeTree43_451All⟩ + +lemma degreeTree43_453All : degreeTree43_453.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29419,degreeTree43_449All,degreeTree43_452All⟩ + +lemma degreeTree43_454All : degreeTree43_454.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29492,⟨sg29488,⟨sg29486,⟨sg29485,⟨sg29484,True.intro,True.intro⟩,True.intro⟩,⟨sg29487,True.intro,True.intro⟩⟩,⟨sg29490,⟨sg29489,True.intro,True.intro⟩,⟨sg29491,True.intro,True.intro⟩⟩⟩,⟨sg29496,⟨sg29494,⟨sg29493,True.intro,True.intro⟩,⟨sg29495,True.intro,True.intro⟩⟩,⟨sg29498,⟨sg29497,True.intro,True.intro⟩,⟨sg29499,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_455All : degreeTree43_455.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29508,⟨sg29504,⟨sg29502,⟨sg29501,True.intro,True.intro⟩,⟨sg29503,True.intro,True.intro⟩⟩,⟨sg29506,⟨sg29505,True.intro,True.intro⟩,⟨sg29507,True.intro,True.intro⟩⟩⟩,⟨sg29512,⟨sg29510,⟨sg29509,True.intro,True.intro⟩,⟨sg29511,True.intro,True.intro⟩⟩,⟨sg29514,⟨sg29513,True.intro,True.intro⟩,⟨sg29515,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_456All : degreeTree43_456.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29500,degreeTree43_454All,degreeTree43_455All⟩ + +lemma degreeTree43_457All : degreeTree43_457.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29532,⟨sg29524,⟨sg29520,⟨sg29518,⟨sg29517,True.intro,True.intro⟩,⟨sg29519,True.intro,True.intro⟩⟩,⟨sg29522,⟨sg29521,True.intro,True.intro⟩,⟨sg29523,True.intro,True.intro⟩⟩⟩,⟨sg29528,⟨sg29526,⟨sg29525,True.intro,True.intro⟩,⟨sg29527,True.intro,True.intro⟩⟩,⟨sg29530,⟨sg29529,True.intro,True.intro⟩,⟨sg29531,True.intro,True.intro⟩⟩⟩⟩,⟨sg29540,⟨sg29536,⟨sg29534,⟨sg29533,True.intro,True.intro⟩,⟨sg29535,True.intro,True.intro⟩⟩,⟨sg29538,⟨sg29537,True.intro,True.intro⟩,⟨sg29539,True.intro,True.intro⟩⟩⟩,⟨sg29544,⟨sg29542,⟨sg29541,True.intro,True.intro⟩,⟨sg29543,True.intro,True.intro⟩⟩,⟨sg29546,⟨sg29545,True.intro,True.intro⟩,⟨sg29547,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_458All : degreeTree43_458.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29516,degreeTree43_456All,degreeTree43_457All⟩ + +lemma degreeTree43_459All : degreeTree43_459.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29564,⟨sg29556,⟨sg29552,⟨sg29550,⟨sg29549,True.intro,True.intro⟩,⟨sg29551,True.intro,True.intro⟩⟩,⟨sg29554,⟨sg29553,True.intro,True.intro⟩,⟨sg29555,True.intro,True.intro⟩⟩⟩,⟨sg29560,⟨sg29558,⟨sg29557,True.intro,True.intro⟩,⟨sg29559,True.intro,True.intro⟩⟩,⟨sg29562,⟨sg29561,True.intro,True.intro⟩,⟨sg29563,True.intro,True.intro⟩⟩⟩⟩,⟨sg29572,⟨sg29568,⟨sg29566,⟨sg29565,True.intro,True.intro⟩,⟨sg29567,True.intro,True.intro⟩⟩,⟨sg29570,⟨sg29569,True.intro,True.intro⟩,⟨sg29571,True.intro,True.intro⟩⟩⟩,⟨sg29576,⟨sg29574,⟨sg29573,True.intro,True.intro⟩,⟨sg29575,True.intro,True.intro⟩⟩,⟨sg29578,⟨sg29577,True.intro,True.intro⟩,⟨sg29579,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_460All : degreeTree43_460.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29596,⟨sg29588,⟨sg29584,⟨sg29582,⟨sg29581,True.intro,True.intro⟩,⟨sg29583,True.intro,True.intro⟩⟩,⟨sg29586,⟨sg29585,True.intro,True.intro⟩,⟨sg29587,True.intro,True.intro⟩⟩⟩,⟨sg29592,⟨sg29590,⟨sg29589,True.intro,True.intro⟩,⟨sg29591,True.intro,True.intro⟩⟩,⟨sg29594,⟨sg29593,True.intro,True.intro⟩,⟨sg29595,True.intro,True.intro⟩⟩⟩⟩,⟨sg29604,⟨sg29600,⟨sg29598,⟨sg29597,True.intro,True.intro⟩,⟨sg29599,True.intro,True.intro⟩⟩,⟨sg29602,⟨sg29601,True.intro,True.intro⟩,⟨sg29603,True.intro,True.intro⟩⟩⟩,⟨sg29608,⟨sg29606,⟨sg29605,True.intro,True.intro⟩,⟨sg29607,True.intro,True.intro⟩⟩,⟨sg29610,⟨sg29609,True.intro,True.intro⟩,⟨sg29611,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_461All : degreeTree43_461.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29580,degreeTree43_459All,degreeTree43_460All⟩ + +lemma degreeTree43_462All : degreeTree43_462.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29548,degreeTree43_458All,degreeTree43_461All⟩ + +lemma degreeTree43_463All : degreeTree43_463.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29483,degreeTree43_453All,degreeTree43_462All⟩ + +lemma degreeTree43_464All : degreeTree43_464.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29621,⟨sg29617,⟨sg29615,⟨sg29614,⟨sg29613,True.intro,True.intro⟩,True.intro⟩,⟨sg29616,True.intro,True.intro⟩⟩,⟨sg29619,⟨sg29618,True.intro,True.intro⟩,⟨sg29620,True.intro,True.intro⟩⟩⟩,⟨sg29625,⟨sg29623,⟨sg29622,True.intro,True.intro⟩,⟨sg29624,True.intro,True.intro⟩⟩,⟨sg29627,⟨sg29626,True.intro,True.intro⟩,⟨sg29628,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_465All : degreeTree43_465.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29637,⟨sg29633,⟨sg29631,⟨sg29630,True.intro,True.intro⟩,⟨sg29632,True.intro,True.intro⟩⟩,⟨sg29635,⟨sg29634,True.intro,True.intro⟩,⟨sg29636,True.intro,True.intro⟩⟩⟩,⟨sg29641,⟨sg29639,⟨sg29638,True.intro,True.intro⟩,⟨sg29640,True.intro,True.intro⟩⟩,⟨sg29643,⟨sg29642,True.intro,True.intro⟩,⟨sg29644,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_466All : degreeTree43_466.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29629,degreeTree43_464All,degreeTree43_465All⟩ + +lemma degreeTree43_467All : degreeTree43_467.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29661,⟨sg29653,⟨sg29649,⟨sg29647,⟨sg29646,True.intro,True.intro⟩,⟨sg29648,True.intro,True.intro⟩⟩,⟨sg29651,⟨sg29650,True.intro,True.intro⟩,⟨sg29652,True.intro,True.intro⟩⟩⟩,⟨sg29657,⟨sg29655,⟨sg29654,True.intro,True.intro⟩,⟨sg29656,True.intro,True.intro⟩⟩,⟨sg29659,⟨sg29658,True.intro,True.intro⟩,⟨sg29660,True.intro,True.intro⟩⟩⟩⟩,⟨sg29669,⟨sg29665,⟨sg29663,⟨sg29662,True.intro,True.intro⟩,⟨sg29664,True.intro,True.intro⟩⟩,⟨sg29667,⟨sg29666,True.intro,True.intro⟩,⟨sg29668,True.intro,True.intro⟩⟩⟩,⟨sg29673,⟨sg29671,⟨sg29670,True.intro,True.intro⟩,⟨sg29672,True.intro,True.intro⟩⟩,⟨sg29675,⟨sg29674,True.intro,True.intro⟩,⟨sg29676,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_468All : degreeTree43_468.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29645,degreeTree43_466All,degreeTree43_467All⟩ + +lemma degreeTree43_469All : degreeTree43_469.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29693,⟨sg29685,⟨sg29681,⟨sg29679,⟨sg29678,True.intro,True.intro⟩,⟨sg29680,True.intro,True.intro⟩⟩,⟨sg29683,⟨sg29682,True.intro,True.intro⟩,⟨sg29684,True.intro,True.intro⟩⟩⟩,⟨sg29689,⟨sg29687,⟨sg29686,True.intro,True.intro⟩,⟨sg29688,True.intro,True.intro⟩⟩,⟨sg29691,⟨sg29690,True.intro,True.intro⟩,⟨sg29692,True.intro,True.intro⟩⟩⟩⟩,⟨sg29701,⟨sg29697,⟨sg29695,⟨sg29694,True.intro,True.intro⟩,⟨sg29696,True.intro,True.intro⟩⟩,⟨sg29699,⟨sg29698,True.intro,True.intro⟩,⟨sg29700,True.intro,True.intro⟩⟩⟩,⟨sg29705,⟨sg29703,⟨sg29702,True.intro,True.intro⟩,⟨sg29704,True.intro,True.intro⟩⟩,⟨sg29707,⟨sg29706,True.intro,True.intro⟩,⟨sg29708,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_470All : degreeTree43_470.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29725,⟨sg29717,⟨sg29713,⟨sg29711,⟨sg29710,True.intro,True.intro⟩,⟨sg29712,True.intro,True.intro⟩⟩,⟨sg29715,⟨sg29714,True.intro,True.intro⟩,⟨sg29716,True.intro,True.intro⟩⟩⟩,⟨sg29721,⟨sg29719,⟨sg29718,True.intro,True.intro⟩,⟨sg29720,True.intro,True.intro⟩⟩,⟨sg29723,⟨sg29722,True.intro,True.intro⟩,⟨sg29724,True.intro,True.intro⟩⟩⟩⟩,⟨sg29733,⟨sg29729,⟨sg29727,⟨sg29726,True.intro,True.intro⟩,⟨sg29728,True.intro,True.intro⟩⟩,⟨sg29731,⟨sg29730,True.intro,True.intro⟩,⟨sg29732,True.intro,True.intro⟩⟩⟩,⟨sg29737,⟨sg29735,⟨sg29734,True.intro,True.intro⟩,⟨sg29736,True.intro,True.intro⟩⟩,⟨sg29739,⟨sg29738,True.intro,True.intro⟩,⟨sg29740,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_471All : degreeTree43_471.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29709,degreeTree43_469All,degreeTree43_470All⟩ + +lemma degreeTree43_472All : degreeTree43_472.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29677,degreeTree43_468All,degreeTree43_471All⟩ + +lemma degreeTree43_473All : degreeTree43_473.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29750,⟨sg29746,⟨sg29744,⟨sg29743,⟨sg29742,True.intro,True.intro⟩,True.intro⟩,⟨sg29745,True.intro,True.intro⟩⟩,⟨sg29748,⟨sg29747,True.intro,True.intro⟩,⟨sg29749,True.intro,True.intro⟩⟩⟩,⟨sg29754,⟨sg29752,⟨sg29751,True.intro,True.intro⟩,⟨sg29753,True.intro,True.intro⟩⟩,⟨sg29756,⟨sg29755,True.intro,True.intro⟩,⟨sg29757,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_474All : degreeTree43_474.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29766,⟨sg29762,⟨sg29760,⟨sg29759,True.intro,True.intro⟩,⟨sg29761,True.intro,True.intro⟩⟩,⟨sg29764,⟨sg29763,True.intro,True.intro⟩,⟨sg29765,True.intro,True.intro⟩⟩⟩,⟨sg29770,⟨sg29768,⟨sg29767,True.intro,True.intro⟩,⟨sg29769,True.intro,True.intro⟩⟩,⟨sg29772,⟨sg29771,True.intro,True.intro⟩,⟨sg29773,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_475All : degreeTree43_475.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29758,degreeTree43_473All,degreeTree43_474All⟩ + +lemma degreeTree43_476All : degreeTree43_476.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29790,⟨sg29782,⟨sg29778,⟨sg29776,⟨sg29775,True.intro,True.intro⟩,⟨sg29777,True.intro,True.intro⟩⟩,⟨sg29780,⟨sg29779,True.intro,True.intro⟩,⟨sg29781,True.intro,True.intro⟩⟩⟩,⟨sg29786,⟨sg29784,⟨sg29783,True.intro,True.intro⟩,⟨sg29785,True.intro,True.intro⟩⟩,⟨sg29788,⟨sg29787,True.intro,True.intro⟩,⟨sg29789,True.intro,True.intro⟩⟩⟩⟩,⟨sg29798,⟨sg29794,⟨sg29792,⟨sg29791,True.intro,True.intro⟩,⟨sg29793,True.intro,True.intro⟩⟩,⟨sg29796,⟨sg29795,True.intro,True.intro⟩,⟨sg29797,True.intro,True.intro⟩⟩⟩,⟨sg29802,⟨sg29800,⟨sg29799,True.intro,True.intro⟩,⟨sg29801,True.intro,True.intro⟩⟩,⟨sg29804,⟨sg29803,True.intro,True.intro⟩,⟨sg29805,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_477All : degreeTree43_477.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29774,degreeTree43_475All,degreeTree43_476All⟩ + +lemma degreeTree43_478All : degreeTree43_478.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29822,⟨sg29814,⟨sg29810,⟨sg29808,⟨sg29807,True.intro,True.intro⟩,⟨sg29809,True.intro,True.intro⟩⟩,⟨sg29812,⟨sg29811,True.intro,True.intro⟩,⟨sg29813,True.intro,True.intro⟩⟩⟩,⟨sg29818,⟨sg29816,⟨sg29815,True.intro,True.intro⟩,⟨sg29817,True.intro,True.intro⟩⟩,⟨sg29820,⟨sg29819,True.intro,True.intro⟩,⟨sg29821,True.intro,True.intro⟩⟩⟩⟩,⟨sg29830,⟨sg29826,⟨sg29824,⟨sg29823,True.intro,True.intro⟩,⟨sg29825,True.intro,True.intro⟩⟩,⟨sg29828,⟨sg29827,True.intro,True.intro⟩,⟨sg29829,True.intro,True.intro⟩⟩⟩,⟨sg29834,⟨sg29832,⟨sg29831,True.intro,True.intro⟩,⟨sg29833,True.intro,True.intro⟩⟩,⟨sg29836,⟨sg29835,True.intro,True.intro⟩,⟨sg29837,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_479All : degreeTree43_479.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29854,⟨sg29846,⟨sg29842,⟨sg29840,⟨sg29839,True.intro,True.intro⟩,⟨sg29841,True.intro,True.intro⟩⟩,⟨sg29844,⟨sg29843,True.intro,True.intro⟩,⟨sg29845,True.intro,True.intro⟩⟩⟩,⟨sg29850,⟨sg29848,⟨sg29847,True.intro,True.intro⟩,⟨sg29849,True.intro,True.intro⟩⟩,⟨sg29852,⟨sg29851,True.intro,True.intro⟩,⟨sg29853,True.intro,True.intro⟩⟩⟩⟩,⟨sg29862,⟨sg29858,⟨sg29856,⟨sg29855,True.intro,True.intro⟩,⟨sg29857,True.intro,True.intro⟩⟩,⟨sg29860,⟨sg29859,True.intro,True.intro⟩,⟨sg29861,True.intro,True.intro⟩⟩⟩,⟨sg29866,⟨sg29864,⟨sg29863,True.intro,True.intro⟩,⟨sg29865,True.intro,True.intro⟩⟩,⟨sg29868,⟨sg29867,True.intro,True.intro⟩,⟨sg29869,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_480All : degreeTree43_480.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29838,degreeTree43_478All,degreeTree43_479All⟩ + +lemma degreeTree43_481All : degreeTree43_481.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29806,degreeTree43_477All,degreeTree43_480All⟩ + +lemma degreeTree43_482All : degreeTree43_482.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29741,degreeTree43_472All,degreeTree43_481All⟩ + +lemma degreeTree43_483All : degreeTree43_483.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29612,degreeTree43_463All,degreeTree43_482All⟩ + +lemma degreeTree43_484All : degreeTree43_484.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29354,degreeTree43_444All,degreeTree43_483All⟩ + +lemma degreeTree43_485All : degreeTree43_485.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg28838,degreeTree43_405All,degreeTree43_484All⟩ + +lemma degreeTree43_486All : degreeTree43_486.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29879,⟨sg29875,⟨sg29873,⟨sg29872,⟨sg29871,True.intro,True.intro⟩,True.intro⟩,⟨sg29874,True.intro,True.intro⟩⟩,⟨sg29877,⟨sg29876,True.intro,True.intro⟩,⟨sg29878,True.intro,True.intro⟩⟩⟩,⟨sg29883,⟨sg29881,⟨sg29880,True.intro,True.intro⟩,⟨sg29882,True.intro,True.intro⟩⟩,⟨sg29885,⟨sg29884,True.intro,True.intro⟩,⟨sg29886,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_487All : degreeTree43_487.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29895,⟨sg29891,⟨sg29889,⟨sg29888,True.intro,True.intro⟩,⟨sg29890,True.intro,True.intro⟩⟩,⟨sg29893,⟨sg29892,True.intro,True.intro⟩,⟨sg29894,True.intro,True.intro⟩⟩⟩,⟨sg29899,⟨sg29897,⟨sg29896,True.intro,True.intro⟩,⟨sg29898,True.intro,True.intro⟩⟩,⟨sg29901,⟨sg29900,True.intro,True.intro⟩,⟨sg29902,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_488All : degreeTree43_488.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29887,degreeTree43_486All,degreeTree43_487All⟩ + +lemma degreeTree43_489All : degreeTree43_489.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29919,⟨sg29911,⟨sg29907,⟨sg29905,⟨sg29904,True.intro,True.intro⟩,⟨sg29906,True.intro,True.intro⟩⟩,⟨sg29909,⟨sg29908,True.intro,True.intro⟩,⟨sg29910,True.intro,True.intro⟩⟩⟩,⟨sg29915,⟨sg29913,⟨sg29912,True.intro,True.intro⟩,⟨sg29914,True.intro,True.intro⟩⟩,⟨sg29917,⟨sg29916,True.intro,True.intro⟩,⟨sg29918,True.intro,True.intro⟩⟩⟩⟩,⟨sg29927,⟨sg29923,⟨sg29921,⟨sg29920,True.intro,True.intro⟩,⟨sg29922,True.intro,True.intro⟩⟩,⟨sg29925,⟨sg29924,True.intro,True.intro⟩,⟨sg29926,True.intro,True.intro⟩⟩⟩,⟨sg29931,⟨sg29929,⟨sg29928,True.intro,True.intro⟩,⟨sg29930,True.intro,True.intro⟩⟩,⟨sg29933,⟨sg29932,True.intro,True.intro⟩,⟨sg29934,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_490All : degreeTree43_490.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29903,degreeTree43_488All,degreeTree43_489All⟩ + +lemma degreeTree43_491All : degreeTree43_491.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29944,⟨sg29940,⟨sg29938,⟨sg29937,⟨sg29936,True.intro,True.intro⟩,True.intro⟩,⟨sg29939,True.intro,True.intro⟩⟩,⟨sg29942,⟨sg29941,True.intro,True.intro⟩,⟨sg29943,True.intro,True.intro⟩⟩⟩,⟨sg29948,⟨sg29946,⟨sg29945,True.intro,True.intro⟩,⟨sg29947,True.intro,True.intro⟩⟩,⟨sg29950,⟨sg29949,True.intro,True.intro⟩,⟨sg29951,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_492All : degreeTree43_492.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29960,⟨sg29956,⟨sg29954,⟨sg29953,True.intro,True.intro⟩,⟨sg29955,True.intro,True.intro⟩⟩,⟨sg29958,⟨sg29957,True.intro,True.intro⟩,⟨sg29959,True.intro,True.intro⟩⟩⟩,⟨sg29964,⟨sg29962,⟨sg29961,True.intro,True.intro⟩,⟨sg29963,True.intro,True.intro⟩⟩,⟨sg29966,⟨sg29965,True.intro,True.intro⟩,⟨sg29967,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_493All : degreeTree43_493.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29952,degreeTree43_491All,degreeTree43_492All⟩ + +lemma degreeTree43_494All : degreeTree43_494.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29984,⟨sg29976,⟨sg29972,⟨sg29970,⟨sg29969,True.intro,True.intro⟩,⟨sg29971,True.intro,True.intro⟩⟩,⟨sg29974,⟨sg29973,True.intro,True.intro⟩,⟨sg29975,True.intro,True.intro⟩⟩⟩,⟨sg29980,⟨sg29978,⟨sg29977,True.intro,True.intro⟩,⟨sg29979,True.intro,True.intro⟩⟩,⟨sg29982,⟨sg29981,True.intro,True.intro⟩,⟨sg29983,True.intro,True.intro⟩⟩⟩⟩,⟨sg29992,⟨sg29988,⟨sg29986,⟨sg29985,True.intro,True.intro⟩,⟨sg29987,True.intro,True.intro⟩⟩,⟨sg29990,⟨sg29989,True.intro,True.intro⟩,⟨sg29991,True.intro,True.intro⟩⟩⟩,⟨sg29996,⟨sg29994,⟨sg29993,True.intro,True.intro⟩,⟨sg29995,True.intro,True.intro⟩⟩,⟨sg29998,⟨sg29997,True.intro,True.intro⟩,⟨sg29999,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_495All : degreeTree43_495.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29968,degreeTree43_493All,degreeTree43_494All⟩ + +lemma degreeTree43_496All : degreeTree43_496.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29935,degreeTree43_490All,degreeTree43_495All⟩ + +lemma degreeTree43_497All : degreeTree43_497.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30009,⟨sg30005,⟨sg30003,⟨sg30002,⟨sg30001,True.intro,True.intro⟩,True.intro⟩,⟨sg30004,True.intro,True.intro⟩⟩,⟨sg30007,⟨sg30006,True.intro,True.intro⟩,⟨sg30008,True.intro,True.intro⟩⟩⟩,⟨sg30013,⟨sg30011,⟨sg30010,True.intro,True.intro⟩,⟨sg30012,True.intro,True.intro⟩⟩,⟨sg30015,⟨sg30014,True.intro,True.intro⟩,⟨sg30016,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_498All : degreeTree43_498.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30025,⟨sg30021,⟨sg30019,⟨sg30018,True.intro,True.intro⟩,⟨sg30020,True.intro,True.intro⟩⟩,⟨sg30023,⟨sg30022,True.intro,True.intro⟩,⟨sg30024,True.intro,True.intro⟩⟩⟩,⟨sg30029,⟨sg30027,⟨sg30026,True.intro,True.intro⟩,⟨sg30028,True.intro,True.intro⟩⟩,⟨sg30031,⟨sg30030,True.intro,True.intro⟩,⟨sg30032,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_499All : degreeTree43_499.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30017,degreeTree43_497All,degreeTree43_498All⟩ + +lemma degreeTree43_500All : degreeTree43_500.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30049,⟨sg30041,⟨sg30037,⟨sg30035,⟨sg30034,True.intro,True.intro⟩,⟨sg30036,True.intro,True.intro⟩⟩,⟨sg30039,⟨sg30038,True.intro,True.intro⟩,⟨sg30040,True.intro,True.intro⟩⟩⟩,⟨sg30045,⟨sg30043,⟨sg30042,True.intro,True.intro⟩,⟨sg30044,True.intro,True.intro⟩⟩,⟨sg30047,⟨sg30046,True.intro,True.intro⟩,⟨sg30048,True.intro,True.intro⟩⟩⟩⟩,⟨sg30057,⟨sg30053,⟨sg30051,⟨sg30050,True.intro,True.intro⟩,⟨sg30052,True.intro,True.intro⟩⟩,⟨sg30055,⟨sg30054,True.intro,True.intro⟩,⟨sg30056,True.intro,True.intro⟩⟩⟩,⟨sg30061,⟨sg30059,⟨sg30058,True.intro,True.intro⟩,⟨sg30060,True.intro,True.intro⟩⟩,⟨sg30063,⟨sg30062,True.intro,True.intro⟩,⟨sg30064,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_501All : degreeTree43_501.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30033,degreeTree43_499All,degreeTree43_500All⟩ + +lemma degreeTree43_502All : degreeTree43_502.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30081,⟨sg30073,⟨sg30069,⟨sg30067,⟨sg30066,True.intro,True.intro⟩,⟨sg30068,True.intro,True.intro⟩⟩,⟨sg30071,⟨sg30070,True.intro,True.intro⟩,⟨sg30072,True.intro,True.intro⟩⟩⟩,⟨sg30077,⟨sg30075,⟨sg30074,True.intro,True.intro⟩,⟨sg30076,True.intro,True.intro⟩⟩,⟨sg30079,⟨sg30078,True.intro,True.intro⟩,⟨sg30080,True.intro,True.intro⟩⟩⟩⟩,⟨sg30089,⟨sg30085,⟨sg30083,⟨sg30082,True.intro,True.intro⟩,⟨sg30084,True.intro,True.intro⟩⟩,⟨sg30087,⟨sg30086,True.intro,True.intro⟩,⟨sg30088,True.intro,True.intro⟩⟩⟩,⟨sg30093,⟨sg30091,⟨sg30090,True.intro,True.intro⟩,⟨sg30092,True.intro,True.intro⟩⟩,⟨sg30095,⟨sg30094,True.intro,True.intro⟩,⟨sg30096,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_503All : degreeTree43_503.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30113,⟨sg30105,⟨sg30101,⟨sg30099,⟨sg30098,True.intro,True.intro⟩,⟨sg30100,True.intro,True.intro⟩⟩,⟨sg30103,⟨sg30102,True.intro,True.intro⟩,⟨sg30104,True.intro,True.intro⟩⟩⟩,⟨sg30109,⟨sg30107,⟨sg30106,True.intro,True.intro⟩,⟨sg30108,True.intro,True.intro⟩⟩,⟨sg30111,⟨sg30110,True.intro,True.intro⟩,⟨sg30112,True.intro,True.intro⟩⟩⟩⟩,⟨sg30121,⟨sg30117,⟨sg30115,⟨sg30114,True.intro,True.intro⟩,⟨sg30116,True.intro,True.intro⟩⟩,⟨sg30119,⟨sg30118,True.intro,True.intro⟩,⟨sg30120,True.intro,True.intro⟩⟩⟩,⟨sg30125,⟨sg30123,⟨sg30122,True.intro,True.intro⟩,⟨sg30124,True.intro,True.intro⟩⟩,⟨sg30127,⟨sg30126,True.intro,True.intro⟩,⟨sg30128,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_504All : degreeTree43_504.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30097,degreeTree43_502All,degreeTree43_503All⟩ + +lemma degreeTree43_505All : degreeTree43_505.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30065,degreeTree43_501All,degreeTree43_504All⟩ + +lemma degreeTree43_506All : degreeTree43_506.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30000,degreeTree43_496All,degreeTree43_505All⟩ + +lemma degreeTree43_507All : degreeTree43_507.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30138,⟨sg30134,⟨sg30132,⟨sg30131,⟨sg30130,True.intro,True.intro⟩,True.intro⟩,⟨sg30133,True.intro,True.intro⟩⟩,⟨sg30136,⟨sg30135,True.intro,True.intro⟩,⟨sg30137,True.intro,True.intro⟩⟩⟩,⟨sg30142,⟨sg30140,⟨sg30139,True.intro,True.intro⟩,⟨sg30141,True.intro,True.intro⟩⟩,⟨sg30144,⟨sg30143,True.intro,True.intro⟩,⟨sg30145,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_508All : degreeTree43_508.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30154,⟨sg30150,⟨sg30148,⟨sg30147,True.intro,True.intro⟩,⟨sg30149,True.intro,True.intro⟩⟩,⟨sg30152,⟨sg30151,True.intro,True.intro⟩,⟨sg30153,True.intro,True.intro⟩⟩⟩,⟨sg30158,⟨sg30156,⟨sg30155,True.intro,True.intro⟩,⟨sg30157,True.intro,True.intro⟩⟩,⟨sg30160,⟨sg30159,True.intro,True.intro⟩,⟨sg30161,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_509All : degreeTree43_509.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30146,degreeTree43_507All,degreeTree43_508All⟩ + +lemma degreeTree43_510All : degreeTree43_510.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30178,⟨sg30170,⟨sg30166,⟨sg30164,⟨sg30163,True.intro,True.intro⟩,⟨sg30165,True.intro,True.intro⟩⟩,⟨sg30168,⟨sg30167,True.intro,True.intro⟩,⟨sg30169,True.intro,True.intro⟩⟩⟩,⟨sg30174,⟨sg30172,⟨sg30171,True.intro,True.intro⟩,⟨sg30173,True.intro,True.intro⟩⟩,⟨sg30176,⟨sg30175,True.intro,True.intro⟩,⟨sg30177,True.intro,True.intro⟩⟩⟩⟩,⟨sg30186,⟨sg30182,⟨sg30180,⟨sg30179,True.intro,True.intro⟩,⟨sg30181,True.intro,True.intro⟩⟩,⟨sg30184,⟨sg30183,True.intro,True.intro⟩,⟨sg30185,True.intro,True.intro⟩⟩⟩,⟨sg30190,⟨sg30188,⟨sg30187,True.intro,True.intro⟩,⟨sg30189,True.intro,True.intro⟩⟩,⟨sg30192,⟨sg30191,True.intro,True.intro⟩,⟨sg30193,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_511All : degreeTree43_511.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30162,degreeTree43_509All,degreeTree43_510All⟩ + +lemma degreeTree43_512All : degreeTree43_512.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30210,⟨sg30202,⟨sg30198,⟨sg30196,⟨sg30195,True.intro,True.intro⟩,⟨sg30197,True.intro,True.intro⟩⟩,⟨sg30200,⟨sg30199,True.intro,True.intro⟩,⟨sg30201,True.intro,True.intro⟩⟩⟩,⟨sg30206,⟨sg30204,⟨sg30203,True.intro,True.intro⟩,⟨sg30205,True.intro,True.intro⟩⟩,⟨sg30208,⟨sg30207,True.intro,True.intro⟩,⟨sg30209,True.intro,True.intro⟩⟩⟩⟩,⟨sg30218,⟨sg30214,⟨sg30212,⟨sg30211,True.intro,True.intro⟩,⟨sg30213,True.intro,True.intro⟩⟩,⟨sg30216,⟨sg30215,True.intro,True.intro⟩,⟨sg30217,True.intro,True.intro⟩⟩⟩,⟨sg30222,⟨sg30220,⟨sg30219,True.intro,True.intro⟩,⟨sg30221,True.intro,True.intro⟩⟩,⟨sg30224,⟨sg30223,True.intro,True.intro⟩,⟨sg30225,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_513All : degreeTree43_513.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30242,⟨sg30234,⟨sg30230,⟨sg30228,⟨sg30227,True.intro,True.intro⟩,⟨sg30229,True.intro,True.intro⟩⟩,⟨sg30232,⟨sg30231,True.intro,True.intro⟩,⟨sg30233,True.intro,True.intro⟩⟩⟩,⟨sg30238,⟨sg30236,⟨sg30235,True.intro,True.intro⟩,⟨sg30237,True.intro,True.intro⟩⟩,⟨sg30240,⟨sg30239,True.intro,True.intro⟩,⟨sg30241,True.intro,True.intro⟩⟩⟩⟩,⟨sg30250,⟨sg30246,⟨sg30244,⟨sg30243,True.intro,True.intro⟩,⟨sg30245,True.intro,True.intro⟩⟩,⟨sg30248,⟨sg30247,True.intro,True.intro⟩,⟨sg30249,True.intro,True.intro⟩⟩⟩,⟨sg30254,⟨sg30252,⟨sg30251,True.intro,True.intro⟩,⟨sg30253,True.intro,True.intro⟩⟩,⟨sg30256,⟨sg30255,True.intro,True.intro⟩,⟨sg30257,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_514All : degreeTree43_514.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30226,degreeTree43_512All,degreeTree43_513All⟩ + +lemma degreeTree43_515All : degreeTree43_515.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30194,degreeTree43_511All,degreeTree43_514All⟩ + +lemma degreeTree43_516All : degreeTree43_516.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30267,⟨sg30263,⟨sg30261,⟨sg30260,⟨sg30259,True.intro,True.intro⟩,True.intro⟩,⟨sg30262,True.intro,True.intro⟩⟩,⟨sg30265,⟨sg30264,True.intro,True.intro⟩,⟨sg30266,True.intro,True.intro⟩⟩⟩,⟨sg30271,⟨sg30269,⟨sg30268,True.intro,True.intro⟩,⟨sg30270,True.intro,True.intro⟩⟩,⟨sg30273,⟨sg30272,True.intro,True.intro⟩,⟨sg30274,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_517All : degreeTree43_517.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30283,⟨sg30279,⟨sg30277,⟨sg30276,True.intro,True.intro⟩,⟨sg30278,True.intro,True.intro⟩⟩,⟨sg30281,⟨sg30280,True.intro,True.intro⟩,⟨sg30282,True.intro,True.intro⟩⟩⟩,⟨sg30287,⟨sg30285,⟨sg30284,True.intro,True.intro⟩,⟨sg30286,True.intro,True.intro⟩⟩,⟨sg30289,⟨sg30288,True.intro,True.intro⟩,⟨sg30290,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_518All : degreeTree43_518.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30275,degreeTree43_516All,degreeTree43_517All⟩ + +lemma degreeTree43_519All : degreeTree43_519.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30307,⟨sg30299,⟨sg30295,⟨sg30293,⟨sg30292,True.intro,True.intro⟩,⟨sg30294,True.intro,True.intro⟩⟩,⟨sg30297,⟨sg30296,True.intro,True.intro⟩,⟨sg30298,True.intro,True.intro⟩⟩⟩,⟨sg30303,⟨sg30301,⟨sg30300,True.intro,True.intro⟩,⟨sg30302,True.intro,True.intro⟩⟩,⟨sg30305,⟨sg30304,True.intro,True.intro⟩,⟨sg30306,True.intro,True.intro⟩⟩⟩⟩,⟨sg30315,⟨sg30311,⟨sg30309,⟨sg30308,True.intro,True.intro⟩,⟨sg30310,True.intro,True.intro⟩⟩,⟨sg30313,⟨sg30312,True.intro,True.intro⟩,⟨sg30314,True.intro,True.intro⟩⟩⟩,⟨sg30319,⟨sg30317,⟨sg30316,True.intro,True.intro⟩,⟨sg30318,True.intro,True.intro⟩⟩,⟨sg30321,⟨sg30320,True.intro,True.intro⟩,⟨sg30322,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_520All : degreeTree43_520.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30291,degreeTree43_518All,degreeTree43_519All⟩ + +lemma degreeTree43_521All : degreeTree43_521.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30339,⟨sg30331,⟨sg30327,⟨sg30325,⟨sg30324,True.intro,True.intro⟩,⟨sg30326,True.intro,True.intro⟩⟩,⟨sg30329,⟨sg30328,True.intro,True.intro⟩,⟨sg30330,True.intro,True.intro⟩⟩⟩,⟨sg30335,⟨sg30333,⟨sg30332,True.intro,True.intro⟩,⟨sg30334,True.intro,True.intro⟩⟩,⟨sg30337,⟨sg30336,True.intro,True.intro⟩,⟨sg30338,True.intro,True.intro⟩⟩⟩⟩,⟨sg30347,⟨sg30343,⟨sg30341,⟨sg30340,True.intro,True.intro⟩,⟨sg30342,True.intro,True.intro⟩⟩,⟨sg30345,⟨sg30344,True.intro,True.intro⟩,⟨sg30346,True.intro,True.intro⟩⟩⟩,⟨sg30351,⟨sg30349,⟨sg30348,True.intro,True.intro⟩,⟨sg30350,True.intro,True.intro⟩⟩,⟨sg30353,⟨sg30352,True.intro,True.intro⟩,⟨sg30354,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_522All : degreeTree43_522.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30371,⟨sg30363,⟨sg30359,⟨sg30357,⟨sg30356,True.intro,True.intro⟩,⟨sg30358,True.intro,True.intro⟩⟩,⟨sg30361,⟨sg30360,True.intro,True.intro⟩,⟨sg30362,True.intro,True.intro⟩⟩⟩,⟨sg30367,⟨sg30365,⟨sg30364,True.intro,True.intro⟩,⟨sg30366,True.intro,True.intro⟩⟩,⟨sg30369,⟨sg30368,True.intro,True.intro⟩,⟨sg30370,True.intro,True.intro⟩⟩⟩⟩,⟨sg30379,⟨sg30375,⟨sg30373,⟨sg30372,True.intro,True.intro⟩,⟨sg30374,True.intro,True.intro⟩⟩,⟨sg30377,⟨sg30376,True.intro,True.intro⟩,⟨sg30378,True.intro,True.intro⟩⟩⟩,⟨sg30383,⟨sg30381,⟨sg30380,True.intro,True.intro⟩,⟨sg30382,True.intro,True.intro⟩⟩,⟨sg30385,⟨sg30384,True.intro,True.intro⟩,⟨sg30386,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_523All : degreeTree43_523.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30355,degreeTree43_521All,degreeTree43_522All⟩ + +lemma degreeTree43_524All : degreeTree43_524.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30323,degreeTree43_520All,degreeTree43_523All⟩ + +lemma degreeTree43_525All : degreeTree43_525.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30258,degreeTree43_515All,degreeTree43_524All⟩ + +lemma degreeTree43_526All : degreeTree43_526.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30129,degreeTree43_506All,degreeTree43_525All⟩ + +lemma degreeTree43_527All : degreeTree43_527.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30396,⟨sg30392,⟨sg30390,⟨sg30389,⟨sg30388,True.intro,True.intro⟩,True.intro⟩,⟨sg30391,True.intro,True.intro⟩⟩,⟨sg30394,⟨sg30393,True.intro,True.intro⟩,⟨sg30395,True.intro,True.intro⟩⟩⟩,⟨sg30400,⟨sg30398,⟨sg30397,True.intro,True.intro⟩,⟨sg30399,True.intro,True.intro⟩⟩,⟨sg30402,⟨sg30401,True.intro,True.intro⟩,⟨sg30403,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_528All : degreeTree43_528.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30412,⟨sg30408,⟨sg30406,⟨sg30405,True.intro,True.intro⟩,⟨sg30407,True.intro,True.intro⟩⟩,⟨sg30410,⟨sg30409,True.intro,True.intro⟩,⟨sg30411,True.intro,True.intro⟩⟩⟩,⟨sg30416,⟨sg30414,⟨sg30413,True.intro,True.intro⟩,⟨sg30415,True.intro,True.intro⟩⟩,⟨sg30418,⟨sg30417,True.intro,True.intro⟩,⟨sg30419,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_529All : degreeTree43_529.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30404,degreeTree43_527All,degreeTree43_528All⟩ + +lemma degreeTree43_530All : degreeTree43_530.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30436,⟨sg30428,⟨sg30424,⟨sg30422,⟨sg30421,True.intro,True.intro⟩,⟨sg30423,True.intro,True.intro⟩⟩,⟨sg30426,⟨sg30425,True.intro,True.intro⟩,⟨sg30427,True.intro,True.intro⟩⟩⟩,⟨sg30432,⟨sg30430,⟨sg30429,True.intro,True.intro⟩,⟨sg30431,True.intro,True.intro⟩⟩,⟨sg30434,⟨sg30433,True.intro,True.intro⟩,⟨sg30435,True.intro,True.intro⟩⟩⟩⟩,⟨sg30444,⟨sg30440,⟨sg30438,⟨sg30437,True.intro,True.intro⟩,⟨sg30439,True.intro,True.intro⟩⟩,⟨sg30442,⟨sg30441,True.intro,True.intro⟩,⟨sg30443,True.intro,True.intro⟩⟩⟩,⟨sg30448,⟨sg30446,⟨sg30445,True.intro,True.intro⟩,⟨sg30447,True.intro,True.intro⟩⟩,⟨sg30450,⟨sg30449,True.intro,True.intro⟩,⟨sg30451,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_531All : degreeTree43_531.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30420,degreeTree43_529All,degreeTree43_530All⟩ + +lemma degreeTree43_532All : degreeTree43_532.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30468,⟨sg30460,⟨sg30456,⟨sg30454,⟨sg30453,True.intro,True.intro⟩,⟨sg30455,True.intro,True.intro⟩⟩,⟨sg30458,⟨sg30457,True.intro,True.intro⟩,⟨sg30459,True.intro,True.intro⟩⟩⟩,⟨sg30464,⟨sg30462,⟨sg30461,True.intro,True.intro⟩,⟨sg30463,True.intro,True.intro⟩⟩,⟨sg30466,⟨sg30465,True.intro,True.intro⟩,⟨sg30467,True.intro,True.intro⟩⟩⟩⟩,⟨sg30476,⟨sg30472,⟨sg30470,⟨sg30469,True.intro,True.intro⟩,⟨sg30471,True.intro,True.intro⟩⟩,⟨sg30474,⟨sg30473,True.intro,True.intro⟩,⟨sg30475,True.intro,True.intro⟩⟩⟩,⟨sg30480,⟨sg30478,⟨sg30477,True.intro,True.intro⟩,⟨sg30479,True.intro,True.intro⟩⟩,⟨sg30482,⟨sg30481,True.intro,True.intro⟩,⟨sg30483,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_533All : degreeTree43_533.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30500,⟨sg30492,⟨sg30488,⟨sg30486,⟨sg30485,True.intro,True.intro⟩,⟨sg30487,True.intro,True.intro⟩⟩,⟨sg30490,⟨sg30489,True.intro,True.intro⟩,⟨sg30491,True.intro,True.intro⟩⟩⟩,⟨sg30496,⟨sg30494,⟨sg30493,True.intro,True.intro⟩,⟨sg30495,True.intro,True.intro⟩⟩,⟨sg30498,⟨sg30497,True.intro,True.intro⟩,⟨sg30499,True.intro,True.intro⟩⟩⟩⟩,⟨sg30508,⟨sg30504,⟨sg30502,⟨sg30501,True.intro,True.intro⟩,⟨sg30503,True.intro,True.intro⟩⟩,⟨sg30506,⟨sg30505,True.intro,True.intro⟩,⟨sg30507,True.intro,True.intro⟩⟩⟩,⟨sg30512,⟨sg30510,⟨sg30509,True.intro,True.intro⟩,⟨sg30511,True.intro,True.intro⟩⟩,⟨sg30514,⟨sg30513,True.intro,True.intro⟩,⟨sg30515,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_534All : degreeTree43_534.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30484,degreeTree43_532All,degreeTree43_533All⟩ + +lemma degreeTree43_535All : degreeTree43_535.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30452,degreeTree43_531All,degreeTree43_534All⟩ + +lemma degreeTree43_536All : degreeTree43_536.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30525,⟨sg30521,⟨sg30519,⟨sg30518,⟨sg30517,True.intro,True.intro⟩,True.intro⟩,⟨sg30520,True.intro,True.intro⟩⟩,⟨sg30523,⟨sg30522,True.intro,True.intro⟩,⟨sg30524,True.intro,True.intro⟩⟩⟩,⟨sg30529,⟨sg30527,⟨sg30526,True.intro,True.intro⟩,⟨sg30528,True.intro,True.intro⟩⟩,⟨sg30531,⟨sg30530,True.intro,True.intro⟩,⟨sg30532,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_537All : degreeTree43_537.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30541,⟨sg30537,⟨sg30535,⟨sg30534,True.intro,True.intro⟩,⟨sg30536,True.intro,True.intro⟩⟩,⟨sg30539,⟨sg30538,True.intro,True.intro⟩,⟨sg30540,True.intro,True.intro⟩⟩⟩,⟨sg30545,⟨sg30543,⟨sg30542,True.intro,True.intro⟩,⟨sg30544,True.intro,True.intro⟩⟩,⟨sg30547,⟨sg30546,True.intro,True.intro⟩,⟨sg30548,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_538All : degreeTree43_538.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30533,degreeTree43_536All,degreeTree43_537All⟩ + +lemma degreeTree43_539All : degreeTree43_539.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30565,⟨sg30557,⟨sg30553,⟨sg30551,⟨sg30550,True.intro,True.intro⟩,⟨sg30552,True.intro,True.intro⟩⟩,⟨sg30555,⟨sg30554,True.intro,True.intro⟩,⟨sg30556,True.intro,True.intro⟩⟩⟩,⟨sg30561,⟨sg30559,⟨sg30558,True.intro,True.intro⟩,⟨sg30560,True.intro,True.intro⟩⟩,⟨sg30563,⟨sg30562,True.intro,True.intro⟩,⟨sg30564,True.intro,True.intro⟩⟩⟩⟩,⟨sg30573,⟨sg30569,⟨sg30567,⟨sg30566,True.intro,True.intro⟩,⟨sg30568,True.intro,True.intro⟩⟩,⟨sg30571,⟨sg30570,True.intro,True.intro⟩,⟨sg30572,True.intro,True.intro⟩⟩⟩,⟨sg30577,⟨sg30575,⟨sg30574,True.intro,True.intro⟩,⟨sg30576,True.intro,True.intro⟩⟩,⟨sg30579,⟨sg30578,True.intro,True.intro⟩,⟨sg30580,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_540All : degreeTree43_540.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30549,degreeTree43_538All,degreeTree43_539All⟩ + +lemma degreeTree43_541All : degreeTree43_541.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30597,⟨sg30589,⟨sg30585,⟨sg30583,⟨sg30582,True.intro,True.intro⟩,⟨sg30584,True.intro,True.intro⟩⟩,⟨sg30587,⟨sg30586,True.intro,True.intro⟩,⟨sg30588,True.intro,True.intro⟩⟩⟩,⟨sg30593,⟨sg30591,⟨sg30590,True.intro,True.intro⟩,⟨sg30592,True.intro,True.intro⟩⟩,⟨sg30595,⟨sg30594,True.intro,True.intro⟩,⟨sg30596,True.intro,True.intro⟩⟩⟩⟩,⟨sg30605,⟨sg30601,⟨sg30599,⟨sg30598,True.intro,True.intro⟩,⟨sg30600,True.intro,True.intro⟩⟩,⟨sg30603,⟨sg30602,True.intro,True.intro⟩,⟨sg30604,True.intro,True.intro⟩⟩⟩,⟨sg30609,⟨sg30607,⟨sg30606,True.intro,True.intro⟩,⟨sg30608,True.intro,True.intro⟩⟩,⟨sg30611,⟨sg30610,True.intro,True.intro⟩,⟨sg30612,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_542All : degreeTree43_542.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30629,⟨sg30621,⟨sg30617,⟨sg30615,⟨sg30614,True.intro,True.intro⟩,⟨sg30616,True.intro,True.intro⟩⟩,⟨sg30619,⟨sg30618,True.intro,True.intro⟩,⟨sg30620,True.intro,True.intro⟩⟩⟩,⟨sg30625,⟨sg30623,⟨sg30622,True.intro,True.intro⟩,⟨sg30624,True.intro,True.intro⟩⟩,⟨sg30627,⟨sg30626,True.intro,True.intro⟩,⟨sg30628,True.intro,True.intro⟩⟩⟩⟩,⟨sg30637,⟨sg30633,⟨sg30631,⟨sg30630,True.intro,True.intro⟩,⟨sg30632,True.intro,True.intro⟩⟩,⟨sg30635,⟨sg30634,True.intro,True.intro⟩,⟨sg30636,True.intro,True.intro⟩⟩⟩,⟨sg30641,⟨sg30639,⟨sg30638,True.intro,True.intro⟩,⟨sg30640,True.intro,True.intro⟩⟩,⟨sg30643,⟨sg30642,True.intro,True.intro⟩,⟨sg30644,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_543All : degreeTree43_543.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30613,degreeTree43_541All,degreeTree43_542All⟩ + +lemma degreeTree43_544All : degreeTree43_544.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30581,degreeTree43_540All,degreeTree43_543All⟩ + +lemma degreeTree43_545All : degreeTree43_545.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30516,degreeTree43_535All,degreeTree43_544All⟩ + +lemma degreeTree43_546All : degreeTree43_546.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30654,⟨sg30650,⟨sg30648,⟨sg30647,⟨sg30646,True.intro,True.intro⟩,True.intro⟩,⟨sg30649,True.intro,True.intro⟩⟩,⟨sg30652,⟨sg30651,True.intro,True.intro⟩,⟨sg30653,True.intro,True.intro⟩⟩⟩,⟨sg30658,⟨sg30656,⟨sg30655,True.intro,True.intro⟩,⟨sg30657,True.intro,True.intro⟩⟩,⟨sg30660,⟨sg30659,True.intro,True.intro⟩,⟨sg30661,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_547All : degreeTree43_547.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30670,⟨sg30666,⟨sg30664,⟨sg30663,True.intro,True.intro⟩,⟨sg30665,True.intro,True.intro⟩⟩,⟨sg30668,⟨sg30667,True.intro,True.intro⟩,⟨sg30669,True.intro,True.intro⟩⟩⟩,⟨sg30674,⟨sg30672,⟨sg30671,True.intro,True.intro⟩,⟨sg30673,True.intro,True.intro⟩⟩,⟨sg30676,⟨sg30675,True.intro,True.intro⟩,⟨sg30677,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_548All : degreeTree43_548.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30662,degreeTree43_546All,degreeTree43_547All⟩ + +lemma degreeTree43_549All : degreeTree43_549.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30694,⟨sg30686,⟨sg30682,⟨sg30680,⟨sg30679,True.intro,True.intro⟩,⟨sg30681,True.intro,True.intro⟩⟩,⟨sg30684,⟨sg30683,True.intro,True.intro⟩,⟨sg30685,True.intro,True.intro⟩⟩⟩,⟨sg30690,⟨sg30688,⟨sg30687,True.intro,True.intro⟩,⟨sg30689,True.intro,True.intro⟩⟩,⟨sg30692,⟨sg30691,True.intro,True.intro⟩,⟨sg30693,True.intro,True.intro⟩⟩⟩⟩,⟨sg30702,⟨sg30698,⟨sg30696,⟨sg30695,True.intro,True.intro⟩,⟨sg30697,True.intro,True.intro⟩⟩,⟨sg30700,⟨sg30699,True.intro,True.intro⟩,⟨sg30701,True.intro,True.intro⟩⟩⟩,⟨sg30706,⟨sg30704,⟨sg30703,True.intro,True.intro⟩,⟨sg30705,True.intro,True.intro⟩⟩,⟨sg30708,⟨sg30707,True.intro,True.intro⟩,⟨sg30709,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_550All : degreeTree43_550.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30678,degreeTree43_548All,degreeTree43_549All⟩ + +lemma degreeTree43_551All : degreeTree43_551.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30726,⟨sg30718,⟨sg30714,⟨sg30712,⟨sg30711,True.intro,True.intro⟩,⟨sg30713,True.intro,True.intro⟩⟩,⟨sg30716,⟨sg30715,True.intro,True.intro⟩,⟨sg30717,True.intro,True.intro⟩⟩⟩,⟨sg30722,⟨sg30720,⟨sg30719,True.intro,True.intro⟩,⟨sg30721,True.intro,True.intro⟩⟩,⟨sg30724,⟨sg30723,True.intro,True.intro⟩,⟨sg30725,True.intro,True.intro⟩⟩⟩⟩,⟨sg30734,⟨sg30730,⟨sg30728,⟨sg30727,True.intro,True.intro⟩,⟨sg30729,True.intro,True.intro⟩⟩,⟨sg30732,⟨sg30731,True.intro,True.intro⟩,⟨sg30733,True.intro,True.intro⟩⟩⟩,⟨sg30738,⟨sg30736,⟨sg30735,True.intro,True.intro⟩,⟨sg30737,True.intro,True.intro⟩⟩,⟨sg30740,⟨sg30739,True.intro,True.intro⟩,⟨sg30741,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_552All : degreeTree43_552.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30758,⟨sg30750,⟨sg30746,⟨sg30744,⟨sg30743,True.intro,True.intro⟩,⟨sg30745,True.intro,True.intro⟩⟩,⟨sg30748,⟨sg30747,True.intro,True.intro⟩,⟨sg30749,True.intro,True.intro⟩⟩⟩,⟨sg30754,⟨sg30752,⟨sg30751,True.intro,True.intro⟩,⟨sg30753,True.intro,True.intro⟩⟩,⟨sg30756,⟨sg30755,True.intro,True.intro⟩,⟨sg30757,True.intro,True.intro⟩⟩⟩⟩,⟨sg30766,⟨sg30762,⟨sg30760,⟨sg30759,True.intro,True.intro⟩,⟨sg30761,True.intro,True.intro⟩⟩,⟨sg30764,⟨sg30763,True.intro,True.intro⟩,⟨sg30765,True.intro,True.intro⟩⟩⟩,⟨sg30770,⟨sg30768,⟨sg30767,True.intro,True.intro⟩,⟨sg30769,True.intro,True.intro⟩⟩,⟨sg30772,⟨sg30771,True.intro,True.intro⟩,⟨sg30773,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_553All : degreeTree43_553.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30742,degreeTree43_551All,degreeTree43_552All⟩ + +lemma degreeTree43_554All : degreeTree43_554.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30710,degreeTree43_550All,degreeTree43_553All⟩ + +lemma degreeTree43_555All : degreeTree43_555.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30783,⟨sg30779,⟨sg30777,⟨sg30776,⟨sg30775,True.intro,True.intro⟩,True.intro⟩,⟨sg30778,True.intro,True.intro⟩⟩,⟨sg30781,⟨sg30780,True.intro,True.intro⟩,⟨sg30782,True.intro,True.intro⟩⟩⟩,⟨sg30787,⟨sg30785,⟨sg30784,True.intro,True.intro⟩,⟨sg30786,True.intro,True.intro⟩⟩,⟨sg30789,⟨sg30788,True.intro,True.intro⟩,⟨sg30790,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_556All : degreeTree43_556.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30799,⟨sg30795,⟨sg30793,⟨sg30792,True.intro,True.intro⟩,⟨sg30794,True.intro,True.intro⟩⟩,⟨sg30797,⟨sg30796,True.intro,True.intro⟩,⟨sg30798,True.intro,True.intro⟩⟩⟩,⟨sg30803,⟨sg30801,⟨sg30800,True.intro,True.intro⟩,⟨sg30802,True.intro,True.intro⟩⟩,⟨sg30805,⟨sg30804,True.intro,True.intro⟩,⟨sg30806,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_557All : degreeTree43_557.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30791,degreeTree43_555All,degreeTree43_556All⟩ + +lemma degreeTree43_558All : degreeTree43_558.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30823,⟨sg30815,⟨sg30811,⟨sg30809,⟨sg30808,True.intro,True.intro⟩,⟨sg30810,True.intro,True.intro⟩⟩,⟨sg30813,⟨sg30812,True.intro,True.intro⟩,⟨sg30814,True.intro,True.intro⟩⟩⟩,⟨sg30819,⟨sg30817,⟨sg30816,True.intro,True.intro⟩,⟨sg30818,True.intro,True.intro⟩⟩,⟨sg30821,⟨sg30820,True.intro,True.intro⟩,⟨sg30822,True.intro,True.intro⟩⟩⟩⟩,⟨sg30831,⟨sg30827,⟨sg30825,⟨sg30824,True.intro,True.intro⟩,⟨sg30826,True.intro,True.intro⟩⟩,⟨sg30829,⟨sg30828,True.intro,True.intro⟩,⟨sg30830,True.intro,True.intro⟩⟩⟩,⟨sg30835,⟨sg30833,⟨sg30832,True.intro,True.intro⟩,⟨sg30834,True.intro,True.intro⟩⟩,⟨sg30837,⟨sg30836,True.intro,True.intro⟩,⟨sg30838,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_559All : degreeTree43_559.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30807,degreeTree43_557All,degreeTree43_558All⟩ + +lemma degreeTree43_560All : degreeTree43_560.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30855,⟨sg30847,⟨sg30843,⟨sg30841,⟨sg30840,True.intro,True.intro⟩,⟨sg30842,True.intro,True.intro⟩⟩,⟨sg30845,⟨sg30844,True.intro,True.intro⟩,⟨sg30846,True.intro,True.intro⟩⟩⟩,⟨sg30851,⟨sg30849,⟨sg30848,True.intro,True.intro⟩,⟨sg30850,True.intro,True.intro⟩⟩,⟨sg30853,⟨sg30852,True.intro,True.intro⟩,⟨sg30854,True.intro,True.intro⟩⟩⟩⟩,⟨sg30863,⟨sg30859,⟨sg30857,⟨sg30856,True.intro,True.intro⟩,⟨sg30858,True.intro,True.intro⟩⟩,⟨sg30861,⟨sg30860,True.intro,True.intro⟩,⟨sg30862,True.intro,True.intro⟩⟩⟩,⟨sg30867,⟨sg30865,⟨sg30864,True.intro,True.intro⟩,⟨sg30866,True.intro,True.intro⟩⟩,⟨sg30869,⟨sg30868,True.intro,True.intro⟩,⟨sg30870,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_561All : degreeTree43_561.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30887,⟨sg30879,⟨sg30875,⟨sg30873,⟨sg30872,True.intro,True.intro⟩,⟨sg30874,True.intro,True.intro⟩⟩,⟨sg30877,⟨sg30876,True.intro,True.intro⟩,⟨sg30878,True.intro,True.intro⟩⟩⟩,⟨sg30883,⟨sg30881,⟨sg30880,True.intro,True.intro⟩,⟨sg30882,True.intro,True.intro⟩⟩,⟨sg30885,⟨sg30884,True.intro,True.intro⟩,⟨sg30886,True.intro,True.intro⟩⟩⟩⟩,⟨sg30895,⟨sg30891,⟨sg30889,⟨sg30888,True.intro,True.intro⟩,⟨sg30890,True.intro,True.intro⟩⟩,⟨sg30893,⟨sg30892,True.intro,True.intro⟩,⟨sg30894,True.intro,True.intro⟩⟩⟩,⟨sg30899,⟨sg30897,⟨sg30896,True.intro,True.intro⟩,⟨sg30898,True.intro,True.intro⟩⟩,⟨sg30901,⟨sg30900,True.intro,True.intro⟩,⟨sg30902,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_562All : degreeTree43_562.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30871,degreeTree43_560All,degreeTree43_561All⟩ + +lemma degreeTree43_563All : degreeTree43_563.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30839,degreeTree43_559All,degreeTree43_562All⟩ + +lemma degreeTree43_564All : degreeTree43_564.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30774,degreeTree43_554All,degreeTree43_563All⟩ + +lemma degreeTree43_565All : degreeTree43_565.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30645,degreeTree43_545All,degreeTree43_564All⟩ + +lemma degreeTree43_566All : degreeTree43_566.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30387,degreeTree43_526All,degreeTree43_565All⟩ + +lemma degreeTree43_567All : degreeTree43_567.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30912,⟨sg30908,⟨sg30906,⟨sg30905,⟨sg30904,True.intro,True.intro⟩,True.intro⟩,⟨sg30907,True.intro,True.intro⟩⟩,⟨sg30910,⟨sg30909,True.intro,True.intro⟩,⟨sg30911,True.intro,True.intro⟩⟩⟩,⟨sg30916,⟨sg30914,⟨sg30913,True.intro,True.intro⟩,⟨sg30915,True.intro,True.intro⟩⟩,⟨sg30918,⟨sg30917,True.intro,True.intro⟩,⟨sg30919,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_568All : degreeTree43_568.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30928,⟨sg30924,⟨sg30922,⟨sg30921,True.intro,True.intro⟩,⟨sg30923,True.intro,True.intro⟩⟩,⟨sg30926,⟨sg30925,True.intro,True.intro⟩,⟨sg30927,True.intro,True.intro⟩⟩⟩,⟨sg30932,⟨sg30930,⟨sg30929,True.intro,True.intro⟩,⟨sg30931,True.intro,True.intro⟩⟩,⟨sg30934,⟨sg30933,True.intro,True.intro⟩,⟨sg30935,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_569All : degreeTree43_569.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30920,degreeTree43_567All,degreeTree43_568All⟩ + +lemma degreeTree43_570All : degreeTree43_570.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30952,⟨sg30944,⟨sg30940,⟨sg30938,⟨sg30937,True.intro,True.intro⟩,⟨sg30939,True.intro,True.intro⟩⟩,⟨sg30942,⟨sg30941,True.intro,True.intro⟩,⟨sg30943,True.intro,True.intro⟩⟩⟩,⟨sg30948,⟨sg30946,⟨sg30945,True.intro,True.intro⟩,⟨sg30947,True.intro,True.intro⟩⟩,⟨sg30950,⟨sg30949,True.intro,True.intro⟩,⟨sg30951,True.intro,True.intro⟩⟩⟩⟩,⟨sg30960,⟨sg30956,⟨sg30954,⟨sg30953,True.intro,True.intro⟩,⟨sg30955,True.intro,True.intro⟩⟩,⟨sg30958,⟨sg30957,True.intro,True.intro⟩,⟨sg30959,True.intro,True.intro⟩⟩⟩,⟨sg30964,⟨sg30962,⟨sg30961,True.intro,True.intro⟩,⟨sg30963,True.intro,True.intro⟩⟩,⟨sg30966,⟨sg30965,True.intro,True.intro⟩,⟨sg30967,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_571All : degreeTree43_571.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30936,degreeTree43_569All,degreeTree43_570All⟩ + +lemma degreeTree43_572All : degreeTree43_572.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30984,⟨sg30976,⟨sg30972,⟨sg30970,⟨sg30969,True.intro,True.intro⟩,⟨sg30971,True.intro,True.intro⟩⟩,⟨sg30974,⟨sg30973,True.intro,True.intro⟩,⟨sg30975,True.intro,True.intro⟩⟩⟩,⟨sg30980,⟨sg30978,⟨sg30977,True.intro,True.intro⟩,⟨sg30979,True.intro,True.intro⟩⟩,⟨sg30982,⟨sg30981,True.intro,True.intro⟩,⟨sg30983,True.intro,True.intro⟩⟩⟩⟩,⟨sg30992,⟨sg30988,⟨sg30986,⟨sg30985,True.intro,True.intro⟩,⟨sg30987,True.intro,True.intro⟩⟩,⟨sg30990,⟨sg30989,True.intro,True.intro⟩,⟨sg30991,True.intro,True.intro⟩⟩⟩,⟨sg30996,⟨sg30994,⟨sg30993,True.intro,True.intro⟩,⟨sg30995,True.intro,True.intro⟩⟩,⟨sg30998,⟨sg30997,True.intro,True.intro⟩,⟨sg30999,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_573All : degreeTree43_573.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31016,⟨sg31008,⟨sg31004,⟨sg31002,⟨sg31001,True.intro,True.intro⟩,⟨sg31003,True.intro,True.intro⟩⟩,⟨sg31006,⟨sg31005,True.intro,True.intro⟩,⟨sg31007,True.intro,True.intro⟩⟩⟩,⟨sg31012,⟨sg31010,⟨sg31009,True.intro,True.intro⟩,⟨sg31011,True.intro,True.intro⟩⟩,⟨sg31014,⟨sg31013,True.intro,True.intro⟩,⟨sg31015,True.intro,True.intro⟩⟩⟩⟩,⟨sg31024,⟨sg31020,⟨sg31018,⟨sg31017,True.intro,True.intro⟩,⟨sg31019,True.intro,True.intro⟩⟩,⟨sg31022,⟨sg31021,True.intro,True.intro⟩,⟨sg31023,True.intro,True.intro⟩⟩⟩,⟨sg31028,⟨sg31026,⟨sg31025,True.intro,True.intro⟩,⟨sg31027,True.intro,True.intro⟩⟩,⟨sg31030,⟨sg31029,True.intro,True.intro⟩,⟨sg31031,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_574All : degreeTree43_574.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31000,degreeTree43_572All,degreeTree43_573All⟩ + +lemma degreeTree43_575All : degreeTree43_575.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30968,degreeTree43_571All,degreeTree43_574All⟩ + +lemma degreeTree43_576All : degreeTree43_576.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31041,⟨sg31037,⟨sg31035,⟨sg31034,⟨sg31033,True.intro,True.intro⟩,True.intro⟩,⟨sg31036,True.intro,True.intro⟩⟩,⟨sg31039,⟨sg31038,True.intro,True.intro⟩,⟨sg31040,True.intro,True.intro⟩⟩⟩,⟨sg31045,⟨sg31043,⟨sg31042,True.intro,True.intro⟩,⟨sg31044,True.intro,True.intro⟩⟩,⟨sg31047,⟨sg31046,True.intro,True.intro⟩,⟨sg31048,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_577All : degreeTree43_577.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31057,⟨sg31053,⟨sg31051,⟨sg31050,True.intro,True.intro⟩,⟨sg31052,True.intro,True.intro⟩⟩,⟨sg31055,⟨sg31054,True.intro,True.intro⟩,⟨sg31056,True.intro,True.intro⟩⟩⟩,⟨sg31061,⟨sg31059,⟨sg31058,True.intro,True.intro⟩,⟨sg31060,True.intro,True.intro⟩⟩,⟨sg31063,⟨sg31062,True.intro,True.intro⟩,⟨sg31064,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_578All : degreeTree43_578.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31049,degreeTree43_576All,degreeTree43_577All⟩ + +lemma degreeTree43_579All : degreeTree43_579.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31081,⟨sg31073,⟨sg31069,⟨sg31067,⟨sg31066,True.intro,True.intro⟩,⟨sg31068,True.intro,True.intro⟩⟩,⟨sg31071,⟨sg31070,True.intro,True.intro⟩,⟨sg31072,True.intro,True.intro⟩⟩⟩,⟨sg31077,⟨sg31075,⟨sg31074,True.intro,True.intro⟩,⟨sg31076,True.intro,True.intro⟩⟩,⟨sg31079,⟨sg31078,True.intro,True.intro⟩,⟨sg31080,True.intro,True.intro⟩⟩⟩⟩,⟨sg31089,⟨sg31085,⟨sg31083,⟨sg31082,True.intro,True.intro⟩,⟨sg31084,True.intro,True.intro⟩⟩,⟨sg31087,⟨sg31086,True.intro,True.intro⟩,⟨sg31088,True.intro,True.intro⟩⟩⟩,⟨sg31093,⟨sg31091,⟨sg31090,True.intro,True.intro⟩,⟨sg31092,True.intro,True.intro⟩⟩,⟨sg31095,⟨sg31094,True.intro,True.intro⟩,⟨sg31096,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_580All : degreeTree43_580.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31065,degreeTree43_578All,degreeTree43_579All⟩ + +lemma degreeTree43_581All : degreeTree43_581.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31113,⟨sg31105,⟨sg31101,⟨sg31099,⟨sg31098,True.intro,True.intro⟩,⟨sg31100,True.intro,True.intro⟩⟩,⟨sg31103,⟨sg31102,True.intro,True.intro⟩,⟨sg31104,True.intro,True.intro⟩⟩⟩,⟨sg31109,⟨sg31107,⟨sg31106,True.intro,True.intro⟩,⟨sg31108,True.intro,True.intro⟩⟩,⟨sg31111,⟨sg31110,True.intro,True.intro⟩,⟨sg31112,True.intro,True.intro⟩⟩⟩⟩,⟨sg31121,⟨sg31117,⟨sg31115,⟨sg31114,True.intro,True.intro⟩,⟨sg31116,True.intro,True.intro⟩⟩,⟨sg31119,⟨sg31118,True.intro,True.intro⟩,⟨sg31120,True.intro,True.intro⟩⟩⟩,⟨sg31125,⟨sg31123,⟨sg31122,True.intro,True.intro⟩,⟨sg31124,True.intro,True.intro⟩⟩,⟨sg31127,⟨sg31126,True.intro,True.intro⟩,⟨sg31128,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_582All : degreeTree43_582.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31145,⟨sg31137,⟨sg31133,⟨sg31131,⟨sg31130,True.intro,True.intro⟩,⟨sg31132,True.intro,True.intro⟩⟩,⟨sg31135,⟨sg31134,True.intro,True.intro⟩,⟨sg31136,True.intro,True.intro⟩⟩⟩,⟨sg31141,⟨sg31139,⟨sg31138,True.intro,True.intro⟩,⟨sg31140,True.intro,True.intro⟩⟩,⟨sg31143,⟨sg31142,True.intro,True.intro⟩,⟨sg31144,True.intro,True.intro⟩⟩⟩⟩,⟨sg31153,⟨sg31149,⟨sg31147,⟨sg31146,True.intro,True.intro⟩,⟨sg31148,True.intro,True.intro⟩⟩,⟨sg31151,⟨sg31150,True.intro,True.intro⟩,⟨sg31152,True.intro,True.intro⟩⟩⟩,⟨sg31157,⟨sg31155,⟨sg31154,True.intro,True.intro⟩,⟨sg31156,True.intro,True.intro⟩⟩,⟨sg31159,⟨sg31158,True.intro,True.intro⟩,⟨sg31160,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_583All : degreeTree43_583.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31129,degreeTree43_581All,degreeTree43_582All⟩ + +lemma degreeTree43_584All : degreeTree43_584.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31097,degreeTree43_580All,degreeTree43_583All⟩ + +lemma degreeTree43_585All : degreeTree43_585.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31032,degreeTree43_575All,degreeTree43_584All⟩ + +lemma degreeTree43_586All : degreeTree43_586.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31170,⟨sg31166,⟨sg31164,⟨sg31163,⟨sg31162,True.intro,True.intro⟩,True.intro⟩,⟨sg31165,True.intro,True.intro⟩⟩,⟨sg31168,⟨sg31167,True.intro,True.intro⟩,⟨sg31169,True.intro,True.intro⟩⟩⟩,⟨sg31174,⟨sg31172,⟨sg31171,True.intro,True.intro⟩,⟨sg31173,True.intro,True.intro⟩⟩,⟨sg31176,⟨sg31175,True.intro,True.intro⟩,⟨sg31177,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_587All : degreeTree43_587.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31186,⟨sg31182,⟨sg31180,⟨sg31179,True.intro,True.intro⟩,⟨sg31181,True.intro,True.intro⟩⟩,⟨sg31184,⟨sg31183,True.intro,True.intro⟩,⟨sg31185,True.intro,True.intro⟩⟩⟩,⟨sg31190,⟨sg31188,⟨sg31187,True.intro,True.intro⟩,⟨sg31189,True.intro,True.intro⟩⟩,⟨sg31192,⟨sg31191,True.intro,True.intro⟩,⟨sg31193,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_588All : degreeTree43_588.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31178,degreeTree43_586All,degreeTree43_587All⟩ + +lemma degreeTree43_589All : degreeTree43_589.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31210,⟨sg31202,⟨sg31198,⟨sg31196,⟨sg31195,True.intro,True.intro⟩,⟨sg31197,True.intro,True.intro⟩⟩,⟨sg31200,⟨sg31199,True.intro,True.intro⟩,⟨sg31201,True.intro,True.intro⟩⟩⟩,⟨sg31206,⟨sg31204,⟨sg31203,True.intro,True.intro⟩,⟨sg31205,True.intro,True.intro⟩⟩,⟨sg31208,⟨sg31207,True.intro,True.intro⟩,⟨sg31209,True.intro,True.intro⟩⟩⟩⟩,⟨sg31218,⟨sg31214,⟨sg31212,⟨sg31211,True.intro,True.intro⟩,⟨sg31213,True.intro,True.intro⟩⟩,⟨sg31216,⟨sg31215,True.intro,True.intro⟩,⟨sg31217,True.intro,True.intro⟩⟩⟩,⟨sg31222,⟨sg31220,⟨sg31219,True.intro,True.intro⟩,⟨sg31221,True.intro,True.intro⟩⟩,⟨sg31224,⟨sg31223,True.intro,True.intro⟩,⟨sg31225,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_590All : degreeTree43_590.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31194,degreeTree43_588All,degreeTree43_589All⟩ + +lemma degreeTree43_591All : degreeTree43_591.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31242,⟨sg31234,⟨sg31230,⟨sg31228,⟨sg31227,True.intro,True.intro⟩,⟨sg31229,True.intro,True.intro⟩⟩,⟨sg31232,⟨sg31231,True.intro,True.intro⟩,⟨sg31233,True.intro,True.intro⟩⟩⟩,⟨sg31238,⟨sg31236,⟨sg31235,True.intro,True.intro⟩,⟨sg31237,True.intro,True.intro⟩⟩,⟨sg31240,⟨sg31239,True.intro,True.intro⟩,⟨sg31241,True.intro,True.intro⟩⟩⟩⟩,⟨sg31250,⟨sg31246,⟨sg31244,⟨sg31243,True.intro,True.intro⟩,⟨sg31245,True.intro,True.intro⟩⟩,⟨sg31248,⟨sg31247,True.intro,True.intro⟩,⟨sg31249,True.intro,True.intro⟩⟩⟩,⟨sg31254,⟨sg31252,⟨sg31251,True.intro,True.intro⟩,⟨sg31253,True.intro,True.intro⟩⟩,⟨sg31256,⟨sg31255,True.intro,True.intro⟩,⟨sg31257,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_592All : degreeTree43_592.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31274,⟨sg31266,⟨sg31262,⟨sg31260,⟨sg31259,True.intro,True.intro⟩,⟨sg31261,True.intro,True.intro⟩⟩,⟨sg31264,⟨sg31263,True.intro,True.intro⟩,⟨sg31265,True.intro,True.intro⟩⟩⟩,⟨sg31270,⟨sg31268,⟨sg31267,True.intro,True.intro⟩,⟨sg31269,True.intro,True.intro⟩⟩,⟨sg31272,⟨sg31271,True.intro,True.intro⟩,⟨sg31273,True.intro,True.intro⟩⟩⟩⟩,⟨sg31282,⟨sg31278,⟨sg31276,⟨sg31275,True.intro,True.intro⟩,⟨sg31277,True.intro,True.intro⟩⟩,⟨sg31280,⟨sg31279,True.intro,True.intro⟩,⟨sg31281,True.intro,True.intro⟩⟩⟩,⟨sg31286,⟨sg31284,⟨sg31283,True.intro,True.intro⟩,⟨sg31285,True.intro,True.intro⟩⟩,⟨sg31288,⟨sg31287,True.intro,True.intro⟩,⟨sg31289,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_593All : degreeTree43_593.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31258,degreeTree43_591All,degreeTree43_592All⟩ + +lemma degreeTree43_594All : degreeTree43_594.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31226,degreeTree43_590All,degreeTree43_593All⟩ + +lemma degreeTree43_595All : degreeTree43_595.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31299,⟨sg31295,⟨sg31293,⟨sg31292,⟨sg31291,True.intro,True.intro⟩,True.intro⟩,⟨sg31294,True.intro,True.intro⟩⟩,⟨sg31297,⟨sg31296,True.intro,True.intro⟩,⟨sg31298,True.intro,True.intro⟩⟩⟩,⟨sg31303,⟨sg31301,⟨sg31300,True.intro,True.intro⟩,⟨sg31302,True.intro,True.intro⟩⟩,⟨sg31305,⟨sg31304,True.intro,True.intro⟩,⟨sg31306,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_596All : degreeTree43_596.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31315,⟨sg31311,⟨sg31309,⟨sg31308,True.intro,True.intro⟩,⟨sg31310,True.intro,True.intro⟩⟩,⟨sg31313,⟨sg31312,True.intro,True.intro⟩,⟨sg31314,True.intro,True.intro⟩⟩⟩,⟨sg31319,⟨sg31317,⟨sg31316,True.intro,True.intro⟩,⟨sg31318,True.intro,True.intro⟩⟩,⟨sg31321,⟨sg31320,True.intro,True.intro⟩,⟨sg31322,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_597All : degreeTree43_597.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31307,degreeTree43_595All,degreeTree43_596All⟩ + +lemma degreeTree43_598All : degreeTree43_598.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31339,⟨sg31331,⟨sg31327,⟨sg31325,⟨sg31324,True.intro,True.intro⟩,⟨sg31326,True.intro,True.intro⟩⟩,⟨sg31329,⟨sg31328,True.intro,True.intro⟩,⟨sg31330,True.intro,True.intro⟩⟩⟩,⟨sg31335,⟨sg31333,⟨sg31332,True.intro,True.intro⟩,⟨sg31334,True.intro,True.intro⟩⟩,⟨sg31337,⟨sg31336,True.intro,True.intro⟩,⟨sg31338,True.intro,True.intro⟩⟩⟩⟩,⟨sg31347,⟨sg31343,⟨sg31341,⟨sg31340,True.intro,True.intro⟩,⟨sg31342,True.intro,True.intro⟩⟩,⟨sg31345,⟨sg31344,True.intro,True.intro⟩,⟨sg31346,True.intro,True.intro⟩⟩⟩,⟨sg31351,⟨sg31349,⟨sg31348,True.intro,True.intro⟩,⟨sg31350,True.intro,True.intro⟩⟩,⟨sg31353,⟨sg31352,True.intro,True.intro⟩,⟨sg31354,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_599All : degreeTree43_599.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31323,degreeTree43_597All,degreeTree43_598All⟩ + +lemma degreeTree43_600All : degreeTree43_600.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31371,⟨sg31363,⟨sg31359,⟨sg31357,⟨sg31356,True.intro,True.intro⟩,⟨sg31358,True.intro,True.intro⟩⟩,⟨sg31361,⟨sg31360,True.intro,True.intro⟩,⟨sg31362,True.intro,True.intro⟩⟩⟩,⟨sg31367,⟨sg31365,⟨sg31364,True.intro,True.intro⟩,⟨sg31366,True.intro,True.intro⟩⟩,⟨sg31369,⟨sg31368,True.intro,True.intro⟩,⟨sg31370,True.intro,True.intro⟩⟩⟩⟩,⟨sg31379,⟨sg31375,⟨sg31373,⟨sg31372,True.intro,True.intro⟩,⟨sg31374,True.intro,True.intro⟩⟩,⟨sg31377,⟨sg31376,True.intro,True.intro⟩,⟨sg31378,True.intro,True.intro⟩⟩⟩,⟨sg31383,⟨sg31381,⟨sg31380,True.intro,True.intro⟩,⟨sg31382,True.intro,True.intro⟩⟩,⟨sg31385,⟨sg31384,True.intro,True.intro⟩,⟨sg31386,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_601All : degreeTree43_601.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31403,⟨sg31395,⟨sg31391,⟨sg31389,⟨sg31388,True.intro,True.intro⟩,⟨sg31390,True.intro,True.intro⟩⟩,⟨sg31393,⟨sg31392,True.intro,True.intro⟩,⟨sg31394,True.intro,True.intro⟩⟩⟩,⟨sg31399,⟨sg31397,⟨sg31396,True.intro,True.intro⟩,⟨sg31398,True.intro,True.intro⟩⟩,⟨sg31401,⟨sg31400,True.intro,True.intro⟩,⟨sg31402,True.intro,True.intro⟩⟩⟩⟩,⟨sg31411,⟨sg31407,⟨sg31405,⟨sg31404,True.intro,True.intro⟩,⟨sg31406,True.intro,True.intro⟩⟩,⟨sg31409,⟨sg31408,True.intro,True.intro⟩,⟨sg31410,True.intro,True.intro⟩⟩⟩,⟨sg31415,⟨sg31413,⟨sg31412,True.intro,True.intro⟩,⟨sg31414,True.intro,True.intro⟩⟩,⟨sg31417,⟨sg31416,True.intro,True.intro⟩,⟨sg31418,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_602All : degreeTree43_602.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31387,degreeTree43_600All,degreeTree43_601All⟩ + +lemma degreeTree43_603All : degreeTree43_603.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31355,degreeTree43_599All,degreeTree43_602All⟩ + +lemma degreeTree43_604All : degreeTree43_604.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31290,degreeTree43_594All,degreeTree43_603All⟩ + +lemma degreeTree43_605All : degreeTree43_605.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31161,degreeTree43_585All,degreeTree43_604All⟩ + +lemma degreeTree43_606All : degreeTree43_606.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31428,⟨sg31424,⟨sg31422,⟨sg31421,⟨sg31420,True.intro,True.intro⟩,True.intro⟩,⟨sg31423,True.intro,True.intro⟩⟩,⟨sg31426,⟨sg31425,True.intro,True.intro⟩,⟨sg31427,True.intro,True.intro⟩⟩⟩,⟨sg31432,⟨sg31430,⟨sg31429,True.intro,True.intro⟩,⟨sg31431,True.intro,True.intro⟩⟩,⟨sg31434,⟨sg31433,True.intro,True.intro⟩,⟨sg31435,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_607All : degreeTree43_607.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31444,⟨sg31440,⟨sg31438,⟨sg31437,True.intro,True.intro⟩,⟨sg31439,True.intro,True.intro⟩⟩,⟨sg31442,⟨sg31441,True.intro,True.intro⟩,⟨sg31443,True.intro,True.intro⟩⟩⟩,⟨sg31448,⟨sg31446,⟨sg31445,True.intro,True.intro⟩,⟨sg31447,True.intro,True.intro⟩⟩,⟨sg31450,⟨sg31449,True.intro,True.intro⟩,⟨sg31451,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_608All : degreeTree43_608.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31436,degreeTree43_606All,degreeTree43_607All⟩ + +lemma degreeTree43_609All : degreeTree43_609.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31468,⟨sg31460,⟨sg31456,⟨sg31454,⟨sg31453,True.intro,True.intro⟩,⟨sg31455,True.intro,True.intro⟩⟩,⟨sg31458,⟨sg31457,True.intro,True.intro⟩,⟨sg31459,True.intro,True.intro⟩⟩⟩,⟨sg31464,⟨sg31462,⟨sg31461,True.intro,True.intro⟩,⟨sg31463,True.intro,True.intro⟩⟩,⟨sg31466,⟨sg31465,True.intro,True.intro⟩,⟨sg31467,True.intro,True.intro⟩⟩⟩⟩,⟨sg31476,⟨sg31472,⟨sg31470,⟨sg31469,True.intro,True.intro⟩,⟨sg31471,True.intro,True.intro⟩⟩,⟨sg31474,⟨sg31473,True.intro,True.intro⟩,⟨sg31475,True.intro,True.intro⟩⟩⟩,⟨sg31480,⟨sg31478,⟨sg31477,True.intro,True.intro⟩,⟨sg31479,True.intro,True.intro⟩⟩,⟨sg31482,⟨sg31481,True.intro,True.intro⟩,⟨sg31483,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_610All : degreeTree43_610.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31452,degreeTree43_608All,degreeTree43_609All⟩ + +lemma degreeTree43_611All : degreeTree43_611.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31500,⟨sg31492,⟨sg31488,⟨sg31486,⟨sg31485,True.intro,True.intro⟩,⟨sg31487,True.intro,True.intro⟩⟩,⟨sg31490,⟨sg31489,True.intro,True.intro⟩,⟨sg31491,True.intro,True.intro⟩⟩⟩,⟨sg31496,⟨sg31494,⟨sg31493,True.intro,True.intro⟩,⟨sg31495,True.intro,True.intro⟩⟩,⟨sg31498,⟨sg31497,True.intro,True.intro⟩,⟨sg31499,True.intro,True.intro⟩⟩⟩⟩,⟨sg31508,⟨sg31504,⟨sg31502,⟨sg31501,True.intro,True.intro⟩,⟨sg31503,True.intro,True.intro⟩⟩,⟨sg31506,⟨sg31505,True.intro,True.intro⟩,⟨sg31507,True.intro,True.intro⟩⟩⟩,⟨sg31512,⟨sg31510,⟨sg31509,True.intro,True.intro⟩,⟨sg31511,True.intro,True.intro⟩⟩,⟨sg31514,⟨sg31513,True.intro,True.intro⟩,⟨sg31515,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_612All : degreeTree43_612.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31532,⟨sg31524,⟨sg31520,⟨sg31518,⟨sg31517,True.intro,True.intro⟩,⟨sg31519,True.intro,True.intro⟩⟩,⟨sg31522,⟨sg31521,True.intro,True.intro⟩,⟨sg31523,True.intro,True.intro⟩⟩⟩,⟨sg31528,⟨sg31526,⟨sg31525,True.intro,True.intro⟩,⟨sg31527,True.intro,True.intro⟩⟩,⟨sg31530,⟨sg31529,True.intro,True.intro⟩,⟨sg31531,True.intro,True.intro⟩⟩⟩⟩,⟨sg31540,⟨sg31536,⟨sg31534,⟨sg31533,True.intro,True.intro⟩,⟨sg31535,True.intro,True.intro⟩⟩,⟨sg31538,⟨sg31537,True.intro,True.intro⟩,⟨sg31539,True.intro,True.intro⟩⟩⟩,⟨sg31544,⟨sg31542,⟨sg31541,True.intro,True.intro⟩,⟨sg31543,True.intro,True.intro⟩⟩,⟨sg31546,⟨sg31545,True.intro,True.intro⟩,⟨sg31547,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_613All : degreeTree43_613.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31516,degreeTree43_611All,degreeTree43_612All⟩ + +lemma degreeTree43_614All : degreeTree43_614.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31484,degreeTree43_610All,degreeTree43_613All⟩ + +lemma degreeTree43_615All : degreeTree43_615.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31557,⟨sg31553,⟨sg31551,⟨sg31550,⟨sg31549,True.intro,True.intro⟩,True.intro⟩,⟨sg31552,True.intro,True.intro⟩⟩,⟨sg31555,⟨sg31554,True.intro,True.intro⟩,⟨sg31556,True.intro,True.intro⟩⟩⟩,⟨sg31561,⟨sg31559,⟨sg31558,True.intro,True.intro⟩,⟨sg31560,True.intro,True.intro⟩⟩,⟨sg31563,⟨sg31562,True.intro,True.intro⟩,⟨sg31564,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_616All : degreeTree43_616.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31573,⟨sg31569,⟨sg31567,⟨sg31566,True.intro,True.intro⟩,⟨sg31568,True.intro,True.intro⟩⟩,⟨sg31571,⟨sg31570,True.intro,True.intro⟩,⟨sg31572,True.intro,True.intro⟩⟩⟩,⟨sg31577,⟨sg31575,⟨sg31574,True.intro,True.intro⟩,⟨sg31576,True.intro,True.intro⟩⟩,⟨sg31579,⟨sg31578,True.intro,True.intro⟩,⟨sg31580,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_617All : degreeTree43_617.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31565,degreeTree43_615All,degreeTree43_616All⟩ + +lemma degreeTree43_618All : degreeTree43_618.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31597,⟨sg31589,⟨sg31585,⟨sg31583,⟨sg31582,True.intro,True.intro⟩,⟨sg31584,True.intro,True.intro⟩⟩,⟨sg31587,⟨sg31586,True.intro,True.intro⟩,⟨sg31588,True.intro,True.intro⟩⟩⟩,⟨sg31593,⟨sg31591,⟨sg31590,True.intro,True.intro⟩,⟨sg31592,True.intro,True.intro⟩⟩,⟨sg31595,⟨sg31594,True.intro,True.intro⟩,⟨sg31596,True.intro,True.intro⟩⟩⟩⟩,⟨sg31605,⟨sg31601,⟨sg31599,⟨sg31598,True.intro,True.intro⟩,⟨sg31600,True.intro,True.intro⟩⟩,⟨sg31603,⟨sg31602,True.intro,True.intro⟩,⟨sg31604,True.intro,True.intro⟩⟩⟩,⟨sg31609,⟨sg31607,⟨sg31606,True.intro,True.intro⟩,⟨sg31608,True.intro,True.intro⟩⟩,⟨sg31611,⟨sg31610,True.intro,True.intro⟩,⟨sg31612,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_619All : degreeTree43_619.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31581,degreeTree43_617All,degreeTree43_618All⟩ + +lemma degreeTree43_620All : degreeTree43_620.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31629,⟨sg31621,⟨sg31617,⟨sg31615,⟨sg31614,True.intro,True.intro⟩,⟨sg31616,True.intro,True.intro⟩⟩,⟨sg31619,⟨sg31618,True.intro,True.intro⟩,⟨sg31620,True.intro,True.intro⟩⟩⟩,⟨sg31625,⟨sg31623,⟨sg31622,True.intro,True.intro⟩,⟨sg31624,True.intro,True.intro⟩⟩,⟨sg31627,⟨sg31626,True.intro,True.intro⟩,⟨sg31628,True.intro,True.intro⟩⟩⟩⟩,⟨sg31637,⟨sg31633,⟨sg31631,⟨sg31630,True.intro,True.intro⟩,⟨sg31632,True.intro,True.intro⟩⟩,⟨sg31635,⟨sg31634,True.intro,True.intro⟩,⟨sg31636,True.intro,True.intro⟩⟩⟩,⟨sg31641,⟨sg31639,⟨sg31638,True.intro,True.intro⟩,⟨sg31640,True.intro,True.intro⟩⟩,⟨sg31643,⟨sg31642,True.intro,True.intro⟩,⟨sg31644,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_621All : degreeTree43_621.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31661,⟨sg31653,⟨sg31649,⟨sg31647,⟨sg31646,True.intro,True.intro⟩,⟨sg31648,True.intro,True.intro⟩⟩,⟨sg31651,⟨sg31650,True.intro,True.intro⟩,⟨sg31652,True.intro,True.intro⟩⟩⟩,⟨sg31657,⟨sg31655,⟨sg31654,True.intro,True.intro⟩,⟨sg31656,True.intro,True.intro⟩⟩,⟨sg31659,⟨sg31658,True.intro,True.intro⟩,⟨sg31660,True.intro,True.intro⟩⟩⟩⟩,⟨sg31669,⟨sg31665,⟨sg31663,⟨sg31662,True.intro,True.intro⟩,⟨sg31664,True.intro,True.intro⟩⟩,⟨sg31667,⟨sg31666,True.intro,True.intro⟩,⟨sg31668,True.intro,True.intro⟩⟩⟩,⟨sg31673,⟨sg31671,⟨sg31670,True.intro,True.intro⟩,⟨sg31672,True.intro,True.intro⟩⟩,⟨sg31675,⟨sg31674,True.intro,True.intro⟩,⟨sg31676,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_622All : degreeTree43_622.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31645,degreeTree43_620All,degreeTree43_621All⟩ + +lemma degreeTree43_623All : degreeTree43_623.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31613,degreeTree43_619All,degreeTree43_622All⟩ + +lemma degreeTree43_624All : degreeTree43_624.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31548,degreeTree43_614All,degreeTree43_623All⟩ + +lemma degreeTree43_625All : degreeTree43_625.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31686,⟨sg31682,⟨sg31680,⟨sg31679,⟨sg31678,True.intro,True.intro⟩,True.intro⟩,⟨sg31681,True.intro,True.intro⟩⟩,⟨sg31684,⟨sg31683,True.intro,True.intro⟩,⟨sg31685,True.intro,True.intro⟩⟩⟩,⟨sg31690,⟨sg31688,⟨sg31687,True.intro,True.intro⟩,⟨sg31689,True.intro,True.intro⟩⟩,⟨sg31692,⟨sg31691,True.intro,True.intro⟩,⟨sg31693,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_626All : degreeTree43_626.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31702,⟨sg31698,⟨sg31696,⟨sg31695,True.intro,True.intro⟩,⟨sg31697,True.intro,True.intro⟩⟩,⟨sg31700,⟨sg31699,True.intro,True.intro⟩,⟨sg31701,True.intro,True.intro⟩⟩⟩,⟨sg31706,⟨sg31704,⟨sg31703,True.intro,True.intro⟩,⟨sg31705,True.intro,True.intro⟩⟩,⟨sg31708,⟨sg31707,True.intro,True.intro⟩,⟨sg31709,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_627All : degreeTree43_627.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31694,degreeTree43_625All,degreeTree43_626All⟩ + +lemma degreeTree43_628All : degreeTree43_628.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31726,⟨sg31718,⟨sg31714,⟨sg31712,⟨sg31711,True.intro,True.intro⟩,⟨sg31713,True.intro,True.intro⟩⟩,⟨sg31716,⟨sg31715,True.intro,True.intro⟩,⟨sg31717,True.intro,True.intro⟩⟩⟩,⟨sg31722,⟨sg31720,⟨sg31719,True.intro,True.intro⟩,⟨sg31721,True.intro,True.intro⟩⟩,⟨sg31724,⟨sg31723,True.intro,True.intro⟩,⟨sg31725,True.intro,True.intro⟩⟩⟩⟩,⟨sg31734,⟨sg31730,⟨sg31728,⟨sg31727,True.intro,True.intro⟩,⟨sg31729,True.intro,True.intro⟩⟩,⟨sg31732,⟨sg31731,True.intro,True.intro⟩,⟨sg31733,True.intro,True.intro⟩⟩⟩,⟨sg31738,⟨sg31736,⟨sg31735,True.intro,True.intro⟩,⟨sg31737,True.intro,True.intro⟩⟩,⟨sg31740,⟨sg31739,True.intro,True.intro⟩,⟨sg31741,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_629All : degreeTree43_629.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31710,degreeTree43_627All,degreeTree43_628All⟩ + +lemma degreeTree43_630All : degreeTree43_630.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31758,⟨sg31750,⟨sg31746,⟨sg31744,⟨sg31743,True.intro,True.intro⟩,⟨sg31745,True.intro,True.intro⟩⟩,⟨sg31748,⟨sg31747,True.intro,True.intro⟩,⟨sg31749,True.intro,True.intro⟩⟩⟩,⟨sg31754,⟨sg31752,⟨sg31751,True.intro,True.intro⟩,⟨sg31753,True.intro,True.intro⟩⟩,⟨sg31756,⟨sg31755,True.intro,True.intro⟩,⟨sg31757,True.intro,True.intro⟩⟩⟩⟩,⟨sg31766,⟨sg31762,⟨sg31760,⟨sg31759,True.intro,True.intro⟩,⟨sg31761,True.intro,True.intro⟩⟩,⟨sg31764,⟨sg31763,True.intro,True.intro⟩,⟨sg31765,True.intro,True.intro⟩⟩⟩,⟨sg31770,⟨sg31768,⟨sg31767,True.intro,True.intro⟩,⟨sg31769,True.intro,True.intro⟩⟩,⟨sg31772,⟨sg31771,True.intro,True.intro⟩,⟨sg31773,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_631All : degreeTree43_631.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31790,⟨sg31782,⟨sg31778,⟨sg31776,⟨sg31775,True.intro,True.intro⟩,⟨sg31777,True.intro,True.intro⟩⟩,⟨sg31780,⟨sg31779,True.intro,True.intro⟩,⟨sg31781,True.intro,True.intro⟩⟩⟩,⟨sg31786,⟨sg31784,⟨sg31783,True.intro,True.intro⟩,⟨sg31785,True.intro,True.intro⟩⟩,⟨sg31788,⟨sg31787,True.intro,True.intro⟩,⟨sg31789,True.intro,True.intro⟩⟩⟩⟩,⟨sg31798,⟨sg31794,⟨sg31792,⟨sg31791,True.intro,True.intro⟩,⟨sg31793,True.intro,True.intro⟩⟩,⟨sg31796,⟨sg31795,True.intro,True.intro⟩,⟨sg31797,True.intro,True.intro⟩⟩⟩,⟨sg31802,⟨sg31800,⟨sg31799,True.intro,True.intro⟩,⟨sg31801,True.intro,True.intro⟩⟩,⟨sg31804,⟨sg31803,True.intro,True.intro⟩,⟨sg31805,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_632All : degreeTree43_632.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31774,degreeTree43_630All,degreeTree43_631All⟩ + +lemma degreeTree43_633All : degreeTree43_633.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31742,degreeTree43_629All,degreeTree43_632All⟩ + +lemma degreeTree43_634All : degreeTree43_634.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31815,⟨sg31811,⟨sg31809,⟨sg31808,⟨sg31807,True.intro,True.intro⟩,True.intro⟩,⟨sg31810,True.intro,True.intro⟩⟩,⟨sg31813,⟨sg31812,True.intro,True.intro⟩,⟨sg31814,True.intro,True.intro⟩⟩⟩,⟨sg31819,⟨sg31817,⟨sg31816,True.intro,True.intro⟩,⟨sg31818,True.intro,True.intro⟩⟩,⟨sg31821,⟨sg31820,True.intro,True.intro⟩,⟨sg31822,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_635All : degreeTree43_635.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31831,⟨sg31827,⟨sg31825,⟨sg31824,True.intro,True.intro⟩,⟨sg31826,True.intro,True.intro⟩⟩,⟨sg31829,⟨sg31828,True.intro,True.intro⟩,⟨sg31830,True.intro,True.intro⟩⟩⟩,⟨sg31835,⟨sg31833,⟨sg31832,True.intro,True.intro⟩,⟨sg31834,True.intro,True.intro⟩⟩,⟨sg31837,⟨sg31836,True.intro,True.intro⟩,⟨sg31838,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree43_636All : degreeTree43_636.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31823,degreeTree43_634All,degreeTree43_635All⟩ + +lemma degreeTree43_637All : degreeTree43_637.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31855,⟨sg31847,⟨sg31843,⟨sg31841,⟨sg31840,True.intro,True.intro⟩,⟨sg31842,True.intro,True.intro⟩⟩,⟨sg31845,⟨sg31844,True.intro,True.intro⟩,⟨sg31846,True.intro,True.intro⟩⟩⟩,⟨sg31851,⟨sg31849,⟨sg31848,True.intro,True.intro⟩,⟨sg31850,True.intro,True.intro⟩⟩,⟨sg31853,⟨sg31852,True.intro,True.intro⟩,⟨sg31854,True.intro,True.intro⟩⟩⟩⟩,⟨sg31863,⟨sg31859,⟨sg31857,⟨sg31856,True.intro,True.intro⟩,⟨sg31858,True.intro,True.intro⟩⟩,⟨sg31861,⟨sg31860,True.intro,True.intro⟩,⟨sg31862,True.intro,True.intro⟩⟩⟩,⟨sg31867,⟨sg31865,⟨sg31864,True.intro,True.intro⟩,⟨sg31866,True.intro,True.intro⟩⟩,⟨sg31869,⟨sg31868,True.intro,True.intro⟩,⟨sg31870,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_638All : degreeTree43_638.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31839,degreeTree43_636All,degreeTree43_637All⟩ + +lemma degreeTree43_639All : degreeTree43_639.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31887,⟨sg31879,⟨sg31875,⟨sg31873,⟨sg31872,True.intro,True.intro⟩,⟨sg31874,True.intro,True.intro⟩⟩,⟨sg31877,⟨sg31876,True.intro,True.intro⟩,⟨sg31878,True.intro,True.intro⟩⟩⟩,⟨sg31883,⟨sg31881,⟨sg31880,True.intro,True.intro⟩,⟨sg31882,True.intro,True.intro⟩⟩,⟨sg31885,⟨sg31884,True.intro,True.intro⟩,⟨sg31886,True.intro,True.intro⟩⟩⟩⟩,⟨sg31895,⟨sg31891,⟨sg31889,⟨sg31888,True.intro,True.intro⟩,⟨sg31890,True.intro,True.intro⟩⟩,⟨sg31893,⟨sg31892,True.intro,True.intro⟩,⟨sg31894,True.intro,True.intro⟩⟩⟩,⟨sg31899,⟨sg31897,⟨sg31896,True.intro,True.intro⟩,⟨sg31898,True.intro,True.intro⟩⟩,⟨sg31901,⟨sg31900,True.intro,True.intro⟩,⟨sg31902,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_640All : degreeTree43_640.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31919,⟨sg31911,⟨sg31907,⟨sg31905,⟨sg31904,True.intro,True.intro⟩,⟨sg31906,True.intro,True.intro⟩⟩,⟨sg31909,⟨sg31908,True.intro,True.intro⟩,⟨sg31910,True.intro,True.intro⟩⟩⟩,⟨sg31915,⟨sg31913,⟨sg31912,True.intro,True.intro⟩,⟨sg31914,True.intro,True.intro⟩⟩,⟨sg31917,⟨sg31916,True.intro,True.intro⟩,⟨sg31918,True.intro,True.intro⟩⟩⟩⟩,⟨sg31927,⟨sg31923,⟨sg31921,⟨sg31920,True.intro,True.intro⟩,⟨sg31922,True.intro,True.intro⟩⟩,⟨sg31925,⟨sg31924,True.intro,True.intro⟩,⟨sg31926,True.intro,True.intro⟩⟩⟩,⟨sg31931,⟨sg31929,⟨sg31928,True.intro,True.intro⟩,⟨sg31930,True.intro,True.intro⟩⟩,⟨sg31933,⟨sg31932,True.intro,True.intro⟩,⟨sg31934,True.intro,True.intro⟩⟩⟩⟩⟩ + +lemma degreeTree43_641All : degreeTree43_641.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31903,degreeTree43_639All,degreeTree43_640All⟩ + +lemma degreeTree43_642All : degreeTree43_642.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31871,degreeTree43_638All,degreeTree43_641All⟩ + +lemma degreeTree43_643All : degreeTree43_643.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31806,degreeTree43_633All,degreeTree43_642All⟩ + +lemma degreeTree43_644All : degreeTree43_644.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31677,degreeTree43_624All,degreeTree43_643All⟩ + +lemma degreeTree43_645All : degreeTree43_645.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31419,degreeTree43_605All,degreeTree43_644All⟩ + +lemma degreeTree43_646All : degreeTree43_646.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg30903,degreeTree43_566All,degreeTree43_645All⟩ + +lemma degreeTree43_647All : degreeTree43_647.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg29870,degreeTree43_485All,degreeTree43_646All⟩ + +lemma degreeTree43_648All : degreeTree43_648.All (RowSquare [12,10,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg27805,degreeTree43_324All,degreeTree43_647All⟩ + +lemma degreeTreeAll43 : degreeTree43.All + (fun rs => SquareOccurs (candidate 6 5 1) (rowDiagram rs)) := by + have hp : rowDiagram [12,10,4,3,2,2,2,2,2,2,1,1] = candidate 6 5 1 := rowDiagram_candidate (M := 6) (b := 5) (δ := 1) (by decide) + rw [← hp] + exact degreeTree43_648All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof58.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof58.lean index 715b9a0012c1ea58b6f3a6dabcb4314f12454aae..244a2f6dbf9b3477550e61916911f2f98bf95c3a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof58.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof58.lean @@ -1,35 +1,35 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData58 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes78 - -namespace OAI - -/-! Degree Tree Proof 58. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree58_0All : degreeTree58_0.All (RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31964,⟨sg31957,⟨sg31954,⟨sg31952,⟨sg31951,True.intro,True.intro⟩,⟨sg31953,True.intro,True.intro⟩⟩,⟨sg31956,⟨sg31955,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg31961,⟨sg31959,⟨sg31958,True.intro,True.intro⟩,⟨sg31960,True.intro,True.intro⟩⟩,⟨sg31963,⟨sg31962,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg31971,⟨sg31968,⟨sg31966,⟨sg31965,True.intro,True.intro⟩,⟨sg31967,True.intro,True.intro⟩⟩,⟨sg31970,⟨sg31969,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg31975,⟨sg31973,⟨sg31972,True.intro,True.intro⟩,⟨sg31974,True.intro,True.intro⟩⟩,⟨sg31977,⟨sg31976,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree58_1All : degreeTree58_1.All (RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31992,⟨sg31985,⟨sg31982,⟨sg31980,⟨sg31979,True.intro,True.intro⟩,⟨sg31981,True.intro,True.intro⟩⟩,⟨sg31984,⟨sg31983,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg31989,⟨sg31987,⟨sg31986,True.intro,True.intro⟩,⟨sg31988,True.intro,True.intro⟩⟩,⟨sg31991,⟨sg31990,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg31999,⟨sg31996,⟨sg31994,⟨sg31993,True.intro,True.intro⟩,⟨sg31995,True.intro,True.intro⟩⟩,⟨sg31998,⟨sg31997,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32003,⟨sg32001,⟨sg32000,True.intro,True.intro⟩,⟨sg32002,True.intro,True.intro⟩⟩,⟨sg32005,⟨sg32004,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ - -lemma degreeTree58_2All : degreeTree58_2.All (RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1]) := by - exact ⟨sg31978,degreeTree58_0All,degreeTree58_1All⟩ - -lemma degreeTreeAll58 : degreeTree58.All - (fun rs => SquareOccurs (candidate 8 5 1) (rowDiagram rs)) := by - have hp : rowDiagram [14,12,6,5,4,3,2,2,2,2,2,2,1,1] = candidate 8 5 1 := rowDiagram_candidate (M := 8) (b := 5) (δ := 1) (by decide) - rw [← hp] - exact degreeTree58_2All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData58 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes78 + +namespace OAI + +/-! Degree Tree Proof 58. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree58_0All : degreeTree58_0.All (RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31964,⟨sg31957,⟨sg31954,⟨sg31952,⟨sg31951,True.intro,True.intro⟩,⟨sg31953,True.intro,True.intro⟩⟩,⟨sg31956,⟨sg31955,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg31961,⟨sg31959,⟨sg31958,True.intro,True.intro⟩,⟨sg31960,True.intro,True.intro⟩⟩,⟨sg31963,⟨sg31962,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg31971,⟨sg31968,⟨sg31966,⟨sg31965,True.intro,True.intro⟩,⟨sg31967,True.intro,True.intro⟩⟩,⟨sg31970,⟨sg31969,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg31975,⟨sg31973,⟨sg31972,True.intro,True.intro⟩,⟨sg31974,True.intro,True.intro⟩⟩,⟨sg31977,⟨sg31976,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree58_1All : degreeTree58_1.All (RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31992,⟨sg31985,⟨sg31982,⟨sg31980,⟨sg31979,True.intro,True.intro⟩,⟨sg31981,True.intro,True.intro⟩⟩,⟨sg31984,⟨sg31983,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg31989,⟨sg31987,⟨sg31986,True.intro,True.intro⟩,⟨sg31988,True.intro,True.intro⟩⟩,⟨sg31991,⟨sg31990,True.intro,True.intro⟩,True.intro⟩⟩⟩,⟨sg31999,⟨sg31996,⟨sg31994,⟨sg31993,True.intro,True.intro⟩,⟨sg31995,True.intro,True.intro⟩⟩,⟨sg31998,⟨sg31997,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32003,⟨sg32001,⟨sg32000,True.intro,True.intro⟩,⟨sg32002,True.intro,True.intro⟩⟩,⟨sg32005,⟨sg32004,True.intro,True.intro⟩,True.intro⟩⟩⟩⟩ + +lemma degreeTree58_2All : degreeTree58_2.All (RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1]) := by + exact ⟨sg31978,degreeTree58_0All,degreeTree58_1All⟩ + +lemma degreeTreeAll58 : degreeTree58.All + (fun rs => SquareOccurs (candidate 8 5 1) (rowDiagram rs)) := by + have hp : rowDiagram [14,12,6,5,4,3,2,2,2,2,2,2,1,1] = candidate 8 5 1 := rowDiagram_candidate (M := 8) (b := 5) (δ := 1) (by decide) + rw [← hp] + exact degreeTree58_2All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof62.lean index 39f811804d990ba4137ffc59be4827e9a1a68f3e..99bc65b763f2ba115e206857f0ea16d273d8ed0f 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof62.lean @@ -1,3123 +1,3123 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData62 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupMissingLeaves -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes100 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes101 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes102 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes103 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes104 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes105 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes106 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes79 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes80 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes81 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes82 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes83 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes84 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes85 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes86 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes87 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes88 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes89 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes90 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes91 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes92 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes93 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes94 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes95 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes96 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes97 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes98 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes99 - -namespace OAI - -/-! Degree Tree Proof 62. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree62_0All : degreeTree62_0.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32016,⟨sg32011,⟨sg32008,⟨sg32007,⟨sg32006,True.intro,True.intro⟩,True.intro⟩,⟨sg32010,⟨sg32009,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32014,⟨sg32013,⟨sg32012,True.intro,True.intro⟩,True.intro⟩,⟨sg32015,True.intro,True.intro⟩⟩⟩,⟨sg32022,⟨sg32019,⟨sg32018,⟨sg32017,True.intro,True.intro⟩,True.intro⟩,⟨sg32021,⟨sg32020,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32025,⟨sg32024,⟨sg32023,True.intro,True.intro⟩,True.intro⟩,⟨sg32026,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_1All : degreeTree62_1.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32038,⟨sg32033,⟨sg32030,⟨sg32029,⟨sg32028,True.intro,True.intro⟩,True.intro⟩,⟨sg32032,⟨sg32031,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32036,⟨sg32035,⟨sg32034,True.intro,True.intro⟩,True.intro⟩,⟨sg32037,True.intro,True.intro⟩⟩⟩,⟨sg32044,⟨sg32041,⟨sg32040,⟨sg32039,True.intro,True.intro⟩,True.intro⟩,⟨sg32043,⟨sg32042,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32047,⟨sg32046,⟨sg32045,True.intro,True.intro⟩,True.intro⟩,⟨sg32048,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_2All : degreeTree62_2.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32027,degreeTree62_0All,degreeTree62_1All⟩ - -lemma degreeTree62_3All : degreeTree62_3.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32060,⟨sg32055,⟨sg32052,⟨sg32051,⟨sg32050,True.intro,True.intro⟩,True.intro⟩,⟨sg32054,⟨sg32053,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32058,⟨sg32057,⟨sg32056,True.intro,True.intro⟩,True.intro⟩,⟨sg32059,True.intro,True.intro⟩⟩⟩,⟨sg32066,⟨sg32063,⟨sg32062,⟨sg32061,True.intro,True.intro⟩,True.intro⟩,⟨sg32065,⟨sg32064,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32069,⟨sg32068,⟨sg32067,True.intro,True.intro⟩,True.intro⟩,⟨sg32070,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_4All : degreeTree62_4.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32082,⟨sg32077,⟨sg32074,⟨sg32073,⟨sg32072,True.intro,True.intro⟩,True.intro⟩,⟨sg32076,⟨sg32075,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32080,⟨sg32079,⟨sg32078,True.intro,True.intro⟩,True.intro⟩,⟨sg32081,True.intro,True.intro⟩⟩⟩,⟨sg32088,⟨sg32085,⟨sg32084,⟨sg32083,True.intro,True.intro⟩,True.intro⟩,⟨sg32087,⟨sg32086,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32091,⟨sg32090,⟨sg32089,True.intro,True.intro⟩,True.intro⟩,⟨sg32092,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_5All : degreeTree62_5.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32071,degreeTree62_3All,degreeTree62_4All⟩ - -lemma degreeTree62_6All : degreeTree62_6.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32049,degreeTree62_2All,degreeTree62_5All⟩ - -lemma degreeTree62_7All : degreeTree62_7.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32104,⟨sg32099,⟨sg32096,⟨sg32095,⟨sg32094,True.intro,True.intro⟩,True.intro⟩,⟨sg32098,⟨sg32097,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32102,⟨sg32101,⟨sg32100,True.intro,True.intro⟩,True.intro⟩,⟨sg32103,True.intro,True.intro⟩⟩⟩,⟨sg32110,⟨sg32107,⟨sg32106,⟨sg32105,True.intro,True.intro⟩,True.intro⟩,⟨sg32109,⟨sg32108,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32113,⟨sg32112,⟨sg32111,True.intro,True.intro⟩,True.intro⟩,⟨sg32114,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_8All : degreeTree62_8.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32126,⟨sg32121,⟨sg32118,⟨sg32117,⟨sg32116,True.intro,True.intro⟩,True.intro⟩,⟨sg32120,⟨sg32119,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32124,⟨sg32123,⟨sg32122,True.intro,True.intro⟩,True.intro⟩,⟨sg32125,True.intro,True.intro⟩⟩⟩,⟨sg32132,⟨sg32129,⟨sg32128,⟨sg32127,True.intro,True.intro⟩,True.intro⟩,⟨sg32131,⟨sg32130,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32135,⟨sg32134,⟨sg32133,True.intro,True.intro⟩,True.intro⟩,⟨sg32136,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_9All : degreeTree62_9.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32115,degreeTree62_7All,degreeTree62_8All⟩ - -lemma degreeTree62_10All : degreeTree62_10.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32148,⟨sg32143,⟨sg32140,⟨sg32139,⟨sg32138,True.intro,True.intro⟩,True.intro⟩,⟨sg32142,⟨sg32141,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32146,⟨sg32145,⟨sg32144,True.intro,True.intro⟩,True.intro⟩,⟨sg32147,True.intro,True.intro⟩⟩⟩,⟨sg32154,⟨sg32151,⟨sg32150,⟨sg32149,True.intro,True.intro⟩,True.intro⟩,⟨sg32153,⟨sg32152,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32157,⟨sg32156,⟨sg32155,True.intro,True.intro⟩,True.intro⟩,⟨sg32158,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_11All : degreeTree62_11.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32170,⟨sg32165,⟨sg32162,⟨sg32161,⟨sg32160,True.intro,True.intro⟩,True.intro⟩,⟨sg32164,⟨sg32163,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32168,⟨sg32167,⟨sg32166,True.intro,True.intro⟩,True.intro⟩,⟨sg32169,True.intro,True.intro⟩⟩⟩,⟨sg32176,⟨sg32173,⟨sg32172,⟨sg32171,True.intro,True.intro⟩,True.intro⟩,⟨sg32175,⟨sg32174,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32179,⟨sg32178,⟨sg32177,True.intro,True.intro⟩,True.intro⟩,⟨sg32180,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_12All : degreeTree62_12.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32159,degreeTree62_10All,degreeTree62_11All⟩ - -lemma degreeTree62_13All : degreeTree62_13.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32137,degreeTree62_9All,degreeTree62_12All⟩ - -lemma degreeTree62_14All : degreeTree62_14.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32093,degreeTree62_6All,degreeTree62_13All⟩ - -lemma degreeTree62_15All : degreeTree62_15.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32192,⟨sg32187,⟨sg32184,⟨sg32183,⟨sg32182,True.intro,True.intro⟩,True.intro⟩,⟨sg32186,⟨sg32185,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32190,⟨sg32189,⟨sg32188,True.intro,True.intro⟩,True.intro⟩,⟨sg32191,True.intro,True.intro⟩⟩⟩,⟨sg32198,⟨sg32195,⟨sg32194,⟨sg32193,True.intro,True.intro⟩,True.intro⟩,⟨sg32197,⟨sg32196,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32201,⟨sg32200,⟨sg32199,True.intro,True.intro⟩,True.intro⟩,⟨sg32202,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_16All : degreeTree62_16.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32214,⟨sg32209,⟨sg32206,⟨sg32205,⟨sg32204,True.intro,True.intro⟩,True.intro⟩,⟨sg32208,⟨sg32207,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32212,⟨sg32211,⟨sg32210,True.intro,True.intro⟩,True.intro⟩,⟨sg32213,True.intro,True.intro⟩⟩⟩,⟨sg32220,⟨sg32217,⟨sg32216,⟨sg32215,True.intro,True.intro⟩,True.intro⟩,⟨sg32219,⟨sg32218,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32223,⟨sg32222,⟨sg32221,True.intro,True.intro⟩,True.intro⟩,⟨sg32224,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_17All : degreeTree62_17.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32203,degreeTree62_15All,degreeTree62_16All⟩ - -lemma degreeTree62_18All : degreeTree62_18.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32236,⟨sg32231,⟨sg32228,⟨sg32227,⟨sg32226,True.intro,True.intro⟩,True.intro⟩,⟨sg32230,⟨sg32229,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32234,⟨sg32233,⟨sg32232,True.intro,True.intro⟩,True.intro⟩,⟨sg32235,True.intro,True.intro⟩⟩⟩,⟨sg32242,⟨sg32239,⟨sg32238,⟨sg32237,True.intro,True.intro⟩,True.intro⟩,⟨sg32241,⟨sg32240,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32245,⟨sg32244,⟨sg32243,True.intro,True.intro⟩,True.intro⟩,⟨sg32246,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_19All : degreeTree62_19.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32258,⟨sg32253,⟨sg32250,⟨sg32249,⟨sg32248,True.intro,True.intro⟩,True.intro⟩,⟨sg32252,⟨sg32251,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32256,⟨sg32255,⟨sg32254,True.intro,True.intro⟩,True.intro⟩,⟨sg32257,True.intro,True.intro⟩⟩⟩,⟨sg32264,⟨sg32261,⟨sg32260,⟨sg32259,True.intro,True.intro⟩,True.intro⟩,⟨sg32263,⟨sg32262,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32267,⟨sg32266,⟨sg32265,True.intro,True.intro⟩,True.intro⟩,⟨sg32268,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_20All : degreeTree62_20.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32247,degreeTree62_18All,degreeTree62_19All⟩ - -lemma degreeTree62_21All : degreeTree62_21.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32225,degreeTree62_17All,degreeTree62_20All⟩ - -lemma degreeTree62_22All : degreeTree62_22.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32280,⟨sg32275,⟨sg32272,⟨sg32271,⟨sg32270,True.intro,True.intro⟩,True.intro⟩,⟨sg32274,⟨sg32273,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32278,⟨sg32277,⟨sg32276,True.intro,True.intro⟩,True.intro⟩,⟨sg32279,True.intro,True.intro⟩⟩⟩,⟨sg32286,⟨sg32283,⟨sg32282,⟨sg32281,True.intro,True.intro⟩,True.intro⟩,⟨sg32285,⟨sg32284,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32289,⟨sg32288,⟨sg32287,True.intro,True.intro⟩,True.intro⟩,⟨sg32290,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_23All : degreeTree62_23.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32302,⟨sg32297,⟨sg32294,⟨sg32293,⟨sg32292,True.intro,True.intro⟩,True.intro⟩,⟨sg32296,⟨sg32295,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32300,⟨sg32299,⟨sg32298,True.intro,True.intro⟩,True.intro⟩,⟨sg32301,True.intro,True.intro⟩⟩⟩,⟨sg32308,⟨sg32305,⟨sg32304,⟨sg32303,True.intro,True.intro⟩,True.intro⟩,⟨sg32307,⟨sg32306,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32311,⟨sg32310,⟨sg32309,True.intro,True.intro⟩,True.intro⟩,⟨sg32312,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_24All : degreeTree62_24.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32291,degreeTree62_22All,degreeTree62_23All⟩ - -lemma degreeTree62_25All : degreeTree62_25.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32324,⟨sg32319,⟨sg32316,⟨sg32315,⟨sg32314,True.intro,True.intro⟩,True.intro⟩,⟨sg32318,⟨sg32317,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32322,⟨sg32321,⟨sg32320,True.intro,True.intro⟩,True.intro⟩,⟨sg32323,True.intro,True.intro⟩⟩⟩,⟨sg32330,⟨sg32327,⟨sg32326,⟨sg32325,True.intro,True.intro⟩,True.intro⟩,⟨sg32329,⟨sg32328,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32333,⟨sg32332,⟨sg32331,True.intro,True.intro⟩,True.intro⟩,⟨sg32334,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_26All : degreeTree62_26.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32346,⟨sg32341,⟨sg32338,⟨sg32337,⟨sg32336,True.intro,True.intro⟩,True.intro⟩,⟨sg32340,⟨sg32339,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32344,⟨sg32343,⟨sg32342,True.intro,True.intro⟩,True.intro⟩,⟨sg32345,True.intro,True.intro⟩⟩⟩,⟨sg32351,⟨sg32349,⟨sg32348,⟨sg32347,True.intro,True.intro⟩,True.intro⟩,⟨sg32350,True.intro,True.intro⟩⟩,⟨sg32354,⟨sg32353,⟨sg32352,True.intro,True.intro⟩,True.intro⟩,⟨sg32355,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_27All : degreeTree62_27.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32335,degreeTree62_25All,degreeTree62_26All⟩ - -lemma degreeTree62_28All : degreeTree62_28.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32313,degreeTree62_24All,degreeTree62_27All⟩ - -lemma degreeTree62_29All : degreeTree62_29.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32269,degreeTree62_21All,degreeTree62_28All⟩ - -lemma degreeTree62_30All : degreeTree62_30.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32181,degreeTree62_14All,degreeTree62_29All⟩ - -lemma degreeTree62_31All : degreeTree62_31.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32367,⟨sg32362,⟨sg32359,⟨sg32358,⟨sg32357,True.intro,True.intro⟩,True.intro⟩,⟨sg32361,⟨sg32360,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32365,⟨sg32364,⟨sg32363,True.intro,True.intro⟩,True.intro⟩,⟨sg32366,True.intro,True.intro⟩⟩⟩,⟨sg32373,⟨sg32370,⟨sg32369,⟨sg32368,True.intro,True.intro⟩,True.intro⟩,⟨sg32372,⟨sg32371,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32376,⟨sg32375,⟨sg32374,True.intro,True.intro⟩,True.intro⟩,⟨sg32377,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_32All : degreeTree62_32.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32389,⟨sg32384,⟨sg32381,⟨sg32380,⟨sg32379,True.intro,True.intro⟩,True.intro⟩,⟨sg32383,⟨sg32382,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32387,⟨sg32386,⟨sg32385,True.intro,True.intro⟩,True.intro⟩,⟨sg32388,True.intro,True.intro⟩⟩⟩,⟨sg32395,⟨sg32392,⟨sg32391,⟨sg32390,True.intro,True.intro⟩,True.intro⟩,⟨sg32394,⟨sg32393,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32398,⟨sg32397,⟨sg32396,True.intro,True.intro⟩,True.intro⟩,⟨sg32399,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_33All : degreeTree62_33.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32378,degreeTree62_31All,degreeTree62_32All⟩ - -lemma degreeTree62_34All : degreeTree62_34.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32411,⟨sg32406,⟨sg32403,⟨sg32402,⟨sg32401,True.intro,True.intro⟩,True.intro⟩,⟨sg32405,⟨sg32404,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32409,⟨sg32408,⟨sg32407,True.intro,True.intro⟩,True.intro⟩,⟨sg32410,True.intro,True.intro⟩⟩⟩,⟨sg32417,⟨sg32414,⟨sg32413,⟨sg32412,True.intro,True.intro⟩,True.intro⟩,⟨sg32416,⟨sg32415,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32420,⟨sg32419,⟨sg32418,True.intro,True.intro⟩,True.intro⟩,⟨sg32421,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_35All : degreeTree62_35.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32433,⟨sg32428,⟨sg32425,⟨sg32424,⟨sg32423,True.intro,True.intro⟩,True.intro⟩,⟨sg32427,⟨sg32426,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32431,⟨sg32430,⟨sg32429,True.intro,True.intro⟩,True.intro⟩,⟨sg32432,True.intro,True.intro⟩⟩⟩,⟨sg32439,⟨sg32436,⟨sg32435,⟨sg32434,True.intro,True.intro⟩,True.intro⟩,⟨sg32438,⟨sg32437,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32442,⟨sg32441,⟨sg32440,True.intro,True.intro⟩,True.intro⟩,⟨sg32443,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_36All : degreeTree62_36.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32422,degreeTree62_34All,degreeTree62_35All⟩ - -lemma degreeTree62_37All : degreeTree62_37.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32400,degreeTree62_33All,degreeTree62_36All⟩ - -lemma degreeTree62_38All : degreeTree62_38.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32455,⟨sg32450,⟨sg32447,⟨sg32446,⟨sg32445,True.intro,True.intro⟩,True.intro⟩,⟨sg32449,⟨sg32448,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32453,⟨sg32452,⟨sg32451,True.intro,True.intro⟩,True.intro⟩,⟨sg32454,True.intro,True.intro⟩⟩⟩,⟨sg32461,⟨sg32458,⟨sg32457,⟨sg32456,True.intro,True.intro⟩,True.intro⟩,⟨sg32460,⟨sg32459,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32464,⟨sg32463,⟨sg32462,True.intro,True.intro⟩,True.intro⟩,⟨sg32465,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_39All : degreeTree62_39.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32477,⟨sg32472,⟨sg32469,⟨sg32468,⟨sg32467,True.intro,True.intro⟩,True.intro⟩,⟨sg32471,⟨sg32470,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32475,⟨sg32474,⟨sg32473,True.intro,True.intro⟩,True.intro⟩,⟨sg32476,True.intro,True.intro⟩⟩⟩,⟨sg32483,⟨sg32480,⟨sg32479,⟨sg32478,True.intro,True.intro⟩,True.intro⟩,⟨sg32482,⟨sg32481,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32486,⟨sg32485,⟨sg32484,True.intro,True.intro⟩,True.intro⟩,⟨sg32487,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_40All : degreeTree62_40.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32466,degreeTree62_38All,degreeTree62_39All⟩ - -lemma degreeTree62_41All : degreeTree62_41.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32499,⟨sg32494,⟨sg32491,⟨sg32490,⟨sg32489,True.intro,True.intro⟩,True.intro⟩,⟨sg32493,⟨sg32492,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32497,⟨sg32496,⟨sg32495,True.intro,True.intro⟩,True.intro⟩,⟨sg32498,True.intro,True.intro⟩⟩⟩,⟨sg32505,⟨sg32502,⟨sg32501,⟨sg32500,True.intro,True.intro⟩,True.intro⟩,⟨sg32504,⟨sg32503,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32508,⟨sg32507,⟨sg32506,True.intro,True.intro⟩,True.intro⟩,⟨sg32509,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_42All : degreeTree62_42.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32521,⟨sg32516,⟨sg32513,⟨sg32512,⟨sg32511,True.intro,True.intro⟩,True.intro⟩,⟨sg32515,⟨sg32514,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32519,⟨sg32518,⟨sg32517,True.intro,True.intro⟩,True.intro⟩,⟨sg32520,True.intro,True.intro⟩⟩⟩,⟨sg32527,⟨sg32524,⟨sg32523,⟨sg32522,True.intro,True.intro⟩,True.intro⟩,⟨sg32526,⟨sg32525,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32530,⟨sg32529,⟨sg32528,True.intro,True.intro⟩,True.intro⟩,⟨sg32531,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_43All : degreeTree62_43.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32510,degreeTree62_41All,degreeTree62_42All⟩ - -lemma degreeTree62_44All : degreeTree62_44.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32488,degreeTree62_40All,degreeTree62_43All⟩ - -lemma degreeTree62_45All : degreeTree62_45.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32444,degreeTree62_37All,degreeTree62_44All⟩ - -lemma degreeTree62_46All : degreeTree62_46.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32543,⟨sg32538,⟨sg32535,⟨sg32534,⟨sg32533,True.intro,True.intro⟩,True.intro⟩,⟨sg32537,⟨sg32536,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32541,⟨sg32540,⟨sg32539,True.intro,True.intro⟩,True.intro⟩,⟨sg32542,True.intro,True.intro⟩⟩⟩,⟨sg32549,⟨sg32546,⟨sg32545,⟨sg32544,True.intro,True.intro⟩,True.intro⟩,⟨sg32548,⟨sg32547,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32552,⟨sg32551,⟨sg32550,True.intro,True.intro⟩,True.intro⟩,⟨sg32553,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_47All : degreeTree62_47.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32565,⟨sg32560,⟨sg32557,⟨sg32556,⟨sg32555,True.intro,True.intro⟩,True.intro⟩,⟨sg32559,⟨sg32558,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32563,⟨sg32562,⟨sg32561,True.intro,True.intro⟩,True.intro⟩,⟨sg32564,True.intro,True.intro⟩⟩⟩,⟨sg32571,⟨sg32568,⟨sg32567,⟨sg32566,True.intro,True.intro⟩,True.intro⟩,⟨sg32570,⟨sg32569,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32574,⟨sg32573,⟨sg32572,True.intro,True.intro⟩,True.intro⟩,⟨sg32575,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_48All : degreeTree62_48.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32554,degreeTree62_46All,degreeTree62_47All⟩ - -lemma degreeTree62_49All : degreeTree62_49.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32587,⟨sg32582,⟨sg32579,⟨sg32578,⟨sg32577,True.intro,True.intro⟩,True.intro⟩,⟨sg32581,⟨sg32580,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32585,⟨sg32584,⟨sg32583,True.intro,True.intro⟩,True.intro⟩,⟨sg32586,True.intro,True.intro⟩⟩⟩,⟨sg32593,⟨sg32590,⟨sg32589,⟨sg32588,True.intro,True.intro⟩,True.intro⟩,⟨sg32592,⟨sg32591,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32596,⟨sg32595,⟨sg32594,True.intro,True.intro⟩,True.intro⟩,⟨sg32597,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_50All : degreeTree62_50.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32609,⟨sg32604,⟨sg32601,⟨sg32600,⟨sg32599,True.intro,True.intro⟩,True.intro⟩,⟨sg32603,⟨sg32602,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32607,⟨sg32606,⟨sg32605,True.intro,True.intro⟩,True.intro⟩,⟨sg32608,True.intro,True.intro⟩⟩⟩,⟨sg32615,⟨sg32612,⟨sg32611,⟨sg32610,True.intro,True.intro⟩,True.intro⟩,⟨sg32614,⟨sg32613,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32618,⟨sg32617,⟨sg32616,True.intro,True.intro⟩,True.intro⟩,⟨sg32619,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_51All : degreeTree62_51.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32598,degreeTree62_49All,degreeTree62_50All⟩ - -lemma degreeTree62_52All : degreeTree62_52.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32576,degreeTree62_48All,degreeTree62_51All⟩ - -lemma degreeTree62_53All : degreeTree62_53.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32631,⟨sg32626,⟨sg32623,⟨sg32622,⟨sg32621,True.intro,True.intro⟩,True.intro⟩,⟨sg32625,⟨sg32624,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32629,⟨sg32628,⟨sg32627,True.intro,True.intro⟩,True.intro⟩,⟨sg32630,True.intro,True.intro⟩⟩⟩,⟨sg32637,⟨sg32634,⟨sg32633,⟨sg32632,True.intro,True.intro⟩,True.intro⟩,⟨sg32636,⟨sg32635,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32640,⟨sg32639,⟨sg32638,True.intro,True.intro⟩,True.intro⟩,⟨sg32641,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_54All : degreeTree62_54.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32653,⟨sg32648,⟨sg32645,⟨sg32644,⟨sg32643,True.intro,True.intro⟩,True.intro⟩,⟨sg32647,⟨sg32646,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32651,⟨sg32650,⟨sg32649,True.intro,True.intro⟩,True.intro⟩,⟨sg32652,True.intro,True.intro⟩⟩⟩,⟨sg32659,⟨sg32656,⟨sg32655,⟨sg32654,True.intro,True.intro⟩,True.intro⟩,⟨sg32658,⟨sg32657,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32662,⟨sg32661,⟨sg32660,True.intro,True.intro⟩,True.intro⟩,⟨sg32663,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_55All : degreeTree62_55.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32642,degreeTree62_53All,degreeTree62_54All⟩ - -lemma degreeTree62_56All : degreeTree62_56.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32675,⟨sg32670,⟨sg32667,⟨sg32666,⟨sg32665,True.intro,True.intro⟩,True.intro⟩,⟨sg32669,⟨sg32668,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32673,⟨sg32672,⟨sg32671,True.intro,True.intro⟩,True.intro⟩,⟨sg32674,True.intro,True.intro⟩⟩⟩,⟨sg32681,⟨sg32678,⟨sg32677,⟨sg32676,True.intro,True.intro⟩,True.intro⟩,⟨sg32680,⟨sg32679,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32684,⟨sg32683,⟨sg32682,True.intro,True.intro⟩,True.intro⟩,⟨sg32685,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_57All : degreeTree62_57.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32697,⟨sg32692,⟨sg32689,⟨sg32688,⟨sg32687,True.intro,True.intro⟩,True.intro⟩,⟨sg32691,⟨sg32690,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32695,⟨sg32694,⟨sg32693,True.intro,True.intro⟩,True.intro⟩,⟨sg32696,True.intro,True.intro⟩⟩⟩,⟨sg32702,⟨sg32700,⟨sg32699,⟨sg32698,True.intro,True.intro⟩,True.intro⟩,⟨sg32701,True.intro,True.intro⟩⟩,⟨sg32705,⟨sg32704,⟨sg32703,True.intro,True.intro⟩,True.intro⟩,⟨sg32706,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_58All : degreeTree62_58.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32686,degreeTree62_56All,degreeTree62_57All⟩ - -lemma degreeTree62_59All : degreeTree62_59.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32664,degreeTree62_55All,degreeTree62_58All⟩ - -lemma degreeTree62_60All : degreeTree62_60.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32620,degreeTree62_52All,degreeTree62_59All⟩ - -lemma degreeTree62_61All : degreeTree62_61.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32532,degreeTree62_45All,degreeTree62_60All⟩ - -lemma degreeTree62_62All : degreeTree62_62.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32356,degreeTree62_30All,degreeTree62_61All⟩ - -lemma degreeTree62_63All : degreeTree62_63.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32718,⟨sg32713,⟨sg32710,⟨sg32709,⟨sg32708,True.intro,True.intro⟩,True.intro⟩,⟨sg32712,⟨sg32711,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32716,⟨sg32715,⟨sg32714,True.intro,True.intro⟩,True.intro⟩,⟨sg32717,True.intro,True.intro⟩⟩⟩,⟨sg32724,⟨sg32721,⟨sg32720,⟨sg32719,True.intro,True.intro⟩,True.intro⟩,⟨sg32723,⟨sg32722,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32727,⟨sg32726,⟨sg32725,True.intro,True.intro⟩,True.intro⟩,⟨sg32728,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_64All : degreeTree62_64.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32740,⟨sg32735,⟨sg32732,⟨sg32731,⟨sg32730,True.intro,True.intro⟩,True.intro⟩,⟨sg32734,⟨sg32733,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32738,⟨sg32737,⟨sg32736,True.intro,True.intro⟩,True.intro⟩,⟨sg32739,True.intro,True.intro⟩⟩⟩,⟨sg32746,⟨sg32743,⟨sg32742,⟨sg32741,True.intro,True.intro⟩,True.intro⟩,⟨sg32745,⟨sg32744,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32749,⟨sg32748,⟨sg32747,True.intro,True.intro⟩,True.intro⟩,⟨sg32750,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_65All : degreeTree62_65.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32729,degreeTree62_63All,degreeTree62_64All⟩ - -lemma degreeTree62_66All : degreeTree62_66.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32762,⟨sg32757,⟨sg32754,⟨sg32753,⟨sg32752,True.intro,True.intro⟩,True.intro⟩,⟨sg32756,⟨sg32755,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32760,⟨sg32759,⟨sg32758,True.intro,True.intro⟩,True.intro⟩,⟨sg32761,True.intro,True.intro⟩⟩⟩,⟨sg32768,⟨sg32765,⟨sg32764,⟨sg32763,True.intro,True.intro⟩,True.intro⟩,⟨sg32767,⟨sg32766,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32771,⟨sg32770,⟨sg32769,True.intro,True.intro⟩,True.intro⟩,⟨sg32772,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_67All : degreeTree62_67.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32784,⟨sg32779,⟨sg32776,⟨sg32775,⟨sg32774,True.intro,True.intro⟩,True.intro⟩,⟨sg32778,⟨sg32777,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32782,⟨sg32781,⟨sg32780,True.intro,True.intro⟩,True.intro⟩,⟨sg32783,True.intro,True.intro⟩⟩⟩,⟨sg32790,⟨sg32787,⟨sg32786,⟨sg32785,True.intro,True.intro⟩,True.intro⟩,⟨sg32789,⟨sg32788,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32793,⟨sg32792,⟨sg32791,True.intro,True.intro⟩,True.intro⟩,⟨sg32794,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_68All : degreeTree62_68.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32773,degreeTree62_66All,degreeTree62_67All⟩ - -lemma degreeTree62_69All : degreeTree62_69.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32751,degreeTree62_65All,degreeTree62_68All⟩ - -lemma degreeTree62_70All : degreeTree62_70.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32806,⟨sg32801,⟨sg32798,⟨sg32797,⟨sg32796,True.intro,True.intro⟩,True.intro⟩,⟨sg32800,⟨sg32799,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32804,⟨sg32803,⟨sg32802,True.intro,True.intro⟩,True.intro⟩,⟨sg32805,True.intro,True.intro⟩⟩⟩,⟨sg32812,⟨sg32809,⟨sg32808,⟨sg32807,True.intro,True.intro⟩,True.intro⟩,⟨sg32811,⟨sg32810,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32815,⟨sg32814,⟨sg32813,True.intro,True.intro⟩,True.intro⟩,⟨sg32816,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_71All : degreeTree62_71.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32828,⟨sg32823,⟨sg32820,⟨sg32819,⟨sg32818,True.intro,True.intro⟩,True.intro⟩,⟨sg32822,⟨sg32821,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32826,⟨sg32825,⟨sg32824,True.intro,True.intro⟩,True.intro⟩,⟨sg32827,True.intro,True.intro⟩⟩⟩,⟨sg32834,⟨sg32831,⟨sg32830,⟨sg32829,True.intro,True.intro⟩,True.intro⟩,⟨sg32833,⟨sg32832,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32837,⟨sg32836,⟨sg32835,True.intro,True.intro⟩,True.intro⟩,⟨sg32838,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_72All : degreeTree62_72.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32817,degreeTree62_70All,degreeTree62_71All⟩ - -lemma degreeTree62_73All : degreeTree62_73.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32850,⟨sg32845,⟨sg32842,⟨sg32841,⟨sg32840,True.intro,True.intro⟩,True.intro⟩,⟨sg32844,⟨sg32843,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32848,⟨sg32847,⟨sg32846,True.intro,True.intro⟩,True.intro⟩,⟨sg32849,True.intro,True.intro⟩⟩⟩,⟨sg32856,⟨sg32853,⟨sg32852,⟨sg32851,True.intro,True.intro⟩,True.intro⟩,⟨sg32855,⟨sg32854,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32859,⟨sg32858,⟨sg32857,True.intro,True.intro⟩,True.intro⟩,⟨sg32860,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_74All : degreeTree62_74.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32872,⟨sg32867,⟨sg32864,⟨sg32863,⟨sg32862,True.intro,True.intro⟩,True.intro⟩,⟨sg32866,⟨sg32865,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32870,⟨sg32869,⟨sg32868,True.intro,True.intro⟩,True.intro⟩,⟨sg32871,True.intro,True.intro⟩⟩⟩,⟨sg32878,⟨sg32875,⟨sg32874,⟨sg32873,True.intro,True.intro⟩,True.intro⟩,⟨sg32877,⟨sg32876,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32881,⟨sg32880,⟨sg32879,True.intro,True.intro⟩,True.intro⟩,⟨sg32882,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_75All : degreeTree62_75.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32861,degreeTree62_73All,degreeTree62_74All⟩ - -lemma degreeTree62_76All : degreeTree62_76.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32839,degreeTree62_72All,degreeTree62_75All⟩ - -lemma degreeTree62_77All : degreeTree62_77.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32795,degreeTree62_69All,degreeTree62_76All⟩ - -lemma degreeTree62_78All : degreeTree62_78.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32894,⟨sg32889,⟨sg32886,⟨sg32885,⟨sg32884,True.intro,True.intro⟩,True.intro⟩,⟨sg32888,⟨sg32887,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32892,⟨sg32891,⟨sg32890,True.intro,True.intro⟩,True.intro⟩,⟨sg32893,True.intro,True.intro⟩⟩⟩,⟨sg32900,⟨sg32897,⟨sg32896,⟨sg32895,True.intro,True.intro⟩,True.intro⟩,⟨sg32899,⟨sg32898,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32903,⟨sg32902,⟨sg32901,True.intro,True.intro⟩,True.intro⟩,⟨sg32904,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_79All : degreeTree62_79.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32916,⟨sg32911,⟨sg32908,⟨sg32907,⟨sg32906,True.intro,True.intro⟩,True.intro⟩,⟨sg32910,⟨sg32909,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32914,⟨sg32913,⟨sg32912,True.intro,True.intro⟩,True.intro⟩,⟨sg32915,True.intro,True.intro⟩⟩⟩,⟨sg32922,⟨sg32919,⟨sg32918,⟨sg32917,True.intro,True.intro⟩,True.intro⟩,⟨sg32921,⟨sg32920,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32925,⟨sg32924,⟨sg32923,True.intro,True.intro⟩,True.intro⟩,⟨sg32926,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_80All : degreeTree62_80.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32905,degreeTree62_78All,degreeTree62_79All⟩ - -lemma degreeTree62_81All : degreeTree62_81.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32938,⟨sg32933,⟨sg32930,⟨sg32929,⟨sg32928,True.intro,True.intro⟩,True.intro⟩,⟨sg32932,⟨sg32931,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32936,⟨sg32935,⟨sg32934,True.intro,True.intro⟩,True.intro⟩,⟨sg32937,True.intro,True.intro⟩⟩⟩,⟨sg32944,⟨sg32941,⟨sg32940,⟨sg32939,True.intro,True.intro⟩,True.intro⟩,⟨sg32943,⟨sg32942,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32947,⟨sg32946,⟨sg32945,True.intro,True.intro⟩,True.intro⟩,⟨sg32948,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_82All : degreeTree62_82.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32960,⟨sg32955,⟨sg32952,⟨sg32951,⟨sg32950,True.intro,True.intro⟩,True.intro⟩,⟨sg32954,⟨sg32953,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32958,⟨sg32957,⟨sg32956,True.intro,True.intro⟩,True.intro⟩,⟨sg32959,True.intro,True.intro⟩⟩⟩,⟨sg32966,⟨sg32963,⟨sg32962,⟨sg32961,True.intro,True.intro⟩,True.intro⟩,⟨sg32965,⟨sg32964,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32969,⟨sg32968,⟨sg32967,True.intro,True.intro⟩,True.intro⟩,⟨sg32970,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_83All : degreeTree62_83.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32949,degreeTree62_81All,degreeTree62_82All⟩ - -lemma degreeTree62_84All : degreeTree62_84.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32927,degreeTree62_80All,degreeTree62_83All⟩ - -lemma degreeTree62_85All : degreeTree62_85.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32982,⟨sg32977,⟨sg32974,⟨sg32973,⟨sg32972,True.intro,True.intro⟩,True.intro⟩,⟨sg32976,⟨sg32975,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32980,⟨sg32979,⟨sg32978,True.intro,True.intro⟩,True.intro⟩,⟨sg32981,True.intro,True.intro⟩⟩⟩,⟨sg32988,⟨sg32985,⟨sg32984,⟨sg32983,True.intro,True.intro⟩,True.intro⟩,⟨sg32987,⟨sg32986,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32991,⟨sg32990,⟨sg32989,True.intro,True.intro⟩,True.intro⟩,⟨sg32992,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_86All : degreeTree62_86.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33004,⟨sg32999,⟨sg32996,⟨sg32995,⟨sg32994,True.intro,True.intro⟩,True.intro⟩,⟨sg32998,⟨sg32997,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33002,⟨sg33001,⟨sg33000,True.intro,True.intro⟩,True.intro⟩,⟨sg33003,True.intro,True.intro⟩⟩⟩,⟨sg33010,⟨sg33007,⟨sg33006,⟨sg33005,True.intro,True.intro⟩,True.intro⟩,⟨sg33009,⟨sg33008,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33013,⟨sg33012,⟨sg33011,True.intro,True.intro⟩,True.intro⟩,⟨sg33014,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_87All : degreeTree62_87.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32993,degreeTree62_85All,degreeTree62_86All⟩ - -lemma degreeTree62_88All : degreeTree62_88.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33026,⟨sg33021,⟨sg33018,⟨sg33017,⟨sg33016,True.intro,True.intro⟩,True.intro⟩,⟨sg33020,⟨sg33019,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33024,⟨sg33023,⟨sg33022,True.intro,True.intro⟩,True.intro⟩,⟨sg33025,True.intro,True.intro⟩⟩⟩,⟨sg33032,⟨sg33029,⟨sg33028,⟨sg33027,True.intro,True.intro⟩,True.intro⟩,⟨sg33031,⟨sg33030,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33035,⟨sg33034,⟨sg33033,True.intro,True.intro⟩,True.intro⟩,⟨sg33036,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_89All : degreeTree62_89.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33048,⟨sg33043,⟨sg33040,⟨sg33039,⟨sg33038,True.intro,True.intro⟩,True.intro⟩,⟨sg33042,⟨sg33041,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33046,⟨sg33045,⟨sg33044,True.intro,True.intro⟩,True.intro⟩,⟨sg33047,True.intro,True.intro⟩⟩⟩,⟨sg33053,⟨sg33051,⟨sg33050,⟨sg33049,True.intro,True.intro⟩,True.intro⟩,⟨sg33052,True.intro,True.intro⟩⟩,⟨sg33056,⟨sg33055,⟨sg33054,True.intro,True.intro⟩,True.intro⟩,⟨sg33057,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_90All : degreeTree62_90.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33037,degreeTree62_88All,degreeTree62_89All⟩ - -lemma degreeTree62_91All : degreeTree62_91.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33015,degreeTree62_87All,degreeTree62_90All⟩ - -lemma degreeTree62_92All : degreeTree62_92.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32971,degreeTree62_84All,degreeTree62_91All⟩ - -lemma degreeTree62_93All : degreeTree62_93.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32883,degreeTree62_77All,degreeTree62_92All⟩ - -lemma degreeTree62_94All : degreeTree62_94.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33069,⟨sg33064,⟨sg33061,⟨sg33060,⟨sg33059,True.intro,True.intro⟩,True.intro⟩,⟨sg33063,⟨sg33062,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33067,⟨sg33066,⟨sg33065,True.intro,True.intro⟩,True.intro⟩,⟨sg33068,True.intro,True.intro⟩⟩⟩,⟨sg33075,⟨sg33072,⟨sg33071,⟨sg33070,True.intro,True.intro⟩,True.intro⟩,⟨sg33074,⟨sg33073,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33078,⟨sg33077,⟨sg33076,True.intro,True.intro⟩,True.intro⟩,⟨sg33079,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_95All : degreeTree62_95.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33091,⟨sg33086,⟨sg33083,⟨sg33082,⟨sg33081,True.intro,True.intro⟩,True.intro⟩,⟨sg33085,⟨sg33084,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33089,⟨sg33088,⟨sg33087,True.intro,True.intro⟩,True.intro⟩,⟨sg33090,True.intro,True.intro⟩⟩⟩,⟨sg33097,⟨sg33094,⟨sg33093,⟨sg33092,True.intro,True.intro⟩,True.intro⟩,⟨sg33096,⟨sg33095,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33100,⟨sg33099,⟨sg33098,True.intro,True.intro⟩,True.intro⟩,⟨sg33101,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_96All : degreeTree62_96.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33080,degreeTree62_94All,degreeTree62_95All⟩ - -lemma degreeTree62_97All : degreeTree62_97.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33113,⟨sg33108,⟨sg33105,⟨sg33104,⟨sg33103,True.intro,True.intro⟩,True.intro⟩,⟨sg33107,⟨sg33106,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33111,⟨sg33110,⟨sg33109,True.intro,True.intro⟩,True.intro⟩,⟨sg33112,True.intro,True.intro⟩⟩⟩,⟨sg33119,⟨sg33116,⟨sg33115,⟨sg33114,True.intro,True.intro⟩,True.intro⟩,⟨sg33118,⟨sg33117,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33122,⟨sg33121,⟨sg33120,True.intro,True.intro⟩,True.intro⟩,⟨sg33123,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_98All : degreeTree62_98.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33135,⟨sg33130,⟨sg33127,⟨sg33126,⟨sg33125,True.intro,True.intro⟩,True.intro⟩,⟨sg33129,⟨sg33128,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33133,⟨sg33132,⟨sg33131,True.intro,True.intro⟩,True.intro⟩,⟨sg33134,True.intro,True.intro⟩⟩⟩,⟨sg33141,⟨sg33138,⟨sg33137,⟨sg33136,True.intro,True.intro⟩,True.intro⟩,⟨sg33140,⟨sg33139,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33144,⟨sg33143,⟨sg33142,True.intro,True.intro⟩,True.intro⟩,⟨sg33145,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_99All : degreeTree62_99.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33124,degreeTree62_97All,degreeTree62_98All⟩ - -lemma degreeTree62_100All : degreeTree62_100.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33102,degreeTree62_96All,degreeTree62_99All⟩ - -lemma degreeTree62_101All : degreeTree62_101.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33157,⟨sg33152,⟨sg33149,⟨sg33148,⟨sg33147,True.intro,True.intro⟩,True.intro⟩,⟨sg33151,⟨sg33150,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33155,⟨sg33154,⟨sg33153,True.intro,True.intro⟩,True.intro⟩,⟨sg33156,True.intro,True.intro⟩⟩⟩,⟨sg33163,⟨sg33160,⟨sg33159,⟨sg33158,True.intro,True.intro⟩,True.intro⟩,⟨sg33162,⟨sg33161,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33166,⟨sg33165,⟨sg33164,True.intro,True.intro⟩,True.intro⟩,⟨sg33167,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_102All : degreeTree62_102.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33179,⟨sg33174,⟨sg33171,⟨sg33170,⟨sg33169,True.intro,True.intro⟩,True.intro⟩,⟨sg33173,⟨sg33172,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33177,⟨sg33176,⟨sg33175,True.intro,True.intro⟩,True.intro⟩,⟨sg33178,True.intro,True.intro⟩⟩⟩,⟨sg33185,⟨sg33182,⟨sg33181,⟨sg33180,True.intro,True.intro⟩,True.intro⟩,⟨sg33184,⟨sg33183,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33188,⟨sg33187,⟨sg33186,True.intro,True.intro⟩,True.intro⟩,⟨sg33189,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_103All : degreeTree62_103.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33168,degreeTree62_101All,degreeTree62_102All⟩ - -lemma degreeTree62_104All : degreeTree62_104.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33201,⟨sg33196,⟨sg33193,⟨sg33192,⟨sg33191,True.intro,True.intro⟩,True.intro⟩,⟨sg33195,⟨sg33194,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33199,⟨sg33198,⟨sg33197,True.intro,True.intro⟩,True.intro⟩,⟨sg33200,True.intro,True.intro⟩⟩⟩,⟨sg33207,⟨sg33204,⟨sg33203,⟨sg33202,True.intro,True.intro⟩,True.intro⟩,⟨sg33206,⟨sg33205,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33210,⟨sg33209,⟨sg33208,True.intro,True.intro⟩,True.intro⟩,⟨sg33211,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_105All : degreeTree62_105.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33223,⟨sg33218,⟨sg33215,⟨sg33214,⟨sg33213,True.intro,True.intro⟩,True.intro⟩,⟨sg33217,⟨sg33216,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33221,⟨sg33220,⟨sg33219,True.intro,True.intro⟩,True.intro⟩,⟨sg33222,True.intro,True.intro⟩⟩⟩,⟨sg33229,⟨sg33226,⟨sg33225,⟨sg33224,True.intro,True.intro⟩,True.intro⟩,⟨sg33228,⟨sg33227,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33232,⟨sg33231,⟨sg33230,True.intro,True.intro⟩,True.intro⟩,⟨sg33233,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_106All : degreeTree62_106.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33212,degreeTree62_104All,degreeTree62_105All⟩ - -lemma degreeTree62_107All : degreeTree62_107.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33190,degreeTree62_103All,degreeTree62_106All⟩ - -lemma degreeTree62_108All : degreeTree62_108.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33146,degreeTree62_100All,degreeTree62_107All⟩ - -lemma degreeTree62_109All : degreeTree62_109.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33245,⟨sg33240,⟨sg33237,⟨sg33236,⟨sg33235,True.intro,True.intro⟩,True.intro⟩,⟨sg33239,⟨sg33238,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33243,⟨sg33242,⟨sg33241,True.intro,True.intro⟩,True.intro⟩,⟨sg33244,True.intro,True.intro⟩⟩⟩,⟨sg33251,⟨sg33248,⟨sg33247,⟨sg33246,True.intro,True.intro⟩,True.intro⟩,⟨sg33250,⟨sg33249,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33254,⟨sg33253,⟨sg33252,True.intro,True.intro⟩,True.intro⟩,⟨sg33255,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_110All : degreeTree62_110.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33267,⟨sg33262,⟨sg33259,⟨sg33258,⟨sg33257,True.intro,True.intro⟩,True.intro⟩,⟨sg33261,⟨sg33260,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33265,⟨sg33264,⟨sg33263,True.intro,True.intro⟩,True.intro⟩,⟨sg33266,True.intro,True.intro⟩⟩⟩,⟨sg33273,⟨sg33270,⟨sg33269,⟨sg33268,True.intro,True.intro⟩,True.intro⟩,⟨sg33272,⟨sg33271,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33276,⟨sg33275,⟨sg33274,True.intro,True.intro⟩,True.intro⟩,⟨sg33277,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_111All : degreeTree62_111.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33256,degreeTree62_109All,degreeTree62_110All⟩ - -lemma degreeTree62_112All : degreeTree62_112.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33289,⟨sg33284,⟨sg33281,⟨sg33280,⟨sg33279,True.intro,True.intro⟩,True.intro⟩,⟨sg33283,⟨sg33282,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33287,⟨sg33286,⟨sg33285,True.intro,True.intro⟩,True.intro⟩,⟨sg33288,True.intro,True.intro⟩⟩⟩,⟨sg33295,⟨sg33292,⟨sg33291,⟨sg33290,True.intro,True.intro⟩,True.intro⟩,⟨sg33294,⟨sg33293,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33298,⟨sg33297,⟨sg33296,True.intro,True.intro⟩,True.intro⟩,⟨sg33299,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_113All : degreeTree62_113.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33311,⟨sg33306,⟨sg33303,⟨sg33302,⟨sg33301,True.intro,True.intro⟩,True.intro⟩,⟨sg33305,⟨sg33304,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33309,⟨sg33308,⟨sg33307,True.intro,True.intro⟩,True.intro⟩,⟨sg33310,True.intro,True.intro⟩⟩⟩,⟨sg33317,⟨sg33314,⟨sg33313,⟨sg33312,True.intro,True.intro⟩,True.intro⟩,⟨sg33316,⟨sg33315,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33320,⟨sg33319,⟨sg33318,True.intro,True.intro⟩,True.intro⟩,⟨sg33321,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_114All : degreeTree62_114.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33300,degreeTree62_112All,degreeTree62_113All⟩ - -lemma degreeTree62_115All : degreeTree62_115.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33278,degreeTree62_111All,degreeTree62_114All⟩ - -lemma degreeTree62_116All : degreeTree62_116.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33333,⟨sg33328,⟨sg33325,⟨sg33324,⟨sg33323,True.intro,True.intro⟩,True.intro⟩,⟨sg33327,⟨sg33326,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33331,⟨sg33330,⟨sg33329,True.intro,True.intro⟩,True.intro⟩,⟨sg33332,True.intro,True.intro⟩⟩⟩,⟨sg33339,⟨sg33336,⟨sg33335,⟨sg33334,True.intro,True.intro⟩,True.intro⟩,⟨sg33338,⟨sg33337,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33342,⟨sg33341,⟨sg33340,True.intro,True.intro⟩,True.intro⟩,⟨sg33343,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_117All : degreeTree62_117.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33355,⟨sg33350,⟨sg33347,⟨sg33346,⟨sg33345,True.intro,True.intro⟩,True.intro⟩,⟨sg33349,⟨sg33348,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33353,⟨sg33352,⟨sg33351,True.intro,True.intro⟩,True.intro⟩,⟨sg33354,True.intro,True.intro⟩⟩⟩,⟨sg33361,⟨sg33358,⟨sg33357,⟨sg33356,True.intro,True.intro⟩,True.intro⟩,⟨sg33360,⟨sg33359,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33364,⟨sg33363,⟨sg33362,True.intro,True.intro⟩,True.intro⟩,⟨sg33365,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_118All : degreeTree62_118.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33344,degreeTree62_116All,degreeTree62_117All⟩ - -lemma degreeTree62_119All : degreeTree62_119.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33377,⟨sg33372,⟨sg33369,⟨sg33368,⟨sg33367,True.intro,True.intro⟩,True.intro⟩,⟨sg33371,⟨sg33370,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33375,⟨sg33374,⟨sg33373,True.intro,True.intro⟩,True.intro⟩,⟨sg33376,True.intro,True.intro⟩⟩⟩,⟨sg33383,⟨sg33380,⟨sg33379,⟨sg33378,True.intro,True.intro⟩,True.intro⟩,⟨sg33382,⟨sg33381,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33386,⟨sg33385,⟨sg33384,True.intro,True.intro⟩,True.intro⟩,⟨sg33387,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_120All : degreeTree62_120.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33399,⟨sg33394,⟨sg33391,⟨sg33390,⟨sg33389,True.intro,True.intro⟩,True.intro⟩,⟨sg33393,⟨sg33392,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33397,⟨sg33396,⟨sg33395,True.intro,True.intro⟩,True.intro⟩,⟨sg33398,True.intro,True.intro⟩⟩⟩,⟨sg33404,⟨sg33402,⟨sg33401,⟨sg33400,True.intro,True.intro⟩,True.intro⟩,⟨sg33403,True.intro,True.intro⟩⟩,⟨sg33407,⟨sg33406,⟨sg33405,True.intro,True.intro⟩,True.intro⟩,⟨sg33408,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_121All : degreeTree62_121.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33388,degreeTree62_119All,degreeTree62_120All⟩ - -lemma degreeTree62_122All : degreeTree62_122.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33366,degreeTree62_118All,degreeTree62_121All⟩ - -lemma degreeTree62_123All : degreeTree62_123.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33322,degreeTree62_115All,degreeTree62_122All⟩ - -lemma degreeTree62_124All : degreeTree62_124.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33234,degreeTree62_108All,degreeTree62_123All⟩ - -lemma degreeTree62_125All : degreeTree62_125.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33058,degreeTree62_93All,degreeTree62_124All⟩ - -lemma degreeTree62_126All : degreeTree62_126.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg32707,degreeTree62_62All,degreeTree62_125All⟩ - -lemma degreeTree62_127All : degreeTree62_127.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33420,⟨sg33415,⟨sg33412,⟨sg33411,⟨sg33410,True.intro,True.intro⟩,True.intro⟩,⟨sg33414,⟨sg33413,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33418,⟨sg33417,⟨sg33416,True.intro,True.intro⟩,True.intro⟩,⟨sg33419,True.intro,True.intro⟩⟩⟩,⟨sg33426,⟨sg33423,⟨sg33422,⟨sg33421,True.intro,True.intro⟩,True.intro⟩,⟨sg33425,⟨sg33424,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33429,⟨sg33428,⟨sg33427,True.intro,True.intro⟩,True.intro⟩,⟨sg33430,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_128All : degreeTree62_128.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33442,⟨sg33437,⟨sg33434,⟨sg33433,⟨sg33432,True.intro,True.intro⟩,True.intro⟩,⟨sg33436,⟨sg33435,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33440,⟨sg33439,⟨sg33438,True.intro,True.intro⟩,True.intro⟩,⟨sg33441,True.intro,True.intro⟩⟩⟩,⟨sg33448,⟨sg33445,⟨sg33444,⟨sg33443,True.intro,True.intro⟩,True.intro⟩,⟨sg33447,⟨sg33446,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33451,⟨sg33450,⟨sg33449,True.intro,True.intro⟩,True.intro⟩,⟨sg33452,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_129All : degreeTree62_129.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33431,degreeTree62_127All,degreeTree62_128All⟩ - -lemma degreeTree62_130All : degreeTree62_130.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33464,⟨sg33459,⟨sg33456,⟨sg33455,⟨sg33454,True.intro,True.intro⟩,True.intro⟩,⟨sg33458,⟨sg33457,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33462,⟨sg33461,⟨sg33460,True.intro,True.intro⟩,True.intro⟩,⟨sg33463,True.intro,True.intro⟩⟩⟩,⟨sg33470,⟨sg33467,⟨sg33466,⟨sg33465,True.intro,True.intro⟩,True.intro⟩,⟨sg33469,⟨sg33468,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33473,⟨sg33472,⟨sg33471,True.intro,True.intro⟩,True.intro⟩,⟨sg33474,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_131All : degreeTree62_131.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33486,⟨sg33481,⟨sg33478,⟨sg33477,⟨sg33476,True.intro,True.intro⟩,True.intro⟩,⟨sg33480,⟨sg33479,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33484,⟨sg33483,⟨sg33482,True.intro,True.intro⟩,True.intro⟩,⟨sg33485,True.intro,True.intro⟩⟩⟩,⟨sg33492,⟨sg33489,⟨sg33488,⟨sg33487,True.intro,True.intro⟩,True.intro⟩,⟨sg33491,⟨sg33490,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33495,⟨sg33494,⟨sg33493,True.intro,True.intro⟩,True.intro⟩,⟨sg33496,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_132All : degreeTree62_132.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33475,degreeTree62_130All,degreeTree62_131All⟩ - -lemma degreeTree62_133All : degreeTree62_133.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33453,degreeTree62_129All,degreeTree62_132All⟩ - -lemma degreeTree62_134All : degreeTree62_134.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33508,⟨sg33503,⟨sg33500,⟨sg33499,⟨sg33498,True.intro,True.intro⟩,True.intro⟩,⟨sg33502,⟨sg33501,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33506,⟨sg33505,⟨sg33504,True.intro,True.intro⟩,True.intro⟩,⟨sg33507,True.intro,True.intro⟩⟩⟩,⟨sg33514,⟨sg33511,⟨sg33510,⟨sg33509,True.intro,True.intro⟩,True.intro⟩,⟨sg33513,⟨sg33512,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33517,⟨sg33516,⟨sg33515,True.intro,True.intro⟩,True.intro⟩,⟨sg33518,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_135All : degreeTree62_135.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33530,⟨sg33525,⟨sg33522,⟨sg33521,⟨sg33520,True.intro,True.intro⟩,True.intro⟩,⟨sg33524,⟨sg33523,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33528,⟨sg33527,⟨sg33526,True.intro,True.intro⟩,True.intro⟩,⟨sg33529,True.intro,True.intro⟩⟩⟩,⟨sg33536,⟨sg33533,⟨sg33532,⟨sg33531,True.intro,True.intro⟩,True.intro⟩,⟨sg33535,⟨sg33534,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33539,⟨sg33538,⟨sg33537,True.intro,True.intro⟩,True.intro⟩,⟨sg33540,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_136All : degreeTree62_136.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33519,degreeTree62_134All,degreeTree62_135All⟩ - -lemma degreeTree62_137All : degreeTree62_137.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33552,⟨sg33547,⟨sg33544,⟨sg33543,⟨sg33542,True.intro,True.intro⟩,True.intro⟩,⟨sg33546,⟨sg33545,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33550,⟨sg33549,⟨sg33548,True.intro,True.intro⟩,True.intro⟩,⟨sg33551,True.intro,True.intro⟩⟩⟩,⟨sg33558,⟨sg33555,⟨sg33554,⟨sg33553,True.intro,True.intro⟩,True.intro⟩,⟨sg33557,⟨sg33556,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33561,⟨sg33560,⟨sg33559,True.intro,True.intro⟩,True.intro⟩,⟨sg33562,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_138All : degreeTree62_138.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33574,⟨sg33569,⟨sg33566,⟨sg33565,⟨sg33564,True.intro,True.intro⟩,True.intro⟩,⟨sg33568,⟨sg33567,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33572,⟨sg33571,⟨sg33570,True.intro,True.intro⟩,True.intro⟩,⟨sg33573,True.intro,True.intro⟩⟩⟩,⟨sg33580,⟨sg33577,⟨sg33576,⟨sg33575,True.intro,True.intro⟩,True.intro⟩,⟨sg33579,⟨sg33578,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33583,⟨sg33582,⟨sg33581,True.intro,True.intro⟩,True.intro⟩,⟨sg33584,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_139All : degreeTree62_139.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33563,degreeTree62_137All,degreeTree62_138All⟩ - -lemma degreeTree62_140All : degreeTree62_140.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33541,degreeTree62_136All,degreeTree62_139All⟩ - -lemma degreeTree62_141All : degreeTree62_141.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33497,degreeTree62_133All,degreeTree62_140All⟩ - -lemma degreeTree62_142All : degreeTree62_142.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33596,⟨sg33591,⟨sg33588,⟨sg33587,⟨sg33586,True.intro,True.intro⟩,True.intro⟩,⟨sg33590,⟨sg33589,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33594,⟨sg33593,⟨sg33592,True.intro,True.intro⟩,True.intro⟩,⟨sg33595,True.intro,True.intro⟩⟩⟩,⟨sg33602,⟨sg33599,⟨sg33598,⟨sg33597,True.intro,True.intro⟩,True.intro⟩,⟨sg33601,⟨sg33600,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33605,⟨sg33604,⟨sg33603,True.intro,True.intro⟩,True.intro⟩,⟨sg33606,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_143All : degreeTree62_143.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33618,⟨sg33613,⟨sg33610,⟨sg33609,⟨sg33608,True.intro,True.intro⟩,True.intro⟩,⟨sg33612,⟨sg33611,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33616,⟨sg33615,⟨sg33614,True.intro,True.intro⟩,True.intro⟩,⟨sg33617,True.intro,True.intro⟩⟩⟩,⟨sg33624,⟨sg33621,⟨sg33620,⟨sg33619,True.intro,True.intro⟩,True.intro⟩,⟨sg33623,⟨sg33622,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33627,⟨sg33626,⟨sg33625,True.intro,True.intro⟩,True.intro⟩,⟨sg33628,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_144All : degreeTree62_144.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33607,degreeTree62_142All,degreeTree62_143All⟩ - -lemma degreeTree62_145All : degreeTree62_145.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33640,⟨sg33635,⟨sg33632,⟨sg33631,⟨sg33630,True.intro,True.intro⟩,True.intro⟩,⟨sg33634,⟨sg33633,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33638,⟨sg33637,⟨sg33636,True.intro,True.intro⟩,True.intro⟩,⟨sg33639,True.intro,True.intro⟩⟩⟩,⟨sg33646,⟨sg33643,⟨sg33642,⟨sg33641,True.intro,True.intro⟩,True.intro⟩,⟨sg33645,⟨sg33644,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33649,⟨sg33648,⟨sg33647,True.intro,True.intro⟩,True.intro⟩,⟨sg33650,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_146All : degreeTree62_146.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33662,⟨sg33657,⟨sg33654,⟨sg33653,⟨sg33652,True.intro,True.intro⟩,True.intro⟩,⟨sg33656,⟨sg33655,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33660,⟨sg33659,⟨sg33658,True.intro,True.intro⟩,True.intro⟩,⟨sg33661,True.intro,True.intro⟩⟩⟩,⟨sg33668,⟨sg33665,⟨sg33664,⟨sg33663,True.intro,True.intro⟩,True.intro⟩,⟨sg33667,⟨sg33666,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33671,⟨sg33670,⟨sg33669,True.intro,True.intro⟩,True.intro⟩,⟨sg33672,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_147All : degreeTree62_147.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33651,degreeTree62_145All,degreeTree62_146All⟩ - -lemma degreeTree62_148All : degreeTree62_148.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33629,degreeTree62_144All,degreeTree62_147All⟩ - -lemma degreeTree62_149All : degreeTree62_149.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33684,⟨sg33679,⟨sg33676,⟨sg33675,⟨sg33674,True.intro,True.intro⟩,True.intro⟩,⟨sg33678,⟨sg33677,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33682,⟨sg33681,⟨sg33680,True.intro,True.intro⟩,True.intro⟩,⟨sg33683,True.intro,True.intro⟩⟩⟩,⟨sg33690,⟨sg33687,⟨sg33686,⟨sg33685,True.intro,True.intro⟩,True.intro⟩,⟨sg33689,⟨sg33688,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33693,⟨sg33692,⟨sg33691,True.intro,True.intro⟩,True.intro⟩,⟨sg33694,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_150All : degreeTree62_150.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33706,⟨sg33701,⟨sg33698,⟨sg33697,⟨sg33696,True.intro,True.intro⟩,True.intro⟩,⟨sg33700,⟨sg33699,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33704,⟨sg33703,⟨sg33702,True.intro,True.intro⟩,True.intro⟩,⟨sg33705,True.intro,True.intro⟩⟩⟩,⟨sg33712,⟨sg33709,⟨sg33708,⟨sg33707,True.intro,True.intro⟩,True.intro⟩,⟨sg33711,⟨sg33710,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33715,⟨sg33714,⟨sg33713,True.intro,True.intro⟩,True.intro⟩,⟨sg33716,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_151All : degreeTree62_151.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33695,degreeTree62_149All,degreeTree62_150All⟩ - -lemma degreeTree62_152All : degreeTree62_152.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33728,⟨sg33723,⟨sg33720,⟨sg33719,⟨sg33718,True.intro,True.intro⟩,True.intro⟩,⟨sg33722,⟨sg33721,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33726,⟨sg33725,⟨sg33724,True.intro,True.intro⟩,True.intro⟩,⟨sg33727,True.intro,True.intro⟩⟩⟩,⟨sg33734,⟨sg33731,⟨sg33730,⟨sg33729,True.intro,True.intro⟩,True.intro⟩,⟨sg33733,⟨sg33732,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33737,⟨sg33736,⟨sg33735,True.intro,True.intro⟩,True.intro⟩,⟨sg33738,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_153All : degreeTree62_153.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33750,⟨sg33745,⟨sg33742,⟨sg33741,⟨sg33740,True.intro,True.intro⟩,True.intro⟩,⟨sg33744,⟨sg33743,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33748,⟨sg33747,⟨sg33746,True.intro,True.intro⟩,True.intro⟩,⟨sg33749,True.intro,True.intro⟩⟩⟩,⟨sg33755,⟨sg33753,⟨sg33752,⟨sg33751,True.intro,True.intro⟩,True.intro⟩,⟨sg33754,True.intro,True.intro⟩⟩,⟨sg33758,⟨sg33757,⟨sg33756,True.intro,True.intro⟩,True.intro⟩,⟨sg33759,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_154All : degreeTree62_154.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33739,degreeTree62_152All,degreeTree62_153All⟩ - -lemma degreeTree62_155All : degreeTree62_155.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33717,degreeTree62_151All,degreeTree62_154All⟩ - -lemma degreeTree62_156All : degreeTree62_156.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33673,degreeTree62_148All,degreeTree62_155All⟩ - -lemma degreeTree62_157All : degreeTree62_157.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33585,degreeTree62_141All,degreeTree62_156All⟩ - -lemma degreeTree62_158All : degreeTree62_158.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33771,⟨sg33766,⟨sg33763,⟨sg33762,⟨sg33761,True.intro,True.intro⟩,True.intro⟩,⟨sg33765,⟨sg33764,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33769,⟨sg33768,⟨sg33767,True.intro,True.intro⟩,True.intro⟩,⟨sg33770,True.intro,True.intro⟩⟩⟩,⟨sg33777,⟨sg33774,⟨sg33773,⟨sg33772,True.intro,True.intro⟩,True.intro⟩,⟨sg33776,⟨sg33775,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33780,⟨sg33779,⟨sg33778,True.intro,True.intro⟩,True.intro⟩,⟨sg33781,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_159All : degreeTree62_159.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33793,⟨sg33788,⟨sg33785,⟨sg33784,⟨sg33783,True.intro,True.intro⟩,True.intro⟩,⟨sg33787,⟨sg33786,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33791,⟨sg33790,⟨sg33789,True.intro,True.intro⟩,True.intro⟩,⟨sg33792,True.intro,True.intro⟩⟩⟩,⟨sg33799,⟨sg33796,⟨sg33795,⟨sg33794,True.intro,True.intro⟩,True.intro⟩,⟨sg33798,⟨sg33797,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33802,⟨sg33801,⟨sg33800,True.intro,True.intro⟩,True.intro⟩,⟨sg33803,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_160All : degreeTree62_160.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33782,degreeTree62_158All,degreeTree62_159All⟩ - -lemma degreeTree62_161All : degreeTree62_161.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33815,⟨sg33810,⟨sg33807,⟨sg33806,⟨sg33805,True.intro,True.intro⟩,True.intro⟩,⟨sg33809,⟨sg33808,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33813,⟨sg33812,⟨sg33811,True.intro,True.intro⟩,True.intro⟩,⟨sg33814,True.intro,True.intro⟩⟩⟩,⟨sg33821,⟨sg33818,⟨sg33817,⟨sg33816,True.intro,True.intro⟩,True.intro⟩,⟨sg33820,⟨sg33819,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33824,⟨sg33823,⟨sg33822,True.intro,True.intro⟩,True.intro⟩,⟨sg33825,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_162All : degreeTree62_162.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33837,⟨sg33832,⟨sg33829,⟨sg33828,⟨sg33827,True.intro,True.intro⟩,True.intro⟩,⟨sg33831,⟨sg33830,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33835,⟨sg33834,⟨sg33833,True.intro,True.intro⟩,True.intro⟩,⟨sg33836,True.intro,True.intro⟩⟩⟩,⟨sg33843,⟨sg33840,⟨sg33839,⟨sg33838,True.intro,True.intro⟩,True.intro⟩,⟨sg33842,⟨sg33841,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33846,⟨sg33845,⟨sg33844,True.intro,True.intro⟩,True.intro⟩,⟨sg33847,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_163All : degreeTree62_163.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33826,degreeTree62_161All,degreeTree62_162All⟩ - -lemma degreeTree62_164All : degreeTree62_164.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33804,degreeTree62_160All,degreeTree62_163All⟩ - -lemma degreeTree62_165All : degreeTree62_165.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33859,⟨sg33854,⟨sg33851,⟨sg33850,⟨sg33849,True.intro,True.intro⟩,True.intro⟩,⟨sg33853,⟨sg33852,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33857,⟨sg33856,⟨sg33855,True.intro,True.intro⟩,True.intro⟩,⟨sg33858,True.intro,True.intro⟩⟩⟩,⟨sg33865,⟨sg33862,⟨sg33861,⟨sg33860,True.intro,True.intro⟩,True.intro⟩,⟨sg33864,⟨sg33863,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33868,⟨sg33867,⟨sg33866,True.intro,True.intro⟩,True.intro⟩,⟨sg33869,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_166All : degreeTree62_166.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33881,⟨sg33876,⟨sg33873,⟨sg33872,⟨sg33871,True.intro,True.intro⟩,True.intro⟩,⟨sg33875,⟨sg33874,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33879,⟨sg33878,⟨sg33877,True.intro,True.intro⟩,True.intro⟩,⟨sg33880,True.intro,True.intro⟩⟩⟩,⟨sg33887,⟨sg33884,⟨sg33883,⟨sg33882,True.intro,True.intro⟩,True.intro⟩,⟨sg33886,⟨sg33885,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33890,⟨sg33889,⟨sg33888,True.intro,True.intro⟩,True.intro⟩,⟨sg33891,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_167All : degreeTree62_167.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33870,degreeTree62_165All,degreeTree62_166All⟩ - -lemma degreeTree62_168All : degreeTree62_168.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33903,⟨sg33898,⟨sg33895,⟨sg33894,⟨sg33893,True.intro,True.intro⟩,True.intro⟩,⟨sg33897,⟨sg33896,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33901,⟨sg33900,⟨sg33899,True.intro,True.intro⟩,True.intro⟩,⟨sg33902,True.intro,True.intro⟩⟩⟩,⟨sg33909,⟨sg33906,⟨sg33905,⟨sg33904,True.intro,True.intro⟩,True.intro⟩,⟨sg33908,⟨sg33907,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33912,⟨sg33911,⟨sg33910,True.intro,True.intro⟩,True.intro⟩,⟨sg33913,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_169All : degreeTree62_169.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33925,⟨sg33920,⟨sg33917,⟨sg33916,⟨sg33915,True.intro,True.intro⟩,True.intro⟩,⟨sg33919,⟨sg33918,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33923,⟨sg33922,⟨sg33921,True.intro,True.intro⟩,True.intro⟩,⟨sg33924,True.intro,True.intro⟩⟩⟩,⟨sg33931,⟨sg33928,⟨sg33927,⟨sg33926,True.intro,True.intro⟩,True.intro⟩,⟨sg33930,⟨sg33929,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33934,⟨sg33933,⟨sg33932,True.intro,True.intro⟩,True.intro⟩,⟨sg33935,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_170All : degreeTree62_170.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33914,degreeTree62_168All,degreeTree62_169All⟩ - -lemma degreeTree62_171All : degreeTree62_171.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33892,degreeTree62_167All,degreeTree62_170All⟩ - -lemma degreeTree62_172All : degreeTree62_172.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33848,degreeTree62_164All,degreeTree62_171All⟩ - -lemma degreeTree62_173All : degreeTree62_173.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33947,⟨sg33942,⟨sg33939,⟨sg33938,⟨sg33937,True.intro,True.intro⟩,True.intro⟩,⟨sg33941,⟨sg33940,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33945,⟨sg33944,⟨sg33943,True.intro,True.intro⟩,True.intro⟩,⟨sg33946,True.intro,True.intro⟩⟩⟩,⟨sg33953,⟨sg33950,⟨sg33949,⟨sg33948,True.intro,True.intro⟩,True.intro⟩,⟨sg33952,⟨sg33951,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33956,⟨sg33955,⟨sg33954,True.intro,True.intro⟩,True.intro⟩,⟨sg33957,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_174All : degreeTree62_174.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33969,⟨sg33964,⟨sg33961,⟨sg33960,⟨sg33959,True.intro,True.intro⟩,True.intro⟩,⟨sg33963,⟨sg33962,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33967,⟨sg33966,⟨sg33965,True.intro,True.intro⟩,True.intro⟩,⟨sg33968,True.intro,True.intro⟩⟩⟩,⟨sg33975,⟨sg33972,⟨sg33971,⟨sg33970,True.intro,True.intro⟩,True.intro⟩,⟨sg33974,⟨sg33973,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33978,⟨sg33977,⟨sg33976,True.intro,True.intro⟩,True.intro⟩,⟨sg33979,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_175All : degreeTree62_175.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33958,degreeTree62_173All,degreeTree62_174All⟩ - -lemma degreeTree62_176All : degreeTree62_176.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33991,⟨sg33986,⟨sg33983,⟨sg33982,⟨sg33981,True.intro,True.intro⟩,True.intro⟩,⟨sg33985,⟨sg33984,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33989,⟨sg33988,⟨sg33987,True.intro,True.intro⟩,True.intro⟩,⟨sg33990,True.intro,True.intro⟩⟩⟩,⟨sg33997,⟨sg33994,⟨sg33993,⟨sg33992,True.intro,True.intro⟩,True.intro⟩,⟨sg33996,⟨sg33995,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34000,⟨sg33999,⟨sg33998,True.intro,True.intro⟩,True.intro⟩,⟨sg34001,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_177All : degreeTree62_177.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34013,⟨sg34008,⟨sg34005,⟨sg34004,⟨sg34003,True.intro,True.intro⟩,True.intro⟩,⟨sg34007,⟨sg34006,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34011,⟨sg34010,⟨sg34009,True.intro,True.intro⟩,True.intro⟩,⟨sg34012,True.intro,True.intro⟩⟩⟩,⟨sg34019,⟨sg34016,⟨sg34015,⟨sg34014,True.intro,True.intro⟩,True.intro⟩,⟨sg34018,⟨sg34017,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34022,⟨sg34021,⟨sg34020,True.intro,True.intro⟩,True.intro⟩,⟨sg34023,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_178All : degreeTree62_178.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34002,degreeTree62_176All,degreeTree62_177All⟩ - -lemma degreeTree62_179All : degreeTree62_179.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33980,degreeTree62_175All,degreeTree62_178All⟩ - -lemma degreeTree62_180All : degreeTree62_180.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34035,⟨sg34030,⟨sg34027,⟨sg34026,⟨sg34025,True.intro,True.intro⟩,True.intro⟩,⟨sg34029,⟨sg34028,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34033,⟨sg34032,⟨sg34031,True.intro,True.intro⟩,True.intro⟩,⟨sg34034,True.intro,True.intro⟩⟩⟩,⟨sg34041,⟨sg34038,⟨sg34037,⟨sg34036,True.intro,True.intro⟩,True.intro⟩,⟨sg34040,⟨sg34039,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34044,⟨sg34043,⟨sg34042,True.intro,True.intro⟩,True.intro⟩,⟨sg34045,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_181All : degreeTree62_181.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34057,⟨sg34052,⟨sg34049,⟨sg34048,⟨sg34047,True.intro,True.intro⟩,True.intro⟩,⟨sg34051,⟨sg34050,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34055,⟨sg34054,⟨sg34053,True.intro,True.intro⟩,True.intro⟩,⟨sg34056,True.intro,True.intro⟩⟩⟩,⟨sg34063,⟨sg34060,⟨sg34059,⟨sg34058,True.intro,True.intro⟩,True.intro⟩,⟨sg34062,⟨sg34061,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34066,⟨sg34065,⟨sg34064,True.intro,True.intro⟩,True.intro⟩,⟨sg34067,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_182All : degreeTree62_182.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34046,degreeTree62_180All,degreeTree62_181All⟩ - -lemma degreeTree62_183All : degreeTree62_183.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34079,⟨sg34074,⟨sg34071,⟨sg34070,⟨sg34069,True.intro,True.intro⟩,True.intro⟩,⟨sg34073,⟨sg34072,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34077,⟨sg34076,⟨sg34075,True.intro,True.intro⟩,True.intro⟩,⟨sg34078,True.intro,True.intro⟩⟩⟩,⟨sg34085,⟨sg34082,⟨sg34081,⟨sg34080,True.intro,True.intro⟩,True.intro⟩,⟨sg34084,⟨sg34083,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34088,⟨sg34087,⟨sg34086,True.intro,True.intro⟩,True.intro⟩,⟨sg34089,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_184All : degreeTree62_184.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34101,⟨sg34096,⟨sg34093,⟨sg34092,⟨sg34091,True.intro,True.intro⟩,True.intro⟩,⟨sg34095,⟨sg34094,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34099,⟨sg34098,⟨sg34097,True.intro,True.intro⟩,True.intro⟩,⟨sg34100,True.intro,True.intro⟩⟩⟩,⟨sg34106,⟨sg34104,⟨sg34103,⟨sg34102,True.intro,True.intro⟩,True.intro⟩,⟨sg34105,True.intro,True.intro⟩⟩,⟨sg34109,⟨sg34108,⟨sg34107,True.intro,True.intro⟩,True.intro⟩,⟨sg34110,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_185All : degreeTree62_185.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34090,degreeTree62_183All,degreeTree62_184All⟩ - -lemma degreeTree62_186All : degreeTree62_186.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34068,degreeTree62_182All,degreeTree62_185All⟩ - -lemma degreeTree62_187All : degreeTree62_187.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34024,degreeTree62_179All,degreeTree62_186All⟩ - -lemma degreeTree62_188All : degreeTree62_188.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33936,degreeTree62_172All,degreeTree62_187All⟩ - -lemma degreeTree62_189All : degreeTree62_189.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33760,degreeTree62_157All,degreeTree62_188All⟩ - -lemma degreeTree62_190All : degreeTree62_190.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34122,⟨sg34117,⟨sg34114,⟨sg34113,⟨sg34112,True.intro,True.intro⟩,True.intro⟩,⟨sg34116,⟨sg34115,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34120,⟨sg34119,⟨sg34118,True.intro,True.intro⟩,True.intro⟩,⟨sg34121,True.intro,True.intro⟩⟩⟩,⟨sg34128,⟨sg34125,⟨sg34124,⟨sg34123,True.intro,True.intro⟩,True.intro⟩,⟨sg34127,⟨sg34126,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34131,⟨sg34130,⟨sg34129,True.intro,True.intro⟩,True.intro⟩,⟨sg34132,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_191All : degreeTree62_191.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34144,⟨sg34139,⟨sg34136,⟨sg34135,⟨sg34134,True.intro,True.intro⟩,True.intro⟩,⟨sg34138,⟨sg34137,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34142,⟨sg34141,⟨sg34140,True.intro,True.intro⟩,True.intro⟩,⟨sg34143,True.intro,True.intro⟩⟩⟩,⟨sg34150,⟨sg34147,⟨sg34146,⟨sg34145,True.intro,True.intro⟩,True.intro⟩,⟨sg34149,⟨sg34148,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34153,⟨sg34152,⟨sg34151,True.intro,True.intro⟩,True.intro⟩,⟨sg34154,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_192All : degreeTree62_192.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34133,degreeTree62_190All,degreeTree62_191All⟩ - -lemma degreeTree62_193All : degreeTree62_193.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34166,⟨sg34161,⟨sg34158,⟨sg34157,⟨sg34156,True.intro,True.intro⟩,True.intro⟩,⟨sg34160,⟨sg34159,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34164,⟨sg34163,⟨sg34162,True.intro,True.intro⟩,True.intro⟩,⟨sg34165,True.intro,True.intro⟩⟩⟩,⟨sg34172,⟨sg34169,⟨sg34168,⟨sg34167,True.intro,True.intro⟩,True.intro⟩,⟨sg34171,⟨sg34170,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34175,⟨sg34174,⟨sg34173,True.intro,True.intro⟩,True.intro⟩,⟨sg34176,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_194All : degreeTree62_194.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34188,⟨sg34183,⟨sg34180,⟨sg34179,⟨sg34178,True.intro,True.intro⟩,True.intro⟩,⟨sg34182,⟨sg34181,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34186,⟨sg34185,⟨sg34184,True.intro,True.intro⟩,True.intro⟩,⟨sg34187,True.intro,True.intro⟩⟩⟩,⟨sg34194,⟨sg34191,⟨sg34190,⟨sg34189,True.intro,True.intro⟩,True.intro⟩,⟨sg34193,⟨sg34192,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34197,⟨sg34196,⟨sg34195,True.intro,True.intro⟩,True.intro⟩,⟨sg34198,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_195All : degreeTree62_195.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34177,degreeTree62_193All,degreeTree62_194All⟩ - -lemma degreeTree62_196All : degreeTree62_196.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34155,degreeTree62_192All,degreeTree62_195All⟩ - -lemma degreeTree62_197All : degreeTree62_197.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34210,⟨sg34205,⟨sg34202,⟨sg34201,⟨sg34200,True.intro,True.intro⟩,True.intro⟩,⟨sg34204,⟨sg34203,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34208,⟨sg34207,⟨sg34206,True.intro,True.intro⟩,True.intro⟩,⟨sg34209,True.intro,True.intro⟩⟩⟩,⟨sg34216,⟨sg34213,⟨sg34212,⟨sg34211,True.intro,True.intro⟩,True.intro⟩,⟨sg34215,⟨sg34214,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34219,⟨sg34218,⟨sg34217,True.intro,True.intro⟩,True.intro⟩,⟨sg34220,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_198All : degreeTree62_198.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34232,⟨sg34227,⟨sg34224,⟨sg34223,⟨sg34222,True.intro,True.intro⟩,True.intro⟩,⟨sg34226,⟨sg34225,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34230,⟨sg34229,⟨sg34228,True.intro,True.intro⟩,True.intro⟩,⟨sg34231,True.intro,True.intro⟩⟩⟩,⟨sg34238,⟨sg34235,⟨sg34234,⟨sg34233,True.intro,True.intro⟩,True.intro⟩,⟨sg34237,⟨sg34236,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34241,⟨sg34240,⟨sg34239,True.intro,True.intro⟩,True.intro⟩,⟨sg34242,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_199All : degreeTree62_199.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34221,degreeTree62_197All,degreeTree62_198All⟩ - -lemma degreeTree62_200All : degreeTree62_200.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34254,⟨sg34249,⟨sg34246,⟨sg34245,⟨sg34244,True.intro,True.intro⟩,True.intro⟩,⟨sg34248,⟨sg34247,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34252,⟨sg34251,⟨sg34250,True.intro,True.intro⟩,True.intro⟩,⟨sg34253,True.intro,True.intro⟩⟩⟩,⟨sg34260,⟨sg34257,⟨sg34256,⟨sg34255,True.intro,True.intro⟩,True.intro⟩,⟨sg34259,⟨sg34258,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34263,⟨sg34262,⟨sg34261,True.intro,True.intro⟩,True.intro⟩,⟨sg34264,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_201All : degreeTree62_201.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34276,⟨sg34271,⟨sg34268,⟨sg34267,⟨sg34266,True.intro,True.intro⟩,True.intro⟩,⟨sg34270,⟨sg34269,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34274,⟨sg34273,⟨sg34272,True.intro,True.intro⟩,True.intro⟩,⟨sg34275,True.intro,True.intro⟩⟩⟩,⟨sg34282,⟨sg34279,⟨sg34278,⟨sg34277,True.intro,True.intro⟩,True.intro⟩,⟨sg34281,⟨sg34280,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34285,⟨sg34284,⟨sg34283,True.intro,True.intro⟩,True.intro⟩,⟨sg34286,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_202All : degreeTree62_202.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34265,degreeTree62_200All,degreeTree62_201All⟩ - -lemma degreeTree62_203All : degreeTree62_203.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34243,degreeTree62_199All,degreeTree62_202All⟩ - -lemma degreeTree62_204All : degreeTree62_204.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34199,degreeTree62_196All,degreeTree62_203All⟩ - -lemma degreeTree62_205All : degreeTree62_205.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34298,⟨sg34293,⟨sg34290,⟨sg34289,⟨sg34288,True.intro,True.intro⟩,True.intro⟩,⟨sg34292,⟨sg34291,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34296,⟨sg34295,⟨sg34294,True.intro,True.intro⟩,True.intro⟩,⟨sg34297,True.intro,True.intro⟩⟩⟩,⟨sg34304,⟨sg34301,⟨sg34300,⟨sg34299,True.intro,True.intro⟩,True.intro⟩,⟨sg34303,⟨sg34302,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34307,⟨sg34306,⟨sg34305,True.intro,True.intro⟩,True.intro⟩,⟨sg34308,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_206All : degreeTree62_206.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34320,⟨sg34315,⟨sg34312,⟨sg34311,⟨sg34310,True.intro,True.intro⟩,True.intro⟩,⟨sg34314,⟨sg34313,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34318,⟨sg34317,⟨sg34316,True.intro,True.intro⟩,True.intro⟩,⟨sg34319,True.intro,True.intro⟩⟩⟩,⟨sg34326,⟨sg34323,⟨sg34322,⟨sg34321,True.intro,True.intro⟩,True.intro⟩,⟨sg34325,⟨sg34324,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34329,⟨sg34328,⟨sg34327,True.intro,True.intro⟩,True.intro⟩,⟨sg34330,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_207All : degreeTree62_207.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34309,degreeTree62_205All,degreeTree62_206All⟩ - -lemma degreeTree62_208All : degreeTree62_208.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34342,⟨sg34337,⟨sg34334,⟨sg34333,⟨sg34332,True.intro,True.intro⟩,True.intro⟩,⟨sg34336,⟨sg34335,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34340,⟨sg34339,⟨sg34338,True.intro,True.intro⟩,True.intro⟩,⟨sg34341,True.intro,True.intro⟩⟩⟩,⟨sg34348,⟨sg34345,⟨sg34344,⟨sg34343,True.intro,True.intro⟩,True.intro⟩,⟨sg34347,⟨sg34346,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34351,⟨sg34350,⟨sg34349,True.intro,True.intro⟩,True.intro⟩,⟨sg34352,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_209All : degreeTree62_209.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34364,⟨sg34359,⟨sg34356,⟨sg34355,⟨sg34354,True.intro,True.intro⟩,True.intro⟩,⟨sg34358,⟨sg34357,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34362,⟨sg34361,⟨sg34360,True.intro,True.intro⟩,True.intro⟩,⟨sg34363,True.intro,True.intro⟩⟩⟩,⟨sg34370,⟨sg34367,⟨sg34366,⟨sg34365,True.intro,True.intro⟩,True.intro⟩,⟨sg34369,⟨sg34368,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34373,⟨sg34372,⟨sg34371,True.intro,True.intro⟩,True.intro⟩,⟨sg34374,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_210All : degreeTree62_210.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34353,degreeTree62_208All,degreeTree62_209All⟩ - -lemma degreeTree62_211All : degreeTree62_211.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34331,degreeTree62_207All,degreeTree62_210All⟩ - -lemma degreeTree62_212All : degreeTree62_212.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34386,⟨sg34381,⟨sg34378,⟨sg34377,⟨sg34376,True.intro,True.intro⟩,True.intro⟩,⟨sg34380,⟨sg34379,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34384,⟨sg34383,⟨sg34382,True.intro,True.intro⟩,True.intro⟩,⟨sg34385,True.intro,True.intro⟩⟩⟩,⟨sg34392,⟨sg34389,⟨sg34388,⟨sg34387,True.intro,True.intro⟩,True.intro⟩,⟨sg34391,⟨sg34390,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34395,⟨sg34394,⟨sg34393,True.intro,True.intro⟩,True.intro⟩,⟨sg34396,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_213All : degreeTree62_213.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34408,⟨sg34403,⟨sg34400,⟨sg34399,⟨sg34398,True.intro,True.intro⟩,True.intro⟩,⟨sg34402,⟨sg34401,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34406,⟨sg34405,⟨sg34404,True.intro,True.intro⟩,True.intro⟩,⟨sg34407,True.intro,True.intro⟩⟩⟩,⟨sg34414,⟨sg34411,⟨sg34410,⟨sg34409,True.intro,True.intro⟩,True.intro⟩,⟨sg34413,⟨sg34412,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34417,⟨sg34416,⟨sg34415,True.intro,True.intro⟩,True.intro⟩,⟨sg34418,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_214All : degreeTree62_214.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34397,degreeTree62_212All,degreeTree62_213All⟩ - -lemma degreeTree62_215All : degreeTree62_215.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34430,⟨sg34425,⟨sg34422,⟨sg34421,⟨sg34420,True.intro,True.intro⟩,True.intro⟩,⟨sg34424,⟨sg34423,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34428,⟨sg34427,⟨sg34426,True.intro,True.intro⟩,True.intro⟩,⟨sg34429,True.intro,True.intro⟩⟩⟩,⟨sg34436,⟨sg34433,⟨sg34432,⟨sg34431,True.intro,True.intro⟩,True.intro⟩,⟨sg34435,⟨sg34434,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34439,⟨sg34438,⟨sg34437,True.intro,True.intro⟩,True.intro⟩,⟨sg34440,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_216All : degreeTree62_216.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34452,⟨sg34447,⟨sg34444,⟨sg34443,⟨sg34442,True.intro,True.intro⟩,True.intro⟩,⟨sg34446,⟨sg34445,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34450,⟨sg34449,⟨sg34448,True.intro,True.intro⟩,True.intro⟩,⟨sg34451,True.intro,True.intro⟩⟩⟩,⟨sg34457,⟨sg34455,⟨sg34454,⟨sg34453,True.intro,True.intro⟩,True.intro⟩,⟨sg34456,True.intro,True.intro⟩⟩,⟨sg34460,⟨sg34459,⟨sg34458,True.intro,True.intro⟩,True.intro⟩,⟨sg34461,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_217All : degreeTree62_217.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34441,degreeTree62_215All,degreeTree62_216All⟩ - -lemma degreeTree62_218All : degreeTree62_218.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34419,degreeTree62_214All,degreeTree62_217All⟩ - -lemma degreeTree62_219All : degreeTree62_219.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34375,degreeTree62_211All,degreeTree62_218All⟩ - -lemma degreeTree62_220All : degreeTree62_220.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34287,degreeTree62_204All,degreeTree62_219All⟩ - -lemma degreeTree62_221All : degreeTree62_221.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34473,⟨sg34468,⟨sg34465,⟨sg34464,⟨sg34463,True.intro,True.intro⟩,True.intro⟩,⟨sg34467,⟨sg34466,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34471,⟨sg34470,⟨sg34469,True.intro,True.intro⟩,True.intro⟩,⟨sg34472,True.intro,True.intro⟩⟩⟩,⟨sg34479,⟨sg34476,⟨sg34475,⟨sg34474,True.intro,True.intro⟩,True.intro⟩,⟨sg34478,⟨sg34477,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34482,⟨sg34481,⟨sg34480,True.intro,True.intro⟩,True.intro⟩,⟨sg34483,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_222All : degreeTree62_222.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34495,⟨sg34490,⟨sg34487,⟨sg34486,⟨sg34485,True.intro,True.intro⟩,True.intro⟩,⟨sg34489,⟨sg34488,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34493,⟨sg34492,⟨sg34491,True.intro,True.intro⟩,True.intro⟩,⟨sg34494,True.intro,True.intro⟩⟩⟩,⟨sg34501,⟨sg34498,⟨sg34497,⟨sg34496,True.intro,True.intro⟩,True.intro⟩,⟨sg34500,⟨sg34499,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34504,⟨sg34503,⟨sg34502,True.intro,True.intro⟩,True.intro⟩,⟨sg34505,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_223All : degreeTree62_223.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34484,degreeTree62_221All,degreeTree62_222All⟩ - -lemma degreeTree62_224All : degreeTree62_224.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34517,⟨sg34512,⟨sg34509,⟨sg34508,⟨sg34507,True.intro,True.intro⟩,True.intro⟩,⟨sg34511,⟨sg34510,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34515,⟨sg34514,⟨sg34513,True.intro,True.intro⟩,True.intro⟩,⟨sg34516,True.intro,True.intro⟩⟩⟩,⟨sg34523,⟨sg34520,⟨sg34519,⟨sg34518,True.intro,True.intro⟩,True.intro⟩,⟨sg34522,⟨sg34521,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34526,⟨sg34525,⟨sg34524,True.intro,True.intro⟩,True.intro⟩,⟨sg34527,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_225All : degreeTree62_225.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34539,⟨sg34534,⟨sg34531,⟨sg34530,⟨sg34529,True.intro,True.intro⟩,True.intro⟩,⟨sg34533,⟨sg34532,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34537,⟨sg34536,⟨sg34535,True.intro,True.intro⟩,True.intro⟩,⟨sg34538,True.intro,True.intro⟩⟩⟩,⟨sg34545,⟨sg34542,⟨sg34541,⟨sg34540,True.intro,True.intro⟩,True.intro⟩,⟨sg34544,⟨sg34543,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34548,⟨sg34547,⟨sg34546,True.intro,True.intro⟩,True.intro⟩,⟨sg34549,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_226All : degreeTree62_226.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34528,degreeTree62_224All,degreeTree62_225All⟩ - -lemma degreeTree62_227All : degreeTree62_227.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34506,degreeTree62_223All,degreeTree62_226All⟩ - -lemma degreeTree62_228All : degreeTree62_228.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34561,⟨sg34556,⟨sg34553,⟨sg34552,⟨sg34551,True.intro,True.intro⟩,True.intro⟩,⟨sg34555,⟨sg34554,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34559,⟨sg34558,⟨sg34557,True.intro,True.intro⟩,True.intro⟩,⟨sg34560,True.intro,True.intro⟩⟩⟩,⟨sg34567,⟨sg34564,⟨sg34563,⟨sg34562,True.intro,True.intro⟩,True.intro⟩,⟨sg34566,⟨sg34565,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34570,⟨sg34569,⟨sg34568,True.intro,True.intro⟩,True.intro⟩,⟨sg34571,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_229All : degreeTree62_229.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34583,⟨sg34578,⟨sg34575,⟨sg34574,⟨sg34573,True.intro,True.intro⟩,True.intro⟩,⟨sg34577,⟨sg34576,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34581,⟨sg34580,⟨sg34579,True.intro,True.intro⟩,True.intro⟩,⟨sg34582,True.intro,True.intro⟩⟩⟩,⟨sg34589,⟨sg34586,⟨sg34585,⟨sg34584,True.intro,True.intro⟩,True.intro⟩,⟨sg34588,⟨sg34587,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34592,⟨sg34591,⟨sg34590,True.intro,True.intro⟩,True.intro⟩,⟨sg34593,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_230All : degreeTree62_230.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34572,degreeTree62_228All,degreeTree62_229All⟩ - -lemma degreeTree62_231All : degreeTree62_231.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34605,⟨sg34600,⟨sg34597,⟨sg34596,⟨sg34595,True.intro,True.intro⟩,True.intro⟩,⟨sg34599,⟨sg34598,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34603,⟨sg34602,⟨sg34601,True.intro,True.intro⟩,True.intro⟩,⟨sg34604,True.intro,True.intro⟩⟩⟩,⟨sg34611,⟨sg34608,⟨sg34607,⟨sg34606,True.intro,True.intro⟩,True.intro⟩,⟨sg34610,⟨sg34609,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34614,⟨sg34613,⟨sg34612,True.intro,True.intro⟩,True.intro⟩,⟨sg34615,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_232All : degreeTree62_232.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34627,⟨sg34622,⟨sg34619,⟨sg34618,⟨sg34617,True.intro,True.intro⟩,True.intro⟩,⟨sg34621,⟨sg34620,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34625,⟨sg34624,⟨sg34623,True.intro,True.intro⟩,True.intro⟩,⟨sg34626,True.intro,True.intro⟩⟩⟩,⟨sg34632,⟨sg34630,⟨sg34629,⟨sg34628,True.intro,True.intro⟩,True.intro⟩,⟨sg34631,True.intro,True.intro⟩⟩,⟨sg34635,⟨sg34634,⟨sg34633,True.intro,True.intro⟩,True.intro⟩,⟨sg34636,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_233All : degreeTree62_233.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34616,degreeTree62_231All,degreeTree62_232All⟩ - -lemma degreeTree62_234All : degreeTree62_234.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34594,degreeTree62_230All,degreeTree62_233All⟩ - -lemma degreeTree62_235All : degreeTree62_235.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34550,degreeTree62_227All,degreeTree62_234All⟩ - -lemma degreeTree62_236All : degreeTree62_236.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34648,⟨sg34643,⟨sg34640,⟨sg34639,⟨sg34638,True.intro,True.intro⟩,True.intro⟩,⟨sg34642,⟨sg34641,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34646,⟨sg34645,⟨sg34644,True.intro,True.intro⟩,True.intro⟩,⟨sg34647,True.intro,True.intro⟩⟩⟩,⟨sg34654,⟨sg34651,⟨sg34650,⟨sg34649,True.intro,True.intro⟩,True.intro⟩,⟨sg34653,⟨sg34652,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34657,⟨sg34656,⟨sg34655,True.intro,True.intro⟩,True.intro⟩,⟨sg34658,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_237All : degreeTree62_237.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34670,⟨sg34665,⟨sg34662,⟨sg34661,⟨sg34660,True.intro,True.intro⟩,True.intro⟩,⟨sg34664,⟨sg34663,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34668,⟨sg34667,⟨sg34666,True.intro,True.intro⟩,True.intro⟩,⟨sg34669,True.intro,True.intro⟩⟩⟩,⟨sg34676,⟨sg34673,⟨sg34672,⟨sg34671,True.intro,True.intro⟩,True.intro⟩,⟨sg34675,⟨sg34674,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34679,⟨sg34678,⟨sg34677,True.intro,True.intro⟩,True.intro⟩,⟨sg34680,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_238All : degreeTree62_238.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34659,degreeTree62_236All,degreeTree62_237All⟩ - -lemma degreeTree62_239All : degreeTree62_239.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34692,⟨sg34687,⟨sg34684,⟨sg34683,⟨sg34682,True.intro,True.intro⟩,True.intro⟩,⟨sg34686,⟨sg34685,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34690,⟨sg34689,⟨sg34688,True.intro,True.intro⟩,True.intro⟩,⟨sg34691,True.intro,True.intro⟩⟩⟩,⟨sg34698,⟨sg34695,⟨sg34694,⟨sg34693,True.intro,True.intro⟩,True.intro⟩,⟨sg34697,⟨sg34696,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34701,⟨sg34700,⟨sg34699,True.intro,True.intro⟩,True.intro⟩,⟨sg34702,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_240All : degreeTree62_240.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34714,⟨sg34709,⟨sg34706,⟨sg34705,⟨sg34704,True.intro,True.intro⟩,True.intro⟩,⟨sg34708,⟨sg34707,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34712,⟨sg34711,⟨sg34710,True.intro,True.intro⟩,True.intro⟩,⟨sg34713,True.intro,True.intro⟩⟩⟩,⟨sg34720,⟨sg34717,⟨sg34716,⟨sg34715,True.intro,True.intro⟩,True.intro⟩,⟨sg34719,⟨sg34718,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34723,⟨sg34722,⟨sg34721,True.intro,True.intro⟩,True.intro⟩,⟨sg34724,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_241All : degreeTree62_241.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34703,degreeTree62_239All,degreeTree62_240All⟩ - -lemma degreeTree62_242All : degreeTree62_242.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34681,degreeTree62_238All,degreeTree62_241All⟩ - -lemma degreeTree62_243All : degreeTree62_243.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34736,⟨sg34731,⟨sg34728,⟨sg34727,⟨sg34726,True.intro,True.intro⟩,True.intro⟩,⟨sg34730,⟨sg34729,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34734,⟨sg34733,⟨sg34732,True.intro,True.intro⟩,True.intro⟩,⟨sg34735,True.intro,True.intro⟩⟩⟩,⟨sg34742,⟨sg34739,⟨sg34738,⟨sg34737,True.intro,True.intro⟩,True.intro⟩,⟨sg34741,⟨sg34740,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34745,⟨sg34744,⟨sg34743,True.intro,True.intro⟩,True.intro⟩,⟨sg34746,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_244All : degreeTree62_244.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34758,⟨sg34753,⟨sg34750,⟨sg34749,⟨sg34748,True.intro,True.intro⟩,True.intro⟩,⟨sg34752,⟨sg34751,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34756,⟨sg34755,⟨sg34754,True.intro,True.intro⟩,True.intro⟩,⟨sg34757,True.intro,True.intro⟩⟩⟩,⟨sg34764,⟨sg34761,⟨sg34760,⟨sg34759,True.intro,True.intro⟩,True.intro⟩,⟨sg34763,⟨sg34762,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34767,⟨sg34766,⟨sg34765,True.intro,True.intro⟩,True.intro⟩,⟨sg34768,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_245All : degreeTree62_245.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34747,degreeTree62_243All,degreeTree62_244All⟩ - -lemma degreeTree62_246All : degreeTree62_246.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34780,⟨sg34775,⟨sg34772,⟨sg34771,⟨sg34770,True.intro,True.intro⟩,True.intro⟩,⟨sg34774,⟨sg34773,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34778,⟨sg34777,⟨sg34776,True.intro,True.intro⟩,True.intro⟩,⟨sg34779,True.intro,True.intro⟩⟩⟩,⟨sg34786,⟨sg34783,⟨sg34782,⟨sg34781,True.intro,True.intro⟩,True.intro⟩,⟨sg34785,⟨sg34784,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34789,⟨sg34788,⟨sg34787,True.intro,True.intro⟩,True.intro⟩,⟨sg34790,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_247All : degreeTree62_247.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34802,⟨sg34797,⟨sg34794,⟨sg34793,⟨sg34792,True.intro,True.intro⟩,True.intro⟩,⟨sg34796,⟨sg34795,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34800,⟨sg34799,⟨sg34798,True.intro,True.intro⟩,True.intro⟩,⟨sg34801,True.intro,True.intro⟩⟩⟩,⟨sg34807,⟨sg34805,⟨sg34804,⟨sg34803,True.intro,True.intro⟩,True.intro⟩,⟨sg34806,True.intro,True.intro⟩⟩,⟨sg34810,⟨sg34809,⟨sg34808,True.intro,True.intro⟩,True.intro⟩,⟨sg34811,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_248All : degreeTree62_248.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34791,degreeTree62_246All,degreeTree62_247All⟩ - -lemma degreeTree62_249All : degreeTree62_249.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34769,degreeTree62_245All,degreeTree62_248All⟩ - -lemma degreeTree62_250All : degreeTree62_250.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34725,degreeTree62_242All,degreeTree62_249All⟩ - -lemma degreeTree62_251All : degreeTree62_251.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34637,degreeTree62_235All,degreeTree62_250All⟩ - -lemma degreeTree62_252All : degreeTree62_252.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34462,degreeTree62_220All,degreeTree62_251All⟩ - -lemma degreeTree62_253All : degreeTree62_253.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34111,degreeTree62_189All,degreeTree62_252All⟩ - -lemma degreeTree62_254All : degreeTree62_254.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg33409,degreeTree62_126All,degreeTree62_253All⟩ - -lemma degreeTree62_255All : degreeTree62_255.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34823,⟨sg34818,⟨sg34815,⟨sg34814,⟨sg34813,True.intro,True.intro⟩,True.intro⟩,⟨sg34817,⟨sg34816,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34821,⟨sg34820,⟨sg34819,True.intro,True.intro⟩,True.intro⟩,⟨sg34822,True.intro,True.intro⟩⟩⟩,⟨sg34829,⟨sg34826,⟨sg34825,⟨sg34824,True.intro,True.intro⟩,True.intro⟩,⟨sg34828,⟨sg34827,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34832,⟨sg34831,⟨sg34830,True.intro,True.intro⟩,True.intro⟩,⟨sg34833,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_256All : degreeTree62_256.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34845,⟨sg34840,⟨sg34837,⟨sg34836,⟨sg34835,True.intro,True.intro⟩,True.intro⟩,⟨sg34839,⟨sg34838,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34843,⟨sg34842,⟨sg34841,True.intro,True.intro⟩,True.intro⟩,⟨sg34844,True.intro,True.intro⟩⟩⟩,⟨sg34851,⟨sg34848,⟨sg34847,⟨sg34846,True.intro,True.intro⟩,True.intro⟩,⟨sg34850,⟨sg34849,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34854,⟨sg34853,⟨sg34852,True.intro,True.intro⟩,True.intro⟩,⟨sg34855,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_257All : degreeTree62_257.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34834,degreeTree62_255All,degreeTree62_256All⟩ - -lemma degreeTree62_258All : degreeTree62_258.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34867,⟨sg34862,⟨sg34859,⟨sg34858,⟨sg34857,True.intro,True.intro⟩,True.intro⟩,⟨sg34861,⟨sg34860,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34865,⟨sg34864,⟨sg34863,True.intro,True.intro⟩,True.intro⟩,⟨sg34866,True.intro,True.intro⟩⟩⟩,⟨sg34873,⟨sg34870,⟨sg34869,⟨sg34868,True.intro,True.intro⟩,True.intro⟩,⟨sg34872,⟨sg34871,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34876,⟨sg34875,⟨sg34874,True.intro,True.intro⟩,True.intro⟩,⟨sg34877,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_259All : degreeTree62_259.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34889,⟨sg34884,⟨sg34881,⟨sg34880,⟨sg34879,True.intro,True.intro⟩,True.intro⟩,⟨sg34883,⟨sg34882,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34887,⟨sg34886,⟨sg34885,True.intro,True.intro⟩,True.intro⟩,⟨sg34888,True.intro,True.intro⟩⟩⟩,⟨sg34895,⟨sg34892,⟨sg34891,⟨sg34890,True.intro,True.intro⟩,True.intro⟩,⟨sg34894,⟨sg34893,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34898,⟨sg34897,⟨sg34896,True.intro,True.intro⟩,True.intro⟩,⟨sg34899,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_260All : degreeTree62_260.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34878,degreeTree62_258All,degreeTree62_259All⟩ - -lemma degreeTree62_261All : degreeTree62_261.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34856,degreeTree62_257All,degreeTree62_260All⟩ - -lemma degreeTree62_262All : degreeTree62_262.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34911,⟨sg34906,⟨sg34903,⟨sg34902,⟨sg34901,True.intro,True.intro⟩,True.intro⟩,⟨sg34905,⟨sg34904,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34909,⟨sg34908,⟨sg34907,True.intro,True.intro⟩,True.intro⟩,⟨sg34910,True.intro,True.intro⟩⟩⟩,⟨sg34917,⟨sg34914,⟨sg34913,⟨sg34912,True.intro,True.intro⟩,True.intro⟩,⟨sg34916,⟨sg34915,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34920,⟨sg34919,⟨sg34918,True.intro,True.intro⟩,True.intro⟩,⟨sg34921,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_263All : degreeTree62_263.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34933,⟨sg34928,⟨sg34925,⟨sg34924,⟨sg34923,True.intro,True.intro⟩,True.intro⟩,⟨sg34927,⟨sg34926,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34931,⟨sg34930,⟨sg34929,True.intro,True.intro⟩,True.intro⟩,⟨sg34932,True.intro,True.intro⟩⟩⟩,⟨sg34939,⟨sg34936,⟨sg34935,⟨sg34934,True.intro,True.intro⟩,True.intro⟩,⟨sg34938,⟨sg34937,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34942,⟨sg34941,⟨sg34940,True.intro,True.intro⟩,True.intro⟩,⟨sg34943,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_264All : degreeTree62_264.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34922,degreeTree62_262All,degreeTree62_263All⟩ - -lemma degreeTree62_265All : degreeTree62_265.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34955,⟨sg34950,⟨sg34947,⟨sg34946,⟨sg34945,True.intro,True.intro⟩,True.intro⟩,⟨sg34949,⟨sg34948,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34953,⟨sg34952,⟨sg34951,True.intro,True.intro⟩,True.intro⟩,⟨sg34954,True.intro,True.intro⟩⟩⟩,⟨sg34961,⟨sg34958,⟨sg34957,⟨sg34956,True.intro,True.intro⟩,True.intro⟩,⟨sg34960,⟨sg34959,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34964,⟨sg34963,⟨sg34962,True.intro,True.intro⟩,True.intro⟩,⟨sg34965,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_266All : degreeTree62_266.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34977,⟨sg34972,⟨sg34969,⟨sg34968,⟨sg34967,True.intro,True.intro⟩,True.intro⟩,⟨sg34971,⟨sg34970,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34975,⟨sg34974,⟨sg34973,True.intro,True.intro⟩,True.intro⟩,⟨sg34976,True.intro,True.intro⟩⟩⟩,⟨sg34983,⟨sg34980,⟨sg34979,⟨sg34978,True.intro,True.intro⟩,True.intro⟩,⟨sg34982,⟨sg34981,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34986,⟨sg34985,⟨sg34984,True.intro,True.intro⟩,True.intro⟩,⟨sg34987,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_267All : degreeTree62_267.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34966,degreeTree62_265All,degreeTree62_266All⟩ - -lemma degreeTree62_268All : degreeTree62_268.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34944,degreeTree62_264All,degreeTree62_267All⟩ - -lemma degreeTree62_269All : degreeTree62_269.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34900,degreeTree62_261All,degreeTree62_268All⟩ - -lemma degreeTree62_270All : degreeTree62_270.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34999,⟨sg34994,⟨sg34991,⟨sg34990,⟨sg34989,True.intro,True.intro⟩,True.intro⟩,⟨sg34993,⟨sg34992,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34997,⟨sg34996,⟨sg34995,True.intro,True.intro⟩,True.intro⟩,⟨sg34998,True.intro,True.intro⟩⟩⟩,⟨sg35005,⟨sg35002,⟨sg35001,⟨sg35000,True.intro,True.intro⟩,True.intro⟩,⟨sg35004,⟨sg35003,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35008,⟨sg35007,⟨sg35006,True.intro,True.intro⟩,True.intro⟩,⟨sg35009,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_271All : degreeTree62_271.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35021,⟨sg35016,⟨sg35013,⟨sg35012,⟨sg35011,True.intro,True.intro⟩,True.intro⟩,⟨sg35015,⟨sg35014,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35019,⟨sg35018,⟨sg35017,True.intro,True.intro⟩,True.intro⟩,⟨sg35020,True.intro,True.intro⟩⟩⟩,⟨sg35027,⟨sg35024,⟨sg35023,⟨sg35022,True.intro,True.intro⟩,True.intro⟩,⟨sg35026,⟨sg35025,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35030,⟨sg35029,⟨sg35028,True.intro,True.intro⟩,True.intro⟩,⟨sg35031,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_272All : degreeTree62_272.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35010,degreeTree62_270All,degreeTree62_271All⟩ - -lemma degreeTree62_273All : degreeTree62_273.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35043,⟨sg35038,⟨sg35035,⟨sg35034,⟨sg35033,True.intro,True.intro⟩,True.intro⟩,⟨sg35037,⟨sg35036,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35041,⟨sg35040,⟨sg35039,True.intro,True.intro⟩,True.intro⟩,⟨sg35042,True.intro,True.intro⟩⟩⟩,⟨sg35049,⟨sg35046,⟨sg35045,⟨sg35044,True.intro,True.intro⟩,True.intro⟩,⟨sg35048,⟨sg35047,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35052,⟨sg35051,⟨sg35050,True.intro,True.intro⟩,True.intro⟩,⟨sg35053,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_274All : degreeTree62_274.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35065,⟨sg35060,⟨sg35057,⟨sg35056,⟨sg35055,True.intro,True.intro⟩,True.intro⟩,⟨sg35059,⟨sg35058,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35063,⟨sg35062,⟨sg35061,True.intro,True.intro⟩,True.intro⟩,⟨sg35064,True.intro,True.intro⟩⟩⟩,⟨sg35071,⟨sg35068,⟨sg35067,⟨sg35066,True.intro,True.intro⟩,True.intro⟩,⟨sg35070,⟨sg35069,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35074,⟨sg35073,⟨sg35072,True.intro,True.intro⟩,True.intro⟩,⟨sg35075,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_275All : degreeTree62_275.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35054,degreeTree62_273All,degreeTree62_274All⟩ - -lemma degreeTree62_276All : degreeTree62_276.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35032,degreeTree62_272All,degreeTree62_275All⟩ - -lemma degreeTree62_277All : degreeTree62_277.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35087,⟨sg35082,⟨sg35079,⟨sg35078,⟨sg35077,True.intro,True.intro⟩,True.intro⟩,⟨sg35081,⟨sg35080,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35085,⟨sg35084,⟨sg35083,True.intro,True.intro⟩,True.intro⟩,⟨sg35086,True.intro,True.intro⟩⟩⟩,⟨sg35093,⟨sg35090,⟨sg35089,⟨sg35088,True.intro,True.intro⟩,True.intro⟩,⟨sg35092,⟨sg35091,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35096,⟨sg35095,⟨sg35094,True.intro,True.intro⟩,True.intro⟩,⟨sg35097,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_278All : degreeTree62_278.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35109,⟨sg35104,⟨sg35101,⟨sg35100,⟨sg35099,True.intro,True.intro⟩,True.intro⟩,⟨sg35103,⟨sg35102,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35107,⟨sg35106,⟨sg35105,True.intro,True.intro⟩,True.intro⟩,⟨sg35108,True.intro,True.intro⟩⟩⟩,⟨sg35115,⟨sg35112,⟨sg35111,⟨sg35110,True.intro,True.intro⟩,True.intro⟩,⟨sg35114,⟨sg35113,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35118,⟨sg35117,⟨sg35116,True.intro,True.intro⟩,True.intro⟩,⟨sg35119,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_279All : degreeTree62_279.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35098,degreeTree62_277All,degreeTree62_278All⟩ - -lemma degreeTree62_280All : degreeTree62_280.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35131,⟨sg35126,⟨sg35123,⟨sg35122,⟨sg35121,True.intro,True.intro⟩,True.intro⟩,⟨sg35125,⟨sg35124,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35129,⟨sg35128,⟨sg35127,True.intro,True.intro⟩,True.intro⟩,⟨sg35130,True.intro,True.intro⟩⟩⟩,⟨sg35137,⟨sg35134,⟨sg35133,⟨sg35132,True.intro,True.intro⟩,True.intro⟩,⟨sg35136,⟨sg35135,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35140,⟨sg35139,⟨sg35138,True.intro,True.intro⟩,True.intro⟩,⟨sg35141,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_281All : degreeTree62_281.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35153,⟨sg35148,⟨sg35145,⟨sg35144,⟨sg35143,True.intro,True.intro⟩,True.intro⟩,⟨sg35147,⟨sg35146,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35151,⟨sg35150,⟨sg35149,True.intro,True.intro⟩,True.intro⟩,⟨sg35152,True.intro,True.intro⟩⟩⟩,⟨sg35158,⟨sg35156,⟨sg35155,⟨sg35154,True.intro,True.intro⟩,True.intro⟩,⟨sg35157,True.intro,True.intro⟩⟩,⟨sg35161,⟨sg35160,⟨sg35159,True.intro,True.intro⟩,True.intro⟩,⟨sg35162,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_282All : degreeTree62_282.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35142,degreeTree62_280All,degreeTree62_281All⟩ - -lemma degreeTree62_283All : degreeTree62_283.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35120,degreeTree62_279All,degreeTree62_282All⟩ - -lemma degreeTree62_284All : degreeTree62_284.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35076,degreeTree62_276All,degreeTree62_283All⟩ - -lemma degreeTree62_285All : degreeTree62_285.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34988,degreeTree62_269All,degreeTree62_284All⟩ - -lemma degreeTree62_286All : degreeTree62_286.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35174,⟨sg35169,⟨sg35166,⟨sg35165,⟨sg35164,True.intro,True.intro⟩,True.intro⟩,⟨sg35168,⟨sg35167,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35172,⟨sg35171,⟨sg35170,True.intro,True.intro⟩,True.intro⟩,⟨sg35173,True.intro,True.intro⟩⟩⟩,⟨sg35180,⟨sg35177,⟨sg35176,⟨sg35175,True.intro,True.intro⟩,True.intro⟩,⟨sg35179,⟨sg35178,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35183,⟨sg35182,⟨sg35181,True.intro,True.intro⟩,True.intro⟩,⟨sg35184,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_287All : degreeTree62_287.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35196,⟨sg35191,⟨sg35188,⟨sg35187,⟨sg35186,True.intro,True.intro⟩,True.intro⟩,⟨sg35190,⟨sg35189,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35194,⟨sg35193,⟨sg35192,True.intro,True.intro⟩,True.intro⟩,⟨sg35195,True.intro,True.intro⟩⟩⟩,⟨sg35202,⟨sg35199,⟨sg35198,⟨sg35197,True.intro,True.intro⟩,True.intro⟩,⟨sg35201,⟨sg35200,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35205,⟨sg35204,⟨sg35203,True.intro,True.intro⟩,True.intro⟩,⟨sg35206,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_288All : degreeTree62_288.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35185,degreeTree62_286All,degreeTree62_287All⟩ - -lemma degreeTree62_289All : degreeTree62_289.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35218,⟨sg35213,⟨sg35210,⟨sg35209,⟨sg35208,True.intro,True.intro⟩,True.intro⟩,⟨sg35212,⟨sg35211,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35216,⟨sg35215,⟨sg35214,True.intro,True.intro⟩,True.intro⟩,⟨sg35217,True.intro,True.intro⟩⟩⟩,⟨sg35224,⟨sg35221,⟨sg35220,⟨sg35219,True.intro,True.intro⟩,True.intro⟩,⟨sg35223,⟨sg35222,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35227,⟨sg35226,⟨sg35225,True.intro,True.intro⟩,True.intro⟩,⟨sg35228,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_290All : degreeTree62_290.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35240,⟨sg35235,⟨sg35232,⟨sg35231,⟨sg35230,True.intro,True.intro⟩,True.intro⟩,⟨sg35234,⟨sg35233,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35238,⟨sg35237,⟨sg35236,True.intro,True.intro⟩,True.intro⟩,⟨sg35239,True.intro,True.intro⟩⟩⟩,⟨sg35246,⟨sg35243,⟨sg35242,⟨sg35241,True.intro,True.intro⟩,True.intro⟩,⟨sg35245,⟨sg35244,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35249,⟨sg35248,⟨sg35247,True.intro,True.intro⟩,True.intro⟩,⟨sg35250,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_291All : degreeTree62_291.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35229,degreeTree62_289All,degreeTree62_290All⟩ - -lemma degreeTree62_292All : degreeTree62_292.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35207,degreeTree62_288All,degreeTree62_291All⟩ - -lemma degreeTree62_293All : degreeTree62_293.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35262,⟨sg35257,⟨sg35254,⟨sg35253,⟨sg35252,True.intro,True.intro⟩,True.intro⟩,⟨sg35256,⟨sg35255,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35260,⟨sg35259,⟨sg35258,True.intro,True.intro⟩,True.intro⟩,⟨sg35261,True.intro,True.intro⟩⟩⟩,⟨sg35268,⟨sg35265,⟨sg35264,⟨sg35263,True.intro,True.intro⟩,True.intro⟩,⟨sg35267,⟨sg35266,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35271,⟨sg35270,⟨sg35269,True.intro,True.intro⟩,True.intro⟩,⟨sg35272,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_294All : degreeTree62_294.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35284,⟨sg35279,⟨sg35276,⟨sg35275,⟨sg35274,True.intro,True.intro⟩,True.intro⟩,⟨sg35278,⟨sg35277,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35282,⟨sg35281,⟨sg35280,True.intro,True.intro⟩,True.intro⟩,⟨sg35283,True.intro,True.intro⟩⟩⟩,⟨sg35290,⟨sg35287,⟨sg35286,⟨sg35285,True.intro,True.intro⟩,True.intro⟩,⟨sg35289,⟨sg35288,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35293,⟨sg35292,⟨sg35291,True.intro,True.intro⟩,True.intro⟩,⟨sg35294,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_295All : degreeTree62_295.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35273,degreeTree62_293All,degreeTree62_294All⟩ - -lemma degreeTree62_296All : degreeTree62_296.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35306,⟨sg35301,⟨sg35298,⟨sg35297,⟨sg35296,True.intro,True.intro⟩,True.intro⟩,⟨sg35300,⟨sg35299,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35304,⟨sg35303,⟨sg35302,True.intro,True.intro⟩,True.intro⟩,⟨sg35305,True.intro,True.intro⟩⟩⟩,⟨sg35312,⟨sg35309,⟨sg35308,⟨sg35307,True.intro,True.intro⟩,True.intro⟩,⟨sg35311,⟨sg35310,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35315,⟨sg35314,⟨sg35313,True.intro,True.intro⟩,True.intro⟩,⟨sg35316,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_297All : degreeTree62_297.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35328,⟨sg35323,⟨sg35320,⟨sg35319,⟨sg35318,True.intro,True.intro⟩,True.intro⟩,⟨sg35322,⟨sg35321,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35326,⟨sg35325,⟨sg35324,True.intro,True.intro⟩,True.intro⟩,⟨sg35327,True.intro,True.intro⟩⟩⟩,⟨sg35334,⟨sg35331,⟨sg35330,⟨sg35329,True.intro,True.intro⟩,True.intro⟩,⟨sg35333,⟨sg35332,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35337,⟨sg35336,⟨sg35335,True.intro,True.intro⟩,True.intro⟩,⟨sg35338,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_298All : degreeTree62_298.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35317,degreeTree62_296All,degreeTree62_297All⟩ - -lemma degreeTree62_299All : degreeTree62_299.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35295,degreeTree62_295All,degreeTree62_298All⟩ - -lemma degreeTree62_300All : degreeTree62_300.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35251,degreeTree62_292All,degreeTree62_299All⟩ - -lemma degreeTree62_301All : degreeTree62_301.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35350,⟨sg35345,⟨sg35342,⟨sg35341,⟨sg35340,True.intro,True.intro⟩,True.intro⟩,⟨sg35344,⟨sg35343,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35348,⟨sg35347,⟨sg35346,True.intro,True.intro⟩,True.intro⟩,⟨sg35349,True.intro,True.intro⟩⟩⟩,⟨sg35356,⟨sg35353,⟨sg35352,⟨sg35351,True.intro,True.intro⟩,True.intro⟩,⟨sg35355,⟨sg35354,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35359,⟨sg35358,⟨sg35357,True.intro,True.intro⟩,True.intro⟩,⟨sg35360,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_302All : degreeTree62_302.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35372,⟨sg35367,⟨sg35364,⟨sg35363,⟨sg35362,True.intro,True.intro⟩,True.intro⟩,⟨sg35366,⟨sg35365,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35370,⟨sg35369,⟨sg35368,True.intro,True.intro⟩,True.intro⟩,⟨sg35371,True.intro,True.intro⟩⟩⟩,⟨sg35378,⟨sg35375,⟨sg35374,⟨sg35373,True.intro,True.intro⟩,True.intro⟩,⟨sg35377,⟨sg35376,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35381,⟨sg35380,⟨sg35379,True.intro,True.intro⟩,True.intro⟩,⟨sg35382,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_303All : degreeTree62_303.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35361,degreeTree62_301All,degreeTree62_302All⟩ - -lemma degreeTree62_304All : degreeTree62_304.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35394,⟨sg35389,⟨sg35386,⟨sg35385,⟨sg35384,True.intro,True.intro⟩,True.intro⟩,⟨sg35388,⟨sg35387,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35392,⟨sg35391,⟨sg35390,True.intro,True.intro⟩,True.intro⟩,⟨sg35393,True.intro,True.intro⟩⟩⟩,⟨sg35400,⟨sg35397,⟨sg35396,⟨sg35395,True.intro,True.intro⟩,True.intro⟩,⟨sg35399,⟨sg35398,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35403,⟨sg35402,⟨sg35401,True.intro,True.intro⟩,True.intro⟩,⟨sg35404,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_305All : degreeTree62_305.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35416,⟨sg35411,⟨sg35408,⟨sg35407,⟨sg35406,True.intro,True.intro⟩,True.intro⟩,⟨sg35410,⟨sg35409,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35414,⟨sg35413,⟨sg35412,True.intro,True.intro⟩,True.intro⟩,⟨sg35415,True.intro,True.intro⟩⟩⟩,⟨sg35422,⟨sg35419,⟨sg35418,⟨sg35417,True.intro,True.intro⟩,True.intro⟩,⟨sg35421,⟨sg35420,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35425,⟨sg35424,⟨sg35423,True.intro,True.intro⟩,True.intro⟩,⟨sg35426,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_306All : degreeTree62_306.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35405,degreeTree62_304All,degreeTree62_305All⟩ - -lemma degreeTree62_307All : degreeTree62_307.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35383,degreeTree62_303All,degreeTree62_306All⟩ - -lemma degreeTree62_308All : degreeTree62_308.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35438,⟨sg35433,⟨sg35430,⟨sg35429,⟨sg35428,True.intro,True.intro⟩,True.intro⟩,⟨sg35432,⟨sg35431,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35436,⟨sg35435,⟨sg35434,True.intro,True.intro⟩,True.intro⟩,⟨sg35437,True.intro,True.intro⟩⟩⟩,⟨sg35444,⟨sg35441,⟨sg35440,⟨sg35439,True.intro,True.intro⟩,True.intro⟩,⟨sg35443,⟨sg35442,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35447,⟨sg35446,⟨sg35445,True.intro,True.intro⟩,True.intro⟩,⟨sg35448,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_309All : degreeTree62_309.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35460,⟨sg35455,⟨sg35452,⟨sg35451,⟨sg35450,True.intro,True.intro⟩,True.intro⟩,⟨sg35454,⟨sg35453,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35458,⟨sg35457,⟨sg35456,True.intro,True.intro⟩,True.intro⟩,⟨sg35459,True.intro,True.intro⟩⟩⟩,⟨sg35466,⟨sg35463,⟨sg35462,⟨sg35461,True.intro,True.intro⟩,True.intro⟩,⟨sg35465,⟨sg35464,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35469,⟨sg35468,⟨sg35467,True.intro,True.intro⟩,True.intro⟩,⟨sg35470,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_310All : degreeTree62_310.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35449,degreeTree62_308All,degreeTree62_309All⟩ - -lemma degreeTree62_311All : degreeTree62_311.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35482,⟨sg35477,⟨sg35474,⟨sg35473,⟨sg35472,True.intro,True.intro⟩,True.intro⟩,⟨sg35476,⟨sg35475,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35480,⟨sg35479,⟨sg35478,True.intro,True.intro⟩,True.intro⟩,⟨sg35481,True.intro,True.intro⟩⟩⟩,⟨sg35488,⟨sg35485,⟨sg35484,⟨sg35483,True.intro,True.intro⟩,True.intro⟩,⟨sg35487,⟨sg35486,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35491,⟨sg35490,⟨sg35489,True.intro,True.intro⟩,True.intro⟩,⟨sg35492,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_312All : degreeTree62_312.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35504,⟨sg35499,⟨sg35496,⟨sg35495,⟨sg35494,True.intro,True.intro⟩,True.intro⟩,⟨sg35498,⟨sg35497,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35502,⟨sg35501,⟨sg35500,True.intro,True.intro⟩,True.intro⟩,⟨sg35503,True.intro,True.intro⟩⟩⟩,⟨sg35509,⟨sg35507,⟨sg35506,⟨sg35505,True.intro,True.intro⟩,True.intro⟩,⟨sg35508,True.intro,True.intro⟩⟩,⟨sg35512,⟨sg35511,⟨sg35510,True.intro,True.intro⟩,True.intro⟩,⟨sg35513,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_313All : degreeTree62_313.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35493,degreeTree62_311All,degreeTree62_312All⟩ - -lemma degreeTree62_314All : degreeTree62_314.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35471,degreeTree62_310All,degreeTree62_313All⟩ - -lemma degreeTree62_315All : degreeTree62_315.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35427,degreeTree62_307All,degreeTree62_314All⟩ - -lemma degreeTree62_316All : degreeTree62_316.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35339,degreeTree62_300All,degreeTree62_315All⟩ - -lemma degreeTree62_317All : degreeTree62_317.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35163,degreeTree62_285All,degreeTree62_316All⟩ - -lemma degreeTree62_318All : degreeTree62_318.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35525,⟨sg35520,⟨sg35517,⟨sg35516,⟨sg35515,True.intro,True.intro⟩,True.intro⟩,⟨sg35519,⟨sg35518,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35523,⟨sg35522,⟨sg35521,True.intro,True.intro⟩,True.intro⟩,⟨sg35524,True.intro,True.intro⟩⟩⟩,⟨sg35531,⟨sg35528,⟨sg35527,⟨sg35526,True.intro,True.intro⟩,True.intro⟩,⟨sg35530,⟨sg35529,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35534,⟨sg35533,⟨sg35532,True.intro,True.intro⟩,True.intro⟩,⟨sg35535,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_319All : degreeTree62_319.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35547,⟨sg35542,⟨sg35539,⟨sg35538,⟨sg35537,True.intro,True.intro⟩,True.intro⟩,⟨sg35541,⟨sg35540,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35545,⟨sg35544,⟨sg35543,True.intro,True.intro⟩,True.intro⟩,⟨sg35546,True.intro,True.intro⟩⟩⟩,⟨sg35553,⟨sg35550,⟨sg35549,⟨sg35548,True.intro,True.intro⟩,True.intro⟩,⟨sg35552,⟨sg35551,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35556,⟨sg35555,⟨sg35554,True.intro,True.intro⟩,True.intro⟩,⟨sg35557,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_320All : degreeTree62_320.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35536,degreeTree62_318All,degreeTree62_319All⟩ - -lemma degreeTree62_321All : degreeTree62_321.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35569,⟨sg35564,⟨sg35561,⟨sg35560,⟨sg35559,True.intro,True.intro⟩,True.intro⟩,⟨sg35563,⟨sg35562,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35567,⟨sg35566,⟨sg35565,True.intro,True.intro⟩,True.intro⟩,⟨sg35568,True.intro,True.intro⟩⟩⟩,⟨sg35575,⟨sg35572,⟨sg35571,⟨sg35570,True.intro,True.intro⟩,True.intro⟩,⟨sg35574,⟨sg35573,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35578,⟨sg35577,⟨sg35576,True.intro,True.intro⟩,True.intro⟩,⟨sg35579,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_322All : degreeTree62_322.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35591,⟨sg35586,⟨sg35583,⟨sg35582,⟨sg35581,True.intro,True.intro⟩,True.intro⟩,⟨sg35585,⟨sg35584,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35589,⟨sg35588,⟨sg35587,True.intro,True.intro⟩,True.intro⟩,⟨sg35590,True.intro,True.intro⟩⟩⟩,⟨sg35597,⟨sg35594,⟨sg35593,⟨sg35592,True.intro,True.intro⟩,True.intro⟩,⟨sg35596,⟨sg35595,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35600,⟨sg35599,⟨sg35598,True.intro,True.intro⟩,True.intro⟩,⟨sg35601,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_323All : degreeTree62_323.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35580,degreeTree62_321All,degreeTree62_322All⟩ - -lemma degreeTree62_324All : degreeTree62_324.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35558,degreeTree62_320All,degreeTree62_323All⟩ - -lemma degreeTree62_325All : degreeTree62_325.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35613,⟨sg35608,⟨sg35605,⟨sg35604,⟨sg35603,True.intro,True.intro⟩,True.intro⟩,⟨sg35607,⟨sg35606,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35611,⟨sg35610,⟨sg35609,True.intro,True.intro⟩,True.intro⟩,⟨sg35612,True.intro,True.intro⟩⟩⟩,⟨sg35619,⟨sg35616,⟨sg35615,⟨sg35614,True.intro,True.intro⟩,True.intro⟩,⟨sg35618,⟨sg35617,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35622,⟨sg35621,⟨sg35620,True.intro,True.intro⟩,True.intro⟩,⟨sg35623,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_326All : degreeTree62_326.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35635,⟨sg35630,⟨sg35627,⟨sg35626,⟨sg35625,True.intro,True.intro⟩,True.intro⟩,⟨sg35629,⟨sg35628,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35633,⟨sg35632,⟨sg35631,True.intro,True.intro⟩,True.intro⟩,⟨sg35634,True.intro,True.intro⟩⟩⟩,⟨sg35641,⟨sg35638,⟨sg35637,⟨sg35636,True.intro,True.intro⟩,True.intro⟩,⟨sg35640,⟨sg35639,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35644,⟨sg35643,⟨sg35642,True.intro,True.intro⟩,True.intro⟩,⟨sg35645,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_327All : degreeTree62_327.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35624,degreeTree62_325All,degreeTree62_326All⟩ - -lemma degreeTree62_328All : degreeTree62_328.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35657,⟨sg35652,⟨sg35649,⟨sg35648,⟨sg35647,True.intro,True.intro⟩,True.intro⟩,⟨sg35651,⟨sg35650,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35655,⟨sg35654,⟨sg35653,True.intro,True.intro⟩,True.intro⟩,⟨sg35656,True.intro,True.intro⟩⟩⟩,⟨sg35663,⟨sg35660,⟨sg35659,⟨sg35658,True.intro,True.intro⟩,True.intro⟩,⟨sg35662,⟨sg35661,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35666,⟨sg35665,⟨sg35664,True.intro,True.intro⟩,True.intro⟩,⟨sg35667,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_329All : degreeTree62_329.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35679,⟨sg35674,⟨sg35671,⟨sg35670,⟨sg35669,True.intro,True.intro⟩,True.intro⟩,⟨sg35673,⟨sg35672,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35677,⟨sg35676,⟨sg35675,True.intro,True.intro⟩,True.intro⟩,⟨sg35678,True.intro,True.intro⟩⟩⟩,⟨sg35685,⟨sg35682,⟨sg35681,⟨sg35680,True.intro,True.intro⟩,True.intro⟩,⟨sg35684,⟨sg35683,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35688,⟨sg35687,⟨sg35686,True.intro,True.intro⟩,True.intro⟩,⟨sg35689,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_330All : degreeTree62_330.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35668,degreeTree62_328All,degreeTree62_329All⟩ - -lemma degreeTree62_331All : degreeTree62_331.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35646,degreeTree62_327All,degreeTree62_330All⟩ - -lemma degreeTree62_332All : degreeTree62_332.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35602,degreeTree62_324All,degreeTree62_331All⟩ - -lemma degreeTree62_333All : degreeTree62_333.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35701,⟨sg35696,⟨sg35693,⟨sg35692,⟨sg35691,True.intro,True.intro⟩,True.intro⟩,⟨sg35695,⟨sg35694,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35699,⟨sg35698,⟨sg35697,True.intro,True.intro⟩,True.intro⟩,⟨sg35700,True.intro,True.intro⟩⟩⟩,⟨sg35707,⟨sg35704,⟨sg35703,⟨sg35702,True.intro,True.intro⟩,True.intro⟩,⟨sg35706,⟨sg35705,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35710,⟨sg35709,⟨sg35708,True.intro,True.intro⟩,True.intro⟩,⟨sg35711,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_334All : degreeTree62_334.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35723,⟨sg35718,⟨sg35715,⟨sg35714,⟨sg35713,True.intro,True.intro⟩,True.intro⟩,⟨sg35717,⟨sg35716,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35721,⟨sg35720,⟨sg35719,True.intro,True.intro⟩,True.intro⟩,⟨sg35722,True.intro,True.intro⟩⟩⟩,⟨sg35729,⟨sg35726,⟨sg35725,⟨sg35724,True.intro,True.intro⟩,True.intro⟩,⟨sg35728,⟨sg35727,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35732,⟨sg35731,⟨sg35730,True.intro,True.intro⟩,True.intro⟩,⟨sg35733,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_335All : degreeTree62_335.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35712,degreeTree62_333All,degreeTree62_334All⟩ - -lemma degreeTree62_336All : degreeTree62_336.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35745,⟨sg35740,⟨sg35737,⟨sg35736,⟨sg35735,True.intro,True.intro⟩,True.intro⟩,⟨sg35739,⟨sg35738,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35743,⟨sg35742,⟨sg35741,True.intro,True.intro⟩,True.intro⟩,⟨sg35744,True.intro,True.intro⟩⟩⟩,⟨sg35751,⟨sg35748,⟨sg35747,⟨sg35746,True.intro,True.intro⟩,True.intro⟩,⟨sg35750,⟨sg35749,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35754,⟨sg35753,⟨sg35752,True.intro,True.intro⟩,True.intro⟩,⟨sg35755,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_337All : degreeTree62_337.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35767,⟨sg35762,⟨sg35759,⟨sg35758,⟨sg35757,True.intro,True.intro⟩,True.intro⟩,⟨sg35761,⟨sg35760,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35765,⟨sg35764,⟨sg35763,True.intro,True.intro⟩,True.intro⟩,⟨sg35766,True.intro,True.intro⟩⟩⟩,⟨sg35773,⟨sg35770,⟨sg35769,⟨sg35768,True.intro,True.intro⟩,True.intro⟩,⟨sg35772,⟨sg35771,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35776,⟨sg35775,⟨sg35774,True.intro,True.intro⟩,True.intro⟩,⟨sg35777,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_338All : degreeTree62_338.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35756,degreeTree62_336All,degreeTree62_337All⟩ - -lemma degreeTree62_339All : degreeTree62_339.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35734,degreeTree62_335All,degreeTree62_338All⟩ - -lemma degreeTree62_340All : degreeTree62_340.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35789,⟨sg35784,⟨sg35781,⟨sg35780,⟨sg35779,True.intro,True.intro⟩,True.intro⟩,⟨sg35783,⟨sg35782,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35787,⟨sg35786,⟨sg35785,True.intro,True.intro⟩,True.intro⟩,⟨sg35788,True.intro,True.intro⟩⟩⟩,⟨sg35795,⟨sg35792,⟨sg35791,⟨sg35790,True.intro,True.intro⟩,True.intro⟩,⟨sg35794,⟨sg35793,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35798,⟨sg35797,⟨sg35796,True.intro,True.intro⟩,True.intro⟩,⟨sg35799,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_341All : degreeTree62_341.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35811,⟨sg35806,⟨sg35803,⟨sg35802,⟨sg35801,True.intro,True.intro⟩,True.intro⟩,⟨sg35805,⟨sg35804,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35809,⟨sg35808,⟨sg35807,True.intro,True.intro⟩,True.intro⟩,⟨sg35810,True.intro,True.intro⟩⟩⟩,⟨sg35817,⟨sg35814,⟨sg35813,⟨sg35812,True.intro,True.intro⟩,True.intro⟩,⟨sg35816,⟨sg35815,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35820,⟨sg35819,⟨sg35818,True.intro,True.intro⟩,True.intro⟩,⟨sg35821,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_342All : degreeTree62_342.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35800,degreeTree62_340All,degreeTree62_341All⟩ - -lemma degreeTree62_343All : degreeTree62_343.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35833,⟨sg35828,⟨sg35825,⟨sg35824,⟨sg35823,True.intro,True.intro⟩,True.intro⟩,⟨sg35827,⟨sg35826,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35831,⟨sg35830,⟨sg35829,True.intro,True.intro⟩,True.intro⟩,⟨sg35832,True.intro,True.intro⟩⟩⟩,⟨sg35839,⟨sg35836,⟨sg35835,⟨sg35834,True.intro,True.intro⟩,True.intro⟩,⟨sg35838,⟨sg35837,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35842,⟨sg35841,⟨sg35840,True.intro,True.intro⟩,True.intro⟩,⟨sg35843,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_344All : degreeTree62_344.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35855,⟨sg35850,⟨sg35847,⟨sg35846,⟨sg35845,True.intro,True.intro⟩,True.intro⟩,⟨sg35849,⟨sg35848,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35853,⟨sg35852,⟨sg35851,True.intro,True.intro⟩,True.intro⟩,⟨sg35854,True.intro,True.intro⟩⟩⟩,⟨sg35860,⟨sg35858,⟨sg35857,⟨sg35856,True.intro,True.intro⟩,True.intro⟩,⟨sg35859,True.intro,True.intro⟩⟩,⟨sg35863,⟨sg35862,⟨sg35861,True.intro,True.intro⟩,True.intro⟩,⟨sg35864,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_345All : degreeTree62_345.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35844,degreeTree62_343All,degreeTree62_344All⟩ - -lemma degreeTree62_346All : degreeTree62_346.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35822,degreeTree62_342All,degreeTree62_345All⟩ - -lemma degreeTree62_347All : degreeTree62_347.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35778,degreeTree62_339All,degreeTree62_346All⟩ - -lemma degreeTree62_348All : degreeTree62_348.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35690,degreeTree62_332All,degreeTree62_347All⟩ - -lemma degreeTree62_349All : degreeTree62_349.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35876,⟨sg35871,⟨sg35868,⟨sg35867,⟨sg35866,True.intro,True.intro⟩,True.intro⟩,⟨sg35870,⟨sg35869,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35874,⟨sg35873,⟨sg35872,True.intro,True.intro⟩,True.intro⟩,⟨sg35875,True.intro,True.intro⟩⟩⟩,⟨sg35882,⟨sg35879,⟨sg35878,⟨sg35877,True.intro,True.intro⟩,True.intro⟩,⟨sg35881,⟨sg35880,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35885,⟨sg35884,⟨sg35883,True.intro,True.intro⟩,True.intro⟩,⟨sg35886,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_350All : degreeTree62_350.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35898,⟨sg35893,⟨sg35890,⟨sg35889,⟨sg35888,True.intro,True.intro⟩,True.intro⟩,⟨sg35892,⟨sg35891,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35896,⟨sg35895,⟨sg35894,True.intro,True.intro⟩,True.intro⟩,⟨sg35897,True.intro,True.intro⟩⟩⟩,⟨sg35904,⟨sg35901,⟨sg35900,⟨sg35899,True.intro,True.intro⟩,True.intro⟩,⟨sg35903,⟨sg35902,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35907,⟨sg35906,⟨sg35905,True.intro,True.intro⟩,True.intro⟩,⟨sg35908,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_351All : degreeTree62_351.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35887,degreeTree62_349All,degreeTree62_350All⟩ - -lemma degreeTree62_352All : degreeTree62_352.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35920,⟨sg35915,⟨sg35912,⟨sg35911,⟨sg35910,True.intro,True.intro⟩,True.intro⟩,⟨sg35914,⟨sg35913,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35918,⟨sg35917,⟨sg35916,True.intro,True.intro⟩,True.intro⟩,⟨sg35919,True.intro,True.intro⟩⟩⟩,⟨sg35926,⟨sg35923,⟨sg35922,⟨sg35921,True.intro,True.intro⟩,True.intro⟩,⟨sg35925,⟨sg35924,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35929,⟨sg35928,⟨sg35927,True.intro,True.intro⟩,True.intro⟩,⟨sg35930,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_353All : degreeTree62_353.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35942,⟨sg35937,⟨sg35934,⟨sg35933,⟨sg35932,True.intro,True.intro⟩,True.intro⟩,⟨sg35936,⟨sg35935,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35940,⟨sg35939,⟨sg35938,True.intro,True.intro⟩,True.intro⟩,⟨sg35941,True.intro,True.intro⟩⟩⟩,⟨sg35948,⟨sg35945,⟨sg35944,⟨sg35943,True.intro,True.intro⟩,True.intro⟩,⟨sg35947,⟨sg35946,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35951,⟨sg35950,⟨sg35949,True.intro,True.intro⟩,True.intro⟩,⟨sg35952,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_354All : degreeTree62_354.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35931,degreeTree62_352All,degreeTree62_353All⟩ - -lemma degreeTree62_355All : degreeTree62_355.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35909,degreeTree62_351All,degreeTree62_354All⟩ - -lemma degreeTree62_356All : degreeTree62_356.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35964,⟨sg35959,⟨sg35956,⟨sg35955,⟨sg35954,True.intro,True.intro⟩,True.intro⟩,⟨sg35958,⟨sg35957,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35962,⟨sg35961,⟨sg35960,True.intro,True.intro⟩,True.intro⟩,⟨sg35963,True.intro,True.intro⟩⟩⟩,⟨sg35970,⟨sg35967,⟨sg35966,⟨sg35965,True.intro,True.intro⟩,True.intro⟩,⟨sg35969,⟨sg35968,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35973,⟨sg35972,⟨sg35971,True.intro,True.intro⟩,True.intro⟩,⟨sg35974,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_357All : degreeTree62_357.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35986,⟨sg35981,⟨sg35978,⟨sg35977,⟨sg35976,True.intro,True.intro⟩,True.intro⟩,⟨sg35980,⟨sg35979,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35984,⟨sg35983,⟨sg35982,True.intro,True.intro⟩,True.intro⟩,⟨sg35985,True.intro,True.intro⟩⟩⟩,⟨sg35992,⟨sg35989,⟨sg35988,⟨sg35987,True.intro,True.intro⟩,True.intro⟩,⟨sg35991,⟨sg35990,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35995,⟨sg35994,⟨sg35993,True.intro,True.intro⟩,True.intro⟩,⟨sg35996,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_358All : degreeTree62_358.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35975,degreeTree62_356All,degreeTree62_357All⟩ - -lemma degreeTree62_359All : degreeTree62_359.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36008,⟨sg36003,⟨sg36000,⟨sg35999,⟨sg35998,True.intro,True.intro⟩,True.intro⟩,⟨sg36002,⟨sg36001,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36006,⟨sg36005,⟨sg36004,True.intro,True.intro⟩,True.intro⟩,⟨sg36007,True.intro,True.intro⟩⟩⟩,⟨sg36014,⟨sg36011,⟨sg36010,⟨sg36009,True.intro,True.intro⟩,True.intro⟩,⟨sg36013,⟨sg36012,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36017,⟨sg36016,⟨sg36015,True.intro,True.intro⟩,True.intro⟩,⟨sg36018,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_360All : degreeTree62_360.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36030,⟨sg36025,⟨sg36022,⟨sg36021,⟨sg36020,True.intro,True.intro⟩,True.intro⟩,⟨sg36024,⟨sg36023,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36028,⟨sg36027,⟨sg36026,True.intro,True.intro⟩,True.intro⟩,⟨sg36029,True.intro,True.intro⟩⟩⟩,⟨sg36036,⟨sg36033,⟨sg36032,⟨sg36031,True.intro,True.intro⟩,True.intro⟩,⟨sg36035,⟨sg36034,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36039,⟨sg36038,⟨sg36037,True.intro,True.intro⟩,True.intro⟩,⟨sg36040,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_361All : degreeTree62_361.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36019,degreeTree62_359All,degreeTree62_360All⟩ - -lemma degreeTree62_362All : degreeTree62_362.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35997,degreeTree62_358All,degreeTree62_361All⟩ - -lemma degreeTree62_363All : degreeTree62_363.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35953,degreeTree62_355All,degreeTree62_362All⟩ - -lemma degreeTree62_364All : degreeTree62_364.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36052,⟨sg36047,⟨sg36044,⟨sg36043,⟨sg36042,True.intro,True.intro⟩,True.intro⟩,⟨sg36046,⟨sg36045,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36050,⟨sg36049,⟨sg36048,True.intro,True.intro⟩,True.intro⟩,⟨sg36051,True.intro,True.intro⟩⟩⟩,⟨sg36058,⟨sg36055,⟨sg36054,⟨sg36053,True.intro,True.intro⟩,True.intro⟩,⟨sg36057,⟨sg36056,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36061,⟨sg36060,⟨sg36059,True.intro,True.intro⟩,True.intro⟩,⟨sg36062,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_365All : degreeTree62_365.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36074,⟨sg36069,⟨sg36066,⟨sg36065,⟨sg36064,True.intro,True.intro⟩,True.intro⟩,⟨sg36068,⟨sg36067,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36072,⟨sg36071,⟨sg36070,True.intro,True.intro⟩,True.intro⟩,⟨sg36073,True.intro,True.intro⟩⟩⟩,⟨sg36080,⟨sg36077,⟨sg36076,⟨sg36075,True.intro,True.intro⟩,True.intro⟩,⟨sg36079,⟨sg36078,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36083,⟨sg36082,⟨sg36081,True.intro,True.intro⟩,True.intro⟩,⟨sg36084,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_366All : degreeTree62_366.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36063,degreeTree62_364All,degreeTree62_365All⟩ - -lemma degreeTree62_367All : degreeTree62_367.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36096,⟨sg36091,⟨sg36088,⟨sg36087,⟨sg36086,True.intro,True.intro⟩,True.intro⟩,⟨sg36090,⟨sg36089,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36094,⟨sg36093,⟨sg36092,True.intro,True.intro⟩,True.intro⟩,⟨sg36095,True.intro,True.intro⟩⟩⟩,⟨sg36102,⟨sg36099,⟨sg36098,⟨sg36097,True.intro,True.intro⟩,True.intro⟩,⟨sg36101,⟨sg36100,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36105,⟨sg36104,⟨sg36103,True.intro,True.intro⟩,True.intro⟩,⟨sg36106,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_368All : degreeTree62_368.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36118,⟨sg36113,⟨sg36110,⟨sg36109,⟨sg36108,True.intro,True.intro⟩,True.intro⟩,⟨sg36112,⟨sg36111,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36116,⟨sg36115,⟨sg36114,True.intro,True.intro⟩,True.intro⟩,⟨sg36117,True.intro,True.intro⟩⟩⟩,⟨sg36124,⟨sg36121,⟨sg36120,⟨sg36119,True.intro,True.intro⟩,True.intro⟩,⟨sg36123,⟨sg36122,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36127,⟨sg36126,⟨sg36125,True.intro,True.intro⟩,True.intro⟩,⟨sg36128,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_369All : degreeTree62_369.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36107,degreeTree62_367All,degreeTree62_368All⟩ - -lemma degreeTree62_370All : degreeTree62_370.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36085,degreeTree62_366All,degreeTree62_369All⟩ - -lemma degreeTree62_371All : degreeTree62_371.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36140,⟨sg36135,⟨sg36132,⟨sg36131,⟨sg36130,True.intro,True.intro⟩,True.intro⟩,⟨sg36134,⟨sg36133,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36138,⟨sg36137,⟨sg36136,True.intro,True.intro⟩,True.intro⟩,⟨sg36139,True.intro,True.intro⟩⟩⟩,⟨sg36146,⟨sg36143,⟨sg36142,⟨sg36141,True.intro,True.intro⟩,True.intro⟩,⟨sg36145,⟨sg36144,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36149,⟨sg36148,⟨sg36147,True.intro,True.intro⟩,True.intro⟩,⟨sg36150,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_372All : degreeTree62_372.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36162,⟨sg36157,⟨sg36154,⟨sg36153,⟨sg36152,True.intro,True.intro⟩,True.intro⟩,⟨sg36156,⟨sg36155,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36160,⟨sg36159,⟨sg36158,True.intro,True.intro⟩,True.intro⟩,⟨sg36161,True.intro,True.intro⟩⟩⟩,⟨sg36168,⟨sg36165,⟨sg36164,⟨sg36163,True.intro,True.intro⟩,True.intro⟩,⟨sg36167,⟨sg36166,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36171,⟨sg36170,⟨sg36169,True.intro,True.intro⟩,True.intro⟩,⟨sg36172,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_373All : degreeTree62_373.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36151,degreeTree62_371All,degreeTree62_372All⟩ - -lemma degreeTree62_374All : degreeTree62_374.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36184,⟨sg36179,⟨sg36176,⟨sg36175,⟨sg36174,True.intro,True.intro⟩,True.intro⟩,⟨sg36178,⟨sg36177,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36182,⟨sg36181,⟨sg36180,True.intro,True.intro⟩,True.intro⟩,⟨sg36183,True.intro,True.intro⟩⟩⟩,⟨sg36190,⟨sg36187,⟨sg36186,⟨sg36185,True.intro,True.intro⟩,True.intro⟩,⟨sg36189,⟨sg36188,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36193,⟨sg36192,⟨sg36191,True.intro,True.intro⟩,True.intro⟩,⟨sg36194,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_375All : degreeTree62_375.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36206,⟨sg36201,⟨sg36198,⟨sg36197,⟨sg36196,True.intro,True.intro⟩,True.intro⟩,⟨sg36200,⟨sg36199,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36204,⟨sg36203,⟨sg36202,True.intro,True.intro⟩,True.intro⟩,⟨sg36205,True.intro,True.intro⟩⟩⟩,⟨sg36211,⟨sg36209,⟨sg36208,⟨sg36207,True.intro,True.intro⟩,True.intro⟩,⟨sg36210,True.intro,True.intro⟩⟩,⟨sg36214,⟨sg36213,⟨sg36212,True.intro,True.intro⟩,True.intro⟩,⟨sg36215,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_376All : degreeTree62_376.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36195,degreeTree62_374All,degreeTree62_375All⟩ - -lemma degreeTree62_377All : degreeTree62_377.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36173,degreeTree62_373All,degreeTree62_376All⟩ - -lemma degreeTree62_378All : degreeTree62_378.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36129,degreeTree62_370All,degreeTree62_377All⟩ - -lemma degreeTree62_379All : degreeTree62_379.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36041,degreeTree62_363All,degreeTree62_378All⟩ - -lemma degreeTree62_380All : degreeTree62_380.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35865,degreeTree62_348All,degreeTree62_379All⟩ - -lemma degreeTree62_381All : degreeTree62_381.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg35514,degreeTree62_317All,degreeTree62_380All⟩ - -lemma degreeTree62_382All : degreeTree62_382.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36227,⟨sg36222,⟨sg36219,⟨sg36218,⟨sg36217,True.intro,True.intro⟩,True.intro⟩,⟨sg36221,⟨sg36220,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36225,⟨sg36224,⟨sg36223,True.intro,True.intro⟩,True.intro⟩,⟨sg36226,True.intro,True.intro⟩⟩⟩,⟨sg36233,⟨sg36230,⟨sg36229,⟨sg36228,True.intro,True.intro⟩,True.intro⟩,⟨sg36232,⟨sg36231,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36236,⟨sg36235,⟨sg36234,True.intro,True.intro⟩,True.intro⟩,⟨sg36237,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_383All : degreeTree62_383.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36249,⟨sg36244,⟨sg36241,⟨sg36240,⟨sg36239,True.intro,True.intro⟩,True.intro⟩,⟨sg36243,⟨sg36242,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36247,⟨sg36246,⟨sg36245,True.intro,True.intro⟩,True.intro⟩,⟨sg36248,True.intro,True.intro⟩⟩⟩,⟨sg36255,⟨sg36252,⟨sg36251,⟨sg36250,True.intro,True.intro⟩,True.intro⟩,⟨sg36254,⟨sg36253,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36258,⟨sg36257,⟨sg36256,True.intro,True.intro⟩,True.intro⟩,⟨sg36259,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_384All : degreeTree62_384.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36238,degreeTree62_382All,degreeTree62_383All⟩ - -lemma degreeTree62_385All : degreeTree62_385.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36271,⟨sg36266,⟨sg36263,⟨sg36262,⟨sg36261,True.intro,True.intro⟩,True.intro⟩,⟨sg36265,⟨sg36264,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36269,⟨sg36268,⟨sg36267,True.intro,True.intro⟩,True.intro⟩,⟨sg36270,True.intro,True.intro⟩⟩⟩,⟨sg36277,⟨sg36274,⟨sg36273,⟨sg36272,True.intro,True.intro⟩,True.intro⟩,⟨sg36276,⟨sg36275,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36280,⟨sg36279,⟨sg36278,True.intro,True.intro⟩,True.intro⟩,⟨sg36281,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_386All : degreeTree62_386.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36293,⟨sg36288,⟨sg36285,⟨sg36284,⟨sg36283,True.intro,True.intro⟩,True.intro⟩,⟨sg36287,⟨sg36286,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36291,⟨sg36290,⟨sg36289,True.intro,True.intro⟩,True.intro⟩,⟨sg36292,True.intro,True.intro⟩⟩⟩,⟨sg36299,⟨sg36296,⟨sg36295,⟨sg36294,True.intro,True.intro⟩,True.intro⟩,⟨sg36298,⟨sg36297,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36302,⟨sg36301,⟨sg36300,True.intro,True.intro⟩,True.intro⟩,⟨sg36303,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_387All : degreeTree62_387.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36282,degreeTree62_385All,degreeTree62_386All⟩ - -lemma degreeTree62_388All : degreeTree62_388.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36260,degreeTree62_384All,degreeTree62_387All⟩ - -lemma degreeTree62_389All : degreeTree62_389.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36315,⟨sg36310,⟨sg36307,⟨sg36306,⟨sg36305,True.intro,True.intro⟩,True.intro⟩,⟨sg36309,⟨sg36308,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36313,⟨sg36312,⟨sg36311,True.intro,True.intro⟩,True.intro⟩,⟨sg36314,True.intro,True.intro⟩⟩⟩,⟨sg36321,⟨sg36318,⟨sg36317,⟨sg36316,True.intro,True.intro⟩,True.intro⟩,⟨sg36320,⟨sg36319,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36324,⟨sg36323,⟨sg36322,True.intro,True.intro⟩,True.intro⟩,⟨sg36325,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_390All : degreeTree62_390.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36337,⟨sg36332,⟨sg36329,⟨sg36328,⟨sg36327,True.intro,True.intro⟩,True.intro⟩,⟨sg36331,⟨sg36330,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36335,⟨sg36334,⟨sg36333,True.intro,True.intro⟩,True.intro⟩,⟨sg36336,True.intro,True.intro⟩⟩⟩,⟨sg36343,⟨sg36340,⟨sg36339,⟨sg36338,True.intro,True.intro⟩,True.intro⟩,⟨sg36342,⟨sg36341,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36346,⟨sg36345,⟨sg36344,True.intro,True.intro⟩,True.intro⟩,⟨sg36347,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_391All : degreeTree62_391.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36326,degreeTree62_389All,degreeTree62_390All⟩ - -lemma degreeTree62_392All : degreeTree62_392.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36359,⟨sg36354,⟨sg36351,⟨sg36350,⟨sg36349,True.intro,True.intro⟩,True.intro⟩,⟨sg36353,⟨sg36352,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36357,⟨sg36356,⟨sg36355,True.intro,True.intro⟩,True.intro⟩,⟨sg36358,True.intro,True.intro⟩⟩⟩,⟨sg36365,⟨sg36362,⟨sg36361,⟨sg36360,True.intro,True.intro⟩,True.intro⟩,⟨sg36364,⟨sg36363,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36368,⟨sg36367,⟨sg36366,True.intro,True.intro⟩,True.intro⟩,⟨sg36369,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_393All : degreeTree62_393.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36381,⟨sg36376,⟨sg36373,⟨sg36372,⟨sg36371,True.intro,True.intro⟩,True.intro⟩,⟨sg36375,⟨sg36374,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36379,⟨sg36378,⟨sg36377,True.intro,True.intro⟩,True.intro⟩,⟨sg36380,True.intro,True.intro⟩⟩⟩,⟨sg36387,⟨sg36384,⟨sg36383,⟨sg36382,True.intro,True.intro⟩,True.intro⟩,⟨sg36386,⟨sg36385,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36390,⟨sg36389,⟨sg36388,True.intro,True.intro⟩,True.intro⟩,⟨sg36391,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_394All : degreeTree62_394.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36370,degreeTree62_392All,degreeTree62_393All⟩ - -lemma degreeTree62_395All : degreeTree62_395.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36348,degreeTree62_391All,degreeTree62_394All⟩ - -lemma degreeTree62_396All : degreeTree62_396.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36304,degreeTree62_388All,degreeTree62_395All⟩ - -lemma degreeTree62_397All : degreeTree62_397.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36403,⟨sg36398,⟨sg36395,⟨sg36394,⟨sg36393,True.intro,True.intro⟩,True.intro⟩,⟨sg36397,⟨sg36396,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36401,⟨sg36400,⟨sg36399,True.intro,True.intro⟩,True.intro⟩,⟨sg36402,True.intro,True.intro⟩⟩⟩,⟨sg36409,⟨sg36406,⟨sg36405,⟨sg36404,True.intro,True.intro⟩,True.intro⟩,⟨sg36408,⟨sg36407,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36412,⟨sg36411,⟨sg36410,True.intro,True.intro⟩,True.intro⟩,⟨sg36413,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_398All : degreeTree62_398.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36425,⟨sg36420,⟨sg36417,⟨sg36416,⟨sg36415,True.intro,True.intro⟩,True.intro⟩,⟨sg36419,⟨sg36418,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36423,⟨sg36422,⟨sg36421,True.intro,True.intro⟩,True.intro⟩,⟨sg36424,True.intro,True.intro⟩⟩⟩,⟨sg36431,⟨sg36428,⟨sg36427,⟨sg36426,True.intro,True.intro⟩,True.intro⟩,⟨sg36430,⟨sg36429,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36434,⟨sg36433,⟨sg36432,True.intro,True.intro⟩,True.intro⟩,⟨sg36435,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_399All : degreeTree62_399.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36414,degreeTree62_397All,degreeTree62_398All⟩ - -lemma degreeTree62_400All : degreeTree62_400.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36447,⟨sg36442,⟨sg36439,⟨sg36438,⟨sg36437,True.intro,True.intro⟩,True.intro⟩,⟨sg36441,⟨sg36440,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36445,⟨sg36444,⟨sg36443,True.intro,True.intro⟩,True.intro⟩,⟨sg36446,True.intro,True.intro⟩⟩⟩,⟨sg36453,⟨sg36450,⟨sg36449,⟨sg36448,True.intro,True.intro⟩,True.intro⟩,⟨sg36452,⟨sg36451,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36456,⟨sg36455,⟨sg36454,True.intro,True.intro⟩,True.intro⟩,⟨sg36457,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_401All : degreeTree62_401.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36469,⟨sg36464,⟨sg36461,⟨sg36460,⟨sg36459,True.intro,True.intro⟩,True.intro⟩,⟨sg36463,⟨sg36462,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36467,⟨sg36466,⟨sg36465,True.intro,True.intro⟩,True.intro⟩,⟨sg36468,True.intro,True.intro⟩⟩⟩,⟨sg36475,⟨sg36472,⟨sg36471,⟨sg36470,True.intro,True.intro⟩,True.intro⟩,⟨sg36474,⟨sg36473,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36478,⟨sg36477,⟨sg36476,True.intro,True.intro⟩,True.intro⟩,⟨sg36479,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_402All : degreeTree62_402.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36458,degreeTree62_400All,degreeTree62_401All⟩ - -lemma degreeTree62_403All : degreeTree62_403.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36436,degreeTree62_399All,degreeTree62_402All⟩ - -lemma degreeTree62_404All : degreeTree62_404.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36491,⟨sg36486,⟨sg36483,⟨sg36482,⟨sg36481,True.intro,True.intro⟩,True.intro⟩,⟨sg36485,⟨sg36484,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36489,⟨sg36488,⟨sg36487,True.intro,True.intro⟩,True.intro⟩,⟨sg36490,True.intro,True.intro⟩⟩⟩,⟨sg36497,⟨sg36494,⟨sg36493,⟨sg36492,True.intro,True.intro⟩,True.intro⟩,⟨sg36496,⟨sg36495,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36500,⟨sg36499,⟨sg36498,True.intro,True.intro⟩,True.intro⟩,⟨sg36501,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_405All : degreeTree62_405.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36513,⟨sg36508,⟨sg36505,⟨sg36504,⟨sg36503,True.intro,True.intro⟩,True.intro⟩,⟨sg36507,⟨sg36506,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36511,⟨sg36510,⟨sg36509,True.intro,True.intro⟩,True.intro⟩,⟨sg36512,True.intro,True.intro⟩⟩⟩,⟨sg36519,⟨sg36516,⟨sg36515,⟨sg36514,True.intro,True.intro⟩,True.intro⟩,⟨sg36518,⟨sg36517,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36522,⟨sg36521,⟨sg36520,True.intro,True.intro⟩,True.intro⟩,⟨sg36523,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_406All : degreeTree62_406.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36502,degreeTree62_404All,degreeTree62_405All⟩ - -lemma degreeTree62_407All : degreeTree62_407.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36535,⟨sg36530,⟨sg36527,⟨sg36526,⟨sg36525,True.intro,True.intro⟩,True.intro⟩,⟨sg36529,⟨sg36528,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36533,⟨sg36532,⟨sg36531,True.intro,True.intro⟩,True.intro⟩,⟨sg36534,True.intro,True.intro⟩⟩⟩,⟨sg36541,⟨sg36538,⟨sg36537,⟨sg36536,True.intro,True.intro⟩,True.intro⟩,⟨sg36540,⟨sg36539,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36544,⟨sg36543,⟨sg36542,True.intro,True.intro⟩,True.intro⟩,⟨sg36545,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_408All : degreeTree62_408.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36557,⟨sg36552,⟨sg36549,⟨sg36548,⟨sg36547,True.intro,True.intro⟩,True.intro⟩,⟨sg36551,⟨sg36550,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36555,⟨sg36554,⟨sg36553,True.intro,True.intro⟩,True.intro⟩,⟨sg36556,True.intro,True.intro⟩⟩⟩,⟨sg36562,⟨sg36560,⟨sg36559,⟨sg36558,True.intro,True.intro⟩,True.intro⟩,⟨sg36561,True.intro,True.intro⟩⟩,⟨sg36565,⟨sg36564,⟨sg36563,True.intro,True.intro⟩,True.intro⟩,⟨sg36566,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_409All : degreeTree62_409.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36546,degreeTree62_407All,degreeTree62_408All⟩ - -lemma degreeTree62_410All : degreeTree62_410.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36524,degreeTree62_406All,degreeTree62_409All⟩ - -lemma degreeTree62_411All : degreeTree62_411.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36480,degreeTree62_403All,degreeTree62_410All⟩ - -lemma degreeTree62_412All : degreeTree62_412.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36392,degreeTree62_396All,degreeTree62_411All⟩ - -lemma degreeTree62_413All : degreeTree62_413.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36578,⟨sg36573,⟨sg36570,⟨sg36569,⟨sg36568,True.intro,True.intro⟩,True.intro⟩,⟨sg36572,⟨sg36571,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36576,⟨sg36575,⟨sg36574,True.intro,True.intro⟩,True.intro⟩,⟨sg36577,True.intro,True.intro⟩⟩⟩,⟨sg36584,⟨sg36581,⟨sg36580,⟨sg36579,True.intro,True.intro⟩,True.intro⟩,⟨sg36583,⟨sg36582,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36587,⟨sg36586,⟨sg36585,True.intro,True.intro⟩,True.intro⟩,⟨sg36588,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_414All : degreeTree62_414.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36600,⟨sg36595,⟨sg36592,⟨sg36591,⟨sg36590,True.intro,True.intro⟩,True.intro⟩,⟨sg36594,⟨sg36593,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36598,⟨sg36597,⟨sg36596,True.intro,True.intro⟩,True.intro⟩,⟨sg36599,True.intro,True.intro⟩⟩⟩,⟨sg36606,⟨sg36603,⟨sg36602,⟨sg36601,True.intro,True.intro⟩,True.intro⟩,⟨sg36605,⟨sg36604,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36609,⟨sg36608,⟨sg36607,True.intro,True.intro⟩,True.intro⟩,⟨sg36610,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_415All : degreeTree62_415.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36589,degreeTree62_413All,degreeTree62_414All⟩ - -lemma degreeTree62_416All : degreeTree62_416.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36622,⟨sg36617,⟨sg36614,⟨sg36613,⟨sg36612,True.intro,True.intro⟩,True.intro⟩,⟨sg36616,⟨sg36615,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36620,⟨sg36619,⟨sg36618,True.intro,True.intro⟩,True.intro⟩,⟨sg36621,True.intro,True.intro⟩⟩⟩,⟨sg36628,⟨sg36625,⟨sg36624,⟨sg36623,True.intro,True.intro⟩,True.intro⟩,⟨sg36627,⟨sg36626,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36631,⟨sg36630,⟨sg36629,True.intro,True.intro⟩,True.intro⟩,⟨sg36632,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_417All : degreeTree62_417.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36644,⟨sg36639,⟨sg36636,⟨sg36635,⟨sg36634,True.intro,True.intro⟩,True.intro⟩,⟨sg36638,⟨sg36637,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36642,⟨sg36641,⟨sg36640,True.intro,True.intro⟩,True.intro⟩,⟨sg36643,True.intro,True.intro⟩⟩⟩,⟨sg36650,⟨sg36647,⟨sg36646,⟨sg36645,True.intro,True.intro⟩,True.intro⟩,⟨sg36649,⟨sg36648,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36653,⟨sg36652,⟨sg36651,True.intro,True.intro⟩,True.intro⟩,⟨sg36654,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_418All : degreeTree62_418.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36633,degreeTree62_416All,degreeTree62_417All⟩ - -lemma degreeTree62_419All : degreeTree62_419.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36611,degreeTree62_415All,degreeTree62_418All⟩ - -lemma degreeTree62_420All : degreeTree62_420.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36666,⟨sg36661,⟨sg36658,⟨sg36657,⟨sg36656,True.intro,True.intro⟩,True.intro⟩,⟨sg36660,⟨sg36659,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36664,⟨sg36663,⟨sg36662,True.intro,True.intro⟩,True.intro⟩,⟨sg36665,True.intro,True.intro⟩⟩⟩,⟨sg36672,⟨sg36669,⟨sg36668,⟨sg36667,True.intro,True.intro⟩,True.intro⟩,⟨sg36671,⟨sg36670,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36675,⟨sg36674,⟨sg36673,True.intro,True.intro⟩,True.intro⟩,⟨sg36676,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_421All : degreeTree62_421.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36688,⟨sg36683,⟨sg36680,⟨sg36679,⟨sg36678,True.intro,True.intro⟩,True.intro⟩,⟨sg36682,⟨sg36681,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36686,⟨sg36685,⟨sg36684,True.intro,True.intro⟩,True.intro⟩,⟨sg36687,True.intro,True.intro⟩⟩⟩,⟨sg36694,⟨sg36691,⟨sg36690,⟨sg36689,True.intro,True.intro⟩,True.intro⟩,⟨sg36693,⟨sg36692,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36697,⟨sg36696,⟨sg36695,True.intro,True.intro⟩,True.intro⟩,⟨sg36698,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_422All : degreeTree62_422.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36677,degreeTree62_420All,degreeTree62_421All⟩ - -lemma degreeTree62_423All : degreeTree62_423.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36710,⟨sg36705,⟨sg36702,⟨sg36701,⟨sg36700,True.intro,True.intro⟩,True.intro⟩,⟨sg36704,⟨sg36703,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36708,⟨sg36707,⟨sg36706,True.intro,True.intro⟩,True.intro⟩,⟨sg36709,True.intro,True.intro⟩⟩⟩,⟨sg36716,⟨sg36713,⟨sg36712,⟨sg36711,True.intro,True.intro⟩,True.intro⟩,⟨sg36715,⟨sg36714,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36719,⟨sg36718,⟨sg36717,True.intro,True.intro⟩,True.intro⟩,⟨sg36720,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_424All : degreeTree62_424.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36732,⟨sg36727,⟨sg36724,⟨sg36723,⟨sg36722,True.intro,True.intro⟩,True.intro⟩,⟨sg36726,⟨sg36725,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36730,⟨sg36729,⟨sg36728,True.intro,True.intro⟩,True.intro⟩,⟨sg36731,True.intro,True.intro⟩⟩⟩,⟨sg36738,⟨sg36735,⟨sg36734,⟨sg36733,True.intro,True.intro⟩,True.intro⟩,⟨sg36737,⟨sg36736,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36741,⟨sg36740,⟨sg36739,True.intro,True.intro⟩,True.intro⟩,⟨sg36742,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_425All : degreeTree62_425.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36721,degreeTree62_423All,degreeTree62_424All⟩ - -lemma degreeTree62_426All : degreeTree62_426.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36699,degreeTree62_422All,degreeTree62_425All⟩ - -lemma degreeTree62_427All : degreeTree62_427.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36655,degreeTree62_419All,degreeTree62_426All⟩ - -lemma degreeTree62_428All : degreeTree62_428.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36754,⟨sg36749,⟨sg36746,⟨sg36745,⟨sg36744,True.intro,True.intro⟩,True.intro⟩,⟨sg36748,⟨sg36747,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36752,⟨sg36751,⟨sg36750,True.intro,True.intro⟩,True.intro⟩,⟨sg36753,True.intro,True.intro⟩⟩⟩,⟨sg36760,⟨sg36757,⟨sg36756,⟨sg36755,True.intro,True.intro⟩,True.intro⟩,⟨sg36759,⟨sg36758,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36763,⟨sg36762,⟨sg36761,True.intro,True.intro⟩,True.intro⟩,⟨sg36764,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_429All : degreeTree62_429.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36776,⟨sg36771,⟨sg36768,⟨sg36767,⟨sg36766,True.intro,True.intro⟩,True.intro⟩,⟨sg36770,⟨sg36769,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36774,⟨sg36773,⟨sg36772,True.intro,True.intro⟩,True.intro⟩,⟨sg36775,True.intro,True.intro⟩⟩⟩,⟨sg36782,⟨sg36779,⟨sg36778,⟨sg36777,True.intro,True.intro⟩,True.intro⟩,⟨sg36781,⟨sg36780,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36785,⟨sg36784,⟨sg36783,True.intro,True.intro⟩,True.intro⟩,⟨sg36786,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_430All : degreeTree62_430.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36765,degreeTree62_428All,degreeTree62_429All⟩ - -lemma degreeTree62_431All : degreeTree62_431.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36798,⟨sg36793,⟨sg36790,⟨sg36789,⟨sg36788,True.intro,True.intro⟩,True.intro⟩,⟨sg36792,⟨sg36791,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36796,⟨sg36795,⟨sg36794,True.intro,True.intro⟩,True.intro⟩,⟨sg36797,True.intro,True.intro⟩⟩⟩,⟨sg36804,⟨sg36801,⟨sg36800,⟨sg36799,True.intro,True.intro⟩,True.intro⟩,⟨sg36803,⟨sg36802,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36807,⟨sg36806,⟨sg36805,True.intro,True.intro⟩,True.intro⟩,⟨sg36808,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_432All : degreeTree62_432.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36820,⟨sg36815,⟨sg36812,⟨sg36811,⟨sg36810,True.intro,True.intro⟩,True.intro⟩,⟨sg36814,⟨sg36813,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36818,⟨sg36817,⟨sg36816,True.intro,True.intro⟩,True.intro⟩,⟨sg36819,True.intro,True.intro⟩⟩⟩,⟨sg36826,⟨sg36823,⟨sg36822,⟨sg36821,True.intro,True.intro⟩,True.intro⟩,⟨sg36825,⟨sg36824,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36829,⟨sg36828,⟨sg36827,True.intro,True.intro⟩,True.intro⟩,⟨sg36830,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_433All : degreeTree62_433.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36809,degreeTree62_431All,degreeTree62_432All⟩ - -lemma degreeTree62_434All : degreeTree62_434.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36787,degreeTree62_430All,degreeTree62_433All⟩ - -lemma degreeTree62_435All : degreeTree62_435.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36842,⟨sg36837,⟨sg36834,⟨sg36833,⟨sg36832,True.intro,True.intro⟩,True.intro⟩,⟨sg36836,⟨sg36835,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36840,⟨sg36839,⟨sg36838,True.intro,True.intro⟩,True.intro⟩,⟨sg36841,True.intro,True.intro⟩⟩⟩,⟨sg36848,⟨sg36845,⟨sg36844,⟨sg36843,True.intro,True.intro⟩,True.intro⟩,⟨sg36847,⟨sg36846,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36851,⟨sg36850,⟨sg36849,True.intro,True.intro⟩,True.intro⟩,⟨sg36852,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_436All : degreeTree62_436.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36864,⟨sg36859,⟨sg36856,⟨sg36855,⟨sg36854,True.intro,True.intro⟩,True.intro⟩,⟨sg36858,⟨sg36857,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36862,⟨sg36861,⟨sg36860,True.intro,True.intro⟩,True.intro⟩,⟨sg36863,True.intro,True.intro⟩⟩⟩,⟨sg36870,⟨sg36867,⟨sg36866,⟨sg36865,True.intro,True.intro⟩,True.intro⟩,⟨sg36869,⟨sg36868,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36873,⟨sg36872,⟨sg36871,True.intro,True.intro⟩,True.intro⟩,⟨sg36874,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_437All : degreeTree62_437.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36853,degreeTree62_435All,degreeTree62_436All⟩ - -lemma degreeTree62_438All : degreeTree62_438.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36886,⟨sg36881,⟨sg36878,⟨sg36877,⟨sg36876,True.intro,True.intro⟩,True.intro⟩,⟨sg36880,⟨sg36879,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36884,⟨sg36883,⟨sg36882,True.intro,True.intro⟩,True.intro⟩,⟨sg36885,True.intro,True.intro⟩⟩⟩,⟨sg36892,⟨sg36889,⟨sg36888,⟨sg36887,True.intro,True.intro⟩,True.intro⟩,⟨sg36891,⟨sg36890,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36895,⟨sg36894,⟨sg36893,True.intro,True.intro⟩,True.intro⟩,⟨sg36896,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_439All : degreeTree62_439.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36908,⟨sg36903,⟨sg36900,⟨sg36899,⟨sg36898,True.intro,True.intro⟩,True.intro⟩,⟨sg36902,⟨sg36901,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36906,⟨sg36905,⟨sg36904,True.intro,True.intro⟩,True.intro⟩,⟨sg36907,True.intro,True.intro⟩⟩⟩,⟨sg36913,⟨sg36911,⟨sg36910,⟨sg36909,True.intro,True.intro⟩,True.intro⟩,⟨sg36912,True.intro,True.intro⟩⟩,⟨sg36916,⟨sg36915,⟨sg36914,True.intro,True.intro⟩,True.intro⟩,⟨sg36917,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_440All : degreeTree62_440.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36897,degreeTree62_438All,degreeTree62_439All⟩ - -lemma degreeTree62_441All : degreeTree62_441.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36875,degreeTree62_437All,degreeTree62_440All⟩ - -lemma degreeTree62_442All : degreeTree62_442.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36831,degreeTree62_434All,degreeTree62_441All⟩ - -lemma degreeTree62_443All : degreeTree62_443.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36743,degreeTree62_427All,degreeTree62_442All⟩ - -lemma degreeTree62_444All : degreeTree62_444.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36567,degreeTree62_412All,degreeTree62_443All⟩ - -lemma degreeTree62_445All : degreeTree62_445.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36929,⟨sg36924,⟨sg36921,⟨sg36920,⟨sg36919,True.intro,True.intro⟩,True.intro⟩,⟨sg36923,⟨sg36922,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36927,⟨sg36926,⟨sg36925,True.intro,True.intro⟩,True.intro⟩,⟨sg36928,True.intro,True.intro⟩⟩⟩,⟨sg36935,⟨sg36932,⟨sg36931,⟨sg36930,True.intro,True.intro⟩,True.intro⟩,⟨sg36934,⟨sg36933,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36938,⟨sg36937,⟨sg36936,True.intro,True.intro⟩,True.intro⟩,⟨sg36939,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_446All : degreeTree62_446.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36951,⟨sg36946,⟨sg36943,⟨sg36942,⟨sg36941,True.intro,True.intro⟩,True.intro⟩,⟨sg36945,⟨sg36944,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36949,⟨sg36948,⟨sg36947,True.intro,True.intro⟩,True.intro⟩,⟨sg36950,True.intro,True.intro⟩⟩⟩,⟨sg36957,⟨sg36954,⟨sg36953,⟨sg36952,True.intro,True.intro⟩,True.intro⟩,⟨sg36956,⟨sg36955,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36960,⟨sg36959,⟨sg36958,True.intro,True.intro⟩,True.intro⟩,⟨sg36961,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_447All : degreeTree62_447.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36940,degreeTree62_445All,degreeTree62_446All⟩ - -lemma degreeTree62_448All : degreeTree62_448.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36973,⟨sg36968,⟨sg36965,⟨sg36964,⟨sg36963,True.intro,True.intro⟩,True.intro⟩,⟨sg36967,⟨sg36966,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36971,⟨sg36970,⟨sg36969,True.intro,True.intro⟩,True.intro⟩,⟨sg36972,True.intro,True.intro⟩⟩⟩,⟨sg36979,⟨sg36976,⟨sg36975,⟨sg36974,True.intro,True.intro⟩,True.intro⟩,⟨sg36978,⟨sg36977,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36982,⟨sg36981,⟨sg36980,True.intro,True.intro⟩,True.intro⟩,⟨sg36983,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_449All : degreeTree62_449.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36995,⟨sg36990,⟨sg36987,⟨sg36986,⟨sg36985,True.intro,True.intro⟩,True.intro⟩,⟨sg36989,⟨sg36988,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36993,⟨sg36992,⟨sg36991,True.intro,True.intro⟩,True.intro⟩,⟨sg36994,True.intro,True.intro⟩⟩⟩,⟨sg37001,⟨sg36998,⟨sg36997,⟨sg36996,True.intro,True.intro⟩,True.intro⟩,⟨sg37000,⟨sg36999,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37004,⟨sg37003,⟨sg37002,True.intro,True.intro⟩,True.intro⟩,⟨sg37005,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_450All : degreeTree62_450.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36984,degreeTree62_448All,degreeTree62_449All⟩ - -lemma degreeTree62_451All : degreeTree62_451.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36962,degreeTree62_447All,degreeTree62_450All⟩ - -lemma degreeTree62_452All : degreeTree62_452.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37017,⟨sg37012,⟨sg37009,⟨sg37008,⟨sg37007,True.intro,True.intro⟩,True.intro⟩,⟨sg37011,⟨sg37010,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37015,⟨sg37014,⟨sg37013,True.intro,True.intro⟩,True.intro⟩,⟨sg37016,True.intro,True.intro⟩⟩⟩,⟨sg37023,⟨sg37020,⟨sg37019,⟨sg37018,True.intro,True.intro⟩,True.intro⟩,⟨sg37022,⟨sg37021,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37026,⟨sg37025,⟨sg37024,True.intro,True.intro⟩,True.intro⟩,⟨sg37027,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_453All : degreeTree62_453.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37039,⟨sg37034,⟨sg37031,⟨sg37030,⟨sg37029,True.intro,True.intro⟩,True.intro⟩,⟨sg37033,⟨sg37032,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37037,⟨sg37036,⟨sg37035,True.intro,True.intro⟩,True.intro⟩,⟨sg37038,True.intro,True.intro⟩⟩⟩,⟨sg37045,⟨sg37042,⟨sg37041,⟨sg37040,True.intro,True.intro⟩,True.intro⟩,⟨sg37044,⟨sg37043,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37048,⟨sg37047,⟨sg37046,True.intro,True.intro⟩,True.intro⟩,⟨sg37049,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_454All : degreeTree62_454.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37028,degreeTree62_452All,degreeTree62_453All⟩ - -lemma degreeTree62_455All : degreeTree62_455.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37061,⟨sg37056,⟨sg37053,⟨sg37052,⟨sg37051,True.intro,True.intro⟩,True.intro⟩,⟨sg37055,⟨sg37054,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37059,⟨sg37058,⟨sg37057,True.intro,True.intro⟩,True.intro⟩,⟨sg37060,True.intro,True.intro⟩⟩⟩,⟨sg37067,⟨sg37064,⟨sg37063,⟨sg37062,True.intro,True.intro⟩,True.intro⟩,⟨sg37066,⟨sg37065,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37070,⟨sg37069,⟨sg37068,True.intro,True.intro⟩,True.intro⟩,⟨sg37071,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_456All : degreeTree62_456.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37083,⟨sg37078,⟨sg37075,⟨sg37074,⟨sg37073,True.intro,True.intro⟩,True.intro⟩,⟨sg37077,⟨sg37076,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37081,⟨sg37080,⟨sg37079,True.intro,True.intro⟩,True.intro⟩,⟨sg37082,True.intro,True.intro⟩⟩⟩,⟨sg37089,⟨sg37086,⟨sg37085,⟨sg37084,True.intro,True.intro⟩,True.intro⟩,⟨sg37088,⟨sg37087,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37092,⟨sg37091,⟨sg37090,True.intro,True.intro⟩,True.intro⟩,⟨sg37093,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_457All : degreeTree62_457.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37072,degreeTree62_455All,degreeTree62_456All⟩ - -lemma degreeTree62_458All : degreeTree62_458.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37050,degreeTree62_454All,degreeTree62_457All⟩ - -lemma degreeTree62_459All : degreeTree62_459.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37006,degreeTree62_451All,degreeTree62_458All⟩ - -lemma degreeTree62_460All : degreeTree62_460.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37105,⟨sg37100,⟨sg37097,⟨sg37096,⟨sg37095,True.intro,True.intro⟩,True.intro⟩,⟨sg37099,⟨sg37098,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37103,⟨sg37102,⟨sg37101,True.intro,True.intro⟩,True.intro⟩,⟨sg37104,True.intro,True.intro⟩⟩⟩,⟨sg37111,⟨sg37108,⟨sg37107,⟨sg37106,True.intro,True.intro⟩,True.intro⟩,⟨sg37110,⟨sg37109,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37114,⟨sg37113,⟨sg37112,True.intro,True.intro⟩,True.intro⟩,⟨sg37115,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_461All : degreeTree62_461.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37127,⟨sg37122,⟨sg37119,⟨sg37118,⟨sg37117,True.intro,True.intro⟩,True.intro⟩,⟨sg37121,⟨sg37120,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37125,⟨sg37124,⟨sg37123,True.intro,True.intro⟩,True.intro⟩,⟨sg37126,True.intro,True.intro⟩⟩⟩,⟨sg37133,⟨sg37130,⟨sg37129,⟨sg37128,True.intro,True.intro⟩,True.intro⟩,⟨sg37132,⟨sg37131,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37136,⟨sg37135,⟨sg37134,True.intro,True.intro⟩,True.intro⟩,⟨sg37137,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_462All : degreeTree62_462.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37116,degreeTree62_460All,degreeTree62_461All⟩ - -lemma degreeTree62_463All : degreeTree62_463.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37149,⟨sg37144,⟨sg37141,⟨sg37140,⟨sg37139,True.intro,True.intro⟩,True.intro⟩,⟨sg37143,⟨sg37142,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37147,⟨sg37146,⟨sg37145,True.intro,True.intro⟩,True.intro⟩,⟨sg37148,True.intro,True.intro⟩⟩⟩,⟨sg37155,⟨sg37152,⟨sg37151,⟨sg37150,True.intro,True.intro⟩,True.intro⟩,⟨sg37154,⟨sg37153,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37158,⟨sg37157,⟨sg37156,True.intro,True.intro⟩,True.intro⟩,⟨sg37159,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_464All : degreeTree62_464.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37171,⟨sg37166,⟨sg37163,⟨sg37162,⟨sg37161,True.intro,True.intro⟩,True.intro⟩,⟨sg37165,⟨sg37164,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37169,⟨sg37168,⟨sg37167,True.intro,True.intro⟩,True.intro⟩,⟨sg37170,True.intro,True.intro⟩⟩⟩,⟨sg37177,⟨sg37174,⟨sg37173,⟨sg37172,True.intro,True.intro⟩,True.intro⟩,⟨sg37176,⟨sg37175,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37180,⟨sg37179,⟨sg37178,True.intro,True.intro⟩,True.intro⟩,⟨sg37181,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_465All : degreeTree62_465.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37160,degreeTree62_463All,degreeTree62_464All⟩ - -lemma degreeTree62_466All : degreeTree62_466.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37138,degreeTree62_462All,degreeTree62_465All⟩ - -lemma degreeTree62_467All : degreeTree62_467.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37193,⟨sg37188,⟨sg37185,⟨sg37184,⟨sg37183,True.intro,True.intro⟩,True.intro⟩,⟨sg37187,⟨sg37186,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37191,⟨sg37190,⟨sg37189,True.intro,True.intro⟩,True.intro⟩,⟨sg37192,True.intro,True.intro⟩⟩⟩,⟨sg37199,⟨sg37196,⟨sg37195,⟨sg37194,True.intro,True.intro⟩,True.intro⟩,⟨sg37198,⟨sg37197,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37202,⟨sg37201,⟨sg37200,True.intro,True.intro⟩,True.intro⟩,⟨sg37203,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_468All : degreeTree62_468.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37215,⟨sg37210,⟨sg37207,⟨sg37206,⟨sg37205,True.intro,True.intro⟩,True.intro⟩,⟨sg37209,⟨sg37208,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37213,⟨sg37212,⟨sg37211,True.intro,True.intro⟩,True.intro⟩,⟨sg37214,True.intro,True.intro⟩⟩⟩,⟨sg37221,⟨sg37218,⟨sg37217,⟨sg37216,True.intro,True.intro⟩,True.intro⟩,⟨sg37220,⟨sg37219,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37224,⟨sg37223,⟨sg37222,True.intro,True.intro⟩,True.intro⟩,⟨sg37225,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_469All : degreeTree62_469.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37204,degreeTree62_467All,degreeTree62_468All⟩ - -lemma degreeTree62_470All : degreeTree62_470.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37237,⟨sg37232,⟨sg37229,⟨sg37228,⟨sg37227,True.intro,True.intro⟩,True.intro⟩,⟨sg37231,⟨sg37230,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37235,⟨sg37234,⟨sg37233,True.intro,True.intro⟩,True.intro⟩,⟨sg37236,True.intro,True.intro⟩⟩⟩,⟨sg37243,⟨sg37240,⟨sg37239,⟨sg37238,True.intro,True.intro⟩,True.intro⟩,⟨sg37242,⟨sg37241,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37246,⟨sg37245,⟨sg37244,True.intro,True.intro⟩,True.intro⟩,⟨sg37247,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_471All : degreeTree62_471.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37259,⟨sg37254,⟨sg37251,⟨sg37250,⟨sg37249,True.intro,True.intro⟩,True.intro⟩,⟨sg37253,⟨sg37252,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37257,⟨sg37256,⟨sg37255,True.intro,True.intro⟩,True.intro⟩,⟨sg37258,True.intro,True.intro⟩⟩⟩,⟨sg37264,⟨sg37262,⟨sg37261,⟨sg37260,True.intro,True.intro⟩,True.intro⟩,⟨sg37263,True.intro,True.intro⟩⟩,⟨sg37267,⟨sg37266,⟨sg37265,True.intro,True.intro⟩,True.intro⟩,⟨sg37268,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_472All : degreeTree62_472.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37248,degreeTree62_470All,degreeTree62_471All⟩ - -lemma degreeTree62_473All : degreeTree62_473.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37226,degreeTree62_469All,degreeTree62_472All⟩ - -lemma degreeTree62_474All : degreeTree62_474.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37182,degreeTree62_466All,degreeTree62_473All⟩ - -lemma degreeTree62_475All : degreeTree62_475.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37094,degreeTree62_459All,degreeTree62_474All⟩ - -lemma degreeTree62_476All : degreeTree62_476.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37280,⟨sg37275,⟨sg37272,⟨sg37271,⟨sg37270,True.intro,True.intro⟩,True.intro⟩,⟨sg37274,⟨sg37273,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37278,⟨sg37277,⟨sg37276,True.intro,True.intro⟩,True.intro⟩,⟨sg37279,True.intro,True.intro⟩⟩⟩,⟨sg37286,⟨sg37283,⟨sg37282,⟨sg37281,True.intro,True.intro⟩,True.intro⟩,⟨sg37285,⟨sg37284,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37289,⟨sg37288,⟨sg37287,True.intro,True.intro⟩,True.intro⟩,⟨sg37290,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_477All : degreeTree62_477.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37302,⟨sg37297,⟨sg37294,⟨sg37293,⟨sg37292,True.intro,True.intro⟩,True.intro⟩,⟨sg37296,⟨sg37295,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37300,⟨sg37299,⟨sg37298,True.intro,True.intro⟩,True.intro⟩,⟨sg37301,True.intro,True.intro⟩⟩⟩,⟨sg37308,⟨sg37305,⟨sg37304,⟨sg37303,True.intro,True.intro⟩,True.intro⟩,⟨sg37307,⟨sg37306,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37311,⟨sg37310,⟨sg37309,True.intro,True.intro⟩,True.intro⟩,⟨sg37312,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_478All : degreeTree62_478.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37291,degreeTree62_476All,degreeTree62_477All⟩ - -lemma degreeTree62_479All : degreeTree62_479.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37324,⟨sg37319,⟨sg37316,⟨sg37315,⟨sg37314,True.intro,True.intro⟩,True.intro⟩,⟨sg37318,⟨sg37317,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37322,⟨sg37321,⟨sg37320,True.intro,True.intro⟩,True.intro⟩,⟨sg37323,True.intro,True.intro⟩⟩⟩,⟨sg37330,⟨sg37327,⟨sg37326,⟨sg37325,True.intro,True.intro⟩,True.intro⟩,⟨sg37329,⟨sg37328,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37333,⟨sg37332,⟨sg37331,True.intro,True.intro⟩,True.intro⟩,⟨sg37334,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_480All : degreeTree62_480.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37346,⟨sg37341,⟨sg37338,⟨sg37337,⟨sg37336,True.intro,True.intro⟩,True.intro⟩,⟨sg37340,⟨sg37339,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37344,⟨sg37343,⟨sg37342,True.intro,True.intro⟩,True.intro⟩,⟨sg37345,True.intro,True.intro⟩⟩⟩,⟨sg37352,⟨sg37349,⟨sg37348,⟨sg37347,True.intro,True.intro⟩,True.intro⟩,⟨sg37351,⟨sg37350,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37355,⟨sg37354,⟨sg37353,True.intro,True.intro⟩,True.intro⟩,⟨sg37356,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_481All : degreeTree62_481.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37335,degreeTree62_479All,degreeTree62_480All⟩ - -lemma degreeTree62_482All : degreeTree62_482.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37313,degreeTree62_478All,degreeTree62_481All⟩ - -lemma degreeTree62_483All : degreeTree62_483.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37368,⟨sg37363,⟨sg37360,⟨sg37359,⟨sg37358,True.intro,True.intro⟩,True.intro⟩,⟨sg37362,⟨sg37361,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37366,⟨sg37365,⟨sg37364,True.intro,True.intro⟩,True.intro⟩,⟨sg37367,True.intro,True.intro⟩⟩⟩,⟨sg37374,⟨sg37371,⟨sg37370,⟨sg37369,True.intro,True.intro⟩,True.intro⟩,⟨sg37373,⟨sg37372,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37377,⟨sg37376,⟨sg37375,True.intro,True.intro⟩,True.intro⟩,⟨sg37378,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_484All : degreeTree62_484.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37390,⟨sg37385,⟨sg37382,⟨sg37381,⟨sg37380,True.intro,True.intro⟩,True.intro⟩,⟨sg37384,⟨sg37383,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37388,⟨sg37387,⟨sg37386,True.intro,True.intro⟩,True.intro⟩,⟨sg37389,True.intro,True.intro⟩⟩⟩,⟨sg37396,⟨sg37393,⟨sg37392,⟨sg37391,True.intro,True.intro⟩,True.intro⟩,⟨sg37395,⟨sg37394,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37399,⟨sg37398,⟨sg37397,True.intro,True.intro⟩,True.intro⟩,⟨sg37400,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_485All : degreeTree62_485.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37379,degreeTree62_483All,degreeTree62_484All⟩ - -lemma degreeTree62_486All : degreeTree62_486.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37412,⟨sg37407,⟨sg37404,⟨sg37403,⟨sg37402,True.intro,True.intro⟩,True.intro⟩,⟨sg37406,⟨sg37405,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37410,⟨sg37409,⟨sg37408,True.intro,True.intro⟩,True.intro⟩,⟨sg37411,True.intro,True.intro⟩⟩⟩,⟨sg37418,⟨sg37415,⟨sg37414,⟨sg37413,True.intro,True.intro⟩,True.intro⟩,⟨sg37417,⟨sg37416,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37421,⟨sg37420,⟨sg37419,True.intro,True.intro⟩,True.intro⟩,⟨sg37422,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_487All : degreeTree62_487.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37434,⟨sg37429,⟨sg37426,⟨sg37425,⟨sg37424,True.intro,True.intro⟩,True.intro⟩,⟨sg37428,⟨sg37427,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37432,⟨sg37431,⟨sg37430,True.intro,True.intro⟩,True.intro⟩,⟨sg37433,True.intro,True.intro⟩⟩⟩,⟨sg37439,⟨sg37437,⟨sg37436,⟨sg37435,True.intro,True.intro⟩,True.intro⟩,⟨sg37438,True.intro,True.intro⟩⟩,⟨sg37442,⟨sg37441,⟨sg37440,True.intro,True.intro⟩,True.intro⟩,⟨sg37443,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_488All : degreeTree62_488.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37423,degreeTree62_486All,degreeTree62_487All⟩ - -lemma degreeTree62_489All : degreeTree62_489.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37401,degreeTree62_485All,degreeTree62_488All⟩ - -lemma degreeTree62_490All : degreeTree62_490.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37357,degreeTree62_482All,degreeTree62_489All⟩ - -lemma degreeTree62_491All : degreeTree62_491.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37455,⟨sg37450,⟨sg37447,⟨sg37446,⟨sg37445,True.intro,True.intro⟩,True.intro⟩,⟨sg37449,⟨sg37448,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37453,⟨sg37452,⟨sg37451,True.intro,True.intro⟩,True.intro⟩,⟨sg37454,True.intro,True.intro⟩⟩⟩,⟨sg37461,⟨sg37458,⟨sg37457,⟨sg37456,True.intro,True.intro⟩,True.intro⟩,⟨sg37460,⟨sg37459,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37464,⟨sg37463,⟨sg37462,True.intro,True.intro⟩,True.intro⟩,⟨sg37465,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_492All : degreeTree62_492.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37477,⟨sg37472,⟨sg37469,⟨sg37468,⟨sg37467,True.intro,True.intro⟩,True.intro⟩,⟨sg37471,⟨sg37470,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37475,⟨sg37474,⟨sg37473,True.intro,True.intro⟩,True.intro⟩,⟨sg37476,True.intro,True.intro⟩⟩⟩,⟨sg37483,⟨sg37480,⟨sg37479,⟨sg37478,True.intro,True.intro⟩,True.intro⟩,⟨sg37482,⟨sg37481,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37486,⟨sg37485,⟨sg37484,True.intro,True.intro⟩,True.intro⟩,⟨sg37487,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_493All : degreeTree62_493.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37466,degreeTree62_491All,degreeTree62_492All⟩ - -lemma degreeTree62_494All : degreeTree62_494.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37499,⟨sg37494,⟨sg37491,⟨sg37490,⟨sg37489,True.intro,True.intro⟩,True.intro⟩,⟨sg37493,⟨sg37492,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37497,⟨sg37496,⟨sg37495,True.intro,True.intro⟩,True.intro⟩,⟨sg37498,True.intro,True.intro⟩⟩⟩,⟨sg37505,⟨sg37502,⟨sg37501,⟨sg37500,True.intro,True.intro⟩,True.intro⟩,⟨sg37504,⟨sg37503,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37508,⟨sg37507,⟨sg37506,True.intro,True.intro⟩,True.intro⟩,⟨sg37509,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_495All : degreeTree62_495.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37521,⟨sg37516,⟨sg37513,⟨sg37512,⟨sg37511,True.intro,True.intro⟩,True.intro⟩,⟨sg37515,⟨sg37514,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37519,⟨sg37518,⟨sg37517,True.intro,True.intro⟩,True.intro⟩,⟨sg37520,True.intro,True.intro⟩⟩⟩,⟨sg37527,⟨sg37524,⟨sg37523,⟨sg37522,True.intro,True.intro⟩,True.intro⟩,⟨sg37526,⟨sg37525,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37530,⟨sg37529,⟨sg37528,True.intro,True.intro⟩,True.intro⟩,⟨sg37531,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_496All : degreeTree62_496.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37510,degreeTree62_494All,degreeTree62_495All⟩ - -lemma degreeTree62_497All : degreeTree62_497.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37488,degreeTree62_493All,degreeTree62_496All⟩ - -lemma degreeTree62_498All : degreeTree62_498.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37543,⟨sg37538,⟨sg37535,⟨sg37534,⟨sg37533,True.intro,True.intro⟩,True.intro⟩,⟨sg37537,⟨sg37536,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37541,⟨sg37540,⟨sg37539,True.intro,True.intro⟩,True.intro⟩,⟨sg37542,True.intro,True.intro⟩⟩⟩,⟨sg37549,⟨sg37546,⟨sg37545,⟨sg37544,True.intro,True.intro⟩,True.intro⟩,⟨sg37548,⟨sg37547,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37552,⟨sg37551,⟨sg37550,True.intro,True.intro⟩,True.intro⟩,⟨sg37553,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_499All : degreeTree62_499.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37565,⟨sg37560,⟨sg37557,⟨sg37556,⟨sg37555,True.intro,True.intro⟩,True.intro⟩,⟨sg37559,⟨sg37558,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37563,⟨sg37562,⟨sg37561,True.intro,True.intro⟩,True.intro⟩,⟨sg37564,True.intro,True.intro⟩⟩⟩,⟨sg37571,⟨sg37568,⟨sg37567,⟨sg37566,True.intro,True.intro⟩,True.intro⟩,⟨sg37570,⟨sg37569,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37574,⟨sg37573,⟨sg37572,True.intro,True.intro⟩,True.intro⟩,⟨sg37575,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_500All : degreeTree62_500.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37554,degreeTree62_498All,degreeTree62_499All⟩ - -lemma degreeTree62_501All : degreeTree62_501.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37587,⟨sg37582,⟨sg37579,⟨sg37578,⟨sg37577,True.intro,True.intro⟩,True.intro⟩,⟨sg37581,⟨sg37580,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37585,⟨sg37584,⟨sg37583,True.intro,True.intro⟩,True.intro⟩,⟨sg37586,True.intro,True.intro⟩⟩⟩,⟨sg37593,⟨sg37590,⟨sg37589,⟨sg37588,True.intro,True.intro⟩,True.intro⟩,⟨sg37592,⟨sg37591,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37596,⟨sg37595,⟨sg37594,True.intro,True.intro⟩,True.intro⟩,⟨sg37597,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_502All : degreeTree62_502.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37609,⟨sg37604,⟨sg37601,⟨sg37600,⟨sg37599,True.intro,True.intro⟩,True.intro⟩,⟨sg37603,⟨sg37602,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37607,⟨sg37606,⟨sg37605,True.intro,True.intro⟩,True.intro⟩,⟨sg37608,True.intro,True.intro⟩⟩⟩,⟨sg37614,⟨sg37612,⟨sg37611,⟨sg37610,True.intro,True.intro⟩,True.intro⟩,⟨sg37613,True.intro,True.intro⟩⟩,⟨sg37617,⟨sg37616,⟨sg37615,True.intro,True.intro⟩,True.intro⟩,⟨sg37618,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_503All : degreeTree62_503.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37598,degreeTree62_501All,degreeTree62_502All⟩ - -lemma degreeTree62_504All : degreeTree62_504.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37576,degreeTree62_500All,degreeTree62_503All⟩ - -lemma degreeTree62_505All : degreeTree62_505.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37532,degreeTree62_497All,degreeTree62_504All⟩ - -lemma degreeTree62_506All : degreeTree62_506.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37444,degreeTree62_490All,degreeTree62_505All⟩ - -lemma degreeTree62_507All : degreeTree62_507.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37269,degreeTree62_475All,degreeTree62_506All⟩ - -lemma degreeTree62_508All : degreeTree62_508.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36918,degreeTree62_444All,degreeTree62_507All⟩ - -lemma degreeTree62_509All : degreeTree62_509.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg36216,degreeTree62_381All,degreeTree62_508All⟩ - -lemma degreeTree62_510All : degreeTree62_510.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg34812,degreeTree62_254All,degreeTree62_509All⟩ - -lemma degreeTree62_511All : degreeTree62_511.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37630,⟨sg37625,⟨sg37622,⟨sg37621,⟨sg37620,True.intro,True.intro⟩,True.intro⟩,⟨sg37624,⟨sg37623,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37628,⟨sg37627,⟨sg37626,True.intro,True.intro⟩,True.intro⟩,⟨sg37629,True.intro,True.intro⟩⟩⟩,⟨sg37636,⟨sg37633,⟨sg37632,⟨sg37631,True.intro,True.intro⟩,True.intro⟩,⟨sg37635,⟨sg37634,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37639,⟨sg37638,⟨sg37637,True.intro,True.intro⟩,True.intro⟩,⟨sg37640,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_512All : degreeTree62_512.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37652,⟨sg37647,⟨sg37644,⟨sg37643,⟨sg37642,True.intro,True.intro⟩,True.intro⟩,⟨sg37646,⟨sg37645,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37650,⟨sg37649,⟨sg37648,True.intro,True.intro⟩,True.intro⟩,⟨sg37651,True.intro,True.intro⟩⟩⟩,⟨sg37658,⟨sg37655,⟨sg37654,⟨sg37653,True.intro,True.intro⟩,True.intro⟩,⟨sg37657,⟨sg37656,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37661,⟨sg37660,⟨sg37659,True.intro,True.intro⟩,True.intro⟩,⟨sg37662,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_513All : degreeTree62_513.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37641,degreeTree62_511All,degreeTree62_512All⟩ - -lemma degreeTree62_514All : degreeTree62_514.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37674,⟨sg37669,⟨sg37666,⟨sg37665,⟨sg37664,True.intro,True.intro⟩,True.intro⟩,⟨sg37668,⟨sg37667,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37672,⟨sg37671,⟨sg37670,True.intro,True.intro⟩,True.intro⟩,⟨sg37673,True.intro,True.intro⟩⟩⟩,⟨sg37680,⟨sg37677,⟨sg37676,⟨sg37675,True.intro,True.intro⟩,True.intro⟩,⟨sg37679,⟨sg37678,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37683,⟨sg37682,⟨sg37681,True.intro,True.intro⟩,True.intro⟩,⟨sg37684,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_515All : degreeTree62_515.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37696,⟨sg37691,⟨sg37688,⟨sg37687,⟨sg37686,True.intro,True.intro⟩,True.intro⟩,⟨sg37690,⟨sg37689,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37694,⟨sg37693,⟨sg37692,True.intro,True.intro⟩,True.intro⟩,⟨sg37695,True.intro,True.intro⟩⟩⟩,⟨sg37702,⟨sg37699,⟨sg37698,⟨sg37697,True.intro,True.intro⟩,True.intro⟩,⟨sg37701,⟨sg37700,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37705,⟨sg37704,⟨sg37703,True.intro,True.intro⟩,True.intro⟩,⟨sg37706,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_516All : degreeTree62_516.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37685,degreeTree62_514All,degreeTree62_515All⟩ - -lemma degreeTree62_517All : degreeTree62_517.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37663,degreeTree62_513All,degreeTree62_516All⟩ - -lemma degreeTree62_518All : degreeTree62_518.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37718,⟨sg37713,⟨sg37710,⟨sg37709,⟨sg37708,True.intro,True.intro⟩,True.intro⟩,⟨sg37712,⟨sg37711,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37716,⟨sg37715,⟨sg37714,True.intro,True.intro⟩,True.intro⟩,⟨sg37717,True.intro,True.intro⟩⟩⟩,⟨sg37724,⟨sg37721,⟨sg37720,⟨sg37719,True.intro,True.intro⟩,True.intro⟩,⟨sg37723,⟨sg37722,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37727,⟨sg37726,⟨sg37725,True.intro,True.intro⟩,True.intro⟩,⟨sg37728,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_519All : degreeTree62_519.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37740,⟨sg37735,⟨sg37732,⟨sg37731,⟨sg37730,True.intro,True.intro⟩,True.intro⟩,⟨sg37734,⟨sg37733,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37738,⟨sg37737,⟨sg37736,True.intro,True.intro⟩,True.intro⟩,⟨sg37739,True.intro,True.intro⟩⟩⟩,⟨sg37746,⟨sg37743,⟨sg37742,⟨sg37741,True.intro,True.intro⟩,True.intro⟩,⟨sg37745,⟨sg37744,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37749,⟨sg37748,⟨sg37747,True.intro,True.intro⟩,True.intro⟩,⟨sg37750,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_520All : degreeTree62_520.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37729,degreeTree62_518All,degreeTree62_519All⟩ - -lemma degreeTree62_521All : degreeTree62_521.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37762,⟨sg37757,⟨sg37754,⟨sg37753,⟨sg37752,True.intro,True.intro⟩,True.intro⟩,⟨sg37756,⟨sg37755,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37760,⟨sg37759,⟨sg37758,True.intro,True.intro⟩,True.intro⟩,⟨sg37761,True.intro,True.intro⟩⟩⟩,⟨sg37768,⟨sg37765,⟨sg37764,⟨sg37763,True.intro,True.intro⟩,True.intro⟩,⟨sg37767,⟨sg37766,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37771,⟨sg37770,⟨sg37769,True.intro,True.intro⟩,True.intro⟩,⟨sg37772,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_522All : degreeTree62_522.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37784,⟨sg37779,⟨sg37776,⟨sg37775,⟨sg37774,True.intro,True.intro⟩,True.intro⟩,⟨sg37778,⟨sg37777,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37782,⟨sg37781,⟨sg37780,True.intro,True.intro⟩,True.intro⟩,⟨sg37783,True.intro,True.intro⟩⟩⟩,⟨sg37790,⟨sg37787,⟨sg37786,⟨sg37785,True.intro,True.intro⟩,True.intro⟩,⟨sg37789,⟨sg37788,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37793,⟨sg37792,⟨sg37791,True.intro,True.intro⟩,True.intro⟩,⟨sg37794,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_523All : degreeTree62_523.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37773,degreeTree62_521All,degreeTree62_522All⟩ - -lemma degreeTree62_524All : degreeTree62_524.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37751,degreeTree62_520All,degreeTree62_523All⟩ - -lemma degreeTree62_525All : degreeTree62_525.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37707,degreeTree62_517All,degreeTree62_524All⟩ - -lemma degreeTree62_526All : degreeTree62_526.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37806,⟨sg37801,⟨sg37798,⟨sg37797,⟨sg37796,True.intro,True.intro⟩,True.intro⟩,⟨sg37800,⟨sg37799,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37804,⟨sg37803,⟨sg37802,True.intro,True.intro⟩,True.intro⟩,⟨sg37805,True.intro,True.intro⟩⟩⟩,⟨sg37812,⟨sg37809,⟨sg37808,⟨sg37807,True.intro,True.intro⟩,True.intro⟩,⟨sg37811,⟨sg37810,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37815,⟨sg37814,⟨sg37813,True.intro,True.intro⟩,True.intro⟩,⟨sg37816,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_527All : degreeTree62_527.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37828,⟨sg37823,⟨sg37820,⟨sg37819,⟨sg37818,True.intro,True.intro⟩,True.intro⟩,⟨sg37822,⟨sg37821,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37826,⟨sg37825,⟨sg37824,True.intro,True.intro⟩,True.intro⟩,⟨sg37827,True.intro,True.intro⟩⟩⟩,⟨sg37834,⟨sg37831,⟨sg37830,⟨sg37829,True.intro,True.intro⟩,True.intro⟩,⟨sg37833,⟨sg37832,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37837,⟨sg37836,⟨sg37835,True.intro,True.intro⟩,True.intro⟩,⟨sg37838,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_528All : degreeTree62_528.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37817,degreeTree62_526All,degreeTree62_527All⟩ - -lemma degreeTree62_529All : degreeTree62_529.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37850,⟨sg37845,⟨sg37842,⟨sg37841,⟨sg37840,True.intro,True.intro⟩,True.intro⟩,⟨sg37844,⟨sg37843,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37848,⟨sg37847,⟨sg37846,True.intro,True.intro⟩,True.intro⟩,⟨sg37849,True.intro,True.intro⟩⟩⟩,⟨sg37856,⟨sg37853,⟨sg37852,⟨sg37851,True.intro,True.intro⟩,True.intro⟩,⟨sg37855,⟨sg37854,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37859,⟨sg37858,⟨sg37857,True.intro,True.intro⟩,True.intro⟩,⟨sg37860,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_530All : degreeTree62_530.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37872,⟨sg37867,⟨sg37864,⟨sg37863,⟨sg37862,True.intro,True.intro⟩,True.intro⟩,⟨sg37866,⟨sg37865,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37870,⟨sg37869,⟨sg37868,True.intro,True.intro⟩,True.intro⟩,⟨sg37871,True.intro,True.intro⟩⟩⟩,⟨sg37878,⟨sg37875,⟨sg37874,⟨sg37873,True.intro,True.intro⟩,True.intro⟩,⟨sg37877,⟨sg37876,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37881,⟨sg37880,⟨sg37879,True.intro,True.intro⟩,True.intro⟩,⟨sg37882,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_531All : degreeTree62_531.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37861,degreeTree62_529All,degreeTree62_530All⟩ - -lemma degreeTree62_532All : degreeTree62_532.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37839,degreeTree62_528All,degreeTree62_531All⟩ - -lemma degreeTree62_533All : degreeTree62_533.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37894,⟨sg37889,⟨sg37886,⟨sg37885,⟨sg37884,True.intro,True.intro⟩,True.intro⟩,⟨sg37888,⟨sg37887,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37892,⟨sg37891,⟨sg37890,True.intro,True.intro⟩,True.intro⟩,⟨sg37893,True.intro,True.intro⟩⟩⟩,⟨sg37900,⟨sg37897,⟨sg37896,⟨sg37895,True.intro,True.intro⟩,True.intro⟩,⟨sg37899,⟨sg37898,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37903,⟨sg37902,⟨sg37901,True.intro,True.intro⟩,True.intro⟩,⟨sg37904,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_534All : degreeTree62_534.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37916,⟨sg37911,⟨sg37908,⟨sg37907,⟨sg37906,True.intro,True.intro⟩,True.intro⟩,⟨sg37910,⟨sg37909,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37914,⟨sg37913,⟨sg37912,True.intro,True.intro⟩,True.intro⟩,⟨sg37915,True.intro,True.intro⟩⟩⟩,⟨sg37922,⟨sg37919,⟨sg37918,⟨sg37917,True.intro,True.intro⟩,True.intro⟩,⟨sg37921,⟨sg37920,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37925,⟨sg37924,⟨sg37923,True.intro,True.intro⟩,True.intro⟩,⟨sg37926,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_535All : degreeTree62_535.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37905,degreeTree62_533All,degreeTree62_534All⟩ - -lemma degreeTree62_536All : degreeTree62_536.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37938,⟨sg37933,⟨sg37930,⟨sg37929,⟨sg37928,True.intro,True.intro⟩,True.intro⟩,⟨sg37932,⟨sg37931,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37936,⟨sg37935,⟨sg37934,True.intro,True.intro⟩,True.intro⟩,⟨sg37937,True.intro,True.intro⟩⟩⟩,⟨sg37944,⟨sg37941,⟨sg37940,⟨sg37939,True.intro,True.intro⟩,True.intro⟩,⟨sg37943,⟨sg37942,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37947,⟨sg37946,⟨sg37945,True.intro,True.intro⟩,True.intro⟩,⟨sg37948,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_537All : degreeTree62_537.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37960,⟨sg37955,⟨sg37952,⟨sg37951,⟨sg37950,True.intro,True.intro⟩,True.intro⟩,⟨sg37954,⟨sg37953,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37958,⟨sg37957,⟨sg37956,True.intro,True.intro⟩,True.intro⟩,⟨sg37959,True.intro,True.intro⟩⟩⟩,⟨sg37965,⟨sg37963,⟨sg37962,⟨sg37961,True.intro,True.intro⟩,True.intro⟩,⟨sg37964,True.intro,True.intro⟩⟩,⟨sg37968,⟨sg37967,⟨sg37966,True.intro,True.intro⟩,True.intro⟩,⟨sg37969,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_538All : degreeTree62_538.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37949,degreeTree62_536All,degreeTree62_537All⟩ - -lemma degreeTree62_539All : degreeTree62_539.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37927,degreeTree62_535All,degreeTree62_538All⟩ - -lemma degreeTree62_540All : degreeTree62_540.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37883,degreeTree62_532All,degreeTree62_539All⟩ - -lemma degreeTree62_541All : degreeTree62_541.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37795,degreeTree62_525All,degreeTree62_540All⟩ - -lemma degreeTree62_542All : degreeTree62_542.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37981,⟨sg37976,⟨sg37973,⟨sg37972,⟨sg37971,True.intro,True.intro⟩,True.intro⟩,⟨sg37975,⟨sg37974,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37979,⟨sg37978,⟨sg37977,True.intro,True.intro⟩,True.intro⟩,⟨sg37980,True.intro,True.intro⟩⟩⟩,⟨sg37987,⟨sg37984,⟨sg37983,⟨sg37982,True.intro,True.intro⟩,True.intro⟩,⟨sg37986,⟨sg37985,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37990,⟨sg37989,⟨sg37988,True.intro,True.intro⟩,True.intro⟩,⟨sg37991,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_543All : degreeTree62_543.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38003,⟨sg37998,⟨sg37995,⟨sg37994,⟨sg37993,True.intro,True.intro⟩,True.intro⟩,⟨sg37997,⟨sg37996,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38001,⟨sg38000,⟨sg37999,True.intro,True.intro⟩,True.intro⟩,⟨sg38002,True.intro,True.intro⟩⟩⟩,⟨sg38009,⟨sg38006,⟨sg38005,⟨sg38004,True.intro,True.intro⟩,True.intro⟩,⟨sg38008,⟨sg38007,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38012,⟨sg38011,⟨sg38010,True.intro,True.intro⟩,True.intro⟩,⟨sg38013,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_544All : degreeTree62_544.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37992,degreeTree62_542All,degreeTree62_543All⟩ - -lemma degreeTree62_545All : degreeTree62_545.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38025,⟨sg38020,⟨sg38017,⟨sg38016,⟨sg38015,True.intro,True.intro⟩,True.intro⟩,⟨sg38019,⟨sg38018,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38023,⟨sg38022,⟨sg38021,True.intro,True.intro⟩,True.intro⟩,⟨sg38024,True.intro,True.intro⟩⟩⟩,⟨sg38031,⟨sg38028,⟨sg38027,⟨sg38026,True.intro,True.intro⟩,True.intro⟩,⟨sg38030,⟨sg38029,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38034,⟨sg38033,⟨sg38032,True.intro,True.intro⟩,True.intro⟩,⟨sg38035,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_546All : degreeTree62_546.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38047,⟨sg38042,⟨sg38039,⟨sg38038,⟨sg38037,True.intro,True.intro⟩,True.intro⟩,⟨sg38041,⟨sg38040,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38045,⟨sg38044,⟨sg38043,True.intro,True.intro⟩,True.intro⟩,⟨sg38046,True.intro,True.intro⟩⟩⟩,⟨sg38053,⟨sg38050,⟨sg38049,⟨sg38048,True.intro,True.intro⟩,True.intro⟩,⟨sg38052,⟨sg38051,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38056,⟨sg38055,⟨sg38054,True.intro,True.intro⟩,True.intro⟩,⟨sg38057,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_547All : degreeTree62_547.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38036,degreeTree62_545All,degreeTree62_546All⟩ - -lemma degreeTree62_548All : degreeTree62_548.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38014,degreeTree62_544All,degreeTree62_547All⟩ - -lemma degreeTree62_549All : degreeTree62_549.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38069,⟨sg38064,⟨sg38061,⟨sg38060,⟨sg38059,True.intro,True.intro⟩,True.intro⟩,⟨sg38063,⟨sg38062,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38067,⟨sg38066,⟨sg38065,True.intro,True.intro⟩,True.intro⟩,⟨sg38068,True.intro,True.intro⟩⟩⟩,⟨sg38075,⟨sg38072,⟨sg38071,⟨sg38070,True.intro,True.intro⟩,True.intro⟩,⟨sg38074,⟨sg38073,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38078,⟨sg38077,⟨sg38076,True.intro,True.intro⟩,True.intro⟩,⟨sg38079,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_550All : degreeTree62_550.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38091,⟨sg38086,⟨sg38083,⟨sg38082,⟨sg38081,True.intro,True.intro⟩,True.intro⟩,⟨sg38085,⟨sg38084,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38089,⟨sg38088,⟨sg38087,True.intro,True.intro⟩,True.intro⟩,⟨sg38090,True.intro,True.intro⟩⟩⟩,⟨sg38097,⟨sg38094,⟨sg38093,⟨sg38092,True.intro,True.intro⟩,True.intro⟩,⟨sg38096,⟨sg38095,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38100,⟨sg38099,⟨sg38098,True.intro,True.intro⟩,True.intro⟩,⟨sg38101,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_551All : degreeTree62_551.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38080,degreeTree62_549All,degreeTree62_550All⟩ - -lemma degreeTree62_552All : degreeTree62_552.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38113,⟨sg38108,⟨sg38105,⟨sg38104,⟨sg38103,True.intro,True.intro⟩,True.intro⟩,⟨sg38107,⟨sg38106,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38111,⟨sg38110,⟨sg38109,True.intro,True.intro⟩,True.intro⟩,⟨sg38112,True.intro,True.intro⟩⟩⟩,⟨sg38119,⟨sg38116,⟨sg38115,⟨sg38114,True.intro,True.intro⟩,True.intro⟩,⟨sg38118,⟨sg38117,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38122,⟨sg38121,⟨sg38120,True.intro,True.intro⟩,True.intro⟩,⟨sg38123,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_553All : degreeTree62_553.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38135,⟨sg38130,⟨sg38127,⟨sg38126,⟨sg38125,True.intro,True.intro⟩,True.intro⟩,⟨sg38129,⟨sg38128,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38133,⟨sg38132,⟨sg38131,True.intro,True.intro⟩,True.intro⟩,⟨sg38134,True.intro,True.intro⟩⟩⟩,⟨sg38141,⟨sg38138,⟨sg38137,⟨sg38136,True.intro,True.intro⟩,True.intro⟩,⟨sg38140,⟨sg38139,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38144,⟨sg38143,⟨sg38142,True.intro,True.intro⟩,True.intro⟩,⟨sg38145,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_554All : degreeTree62_554.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38124,degreeTree62_552All,degreeTree62_553All⟩ - -lemma degreeTree62_555All : degreeTree62_555.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38102,degreeTree62_551All,degreeTree62_554All⟩ - -lemma degreeTree62_556All : degreeTree62_556.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38058,degreeTree62_548All,degreeTree62_555All⟩ - -lemma degreeTree62_557All : degreeTree62_557.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38157,⟨sg38152,⟨sg38149,⟨sg38148,⟨sg38147,True.intro,True.intro⟩,True.intro⟩,⟨sg38151,⟨sg38150,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38155,⟨sg38154,⟨sg38153,True.intro,True.intro⟩,True.intro⟩,⟨sg38156,True.intro,True.intro⟩⟩⟩,⟨sg38163,⟨sg38160,⟨sg38159,⟨sg38158,True.intro,True.intro⟩,True.intro⟩,⟨sg38162,⟨sg38161,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38166,⟨sg38165,⟨sg38164,True.intro,True.intro⟩,True.intro⟩,⟨sg38167,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_558All : degreeTree62_558.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38179,⟨sg38174,⟨sg38171,⟨sg38170,⟨sg38169,True.intro,True.intro⟩,True.intro⟩,⟨sg38173,⟨sg38172,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38177,⟨sg38176,⟨sg38175,True.intro,True.intro⟩,True.intro⟩,⟨sg38178,True.intro,True.intro⟩⟩⟩,⟨sg38185,⟨sg38182,⟨sg38181,⟨sg38180,True.intro,True.intro⟩,True.intro⟩,⟨sg38184,⟨sg38183,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38188,⟨sg38187,⟨sg38186,True.intro,True.intro⟩,True.intro⟩,⟨sg38189,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_559All : degreeTree62_559.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38168,degreeTree62_557All,degreeTree62_558All⟩ - -lemma degreeTree62_560All : degreeTree62_560.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38201,⟨sg38196,⟨sg38193,⟨sg38192,⟨sg38191,True.intro,True.intro⟩,True.intro⟩,⟨sg38195,⟨sg38194,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38199,⟨sg38198,⟨sg38197,True.intro,True.intro⟩,True.intro⟩,⟨sg38200,True.intro,True.intro⟩⟩⟩,⟨sg38207,⟨sg38204,⟨sg38203,⟨sg38202,True.intro,True.intro⟩,True.intro⟩,⟨sg38206,⟨sg38205,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38210,⟨sg38209,⟨sg38208,True.intro,True.intro⟩,True.intro⟩,⟨sg38211,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_561All : degreeTree62_561.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38223,⟨sg38218,⟨sg38215,⟨sg38214,⟨sg38213,True.intro,True.intro⟩,True.intro⟩,⟨sg38217,⟨sg38216,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38221,⟨sg38220,⟨sg38219,True.intro,True.intro⟩,True.intro⟩,⟨sg38222,True.intro,True.intro⟩⟩⟩,⟨sg38229,⟨sg38226,⟨sg38225,⟨sg38224,True.intro,True.intro⟩,True.intro⟩,⟨sg38228,⟨sg38227,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38232,⟨sg38231,⟨sg38230,True.intro,True.intro⟩,True.intro⟩,⟨sg38233,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_562All : degreeTree62_562.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38212,degreeTree62_560All,degreeTree62_561All⟩ - -lemma degreeTree62_563All : degreeTree62_563.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38190,degreeTree62_559All,degreeTree62_562All⟩ - -lemma degreeTree62_564All : degreeTree62_564.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38245,⟨sg38240,⟨sg38237,⟨sg38236,⟨sg38235,True.intro,True.intro⟩,True.intro⟩,⟨sg38239,⟨sg38238,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38243,⟨sg38242,⟨sg38241,True.intro,True.intro⟩,True.intro⟩,⟨sg38244,True.intro,True.intro⟩⟩⟩,⟨sg38251,⟨sg38248,⟨sg38247,⟨sg38246,True.intro,True.intro⟩,True.intro⟩,⟨sg38250,⟨sg38249,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38254,⟨sg38253,⟨sg38252,True.intro,True.intro⟩,True.intro⟩,⟨sg38255,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_565All : degreeTree62_565.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38267,⟨sg38262,⟨sg38259,⟨sg38258,⟨sg38257,True.intro,True.intro⟩,True.intro⟩,⟨sg38261,⟨sg38260,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38265,⟨sg38264,⟨sg38263,True.intro,True.intro⟩,True.intro⟩,⟨sg38266,True.intro,True.intro⟩⟩⟩,⟨sg38273,⟨sg38270,⟨sg38269,⟨sg38268,True.intro,True.intro⟩,True.intro⟩,⟨sg38272,⟨sg38271,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38276,⟨sg38275,⟨sg38274,True.intro,True.intro⟩,True.intro⟩,⟨sg38277,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_566All : degreeTree62_566.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38256,degreeTree62_564All,degreeTree62_565All⟩ - -lemma degreeTree62_567All : degreeTree62_567.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38289,⟨sg38284,⟨sg38281,⟨sg38280,⟨sg38279,True.intro,True.intro⟩,True.intro⟩,⟨sg38283,⟨sg38282,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38287,⟨sg38286,⟨sg38285,True.intro,True.intro⟩,True.intro⟩,⟨sg38288,True.intro,True.intro⟩⟩⟩,⟨sg38295,⟨sg38292,⟨sg38291,⟨sg38290,True.intro,True.intro⟩,True.intro⟩,⟨sg38294,⟨sg38293,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38298,⟨sg38297,⟨sg38296,True.intro,True.intro⟩,True.intro⟩,⟨sg38299,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_568All : degreeTree62_568.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38311,⟨sg38306,⟨sg38303,⟨sg38302,⟨sg38301,True.intro,True.intro⟩,True.intro⟩,⟨sg38305,⟨sg38304,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38309,⟨sg38308,⟨sg38307,True.intro,True.intro⟩,True.intro⟩,⟨sg38310,True.intro,True.intro⟩⟩⟩,⟨sg38316,⟨sg38314,⟨sg38313,⟨sg38312,True.intro,True.intro⟩,True.intro⟩,⟨sg38315,True.intro,True.intro⟩⟩,⟨sg38319,⟨sg38318,⟨sg38317,True.intro,True.intro⟩,True.intro⟩,⟨sg38320,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_569All : degreeTree62_569.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38300,degreeTree62_567All,degreeTree62_568All⟩ - -lemma degreeTree62_570All : degreeTree62_570.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38278,degreeTree62_566All,degreeTree62_569All⟩ - -lemma degreeTree62_571All : degreeTree62_571.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38234,degreeTree62_563All,degreeTree62_570All⟩ - -lemma degreeTree62_572All : degreeTree62_572.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38146,degreeTree62_556All,degreeTree62_571All⟩ - -lemma degreeTree62_573All : degreeTree62_573.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37970,degreeTree62_541All,degreeTree62_572All⟩ - -lemma degreeTree62_574All : degreeTree62_574.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38332,⟨sg38327,⟨sg38324,⟨sg38323,⟨sg38322,True.intro,True.intro⟩,True.intro⟩,⟨sg38326,⟨sg38325,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38330,⟨sg38329,⟨sg38328,True.intro,True.intro⟩,True.intro⟩,⟨sg38331,True.intro,True.intro⟩⟩⟩,⟨sg38338,⟨sg38335,⟨sg38334,⟨sg38333,True.intro,True.intro⟩,True.intro⟩,⟨sg38337,⟨sg38336,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38341,⟨sg38340,⟨sg38339,True.intro,True.intro⟩,True.intro⟩,⟨sg38342,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_575All : degreeTree62_575.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38354,⟨sg38349,⟨sg38346,⟨sg38345,⟨sg38344,True.intro,True.intro⟩,True.intro⟩,⟨sg38348,⟨sg38347,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38352,⟨sg38351,⟨sg38350,True.intro,True.intro⟩,True.intro⟩,⟨sg38353,True.intro,True.intro⟩⟩⟩,⟨sg38360,⟨sg38357,⟨sg38356,⟨sg38355,True.intro,True.intro⟩,True.intro⟩,⟨sg38359,⟨sg38358,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38363,⟨sg38362,⟨sg38361,True.intro,True.intro⟩,True.intro⟩,⟨sg38364,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_576All : degreeTree62_576.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38343,degreeTree62_574All,degreeTree62_575All⟩ - -lemma degreeTree62_577All : degreeTree62_577.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38376,⟨sg38371,⟨sg38368,⟨sg38367,⟨sg38366,True.intro,True.intro⟩,True.intro⟩,⟨sg38370,⟨sg38369,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38374,⟨sg38373,⟨sg38372,True.intro,True.intro⟩,True.intro⟩,⟨sg38375,True.intro,True.intro⟩⟩⟩,⟨sg38382,⟨sg38379,⟨sg38378,⟨sg38377,True.intro,True.intro⟩,True.intro⟩,⟨sg38381,⟨sg38380,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38385,⟨sg38384,⟨sg38383,True.intro,True.intro⟩,True.intro⟩,⟨sg38386,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_578All : degreeTree62_578.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38398,⟨sg38393,⟨sg38390,⟨sg38389,⟨sg38388,True.intro,True.intro⟩,True.intro⟩,⟨sg38392,⟨sg38391,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38396,⟨sg38395,⟨sg38394,True.intro,True.intro⟩,True.intro⟩,⟨sg38397,True.intro,True.intro⟩⟩⟩,⟨sg38404,⟨sg38401,⟨sg38400,⟨sg38399,True.intro,True.intro⟩,True.intro⟩,⟨sg38403,⟨sg38402,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38407,⟨sg38406,⟨sg38405,True.intro,True.intro⟩,True.intro⟩,⟨sg38408,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_579All : degreeTree62_579.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38387,degreeTree62_577All,degreeTree62_578All⟩ - -lemma degreeTree62_580All : degreeTree62_580.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38365,degreeTree62_576All,degreeTree62_579All⟩ - -lemma degreeTree62_581All : degreeTree62_581.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38420,⟨sg38415,⟨sg38412,⟨sg38411,⟨sg38410,True.intro,True.intro⟩,True.intro⟩,⟨sg38414,⟨sg38413,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38418,⟨sg38417,⟨sg38416,True.intro,True.intro⟩,True.intro⟩,⟨sg38419,True.intro,True.intro⟩⟩⟩,⟨sg38426,⟨sg38423,⟨sg38422,⟨sg38421,True.intro,True.intro⟩,True.intro⟩,⟨sg38425,⟨sg38424,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38429,⟨sg38428,⟨sg38427,True.intro,True.intro⟩,True.intro⟩,⟨sg38430,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_582All : degreeTree62_582.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38442,⟨sg38437,⟨sg38434,⟨sg38433,⟨sg38432,True.intro,True.intro⟩,True.intro⟩,⟨sg38436,⟨sg38435,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38440,⟨sg38439,⟨sg38438,True.intro,True.intro⟩,True.intro⟩,⟨sg38441,True.intro,True.intro⟩⟩⟩,⟨sg38448,⟨sg38445,⟨sg38444,⟨sg38443,True.intro,True.intro⟩,True.intro⟩,⟨sg38447,⟨sg38446,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38451,⟨sg38450,⟨sg38449,True.intro,True.intro⟩,True.intro⟩,⟨sg38452,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_583All : degreeTree62_583.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38431,degreeTree62_581All,degreeTree62_582All⟩ - -lemma degreeTree62_584All : degreeTree62_584.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38464,⟨sg38459,⟨sg38456,⟨sg38455,⟨sg38454,True.intro,True.intro⟩,True.intro⟩,⟨sg38458,⟨sg38457,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38462,⟨sg38461,⟨sg38460,True.intro,True.intro⟩,True.intro⟩,⟨sg38463,True.intro,True.intro⟩⟩⟩,⟨sg38470,⟨sg38467,⟨sg38466,⟨sg38465,True.intro,True.intro⟩,True.intro⟩,⟨sg38469,⟨sg38468,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38473,⟨sg38472,⟨sg38471,True.intro,True.intro⟩,True.intro⟩,⟨sg38474,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_585All : degreeTree62_585.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38486,⟨sg38481,⟨sg38478,⟨sg38477,⟨sg38476,True.intro,True.intro⟩,True.intro⟩,⟨sg38480,⟨sg38479,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38484,⟨sg38483,⟨sg38482,True.intro,True.intro⟩,True.intro⟩,⟨sg38485,True.intro,True.intro⟩⟩⟩,⟨sg38492,⟨sg38489,⟨sg38488,⟨sg38487,True.intro,True.intro⟩,True.intro⟩,⟨sg38491,⟨sg38490,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38495,⟨sg38494,⟨sg38493,True.intro,True.intro⟩,True.intro⟩,⟨sg38496,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_586All : degreeTree62_586.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38475,degreeTree62_584All,degreeTree62_585All⟩ - -lemma degreeTree62_587All : degreeTree62_587.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38453,degreeTree62_583All,degreeTree62_586All⟩ - -lemma degreeTree62_588All : degreeTree62_588.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38409,degreeTree62_580All,degreeTree62_587All⟩ - -lemma degreeTree62_589All : degreeTree62_589.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38508,⟨sg38503,⟨sg38500,⟨sg38499,⟨sg38498,True.intro,True.intro⟩,True.intro⟩,⟨sg38502,⟨sg38501,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38506,⟨sg38505,⟨sg38504,True.intro,True.intro⟩,True.intro⟩,⟨sg38507,True.intro,True.intro⟩⟩⟩,⟨sg38514,⟨sg38511,⟨sg38510,⟨sg38509,True.intro,True.intro⟩,True.intro⟩,⟨sg38513,⟨sg38512,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38517,⟨sg38516,⟨sg38515,True.intro,True.intro⟩,True.intro⟩,⟨sg38518,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_590All : degreeTree62_590.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38530,⟨sg38525,⟨sg38522,⟨sg38521,⟨sg38520,True.intro,True.intro⟩,True.intro⟩,⟨sg38524,⟨sg38523,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38528,⟨sg38527,⟨sg38526,True.intro,True.intro⟩,True.intro⟩,⟨sg38529,True.intro,True.intro⟩⟩⟩,⟨sg38536,⟨sg38533,⟨sg38532,⟨sg38531,True.intro,True.intro⟩,True.intro⟩,⟨sg38535,⟨sg38534,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38539,⟨sg38538,⟨sg38537,True.intro,True.intro⟩,True.intro⟩,⟨sg38540,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_591All : degreeTree62_591.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38519,degreeTree62_589All,degreeTree62_590All⟩ - -lemma degreeTree62_592All : degreeTree62_592.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38552,⟨sg38547,⟨sg38544,⟨sg38543,⟨sg38542,True.intro,True.intro⟩,True.intro⟩,⟨sg38546,⟨sg38545,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38550,⟨sg38549,⟨sg38548,True.intro,True.intro⟩,True.intro⟩,⟨sg38551,True.intro,True.intro⟩⟩⟩,⟨sg38558,⟨sg38555,⟨sg38554,⟨sg38553,True.intro,True.intro⟩,True.intro⟩,⟨sg38557,⟨sg38556,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38561,⟨sg38560,⟨sg38559,True.intro,True.intro⟩,True.intro⟩,⟨sg38562,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_593All : degreeTree62_593.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38574,⟨sg38569,⟨sg38566,⟨sg38565,⟨sg38564,True.intro,True.intro⟩,True.intro⟩,⟨sg38568,⟨sg38567,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38572,⟨sg38571,⟨sg38570,True.intro,True.intro⟩,True.intro⟩,⟨sg38573,True.intro,True.intro⟩⟩⟩,⟨sg38580,⟨sg38577,⟨sg38576,⟨sg38575,True.intro,True.intro⟩,True.intro⟩,⟨sg38579,⟨sg38578,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38583,⟨sg38582,⟨sg38581,True.intro,True.intro⟩,True.intro⟩,⟨sg38584,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_594All : degreeTree62_594.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38563,degreeTree62_592All,degreeTree62_593All⟩ - -lemma degreeTree62_595All : degreeTree62_595.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38541,degreeTree62_591All,degreeTree62_594All⟩ - -lemma degreeTree62_596All : degreeTree62_596.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38596,⟨sg38591,⟨sg38588,⟨sg38587,⟨sg38586,True.intro,True.intro⟩,True.intro⟩,⟨sg38590,⟨sg38589,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38594,⟨sg38593,⟨sg38592,True.intro,True.intro⟩,True.intro⟩,⟨sg38595,True.intro,True.intro⟩⟩⟩,⟨sg38602,⟨sg38599,⟨sg38598,⟨sg38597,True.intro,True.intro⟩,True.intro⟩,⟨sg38601,⟨sg38600,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38605,⟨sg38604,⟨sg38603,True.intro,True.intro⟩,True.intro⟩,⟨sg38606,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_597All : degreeTree62_597.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38618,⟨sg38613,⟨sg38610,⟨sg38609,⟨sg38608,True.intro,True.intro⟩,True.intro⟩,⟨sg38612,⟨sg38611,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38616,⟨sg38615,⟨sg38614,True.intro,True.intro⟩,True.intro⟩,⟨sg38617,True.intro,True.intro⟩⟩⟩,⟨sg38624,⟨sg38621,⟨sg38620,⟨sg38619,True.intro,True.intro⟩,True.intro⟩,⟨sg38623,⟨sg38622,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38627,⟨sg38626,⟨sg38625,True.intro,True.intro⟩,True.intro⟩,⟨sg38628,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_598All : degreeTree62_598.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38607,degreeTree62_596All,degreeTree62_597All⟩ - -lemma degreeTree62_599All : degreeTree62_599.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38640,⟨sg38635,⟨sg38632,⟨sg38631,⟨sg38630,True.intro,True.intro⟩,True.intro⟩,⟨sg38634,⟨sg38633,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38638,⟨sg38637,⟨sg38636,True.intro,True.intro⟩,True.intro⟩,⟨sg38639,True.intro,True.intro⟩⟩⟩,⟨sg38646,⟨sg38643,⟨sg38642,⟨sg38641,True.intro,True.intro⟩,True.intro⟩,⟨sg38645,⟨sg38644,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38649,⟨sg38648,⟨sg38647,True.intro,True.intro⟩,True.intro⟩,⟨sg38650,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_600All : degreeTree62_600.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38662,⟨sg38657,⟨sg38654,⟨sg38653,⟨sg38652,True.intro,True.intro⟩,True.intro⟩,⟨sg38656,⟨sg38655,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38660,⟨sg38659,⟨sg38658,True.intro,True.intro⟩,True.intro⟩,⟨sg38661,True.intro,True.intro⟩⟩⟩,⟨sg38667,⟨sg38665,⟨sg38664,⟨sg38663,True.intro,True.intro⟩,True.intro⟩,⟨sg38666,True.intro,True.intro⟩⟩,⟨sg38670,⟨sg38669,⟨sg38668,True.intro,True.intro⟩,True.intro⟩,⟨sg38671,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_601All : degreeTree62_601.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38651,degreeTree62_599All,degreeTree62_600All⟩ - -lemma degreeTree62_602All : degreeTree62_602.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38629,degreeTree62_598All,degreeTree62_601All⟩ - -lemma degreeTree62_603All : degreeTree62_603.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38585,degreeTree62_595All,degreeTree62_602All⟩ - -lemma degreeTree62_604All : degreeTree62_604.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38497,degreeTree62_588All,degreeTree62_603All⟩ - -lemma degreeTree62_605All : degreeTree62_605.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38683,⟨sg38678,⟨sg38675,⟨sg38674,⟨sg38673,True.intro,True.intro⟩,True.intro⟩,⟨sg38677,⟨sg38676,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38681,⟨sg38680,⟨sg38679,True.intro,True.intro⟩,True.intro⟩,⟨sg38682,True.intro,True.intro⟩⟩⟩,⟨sg38689,⟨sg38686,⟨sg38685,⟨sg38684,True.intro,True.intro⟩,True.intro⟩,⟨sg38688,⟨sg38687,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38692,⟨sg38691,⟨sg38690,True.intro,True.intro⟩,True.intro⟩,⟨sg38693,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_606All : degreeTree62_606.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38705,⟨sg38700,⟨sg38697,⟨sg38696,⟨sg38695,True.intro,True.intro⟩,True.intro⟩,⟨sg38699,⟨sg38698,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38703,⟨sg38702,⟨sg38701,True.intro,True.intro⟩,True.intro⟩,⟨sg38704,True.intro,True.intro⟩⟩⟩,⟨sg38711,⟨sg38708,⟨sg38707,⟨sg38706,True.intro,True.intro⟩,True.intro⟩,⟨sg38710,⟨sg38709,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38714,⟨sg38713,⟨sg38712,True.intro,True.intro⟩,True.intro⟩,⟨sg38715,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_607All : degreeTree62_607.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38694,degreeTree62_605All,degreeTree62_606All⟩ - -lemma degreeTree62_608All : degreeTree62_608.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38727,⟨sg38722,⟨sg38719,⟨sg38718,⟨sg38717,True.intro,True.intro⟩,True.intro⟩,⟨sg38721,⟨sg38720,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38725,⟨sg38724,⟨sg38723,True.intro,True.intro⟩,True.intro⟩,⟨sg38726,True.intro,True.intro⟩⟩⟩,⟨sg38733,⟨sg38730,⟨sg38729,⟨sg38728,True.intro,True.intro⟩,True.intro⟩,⟨sg38732,⟨sg38731,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38736,⟨sg38735,⟨sg38734,True.intro,True.intro⟩,True.intro⟩,⟨sg38737,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_609All : degreeTree62_609.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38749,⟨sg38744,⟨sg38741,⟨sg38740,⟨sg38739,True.intro,True.intro⟩,True.intro⟩,⟨sg38743,⟨sg38742,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38747,⟨sg38746,⟨sg38745,True.intro,True.intro⟩,True.intro⟩,⟨sg38748,True.intro,True.intro⟩⟩⟩,⟨sg38755,⟨sg38752,⟨sg38751,⟨sg38750,True.intro,True.intro⟩,True.intro⟩,⟨sg38754,⟨sg38753,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38758,⟨sg38757,⟨sg38756,True.intro,True.intro⟩,True.intro⟩,⟨sg38759,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_610All : degreeTree62_610.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38738,degreeTree62_608All,degreeTree62_609All⟩ - -lemma degreeTree62_611All : degreeTree62_611.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38716,degreeTree62_607All,degreeTree62_610All⟩ - -lemma degreeTree62_612All : degreeTree62_612.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38771,⟨sg38766,⟨sg38763,⟨sg38762,⟨sg38761,True.intro,True.intro⟩,True.intro⟩,⟨sg38765,⟨sg38764,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38769,⟨sg38768,⟨sg38767,True.intro,True.intro⟩,True.intro⟩,⟨sg38770,True.intro,True.intro⟩⟩⟩,⟨sg38777,⟨sg38774,⟨sg38773,⟨sg38772,True.intro,True.intro⟩,True.intro⟩,⟨sg38776,⟨sg38775,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38780,⟨sg38779,⟨sg38778,True.intro,True.intro⟩,True.intro⟩,⟨sg38781,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_613All : degreeTree62_613.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38793,⟨sg38788,⟨sg38785,⟨sg38784,⟨sg38783,True.intro,True.intro⟩,True.intro⟩,⟨sg38787,⟨sg38786,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38791,⟨sg38790,⟨sg38789,True.intro,True.intro⟩,True.intro⟩,⟨sg38792,True.intro,True.intro⟩⟩⟩,⟨sg38799,⟨sg38796,⟨sg38795,⟨sg38794,True.intro,True.intro⟩,True.intro⟩,⟨sg38798,⟨sg38797,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38802,⟨sg38801,⟨sg38800,True.intro,True.intro⟩,True.intro⟩,⟨sg38803,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_614All : degreeTree62_614.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38782,degreeTree62_612All,degreeTree62_613All⟩ - -lemma degreeTree62_615All : degreeTree62_615.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38815,⟨sg38810,⟨sg38807,⟨sg38806,⟨sg38805,True.intro,True.intro⟩,True.intro⟩,⟨sg38809,⟨sg38808,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38813,⟨sg38812,⟨sg38811,True.intro,True.intro⟩,True.intro⟩,⟨sg38814,True.intro,True.intro⟩⟩⟩,⟨sg38821,⟨sg38818,⟨sg38817,⟨sg38816,True.intro,True.intro⟩,True.intro⟩,⟨sg38820,⟨sg38819,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38824,⟨sg38823,⟨sg38822,True.intro,True.intro⟩,True.intro⟩,⟨sg38825,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_616All : degreeTree62_616.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38837,⟨sg38832,⟨sg38829,⟨sg38828,⟨sg38827,True.intro,True.intro⟩,True.intro⟩,⟨sg38831,⟨sg38830,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38835,⟨sg38834,⟨sg38833,True.intro,True.intro⟩,True.intro⟩,⟨sg38836,True.intro,True.intro⟩⟩⟩,⟨sg38843,⟨sg38840,⟨sg38839,⟨sg38838,True.intro,True.intro⟩,True.intro⟩,⟨sg38842,⟨sg38841,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38846,⟨sg38845,⟨sg38844,True.intro,True.intro⟩,True.intro⟩,⟨sg38847,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_617All : degreeTree62_617.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38826,degreeTree62_615All,degreeTree62_616All⟩ - -lemma degreeTree62_618All : degreeTree62_618.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38804,degreeTree62_614All,degreeTree62_617All⟩ - -lemma degreeTree62_619All : degreeTree62_619.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38760,degreeTree62_611All,degreeTree62_618All⟩ - -lemma degreeTree62_620All : degreeTree62_620.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38859,⟨sg38854,⟨sg38851,⟨sg38850,⟨sg38849,True.intro,True.intro⟩,True.intro⟩,⟨sg38853,⟨sg38852,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38857,⟨sg38856,⟨sg38855,True.intro,True.intro⟩,True.intro⟩,⟨sg38858,True.intro,True.intro⟩⟩⟩,⟨sg38865,⟨sg38862,⟨sg38861,⟨sg38860,True.intro,True.intro⟩,True.intro⟩,⟨sg38864,⟨sg38863,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38868,⟨sg38867,⟨sg38866,True.intro,True.intro⟩,True.intro⟩,⟨sg38869,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_621All : degreeTree62_621.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38881,⟨sg38876,⟨sg38873,⟨sg38872,⟨sg38871,True.intro,True.intro⟩,True.intro⟩,⟨sg38875,⟨sg38874,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38879,⟨sg38878,⟨sg38877,True.intro,True.intro⟩,True.intro⟩,⟨sg38880,True.intro,True.intro⟩⟩⟩,⟨sg38887,⟨sg38884,⟨sg38883,⟨sg38882,True.intro,True.intro⟩,True.intro⟩,⟨sg38886,⟨sg38885,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38890,⟨sg38889,⟨sg38888,True.intro,True.intro⟩,True.intro⟩,⟨sg38891,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_622All : degreeTree62_622.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38870,degreeTree62_620All,degreeTree62_621All⟩ - -lemma degreeTree62_623All : degreeTree62_623.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38903,⟨sg38898,⟨sg38895,⟨sg38894,⟨sg38893,True.intro,True.intro⟩,True.intro⟩,⟨sg38897,⟨sg38896,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38901,⟨sg38900,⟨sg38899,True.intro,True.intro⟩,True.intro⟩,⟨sg38902,True.intro,True.intro⟩⟩⟩,⟨sg38909,⟨sg38906,⟨sg38905,⟨sg38904,True.intro,True.intro⟩,True.intro⟩,⟨sg38908,⟨sg38907,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38912,⟨sg38911,⟨sg38910,True.intro,True.intro⟩,True.intro⟩,⟨sg38913,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_624All : degreeTree62_624.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38925,⟨sg38920,⟨sg38917,⟨sg38916,⟨sg38915,True.intro,True.intro⟩,True.intro⟩,⟨sg38919,⟨sg38918,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38923,⟨sg38922,⟨sg38921,True.intro,True.intro⟩,True.intro⟩,⟨sg38924,True.intro,True.intro⟩⟩⟩,⟨sg38931,⟨sg38928,⟨sg38927,⟨sg38926,True.intro,True.intro⟩,True.intro⟩,⟨sg38930,⟨sg38929,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38934,⟨sg38933,⟨sg38932,True.intro,True.intro⟩,True.intro⟩,⟨sg38935,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_625All : degreeTree62_625.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38914,degreeTree62_623All,degreeTree62_624All⟩ - -lemma degreeTree62_626All : degreeTree62_626.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38892,degreeTree62_622All,degreeTree62_625All⟩ - -lemma degreeTree62_627All : degreeTree62_627.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38947,⟨sg38942,⟨sg38939,⟨sg38938,⟨sg38937,True.intro,True.intro⟩,True.intro⟩,⟨sg38941,⟨sg38940,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38945,⟨sg38944,⟨sg38943,True.intro,True.intro⟩,True.intro⟩,⟨sg38946,True.intro,True.intro⟩⟩⟩,⟨sg38953,⟨sg38950,⟨sg38949,⟨sg38948,True.intro,True.intro⟩,True.intro⟩,⟨sg38952,⟨sg38951,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38956,⟨sg38955,⟨sg38954,True.intro,True.intro⟩,True.intro⟩,⟨sg38957,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_628All : degreeTree62_628.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38969,⟨sg38964,⟨sg38961,⟨sg38960,⟨sg38959,True.intro,True.intro⟩,True.intro⟩,⟨sg38963,⟨sg38962,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38967,⟨sg38966,⟨sg38965,True.intro,True.intro⟩,True.intro⟩,⟨sg38968,True.intro,True.intro⟩⟩⟩,⟨sg38975,⟨sg38972,⟨sg38971,⟨sg38970,True.intro,True.intro⟩,True.intro⟩,⟨sg38974,⟨sg38973,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38978,⟨sg38977,⟨sg38976,True.intro,True.intro⟩,True.intro⟩,⟨sg38979,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_629All : degreeTree62_629.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38958,degreeTree62_627All,degreeTree62_628All⟩ - -lemma degreeTree62_630All : degreeTree62_630.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38991,⟨sg38986,⟨sg38983,⟨sg38982,⟨sg38981,True.intro,True.intro⟩,True.intro⟩,⟨sg38985,⟨sg38984,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38989,⟨sg38988,⟨sg38987,True.intro,True.intro⟩,True.intro⟩,⟨sg38990,True.intro,True.intro⟩⟩⟩,⟨sg38997,⟨sg38994,⟨sg38993,⟨sg38992,True.intro,True.intro⟩,True.intro⟩,⟨sg38996,⟨sg38995,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39000,⟨sg38999,⟨sg38998,True.intro,True.intro⟩,True.intro⟩,⟨sg39001,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_631All : degreeTree62_631.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39013,⟨sg39008,⟨sg39005,⟨sg39004,⟨sg39003,True.intro,True.intro⟩,True.intro⟩,⟨sg39007,⟨sg39006,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39011,⟨sg39010,⟨sg39009,True.intro,True.intro⟩,True.intro⟩,⟨sg39012,True.intro,True.intro⟩⟩⟩,⟨sg39018,⟨sg39016,⟨sg39015,⟨sg39014,True.intro,True.intro⟩,True.intro⟩,⟨sg39017,True.intro,True.intro⟩⟩,⟨sg39021,⟨sg39020,⟨sg39019,True.intro,True.intro⟩,True.intro⟩,⟨sg39022,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_632All : degreeTree62_632.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39002,degreeTree62_630All,degreeTree62_631All⟩ - -lemma degreeTree62_633All : degreeTree62_633.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38980,degreeTree62_629All,degreeTree62_632All⟩ - -lemma degreeTree62_634All : degreeTree62_634.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38936,degreeTree62_626All,degreeTree62_633All⟩ - -lemma degreeTree62_635All : degreeTree62_635.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38848,degreeTree62_619All,degreeTree62_634All⟩ - -lemma degreeTree62_636All : degreeTree62_636.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38672,degreeTree62_604All,degreeTree62_635All⟩ - -lemma degreeTree62_637All : degreeTree62_637.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg38321,degreeTree62_573All,degreeTree62_636All⟩ - -lemma degreeTree62_638All : degreeTree62_638.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39034,⟨sg39029,⟨sg39026,⟨sg39025,⟨sg39024,True.intro,True.intro⟩,True.intro⟩,⟨sg39028,⟨sg39027,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39032,⟨sg39031,⟨sg39030,True.intro,True.intro⟩,True.intro⟩,⟨sg39033,True.intro,True.intro⟩⟩⟩,⟨sg39040,⟨sg39037,⟨sg39036,⟨sg39035,True.intro,True.intro⟩,True.intro⟩,⟨sg39039,⟨sg39038,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39043,⟨sg39042,⟨sg39041,True.intro,True.intro⟩,True.intro⟩,⟨sg39044,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_639All : degreeTree62_639.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39056,⟨sg39051,⟨sg39048,⟨sg39047,⟨sg39046,True.intro,True.intro⟩,True.intro⟩,⟨sg39050,⟨sg39049,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39054,⟨sg39053,⟨sg39052,True.intro,True.intro⟩,True.intro⟩,⟨sg39055,True.intro,True.intro⟩⟩⟩,⟨sg39062,⟨sg39059,⟨sg39058,⟨sg39057,True.intro,True.intro⟩,True.intro⟩,⟨sg39061,⟨sg39060,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39065,⟨sg39064,⟨sg39063,True.intro,True.intro⟩,True.intro⟩,⟨sg39066,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_640All : degreeTree62_640.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39045,degreeTree62_638All,degreeTree62_639All⟩ - -lemma degreeTree62_641All : degreeTree62_641.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39078,⟨sg39073,⟨sg39070,⟨sg39069,⟨sg39068,True.intro,True.intro⟩,True.intro⟩,⟨sg39072,⟨sg39071,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39076,⟨sg39075,⟨sg39074,True.intro,True.intro⟩,True.intro⟩,⟨sg39077,True.intro,True.intro⟩⟩⟩,⟨sg39084,⟨sg39081,⟨sg39080,⟨sg39079,True.intro,True.intro⟩,True.intro⟩,⟨sg39083,⟨sg39082,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39087,⟨sg39086,⟨sg39085,True.intro,True.intro⟩,True.intro⟩,⟨sg39088,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_642All : degreeTree62_642.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39100,⟨sg39095,⟨sg39092,⟨sg39091,⟨sg39090,True.intro,True.intro⟩,True.intro⟩,⟨sg39094,⟨sg39093,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39098,⟨sg39097,⟨sg39096,True.intro,True.intro⟩,True.intro⟩,⟨sg39099,True.intro,True.intro⟩⟩⟩,⟨sg39106,⟨sg39103,⟨sg39102,⟨sg39101,True.intro,True.intro⟩,True.intro⟩,⟨sg39105,⟨sg39104,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39109,⟨sg39108,⟨sg39107,True.intro,True.intro⟩,True.intro⟩,⟨sg39110,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_643All : degreeTree62_643.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39089,degreeTree62_641All,degreeTree62_642All⟩ - -lemma degreeTree62_644All : degreeTree62_644.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39067,degreeTree62_640All,degreeTree62_643All⟩ - -lemma degreeTree62_645All : degreeTree62_645.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39122,⟨sg39117,⟨sg39114,⟨sg39113,⟨sg39112,True.intro,True.intro⟩,True.intro⟩,⟨sg39116,⟨sg39115,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39120,⟨sg39119,⟨sg39118,True.intro,True.intro⟩,True.intro⟩,⟨sg39121,True.intro,True.intro⟩⟩⟩,⟨sg39128,⟨sg39125,⟨sg39124,⟨sg39123,True.intro,True.intro⟩,True.intro⟩,⟨sg39127,⟨sg39126,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39131,⟨sg39130,⟨sg39129,True.intro,True.intro⟩,True.intro⟩,⟨sg39132,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_646All : degreeTree62_646.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39144,⟨sg39139,⟨sg39136,⟨sg39135,⟨sg39134,True.intro,True.intro⟩,True.intro⟩,⟨sg39138,⟨sg39137,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39142,⟨sg39141,⟨sg39140,True.intro,True.intro⟩,True.intro⟩,⟨sg39143,True.intro,True.intro⟩⟩⟩,⟨sg39150,⟨sg39147,⟨sg39146,⟨sg39145,True.intro,True.intro⟩,True.intro⟩,⟨sg39149,⟨sg39148,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39153,⟨sg39152,⟨sg39151,True.intro,True.intro⟩,True.intro⟩,⟨sg39154,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_647All : degreeTree62_647.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39133,degreeTree62_645All,degreeTree62_646All⟩ - -lemma degreeTree62_648All : degreeTree62_648.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39166,⟨sg39161,⟨sg39158,⟨sg39157,⟨sg39156,True.intro,True.intro⟩,True.intro⟩,⟨sg39160,⟨sg39159,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39164,⟨sg39163,⟨sg39162,True.intro,True.intro⟩,True.intro⟩,⟨sg39165,True.intro,True.intro⟩⟩⟩,⟨sg39172,⟨sg39169,⟨sg39168,⟨sg39167,True.intro,True.intro⟩,True.intro⟩,⟨sg39171,⟨sg39170,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39175,⟨sg39174,⟨sg39173,True.intro,True.intro⟩,True.intro⟩,⟨sg39176,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_649All : degreeTree62_649.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39188,⟨sg39183,⟨sg39180,⟨sg39179,⟨sg39178,True.intro,True.intro⟩,True.intro⟩,⟨sg39182,⟨sg39181,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39186,⟨sg39185,⟨sg39184,True.intro,True.intro⟩,True.intro⟩,⟨sg39187,True.intro,True.intro⟩⟩⟩,⟨sg39194,⟨sg39191,⟨sg39190,⟨sg39189,True.intro,True.intro⟩,True.intro⟩,⟨sg39193,⟨sg39192,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39197,⟨sg39196,⟨sg39195,True.intro,True.intro⟩,True.intro⟩,⟨sg39198,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_650All : degreeTree62_650.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39177,degreeTree62_648All,degreeTree62_649All⟩ - -lemma degreeTree62_651All : degreeTree62_651.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39155,degreeTree62_647All,degreeTree62_650All⟩ - -lemma degreeTree62_652All : degreeTree62_652.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39111,degreeTree62_644All,degreeTree62_651All⟩ - -lemma degreeTree62_653All : degreeTree62_653.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39210,⟨sg39205,⟨sg39202,⟨sg39201,⟨sg39200,True.intro,True.intro⟩,True.intro⟩,⟨sg39204,⟨sg39203,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39208,⟨sg39207,⟨sg39206,True.intro,True.intro⟩,True.intro⟩,⟨sg39209,True.intro,True.intro⟩⟩⟩,⟨sg39216,⟨sg39213,⟨sg39212,⟨sg39211,True.intro,True.intro⟩,True.intro⟩,⟨sg39215,⟨sg39214,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39219,⟨sg39218,⟨sg39217,True.intro,True.intro⟩,True.intro⟩,⟨sg39220,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_654All : degreeTree62_654.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39232,⟨sg39227,⟨sg39224,⟨sg39223,⟨sg39222,True.intro,True.intro⟩,True.intro⟩,⟨sg39226,⟨sg39225,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39230,⟨sg39229,⟨sg39228,True.intro,True.intro⟩,True.intro⟩,⟨sg39231,True.intro,True.intro⟩⟩⟩,⟨sg39238,⟨sg39235,⟨sg39234,⟨sg39233,True.intro,True.intro⟩,True.intro⟩,⟨sg39237,⟨sg39236,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39241,⟨sg39240,⟨sg39239,True.intro,True.intro⟩,True.intro⟩,⟨sg39242,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_655All : degreeTree62_655.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39221,degreeTree62_653All,degreeTree62_654All⟩ - -lemma degreeTree62_656All : degreeTree62_656.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39254,⟨sg39249,⟨sg39246,⟨sg39245,⟨sg39244,True.intro,True.intro⟩,True.intro⟩,⟨sg39248,⟨sg39247,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39252,⟨sg39251,⟨sg39250,True.intro,True.intro⟩,True.intro⟩,⟨sg39253,True.intro,True.intro⟩⟩⟩,⟨sg39260,⟨sg39257,⟨sg39256,⟨sg39255,True.intro,True.intro⟩,True.intro⟩,⟨sg39259,⟨sg39258,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39263,⟨sg39262,⟨sg39261,True.intro,True.intro⟩,True.intro⟩,⟨sg39264,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_657All : degreeTree62_657.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39276,⟨sg39271,⟨sg39268,⟨sg39267,⟨sg39266,True.intro,True.intro⟩,True.intro⟩,⟨sg39270,⟨sg39269,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39274,⟨sg39273,⟨sg39272,True.intro,True.intro⟩,True.intro⟩,⟨sg39275,True.intro,True.intro⟩⟩⟩,⟨sg39282,⟨sg39279,⟨sg39278,⟨sg39277,True.intro,True.intro⟩,True.intro⟩,⟨sg39281,⟨sg39280,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39285,⟨sg39284,⟨sg39283,True.intro,True.intro⟩,True.intro⟩,⟨sg39286,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_658All : degreeTree62_658.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39265,degreeTree62_656All,degreeTree62_657All⟩ - -lemma degreeTree62_659All : degreeTree62_659.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39243,degreeTree62_655All,degreeTree62_658All⟩ - -lemma degreeTree62_660All : degreeTree62_660.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39298,⟨sg39293,⟨sg39290,⟨sg39289,⟨sg39288,True.intro,True.intro⟩,True.intro⟩,⟨sg39292,⟨sg39291,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39296,⟨sg39295,⟨sg39294,True.intro,True.intro⟩,True.intro⟩,⟨sg39297,True.intro,True.intro⟩⟩⟩,⟨sg39304,⟨sg39301,⟨sg39300,⟨sg39299,True.intro,True.intro⟩,True.intro⟩,⟨sg39303,⟨sg39302,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39307,⟨sg39306,⟨sg39305,True.intro,True.intro⟩,True.intro⟩,⟨sg39308,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_661All : degreeTree62_661.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39320,⟨sg39315,⟨sg39312,⟨sg39311,⟨sg39310,True.intro,True.intro⟩,True.intro⟩,⟨sg39314,⟨sg39313,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39318,⟨sg39317,⟨sg39316,True.intro,True.intro⟩,True.intro⟩,⟨sg39319,True.intro,True.intro⟩⟩⟩,⟨sg39326,⟨sg39323,⟨sg39322,⟨sg39321,True.intro,True.intro⟩,True.intro⟩,⟨sg39325,⟨sg39324,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39329,⟨sg39328,⟨sg39327,True.intro,True.intro⟩,True.intro⟩,⟨sg39330,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_662All : degreeTree62_662.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39309,degreeTree62_660All,degreeTree62_661All⟩ - -lemma degreeTree62_663All : degreeTree62_663.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39342,⟨sg39337,⟨sg39334,⟨sg39333,⟨sg39332,True.intro,True.intro⟩,True.intro⟩,⟨sg39336,⟨sg39335,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39340,⟨sg39339,⟨sg39338,True.intro,True.intro⟩,True.intro⟩,⟨sg39341,True.intro,True.intro⟩⟩⟩,⟨sg39348,⟨sg39345,⟨sg39344,⟨sg39343,True.intro,True.intro⟩,True.intro⟩,⟨sg39347,⟨sg39346,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39351,⟨sg39350,⟨sg39349,True.intro,True.intro⟩,True.intro⟩,⟨sg39352,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_664All : degreeTree62_664.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39364,⟨sg39359,⟨sg39356,⟨sg39355,⟨sg39354,True.intro,True.intro⟩,True.intro⟩,⟨sg39358,⟨sg39357,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39362,⟨sg39361,⟨sg39360,True.intro,True.intro⟩,True.intro⟩,⟨sg39363,True.intro,True.intro⟩⟩⟩,⟨sg39369,⟨sg39367,⟨sg39366,⟨sg39365,True.intro,True.intro⟩,True.intro⟩,⟨sg39368,True.intro,True.intro⟩⟩,⟨sg39372,⟨sg39371,⟨sg39370,True.intro,True.intro⟩,True.intro⟩,⟨sg39373,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_665All : degreeTree62_665.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39353,degreeTree62_663All,degreeTree62_664All⟩ - -lemma degreeTree62_666All : degreeTree62_666.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39331,degreeTree62_662All,degreeTree62_665All⟩ - -lemma degreeTree62_667All : degreeTree62_667.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39287,degreeTree62_659All,degreeTree62_666All⟩ - -lemma degreeTree62_668All : degreeTree62_668.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39199,degreeTree62_652All,degreeTree62_667All⟩ - -lemma degreeTree62_669All : degreeTree62_669.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39385,⟨sg39380,⟨sg39377,⟨sg39376,⟨sg39375,True.intro,True.intro⟩,True.intro⟩,⟨sg39379,⟨sg39378,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39383,⟨sg39382,⟨sg39381,True.intro,True.intro⟩,True.intro⟩,⟨sg39384,True.intro,True.intro⟩⟩⟩,⟨sg39391,⟨sg39388,⟨sg39387,⟨sg39386,True.intro,True.intro⟩,True.intro⟩,⟨sg39390,⟨sg39389,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39394,⟨sg39393,⟨sg39392,True.intro,True.intro⟩,True.intro⟩,⟨sg39395,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_670All : degreeTree62_670.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39407,⟨sg39402,⟨sg39399,⟨sg39398,⟨sg39397,True.intro,True.intro⟩,True.intro⟩,⟨sg39401,⟨sg39400,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39405,⟨sg39404,⟨sg39403,True.intro,True.intro⟩,True.intro⟩,⟨sg39406,True.intro,True.intro⟩⟩⟩,⟨sg39413,⟨sg39410,⟨sg39409,⟨sg39408,True.intro,True.intro⟩,True.intro⟩,⟨sg39412,⟨sg39411,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39416,⟨sg39415,⟨sg39414,True.intro,True.intro⟩,True.intro⟩,⟨sg39417,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_671All : degreeTree62_671.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39396,degreeTree62_669All,degreeTree62_670All⟩ - -lemma degreeTree62_672All : degreeTree62_672.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39429,⟨sg39424,⟨sg39421,⟨sg39420,⟨sg39419,True.intro,True.intro⟩,True.intro⟩,⟨sg39423,⟨sg39422,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39427,⟨sg39426,⟨sg39425,True.intro,True.intro⟩,True.intro⟩,⟨sg39428,True.intro,True.intro⟩⟩⟩,⟨sg39435,⟨sg39432,⟨sg39431,⟨sg39430,True.intro,True.intro⟩,True.intro⟩,⟨sg39434,⟨sg39433,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39438,⟨sg39437,⟨sg39436,True.intro,True.intro⟩,True.intro⟩,⟨sg39439,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_673All : degreeTree62_673.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39451,⟨sg39446,⟨sg39443,⟨sg39442,⟨sg39441,True.intro,True.intro⟩,True.intro⟩,⟨sg39445,⟨sg39444,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39449,⟨sg39448,⟨sg39447,True.intro,True.intro⟩,True.intro⟩,⟨sg39450,True.intro,True.intro⟩⟩⟩,⟨sg39457,⟨sg39454,⟨sg39453,⟨sg39452,True.intro,True.intro⟩,True.intro⟩,⟨sg39456,⟨sg39455,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39460,⟨sg39459,⟨sg39458,True.intro,True.intro⟩,True.intro⟩,⟨sg39461,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_674All : degreeTree62_674.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39440,degreeTree62_672All,degreeTree62_673All⟩ - -lemma degreeTree62_675All : degreeTree62_675.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39418,degreeTree62_671All,degreeTree62_674All⟩ - -lemma degreeTree62_676All : degreeTree62_676.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39473,⟨sg39468,⟨sg39465,⟨sg39464,⟨sg39463,True.intro,True.intro⟩,True.intro⟩,⟨sg39467,⟨sg39466,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39471,⟨sg39470,⟨sg39469,True.intro,True.intro⟩,True.intro⟩,⟨sg39472,True.intro,True.intro⟩⟩⟩,⟨sg39479,⟨sg39476,⟨sg39475,⟨sg39474,True.intro,True.intro⟩,True.intro⟩,⟨sg39478,⟨sg39477,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39482,⟨sg39481,⟨sg39480,True.intro,True.intro⟩,True.intro⟩,⟨sg39483,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_677All : degreeTree62_677.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39495,⟨sg39490,⟨sg39487,⟨sg39486,⟨sg39485,True.intro,True.intro⟩,True.intro⟩,⟨sg39489,⟨sg39488,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39493,⟨sg39492,⟨sg39491,True.intro,True.intro⟩,True.intro⟩,⟨sg39494,True.intro,True.intro⟩⟩⟩,⟨sg39501,⟨sg39498,⟨sg39497,⟨sg39496,True.intro,True.intro⟩,True.intro⟩,⟨sg39500,⟨sg39499,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39504,⟨sg39503,⟨sg39502,True.intro,True.intro⟩,True.intro⟩,⟨sg39505,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_678All : degreeTree62_678.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39484,degreeTree62_676All,degreeTree62_677All⟩ - -lemma degreeTree62_679All : degreeTree62_679.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39517,⟨sg39512,⟨sg39509,⟨sg39508,⟨sg39507,True.intro,True.intro⟩,True.intro⟩,⟨sg39511,⟨sg39510,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39515,⟨sg39514,⟨sg39513,True.intro,True.intro⟩,True.intro⟩,⟨sg39516,True.intro,True.intro⟩⟩⟩,⟨sg39523,⟨sg39520,⟨sg39519,⟨sg39518,True.intro,True.intro⟩,True.intro⟩,⟨sg39522,⟨sg39521,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39526,⟨sg39525,⟨sg39524,True.intro,True.intro⟩,True.intro⟩,⟨sg39527,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_680All : degreeTree62_680.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39539,⟨sg39534,⟨sg39531,⟨sg39530,⟨sg39529,True.intro,True.intro⟩,True.intro⟩,⟨sg39533,⟨sg39532,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39537,⟨sg39536,⟨sg39535,True.intro,True.intro⟩,True.intro⟩,⟨sg39538,True.intro,True.intro⟩⟩⟩,⟨sg39545,⟨sg39542,⟨sg39541,⟨sg39540,True.intro,True.intro⟩,True.intro⟩,⟨sg39544,⟨sg39543,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39548,⟨sg39547,⟨sg39546,True.intro,True.intro⟩,True.intro⟩,⟨sg39549,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_681All : degreeTree62_681.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39528,degreeTree62_679All,degreeTree62_680All⟩ - -lemma degreeTree62_682All : degreeTree62_682.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39506,degreeTree62_678All,degreeTree62_681All⟩ - -lemma degreeTree62_683All : degreeTree62_683.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39462,degreeTree62_675All,degreeTree62_682All⟩ - -lemma degreeTree62_684All : degreeTree62_684.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39561,⟨sg39556,⟨sg39553,⟨sg39552,⟨sg39551,True.intro,True.intro⟩,True.intro⟩,⟨sg39555,⟨sg39554,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39559,⟨sg39558,⟨sg39557,True.intro,True.intro⟩,True.intro⟩,⟨sg39560,True.intro,True.intro⟩⟩⟩,⟨sg39567,⟨sg39564,⟨sg39563,⟨sg39562,True.intro,True.intro⟩,True.intro⟩,⟨sg39566,⟨sg39565,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39570,⟨sg39569,⟨sg39568,True.intro,True.intro⟩,True.intro⟩,⟨sg39571,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_685All : degreeTree62_685.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39583,⟨sg39578,⟨sg39575,⟨sg39574,⟨sg39573,True.intro,True.intro⟩,True.intro⟩,⟨sg39577,⟨sg39576,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39581,⟨sg39580,⟨sg39579,True.intro,True.intro⟩,True.intro⟩,⟨sg39582,True.intro,True.intro⟩⟩⟩,⟨sg39589,⟨sg39586,⟨sg39585,⟨sg39584,True.intro,True.intro⟩,True.intro⟩,⟨sg39588,⟨sg39587,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39592,⟨sg39591,⟨sg39590,True.intro,True.intro⟩,True.intro⟩,⟨sg39593,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_686All : degreeTree62_686.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39572,degreeTree62_684All,degreeTree62_685All⟩ - -lemma degreeTree62_687All : degreeTree62_687.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39605,⟨sg39600,⟨sg39597,⟨sg39596,⟨sg39595,True.intro,True.intro⟩,True.intro⟩,⟨sg39599,⟨sg39598,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39603,⟨sg39602,⟨sg39601,True.intro,True.intro⟩,True.intro⟩,⟨sg39604,True.intro,True.intro⟩⟩⟩,⟨sg39611,⟨sg39608,⟨sg39607,⟨sg39606,True.intro,True.intro⟩,True.intro⟩,⟨sg39610,⟨sg39609,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39614,⟨sg39613,⟨sg39612,True.intro,True.intro⟩,True.intro⟩,⟨sg39615,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_688All : degreeTree62_688.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39627,⟨sg39622,⟨sg39619,⟨sg39618,⟨sg39617,True.intro,True.intro⟩,True.intro⟩,⟨sg39621,⟨sg39620,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39625,⟨sg39624,⟨sg39623,True.intro,True.intro⟩,True.intro⟩,⟨sg39626,True.intro,True.intro⟩⟩⟩,⟨sg39633,⟨sg39630,⟨sg39629,⟨sg39628,True.intro,True.intro⟩,True.intro⟩,⟨sg39632,⟨sg39631,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39636,⟨sg39635,⟨sg39634,True.intro,True.intro⟩,True.intro⟩,⟨sg39637,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_689All : degreeTree62_689.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39616,degreeTree62_687All,degreeTree62_688All⟩ - -lemma degreeTree62_690All : degreeTree62_690.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39594,degreeTree62_686All,degreeTree62_689All⟩ - -lemma degreeTree62_691All : degreeTree62_691.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39649,⟨sg39644,⟨sg39641,⟨sg39640,⟨sg39639,True.intro,True.intro⟩,True.intro⟩,⟨sg39643,⟨sg39642,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39647,⟨sg39646,⟨sg39645,True.intro,True.intro⟩,True.intro⟩,⟨sg39648,True.intro,True.intro⟩⟩⟩,⟨sg39655,⟨sg39652,⟨sg39651,⟨sg39650,True.intro,True.intro⟩,True.intro⟩,⟨sg39654,⟨sg39653,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39658,⟨sg39657,⟨sg39656,True.intro,True.intro⟩,True.intro⟩,⟨sg39659,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_692All : degreeTree62_692.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39671,⟨sg39666,⟨sg39663,⟨sg39662,⟨sg39661,True.intro,True.intro⟩,True.intro⟩,⟨sg39665,⟨sg39664,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39669,⟨sg39668,⟨sg39667,True.intro,True.intro⟩,True.intro⟩,⟨sg39670,True.intro,True.intro⟩⟩⟩,⟨sg39677,⟨sg39674,⟨sg39673,⟨sg39672,True.intro,True.intro⟩,True.intro⟩,⟨sg39676,⟨sg39675,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39680,⟨sg39679,⟨sg39678,True.intro,True.intro⟩,True.intro⟩,⟨sg39681,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_693All : degreeTree62_693.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39660,degreeTree62_691All,degreeTree62_692All⟩ - -lemma degreeTree62_694All : degreeTree62_694.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39693,⟨sg39688,⟨sg39685,⟨sg39684,⟨sg39683,True.intro,True.intro⟩,True.intro⟩,⟨sg39687,⟨sg39686,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39691,⟨sg39690,⟨sg39689,True.intro,True.intro⟩,True.intro⟩,⟨sg39692,True.intro,True.intro⟩⟩⟩,⟨sg39699,⟨sg39696,⟨sg39695,⟨sg39694,True.intro,True.intro⟩,True.intro⟩,⟨sg39698,⟨sg39697,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39702,⟨sg39701,⟨sg39700,True.intro,True.intro⟩,True.intro⟩,⟨sg39703,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_695All : degreeTree62_695.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39715,⟨sg39710,⟨sg39707,⟨sg39706,⟨sg39705,True.intro,True.intro⟩,True.intro⟩,⟨sg39709,⟨sg39708,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39713,⟨sg39712,⟨sg39711,True.intro,True.intro⟩,True.intro⟩,⟨sg39714,True.intro,True.intro⟩⟩⟩,⟨sg39720,⟨sg39718,⟨sg39717,⟨sg39716,True.intro,True.intro⟩,True.intro⟩,⟨sg39719,True.intro,True.intro⟩⟩,⟨sg39723,⟨sg39722,⟨sg39721,True.intro,True.intro⟩,True.intro⟩,⟨sg39724,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_696All : degreeTree62_696.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39704,degreeTree62_694All,degreeTree62_695All⟩ - -lemma degreeTree62_697All : degreeTree62_697.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39682,degreeTree62_693All,degreeTree62_696All⟩ - -lemma degreeTree62_698All : degreeTree62_698.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39638,degreeTree62_690All,degreeTree62_697All⟩ - -lemma degreeTree62_699All : degreeTree62_699.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39550,degreeTree62_683All,degreeTree62_698All⟩ - -lemma degreeTree62_700All : degreeTree62_700.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39374,degreeTree62_668All,degreeTree62_699All⟩ - -lemma degreeTree62_701All : degreeTree62_701.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39736,⟨sg39731,⟨sg39728,⟨sg39727,⟨sg39726,True.intro,True.intro⟩,True.intro⟩,⟨sg39730,⟨sg39729,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39734,⟨sg39733,⟨sg39732,True.intro,True.intro⟩,True.intro⟩,⟨sg39735,True.intro,True.intro⟩⟩⟩,⟨sg39742,⟨sg39739,⟨sg39738,⟨sg39737,True.intro,True.intro⟩,True.intro⟩,⟨sg39741,⟨sg39740,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39745,⟨sg39744,⟨sg39743,True.intro,True.intro⟩,True.intro⟩,⟨sg39746,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_702All : degreeTree62_702.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39758,⟨sg39753,⟨sg39750,⟨sg39749,⟨sg39748,True.intro,True.intro⟩,True.intro⟩,⟨sg39752,⟨sg39751,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39756,⟨sg39755,⟨sg39754,True.intro,True.intro⟩,True.intro⟩,⟨sg39757,True.intro,True.intro⟩⟩⟩,⟨sg39764,⟨sg39761,⟨sg39760,⟨sg39759,True.intro,True.intro⟩,True.intro⟩,⟨sg39763,⟨sg39762,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39767,⟨sg39766,⟨sg39765,True.intro,True.intro⟩,True.intro⟩,⟨sg39768,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_703All : degreeTree62_703.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39747,degreeTree62_701All,degreeTree62_702All⟩ - -lemma degreeTree62_704All : degreeTree62_704.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39780,⟨sg39775,⟨sg39772,⟨sg39771,⟨sg39770,True.intro,True.intro⟩,True.intro⟩,⟨sg39774,⟨sg39773,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39778,⟨sg39777,⟨sg39776,True.intro,True.intro⟩,True.intro⟩,⟨sg39779,True.intro,True.intro⟩⟩⟩,⟨sg39786,⟨sg39783,⟨sg39782,⟨sg39781,True.intro,True.intro⟩,True.intro⟩,⟨sg39785,⟨sg39784,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39789,⟨sg39788,⟨sg39787,True.intro,True.intro⟩,True.intro⟩,⟨sg39790,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_705All : degreeTree62_705.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39802,⟨sg39797,⟨sg39794,⟨sg39793,⟨sg39792,True.intro,True.intro⟩,True.intro⟩,⟨sg39796,⟨sg39795,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39800,⟨sg39799,⟨sg39798,True.intro,True.intro⟩,True.intro⟩,⟨sg39801,True.intro,True.intro⟩⟩⟩,⟨sg39808,⟨sg39805,⟨sg39804,⟨sg39803,True.intro,True.intro⟩,True.intro⟩,⟨sg39807,⟨sg39806,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39811,⟨sg39810,⟨sg39809,True.intro,True.intro⟩,True.intro⟩,⟨sg39812,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_706All : degreeTree62_706.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39791,degreeTree62_704All,degreeTree62_705All⟩ - -lemma degreeTree62_707All : degreeTree62_707.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39769,degreeTree62_703All,degreeTree62_706All⟩ - -lemma degreeTree62_708All : degreeTree62_708.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39824,⟨sg39819,⟨sg39816,⟨sg39815,⟨sg39814,True.intro,True.intro⟩,True.intro⟩,⟨sg39818,⟨sg39817,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39822,⟨sg39821,⟨sg39820,True.intro,True.intro⟩,True.intro⟩,⟨sg39823,True.intro,True.intro⟩⟩⟩,⟨sg39830,⟨sg39827,⟨sg39826,⟨sg39825,True.intro,True.intro⟩,True.intro⟩,⟨sg39829,⟨sg39828,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39833,⟨sg39832,⟨sg39831,True.intro,True.intro⟩,True.intro⟩,⟨sg39834,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_709All : degreeTree62_709.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39846,⟨sg39841,⟨sg39838,⟨sg39837,⟨sg39836,True.intro,True.intro⟩,True.intro⟩,⟨sg39840,⟨sg39839,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39844,⟨sg39843,⟨sg39842,True.intro,True.intro⟩,True.intro⟩,⟨sg39845,True.intro,True.intro⟩⟩⟩,⟨sg39852,⟨sg39849,⟨sg39848,⟨sg39847,True.intro,True.intro⟩,True.intro⟩,⟨sg39851,⟨sg39850,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39855,⟨sg39854,⟨sg39853,True.intro,True.intro⟩,True.intro⟩,⟨sg39856,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_710All : degreeTree62_710.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39835,degreeTree62_708All,degreeTree62_709All⟩ - -lemma degreeTree62_711All : degreeTree62_711.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39868,⟨sg39863,⟨sg39860,⟨sg39859,⟨sg39858,True.intro,True.intro⟩,True.intro⟩,⟨sg39862,⟨sg39861,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39866,⟨sg39865,⟨sg39864,True.intro,True.intro⟩,True.intro⟩,⟨sg39867,True.intro,True.intro⟩⟩⟩,⟨sg39874,⟨sg39871,⟨sg39870,⟨sg39869,True.intro,True.intro⟩,True.intro⟩,⟨sg39873,⟨sg39872,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39877,⟨sg39876,⟨sg39875,True.intro,True.intro⟩,True.intro⟩,⟨sg39878,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_712All : degreeTree62_712.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39890,⟨sg39885,⟨sg39882,⟨sg39881,⟨sg39880,True.intro,True.intro⟩,True.intro⟩,⟨sg39884,⟨sg39883,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39888,⟨sg39887,⟨sg39886,True.intro,True.intro⟩,True.intro⟩,⟨sg39889,True.intro,True.intro⟩⟩⟩,⟨sg39896,⟨sg39893,⟨sg39892,⟨sg39891,True.intro,True.intro⟩,True.intro⟩,⟨sg39895,⟨sg39894,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39899,⟨sg39898,⟨sg39897,True.intro,True.intro⟩,True.intro⟩,⟨sg39900,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_713All : degreeTree62_713.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39879,degreeTree62_711All,degreeTree62_712All⟩ - -lemma degreeTree62_714All : degreeTree62_714.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39857,degreeTree62_710All,degreeTree62_713All⟩ - -lemma degreeTree62_715All : degreeTree62_715.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39813,degreeTree62_707All,degreeTree62_714All⟩ - -lemma degreeTree62_716All : degreeTree62_716.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39912,⟨sg39907,⟨sg39904,⟨sg39903,⟨sg39902,True.intro,True.intro⟩,True.intro⟩,⟨sg39906,⟨sg39905,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39910,⟨sg39909,⟨sg39908,True.intro,True.intro⟩,True.intro⟩,⟨sg39911,True.intro,True.intro⟩⟩⟩,⟨sg39918,⟨sg39915,⟨sg39914,⟨sg39913,True.intro,True.intro⟩,True.intro⟩,⟨sg39917,⟨sg39916,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39921,⟨sg39920,⟨sg39919,True.intro,True.intro⟩,True.intro⟩,⟨sg39922,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_717All : degreeTree62_717.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39934,⟨sg39929,⟨sg39926,⟨sg39925,⟨sg39924,True.intro,True.intro⟩,True.intro⟩,⟨sg39928,⟨sg39927,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39932,⟨sg39931,⟨sg39930,True.intro,True.intro⟩,True.intro⟩,⟨sg39933,True.intro,True.intro⟩⟩⟩,⟨sg39940,⟨sg39937,⟨sg39936,⟨sg39935,True.intro,True.intro⟩,True.intro⟩,⟨sg39939,⟨sg39938,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39943,⟨sg39942,⟨sg39941,True.intro,True.intro⟩,True.intro⟩,⟨sg39944,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_718All : degreeTree62_718.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39923,degreeTree62_716All,degreeTree62_717All⟩ - -lemma degreeTree62_719All : degreeTree62_719.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39956,⟨sg39951,⟨sg39948,⟨sg39947,⟨sg39946,True.intro,True.intro⟩,True.intro⟩,⟨sg39950,⟨sg39949,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39954,⟨sg39953,⟨sg39952,True.intro,True.intro⟩,True.intro⟩,⟨sg39955,True.intro,True.intro⟩⟩⟩,⟨sg39962,⟨sg39959,⟨sg39958,⟨sg39957,True.intro,True.intro⟩,True.intro⟩,⟨sg39961,⟨sg39960,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39965,⟨sg39964,⟨sg39963,True.intro,True.intro⟩,True.intro⟩,⟨sg39966,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_720All : degreeTree62_720.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39978,⟨sg39973,⟨sg39970,⟨sg39969,⟨sg39968,True.intro,True.intro⟩,True.intro⟩,⟨sg39972,⟨sg39971,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39976,⟨sg39975,⟨sg39974,True.intro,True.intro⟩,True.intro⟩,⟨sg39977,True.intro,True.intro⟩⟩⟩,⟨sg39984,⟨sg39981,⟨sg39980,⟨sg39979,True.intro,True.intro⟩,True.intro⟩,⟨sg39983,⟨sg39982,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39987,⟨sg39986,⟨sg39985,True.intro,True.intro⟩,True.intro⟩,⟨sg39988,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_721All : degreeTree62_721.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39967,degreeTree62_719All,degreeTree62_720All⟩ - -lemma degreeTree62_722All : degreeTree62_722.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39945,degreeTree62_718All,degreeTree62_721All⟩ - -lemma degreeTree62_723All : degreeTree62_723.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40000,⟨sg39995,⟨sg39992,⟨sg39991,⟨sg39990,True.intro,True.intro⟩,True.intro⟩,⟨sg39994,⟨sg39993,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39998,⟨sg39997,⟨sg39996,True.intro,True.intro⟩,True.intro⟩,⟨sg39999,True.intro,True.intro⟩⟩⟩,⟨sg40006,⟨sg40003,⟨sg40002,⟨sg40001,True.intro,True.intro⟩,True.intro⟩,⟨sg40005,⟨sg40004,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40009,⟨sg40008,⟨sg40007,True.intro,True.intro⟩,True.intro⟩,⟨sg40010,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_724All : degreeTree62_724.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40022,⟨sg40017,⟨sg40014,⟨sg40013,⟨sg40012,True.intro,True.intro⟩,True.intro⟩,⟨sg40016,⟨sg40015,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40020,⟨sg40019,⟨sg40018,True.intro,True.intro⟩,True.intro⟩,⟨sg40021,True.intro,True.intro⟩⟩⟩,⟨sg40028,⟨sg40025,⟨sg40024,⟨sg40023,True.intro,True.intro⟩,True.intro⟩,⟨sg40027,⟨sg40026,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40031,⟨sg40030,⟨sg40029,True.intro,True.intro⟩,True.intro⟩,⟨sg40032,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_725All : degreeTree62_725.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40011,degreeTree62_723All,degreeTree62_724All⟩ - -lemma degreeTree62_726All : degreeTree62_726.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40044,⟨sg40039,⟨sg40036,⟨sg40035,⟨sg40034,True.intro,True.intro⟩,True.intro⟩,⟨sg40038,⟨sg40037,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40042,⟨sg40041,⟨sg40040,True.intro,True.intro⟩,True.intro⟩,⟨sg40043,True.intro,True.intro⟩⟩⟩,⟨sg40050,⟨sg40047,⟨sg40046,⟨sg40045,True.intro,True.intro⟩,True.intro⟩,⟨sg40049,⟨sg40048,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40053,⟨sg40052,⟨sg40051,True.intro,True.intro⟩,True.intro⟩,⟨sg40054,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_727All : degreeTree62_727.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40066,⟨sg40061,⟨sg40058,⟨sg40057,⟨sg40056,True.intro,True.intro⟩,True.intro⟩,⟨sg40060,⟨sg40059,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40064,⟨sg40063,⟨sg40062,True.intro,True.intro⟩,True.intro⟩,⟨sg40065,True.intro,True.intro⟩⟩⟩,⟨sg40071,⟨sg40069,⟨sg40068,⟨sg40067,True.intro,True.intro⟩,True.intro⟩,⟨sg40070,True.intro,True.intro⟩⟩,⟨sg40074,⟨sg40073,⟨sg40072,True.intro,True.intro⟩,True.intro⟩,⟨sg40075,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_728All : degreeTree62_728.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40055,degreeTree62_726All,degreeTree62_727All⟩ - -lemma degreeTree62_729All : degreeTree62_729.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40033,degreeTree62_725All,degreeTree62_728All⟩ - -lemma degreeTree62_730All : degreeTree62_730.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39989,degreeTree62_722All,degreeTree62_729All⟩ - -lemma degreeTree62_731All : degreeTree62_731.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39901,degreeTree62_715All,degreeTree62_730All⟩ - -lemma degreeTree62_732All : degreeTree62_732.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40087,⟨sg40082,⟨sg40079,⟨sg40078,⟨sg40077,True.intro,True.intro⟩,True.intro⟩,⟨sg40081,⟨sg40080,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40085,⟨sg40084,⟨sg40083,True.intro,True.intro⟩,True.intro⟩,⟨sg40086,True.intro,True.intro⟩⟩⟩,⟨sg40093,⟨sg40090,⟨sg40089,⟨sg40088,True.intro,True.intro⟩,True.intro⟩,⟨sg40092,⟨sg40091,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40096,⟨sg40095,⟨sg40094,True.intro,True.intro⟩,True.intro⟩,⟨sg40097,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_733All : degreeTree62_733.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40109,⟨sg40104,⟨sg40101,⟨sg40100,⟨sg40099,True.intro,True.intro⟩,True.intro⟩,⟨sg40103,⟨sg40102,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40107,⟨sg40106,⟨sg40105,True.intro,True.intro⟩,True.intro⟩,⟨sg40108,True.intro,True.intro⟩⟩⟩,⟨sg40115,⟨sg40112,⟨sg40111,⟨sg40110,True.intro,True.intro⟩,True.intro⟩,⟨sg40114,⟨sg40113,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40118,⟨sg40117,⟨sg40116,True.intro,True.intro⟩,True.intro⟩,⟨sg40119,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_734All : degreeTree62_734.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40098,degreeTree62_732All,degreeTree62_733All⟩ - -lemma degreeTree62_735All : degreeTree62_735.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40131,⟨sg40126,⟨sg40123,⟨sg40122,⟨sg40121,True.intro,True.intro⟩,True.intro⟩,⟨sg40125,⟨sg40124,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40129,⟨sg40128,⟨sg40127,True.intro,True.intro⟩,True.intro⟩,⟨sg40130,True.intro,True.intro⟩⟩⟩,⟨sg40137,⟨sg40134,⟨sg40133,⟨sg40132,True.intro,True.intro⟩,True.intro⟩,⟨sg40136,⟨sg40135,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40140,⟨sg40139,⟨sg40138,True.intro,True.intro⟩,True.intro⟩,⟨sg40141,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_736All : degreeTree62_736.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40153,⟨sg40148,⟨sg40145,⟨sg40144,⟨sg40143,True.intro,True.intro⟩,True.intro⟩,⟨sg40147,⟨sg40146,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40151,⟨sg40150,⟨sg40149,True.intro,True.intro⟩,True.intro⟩,⟨sg40152,True.intro,True.intro⟩⟩⟩,⟨sg40159,⟨sg40156,⟨sg40155,⟨sg40154,True.intro,True.intro⟩,True.intro⟩,⟨sg40158,⟨sg40157,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40162,⟨sg40161,⟨sg40160,True.intro,True.intro⟩,True.intro⟩,⟨sg40163,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_737All : degreeTree62_737.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40142,degreeTree62_735All,degreeTree62_736All⟩ - -lemma degreeTree62_738All : degreeTree62_738.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40120,degreeTree62_734All,degreeTree62_737All⟩ - -lemma degreeTree62_739All : degreeTree62_739.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40175,⟨sg40170,⟨sg40167,⟨sg40166,⟨sg40165,True.intro,True.intro⟩,True.intro⟩,⟨sg40169,⟨sg40168,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40173,⟨sg40172,⟨sg40171,True.intro,True.intro⟩,True.intro⟩,⟨sg40174,True.intro,True.intro⟩⟩⟩,⟨sg40181,⟨sg40178,⟨sg40177,⟨sg40176,True.intro,True.intro⟩,True.intro⟩,⟨sg40180,⟨sg40179,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40184,⟨sg40183,⟨sg40182,True.intro,True.intro⟩,True.intro⟩,⟨sg40185,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_740All : degreeTree62_740.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40197,⟨sg40192,⟨sg40189,⟨sg40188,⟨sg40187,True.intro,True.intro⟩,True.intro⟩,⟨sg40191,⟨sg40190,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40195,⟨sg40194,⟨sg40193,True.intro,True.intro⟩,True.intro⟩,⟨sg40196,True.intro,True.intro⟩⟩⟩,⟨sg40203,⟨sg40200,⟨sg40199,⟨sg40198,True.intro,True.intro⟩,True.intro⟩,⟨sg40202,⟨sg40201,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40206,⟨sg40205,⟨sg40204,True.intro,True.intro⟩,True.intro⟩,⟨sg40207,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_741All : degreeTree62_741.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40186,degreeTree62_739All,degreeTree62_740All⟩ - -lemma degreeTree62_742All : degreeTree62_742.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40219,⟨sg40214,⟨sg40211,⟨sg40210,⟨sg40209,True.intro,True.intro⟩,True.intro⟩,⟨sg40213,⟨sg40212,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40217,⟨sg40216,⟨sg40215,True.intro,True.intro⟩,True.intro⟩,⟨sg40218,True.intro,True.intro⟩⟩⟩,⟨sg40225,⟨sg40222,⟨sg40221,⟨sg40220,True.intro,True.intro⟩,True.intro⟩,⟨sg40224,⟨sg40223,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40228,⟨sg40227,⟨sg40226,True.intro,True.intro⟩,True.intro⟩,⟨sg40229,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_743All : degreeTree62_743.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40241,⟨sg40236,⟨sg40233,⟨sg40232,⟨sg40231,True.intro,True.intro⟩,True.intro⟩,⟨sg40235,⟨sg40234,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40239,⟨sg40238,⟨sg40237,True.intro,True.intro⟩,True.intro⟩,⟨sg40240,True.intro,True.intro⟩⟩⟩,⟨sg40246,⟨sg40244,⟨sg40243,⟨sg40242,True.intro,True.intro⟩,True.intro⟩,⟨sg40245,True.intro,True.intro⟩⟩,⟨sg40249,⟨sg40248,⟨sg40247,True.intro,True.intro⟩,True.intro⟩,⟨sg40250,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_744All : degreeTree62_744.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40230,degreeTree62_742All,degreeTree62_743All⟩ - -lemma degreeTree62_745All : degreeTree62_745.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40208,degreeTree62_741All,degreeTree62_744All⟩ - -lemma degreeTree62_746All : degreeTree62_746.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40164,degreeTree62_738All,degreeTree62_745All⟩ - -lemma degreeTree62_747All : degreeTree62_747.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40262,⟨sg40257,⟨sg40254,⟨sg40253,⟨sg40252,True.intro,True.intro⟩,True.intro⟩,⟨sg40256,⟨sg40255,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40260,⟨sg40259,⟨sg40258,True.intro,True.intro⟩,True.intro⟩,⟨sg40261,True.intro,True.intro⟩⟩⟩,⟨sg40268,⟨sg40265,⟨sg40264,⟨sg40263,True.intro,True.intro⟩,True.intro⟩,⟨sg40267,⟨sg40266,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40271,⟨sg40270,⟨sg40269,True.intro,True.intro⟩,True.intro⟩,⟨sg40272,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_748All : degreeTree62_748.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40284,⟨sg40279,⟨sg40276,⟨sg40275,⟨sg40274,True.intro,True.intro⟩,True.intro⟩,⟨sg40278,⟨sg40277,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40282,⟨sg40281,⟨sg40280,True.intro,True.intro⟩,True.intro⟩,⟨sg40283,True.intro,True.intro⟩⟩⟩,⟨sg40290,⟨sg40287,⟨sg40286,⟨sg40285,True.intro,True.intro⟩,True.intro⟩,⟨sg40289,⟨sg40288,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40293,⟨sg40292,⟨sg40291,True.intro,True.intro⟩,True.intro⟩,⟨sg40294,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_749All : degreeTree62_749.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40273,degreeTree62_747All,degreeTree62_748All⟩ - -lemma degreeTree62_750All : degreeTree62_750.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40306,⟨sg40301,⟨sg40298,⟨sg40297,⟨sg40296,True.intro,True.intro⟩,True.intro⟩,⟨sg40300,⟨sg40299,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40304,⟨sg40303,⟨sg40302,True.intro,True.intro⟩,True.intro⟩,⟨sg40305,True.intro,True.intro⟩⟩⟩,⟨sg40312,⟨sg40309,⟨sg40308,⟨sg40307,True.intro,True.intro⟩,True.intro⟩,⟨sg40311,⟨sg40310,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40315,⟨sg40314,⟨sg40313,True.intro,True.intro⟩,True.intro⟩,⟨sg40316,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_751All : degreeTree62_751.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40328,⟨sg40323,⟨sg40320,⟨sg40319,⟨sg40318,True.intro,True.intro⟩,True.intro⟩,⟨sg40322,⟨sg40321,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40326,⟨sg40325,⟨sg40324,True.intro,True.intro⟩,True.intro⟩,⟨sg40327,True.intro,True.intro⟩⟩⟩,⟨sg40334,⟨sg40331,⟨sg40330,⟨sg40329,True.intro,True.intro⟩,True.intro⟩,⟨sg40333,⟨sg40332,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40337,⟨sg40336,⟨sg40335,True.intro,True.intro⟩,True.intro⟩,⟨sg40338,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_752All : degreeTree62_752.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40317,degreeTree62_750All,degreeTree62_751All⟩ - -lemma degreeTree62_753All : degreeTree62_753.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40295,degreeTree62_749All,degreeTree62_752All⟩ - -lemma degreeTree62_754All : degreeTree62_754.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40350,⟨sg40345,⟨sg40342,⟨sg40341,⟨sg40340,True.intro,True.intro⟩,True.intro⟩,⟨sg40344,⟨sg40343,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40348,⟨sg40347,⟨sg40346,True.intro,True.intro⟩,True.intro⟩,⟨sg40349,True.intro,True.intro⟩⟩⟩,⟨sg40356,⟨sg40353,⟨sg40352,⟨sg40351,True.intro,True.intro⟩,True.intro⟩,⟨sg40355,⟨sg40354,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40359,⟨sg40358,⟨sg40357,True.intro,True.intro⟩,True.intro⟩,⟨sg40360,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_755All : degreeTree62_755.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40372,⟨sg40367,⟨sg40364,⟨sg40363,⟨sg40362,True.intro,True.intro⟩,True.intro⟩,⟨sg40366,⟨sg40365,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40370,⟨sg40369,⟨sg40368,True.intro,True.intro⟩,True.intro⟩,⟨sg40371,True.intro,True.intro⟩⟩⟩,⟨sg40378,⟨sg40375,⟨sg40374,⟨sg40373,True.intro,True.intro⟩,True.intro⟩,⟨sg40377,⟨sg40376,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40381,⟨sg40380,⟨sg40379,True.intro,True.intro⟩,True.intro⟩,⟨sg40382,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_756All : degreeTree62_756.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40361,degreeTree62_754All,degreeTree62_755All⟩ - -lemma degreeTree62_757All : degreeTree62_757.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40394,⟨sg40389,⟨sg40386,⟨sg40385,⟨sg40384,True.intro,True.intro⟩,True.intro⟩,⟨sg40388,⟨sg40387,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40392,⟨sg40391,⟨sg40390,True.intro,True.intro⟩,True.intro⟩,⟨sg40393,True.intro,True.intro⟩⟩⟩,⟨sg40400,⟨sg40397,⟨sg40396,⟨sg40395,True.intro,True.intro⟩,True.intro⟩,⟨sg40399,⟨sg40398,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40403,⟨sg40402,⟨sg40401,True.intro,True.intro⟩,True.intro⟩,⟨sg40404,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_758All : degreeTree62_758.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40416,⟨sg40411,⟨sg40408,⟨sg40407,⟨sg40406,True.intro,True.intro⟩,True.intro⟩,⟨sg40410,⟨sg40409,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40414,⟨sg40413,⟨sg40412,True.intro,True.intro⟩,True.intro⟩,⟨sg40415,True.intro,True.intro⟩⟩⟩,⟨sg40421,⟨sg40419,⟨sg40418,⟨sg40417,True.intro,True.intro⟩,True.intro⟩,⟨sg40420,True.intro,True.intro⟩⟩,⟨sg40424,⟨sg40423,⟨sg40422,True.intro,True.intro⟩,True.intro⟩,⟨sg40425,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_759All : degreeTree62_759.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40405,degreeTree62_757All,degreeTree62_758All⟩ - -lemma degreeTree62_760All : degreeTree62_760.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40383,degreeTree62_756All,degreeTree62_759All⟩ - -lemma degreeTree62_761All : degreeTree62_761.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40339,degreeTree62_753All,degreeTree62_760All⟩ - -lemma degreeTree62_762All : degreeTree62_762.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40251,degreeTree62_746All,degreeTree62_761All⟩ - -lemma degreeTree62_763All : degreeTree62_763.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40076,degreeTree62_731All,degreeTree62_762All⟩ - -lemma degreeTree62_764All : degreeTree62_764.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39725,degreeTree62_700All,degreeTree62_763All⟩ - -lemma degreeTree62_765All : degreeTree62_765.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg39023,degreeTree62_637All,degreeTree62_764All⟩ - -lemma degreeTree62_766All : degreeTree62_766.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40437,⟨sg40432,⟨sg40429,⟨sg40428,⟨sg40427,True.intro,True.intro⟩,True.intro⟩,⟨sg40431,⟨sg40430,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40435,⟨sg40434,⟨sg40433,True.intro,True.intro⟩,True.intro⟩,⟨sg40436,True.intro,True.intro⟩⟩⟩,⟨sg40443,⟨sg40440,⟨sg40439,⟨sg40438,True.intro,True.intro⟩,True.intro⟩,⟨sg40442,⟨sg40441,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40446,⟨sg40445,⟨sg40444,True.intro,True.intro⟩,True.intro⟩,⟨sg40447,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_767All : degreeTree62_767.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40459,⟨sg40454,⟨sg40451,⟨sg40450,⟨sg40449,True.intro,True.intro⟩,True.intro⟩,⟨sg40453,⟨sg40452,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40457,⟨sg40456,⟨sg40455,True.intro,True.intro⟩,True.intro⟩,⟨sg40458,True.intro,True.intro⟩⟩⟩,⟨sg40465,⟨sg40462,⟨sg40461,⟨sg40460,True.intro,True.intro⟩,True.intro⟩,⟨sg40464,⟨sg40463,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40468,⟨sg40467,⟨sg40466,True.intro,True.intro⟩,True.intro⟩,⟨sg40469,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_768All : degreeTree62_768.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40448,degreeTree62_766All,degreeTree62_767All⟩ - -lemma degreeTree62_769All : degreeTree62_769.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40481,⟨sg40476,⟨sg40473,⟨sg40472,⟨sg40471,True.intro,True.intro⟩,True.intro⟩,⟨sg40475,⟨sg40474,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40479,⟨sg40478,⟨sg40477,True.intro,True.intro⟩,True.intro⟩,⟨sg40480,True.intro,True.intro⟩⟩⟩,⟨sg40487,⟨sg40484,⟨sg40483,⟨sg40482,True.intro,True.intro⟩,True.intro⟩,⟨sg40486,⟨sg40485,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40490,⟨sg40489,⟨sg40488,True.intro,True.intro⟩,True.intro⟩,⟨sg40491,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_770All : degreeTree62_770.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40503,⟨sg40498,⟨sg40495,⟨sg40494,⟨sg40493,True.intro,True.intro⟩,True.intro⟩,⟨sg40497,⟨sg40496,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40501,⟨sg40500,⟨sg40499,True.intro,True.intro⟩,True.intro⟩,⟨sg40502,True.intro,True.intro⟩⟩⟩,⟨sg40509,⟨sg40506,⟨sg40505,⟨sg40504,True.intro,True.intro⟩,True.intro⟩,⟨sg40508,⟨sg40507,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40512,⟨sg40511,⟨sg40510,True.intro,True.intro⟩,True.intro⟩,⟨sg40513,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_771All : degreeTree62_771.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40492,degreeTree62_769All,degreeTree62_770All⟩ - -lemma degreeTree62_772All : degreeTree62_772.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40470,degreeTree62_768All,degreeTree62_771All⟩ - -lemma degreeTree62_773All : degreeTree62_773.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40525,⟨sg40520,⟨sg40517,⟨sg40516,⟨sg40515,True.intro,True.intro⟩,True.intro⟩,⟨sg40519,⟨sg40518,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40523,⟨sg40522,⟨sg40521,True.intro,True.intro⟩,True.intro⟩,⟨sg40524,True.intro,True.intro⟩⟩⟩,⟨sg40531,⟨sg40528,⟨sg40527,⟨sg40526,True.intro,True.intro⟩,True.intro⟩,⟨sg40530,⟨sg40529,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40534,⟨sg40533,⟨sg40532,True.intro,True.intro⟩,True.intro⟩,⟨sg40535,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_774All : degreeTree62_774.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40547,⟨sg40542,⟨sg40539,⟨sg40538,⟨sg40537,True.intro,True.intro⟩,True.intro⟩,⟨sg40541,⟨sg40540,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40545,⟨sg40544,⟨sg40543,True.intro,True.intro⟩,True.intro⟩,⟨sg40546,True.intro,True.intro⟩⟩⟩,⟨sg40553,⟨sg40550,⟨sg40549,⟨sg40548,True.intro,True.intro⟩,True.intro⟩,⟨sg40552,⟨sg40551,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40556,⟨sg40555,⟨sg40554,True.intro,True.intro⟩,True.intro⟩,⟨sg40557,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_775All : degreeTree62_775.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40536,degreeTree62_773All,degreeTree62_774All⟩ - -lemma degreeTree62_776All : degreeTree62_776.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40569,⟨sg40564,⟨sg40561,⟨sg40560,⟨sg40559,True.intro,True.intro⟩,True.intro⟩,⟨sg40563,⟨sg40562,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40567,⟨sg40566,⟨sg40565,True.intro,True.intro⟩,True.intro⟩,⟨sg40568,True.intro,True.intro⟩⟩⟩,⟨sg40575,⟨sg40572,⟨sg40571,⟨sg40570,True.intro,True.intro⟩,True.intro⟩,⟨sg40574,⟨sg40573,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40578,⟨sg40577,⟨sg40576,True.intro,True.intro⟩,True.intro⟩,⟨sg40579,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_777All : degreeTree62_777.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40591,⟨sg40586,⟨sg40583,⟨sg40582,⟨sg40581,True.intro,True.intro⟩,True.intro⟩,⟨sg40585,⟨sg40584,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40589,⟨sg40588,⟨sg40587,True.intro,True.intro⟩,True.intro⟩,⟨sg40590,True.intro,True.intro⟩⟩⟩,⟨sg40597,⟨sg40594,⟨sg40593,⟨sg40592,True.intro,True.intro⟩,True.intro⟩,⟨sg40596,⟨sg40595,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40600,⟨sg40599,⟨sg40598,True.intro,True.intro⟩,True.intro⟩,⟨sg40601,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_778All : degreeTree62_778.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40580,degreeTree62_776All,degreeTree62_777All⟩ - -lemma degreeTree62_779All : degreeTree62_779.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40558,degreeTree62_775All,degreeTree62_778All⟩ - -lemma degreeTree62_780All : degreeTree62_780.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40514,degreeTree62_772All,degreeTree62_779All⟩ - -lemma degreeTree62_781All : degreeTree62_781.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40613,⟨sg40608,⟨sg40605,⟨sg40604,⟨sg40603,True.intro,True.intro⟩,True.intro⟩,⟨sg40607,⟨sg40606,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40611,⟨sg40610,⟨sg40609,True.intro,True.intro⟩,True.intro⟩,⟨sg40612,True.intro,True.intro⟩⟩⟩,⟨sg40619,⟨sg40616,⟨sg40615,⟨sg40614,True.intro,True.intro⟩,True.intro⟩,⟨sg40618,⟨sg40617,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40622,⟨sg40621,⟨sg40620,True.intro,True.intro⟩,True.intro⟩,⟨sg40623,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_782All : degreeTree62_782.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40635,⟨sg40630,⟨sg40627,⟨sg40626,⟨sg40625,True.intro,True.intro⟩,True.intro⟩,⟨sg40629,⟨sg40628,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40633,⟨sg40632,⟨sg40631,True.intro,True.intro⟩,True.intro⟩,⟨sg40634,True.intro,True.intro⟩⟩⟩,⟨sg40641,⟨sg40638,⟨sg40637,⟨sg40636,True.intro,True.intro⟩,True.intro⟩,⟨sg40640,⟨sg40639,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40644,⟨sg40643,⟨sg40642,True.intro,True.intro⟩,True.intro⟩,⟨sg40645,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_783All : degreeTree62_783.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40624,degreeTree62_781All,degreeTree62_782All⟩ - -lemma degreeTree62_784All : degreeTree62_784.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40657,⟨sg40652,⟨sg40649,⟨sg40648,⟨sg40647,True.intro,True.intro⟩,True.intro⟩,⟨sg40651,⟨sg40650,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40655,⟨sg40654,⟨sg40653,True.intro,True.intro⟩,True.intro⟩,⟨sg40656,True.intro,True.intro⟩⟩⟩,⟨sg40663,⟨sg40660,⟨sg40659,⟨sg40658,True.intro,True.intro⟩,True.intro⟩,⟨sg40662,⟨sg40661,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40666,⟨sg40665,⟨sg40664,True.intro,True.intro⟩,True.intro⟩,⟨sg40667,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_785All : degreeTree62_785.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40679,⟨sg40674,⟨sg40671,⟨sg40670,⟨sg40669,True.intro,True.intro⟩,True.intro⟩,⟨sg40673,⟨sg40672,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40677,⟨sg40676,⟨sg40675,True.intro,True.intro⟩,True.intro⟩,⟨sg40678,True.intro,True.intro⟩⟩⟩,⟨sg40685,⟨sg40682,⟨sg40681,⟨sg40680,True.intro,True.intro⟩,True.intro⟩,⟨sg40684,⟨sg40683,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40688,⟨sg40687,⟨sg40686,True.intro,True.intro⟩,True.intro⟩,⟨sg40689,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_786All : degreeTree62_786.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40668,degreeTree62_784All,degreeTree62_785All⟩ - -lemma degreeTree62_787All : degreeTree62_787.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40646,degreeTree62_783All,degreeTree62_786All⟩ - -lemma degreeTree62_788All : degreeTree62_788.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40701,⟨sg40696,⟨sg40693,⟨sg40692,⟨sg40691,True.intro,True.intro⟩,True.intro⟩,⟨sg40695,⟨sg40694,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40699,⟨sg40698,⟨sg40697,True.intro,True.intro⟩,True.intro⟩,⟨sg40700,True.intro,True.intro⟩⟩⟩,⟨sg40707,⟨sg40704,⟨sg40703,⟨sg40702,True.intro,True.intro⟩,True.intro⟩,⟨sg40706,⟨sg40705,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40710,⟨sg40709,⟨sg40708,True.intro,True.intro⟩,True.intro⟩,⟨sg40711,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_789All : degreeTree62_789.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40723,⟨sg40718,⟨sg40715,⟨sg40714,⟨sg40713,True.intro,True.intro⟩,True.intro⟩,⟨sg40717,⟨sg40716,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40721,⟨sg40720,⟨sg40719,True.intro,True.intro⟩,True.intro⟩,⟨sg40722,True.intro,True.intro⟩⟩⟩,⟨sg40729,⟨sg40726,⟨sg40725,⟨sg40724,True.intro,True.intro⟩,True.intro⟩,⟨sg40728,⟨sg40727,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40732,⟨sg40731,⟨sg40730,True.intro,True.intro⟩,True.intro⟩,⟨sg40733,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_790All : degreeTree62_790.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40712,degreeTree62_788All,degreeTree62_789All⟩ - -lemma degreeTree62_791All : degreeTree62_791.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40745,⟨sg40740,⟨sg40737,⟨sg40736,⟨sg40735,True.intro,True.intro⟩,True.intro⟩,⟨sg40739,⟨sg40738,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40743,⟨sg40742,⟨sg40741,True.intro,True.intro⟩,True.intro⟩,⟨sg40744,True.intro,True.intro⟩⟩⟩,⟨sg40751,⟨sg40748,⟨sg40747,⟨sg40746,True.intro,True.intro⟩,True.intro⟩,⟨sg40750,⟨sg40749,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40754,⟨sg40753,⟨sg40752,True.intro,True.intro⟩,True.intro⟩,⟨sg40755,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_792All : degreeTree62_792.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40767,⟨sg40762,⟨sg40759,⟨sg40758,⟨sg40757,True.intro,True.intro⟩,True.intro⟩,⟨sg40761,⟨sg40760,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40765,⟨sg40764,⟨sg40763,True.intro,True.intro⟩,True.intro⟩,⟨sg40766,True.intro,True.intro⟩⟩⟩,⟨sg40772,⟨sg40770,⟨sg40769,⟨sg40768,True.intro,True.intro⟩,True.intro⟩,⟨sg40771,True.intro,True.intro⟩⟩,⟨sg40775,⟨sg40774,⟨sg40773,True.intro,True.intro⟩,True.intro⟩,⟨sg40776,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_793All : degreeTree62_793.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40756,degreeTree62_791All,degreeTree62_792All⟩ - -lemma degreeTree62_794All : degreeTree62_794.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40734,degreeTree62_790All,degreeTree62_793All⟩ - -lemma degreeTree62_795All : degreeTree62_795.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40690,degreeTree62_787All,degreeTree62_794All⟩ - -lemma degreeTree62_796All : degreeTree62_796.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40602,degreeTree62_780All,degreeTree62_795All⟩ - -lemma degreeTree62_797All : degreeTree62_797.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40788,⟨sg40783,⟨sg40780,⟨sg40779,⟨sg40778,True.intro,True.intro⟩,True.intro⟩,⟨sg40782,⟨sg40781,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40786,⟨sg40785,⟨sg40784,True.intro,True.intro⟩,True.intro⟩,⟨sg40787,True.intro,True.intro⟩⟩⟩,⟨sg40794,⟨sg40791,⟨sg40790,⟨sg40789,True.intro,True.intro⟩,True.intro⟩,⟨sg40793,⟨sg40792,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40797,⟨sg40796,⟨sg40795,True.intro,True.intro⟩,True.intro⟩,⟨sg40798,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_798All : degreeTree62_798.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40810,⟨sg40805,⟨sg40802,⟨sg40801,⟨sg40800,True.intro,True.intro⟩,True.intro⟩,⟨sg40804,⟨sg40803,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40808,⟨sg40807,⟨sg40806,True.intro,True.intro⟩,True.intro⟩,⟨sg40809,True.intro,True.intro⟩⟩⟩,⟨sg40816,⟨sg40813,⟨sg40812,⟨sg40811,True.intro,True.intro⟩,True.intro⟩,⟨sg40815,⟨sg40814,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40819,⟨sg40818,⟨sg40817,True.intro,True.intro⟩,True.intro⟩,⟨sg40820,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_799All : degreeTree62_799.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40799,degreeTree62_797All,degreeTree62_798All⟩ - -lemma degreeTree62_800All : degreeTree62_800.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40832,⟨sg40827,⟨sg40824,⟨sg40823,⟨sg40822,True.intro,True.intro⟩,True.intro⟩,⟨sg40826,⟨sg40825,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40830,⟨sg40829,⟨sg40828,True.intro,True.intro⟩,True.intro⟩,⟨sg40831,True.intro,True.intro⟩⟩⟩,⟨sg40838,⟨sg40835,⟨sg40834,⟨sg40833,True.intro,True.intro⟩,True.intro⟩,⟨sg40837,⟨sg40836,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40841,⟨sg40840,⟨sg40839,True.intro,True.intro⟩,True.intro⟩,⟨sg40842,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_801All : degreeTree62_801.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40854,⟨sg40849,⟨sg40846,⟨sg40845,⟨sg40844,True.intro,True.intro⟩,True.intro⟩,⟨sg40848,⟨sg40847,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40852,⟨sg40851,⟨sg40850,True.intro,True.intro⟩,True.intro⟩,⟨sg40853,True.intro,True.intro⟩⟩⟩,⟨sg40860,⟨sg40857,⟨sg40856,⟨sg40855,True.intro,True.intro⟩,True.intro⟩,⟨sg40859,⟨sg40858,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40863,⟨sg40862,⟨sg40861,True.intro,True.intro⟩,True.intro⟩,⟨sg40864,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_802All : degreeTree62_802.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40843,degreeTree62_800All,degreeTree62_801All⟩ - -lemma degreeTree62_803All : degreeTree62_803.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40821,degreeTree62_799All,degreeTree62_802All⟩ - -lemma degreeTree62_804All : degreeTree62_804.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40876,⟨sg40871,⟨sg40868,⟨sg40867,⟨sg40866,True.intro,True.intro⟩,True.intro⟩,⟨sg40870,⟨sg40869,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40874,⟨sg40873,⟨sg40872,True.intro,True.intro⟩,True.intro⟩,⟨sg40875,True.intro,True.intro⟩⟩⟩,⟨sg40882,⟨sg40879,⟨sg40878,⟨sg40877,True.intro,True.intro⟩,True.intro⟩,⟨sg40881,⟨sg40880,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40885,⟨sg40884,⟨sg40883,True.intro,True.intro⟩,True.intro⟩,⟨sg40886,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_805All : degreeTree62_805.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40898,⟨sg40893,⟨sg40890,⟨sg40889,⟨sg40888,True.intro,True.intro⟩,True.intro⟩,⟨sg40892,⟨sg40891,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40896,⟨sg40895,⟨sg40894,True.intro,True.intro⟩,True.intro⟩,⟨sg40897,True.intro,True.intro⟩⟩⟩,⟨sg40904,⟨sg40901,⟨sg40900,⟨sg40899,True.intro,True.intro⟩,True.intro⟩,⟨sg40903,⟨sg40902,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40907,⟨sg40906,⟨sg40905,True.intro,True.intro⟩,True.intro⟩,⟨sg40908,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_806All : degreeTree62_806.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40887,degreeTree62_804All,degreeTree62_805All⟩ - -lemma degreeTree62_807All : degreeTree62_807.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40920,⟨sg40915,⟨sg40912,⟨sg40911,⟨sg40910,True.intro,True.intro⟩,True.intro⟩,⟨sg40914,⟨sg40913,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40918,⟨sg40917,⟨sg40916,True.intro,True.intro⟩,True.intro⟩,⟨sg40919,True.intro,True.intro⟩⟩⟩,⟨sg40926,⟨sg40923,⟨sg40922,⟨sg40921,True.intro,True.intro⟩,True.intro⟩,⟨sg40925,⟨sg40924,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40929,⟨sg40928,⟨sg40927,True.intro,True.intro⟩,True.intro⟩,⟨sg40930,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_808All : degreeTree62_808.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40942,⟨sg40937,⟨sg40934,⟨sg40933,⟨sg40932,True.intro,True.intro⟩,True.intro⟩,⟨sg40936,⟨sg40935,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40940,⟨sg40939,⟨sg40938,True.intro,True.intro⟩,True.intro⟩,⟨sg40941,True.intro,True.intro⟩⟩⟩,⟨sg40948,⟨sg40945,⟨sg40944,⟨sg40943,True.intro,True.intro⟩,True.intro⟩,⟨sg40947,⟨sg40946,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40951,⟨sg40950,⟨sg40949,True.intro,True.intro⟩,True.intro⟩,⟨sg40952,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_809All : degreeTree62_809.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40931,degreeTree62_807All,degreeTree62_808All⟩ - -lemma degreeTree62_810All : degreeTree62_810.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40909,degreeTree62_806All,degreeTree62_809All⟩ - -lemma degreeTree62_811All : degreeTree62_811.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40865,degreeTree62_803All,degreeTree62_810All⟩ - -lemma degreeTree62_812All : degreeTree62_812.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40964,⟨sg40959,⟨sg40956,⟨sg40955,⟨sg40954,True.intro,True.intro⟩,True.intro⟩,⟨sg40958,⟨sg40957,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40962,⟨sg40961,⟨sg40960,True.intro,True.intro⟩,True.intro⟩,⟨sg40963,True.intro,True.intro⟩⟩⟩,⟨sg40970,⟨sg40967,⟨sg40966,⟨sg40965,True.intro,True.intro⟩,True.intro⟩,⟨sg40969,⟨sg40968,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40973,⟨sg40972,⟨sg40971,True.intro,True.intro⟩,True.intro⟩,⟨sg40974,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_813All : degreeTree62_813.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40986,⟨sg40981,⟨sg40978,⟨sg40977,⟨sg40976,True.intro,True.intro⟩,True.intro⟩,⟨sg40980,⟨sg40979,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40984,⟨sg40983,⟨sg40982,True.intro,True.intro⟩,True.intro⟩,⟨sg40985,True.intro,True.intro⟩⟩⟩,⟨sg40992,⟨sg40989,⟨sg40988,⟨sg40987,True.intro,True.intro⟩,True.intro⟩,⟨sg40991,⟨sg40990,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40995,⟨sg40994,⟨sg40993,True.intro,True.intro⟩,True.intro⟩,⟨sg40996,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_814All : degreeTree62_814.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40975,degreeTree62_812All,degreeTree62_813All⟩ - -lemma degreeTree62_815All : degreeTree62_815.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41008,⟨sg41003,⟨sg41000,⟨sg40999,⟨sg40998,True.intro,True.intro⟩,True.intro⟩,⟨sg41002,⟨sg41001,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41006,⟨sg41005,⟨sg41004,True.intro,True.intro⟩,True.intro⟩,⟨sg41007,True.intro,True.intro⟩⟩⟩,⟨sg41014,⟨sg41011,⟨sg41010,⟨sg41009,True.intro,True.intro⟩,True.intro⟩,⟨sg41013,⟨sg41012,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41017,⟨sg41016,⟨sg41015,True.intro,True.intro⟩,True.intro⟩,⟨sg41018,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_816All : degreeTree62_816.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41030,⟨sg41025,⟨sg41022,⟨sg41021,⟨sg41020,True.intro,True.intro⟩,True.intro⟩,⟨sg41024,⟨sg41023,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41028,⟨sg41027,⟨sg41026,True.intro,True.intro⟩,True.intro⟩,⟨sg41029,True.intro,True.intro⟩⟩⟩,⟨sg41036,⟨sg41033,⟨sg41032,⟨sg41031,True.intro,True.intro⟩,True.intro⟩,⟨sg41035,⟨sg41034,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41039,⟨sg41038,⟨sg41037,True.intro,True.intro⟩,True.intro⟩,⟨sg41040,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_817All : degreeTree62_817.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41019,degreeTree62_815All,degreeTree62_816All⟩ - -lemma degreeTree62_818All : degreeTree62_818.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40997,degreeTree62_814All,degreeTree62_817All⟩ - -lemma degreeTree62_819All : degreeTree62_819.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41052,⟨sg41047,⟨sg41044,⟨sg41043,⟨sg41042,True.intro,True.intro⟩,True.intro⟩,⟨sg41046,⟨sg41045,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41050,⟨sg41049,⟨sg41048,True.intro,True.intro⟩,True.intro⟩,⟨sg41051,True.intro,True.intro⟩⟩⟩,⟨sg41058,⟨sg41055,⟨sg41054,⟨sg41053,True.intro,True.intro⟩,True.intro⟩,⟨sg41057,⟨sg41056,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41061,⟨sg41060,⟨sg41059,True.intro,True.intro⟩,True.intro⟩,⟨sg41062,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_820All : degreeTree62_820.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41074,⟨sg41069,⟨sg41066,⟨sg41065,⟨sg41064,True.intro,True.intro⟩,True.intro⟩,⟨sg41068,⟨sg41067,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41072,⟨sg41071,⟨sg41070,True.intro,True.intro⟩,True.intro⟩,⟨sg41073,True.intro,True.intro⟩⟩⟩,⟨sg41080,⟨sg41077,⟨sg41076,⟨sg41075,True.intro,True.intro⟩,True.intro⟩,⟨sg41079,⟨sg41078,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41083,⟨sg41082,⟨sg41081,True.intro,True.intro⟩,True.intro⟩,⟨sg41084,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_821All : degreeTree62_821.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41063,degreeTree62_819All,degreeTree62_820All⟩ - -lemma degreeTree62_822All : degreeTree62_822.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41096,⟨sg41091,⟨sg41088,⟨sg41087,⟨sg41086,True.intro,True.intro⟩,True.intro⟩,⟨sg41090,⟨sg41089,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41094,⟨sg41093,⟨sg41092,True.intro,True.intro⟩,True.intro⟩,⟨sg41095,True.intro,True.intro⟩⟩⟩,⟨sg41102,⟨sg41099,⟨sg41098,⟨sg41097,True.intro,True.intro⟩,True.intro⟩,⟨sg41101,⟨sg41100,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41105,⟨sg41104,⟨sg41103,True.intro,True.intro⟩,True.intro⟩,⟨sg41106,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_823All : degreeTree62_823.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41118,⟨sg41113,⟨sg41110,⟨sg41109,⟨sg41108,True.intro,True.intro⟩,True.intro⟩,⟨sg41112,⟨sg41111,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41116,⟨sg41115,⟨sg41114,True.intro,True.intro⟩,True.intro⟩,⟨sg41117,True.intro,True.intro⟩⟩⟩,⟨sg41123,⟨sg41121,⟨sg41120,⟨sg41119,True.intro,True.intro⟩,True.intro⟩,⟨sg41122,True.intro,True.intro⟩⟩,⟨sg41126,⟨sg41125,⟨sg41124,True.intro,True.intro⟩,True.intro⟩,⟨sg41127,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_824All : degreeTree62_824.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41107,degreeTree62_822All,degreeTree62_823All⟩ - -lemma degreeTree62_825All : degreeTree62_825.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41085,degreeTree62_821All,degreeTree62_824All⟩ - -lemma degreeTree62_826All : degreeTree62_826.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41041,degreeTree62_818All,degreeTree62_825All⟩ - -lemma degreeTree62_827All : degreeTree62_827.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40953,degreeTree62_811All,degreeTree62_826All⟩ - -lemma degreeTree62_828All : degreeTree62_828.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40777,degreeTree62_796All,degreeTree62_827All⟩ - -lemma degreeTree62_829All : degreeTree62_829.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41139,⟨sg41134,⟨sg41131,⟨sg41130,⟨sg41129,True.intro,True.intro⟩,True.intro⟩,⟨sg41133,⟨sg41132,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41137,⟨sg41136,⟨sg41135,True.intro,True.intro⟩,True.intro⟩,⟨sg41138,True.intro,True.intro⟩⟩⟩,⟨sg41145,⟨sg41142,⟨sg41141,⟨sg41140,True.intro,True.intro⟩,True.intro⟩,⟨sg41144,⟨sg41143,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41148,⟨sg41147,⟨sg41146,True.intro,True.intro⟩,True.intro⟩,⟨sg41149,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_830All : degreeTree62_830.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41161,⟨sg41156,⟨sg41153,⟨sg41152,⟨sg41151,True.intro,True.intro⟩,True.intro⟩,⟨sg41155,⟨sg41154,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41159,⟨sg41158,⟨sg41157,True.intro,True.intro⟩,True.intro⟩,⟨sg41160,True.intro,True.intro⟩⟩⟩,⟨sg41167,⟨sg41164,⟨sg41163,⟨sg41162,True.intro,True.intro⟩,True.intro⟩,⟨sg41166,⟨sg41165,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41170,⟨sg41169,⟨sg41168,True.intro,True.intro⟩,True.intro⟩,⟨sg41171,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_831All : degreeTree62_831.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41150,degreeTree62_829All,degreeTree62_830All⟩ - -lemma degreeTree62_832All : degreeTree62_832.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41183,⟨sg41178,⟨sg41175,⟨sg41174,⟨sg41173,True.intro,True.intro⟩,True.intro⟩,⟨sg41177,⟨sg41176,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41181,⟨sg41180,⟨sg41179,True.intro,True.intro⟩,True.intro⟩,⟨sg41182,True.intro,True.intro⟩⟩⟩,⟨sg41189,⟨sg41186,⟨sg41185,⟨sg41184,True.intro,True.intro⟩,True.intro⟩,⟨sg41188,⟨sg41187,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41192,⟨sg41191,⟨sg41190,True.intro,True.intro⟩,True.intro⟩,⟨sg41193,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_833All : degreeTree62_833.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41205,⟨sg41200,⟨sg41197,⟨sg41196,⟨sg41195,True.intro,True.intro⟩,True.intro⟩,⟨sg41199,⟨sg41198,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41203,⟨sg41202,⟨sg41201,True.intro,True.intro⟩,True.intro⟩,⟨sg41204,True.intro,True.intro⟩⟩⟩,⟨sg41211,⟨sg41208,⟨sg41207,⟨sg41206,True.intro,True.intro⟩,True.intro⟩,⟨sg41210,⟨sg41209,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41214,⟨sg41213,⟨sg41212,True.intro,True.intro⟩,True.intro⟩,⟨sg41215,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_834All : degreeTree62_834.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41194,degreeTree62_832All,degreeTree62_833All⟩ - -lemma degreeTree62_835All : degreeTree62_835.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41172,degreeTree62_831All,degreeTree62_834All⟩ - -lemma degreeTree62_836All : degreeTree62_836.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41227,⟨sg41222,⟨sg41219,⟨sg41218,⟨sg41217,True.intro,True.intro⟩,True.intro⟩,⟨sg41221,⟨sg41220,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41225,⟨sg41224,⟨sg41223,True.intro,True.intro⟩,True.intro⟩,⟨sg41226,True.intro,True.intro⟩⟩⟩,⟨sg41233,⟨sg41230,⟨sg41229,⟨sg41228,True.intro,True.intro⟩,True.intro⟩,⟨sg41232,⟨sg41231,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41236,⟨sg41235,⟨sg41234,True.intro,True.intro⟩,True.intro⟩,⟨sg41237,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_837All : degreeTree62_837.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41249,⟨sg41244,⟨sg41241,⟨sg41240,⟨sg41239,True.intro,True.intro⟩,True.intro⟩,⟨sg41243,⟨sg41242,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41247,⟨sg41246,⟨sg41245,True.intro,True.intro⟩,True.intro⟩,⟨sg41248,True.intro,True.intro⟩⟩⟩,⟨sg41255,⟨sg41252,⟨sg41251,⟨sg41250,True.intro,True.intro⟩,True.intro⟩,⟨sg41254,⟨sg41253,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41258,⟨sg41257,⟨sg41256,True.intro,True.intro⟩,True.intro⟩,⟨sg41259,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_838All : degreeTree62_838.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41238,degreeTree62_836All,degreeTree62_837All⟩ - -lemma degreeTree62_839All : degreeTree62_839.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41271,⟨sg41266,⟨sg41263,⟨sg41262,⟨sg41261,True.intro,True.intro⟩,True.intro⟩,⟨sg41265,⟨sg41264,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41269,⟨sg41268,⟨sg41267,True.intro,True.intro⟩,True.intro⟩,⟨sg41270,True.intro,True.intro⟩⟩⟩,⟨sg41277,⟨sg41274,⟨sg41273,⟨sg41272,True.intro,True.intro⟩,True.intro⟩,⟨sg41276,⟨sg41275,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41280,⟨sg41279,⟨sg41278,True.intro,True.intro⟩,True.intro⟩,⟨sg41281,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_840All : degreeTree62_840.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41293,⟨sg41288,⟨sg41285,⟨sg41284,⟨sg41283,True.intro,True.intro⟩,True.intro⟩,⟨sg41287,⟨sg41286,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41291,⟨sg41290,⟨sg41289,True.intro,True.intro⟩,True.intro⟩,⟨sg41292,True.intro,True.intro⟩⟩⟩,⟨sg41299,⟨sg41296,⟨sg41295,⟨sg41294,True.intro,True.intro⟩,True.intro⟩,⟨sg41298,⟨sg41297,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41302,⟨sg41301,⟨sg41300,True.intro,True.intro⟩,True.intro⟩,⟨sg41303,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_841All : degreeTree62_841.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41282,degreeTree62_839All,degreeTree62_840All⟩ - -lemma degreeTree62_842All : degreeTree62_842.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41260,degreeTree62_838All,degreeTree62_841All⟩ - -lemma degreeTree62_843All : degreeTree62_843.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41216,degreeTree62_835All,degreeTree62_842All⟩ - -lemma degreeTree62_844All : degreeTree62_844.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41315,⟨sg41310,⟨sg41307,⟨sg41306,⟨sg41305,True.intro,True.intro⟩,True.intro⟩,⟨sg41309,⟨sg41308,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41313,⟨sg41312,⟨sg41311,True.intro,True.intro⟩,True.intro⟩,⟨sg41314,True.intro,True.intro⟩⟩⟩,⟨sg41321,⟨sg41318,⟨sg41317,⟨sg41316,True.intro,True.intro⟩,True.intro⟩,⟨sg41320,⟨sg41319,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41324,⟨sg41323,⟨sg41322,True.intro,True.intro⟩,True.intro⟩,⟨sg41325,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_845All : degreeTree62_845.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41337,⟨sg41332,⟨sg41329,⟨sg41328,⟨sg41327,True.intro,True.intro⟩,True.intro⟩,⟨sg41331,⟨sg41330,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41335,⟨sg41334,⟨sg41333,True.intro,True.intro⟩,True.intro⟩,⟨sg41336,True.intro,True.intro⟩⟩⟩,⟨sg41343,⟨sg41340,⟨sg41339,⟨sg41338,True.intro,True.intro⟩,True.intro⟩,⟨sg41342,⟨sg41341,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41346,⟨sg41345,⟨sg41344,True.intro,True.intro⟩,True.intro⟩,⟨sg41347,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_846All : degreeTree62_846.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41326,degreeTree62_844All,degreeTree62_845All⟩ - -lemma degreeTree62_847All : degreeTree62_847.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41359,⟨sg41354,⟨sg41351,⟨sg41350,⟨sg41349,True.intro,True.intro⟩,True.intro⟩,⟨sg41353,⟨sg41352,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41357,⟨sg41356,⟨sg41355,True.intro,True.intro⟩,True.intro⟩,⟨sg41358,True.intro,True.intro⟩⟩⟩,⟨sg41365,⟨sg41362,⟨sg41361,⟨sg41360,True.intro,True.intro⟩,True.intro⟩,⟨sg41364,⟨sg41363,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41368,⟨sg41367,⟨sg41366,True.intro,True.intro⟩,True.intro⟩,⟨sg41369,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_848All : degreeTree62_848.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41381,⟨sg41376,⟨sg41373,⟨sg41372,⟨sg41371,True.intro,True.intro⟩,True.intro⟩,⟨sg41375,⟨sg41374,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41379,⟨sg41378,⟨sg41377,True.intro,True.intro⟩,True.intro⟩,⟨sg41380,True.intro,True.intro⟩⟩⟩,⟨sg41387,⟨sg41384,⟨sg41383,⟨sg41382,True.intro,True.intro⟩,True.intro⟩,⟨sg41386,⟨sg41385,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41390,⟨sg41389,⟨sg41388,True.intro,True.intro⟩,True.intro⟩,⟨sg41391,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_849All : degreeTree62_849.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41370,degreeTree62_847All,degreeTree62_848All⟩ - -lemma degreeTree62_850All : degreeTree62_850.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41348,degreeTree62_846All,degreeTree62_849All⟩ - -lemma degreeTree62_851All : degreeTree62_851.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41403,⟨sg41398,⟨sg41395,⟨sg41394,⟨sg41393,True.intro,True.intro⟩,True.intro⟩,⟨sg41397,⟨sg41396,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41401,⟨sg41400,⟨sg41399,True.intro,True.intro⟩,True.intro⟩,⟨sg41402,True.intro,True.intro⟩⟩⟩,⟨sg41409,⟨sg41406,⟨sg41405,⟨sg41404,True.intro,True.intro⟩,True.intro⟩,⟨sg41408,⟨sg41407,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41412,⟨sg41411,⟨sg41410,True.intro,True.intro⟩,True.intro⟩,⟨sg41413,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_852All : degreeTree62_852.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41425,⟨sg41420,⟨sg41417,⟨sg41416,⟨sg41415,True.intro,True.intro⟩,True.intro⟩,⟨sg41419,⟨sg41418,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41423,⟨sg41422,⟨sg41421,True.intro,True.intro⟩,True.intro⟩,⟨sg41424,True.intro,True.intro⟩⟩⟩,⟨sg41431,⟨sg41428,⟨sg41427,⟨sg41426,True.intro,True.intro⟩,True.intro⟩,⟨sg41430,⟨sg41429,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41434,⟨sg41433,⟨sg41432,True.intro,True.intro⟩,True.intro⟩,⟨sg41435,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_853All : degreeTree62_853.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41414,degreeTree62_851All,degreeTree62_852All⟩ - -lemma degreeTree62_854All : degreeTree62_854.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41447,⟨sg41442,⟨sg41439,⟨sg41438,⟨sg41437,True.intro,True.intro⟩,True.intro⟩,⟨sg41441,⟨sg41440,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41445,⟨sg41444,⟨sg41443,True.intro,True.intro⟩,True.intro⟩,⟨sg41446,True.intro,True.intro⟩⟩⟩,⟨sg41453,⟨sg41450,⟨sg41449,⟨sg41448,True.intro,True.intro⟩,True.intro⟩,⟨sg41452,⟨sg41451,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41456,⟨sg41455,⟨sg41454,True.intro,True.intro⟩,True.intro⟩,⟨sg41457,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_855All : degreeTree62_855.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41469,⟨sg41464,⟨sg41461,⟨sg41460,⟨sg41459,True.intro,True.intro⟩,True.intro⟩,⟨sg41463,⟨sg41462,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41467,⟨sg41466,⟨sg41465,True.intro,True.intro⟩,True.intro⟩,⟨sg41468,True.intro,True.intro⟩⟩⟩,⟨sg41474,⟨sg41472,⟨sg41471,⟨sg41470,True.intro,True.intro⟩,True.intro⟩,⟨sg41473,True.intro,True.intro⟩⟩,⟨sg41477,⟨sg41476,⟨sg41475,True.intro,True.intro⟩,True.intro⟩,⟨sg41478,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_856All : degreeTree62_856.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41458,degreeTree62_854All,degreeTree62_855All⟩ - -lemma degreeTree62_857All : degreeTree62_857.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41436,degreeTree62_853All,degreeTree62_856All⟩ - -lemma degreeTree62_858All : degreeTree62_858.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41392,degreeTree62_850All,degreeTree62_857All⟩ - -lemma degreeTree62_859All : degreeTree62_859.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41304,degreeTree62_843All,degreeTree62_858All⟩ - -lemma degreeTree62_860All : degreeTree62_860.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41490,⟨sg41485,⟨sg41482,⟨sg41481,⟨sg41480,True.intro,True.intro⟩,True.intro⟩,⟨sg41484,⟨sg41483,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41488,⟨sg41487,⟨sg41486,True.intro,True.intro⟩,True.intro⟩,⟨sg41489,True.intro,True.intro⟩⟩⟩,⟨sg41496,⟨sg41493,⟨sg41492,⟨sg41491,True.intro,True.intro⟩,True.intro⟩,⟨sg41495,⟨sg41494,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41499,⟨sg41498,⟨sg41497,True.intro,True.intro⟩,True.intro⟩,⟨sg41500,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_861All : degreeTree62_861.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41512,⟨sg41507,⟨sg41504,⟨sg41503,⟨sg41502,True.intro,True.intro⟩,True.intro⟩,⟨sg41506,⟨sg41505,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41510,⟨sg41509,⟨sg41508,True.intro,True.intro⟩,True.intro⟩,⟨sg41511,True.intro,True.intro⟩⟩⟩,⟨sg41518,⟨sg41515,⟨sg41514,⟨sg41513,True.intro,True.intro⟩,True.intro⟩,⟨sg41517,⟨sg41516,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41521,⟨sg41520,⟨sg41519,True.intro,True.intro⟩,True.intro⟩,⟨sg41522,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_862All : degreeTree62_862.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41501,degreeTree62_860All,degreeTree62_861All⟩ - -lemma degreeTree62_863All : degreeTree62_863.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41534,⟨sg41529,⟨sg41526,⟨sg41525,⟨sg41524,True.intro,True.intro⟩,True.intro⟩,⟨sg41528,⟨sg41527,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41532,⟨sg41531,⟨sg41530,True.intro,True.intro⟩,True.intro⟩,⟨sg41533,True.intro,True.intro⟩⟩⟩,⟨sg41540,⟨sg41537,⟨sg41536,⟨sg41535,True.intro,True.intro⟩,True.intro⟩,⟨sg41539,⟨sg41538,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41543,⟨sg41542,⟨sg41541,True.intro,True.intro⟩,True.intro⟩,⟨sg41544,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_864All : degreeTree62_864.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41556,⟨sg41551,⟨sg41548,⟨sg41547,⟨sg41546,True.intro,True.intro⟩,True.intro⟩,⟨sg41550,⟨sg41549,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41554,⟨sg41553,⟨sg41552,True.intro,True.intro⟩,True.intro⟩,⟨sg41555,True.intro,True.intro⟩⟩⟩,⟨sg41562,⟨sg41559,⟨sg41558,⟨sg41557,True.intro,True.intro⟩,True.intro⟩,⟨sg41561,⟨sg41560,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41565,⟨sg41564,⟨sg41563,True.intro,True.intro⟩,True.intro⟩,⟨sg41566,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_865All : degreeTree62_865.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41545,degreeTree62_863All,degreeTree62_864All⟩ - -lemma degreeTree62_866All : degreeTree62_866.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41523,degreeTree62_862All,degreeTree62_865All⟩ - -lemma degreeTree62_867All : degreeTree62_867.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41578,⟨sg41573,⟨sg41570,⟨sg41569,⟨sg41568,True.intro,True.intro⟩,True.intro⟩,⟨sg41572,⟨sg41571,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41576,⟨sg41575,⟨sg41574,True.intro,True.intro⟩,True.intro⟩,⟨sg41577,True.intro,True.intro⟩⟩⟩,⟨sg41584,⟨sg41581,⟨sg41580,⟨sg41579,True.intro,True.intro⟩,True.intro⟩,⟨sg41583,⟨sg41582,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41587,⟨sg41586,⟨sg41585,True.intro,True.intro⟩,True.intro⟩,⟨sg41588,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_868All : degreeTree62_868.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41600,⟨sg41595,⟨sg41592,⟨sg41591,⟨sg41590,True.intro,True.intro⟩,True.intro⟩,⟨sg41594,⟨sg41593,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41598,⟨sg41597,⟨sg41596,True.intro,True.intro⟩,True.intro⟩,⟨sg41599,True.intro,True.intro⟩⟩⟩,⟨sg41606,⟨sg41603,⟨sg41602,⟨sg41601,True.intro,True.intro⟩,True.intro⟩,⟨sg41605,⟨sg41604,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41609,⟨sg41608,⟨sg41607,True.intro,True.intro⟩,True.intro⟩,⟨sg41610,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_869All : degreeTree62_869.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41589,degreeTree62_867All,degreeTree62_868All⟩ - -lemma degreeTree62_870All : degreeTree62_870.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41622,⟨sg41617,⟨sg41614,⟨sg41613,⟨sg41612,True.intro,True.intro⟩,True.intro⟩,⟨sg41616,⟨sg41615,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41620,⟨sg41619,⟨sg41618,True.intro,True.intro⟩,True.intro⟩,⟨sg41621,True.intro,True.intro⟩⟩⟩,⟨sg41628,⟨sg41625,⟨sg41624,⟨sg41623,True.intro,True.intro⟩,True.intro⟩,⟨sg41627,⟨sg41626,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41631,⟨sg41630,⟨sg41629,True.intro,True.intro⟩,True.intro⟩,⟨sg41632,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_871All : degreeTree62_871.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41644,⟨sg41639,⟨sg41636,⟨sg41635,⟨sg41634,True.intro,True.intro⟩,True.intro⟩,⟨sg41638,⟨sg41637,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41642,⟨sg41641,⟨sg41640,True.intro,True.intro⟩,True.intro⟩,⟨sg41643,True.intro,True.intro⟩⟩⟩,⟨sg41650,⟨sg41647,⟨sg41646,⟨sg41645,True.intro,True.intro⟩,True.intro⟩,⟨sg41649,⟨sg41648,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41653,⟨sg41652,⟨sg41651,True.intro,True.intro⟩,True.intro⟩,⟨sg41654,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_872All : degreeTree62_872.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41633,degreeTree62_870All,degreeTree62_871All⟩ - -lemma degreeTree62_873All : degreeTree62_873.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41611,degreeTree62_869All,degreeTree62_872All⟩ - -lemma degreeTree62_874All : degreeTree62_874.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41567,degreeTree62_866All,degreeTree62_873All⟩ - -lemma degreeTree62_875All : degreeTree62_875.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41666,⟨sg41661,⟨sg41658,⟨sg41657,⟨sg41656,True.intro,True.intro⟩,True.intro⟩,⟨sg41660,⟨sg41659,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41664,⟨sg41663,⟨sg41662,True.intro,True.intro⟩,True.intro⟩,⟨sg41665,True.intro,True.intro⟩⟩⟩,⟨sg41672,⟨sg41669,⟨sg41668,⟨sg41667,True.intro,True.intro⟩,True.intro⟩,⟨sg41671,⟨sg41670,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41675,⟨sg41674,⟨sg41673,True.intro,True.intro⟩,True.intro⟩,⟨sg41676,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_876All : degreeTree62_876.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41688,⟨sg41683,⟨sg41680,⟨sg41679,⟨sg41678,True.intro,True.intro⟩,True.intro⟩,⟨sg41682,⟨sg41681,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41686,⟨sg41685,⟨sg41684,True.intro,True.intro⟩,True.intro⟩,⟨sg41687,True.intro,True.intro⟩⟩⟩,⟨sg41694,⟨sg41691,⟨sg41690,⟨sg41689,True.intro,True.intro⟩,True.intro⟩,⟨sg41693,⟨sg41692,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41697,⟨sg41696,⟨sg41695,True.intro,True.intro⟩,True.intro⟩,⟨sg41698,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_877All : degreeTree62_877.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41677,degreeTree62_875All,degreeTree62_876All⟩ - -lemma degreeTree62_878All : degreeTree62_878.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41710,⟨sg41705,⟨sg41702,⟨sg41701,⟨sg41700,True.intro,True.intro⟩,True.intro⟩,⟨sg41704,⟨sg41703,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41708,⟨sg41707,⟨sg41706,True.intro,True.intro⟩,True.intro⟩,⟨sg41709,True.intro,True.intro⟩⟩⟩,⟨sg41716,⟨sg41713,⟨sg41712,⟨sg41711,True.intro,True.intro⟩,True.intro⟩,⟨sg41715,⟨sg41714,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41719,⟨sg41718,⟨sg41717,True.intro,True.intro⟩,True.intro⟩,⟨sg41720,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_879All : degreeTree62_879.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41732,⟨sg41727,⟨sg41724,⟨sg41723,⟨sg41722,True.intro,True.intro⟩,True.intro⟩,⟨sg41726,⟨sg41725,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41730,⟨sg41729,⟨sg41728,True.intro,True.intro⟩,True.intro⟩,⟨sg41731,True.intro,True.intro⟩⟩⟩,⟨sg41738,⟨sg41735,⟨sg41734,⟨sg41733,True.intro,True.intro⟩,True.intro⟩,⟨sg41737,⟨sg41736,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41741,⟨sg41740,⟨sg41739,True.intro,True.intro⟩,True.intro⟩,⟨sg41742,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_880All : degreeTree62_880.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41721,degreeTree62_878All,degreeTree62_879All⟩ - -lemma degreeTree62_881All : degreeTree62_881.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41699,degreeTree62_877All,degreeTree62_880All⟩ - -lemma degreeTree62_882All : degreeTree62_882.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41754,⟨sg41749,⟨sg41746,⟨sg41745,⟨sg41744,True.intro,True.intro⟩,True.intro⟩,⟨sg41748,⟨sg41747,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41752,⟨sg41751,⟨sg41750,True.intro,True.intro⟩,True.intro⟩,⟨sg41753,True.intro,True.intro⟩⟩⟩,⟨sg41760,⟨sg41757,⟨sg41756,⟨sg41755,True.intro,True.intro⟩,True.intro⟩,⟨sg41759,⟨sg41758,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41763,⟨sg41762,⟨sg41761,True.intro,True.intro⟩,True.intro⟩,⟨sg41764,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_883All : degreeTree62_883.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41776,⟨sg41771,⟨sg41768,⟨sg41767,⟨sg41766,True.intro,True.intro⟩,True.intro⟩,⟨sg41770,⟨sg41769,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41774,⟨sg41773,⟨sg41772,True.intro,True.intro⟩,True.intro⟩,⟨sg41775,True.intro,True.intro⟩⟩⟩,⟨sg41782,⟨sg41779,⟨sg41778,⟨sg41777,True.intro,True.intro⟩,True.intro⟩,⟨sg41781,⟨sg41780,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41785,⟨sg41784,⟨sg41783,True.intro,True.intro⟩,True.intro⟩,⟨sg41786,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_884All : degreeTree62_884.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41765,degreeTree62_882All,degreeTree62_883All⟩ - -lemma degreeTree62_885All : degreeTree62_885.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41798,⟨sg41793,⟨sg41790,⟨sg41789,⟨sg41788,True.intro,True.intro⟩,True.intro⟩,⟨sg41792,⟨sg41791,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41796,⟨sg41795,⟨sg41794,True.intro,True.intro⟩,True.intro⟩,⟨sg41797,True.intro,True.intro⟩⟩⟩,⟨sg41804,⟨sg41801,⟨sg41800,⟨sg41799,True.intro,True.intro⟩,True.intro⟩,⟨sg41803,⟨sg41802,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41807,⟨sg41806,⟨sg41805,True.intro,True.intro⟩,True.intro⟩,⟨sg41808,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_886All : degreeTree62_886.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41820,⟨sg41815,⟨sg41812,⟨sg41811,⟨sg41810,True.intro,True.intro⟩,True.intro⟩,⟨sg41814,⟨sg41813,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41818,⟨sg41817,⟨sg41816,True.intro,True.intro⟩,True.intro⟩,⟨sg41819,True.intro,True.intro⟩⟩⟩,⟨sg41825,⟨sg41823,⟨sg41822,⟨sg41821,True.intro,True.intro⟩,True.intro⟩,⟨sg41824,True.intro,True.intro⟩⟩,⟨sg41828,⟨sg41827,⟨sg41826,True.intro,True.intro⟩,True.intro⟩,⟨sg41829,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_887All : degreeTree62_887.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41809,degreeTree62_885All,degreeTree62_886All⟩ - -lemma degreeTree62_888All : degreeTree62_888.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41787,degreeTree62_884All,degreeTree62_887All⟩ - -lemma degreeTree62_889All : degreeTree62_889.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41743,degreeTree62_881All,degreeTree62_888All⟩ - -lemma degreeTree62_890All : degreeTree62_890.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41655,degreeTree62_874All,degreeTree62_889All⟩ - -lemma degreeTree62_891All : degreeTree62_891.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41479,degreeTree62_859All,degreeTree62_890All⟩ - -lemma degreeTree62_892All : degreeTree62_892.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41128,degreeTree62_828All,degreeTree62_891All⟩ - -lemma degreeTree62_893All : degreeTree62_893.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41841,⟨sg41836,⟨sg41833,⟨sg41832,⟨sg41831,True.intro,True.intro⟩,True.intro⟩,⟨sg41835,⟨sg41834,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41839,⟨sg41838,⟨sg41837,True.intro,True.intro⟩,True.intro⟩,⟨sg41840,True.intro,True.intro⟩⟩⟩,⟨sg41847,⟨sg41844,⟨sg41843,⟨sg41842,True.intro,True.intro⟩,True.intro⟩,⟨sg41846,⟨sg41845,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41850,⟨sg41849,⟨sg41848,True.intro,True.intro⟩,True.intro⟩,⟨sg41851,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_894All : degreeTree62_894.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41863,⟨sg41858,⟨sg41855,⟨sg41854,⟨sg41853,True.intro,True.intro⟩,True.intro⟩,⟨sg41857,⟨sg41856,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41861,⟨sg41860,⟨sg41859,True.intro,True.intro⟩,True.intro⟩,⟨sg41862,True.intro,True.intro⟩⟩⟩,⟨sg41869,⟨sg41866,⟨sg41865,⟨sg41864,True.intro,True.intro⟩,True.intro⟩,⟨sg41868,⟨sg41867,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41872,⟨sg41871,⟨sg41870,True.intro,True.intro⟩,True.intro⟩,⟨sg41873,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_895All : degreeTree62_895.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41852,degreeTree62_893All,degreeTree62_894All⟩ - -lemma degreeTree62_896All : degreeTree62_896.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41885,⟨sg41880,⟨sg41877,⟨sg41876,⟨sg41875,True.intro,True.intro⟩,True.intro⟩,⟨sg41879,⟨sg41878,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41883,⟨sg41882,⟨sg41881,True.intro,True.intro⟩,True.intro⟩,⟨sg41884,True.intro,True.intro⟩⟩⟩,⟨sg41891,⟨sg41888,⟨sg41887,⟨sg41886,True.intro,True.intro⟩,True.intro⟩,⟨sg41890,⟨sg41889,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41894,⟨sg41893,⟨sg41892,True.intro,True.intro⟩,True.intro⟩,⟨sg41895,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_897All : degreeTree62_897.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41907,⟨sg41902,⟨sg41899,⟨sg41898,⟨sg41897,True.intro,True.intro⟩,True.intro⟩,⟨sg41901,⟨sg41900,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41905,⟨sg41904,⟨sg41903,True.intro,True.intro⟩,True.intro⟩,⟨sg41906,True.intro,True.intro⟩⟩⟩,⟨sg41913,⟨sg41910,⟨sg41909,⟨sg41908,True.intro,True.intro⟩,True.intro⟩,⟨sg41912,⟨sg41911,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41916,⟨sg41915,⟨sg41914,True.intro,True.intro⟩,True.intro⟩,⟨sg41917,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_898All : degreeTree62_898.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41896,degreeTree62_896All,degreeTree62_897All⟩ - -lemma degreeTree62_899All : degreeTree62_899.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41874,degreeTree62_895All,degreeTree62_898All⟩ - -lemma degreeTree62_900All : degreeTree62_900.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41929,⟨sg41924,⟨sg41921,⟨sg41920,⟨sg41919,True.intro,True.intro⟩,True.intro⟩,⟨sg41923,⟨sg41922,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41927,⟨sg41926,⟨sg41925,True.intro,True.intro⟩,True.intro⟩,⟨sg41928,True.intro,True.intro⟩⟩⟩,⟨sg41935,⟨sg41932,⟨sg41931,⟨sg41930,True.intro,True.intro⟩,True.intro⟩,⟨sg41934,⟨sg41933,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41938,⟨sg41937,⟨sg41936,True.intro,True.intro⟩,True.intro⟩,⟨sg41939,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_901All : degreeTree62_901.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41951,⟨sg41946,⟨sg41943,⟨sg41942,⟨sg41941,True.intro,True.intro⟩,True.intro⟩,⟨sg41945,⟨sg41944,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41949,⟨sg41948,⟨sg41947,True.intro,True.intro⟩,True.intro⟩,⟨sg41950,True.intro,True.intro⟩⟩⟩,⟨sg41957,⟨sg41954,⟨sg41953,⟨sg41952,True.intro,True.intro⟩,True.intro⟩,⟨sg41956,⟨sg41955,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41960,⟨sg41959,⟨sg41958,True.intro,True.intro⟩,True.intro⟩,⟨sg41961,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_902All : degreeTree62_902.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41940,degreeTree62_900All,degreeTree62_901All⟩ - -lemma degreeTree62_903All : degreeTree62_903.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41973,⟨sg41968,⟨sg41965,⟨sg41964,⟨sg41963,True.intro,True.intro⟩,True.intro⟩,⟨sg41967,⟨sg41966,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41971,⟨sg41970,⟨sg41969,True.intro,True.intro⟩,True.intro⟩,⟨sg41972,True.intro,True.intro⟩⟩⟩,⟨sg41979,⟨sg41976,⟨sg41975,⟨sg41974,True.intro,True.intro⟩,True.intro⟩,⟨sg41978,⟨sg41977,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41982,⟨sg41981,⟨sg41980,True.intro,True.intro⟩,True.intro⟩,⟨sg41983,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_904All : degreeTree62_904.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41995,⟨sg41990,⟨sg41987,⟨sg41986,⟨sg41985,True.intro,True.intro⟩,True.intro⟩,⟨sg41989,⟨sg41988,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41993,⟨sg41992,⟨sg41991,True.intro,True.intro⟩,True.intro⟩,⟨sg41994,True.intro,True.intro⟩⟩⟩,⟨sg42001,⟨sg41998,⟨sg41997,⟨sg41996,True.intro,True.intro⟩,True.intro⟩,⟨sg42000,⟨sg41999,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42004,⟨sg42003,⟨sg42002,True.intro,True.intro⟩,True.intro⟩,⟨sg42005,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_905All : degreeTree62_905.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41984,degreeTree62_903All,degreeTree62_904All⟩ - -lemma degreeTree62_906All : degreeTree62_906.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41962,degreeTree62_902All,degreeTree62_905All⟩ - -lemma degreeTree62_907All : degreeTree62_907.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41918,degreeTree62_899All,degreeTree62_906All⟩ - -lemma degreeTree62_908All : degreeTree62_908.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42017,⟨sg42012,⟨sg42009,⟨sg42008,⟨sg42007,True.intro,True.intro⟩,True.intro⟩,⟨sg42011,⟨sg42010,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42015,⟨sg42014,⟨sg42013,True.intro,True.intro⟩,True.intro⟩,⟨sg42016,True.intro,True.intro⟩⟩⟩,⟨sg42023,⟨sg42020,⟨sg42019,⟨sg42018,True.intro,True.intro⟩,True.intro⟩,⟨sg42022,⟨sg42021,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42026,⟨sg42025,⟨sg42024,True.intro,True.intro⟩,True.intro⟩,⟨sg42027,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_909All : degreeTree62_909.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42039,⟨sg42034,⟨sg42031,⟨sg42030,⟨sg42029,True.intro,True.intro⟩,True.intro⟩,⟨sg42033,⟨sg42032,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42037,⟨sg42036,⟨sg42035,True.intro,True.intro⟩,True.intro⟩,⟨sg42038,True.intro,True.intro⟩⟩⟩,⟨sg42045,⟨sg42042,⟨sg42041,⟨sg42040,True.intro,True.intro⟩,True.intro⟩,⟨sg42044,⟨sg42043,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42048,⟨sg42047,⟨sg42046,True.intro,True.intro⟩,True.intro⟩,⟨sg42049,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_910All : degreeTree62_910.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42028,degreeTree62_908All,degreeTree62_909All⟩ - -lemma degreeTree62_911All : degreeTree62_911.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42061,⟨sg42056,⟨sg42053,⟨sg42052,⟨sg42051,True.intro,True.intro⟩,True.intro⟩,⟨sg42055,⟨sg42054,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42059,⟨sg42058,⟨sg42057,True.intro,True.intro⟩,True.intro⟩,⟨sg42060,True.intro,True.intro⟩⟩⟩,⟨sg42067,⟨sg42064,⟨sg42063,⟨sg42062,True.intro,True.intro⟩,True.intro⟩,⟨sg42066,⟨sg42065,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42070,⟨sg42069,⟨sg42068,True.intro,True.intro⟩,True.intro⟩,⟨sg42071,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_912All : degreeTree62_912.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42083,⟨sg42078,⟨sg42075,⟨sg42074,⟨sg42073,True.intro,True.intro⟩,True.intro⟩,⟨sg42077,⟨sg42076,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42081,⟨sg42080,⟨sg42079,True.intro,True.intro⟩,True.intro⟩,⟨sg42082,True.intro,True.intro⟩⟩⟩,⟨sg42089,⟨sg42086,⟨sg42085,⟨sg42084,True.intro,True.intro⟩,True.intro⟩,⟨sg42088,⟨sg42087,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42092,⟨sg42091,⟨sg42090,True.intro,True.intro⟩,True.intro⟩,⟨sg42093,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_913All : degreeTree62_913.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42072,degreeTree62_911All,degreeTree62_912All⟩ - -lemma degreeTree62_914All : degreeTree62_914.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42050,degreeTree62_910All,degreeTree62_913All⟩ - -lemma degreeTree62_915All : degreeTree62_915.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42105,⟨sg42100,⟨sg42097,⟨sg42096,⟨sg42095,True.intro,True.intro⟩,True.intro⟩,⟨sg42099,⟨sg42098,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42103,⟨sg42102,⟨sg42101,True.intro,True.intro⟩,True.intro⟩,⟨sg42104,True.intro,True.intro⟩⟩⟩,⟨sg42111,⟨sg42108,⟨sg42107,⟨sg42106,True.intro,True.intro⟩,True.intro⟩,⟨sg42110,⟨sg42109,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42114,⟨sg42113,⟨sg42112,True.intro,True.intro⟩,True.intro⟩,⟨sg42115,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_916All : degreeTree62_916.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42127,⟨sg42122,⟨sg42119,⟨sg42118,⟨sg42117,True.intro,True.intro⟩,True.intro⟩,⟨sg42121,⟨sg42120,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42125,⟨sg42124,⟨sg42123,True.intro,True.intro⟩,True.intro⟩,⟨sg42126,True.intro,True.intro⟩⟩⟩,⟨sg42133,⟨sg42130,⟨sg42129,⟨sg42128,True.intro,True.intro⟩,True.intro⟩,⟨sg42132,⟨sg42131,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42136,⟨sg42135,⟨sg42134,True.intro,True.intro⟩,True.intro⟩,⟨sg42137,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_917All : degreeTree62_917.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42116,degreeTree62_915All,degreeTree62_916All⟩ - -lemma degreeTree62_918All : degreeTree62_918.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42149,⟨sg42144,⟨sg42141,⟨sg42140,⟨sg42139,True.intro,True.intro⟩,True.intro⟩,⟨sg42143,⟨sg42142,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42147,⟨sg42146,⟨sg42145,True.intro,True.intro⟩,True.intro⟩,⟨sg42148,True.intro,True.intro⟩⟩⟩,⟨sg42155,⟨sg42152,⟨sg42151,⟨sg42150,True.intro,True.intro⟩,True.intro⟩,⟨sg42154,⟨sg42153,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42158,⟨sg42157,⟨sg42156,True.intro,True.intro⟩,True.intro⟩,⟨sg42159,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_919All : degreeTree62_919.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42171,⟨sg42166,⟨sg42163,⟨sg42162,⟨sg42161,True.intro,True.intro⟩,True.intro⟩,⟨sg42165,⟨sg42164,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42169,⟨sg42168,⟨sg42167,True.intro,True.intro⟩,True.intro⟩,⟨sg42170,True.intro,True.intro⟩⟩⟩,⟨sg42176,⟨sg42174,⟨sg42173,⟨sg42172,True.intro,True.intro⟩,True.intro⟩,⟨sg42175,True.intro,True.intro⟩⟩,⟨sg42179,⟨sg42178,⟨sg42177,True.intro,True.intro⟩,True.intro⟩,⟨sg42180,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_920All : degreeTree62_920.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42160,degreeTree62_918All,degreeTree62_919All⟩ - -lemma degreeTree62_921All : degreeTree62_921.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42138,degreeTree62_917All,degreeTree62_920All⟩ - -lemma degreeTree62_922All : degreeTree62_922.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42094,degreeTree62_914All,degreeTree62_921All⟩ - -lemma degreeTree62_923All : degreeTree62_923.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42006,degreeTree62_907All,degreeTree62_922All⟩ - -lemma degreeTree62_924All : degreeTree62_924.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42192,⟨sg42187,⟨sg42184,⟨sg42183,⟨sg42182,True.intro,True.intro⟩,True.intro⟩,⟨sg42186,⟨sg42185,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42190,⟨sg42189,⟨sg42188,True.intro,True.intro⟩,True.intro⟩,⟨sg42191,True.intro,True.intro⟩⟩⟩,⟨sg42198,⟨sg42195,⟨sg42194,⟨sg42193,True.intro,True.intro⟩,True.intro⟩,⟨sg42197,⟨sg42196,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42201,⟨sg42200,⟨sg42199,True.intro,True.intro⟩,True.intro⟩,⟨sg42202,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_925All : degreeTree62_925.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42214,⟨sg42209,⟨sg42206,⟨sg42205,⟨sg42204,True.intro,True.intro⟩,True.intro⟩,⟨sg42208,⟨sg42207,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42212,⟨sg42211,⟨sg42210,True.intro,True.intro⟩,True.intro⟩,⟨sg42213,True.intro,True.intro⟩⟩⟩,⟨sg42220,⟨sg42217,⟨sg42216,⟨sg42215,True.intro,True.intro⟩,True.intro⟩,⟨sg42219,⟨sg42218,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42223,⟨sg42222,⟨sg42221,True.intro,True.intro⟩,True.intro⟩,⟨sg42224,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_926All : degreeTree62_926.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42203,degreeTree62_924All,degreeTree62_925All⟩ - -lemma degreeTree62_927All : degreeTree62_927.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42236,⟨sg42231,⟨sg42228,⟨sg42227,⟨sg42226,True.intro,True.intro⟩,True.intro⟩,⟨sg42230,⟨sg42229,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42234,⟨sg42233,⟨sg42232,True.intro,True.intro⟩,True.intro⟩,⟨sg42235,True.intro,True.intro⟩⟩⟩,⟨sg42242,⟨sg42239,⟨sg42238,⟨sg42237,True.intro,True.intro⟩,True.intro⟩,⟨sg42241,⟨sg42240,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42245,⟨sg42244,⟨sg42243,True.intro,True.intro⟩,True.intro⟩,⟨sg42246,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_928All : degreeTree62_928.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42258,⟨sg42253,⟨sg42250,⟨sg42249,⟨sg42248,True.intro,True.intro⟩,True.intro⟩,⟨sg42252,⟨sg42251,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42256,⟨sg42255,⟨sg42254,True.intro,True.intro⟩,True.intro⟩,⟨sg42257,True.intro,True.intro⟩⟩⟩,⟨sg42264,⟨sg42261,⟨sg42260,⟨sg42259,True.intro,True.intro⟩,True.intro⟩,⟨sg42263,⟨sg42262,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42267,⟨sg42266,⟨sg42265,True.intro,True.intro⟩,True.intro⟩,⟨sg42268,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_929All : degreeTree62_929.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42247,degreeTree62_927All,degreeTree62_928All⟩ - -lemma degreeTree62_930All : degreeTree62_930.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42225,degreeTree62_926All,degreeTree62_929All⟩ - -lemma degreeTree62_931All : degreeTree62_931.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42280,⟨sg42275,⟨sg42272,⟨sg42271,⟨sg42270,True.intro,True.intro⟩,True.intro⟩,⟨sg42274,⟨sg42273,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42278,⟨sg42277,⟨sg42276,True.intro,True.intro⟩,True.intro⟩,⟨sg42279,True.intro,True.intro⟩⟩⟩,⟨sg42286,⟨sg42283,⟨sg42282,⟨sg42281,True.intro,True.intro⟩,True.intro⟩,⟨sg42285,⟨sg42284,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42289,⟨sg42288,⟨sg42287,True.intro,True.intro⟩,True.intro⟩,⟨sg42290,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_932All : degreeTree62_932.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42302,⟨sg42297,⟨sg42294,⟨sg42293,⟨sg42292,True.intro,True.intro⟩,True.intro⟩,⟨sg42296,⟨sg42295,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42300,⟨sg42299,⟨sg42298,True.intro,True.intro⟩,True.intro⟩,⟨sg42301,True.intro,True.intro⟩⟩⟩,⟨sg42308,⟨sg42305,⟨sg42304,⟨sg42303,True.intro,True.intro⟩,True.intro⟩,⟨sg42307,⟨sg42306,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42311,⟨sg42310,⟨sg42309,True.intro,True.intro⟩,True.intro⟩,⟨sg42312,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_933All : degreeTree62_933.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42291,degreeTree62_931All,degreeTree62_932All⟩ - -lemma degreeTree62_934All : degreeTree62_934.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42324,⟨sg42319,⟨sg42316,⟨sg42315,⟨sg42314,True.intro,True.intro⟩,True.intro⟩,⟨sg42318,⟨sg42317,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42322,⟨sg42321,⟨sg42320,True.intro,True.intro⟩,True.intro⟩,⟨sg42323,True.intro,True.intro⟩⟩⟩,⟨sg42330,⟨sg42327,⟨sg42326,⟨sg42325,True.intro,True.intro⟩,True.intro⟩,⟨sg42329,⟨sg42328,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42333,⟨sg42332,⟨sg42331,True.intro,True.intro⟩,True.intro⟩,⟨sg42334,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_935All : degreeTree62_935.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42346,⟨sg42341,⟨sg42338,⟨sg42337,⟨sg42336,True.intro,True.intro⟩,True.intro⟩,⟨sg42340,⟨sg42339,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42344,⟨sg42343,⟨sg42342,True.intro,True.intro⟩,True.intro⟩,⟨sg42345,True.intro,True.intro⟩⟩⟩,⟨sg42352,⟨sg42349,⟨sg42348,⟨sg42347,True.intro,True.intro⟩,True.intro⟩,⟨sg42351,⟨sg42350,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42355,⟨sg42354,⟨sg42353,True.intro,True.intro⟩,True.intro⟩,⟨sg42356,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_936All : degreeTree62_936.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42335,degreeTree62_934All,degreeTree62_935All⟩ - -lemma degreeTree62_937All : degreeTree62_937.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42313,degreeTree62_933All,degreeTree62_936All⟩ - -lemma degreeTree62_938All : degreeTree62_938.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42269,degreeTree62_930All,degreeTree62_937All⟩ - -lemma degreeTree62_939All : degreeTree62_939.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42368,⟨sg42363,⟨sg42360,⟨sg42359,⟨sg42358,True.intro,True.intro⟩,True.intro⟩,⟨sg42362,⟨sg42361,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42366,⟨sg42365,⟨sg42364,True.intro,True.intro⟩,True.intro⟩,⟨sg42367,True.intro,True.intro⟩⟩⟩,⟨sg42374,⟨sg42371,⟨sg42370,⟨sg42369,True.intro,True.intro⟩,True.intro⟩,⟨sg42373,⟨sg42372,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42377,⟨sg42376,⟨sg42375,True.intro,True.intro⟩,True.intro⟩,⟨sg42378,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_940All : degreeTree62_940.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42390,⟨sg42385,⟨sg42382,⟨sg42381,⟨sg42380,True.intro,True.intro⟩,True.intro⟩,⟨sg42384,⟨sg42383,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42388,⟨sg42387,⟨sg42386,True.intro,True.intro⟩,True.intro⟩,⟨sg42389,True.intro,True.intro⟩⟩⟩,⟨sg42396,⟨sg42393,⟨sg42392,⟨sg42391,True.intro,True.intro⟩,True.intro⟩,⟨sg42395,⟨sg42394,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42399,⟨sg42398,⟨sg42397,True.intro,True.intro⟩,True.intro⟩,⟨sg42400,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_941All : degreeTree62_941.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42379,degreeTree62_939All,degreeTree62_940All⟩ - -lemma degreeTree62_942All : degreeTree62_942.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42412,⟨sg42407,⟨sg42404,⟨sg42403,⟨sg42402,True.intro,True.intro⟩,True.intro⟩,⟨sg42406,⟨sg42405,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42410,⟨sg42409,⟨sg42408,True.intro,True.intro⟩,True.intro⟩,⟨sg42411,True.intro,True.intro⟩⟩⟩,⟨sg42418,⟨sg42415,⟨sg42414,⟨sg42413,True.intro,True.intro⟩,True.intro⟩,⟨sg42417,⟨sg42416,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42421,⟨sg42420,⟨sg42419,True.intro,True.intro⟩,True.intro⟩,⟨sg42422,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_943All : degreeTree62_943.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42434,⟨sg42429,⟨sg42426,⟨sg42425,⟨sg42424,True.intro,True.intro⟩,True.intro⟩,⟨sg42428,⟨sg42427,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42432,⟨sg42431,⟨sg42430,True.intro,True.intro⟩,True.intro⟩,⟨sg42433,True.intro,True.intro⟩⟩⟩,⟨sg42440,⟨sg42437,⟨sg42436,⟨sg42435,True.intro,True.intro⟩,True.intro⟩,⟨sg42439,⟨sg42438,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42443,⟨sg42442,⟨sg42441,True.intro,True.intro⟩,True.intro⟩,⟨sg42444,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_944All : degreeTree62_944.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42423,degreeTree62_942All,degreeTree62_943All⟩ - -lemma degreeTree62_945All : degreeTree62_945.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42401,degreeTree62_941All,degreeTree62_944All⟩ - -lemma degreeTree62_946All : degreeTree62_946.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42456,⟨sg42451,⟨sg42448,⟨sg42447,⟨sg42446,True.intro,True.intro⟩,True.intro⟩,⟨sg42450,⟨sg42449,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42454,⟨sg42453,⟨sg42452,True.intro,True.intro⟩,True.intro⟩,⟨sg42455,True.intro,True.intro⟩⟩⟩,⟨sg42462,⟨sg42459,⟨sg42458,⟨sg42457,True.intro,True.intro⟩,True.intro⟩,⟨sg42461,⟨sg42460,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42465,⟨sg42464,⟨sg42463,True.intro,True.intro⟩,True.intro⟩,⟨sg42466,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_947All : degreeTree62_947.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42478,⟨sg42473,⟨sg42470,⟨sg42469,⟨sg42468,True.intro,True.intro⟩,True.intro⟩,⟨sg42472,⟨sg42471,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42476,⟨sg42475,⟨sg42474,True.intro,True.intro⟩,True.intro⟩,⟨sg42477,True.intro,True.intro⟩⟩⟩,⟨sg42484,⟨sg42481,⟨sg42480,⟨sg42479,True.intro,True.intro⟩,True.intro⟩,⟨sg42483,⟨sg42482,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42487,⟨sg42486,⟨sg42485,True.intro,True.intro⟩,True.intro⟩,⟨sg42488,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_948All : degreeTree62_948.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42467,degreeTree62_946All,degreeTree62_947All⟩ - -lemma degreeTree62_949All : degreeTree62_949.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42500,⟨sg42495,⟨sg42492,⟨sg42491,⟨sg42490,True.intro,True.intro⟩,True.intro⟩,⟨sg42494,⟨sg42493,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42498,⟨sg42497,⟨sg42496,True.intro,True.intro⟩,True.intro⟩,⟨sg42499,True.intro,True.intro⟩⟩⟩,⟨sg42506,⟨sg42503,⟨sg42502,⟨sg42501,True.intro,True.intro⟩,True.intro⟩,⟨sg42505,⟨sg42504,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42509,⟨sg42508,⟨sg42507,True.intro,True.intro⟩,True.intro⟩,⟨sg42510,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_950All : degreeTree62_950.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42522,⟨sg42517,⟨sg42514,⟨sg42513,⟨sg42512,True.intro,True.intro⟩,True.intro⟩,⟨sg42516,⟨sg42515,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42520,⟨sg42519,⟨sg42518,True.intro,True.intro⟩,True.intro⟩,⟨sg42521,True.intro,True.intro⟩⟩⟩,⟨sg42527,⟨sg42525,⟨sg42524,⟨sg42523,True.intro,True.intro⟩,True.intro⟩,⟨sg42526,True.intro,True.intro⟩⟩,⟨sg42530,⟨sg42529,⟨sg42528,True.intro,True.intro⟩,True.intro⟩,⟨sg42531,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_951All : degreeTree62_951.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42511,degreeTree62_949All,degreeTree62_950All⟩ - -lemma degreeTree62_952All : degreeTree62_952.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42489,degreeTree62_948All,degreeTree62_951All⟩ - -lemma degreeTree62_953All : degreeTree62_953.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42445,degreeTree62_945All,degreeTree62_952All⟩ - -lemma degreeTree62_954All : degreeTree62_954.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42357,degreeTree62_938All,degreeTree62_953All⟩ - -lemma degreeTree62_955All : degreeTree62_955.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42181,degreeTree62_923All,degreeTree62_954All⟩ - -lemma degreeTree62_956All : degreeTree62_956.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42543,⟨sg42538,⟨sg42535,⟨sg42534,⟨sg42533,True.intro,True.intro⟩,True.intro⟩,⟨sg42537,⟨sg42536,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42541,⟨sg42540,⟨sg42539,True.intro,True.intro⟩,True.intro⟩,⟨sg42542,True.intro,True.intro⟩⟩⟩,⟨sg42549,⟨sg42546,⟨sg42545,⟨sg42544,True.intro,True.intro⟩,True.intro⟩,⟨sg42548,⟨sg42547,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42552,⟨sg42551,⟨sg42550,True.intro,True.intro⟩,True.intro⟩,⟨sg42553,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_957All : degreeTree62_957.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42565,⟨sg42560,⟨sg42557,⟨sg42556,⟨sg42555,True.intro,True.intro⟩,True.intro⟩,⟨sg42559,⟨sg42558,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42563,⟨sg42562,⟨sg42561,True.intro,True.intro⟩,True.intro⟩,⟨sg42564,True.intro,True.intro⟩⟩⟩,⟨sg42571,⟨sg42568,⟨sg42567,⟨sg42566,True.intro,True.intro⟩,True.intro⟩,⟨sg42570,⟨sg42569,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42574,⟨sg42573,⟨sg42572,True.intro,True.intro⟩,True.intro⟩,⟨sg42575,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_958All : degreeTree62_958.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42554,degreeTree62_956All,degreeTree62_957All⟩ - -lemma degreeTree62_959All : degreeTree62_959.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42587,⟨sg42582,⟨sg42579,⟨sg42578,⟨sg42577,True.intro,True.intro⟩,True.intro⟩,⟨sg42581,⟨sg42580,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42585,⟨sg42584,⟨sg42583,True.intro,True.intro⟩,True.intro⟩,⟨sg42586,True.intro,True.intro⟩⟩⟩,⟨sg42593,⟨sg42590,⟨sg42589,⟨sg42588,True.intro,True.intro⟩,True.intro⟩,⟨sg42592,⟨sg42591,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42596,⟨sg42595,⟨sg42594,True.intro,True.intro⟩,True.intro⟩,⟨sg42597,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_960All : degreeTree62_960.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42609,⟨sg42604,⟨sg42601,⟨sg42600,⟨sg42599,True.intro,True.intro⟩,True.intro⟩,⟨sg42603,⟨sg42602,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42607,⟨sg42606,⟨sg42605,True.intro,True.intro⟩,True.intro⟩,⟨sg42608,True.intro,True.intro⟩⟩⟩,⟨sg42615,⟨sg42612,⟨sg42611,⟨sg42610,True.intro,True.intro⟩,True.intro⟩,⟨sg42614,⟨sg42613,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42618,⟨sg42617,⟨sg42616,True.intro,True.intro⟩,True.intro⟩,⟨sg42619,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_961All : degreeTree62_961.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42598,degreeTree62_959All,degreeTree62_960All⟩ - -lemma degreeTree62_962All : degreeTree62_962.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42576,degreeTree62_958All,degreeTree62_961All⟩ - -lemma degreeTree62_963All : degreeTree62_963.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42631,⟨sg42626,⟨sg42623,⟨sg42622,⟨sg42621,True.intro,True.intro⟩,True.intro⟩,⟨sg42625,⟨sg42624,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42629,⟨sg42628,⟨sg42627,True.intro,True.intro⟩,True.intro⟩,⟨sg42630,True.intro,True.intro⟩⟩⟩,⟨sg42637,⟨sg42634,⟨sg42633,⟨sg42632,True.intro,True.intro⟩,True.intro⟩,⟨sg42636,⟨sg42635,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42640,⟨sg42639,⟨sg42638,True.intro,True.intro⟩,True.intro⟩,⟨sg42641,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_964All : degreeTree62_964.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42653,⟨sg42648,⟨sg42645,⟨sg42644,⟨sg42643,True.intro,True.intro⟩,True.intro⟩,⟨sg42647,⟨sg42646,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42651,⟨sg42650,⟨sg42649,True.intro,True.intro⟩,True.intro⟩,⟨sg42652,True.intro,True.intro⟩⟩⟩,⟨sg42659,⟨sg42656,⟨sg42655,⟨sg42654,True.intro,True.intro⟩,True.intro⟩,⟨sg42658,⟨sg42657,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42662,⟨sg42661,⟨sg42660,True.intro,True.intro⟩,True.intro⟩,⟨sg42663,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_965All : degreeTree62_965.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42642,degreeTree62_963All,degreeTree62_964All⟩ - -lemma degreeTree62_966All : degreeTree62_966.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42675,⟨sg42670,⟨sg42667,⟨sg42666,⟨sg42665,True.intro,True.intro⟩,True.intro⟩,⟨sg42669,⟨sg42668,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42673,⟨sg42672,⟨sg42671,True.intro,True.intro⟩,True.intro⟩,⟨sg42674,True.intro,True.intro⟩⟩⟩,⟨sg42681,⟨sg42678,⟨sg42677,⟨sg42676,True.intro,True.intro⟩,True.intro⟩,⟨sg42680,⟨sg42679,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42684,⟨sg42683,⟨sg42682,True.intro,True.intro⟩,True.intro⟩,⟨sg42685,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_967All : degreeTree62_967.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42697,⟨sg42692,⟨sg42689,⟨sg42688,⟨sg42687,True.intro,True.intro⟩,True.intro⟩,⟨sg42691,⟨sg42690,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42695,⟨sg42694,⟨sg42693,True.intro,True.intro⟩,True.intro⟩,⟨sg42696,True.intro,True.intro⟩⟩⟩,⟨sg42703,⟨sg42700,⟨sg42699,⟨sg42698,True.intro,True.intro⟩,True.intro⟩,⟨sg42702,⟨sg42701,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42706,⟨sg42705,⟨sg42704,True.intro,True.intro⟩,True.intro⟩,⟨sg42707,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_968All : degreeTree62_968.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42686,degreeTree62_966All,degreeTree62_967All⟩ - -lemma degreeTree62_969All : degreeTree62_969.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42664,degreeTree62_965All,degreeTree62_968All⟩ - -lemma degreeTree62_970All : degreeTree62_970.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42620,degreeTree62_962All,degreeTree62_969All⟩ - -lemma degreeTree62_971All : degreeTree62_971.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42719,⟨sg42714,⟨sg42711,⟨sg42710,⟨sg42709,True.intro,True.intro⟩,True.intro⟩,⟨sg42713,⟨sg42712,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42717,⟨sg42716,⟨sg42715,True.intro,True.intro⟩,True.intro⟩,⟨sg42718,True.intro,True.intro⟩⟩⟩,⟨sg42725,⟨sg42722,⟨sg42721,⟨sg42720,True.intro,True.intro⟩,True.intro⟩,⟨sg42724,⟨sg42723,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42728,⟨sg42727,⟨sg42726,True.intro,True.intro⟩,True.intro⟩,⟨sg42729,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_972All : degreeTree62_972.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42741,⟨sg42736,⟨sg42733,⟨sg42732,⟨sg42731,True.intro,True.intro⟩,True.intro⟩,⟨sg42735,⟨sg42734,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42739,⟨sg42738,⟨sg42737,True.intro,True.intro⟩,True.intro⟩,⟨sg42740,True.intro,True.intro⟩⟩⟩,⟨sg42747,⟨sg42744,⟨sg42743,⟨sg42742,True.intro,True.intro⟩,True.intro⟩,⟨sg42746,⟨sg42745,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42750,⟨sg42749,⟨sg42748,True.intro,True.intro⟩,True.intro⟩,⟨sg42751,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_973All : degreeTree62_973.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42730,degreeTree62_971All,degreeTree62_972All⟩ - -lemma degreeTree62_974All : degreeTree62_974.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42763,⟨sg42758,⟨sg42755,⟨sg42754,⟨sg42753,True.intro,True.intro⟩,True.intro⟩,⟨sg42757,⟨sg42756,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42761,⟨sg42760,⟨sg42759,True.intro,True.intro⟩,True.intro⟩,⟨sg42762,True.intro,True.intro⟩⟩⟩,⟨sg42769,⟨sg42766,⟨sg42765,⟨sg42764,True.intro,True.intro⟩,True.intro⟩,⟨sg42768,⟨sg42767,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42772,⟨sg42771,⟨sg42770,True.intro,True.intro⟩,True.intro⟩,⟨sg42773,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_975All : degreeTree62_975.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42785,⟨sg42780,⟨sg42777,⟨sg42776,⟨sg42775,True.intro,True.intro⟩,True.intro⟩,⟨sg42779,⟨sg42778,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42783,⟨sg42782,⟨sg42781,True.intro,True.intro⟩,True.intro⟩,⟨sg42784,True.intro,True.intro⟩⟩⟩,⟨sg42791,⟨sg42788,⟨sg42787,⟨sg42786,True.intro,True.intro⟩,True.intro⟩,⟨sg42790,⟨sg42789,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42794,⟨sg42793,⟨sg42792,True.intro,True.intro⟩,True.intro⟩,⟨sg42795,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_976All : degreeTree62_976.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42774,degreeTree62_974All,degreeTree62_975All⟩ - -lemma degreeTree62_977All : degreeTree62_977.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42752,degreeTree62_973All,degreeTree62_976All⟩ - -lemma degreeTree62_978All : degreeTree62_978.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42807,⟨sg42802,⟨sg42799,⟨sg42798,⟨sg42797,True.intro,True.intro⟩,True.intro⟩,⟨sg42801,⟨sg42800,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42805,⟨sg42804,⟨sg42803,True.intro,True.intro⟩,True.intro⟩,⟨sg42806,True.intro,True.intro⟩⟩⟩,⟨sg42813,⟨sg42810,⟨sg42809,⟨sg42808,True.intro,True.intro⟩,True.intro⟩,⟨sg42812,⟨sg42811,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42816,⟨sg42815,⟨sg42814,True.intro,True.intro⟩,True.intro⟩,⟨sg42817,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_979All : degreeTree62_979.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42829,⟨sg42824,⟨sg42821,⟨sg42820,⟨sg42819,True.intro,True.intro⟩,True.intro⟩,⟨sg42823,⟨sg42822,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42827,⟨sg42826,⟨sg42825,True.intro,True.intro⟩,True.intro⟩,⟨sg42828,True.intro,True.intro⟩⟩⟩,⟨sg42835,⟨sg42832,⟨sg42831,⟨sg42830,True.intro,True.intro⟩,True.intro⟩,⟨sg42834,⟨sg42833,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42838,⟨sg42837,⟨sg42836,True.intro,True.intro⟩,True.intro⟩,⟨sg42839,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_980All : degreeTree62_980.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42818,degreeTree62_978All,degreeTree62_979All⟩ - -lemma degreeTree62_981All : degreeTree62_981.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42851,⟨sg42846,⟨sg42843,⟨sg42842,⟨sg42841,True.intro,True.intro⟩,True.intro⟩,⟨sg42845,⟨sg42844,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42849,⟨sg42848,⟨sg42847,True.intro,True.intro⟩,True.intro⟩,⟨sg42850,True.intro,True.intro⟩⟩⟩,⟨sg42857,⟨sg42854,⟨sg42853,⟨sg42852,True.intro,True.intro⟩,True.intro⟩,⟨sg42856,⟨sg42855,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42860,⟨sg42859,⟨sg42858,True.intro,True.intro⟩,True.intro⟩,⟨sg42861,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_982All : degreeTree62_982.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42873,⟨sg42868,⟨sg42865,⟨sg42864,⟨sg42863,True.intro,True.intro⟩,True.intro⟩,⟨sg42867,⟨sg42866,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42871,⟨sg42870,⟨sg42869,True.intro,True.intro⟩,True.intro⟩,⟨sg42872,True.intro,True.intro⟩⟩⟩,⟨sg42878,⟨sg42876,⟨sg42875,⟨sg42874,True.intro,True.intro⟩,True.intro⟩,⟨sg42877,True.intro,True.intro⟩⟩,⟨sg42881,⟨sg42880,⟨sg42879,True.intro,True.intro⟩,True.intro⟩,⟨sg42882,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_983All : degreeTree62_983.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42862,degreeTree62_981All,degreeTree62_982All⟩ - -lemma degreeTree62_984All : degreeTree62_984.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42840,degreeTree62_980All,degreeTree62_983All⟩ - -lemma degreeTree62_985All : degreeTree62_985.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42796,degreeTree62_977All,degreeTree62_984All⟩ - -lemma degreeTree62_986All : degreeTree62_986.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42708,degreeTree62_970All,degreeTree62_985All⟩ - -lemma degreeTree62_987All : degreeTree62_987.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42894,⟨sg42889,⟨sg42886,⟨sg42885,⟨sg42884,True.intro,True.intro⟩,True.intro⟩,⟨sg42888,⟨sg42887,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42892,⟨sg42891,⟨sg42890,True.intro,True.intro⟩,True.intro⟩,⟨sg42893,True.intro,True.intro⟩⟩⟩,⟨sg42900,⟨sg42897,⟨sg42896,⟨sg42895,True.intro,True.intro⟩,True.intro⟩,⟨sg42899,⟨sg42898,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42903,⟨sg42902,⟨sg42901,True.intro,True.intro⟩,True.intro⟩,⟨sg42904,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_988All : degreeTree62_988.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42916,⟨sg42911,⟨sg42908,⟨sg42907,⟨sg42906,True.intro,True.intro⟩,True.intro⟩,⟨sg42910,⟨sg42909,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42914,⟨sg42913,⟨sg42912,True.intro,True.intro⟩,True.intro⟩,⟨sg42915,True.intro,True.intro⟩⟩⟩,⟨sg42922,⟨sg42919,⟨sg42918,⟨sg42917,True.intro,True.intro⟩,True.intro⟩,⟨sg42921,⟨sg42920,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42925,⟨sg42924,⟨sg42923,True.intro,True.intro⟩,True.intro⟩,⟨sg42926,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_989All : degreeTree62_989.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42905,degreeTree62_987All,degreeTree62_988All⟩ - -lemma degreeTree62_990All : degreeTree62_990.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42938,⟨sg42933,⟨sg42930,⟨sg42929,⟨sg42928,True.intro,True.intro⟩,True.intro⟩,⟨sg42932,⟨sg42931,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42936,⟨sg42935,⟨sg42934,True.intro,True.intro⟩,True.intro⟩,⟨sg42937,True.intro,True.intro⟩⟩⟩,⟨sg42944,⟨sg42941,⟨sg42940,⟨sg42939,True.intro,True.intro⟩,True.intro⟩,⟨sg42943,⟨sg42942,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42947,⟨sg42946,⟨sg42945,True.intro,True.intro⟩,True.intro⟩,⟨sg42948,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_991All : degreeTree62_991.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42960,⟨sg42955,⟨sg42952,⟨sg42951,⟨sg42950,True.intro,True.intro⟩,True.intro⟩,⟨sg42954,⟨sg42953,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42958,⟨sg42957,⟨sg42956,True.intro,True.intro⟩,True.intro⟩,⟨sg42959,True.intro,True.intro⟩⟩⟩,⟨sg42966,⟨sg42963,⟨sg42962,⟨sg42961,True.intro,True.intro⟩,True.intro⟩,⟨sg42965,⟨sg42964,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42969,⟨sg42968,⟨sg42967,True.intro,True.intro⟩,True.intro⟩,⟨sg42970,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_992All : degreeTree62_992.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42949,degreeTree62_990All,degreeTree62_991All⟩ - -lemma degreeTree62_993All : degreeTree62_993.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42927,degreeTree62_989All,degreeTree62_992All⟩ - -lemma degreeTree62_994All : degreeTree62_994.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42982,⟨sg42977,⟨sg42974,⟨sg42973,⟨sg42972,True.intro,True.intro⟩,True.intro⟩,⟨sg42976,⟨sg42975,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42980,⟨sg42979,⟨sg42978,True.intro,True.intro⟩,True.intro⟩,⟨sg42981,True.intro,True.intro⟩⟩⟩,⟨sg42988,⟨sg42985,⟨sg42984,⟨sg42983,True.intro,True.intro⟩,True.intro⟩,⟨sg42987,⟨sg42986,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42991,⟨sg42990,⟨sg42989,True.intro,True.intro⟩,True.intro⟩,⟨sg42992,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_995All : degreeTree62_995.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43004,⟨sg42999,⟨sg42996,⟨sg42995,⟨sg42994,True.intro,True.intro⟩,True.intro⟩,⟨sg42998,⟨sg42997,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43002,⟨sg43001,⟨sg43000,True.intro,True.intro⟩,True.intro⟩,⟨sg43003,True.intro,True.intro⟩⟩⟩,⟨sg43010,⟨sg43007,⟨sg43006,⟨sg43005,True.intro,True.intro⟩,True.intro⟩,⟨sg43009,⟨sg43008,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43013,⟨sg43012,⟨sg43011,True.intro,True.intro⟩,True.intro⟩,⟨sg43014,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_996All : degreeTree62_996.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42993,degreeTree62_994All,degreeTree62_995All⟩ - -lemma degreeTree62_997All : degreeTree62_997.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43026,⟨sg43021,⟨sg43018,⟨sg43017,⟨sg43016,True.intro,True.intro⟩,True.intro⟩,⟨sg43020,⟨sg43019,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43024,⟨sg43023,⟨sg43022,True.intro,True.intro⟩,True.intro⟩,⟨sg43025,True.intro,True.intro⟩⟩⟩,⟨sg43032,⟨sg43029,⟨sg43028,⟨sg43027,True.intro,True.intro⟩,True.intro⟩,⟨sg43031,⟨sg43030,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43035,⟨sg43034,⟨sg43033,True.intro,True.intro⟩,True.intro⟩,⟨sg43036,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_998All : degreeTree62_998.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43048,⟨sg43043,⟨sg43040,⟨sg43039,⟨sg43038,True.intro,True.intro⟩,True.intro⟩,⟨sg43042,⟨sg43041,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43046,⟨sg43045,⟨sg43044,True.intro,True.intro⟩,True.intro⟩,⟨sg43047,True.intro,True.intro⟩⟩⟩,⟨sg43053,⟨sg43051,⟨sg43050,⟨sg43049,True.intro,True.intro⟩,True.intro⟩,⟨sg43052,True.intro,True.intro⟩⟩,⟨sg43056,⟨sg43055,⟨sg43054,True.intro,True.intro⟩,True.intro⟩,⟨sg43057,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_999All : degreeTree62_999.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43037,degreeTree62_997All,degreeTree62_998All⟩ - -lemma degreeTree62_1000All : degreeTree62_1000.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43015,degreeTree62_996All,degreeTree62_999All⟩ - -lemma degreeTree62_1001All : degreeTree62_1001.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42971,degreeTree62_993All,degreeTree62_1000All⟩ - -lemma degreeTree62_1002All : degreeTree62_1002.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43069,⟨sg43064,⟨sg43061,⟨sg43060,⟨sg43059,True.intro,True.intro⟩,True.intro⟩,⟨sg43063,⟨sg43062,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43067,⟨sg43066,⟨sg43065,True.intro,True.intro⟩,True.intro⟩,⟨sg43068,True.intro,True.intro⟩⟩⟩,⟨sg43075,⟨sg43072,⟨sg43071,⟨sg43070,True.intro,True.intro⟩,True.intro⟩,⟨sg43074,⟨sg43073,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43078,⟨sg43077,⟨sg43076,True.intro,True.intro⟩,True.intro⟩,⟨sg43079,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_1003All : degreeTree62_1003.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43091,⟨sg43086,⟨sg43083,⟨sg43082,⟨sg43081,True.intro,True.intro⟩,True.intro⟩,⟨sg43085,⟨sg43084,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43089,⟨sg43088,⟨sg43087,True.intro,True.intro⟩,True.intro⟩,⟨sg43090,True.intro,True.intro⟩⟩⟩,⟨sg43097,⟨sg43094,⟨sg43093,⟨sg43092,True.intro,True.intro⟩,True.intro⟩,⟨sg43096,⟨sg43095,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43100,⟨sg43099,⟨sg43098,True.intro,True.intro⟩,True.intro⟩,⟨sg43101,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_1004All : degreeTree62_1004.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43080,degreeTree62_1002All,degreeTree62_1003All⟩ - -lemma degreeTree62_1005All : degreeTree62_1005.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43113,⟨sg43108,⟨sg43105,⟨sg43104,⟨sg43103,True.intro,True.intro⟩,True.intro⟩,⟨sg43107,⟨sg43106,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43111,⟨sg43110,⟨sg43109,True.intro,True.intro⟩,True.intro⟩,⟨sg43112,True.intro,True.intro⟩⟩⟩,⟨sg43119,⟨sg43116,⟨sg43115,⟨sg43114,True.intro,True.intro⟩,True.intro⟩,⟨sg43118,⟨sg43117,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43122,⟨sg43121,⟨sg43120,True.intro,True.intro⟩,True.intro⟩,⟨sg43123,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_1006All : degreeTree62_1006.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43135,⟨sg43130,⟨sg43127,⟨sg43126,⟨sg43125,True.intro,True.intro⟩,True.intro⟩,⟨sg43129,⟨sg43128,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43133,⟨sg43132,⟨sg43131,True.intro,True.intro⟩,True.intro⟩,⟨sg43134,True.intro,True.intro⟩⟩⟩,⟨sg43141,⟨sg43138,⟨sg43137,⟨sg43136,True.intro,True.intro⟩,True.intro⟩,⟨sg43140,⟨sg43139,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43144,⟨sg43143,⟨sg43142,True.intro,True.intro⟩,True.intro⟩,⟨sg43145,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_1007All : degreeTree62_1007.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43124,degreeTree62_1005All,degreeTree62_1006All⟩ - -lemma degreeTree62_1008All : degreeTree62_1008.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43102,degreeTree62_1004All,degreeTree62_1007All⟩ - -lemma degreeTree62_1009All : degreeTree62_1009.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43157,⟨sg43152,⟨sg43149,⟨sg43148,⟨sg43147,True.intro,True.intro⟩,True.intro⟩,⟨sg43151,⟨sg43150,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43155,⟨sg43154,⟨sg43153,True.intro,True.intro⟩,True.intro⟩,⟨sg43156,True.intro,True.intro⟩⟩⟩,⟨sg43163,⟨sg43160,⟨sg43159,⟨sg43158,True.intro,True.intro⟩,True.intro⟩,⟨sg43162,⟨sg43161,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43166,⟨sg43165,⟨sg43164,True.intro,True.intro⟩,True.intro⟩,⟨sg43167,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_1010All : degreeTree62_1010.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43179,⟨sg43174,⟨sg43171,⟨sg43170,⟨sg43169,True.intro,True.intro⟩,True.intro⟩,⟨sg43173,⟨sg43172,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43177,⟨sg43176,⟨sg43175,True.intro,True.intro⟩,True.intro⟩,⟨sg43178,True.intro,True.intro⟩⟩⟩,⟨sg43185,⟨sg43182,⟨sg43181,⟨sg43180,True.intro,True.intro⟩,True.intro⟩,⟨sg43184,⟨sg43183,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43188,⟨sg43187,⟨sg43186,True.intro,True.intro⟩,True.intro⟩,⟨sg43189,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_1011All : degreeTree62_1011.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43168,degreeTree62_1009All,degreeTree62_1010All⟩ - -lemma degreeTree62_1012All : degreeTree62_1012.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43201,⟨sg43196,⟨sg43193,⟨sg43192,⟨sg43191,True.intro,True.intro⟩,True.intro⟩,⟨sg43195,⟨sg43194,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43199,⟨sg43198,⟨sg43197,True.intro,True.intro⟩,True.intro⟩,⟨sg43200,True.intro,True.intro⟩⟩⟩,⟨sg43207,⟨sg43204,⟨sg43203,⟨sg43202,True.intro,True.intro⟩,True.intro⟩,⟨sg43206,⟨sg43205,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43210,⟨sg43209,⟨sg43208,True.intro,True.intro⟩,True.intro⟩,⟨sg43211,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_1013All : degreeTree62_1013.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43223,⟨sg43218,⟨sg43215,⟨sg43214,⟨sg43213,True.intro,True.intro⟩,True.intro⟩,⟨sg43217,⟨sg43216,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43221,⟨sg43220,⟨sg43219,True.intro,True.intro⟩,True.intro⟩,⟨sg43222,True.intro,True.intro⟩⟩⟩,⟨sg43228,⟨sg43226,⟨sg43225,⟨sg43224,True.intro,True.intro⟩,True.intro⟩,⟨sg43227,True.intro,True.intro⟩⟩,⟨sg43231,⟨sg43230,⟨sg43229,True.intro,True.intro⟩,True.intro⟩,⟨sg43232,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTree62_1014All : degreeTree62_1014.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43212,degreeTree62_1012All,degreeTree62_1013All⟩ - -lemma degreeTree62_1015All : degreeTree62_1015.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43190,degreeTree62_1011All,degreeTree62_1014All⟩ - -lemma degreeTree62_1016All : degreeTree62_1016.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43146,degreeTree62_1008All,degreeTree62_1015All⟩ - -lemma degreeTree62_1017All : degreeTree62_1017.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg43058,degreeTree62_1001All,degreeTree62_1016All⟩ - -lemma degreeTree62_1018All : degreeTree62_1018.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42883,degreeTree62_986All,degreeTree62_1017All⟩ - -lemma degreeTree62_1019All : degreeTree62_1019.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg42532,degreeTree62_955All,degreeTree62_1018All⟩ - -lemma degreeTree62_1020All : degreeTree62_1020.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg41830,degreeTree62_892All,degreeTree62_1019All⟩ - -lemma degreeTree62_1021All : degreeTree62_1021.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg40426,degreeTree62_765All,degreeTree62_1020All⟩ - -lemma degreeTree62_1022All : degreeTree62_1022.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by - exact ⟨sg37619,degreeTree62_510All,degreeTree62_1021All⟩ - -lemma degreeTreeAll62 : degreeTree62.All - (fun rs => SquareOccurs (candidate 8 6 1) (rowDiagram rs)) := by - have hp : rowDiagram [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] = candidate 8 6 1 := rowDiagram_candidate (M := 8) (b := 6) (δ := 1) (by decide) - rw [← hp] - exact degreeTree62_1022All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData62 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupMissingLeaves +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes100 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes101 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes102 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes103 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes104 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes105 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes106 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes79 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes80 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes81 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes82 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes83 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes84 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes85 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes86 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes87 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes88 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes89 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes90 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes91 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes92 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes93 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes94 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes95 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes96 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes97 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes98 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes99 + +namespace OAI + +/-! Degree Tree Proof 62. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree62_0All : degreeTree62_0.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32016,⟨sg32011,⟨sg32008,⟨sg32007,⟨sg32006,True.intro,True.intro⟩,True.intro⟩,⟨sg32010,⟨sg32009,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32014,⟨sg32013,⟨sg32012,True.intro,True.intro⟩,True.intro⟩,⟨sg32015,True.intro,True.intro⟩⟩⟩,⟨sg32022,⟨sg32019,⟨sg32018,⟨sg32017,True.intro,True.intro⟩,True.intro⟩,⟨sg32021,⟨sg32020,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32025,⟨sg32024,⟨sg32023,True.intro,True.intro⟩,True.intro⟩,⟨sg32026,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_1All : degreeTree62_1.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32038,⟨sg32033,⟨sg32030,⟨sg32029,⟨sg32028,True.intro,True.intro⟩,True.intro⟩,⟨sg32032,⟨sg32031,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32036,⟨sg32035,⟨sg32034,True.intro,True.intro⟩,True.intro⟩,⟨sg32037,True.intro,True.intro⟩⟩⟩,⟨sg32044,⟨sg32041,⟨sg32040,⟨sg32039,True.intro,True.intro⟩,True.intro⟩,⟨sg32043,⟨sg32042,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32047,⟨sg32046,⟨sg32045,True.intro,True.intro⟩,True.intro⟩,⟨sg32048,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_2All : degreeTree62_2.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32027,degreeTree62_0All,degreeTree62_1All⟩ + +lemma degreeTree62_3All : degreeTree62_3.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32060,⟨sg32055,⟨sg32052,⟨sg32051,⟨sg32050,True.intro,True.intro⟩,True.intro⟩,⟨sg32054,⟨sg32053,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32058,⟨sg32057,⟨sg32056,True.intro,True.intro⟩,True.intro⟩,⟨sg32059,True.intro,True.intro⟩⟩⟩,⟨sg32066,⟨sg32063,⟨sg32062,⟨sg32061,True.intro,True.intro⟩,True.intro⟩,⟨sg32065,⟨sg32064,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32069,⟨sg32068,⟨sg32067,True.intro,True.intro⟩,True.intro⟩,⟨sg32070,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_4All : degreeTree62_4.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32082,⟨sg32077,⟨sg32074,⟨sg32073,⟨sg32072,True.intro,True.intro⟩,True.intro⟩,⟨sg32076,⟨sg32075,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32080,⟨sg32079,⟨sg32078,True.intro,True.intro⟩,True.intro⟩,⟨sg32081,True.intro,True.intro⟩⟩⟩,⟨sg32088,⟨sg32085,⟨sg32084,⟨sg32083,True.intro,True.intro⟩,True.intro⟩,⟨sg32087,⟨sg32086,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32091,⟨sg32090,⟨sg32089,True.intro,True.intro⟩,True.intro⟩,⟨sg32092,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_5All : degreeTree62_5.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32071,degreeTree62_3All,degreeTree62_4All⟩ + +lemma degreeTree62_6All : degreeTree62_6.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32049,degreeTree62_2All,degreeTree62_5All⟩ + +lemma degreeTree62_7All : degreeTree62_7.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32104,⟨sg32099,⟨sg32096,⟨sg32095,⟨sg32094,True.intro,True.intro⟩,True.intro⟩,⟨sg32098,⟨sg32097,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32102,⟨sg32101,⟨sg32100,True.intro,True.intro⟩,True.intro⟩,⟨sg32103,True.intro,True.intro⟩⟩⟩,⟨sg32110,⟨sg32107,⟨sg32106,⟨sg32105,True.intro,True.intro⟩,True.intro⟩,⟨sg32109,⟨sg32108,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32113,⟨sg32112,⟨sg32111,True.intro,True.intro⟩,True.intro⟩,⟨sg32114,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_8All : degreeTree62_8.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32126,⟨sg32121,⟨sg32118,⟨sg32117,⟨sg32116,True.intro,True.intro⟩,True.intro⟩,⟨sg32120,⟨sg32119,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32124,⟨sg32123,⟨sg32122,True.intro,True.intro⟩,True.intro⟩,⟨sg32125,True.intro,True.intro⟩⟩⟩,⟨sg32132,⟨sg32129,⟨sg32128,⟨sg32127,True.intro,True.intro⟩,True.intro⟩,⟨sg32131,⟨sg32130,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32135,⟨sg32134,⟨sg32133,True.intro,True.intro⟩,True.intro⟩,⟨sg32136,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_9All : degreeTree62_9.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32115,degreeTree62_7All,degreeTree62_8All⟩ + +lemma degreeTree62_10All : degreeTree62_10.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32148,⟨sg32143,⟨sg32140,⟨sg32139,⟨sg32138,True.intro,True.intro⟩,True.intro⟩,⟨sg32142,⟨sg32141,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32146,⟨sg32145,⟨sg32144,True.intro,True.intro⟩,True.intro⟩,⟨sg32147,True.intro,True.intro⟩⟩⟩,⟨sg32154,⟨sg32151,⟨sg32150,⟨sg32149,True.intro,True.intro⟩,True.intro⟩,⟨sg32153,⟨sg32152,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32157,⟨sg32156,⟨sg32155,True.intro,True.intro⟩,True.intro⟩,⟨sg32158,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_11All : degreeTree62_11.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32170,⟨sg32165,⟨sg32162,⟨sg32161,⟨sg32160,True.intro,True.intro⟩,True.intro⟩,⟨sg32164,⟨sg32163,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32168,⟨sg32167,⟨sg32166,True.intro,True.intro⟩,True.intro⟩,⟨sg32169,True.intro,True.intro⟩⟩⟩,⟨sg32176,⟨sg32173,⟨sg32172,⟨sg32171,True.intro,True.intro⟩,True.intro⟩,⟨sg32175,⟨sg32174,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32179,⟨sg32178,⟨sg32177,True.intro,True.intro⟩,True.intro⟩,⟨sg32180,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_12All : degreeTree62_12.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32159,degreeTree62_10All,degreeTree62_11All⟩ + +lemma degreeTree62_13All : degreeTree62_13.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32137,degreeTree62_9All,degreeTree62_12All⟩ + +lemma degreeTree62_14All : degreeTree62_14.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32093,degreeTree62_6All,degreeTree62_13All⟩ + +lemma degreeTree62_15All : degreeTree62_15.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32192,⟨sg32187,⟨sg32184,⟨sg32183,⟨sg32182,True.intro,True.intro⟩,True.intro⟩,⟨sg32186,⟨sg32185,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32190,⟨sg32189,⟨sg32188,True.intro,True.intro⟩,True.intro⟩,⟨sg32191,True.intro,True.intro⟩⟩⟩,⟨sg32198,⟨sg32195,⟨sg32194,⟨sg32193,True.intro,True.intro⟩,True.intro⟩,⟨sg32197,⟨sg32196,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32201,⟨sg32200,⟨sg32199,True.intro,True.intro⟩,True.intro⟩,⟨sg32202,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_16All : degreeTree62_16.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32214,⟨sg32209,⟨sg32206,⟨sg32205,⟨sg32204,True.intro,True.intro⟩,True.intro⟩,⟨sg32208,⟨sg32207,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32212,⟨sg32211,⟨sg32210,True.intro,True.intro⟩,True.intro⟩,⟨sg32213,True.intro,True.intro⟩⟩⟩,⟨sg32220,⟨sg32217,⟨sg32216,⟨sg32215,True.intro,True.intro⟩,True.intro⟩,⟨sg32219,⟨sg32218,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32223,⟨sg32222,⟨sg32221,True.intro,True.intro⟩,True.intro⟩,⟨sg32224,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_17All : degreeTree62_17.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32203,degreeTree62_15All,degreeTree62_16All⟩ + +lemma degreeTree62_18All : degreeTree62_18.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32236,⟨sg32231,⟨sg32228,⟨sg32227,⟨sg32226,True.intro,True.intro⟩,True.intro⟩,⟨sg32230,⟨sg32229,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32234,⟨sg32233,⟨sg32232,True.intro,True.intro⟩,True.intro⟩,⟨sg32235,True.intro,True.intro⟩⟩⟩,⟨sg32242,⟨sg32239,⟨sg32238,⟨sg32237,True.intro,True.intro⟩,True.intro⟩,⟨sg32241,⟨sg32240,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32245,⟨sg32244,⟨sg32243,True.intro,True.intro⟩,True.intro⟩,⟨sg32246,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_19All : degreeTree62_19.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32258,⟨sg32253,⟨sg32250,⟨sg32249,⟨sg32248,True.intro,True.intro⟩,True.intro⟩,⟨sg32252,⟨sg32251,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32256,⟨sg32255,⟨sg32254,True.intro,True.intro⟩,True.intro⟩,⟨sg32257,True.intro,True.intro⟩⟩⟩,⟨sg32264,⟨sg32261,⟨sg32260,⟨sg32259,True.intro,True.intro⟩,True.intro⟩,⟨sg32263,⟨sg32262,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32267,⟨sg32266,⟨sg32265,True.intro,True.intro⟩,True.intro⟩,⟨sg32268,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_20All : degreeTree62_20.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32247,degreeTree62_18All,degreeTree62_19All⟩ + +lemma degreeTree62_21All : degreeTree62_21.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32225,degreeTree62_17All,degreeTree62_20All⟩ + +lemma degreeTree62_22All : degreeTree62_22.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32280,⟨sg32275,⟨sg32272,⟨sg32271,⟨sg32270,True.intro,True.intro⟩,True.intro⟩,⟨sg32274,⟨sg32273,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32278,⟨sg32277,⟨sg32276,True.intro,True.intro⟩,True.intro⟩,⟨sg32279,True.intro,True.intro⟩⟩⟩,⟨sg32286,⟨sg32283,⟨sg32282,⟨sg32281,True.intro,True.intro⟩,True.intro⟩,⟨sg32285,⟨sg32284,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32289,⟨sg32288,⟨sg32287,True.intro,True.intro⟩,True.intro⟩,⟨sg32290,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_23All : degreeTree62_23.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32302,⟨sg32297,⟨sg32294,⟨sg32293,⟨sg32292,True.intro,True.intro⟩,True.intro⟩,⟨sg32296,⟨sg32295,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32300,⟨sg32299,⟨sg32298,True.intro,True.intro⟩,True.intro⟩,⟨sg32301,True.intro,True.intro⟩⟩⟩,⟨sg32308,⟨sg32305,⟨sg32304,⟨sg32303,True.intro,True.intro⟩,True.intro⟩,⟨sg32307,⟨sg32306,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32311,⟨sg32310,⟨sg32309,True.intro,True.intro⟩,True.intro⟩,⟨sg32312,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_24All : degreeTree62_24.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32291,degreeTree62_22All,degreeTree62_23All⟩ + +lemma degreeTree62_25All : degreeTree62_25.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32324,⟨sg32319,⟨sg32316,⟨sg32315,⟨sg32314,True.intro,True.intro⟩,True.intro⟩,⟨sg32318,⟨sg32317,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32322,⟨sg32321,⟨sg32320,True.intro,True.intro⟩,True.intro⟩,⟨sg32323,True.intro,True.intro⟩⟩⟩,⟨sg32330,⟨sg32327,⟨sg32326,⟨sg32325,True.intro,True.intro⟩,True.intro⟩,⟨sg32329,⟨sg32328,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32333,⟨sg32332,⟨sg32331,True.intro,True.intro⟩,True.intro⟩,⟨sg32334,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_26All : degreeTree62_26.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32346,⟨sg32341,⟨sg32338,⟨sg32337,⟨sg32336,True.intro,True.intro⟩,True.intro⟩,⟨sg32340,⟨sg32339,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32344,⟨sg32343,⟨sg32342,True.intro,True.intro⟩,True.intro⟩,⟨sg32345,True.intro,True.intro⟩⟩⟩,⟨sg32351,⟨sg32349,⟨sg32348,⟨sg32347,True.intro,True.intro⟩,True.intro⟩,⟨sg32350,True.intro,True.intro⟩⟩,⟨sg32354,⟨sg32353,⟨sg32352,True.intro,True.intro⟩,True.intro⟩,⟨sg32355,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_27All : degreeTree62_27.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32335,degreeTree62_25All,degreeTree62_26All⟩ + +lemma degreeTree62_28All : degreeTree62_28.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32313,degreeTree62_24All,degreeTree62_27All⟩ + +lemma degreeTree62_29All : degreeTree62_29.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32269,degreeTree62_21All,degreeTree62_28All⟩ + +lemma degreeTree62_30All : degreeTree62_30.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32181,degreeTree62_14All,degreeTree62_29All⟩ + +lemma degreeTree62_31All : degreeTree62_31.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32367,⟨sg32362,⟨sg32359,⟨sg32358,⟨sg32357,True.intro,True.intro⟩,True.intro⟩,⟨sg32361,⟨sg32360,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32365,⟨sg32364,⟨sg32363,True.intro,True.intro⟩,True.intro⟩,⟨sg32366,True.intro,True.intro⟩⟩⟩,⟨sg32373,⟨sg32370,⟨sg32369,⟨sg32368,True.intro,True.intro⟩,True.intro⟩,⟨sg32372,⟨sg32371,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32376,⟨sg32375,⟨sg32374,True.intro,True.intro⟩,True.intro⟩,⟨sg32377,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_32All : degreeTree62_32.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32389,⟨sg32384,⟨sg32381,⟨sg32380,⟨sg32379,True.intro,True.intro⟩,True.intro⟩,⟨sg32383,⟨sg32382,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32387,⟨sg32386,⟨sg32385,True.intro,True.intro⟩,True.intro⟩,⟨sg32388,True.intro,True.intro⟩⟩⟩,⟨sg32395,⟨sg32392,⟨sg32391,⟨sg32390,True.intro,True.intro⟩,True.intro⟩,⟨sg32394,⟨sg32393,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32398,⟨sg32397,⟨sg32396,True.intro,True.intro⟩,True.intro⟩,⟨sg32399,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_33All : degreeTree62_33.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32378,degreeTree62_31All,degreeTree62_32All⟩ + +lemma degreeTree62_34All : degreeTree62_34.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32411,⟨sg32406,⟨sg32403,⟨sg32402,⟨sg32401,True.intro,True.intro⟩,True.intro⟩,⟨sg32405,⟨sg32404,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32409,⟨sg32408,⟨sg32407,True.intro,True.intro⟩,True.intro⟩,⟨sg32410,True.intro,True.intro⟩⟩⟩,⟨sg32417,⟨sg32414,⟨sg32413,⟨sg32412,True.intro,True.intro⟩,True.intro⟩,⟨sg32416,⟨sg32415,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32420,⟨sg32419,⟨sg32418,True.intro,True.intro⟩,True.intro⟩,⟨sg32421,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_35All : degreeTree62_35.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32433,⟨sg32428,⟨sg32425,⟨sg32424,⟨sg32423,True.intro,True.intro⟩,True.intro⟩,⟨sg32427,⟨sg32426,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32431,⟨sg32430,⟨sg32429,True.intro,True.intro⟩,True.intro⟩,⟨sg32432,True.intro,True.intro⟩⟩⟩,⟨sg32439,⟨sg32436,⟨sg32435,⟨sg32434,True.intro,True.intro⟩,True.intro⟩,⟨sg32438,⟨sg32437,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32442,⟨sg32441,⟨sg32440,True.intro,True.intro⟩,True.intro⟩,⟨sg32443,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_36All : degreeTree62_36.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32422,degreeTree62_34All,degreeTree62_35All⟩ + +lemma degreeTree62_37All : degreeTree62_37.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32400,degreeTree62_33All,degreeTree62_36All⟩ + +lemma degreeTree62_38All : degreeTree62_38.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32455,⟨sg32450,⟨sg32447,⟨sg32446,⟨sg32445,True.intro,True.intro⟩,True.intro⟩,⟨sg32449,⟨sg32448,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32453,⟨sg32452,⟨sg32451,True.intro,True.intro⟩,True.intro⟩,⟨sg32454,True.intro,True.intro⟩⟩⟩,⟨sg32461,⟨sg32458,⟨sg32457,⟨sg32456,True.intro,True.intro⟩,True.intro⟩,⟨sg32460,⟨sg32459,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32464,⟨sg32463,⟨sg32462,True.intro,True.intro⟩,True.intro⟩,⟨sg32465,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_39All : degreeTree62_39.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32477,⟨sg32472,⟨sg32469,⟨sg32468,⟨sg32467,True.intro,True.intro⟩,True.intro⟩,⟨sg32471,⟨sg32470,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32475,⟨sg32474,⟨sg32473,True.intro,True.intro⟩,True.intro⟩,⟨sg32476,True.intro,True.intro⟩⟩⟩,⟨sg32483,⟨sg32480,⟨sg32479,⟨sg32478,True.intro,True.intro⟩,True.intro⟩,⟨sg32482,⟨sg32481,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32486,⟨sg32485,⟨sg32484,True.intro,True.intro⟩,True.intro⟩,⟨sg32487,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_40All : degreeTree62_40.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32466,degreeTree62_38All,degreeTree62_39All⟩ + +lemma degreeTree62_41All : degreeTree62_41.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32499,⟨sg32494,⟨sg32491,⟨sg32490,⟨sg32489,True.intro,True.intro⟩,True.intro⟩,⟨sg32493,⟨sg32492,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32497,⟨sg32496,⟨sg32495,True.intro,True.intro⟩,True.intro⟩,⟨sg32498,True.intro,True.intro⟩⟩⟩,⟨sg32505,⟨sg32502,⟨sg32501,⟨sg32500,True.intro,True.intro⟩,True.intro⟩,⟨sg32504,⟨sg32503,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32508,⟨sg32507,⟨sg32506,True.intro,True.intro⟩,True.intro⟩,⟨sg32509,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_42All : degreeTree62_42.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32521,⟨sg32516,⟨sg32513,⟨sg32512,⟨sg32511,True.intro,True.intro⟩,True.intro⟩,⟨sg32515,⟨sg32514,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32519,⟨sg32518,⟨sg32517,True.intro,True.intro⟩,True.intro⟩,⟨sg32520,True.intro,True.intro⟩⟩⟩,⟨sg32527,⟨sg32524,⟨sg32523,⟨sg32522,True.intro,True.intro⟩,True.intro⟩,⟨sg32526,⟨sg32525,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32530,⟨sg32529,⟨sg32528,True.intro,True.intro⟩,True.intro⟩,⟨sg32531,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_43All : degreeTree62_43.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32510,degreeTree62_41All,degreeTree62_42All⟩ + +lemma degreeTree62_44All : degreeTree62_44.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32488,degreeTree62_40All,degreeTree62_43All⟩ + +lemma degreeTree62_45All : degreeTree62_45.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32444,degreeTree62_37All,degreeTree62_44All⟩ + +lemma degreeTree62_46All : degreeTree62_46.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32543,⟨sg32538,⟨sg32535,⟨sg32534,⟨sg32533,True.intro,True.intro⟩,True.intro⟩,⟨sg32537,⟨sg32536,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32541,⟨sg32540,⟨sg32539,True.intro,True.intro⟩,True.intro⟩,⟨sg32542,True.intro,True.intro⟩⟩⟩,⟨sg32549,⟨sg32546,⟨sg32545,⟨sg32544,True.intro,True.intro⟩,True.intro⟩,⟨sg32548,⟨sg32547,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32552,⟨sg32551,⟨sg32550,True.intro,True.intro⟩,True.intro⟩,⟨sg32553,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_47All : degreeTree62_47.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32565,⟨sg32560,⟨sg32557,⟨sg32556,⟨sg32555,True.intro,True.intro⟩,True.intro⟩,⟨sg32559,⟨sg32558,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32563,⟨sg32562,⟨sg32561,True.intro,True.intro⟩,True.intro⟩,⟨sg32564,True.intro,True.intro⟩⟩⟩,⟨sg32571,⟨sg32568,⟨sg32567,⟨sg32566,True.intro,True.intro⟩,True.intro⟩,⟨sg32570,⟨sg32569,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32574,⟨sg32573,⟨sg32572,True.intro,True.intro⟩,True.intro⟩,⟨sg32575,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_48All : degreeTree62_48.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32554,degreeTree62_46All,degreeTree62_47All⟩ + +lemma degreeTree62_49All : degreeTree62_49.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32587,⟨sg32582,⟨sg32579,⟨sg32578,⟨sg32577,True.intro,True.intro⟩,True.intro⟩,⟨sg32581,⟨sg32580,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32585,⟨sg32584,⟨sg32583,True.intro,True.intro⟩,True.intro⟩,⟨sg32586,True.intro,True.intro⟩⟩⟩,⟨sg32593,⟨sg32590,⟨sg32589,⟨sg32588,True.intro,True.intro⟩,True.intro⟩,⟨sg32592,⟨sg32591,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32596,⟨sg32595,⟨sg32594,True.intro,True.intro⟩,True.intro⟩,⟨sg32597,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_50All : degreeTree62_50.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32609,⟨sg32604,⟨sg32601,⟨sg32600,⟨sg32599,True.intro,True.intro⟩,True.intro⟩,⟨sg32603,⟨sg32602,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32607,⟨sg32606,⟨sg32605,True.intro,True.intro⟩,True.intro⟩,⟨sg32608,True.intro,True.intro⟩⟩⟩,⟨sg32615,⟨sg32612,⟨sg32611,⟨sg32610,True.intro,True.intro⟩,True.intro⟩,⟨sg32614,⟨sg32613,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32618,⟨sg32617,⟨sg32616,True.intro,True.intro⟩,True.intro⟩,⟨sg32619,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_51All : degreeTree62_51.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32598,degreeTree62_49All,degreeTree62_50All⟩ + +lemma degreeTree62_52All : degreeTree62_52.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32576,degreeTree62_48All,degreeTree62_51All⟩ + +lemma degreeTree62_53All : degreeTree62_53.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32631,⟨sg32626,⟨sg32623,⟨sg32622,⟨sg32621,True.intro,True.intro⟩,True.intro⟩,⟨sg32625,⟨sg32624,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32629,⟨sg32628,⟨sg32627,True.intro,True.intro⟩,True.intro⟩,⟨sg32630,True.intro,True.intro⟩⟩⟩,⟨sg32637,⟨sg32634,⟨sg32633,⟨sg32632,True.intro,True.intro⟩,True.intro⟩,⟨sg32636,⟨sg32635,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32640,⟨sg32639,⟨sg32638,True.intro,True.intro⟩,True.intro⟩,⟨sg32641,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_54All : degreeTree62_54.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32653,⟨sg32648,⟨sg32645,⟨sg32644,⟨sg32643,True.intro,True.intro⟩,True.intro⟩,⟨sg32647,⟨sg32646,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32651,⟨sg32650,⟨sg32649,True.intro,True.intro⟩,True.intro⟩,⟨sg32652,True.intro,True.intro⟩⟩⟩,⟨sg32659,⟨sg32656,⟨sg32655,⟨sg32654,True.intro,True.intro⟩,True.intro⟩,⟨sg32658,⟨sg32657,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32662,⟨sg32661,⟨sg32660,True.intro,True.intro⟩,True.intro⟩,⟨sg32663,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_55All : degreeTree62_55.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32642,degreeTree62_53All,degreeTree62_54All⟩ + +lemma degreeTree62_56All : degreeTree62_56.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32675,⟨sg32670,⟨sg32667,⟨sg32666,⟨sg32665,True.intro,True.intro⟩,True.intro⟩,⟨sg32669,⟨sg32668,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32673,⟨sg32672,⟨sg32671,True.intro,True.intro⟩,True.intro⟩,⟨sg32674,True.intro,True.intro⟩⟩⟩,⟨sg32681,⟨sg32678,⟨sg32677,⟨sg32676,True.intro,True.intro⟩,True.intro⟩,⟨sg32680,⟨sg32679,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32684,⟨sg32683,⟨sg32682,True.intro,True.intro⟩,True.intro⟩,⟨sg32685,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_57All : degreeTree62_57.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32697,⟨sg32692,⟨sg32689,⟨sg32688,⟨sg32687,True.intro,True.intro⟩,True.intro⟩,⟨sg32691,⟨sg32690,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32695,⟨sg32694,⟨sg32693,True.intro,True.intro⟩,True.intro⟩,⟨sg32696,True.intro,True.intro⟩⟩⟩,⟨sg32702,⟨sg32700,⟨sg32699,⟨sg32698,True.intro,True.intro⟩,True.intro⟩,⟨sg32701,True.intro,True.intro⟩⟩,⟨sg32705,⟨sg32704,⟨sg32703,True.intro,True.intro⟩,True.intro⟩,⟨sg32706,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_58All : degreeTree62_58.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32686,degreeTree62_56All,degreeTree62_57All⟩ + +lemma degreeTree62_59All : degreeTree62_59.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32664,degreeTree62_55All,degreeTree62_58All⟩ + +lemma degreeTree62_60All : degreeTree62_60.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32620,degreeTree62_52All,degreeTree62_59All⟩ + +lemma degreeTree62_61All : degreeTree62_61.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32532,degreeTree62_45All,degreeTree62_60All⟩ + +lemma degreeTree62_62All : degreeTree62_62.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32356,degreeTree62_30All,degreeTree62_61All⟩ + +lemma degreeTree62_63All : degreeTree62_63.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32718,⟨sg32713,⟨sg32710,⟨sg32709,⟨sg32708,True.intro,True.intro⟩,True.intro⟩,⟨sg32712,⟨sg32711,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32716,⟨sg32715,⟨sg32714,True.intro,True.intro⟩,True.intro⟩,⟨sg32717,True.intro,True.intro⟩⟩⟩,⟨sg32724,⟨sg32721,⟨sg32720,⟨sg32719,True.intro,True.intro⟩,True.intro⟩,⟨sg32723,⟨sg32722,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32727,⟨sg32726,⟨sg32725,True.intro,True.intro⟩,True.intro⟩,⟨sg32728,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_64All : degreeTree62_64.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32740,⟨sg32735,⟨sg32732,⟨sg32731,⟨sg32730,True.intro,True.intro⟩,True.intro⟩,⟨sg32734,⟨sg32733,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32738,⟨sg32737,⟨sg32736,True.intro,True.intro⟩,True.intro⟩,⟨sg32739,True.intro,True.intro⟩⟩⟩,⟨sg32746,⟨sg32743,⟨sg32742,⟨sg32741,True.intro,True.intro⟩,True.intro⟩,⟨sg32745,⟨sg32744,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32749,⟨sg32748,⟨sg32747,True.intro,True.intro⟩,True.intro⟩,⟨sg32750,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_65All : degreeTree62_65.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32729,degreeTree62_63All,degreeTree62_64All⟩ + +lemma degreeTree62_66All : degreeTree62_66.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32762,⟨sg32757,⟨sg32754,⟨sg32753,⟨sg32752,True.intro,True.intro⟩,True.intro⟩,⟨sg32756,⟨sg32755,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32760,⟨sg32759,⟨sg32758,True.intro,True.intro⟩,True.intro⟩,⟨sg32761,True.intro,True.intro⟩⟩⟩,⟨sg32768,⟨sg32765,⟨sg32764,⟨sg32763,True.intro,True.intro⟩,True.intro⟩,⟨sg32767,⟨sg32766,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32771,⟨sg32770,⟨sg32769,True.intro,True.intro⟩,True.intro⟩,⟨sg32772,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_67All : degreeTree62_67.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32784,⟨sg32779,⟨sg32776,⟨sg32775,⟨sg32774,True.intro,True.intro⟩,True.intro⟩,⟨sg32778,⟨sg32777,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32782,⟨sg32781,⟨sg32780,True.intro,True.intro⟩,True.intro⟩,⟨sg32783,True.intro,True.intro⟩⟩⟩,⟨sg32790,⟨sg32787,⟨sg32786,⟨sg32785,True.intro,True.intro⟩,True.intro⟩,⟨sg32789,⟨sg32788,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32793,⟨sg32792,⟨sg32791,True.intro,True.intro⟩,True.intro⟩,⟨sg32794,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_68All : degreeTree62_68.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32773,degreeTree62_66All,degreeTree62_67All⟩ + +lemma degreeTree62_69All : degreeTree62_69.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32751,degreeTree62_65All,degreeTree62_68All⟩ + +lemma degreeTree62_70All : degreeTree62_70.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32806,⟨sg32801,⟨sg32798,⟨sg32797,⟨sg32796,True.intro,True.intro⟩,True.intro⟩,⟨sg32800,⟨sg32799,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32804,⟨sg32803,⟨sg32802,True.intro,True.intro⟩,True.intro⟩,⟨sg32805,True.intro,True.intro⟩⟩⟩,⟨sg32812,⟨sg32809,⟨sg32808,⟨sg32807,True.intro,True.intro⟩,True.intro⟩,⟨sg32811,⟨sg32810,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32815,⟨sg32814,⟨sg32813,True.intro,True.intro⟩,True.intro⟩,⟨sg32816,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_71All : degreeTree62_71.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32828,⟨sg32823,⟨sg32820,⟨sg32819,⟨sg32818,True.intro,True.intro⟩,True.intro⟩,⟨sg32822,⟨sg32821,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32826,⟨sg32825,⟨sg32824,True.intro,True.intro⟩,True.intro⟩,⟨sg32827,True.intro,True.intro⟩⟩⟩,⟨sg32834,⟨sg32831,⟨sg32830,⟨sg32829,True.intro,True.intro⟩,True.intro⟩,⟨sg32833,⟨sg32832,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32837,⟨sg32836,⟨sg32835,True.intro,True.intro⟩,True.intro⟩,⟨sg32838,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_72All : degreeTree62_72.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32817,degreeTree62_70All,degreeTree62_71All⟩ + +lemma degreeTree62_73All : degreeTree62_73.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32850,⟨sg32845,⟨sg32842,⟨sg32841,⟨sg32840,True.intro,True.intro⟩,True.intro⟩,⟨sg32844,⟨sg32843,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32848,⟨sg32847,⟨sg32846,True.intro,True.intro⟩,True.intro⟩,⟨sg32849,True.intro,True.intro⟩⟩⟩,⟨sg32856,⟨sg32853,⟨sg32852,⟨sg32851,True.intro,True.intro⟩,True.intro⟩,⟨sg32855,⟨sg32854,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32859,⟨sg32858,⟨sg32857,True.intro,True.intro⟩,True.intro⟩,⟨sg32860,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_74All : degreeTree62_74.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32872,⟨sg32867,⟨sg32864,⟨sg32863,⟨sg32862,True.intro,True.intro⟩,True.intro⟩,⟨sg32866,⟨sg32865,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32870,⟨sg32869,⟨sg32868,True.intro,True.intro⟩,True.intro⟩,⟨sg32871,True.intro,True.intro⟩⟩⟩,⟨sg32878,⟨sg32875,⟨sg32874,⟨sg32873,True.intro,True.intro⟩,True.intro⟩,⟨sg32877,⟨sg32876,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32881,⟨sg32880,⟨sg32879,True.intro,True.intro⟩,True.intro⟩,⟨sg32882,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_75All : degreeTree62_75.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32861,degreeTree62_73All,degreeTree62_74All⟩ + +lemma degreeTree62_76All : degreeTree62_76.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32839,degreeTree62_72All,degreeTree62_75All⟩ + +lemma degreeTree62_77All : degreeTree62_77.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32795,degreeTree62_69All,degreeTree62_76All⟩ + +lemma degreeTree62_78All : degreeTree62_78.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32894,⟨sg32889,⟨sg32886,⟨sg32885,⟨sg32884,True.intro,True.intro⟩,True.intro⟩,⟨sg32888,⟨sg32887,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32892,⟨sg32891,⟨sg32890,True.intro,True.intro⟩,True.intro⟩,⟨sg32893,True.intro,True.intro⟩⟩⟩,⟨sg32900,⟨sg32897,⟨sg32896,⟨sg32895,True.intro,True.intro⟩,True.intro⟩,⟨sg32899,⟨sg32898,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32903,⟨sg32902,⟨sg32901,True.intro,True.intro⟩,True.intro⟩,⟨sg32904,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_79All : degreeTree62_79.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32916,⟨sg32911,⟨sg32908,⟨sg32907,⟨sg32906,True.intro,True.intro⟩,True.intro⟩,⟨sg32910,⟨sg32909,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32914,⟨sg32913,⟨sg32912,True.intro,True.intro⟩,True.intro⟩,⟨sg32915,True.intro,True.intro⟩⟩⟩,⟨sg32922,⟨sg32919,⟨sg32918,⟨sg32917,True.intro,True.intro⟩,True.intro⟩,⟨sg32921,⟨sg32920,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32925,⟨sg32924,⟨sg32923,True.intro,True.intro⟩,True.intro⟩,⟨sg32926,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_80All : degreeTree62_80.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32905,degreeTree62_78All,degreeTree62_79All⟩ + +lemma degreeTree62_81All : degreeTree62_81.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32938,⟨sg32933,⟨sg32930,⟨sg32929,⟨sg32928,True.intro,True.intro⟩,True.intro⟩,⟨sg32932,⟨sg32931,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32936,⟨sg32935,⟨sg32934,True.intro,True.intro⟩,True.intro⟩,⟨sg32937,True.intro,True.intro⟩⟩⟩,⟨sg32944,⟨sg32941,⟨sg32940,⟨sg32939,True.intro,True.intro⟩,True.intro⟩,⟨sg32943,⟨sg32942,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32947,⟨sg32946,⟨sg32945,True.intro,True.intro⟩,True.intro⟩,⟨sg32948,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_82All : degreeTree62_82.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32960,⟨sg32955,⟨sg32952,⟨sg32951,⟨sg32950,True.intro,True.intro⟩,True.intro⟩,⟨sg32954,⟨sg32953,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32958,⟨sg32957,⟨sg32956,True.intro,True.intro⟩,True.intro⟩,⟨sg32959,True.intro,True.intro⟩⟩⟩,⟨sg32966,⟨sg32963,⟨sg32962,⟨sg32961,True.intro,True.intro⟩,True.intro⟩,⟨sg32965,⟨sg32964,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32969,⟨sg32968,⟨sg32967,True.intro,True.intro⟩,True.intro⟩,⟨sg32970,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_83All : degreeTree62_83.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32949,degreeTree62_81All,degreeTree62_82All⟩ + +lemma degreeTree62_84All : degreeTree62_84.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32927,degreeTree62_80All,degreeTree62_83All⟩ + +lemma degreeTree62_85All : degreeTree62_85.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32982,⟨sg32977,⟨sg32974,⟨sg32973,⟨sg32972,True.intro,True.intro⟩,True.intro⟩,⟨sg32976,⟨sg32975,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32980,⟨sg32979,⟨sg32978,True.intro,True.intro⟩,True.intro⟩,⟨sg32981,True.intro,True.intro⟩⟩⟩,⟨sg32988,⟨sg32985,⟨sg32984,⟨sg32983,True.intro,True.intro⟩,True.intro⟩,⟨sg32987,⟨sg32986,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg32991,⟨sg32990,⟨sg32989,True.intro,True.intro⟩,True.intro⟩,⟨sg32992,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_86All : degreeTree62_86.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33004,⟨sg32999,⟨sg32996,⟨sg32995,⟨sg32994,True.intro,True.intro⟩,True.intro⟩,⟨sg32998,⟨sg32997,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33002,⟨sg33001,⟨sg33000,True.intro,True.intro⟩,True.intro⟩,⟨sg33003,True.intro,True.intro⟩⟩⟩,⟨sg33010,⟨sg33007,⟨sg33006,⟨sg33005,True.intro,True.intro⟩,True.intro⟩,⟨sg33009,⟨sg33008,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33013,⟨sg33012,⟨sg33011,True.intro,True.intro⟩,True.intro⟩,⟨sg33014,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_87All : degreeTree62_87.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32993,degreeTree62_85All,degreeTree62_86All⟩ + +lemma degreeTree62_88All : degreeTree62_88.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33026,⟨sg33021,⟨sg33018,⟨sg33017,⟨sg33016,True.intro,True.intro⟩,True.intro⟩,⟨sg33020,⟨sg33019,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33024,⟨sg33023,⟨sg33022,True.intro,True.intro⟩,True.intro⟩,⟨sg33025,True.intro,True.intro⟩⟩⟩,⟨sg33032,⟨sg33029,⟨sg33028,⟨sg33027,True.intro,True.intro⟩,True.intro⟩,⟨sg33031,⟨sg33030,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33035,⟨sg33034,⟨sg33033,True.intro,True.intro⟩,True.intro⟩,⟨sg33036,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_89All : degreeTree62_89.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33048,⟨sg33043,⟨sg33040,⟨sg33039,⟨sg33038,True.intro,True.intro⟩,True.intro⟩,⟨sg33042,⟨sg33041,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33046,⟨sg33045,⟨sg33044,True.intro,True.intro⟩,True.intro⟩,⟨sg33047,True.intro,True.intro⟩⟩⟩,⟨sg33053,⟨sg33051,⟨sg33050,⟨sg33049,True.intro,True.intro⟩,True.intro⟩,⟨sg33052,True.intro,True.intro⟩⟩,⟨sg33056,⟨sg33055,⟨sg33054,True.intro,True.intro⟩,True.intro⟩,⟨sg33057,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_90All : degreeTree62_90.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33037,degreeTree62_88All,degreeTree62_89All⟩ + +lemma degreeTree62_91All : degreeTree62_91.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33015,degreeTree62_87All,degreeTree62_90All⟩ + +lemma degreeTree62_92All : degreeTree62_92.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32971,degreeTree62_84All,degreeTree62_91All⟩ + +lemma degreeTree62_93All : degreeTree62_93.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32883,degreeTree62_77All,degreeTree62_92All⟩ + +lemma degreeTree62_94All : degreeTree62_94.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33069,⟨sg33064,⟨sg33061,⟨sg33060,⟨sg33059,True.intro,True.intro⟩,True.intro⟩,⟨sg33063,⟨sg33062,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33067,⟨sg33066,⟨sg33065,True.intro,True.intro⟩,True.intro⟩,⟨sg33068,True.intro,True.intro⟩⟩⟩,⟨sg33075,⟨sg33072,⟨sg33071,⟨sg33070,True.intro,True.intro⟩,True.intro⟩,⟨sg33074,⟨sg33073,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33078,⟨sg33077,⟨sg33076,True.intro,True.intro⟩,True.intro⟩,⟨sg33079,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_95All : degreeTree62_95.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33091,⟨sg33086,⟨sg33083,⟨sg33082,⟨sg33081,True.intro,True.intro⟩,True.intro⟩,⟨sg33085,⟨sg33084,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33089,⟨sg33088,⟨sg33087,True.intro,True.intro⟩,True.intro⟩,⟨sg33090,True.intro,True.intro⟩⟩⟩,⟨sg33097,⟨sg33094,⟨sg33093,⟨sg33092,True.intro,True.intro⟩,True.intro⟩,⟨sg33096,⟨sg33095,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33100,⟨sg33099,⟨sg33098,True.intro,True.intro⟩,True.intro⟩,⟨sg33101,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_96All : degreeTree62_96.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33080,degreeTree62_94All,degreeTree62_95All⟩ + +lemma degreeTree62_97All : degreeTree62_97.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33113,⟨sg33108,⟨sg33105,⟨sg33104,⟨sg33103,True.intro,True.intro⟩,True.intro⟩,⟨sg33107,⟨sg33106,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33111,⟨sg33110,⟨sg33109,True.intro,True.intro⟩,True.intro⟩,⟨sg33112,True.intro,True.intro⟩⟩⟩,⟨sg33119,⟨sg33116,⟨sg33115,⟨sg33114,True.intro,True.intro⟩,True.intro⟩,⟨sg33118,⟨sg33117,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33122,⟨sg33121,⟨sg33120,True.intro,True.intro⟩,True.intro⟩,⟨sg33123,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_98All : degreeTree62_98.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33135,⟨sg33130,⟨sg33127,⟨sg33126,⟨sg33125,True.intro,True.intro⟩,True.intro⟩,⟨sg33129,⟨sg33128,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33133,⟨sg33132,⟨sg33131,True.intro,True.intro⟩,True.intro⟩,⟨sg33134,True.intro,True.intro⟩⟩⟩,⟨sg33141,⟨sg33138,⟨sg33137,⟨sg33136,True.intro,True.intro⟩,True.intro⟩,⟨sg33140,⟨sg33139,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33144,⟨sg33143,⟨sg33142,True.intro,True.intro⟩,True.intro⟩,⟨sg33145,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_99All : degreeTree62_99.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33124,degreeTree62_97All,degreeTree62_98All⟩ + +lemma degreeTree62_100All : degreeTree62_100.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33102,degreeTree62_96All,degreeTree62_99All⟩ + +lemma degreeTree62_101All : degreeTree62_101.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33157,⟨sg33152,⟨sg33149,⟨sg33148,⟨sg33147,True.intro,True.intro⟩,True.intro⟩,⟨sg33151,⟨sg33150,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33155,⟨sg33154,⟨sg33153,True.intro,True.intro⟩,True.intro⟩,⟨sg33156,True.intro,True.intro⟩⟩⟩,⟨sg33163,⟨sg33160,⟨sg33159,⟨sg33158,True.intro,True.intro⟩,True.intro⟩,⟨sg33162,⟨sg33161,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33166,⟨sg33165,⟨sg33164,True.intro,True.intro⟩,True.intro⟩,⟨sg33167,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_102All : degreeTree62_102.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33179,⟨sg33174,⟨sg33171,⟨sg33170,⟨sg33169,True.intro,True.intro⟩,True.intro⟩,⟨sg33173,⟨sg33172,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33177,⟨sg33176,⟨sg33175,True.intro,True.intro⟩,True.intro⟩,⟨sg33178,True.intro,True.intro⟩⟩⟩,⟨sg33185,⟨sg33182,⟨sg33181,⟨sg33180,True.intro,True.intro⟩,True.intro⟩,⟨sg33184,⟨sg33183,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33188,⟨sg33187,⟨sg33186,True.intro,True.intro⟩,True.intro⟩,⟨sg33189,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_103All : degreeTree62_103.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33168,degreeTree62_101All,degreeTree62_102All⟩ + +lemma degreeTree62_104All : degreeTree62_104.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33201,⟨sg33196,⟨sg33193,⟨sg33192,⟨sg33191,True.intro,True.intro⟩,True.intro⟩,⟨sg33195,⟨sg33194,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33199,⟨sg33198,⟨sg33197,True.intro,True.intro⟩,True.intro⟩,⟨sg33200,True.intro,True.intro⟩⟩⟩,⟨sg33207,⟨sg33204,⟨sg33203,⟨sg33202,True.intro,True.intro⟩,True.intro⟩,⟨sg33206,⟨sg33205,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33210,⟨sg33209,⟨sg33208,True.intro,True.intro⟩,True.intro⟩,⟨sg33211,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_105All : degreeTree62_105.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33223,⟨sg33218,⟨sg33215,⟨sg33214,⟨sg33213,True.intro,True.intro⟩,True.intro⟩,⟨sg33217,⟨sg33216,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33221,⟨sg33220,⟨sg33219,True.intro,True.intro⟩,True.intro⟩,⟨sg33222,True.intro,True.intro⟩⟩⟩,⟨sg33229,⟨sg33226,⟨sg33225,⟨sg33224,True.intro,True.intro⟩,True.intro⟩,⟨sg33228,⟨sg33227,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33232,⟨sg33231,⟨sg33230,True.intro,True.intro⟩,True.intro⟩,⟨sg33233,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_106All : degreeTree62_106.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33212,degreeTree62_104All,degreeTree62_105All⟩ + +lemma degreeTree62_107All : degreeTree62_107.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33190,degreeTree62_103All,degreeTree62_106All⟩ + +lemma degreeTree62_108All : degreeTree62_108.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33146,degreeTree62_100All,degreeTree62_107All⟩ + +lemma degreeTree62_109All : degreeTree62_109.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33245,⟨sg33240,⟨sg33237,⟨sg33236,⟨sg33235,True.intro,True.intro⟩,True.intro⟩,⟨sg33239,⟨sg33238,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33243,⟨sg33242,⟨sg33241,True.intro,True.intro⟩,True.intro⟩,⟨sg33244,True.intro,True.intro⟩⟩⟩,⟨sg33251,⟨sg33248,⟨sg33247,⟨sg33246,True.intro,True.intro⟩,True.intro⟩,⟨sg33250,⟨sg33249,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33254,⟨sg33253,⟨sg33252,True.intro,True.intro⟩,True.intro⟩,⟨sg33255,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_110All : degreeTree62_110.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33267,⟨sg33262,⟨sg33259,⟨sg33258,⟨sg33257,True.intro,True.intro⟩,True.intro⟩,⟨sg33261,⟨sg33260,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33265,⟨sg33264,⟨sg33263,True.intro,True.intro⟩,True.intro⟩,⟨sg33266,True.intro,True.intro⟩⟩⟩,⟨sg33273,⟨sg33270,⟨sg33269,⟨sg33268,True.intro,True.intro⟩,True.intro⟩,⟨sg33272,⟨sg33271,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33276,⟨sg33275,⟨sg33274,True.intro,True.intro⟩,True.intro⟩,⟨sg33277,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_111All : degreeTree62_111.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33256,degreeTree62_109All,degreeTree62_110All⟩ + +lemma degreeTree62_112All : degreeTree62_112.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33289,⟨sg33284,⟨sg33281,⟨sg33280,⟨sg33279,True.intro,True.intro⟩,True.intro⟩,⟨sg33283,⟨sg33282,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33287,⟨sg33286,⟨sg33285,True.intro,True.intro⟩,True.intro⟩,⟨sg33288,True.intro,True.intro⟩⟩⟩,⟨sg33295,⟨sg33292,⟨sg33291,⟨sg33290,True.intro,True.intro⟩,True.intro⟩,⟨sg33294,⟨sg33293,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33298,⟨sg33297,⟨sg33296,True.intro,True.intro⟩,True.intro⟩,⟨sg33299,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_113All : degreeTree62_113.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33311,⟨sg33306,⟨sg33303,⟨sg33302,⟨sg33301,True.intro,True.intro⟩,True.intro⟩,⟨sg33305,⟨sg33304,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33309,⟨sg33308,⟨sg33307,True.intro,True.intro⟩,True.intro⟩,⟨sg33310,True.intro,True.intro⟩⟩⟩,⟨sg33317,⟨sg33314,⟨sg33313,⟨sg33312,True.intro,True.intro⟩,True.intro⟩,⟨sg33316,⟨sg33315,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33320,⟨sg33319,⟨sg33318,True.intro,True.intro⟩,True.intro⟩,⟨sg33321,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_114All : degreeTree62_114.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33300,degreeTree62_112All,degreeTree62_113All⟩ + +lemma degreeTree62_115All : degreeTree62_115.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33278,degreeTree62_111All,degreeTree62_114All⟩ + +lemma degreeTree62_116All : degreeTree62_116.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33333,⟨sg33328,⟨sg33325,⟨sg33324,⟨sg33323,True.intro,True.intro⟩,True.intro⟩,⟨sg33327,⟨sg33326,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33331,⟨sg33330,⟨sg33329,True.intro,True.intro⟩,True.intro⟩,⟨sg33332,True.intro,True.intro⟩⟩⟩,⟨sg33339,⟨sg33336,⟨sg33335,⟨sg33334,True.intro,True.intro⟩,True.intro⟩,⟨sg33338,⟨sg33337,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33342,⟨sg33341,⟨sg33340,True.intro,True.intro⟩,True.intro⟩,⟨sg33343,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_117All : degreeTree62_117.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33355,⟨sg33350,⟨sg33347,⟨sg33346,⟨sg33345,True.intro,True.intro⟩,True.intro⟩,⟨sg33349,⟨sg33348,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33353,⟨sg33352,⟨sg33351,True.intro,True.intro⟩,True.intro⟩,⟨sg33354,True.intro,True.intro⟩⟩⟩,⟨sg33361,⟨sg33358,⟨sg33357,⟨sg33356,True.intro,True.intro⟩,True.intro⟩,⟨sg33360,⟨sg33359,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33364,⟨sg33363,⟨sg33362,True.intro,True.intro⟩,True.intro⟩,⟨sg33365,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_118All : degreeTree62_118.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33344,degreeTree62_116All,degreeTree62_117All⟩ + +lemma degreeTree62_119All : degreeTree62_119.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33377,⟨sg33372,⟨sg33369,⟨sg33368,⟨sg33367,True.intro,True.intro⟩,True.intro⟩,⟨sg33371,⟨sg33370,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33375,⟨sg33374,⟨sg33373,True.intro,True.intro⟩,True.intro⟩,⟨sg33376,True.intro,True.intro⟩⟩⟩,⟨sg33383,⟨sg33380,⟨sg33379,⟨sg33378,True.intro,True.intro⟩,True.intro⟩,⟨sg33382,⟨sg33381,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33386,⟨sg33385,⟨sg33384,True.intro,True.intro⟩,True.intro⟩,⟨sg33387,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_120All : degreeTree62_120.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33399,⟨sg33394,⟨sg33391,⟨sg33390,⟨sg33389,True.intro,True.intro⟩,True.intro⟩,⟨sg33393,⟨sg33392,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33397,⟨sg33396,⟨sg33395,True.intro,True.intro⟩,True.intro⟩,⟨sg33398,True.intro,True.intro⟩⟩⟩,⟨sg33404,⟨sg33402,⟨sg33401,⟨sg33400,True.intro,True.intro⟩,True.intro⟩,⟨sg33403,True.intro,True.intro⟩⟩,⟨sg33407,⟨sg33406,⟨sg33405,True.intro,True.intro⟩,True.intro⟩,⟨sg33408,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_121All : degreeTree62_121.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33388,degreeTree62_119All,degreeTree62_120All⟩ + +lemma degreeTree62_122All : degreeTree62_122.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33366,degreeTree62_118All,degreeTree62_121All⟩ + +lemma degreeTree62_123All : degreeTree62_123.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33322,degreeTree62_115All,degreeTree62_122All⟩ + +lemma degreeTree62_124All : degreeTree62_124.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33234,degreeTree62_108All,degreeTree62_123All⟩ + +lemma degreeTree62_125All : degreeTree62_125.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33058,degreeTree62_93All,degreeTree62_124All⟩ + +lemma degreeTree62_126All : degreeTree62_126.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg32707,degreeTree62_62All,degreeTree62_125All⟩ + +lemma degreeTree62_127All : degreeTree62_127.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33420,⟨sg33415,⟨sg33412,⟨sg33411,⟨sg33410,True.intro,True.intro⟩,True.intro⟩,⟨sg33414,⟨sg33413,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33418,⟨sg33417,⟨sg33416,True.intro,True.intro⟩,True.intro⟩,⟨sg33419,True.intro,True.intro⟩⟩⟩,⟨sg33426,⟨sg33423,⟨sg33422,⟨sg33421,True.intro,True.intro⟩,True.intro⟩,⟨sg33425,⟨sg33424,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33429,⟨sg33428,⟨sg33427,True.intro,True.intro⟩,True.intro⟩,⟨sg33430,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_128All : degreeTree62_128.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33442,⟨sg33437,⟨sg33434,⟨sg33433,⟨sg33432,True.intro,True.intro⟩,True.intro⟩,⟨sg33436,⟨sg33435,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33440,⟨sg33439,⟨sg33438,True.intro,True.intro⟩,True.intro⟩,⟨sg33441,True.intro,True.intro⟩⟩⟩,⟨sg33448,⟨sg33445,⟨sg33444,⟨sg33443,True.intro,True.intro⟩,True.intro⟩,⟨sg33447,⟨sg33446,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33451,⟨sg33450,⟨sg33449,True.intro,True.intro⟩,True.intro⟩,⟨sg33452,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_129All : degreeTree62_129.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33431,degreeTree62_127All,degreeTree62_128All⟩ + +lemma degreeTree62_130All : degreeTree62_130.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33464,⟨sg33459,⟨sg33456,⟨sg33455,⟨sg33454,True.intro,True.intro⟩,True.intro⟩,⟨sg33458,⟨sg33457,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33462,⟨sg33461,⟨sg33460,True.intro,True.intro⟩,True.intro⟩,⟨sg33463,True.intro,True.intro⟩⟩⟩,⟨sg33470,⟨sg33467,⟨sg33466,⟨sg33465,True.intro,True.intro⟩,True.intro⟩,⟨sg33469,⟨sg33468,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33473,⟨sg33472,⟨sg33471,True.intro,True.intro⟩,True.intro⟩,⟨sg33474,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_131All : degreeTree62_131.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33486,⟨sg33481,⟨sg33478,⟨sg33477,⟨sg33476,True.intro,True.intro⟩,True.intro⟩,⟨sg33480,⟨sg33479,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33484,⟨sg33483,⟨sg33482,True.intro,True.intro⟩,True.intro⟩,⟨sg33485,True.intro,True.intro⟩⟩⟩,⟨sg33492,⟨sg33489,⟨sg33488,⟨sg33487,True.intro,True.intro⟩,True.intro⟩,⟨sg33491,⟨sg33490,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33495,⟨sg33494,⟨sg33493,True.intro,True.intro⟩,True.intro⟩,⟨sg33496,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_132All : degreeTree62_132.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33475,degreeTree62_130All,degreeTree62_131All⟩ + +lemma degreeTree62_133All : degreeTree62_133.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33453,degreeTree62_129All,degreeTree62_132All⟩ + +lemma degreeTree62_134All : degreeTree62_134.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33508,⟨sg33503,⟨sg33500,⟨sg33499,⟨sg33498,True.intro,True.intro⟩,True.intro⟩,⟨sg33502,⟨sg33501,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33506,⟨sg33505,⟨sg33504,True.intro,True.intro⟩,True.intro⟩,⟨sg33507,True.intro,True.intro⟩⟩⟩,⟨sg33514,⟨sg33511,⟨sg33510,⟨sg33509,True.intro,True.intro⟩,True.intro⟩,⟨sg33513,⟨sg33512,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33517,⟨sg33516,⟨sg33515,True.intro,True.intro⟩,True.intro⟩,⟨sg33518,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_135All : degreeTree62_135.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33530,⟨sg33525,⟨sg33522,⟨sg33521,⟨sg33520,True.intro,True.intro⟩,True.intro⟩,⟨sg33524,⟨sg33523,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33528,⟨sg33527,⟨sg33526,True.intro,True.intro⟩,True.intro⟩,⟨sg33529,True.intro,True.intro⟩⟩⟩,⟨sg33536,⟨sg33533,⟨sg33532,⟨sg33531,True.intro,True.intro⟩,True.intro⟩,⟨sg33535,⟨sg33534,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33539,⟨sg33538,⟨sg33537,True.intro,True.intro⟩,True.intro⟩,⟨sg33540,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_136All : degreeTree62_136.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33519,degreeTree62_134All,degreeTree62_135All⟩ + +lemma degreeTree62_137All : degreeTree62_137.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33552,⟨sg33547,⟨sg33544,⟨sg33543,⟨sg33542,True.intro,True.intro⟩,True.intro⟩,⟨sg33546,⟨sg33545,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33550,⟨sg33549,⟨sg33548,True.intro,True.intro⟩,True.intro⟩,⟨sg33551,True.intro,True.intro⟩⟩⟩,⟨sg33558,⟨sg33555,⟨sg33554,⟨sg33553,True.intro,True.intro⟩,True.intro⟩,⟨sg33557,⟨sg33556,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33561,⟨sg33560,⟨sg33559,True.intro,True.intro⟩,True.intro⟩,⟨sg33562,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_138All : degreeTree62_138.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33574,⟨sg33569,⟨sg33566,⟨sg33565,⟨sg33564,True.intro,True.intro⟩,True.intro⟩,⟨sg33568,⟨sg33567,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33572,⟨sg33571,⟨sg33570,True.intro,True.intro⟩,True.intro⟩,⟨sg33573,True.intro,True.intro⟩⟩⟩,⟨sg33580,⟨sg33577,⟨sg33576,⟨sg33575,True.intro,True.intro⟩,True.intro⟩,⟨sg33579,⟨sg33578,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33583,⟨sg33582,⟨sg33581,True.intro,True.intro⟩,True.intro⟩,⟨sg33584,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_139All : degreeTree62_139.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33563,degreeTree62_137All,degreeTree62_138All⟩ + +lemma degreeTree62_140All : degreeTree62_140.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33541,degreeTree62_136All,degreeTree62_139All⟩ + +lemma degreeTree62_141All : degreeTree62_141.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33497,degreeTree62_133All,degreeTree62_140All⟩ + +lemma degreeTree62_142All : degreeTree62_142.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33596,⟨sg33591,⟨sg33588,⟨sg33587,⟨sg33586,True.intro,True.intro⟩,True.intro⟩,⟨sg33590,⟨sg33589,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33594,⟨sg33593,⟨sg33592,True.intro,True.intro⟩,True.intro⟩,⟨sg33595,True.intro,True.intro⟩⟩⟩,⟨sg33602,⟨sg33599,⟨sg33598,⟨sg33597,True.intro,True.intro⟩,True.intro⟩,⟨sg33601,⟨sg33600,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33605,⟨sg33604,⟨sg33603,True.intro,True.intro⟩,True.intro⟩,⟨sg33606,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_143All : degreeTree62_143.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33618,⟨sg33613,⟨sg33610,⟨sg33609,⟨sg33608,True.intro,True.intro⟩,True.intro⟩,⟨sg33612,⟨sg33611,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33616,⟨sg33615,⟨sg33614,True.intro,True.intro⟩,True.intro⟩,⟨sg33617,True.intro,True.intro⟩⟩⟩,⟨sg33624,⟨sg33621,⟨sg33620,⟨sg33619,True.intro,True.intro⟩,True.intro⟩,⟨sg33623,⟨sg33622,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33627,⟨sg33626,⟨sg33625,True.intro,True.intro⟩,True.intro⟩,⟨sg33628,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_144All : degreeTree62_144.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33607,degreeTree62_142All,degreeTree62_143All⟩ + +lemma degreeTree62_145All : degreeTree62_145.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33640,⟨sg33635,⟨sg33632,⟨sg33631,⟨sg33630,True.intro,True.intro⟩,True.intro⟩,⟨sg33634,⟨sg33633,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33638,⟨sg33637,⟨sg33636,True.intro,True.intro⟩,True.intro⟩,⟨sg33639,True.intro,True.intro⟩⟩⟩,⟨sg33646,⟨sg33643,⟨sg33642,⟨sg33641,True.intro,True.intro⟩,True.intro⟩,⟨sg33645,⟨sg33644,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33649,⟨sg33648,⟨sg33647,True.intro,True.intro⟩,True.intro⟩,⟨sg33650,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_146All : degreeTree62_146.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33662,⟨sg33657,⟨sg33654,⟨sg33653,⟨sg33652,True.intro,True.intro⟩,True.intro⟩,⟨sg33656,⟨sg33655,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33660,⟨sg33659,⟨sg33658,True.intro,True.intro⟩,True.intro⟩,⟨sg33661,True.intro,True.intro⟩⟩⟩,⟨sg33668,⟨sg33665,⟨sg33664,⟨sg33663,True.intro,True.intro⟩,True.intro⟩,⟨sg33667,⟨sg33666,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33671,⟨sg33670,⟨sg33669,True.intro,True.intro⟩,True.intro⟩,⟨sg33672,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_147All : degreeTree62_147.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33651,degreeTree62_145All,degreeTree62_146All⟩ + +lemma degreeTree62_148All : degreeTree62_148.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33629,degreeTree62_144All,degreeTree62_147All⟩ + +lemma degreeTree62_149All : degreeTree62_149.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33684,⟨sg33679,⟨sg33676,⟨sg33675,⟨sg33674,True.intro,True.intro⟩,True.intro⟩,⟨sg33678,⟨sg33677,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33682,⟨sg33681,⟨sg33680,True.intro,True.intro⟩,True.intro⟩,⟨sg33683,True.intro,True.intro⟩⟩⟩,⟨sg33690,⟨sg33687,⟨sg33686,⟨sg33685,True.intro,True.intro⟩,True.intro⟩,⟨sg33689,⟨sg33688,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33693,⟨sg33692,⟨sg33691,True.intro,True.intro⟩,True.intro⟩,⟨sg33694,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_150All : degreeTree62_150.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33706,⟨sg33701,⟨sg33698,⟨sg33697,⟨sg33696,True.intro,True.intro⟩,True.intro⟩,⟨sg33700,⟨sg33699,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33704,⟨sg33703,⟨sg33702,True.intro,True.intro⟩,True.intro⟩,⟨sg33705,True.intro,True.intro⟩⟩⟩,⟨sg33712,⟨sg33709,⟨sg33708,⟨sg33707,True.intro,True.intro⟩,True.intro⟩,⟨sg33711,⟨sg33710,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33715,⟨sg33714,⟨sg33713,True.intro,True.intro⟩,True.intro⟩,⟨sg33716,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_151All : degreeTree62_151.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33695,degreeTree62_149All,degreeTree62_150All⟩ + +lemma degreeTree62_152All : degreeTree62_152.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33728,⟨sg33723,⟨sg33720,⟨sg33719,⟨sg33718,True.intro,True.intro⟩,True.intro⟩,⟨sg33722,⟨sg33721,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33726,⟨sg33725,⟨sg33724,True.intro,True.intro⟩,True.intro⟩,⟨sg33727,True.intro,True.intro⟩⟩⟩,⟨sg33734,⟨sg33731,⟨sg33730,⟨sg33729,True.intro,True.intro⟩,True.intro⟩,⟨sg33733,⟨sg33732,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33737,⟨sg33736,⟨sg33735,True.intro,True.intro⟩,True.intro⟩,⟨sg33738,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_153All : degreeTree62_153.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33750,⟨sg33745,⟨sg33742,⟨sg33741,⟨sg33740,True.intro,True.intro⟩,True.intro⟩,⟨sg33744,⟨sg33743,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33748,⟨sg33747,⟨sg33746,True.intro,True.intro⟩,True.intro⟩,⟨sg33749,True.intro,True.intro⟩⟩⟩,⟨sg33755,⟨sg33753,⟨sg33752,⟨sg33751,True.intro,True.intro⟩,True.intro⟩,⟨sg33754,True.intro,True.intro⟩⟩,⟨sg33758,⟨sg33757,⟨sg33756,True.intro,True.intro⟩,True.intro⟩,⟨sg33759,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_154All : degreeTree62_154.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33739,degreeTree62_152All,degreeTree62_153All⟩ + +lemma degreeTree62_155All : degreeTree62_155.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33717,degreeTree62_151All,degreeTree62_154All⟩ + +lemma degreeTree62_156All : degreeTree62_156.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33673,degreeTree62_148All,degreeTree62_155All⟩ + +lemma degreeTree62_157All : degreeTree62_157.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33585,degreeTree62_141All,degreeTree62_156All⟩ + +lemma degreeTree62_158All : degreeTree62_158.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33771,⟨sg33766,⟨sg33763,⟨sg33762,⟨sg33761,True.intro,True.intro⟩,True.intro⟩,⟨sg33765,⟨sg33764,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33769,⟨sg33768,⟨sg33767,True.intro,True.intro⟩,True.intro⟩,⟨sg33770,True.intro,True.intro⟩⟩⟩,⟨sg33777,⟨sg33774,⟨sg33773,⟨sg33772,True.intro,True.intro⟩,True.intro⟩,⟨sg33776,⟨sg33775,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33780,⟨sg33779,⟨sg33778,True.intro,True.intro⟩,True.intro⟩,⟨sg33781,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_159All : degreeTree62_159.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33793,⟨sg33788,⟨sg33785,⟨sg33784,⟨sg33783,True.intro,True.intro⟩,True.intro⟩,⟨sg33787,⟨sg33786,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33791,⟨sg33790,⟨sg33789,True.intro,True.intro⟩,True.intro⟩,⟨sg33792,True.intro,True.intro⟩⟩⟩,⟨sg33799,⟨sg33796,⟨sg33795,⟨sg33794,True.intro,True.intro⟩,True.intro⟩,⟨sg33798,⟨sg33797,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33802,⟨sg33801,⟨sg33800,True.intro,True.intro⟩,True.intro⟩,⟨sg33803,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_160All : degreeTree62_160.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33782,degreeTree62_158All,degreeTree62_159All⟩ + +lemma degreeTree62_161All : degreeTree62_161.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33815,⟨sg33810,⟨sg33807,⟨sg33806,⟨sg33805,True.intro,True.intro⟩,True.intro⟩,⟨sg33809,⟨sg33808,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33813,⟨sg33812,⟨sg33811,True.intro,True.intro⟩,True.intro⟩,⟨sg33814,True.intro,True.intro⟩⟩⟩,⟨sg33821,⟨sg33818,⟨sg33817,⟨sg33816,True.intro,True.intro⟩,True.intro⟩,⟨sg33820,⟨sg33819,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33824,⟨sg33823,⟨sg33822,True.intro,True.intro⟩,True.intro⟩,⟨sg33825,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_162All : degreeTree62_162.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33837,⟨sg33832,⟨sg33829,⟨sg33828,⟨sg33827,True.intro,True.intro⟩,True.intro⟩,⟨sg33831,⟨sg33830,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33835,⟨sg33834,⟨sg33833,True.intro,True.intro⟩,True.intro⟩,⟨sg33836,True.intro,True.intro⟩⟩⟩,⟨sg33843,⟨sg33840,⟨sg33839,⟨sg33838,True.intro,True.intro⟩,True.intro⟩,⟨sg33842,⟨sg33841,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33846,⟨sg33845,⟨sg33844,True.intro,True.intro⟩,True.intro⟩,⟨sg33847,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_163All : degreeTree62_163.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33826,degreeTree62_161All,degreeTree62_162All⟩ + +lemma degreeTree62_164All : degreeTree62_164.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33804,degreeTree62_160All,degreeTree62_163All⟩ + +lemma degreeTree62_165All : degreeTree62_165.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33859,⟨sg33854,⟨sg33851,⟨sg33850,⟨sg33849,True.intro,True.intro⟩,True.intro⟩,⟨sg33853,⟨sg33852,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33857,⟨sg33856,⟨sg33855,True.intro,True.intro⟩,True.intro⟩,⟨sg33858,True.intro,True.intro⟩⟩⟩,⟨sg33865,⟨sg33862,⟨sg33861,⟨sg33860,True.intro,True.intro⟩,True.intro⟩,⟨sg33864,⟨sg33863,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33868,⟨sg33867,⟨sg33866,True.intro,True.intro⟩,True.intro⟩,⟨sg33869,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_166All : degreeTree62_166.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33881,⟨sg33876,⟨sg33873,⟨sg33872,⟨sg33871,True.intro,True.intro⟩,True.intro⟩,⟨sg33875,⟨sg33874,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33879,⟨sg33878,⟨sg33877,True.intro,True.intro⟩,True.intro⟩,⟨sg33880,True.intro,True.intro⟩⟩⟩,⟨sg33887,⟨sg33884,⟨sg33883,⟨sg33882,True.intro,True.intro⟩,True.intro⟩,⟨sg33886,⟨sg33885,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33890,⟨sg33889,⟨sg33888,True.intro,True.intro⟩,True.intro⟩,⟨sg33891,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_167All : degreeTree62_167.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33870,degreeTree62_165All,degreeTree62_166All⟩ + +lemma degreeTree62_168All : degreeTree62_168.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33903,⟨sg33898,⟨sg33895,⟨sg33894,⟨sg33893,True.intro,True.intro⟩,True.intro⟩,⟨sg33897,⟨sg33896,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33901,⟨sg33900,⟨sg33899,True.intro,True.intro⟩,True.intro⟩,⟨sg33902,True.intro,True.intro⟩⟩⟩,⟨sg33909,⟨sg33906,⟨sg33905,⟨sg33904,True.intro,True.intro⟩,True.intro⟩,⟨sg33908,⟨sg33907,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33912,⟨sg33911,⟨sg33910,True.intro,True.intro⟩,True.intro⟩,⟨sg33913,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_169All : degreeTree62_169.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33925,⟨sg33920,⟨sg33917,⟨sg33916,⟨sg33915,True.intro,True.intro⟩,True.intro⟩,⟨sg33919,⟨sg33918,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33923,⟨sg33922,⟨sg33921,True.intro,True.intro⟩,True.intro⟩,⟨sg33924,True.intro,True.intro⟩⟩⟩,⟨sg33931,⟨sg33928,⟨sg33927,⟨sg33926,True.intro,True.intro⟩,True.intro⟩,⟨sg33930,⟨sg33929,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33934,⟨sg33933,⟨sg33932,True.intro,True.intro⟩,True.intro⟩,⟨sg33935,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_170All : degreeTree62_170.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33914,degreeTree62_168All,degreeTree62_169All⟩ + +lemma degreeTree62_171All : degreeTree62_171.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33892,degreeTree62_167All,degreeTree62_170All⟩ + +lemma degreeTree62_172All : degreeTree62_172.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33848,degreeTree62_164All,degreeTree62_171All⟩ + +lemma degreeTree62_173All : degreeTree62_173.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33947,⟨sg33942,⟨sg33939,⟨sg33938,⟨sg33937,True.intro,True.intro⟩,True.intro⟩,⟨sg33941,⟨sg33940,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33945,⟨sg33944,⟨sg33943,True.intro,True.intro⟩,True.intro⟩,⟨sg33946,True.intro,True.intro⟩⟩⟩,⟨sg33953,⟨sg33950,⟨sg33949,⟨sg33948,True.intro,True.intro⟩,True.intro⟩,⟨sg33952,⟨sg33951,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33956,⟨sg33955,⟨sg33954,True.intro,True.intro⟩,True.intro⟩,⟨sg33957,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_174All : degreeTree62_174.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33969,⟨sg33964,⟨sg33961,⟨sg33960,⟨sg33959,True.intro,True.intro⟩,True.intro⟩,⟨sg33963,⟨sg33962,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33967,⟨sg33966,⟨sg33965,True.intro,True.intro⟩,True.intro⟩,⟨sg33968,True.intro,True.intro⟩⟩⟩,⟨sg33975,⟨sg33972,⟨sg33971,⟨sg33970,True.intro,True.intro⟩,True.intro⟩,⟨sg33974,⟨sg33973,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33978,⟨sg33977,⟨sg33976,True.intro,True.intro⟩,True.intro⟩,⟨sg33979,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_175All : degreeTree62_175.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33958,degreeTree62_173All,degreeTree62_174All⟩ + +lemma degreeTree62_176All : degreeTree62_176.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33991,⟨sg33986,⟨sg33983,⟨sg33982,⟨sg33981,True.intro,True.intro⟩,True.intro⟩,⟨sg33985,⟨sg33984,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg33989,⟨sg33988,⟨sg33987,True.intro,True.intro⟩,True.intro⟩,⟨sg33990,True.intro,True.intro⟩⟩⟩,⟨sg33997,⟨sg33994,⟨sg33993,⟨sg33992,True.intro,True.intro⟩,True.intro⟩,⟨sg33996,⟨sg33995,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34000,⟨sg33999,⟨sg33998,True.intro,True.intro⟩,True.intro⟩,⟨sg34001,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_177All : degreeTree62_177.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34013,⟨sg34008,⟨sg34005,⟨sg34004,⟨sg34003,True.intro,True.intro⟩,True.intro⟩,⟨sg34007,⟨sg34006,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34011,⟨sg34010,⟨sg34009,True.intro,True.intro⟩,True.intro⟩,⟨sg34012,True.intro,True.intro⟩⟩⟩,⟨sg34019,⟨sg34016,⟨sg34015,⟨sg34014,True.intro,True.intro⟩,True.intro⟩,⟨sg34018,⟨sg34017,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34022,⟨sg34021,⟨sg34020,True.intro,True.intro⟩,True.intro⟩,⟨sg34023,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_178All : degreeTree62_178.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34002,degreeTree62_176All,degreeTree62_177All⟩ + +lemma degreeTree62_179All : degreeTree62_179.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33980,degreeTree62_175All,degreeTree62_178All⟩ + +lemma degreeTree62_180All : degreeTree62_180.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34035,⟨sg34030,⟨sg34027,⟨sg34026,⟨sg34025,True.intro,True.intro⟩,True.intro⟩,⟨sg34029,⟨sg34028,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34033,⟨sg34032,⟨sg34031,True.intro,True.intro⟩,True.intro⟩,⟨sg34034,True.intro,True.intro⟩⟩⟩,⟨sg34041,⟨sg34038,⟨sg34037,⟨sg34036,True.intro,True.intro⟩,True.intro⟩,⟨sg34040,⟨sg34039,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34044,⟨sg34043,⟨sg34042,True.intro,True.intro⟩,True.intro⟩,⟨sg34045,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_181All : degreeTree62_181.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34057,⟨sg34052,⟨sg34049,⟨sg34048,⟨sg34047,True.intro,True.intro⟩,True.intro⟩,⟨sg34051,⟨sg34050,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34055,⟨sg34054,⟨sg34053,True.intro,True.intro⟩,True.intro⟩,⟨sg34056,True.intro,True.intro⟩⟩⟩,⟨sg34063,⟨sg34060,⟨sg34059,⟨sg34058,True.intro,True.intro⟩,True.intro⟩,⟨sg34062,⟨sg34061,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34066,⟨sg34065,⟨sg34064,True.intro,True.intro⟩,True.intro⟩,⟨sg34067,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_182All : degreeTree62_182.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34046,degreeTree62_180All,degreeTree62_181All⟩ + +lemma degreeTree62_183All : degreeTree62_183.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34079,⟨sg34074,⟨sg34071,⟨sg34070,⟨sg34069,True.intro,True.intro⟩,True.intro⟩,⟨sg34073,⟨sg34072,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34077,⟨sg34076,⟨sg34075,True.intro,True.intro⟩,True.intro⟩,⟨sg34078,True.intro,True.intro⟩⟩⟩,⟨sg34085,⟨sg34082,⟨sg34081,⟨sg34080,True.intro,True.intro⟩,True.intro⟩,⟨sg34084,⟨sg34083,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34088,⟨sg34087,⟨sg34086,True.intro,True.intro⟩,True.intro⟩,⟨sg34089,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_184All : degreeTree62_184.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34101,⟨sg34096,⟨sg34093,⟨sg34092,⟨sg34091,True.intro,True.intro⟩,True.intro⟩,⟨sg34095,⟨sg34094,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34099,⟨sg34098,⟨sg34097,True.intro,True.intro⟩,True.intro⟩,⟨sg34100,True.intro,True.intro⟩⟩⟩,⟨sg34106,⟨sg34104,⟨sg34103,⟨sg34102,True.intro,True.intro⟩,True.intro⟩,⟨sg34105,True.intro,True.intro⟩⟩,⟨sg34109,⟨sg34108,⟨sg34107,True.intro,True.intro⟩,True.intro⟩,⟨sg34110,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_185All : degreeTree62_185.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34090,degreeTree62_183All,degreeTree62_184All⟩ + +lemma degreeTree62_186All : degreeTree62_186.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34068,degreeTree62_182All,degreeTree62_185All⟩ + +lemma degreeTree62_187All : degreeTree62_187.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34024,degreeTree62_179All,degreeTree62_186All⟩ + +lemma degreeTree62_188All : degreeTree62_188.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33936,degreeTree62_172All,degreeTree62_187All⟩ + +lemma degreeTree62_189All : degreeTree62_189.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33760,degreeTree62_157All,degreeTree62_188All⟩ + +lemma degreeTree62_190All : degreeTree62_190.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34122,⟨sg34117,⟨sg34114,⟨sg34113,⟨sg34112,True.intro,True.intro⟩,True.intro⟩,⟨sg34116,⟨sg34115,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34120,⟨sg34119,⟨sg34118,True.intro,True.intro⟩,True.intro⟩,⟨sg34121,True.intro,True.intro⟩⟩⟩,⟨sg34128,⟨sg34125,⟨sg34124,⟨sg34123,True.intro,True.intro⟩,True.intro⟩,⟨sg34127,⟨sg34126,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34131,⟨sg34130,⟨sg34129,True.intro,True.intro⟩,True.intro⟩,⟨sg34132,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_191All : degreeTree62_191.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34144,⟨sg34139,⟨sg34136,⟨sg34135,⟨sg34134,True.intro,True.intro⟩,True.intro⟩,⟨sg34138,⟨sg34137,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34142,⟨sg34141,⟨sg34140,True.intro,True.intro⟩,True.intro⟩,⟨sg34143,True.intro,True.intro⟩⟩⟩,⟨sg34150,⟨sg34147,⟨sg34146,⟨sg34145,True.intro,True.intro⟩,True.intro⟩,⟨sg34149,⟨sg34148,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34153,⟨sg34152,⟨sg34151,True.intro,True.intro⟩,True.intro⟩,⟨sg34154,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_192All : degreeTree62_192.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34133,degreeTree62_190All,degreeTree62_191All⟩ + +lemma degreeTree62_193All : degreeTree62_193.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34166,⟨sg34161,⟨sg34158,⟨sg34157,⟨sg34156,True.intro,True.intro⟩,True.intro⟩,⟨sg34160,⟨sg34159,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34164,⟨sg34163,⟨sg34162,True.intro,True.intro⟩,True.intro⟩,⟨sg34165,True.intro,True.intro⟩⟩⟩,⟨sg34172,⟨sg34169,⟨sg34168,⟨sg34167,True.intro,True.intro⟩,True.intro⟩,⟨sg34171,⟨sg34170,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34175,⟨sg34174,⟨sg34173,True.intro,True.intro⟩,True.intro⟩,⟨sg34176,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_194All : degreeTree62_194.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34188,⟨sg34183,⟨sg34180,⟨sg34179,⟨sg34178,True.intro,True.intro⟩,True.intro⟩,⟨sg34182,⟨sg34181,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34186,⟨sg34185,⟨sg34184,True.intro,True.intro⟩,True.intro⟩,⟨sg34187,True.intro,True.intro⟩⟩⟩,⟨sg34194,⟨sg34191,⟨sg34190,⟨sg34189,True.intro,True.intro⟩,True.intro⟩,⟨sg34193,⟨sg34192,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34197,⟨sg34196,⟨sg34195,True.intro,True.intro⟩,True.intro⟩,⟨sg34198,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_195All : degreeTree62_195.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34177,degreeTree62_193All,degreeTree62_194All⟩ + +lemma degreeTree62_196All : degreeTree62_196.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34155,degreeTree62_192All,degreeTree62_195All⟩ + +lemma degreeTree62_197All : degreeTree62_197.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34210,⟨sg34205,⟨sg34202,⟨sg34201,⟨sg34200,True.intro,True.intro⟩,True.intro⟩,⟨sg34204,⟨sg34203,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34208,⟨sg34207,⟨sg34206,True.intro,True.intro⟩,True.intro⟩,⟨sg34209,True.intro,True.intro⟩⟩⟩,⟨sg34216,⟨sg34213,⟨sg34212,⟨sg34211,True.intro,True.intro⟩,True.intro⟩,⟨sg34215,⟨sg34214,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34219,⟨sg34218,⟨sg34217,True.intro,True.intro⟩,True.intro⟩,⟨sg34220,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_198All : degreeTree62_198.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34232,⟨sg34227,⟨sg34224,⟨sg34223,⟨sg34222,True.intro,True.intro⟩,True.intro⟩,⟨sg34226,⟨sg34225,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34230,⟨sg34229,⟨sg34228,True.intro,True.intro⟩,True.intro⟩,⟨sg34231,True.intro,True.intro⟩⟩⟩,⟨sg34238,⟨sg34235,⟨sg34234,⟨sg34233,True.intro,True.intro⟩,True.intro⟩,⟨sg34237,⟨sg34236,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34241,⟨sg34240,⟨sg34239,True.intro,True.intro⟩,True.intro⟩,⟨sg34242,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_199All : degreeTree62_199.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34221,degreeTree62_197All,degreeTree62_198All⟩ + +lemma degreeTree62_200All : degreeTree62_200.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34254,⟨sg34249,⟨sg34246,⟨sg34245,⟨sg34244,True.intro,True.intro⟩,True.intro⟩,⟨sg34248,⟨sg34247,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34252,⟨sg34251,⟨sg34250,True.intro,True.intro⟩,True.intro⟩,⟨sg34253,True.intro,True.intro⟩⟩⟩,⟨sg34260,⟨sg34257,⟨sg34256,⟨sg34255,True.intro,True.intro⟩,True.intro⟩,⟨sg34259,⟨sg34258,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34263,⟨sg34262,⟨sg34261,True.intro,True.intro⟩,True.intro⟩,⟨sg34264,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_201All : degreeTree62_201.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34276,⟨sg34271,⟨sg34268,⟨sg34267,⟨sg34266,True.intro,True.intro⟩,True.intro⟩,⟨sg34270,⟨sg34269,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34274,⟨sg34273,⟨sg34272,True.intro,True.intro⟩,True.intro⟩,⟨sg34275,True.intro,True.intro⟩⟩⟩,⟨sg34282,⟨sg34279,⟨sg34278,⟨sg34277,True.intro,True.intro⟩,True.intro⟩,⟨sg34281,⟨sg34280,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34285,⟨sg34284,⟨sg34283,True.intro,True.intro⟩,True.intro⟩,⟨sg34286,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_202All : degreeTree62_202.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34265,degreeTree62_200All,degreeTree62_201All⟩ + +lemma degreeTree62_203All : degreeTree62_203.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34243,degreeTree62_199All,degreeTree62_202All⟩ + +lemma degreeTree62_204All : degreeTree62_204.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34199,degreeTree62_196All,degreeTree62_203All⟩ + +lemma degreeTree62_205All : degreeTree62_205.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34298,⟨sg34293,⟨sg34290,⟨sg34289,⟨sg34288,True.intro,True.intro⟩,True.intro⟩,⟨sg34292,⟨sg34291,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34296,⟨sg34295,⟨sg34294,True.intro,True.intro⟩,True.intro⟩,⟨sg34297,True.intro,True.intro⟩⟩⟩,⟨sg34304,⟨sg34301,⟨sg34300,⟨sg34299,True.intro,True.intro⟩,True.intro⟩,⟨sg34303,⟨sg34302,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34307,⟨sg34306,⟨sg34305,True.intro,True.intro⟩,True.intro⟩,⟨sg34308,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_206All : degreeTree62_206.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34320,⟨sg34315,⟨sg34312,⟨sg34311,⟨sg34310,True.intro,True.intro⟩,True.intro⟩,⟨sg34314,⟨sg34313,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34318,⟨sg34317,⟨sg34316,True.intro,True.intro⟩,True.intro⟩,⟨sg34319,True.intro,True.intro⟩⟩⟩,⟨sg34326,⟨sg34323,⟨sg34322,⟨sg34321,True.intro,True.intro⟩,True.intro⟩,⟨sg34325,⟨sg34324,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34329,⟨sg34328,⟨sg34327,True.intro,True.intro⟩,True.intro⟩,⟨sg34330,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_207All : degreeTree62_207.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34309,degreeTree62_205All,degreeTree62_206All⟩ + +lemma degreeTree62_208All : degreeTree62_208.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34342,⟨sg34337,⟨sg34334,⟨sg34333,⟨sg34332,True.intro,True.intro⟩,True.intro⟩,⟨sg34336,⟨sg34335,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34340,⟨sg34339,⟨sg34338,True.intro,True.intro⟩,True.intro⟩,⟨sg34341,True.intro,True.intro⟩⟩⟩,⟨sg34348,⟨sg34345,⟨sg34344,⟨sg34343,True.intro,True.intro⟩,True.intro⟩,⟨sg34347,⟨sg34346,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34351,⟨sg34350,⟨sg34349,True.intro,True.intro⟩,True.intro⟩,⟨sg34352,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_209All : degreeTree62_209.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34364,⟨sg34359,⟨sg34356,⟨sg34355,⟨sg34354,True.intro,True.intro⟩,True.intro⟩,⟨sg34358,⟨sg34357,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34362,⟨sg34361,⟨sg34360,True.intro,True.intro⟩,True.intro⟩,⟨sg34363,True.intro,True.intro⟩⟩⟩,⟨sg34370,⟨sg34367,⟨sg34366,⟨sg34365,True.intro,True.intro⟩,True.intro⟩,⟨sg34369,⟨sg34368,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34373,⟨sg34372,⟨sg34371,True.intro,True.intro⟩,True.intro⟩,⟨sg34374,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_210All : degreeTree62_210.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34353,degreeTree62_208All,degreeTree62_209All⟩ + +lemma degreeTree62_211All : degreeTree62_211.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34331,degreeTree62_207All,degreeTree62_210All⟩ + +lemma degreeTree62_212All : degreeTree62_212.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34386,⟨sg34381,⟨sg34378,⟨sg34377,⟨sg34376,True.intro,True.intro⟩,True.intro⟩,⟨sg34380,⟨sg34379,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34384,⟨sg34383,⟨sg34382,True.intro,True.intro⟩,True.intro⟩,⟨sg34385,True.intro,True.intro⟩⟩⟩,⟨sg34392,⟨sg34389,⟨sg34388,⟨sg34387,True.intro,True.intro⟩,True.intro⟩,⟨sg34391,⟨sg34390,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34395,⟨sg34394,⟨sg34393,True.intro,True.intro⟩,True.intro⟩,⟨sg34396,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_213All : degreeTree62_213.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34408,⟨sg34403,⟨sg34400,⟨sg34399,⟨sg34398,True.intro,True.intro⟩,True.intro⟩,⟨sg34402,⟨sg34401,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34406,⟨sg34405,⟨sg34404,True.intro,True.intro⟩,True.intro⟩,⟨sg34407,True.intro,True.intro⟩⟩⟩,⟨sg34414,⟨sg34411,⟨sg34410,⟨sg34409,True.intro,True.intro⟩,True.intro⟩,⟨sg34413,⟨sg34412,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34417,⟨sg34416,⟨sg34415,True.intro,True.intro⟩,True.intro⟩,⟨sg34418,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_214All : degreeTree62_214.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34397,degreeTree62_212All,degreeTree62_213All⟩ + +lemma degreeTree62_215All : degreeTree62_215.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34430,⟨sg34425,⟨sg34422,⟨sg34421,⟨sg34420,True.intro,True.intro⟩,True.intro⟩,⟨sg34424,⟨sg34423,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34428,⟨sg34427,⟨sg34426,True.intro,True.intro⟩,True.intro⟩,⟨sg34429,True.intro,True.intro⟩⟩⟩,⟨sg34436,⟨sg34433,⟨sg34432,⟨sg34431,True.intro,True.intro⟩,True.intro⟩,⟨sg34435,⟨sg34434,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34439,⟨sg34438,⟨sg34437,True.intro,True.intro⟩,True.intro⟩,⟨sg34440,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_216All : degreeTree62_216.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34452,⟨sg34447,⟨sg34444,⟨sg34443,⟨sg34442,True.intro,True.intro⟩,True.intro⟩,⟨sg34446,⟨sg34445,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34450,⟨sg34449,⟨sg34448,True.intro,True.intro⟩,True.intro⟩,⟨sg34451,True.intro,True.intro⟩⟩⟩,⟨sg34457,⟨sg34455,⟨sg34454,⟨sg34453,True.intro,True.intro⟩,True.intro⟩,⟨sg34456,True.intro,True.intro⟩⟩,⟨sg34460,⟨sg34459,⟨sg34458,True.intro,True.intro⟩,True.intro⟩,⟨sg34461,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_217All : degreeTree62_217.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34441,degreeTree62_215All,degreeTree62_216All⟩ + +lemma degreeTree62_218All : degreeTree62_218.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34419,degreeTree62_214All,degreeTree62_217All⟩ + +lemma degreeTree62_219All : degreeTree62_219.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34375,degreeTree62_211All,degreeTree62_218All⟩ + +lemma degreeTree62_220All : degreeTree62_220.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34287,degreeTree62_204All,degreeTree62_219All⟩ + +lemma degreeTree62_221All : degreeTree62_221.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34473,⟨sg34468,⟨sg34465,⟨sg34464,⟨sg34463,True.intro,True.intro⟩,True.intro⟩,⟨sg34467,⟨sg34466,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34471,⟨sg34470,⟨sg34469,True.intro,True.intro⟩,True.intro⟩,⟨sg34472,True.intro,True.intro⟩⟩⟩,⟨sg34479,⟨sg34476,⟨sg34475,⟨sg34474,True.intro,True.intro⟩,True.intro⟩,⟨sg34478,⟨sg34477,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34482,⟨sg34481,⟨sg34480,True.intro,True.intro⟩,True.intro⟩,⟨sg34483,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_222All : degreeTree62_222.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34495,⟨sg34490,⟨sg34487,⟨sg34486,⟨sg34485,True.intro,True.intro⟩,True.intro⟩,⟨sg34489,⟨sg34488,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34493,⟨sg34492,⟨sg34491,True.intro,True.intro⟩,True.intro⟩,⟨sg34494,True.intro,True.intro⟩⟩⟩,⟨sg34501,⟨sg34498,⟨sg34497,⟨sg34496,True.intro,True.intro⟩,True.intro⟩,⟨sg34500,⟨sg34499,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34504,⟨sg34503,⟨sg34502,True.intro,True.intro⟩,True.intro⟩,⟨sg34505,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_223All : degreeTree62_223.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34484,degreeTree62_221All,degreeTree62_222All⟩ + +lemma degreeTree62_224All : degreeTree62_224.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34517,⟨sg34512,⟨sg34509,⟨sg34508,⟨sg34507,True.intro,True.intro⟩,True.intro⟩,⟨sg34511,⟨sg34510,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34515,⟨sg34514,⟨sg34513,True.intro,True.intro⟩,True.intro⟩,⟨sg34516,True.intro,True.intro⟩⟩⟩,⟨sg34523,⟨sg34520,⟨sg34519,⟨sg34518,True.intro,True.intro⟩,True.intro⟩,⟨sg34522,⟨sg34521,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34526,⟨sg34525,⟨sg34524,True.intro,True.intro⟩,True.intro⟩,⟨sg34527,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_225All : degreeTree62_225.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34539,⟨sg34534,⟨sg34531,⟨sg34530,⟨sg34529,True.intro,True.intro⟩,True.intro⟩,⟨sg34533,⟨sg34532,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34537,⟨sg34536,⟨sg34535,True.intro,True.intro⟩,True.intro⟩,⟨sg34538,True.intro,True.intro⟩⟩⟩,⟨sg34545,⟨sg34542,⟨sg34541,⟨sg34540,True.intro,True.intro⟩,True.intro⟩,⟨sg34544,⟨sg34543,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34548,⟨sg34547,⟨sg34546,True.intro,True.intro⟩,True.intro⟩,⟨sg34549,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_226All : degreeTree62_226.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34528,degreeTree62_224All,degreeTree62_225All⟩ + +lemma degreeTree62_227All : degreeTree62_227.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34506,degreeTree62_223All,degreeTree62_226All⟩ + +lemma degreeTree62_228All : degreeTree62_228.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34561,⟨sg34556,⟨sg34553,⟨sg34552,⟨sg34551,True.intro,True.intro⟩,True.intro⟩,⟨sg34555,⟨sg34554,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34559,⟨sg34558,⟨sg34557,True.intro,True.intro⟩,True.intro⟩,⟨sg34560,True.intro,True.intro⟩⟩⟩,⟨sg34567,⟨sg34564,⟨sg34563,⟨sg34562,True.intro,True.intro⟩,True.intro⟩,⟨sg34566,⟨sg34565,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34570,⟨sg34569,⟨sg34568,True.intro,True.intro⟩,True.intro⟩,⟨sg34571,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_229All : degreeTree62_229.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34583,⟨sg34578,⟨sg34575,⟨sg34574,⟨sg34573,True.intro,True.intro⟩,True.intro⟩,⟨sg34577,⟨sg34576,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34581,⟨sg34580,⟨sg34579,True.intro,True.intro⟩,True.intro⟩,⟨sg34582,True.intro,True.intro⟩⟩⟩,⟨sg34589,⟨sg34586,⟨sg34585,⟨sg34584,True.intro,True.intro⟩,True.intro⟩,⟨sg34588,⟨sg34587,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34592,⟨sg34591,⟨sg34590,True.intro,True.intro⟩,True.intro⟩,⟨sg34593,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_230All : degreeTree62_230.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34572,degreeTree62_228All,degreeTree62_229All⟩ + +lemma degreeTree62_231All : degreeTree62_231.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34605,⟨sg34600,⟨sg34597,⟨sg34596,⟨sg34595,True.intro,True.intro⟩,True.intro⟩,⟨sg34599,⟨sg34598,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34603,⟨sg34602,⟨sg34601,True.intro,True.intro⟩,True.intro⟩,⟨sg34604,True.intro,True.intro⟩⟩⟩,⟨sg34611,⟨sg34608,⟨sg34607,⟨sg34606,True.intro,True.intro⟩,True.intro⟩,⟨sg34610,⟨sg34609,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34614,⟨sg34613,⟨sg34612,True.intro,True.intro⟩,True.intro⟩,⟨sg34615,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_232All : degreeTree62_232.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34627,⟨sg34622,⟨sg34619,⟨sg34618,⟨sg34617,True.intro,True.intro⟩,True.intro⟩,⟨sg34621,⟨sg34620,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34625,⟨sg34624,⟨sg34623,True.intro,True.intro⟩,True.intro⟩,⟨sg34626,True.intro,True.intro⟩⟩⟩,⟨sg34632,⟨sg34630,⟨sg34629,⟨sg34628,True.intro,True.intro⟩,True.intro⟩,⟨sg34631,True.intro,True.intro⟩⟩,⟨sg34635,⟨sg34634,⟨sg34633,True.intro,True.intro⟩,True.intro⟩,⟨sg34636,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_233All : degreeTree62_233.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34616,degreeTree62_231All,degreeTree62_232All⟩ + +lemma degreeTree62_234All : degreeTree62_234.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34594,degreeTree62_230All,degreeTree62_233All⟩ + +lemma degreeTree62_235All : degreeTree62_235.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34550,degreeTree62_227All,degreeTree62_234All⟩ + +lemma degreeTree62_236All : degreeTree62_236.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34648,⟨sg34643,⟨sg34640,⟨sg34639,⟨sg34638,True.intro,True.intro⟩,True.intro⟩,⟨sg34642,⟨sg34641,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34646,⟨sg34645,⟨sg34644,True.intro,True.intro⟩,True.intro⟩,⟨sg34647,True.intro,True.intro⟩⟩⟩,⟨sg34654,⟨sg34651,⟨sg34650,⟨sg34649,True.intro,True.intro⟩,True.intro⟩,⟨sg34653,⟨sg34652,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34657,⟨sg34656,⟨sg34655,True.intro,True.intro⟩,True.intro⟩,⟨sg34658,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_237All : degreeTree62_237.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34670,⟨sg34665,⟨sg34662,⟨sg34661,⟨sg34660,True.intro,True.intro⟩,True.intro⟩,⟨sg34664,⟨sg34663,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34668,⟨sg34667,⟨sg34666,True.intro,True.intro⟩,True.intro⟩,⟨sg34669,True.intro,True.intro⟩⟩⟩,⟨sg34676,⟨sg34673,⟨sg34672,⟨sg34671,True.intro,True.intro⟩,True.intro⟩,⟨sg34675,⟨sg34674,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34679,⟨sg34678,⟨sg34677,True.intro,True.intro⟩,True.intro⟩,⟨sg34680,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_238All : degreeTree62_238.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34659,degreeTree62_236All,degreeTree62_237All⟩ + +lemma degreeTree62_239All : degreeTree62_239.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34692,⟨sg34687,⟨sg34684,⟨sg34683,⟨sg34682,True.intro,True.intro⟩,True.intro⟩,⟨sg34686,⟨sg34685,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34690,⟨sg34689,⟨sg34688,True.intro,True.intro⟩,True.intro⟩,⟨sg34691,True.intro,True.intro⟩⟩⟩,⟨sg34698,⟨sg34695,⟨sg34694,⟨sg34693,True.intro,True.intro⟩,True.intro⟩,⟨sg34697,⟨sg34696,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34701,⟨sg34700,⟨sg34699,True.intro,True.intro⟩,True.intro⟩,⟨sg34702,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_240All : degreeTree62_240.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34714,⟨sg34709,⟨sg34706,⟨sg34705,⟨sg34704,True.intro,True.intro⟩,True.intro⟩,⟨sg34708,⟨sg34707,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34712,⟨sg34711,⟨sg34710,True.intro,True.intro⟩,True.intro⟩,⟨sg34713,True.intro,True.intro⟩⟩⟩,⟨sg34720,⟨sg34717,⟨sg34716,⟨sg34715,True.intro,True.intro⟩,True.intro⟩,⟨sg34719,⟨sg34718,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34723,⟨sg34722,⟨sg34721,True.intro,True.intro⟩,True.intro⟩,⟨sg34724,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_241All : degreeTree62_241.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34703,degreeTree62_239All,degreeTree62_240All⟩ + +lemma degreeTree62_242All : degreeTree62_242.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34681,degreeTree62_238All,degreeTree62_241All⟩ + +lemma degreeTree62_243All : degreeTree62_243.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34736,⟨sg34731,⟨sg34728,⟨sg34727,⟨sg34726,True.intro,True.intro⟩,True.intro⟩,⟨sg34730,⟨sg34729,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34734,⟨sg34733,⟨sg34732,True.intro,True.intro⟩,True.intro⟩,⟨sg34735,True.intro,True.intro⟩⟩⟩,⟨sg34742,⟨sg34739,⟨sg34738,⟨sg34737,True.intro,True.intro⟩,True.intro⟩,⟨sg34741,⟨sg34740,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34745,⟨sg34744,⟨sg34743,True.intro,True.intro⟩,True.intro⟩,⟨sg34746,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_244All : degreeTree62_244.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34758,⟨sg34753,⟨sg34750,⟨sg34749,⟨sg34748,True.intro,True.intro⟩,True.intro⟩,⟨sg34752,⟨sg34751,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34756,⟨sg34755,⟨sg34754,True.intro,True.intro⟩,True.intro⟩,⟨sg34757,True.intro,True.intro⟩⟩⟩,⟨sg34764,⟨sg34761,⟨sg34760,⟨sg34759,True.intro,True.intro⟩,True.intro⟩,⟨sg34763,⟨sg34762,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34767,⟨sg34766,⟨sg34765,True.intro,True.intro⟩,True.intro⟩,⟨sg34768,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_245All : degreeTree62_245.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34747,degreeTree62_243All,degreeTree62_244All⟩ + +lemma degreeTree62_246All : degreeTree62_246.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34780,⟨sg34775,⟨sg34772,⟨sg34771,⟨sg34770,True.intro,True.intro⟩,True.intro⟩,⟨sg34774,⟨sg34773,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34778,⟨sg34777,⟨sg34776,True.intro,True.intro⟩,True.intro⟩,⟨sg34779,True.intro,True.intro⟩⟩⟩,⟨sg34786,⟨sg34783,⟨sg34782,⟨sg34781,True.intro,True.intro⟩,True.intro⟩,⟨sg34785,⟨sg34784,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34789,⟨sg34788,⟨sg34787,True.intro,True.intro⟩,True.intro⟩,⟨sg34790,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_247All : degreeTree62_247.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34802,⟨sg34797,⟨sg34794,⟨sg34793,⟨sg34792,True.intro,True.intro⟩,True.intro⟩,⟨sg34796,⟨sg34795,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34800,⟨sg34799,⟨sg34798,True.intro,True.intro⟩,True.intro⟩,⟨sg34801,True.intro,True.intro⟩⟩⟩,⟨sg34807,⟨sg34805,⟨sg34804,⟨sg34803,True.intro,True.intro⟩,True.intro⟩,⟨sg34806,True.intro,True.intro⟩⟩,⟨sg34810,⟨sg34809,⟨sg34808,True.intro,True.intro⟩,True.intro⟩,⟨sg34811,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_248All : degreeTree62_248.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34791,degreeTree62_246All,degreeTree62_247All⟩ + +lemma degreeTree62_249All : degreeTree62_249.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34769,degreeTree62_245All,degreeTree62_248All⟩ + +lemma degreeTree62_250All : degreeTree62_250.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34725,degreeTree62_242All,degreeTree62_249All⟩ + +lemma degreeTree62_251All : degreeTree62_251.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34637,degreeTree62_235All,degreeTree62_250All⟩ + +lemma degreeTree62_252All : degreeTree62_252.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34462,degreeTree62_220All,degreeTree62_251All⟩ + +lemma degreeTree62_253All : degreeTree62_253.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34111,degreeTree62_189All,degreeTree62_252All⟩ + +lemma degreeTree62_254All : degreeTree62_254.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg33409,degreeTree62_126All,degreeTree62_253All⟩ + +lemma degreeTree62_255All : degreeTree62_255.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34823,⟨sg34818,⟨sg34815,⟨sg34814,⟨sg34813,True.intro,True.intro⟩,True.intro⟩,⟨sg34817,⟨sg34816,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34821,⟨sg34820,⟨sg34819,True.intro,True.intro⟩,True.intro⟩,⟨sg34822,True.intro,True.intro⟩⟩⟩,⟨sg34829,⟨sg34826,⟨sg34825,⟨sg34824,True.intro,True.intro⟩,True.intro⟩,⟨sg34828,⟨sg34827,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34832,⟨sg34831,⟨sg34830,True.intro,True.intro⟩,True.intro⟩,⟨sg34833,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_256All : degreeTree62_256.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34845,⟨sg34840,⟨sg34837,⟨sg34836,⟨sg34835,True.intro,True.intro⟩,True.intro⟩,⟨sg34839,⟨sg34838,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34843,⟨sg34842,⟨sg34841,True.intro,True.intro⟩,True.intro⟩,⟨sg34844,True.intro,True.intro⟩⟩⟩,⟨sg34851,⟨sg34848,⟨sg34847,⟨sg34846,True.intro,True.intro⟩,True.intro⟩,⟨sg34850,⟨sg34849,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34854,⟨sg34853,⟨sg34852,True.intro,True.intro⟩,True.intro⟩,⟨sg34855,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_257All : degreeTree62_257.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34834,degreeTree62_255All,degreeTree62_256All⟩ + +lemma degreeTree62_258All : degreeTree62_258.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34867,⟨sg34862,⟨sg34859,⟨sg34858,⟨sg34857,True.intro,True.intro⟩,True.intro⟩,⟨sg34861,⟨sg34860,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34865,⟨sg34864,⟨sg34863,True.intro,True.intro⟩,True.intro⟩,⟨sg34866,True.intro,True.intro⟩⟩⟩,⟨sg34873,⟨sg34870,⟨sg34869,⟨sg34868,True.intro,True.intro⟩,True.intro⟩,⟨sg34872,⟨sg34871,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34876,⟨sg34875,⟨sg34874,True.intro,True.intro⟩,True.intro⟩,⟨sg34877,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_259All : degreeTree62_259.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34889,⟨sg34884,⟨sg34881,⟨sg34880,⟨sg34879,True.intro,True.intro⟩,True.intro⟩,⟨sg34883,⟨sg34882,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34887,⟨sg34886,⟨sg34885,True.intro,True.intro⟩,True.intro⟩,⟨sg34888,True.intro,True.intro⟩⟩⟩,⟨sg34895,⟨sg34892,⟨sg34891,⟨sg34890,True.intro,True.intro⟩,True.intro⟩,⟨sg34894,⟨sg34893,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34898,⟨sg34897,⟨sg34896,True.intro,True.intro⟩,True.intro⟩,⟨sg34899,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_260All : degreeTree62_260.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34878,degreeTree62_258All,degreeTree62_259All⟩ + +lemma degreeTree62_261All : degreeTree62_261.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34856,degreeTree62_257All,degreeTree62_260All⟩ + +lemma degreeTree62_262All : degreeTree62_262.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34911,⟨sg34906,⟨sg34903,⟨sg34902,⟨sg34901,True.intro,True.intro⟩,True.intro⟩,⟨sg34905,⟨sg34904,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34909,⟨sg34908,⟨sg34907,True.intro,True.intro⟩,True.intro⟩,⟨sg34910,True.intro,True.intro⟩⟩⟩,⟨sg34917,⟨sg34914,⟨sg34913,⟨sg34912,True.intro,True.intro⟩,True.intro⟩,⟨sg34916,⟨sg34915,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34920,⟨sg34919,⟨sg34918,True.intro,True.intro⟩,True.intro⟩,⟨sg34921,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_263All : degreeTree62_263.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34933,⟨sg34928,⟨sg34925,⟨sg34924,⟨sg34923,True.intro,True.intro⟩,True.intro⟩,⟨sg34927,⟨sg34926,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34931,⟨sg34930,⟨sg34929,True.intro,True.intro⟩,True.intro⟩,⟨sg34932,True.intro,True.intro⟩⟩⟩,⟨sg34939,⟨sg34936,⟨sg34935,⟨sg34934,True.intro,True.intro⟩,True.intro⟩,⟨sg34938,⟨sg34937,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34942,⟨sg34941,⟨sg34940,True.intro,True.intro⟩,True.intro⟩,⟨sg34943,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_264All : degreeTree62_264.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34922,degreeTree62_262All,degreeTree62_263All⟩ + +lemma degreeTree62_265All : degreeTree62_265.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34955,⟨sg34950,⟨sg34947,⟨sg34946,⟨sg34945,True.intro,True.intro⟩,True.intro⟩,⟨sg34949,⟨sg34948,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34953,⟨sg34952,⟨sg34951,True.intro,True.intro⟩,True.intro⟩,⟨sg34954,True.intro,True.intro⟩⟩⟩,⟨sg34961,⟨sg34958,⟨sg34957,⟨sg34956,True.intro,True.intro⟩,True.intro⟩,⟨sg34960,⟨sg34959,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34964,⟨sg34963,⟨sg34962,True.intro,True.intro⟩,True.intro⟩,⟨sg34965,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_266All : degreeTree62_266.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34977,⟨sg34972,⟨sg34969,⟨sg34968,⟨sg34967,True.intro,True.intro⟩,True.intro⟩,⟨sg34971,⟨sg34970,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34975,⟨sg34974,⟨sg34973,True.intro,True.intro⟩,True.intro⟩,⟨sg34976,True.intro,True.intro⟩⟩⟩,⟨sg34983,⟨sg34980,⟨sg34979,⟨sg34978,True.intro,True.intro⟩,True.intro⟩,⟨sg34982,⟨sg34981,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34986,⟨sg34985,⟨sg34984,True.intro,True.intro⟩,True.intro⟩,⟨sg34987,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_267All : degreeTree62_267.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34966,degreeTree62_265All,degreeTree62_266All⟩ + +lemma degreeTree62_268All : degreeTree62_268.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34944,degreeTree62_264All,degreeTree62_267All⟩ + +lemma degreeTree62_269All : degreeTree62_269.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34900,degreeTree62_261All,degreeTree62_268All⟩ + +lemma degreeTree62_270All : degreeTree62_270.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34999,⟨sg34994,⟨sg34991,⟨sg34990,⟨sg34989,True.intro,True.intro⟩,True.intro⟩,⟨sg34993,⟨sg34992,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg34997,⟨sg34996,⟨sg34995,True.intro,True.intro⟩,True.intro⟩,⟨sg34998,True.intro,True.intro⟩⟩⟩,⟨sg35005,⟨sg35002,⟨sg35001,⟨sg35000,True.intro,True.intro⟩,True.intro⟩,⟨sg35004,⟨sg35003,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35008,⟨sg35007,⟨sg35006,True.intro,True.intro⟩,True.intro⟩,⟨sg35009,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_271All : degreeTree62_271.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35021,⟨sg35016,⟨sg35013,⟨sg35012,⟨sg35011,True.intro,True.intro⟩,True.intro⟩,⟨sg35015,⟨sg35014,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35019,⟨sg35018,⟨sg35017,True.intro,True.intro⟩,True.intro⟩,⟨sg35020,True.intro,True.intro⟩⟩⟩,⟨sg35027,⟨sg35024,⟨sg35023,⟨sg35022,True.intro,True.intro⟩,True.intro⟩,⟨sg35026,⟨sg35025,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35030,⟨sg35029,⟨sg35028,True.intro,True.intro⟩,True.intro⟩,⟨sg35031,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_272All : degreeTree62_272.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35010,degreeTree62_270All,degreeTree62_271All⟩ + +lemma degreeTree62_273All : degreeTree62_273.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35043,⟨sg35038,⟨sg35035,⟨sg35034,⟨sg35033,True.intro,True.intro⟩,True.intro⟩,⟨sg35037,⟨sg35036,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35041,⟨sg35040,⟨sg35039,True.intro,True.intro⟩,True.intro⟩,⟨sg35042,True.intro,True.intro⟩⟩⟩,⟨sg35049,⟨sg35046,⟨sg35045,⟨sg35044,True.intro,True.intro⟩,True.intro⟩,⟨sg35048,⟨sg35047,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35052,⟨sg35051,⟨sg35050,True.intro,True.intro⟩,True.intro⟩,⟨sg35053,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_274All : degreeTree62_274.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35065,⟨sg35060,⟨sg35057,⟨sg35056,⟨sg35055,True.intro,True.intro⟩,True.intro⟩,⟨sg35059,⟨sg35058,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35063,⟨sg35062,⟨sg35061,True.intro,True.intro⟩,True.intro⟩,⟨sg35064,True.intro,True.intro⟩⟩⟩,⟨sg35071,⟨sg35068,⟨sg35067,⟨sg35066,True.intro,True.intro⟩,True.intro⟩,⟨sg35070,⟨sg35069,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35074,⟨sg35073,⟨sg35072,True.intro,True.intro⟩,True.intro⟩,⟨sg35075,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_275All : degreeTree62_275.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35054,degreeTree62_273All,degreeTree62_274All⟩ + +lemma degreeTree62_276All : degreeTree62_276.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35032,degreeTree62_272All,degreeTree62_275All⟩ + +lemma degreeTree62_277All : degreeTree62_277.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35087,⟨sg35082,⟨sg35079,⟨sg35078,⟨sg35077,True.intro,True.intro⟩,True.intro⟩,⟨sg35081,⟨sg35080,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35085,⟨sg35084,⟨sg35083,True.intro,True.intro⟩,True.intro⟩,⟨sg35086,True.intro,True.intro⟩⟩⟩,⟨sg35093,⟨sg35090,⟨sg35089,⟨sg35088,True.intro,True.intro⟩,True.intro⟩,⟨sg35092,⟨sg35091,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35096,⟨sg35095,⟨sg35094,True.intro,True.intro⟩,True.intro⟩,⟨sg35097,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_278All : degreeTree62_278.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35109,⟨sg35104,⟨sg35101,⟨sg35100,⟨sg35099,True.intro,True.intro⟩,True.intro⟩,⟨sg35103,⟨sg35102,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35107,⟨sg35106,⟨sg35105,True.intro,True.intro⟩,True.intro⟩,⟨sg35108,True.intro,True.intro⟩⟩⟩,⟨sg35115,⟨sg35112,⟨sg35111,⟨sg35110,True.intro,True.intro⟩,True.intro⟩,⟨sg35114,⟨sg35113,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35118,⟨sg35117,⟨sg35116,True.intro,True.intro⟩,True.intro⟩,⟨sg35119,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_279All : degreeTree62_279.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35098,degreeTree62_277All,degreeTree62_278All⟩ + +lemma degreeTree62_280All : degreeTree62_280.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35131,⟨sg35126,⟨sg35123,⟨sg35122,⟨sg35121,True.intro,True.intro⟩,True.intro⟩,⟨sg35125,⟨sg35124,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35129,⟨sg35128,⟨sg35127,True.intro,True.intro⟩,True.intro⟩,⟨sg35130,True.intro,True.intro⟩⟩⟩,⟨sg35137,⟨sg35134,⟨sg35133,⟨sg35132,True.intro,True.intro⟩,True.intro⟩,⟨sg35136,⟨sg35135,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35140,⟨sg35139,⟨sg35138,True.intro,True.intro⟩,True.intro⟩,⟨sg35141,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_281All : degreeTree62_281.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35153,⟨sg35148,⟨sg35145,⟨sg35144,⟨sg35143,True.intro,True.intro⟩,True.intro⟩,⟨sg35147,⟨sg35146,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35151,⟨sg35150,⟨sg35149,True.intro,True.intro⟩,True.intro⟩,⟨sg35152,True.intro,True.intro⟩⟩⟩,⟨sg35158,⟨sg35156,⟨sg35155,⟨sg35154,True.intro,True.intro⟩,True.intro⟩,⟨sg35157,True.intro,True.intro⟩⟩,⟨sg35161,⟨sg35160,⟨sg35159,True.intro,True.intro⟩,True.intro⟩,⟨sg35162,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_282All : degreeTree62_282.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35142,degreeTree62_280All,degreeTree62_281All⟩ + +lemma degreeTree62_283All : degreeTree62_283.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35120,degreeTree62_279All,degreeTree62_282All⟩ + +lemma degreeTree62_284All : degreeTree62_284.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35076,degreeTree62_276All,degreeTree62_283All⟩ + +lemma degreeTree62_285All : degreeTree62_285.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34988,degreeTree62_269All,degreeTree62_284All⟩ + +lemma degreeTree62_286All : degreeTree62_286.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35174,⟨sg35169,⟨sg35166,⟨sg35165,⟨sg35164,True.intro,True.intro⟩,True.intro⟩,⟨sg35168,⟨sg35167,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35172,⟨sg35171,⟨sg35170,True.intro,True.intro⟩,True.intro⟩,⟨sg35173,True.intro,True.intro⟩⟩⟩,⟨sg35180,⟨sg35177,⟨sg35176,⟨sg35175,True.intro,True.intro⟩,True.intro⟩,⟨sg35179,⟨sg35178,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35183,⟨sg35182,⟨sg35181,True.intro,True.intro⟩,True.intro⟩,⟨sg35184,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_287All : degreeTree62_287.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35196,⟨sg35191,⟨sg35188,⟨sg35187,⟨sg35186,True.intro,True.intro⟩,True.intro⟩,⟨sg35190,⟨sg35189,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35194,⟨sg35193,⟨sg35192,True.intro,True.intro⟩,True.intro⟩,⟨sg35195,True.intro,True.intro⟩⟩⟩,⟨sg35202,⟨sg35199,⟨sg35198,⟨sg35197,True.intro,True.intro⟩,True.intro⟩,⟨sg35201,⟨sg35200,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35205,⟨sg35204,⟨sg35203,True.intro,True.intro⟩,True.intro⟩,⟨sg35206,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_288All : degreeTree62_288.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35185,degreeTree62_286All,degreeTree62_287All⟩ + +lemma degreeTree62_289All : degreeTree62_289.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35218,⟨sg35213,⟨sg35210,⟨sg35209,⟨sg35208,True.intro,True.intro⟩,True.intro⟩,⟨sg35212,⟨sg35211,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35216,⟨sg35215,⟨sg35214,True.intro,True.intro⟩,True.intro⟩,⟨sg35217,True.intro,True.intro⟩⟩⟩,⟨sg35224,⟨sg35221,⟨sg35220,⟨sg35219,True.intro,True.intro⟩,True.intro⟩,⟨sg35223,⟨sg35222,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35227,⟨sg35226,⟨sg35225,True.intro,True.intro⟩,True.intro⟩,⟨sg35228,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_290All : degreeTree62_290.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35240,⟨sg35235,⟨sg35232,⟨sg35231,⟨sg35230,True.intro,True.intro⟩,True.intro⟩,⟨sg35234,⟨sg35233,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35238,⟨sg35237,⟨sg35236,True.intro,True.intro⟩,True.intro⟩,⟨sg35239,True.intro,True.intro⟩⟩⟩,⟨sg35246,⟨sg35243,⟨sg35242,⟨sg35241,True.intro,True.intro⟩,True.intro⟩,⟨sg35245,⟨sg35244,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35249,⟨sg35248,⟨sg35247,True.intro,True.intro⟩,True.intro⟩,⟨sg35250,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_291All : degreeTree62_291.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35229,degreeTree62_289All,degreeTree62_290All⟩ + +lemma degreeTree62_292All : degreeTree62_292.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35207,degreeTree62_288All,degreeTree62_291All⟩ + +lemma degreeTree62_293All : degreeTree62_293.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35262,⟨sg35257,⟨sg35254,⟨sg35253,⟨sg35252,True.intro,True.intro⟩,True.intro⟩,⟨sg35256,⟨sg35255,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35260,⟨sg35259,⟨sg35258,True.intro,True.intro⟩,True.intro⟩,⟨sg35261,True.intro,True.intro⟩⟩⟩,⟨sg35268,⟨sg35265,⟨sg35264,⟨sg35263,True.intro,True.intro⟩,True.intro⟩,⟨sg35267,⟨sg35266,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35271,⟨sg35270,⟨sg35269,True.intro,True.intro⟩,True.intro⟩,⟨sg35272,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_294All : degreeTree62_294.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35284,⟨sg35279,⟨sg35276,⟨sg35275,⟨sg35274,True.intro,True.intro⟩,True.intro⟩,⟨sg35278,⟨sg35277,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35282,⟨sg35281,⟨sg35280,True.intro,True.intro⟩,True.intro⟩,⟨sg35283,True.intro,True.intro⟩⟩⟩,⟨sg35290,⟨sg35287,⟨sg35286,⟨sg35285,True.intro,True.intro⟩,True.intro⟩,⟨sg35289,⟨sg35288,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35293,⟨sg35292,⟨sg35291,True.intro,True.intro⟩,True.intro⟩,⟨sg35294,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_295All : degreeTree62_295.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35273,degreeTree62_293All,degreeTree62_294All⟩ + +lemma degreeTree62_296All : degreeTree62_296.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35306,⟨sg35301,⟨sg35298,⟨sg35297,⟨sg35296,True.intro,True.intro⟩,True.intro⟩,⟨sg35300,⟨sg35299,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35304,⟨sg35303,⟨sg35302,True.intro,True.intro⟩,True.intro⟩,⟨sg35305,True.intro,True.intro⟩⟩⟩,⟨sg35312,⟨sg35309,⟨sg35308,⟨sg35307,True.intro,True.intro⟩,True.intro⟩,⟨sg35311,⟨sg35310,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35315,⟨sg35314,⟨sg35313,True.intro,True.intro⟩,True.intro⟩,⟨sg35316,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_297All : degreeTree62_297.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35328,⟨sg35323,⟨sg35320,⟨sg35319,⟨sg35318,True.intro,True.intro⟩,True.intro⟩,⟨sg35322,⟨sg35321,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35326,⟨sg35325,⟨sg35324,True.intro,True.intro⟩,True.intro⟩,⟨sg35327,True.intro,True.intro⟩⟩⟩,⟨sg35334,⟨sg35331,⟨sg35330,⟨sg35329,True.intro,True.intro⟩,True.intro⟩,⟨sg35333,⟨sg35332,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35337,⟨sg35336,⟨sg35335,True.intro,True.intro⟩,True.intro⟩,⟨sg35338,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_298All : degreeTree62_298.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35317,degreeTree62_296All,degreeTree62_297All⟩ + +lemma degreeTree62_299All : degreeTree62_299.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35295,degreeTree62_295All,degreeTree62_298All⟩ + +lemma degreeTree62_300All : degreeTree62_300.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35251,degreeTree62_292All,degreeTree62_299All⟩ + +lemma degreeTree62_301All : degreeTree62_301.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35350,⟨sg35345,⟨sg35342,⟨sg35341,⟨sg35340,True.intro,True.intro⟩,True.intro⟩,⟨sg35344,⟨sg35343,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35348,⟨sg35347,⟨sg35346,True.intro,True.intro⟩,True.intro⟩,⟨sg35349,True.intro,True.intro⟩⟩⟩,⟨sg35356,⟨sg35353,⟨sg35352,⟨sg35351,True.intro,True.intro⟩,True.intro⟩,⟨sg35355,⟨sg35354,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35359,⟨sg35358,⟨sg35357,True.intro,True.intro⟩,True.intro⟩,⟨sg35360,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_302All : degreeTree62_302.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35372,⟨sg35367,⟨sg35364,⟨sg35363,⟨sg35362,True.intro,True.intro⟩,True.intro⟩,⟨sg35366,⟨sg35365,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35370,⟨sg35369,⟨sg35368,True.intro,True.intro⟩,True.intro⟩,⟨sg35371,True.intro,True.intro⟩⟩⟩,⟨sg35378,⟨sg35375,⟨sg35374,⟨sg35373,True.intro,True.intro⟩,True.intro⟩,⟨sg35377,⟨sg35376,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35381,⟨sg35380,⟨sg35379,True.intro,True.intro⟩,True.intro⟩,⟨sg35382,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_303All : degreeTree62_303.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35361,degreeTree62_301All,degreeTree62_302All⟩ + +lemma degreeTree62_304All : degreeTree62_304.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35394,⟨sg35389,⟨sg35386,⟨sg35385,⟨sg35384,True.intro,True.intro⟩,True.intro⟩,⟨sg35388,⟨sg35387,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35392,⟨sg35391,⟨sg35390,True.intro,True.intro⟩,True.intro⟩,⟨sg35393,True.intro,True.intro⟩⟩⟩,⟨sg35400,⟨sg35397,⟨sg35396,⟨sg35395,True.intro,True.intro⟩,True.intro⟩,⟨sg35399,⟨sg35398,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35403,⟨sg35402,⟨sg35401,True.intro,True.intro⟩,True.intro⟩,⟨sg35404,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_305All : degreeTree62_305.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35416,⟨sg35411,⟨sg35408,⟨sg35407,⟨sg35406,True.intro,True.intro⟩,True.intro⟩,⟨sg35410,⟨sg35409,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35414,⟨sg35413,⟨sg35412,True.intro,True.intro⟩,True.intro⟩,⟨sg35415,True.intro,True.intro⟩⟩⟩,⟨sg35422,⟨sg35419,⟨sg35418,⟨sg35417,True.intro,True.intro⟩,True.intro⟩,⟨sg35421,⟨sg35420,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35425,⟨sg35424,⟨sg35423,True.intro,True.intro⟩,True.intro⟩,⟨sg35426,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_306All : degreeTree62_306.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35405,degreeTree62_304All,degreeTree62_305All⟩ + +lemma degreeTree62_307All : degreeTree62_307.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35383,degreeTree62_303All,degreeTree62_306All⟩ + +lemma degreeTree62_308All : degreeTree62_308.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35438,⟨sg35433,⟨sg35430,⟨sg35429,⟨sg35428,True.intro,True.intro⟩,True.intro⟩,⟨sg35432,⟨sg35431,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35436,⟨sg35435,⟨sg35434,True.intro,True.intro⟩,True.intro⟩,⟨sg35437,True.intro,True.intro⟩⟩⟩,⟨sg35444,⟨sg35441,⟨sg35440,⟨sg35439,True.intro,True.intro⟩,True.intro⟩,⟨sg35443,⟨sg35442,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35447,⟨sg35446,⟨sg35445,True.intro,True.intro⟩,True.intro⟩,⟨sg35448,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_309All : degreeTree62_309.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35460,⟨sg35455,⟨sg35452,⟨sg35451,⟨sg35450,True.intro,True.intro⟩,True.intro⟩,⟨sg35454,⟨sg35453,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35458,⟨sg35457,⟨sg35456,True.intro,True.intro⟩,True.intro⟩,⟨sg35459,True.intro,True.intro⟩⟩⟩,⟨sg35466,⟨sg35463,⟨sg35462,⟨sg35461,True.intro,True.intro⟩,True.intro⟩,⟨sg35465,⟨sg35464,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35469,⟨sg35468,⟨sg35467,True.intro,True.intro⟩,True.intro⟩,⟨sg35470,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_310All : degreeTree62_310.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35449,degreeTree62_308All,degreeTree62_309All⟩ + +lemma degreeTree62_311All : degreeTree62_311.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35482,⟨sg35477,⟨sg35474,⟨sg35473,⟨sg35472,True.intro,True.intro⟩,True.intro⟩,⟨sg35476,⟨sg35475,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35480,⟨sg35479,⟨sg35478,True.intro,True.intro⟩,True.intro⟩,⟨sg35481,True.intro,True.intro⟩⟩⟩,⟨sg35488,⟨sg35485,⟨sg35484,⟨sg35483,True.intro,True.intro⟩,True.intro⟩,⟨sg35487,⟨sg35486,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35491,⟨sg35490,⟨sg35489,True.intro,True.intro⟩,True.intro⟩,⟨sg35492,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_312All : degreeTree62_312.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35504,⟨sg35499,⟨sg35496,⟨sg35495,⟨sg35494,True.intro,True.intro⟩,True.intro⟩,⟨sg35498,⟨sg35497,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35502,⟨sg35501,⟨sg35500,True.intro,True.intro⟩,True.intro⟩,⟨sg35503,True.intro,True.intro⟩⟩⟩,⟨sg35509,⟨sg35507,⟨sg35506,⟨sg35505,True.intro,True.intro⟩,True.intro⟩,⟨sg35508,True.intro,True.intro⟩⟩,⟨sg35512,⟨sg35511,⟨sg35510,True.intro,True.intro⟩,True.intro⟩,⟨sg35513,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_313All : degreeTree62_313.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35493,degreeTree62_311All,degreeTree62_312All⟩ + +lemma degreeTree62_314All : degreeTree62_314.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35471,degreeTree62_310All,degreeTree62_313All⟩ + +lemma degreeTree62_315All : degreeTree62_315.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35427,degreeTree62_307All,degreeTree62_314All⟩ + +lemma degreeTree62_316All : degreeTree62_316.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35339,degreeTree62_300All,degreeTree62_315All⟩ + +lemma degreeTree62_317All : degreeTree62_317.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35163,degreeTree62_285All,degreeTree62_316All⟩ + +lemma degreeTree62_318All : degreeTree62_318.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35525,⟨sg35520,⟨sg35517,⟨sg35516,⟨sg35515,True.intro,True.intro⟩,True.intro⟩,⟨sg35519,⟨sg35518,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35523,⟨sg35522,⟨sg35521,True.intro,True.intro⟩,True.intro⟩,⟨sg35524,True.intro,True.intro⟩⟩⟩,⟨sg35531,⟨sg35528,⟨sg35527,⟨sg35526,True.intro,True.intro⟩,True.intro⟩,⟨sg35530,⟨sg35529,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35534,⟨sg35533,⟨sg35532,True.intro,True.intro⟩,True.intro⟩,⟨sg35535,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_319All : degreeTree62_319.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35547,⟨sg35542,⟨sg35539,⟨sg35538,⟨sg35537,True.intro,True.intro⟩,True.intro⟩,⟨sg35541,⟨sg35540,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35545,⟨sg35544,⟨sg35543,True.intro,True.intro⟩,True.intro⟩,⟨sg35546,True.intro,True.intro⟩⟩⟩,⟨sg35553,⟨sg35550,⟨sg35549,⟨sg35548,True.intro,True.intro⟩,True.intro⟩,⟨sg35552,⟨sg35551,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35556,⟨sg35555,⟨sg35554,True.intro,True.intro⟩,True.intro⟩,⟨sg35557,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_320All : degreeTree62_320.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35536,degreeTree62_318All,degreeTree62_319All⟩ + +lemma degreeTree62_321All : degreeTree62_321.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35569,⟨sg35564,⟨sg35561,⟨sg35560,⟨sg35559,True.intro,True.intro⟩,True.intro⟩,⟨sg35563,⟨sg35562,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35567,⟨sg35566,⟨sg35565,True.intro,True.intro⟩,True.intro⟩,⟨sg35568,True.intro,True.intro⟩⟩⟩,⟨sg35575,⟨sg35572,⟨sg35571,⟨sg35570,True.intro,True.intro⟩,True.intro⟩,⟨sg35574,⟨sg35573,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35578,⟨sg35577,⟨sg35576,True.intro,True.intro⟩,True.intro⟩,⟨sg35579,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_322All : degreeTree62_322.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35591,⟨sg35586,⟨sg35583,⟨sg35582,⟨sg35581,True.intro,True.intro⟩,True.intro⟩,⟨sg35585,⟨sg35584,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35589,⟨sg35588,⟨sg35587,True.intro,True.intro⟩,True.intro⟩,⟨sg35590,True.intro,True.intro⟩⟩⟩,⟨sg35597,⟨sg35594,⟨sg35593,⟨sg35592,True.intro,True.intro⟩,True.intro⟩,⟨sg35596,⟨sg35595,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35600,⟨sg35599,⟨sg35598,True.intro,True.intro⟩,True.intro⟩,⟨sg35601,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_323All : degreeTree62_323.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35580,degreeTree62_321All,degreeTree62_322All⟩ + +lemma degreeTree62_324All : degreeTree62_324.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35558,degreeTree62_320All,degreeTree62_323All⟩ + +lemma degreeTree62_325All : degreeTree62_325.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35613,⟨sg35608,⟨sg35605,⟨sg35604,⟨sg35603,True.intro,True.intro⟩,True.intro⟩,⟨sg35607,⟨sg35606,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35611,⟨sg35610,⟨sg35609,True.intro,True.intro⟩,True.intro⟩,⟨sg35612,True.intro,True.intro⟩⟩⟩,⟨sg35619,⟨sg35616,⟨sg35615,⟨sg35614,True.intro,True.intro⟩,True.intro⟩,⟨sg35618,⟨sg35617,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35622,⟨sg35621,⟨sg35620,True.intro,True.intro⟩,True.intro⟩,⟨sg35623,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_326All : degreeTree62_326.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35635,⟨sg35630,⟨sg35627,⟨sg35626,⟨sg35625,True.intro,True.intro⟩,True.intro⟩,⟨sg35629,⟨sg35628,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35633,⟨sg35632,⟨sg35631,True.intro,True.intro⟩,True.intro⟩,⟨sg35634,True.intro,True.intro⟩⟩⟩,⟨sg35641,⟨sg35638,⟨sg35637,⟨sg35636,True.intro,True.intro⟩,True.intro⟩,⟨sg35640,⟨sg35639,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35644,⟨sg35643,⟨sg35642,True.intro,True.intro⟩,True.intro⟩,⟨sg35645,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_327All : degreeTree62_327.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35624,degreeTree62_325All,degreeTree62_326All⟩ + +lemma degreeTree62_328All : degreeTree62_328.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35657,⟨sg35652,⟨sg35649,⟨sg35648,⟨sg35647,True.intro,True.intro⟩,True.intro⟩,⟨sg35651,⟨sg35650,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35655,⟨sg35654,⟨sg35653,True.intro,True.intro⟩,True.intro⟩,⟨sg35656,True.intro,True.intro⟩⟩⟩,⟨sg35663,⟨sg35660,⟨sg35659,⟨sg35658,True.intro,True.intro⟩,True.intro⟩,⟨sg35662,⟨sg35661,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35666,⟨sg35665,⟨sg35664,True.intro,True.intro⟩,True.intro⟩,⟨sg35667,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_329All : degreeTree62_329.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35679,⟨sg35674,⟨sg35671,⟨sg35670,⟨sg35669,True.intro,True.intro⟩,True.intro⟩,⟨sg35673,⟨sg35672,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35677,⟨sg35676,⟨sg35675,True.intro,True.intro⟩,True.intro⟩,⟨sg35678,True.intro,True.intro⟩⟩⟩,⟨sg35685,⟨sg35682,⟨sg35681,⟨sg35680,True.intro,True.intro⟩,True.intro⟩,⟨sg35684,⟨sg35683,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35688,⟨sg35687,⟨sg35686,True.intro,True.intro⟩,True.intro⟩,⟨sg35689,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_330All : degreeTree62_330.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35668,degreeTree62_328All,degreeTree62_329All⟩ + +lemma degreeTree62_331All : degreeTree62_331.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35646,degreeTree62_327All,degreeTree62_330All⟩ + +lemma degreeTree62_332All : degreeTree62_332.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35602,degreeTree62_324All,degreeTree62_331All⟩ + +lemma degreeTree62_333All : degreeTree62_333.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35701,⟨sg35696,⟨sg35693,⟨sg35692,⟨sg35691,True.intro,True.intro⟩,True.intro⟩,⟨sg35695,⟨sg35694,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35699,⟨sg35698,⟨sg35697,True.intro,True.intro⟩,True.intro⟩,⟨sg35700,True.intro,True.intro⟩⟩⟩,⟨sg35707,⟨sg35704,⟨sg35703,⟨sg35702,True.intro,True.intro⟩,True.intro⟩,⟨sg35706,⟨sg35705,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35710,⟨sg35709,⟨sg35708,True.intro,True.intro⟩,True.intro⟩,⟨sg35711,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_334All : degreeTree62_334.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35723,⟨sg35718,⟨sg35715,⟨sg35714,⟨sg35713,True.intro,True.intro⟩,True.intro⟩,⟨sg35717,⟨sg35716,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35721,⟨sg35720,⟨sg35719,True.intro,True.intro⟩,True.intro⟩,⟨sg35722,True.intro,True.intro⟩⟩⟩,⟨sg35729,⟨sg35726,⟨sg35725,⟨sg35724,True.intro,True.intro⟩,True.intro⟩,⟨sg35728,⟨sg35727,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35732,⟨sg35731,⟨sg35730,True.intro,True.intro⟩,True.intro⟩,⟨sg35733,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_335All : degreeTree62_335.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35712,degreeTree62_333All,degreeTree62_334All⟩ + +lemma degreeTree62_336All : degreeTree62_336.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35745,⟨sg35740,⟨sg35737,⟨sg35736,⟨sg35735,True.intro,True.intro⟩,True.intro⟩,⟨sg35739,⟨sg35738,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35743,⟨sg35742,⟨sg35741,True.intro,True.intro⟩,True.intro⟩,⟨sg35744,True.intro,True.intro⟩⟩⟩,⟨sg35751,⟨sg35748,⟨sg35747,⟨sg35746,True.intro,True.intro⟩,True.intro⟩,⟨sg35750,⟨sg35749,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35754,⟨sg35753,⟨sg35752,True.intro,True.intro⟩,True.intro⟩,⟨sg35755,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_337All : degreeTree62_337.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35767,⟨sg35762,⟨sg35759,⟨sg35758,⟨sg35757,True.intro,True.intro⟩,True.intro⟩,⟨sg35761,⟨sg35760,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35765,⟨sg35764,⟨sg35763,True.intro,True.intro⟩,True.intro⟩,⟨sg35766,True.intro,True.intro⟩⟩⟩,⟨sg35773,⟨sg35770,⟨sg35769,⟨sg35768,True.intro,True.intro⟩,True.intro⟩,⟨sg35772,⟨sg35771,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35776,⟨sg35775,⟨sg35774,True.intro,True.intro⟩,True.intro⟩,⟨sg35777,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_338All : degreeTree62_338.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35756,degreeTree62_336All,degreeTree62_337All⟩ + +lemma degreeTree62_339All : degreeTree62_339.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35734,degreeTree62_335All,degreeTree62_338All⟩ + +lemma degreeTree62_340All : degreeTree62_340.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35789,⟨sg35784,⟨sg35781,⟨sg35780,⟨sg35779,True.intro,True.intro⟩,True.intro⟩,⟨sg35783,⟨sg35782,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35787,⟨sg35786,⟨sg35785,True.intro,True.intro⟩,True.intro⟩,⟨sg35788,True.intro,True.intro⟩⟩⟩,⟨sg35795,⟨sg35792,⟨sg35791,⟨sg35790,True.intro,True.intro⟩,True.intro⟩,⟨sg35794,⟨sg35793,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35798,⟨sg35797,⟨sg35796,True.intro,True.intro⟩,True.intro⟩,⟨sg35799,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_341All : degreeTree62_341.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35811,⟨sg35806,⟨sg35803,⟨sg35802,⟨sg35801,True.intro,True.intro⟩,True.intro⟩,⟨sg35805,⟨sg35804,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35809,⟨sg35808,⟨sg35807,True.intro,True.intro⟩,True.intro⟩,⟨sg35810,True.intro,True.intro⟩⟩⟩,⟨sg35817,⟨sg35814,⟨sg35813,⟨sg35812,True.intro,True.intro⟩,True.intro⟩,⟨sg35816,⟨sg35815,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35820,⟨sg35819,⟨sg35818,True.intro,True.intro⟩,True.intro⟩,⟨sg35821,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_342All : degreeTree62_342.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35800,degreeTree62_340All,degreeTree62_341All⟩ + +lemma degreeTree62_343All : degreeTree62_343.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35833,⟨sg35828,⟨sg35825,⟨sg35824,⟨sg35823,True.intro,True.intro⟩,True.intro⟩,⟨sg35827,⟨sg35826,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35831,⟨sg35830,⟨sg35829,True.intro,True.intro⟩,True.intro⟩,⟨sg35832,True.intro,True.intro⟩⟩⟩,⟨sg35839,⟨sg35836,⟨sg35835,⟨sg35834,True.intro,True.intro⟩,True.intro⟩,⟨sg35838,⟨sg35837,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35842,⟨sg35841,⟨sg35840,True.intro,True.intro⟩,True.intro⟩,⟨sg35843,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_344All : degreeTree62_344.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35855,⟨sg35850,⟨sg35847,⟨sg35846,⟨sg35845,True.intro,True.intro⟩,True.intro⟩,⟨sg35849,⟨sg35848,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35853,⟨sg35852,⟨sg35851,True.intro,True.intro⟩,True.intro⟩,⟨sg35854,True.intro,True.intro⟩⟩⟩,⟨sg35860,⟨sg35858,⟨sg35857,⟨sg35856,True.intro,True.intro⟩,True.intro⟩,⟨sg35859,True.intro,True.intro⟩⟩,⟨sg35863,⟨sg35862,⟨sg35861,True.intro,True.intro⟩,True.intro⟩,⟨sg35864,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_345All : degreeTree62_345.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35844,degreeTree62_343All,degreeTree62_344All⟩ + +lemma degreeTree62_346All : degreeTree62_346.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35822,degreeTree62_342All,degreeTree62_345All⟩ + +lemma degreeTree62_347All : degreeTree62_347.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35778,degreeTree62_339All,degreeTree62_346All⟩ + +lemma degreeTree62_348All : degreeTree62_348.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35690,degreeTree62_332All,degreeTree62_347All⟩ + +lemma degreeTree62_349All : degreeTree62_349.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35876,⟨sg35871,⟨sg35868,⟨sg35867,⟨sg35866,True.intro,True.intro⟩,True.intro⟩,⟨sg35870,⟨sg35869,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35874,⟨sg35873,⟨sg35872,True.intro,True.intro⟩,True.intro⟩,⟨sg35875,True.intro,True.intro⟩⟩⟩,⟨sg35882,⟨sg35879,⟨sg35878,⟨sg35877,True.intro,True.intro⟩,True.intro⟩,⟨sg35881,⟨sg35880,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35885,⟨sg35884,⟨sg35883,True.intro,True.intro⟩,True.intro⟩,⟨sg35886,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_350All : degreeTree62_350.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35898,⟨sg35893,⟨sg35890,⟨sg35889,⟨sg35888,True.intro,True.intro⟩,True.intro⟩,⟨sg35892,⟨sg35891,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35896,⟨sg35895,⟨sg35894,True.intro,True.intro⟩,True.intro⟩,⟨sg35897,True.intro,True.intro⟩⟩⟩,⟨sg35904,⟨sg35901,⟨sg35900,⟨sg35899,True.intro,True.intro⟩,True.intro⟩,⟨sg35903,⟨sg35902,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35907,⟨sg35906,⟨sg35905,True.intro,True.intro⟩,True.intro⟩,⟨sg35908,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_351All : degreeTree62_351.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35887,degreeTree62_349All,degreeTree62_350All⟩ + +lemma degreeTree62_352All : degreeTree62_352.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35920,⟨sg35915,⟨sg35912,⟨sg35911,⟨sg35910,True.intro,True.intro⟩,True.intro⟩,⟨sg35914,⟨sg35913,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35918,⟨sg35917,⟨sg35916,True.intro,True.intro⟩,True.intro⟩,⟨sg35919,True.intro,True.intro⟩⟩⟩,⟨sg35926,⟨sg35923,⟨sg35922,⟨sg35921,True.intro,True.intro⟩,True.intro⟩,⟨sg35925,⟨sg35924,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35929,⟨sg35928,⟨sg35927,True.intro,True.intro⟩,True.intro⟩,⟨sg35930,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_353All : degreeTree62_353.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35942,⟨sg35937,⟨sg35934,⟨sg35933,⟨sg35932,True.intro,True.intro⟩,True.intro⟩,⟨sg35936,⟨sg35935,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35940,⟨sg35939,⟨sg35938,True.intro,True.intro⟩,True.intro⟩,⟨sg35941,True.intro,True.intro⟩⟩⟩,⟨sg35948,⟨sg35945,⟨sg35944,⟨sg35943,True.intro,True.intro⟩,True.intro⟩,⟨sg35947,⟨sg35946,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35951,⟨sg35950,⟨sg35949,True.intro,True.intro⟩,True.intro⟩,⟨sg35952,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_354All : degreeTree62_354.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35931,degreeTree62_352All,degreeTree62_353All⟩ + +lemma degreeTree62_355All : degreeTree62_355.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35909,degreeTree62_351All,degreeTree62_354All⟩ + +lemma degreeTree62_356All : degreeTree62_356.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35964,⟨sg35959,⟨sg35956,⟨sg35955,⟨sg35954,True.intro,True.intro⟩,True.intro⟩,⟨sg35958,⟨sg35957,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35962,⟨sg35961,⟨sg35960,True.intro,True.intro⟩,True.intro⟩,⟨sg35963,True.intro,True.intro⟩⟩⟩,⟨sg35970,⟨sg35967,⟨sg35966,⟨sg35965,True.intro,True.intro⟩,True.intro⟩,⟨sg35969,⟨sg35968,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35973,⟨sg35972,⟨sg35971,True.intro,True.intro⟩,True.intro⟩,⟨sg35974,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_357All : degreeTree62_357.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35986,⟨sg35981,⟨sg35978,⟨sg35977,⟨sg35976,True.intro,True.intro⟩,True.intro⟩,⟨sg35980,⟨sg35979,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35984,⟨sg35983,⟨sg35982,True.intro,True.intro⟩,True.intro⟩,⟨sg35985,True.intro,True.intro⟩⟩⟩,⟨sg35992,⟨sg35989,⟨sg35988,⟨sg35987,True.intro,True.intro⟩,True.intro⟩,⟨sg35991,⟨sg35990,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg35995,⟨sg35994,⟨sg35993,True.intro,True.intro⟩,True.intro⟩,⟨sg35996,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_358All : degreeTree62_358.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35975,degreeTree62_356All,degreeTree62_357All⟩ + +lemma degreeTree62_359All : degreeTree62_359.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36008,⟨sg36003,⟨sg36000,⟨sg35999,⟨sg35998,True.intro,True.intro⟩,True.intro⟩,⟨sg36002,⟨sg36001,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36006,⟨sg36005,⟨sg36004,True.intro,True.intro⟩,True.intro⟩,⟨sg36007,True.intro,True.intro⟩⟩⟩,⟨sg36014,⟨sg36011,⟨sg36010,⟨sg36009,True.intro,True.intro⟩,True.intro⟩,⟨sg36013,⟨sg36012,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36017,⟨sg36016,⟨sg36015,True.intro,True.intro⟩,True.intro⟩,⟨sg36018,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_360All : degreeTree62_360.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36030,⟨sg36025,⟨sg36022,⟨sg36021,⟨sg36020,True.intro,True.intro⟩,True.intro⟩,⟨sg36024,⟨sg36023,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36028,⟨sg36027,⟨sg36026,True.intro,True.intro⟩,True.intro⟩,⟨sg36029,True.intro,True.intro⟩⟩⟩,⟨sg36036,⟨sg36033,⟨sg36032,⟨sg36031,True.intro,True.intro⟩,True.intro⟩,⟨sg36035,⟨sg36034,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36039,⟨sg36038,⟨sg36037,True.intro,True.intro⟩,True.intro⟩,⟨sg36040,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_361All : degreeTree62_361.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36019,degreeTree62_359All,degreeTree62_360All⟩ + +lemma degreeTree62_362All : degreeTree62_362.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35997,degreeTree62_358All,degreeTree62_361All⟩ + +lemma degreeTree62_363All : degreeTree62_363.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35953,degreeTree62_355All,degreeTree62_362All⟩ + +lemma degreeTree62_364All : degreeTree62_364.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36052,⟨sg36047,⟨sg36044,⟨sg36043,⟨sg36042,True.intro,True.intro⟩,True.intro⟩,⟨sg36046,⟨sg36045,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36050,⟨sg36049,⟨sg36048,True.intro,True.intro⟩,True.intro⟩,⟨sg36051,True.intro,True.intro⟩⟩⟩,⟨sg36058,⟨sg36055,⟨sg36054,⟨sg36053,True.intro,True.intro⟩,True.intro⟩,⟨sg36057,⟨sg36056,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36061,⟨sg36060,⟨sg36059,True.intro,True.intro⟩,True.intro⟩,⟨sg36062,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_365All : degreeTree62_365.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36074,⟨sg36069,⟨sg36066,⟨sg36065,⟨sg36064,True.intro,True.intro⟩,True.intro⟩,⟨sg36068,⟨sg36067,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36072,⟨sg36071,⟨sg36070,True.intro,True.intro⟩,True.intro⟩,⟨sg36073,True.intro,True.intro⟩⟩⟩,⟨sg36080,⟨sg36077,⟨sg36076,⟨sg36075,True.intro,True.intro⟩,True.intro⟩,⟨sg36079,⟨sg36078,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36083,⟨sg36082,⟨sg36081,True.intro,True.intro⟩,True.intro⟩,⟨sg36084,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_366All : degreeTree62_366.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36063,degreeTree62_364All,degreeTree62_365All⟩ + +lemma degreeTree62_367All : degreeTree62_367.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36096,⟨sg36091,⟨sg36088,⟨sg36087,⟨sg36086,True.intro,True.intro⟩,True.intro⟩,⟨sg36090,⟨sg36089,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36094,⟨sg36093,⟨sg36092,True.intro,True.intro⟩,True.intro⟩,⟨sg36095,True.intro,True.intro⟩⟩⟩,⟨sg36102,⟨sg36099,⟨sg36098,⟨sg36097,True.intro,True.intro⟩,True.intro⟩,⟨sg36101,⟨sg36100,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36105,⟨sg36104,⟨sg36103,True.intro,True.intro⟩,True.intro⟩,⟨sg36106,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_368All : degreeTree62_368.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36118,⟨sg36113,⟨sg36110,⟨sg36109,⟨sg36108,True.intro,True.intro⟩,True.intro⟩,⟨sg36112,⟨sg36111,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36116,⟨sg36115,⟨sg36114,True.intro,True.intro⟩,True.intro⟩,⟨sg36117,True.intro,True.intro⟩⟩⟩,⟨sg36124,⟨sg36121,⟨sg36120,⟨sg36119,True.intro,True.intro⟩,True.intro⟩,⟨sg36123,⟨sg36122,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36127,⟨sg36126,⟨sg36125,True.intro,True.intro⟩,True.intro⟩,⟨sg36128,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_369All : degreeTree62_369.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36107,degreeTree62_367All,degreeTree62_368All⟩ + +lemma degreeTree62_370All : degreeTree62_370.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36085,degreeTree62_366All,degreeTree62_369All⟩ + +lemma degreeTree62_371All : degreeTree62_371.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36140,⟨sg36135,⟨sg36132,⟨sg36131,⟨sg36130,True.intro,True.intro⟩,True.intro⟩,⟨sg36134,⟨sg36133,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36138,⟨sg36137,⟨sg36136,True.intro,True.intro⟩,True.intro⟩,⟨sg36139,True.intro,True.intro⟩⟩⟩,⟨sg36146,⟨sg36143,⟨sg36142,⟨sg36141,True.intro,True.intro⟩,True.intro⟩,⟨sg36145,⟨sg36144,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36149,⟨sg36148,⟨sg36147,True.intro,True.intro⟩,True.intro⟩,⟨sg36150,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_372All : degreeTree62_372.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36162,⟨sg36157,⟨sg36154,⟨sg36153,⟨sg36152,True.intro,True.intro⟩,True.intro⟩,⟨sg36156,⟨sg36155,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36160,⟨sg36159,⟨sg36158,True.intro,True.intro⟩,True.intro⟩,⟨sg36161,True.intro,True.intro⟩⟩⟩,⟨sg36168,⟨sg36165,⟨sg36164,⟨sg36163,True.intro,True.intro⟩,True.intro⟩,⟨sg36167,⟨sg36166,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36171,⟨sg36170,⟨sg36169,True.intro,True.intro⟩,True.intro⟩,⟨sg36172,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_373All : degreeTree62_373.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36151,degreeTree62_371All,degreeTree62_372All⟩ + +lemma degreeTree62_374All : degreeTree62_374.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36184,⟨sg36179,⟨sg36176,⟨sg36175,⟨sg36174,True.intro,True.intro⟩,True.intro⟩,⟨sg36178,⟨sg36177,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36182,⟨sg36181,⟨sg36180,True.intro,True.intro⟩,True.intro⟩,⟨sg36183,True.intro,True.intro⟩⟩⟩,⟨sg36190,⟨sg36187,⟨sg36186,⟨sg36185,True.intro,True.intro⟩,True.intro⟩,⟨sg36189,⟨sg36188,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36193,⟨sg36192,⟨sg36191,True.intro,True.intro⟩,True.intro⟩,⟨sg36194,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_375All : degreeTree62_375.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36206,⟨sg36201,⟨sg36198,⟨sg36197,⟨sg36196,True.intro,True.intro⟩,True.intro⟩,⟨sg36200,⟨sg36199,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36204,⟨sg36203,⟨sg36202,True.intro,True.intro⟩,True.intro⟩,⟨sg36205,True.intro,True.intro⟩⟩⟩,⟨sg36211,⟨sg36209,⟨sg36208,⟨sg36207,True.intro,True.intro⟩,True.intro⟩,⟨sg36210,True.intro,True.intro⟩⟩,⟨sg36214,⟨sg36213,⟨sg36212,True.intro,True.intro⟩,True.intro⟩,⟨sg36215,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_376All : degreeTree62_376.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36195,degreeTree62_374All,degreeTree62_375All⟩ + +lemma degreeTree62_377All : degreeTree62_377.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36173,degreeTree62_373All,degreeTree62_376All⟩ + +lemma degreeTree62_378All : degreeTree62_378.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36129,degreeTree62_370All,degreeTree62_377All⟩ + +lemma degreeTree62_379All : degreeTree62_379.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36041,degreeTree62_363All,degreeTree62_378All⟩ + +lemma degreeTree62_380All : degreeTree62_380.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35865,degreeTree62_348All,degreeTree62_379All⟩ + +lemma degreeTree62_381All : degreeTree62_381.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg35514,degreeTree62_317All,degreeTree62_380All⟩ + +lemma degreeTree62_382All : degreeTree62_382.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36227,⟨sg36222,⟨sg36219,⟨sg36218,⟨sg36217,True.intro,True.intro⟩,True.intro⟩,⟨sg36221,⟨sg36220,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36225,⟨sg36224,⟨sg36223,True.intro,True.intro⟩,True.intro⟩,⟨sg36226,True.intro,True.intro⟩⟩⟩,⟨sg36233,⟨sg36230,⟨sg36229,⟨sg36228,True.intro,True.intro⟩,True.intro⟩,⟨sg36232,⟨sg36231,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36236,⟨sg36235,⟨sg36234,True.intro,True.intro⟩,True.intro⟩,⟨sg36237,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_383All : degreeTree62_383.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36249,⟨sg36244,⟨sg36241,⟨sg36240,⟨sg36239,True.intro,True.intro⟩,True.intro⟩,⟨sg36243,⟨sg36242,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36247,⟨sg36246,⟨sg36245,True.intro,True.intro⟩,True.intro⟩,⟨sg36248,True.intro,True.intro⟩⟩⟩,⟨sg36255,⟨sg36252,⟨sg36251,⟨sg36250,True.intro,True.intro⟩,True.intro⟩,⟨sg36254,⟨sg36253,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36258,⟨sg36257,⟨sg36256,True.intro,True.intro⟩,True.intro⟩,⟨sg36259,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_384All : degreeTree62_384.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36238,degreeTree62_382All,degreeTree62_383All⟩ + +lemma degreeTree62_385All : degreeTree62_385.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36271,⟨sg36266,⟨sg36263,⟨sg36262,⟨sg36261,True.intro,True.intro⟩,True.intro⟩,⟨sg36265,⟨sg36264,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36269,⟨sg36268,⟨sg36267,True.intro,True.intro⟩,True.intro⟩,⟨sg36270,True.intro,True.intro⟩⟩⟩,⟨sg36277,⟨sg36274,⟨sg36273,⟨sg36272,True.intro,True.intro⟩,True.intro⟩,⟨sg36276,⟨sg36275,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36280,⟨sg36279,⟨sg36278,True.intro,True.intro⟩,True.intro⟩,⟨sg36281,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_386All : degreeTree62_386.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36293,⟨sg36288,⟨sg36285,⟨sg36284,⟨sg36283,True.intro,True.intro⟩,True.intro⟩,⟨sg36287,⟨sg36286,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36291,⟨sg36290,⟨sg36289,True.intro,True.intro⟩,True.intro⟩,⟨sg36292,True.intro,True.intro⟩⟩⟩,⟨sg36299,⟨sg36296,⟨sg36295,⟨sg36294,True.intro,True.intro⟩,True.intro⟩,⟨sg36298,⟨sg36297,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36302,⟨sg36301,⟨sg36300,True.intro,True.intro⟩,True.intro⟩,⟨sg36303,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_387All : degreeTree62_387.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36282,degreeTree62_385All,degreeTree62_386All⟩ + +lemma degreeTree62_388All : degreeTree62_388.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36260,degreeTree62_384All,degreeTree62_387All⟩ + +lemma degreeTree62_389All : degreeTree62_389.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36315,⟨sg36310,⟨sg36307,⟨sg36306,⟨sg36305,True.intro,True.intro⟩,True.intro⟩,⟨sg36309,⟨sg36308,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36313,⟨sg36312,⟨sg36311,True.intro,True.intro⟩,True.intro⟩,⟨sg36314,True.intro,True.intro⟩⟩⟩,⟨sg36321,⟨sg36318,⟨sg36317,⟨sg36316,True.intro,True.intro⟩,True.intro⟩,⟨sg36320,⟨sg36319,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36324,⟨sg36323,⟨sg36322,True.intro,True.intro⟩,True.intro⟩,⟨sg36325,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_390All : degreeTree62_390.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36337,⟨sg36332,⟨sg36329,⟨sg36328,⟨sg36327,True.intro,True.intro⟩,True.intro⟩,⟨sg36331,⟨sg36330,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36335,⟨sg36334,⟨sg36333,True.intro,True.intro⟩,True.intro⟩,⟨sg36336,True.intro,True.intro⟩⟩⟩,⟨sg36343,⟨sg36340,⟨sg36339,⟨sg36338,True.intro,True.intro⟩,True.intro⟩,⟨sg36342,⟨sg36341,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36346,⟨sg36345,⟨sg36344,True.intro,True.intro⟩,True.intro⟩,⟨sg36347,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_391All : degreeTree62_391.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36326,degreeTree62_389All,degreeTree62_390All⟩ + +lemma degreeTree62_392All : degreeTree62_392.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36359,⟨sg36354,⟨sg36351,⟨sg36350,⟨sg36349,True.intro,True.intro⟩,True.intro⟩,⟨sg36353,⟨sg36352,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36357,⟨sg36356,⟨sg36355,True.intro,True.intro⟩,True.intro⟩,⟨sg36358,True.intro,True.intro⟩⟩⟩,⟨sg36365,⟨sg36362,⟨sg36361,⟨sg36360,True.intro,True.intro⟩,True.intro⟩,⟨sg36364,⟨sg36363,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36368,⟨sg36367,⟨sg36366,True.intro,True.intro⟩,True.intro⟩,⟨sg36369,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_393All : degreeTree62_393.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36381,⟨sg36376,⟨sg36373,⟨sg36372,⟨sg36371,True.intro,True.intro⟩,True.intro⟩,⟨sg36375,⟨sg36374,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36379,⟨sg36378,⟨sg36377,True.intro,True.intro⟩,True.intro⟩,⟨sg36380,True.intro,True.intro⟩⟩⟩,⟨sg36387,⟨sg36384,⟨sg36383,⟨sg36382,True.intro,True.intro⟩,True.intro⟩,⟨sg36386,⟨sg36385,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36390,⟨sg36389,⟨sg36388,True.intro,True.intro⟩,True.intro⟩,⟨sg36391,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_394All : degreeTree62_394.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36370,degreeTree62_392All,degreeTree62_393All⟩ + +lemma degreeTree62_395All : degreeTree62_395.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36348,degreeTree62_391All,degreeTree62_394All⟩ + +lemma degreeTree62_396All : degreeTree62_396.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36304,degreeTree62_388All,degreeTree62_395All⟩ + +lemma degreeTree62_397All : degreeTree62_397.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36403,⟨sg36398,⟨sg36395,⟨sg36394,⟨sg36393,True.intro,True.intro⟩,True.intro⟩,⟨sg36397,⟨sg36396,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36401,⟨sg36400,⟨sg36399,True.intro,True.intro⟩,True.intro⟩,⟨sg36402,True.intro,True.intro⟩⟩⟩,⟨sg36409,⟨sg36406,⟨sg36405,⟨sg36404,True.intro,True.intro⟩,True.intro⟩,⟨sg36408,⟨sg36407,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36412,⟨sg36411,⟨sg36410,True.intro,True.intro⟩,True.intro⟩,⟨sg36413,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_398All : degreeTree62_398.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36425,⟨sg36420,⟨sg36417,⟨sg36416,⟨sg36415,True.intro,True.intro⟩,True.intro⟩,⟨sg36419,⟨sg36418,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36423,⟨sg36422,⟨sg36421,True.intro,True.intro⟩,True.intro⟩,⟨sg36424,True.intro,True.intro⟩⟩⟩,⟨sg36431,⟨sg36428,⟨sg36427,⟨sg36426,True.intro,True.intro⟩,True.intro⟩,⟨sg36430,⟨sg36429,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36434,⟨sg36433,⟨sg36432,True.intro,True.intro⟩,True.intro⟩,⟨sg36435,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_399All : degreeTree62_399.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36414,degreeTree62_397All,degreeTree62_398All⟩ + +lemma degreeTree62_400All : degreeTree62_400.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36447,⟨sg36442,⟨sg36439,⟨sg36438,⟨sg36437,True.intro,True.intro⟩,True.intro⟩,⟨sg36441,⟨sg36440,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36445,⟨sg36444,⟨sg36443,True.intro,True.intro⟩,True.intro⟩,⟨sg36446,True.intro,True.intro⟩⟩⟩,⟨sg36453,⟨sg36450,⟨sg36449,⟨sg36448,True.intro,True.intro⟩,True.intro⟩,⟨sg36452,⟨sg36451,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36456,⟨sg36455,⟨sg36454,True.intro,True.intro⟩,True.intro⟩,⟨sg36457,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_401All : degreeTree62_401.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36469,⟨sg36464,⟨sg36461,⟨sg36460,⟨sg36459,True.intro,True.intro⟩,True.intro⟩,⟨sg36463,⟨sg36462,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36467,⟨sg36466,⟨sg36465,True.intro,True.intro⟩,True.intro⟩,⟨sg36468,True.intro,True.intro⟩⟩⟩,⟨sg36475,⟨sg36472,⟨sg36471,⟨sg36470,True.intro,True.intro⟩,True.intro⟩,⟨sg36474,⟨sg36473,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36478,⟨sg36477,⟨sg36476,True.intro,True.intro⟩,True.intro⟩,⟨sg36479,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_402All : degreeTree62_402.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36458,degreeTree62_400All,degreeTree62_401All⟩ + +lemma degreeTree62_403All : degreeTree62_403.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36436,degreeTree62_399All,degreeTree62_402All⟩ + +lemma degreeTree62_404All : degreeTree62_404.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36491,⟨sg36486,⟨sg36483,⟨sg36482,⟨sg36481,True.intro,True.intro⟩,True.intro⟩,⟨sg36485,⟨sg36484,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36489,⟨sg36488,⟨sg36487,True.intro,True.intro⟩,True.intro⟩,⟨sg36490,True.intro,True.intro⟩⟩⟩,⟨sg36497,⟨sg36494,⟨sg36493,⟨sg36492,True.intro,True.intro⟩,True.intro⟩,⟨sg36496,⟨sg36495,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36500,⟨sg36499,⟨sg36498,True.intro,True.intro⟩,True.intro⟩,⟨sg36501,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_405All : degreeTree62_405.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36513,⟨sg36508,⟨sg36505,⟨sg36504,⟨sg36503,True.intro,True.intro⟩,True.intro⟩,⟨sg36507,⟨sg36506,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36511,⟨sg36510,⟨sg36509,True.intro,True.intro⟩,True.intro⟩,⟨sg36512,True.intro,True.intro⟩⟩⟩,⟨sg36519,⟨sg36516,⟨sg36515,⟨sg36514,True.intro,True.intro⟩,True.intro⟩,⟨sg36518,⟨sg36517,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36522,⟨sg36521,⟨sg36520,True.intro,True.intro⟩,True.intro⟩,⟨sg36523,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_406All : degreeTree62_406.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36502,degreeTree62_404All,degreeTree62_405All⟩ + +lemma degreeTree62_407All : degreeTree62_407.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36535,⟨sg36530,⟨sg36527,⟨sg36526,⟨sg36525,True.intro,True.intro⟩,True.intro⟩,⟨sg36529,⟨sg36528,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36533,⟨sg36532,⟨sg36531,True.intro,True.intro⟩,True.intro⟩,⟨sg36534,True.intro,True.intro⟩⟩⟩,⟨sg36541,⟨sg36538,⟨sg36537,⟨sg36536,True.intro,True.intro⟩,True.intro⟩,⟨sg36540,⟨sg36539,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36544,⟨sg36543,⟨sg36542,True.intro,True.intro⟩,True.intro⟩,⟨sg36545,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_408All : degreeTree62_408.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36557,⟨sg36552,⟨sg36549,⟨sg36548,⟨sg36547,True.intro,True.intro⟩,True.intro⟩,⟨sg36551,⟨sg36550,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36555,⟨sg36554,⟨sg36553,True.intro,True.intro⟩,True.intro⟩,⟨sg36556,True.intro,True.intro⟩⟩⟩,⟨sg36562,⟨sg36560,⟨sg36559,⟨sg36558,True.intro,True.intro⟩,True.intro⟩,⟨sg36561,True.intro,True.intro⟩⟩,⟨sg36565,⟨sg36564,⟨sg36563,True.intro,True.intro⟩,True.intro⟩,⟨sg36566,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_409All : degreeTree62_409.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36546,degreeTree62_407All,degreeTree62_408All⟩ + +lemma degreeTree62_410All : degreeTree62_410.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36524,degreeTree62_406All,degreeTree62_409All⟩ + +lemma degreeTree62_411All : degreeTree62_411.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36480,degreeTree62_403All,degreeTree62_410All⟩ + +lemma degreeTree62_412All : degreeTree62_412.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36392,degreeTree62_396All,degreeTree62_411All⟩ + +lemma degreeTree62_413All : degreeTree62_413.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36578,⟨sg36573,⟨sg36570,⟨sg36569,⟨sg36568,True.intro,True.intro⟩,True.intro⟩,⟨sg36572,⟨sg36571,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36576,⟨sg36575,⟨sg36574,True.intro,True.intro⟩,True.intro⟩,⟨sg36577,True.intro,True.intro⟩⟩⟩,⟨sg36584,⟨sg36581,⟨sg36580,⟨sg36579,True.intro,True.intro⟩,True.intro⟩,⟨sg36583,⟨sg36582,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36587,⟨sg36586,⟨sg36585,True.intro,True.intro⟩,True.intro⟩,⟨sg36588,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_414All : degreeTree62_414.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36600,⟨sg36595,⟨sg36592,⟨sg36591,⟨sg36590,True.intro,True.intro⟩,True.intro⟩,⟨sg36594,⟨sg36593,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36598,⟨sg36597,⟨sg36596,True.intro,True.intro⟩,True.intro⟩,⟨sg36599,True.intro,True.intro⟩⟩⟩,⟨sg36606,⟨sg36603,⟨sg36602,⟨sg36601,True.intro,True.intro⟩,True.intro⟩,⟨sg36605,⟨sg36604,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36609,⟨sg36608,⟨sg36607,True.intro,True.intro⟩,True.intro⟩,⟨sg36610,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_415All : degreeTree62_415.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36589,degreeTree62_413All,degreeTree62_414All⟩ + +lemma degreeTree62_416All : degreeTree62_416.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36622,⟨sg36617,⟨sg36614,⟨sg36613,⟨sg36612,True.intro,True.intro⟩,True.intro⟩,⟨sg36616,⟨sg36615,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36620,⟨sg36619,⟨sg36618,True.intro,True.intro⟩,True.intro⟩,⟨sg36621,True.intro,True.intro⟩⟩⟩,⟨sg36628,⟨sg36625,⟨sg36624,⟨sg36623,True.intro,True.intro⟩,True.intro⟩,⟨sg36627,⟨sg36626,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36631,⟨sg36630,⟨sg36629,True.intro,True.intro⟩,True.intro⟩,⟨sg36632,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_417All : degreeTree62_417.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36644,⟨sg36639,⟨sg36636,⟨sg36635,⟨sg36634,True.intro,True.intro⟩,True.intro⟩,⟨sg36638,⟨sg36637,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36642,⟨sg36641,⟨sg36640,True.intro,True.intro⟩,True.intro⟩,⟨sg36643,True.intro,True.intro⟩⟩⟩,⟨sg36650,⟨sg36647,⟨sg36646,⟨sg36645,True.intro,True.intro⟩,True.intro⟩,⟨sg36649,⟨sg36648,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36653,⟨sg36652,⟨sg36651,True.intro,True.intro⟩,True.intro⟩,⟨sg36654,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_418All : degreeTree62_418.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36633,degreeTree62_416All,degreeTree62_417All⟩ + +lemma degreeTree62_419All : degreeTree62_419.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36611,degreeTree62_415All,degreeTree62_418All⟩ + +lemma degreeTree62_420All : degreeTree62_420.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36666,⟨sg36661,⟨sg36658,⟨sg36657,⟨sg36656,True.intro,True.intro⟩,True.intro⟩,⟨sg36660,⟨sg36659,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36664,⟨sg36663,⟨sg36662,True.intro,True.intro⟩,True.intro⟩,⟨sg36665,True.intro,True.intro⟩⟩⟩,⟨sg36672,⟨sg36669,⟨sg36668,⟨sg36667,True.intro,True.intro⟩,True.intro⟩,⟨sg36671,⟨sg36670,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36675,⟨sg36674,⟨sg36673,True.intro,True.intro⟩,True.intro⟩,⟨sg36676,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_421All : degreeTree62_421.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36688,⟨sg36683,⟨sg36680,⟨sg36679,⟨sg36678,True.intro,True.intro⟩,True.intro⟩,⟨sg36682,⟨sg36681,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36686,⟨sg36685,⟨sg36684,True.intro,True.intro⟩,True.intro⟩,⟨sg36687,True.intro,True.intro⟩⟩⟩,⟨sg36694,⟨sg36691,⟨sg36690,⟨sg36689,True.intro,True.intro⟩,True.intro⟩,⟨sg36693,⟨sg36692,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36697,⟨sg36696,⟨sg36695,True.intro,True.intro⟩,True.intro⟩,⟨sg36698,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_422All : degreeTree62_422.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36677,degreeTree62_420All,degreeTree62_421All⟩ + +lemma degreeTree62_423All : degreeTree62_423.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36710,⟨sg36705,⟨sg36702,⟨sg36701,⟨sg36700,True.intro,True.intro⟩,True.intro⟩,⟨sg36704,⟨sg36703,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36708,⟨sg36707,⟨sg36706,True.intro,True.intro⟩,True.intro⟩,⟨sg36709,True.intro,True.intro⟩⟩⟩,⟨sg36716,⟨sg36713,⟨sg36712,⟨sg36711,True.intro,True.intro⟩,True.intro⟩,⟨sg36715,⟨sg36714,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36719,⟨sg36718,⟨sg36717,True.intro,True.intro⟩,True.intro⟩,⟨sg36720,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_424All : degreeTree62_424.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36732,⟨sg36727,⟨sg36724,⟨sg36723,⟨sg36722,True.intro,True.intro⟩,True.intro⟩,⟨sg36726,⟨sg36725,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36730,⟨sg36729,⟨sg36728,True.intro,True.intro⟩,True.intro⟩,⟨sg36731,True.intro,True.intro⟩⟩⟩,⟨sg36738,⟨sg36735,⟨sg36734,⟨sg36733,True.intro,True.intro⟩,True.intro⟩,⟨sg36737,⟨sg36736,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36741,⟨sg36740,⟨sg36739,True.intro,True.intro⟩,True.intro⟩,⟨sg36742,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_425All : degreeTree62_425.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36721,degreeTree62_423All,degreeTree62_424All⟩ + +lemma degreeTree62_426All : degreeTree62_426.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36699,degreeTree62_422All,degreeTree62_425All⟩ + +lemma degreeTree62_427All : degreeTree62_427.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36655,degreeTree62_419All,degreeTree62_426All⟩ + +lemma degreeTree62_428All : degreeTree62_428.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36754,⟨sg36749,⟨sg36746,⟨sg36745,⟨sg36744,True.intro,True.intro⟩,True.intro⟩,⟨sg36748,⟨sg36747,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36752,⟨sg36751,⟨sg36750,True.intro,True.intro⟩,True.intro⟩,⟨sg36753,True.intro,True.intro⟩⟩⟩,⟨sg36760,⟨sg36757,⟨sg36756,⟨sg36755,True.intro,True.intro⟩,True.intro⟩,⟨sg36759,⟨sg36758,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36763,⟨sg36762,⟨sg36761,True.intro,True.intro⟩,True.intro⟩,⟨sg36764,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_429All : degreeTree62_429.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36776,⟨sg36771,⟨sg36768,⟨sg36767,⟨sg36766,True.intro,True.intro⟩,True.intro⟩,⟨sg36770,⟨sg36769,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36774,⟨sg36773,⟨sg36772,True.intro,True.intro⟩,True.intro⟩,⟨sg36775,True.intro,True.intro⟩⟩⟩,⟨sg36782,⟨sg36779,⟨sg36778,⟨sg36777,True.intro,True.intro⟩,True.intro⟩,⟨sg36781,⟨sg36780,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36785,⟨sg36784,⟨sg36783,True.intro,True.intro⟩,True.intro⟩,⟨sg36786,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_430All : degreeTree62_430.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36765,degreeTree62_428All,degreeTree62_429All⟩ + +lemma degreeTree62_431All : degreeTree62_431.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36798,⟨sg36793,⟨sg36790,⟨sg36789,⟨sg36788,True.intro,True.intro⟩,True.intro⟩,⟨sg36792,⟨sg36791,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36796,⟨sg36795,⟨sg36794,True.intro,True.intro⟩,True.intro⟩,⟨sg36797,True.intro,True.intro⟩⟩⟩,⟨sg36804,⟨sg36801,⟨sg36800,⟨sg36799,True.intro,True.intro⟩,True.intro⟩,⟨sg36803,⟨sg36802,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36807,⟨sg36806,⟨sg36805,True.intro,True.intro⟩,True.intro⟩,⟨sg36808,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_432All : degreeTree62_432.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36820,⟨sg36815,⟨sg36812,⟨sg36811,⟨sg36810,True.intro,True.intro⟩,True.intro⟩,⟨sg36814,⟨sg36813,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36818,⟨sg36817,⟨sg36816,True.intro,True.intro⟩,True.intro⟩,⟨sg36819,True.intro,True.intro⟩⟩⟩,⟨sg36826,⟨sg36823,⟨sg36822,⟨sg36821,True.intro,True.intro⟩,True.intro⟩,⟨sg36825,⟨sg36824,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36829,⟨sg36828,⟨sg36827,True.intro,True.intro⟩,True.intro⟩,⟨sg36830,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_433All : degreeTree62_433.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36809,degreeTree62_431All,degreeTree62_432All⟩ + +lemma degreeTree62_434All : degreeTree62_434.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36787,degreeTree62_430All,degreeTree62_433All⟩ + +lemma degreeTree62_435All : degreeTree62_435.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36842,⟨sg36837,⟨sg36834,⟨sg36833,⟨sg36832,True.intro,True.intro⟩,True.intro⟩,⟨sg36836,⟨sg36835,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36840,⟨sg36839,⟨sg36838,True.intro,True.intro⟩,True.intro⟩,⟨sg36841,True.intro,True.intro⟩⟩⟩,⟨sg36848,⟨sg36845,⟨sg36844,⟨sg36843,True.intro,True.intro⟩,True.intro⟩,⟨sg36847,⟨sg36846,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36851,⟨sg36850,⟨sg36849,True.intro,True.intro⟩,True.intro⟩,⟨sg36852,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_436All : degreeTree62_436.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36864,⟨sg36859,⟨sg36856,⟨sg36855,⟨sg36854,True.intro,True.intro⟩,True.intro⟩,⟨sg36858,⟨sg36857,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36862,⟨sg36861,⟨sg36860,True.intro,True.intro⟩,True.intro⟩,⟨sg36863,True.intro,True.intro⟩⟩⟩,⟨sg36870,⟨sg36867,⟨sg36866,⟨sg36865,True.intro,True.intro⟩,True.intro⟩,⟨sg36869,⟨sg36868,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36873,⟨sg36872,⟨sg36871,True.intro,True.intro⟩,True.intro⟩,⟨sg36874,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_437All : degreeTree62_437.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36853,degreeTree62_435All,degreeTree62_436All⟩ + +lemma degreeTree62_438All : degreeTree62_438.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36886,⟨sg36881,⟨sg36878,⟨sg36877,⟨sg36876,True.intro,True.intro⟩,True.intro⟩,⟨sg36880,⟨sg36879,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36884,⟨sg36883,⟨sg36882,True.intro,True.intro⟩,True.intro⟩,⟨sg36885,True.intro,True.intro⟩⟩⟩,⟨sg36892,⟨sg36889,⟨sg36888,⟨sg36887,True.intro,True.intro⟩,True.intro⟩,⟨sg36891,⟨sg36890,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36895,⟨sg36894,⟨sg36893,True.intro,True.intro⟩,True.intro⟩,⟨sg36896,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_439All : degreeTree62_439.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36908,⟨sg36903,⟨sg36900,⟨sg36899,⟨sg36898,True.intro,True.intro⟩,True.intro⟩,⟨sg36902,⟨sg36901,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36906,⟨sg36905,⟨sg36904,True.intro,True.intro⟩,True.intro⟩,⟨sg36907,True.intro,True.intro⟩⟩⟩,⟨sg36913,⟨sg36911,⟨sg36910,⟨sg36909,True.intro,True.intro⟩,True.intro⟩,⟨sg36912,True.intro,True.intro⟩⟩,⟨sg36916,⟨sg36915,⟨sg36914,True.intro,True.intro⟩,True.intro⟩,⟨sg36917,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_440All : degreeTree62_440.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36897,degreeTree62_438All,degreeTree62_439All⟩ + +lemma degreeTree62_441All : degreeTree62_441.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36875,degreeTree62_437All,degreeTree62_440All⟩ + +lemma degreeTree62_442All : degreeTree62_442.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36831,degreeTree62_434All,degreeTree62_441All⟩ + +lemma degreeTree62_443All : degreeTree62_443.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36743,degreeTree62_427All,degreeTree62_442All⟩ + +lemma degreeTree62_444All : degreeTree62_444.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36567,degreeTree62_412All,degreeTree62_443All⟩ + +lemma degreeTree62_445All : degreeTree62_445.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36929,⟨sg36924,⟨sg36921,⟨sg36920,⟨sg36919,True.intro,True.intro⟩,True.intro⟩,⟨sg36923,⟨sg36922,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36927,⟨sg36926,⟨sg36925,True.intro,True.intro⟩,True.intro⟩,⟨sg36928,True.intro,True.intro⟩⟩⟩,⟨sg36935,⟨sg36932,⟨sg36931,⟨sg36930,True.intro,True.intro⟩,True.intro⟩,⟨sg36934,⟨sg36933,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36938,⟨sg36937,⟨sg36936,True.intro,True.intro⟩,True.intro⟩,⟨sg36939,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_446All : degreeTree62_446.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36951,⟨sg36946,⟨sg36943,⟨sg36942,⟨sg36941,True.intro,True.intro⟩,True.intro⟩,⟨sg36945,⟨sg36944,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36949,⟨sg36948,⟨sg36947,True.intro,True.intro⟩,True.intro⟩,⟨sg36950,True.intro,True.intro⟩⟩⟩,⟨sg36957,⟨sg36954,⟨sg36953,⟨sg36952,True.intro,True.intro⟩,True.intro⟩,⟨sg36956,⟨sg36955,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36960,⟨sg36959,⟨sg36958,True.intro,True.intro⟩,True.intro⟩,⟨sg36961,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_447All : degreeTree62_447.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36940,degreeTree62_445All,degreeTree62_446All⟩ + +lemma degreeTree62_448All : degreeTree62_448.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36973,⟨sg36968,⟨sg36965,⟨sg36964,⟨sg36963,True.intro,True.intro⟩,True.intro⟩,⟨sg36967,⟨sg36966,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36971,⟨sg36970,⟨sg36969,True.intro,True.intro⟩,True.intro⟩,⟨sg36972,True.intro,True.intro⟩⟩⟩,⟨sg36979,⟨sg36976,⟨sg36975,⟨sg36974,True.intro,True.intro⟩,True.intro⟩,⟨sg36978,⟨sg36977,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36982,⟨sg36981,⟨sg36980,True.intro,True.intro⟩,True.intro⟩,⟨sg36983,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_449All : degreeTree62_449.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36995,⟨sg36990,⟨sg36987,⟨sg36986,⟨sg36985,True.intro,True.intro⟩,True.intro⟩,⟨sg36989,⟨sg36988,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg36993,⟨sg36992,⟨sg36991,True.intro,True.intro⟩,True.intro⟩,⟨sg36994,True.intro,True.intro⟩⟩⟩,⟨sg37001,⟨sg36998,⟨sg36997,⟨sg36996,True.intro,True.intro⟩,True.intro⟩,⟨sg37000,⟨sg36999,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37004,⟨sg37003,⟨sg37002,True.intro,True.intro⟩,True.intro⟩,⟨sg37005,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_450All : degreeTree62_450.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36984,degreeTree62_448All,degreeTree62_449All⟩ + +lemma degreeTree62_451All : degreeTree62_451.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36962,degreeTree62_447All,degreeTree62_450All⟩ + +lemma degreeTree62_452All : degreeTree62_452.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37017,⟨sg37012,⟨sg37009,⟨sg37008,⟨sg37007,True.intro,True.intro⟩,True.intro⟩,⟨sg37011,⟨sg37010,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37015,⟨sg37014,⟨sg37013,True.intro,True.intro⟩,True.intro⟩,⟨sg37016,True.intro,True.intro⟩⟩⟩,⟨sg37023,⟨sg37020,⟨sg37019,⟨sg37018,True.intro,True.intro⟩,True.intro⟩,⟨sg37022,⟨sg37021,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37026,⟨sg37025,⟨sg37024,True.intro,True.intro⟩,True.intro⟩,⟨sg37027,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_453All : degreeTree62_453.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37039,⟨sg37034,⟨sg37031,⟨sg37030,⟨sg37029,True.intro,True.intro⟩,True.intro⟩,⟨sg37033,⟨sg37032,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37037,⟨sg37036,⟨sg37035,True.intro,True.intro⟩,True.intro⟩,⟨sg37038,True.intro,True.intro⟩⟩⟩,⟨sg37045,⟨sg37042,⟨sg37041,⟨sg37040,True.intro,True.intro⟩,True.intro⟩,⟨sg37044,⟨sg37043,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37048,⟨sg37047,⟨sg37046,True.intro,True.intro⟩,True.intro⟩,⟨sg37049,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_454All : degreeTree62_454.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37028,degreeTree62_452All,degreeTree62_453All⟩ + +lemma degreeTree62_455All : degreeTree62_455.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37061,⟨sg37056,⟨sg37053,⟨sg37052,⟨sg37051,True.intro,True.intro⟩,True.intro⟩,⟨sg37055,⟨sg37054,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37059,⟨sg37058,⟨sg37057,True.intro,True.intro⟩,True.intro⟩,⟨sg37060,True.intro,True.intro⟩⟩⟩,⟨sg37067,⟨sg37064,⟨sg37063,⟨sg37062,True.intro,True.intro⟩,True.intro⟩,⟨sg37066,⟨sg37065,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37070,⟨sg37069,⟨sg37068,True.intro,True.intro⟩,True.intro⟩,⟨sg37071,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_456All : degreeTree62_456.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37083,⟨sg37078,⟨sg37075,⟨sg37074,⟨sg37073,True.intro,True.intro⟩,True.intro⟩,⟨sg37077,⟨sg37076,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37081,⟨sg37080,⟨sg37079,True.intro,True.intro⟩,True.intro⟩,⟨sg37082,True.intro,True.intro⟩⟩⟩,⟨sg37089,⟨sg37086,⟨sg37085,⟨sg37084,True.intro,True.intro⟩,True.intro⟩,⟨sg37088,⟨sg37087,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37092,⟨sg37091,⟨sg37090,True.intro,True.intro⟩,True.intro⟩,⟨sg37093,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_457All : degreeTree62_457.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37072,degreeTree62_455All,degreeTree62_456All⟩ + +lemma degreeTree62_458All : degreeTree62_458.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37050,degreeTree62_454All,degreeTree62_457All⟩ + +lemma degreeTree62_459All : degreeTree62_459.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37006,degreeTree62_451All,degreeTree62_458All⟩ + +lemma degreeTree62_460All : degreeTree62_460.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37105,⟨sg37100,⟨sg37097,⟨sg37096,⟨sg37095,True.intro,True.intro⟩,True.intro⟩,⟨sg37099,⟨sg37098,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37103,⟨sg37102,⟨sg37101,True.intro,True.intro⟩,True.intro⟩,⟨sg37104,True.intro,True.intro⟩⟩⟩,⟨sg37111,⟨sg37108,⟨sg37107,⟨sg37106,True.intro,True.intro⟩,True.intro⟩,⟨sg37110,⟨sg37109,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37114,⟨sg37113,⟨sg37112,True.intro,True.intro⟩,True.intro⟩,⟨sg37115,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_461All : degreeTree62_461.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37127,⟨sg37122,⟨sg37119,⟨sg37118,⟨sg37117,True.intro,True.intro⟩,True.intro⟩,⟨sg37121,⟨sg37120,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37125,⟨sg37124,⟨sg37123,True.intro,True.intro⟩,True.intro⟩,⟨sg37126,True.intro,True.intro⟩⟩⟩,⟨sg37133,⟨sg37130,⟨sg37129,⟨sg37128,True.intro,True.intro⟩,True.intro⟩,⟨sg37132,⟨sg37131,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37136,⟨sg37135,⟨sg37134,True.intro,True.intro⟩,True.intro⟩,⟨sg37137,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_462All : degreeTree62_462.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37116,degreeTree62_460All,degreeTree62_461All⟩ + +lemma degreeTree62_463All : degreeTree62_463.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37149,⟨sg37144,⟨sg37141,⟨sg37140,⟨sg37139,True.intro,True.intro⟩,True.intro⟩,⟨sg37143,⟨sg37142,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37147,⟨sg37146,⟨sg37145,True.intro,True.intro⟩,True.intro⟩,⟨sg37148,True.intro,True.intro⟩⟩⟩,⟨sg37155,⟨sg37152,⟨sg37151,⟨sg37150,True.intro,True.intro⟩,True.intro⟩,⟨sg37154,⟨sg37153,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37158,⟨sg37157,⟨sg37156,True.intro,True.intro⟩,True.intro⟩,⟨sg37159,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_464All : degreeTree62_464.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37171,⟨sg37166,⟨sg37163,⟨sg37162,⟨sg37161,True.intro,True.intro⟩,True.intro⟩,⟨sg37165,⟨sg37164,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37169,⟨sg37168,⟨sg37167,True.intro,True.intro⟩,True.intro⟩,⟨sg37170,True.intro,True.intro⟩⟩⟩,⟨sg37177,⟨sg37174,⟨sg37173,⟨sg37172,True.intro,True.intro⟩,True.intro⟩,⟨sg37176,⟨sg37175,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37180,⟨sg37179,⟨sg37178,True.intro,True.intro⟩,True.intro⟩,⟨sg37181,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_465All : degreeTree62_465.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37160,degreeTree62_463All,degreeTree62_464All⟩ + +lemma degreeTree62_466All : degreeTree62_466.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37138,degreeTree62_462All,degreeTree62_465All⟩ + +lemma degreeTree62_467All : degreeTree62_467.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37193,⟨sg37188,⟨sg37185,⟨sg37184,⟨sg37183,True.intro,True.intro⟩,True.intro⟩,⟨sg37187,⟨sg37186,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37191,⟨sg37190,⟨sg37189,True.intro,True.intro⟩,True.intro⟩,⟨sg37192,True.intro,True.intro⟩⟩⟩,⟨sg37199,⟨sg37196,⟨sg37195,⟨sg37194,True.intro,True.intro⟩,True.intro⟩,⟨sg37198,⟨sg37197,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37202,⟨sg37201,⟨sg37200,True.intro,True.intro⟩,True.intro⟩,⟨sg37203,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_468All : degreeTree62_468.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37215,⟨sg37210,⟨sg37207,⟨sg37206,⟨sg37205,True.intro,True.intro⟩,True.intro⟩,⟨sg37209,⟨sg37208,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37213,⟨sg37212,⟨sg37211,True.intro,True.intro⟩,True.intro⟩,⟨sg37214,True.intro,True.intro⟩⟩⟩,⟨sg37221,⟨sg37218,⟨sg37217,⟨sg37216,True.intro,True.intro⟩,True.intro⟩,⟨sg37220,⟨sg37219,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37224,⟨sg37223,⟨sg37222,True.intro,True.intro⟩,True.intro⟩,⟨sg37225,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_469All : degreeTree62_469.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37204,degreeTree62_467All,degreeTree62_468All⟩ + +lemma degreeTree62_470All : degreeTree62_470.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37237,⟨sg37232,⟨sg37229,⟨sg37228,⟨sg37227,True.intro,True.intro⟩,True.intro⟩,⟨sg37231,⟨sg37230,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37235,⟨sg37234,⟨sg37233,True.intro,True.intro⟩,True.intro⟩,⟨sg37236,True.intro,True.intro⟩⟩⟩,⟨sg37243,⟨sg37240,⟨sg37239,⟨sg37238,True.intro,True.intro⟩,True.intro⟩,⟨sg37242,⟨sg37241,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37246,⟨sg37245,⟨sg37244,True.intro,True.intro⟩,True.intro⟩,⟨sg37247,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_471All : degreeTree62_471.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37259,⟨sg37254,⟨sg37251,⟨sg37250,⟨sg37249,True.intro,True.intro⟩,True.intro⟩,⟨sg37253,⟨sg37252,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37257,⟨sg37256,⟨sg37255,True.intro,True.intro⟩,True.intro⟩,⟨sg37258,True.intro,True.intro⟩⟩⟩,⟨sg37264,⟨sg37262,⟨sg37261,⟨sg37260,True.intro,True.intro⟩,True.intro⟩,⟨sg37263,True.intro,True.intro⟩⟩,⟨sg37267,⟨sg37266,⟨sg37265,True.intro,True.intro⟩,True.intro⟩,⟨sg37268,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_472All : degreeTree62_472.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37248,degreeTree62_470All,degreeTree62_471All⟩ + +lemma degreeTree62_473All : degreeTree62_473.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37226,degreeTree62_469All,degreeTree62_472All⟩ + +lemma degreeTree62_474All : degreeTree62_474.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37182,degreeTree62_466All,degreeTree62_473All⟩ + +lemma degreeTree62_475All : degreeTree62_475.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37094,degreeTree62_459All,degreeTree62_474All⟩ + +lemma degreeTree62_476All : degreeTree62_476.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37280,⟨sg37275,⟨sg37272,⟨sg37271,⟨sg37270,True.intro,True.intro⟩,True.intro⟩,⟨sg37274,⟨sg37273,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37278,⟨sg37277,⟨sg37276,True.intro,True.intro⟩,True.intro⟩,⟨sg37279,True.intro,True.intro⟩⟩⟩,⟨sg37286,⟨sg37283,⟨sg37282,⟨sg37281,True.intro,True.intro⟩,True.intro⟩,⟨sg37285,⟨sg37284,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37289,⟨sg37288,⟨sg37287,True.intro,True.intro⟩,True.intro⟩,⟨sg37290,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_477All : degreeTree62_477.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37302,⟨sg37297,⟨sg37294,⟨sg37293,⟨sg37292,True.intro,True.intro⟩,True.intro⟩,⟨sg37296,⟨sg37295,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37300,⟨sg37299,⟨sg37298,True.intro,True.intro⟩,True.intro⟩,⟨sg37301,True.intro,True.intro⟩⟩⟩,⟨sg37308,⟨sg37305,⟨sg37304,⟨sg37303,True.intro,True.intro⟩,True.intro⟩,⟨sg37307,⟨sg37306,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37311,⟨sg37310,⟨sg37309,True.intro,True.intro⟩,True.intro⟩,⟨sg37312,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_478All : degreeTree62_478.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37291,degreeTree62_476All,degreeTree62_477All⟩ + +lemma degreeTree62_479All : degreeTree62_479.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37324,⟨sg37319,⟨sg37316,⟨sg37315,⟨sg37314,True.intro,True.intro⟩,True.intro⟩,⟨sg37318,⟨sg37317,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37322,⟨sg37321,⟨sg37320,True.intro,True.intro⟩,True.intro⟩,⟨sg37323,True.intro,True.intro⟩⟩⟩,⟨sg37330,⟨sg37327,⟨sg37326,⟨sg37325,True.intro,True.intro⟩,True.intro⟩,⟨sg37329,⟨sg37328,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37333,⟨sg37332,⟨sg37331,True.intro,True.intro⟩,True.intro⟩,⟨sg37334,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_480All : degreeTree62_480.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37346,⟨sg37341,⟨sg37338,⟨sg37337,⟨sg37336,True.intro,True.intro⟩,True.intro⟩,⟨sg37340,⟨sg37339,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37344,⟨sg37343,⟨sg37342,True.intro,True.intro⟩,True.intro⟩,⟨sg37345,True.intro,True.intro⟩⟩⟩,⟨sg37352,⟨sg37349,⟨sg37348,⟨sg37347,True.intro,True.intro⟩,True.intro⟩,⟨sg37351,⟨sg37350,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37355,⟨sg37354,⟨sg37353,True.intro,True.intro⟩,True.intro⟩,⟨sg37356,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_481All : degreeTree62_481.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37335,degreeTree62_479All,degreeTree62_480All⟩ + +lemma degreeTree62_482All : degreeTree62_482.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37313,degreeTree62_478All,degreeTree62_481All⟩ + +lemma degreeTree62_483All : degreeTree62_483.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37368,⟨sg37363,⟨sg37360,⟨sg37359,⟨sg37358,True.intro,True.intro⟩,True.intro⟩,⟨sg37362,⟨sg37361,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37366,⟨sg37365,⟨sg37364,True.intro,True.intro⟩,True.intro⟩,⟨sg37367,True.intro,True.intro⟩⟩⟩,⟨sg37374,⟨sg37371,⟨sg37370,⟨sg37369,True.intro,True.intro⟩,True.intro⟩,⟨sg37373,⟨sg37372,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37377,⟨sg37376,⟨sg37375,True.intro,True.intro⟩,True.intro⟩,⟨sg37378,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_484All : degreeTree62_484.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37390,⟨sg37385,⟨sg37382,⟨sg37381,⟨sg37380,True.intro,True.intro⟩,True.intro⟩,⟨sg37384,⟨sg37383,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37388,⟨sg37387,⟨sg37386,True.intro,True.intro⟩,True.intro⟩,⟨sg37389,True.intro,True.intro⟩⟩⟩,⟨sg37396,⟨sg37393,⟨sg37392,⟨sg37391,True.intro,True.intro⟩,True.intro⟩,⟨sg37395,⟨sg37394,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37399,⟨sg37398,⟨sg37397,True.intro,True.intro⟩,True.intro⟩,⟨sg37400,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_485All : degreeTree62_485.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37379,degreeTree62_483All,degreeTree62_484All⟩ + +lemma degreeTree62_486All : degreeTree62_486.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37412,⟨sg37407,⟨sg37404,⟨sg37403,⟨sg37402,True.intro,True.intro⟩,True.intro⟩,⟨sg37406,⟨sg37405,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37410,⟨sg37409,⟨sg37408,True.intro,True.intro⟩,True.intro⟩,⟨sg37411,True.intro,True.intro⟩⟩⟩,⟨sg37418,⟨sg37415,⟨sg37414,⟨sg37413,True.intro,True.intro⟩,True.intro⟩,⟨sg37417,⟨sg37416,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37421,⟨sg37420,⟨sg37419,True.intro,True.intro⟩,True.intro⟩,⟨sg37422,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_487All : degreeTree62_487.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37434,⟨sg37429,⟨sg37426,⟨sg37425,⟨sg37424,True.intro,True.intro⟩,True.intro⟩,⟨sg37428,⟨sg37427,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37432,⟨sg37431,⟨sg37430,True.intro,True.intro⟩,True.intro⟩,⟨sg37433,True.intro,True.intro⟩⟩⟩,⟨sg37439,⟨sg37437,⟨sg37436,⟨sg37435,True.intro,True.intro⟩,True.intro⟩,⟨sg37438,True.intro,True.intro⟩⟩,⟨sg37442,⟨sg37441,⟨sg37440,True.intro,True.intro⟩,True.intro⟩,⟨sg37443,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_488All : degreeTree62_488.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37423,degreeTree62_486All,degreeTree62_487All⟩ + +lemma degreeTree62_489All : degreeTree62_489.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37401,degreeTree62_485All,degreeTree62_488All⟩ + +lemma degreeTree62_490All : degreeTree62_490.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37357,degreeTree62_482All,degreeTree62_489All⟩ + +lemma degreeTree62_491All : degreeTree62_491.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37455,⟨sg37450,⟨sg37447,⟨sg37446,⟨sg37445,True.intro,True.intro⟩,True.intro⟩,⟨sg37449,⟨sg37448,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37453,⟨sg37452,⟨sg37451,True.intro,True.intro⟩,True.intro⟩,⟨sg37454,True.intro,True.intro⟩⟩⟩,⟨sg37461,⟨sg37458,⟨sg37457,⟨sg37456,True.intro,True.intro⟩,True.intro⟩,⟨sg37460,⟨sg37459,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37464,⟨sg37463,⟨sg37462,True.intro,True.intro⟩,True.intro⟩,⟨sg37465,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_492All : degreeTree62_492.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37477,⟨sg37472,⟨sg37469,⟨sg37468,⟨sg37467,True.intro,True.intro⟩,True.intro⟩,⟨sg37471,⟨sg37470,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37475,⟨sg37474,⟨sg37473,True.intro,True.intro⟩,True.intro⟩,⟨sg37476,True.intro,True.intro⟩⟩⟩,⟨sg37483,⟨sg37480,⟨sg37479,⟨sg37478,True.intro,True.intro⟩,True.intro⟩,⟨sg37482,⟨sg37481,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37486,⟨sg37485,⟨sg37484,True.intro,True.intro⟩,True.intro⟩,⟨sg37487,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_493All : degreeTree62_493.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37466,degreeTree62_491All,degreeTree62_492All⟩ + +lemma degreeTree62_494All : degreeTree62_494.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37499,⟨sg37494,⟨sg37491,⟨sg37490,⟨sg37489,True.intro,True.intro⟩,True.intro⟩,⟨sg37493,⟨sg37492,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37497,⟨sg37496,⟨sg37495,True.intro,True.intro⟩,True.intro⟩,⟨sg37498,True.intro,True.intro⟩⟩⟩,⟨sg37505,⟨sg37502,⟨sg37501,⟨sg37500,True.intro,True.intro⟩,True.intro⟩,⟨sg37504,⟨sg37503,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37508,⟨sg37507,⟨sg37506,True.intro,True.intro⟩,True.intro⟩,⟨sg37509,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_495All : degreeTree62_495.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37521,⟨sg37516,⟨sg37513,⟨sg37512,⟨sg37511,True.intro,True.intro⟩,True.intro⟩,⟨sg37515,⟨sg37514,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37519,⟨sg37518,⟨sg37517,True.intro,True.intro⟩,True.intro⟩,⟨sg37520,True.intro,True.intro⟩⟩⟩,⟨sg37527,⟨sg37524,⟨sg37523,⟨sg37522,True.intro,True.intro⟩,True.intro⟩,⟨sg37526,⟨sg37525,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37530,⟨sg37529,⟨sg37528,True.intro,True.intro⟩,True.intro⟩,⟨sg37531,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_496All : degreeTree62_496.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37510,degreeTree62_494All,degreeTree62_495All⟩ + +lemma degreeTree62_497All : degreeTree62_497.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37488,degreeTree62_493All,degreeTree62_496All⟩ + +lemma degreeTree62_498All : degreeTree62_498.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37543,⟨sg37538,⟨sg37535,⟨sg37534,⟨sg37533,True.intro,True.intro⟩,True.intro⟩,⟨sg37537,⟨sg37536,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37541,⟨sg37540,⟨sg37539,True.intro,True.intro⟩,True.intro⟩,⟨sg37542,True.intro,True.intro⟩⟩⟩,⟨sg37549,⟨sg37546,⟨sg37545,⟨sg37544,True.intro,True.intro⟩,True.intro⟩,⟨sg37548,⟨sg37547,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37552,⟨sg37551,⟨sg37550,True.intro,True.intro⟩,True.intro⟩,⟨sg37553,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_499All : degreeTree62_499.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37565,⟨sg37560,⟨sg37557,⟨sg37556,⟨sg37555,True.intro,True.intro⟩,True.intro⟩,⟨sg37559,⟨sg37558,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37563,⟨sg37562,⟨sg37561,True.intro,True.intro⟩,True.intro⟩,⟨sg37564,True.intro,True.intro⟩⟩⟩,⟨sg37571,⟨sg37568,⟨sg37567,⟨sg37566,True.intro,True.intro⟩,True.intro⟩,⟨sg37570,⟨sg37569,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37574,⟨sg37573,⟨sg37572,True.intro,True.intro⟩,True.intro⟩,⟨sg37575,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_500All : degreeTree62_500.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37554,degreeTree62_498All,degreeTree62_499All⟩ + +lemma degreeTree62_501All : degreeTree62_501.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37587,⟨sg37582,⟨sg37579,⟨sg37578,⟨sg37577,True.intro,True.intro⟩,True.intro⟩,⟨sg37581,⟨sg37580,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37585,⟨sg37584,⟨sg37583,True.intro,True.intro⟩,True.intro⟩,⟨sg37586,True.intro,True.intro⟩⟩⟩,⟨sg37593,⟨sg37590,⟨sg37589,⟨sg37588,True.intro,True.intro⟩,True.intro⟩,⟨sg37592,⟨sg37591,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37596,⟨sg37595,⟨sg37594,True.intro,True.intro⟩,True.intro⟩,⟨sg37597,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_502All : degreeTree62_502.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37609,⟨sg37604,⟨sg37601,⟨sg37600,⟨sg37599,True.intro,True.intro⟩,True.intro⟩,⟨sg37603,⟨sg37602,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37607,⟨sg37606,⟨sg37605,True.intro,True.intro⟩,True.intro⟩,⟨sg37608,True.intro,True.intro⟩⟩⟩,⟨sg37614,⟨sg37612,⟨sg37611,⟨sg37610,True.intro,True.intro⟩,True.intro⟩,⟨sg37613,True.intro,True.intro⟩⟩,⟨sg37617,⟨sg37616,⟨sg37615,True.intro,True.intro⟩,True.intro⟩,⟨sg37618,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_503All : degreeTree62_503.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37598,degreeTree62_501All,degreeTree62_502All⟩ + +lemma degreeTree62_504All : degreeTree62_504.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37576,degreeTree62_500All,degreeTree62_503All⟩ + +lemma degreeTree62_505All : degreeTree62_505.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37532,degreeTree62_497All,degreeTree62_504All⟩ + +lemma degreeTree62_506All : degreeTree62_506.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37444,degreeTree62_490All,degreeTree62_505All⟩ + +lemma degreeTree62_507All : degreeTree62_507.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37269,degreeTree62_475All,degreeTree62_506All⟩ + +lemma degreeTree62_508All : degreeTree62_508.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36918,degreeTree62_444All,degreeTree62_507All⟩ + +lemma degreeTree62_509All : degreeTree62_509.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg36216,degreeTree62_381All,degreeTree62_508All⟩ + +lemma degreeTree62_510All : degreeTree62_510.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg34812,degreeTree62_254All,degreeTree62_509All⟩ + +lemma degreeTree62_511All : degreeTree62_511.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37630,⟨sg37625,⟨sg37622,⟨sg37621,⟨sg37620,True.intro,True.intro⟩,True.intro⟩,⟨sg37624,⟨sg37623,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37628,⟨sg37627,⟨sg37626,True.intro,True.intro⟩,True.intro⟩,⟨sg37629,True.intro,True.intro⟩⟩⟩,⟨sg37636,⟨sg37633,⟨sg37632,⟨sg37631,True.intro,True.intro⟩,True.intro⟩,⟨sg37635,⟨sg37634,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37639,⟨sg37638,⟨sg37637,True.intro,True.intro⟩,True.intro⟩,⟨sg37640,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_512All : degreeTree62_512.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37652,⟨sg37647,⟨sg37644,⟨sg37643,⟨sg37642,True.intro,True.intro⟩,True.intro⟩,⟨sg37646,⟨sg37645,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37650,⟨sg37649,⟨sg37648,True.intro,True.intro⟩,True.intro⟩,⟨sg37651,True.intro,True.intro⟩⟩⟩,⟨sg37658,⟨sg37655,⟨sg37654,⟨sg37653,True.intro,True.intro⟩,True.intro⟩,⟨sg37657,⟨sg37656,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37661,⟨sg37660,⟨sg37659,True.intro,True.intro⟩,True.intro⟩,⟨sg37662,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_513All : degreeTree62_513.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37641,degreeTree62_511All,degreeTree62_512All⟩ + +lemma degreeTree62_514All : degreeTree62_514.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37674,⟨sg37669,⟨sg37666,⟨sg37665,⟨sg37664,True.intro,True.intro⟩,True.intro⟩,⟨sg37668,⟨sg37667,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37672,⟨sg37671,⟨sg37670,True.intro,True.intro⟩,True.intro⟩,⟨sg37673,True.intro,True.intro⟩⟩⟩,⟨sg37680,⟨sg37677,⟨sg37676,⟨sg37675,True.intro,True.intro⟩,True.intro⟩,⟨sg37679,⟨sg37678,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37683,⟨sg37682,⟨sg37681,True.intro,True.intro⟩,True.intro⟩,⟨sg37684,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_515All : degreeTree62_515.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37696,⟨sg37691,⟨sg37688,⟨sg37687,⟨sg37686,True.intro,True.intro⟩,True.intro⟩,⟨sg37690,⟨sg37689,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37694,⟨sg37693,⟨sg37692,True.intro,True.intro⟩,True.intro⟩,⟨sg37695,True.intro,True.intro⟩⟩⟩,⟨sg37702,⟨sg37699,⟨sg37698,⟨sg37697,True.intro,True.intro⟩,True.intro⟩,⟨sg37701,⟨sg37700,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37705,⟨sg37704,⟨sg37703,True.intro,True.intro⟩,True.intro⟩,⟨sg37706,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_516All : degreeTree62_516.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37685,degreeTree62_514All,degreeTree62_515All⟩ + +lemma degreeTree62_517All : degreeTree62_517.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37663,degreeTree62_513All,degreeTree62_516All⟩ + +lemma degreeTree62_518All : degreeTree62_518.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37718,⟨sg37713,⟨sg37710,⟨sg37709,⟨sg37708,True.intro,True.intro⟩,True.intro⟩,⟨sg37712,⟨sg37711,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37716,⟨sg37715,⟨sg37714,True.intro,True.intro⟩,True.intro⟩,⟨sg37717,True.intro,True.intro⟩⟩⟩,⟨sg37724,⟨sg37721,⟨sg37720,⟨sg37719,True.intro,True.intro⟩,True.intro⟩,⟨sg37723,⟨sg37722,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37727,⟨sg37726,⟨sg37725,True.intro,True.intro⟩,True.intro⟩,⟨sg37728,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_519All : degreeTree62_519.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37740,⟨sg37735,⟨sg37732,⟨sg37731,⟨sg37730,True.intro,True.intro⟩,True.intro⟩,⟨sg37734,⟨sg37733,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37738,⟨sg37737,⟨sg37736,True.intro,True.intro⟩,True.intro⟩,⟨sg37739,True.intro,True.intro⟩⟩⟩,⟨sg37746,⟨sg37743,⟨sg37742,⟨sg37741,True.intro,True.intro⟩,True.intro⟩,⟨sg37745,⟨sg37744,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37749,⟨sg37748,⟨sg37747,True.intro,True.intro⟩,True.intro⟩,⟨sg37750,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_520All : degreeTree62_520.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37729,degreeTree62_518All,degreeTree62_519All⟩ + +lemma degreeTree62_521All : degreeTree62_521.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37762,⟨sg37757,⟨sg37754,⟨sg37753,⟨sg37752,True.intro,True.intro⟩,True.intro⟩,⟨sg37756,⟨sg37755,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37760,⟨sg37759,⟨sg37758,True.intro,True.intro⟩,True.intro⟩,⟨sg37761,True.intro,True.intro⟩⟩⟩,⟨sg37768,⟨sg37765,⟨sg37764,⟨sg37763,True.intro,True.intro⟩,True.intro⟩,⟨sg37767,⟨sg37766,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37771,⟨sg37770,⟨sg37769,True.intro,True.intro⟩,True.intro⟩,⟨sg37772,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_522All : degreeTree62_522.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37784,⟨sg37779,⟨sg37776,⟨sg37775,⟨sg37774,True.intro,True.intro⟩,True.intro⟩,⟨sg37778,⟨sg37777,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37782,⟨sg37781,⟨sg37780,True.intro,True.intro⟩,True.intro⟩,⟨sg37783,True.intro,True.intro⟩⟩⟩,⟨sg37790,⟨sg37787,⟨sg37786,⟨sg37785,True.intro,True.intro⟩,True.intro⟩,⟨sg37789,⟨sg37788,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37793,⟨sg37792,⟨sg37791,True.intro,True.intro⟩,True.intro⟩,⟨sg37794,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_523All : degreeTree62_523.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37773,degreeTree62_521All,degreeTree62_522All⟩ + +lemma degreeTree62_524All : degreeTree62_524.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37751,degreeTree62_520All,degreeTree62_523All⟩ + +lemma degreeTree62_525All : degreeTree62_525.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37707,degreeTree62_517All,degreeTree62_524All⟩ + +lemma degreeTree62_526All : degreeTree62_526.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37806,⟨sg37801,⟨sg37798,⟨sg37797,⟨sg37796,True.intro,True.intro⟩,True.intro⟩,⟨sg37800,⟨sg37799,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37804,⟨sg37803,⟨sg37802,True.intro,True.intro⟩,True.intro⟩,⟨sg37805,True.intro,True.intro⟩⟩⟩,⟨sg37812,⟨sg37809,⟨sg37808,⟨sg37807,True.intro,True.intro⟩,True.intro⟩,⟨sg37811,⟨sg37810,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37815,⟨sg37814,⟨sg37813,True.intro,True.intro⟩,True.intro⟩,⟨sg37816,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_527All : degreeTree62_527.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37828,⟨sg37823,⟨sg37820,⟨sg37819,⟨sg37818,True.intro,True.intro⟩,True.intro⟩,⟨sg37822,⟨sg37821,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37826,⟨sg37825,⟨sg37824,True.intro,True.intro⟩,True.intro⟩,⟨sg37827,True.intro,True.intro⟩⟩⟩,⟨sg37834,⟨sg37831,⟨sg37830,⟨sg37829,True.intro,True.intro⟩,True.intro⟩,⟨sg37833,⟨sg37832,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37837,⟨sg37836,⟨sg37835,True.intro,True.intro⟩,True.intro⟩,⟨sg37838,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_528All : degreeTree62_528.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37817,degreeTree62_526All,degreeTree62_527All⟩ + +lemma degreeTree62_529All : degreeTree62_529.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37850,⟨sg37845,⟨sg37842,⟨sg37841,⟨sg37840,True.intro,True.intro⟩,True.intro⟩,⟨sg37844,⟨sg37843,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37848,⟨sg37847,⟨sg37846,True.intro,True.intro⟩,True.intro⟩,⟨sg37849,True.intro,True.intro⟩⟩⟩,⟨sg37856,⟨sg37853,⟨sg37852,⟨sg37851,True.intro,True.intro⟩,True.intro⟩,⟨sg37855,⟨sg37854,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37859,⟨sg37858,⟨sg37857,True.intro,True.intro⟩,True.intro⟩,⟨sg37860,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_530All : degreeTree62_530.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37872,⟨sg37867,⟨sg37864,⟨sg37863,⟨sg37862,True.intro,True.intro⟩,True.intro⟩,⟨sg37866,⟨sg37865,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37870,⟨sg37869,⟨sg37868,True.intro,True.intro⟩,True.intro⟩,⟨sg37871,True.intro,True.intro⟩⟩⟩,⟨sg37878,⟨sg37875,⟨sg37874,⟨sg37873,True.intro,True.intro⟩,True.intro⟩,⟨sg37877,⟨sg37876,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37881,⟨sg37880,⟨sg37879,True.intro,True.intro⟩,True.intro⟩,⟨sg37882,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_531All : degreeTree62_531.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37861,degreeTree62_529All,degreeTree62_530All⟩ + +lemma degreeTree62_532All : degreeTree62_532.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37839,degreeTree62_528All,degreeTree62_531All⟩ + +lemma degreeTree62_533All : degreeTree62_533.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37894,⟨sg37889,⟨sg37886,⟨sg37885,⟨sg37884,True.intro,True.intro⟩,True.intro⟩,⟨sg37888,⟨sg37887,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37892,⟨sg37891,⟨sg37890,True.intro,True.intro⟩,True.intro⟩,⟨sg37893,True.intro,True.intro⟩⟩⟩,⟨sg37900,⟨sg37897,⟨sg37896,⟨sg37895,True.intro,True.intro⟩,True.intro⟩,⟨sg37899,⟨sg37898,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37903,⟨sg37902,⟨sg37901,True.intro,True.intro⟩,True.intro⟩,⟨sg37904,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_534All : degreeTree62_534.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37916,⟨sg37911,⟨sg37908,⟨sg37907,⟨sg37906,True.intro,True.intro⟩,True.intro⟩,⟨sg37910,⟨sg37909,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37914,⟨sg37913,⟨sg37912,True.intro,True.intro⟩,True.intro⟩,⟨sg37915,True.intro,True.intro⟩⟩⟩,⟨sg37922,⟨sg37919,⟨sg37918,⟨sg37917,True.intro,True.intro⟩,True.intro⟩,⟨sg37921,⟨sg37920,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37925,⟨sg37924,⟨sg37923,True.intro,True.intro⟩,True.intro⟩,⟨sg37926,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_535All : degreeTree62_535.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37905,degreeTree62_533All,degreeTree62_534All⟩ + +lemma degreeTree62_536All : degreeTree62_536.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37938,⟨sg37933,⟨sg37930,⟨sg37929,⟨sg37928,True.intro,True.intro⟩,True.intro⟩,⟨sg37932,⟨sg37931,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37936,⟨sg37935,⟨sg37934,True.intro,True.intro⟩,True.intro⟩,⟨sg37937,True.intro,True.intro⟩⟩⟩,⟨sg37944,⟨sg37941,⟨sg37940,⟨sg37939,True.intro,True.intro⟩,True.intro⟩,⟨sg37943,⟨sg37942,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37947,⟨sg37946,⟨sg37945,True.intro,True.intro⟩,True.intro⟩,⟨sg37948,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_537All : degreeTree62_537.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37960,⟨sg37955,⟨sg37952,⟨sg37951,⟨sg37950,True.intro,True.intro⟩,True.intro⟩,⟨sg37954,⟨sg37953,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37958,⟨sg37957,⟨sg37956,True.intro,True.intro⟩,True.intro⟩,⟨sg37959,True.intro,True.intro⟩⟩⟩,⟨sg37965,⟨sg37963,⟨sg37962,⟨sg37961,True.intro,True.intro⟩,True.intro⟩,⟨sg37964,True.intro,True.intro⟩⟩,⟨sg37968,⟨sg37967,⟨sg37966,True.intro,True.intro⟩,True.intro⟩,⟨sg37969,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_538All : degreeTree62_538.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37949,degreeTree62_536All,degreeTree62_537All⟩ + +lemma degreeTree62_539All : degreeTree62_539.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37927,degreeTree62_535All,degreeTree62_538All⟩ + +lemma degreeTree62_540All : degreeTree62_540.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37883,degreeTree62_532All,degreeTree62_539All⟩ + +lemma degreeTree62_541All : degreeTree62_541.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37795,degreeTree62_525All,degreeTree62_540All⟩ + +lemma degreeTree62_542All : degreeTree62_542.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37981,⟨sg37976,⟨sg37973,⟨sg37972,⟨sg37971,True.intro,True.intro⟩,True.intro⟩,⟨sg37975,⟨sg37974,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37979,⟨sg37978,⟨sg37977,True.intro,True.intro⟩,True.intro⟩,⟨sg37980,True.intro,True.intro⟩⟩⟩,⟨sg37987,⟨sg37984,⟨sg37983,⟨sg37982,True.intro,True.intro⟩,True.intro⟩,⟨sg37986,⟨sg37985,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg37990,⟨sg37989,⟨sg37988,True.intro,True.intro⟩,True.intro⟩,⟨sg37991,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_543All : degreeTree62_543.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38003,⟨sg37998,⟨sg37995,⟨sg37994,⟨sg37993,True.intro,True.intro⟩,True.intro⟩,⟨sg37997,⟨sg37996,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38001,⟨sg38000,⟨sg37999,True.intro,True.intro⟩,True.intro⟩,⟨sg38002,True.intro,True.intro⟩⟩⟩,⟨sg38009,⟨sg38006,⟨sg38005,⟨sg38004,True.intro,True.intro⟩,True.intro⟩,⟨sg38008,⟨sg38007,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38012,⟨sg38011,⟨sg38010,True.intro,True.intro⟩,True.intro⟩,⟨sg38013,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_544All : degreeTree62_544.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37992,degreeTree62_542All,degreeTree62_543All⟩ + +lemma degreeTree62_545All : degreeTree62_545.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38025,⟨sg38020,⟨sg38017,⟨sg38016,⟨sg38015,True.intro,True.intro⟩,True.intro⟩,⟨sg38019,⟨sg38018,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38023,⟨sg38022,⟨sg38021,True.intro,True.intro⟩,True.intro⟩,⟨sg38024,True.intro,True.intro⟩⟩⟩,⟨sg38031,⟨sg38028,⟨sg38027,⟨sg38026,True.intro,True.intro⟩,True.intro⟩,⟨sg38030,⟨sg38029,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38034,⟨sg38033,⟨sg38032,True.intro,True.intro⟩,True.intro⟩,⟨sg38035,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_546All : degreeTree62_546.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38047,⟨sg38042,⟨sg38039,⟨sg38038,⟨sg38037,True.intro,True.intro⟩,True.intro⟩,⟨sg38041,⟨sg38040,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38045,⟨sg38044,⟨sg38043,True.intro,True.intro⟩,True.intro⟩,⟨sg38046,True.intro,True.intro⟩⟩⟩,⟨sg38053,⟨sg38050,⟨sg38049,⟨sg38048,True.intro,True.intro⟩,True.intro⟩,⟨sg38052,⟨sg38051,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38056,⟨sg38055,⟨sg38054,True.intro,True.intro⟩,True.intro⟩,⟨sg38057,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_547All : degreeTree62_547.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38036,degreeTree62_545All,degreeTree62_546All⟩ + +lemma degreeTree62_548All : degreeTree62_548.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38014,degreeTree62_544All,degreeTree62_547All⟩ + +lemma degreeTree62_549All : degreeTree62_549.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38069,⟨sg38064,⟨sg38061,⟨sg38060,⟨sg38059,True.intro,True.intro⟩,True.intro⟩,⟨sg38063,⟨sg38062,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38067,⟨sg38066,⟨sg38065,True.intro,True.intro⟩,True.intro⟩,⟨sg38068,True.intro,True.intro⟩⟩⟩,⟨sg38075,⟨sg38072,⟨sg38071,⟨sg38070,True.intro,True.intro⟩,True.intro⟩,⟨sg38074,⟨sg38073,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38078,⟨sg38077,⟨sg38076,True.intro,True.intro⟩,True.intro⟩,⟨sg38079,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_550All : degreeTree62_550.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38091,⟨sg38086,⟨sg38083,⟨sg38082,⟨sg38081,True.intro,True.intro⟩,True.intro⟩,⟨sg38085,⟨sg38084,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38089,⟨sg38088,⟨sg38087,True.intro,True.intro⟩,True.intro⟩,⟨sg38090,True.intro,True.intro⟩⟩⟩,⟨sg38097,⟨sg38094,⟨sg38093,⟨sg38092,True.intro,True.intro⟩,True.intro⟩,⟨sg38096,⟨sg38095,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38100,⟨sg38099,⟨sg38098,True.intro,True.intro⟩,True.intro⟩,⟨sg38101,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_551All : degreeTree62_551.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38080,degreeTree62_549All,degreeTree62_550All⟩ + +lemma degreeTree62_552All : degreeTree62_552.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38113,⟨sg38108,⟨sg38105,⟨sg38104,⟨sg38103,True.intro,True.intro⟩,True.intro⟩,⟨sg38107,⟨sg38106,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38111,⟨sg38110,⟨sg38109,True.intro,True.intro⟩,True.intro⟩,⟨sg38112,True.intro,True.intro⟩⟩⟩,⟨sg38119,⟨sg38116,⟨sg38115,⟨sg38114,True.intro,True.intro⟩,True.intro⟩,⟨sg38118,⟨sg38117,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38122,⟨sg38121,⟨sg38120,True.intro,True.intro⟩,True.intro⟩,⟨sg38123,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_553All : degreeTree62_553.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38135,⟨sg38130,⟨sg38127,⟨sg38126,⟨sg38125,True.intro,True.intro⟩,True.intro⟩,⟨sg38129,⟨sg38128,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38133,⟨sg38132,⟨sg38131,True.intro,True.intro⟩,True.intro⟩,⟨sg38134,True.intro,True.intro⟩⟩⟩,⟨sg38141,⟨sg38138,⟨sg38137,⟨sg38136,True.intro,True.intro⟩,True.intro⟩,⟨sg38140,⟨sg38139,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38144,⟨sg38143,⟨sg38142,True.intro,True.intro⟩,True.intro⟩,⟨sg38145,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_554All : degreeTree62_554.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38124,degreeTree62_552All,degreeTree62_553All⟩ + +lemma degreeTree62_555All : degreeTree62_555.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38102,degreeTree62_551All,degreeTree62_554All⟩ + +lemma degreeTree62_556All : degreeTree62_556.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38058,degreeTree62_548All,degreeTree62_555All⟩ + +lemma degreeTree62_557All : degreeTree62_557.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38157,⟨sg38152,⟨sg38149,⟨sg38148,⟨sg38147,True.intro,True.intro⟩,True.intro⟩,⟨sg38151,⟨sg38150,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38155,⟨sg38154,⟨sg38153,True.intro,True.intro⟩,True.intro⟩,⟨sg38156,True.intro,True.intro⟩⟩⟩,⟨sg38163,⟨sg38160,⟨sg38159,⟨sg38158,True.intro,True.intro⟩,True.intro⟩,⟨sg38162,⟨sg38161,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38166,⟨sg38165,⟨sg38164,True.intro,True.intro⟩,True.intro⟩,⟨sg38167,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_558All : degreeTree62_558.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38179,⟨sg38174,⟨sg38171,⟨sg38170,⟨sg38169,True.intro,True.intro⟩,True.intro⟩,⟨sg38173,⟨sg38172,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38177,⟨sg38176,⟨sg38175,True.intro,True.intro⟩,True.intro⟩,⟨sg38178,True.intro,True.intro⟩⟩⟩,⟨sg38185,⟨sg38182,⟨sg38181,⟨sg38180,True.intro,True.intro⟩,True.intro⟩,⟨sg38184,⟨sg38183,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38188,⟨sg38187,⟨sg38186,True.intro,True.intro⟩,True.intro⟩,⟨sg38189,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_559All : degreeTree62_559.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38168,degreeTree62_557All,degreeTree62_558All⟩ + +lemma degreeTree62_560All : degreeTree62_560.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38201,⟨sg38196,⟨sg38193,⟨sg38192,⟨sg38191,True.intro,True.intro⟩,True.intro⟩,⟨sg38195,⟨sg38194,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38199,⟨sg38198,⟨sg38197,True.intro,True.intro⟩,True.intro⟩,⟨sg38200,True.intro,True.intro⟩⟩⟩,⟨sg38207,⟨sg38204,⟨sg38203,⟨sg38202,True.intro,True.intro⟩,True.intro⟩,⟨sg38206,⟨sg38205,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38210,⟨sg38209,⟨sg38208,True.intro,True.intro⟩,True.intro⟩,⟨sg38211,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_561All : degreeTree62_561.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38223,⟨sg38218,⟨sg38215,⟨sg38214,⟨sg38213,True.intro,True.intro⟩,True.intro⟩,⟨sg38217,⟨sg38216,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38221,⟨sg38220,⟨sg38219,True.intro,True.intro⟩,True.intro⟩,⟨sg38222,True.intro,True.intro⟩⟩⟩,⟨sg38229,⟨sg38226,⟨sg38225,⟨sg38224,True.intro,True.intro⟩,True.intro⟩,⟨sg38228,⟨sg38227,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38232,⟨sg38231,⟨sg38230,True.intro,True.intro⟩,True.intro⟩,⟨sg38233,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_562All : degreeTree62_562.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38212,degreeTree62_560All,degreeTree62_561All⟩ + +lemma degreeTree62_563All : degreeTree62_563.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38190,degreeTree62_559All,degreeTree62_562All⟩ + +lemma degreeTree62_564All : degreeTree62_564.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38245,⟨sg38240,⟨sg38237,⟨sg38236,⟨sg38235,True.intro,True.intro⟩,True.intro⟩,⟨sg38239,⟨sg38238,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38243,⟨sg38242,⟨sg38241,True.intro,True.intro⟩,True.intro⟩,⟨sg38244,True.intro,True.intro⟩⟩⟩,⟨sg38251,⟨sg38248,⟨sg38247,⟨sg38246,True.intro,True.intro⟩,True.intro⟩,⟨sg38250,⟨sg38249,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38254,⟨sg38253,⟨sg38252,True.intro,True.intro⟩,True.intro⟩,⟨sg38255,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_565All : degreeTree62_565.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38267,⟨sg38262,⟨sg38259,⟨sg38258,⟨sg38257,True.intro,True.intro⟩,True.intro⟩,⟨sg38261,⟨sg38260,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38265,⟨sg38264,⟨sg38263,True.intro,True.intro⟩,True.intro⟩,⟨sg38266,True.intro,True.intro⟩⟩⟩,⟨sg38273,⟨sg38270,⟨sg38269,⟨sg38268,True.intro,True.intro⟩,True.intro⟩,⟨sg38272,⟨sg38271,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38276,⟨sg38275,⟨sg38274,True.intro,True.intro⟩,True.intro⟩,⟨sg38277,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_566All : degreeTree62_566.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38256,degreeTree62_564All,degreeTree62_565All⟩ + +lemma degreeTree62_567All : degreeTree62_567.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38289,⟨sg38284,⟨sg38281,⟨sg38280,⟨sg38279,True.intro,True.intro⟩,True.intro⟩,⟨sg38283,⟨sg38282,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38287,⟨sg38286,⟨sg38285,True.intro,True.intro⟩,True.intro⟩,⟨sg38288,True.intro,True.intro⟩⟩⟩,⟨sg38295,⟨sg38292,⟨sg38291,⟨sg38290,True.intro,True.intro⟩,True.intro⟩,⟨sg38294,⟨sg38293,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38298,⟨sg38297,⟨sg38296,True.intro,True.intro⟩,True.intro⟩,⟨sg38299,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_568All : degreeTree62_568.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38311,⟨sg38306,⟨sg38303,⟨sg38302,⟨sg38301,True.intro,True.intro⟩,True.intro⟩,⟨sg38305,⟨sg38304,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38309,⟨sg38308,⟨sg38307,True.intro,True.intro⟩,True.intro⟩,⟨sg38310,True.intro,True.intro⟩⟩⟩,⟨sg38316,⟨sg38314,⟨sg38313,⟨sg38312,True.intro,True.intro⟩,True.intro⟩,⟨sg38315,True.intro,True.intro⟩⟩,⟨sg38319,⟨sg38318,⟨sg38317,True.intro,True.intro⟩,True.intro⟩,⟨sg38320,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_569All : degreeTree62_569.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38300,degreeTree62_567All,degreeTree62_568All⟩ + +lemma degreeTree62_570All : degreeTree62_570.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38278,degreeTree62_566All,degreeTree62_569All⟩ + +lemma degreeTree62_571All : degreeTree62_571.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38234,degreeTree62_563All,degreeTree62_570All⟩ + +lemma degreeTree62_572All : degreeTree62_572.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38146,degreeTree62_556All,degreeTree62_571All⟩ + +lemma degreeTree62_573All : degreeTree62_573.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37970,degreeTree62_541All,degreeTree62_572All⟩ + +lemma degreeTree62_574All : degreeTree62_574.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38332,⟨sg38327,⟨sg38324,⟨sg38323,⟨sg38322,True.intro,True.intro⟩,True.intro⟩,⟨sg38326,⟨sg38325,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38330,⟨sg38329,⟨sg38328,True.intro,True.intro⟩,True.intro⟩,⟨sg38331,True.intro,True.intro⟩⟩⟩,⟨sg38338,⟨sg38335,⟨sg38334,⟨sg38333,True.intro,True.intro⟩,True.intro⟩,⟨sg38337,⟨sg38336,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38341,⟨sg38340,⟨sg38339,True.intro,True.intro⟩,True.intro⟩,⟨sg38342,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_575All : degreeTree62_575.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38354,⟨sg38349,⟨sg38346,⟨sg38345,⟨sg38344,True.intro,True.intro⟩,True.intro⟩,⟨sg38348,⟨sg38347,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38352,⟨sg38351,⟨sg38350,True.intro,True.intro⟩,True.intro⟩,⟨sg38353,True.intro,True.intro⟩⟩⟩,⟨sg38360,⟨sg38357,⟨sg38356,⟨sg38355,True.intro,True.intro⟩,True.intro⟩,⟨sg38359,⟨sg38358,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38363,⟨sg38362,⟨sg38361,True.intro,True.intro⟩,True.intro⟩,⟨sg38364,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_576All : degreeTree62_576.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38343,degreeTree62_574All,degreeTree62_575All⟩ + +lemma degreeTree62_577All : degreeTree62_577.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38376,⟨sg38371,⟨sg38368,⟨sg38367,⟨sg38366,True.intro,True.intro⟩,True.intro⟩,⟨sg38370,⟨sg38369,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38374,⟨sg38373,⟨sg38372,True.intro,True.intro⟩,True.intro⟩,⟨sg38375,True.intro,True.intro⟩⟩⟩,⟨sg38382,⟨sg38379,⟨sg38378,⟨sg38377,True.intro,True.intro⟩,True.intro⟩,⟨sg38381,⟨sg38380,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38385,⟨sg38384,⟨sg38383,True.intro,True.intro⟩,True.intro⟩,⟨sg38386,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_578All : degreeTree62_578.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38398,⟨sg38393,⟨sg38390,⟨sg38389,⟨sg38388,True.intro,True.intro⟩,True.intro⟩,⟨sg38392,⟨sg38391,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38396,⟨sg38395,⟨sg38394,True.intro,True.intro⟩,True.intro⟩,⟨sg38397,True.intro,True.intro⟩⟩⟩,⟨sg38404,⟨sg38401,⟨sg38400,⟨sg38399,True.intro,True.intro⟩,True.intro⟩,⟨sg38403,⟨sg38402,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38407,⟨sg38406,⟨sg38405,True.intro,True.intro⟩,True.intro⟩,⟨sg38408,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_579All : degreeTree62_579.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38387,degreeTree62_577All,degreeTree62_578All⟩ + +lemma degreeTree62_580All : degreeTree62_580.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38365,degreeTree62_576All,degreeTree62_579All⟩ + +lemma degreeTree62_581All : degreeTree62_581.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38420,⟨sg38415,⟨sg38412,⟨sg38411,⟨sg38410,True.intro,True.intro⟩,True.intro⟩,⟨sg38414,⟨sg38413,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38418,⟨sg38417,⟨sg38416,True.intro,True.intro⟩,True.intro⟩,⟨sg38419,True.intro,True.intro⟩⟩⟩,⟨sg38426,⟨sg38423,⟨sg38422,⟨sg38421,True.intro,True.intro⟩,True.intro⟩,⟨sg38425,⟨sg38424,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38429,⟨sg38428,⟨sg38427,True.intro,True.intro⟩,True.intro⟩,⟨sg38430,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_582All : degreeTree62_582.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38442,⟨sg38437,⟨sg38434,⟨sg38433,⟨sg38432,True.intro,True.intro⟩,True.intro⟩,⟨sg38436,⟨sg38435,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38440,⟨sg38439,⟨sg38438,True.intro,True.intro⟩,True.intro⟩,⟨sg38441,True.intro,True.intro⟩⟩⟩,⟨sg38448,⟨sg38445,⟨sg38444,⟨sg38443,True.intro,True.intro⟩,True.intro⟩,⟨sg38447,⟨sg38446,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38451,⟨sg38450,⟨sg38449,True.intro,True.intro⟩,True.intro⟩,⟨sg38452,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_583All : degreeTree62_583.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38431,degreeTree62_581All,degreeTree62_582All⟩ + +lemma degreeTree62_584All : degreeTree62_584.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38464,⟨sg38459,⟨sg38456,⟨sg38455,⟨sg38454,True.intro,True.intro⟩,True.intro⟩,⟨sg38458,⟨sg38457,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38462,⟨sg38461,⟨sg38460,True.intro,True.intro⟩,True.intro⟩,⟨sg38463,True.intro,True.intro⟩⟩⟩,⟨sg38470,⟨sg38467,⟨sg38466,⟨sg38465,True.intro,True.intro⟩,True.intro⟩,⟨sg38469,⟨sg38468,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38473,⟨sg38472,⟨sg38471,True.intro,True.intro⟩,True.intro⟩,⟨sg38474,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_585All : degreeTree62_585.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38486,⟨sg38481,⟨sg38478,⟨sg38477,⟨sg38476,True.intro,True.intro⟩,True.intro⟩,⟨sg38480,⟨sg38479,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38484,⟨sg38483,⟨sg38482,True.intro,True.intro⟩,True.intro⟩,⟨sg38485,True.intro,True.intro⟩⟩⟩,⟨sg38492,⟨sg38489,⟨sg38488,⟨sg38487,True.intro,True.intro⟩,True.intro⟩,⟨sg38491,⟨sg38490,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38495,⟨sg38494,⟨sg38493,True.intro,True.intro⟩,True.intro⟩,⟨sg38496,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_586All : degreeTree62_586.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38475,degreeTree62_584All,degreeTree62_585All⟩ + +lemma degreeTree62_587All : degreeTree62_587.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38453,degreeTree62_583All,degreeTree62_586All⟩ + +lemma degreeTree62_588All : degreeTree62_588.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38409,degreeTree62_580All,degreeTree62_587All⟩ + +lemma degreeTree62_589All : degreeTree62_589.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38508,⟨sg38503,⟨sg38500,⟨sg38499,⟨sg38498,True.intro,True.intro⟩,True.intro⟩,⟨sg38502,⟨sg38501,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38506,⟨sg38505,⟨sg38504,True.intro,True.intro⟩,True.intro⟩,⟨sg38507,True.intro,True.intro⟩⟩⟩,⟨sg38514,⟨sg38511,⟨sg38510,⟨sg38509,True.intro,True.intro⟩,True.intro⟩,⟨sg38513,⟨sg38512,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38517,⟨sg38516,⟨sg38515,True.intro,True.intro⟩,True.intro⟩,⟨sg38518,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_590All : degreeTree62_590.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38530,⟨sg38525,⟨sg38522,⟨sg38521,⟨sg38520,True.intro,True.intro⟩,True.intro⟩,⟨sg38524,⟨sg38523,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38528,⟨sg38527,⟨sg38526,True.intro,True.intro⟩,True.intro⟩,⟨sg38529,True.intro,True.intro⟩⟩⟩,⟨sg38536,⟨sg38533,⟨sg38532,⟨sg38531,True.intro,True.intro⟩,True.intro⟩,⟨sg38535,⟨sg38534,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38539,⟨sg38538,⟨sg38537,True.intro,True.intro⟩,True.intro⟩,⟨sg38540,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_591All : degreeTree62_591.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38519,degreeTree62_589All,degreeTree62_590All⟩ + +lemma degreeTree62_592All : degreeTree62_592.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38552,⟨sg38547,⟨sg38544,⟨sg38543,⟨sg38542,True.intro,True.intro⟩,True.intro⟩,⟨sg38546,⟨sg38545,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38550,⟨sg38549,⟨sg38548,True.intro,True.intro⟩,True.intro⟩,⟨sg38551,True.intro,True.intro⟩⟩⟩,⟨sg38558,⟨sg38555,⟨sg38554,⟨sg38553,True.intro,True.intro⟩,True.intro⟩,⟨sg38557,⟨sg38556,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38561,⟨sg38560,⟨sg38559,True.intro,True.intro⟩,True.intro⟩,⟨sg38562,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_593All : degreeTree62_593.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38574,⟨sg38569,⟨sg38566,⟨sg38565,⟨sg38564,True.intro,True.intro⟩,True.intro⟩,⟨sg38568,⟨sg38567,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38572,⟨sg38571,⟨sg38570,True.intro,True.intro⟩,True.intro⟩,⟨sg38573,True.intro,True.intro⟩⟩⟩,⟨sg38580,⟨sg38577,⟨sg38576,⟨sg38575,True.intro,True.intro⟩,True.intro⟩,⟨sg38579,⟨sg38578,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38583,⟨sg38582,⟨sg38581,True.intro,True.intro⟩,True.intro⟩,⟨sg38584,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_594All : degreeTree62_594.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38563,degreeTree62_592All,degreeTree62_593All⟩ + +lemma degreeTree62_595All : degreeTree62_595.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38541,degreeTree62_591All,degreeTree62_594All⟩ + +lemma degreeTree62_596All : degreeTree62_596.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38596,⟨sg38591,⟨sg38588,⟨sg38587,⟨sg38586,True.intro,True.intro⟩,True.intro⟩,⟨sg38590,⟨sg38589,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38594,⟨sg38593,⟨sg38592,True.intro,True.intro⟩,True.intro⟩,⟨sg38595,True.intro,True.intro⟩⟩⟩,⟨sg38602,⟨sg38599,⟨sg38598,⟨sg38597,True.intro,True.intro⟩,True.intro⟩,⟨sg38601,⟨sg38600,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38605,⟨sg38604,⟨sg38603,True.intro,True.intro⟩,True.intro⟩,⟨sg38606,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_597All : degreeTree62_597.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38618,⟨sg38613,⟨sg38610,⟨sg38609,⟨sg38608,True.intro,True.intro⟩,True.intro⟩,⟨sg38612,⟨sg38611,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38616,⟨sg38615,⟨sg38614,True.intro,True.intro⟩,True.intro⟩,⟨sg38617,True.intro,True.intro⟩⟩⟩,⟨sg38624,⟨sg38621,⟨sg38620,⟨sg38619,True.intro,True.intro⟩,True.intro⟩,⟨sg38623,⟨sg38622,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38627,⟨sg38626,⟨sg38625,True.intro,True.intro⟩,True.intro⟩,⟨sg38628,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_598All : degreeTree62_598.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38607,degreeTree62_596All,degreeTree62_597All⟩ + +lemma degreeTree62_599All : degreeTree62_599.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38640,⟨sg38635,⟨sg38632,⟨sg38631,⟨sg38630,True.intro,True.intro⟩,True.intro⟩,⟨sg38634,⟨sg38633,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38638,⟨sg38637,⟨sg38636,True.intro,True.intro⟩,True.intro⟩,⟨sg38639,True.intro,True.intro⟩⟩⟩,⟨sg38646,⟨sg38643,⟨sg38642,⟨sg38641,True.intro,True.intro⟩,True.intro⟩,⟨sg38645,⟨sg38644,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38649,⟨sg38648,⟨sg38647,True.intro,True.intro⟩,True.intro⟩,⟨sg38650,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_600All : degreeTree62_600.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38662,⟨sg38657,⟨sg38654,⟨sg38653,⟨sg38652,True.intro,True.intro⟩,True.intro⟩,⟨sg38656,⟨sg38655,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38660,⟨sg38659,⟨sg38658,True.intro,True.intro⟩,True.intro⟩,⟨sg38661,True.intro,True.intro⟩⟩⟩,⟨sg38667,⟨sg38665,⟨sg38664,⟨sg38663,True.intro,True.intro⟩,True.intro⟩,⟨sg38666,True.intro,True.intro⟩⟩,⟨sg38670,⟨sg38669,⟨sg38668,True.intro,True.intro⟩,True.intro⟩,⟨sg38671,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_601All : degreeTree62_601.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38651,degreeTree62_599All,degreeTree62_600All⟩ + +lemma degreeTree62_602All : degreeTree62_602.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38629,degreeTree62_598All,degreeTree62_601All⟩ + +lemma degreeTree62_603All : degreeTree62_603.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38585,degreeTree62_595All,degreeTree62_602All⟩ + +lemma degreeTree62_604All : degreeTree62_604.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38497,degreeTree62_588All,degreeTree62_603All⟩ + +lemma degreeTree62_605All : degreeTree62_605.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38683,⟨sg38678,⟨sg38675,⟨sg38674,⟨sg38673,True.intro,True.intro⟩,True.intro⟩,⟨sg38677,⟨sg38676,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38681,⟨sg38680,⟨sg38679,True.intro,True.intro⟩,True.intro⟩,⟨sg38682,True.intro,True.intro⟩⟩⟩,⟨sg38689,⟨sg38686,⟨sg38685,⟨sg38684,True.intro,True.intro⟩,True.intro⟩,⟨sg38688,⟨sg38687,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38692,⟨sg38691,⟨sg38690,True.intro,True.intro⟩,True.intro⟩,⟨sg38693,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_606All : degreeTree62_606.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38705,⟨sg38700,⟨sg38697,⟨sg38696,⟨sg38695,True.intro,True.intro⟩,True.intro⟩,⟨sg38699,⟨sg38698,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38703,⟨sg38702,⟨sg38701,True.intro,True.intro⟩,True.intro⟩,⟨sg38704,True.intro,True.intro⟩⟩⟩,⟨sg38711,⟨sg38708,⟨sg38707,⟨sg38706,True.intro,True.intro⟩,True.intro⟩,⟨sg38710,⟨sg38709,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38714,⟨sg38713,⟨sg38712,True.intro,True.intro⟩,True.intro⟩,⟨sg38715,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_607All : degreeTree62_607.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38694,degreeTree62_605All,degreeTree62_606All⟩ + +lemma degreeTree62_608All : degreeTree62_608.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38727,⟨sg38722,⟨sg38719,⟨sg38718,⟨sg38717,True.intro,True.intro⟩,True.intro⟩,⟨sg38721,⟨sg38720,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38725,⟨sg38724,⟨sg38723,True.intro,True.intro⟩,True.intro⟩,⟨sg38726,True.intro,True.intro⟩⟩⟩,⟨sg38733,⟨sg38730,⟨sg38729,⟨sg38728,True.intro,True.intro⟩,True.intro⟩,⟨sg38732,⟨sg38731,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38736,⟨sg38735,⟨sg38734,True.intro,True.intro⟩,True.intro⟩,⟨sg38737,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_609All : degreeTree62_609.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38749,⟨sg38744,⟨sg38741,⟨sg38740,⟨sg38739,True.intro,True.intro⟩,True.intro⟩,⟨sg38743,⟨sg38742,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38747,⟨sg38746,⟨sg38745,True.intro,True.intro⟩,True.intro⟩,⟨sg38748,True.intro,True.intro⟩⟩⟩,⟨sg38755,⟨sg38752,⟨sg38751,⟨sg38750,True.intro,True.intro⟩,True.intro⟩,⟨sg38754,⟨sg38753,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38758,⟨sg38757,⟨sg38756,True.intro,True.intro⟩,True.intro⟩,⟨sg38759,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_610All : degreeTree62_610.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38738,degreeTree62_608All,degreeTree62_609All⟩ + +lemma degreeTree62_611All : degreeTree62_611.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38716,degreeTree62_607All,degreeTree62_610All⟩ + +lemma degreeTree62_612All : degreeTree62_612.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38771,⟨sg38766,⟨sg38763,⟨sg38762,⟨sg38761,True.intro,True.intro⟩,True.intro⟩,⟨sg38765,⟨sg38764,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38769,⟨sg38768,⟨sg38767,True.intro,True.intro⟩,True.intro⟩,⟨sg38770,True.intro,True.intro⟩⟩⟩,⟨sg38777,⟨sg38774,⟨sg38773,⟨sg38772,True.intro,True.intro⟩,True.intro⟩,⟨sg38776,⟨sg38775,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38780,⟨sg38779,⟨sg38778,True.intro,True.intro⟩,True.intro⟩,⟨sg38781,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_613All : degreeTree62_613.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38793,⟨sg38788,⟨sg38785,⟨sg38784,⟨sg38783,True.intro,True.intro⟩,True.intro⟩,⟨sg38787,⟨sg38786,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38791,⟨sg38790,⟨sg38789,True.intro,True.intro⟩,True.intro⟩,⟨sg38792,True.intro,True.intro⟩⟩⟩,⟨sg38799,⟨sg38796,⟨sg38795,⟨sg38794,True.intro,True.intro⟩,True.intro⟩,⟨sg38798,⟨sg38797,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38802,⟨sg38801,⟨sg38800,True.intro,True.intro⟩,True.intro⟩,⟨sg38803,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_614All : degreeTree62_614.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38782,degreeTree62_612All,degreeTree62_613All⟩ + +lemma degreeTree62_615All : degreeTree62_615.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38815,⟨sg38810,⟨sg38807,⟨sg38806,⟨sg38805,True.intro,True.intro⟩,True.intro⟩,⟨sg38809,⟨sg38808,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38813,⟨sg38812,⟨sg38811,True.intro,True.intro⟩,True.intro⟩,⟨sg38814,True.intro,True.intro⟩⟩⟩,⟨sg38821,⟨sg38818,⟨sg38817,⟨sg38816,True.intro,True.intro⟩,True.intro⟩,⟨sg38820,⟨sg38819,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38824,⟨sg38823,⟨sg38822,True.intro,True.intro⟩,True.intro⟩,⟨sg38825,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_616All : degreeTree62_616.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38837,⟨sg38832,⟨sg38829,⟨sg38828,⟨sg38827,True.intro,True.intro⟩,True.intro⟩,⟨sg38831,⟨sg38830,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38835,⟨sg38834,⟨sg38833,True.intro,True.intro⟩,True.intro⟩,⟨sg38836,True.intro,True.intro⟩⟩⟩,⟨sg38843,⟨sg38840,⟨sg38839,⟨sg38838,True.intro,True.intro⟩,True.intro⟩,⟨sg38842,⟨sg38841,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38846,⟨sg38845,⟨sg38844,True.intro,True.intro⟩,True.intro⟩,⟨sg38847,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_617All : degreeTree62_617.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38826,degreeTree62_615All,degreeTree62_616All⟩ + +lemma degreeTree62_618All : degreeTree62_618.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38804,degreeTree62_614All,degreeTree62_617All⟩ + +lemma degreeTree62_619All : degreeTree62_619.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38760,degreeTree62_611All,degreeTree62_618All⟩ + +lemma degreeTree62_620All : degreeTree62_620.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38859,⟨sg38854,⟨sg38851,⟨sg38850,⟨sg38849,True.intro,True.intro⟩,True.intro⟩,⟨sg38853,⟨sg38852,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38857,⟨sg38856,⟨sg38855,True.intro,True.intro⟩,True.intro⟩,⟨sg38858,True.intro,True.intro⟩⟩⟩,⟨sg38865,⟨sg38862,⟨sg38861,⟨sg38860,True.intro,True.intro⟩,True.intro⟩,⟨sg38864,⟨sg38863,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38868,⟨sg38867,⟨sg38866,True.intro,True.intro⟩,True.intro⟩,⟨sg38869,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_621All : degreeTree62_621.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38881,⟨sg38876,⟨sg38873,⟨sg38872,⟨sg38871,True.intro,True.intro⟩,True.intro⟩,⟨sg38875,⟨sg38874,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38879,⟨sg38878,⟨sg38877,True.intro,True.intro⟩,True.intro⟩,⟨sg38880,True.intro,True.intro⟩⟩⟩,⟨sg38887,⟨sg38884,⟨sg38883,⟨sg38882,True.intro,True.intro⟩,True.intro⟩,⟨sg38886,⟨sg38885,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38890,⟨sg38889,⟨sg38888,True.intro,True.intro⟩,True.intro⟩,⟨sg38891,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_622All : degreeTree62_622.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38870,degreeTree62_620All,degreeTree62_621All⟩ + +lemma degreeTree62_623All : degreeTree62_623.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38903,⟨sg38898,⟨sg38895,⟨sg38894,⟨sg38893,True.intro,True.intro⟩,True.intro⟩,⟨sg38897,⟨sg38896,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38901,⟨sg38900,⟨sg38899,True.intro,True.intro⟩,True.intro⟩,⟨sg38902,True.intro,True.intro⟩⟩⟩,⟨sg38909,⟨sg38906,⟨sg38905,⟨sg38904,True.intro,True.intro⟩,True.intro⟩,⟨sg38908,⟨sg38907,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38912,⟨sg38911,⟨sg38910,True.intro,True.intro⟩,True.intro⟩,⟨sg38913,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_624All : degreeTree62_624.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38925,⟨sg38920,⟨sg38917,⟨sg38916,⟨sg38915,True.intro,True.intro⟩,True.intro⟩,⟨sg38919,⟨sg38918,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38923,⟨sg38922,⟨sg38921,True.intro,True.intro⟩,True.intro⟩,⟨sg38924,True.intro,True.intro⟩⟩⟩,⟨sg38931,⟨sg38928,⟨sg38927,⟨sg38926,True.intro,True.intro⟩,True.intro⟩,⟨sg38930,⟨sg38929,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38934,⟨sg38933,⟨sg38932,True.intro,True.intro⟩,True.intro⟩,⟨sg38935,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_625All : degreeTree62_625.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38914,degreeTree62_623All,degreeTree62_624All⟩ + +lemma degreeTree62_626All : degreeTree62_626.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38892,degreeTree62_622All,degreeTree62_625All⟩ + +lemma degreeTree62_627All : degreeTree62_627.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38947,⟨sg38942,⟨sg38939,⟨sg38938,⟨sg38937,True.intro,True.intro⟩,True.intro⟩,⟨sg38941,⟨sg38940,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38945,⟨sg38944,⟨sg38943,True.intro,True.intro⟩,True.intro⟩,⟨sg38946,True.intro,True.intro⟩⟩⟩,⟨sg38953,⟨sg38950,⟨sg38949,⟨sg38948,True.intro,True.intro⟩,True.intro⟩,⟨sg38952,⟨sg38951,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38956,⟨sg38955,⟨sg38954,True.intro,True.intro⟩,True.intro⟩,⟨sg38957,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_628All : degreeTree62_628.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38969,⟨sg38964,⟨sg38961,⟨sg38960,⟨sg38959,True.intro,True.intro⟩,True.intro⟩,⟨sg38963,⟨sg38962,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38967,⟨sg38966,⟨sg38965,True.intro,True.intro⟩,True.intro⟩,⟨sg38968,True.intro,True.intro⟩⟩⟩,⟨sg38975,⟨sg38972,⟨sg38971,⟨sg38970,True.intro,True.intro⟩,True.intro⟩,⟨sg38974,⟨sg38973,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38978,⟨sg38977,⟨sg38976,True.intro,True.intro⟩,True.intro⟩,⟨sg38979,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_629All : degreeTree62_629.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38958,degreeTree62_627All,degreeTree62_628All⟩ + +lemma degreeTree62_630All : degreeTree62_630.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38991,⟨sg38986,⟨sg38983,⟨sg38982,⟨sg38981,True.intro,True.intro⟩,True.intro⟩,⟨sg38985,⟨sg38984,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg38989,⟨sg38988,⟨sg38987,True.intro,True.intro⟩,True.intro⟩,⟨sg38990,True.intro,True.intro⟩⟩⟩,⟨sg38997,⟨sg38994,⟨sg38993,⟨sg38992,True.intro,True.intro⟩,True.intro⟩,⟨sg38996,⟨sg38995,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39000,⟨sg38999,⟨sg38998,True.intro,True.intro⟩,True.intro⟩,⟨sg39001,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_631All : degreeTree62_631.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39013,⟨sg39008,⟨sg39005,⟨sg39004,⟨sg39003,True.intro,True.intro⟩,True.intro⟩,⟨sg39007,⟨sg39006,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39011,⟨sg39010,⟨sg39009,True.intro,True.intro⟩,True.intro⟩,⟨sg39012,True.intro,True.intro⟩⟩⟩,⟨sg39018,⟨sg39016,⟨sg39015,⟨sg39014,True.intro,True.intro⟩,True.intro⟩,⟨sg39017,True.intro,True.intro⟩⟩,⟨sg39021,⟨sg39020,⟨sg39019,True.intro,True.intro⟩,True.intro⟩,⟨sg39022,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_632All : degreeTree62_632.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39002,degreeTree62_630All,degreeTree62_631All⟩ + +lemma degreeTree62_633All : degreeTree62_633.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38980,degreeTree62_629All,degreeTree62_632All⟩ + +lemma degreeTree62_634All : degreeTree62_634.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38936,degreeTree62_626All,degreeTree62_633All⟩ + +lemma degreeTree62_635All : degreeTree62_635.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38848,degreeTree62_619All,degreeTree62_634All⟩ + +lemma degreeTree62_636All : degreeTree62_636.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38672,degreeTree62_604All,degreeTree62_635All⟩ + +lemma degreeTree62_637All : degreeTree62_637.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg38321,degreeTree62_573All,degreeTree62_636All⟩ + +lemma degreeTree62_638All : degreeTree62_638.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39034,⟨sg39029,⟨sg39026,⟨sg39025,⟨sg39024,True.intro,True.intro⟩,True.intro⟩,⟨sg39028,⟨sg39027,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39032,⟨sg39031,⟨sg39030,True.intro,True.intro⟩,True.intro⟩,⟨sg39033,True.intro,True.intro⟩⟩⟩,⟨sg39040,⟨sg39037,⟨sg39036,⟨sg39035,True.intro,True.intro⟩,True.intro⟩,⟨sg39039,⟨sg39038,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39043,⟨sg39042,⟨sg39041,True.intro,True.intro⟩,True.intro⟩,⟨sg39044,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_639All : degreeTree62_639.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39056,⟨sg39051,⟨sg39048,⟨sg39047,⟨sg39046,True.intro,True.intro⟩,True.intro⟩,⟨sg39050,⟨sg39049,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39054,⟨sg39053,⟨sg39052,True.intro,True.intro⟩,True.intro⟩,⟨sg39055,True.intro,True.intro⟩⟩⟩,⟨sg39062,⟨sg39059,⟨sg39058,⟨sg39057,True.intro,True.intro⟩,True.intro⟩,⟨sg39061,⟨sg39060,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39065,⟨sg39064,⟨sg39063,True.intro,True.intro⟩,True.intro⟩,⟨sg39066,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_640All : degreeTree62_640.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39045,degreeTree62_638All,degreeTree62_639All⟩ + +lemma degreeTree62_641All : degreeTree62_641.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39078,⟨sg39073,⟨sg39070,⟨sg39069,⟨sg39068,True.intro,True.intro⟩,True.intro⟩,⟨sg39072,⟨sg39071,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39076,⟨sg39075,⟨sg39074,True.intro,True.intro⟩,True.intro⟩,⟨sg39077,True.intro,True.intro⟩⟩⟩,⟨sg39084,⟨sg39081,⟨sg39080,⟨sg39079,True.intro,True.intro⟩,True.intro⟩,⟨sg39083,⟨sg39082,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39087,⟨sg39086,⟨sg39085,True.intro,True.intro⟩,True.intro⟩,⟨sg39088,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_642All : degreeTree62_642.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39100,⟨sg39095,⟨sg39092,⟨sg39091,⟨sg39090,True.intro,True.intro⟩,True.intro⟩,⟨sg39094,⟨sg39093,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39098,⟨sg39097,⟨sg39096,True.intro,True.intro⟩,True.intro⟩,⟨sg39099,True.intro,True.intro⟩⟩⟩,⟨sg39106,⟨sg39103,⟨sg39102,⟨sg39101,True.intro,True.intro⟩,True.intro⟩,⟨sg39105,⟨sg39104,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39109,⟨sg39108,⟨sg39107,True.intro,True.intro⟩,True.intro⟩,⟨sg39110,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_643All : degreeTree62_643.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39089,degreeTree62_641All,degreeTree62_642All⟩ + +lemma degreeTree62_644All : degreeTree62_644.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39067,degreeTree62_640All,degreeTree62_643All⟩ + +lemma degreeTree62_645All : degreeTree62_645.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39122,⟨sg39117,⟨sg39114,⟨sg39113,⟨sg39112,True.intro,True.intro⟩,True.intro⟩,⟨sg39116,⟨sg39115,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39120,⟨sg39119,⟨sg39118,True.intro,True.intro⟩,True.intro⟩,⟨sg39121,True.intro,True.intro⟩⟩⟩,⟨sg39128,⟨sg39125,⟨sg39124,⟨sg39123,True.intro,True.intro⟩,True.intro⟩,⟨sg39127,⟨sg39126,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39131,⟨sg39130,⟨sg39129,True.intro,True.intro⟩,True.intro⟩,⟨sg39132,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_646All : degreeTree62_646.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39144,⟨sg39139,⟨sg39136,⟨sg39135,⟨sg39134,True.intro,True.intro⟩,True.intro⟩,⟨sg39138,⟨sg39137,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39142,⟨sg39141,⟨sg39140,True.intro,True.intro⟩,True.intro⟩,⟨sg39143,True.intro,True.intro⟩⟩⟩,⟨sg39150,⟨sg39147,⟨sg39146,⟨sg39145,True.intro,True.intro⟩,True.intro⟩,⟨sg39149,⟨sg39148,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39153,⟨sg39152,⟨sg39151,True.intro,True.intro⟩,True.intro⟩,⟨sg39154,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_647All : degreeTree62_647.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39133,degreeTree62_645All,degreeTree62_646All⟩ + +lemma degreeTree62_648All : degreeTree62_648.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39166,⟨sg39161,⟨sg39158,⟨sg39157,⟨sg39156,True.intro,True.intro⟩,True.intro⟩,⟨sg39160,⟨sg39159,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39164,⟨sg39163,⟨sg39162,True.intro,True.intro⟩,True.intro⟩,⟨sg39165,True.intro,True.intro⟩⟩⟩,⟨sg39172,⟨sg39169,⟨sg39168,⟨sg39167,True.intro,True.intro⟩,True.intro⟩,⟨sg39171,⟨sg39170,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39175,⟨sg39174,⟨sg39173,True.intro,True.intro⟩,True.intro⟩,⟨sg39176,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_649All : degreeTree62_649.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39188,⟨sg39183,⟨sg39180,⟨sg39179,⟨sg39178,True.intro,True.intro⟩,True.intro⟩,⟨sg39182,⟨sg39181,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39186,⟨sg39185,⟨sg39184,True.intro,True.intro⟩,True.intro⟩,⟨sg39187,True.intro,True.intro⟩⟩⟩,⟨sg39194,⟨sg39191,⟨sg39190,⟨sg39189,True.intro,True.intro⟩,True.intro⟩,⟨sg39193,⟨sg39192,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39197,⟨sg39196,⟨sg39195,True.intro,True.intro⟩,True.intro⟩,⟨sg39198,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_650All : degreeTree62_650.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39177,degreeTree62_648All,degreeTree62_649All⟩ + +lemma degreeTree62_651All : degreeTree62_651.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39155,degreeTree62_647All,degreeTree62_650All⟩ + +lemma degreeTree62_652All : degreeTree62_652.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39111,degreeTree62_644All,degreeTree62_651All⟩ + +lemma degreeTree62_653All : degreeTree62_653.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39210,⟨sg39205,⟨sg39202,⟨sg39201,⟨sg39200,True.intro,True.intro⟩,True.intro⟩,⟨sg39204,⟨sg39203,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39208,⟨sg39207,⟨sg39206,True.intro,True.intro⟩,True.intro⟩,⟨sg39209,True.intro,True.intro⟩⟩⟩,⟨sg39216,⟨sg39213,⟨sg39212,⟨sg39211,True.intro,True.intro⟩,True.intro⟩,⟨sg39215,⟨sg39214,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39219,⟨sg39218,⟨sg39217,True.intro,True.intro⟩,True.intro⟩,⟨sg39220,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_654All : degreeTree62_654.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39232,⟨sg39227,⟨sg39224,⟨sg39223,⟨sg39222,True.intro,True.intro⟩,True.intro⟩,⟨sg39226,⟨sg39225,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39230,⟨sg39229,⟨sg39228,True.intro,True.intro⟩,True.intro⟩,⟨sg39231,True.intro,True.intro⟩⟩⟩,⟨sg39238,⟨sg39235,⟨sg39234,⟨sg39233,True.intro,True.intro⟩,True.intro⟩,⟨sg39237,⟨sg39236,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39241,⟨sg39240,⟨sg39239,True.intro,True.intro⟩,True.intro⟩,⟨sg39242,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_655All : degreeTree62_655.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39221,degreeTree62_653All,degreeTree62_654All⟩ + +lemma degreeTree62_656All : degreeTree62_656.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39254,⟨sg39249,⟨sg39246,⟨sg39245,⟨sg39244,True.intro,True.intro⟩,True.intro⟩,⟨sg39248,⟨sg39247,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39252,⟨sg39251,⟨sg39250,True.intro,True.intro⟩,True.intro⟩,⟨sg39253,True.intro,True.intro⟩⟩⟩,⟨sg39260,⟨sg39257,⟨sg39256,⟨sg39255,True.intro,True.intro⟩,True.intro⟩,⟨sg39259,⟨sg39258,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39263,⟨sg39262,⟨sg39261,True.intro,True.intro⟩,True.intro⟩,⟨sg39264,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_657All : degreeTree62_657.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39276,⟨sg39271,⟨sg39268,⟨sg39267,⟨sg39266,True.intro,True.intro⟩,True.intro⟩,⟨sg39270,⟨sg39269,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39274,⟨sg39273,⟨sg39272,True.intro,True.intro⟩,True.intro⟩,⟨sg39275,True.intro,True.intro⟩⟩⟩,⟨sg39282,⟨sg39279,⟨sg39278,⟨sg39277,True.intro,True.intro⟩,True.intro⟩,⟨sg39281,⟨sg39280,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39285,⟨sg39284,⟨sg39283,True.intro,True.intro⟩,True.intro⟩,⟨sg39286,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_658All : degreeTree62_658.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39265,degreeTree62_656All,degreeTree62_657All⟩ + +lemma degreeTree62_659All : degreeTree62_659.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39243,degreeTree62_655All,degreeTree62_658All⟩ + +lemma degreeTree62_660All : degreeTree62_660.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39298,⟨sg39293,⟨sg39290,⟨sg39289,⟨sg39288,True.intro,True.intro⟩,True.intro⟩,⟨sg39292,⟨sg39291,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39296,⟨sg39295,⟨sg39294,True.intro,True.intro⟩,True.intro⟩,⟨sg39297,True.intro,True.intro⟩⟩⟩,⟨sg39304,⟨sg39301,⟨sg39300,⟨sg39299,True.intro,True.intro⟩,True.intro⟩,⟨sg39303,⟨sg39302,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39307,⟨sg39306,⟨sg39305,True.intro,True.intro⟩,True.intro⟩,⟨sg39308,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_661All : degreeTree62_661.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39320,⟨sg39315,⟨sg39312,⟨sg39311,⟨sg39310,True.intro,True.intro⟩,True.intro⟩,⟨sg39314,⟨sg39313,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39318,⟨sg39317,⟨sg39316,True.intro,True.intro⟩,True.intro⟩,⟨sg39319,True.intro,True.intro⟩⟩⟩,⟨sg39326,⟨sg39323,⟨sg39322,⟨sg39321,True.intro,True.intro⟩,True.intro⟩,⟨sg39325,⟨sg39324,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39329,⟨sg39328,⟨sg39327,True.intro,True.intro⟩,True.intro⟩,⟨sg39330,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_662All : degreeTree62_662.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39309,degreeTree62_660All,degreeTree62_661All⟩ + +lemma degreeTree62_663All : degreeTree62_663.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39342,⟨sg39337,⟨sg39334,⟨sg39333,⟨sg39332,True.intro,True.intro⟩,True.intro⟩,⟨sg39336,⟨sg39335,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39340,⟨sg39339,⟨sg39338,True.intro,True.intro⟩,True.intro⟩,⟨sg39341,True.intro,True.intro⟩⟩⟩,⟨sg39348,⟨sg39345,⟨sg39344,⟨sg39343,True.intro,True.intro⟩,True.intro⟩,⟨sg39347,⟨sg39346,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39351,⟨sg39350,⟨sg39349,True.intro,True.intro⟩,True.intro⟩,⟨sg39352,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_664All : degreeTree62_664.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39364,⟨sg39359,⟨sg39356,⟨sg39355,⟨sg39354,True.intro,True.intro⟩,True.intro⟩,⟨sg39358,⟨sg39357,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39362,⟨sg39361,⟨sg39360,True.intro,True.intro⟩,True.intro⟩,⟨sg39363,True.intro,True.intro⟩⟩⟩,⟨sg39369,⟨sg39367,⟨sg39366,⟨sg39365,True.intro,True.intro⟩,True.intro⟩,⟨sg39368,True.intro,True.intro⟩⟩,⟨sg39372,⟨sg39371,⟨sg39370,True.intro,True.intro⟩,True.intro⟩,⟨sg39373,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_665All : degreeTree62_665.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39353,degreeTree62_663All,degreeTree62_664All⟩ + +lemma degreeTree62_666All : degreeTree62_666.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39331,degreeTree62_662All,degreeTree62_665All⟩ + +lemma degreeTree62_667All : degreeTree62_667.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39287,degreeTree62_659All,degreeTree62_666All⟩ + +lemma degreeTree62_668All : degreeTree62_668.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39199,degreeTree62_652All,degreeTree62_667All⟩ + +lemma degreeTree62_669All : degreeTree62_669.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39385,⟨sg39380,⟨sg39377,⟨sg39376,⟨sg39375,True.intro,True.intro⟩,True.intro⟩,⟨sg39379,⟨sg39378,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39383,⟨sg39382,⟨sg39381,True.intro,True.intro⟩,True.intro⟩,⟨sg39384,True.intro,True.intro⟩⟩⟩,⟨sg39391,⟨sg39388,⟨sg39387,⟨sg39386,True.intro,True.intro⟩,True.intro⟩,⟨sg39390,⟨sg39389,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39394,⟨sg39393,⟨sg39392,True.intro,True.intro⟩,True.intro⟩,⟨sg39395,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_670All : degreeTree62_670.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39407,⟨sg39402,⟨sg39399,⟨sg39398,⟨sg39397,True.intro,True.intro⟩,True.intro⟩,⟨sg39401,⟨sg39400,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39405,⟨sg39404,⟨sg39403,True.intro,True.intro⟩,True.intro⟩,⟨sg39406,True.intro,True.intro⟩⟩⟩,⟨sg39413,⟨sg39410,⟨sg39409,⟨sg39408,True.intro,True.intro⟩,True.intro⟩,⟨sg39412,⟨sg39411,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39416,⟨sg39415,⟨sg39414,True.intro,True.intro⟩,True.intro⟩,⟨sg39417,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_671All : degreeTree62_671.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39396,degreeTree62_669All,degreeTree62_670All⟩ + +lemma degreeTree62_672All : degreeTree62_672.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39429,⟨sg39424,⟨sg39421,⟨sg39420,⟨sg39419,True.intro,True.intro⟩,True.intro⟩,⟨sg39423,⟨sg39422,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39427,⟨sg39426,⟨sg39425,True.intro,True.intro⟩,True.intro⟩,⟨sg39428,True.intro,True.intro⟩⟩⟩,⟨sg39435,⟨sg39432,⟨sg39431,⟨sg39430,True.intro,True.intro⟩,True.intro⟩,⟨sg39434,⟨sg39433,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39438,⟨sg39437,⟨sg39436,True.intro,True.intro⟩,True.intro⟩,⟨sg39439,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_673All : degreeTree62_673.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39451,⟨sg39446,⟨sg39443,⟨sg39442,⟨sg39441,True.intro,True.intro⟩,True.intro⟩,⟨sg39445,⟨sg39444,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39449,⟨sg39448,⟨sg39447,True.intro,True.intro⟩,True.intro⟩,⟨sg39450,True.intro,True.intro⟩⟩⟩,⟨sg39457,⟨sg39454,⟨sg39453,⟨sg39452,True.intro,True.intro⟩,True.intro⟩,⟨sg39456,⟨sg39455,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39460,⟨sg39459,⟨sg39458,True.intro,True.intro⟩,True.intro⟩,⟨sg39461,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_674All : degreeTree62_674.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39440,degreeTree62_672All,degreeTree62_673All⟩ + +lemma degreeTree62_675All : degreeTree62_675.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39418,degreeTree62_671All,degreeTree62_674All⟩ + +lemma degreeTree62_676All : degreeTree62_676.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39473,⟨sg39468,⟨sg39465,⟨sg39464,⟨sg39463,True.intro,True.intro⟩,True.intro⟩,⟨sg39467,⟨sg39466,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39471,⟨sg39470,⟨sg39469,True.intro,True.intro⟩,True.intro⟩,⟨sg39472,True.intro,True.intro⟩⟩⟩,⟨sg39479,⟨sg39476,⟨sg39475,⟨sg39474,True.intro,True.intro⟩,True.intro⟩,⟨sg39478,⟨sg39477,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39482,⟨sg39481,⟨sg39480,True.intro,True.intro⟩,True.intro⟩,⟨sg39483,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_677All : degreeTree62_677.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39495,⟨sg39490,⟨sg39487,⟨sg39486,⟨sg39485,True.intro,True.intro⟩,True.intro⟩,⟨sg39489,⟨sg39488,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39493,⟨sg39492,⟨sg39491,True.intro,True.intro⟩,True.intro⟩,⟨sg39494,True.intro,True.intro⟩⟩⟩,⟨sg39501,⟨sg39498,⟨sg39497,⟨sg39496,True.intro,True.intro⟩,True.intro⟩,⟨sg39500,⟨sg39499,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39504,⟨sg39503,⟨sg39502,True.intro,True.intro⟩,True.intro⟩,⟨sg39505,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_678All : degreeTree62_678.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39484,degreeTree62_676All,degreeTree62_677All⟩ + +lemma degreeTree62_679All : degreeTree62_679.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39517,⟨sg39512,⟨sg39509,⟨sg39508,⟨sg39507,True.intro,True.intro⟩,True.intro⟩,⟨sg39511,⟨sg39510,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39515,⟨sg39514,⟨sg39513,True.intro,True.intro⟩,True.intro⟩,⟨sg39516,True.intro,True.intro⟩⟩⟩,⟨sg39523,⟨sg39520,⟨sg39519,⟨sg39518,True.intro,True.intro⟩,True.intro⟩,⟨sg39522,⟨sg39521,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39526,⟨sg39525,⟨sg39524,True.intro,True.intro⟩,True.intro⟩,⟨sg39527,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_680All : degreeTree62_680.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39539,⟨sg39534,⟨sg39531,⟨sg39530,⟨sg39529,True.intro,True.intro⟩,True.intro⟩,⟨sg39533,⟨sg39532,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39537,⟨sg39536,⟨sg39535,True.intro,True.intro⟩,True.intro⟩,⟨sg39538,True.intro,True.intro⟩⟩⟩,⟨sg39545,⟨sg39542,⟨sg39541,⟨sg39540,True.intro,True.intro⟩,True.intro⟩,⟨sg39544,⟨sg39543,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39548,⟨sg39547,⟨sg39546,True.intro,True.intro⟩,True.intro⟩,⟨sg39549,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_681All : degreeTree62_681.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39528,degreeTree62_679All,degreeTree62_680All⟩ + +lemma degreeTree62_682All : degreeTree62_682.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39506,degreeTree62_678All,degreeTree62_681All⟩ + +lemma degreeTree62_683All : degreeTree62_683.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39462,degreeTree62_675All,degreeTree62_682All⟩ + +lemma degreeTree62_684All : degreeTree62_684.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39561,⟨sg39556,⟨sg39553,⟨sg39552,⟨sg39551,True.intro,True.intro⟩,True.intro⟩,⟨sg39555,⟨sg39554,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39559,⟨sg39558,⟨sg39557,True.intro,True.intro⟩,True.intro⟩,⟨sg39560,True.intro,True.intro⟩⟩⟩,⟨sg39567,⟨sg39564,⟨sg39563,⟨sg39562,True.intro,True.intro⟩,True.intro⟩,⟨sg39566,⟨sg39565,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39570,⟨sg39569,⟨sg39568,True.intro,True.intro⟩,True.intro⟩,⟨sg39571,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_685All : degreeTree62_685.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39583,⟨sg39578,⟨sg39575,⟨sg39574,⟨sg39573,True.intro,True.intro⟩,True.intro⟩,⟨sg39577,⟨sg39576,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39581,⟨sg39580,⟨sg39579,True.intro,True.intro⟩,True.intro⟩,⟨sg39582,True.intro,True.intro⟩⟩⟩,⟨sg39589,⟨sg39586,⟨sg39585,⟨sg39584,True.intro,True.intro⟩,True.intro⟩,⟨sg39588,⟨sg39587,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39592,⟨sg39591,⟨sg39590,True.intro,True.intro⟩,True.intro⟩,⟨sg39593,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_686All : degreeTree62_686.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39572,degreeTree62_684All,degreeTree62_685All⟩ + +lemma degreeTree62_687All : degreeTree62_687.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39605,⟨sg39600,⟨sg39597,⟨sg39596,⟨sg39595,True.intro,True.intro⟩,True.intro⟩,⟨sg39599,⟨sg39598,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39603,⟨sg39602,⟨sg39601,True.intro,True.intro⟩,True.intro⟩,⟨sg39604,True.intro,True.intro⟩⟩⟩,⟨sg39611,⟨sg39608,⟨sg39607,⟨sg39606,True.intro,True.intro⟩,True.intro⟩,⟨sg39610,⟨sg39609,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39614,⟨sg39613,⟨sg39612,True.intro,True.intro⟩,True.intro⟩,⟨sg39615,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_688All : degreeTree62_688.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39627,⟨sg39622,⟨sg39619,⟨sg39618,⟨sg39617,True.intro,True.intro⟩,True.intro⟩,⟨sg39621,⟨sg39620,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39625,⟨sg39624,⟨sg39623,True.intro,True.intro⟩,True.intro⟩,⟨sg39626,True.intro,True.intro⟩⟩⟩,⟨sg39633,⟨sg39630,⟨sg39629,⟨sg39628,True.intro,True.intro⟩,True.intro⟩,⟨sg39632,⟨sg39631,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39636,⟨sg39635,⟨sg39634,True.intro,True.intro⟩,True.intro⟩,⟨sg39637,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_689All : degreeTree62_689.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39616,degreeTree62_687All,degreeTree62_688All⟩ + +lemma degreeTree62_690All : degreeTree62_690.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39594,degreeTree62_686All,degreeTree62_689All⟩ + +lemma degreeTree62_691All : degreeTree62_691.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39649,⟨sg39644,⟨sg39641,⟨sg39640,⟨sg39639,True.intro,True.intro⟩,True.intro⟩,⟨sg39643,⟨sg39642,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39647,⟨sg39646,⟨sg39645,True.intro,True.intro⟩,True.intro⟩,⟨sg39648,True.intro,True.intro⟩⟩⟩,⟨sg39655,⟨sg39652,⟨sg39651,⟨sg39650,True.intro,True.intro⟩,True.intro⟩,⟨sg39654,⟨sg39653,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39658,⟨sg39657,⟨sg39656,True.intro,True.intro⟩,True.intro⟩,⟨sg39659,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_692All : degreeTree62_692.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39671,⟨sg39666,⟨sg39663,⟨sg39662,⟨sg39661,True.intro,True.intro⟩,True.intro⟩,⟨sg39665,⟨sg39664,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39669,⟨sg39668,⟨sg39667,True.intro,True.intro⟩,True.intro⟩,⟨sg39670,True.intro,True.intro⟩⟩⟩,⟨sg39677,⟨sg39674,⟨sg39673,⟨sg39672,True.intro,True.intro⟩,True.intro⟩,⟨sg39676,⟨sg39675,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39680,⟨sg39679,⟨sg39678,True.intro,True.intro⟩,True.intro⟩,⟨sg39681,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_693All : degreeTree62_693.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39660,degreeTree62_691All,degreeTree62_692All⟩ + +lemma degreeTree62_694All : degreeTree62_694.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39693,⟨sg39688,⟨sg39685,⟨sg39684,⟨sg39683,True.intro,True.intro⟩,True.intro⟩,⟨sg39687,⟨sg39686,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39691,⟨sg39690,⟨sg39689,True.intro,True.intro⟩,True.intro⟩,⟨sg39692,True.intro,True.intro⟩⟩⟩,⟨sg39699,⟨sg39696,⟨sg39695,⟨sg39694,True.intro,True.intro⟩,True.intro⟩,⟨sg39698,⟨sg39697,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39702,⟨sg39701,⟨sg39700,True.intro,True.intro⟩,True.intro⟩,⟨sg39703,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_695All : degreeTree62_695.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39715,⟨sg39710,⟨sg39707,⟨sg39706,⟨sg39705,True.intro,True.intro⟩,True.intro⟩,⟨sg39709,⟨sg39708,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39713,⟨sg39712,⟨sg39711,True.intro,True.intro⟩,True.intro⟩,⟨sg39714,True.intro,True.intro⟩⟩⟩,⟨sg39720,⟨sg39718,⟨sg39717,⟨sg39716,True.intro,True.intro⟩,True.intro⟩,⟨sg39719,True.intro,True.intro⟩⟩,⟨sg39723,⟨sg39722,⟨sg39721,True.intro,True.intro⟩,True.intro⟩,⟨sg39724,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_696All : degreeTree62_696.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39704,degreeTree62_694All,degreeTree62_695All⟩ + +lemma degreeTree62_697All : degreeTree62_697.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39682,degreeTree62_693All,degreeTree62_696All⟩ + +lemma degreeTree62_698All : degreeTree62_698.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39638,degreeTree62_690All,degreeTree62_697All⟩ + +lemma degreeTree62_699All : degreeTree62_699.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39550,degreeTree62_683All,degreeTree62_698All⟩ + +lemma degreeTree62_700All : degreeTree62_700.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39374,degreeTree62_668All,degreeTree62_699All⟩ + +lemma degreeTree62_701All : degreeTree62_701.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39736,⟨sg39731,⟨sg39728,⟨sg39727,⟨sg39726,True.intro,True.intro⟩,True.intro⟩,⟨sg39730,⟨sg39729,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39734,⟨sg39733,⟨sg39732,True.intro,True.intro⟩,True.intro⟩,⟨sg39735,True.intro,True.intro⟩⟩⟩,⟨sg39742,⟨sg39739,⟨sg39738,⟨sg39737,True.intro,True.intro⟩,True.intro⟩,⟨sg39741,⟨sg39740,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39745,⟨sg39744,⟨sg39743,True.intro,True.intro⟩,True.intro⟩,⟨sg39746,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_702All : degreeTree62_702.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39758,⟨sg39753,⟨sg39750,⟨sg39749,⟨sg39748,True.intro,True.intro⟩,True.intro⟩,⟨sg39752,⟨sg39751,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39756,⟨sg39755,⟨sg39754,True.intro,True.intro⟩,True.intro⟩,⟨sg39757,True.intro,True.intro⟩⟩⟩,⟨sg39764,⟨sg39761,⟨sg39760,⟨sg39759,True.intro,True.intro⟩,True.intro⟩,⟨sg39763,⟨sg39762,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39767,⟨sg39766,⟨sg39765,True.intro,True.intro⟩,True.intro⟩,⟨sg39768,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_703All : degreeTree62_703.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39747,degreeTree62_701All,degreeTree62_702All⟩ + +lemma degreeTree62_704All : degreeTree62_704.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39780,⟨sg39775,⟨sg39772,⟨sg39771,⟨sg39770,True.intro,True.intro⟩,True.intro⟩,⟨sg39774,⟨sg39773,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39778,⟨sg39777,⟨sg39776,True.intro,True.intro⟩,True.intro⟩,⟨sg39779,True.intro,True.intro⟩⟩⟩,⟨sg39786,⟨sg39783,⟨sg39782,⟨sg39781,True.intro,True.intro⟩,True.intro⟩,⟨sg39785,⟨sg39784,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39789,⟨sg39788,⟨sg39787,True.intro,True.intro⟩,True.intro⟩,⟨sg39790,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_705All : degreeTree62_705.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39802,⟨sg39797,⟨sg39794,⟨sg39793,⟨sg39792,True.intro,True.intro⟩,True.intro⟩,⟨sg39796,⟨sg39795,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39800,⟨sg39799,⟨sg39798,True.intro,True.intro⟩,True.intro⟩,⟨sg39801,True.intro,True.intro⟩⟩⟩,⟨sg39808,⟨sg39805,⟨sg39804,⟨sg39803,True.intro,True.intro⟩,True.intro⟩,⟨sg39807,⟨sg39806,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39811,⟨sg39810,⟨sg39809,True.intro,True.intro⟩,True.intro⟩,⟨sg39812,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_706All : degreeTree62_706.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39791,degreeTree62_704All,degreeTree62_705All⟩ + +lemma degreeTree62_707All : degreeTree62_707.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39769,degreeTree62_703All,degreeTree62_706All⟩ + +lemma degreeTree62_708All : degreeTree62_708.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39824,⟨sg39819,⟨sg39816,⟨sg39815,⟨sg39814,True.intro,True.intro⟩,True.intro⟩,⟨sg39818,⟨sg39817,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39822,⟨sg39821,⟨sg39820,True.intro,True.intro⟩,True.intro⟩,⟨sg39823,True.intro,True.intro⟩⟩⟩,⟨sg39830,⟨sg39827,⟨sg39826,⟨sg39825,True.intro,True.intro⟩,True.intro⟩,⟨sg39829,⟨sg39828,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39833,⟨sg39832,⟨sg39831,True.intro,True.intro⟩,True.intro⟩,⟨sg39834,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_709All : degreeTree62_709.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39846,⟨sg39841,⟨sg39838,⟨sg39837,⟨sg39836,True.intro,True.intro⟩,True.intro⟩,⟨sg39840,⟨sg39839,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39844,⟨sg39843,⟨sg39842,True.intro,True.intro⟩,True.intro⟩,⟨sg39845,True.intro,True.intro⟩⟩⟩,⟨sg39852,⟨sg39849,⟨sg39848,⟨sg39847,True.intro,True.intro⟩,True.intro⟩,⟨sg39851,⟨sg39850,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39855,⟨sg39854,⟨sg39853,True.intro,True.intro⟩,True.intro⟩,⟨sg39856,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_710All : degreeTree62_710.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39835,degreeTree62_708All,degreeTree62_709All⟩ + +lemma degreeTree62_711All : degreeTree62_711.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39868,⟨sg39863,⟨sg39860,⟨sg39859,⟨sg39858,True.intro,True.intro⟩,True.intro⟩,⟨sg39862,⟨sg39861,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39866,⟨sg39865,⟨sg39864,True.intro,True.intro⟩,True.intro⟩,⟨sg39867,True.intro,True.intro⟩⟩⟩,⟨sg39874,⟨sg39871,⟨sg39870,⟨sg39869,True.intro,True.intro⟩,True.intro⟩,⟨sg39873,⟨sg39872,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39877,⟨sg39876,⟨sg39875,True.intro,True.intro⟩,True.intro⟩,⟨sg39878,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_712All : degreeTree62_712.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39890,⟨sg39885,⟨sg39882,⟨sg39881,⟨sg39880,True.intro,True.intro⟩,True.intro⟩,⟨sg39884,⟨sg39883,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39888,⟨sg39887,⟨sg39886,True.intro,True.intro⟩,True.intro⟩,⟨sg39889,True.intro,True.intro⟩⟩⟩,⟨sg39896,⟨sg39893,⟨sg39892,⟨sg39891,True.intro,True.intro⟩,True.intro⟩,⟨sg39895,⟨sg39894,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39899,⟨sg39898,⟨sg39897,True.intro,True.intro⟩,True.intro⟩,⟨sg39900,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_713All : degreeTree62_713.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39879,degreeTree62_711All,degreeTree62_712All⟩ + +lemma degreeTree62_714All : degreeTree62_714.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39857,degreeTree62_710All,degreeTree62_713All⟩ + +lemma degreeTree62_715All : degreeTree62_715.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39813,degreeTree62_707All,degreeTree62_714All⟩ + +lemma degreeTree62_716All : degreeTree62_716.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39912,⟨sg39907,⟨sg39904,⟨sg39903,⟨sg39902,True.intro,True.intro⟩,True.intro⟩,⟨sg39906,⟨sg39905,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39910,⟨sg39909,⟨sg39908,True.intro,True.intro⟩,True.intro⟩,⟨sg39911,True.intro,True.intro⟩⟩⟩,⟨sg39918,⟨sg39915,⟨sg39914,⟨sg39913,True.intro,True.intro⟩,True.intro⟩,⟨sg39917,⟨sg39916,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39921,⟨sg39920,⟨sg39919,True.intro,True.intro⟩,True.intro⟩,⟨sg39922,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_717All : degreeTree62_717.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39934,⟨sg39929,⟨sg39926,⟨sg39925,⟨sg39924,True.intro,True.intro⟩,True.intro⟩,⟨sg39928,⟨sg39927,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39932,⟨sg39931,⟨sg39930,True.intro,True.intro⟩,True.intro⟩,⟨sg39933,True.intro,True.intro⟩⟩⟩,⟨sg39940,⟨sg39937,⟨sg39936,⟨sg39935,True.intro,True.intro⟩,True.intro⟩,⟨sg39939,⟨sg39938,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39943,⟨sg39942,⟨sg39941,True.intro,True.intro⟩,True.intro⟩,⟨sg39944,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_718All : degreeTree62_718.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39923,degreeTree62_716All,degreeTree62_717All⟩ + +lemma degreeTree62_719All : degreeTree62_719.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39956,⟨sg39951,⟨sg39948,⟨sg39947,⟨sg39946,True.intro,True.intro⟩,True.intro⟩,⟨sg39950,⟨sg39949,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39954,⟨sg39953,⟨sg39952,True.intro,True.intro⟩,True.intro⟩,⟨sg39955,True.intro,True.intro⟩⟩⟩,⟨sg39962,⟨sg39959,⟨sg39958,⟨sg39957,True.intro,True.intro⟩,True.intro⟩,⟨sg39961,⟨sg39960,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39965,⟨sg39964,⟨sg39963,True.intro,True.intro⟩,True.intro⟩,⟨sg39966,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_720All : degreeTree62_720.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39978,⟨sg39973,⟨sg39970,⟨sg39969,⟨sg39968,True.intro,True.intro⟩,True.intro⟩,⟨sg39972,⟨sg39971,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39976,⟨sg39975,⟨sg39974,True.intro,True.intro⟩,True.intro⟩,⟨sg39977,True.intro,True.intro⟩⟩⟩,⟨sg39984,⟨sg39981,⟨sg39980,⟨sg39979,True.intro,True.intro⟩,True.intro⟩,⟨sg39983,⟨sg39982,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39987,⟨sg39986,⟨sg39985,True.intro,True.intro⟩,True.intro⟩,⟨sg39988,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_721All : degreeTree62_721.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39967,degreeTree62_719All,degreeTree62_720All⟩ + +lemma degreeTree62_722All : degreeTree62_722.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39945,degreeTree62_718All,degreeTree62_721All⟩ + +lemma degreeTree62_723All : degreeTree62_723.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40000,⟨sg39995,⟨sg39992,⟨sg39991,⟨sg39990,True.intro,True.intro⟩,True.intro⟩,⟨sg39994,⟨sg39993,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg39998,⟨sg39997,⟨sg39996,True.intro,True.intro⟩,True.intro⟩,⟨sg39999,True.intro,True.intro⟩⟩⟩,⟨sg40006,⟨sg40003,⟨sg40002,⟨sg40001,True.intro,True.intro⟩,True.intro⟩,⟨sg40005,⟨sg40004,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40009,⟨sg40008,⟨sg40007,True.intro,True.intro⟩,True.intro⟩,⟨sg40010,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_724All : degreeTree62_724.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40022,⟨sg40017,⟨sg40014,⟨sg40013,⟨sg40012,True.intro,True.intro⟩,True.intro⟩,⟨sg40016,⟨sg40015,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40020,⟨sg40019,⟨sg40018,True.intro,True.intro⟩,True.intro⟩,⟨sg40021,True.intro,True.intro⟩⟩⟩,⟨sg40028,⟨sg40025,⟨sg40024,⟨sg40023,True.intro,True.intro⟩,True.intro⟩,⟨sg40027,⟨sg40026,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40031,⟨sg40030,⟨sg40029,True.intro,True.intro⟩,True.intro⟩,⟨sg40032,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_725All : degreeTree62_725.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40011,degreeTree62_723All,degreeTree62_724All⟩ + +lemma degreeTree62_726All : degreeTree62_726.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40044,⟨sg40039,⟨sg40036,⟨sg40035,⟨sg40034,True.intro,True.intro⟩,True.intro⟩,⟨sg40038,⟨sg40037,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40042,⟨sg40041,⟨sg40040,True.intro,True.intro⟩,True.intro⟩,⟨sg40043,True.intro,True.intro⟩⟩⟩,⟨sg40050,⟨sg40047,⟨sg40046,⟨sg40045,True.intro,True.intro⟩,True.intro⟩,⟨sg40049,⟨sg40048,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40053,⟨sg40052,⟨sg40051,True.intro,True.intro⟩,True.intro⟩,⟨sg40054,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_727All : degreeTree62_727.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40066,⟨sg40061,⟨sg40058,⟨sg40057,⟨sg40056,True.intro,True.intro⟩,True.intro⟩,⟨sg40060,⟨sg40059,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40064,⟨sg40063,⟨sg40062,True.intro,True.intro⟩,True.intro⟩,⟨sg40065,True.intro,True.intro⟩⟩⟩,⟨sg40071,⟨sg40069,⟨sg40068,⟨sg40067,True.intro,True.intro⟩,True.intro⟩,⟨sg40070,True.intro,True.intro⟩⟩,⟨sg40074,⟨sg40073,⟨sg40072,True.intro,True.intro⟩,True.intro⟩,⟨sg40075,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_728All : degreeTree62_728.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40055,degreeTree62_726All,degreeTree62_727All⟩ + +lemma degreeTree62_729All : degreeTree62_729.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40033,degreeTree62_725All,degreeTree62_728All⟩ + +lemma degreeTree62_730All : degreeTree62_730.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39989,degreeTree62_722All,degreeTree62_729All⟩ + +lemma degreeTree62_731All : degreeTree62_731.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39901,degreeTree62_715All,degreeTree62_730All⟩ + +lemma degreeTree62_732All : degreeTree62_732.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40087,⟨sg40082,⟨sg40079,⟨sg40078,⟨sg40077,True.intro,True.intro⟩,True.intro⟩,⟨sg40081,⟨sg40080,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40085,⟨sg40084,⟨sg40083,True.intro,True.intro⟩,True.intro⟩,⟨sg40086,True.intro,True.intro⟩⟩⟩,⟨sg40093,⟨sg40090,⟨sg40089,⟨sg40088,True.intro,True.intro⟩,True.intro⟩,⟨sg40092,⟨sg40091,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40096,⟨sg40095,⟨sg40094,True.intro,True.intro⟩,True.intro⟩,⟨sg40097,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_733All : degreeTree62_733.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40109,⟨sg40104,⟨sg40101,⟨sg40100,⟨sg40099,True.intro,True.intro⟩,True.intro⟩,⟨sg40103,⟨sg40102,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40107,⟨sg40106,⟨sg40105,True.intro,True.intro⟩,True.intro⟩,⟨sg40108,True.intro,True.intro⟩⟩⟩,⟨sg40115,⟨sg40112,⟨sg40111,⟨sg40110,True.intro,True.intro⟩,True.intro⟩,⟨sg40114,⟨sg40113,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40118,⟨sg40117,⟨sg40116,True.intro,True.intro⟩,True.intro⟩,⟨sg40119,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_734All : degreeTree62_734.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40098,degreeTree62_732All,degreeTree62_733All⟩ + +lemma degreeTree62_735All : degreeTree62_735.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40131,⟨sg40126,⟨sg40123,⟨sg40122,⟨sg40121,True.intro,True.intro⟩,True.intro⟩,⟨sg40125,⟨sg40124,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40129,⟨sg40128,⟨sg40127,True.intro,True.intro⟩,True.intro⟩,⟨sg40130,True.intro,True.intro⟩⟩⟩,⟨sg40137,⟨sg40134,⟨sg40133,⟨sg40132,True.intro,True.intro⟩,True.intro⟩,⟨sg40136,⟨sg40135,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40140,⟨sg40139,⟨sg40138,True.intro,True.intro⟩,True.intro⟩,⟨sg40141,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_736All : degreeTree62_736.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40153,⟨sg40148,⟨sg40145,⟨sg40144,⟨sg40143,True.intro,True.intro⟩,True.intro⟩,⟨sg40147,⟨sg40146,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40151,⟨sg40150,⟨sg40149,True.intro,True.intro⟩,True.intro⟩,⟨sg40152,True.intro,True.intro⟩⟩⟩,⟨sg40159,⟨sg40156,⟨sg40155,⟨sg40154,True.intro,True.intro⟩,True.intro⟩,⟨sg40158,⟨sg40157,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40162,⟨sg40161,⟨sg40160,True.intro,True.intro⟩,True.intro⟩,⟨sg40163,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_737All : degreeTree62_737.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40142,degreeTree62_735All,degreeTree62_736All⟩ + +lemma degreeTree62_738All : degreeTree62_738.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40120,degreeTree62_734All,degreeTree62_737All⟩ + +lemma degreeTree62_739All : degreeTree62_739.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40175,⟨sg40170,⟨sg40167,⟨sg40166,⟨sg40165,True.intro,True.intro⟩,True.intro⟩,⟨sg40169,⟨sg40168,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40173,⟨sg40172,⟨sg40171,True.intro,True.intro⟩,True.intro⟩,⟨sg40174,True.intro,True.intro⟩⟩⟩,⟨sg40181,⟨sg40178,⟨sg40177,⟨sg40176,True.intro,True.intro⟩,True.intro⟩,⟨sg40180,⟨sg40179,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40184,⟨sg40183,⟨sg40182,True.intro,True.intro⟩,True.intro⟩,⟨sg40185,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_740All : degreeTree62_740.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40197,⟨sg40192,⟨sg40189,⟨sg40188,⟨sg40187,True.intro,True.intro⟩,True.intro⟩,⟨sg40191,⟨sg40190,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40195,⟨sg40194,⟨sg40193,True.intro,True.intro⟩,True.intro⟩,⟨sg40196,True.intro,True.intro⟩⟩⟩,⟨sg40203,⟨sg40200,⟨sg40199,⟨sg40198,True.intro,True.intro⟩,True.intro⟩,⟨sg40202,⟨sg40201,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40206,⟨sg40205,⟨sg40204,True.intro,True.intro⟩,True.intro⟩,⟨sg40207,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_741All : degreeTree62_741.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40186,degreeTree62_739All,degreeTree62_740All⟩ + +lemma degreeTree62_742All : degreeTree62_742.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40219,⟨sg40214,⟨sg40211,⟨sg40210,⟨sg40209,True.intro,True.intro⟩,True.intro⟩,⟨sg40213,⟨sg40212,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40217,⟨sg40216,⟨sg40215,True.intro,True.intro⟩,True.intro⟩,⟨sg40218,True.intro,True.intro⟩⟩⟩,⟨sg40225,⟨sg40222,⟨sg40221,⟨sg40220,True.intro,True.intro⟩,True.intro⟩,⟨sg40224,⟨sg40223,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40228,⟨sg40227,⟨sg40226,True.intro,True.intro⟩,True.intro⟩,⟨sg40229,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_743All : degreeTree62_743.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40241,⟨sg40236,⟨sg40233,⟨sg40232,⟨sg40231,True.intro,True.intro⟩,True.intro⟩,⟨sg40235,⟨sg40234,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40239,⟨sg40238,⟨sg40237,True.intro,True.intro⟩,True.intro⟩,⟨sg40240,True.intro,True.intro⟩⟩⟩,⟨sg40246,⟨sg40244,⟨sg40243,⟨sg40242,True.intro,True.intro⟩,True.intro⟩,⟨sg40245,True.intro,True.intro⟩⟩,⟨sg40249,⟨sg40248,⟨sg40247,True.intro,True.intro⟩,True.intro⟩,⟨sg40250,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_744All : degreeTree62_744.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40230,degreeTree62_742All,degreeTree62_743All⟩ + +lemma degreeTree62_745All : degreeTree62_745.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40208,degreeTree62_741All,degreeTree62_744All⟩ + +lemma degreeTree62_746All : degreeTree62_746.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40164,degreeTree62_738All,degreeTree62_745All⟩ + +lemma degreeTree62_747All : degreeTree62_747.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40262,⟨sg40257,⟨sg40254,⟨sg40253,⟨sg40252,True.intro,True.intro⟩,True.intro⟩,⟨sg40256,⟨sg40255,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40260,⟨sg40259,⟨sg40258,True.intro,True.intro⟩,True.intro⟩,⟨sg40261,True.intro,True.intro⟩⟩⟩,⟨sg40268,⟨sg40265,⟨sg40264,⟨sg40263,True.intro,True.intro⟩,True.intro⟩,⟨sg40267,⟨sg40266,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40271,⟨sg40270,⟨sg40269,True.intro,True.intro⟩,True.intro⟩,⟨sg40272,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_748All : degreeTree62_748.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40284,⟨sg40279,⟨sg40276,⟨sg40275,⟨sg40274,True.intro,True.intro⟩,True.intro⟩,⟨sg40278,⟨sg40277,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40282,⟨sg40281,⟨sg40280,True.intro,True.intro⟩,True.intro⟩,⟨sg40283,True.intro,True.intro⟩⟩⟩,⟨sg40290,⟨sg40287,⟨sg40286,⟨sg40285,True.intro,True.intro⟩,True.intro⟩,⟨sg40289,⟨sg40288,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40293,⟨sg40292,⟨sg40291,True.intro,True.intro⟩,True.intro⟩,⟨sg40294,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_749All : degreeTree62_749.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40273,degreeTree62_747All,degreeTree62_748All⟩ + +lemma degreeTree62_750All : degreeTree62_750.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40306,⟨sg40301,⟨sg40298,⟨sg40297,⟨sg40296,True.intro,True.intro⟩,True.intro⟩,⟨sg40300,⟨sg40299,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40304,⟨sg40303,⟨sg40302,True.intro,True.intro⟩,True.intro⟩,⟨sg40305,True.intro,True.intro⟩⟩⟩,⟨sg40312,⟨sg40309,⟨sg40308,⟨sg40307,True.intro,True.intro⟩,True.intro⟩,⟨sg40311,⟨sg40310,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40315,⟨sg40314,⟨sg40313,True.intro,True.intro⟩,True.intro⟩,⟨sg40316,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_751All : degreeTree62_751.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40328,⟨sg40323,⟨sg40320,⟨sg40319,⟨sg40318,True.intro,True.intro⟩,True.intro⟩,⟨sg40322,⟨sg40321,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40326,⟨sg40325,⟨sg40324,True.intro,True.intro⟩,True.intro⟩,⟨sg40327,True.intro,True.intro⟩⟩⟩,⟨sg40334,⟨sg40331,⟨sg40330,⟨sg40329,True.intro,True.intro⟩,True.intro⟩,⟨sg40333,⟨sg40332,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40337,⟨sg40336,⟨sg40335,True.intro,True.intro⟩,True.intro⟩,⟨sg40338,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_752All : degreeTree62_752.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40317,degreeTree62_750All,degreeTree62_751All⟩ + +lemma degreeTree62_753All : degreeTree62_753.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40295,degreeTree62_749All,degreeTree62_752All⟩ + +lemma degreeTree62_754All : degreeTree62_754.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40350,⟨sg40345,⟨sg40342,⟨sg40341,⟨sg40340,True.intro,True.intro⟩,True.intro⟩,⟨sg40344,⟨sg40343,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40348,⟨sg40347,⟨sg40346,True.intro,True.intro⟩,True.intro⟩,⟨sg40349,True.intro,True.intro⟩⟩⟩,⟨sg40356,⟨sg40353,⟨sg40352,⟨sg40351,True.intro,True.intro⟩,True.intro⟩,⟨sg40355,⟨sg40354,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40359,⟨sg40358,⟨sg40357,True.intro,True.intro⟩,True.intro⟩,⟨sg40360,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_755All : degreeTree62_755.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40372,⟨sg40367,⟨sg40364,⟨sg40363,⟨sg40362,True.intro,True.intro⟩,True.intro⟩,⟨sg40366,⟨sg40365,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40370,⟨sg40369,⟨sg40368,True.intro,True.intro⟩,True.intro⟩,⟨sg40371,True.intro,True.intro⟩⟩⟩,⟨sg40378,⟨sg40375,⟨sg40374,⟨sg40373,True.intro,True.intro⟩,True.intro⟩,⟨sg40377,⟨sg40376,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40381,⟨sg40380,⟨sg40379,True.intro,True.intro⟩,True.intro⟩,⟨sg40382,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_756All : degreeTree62_756.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40361,degreeTree62_754All,degreeTree62_755All⟩ + +lemma degreeTree62_757All : degreeTree62_757.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40394,⟨sg40389,⟨sg40386,⟨sg40385,⟨sg40384,True.intro,True.intro⟩,True.intro⟩,⟨sg40388,⟨sg40387,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40392,⟨sg40391,⟨sg40390,True.intro,True.intro⟩,True.intro⟩,⟨sg40393,True.intro,True.intro⟩⟩⟩,⟨sg40400,⟨sg40397,⟨sg40396,⟨sg40395,True.intro,True.intro⟩,True.intro⟩,⟨sg40399,⟨sg40398,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40403,⟨sg40402,⟨sg40401,True.intro,True.intro⟩,True.intro⟩,⟨sg40404,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_758All : degreeTree62_758.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40416,⟨sg40411,⟨sg40408,⟨sg40407,⟨sg40406,True.intro,True.intro⟩,True.intro⟩,⟨sg40410,⟨sg40409,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40414,⟨sg40413,⟨sg40412,True.intro,True.intro⟩,True.intro⟩,⟨sg40415,True.intro,True.intro⟩⟩⟩,⟨sg40421,⟨sg40419,⟨sg40418,⟨sg40417,True.intro,True.intro⟩,True.intro⟩,⟨sg40420,True.intro,True.intro⟩⟩,⟨sg40424,⟨sg40423,⟨sg40422,True.intro,True.intro⟩,True.intro⟩,⟨sg40425,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_759All : degreeTree62_759.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40405,degreeTree62_757All,degreeTree62_758All⟩ + +lemma degreeTree62_760All : degreeTree62_760.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40383,degreeTree62_756All,degreeTree62_759All⟩ + +lemma degreeTree62_761All : degreeTree62_761.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40339,degreeTree62_753All,degreeTree62_760All⟩ + +lemma degreeTree62_762All : degreeTree62_762.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40251,degreeTree62_746All,degreeTree62_761All⟩ + +lemma degreeTree62_763All : degreeTree62_763.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40076,degreeTree62_731All,degreeTree62_762All⟩ + +lemma degreeTree62_764All : degreeTree62_764.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39725,degreeTree62_700All,degreeTree62_763All⟩ + +lemma degreeTree62_765All : degreeTree62_765.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg39023,degreeTree62_637All,degreeTree62_764All⟩ + +lemma degreeTree62_766All : degreeTree62_766.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40437,⟨sg40432,⟨sg40429,⟨sg40428,⟨sg40427,True.intro,True.intro⟩,True.intro⟩,⟨sg40431,⟨sg40430,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40435,⟨sg40434,⟨sg40433,True.intro,True.intro⟩,True.intro⟩,⟨sg40436,True.intro,True.intro⟩⟩⟩,⟨sg40443,⟨sg40440,⟨sg40439,⟨sg40438,True.intro,True.intro⟩,True.intro⟩,⟨sg40442,⟨sg40441,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40446,⟨sg40445,⟨sg40444,True.intro,True.intro⟩,True.intro⟩,⟨sg40447,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_767All : degreeTree62_767.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40459,⟨sg40454,⟨sg40451,⟨sg40450,⟨sg40449,True.intro,True.intro⟩,True.intro⟩,⟨sg40453,⟨sg40452,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40457,⟨sg40456,⟨sg40455,True.intro,True.intro⟩,True.intro⟩,⟨sg40458,True.intro,True.intro⟩⟩⟩,⟨sg40465,⟨sg40462,⟨sg40461,⟨sg40460,True.intro,True.intro⟩,True.intro⟩,⟨sg40464,⟨sg40463,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40468,⟨sg40467,⟨sg40466,True.intro,True.intro⟩,True.intro⟩,⟨sg40469,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_768All : degreeTree62_768.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40448,degreeTree62_766All,degreeTree62_767All⟩ + +lemma degreeTree62_769All : degreeTree62_769.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40481,⟨sg40476,⟨sg40473,⟨sg40472,⟨sg40471,True.intro,True.intro⟩,True.intro⟩,⟨sg40475,⟨sg40474,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40479,⟨sg40478,⟨sg40477,True.intro,True.intro⟩,True.intro⟩,⟨sg40480,True.intro,True.intro⟩⟩⟩,⟨sg40487,⟨sg40484,⟨sg40483,⟨sg40482,True.intro,True.intro⟩,True.intro⟩,⟨sg40486,⟨sg40485,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40490,⟨sg40489,⟨sg40488,True.intro,True.intro⟩,True.intro⟩,⟨sg40491,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_770All : degreeTree62_770.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40503,⟨sg40498,⟨sg40495,⟨sg40494,⟨sg40493,True.intro,True.intro⟩,True.intro⟩,⟨sg40497,⟨sg40496,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40501,⟨sg40500,⟨sg40499,True.intro,True.intro⟩,True.intro⟩,⟨sg40502,True.intro,True.intro⟩⟩⟩,⟨sg40509,⟨sg40506,⟨sg40505,⟨sg40504,True.intro,True.intro⟩,True.intro⟩,⟨sg40508,⟨sg40507,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40512,⟨sg40511,⟨sg40510,True.intro,True.intro⟩,True.intro⟩,⟨sg40513,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_771All : degreeTree62_771.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40492,degreeTree62_769All,degreeTree62_770All⟩ + +lemma degreeTree62_772All : degreeTree62_772.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40470,degreeTree62_768All,degreeTree62_771All⟩ + +lemma degreeTree62_773All : degreeTree62_773.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40525,⟨sg40520,⟨sg40517,⟨sg40516,⟨sg40515,True.intro,True.intro⟩,True.intro⟩,⟨sg40519,⟨sg40518,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40523,⟨sg40522,⟨sg40521,True.intro,True.intro⟩,True.intro⟩,⟨sg40524,True.intro,True.intro⟩⟩⟩,⟨sg40531,⟨sg40528,⟨sg40527,⟨sg40526,True.intro,True.intro⟩,True.intro⟩,⟨sg40530,⟨sg40529,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40534,⟨sg40533,⟨sg40532,True.intro,True.intro⟩,True.intro⟩,⟨sg40535,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_774All : degreeTree62_774.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40547,⟨sg40542,⟨sg40539,⟨sg40538,⟨sg40537,True.intro,True.intro⟩,True.intro⟩,⟨sg40541,⟨sg40540,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40545,⟨sg40544,⟨sg40543,True.intro,True.intro⟩,True.intro⟩,⟨sg40546,True.intro,True.intro⟩⟩⟩,⟨sg40553,⟨sg40550,⟨sg40549,⟨sg40548,True.intro,True.intro⟩,True.intro⟩,⟨sg40552,⟨sg40551,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40556,⟨sg40555,⟨sg40554,True.intro,True.intro⟩,True.intro⟩,⟨sg40557,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_775All : degreeTree62_775.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40536,degreeTree62_773All,degreeTree62_774All⟩ + +lemma degreeTree62_776All : degreeTree62_776.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40569,⟨sg40564,⟨sg40561,⟨sg40560,⟨sg40559,True.intro,True.intro⟩,True.intro⟩,⟨sg40563,⟨sg40562,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40567,⟨sg40566,⟨sg40565,True.intro,True.intro⟩,True.intro⟩,⟨sg40568,True.intro,True.intro⟩⟩⟩,⟨sg40575,⟨sg40572,⟨sg40571,⟨sg40570,True.intro,True.intro⟩,True.intro⟩,⟨sg40574,⟨sg40573,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40578,⟨sg40577,⟨sg40576,True.intro,True.intro⟩,True.intro⟩,⟨sg40579,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_777All : degreeTree62_777.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40591,⟨sg40586,⟨sg40583,⟨sg40582,⟨sg40581,True.intro,True.intro⟩,True.intro⟩,⟨sg40585,⟨sg40584,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40589,⟨sg40588,⟨sg40587,True.intro,True.intro⟩,True.intro⟩,⟨sg40590,True.intro,True.intro⟩⟩⟩,⟨sg40597,⟨sg40594,⟨sg40593,⟨sg40592,True.intro,True.intro⟩,True.intro⟩,⟨sg40596,⟨sg40595,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40600,⟨sg40599,⟨sg40598,True.intro,True.intro⟩,True.intro⟩,⟨sg40601,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_778All : degreeTree62_778.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40580,degreeTree62_776All,degreeTree62_777All⟩ + +lemma degreeTree62_779All : degreeTree62_779.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40558,degreeTree62_775All,degreeTree62_778All⟩ + +lemma degreeTree62_780All : degreeTree62_780.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40514,degreeTree62_772All,degreeTree62_779All⟩ + +lemma degreeTree62_781All : degreeTree62_781.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40613,⟨sg40608,⟨sg40605,⟨sg40604,⟨sg40603,True.intro,True.intro⟩,True.intro⟩,⟨sg40607,⟨sg40606,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40611,⟨sg40610,⟨sg40609,True.intro,True.intro⟩,True.intro⟩,⟨sg40612,True.intro,True.intro⟩⟩⟩,⟨sg40619,⟨sg40616,⟨sg40615,⟨sg40614,True.intro,True.intro⟩,True.intro⟩,⟨sg40618,⟨sg40617,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40622,⟨sg40621,⟨sg40620,True.intro,True.intro⟩,True.intro⟩,⟨sg40623,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_782All : degreeTree62_782.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40635,⟨sg40630,⟨sg40627,⟨sg40626,⟨sg40625,True.intro,True.intro⟩,True.intro⟩,⟨sg40629,⟨sg40628,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40633,⟨sg40632,⟨sg40631,True.intro,True.intro⟩,True.intro⟩,⟨sg40634,True.intro,True.intro⟩⟩⟩,⟨sg40641,⟨sg40638,⟨sg40637,⟨sg40636,True.intro,True.intro⟩,True.intro⟩,⟨sg40640,⟨sg40639,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40644,⟨sg40643,⟨sg40642,True.intro,True.intro⟩,True.intro⟩,⟨sg40645,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_783All : degreeTree62_783.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40624,degreeTree62_781All,degreeTree62_782All⟩ + +lemma degreeTree62_784All : degreeTree62_784.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40657,⟨sg40652,⟨sg40649,⟨sg40648,⟨sg40647,True.intro,True.intro⟩,True.intro⟩,⟨sg40651,⟨sg40650,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40655,⟨sg40654,⟨sg40653,True.intro,True.intro⟩,True.intro⟩,⟨sg40656,True.intro,True.intro⟩⟩⟩,⟨sg40663,⟨sg40660,⟨sg40659,⟨sg40658,True.intro,True.intro⟩,True.intro⟩,⟨sg40662,⟨sg40661,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40666,⟨sg40665,⟨sg40664,True.intro,True.intro⟩,True.intro⟩,⟨sg40667,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_785All : degreeTree62_785.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40679,⟨sg40674,⟨sg40671,⟨sg40670,⟨sg40669,True.intro,True.intro⟩,True.intro⟩,⟨sg40673,⟨sg40672,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40677,⟨sg40676,⟨sg40675,True.intro,True.intro⟩,True.intro⟩,⟨sg40678,True.intro,True.intro⟩⟩⟩,⟨sg40685,⟨sg40682,⟨sg40681,⟨sg40680,True.intro,True.intro⟩,True.intro⟩,⟨sg40684,⟨sg40683,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40688,⟨sg40687,⟨sg40686,True.intro,True.intro⟩,True.intro⟩,⟨sg40689,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_786All : degreeTree62_786.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40668,degreeTree62_784All,degreeTree62_785All⟩ + +lemma degreeTree62_787All : degreeTree62_787.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40646,degreeTree62_783All,degreeTree62_786All⟩ + +lemma degreeTree62_788All : degreeTree62_788.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40701,⟨sg40696,⟨sg40693,⟨sg40692,⟨sg40691,True.intro,True.intro⟩,True.intro⟩,⟨sg40695,⟨sg40694,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40699,⟨sg40698,⟨sg40697,True.intro,True.intro⟩,True.intro⟩,⟨sg40700,True.intro,True.intro⟩⟩⟩,⟨sg40707,⟨sg40704,⟨sg40703,⟨sg40702,True.intro,True.intro⟩,True.intro⟩,⟨sg40706,⟨sg40705,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40710,⟨sg40709,⟨sg40708,True.intro,True.intro⟩,True.intro⟩,⟨sg40711,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_789All : degreeTree62_789.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40723,⟨sg40718,⟨sg40715,⟨sg40714,⟨sg40713,True.intro,True.intro⟩,True.intro⟩,⟨sg40717,⟨sg40716,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40721,⟨sg40720,⟨sg40719,True.intro,True.intro⟩,True.intro⟩,⟨sg40722,True.intro,True.intro⟩⟩⟩,⟨sg40729,⟨sg40726,⟨sg40725,⟨sg40724,True.intro,True.intro⟩,True.intro⟩,⟨sg40728,⟨sg40727,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40732,⟨sg40731,⟨sg40730,True.intro,True.intro⟩,True.intro⟩,⟨sg40733,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_790All : degreeTree62_790.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40712,degreeTree62_788All,degreeTree62_789All⟩ + +lemma degreeTree62_791All : degreeTree62_791.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40745,⟨sg40740,⟨sg40737,⟨sg40736,⟨sg40735,True.intro,True.intro⟩,True.intro⟩,⟨sg40739,⟨sg40738,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40743,⟨sg40742,⟨sg40741,True.intro,True.intro⟩,True.intro⟩,⟨sg40744,True.intro,True.intro⟩⟩⟩,⟨sg40751,⟨sg40748,⟨sg40747,⟨sg40746,True.intro,True.intro⟩,True.intro⟩,⟨sg40750,⟨sg40749,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40754,⟨sg40753,⟨sg40752,True.intro,True.intro⟩,True.intro⟩,⟨sg40755,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_792All : degreeTree62_792.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40767,⟨sg40762,⟨sg40759,⟨sg40758,⟨sg40757,True.intro,True.intro⟩,True.intro⟩,⟨sg40761,⟨sg40760,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40765,⟨sg40764,⟨sg40763,True.intro,True.intro⟩,True.intro⟩,⟨sg40766,True.intro,True.intro⟩⟩⟩,⟨sg40772,⟨sg40770,⟨sg40769,⟨sg40768,True.intro,True.intro⟩,True.intro⟩,⟨sg40771,True.intro,True.intro⟩⟩,⟨sg40775,⟨sg40774,⟨sg40773,True.intro,True.intro⟩,True.intro⟩,⟨sg40776,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_793All : degreeTree62_793.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40756,degreeTree62_791All,degreeTree62_792All⟩ + +lemma degreeTree62_794All : degreeTree62_794.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40734,degreeTree62_790All,degreeTree62_793All⟩ + +lemma degreeTree62_795All : degreeTree62_795.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40690,degreeTree62_787All,degreeTree62_794All⟩ + +lemma degreeTree62_796All : degreeTree62_796.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40602,degreeTree62_780All,degreeTree62_795All⟩ + +lemma degreeTree62_797All : degreeTree62_797.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40788,⟨sg40783,⟨sg40780,⟨sg40779,⟨sg40778,True.intro,True.intro⟩,True.intro⟩,⟨sg40782,⟨sg40781,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40786,⟨sg40785,⟨sg40784,True.intro,True.intro⟩,True.intro⟩,⟨sg40787,True.intro,True.intro⟩⟩⟩,⟨sg40794,⟨sg40791,⟨sg40790,⟨sg40789,True.intro,True.intro⟩,True.intro⟩,⟨sg40793,⟨sg40792,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40797,⟨sg40796,⟨sg40795,True.intro,True.intro⟩,True.intro⟩,⟨sg40798,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_798All : degreeTree62_798.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40810,⟨sg40805,⟨sg40802,⟨sg40801,⟨sg40800,True.intro,True.intro⟩,True.intro⟩,⟨sg40804,⟨sg40803,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40808,⟨sg40807,⟨sg40806,True.intro,True.intro⟩,True.intro⟩,⟨sg40809,True.intro,True.intro⟩⟩⟩,⟨sg40816,⟨sg40813,⟨sg40812,⟨sg40811,True.intro,True.intro⟩,True.intro⟩,⟨sg40815,⟨sg40814,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40819,⟨sg40818,⟨sg40817,True.intro,True.intro⟩,True.intro⟩,⟨sg40820,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_799All : degreeTree62_799.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40799,degreeTree62_797All,degreeTree62_798All⟩ + +lemma degreeTree62_800All : degreeTree62_800.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40832,⟨sg40827,⟨sg40824,⟨sg40823,⟨sg40822,True.intro,True.intro⟩,True.intro⟩,⟨sg40826,⟨sg40825,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40830,⟨sg40829,⟨sg40828,True.intro,True.intro⟩,True.intro⟩,⟨sg40831,True.intro,True.intro⟩⟩⟩,⟨sg40838,⟨sg40835,⟨sg40834,⟨sg40833,True.intro,True.intro⟩,True.intro⟩,⟨sg40837,⟨sg40836,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40841,⟨sg40840,⟨sg40839,True.intro,True.intro⟩,True.intro⟩,⟨sg40842,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_801All : degreeTree62_801.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40854,⟨sg40849,⟨sg40846,⟨sg40845,⟨sg40844,True.intro,True.intro⟩,True.intro⟩,⟨sg40848,⟨sg40847,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40852,⟨sg40851,⟨sg40850,True.intro,True.intro⟩,True.intro⟩,⟨sg40853,True.intro,True.intro⟩⟩⟩,⟨sg40860,⟨sg40857,⟨sg40856,⟨sg40855,True.intro,True.intro⟩,True.intro⟩,⟨sg40859,⟨sg40858,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40863,⟨sg40862,⟨sg40861,True.intro,True.intro⟩,True.intro⟩,⟨sg40864,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_802All : degreeTree62_802.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40843,degreeTree62_800All,degreeTree62_801All⟩ + +lemma degreeTree62_803All : degreeTree62_803.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40821,degreeTree62_799All,degreeTree62_802All⟩ + +lemma degreeTree62_804All : degreeTree62_804.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40876,⟨sg40871,⟨sg40868,⟨sg40867,⟨sg40866,True.intro,True.intro⟩,True.intro⟩,⟨sg40870,⟨sg40869,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40874,⟨sg40873,⟨sg40872,True.intro,True.intro⟩,True.intro⟩,⟨sg40875,True.intro,True.intro⟩⟩⟩,⟨sg40882,⟨sg40879,⟨sg40878,⟨sg40877,True.intro,True.intro⟩,True.intro⟩,⟨sg40881,⟨sg40880,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40885,⟨sg40884,⟨sg40883,True.intro,True.intro⟩,True.intro⟩,⟨sg40886,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_805All : degreeTree62_805.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40898,⟨sg40893,⟨sg40890,⟨sg40889,⟨sg40888,True.intro,True.intro⟩,True.intro⟩,⟨sg40892,⟨sg40891,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40896,⟨sg40895,⟨sg40894,True.intro,True.intro⟩,True.intro⟩,⟨sg40897,True.intro,True.intro⟩⟩⟩,⟨sg40904,⟨sg40901,⟨sg40900,⟨sg40899,True.intro,True.intro⟩,True.intro⟩,⟨sg40903,⟨sg40902,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40907,⟨sg40906,⟨sg40905,True.intro,True.intro⟩,True.intro⟩,⟨sg40908,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_806All : degreeTree62_806.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40887,degreeTree62_804All,degreeTree62_805All⟩ + +lemma degreeTree62_807All : degreeTree62_807.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40920,⟨sg40915,⟨sg40912,⟨sg40911,⟨sg40910,True.intro,True.intro⟩,True.intro⟩,⟨sg40914,⟨sg40913,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40918,⟨sg40917,⟨sg40916,True.intro,True.intro⟩,True.intro⟩,⟨sg40919,True.intro,True.intro⟩⟩⟩,⟨sg40926,⟨sg40923,⟨sg40922,⟨sg40921,True.intro,True.intro⟩,True.intro⟩,⟨sg40925,⟨sg40924,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40929,⟨sg40928,⟨sg40927,True.intro,True.intro⟩,True.intro⟩,⟨sg40930,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_808All : degreeTree62_808.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40942,⟨sg40937,⟨sg40934,⟨sg40933,⟨sg40932,True.intro,True.intro⟩,True.intro⟩,⟨sg40936,⟨sg40935,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40940,⟨sg40939,⟨sg40938,True.intro,True.intro⟩,True.intro⟩,⟨sg40941,True.intro,True.intro⟩⟩⟩,⟨sg40948,⟨sg40945,⟨sg40944,⟨sg40943,True.intro,True.intro⟩,True.intro⟩,⟨sg40947,⟨sg40946,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40951,⟨sg40950,⟨sg40949,True.intro,True.intro⟩,True.intro⟩,⟨sg40952,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_809All : degreeTree62_809.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40931,degreeTree62_807All,degreeTree62_808All⟩ + +lemma degreeTree62_810All : degreeTree62_810.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40909,degreeTree62_806All,degreeTree62_809All⟩ + +lemma degreeTree62_811All : degreeTree62_811.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40865,degreeTree62_803All,degreeTree62_810All⟩ + +lemma degreeTree62_812All : degreeTree62_812.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40964,⟨sg40959,⟨sg40956,⟨sg40955,⟨sg40954,True.intro,True.intro⟩,True.intro⟩,⟨sg40958,⟨sg40957,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40962,⟨sg40961,⟨sg40960,True.intro,True.intro⟩,True.intro⟩,⟨sg40963,True.intro,True.intro⟩⟩⟩,⟨sg40970,⟨sg40967,⟨sg40966,⟨sg40965,True.intro,True.intro⟩,True.intro⟩,⟨sg40969,⟨sg40968,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40973,⟨sg40972,⟨sg40971,True.intro,True.intro⟩,True.intro⟩,⟨sg40974,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_813All : degreeTree62_813.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40986,⟨sg40981,⟨sg40978,⟨sg40977,⟨sg40976,True.intro,True.intro⟩,True.intro⟩,⟨sg40980,⟨sg40979,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40984,⟨sg40983,⟨sg40982,True.intro,True.intro⟩,True.intro⟩,⟨sg40985,True.intro,True.intro⟩⟩⟩,⟨sg40992,⟨sg40989,⟨sg40988,⟨sg40987,True.intro,True.intro⟩,True.intro⟩,⟨sg40991,⟨sg40990,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg40995,⟨sg40994,⟨sg40993,True.intro,True.intro⟩,True.intro⟩,⟨sg40996,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_814All : degreeTree62_814.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40975,degreeTree62_812All,degreeTree62_813All⟩ + +lemma degreeTree62_815All : degreeTree62_815.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41008,⟨sg41003,⟨sg41000,⟨sg40999,⟨sg40998,True.intro,True.intro⟩,True.intro⟩,⟨sg41002,⟨sg41001,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41006,⟨sg41005,⟨sg41004,True.intro,True.intro⟩,True.intro⟩,⟨sg41007,True.intro,True.intro⟩⟩⟩,⟨sg41014,⟨sg41011,⟨sg41010,⟨sg41009,True.intro,True.intro⟩,True.intro⟩,⟨sg41013,⟨sg41012,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41017,⟨sg41016,⟨sg41015,True.intro,True.intro⟩,True.intro⟩,⟨sg41018,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_816All : degreeTree62_816.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41030,⟨sg41025,⟨sg41022,⟨sg41021,⟨sg41020,True.intro,True.intro⟩,True.intro⟩,⟨sg41024,⟨sg41023,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41028,⟨sg41027,⟨sg41026,True.intro,True.intro⟩,True.intro⟩,⟨sg41029,True.intro,True.intro⟩⟩⟩,⟨sg41036,⟨sg41033,⟨sg41032,⟨sg41031,True.intro,True.intro⟩,True.intro⟩,⟨sg41035,⟨sg41034,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41039,⟨sg41038,⟨sg41037,True.intro,True.intro⟩,True.intro⟩,⟨sg41040,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_817All : degreeTree62_817.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41019,degreeTree62_815All,degreeTree62_816All⟩ + +lemma degreeTree62_818All : degreeTree62_818.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40997,degreeTree62_814All,degreeTree62_817All⟩ + +lemma degreeTree62_819All : degreeTree62_819.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41052,⟨sg41047,⟨sg41044,⟨sg41043,⟨sg41042,True.intro,True.intro⟩,True.intro⟩,⟨sg41046,⟨sg41045,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41050,⟨sg41049,⟨sg41048,True.intro,True.intro⟩,True.intro⟩,⟨sg41051,True.intro,True.intro⟩⟩⟩,⟨sg41058,⟨sg41055,⟨sg41054,⟨sg41053,True.intro,True.intro⟩,True.intro⟩,⟨sg41057,⟨sg41056,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41061,⟨sg41060,⟨sg41059,True.intro,True.intro⟩,True.intro⟩,⟨sg41062,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_820All : degreeTree62_820.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41074,⟨sg41069,⟨sg41066,⟨sg41065,⟨sg41064,True.intro,True.intro⟩,True.intro⟩,⟨sg41068,⟨sg41067,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41072,⟨sg41071,⟨sg41070,True.intro,True.intro⟩,True.intro⟩,⟨sg41073,True.intro,True.intro⟩⟩⟩,⟨sg41080,⟨sg41077,⟨sg41076,⟨sg41075,True.intro,True.intro⟩,True.intro⟩,⟨sg41079,⟨sg41078,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41083,⟨sg41082,⟨sg41081,True.intro,True.intro⟩,True.intro⟩,⟨sg41084,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_821All : degreeTree62_821.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41063,degreeTree62_819All,degreeTree62_820All⟩ + +lemma degreeTree62_822All : degreeTree62_822.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41096,⟨sg41091,⟨sg41088,⟨sg41087,⟨sg41086,True.intro,True.intro⟩,True.intro⟩,⟨sg41090,⟨sg41089,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41094,⟨sg41093,⟨sg41092,True.intro,True.intro⟩,True.intro⟩,⟨sg41095,True.intro,True.intro⟩⟩⟩,⟨sg41102,⟨sg41099,⟨sg41098,⟨sg41097,True.intro,True.intro⟩,True.intro⟩,⟨sg41101,⟨sg41100,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41105,⟨sg41104,⟨sg41103,True.intro,True.intro⟩,True.intro⟩,⟨sg41106,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_823All : degreeTree62_823.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41118,⟨sg41113,⟨sg41110,⟨sg41109,⟨sg41108,True.intro,True.intro⟩,True.intro⟩,⟨sg41112,⟨sg41111,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41116,⟨sg41115,⟨sg41114,True.intro,True.intro⟩,True.intro⟩,⟨sg41117,True.intro,True.intro⟩⟩⟩,⟨sg41123,⟨sg41121,⟨sg41120,⟨sg41119,True.intro,True.intro⟩,True.intro⟩,⟨sg41122,True.intro,True.intro⟩⟩,⟨sg41126,⟨sg41125,⟨sg41124,True.intro,True.intro⟩,True.intro⟩,⟨sg41127,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_824All : degreeTree62_824.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41107,degreeTree62_822All,degreeTree62_823All⟩ + +lemma degreeTree62_825All : degreeTree62_825.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41085,degreeTree62_821All,degreeTree62_824All⟩ + +lemma degreeTree62_826All : degreeTree62_826.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41041,degreeTree62_818All,degreeTree62_825All⟩ + +lemma degreeTree62_827All : degreeTree62_827.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40953,degreeTree62_811All,degreeTree62_826All⟩ + +lemma degreeTree62_828All : degreeTree62_828.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40777,degreeTree62_796All,degreeTree62_827All⟩ + +lemma degreeTree62_829All : degreeTree62_829.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41139,⟨sg41134,⟨sg41131,⟨sg41130,⟨sg41129,True.intro,True.intro⟩,True.intro⟩,⟨sg41133,⟨sg41132,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41137,⟨sg41136,⟨sg41135,True.intro,True.intro⟩,True.intro⟩,⟨sg41138,True.intro,True.intro⟩⟩⟩,⟨sg41145,⟨sg41142,⟨sg41141,⟨sg41140,True.intro,True.intro⟩,True.intro⟩,⟨sg41144,⟨sg41143,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41148,⟨sg41147,⟨sg41146,True.intro,True.intro⟩,True.intro⟩,⟨sg41149,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_830All : degreeTree62_830.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41161,⟨sg41156,⟨sg41153,⟨sg41152,⟨sg41151,True.intro,True.intro⟩,True.intro⟩,⟨sg41155,⟨sg41154,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41159,⟨sg41158,⟨sg41157,True.intro,True.intro⟩,True.intro⟩,⟨sg41160,True.intro,True.intro⟩⟩⟩,⟨sg41167,⟨sg41164,⟨sg41163,⟨sg41162,True.intro,True.intro⟩,True.intro⟩,⟨sg41166,⟨sg41165,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41170,⟨sg41169,⟨sg41168,True.intro,True.intro⟩,True.intro⟩,⟨sg41171,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_831All : degreeTree62_831.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41150,degreeTree62_829All,degreeTree62_830All⟩ + +lemma degreeTree62_832All : degreeTree62_832.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41183,⟨sg41178,⟨sg41175,⟨sg41174,⟨sg41173,True.intro,True.intro⟩,True.intro⟩,⟨sg41177,⟨sg41176,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41181,⟨sg41180,⟨sg41179,True.intro,True.intro⟩,True.intro⟩,⟨sg41182,True.intro,True.intro⟩⟩⟩,⟨sg41189,⟨sg41186,⟨sg41185,⟨sg41184,True.intro,True.intro⟩,True.intro⟩,⟨sg41188,⟨sg41187,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41192,⟨sg41191,⟨sg41190,True.intro,True.intro⟩,True.intro⟩,⟨sg41193,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_833All : degreeTree62_833.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41205,⟨sg41200,⟨sg41197,⟨sg41196,⟨sg41195,True.intro,True.intro⟩,True.intro⟩,⟨sg41199,⟨sg41198,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41203,⟨sg41202,⟨sg41201,True.intro,True.intro⟩,True.intro⟩,⟨sg41204,True.intro,True.intro⟩⟩⟩,⟨sg41211,⟨sg41208,⟨sg41207,⟨sg41206,True.intro,True.intro⟩,True.intro⟩,⟨sg41210,⟨sg41209,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41214,⟨sg41213,⟨sg41212,True.intro,True.intro⟩,True.intro⟩,⟨sg41215,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_834All : degreeTree62_834.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41194,degreeTree62_832All,degreeTree62_833All⟩ + +lemma degreeTree62_835All : degreeTree62_835.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41172,degreeTree62_831All,degreeTree62_834All⟩ + +lemma degreeTree62_836All : degreeTree62_836.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41227,⟨sg41222,⟨sg41219,⟨sg41218,⟨sg41217,True.intro,True.intro⟩,True.intro⟩,⟨sg41221,⟨sg41220,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41225,⟨sg41224,⟨sg41223,True.intro,True.intro⟩,True.intro⟩,⟨sg41226,True.intro,True.intro⟩⟩⟩,⟨sg41233,⟨sg41230,⟨sg41229,⟨sg41228,True.intro,True.intro⟩,True.intro⟩,⟨sg41232,⟨sg41231,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41236,⟨sg41235,⟨sg41234,True.intro,True.intro⟩,True.intro⟩,⟨sg41237,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_837All : degreeTree62_837.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41249,⟨sg41244,⟨sg41241,⟨sg41240,⟨sg41239,True.intro,True.intro⟩,True.intro⟩,⟨sg41243,⟨sg41242,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41247,⟨sg41246,⟨sg41245,True.intro,True.intro⟩,True.intro⟩,⟨sg41248,True.intro,True.intro⟩⟩⟩,⟨sg41255,⟨sg41252,⟨sg41251,⟨sg41250,True.intro,True.intro⟩,True.intro⟩,⟨sg41254,⟨sg41253,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41258,⟨sg41257,⟨sg41256,True.intro,True.intro⟩,True.intro⟩,⟨sg41259,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_838All : degreeTree62_838.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41238,degreeTree62_836All,degreeTree62_837All⟩ + +lemma degreeTree62_839All : degreeTree62_839.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41271,⟨sg41266,⟨sg41263,⟨sg41262,⟨sg41261,True.intro,True.intro⟩,True.intro⟩,⟨sg41265,⟨sg41264,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41269,⟨sg41268,⟨sg41267,True.intro,True.intro⟩,True.intro⟩,⟨sg41270,True.intro,True.intro⟩⟩⟩,⟨sg41277,⟨sg41274,⟨sg41273,⟨sg41272,True.intro,True.intro⟩,True.intro⟩,⟨sg41276,⟨sg41275,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41280,⟨sg41279,⟨sg41278,True.intro,True.intro⟩,True.intro⟩,⟨sg41281,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_840All : degreeTree62_840.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41293,⟨sg41288,⟨sg41285,⟨sg41284,⟨sg41283,True.intro,True.intro⟩,True.intro⟩,⟨sg41287,⟨sg41286,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41291,⟨sg41290,⟨sg41289,True.intro,True.intro⟩,True.intro⟩,⟨sg41292,True.intro,True.intro⟩⟩⟩,⟨sg41299,⟨sg41296,⟨sg41295,⟨sg41294,True.intro,True.intro⟩,True.intro⟩,⟨sg41298,⟨sg41297,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41302,⟨sg41301,⟨sg41300,True.intro,True.intro⟩,True.intro⟩,⟨sg41303,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_841All : degreeTree62_841.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41282,degreeTree62_839All,degreeTree62_840All⟩ + +lemma degreeTree62_842All : degreeTree62_842.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41260,degreeTree62_838All,degreeTree62_841All⟩ + +lemma degreeTree62_843All : degreeTree62_843.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41216,degreeTree62_835All,degreeTree62_842All⟩ + +lemma degreeTree62_844All : degreeTree62_844.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41315,⟨sg41310,⟨sg41307,⟨sg41306,⟨sg41305,True.intro,True.intro⟩,True.intro⟩,⟨sg41309,⟨sg41308,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41313,⟨sg41312,⟨sg41311,True.intro,True.intro⟩,True.intro⟩,⟨sg41314,True.intro,True.intro⟩⟩⟩,⟨sg41321,⟨sg41318,⟨sg41317,⟨sg41316,True.intro,True.intro⟩,True.intro⟩,⟨sg41320,⟨sg41319,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41324,⟨sg41323,⟨sg41322,True.intro,True.intro⟩,True.intro⟩,⟨sg41325,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_845All : degreeTree62_845.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41337,⟨sg41332,⟨sg41329,⟨sg41328,⟨sg41327,True.intro,True.intro⟩,True.intro⟩,⟨sg41331,⟨sg41330,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41335,⟨sg41334,⟨sg41333,True.intro,True.intro⟩,True.intro⟩,⟨sg41336,True.intro,True.intro⟩⟩⟩,⟨sg41343,⟨sg41340,⟨sg41339,⟨sg41338,True.intro,True.intro⟩,True.intro⟩,⟨sg41342,⟨sg41341,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41346,⟨sg41345,⟨sg41344,True.intro,True.intro⟩,True.intro⟩,⟨sg41347,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_846All : degreeTree62_846.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41326,degreeTree62_844All,degreeTree62_845All⟩ + +lemma degreeTree62_847All : degreeTree62_847.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41359,⟨sg41354,⟨sg41351,⟨sg41350,⟨sg41349,True.intro,True.intro⟩,True.intro⟩,⟨sg41353,⟨sg41352,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41357,⟨sg41356,⟨sg41355,True.intro,True.intro⟩,True.intro⟩,⟨sg41358,True.intro,True.intro⟩⟩⟩,⟨sg41365,⟨sg41362,⟨sg41361,⟨sg41360,True.intro,True.intro⟩,True.intro⟩,⟨sg41364,⟨sg41363,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41368,⟨sg41367,⟨sg41366,True.intro,True.intro⟩,True.intro⟩,⟨sg41369,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_848All : degreeTree62_848.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41381,⟨sg41376,⟨sg41373,⟨sg41372,⟨sg41371,True.intro,True.intro⟩,True.intro⟩,⟨sg41375,⟨sg41374,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41379,⟨sg41378,⟨sg41377,True.intro,True.intro⟩,True.intro⟩,⟨sg41380,True.intro,True.intro⟩⟩⟩,⟨sg41387,⟨sg41384,⟨sg41383,⟨sg41382,True.intro,True.intro⟩,True.intro⟩,⟨sg41386,⟨sg41385,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41390,⟨sg41389,⟨sg41388,True.intro,True.intro⟩,True.intro⟩,⟨sg41391,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_849All : degreeTree62_849.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41370,degreeTree62_847All,degreeTree62_848All⟩ + +lemma degreeTree62_850All : degreeTree62_850.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41348,degreeTree62_846All,degreeTree62_849All⟩ + +lemma degreeTree62_851All : degreeTree62_851.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41403,⟨sg41398,⟨sg41395,⟨sg41394,⟨sg41393,True.intro,True.intro⟩,True.intro⟩,⟨sg41397,⟨sg41396,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41401,⟨sg41400,⟨sg41399,True.intro,True.intro⟩,True.intro⟩,⟨sg41402,True.intro,True.intro⟩⟩⟩,⟨sg41409,⟨sg41406,⟨sg41405,⟨sg41404,True.intro,True.intro⟩,True.intro⟩,⟨sg41408,⟨sg41407,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41412,⟨sg41411,⟨sg41410,True.intro,True.intro⟩,True.intro⟩,⟨sg41413,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_852All : degreeTree62_852.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41425,⟨sg41420,⟨sg41417,⟨sg41416,⟨sg41415,True.intro,True.intro⟩,True.intro⟩,⟨sg41419,⟨sg41418,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41423,⟨sg41422,⟨sg41421,True.intro,True.intro⟩,True.intro⟩,⟨sg41424,True.intro,True.intro⟩⟩⟩,⟨sg41431,⟨sg41428,⟨sg41427,⟨sg41426,True.intro,True.intro⟩,True.intro⟩,⟨sg41430,⟨sg41429,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41434,⟨sg41433,⟨sg41432,True.intro,True.intro⟩,True.intro⟩,⟨sg41435,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_853All : degreeTree62_853.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41414,degreeTree62_851All,degreeTree62_852All⟩ + +lemma degreeTree62_854All : degreeTree62_854.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41447,⟨sg41442,⟨sg41439,⟨sg41438,⟨sg41437,True.intro,True.intro⟩,True.intro⟩,⟨sg41441,⟨sg41440,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41445,⟨sg41444,⟨sg41443,True.intro,True.intro⟩,True.intro⟩,⟨sg41446,True.intro,True.intro⟩⟩⟩,⟨sg41453,⟨sg41450,⟨sg41449,⟨sg41448,True.intro,True.intro⟩,True.intro⟩,⟨sg41452,⟨sg41451,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41456,⟨sg41455,⟨sg41454,True.intro,True.intro⟩,True.intro⟩,⟨sg41457,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_855All : degreeTree62_855.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41469,⟨sg41464,⟨sg41461,⟨sg41460,⟨sg41459,True.intro,True.intro⟩,True.intro⟩,⟨sg41463,⟨sg41462,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41467,⟨sg41466,⟨sg41465,True.intro,True.intro⟩,True.intro⟩,⟨sg41468,True.intro,True.intro⟩⟩⟩,⟨sg41474,⟨sg41472,⟨sg41471,⟨sg41470,True.intro,True.intro⟩,True.intro⟩,⟨sg41473,True.intro,True.intro⟩⟩,⟨sg41477,⟨sg41476,⟨sg41475,True.intro,True.intro⟩,True.intro⟩,⟨sg41478,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_856All : degreeTree62_856.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41458,degreeTree62_854All,degreeTree62_855All⟩ + +lemma degreeTree62_857All : degreeTree62_857.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41436,degreeTree62_853All,degreeTree62_856All⟩ + +lemma degreeTree62_858All : degreeTree62_858.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41392,degreeTree62_850All,degreeTree62_857All⟩ + +lemma degreeTree62_859All : degreeTree62_859.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41304,degreeTree62_843All,degreeTree62_858All⟩ + +lemma degreeTree62_860All : degreeTree62_860.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41490,⟨sg41485,⟨sg41482,⟨sg41481,⟨sg41480,True.intro,True.intro⟩,True.intro⟩,⟨sg41484,⟨sg41483,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41488,⟨sg41487,⟨sg41486,True.intro,True.intro⟩,True.intro⟩,⟨sg41489,True.intro,True.intro⟩⟩⟩,⟨sg41496,⟨sg41493,⟨sg41492,⟨sg41491,True.intro,True.intro⟩,True.intro⟩,⟨sg41495,⟨sg41494,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41499,⟨sg41498,⟨sg41497,True.intro,True.intro⟩,True.intro⟩,⟨sg41500,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_861All : degreeTree62_861.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41512,⟨sg41507,⟨sg41504,⟨sg41503,⟨sg41502,True.intro,True.intro⟩,True.intro⟩,⟨sg41506,⟨sg41505,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41510,⟨sg41509,⟨sg41508,True.intro,True.intro⟩,True.intro⟩,⟨sg41511,True.intro,True.intro⟩⟩⟩,⟨sg41518,⟨sg41515,⟨sg41514,⟨sg41513,True.intro,True.intro⟩,True.intro⟩,⟨sg41517,⟨sg41516,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41521,⟨sg41520,⟨sg41519,True.intro,True.intro⟩,True.intro⟩,⟨sg41522,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_862All : degreeTree62_862.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41501,degreeTree62_860All,degreeTree62_861All⟩ + +lemma degreeTree62_863All : degreeTree62_863.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41534,⟨sg41529,⟨sg41526,⟨sg41525,⟨sg41524,True.intro,True.intro⟩,True.intro⟩,⟨sg41528,⟨sg41527,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41532,⟨sg41531,⟨sg41530,True.intro,True.intro⟩,True.intro⟩,⟨sg41533,True.intro,True.intro⟩⟩⟩,⟨sg41540,⟨sg41537,⟨sg41536,⟨sg41535,True.intro,True.intro⟩,True.intro⟩,⟨sg41539,⟨sg41538,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41543,⟨sg41542,⟨sg41541,True.intro,True.intro⟩,True.intro⟩,⟨sg41544,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_864All : degreeTree62_864.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41556,⟨sg41551,⟨sg41548,⟨sg41547,⟨sg41546,True.intro,True.intro⟩,True.intro⟩,⟨sg41550,⟨sg41549,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41554,⟨sg41553,⟨sg41552,True.intro,True.intro⟩,True.intro⟩,⟨sg41555,True.intro,True.intro⟩⟩⟩,⟨sg41562,⟨sg41559,⟨sg41558,⟨sg41557,True.intro,True.intro⟩,True.intro⟩,⟨sg41561,⟨sg41560,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41565,⟨sg41564,⟨sg41563,True.intro,True.intro⟩,True.intro⟩,⟨sg41566,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_865All : degreeTree62_865.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41545,degreeTree62_863All,degreeTree62_864All⟩ + +lemma degreeTree62_866All : degreeTree62_866.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41523,degreeTree62_862All,degreeTree62_865All⟩ + +lemma degreeTree62_867All : degreeTree62_867.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41578,⟨sg41573,⟨sg41570,⟨sg41569,⟨sg41568,True.intro,True.intro⟩,True.intro⟩,⟨sg41572,⟨sg41571,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41576,⟨sg41575,⟨sg41574,True.intro,True.intro⟩,True.intro⟩,⟨sg41577,True.intro,True.intro⟩⟩⟩,⟨sg41584,⟨sg41581,⟨sg41580,⟨sg41579,True.intro,True.intro⟩,True.intro⟩,⟨sg41583,⟨sg41582,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41587,⟨sg41586,⟨sg41585,True.intro,True.intro⟩,True.intro⟩,⟨sg41588,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_868All : degreeTree62_868.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41600,⟨sg41595,⟨sg41592,⟨sg41591,⟨sg41590,True.intro,True.intro⟩,True.intro⟩,⟨sg41594,⟨sg41593,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41598,⟨sg41597,⟨sg41596,True.intro,True.intro⟩,True.intro⟩,⟨sg41599,True.intro,True.intro⟩⟩⟩,⟨sg41606,⟨sg41603,⟨sg41602,⟨sg41601,True.intro,True.intro⟩,True.intro⟩,⟨sg41605,⟨sg41604,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41609,⟨sg41608,⟨sg41607,True.intro,True.intro⟩,True.intro⟩,⟨sg41610,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_869All : degreeTree62_869.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41589,degreeTree62_867All,degreeTree62_868All⟩ + +lemma degreeTree62_870All : degreeTree62_870.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41622,⟨sg41617,⟨sg41614,⟨sg41613,⟨sg41612,True.intro,True.intro⟩,True.intro⟩,⟨sg41616,⟨sg41615,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41620,⟨sg41619,⟨sg41618,True.intro,True.intro⟩,True.intro⟩,⟨sg41621,True.intro,True.intro⟩⟩⟩,⟨sg41628,⟨sg41625,⟨sg41624,⟨sg41623,True.intro,True.intro⟩,True.intro⟩,⟨sg41627,⟨sg41626,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41631,⟨sg41630,⟨sg41629,True.intro,True.intro⟩,True.intro⟩,⟨sg41632,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_871All : degreeTree62_871.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41644,⟨sg41639,⟨sg41636,⟨sg41635,⟨sg41634,True.intro,True.intro⟩,True.intro⟩,⟨sg41638,⟨sg41637,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41642,⟨sg41641,⟨sg41640,True.intro,True.intro⟩,True.intro⟩,⟨sg41643,True.intro,True.intro⟩⟩⟩,⟨sg41650,⟨sg41647,⟨sg41646,⟨sg41645,True.intro,True.intro⟩,True.intro⟩,⟨sg41649,⟨sg41648,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41653,⟨sg41652,⟨sg41651,True.intro,True.intro⟩,True.intro⟩,⟨sg41654,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_872All : degreeTree62_872.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41633,degreeTree62_870All,degreeTree62_871All⟩ + +lemma degreeTree62_873All : degreeTree62_873.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41611,degreeTree62_869All,degreeTree62_872All⟩ + +lemma degreeTree62_874All : degreeTree62_874.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41567,degreeTree62_866All,degreeTree62_873All⟩ + +lemma degreeTree62_875All : degreeTree62_875.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41666,⟨sg41661,⟨sg41658,⟨sg41657,⟨sg41656,True.intro,True.intro⟩,True.intro⟩,⟨sg41660,⟨sg41659,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41664,⟨sg41663,⟨sg41662,True.intro,True.intro⟩,True.intro⟩,⟨sg41665,True.intro,True.intro⟩⟩⟩,⟨sg41672,⟨sg41669,⟨sg41668,⟨sg41667,True.intro,True.intro⟩,True.intro⟩,⟨sg41671,⟨sg41670,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41675,⟨sg41674,⟨sg41673,True.intro,True.intro⟩,True.intro⟩,⟨sg41676,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_876All : degreeTree62_876.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41688,⟨sg41683,⟨sg41680,⟨sg41679,⟨sg41678,True.intro,True.intro⟩,True.intro⟩,⟨sg41682,⟨sg41681,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41686,⟨sg41685,⟨sg41684,True.intro,True.intro⟩,True.intro⟩,⟨sg41687,True.intro,True.intro⟩⟩⟩,⟨sg41694,⟨sg41691,⟨sg41690,⟨sg41689,True.intro,True.intro⟩,True.intro⟩,⟨sg41693,⟨sg41692,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41697,⟨sg41696,⟨sg41695,True.intro,True.intro⟩,True.intro⟩,⟨sg41698,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_877All : degreeTree62_877.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41677,degreeTree62_875All,degreeTree62_876All⟩ + +lemma degreeTree62_878All : degreeTree62_878.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41710,⟨sg41705,⟨sg41702,⟨sg41701,⟨sg41700,True.intro,True.intro⟩,True.intro⟩,⟨sg41704,⟨sg41703,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41708,⟨sg41707,⟨sg41706,True.intro,True.intro⟩,True.intro⟩,⟨sg41709,True.intro,True.intro⟩⟩⟩,⟨sg41716,⟨sg41713,⟨sg41712,⟨sg41711,True.intro,True.intro⟩,True.intro⟩,⟨sg41715,⟨sg41714,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41719,⟨sg41718,⟨sg41717,True.intro,True.intro⟩,True.intro⟩,⟨sg41720,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_879All : degreeTree62_879.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41732,⟨sg41727,⟨sg41724,⟨sg41723,⟨sg41722,True.intro,True.intro⟩,True.intro⟩,⟨sg41726,⟨sg41725,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41730,⟨sg41729,⟨sg41728,True.intro,True.intro⟩,True.intro⟩,⟨sg41731,True.intro,True.intro⟩⟩⟩,⟨sg41738,⟨sg41735,⟨sg41734,⟨sg41733,True.intro,True.intro⟩,True.intro⟩,⟨sg41737,⟨sg41736,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41741,⟨sg41740,⟨sg41739,True.intro,True.intro⟩,True.intro⟩,⟨sg41742,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_880All : degreeTree62_880.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41721,degreeTree62_878All,degreeTree62_879All⟩ + +lemma degreeTree62_881All : degreeTree62_881.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41699,degreeTree62_877All,degreeTree62_880All⟩ + +lemma degreeTree62_882All : degreeTree62_882.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41754,⟨sg41749,⟨sg41746,⟨sg41745,⟨sg41744,True.intro,True.intro⟩,True.intro⟩,⟨sg41748,⟨sg41747,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41752,⟨sg41751,⟨sg41750,True.intro,True.intro⟩,True.intro⟩,⟨sg41753,True.intro,True.intro⟩⟩⟩,⟨sg41760,⟨sg41757,⟨sg41756,⟨sg41755,True.intro,True.intro⟩,True.intro⟩,⟨sg41759,⟨sg41758,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41763,⟨sg41762,⟨sg41761,True.intro,True.intro⟩,True.intro⟩,⟨sg41764,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_883All : degreeTree62_883.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41776,⟨sg41771,⟨sg41768,⟨sg41767,⟨sg41766,True.intro,True.intro⟩,True.intro⟩,⟨sg41770,⟨sg41769,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41774,⟨sg41773,⟨sg41772,True.intro,True.intro⟩,True.intro⟩,⟨sg41775,True.intro,True.intro⟩⟩⟩,⟨sg41782,⟨sg41779,⟨sg41778,⟨sg41777,True.intro,True.intro⟩,True.intro⟩,⟨sg41781,⟨sg41780,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41785,⟨sg41784,⟨sg41783,True.intro,True.intro⟩,True.intro⟩,⟨sg41786,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_884All : degreeTree62_884.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41765,degreeTree62_882All,degreeTree62_883All⟩ + +lemma degreeTree62_885All : degreeTree62_885.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41798,⟨sg41793,⟨sg41790,⟨sg41789,⟨sg41788,True.intro,True.intro⟩,True.intro⟩,⟨sg41792,⟨sg41791,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41796,⟨sg41795,⟨sg41794,True.intro,True.intro⟩,True.intro⟩,⟨sg41797,True.intro,True.intro⟩⟩⟩,⟨sg41804,⟨sg41801,⟨sg41800,⟨sg41799,True.intro,True.intro⟩,True.intro⟩,⟨sg41803,⟨sg41802,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41807,⟨sg41806,⟨sg41805,True.intro,True.intro⟩,True.intro⟩,⟨sg41808,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_886All : degreeTree62_886.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41820,⟨sg41815,⟨sg41812,⟨sg41811,⟨sg41810,True.intro,True.intro⟩,True.intro⟩,⟨sg41814,⟨sg41813,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41818,⟨sg41817,⟨sg41816,True.intro,True.intro⟩,True.intro⟩,⟨sg41819,True.intro,True.intro⟩⟩⟩,⟨sg41825,⟨sg41823,⟨sg41822,⟨sg41821,True.intro,True.intro⟩,True.intro⟩,⟨sg41824,True.intro,True.intro⟩⟩,⟨sg41828,⟨sg41827,⟨sg41826,True.intro,True.intro⟩,True.intro⟩,⟨sg41829,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_887All : degreeTree62_887.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41809,degreeTree62_885All,degreeTree62_886All⟩ + +lemma degreeTree62_888All : degreeTree62_888.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41787,degreeTree62_884All,degreeTree62_887All⟩ + +lemma degreeTree62_889All : degreeTree62_889.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41743,degreeTree62_881All,degreeTree62_888All⟩ + +lemma degreeTree62_890All : degreeTree62_890.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41655,degreeTree62_874All,degreeTree62_889All⟩ + +lemma degreeTree62_891All : degreeTree62_891.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41479,degreeTree62_859All,degreeTree62_890All⟩ + +lemma degreeTree62_892All : degreeTree62_892.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41128,degreeTree62_828All,degreeTree62_891All⟩ + +lemma degreeTree62_893All : degreeTree62_893.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41841,⟨sg41836,⟨sg41833,⟨sg41832,⟨sg41831,True.intro,True.intro⟩,True.intro⟩,⟨sg41835,⟨sg41834,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41839,⟨sg41838,⟨sg41837,True.intro,True.intro⟩,True.intro⟩,⟨sg41840,True.intro,True.intro⟩⟩⟩,⟨sg41847,⟨sg41844,⟨sg41843,⟨sg41842,True.intro,True.intro⟩,True.intro⟩,⟨sg41846,⟨sg41845,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41850,⟨sg41849,⟨sg41848,True.intro,True.intro⟩,True.intro⟩,⟨sg41851,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_894All : degreeTree62_894.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41863,⟨sg41858,⟨sg41855,⟨sg41854,⟨sg41853,True.intro,True.intro⟩,True.intro⟩,⟨sg41857,⟨sg41856,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41861,⟨sg41860,⟨sg41859,True.intro,True.intro⟩,True.intro⟩,⟨sg41862,True.intro,True.intro⟩⟩⟩,⟨sg41869,⟨sg41866,⟨sg41865,⟨sg41864,True.intro,True.intro⟩,True.intro⟩,⟨sg41868,⟨sg41867,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41872,⟨sg41871,⟨sg41870,True.intro,True.intro⟩,True.intro⟩,⟨sg41873,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_895All : degreeTree62_895.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41852,degreeTree62_893All,degreeTree62_894All⟩ + +lemma degreeTree62_896All : degreeTree62_896.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41885,⟨sg41880,⟨sg41877,⟨sg41876,⟨sg41875,True.intro,True.intro⟩,True.intro⟩,⟨sg41879,⟨sg41878,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41883,⟨sg41882,⟨sg41881,True.intro,True.intro⟩,True.intro⟩,⟨sg41884,True.intro,True.intro⟩⟩⟩,⟨sg41891,⟨sg41888,⟨sg41887,⟨sg41886,True.intro,True.intro⟩,True.intro⟩,⟨sg41890,⟨sg41889,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41894,⟨sg41893,⟨sg41892,True.intro,True.intro⟩,True.intro⟩,⟨sg41895,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_897All : degreeTree62_897.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41907,⟨sg41902,⟨sg41899,⟨sg41898,⟨sg41897,True.intro,True.intro⟩,True.intro⟩,⟨sg41901,⟨sg41900,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41905,⟨sg41904,⟨sg41903,True.intro,True.intro⟩,True.intro⟩,⟨sg41906,True.intro,True.intro⟩⟩⟩,⟨sg41913,⟨sg41910,⟨sg41909,⟨sg41908,True.intro,True.intro⟩,True.intro⟩,⟨sg41912,⟨sg41911,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41916,⟨sg41915,⟨sg41914,True.intro,True.intro⟩,True.intro⟩,⟨sg41917,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_898All : degreeTree62_898.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41896,degreeTree62_896All,degreeTree62_897All⟩ + +lemma degreeTree62_899All : degreeTree62_899.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41874,degreeTree62_895All,degreeTree62_898All⟩ + +lemma degreeTree62_900All : degreeTree62_900.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41929,⟨sg41924,⟨sg41921,⟨sg41920,⟨sg41919,True.intro,True.intro⟩,True.intro⟩,⟨sg41923,⟨sg41922,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41927,⟨sg41926,⟨sg41925,True.intro,True.intro⟩,True.intro⟩,⟨sg41928,True.intro,True.intro⟩⟩⟩,⟨sg41935,⟨sg41932,⟨sg41931,⟨sg41930,True.intro,True.intro⟩,True.intro⟩,⟨sg41934,⟨sg41933,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41938,⟨sg41937,⟨sg41936,True.intro,True.intro⟩,True.intro⟩,⟨sg41939,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_901All : degreeTree62_901.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41951,⟨sg41946,⟨sg41943,⟨sg41942,⟨sg41941,True.intro,True.intro⟩,True.intro⟩,⟨sg41945,⟨sg41944,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41949,⟨sg41948,⟨sg41947,True.intro,True.intro⟩,True.intro⟩,⟨sg41950,True.intro,True.intro⟩⟩⟩,⟨sg41957,⟨sg41954,⟨sg41953,⟨sg41952,True.intro,True.intro⟩,True.intro⟩,⟨sg41956,⟨sg41955,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41960,⟨sg41959,⟨sg41958,True.intro,True.intro⟩,True.intro⟩,⟨sg41961,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_902All : degreeTree62_902.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41940,degreeTree62_900All,degreeTree62_901All⟩ + +lemma degreeTree62_903All : degreeTree62_903.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41973,⟨sg41968,⟨sg41965,⟨sg41964,⟨sg41963,True.intro,True.intro⟩,True.intro⟩,⟨sg41967,⟨sg41966,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41971,⟨sg41970,⟨sg41969,True.intro,True.intro⟩,True.intro⟩,⟨sg41972,True.intro,True.intro⟩⟩⟩,⟨sg41979,⟨sg41976,⟨sg41975,⟨sg41974,True.intro,True.intro⟩,True.intro⟩,⟨sg41978,⟨sg41977,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41982,⟨sg41981,⟨sg41980,True.intro,True.intro⟩,True.intro⟩,⟨sg41983,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_904All : degreeTree62_904.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41995,⟨sg41990,⟨sg41987,⟨sg41986,⟨sg41985,True.intro,True.intro⟩,True.intro⟩,⟨sg41989,⟨sg41988,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg41993,⟨sg41992,⟨sg41991,True.intro,True.intro⟩,True.intro⟩,⟨sg41994,True.intro,True.intro⟩⟩⟩,⟨sg42001,⟨sg41998,⟨sg41997,⟨sg41996,True.intro,True.intro⟩,True.intro⟩,⟨sg42000,⟨sg41999,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42004,⟨sg42003,⟨sg42002,True.intro,True.intro⟩,True.intro⟩,⟨sg42005,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_905All : degreeTree62_905.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41984,degreeTree62_903All,degreeTree62_904All⟩ + +lemma degreeTree62_906All : degreeTree62_906.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41962,degreeTree62_902All,degreeTree62_905All⟩ + +lemma degreeTree62_907All : degreeTree62_907.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41918,degreeTree62_899All,degreeTree62_906All⟩ + +lemma degreeTree62_908All : degreeTree62_908.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42017,⟨sg42012,⟨sg42009,⟨sg42008,⟨sg42007,True.intro,True.intro⟩,True.intro⟩,⟨sg42011,⟨sg42010,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42015,⟨sg42014,⟨sg42013,True.intro,True.intro⟩,True.intro⟩,⟨sg42016,True.intro,True.intro⟩⟩⟩,⟨sg42023,⟨sg42020,⟨sg42019,⟨sg42018,True.intro,True.intro⟩,True.intro⟩,⟨sg42022,⟨sg42021,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42026,⟨sg42025,⟨sg42024,True.intro,True.intro⟩,True.intro⟩,⟨sg42027,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_909All : degreeTree62_909.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42039,⟨sg42034,⟨sg42031,⟨sg42030,⟨sg42029,True.intro,True.intro⟩,True.intro⟩,⟨sg42033,⟨sg42032,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42037,⟨sg42036,⟨sg42035,True.intro,True.intro⟩,True.intro⟩,⟨sg42038,True.intro,True.intro⟩⟩⟩,⟨sg42045,⟨sg42042,⟨sg42041,⟨sg42040,True.intro,True.intro⟩,True.intro⟩,⟨sg42044,⟨sg42043,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42048,⟨sg42047,⟨sg42046,True.intro,True.intro⟩,True.intro⟩,⟨sg42049,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_910All : degreeTree62_910.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42028,degreeTree62_908All,degreeTree62_909All⟩ + +lemma degreeTree62_911All : degreeTree62_911.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42061,⟨sg42056,⟨sg42053,⟨sg42052,⟨sg42051,True.intro,True.intro⟩,True.intro⟩,⟨sg42055,⟨sg42054,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42059,⟨sg42058,⟨sg42057,True.intro,True.intro⟩,True.intro⟩,⟨sg42060,True.intro,True.intro⟩⟩⟩,⟨sg42067,⟨sg42064,⟨sg42063,⟨sg42062,True.intro,True.intro⟩,True.intro⟩,⟨sg42066,⟨sg42065,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42070,⟨sg42069,⟨sg42068,True.intro,True.intro⟩,True.intro⟩,⟨sg42071,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_912All : degreeTree62_912.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42083,⟨sg42078,⟨sg42075,⟨sg42074,⟨sg42073,True.intro,True.intro⟩,True.intro⟩,⟨sg42077,⟨sg42076,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42081,⟨sg42080,⟨sg42079,True.intro,True.intro⟩,True.intro⟩,⟨sg42082,True.intro,True.intro⟩⟩⟩,⟨sg42089,⟨sg42086,⟨sg42085,⟨sg42084,True.intro,True.intro⟩,True.intro⟩,⟨sg42088,⟨sg42087,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42092,⟨sg42091,⟨sg42090,True.intro,True.intro⟩,True.intro⟩,⟨sg42093,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_913All : degreeTree62_913.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42072,degreeTree62_911All,degreeTree62_912All⟩ + +lemma degreeTree62_914All : degreeTree62_914.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42050,degreeTree62_910All,degreeTree62_913All⟩ + +lemma degreeTree62_915All : degreeTree62_915.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42105,⟨sg42100,⟨sg42097,⟨sg42096,⟨sg42095,True.intro,True.intro⟩,True.intro⟩,⟨sg42099,⟨sg42098,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42103,⟨sg42102,⟨sg42101,True.intro,True.intro⟩,True.intro⟩,⟨sg42104,True.intro,True.intro⟩⟩⟩,⟨sg42111,⟨sg42108,⟨sg42107,⟨sg42106,True.intro,True.intro⟩,True.intro⟩,⟨sg42110,⟨sg42109,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42114,⟨sg42113,⟨sg42112,True.intro,True.intro⟩,True.intro⟩,⟨sg42115,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_916All : degreeTree62_916.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42127,⟨sg42122,⟨sg42119,⟨sg42118,⟨sg42117,True.intro,True.intro⟩,True.intro⟩,⟨sg42121,⟨sg42120,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42125,⟨sg42124,⟨sg42123,True.intro,True.intro⟩,True.intro⟩,⟨sg42126,True.intro,True.intro⟩⟩⟩,⟨sg42133,⟨sg42130,⟨sg42129,⟨sg42128,True.intro,True.intro⟩,True.intro⟩,⟨sg42132,⟨sg42131,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42136,⟨sg42135,⟨sg42134,True.intro,True.intro⟩,True.intro⟩,⟨sg42137,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_917All : degreeTree62_917.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42116,degreeTree62_915All,degreeTree62_916All⟩ + +lemma degreeTree62_918All : degreeTree62_918.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42149,⟨sg42144,⟨sg42141,⟨sg42140,⟨sg42139,True.intro,True.intro⟩,True.intro⟩,⟨sg42143,⟨sg42142,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42147,⟨sg42146,⟨sg42145,True.intro,True.intro⟩,True.intro⟩,⟨sg42148,True.intro,True.intro⟩⟩⟩,⟨sg42155,⟨sg42152,⟨sg42151,⟨sg42150,True.intro,True.intro⟩,True.intro⟩,⟨sg42154,⟨sg42153,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42158,⟨sg42157,⟨sg42156,True.intro,True.intro⟩,True.intro⟩,⟨sg42159,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_919All : degreeTree62_919.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42171,⟨sg42166,⟨sg42163,⟨sg42162,⟨sg42161,True.intro,True.intro⟩,True.intro⟩,⟨sg42165,⟨sg42164,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42169,⟨sg42168,⟨sg42167,True.intro,True.intro⟩,True.intro⟩,⟨sg42170,True.intro,True.intro⟩⟩⟩,⟨sg42176,⟨sg42174,⟨sg42173,⟨sg42172,True.intro,True.intro⟩,True.intro⟩,⟨sg42175,True.intro,True.intro⟩⟩,⟨sg42179,⟨sg42178,⟨sg42177,True.intro,True.intro⟩,True.intro⟩,⟨sg42180,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_920All : degreeTree62_920.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42160,degreeTree62_918All,degreeTree62_919All⟩ + +lemma degreeTree62_921All : degreeTree62_921.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42138,degreeTree62_917All,degreeTree62_920All⟩ + +lemma degreeTree62_922All : degreeTree62_922.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42094,degreeTree62_914All,degreeTree62_921All⟩ + +lemma degreeTree62_923All : degreeTree62_923.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42006,degreeTree62_907All,degreeTree62_922All⟩ + +lemma degreeTree62_924All : degreeTree62_924.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42192,⟨sg42187,⟨sg42184,⟨sg42183,⟨sg42182,True.intro,True.intro⟩,True.intro⟩,⟨sg42186,⟨sg42185,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42190,⟨sg42189,⟨sg42188,True.intro,True.intro⟩,True.intro⟩,⟨sg42191,True.intro,True.intro⟩⟩⟩,⟨sg42198,⟨sg42195,⟨sg42194,⟨sg42193,True.intro,True.intro⟩,True.intro⟩,⟨sg42197,⟨sg42196,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42201,⟨sg42200,⟨sg42199,True.intro,True.intro⟩,True.intro⟩,⟨sg42202,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_925All : degreeTree62_925.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42214,⟨sg42209,⟨sg42206,⟨sg42205,⟨sg42204,True.intro,True.intro⟩,True.intro⟩,⟨sg42208,⟨sg42207,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42212,⟨sg42211,⟨sg42210,True.intro,True.intro⟩,True.intro⟩,⟨sg42213,True.intro,True.intro⟩⟩⟩,⟨sg42220,⟨sg42217,⟨sg42216,⟨sg42215,True.intro,True.intro⟩,True.intro⟩,⟨sg42219,⟨sg42218,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42223,⟨sg42222,⟨sg42221,True.intro,True.intro⟩,True.intro⟩,⟨sg42224,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_926All : degreeTree62_926.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42203,degreeTree62_924All,degreeTree62_925All⟩ + +lemma degreeTree62_927All : degreeTree62_927.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42236,⟨sg42231,⟨sg42228,⟨sg42227,⟨sg42226,True.intro,True.intro⟩,True.intro⟩,⟨sg42230,⟨sg42229,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42234,⟨sg42233,⟨sg42232,True.intro,True.intro⟩,True.intro⟩,⟨sg42235,True.intro,True.intro⟩⟩⟩,⟨sg42242,⟨sg42239,⟨sg42238,⟨sg42237,True.intro,True.intro⟩,True.intro⟩,⟨sg42241,⟨sg42240,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42245,⟨sg42244,⟨sg42243,True.intro,True.intro⟩,True.intro⟩,⟨sg42246,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_928All : degreeTree62_928.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42258,⟨sg42253,⟨sg42250,⟨sg42249,⟨sg42248,True.intro,True.intro⟩,True.intro⟩,⟨sg42252,⟨sg42251,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42256,⟨sg42255,⟨sg42254,True.intro,True.intro⟩,True.intro⟩,⟨sg42257,True.intro,True.intro⟩⟩⟩,⟨sg42264,⟨sg42261,⟨sg42260,⟨sg42259,True.intro,True.intro⟩,True.intro⟩,⟨sg42263,⟨sg42262,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42267,⟨sg42266,⟨sg42265,True.intro,True.intro⟩,True.intro⟩,⟨sg42268,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_929All : degreeTree62_929.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42247,degreeTree62_927All,degreeTree62_928All⟩ + +lemma degreeTree62_930All : degreeTree62_930.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42225,degreeTree62_926All,degreeTree62_929All⟩ + +lemma degreeTree62_931All : degreeTree62_931.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42280,⟨sg42275,⟨sg42272,⟨sg42271,⟨sg42270,True.intro,True.intro⟩,True.intro⟩,⟨sg42274,⟨sg42273,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42278,⟨sg42277,⟨sg42276,True.intro,True.intro⟩,True.intro⟩,⟨sg42279,True.intro,True.intro⟩⟩⟩,⟨sg42286,⟨sg42283,⟨sg42282,⟨sg42281,True.intro,True.intro⟩,True.intro⟩,⟨sg42285,⟨sg42284,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42289,⟨sg42288,⟨sg42287,True.intro,True.intro⟩,True.intro⟩,⟨sg42290,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_932All : degreeTree62_932.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42302,⟨sg42297,⟨sg42294,⟨sg42293,⟨sg42292,True.intro,True.intro⟩,True.intro⟩,⟨sg42296,⟨sg42295,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42300,⟨sg42299,⟨sg42298,True.intro,True.intro⟩,True.intro⟩,⟨sg42301,True.intro,True.intro⟩⟩⟩,⟨sg42308,⟨sg42305,⟨sg42304,⟨sg42303,True.intro,True.intro⟩,True.intro⟩,⟨sg42307,⟨sg42306,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42311,⟨sg42310,⟨sg42309,True.intro,True.intro⟩,True.intro⟩,⟨sg42312,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_933All : degreeTree62_933.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42291,degreeTree62_931All,degreeTree62_932All⟩ + +lemma degreeTree62_934All : degreeTree62_934.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42324,⟨sg42319,⟨sg42316,⟨sg42315,⟨sg42314,True.intro,True.intro⟩,True.intro⟩,⟨sg42318,⟨sg42317,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42322,⟨sg42321,⟨sg42320,True.intro,True.intro⟩,True.intro⟩,⟨sg42323,True.intro,True.intro⟩⟩⟩,⟨sg42330,⟨sg42327,⟨sg42326,⟨sg42325,True.intro,True.intro⟩,True.intro⟩,⟨sg42329,⟨sg42328,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42333,⟨sg42332,⟨sg42331,True.intro,True.intro⟩,True.intro⟩,⟨sg42334,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_935All : degreeTree62_935.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42346,⟨sg42341,⟨sg42338,⟨sg42337,⟨sg42336,True.intro,True.intro⟩,True.intro⟩,⟨sg42340,⟨sg42339,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42344,⟨sg42343,⟨sg42342,True.intro,True.intro⟩,True.intro⟩,⟨sg42345,True.intro,True.intro⟩⟩⟩,⟨sg42352,⟨sg42349,⟨sg42348,⟨sg42347,True.intro,True.intro⟩,True.intro⟩,⟨sg42351,⟨sg42350,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42355,⟨sg42354,⟨sg42353,True.intro,True.intro⟩,True.intro⟩,⟨sg42356,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_936All : degreeTree62_936.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42335,degreeTree62_934All,degreeTree62_935All⟩ + +lemma degreeTree62_937All : degreeTree62_937.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42313,degreeTree62_933All,degreeTree62_936All⟩ + +lemma degreeTree62_938All : degreeTree62_938.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42269,degreeTree62_930All,degreeTree62_937All⟩ + +lemma degreeTree62_939All : degreeTree62_939.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42368,⟨sg42363,⟨sg42360,⟨sg42359,⟨sg42358,True.intro,True.intro⟩,True.intro⟩,⟨sg42362,⟨sg42361,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42366,⟨sg42365,⟨sg42364,True.intro,True.intro⟩,True.intro⟩,⟨sg42367,True.intro,True.intro⟩⟩⟩,⟨sg42374,⟨sg42371,⟨sg42370,⟨sg42369,True.intro,True.intro⟩,True.intro⟩,⟨sg42373,⟨sg42372,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42377,⟨sg42376,⟨sg42375,True.intro,True.intro⟩,True.intro⟩,⟨sg42378,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_940All : degreeTree62_940.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42390,⟨sg42385,⟨sg42382,⟨sg42381,⟨sg42380,True.intro,True.intro⟩,True.intro⟩,⟨sg42384,⟨sg42383,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42388,⟨sg42387,⟨sg42386,True.intro,True.intro⟩,True.intro⟩,⟨sg42389,True.intro,True.intro⟩⟩⟩,⟨sg42396,⟨sg42393,⟨sg42392,⟨sg42391,True.intro,True.intro⟩,True.intro⟩,⟨sg42395,⟨sg42394,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42399,⟨sg42398,⟨sg42397,True.intro,True.intro⟩,True.intro⟩,⟨sg42400,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_941All : degreeTree62_941.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42379,degreeTree62_939All,degreeTree62_940All⟩ + +lemma degreeTree62_942All : degreeTree62_942.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42412,⟨sg42407,⟨sg42404,⟨sg42403,⟨sg42402,True.intro,True.intro⟩,True.intro⟩,⟨sg42406,⟨sg42405,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42410,⟨sg42409,⟨sg42408,True.intro,True.intro⟩,True.intro⟩,⟨sg42411,True.intro,True.intro⟩⟩⟩,⟨sg42418,⟨sg42415,⟨sg42414,⟨sg42413,True.intro,True.intro⟩,True.intro⟩,⟨sg42417,⟨sg42416,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42421,⟨sg42420,⟨sg42419,True.intro,True.intro⟩,True.intro⟩,⟨sg42422,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_943All : degreeTree62_943.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42434,⟨sg42429,⟨sg42426,⟨sg42425,⟨sg42424,True.intro,True.intro⟩,True.intro⟩,⟨sg42428,⟨sg42427,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42432,⟨sg42431,⟨sg42430,True.intro,True.intro⟩,True.intro⟩,⟨sg42433,True.intro,True.intro⟩⟩⟩,⟨sg42440,⟨sg42437,⟨sg42436,⟨sg42435,True.intro,True.intro⟩,True.intro⟩,⟨sg42439,⟨sg42438,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42443,⟨sg42442,⟨sg42441,True.intro,True.intro⟩,True.intro⟩,⟨sg42444,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_944All : degreeTree62_944.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42423,degreeTree62_942All,degreeTree62_943All⟩ + +lemma degreeTree62_945All : degreeTree62_945.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42401,degreeTree62_941All,degreeTree62_944All⟩ + +lemma degreeTree62_946All : degreeTree62_946.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42456,⟨sg42451,⟨sg42448,⟨sg42447,⟨sg42446,True.intro,True.intro⟩,True.intro⟩,⟨sg42450,⟨sg42449,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42454,⟨sg42453,⟨sg42452,True.intro,True.intro⟩,True.intro⟩,⟨sg42455,True.intro,True.intro⟩⟩⟩,⟨sg42462,⟨sg42459,⟨sg42458,⟨sg42457,True.intro,True.intro⟩,True.intro⟩,⟨sg42461,⟨sg42460,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42465,⟨sg42464,⟨sg42463,True.intro,True.intro⟩,True.intro⟩,⟨sg42466,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_947All : degreeTree62_947.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42478,⟨sg42473,⟨sg42470,⟨sg42469,⟨sg42468,True.intro,True.intro⟩,True.intro⟩,⟨sg42472,⟨sg42471,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42476,⟨sg42475,⟨sg42474,True.intro,True.intro⟩,True.intro⟩,⟨sg42477,True.intro,True.intro⟩⟩⟩,⟨sg42484,⟨sg42481,⟨sg42480,⟨sg42479,True.intro,True.intro⟩,True.intro⟩,⟨sg42483,⟨sg42482,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42487,⟨sg42486,⟨sg42485,True.intro,True.intro⟩,True.intro⟩,⟨sg42488,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_948All : degreeTree62_948.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42467,degreeTree62_946All,degreeTree62_947All⟩ + +lemma degreeTree62_949All : degreeTree62_949.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42500,⟨sg42495,⟨sg42492,⟨sg42491,⟨sg42490,True.intro,True.intro⟩,True.intro⟩,⟨sg42494,⟨sg42493,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42498,⟨sg42497,⟨sg42496,True.intro,True.intro⟩,True.intro⟩,⟨sg42499,True.intro,True.intro⟩⟩⟩,⟨sg42506,⟨sg42503,⟨sg42502,⟨sg42501,True.intro,True.intro⟩,True.intro⟩,⟨sg42505,⟨sg42504,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42509,⟨sg42508,⟨sg42507,True.intro,True.intro⟩,True.intro⟩,⟨sg42510,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_950All : degreeTree62_950.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42522,⟨sg42517,⟨sg42514,⟨sg42513,⟨sg42512,True.intro,True.intro⟩,True.intro⟩,⟨sg42516,⟨sg42515,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42520,⟨sg42519,⟨sg42518,True.intro,True.intro⟩,True.intro⟩,⟨sg42521,True.intro,True.intro⟩⟩⟩,⟨sg42527,⟨sg42525,⟨sg42524,⟨sg42523,True.intro,True.intro⟩,True.intro⟩,⟨sg42526,True.intro,True.intro⟩⟩,⟨sg42530,⟨sg42529,⟨sg42528,True.intro,True.intro⟩,True.intro⟩,⟨sg42531,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_951All : degreeTree62_951.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42511,degreeTree62_949All,degreeTree62_950All⟩ + +lemma degreeTree62_952All : degreeTree62_952.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42489,degreeTree62_948All,degreeTree62_951All⟩ + +lemma degreeTree62_953All : degreeTree62_953.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42445,degreeTree62_945All,degreeTree62_952All⟩ + +lemma degreeTree62_954All : degreeTree62_954.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42357,degreeTree62_938All,degreeTree62_953All⟩ + +lemma degreeTree62_955All : degreeTree62_955.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42181,degreeTree62_923All,degreeTree62_954All⟩ + +lemma degreeTree62_956All : degreeTree62_956.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42543,⟨sg42538,⟨sg42535,⟨sg42534,⟨sg42533,True.intro,True.intro⟩,True.intro⟩,⟨sg42537,⟨sg42536,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42541,⟨sg42540,⟨sg42539,True.intro,True.intro⟩,True.intro⟩,⟨sg42542,True.intro,True.intro⟩⟩⟩,⟨sg42549,⟨sg42546,⟨sg42545,⟨sg42544,True.intro,True.intro⟩,True.intro⟩,⟨sg42548,⟨sg42547,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42552,⟨sg42551,⟨sg42550,True.intro,True.intro⟩,True.intro⟩,⟨sg42553,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_957All : degreeTree62_957.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42565,⟨sg42560,⟨sg42557,⟨sg42556,⟨sg42555,True.intro,True.intro⟩,True.intro⟩,⟨sg42559,⟨sg42558,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42563,⟨sg42562,⟨sg42561,True.intro,True.intro⟩,True.intro⟩,⟨sg42564,True.intro,True.intro⟩⟩⟩,⟨sg42571,⟨sg42568,⟨sg42567,⟨sg42566,True.intro,True.intro⟩,True.intro⟩,⟨sg42570,⟨sg42569,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42574,⟨sg42573,⟨sg42572,True.intro,True.intro⟩,True.intro⟩,⟨sg42575,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_958All : degreeTree62_958.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42554,degreeTree62_956All,degreeTree62_957All⟩ + +lemma degreeTree62_959All : degreeTree62_959.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42587,⟨sg42582,⟨sg42579,⟨sg42578,⟨sg42577,True.intro,True.intro⟩,True.intro⟩,⟨sg42581,⟨sg42580,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42585,⟨sg42584,⟨sg42583,True.intro,True.intro⟩,True.intro⟩,⟨sg42586,True.intro,True.intro⟩⟩⟩,⟨sg42593,⟨sg42590,⟨sg42589,⟨sg42588,True.intro,True.intro⟩,True.intro⟩,⟨sg42592,⟨sg42591,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42596,⟨sg42595,⟨sg42594,True.intro,True.intro⟩,True.intro⟩,⟨sg42597,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_960All : degreeTree62_960.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42609,⟨sg42604,⟨sg42601,⟨sg42600,⟨sg42599,True.intro,True.intro⟩,True.intro⟩,⟨sg42603,⟨sg42602,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42607,⟨sg42606,⟨sg42605,True.intro,True.intro⟩,True.intro⟩,⟨sg42608,True.intro,True.intro⟩⟩⟩,⟨sg42615,⟨sg42612,⟨sg42611,⟨sg42610,True.intro,True.intro⟩,True.intro⟩,⟨sg42614,⟨sg42613,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42618,⟨sg42617,⟨sg42616,True.intro,True.intro⟩,True.intro⟩,⟨sg42619,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_961All : degreeTree62_961.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42598,degreeTree62_959All,degreeTree62_960All⟩ + +lemma degreeTree62_962All : degreeTree62_962.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42576,degreeTree62_958All,degreeTree62_961All⟩ + +lemma degreeTree62_963All : degreeTree62_963.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42631,⟨sg42626,⟨sg42623,⟨sg42622,⟨sg42621,True.intro,True.intro⟩,True.intro⟩,⟨sg42625,⟨sg42624,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42629,⟨sg42628,⟨sg42627,True.intro,True.intro⟩,True.intro⟩,⟨sg42630,True.intro,True.intro⟩⟩⟩,⟨sg42637,⟨sg42634,⟨sg42633,⟨sg42632,True.intro,True.intro⟩,True.intro⟩,⟨sg42636,⟨sg42635,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42640,⟨sg42639,⟨sg42638,True.intro,True.intro⟩,True.intro⟩,⟨sg42641,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_964All : degreeTree62_964.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42653,⟨sg42648,⟨sg42645,⟨sg42644,⟨sg42643,True.intro,True.intro⟩,True.intro⟩,⟨sg42647,⟨sg42646,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42651,⟨sg42650,⟨sg42649,True.intro,True.intro⟩,True.intro⟩,⟨sg42652,True.intro,True.intro⟩⟩⟩,⟨sg42659,⟨sg42656,⟨sg42655,⟨sg42654,True.intro,True.intro⟩,True.intro⟩,⟨sg42658,⟨sg42657,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42662,⟨sg42661,⟨sg42660,True.intro,True.intro⟩,True.intro⟩,⟨sg42663,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_965All : degreeTree62_965.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42642,degreeTree62_963All,degreeTree62_964All⟩ + +lemma degreeTree62_966All : degreeTree62_966.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42675,⟨sg42670,⟨sg42667,⟨sg42666,⟨sg42665,True.intro,True.intro⟩,True.intro⟩,⟨sg42669,⟨sg42668,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42673,⟨sg42672,⟨sg42671,True.intro,True.intro⟩,True.intro⟩,⟨sg42674,True.intro,True.intro⟩⟩⟩,⟨sg42681,⟨sg42678,⟨sg42677,⟨sg42676,True.intro,True.intro⟩,True.intro⟩,⟨sg42680,⟨sg42679,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42684,⟨sg42683,⟨sg42682,True.intro,True.intro⟩,True.intro⟩,⟨sg42685,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_967All : degreeTree62_967.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42697,⟨sg42692,⟨sg42689,⟨sg42688,⟨sg42687,True.intro,True.intro⟩,True.intro⟩,⟨sg42691,⟨sg42690,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42695,⟨sg42694,⟨sg42693,True.intro,True.intro⟩,True.intro⟩,⟨sg42696,True.intro,True.intro⟩⟩⟩,⟨sg42703,⟨sg42700,⟨sg42699,⟨sg42698,True.intro,True.intro⟩,True.intro⟩,⟨sg42702,⟨sg42701,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42706,⟨sg42705,⟨sg42704,True.intro,True.intro⟩,True.intro⟩,⟨sg42707,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_968All : degreeTree62_968.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42686,degreeTree62_966All,degreeTree62_967All⟩ + +lemma degreeTree62_969All : degreeTree62_969.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42664,degreeTree62_965All,degreeTree62_968All⟩ + +lemma degreeTree62_970All : degreeTree62_970.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42620,degreeTree62_962All,degreeTree62_969All⟩ + +lemma degreeTree62_971All : degreeTree62_971.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42719,⟨sg42714,⟨sg42711,⟨sg42710,⟨sg42709,True.intro,True.intro⟩,True.intro⟩,⟨sg42713,⟨sg42712,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42717,⟨sg42716,⟨sg42715,True.intro,True.intro⟩,True.intro⟩,⟨sg42718,True.intro,True.intro⟩⟩⟩,⟨sg42725,⟨sg42722,⟨sg42721,⟨sg42720,True.intro,True.intro⟩,True.intro⟩,⟨sg42724,⟨sg42723,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42728,⟨sg42727,⟨sg42726,True.intro,True.intro⟩,True.intro⟩,⟨sg42729,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_972All : degreeTree62_972.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42741,⟨sg42736,⟨sg42733,⟨sg42732,⟨sg42731,True.intro,True.intro⟩,True.intro⟩,⟨sg42735,⟨sg42734,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42739,⟨sg42738,⟨sg42737,True.intro,True.intro⟩,True.intro⟩,⟨sg42740,True.intro,True.intro⟩⟩⟩,⟨sg42747,⟨sg42744,⟨sg42743,⟨sg42742,True.intro,True.intro⟩,True.intro⟩,⟨sg42746,⟨sg42745,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42750,⟨sg42749,⟨sg42748,True.intro,True.intro⟩,True.intro⟩,⟨sg42751,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_973All : degreeTree62_973.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42730,degreeTree62_971All,degreeTree62_972All⟩ + +lemma degreeTree62_974All : degreeTree62_974.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42763,⟨sg42758,⟨sg42755,⟨sg42754,⟨sg42753,True.intro,True.intro⟩,True.intro⟩,⟨sg42757,⟨sg42756,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42761,⟨sg42760,⟨sg42759,True.intro,True.intro⟩,True.intro⟩,⟨sg42762,True.intro,True.intro⟩⟩⟩,⟨sg42769,⟨sg42766,⟨sg42765,⟨sg42764,True.intro,True.intro⟩,True.intro⟩,⟨sg42768,⟨sg42767,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42772,⟨sg42771,⟨sg42770,True.intro,True.intro⟩,True.intro⟩,⟨sg42773,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_975All : degreeTree62_975.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42785,⟨sg42780,⟨sg42777,⟨sg42776,⟨sg42775,True.intro,True.intro⟩,True.intro⟩,⟨sg42779,⟨sg42778,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42783,⟨sg42782,⟨sg42781,True.intro,True.intro⟩,True.intro⟩,⟨sg42784,True.intro,True.intro⟩⟩⟩,⟨sg42791,⟨sg42788,⟨sg42787,⟨sg42786,True.intro,True.intro⟩,True.intro⟩,⟨sg42790,⟨sg42789,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42794,⟨sg42793,⟨sg42792,True.intro,True.intro⟩,True.intro⟩,⟨sg42795,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_976All : degreeTree62_976.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42774,degreeTree62_974All,degreeTree62_975All⟩ + +lemma degreeTree62_977All : degreeTree62_977.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42752,degreeTree62_973All,degreeTree62_976All⟩ + +lemma degreeTree62_978All : degreeTree62_978.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42807,⟨sg42802,⟨sg42799,⟨sg42798,⟨sg42797,True.intro,True.intro⟩,True.intro⟩,⟨sg42801,⟨sg42800,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42805,⟨sg42804,⟨sg42803,True.intro,True.intro⟩,True.intro⟩,⟨sg42806,True.intro,True.intro⟩⟩⟩,⟨sg42813,⟨sg42810,⟨sg42809,⟨sg42808,True.intro,True.intro⟩,True.intro⟩,⟨sg42812,⟨sg42811,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42816,⟨sg42815,⟨sg42814,True.intro,True.intro⟩,True.intro⟩,⟨sg42817,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_979All : degreeTree62_979.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42829,⟨sg42824,⟨sg42821,⟨sg42820,⟨sg42819,True.intro,True.intro⟩,True.intro⟩,⟨sg42823,⟨sg42822,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42827,⟨sg42826,⟨sg42825,True.intro,True.intro⟩,True.intro⟩,⟨sg42828,True.intro,True.intro⟩⟩⟩,⟨sg42835,⟨sg42832,⟨sg42831,⟨sg42830,True.intro,True.intro⟩,True.intro⟩,⟨sg42834,⟨sg42833,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42838,⟨sg42837,⟨sg42836,True.intro,True.intro⟩,True.intro⟩,⟨sg42839,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_980All : degreeTree62_980.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42818,degreeTree62_978All,degreeTree62_979All⟩ + +lemma degreeTree62_981All : degreeTree62_981.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42851,⟨sg42846,⟨sg42843,⟨sg42842,⟨sg42841,True.intro,True.intro⟩,True.intro⟩,⟨sg42845,⟨sg42844,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42849,⟨sg42848,⟨sg42847,True.intro,True.intro⟩,True.intro⟩,⟨sg42850,True.intro,True.intro⟩⟩⟩,⟨sg42857,⟨sg42854,⟨sg42853,⟨sg42852,True.intro,True.intro⟩,True.intro⟩,⟨sg42856,⟨sg42855,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42860,⟨sg42859,⟨sg42858,True.intro,True.intro⟩,True.intro⟩,⟨sg42861,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_982All : degreeTree62_982.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42873,⟨sg42868,⟨sg42865,⟨sg42864,⟨sg42863,True.intro,True.intro⟩,True.intro⟩,⟨sg42867,⟨sg42866,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42871,⟨sg42870,⟨sg42869,True.intro,True.intro⟩,True.intro⟩,⟨sg42872,True.intro,True.intro⟩⟩⟩,⟨sg42878,⟨sg42876,⟨sg42875,⟨sg42874,True.intro,True.intro⟩,True.intro⟩,⟨sg42877,True.intro,True.intro⟩⟩,⟨sg42881,⟨sg42880,⟨sg42879,True.intro,True.intro⟩,True.intro⟩,⟨sg42882,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_983All : degreeTree62_983.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42862,degreeTree62_981All,degreeTree62_982All⟩ + +lemma degreeTree62_984All : degreeTree62_984.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42840,degreeTree62_980All,degreeTree62_983All⟩ + +lemma degreeTree62_985All : degreeTree62_985.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42796,degreeTree62_977All,degreeTree62_984All⟩ + +lemma degreeTree62_986All : degreeTree62_986.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42708,degreeTree62_970All,degreeTree62_985All⟩ + +lemma degreeTree62_987All : degreeTree62_987.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42894,⟨sg42889,⟨sg42886,⟨sg42885,⟨sg42884,True.intro,True.intro⟩,True.intro⟩,⟨sg42888,⟨sg42887,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42892,⟨sg42891,⟨sg42890,True.intro,True.intro⟩,True.intro⟩,⟨sg42893,True.intro,True.intro⟩⟩⟩,⟨sg42900,⟨sg42897,⟨sg42896,⟨sg42895,True.intro,True.intro⟩,True.intro⟩,⟨sg42899,⟨sg42898,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42903,⟨sg42902,⟨sg42901,True.intro,True.intro⟩,True.intro⟩,⟨sg42904,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_988All : degreeTree62_988.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42916,⟨sg42911,⟨sg42908,⟨sg42907,⟨sg42906,True.intro,True.intro⟩,True.intro⟩,⟨sg42910,⟨sg42909,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42914,⟨sg42913,⟨sg42912,True.intro,True.intro⟩,True.intro⟩,⟨sg42915,True.intro,True.intro⟩⟩⟩,⟨sg42922,⟨sg42919,⟨sg42918,⟨sg42917,True.intro,True.intro⟩,True.intro⟩,⟨sg42921,⟨sg42920,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42925,⟨sg42924,⟨sg42923,True.intro,True.intro⟩,True.intro⟩,⟨sg42926,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_989All : degreeTree62_989.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42905,degreeTree62_987All,degreeTree62_988All⟩ + +lemma degreeTree62_990All : degreeTree62_990.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42938,⟨sg42933,⟨sg42930,⟨sg42929,⟨sg42928,True.intro,True.intro⟩,True.intro⟩,⟨sg42932,⟨sg42931,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42936,⟨sg42935,⟨sg42934,True.intro,True.intro⟩,True.intro⟩,⟨sg42937,True.intro,True.intro⟩⟩⟩,⟨sg42944,⟨sg42941,⟨sg42940,⟨sg42939,True.intro,True.intro⟩,True.intro⟩,⟨sg42943,⟨sg42942,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42947,⟨sg42946,⟨sg42945,True.intro,True.intro⟩,True.intro⟩,⟨sg42948,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_991All : degreeTree62_991.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42960,⟨sg42955,⟨sg42952,⟨sg42951,⟨sg42950,True.intro,True.intro⟩,True.intro⟩,⟨sg42954,⟨sg42953,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42958,⟨sg42957,⟨sg42956,True.intro,True.intro⟩,True.intro⟩,⟨sg42959,True.intro,True.intro⟩⟩⟩,⟨sg42966,⟨sg42963,⟨sg42962,⟨sg42961,True.intro,True.intro⟩,True.intro⟩,⟨sg42965,⟨sg42964,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42969,⟨sg42968,⟨sg42967,True.intro,True.intro⟩,True.intro⟩,⟨sg42970,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_992All : degreeTree62_992.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42949,degreeTree62_990All,degreeTree62_991All⟩ + +lemma degreeTree62_993All : degreeTree62_993.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42927,degreeTree62_989All,degreeTree62_992All⟩ + +lemma degreeTree62_994All : degreeTree62_994.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42982,⟨sg42977,⟨sg42974,⟨sg42973,⟨sg42972,True.intro,True.intro⟩,True.intro⟩,⟨sg42976,⟨sg42975,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42980,⟨sg42979,⟨sg42978,True.intro,True.intro⟩,True.intro⟩,⟨sg42981,True.intro,True.intro⟩⟩⟩,⟨sg42988,⟨sg42985,⟨sg42984,⟨sg42983,True.intro,True.intro⟩,True.intro⟩,⟨sg42987,⟨sg42986,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg42991,⟨sg42990,⟨sg42989,True.intro,True.intro⟩,True.intro⟩,⟨sg42992,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_995All : degreeTree62_995.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43004,⟨sg42999,⟨sg42996,⟨sg42995,⟨sg42994,True.intro,True.intro⟩,True.intro⟩,⟨sg42998,⟨sg42997,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43002,⟨sg43001,⟨sg43000,True.intro,True.intro⟩,True.intro⟩,⟨sg43003,True.intro,True.intro⟩⟩⟩,⟨sg43010,⟨sg43007,⟨sg43006,⟨sg43005,True.intro,True.intro⟩,True.intro⟩,⟨sg43009,⟨sg43008,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43013,⟨sg43012,⟨sg43011,True.intro,True.intro⟩,True.intro⟩,⟨sg43014,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_996All : degreeTree62_996.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42993,degreeTree62_994All,degreeTree62_995All⟩ + +lemma degreeTree62_997All : degreeTree62_997.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43026,⟨sg43021,⟨sg43018,⟨sg43017,⟨sg43016,True.intro,True.intro⟩,True.intro⟩,⟨sg43020,⟨sg43019,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43024,⟨sg43023,⟨sg43022,True.intro,True.intro⟩,True.intro⟩,⟨sg43025,True.intro,True.intro⟩⟩⟩,⟨sg43032,⟨sg43029,⟨sg43028,⟨sg43027,True.intro,True.intro⟩,True.intro⟩,⟨sg43031,⟨sg43030,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43035,⟨sg43034,⟨sg43033,True.intro,True.intro⟩,True.intro⟩,⟨sg43036,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_998All : degreeTree62_998.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43048,⟨sg43043,⟨sg43040,⟨sg43039,⟨sg43038,True.intro,True.intro⟩,True.intro⟩,⟨sg43042,⟨sg43041,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43046,⟨sg43045,⟨sg43044,True.intro,True.intro⟩,True.intro⟩,⟨sg43047,True.intro,True.intro⟩⟩⟩,⟨sg43053,⟨sg43051,⟨sg43050,⟨sg43049,True.intro,True.intro⟩,True.intro⟩,⟨sg43052,True.intro,True.intro⟩⟩,⟨sg43056,⟨sg43055,⟨sg43054,True.intro,True.intro⟩,True.intro⟩,⟨sg43057,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_999All : degreeTree62_999.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43037,degreeTree62_997All,degreeTree62_998All⟩ + +lemma degreeTree62_1000All : degreeTree62_1000.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43015,degreeTree62_996All,degreeTree62_999All⟩ + +lemma degreeTree62_1001All : degreeTree62_1001.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42971,degreeTree62_993All,degreeTree62_1000All⟩ + +lemma degreeTree62_1002All : degreeTree62_1002.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43069,⟨sg43064,⟨sg43061,⟨sg43060,⟨sg43059,True.intro,True.intro⟩,True.intro⟩,⟨sg43063,⟨sg43062,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43067,⟨sg43066,⟨sg43065,True.intro,True.intro⟩,True.intro⟩,⟨sg43068,True.intro,True.intro⟩⟩⟩,⟨sg43075,⟨sg43072,⟨sg43071,⟨sg43070,True.intro,True.intro⟩,True.intro⟩,⟨sg43074,⟨sg43073,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43078,⟨sg43077,⟨sg43076,True.intro,True.intro⟩,True.intro⟩,⟨sg43079,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_1003All : degreeTree62_1003.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43091,⟨sg43086,⟨sg43083,⟨sg43082,⟨sg43081,True.intro,True.intro⟩,True.intro⟩,⟨sg43085,⟨sg43084,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43089,⟨sg43088,⟨sg43087,True.intro,True.intro⟩,True.intro⟩,⟨sg43090,True.intro,True.intro⟩⟩⟩,⟨sg43097,⟨sg43094,⟨sg43093,⟨sg43092,True.intro,True.intro⟩,True.intro⟩,⟨sg43096,⟨sg43095,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43100,⟨sg43099,⟨sg43098,True.intro,True.intro⟩,True.intro⟩,⟨sg43101,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_1004All : degreeTree62_1004.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43080,degreeTree62_1002All,degreeTree62_1003All⟩ + +lemma degreeTree62_1005All : degreeTree62_1005.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43113,⟨sg43108,⟨sg43105,⟨sg43104,⟨sg43103,True.intro,True.intro⟩,True.intro⟩,⟨sg43107,⟨sg43106,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43111,⟨sg43110,⟨sg43109,True.intro,True.intro⟩,True.intro⟩,⟨sg43112,True.intro,True.intro⟩⟩⟩,⟨sg43119,⟨sg43116,⟨sg43115,⟨sg43114,True.intro,True.intro⟩,True.intro⟩,⟨sg43118,⟨sg43117,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43122,⟨sg43121,⟨sg43120,True.intro,True.intro⟩,True.intro⟩,⟨sg43123,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_1006All : degreeTree62_1006.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43135,⟨sg43130,⟨sg43127,⟨sg43126,⟨sg43125,True.intro,True.intro⟩,True.intro⟩,⟨sg43129,⟨sg43128,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43133,⟨sg43132,⟨sg43131,True.intro,True.intro⟩,True.intro⟩,⟨sg43134,True.intro,True.intro⟩⟩⟩,⟨sg43141,⟨sg43138,⟨sg43137,⟨sg43136,True.intro,True.intro⟩,True.intro⟩,⟨sg43140,⟨sg43139,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43144,⟨sg43143,⟨sg43142,True.intro,True.intro⟩,True.intro⟩,⟨sg43145,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_1007All : degreeTree62_1007.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43124,degreeTree62_1005All,degreeTree62_1006All⟩ + +lemma degreeTree62_1008All : degreeTree62_1008.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43102,degreeTree62_1004All,degreeTree62_1007All⟩ + +lemma degreeTree62_1009All : degreeTree62_1009.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43157,⟨sg43152,⟨sg43149,⟨sg43148,⟨sg43147,True.intro,True.intro⟩,True.intro⟩,⟨sg43151,⟨sg43150,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43155,⟨sg43154,⟨sg43153,True.intro,True.intro⟩,True.intro⟩,⟨sg43156,True.intro,True.intro⟩⟩⟩,⟨sg43163,⟨sg43160,⟨sg43159,⟨sg43158,True.intro,True.intro⟩,True.intro⟩,⟨sg43162,⟨sg43161,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43166,⟨sg43165,⟨sg43164,True.intro,True.intro⟩,True.intro⟩,⟨sg43167,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_1010All : degreeTree62_1010.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43179,⟨sg43174,⟨sg43171,⟨sg43170,⟨sg43169,True.intro,True.intro⟩,True.intro⟩,⟨sg43173,⟨sg43172,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43177,⟨sg43176,⟨sg43175,True.intro,True.intro⟩,True.intro⟩,⟨sg43178,True.intro,True.intro⟩⟩⟩,⟨sg43185,⟨sg43182,⟨sg43181,⟨sg43180,True.intro,True.intro⟩,True.intro⟩,⟨sg43184,⟨sg43183,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43188,⟨sg43187,⟨sg43186,True.intro,True.intro⟩,True.intro⟩,⟨sg43189,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_1011All : degreeTree62_1011.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43168,degreeTree62_1009All,degreeTree62_1010All⟩ + +lemma degreeTree62_1012All : degreeTree62_1012.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43201,⟨sg43196,⟨sg43193,⟨sg43192,⟨sg43191,True.intro,True.intro⟩,True.intro⟩,⟨sg43195,⟨sg43194,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43199,⟨sg43198,⟨sg43197,True.intro,True.intro⟩,True.intro⟩,⟨sg43200,True.intro,True.intro⟩⟩⟩,⟨sg43207,⟨sg43204,⟨sg43203,⟨sg43202,True.intro,True.intro⟩,True.intro⟩,⟨sg43206,⟨sg43205,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43210,⟨sg43209,⟨sg43208,True.intro,True.intro⟩,True.intro⟩,⟨sg43211,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_1013All : degreeTree62_1013.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43223,⟨sg43218,⟨sg43215,⟨sg43214,⟨sg43213,True.intro,True.intro⟩,True.intro⟩,⟨sg43217,⟨sg43216,True.intro,True.intro⟩,True.intro⟩⟩,⟨sg43221,⟨sg43220,⟨sg43219,True.intro,True.intro⟩,True.intro⟩,⟨sg43222,True.intro,True.intro⟩⟩⟩,⟨sg43228,⟨sg43226,⟨sg43225,⟨sg43224,True.intro,True.intro⟩,True.intro⟩,⟨sg43227,True.intro,True.intro⟩⟩,⟨sg43231,⟨sg43230,⟨sg43229,True.intro,True.intro⟩,True.intro⟩,⟨sg43232,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTree62_1014All : degreeTree62_1014.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43212,degreeTree62_1012All,degreeTree62_1013All⟩ + +lemma degreeTree62_1015All : degreeTree62_1015.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43190,degreeTree62_1011All,degreeTree62_1014All⟩ + +lemma degreeTree62_1016All : degreeTree62_1016.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43146,degreeTree62_1008All,degreeTree62_1015All⟩ + +lemma degreeTree62_1017All : degreeTree62_1017.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg43058,degreeTree62_1001All,degreeTree62_1016All⟩ + +lemma degreeTree62_1018All : degreeTree62_1018.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42883,degreeTree62_986All,degreeTree62_1017All⟩ + +lemma degreeTree62_1019All : degreeTree62_1019.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg42532,degreeTree62_955All,degreeTree62_1018All⟩ + +lemma degreeTree62_1020All : degreeTree62_1020.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg41830,degreeTree62_892All,degreeTree62_1019All⟩ + +lemma degreeTree62_1021All : degreeTree62_1021.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg40426,degreeTree62_765All,degreeTree62_1020All⟩ + +lemma degreeTree62_1022All : degreeTree62_1022.All (RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1]) := by + exact ⟨sg37619,degreeTree62_510All,degreeTree62_1021All⟩ + +lemma degreeTreeAll62 : degreeTree62.All + (fun rs => SquareOccurs (candidate 8 6 1) (rowDiagram rs)) := by + have hp : rowDiagram [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] = candidate 8 6 1 := rowDiagram_candidate (M := 8) (b := 6) (δ := 1) (by decide) + rw [← hp] + exact degreeTree62_1022All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof64.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof64.lean index 6ddc5f3007174150357e6a10fac9a5cdf318d5c4..48b2fd0b139bb29c540f51239b8efff7dbff9e67 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof64.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof64.lean @@ -1,30 +1,30 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData64 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupMissingLeaves -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes106 - -namespace OAI - -/-! Degree Tree Proof 64. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree64_0All : degreeTree64_0.All (RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1]) := by - exact ⟨sg43240,⟨sg43236,⟨sg43234,⟨sg43233,True.intro,True.intro⟩,⟨sg43235,True.intro,True.intro⟩⟩,⟨sg43238,⟨sg43237,True.intro,True.intro⟩,⟨sg43239,True.intro,True.intro⟩⟩⟩,⟨sg43244,⟨sg43242,⟨sg43241,True.intro,True.intro⟩,⟨sg43243,True.intro,True.intro⟩⟩,⟨sg43246,⟨sg43245,True.intro,True.intro⟩,⟨sg43247,True.intro,True.intro⟩⟩⟩⟩ - -lemma degreeTreeAll64 : degreeTree64.All - (fun rs => SquareOccurs (candidate 8 7 0) (rowDiagram rs)) := by - have hp : rowDiagram [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] = candidate 8 7 0 := rowDiagram_candidate (M := 8) (b := 7) (δ := 0) (by decide) - rw [← hp] - exact degreeTree64_0All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData64 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupMissingLeaves +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes106 + +namespace OAI + +/-! Degree Tree Proof 64. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree64_0All : degreeTree64_0.All (RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1]) := by + exact ⟨sg43240,⟨sg43236,⟨sg43234,⟨sg43233,True.intro,True.intro⟩,⟨sg43235,True.intro,True.intro⟩⟩,⟨sg43238,⟨sg43237,True.intro,True.intro⟩,⟨sg43239,True.intro,True.intro⟩⟩⟩,⟨sg43244,⟨sg43242,⟨sg43241,True.intro,True.intro⟩,⟨sg43243,True.intro,True.intro⟩⟩,⟨sg43246,⟨sg43245,True.intro,True.intro⟩,⟨sg43247,True.intro,True.intro⟩⟩⟩⟩ + +lemma degreeTreeAll64 : degreeTree64.All + (fun rs => SquareOccurs (candidate 8 7 0) (rowDiagram rs)) := by + have hp : rowDiagram [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] = candidate 8 7 0 := rowDiagram_candidate (M := 8) (b := 7) (δ := 0) (by decide) + rw [← hp] + exact degreeTree64_0All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof89.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof89.lean index 8036f9a2bacf94aa52dffc328499a08689202449..f41ef99ac3be893e791831068b4618e752c53312 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof89.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeTreeProof89.lean @@ -1,29 +1,29 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData89 -import OAI.RepresentationTheory.UniversalSquare.Finite.PieriRows89 - -namespace OAI - -/-! Degree Tree Proof 89. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeTree89_0All : degreeTree89_0.All (RowSquare [19,17,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,1,1]) := by - exact ⟨pieriSquare89_0,True.intro,True.intro⟩ - -lemma degreeTreeAll89 : degreeTree89.All - (fun rs => SquareOccurs (candidate 10 8 1) (rowDiagram rs)) := by - have hp : rowDiagram [19,17,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,1,1] = candidate 10 8 1 := rowDiagram_candidate (M := 10) (b := 8) (δ := 1) (by decide) - rw [← hp] - exact degreeTree89_0All - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeData89 +import OAI.RepresentationTheory.UniversalSquare.Finite.PieriRows89 + +namespace OAI + +/-! Degree Tree Proof 89. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeTree89_0All : degreeTree89_0.All (RowSquare [19,17,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,1,1]) := by + exact ⟨pieriSquare89_0,True.intro,True.intro⟩ + +lemma degreeTreeAll89 : degreeTree89.All + (fun rs => SquareOccurs (candidate 10 8 1) (rowDiagram rs)) := by + have hp : rowDiagram [19,17,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,1,1] = candidate 10 8 1 := rowDiagram_candidate (M := 10) (b := 8) (δ := 1) (by decide) + rw [← hp] + exact degreeTree89_0All + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData116.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData116.lean index accf4e2fee936e89cebcb8a31fb408e88f3c1f6b..ac4247cb60deb53cd138e94c2575867fe793d31f 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData116.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData116.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData116 - -namespace OAI - -/-! Degree Union Data 116. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions116 : List PrefixRegion := [degreeRegion116_0] - -lemma degreeHalfHeight116 : ∀ R ∈ degreeHalfRegions116, firstBound 116 R.1 ≤ 22 := by decide +kernel - -lemma degreeHalfWidth116 : ∀ R ∈ degreeHalfRegions116, firstBound 116 R.2 ≤ 22 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData116 + +namespace OAI + +/-! Degree Union Data 116. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions116 : List PrefixRegion := [degreeRegion116_0] + +lemma degreeHalfHeight116 : ∀ R ∈ degreeHalfRegions116, firstBound 116 R.1 ≤ 22 := by decide +kernel + +lemma degreeHalfWidth116 : ∀ R ∈ degreeHalfRegions116, firstBound 116 R.2 ≤ 22 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData118.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData118.lean index 4f10d92350f3a0f161d20c7542c3b0f9926aa851..0727379ecf5a0b1b821dc63d3969349b61c0d38b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData118.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData118.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData118 - -namespace OAI - -/-! Degree Union Data 118. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions118 : List PrefixRegion := [degreeRegion118_0] - -lemma degreeHalfHeight118 : ∀ R ∈ degreeHalfRegions118, firstBound 118 R.1 ≤ 22 := by decide +kernel - -lemma degreeHalfWidth118 : ∀ R ∈ degreeHalfRegions118, firstBound 118 R.2 ≤ 22 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData118 + +namespace OAI + +/-! Degree Union Data 118. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions118 : List PrefixRegion := [degreeRegion118_0] + +lemma degreeHalfHeight118 : ∀ R ∈ degreeHalfRegions118, firstBound 118 R.1 ≤ 22 := by decide +kernel + +lemma degreeHalfWidth118 : ∀ R ∈ degreeHalfRegions118, firstBound 118 R.2 ≤ 22 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData14.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData14.lean index 37e04066bd52286255f7874e031d3dbc7de3642e..9ba3a20386fad634ab9195591efe8b02c3007f89 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData14.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData14.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData14 - -namespace OAI - -/-! Degree Union Data 14. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions14 : List PrefixRegion := [degreeRegion14_0,degreeRegion14_2] - -lemma degreeHalfHeight14 : ∀ R ∈ degreeHalfRegions14, firstBound 14 R.1 ≤ 13 := by decide +kernel - -lemma degreeHalfWidth14 : ∀ R ∈ degreeHalfRegions14, firstBound 14 R.2 ≤ 13 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData14 + +namespace OAI + +/-! Degree Union Data 14. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions14 : List PrefixRegion := [degreeRegion14_0,degreeRegion14_2] + +lemma degreeHalfHeight14 : ∀ R ∈ degreeHalfRegions14, firstBound 14 R.1 ≤ 13 := by decide +kernel + +lemma degreeHalfWidth14 : ∀ R ∈ degreeHalfRegions14, firstBound 14 R.2 ≤ 13 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData16.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData16.lean index f09e5dc66e2a5870d7427e8b0d91fc4aadf0e99c..92002fade4268d83b00bcf1909fe539c68396786 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData16.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData16.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData16 - -namespace OAI - -/-! Degree Union Data 16. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions16 : List PrefixRegion := [degreeRegion16_0,degreeRegion16_1,degreeRegion16_2,degreeRegion16_5] - -lemma degreeHalfHeight16 : ∀ R ∈ degreeHalfRegions16, firstBound 16 R.1 ≤ 15 := by decide +kernel - -lemma degreeHalfWidth16 : ∀ R ∈ degreeHalfRegions16, firstBound 16 R.2 ≤ 15 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData16 + +namespace OAI + +/-! Degree Union Data 16. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions16 : List PrefixRegion := [degreeRegion16_0,degreeRegion16_1,degreeRegion16_2,degreeRegion16_5] + +lemma degreeHalfHeight16 : ∀ R ∈ degreeHalfRegions16, firstBound 16 R.1 ≤ 15 := by decide +kernel + +lemma degreeHalfWidth16 : ∀ R ∈ degreeHalfRegions16, firstBound 16 R.2 ≤ 15 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData18.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData18.lean index b2cf0598ed168e6e1ab02876549d93e31dd4b4b8..ec016b38b43b15bada9d36dd04efc21ec43ada42 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData18.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData18.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData18 - -namespace OAI - -/-! Degree Union Data 18. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions18 : List PrefixRegion := [degreeRegion18_0,degreeRegion18_1,degreeRegion18_2,degreeRegion18_4,degreeRegion18_5,degreeRegion18_9] - -lemma degreeHalfHeight18 : ∀ R ∈ degreeHalfRegions18, firstBound 18 R.1 ≤ 17 := by decide +kernel - -lemma degreeHalfWidth18 : ∀ R ∈ degreeHalfRegions18, firstBound 18 R.2 ≤ 17 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData18 + +namespace OAI + +/-! Degree Union Data 18. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions18 : List PrefixRegion := [degreeRegion18_0,degreeRegion18_1,degreeRegion18_2,degreeRegion18_4,degreeRegion18_5,degreeRegion18_9] + +lemma degreeHalfHeight18 : ∀ R ∈ degreeHalfRegions18, firstBound 18 R.1 ≤ 17 := by decide +kernel + +lemma degreeHalfWidth18 : ∀ R ∈ degreeHalfRegions18, firstBound 18 R.2 ≤ 17 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData19.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData19.lean index ddc76d44f3674780b2cbdb93d53d01dd7661ee19..9baa9c9f550c979334e2224db8827fcc0b427f94 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData19.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData19.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData19 - -namespace OAI - -/-! Degree Union Data 19. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions19 : List PrefixRegion := [degreeRegion19_0,degreeRegion19_1] - -lemma degreeHalfHeight19 : ∀ R ∈ degreeHalfRegions19, firstBound 19 R.1 ≤ 8 := by decide +kernel - -lemma degreeHalfWidth19 : ∀ R ∈ degreeHalfRegions19, firstBound 19 R.2 ≤ 8 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData19 + +namespace OAI + +/-! Degree Union Data 19. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions19 : List PrefixRegion := [degreeRegion19_0,degreeRegion19_1] + +lemma degreeHalfHeight19 : ∀ R ∈ degreeHalfRegions19, firstBound 19 R.1 ≤ 8 := by decide +kernel + +lemma degreeHalfWidth19 : ∀ R ∈ degreeHalfRegions19, firstBound 19 R.2 ≤ 8 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData20.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData20.lean index ca227189830608c4375a752533206de96821f60d..ff8bfa700b026128fd26a1309716c0b508f43c91 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData20.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData20.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData20 - -namespace OAI - -/-! Degree Union Data 20. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions20 : List PrefixRegion := [degreeRegion20_0,degreeRegion20_1,degreeRegion20_2,degreeRegion20_3,degreeRegion20_5,degreeRegion20_6,degreeRegion20_8,degreeRegion20_9,degreeRegion20_10,degreeRegion20_14,degreeRegion20_15,degreeRegion20_19] - -lemma degreeHalfHeight20 : ∀ R ∈ degreeHalfRegions20, firstBound 20 R.1 ≤ 19 := by decide +kernel - -lemma degreeHalfWidth20 : ∀ R ∈ degreeHalfRegions20, firstBound 20 R.2 ≤ 19 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData20 + +namespace OAI + +/-! Degree Union Data 20. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions20 : List PrefixRegion := [degreeRegion20_0,degreeRegion20_1,degreeRegion20_2,degreeRegion20_3,degreeRegion20_5,degreeRegion20_6,degreeRegion20_8,degreeRegion20_9,degreeRegion20_10,degreeRegion20_14,degreeRegion20_15,degreeRegion20_19] + +lemma degreeHalfHeight20 : ∀ R ∈ degreeHalfRegions20, firstBound 20 R.1 ≤ 19 := by decide +kernel + +lemma degreeHalfWidth20 : ∀ R ∈ degreeHalfRegions20, firstBound 20 R.2 ≤ 19 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData22.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData22.lean index 1263e48a273e5b688cefb157246add74042f5f7e..b9d252829ebeb61468a320b44748257855059c96 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData22.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData22.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData22 - -namespace OAI - -/-! Degree Union Data 22. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions22 : List PrefixRegion := [degreeRegion22_0,degreeRegion22_1,degreeRegion22_2,degreeRegion22_3,degreeRegion22_4,degreeRegion22_5,degreeRegion22_8,degreeRegion22_9,degreeRegion22_14] - -lemma degreeHalfHeight22 : ∀ R ∈ degreeHalfRegions22, firstBound 22 R.1 ≤ 21 := by decide +kernel - -lemma degreeHalfWidth22 : ∀ R ∈ degreeHalfRegions22, firstBound 22 R.2 ≤ 21 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData22 + +namespace OAI + +/-! Degree Union Data 22. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions22 : List PrefixRegion := [degreeRegion22_0,degreeRegion22_1,degreeRegion22_2,degreeRegion22_3,degreeRegion22_4,degreeRegion22_5,degreeRegion22_8,degreeRegion22_9,degreeRegion22_14] + +lemma degreeHalfHeight22 : ∀ R ∈ degreeHalfRegions22, firstBound 22 R.1 ≤ 21 := by decide +kernel + +lemma degreeHalfWidth22 : ∀ R ∈ degreeHalfRegions22, firstBound 22 R.2 ≤ 21 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData24.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData24.lean index 507eb83d63a495a3faeb36066532259ca8cf0fc6..ba417741e6dc7a43d0d3eee3f77674ba14453f4f 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData24.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData24.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData24 - -namespace OAI - -/-! Degree Union Data 24. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions24 : List PrefixRegion := [degreeRegion24_0,degreeRegion24_1,degreeRegion24_2,degreeRegion24_3,degreeRegion24_4,degreeRegion24_6,degreeRegion24_7,degreeRegion24_8,degreeRegion24_9,degreeRegion24_12,degreeRegion24_13,degreeRegion24_14,degreeRegion24_18,degreeRegion24_19,degreeRegion24_24] - -lemma degreeHalfHeight24 : ∀ R ∈ degreeHalfRegions24, firstBound 24 R.1 ≤ 23 := by decide +kernel - -lemma degreeHalfWidth24 : ∀ R ∈ degreeHalfRegions24, firstBound 24 R.2 ≤ 23 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData24 + +namespace OAI + +/-! Degree Union Data 24. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions24 : List PrefixRegion := [degreeRegion24_0,degreeRegion24_1,degreeRegion24_2,degreeRegion24_3,degreeRegion24_4,degreeRegion24_6,degreeRegion24_7,degreeRegion24_8,degreeRegion24_9,degreeRegion24_12,degreeRegion24_13,degreeRegion24_14,degreeRegion24_18,degreeRegion24_19,degreeRegion24_24] + +lemma degreeHalfHeight24 : ∀ R ∈ degreeHalfRegions24, firstBound 24 R.1 ≤ 23 := by decide +kernel + +lemma degreeHalfWidth24 : ∀ R ∈ degreeHalfRegions24, firstBound 24 R.2 ≤ 23 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData26.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData26.lean index 5d5b93f8cd305c2596119fcf61f238f9ebdf7be8..f90a691a3e09b9492c8b6f80314da31f372bc5f6 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData26.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData26.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData26 - -namespace OAI - -/-! Degree Union Data 26. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions26 : List PrefixRegion := [degreeRegion26_0,degreeRegion26_1,degreeRegion26_2,degreeRegion26_3,degreeRegion26_4,degreeRegion26_6,degreeRegion26_7,degreeRegion26_8,degreeRegion26_12,degreeRegion26_13,degreeRegion26_18] - -lemma degreeHalfHeight26 : ∀ R ∈ degreeHalfRegions26, firstBound 26 R.1 ≤ 25 := by decide +kernel - -lemma degreeHalfWidth26 : ∀ R ∈ degreeHalfRegions26, firstBound 26 R.2 ≤ 25 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData26 + +namespace OAI + +/-! Degree Union Data 26. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions26 : List PrefixRegion := [degreeRegion26_0,degreeRegion26_1,degreeRegion26_2,degreeRegion26_3,degreeRegion26_4,degreeRegion26_6,degreeRegion26_7,degreeRegion26_8,degreeRegion26_12,degreeRegion26_13,degreeRegion26_18] + +lemma degreeHalfHeight26 : ∀ R ∈ degreeHalfRegions26, firstBound 26 R.1 ≤ 25 := by decide +kernel + +lemma degreeHalfWidth26 : ∀ R ∈ degreeHalfRegions26, firstBound 26 R.2 ≤ 25 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData31.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData31.lean index 3abf59d3d35640634edc76c6733a5b9105310fe8..508ce93b668ab4ec1110c6bc7a32179501b93414 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData31.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData31.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData31 - -namespace OAI - -/-! Degree Union Data 31. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions31 : List PrefixRegion := [degreeRegion31_0,degreeRegion31_1,degreeRegion31_2,degreeRegion31_3,degreeRegion31_4,degreeRegion31_6,degreeRegion31_7,degreeRegion31_8,degreeRegion31_11,degreeRegion31_12,degreeRegion31_16,degreeRegion31_19] - -lemma degreeHalfHeight31 : ∀ R ∈ degreeHalfRegions31, firstBound 31 R.1 ≤ 10 := by decide +kernel - -lemma degreeHalfWidth31 : ∀ R ∈ degreeHalfRegions31, firstBound 31 R.2 ≤ 30 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData31 + +namespace OAI + +/-! Degree Union Data 31. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions31 : List PrefixRegion := [degreeRegion31_0,degreeRegion31_1,degreeRegion31_2,degreeRegion31_3,degreeRegion31_4,degreeRegion31_6,degreeRegion31_7,degreeRegion31_8,degreeRegion31_11,degreeRegion31_12,degreeRegion31_16,degreeRegion31_19] + +lemma degreeHalfHeight31 : ∀ R ∈ degreeHalfRegions31, firstBound 31 R.1 ≤ 10 := by decide +kernel + +lemma degreeHalfWidth31 : ∀ R ∈ degreeHalfRegions31, firstBound 31 R.2 ≤ 30 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData35.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData35.lean index 6a87bf231b58c478b72c29855d04bec5173c784c..ebb56a8a485075396df6c913016aa977ea777d05 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData35.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData35.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData35 - -namespace OAI - -/-! Degree Union Data 35. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions35 : List PrefixRegion := [degreeRegion35_0,degreeRegion35_1,degreeRegion35_2,degreeRegion35_3,degreeRegion35_4,degreeRegion35_5,degreeRegion35_6,degreeRegion35_7,degreeRegion35_8,degreeRegion35_9,degreeRegion35_10,degreeRegion35_11,degreeRegion35_12,degreeRegion35_13,degreeRegion35_14,degreeRegion35_15,degreeRegion35_16,degreeRegion35_18,degreeRegion35_19,degreeRegion35_20,degreeRegion35_23,degreeRegion35_24,degreeRegion35_28,degreeRegion35_29,degreeRegion35_44] - -lemma degreeHalfHeight35 : ∀ R ∈ degreeHalfRegions35, firstBound 35 R.1 ≤ 15 := by decide +kernel - -lemma degreeHalfWidth35 : ∀ R ∈ degreeHalfRegions35, firstBound 35 R.2 ≤ 34 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData35 + +namespace OAI + +/-! Degree Union Data 35. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions35 : List PrefixRegion := [degreeRegion35_0,degreeRegion35_1,degreeRegion35_2,degreeRegion35_3,degreeRegion35_4,degreeRegion35_5,degreeRegion35_6,degreeRegion35_7,degreeRegion35_8,degreeRegion35_9,degreeRegion35_10,degreeRegion35_11,degreeRegion35_12,degreeRegion35_13,degreeRegion35_14,degreeRegion35_15,degreeRegion35_16,degreeRegion35_18,degreeRegion35_19,degreeRegion35_20,degreeRegion35_23,degreeRegion35_24,degreeRegion35_28,degreeRegion35_29,degreeRegion35_44] + +lemma degreeHalfHeight35 : ∀ R ∈ degreeHalfRegions35, firstBound 35 R.1 ≤ 15 := by decide +kernel + +lemma degreeHalfWidth35 : ∀ R ∈ degreeHalfRegions35, firstBound 35 R.2 ≤ 34 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData37.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData37.lean index 62f1a5eeb96b5ffcef4f5d69bfdf29de05a13c0f..5c33efae3022a6dcb29637689a7eb83dca388ce3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData37.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData37.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData37 - -namespace OAI - -/-! Degree Union Data 37. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions37 : List PrefixRegion := [degreeRegion37_0,degreeRegion37_1,degreeRegion37_2,degreeRegion37_3,degreeRegion37_4,degreeRegion37_5,degreeRegion37_6,degreeRegion37_7,degreeRegion37_8,degreeRegion37_9,degreeRegion37_10,degreeRegion37_11,degreeRegion37_12,degreeRegion37_13,degreeRegion37_14,degreeRegion37_15,degreeRegion37_16,degreeRegion37_17,degreeRegion37_18,degreeRegion37_19,degreeRegion37_20,degreeRegion37_21,degreeRegion37_22,degreeRegion37_23,degreeRegion37_24,degreeRegion37_25,degreeRegion37_26,degreeRegion37_27,degreeRegion37_28,degreeRegion37_29,degreeRegion37_30,degreeRegion37_31,degreeRegion37_32,degreeRegion37_33,degreeRegion37_34,degreeRegion37_35,degreeRegion37_36,degreeRegion37_37,degreeRegion37_38,degreeRegion37_39,degreeRegion37_40,degreeRegion37_41,degreeRegion37_42,degreeRegion37_44,degreeRegion37_45,degreeRegion37_46,degreeRegion37_47,degreeRegion37_50,degreeRegion37_51,degreeRegion37_52,degreeRegion37_56,degreeRegion37_57,degreeRegion37_62,degreeRegion37_63,degreeRegion37_64,degreeRegion37_65,degreeRegion37_66,degreeRegion37_67,degreeRegion37_69,degreeRegion37_70,degreeRegion37_71,degreeRegion37_72,degreeRegion37_75,degreeRegion37_76,degreeRegion37_77] - -lemma degreeHalfHeight37 : ∀ R ∈ degreeHalfRegions37, firstBound 37 R.1 ≤ 17 := by decide +kernel - -lemma degreeHalfWidth37 : ∀ R ∈ degreeHalfRegions37, firstBound 37 R.2 ≤ 17 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData37 + +namespace OAI + +/-! Degree Union Data 37. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions37 : List PrefixRegion := [degreeRegion37_0,degreeRegion37_1,degreeRegion37_2,degreeRegion37_3,degreeRegion37_4,degreeRegion37_5,degreeRegion37_6,degreeRegion37_7,degreeRegion37_8,degreeRegion37_9,degreeRegion37_10,degreeRegion37_11,degreeRegion37_12,degreeRegion37_13,degreeRegion37_14,degreeRegion37_15,degreeRegion37_16,degreeRegion37_17,degreeRegion37_18,degreeRegion37_19,degreeRegion37_20,degreeRegion37_21,degreeRegion37_22,degreeRegion37_23,degreeRegion37_24,degreeRegion37_25,degreeRegion37_26,degreeRegion37_27,degreeRegion37_28,degreeRegion37_29,degreeRegion37_30,degreeRegion37_31,degreeRegion37_32,degreeRegion37_33,degreeRegion37_34,degreeRegion37_35,degreeRegion37_36,degreeRegion37_37,degreeRegion37_38,degreeRegion37_39,degreeRegion37_40,degreeRegion37_41,degreeRegion37_42,degreeRegion37_44,degreeRegion37_45,degreeRegion37_46,degreeRegion37_47,degreeRegion37_50,degreeRegion37_51,degreeRegion37_52,degreeRegion37_56,degreeRegion37_57,degreeRegion37_62,degreeRegion37_63,degreeRegion37_64,degreeRegion37_65,degreeRegion37_66,degreeRegion37_67,degreeRegion37_69,degreeRegion37_70,degreeRegion37_71,degreeRegion37_72,degreeRegion37_75,degreeRegion37_76,degreeRegion37_77] + +lemma degreeHalfHeight37 : ∀ R ∈ degreeHalfRegions37, firstBound 37 R.1 ≤ 17 := by decide +kernel + +lemma degreeHalfWidth37 : ∀ R ∈ degreeHalfRegions37, firstBound 37 R.2 ≤ 17 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData39.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData39.lean index e5b0b386153c1c361eb92c2220f9c761bdd3d45d..3ee813c7f8d855b28e1fe847c9de22f9a0641d1c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData39.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData39.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData39 - -namespace OAI - -/-! Degree Union Data 39. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions39 : List PrefixRegion := [degreeRegion39_0,degreeRegion39_1,degreeRegion39_2,degreeRegion39_3,degreeRegion39_4,degreeRegion39_5,degreeRegion39_6,degreeRegion39_7,degreeRegion39_8,degreeRegion39_9,degreeRegion39_10,degreeRegion39_11,degreeRegion39_12,degreeRegion39_13,degreeRegion39_14,degreeRegion39_15,degreeRegion39_16,degreeRegion39_17,degreeRegion39_18,degreeRegion39_19,degreeRegion39_20,degreeRegion39_21,degreeRegion39_22,degreeRegion39_23,degreeRegion39_24,degreeRegion39_25,degreeRegion39_26,degreeRegion39_28,degreeRegion39_29,degreeRegion39_30,degreeRegion39_34,degreeRegion39_35,degreeRegion39_40,degreeRegion39_41,degreeRegion39_42,degreeRegion39_43,degreeRegion39_44,degreeRegion39_46,degreeRegion39_47,degreeRegion39_48,degreeRegion39_49,degreeRegion39_52,degreeRegion39_53,degreeRegion39_54,degreeRegion39_58,degreeRegion39_59,degreeRegion39_81] - -lemma degreeHalfHeight39 : ∀ R ∈ degreeHalfRegions39, firstBound 39 R.1 ≤ 19 := by decide +kernel - -lemma degreeHalfWidth39 : ∀ R ∈ degreeHalfRegions39, firstBound 39 R.2 ≤ 38 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData39 + +namespace OAI + +/-! Degree Union Data 39. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions39 : List PrefixRegion := [degreeRegion39_0,degreeRegion39_1,degreeRegion39_2,degreeRegion39_3,degreeRegion39_4,degreeRegion39_5,degreeRegion39_6,degreeRegion39_7,degreeRegion39_8,degreeRegion39_9,degreeRegion39_10,degreeRegion39_11,degreeRegion39_12,degreeRegion39_13,degreeRegion39_14,degreeRegion39_15,degreeRegion39_16,degreeRegion39_17,degreeRegion39_18,degreeRegion39_19,degreeRegion39_20,degreeRegion39_21,degreeRegion39_22,degreeRegion39_23,degreeRegion39_24,degreeRegion39_25,degreeRegion39_26,degreeRegion39_28,degreeRegion39_29,degreeRegion39_30,degreeRegion39_34,degreeRegion39_35,degreeRegion39_40,degreeRegion39_41,degreeRegion39_42,degreeRegion39_43,degreeRegion39_44,degreeRegion39_46,degreeRegion39_47,degreeRegion39_48,degreeRegion39_49,degreeRegion39_52,degreeRegion39_53,degreeRegion39_54,degreeRegion39_58,degreeRegion39_59,degreeRegion39_81] + +lemma degreeHalfHeight39 : ∀ R ∈ degreeHalfRegions39, firstBound 39 R.1 ≤ 19 := by decide +kernel + +lemma degreeHalfWidth39 : ∀ R ∈ degreeHalfRegions39, firstBound 39 R.2 ≤ 38 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData41.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData41.lean index cf090a93cc528328f15adcd209c3ddcb11db307e..921464ea0c11dc2edfd2a51a79298cf96d8795d9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData41.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData41.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData41 - -namespace OAI - -/-! Degree Union Data 41. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions41 : List PrefixRegion := [degreeRegion41_0,degreeRegion41_1,degreeRegion41_2,degreeRegion41_3,degreeRegion41_4,degreeRegion41_5,degreeRegion41_6,degreeRegion41_7,degreeRegion41_8,degreeRegion41_9,degreeRegion41_10,degreeRegion41_11,degreeRegion41_12,degreeRegion41_13,degreeRegion41_14,degreeRegion41_15,degreeRegion41_16,degreeRegion41_17,degreeRegion41_18,degreeRegion41_19,degreeRegion41_20,degreeRegion41_21,degreeRegion41_22,degreeRegion41_23,degreeRegion41_24,degreeRegion41_25,degreeRegion41_26,degreeRegion41_27,degreeRegion41_28,degreeRegion41_29,degreeRegion41_30,degreeRegion41_31,degreeRegion41_32,degreeRegion41_33,degreeRegion41_34,degreeRegion41_35,degreeRegion41_36,degreeRegion41_37,degreeRegion41_38,degreeRegion41_39,degreeRegion41_40,degreeRegion41_41,degreeRegion41_42,degreeRegion41_43,degreeRegion41_44,degreeRegion41_46,degreeRegion41_47,degreeRegion41_48,degreeRegion41_49,degreeRegion41_52,degreeRegion41_53,degreeRegion41_54,degreeRegion41_58,degreeRegion41_59,degreeRegion41_64,degreeRegion41_65,degreeRegion41_66,degreeRegion41_67,degreeRegion41_68,degreeRegion41_69,degreeRegion41_70,degreeRegion41_71,degreeRegion41_73,degreeRegion41_74,degreeRegion41_75,degreeRegion41_76,degreeRegion41_77,degreeRegion41_78,degreeRegion41_79,degreeRegion41_82,degreeRegion41_83,degreeRegion41_84,degreeRegion41_85,degreeRegion41_86,degreeRegion41_87,degreeRegion41_91,degreeRegion41_92,degreeRegion41_93,degreeRegion41_94,degreeRegion41_99,degreeRegion41_100,degreeRegion41_101,degreeRegion41_107,degreeRegion41_108] - -lemma degreeHalfHeight41 : ∀ R ∈ degreeHalfRegions41, firstBound 41 R.1 ≤ 21 := by decide +kernel - -lemma degreeHalfWidth41 : ∀ R ∈ degreeHalfRegions41, firstBound 41 R.2 ≤ 21 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData41 + +namespace OAI + +/-! Degree Union Data 41. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions41 : List PrefixRegion := [degreeRegion41_0,degreeRegion41_1,degreeRegion41_2,degreeRegion41_3,degreeRegion41_4,degreeRegion41_5,degreeRegion41_6,degreeRegion41_7,degreeRegion41_8,degreeRegion41_9,degreeRegion41_10,degreeRegion41_11,degreeRegion41_12,degreeRegion41_13,degreeRegion41_14,degreeRegion41_15,degreeRegion41_16,degreeRegion41_17,degreeRegion41_18,degreeRegion41_19,degreeRegion41_20,degreeRegion41_21,degreeRegion41_22,degreeRegion41_23,degreeRegion41_24,degreeRegion41_25,degreeRegion41_26,degreeRegion41_27,degreeRegion41_28,degreeRegion41_29,degreeRegion41_30,degreeRegion41_31,degreeRegion41_32,degreeRegion41_33,degreeRegion41_34,degreeRegion41_35,degreeRegion41_36,degreeRegion41_37,degreeRegion41_38,degreeRegion41_39,degreeRegion41_40,degreeRegion41_41,degreeRegion41_42,degreeRegion41_43,degreeRegion41_44,degreeRegion41_46,degreeRegion41_47,degreeRegion41_48,degreeRegion41_49,degreeRegion41_52,degreeRegion41_53,degreeRegion41_54,degreeRegion41_58,degreeRegion41_59,degreeRegion41_64,degreeRegion41_65,degreeRegion41_66,degreeRegion41_67,degreeRegion41_68,degreeRegion41_69,degreeRegion41_70,degreeRegion41_71,degreeRegion41_73,degreeRegion41_74,degreeRegion41_75,degreeRegion41_76,degreeRegion41_77,degreeRegion41_78,degreeRegion41_79,degreeRegion41_82,degreeRegion41_83,degreeRegion41_84,degreeRegion41_85,degreeRegion41_86,degreeRegion41_87,degreeRegion41_91,degreeRegion41_92,degreeRegion41_93,degreeRegion41_94,degreeRegion41_99,degreeRegion41_100,degreeRegion41_101,degreeRegion41_107,degreeRegion41_108] + +lemma degreeHalfHeight41 : ∀ R ∈ degreeHalfRegions41, firstBound 41 R.1 ≤ 21 := by decide +kernel + +lemma degreeHalfWidth41 : ∀ R ∈ degreeHalfRegions41, firstBound 41 R.2 ≤ 21 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData43.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData43.lean index f3b8f63580db72aecc4fd0844dbcf82ed3453f77..76f12f84188aa6808c64601f0c4853cf37670bfc 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData43.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData43.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData43 - -namespace OAI - -/-! Degree Union Data 43. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions43 : List PrefixRegion := [degreeRegion43_0,degreeRegion43_1,degreeRegion43_2,degreeRegion43_3,degreeRegion43_4,degreeRegion43_5,degreeRegion43_6,degreeRegion43_7,degreeRegion43_8,degreeRegion43_9,degreeRegion43_10,degreeRegion43_12,degreeRegion43_13,degreeRegion43_14,degreeRegion43_15,degreeRegion43_16,degreeRegion43_17,degreeRegion43_18,degreeRegion43_19,degreeRegion43_21,degreeRegion43_22,degreeRegion43_23,degreeRegion43_24,degreeRegion43_25,degreeRegion43_26,degreeRegion43_27,degreeRegion43_28,degreeRegion43_29,degreeRegion43_30,degreeRegion43_31,degreeRegion43_32,degreeRegion43_33,degreeRegion43_34,degreeRegion43_35,degreeRegion43_36,degreeRegion43_38,degreeRegion43_39,degreeRegion43_40,degreeRegion43_41,degreeRegion43_44,degreeRegion43_45,degreeRegion43_46,degreeRegion43_50,degreeRegion43_51,degreeRegion43_55,degreeRegion43_56,degreeRegion43_57,degreeRegion43_58,degreeRegion43_59,degreeRegion43_60,degreeRegion43_61,degreeRegion43_63,degreeRegion43_64,degreeRegion43_65,degreeRegion43_66,degreeRegion43_67,degreeRegion43_70,degreeRegion43_71,degreeRegion43_72,degreeRegion43_73,degreeRegion43_78,degreeRegion43_79,degreeRegion43_100,degreeRegion43_112,degreeRegion43_113] - -lemma degreeHalfHeight43 : ∀ R ∈ degreeHalfRegions43, firstBound 43 R.1 ≤ 23 := by decide +kernel - -lemma degreeHalfWidth43 : ∀ R ∈ degreeHalfRegions43, firstBound 43 R.2 ≤ 42 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData43 + +namespace OAI + +/-! Degree Union Data 43. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions43 : List PrefixRegion := [degreeRegion43_0,degreeRegion43_1,degreeRegion43_2,degreeRegion43_3,degreeRegion43_4,degreeRegion43_5,degreeRegion43_6,degreeRegion43_7,degreeRegion43_8,degreeRegion43_9,degreeRegion43_10,degreeRegion43_12,degreeRegion43_13,degreeRegion43_14,degreeRegion43_15,degreeRegion43_16,degreeRegion43_17,degreeRegion43_18,degreeRegion43_19,degreeRegion43_21,degreeRegion43_22,degreeRegion43_23,degreeRegion43_24,degreeRegion43_25,degreeRegion43_26,degreeRegion43_27,degreeRegion43_28,degreeRegion43_29,degreeRegion43_30,degreeRegion43_31,degreeRegion43_32,degreeRegion43_33,degreeRegion43_34,degreeRegion43_35,degreeRegion43_36,degreeRegion43_38,degreeRegion43_39,degreeRegion43_40,degreeRegion43_41,degreeRegion43_44,degreeRegion43_45,degreeRegion43_46,degreeRegion43_50,degreeRegion43_51,degreeRegion43_55,degreeRegion43_56,degreeRegion43_57,degreeRegion43_58,degreeRegion43_59,degreeRegion43_60,degreeRegion43_61,degreeRegion43_63,degreeRegion43_64,degreeRegion43_65,degreeRegion43_66,degreeRegion43_67,degreeRegion43_70,degreeRegion43_71,degreeRegion43_72,degreeRegion43_73,degreeRegion43_78,degreeRegion43_79,degreeRegion43_100,degreeRegion43_112,degreeRegion43_113] + +lemma degreeHalfHeight43 : ∀ R ∈ degreeHalfRegions43, firstBound 43 R.1 ≤ 23 := by decide +kernel + +lemma degreeHalfWidth43 : ∀ R ∈ degreeHalfRegions43, firstBound 43 R.2 ≤ 42 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData58.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData58.lean index 658cf6f99b21c9630ff71e7428ee11a5693aeaed..d6ce6d11b47a676a131029d7358381a711402a18 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData58.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData58.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData58 - -namespace OAI - -/-! Degree Union Data 58. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions58 : List PrefixRegion := [degreeRegion58_0,degreeRegion58_1,degreeRegion58_2,degreeRegion58_3,degreeRegion58_4,degreeRegion58_5,degreeRegion58_6,degreeRegion58_7,degreeRegion58_9,degreeRegion58_10,degreeRegion58_11,degreeRegion58_12,degreeRegion58_13,degreeRegion58_14,degreeRegion58_15,degreeRegion58_19,degreeRegion58_20,degreeRegion58_21,degreeRegion58_22,degreeRegion58_23,degreeRegion58_24,degreeRegion58_29,degreeRegion58_30,degreeRegion58_31,degreeRegion58_32,degreeRegion58_33,degreeRegion58_38,degreeRegion58_39,degreeRegion58_40,degreeRegion58_41,degreeRegion58_47,degreeRegion58_48,degreeRegion58_54,degreeRegion58_59,degreeRegion58_60] - -lemma degreeHalfHeight58 : ∀ R ∈ degreeHalfRegions58, firstBound 58 R.1 ≤ 24 := by decide +kernel - -lemma degreeHalfWidth58 : ∀ R ∈ degreeHalfRegions58, firstBound 58 R.2 ≤ 14 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData58 + +namespace OAI + +/-! Degree Union Data 58. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions58 : List PrefixRegion := [degreeRegion58_0,degreeRegion58_1,degreeRegion58_2,degreeRegion58_3,degreeRegion58_4,degreeRegion58_5,degreeRegion58_6,degreeRegion58_7,degreeRegion58_9,degreeRegion58_10,degreeRegion58_11,degreeRegion58_12,degreeRegion58_13,degreeRegion58_14,degreeRegion58_15,degreeRegion58_19,degreeRegion58_20,degreeRegion58_21,degreeRegion58_22,degreeRegion58_23,degreeRegion58_24,degreeRegion58_29,degreeRegion58_30,degreeRegion58_31,degreeRegion58_32,degreeRegion58_33,degreeRegion58_38,degreeRegion58_39,degreeRegion58_40,degreeRegion58_41,degreeRegion58_47,degreeRegion58_48,degreeRegion58_54,degreeRegion58_59,degreeRegion58_60] + +lemma degreeHalfHeight58 : ∀ R ∈ degreeHalfRegions58, firstBound 58 R.1 ≤ 24 := by decide +kernel + +lemma degreeHalfWidth58 : ∀ R ∈ degreeHalfRegions58, firstBound 58 R.2 ≤ 14 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData62.lean index 9e5e972cab987ff501f9a3e41e2f647c5f37b090..825e5ef57307e7505f17ba83d7fb18465cb3311e 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData62.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData62 - -namespace OAI - -/-! Degree Union Data 62. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions62 : List PrefixRegion := [degreeRegion62_0,degreeRegion62_1,degreeRegion62_2,degreeRegion62_3,degreeRegion62_5,degreeRegion62_6,degreeRegion62_7,degreeRegion62_8,degreeRegion62_11,degreeRegion62_12,degreeRegion62_13,degreeRegion62_14,degreeRegion62_15,degreeRegion62_16,degreeRegion62_17,degreeRegion62_18,degreeRegion62_19,degreeRegion62_20,degreeRegion62_21,degreeRegion62_22,degreeRegion62_23,degreeRegion62_24,degreeRegion62_25,degreeRegion62_26,degreeRegion62_29,degreeRegion62_30,degreeRegion62_31,degreeRegion62_32,degreeRegion62_33,degreeRegion62_34,degreeRegion62_35,degreeRegion62_36,degreeRegion62_37,degreeRegion62_38,degreeRegion62_39,degreeRegion62_40,degreeRegion62_41,degreeRegion62_42,degreeRegion62_46,degreeRegion62_47,degreeRegion62_48,degreeRegion62_49,degreeRegion62_50,degreeRegion62_51,degreeRegion62_56,degreeRegion62_57,degreeRegion62_58,degreeRegion62_59,degreeRegion62_60,degreeRegion62_67,degreeRegion62_68,degreeRegion62_69,degreeRegion62_70,degreeRegion62_77,degreeRegion62_78,degreeRegion62_79,degreeRegion62_87,degreeRegion62_88,degreeRegion62_99,degreeRegion62_102,degreeRegion62_108,degreeRegion62_109] - -lemma degreeHalfHeight62 : ∀ R ∈ degreeHalfRegions62, firstBound 62 R.1 ≤ 28 := by decide +kernel - -lemma degreeHalfWidth62 : ∀ R ∈ degreeHalfRegions62, firstBound 62 R.2 ≤ 28 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData62 + +namespace OAI + +/-! Degree Union Data 62. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions62 : List PrefixRegion := [degreeRegion62_0,degreeRegion62_1,degreeRegion62_2,degreeRegion62_3,degreeRegion62_5,degreeRegion62_6,degreeRegion62_7,degreeRegion62_8,degreeRegion62_11,degreeRegion62_12,degreeRegion62_13,degreeRegion62_14,degreeRegion62_15,degreeRegion62_16,degreeRegion62_17,degreeRegion62_18,degreeRegion62_19,degreeRegion62_20,degreeRegion62_21,degreeRegion62_22,degreeRegion62_23,degreeRegion62_24,degreeRegion62_25,degreeRegion62_26,degreeRegion62_29,degreeRegion62_30,degreeRegion62_31,degreeRegion62_32,degreeRegion62_33,degreeRegion62_34,degreeRegion62_35,degreeRegion62_36,degreeRegion62_37,degreeRegion62_38,degreeRegion62_39,degreeRegion62_40,degreeRegion62_41,degreeRegion62_42,degreeRegion62_46,degreeRegion62_47,degreeRegion62_48,degreeRegion62_49,degreeRegion62_50,degreeRegion62_51,degreeRegion62_56,degreeRegion62_57,degreeRegion62_58,degreeRegion62_59,degreeRegion62_60,degreeRegion62_67,degreeRegion62_68,degreeRegion62_69,degreeRegion62_70,degreeRegion62_77,degreeRegion62_78,degreeRegion62_79,degreeRegion62_87,degreeRegion62_88,degreeRegion62_99,degreeRegion62_102,degreeRegion62_108,degreeRegion62_109] + +lemma degreeHalfHeight62 : ∀ R ∈ degreeHalfRegions62, firstBound 62 R.1 ≤ 28 := by decide +kernel + +lemma degreeHalfWidth62 : ∀ R ∈ degreeHalfRegions62, firstBound 62 R.2 ≤ 28 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData64.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData64.lean index 3ca4ce79eb68a1db0117597827880bc97ef923b7..fb412335a72c4b5293d8b221641145195efeeb44 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData64.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData64.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData64 - -namespace OAI - -/-! Degree Union Data 64. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions64 : List PrefixRegion := [degreeRegion64_0,degreeRegion64_1,degreeRegion64_2,degreeRegion64_4,degreeRegion64_5,degreeRegion64_8,degreeRegion64_9,degreeRegion64_10,degreeRegion64_11,degreeRegion64_12,degreeRegion64_13,degreeRegion64_14,degreeRegion64_15,degreeRegion64_16,degreeRegion64_17,degreeRegion64_18,degreeRegion64_19,degreeRegion64_20,degreeRegion64_21,degreeRegion64_22,degreeRegion64_23,degreeRegion64_25,degreeRegion64_26,degreeRegion64_27,degreeRegion64_28,degreeRegion64_29,degreeRegion64_30,degreeRegion64_31,degreeRegion64_32,degreeRegion64_33,degreeRegion64_34,degreeRegion64_35,degreeRegion64_36,degreeRegion64_37,degreeRegion64_38,degreeRegion64_39,degreeRegion64_40,degreeRegion64_41,degreeRegion64_42,degreeRegion64_45,degreeRegion64_46,degreeRegion64_47,degreeRegion64_48,degreeRegion64_49,degreeRegion64_50,degreeRegion64_51,degreeRegion64_52,degreeRegion64_57,degreeRegion64_58,degreeRegion64_59,degreeRegion64_60,degreeRegion64_61,degreeRegion64_62,degreeRegion64_63,degreeRegion64_69,degreeRegion64_70,degreeRegion64_71,degreeRegion64_72,degreeRegion64_73,degreeRegion64_74,degreeRegion64_81,degreeRegion64_82,degreeRegion64_83,degreeRegion64_84,degreeRegion64_85,degreeRegion64_93,degreeRegion64_94,degreeRegion64_95,degreeRegion64_96,degreeRegion64_105,degreeRegion64_106,degreeRegion64_107,degreeRegion64_117,degreeRegion64_118,degreeRegion64_129] - -lemma degreeHalfHeight64 : ∀ R ∈ degreeHalfRegions64, firstBound 64 R.1 ≤ 30 := by decide +kernel - -lemma degreeHalfWidth64 : ∀ R ∈ degreeHalfRegions64, firstBound 64 R.2 ≤ 30 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData64 + +namespace OAI + +/-! Degree Union Data 64. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions64 : List PrefixRegion := [degreeRegion64_0,degreeRegion64_1,degreeRegion64_2,degreeRegion64_4,degreeRegion64_5,degreeRegion64_8,degreeRegion64_9,degreeRegion64_10,degreeRegion64_11,degreeRegion64_12,degreeRegion64_13,degreeRegion64_14,degreeRegion64_15,degreeRegion64_16,degreeRegion64_17,degreeRegion64_18,degreeRegion64_19,degreeRegion64_20,degreeRegion64_21,degreeRegion64_22,degreeRegion64_23,degreeRegion64_25,degreeRegion64_26,degreeRegion64_27,degreeRegion64_28,degreeRegion64_29,degreeRegion64_30,degreeRegion64_31,degreeRegion64_32,degreeRegion64_33,degreeRegion64_34,degreeRegion64_35,degreeRegion64_36,degreeRegion64_37,degreeRegion64_38,degreeRegion64_39,degreeRegion64_40,degreeRegion64_41,degreeRegion64_42,degreeRegion64_45,degreeRegion64_46,degreeRegion64_47,degreeRegion64_48,degreeRegion64_49,degreeRegion64_50,degreeRegion64_51,degreeRegion64_52,degreeRegion64_57,degreeRegion64_58,degreeRegion64_59,degreeRegion64_60,degreeRegion64_61,degreeRegion64_62,degreeRegion64_63,degreeRegion64_69,degreeRegion64_70,degreeRegion64_71,degreeRegion64_72,degreeRegion64_73,degreeRegion64_74,degreeRegion64_81,degreeRegion64_82,degreeRegion64_83,degreeRegion64_84,degreeRegion64_85,degreeRegion64_93,degreeRegion64_94,degreeRegion64_95,degreeRegion64_96,degreeRegion64_105,degreeRegion64_106,degreeRegion64_107,degreeRegion64_117,degreeRegion64_118,degreeRegion64_129] + +lemma degreeHalfHeight64 : ∀ R ∈ degreeHalfRegions64, firstBound 64 R.1 ≤ 30 := by decide +kernel + +lemma degreeHalfWidth64 : ∀ R ∈ degreeHalfRegions64, firstBound 64 R.2 ≤ 30 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData89.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData89.lean index 60e12dc7d40d39bc4f328a7b748c7ab1605112c7..c4446f392b9e77b61aeba766705929b4b29aba6d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData89.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionData89.lean @@ -1,22 +1,22 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData89 - -namespace OAI - -/-! Degree Union Data 89. -/ - -section - -namespace UniversalTensorSquare - -def degreeHalfRegions89 : List PrefixRegion := [degreeRegion89_0,degreeRegion89_1,degreeRegion89_2,degreeRegion89_3] - -lemma degreeHalfHeight89 : ∀ R ∈ degreeHalfRegions89, firstBound 89 R.1 ≤ 18 := by decide +kernel - -lemma degreeHalfWidth89 : ∀ R ∈ degreeHalfRegions89, firstBound 89 R.2 ≤ 18 := by decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeRegionData89 + +namespace OAI + +/-! Degree Union Data 89. -/ + +section + +namespace UniversalTensorSquare + +def degreeHalfRegions89 : List PrefixRegion := [degreeRegion89_0,degreeRegion89_1,degreeRegion89_2,degreeRegion89_3] + +lemma degreeHalfHeight89 : ∀ R ∈ degreeHalfRegions89, firstBound 89 R.1 ≤ 18 := by decide +kernel + +lemma degreeHalfWidth89 : ∀ R ∈ degreeHalfRegions89, firstBound 89 R.2 ≤ 18 := by decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates24.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates24.lean index 76d5bb8676739507d7ee275ddc24b25362fee811..b622c2c0cde82417c6d9d235beced169ba57a323 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates24.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates24.lean @@ -1,139 +1,139 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData24 - -namespace OAI - -/-! Degree Union States 24. -/ - -section - -namespace UniversalTensorSquare - -def degreeUnionState24_7 : List PrefixRegion := nextRegions 4 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_8 : List PrefixRegion := nextRegions 5 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_9 : List PrefixRegion := nextRegions 6 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_10 : List PrefixRegion := nextRegions 7 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_11 : List PrefixRegion := nextRegions 8 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_12 : List PrefixRegion := nextRegions 9 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_13 : List PrefixRegion := nextRegions 10 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_14 : List PrefixRegion := nextRegions 11 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_15 : List PrefixRegion := nextRegions 12 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_16 : List PrefixRegion := nextRegions 13 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_17 : List PrefixRegion := nextRegions 14 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_18 : List PrefixRegion := nextRegions 15 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_19 : List PrefixRegion := nextRegions 16 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_20 : List PrefixRegion := nextRegions 17 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_21 : List PrefixRegion := nextRegions 18 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_22 : List PrefixRegion := nextRegions 19 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_23 : List PrefixRegion := nextRegions 20 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_24 : List PrefixRegion := nextRegions 21 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_25 : List PrefixRegion := nextRegions 22 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_26 : List PrefixRegion := nextRegions 23 (liveRegions 6 24 23 degreeHalfRegions24) - -def degreeUnionState24_28 : List PrefixRegion := nextRegions 4 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_29 : List PrefixRegion := nextRegions 5 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_30 : List PrefixRegion := nextRegions 6 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_31 : List PrefixRegion := nextRegions 7 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_32 : List PrefixRegion := nextRegions 8 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_33 : List PrefixRegion := nextRegions 9 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_34 : List PrefixRegion := nextRegions 10 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_35 : List PrefixRegion := nextRegions 11 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_36 : List PrefixRegion := nextRegions 12 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_37 : List PrefixRegion := nextRegions 13 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_38 : List PrefixRegion := nextRegions 14 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_39 : List PrefixRegion := nextRegions 15 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_40 : List PrefixRegion := nextRegions 16 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_41 : List PrefixRegion := nextRegions 17 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_42 : List PrefixRegion := nextRegions 18 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_43 : List PrefixRegion := nextRegions 19 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_44 : List PrefixRegion := nextRegions 20 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_45 : List PrefixRegion := nextRegions 21 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_46 : List PrefixRegion := nextRegions 22 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_47 : List PrefixRegion := nextRegions 23 (liveRegions 7 24 23 degreeHalfRegions24) - -def degreeUnionState24_49 : List PrefixRegion := nextRegions 3 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_50 : List PrefixRegion := nextRegions 4 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_51 : List PrefixRegion := nextRegions 5 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_52 : List PrefixRegion := nextRegions 6 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_53 : List PrefixRegion := nextRegions 7 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_54 : List PrefixRegion := nextRegions 8 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_55 : List PrefixRegion := nextRegions 9 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_56 : List PrefixRegion := nextRegions 10 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_57 : List PrefixRegion := nextRegions 11 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_58 : List PrefixRegion := nextRegions 12 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_59 : List PrefixRegion := nextRegions 13 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_60 : List PrefixRegion := nextRegions 14 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_61 : List PrefixRegion := nextRegions 15 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_62 : List PrefixRegion := nextRegions 16 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_63 : List PrefixRegion := nextRegions 17 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_64 : List PrefixRegion := nextRegions 18 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_65 : List PrefixRegion := nextRegions 19 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_66 : List PrefixRegion := nextRegions 20 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_67 : List PrefixRegion := nextRegions 21 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_68 : List PrefixRegion := nextRegions 22 (liveRegions 8 24 23 degreeHalfRegions24) - -def degreeUnionState24_69 : List PrefixRegion := nextRegions 23 (liveRegions 8 24 23 degreeHalfRegions24) - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData24 + +namespace OAI + +/-! Degree Union States 24. -/ + +section + +namespace UniversalTensorSquare + +def degreeUnionState24_7 : List PrefixRegion := nextRegions 4 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_8 : List PrefixRegion := nextRegions 5 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_9 : List PrefixRegion := nextRegions 6 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_10 : List PrefixRegion := nextRegions 7 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_11 : List PrefixRegion := nextRegions 8 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_12 : List PrefixRegion := nextRegions 9 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_13 : List PrefixRegion := nextRegions 10 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_14 : List PrefixRegion := nextRegions 11 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_15 : List PrefixRegion := nextRegions 12 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_16 : List PrefixRegion := nextRegions 13 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_17 : List PrefixRegion := nextRegions 14 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_18 : List PrefixRegion := nextRegions 15 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_19 : List PrefixRegion := nextRegions 16 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_20 : List PrefixRegion := nextRegions 17 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_21 : List PrefixRegion := nextRegions 18 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_22 : List PrefixRegion := nextRegions 19 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_23 : List PrefixRegion := nextRegions 20 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_24 : List PrefixRegion := nextRegions 21 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_25 : List PrefixRegion := nextRegions 22 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_26 : List PrefixRegion := nextRegions 23 (liveRegions 6 24 23 degreeHalfRegions24) + +def degreeUnionState24_28 : List PrefixRegion := nextRegions 4 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_29 : List PrefixRegion := nextRegions 5 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_30 : List PrefixRegion := nextRegions 6 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_31 : List PrefixRegion := nextRegions 7 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_32 : List PrefixRegion := nextRegions 8 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_33 : List PrefixRegion := nextRegions 9 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_34 : List PrefixRegion := nextRegions 10 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_35 : List PrefixRegion := nextRegions 11 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_36 : List PrefixRegion := nextRegions 12 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_37 : List PrefixRegion := nextRegions 13 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_38 : List PrefixRegion := nextRegions 14 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_39 : List PrefixRegion := nextRegions 15 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_40 : List PrefixRegion := nextRegions 16 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_41 : List PrefixRegion := nextRegions 17 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_42 : List PrefixRegion := nextRegions 18 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_43 : List PrefixRegion := nextRegions 19 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_44 : List PrefixRegion := nextRegions 20 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_45 : List PrefixRegion := nextRegions 21 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_46 : List PrefixRegion := nextRegions 22 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_47 : List PrefixRegion := nextRegions 23 (liveRegions 7 24 23 degreeHalfRegions24) + +def degreeUnionState24_49 : List PrefixRegion := nextRegions 3 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_50 : List PrefixRegion := nextRegions 4 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_51 : List PrefixRegion := nextRegions 5 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_52 : List PrefixRegion := nextRegions 6 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_53 : List PrefixRegion := nextRegions 7 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_54 : List PrefixRegion := nextRegions 8 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_55 : List PrefixRegion := nextRegions 9 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_56 : List PrefixRegion := nextRegions 10 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_57 : List PrefixRegion := nextRegions 11 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_58 : List PrefixRegion := nextRegions 12 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_59 : List PrefixRegion := nextRegions 13 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_60 : List PrefixRegion := nextRegions 14 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_61 : List PrefixRegion := nextRegions 15 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_62 : List PrefixRegion := nextRegions 16 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_63 : List PrefixRegion := nextRegions 17 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_64 : List PrefixRegion := nextRegions 18 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_65 : List PrefixRegion := nextRegions 19 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_66 : List PrefixRegion := nextRegions 20 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_67 : List PrefixRegion := nextRegions 21 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_68 : List PrefixRegion := nextRegions 22 (liveRegions 8 24 23 degreeHalfRegions24) + +def degreeUnionState24_69 : List PrefixRegion := nextRegions 23 (liveRegions 8 24 23 degreeHalfRegions24) + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates26.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates26.lean index fe56d01ad9c726369a457a43947850d3dfb46c08..3c1882f193269c5baecee90627315a66024333a3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates26.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates26.lean @@ -1,151 +1,151 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData26 - -namespace OAI - -/-! Degree Union States 26. -/ - -section - -namespace UniversalTensorSquare - -def degreeUnionState26_8 : List PrefixRegion := nextRegions 4 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_9 : List PrefixRegion := nextRegions 5 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_10 : List PrefixRegion := nextRegions 6 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_11 : List PrefixRegion := nextRegions 7 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_12 : List PrefixRegion := nextRegions 8 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_13 : List PrefixRegion := nextRegions 9 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_14 : List PrefixRegion := nextRegions 10 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_15 : List PrefixRegion := nextRegions 11 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_16 : List PrefixRegion := nextRegions 12 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_17 : List PrefixRegion := nextRegions 13 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_18 : List PrefixRegion := nextRegions 14 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_19 : List PrefixRegion := nextRegions 15 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_20 : List PrefixRegion := nextRegions 16 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_21 : List PrefixRegion := nextRegions 17 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_22 : List PrefixRegion := nextRegions 18 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_23 : List PrefixRegion := nextRegions 19 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_24 : List PrefixRegion := nextRegions 20 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_25 : List PrefixRegion := nextRegions 21 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_26 : List PrefixRegion := nextRegions 22 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_27 : List PrefixRegion := nextRegions 23 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_28 : List PrefixRegion := nextRegions 24 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_29 : List PrefixRegion := nextRegions 25 (liveRegions 7 26 25 degreeHalfRegions26) - -def degreeUnionState26_31 : List PrefixRegion := nextRegions 4 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_32 : List PrefixRegion := nextRegions 5 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_33 : List PrefixRegion := nextRegions 6 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_34 : List PrefixRegion := nextRegions 7 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_35 : List PrefixRegion := nextRegions 8 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_36 : List PrefixRegion := nextRegions 9 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_37 : List PrefixRegion := nextRegions 10 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_38 : List PrefixRegion := nextRegions 11 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_39 : List PrefixRegion := nextRegions 12 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_40 : List PrefixRegion := nextRegions 13 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_41 : List PrefixRegion := nextRegions 14 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_42 : List PrefixRegion := nextRegions 15 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_43 : List PrefixRegion := nextRegions 16 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_44 : List PrefixRegion := nextRegions 17 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_45 : List PrefixRegion := nextRegions 18 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_46 : List PrefixRegion := nextRegions 19 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_47 : List PrefixRegion := nextRegions 20 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_48 : List PrefixRegion := nextRegions 21 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_49 : List PrefixRegion := nextRegions 22 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_50 : List PrefixRegion := nextRegions 23 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_51 : List PrefixRegion := nextRegions 24 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_52 : List PrefixRegion := nextRegions 25 (liveRegions 8 26 25 degreeHalfRegions26) - -def degreeUnionState26_54 : List PrefixRegion := nextRegions 3 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_55 : List PrefixRegion := nextRegions 4 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_56 : List PrefixRegion := nextRegions 5 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_57 : List PrefixRegion := nextRegions 6 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_58 : List PrefixRegion := nextRegions 7 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_59 : List PrefixRegion := nextRegions 8 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_60 : List PrefixRegion := nextRegions 9 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_61 : List PrefixRegion := nextRegions 10 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_62 : List PrefixRegion := nextRegions 11 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_63 : List PrefixRegion := nextRegions 12 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_64 : List PrefixRegion := nextRegions 13 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_65 : List PrefixRegion := nextRegions 14 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_66 : List PrefixRegion := nextRegions 15 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_67 : List PrefixRegion := nextRegions 16 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_68 : List PrefixRegion := nextRegions 17 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_69 : List PrefixRegion := nextRegions 18 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_70 : List PrefixRegion := nextRegions 19 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_71 : List PrefixRegion := nextRegions 20 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_72 : List PrefixRegion := nextRegions 21 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_73 : List PrefixRegion := nextRegions 22 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_74 : List PrefixRegion := nextRegions 23 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_75 : List PrefixRegion := nextRegions 24 (liveRegions 9 26 25 degreeHalfRegions26) - -def degreeUnionState26_76 : List PrefixRegion := nextRegions 25 (liveRegions 9 26 25 degreeHalfRegions26) - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData26 + +namespace OAI + +/-! Degree Union States 26. -/ + +section + +namespace UniversalTensorSquare + +def degreeUnionState26_8 : List PrefixRegion := nextRegions 4 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_9 : List PrefixRegion := nextRegions 5 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_10 : List PrefixRegion := nextRegions 6 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_11 : List PrefixRegion := nextRegions 7 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_12 : List PrefixRegion := nextRegions 8 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_13 : List PrefixRegion := nextRegions 9 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_14 : List PrefixRegion := nextRegions 10 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_15 : List PrefixRegion := nextRegions 11 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_16 : List PrefixRegion := nextRegions 12 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_17 : List PrefixRegion := nextRegions 13 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_18 : List PrefixRegion := nextRegions 14 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_19 : List PrefixRegion := nextRegions 15 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_20 : List PrefixRegion := nextRegions 16 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_21 : List PrefixRegion := nextRegions 17 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_22 : List PrefixRegion := nextRegions 18 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_23 : List PrefixRegion := nextRegions 19 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_24 : List PrefixRegion := nextRegions 20 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_25 : List PrefixRegion := nextRegions 21 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_26 : List PrefixRegion := nextRegions 22 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_27 : List PrefixRegion := nextRegions 23 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_28 : List PrefixRegion := nextRegions 24 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_29 : List PrefixRegion := nextRegions 25 (liveRegions 7 26 25 degreeHalfRegions26) + +def degreeUnionState26_31 : List PrefixRegion := nextRegions 4 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_32 : List PrefixRegion := nextRegions 5 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_33 : List PrefixRegion := nextRegions 6 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_34 : List PrefixRegion := nextRegions 7 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_35 : List PrefixRegion := nextRegions 8 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_36 : List PrefixRegion := nextRegions 9 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_37 : List PrefixRegion := nextRegions 10 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_38 : List PrefixRegion := nextRegions 11 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_39 : List PrefixRegion := nextRegions 12 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_40 : List PrefixRegion := nextRegions 13 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_41 : List PrefixRegion := nextRegions 14 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_42 : List PrefixRegion := nextRegions 15 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_43 : List PrefixRegion := nextRegions 16 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_44 : List PrefixRegion := nextRegions 17 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_45 : List PrefixRegion := nextRegions 18 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_46 : List PrefixRegion := nextRegions 19 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_47 : List PrefixRegion := nextRegions 20 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_48 : List PrefixRegion := nextRegions 21 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_49 : List PrefixRegion := nextRegions 22 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_50 : List PrefixRegion := nextRegions 23 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_51 : List PrefixRegion := nextRegions 24 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_52 : List PrefixRegion := nextRegions 25 (liveRegions 8 26 25 degreeHalfRegions26) + +def degreeUnionState26_54 : List PrefixRegion := nextRegions 3 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_55 : List PrefixRegion := nextRegions 4 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_56 : List PrefixRegion := nextRegions 5 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_57 : List PrefixRegion := nextRegions 6 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_58 : List PrefixRegion := nextRegions 7 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_59 : List PrefixRegion := nextRegions 8 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_60 : List PrefixRegion := nextRegions 9 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_61 : List PrefixRegion := nextRegions 10 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_62 : List PrefixRegion := nextRegions 11 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_63 : List PrefixRegion := nextRegions 12 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_64 : List PrefixRegion := nextRegions 13 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_65 : List PrefixRegion := nextRegions 14 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_66 : List PrefixRegion := nextRegions 15 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_67 : List PrefixRegion := nextRegions 16 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_68 : List PrefixRegion := nextRegions 17 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_69 : List PrefixRegion := nextRegions 18 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_70 : List PrefixRegion := nextRegions 19 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_71 : List PrefixRegion := nextRegions 20 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_72 : List PrefixRegion := nextRegions 21 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_73 : List PrefixRegion := nextRegions 22 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_74 : List PrefixRegion := nextRegions 23 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_75 : List PrefixRegion := nextRegions 24 (liveRegions 9 26 25 degreeHalfRegions26) + +def degreeUnionState26_76 : List PrefixRegion := nextRegions 25 (liveRegions 9 26 25 degreeHalfRegions26) + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates31.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates31.lean index 030973169943b2b9174074f207de97567226ddd8..25cce87063951f290f6e01bfeed68b2c2151d223 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates31.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates31.lean @@ -1,179 +1,179 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData31 - -namespace OAI - -/-! Degree Union States 31. -/ - -section - -namespace UniversalTensorSquare - -def degreeUnionState31_9 : List PrefixRegion := nextRegions 4 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_10 : List PrefixRegion := nextRegions 5 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_11 : List PrefixRegion := nextRegions 6 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_12 : List PrefixRegion := nextRegions 7 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_13 : List PrefixRegion := nextRegions 8 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_14 : List PrefixRegion := nextRegions 9 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_15 : List PrefixRegion := nextRegions 10 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_16 : List PrefixRegion := nextRegions 11 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_17 : List PrefixRegion := nextRegions 12 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_18 : List PrefixRegion := nextRegions 13 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_19 : List PrefixRegion := nextRegions 14 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_20 : List PrefixRegion := nextRegions 15 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_21 : List PrefixRegion := nextRegions 16 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_22 : List PrefixRegion := nextRegions 17 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_23 : List PrefixRegion := nextRegions 18 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_24 : List PrefixRegion := nextRegions 19 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_25 : List PrefixRegion := nextRegions 20 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_26 : List PrefixRegion := nextRegions 21 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_27 : List PrefixRegion := nextRegions 22 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_28 : List PrefixRegion := nextRegions 23 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_29 : List PrefixRegion := nextRegions 24 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_30 : List PrefixRegion := nextRegions 25 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_31 : List PrefixRegion := nextRegions 26 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_32 : List PrefixRegion := nextRegions 27 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_33 : List PrefixRegion := nextRegions 28 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_34 : List PrefixRegion := nextRegions 29 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_35 : List PrefixRegion := nextRegions 30 (liveRegions 8 31 30 degreeHalfRegions31) - -def degreeUnionState31_37 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_38 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_39 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_40 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_41 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_42 : List PrefixRegion := nextRegions 9 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_43 : List PrefixRegion := nextRegions 10 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_44 : List PrefixRegion := nextRegions 11 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_45 : List PrefixRegion := nextRegions 12 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_46 : List PrefixRegion := nextRegions 13 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_47 : List PrefixRegion := nextRegions 14 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_48 : List PrefixRegion := nextRegions 15 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_49 : List PrefixRegion := nextRegions 16 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_50 : List PrefixRegion := nextRegions 17 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_51 : List PrefixRegion := nextRegions 18 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_52 : List PrefixRegion := nextRegions 19 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_53 : List PrefixRegion := nextRegions 20 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_54 : List PrefixRegion := nextRegions 21 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_55 : List PrefixRegion := nextRegions 22 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_56 : List PrefixRegion := nextRegions 23 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_57 : List PrefixRegion := nextRegions 24 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_58 : List PrefixRegion := nextRegions 25 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_59 : List PrefixRegion := nextRegions 26 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_60 : List PrefixRegion := nextRegions 27 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_61 : List PrefixRegion := nextRegions 28 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_62 : List PrefixRegion := nextRegions 29 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_63 : List PrefixRegion := nextRegions 30 (liveRegions 9 31 30 degreeHalfRegions31) - -def degreeUnionState31_65 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_66 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_67 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_68 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_69 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_70 : List PrefixRegion := nextRegions 9 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_71 : List PrefixRegion := nextRegions 10 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_72 : List PrefixRegion := nextRegions 11 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_73 : List PrefixRegion := nextRegions 12 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_74 : List PrefixRegion := nextRegions 13 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_75 : List PrefixRegion := nextRegions 14 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_76 : List PrefixRegion := nextRegions 15 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_77 : List PrefixRegion := nextRegions 16 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_78 : List PrefixRegion := nextRegions 17 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_79 : List PrefixRegion := nextRegions 18 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_80 : List PrefixRegion := nextRegions 19 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_81 : List PrefixRegion := nextRegions 20 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_82 : List PrefixRegion := nextRegions 21 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_83 : List PrefixRegion := nextRegions 22 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_84 : List PrefixRegion := nextRegions 23 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_85 : List PrefixRegion := nextRegions 24 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_86 : List PrefixRegion := nextRegions 25 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_87 : List PrefixRegion := nextRegions 26 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_88 : List PrefixRegion := nextRegions 27 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_89 : List PrefixRegion := nextRegions 28 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_90 : List PrefixRegion := nextRegions 29 (liveRegions 10 31 30 degreeHalfRegions31) - -def degreeUnionState31_91 : List PrefixRegion := nextRegions 30 (liveRegions 10 31 30 degreeHalfRegions31) - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData31 + +namespace OAI + +/-! Degree Union States 31. -/ + +section + +namespace UniversalTensorSquare + +def degreeUnionState31_9 : List PrefixRegion := nextRegions 4 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_10 : List PrefixRegion := nextRegions 5 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_11 : List PrefixRegion := nextRegions 6 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_12 : List PrefixRegion := nextRegions 7 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_13 : List PrefixRegion := nextRegions 8 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_14 : List PrefixRegion := nextRegions 9 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_15 : List PrefixRegion := nextRegions 10 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_16 : List PrefixRegion := nextRegions 11 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_17 : List PrefixRegion := nextRegions 12 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_18 : List PrefixRegion := nextRegions 13 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_19 : List PrefixRegion := nextRegions 14 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_20 : List PrefixRegion := nextRegions 15 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_21 : List PrefixRegion := nextRegions 16 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_22 : List PrefixRegion := nextRegions 17 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_23 : List PrefixRegion := nextRegions 18 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_24 : List PrefixRegion := nextRegions 19 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_25 : List PrefixRegion := nextRegions 20 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_26 : List PrefixRegion := nextRegions 21 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_27 : List PrefixRegion := nextRegions 22 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_28 : List PrefixRegion := nextRegions 23 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_29 : List PrefixRegion := nextRegions 24 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_30 : List PrefixRegion := nextRegions 25 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_31 : List PrefixRegion := nextRegions 26 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_32 : List PrefixRegion := nextRegions 27 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_33 : List PrefixRegion := nextRegions 28 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_34 : List PrefixRegion := nextRegions 29 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_35 : List PrefixRegion := nextRegions 30 (liveRegions 8 31 30 degreeHalfRegions31) + +def degreeUnionState31_37 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_38 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_39 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_40 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_41 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_42 : List PrefixRegion := nextRegions 9 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_43 : List PrefixRegion := nextRegions 10 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_44 : List PrefixRegion := nextRegions 11 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_45 : List PrefixRegion := nextRegions 12 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_46 : List PrefixRegion := nextRegions 13 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_47 : List PrefixRegion := nextRegions 14 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_48 : List PrefixRegion := nextRegions 15 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_49 : List PrefixRegion := nextRegions 16 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_50 : List PrefixRegion := nextRegions 17 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_51 : List PrefixRegion := nextRegions 18 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_52 : List PrefixRegion := nextRegions 19 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_53 : List PrefixRegion := nextRegions 20 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_54 : List PrefixRegion := nextRegions 21 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_55 : List PrefixRegion := nextRegions 22 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_56 : List PrefixRegion := nextRegions 23 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_57 : List PrefixRegion := nextRegions 24 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_58 : List PrefixRegion := nextRegions 25 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_59 : List PrefixRegion := nextRegions 26 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_60 : List PrefixRegion := nextRegions 27 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_61 : List PrefixRegion := nextRegions 28 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_62 : List PrefixRegion := nextRegions 29 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_63 : List PrefixRegion := nextRegions 30 (liveRegions 9 31 30 degreeHalfRegions31) + +def degreeUnionState31_65 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_66 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_67 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_68 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_69 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_70 : List PrefixRegion := nextRegions 9 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_71 : List PrefixRegion := nextRegions 10 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_72 : List PrefixRegion := nextRegions 11 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_73 : List PrefixRegion := nextRegions 12 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_74 : List PrefixRegion := nextRegions 13 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_75 : List PrefixRegion := nextRegions 14 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_76 : List PrefixRegion := nextRegions 15 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_77 : List PrefixRegion := nextRegions 16 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_78 : List PrefixRegion := nextRegions 17 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_79 : List PrefixRegion := nextRegions 18 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_80 : List PrefixRegion := nextRegions 19 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_81 : List PrefixRegion := nextRegions 20 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_82 : List PrefixRegion := nextRegions 21 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_83 : List PrefixRegion := nextRegions 22 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_84 : List PrefixRegion := nextRegions 23 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_85 : List PrefixRegion := nextRegions 24 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_86 : List PrefixRegion := nextRegions 25 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_87 : List PrefixRegion := nextRegions 26 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_88 : List PrefixRegion := nextRegions 27 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_89 : List PrefixRegion := nextRegions 28 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_90 : List PrefixRegion := nextRegions 29 (liveRegions 10 31 30 degreeHalfRegions31) + +def degreeUnionState31_91 : List PrefixRegion := nextRegions 30 (liveRegions 10 31 30 degreeHalfRegions31) + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates35.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates35.lean index da92a5e7bb65634ef8e0c3b0d229e9218e789873..e9e84bf9a567046fbfee05e34e3e2ee0fbb2d2eb 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates35.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates35.lean @@ -1,305 +1,305 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData35 - -namespace OAI - -/-! Degree Union States 35. -/ - -section - -namespace UniversalTensorSquare - -def degreeUnionState35_9 : List PrefixRegion := nextRegions 5 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_10 : List PrefixRegion := nextRegions 6 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_11 : List PrefixRegion := nextRegions 7 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_12 : List PrefixRegion := nextRegions 8 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_13 : List PrefixRegion := nextRegions 9 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_14 : List PrefixRegion := nextRegions 4 (liveRegions 7 26 9 degreeUnionState35_13) - -def degreeUnionState35_15 : List PrefixRegion := nextRegions 5 (liveRegions 7 26 9 degreeUnionState35_13) - -def degreeUnionState35_16 : List PrefixRegion := nextRegions 6 (liveRegions 7 26 9 degreeUnionState35_13) - -def degreeUnionState35_17 : List PrefixRegion := nextRegions 7 (liveRegions 7 26 9 degreeUnionState35_13) - -def degreeUnionState35_18 : List PrefixRegion := nextRegions 8 (liveRegions 7 26 9 degreeUnionState35_13) - -def degreeUnionState35_19 : List PrefixRegion := nextRegions 9 (liveRegions 7 26 9 degreeUnionState35_13) - -def degreeUnionState35_20 : List PrefixRegion := nextRegions 10 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_21 : List PrefixRegion := nextRegions 4 (liveRegions 7 25 10 degreeUnionState35_20) - -def degreeUnionState35_22 : List PrefixRegion := nextRegions 5 (liveRegions 7 25 10 degreeUnionState35_20) - -def degreeUnionState35_23 : List PrefixRegion := nextRegions 6 (liveRegions 7 25 10 degreeUnionState35_20) - -def degreeUnionState35_24 : List PrefixRegion := nextRegions 7 (liveRegions 7 25 10 degreeUnionState35_20) - -def degreeUnionState35_25 : List PrefixRegion := nextRegions 8 (liveRegions 7 25 10 degreeUnionState35_20) - -def degreeUnionState35_26 : List PrefixRegion := nextRegions 9 (liveRegions 7 25 10 degreeUnionState35_20) - -def degreeUnionState35_27 : List PrefixRegion := nextRegions 10 (liveRegions 7 25 10 degreeUnionState35_20) - -def degreeUnionState35_28 : List PrefixRegion := nextRegions 11 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_29 : List PrefixRegion := nextRegions 12 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_30 : List PrefixRegion := nextRegions 13 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_31 : List PrefixRegion := nextRegions 14 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_32 : List PrefixRegion := nextRegions 15 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_33 : List PrefixRegion := nextRegions 16 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_34 : List PrefixRegion := nextRegions 17 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_35 : List PrefixRegion := nextRegions 18 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_36 : List PrefixRegion := nextRegions 19 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_37 : List PrefixRegion := nextRegions 20 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_38 : List PrefixRegion := nextRegions 21 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_39 : List PrefixRegion := nextRegions 22 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_40 : List PrefixRegion := nextRegions 23 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_41 : List PrefixRegion := nextRegions 24 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_42 : List PrefixRegion := nextRegions 25 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_43 : List PrefixRegion := nextRegions 26 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_44 : List PrefixRegion := nextRegions 27 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_45 : List PrefixRegion := nextRegions 28 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_46 : List PrefixRegion := nextRegions 29 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_47 : List PrefixRegion := nextRegions 30 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_48 : List PrefixRegion := nextRegions 31 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_49 : List PrefixRegion := nextRegions 32 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_50 : List PrefixRegion := nextRegions 33 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_51 : List PrefixRegion := nextRegions 34 (liveRegions 8 35 34 degreeHalfRegions35) - -def degreeUnionState35_53 : List PrefixRegion := nextRegions 4 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_54 : List PrefixRegion := nextRegions 5 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_55 : List PrefixRegion := nextRegions 6 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_56 : List PrefixRegion := nextRegions 7 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_57 : List PrefixRegion := nextRegions 8 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_58 : List PrefixRegion := nextRegions 4 (liveRegions 8 27 8 degreeUnionState35_57) - -def degreeUnionState35_59 : List PrefixRegion := nextRegions 5 (liveRegions 8 27 8 degreeUnionState35_57) - -def degreeUnionState35_60 : List PrefixRegion := nextRegions 6 (liveRegions 8 27 8 degreeUnionState35_57) - -def degreeUnionState35_61 : List PrefixRegion := nextRegions 7 (liveRegions 8 27 8 degreeUnionState35_57) - -def degreeUnionState35_62 : List PrefixRegion := nextRegions 8 (liveRegions 8 27 8 degreeUnionState35_57) - -def degreeUnionState35_63 : List PrefixRegion := nextRegions 9 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_64 : List PrefixRegion := nextRegions 4 (liveRegions 8 26 9 degreeUnionState35_63) - -def degreeUnionState35_65 : List PrefixRegion := nextRegions 5 (liveRegions 8 26 9 degreeUnionState35_63) - -def degreeUnionState35_66 : List PrefixRegion := nextRegions 6 (liveRegions 8 26 9 degreeUnionState35_63) - -def degreeUnionState35_67 : List PrefixRegion := nextRegions 7 (liveRegions 8 26 9 degreeUnionState35_63) - -def degreeUnionState35_68 : List PrefixRegion := nextRegions 8 (liveRegions 8 26 9 degreeUnionState35_63) - -def degreeUnionState35_69 : List PrefixRegion := nextRegions 9 (liveRegions 8 26 9 degreeUnionState35_63) - -def degreeUnionState35_70 : List PrefixRegion := nextRegions 10 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_71 : List PrefixRegion := nextRegions 4 (liveRegions 8 25 10 degreeUnionState35_70) - -def degreeUnionState35_72 : List PrefixRegion := nextRegions 5 (liveRegions 8 25 10 degreeUnionState35_70) - -def degreeUnionState35_73 : List PrefixRegion := nextRegions 6 (liveRegions 8 25 10 degreeUnionState35_70) - -def degreeUnionState35_74 : List PrefixRegion := nextRegions 7 (liveRegions 8 25 10 degreeUnionState35_70) - -def degreeUnionState35_75 : List PrefixRegion := nextRegions 8 (liveRegions 8 25 10 degreeUnionState35_70) - -def degreeUnionState35_76 : List PrefixRegion := nextRegions 9 (liveRegions 8 25 10 degreeUnionState35_70) - -def degreeUnionState35_77 : List PrefixRegion := nextRegions 10 (liveRegions 8 25 10 degreeUnionState35_70) - -def degreeUnionState35_78 : List PrefixRegion := nextRegions 11 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_79 : List PrefixRegion := nextRegions 12 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_80 : List PrefixRegion := nextRegions 13 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_81 : List PrefixRegion := nextRegions 14 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_82 : List PrefixRegion := nextRegions 15 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_83 : List PrefixRegion := nextRegions 16 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_84 : List PrefixRegion := nextRegions 17 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_85 : List PrefixRegion := nextRegions 18 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_86 : List PrefixRegion := nextRegions 19 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_87 : List PrefixRegion := nextRegions 20 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_88 : List PrefixRegion := nextRegions 21 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_89 : List PrefixRegion := nextRegions 22 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_90 : List PrefixRegion := nextRegions 23 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_91 : List PrefixRegion := nextRegions 24 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_92 : List PrefixRegion := nextRegions 25 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_93 : List PrefixRegion := nextRegions 26 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_94 : List PrefixRegion := nextRegions 27 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_95 : List PrefixRegion := nextRegions 28 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_96 : List PrefixRegion := nextRegions 29 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_97 : List PrefixRegion := nextRegions 30 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_98 : List PrefixRegion := nextRegions 31 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_99 : List PrefixRegion := nextRegions 32 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_100 : List PrefixRegion := nextRegions 33 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_101 : List PrefixRegion := nextRegions 34 (liveRegions 9 35 34 degreeHalfRegions35) - -def degreeUnionState35_103 : List PrefixRegion := nextRegions 4 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_104 : List PrefixRegion := nextRegions 5 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_105 : List PrefixRegion := nextRegions 6 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_106 : List PrefixRegion := nextRegions 7 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_107 : List PrefixRegion := nextRegions 8 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_108 : List PrefixRegion := nextRegions 3 (liveRegions 9 27 8 degreeUnionState35_107) - -def degreeUnionState35_109 : List PrefixRegion := nextRegions 4 (liveRegions 9 27 8 degreeUnionState35_107) - -def degreeUnionState35_110 : List PrefixRegion := nextRegions 5 (liveRegions 9 27 8 degreeUnionState35_107) - -def degreeUnionState35_111 : List PrefixRegion := nextRegions 6 (liveRegions 9 27 8 degreeUnionState35_107) - -def degreeUnionState35_112 : List PrefixRegion := nextRegions 7 (liveRegions 9 27 8 degreeUnionState35_107) - -def degreeUnionState35_113 : List PrefixRegion := nextRegions 8 (liveRegions 9 27 8 degreeUnionState35_107) - -def degreeUnionState35_114 : List PrefixRegion := nextRegions 9 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_115 : List PrefixRegion := nextRegions 3 (liveRegions 9 26 9 degreeUnionState35_114) - -def degreeUnionState35_116 : List PrefixRegion := nextRegions 4 (liveRegions 9 26 9 degreeUnionState35_114) - -def degreeUnionState35_117 : List PrefixRegion := nextRegions 5 (liveRegions 9 26 9 degreeUnionState35_114) - -def degreeUnionState35_118 : List PrefixRegion := nextRegions 6 (liveRegions 9 26 9 degreeUnionState35_114) - -def degreeUnionState35_119 : List PrefixRegion := nextRegions 7 (liveRegions 9 26 9 degreeUnionState35_114) - -def degreeUnionState35_120 : List PrefixRegion := nextRegions 8 (liveRegions 9 26 9 degreeUnionState35_114) - -def degreeUnionState35_121 : List PrefixRegion := nextRegions 9 (liveRegions 9 26 9 degreeUnionState35_114) - -def degreeUnionState35_122 : List PrefixRegion := nextRegions 10 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_123 : List PrefixRegion := nextRegions 3 (liveRegions 9 25 10 degreeUnionState35_122) - -def degreeUnionState35_124 : List PrefixRegion := nextRegions 4 (liveRegions 9 25 10 degreeUnionState35_122) - -def degreeUnionState35_125 : List PrefixRegion := nextRegions 5 (liveRegions 9 25 10 degreeUnionState35_122) - -def degreeUnionState35_126 : List PrefixRegion := nextRegions 6 (liveRegions 9 25 10 degreeUnionState35_122) - -def degreeUnionState35_127 : List PrefixRegion := nextRegions 7 (liveRegions 9 25 10 degreeUnionState35_122) - -def degreeUnionState35_128 : List PrefixRegion := nextRegions 8 (liveRegions 9 25 10 degreeUnionState35_122) - -def degreeUnionState35_129 : List PrefixRegion := nextRegions 9 (liveRegions 9 25 10 degreeUnionState35_122) - -def degreeUnionState35_130 : List PrefixRegion := nextRegions 10 (liveRegions 9 25 10 degreeUnionState35_122) - -def degreeUnionState35_131 : List PrefixRegion := nextRegions 11 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_132 : List PrefixRegion := nextRegions 12 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_133 : List PrefixRegion := nextRegions 13 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_134 : List PrefixRegion := nextRegions 14 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_135 : List PrefixRegion := nextRegions 15 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_136 : List PrefixRegion := nextRegions 16 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_137 : List PrefixRegion := nextRegions 17 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_138 : List PrefixRegion := nextRegions 18 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_139 : List PrefixRegion := nextRegions 19 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_140 : List PrefixRegion := nextRegions 20 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_141 : List PrefixRegion := nextRegions 21 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_142 : List PrefixRegion := nextRegions 22 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_143 : List PrefixRegion := nextRegions 23 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_144 : List PrefixRegion := nextRegions 24 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_145 : List PrefixRegion := nextRegions 25 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_146 : List PrefixRegion := nextRegions 26 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_147 : List PrefixRegion := nextRegions 27 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_148 : List PrefixRegion := nextRegions 28 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_149 : List PrefixRegion := nextRegions 29 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_150 : List PrefixRegion := nextRegions 30 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_151 : List PrefixRegion := nextRegions 31 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_152 : List PrefixRegion := nextRegions 32 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_153 : List PrefixRegion := nextRegions 33 (liveRegions 10 35 34 degreeHalfRegions35) - -def degreeUnionState35_154 : List PrefixRegion := nextRegions 34 (liveRegions 10 35 34 degreeHalfRegions35) - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData35 + +namespace OAI + +/-! Degree Union States 35. -/ + +section + +namespace UniversalTensorSquare + +def degreeUnionState35_9 : List PrefixRegion := nextRegions 5 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_10 : List PrefixRegion := nextRegions 6 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_11 : List PrefixRegion := nextRegions 7 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_12 : List PrefixRegion := nextRegions 8 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_13 : List PrefixRegion := nextRegions 9 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_14 : List PrefixRegion := nextRegions 4 (liveRegions 7 26 9 degreeUnionState35_13) + +def degreeUnionState35_15 : List PrefixRegion := nextRegions 5 (liveRegions 7 26 9 degreeUnionState35_13) + +def degreeUnionState35_16 : List PrefixRegion := nextRegions 6 (liveRegions 7 26 9 degreeUnionState35_13) + +def degreeUnionState35_17 : List PrefixRegion := nextRegions 7 (liveRegions 7 26 9 degreeUnionState35_13) + +def degreeUnionState35_18 : List PrefixRegion := nextRegions 8 (liveRegions 7 26 9 degreeUnionState35_13) + +def degreeUnionState35_19 : List PrefixRegion := nextRegions 9 (liveRegions 7 26 9 degreeUnionState35_13) + +def degreeUnionState35_20 : List PrefixRegion := nextRegions 10 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_21 : List PrefixRegion := nextRegions 4 (liveRegions 7 25 10 degreeUnionState35_20) + +def degreeUnionState35_22 : List PrefixRegion := nextRegions 5 (liveRegions 7 25 10 degreeUnionState35_20) + +def degreeUnionState35_23 : List PrefixRegion := nextRegions 6 (liveRegions 7 25 10 degreeUnionState35_20) + +def degreeUnionState35_24 : List PrefixRegion := nextRegions 7 (liveRegions 7 25 10 degreeUnionState35_20) + +def degreeUnionState35_25 : List PrefixRegion := nextRegions 8 (liveRegions 7 25 10 degreeUnionState35_20) + +def degreeUnionState35_26 : List PrefixRegion := nextRegions 9 (liveRegions 7 25 10 degreeUnionState35_20) + +def degreeUnionState35_27 : List PrefixRegion := nextRegions 10 (liveRegions 7 25 10 degreeUnionState35_20) + +def degreeUnionState35_28 : List PrefixRegion := nextRegions 11 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_29 : List PrefixRegion := nextRegions 12 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_30 : List PrefixRegion := nextRegions 13 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_31 : List PrefixRegion := nextRegions 14 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_32 : List PrefixRegion := nextRegions 15 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_33 : List PrefixRegion := nextRegions 16 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_34 : List PrefixRegion := nextRegions 17 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_35 : List PrefixRegion := nextRegions 18 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_36 : List PrefixRegion := nextRegions 19 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_37 : List PrefixRegion := nextRegions 20 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_38 : List PrefixRegion := nextRegions 21 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_39 : List PrefixRegion := nextRegions 22 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_40 : List PrefixRegion := nextRegions 23 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_41 : List PrefixRegion := nextRegions 24 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_42 : List PrefixRegion := nextRegions 25 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_43 : List PrefixRegion := nextRegions 26 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_44 : List PrefixRegion := nextRegions 27 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_45 : List PrefixRegion := nextRegions 28 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_46 : List PrefixRegion := nextRegions 29 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_47 : List PrefixRegion := nextRegions 30 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_48 : List PrefixRegion := nextRegions 31 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_49 : List PrefixRegion := nextRegions 32 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_50 : List PrefixRegion := nextRegions 33 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_51 : List PrefixRegion := nextRegions 34 (liveRegions 8 35 34 degreeHalfRegions35) + +def degreeUnionState35_53 : List PrefixRegion := nextRegions 4 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_54 : List PrefixRegion := nextRegions 5 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_55 : List PrefixRegion := nextRegions 6 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_56 : List PrefixRegion := nextRegions 7 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_57 : List PrefixRegion := nextRegions 8 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_58 : List PrefixRegion := nextRegions 4 (liveRegions 8 27 8 degreeUnionState35_57) + +def degreeUnionState35_59 : List PrefixRegion := nextRegions 5 (liveRegions 8 27 8 degreeUnionState35_57) + +def degreeUnionState35_60 : List PrefixRegion := nextRegions 6 (liveRegions 8 27 8 degreeUnionState35_57) + +def degreeUnionState35_61 : List PrefixRegion := nextRegions 7 (liveRegions 8 27 8 degreeUnionState35_57) + +def degreeUnionState35_62 : List PrefixRegion := nextRegions 8 (liveRegions 8 27 8 degreeUnionState35_57) + +def degreeUnionState35_63 : List PrefixRegion := nextRegions 9 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_64 : List PrefixRegion := nextRegions 4 (liveRegions 8 26 9 degreeUnionState35_63) + +def degreeUnionState35_65 : List PrefixRegion := nextRegions 5 (liveRegions 8 26 9 degreeUnionState35_63) + +def degreeUnionState35_66 : List PrefixRegion := nextRegions 6 (liveRegions 8 26 9 degreeUnionState35_63) + +def degreeUnionState35_67 : List PrefixRegion := nextRegions 7 (liveRegions 8 26 9 degreeUnionState35_63) + +def degreeUnionState35_68 : List PrefixRegion := nextRegions 8 (liveRegions 8 26 9 degreeUnionState35_63) + +def degreeUnionState35_69 : List PrefixRegion := nextRegions 9 (liveRegions 8 26 9 degreeUnionState35_63) + +def degreeUnionState35_70 : List PrefixRegion := nextRegions 10 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_71 : List PrefixRegion := nextRegions 4 (liveRegions 8 25 10 degreeUnionState35_70) + +def degreeUnionState35_72 : List PrefixRegion := nextRegions 5 (liveRegions 8 25 10 degreeUnionState35_70) + +def degreeUnionState35_73 : List PrefixRegion := nextRegions 6 (liveRegions 8 25 10 degreeUnionState35_70) + +def degreeUnionState35_74 : List PrefixRegion := nextRegions 7 (liveRegions 8 25 10 degreeUnionState35_70) + +def degreeUnionState35_75 : List PrefixRegion := nextRegions 8 (liveRegions 8 25 10 degreeUnionState35_70) + +def degreeUnionState35_76 : List PrefixRegion := nextRegions 9 (liveRegions 8 25 10 degreeUnionState35_70) + +def degreeUnionState35_77 : List PrefixRegion := nextRegions 10 (liveRegions 8 25 10 degreeUnionState35_70) + +def degreeUnionState35_78 : List PrefixRegion := nextRegions 11 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_79 : List PrefixRegion := nextRegions 12 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_80 : List PrefixRegion := nextRegions 13 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_81 : List PrefixRegion := nextRegions 14 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_82 : List PrefixRegion := nextRegions 15 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_83 : List PrefixRegion := nextRegions 16 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_84 : List PrefixRegion := nextRegions 17 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_85 : List PrefixRegion := nextRegions 18 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_86 : List PrefixRegion := nextRegions 19 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_87 : List PrefixRegion := nextRegions 20 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_88 : List PrefixRegion := nextRegions 21 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_89 : List PrefixRegion := nextRegions 22 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_90 : List PrefixRegion := nextRegions 23 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_91 : List PrefixRegion := nextRegions 24 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_92 : List PrefixRegion := nextRegions 25 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_93 : List PrefixRegion := nextRegions 26 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_94 : List PrefixRegion := nextRegions 27 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_95 : List PrefixRegion := nextRegions 28 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_96 : List PrefixRegion := nextRegions 29 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_97 : List PrefixRegion := nextRegions 30 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_98 : List PrefixRegion := nextRegions 31 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_99 : List PrefixRegion := nextRegions 32 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_100 : List PrefixRegion := nextRegions 33 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_101 : List PrefixRegion := nextRegions 34 (liveRegions 9 35 34 degreeHalfRegions35) + +def degreeUnionState35_103 : List PrefixRegion := nextRegions 4 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_104 : List PrefixRegion := nextRegions 5 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_105 : List PrefixRegion := nextRegions 6 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_106 : List PrefixRegion := nextRegions 7 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_107 : List PrefixRegion := nextRegions 8 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_108 : List PrefixRegion := nextRegions 3 (liveRegions 9 27 8 degreeUnionState35_107) + +def degreeUnionState35_109 : List PrefixRegion := nextRegions 4 (liveRegions 9 27 8 degreeUnionState35_107) + +def degreeUnionState35_110 : List PrefixRegion := nextRegions 5 (liveRegions 9 27 8 degreeUnionState35_107) + +def degreeUnionState35_111 : List PrefixRegion := nextRegions 6 (liveRegions 9 27 8 degreeUnionState35_107) + +def degreeUnionState35_112 : List PrefixRegion := nextRegions 7 (liveRegions 9 27 8 degreeUnionState35_107) + +def degreeUnionState35_113 : List PrefixRegion := nextRegions 8 (liveRegions 9 27 8 degreeUnionState35_107) + +def degreeUnionState35_114 : List PrefixRegion := nextRegions 9 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_115 : List PrefixRegion := nextRegions 3 (liveRegions 9 26 9 degreeUnionState35_114) + +def degreeUnionState35_116 : List PrefixRegion := nextRegions 4 (liveRegions 9 26 9 degreeUnionState35_114) + +def degreeUnionState35_117 : List PrefixRegion := nextRegions 5 (liveRegions 9 26 9 degreeUnionState35_114) + +def degreeUnionState35_118 : List PrefixRegion := nextRegions 6 (liveRegions 9 26 9 degreeUnionState35_114) + +def degreeUnionState35_119 : List PrefixRegion := nextRegions 7 (liveRegions 9 26 9 degreeUnionState35_114) + +def degreeUnionState35_120 : List PrefixRegion := nextRegions 8 (liveRegions 9 26 9 degreeUnionState35_114) + +def degreeUnionState35_121 : List PrefixRegion := nextRegions 9 (liveRegions 9 26 9 degreeUnionState35_114) + +def degreeUnionState35_122 : List PrefixRegion := nextRegions 10 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_123 : List PrefixRegion := nextRegions 3 (liveRegions 9 25 10 degreeUnionState35_122) + +def degreeUnionState35_124 : List PrefixRegion := nextRegions 4 (liveRegions 9 25 10 degreeUnionState35_122) + +def degreeUnionState35_125 : List PrefixRegion := nextRegions 5 (liveRegions 9 25 10 degreeUnionState35_122) + +def degreeUnionState35_126 : List PrefixRegion := nextRegions 6 (liveRegions 9 25 10 degreeUnionState35_122) + +def degreeUnionState35_127 : List PrefixRegion := nextRegions 7 (liveRegions 9 25 10 degreeUnionState35_122) + +def degreeUnionState35_128 : List PrefixRegion := nextRegions 8 (liveRegions 9 25 10 degreeUnionState35_122) + +def degreeUnionState35_129 : List PrefixRegion := nextRegions 9 (liveRegions 9 25 10 degreeUnionState35_122) + +def degreeUnionState35_130 : List PrefixRegion := nextRegions 10 (liveRegions 9 25 10 degreeUnionState35_122) + +def degreeUnionState35_131 : List PrefixRegion := nextRegions 11 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_132 : List PrefixRegion := nextRegions 12 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_133 : List PrefixRegion := nextRegions 13 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_134 : List PrefixRegion := nextRegions 14 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_135 : List PrefixRegion := nextRegions 15 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_136 : List PrefixRegion := nextRegions 16 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_137 : List PrefixRegion := nextRegions 17 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_138 : List PrefixRegion := nextRegions 18 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_139 : List PrefixRegion := nextRegions 19 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_140 : List PrefixRegion := nextRegions 20 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_141 : List PrefixRegion := nextRegions 21 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_142 : List PrefixRegion := nextRegions 22 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_143 : List PrefixRegion := nextRegions 23 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_144 : List PrefixRegion := nextRegions 24 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_145 : List PrefixRegion := nextRegions 25 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_146 : List PrefixRegion := nextRegions 26 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_147 : List PrefixRegion := nextRegions 27 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_148 : List PrefixRegion := nextRegions 28 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_149 : List PrefixRegion := nextRegions 29 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_150 : List PrefixRegion := nextRegions 30 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_151 : List PrefixRegion := nextRegions 31 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_152 : List PrefixRegion := nextRegions 32 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_153 : List PrefixRegion := nextRegions 33 (liveRegions 10 35 34 degreeHalfRegions35) + +def degreeUnionState35_154 : List PrefixRegion := nextRegions 34 (liveRegions 10 35 34 degreeHalfRegions35) + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates39.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates39.lean index b467de82334255a3bdde63891c40bbf8b42fef64..59b7659ebb3cacc7028ab674f4b15d117eb04a0e 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates39.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates39.lean @@ -1,611 +1,611 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData39 - -namespace OAI - -/-! Degree Union States 39. -/ - -section - -namespace UniversalTensorSquare - -def degreeUnionState39_9 : List PrefixRegion := nextRegions 5 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_10 : List PrefixRegion := nextRegions 6 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_11 : List PrefixRegion := nextRegions 7 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_12 : List PrefixRegion := nextRegions 8 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_13 : List PrefixRegion := nextRegions 5 (liveRegions 7 31 8 degreeUnionState39_12) - -def degreeUnionState39_14 : List PrefixRegion := nextRegions 6 (liveRegions 7 31 8 degreeUnionState39_12) - -def degreeUnionState39_15 : List PrefixRegion := nextRegions 7 (liveRegions 7 31 8 degreeUnionState39_12) - -def degreeUnionState39_16 : List PrefixRegion := nextRegions 8 (liveRegions 7 31 8 degreeUnionState39_12) - -def degreeUnionState39_17 : List PrefixRegion := nextRegions 9 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_18 : List PrefixRegion := nextRegions 5 (liveRegions 7 30 9 degreeUnionState39_17) - -def degreeUnionState39_19 : List PrefixRegion := nextRegions 6 (liveRegions 7 30 9 degreeUnionState39_17) - -def degreeUnionState39_20 : List PrefixRegion := nextRegions 7 (liveRegions 7 30 9 degreeUnionState39_17) - -def degreeUnionState39_21 : List PrefixRegion := nextRegions 8 (liveRegions 7 30 9 degreeUnionState39_17) - -def degreeUnionState39_22 : List PrefixRegion := nextRegions 9 (liveRegions 7 30 9 degreeUnionState39_17) - -def degreeUnionState39_23 : List PrefixRegion := nextRegions 10 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_24 : List PrefixRegion := nextRegions 5 (liveRegions 7 29 10 degreeUnionState39_23) - -def degreeUnionState39_25 : List PrefixRegion := nextRegions 6 (liveRegions 7 29 10 degreeUnionState39_23) - -def degreeUnionState39_26 : List PrefixRegion := nextRegions 7 (liveRegions 7 29 10 degreeUnionState39_23) - -def degreeUnionState39_27 : List PrefixRegion := nextRegions 8 (liveRegions 7 29 10 degreeUnionState39_23) - -def degreeUnionState39_28 : List PrefixRegion := nextRegions 9 (liveRegions 7 29 10 degreeUnionState39_23) - -def degreeUnionState39_29 : List PrefixRegion := nextRegions 10 (liveRegions 7 29 10 degreeUnionState39_23) - -def degreeUnionState39_30 : List PrefixRegion := nextRegions 11 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_31 : List PrefixRegion := nextRegions 4 (liveRegions 7 28 11 degreeUnionState39_30) - -def degreeUnionState39_32 : List PrefixRegion := nextRegions 5 (liveRegions 7 28 11 degreeUnionState39_30) - -def degreeUnionState39_33 : List PrefixRegion := nextRegions 6 (liveRegions 7 28 11 degreeUnionState39_30) - -def degreeUnionState39_34 : List PrefixRegion := nextRegions 7 (liveRegions 7 28 11 degreeUnionState39_30) - -def degreeUnionState39_35 : List PrefixRegion := nextRegions 8 (liveRegions 7 28 11 degreeUnionState39_30) - -def degreeUnionState39_36 : List PrefixRegion := nextRegions 9 (liveRegions 7 28 11 degreeUnionState39_30) - -def degreeUnionState39_37 : List PrefixRegion := nextRegions 10 (liveRegions 7 28 11 degreeUnionState39_30) - -def degreeUnionState39_38 : List PrefixRegion := nextRegions 11 (liveRegions 7 28 11 degreeUnionState39_30) - -def degreeUnionState39_39 : List PrefixRegion := nextRegions 12 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_40 : List PrefixRegion := nextRegions 4 (liveRegions 7 27 12 degreeUnionState39_39) - -def degreeUnionState39_41 : List PrefixRegion := nextRegions 5 (liveRegions 7 27 12 degreeUnionState39_39) - -def degreeUnionState39_42 : List PrefixRegion := nextRegions 6 (liveRegions 7 27 12 degreeUnionState39_39) - -def degreeUnionState39_43 : List PrefixRegion := nextRegions 7 (liveRegions 7 27 12 degreeUnionState39_39) - -def degreeUnionState39_44 : List PrefixRegion := nextRegions 8 (liveRegions 7 27 12 degreeUnionState39_39) - -def degreeUnionState39_45 : List PrefixRegion := nextRegions 9 (liveRegions 7 27 12 degreeUnionState39_39) - -def degreeUnionState39_46 : List PrefixRegion := nextRegions 10 (liveRegions 7 27 12 degreeUnionState39_39) - -def degreeUnionState39_47 : List PrefixRegion := nextRegions 11 (liveRegions 7 27 12 degreeUnionState39_39) - -def degreeUnionState39_48 : List PrefixRegion := nextRegions 12 (liveRegions 7 27 12 degreeUnionState39_39) - -def degreeUnionState39_49 : List PrefixRegion := nextRegions 13 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_50 : List PrefixRegion := nextRegions 4 (liveRegions 7 26 13 degreeUnionState39_49) - -def degreeUnionState39_51 : List PrefixRegion := nextRegions 5 (liveRegions 7 26 13 degreeUnionState39_49) - -def degreeUnionState39_52 : List PrefixRegion := nextRegions 6 (liveRegions 7 26 13 degreeUnionState39_49) - -def degreeUnionState39_53 : List PrefixRegion := nextRegions 7 (liveRegions 7 26 13 degreeUnionState39_49) - -def degreeUnionState39_54 : List PrefixRegion := nextRegions 8 (liveRegions 7 26 13 degreeUnionState39_49) - -def degreeUnionState39_55 : List PrefixRegion := nextRegions 9 (liveRegions 7 26 13 degreeUnionState39_49) - -def degreeUnionState39_56 : List PrefixRegion := nextRegions 10 (liveRegions 7 26 13 degreeUnionState39_49) - -def degreeUnionState39_57 : List PrefixRegion := nextRegions 11 (liveRegions 7 26 13 degreeUnionState39_49) - -def degreeUnionState39_58 : List PrefixRegion := nextRegions 12 (liveRegions 7 26 13 degreeUnionState39_49) - -def degreeUnionState39_59 : List PrefixRegion := nextRegions 13 (liveRegions 7 26 13 degreeUnionState39_49) - -def degreeUnionState39_60 : List PrefixRegion := nextRegions 14 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_61 : List PrefixRegion := nextRegions 4 (liveRegions 7 25 14 degreeUnionState39_60) - -def degreeUnionState39_62 : List PrefixRegion := nextRegions 5 (liveRegions 7 25 14 degreeUnionState39_60) - -def degreeUnionState39_63 : List PrefixRegion := nextRegions 6 (liveRegions 7 25 14 degreeUnionState39_60) - -def degreeUnionState39_64 : List PrefixRegion := nextRegions 7 (liveRegions 7 25 14 degreeUnionState39_60) - -def degreeUnionState39_65 : List PrefixRegion := nextRegions 8 (liveRegions 7 25 14 degreeUnionState39_60) - -def degreeUnionState39_66 : List PrefixRegion := nextRegions 9 (liveRegions 7 25 14 degreeUnionState39_60) - -def degreeUnionState39_67 : List PrefixRegion := nextRegions 10 (liveRegions 7 25 14 degreeUnionState39_60) - -def degreeUnionState39_68 : List PrefixRegion := nextRegions 11 (liveRegions 7 25 14 degreeUnionState39_60) - -def degreeUnionState39_69 : List PrefixRegion := nextRegions 12 (liveRegions 7 25 14 degreeUnionState39_60) - -def degreeUnionState39_70 : List PrefixRegion := nextRegions 13 (liveRegions 7 25 14 degreeUnionState39_60) - -def degreeUnionState39_71 : List PrefixRegion := nextRegions 14 (liveRegions 7 25 14 degreeUnionState39_60) - -def degreeUnionState39_72 : List PrefixRegion := nextRegions 15 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_73 : List PrefixRegion := nextRegions 4 (liveRegions 7 24 15 degreeUnionState39_72) - -def degreeUnionState39_74 : List PrefixRegion := nextRegions 5 (liveRegions 7 24 15 degreeUnionState39_72) - -def degreeUnionState39_75 : List PrefixRegion := nextRegions 6 (liveRegions 7 24 15 degreeUnionState39_72) - -def degreeUnionState39_76 : List PrefixRegion := nextRegions 7 (liveRegions 7 24 15 degreeUnionState39_72) - -def degreeUnionState39_77 : List PrefixRegion := nextRegions 8 (liveRegions 7 24 15 degreeUnionState39_72) - -def degreeUnionState39_78 : List PrefixRegion := nextRegions 9 (liveRegions 7 24 15 degreeUnionState39_72) - -def degreeUnionState39_79 : List PrefixRegion := nextRegions 10 (liveRegions 7 24 15 degreeUnionState39_72) - -def degreeUnionState39_80 : List PrefixRegion := nextRegions 11 (liveRegions 7 24 15 degreeUnionState39_72) - -def degreeUnionState39_81 : List PrefixRegion := nextRegions 12 (liveRegions 7 24 15 degreeUnionState39_72) - -def degreeUnionState39_82 : List PrefixRegion := nextRegions 13 (liveRegions 7 24 15 degreeUnionState39_72) - -def degreeUnionState39_83 : List PrefixRegion := nextRegions 14 (liveRegions 7 24 15 degreeUnionState39_72) - -def degreeUnionState39_84 : List PrefixRegion := nextRegions 15 (liveRegions 7 24 15 degreeUnionState39_72) - -def degreeUnionState39_85 : List PrefixRegion := nextRegions 16 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_86 : List PrefixRegion := nextRegions 4 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_87 : List PrefixRegion := nextRegions 5 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_88 : List PrefixRegion := nextRegions 6 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_89 : List PrefixRegion := nextRegions 7 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_90 : List PrefixRegion := nextRegions 8 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_91 : List PrefixRegion := nextRegions 9 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_92 : List PrefixRegion := nextRegions 10 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_93 : List PrefixRegion := nextRegions 11 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_94 : List PrefixRegion := nextRegions 12 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_95 : List PrefixRegion := nextRegions 13 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_96 : List PrefixRegion := nextRegions 14 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_97 : List PrefixRegion := nextRegions 15 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_98 : List PrefixRegion := nextRegions 16 (liveRegions 7 23 16 degreeUnionState39_85) - -def degreeUnionState39_99 : List PrefixRegion := nextRegions 17 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_100 : List PrefixRegion := nextRegions 18 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_101 : List PrefixRegion := nextRegions 19 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_102 : List PrefixRegion := nextRegions 20 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_103 : List PrefixRegion := nextRegions 21 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_104 : List PrefixRegion := nextRegions 22 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_105 : List PrefixRegion := nextRegions 23 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_106 : List PrefixRegion := nextRegions 24 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_107 : List PrefixRegion := nextRegions 25 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_108 : List PrefixRegion := nextRegions 26 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_109 : List PrefixRegion := nextRegions 27 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_110 : List PrefixRegion := nextRegions 28 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_111 : List PrefixRegion := nextRegions 29 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_112 : List PrefixRegion := nextRegions 30 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_113 : List PrefixRegion := nextRegions 31 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_114 : List PrefixRegion := nextRegions 32 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_115 : List PrefixRegion := nextRegions 33 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_116 : List PrefixRegion := nextRegions 34 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_117 : List PrefixRegion := nextRegions 35 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_118 : List PrefixRegion := nextRegions 36 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_119 : List PrefixRegion := nextRegions 37 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_120 : List PrefixRegion := nextRegions 38 (liveRegions 8 39 38 degreeHalfRegions39) - -def degreeUnionState39_122 : List PrefixRegion := nextRegions 5 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_123 : List PrefixRegion := nextRegions 6 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_124 : List PrefixRegion := nextRegions 7 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_125 : List PrefixRegion := nextRegions 8 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_126 : List PrefixRegion := nextRegions 4 (liveRegions 8 31 8 degreeUnionState39_125) - -def degreeUnionState39_127 : List PrefixRegion := nextRegions 5 (liveRegions 8 31 8 degreeUnionState39_125) - -def degreeUnionState39_128 : List PrefixRegion := nextRegions 6 (liveRegions 8 31 8 degreeUnionState39_125) - -def degreeUnionState39_129 : List PrefixRegion := nextRegions 7 (liveRegions 8 31 8 degreeUnionState39_125) - -def degreeUnionState39_130 : List PrefixRegion := nextRegions 8 (liveRegions 8 31 8 degreeUnionState39_125) - -def degreeUnionState39_131 : List PrefixRegion := nextRegions 9 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_132 : List PrefixRegion := nextRegions 4 (liveRegions 8 30 9 degreeUnionState39_131) - -def degreeUnionState39_133 : List PrefixRegion := nextRegions 5 (liveRegions 8 30 9 degreeUnionState39_131) - -def degreeUnionState39_134 : List PrefixRegion := nextRegions 6 (liveRegions 8 30 9 degreeUnionState39_131) - -def degreeUnionState39_135 : List PrefixRegion := nextRegions 7 (liveRegions 8 30 9 degreeUnionState39_131) - -def degreeUnionState39_136 : List PrefixRegion := nextRegions 8 (liveRegions 8 30 9 degreeUnionState39_131) - -def degreeUnionState39_137 : List PrefixRegion := nextRegions 9 (liveRegions 8 30 9 degreeUnionState39_131) - -def degreeUnionState39_138 : List PrefixRegion := nextRegions 10 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_139 : List PrefixRegion := nextRegions 4 (liveRegions 8 29 10 degreeUnionState39_138) - -def degreeUnionState39_140 : List PrefixRegion := nextRegions 5 (liveRegions 8 29 10 degreeUnionState39_138) - -def degreeUnionState39_141 : List PrefixRegion := nextRegions 6 (liveRegions 8 29 10 degreeUnionState39_138) - -def degreeUnionState39_142 : List PrefixRegion := nextRegions 7 (liveRegions 8 29 10 degreeUnionState39_138) - -def degreeUnionState39_143 : List PrefixRegion := nextRegions 8 (liveRegions 8 29 10 degreeUnionState39_138) - -def degreeUnionState39_144 : List PrefixRegion := nextRegions 9 (liveRegions 8 29 10 degreeUnionState39_138) - -def degreeUnionState39_145 : List PrefixRegion := nextRegions 10 (liveRegions 8 29 10 degreeUnionState39_138) - -def degreeUnionState39_146 : List PrefixRegion := nextRegions 11 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_147 : List PrefixRegion := nextRegions 4 (liveRegions 8 28 11 degreeUnionState39_146) - -def degreeUnionState39_148 : List PrefixRegion := nextRegions 5 (liveRegions 8 28 11 degreeUnionState39_146) - -def degreeUnionState39_149 : List PrefixRegion := nextRegions 6 (liveRegions 8 28 11 degreeUnionState39_146) - -def degreeUnionState39_150 : List PrefixRegion := nextRegions 7 (liveRegions 8 28 11 degreeUnionState39_146) - -def degreeUnionState39_151 : List PrefixRegion := nextRegions 8 (liveRegions 8 28 11 degreeUnionState39_146) - -def degreeUnionState39_152 : List PrefixRegion := nextRegions 9 (liveRegions 8 28 11 degreeUnionState39_146) - -def degreeUnionState39_153 : List PrefixRegion := nextRegions 10 (liveRegions 8 28 11 degreeUnionState39_146) - -def degreeUnionState39_154 : List PrefixRegion := nextRegions 11 (liveRegions 8 28 11 degreeUnionState39_146) - -def degreeUnionState39_155 : List PrefixRegion := nextRegions 12 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_156 : List PrefixRegion := nextRegions 4 (liveRegions 8 27 12 degreeUnionState39_155) - -def degreeUnionState39_157 : List PrefixRegion := nextRegions 5 (liveRegions 8 27 12 degreeUnionState39_155) - -def degreeUnionState39_158 : List PrefixRegion := nextRegions 6 (liveRegions 8 27 12 degreeUnionState39_155) - -def degreeUnionState39_159 : List PrefixRegion := nextRegions 7 (liveRegions 8 27 12 degreeUnionState39_155) - -def degreeUnionState39_160 : List PrefixRegion := nextRegions 8 (liveRegions 8 27 12 degreeUnionState39_155) - -def degreeUnionState39_161 : List PrefixRegion := nextRegions 9 (liveRegions 8 27 12 degreeUnionState39_155) - -def degreeUnionState39_162 : List PrefixRegion := nextRegions 10 (liveRegions 8 27 12 degreeUnionState39_155) - -def degreeUnionState39_163 : List PrefixRegion := nextRegions 11 (liveRegions 8 27 12 degreeUnionState39_155) - -def degreeUnionState39_164 : List PrefixRegion := nextRegions 12 (liveRegions 8 27 12 degreeUnionState39_155) - -def degreeUnionState39_165 : List PrefixRegion := nextRegions 13 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_166 : List PrefixRegion := nextRegions 4 (liveRegions 8 26 13 degreeUnionState39_165) - -def degreeUnionState39_167 : List PrefixRegion := nextRegions 5 (liveRegions 8 26 13 degreeUnionState39_165) - -def degreeUnionState39_168 : List PrefixRegion := nextRegions 6 (liveRegions 8 26 13 degreeUnionState39_165) - -def degreeUnionState39_169 : List PrefixRegion := nextRegions 7 (liveRegions 8 26 13 degreeUnionState39_165) - -def degreeUnionState39_170 : List PrefixRegion := nextRegions 8 (liveRegions 8 26 13 degreeUnionState39_165) - -def degreeUnionState39_171 : List PrefixRegion := nextRegions 9 (liveRegions 8 26 13 degreeUnionState39_165) - -def degreeUnionState39_172 : List PrefixRegion := nextRegions 10 (liveRegions 8 26 13 degreeUnionState39_165) - -def degreeUnionState39_173 : List PrefixRegion := nextRegions 11 (liveRegions 8 26 13 degreeUnionState39_165) - -def degreeUnionState39_174 : List PrefixRegion := nextRegions 12 (liveRegions 8 26 13 degreeUnionState39_165) - -def degreeUnionState39_175 : List PrefixRegion := nextRegions 13 (liveRegions 8 26 13 degreeUnionState39_165) - -def degreeUnionState39_176 : List PrefixRegion := nextRegions 14 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_177 : List PrefixRegion := nextRegions 4 (liveRegions 8 25 14 degreeUnionState39_176) - -def degreeUnionState39_178 : List PrefixRegion := nextRegions 5 (liveRegions 8 25 14 degreeUnionState39_176) - -def degreeUnionState39_179 : List PrefixRegion := nextRegions 6 (liveRegions 8 25 14 degreeUnionState39_176) - -def degreeUnionState39_180 : List PrefixRegion := nextRegions 7 (liveRegions 8 25 14 degreeUnionState39_176) - -def degreeUnionState39_181 : List PrefixRegion := nextRegions 8 (liveRegions 8 25 14 degreeUnionState39_176) - -def degreeUnionState39_182 : List PrefixRegion := nextRegions 9 (liveRegions 8 25 14 degreeUnionState39_176) - -def degreeUnionState39_183 : List PrefixRegion := nextRegions 10 (liveRegions 8 25 14 degreeUnionState39_176) - -def degreeUnionState39_184 : List PrefixRegion := nextRegions 11 (liveRegions 8 25 14 degreeUnionState39_176) - -def degreeUnionState39_185 : List PrefixRegion := nextRegions 12 (liveRegions 8 25 14 degreeUnionState39_176) - -def degreeUnionState39_186 : List PrefixRegion := nextRegions 13 (liveRegions 8 25 14 degreeUnionState39_176) - -def degreeUnionState39_187 : List PrefixRegion := nextRegions 14 (liveRegions 8 25 14 degreeUnionState39_176) - -def degreeUnionState39_188 : List PrefixRegion := nextRegions 15 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_189 : List PrefixRegion := nextRegions 3 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_190 : List PrefixRegion := nextRegions 4 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_191 : List PrefixRegion := nextRegions 5 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_192 : List PrefixRegion := nextRegions 6 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_193 : List PrefixRegion := nextRegions 7 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_194 : List PrefixRegion := nextRegions 8 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_195 : List PrefixRegion := nextRegions 9 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_196 : List PrefixRegion := nextRegions 10 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_197 : List PrefixRegion := nextRegions 11 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_198 : List PrefixRegion := nextRegions 12 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_199 : List PrefixRegion := nextRegions 13 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_200 : List PrefixRegion := nextRegions 14 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_201 : List PrefixRegion := nextRegions 15 (liveRegions 8 24 15 degreeUnionState39_188) - -def degreeUnionState39_202 : List PrefixRegion := nextRegions 16 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_203 : List PrefixRegion := nextRegions 17 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_204 : List PrefixRegion := nextRegions 18 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_205 : List PrefixRegion := nextRegions 19 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_206 : List PrefixRegion := nextRegions 20 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_207 : List PrefixRegion := nextRegions 21 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_208 : List PrefixRegion := nextRegions 22 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_209 : List PrefixRegion := nextRegions 23 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_210 : List PrefixRegion := nextRegions 24 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_211 : List PrefixRegion := nextRegions 25 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_212 : List PrefixRegion := nextRegions 26 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_213 : List PrefixRegion := nextRegions 27 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_214 : List PrefixRegion := nextRegions 28 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_215 : List PrefixRegion := nextRegions 29 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_216 : List PrefixRegion := nextRegions 30 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_217 : List PrefixRegion := nextRegions 31 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_218 : List PrefixRegion := nextRegions 32 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_219 : List PrefixRegion := nextRegions 33 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_220 : List PrefixRegion := nextRegions 34 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_221 : List PrefixRegion := nextRegions 35 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_222 : List PrefixRegion := nextRegions 36 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_223 : List PrefixRegion := nextRegions 37 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_224 : List PrefixRegion := nextRegions 38 (liveRegions 9 39 38 degreeHalfRegions39) - -def degreeUnionState39_226 : List PrefixRegion := nextRegions 4 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_227 : List PrefixRegion := nextRegions 5 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_228 : List PrefixRegion := nextRegions 6 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_229 : List PrefixRegion := nextRegions 7 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_230 : List PrefixRegion := nextRegions 8 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_231 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 8 degreeUnionState39_230) - -def degreeUnionState39_232 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 8 degreeUnionState39_230) - -def degreeUnionState39_233 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 8 degreeUnionState39_230) - -def degreeUnionState39_234 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 8 degreeUnionState39_230) - -def degreeUnionState39_235 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 8 degreeUnionState39_230) - -def degreeUnionState39_236 : List PrefixRegion := nextRegions 9 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_237 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 9 degreeUnionState39_236) - -def degreeUnionState39_238 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 9 degreeUnionState39_236) - -def degreeUnionState39_239 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 9 degreeUnionState39_236) - -def degreeUnionState39_240 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 9 degreeUnionState39_236) - -def degreeUnionState39_241 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 9 degreeUnionState39_236) - -def degreeUnionState39_242 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 9 degreeUnionState39_236) - -def degreeUnionState39_243 : List PrefixRegion := nextRegions 10 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_244 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 10 degreeUnionState39_243) - -def degreeUnionState39_245 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 10 degreeUnionState39_243) - -def degreeUnionState39_246 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 10 degreeUnionState39_243) - -def degreeUnionState39_247 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 10 degreeUnionState39_243) - -def degreeUnionState39_248 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 10 degreeUnionState39_243) - -def degreeUnionState39_249 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 10 degreeUnionState39_243) - -def degreeUnionState39_250 : List PrefixRegion := nextRegions 10 (liveRegions 9 29 10 degreeUnionState39_243) - -def degreeUnionState39_251 : List PrefixRegion := nextRegions 11 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_252 : List PrefixRegion := nextRegions 4 (liveRegions 9 28 11 degreeUnionState39_251) - -def degreeUnionState39_253 : List PrefixRegion := nextRegions 5 (liveRegions 9 28 11 degreeUnionState39_251) - -def degreeUnionState39_254 : List PrefixRegion := nextRegions 6 (liveRegions 9 28 11 degreeUnionState39_251) - -def degreeUnionState39_255 : List PrefixRegion := nextRegions 7 (liveRegions 9 28 11 degreeUnionState39_251) - -def degreeUnionState39_256 : List PrefixRegion := nextRegions 8 (liveRegions 9 28 11 degreeUnionState39_251) - -def degreeUnionState39_257 : List PrefixRegion := nextRegions 9 (liveRegions 9 28 11 degreeUnionState39_251) - -def degreeUnionState39_258 : List PrefixRegion := nextRegions 10 (liveRegions 9 28 11 degreeUnionState39_251) - -def degreeUnionState39_259 : List PrefixRegion := nextRegions 11 (liveRegions 9 28 11 degreeUnionState39_251) - -def degreeUnionState39_260 : List PrefixRegion := nextRegions 12 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_261 : List PrefixRegion := nextRegions 3 (liveRegions 9 27 12 degreeUnionState39_260) - -def degreeUnionState39_262 : List PrefixRegion := nextRegions 4 (liveRegions 9 27 12 degreeUnionState39_260) - -def degreeUnionState39_263 : List PrefixRegion := nextRegions 5 (liveRegions 9 27 12 degreeUnionState39_260) - -def degreeUnionState39_264 : List PrefixRegion := nextRegions 6 (liveRegions 9 27 12 degreeUnionState39_260) - -def degreeUnionState39_265 : List PrefixRegion := nextRegions 7 (liveRegions 9 27 12 degreeUnionState39_260) - -def degreeUnionState39_266 : List PrefixRegion := nextRegions 8 (liveRegions 9 27 12 degreeUnionState39_260) - -def degreeUnionState39_267 : List PrefixRegion := nextRegions 9 (liveRegions 9 27 12 degreeUnionState39_260) - -def degreeUnionState39_268 : List PrefixRegion := nextRegions 10 (liveRegions 9 27 12 degreeUnionState39_260) - -def degreeUnionState39_269 : List PrefixRegion := nextRegions 11 (liveRegions 9 27 12 degreeUnionState39_260) - -def degreeUnionState39_270 : List PrefixRegion := nextRegions 12 (liveRegions 9 27 12 degreeUnionState39_260) - -def degreeUnionState39_271 : List PrefixRegion := nextRegions 13 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_272 : List PrefixRegion := nextRegions 3 (liveRegions 9 26 13 degreeUnionState39_271) - -def degreeUnionState39_273 : List PrefixRegion := nextRegions 4 (liveRegions 9 26 13 degreeUnionState39_271) - -def degreeUnionState39_274 : List PrefixRegion := nextRegions 5 (liveRegions 9 26 13 degreeUnionState39_271) - -def degreeUnionState39_275 : List PrefixRegion := nextRegions 6 (liveRegions 9 26 13 degreeUnionState39_271) - -def degreeUnionState39_276 : List PrefixRegion := nextRegions 7 (liveRegions 9 26 13 degreeUnionState39_271) - -def degreeUnionState39_277 : List PrefixRegion := nextRegions 8 (liveRegions 9 26 13 degreeUnionState39_271) - -def degreeUnionState39_278 : List PrefixRegion := nextRegions 9 (liveRegions 9 26 13 degreeUnionState39_271) - -def degreeUnionState39_279 : List PrefixRegion := nextRegions 10 (liveRegions 9 26 13 degreeUnionState39_271) - -def degreeUnionState39_280 : List PrefixRegion := nextRegions 11 (liveRegions 9 26 13 degreeUnionState39_271) - -def degreeUnionState39_281 : List PrefixRegion := nextRegions 12 (liveRegions 9 26 13 degreeUnionState39_271) - -def degreeUnionState39_282 : List PrefixRegion := nextRegions 13 (liveRegions 9 26 13 degreeUnionState39_271) - -def degreeUnionState39_283 : List PrefixRegion := nextRegions 14 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_284 : List PrefixRegion := nextRegions 15 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_285 : List PrefixRegion := nextRegions 16 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_286 : List PrefixRegion := nextRegions 17 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_287 : List PrefixRegion := nextRegions 18 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_288 : List PrefixRegion := nextRegions 19 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_289 : List PrefixRegion := nextRegions 20 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_290 : List PrefixRegion := nextRegions 21 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_291 : List PrefixRegion := nextRegions 22 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_292 : List PrefixRegion := nextRegions 23 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_293 : List PrefixRegion := nextRegions 24 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_294 : List PrefixRegion := nextRegions 25 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_295 : List PrefixRegion := nextRegions 26 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_296 : List PrefixRegion := nextRegions 27 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_297 : List PrefixRegion := nextRegions 28 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_298 : List PrefixRegion := nextRegions 29 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_299 : List PrefixRegion := nextRegions 30 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_300 : List PrefixRegion := nextRegions 31 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_301 : List PrefixRegion := nextRegions 32 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_302 : List PrefixRegion := nextRegions 33 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_303 : List PrefixRegion := nextRegions 34 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_304 : List PrefixRegion := nextRegions 35 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_305 : List PrefixRegion := nextRegions 36 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_306 : List PrefixRegion := nextRegions 37 (liveRegions 10 39 38 degreeHalfRegions39) - -def degreeUnionState39_307 : List PrefixRegion := nextRegions 38 (liveRegions 10 39 38 degreeHalfRegions39) - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData39 + +namespace OAI + +/-! Degree Union States 39. -/ + +section + +namespace UniversalTensorSquare + +def degreeUnionState39_9 : List PrefixRegion := nextRegions 5 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_10 : List PrefixRegion := nextRegions 6 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_11 : List PrefixRegion := nextRegions 7 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_12 : List PrefixRegion := nextRegions 8 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_13 : List PrefixRegion := nextRegions 5 (liveRegions 7 31 8 degreeUnionState39_12) + +def degreeUnionState39_14 : List PrefixRegion := nextRegions 6 (liveRegions 7 31 8 degreeUnionState39_12) + +def degreeUnionState39_15 : List PrefixRegion := nextRegions 7 (liveRegions 7 31 8 degreeUnionState39_12) + +def degreeUnionState39_16 : List PrefixRegion := nextRegions 8 (liveRegions 7 31 8 degreeUnionState39_12) + +def degreeUnionState39_17 : List PrefixRegion := nextRegions 9 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_18 : List PrefixRegion := nextRegions 5 (liveRegions 7 30 9 degreeUnionState39_17) + +def degreeUnionState39_19 : List PrefixRegion := nextRegions 6 (liveRegions 7 30 9 degreeUnionState39_17) + +def degreeUnionState39_20 : List PrefixRegion := nextRegions 7 (liveRegions 7 30 9 degreeUnionState39_17) + +def degreeUnionState39_21 : List PrefixRegion := nextRegions 8 (liveRegions 7 30 9 degreeUnionState39_17) + +def degreeUnionState39_22 : List PrefixRegion := nextRegions 9 (liveRegions 7 30 9 degreeUnionState39_17) + +def degreeUnionState39_23 : List PrefixRegion := nextRegions 10 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_24 : List PrefixRegion := nextRegions 5 (liveRegions 7 29 10 degreeUnionState39_23) + +def degreeUnionState39_25 : List PrefixRegion := nextRegions 6 (liveRegions 7 29 10 degreeUnionState39_23) + +def degreeUnionState39_26 : List PrefixRegion := nextRegions 7 (liveRegions 7 29 10 degreeUnionState39_23) + +def degreeUnionState39_27 : List PrefixRegion := nextRegions 8 (liveRegions 7 29 10 degreeUnionState39_23) + +def degreeUnionState39_28 : List PrefixRegion := nextRegions 9 (liveRegions 7 29 10 degreeUnionState39_23) + +def degreeUnionState39_29 : List PrefixRegion := nextRegions 10 (liveRegions 7 29 10 degreeUnionState39_23) + +def degreeUnionState39_30 : List PrefixRegion := nextRegions 11 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_31 : List PrefixRegion := nextRegions 4 (liveRegions 7 28 11 degreeUnionState39_30) + +def degreeUnionState39_32 : List PrefixRegion := nextRegions 5 (liveRegions 7 28 11 degreeUnionState39_30) + +def degreeUnionState39_33 : List PrefixRegion := nextRegions 6 (liveRegions 7 28 11 degreeUnionState39_30) + +def degreeUnionState39_34 : List PrefixRegion := nextRegions 7 (liveRegions 7 28 11 degreeUnionState39_30) + +def degreeUnionState39_35 : List PrefixRegion := nextRegions 8 (liveRegions 7 28 11 degreeUnionState39_30) + +def degreeUnionState39_36 : List PrefixRegion := nextRegions 9 (liveRegions 7 28 11 degreeUnionState39_30) + +def degreeUnionState39_37 : List PrefixRegion := nextRegions 10 (liveRegions 7 28 11 degreeUnionState39_30) + +def degreeUnionState39_38 : List PrefixRegion := nextRegions 11 (liveRegions 7 28 11 degreeUnionState39_30) + +def degreeUnionState39_39 : List PrefixRegion := nextRegions 12 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_40 : List PrefixRegion := nextRegions 4 (liveRegions 7 27 12 degreeUnionState39_39) + +def degreeUnionState39_41 : List PrefixRegion := nextRegions 5 (liveRegions 7 27 12 degreeUnionState39_39) + +def degreeUnionState39_42 : List PrefixRegion := nextRegions 6 (liveRegions 7 27 12 degreeUnionState39_39) + +def degreeUnionState39_43 : List PrefixRegion := nextRegions 7 (liveRegions 7 27 12 degreeUnionState39_39) + +def degreeUnionState39_44 : List PrefixRegion := nextRegions 8 (liveRegions 7 27 12 degreeUnionState39_39) + +def degreeUnionState39_45 : List PrefixRegion := nextRegions 9 (liveRegions 7 27 12 degreeUnionState39_39) + +def degreeUnionState39_46 : List PrefixRegion := nextRegions 10 (liveRegions 7 27 12 degreeUnionState39_39) + +def degreeUnionState39_47 : List PrefixRegion := nextRegions 11 (liveRegions 7 27 12 degreeUnionState39_39) + +def degreeUnionState39_48 : List PrefixRegion := nextRegions 12 (liveRegions 7 27 12 degreeUnionState39_39) + +def degreeUnionState39_49 : List PrefixRegion := nextRegions 13 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_50 : List PrefixRegion := nextRegions 4 (liveRegions 7 26 13 degreeUnionState39_49) + +def degreeUnionState39_51 : List PrefixRegion := nextRegions 5 (liveRegions 7 26 13 degreeUnionState39_49) + +def degreeUnionState39_52 : List PrefixRegion := nextRegions 6 (liveRegions 7 26 13 degreeUnionState39_49) + +def degreeUnionState39_53 : List PrefixRegion := nextRegions 7 (liveRegions 7 26 13 degreeUnionState39_49) + +def degreeUnionState39_54 : List PrefixRegion := nextRegions 8 (liveRegions 7 26 13 degreeUnionState39_49) + +def degreeUnionState39_55 : List PrefixRegion := nextRegions 9 (liveRegions 7 26 13 degreeUnionState39_49) + +def degreeUnionState39_56 : List PrefixRegion := nextRegions 10 (liveRegions 7 26 13 degreeUnionState39_49) + +def degreeUnionState39_57 : List PrefixRegion := nextRegions 11 (liveRegions 7 26 13 degreeUnionState39_49) + +def degreeUnionState39_58 : List PrefixRegion := nextRegions 12 (liveRegions 7 26 13 degreeUnionState39_49) + +def degreeUnionState39_59 : List PrefixRegion := nextRegions 13 (liveRegions 7 26 13 degreeUnionState39_49) + +def degreeUnionState39_60 : List PrefixRegion := nextRegions 14 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_61 : List PrefixRegion := nextRegions 4 (liveRegions 7 25 14 degreeUnionState39_60) + +def degreeUnionState39_62 : List PrefixRegion := nextRegions 5 (liveRegions 7 25 14 degreeUnionState39_60) + +def degreeUnionState39_63 : List PrefixRegion := nextRegions 6 (liveRegions 7 25 14 degreeUnionState39_60) + +def degreeUnionState39_64 : List PrefixRegion := nextRegions 7 (liveRegions 7 25 14 degreeUnionState39_60) + +def degreeUnionState39_65 : List PrefixRegion := nextRegions 8 (liveRegions 7 25 14 degreeUnionState39_60) + +def degreeUnionState39_66 : List PrefixRegion := nextRegions 9 (liveRegions 7 25 14 degreeUnionState39_60) + +def degreeUnionState39_67 : List PrefixRegion := nextRegions 10 (liveRegions 7 25 14 degreeUnionState39_60) + +def degreeUnionState39_68 : List PrefixRegion := nextRegions 11 (liveRegions 7 25 14 degreeUnionState39_60) + +def degreeUnionState39_69 : List PrefixRegion := nextRegions 12 (liveRegions 7 25 14 degreeUnionState39_60) + +def degreeUnionState39_70 : List PrefixRegion := nextRegions 13 (liveRegions 7 25 14 degreeUnionState39_60) + +def degreeUnionState39_71 : List PrefixRegion := nextRegions 14 (liveRegions 7 25 14 degreeUnionState39_60) + +def degreeUnionState39_72 : List PrefixRegion := nextRegions 15 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_73 : List PrefixRegion := nextRegions 4 (liveRegions 7 24 15 degreeUnionState39_72) + +def degreeUnionState39_74 : List PrefixRegion := nextRegions 5 (liveRegions 7 24 15 degreeUnionState39_72) + +def degreeUnionState39_75 : List PrefixRegion := nextRegions 6 (liveRegions 7 24 15 degreeUnionState39_72) + +def degreeUnionState39_76 : List PrefixRegion := nextRegions 7 (liveRegions 7 24 15 degreeUnionState39_72) + +def degreeUnionState39_77 : List PrefixRegion := nextRegions 8 (liveRegions 7 24 15 degreeUnionState39_72) + +def degreeUnionState39_78 : List PrefixRegion := nextRegions 9 (liveRegions 7 24 15 degreeUnionState39_72) + +def degreeUnionState39_79 : List PrefixRegion := nextRegions 10 (liveRegions 7 24 15 degreeUnionState39_72) + +def degreeUnionState39_80 : List PrefixRegion := nextRegions 11 (liveRegions 7 24 15 degreeUnionState39_72) + +def degreeUnionState39_81 : List PrefixRegion := nextRegions 12 (liveRegions 7 24 15 degreeUnionState39_72) + +def degreeUnionState39_82 : List PrefixRegion := nextRegions 13 (liveRegions 7 24 15 degreeUnionState39_72) + +def degreeUnionState39_83 : List PrefixRegion := nextRegions 14 (liveRegions 7 24 15 degreeUnionState39_72) + +def degreeUnionState39_84 : List PrefixRegion := nextRegions 15 (liveRegions 7 24 15 degreeUnionState39_72) + +def degreeUnionState39_85 : List PrefixRegion := nextRegions 16 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_86 : List PrefixRegion := nextRegions 4 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_87 : List PrefixRegion := nextRegions 5 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_88 : List PrefixRegion := nextRegions 6 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_89 : List PrefixRegion := nextRegions 7 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_90 : List PrefixRegion := nextRegions 8 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_91 : List PrefixRegion := nextRegions 9 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_92 : List PrefixRegion := nextRegions 10 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_93 : List PrefixRegion := nextRegions 11 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_94 : List PrefixRegion := nextRegions 12 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_95 : List PrefixRegion := nextRegions 13 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_96 : List PrefixRegion := nextRegions 14 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_97 : List PrefixRegion := nextRegions 15 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_98 : List PrefixRegion := nextRegions 16 (liveRegions 7 23 16 degreeUnionState39_85) + +def degreeUnionState39_99 : List PrefixRegion := nextRegions 17 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_100 : List PrefixRegion := nextRegions 18 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_101 : List PrefixRegion := nextRegions 19 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_102 : List PrefixRegion := nextRegions 20 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_103 : List PrefixRegion := nextRegions 21 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_104 : List PrefixRegion := nextRegions 22 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_105 : List PrefixRegion := nextRegions 23 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_106 : List PrefixRegion := nextRegions 24 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_107 : List PrefixRegion := nextRegions 25 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_108 : List PrefixRegion := nextRegions 26 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_109 : List PrefixRegion := nextRegions 27 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_110 : List PrefixRegion := nextRegions 28 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_111 : List PrefixRegion := nextRegions 29 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_112 : List PrefixRegion := nextRegions 30 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_113 : List PrefixRegion := nextRegions 31 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_114 : List PrefixRegion := nextRegions 32 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_115 : List PrefixRegion := nextRegions 33 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_116 : List PrefixRegion := nextRegions 34 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_117 : List PrefixRegion := nextRegions 35 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_118 : List PrefixRegion := nextRegions 36 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_119 : List PrefixRegion := nextRegions 37 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_120 : List PrefixRegion := nextRegions 38 (liveRegions 8 39 38 degreeHalfRegions39) + +def degreeUnionState39_122 : List PrefixRegion := nextRegions 5 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_123 : List PrefixRegion := nextRegions 6 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_124 : List PrefixRegion := nextRegions 7 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_125 : List PrefixRegion := nextRegions 8 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_126 : List PrefixRegion := nextRegions 4 (liveRegions 8 31 8 degreeUnionState39_125) + +def degreeUnionState39_127 : List PrefixRegion := nextRegions 5 (liveRegions 8 31 8 degreeUnionState39_125) + +def degreeUnionState39_128 : List PrefixRegion := nextRegions 6 (liveRegions 8 31 8 degreeUnionState39_125) + +def degreeUnionState39_129 : List PrefixRegion := nextRegions 7 (liveRegions 8 31 8 degreeUnionState39_125) + +def degreeUnionState39_130 : List PrefixRegion := nextRegions 8 (liveRegions 8 31 8 degreeUnionState39_125) + +def degreeUnionState39_131 : List PrefixRegion := nextRegions 9 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_132 : List PrefixRegion := nextRegions 4 (liveRegions 8 30 9 degreeUnionState39_131) + +def degreeUnionState39_133 : List PrefixRegion := nextRegions 5 (liveRegions 8 30 9 degreeUnionState39_131) + +def degreeUnionState39_134 : List PrefixRegion := nextRegions 6 (liveRegions 8 30 9 degreeUnionState39_131) + +def degreeUnionState39_135 : List PrefixRegion := nextRegions 7 (liveRegions 8 30 9 degreeUnionState39_131) + +def degreeUnionState39_136 : List PrefixRegion := nextRegions 8 (liveRegions 8 30 9 degreeUnionState39_131) + +def degreeUnionState39_137 : List PrefixRegion := nextRegions 9 (liveRegions 8 30 9 degreeUnionState39_131) + +def degreeUnionState39_138 : List PrefixRegion := nextRegions 10 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_139 : List PrefixRegion := nextRegions 4 (liveRegions 8 29 10 degreeUnionState39_138) + +def degreeUnionState39_140 : List PrefixRegion := nextRegions 5 (liveRegions 8 29 10 degreeUnionState39_138) + +def degreeUnionState39_141 : List PrefixRegion := nextRegions 6 (liveRegions 8 29 10 degreeUnionState39_138) + +def degreeUnionState39_142 : List PrefixRegion := nextRegions 7 (liveRegions 8 29 10 degreeUnionState39_138) + +def degreeUnionState39_143 : List PrefixRegion := nextRegions 8 (liveRegions 8 29 10 degreeUnionState39_138) + +def degreeUnionState39_144 : List PrefixRegion := nextRegions 9 (liveRegions 8 29 10 degreeUnionState39_138) + +def degreeUnionState39_145 : List PrefixRegion := nextRegions 10 (liveRegions 8 29 10 degreeUnionState39_138) + +def degreeUnionState39_146 : List PrefixRegion := nextRegions 11 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_147 : List PrefixRegion := nextRegions 4 (liveRegions 8 28 11 degreeUnionState39_146) + +def degreeUnionState39_148 : List PrefixRegion := nextRegions 5 (liveRegions 8 28 11 degreeUnionState39_146) + +def degreeUnionState39_149 : List PrefixRegion := nextRegions 6 (liveRegions 8 28 11 degreeUnionState39_146) + +def degreeUnionState39_150 : List PrefixRegion := nextRegions 7 (liveRegions 8 28 11 degreeUnionState39_146) + +def degreeUnionState39_151 : List PrefixRegion := nextRegions 8 (liveRegions 8 28 11 degreeUnionState39_146) + +def degreeUnionState39_152 : List PrefixRegion := nextRegions 9 (liveRegions 8 28 11 degreeUnionState39_146) + +def degreeUnionState39_153 : List PrefixRegion := nextRegions 10 (liveRegions 8 28 11 degreeUnionState39_146) + +def degreeUnionState39_154 : List PrefixRegion := nextRegions 11 (liveRegions 8 28 11 degreeUnionState39_146) + +def degreeUnionState39_155 : List PrefixRegion := nextRegions 12 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_156 : List PrefixRegion := nextRegions 4 (liveRegions 8 27 12 degreeUnionState39_155) + +def degreeUnionState39_157 : List PrefixRegion := nextRegions 5 (liveRegions 8 27 12 degreeUnionState39_155) + +def degreeUnionState39_158 : List PrefixRegion := nextRegions 6 (liveRegions 8 27 12 degreeUnionState39_155) + +def degreeUnionState39_159 : List PrefixRegion := nextRegions 7 (liveRegions 8 27 12 degreeUnionState39_155) + +def degreeUnionState39_160 : List PrefixRegion := nextRegions 8 (liveRegions 8 27 12 degreeUnionState39_155) + +def degreeUnionState39_161 : List PrefixRegion := nextRegions 9 (liveRegions 8 27 12 degreeUnionState39_155) + +def degreeUnionState39_162 : List PrefixRegion := nextRegions 10 (liveRegions 8 27 12 degreeUnionState39_155) + +def degreeUnionState39_163 : List PrefixRegion := nextRegions 11 (liveRegions 8 27 12 degreeUnionState39_155) + +def degreeUnionState39_164 : List PrefixRegion := nextRegions 12 (liveRegions 8 27 12 degreeUnionState39_155) + +def degreeUnionState39_165 : List PrefixRegion := nextRegions 13 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_166 : List PrefixRegion := nextRegions 4 (liveRegions 8 26 13 degreeUnionState39_165) + +def degreeUnionState39_167 : List PrefixRegion := nextRegions 5 (liveRegions 8 26 13 degreeUnionState39_165) + +def degreeUnionState39_168 : List PrefixRegion := nextRegions 6 (liveRegions 8 26 13 degreeUnionState39_165) + +def degreeUnionState39_169 : List PrefixRegion := nextRegions 7 (liveRegions 8 26 13 degreeUnionState39_165) + +def degreeUnionState39_170 : List PrefixRegion := nextRegions 8 (liveRegions 8 26 13 degreeUnionState39_165) + +def degreeUnionState39_171 : List PrefixRegion := nextRegions 9 (liveRegions 8 26 13 degreeUnionState39_165) + +def degreeUnionState39_172 : List PrefixRegion := nextRegions 10 (liveRegions 8 26 13 degreeUnionState39_165) + +def degreeUnionState39_173 : List PrefixRegion := nextRegions 11 (liveRegions 8 26 13 degreeUnionState39_165) + +def degreeUnionState39_174 : List PrefixRegion := nextRegions 12 (liveRegions 8 26 13 degreeUnionState39_165) + +def degreeUnionState39_175 : List PrefixRegion := nextRegions 13 (liveRegions 8 26 13 degreeUnionState39_165) + +def degreeUnionState39_176 : List PrefixRegion := nextRegions 14 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_177 : List PrefixRegion := nextRegions 4 (liveRegions 8 25 14 degreeUnionState39_176) + +def degreeUnionState39_178 : List PrefixRegion := nextRegions 5 (liveRegions 8 25 14 degreeUnionState39_176) + +def degreeUnionState39_179 : List PrefixRegion := nextRegions 6 (liveRegions 8 25 14 degreeUnionState39_176) + +def degreeUnionState39_180 : List PrefixRegion := nextRegions 7 (liveRegions 8 25 14 degreeUnionState39_176) + +def degreeUnionState39_181 : List PrefixRegion := nextRegions 8 (liveRegions 8 25 14 degreeUnionState39_176) + +def degreeUnionState39_182 : List PrefixRegion := nextRegions 9 (liveRegions 8 25 14 degreeUnionState39_176) + +def degreeUnionState39_183 : List PrefixRegion := nextRegions 10 (liveRegions 8 25 14 degreeUnionState39_176) + +def degreeUnionState39_184 : List PrefixRegion := nextRegions 11 (liveRegions 8 25 14 degreeUnionState39_176) + +def degreeUnionState39_185 : List PrefixRegion := nextRegions 12 (liveRegions 8 25 14 degreeUnionState39_176) + +def degreeUnionState39_186 : List PrefixRegion := nextRegions 13 (liveRegions 8 25 14 degreeUnionState39_176) + +def degreeUnionState39_187 : List PrefixRegion := nextRegions 14 (liveRegions 8 25 14 degreeUnionState39_176) + +def degreeUnionState39_188 : List PrefixRegion := nextRegions 15 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_189 : List PrefixRegion := nextRegions 3 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_190 : List PrefixRegion := nextRegions 4 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_191 : List PrefixRegion := nextRegions 5 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_192 : List PrefixRegion := nextRegions 6 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_193 : List PrefixRegion := nextRegions 7 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_194 : List PrefixRegion := nextRegions 8 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_195 : List PrefixRegion := nextRegions 9 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_196 : List PrefixRegion := nextRegions 10 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_197 : List PrefixRegion := nextRegions 11 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_198 : List PrefixRegion := nextRegions 12 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_199 : List PrefixRegion := nextRegions 13 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_200 : List PrefixRegion := nextRegions 14 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_201 : List PrefixRegion := nextRegions 15 (liveRegions 8 24 15 degreeUnionState39_188) + +def degreeUnionState39_202 : List PrefixRegion := nextRegions 16 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_203 : List PrefixRegion := nextRegions 17 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_204 : List PrefixRegion := nextRegions 18 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_205 : List PrefixRegion := nextRegions 19 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_206 : List PrefixRegion := nextRegions 20 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_207 : List PrefixRegion := nextRegions 21 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_208 : List PrefixRegion := nextRegions 22 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_209 : List PrefixRegion := nextRegions 23 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_210 : List PrefixRegion := nextRegions 24 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_211 : List PrefixRegion := nextRegions 25 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_212 : List PrefixRegion := nextRegions 26 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_213 : List PrefixRegion := nextRegions 27 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_214 : List PrefixRegion := nextRegions 28 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_215 : List PrefixRegion := nextRegions 29 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_216 : List PrefixRegion := nextRegions 30 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_217 : List PrefixRegion := nextRegions 31 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_218 : List PrefixRegion := nextRegions 32 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_219 : List PrefixRegion := nextRegions 33 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_220 : List PrefixRegion := nextRegions 34 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_221 : List PrefixRegion := nextRegions 35 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_222 : List PrefixRegion := nextRegions 36 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_223 : List PrefixRegion := nextRegions 37 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_224 : List PrefixRegion := nextRegions 38 (liveRegions 9 39 38 degreeHalfRegions39) + +def degreeUnionState39_226 : List PrefixRegion := nextRegions 4 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_227 : List PrefixRegion := nextRegions 5 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_228 : List PrefixRegion := nextRegions 6 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_229 : List PrefixRegion := nextRegions 7 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_230 : List PrefixRegion := nextRegions 8 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_231 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 8 degreeUnionState39_230) + +def degreeUnionState39_232 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 8 degreeUnionState39_230) + +def degreeUnionState39_233 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 8 degreeUnionState39_230) + +def degreeUnionState39_234 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 8 degreeUnionState39_230) + +def degreeUnionState39_235 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 8 degreeUnionState39_230) + +def degreeUnionState39_236 : List PrefixRegion := nextRegions 9 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_237 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 9 degreeUnionState39_236) + +def degreeUnionState39_238 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 9 degreeUnionState39_236) + +def degreeUnionState39_239 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 9 degreeUnionState39_236) + +def degreeUnionState39_240 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 9 degreeUnionState39_236) + +def degreeUnionState39_241 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 9 degreeUnionState39_236) + +def degreeUnionState39_242 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 9 degreeUnionState39_236) + +def degreeUnionState39_243 : List PrefixRegion := nextRegions 10 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_244 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 10 degreeUnionState39_243) + +def degreeUnionState39_245 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 10 degreeUnionState39_243) + +def degreeUnionState39_246 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 10 degreeUnionState39_243) + +def degreeUnionState39_247 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 10 degreeUnionState39_243) + +def degreeUnionState39_248 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 10 degreeUnionState39_243) + +def degreeUnionState39_249 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 10 degreeUnionState39_243) + +def degreeUnionState39_250 : List PrefixRegion := nextRegions 10 (liveRegions 9 29 10 degreeUnionState39_243) + +def degreeUnionState39_251 : List PrefixRegion := nextRegions 11 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_252 : List PrefixRegion := nextRegions 4 (liveRegions 9 28 11 degreeUnionState39_251) + +def degreeUnionState39_253 : List PrefixRegion := nextRegions 5 (liveRegions 9 28 11 degreeUnionState39_251) + +def degreeUnionState39_254 : List PrefixRegion := nextRegions 6 (liveRegions 9 28 11 degreeUnionState39_251) + +def degreeUnionState39_255 : List PrefixRegion := nextRegions 7 (liveRegions 9 28 11 degreeUnionState39_251) + +def degreeUnionState39_256 : List PrefixRegion := nextRegions 8 (liveRegions 9 28 11 degreeUnionState39_251) + +def degreeUnionState39_257 : List PrefixRegion := nextRegions 9 (liveRegions 9 28 11 degreeUnionState39_251) + +def degreeUnionState39_258 : List PrefixRegion := nextRegions 10 (liveRegions 9 28 11 degreeUnionState39_251) + +def degreeUnionState39_259 : List PrefixRegion := nextRegions 11 (liveRegions 9 28 11 degreeUnionState39_251) + +def degreeUnionState39_260 : List PrefixRegion := nextRegions 12 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_261 : List PrefixRegion := nextRegions 3 (liveRegions 9 27 12 degreeUnionState39_260) + +def degreeUnionState39_262 : List PrefixRegion := nextRegions 4 (liveRegions 9 27 12 degreeUnionState39_260) + +def degreeUnionState39_263 : List PrefixRegion := nextRegions 5 (liveRegions 9 27 12 degreeUnionState39_260) + +def degreeUnionState39_264 : List PrefixRegion := nextRegions 6 (liveRegions 9 27 12 degreeUnionState39_260) + +def degreeUnionState39_265 : List PrefixRegion := nextRegions 7 (liveRegions 9 27 12 degreeUnionState39_260) + +def degreeUnionState39_266 : List PrefixRegion := nextRegions 8 (liveRegions 9 27 12 degreeUnionState39_260) + +def degreeUnionState39_267 : List PrefixRegion := nextRegions 9 (liveRegions 9 27 12 degreeUnionState39_260) + +def degreeUnionState39_268 : List PrefixRegion := nextRegions 10 (liveRegions 9 27 12 degreeUnionState39_260) + +def degreeUnionState39_269 : List PrefixRegion := nextRegions 11 (liveRegions 9 27 12 degreeUnionState39_260) + +def degreeUnionState39_270 : List PrefixRegion := nextRegions 12 (liveRegions 9 27 12 degreeUnionState39_260) + +def degreeUnionState39_271 : List PrefixRegion := nextRegions 13 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_272 : List PrefixRegion := nextRegions 3 (liveRegions 9 26 13 degreeUnionState39_271) + +def degreeUnionState39_273 : List PrefixRegion := nextRegions 4 (liveRegions 9 26 13 degreeUnionState39_271) + +def degreeUnionState39_274 : List PrefixRegion := nextRegions 5 (liveRegions 9 26 13 degreeUnionState39_271) + +def degreeUnionState39_275 : List PrefixRegion := nextRegions 6 (liveRegions 9 26 13 degreeUnionState39_271) + +def degreeUnionState39_276 : List PrefixRegion := nextRegions 7 (liveRegions 9 26 13 degreeUnionState39_271) + +def degreeUnionState39_277 : List PrefixRegion := nextRegions 8 (liveRegions 9 26 13 degreeUnionState39_271) + +def degreeUnionState39_278 : List PrefixRegion := nextRegions 9 (liveRegions 9 26 13 degreeUnionState39_271) + +def degreeUnionState39_279 : List PrefixRegion := nextRegions 10 (liveRegions 9 26 13 degreeUnionState39_271) + +def degreeUnionState39_280 : List PrefixRegion := nextRegions 11 (liveRegions 9 26 13 degreeUnionState39_271) + +def degreeUnionState39_281 : List PrefixRegion := nextRegions 12 (liveRegions 9 26 13 degreeUnionState39_271) + +def degreeUnionState39_282 : List PrefixRegion := nextRegions 13 (liveRegions 9 26 13 degreeUnionState39_271) + +def degreeUnionState39_283 : List PrefixRegion := nextRegions 14 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_284 : List PrefixRegion := nextRegions 15 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_285 : List PrefixRegion := nextRegions 16 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_286 : List PrefixRegion := nextRegions 17 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_287 : List PrefixRegion := nextRegions 18 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_288 : List PrefixRegion := nextRegions 19 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_289 : List PrefixRegion := nextRegions 20 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_290 : List PrefixRegion := nextRegions 21 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_291 : List PrefixRegion := nextRegions 22 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_292 : List PrefixRegion := nextRegions 23 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_293 : List PrefixRegion := nextRegions 24 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_294 : List PrefixRegion := nextRegions 25 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_295 : List PrefixRegion := nextRegions 26 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_296 : List PrefixRegion := nextRegions 27 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_297 : List PrefixRegion := nextRegions 28 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_298 : List PrefixRegion := nextRegions 29 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_299 : List PrefixRegion := nextRegions 30 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_300 : List PrefixRegion := nextRegions 31 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_301 : List PrefixRegion := nextRegions 32 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_302 : List PrefixRegion := nextRegions 33 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_303 : List PrefixRegion := nextRegions 34 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_304 : List PrefixRegion := nextRegions 35 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_305 : List PrefixRegion := nextRegions 36 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_306 : List PrefixRegion := nextRegions 37 (liveRegions 10 39 38 degreeHalfRegions39) + +def degreeUnionState39_307 : List PrefixRegion := nextRegions 38 (liveRegions 10 39 38 degreeHalfRegions39) + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates43.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates43.lean index bf9a843506f550f5fcafbfa781399d8fbed638a7..2db6a0b31de2ec87b768d8efce92a8eea4a7b468 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates43.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates43.lean @@ -1,1771 +1,1771 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData43 - -namespace OAI - -/-! Degree Union States 43. -/ - -section - -namespace UniversalTensorSquare - -def degreeUnionState43_9 : List PrefixRegion := nextRegions 6 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_10 : List PrefixRegion := nextRegions 7 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_11 : List PrefixRegion := nextRegions 8 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_12 : List PrefixRegion := nextRegions 5 (liveRegions 7 35 8 degreeUnionState43_11) - -def degreeUnionState43_13 : List PrefixRegion := nextRegions 6 (liveRegions 7 35 8 degreeUnionState43_11) - -def degreeUnionState43_14 : List PrefixRegion := nextRegions 7 (liveRegions 7 35 8 degreeUnionState43_11) - -def degreeUnionState43_15 : List PrefixRegion := nextRegions 8 (liveRegions 7 35 8 degreeUnionState43_11) - -def degreeUnionState43_16 : List PrefixRegion := nextRegions 9 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_17 : List PrefixRegion := nextRegions 5 (liveRegions 7 34 9 degreeUnionState43_16) - -def degreeUnionState43_18 : List PrefixRegion := nextRegions 6 (liveRegions 7 34 9 degreeUnionState43_16) - -def degreeUnionState43_19 : List PrefixRegion := nextRegions 7 (liveRegions 7 34 9 degreeUnionState43_16) - -def degreeUnionState43_20 : List PrefixRegion := nextRegions 8 (liveRegions 7 34 9 degreeUnionState43_16) - -def degreeUnionState43_21 : List PrefixRegion := nextRegions 9 (liveRegions 7 34 9 degreeUnionState43_16) - -def degreeUnionState43_22 : List PrefixRegion := nextRegions 10 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_23 : List PrefixRegion := nextRegions 5 (liveRegions 7 33 10 degreeUnionState43_22) - -def degreeUnionState43_24 : List PrefixRegion := nextRegions 6 (liveRegions 7 33 10 degreeUnionState43_22) - -def degreeUnionState43_25 : List PrefixRegion := nextRegions 7 (liveRegions 7 33 10 degreeUnionState43_22) - -def degreeUnionState43_26 : List PrefixRegion := nextRegions 8 (liveRegions 7 33 10 degreeUnionState43_22) - -def degreeUnionState43_27 : List PrefixRegion := nextRegions 9 (liveRegions 7 33 10 degreeUnionState43_22) - -def degreeUnionState43_28 : List PrefixRegion := nextRegions 10 (liveRegions 7 33 10 degreeUnionState43_22) - -def degreeUnionState43_29 : List PrefixRegion := nextRegions 11 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_30 : List PrefixRegion := nextRegions 5 (liveRegions 7 32 11 degreeUnionState43_29) - -def degreeUnionState43_31 : List PrefixRegion := nextRegions 6 (liveRegions 7 32 11 degreeUnionState43_29) - -def degreeUnionState43_32 : List PrefixRegion := nextRegions 7 (liveRegions 7 32 11 degreeUnionState43_29) - -def degreeUnionState43_33 : List PrefixRegion := nextRegions 8 (liveRegions 7 32 11 degreeUnionState43_29) - -def degreeUnionState43_34 : List PrefixRegion := nextRegions 9 (liveRegions 7 32 11 degreeUnionState43_29) - -def degreeUnionState43_35 : List PrefixRegion := nextRegions 10 (liveRegions 7 32 11 degreeUnionState43_29) - -def degreeUnionState43_36 : List PrefixRegion := nextRegions 11 (liveRegions 7 32 11 degreeUnionState43_29) - -def degreeUnionState43_37 : List PrefixRegion := nextRegions 12 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_38 : List PrefixRegion := nextRegions 5 (liveRegions 7 31 12 degreeUnionState43_37) - -def degreeUnionState43_39 : List PrefixRegion := nextRegions 6 (liveRegions 7 31 12 degreeUnionState43_37) - -def degreeUnionState43_40 : List PrefixRegion := nextRegions 7 (liveRegions 7 31 12 degreeUnionState43_37) - -def degreeUnionState43_41 : List PrefixRegion := nextRegions 8 (liveRegions 7 31 12 degreeUnionState43_37) - -def degreeUnionState43_42 : List PrefixRegion := nextRegions 9 (liveRegions 7 31 12 degreeUnionState43_37) - -def degreeUnionState43_43 : List PrefixRegion := nextRegions 10 (liveRegions 7 31 12 degreeUnionState43_37) - -def degreeUnionState43_44 : List PrefixRegion := nextRegions 11 (liveRegions 7 31 12 degreeUnionState43_37) - -def degreeUnionState43_45 : List PrefixRegion := nextRegions 12 (liveRegions 7 31 12 degreeUnionState43_37) - -def degreeUnionState43_46 : List PrefixRegion := nextRegions 13 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_47 : List PrefixRegion := nextRegions 5 (liveRegions 7 30 13 degreeUnionState43_46) - -def degreeUnionState43_48 : List PrefixRegion := nextRegions 6 (liveRegions 7 30 13 degreeUnionState43_46) - -def degreeUnionState43_49 : List PrefixRegion := nextRegions 7 (liveRegions 7 30 13 degreeUnionState43_46) - -def degreeUnionState43_50 : List PrefixRegion := nextRegions 8 (liveRegions 7 30 13 degreeUnionState43_46) - -def degreeUnionState43_51 : List PrefixRegion := nextRegions 9 (liveRegions 7 30 13 degreeUnionState43_46) - -def degreeUnionState43_52 : List PrefixRegion := nextRegions 10 (liveRegions 7 30 13 degreeUnionState43_46) - -def degreeUnionState43_53 : List PrefixRegion := nextRegions 11 (liveRegions 7 30 13 degreeUnionState43_46) - -def degreeUnionState43_54 : List PrefixRegion := nextRegions 12 (liveRegions 7 30 13 degreeUnionState43_46) - -def degreeUnionState43_55 : List PrefixRegion := nextRegions 13 (liveRegions 7 30 13 degreeUnionState43_46) - -def degreeUnionState43_56 : List PrefixRegion := nextRegions 14 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_57 : List PrefixRegion := nextRegions 5 (liveRegions 7 29 14 degreeUnionState43_56) - -def degreeUnionState43_58 : List PrefixRegion := nextRegions 6 (liveRegions 7 29 14 degreeUnionState43_56) - -def degreeUnionState43_59 : List PrefixRegion := nextRegions 7 (liveRegions 7 29 14 degreeUnionState43_56) - -def degreeUnionState43_60 : List PrefixRegion := nextRegions 8 (liveRegions 7 29 14 degreeUnionState43_56) - -def degreeUnionState43_61 : List PrefixRegion := nextRegions 9 (liveRegions 7 29 14 degreeUnionState43_56) - -def degreeUnionState43_62 : List PrefixRegion := nextRegions 10 (liveRegions 7 29 14 degreeUnionState43_56) - -def degreeUnionState43_63 : List PrefixRegion := nextRegions 11 (liveRegions 7 29 14 degreeUnionState43_56) - -def degreeUnionState43_64 : List PrefixRegion := nextRegions 12 (liveRegions 7 29 14 degreeUnionState43_56) - -def degreeUnionState43_65 : List PrefixRegion := nextRegions 13 (liveRegions 7 29 14 degreeUnionState43_56) - -def degreeUnionState43_66 : List PrefixRegion := nextRegions 14 (liveRegions 7 29 14 degreeUnionState43_56) - -def degreeUnionState43_67 : List PrefixRegion := nextRegions 15 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_68 : List PrefixRegion := nextRegions 4 (liveRegions 7 28 15 degreeUnionState43_67) - -def degreeUnionState43_69 : List PrefixRegion := nextRegions 5 (liveRegions 7 28 15 degreeUnionState43_67) - -def degreeUnionState43_70 : List PrefixRegion := nextRegions 6 (liveRegions 7 28 15 degreeUnionState43_67) - -def degreeUnionState43_71 : List PrefixRegion := nextRegions 7 (liveRegions 7 28 15 degreeUnionState43_67) - -def degreeUnionState43_72 : List PrefixRegion := nextRegions 8 (liveRegions 7 28 15 degreeUnionState43_67) - -def degreeUnionState43_73 : List PrefixRegion := nextRegions 9 (liveRegions 7 28 15 degreeUnionState43_67) - -def degreeUnionState43_74 : List PrefixRegion := nextRegions 10 (liveRegions 7 28 15 degreeUnionState43_67) - -def degreeUnionState43_75 : List PrefixRegion := nextRegions 11 (liveRegions 7 28 15 degreeUnionState43_67) - -def degreeUnionState43_76 : List PrefixRegion := nextRegions 12 (liveRegions 7 28 15 degreeUnionState43_67) - -def degreeUnionState43_77 : List PrefixRegion := nextRegions 13 (liveRegions 7 28 15 degreeUnionState43_67) - -def degreeUnionState43_78 : List PrefixRegion := nextRegions 14 (liveRegions 7 28 15 degreeUnionState43_67) - -def degreeUnionState43_79 : List PrefixRegion := nextRegions 15 (liveRegions 7 28 15 degreeUnionState43_67) - -def degreeUnionState43_80 : List PrefixRegion := nextRegions 16 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_81 : List PrefixRegion := nextRegions 4 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_82 : List PrefixRegion := nextRegions 5 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_83 : List PrefixRegion := nextRegions 6 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_84 : List PrefixRegion := nextRegions 7 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_85 : List PrefixRegion := nextRegions 8 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_86 : List PrefixRegion := nextRegions 9 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_87 : List PrefixRegion := nextRegions 10 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_88 : List PrefixRegion := nextRegions 11 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_89 : List PrefixRegion := nextRegions 12 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_90 : List PrefixRegion := nextRegions 13 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_91 : List PrefixRegion := nextRegions 14 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_92 : List PrefixRegion := nextRegions 15 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_93 : List PrefixRegion := nextRegions 16 (liveRegions 7 27 16 degreeUnionState43_80) - -def degreeUnionState43_94 : List PrefixRegion := nextRegions 17 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_95 : List PrefixRegion := nextRegions 4 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_96 : List PrefixRegion := nextRegions 5 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_97 : List PrefixRegion := nextRegions 6 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_98 : List PrefixRegion := nextRegions 7 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_99 : List PrefixRegion := nextRegions 8 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_100 : List PrefixRegion := nextRegions 9 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_101 : List PrefixRegion := nextRegions 10 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_102 : List PrefixRegion := nextRegions 11 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_103 : List PrefixRegion := nextRegions 12 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_104 : List PrefixRegion := nextRegions 13 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_105 : List PrefixRegion := nextRegions 14 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_106 : List PrefixRegion := nextRegions 15 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_107 : List PrefixRegion := nextRegions 16 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_108 : List PrefixRegion := nextRegions 17 (liveRegions 7 26 17 degreeUnionState43_94) - -def degreeUnionState43_109 : List PrefixRegion := nextRegions 18 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_110 : List PrefixRegion := nextRegions 4 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_111 : List PrefixRegion := nextRegions 5 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_112 : List PrefixRegion := nextRegions 6 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_113 : List PrefixRegion := nextRegions 7 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_114 : List PrefixRegion := nextRegions 8 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_115 : List PrefixRegion := nextRegions 9 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_116 : List PrefixRegion := nextRegions 10 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_117 : List PrefixRegion := nextRegions 11 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_118 : List PrefixRegion := nextRegions 12 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_119 : List PrefixRegion := nextRegions 13 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_120 : List PrefixRegion := nextRegions 14 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_121 : List PrefixRegion := nextRegions 15 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_122 : List PrefixRegion := nextRegions 16 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_123 : List PrefixRegion := nextRegions 17 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_124 : List PrefixRegion := nextRegions 18 (liveRegions 7 25 18 degreeUnionState43_109) - -def degreeUnionState43_125 : List PrefixRegion := nextRegions 19 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_126 : List PrefixRegion := nextRegions 4 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_127 : List PrefixRegion := nextRegions 5 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_128 : List PrefixRegion := nextRegions 6 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_129 : List PrefixRegion := nextRegions 7 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_130 : List PrefixRegion := nextRegions 8 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_131 : List PrefixRegion := nextRegions 9 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_132 : List PrefixRegion := nextRegions 10 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_133 : List PrefixRegion := nextRegions 11 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_134 : List PrefixRegion := nextRegions 12 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_135 : List PrefixRegion := nextRegions 13 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_136 : List PrefixRegion := nextRegions 14 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_137 : List PrefixRegion := nextRegions 15 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_138 : List PrefixRegion := nextRegions 16 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_139 : List PrefixRegion := nextRegions 17 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_140 : List PrefixRegion := nextRegions 18 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_141 : List PrefixRegion := nextRegions 19 (liveRegions 7 24 19 degreeUnionState43_125) - -def degreeUnionState43_142 : List PrefixRegion := nextRegions 20 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_143 : List PrefixRegion := nextRegions 4 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_144 : List PrefixRegion := nextRegions 5 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_145 : List PrefixRegion := nextRegions 6 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_146 : List PrefixRegion := nextRegions 7 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_147 : List PrefixRegion := nextRegions 8 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_148 : List PrefixRegion := nextRegions 9 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_149 : List PrefixRegion := nextRegions 10 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_150 : List PrefixRegion := nextRegions 11 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_151 : List PrefixRegion := nextRegions 12 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_152 : List PrefixRegion := nextRegions 13 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_153 : List PrefixRegion := nextRegions 14 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_154 : List PrefixRegion := nextRegions 15 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_155 : List PrefixRegion := nextRegions 16 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_156 : List PrefixRegion := nextRegions 17 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_157 : List PrefixRegion := nextRegions 18 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_158 : List PrefixRegion := nextRegions 19 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_159 : List PrefixRegion := nextRegions 20 (liveRegions 7 23 20 degreeUnionState43_142) - -def degreeUnionState43_160 : List PrefixRegion := nextRegions 21 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_161 : List PrefixRegion := nextRegions 22 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_162 : List PrefixRegion := nextRegions 23 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_163 : List PrefixRegion := nextRegions 24 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_164 : List PrefixRegion := nextRegions 25 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_165 : List PrefixRegion := nextRegions 26 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_166 : List PrefixRegion := nextRegions 27 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_167 : List PrefixRegion := nextRegions 28 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_168 : List PrefixRegion := nextRegions 29 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_169 : List PrefixRegion := nextRegions 30 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_170 : List PrefixRegion := nextRegions 31 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_171 : List PrefixRegion := nextRegions 32 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_172 : List PrefixRegion := nextRegions 33 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_173 : List PrefixRegion := nextRegions 34 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_174 : List PrefixRegion := nextRegions 35 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_175 : List PrefixRegion := nextRegions 36 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_176 : List PrefixRegion := nextRegions 37 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_177 : List PrefixRegion := nextRegions 38 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_178 : List PrefixRegion := nextRegions 39 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_179 : List PrefixRegion := nextRegions 40 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_180 : List PrefixRegion := nextRegions 41 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_181 : List PrefixRegion := nextRegions 42 (liveRegions 8 43 42 degreeHalfRegions43) - -def degreeUnionState43_183 : List PrefixRegion := nextRegions 5 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_184 : List PrefixRegion := nextRegions 6 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_185 : List PrefixRegion := nextRegions 7 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_186 : List PrefixRegion := nextRegions 8 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_187 : List PrefixRegion := nextRegions 5 (liveRegions 8 35 8 degreeUnionState43_186) - -def degreeUnionState43_188 : List PrefixRegion := nextRegions 6 (liveRegions 8 35 8 degreeUnionState43_186) - -def degreeUnionState43_189 : List PrefixRegion := nextRegions 7 (liveRegions 8 35 8 degreeUnionState43_186) - -def degreeUnionState43_190 : List PrefixRegion := nextRegions 8 (liveRegions 8 35 8 degreeUnionState43_186) - -def degreeUnionState43_191 : List PrefixRegion := nextRegions 9 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_192 : List PrefixRegion := nextRegions 5 (liveRegions 8 34 9 degreeUnionState43_191) - -def degreeUnionState43_193 : List PrefixRegion := nextRegions 6 (liveRegions 8 34 9 degreeUnionState43_191) - -def degreeUnionState43_194 : List PrefixRegion := nextRegions 7 (liveRegions 8 34 9 degreeUnionState43_191) - -def degreeUnionState43_195 : List PrefixRegion := nextRegions 8 (liveRegions 8 34 9 degreeUnionState43_191) - -def degreeUnionState43_196 : List PrefixRegion := nextRegions 9 (liveRegions 8 34 9 degreeUnionState43_191) - -def degreeUnionState43_197 : List PrefixRegion := nextRegions 4 (liveRegions 7 25 9 degreeUnionState43_196) - -def degreeUnionState43_198 : List PrefixRegion := nextRegions 5 (liveRegions 7 25 9 degreeUnionState43_196) - -def degreeUnionState43_199 : List PrefixRegion := nextRegions 6 (liveRegions 7 25 9 degreeUnionState43_196) - -def degreeUnionState43_200 : List PrefixRegion := nextRegions 7 (liveRegions 7 25 9 degreeUnionState43_196) - -def degreeUnionState43_201 : List PrefixRegion := nextRegions 8 (liveRegions 7 25 9 degreeUnionState43_196) - -def degreeUnionState43_202 : List PrefixRegion := nextRegions 9 (liveRegions 7 25 9 degreeUnionState43_196) - -def degreeUnionState43_203 : List PrefixRegion := nextRegions 10 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_204 : List PrefixRegion := nextRegions 5 (liveRegions 8 33 10 degreeUnionState43_203) - -def degreeUnionState43_205 : List PrefixRegion := nextRegions 6 (liveRegions 8 33 10 degreeUnionState43_203) - -def degreeUnionState43_206 : List PrefixRegion := nextRegions 7 (liveRegions 8 33 10 degreeUnionState43_203) - -def degreeUnionState43_207 : List PrefixRegion := nextRegions 8 (liveRegions 8 33 10 degreeUnionState43_203) - -def degreeUnionState43_208 : List PrefixRegion := nextRegions 9 (liveRegions 8 33 10 degreeUnionState43_203) - -def degreeUnionState43_209 : List PrefixRegion := nextRegions 10 (liveRegions 8 33 10 degreeUnionState43_203) - -def degreeUnionState43_210 : List PrefixRegion := nextRegions 11 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_211 : List PrefixRegion := nextRegions 4 (liveRegions 8 32 11 degreeUnionState43_210) - -def degreeUnionState43_212 : List PrefixRegion := nextRegions 5 (liveRegions 8 32 11 degreeUnionState43_210) - -def degreeUnionState43_213 : List PrefixRegion := nextRegions 6 (liveRegions 8 32 11 degreeUnionState43_210) - -def degreeUnionState43_214 : List PrefixRegion := nextRegions 7 (liveRegions 8 32 11 degreeUnionState43_210) - -def degreeUnionState43_215 : List PrefixRegion := nextRegions 8 (liveRegions 8 32 11 degreeUnionState43_210) - -def degreeUnionState43_216 : List PrefixRegion := nextRegions 9 (liveRegions 8 32 11 degreeUnionState43_210) - -def degreeUnionState43_217 : List PrefixRegion := nextRegions 10 (liveRegions 8 32 11 degreeUnionState43_210) - -def degreeUnionState43_218 : List PrefixRegion := nextRegions 11 (liveRegions 8 32 11 degreeUnionState43_210) - -def degreeUnionState43_219 : List PrefixRegion := nextRegions 12 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_220 : List PrefixRegion := nextRegions 4 (liveRegions 8 31 12 degreeUnionState43_219) - -def degreeUnionState43_221 : List PrefixRegion := nextRegions 5 (liveRegions 8 31 12 degreeUnionState43_219) - -def degreeUnionState43_222 : List PrefixRegion := nextRegions 6 (liveRegions 8 31 12 degreeUnionState43_219) - -def degreeUnionState43_223 : List PrefixRegion := nextRegions 7 (liveRegions 8 31 12 degreeUnionState43_219) - -def degreeUnionState43_224 : List PrefixRegion := nextRegions 8 (liveRegions 8 31 12 degreeUnionState43_219) - -def degreeUnionState43_225 : List PrefixRegion := nextRegions 9 (liveRegions 8 31 12 degreeUnionState43_219) - -def degreeUnionState43_226 : List PrefixRegion := nextRegions 10 (liveRegions 8 31 12 degreeUnionState43_219) - -def degreeUnionState43_227 : List PrefixRegion := nextRegions 11 (liveRegions 8 31 12 degreeUnionState43_219) - -def degreeUnionState43_228 : List PrefixRegion := nextRegions 12 (liveRegions 8 31 12 degreeUnionState43_219) - -def degreeUnionState43_229 : List PrefixRegion := nextRegions 13 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_230 : List PrefixRegion := nextRegions 4 (liveRegions 8 30 13 degreeUnionState43_229) - -def degreeUnionState43_231 : List PrefixRegion := nextRegions 5 (liveRegions 8 30 13 degreeUnionState43_229) - -def degreeUnionState43_232 : List PrefixRegion := nextRegions 6 (liveRegions 8 30 13 degreeUnionState43_229) - -def degreeUnionState43_233 : List PrefixRegion := nextRegions 7 (liveRegions 8 30 13 degreeUnionState43_229) - -def degreeUnionState43_234 : List PrefixRegion := nextRegions 8 (liveRegions 8 30 13 degreeUnionState43_229) - -def degreeUnionState43_235 : List PrefixRegion := nextRegions 9 (liveRegions 8 30 13 degreeUnionState43_229) - -def degreeUnionState43_236 : List PrefixRegion := nextRegions 10 (liveRegions 8 30 13 degreeUnionState43_229) - -def degreeUnionState43_237 : List PrefixRegion := nextRegions 11 (liveRegions 8 30 13 degreeUnionState43_229) - -def degreeUnionState43_238 : List PrefixRegion := nextRegions 12 (liveRegions 8 30 13 degreeUnionState43_229) - -def degreeUnionState43_239 : List PrefixRegion := nextRegions 13 (liveRegions 8 30 13 degreeUnionState43_229) - -def degreeUnionState43_240 : List PrefixRegion := nextRegions 14 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_241 : List PrefixRegion := nextRegions 4 (liveRegions 8 29 14 degreeUnionState43_240) - -def degreeUnionState43_242 : List PrefixRegion := nextRegions 5 (liveRegions 8 29 14 degreeUnionState43_240) - -def degreeUnionState43_243 : List PrefixRegion := nextRegions 6 (liveRegions 8 29 14 degreeUnionState43_240) - -def degreeUnionState43_244 : List PrefixRegion := nextRegions 7 (liveRegions 8 29 14 degreeUnionState43_240) - -def degreeUnionState43_245 : List PrefixRegion := nextRegions 8 (liveRegions 8 29 14 degreeUnionState43_240) - -def degreeUnionState43_246 : List PrefixRegion := nextRegions 9 (liveRegions 8 29 14 degreeUnionState43_240) - -def degreeUnionState43_247 : List PrefixRegion := nextRegions 10 (liveRegions 8 29 14 degreeUnionState43_240) - -def degreeUnionState43_248 : List PrefixRegion := nextRegions 11 (liveRegions 8 29 14 degreeUnionState43_240) - -def degreeUnionState43_249 : List PrefixRegion := nextRegions 12 (liveRegions 8 29 14 degreeUnionState43_240) - -def degreeUnionState43_250 : List PrefixRegion := nextRegions 13 (liveRegions 8 29 14 degreeUnionState43_240) - -def degreeUnionState43_251 : List PrefixRegion := nextRegions 14 (liveRegions 8 29 14 degreeUnionState43_240) - -def degreeUnionState43_252 : List PrefixRegion := nextRegions 15 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_253 : List PrefixRegion := nextRegions 4 (liveRegions 8 28 15 degreeUnionState43_252) - -def degreeUnionState43_254 : List PrefixRegion := nextRegions 5 (liveRegions 8 28 15 degreeUnionState43_252) - -def degreeUnionState43_255 : List PrefixRegion := nextRegions 6 (liveRegions 8 28 15 degreeUnionState43_252) - -def degreeUnionState43_256 : List PrefixRegion := nextRegions 7 (liveRegions 8 28 15 degreeUnionState43_252) - -def degreeUnionState43_257 : List PrefixRegion := nextRegions 8 (liveRegions 8 28 15 degreeUnionState43_252) - -def degreeUnionState43_258 : List PrefixRegion := nextRegions 9 (liveRegions 8 28 15 degreeUnionState43_252) - -def degreeUnionState43_259 : List PrefixRegion := nextRegions 10 (liveRegions 8 28 15 degreeUnionState43_252) - -def degreeUnionState43_260 : List PrefixRegion := nextRegions 11 (liveRegions 8 28 15 degreeUnionState43_252) - -def degreeUnionState43_261 : List PrefixRegion := nextRegions 12 (liveRegions 8 28 15 degreeUnionState43_252) - -def degreeUnionState43_262 : List PrefixRegion := nextRegions 13 (liveRegions 8 28 15 degreeUnionState43_252) - -def degreeUnionState43_263 : List PrefixRegion := nextRegions 14 (liveRegions 8 28 15 degreeUnionState43_252) - -def degreeUnionState43_264 : List PrefixRegion := nextRegions 15 (liveRegions 8 28 15 degreeUnionState43_252) - -def degreeUnionState43_265 : List PrefixRegion := nextRegions 16 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_266 : List PrefixRegion := nextRegions 4 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_267 : List PrefixRegion := nextRegions 5 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_268 : List PrefixRegion := nextRegions 6 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_269 : List PrefixRegion := nextRegions 7 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_270 : List PrefixRegion := nextRegions 8 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_271 : List PrefixRegion := nextRegions 9 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_272 : List PrefixRegion := nextRegions 10 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_273 : List PrefixRegion := nextRegions 11 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_274 : List PrefixRegion := nextRegions 12 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_275 : List PrefixRegion := nextRegions 13 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_276 : List PrefixRegion := nextRegions 14 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_277 : List PrefixRegion := nextRegions 15 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_278 : List PrefixRegion := nextRegions 16 (liveRegions 8 27 16 degreeUnionState43_265) - -def degreeUnionState43_279 : List PrefixRegion := nextRegions 17 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_280 : List PrefixRegion := nextRegions 4 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_281 : List PrefixRegion := nextRegions 5 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_282 : List PrefixRegion := nextRegions 6 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_283 : List PrefixRegion := nextRegions 7 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_284 : List PrefixRegion := nextRegions 8 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_285 : List PrefixRegion := nextRegions 9 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_286 : List PrefixRegion := nextRegions 10 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_287 : List PrefixRegion := nextRegions 11 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_288 : List PrefixRegion := nextRegions 12 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_289 : List PrefixRegion := nextRegions 13 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_290 : List PrefixRegion := nextRegions 14 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_291 : List PrefixRegion := nextRegions 15 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_292 : List PrefixRegion := nextRegions 16 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_293 : List PrefixRegion := nextRegions 17 (liveRegions 8 26 17 degreeUnionState43_279) - -def degreeUnionState43_294 : List PrefixRegion := nextRegions 18 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_295 : List PrefixRegion := nextRegions 4 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_296 : List PrefixRegion := nextRegions 5 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_297 : List PrefixRegion := nextRegions 6 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_298 : List PrefixRegion := nextRegions 7 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_299 : List PrefixRegion := nextRegions 8 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_300 : List PrefixRegion := nextRegions 9 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_301 : List PrefixRegion := nextRegions 10 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_302 : List PrefixRegion := nextRegions 11 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_303 : List PrefixRegion := nextRegions 12 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_304 : List PrefixRegion := nextRegions 13 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_305 : List PrefixRegion := nextRegions 14 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_306 : List PrefixRegion := nextRegions 15 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_307 : List PrefixRegion := nextRegions 16 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_308 : List PrefixRegion := nextRegions 17 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_309 : List PrefixRegion := nextRegions 18 (liveRegions 8 25 18 degreeUnionState43_294) - -def degreeUnionState43_310 : List PrefixRegion := nextRegions 19 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_311 : List PrefixRegion := nextRegions 3 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_312 : List PrefixRegion := nextRegions 4 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_313 : List PrefixRegion := nextRegions 5 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_314 : List PrefixRegion := nextRegions 6 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_315 : List PrefixRegion := nextRegions 7 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_316 : List PrefixRegion := nextRegions 8 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_317 : List PrefixRegion := nextRegions 9 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_318 : List PrefixRegion := nextRegions 10 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_319 : List PrefixRegion := nextRegions 11 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_320 : List PrefixRegion := nextRegions 12 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_321 : List PrefixRegion := nextRegions 13 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_322 : List PrefixRegion := nextRegions 14 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_323 : List PrefixRegion := nextRegions 15 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_324 : List PrefixRegion := nextRegions 16 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_325 : List PrefixRegion := nextRegions 17 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_326 : List PrefixRegion := nextRegions 18 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_327 : List PrefixRegion := nextRegions 19 (liveRegions 8 24 19 degreeUnionState43_310) - -def degreeUnionState43_328 : List PrefixRegion := nextRegions 20 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_329 : List PrefixRegion := nextRegions 21 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_330 : List PrefixRegion := nextRegions 22 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_331 : List PrefixRegion := nextRegions 23 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_332 : List PrefixRegion := nextRegions 24 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_333 : List PrefixRegion := nextRegions 25 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_334 : List PrefixRegion := nextRegions 26 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_335 : List PrefixRegion := nextRegions 27 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_336 : List PrefixRegion := nextRegions 28 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_337 : List PrefixRegion := nextRegions 29 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_338 : List PrefixRegion := nextRegions 30 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_339 : List PrefixRegion := nextRegions 31 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_340 : List PrefixRegion := nextRegions 32 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_341 : List PrefixRegion := nextRegions 33 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_342 : List PrefixRegion := nextRegions 34 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_343 : List PrefixRegion := nextRegions 35 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_344 : List PrefixRegion := nextRegions 36 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_345 : List PrefixRegion := nextRegions 37 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_346 : List PrefixRegion := nextRegions 38 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_347 : List PrefixRegion := nextRegions 39 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_348 : List PrefixRegion := nextRegions 40 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_349 : List PrefixRegion := nextRegions 41 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_350 : List PrefixRegion := nextRegions 42 (liveRegions 9 43 42 degreeHalfRegions43) - -def degreeUnionState43_352 : List PrefixRegion := nextRegions 5 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_353 : List PrefixRegion := nextRegions 6 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_354 : List PrefixRegion := nextRegions 7 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_355 : List PrefixRegion := nextRegions 8 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_356 : List PrefixRegion := nextRegions 4 (liveRegions 9 35 8 degreeUnionState43_355) - -def degreeUnionState43_357 : List PrefixRegion := nextRegions 5 (liveRegions 9 35 8 degreeUnionState43_355) - -def degreeUnionState43_358 : List PrefixRegion := nextRegions 6 (liveRegions 9 35 8 degreeUnionState43_355) - -def degreeUnionState43_359 : List PrefixRegion := nextRegions 7 (liveRegions 9 35 8 degreeUnionState43_355) - -def degreeUnionState43_360 : List PrefixRegion := nextRegions 8 (liveRegions 9 35 8 degreeUnionState43_355) - -def degreeUnionState43_361 : List PrefixRegion := nextRegions 4 (liveRegions 8 27 8 degreeUnionState43_360) - -def degreeUnionState43_362 : List PrefixRegion := nextRegions 5 (liveRegions 8 27 8 degreeUnionState43_360) - -def degreeUnionState43_363 : List PrefixRegion := nextRegions 6 (liveRegions 8 27 8 degreeUnionState43_360) - -def degreeUnionState43_364 : List PrefixRegion := nextRegions 7 (liveRegions 8 27 8 degreeUnionState43_360) - -def degreeUnionState43_365 : List PrefixRegion := nextRegions 8 (liveRegions 8 27 8 degreeUnionState43_360) - -def degreeUnionState43_366 : List PrefixRegion := nextRegions 9 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_367 : List PrefixRegion := nextRegions 4 (liveRegions 9 34 9 degreeUnionState43_366) - -def degreeUnionState43_368 : List PrefixRegion := nextRegions 5 (liveRegions 9 34 9 degreeUnionState43_366) - -def degreeUnionState43_369 : List PrefixRegion := nextRegions 6 (liveRegions 9 34 9 degreeUnionState43_366) - -def degreeUnionState43_370 : List PrefixRegion := nextRegions 7 (liveRegions 9 34 9 degreeUnionState43_366) - -def degreeUnionState43_371 : List PrefixRegion := nextRegions 8 (liveRegions 9 34 9 degreeUnionState43_366) - -def degreeUnionState43_372 : List PrefixRegion := nextRegions 4 (liveRegions 8 26 8 degreeUnionState43_371) - -def degreeUnionState43_373 : List PrefixRegion := nextRegions 5 (liveRegions 8 26 8 degreeUnionState43_371) - -def degreeUnionState43_374 : List PrefixRegion := nextRegions 6 (liveRegions 8 26 8 degreeUnionState43_371) - -def degreeUnionState43_375 : List PrefixRegion := nextRegions 7 (liveRegions 8 26 8 degreeUnionState43_371) - -def degreeUnionState43_376 : List PrefixRegion := nextRegions 8 (liveRegions 8 26 8 degreeUnionState43_371) - -def degreeUnionState43_377 : List PrefixRegion := nextRegions 9 (liveRegions 9 34 9 degreeUnionState43_366) - -def degreeUnionState43_378 : List PrefixRegion := nextRegions 4 (liveRegions 8 25 9 degreeUnionState43_377) - -def degreeUnionState43_379 : List PrefixRegion := nextRegions 5 (liveRegions 8 25 9 degreeUnionState43_377) - -def degreeUnionState43_380 : List PrefixRegion := nextRegions 6 (liveRegions 8 25 9 degreeUnionState43_377) - -def degreeUnionState43_381 : List PrefixRegion := nextRegions 7 (liveRegions 8 25 9 degreeUnionState43_377) - -def degreeUnionState43_382 : List PrefixRegion := nextRegions 8 (liveRegions 8 25 9 degreeUnionState43_377) - -def degreeUnionState43_383 : List PrefixRegion := nextRegions 9 (liveRegions 8 25 9 degreeUnionState43_377) - -def degreeUnionState43_384 : List PrefixRegion := nextRegions 10 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_385 : List PrefixRegion := nextRegions 4 (liveRegions 9 33 10 degreeUnionState43_384) - -def degreeUnionState43_386 : List PrefixRegion := nextRegions 5 (liveRegions 9 33 10 degreeUnionState43_384) - -def degreeUnionState43_387 : List PrefixRegion := nextRegions 6 (liveRegions 9 33 10 degreeUnionState43_384) - -def degreeUnionState43_388 : List PrefixRegion := nextRegions 7 (liveRegions 9 33 10 degreeUnionState43_384) - -def degreeUnionState43_389 : List PrefixRegion := nextRegions 8 (liveRegions 9 33 10 degreeUnionState43_384) - -def degreeUnionState43_390 : List PrefixRegion := nextRegions 9 (liveRegions 9 33 10 degreeUnionState43_384) - -def degreeUnionState43_391 : List PrefixRegion := nextRegions 10 (liveRegions 9 33 10 degreeUnionState43_384) - -def degreeUnionState43_392 : List PrefixRegion := nextRegions 11 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_393 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 11 degreeUnionState43_392) - -def degreeUnionState43_394 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 11 degreeUnionState43_392) - -def degreeUnionState43_395 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 11 degreeUnionState43_392) - -def degreeUnionState43_396 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 11 degreeUnionState43_392) - -def degreeUnionState43_397 : List PrefixRegion := nextRegions 8 (liveRegions 9 32 11 degreeUnionState43_392) - -def degreeUnionState43_398 : List PrefixRegion := nextRegions 9 (liveRegions 9 32 11 degreeUnionState43_392) - -def degreeUnionState43_399 : List PrefixRegion := nextRegions 10 (liveRegions 9 32 11 degreeUnionState43_392) - -def degreeUnionState43_400 : List PrefixRegion := nextRegions 11 (liveRegions 9 32 11 degreeUnionState43_392) - -def degreeUnionState43_401 : List PrefixRegion := nextRegions 12 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_402 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 12 degreeUnionState43_401) - -def degreeUnionState43_403 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 12 degreeUnionState43_401) - -def degreeUnionState43_404 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 12 degreeUnionState43_401) - -def degreeUnionState43_405 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 12 degreeUnionState43_401) - -def degreeUnionState43_406 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 12 degreeUnionState43_401) - -def degreeUnionState43_407 : List PrefixRegion := nextRegions 9 (liveRegions 9 31 12 degreeUnionState43_401) - -def degreeUnionState43_408 : List PrefixRegion := nextRegions 10 (liveRegions 9 31 12 degreeUnionState43_401) - -def degreeUnionState43_409 : List PrefixRegion := nextRegions 11 (liveRegions 9 31 12 degreeUnionState43_401) - -def degreeUnionState43_410 : List PrefixRegion := nextRegions 12 (liveRegions 9 31 12 degreeUnionState43_401) - -def degreeUnionState43_411 : List PrefixRegion := nextRegions 13 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_412 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 13 degreeUnionState43_411) - -def degreeUnionState43_413 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 13 degreeUnionState43_411) - -def degreeUnionState43_414 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 13 degreeUnionState43_411) - -def degreeUnionState43_415 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 13 degreeUnionState43_411) - -def degreeUnionState43_416 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 13 degreeUnionState43_411) - -def degreeUnionState43_417 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 13 degreeUnionState43_411) - -def degreeUnionState43_418 : List PrefixRegion := nextRegions 10 (liveRegions 9 30 13 degreeUnionState43_411) - -def degreeUnionState43_419 : List PrefixRegion := nextRegions 11 (liveRegions 9 30 13 degreeUnionState43_411) - -def degreeUnionState43_420 : List PrefixRegion := nextRegions 12 (liveRegions 9 30 13 degreeUnionState43_411) - -def degreeUnionState43_421 : List PrefixRegion := nextRegions 13 (liveRegions 9 30 13 degreeUnionState43_411) - -def degreeUnionState43_422 : List PrefixRegion := nextRegions 14 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_423 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 14 degreeUnionState43_422) - -def degreeUnionState43_424 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 14 degreeUnionState43_422) - -def degreeUnionState43_425 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 14 degreeUnionState43_422) - -def degreeUnionState43_426 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 14 degreeUnionState43_422) - -def degreeUnionState43_427 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 14 degreeUnionState43_422) - -def degreeUnionState43_428 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 14 degreeUnionState43_422) - -def degreeUnionState43_429 : List PrefixRegion := nextRegions 10 (liveRegions 9 29 14 degreeUnionState43_422) - -def degreeUnionState43_430 : List PrefixRegion := nextRegions 11 (liveRegions 9 29 14 degreeUnionState43_422) - -def degreeUnionState43_431 : List PrefixRegion := nextRegions 12 (liveRegions 9 29 14 degreeUnionState43_422) - -def degreeUnionState43_432 : List PrefixRegion := nextRegions 13 (liveRegions 9 29 14 degreeUnionState43_422) - -def degreeUnionState43_433 : List PrefixRegion := nextRegions 14 (liveRegions 9 29 14 degreeUnionState43_422) - -def degreeUnionState43_434 : List PrefixRegion := nextRegions 15 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_435 : List PrefixRegion := nextRegions 4 (liveRegions 9 28 15 degreeUnionState43_434) - -def degreeUnionState43_436 : List PrefixRegion := nextRegions 5 (liveRegions 9 28 15 degreeUnionState43_434) - -def degreeUnionState43_437 : List PrefixRegion := nextRegions 6 (liveRegions 9 28 15 degreeUnionState43_434) - -def degreeUnionState43_438 : List PrefixRegion := nextRegions 7 (liveRegions 9 28 15 degreeUnionState43_434) - -def degreeUnionState43_439 : List PrefixRegion := nextRegions 8 (liveRegions 9 28 15 degreeUnionState43_434) - -def degreeUnionState43_440 : List PrefixRegion := nextRegions 9 (liveRegions 9 28 15 degreeUnionState43_434) - -def degreeUnionState43_441 : List PrefixRegion := nextRegions 10 (liveRegions 9 28 15 degreeUnionState43_434) - -def degreeUnionState43_442 : List PrefixRegion := nextRegions 11 (liveRegions 9 28 15 degreeUnionState43_434) - -def degreeUnionState43_443 : List PrefixRegion := nextRegions 12 (liveRegions 9 28 15 degreeUnionState43_434) - -def degreeUnionState43_444 : List PrefixRegion := nextRegions 13 (liveRegions 9 28 15 degreeUnionState43_434) - -def degreeUnionState43_445 : List PrefixRegion := nextRegions 14 (liveRegions 9 28 15 degreeUnionState43_434) - -def degreeUnionState43_446 : List PrefixRegion := nextRegions 15 (liveRegions 9 28 15 degreeUnionState43_434) - -def degreeUnionState43_447 : List PrefixRegion := nextRegions 16 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_448 : List PrefixRegion := nextRegions 3 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_449 : List PrefixRegion := nextRegions 4 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_450 : List PrefixRegion := nextRegions 5 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_451 : List PrefixRegion := nextRegions 6 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_452 : List PrefixRegion := nextRegions 7 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_453 : List PrefixRegion := nextRegions 8 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_454 : List PrefixRegion := nextRegions 9 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_455 : List PrefixRegion := nextRegions 10 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_456 : List PrefixRegion := nextRegions 11 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_457 : List PrefixRegion := nextRegions 12 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_458 : List PrefixRegion := nextRegions 13 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_459 : List PrefixRegion := nextRegions 14 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_460 : List PrefixRegion := nextRegions 15 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_461 : List PrefixRegion := nextRegions 16 (liveRegions 9 27 16 degreeUnionState43_447) - -def degreeUnionState43_462 : List PrefixRegion := nextRegions 17 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_463 : List PrefixRegion := nextRegions 3 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_464 : List PrefixRegion := nextRegions 4 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_465 : List PrefixRegion := nextRegions 5 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_466 : List PrefixRegion := nextRegions 6 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_467 : List PrefixRegion := nextRegions 7 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_468 : List PrefixRegion := nextRegions 8 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_469 : List PrefixRegion := nextRegions 9 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_470 : List PrefixRegion := nextRegions 10 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_471 : List PrefixRegion := nextRegions 11 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_472 : List PrefixRegion := nextRegions 12 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_473 : List PrefixRegion := nextRegions 13 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_474 : List PrefixRegion := nextRegions 14 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_475 : List PrefixRegion := nextRegions 15 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_476 : List PrefixRegion := nextRegions 16 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_477 : List PrefixRegion := nextRegions 17 (liveRegions 9 26 17 degreeUnionState43_462) - -def degreeUnionState43_478 : List PrefixRegion := nextRegions 18 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_479 : List PrefixRegion := nextRegions 3 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_480 : List PrefixRegion := nextRegions 4 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_481 : List PrefixRegion := nextRegions 5 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_482 : List PrefixRegion := nextRegions 6 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_483 : List PrefixRegion := nextRegions 7 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_484 : List PrefixRegion := nextRegions 8 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_485 : List PrefixRegion := nextRegions 9 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_486 : List PrefixRegion := nextRegions 10 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_487 : List PrefixRegion := nextRegions 11 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_488 : List PrefixRegion := nextRegions 12 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_489 : List PrefixRegion := nextRegions 13 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_490 : List PrefixRegion := nextRegions 14 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_491 : List PrefixRegion := nextRegions 15 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_492 : List PrefixRegion := nextRegions 16 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_493 : List PrefixRegion := nextRegions 17 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_494 : List PrefixRegion := nextRegions 18 (liveRegions 9 25 18 degreeUnionState43_478) - -def degreeUnionState43_495 : List PrefixRegion := nextRegions 19 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_496 : List PrefixRegion := nextRegions 3 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_497 : List PrefixRegion := nextRegions 4 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_498 : List PrefixRegion := nextRegions 5 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_499 : List PrefixRegion := nextRegions 6 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_500 : List PrefixRegion := nextRegions 7 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_501 : List PrefixRegion := nextRegions 8 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_502 : List PrefixRegion := nextRegions 9 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_503 : List PrefixRegion := nextRegions 10 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_504 : List PrefixRegion := nextRegions 11 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_505 : List PrefixRegion := nextRegions 12 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_506 : List PrefixRegion := nextRegions 13 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_507 : List PrefixRegion := nextRegions 14 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_508 : List PrefixRegion := nextRegions 15 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_509 : List PrefixRegion := nextRegions 16 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_510 : List PrefixRegion := nextRegions 17 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_511 : List PrefixRegion := nextRegions 18 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_512 : List PrefixRegion := nextRegions 19 (liveRegions 9 24 19 degreeUnionState43_495) - -def degreeUnionState43_513 : List PrefixRegion := nextRegions 20 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_514 : List PrefixRegion := nextRegions 21 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_515 : List PrefixRegion := nextRegions 22 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_516 : List PrefixRegion := nextRegions 23 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_517 : List PrefixRegion := nextRegions 24 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_518 : List PrefixRegion := nextRegions 25 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_519 : List PrefixRegion := nextRegions 26 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_520 : List PrefixRegion := nextRegions 27 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_521 : List PrefixRegion := nextRegions 28 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_522 : List PrefixRegion := nextRegions 29 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_523 : List PrefixRegion := nextRegions 30 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_524 : List PrefixRegion := nextRegions 31 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_525 : List PrefixRegion := nextRegions 32 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_526 : List PrefixRegion := nextRegions 33 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_527 : List PrefixRegion := nextRegions 34 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_528 : List PrefixRegion := nextRegions 35 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_529 : List PrefixRegion := nextRegions 36 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_530 : List PrefixRegion := nextRegions 37 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_531 : List PrefixRegion := nextRegions 38 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_532 : List PrefixRegion := nextRegions 39 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_533 : List PrefixRegion := nextRegions 40 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_534 : List PrefixRegion := nextRegions 41 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_535 : List PrefixRegion := nextRegions 42 (liveRegions 10 43 42 degreeHalfRegions43) - -def degreeUnionState43_537 : List PrefixRegion := nextRegions 4 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_538 : List PrefixRegion := nextRegions 5 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_539 : List PrefixRegion := nextRegions 6 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_540 : List PrefixRegion := nextRegions 7 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_541 : List PrefixRegion := nextRegions 8 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_542 : List PrefixRegion := nextRegions 4 (liveRegions 10 35 8 degreeUnionState43_541) - -def degreeUnionState43_543 : List PrefixRegion := nextRegions 5 (liveRegions 10 35 8 degreeUnionState43_541) - -def degreeUnionState43_544 : List PrefixRegion := nextRegions 6 (liveRegions 10 35 8 degreeUnionState43_541) - -def degreeUnionState43_545 : List PrefixRegion := nextRegions 7 (liveRegions 10 35 8 degreeUnionState43_541) - -def degreeUnionState43_546 : List PrefixRegion := nextRegions 8 (liveRegions 10 35 8 degreeUnionState43_541) - -def degreeUnionState43_547 : List PrefixRegion := nextRegions 9 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_548 : List PrefixRegion := nextRegions 4 (liveRegions 10 34 9 degreeUnionState43_547) - -def degreeUnionState43_549 : List PrefixRegion := nextRegions 5 (liveRegions 10 34 9 degreeUnionState43_547) - -def degreeUnionState43_550 : List PrefixRegion := nextRegions 6 (liveRegions 10 34 9 degreeUnionState43_547) - -def degreeUnionState43_551 : List PrefixRegion := nextRegions 7 (liveRegions 10 34 9 degreeUnionState43_547) - -def degreeUnionState43_552 : List PrefixRegion := nextRegions 8 (liveRegions 10 34 9 degreeUnionState43_547) - -def degreeUnionState43_553 : List PrefixRegion := nextRegions 9 (liveRegions 10 34 9 degreeUnionState43_547) - -def degreeUnionState43_554 : List PrefixRegion := nextRegions 10 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_555 : List PrefixRegion := nextRegions 4 (liveRegions 10 33 10 degreeUnionState43_554) - -def degreeUnionState43_556 : List PrefixRegion := nextRegions 5 (liveRegions 10 33 10 degreeUnionState43_554) - -def degreeUnionState43_557 : List PrefixRegion := nextRegions 6 (liveRegions 10 33 10 degreeUnionState43_554) - -def degreeUnionState43_558 : List PrefixRegion := nextRegions 7 (liveRegions 10 33 10 degreeUnionState43_554) - -def degreeUnionState43_559 : List PrefixRegion := nextRegions 8 (liveRegions 10 33 10 degreeUnionState43_554) - -def degreeUnionState43_560 : List PrefixRegion := nextRegions 9 (liveRegions 10 33 10 degreeUnionState43_554) - -def degreeUnionState43_561 : List PrefixRegion := nextRegions 10 (liveRegions 10 33 10 degreeUnionState43_554) - -def degreeUnionState43_562 : List PrefixRegion := nextRegions 11 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_563 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 11 degreeUnionState43_562) - -def degreeUnionState43_564 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 11 degreeUnionState43_562) - -def degreeUnionState43_565 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 11 degreeUnionState43_562) - -def degreeUnionState43_566 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 11 degreeUnionState43_562) - -def degreeUnionState43_567 : List PrefixRegion := nextRegions 8 (liveRegions 10 32 11 degreeUnionState43_562) - -def degreeUnionState43_568 : List PrefixRegion := nextRegions 9 (liveRegions 10 32 11 degreeUnionState43_562) - -def degreeUnionState43_569 : List PrefixRegion := nextRegions 10 (liveRegions 10 32 11 degreeUnionState43_562) - -def degreeUnionState43_570 : List PrefixRegion := nextRegions 11 (liveRegions 10 32 11 degreeUnionState43_562) - -def degreeUnionState43_571 : List PrefixRegion := nextRegions 12 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_572 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 12 degreeUnionState43_571) - -def degreeUnionState43_573 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 12 degreeUnionState43_571) - -def degreeUnionState43_574 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 12 degreeUnionState43_571) - -def degreeUnionState43_575 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 12 degreeUnionState43_571) - -def degreeUnionState43_576 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 12 degreeUnionState43_571) - -def degreeUnionState43_577 : List PrefixRegion := nextRegions 9 (liveRegions 10 31 12 degreeUnionState43_571) - -def degreeUnionState43_578 : List PrefixRegion := nextRegions 10 (liveRegions 10 31 12 degreeUnionState43_571) - -def degreeUnionState43_579 : List PrefixRegion := nextRegions 11 (liveRegions 10 31 12 degreeUnionState43_571) - -def degreeUnionState43_580 : List PrefixRegion := nextRegions 12 (liveRegions 10 31 12 degreeUnionState43_571) - -def degreeUnionState43_581 : List PrefixRegion := nextRegions 13 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_582 : List PrefixRegion := nextRegions 14 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_583 : List PrefixRegion := nextRegions 15 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_584 : List PrefixRegion := nextRegions 16 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_585 : List PrefixRegion := nextRegions 17 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_586 : List PrefixRegion := nextRegions 18 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_587 : List PrefixRegion := nextRegions 19 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_588 : List PrefixRegion := nextRegions 20 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_589 : List PrefixRegion := nextRegions 21 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_590 : List PrefixRegion := nextRegions 22 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_591 : List PrefixRegion := nextRegions 23 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_592 : List PrefixRegion := nextRegions 24 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_593 : List PrefixRegion := nextRegions 25 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_594 : List PrefixRegion := nextRegions 26 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_595 : List PrefixRegion := nextRegions 27 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_596 : List PrefixRegion := nextRegions 28 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_597 : List PrefixRegion := nextRegions 29 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_598 : List PrefixRegion := nextRegions 30 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_599 : List PrefixRegion := nextRegions 31 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_600 : List PrefixRegion := nextRegions 32 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_601 : List PrefixRegion := nextRegions 33 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_602 : List PrefixRegion := nextRegions 34 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_603 : List PrefixRegion := nextRegions 35 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_604 : List PrefixRegion := nextRegions 36 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_605 : List PrefixRegion := nextRegions 37 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_606 : List PrefixRegion := nextRegions 38 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_607 : List PrefixRegion := nextRegions 39 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_608 : List PrefixRegion := nextRegions 40 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_609 : List PrefixRegion := nextRegions 41 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_610 : List PrefixRegion := nextRegions 42 (liveRegions 11 43 42 degreeHalfRegions43) - -def degreeUnionState43_612 : List PrefixRegion := nextRegions 4 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_613 : List PrefixRegion := nextRegions 5 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_614 : List PrefixRegion := nextRegions 6 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_615 : List PrefixRegion := nextRegions 7 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_616 : List PrefixRegion := nextRegions 8 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_617 : List PrefixRegion := nextRegions 9 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_618 : List PrefixRegion := nextRegions 4 (liveRegions 11 34 9 degreeUnionState43_617) - -def degreeUnionState43_619 : List PrefixRegion := nextRegions 5 (liveRegions 11 34 9 degreeUnionState43_617) - -def degreeUnionState43_620 : List PrefixRegion := nextRegions 6 (liveRegions 11 34 9 degreeUnionState43_617) - -def degreeUnionState43_621 : List PrefixRegion := nextRegions 7 (liveRegions 11 34 9 degreeUnionState43_617) - -def degreeUnionState43_622 : List PrefixRegion := nextRegions 8 (liveRegions 11 34 9 degreeUnionState43_617) - -def degreeUnionState43_623 : List PrefixRegion := nextRegions 9 (liveRegions 11 34 9 degreeUnionState43_617) - -def degreeUnionState43_624 : List PrefixRegion := nextRegions 10 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_625 : List PrefixRegion := nextRegions 3 (liveRegions 11 33 10 degreeUnionState43_624) - -def degreeUnionState43_626 : List PrefixRegion := nextRegions 4 (liveRegions 11 33 10 degreeUnionState43_624) - -def degreeUnionState43_627 : List PrefixRegion := nextRegions 5 (liveRegions 11 33 10 degreeUnionState43_624) - -def degreeUnionState43_628 : List PrefixRegion := nextRegions 6 (liveRegions 11 33 10 degreeUnionState43_624) - -def degreeUnionState43_629 : List PrefixRegion := nextRegions 7 (liveRegions 11 33 10 degreeUnionState43_624) - -def degreeUnionState43_630 : List PrefixRegion := nextRegions 8 (liveRegions 11 33 10 degreeUnionState43_624) - -def degreeUnionState43_631 : List PrefixRegion := nextRegions 9 (liveRegions 11 33 10 degreeUnionState43_624) - -def degreeUnionState43_632 : List PrefixRegion := nextRegions 10 (liveRegions 11 33 10 degreeUnionState43_624) - -def degreeUnionState43_633 : List PrefixRegion := nextRegions 11 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_634 : List PrefixRegion := nextRegions 3 (liveRegions 11 32 11 degreeUnionState43_633) - -def degreeUnionState43_635 : List PrefixRegion := nextRegions 4 (liveRegions 11 32 11 degreeUnionState43_633) - -def degreeUnionState43_636 : List PrefixRegion := nextRegions 5 (liveRegions 11 32 11 degreeUnionState43_633) - -def degreeUnionState43_637 : List PrefixRegion := nextRegions 6 (liveRegions 11 32 11 degreeUnionState43_633) - -def degreeUnionState43_638 : List PrefixRegion := nextRegions 7 (liveRegions 11 32 11 degreeUnionState43_633) - -def degreeUnionState43_639 : List PrefixRegion := nextRegions 8 (liveRegions 11 32 11 degreeUnionState43_633) - -def degreeUnionState43_640 : List PrefixRegion := nextRegions 9 (liveRegions 11 32 11 degreeUnionState43_633) - -def degreeUnionState43_641 : List PrefixRegion := nextRegions 10 (liveRegions 11 32 11 degreeUnionState43_633) - -def degreeUnionState43_642 : List PrefixRegion := nextRegions 11 (liveRegions 11 32 11 degreeUnionState43_633) - -def degreeUnionState43_643 : List PrefixRegion := nextRegions 12 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_644 : List PrefixRegion := nextRegions 3 (liveRegions 11 31 12 degreeUnionState43_643) - -def degreeUnionState43_645 : List PrefixRegion := nextRegions 4 (liveRegions 11 31 12 degreeUnionState43_643) - -def degreeUnionState43_646 : List PrefixRegion := nextRegions 5 (liveRegions 11 31 12 degreeUnionState43_643) - -def degreeUnionState43_647 : List PrefixRegion := nextRegions 6 (liveRegions 11 31 12 degreeUnionState43_643) - -def degreeUnionState43_648 : List PrefixRegion := nextRegions 7 (liveRegions 11 31 12 degreeUnionState43_643) - -def degreeUnionState43_649 : List PrefixRegion := nextRegions 8 (liveRegions 11 31 12 degreeUnionState43_643) - -def degreeUnionState43_650 : List PrefixRegion := nextRegions 9 (liveRegions 11 31 12 degreeUnionState43_643) - -def degreeUnionState43_651 : List PrefixRegion := nextRegions 10 (liveRegions 11 31 12 degreeUnionState43_643) - -def degreeUnionState43_652 : List PrefixRegion := nextRegions 11 (liveRegions 11 31 12 degreeUnionState43_643) - -def degreeUnionState43_653 : List PrefixRegion := nextRegions 12 (liveRegions 11 31 12 degreeUnionState43_643) - -def degreeUnionState43_654 : List PrefixRegion := nextRegions 13 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_655 : List PrefixRegion := nextRegions 14 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_656 : List PrefixRegion := nextRegions 15 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_657 : List PrefixRegion := nextRegions 16 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_658 : List PrefixRegion := nextRegions 17 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_659 : List PrefixRegion := nextRegions 18 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_660 : List PrefixRegion := nextRegions 19 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_661 : List PrefixRegion := nextRegions 20 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_662 : List PrefixRegion := nextRegions 21 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_663 : List PrefixRegion := nextRegions 22 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_664 : List PrefixRegion := nextRegions 23 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_665 : List PrefixRegion := nextRegions 24 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_666 : List PrefixRegion := nextRegions 25 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_667 : List PrefixRegion := nextRegions 26 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_668 : List PrefixRegion := nextRegions 27 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_669 : List PrefixRegion := nextRegions 28 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_670 : List PrefixRegion := nextRegions 29 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_671 : List PrefixRegion := nextRegions 30 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_672 : List PrefixRegion := nextRegions 31 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_673 : List PrefixRegion := nextRegions 32 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_674 : List PrefixRegion := nextRegions 33 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_675 : List PrefixRegion := nextRegions 34 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_676 : List PrefixRegion := nextRegions 35 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_677 : List PrefixRegion := nextRegions 36 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_678 : List PrefixRegion := nextRegions 37 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_679 : List PrefixRegion := nextRegions 38 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_680 : List PrefixRegion := nextRegions 39 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_681 : List PrefixRegion := nextRegions 40 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_682 : List PrefixRegion := nextRegions 41 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_683 : List PrefixRegion := nextRegions 42 (liveRegions 12 43 42 degreeHalfRegions43) - -def degreeUnionState43_685 : List PrefixRegion := nextRegions 4 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_686 : List PrefixRegion := nextRegions 5 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_687 : List PrefixRegion := nextRegions 6 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_688 : List PrefixRegion := nextRegions 7 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_689 : List PrefixRegion := nextRegions 8 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_690 : List PrefixRegion := nextRegions 9 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_691 : List PrefixRegion := nextRegions 10 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_692 : List PrefixRegion := nextRegions 3 (liveRegions 12 33 10 degreeUnionState43_691) - -def degreeUnionState43_693 : List PrefixRegion := nextRegions 4 (liveRegions 12 33 10 degreeUnionState43_691) - -def degreeUnionState43_694 : List PrefixRegion := nextRegions 5 (liveRegions 12 33 10 degreeUnionState43_691) - -def degreeUnionState43_695 : List PrefixRegion := nextRegions 6 (liveRegions 12 33 10 degreeUnionState43_691) - -def degreeUnionState43_696 : List PrefixRegion := nextRegions 7 (liveRegions 12 33 10 degreeUnionState43_691) - -def degreeUnionState43_697 : List PrefixRegion := nextRegions 8 (liveRegions 12 33 10 degreeUnionState43_691) - -def degreeUnionState43_698 : List PrefixRegion := nextRegions 9 (liveRegions 12 33 10 degreeUnionState43_691) - -def degreeUnionState43_699 : List PrefixRegion := nextRegions 10 (liveRegions 12 33 10 degreeUnionState43_691) - -def degreeUnionState43_700 : List PrefixRegion := nextRegions 11 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_701 : List PrefixRegion := nextRegions 12 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_702 : List PrefixRegion := nextRegions 13 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_703 : List PrefixRegion := nextRegions 14 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_704 : List PrefixRegion := nextRegions 15 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_705 : List PrefixRegion := nextRegions 16 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_706 : List PrefixRegion := nextRegions 17 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_707 : List PrefixRegion := nextRegions 18 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_708 : List PrefixRegion := nextRegions 19 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_709 : List PrefixRegion := nextRegions 20 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_710 : List PrefixRegion := nextRegions 21 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_711 : List PrefixRegion := nextRegions 22 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_712 : List PrefixRegion := nextRegions 23 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_713 : List PrefixRegion := nextRegions 24 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_714 : List PrefixRegion := nextRegions 25 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_715 : List PrefixRegion := nextRegions 26 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_716 : List PrefixRegion := nextRegions 27 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_717 : List PrefixRegion := nextRegions 28 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_718 : List PrefixRegion := nextRegions 29 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_719 : List PrefixRegion := nextRegions 30 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_720 : List PrefixRegion := nextRegions 31 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_721 : List PrefixRegion := nextRegions 32 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_722 : List PrefixRegion := nextRegions 33 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_723 : List PrefixRegion := nextRegions 34 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_724 : List PrefixRegion := nextRegions 35 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_725 : List PrefixRegion := nextRegions 36 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_726 : List PrefixRegion := nextRegions 37 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_727 : List PrefixRegion := nextRegions 38 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_728 : List PrefixRegion := nextRegions 39 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_729 : List PrefixRegion := nextRegions 40 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_730 : List PrefixRegion := nextRegions 41 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_731 : List PrefixRegion := nextRegions 42 (liveRegions 13 43 42 degreeHalfRegions43) - -def degreeUnionState43_733 : List PrefixRegion := nextRegions 4 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_734 : List PrefixRegion := nextRegions 5 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_735 : List PrefixRegion := nextRegions 6 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_736 : List PrefixRegion := nextRegions 7 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_737 : List PrefixRegion := nextRegions 8 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_738 : List PrefixRegion := nextRegions 9 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_739 : List PrefixRegion := nextRegions 10 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_740 : List PrefixRegion := nextRegions 11 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_741 : List PrefixRegion := nextRegions 12 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_742 : List PrefixRegion := nextRegions 13 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_743 : List PrefixRegion := nextRegions 14 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_744 : List PrefixRegion := nextRegions 15 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_745 : List PrefixRegion := nextRegions 16 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_746 : List PrefixRegion := nextRegions 17 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_747 : List PrefixRegion := nextRegions 18 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_748 : List PrefixRegion := nextRegions 19 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_749 : List PrefixRegion := nextRegions 20 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_750 : List PrefixRegion := nextRegions 21 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_751 : List PrefixRegion := nextRegions 22 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_752 : List PrefixRegion := nextRegions 23 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_753 : List PrefixRegion := nextRegions 24 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_754 : List PrefixRegion := nextRegions 25 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_755 : List PrefixRegion := nextRegions 26 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_756 : List PrefixRegion := nextRegions 27 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_757 : List PrefixRegion := nextRegions 28 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_758 : List PrefixRegion := nextRegions 29 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_759 : List PrefixRegion := nextRegions 30 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_760 : List PrefixRegion := nextRegions 31 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_761 : List PrefixRegion := nextRegions 32 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_762 : List PrefixRegion := nextRegions 33 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_763 : List PrefixRegion := nextRegions 34 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_764 : List PrefixRegion := nextRegions 35 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_765 : List PrefixRegion := nextRegions 36 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_766 : List PrefixRegion := nextRegions 37 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_767 : List PrefixRegion := nextRegions 38 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_768 : List PrefixRegion := nextRegions 39 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_769 : List PrefixRegion := nextRegions 40 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_770 : List PrefixRegion := nextRegions 41 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_771 : List PrefixRegion := nextRegions 42 (liveRegions 14 43 42 degreeHalfRegions43) - -def degreeUnionState43_773 : List PrefixRegion := nextRegions 3 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_774 : List PrefixRegion := nextRegions 4 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_775 : List PrefixRegion := nextRegions 5 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_776 : List PrefixRegion := nextRegions 6 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_777 : List PrefixRegion := nextRegions 7 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_778 : List PrefixRegion := nextRegions 8 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_779 : List PrefixRegion := nextRegions 9 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_780 : List PrefixRegion := nextRegions 10 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_781 : List PrefixRegion := nextRegions 11 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_782 : List PrefixRegion := nextRegions 12 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_783 : List PrefixRegion := nextRegions 13 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_784 : List PrefixRegion := nextRegions 14 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_785 : List PrefixRegion := nextRegions 15 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_786 : List PrefixRegion := nextRegions 16 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_787 : List PrefixRegion := nextRegions 17 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_788 : List PrefixRegion := nextRegions 18 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_789 : List PrefixRegion := nextRegions 19 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_790 : List PrefixRegion := nextRegions 20 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_791 : List PrefixRegion := nextRegions 21 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_792 : List PrefixRegion := nextRegions 22 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_793 : List PrefixRegion := nextRegions 23 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_794 : List PrefixRegion := nextRegions 24 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_795 : List PrefixRegion := nextRegions 25 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_796 : List PrefixRegion := nextRegions 26 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_797 : List PrefixRegion := nextRegions 27 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_798 : List PrefixRegion := nextRegions 28 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_799 : List PrefixRegion := nextRegions 29 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_800 : List PrefixRegion := nextRegions 30 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_801 : List PrefixRegion := nextRegions 31 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_802 : List PrefixRegion := nextRegions 32 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_803 : List PrefixRegion := nextRegions 33 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_804 : List PrefixRegion := nextRegions 34 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_805 : List PrefixRegion := nextRegions 35 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_806 : List PrefixRegion := nextRegions 36 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_807 : List PrefixRegion := nextRegions 37 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_808 : List PrefixRegion := nextRegions 38 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_809 : List PrefixRegion := nextRegions 39 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_810 : List PrefixRegion := nextRegions 40 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_811 : List PrefixRegion := nextRegions 41 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_812 : List PrefixRegion := nextRegions 42 (liveRegions 15 43 42 degreeHalfRegions43) - -def degreeUnionState43_814 : List PrefixRegion := nextRegions 3 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_815 : List PrefixRegion := nextRegions 4 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_816 : List PrefixRegion := nextRegions 5 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_817 : List PrefixRegion := nextRegions 6 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_818 : List PrefixRegion := nextRegions 7 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_819 : List PrefixRegion := nextRegions 8 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_820 : List PrefixRegion := nextRegions 9 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_821 : List PrefixRegion := nextRegions 10 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_822 : List PrefixRegion := nextRegions 11 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_823 : List PrefixRegion := nextRegions 12 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_824 : List PrefixRegion := nextRegions 13 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_825 : List PrefixRegion := nextRegions 14 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_826 : List PrefixRegion := nextRegions 15 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_827 : List PrefixRegion := nextRegions 16 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_828 : List PrefixRegion := nextRegions 17 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_829 : List PrefixRegion := nextRegions 18 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_830 : List PrefixRegion := nextRegions 19 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_831 : List PrefixRegion := nextRegions 20 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_832 : List PrefixRegion := nextRegions 21 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_833 : List PrefixRegion := nextRegions 22 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_834 : List PrefixRegion := nextRegions 23 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_835 : List PrefixRegion := nextRegions 24 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_836 : List PrefixRegion := nextRegions 25 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_837 : List PrefixRegion := nextRegions 26 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_838 : List PrefixRegion := nextRegions 27 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_839 : List PrefixRegion := nextRegions 28 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_840 : List PrefixRegion := nextRegions 29 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_841 : List PrefixRegion := nextRegions 30 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_842 : List PrefixRegion := nextRegions 31 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_843 : List PrefixRegion := nextRegions 32 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_844 : List PrefixRegion := nextRegions 33 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_845 : List PrefixRegion := nextRegions 34 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_846 : List PrefixRegion := nextRegions 35 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_847 : List PrefixRegion := nextRegions 36 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_848 : List PrefixRegion := nextRegions 37 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_849 : List PrefixRegion := nextRegions 38 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_850 : List PrefixRegion := nextRegions 39 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_851 : List PrefixRegion := nextRegions 40 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_852 : List PrefixRegion := nextRegions 41 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_853 : List PrefixRegion := nextRegions 42 (liveRegions 16 43 42 degreeHalfRegions43) - -def degreeUnionState43_855 : List PrefixRegion := nextRegions 3 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_856 : List PrefixRegion := nextRegions 4 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_857 : List PrefixRegion := nextRegions 5 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_858 : List PrefixRegion := nextRegions 6 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_859 : List PrefixRegion := nextRegions 7 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_860 : List PrefixRegion := nextRegions 8 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_861 : List PrefixRegion := nextRegions 9 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_862 : List PrefixRegion := nextRegions 10 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_863 : List PrefixRegion := nextRegions 11 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_864 : List PrefixRegion := nextRegions 12 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_865 : List PrefixRegion := nextRegions 13 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_866 : List PrefixRegion := nextRegions 14 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_867 : List PrefixRegion := nextRegions 15 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_868 : List PrefixRegion := nextRegions 16 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_869 : List PrefixRegion := nextRegions 17 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_870 : List PrefixRegion := nextRegions 18 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_871 : List PrefixRegion := nextRegions 19 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_872 : List PrefixRegion := nextRegions 20 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_873 : List PrefixRegion := nextRegions 21 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_874 : List PrefixRegion := nextRegions 22 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_875 : List PrefixRegion := nextRegions 23 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_876 : List PrefixRegion := nextRegions 24 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_877 : List PrefixRegion := nextRegions 25 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_878 : List PrefixRegion := nextRegions 26 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_879 : List PrefixRegion := nextRegions 27 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_880 : List PrefixRegion := nextRegions 28 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_881 : List PrefixRegion := nextRegions 29 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_882 : List PrefixRegion := nextRegions 30 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_883 : List PrefixRegion := nextRegions 31 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_884 : List PrefixRegion := nextRegions 32 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_885 : List PrefixRegion := nextRegions 33 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_886 : List PrefixRegion := nextRegions 34 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_887 : List PrefixRegion := nextRegions 35 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_888 : List PrefixRegion := nextRegions 36 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_889 : List PrefixRegion := nextRegions 37 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_890 : List PrefixRegion := nextRegions 38 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_891 : List PrefixRegion := nextRegions 39 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_892 : List PrefixRegion := nextRegions 40 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_893 : List PrefixRegion := nextRegions 41 (liveRegions 17 43 42 degreeHalfRegions43) - -def degreeUnionState43_894 : List PrefixRegion := nextRegions 42 (liveRegions 17 43 42 degreeHalfRegions43) - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData43 + +namespace OAI + +/-! Degree Union States 43. -/ + +section + +namespace UniversalTensorSquare + +def degreeUnionState43_9 : List PrefixRegion := nextRegions 6 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_10 : List PrefixRegion := nextRegions 7 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_11 : List PrefixRegion := nextRegions 8 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_12 : List PrefixRegion := nextRegions 5 (liveRegions 7 35 8 degreeUnionState43_11) + +def degreeUnionState43_13 : List PrefixRegion := nextRegions 6 (liveRegions 7 35 8 degreeUnionState43_11) + +def degreeUnionState43_14 : List PrefixRegion := nextRegions 7 (liveRegions 7 35 8 degreeUnionState43_11) + +def degreeUnionState43_15 : List PrefixRegion := nextRegions 8 (liveRegions 7 35 8 degreeUnionState43_11) + +def degreeUnionState43_16 : List PrefixRegion := nextRegions 9 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_17 : List PrefixRegion := nextRegions 5 (liveRegions 7 34 9 degreeUnionState43_16) + +def degreeUnionState43_18 : List PrefixRegion := nextRegions 6 (liveRegions 7 34 9 degreeUnionState43_16) + +def degreeUnionState43_19 : List PrefixRegion := nextRegions 7 (liveRegions 7 34 9 degreeUnionState43_16) + +def degreeUnionState43_20 : List PrefixRegion := nextRegions 8 (liveRegions 7 34 9 degreeUnionState43_16) + +def degreeUnionState43_21 : List PrefixRegion := nextRegions 9 (liveRegions 7 34 9 degreeUnionState43_16) + +def degreeUnionState43_22 : List PrefixRegion := nextRegions 10 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_23 : List PrefixRegion := nextRegions 5 (liveRegions 7 33 10 degreeUnionState43_22) + +def degreeUnionState43_24 : List PrefixRegion := nextRegions 6 (liveRegions 7 33 10 degreeUnionState43_22) + +def degreeUnionState43_25 : List PrefixRegion := nextRegions 7 (liveRegions 7 33 10 degreeUnionState43_22) + +def degreeUnionState43_26 : List PrefixRegion := nextRegions 8 (liveRegions 7 33 10 degreeUnionState43_22) + +def degreeUnionState43_27 : List PrefixRegion := nextRegions 9 (liveRegions 7 33 10 degreeUnionState43_22) + +def degreeUnionState43_28 : List PrefixRegion := nextRegions 10 (liveRegions 7 33 10 degreeUnionState43_22) + +def degreeUnionState43_29 : List PrefixRegion := nextRegions 11 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_30 : List PrefixRegion := nextRegions 5 (liveRegions 7 32 11 degreeUnionState43_29) + +def degreeUnionState43_31 : List PrefixRegion := nextRegions 6 (liveRegions 7 32 11 degreeUnionState43_29) + +def degreeUnionState43_32 : List PrefixRegion := nextRegions 7 (liveRegions 7 32 11 degreeUnionState43_29) + +def degreeUnionState43_33 : List PrefixRegion := nextRegions 8 (liveRegions 7 32 11 degreeUnionState43_29) + +def degreeUnionState43_34 : List PrefixRegion := nextRegions 9 (liveRegions 7 32 11 degreeUnionState43_29) + +def degreeUnionState43_35 : List PrefixRegion := nextRegions 10 (liveRegions 7 32 11 degreeUnionState43_29) + +def degreeUnionState43_36 : List PrefixRegion := nextRegions 11 (liveRegions 7 32 11 degreeUnionState43_29) + +def degreeUnionState43_37 : List PrefixRegion := nextRegions 12 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_38 : List PrefixRegion := nextRegions 5 (liveRegions 7 31 12 degreeUnionState43_37) + +def degreeUnionState43_39 : List PrefixRegion := nextRegions 6 (liveRegions 7 31 12 degreeUnionState43_37) + +def degreeUnionState43_40 : List PrefixRegion := nextRegions 7 (liveRegions 7 31 12 degreeUnionState43_37) + +def degreeUnionState43_41 : List PrefixRegion := nextRegions 8 (liveRegions 7 31 12 degreeUnionState43_37) + +def degreeUnionState43_42 : List PrefixRegion := nextRegions 9 (liveRegions 7 31 12 degreeUnionState43_37) + +def degreeUnionState43_43 : List PrefixRegion := nextRegions 10 (liveRegions 7 31 12 degreeUnionState43_37) + +def degreeUnionState43_44 : List PrefixRegion := nextRegions 11 (liveRegions 7 31 12 degreeUnionState43_37) + +def degreeUnionState43_45 : List PrefixRegion := nextRegions 12 (liveRegions 7 31 12 degreeUnionState43_37) + +def degreeUnionState43_46 : List PrefixRegion := nextRegions 13 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_47 : List PrefixRegion := nextRegions 5 (liveRegions 7 30 13 degreeUnionState43_46) + +def degreeUnionState43_48 : List PrefixRegion := nextRegions 6 (liveRegions 7 30 13 degreeUnionState43_46) + +def degreeUnionState43_49 : List PrefixRegion := nextRegions 7 (liveRegions 7 30 13 degreeUnionState43_46) + +def degreeUnionState43_50 : List PrefixRegion := nextRegions 8 (liveRegions 7 30 13 degreeUnionState43_46) + +def degreeUnionState43_51 : List PrefixRegion := nextRegions 9 (liveRegions 7 30 13 degreeUnionState43_46) + +def degreeUnionState43_52 : List PrefixRegion := nextRegions 10 (liveRegions 7 30 13 degreeUnionState43_46) + +def degreeUnionState43_53 : List PrefixRegion := nextRegions 11 (liveRegions 7 30 13 degreeUnionState43_46) + +def degreeUnionState43_54 : List PrefixRegion := nextRegions 12 (liveRegions 7 30 13 degreeUnionState43_46) + +def degreeUnionState43_55 : List PrefixRegion := nextRegions 13 (liveRegions 7 30 13 degreeUnionState43_46) + +def degreeUnionState43_56 : List PrefixRegion := nextRegions 14 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_57 : List PrefixRegion := nextRegions 5 (liveRegions 7 29 14 degreeUnionState43_56) + +def degreeUnionState43_58 : List PrefixRegion := nextRegions 6 (liveRegions 7 29 14 degreeUnionState43_56) + +def degreeUnionState43_59 : List PrefixRegion := nextRegions 7 (liveRegions 7 29 14 degreeUnionState43_56) + +def degreeUnionState43_60 : List PrefixRegion := nextRegions 8 (liveRegions 7 29 14 degreeUnionState43_56) + +def degreeUnionState43_61 : List PrefixRegion := nextRegions 9 (liveRegions 7 29 14 degreeUnionState43_56) + +def degreeUnionState43_62 : List PrefixRegion := nextRegions 10 (liveRegions 7 29 14 degreeUnionState43_56) + +def degreeUnionState43_63 : List PrefixRegion := nextRegions 11 (liveRegions 7 29 14 degreeUnionState43_56) + +def degreeUnionState43_64 : List PrefixRegion := nextRegions 12 (liveRegions 7 29 14 degreeUnionState43_56) + +def degreeUnionState43_65 : List PrefixRegion := nextRegions 13 (liveRegions 7 29 14 degreeUnionState43_56) + +def degreeUnionState43_66 : List PrefixRegion := nextRegions 14 (liveRegions 7 29 14 degreeUnionState43_56) + +def degreeUnionState43_67 : List PrefixRegion := nextRegions 15 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_68 : List PrefixRegion := nextRegions 4 (liveRegions 7 28 15 degreeUnionState43_67) + +def degreeUnionState43_69 : List PrefixRegion := nextRegions 5 (liveRegions 7 28 15 degreeUnionState43_67) + +def degreeUnionState43_70 : List PrefixRegion := nextRegions 6 (liveRegions 7 28 15 degreeUnionState43_67) + +def degreeUnionState43_71 : List PrefixRegion := nextRegions 7 (liveRegions 7 28 15 degreeUnionState43_67) + +def degreeUnionState43_72 : List PrefixRegion := nextRegions 8 (liveRegions 7 28 15 degreeUnionState43_67) + +def degreeUnionState43_73 : List PrefixRegion := nextRegions 9 (liveRegions 7 28 15 degreeUnionState43_67) + +def degreeUnionState43_74 : List PrefixRegion := nextRegions 10 (liveRegions 7 28 15 degreeUnionState43_67) + +def degreeUnionState43_75 : List PrefixRegion := nextRegions 11 (liveRegions 7 28 15 degreeUnionState43_67) + +def degreeUnionState43_76 : List PrefixRegion := nextRegions 12 (liveRegions 7 28 15 degreeUnionState43_67) + +def degreeUnionState43_77 : List PrefixRegion := nextRegions 13 (liveRegions 7 28 15 degreeUnionState43_67) + +def degreeUnionState43_78 : List PrefixRegion := nextRegions 14 (liveRegions 7 28 15 degreeUnionState43_67) + +def degreeUnionState43_79 : List PrefixRegion := nextRegions 15 (liveRegions 7 28 15 degreeUnionState43_67) + +def degreeUnionState43_80 : List PrefixRegion := nextRegions 16 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_81 : List PrefixRegion := nextRegions 4 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_82 : List PrefixRegion := nextRegions 5 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_83 : List PrefixRegion := nextRegions 6 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_84 : List PrefixRegion := nextRegions 7 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_85 : List PrefixRegion := nextRegions 8 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_86 : List PrefixRegion := nextRegions 9 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_87 : List PrefixRegion := nextRegions 10 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_88 : List PrefixRegion := nextRegions 11 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_89 : List PrefixRegion := nextRegions 12 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_90 : List PrefixRegion := nextRegions 13 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_91 : List PrefixRegion := nextRegions 14 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_92 : List PrefixRegion := nextRegions 15 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_93 : List PrefixRegion := nextRegions 16 (liveRegions 7 27 16 degreeUnionState43_80) + +def degreeUnionState43_94 : List PrefixRegion := nextRegions 17 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_95 : List PrefixRegion := nextRegions 4 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_96 : List PrefixRegion := nextRegions 5 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_97 : List PrefixRegion := nextRegions 6 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_98 : List PrefixRegion := nextRegions 7 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_99 : List PrefixRegion := nextRegions 8 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_100 : List PrefixRegion := nextRegions 9 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_101 : List PrefixRegion := nextRegions 10 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_102 : List PrefixRegion := nextRegions 11 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_103 : List PrefixRegion := nextRegions 12 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_104 : List PrefixRegion := nextRegions 13 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_105 : List PrefixRegion := nextRegions 14 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_106 : List PrefixRegion := nextRegions 15 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_107 : List PrefixRegion := nextRegions 16 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_108 : List PrefixRegion := nextRegions 17 (liveRegions 7 26 17 degreeUnionState43_94) + +def degreeUnionState43_109 : List PrefixRegion := nextRegions 18 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_110 : List PrefixRegion := nextRegions 4 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_111 : List PrefixRegion := nextRegions 5 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_112 : List PrefixRegion := nextRegions 6 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_113 : List PrefixRegion := nextRegions 7 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_114 : List PrefixRegion := nextRegions 8 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_115 : List PrefixRegion := nextRegions 9 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_116 : List PrefixRegion := nextRegions 10 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_117 : List PrefixRegion := nextRegions 11 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_118 : List PrefixRegion := nextRegions 12 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_119 : List PrefixRegion := nextRegions 13 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_120 : List PrefixRegion := nextRegions 14 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_121 : List PrefixRegion := nextRegions 15 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_122 : List PrefixRegion := nextRegions 16 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_123 : List PrefixRegion := nextRegions 17 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_124 : List PrefixRegion := nextRegions 18 (liveRegions 7 25 18 degreeUnionState43_109) + +def degreeUnionState43_125 : List PrefixRegion := nextRegions 19 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_126 : List PrefixRegion := nextRegions 4 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_127 : List PrefixRegion := nextRegions 5 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_128 : List PrefixRegion := nextRegions 6 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_129 : List PrefixRegion := nextRegions 7 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_130 : List PrefixRegion := nextRegions 8 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_131 : List PrefixRegion := nextRegions 9 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_132 : List PrefixRegion := nextRegions 10 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_133 : List PrefixRegion := nextRegions 11 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_134 : List PrefixRegion := nextRegions 12 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_135 : List PrefixRegion := nextRegions 13 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_136 : List PrefixRegion := nextRegions 14 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_137 : List PrefixRegion := nextRegions 15 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_138 : List PrefixRegion := nextRegions 16 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_139 : List PrefixRegion := nextRegions 17 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_140 : List PrefixRegion := nextRegions 18 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_141 : List PrefixRegion := nextRegions 19 (liveRegions 7 24 19 degreeUnionState43_125) + +def degreeUnionState43_142 : List PrefixRegion := nextRegions 20 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_143 : List PrefixRegion := nextRegions 4 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_144 : List PrefixRegion := nextRegions 5 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_145 : List PrefixRegion := nextRegions 6 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_146 : List PrefixRegion := nextRegions 7 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_147 : List PrefixRegion := nextRegions 8 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_148 : List PrefixRegion := nextRegions 9 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_149 : List PrefixRegion := nextRegions 10 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_150 : List PrefixRegion := nextRegions 11 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_151 : List PrefixRegion := nextRegions 12 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_152 : List PrefixRegion := nextRegions 13 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_153 : List PrefixRegion := nextRegions 14 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_154 : List PrefixRegion := nextRegions 15 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_155 : List PrefixRegion := nextRegions 16 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_156 : List PrefixRegion := nextRegions 17 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_157 : List PrefixRegion := nextRegions 18 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_158 : List PrefixRegion := nextRegions 19 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_159 : List PrefixRegion := nextRegions 20 (liveRegions 7 23 20 degreeUnionState43_142) + +def degreeUnionState43_160 : List PrefixRegion := nextRegions 21 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_161 : List PrefixRegion := nextRegions 22 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_162 : List PrefixRegion := nextRegions 23 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_163 : List PrefixRegion := nextRegions 24 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_164 : List PrefixRegion := nextRegions 25 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_165 : List PrefixRegion := nextRegions 26 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_166 : List PrefixRegion := nextRegions 27 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_167 : List PrefixRegion := nextRegions 28 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_168 : List PrefixRegion := nextRegions 29 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_169 : List PrefixRegion := nextRegions 30 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_170 : List PrefixRegion := nextRegions 31 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_171 : List PrefixRegion := nextRegions 32 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_172 : List PrefixRegion := nextRegions 33 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_173 : List PrefixRegion := nextRegions 34 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_174 : List PrefixRegion := nextRegions 35 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_175 : List PrefixRegion := nextRegions 36 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_176 : List PrefixRegion := nextRegions 37 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_177 : List PrefixRegion := nextRegions 38 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_178 : List PrefixRegion := nextRegions 39 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_179 : List PrefixRegion := nextRegions 40 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_180 : List PrefixRegion := nextRegions 41 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_181 : List PrefixRegion := nextRegions 42 (liveRegions 8 43 42 degreeHalfRegions43) + +def degreeUnionState43_183 : List PrefixRegion := nextRegions 5 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_184 : List PrefixRegion := nextRegions 6 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_185 : List PrefixRegion := nextRegions 7 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_186 : List PrefixRegion := nextRegions 8 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_187 : List PrefixRegion := nextRegions 5 (liveRegions 8 35 8 degreeUnionState43_186) + +def degreeUnionState43_188 : List PrefixRegion := nextRegions 6 (liveRegions 8 35 8 degreeUnionState43_186) + +def degreeUnionState43_189 : List PrefixRegion := nextRegions 7 (liveRegions 8 35 8 degreeUnionState43_186) + +def degreeUnionState43_190 : List PrefixRegion := nextRegions 8 (liveRegions 8 35 8 degreeUnionState43_186) + +def degreeUnionState43_191 : List PrefixRegion := nextRegions 9 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_192 : List PrefixRegion := nextRegions 5 (liveRegions 8 34 9 degreeUnionState43_191) + +def degreeUnionState43_193 : List PrefixRegion := nextRegions 6 (liveRegions 8 34 9 degreeUnionState43_191) + +def degreeUnionState43_194 : List PrefixRegion := nextRegions 7 (liveRegions 8 34 9 degreeUnionState43_191) + +def degreeUnionState43_195 : List PrefixRegion := nextRegions 8 (liveRegions 8 34 9 degreeUnionState43_191) + +def degreeUnionState43_196 : List PrefixRegion := nextRegions 9 (liveRegions 8 34 9 degreeUnionState43_191) + +def degreeUnionState43_197 : List PrefixRegion := nextRegions 4 (liveRegions 7 25 9 degreeUnionState43_196) + +def degreeUnionState43_198 : List PrefixRegion := nextRegions 5 (liveRegions 7 25 9 degreeUnionState43_196) + +def degreeUnionState43_199 : List PrefixRegion := nextRegions 6 (liveRegions 7 25 9 degreeUnionState43_196) + +def degreeUnionState43_200 : List PrefixRegion := nextRegions 7 (liveRegions 7 25 9 degreeUnionState43_196) + +def degreeUnionState43_201 : List PrefixRegion := nextRegions 8 (liveRegions 7 25 9 degreeUnionState43_196) + +def degreeUnionState43_202 : List PrefixRegion := nextRegions 9 (liveRegions 7 25 9 degreeUnionState43_196) + +def degreeUnionState43_203 : List PrefixRegion := nextRegions 10 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_204 : List PrefixRegion := nextRegions 5 (liveRegions 8 33 10 degreeUnionState43_203) + +def degreeUnionState43_205 : List PrefixRegion := nextRegions 6 (liveRegions 8 33 10 degreeUnionState43_203) + +def degreeUnionState43_206 : List PrefixRegion := nextRegions 7 (liveRegions 8 33 10 degreeUnionState43_203) + +def degreeUnionState43_207 : List PrefixRegion := nextRegions 8 (liveRegions 8 33 10 degreeUnionState43_203) + +def degreeUnionState43_208 : List PrefixRegion := nextRegions 9 (liveRegions 8 33 10 degreeUnionState43_203) + +def degreeUnionState43_209 : List PrefixRegion := nextRegions 10 (liveRegions 8 33 10 degreeUnionState43_203) + +def degreeUnionState43_210 : List PrefixRegion := nextRegions 11 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_211 : List PrefixRegion := nextRegions 4 (liveRegions 8 32 11 degreeUnionState43_210) + +def degreeUnionState43_212 : List PrefixRegion := nextRegions 5 (liveRegions 8 32 11 degreeUnionState43_210) + +def degreeUnionState43_213 : List PrefixRegion := nextRegions 6 (liveRegions 8 32 11 degreeUnionState43_210) + +def degreeUnionState43_214 : List PrefixRegion := nextRegions 7 (liveRegions 8 32 11 degreeUnionState43_210) + +def degreeUnionState43_215 : List PrefixRegion := nextRegions 8 (liveRegions 8 32 11 degreeUnionState43_210) + +def degreeUnionState43_216 : List PrefixRegion := nextRegions 9 (liveRegions 8 32 11 degreeUnionState43_210) + +def degreeUnionState43_217 : List PrefixRegion := nextRegions 10 (liveRegions 8 32 11 degreeUnionState43_210) + +def degreeUnionState43_218 : List PrefixRegion := nextRegions 11 (liveRegions 8 32 11 degreeUnionState43_210) + +def degreeUnionState43_219 : List PrefixRegion := nextRegions 12 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_220 : List PrefixRegion := nextRegions 4 (liveRegions 8 31 12 degreeUnionState43_219) + +def degreeUnionState43_221 : List PrefixRegion := nextRegions 5 (liveRegions 8 31 12 degreeUnionState43_219) + +def degreeUnionState43_222 : List PrefixRegion := nextRegions 6 (liveRegions 8 31 12 degreeUnionState43_219) + +def degreeUnionState43_223 : List PrefixRegion := nextRegions 7 (liveRegions 8 31 12 degreeUnionState43_219) + +def degreeUnionState43_224 : List PrefixRegion := nextRegions 8 (liveRegions 8 31 12 degreeUnionState43_219) + +def degreeUnionState43_225 : List PrefixRegion := nextRegions 9 (liveRegions 8 31 12 degreeUnionState43_219) + +def degreeUnionState43_226 : List PrefixRegion := nextRegions 10 (liveRegions 8 31 12 degreeUnionState43_219) + +def degreeUnionState43_227 : List PrefixRegion := nextRegions 11 (liveRegions 8 31 12 degreeUnionState43_219) + +def degreeUnionState43_228 : List PrefixRegion := nextRegions 12 (liveRegions 8 31 12 degreeUnionState43_219) + +def degreeUnionState43_229 : List PrefixRegion := nextRegions 13 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_230 : List PrefixRegion := nextRegions 4 (liveRegions 8 30 13 degreeUnionState43_229) + +def degreeUnionState43_231 : List PrefixRegion := nextRegions 5 (liveRegions 8 30 13 degreeUnionState43_229) + +def degreeUnionState43_232 : List PrefixRegion := nextRegions 6 (liveRegions 8 30 13 degreeUnionState43_229) + +def degreeUnionState43_233 : List PrefixRegion := nextRegions 7 (liveRegions 8 30 13 degreeUnionState43_229) + +def degreeUnionState43_234 : List PrefixRegion := nextRegions 8 (liveRegions 8 30 13 degreeUnionState43_229) + +def degreeUnionState43_235 : List PrefixRegion := nextRegions 9 (liveRegions 8 30 13 degreeUnionState43_229) + +def degreeUnionState43_236 : List PrefixRegion := nextRegions 10 (liveRegions 8 30 13 degreeUnionState43_229) + +def degreeUnionState43_237 : List PrefixRegion := nextRegions 11 (liveRegions 8 30 13 degreeUnionState43_229) + +def degreeUnionState43_238 : List PrefixRegion := nextRegions 12 (liveRegions 8 30 13 degreeUnionState43_229) + +def degreeUnionState43_239 : List PrefixRegion := nextRegions 13 (liveRegions 8 30 13 degreeUnionState43_229) + +def degreeUnionState43_240 : List PrefixRegion := nextRegions 14 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_241 : List PrefixRegion := nextRegions 4 (liveRegions 8 29 14 degreeUnionState43_240) + +def degreeUnionState43_242 : List PrefixRegion := nextRegions 5 (liveRegions 8 29 14 degreeUnionState43_240) + +def degreeUnionState43_243 : List PrefixRegion := nextRegions 6 (liveRegions 8 29 14 degreeUnionState43_240) + +def degreeUnionState43_244 : List PrefixRegion := nextRegions 7 (liveRegions 8 29 14 degreeUnionState43_240) + +def degreeUnionState43_245 : List PrefixRegion := nextRegions 8 (liveRegions 8 29 14 degreeUnionState43_240) + +def degreeUnionState43_246 : List PrefixRegion := nextRegions 9 (liveRegions 8 29 14 degreeUnionState43_240) + +def degreeUnionState43_247 : List PrefixRegion := nextRegions 10 (liveRegions 8 29 14 degreeUnionState43_240) + +def degreeUnionState43_248 : List PrefixRegion := nextRegions 11 (liveRegions 8 29 14 degreeUnionState43_240) + +def degreeUnionState43_249 : List PrefixRegion := nextRegions 12 (liveRegions 8 29 14 degreeUnionState43_240) + +def degreeUnionState43_250 : List PrefixRegion := nextRegions 13 (liveRegions 8 29 14 degreeUnionState43_240) + +def degreeUnionState43_251 : List PrefixRegion := nextRegions 14 (liveRegions 8 29 14 degreeUnionState43_240) + +def degreeUnionState43_252 : List PrefixRegion := nextRegions 15 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_253 : List PrefixRegion := nextRegions 4 (liveRegions 8 28 15 degreeUnionState43_252) + +def degreeUnionState43_254 : List PrefixRegion := nextRegions 5 (liveRegions 8 28 15 degreeUnionState43_252) + +def degreeUnionState43_255 : List PrefixRegion := nextRegions 6 (liveRegions 8 28 15 degreeUnionState43_252) + +def degreeUnionState43_256 : List PrefixRegion := nextRegions 7 (liveRegions 8 28 15 degreeUnionState43_252) + +def degreeUnionState43_257 : List PrefixRegion := nextRegions 8 (liveRegions 8 28 15 degreeUnionState43_252) + +def degreeUnionState43_258 : List PrefixRegion := nextRegions 9 (liveRegions 8 28 15 degreeUnionState43_252) + +def degreeUnionState43_259 : List PrefixRegion := nextRegions 10 (liveRegions 8 28 15 degreeUnionState43_252) + +def degreeUnionState43_260 : List PrefixRegion := nextRegions 11 (liveRegions 8 28 15 degreeUnionState43_252) + +def degreeUnionState43_261 : List PrefixRegion := nextRegions 12 (liveRegions 8 28 15 degreeUnionState43_252) + +def degreeUnionState43_262 : List PrefixRegion := nextRegions 13 (liveRegions 8 28 15 degreeUnionState43_252) + +def degreeUnionState43_263 : List PrefixRegion := nextRegions 14 (liveRegions 8 28 15 degreeUnionState43_252) + +def degreeUnionState43_264 : List PrefixRegion := nextRegions 15 (liveRegions 8 28 15 degreeUnionState43_252) + +def degreeUnionState43_265 : List PrefixRegion := nextRegions 16 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_266 : List PrefixRegion := nextRegions 4 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_267 : List PrefixRegion := nextRegions 5 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_268 : List PrefixRegion := nextRegions 6 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_269 : List PrefixRegion := nextRegions 7 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_270 : List PrefixRegion := nextRegions 8 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_271 : List PrefixRegion := nextRegions 9 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_272 : List PrefixRegion := nextRegions 10 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_273 : List PrefixRegion := nextRegions 11 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_274 : List PrefixRegion := nextRegions 12 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_275 : List PrefixRegion := nextRegions 13 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_276 : List PrefixRegion := nextRegions 14 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_277 : List PrefixRegion := nextRegions 15 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_278 : List PrefixRegion := nextRegions 16 (liveRegions 8 27 16 degreeUnionState43_265) + +def degreeUnionState43_279 : List PrefixRegion := nextRegions 17 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_280 : List PrefixRegion := nextRegions 4 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_281 : List PrefixRegion := nextRegions 5 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_282 : List PrefixRegion := nextRegions 6 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_283 : List PrefixRegion := nextRegions 7 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_284 : List PrefixRegion := nextRegions 8 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_285 : List PrefixRegion := nextRegions 9 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_286 : List PrefixRegion := nextRegions 10 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_287 : List PrefixRegion := nextRegions 11 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_288 : List PrefixRegion := nextRegions 12 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_289 : List PrefixRegion := nextRegions 13 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_290 : List PrefixRegion := nextRegions 14 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_291 : List PrefixRegion := nextRegions 15 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_292 : List PrefixRegion := nextRegions 16 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_293 : List PrefixRegion := nextRegions 17 (liveRegions 8 26 17 degreeUnionState43_279) + +def degreeUnionState43_294 : List PrefixRegion := nextRegions 18 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_295 : List PrefixRegion := nextRegions 4 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_296 : List PrefixRegion := nextRegions 5 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_297 : List PrefixRegion := nextRegions 6 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_298 : List PrefixRegion := nextRegions 7 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_299 : List PrefixRegion := nextRegions 8 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_300 : List PrefixRegion := nextRegions 9 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_301 : List PrefixRegion := nextRegions 10 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_302 : List PrefixRegion := nextRegions 11 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_303 : List PrefixRegion := nextRegions 12 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_304 : List PrefixRegion := nextRegions 13 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_305 : List PrefixRegion := nextRegions 14 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_306 : List PrefixRegion := nextRegions 15 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_307 : List PrefixRegion := nextRegions 16 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_308 : List PrefixRegion := nextRegions 17 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_309 : List PrefixRegion := nextRegions 18 (liveRegions 8 25 18 degreeUnionState43_294) + +def degreeUnionState43_310 : List PrefixRegion := nextRegions 19 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_311 : List PrefixRegion := nextRegions 3 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_312 : List PrefixRegion := nextRegions 4 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_313 : List PrefixRegion := nextRegions 5 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_314 : List PrefixRegion := nextRegions 6 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_315 : List PrefixRegion := nextRegions 7 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_316 : List PrefixRegion := nextRegions 8 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_317 : List PrefixRegion := nextRegions 9 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_318 : List PrefixRegion := nextRegions 10 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_319 : List PrefixRegion := nextRegions 11 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_320 : List PrefixRegion := nextRegions 12 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_321 : List PrefixRegion := nextRegions 13 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_322 : List PrefixRegion := nextRegions 14 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_323 : List PrefixRegion := nextRegions 15 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_324 : List PrefixRegion := nextRegions 16 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_325 : List PrefixRegion := nextRegions 17 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_326 : List PrefixRegion := nextRegions 18 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_327 : List PrefixRegion := nextRegions 19 (liveRegions 8 24 19 degreeUnionState43_310) + +def degreeUnionState43_328 : List PrefixRegion := nextRegions 20 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_329 : List PrefixRegion := nextRegions 21 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_330 : List PrefixRegion := nextRegions 22 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_331 : List PrefixRegion := nextRegions 23 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_332 : List PrefixRegion := nextRegions 24 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_333 : List PrefixRegion := nextRegions 25 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_334 : List PrefixRegion := nextRegions 26 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_335 : List PrefixRegion := nextRegions 27 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_336 : List PrefixRegion := nextRegions 28 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_337 : List PrefixRegion := nextRegions 29 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_338 : List PrefixRegion := nextRegions 30 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_339 : List PrefixRegion := nextRegions 31 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_340 : List PrefixRegion := nextRegions 32 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_341 : List PrefixRegion := nextRegions 33 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_342 : List PrefixRegion := nextRegions 34 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_343 : List PrefixRegion := nextRegions 35 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_344 : List PrefixRegion := nextRegions 36 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_345 : List PrefixRegion := nextRegions 37 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_346 : List PrefixRegion := nextRegions 38 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_347 : List PrefixRegion := nextRegions 39 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_348 : List PrefixRegion := nextRegions 40 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_349 : List PrefixRegion := nextRegions 41 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_350 : List PrefixRegion := nextRegions 42 (liveRegions 9 43 42 degreeHalfRegions43) + +def degreeUnionState43_352 : List PrefixRegion := nextRegions 5 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_353 : List PrefixRegion := nextRegions 6 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_354 : List PrefixRegion := nextRegions 7 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_355 : List PrefixRegion := nextRegions 8 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_356 : List PrefixRegion := nextRegions 4 (liveRegions 9 35 8 degreeUnionState43_355) + +def degreeUnionState43_357 : List PrefixRegion := nextRegions 5 (liveRegions 9 35 8 degreeUnionState43_355) + +def degreeUnionState43_358 : List PrefixRegion := nextRegions 6 (liveRegions 9 35 8 degreeUnionState43_355) + +def degreeUnionState43_359 : List PrefixRegion := nextRegions 7 (liveRegions 9 35 8 degreeUnionState43_355) + +def degreeUnionState43_360 : List PrefixRegion := nextRegions 8 (liveRegions 9 35 8 degreeUnionState43_355) + +def degreeUnionState43_361 : List PrefixRegion := nextRegions 4 (liveRegions 8 27 8 degreeUnionState43_360) + +def degreeUnionState43_362 : List PrefixRegion := nextRegions 5 (liveRegions 8 27 8 degreeUnionState43_360) + +def degreeUnionState43_363 : List PrefixRegion := nextRegions 6 (liveRegions 8 27 8 degreeUnionState43_360) + +def degreeUnionState43_364 : List PrefixRegion := nextRegions 7 (liveRegions 8 27 8 degreeUnionState43_360) + +def degreeUnionState43_365 : List PrefixRegion := nextRegions 8 (liveRegions 8 27 8 degreeUnionState43_360) + +def degreeUnionState43_366 : List PrefixRegion := nextRegions 9 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_367 : List PrefixRegion := nextRegions 4 (liveRegions 9 34 9 degreeUnionState43_366) + +def degreeUnionState43_368 : List PrefixRegion := nextRegions 5 (liveRegions 9 34 9 degreeUnionState43_366) + +def degreeUnionState43_369 : List PrefixRegion := nextRegions 6 (liveRegions 9 34 9 degreeUnionState43_366) + +def degreeUnionState43_370 : List PrefixRegion := nextRegions 7 (liveRegions 9 34 9 degreeUnionState43_366) + +def degreeUnionState43_371 : List PrefixRegion := nextRegions 8 (liveRegions 9 34 9 degreeUnionState43_366) + +def degreeUnionState43_372 : List PrefixRegion := nextRegions 4 (liveRegions 8 26 8 degreeUnionState43_371) + +def degreeUnionState43_373 : List PrefixRegion := nextRegions 5 (liveRegions 8 26 8 degreeUnionState43_371) + +def degreeUnionState43_374 : List PrefixRegion := nextRegions 6 (liveRegions 8 26 8 degreeUnionState43_371) + +def degreeUnionState43_375 : List PrefixRegion := nextRegions 7 (liveRegions 8 26 8 degreeUnionState43_371) + +def degreeUnionState43_376 : List PrefixRegion := nextRegions 8 (liveRegions 8 26 8 degreeUnionState43_371) + +def degreeUnionState43_377 : List PrefixRegion := nextRegions 9 (liveRegions 9 34 9 degreeUnionState43_366) + +def degreeUnionState43_378 : List PrefixRegion := nextRegions 4 (liveRegions 8 25 9 degreeUnionState43_377) + +def degreeUnionState43_379 : List PrefixRegion := nextRegions 5 (liveRegions 8 25 9 degreeUnionState43_377) + +def degreeUnionState43_380 : List PrefixRegion := nextRegions 6 (liveRegions 8 25 9 degreeUnionState43_377) + +def degreeUnionState43_381 : List PrefixRegion := nextRegions 7 (liveRegions 8 25 9 degreeUnionState43_377) + +def degreeUnionState43_382 : List PrefixRegion := nextRegions 8 (liveRegions 8 25 9 degreeUnionState43_377) + +def degreeUnionState43_383 : List PrefixRegion := nextRegions 9 (liveRegions 8 25 9 degreeUnionState43_377) + +def degreeUnionState43_384 : List PrefixRegion := nextRegions 10 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_385 : List PrefixRegion := nextRegions 4 (liveRegions 9 33 10 degreeUnionState43_384) + +def degreeUnionState43_386 : List PrefixRegion := nextRegions 5 (liveRegions 9 33 10 degreeUnionState43_384) + +def degreeUnionState43_387 : List PrefixRegion := nextRegions 6 (liveRegions 9 33 10 degreeUnionState43_384) + +def degreeUnionState43_388 : List PrefixRegion := nextRegions 7 (liveRegions 9 33 10 degreeUnionState43_384) + +def degreeUnionState43_389 : List PrefixRegion := nextRegions 8 (liveRegions 9 33 10 degreeUnionState43_384) + +def degreeUnionState43_390 : List PrefixRegion := nextRegions 9 (liveRegions 9 33 10 degreeUnionState43_384) + +def degreeUnionState43_391 : List PrefixRegion := nextRegions 10 (liveRegions 9 33 10 degreeUnionState43_384) + +def degreeUnionState43_392 : List PrefixRegion := nextRegions 11 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_393 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 11 degreeUnionState43_392) + +def degreeUnionState43_394 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 11 degreeUnionState43_392) + +def degreeUnionState43_395 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 11 degreeUnionState43_392) + +def degreeUnionState43_396 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 11 degreeUnionState43_392) + +def degreeUnionState43_397 : List PrefixRegion := nextRegions 8 (liveRegions 9 32 11 degreeUnionState43_392) + +def degreeUnionState43_398 : List PrefixRegion := nextRegions 9 (liveRegions 9 32 11 degreeUnionState43_392) + +def degreeUnionState43_399 : List PrefixRegion := nextRegions 10 (liveRegions 9 32 11 degreeUnionState43_392) + +def degreeUnionState43_400 : List PrefixRegion := nextRegions 11 (liveRegions 9 32 11 degreeUnionState43_392) + +def degreeUnionState43_401 : List PrefixRegion := nextRegions 12 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_402 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 12 degreeUnionState43_401) + +def degreeUnionState43_403 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 12 degreeUnionState43_401) + +def degreeUnionState43_404 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 12 degreeUnionState43_401) + +def degreeUnionState43_405 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 12 degreeUnionState43_401) + +def degreeUnionState43_406 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 12 degreeUnionState43_401) + +def degreeUnionState43_407 : List PrefixRegion := nextRegions 9 (liveRegions 9 31 12 degreeUnionState43_401) + +def degreeUnionState43_408 : List PrefixRegion := nextRegions 10 (liveRegions 9 31 12 degreeUnionState43_401) + +def degreeUnionState43_409 : List PrefixRegion := nextRegions 11 (liveRegions 9 31 12 degreeUnionState43_401) + +def degreeUnionState43_410 : List PrefixRegion := nextRegions 12 (liveRegions 9 31 12 degreeUnionState43_401) + +def degreeUnionState43_411 : List PrefixRegion := nextRegions 13 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_412 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 13 degreeUnionState43_411) + +def degreeUnionState43_413 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 13 degreeUnionState43_411) + +def degreeUnionState43_414 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 13 degreeUnionState43_411) + +def degreeUnionState43_415 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 13 degreeUnionState43_411) + +def degreeUnionState43_416 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 13 degreeUnionState43_411) + +def degreeUnionState43_417 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 13 degreeUnionState43_411) + +def degreeUnionState43_418 : List PrefixRegion := nextRegions 10 (liveRegions 9 30 13 degreeUnionState43_411) + +def degreeUnionState43_419 : List PrefixRegion := nextRegions 11 (liveRegions 9 30 13 degreeUnionState43_411) + +def degreeUnionState43_420 : List PrefixRegion := nextRegions 12 (liveRegions 9 30 13 degreeUnionState43_411) + +def degreeUnionState43_421 : List PrefixRegion := nextRegions 13 (liveRegions 9 30 13 degreeUnionState43_411) + +def degreeUnionState43_422 : List PrefixRegion := nextRegions 14 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_423 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 14 degreeUnionState43_422) + +def degreeUnionState43_424 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 14 degreeUnionState43_422) + +def degreeUnionState43_425 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 14 degreeUnionState43_422) + +def degreeUnionState43_426 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 14 degreeUnionState43_422) + +def degreeUnionState43_427 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 14 degreeUnionState43_422) + +def degreeUnionState43_428 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 14 degreeUnionState43_422) + +def degreeUnionState43_429 : List PrefixRegion := nextRegions 10 (liveRegions 9 29 14 degreeUnionState43_422) + +def degreeUnionState43_430 : List PrefixRegion := nextRegions 11 (liveRegions 9 29 14 degreeUnionState43_422) + +def degreeUnionState43_431 : List PrefixRegion := nextRegions 12 (liveRegions 9 29 14 degreeUnionState43_422) + +def degreeUnionState43_432 : List PrefixRegion := nextRegions 13 (liveRegions 9 29 14 degreeUnionState43_422) + +def degreeUnionState43_433 : List PrefixRegion := nextRegions 14 (liveRegions 9 29 14 degreeUnionState43_422) + +def degreeUnionState43_434 : List PrefixRegion := nextRegions 15 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_435 : List PrefixRegion := nextRegions 4 (liveRegions 9 28 15 degreeUnionState43_434) + +def degreeUnionState43_436 : List PrefixRegion := nextRegions 5 (liveRegions 9 28 15 degreeUnionState43_434) + +def degreeUnionState43_437 : List PrefixRegion := nextRegions 6 (liveRegions 9 28 15 degreeUnionState43_434) + +def degreeUnionState43_438 : List PrefixRegion := nextRegions 7 (liveRegions 9 28 15 degreeUnionState43_434) + +def degreeUnionState43_439 : List PrefixRegion := nextRegions 8 (liveRegions 9 28 15 degreeUnionState43_434) + +def degreeUnionState43_440 : List PrefixRegion := nextRegions 9 (liveRegions 9 28 15 degreeUnionState43_434) + +def degreeUnionState43_441 : List PrefixRegion := nextRegions 10 (liveRegions 9 28 15 degreeUnionState43_434) + +def degreeUnionState43_442 : List PrefixRegion := nextRegions 11 (liveRegions 9 28 15 degreeUnionState43_434) + +def degreeUnionState43_443 : List PrefixRegion := nextRegions 12 (liveRegions 9 28 15 degreeUnionState43_434) + +def degreeUnionState43_444 : List PrefixRegion := nextRegions 13 (liveRegions 9 28 15 degreeUnionState43_434) + +def degreeUnionState43_445 : List PrefixRegion := nextRegions 14 (liveRegions 9 28 15 degreeUnionState43_434) + +def degreeUnionState43_446 : List PrefixRegion := nextRegions 15 (liveRegions 9 28 15 degreeUnionState43_434) + +def degreeUnionState43_447 : List PrefixRegion := nextRegions 16 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_448 : List PrefixRegion := nextRegions 3 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_449 : List PrefixRegion := nextRegions 4 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_450 : List PrefixRegion := nextRegions 5 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_451 : List PrefixRegion := nextRegions 6 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_452 : List PrefixRegion := nextRegions 7 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_453 : List PrefixRegion := nextRegions 8 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_454 : List PrefixRegion := nextRegions 9 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_455 : List PrefixRegion := nextRegions 10 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_456 : List PrefixRegion := nextRegions 11 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_457 : List PrefixRegion := nextRegions 12 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_458 : List PrefixRegion := nextRegions 13 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_459 : List PrefixRegion := nextRegions 14 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_460 : List PrefixRegion := nextRegions 15 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_461 : List PrefixRegion := nextRegions 16 (liveRegions 9 27 16 degreeUnionState43_447) + +def degreeUnionState43_462 : List PrefixRegion := nextRegions 17 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_463 : List PrefixRegion := nextRegions 3 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_464 : List PrefixRegion := nextRegions 4 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_465 : List PrefixRegion := nextRegions 5 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_466 : List PrefixRegion := nextRegions 6 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_467 : List PrefixRegion := nextRegions 7 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_468 : List PrefixRegion := nextRegions 8 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_469 : List PrefixRegion := nextRegions 9 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_470 : List PrefixRegion := nextRegions 10 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_471 : List PrefixRegion := nextRegions 11 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_472 : List PrefixRegion := nextRegions 12 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_473 : List PrefixRegion := nextRegions 13 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_474 : List PrefixRegion := nextRegions 14 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_475 : List PrefixRegion := nextRegions 15 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_476 : List PrefixRegion := nextRegions 16 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_477 : List PrefixRegion := nextRegions 17 (liveRegions 9 26 17 degreeUnionState43_462) + +def degreeUnionState43_478 : List PrefixRegion := nextRegions 18 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_479 : List PrefixRegion := nextRegions 3 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_480 : List PrefixRegion := nextRegions 4 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_481 : List PrefixRegion := nextRegions 5 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_482 : List PrefixRegion := nextRegions 6 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_483 : List PrefixRegion := nextRegions 7 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_484 : List PrefixRegion := nextRegions 8 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_485 : List PrefixRegion := nextRegions 9 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_486 : List PrefixRegion := nextRegions 10 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_487 : List PrefixRegion := nextRegions 11 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_488 : List PrefixRegion := nextRegions 12 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_489 : List PrefixRegion := nextRegions 13 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_490 : List PrefixRegion := nextRegions 14 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_491 : List PrefixRegion := nextRegions 15 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_492 : List PrefixRegion := nextRegions 16 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_493 : List PrefixRegion := nextRegions 17 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_494 : List PrefixRegion := nextRegions 18 (liveRegions 9 25 18 degreeUnionState43_478) + +def degreeUnionState43_495 : List PrefixRegion := nextRegions 19 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_496 : List PrefixRegion := nextRegions 3 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_497 : List PrefixRegion := nextRegions 4 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_498 : List PrefixRegion := nextRegions 5 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_499 : List PrefixRegion := nextRegions 6 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_500 : List PrefixRegion := nextRegions 7 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_501 : List PrefixRegion := nextRegions 8 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_502 : List PrefixRegion := nextRegions 9 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_503 : List PrefixRegion := nextRegions 10 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_504 : List PrefixRegion := nextRegions 11 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_505 : List PrefixRegion := nextRegions 12 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_506 : List PrefixRegion := nextRegions 13 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_507 : List PrefixRegion := nextRegions 14 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_508 : List PrefixRegion := nextRegions 15 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_509 : List PrefixRegion := nextRegions 16 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_510 : List PrefixRegion := nextRegions 17 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_511 : List PrefixRegion := nextRegions 18 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_512 : List PrefixRegion := nextRegions 19 (liveRegions 9 24 19 degreeUnionState43_495) + +def degreeUnionState43_513 : List PrefixRegion := nextRegions 20 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_514 : List PrefixRegion := nextRegions 21 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_515 : List PrefixRegion := nextRegions 22 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_516 : List PrefixRegion := nextRegions 23 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_517 : List PrefixRegion := nextRegions 24 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_518 : List PrefixRegion := nextRegions 25 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_519 : List PrefixRegion := nextRegions 26 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_520 : List PrefixRegion := nextRegions 27 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_521 : List PrefixRegion := nextRegions 28 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_522 : List PrefixRegion := nextRegions 29 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_523 : List PrefixRegion := nextRegions 30 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_524 : List PrefixRegion := nextRegions 31 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_525 : List PrefixRegion := nextRegions 32 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_526 : List PrefixRegion := nextRegions 33 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_527 : List PrefixRegion := nextRegions 34 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_528 : List PrefixRegion := nextRegions 35 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_529 : List PrefixRegion := nextRegions 36 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_530 : List PrefixRegion := nextRegions 37 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_531 : List PrefixRegion := nextRegions 38 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_532 : List PrefixRegion := nextRegions 39 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_533 : List PrefixRegion := nextRegions 40 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_534 : List PrefixRegion := nextRegions 41 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_535 : List PrefixRegion := nextRegions 42 (liveRegions 10 43 42 degreeHalfRegions43) + +def degreeUnionState43_537 : List PrefixRegion := nextRegions 4 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_538 : List PrefixRegion := nextRegions 5 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_539 : List PrefixRegion := nextRegions 6 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_540 : List PrefixRegion := nextRegions 7 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_541 : List PrefixRegion := nextRegions 8 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_542 : List PrefixRegion := nextRegions 4 (liveRegions 10 35 8 degreeUnionState43_541) + +def degreeUnionState43_543 : List PrefixRegion := nextRegions 5 (liveRegions 10 35 8 degreeUnionState43_541) + +def degreeUnionState43_544 : List PrefixRegion := nextRegions 6 (liveRegions 10 35 8 degreeUnionState43_541) + +def degreeUnionState43_545 : List PrefixRegion := nextRegions 7 (liveRegions 10 35 8 degreeUnionState43_541) + +def degreeUnionState43_546 : List PrefixRegion := nextRegions 8 (liveRegions 10 35 8 degreeUnionState43_541) + +def degreeUnionState43_547 : List PrefixRegion := nextRegions 9 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_548 : List PrefixRegion := nextRegions 4 (liveRegions 10 34 9 degreeUnionState43_547) + +def degreeUnionState43_549 : List PrefixRegion := nextRegions 5 (liveRegions 10 34 9 degreeUnionState43_547) + +def degreeUnionState43_550 : List PrefixRegion := nextRegions 6 (liveRegions 10 34 9 degreeUnionState43_547) + +def degreeUnionState43_551 : List PrefixRegion := nextRegions 7 (liveRegions 10 34 9 degreeUnionState43_547) + +def degreeUnionState43_552 : List PrefixRegion := nextRegions 8 (liveRegions 10 34 9 degreeUnionState43_547) + +def degreeUnionState43_553 : List PrefixRegion := nextRegions 9 (liveRegions 10 34 9 degreeUnionState43_547) + +def degreeUnionState43_554 : List PrefixRegion := nextRegions 10 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_555 : List PrefixRegion := nextRegions 4 (liveRegions 10 33 10 degreeUnionState43_554) + +def degreeUnionState43_556 : List PrefixRegion := nextRegions 5 (liveRegions 10 33 10 degreeUnionState43_554) + +def degreeUnionState43_557 : List PrefixRegion := nextRegions 6 (liveRegions 10 33 10 degreeUnionState43_554) + +def degreeUnionState43_558 : List PrefixRegion := nextRegions 7 (liveRegions 10 33 10 degreeUnionState43_554) + +def degreeUnionState43_559 : List PrefixRegion := nextRegions 8 (liveRegions 10 33 10 degreeUnionState43_554) + +def degreeUnionState43_560 : List PrefixRegion := nextRegions 9 (liveRegions 10 33 10 degreeUnionState43_554) + +def degreeUnionState43_561 : List PrefixRegion := nextRegions 10 (liveRegions 10 33 10 degreeUnionState43_554) + +def degreeUnionState43_562 : List PrefixRegion := nextRegions 11 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_563 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 11 degreeUnionState43_562) + +def degreeUnionState43_564 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 11 degreeUnionState43_562) + +def degreeUnionState43_565 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 11 degreeUnionState43_562) + +def degreeUnionState43_566 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 11 degreeUnionState43_562) + +def degreeUnionState43_567 : List PrefixRegion := nextRegions 8 (liveRegions 10 32 11 degreeUnionState43_562) + +def degreeUnionState43_568 : List PrefixRegion := nextRegions 9 (liveRegions 10 32 11 degreeUnionState43_562) + +def degreeUnionState43_569 : List PrefixRegion := nextRegions 10 (liveRegions 10 32 11 degreeUnionState43_562) + +def degreeUnionState43_570 : List PrefixRegion := nextRegions 11 (liveRegions 10 32 11 degreeUnionState43_562) + +def degreeUnionState43_571 : List PrefixRegion := nextRegions 12 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_572 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 12 degreeUnionState43_571) + +def degreeUnionState43_573 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 12 degreeUnionState43_571) + +def degreeUnionState43_574 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 12 degreeUnionState43_571) + +def degreeUnionState43_575 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 12 degreeUnionState43_571) + +def degreeUnionState43_576 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 12 degreeUnionState43_571) + +def degreeUnionState43_577 : List PrefixRegion := nextRegions 9 (liveRegions 10 31 12 degreeUnionState43_571) + +def degreeUnionState43_578 : List PrefixRegion := nextRegions 10 (liveRegions 10 31 12 degreeUnionState43_571) + +def degreeUnionState43_579 : List PrefixRegion := nextRegions 11 (liveRegions 10 31 12 degreeUnionState43_571) + +def degreeUnionState43_580 : List PrefixRegion := nextRegions 12 (liveRegions 10 31 12 degreeUnionState43_571) + +def degreeUnionState43_581 : List PrefixRegion := nextRegions 13 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_582 : List PrefixRegion := nextRegions 14 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_583 : List PrefixRegion := nextRegions 15 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_584 : List PrefixRegion := nextRegions 16 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_585 : List PrefixRegion := nextRegions 17 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_586 : List PrefixRegion := nextRegions 18 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_587 : List PrefixRegion := nextRegions 19 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_588 : List PrefixRegion := nextRegions 20 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_589 : List PrefixRegion := nextRegions 21 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_590 : List PrefixRegion := nextRegions 22 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_591 : List PrefixRegion := nextRegions 23 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_592 : List PrefixRegion := nextRegions 24 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_593 : List PrefixRegion := nextRegions 25 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_594 : List PrefixRegion := nextRegions 26 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_595 : List PrefixRegion := nextRegions 27 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_596 : List PrefixRegion := nextRegions 28 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_597 : List PrefixRegion := nextRegions 29 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_598 : List PrefixRegion := nextRegions 30 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_599 : List PrefixRegion := nextRegions 31 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_600 : List PrefixRegion := nextRegions 32 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_601 : List PrefixRegion := nextRegions 33 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_602 : List PrefixRegion := nextRegions 34 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_603 : List PrefixRegion := nextRegions 35 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_604 : List PrefixRegion := nextRegions 36 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_605 : List PrefixRegion := nextRegions 37 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_606 : List PrefixRegion := nextRegions 38 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_607 : List PrefixRegion := nextRegions 39 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_608 : List PrefixRegion := nextRegions 40 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_609 : List PrefixRegion := nextRegions 41 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_610 : List PrefixRegion := nextRegions 42 (liveRegions 11 43 42 degreeHalfRegions43) + +def degreeUnionState43_612 : List PrefixRegion := nextRegions 4 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_613 : List PrefixRegion := nextRegions 5 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_614 : List PrefixRegion := nextRegions 6 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_615 : List PrefixRegion := nextRegions 7 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_616 : List PrefixRegion := nextRegions 8 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_617 : List PrefixRegion := nextRegions 9 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_618 : List PrefixRegion := nextRegions 4 (liveRegions 11 34 9 degreeUnionState43_617) + +def degreeUnionState43_619 : List PrefixRegion := nextRegions 5 (liveRegions 11 34 9 degreeUnionState43_617) + +def degreeUnionState43_620 : List PrefixRegion := nextRegions 6 (liveRegions 11 34 9 degreeUnionState43_617) + +def degreeUnionState43_621 : List PrefixRegion := nextRegions 7 (liveRegions 11 34 9 degreeUnionState43_617) + +def degreeUnionState43_622 : List PrefixRegion := nextRegions 8 (liveRegions 11 34 9 degreeUnionState43_617) + +def degreeUnionState43_623 : List PrefixRegion := nextRegions 9 (liveRegions 11 34 9 degreeUnionState43_617) + +def degreeUnionState43_624 : List PrefixRegion := nextRegions 10 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_625 : List PrefixRegion := nextRegions 3 (liveRegions 11 33 10 degreeUnionState43_624) + +def degreeUnionState43_626 : List PrefixRegion := nextRegions 4 (liveRegions 11 33 10 degreeUnionState43_624) + +def degreeUnionState43_627 : List PrefixRegion := nextRegions 5 (liveRegions 11 33 10 degreeUnionState43_624) + +def degreeUnionState43_628 : List PrefixRegion := nextRegions 6 (liveRegions 11 33 10 degreeUnionState43_624) + +def degreeUnionState43_629 : List PrefixRegion := nextRegions 7 (liveRegions 11 33 10 degreeUnionState43_624) + +def degreeUnionState43_630 : List PrefixRegion := nextRegions 8 (liveRegions 11 33 10 degreeUnionState43_624) + +def degreeUnionState43_631 : List PrefixRegion := nextRegions 9 (liveRegions 11 33 10 degreeUnionState43_624) + +def degreeUnionState43_632 : List PrefixRegion := nextRegions 10 (liveRegions 11 33 10 degreeUnionState43_624) + +def degreeUnionState43_633 : List PrefixRegion := nextRegions 11 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_634 : List PrefixRegion := nextRegions 3 (liveRegions 11 32 11 degreeUnionState43_633) + +def degreeUnionState43_635 : List PrefixRegion := nextRegions 4 (liveRegions 11 32 11 degreeUnionState43_633) + +def degreeUnionState43_636 : List PrefixRegion := nextRegions 5 (liveRegions 11 32 11 degreeUnionState43_633) + +def degreeUnionState43_637 : List PrefixRegion := nextRegions 6 (liveRegions 11 32 11 degreeUnionState43_633) + +def degreeUnionState43_638 : List PrefixRegion := nextRegions 7 (liveRegions 11 32 11 degreeUnionState43_633) + +def degreeUnionState43_639 : List PrefixRegion := nextRegions 8 (liveRegions 11 32 11 degreeUnionState43_633) + +def degreeUnionState43_640 : List PrefixRegion := nextRegions 9 (liveRegions 11 32 11 degreeUnionState43_633) + +def degreeUnionState43_641 : List PrefixRegion := nextRegions 10 (liveRegions 11 32 11 degreeUnionState43_633) + +def degreeUnionState43_642 : List PrefixRegion := nextRegions 11 (liveRegions 11 32 11 degreeUnionState43_633) + +def degreeUnionState43_643 : List PrefixRegion := nextRegions 12 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_644 : List PrefixRegion := nextRegions 3 (liveRegions 11 31 12 degreeUnionState43_643) + +def degreeUnionState43_645 : List PrefixRegion := nextRegions 4 (liveRegions 11 31 12 degreeUnionState43_643) + +def degreeUnionState43_646 : List PrefixRegion := nextRegions 5 (liveRegions 11 31 12 degreeUnionState43_643) + +def degreeUnionState43_647 : List PrefixRegion := nextRegions 6 (liveRegions 11 31 12 degreeUnionState43_643) + +def degreeUnionState43_648 : List PrefixRegion := nextRegions 7 (liveRegions 11 31 12 degreeUnionState43_643) + +def degreeUnionState43_649 : List PrefixRegion := nextRegions 8 (liveRegions 11 31 12 degreeUnionState43_643) + +def degreeUnionState43_650 : List PrefixRegion := nextRegions 9 (liveRegions 11 31 12 degreeUnionState43_643) + +def degreeUnionState43_651 : List PrefixRegion := nextRegions 10 (liveRegions 11 31 12 degreeUnionState43_643) + +def degreeUnionState43_652 : List PrefixRegion := nextRegions 11 (liveRegions 11 31 12 degreeUnionState43_643) + +def degreeUnionState43_653 : List PrefixRegion := nextRegions 12 (liveRegions 11 31 12 degreeUnionState43_643) + +def degreeUnionState43_654 : List PrefixRegion := nextRegions 13 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_655 : List PrefixRegion := nextRegions 14 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_656 : List PrefixRegion := nextRegions 15 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_657 : List PrefixRegion := nextRegions 16 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_658 : List PrefixRegion := nextRegions 17 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_659 : List PrefixRegion := nextRegions 18 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_660 : List PrefixRegion := nextRegions 19 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_661 : List PrefixRegion := nextRegions 20 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_662 : List PrefixRegion := nextRegions 21 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_663 : List PrefixRegion := nextRegions 22 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_664 : List PrefixRegion := nextRegions 23 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_665 : List PrefixRegion := nextRegions 24 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_666 : List PrefixRegion := nextRegions 25 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_667 : List PrefixRegion := nextRegions 26 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_668 : List PrefixRegion := nextRegions 27 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_669 : List PrefixRegion := nextRegions 28 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_670 : List PrefixRegion := nextRegions 29 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_671 : List PrefixRegion := nextRegions 30 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_672 : List PrefixRegion := nextRegions 31 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_673 : List PrefixRegion := nextRegions 32 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_674 : List PrefixRegion := nextRegions 33 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_675 : List PrefixRegion := nextRegions 34 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_676 : List PrefixRegion := nextRegions 35 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_677 : List PrefixRegion := nextRegions 36 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_678 : List PrefixRegion := nextRegions 37 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_679 : List PrefixRegion := nextRegions 38 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_680 : List PrefixRegion := nextRegions 39 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_681 : List PrefixRegion := nextRegions 40 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_682 : List PrefixRegion := nextRegions 41 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_683 : List PrefixRegion := nextRegions 42 (liveRegions 12 43 42 degreeHalfRegions43) + +def degreeUnionState43_685 : List PrefixRegion := nextRegions 4 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_686 : List PrefixRegion := nextRegions 5 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_687 : List PrefixRegion := nextRegions 6 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_688 : List PrefixRegion := nextRegions 7 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_689 : List PrefixRegion := nextRegions 8 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_690 : List PrefixRegion := nextRegions 9 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_691 : List PrefixRegion := nextRegions 10 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_692 : List PrefixRegion := nextRegions 3 (liveRegions 12 33 10 degreeUnionState43_691) + +def degreeUnionState43_693 : List PrefixRegion := nextRegions 4 (liveRegions 12 33 10 degreeUnionState43_691) + +def degreeUnionState43_694 : List PrefixRegion := nextRegions 5 (liveRegions 12 33 10 degreeUnionState43_691) + +def degreeUnionState43_695 : List PrefixRegion := nextRegions 6 (liveRegions 12 33 10 degreeUnionState43_691) + +def degreeUnionState43_696 : List PrefixRegion := nextRegions 7 (liveRegions 12 33 10 degreeUnionState43_691) + +def degreeUnionState43_697 : List PrefixRegion := nextRegions 8 (liveRegions 12 33 10 degreeUnionState43_691) + +def degreeUnionState43_698 : List PrefixRegion := nextRegions 9 (liveRegions 12 33 10 degreeUnionState43_691) + +def degreeUnionState43_699 : List PrefixRegion := nextRegions 10 (liveRegions 12 33 10 degreeUnionState43_691) + +def degreeUnionState43_700 : List PrefixRegion := nextRegions 11 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_701 : List PrefixRegion := nextRegions 12 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_702 : List PrefixRegion := nextRegions 13 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_703 : List PrefixRegion := nextRegions 14 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_704 : List PrefixRegion := nextRegions 15 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_705 : List PrefixRegion := nextRegions 16 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_706 : List PrefixRegion := nextRegions 17 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_707 : List PrefixRegion := nextRegions 18 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_708 : List PrefixRegion := nextRegions 19 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_709 : List PrefixRegion := nextRegions 20 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_710 : List PrefixRegion := nextRegions 21 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_711 : List PrefixRegion := nextRegions 22 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_712 : List PrefixRegion := nextRegions 23 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_713 : List PrefixRegion := nextRegions 24 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_714 : List PrefixRegion := nextRegions 25 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_715 : List PrefixRegion := nextRegions 26 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_716 : List PrefixRegion := nextRegions 27 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_717 : List PrefixRegion := nextRegions 28 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_718 : List PrefixRegion := nextRegions 29 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_719 : List PrefixRegion := nextRegions 30 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_720 : List PrefixRegion := nextRegions 31 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_721 : List PrefixRegion := nextRegions 32 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_722 : List PrefixRegion := nextRegions 33 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_723 : List PrefixRegion := nextRegions 34 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_724 : List PrefixRegion := nextRegions 35 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_725 : List PrefixRegion := nextRegions 36 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_726 : List PrefixRegion := nextRegions 37 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_727 : List PrefixRegion := nextRegions 38 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_728 : List PrefixRegion := nextRegions 39 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_729 : List PrefixRegion := nextRegions 40 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_730 : List PrefixRegion := nextRegions 41 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_731 : List PrefixRegion := nextRegions 42 (liveRegions 13 43 42 degreeHalfRegions43) + +def degreeUnionState43_733 : List PrefixRegion := nextRegions 4 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_734 : List PrefixRegion := nextRegions 5 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_735 : List PrefixRegion := nextRegions 6 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_736 : List PrefixRegion := nextRegions 7 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_737 : List PrefixRegion := nextRegions 8 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_738 : List PrefixRegion := nextRegions 9 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_739 : List PrefixRegion := nextRegions 10 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_740 : List PrefixRegion := nextRegions 11 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_741 : List PrefixRegion := nextRegions 12 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_742 : List PrefixRegion := nextRegions 13 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_743 : List PrefixRegion := nextRegions 14 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_744 : List PrefixRegion := nextRegions 15 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_745 : List PrefixRegion := nextRegions 16 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_746 : List PrefixRegion := nextRegions 17 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_747 : List PrefixRegion := nextRegions 18 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_748 : List PrefixRegion := nextRegions 19 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_749 : List PrefixRegion := nextRegions 20 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_750 : List PrefixRegion := nextRegions 21 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_751 : List PrefixRegion := nextRegions 22 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_752 : List PrefixRegion := nextRegions 23 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_753 : List PrefixRegion := nextRegions 24 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_754 : List PrefixRegion := nextRegions 25 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_755 : List PrefixRegion := nextRegions 26 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_756 : List PrefixRegion := nextRegions 27 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_757 : List PrefixRegion := nextRegions 28 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_758 : List PrefixRegion := nextRegions 29 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_759 : List PrefixRegion := nextRegions 30 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_760 : List PrefixRegion := nextRegions 31 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_761 : List PrefixRegion := nextRegions 32 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_762 : List PrefixRegion := nextRegions 33 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_763 : List PrefixRegion := nextRegions 34 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_764 : List PrefixRegion := nextRegions 35 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_765 : List PrefixRegion := nextRegions 36 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_766 : List PrefixRegion := nextRegions 37 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_767 : List PrefixRegion := nextRegions 38 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_768 : List PrefixRegion := nextRegions 39 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_769 : List PrefixRegion := nextRegions 40 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_770 : List PrefixRegion := nextRegions 41 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_771 : List PrefixRegion := nextRegions 42 (liveRegions 14 43 42 degreeHalfRegions43) + +def degreeUnionState43_773 : List PrefixRegion := nextRegions 3 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_774 : List PrefixRegion := nextRegions 4 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_775 : List PrefixRegion := nextRegions 5 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_776 : List PrefixRegion := nextRegions 6 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_777 : List PrefixRegion := nextRegions 7 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_778 : List PrefixRegion := nextRegions 8 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_779 : List PrefixRegion := nextRegions 9 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_780 : List PrefixRegion := nextRegions 10 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_781 : List PrefixRegion := nextRegions 11 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_782 : List PrefixRegion := nextRegions 12 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_783 : List PrefixRegion := nextRegions 13 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_784 : List PrefixRegion := nextRegions 14 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_785 : List PrefixRegion := nextRegions 15 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_786 : List PrefixRegion := nextRegions 16 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_787 : List PrefixRegion := nextRegions 17 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_788 : List PrefixRegion := nextRegions 18 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_789 : List PrefixRegion := nextRegions 19 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_790 : List PrefixRegion := nextRegions 20 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_791 : List PrefixRegion := nextRegions 21 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_792 : List PrefixRegion := nextRegions 22 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_793 : List PrefixRegion := nextRegions 23 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_794 : List PrefixRegion := nextRegions 24 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_795 : List PrefixRegion := nextRegions 25 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_796 : List PrefixRegion := nextRegions 26 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_797 : List PrefixRegion := nextRegions 27 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_798 : List PrefixRegion := nextRegions 28 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_799 : List PrefixRegion := nextRegions 29 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_800 : List PrefixRegion := nextRegions 30 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_801 : List PrefixRegion := nextRegions 31 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_802 : List PrefixRegion := nextRegions 32 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_803 : List PrefixRegion := nextRegions 33 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_804 : List PrefixRegion := nextRegions 34 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_805 : List PrefixRegion := nextRegions 35 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_806 : List PrefixRegion := nextRegions 36 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_807 : List PrefixRegion := nextRegions 37 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_808 : List PrefixRegion := nextRegions 38 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_809 : List PrefixRegion := nextRegions 39 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_810 : List PrefixRegion := nextRegions 40 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_811 : List PrefixRegion := nextRegions 41 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_812 : List PrefixRegion := nextRegions 42 (liveRegions 15 43 42 degreeHalfRegions43) + +def degreeUnionState43_814 : List PrefixRegion := nextRegions 3 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_815 : List PrefixRegion := nextRegions 4 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_816 : List PrefixRegion := nextRegions 5 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_817 : List PrefixRegion := nextRegions 6 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_818 : List PrefixRegion := nextRegions 7 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_819 : List PrefixRegion := nextRegions 8 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_820 : List PrefixRegion := nextRegions 9 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_821 : List PrefixRegion := nextRegions 10 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_822 : List PrefixRegion := nextRegions 11 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_823 : List PrefixRegion := nextRegions 12 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_824 : List PrefixRegion := nextRegions 13 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_825 : List PrefixRegion := nextRegions 14 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_826 : List PrefixRegion := nextRegions 15 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_827 : List PrefixRegion := nextRegions 16 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_828 : List PrefixRegion := nextRegions 17 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_829 : List PrefixRegion := nextRegions 18 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_830 : List PrefixRegion := nextRegions 19 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_831 : List PrefixRegion := nextRegions 20 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_832 : List PrefixRegion := nextRegions 21 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_833 : List PrefixRegion := nextRegions 22 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_834 : List PrefixRegion := nextRegions 23 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_835 : List PrefixRegion := nextRegions 24 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_836 : List PrefixRegion := nextRegions 25 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_837 : List PrefixRegion := nextRegions 26 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_838 : List PrefixRegion := nextRegions 27 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_839 : List PrefixRegion := nextRegions 28 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_840 : List PrefixRegion := nextRegions 29 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_841 : List PrefixRegion := nextRegions 30 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_842 : List PrefixRegion := nextRegions 31 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_843 : List PrefixRegion := nextRegions 32 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_844 : List PrefixRegion := nextRegions 33 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_845 : List PrefixRegion := nextRegions 34 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_846 : List PrefixRegion := nextRegions 35 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_847 : List PrefixRegion := nextRegions 36 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_848 : List PrefixRegion := nextRegions 37 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_849 : List PrefixRegion := nextRegions 38 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_850 : List PrefixRegion := nextRegions 39 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_851 : List PrefixRegion := nextRegions 40 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_852 : List PrefixRegion := nextRegions 41 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_853 : List PrefixRegion := nextRegions 42 (liveRegions 16 43 42 degreeHalfRegions43) + +def degreeUnionState43_855 : List PrefixRegion := nextRegions 3 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_856 : List PrefixRegion := nextRegions 4 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_857 : List PrefixRegion := nextRegions 5 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_858 : List PrefixRegion := nextRegions 6 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_859 : List PrefixRegion := nextRegions 7 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_860 : List PrefixRegion := nextRegions 8 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_861 : List PrefixRegion := nextRegions 9 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_862 : List PrefixRegion := nextRegions 10 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_863 : List PrefixRegion := nextRegions 11 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_864 : List PrefixRegion := nextRegions 12 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_865 : List PrefixRegion := nextRegions 13 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_866 : List PrefixRegion := nextRegions 14 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_867 : List PrefixRegion := nextRegions 15 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_868 : List PrefixRegion := nextRegions 16 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_869 : List PrefixRegion := nextRegions 17 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_870 : List PrefixRegion := nextRegions 18 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_871 : List PrefixRegion := nextRegions 19 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_872 : List PrefixRegion := nextRegions 20 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_873 : List PrefixRegion := nextRegions 21 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_874 : List PrefixRegion := nextRegions 22 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_875 : List PrefixRegion := nextRegions 23 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_876 : List PrefixRegion := nextRegions 24 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_877 : List PrefixRegion := nextRegions 25 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_878 : List PrefixRegion := nextRegions 26 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_879 : List PrefixRegion := nextRegions 27 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_880 : List PrefixRegion := nextRegions 28 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_881 : List PrefixRegion := nextRegions 29 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_882 : List PrefixRegion := nextRegions 30 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_883 : List PrefixRegion := nextRegions 31 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_884 : List PrefixRegion := nextRegions 32 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_885 : List PrefixRegion := nextRegions 33 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_886 : List PrefixRegion := nextRegions 34 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_887 : List PrefixRegion := nextRegions 35 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_888 : List PrefixRegion := nextRegions 36 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_889 : List PrefixRegion := nextRegions 37 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_890 : List PrefixRegion := nextRegions 38 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_891 : List PrefixRegion := nextRegions 39 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_892 : List PrefixRegion := nextRegions 40 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_893 : List PrefixRegion := nextRegions 41 (liveRegions 17 43 42 degreeHalfRegions43) + +def degreeUnionState43_894 : List PrefixRegion := nextRegions 42 (liveRegions 17 43 42 degreeHalfRegions43) + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates58.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates58.lean index 78d96381eb324cc1f10099181e113e446eedf2e3..ef9773a7139cfe19a5eb1045bf2eee05d3a47226 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates58.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates58.lean @@ -1,211 +1,211 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData58 - -namespace OAI - -/-! Degree Union States 58. -/ - -section - -namespace UniversalTensorSquare - -def degreeUnionState58_13 : List PrefixRegion := nextRegions 5 (liveRegions 12 58 14 degreeHalfRegions58) - -def degreeUnionState58_14 : List PrefixRegion := nextRegions 6 (liveRegions 12 58 14 degreeHalfRegions58) - -def degreeUnionState58_15 : List PrefixRegion := nextRegions 7 (liveRegions 12 58 14 degreeHalfRegions58) - -def degreeUnionState58_16 : List PrefixRegion := nextRegions 8 (liveRegions 12 58 14 degreeHalfRegions58) - -def degreeUnionState58_17 : List PrefixRegion := nextRegions 9 (liveRegions 12 58 14 degreeHalfRegions58) - -def degreeUnionState58_18 : List PrefixRegion := nextRegions 10 (liveRegions 12 58 14 degreeHalfRegions58) - -def degreeUnionState58_19 : List PrefixRegion := nextRegions 11 (liveRegions 12 58 14 degreeHalfRegions58) - -def degreeUnionState58_20 : List PrefixRegion := nextRegions 12 (liveRegions 12 58 14 degreeHalfRegions58) - -def degreeUnionState58_21 : List PrefixRegion := nextRegions 5 (liveRegions 11 46 12 degreeUnionState58_20) - -def degreeUnionState58_22 : List PrefixRegion := nextRegions 6 (liveRegions 11 46 12 degreeUnionState58_20) - -def degreeUnionState58_23 : List PrefixRegion := nextRegions 7 (liveRegions 11 46 12 degreeUnionState58_20) - -def degreeUnionState58_24 : List PrefixRegion := nextRegions 8 (liveRegions 11 46 12 degreeUnionState58_20) - -def degreeUnionState58_25 : List PrefixRegion := nextRegions 9 (liveRegions 11 46 12 degreeUnionState58_20) - -def degreeUnionState58_26 : List PrefixRegion := nextRegions 4 (liveRegions 10 37 9 degreeUnionState58_25) - -def degreeUnionState58_27 : List PrefixRegion := nextRegions 5 (liveRegions 10 37 9 degreeUnionState58_25) - -def degreeUnionState58_28 : List PrefixRegion := nextRegions 6 (liveRegions 10 37 9 degreeUnionState58_25) - -def degreeUnionState58_29 : List PrefixRegion := nextRegions 7 (liveRegions 10 37 9 degreeUnionState58_25) - -def degreeUnionState58_30 : List PrefixRegion := nextRegions 8 (liveRegions 10 37 9 degreeUnionState58_25) - -def degreeUnionState58_31 : List PrefixRegion := nextRegions 9 (liveRegions 10 37 9 degreeUnionState58_25) - -def degreeUnionState58_32 : List PrefixRegion := nextRegions 10 (liveRegions 11 46 12 degreeUnionState58_20) - -def degreeUnionState58_33 : List PrefixRegion := nextRegions 11 (liveRegions 11 46 12 degreeUnionState58_20) - -def degreeUnionState58_34 : List PrefixRegion := nextRegions 12 (liveRegions 11 46 12 degreeUnionState58_20) - -def degreeUnionState58_35 : List PrefixRegion := nextRegions 13 (liveRegions 12 58 14 degreeHalfRegions58) - -def degreeUnionState58_36 : List PrefixRegion := nextRegions 5 (liveRegions 11 45 13 degreeUnionState58_35) - -def degreeUnionState58_37 : List PrefixRegion := nextRegions 6 (liveRegions 11 45 13 degreeUnionState58_35) - -def degreeUnionState58_38 : List PrefixRegion := nextRegions 7 (liveRegions 11 45 13 degreeUnionState58_35) - -def degreeUnionState58_39 : List PrefixRegion := nextRegions 8 (liveRegions 11 45 13 degreeUnionState58_35) - -def degreeUnionState58_40 : List PrefixRegion := nextRegions 4 (liveRegions 10 37 8 degreeUnionState58_39) - -def degreeUnionState58_41 : List PrefixRegion := nextRegions 5 (liveRegions 10 37 8 degreeUnionState58_39) - -def degreeUnionState58_42 : List PrefixRegion := nextRegions 6 (liveRegions 10 37 8 degreeUnionState58_39) - -def degreeUnionState58_43 : List PrefixRegion := nextRegions 7 (liveRegions 10 37 8 degreeUnionState58_39) - -def degreeUnionState58_44 : List PrefixRegion := nextRegions 8 (liveRegions 10 37 8 degreeUnionState58_39) - -def degreeUnionState58_45 : List PrefixRegion := nextRegions 9 (liveRegions 11 45 13 degreeUnionState58_35) - -def degreeUnionState58_46 : List PrefixRegion := nextRegions 10 (liveRegions 11 45 13 degreeUnionState58_35) - -def degreeUnionState58_47 : List PrefixRegion := nextRegions 11 (liveRegions 11 45 13 degreeUnionState58_35) - -def degreeUnionState58_48 : List PrefixRegion := nextRegions 12 (liveRegions 11 45 13 degreeUnionState58_35) - -def degreeUnionState58_49 : List PrefixRegion := nextRegions 13 (liveRegions 11 45 13 degreeUnionState58_35) - -def degreeUnionState58_50 : List PrefixRegion := nextRegions 14 (liveRegions 12 58 14 degreeHalfRegions58) - -def degreeUnionState58_51 : List PrefixRegion := nextRegions 4 (liveRegions 11 44 14 degreeUnionState58_50) - -def degreeUnionState58_52 : List PrefixRegion := nextRegions 5 (liveRegions 11 44 14 degreeUnionState58_50) - -def degreeUnionState58_53 : List PrefixRegion := nextRegions 6 (liveRegions 11 44 14 degreeUnionState58_50) - -def degreeUnionState58_54 : List PrefixRegion := nextRegions 7 (liveRegions 11 44 14 degreeUnionState58_50) - -def degreeUnionState58_55 : List PrefixRegion := nextRegions 8 (liveRegions 11 44 14 degreeUnionState58_50) - -def degreeUnionState58_56 : List PrefixRegion := nextRegions 9 (liveRegions 11 44 14 degreeUnionState58_50) - -def degreeUnionState58_57 : List PrefixRegion := nextRegions 10 (liveRegions 11 44 14 degreeUnionState58_50) - -def degreeUnionState58_58 : List PrefixRegion := nextRegions 11 (liveRegions 11 44 14 degreeUnionState58_50) - -def degreeUnionState58_59 : List PrefixRegion := nextRegions 12 (liveRegions 11 44 14 degreeUnionState58_50) - -def degreeUnionState58_60 : List PrefixRegion := nextRegions 13 (liveRegions 11 44 14 degreeUnionState58_50) - -def degreeUnionState58_61 : List PrefixRegion := nextRegions 14 (liveRegions 11 44 14 degreeUnionState58_50) - -def degreeUnionState58_63 : List PrefixRegion := nextRegions 5 (liveRegions 13 58 14 degreeHalfRegions58) - -def degreeUnionState58_64 : List PrefixRegion := nextRegions 6 (liveRegions 13 58 14 degreeHalfRegions58) - -def degreeUnionState58_65 : List PrefixRegion := nextRegions 7 (liveRegions 13 58 14 degreeHalfRegions58) - -def degreeUnionState58_66 : List PrefixRegion := nextRegions 8 (liveRegions 13 58 14 degreeHalfRegions58) - -def degreeUnionState58_67 : List PrefixRegion := nextRegions 9 (liveRegions 13 58 14 degreeHalfRegions58) - -def degreeUnionState58_68 : List PrefixRegion := nextRegions 10 (liveRegions 13 58 14 degreeHalfRegions58) - -def degreeUnionState58_69 : List PrefixRegion := nextRegions 11 (liveRegions 13 58 14 degreeHalfRegions58) - -def degreeUnionState58_70 : List PrefixRegion := nextRegions 12 (liveRegions 13 58 14 degreeHalfRegions58) - -def degreeUnionState58_71 : List PrefixRegion := nextRegions 4 (liveRegions 12 46 12 degreeUnionState58_70) - -def degreeUnionState58_72 : List PrefixRegion := nextRegions 5 (liveRegions 12 46 12 degreeUnionState58_70) - -def degreeUnionState58_73 : List PrefixRegion := nextRegions 6 (liveRegions 12 46 12 degreeUnionState58_70) - -def degreeUnionState58_74 : List PrefixRegion := nextRegions 7 (liveRegions 12 46 12 degreeUnionState58_70) - -def degreeUnionState58_75 : List PrefixRegion := nextRegions 8 (liveRegions 12 46 12 degreeUnionState58_70) - -def degreeUnionState58_76 : List PrefixRegion := nextRegions 9 (liveRegions 12 46 12 degreeUnionState58_70) - -def degreeUnionState58_77 : List PrefixRegion := nextRegions 10 (liveRegions 12 46 12 degreeUnionState58_70) - -def degreeUnionState58_78 : List PrefixRegion := nextRegions 11 (liveRegions 12 46 12 degreeUnionState58_70) - -def degreeUnionState58_79 : List PrefixRegion := nextRegions 12 (liveRegions 12 46 12 degreeUnionState58_70) - -def degreeUnionState58_80 : List PrefixRegion := nextRegions 13 (liveRegions 13 58 14 degreeHalfRegions58) - -def degreeUnionState58_81 : List PrefixRegion := nextRegions 4 (liveRegions 12 45 13 degreeUnionState58_80) - -def degreeUnionState58_82 : List PrefixRegion := nextRegions 5 (liveRegions 12 45 13 degreeUnionState58_80) - -def degreeUnionState58_83 : List PrefixRegion := nextRegions 6 (liveRegions 12 45 13 degreeUnionState58_80) - -def degreeUnionState58_84 : List PrefixRegion := nextRegions 7 (liveRegions 12 45 13 degreeUnionState58_80) - -def degreeUnionState58_85 : List PrefixRegion := nextRegions 8 (liveRegions 12 45 13 degreeUnionState58_80) - -def degreeUnionState58_86 : List PrefixRegion := nextRegions 9 (liveRegions 12 45 13 degreeUnionState58_80) - -def degreeUnionState58_87 : List PrefixRegion := nextRegions 10 (liveRegions 12 45 13 degreeUnionState58_80) - -def degreeUnionState58_88 : List PrefixRegion := nextRegions 11 (liveRegions 12 45 13 degreeUnionState58_80) - -def degreeUnionState58_89 : List PrefixRegion := nextRegions 12 (liveRegions 12 45 13 degreeUnionState58_80) - -def degreeUnionState58_90 : List PrefixRegion := nextRegions 13 (liveRegions 12 45 13 degreeUnionState58_80) - -def degreeUnionState58_91 : List PrefixRegion := nextRegions 14 (liveRegions 13 58 14 degreeHalfRegions58) - -def degreeUnionState58_93 : List PrefixRegion := nextRegions 5 (liveRegions 14 58 14 degreeHalfRegions58) - -def degreeUnionState58_94 : List PrefixRegion := nextRegions 6 (liveRegions 14 58 14 degreeHalfRegions58) - -def degreeUnionState58_95 : List PrefixRegion := nextRegions 7 (liveRegions 14 58 14 degreeHalfRegions58) - -def degreeUnionState58_96 : List PrefixRegion := nextRegions 8 (liveRegions 14 58 14 degreeHalfRegions58) - -def degreeUnionState58_97 : List PrefixRegion := nextRegions 9 (liveRegions 14 58 14 degreeHalfRegions58) - -def degreeUnionState58_98 : List PrefixRegion := nextRegions 10 (liveRegions 14 58 14 degreeHalfRegions58) - -def degreeUnionState58_99 : List PrefixRegion := nextRegions 11 (liveRegions 14 58 14 degreeHalfRegions58) - -def degreeUnionState58_100 : List PrefixRegion := nextRegions 12 (liveRegions 14 58 14 degreeHalfRegions58) - -def degreeUnionState58_101 : List PrefixRegion := nextRegions 4 (liveRegions 13 46 12 degreeUnionState58_100) - -def degreeUnionState58_102 : List PrefixRegion := nextRegions 5 (liveRegions 13 46 12 degreeUnionState58_100) - -def degreeUnionState58_103 : List PrefixRegion := nextRegions 6 (liveRegions 13 46 12 degreeUnionState58_100) - -def degreeUnionState58_104 : List PrefixRegion := nextRegions 7 (liveRegions 13 46 12 degreeUnionState58_100) - -def degreeUnionState58_105 : List PrefixRegion := nextRegions 8 (liveRegions 13 46 12 degreeUnionState58_100) - -def degreeUnionState58_106 : List PrefixRegion := nextRegions 9 (liveRegions 13 46 12 degreeUnionState58_100) - -def degreeUnionState58_107 : List PrefixRegion := nextRegions 10 (liveRegions 13 46 12 degreeUnionState58_100) - -def degreeUnionState58_108 : List PrefixRegion := nextRegions 11 (liveRegions 13 46 12 degreeUnionState58_100) - -def degreeUnionState58_109 : List PrefixRegion := nextRegions 12 (liveRegions 13 46 12 degreeUnionState58_100) - -def degreeUnionState58_110 : List PrefixRegion := nextRegions 13 (liveRegions 14 58 14 degreeHalfRegions58) - -def degreeUnionState58_111 : List PrefixRegion := nextRegions 14 (liveRegions 14 58 14 degreeHalfRegions58) - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData58 + +namespace OAI + +/-! Degree Union States 58. -/ + +section + +namespace UniversalTensorSquare + +def degreeUnionState58_13 : List PrefixRegion := nextRegions 5 (liveRegions 12 58 14 degreeHalfRegions58) + +def degreeUnionState58_14 : List PrefixRegion := nextRegions 6 (liveRegions 12 58 14 degreeHalfRegions58) + +def degreeUnionState58_15 : List PrefixRegion := nextRegions 7 (liveRegions 12 58 14 degreeHalfRegions58) + +def degreeUnionState58_16 : List PrefixRegion := nextRegions 8 (liveRegions 12 58 14 degreeHalfRegions58) + +def degreeUnionState58_17 : List PrefixRegion := nextRegions 9 (liveRegions 12 58 14 degreeHalfRegions58) + +def degreeUnionState58_18 : List PrefixRegion := nextRegions 10 (liveRegions 12 58 14 degreeHalfRegions58) + +def degreeUnionState58_19 : List PrefixRegion := nextRegions 11 (liveRegions 12 58 14 degreeHalfRegions58) + +def degreeUnionState58_20 : List PrefixRegion := nextRegions 12 (liveRegions 12 58 14 degreeHalfRegions58) + +def degreeUnionState58_21 : List PrefixRegion := nextRegions 5 (liveRegions 11 46 12 degreeUnionState58_20) + +def degreeUnionState58_22 : List PrefixRegion := nextRegions 6 (liveRegions 11 46 12 degreeUnionState58_20) + +def degreeUnionState58_23 : List PrefixRegion := nextRegions 7 (liveRegions 11 46 12 degreeUnionState58_20) + +def degreeUnionState58_24 : List PrefixRegion := nextRegions 8 (liveRegions 11 46 12 degreeUnionState58_20) + +def degreeUnionState58_25 : List PrefixRegion := nextRegions 9 (liveRegions 11 46 12 degreeUnionState58_20) + +def degreeUnionState58_26 : List PrefixRegion := nextRegions 4 (liveRegions 10 37 9 degreeUnionState58_25) + +def degreeUnionState58_27 : List PrefixRegion := nextRegions 5 (liveRegions 10 37 9 degreeUnionState58_25) + +def degreeUnionState58_28 : List PrefixRegion := nextRegions 6 (liveRegions 10 37 9 degreeUnionState58_25) + +def degreeUnionState58_29 : List PrefixRegion := nextRegions 7 (liveRegions 10 37 9 degreeUnionState58_25) + +def degreeUnionState58_30 : List PrefixRegion := nextRegions 8 (liveRegions 10 37 9 degreeUnionState58_25) + +def degreeUnionState58_31 : List PrefixRegion := nextRegions 9 (liveRegions 10 37 9 degreeUnionState58_25) + +def degreeUnionState58_32 : List PrefixRegion := nextRegions 10 (liveRegions 11 46 12 degreeUnionState58_20) + +def degreeUnionState58_33 : List PrefixRegion := nextRegions 11 (liveRegions 11 46 12 degreeUnionState58_20) + +def degreeUnionState58_34 : List PrefixRegion := nextRegions 12 (liveRegions 11 46 12 degreeUnionState58_20) + +def degreeUnionState58_35 : List PrefixRegion := nextRegions 13 (liveRegions 12 58 14 degreeHalfRegions58) + +def degreeUnionState58_36 : List PrefixRegion := nextRegions 5 (liveRegions 11 45 13 degreeUnionState58_35) + +def degreeUnionState58_37 : List PrefixRegion := nextRegions 6 (liveRegions 11 45 13 degreeUnionState58_35) + +def degreeUnionState58_38 : List PrefixRegion := nextRegions 7 (liveRegions 11 45 13 degreeUnionState58_35) + +def degreeUnionState58_39 : List PrefixRegion := nextRegions 8 (liveRegions 11 45 13 degreeUnionState58_35) + +def degreeUnionState58_40 : List PrefixRegion := nextRegions 4 (liveRegions 10 37 8 degreeUnionState58_39) + +def degreeUnionState58_41 : List PrefixRegion := nextRegions 5 (liveRegions 10 37 8 degreeUnionState58_39) + +def degreeUnionState58_42 : List PrefixRegion := nextRegions 6 (liveRegions 10 37 8 degreeUnionState58_39) + +def degreeUnionState58_43 : List PrefixRegion := nextRegions 7 (liveRegions 10 37 8 degreeUnionState58_39) + +def degreeUnionState58_44 : List PrefixRegion := nextRegions 8 (liveRegions 10 37 8 degreeUnionState58_39) + +def degreeUnionState58_45 : List PrefixRegion := nextRegions 9 (liveRegions 11 45 13 degreeUnionState58_35) + +def degreeUnionState58_46 : List PrefixRegion := nextRegions 10 (liveRegions 11 45 13 degreeUnionState58_35) + +def degreeUnionState58_47 : List PrefixRegion := nextRegions 11 (liveRegions 11 45 13 degreeUnionState58_35) + +def degreeUnionState58_48 : List PrefixRegion := nextRegions 12 (liveRegions 11 45 13 degreeUnionState58_35) + +def degreeUnionState58_49 : List PrefixRegion := nextRegions 13 (liveRegions 11 45 13 degreeUnionState58_35) + +def degreeUnionState58_50 : List PrefixRegion := nextRegions 14 (liveRegions 12 58 14 degreeHalfRegions58) + +def degreeUnionState58_51 : List PrefixRegion := nextRegions 4 (liveRegions 11 44 14 degreeUnionState58_50) + +def degreeUnionState58_52 : List PrefixRegion := nextRegions 5 (liveRegions 11 44 14 degreeUnionState58_50) + +def degreeUnionState58_53 : List PrefixRegion := nextRegions 6 (liveRegions 11 44 14 degreeUnionState58_50) + +def degreeUnionState58_54 : List PrefixRegion := nextRegions 7 (liveRegions 11 44 14 degreeUnionState58_50) + +def degreeUnionState58_55 : List PrefixRegion := nextRegions 8 (liveRegions 11 44 14 degreeUnionState58_50) + +def degreeUnionState58_56 : List PrefixRegion := nextRegions 9 (liveRegions 11 44 14 degreeUnionState58_50) + +def degreeUnionState58_57 : List PrefixRegion := nextRegions 10 (liveRegions 11 44 14 degreeUnionState58_50) + +def degreeUnionState58_58 : List PrefixRegion := nextRegions 11 (liveRegions 11 44 14 degreeUnionState58_50) + +def degreeUnionState58_59 : List PrefixRegion := nextRegions 12 (liveRegions 11 44 14 degreeUnionState58_50) + +def degreeUnionState58_60 : List PrefixRegion := nextRegions 13 (liveRegions 11 44 14 degreeUnionState58_50) + +def degreeUnionState58_61 : List PrefixRegion := nextRegions 14 (liveRegions 11 44 14 degreeUnionState58_50) + +def degreeUnionState58_63 : List PrefixRegion := nextRegions 5 (liveRegions 13 58 14 degreeHalfRegions58) + +def degreeUnionState58_64 : List PrefixRegion := nextRegions 6 (liveRegions 13 58 14 degreeHalfRegions58) + +def degreeUnionState58_65 : List PrefixRegion := nextRegions 7 (liveRegions 13 58 14 degreeHalfRegions58) + +def degreeUnionState58_66 : List PrefixRegion := nextRegions 8 (liveRegions 13 58 14 degreeHalfRegions58) + +def degreeUnionState58_67 : List PrefixRegion := nextRegions 9 (liveRegions 13 58 14 degreeHalfRegions58) + +def degreeUnionState58_68 : List PrefixRegion := nextRegions 10 (liveRegions 13 58 14 degreeHalfRegions58) + +def degreeUnionState58_69 : List PrefixRegion := nextRegions 11 (liveRegions 13 58 14 degreeHalfRegions58) + +def degreeUnionState58_70 : List PrefixRegion := nextRegions 12 (liveRegions 13 58 14 degreeHalfRegions58) + +def degreeUnionState58_71 : List PrefixRegion := nextRegions 4 (liveRegions 12 46 12 degreeUnionState58_70) + +def degreeUnionState58_72 : List PrefixRegion := nextRegions 5 (liveRegions 12 46 12 degreeUnionState58_70) + +def degreeUnionState58_73 : List PrefixRegion := nextRegions 6 (liveRegions 12 46 12 degreeUnionState58_70) + +def degreeUnionState58_74 : List PrefixRegion := nextRegions 7 (liveRegions 12 46 12 degreeUnionState58_70) + +def degreeUnionState58_75 : List PrefixRegion := nextRegions 8 (liveRegions 12 46 12 degreeUnionState58_70) + +def degreeUnionState58_76 : List PrefixRegion := nextRegions 9 (liveRegions 12 46 12 degreeUnionState58_70) + +def degreeUnionState58_77 : List PrefixRegion := nextRegions 10 (liveRegions 12 46 12 degreeUnionState58_70) + +def degreeUnionState58_78 : List PrefixRegion := nextRegions 11 (liveRegions 12 46 12 degreeUnionState58_70) + +def degreeUnionState58_79 : List PrefixRegion := nextRegions 12 (liveRegions 12 46 12 degreeUnionState58_70) + +def degreeUnionState58_80 : List PrefixRegion := nextRegions 13 (liveRegions 13 58 14 degreeHalfRegions58) + +def degreeUnionState58_81 : List PrefixRegion := nextRegions 4 (liveRegions 12 45 13 degreeUnionState58_80) + +def degreeUnionState58_82 : List PrefixRegion := nextRegions 5 (liveRegions 12 45 13 degreeUnionState58_80) + +def degreeUnionState58_83 : List PrefixRegion := nextRegions 6 (liveRegions 12 45 13 degreeUnionState58_80) + +def degreeUnionState58_84 : List PrefixRegion := nextRegions 7 (liveRegions 12 45 13 degreeUnionState58_80) + +def degreeUnionState58_85 : List PrefixRegion := nextRegions 8 (liveRegions 12 45 13 degreeUnionState58_80) + +def degreeUnionState58_86 : List PrefixRegion := nextRegions 9 (liveRegions 12 45 13 degreeUnionState58_80) + +def degreeUnionState58_87 : List PrefixRegion := nextRegions 10 (liveRegions 12 45 13 degreeUnionState58_80) + +def degreeUnionState58_88 : List PrefixRegion := nextRegions 11 (liveRegions 12 45 13 degreeUnionState58_80) + +def degreeUnionState58_89 : List PrefixRegion := nextRegions 12 (liveRegions 12 45 13 degreeUnionState58_80) + +def degreeUnionState58_90 : List PrefixRegion := nextRegions 13 (liveRegions 12 45 13 degreeUnionState58_80) + +def degreeUnionState58_91 : List PrefixRegion := nextRegions 14 (liveRegions 13 58 14 degreeHalfRegions58) + +def degreeUnionState58_93 : List PrefixRegion := nextRegions 5 (liveRegions 14 58 14 degreeHalfRegions58) + +def degreeUnionState58_94 : List PrefixRegion := nextRegions 6 (liveRegions 14 58 14 degreeHalfRegions58) + +def degreeUnionState58_95 : List PrefixRegion := nextRegions 7 (liveRegions 14 58 14 degreeHalfRegions58) + +def degreeUnionState58_96 : List PrefixRegion := nextRegions 8 (liveRegions 14 58 14 degreeHalfRegions58) + +def degreeUnionState58_97 : List PrefixRegion := nextRegions 9 (liveRegions 14 58 14 degreeHalfRegions58) + +def degreeUnionState58_98 : List PrefixRegion := nextRegions 10 (liveRegions 14 58 14 degreeHalfRegions58) + +def degreeUnionState58_99 : List PrefixRegion := nextRegions 11 (liveRegions 14 58 14 degreeHalfRegions58) + +def degreeUnionState58_100 : List PrefixRegion := nextRegions 12 (liveRegions 14 58 14 degreeHalfRegions58) + +def degreeUnionState58_101 : List PrefixRegion := nextRegions 4 (liveRegions 13 46 12 degreeUnionState58_100) + +def degreeUnionState58_102 : List PrefixRegion := nextRegions 5 (liveRegions 13 46 12 degreeUnionState58_100) + +def degreeUnionState58_103 : List PrefixRegion := nextRegions 6 (liveRegions 13 46 12 degreeUnionState58_100) + +def degreeUnionState58_104 : List PrefixRegion := nextRegions 7 (liveRegions 13 46 12 degreeUnionState58_100) + +def degreeUnionState58_105 : List PrefixRegion := nextRegions 8 (liveRegions 13 46 12 degreeUnionState58_100) + +def degreeUnionState58_106 : List PrefixRegion := nextRegions 9 (liveRegions 13 46 12 degreeUnionState58_100) + +def degreeUnionState58_107 : List PrefixRegion := nextRegions 10 (liveRegions 13 46 12 degreeUnionState58_100) + +def degreeUnionState58_108 : List PrefixRegion := nextRegions 11 (liveRegions 13 46 12 degreeUnionState58_100) + +def degreeUnionState58_109 : List PrefixRegion := nextRegions 12 (liveRegions 13 46 12 degreeUnionState58_100) + +def degreeUnionState58_110 : List PrefixRegion := nextRegions 13 (liveRegions 14 58 14 degreeHalfRegions58) + +def degreeUnionState58_111 : List PrefixRegion := nextRegions 14 (liveRegions 14 58 14 degreeHalfRegions58) + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates62.lean index 733744b4ce73da9a21a3c7708f3970bb1e6c637e..5bead31632a234d31ac2e5757455c742b9f4e094 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/DegreeUnionStates62.lean @@ -1,2661 +1,2661 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData62 - -namespace OAI - -/-! Degree Union States 62. -/ - -section - -namespace UniversalTensorSquare - -def degreeUnionState62_12 : List PrefixRegion := nextRegions 6 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_13 : List PrefixRegion := nextRegions 7 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_14 : List PrefixRegion := nextRegions 8 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_15 : List PrefixRegion := nextRegions 9 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_16 : List PrefixRegion := nextRegions 10 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_17 : List PrefixRegion := nextRegions 11 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_18 : List PrefixRegion := nextRegions 12 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_19 : List PrefixRegion := nextRegions 5 (liveRegions 10 50 12 degreeUnionState62_18) - -def degreeUnionState62_20 : List PrefixRegion := nextRegions 6 (liveRegions 10 50 12 degreeUnionState62_18) - -def degreeUnionState62_21 : List PrefixRegion := nextRegions 7 (liveRegions 10 50 12 degreeUnionState62_18) - -def degreeUnionState62_22 : List PrefixRegion := nextRegions 8 (liveRegions 10 50 12 degreeUnionState62_18) - -def degreeUnionState62_23 : List PrefixRegion := nextRegions 9 (liveRegions 10 50 12 degreeUnionState62_18) - -def degreeUnionState62_24 : List PrefixRegion := nextRegions 10 (liveRegions 10 50 12 degreeUnionState62_18) - -def degreeUnionState62_25 : List PrefixRegion := nextRegions 11 (liveRegions 10 50 12 degreeUnionState62_18) - -def degreeUnionState62_26 : List PrefixRegion := nextRegions 12 (liveRegions 10 50 12 degreeUnionState62_18) - -def degreeUnionState62_27 : List PrefixRegion := nextRegions 13 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_28 : List PrefixRegion := nextRegions 5 (liveRegions 10 49 13 degreeUnionState62_27) - -def degreeUnionState62_29 : List PrefixRegion := nextRegions 6 (liveRegions 10 49 13 degreeUnionState62_27) - -def degreeUnionState62_30 : List PrefixRegion := nextRegions 7 (liveRegions 10 49 13 degreeUnionState62_27) - -def degreeUnionState62_31 : List PrefixRegion := nextRegions 8 (liveRegions 10 49 13 degreeUnionState62_27) - -def degreeUnionState62_32 : List PrefixRegion := nextRegions 9 (liveRegions 10 49 13 degreeUnionState62_27) - -def degreeUnionState62_33 : List PrefixRegion := nextRegions 10 (liveRegions 10 49 13 degreeUnionState62_27) - -def degreeUnionState62_34 : List PrefixRegion := nextRegions 11 (liveRegions 10 49 13 degreeUnionState62_27) - -def degreeUnionState62_35 : List PrefixRegion := nextRegions 12 (liveRegions 10 49 13 degreeUnionState62_27) - -def degreeUnionState62_36 : List PrefixRegion := nextRegions 13 (liveRegions 10 49 13 degreeUnionState62_27) - -def degreeUnionState62_37 : List PrefixRegion := nextRegions 14 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_38 : List PrefixRegion := nextRegions 5 (liveRegions 10 48 14 degreeUnionState62_37) - -def degreeUnionState62_39 : List PrefixRegion := nextRegions 6 (liveRegions 10 48 14 degreeUnionState62_37) - -def degreeUnionState62_40 : List PrefixRegion := nextRegions 7 (liveRegions 10 48 14 degreeUnionState62_37) - -def degreeUnionState62_41 : List PrefixRegion := nextRegions 8 (liveRegions 10 48 14 degreeUnionState62_37) - -def degreeUnionState62_42 : List PrefixRegion := nextRegions 9 (liveRegions 10 48 14 degreeUnionState62_37) - -def degreeUnionState62_43 : List PrefixRegion := nextRegions 10 (liveRegions 10 48 14 degreeUnionState62_37) - -def degreeUnionState62_44 : List PrefixRegion := nextRegions 11 (liveRegions 10 48 14 degreeUnionState62_37) - -def degreeUnionState62_45 : List PrefixRegion := nextRegions 12 (liveRegions 10 48 14 degreeUnionState62_37) - -def degreeUnionState62_46 : List PrefixRegion := nextRegions 13 (liveRegions 10 48 14 degreeUnionState62_37) - -def degreeUnionState62_47 : List PrefixRegion := nextRegions 14 (liveRegions 10 48 14 degreeUnionState62_37) - -def degreeUnionState62_48 : List PrefixRegion := nextRegions 15 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_49 : List PrefixRegion := nextRegions 16 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_50 : List PrefixRegion := nextRegions 17 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_51 : List PrefixRegion := nextRegions 18 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_52 : List PrefixRegion := nextRegions 19 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_53 : List PrefixRegion := nextRegions 20 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_54 : List PrefixRegion := nextRegions 21 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_55 : List PrefixRegion := nextRegions 22 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_56 : List PrefixRegion := nextRegions 23 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_57 : List PrefixRegion := nextRegions 24 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_58 : List PrefixRegion := nextRegions 25 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_59 : List PrefixRegion := nextRegions 26 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_60 : List PrefixRegion := nextRegions 27 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_61 : List PrefixRegion := nextRegions 28 (liveRegions 11 62 28 degreeHalfRegions62) - -def degreeUnionState62_63 : List PrefixRegion := nextRegions 6 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_64 : List PrefixRegion := nextRegions 7 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_65 : List PrefixRegion := nextRegions 8 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_66 : List PrefixRegion := nextRegions 9 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_67 : List PrefixRegion := nextRegions 10 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_68 : List PrefixRegion := nextRegions 5 (liveRegions 11 52 10 degreeUnionState62_67) - -def degreeUnionState62_69 : List PrefixRegion := nextRegions 6 (liveRegions 11 52 10 degreeUnionState62_67) - -def degreeUnionState62_70 : List PrefixRegion := nextRegions 7 (liveRegions 11 52 10 degreeUnionState62_67) - -def degreeUnionState62_71 : List PrefixRegion := nextRegions 8 (liveRegions 11 52 10 degreeUnionState62_67) - -def degreeUnionState62_72 : List PrefixRegion := nextRegions 9 (liveRegions 11 52 10 degreeUnionState62_67) - -def degreeUnionState62_73 : List PrefixRegion := nextRegions 10 (liveRegions 11 52 10 degreeUnionState62_67) - -def degreeUnionState62_74 : List PrefixRegion := nextRegions 5 (liveRegions 10 42 10 degreeUnionState62_73) - -def degreeUnionState62_75 : List PrefixRegion := nextRegions 6 (liveRegions 10 42 10 degreeUnionState62_73) - -def degreeUnionState62_76 : List PrefixRegion := nextRegions 7 (liveRegions 10 42 10 degreeUnionState62_73) - -def degreeUnionState62_77 : List PrefixRegion := nextRegions 8 (liveRegions 10 42 10 degreeUnionState62_73) - -def degreeUnionState62_78 : List PrefixRegion := nextRegions 9 (liveRegions 10 42 10 degreeUnionState62_73) - -def degreeUnionState62_79 : List PrefixRegion := nextRegions 10 (liveRegions 10 42 10 degreeUnionState62_73) - -def degreeUnionState62_80 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 10 degreeUnionState62_79) - -def degreeUnionState62_81 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 10 degreeUnionState62_79) - -def degreeUnionState62_82 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 10 degreeUnionState62_79) - -def degreeUnionState62_83 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 10 degreeUnionState62_79) - -def degreeUnionState62_84 : List PrefixRegion := nextRegions 8 (liveRegions 9 32 10 degreeUnionState62_79) - -def degreeUnionState62_85 : List PrefixRegion := nextRegions 9 (liveRegions 9 32 10 degreeUnionState62_79) - -def degreeUnionState62_86 : List PrefixRegion := nextRegions 10 (liveRegions 9 32 10 degreeUnionState62_79) - -def degreeUnionState62_87 : List PrefixRegion := nextRegions 11 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_88 : List PrefixRegion := nextRegions 5 (liveRegions 11 51 11 degreeUnionState62_87) - -def degreeUnionState62_89 : List PrefixRegion := nextRegions 6 (liveRegions 11 51 11 degreeUnionState62_87) - -def degreeUnionState62_90 : List PrefixRegion := nextRegions 7 (liveRegions 11 51 11 degreeUnionState62_87) - -def degreeUnionState62_91 : List PrefixRegion := nextRegions 8 (liveRegions 11 51 11 degreeUnionState62_87) - -def degreeUnionState62_92 : List PrefixRegion := nextRegions 9 (liveRegions 11 51 11 degreeUnionState62_87) - -def degreeUnionState62_93 : List PrefixRegion := nextRegions 10 (liveRegions 11 51 11 degreeUnionState62_87) - -def degreeUnionState62_94 : List PrefixRegion := nextRegions 5 (liveRegions 10 41 10 degreeUnionState62_93) - -def degreeUnionState62_95 : List PrefixRegion := nextRegions 6 (liveRegions 10 41 10 degreeUnionState62_93) - -def degreeUnionState62_96 : List PrefixRegion := nextRegions 7 (liveRegions 10 41 10 degreeUnionState62_93) - -def degreeUnionState62_97 : List PrefixRegion := nextRegions 8 (liveRegions 10 41 10 degreeUnionState62_93) - -def degreeUnionState62_98 : List PrefixRegion := nextRegions 9 (liveRegions 10 41 10 degreeUnionState62_93) - -def degreeUnionState62_99 : List PrefixRegion := nextRegions 10 (liveRegions 10 41 10 degreeUnionState62_93) - -def degreeUnionState62_100 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 10 degreeUnionState62_99) - -def degreeUnionState62_101 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 10 degreeUnionState62_99) - -def degreeUnionState62_102 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 10 degreeUnionState62_99) - -def degreeUnionState62_103 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 10 degreeUnionState62_99) - -def degreeUnionState62_104 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 10 degreeUnionState62_99) - -def degreeUnionState62_105 : List PrefixRegion := nextRegions 9 (liveRegions 9 31 10 degreeUnionState62_99) - -def degreeUnionState62_106 : List PrefixRegion := nextRegions 10 (liveRegions 9 31 10 degreeUnionState62_99) - -def degreeUnionState62_107 : List PrefixRegion := nextRegions 11 (liveRegions 11 51 11 degreeUnionState62_87) - -def degreeUnionState62_108 : List PrefixRegion := nextRegions 4 (liveRegions 10 40 11 degreeUnionState62_107) - -def degreeUnionState62_109 : List PrefixRegion := nextRegions 5 (liveRegions 10 40 11 degreeUnionState62_107) - -def degreeUnionState62_110 : List PrefixRegion := nextRegions 6 (liveRegions 10 40 11 degreeUnionState62_107) - -def degreeUnionState62_111 : List PrefixRegion := nextRegions 7 (liveRegions 10 40 11 degreeUnionState62_107) - -def degreeUnionState62_112 : List PrefixRegion := nextRegions 8 (liveRegions 10 40 11 degreeUnionState62_107) - -def degreeUnionState62_113 : List PrefixRegion := nextRegions 9 (liveRegions 10 40 11 degreeUnionState62_107) - -def degreeUnionState62_114 : List PrefixRegion := nextRegions 10 (liveRegions 10 40 11 degreeUnionState62_107) - -def degreeUnionState62_115 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 10 degreeUnionState62_114) - -def degreeUnionState62_116 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 10 degreeUnionState62_114) - -def degreeUnionState62_117 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 10 degreeUnionState62_114) - -def degreeUnionState62_118 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 10 degreeUnionState62_114) - -def degreeUnionState62_119 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 10 degreeUnionState62_114) - -def degreeUnionState62_120 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 10 degreeUnionState62_114) - -def degreeUnionState62_121 : List PrefixRegion := nextRegions 10 (liveRegions 9 30 10 degreeUnionState62_114) - -def degreeUnionState62_122 : List PrefixRegion := nextRegions 11 (liveRegions 10 40 11 degreeUnionState62_107) - -def degreeUnionState62_123 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 11 degreeUnionState62_122) - -def degreeUnionState62_124 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 11 degreeUnionState62_122) - -def degreeUnionState62_125 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 11 degreeUnionState62_122) - -def degreeUnionState62_126 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 11 degreeUnionState62_122) - -def degreeUnionState62_127 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 11 degreeUnionState62_122) - -def degreeUnionState62_128 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 11 degreeUnionState62_122) - -def degreeUnionState62_129 : List PrefixRegion := nextRegions 10 (liveRegions 9 29 11 degreeUnionState62_122) - -def degreeUnionState62_130 : List PrefixRegion := nextRegions 11 (liveRegions 9 29 11 degreeUnionState62_122) - -def degreeUnionState62_131 : List PrefixRegion := nextRegions 12 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_132 : List PrefixRegion := nextRegions 5 (liveRegions 11 50 12 degreeUnionState62_131) - -def degreeUnionState62_133 : List PrefixRegion := nextRegions 6 (liveRegions 11 50 12 degreeUnionState62_131) - -def degreeUnionState62_134 : List PrefixRegion := nextRegions 7 (liveRegions 11 50 12 degreeUnionState62_131) - -def degreeUnionState62_135 : List PrefixRegion := nextRegions 5 (liveRegions 10 43 7 degreeUnionState62_134) - -def degreeUnionState62_136 : List PrefixRegion := nextRegions 6 (liveRegions 10 43 7 degreeUnionState62_134) - -def degreeUnionState62_137 : List PrefixRegion := nextRegions 7 (liveRegions 10 43 7 degreeUnionState62_134) - -def degreeUnionState62_138 : List PrefixRegion := nextRegions 8 (liveRegions 11 50 12 degreeUnionState62_131) - -def degreeUnionState62_139 : List PrefixRegion := nextRegions 5 (liveRegions 10 42 8 degreeUnionState62_138) - -def degreeUnionState62_140 : List PrefixRegion := nextRegions 6 (liveRegions 10 42 8 degreeUnionState62_138) - -def degreeUnionState62_141 : List PrefixRegion := nextRegions 7 (liveRegions 10 42 8 degreeUnionState62_138) - -def degreeUnionState62_142 : List PrefixRegion := nextRegions 4 (liveRegions 9 35 7 degreeUnionState62_141) - -def degreeUnionState62_143 : List PrefixRegion := nextRegions 5 (liveRegions 9 35 7 degreeUnionState62_141) - -def degreeUnionState62_144 : List PrefixRegion := nextRegions 6 (liveRegions 9 35 7 degreeUnionState62_141) - -def degreeUnionState62_145 : List PrefixRegion := nextRegions 7 (liveRegions 9 35 7 degreeUnionState62_141) - -def degreeUnionState62_146 : List PrefixRegion := nextRegions 8 (liveRegions 10 42 8 degreeUnionState62_138) - -def degreeUnionState62_147 : List PrefixRegion := nextRegions 4 (liveRegions 9 34 8 degreeUnionState62_146) - -def degreeUnionState62_148 : List PrefixRegion := nextRegions 5 (liveRegions 9 34 8 degreeUnionState62_146) - -def degreeUnionState62_149 : List PrefixRegion := nextRegions 6 (liveRegions 9 34 8 degreeUnionState62_146) - -def degreeUnionState62_150 : List PrefixRegion := nextRegions 7 (liveRegions 9 34 8 degreeUnionState62_146) - -def degreeUnionState62_151 : List PrefixRegion := nextRegions 8 (liveRegions 9 34 8 degreeUnionState62_146) - -def degreeUnionState62_152 : List PrefixRegion := nextRegions 9 (liveRegions 11 50 12 degreeUnionState62_131) - -def degreeUnionState62_153 : List PrefixRegion := nextRegions 5 (liveRegions 10 41 9 degreeUnionState62_152) - -def degreeUnionState62_154 : List PrefixRegion := nextRegions 6 (liveRegions 10 41 9 degreeUnionState62_152) - -def degreeUnionState62_155 : List PrefixRegion := nextRegions 7 (liveRegions 10 41 9 degreeUnionState62_152) - -def degreeUnionState62_156 : List PrefixRegion := nextRegions 4 (liveRegions 9 34 7 degreeUnionState62_155) - -def degreeUnionState62_157 : List PrefixRegion := nextRegions 5 (liveRegions 9 34 7 degreeUnionState62_155) - -def degreeUnionState62_158 : List PrefixRegion := nextRegions 6 (liveRegions 9 34 7 degreeUnionState62_155) - -def degreeUnionState62_159 : List PrefixRegion := nextRegions 7 (liveRegions 9 34 7 degreeUnionState62_155) - -def degreeUnionState62_160 : List PrefixRegion := nextRegions 8 (liveRegions 10 41 9 degreeUnionState62_152) - -def degreeUnionState62_161 : List PrefixRegion := nextRegions 4 (liveRegions 9 33 8 degreeUnionState62_160) - -def degreeUnionState62_162 : List PrefixRegion := nextRegions 5 (liveRegions 9 33 8 degreeUnionState62_160) - -def degreeUnionState62_163 : List PrefixRegion := nextRegions 6 (liveRegions 9 33 8 degreeUnionState62_160) - -def degreeUnionState62_164 : List PrefixRegion := nextRegions 7 (liveRegions 9 33 8 degreeUnionState62_160) - -def degreeUnionState62_165 : List PrefixRegion := nextRegions 8 (liveRegions 9 33 8 degreeUnionState62_160) - -def degreeUnionState62_166 : List PrefixRegion := nextRegions 9 (liveRegions 10 41 9 degreeUnionState62_152) - -def degreeUnionState62_167 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 9 degreeUnionState62_166) - -def degreeUnionState62_168 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 9 degreeUnionState62_166) - -def degreeUnionState62_169 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 9 degreeUnionState62_166) - -def degreeUnionState62_170 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 9 degreeUnionState62_166) - -def degreeUnionState62_171 : List PrefixRegion := nextRegions 8 (liveRegions 9 32 9 degreeUnionState62_166) - -def degreeUnionState62_172 : List PrefixRegion := nextRegions 9 (liveRegions 9 32 9 degreeUnionState62_166) - -def degreeUnionState62_173 : List PrefixRegion := nextRegions 10 (liveRegions 11 50 12 degreeUnionState62_131) - -def degreeUnionState62_174 : List PrefixRegion := nextRegions 4 (liveRegions 10 40 10 degreeUnionState62_173) - -def degreeUnionState62_175 : List PrefixRegion := nextRegions 5 (liveRegions 10 40 10 degreeUnionState62_173) - -def degreeUnionState62_176 : List PrefixRegion := nextRegions 6 (liveRegions 10 40 10 degreeUnionState62_173) - -def degreeUnionState62_177 : List PrefixRegion := nextRegions 7 (liveRegions 10 40 10 degreeUnionState62_173) - -def degreeUnionState62_178 : List PrefixRegion := nextRegions 4 (liveRegions 9 33 7 degreeUnionState62_177) - -def degreeUnionState62_179 : List PrefixRegion := nextRegions 5 (liveRegions 9 33 7 degreeUnionState62_177) - -def degreeUnionState62_180 : List PrefixRegion := nextRegions 6 (liveRegions 9 33 7 degreeUnionState62_177) - -def degreeUnionState62_181 : List PrefixRegion := nextRegions 7 (liveRegions 9 33 7 degreeUnionState62_177) - -def degreeUnionState62_182 : List PrefixRegion := nextRegions 8 (liveRegions 10 40 10 degreeUnionState62_173) - -def degreeUnionState62_183 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 8 degreeUnionState62_182) - -def degreeUnionState62_184 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 8 degreeUnionState62_182) - -def degreeUnionState62_185 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 8 degreeUnionState62_182) - -def degreeUnionState62_186 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 8 degreeUnionState62_182) - -def degreeUnionState62_187 : List PrefixRegion := nextRegions 8 (liveRegions 9 32 8 degreeUnionState62_182) - -def degreeUnionState62_188 : List PrefixRegion := nextRegions 9 (liveRegions 10 40 10 degreeUnionState62_173) - -def degreeUnionState62_189 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 9 degreeUnionState62_188) - -def degreeUnionState62_190 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 9 degreeUnionState62_188) - -def degreeUnionState62_191 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 9 degreeUnionState62_188) - -def degreeUnionState62_192 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 9 degreeUnionState62_188) - -def degreeUnionState62_193 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 9 degreeUnionState62_188) - -def degreeUnionState62_194 : List PrefixRegion := nextRegions 9 (liveRegions 9 31 9 degreeUnionState62_188) - -def degreeUnionState62_195 : List PrefixRegion := nextRegions 10 (liveRegions 10 40 10 degreeUnionState62_173) - -def degreeUnionState62_196 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 10 degreeUnionState62_195) - -def degreeUnionState62_197 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 10 degreeUnionState62_195) - -def degreeUnionState62_198 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 10 degreeUnionState62_195) - -def degreeUnionState62_199 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 10 degreeUnionState62_195) - -def degreeUnionState62_200 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 10 degreeUnionState62_195) - -def degreeUnionState62_201 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 10 degreeUnionState62_195) - -def degreeUnionState62_202 : List PrefixRegion := nextRegions 10 (liveRegions 9 30 10 degreeUnionState62_195) - -def degreeUnionState62_203 : List PrefixRegion := nextRegions 11 (liveRegions 11 50 12 degreeUnionState62_131) - -def degreeUnionState62_204 : List PrefixRegion := nextRegions 4 (liveRegions 10 39 11 degreeUnionState62_203) - -def degreeUnionState62_205 : List PrefixRegion := nextRegions 5 (liveRegions 10 39 11 degreeUnionState62_203) - -def degreeUnionState62_206 : List PrefixRegion := nextRegions 6 (liveRegions 10 39 11 degreeUnionState62_203) - -def degreeUnionState62_207 : List PrefixRegion := nextRegions 7 (liveRegions 10 39 11 degreeUnionState62_203) - -def degreeUnionState62_208 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 7 degreeUnionState62_207) - -def degreeUnionState62_209 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 7 degreeUnionState62_207) - -def degreeUnionState62_210 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 7 degreeUnionState62_207) - -def degreeUnionState62_211 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 7 degreeUnionState62_207) - -def degreeUnionState62_212 : List PrefixRegion := nextRegions 8 (liveRegions 10 39 11 degreeUnionState62_203) - -def degreeUnionState62_213 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 8 degreeUnionState62_212) - -def degreeUnionState62_214 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 8 degreeUnionState62_212) - -def degreeUnionState62_215 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 8 degreeUnionState62_212) - -def degreeUnionState62_216 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 8 degreeUnionState62_212) - -def degreeUnionState62_217 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 8 degreeUnionState62_212) - -def degreeUnionState62_218 : List PrefixRegion := nextRegions 9 (liveRegions 10 39 11 degreeUnionState62_203) - -def degreeUnionState62_219 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 9 degreeUnionState62_218) - -def degreeUnionState62_220 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 9 degreeUnionState62_218) - -def degreeUnionState62_221 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 9 degreeUnionState62_218) - -def degreeUnionState62_222 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 9 degreeUnionState62_218) - -def degreeUnionState62_223 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 9 degreeUnionState62_218) - -def degreeUnionState62_224 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 9 degreeUnionState62_218) - -def degreeUnionState62_225 : List PrefixRegion := nextRegions 10 (liveRegions 10 39 11 degreeUnionState62_203) - -def degreeUnionState62_226 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 10 degreeUnionState62_225) - -def degreeUnionState62_227 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 10 degreeUnionState62_225) - -def degreeUnionState62_228 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 10 degreeUnionState62_225) - -def degreeUnionState62_229 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 10 degreeUnionState62_225) - -def degreeUnionState62_230 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 10 degreeUnionState62_225) - -def degreeUnionState62_231 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 10 degreeUnionState62_225) - -def degreeUnionState62_232 : List PrefixRegion := nextRegions 10 (liveRegions 9 29 10 degreeUnionState62_225) - -def degreeUnionState62_233 : List PrefixRegion := nextRegions 11 (liveRegions 10 39 11 degreeUnionState62_203) - -def degreeUnionState62_234 : List PrefixRegion := nextRegions 12 (liveRegions 11 50 12 degreeUnionState62_131) - -def degreeUnionState62_235 : List PrefixRegion := nextRegions 4 (liveRegions 10 38 12 degreeUnionState62_234) - -def degreeUnionState62_236 : List PrefixRegion := nextRegions 5 (liveRegions 10 38 12 degreeUnionState62_234) - -def degreeUnionState62_237 : List PrefixRegion := nextRegions 6 (liveRegions 10 38 12 degreeUnionState62_234) - -def degreeUnionState62_238 : List PrefixRegion := nextRegions 7 (liveRegions 10 38 12 degreeUnionState62_234) - -def degreeUnionState62_239 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 7 degreeUnionState62_238) - -def degreeUnionState62_240 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 7 degreeUnionState62_238) - -def degreeUnionState62_241 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 7 degreeUnionState62_238) - -def degreeUnionState62_242 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 7 degreeUnionState62_238) - -def degreeUnionState62_243 : List PrefixRegion := nextRegions 8 (liveRegions 10 38 12 degreeUnionState62_234) - -def degreeUnionState62_244 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 8 degreeUnionState62_243) - -def degreeUnionState62_245 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 8 degreeUnionState62_243) - -def degreeUnionState62_246 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 8 degreeUnionState62_243) - -def degreeUnionState62_247 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 8 degreeUnionState62_243) - -def degreeUnionState62_248 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 8 degreeUnionState62_243) - -def degreeUnionState62_249 : List PrefixRegion := nextRegions 9 (liveRegions 10 38 12 degreeUnionState62_234) - -def degreeUnionState62_250 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 9 degreeUnionState62_249) - -def degreeUnionState62_251 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 9 degreeUnionState62_249) - -def degreeUnionState62_252 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 9 degreeUnionState62_249) - -def degreeUnionState62_253 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 9 degreeUnionState62_249) - -def degreeUnionState62_254 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 9 degreeUnionState62_249) - -def degreeUnionState62_255 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 9 degreeUnionState62_249) - -def degreeUnionState62_256 : List PrefixRegion := nextRegions 10 (liveRegions 10 38 12 degreeUnionState62_234) - -def degreeUnionState62_257 : List PrefixRegion := nextRegions 11 (liveRegions 10 38 12 degreeUnionState62_234) - -def degreeUnionState62_258 : List PrefixRegion := nextRegions 12 (liveRegions 10 38 12 degreeUnionState62_234) - -def degreeUnionState62_259 : List PrefixRegion := nextRegions 13 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_260 : List PrefixRegion := nextRegions 5 (liveRegions 11 49 13 degreeUnionState62_259) - -def degreeUnionState62_261 : List PrefixRegion := nextRegions 6 (liveRegions 11 49 13 degreeUnionState62_259) - -def degreeUnionState62_262 : List PrefixRegion := nextRegions 7 (liveRegions 11 49 13 degreeUnionState62_259) - -def degreeUnionState62_263 : List PrefixRegion := nextRegions 5 (liveRegions 10 42 7 degreeUnionState62_262) - -def degreeUnionState62_264 : List PrefixRegion := nextRegions 6 (liveRegions 10 42 7 degreeUnionState62_262) - -def degreeUnionState62_265 : List PrefixRegion := nextRegions 7 (liveRegions 10 42 7 degreeUnionState62_262) - -def degreeUnionState62_266 : List PrefixRegion := nextRegions 4 (liveRegions 9 35 7 degreeUnionState62_265) - -def degreeUnionState62_267 : List PrefixRegion := nextRegions 5 (liveRegions 9 35 7 degreeUnionState62_265) - -def degreeUnionState62_268 : List PrefixRegion := nextRegions 6 (liveRegions 9 35 7 degreeUnionState62_265) - -def degreeUnionState62_269 : List PrefixRegion := nextRegions 7 (liveRegions 9 35 7 degreeUnionState62_265) - -def degreeUnionState62_270 : List PrefixRegion := nextRegions 8 (liveRegions 11 49 13 degreeUnionState62_259) - -def degreeUnionState62_271 : List PrefixRegion := nextRegions 5 (liveRegions 10 41 8 degreeUnionState62_270) - -def degreeUnionState62_272 : List PrefixRegion := nextRegions 6 (liveRegions 10 41 8 degreeUnionState62_270) - -def degreeUnionState62_273 : List PrefixRegion := nextRegions 7 (liveRegions 10 41 8 degreeUnionState62_270) - -def degreeUnionState62_274 : List PrefixRegion := nextRegions 4 (liveRegions 9 34 7 degreeUnionState62_273) - -def degreeUnionState62_275 : List PrefixRegion := nextRegions 5 (liveRegions 9 34 7 degreeUnionState62_273) - -def degreeUnionState62_276 : List PrefixRegion := nextRegions 6 (liveRegions 9 34 7 degreeUnionState62_273) - -def degreeUnionState62_277 : List PrefixRegion := nextRegions 7 (liveRegions 9 34 7 degreeUnionState62_273) - -def degreeUnionState62_278 : List PrefixRegion := nextRegions 8 (liveRegions 10 41 8 degreeUnionState62_270) - -def degreeUnionState62_279 : List PrefixRegion := nextRegions 4 (liveRegions 9 33 8 degreeUnionState62_278) - -def degreeUnionState62_280 : List PrefixRegion := nextRegions 5 (liveRegions 9 33 8 degreeUnionState62_278) - -def degreeUnionState62_281 : List PrefixRegion := nextRegions 6 (liveRegions 9 33 8 degreeUnionState62_278) - -def degreeUnionState62_282 : List PrefixRegion := nextRegions 7 (liveRegions 9 33 8 degreeUnionState62_278) - -def degreeUnionState62_283 : List PrefixRegion := nextRegions 8 (liveRegions 9 33 8 degreeUnionState62_278) - -def degreeUnionState62_284 : List PrefixRegion := nextRegions 9 (liveRegions 11 49 13 degreeUnionState62_259) - -def degreeUnionState62_285 : List PrefixRegion := nextRegions 4 (liveRegions 10 40 9 degreeUnionState62_284) - -def degreeUnionState62_286 : List PrefixRegion := nextRegions 5 (liveRegions 10 40 9 degreeUnionState62_284) - -def degreeUnionState62_287 : List PrefixRegion := nextRegions 6 (liveRegions 10 40 9 degreeUnionState62_284) - -def degreeUnionState62_288 : List PrefixRegion := nextRegions 7 (liveRegions 10 40 9 degreeUnionState62_284) - -def degreeUnionState62_289 : List PrefixRegion := nextRegions 4 (liveRegions 9 33 7 degreeUnionState62_288) - -def degreeUnionState62_290 : List PrefixRegion := nextRegions 5 (liveRegions 9 33 7 degreeUnionState62_288) - -def degreeUnionState62_291 : List PrefixRegion := nextRegions 6 (liveRegions 9 33 7 degreeUnionState62_288) - -def degreeUnionState62_292 : List PrefixRegion := nextRegions 7 (liveRegions 9 33 7 degreeUnionState62_288) - -def degreeUnionState62_293 : List PrefixRegion := nextRegions 8 (liveRegions 10 40 9 degreeUnionState62_284) - -def degreeUnionState62_294 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 8 degreeUnionState62_293) - -def degreeUnionState62_295 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 8 degreeUnionState62_293) - -def degreeUnionState62_296 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 8 degreeUnionState62_293) - -def degreeUnionState62_297 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 8 degreeUnionState62_293) - -def degreeUnionState62_298 : List PrefixRegion := nextRegions 8 (liveRegions 9 32 8 degreeUnionState62_293) - -def degreeUnionState62_299 : List PrefixRegion := nextRegions 9 (liveRegions 10 40 9 degreeUnionState62_284) - -def degreeUnionState62_300 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 9 degreeUnionState62_299) - -def degreeUnionState62_301 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 9 degreeUnionState62_299) - -def degreeUnionState62_302 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 9 degreeUnionState62_299) - -def degreeUnionState62_303 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 9 degreeUnionState62_299) - -def degreeUnionState62_304 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 9 degreeUnionState62_299) - -def degreeUnionState62_305 : List PrefixRegion := nextRegions 9 (liveRegions 9 31 9 degreeUnionState62_299) - -def degreeUnionState62_306 : List PrefixRegion := nextRegions 10 (liveRegions 11 49 13 degreeUnionState62_259) - -def degreeUnionState62_307 : List PrefixRegion := nextRegions 4 (liveRegions 10 39 10 degreeUnionState62_306) - -def degreeUnionState62_308 : List PrefixRegion := nextRegions 5 (liveRegions 10 39 10 degreeUnionState62_306) - -def degreeUnionState62_309 : List PrefixRegion := nextRegions 6 (liveRegions 10 39 10 degreeUnionState62_306) - -def degreeUnionState62_310 : List PrefixRegion := nextRegions 7 (liveRegions 10 39 10 degreeUnionState62_306) - -def degreeUnionState62_311 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 7 degreeUnionState62_310) - -def degreeUnionState62_312 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 7 degreeUnionState62_310) - -def degreeUnionState62_313 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 7 degreeUnionState62_310) - -def degreeUnionState62_314 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 7 degreeUnionState62_310) - -def degreeUnionState62_315 : List PrefixRegion := nextRegions 8 (liveRegions 10 39 10 degreeUnionState62_306) - -def degreeUnionState62_316 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 8 degreeUnionState62_315) - -def degreeUnionState62_317 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 8 degreeUnionState62_315) - -def degreeUnionState62_318 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 8 degreeUnionState62_315) - -def degreeUnionState62_319 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 8 degreeUnionState62_315) - -def degreeUnionState62_320 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 8 degreeUnionState62_315) - -def degreeUnionState62_321 : List PrefixRegion := nextRegions 9 (liveRegions 10 39 10 degreeUnionState62_306) - -def degreeUnionState62_322 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 9 degreeUnionState62_321) - -def degreeUnionState62_323 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 9 degreeUnionState62_321) - -def degreeUnionState62_324 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 9 degreeUnionState62_321) - -def degreeUnionState62_325 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 9 degreeUnionState62_321) - -def degreeUnionState62_326 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 9 degreeUnionState62_321) - -def degreeUnionState62_327 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 9 degreeUnionState62_321) - -def degreeUnionState62_328 : List PrefixRegion := nextRegions 10 (liveRegions 10 39 10 degreeUnionState62_306) - -def degreeUnionState62_329 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 10 degreeUnionState62_328) - -def degreeUnionState62_330 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 10 degreeUnionState62_328) - -def degreeUnionState62_331 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 10 degreeUnionState62_328) - -def degreeUnionState62_332 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 10 degreeUnionState62_328) - -def degreeUnionState62_333 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 10 degreeUnionState62_328) - -def degreeUnionState62_334 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 10 degreeUnionState62_328) - -def degreeUnionState62_335 : List PrefixRegion := nextRegions 10 (liveRegions 9 29 10 degreeUnionState62_328) - -def degreeUnionState62_336 : List PrefixRegion := nextRegions 11 (liveRegions 11 49 13 degreeUnionState62_259) - -def degreeUnionState62_337 : List PrefixRegion := nextRegions 4 (liveRegions 10 38 11 degreeUnionState62_336) - -def degreeUnionState62_338 : List PrefixRegion := nextRegions 5 (liveRegions 10 38 11 degreeUnionState62_336) - -def degreeUnionState62_339 : List PrefixRegion := nextRegions 6 (liveRegions 10 38 11 degreeUnionState62_336) - -def degreeUnionState62_340 : List PrefixRegion := nextRegions 7 (liveRegions 10 38 11 degreeUnionState62_336) - -def degreeUnionState62_341 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 7 degreeUnionState62_340) - -def degreeUnionState62_342 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 7 degreeUnionState62_340) - -def degreeUnionState62_343 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 7 degreeUnionState62_340) - -def degreeUnionState62_344 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 7 degreeUnionState62_340) - -def degreeUnionState62_345 : List PrefixRegion := nextRegions 8 (liveRegions 10 38 11 degreeUnionState62_336) - -def degreeUnionState62_346 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 8 degreeUnionState62_345) - -def degreeUnionState62_347 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 8 degreeUnionState62_345) - -def degreeUnionState62_348 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 8 degreeUnionState62_345) - -def degreeUnionState62_349 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 8 degreeUnionState62_345) - -def degreeUnionState62_350 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 8 degreeUnionState62_345) - -def degreeUnionState62_351 : List PrefixRegion := nextRegions 9 (liveRegions 10 38 11 degreeUnionState62_336) - -def degreeUnionState62_352 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 9 degreeUnionState62_351) - -def degreeUnionState62_353 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 9 degreeUnionState62_351) - -def degreeUnionState62_354 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 9 degreeUnionState62_351) - -def degreeUnionState62_355 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 9 degreeUnionState62_351) - -def degreeUnionState62_356 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 9 degreeUnionState62_351) - -def degreeUnionState62_357 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 9 degreeUnionState62_351) - -def degreeUnionState62_358 : List PrefixRegion := nextRegions 10 (liveRegions 10 38 11 degreeUnionState62_336) - -def degreeUnionState62_359 : List PrefixRegion := nextRegions 11 (liveRegions 10 38 11 degreeUnionState62_336) - -def degreeUnionState62_360 : List PrefixRegion := nextRegions 12 (liveRegions 11 49 13 degreeUnionState62_259) - -def degreeUnionState62_361 : List PrefixRegion := nextRegions 4 (liveRegions 10 37 12 degreeUnionState62_360) - -def degreeUnionState62_362 : List PrefixRegion := nextRegions 5 (liveRegions 10 37 12 degreeUnionState62_360) - -def degreeUnionState62_363 : List PrefixRegion := nextRegions 6 (liveRegions 10 37 12 degreeUnionState62_360) - -def degreeUnionState62_364 : List PrefixRegion := nextRegions 7 (liveRegions 10 37 12 degreeUnionState62_360) - -def degreeUnionState62_365 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 7 degreeUnionState62_364) - -def degreeUnionState62_366 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 7 degreeUnionState62_364) - -def degreeUnionState62_367 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 7 degreeUnionState62_364) - -def degreeUnionState62_368 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 7 degreeUnionState62_364) - -def degreeUnionState62_369 : List PrefixRegion := nextRegions 8 (liveRegions 10 37 12 degreeUnionState62_360) - -def degreeUnionState62_370 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 8 degreeUnionState62_369) - -def degreeUnionState62_371 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 8 degreeUnionState62_369) - -def degreeUnionState62_372 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 8 degreeUnionState62_369) - -def degreeUnionState62_373 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 8 degreeUnionState62_369) - -def degreeUnionState62_374 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 8 degreeUnionState62_369) - -def degreeUnionState62_375 : List PrefixRegion := nextRegions 9 (liveRegions 10 37 12 degreeUnionState62_360) - -def degreeUnionState62_376 : List PrefixRegion := nextRegions 10 (liveRegions 10 37 12 degreeUnionState62_360) - -def degreeUnionState62_377 : List PrefixRegion := nextRegions 11 (liveRegions 10 37 12 degreeUnionState62_360) - -def degreeUnionState62_378 : List PrefixRegion := nextRegions 12 (liveRegions 10 37 12 degreeUnionState62_360) - -def degreeUnionState62_379 : List PrefixRegion := nextRegions 13 (liveRegions 11 49 13 degreeUnionState62_259) - -def degreeUnionState62_380 : List PrefixRegion := nextRegions 4 (liveRegions 10 36 13 degreeUnionState62_379) - -def degreeUnionState62_381 : List PrefixRegion := nextRegions 5 (liveRegions 10 36 13 degreeUnionState62_379) - -def degreeUnionState62_382 : List PrefixRegion := nextRegions 6 (liveRegions 10 36 13 degreeUnionState62_379) - -def degreeUnionState62_383 : List PrefixRegion := nextRegions 7 (liveRegions 10 36 13 degreeUnionState62_379) - -def degreeUnionState62_384 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 7 degreeUnionState62_383) - -def degreeUnionState62_385 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 7 degreeUnionState62_383) - -def degreeUnionState62_386 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 7 degreeUnionState62_383) - -def degreeUnionState62_387 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 7 degreeUnionState62_383) - -def degreeUnionState62_388 : List PrefixRegion := nextRegions 8 (liveRegions 10 36 13 degreeUnionState62_379) - -def degreeUnionState62_389 : List PrefixRegion := nextRegions 9 (liveRegions 10 36 13 degreeUnionState62_379) - -def degreeUnionState62_390 : List PrefixRegion := nextRegions 10 (liveRegions 10 36 13 degreeUnionState62_379) - -def degreeUnionState62_391 : List PrefixRegion := nextRegions 11 (liveRegions 10 36 13 degreeUnionState62_379) - -def degreeUnionState62_392 : List PrefixRegion := nextRegions 12 (liveRegions 10 36 13 degreeUnionState62_379) - -def degreeUnionState62_393 : List PrefixRegion := nextRegions 13 (liveRegions 10 36 13 degreeUnionState62_379) - -def degreeUnionState62_394 : List PrefixRegion := nextRegions 14 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_395 : List PrefixRegion := nextRegions 5 (liveRegions 11 48 14 degreeUnionState62_394) - -def degreeUnionState62_396 : List PrefixRegion := nextRegions 6 (liveRegions 11 48 14 degreeUnionState62_394) - -def degreeUnionState62_397 : List PrefixRegion := nextRegions 7 (liveRegions 11 48 14 degreeUnionState62_394) - -def degreeUnionState62_398 : List PrefixRegion := nextRegions 5 (liveRegions 10 41 7 degreeUnionState62_397) - -def degreeUnionState62_399 : List PrefixRegion := nextRegions 6 (liveRegions 10 41 7 degreeUnionState62_397) - -def degreeUnionState62_400 : List PrefixRegion := nextRegions 7 (liveRegions 10 41 7 degreeUnionState62_397) - -def degreeUnionState62_401 : List PrefixRegion := nextRegions 4 (liveRegions 9 34 7 degreeUnionState62_400) - -def degreeUnionState62_402 : List PrefixRegion := nextRegions 5 (liveRegions 9 34 7 degreeUnionState62_400) - -def degreeUnionState62_403 : List PrefixRegion := nextRegions 6 (liveRegions 9 34 7 degreeUnionState62_400) - -def degreeUnionState62_404 : List PrefixRegion := nextRegions 7 (liveRegions 9 34 7 degreeUnionState62_400) - -def degreeUnionState62_405 : List PrefixRegion := nextRegions 8 (liveRegions 11 48 14 degreeUnionState62_394) - -def degreeUnionState62_406 : List PrefixRegion := nextRegions 4 (liveRegions 10 40 8 degreeUnionState62_405) - -def degreeUnionState62_407 : List PrefixRegion := nextRegions 5 (liveRegions 10 40 8 degreeUnionState62_405) - -def degreeUnionState62_408 : List PrefixRegion := nextRegions 6 (liveRegions 10 40 8 degreeUnionState62_405) - -def degreeUnionState62_409 : List PrefixRegion := nextRegions 7 (liveRegions 10 40 8 degreeUnionState62_405) - -def degreeUnionState62_410 : List PrefixRegion := nextRegions 4 (liveRegions 9 33 7 degreeUnionState62_409) - -def degreeUnionState62_411 : List PrefixRegion := nextRegions 5 (liveRegions 9 33 7 degreeUnionState62_409) - -def degreeUnionState62_412 : List PrefixRegion := nextRegions 6 (liveRegions 9 33 7 degreeUnionState62_409) - -def degreeUnionState62_413 : List PrefixRegion := nextRegions 7 (liveRegions 9 33 7 degreeUnionState62_409) - -def degreeUnionState62_414 : List PrefixRegion := nextRegions 8 (liveRegions 10 40 8 degreeUnionState62_405) - -def degreeUnionState62_415 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 8 degreeUnionState62_414) - -def degreeUnionState62_416 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 8 degreeUnionState62_414) - -def degreeUnionState62_417 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 8 degreeUnionState62_414) - -def degreeUnionState62_418 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 8 degreeUnionState62_414) - -def degreeUnionState62_419 : List PrefixRegion := nextRegions 8 (liveRegions 9 32 8 degreeUnionState62_414) - -def degreeUnionState62_420 : List PrefixRegion := nextRegions 9 (liveRegions 11 48 14 degreeUnionState62_394) - -def degreeUnionState62_421 : List PrefixRegion := nextRegions 4 (liveRegions 10 39 9 degreeUnionState62_420) - -def degreeUnionState62_422 : List PrefixRegion := nextRegions 5 (liveRegions 10 39 9 degreeUnionState62_420) - -def degreeUnionState62_423 : List PrefixRegion := nextRegions 6 (liveRegions 10 39 9 degreeUnionState62_420) - -def degreeUnionState62_424 : List PrefixRegion := nextRegions 7 (liveRegions 10 39 9 degreeUnionState62_420) - -def degreeUnionState62_425 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 7 degreeUnionState62_424) - -def degreeUnionState62_426 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 7 degreeUnionState62_424) - -def degreeUnionState62_427 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 7 degreeUnionState62_424) - -def degreeUnionState62_428 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 7 degreeUnionState62_424) - -def degreeUnionState62_429 : List PrefixRegion := nextRegions 8 (liveRegions 10 39 9 degreeUnionState62_420) - -def degreeUnionState62_430 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 8 degreeUnionState62_429) - -def degreeUnionState62_431 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 8 degreeUnionState62_429) - -def degreeUnionState62_432 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 8 degreeUnionState62_429) - -def degreeUnionState62_433 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 8 degreeUnionState62_429) - -def degreeUnionState62_434 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 8 degreeUnionState62_429) - -def degreeUnionState62_435 : List PrefixRegion := nextRegions 9 (liveRegions 10 39 9 degreeUnionState62_420) - -def degreeUnionState62_436 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 9 degreeUnionState62_435) - -def degreeUnionState62_437 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 9 degreeUnionState62_435) - -def degreeUnionState62_438 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 9 degreeUnionState62_435) - -def degreeUnionState62_439 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 9 degreeUnionState62_435) - -def degreeUnionState62_440 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 9 degreeUnionState62_435) - -def degreeUnionState62_441 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 9 degreeUnionState62_435) - -def degreeUnionState62_442 : List PrefixRegion := nextRegions 10 (liveRegions 11 48 14 degreeUnionState62_394) - -def degreeUnionState62_443 : List PrefixRegion := nextRegions 4 (liveRegions 10 38 10 degreeUnionState62_442) - -def degreeUnionState62_444 : List PrefixRegion := nextRegions 5 (liveRegions 10 38 10 degreeUnionState62_442) - -def degreeUnionState62_445 : List PrefixRegion := nextRegions 6 (liveRegions 10 38 10 degreeUnionState62_442) - -def degreeUnionState62_446 : List PrefixRegion := nextRegions 7 (liveRegions 10 38 10 degreeUnionState62_442) - -def degreeUnionState62_447 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 7 degreeUnionState62_446) - -def degreeUnionState62_448 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 7 degreeUnionState62_446) - -def degreeUnionState62_449 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 7 degreeUnionState62_446) - -def degreeUnionState62_450 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 7 degreeUnionState62_446) - -def degreeUnionState62_451 : List PrefixRegion := nextRegions 8 (liveRegions 10 38 10 degreeUnionState62_442) - -def degreeUnionState62_452 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 8 degreeUnionState62_451) - -def degreeUnionState62_453 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 8 degreeUnionState62_451) - -def degreeUnionState62_454 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 8 degreeUnionState62_451) - -def degreeUnionState62_455 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 8 degreeUnionState62_451) - -def degreeUnionState62_456 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 8 degreeUnionState62_451) - -def degreeUnionState62_457 : List PrefixRegion := nextRegions 9 (liveRegions 10 38 10 degreeUnionState62_442) - -def degreeUnionState62_458 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 9 degreeUnionState62_457) - -def degreeUnionState62_459 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 9 degreeUnionState62_457) - -def degreeUnionState62_460 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 9 degreeUnionState62_457) - -def degreeUnionState62_461 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 9 degreeUnionState62_457) - -def degreeUnionState62_462 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 9 degreeUnionState62_457) - -def degreeUnionState62_463 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 9 degreeUnionState62_457) - -def degreeUnionState62_464 : List PrefixRegion := nextRegions 10 (liveRegions 10 38 10 degreeUnionState62_442) - -def degreeUnionState62_465 : List PrefixRegion := nextRegions 11 (liveRegions 11 48 14 degreeUnionState62_394) - -def degreeUnionState62_466 : List PrefixRegion := nextRegions 4 (liveRegions 10 37 11 degreeUnionState62_465) - -def degreeUnionState62_467 : List PrefixRegion := nextRegions 5 (liveRegions 10 37 11 degreeUnionState62_465) - -def degreeUnionState62_468 : List PrefixRegion := nextRegions 6 (liveRegions 10 37 11 degreeUnionState62_465) - -def degreeUnionState62_469 : List PrefixRegion := nextRegions 7 (liveRegions 10 37 11 degreeUnionState62_465) - -def degreeUnionState62_470 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 7 degreeUnionState62_469) - -def degreeUnionState62_471 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 7 degreeUnionState62_469) - -def degreeUnionState62_472 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 7 degreeUnionState62_469) - -def degreeUnionState62_473 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 7 degreeUnionState62_469) - -def degreeUnionState62_474 : List PrefixRegion := nextRegions 8 (liveRegions 10 37 11 degreeUnionState62_465) - -def degreeUnionState62_475 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 8 degreeUnionState62_474) - -def degreeUnionState62_476 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 8 degreeUnionState62_474) - -def degreeUnionState62_477 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 8 degreeUnionState62_474) - -def degreeUnionState62_478 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 8 degreeUnionState62_474) - -def degreeUnionState62_479 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 8 degreeUnionState62_474) - -def degreeUnionState62_480 : List PrefixRegion := nextRegions 9 (liveRegions 10 37 11 degreeUnionState62_465) - -def degreeUnionState62_481 : List PrefixRegion := nextRegions 10 (liveRegions 10 37 11 degreeUnionState62_465) - -def degreeUnionState62_482 : List PrefixRegion := nextRegions 11 (liveRegions 10 37 11 degreeUnionState62_465) - -def degreeUnionState62_483 : List PrefixRegion := nextRegions 12 (liveRegions 11 48 14 degreeUnionState62_394) - -def degreeUnionState62_484 : List PrefixRegion := nextRegions 4 (liveRegions 10 36 12 degreeUnionState62_483) - -def degreeUnionState62_485 : List PrefixRegion := nextRegions 5 (liveRegions 10 36 12 degreeUnionState62_483) - -def degreeUnionState62_486 : List PrefixRegion := nextRegions 6 (liveRegions 10 36 12 degreeUnionState62_483) - -def degreeUnionState62_487 : List PrefixRegion := nextRegions 7 (liveRegions 10 36 12 degreeUnionState62_483) - -def degreeUnionState62_488 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 7 degreeUnionState62_487) - -def degreeUnionState62_489 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 7 degreeUnionState62_487) - -def degreeUnionState62_490 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 7 degreeUnionState62_487) - -def degreeUnionState62_491 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 7 degreeUnionState62_487) - -def degreeUnionState62_492 : List PrefixRegion := nextRegions 8 (liveRegions 10 36 12 degreeUnionState62_483) - -def degreeUnionState62_493 : List PrefixRegion := nextRegions 9 (liveRegions 10 36 12 degreeUnionState62_483) - -def degreeUnionState62_494 : List PrefixRegion := nextRegions 10 (liveRegions 10 36 12 degreeUnionState62_483) - -def degreeUnionState62_495 : List PrefixRegion := nextRegions 11 (liveRegions 10 36 12 degreeUnionState62_483) - -def degreeUnionState62_496 : List PrefixRegion := nextRegions 12 (liveRegions 10 36 12 degreeUnionState62_483) - -def degreeUnionState62_497 : List PrefixRegion := nextRegions 13 (liveRegions 11 48 14 degreeUnionState62_394) - -def degreeUnionState62_498 : List PrefixRegion := nextRegions 14 (liveRegions 11 48 14 degreeUnionState62_394) - -def degreeUnionState62_499 : List PrefixRegion := nextRegions 15 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_500 : List PrefixRegion := nextRegions 16 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_501 : List PrefixRegion := nextRegions 17 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_502 : List PrefixRegion := nextRegions 18 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_503 : List PrefixRegion := nextRegions 19 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_504 : List PrefixRegion := nextRegions 20 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_505 : List PrefixRegion := nextRegions 21 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_506 : List PrefixRegion := nextRegions 22 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_507 : List PrefixRegion := nextRegions 23 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_508 : List PrefixRegion := nextRegions 24 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_509 : List PrefixRegion := nextRegions 25 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_510 : List PrefixRegion := nextRegions 26 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_511 : List PrefixRegion := nextRegions 27 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_512 : List PrefixRegion := nextRegions 28 (liveRegions 12 62 28 degreeHalfRegions62) - -def degreeUnionState62_514 : List PrefixRegion := nextRegions 5 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_515 : List PrefixRegion := nextRegions 6 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_516 : List PrefixRegion := nextRegions 7 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_517 : List PrefixRegion := nextRegions 8 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_518 : List PrefixRegion := nextRegions 9 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_519 : List PrefixRegion := nextRegions 10 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_520 : List PrefixRegion := nextRegions 5 (liveRegions 12 52 10 degreeUnionState62_519) - -def degreeUnionState62_521 : List PrefixRegion := nextRegions 6 (liveRegions 12 52 10 degreeUnionState62_519) - -def degreeUnionState62_522 : List PrefixRegion := nextRegions 7 (liveRegions 12 52 10 degreeUnionState62_519) - -def degreeUnionState62_523 : List PrefixRegion := nextRegions 8 (liveRegions 12 52 10 degreeUnionState62_519) - -def degreeUnionState62_524 : List PrefixRegion := nextRegions 9 (liveRegions 12 52 10 degreeUnionState62_519) - -def degreeUnionState62_525 : List PrefixRegion := nextRegions 10 (liveRegions 12 52 10 degreeUnionState62_519) - -def degreeUnionState62_526 : List PrefixRegion := nextRegions 4 (liveRegions 11 42 10 degreeUnionState62_525) - -def degreeUnionState62_527 : List PrefixRegion := nextRegions 5 (liveRegions 11 42 10 degreeUnionState62_525) - -def degreeUnionState62_528 : List PrefixRegion := nextRegions 6 (liveRegions 11 42 10 degreeUnionState62_525) - -def degreeUnionState62_529 : List PrefixRegion := nextRegions 7 (liveRegions 11 42 10 degreeUnionState62_525) - -def degreeUnionState62_530 : List PrefixRegion := nextRegions 8 (liveRegions 11 42 10 degreeUnionState62_525) - -def degreeUnionState62_531 : List PrefixRegion := nextRegions 9 (liveRegions 11 42 10 degreeUnionState62_525) - -def degreeUnionState62_532 : List PrefixRegion := nextRegions 10 (liveRegions 11 42 10 degreeUnionState62_525) - -def degreeUnionState62_533 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 10 degreeUnionState62_532) - -def degreeUnionState62_534 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 10 degreeUnionState62_532) - -def degreeUnionState62_535 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 10 degreeUnionState62_532) - -def degreeUnionState62_536 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 10 degreeUnionState62_532) - -def degreeUnionState62_537 : List PrefixRegion := nextRegions 8 (liveRegions 10 32 10 degreeUnionState62_532) - -def degreeUnionState62_538 : List PrefixRegion := nextRegions 9 (liveRegions 10 32 10 degreeUnionState62_532) - -def degreeUnionState62_539 : List PrefixRegion := nextRegions 10 (liveRegions 10 32 10 degreeUnionState62_532) - -def degreeUnionState62_540 : List PrefixRegion := nextRegions 11 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_541 : List PrefixRegion := nextRegions 5 (liveRegions 12 51 11 degreeUnionState62_540) - -def degreeUnionState62_542 : List PrefixRegion := nextRegions 6 (liveRegions 12 51 11 degreeUnionState62_540) - -def degreeUnionState62_543 : List PrefixRegion := nextRegions 7 (liveRegions 12 51 11 degreeUnionState62_540) - -def degreeUnionState62_544 : List PrefixRegion := nextRegions 8 (liveRegions 12 51 11 degreeUnionState62_540) - -def degreeUnionState62_545 : List PrefixRegion := nextRegions 9 (liveRegions 12 51 11 degreeUnionState62_540) - -def degreeUnionState62_546 : List PrefixRegion := nextRegions 10 (liveRegions 12 51 11 degreeUnionState62_540) - -def degreeUnionState62_547 : List PrefixRegion := nextRegions 4 (liveRegions 11 41 10 degreeUnionState62_546) - -def degreeUnionState62_548 : List PrefixRegion := nextRegions 5 (liveRegions 11 41 10 degreeUnionState62_546) - -def degreeUnionState62_549 : List PrefixRegion := nextRegions 6 (liveRegions 11 41 10 degreeUnionState62_546) - -def degreeUnionState62_550 : List PrefixRegion := nextRegions 7 (liveRegions 11 41 10 degreeUnionState62_546) - -def degreeUnionState62_551 : List PrefixRegion := nextRegions 8 (liveRegions 11 41 10 degreeUnionState62_546) - -def degreeUnionState62_552 : List PrefixRegion := nextRegions 9 (liveRegions 11 41 10 degreeUnionState62_546) - -def degreeUnionState62_553 : List PrefixRegion := nextRegions 10 (liveRegions 11 41 10 degreeUnionState62_546) - -def degreeUnionState62_554 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 10 degreeUnionState62_553) - -def degreeUnionState62_555 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 10 degreeUnionState62_553) - -def degreeUnionState62_556 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 10 degreeUnionState62_553) - -def degreeUnionState62_557 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 10 degreeUnionState62_553) - -def degreeUnionState62_558 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 10 degreeUnionState62_553) - -def degreeUnionState62_559 : List PrefixRegion := nextRegions 9 (liveRegions 10 31 10 degreeUnionState62_553) - -def degreeUnionState62_560 : List PrefixRegion := nextRegions 10 (liveRegions 10 31 10 degreeUnionState62_553) - -def degreeUnionState62_561 : List PrefixRegion := nextRegions 11 (liveRegions 12 51 11 degreeUnionState62_540) - -def degreeUnionState62_562 : List PrefixRegion := nextRegions 4 (liveRegions 11 40 11 degreeUnionState62_561) - -def degreeUnionState62_563 : List PrefixRegion := nextRegions 5 (liveRegions 11 40 11 degreeUnionState62_561) - -def degreeUnionState62_564 : List PrefixRegion := nextRegions 6 (liveRegions 11 40 11 degreeUnionState62_561) - -def degreeUnionState62_565 : List PrefixRegion := nextRegions 7 (liveRegions 11 40 11 degreeUnionState62_561) - -def degreeUnionState62_566 : List PrefixRegion := nextRegions 8 (liveRegions 11 40 11 degreeUnionState62_561) - -def degreeUnionState62_567 : List PrefixRegion := nextRegions 9 (liveRegions 11 40 11 degreeUnionState62_561) - -def degreeUnionState62_568 : List PrefixRegion := nextRegions 10 (liveRegions 11 40 11 degreeUnionState62_561) - -def degreeUnionState62_569 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 10 degreeUnionState62_568) - -def degreeUnionState62_570 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 10 degreeUnionState62_568) - -def degreeUnionState62_571 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 10 degreeUnionState62_568) - -def degreeUnionState62_572 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 10 degreeUnionState62_568) - -def degreeUnionState62_573 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 10 degreeUnionState62_568) - -def degreeUnionState62_574 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 10 degreeUnionState62_568) - -def degreeUnionState62_575 : List PrefixRegion := nextRegions 9 (liveRegions 10 30 10 degreeUnionState62_568) - -def degreeUnionState62_576 : List PrefixRegion := nextRegions 10 (liveRegions 10 30 10 degreeUnionState62_568) - -def degreeUnionState62_577 : List PrefixRegion := nextRegions 11 (liveRegions 11 40 11 degreeUnionState62_561) - -def degreeUnionState62_578 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 11 degreeUnionState62_577) - -def degreeUnionState62_579 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 11 degreeUnionState62_577) - -def degreeUnionState62_580 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 11 degreeUnionState62_577) - -def degreeUnionState62_581 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 11 degreeUnionState62_577) - -def degreeUnionState62_582 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 11 degreeUnionState62_577) - -def degreeUnionState62_583 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 11 degreeUnionState62_577) - -def degreeUnionState62_584 : List PrefixRegion := nextRegions 9 (liveRegions 10 29 11 degreeUnionState62_577) - -def degreeUnionState62_585 : List PrefixRegion := nextRegions 10 (liveRegions 10 29 11 degreeUnionState62_577) - -def degreeUnionState62_586 : List PrefixRegion := nextRegions 11 (liveRegions 10 29 11 degreeUnionState62_577) - -def degreeUnionState62_587 : List PrefixRegion := nextRegions 12 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_588 : List PrefixRegion := nextRegions 5 (liveRegions 12 50 12 degreeUnionState62_587) - -def degreeUnionState62_589 : List PrefixRegion := nextRegions 6 (liveRegions 12 50 12 degreeUnionState62_587) - -def degreeUnionState62_590 : List PrefixRegion := nextRegions 7 (liveRegions 12 50 12 degreeUnionState62_587) - -def degreeUnionState62_591 : List PrefixRegion := nextRegions 8 (liveRegions 12 50 12 degreeUnionState62_587) - -def degreeUnionState62_592 : List PrefixRegion := nextRegions 4 (liveRegions 11 42 8 degreeUnionState62_591) - -def degreeUnionState62_593 : List PrefixRegion := nextRegions 5 (liveRegions 11 42 8 degreeUnionState62_591) - -def degreeUnionState62_594 : List PrefixRegion := nextRegions 6 (liveRegions 11 42 8 degreeUnionState62_591) - -def degreeUnionState62_595 : List PrefixRegion := nextRegions 7 (liveRegions 11 42 8 degreeUnionState62_591) - -def degreeUnionState62_596 : List PrefixRegion := nextRegions 8 (liveRegions 11 42 8 degreeUnionState62_591) - -def degreeUnionState62_597 : List PrefixRegion := nextRegions 4 (liveRegions 10 34 8 degreeUnionState62_596) - -def degreeUnionState62_598 : List PrefixRegion := nextRegions 5 (liveRegions 10 34 8 degreeUnionState62_596) - -def degreeUnionState62_599 : List PrefixRegion := nextRegions 6 (liveRegions 10 34 8 degreeUnionState62_596) - -def degreeUnionState62_600 : List PrefixRegion := nextRegions 7 (liveRegions 10 34 8 degreeUnionState62_596) - -def degreeUnionState62_601 : List PrefixRegion := nextRegions 8 (liveRegions 10 34 8 degreeUnionState62_596) - -def degreeUnionState62_602 : List PrefixRegion := nextRegions 9 (liveRegions 12 50 12 degreeUnionState62_587) - -def degreeUnionState62_603 : List PrefixRegion := nextRegions 4 (liveRegions 11 41 9 degreeUnionState62_602) - -def degreeUnionState62_604 : List PrefixRegion := nextRegions 5 (liveRegions 11 41 9 degreeUnionState62_602) - -def degreeUnionState62_605 : List PrefixRegion := nextRegions 6 (liveRegions 11 41 9 degreeUnionState62_602) - -def degreeUnionState62_606 : List PrefixRegion := nextRegions 7 (liveRegions 11 41 9 degreeUnionState62_602) - -def degreeUnionState62_607 : List PrefixRegion := nextRegions 8 (liveRegions 11 41 9 degreeUnionState62_602) - -def degreeUnionState62_608 : List PrefixRegion := nextRegions 4 (liveRegions 10 33 8 degreeUnionState62_607) - -def degreeUnionState62_609 : List PrefixRegion := nextRegions 5 (liveRegions 10 33 8 degreeUnionState62_607) - -def degreeUnionState62_610 : List PrefixRegion := nextRegions 6 (liveRegions 10 33 8 degreeUnionState62_607) - -def degreeUnionState62_611 : List PrefixRegion := nextRegions 7 (liveRegions 10 33 8 degreeUnionState62_607) - -def degreeUnionState62_612 : List PrefixRegion := nextRegions 8 (liveRegions 10 33 8 degreeUnionState62_607) - -def degreeUnionState62_613 : List PrefixRegion := nextRegions 9 (liveRegions 11 41 9 degreeUnionState62_602) - -def degreeUnionState62_614 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 9 degreeUnionState62_613) - -def degreeUnionState62_615 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 9 degreeUnionState62_613) - -def degreeUnionState62_616 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 9 degreeUnionState62_613) - -def degreeUnionState62_617 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 9 degreeUnionState62_613) - -def degreeUnionState62_618 : List PrefixRegion := nextRegions 8 (liveRegions 10 32 9 degreeUnionState62_613) - -def degreeUnionState62_619 : List PrefixRegion := nextRegions 9 (liveRegions 10 32 9 degreeUnionState62_613) - -def degreeUnionState62_620 : List PrefixRegion := nextRegions 10 (liveRegions 12 50 12 degreeUnionState62_587) - -def degreeUnionState62_621 : List PrefixRegion := nextRegions 4 (liveRegions 11 40 10 degreeUnionState62_620) - -def degreeUnionState62_622 : List PrefixRegion := nextRegions 5 (liveRegions 11 40 10 degreeUnionState62_620) - -def degreeUnionState62_623 : List PrefixRegion := nextRegions 6 (liveRegions 11 40 10 degreeUnionState62_620) - -def degreeUnionState62_624 : List PrefixRegion := nextRegions 7 (liveRegions 11 40 10 degreeUnionState62_620) - -def degreeUnionState62_625 : List PrefixRegion := nextRegions 8 (liveRegions 11 40 10 degreeUnionState62_620) - -def degreeUnionState62_626 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 8 degreeUnionState62_625) - -def degreeUnionState62_627 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 8 degreeUnionState62_625) - -def degreeUnionState62_628 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 8 degreeUnionState62_625) - -def degreeUnionState62_629 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 8 degreeUnionState62_625) - -def degreeUnionState62_630 : List PrefixRegion := nextRegions 8 (liveRegions 10 32 8 degreeUnionState62_625) - -def degreeUnionState62_631 : List PrefixRegion := nextRegions 9 (liveRegions 11 40 10 degreeUnionState62_620) - -def degreeUnionState62_632 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 9 degreeUnionState62_631) - -def degreeUnionState62_633 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 9 degreeUnionState62_631) - -def degreeUnionState62_634 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 9 degreeUnionState62_631) - -def degreeUnionState62_635 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 9 degreeUnionState62_631) - -def degreeUnionState62_636 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 9 degreeUnionState62_631) - -def degreeUnionState62_637 : List PrefixRegion := nextRegions 9 (liveRegions 10 31 9 degreeUnionState62_631) - -def degreeUnionState62_638 : List PrefixRegion := nextRegions 10 (liveRegions 11 40 10 degreeUnionState62_620) - -def degreeUnionState62_639 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 10 degreeUnionState62_638) - -def degreeUnionState62_640 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 10 degreeUnionState62_638) - -def degreeUnionState62_641 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 10 degreeUnionState62_638) - -def degreeUnionState62_642 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 10 degreeUnionState62_638) - -def degreeUnionState62_643 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 10 degreeUnionState62_638) - -def degreeUnionState62_644 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 10 degreeUnionState62_638) - -def degreeUnionState62_645 : List PrefixRegion := nextRegions 9 (liveRegions 10 30 10 degreeUnionState62_638) - -def degreeUnionState62_646 : List PrefixRegion := nextRegions 10 (liveRegions 10 30 10 degreeUnionState62_638) - -def degreeUnionState62_647 : List PrefixRegion := nextRegions 11 (liveRegions 12 50 12 degreeUnionState62_587) - -def degreeUnionState62_648 : List PrefixRegion := nextRegions 4 (liveRegions 11 39 11 degreeUnionState62_647) - -def degreeUnionState62_649 : List PrefixRegion := nextRegions 5 (liveRegions 11 39 11 degreeUnionState62_647) - -def degreeUnionState62_650 : List PrefixRegion := nextRegions 6 (liveRegions 11 39 11 degreeUnionState62_647) - -def degreeUnionState62_651 : List PrefixRegion := nextRegions 7 (liveRegions 11 39 11 degreeUnionState62_647) - -def degreeUnionState62_652 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 7 degreeUnionState62_651) - -def degreeUnionState62_653 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 7 degreeUnionState62_651) - -def degreeUnionState62_654 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 7 degreeUnionState62_651) - -def degreeUnionState62_655 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 7 degreeUnionState62_651) - -def degreeUnionState62_656 : List PrefixRegion := nextRegions 8 (liveRegions 11 39 11 degreeUnionState62_647) - -def degreeUnionState62_657 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 8 degreeUnionState62_656) - -def degreeUnionState62_658 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 8 degreeUnionState62_656) - -def degreeUnionState62_659 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 8 degreeUnionState62_656) - -def degreeUnionState62_660 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 8 degreeUnionState62_656) - -def degreeUnionState62_661 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 8 degreeUnionState62_656) - -def degreeUnionState62_662 : List PrefixRegion := nextRegions 9 (liveRegions 11 39 11 degreeUnionState62_647) - -def degreeUnionState62_663 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 9 degreeUnionState62_662) - -def degreeUnionState62_664 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 9 degreeUnionState62_662) - -def degreeUnionState62_665 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 9 degreeUnionState62_662) - -def degreeUnionState62_666 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 9 degreeUnionState62_662) - -def degreeUnionState62_667 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 9 degreeUnionState62_662) - -def degreeUnionState62_668 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 9 degreeUnionState62_662) - -def degreeUnionState62_669 : List PrefixRegion := nextRegions 9 (liveRegions 10 30 9 degreeUnionState62_662) - -def degreeUnionState62_670 : List PrefixRegion := nextRegions 10 (liveRegions 11 39 11 degreeUnionState62_647) - -def degreeUnionState62_671 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 10 degreeUnionState62_670) - -def degreeUnionState62_672 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 10 degreeUnionState62_670) - -def degreeUnionState62_673 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 10 degreeUnionState62_670) - -def degreeUnionState62_674 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 10 degreeUnionState62_670) - -def degreeUnionState62_675 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 10 degreeUnionState62_670) - -def degreeUnionState62_676 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 10 degreeUnionState62_670) - -def degreeUnionState62_677 : List PrefixRegion := nextRegions 9 (liveRegions 10 29 10 degreeUnionState62_670) - -def degreeUnionState62_678 : List PrefixRegion := nextRegions 10 (liveRegions 10 29 10 degreeUnionState62_670) - -def degreeUnionState62_679 : List PrefixRegion := nextRegions 11 (liveRegions 11 39 11 degreeUnionState62_647) - -def degreeUnionState62_680 : List PrefixRegion := nextRegions 12 (liveRegions 12 50 12 degreeUnionState62_587) - -def degreeUnionState62_681 : List PrefixRegion := nextRegions 4 (liveRegions 11 38 12 degreeUnionState62_680) - -def degreeUnionState62_682 : List PrefixRegion := nextRegions 5 (liveRegions 11 38 12 degreeUnionState62_680) - -def degreeUnionState62_683 : List PrefixRegion := nextRegions 6 (liveRegions 11 38 12 degreeUnionState62_680) - -def degreeUnionState62_684 : List PrefixRegion := nextRegions 7 (liveRegions 11 38 12 degreeUnionState62_680) - -def degreeUnionState62_685 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 7 degreeUnionState62_684) - -def degreeUnionState62_686 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 7 degreeUnionState62_684) - -def degreeUnionState62_687 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 7 degreeUnionState62_684) - -def degreeUnionState62_688 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 7 degreeUnionState62_684) - -def degreeUnionState62_689 : List PrefixRegion := nextRegions 8 (liveRegions 11 38 12 degreeUnionState62_680) - -def degreeUnionState62_690 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 8 degreeUnionState62_689) - -def degreeUnionState62_691 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 8 degreeUnionState62_689) - -def degreeUnionState62_692 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 8 degreeUnionState62_689) - -def degreeUnionState62_693 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 8 degreeUnionState62_689) - -def degreeUnionState62_694 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 8 degreeUnionState62_689) - -def degreeUnionState62_695 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 8 degreeUnionState62_689) - -def degreeUnionState62_696 : List PrefixRegion := nextRegions 9 (liveRegions 11 38 12 degreeUnionState62_680) - -def degreeUnionState62_697 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 9 degreeUnionState62_696) - -def degreeUnionState62_698 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 9 degreeUnionState62_696) - -def degreeUnionState62_699 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 9 degreeUnionState62_696) - -def degreeUnionState62_700 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 9 degreeUnionState62_696) - -def degreeUnionState62_701 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 9 degreeUnionState62_696) - -def degreeUnionState62_702 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 9 degreeUnionState62_696) - -def degreeUnionState62_703 : List PrefixRegion := nextRegions 9 (liveRegions 10 29 9 degreeUnionState62_696) - -def degreeUnionState62_704 : List PrefixRegion := nextRegions 10 (liveRegions 11 38 12 degreeUnionState62_680) - -def degreeUnionState62_705 : List PrefixRegion := nextRegions 11 (liveRegions 11 38 12 degreeUnionState62_680) - -def degreeUnionState62_706 : List PrefixRegion := nextRegions 12 (liveRegions 11 38 12 degreeUnionState62_680) - -def degreeUnionState62_707 : List PrefixRegion := nextRegions 13 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_708 : List PrefixRegion := nextRegions 5 (liveRegions 12 49 13 degreeUnionState62_707) - -def degreeUnionState62_709 : List PrefixRegion := nextRegions 6 (liveRegions 12 49 13 degreeUnionState62_707) - -def degreeUnionState62_710 : List PrefixRegion := nextRegions 7 (liveRegions 12 49 13 degreeUnionState62_707) - -def degreeUnionState62_711 : List PrefixRegion := nextRegions 4 (liveRegions 11 42 7 degreeUnionState62_710) - -def degreeUnionState62_712 : List PrefixRegion := nextRegions 5 (liveRegions 11 42 7 degreeUnionState62_710) - -def degreeUnionState62_713 : List PrefixRegion := nextRegions 6 (liveRegions 11 42 7 degreeUnionState62_710) - -def degreeUnionState62_714 : List PrefixRegion := nextRegions 7 (liveRegions 11 42 7 degreeUnionState62_710) - -def degreeUnionState62_715 : List PrefixRegion := nextRegions 8 (liveRegions 12 49 13 degreeUnionState62_707) - -def degreeUnionState62_716 : List PrefixRegion := nextRegions 4 (liveRegions 11 41 8 degreeUnionState62_715) - -def degreeUnionState62_717 : List PrefixRegion := nextRegions 5 (liveRegions 11 41 8 degreeUnionState62_715) - -def degreeUnionState62_718 : List PrefixRegion := nextRegions 6 (liveRegions 11 41 8 degreeUnionState62_715) - -def degreeUnionState62_719 : List PrefixRegion := nextRegions 7 (liveRegions 11 41 8 degreeUnionState62_715) - -def degreeUnionState62_720 : List PrefixRegion := nextRegions 8 (liveRegions 11 41 8 degreeUnionState62_715) - -def degreeUnionState62_721 : List PrefixRegion := nextRegions 4 (liveRegions 10 33 8 degreeUnionState62_720) - -def degreeUnionState62_722 : List PrefixRegion := nextRegions 5 (liveRegions 10 33 8 degreeUnionState62_720) - -def degreeUnionState62_723 : List PrefixRegion := nextRegions 6 (liveRegions 10 33 8 degreeUnionState62_720) - -def degreeUnionState62_724 : List PrefixRegion := nextRegions 7 (liveRegions 10 33 8 degreeUnionState62_720) - -def degreeUnionState62_725 : List PrefixRegion := nextRegions 8 (liveRegions 10 33 8 degreeUnionState62_720) - -def degreeUnionState62_726 : List PrefixRegion := nextRegions 9 (liveRegions 12 49 13 degreeUnionState62_707) - -def degreeUnionState62_727 : List PrefixRegion := nextRegions 4 (liveRegions 11 40 9 degreeUnionState62_726) - -def degreeUnionState62_728 : List PrefixRegion := nextRegions 5 (liveRegions 11 40 9 degreeUnionState62_726) - -def degreeUnionState62_729 : List PrefixRegion := nextRegions 6 (liveRegions 11 40 9 degreeUnionState62_726) - -def degreeUnionState62_730 : List PrefixRegion := nextRegions 7 (liveRegions 11 40 9 degreeUnionState62_726) - -def degreeUnionState62_731 : List PrefixRegion := nextRegions 8 (liveRegions 11 40 9 degreeUnionState62_726) - -def degreeUnionState62_732 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 8 degreeUnionState62_731) - -def degreeUnionState62_733 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 8 degreeUnionState62_731) - -def degreeUnionState62_734 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 8 degreeUnionState62_731) - -def degreeUnionState62_735 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 8 degreeUnionState62_731) - -def degreeUnionState62_736 : List PrefixRegion := nextRegions 8 (liveRegions 10 32 8 degreeUnionState62_731) - -def degreeUnionState62_737 : List PrefixRegion := nextRegions 9 (liveRegions 11 40 9 degreeUnionState62_726) - -def degreeUnionState62_738 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 9 degreeUnionState62_737) - -def degreeUnionState62_739 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 9 degreeUnionState62_737) - -def degreeUnionState62_740 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 9 degreeUnionState62_737) - -def degreeUnionState62_741 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 9 degreeUnionState62_737) - -def degreeUnionState62_742 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 9 degreeUnionState62_737) - -def degreeUnionState62_743 : List PrefixRegion := nextRegions 9 (liveRegions 10 31 9 degreeUnionState62_737) - -def degreeUnionState62_744 : List PrefixRegion := nextRegions 10 (liveRegions 12 49 13 degreeUnionState62_707) - -def degreeUnionState62_745 : List PrefixRegion := nextRegions 4 (liveRegions 11 39 10 degreeUnionState62_744) - -def degreeUnionState62_746 : List PrefixRegion := nextRegions 5 (liveRegions 11 39 10 degreeUnionState62_744) - -def degreeUnionState62_747 : List PrefixRegion := nextRegions 6 (liveRegions 11 39 10 degreeUnionState62_744) - -def degreeUnionState62_748 : List PrefixRegion := nextRegions 7 (liveRegions 11 39 10 degreeUnionState62_744) - -def degreeUnionState62_749 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 7 degreeUnionState62_748) - -def degreeUnionState62_750 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 7 degreeUnionState62_748) - -def degreeUnionState62_751 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 7 degreeUnionState62_748) - -def degreeUnionState62_752 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 7 degreeUnionState62_748) - -def degreeUnionState62_753 : List PrefixRegion := nextRegions 8 (liveRegions 11 39 10 degreeUnionState62_744) - -def degreeUnionState62_754 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 8 degreeUnionState62_753) - -def degreeUnionState62_755 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 8 degreeUnionState62_753) - -def degreeUnionState62_756 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 8 degreeUnionState62_753) - -def degreeUnionState62_757 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 8 degreeUnionState62_753) - -def degreeUnionState62_758 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 8 degreeUnionState62_753) - -def degreeUnionState62_759 : List PrefixRegion := nextRegions 9 (liveRegions 11 39 10 degreeUnionState62_744) - -def degreeUnionState62_760 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 9 degreeUnionState62_759) - -def degreeUnionState62_761 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 9 degreeUnionState62_759) - -def degreeUnionState62_762 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 9 degreeUnionState62_759) - -def degreeUnionState62_763 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 9 degreeUnionState62_759) - -def degreeUnionState62_764 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 9 degreeUnionState62_759) - -def degreeUnionState62_765 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 9 degreeUnionState62_759) - -def degreeUnionState62_766 : List PrefixRegion := nextRegions 9 (liveRegions 10 30 9 degreeUnionState62_759) - -def degreeUnionState62_767 : List PrefixRegion := nextRegions 10 (liveRegions 11 39 10 degreeUnionState62_744) - -def degreeUnionState62_768 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 10 degreeUnionState62_767) - -def degreeUnionState62_769 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 10 degreeUnionState62_767) - -def degreeUnionState62_770 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 10 degreeUnionState62_767) - -def degreeUnionState62_771 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 10 degreeUnionState62_767) - -def degreeUnionState62_772 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 10 degreeUnionState62_767) - -def degreeUnionState62_773 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 10 degreeUnionState62_767) - -def degreeUnionState62_774 : List PrefixRegion := nextRegions 9 (liveRegions 10 29 10 degreeUnionState62_767) - -def degreeUnionState62_775 : List PrefixRegion := nextRegions 10 (liveRegions 10 29 10 degreeUnionState62_767) - -def degreeUnionState62_776 : List PrefixRegion := nextRegions 11 (liveRegions 12 49 13 degreeUnionState62_707) - -def degreeUnionState62_777 : List PrefixRegion := nextRegions 4 (liveRegions 11 38 11 degreeUnionState62_776) - -def degreeUnionState62_778 : List PrefixRegion := nextRegions 5 (liveRegions 11 38 11 degreeUnionState62_776) - -def degreeUnionState62_779 : List PrefixRegion := nextRegions 6 (liveRegions 11 38 11 degreeUnionState62_776) - -def degreeUnionState62_780 : List PrefixRegion := nextRegions 7 (liveRegions 11 38 11 degreeUnionState62_776) - -def degreeUnionState62_781 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 7 degreeUnionState62_780) - -def degreeUnionState62_782 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 7 degreeUnionState62_780) - -def degreeUnionState62_783 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 7 degreeUnionState62_780) - -def degreeUnionState62_784 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 7 degreeUnionState62_780) - -def degreeUnionState62_785 : List PrefixRegion := nextRegions 8 (liveRegions 11 38 11 degreeUnionState62_776) - -def degreeUnionState62_786 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 8 degreeUnionState62_785) - -def degreeUnionState62_787 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 8 degreeUnionState62_785) - -def degreeUnionState62_788 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 8 degreeUnionState62_785) - -def degreeUnionState62_789 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 8 degreeUnionState62_785) - -def degreeUnionState62_790 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 8 degreeUnionState62_785) - -def degreeUnionState62_791 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 8 degreeUnionState62_785) - -def degreeUnionState62_792 : List PrefixRegion := nextRegions 9 (liveRegions 11 38 11 degreeUnionState62_776) - -def degreeUnionState62_793 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 9 degreeUnionState62_792) - -def degreeUnionState62_794 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 9 degreeUnionState62_792) - -def degreeUnionState62_795 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 9 degreeUnionState62_792) - -def degreeUnionState62_796 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 9 degreeUnionState62_792) - -def degreeUnionState62_797 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 9 degreeUnionState62_792) - -def degreeUnionState62_798 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 9 degreeUnionState62_792) - -def degreeUnionState62_799 : List PrefixRegion := nextRegions 9 (liveRegions 10 29 9 degreeUnionState62_792) - -def degreeUnionState62_800 : List PrefixRegion := nextRegions 10 (liveRegions 11 38 11 degreeUnionState62_776) - -def degreeUnionState62_801 : List PrefixRegion := nextRegions 11 (liveRegions 11 38 11 degreeUnionState62_776) - -def degreeUnionState62_802 : List PrefixRegion := nextRegions 12 (liveRegions 12 49 13 degreeUnionState62_707) - -def degreeUnionState62_803 : List PrefixRegion := nextRegions 4 (liveRegions 11 37 12 degreeUnionState62_802) - -def degreeUnionState62_804 : List PrefixRegion := nextRegions 5 (liveRegions 11 37 12 degreeUnionState62_802) - -def degreeUnionState62_805 : List PrefixRegion := nextRegions 6 (liveRegions 11 37 12 degreeUnionState62_802) - -def degreeUnionState62_806 : List PrefixRegion := nextRegions 7 (liveRegions 11 37 12 degreeUnionState62_802) - -def degreeUnionState62_807 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 7 degreeUnionState62_806) - -def degreeUnionState62_808 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 7 degreeUnionState62_806) - -def degreeUnionState62_809 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 7 degreeUnionState62_806) - -def degreeUnionState62_810 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 7 degreeUnionState62_806) - -def degreeUnionState62_811 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 7 degreeUnionState62_806) - -def degreeUnionState62_812 : List PrefixRegion := nextRegions 8 (liveRegions 11 37 12 degreeUnionState62_802) - -def degreeUnionState62_813 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 8 degreeUnionState62_812) - -def degreeUnionState62_814 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 8 degreeUnionState62_812) - -def degreeUnionState62_815 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 8 degreeUnionState62_812) - -def degreeUnionState62_816 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 8 degreeUnionState62_812) - -def degreeUnionState62_817 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 8 degreeUnionState62_812) - -def degreeUnionState62_818 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 8 degreeUnionState62_812) - -def degreeUnionState62_819 : List PrefixRegion := nextRegions 9 (liveRegions 11 37 12 degreeUnionState62_802) - -def degreeUnionState62_820 : List PrefixRegion := nextRegions 10 (liveRegions 11 37 12 degreeUnionState62_802) - -def degreeUnionState62_821 : List PrefixRegion := nextRegions 11 (liveRegions 11 37 12 degreeUnionState62_802) - -def degreeUnionState62_822 : List PrefixRegion := nextRegions 12 (liveRegions 11 37 12 degreeUnionState62_802) - -def degreeUnionState62_823 : List PrefixRegion := nextRegions 13 (liveRegions 12 49 13 degreeUnionState62_707) - -def degreeUnionState62_824 : List PrefixRegion := nextRegions 4 (liveRegions 11 36 13 degreeUnionState62_823) - -def degreeUnionState62_825 : List PrefixRegion := nextRegions 5 (liveRegions 11 36 13 degreeUnionState62_823) - -def degreeUnionState62_826 : List PrefixRegion := nextRegions 6 (liveRegions 11 36 13 degreeUnionState62_823) - -def degreeUnionState62_827 : List PrefixRegion := nextRegions 7 (liveRegions 11 36 13 degreeUnionState62_823) - -def degreeUnionState62_828 : List PrefixRegion := nextRegions 8 (liveRegions 11 36 13 degreeUnionState62_823) - -def degreeUnionState62_829 : List PrefixRegion := nextRegions 9 (liveRegions 11 36 13 degreeUnionState62_823) - -def degreeUnionState62_830 : List PrefixRegion := nextRegions 10 (liveRegions 11 36 13 degreeUnionState62_823) - -def degreeUnionState62_831 : List PrefixRegion := nextRegions 11 (liveRegions 11 36 13 degreeUnionState62_823) - -def degreeUnionState62_832 : List PrefixRegion := nextRegions 12 (liveRegions 11 36 13 degreeUnionState62_823) - -def degreeUnionState62_833 : List PrefixRegion := nextRegions 13 (liveRegions 11 36 13 degreeUnionState62_823) - -def degreeUnionState62_834 : List PrefixRegion := nextRegions 14 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_835 : List PrefixRegion := nextRegions 4 (liveRegions 12 48 14 degreeUnionState62_834) - -def degreeUnionState62_836 : List PrefixRegion := nextRegions 5 (liveRegions 12 48 14 degreeUnionState62_834) - -def degreeUnionState62_837 : List PrefixRegion := nextRegions 6 (liveRegions 12 48 14 degreeUnionState62_834) - -def degreeUnionState62_838 : List PrefixRegion := nextRegions 7 (liveRegions 12 48 14 degreeUnionState62_834) - -def degreeUnionState62_839 : List PrefixRegion := nextRegions 4 (liveRegions 11 41 7 degreeUnionState62_838) - -def degreeUnionState62_840 : List PrefixRegion := nextRegions 5 (liveRegions 11 41 7 degreeUnionState62_838) - -def degreeUnionState62_841 : List PrefixRegion := nextRegions 6 (liveRegions 11 41 7 degreeUnionState62_838) - -def degreeUnionState62_842 : List PrefixRegion := nextRegions 7 (liveRegions 11 41 7 degreeUnionState62_838) - -def degreeUnionState62_843 : List PrefixRegion := nextRegions 8 (liveRegions 12 48 14 degreeUnionState62_834) - -def degreeUnionState62_844 : List PrefixRegion := nextRegions 4 (liveRegions 11 40 8 degreeUnionState62_843) - -def degreeUnionState62_845 : List PrefixRegion := nextRegions 5 (liveRegions 11 40 8 degreeUnionState62_843) - -def degreeUnionState62_846 : List PrefixRegion := nextRegions 6 (liveRegions 11 40 8 degreeUnionState62_843) - -def degreeUnionState62_847 : List PrefixRegion := nextRegions 7 (liveRegions 11 40 8 degreeUnionState62_843) - -def degreeUnionState62_848 : List PrefixRegion := nextRegions 8 (liveRegions 11 40 8 degreeUnionState62_843) - -def degreeUnionState62_849 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 8 degreeUnionState62_848) - -def degreeUnionState62_850 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 8 degreeUnionState62_848) - -def degreeUnionState62_851 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 8 degreeUnionState62_848) - -def degreeUnionState62_852 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 8 degreeUnionState62_848) - -def degreeUnionState62_853 : List PrefixRegion := nextRegions 8 (liveRegions 10 32 8 degreeUnionState62_848) - -def degreeUnionState62_854 : List PrefixRegion := nextRegions 9 (liveRegions 12 48 14 degreeUnionState62_834) - -def degreeUnionState62_855 : List PrefixRegion := nextRegions 4 (liveRegions 11 39 9 degreeUnionState62_854) - -def degreeUnionState62_856 : List PrefixRegion := nextRegions 5 (liveRegions 11 39 9 degreeUnionState62_854) - -def degreeUnionState62_857 : List PrefixRegion := nextRegions 6 (liveRegions 11 39 9 degreeUnionState62_854) - -def degreeUnionState62_858 : List PrefixRegion := nextRegions 7 (liveRegions 11 39 9 degreeUnionState62_854) - -def degreeUnionState62_859 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 7 degreeUnionState62_858) - -def degreeUnionState62_860 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 7 degreeUnionState62_858) - -def degreeUnionState62_861 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 7 degreeUnionState62_858) - -def degreeUnionState62_862 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 7 degreeUnionState62_858) - -def degreeUnionState62_863 : List PrefixRegion := nextRegions 8 (liveRegions 11 39 9 degreeUnionState62_854) - -def degreeUnionState62_864 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 8 degreeUnionState62_863) - -def degreeUnionState62_865 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 8 degreeUnionState62_863) - -def degreeUnionState62_866 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 8 degreeUnionState62_863) - -def degreeUnionState62_867 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 8 degreeUnionState62_863) - -def degreeUnionState62_868 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 8 degreeUnionState62_863) - -def degreeUnionState62_869 : List PrefixRegion := nextRegions 9 (liveRegions 11 39 9 degreeUnionState62_854) - -def degreeUnionState62_870 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 9 degreeUnionState62_869) - -def degreeUnionState62_871 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 9 degreeUnionState62_869) - -def degreeUnionState62_872 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 9 degreeUnionState62_869) - -def degreeUnionState62_873 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 9 degreeUnionState62_869) - -def degreeUnionState62_874 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 9 degreeUnionState62_869) - -def degreeUnionState62_875 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 9 degreeUnionState62_869) - -def degreeUnionState62_876 : List PrefixRegion := nextRegions 9 (liveRegions 10 30 9 degreeUnionState62_869) - -def degreeUnionState62_877 : List PrefixRegion := nextRegions 10 (liveRegions 12 48 14 degreeUnionState62_834) - -def degreeUnionState62_878 : List PrefixRegion := nextRegions 4 (liveRegions 11 38 10 degreeUnionState62_877) - -def degreeUnionState62_879 : List PrefixRegion := nextRegions 5 (liveRegions 11 38 10 degreeUnionState62_877) - -def degreeUnionState62_880 : List PrefixRegion := nextRegions 6 (liveRegions 11 38 10 degreeUnionState62_877) - -def degreeUnionState62_881 : List PrefixRegion := nextRegions 7 (liveRegions 11 38 10 degreeUnionState62_877) - -def degreeUnionState62_882 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 7 degreeUnionState62_881) - -def degreeUnionState62_883 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 7 degreeUnionState62_881) - -def degreeUnionState62_884 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 7 degreeUnionState62_881) - -def degreeUnionState62_885 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 7 degreeUnionState62_881) - -def degreeUnionState62_886 : List PrefixRegion := nextRegions 8 (liveRegions 11 38 10 degreeUnionState62_877) - -def degreeUnionState62_887 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 8 degreeUnionState62_886) - -def degreeUnionState62_888 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 8 degreeUnionState62_886) - -def degreeUnionState62_889 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 8 degreeUnionState62_886) - -def degreeUnionState62_890 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 8 degreeUnionState62_886) - -def degreeUnionState62_891 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 8 degreeUnionState62_886) - -def degreeUnionState62_892 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 8 degreeUnionState62_886) - -def degreeUnionState62_893 : List PrefixRegion := nextRegions 9 (liveRegions 11 38 10 degreeUnionState62_877) - -def degreeUnionState62_894 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 9 degreeUnionState62_893) - -def degreeUnionState62_895 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 9 degreeUnionState62_893) - -def degreeUnionState62_896 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 9 degreeUnionState62_893) - -def degreeUnionState62_897 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 9 degreeUnionState62_893) - -def degreeUnionState62_898 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 9 degreeUnionState62_893) - -def degreeUnionState62_899 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 9 degreeUnionState62_893) - -def degreeUnionState62_900 : List PrefixRegion := nextRegions 9 (liveRegions 10 29 9 degreeUnionState62_893) - -def degreeUnionState62_901 : List PrefixRegion := nextRegions 10 (liveRegions 11 38 10 degreeUnionState62_877) - -def degreeUnionState62_902 : List PrefixRegion := nextRegions 11 (liveRegions 12 48 14 degreeUnionState62_834) - -def degreeUnionState62_903 : List PrefixRegion := nextRegions 4 (liveRegions 11 37 11 degreeUnionState62_902) - -def degreeUnionState62_904 : List PrefixRegion := nextRegions 5 (liveRegions 11 37 11 degreeUnionState62_902) - -def degreeUnionState62_905 : List PrefixRegion := nextRegions 6 (liveRegions 11 37 11 degreeUnionState62_902) - -def degreeUnionState62_906 : List PrefixRegion := nextRegions 7 (liveRegions 11 37 11 degreeUnionState62_902) - -def degreeUnionState62_907 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 7 degreeUnionState62_906) - -def degreeUnionState62_908 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 7 degreeUnionState62_906) - -def degreeUnionState62_909 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 7 degreeUnionState62_906) - -def degreeUnionState62_910 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 7 degreeUnionState62_906) - -def degreeUnionState62_911 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 7 degreeUnionState62_906) - -def degreeUnionState62_912 : List PrefixRegion := nextRegions 8 (liveRegions 11 37 11 degreeUnionState62_902) - -def degreeUnionState62_913 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 8 degreeUnionState62_912) - -def degreeUnionState62_914 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 8 degreeUnionState62_912) - -def degreeUnionState62_915 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 8 degreeUnionState62_912) - -def degreeUnionState62_916 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 8 degreeUnionState62_912) - -def degreeUnionState62_917 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 8 degreeUnionState62_912) - -def degreeUnionState62_918 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 8 degreeUnionState62_912) - -def degreeUnionState62_919 : List PrefixRegion := nextRegions 9 (liveRegions 11 37 11 degreeUnionState62_902) - -def degreeUnionState62_920 : List PrefixRegion := nextRegions 10 (liveRegions 11 37 11 degreeUnionState62_902) - -def degreeUnionState62_921 : List PrefixRegion := nextRegions 11 (liveRegions 11 37 11 degreeUnionState62_902) - -def degreeUnionState62_922 : List PrefixRegion := nextRegions 12 (liveRegions 12 48 14 degreeUnionState62_834) - -def degreeUnionState62_923 : List PrefixRegion := nextRegions 4 (liveRegions 11 36 12 degreeUnionState62_922) - -def degreeUnionState62_924 : List PrefixRegion := nextRegions 5 (liveRegions 11 36 12 degreeUnionState62_922) - -def degreeUnionState62_925 : List PrefixRegion := nextRegions 6 (liveRegions 11 36 12 degreeUnionState62_922) - -def degreeUnionState62_926 : List PrefixRegion := nextRegions 7 (liveRegions 11 36 12 degreeUnionState62_922) - -def degreeUnionState62_927 : List PrefixRegion := nextRegions 8 (liveRegions 11 36 12 degreeUnionState62_922) - -def degreeUnionState62_928 : List PrefixRegion := nextRegions 9 (liveRegions 11 36 12 degreeUnionState62_922) - -def degreeUnionState62_929 : List PrefixRegion := nextRegions 10 (liveRegions 11 36 12 degreeUnionState62_922) - -def degreeUnionState62_930 : List PrefixRegion := nextRegions 11 (liveRegions 11 36 12 degreeUnionState62_922) - -def degreeUnionState62_931 : List PrefixRegion := nextRegions 12 (liveRegions 11 36 12 degreeUnionState62_922) - -def degreeUnionState62_932 : List PrefixRegion := nextRegions 13 (liveRegions 12 48 14 degreeUnionState62_834) - -def degreeUnionState62_933 : List PrefixRegion := nextRegions 14 (liveRegions 12 48 14 degreeUnionState62_834) - -def degreeUnionState62_934 : List PrefixRegion := nextRegions 15 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_935 : List PrefixRegion := nextRegions 16 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_936 : List PrefixRegion := nextRegions 17 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_937 : List PrefixRegion := nextRegions 18 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_938 : List PrefixRegion := nextRegions 19 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_939 : List PrefixRegion := nextRegions 20 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_940 : List PrefixRegion := nextRegions 21 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_941 : List PrefixRegion := nextRegions 22 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_942 : List PrefixRegion := nextRegions 23 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_943 : List PrefixRegion := nextRegions 24 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_944 : List PrefixRegion := nextRegions 25 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_945 : List PrefixRegion := nextRegions 26 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_946 : List PrefixRegion := nextRegions 27 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_947 : List PrefixRegion := nextRegions 28 (liveRegions 13 62 28 degreeHalfRegions62) - -def degreeUnionState62_949 : List PrefixRegion := nextRegions 5 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_950 : List PrefixRegion := nextRegions 6 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_951 : List PrefixRegion := nextRegions 7 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_952 : List PrefixRegion := nextRegions 8 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_953 : List PrefixRegion := nextRegions 9 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_954 : List PrefixRegion := nextRegions 10 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_955 : List PrefixRegion := nextRegions 4 (liveRegions 13 52 10 degreeUnionState62_954) - -def degreeUnionState62_956 : List PrefixRegion := nextRegions 5 (liveRegions 13 52 10 degreeUnionState62_954) - -def degreeUnionState62_957 : List PrefixRegion := nextRegions 6 (liveRegions 13 52 10 degreeUnionState62_954) - -def degreeUnionState62_958 : List PrefixRegion := nextRegions 7 (liveRegions 13 52 10 degreeUnionState62_954) - -def degreeUnionState62_959 : List PrefixRegion := nextRegions 8 (liveRegions 13 52 10 degreeUnionState62_954) - -def degreeUnionState62_960 : List PrefixRegion := nextRegions 9 (liveRegions 13 52 10 degreeUnionState62_954) - -def degreeUnionState62_961 : List PrefixRegion := nextRegions 10 (liveRegions 13 52 10 degreeUnionState62_954) - -def degreeUnionState62_962 : List PrefixRegion := nextRegions 11 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_963 : List PrefixRegion := nextRegions 4 (liveRegions 13 51 11 degreeUnionState62_962) - -def degreeUnionState62_964 : List PrefixRegion := nextRegions 5 (liveRegions 13 51 11 degreeUnionState62_962) - -def degreeUnionState62_965 : List PrefixRegion := nextRegions 6 (liveRegions 13 51 11 degreeUnionState62_962) - -def degreeUnionState62_966 : List PrefixRegion := nextRegions 7 (liveRegions 13 51 11 degreeUnionState62_962) - -def degreeUnionState62_967 : List PrefixRegion := nextRegions 8 (liveRegions 13 51 11 degreeUnionState62_962) - -def degreeUnionState62_968 : List PrefixRegion := nextRegions 9 (liveRegions 13 51 11 degreeUnionState62_962) - -def degreeUnionState62_969 : List PrefixRegion := nextRegions 10 (liveRegions 13 51 11 degreeUnionState62_962) - -def degreeUnionState62_970 : List PrefixRegion := nextRegions 4 (liveRegions 12 41 10 degreeUnionState62_969) - -def degreeUnionState62_971 : List PrefixRegion := nextRegions 5 (liveRegions 12 41 10 degreeUnionState62_969) - -def degreeUnionState62_972 : List PrefixRegion := nextRegions 6 (liveRegions 12 41 10 degreeUnionState62_969) - -def degreeUnionState62_973 : List PrefixRegion := nextRegions 7 (liveRegions 12 41 10 degreeUnionState62_969) - -def degreeUnionState62_974 : List PrefixRegion := nextRegions 8 (liveRegions 12 41 10 degreeUnionState62_969) - -def degreeUnionState62_975 : List PrefixRegion := nextRegions 9 (liveRegions 12 41 10 degreeUnionState62_969) - -def degreeUnionState62_976 : List PrefixRegion := nextRegions 10 (liveRegions 12 41 10 degreeUnionState62_969) - -def degreeUnionState62_977 : List PrefixRegion := nextRegions 11 (liveRegions 13 51 11 degreeUnionState62_962) - -def degreeUnionState62_978 : List PrefixRegion := nextRegions 4 (liveRegions 12 40 11 degreeUnionState62_977) - -def degreeUnionState62_979 : List PrefixRegion := nextRegions 5 (liveRegions 12 40 11 degreeUnionState62_977) - -def degreeUnionState62_980 : List PrefixRegion := nextRegions 6 (liveRegions 12 40 11 degreeUnionState62_977) - -def degreeUnionState62_981 : List PrefixRegion := nextRegions 7 (liveRegions 12 40 11 degreeUnionState62_977) - -def degreeUnionState62_982 : List PrefixRegion := nextRegions 8 (liveRegions 12 40 11 degreeUnionState62_977) - -def degreeUnionState62_983 : List PrefixRegion := nextRegions 9 (liveRegions 12 40 11 degreeUnionState62_977) - -def degreeUnionState62_984 : List PrefixRegion := nextRegions 10 (liveRegions 12 40 11 degreeUnionState62_977) - -def degreeUnionState62_985 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 10 degreeUnionState62_984) - -def degreeUnionState62_986 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 10 degreeUnionState62_984) - -def degreeUnionState62_987 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 10 degreeUnionState62_984) - -def degreeUnionState62_988 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 10 degreeUnionState62_984) - -def degreeUnionState62_989 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 10 degreeUnionState62_984) - -def degreeUnionState62_990 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 10 degreeUnionState62_984) - -def degreeUnionState62_991 : List PrefixRegion := nextRegions 9 (liveRegions 11 30 10 degreeUnionState62_984) - -def degreeUnionState62_992 : List PrefixRegion := nextRegions 10 (liveRegions 11 30 10 degreeUnionState62_984) - -def degreeUnionState62_993 : List PrefixRegion := nextRegions 11 (liveRegions 12 40 11 degreeUnionState62_977) - -def degreeUnionState62_994 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 11 degreeUnionState62_993) - -def degreeUnionState62_995 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 11 degreeUnionState62_993) - -def degreeUnionState62_996 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 11 degreeUnionState62_993) - -def degreeUnionState62_997 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 11 degreeUnionState62_993) - -def degreeUnionState62_998 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 11 degreeUnionState62_993) - -def degreeUnionState62_999 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 11 degreeUnionState62_993) - -def degreeUnionState62_1000 : List PrefixRegion := nextRegions 9 (liveRegions 11 29 11 degreeUnionState62_993) - -def degreeUnionState62_1001 : List PrefixRegion := nextRegions 10 (liveRegions 11 29 11 degreeUnionState62_993) - -def degreeUnionState62_1002 : List PrefixRegion := nextRegions 11 (liveRegions 11 29 11 degreeUnionState62_993) - -def degreeUnionState62_1003 : List PrefixRegion := nextRegions 12 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1004 : List PrefixRegion := nextRegions 4 (liveRegions 13 50 12 degreeUnionState62_1003) - -def degreeUnionState62_1005 : List PrefixRegion := nextRegions 5 (liveRegions 13 50 12 degreeUnionState62_1003) - -def degreeUnionState62_1006 : List PrefixRegion := nextRegions 6 (liveRegions 13 50 12 degreeUnionState62_1003) - -def degreeUnionState62_1007 : List PrefixRegion := nextRegions 7 (liveRegions 13 50 12 degreeUnionState62_1003) - -def degreeUnionState62_1008 : List PrefixRegion := nextRegions 8 (liveRegions 13 50 12 degreeUnionState62_1003) - -def degreeUnionState62_1009 : List PrefixRegion := nextRegions 4 (liveRegions 12 42 8 degreeUnionState62_1008) - -def degreeUnionState62_1010 : List PrefixRegion := nextRegions 5 (liveRegions 12 42 8 degreeUnionState62_1008) - -def degreeUnionState62_1011 : List PrefixRegion := nextRegions 6 (liveRegions 12 42 8 degreeUnionState62_1008) - -def degreeUnionState62_1012 : List PrefixRegion := nextRegions 7 (liveRegions 12 42 8 degreeUnionState62_1008) - -def degreeUnionState62_1013 : List PrefixRegion := nextRegions 8 (liveRegions 12 42 8 degreeUnionState62_1008) - -def degreeUnionState62_1014 : List PrefixRegion := nextRegions 4 (liveRegions 11 34 8 degreeUnionState62_1013) - -def degreeUnionState62_1015 : List PrefixRegion := nextRegions 5 (liveRegions 11 34 8 degreeUnionState62_1013) - -def degreeUnionState62_1016 : List PrefixRegion := nextRegions 6 (liveRegions 11 34 8 degreeUnionState62_1013) - -def degreeUnionState62_1017 : List PrefixRegion := nextRegions 7 (liveRegions 11 34 8 degreeUnionState62_1013) - -def degreeUnionState62_1018 : List PrefixRegion := nextRegions 8 (liveRegions 11 34 8 degreeUnionState62_1013) - -def degreeUnionState62_1019 : List PrefixRegion := nextRegions 9 (liveRegions 13 50 12 degreeUnionState62_1003) - -def degreeUnionState62_1020 : List PrefixRegion := nextRegions 4 (liveRegions 12 41 9 degreeUnionState62_1019) - -def degreeUnionState62_1021 : List PrefixRegion := nextRegions 5 (liveRegions 12 41 9 degreeUnionState62_1019) - -def degreeUnionState62_1022 : List PrefixRegion := nextRegions 6 (liveRegions 12 41 9 degreeUnionState62_1019) - -def degreeUnionState62_1023 : List PrefixRegion := nextRegions 7 (liveRegions 12 41 9 degreeUnionState62_1019) - -def degreeUnionState62_1024 : List PrefixRegion := nextRegions 8 (liveRegions 12 41 9 degreeUnionState62_1019) - -def degreeUnionState62_1025 : List PrefixRegion := nextRegions 3 (liveRegions 11 33 8 degreeUnionState62_1024) - -def degreeUnionState62_1026 : List PrefixRegion := nextRegions 4 (liveRegions 11 33 8 degreeUnionState62_1024) - -def degreeUnionState62_1027 : List PrefixRegion := nextRegions 5 (liveRegions 11 33 8 degreeUnionState62_1024) - -def degreeUnionState62_1028 : List PrefixRegion := nextRegions 6 (liveRegions 11 33 8 degreeUnionState62_1024) - -def degreeUnionState62_1029 : List PrefixRegion := nextRegions 7 (liveRegions 11 33 8 degreeUnionState62_1024) - -def degreeUnionState62_1030 : List PrefixRegion := nextRegions 8 (liveRegions 11 33 8 degreeUnionState62_1024) - -def degreeUnionState62_1031 : List PrefixRegion := nextRegions 9 (liveRegions 12 41 9 degreeUnionState62_1019) - -def degreeUnionState62_1032 : List PrefixRegion := nextRegions 3 (liveRegions 11 32 9 degreeUnionState62_1031) - -def degreeUnionState62_1033 : List PrefixRegion := nextRegions 4 (liveRegions 11 32 9 degreeUnionState62_1031) - -def degreeUnionState62_1034 : List PrefixRegion := nextRegions 5 (liveRegions 11 32 9 degreeUnionState62_1031) - -def degreeUnionState62_1035 : List PrefixRegion := nextRegions 6 (liveRegions 11 32 9 degreeUnionState62_1031) - -def degreeUnionState62_1036 : List PrefixRegion := nextRegions 7 (liveRegions 11 32 9 degreeUnionState62_1031) - -def degreeUnionState62_1037 : List PrefixRegion := nextRegions 8 (liveRegions 11 32 9 degreeUnionState62_1031) - -def degreeUnionState62_1038 : List PrefixRegion := nextRegions 9 (liveRegions 11 32 9 degreeUnionState62_1031) - -def degreeUnionState62_1039 : List PrefixRegion := nextRegions 10 (liveRegions 13 50 12 degreeUnionState62_1003) - -def degreeUnionState62_1040 : List PrefixRegion := nextRegions 4 (liveRegions 12 40 10 degreeUnionState62_1039) - -def degreeUnionState62_1041 : List PrefixRegion := nextRegions 5 (liveRegions 12 40 10 degreeUnionState62_1039) - -def degreeUnionState62_1042 : List PrefixRegion := nextRegions 6 (liveRegions 12 40 10 degreeUnionState62_1039) - -def degreeUnionState62_1043 : List PrefixRegion := nextRegions 7 (liveRegions 12 40 10 degreeUnionState62_1039) - -def degreeUnionState62_1044 : List PrefixRegion := nextRegions 8 (liveRegions 12 40 10 degreeUnionState62_1039) - -def degreeUnionState62_1045 : List PrefixRegion := nextRegions 3 (liveRegions 11 32 8 degreeUnionState62_1044) - -def degreeUnionState62_1046 : List PrefixRegion := nextRegions 4 (liveRegions 11 32 8 degreeUnionState62_1044) - -def degreeUnionState62_1047 : List PrefixRegion := nextRegions 5 (liveRegions 11 32 8 degreeUnionState62_1044) - -def degreeUnionState62_1048 : List PrefixRegion := nextRegions 6 (liveRegions 11 32 8 degreeUnionState62_1044) - -def degreeUnionState62_1049 : List PrefixRegion := nextRegions 7 (liveRegions 11 32 8 degreeUnionState62_1044) - -def degreeUnionState62_1050 : List PrefixRegion := nextRegions 8 (liveRegions 11 32 8 degreeUnionState62_1044) - -def degreeUnionState62_1051 : List PrefixRegion := nextRegions 9 (liveRegions 12 40 10 degreeUnionState62_1039) - -def degreeUnionState62_1052 : List PrefixRegion := nextRegions 3 (liveRegions 11 31 9 degreeUnionState62_1051) - -def degreeUnionState62_1053 : List PrefixRegion := nextRegions 4 (liveRegions 11 31 9 degreeUnionState62_1051) - -def degreeUnionState62_1054 : List PrefixRegion := nextRegions 5 (liveRegions 11 31 9 degreeUnionState62_1051) - -def degreeUnionState62_1055 : List PrefixRegion := nextRegions 6 (liveRegions 11 31 9 degreeUnionState62_1051) - -def degreeUnionState62_1056 : List PrefixRegion := nextRegions 7 (liveRegions 11 31 9 degreeUnionState62_1051) - -def degreeUnionState62_1057 : List PrefixRegion := nextRegions 8 (liveRegions 11 31 9 degreeUnionState62_1051) - -def degreeUnionState62_1058 : List PrefixRegion := nextRegions 9 (liveRegions 11 31 9 degreeUnionState62_1051) - -def degreeUnionState62_1059 : List PrefixRegion := nextRegions 10 (liveRegions 12 40 10 degreeUnionState62_1039) - -def degreeUnionState62_1060 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 10 degreeUnionState62_1059) - -def degreeUnionState62_1061 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 10 degreeUnionState62_1059) - -def degreeUnionState62_1062 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 10 degreeUnionState62_1059) - -def degreeUnionState62_1063 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 10 degreeUnionState62_1059) - -def degreeUnionState62_1064 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 10 degreeUnionState62_1059) - -def degreeUnionState62_1065 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 10 degreeUnionState62_1059) - -def degreeUnionState62_1066 : List PrefixRegion := nextRegions 9 (liveRegions 11 30 10 degreeUnionState62_1059) - -def degreeUnionState62_1067 : List PrefixRegion := nextRegions 10 (liveRegions 11 30 10 degreeUnionState62_1059) - -def degreeUnionState62_1068 : List PrefixRegion := nextRegions 11 (liveRegions 13 50 12 degreeUnionState62_1003) - -def degreeUnionState62_1069 : List PrefixRegion := nextRegions 4 (liveRegions 12 39 11 degreeUnionState62_1068) - -def degreeUnionState62_1070 : List PrefixRegion := nextRegions 5 (liveRegions 12 39 11 degreeUnionState62_1068) - -def degreeUnionState62_1071 : List PrefixRegion := nextRegions 6 (liveRegions 12 39 11 degreeUnionState62_1068) - -def degreeUnionState62_1072 : List PrefixRegion := nextRegions 7 (liveRegions 12 39 11 degreeUnionState62_1068) - -def degreeUnionState62_1073 : List PrefixRegion := nextRegions 8 (liveRegions 12 39 11 degreeUnionState62_1068) - -def degreeUnionState62_1074 : List PrefixRegion := nextRegions 3 (liveRegions 11 31 8 degreeUnionState62_1073) - -def degreeUnionState62_1075 : List PrefixRegion := nextRegions 4 (liveRegions 11 31 8 degreeUnionState62_1073) - -def degreeUnionState62_1076 : List PrefixRegion := nextRegions 5 (liveRegions 11 31 8 degreeUnionState62_1073) - -def degreeUnionState62_1077 : List PrefixRegion := nextRegions 6 (liveRegions 11 31 8 degreeUnionState62_1073) - -def degreeUnionState62_1078 : List PrefixRegion := nextRegions 7 (liveRegions 11 31 8 degreeUnionState62_1073) - -def degreeUnionState62_1079 : List PrefixRegion := nextRegions 8 (liveRegions 11 31 8 degreeUnionState62_1073) - -def degreeUnionState62_1080 : List PrefixRegion := nextRegions 9 (liveRegions 12 39 11 degreeUnionState62_1068) - -def degreeUnionState62_1081 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 9 degreeUnionState62_1080) - -def degreeUnionState62_1082 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 9 degreeUnionState62_1080) - -def degreeUnionState62_1083 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 9 degreeUnionState62_1080) - -def degreeUnionState62_1084 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 9 degreeUnionState62_1080) - -def degreeUnionState62_1085 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 9 degreeUnionState62_1080) - -def degreeUnionState62_1086 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 9 degreeUnionState62_1080) - -def degreeUnionState62_1087 : List PrefixRegion := nextRegions 9 (liveRegions 11 30 9 degreeUnionState62_1080) - -def degreeUnionState62_1088 : List PrefixRegion := nextRegions 10 (liveRegions 12 39 11 degreeUnionState62_1068) - -def degreeUnionState62_1089 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 10 degreeUnionState62_1088) - -def degreeUnionState62_1090 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 10 degreeUnionState62_1088) - -def degreeUnionState62_1091 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 10 degreeUnionState62_1088) - -def degreeUnionState62_1092 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 10 degreeUnionState62_1088) - -def degreeUnionState62_1093 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 10 degreeUnionState62_1088) - -def degreeUnionState62_1094 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 10 degreeUnionState62_1088) - -def degreeUnionState62_1095 : List PrefixRegion := nextRegions 9 (liveRegions 11 29 10 degreeUnionState62_1088) - -def degreeUnionState62_1096 : List PrefixRegion := nextRegions 10 (liveRegions 11 29 10 degreeUnionState62_1088) - -def degreeUnionState62_1097 : List PrefixRegion := nextRegions 11 (liveRegions 12 39 11 degreeUnionState62_1068) - -def degreeUnionState62_1098 : List PrefixRegion := nextRegions 12 (liveRegions 13 50 12 degreeUnionState62_1003) - -def degreeUnionState62_1099 : List PrefixRegion := nextRegions 4 (liveRegions 12 38 12 degreeUnionState62_1098) - -def degreeUnionState62_1100 : List PrefixRegion := nextRegions 5 (liveRegions 12 38 12 degreeUnionState62_1098) - -def degreeUnionState62_1101 : List PrefixRegion := nextRegions 6 (liveRegions 12 38 12 degreeUnionState62_1098) - -def degreeUnionState62_1102 : List PrefixRegion := nextRegions 7 (liveRegions 12 38 12 degreeUnionState62_1098) - -def degreeUnionState62_1103 : List PrefixRegion := nextRegions 8 (liveRegions 12 38 12 degreeUnionState62_1098) - -def degreeUnionState62_1104 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 8 degreeUnionState62_1103) - -def degreeUnionState62_1105 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 8 degreeUnionState62_1103) - -def degreeUnionState62_1106 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 8 degreeUnionState62_1103) - -def degreeUnionState62_1107 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 8 degreeUnionState62_1103) - -def degreeUnionState62_1108 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 8 degreeUnionState62_1103) - -def degreeUnionState62_1109 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 8 degreeUnionState62_1103) - -def degreeUnionState62_1110 : List PrefixRegion := nextRegions 9 (liveRegions 12 38 12 degreeUnionState62_1098) - -def degreeUnionState62_1111 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 9 degreeUnionState62_1110) - -def degreeUnionState62_1112 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 9 degreeUnionState62_1110) - -def degreeUnionState62_1113 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 9 degreeUnionState62_1110) - -def degreeUnionState62_1114 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 9 degreeUnionState62_1110) - -def degreeUnionState62_1115 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 9 degreeUnionState62_1110) - -def degreeUnionState62_1116 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 9 degreeUnionState62_1110) - -def degreeUnionState62_1117 : List PrefixRegion := nextRegions 9 (liveRegions 11 29 9 degreeUnionState62_1110) - -def degreeUnionState62_1118 : List PrefixRegion := nextRegions 10 (liveRegions 12 38 12 degreeUnionState62_1098) - -def degreeUnionState62_1119 : List PrefixRegion := nextRegions 11 (liveRegions 12 38 12 degreeUnionState62_1098) - -def degreeUnionState62_1120 : List PrefixRegion := nextRegions 12 (liveRegions 12 38 12 degreeUnionState62_1098) - -def degreeUnionState62_1121 : List PrefixRegion := nextRegions 13 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1122 : List PrefixRegion := nextRegions 4 (liveRegions 13 49 13 degreeUnionState62_1121) - -def degreeUnionState62_1123 : List PrefixRegion := nextRegions 5 (liveRegions 13 49 13 degreeUnionState62_1121) - -def degreeUnionState62_1124 : List PrefixRegion := nextRegions 6 (liveRegions 13 49 13 degreeUnionState62_1121) - -def degreeUnionState62_1125 : List PrefixRegion := nextRegions 7 (liveRegions 13 49 13 degreeUnionState62_1121) - -def degreeUnionState62_1126 : List PrefixRegion := nextRegions 8 (liveRegions 13 49 13 degreeUnionState62_1121) - -def degreeUnionState62_1127 : List PrefixRegion := nextRegions 4 (liveRegions 12 41 8 degreeUnionState62_1126) - -def degreeUnionState62_1128 : List PrefixRegion := nextRegions 5 (liveRegions 12 41 8 degreeUnionState62_1126) - -def degreeUnionState62_1129 : List PrefixRegion := nextRegions 6 (liveRegions 12 41 8 degreeUnionState62_1126) - -def degreeUnionState62_1130 : List PrefixRegion := nextRegions 7 (liveRegions 12 41 8 degreeUnionState62_1126) - -def degreeUnionState62_1131 : List PrefixRegion := nextRegions 8 (liveRegions 12 41 8 degreeUnionState62_1126) - -def degreeUnionState62_1132 : List PrefixRegion := nextRegions 3 (liveRegions 11 33 8 degreeUnionState62_1131) - -def degreeUnionState62_1133 : List PrefixRegion := nextRegions 4 (liveRegions 11 33 8 degreeUnionState62_1131) - -def degreeUnionState62_1134 : List PrefixRegion := nextRegions 5 (liveRegions 11 33 8 degreeUnionState62_1131) - -def degreeUnionState62_1135 : List PrefixRegion := nextRegions 6 (liveRegions 11 33 8 degreeUnionState62_1131) - -def degreeUnionState62_1136 : List PrefixRegion := nextRegions 7 (liveRegions 11 33 8 degreeUnionState62_1131) - -def degreeUnionState62_1137 : List PrefixRegion := nextRegions 8 (liveRegions 11 33 8 degreeUnionState62_1131) - -def degreeUnionState62_1138 : List PrefixRegion := nextRegions 9 (liveRegions 13 49 13 degreeUnionState62_1121) - -def degreeUnionState62_1139 : List PrefixRegion := nextRegions 4 (liveRegions 12 40 9 degreeUnionState62_1138) - -def degreeUnionState62_1140 : List PrefixRegion := nextRegions 5 (liveRegions 12 40 9 degreeUnionState62_1138) - -def degreeUnionState62_1141 : List PrefixRegion := nextRegions 6 (liveRegions 12 40 9 degreeUnionState62_1138) - -def degreeUnionState62_1142 : List PrefixRegion := nextRegions 7 (liveRegions 12 40 9 degreeUnionState62_1138) - -def degreeUnionState62_1143 : List PrefixRegion := nextRegions 8 (liveRegions 12 40 9 degreeUnionState62_1138) - -def degreeUnionState62_1144 : List PrefixRegion := nextRegions 3 (liveRegions 11 32 8 degreeUnionState62_1143) - -def degreeUnionState62_1145 : List PrefixRegion := nextRegions 4 (liveRegions 11 32 8 degreeUnionState62_1143) - -def degreeUnionState62_1146 : List PrefixRegion := nextRegions 5 (liveRegions 11 32 8 degreeUnionState62_1143) - -def degreeUnionState62_1147 : List PrefixRegion := nextRegions 6 (liveRegions 11 32 8 degreeUnionState62_1143) - -def degreeUnionState62_1148 : List PrefixRegion := nextRegions 7 (liveRegions 11 32 8 degreeUnionState62_1143) - -def degreeUnionState62_1149 : List PrefixRegion := nextRegions 8 (liveRegions 11 32 8 degreeUnionState62_1143) - -def degreeUnionState62_1150 : List PrefixRegion := nextRegions 9 (liveRegions 12 40 9 degreeUnionState62_1138) - -def degreeUnionState62_1151 : List PrefixRegion := nextRegions 3 (liveRegions 11 31 9 degreeUnionState62_1150) - -def degreeUnionState62_1152 : List PrefixRegion := nextRegions 4 (liveRegions 11 31 9 degreeUnionState62_1150) - -def degreeUnionState62_1153 : List PrefixRegion := nextRegions 5 (liveRegions 11 31 9 degreeUnionState62_1150) - -def degreeUnionState62_1154 : List PrefixRegion := nextRegions 6 (liveRegions 11 31 9 degreeUnionState62_1150) - -def degreeUnionState62_1155 : List PrefixRegion := nextRegions 7 (liveRegions 11 31 9 degreeUnionState62_1150) - -def degreeUnionState62_1156 : List PrefixRegion := nextRegions 8 (liveRegions 11 31 9 degreeUnionState62_1150) - -def degreeUnionState62_1157 : List PrefixRegion := nextRegions 9 (liveRegions 11 31 9 degreeUnionState62_1150) - -def degreeUnionState62_1158 : List PrefixRegion := nextRegions 10 (liveRegions 13 49 13 degreeUnionState62_1121) - -def degreeUnionState62_1159 : List PrefixRegion := nextRegions 4 (liveRegions 12 39 10 degreeUnionState62_1158) - -def degreeUnionState62_1160 : List PrefixRegion := nextRegions 5 (liveRegions 12 39 10 degreeUnionState62_1158) - -def degreeUnionState62_1161 : List PrefixRegion := nextRegions 6 (liveRegions 12 39 10 degreeUnionState62_1158) - -def degreeUnionState62_1162 : List PrefixRegion := nextRegions 7 (liveRegions 12 39 10 degreeUnionState62_1158) - -def degreeUnionState62_1163 : List PrefixRegion := nextRegions 8 (liveRegions 12 39 10 degreeUnionState62_1158) - -def degreeUnionState62_1164 : List PrefixRegion := nextRegions 3 (liveRegions 11 31 8 degreeUnionState62_1163) - -def degreeUnionState62_1165 : List PrefixRegion := nextRegions 4 (liveRegions 11 31 8 degreeUnionState62_1163) - -def degreeUnionState62_1166 : List PrefixRegion := nextRegions 5 (liveRegions 11 31 8 degreeUnionState62_1163) - -def degreeUnionState62_1167 : List PrefixRegion := nextRegions 6 (liveRegions 11 31 8 degreeUnionState62_1163) - -def degreeUnionState62_1168 : List PrefixRegion := nextRegions 7 (liveRegions 11 31 8 degreeUnionState62_1163) - -def degreeUnionState62_1169 : List PrefixRegion := nextRegions 8 (liveRegions 11 31 8 degreeUnionState62_1163) - -def degreeUnionState62_1170 : List PrefixRegion := nextRegions 9 (liveRegions 12 39 10 degreeUnionState62_1158) - -def degreeUnionState62_1171 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 9 degreeUnionState62_1170) - -def degreeUnionState62_1172 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 9 degreeUnionState62_1170) - -def degreeUnionState62_1173 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 9 degreeUnionState62_1170) - -def degreeUnionState62_1174 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 9 degreeUnionState62_1170) - -def degreeUnionState62_1175 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 9 degreeUnionState62_1170) - -def degreeUnionState62_1176 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 9 degreeUnionState62_1170) - -def degreeUnionState62_1177 : List PrefixRegion := nextRegions 9 (liveRegions 11 30 9 degreeUnionState62_1170) - -def degreeUnionState62_1178 : List PrefixRegion := nextRegions 10 (liveRegions 12 39 10 degreeUnionState62_1158) - -def degreeUnionState62_1179 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 10 degreeUnionState62_1178) - -def degreeUnionState62_1180 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 10 degreeUnionState62_1178) - -def degreeUnionState62_1181 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 10 degreeUnionState62_1178) - -def degreeUnionState62_1182 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 10 degreeUnionState62_1178) - -def degreeUnionState62_1183 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 10 degreeUnionState62_1178) - -def degreeUnionState62_1184 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 10 degreeUnionState62_1178) - -def degreeUnionState62_1185 : List PrefixRegion := nextRegions 9 (liveRegions 11 29 10 degreeUnionState62_1178) - -def degreeUnionState62_1186 : List PrefixRegion := nextRegions 10 (liveRegions 11 29 10 degreeUnionState62_1178) - -def degreeUnionState62_1187 : List PrefixRegion := nextRegions 11 (liveRegions 13 49 13 degreeUnionState62_1121) - -def degreeUnionState62_1188 : List PrefixRegion := nextRegions 4 (liveRegions 12 38 11 degreeUnionState62_1187) - -def degreeUnionState62_1189 : List PrefixRegion := nextRegions 5 (liveRegions 12 38 11 degreeUnionState62_1187) - -def degreeUnionState62_1190 : List PrefixRegion := nextRegions 6 (liveRegions 12 38 11 degreeUnionState62_1187) - -def degreeUnionState62_1191 : List PrefixRegion := nextRegions 7 (liveRegions 12 38 11 degreeUnionState62_1187) - -def degreeUnionState62_1192 : List PrefixRegion := nextRegions 8 (liveRegions 12 38 11 degreeUnionState62_1187) - -def degreeUnionState62_1193 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 8 degreeUnionState62_1192) - -def degreeUnionState62_1194 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 8 degreeUnionState62_1192) - -def degreeUnionState62_1195 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 8 degreeUnionState62_1192) - -def degreeUnionState62_1196 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 8 degreeUnionState62_1192) - -def degreeUnionState62_1197 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 8 degreeUnionState62_1192) - -def degreeUnionState62_1198 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 8 degreeUnionState62_1192) - -def degreeUnionState62_1199 : List PrefixRegion := nextRegions 9 (liveRegions 12 38 11 degreeUnionState62_1187) - -def degreeUnionState62_1200 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 9 degreeUnionState62_1199) - -def degreeUnionState62_1201 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 9 degreeUnionState62_1199) - -def degreeUnionState62_1202 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 9 degreeUnionState62_1199) - -def degreeUnionState62_1203 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 9 degreeUnionState62_1199) - -def degreeUnionState62_1204 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 9 degreeUnionState62_1199) - -def degreeUnionState62_1205 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 9 degreeUnionState62_1199) - -def degreeUnionState62_1206 : List PrefixRegion := nextRegions 9 (liveRegions 11 29 9 degreeUnionState62_1199) - -def degreeUnionState62_1207 : List PrefixRegion := nextRegions 10 (liveRegions 12 38 11 degreeUnionState62_1187) - -def degreeUnionState62_1208 : List PrefixRegion := nextRegions 11 (liveRegions 12 38 11 degreeUnionState62_1187) - -def degreeUnionState62_1209 : List PrefixRegion := nextRegions 12 (liveRegions 13 49 13 degreeUnionState62_1121) - -def degreeUnionState62_1210 : List PrefixRegion := nextRegions 4 (liveRegions 12 37 12 degreeUnionState62_1209) - -def degreeUnionState62_1211 : List PrefixRegion := nextRegions 5 (liveRegions 12 37 12 degreeUnionState62_1209) - -def degreeUnionState62_1212 : List PrefixRegion := nextRegions 6 (liveRegions 12 37 12 degreeUnionState62_1209) - -def degreeUnionState62_1213 : List PrefixRegion := nextRegions 7 (liveRegions 12 37 12 degreeUnionState62_1209) - -def degreeUnionState62_1214 : List PrefixRegion := nextRegions 8 (liveRegions 12 37 12 degreeUnionState62_1209) - -def degreeUnionState62_1215 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 8 degreeUnionState62_1214) - -def degreeUnionState62_1216 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 8 degreeUnionState62_1214) - -def degreeUnionState62_1217 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 8 degreeUnionState62_1214) - -def degreeUnionState62_1218 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 8 degreeUnionState62_1214) - -def degreeUnionState62_1219 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 8 degreeUnionState62_1214) - -def degreeUnionState62_1220 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 8 degreeUnionState62_1214) - -def degreeUnionState62_1221 : List PrefixRegion := nextRegions 9 (liveRegions 12 37 12 degreeUnionState62_1209) - -def degreeUnionState62_1222 : List PrefixRegion := nextRegions 10 (liveRegions 12 37 12 degreeUnionState62_1209) - -def degreeUnionState62_1223 : List PrefixRegion := nextRegions 11 (liveRegions 12 37 12 degreeUnionState62_1209) - -def degreeUnionState62_1224 : List PrefixRegion := nextRegions 12 (liveRegions 12 37 12 degreeUnionState62_1209) - -def degreeUnionState62_1225 : List PrefixRegion := nextRegions 13 (liveRegions 13 49 13 degreeUnionState62_1121) - -def degreeUnionState62_1226 : List PrefixRegion := nextRegions 3 (liveRegions 12 36 13 degreeUnionState62_1225) - -def degreeUnionState62_1227 : List PrefixRegion := nextRegions 4 (liveRegions 12 36 13 degreeUnionState62_1225) - -def degreeUnionState62_1228 : List PrefixRegion := nextRegions 5 (liveRegions 12 36 13 degreeUnionState62_1225) - -def degreeUnionState62_1229 : List PrefixRegion := nextRegions 6 (liveRegions 12 36 13 degreeUnionState62_1225) - -def degreeUnionState62_1230 : List PrefixRegion := nextRegions 7 (liveRegions 12 36 13 degreeUnionState62_1225) - -def degreeUnionState62_1231 : List PrefixRegion := nextRegions 8 (liveRegions 12 36 13 degreeUnionState62_1225) - -def degreeUnionState62_1232 : List PrefixRegion := nextRegions 9 (liveRegions 12 36 13 degreeUnionState62_1225) - -def degreeUnionState62_1233 : List PrefixRegion := nextRegions 10 (liveRegions 12 36 13 degreeUnionState62_1225) - -def degreeUnionState62_1234 : List PrefixRegion := nextRegions 11 (liveRegions 12 36 13 degreeUnionState62_1225) - -def degreeUnionState62_1235 : List PrefixRegion := nextRegions 12 (liveRegions 12 36 13 degreeUnionState62_1225) - -def degreeUnionState62_1236 : List PrefixRegion := nextRegions 13 (liveRegions 12 36 13 degreeUnionState62_1225) - -def degreeUnionState62_1237 : List PrefixRegion := nextRegions 14 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1238 : List PrefixRegion := nextRegions 4 (liveRegions 13 48 14 degreeUnionState62_1237) - -def degreeUnionState62_1239 : List PrefixRegion := nextRegions 5 (liveRegions 13 48 14 degreeUnionState62_1237) - -def degreeUnionState62_1240 : List PrefixRegion := nextRegions 6 (liveRegions 13 48 14 degreeUnionState62_1237) - -def degreeUnionState62_1241 : List PrefixRegion := nextRegions 7 (liveRegions 13 48 14 degreeUnionState62_1237) - -def degreeUnionState62_1242 : List PrefixRegion := nextRegions 8 (liveRegions 13 48 14 degreeUnionState62_1237) - -def degreeUnionState62_1243 : List PrefixRegion := nextRegions 4 (liveRegions 12 40 8 degreeUnionState62_1242) - -def degreeUnionState62_1244 : List PrefixRegion := nextRegions 5 (liveRegions 12 40 8 degreeUnionState62_1242) - -def degreeUnionState62_1245 : List PrefixRegion := nextRegions 6 (liveRegions 12 40 8 degreeUnionState62_1242) - -def degreeUnionState62_1246 : List PrefixRegion := nextRegions 7 (liveRegions 12 40 8 degreeUnionState62_1242) - -def degreeUnionState62_1247 : List PrefixRegion := nextRegions 8 (liveRegions 12 40 8 degreeUnionState62_1242) - -def degreeUnionState62_1248 : List PrefixRegion := nextRegions 3 (liveRegions 11 32 8 degreeUnionState62_1247) - -def degreeUnionState62_1249 : List PrefixRegion := nextRegions 4 (liveRegions 11 32 8 degreeUnionState62_1247) - -def degreeUnionState62_1250 : List PrefixRegion := nextRegions 5 (liveRegions 11 32 8 degreeUnionState62_1247) - -def degreeUnionState62_1251 : List PrefixRegion := nextRegions 6 (liveRegions 11 32 8 degreeUnionState62_1247) - -def degreeUnionState62_1252 : List PrefixRegion := nextRegions 7 (liveRegions 11 32 8 degreeUnionState62_1247) - -def degreeUnionState62_1253 : List PrefixRegion := nextRegions 8 (liveRegions 11 32 8 degreeUnionState62_1247) - -def degreeUnionState62_1254 : List PrefixRegion := nextRegions 9 (liveRegions 13 48 14 degreeUnionState62_1237) - -def degreeUnionState62_1255 : List PrefixRegion := nextRegions 4 (liveRegions 12 39 9 degreeUnionState62_1254) - -def degreeUnionState62_1256 : List PrefixRegion := nextRegions 5 (liveRegions 12 39 9 degreeUnionState62_1254) - -def degreeUnionState62_1257 : List PrefixRegion := nextRegions 6 (liveRegions 12 39 9 degreeUnionState62_1254) - -def degreeUnionState62_1258 : List PrefixRegion := nextRegions 7 (liveRegions 12 39 9 degreeUnionState62_1254) - -def degreeUnionState62_1259 : List PrefixRegion := nextRegions 8 (liveRegions 12 39 9 degreeUnionState62_1254) - -def degreeUnionState62_1260 : List PrefixRegion := nextRegions 3 (liveRegions 11 31 8 degreeUnionState62_1259) - -def degreeUnionState62_1261 : List PrefixRegion := nextRegions 4 (liveRegions 11 31 8 degreeUnionState62_1259) - -def degreeUnionState62_1262 : List PrefixRegion := nextRegions 5 (liveRegions 11 31 8 degreeUnionState62_1259) - -def degreeUnionState62_1263 : List PrefixRegion := nextRegions 6 (liveRegions 11 31 8 degreeUnionState62_1259) - -def degreeUnionState62_1264 : List PrefixRegion := nextRegions 7 (liveRegions 11 31 8 degreeUnionState62_1259) - -def degreeUnionState62_1265 : List PrefixRegion := nextRegions 8 (liveRegions 11 31 8 degreeUnionState62_1259) - -def degreeUnionState62_1266 : List PrefixRegion := nextRegions 9 (liveRegions 12 39 9 degreeUnionState62_1254) - -def degreeUnionState62_1267 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 9 degreeUnionState62_1266) - -def degreeUnionState62_1268 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 9 degreeUnionState62_1266) - -def degreeUnionState62_1269 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 9 degreeUnionState62_1266) - -def degreeUnionState62_1270 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 9 degreeUnionState62_1266) - -def degreeUnionState62_1271 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 9 degreeUnionState62_1266) - -def degreeUnionState62_1272 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 9 degreeUnionState62_1266) - -def degreeUnionState62_1273 : List PrefixRegion := nextRegions 9 (liveRegions 11 30 9 degreeUnionState62_1266) - -def degreeUnionState62_1274 : List PrefixRegion := nextRegions 10 (liveRegions 13 48 14 degreeUnionState62_1237) - -def degreeUnionState62_1275 : List PrefixRegion := nextRegions 4 (liveRegions 12 38 10 degreeUnionState62_1274) - -def degreeUnionState62_1276 : List PrefixRegion := nextRegions 5 (liveRegions 12 38 10 degreeUnionState62_1274) - -def degreeUnionState62_1277 : List PrefixRegion := nextRegions 6 (liveRegions 12 38 10 degreeUnionState62_1274) - -def degreeUnionState62_1278 : List PrefixRegion := nextRegions 7 (liveRegions 12 38 10 degreeUnionState62_1274) - -def degreeUnionState62_1279 : List PrefixRegion := nextRegions 8 (liveRegions 12 38 10 degreeUnionState62_1274) - -def degreeUnionState62_1280 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 8 degreeUnionState62_1279) - -def degreeUnionState62_1281 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 8 degreeUnionState62_1279) - -def degreeUnionState62_1282 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 8 degreeUnionState62_1279) - -def degreeUnionState62_1283 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 8 degreeUnionState62_1279) - -def degreeUnionState62_1284 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 8 degreeUnionState62_1279) - -def degreeUnionState62_1285 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 8 degreeUnionState62_1279) - -def degreeUnionState62_1286 : List PrefixRegion := nextRegions 9 (liveRegions 12 38 10 degreeUnionState62_1274) - -def degreeUnionState62_1287 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 9 degreeUnionState62_1286) - -def degreeUnionState62_1288 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 9 degreeUnionState62_1286) - -def degreeUnionState62_1289 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 9 degreeUnionState62_1286) - -def degreeUnionState62_1290 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 9 degreeUnionState62_1286) - -def degreeUnionState62_1291 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 9 degreeUnionState62_1286) - -def degreeUnionState62_1292 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 9 degreeUnionState62_1286) - -def degreeUnionState62_1293 : List PrefixRegion := nextRegions 9 (liveRegions 11 29 9 degreeUnionState62_1286) - -def degreeUnionState62_1294 : List PrefixRegion := nextRegions 10 (liveRegions 12 38 10 degreeUnionState62_1274) - -def degreeUnionState62_1295 : List PrefixRegion := nextRegions 11 (liveRegions 13 48 14 degreeUnionState62_1237) - -def degreeUnionState62_1296 : List PrefixRegion := nextRegions 4 (liveRegions 12 37 11 degreeUnionState62_1295) - -def degreeUnionState62_1297 : List PrefixRegion := nextRegions 5 (liveRegions 12 37 11 degreeUnionState62_1295) - -def degreeUnionState62_1298 : List PrefixRegion := nextRegions 6 (liveRegions 12 37 11 degreeUnionState62_1295) - -def degreeUnionState62_1299 : List PrefixRegion := nextRegions 7 (liveRegions 12 37 11 degreeUnionState62_1295) - -def degreeUnionState62_1300 : List PrefixRegion := nextRegions 8 (liveRegions 12 37 11 degreeUnionState62_1295) - -def degreeUnionState62_1301 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 8 degreeUnionState62_1300) - -def degreeUnionState62_1302 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 8 degreeUnionState62_1300) - -def degreeUnionState62_1303 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 8 degreeUnionState62_1300) - -def degreeUnionState62_1304 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 8 degreeUnionState62_1300) - -def degreeUnionState62_1305 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 8 degreeUnionState62_1300) - -def degreeUnionState62_1306 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 8 degreeUnionState62_1300) - -def degreeUnionState62_1307 : List PrefixRegion := nextRegions 9 (liveRegions 12 37 11 degreeUnionState62_1295) - -def degreeUnionState62_1308 : List PrefixRegion := nextRegions 10 (liveRegions 12 37 11 degreeUnionState62_1295) - -def degreeUnionState62_1309 : List PrefixRegion := nextRegions 11 (liveRegions 12 37 11 degreeUnionState62_1295) - -def degreeUnionState62_1310 : List PrefixRegion := nextRegions 12 (liveRegions 13 48 14 degreeUnionState62_1237) - -def degreeUnionState62_1311 : List PrefixRegion := nextRegions 3 (liveRegions 12 36 12 degreeUnionState62_1310) - -def degreeUnionState62_1312 : List PrefixRegion := nextRegions 4 (liveRegions 12 36 12 degreeUnionState62_1310) - -def degreeUnionState62_1313 : List PrefixRegion := nextRegions 5 (liveRegions 12 36 12 degreeUnionState62_1310) - -def degreeUnionState62_1314 : List PrefixRegion := nextRegions 6 (liveRegions 12 36 12 degreeUnionState62_1310) - -def degreeUnionState62_1315 : List PrefixRegion := nextRegions 7 (liveRegions 12 36 12 degreeUnionState62_1310) - -def degreeUnionState62_1316 : List PrefixRegion := nextRegions 8 (liveRegions 12 36 12 degreeUnionState62_1310) - -def degreeUnionState62_1317 : List PrefixRegion := nextRegions 9 (liveRegions 12 36 12 degreeUnionState62_1310) - -def degreeUnionState62_1318 : List PrefixRegion := nextRegions 10 (liveRegions 12 36 12 degreeUnionState62_1310) - -def degreeUnionState62_1319 : List PrefixRegion := nextRegions 11 (liveRegions 12 36 12 degreeUnionState62_1310) - -def degreeUnionState62_1320 : List PrefixRegion := nextRegions 12 (liveRegions 12 36 12 degreeUnionState62_1310) - -def degreeUnionState62_1321 : List PrefixRegion := nextRegions 13 (liveRegions 13 48 14 degreeUnionState62_1237) - -def degreeUnionState62_1322 : List PrefixRegion := nextRegions 14 (liveRegions 13 48 14 degreeUnionState62_1237) - -def degreeUnionState62_1323 : List PrefixRegion := nextRegions 15 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1324 : List PrefixRegion := nextRegions 16 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1325 : List PrefixRegion := nextRegions 17 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1326 : List PrefixRegion := nextRegions 18 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1327 : List PrefixRegion := nextRegions 19 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1328 : List PrefixRegion := nextRegions 20 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1329 : List PrefixRegion := nextRegions 21 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1330 : List PrefixRegion := nextRegions 22 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1331 : List PrefixRegion := nextRegions 23 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1332 : List PrefixRegion := nextRegions 24 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1333 : List PrefixRegion := nextRegions 25 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1334 : List PrefixRegion := nextRegions 26 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1335 : List PrefixRegion := nextRegions 27 (liveRegions 14 62 28 degreeHalfRegions62) - -def degreeUnionState62_1336 : List PrefixRegion := nextRegions 28 (liveRegions 14 62 28 degreeHalfRegions62) - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.UnionRowChecker +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeUnionData62 + +namespace OAI + +/-! Degree Union States 62. -/ + +section + +namespace UniversalTensorSquare + +def degreeUnionState62_12 : List PrefixRegion := nextRegions 6 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_13 : List PrefixRegion := nextRegions 7 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_14 : List PrefixRegion := nextRegions 8 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_15 : List PrefixRegion := nextRegions 9 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_16 : List PrefixRegion := nextRegions 10 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_17 : List PrefixRegion := nextRegions 11 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_18 : List PrefixRegion := nextRegions 12 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_19 : List PrefixRegion := nextRegions 5 (liveRegions 10 50 12 degreeUnionState62_18) + +def degreeUnionState62_20 : List PrefixRegion := nextRegions 6 (liveRegions 10 50 12 degreeUnionState62_18) + +def degreeUnionState62_21 : List PrefixRegion := nextRegions 7 (liveRegions 10 50 12 degreeUnionState62_18) + +def degreeUnionState62_22 : List PrefixRegion := nextRegions 8 (liveRegions 10 50 12 degreeUnionState62_18) + +def degreeUnionState62_23 : List PrefixRegion := nextRegions 9 (liveRegions 10 50 12 degreeUnionState62_18) + +def degreeUnionState62_24 : List PrefixRegion := nextRegions 10 (liveRegions 10 50 12 degreeUnionState62_18) + +def degreeUnionState62_25 : List PrefixRegion := nextRegions 11 (liveRegions 10 50 12 degreeUnionState62_18) + +def degreeUnionState62_26 : List PrefixRegion := nextRegions 12 (liveRegions 10 50 12 degreeUnionState62_18) + +def degreeUnionState62_27 : List PrefixRegion := nextRegions 13 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_28 : List PrefixRegion := nextRegions 5 (liveRegions 10 49 13 degreeUnionState62_27) + +def degreeUnionState62_29 : List PrefixRegion := nextRegions 6 (liveRegions 10 49 13 degreeUnionState62_27) + +def degreeUnionState62_30 : List PrefixRegion := nextRegions 7 (liveRegions 10 49 13 degreeUnionState62_27) + +def degreeUnionState62_31 : List PrefixRegion := nextRegions 8 (liveRegions 10 49 13 degreeUnionState62_27) + +def degreeUnionState62_32 : List PrefixRegion := nextRegions 9 (liveRegions 10 49 13 degreeUnionState62_27) + +def degreeUnionState62_33 : List PrefixRegion := nextRegions 10 (liveRegions 10 49 13 degreeUnionState62_27) + +def degreeUnionState62_34 : List PrefixRegion := nextRegions 11 (liveRegions 10 49 13 degreeUnionState62_27) + +def degreeUnionState62_35 : List PrefixRegion := nextRegions 12 (liveRegions 10 49 13 degreeUnionState62_27) + +def degreeUnionState62_36 : List PrefixRegion := nextRegions 13 (liveRegions 10 49 13 degreeUnionState62_27) + +def degreeUnionState62_37 : List PrefixRegion := nextRegions 14 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_38 : List PrefixRegion := nextRegions 5 (liveRegions 10 48 14 degreeUnionState62_37) + +def degreeUnionState62_39 : List PrefixRegion := nextRegions 6 (liveRegions 10 48 14 degreeUnionState62_37) + +def degreeUnionState62_40 : List PrefixRegion := nextRegions 7 (liveRegions 10 48 14 degreeUnionState62_37) + +def degreeUnionState62_41 : List PrefixRegion := nextRegions 8 (liveRegions 10 48 14 degreeUnionState62_37) + +def degreeUnionState62_42 : List PrefixRegion := nextRegions 9 (liveRegions 10 48 14 degreeUnionState62_37) + +def degreeUnionState62_43 : List PrefixRegion := nextRegions 10 (liveRegions 10 48 14 degreeUnionState62_37) + +def degreeUnionState62_44 : List PrefixRegion := nextRegions 11 (liveRegions 10 48 14 degreeUnionState62_37) + +def degreeUnionState62_45 : List PrefixRegion := nextRegions 12 (liveRegions 10 48 14 degreeUnionState62_37) + +def degreeUnionState62_46 : List PrefixRegion := nextRegions 13 (liveRegions 10 48 14 degreeUnionState62_37) + +def degreeUnionState62_47 : List PrefixRegion := nextRegions 14 (liveRegions 10 48 14 degreeUnionState62_37) + +def degreeUnionState62_48 : List PrefixRegion := nextRegions 15 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_49 : List PrefixRegion := nextRegions 16 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_50 : List PrefixRegion := nextRegions 17 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_51 : List PrefixRegion := nextRegions 18 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_52 : List PrefixRegion := nextRegions 19 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_53 : List PrefixRegion := nextRegions 20 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_54 : List PrefixRegion := nextRegions 21 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_55 : List PrefixRegion := nextRegions 22 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_56 : List PrefixRegion := nextRegions 23 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_57 : List PrefixRegion := nextRegions 24 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_58 : List PrefixRegion := nextRegions 25 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_59 : List PrefixRegion := nextRegions 26 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_60 : List PrefixRegion := nextRegions 27 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_61 : List PrefixRegion := nextRegions 28 (liveRegions 11 62 28 degreeHalfRegions62) + +def degreeUnionState62_63 : List PrefixRegion := nextRegions 6 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_64 : List PrefixRegion := nextRegions 7 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_65 : List PrefixRegion := nextRegions 8 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_66 : List PrefixRegion := nextRegions 9 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_67 : List PrefixRegion := nextRegions 10 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_68 : List PrefixRegion := nextRegions 5 (liveRegions 11 52 10 degreeUnionState62_67) + +def degreeUnionState62_69 : List PrefixRegion := nextRegions 6 (liveRegions 11 52 10 degreeUnionState62_67) + +def degreeUnionState62_70 : List PrefixRegion := nextRegions 7 (liveRegions 11 52 10 degreeUnionState62_67) + +def degreeUnionState62_71 : List PrefixRegion := nextRegions 8 (liveRegions 11 52 10 degreeUnionState62_67) + +def degreeUnionState62_72 : List PrefixRegion := nextRegions 9 (liveRegions 11 52 10 degreeUnionState62_67) + +def degreeUnionState62_73 : List PrefixRegion := nextRegions 10 (liveRegions 11 52 10 degreeUnionState62_67) + +def degreeUnionState62_74 : List PrefixRegion := nextRegions 5 (liveRegions 10 42 10 degreeUnionState62_73) + +def degreeUnionState62_75 : List PrefixRegion := nextRegions 6 (liveRegions 10 42 10 degreeUnionState62_73) + +def degreeUnionState62_76 : List PrefixRegion := nextRegions 7 (liveRegions 10 42 10 degreeUnionState62_73) + +def degreeUnionState62_77 : List PrefixRegion := nextRegions 8 (liveRegions 10 42 10 degreeUnionState62_73) + +def degreeUnionState62_78 : List PrefixRegion := nextRegions 9 (liveRegions 10 42 10 degreeUnionState62_73) + +def degreeUnionState62_79 : List PrefixRegion := nextRegions 10 (liveRegions 10 42 10 degreeUnionState62_73) + +def degreeUnionState62_80 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 10 degreeUnionState62_79) + +def degreeUnionState62_81 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 10 degreeUnionState62_79) + +def degreeUnionState62_82 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 10 degreeUnionState62_79) + +def degreeUnionState62_83 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 10 degreeUnionState62_79) + +def degreeUnionState62_84 : List PrefixRegion := nextRegions 8 (liveRegions 9 32 10 degreeUnionState62_79) + +def degreeUnionState62_85 : List PrefixRegion := nextRegions 9 (liveRegions 9 32 10 degreeUnionState62_79) + +def degreeUnionState62_86 : List PrefixRegion := nextRegions 10 (liveRegions 9 32 10 degreeUnionState62_79) + +def degreeUnionState62_87 : List PrefixRegion := nextRegions 11 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_88 : List PrefixRegion := nextRegions 5 (liveRegions 11 51 11 degreeUnionState62_87) + +def degreeUnionState62_89 : List PrefixRegion := nextRegions 6 (liveRegions 11 51 11 degreeUnionState62_87) + +def degreeUnionState62_90 : List PrefixRegion := nextRegions 7 (liveRegions 11 51 11 degreeUnionState62_87) + +def degreeUnionState62_91 : List PrefixRegion := nextRegions 8 (liveRegions 11 51 11 degreeUnionState62_87) + +def degreeUnionState62_92 : List PrefixRegion := nextRegions 9 (liveRegions 11 51 11 degreeUnionState62_87) + +def degreeUnionState62_93 : List PrefixRegion := nextRegions 10 (liveRegions 11 51 11 degreeUnionState62_87) + +def degreeUnionState62_94 : List PrefixRegion := nextRegions 5 (liveRegions 10 41 10 degreeUnionState62_93) + +def degreeUnionState62_95 : List PrefixRegion := nextRegions 6 (liveRegions 10 41 10 degreeUnionState62_93) + +def degreeUnionState62_96 : List PrefixRegion := nextRegions 7 (liveRegions 10 41 10 degreeUnionState62_93) + +def degreeUnionState62_97 : List PrefixRegion := nextRegions 8 (liveRegions 10 41 10 degreeUnionState62_93) + +def degreeUnionState62_98 : List PrefixRegion := nextRegions 9 (liveRegions 10 41 10 degreeUnionState62_93) + +def degreeUnionState62_99 : List PrefixRegion := nextRegions 10 (liveRegions 10 41 10 degreeUnionState62_93) + +def degreeUnionState62_100 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 10 degreeUnionState62_99) + +def degreeUnionState62_101 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 10 degreeUnionState62_99) + +def degreeUnionState62_102 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 10 degreeUnionState62_99) + +def degreeUnionState62_103 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 10 degreeUnionState62_99) + +def degreeUnionState62_104 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 10 degreeUnionState62_99) + +def degreeUnionState62_105 : List PrefixRegion := nextRegions 9 (liveRegions 9 31 10 degreeUnionState62_99) + +def degreeUnionState62_106 : List PrefixRegion := nextRegions 10 (liveRegions 9 31 10 degreeUnionState62_99) + +def degreeUnionState62_107 : List PrefixRegion := nextRegions 11 (liveRegions 11 51 11 degreeUnionState62_87) + +def degreeUnionState62_108 : List PrefixRegion := nextRegions 4 (liveRegions 10 40 11 degreeUnionState62_107) + +def degreeUnionState62_109 : List PrefixRegion := nextRegions 5 (liveRegions 10 40 11 degreeUnionState62_107) + +def degreeUnionState62_110 : List PrefixRegion := nextRegions 6 (liveRegions 10 40 11 degreeUnionState62_107) + +def degreeUnionState62_111 : List PrefixRegion := nextRegions 7 (liveRegions 10 40 11 degreeUnionState62_107) + +def degreeUnionState62_112 : List PrefixRegion := nextRegions 8 (liveRegions 10 40 11 degreeUnionState62_107) + +def degreeUnionState62_113 : List PrefixRegion := nextRegions 9 (liveRegions 10 40 11 degreeUnionState62_107) + +def degreeUnionState62_114 : List PrefixRegion := nextRegions 10 (liveRegions 10 40 11 degreeUnionState62_107) + +def degreeUnionState62_115 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 10 degreeUnionState62_114) + +def degreeUnionState62_116 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 10 degreeUnionState62_114) + +def degreeUnionState62_117 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 10 degreeUnionState62_114) + +def degreeUnionState62_118 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 10 degreeUnionState62_114) + +def degreeUnionState62_119 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 10 degreeUnionState62_114) + +def degreeUnionState62_120 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 10 degreeUnionState62_114) + +def degreeUnionState62_121 : List PrefixRegion := nextRegions 10 (liveRegions 9 30 10 degreeUnionState62_114) + +def degreeUnionState62_122 : List PrefixRegion := nextRegions 11 (liveRegions 10 40 11 degreeUnionState62_107) + +def degreeUnionState62_123 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 11 degreeUnionState62_122) + +def degreeUnionState62_124 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 11 degreeUnionState62_122) + +def degreeUnionState62_125 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 11 degreeUnionState62_122) + +def degreeUnionState62_126 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 11 degreeUnionState62_122) + +def degreeUnionState62_127 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 11 degreeUnionState62_122) + +def degreeUnionState62_128 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 11 degreeUnionState62_122) + +def degreeUnionState62_129 : List PrefixRegion := nextRegions 10 (liveRegions 9 29 11 degreeUnionState62_122) + +def degreeUnionState62_130 : List PrefixRegion := nextRegions 11 (liveRegions 9 29 11 degreeUnionState62_122) + +def degreeUnionState62_131 : List PrefixRegion := nextRegions 12 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_132 : List PrefixRegion := nextRegions 5 (liveRegions 11 50 12 degreeUnionState62_131) + +def degreeUnionState62_133 : List PrefixRegion := nextRegions 6 (liveRegions 11 50 12 degreeUnionState62_131) + +def degreeUnionState62_134 : List PrefixRegion := nextRegions 7 (liveRegions 11 50 12 degreeUnionState62_131) + +def degreeUnionState62_135 : List PrefixRegion := nextRegions 5 (liveRegions 10 43 7 degreeUnionState62_134) + +def degreeUnionState62_136 : List PrefixRegion := nextRegions 6 (liveRegions 10 43 7 degreeUnionState62_134) + +def degreeUnionState62_137 : List PrefixRegion := nextRegions 7 (liveRegions 10 43 7 degreeUnionState62_134) + +def degreeUnionState62_138 : List PrefixRegion := nextRegions 8 (liveRegions 11 50 12 degreeUnionState62_131) + +def degreeUnionState62_139 : List PrefixRegion := nextRegions 5 (liveRegions 10 42 8 degreeUnionState62_138) + +def degreeUnionState62_140 : List PrefixRegion := nextRegions 6 (liveRegions 10 42 8 degreeUnionState62_138) + +def degreeUnionState62_141 : List PrefixRegion := nextRegions 7 (liveRegions 10 42 8 degreeUnionState62_138) + +def degreeUnionState62_142 : List PrefixRegion := nextRegions 4 (liveRegions 9 35 7 degreeUnionState62_141) + +def degreeUnionState62_143 : List PrefixRegion := nextRegions 5 (liveRegions 9 35 7 degreeUnionState62_141) + +def degreeUnionState62_144 : List PrefixRegion := nextRegions 6 (liveRegions 9 35 7 degreeUnionState62_141) + +def degreeUnionState62_145 : List PrefixRegion := nextRegions 7 (liveRegions 9 35 7 degreeUnionState62_141) + +def degreeUnionState62_146 : List PrefixRegion := nextRegions 8 (liveRegions 10 42 8 degreeUnionState62_138) + +def degreeUnionState62_147 : List PrefixRegion := nextRegions 4 (liveRegions 9 34 8 degreeUnionState62_146) + +def degreeUnionState62_148 : List PrefixRegion := nextRegions 5 (liveRegions 9 34 8 degreeUnionState62_146) + +def degreeUnionState62_149 : List PrefixRegion := nextRegions 6 (liveRegions 9 34 8 degreeUnionState62_146) + +def degreeUnionState62_150 : List PrefixRegion := nextRegions 7 (liveRegions 9 34 8 degreeUnionState62_146) + +def degreeUnionState62_151 : List PrefixRegion := nextRegions 8 (liveRegions 9 34 8 degreeUnionState62_146) + +def degreeUnionState62_152 : List PrefixRegion := nextRegions 9 (liveRegions 11 50 12 degreeUnionState62_131) + +def degreeUnionState62_153 : List PrefixRegion := nextRegions 5 (liveRegions 10 41 9 degreeUnionState62_152) + +def degreeUnionState62_154 : List PrefixRegion := nextRegions 6 (liveRegions 10 41 9 degreeUnionState62_152) + +def degreeUnionState62_155 : List PrefixRegion := nextRegions 7 (liveRegions 10 41 9 degreeUnionState62_152) + +def degreeUnionState62_156 : List PrefixRegion := nextRegions 4 (liveRegions 9 34 7 degreeUnionState62_155) + +def degreeUnionState62_157 : List PrefixRegion := nextRegions 5 (liveRegions 9 34 7 degreeUnionState62_155) + +def degreeUnionState62_158 : List PrefixRegion := nextRegions 6 (liveRegions 9 34 7 degreeUnionState62_155) + +def degreeUnionState62_159 : List PrefixRegion := nextRegions 7 (liveRegions 9 34 7 degreeUnionState62_155) + +def degreeUnionState62_160 : List PrefixRegion := nextRegions 8 (liveRegions 10 41 9 degreeUnionState62_152) + +def degreeUnionState62_161 : List PrefixRegion := nextRegions 4 (liveRegions 9 33 8 degreeUnionState62_160) + +def degreeUnionState62_162 : List PrefixRegion := nextRegions 5 (liveRegions 9 33 8 degreeUnionState62_160) + +def degreeUnionState62_163 : List PrefixRegion := nextRegions 6 (liveRegions 9 33 8 degreeUnionState62_160) + +def degreeUnionState62_164 : List PrefixRegion := nextRegions 7 (liveRegions 9 33 8 degreeUnionState62_160) + +def degreeUnionState62_165 : List PrefixRegion := nextRegions 8 (liveRegions 9 33 8 degreeUnionState62_160) + +def degreeUnionState62_166 : List PrefixRegion := nextRegions 9 (liveRegions 10 41 9 degreeUnionState62_152) + +def degreeUnionState62_167 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 9 degreeUnionState62_166) + +def degreeUnionState62_168 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 9 degreeUnionState62_166) + +def degreeUnionState62_169 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 9 degreeUnionState62_166) + +def degreeUnionState62_170 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 9 degreeUnionState62_166) + +def degreeUnionState62_171 : List PrefixRegion := nextRegions 8 (liveRegions 9 32 9 degreeUnionState62_166) + +def degreeUnionState62_172 : List PrefixRegion := nextRegions 9 (liveRegions 9 32 9 degreeUnionState62_166) + +def degreeUnionState62_173 : List PrefixRegion := nextRegions 10 (liveRegions 11 50 12 degreeUnionState62_131) + +def degreeUnionState62_174 : List PrefixRegion := nextRegions 4 (liveRegions 10 40 10 degreeUnionState62_173) + +def degreeUnionState62_175 : List PrefixRegion := nextRegions 5 (liveRegions 10 40 10 degreeUnionState62_173) + +def degreeUnionState62_176 : List PrefixRegion := nextRegions 6 (liveRegions 10 40 10 degreeUnionState62_173) + +def degreeUnionState62_177 : List PrefixRegion := nextRegions 7 (liveRegions 10 40 10 degreeUnionState62_173) + +def degreeUnionState62_178 : List PrefixRegion := nextRegions 4 (liveRegions 9 33 7 degreeUnionState62_177) + +def degreeUnionState62_179 : List PrefixRegion := nextRegions 5 (liveRegions 9 33 7 degreeUnionState62_177) + +def degreeUnionState62_180 : List PrefixRegion := nextRegions 6 (liveRegions 9 33 7 degreeUnionState62_177) + +def degreeUnionState62_181 : List PrefixRegion := nextRegions 7 (liveRegions 9 33 7 degreeUnionState62_177) + +def degreeUnionState62_182 : List PrefixRegion := nextRegions 8 (liveRegions 10 40 10 degreeUnionState62_173) + +def degreeUnionState62_183 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 8 degreeUnionState62_182) + +def degreeUnionState62_184 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 8 degreeUnionState62_182) + +def degreeUnionState62_185 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 8 degreeUnionState62_182) + +def degreeUnionState62_186 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 8 degreeUnionState62_182) + +def degreeUnionState62_187 : List PrefixRegion := nextRegions 8 (liveRegions 9 32 8 degreeUnionState62_182) + +def degreeUnionState62_188 : List PrefixRegion := nextRegions 9 (liveRegions 10 40 10 degreeUnionState62_173) + +def degreeUnionState62_189 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 9 degreeUnionState62_188) + +def degreeUnionState62_190 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 9 degreeUnionState62_188) + +def degreeUnionState62_191 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 9 degreeUnionState62_188) + +def degreeUnionState62_192 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 9 degreeUnionState62_188) + +def degreeUnionState62_193 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 9 degreeUnionState62_188) + +def degreeUnionState62_194 : List PrefixRegion := nextRegions 9 (liveRegions 9 31 9 degreeUnionState62_188) + +def degreeUnionState62_195 : List PrefixRegion := nextRegions 10 (liveRegions 10 40 10 degreeUnionState62_173) + +def degreeUnionState62_196 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 10 degreeUnionState62_195) + +def degreeUnionState62_197 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 10 degreeUnionState62_195) + +def degreeUnionState62_198 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 10 degreeUnionState62_195) + +def degreeUnionState62_199 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 10 degreeUnionState62_195) + +def degreeUnionState62_200 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 10 degreeUnionState62_195) + +def degreeUnionState62_201 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 10 degreeUnionState62_195) + +def degreeUnionState62_202 : List PrefixRegion := nextRegions 10 (liveRegions 9 30 10 degreeUnionState62_195) + +def degreeUnionState62_203 : List PrefixRegion := nextRegions 11 (liveRegions 11 50 12 degreeUnionState62_131) + +def degreeUnionState62_204 : List PrefixRegion := nextRegions 4 (liveRegions 10 39 11 degreeUnionState62_203) + +def degreeUnionState62_205 : List PrefixRegion := nextRegions 5 (liveRegions 10 39 11 degreeUnionState62_203) + +def degreeUnionState62_206 : List PrefixRegion := nextRegions 6 (liveRegions 10 39 11 degreeUnionState62_203) + +def degreeUnionState62_207 : List PrefixRegion := nextRegions 7 (liveRegions 10 39 11 degreeUnionState62_203) + +def degreeUnionState62_208 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 7 degreeUnionState62_207) + +def degreeUnionState62_209 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 7 degreeUnionState62_207) + +def degreeUnionState62_210 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 7 degreeUnionState62_207) + +def degreeUnionState62_211 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 7 degreeUnionState62_207) + +def degreeUnionState62_212 : List PrefixRegion := nextRegions 8 (liveRegions 10 39 11 degreeUnionState62_203) + +def degreeUnionState62_213 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 8 degreeUnionState62_212) + +def degreeUnionState62_214 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 8 degreeUnionState62_212) + +def degreeUnionState62_215 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 8 degreeUnionState62_212) + +def degreeUnionState62_216 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 8 degreeUnionState62_212) + +def degreeUnionState62_217 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 8 degreeUnionState62_212) + +def degreeUnionState62_218 : List PrefixRegion := nextRegions 9 (liveRegions 10 39 11 degreeUnionState62_203) + +def degreeUnionState62_219 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 9 degreeUnionState62_218) + +def degreeUnionState62_220 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 9 degreeUnionState62_218) + +def degreeUnionState62_221 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 9 degreeUnionState62_218) + +def degreeUnionState62_222 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 9 degreeUnionState62_218) + +def degreeUnionState62_223 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 9 degreeUnionState62_218) + +def degreeUnionState62_224 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 9 degreeUnionState62_218) + +def degreeUnionState62_225 : List PrefixRegion := nextRegions 10 (liveRegions 10 39 11 degreeUnionState62_203) + +def degreeUnionState62_226 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 10 degreeUnionState62_225) + +def degreeUnionState62_227 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 10 degreeUnionState62_225) + +def degreeUnionState62_228 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 10 degreeUnionState62_225) + +def degreeUnionState62_229 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 10 degreeUnionState62_225) + +def degreeUnionState62_230 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 10 degreeUnionState62_225) + +def degreeUnionState62_231 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 10 degreeUnionState62_225) + +def degreeUnionState62_232 : List PrefixRegion := nextRegions 10 (liveRegions 9 29 10 degreeUnionState62_225) + +def degreeUnionState62_233 : List PrefixRegion := nextRegions 11 (liveRegions 10 39 11 degreeUnionState62_203) + +def degreeUnionState62_234 : List PrefixRegion := nextRegions 12 (liveRegions 11 50 12 degreeUnionState62_131) + +def degreeUnionState62_235 : List PrefixRegion := nextRegions 4 (liveRegions 10 38 12 degreeUnionState62_234) + +def degreeUnionState62_236 : List PrefixRegion := nextRegions 5 (liveRegions 10 38 12 degreeUnionState62_234) + +def degreeUnionState62_237 : List PrefixRegion := nextRegions 6 (liveRegions 10 38 12 degreeUnionState62_234) + +def degreeUnionState62_238 : List PrefixRegion := nextRegions 7 (liveRegions 10 38 12 degreeUnionState62_234) + +def degreeUnionState62_239 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 7 degreeUnionState62_238) + +def degreeUnionState62_240 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 7 degreeUnionState62_238) + +def degreeUnionState62_241 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 7 degreeUnionState62_238) + +def degreeUnionState62_242 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 7 degreeUnionState62_238) + +def degreeUnionState62_243 : List PrefixRegion := nextRegions 8 (liveRegions 10 38 12 degreeUnionState62_234) + +def degreeUnionState62_244 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 8 degreeUnionState62_243) + +def degreeUnionState62_245 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 8 degreeUnionState62_243) + +def degreeUnionState62_246 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 8 degreeUnionState62_243) + +def degreeUnionState62_247 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 8 degreeUnionState62_243) + +def degreeUnionState62_248 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 8 degreeUnionState62_243) + +def degreeUnionState62_249 : List PrefixRegion := nextRegions 9 (liveRegions 10 38 12 degreeUnionState62_234) + +def degreeUnionState62_250 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 9 degreeUnionState62_249) + +def degreeUnionState62_251 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 9 degreeUnionState62_249) + +def degreeUnionState62_252 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 9 degreeUnionState62_249) + +def degreeUnionState62_253 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 9 degreeUnionState62_249) + +def degreeUnionState62_254 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 9 degreeUnionState62_249) + +def degreeUnionState62_255 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 9 degreeUnionState62_249) + +def degreeUnionState62_256 : List PrefixRegion := nextRegions 10 (liveRegions 10 38 12 degreeUnionState62_234) + +def degreeUnionState62_257 : List PrefixRegion := nextRegions 11 (liveRegions 10 38 12 degreeUnionState62_234) + +def degreeUnionState62_258 : List PrefixRegion := nextRegions 12 (liveRegions 10 38 12 degreeUnionState62_234) + +def degreeUnionState62_259 : List PrefixRegion := nextRegions 13 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_260 : List PrefixRegion := nextRegions 5 (liveRegions 11 49 13 degreeUnionState62_259) + +def degreeUnionState62_261 : List PrefixRegion := nextRegions 6 (liveRegions 11 49 13 degreeUnionState62_259) + +def degreeUnionState62_262 : List PrefixRegion := nextRegions 7 (liveRegions 11 49 13 degreeUnionState62_259) + +def degreeUnionState62_263 : List PrefixRegion := nextRegions 5 (liveRegions 10 42 7 degreeUnionState62_262) + +def degreeUnionState62_264 : List PrefixRegion := nextRegions 6 (liveRegions 10 42 7 degreeUnionState62_262) + +def degreeUnionState62_265 : List PrefixRegion := nextRegions 7 (liveRegions 10 42 7 degreeUnionState62_262) + +def degreeUnionState62_266 : List PrefixRegion := nextRegions 4 (liveRegions 9 35 7 degreeUnionState62_265) + +def degreeUnionState62_267 : List PrefixRegion := nextRegions 5 (liveRegions 9 35 7 degreeUnionState62_265) + +def degreeUnionState62_268 : List PrefixRegion := nextRegions 6 (liveRegions 9 35 7 degreeUnionState62_265) + +def degreeUnionState62_269 : List PrefixRegion := nextRegions 7 (liveRegions 9 35 7 degreeUnionState62_265) + +def degreeUnionState62_270 : List PrefixRegion := nextRegions 8 (liveRegions 11 49 13 degreeUnionState62_259) + +def degreeUnionState62_271 : List PrefixRegion := nextRegions 5 (liveRegions 10 41 8 degreeUnionState62_270) + +def degreeUnionState62_272 : List PrefixRegion := nextRegions 6 (liveRegions 10 41 8 degreeUnionState62_270) + +def degreeUnionState62_273 : List PrefixRegion := nextRegions 7 (liveRegions 10 41 8 degreeUnionState62_270) + +def degreeUnionState62_274 : List PrefixRegion := nextRegions 4 (liveRegions 9 34 7 degreeUnionState62_273) + +def degreeUnionState62_275 : List PrefixRegion := nextRegions 5 (liveRegions 9 34 7 degreeUnionState62_273) + +def degreeUnionState62_276 : List PrefixRegion := nextRegions 6 (liveRegions 9 34 7 degreeUnionState62_273) + +def degreeUnionState62_277 : List PrefixRegion := nextRegions 7 (liveRegions 9 34 7 degreeUnionState62_273) + +def degreeUnionState62_278 : List PrefixRegion := nextRegions 8 (liveRegions 10 41 8 degreeUnionState62_270) + +def degreeUnionState62_279 : List PrefixRegion := nextRegions 4 (liveRegions 9 33 8 degreeUnionState62_278) + +def degreeUnionState62_280 : List PrefixRegion := nextRegions 5 (liveRegions 9 33 8 degreeUnionState62_278) + +def degreeUnionState62_281 : List PrefixRegion := nextRegions 6 (liveRegions 9 33 8 degreeUnionState62_278) + +def degreeUnionState62_282 : List PrefixRegion := nextRegions 7 (liveRegions 9 33 8 degreeUnionState62_278) + +def degreeUnionState62_283 : List PrefixRegion := nextRegions 8 (liveRegions 9 33 8 degreeUnionState62_278) + +def degreeUnionState62_284 : List PrefixRegion := nextRegions 9 (liveRegions 11 49 13 degreeUnionState62_259) + +def degreeUnionState62_285 : List PrefixRegion := nextRegions 4 (liveRegions 10 40 9 degreeUnionState62_284) + +def degreeUnionState62_286 : List PrefixRegion := nextRegions 5 (liveRegions 10 40 9 degreeUnionState62_284) + +def degreeUnionState62_287 : List PrefixRegion := nextRegions 6 (liveRegions 10 40 9 degreeUnionState62_284) + +def degreeUnionState62_288 : List PrefixRegion := nextRegions 7 (liveRegions 10 40 9 degreeUnionState62_284) + +def degreeUnionState62_289 : List PrefixRegion := nextRegions 4 (liveRegions 9 33 7 degreeUnionState62_288) + +def degreeUnionState62_290 : List PrefixRegion := nextRegions 5 (liveRegions 9 33 7 degreeUnionState62_288) + +def degreeUnionState62_291 : List PrefixRegion := nextRegions 6 (liveRegions 9 33 7 degreeUnionState62_288) + +def degreeUnionState62_292 : List PrefixRegion := nextRegions 7 (liveRegions 9 33 7 degreeUnionState62_288) + +def degreeUnionState62_293 : List PrefixRegion := nextRegions 8 (liveRegions 10 40 9 degreeUnionState62_284) + +def degreeUnionState62_294 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 8 degreeUnionState62_293) + +def degreeUnionState62_295 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 8 degreeUnionState62_293) + +def degreeUnionState62_296 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 8 degreeUnionState62_293) + +def degreeUnionState62_297 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 8 degreeUnionState62_293) + +def degreeUnionState62_298 : List PrefixRegion := nextRegions 8 (liveRegions 9 32 8 degreeUnionState62_293) + +def degreeUnionState62_299 : List PrefixRegion := nextRegions 9 (liveRegions 10 40 9 degreeUnionState62_284) + +def degreeUnionState62_300 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 9 degreeUnionState62_299) + +def degreeUnionState62_301 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 9 degreeUnionState62_299) + +def degreeUnionState62_302 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 9 degreeUnionState62_299) + +def degreeUnionState62_303 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 9 degreeUnionState62_299) + +def degreeUnionState62_304 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 9 degreeUnionState62_299) + +def degreeUnionState62_305 : List PrefixRegion := nextRegions 9 (liveRegions 9 31 9 degreeUnionState62_299) + +def degreeUnionState62_306 : List PrefixRegion := nextRegions 10 (liveRegions 11 49 13 degreeUnionState62_259) + +def degreeUnionState62_307 : List PrefixRegion := nextRegions 4 (liveRegions 10 39 10 degreeUnionState62_306) + +def degreeUnionState62_308 : List PrefixRegion := nextRegions 5 (liveRegions 10 39 10 degreeUnionState62_306) + +def degreeUnionState62_309 : List PrefixRegion := nextRegions 6 (liveRegions 10 39 10 degreeUnionState62_306) + +def degreeUnionState62_310 : List PrefixRegion := nextRegions 7 (liveRegions 10 39 10 degreeUnionState62_306) + +def degreeUnionState62_311 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 7 degreeUnionState62_310) + +def degreeUnionState62_312 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 7 degreeUnionState62_310) + +def degreeUnionState62_313 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 7 degreeUnionState62_310) + +def degreeUnionState62_314 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 7 degreeUnionState62_310) + +def degreeUnionState62_315 : List PrefixRegion := nextRegions 8 (liveRegions 10 39 10 degreeUnionState62_306) + +def degreeUnionState62_316 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 8 degreeUnionState62_315) + +def degreeUnionState62_317 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 8 degreeUnionState62_315) + +def degreeUnionState62_318 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 8 degreeUnionState62_315) + +def degreeUnionState62_319 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 8 degreeUnionState62_315) + +def degreeUnionState62_320 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 8 degreeUnionState62_315) + +def degreeUnionState62_321 : List PrefixRegion := nextRegions 9 (liveRegions 10 39 10 degreeUnionState62_306) + +def degreeUnionState62_322 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 9 degreeUnionState62_321) + +def degreeUnionState62_323 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 9 degreeUnionState62_321) + +def degreeUnionState62_324 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 9 degreeUnionState62_321) + +def degreeUnionState62_325 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 9 degreeUnionState62_321) + +def degreeUnionState62_326 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 9 degreeUnionState62_321) + +def degreeUnionState62_327 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 9 degreeUnionState62_321) + +def degreeUnionState62_328 : List PrefixRegion := nextRegions 10 (liveRegions 10 39 10 degreeUnionState62_306) + +def degreeUnionState62_329 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 10 degreeUnionState62_328) + +def degreeUnionState62_330 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 10 degreeUnionState62_328) + +def degreeUnionState62_331 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 10 degreeUnionState62_328) + +def degreeUnionState62_332 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 10 degreeUnionState62_328) + +def degreeUnionState62_333 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 10 degreeUnionState62_328) + +def degreeUnionState62_334 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 10 degreeUnionState62_328) + +def degreeUnionState62_335 : List PrefixRegion := nextRegions 10 (liveRegions 9 29 10 degreeUnionState62_328) + +def degreeUnionState62_336 : List PrefixRegion := nextRegions 11 (liveRegions 11 49 13 degreeUnionState62_259) + +def degreeUnionState62_337 : List PrefixRegion := nextRegions 4 (liveRegions 10 38 11 degreeUnionState62_336) + +def degreeUnionState62_338 : List PrefixRegion := nextRegions 5 (liveRegions 10 38 11 degreeUnionState62_336) + +def degreeUnionState62_339 : List PrefixRegion := nextRegions 6 (liveRegions 10 38 11 degreeUnionState62_336) + +def degreeUnionState62_340 : List PrefixRegion := nextRegions 7 (liveRegions 10 38 11 degreeUnionState62_336) + +def degreeUnionState62_341 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 7 degreeUnionState62_340) + +def degreeUnionState62_342 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 7 degreeUnionState62_340) + +def degreeUnionState62_343 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 7 degreeUnionState62_340) + +def degreeUnionState62_344 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 7 degreeUnionState62_340) + +def degreeUnionState62_345 : List PrefixRegion := nextRegions 8 (liveRegions 10 38 11 degreeUnionState62_336) + +def degreeUnionState62_346 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 8 degreeUnionState62_345) + +def degreeUnionState62_347 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 8 degreeUnionState62_345) + +def degreeUnionState62_348 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 8 degreeUnionState62_345) + +def degreeUnionState62_349 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 8 degreeUnionState62_345) + +def degreeUnionState62_350 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 8 degreeUnionState62_345) + +def degreeUnionState62_351 : List PrefixRegion := nextRegions 9 (liveRegions 10 38 11 degreeUnionState62_336) + +def degreeUnionState62_352 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 9 degreeUnionState62_351) + +def degreeUnionState62_353 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 9 degreeUnionState62_351) + +def degreeUnionState62_354 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 9 degreeUnionState62_351) + +def degreeUnionState62_355 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 9 degreeUnionState62_351) + +def degreeUnionState62_356 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 9 degreeUnionState62_351) + +def degreeUnionState62_357 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 9 degreeUnionState62_351) + +def degreeUnionState62_358 : List PrefixRegion := nextRegions 10 (liveRegions 10 38 11 degreeUnionState62_336) + +def degreeUnionState62_359 : List PrefixRegion := nextRegions 11 (liveRegions 10 38 11 degreeUnionState62_336) + +def degreeUnionState62_360 : List PrefixRegion := nextRegions 12 (liveRegions 11 49 13 degreeUnionState62_259) + +def degreeUnionState62_361 : List PrefixRegion := nextRegions 4 (liveRegions 10 37 12 degreeUnionState62_360) + +def degreeUnionState62_362 : List PrefixRegion := nextRegions 5 (liveRegions 10 37 12 degreeUnionState62_360) + +def degreeUnionState62_363 : List PrefixRegion := nextRegions 6 (liveRegions 10 37 12 degreeUnionState62_360) + +def degreeUnionState62_364 : List PrefixRegion := nextRegions 7 (liveRegions 10 37 12 degreeUnionState62_360) + +def degreeUnionState62_365 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 7 degreeUnionState62_364) + +def degreeUnionState62_366 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 7 degreeUnionState62_364) + +def degreeUnionState62_367 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 7 degreeUnionState62_364) + +def degreeUnionState62_368 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 7 degreeUnionState62_364) + +def degreeUnionState62_369 : List PrefixRegion := nextRegions 8 (liveRegions 10 37 12 degreeUnionState62_360) + +def degreeUnionState62_370 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 8 degreeUnionState62_369) + +def degreeUnionState62_371 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 8 degreeUnionState62_369) + +def degreeUnionState62_372 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 8 degreeUnionState62_369) + +def degreeUnionState62_373 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 8 degreeUnionState62_369) + +def degreeUnionState62_374 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 8 degreeUnionState62_369) + +def degreeUnionState62_375 : List PrefixRegion := nextRegions 9 (liveRegions 10 37 12 degreeUnionState62_360) + +def degreeUnionState62_376 : List PrefixRegion := nextRegions 10 (liveRegions 10 37 12 degreeUnionState62_360) + +def degreeUnionState62_377 : List PrefixRegion := nextRegions 11 (liveRegions 10 37 12 degreeUnionState62_360) + +def degreeUnionState62_378 : List PrefixRegion := nextRegions 12 (liveRegions 10 37 12 degreeUnionState62_360) + +def degreeUnionState62_379 : List PrefixRegion := nextRegions 13 (liveRegions 11 49 13 degreeUnionState62_259) + +def degreeUnionState62_380 : List PrefixRegion := nextRegions 4 (liveRegions 10 36 13 degreeUnionState62_379) + +def degreeUnionState62_381 : List PrefixRegion := nextRegions 5 (liveRegions 10 36 13 degreeUnionState62_379) + +def degreeUnionState62_382 : List PrefixRegion := nextRegions 6 (liveRegions 10 36 13 degreeUnionState62_379) + +def degreeUnionState62_383 : List PrefixRegion := nextRegions 7 (liveRegions 10 36 13 degreeUnionState62_379) + +def degreeUnionState62_384 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 7 degreeUnionState62_383) + +def degreeUnionState62_385 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 7 degreeUnionState62_383) + +def degreeUnionState62_386 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 7 degreeUnionState62_383) + +def degreeUnionState62_387 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 7 degreeUnionState62_383) + +def degreeUnionState62_388 : List PrefixRegion := nextRegions 8 (liveRegions 10 36 13 degreeUnionState62_379) + +def degreeUnionState62_389 : List PrefixRegion := nextRegions 9 (liveRegions 10 36 13 degreeUnionState62_379) + +def degreeUnionState62_390 : List PrefixRegion := nextRegions 10 (liveRegions 10 36 13 degreeUnionState62_379) + +def degreeUnionState62_391 : List PrefixRegion := nextRegions 11 (liveRegions 10 36 13 degreeUnionState62_379) + +def degreeUnionState62_392 : List PrefixRegion := nextRegions 12 (liveRegions 10 36 13 degreeUnionState62_379) + +def degreeUnionState62_393 : List PrefixRegion := nextRegions 13 (liveRegions 10 36 13 degreeUnionState62_379) + +def degreeUnionState62_394 : List PrefixRegion := nextRegions 14 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_395 : List PrefixRegion := nextRegions 5 (liveRegions 11 48 14 degreeUnionState62_394) + +def degreeUnionState62_396 : List PrefixRegion := nextRegions 6 (liveRegions 11 48 14 degreeUnionState62_394) + +def degreeUnionState62_397 : List PrefixRegion := nextRegions 7 (liveRegions 11 48 14 degreeUnionState62_394) + +def degreeUnionState62_398 : List PrefixRegion := nextRegions 5 (liveRegions 10 41 7 degreeUnionState62_397) + +def degreeUnionState62_399 : List PrefixRegion := nextRegions 6 (liveRegions 10 41 7 degreeUnionState62_397) + +def degreeUnionState62_400 : List PrefixRegion := nextRegions 7 (liveRegions 10 41 7 degreeUnionState62_397) + +def degreeUnionState62_401 : List PrefixRegion := nextRegions 4 (liveRegions 9 34 7 degreeUnionState62_400) + +def degreeUnionState62_402 : List PrefixRegion := nextRegions 5 (liveRegions 9 34 7 degreeUnionState62_400) + +def degreeUnionState62_403 : List PrefixRegion := nextRegions 6 (liveRegions 9 34 7 degreeUnionState62_400) + +def degreeUnionState62_404 : List PrefixRegion := nextRegions 7 (liveRegions 9 34 7 degreeUnionState62_400) + +def degreeUnionState62_405 : List PrefixRegion := nextRegions 8 (liveRegions 11 48 14 degreeUnionState62_394) + +def degreeUnionState62_406 : List PrefixRegion := nextRegions 4 (liveRegions 10 40 8 degreeUnionState62_405) + +def degreeUnionState62_407 : List PrefixRegion := nextRegions 5 (liveRegions 10 40 8 degreeUnionState62_405) + +def degreeUnionState62_408 : List PrefixRegion := nextRegions 6 (liveRegions 10 40 8 degreeUnionState62_405) + +def degreeUnionState62_409 : List PrefixRegion := nextRegions 7 (liveRegions 10 40 8 degreeUnionState62_405) + +def degreeUnionState62_410 : List PrefixRegion := nextRegions 4 (liveRegions 9 33 7 degreeUnionState62_409) + +def degreeUnionState62_411 : List PrefixRegion := nextRegions 5 (liveRegions 9 33 7 degreeUnionState62_409) + +def degreeUnionState62_412 : List PrefixRegion := nextRegions 6 (liveRegions 9 33 7 degreeUnionState62_409) + +def degreeUnionState62_413 : List PrefixRegion := nextRegions 7 (liveRegions 9 33 7 degreeUnionState62_409) + +def degreeUnionState62_414 : List PrefixRegion := nextRegions 8 (liveRegions 10 40 8 degreeUnionState62_405) + +def degreeUnionState62_415 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 8 degreeUnionState62_414) + +def degreeUnionState62_416 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 8 degreeUnionState62_414) + +def degreeUnionState62_417 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 8 degreeUnionState62_414) + +def degreeUnionState62_418 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 8 degreeUnionState62_414) + +def degreeUnionState62_419 : List PrefixRegion := nextRegions 8 (liveRegions 9 32 8 degreeUnionState62_414) + +def degreeUnionState62_420 : List PrefixRegion := nextRegions 9 (liveRegions 11 48 14 degreeUnionState62_394) + +def degreeUnionState62_421 : List PrefixRegion := nextRegions 4 (liveRegions 10 39 9 degreeUnionState62_420) + +def degreeUnionState62_422 : List PrefixRegion := nextRegions 5 (liveRegions 10 39 9 degreeUnionState62_420) + +def degreeUnionState62_423 : List PrefixRegion := nextRegions 6 (liveRegions 10 39 9 degreeUnionState62_420) + +def degreeUnionState62_424 : List PrefixRegion := nextRegions 7 (liveRegions 10 39 9 degreeUnionState62_420) + +def degreeUnionState62_425 : List PrefixRegion := nextRegions 4 (liveRegions 9 32 7 degreeUnionState62_424) + +def degreeUnionState62_426 : List PrefixRegion := nextRegions 5 (liveRegions 9 32 7 degreeUnionState62_424) + +def degreeUnionState62_427 : List PrefixRegion := nextRegions 6 (liveRegions 9 32 7 degreeUnionState62_424) + +def degreeUnionState62_428 : List PrefixRegion := nextRegions 7 (liveRegions 9 32 7 degreeUnionState62_424) + +def degreeUnionState62_429 : List PrefixRegion := nextRegions 8 (liveRegions 10 39 9 degreeUnionState62_420) + +def degreeUnionState62_430 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 8 degreeUnionState62_429) + +def degreeUnionState62_431 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 8 degreeUnionState62_429) + +def degreeUnionState62_432 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 8 degreeUnionState62_429) + +def degreeUnionState62_433 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 8 degreeUnionState62_429) + +def degreeUnionState62_434 : List PrefixRegion := nextRegions 8 (liveRegions 9 31 8 degreeUnionState62_429) + +def degreeUnionState62_435 : List PrefixRegion := nextRegions 9 (liveRegions 10 39 9 degreeUnionState62_420) + +def degreeUnionState62_436 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 9 degreeUnionState62_435) + +def degreeUnionState62_437 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 9 degreeUnionState62_435) + +def degreeUnionState62_438 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 9 degreeUnionState62_435) + +def degreeUnionState62_439 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 9 degreeUnionState62_435) + +def degreeUnionState62_440 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 9 degreeUnionState62_435) + +def degreeUnionState62_441 : List PrefixRegion := nextRegions 9 (liveRegions 9 30 9 degreeUnionState62_435) + +def degreeUnionState62_442 : List PrefixRegion := nextRegions 10 (liveRegions 11 48 14 degreeUnionState62_394) + +def degreeUnionState62_443 : List PrefixRegion := nextRegions 4 (liveRegions 10 38 10 degreeUnionState62_442) + +def degreeUnionState62_444 : List PrefixRegion := nextRegions 5 (liveRegions 10 38 10 degreeUnionState62_442) + +def degreeUnionState62_445 : List PrefixRegion := nextRegions 6 (liveRegions 10 38 10 degreeUnionState62_442) + +def degreeUnionState62_446 : List PrefixRegion := nextRegions 7 (liveRegions 10 38 10 degreeUnionState62_442) + +def degreeUnionState62_447 : List PrefixRegion := nextRegions 4 (liveRegions 9 31 7 degreeUnionState62_446) + +def degreeUnionState62_448 : List PrefixRegion := nextRegions 5 (liveRegions 9 31 7 degreeUnionState62_446) + +def degreeUnionState62_449 : List PrefixRegion := nextRegions 6 (liveRegions 9 31 7 degreeUnionState62_446) + +def degreeUnionState62_450 : List PrefixRegion := nextRegions 7 (liveRegions 9 31 7 degreeUnionState62_446) + +def degreeUnionState62_451 : List PrefixRegion := nextRegions 8 (liveRegions 10 38 10 degreeUnionState62_442) + +def degreeUnionState62_452 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 8 degreeUnionState62_451) + +def degreeUnionState62_453 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 8 degreeUnionState62_451) + +def degreeUnionState62_454 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 8 degreeUnionState62_451) + +def degreeUnionState62_455 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 8 degreeUnionState62_451) + +def degreeUnionState62_456 : List PrefixRegion := nextRegions 8 (liveRegions 9 30 8 degreeUnionState62_451) + +def degreeUnionState62_457 : List PrefixRegion := nextRegions 9 (liveRegions 10 38 10 degreeUnionState62_442) + +def degreeUnionState62_458 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 9 degreeUnionState62_457) + +def degreeUnionState62_459 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 9 degreeUnionState62_457) + +def degreeUnionState62_460 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 9 degreeUnionState62_457) + +def degreeUnionState62_461 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 9 degreeUnionState62_457) + +def degreeUnionState62_462 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 9 degreeUnionState62_457) + +def degreeUnionState62_463 : List PrefixRegion := nextRegions 9 (liveRegions 9 29 9 degreeUnionState62_457) + +def degreeUnionState62_464 : List PrefixRegion := nextRegions 10 (liveRegions 10 38 10 degreeUnionState62_442) + +def degreeUnionState62_465 : List PrefixRegion := nextRegions 11 (liveRegions 11 48 14 degreeUnionState62_394) + +def degreeUnionState62_466 : List PrefixRegion := nextRegions 4 (liveRegions 10 37 11 degreeUnionState62_465) + +def degreeUnionState62_467 : List PrefixRegion := nextRegions 5 (liveRegions 10 37 11 degreeUnionState62_465) + +def degreeUnionState62_468 : List PrefixRegion := nextRegions 6 (liveRegions 10 37 11 degreeUnionState62_465) + +def degreeUnionState62_469 : List PrefixRegion := nextRegions 7 (liveRegions 10 37 11 degreeUnionState62_465) + +def degreeUnionState62_470 : List PrefixRegion := nextRegions 4 (liveRegions 9 30 7 degreeUnionState62_469) + +def degreeUnionState62_471 : List PrefixRegion := nextRegions 5 (liveRegions 9 30 7 degreeUnionState62_469) + +def degreeUnionState62_472 : List PrefixRegion := nextRegions 6 (liveRegions 9 30 7 degreeUnionState62_469) + +def degreeUnionState62_473 : List PrefixRegion := nextRegions 7 (liveRegions 9 30 7 degreeUnionState62_469) + +def degreeUnionState62_474 : List PrefixRegion := nextRegions 8 (liveRegions 10 37 11 degreeUnionState62_465) + +def degreeUnionState62_475 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 8 degreeUnionState62_474) + +def degreeUnionState62_476 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 8 degreeUnionState62_474) + +def degreeUnionState62_477 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 8 degreeUnionState62_474) + +def degreeUnionState62_478 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 8 degreeUnionState62_474) + +def degreeUnionState62_479 : List PrefixRegion := nextRegions 8 (liveRegions 9 29 8 degreeUnionState62_474) + +def degreeUnionState62_480 : List PrefixRegion := nextRegions 9 (liveRegions 10 37 11 degreeUnionState62_465) + +def degreeUnionState62_481 : List PrefixRegion := nextRegions 10 (liveRegions 10 37 11 degreeUnionState62_465) + +def degreeUnionState62_482 : List PrefixRegion := nextRegions 11 (liveRegions 10 37 11 degreeUnionState62_465) + +def degreeUnionState62_483 : List PrefixRegion := nextRegions 12 (liveRegions 11 48 14 degreeUnionState62_394) + +def degreeUnionState62_484 : List PrefixRegion := nextRegions 4 (liveRegions 10 36 12 degreeUnionState62_483) + +def degreeUnionState62_485 : List PrefixRegion := nextRegions 5 (liveRegions 10 36 12 degreeUnionState62_483) + +def degreeUnionState62_486 : List PrefixRegion := nextRegions 6 (liveRegions 10 36 12 degreeUnionState62_483) + +def degreeUnionState62_487 : List PrefixRegion := nextRegions 7 (liveRegions 10 36 12 degreeUnionState62_483) + +def degreeUnionState62_488 : List PrefixRegion := nextRegions 4 (liveRegions 9 29 7 degreeUnionState62_487) + +def degreeUnionState62_489 : List PrefixRegion := nextRegions 5 (liveRegions 9 29 7 degreeUnionState62_487) + +def degreeUnionState62_490 : List PrefixRegion := nextRegions 6 (liveRegions 9 29 7 degreeUnionState62_487) + +def degreeUnionState62_491 : List PrefixRegion := nextRegions 7 (liveRegions 9 29 7 degreeUnionState62_487) + +def degreeUnionState62_492 : List PrefixRegion := nextRegions 8 (liveRegions 10 36 12 degreeUnionState62_483) + +def degreeUnionState62_493 : List PrefixRegion := nextRegions 9 (liveRegions 10 36 12 degreeUnionState62_483) + +def degreeUnionState62_494 : List PrefixRegion := nextRegions 10 (liveRegions 10 36 12 degreeUnionState62_483) + +def degreeUnionState62_495 : List PrefixRegion := nextRegions 11 (liveRegions 10 36 12 degreeUnionState62_483) + +def degreeUnionState62_496 : List PrefixRegion := nextRegions 12 (liveRegions 10 36 12 degreeUnionState62_483) + +def degreeUnionState62_497 : List PrefixRegion := nextRegions 13 (liveRegions 11 48 14 degreeUnionState62_394) + +def degreeUnionState62_498 : List PrefixRegion := nextRegions 14 (liveRegions 11 48 14 degreeUnionState62_394) + +def degreeUnionState62_499 : List PrefixRegion := nextRegions 15 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_500 : List PrefixRegion := nextRegions 16 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_501 : List PrefixRegion := nextRegions 17 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_502 : List PrefixRegion := nextRegions 18 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_503 : List PrefixRegion := nextRegions 19 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_504 : List PrefixRegion := nextRegions 20 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_505 : List PrefixRegion := nextRegions 21 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_506 : List PrefixRegion := nextRegions 22 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_507 : List PrefixRegion := nextRegions 23 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_508 : List PrefixRegion := nextRegions 24 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_509 : List PrefixRegion := nextRegions 25 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_510 : List PrefixRegion := nextRegions 26 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_511 : List PrefixRegion := nextRegions 27 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_512 : List PrefixRegion := nextRegions 28 (liveRegions 12 62 28 degreeHalfRegions62) + +def degreeUnionState62_514 : List PrefixRegion := nextRegions 5 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_515 : List PrefixRegion := nextRegions 6 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_516 : List PrefixRegion := nextRegions 7 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_517 : List PrefixRegion := nextRegions 8 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_518 : List PrefixRegion := nextRegions 9 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_519 : List PrefixRegion := nextRegions 10 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_520 : List PrefixRegion := nextRegions 5 (liveRegions 12 52 10 degreeUnionState62_519) + +def degreeUnionState62_521 : List PrefixRegion := nextRegions 6 (liveRegions 12 52 10 degreeUnionState62_519) + +def degreeUnionState62_522 : List PrefixRegion := nextRegions 7 (liveRegions 12 52 10 degreeUnionState62_519) + +def degreeUnionState62_523 : List PrefixRegion := nextRegions 8 (liveRegions 12 52 10 degreeUnionState62_519) + +def degreeUnionState62_524 : List PrefixRegion := nextRegions 9 (liveRegions 12 52 10 degreeUnionState62_519) + +def degreeUnionState62_525 : List PrefixRegion := nextRegions 10 (liveRegions 12 52 10 degreeUnionState62_519) + +def degreeUnionState62_526 : List PrefixRegion := nextRegions 4 (liveRegions 11 42 10 degreeUnionState62_525) + +def degreeUnionState62_527 : List PrefixRegion := nextRegions 5 (liveRegions 11 42 10 degreeUnionState62_525) + +def degreeUnionState62_528 : List PrefixRegion := nextRegions 6 (liveRegions 11 42 10 degreeUnionState62_525) + +def degreeUnionState62_529 : List PrefixRegion := nextRegions 7 (liveRegions 11 42 10 degreeUnionState62_525) + +def degreeUnionState62_530 : List PrefixRegion := nextRegions 8 (liveRegions 11 42 10 degreeUnionState62_525) + +def degreeUnionState62_531 : List PrefixRegion := nextRegions 9 (liveRegions 11 42 10 degreeUnionState62_525) + +def degreeUnionState62_532 : List PrefixRegion := nextRegions 10 (liveRegions 11 42 10 degreeUnionState62_525) + +def degreeUnionState62_533 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 10 degreeUnionState62_532) + +def degreeUnionState62_534 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 10 degreeUnionState62_532) + +def degreeUnionState62_535 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 10 degreeUnionState62_532) + +def degreeUnionState62_536 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 10 degreeUnionState62_532) + +def degreeUnionState62_537 : List PrefixRegion := nextRegions 8 (liveRegions 10 32 10 degreeUnionState62_532) + +def degreeUnionState62_538 : List PrefixRegion := nextRegions 9 (liveRegions 10 32 10 degreeUnionState62_532) + +def degreeUnionState62_539 : List PrefixRegion := nextRegions 10 (liveRegions 10 32 10 degreeUnionState62_532) + +def degreeUnionState62_540 : List PrefixRegion := nextRegions 11 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_541 : List PrefixRegion := nextRegions 5 (liveRegions 12 51 11 degreeUnionState62_540) + +def degreeUnionState62_542 : List PrefixRegion := nextRegions 6 (liveRegions 12 51 11 degreeUnionState62_540) + +def degreeUnionState62_543 : List PrefixRegion := nextRegions 7 (liveRegions 12 51 11 degreeUnionState62_540) + +def degreeUnionState62_544 : List PrefixRegion := nextRegions 8 (liveRegions 12 51 11 degreeUnionState62_540) + +def degreeUnionState62_545 : List PrefixRegion := nextRegions 9 (liveRegions 12 51 11 degreeUnionState62_540) + +def degreeUnionState62_546 : List PrefixRegion := nextRegions 10 (liveRegions 12 51 11 degreeUnionState62_540) + +def degreeUnionState62_547 : List PrefixRegion := nextRegions 4 (liveRegions 11 41 10 degreeUnionState62_546) + +def degreeUnionState62_548 : List PrefixRegion := nextRegions 5 (liveRegions 11 41 10 degreeUnionState62_546) + +def degreeUnionState62_549 : List PrefixRegion := nextRegions 6 (liveRegions 11 41 10 degreeUnionState62_546) + +def degreeUnionState62_550 : List PrefixRegion := nextRegions 7 (liveRegions 11 41 10 degreeUnionState62_546) + +def degreeUnionState62_551 : List PrefixRegion := nextRegions 8 (liveRegions 11 41 10 degreeUnionState62_546) + +def degreeUnionState62_552 : List PrefixRegion := nextRegions 9 (liveRegions 11 41 10 degreeUnionState62_546) + +def degreeUnionState62_553 : List PrefixRegion := nextRegions 10 (liveRegions 11 41 10 degreeUnionState62_546) + +def degreeUnionState62_554 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 10 degreeUnionState62_553) + +def degreeUnionState62_555 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 10 degreeUnionState62_553) + +def degreeUnionState62_556 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 10 degreeUnionState62_553) + +def degreeUnionState62_557 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 10 degreeUnionState62_553) + +def degreeUnionState62_558 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 10 degreeUnionState62_553) + +def degreeUnionState62_559 : List PrefixRegion := nextRegions 9 (liveRegions 10 31 10 degreeUnionState62_553) + +def degreeUnionState62_560 : List PrefixRegion := nextRegions 10 (liveRegions 10 31 10 degreeUnionState62_553) + +def degreeUnionState62_561 : List PrefixRegion := nextRegions 11 (liveRegions 12 51 11 degreeUnionState62_540) + +def degreeUnionState62_562 : List PrefixRegion := nextRegions 4 (liveRegions 11 40 11 degreeUnionState62_561) + +def degreeUnionState62_563 : List PrefixRegion := nextRegions 5 (liveRegions 11 40 11 degreeUnionState62_561) + +def degreeUnionState62_564 : List PrefixRegion := nextRegions 6 (liveRegions 11 40 11 degreeUnionState62_561) + +def degreeUnionState62_565 : List PrefixRegion := nextRegions 7 (liveRegions 11 40 11 degreeUnionState62_561) + +def degreeUnionState62_566 : List PrefixRegion := nextRegions 8 (liveRegions 11 40 11 degreeUnionState62_561) + +def degreeUnionState62_567 : List PrefixRegion := nextRegions 9 (liveRegions 11 40 11 degreeUnionState62_561) + +def degreeUnionState62_568 : List PrefixRegion := nextRegions 10 (liveRegions 11 40 11 degreeUnionState62_561) + +def degreeUnionState62_569 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 10 degreeUnionState62_568) + +def degreeUnionState62_570 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 10 degreeUnionState62_568) + +def degreeUnionState62_571 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 10 degreeUnionState62_568) + +def degreeUnionState62_572 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 10 degreeUnionState62_568) + +def degreeUnionState62_573 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 10 degreeUnionState62_568) + +def degreeUnionState62_574 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 10 degreeUnionState62_568) + +def degreeUnionState62_575 : List PrefixRegion := nextRegions 9 (liveRegions 10 30 10 degreeUnionState62_568) + +def degreeUnionState62_576 : List PrefixRegion := nextRegions 10 (liveRegions 10 30 10 degreeUnionState62_568) + +def degreeUnionState62_577 : List PrefixRegion := nextRegions 11 (liveRegions 11 40 11 degreeUnionState62_561) + +def degreeUnionState62_578 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 11 degreeUnionState62_577) + +def degreeUnionState62_579 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 11 degreeUnionState62_577) + +def degreeUnionState62_580 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 11 degreeUnionState62_577) + +def degreeUnionState62_581 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 11 degreeUnionState62_577) + +def degreeUnionState62_582 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 11 degreeUnionState62_577) + +def degreeUnionState62_583 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 11 degreeUnionState62_577) + +def degreeUnionState62_584 : List PrefixRegion := nextRegions 9 (liveRegions 10 29 11 degreeUnionState62_577) + +def degreeUnionState62_585 : List PrefixRegion := nextRegions 10 (liveRegions 10 29 11 degreeUnionState62_577) + +def degreeUnionState62_586 : List PrefixRegion := nextRegions 11 (liveRegions 10 29 11 degreeUnionState62_577) + +def degreeUnionState62_587 : List PrefixRegion := nextRegions 12 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_588 : List PrefixRegion := nextRegions 5 (liveRegions 12 50 12 degreeUnionState62_587) + +def degreeUnionState62_589 : List PrefixRegion := nextRegions 6 (liveRegions 12 50 12 degreeUnionState62_587) + +def degreeUnionState62_590 : List PrefixRegion := nextRegions 7 (liveRegions 12 50 12 degreeUnionState62_587) + +def degreeUnionState62_591 : List PrefixRegion := nextRegions 8 (liveRegions 12 50 12 degreeUnionState62_587) + +def degreeUnionState62_592 : List PrefixRegion := nextRegions 4 (liveRegions 11 42 8 degreeUnionState62_591) + +def degreeUnionState62_593 : List PrefixRegion := nextRegions 5 (liveRegions 11 42 8 degreeUnionState62_591) + +def degreeUnionState62_594 : List PrefixRegion := nextRegions 6 (liveRegions 11 42 8 degreeUnionState62_591) + +def degreeUnionState62_595 : List PrefixRegion := nextRegions 7 (liveRegions 11 42 8 degreeUnionState62_591) + +def degreeUnionState62_596 : List PrefixRegion := nextRegions 8 (liveRegions 11 42 8 degreeUnionState62_591) + +def degreeUnionState62_597 : List PrefixRegion := nextRegions 4 (liveRegions 10 34 8 degreeUnionState62_596) + +def degreeUnionState62_598 : List PrefixRegion := nextRegions 5 (liveRegions 10 34 8 degreeUnionState62_596) + +def degreeUnionState62_599 : List PrefixRegion := nextRegions 6 (liveRegions 10 34 8 degreeUnionState62_596) + +def degreeUnionState62_600 : List PrefixRegion := nextRegions 7 (liveRegions 10 34 8 degreeUnionState62_596) + +def degreeUnionState62_601 : List PrefixRegion := nextRegions 8 (liveRegions 10 34 8 degreeUnionState62_596) + +def degreeUnionState62_602 : List PrefixRegion := nextRegions 9 (liveRegions 12 50 12 degreeUnionState62_587) + +def degreeUnionState62_603 : List PrefixRegion := nextRegions 4 (liveRegions 11 41 9 degreeUnionState62_602) + +def degreeUnionState62_604 : List PrefixRegion := nextRegions 5 (liveRegions 11 41 9 degreeUnionState62_602) + +def degreeUnionState62_605 : List PrefixRegion := nextRegions 6 (liveRegions 11 41 9 degreeUnionState62_602) + +def degreeUnionState62_606 : List PrefixRegion := nextRegions 7 (liveRegions 11 41 9 degreeUnionState62_602) + +def degreeUnionState62_607 : List PrefixRegion := nextRegions 8 (liveRegions 11 41 9 degreeUnionState62_602) + +def degreeUnionState62_608 : List PrefixRegion := nextRegions 4 (liveRegions 10 33 8 degreeUnionState62_607) + +def degreeUnionState62_609 : List PrefixRegion := nextRegions 5 (liveRegions 10 33 8 degreeUnionState62_607) + +def degreeUnionState62_610 : List PrefixRegion := nextRegions 6 (liveRegions 10 33 8 degreeUnionState62_607) + +def degreeUnionState62_611 : List PrefixRegion := nextRegions 7 (liveRegions 10 33 8 degreeUnionState62_607) + +def degreeUnionState62_612 : List PrefixRegion := nextRegions 8 (liveRegions 10 33 8 degreeUnionState62_607) + +def degreeUnionState62_613 : List PrefixRegion := nextRegions 9 (liveRegions 11 41 9 degreeUnionState62_602) + +def degreeUnionState62_614 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 9 degreeUnionState62_613) + +def degreeUnionState62_615 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 9 degreeUnionState62_613) + +def degreeUnionState62_616 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 9 degreeUnionState62_613) + +def degreeUnionState62_617 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 9 degreeUnionState62_613) + +def degreeUnionState62_618 : List PrefixRegion := nextRegions 8 (liveRegions 10 32 9 degreeUnionState62_613) + +def degreeUnionState62_619 : List PrefixRegion := nextRegions 9 (liveRegions 10 32 9 degreeUnionState62_613) + +def degreeUnionState62_620 : List PrefixRegion := nextRegions 10 (liveRegions 12 50 12 degreeUnionState62_587) + +def degreeUnionState62_621 : List PrefixRegion := nextRegions 4 (liveRegions 11 40 10 degreeUnionState62_620) + +def degreeUnionState62_622 : List PrefixRegion := nextRegions 5 (liveRegions 11 40 10 degreeUnionState62_620) + +def degreeUnionState62_623 : List PrefixRegion := nextRegions 6 (liveRegions 11 40 10 degreeUnionState62_620) + +def degreeUnionState62_624 : List PrefixRegion := nextRegions 7 (liveRegions 11 40 10 degreeUnionState62_620) + +def degreeUnionState62_625 : List PrefixRegion := nextRegions 8 (liveRegions 11 40 10 degreeUnionState62_620) + +def degreeUnionState62_626 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 8 degreeUnionState62_625) + +def degreeUnionState62_627 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 8 degreeUnionState62_625) + +def degreeUnionState62_628 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 8 degreeUnionState62_625) + +def degreeUnionState62_629 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 8 degreeUnionState62_625) + +def degreeUnionState62_630 : List PrefixRegion := nextRegions 8 (liveRegions 10 32 8 degreeUnionState62_625) + +def degreeUnionState62_631 : List PrefixRegion := nextRegions 9 (liveRegions 11 40 10 degreeUnionState62_620) + +def degreeUnionState62_632 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 9 degreeUnionState62_631) + +def degreeUnionState62_633 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 9 degreeUnionState62_631) + +def degreeUnionState62_634 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 9 degreeUnionState62_631) + +def degreeUnionState62_635 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 9 degreeUnionState62_631) + +def degreeUnionState62_636 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 9 degreeUnionState62_631) + +def degreeUnionState62_637 : List PrefixRegion := nextRegions 9 (liveRegions 10 31 9 degreeUnionState62_631) + +def degreeUnionState62_638 : List PrefixRegion := nextRegions 10 (liveRegions 11 40 10 degreeUnionState62_620) + +def degreeUnionState62_639 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 10 degreeUnionState62_638) + +def degreeUnionState62_640 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 10 degreeUnionState62_638) + +def degreeUnionState62_641 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 10 degreeUnionState62_638) + +def degreeUnionState62_642 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 10 degreeUnionState62_638) + +def degreeUnionState62_643 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 10 degreeUnionState62_638) + +def degreeUnionState62_644 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 10 degreeUnionState62_638) + +def degreeUnionState62_645 : List PrefixRegion := nextRegions 9 (liveRegions 10 30 10 degreeUnionState62_638) + +def degreeUnionState62_646 : List PrefixRegion := nextRegions 10 (liveRegions 10 30 10 degreeUnionState62_638) + +def degreeUnionState62_647 : List PrefixRegion := nextRegions 11 (liveRegions 12 50 12 degreeUnionState62_587) + +def degreeUnionState62_648 : List PrefixRegion := nextRegions 4 (liveRegions 11 39 11 degreeUnionState62_647) + +def degreeUnionState62_649 : List PrefixRegion := nextRegions 5 (liveRegions 11 39 11 degreeUnionState62_647) + +def degreeUnionState62_650 : List PrefixRegion := nextRegions 6 (liveRegions 11 39 11 degreeUnionState62_647) + +def degreeUnionState62_651 : List PrefixRegion := nextRegions 7 (liveRegions 11 39 11 degreeUnionState62_647) + +def degreeUnionState62_652 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 7 degreeUnionState62_651) + +def degreeUnionState62_653 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 7 degreeUnionState62_651) + +def degreeUnionState62_654 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 7 degreeUnionState62_651) + +def degreeUnionState62_655 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 7 degreeUnionState62_651) + +def degreeUnionState62_656 : List PrefixRegion := nextRegions 8 (liveRegions 11 39 11 degreeUnionState62_647) + +def degreeUnionState62_657 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 8 degreeUnionState62_656) + +def degreeUnionState62_658 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 8 degreeUnionState62_656) + +def degreeUnionState62_659 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 8 degreeUnionState62_656) + +def degreeUnionState62_660 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 8 degreeUnionState62_656) + +def degreeUnionState62_661 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 8 degreeUnionState62_656) + +def degreeUnionState62_662 : List PrefixRegion := nextRegions 9 (liveRegions 11 39 11 degreeUnionState62_647) + +def degreeUnionState62_663 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 9 degreeUnionState62_662) + +def degreeUnionState62_664 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 9 degreeUnionState62_662) + +def degreeUnionState62_665 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 9 degreeUnionState62_662) + +def degreeUnionState62_666 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 9 degreeUnionState62_662) + +def degreeUnionState62_667 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 9 degreeUnionState62_662) + +def degreeUnionState62_668 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 9 degreeUnionState62_662) + +def degreeUnionState62_669 : List PrefixRegion := nextRegions 9 (liveRegions 10 30 9 degreeUnionState62_662) + +def degreeUnionState62_670 : List PrefixRegion := nextRegions 10 (liveRegions 11 39 11 degreeUnionState62_647) + +def degreeUnionState62_671 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 10 degreeUnionState62_670) + +def degreeUnionState62_672 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 10 degreeUnionState62_670) + +def degreeUnionState62_673 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 10 degreeUnionState62_670) + +def degreeUnionState62_674 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 10 degreeUnionState62_670) + +def degreeUnionState62_675 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 10 degreeUnionState62_670) + +def degreeUnionState62_676 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 10 degreeUnionState62_670) + +def degreeUnionState62_677 : List PrefixRegion := nextRegions 9 (liveRegions 10 29 10 degreeUnionState62_670) + +def degreeUnionState62_678 : List PrefixRegion := nextRegions 10 (liveRegions 10 29 10 degreeUnionState62_670) + +def degreeUnionState62_679 : List PrefixRegion := nextRegions 11 (liveRegions 11 39 11 degreeUnionState62_647) + +def degreeUnionState62_680 : List PrefixRegion := nextRegions 12 (liveRegions 12 50 12 degreeUnionState62_587) + +def degreeUnionState62_681 : List PrefixRegion := nextRegions 4 (liveRegions 11 38 12 degreeUnionState62_680) + +def degreeUnionState62_682 : List PrefixRegion := nextRegions 5 (liveRegions 11 38 12 degreeUnionState62_680) + +def degreeUnionState62_683 : List PrefixRegion := nextRegions 6 (liveRegions 11 38 12 degreeUnionState62_680) + +def degreeUnionState62_684 : List PrefixRegion := nextRegions 7 (liveRegions 11 38 12 degreeUnionState62_680) + +def degreeUnionState62_685 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 7 degreeUnionState62_684) + +def degreeUnionState62_686 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 7 degreeUnionState62_684) + +def degreeUnionState62_687 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 7 degreeUnionState62_684) + +def degreeUnionState62_688 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 7 degreeUnionState62_684) + +def degreeUnionState62_689 : List PrefixRegion := nextRegions 8 (liveRegions 11 38 12 degreeUnionState62_680) + +def degreeUnionState62_690 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 8 degreeUnionState62_689) + +def degreeUnionState62_691 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 8 degreeUnionState62_689) + +def degreeUnionState62_692 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 8 degreeUnionState62_689) + +def degreeUnionState62_693 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 8 degreeUnionState62_689) + +def degreeUnionState62_694 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 8 degreeUnionState62_689) + +def degreeUnionState62_695 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 8 degreeUnionState62_689) + +def degreeUnionState62_696 : List PrefixRegion := nextRegions 9 (liveRegions 11 38 12 degreeUnionState62_680) + +def degreeUnionState62_697 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 9 degreeUnionState62_696) + +def degreeUnionState62_698 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 9 degreeUnionState62_696) + +def degreeUnionState62_699 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 9 degreeUnionState62_696) + +def degreeUnionState62_700 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 9 degreeUnionState62_696) + +def degreeUnionState62_701 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 9 degreeUnionState62_696) + +def degreeUnionState62_702 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 9 degreeUnionState62_696) + +def degreeUnionState62_703 : List PrefixRegion := nextRegions 9 (liveRegions 10 29 9 degreeUnionState62_696) + +def degreeUnionState62_704 : List PrefixRegion := nextRegions 10 (liveRegions 11 38 12 degreeUnionState62_680) + +def degreeUnionState62_705 : List PrefixRegion := nextRegions 11 (liveRegions 11 38 12 degreeUnionState62_680) + +def degreeUnionState62_706 : List PrefixRegion := nextRegions 12 (liveRegions 11 38 12 degreeUnionState62_680) + +def degreeUnionState62_707 : List PrefixRegion := nextRegions 13 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_708 : List PrefixRegion := nextRegions 5 (liveRegions 12 49 13 degreeUnionState62_707) + +def degreeUnionState62_709 : List PrefixRegion := nextRegions 6 (liveRegions 12 49 13 degreeUnionState62_707) + +def degreeUnionState62_710 : List PrefixRegion := nextRegions 7 (liveRegions 12 49 13 degreeUnionState62_707) + +def degreeUnionState62_711 : List PrefixRegion := nextRegions 4 (liveRegions 11 42 7 degreeUnionState62_710) + +def degreeUnionState62_712 : List PrefixRegion := nextRegions 5 (liveRegions 11 42 7 degreeUnionState62_710) + +def degreeUnionState62_713 : List PrefixRegion := nextRegions 6 (liveRegions 11 42 7 degreeUnionState62_710) + +def degreeUnionState62_714 : List PrefixRegion := nextRegions 7 (liveRegions 11 42 7 degreeUnionState62_710) + +def degreeUnionState62_715 : List PrefixRegion := nextRegions 8 (liveRegions 12 49 13 degreeUnionState62_707) + +def degreeUnionState62_716 : List PrefixRegion := nextRegions 4 (liveRegions 11 41 8 degreeUnionState62_715) + +def degreeUnionState62_717 : List PrefixRegion := nextRegions 5 (liveRegions 11 41 8 degreeUnionState62_715) + +def degreeUnionState62_718 : List PrefixRegion := nextRegions 6 (liveRegions 11 41 8 degreeUnionState62_715) + +def degreeUnionState62_719 : List PrefixRegion := nextRegions 7 (liveRegions 11 41 8 degreeUnionState62_715) + +def degreeUnionState62_720 : List PrefixRegion := nextRegions 8 (liveRegions 11 41 8 degreeUnionState62_715) + +def degreeUnionState62_721 : List PrefixRegion := nextRegions 4 (liveRegions 10 33 8 degreeUnionState62_720) + +def degreeUnionState62_722 : List PrefixRegion := nextRegions 5 (liveRegions 10 33 8 degreeUnionState62_720) + +def degreeUnionState62_723 : List PrefixRegion := nextRegions 6 (liveRegions 10 33 8 degreeUnionState62_720) + +def degreeUnionState62_724 : List PrefixRegion := nextRegions 7 (liveRegions 10 33 8 degreeUnionState62_720) + +def degreeUnionState62_725 : List PrefixRegion := nextRegions 8 (liveRegions 10 33 8 degreeUnionState62_720) + +def degreeUnionState62_726 : List PrefixRegion := nextRegions 9 (liveRegions 12 49 13 degreeUnionState62_707) + +def degreeUnionState62_727 : List PrefixRegion := nextRegions 4 (liveRegions 11 40 9 degreeUnionState62_726) + +def degreeUnionState62_728 : List PrefixRegion := nextRegions 5 (liveRegions 11 40 9 degreeUnionState62_726) + +def degreeUnionState62_729 : List PrefixRegion := nextRegions 6 (liveRegions 11 40 9 degreeUnionState62_726) + +def degreeUnionState62_730 : List PrefixRegion := nextRegions 7 (liveRegions 11 40 9 degreeUnionState62_726) + +def degreeUnionState62_731 : List PrefixRegion := nextRegions 8 (liveRegions 11 40 9 degreeUnionState62_726) + +def degreeUnionState62_732 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 8 degreeUnionState62_731) + +def degreeUnionState62_733 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 8 degreeUnionState62_731) + +def degreeUnionState62_734 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 8 degreeUnionState62_731) + +def degreeUnionState62_735 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 8 degreeUnionState62_731) + +def degreeUnionState62_736 : List PrefixRegion := nextRegions 8 (liveRegions 10 32 8 degreeUnionState62_731) + +def degreeUnionState62_737 : List PrefixRegion := nextRegions 9 (liveRegions 11 40 9 degreeUnionState62_726) + +def degreeUnionState62_738 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 9 degreeUnionState62_737) + +def degreeUnionState62_739 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 9 degreeUnionState62_737) + +def degreeUnionState62_740 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 9 degreeUnionState62_737) + +def degreeUnionState62_741 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 9 degreeUnionState62_737) + +def degreeUnionState62_742 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 9 degreeUnionState62_737) + +def degreeUnionState62_743 : List PrefixRegion := nextRegions 9 (liveRegions 10 31 9 degreeUnionState62_737) + +def degreeUnionState62_744 : List PrefixRegion := nextRegions 10 (liveRegions 12 49 13 degreeUnionState62_707) + +def degreeUnionState62_745 : List PrefixRegion := nextRegions 4 (liveRegions 11 39 10 degreeUnionState62_744) + +def degreeUnionState62_746 : List PrefixRegion := nextRegions 5 (liveRegions 11 39 10 degreeUnionState62_744) + +def degreeUnionState62_747 : List PrefixRegion := nextRegions 6 (liveRegions 11 39 10 degreeUnionState62_744) + +def degreeUnionState62_748 : List PrefixRegion := nextRegions 7 (liveRegions 11 39 10 degreeUnionState62_744) + +def degreeUnionState62_749 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 7 degreeUnionState62_748) + +def degreeUnionState62_750 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 7 degreeUnionState62_748) + +def degreeUnionState62_751 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 7 degreeUnionState62_748) + +def degreeUnionState62_752 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 7 degreeUnionState62_748) + +def degreeUnionState62_753 : List PrefixRegion := nextRegions 8 (liveRegions 11 39 10 degreeUnionState62_744) + +def degreeUnionState62_754 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 8 degreeUnionState62_753) + +def degreeUnionState62_755 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 8 degreeUnionState62_753) + +def degreeUnionState62_756 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 8 degreeUnionState62_753) + +def degreeUnionState62_757 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 8 degreeUnionState62_753) + +def degreeUnionState62_758 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 8 degreeUnionState62_753) + +def degreeUnionState62_759 : List PrefixRegion := nextRegions 9 (liveRegions 11 39 10 degreeUnionState62_744) + +def degreeUnionState62_760 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 9 degreeUnionState62_759) + +def degreeUnionState62_761 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 9 degreeUnionState62_759) + +def degreeUnionState62_762 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 9 degreeUnionState62_759) + +def degreeUnionState62_763 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 9 degreeUnionState62_759) + +def degreeUnionState62_764 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 9 degreeUnionState62_759) + +def degreeUnionState62_765 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 9 degreeUnionState62_759) + +def degreeUnionState62_766 : List PrefixRegion := nextRegions 9 (liveRegions 10 30 9 degreeUnionState62_759) + +def degreeUnionState62_767 : List PrefixRegion := nextRegions 10 (liveRegions 11 39 10 degreeUnionState62_744) + +def degreeUnionState62_768 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 10 degreeUnionState62_767) + +def degreeUnionState62_769 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 10 degreeUnionState62_767) + +def degreeUnionState62_770 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 10 degreeUnionState62_767) + +def degreeUnionState62_771 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 10 degreeUnionState62_767) + +def degreeUnionState62_772 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 10 degreeUnionState62_767) + +def degreeUnionState62_773 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 10 degreeUnionState62_767) + +def degreeUnionState62_774 : List PrefixRegion := nextRegions 9 (liveRegions 10 29 10 degreeUnionState62_767) + +def degreeUnionState62_775 : List PrefixRegion := nextRegions 10 (liveRegions 10 29 10 degreeUnionState62_767) + +def degreeUnionState62_776 : List PrefixRegion := nextRegions 11 (liveRegions 12 49 13 degreeUnionState62_707) + +def degreeUnionState62_777 : List PrefixRegion := nextRegions 4 (liveRegions 11 38 11 degreeUnionState62_776) + +def degreeUnionState62_778 : List PrefixRegion := nextRegions 5 (liveRegions 11 38 11 degreeUnionState62_776) + +def degreeUnionState62_779 : List PrefixRegion := nextRegions 6 (liveRegions 11 38 11 degreeUnionState62_776) + +def degreeUnionState62_780 : List PrefixRegion := nextRegions 7 (liveRegions 11 38 11 degreeUnionState62_776) + +def degreeUnionState62_781 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 7 degreeUnionState62_780) + +def degreeUnionState62_782 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 7 degreeUnionState62_780) + +def degreeUnionState62_783 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 7 degreeUnionState62_780) + +def degreeUnionState62_784 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 7 degreeUnionState62_780) + +def degreeUnionState62_785 : List PrefixRegion := nextRegions 8 (liveRegions 11 38 11 degreeUnionState62_776) + +def degreeUnionState62_786 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 8 degreeUnionState62_785) + +def degreeUnionState62_787 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 8 degreeUnionState62_785) + +def degreeUnionState62_788 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 8 degreeUnionState62_785) + +def degreeUnionState62_789 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 8 degreeUnionState62_785) + +def degreeUnionState62_790 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 8 degreeUnionState62_785) + +def degreeUnionState62_791 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 8 degreeUnionState62_785) + +def degreeUnionState62_792 : List PrefixRegion := nextRegions 9 (liveRegions 11 38 11 degreeUnionState62_776) + +def degreeUnionState62_793 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 9 degreeUnionState62_792) + +def degreeUnionState62_794 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 9 degreeUnionState62_792) + +def degreeUnionState62_795 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 9 degreeUnionState62_792) + +def degreeUnionState62_796 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 9 degreeUnionState62_792) + +def degreeUnionState62_797 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 9 degreeUnionState62_792) + +def degreeUnionState62_798 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 9 degreeUnionState62_792) + +def degreeUnionState62_799 : List PrefixRegion := nextRegions 9 (liveRegions 10 29 9 degreeUnionState62_792) + +def degreeUnionState62_800 : List PrefixRegion := nextRegions 10 (liveRegions 11 38 11 degreeUnionState62_776) + +def degreeUnionState62_801 : List PrefixRegion := nextRegions 11 (liveRegions 11 38 11 degreeUnionState62_776) + +def degreeUnionState62_802 : List PrefixRegion := nextRegions 12 (liveRegions 12 49 13 degreeUnionState62_707) + +def degreeUnionState62_803 : List PrefixRegion := nextRegions 4 (liveRegions 11 37 12 degreeUnionState62_802) + +def degreeUnionState62_804 : List PrefixRegion := nextRegions 5 (liveRegions 11 37 12 degreeUnionState62_802) + +def degreeUnionState62_805 : List PrefixRegion := nextRegions 6 (liveRegions 11 37 12 degreeUnionState62_802) + +def degreeUnionState62_806 : List PrefixRegion := nextRegions 7 (liveRegions 11 37 12 degreeUnionState62_802) + +def degreeUnionState62_807 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 7 degreeUnionState62_806) + +def degreeUnionState62_808 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 7 degreeUnionState62_806) + +def degreeUnionState62_809 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 7 degreeUnionState62_806) + +def degreeUnionState62_810 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 7 degreeUnionState62_806) + +def degreeUnionState62_811 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 7 degreeUnionState62_806) + +def degreeUnionState62_812 : List PrefixRegion := nextRegions 8 (liveRegions 11 37 12 degreeUnionState62_802) + +def degreeUnionState62_813 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 8 degreeUnionState62_812) + +def degreeUnionState62_814 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 8 degreeUnionState62_812) + +def degreeUnionState62_815 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 8 degreeUnionState62_812) + +def degreeUnionState62_816 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 8 degreeUnionState62_812) + +def degreeUnionState62_817 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 8 degreeUnionState62_812) + +def degreeUnionState62_818 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 8 degreeUnionState62_812) + +def degreeUnionState62_819 : List PrefixRegion := nextRegions 9 (liveRegions 11 37 12 degreeUnionState62_802) + +def degreeUnionState62_820 : List PrefixRegion := nextRegions 10 (liveRegions 11 37 12 degreeUnionState62_802) + +def degreeUnionState62_821 : List PrefixRegion := nextRegions 11 (liveRegions 11 37 12 degreeUnionState62_802) + +def degreeUnionState62_822 : List PrefixRegion := nextRegions 12 (liveRegions 11 37 12 degreeUnionState62_802) + +def degreeUnionState62_823 : List PrefixRegion := nextRegions 13 (liveRegions 12 49 13 degreeUnionState62_707) + +def degreeUnionState62_824 : List PrefixRegion := nextRegions 4 (liveRegions 11 36 13 degreeUnionState62_823) + +def degreeUnionState62_825 : List PrefixRegion := nextRegions 5 (liveRegions 11 36 13 degreeUnionState62_823) + +def degreeUnionState62_826 : List PrefixRegion := nextRegions 6 (liveRegions 11 36 13 degreeUnionState62_823) + +def degreeUnionState62_827 : List PrefixRegion := nextRegions 7 (liveRegions 11 36 13 degreeUnionState62_823) + +def degreeUnionState62_828 : List PrefixRegion := nextRegions 8 (liveRegions 11 36 13 degreeUnionState62_823) + +def degreeUnionState62_829 : List PrefixRegion := nextRegions 9 (liveRegions 11 36 13 degreeUnionState62_823) + +def degreeUnionState62_830 : List PrefixRegion := nextRegions 10 (liveRegions 11 36 13 degreeUnionState62_823) + +def degreeUnionState62_831 : List PrefixRegion := nextRegions 11 (liveRegions 11 36 13 degreeUnionState62_823) + +def degreeUnionState62_832 : List PrefixRegion := nextRegions 12 (liveRegions 11 36 13 degreeUnionState62_823) + +def degreeUnionState62_833 : List PrefixRegion := nextRegions 13 (liveRegions 11 36 13 degreeUnionState62_823) + +def degreeUnionState62_834 : List PrefixRegion := nextRegions 14 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_835 : List PrefixRegion := nextRegions 4 (liveRegions 12 48 14 degreeUnionState62_834) + +def degreeUnionState62_836 : List PrefixRegion := nextRegions 5 (liveRegions 12 48 14 degreeUnionState62_834) + +def degreeUnionState62_837 : List PrefixRegion := nextRegions 6 (liveRegions 12 48 14 degreeUnionState62_834) + +def degreeUnionState62_838 : List PrefixRegion := nextRegions 7 (liveRegions 12 48 14 degreeUnionState62_834) + +def degreeUnionState62_839 : List PrefixRegion := nextRegions 4 (liveRegions 11 41 7 degreeUnionState62_838) + +def degreeUnionState62_840 : List PrefixRegion := nextRegions 5 (liveRegions 11 41 7 degreeUnionState62_838) + +def degreeUnionState62_841 : List PrefixRegion := nextRegions 6 (liveRegions 11 41 7 degreeUnionState62_838) + +def degreeUnionState62_842 : List PrefixRegion := nextRegions 7 (liveRegions 11 41 7 degreeUnionState62_838) + +def degreeUnionState62_843 : List PrefixRegion := nextRegions 8 (liveRegions 12 48 14 degreeUnionState62_834) + +def degreeUnionState62_844 : List PrefixRegion := nextRegions 4 (liveRegions 11 40 8 degreeUnionState62_843) + +def degreeUnionState62_845 : List PrefixRegion := nextRegions 5 (liveRegions 11 40 8 degreeUnionState62_843) + +def degreeUnionState62_846 : List PrefixRegion := nextRegions 6 (liveRegions 11 40 8 degreeUnionState62_843) + +def degreeUnionState62_847 : List PrefixRegion := nextRegions 7 (liveRegions 11 40 8 degreeUnionState62_843) + +def degreeUnionState62_848 : List PrefixRegion := nextRegions 8 (liveRegions 11 40 8 degreeUnionState62_843) + +def degreeUnionState62_849 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 8 degreeUnionState62_848) + +def degreeUnionState62_850 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 8 degreeUnionState62_848) + +def degreeUnionState62_851 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 8 degreeUnionState62_848) + +def degreeUnionState62_852 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 8 degreeUnionState62_848) + +def degreeUnionState62_853 : List PrefixRegion := nextRegions 8 (liveRegions 10 32 8 degreeUnionState62_848) + +def degreeUnionState62_854 : List PrefixRegion := nextRegions 9 (liveRegions 12 48 14 degreeUnionState62_834) + +def degreeUnionState62_855 : List PrefixRegion := nextRegions 4 (liveRegions 11 39 9 degreeUnionState62_854) + +def degreeUnionState62_856 : List PrefixRegion := nextRegions 5 (liveRegions 11 39 9 degreeUnionState62_854) + +def degreeUnionState62_857 : List PrefixRegion := nextRegions 6 (liveRegions 11 39 9 degreeUnionState62_854) + +def degreeUnionState62_858 : List PrefixRegion := nextRegions 7 (liveRegions 11 39 9 degreeUnionState62_854) + +def degreeUnionState62_859 : List PrefixRegion := nextRegions 4 (liveRegions 10 32 7 degreeUnionState62_858) + +def degreeUnionState62_860 : List PrefixRegion := nextRegions 5 (liveRegions 10 32 7 degreeUnionState62_858) + +def degreeUnionState62_861 : List PrefixRegion := nextRegions 6 (liveRegions 10 32 7 degreeUnionState62_858) + +def degreeUnionState62_862 : List PrefixRegion := nextRegions 7 (liveRegions 10 32 7 degreeUnionState62_858) + +def degreeUnionState62_863 : List PrefixRegion := nextRegions 8 (liveRegions 11 39 9 degreeUnionState62_854) + +def degreeUnionState62_864 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 8 degreeUnionState62_863) + +def degreeUnionState62_865 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 8 degreeUnionState62_863) + +def degreeUnionState62_866 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 8 degreeUnionState62_863) + +def degreeUnionState62_867 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 8 degreeUnionState62_863) + +def degreeUnionState62_868 : List PrefixRegion := nextRegions 8 (liveRegions 10 31 8 degreeUnionState62_863) + +def degreeUnionState62_869 : List PrefixRegion := nextRegions 9 (liveRegions 11 39 9 degreeUnionState62_854) + +def degreeUnionState62_870 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 9 degreeUnionState62_869) + +def degreeUnionState62_871 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 9 degreeUnionState62_869) + +def degreeUnionState62_872 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 9 degreeUnionState62_869) + +def degreeUnionState62_873 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 9 degreeUnionState62_869) + +def degreeUnionState62_874 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 9 degreeUnionState62_869) + +def degreeUnionState62_875 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 9 degreeUnionState62_869) + +def degreeUnionState62_876 : List PrefixRegion := nextRegions 9 (liveRegions 10 30 9 degreeUnionState62_869) + +def degreeUnionState62_877 : List PrefixRegion := nextRegions 10 (liveRegions 12 48 14 degreeUnionState62_834) + +def degreeUnionState62_878 : List PrefixRegion := nextRegions 4 (liveRegions 11 38 10 degreeUnionState62_877) + +def degreeUnionState62_879 : List PrefixRegion := nextRegions 5 (liveRegions 11 38 10 degreeUnionState62_877) + +def degreeUnionState62_880 : List PrefixRegion := nextRegions 6 (liveRegions 11 38 10 degreeUnionState62_877) + +def degreeUnionState62_881 : List PrefixRegion := nextRegions 7 (liveRegions 11 38 10 degreeUnionState62_877) + +def degreeUnionState62_882 : List PrefixRegion := nextRegions 4 (liveRegions 10 31 7 degreeUnionState62_881) + +def degreeUnionState62_883 : List PrefixRegion := nextRegions 5 (liveRegions 10 31 7 degreeUnionState62_881) + +def degreeUnionState62_884 : List PrefixRegion := nextRegions 6 (liveRegions 10 31 7 degreeUnionState62_881) + +def degreeUnionState62_885 : List PrefixRegion := nextRegions 7 (liveRegions 10 31 7 degreeUnionState62_881) + +def degreeUnionState62_886 : List PrefixRegion := nextRegions 8 (liveRegions 11 38 10 degreeUnionState62_877) + +def degreeUnionState62_887 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 8 degreeUnionState62_886) + +def degreeUnionState62_888 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 8 degreeUnionState62_886) + +def degreeUnionState62_889 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 8 degreeUnionState62_886) + +def degreeUnionState62_890 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 8 degreeUnionState62_886) + +def degreeUnionState62_891 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 8 degreeUnionState62_886) + +def degreeUnionState62_892 : List PrefixRegion := nextRegions 8 (liveRegions 10 30 8 degreeUnionState62_886) + +def degreeUnionState62_893 : List PrefixRegion := nextRegions 9 (liveRegions 11 38 10 degreeUnionState62_877) + +def degreeUnionState62_894 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 9 degreeUnionState62_893) + +def degreeUnionState62_895 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 9 degreeUnionState62_893) + +def degreeUnionState62_896 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 9 degreeUnionState62_893) + +def degreeUnionState62_897 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 9 degreeUnionState62_893) + +def degreeUnionState62_898 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 9 degreeUnionState62_893) + +def degreeUnionState62_899 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 9 degreeUnionState62_893) + +def degreeUnionState62_900 : List PrefixRegion := nextRegions 9 (liveRegions 10 29 9 degreeUnionState62_893) + +def degreeUnionState62_901 : List PrefixRegion := nextRegions 10 (liveRegions 11 38 10 degreeUnionState62_877) + +def degreeUnionState62_902 : List PrefixRegion := nextRegions 11 (liveRegions 12 48 14 degreeUnionState62_834) + +def degreeUnionState62_903 : List PrefixRegion := nextRegions 4 (liveRegions 11 37 11 degreeUnionState62_902) + +def degreeUnionState62_904 : List PrefixRegion := nextRegions 5 (liveRegions 11 37 11 degreeUnionState62_902) + +def degreeUnionState62_905 : List PrefixRegion := nextRegions 6 (liveRegions 11 37 11 degreeUnionState62_902) + +def degreeUnionState62_906 : List PrefixRegion := nextRegions 7 (liveRegions 11 37 11 degreeUnionState62_902) + +def degreeUnionState62_907 : List PrefixRegion := nextRegions 3 (liveRegions 10 30 7 degreeUnionState62_906) + +def degreeUnionState62_908 : List PrefixRegion := nextRegions 4 (liveRegions 10 30 7 degreeUnionState62_906) + +def degreeUnionState62_909 : List PrefixRegion := nextRegions 5 (liveRegions 10 30 7 degreeUnionState62_906) + +def degreeUnionState62_910 : List PrefixRegion := nextRegions 6 (liveRegions 10 30 7 degreeUnionState62_906) + +def degreeUnionState62_911 : List PrefixRegion := nextRegions 7 (liveRegions 10 30 7 degreeUnionState62_906) + +def degreeUnionState62_912 : List PrefixRegion := nextRegions 8 (liveRegions 11 37 11 degreeUnionState62_902) + +def degreeUnionState62_913 : List PrefixRegion := nextRegions 3 (liveRegions 10 29 8 degreeUnionState62_912) + +def degreeUnionState62_914 : List PrefixRegion := nextRegions 4 (liveRegions 10 29 8 degreeUnionState62_912) + +def degreeUnionState62_915 : List PrefixRegion := nextRegions 5 (liveRegions 10 29 8 degreeUnionState62_912) + +def degreeUnionState62_916 : List PrefixRegion := nextRegions 6 (liveRegions 10 29 8 degreeUnionState62_912) + +def degreeUnionState62_917 : List PrefixRegion := nextRegions 7 (liveRegions 10 29 8 degreeUnionState62_912) + +def degreeUnionState62_918 : List PrefixRegion := nextRegions 8 (liveRegions 10 29 8 degreeUnionState62_912) + +def degreeUnionState62_919 : List PrefixRegion := nextRegions 9 (liveRegions 11 37 11 degreeUnionState62_902) + +def degreeUnionState62_920 : List PrefixRegion := nextRegions 10 (liveRegions 11 37 11 degreeUnionState62_902) + +def degreeUnionState62_921 : List PrefixRegion := nextRegions 11 (liveRegions 11 37 11 degreeUnionState62_902) + +def degreeUnionState62_922 : List PrefixRegion := nextRegions 12 (liveRegions 12 48 14 degreeUnionState62_834) + +def degreeUnionState62_923 : List PrefixRegion := nextRegions 4 (liveRegions 11 36 12 degreeUnionState62_922) + +def degreeUnionState62_924 : List PrefixRegion := nextRegions 5 (liveRegions 11 36 12 degreeUnionState62_922) + +def degreeUnionState62_925 : List PrefixRegion := nextRegions 6 (liveRegions 11 36 12 degreeUnionState62_922) + +def degreeUnionState62_926 : List PrefixRegion := nextRegions 7 (liveRegions 11 36 12 degreeUnionState62_922) + +def degreeUnionState62_927 : List PrefixRegion := nextRegions 8 (liveRegions 11 36 12 degreeUnionState62_922) + +def degreeUnionState62_928 : List PrefixRegion := nextRegions 9 (liveRegions 11 36 12 degreeUnionState62_922) + +def degreeUnionState62_929 : List PrefixRegion := nextRegions 10 (liveRegions 11 36 12 degreeUnionState62_922) + +def degreeUnionState62_930 : List PrefixRegion := nextRegions 11 (liveRegions 11 36 12 degreeUnionState62_922) + +def degreeUnionState62_931 : List PrefixRegion := nextRegions 12 (liveRegions 11 36 12 degreeUnionState62_922) + +def degreeUnionState62_932 : List PrefixRegion := nextRegions 13 (liveRegions 12 48 14 degreeUnionState62_834) + +def degreeUnionState62_933 : List PrefixRegion := nextRegions 14 (liveRegions 12 48 14 degreeUnionState62_834) + +def degreeUnionState62_934 : List PrefixRegion := nextRegions 15 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_935 : List PrefixRegion := nextRegions 16 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_936 : List PrefixRegion := nextRegions 17 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_937 : List PrefixRegion := nextRegions 18 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_938 : List PrefixRegion := nextRegions 19 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_939 : List PrefixRegion := nextRegions 20 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_940 : List PrefixRegion := nextRegions 21 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_941 : List PrefixRegion := nextRegions 22 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_942 : List PrefixRegion := nextRegions 23 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_943 : List PrefixRegion := nextRegions 24 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_944 : List PrefixRegion := nextRegions 25 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_945 : List PrefixRegion := nextRegions 26 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_946 : List PrefixRegion := nextRegions 27 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_947 : List PrefixRegion := nextRegions 28 (liveRegions 13 62 28 degreeHalfRegions62) + +def degreeUnionState62_949 : List PrefixRegion := nextRegions 5 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_950 : List PrefixRegion := nextRegions 6 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_951 : List PrefixRegion := nextRegions 7 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_952 : List PrefixRegion := nextRegions 8 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_953 : List PrefixRegion := nextRegions 9 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_954 : List PrefixRegion := nextRegions 10 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_955 : List PrefixRegion := nextRegions 4 (liveRegions 13 52 10 degreeUnionState62_954) + +def degreeUnionState62_956 : List PrefixRegion := nextRegions 5 (liveRegions 13 52 10 degreeUnionState62_954) + +def degreeUnionState62_957 : List PrefixRegion := nextRegions 6 (liveRegions 13 52 10 degreeUnionState62_954) + +def degreeUnionState62_958 : List PrefixRegion := nextRegions 7 (liveRegions 13 52 10 degreeUnionState62_954) + +def degreeUnionState62_959 : List PrefixRegion := nextRegions 8 (liveRegions 13 52 10 degreeUnionState62_954) + +def degreeUnionState62_960 : List PrefixRegion := nextRegions 9 (liveRegions 13 52 10 degreeUnionState62_954) + +def degreeUnionState62_961 : List PrefixRegion := nextRegions 10 (liveRegions 13 52 10 degreeUnionState62_954) + +def degreeUnionState62_962 : List PrefixRegion := nextRegions 11 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_963 : List PrefixRegion := nextRegions 4 (liveRegions 13 51 11 degreeUnionState62_962) + +def degreeUnionState62_964 : List PrefixRegion := nextRegions 5 (liveRegions 13 51 11 degreeUnionState62_962) + +def degreeUnionState62_965 : List PrefixRegion := nextRegions 6 (liveRegions 13 51 11 degreeUnionState62_962) + +def degreeUnionState62_966 : List PrefixRegion := nextRegions 7 (liveRegions 13 51 11 degreeUnionState62_962) + +def degreeUnionState62_967 : List PrefixRegion := nextRegions 8 (liveRegions 13 51 11 degreeUnionState62_962) + +def degreeUnionState62_968 : List PrefixRegion := nextRegions 9 (liveRegions 13 51 11 degreeUnionState62_962) + +def degreeUnionState62_969 : List PrefixRegion := nextRegions 10 (liveRegions 13 51 11 degreeUnionState62_962) + +def degreeUnionState62_970 : List PrefixRegion := nextRegions 4 (liveRegions 12 41 10 degreeUnionState62_969) + +def degreeUnionState62_971 : List PrefixRegion := nextRegions 5 (liveRegions 12 41 10 degreeUnionState62_969) + +def degreeUnionState62_972 : List PrefixRegion := nextRegions 6 (liveRegions 12 41 10 degreeUnionState62_969) + +def degreeUnionState62_973 : List PrefixRegion := nextRegions 7 (liveRegions 12 41 10 degreeUnionState62_969) + +def degreeUnionState62_974 : List PrefixRegion := nextRegions 8 (liveRegions 12 41 10 degreeUnionState62_969) + +def degreeUnionState62_975 : List PrefixRegion := nextRegions 9 (liveRegions 12 41 10 degreeUnionState62_969) + +def degreeUnionState62_976 : List PrefixRegion := nextRegions 10 (liveRegions 12 41 10 degreeUnionState62_969) + +def degreeUnionState62_977 : List PrefixRegion := nextRegions 11 (liveRegions 13 51 11 degreeUnionState62_962) + +def degreeUnionState62_978 : List PrefixRegion := nextRegions 4 (liveRegions 12 40 11 degreeUnionState62_977) + +def degreeUnionState62_979 : List PrefixRegion := nextRegions 5 (liveRegions 12 40 11 degreeUnionState62_977) + +def degreeUnionState62_980 : List PrefixRegion := nextRegions 6 (liveRegions 12 40 11 degreeUnionState62_977) + +def degreeUnionState62_981 : List PrefixRegion := nextRegions 7 (liveRegions 12 40 11 degreeUnionState62_977) + +def degreeUnionState62_982 : List PrefixRegion := nextRegions 8 (liveRegions 12 40 11 degreeUnionState62_977) + +def degreeUnionState62_983 : List PrefixRegion := nextRegions 9 (liveRegions 12 40 11 degreeUnionState62_977) + +def degreeUnionState62_984 : List PrefixRegion := nextRegions 10 (liveRegions 12 40 11 degreeUnionState62_977) + +def degreeUnionState62_985 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 10 degreeUnionState62_984) + +def degreeUnionState62_986 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 10 degreeUnionState62_984) + +def degreeUnionState62_987 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 10 degreeUnionState62_984) + +def degreeUnionState62_988 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 10 degreeUnionState62_984) + +def degreeUnionState62_989 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 10 degreeUnionState62_984) + +def degreeUnionState62_990 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 10 degreeUnionState62_984) + +def degreeUnionState62_991 : List PrefixRegion := nextRegions 9 (liveRegions 11 30 10 degreeUnionState62_984) + +def degreeUnionState62_992 : List PrefixRegion := nextRegions 10 (liveRegions 11 30 10 degreeUnionState62_984) + +def degreeUnionState62_993 : List PrefixRegion := nextRegions 11 (liveRegions 12 40 11 degreeUnionState62_977) + +def degreeUnionState62_994 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 11 degreeUnionState62_993) + +def degreeUnionState62_995 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 11 degreeUnionState62_993) + +def degreeUnionState62_996 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 11 degreeUnionState62_993) + +def degreeUnionState62_997 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 11 degreeUnionState62_993) + +def degreeUnionState62_998 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 11 degreeUnionState62_993) + +def degreeUnionState62_999 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 11 degreeUnionState62_993) + +def degreeUnionState62_1000 : List PrefixRegion := nextRegions 9 (liveRegions 11 29 11 degreeUnionState62_993) + +def degreeUnionState62_1001 : List PrefixRegion := nextRegions 10 (liveRegions 11 29 11 degreeUnionState62_993) + +def degreeUnionState62_1002 : List PrefixRegion := nextRegions 11 (liveRegions 11 29 11 degreeUnionState62_993) + +def degreeUnionState62_1003 : List PrefixRegion := nextRegions 12 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1004 : List PrefixRegion := nextRegions 4 (liveRegions 13 50 12 degreeUnionState62_1003) + +def degreeUnionState62_1005 : List PrefixRegion := nextRegions 5 (liveRegions 13 50 12 degreeUnionState62_1003) + +def degreeUnionState62_1006 : List PrefixRegion := nextRegions 6 (liveRegions 13 50 12 degreeUnionState62_1003) + +def degreeUnionState62_1007 : List PrefixRegion := nextRegions 7 (liveRegions 13 50 12 degreeUnionState62_1003) + +def degreeUnionState62_1008 : List PrefixRegion := nextRegions 8 (liveRegions 13 50 12 degreeUnionState62_1003) + +def degreeUnionState62_1009 : List PrefixRegion := nextRegions 4 (liveRegions 12 42 8 degreeUnionState62_1008) + +def degreeUnionState62_1010 : List PrefixRegion := nextRegions 5 (liveRegions 12 42 8 degreeUnionState62_1008) + +def degreeUnionState62_1011 : List PrefixRegion := nextRegions 6 (liveRegions 12 42 8 degreeUnionState62_1008) + +def degreeUnionState62_1012 : List PrefixRegion := nextRegions 7 (liveRegions 12 42 8 degreeUnionState62_1008) + +def degreeUnionState62_1013 : List PrefixRegion := nextRegions 8 (liveRegions 12 42 8 degreeUnionState62_1008) + +def degreeUnionState62_1014 : List PrefixRegion := nextRegions 4 (liveRegions 11 34 8 degreeUnionState62_1013) + +def degreeUnionState62_1015 : List PrefixRegion := nextRegions 5 (liveRegions 11 34 8 degreeUnionState62_1013) + +def degreeUnionState62_1016 : List PrefixRegion := nextRegions 6 (liveRegions 11 34 8 degreeUnionState62_1013) + +def degreeUnionState62_1017 : List PrefixRegion := nextRegions 7 (liveRegions 11 34 8 degreeUnionState62_1013) + +def degreeUnionState62_1018 : List PrefixRegion := nextRegions 8 (liveRegions 11 34 8 degreeUnionState62_1013) + +def degreeUnionState62_1019 : List PrefixRegion := nextRegions 9 (liveRegions 13 50 12 degreeUnionState62_1003) + +def degreeUnionState62_1020 : List PrefixRegion := nextRegions 4 (liveRegions 12 41 9 degreeUnionState62_1019) + +def degreeUnionState62_1021 : List PrefixRegion := nextRegions 5 (liveRegions 12 41 9 degreeUnionState62_1019) + +def degreeUnionState62_1022 : List PrefixRegion := nextRegions 6 (liveRegions 12 41 9 degreeUnionState62_1019) + +def degreeUnionState62_1023 : List PrefixRegion := nextRegions 7 (liveRegions 12 41 9 degreeUnionState62_1019) + +def degreeUnionState62_1024 : List PrefixRegion := nextRegions 8 (liveRegions 12 41 9 degreeUnionState62_1019) + +def degreeUnionState62_1025 : List PrefixRegion := nextRegions 3 (liveRegions 11 33 8 degreeUnionState62_1024) + +def degreeUnionState62_1026 : List PrefixRegion := nextRegions 4 (liveRegions 11 33 8 degreeUnionState62_1024) + +def degreeUnionState62_1027 : List PrefixRegion := nextRegions 5 (liveRegions 11 33 8 degreeUnionState62_1024) + +def degreeUnionState62_1028 : List PrefixRegion := nextRegions 6 (liveRegions 11 33 8 degreeUnionState62_1024) + +def degreeUnionState62_1029 : List PrefixRegion := nextRegions 7 (liveRegions 11 33 8 degreeUnionState62_1024) + +def degreeUnionState62_1030 : List PrefixRegion := nextRegions 8 (liveRegions 11 33 8 degreeUnionState62_1024) + +def degreeUnionState62_1031 : List PrefixRegion := nextRegions 9 (liveRegions 12 41 9 degreeUnionState62_1019) + +def degreeUnionState62_1032 : List PrefixRegion := nextRegions 3 (liveRegions 11 32 9 degreeUnionState62_1031) + +def degreeUnionState62_1033 : List PrefixRegion := nextRegions 4 (liveRegions 11 32 9 degreeUnionState62_1031) + +def degreeUnionState62_1034 : List PrefixRegion := nextRegions 5 (liveRegions 11 32 9 degreeUnionState62_1031) + +def degreeUnionState62_1035 : List PrefixRegion := nextRegions 6 (liveRegions 11 32 9 degreeUnionState62_1031) + +def degreeUnionState62_1036 : List PrefixRegion := nextRegions 7 (liveRegions 11 32 9 degreeUnionState62_1031) + +def degreeUnionState62_1037 : List PrefixRegion := nextRegions 8 (liveRegions 11 32 9 degreeUnionState62_1031) + +def degreeUnionState62_1038 : List PrefixRegion := nextRegions 9 (liveRegions 11 32 9 degreeUnionState62_1031) + +def degreeUnionState62_1039 : List PrefixRegion := nextRegions 10 (liveRegions 13 50 12 degreeUnionState62_1003) + +def degreeUnionState62_1040 : List PrefixRegion := nextRegions 4 (liveRegions 12 40 10 degreeUnionState62_1039) + +def degreeUnionState62_1041 : List PrefixRegion := nextRegions 5 (liveRegions 12 40 10 degreeUnionState62_1039) + +def degreeUnionState62_1042 : List PrefixRegion := nextRegions 6 (liveRegions 12 40 10 degreeUnionState62_1039) + +def degreeUnionState62_1043 : List PrefixRegion := nextRegions 7 (liveRegions 12 40 10 degreeUnionState62_1039) + +def degreeUnionState62_1044 : List PrefixRegion := nextRegions 8 (liveRegions 12 40 10 degreeUnionState62_1039) + +def degreeUnionState62_1045 : List PrefixRegion := nextRegions 3 (liveRegions 11 32 8 degreeUnionState62_1044) + +def degreeUnionState62_1046 : List PrefixRegion := nextRegions 4 (liveRegions 11 32 8 degreeUnionState62_1044) + +def degreeUnionState62_1047 : List PrefixRegion := nextRegions 5 (liveRegions 11 32 8 degreeUnionState62_1044) + +def degreeUnionState62_1048 : List PrefixRegion := nextRegions 6 (liveRegions 11 32 8 degreeUnionState62_1044) + +def degreeUnionState62_1049 : List PrefixRegion := nextRegions 7 (liveRegions 11 32 8 degreeUnionState62_1044) + +def degreeUnionState62_1050 : List PrefixRegion := nextRegions 8 (liveRegions 11 32 8 degreeUnionState62_1044) + +def degreeUnionState62_1051 : List PrefixRegion := nextRegions 9 (liveRegions 12 40 10 degreeUnionState62_1039) + +def degreeUnionState62_1052 : List PrefixRegion := nextRegions 3 (liveRegions 11 31 9 degreeUnionState62_1051) + +def degreeUnionState62_1053 : List PrefixRegion := nextRegions 4 (liveRegions 11 31 9 degreeUnionState62_1051) + +def degreeUnionState62_1054 : List PrefixRegion := nextRegions 5 (liveRegions 11 31 9 degreeUnionState62_1051) + +def degreeUnionState62_1055 : List PrefixRegion := nextRegions 6 (liveRegions 11 31 9 degreeUnionState62_1051) + +def degreeUnionState62_1056 : List PrefixRegion := nextRegions 7 (liveRegions 11 31 9 degreeUnionState62_1051) + +def degreeUnionState62_1057 : List PrefixRegion := nextRegions 8 (liveRegions 11 31 9 degreeUnionState62_1051) + +def degreeUnionState62_1058 : List PrefixRegion := nextRegions 9 (liveRegions 11 31 9 degreeUnionState62_1051) + +def degreeUnionState62_1059 : List PrefixRegion := nextRegions 10 (liveRegions 12 40 10 degreeUnionState62_1039) + +def degreeUnionState62_1060 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 10 degreeUnionState62_1059) + +def degreeUnionState62_1061 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 10 degreeUnionState62_1059) + +def degreeUnionState62_1062 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 10 degreeUnionState62_1059) + +def degreeUnionState62_1063 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 10 degreeUnionState62_1059) + +def degreeUnionState62_1064 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 10 degreeUnionState62_1059) + +def degreeUnionState62_1065 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 10 degreeUnionState62_1059) + +def degreeUnionState62_1066 : List PrefixRegion := nextRegions 9 (liveRegions 11 30 10 degreeUnionState62_1059) + +def degreeUnionState62_1067 : List PrefixRegion := nextRegions 10 (liveRegions 11 30 10 degreeUnionState62_1059) + +def degreeUnionState62_1068 : List PrefixRegion := nextRegions 11 (liveRegions 13 50 12 degreeUnionState62_1003) + +def degreeUnionState62_1069 : List PrefixRegion := nextRegions 4 (liveRegions 12 39 11 degreeUnionState62_1068) + +def degreeUnionState62_1070 : List PrefixRegion := nextRegions 5 (liveRegions 12 39 11 degreeUnionState62_1068) + +def degreeUnionState62_1071 : List PrefixRegion := nextRegions 6 (liveRegions 12 39 11 degreeUnionState62_1068) + +def degreeUnionState62_1072 : List PrefixRegion := nextRegions 7 (liveRegions 12 39 11 degreeUnionState62_1068) + +def degreeUnionState62_1073 : List PrefixRegion := nextRegions 8 (liveRegions 12 39 11 degreeUnionState62_1068) + +def degreeUnionState62_1074 : List PrefixRegion := nextRegions 3 (liveRegions 11 31 8 degreeUnionState62_1073) + +def degreeUnionState62_1075 : List PrefixRegion := nextRegions 4 (liveRegions 11 31 8 degreeUnionState62_1073) + +def degreeUnionState62_1076 : List PrefixRegion := nextRegions 5 (liveRegions 11 31 8 degreeUnionState62_1073) + +def degreeUnionState62_1077 : List PrefixRegion := nextRegions 6 (liveRegions 11 31 8 degreeUnionState62_1073) + +def degreeUnionState62_1078 : List PrefixRegion := nextRegions 7 (liveRegions 11 31 8 degreeUnionState62_1073) + +def degreeUnionState62_1079 : List PrefixRegion := nextRegions 8 (liveRegions 11 31 8 degreeUnionState62_1073) + +def degreeUnionState62_1080 : List PrefixRegion := nextRegions 9 (liveRegions 12 39 11 degreeUnionState62_1068) + +def degreeUnionState62_1081 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 9 degreeUnionState62_1080) + +def degreeUnionState62_1082 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 9 degreeUnionState62_1080) + +def degreeUnionState62_1083 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 9 degreeUnionState62_1080) + +def degreeUnionState62_1084 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 9 degreeUnionState62_1080) + +def degreeUnionState62_1085 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 9 degreeUnionState62_1080) + +def degreeUnionState62_1086 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 9 degreeUnionState62_1080) + +def degreeUnionState62_1087 : List PrefixRegion := nextRegions 9 (liveRegions 11 30 9 degreeUnionState62_1080) + +def degreeUnionState62_1088 : List PrefixRegion := nextRegions 10 (liveRegions 12 39 11 degreeUnionState62_1068) + +def degreeUnionState62_1089 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 10 degreeUnionState62_1088) + +def degreeUnionState62_1090 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 10 degreeUnionState62_1088) + +def degreeUnionState62_1091 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 10 degreeUnionState62_1088) + +def degreeUnionState62_1092 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 10 degreeUnionState62_1088) + +def degreeUnionState62_1093 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 10 degreeUnionState62_1088) + +def degreeUnionState62_1094 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 10 degreeUnionState62_1088) + +def degreeUnionState62_1095 : List PrefixRegion := nextRegions 9 (liveRegions 11 29 10 degreeUnionState62_1088) + +def degreeUnionState62_1096 : List PrefixRegion := nextRegions 10 (liveRegions 11 29 10 degreeUnionState62_1088) + +def degreeUnionState62_1097 : List PrefixRegion := nextRegions 11 (liveRegions 12 39 11 degreeUnionState62_1068) + +def degreeUnionState62_1098 : List PrefixRegion := nextRegions 12 (liveRegions 13 50 12 degreeUnionState62_1003) + +def degreeUnionState62_1099 : List PrefixRegion := nextRegions 4 (liveRegions 12 38 12 degreeUnionState62_1098) + +def degreeUnionState62_1100 : List PrefixRegion := nextRegions 5 (liveRegions 12 38 12 degreeUnionState62_1098) + +def degreeUnionState62_1101 : List PrefixRegion := nextRegions 6 (liveRegions 12 38 12 degreeUnionState62_1098) + +def degreeUnionState62_1102 : List PrefixRegion := nextRegions 7 (liveRegions 12 38 12 degreeUnionState62_1098) + +def degreeUnionState62_1103 : List PrefixRegion := nextRegions 8 (liveRegions 12 38 12 degreeUnionState62_1098) + +def degreeUnionState62_1104 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 8 degreeUnionState62_1103) + +def degreeUnionState62_1105 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 8 degreeUnionState62_1103) + +def degreeUnionState62_1106 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 8 degreeUnionState62_1103) + +def degreeUnionState62_1107 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 8 degreeUnionState62_1103) + +def degreeUnionState62_1108 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 8 degreeUnionState62_1103) + +def degreeUnionState62_1109 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 8 degreeUnionState62_1103) + +def degreeUnionState62_1110 : List PrefixRegion := nextRegions 9 (liveRegions 12 38 12 degreeUnionState62_1098) + +def degreeUnionState62_1111 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 9 degreeUnionState62_1110) + +def degreeUnionState62_1112 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 9 degreeUnionState62_1110) + +def degreeUnionState62_1113 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 9 degreeUnionState62_1110) + +def degreeUnionState62_1114 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 9 degreeUnionState62_1110) + +def degreeUnionState62_1115 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 9 degreeUnionState62_1110) + +def degreeUnionState62_1116 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 9 degreeUnionState62_1110) + +def degreeUnionState62_1117 : List PrefixRegion := nextRegions 9 (liveRegions 11 29 9 degreeUnionState62_1110) + +def degreeUnionState62_1118 : List PrefixRegion := nextRegions 10 (liveRegions 12 38 12 degreeUnionState62_1098) + +def degreeUnionState62_1119 : List PrefixRegion := nextRegions 11 (liveRegions 12 38 12 degreeUnionState62_1098) + +def degreeUnionState62_1120 : List PrefixRegion := nextRegions 12 (liveRegions 12 38 12 degreeUnionState62_1098) + +def degreeUnionState62_1121 : List PrefixRegion := nextRegions 13 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1122 : List PrefixRegion := nextRegions 4 (liveRegions 13 49 13 degreeUnionState62_1121) + +def degreeUnionState62_1123 : List PrefixRegion := nextRegions 5 (liveRegions 13 49 13 degreeUnionState62_1121) + +def degreeUnionState62_1124 : List PrefixRegion := nextRegions 6 (liveRegions 13 49 13 degreeUnionState62_1121) + +def degreeUnionState62_1125 : List PrefixRegion := nextRegions 7 (liveRegions 13 49 13 degreeUnionState62_1121) + +def degreeUnionState62_1126 : List PrefixRegion := nextRegions 8 (liveRegions 13 49 13 degreeUnionState62_1121) + +def degreeUnionState62_1127 : List PrefixRegion := nextRegions 4 (liveRegions 12 41 8 degreeUnionState62_1126) + +def degreeUnionState62_1128 : List PrefixRegion := nextRegions 5 (liveRegions 12 41 8 degreeUnionState62_1126) + +def degreeUnionState62_1129 : List PrefixRegion := nextRegions 6 (liveRegions 12 41 8 degreeUnionState62_1126) + +def degreeUnionState62_1130 : List PrefixRegion := nextRegions 7 (liveRegions 12 41 8 degreeUnionState62_1126) + +def degreeUnionState62_1131 : List PrefixRegion := nextRegions 8 (liveRegions 12 41 8 degreeUnionState62_1126) + +def degreeUnionState62_1132 : List PrefixRegion := nextRegions 3 (liveRegions 11 33 8 degreeUnionState62_1131) + +def degreeUnionState62_1133 : List PrefixRegion := nextRegions 4 (liveRegions 11 33 8 degreeUnionState62_1131) + +def degreeUnionState62_1134 : List PrefixRegion := nextRegions 5 (liveRegions 11 33 8 degreeUnionState62_1131) + +def degreeUnionState62_1135 : List PrefixRegion := nextRegions 6 (liveRegions 11 33 8 degreeUnionState62_1131) + +def degreeUnionState62_1136 : List PrefixRegion := nextRegions 7 (liveRegions 11 33 8 degreeUnionState62_1131) + +def degreeUnionState62_1137 : List PrefixRegion := nextRegions 8 (liveRegions 11 33 8 degreeUnionState62_1131) + +def degreeUnionState62_1138 : List PrefixRegion := nextRegions 9 (liveRegions 13 49 13 degreeUnionState62_1121) + +def degreeUnionState62_1139 : List PrefixRegion := nextRegions 4 (liveRegions 12 40 9 degreeUnionState62_1138) + +def degreeUnionState62_1140 : List PrefixRegion := nextRegions 5 (liveRegions 12 40 9 degreeUnionState62_1138) + +def degreeUnionState62_1141 : List PrefixRegion := nextRegions 6 (liveRegions 12 40 9 degreeUnionState62_1138) + +def degreeUnionState62_1142 : List PrefixRegion := nextRegions 7 (liveRegions 12 40 9 degreeUnionState62_1138) + +def degreeUnionState62_1143 : List PrefixRegion := nextRegions 8 (liveRegions 12 40 9 degreeUnionState62_1138) + +def degreeUnionState62_1144 : List PrefixRegion := nextRegions 3 (liveRegions 11 32 8 degreeUnionState62_1143) + +def degreeUnionState62_1145 : List PrefixRegion := nextRegions 4 (liveRegions 11 32 8 degreeUnionState62_1143) + +def degreeUnionState62_1146 : List PrefixRegion := nextRegions 5 (liveRegions 11 32 8 degreeUnionState62_1143) + +def degreeUnionState62_1147 : List PrefixRegion := nextRegions 6 (liveRegions 11 32 8 degreeUnionState62_1143) + +def degreeUnionState62_1148 : List PrefixRegion := nextRegions 7 (liveRegions 11 32 8 degreeUnionState62_1143) + +def degreeUnionState62_1149 : List PrefixRegion := nextRegions 8 (liveRegions 11 32 8 degreeUnionState62_1143) + +def degreeUnionState62_1150 : List PrefixRegion := nextRegions 9 (liveRegions 12 40 9 degreeUnionState62_1138) + +def degreeUnionState62_1151 : List PrefixRegion := nextRegions 3 (liveRegions 11 31 9 degreeUnionState62_1150) + +def degreeUnionState62_1152 : List PrefixRegion := nextRegions 4 (liveRegions 11 31 9 degreeUnionState62_1150) + +def degreeUnionState62_1153 : List PrefixRegion := nextRegions 5 (liveRegions 11 31 9 degreeUnionState62_1150) + +def degreeUnionState62_1154 : List PrefixRegion := nextRegions 6 (liveRegions 11 31 9 degreeUnionState62_1150) + +def degreeUnionState62_1155 : List PrefixRegion := nextRegions 7 (liveRegions 11 31 9 degreeUnionState62_1150) + +def degreeUnionState62_1156 : List PrefixRegion := nextRegions 8 (liveRegions 11 31 9 degreeUnionState62_1150) + +def degreeUnionState62_1157 : List PrefixRegion := nextRegions 9 (liveRegions 11 31 9 degreeUnionState62_1150) + +def degreeUnionState62_1158 : List PrefixRegion := nextRegions 10 (liveRegions 13 49 13 degreeUnionState62_1121) + +def degreeUnionState62_1159 : List PrefixRegion := nextRegions 4 (liveRegions 12 39 10 degreeUnionState62_1158) + +def degreeUnionState62_1160 : List PrefixRegion := nextRegions 5 (liveRegions 12 39 10 degreeUnionState62_1158) + +def degreeUnionState62_1161 : List PrefixRegion := nextRegions 6 (liveRegions 12 39 10 degreeUnionState62_1158) + +def degreeUnionState62_1162 : List PrefixRegion := nextRegions 7 (liveRegions 12 39 10 degreeUnionState62_1158) + +def degreeUnionState62_1163 : List PrefixRegion := nextRegions 8 (liveRegions 12 39 10 degreeUnionState62_1158) + +def degreeUnionState62_1164 : List PrefixRegion := nextRegions 3 (liveRegions 11 31 8 degreeUnionState62_1163) + +def degreeUnionState62_1165 : List PrefixRegion := nextRegions 4 (liveRegions 11 31 8 degreeUnionState62_1163) + +def degreeUnionState62_1166 : List PrefixRegion := nextRegions 5 (liveRegions 11 31 8 degreeUnionState62_1163) + +def degreeUnionState62_1167 : List PrefixRegion := nextRegions 6 (liveRegions 11 31 8 degreeUnionState62_1163) + +def degreeUnionState62_1168 : List PrefixRegion := nextRegions 7 (liveRegions 11 31 8 degreeUnionState62_1163) + +def degreeUnionState62_1169 : List PrefixRegion := nextRegions 8 (liveRegions 11 31 8 degreeUnionState62_1163) + +def degreeUnionState62_1170 : List PrefixRegion := nextRegions 9 (liveRegions 12 39 10 degreeUnionState62_1158) + +def degreeUnionState62_1171 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 9 degreeUnionState62_1170) + +def degreeUnionState62_1172 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 9 degreeUnionState62_1170) + +def degreeUnionState62_1173 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 9 degreeUnionState62_1170) + +def degreeUnionState62_1174 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 9 degreeUnionState62_1170) + +def degreeUnionState62_1175 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 9 degreeUnionState62_1170) + +def degreeUnionState62_1176 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 9 degreeUnionState62_1170) + +def degreeUnionState62_1177 : List PrefixRegion := nextRegions 9 (liveRegions 11 30 9 degreeUnionState62_1170) + +def degreeUnionState62_1178 : List PrefixRegion := nextRegions 10 (liveRegions 12 39 10 degreeUnionState62_1158) + +def degreeUnionState62_1179 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 10 degreeUnionState62_1178) + +def degreeUnionState62_1180 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 10 degreeUnionState62_1178) + +def degreeUnionState62_1181 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 10 degreeUnionState62_1178) + +def degreeUnionState62_1182 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 10 degreeUnionState62_1178) + +def degreeUnionState62_1183 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 10 degreeUnionState62_1178) + +def degreeUnionState62_1184 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 10 degreeUnionState62_1178) + +def degreeUnionState62_1185 : List PrefixRegion := nextRegions 9 (liveRegions 11 29 10 degreeUnionState62_1178) + +def degreeUnionState62_1186 : List PrefixRegion := nextRegions 10 (liveRegions 11 29 10 degreeUnionState62_1178) + +def degreeUnionState62_1187 : List PrefixRegion := nextRegions 11 (liveRegions 13 49 13 degreeUnionState62_1121) + +def degreeUnionState62_1188 : List PrefixRegion := nextRegions 4 (liveRegions 12 38 11 degreeUnionState62_1187) + +def degreeUnionState62_1189 : List PrefixRegion := nextRegions 5 (liveRegions 12 38 11 degreeUnionState62_1187) + +def degreeUnionState62_1190 : List PrefixRegion := nextRegions 6 (liveRegions 12 38 11 degreeUnionState62_1187) + +def degreeUnionState62_1191 : List PrefixRegion := nextRegions 7 (liveRegions 12 38 11 degreeUnionState62_1187) + +def degreeUnionState62_1192 : List PrefixRegion := nextRegions 8 (liveRegions 12 38 11 degreeUnionState62_1187) + +def degreeUnionState62_1193 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 8 degreeUnionState62_1192) + +def degreeUnionState62_1194 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 8 degreeUnionState62_1192) + +def degreeUnionState62_1195 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 8 degreeUnionState62_1192) + +def degreeUnionState62_1196 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 8 degreeUnionState62_1192) + +def degreeUnionState62_1197 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 8 degreeUnionState62_1192) + +def degreeUnionState62_1198 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 8 degreeUnionState62_1192) + +def degreeUnionState62_1199 : List PrefixRegion := nextRegions 9 (liveRegions 12 38 11 degreeUnionState62_1187) + +def degreeUnionState62_1200 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 9 degreeUnionState62_1199) + +def degreeUnionState62_1201 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 9 degreeUnionState62_1199) + +def degreeUnionState62_1202 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 9 degreeUnionState62_1199) + +def degreeUnionState62_1203 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 9 degreeUnionState62_1199) + +def degreeUnionState62_1204 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 9 degreeUnionState62_1199) + +def degreeUnionState62_1205 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 9 degreeUnionState62_1199) + +def degreeUnionState62_1206 : List PrefixRegion := nextRegions 9 (liveRegions 11 29 9 degreeUnionState62_1199) + +def degreeUnionState62_1207 : List PrefixRegion := nextRegions 10 (liveRegions 12 38 11 degreeUnionState62_1187) + +def degreeUnionState62_1208 : List PrefixRegion := nextRegions 11 (liveRegions 12 38 11 degreeUnionState62_1187) + +def degreeUnionState62_1209 : List PrefixRegion := nextRegions 12 (liveRegions 13 49 13 degreeUnionState62_1121) + +def degreeUnionState62_1210 : List PrefixRegion := nextRegions 4 (liveRegions 12 37 12 degreeUnionState62_1209) + +def degreeUnionState62_1211 : List PrefixRegion := nextRegions 5 (liveRegions 12 37 12 degreeUnionState62_1209) + +def degreeUnionState62_1212 : List PrefixRegion := nextRegions 6 (liveRegions 12 37 12 degreeUnionState62_1209) + +def degreeUnionState62_1213 : List PrefixRegion := nextRegions 7 (liveRegions 12 37 12 degreeUnionState62_1209) + +def degreeUnionState62_1214 : List PrefixRegion := nextRegions 8 (liveRegions 12 37 12 degreeUnionState62_1209) + +def degreeUnionState62_1215 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 8 degreeUnionState62_1214) + +def degreeUnionState62_1216 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 8 degreeUnionState62_1214) + +def degreeUnionState62_1217 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 8 degreeUnionState62_1214) + +def degreeUnionState62_1218 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 8 degreeUnionState62_1214) + +def degreeUnionState62_1219 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 8 degreeUnionState62_1214) + +def degreeUnionState62_1220 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 8 degreeUnionState62_1214) + +def degreeUnionState62_1221 : List PrefixRegion := nextRegions 9 (liveRegions 12 37 12 degreeUnionState62_1209) + +def degreeUnionState62_1222 : List PrefixRegion := nextRegions 10 (liveRegions 12 37 12 degreeUnionState62_1209) + +def degreeUnionState62_1223 : List PrefixRegion := nextRegions 11 (liveRegions 12 37 12 degreeUnionState62_1209) + +def degreeUnionState62_1224 : List PrefixRegion := nextRegions 12 (liveRegions 12 37 12 degreeUnionState62_1209) + +def degreeUnionState62_1225 : List PrefixRegion := nextRegions 13 (liveRegions 13 49 13 degreeUnionState62_1121) + +def degreeUnionState62_1226 : List PrefixRegion := nextRegions 3 (liveRegions 12 36 13 degreeUnionState62_1225) + +def degreeUnionState62_1227 : List PrefixRegion := nextRegions 4 (liveRegions 12 36 13 degreeUnionState62_1225) + +def degreeUnionState62_1228 : List PrefixRegion := nextRegions 5 (liveRegions 12 36 13 degreeUnionState62_1225) + +def degreeUnionState62_1229 : List PrefixRegion := nextRegions 6 (liveRegions 12 36 13 degreeUnionState62_1225) + +def degreeUnionState62_1230 : List PrefixRegion := nextRegions 7 (liveRegions 12 36 13 degreeUnionState62_1225) + +def degreeUnionState62_1231 : List PrefixRegion := nextRegions 8 (liveRegions 12 36 13 degreeUnionState62_1225) + +def degreeUnionState62_1232 : List PrefixRegion := nextRegions 9 (liveRegions 12 36 13 degreeUnionState62_1225) + +def degreeUnionState62_1233 : List PrefixRegion := nextRegions 10 (liveRegions 12 36 13 degreeUnionState62_1225) + +def degreeUnionState62_1234 : List PrefixRegion := nextRegions 11 (liveRegions 12 36 13 degreeUnionState62_1225) + +def degreeUnionState62_1235 : List PrefixRegion := nextRegions 12 (liveRegions 12 36 13 degreeUnionState62_1225) + +def degreeUnionState62_1236 : List PrefixRegion := nextRegions 13 (liveRegions 12 36 13 degreeUnionState62_1225) + +def degreeUnionState62_1237 : List PrefixRegion := nextRegions 14 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1238 : List PrefixRegion := nextRegions 4 (liveRegions 13 48 14 degreeUnionState62_1237) + +def degreeUnionState62_1239 : List PrefixRegion := nextRegions 5 (liveRegions 13 48 14 degreeUnionState62_1237) + +def degreeUnionState62_1240 : List PrefixRegion := nextRegions 6 (liveRegions 13 48 14 degreeUnionState62_1237) + +def degreeUnionState62_1241 : List PrefixRegion := nextRegions 7 (liveRegions 13 48 14 degreeUnionState62_1237) + +def degreeUnionState62_1242 : List PrefixRegion := nextRegions 8 (liveRegions 13 48 14 degreeUnionState62_1237) + +def degreeUnionState62_1243 : List PrefixRegion := nextRegions 4 (liveRegions 12 40 8 degreeUnionState62_1242) + +def degreeUnionState62_1244 : List PrefixRegion := nextRegions 5 (liveRegions 12 40 8 degreeUnionState62_1242) + +def degreeUnionState62_1245 : List PrefixRegion := nextRegions 6 (liveRegions 12 40 8 degreeUnionState62_1242) + +def degreeUnionState62_1246 : List PrefixRegion := nextRegions 7 (liveRegions 12 40 8 degreeUnionState62_1242) + +def degreeUnionState62_1247 : List PrefixRegion := nextRegions 8 (liveRegions 12 40 8 degreeUnionState62_1242) + +def degreeUnionState62_1248 : List PrefixRegion := nextRegions 3 (liveRegions 11 32 8 degreeUnionState62_1247) + +def degreeUnionState62_1249 : List PrefixRegion := nextRegions 4 (liveRegions 11 32 8 degreeUnionState62_1247) + +def degreeUnionState62_1250 : List PrefixRegion := nextRegions 5 (liveRegions 11 32 8 degreeUnionState62_1247) + +def degreeUnionState62_1251 : List PrefixRegion := nextRegions 6 (liveRegions 11 32 8 degreeUnionState62_1247) + +def degreeUnionState62_1252 : List PrefixRegion := nextRegions 7 (liveRegions 11 32 8 degreeUnionState62_1247) + +def degreeUnionState62_1253 : List PrefixRegion := nextRegions 8 (liveRegions 11 32 8 degreeUnionState62_1247) + +def degreeUnionState62_1254 : List PrefixRegion := nextRegions 9 (liveRegions 13 48 14 degreeUnionState62_1237) + +def degreeUnionState62_1255 : List PrefixRegion := nextRegions 4 (liveRegions 12 39 9 degreeUnionState62_1254) + +def degreeUnionState62_1256 : List PrefixRegion := nextRegions 5 (liveRegions 12 39 9 degreeUnionState62_1254) + +def degreeUnionState62_1257 : List PrefixRegion := nextRegions 6 (liveRegions 12 39 9 degreeUnionState62_1254) + +def degreeUnionState62_1258 : List PrefixRegion := nextRegions 7 (liveRegions 12 39 9 degreeUnionState62_1254) + +def degreeUnionState62_1259 : List PrefixRegion := nextRegions 8 (liveRegions 12 39 9 degreeUnionState62_1254) + +def degreeUnionState62_1260 : List PrefixRegion := nextRegions 3 (liveRegions 11 31 8 degreeUnionState62_1259) + +def degreeUnionState62_1261 : List PrefixRegion := nextRegions 4 (liveRegions 11 31 8 degreeUnionState62_1259) + +def degreeUnionState62_1262 : List PrefixRegion := nextRegions 5 (liveRegions 11 31 8 degreeUnionState62_1259) + +def degreeUnionState62_1263 : List PrefixRegion := nextRegions 6 (liveRegions 11 31 8 degreeUnionState62_1259) + +def degreeUnionState62_1264 : List PrefixRegion := nextRegions 7 (liveRegions 11 31 8 degreeUnionState62_1259) + +def degreeUnionState62_1265 : List PrefixRegion := nextRegions 8 (liveRegions 11 31 8 degreeUnionState62_1259) + +def degreeUnionState62_1266 : List PrefixRegion := nextRegions 9 (liveRegions 12 39 9 degreeUnionState62_1254) + +def degreeUnionState62_1267 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 9 degreeUnionState62_1266) + +def degreeUnionState62_1268 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 9 degreeUnionState62_1266) + +def degreeUnionState62_1269 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 9 degreeUnionState62_1266) + +def degreeUnionState62_1270 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 9 degreeUnionState62_1266) + +def degreeUnionState62_1271 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 9 degreeUnionState62_1266) + +def degreeUnionState62_1272 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 9 degreeUnionState62_1266) + +def degreeUnionState62_1273 : List PrefixRegion := nextRegions 9 (liveRegions 11 30 9 degreeUnionState62_1266) + +def degreeUnionState62_1274 : List PrefixRegion := nextRegions 10 (liveRegions 13 48 14 degreeUnionState62_1237) + +def degreeUnionState62_1275 : List PrefixRegion := nextRegions 4 (liveRegions 12 38 10 degreeUnionState62_1274) + +def degreeUnionState62_1276 : List PrefixRegion := nextRegions 5 (liveRegions 12 38 10 degreeUnionState62_1274) + +def degreeUnionState62_1277 : List PrefixRegion := nextRegions 6 (liveRegions 12 38 10 degreeUnionState62_1274) + +def degreeUnionState62_1278 : List PrefixRegion := nextRegions 7 (liveRegions 12 38 10 degreeUnionState62_1274) + +def degreeUnionState62_1279 : List PrefixRegion := nextRegions 8 (liveRegions 12 38 10 degreeUnionState62_1274) + +def degreeUnionState62_1280 : List PrefixRegion := nextRegions 3 (liveRegions 11 30 8 degreeUnionState62_1279) + +def degreeUnionState62_1281 : List PrefixRegion := nextRegions 4 (liveRegions 11 30 8 degreeUnionState62_1279) + +def degreeUnionState62_1282 : List PrefixRegion := nextRegions 5 (liveRegions 11 30 8 degreeUnionState62_1279) + +def degreeUnionState62_1283 : List PrefixRegion := nextRegions 6 (liveRegions 11 30 8 degreeUnionState62_1279) + +def degreeUnionState62_1284 : List PrefixRegion := nextRegions 7 (liveRegions 11 30 8 degreeUnionState62_1279) + +def degreeUnionState62_1285 : List PrefixRegion := nextRegions 8 (liveRegions 11 30 8 degreeUnionState62_1279) + +def degreeUnionState62_1286 : List PrefixRegion := nextRegions 9 (liveRegions 12 38 10 degreeUnionState62_1274) + +def degreeUnionState62_1287 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 9 degreeUnionState62_1286) + +def degreeUnionState62_1288 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 9 degreeUnionState62_1286) + +def degreeUnionState62_1289 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 9 degreeUnionState62_1286) + +def degreeUnionState62_1290 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 9 degreeUnionState62_1286) + +def degreeUnionState62_1291 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 9 degreeUnionState62_1286) + +def degreeUnionState62_1292 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 9 degreeUnionState62_1286) + +def degreeUnionState62_1293 : List PrefixRegion := nextRegions 9 (liveRegions 11 29 9 degreeUnionState62_1286) + +def degreeUnionState62_1294 : List PrefixRegion := nextRegions 10 (liveRegions 12 38 10 degreeUnionState62_1274) + +def degreeUnionState62_1295 : List PrefixRegion := nextRegions 11 (liveRegions 13 48 14 degreeUnionState62_1237) + +def degreeUnionState62_1296 : List PrefixRegion := nextRegions 4 (liveRegions 12 37 11 degreeUnionState62_1295) + +def degreeUnionState62_1297 : List PrefixRegion := nextRegions 5 (liveRegions 12 37 11 degreeUnionState62_1295) + +def degreeUnionState62_1298 : List PrefixRegion := nextRegions 6 (liveRegions 12 37 11 degreeUnionState62_1295) + +def degreeUnionState62_1299 : List PrefixRegion := nextRegions 7 (liveRegions 12 37 11 degreeUnionState62_1295) + +def degreeUnionState62_1300 : List PrefixRegion := nextRegions 8 (liveRegions 12 37 11 degreeUnionState62_1295) + +def degreeUnionState62_1301 : List PrefixRegion := nextRegions 3 (liveRegions 11 29 8 degreeUnionState62_1300) + +def degreeUnionState62_1302 : List PrefixRegion := nextRegions 4 (liveRegions 11 29 8 degreeUnionState62_1300) + +def degreeUnionState62_1303 : List PrefixRegion := nextRegions 5 (liveRegions 11 29 8 degreeUnionState62_1300) + +def degreeUnionState62_1304 : List PrefixRegion := nextRegions 6 (liveRegions 11 29 8 degreeUnionState62_1300) + +def degreeUnionState62_1305 : List PrefixRegion := nextRegions 7 (liveRegions 11 29 8 degreeUnionState62_1300) + +def degreeUnionState62_1306 : List PrefixRegion := nextRegions 8 (liveRegions 11 29 8 degreeUnionState62_1300) + +def degreeUnionState62_1307 : List PrefixRegion := nextRegions 9 (liveRegions 12 37 11 degreeUnionState62_1295) + +def degreeUnionState62_1308 : List PrefixRegion := nextRegions 10 (liveRegions 12 37 11 degreeUnionState62_1295) + +def degreeUnionState62_1309 : List PrefixRegion := nextRegions 11 (liveRegions 12 37 11 degreeUnionState62_1295) + +def degreeUnionState62_1310 : List PrefixRegion := nextRegions 12 (liveRegions 13 48 14 degreeUnionState62_1237) + +def degreeUnionState62_1311 : List PrefixRegion := nextRegions 3 (liveRegions 12 36 12 degreeUnionState62_1310) + +def degreeUnionState62_1312 : List PrefixRegion := nextRegions 4 (liveRegions 12 36 12 degreeUnionState62_1310) + +def degreeUnionState62_1313 : List PrefixRegion := nextRegions 5 (liveRegions 12 36 12 degreeUnionState62_1310) + +def degreeUnionState62_1314 : List PrefixRegion := nextRegions 6 (liveRegions 12 36 12 degreeUnionState62_1310) + +def degreeUnionState62_1315 : List PrefixRegion := nextRegions 7 (liveRegions 12 36 12 degreeUnionState62_1310) + +def degreeUnionState62_1316 : List PrefixRegion := nextRegions 8 (liveRegions 12 36 12 degreeUnionState62_1310) + +def degreeUnionState62_1317 : List PrefixRegion := nextRegions 9 (liveRegions 12 36 12 degreeUnionState62_1310) + +def degreeUnionState62_1318 : List PrefixRegion := nextRegions 10 (liveRegions 12 36 12 degreeUnionState62_1310) + +def degreeUnionState62_1319 : List PrefixRegion := nextRegions 11 (liveRegions 12 36 12 degreeUnionState62_1310) + +def degreeUnionState62_1320 : List PrefixRegion := nextRegions 12 (liveRegions 12 36 12 degreeUnionState62_1310) + +def degreeUnionState62_1321 : List PrefixRegion := nextRegions 13 (liveRegions 13 48 14 degreeUnionState62_1237) + +def degreeUnionState62_1322 : List PrefixRegion := nextRegions 14 (liveRegions 13 48 14 degreeUnionState62_1237) + +def degreeUnionState62_1323 : List PrefixRegion := nextRegions 15 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1324 : List PrefixRegion := nextRegions 16 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1325 : List PrefixRegion := nextRegions 17 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1326 : List PrefixRegion := nextRegions 18 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1327 : List PrefixRegion := nextRegions 19 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1328 : List PrefixRegion := nextRegions 20 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1329 : List PrefixRegion := nextRegions 21 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1330 : List PrefixRegion := nextRegions 22 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1331 : List PrefixRegion := nextRegions 23 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1332 : List PrefixRegion := nextRegions 24 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1333 : List PrefixRegion := nextRegions 25 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1334 : List PrefixRegion := nextRegions 26 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1335 : List PrefixRegion := nextRegions 27 (liveRegions 14 62 28 degreeHalfRegions62) + +def degreeUnionState62_1336 : List PrefixRegion := nextRegions 28 (liveRegions 14 62 28 degreeHalfRegions62) + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/EightSplitCertificate.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/EightSplitCertificate.lean index 852b5c208fb5b4d86260f8619aec4fe6610ddb50..4ca68d94926278487c2d6ff4ef2e1956d6686409 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/EightSplitCertificate.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/EightSplitCertificate.lean @@ -1,32 +1,32 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomainsCore -import OAI.RepresentationTheory.UniversalSquare.Support.NumericalSupport - -namespace OAI - -/-! Eight Split Certificate. -/ - -section - -open Saxl Saxl.Columns -namespace UniversalTensorSquare - -def eightPlaceB10 : Equiv.Perm (Fin 8) := Equiv.swap 0 3 * (Equiv.swap 1 7 * (Equiv.swap 3 6 * (Equiv.swap 1 4 * (Equiv.swap 0 5)))) - -def eightPlaceT10 : Equiv.Perm (Fin 8) := Equiv.swap 2 5 * (Equiv.swap 2 4 * (Equiv.swap 1 6 * (Equiv.swap 0 7))) - -def eightFlag10 (r a b : ℕ) : ℤ := - if (r,a,b) ∈ ([(0,0,0),(0,2,1),(0,3,3),(1,0,0),(1,1,0),(2,1,1),(3,0,2)] : List (ℕ × ℕ × ℕ)) then 1 else 0 - -lemma eightCertificate10 : contractionInteger [4,2,1,1] [4,2,1,1] [4,2,1,1] - (Equiv.refl (Fin 8)) eightPlaceB10 eightPlaceT10 eightFlag10 = -4 := by - unfold eightFlag10 - simp_rw [← List.mem_toFinset] - erw [contractionInteger_compact] - decide +kernel - -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomainsCore +import OAI.RepresentationTheory.UniversalSquare.Support.NumericalSupport + +namespace OAI + +/-! Eight Split Certificate. -/ + +section + +open Saxl Saxl.Columns +namespace UniversalTensorSquare + +def eightPlaceB10 : Equiv.Perm (Fin 8) := Equiv.swap 0 3 * (Equiv.swap 1 7 * (Equiv.swap 3 6 * (Equiv.swap 1 4 * (Equiv.swap 0 5)))) + +def eightPlaceT10 : Equiv.Perm (Fin 8) := Equiv.swap 2 5 * (Equiv.swap 2 4 * (Equiv.swap 1 6 * (Equiv.swap 0 7))) + +def eightFlag10 (r a b : ℕ) : ℤ := + if (r,a,b) ∈ ([(0,0,0),(0,2,1),(0,3,3),(1,0,0),(1,1,0),(2,1,1),(3,0,2)] : List (ℕ × ℕ × ℕ)) then 1 else 0 + +lemma eightCertificate10 : contractionInteger [4,2,1,1] [4,2,1,1] [4,2,1,1] + (Equiv.refl (Fin 8)) eightPlaceB10 eightPlaceT10 eightFlag10 = -4 := by + unfold eightFlag10 + simp_rw [← List.mem_toFinset] + erw [contractionInteger_compact] + decide +kernel + +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree11.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree11.lean index 126ef4bbd4006f47b29e9537a39f603791b2a711..c04772d8a801cd4ea273da2f9ca20adbdbb6cf3d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree11.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree11.lean @@ -1,72 +1,72 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_0 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_1 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_2 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_3 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_4 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_5 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_6 -import OAI.RepresentationTheory.UniversalSquare.Support.FiniteRowSquares - -namespace OAI - -/-! Numerical Degree 11. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallKeys11 : List (List ℕ) := [[11],[6,1,1,1,1,1],[5,3,1,1,1],[6,2,1,1,1],[7,1,1,1,1],[5,2,2,2],[4,3,3,1],[4,4,2,1],[5,3,2,1],[6,2,2,1],[5,4,1,1],[6,3,1,1],[7,2,1,1],[8,1,1,1],[4,4,3],[5,3,3],[5,4,2],[6,3,2],[7,2,2],[5,5,1],[6,4,1],[7,3,1],[8,2,1],[9,1,1],[6,5],[7,4],[8,3],[9,2],[10,1]] -lemma smallCover11 : ∀ rs ∈ rowsWithin 11 [] [], - rs ∈ smallKeys11 ∨ transposeRows rs ∈ smallKeys11 := by - decide +kernel -lemma smallSupports11 : ∀ q ∈ smallKeys11, RowSquare [4,3,3,1] q := by - intro q hq - simp only [smallKeys11, List.mem_cons, List.not_mem_nil, or_false] at hq - rcases hq with rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl - · exact rowSquare_trivial _ (by decide) - · exact smallSupport11_0 - · exact smallSupport11_1 - · exact smallSupport11_2 - · exact smallSupport11_3 - · exact smallSupport11_4 - · exact smallSupport11_5 - · exact smallSupport11_6 - · exact smallSupport11_7 - · exact smallSupport11_8 - · exact smallSupport11_9 - · exact smallSupport11_10 - · exact smallSupport11_11 - · exact smallSupport11_12 - · exact smallSupport11_13 - · exact smallSupport11_14 - · exact smallSupport11_15 - · exact smallSupport11_16 - · exact smallSupport11_17 - · exact smallSupport11_18 - · exact smallSupport11_19 - · exact smallSupport11_20 - · exact smallSupport11_21 - · exact smallSupport11_22 - · exact smallSupport11_23 - · exact smallSupport11_24 - · exact smallSupport11_25 - · exact smallSupport11_26 - · exact smallSupport11_27 - -lemma degreeCard11 : (rowDiagram [4,3,3,1]).card = 11 := rowDiagram_card _ - -lemma degree_pos11 (μ : YoungDiagram) (hμ : μ.card = 11) : - 0 < kronecker (canonicalTableau (rowDiagram [4,3,3,1]) degreeCard11) - (canonicalTableau (rowDiagram [4,3,3,1]) degreeCard11) (canonicalTableau μ hμ) := by - exact (rowSquare_of_exhaustion (by decide) (by decide) (by decide) - smallKeys11 smallSupports11 smallCover11 μ hμ).pos _ _ - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_0 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_1 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_2 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_3 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_4 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_5 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts11_6 +import OAI.RepresentationTheory.UniversalSquare.Support.FiniteRowSquares + +namespace OAI + +/-! Numerical Degree 11. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallKeys11 : List (List ℕ) := [[11],[6,1,1,1,1,1],[5,3,1,1,1],[6,2,1,1,1],[7,1,1,1,1],[5,2,2,2],[4,3,3,1],[4,4,2,1],[5,3,2,1],[6,2,2,1],[5,4,1,1],[6,3,1,1],[7,2,1,1],[8,1,1,1],[4,4,3],[5,3,3],[5,4,2],[6,3,2],[7,2,2],[5,5,1],[6,4,1],[7,3,1],[8,2,1],[9,1,1],[6,5],[7,4],[8,3],[9,2],[10,1]] +lemma smallCover11 : ∀ rs ∈ rowsWithin 11 [] [], + rs ∈ smallKeys11 ∨ transposeRows rs ∈ smallKeys11 := by + decide +kernel +lemma smallSupports11 : ∀ q ∈ smallKeys11, RowSquare [4,3,3,1] q := by + intro q hq + simp only [smallKeys11, List.mem_cons, List.not_mem_nil, or_false] at hq + rcases hq with rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl + · exact rowSquare_trivial _ (by decide) + · exact smallSupport11_0 + · exact smallSupport11_1 + · exact smallSupport11_2 + · exact smallSupport11_3 + · exact smallSupport11_4 + · exact smallSupport11_5 + · exact smallSupport11_6 + · exact smallSupport11_7 + · exact smallSupport11_8 + · exact smallSupport11_9 + · exact smallSupport11_10 + · exact smallSupport11_11 + · exact smallSupport11_12 + · exact smallSupport11_13 + · exact smallSupport11_14 + · exact smallSupport11_15 + · exact smallSupport11_16 + · exact smallSupport11_17 + · exact smallSupport11_18 + · exact smallSupport11_19 + · exact smallSupport11_20 + · exact smallSupport11_21 + · exact smallSupport11_22 + · exact smallSupport11_23 + · exact smallSupport11_24 + · exact smallSupport11_25 + · exact smallSupport11_26 + · exact smallSupport11_27 + +lemma degreeCard11 : (rowDiagram [4,3,3,1]).card = 11 := rowDiagram_card _ + +lemma degree_pos11 (μ : YoungDiagram) (hμ : μ.card = 11) : + 0 < kronecker (canonicalTableau (rowDiagram [4,3,3,1]) degreeCard11) + (canonicalTableau (rowDiagram [4,3,3,1]) degreeCard11) (canonicalTableau μ hμ) := by + exact (rowSquare_of_exhaustion (by decide) (by decide) (by decide) + smallKeys11 smallSupports11 smallCover11 μ hμ).pos _ _ + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree112.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree112.lean index 5361c06dfef519741821c258f85a79cf49440a1d..8777084acd365e562c3c7fb8675a04179eb89adc 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree112.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree112.lean @@ -1,218 +1,218 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 112. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard112 : (candidate 12 8 1).card = 112 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan112_0 : PackingPlan := (.join (.twoPaths 19 [11,11,10,10]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 9 3 [11,10])))))) -def degreeRows112_0 : List ℕ := [11,11,11,10,10,10,5,5,5,4,4,4,4,4,3,3,3,3,2] - -lemma degreeCone112_0 (μ : YoungDiagram) (hμ : μ.card = 112) - (hd : RowsDom μ.rowLens degreeRows112_0) : SquareOccurs (candidate 12 8 1) μ := by - exact candidate_cone (by decide) degreeCard112 degreePlan112_0 degreeRows112_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan112_1 : PackingPlan := (.join (.twoPaths 19 [11,11,10,10]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 9 2)))))) -def degreeRows112_1 : List ℕ := [18,11,11,10,10,5,5,5,4,4,4,4,3,3,3,3,2,2,2,2,1] - -lemma degreeCone112_1 (μ : YoungDiagram) (hμ : μ.card = 112) - (hd : RowsDom μ.rowLens degreeRows112_1) : SquareOccurs (candidate 12 8 1) μ := by - exact candidate_cone (by decide) degreeCard112 degreePlan112_1 degreeRows112_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs112 : List (List ℕ) := [degreeRows112_1] - -lemma degreeCones112 : ∀ q ∈ degreeQs112, ∀ μ : YoungDiagram, μ.card = 112 → - RowsDom μ.rowLens q → SquareOccurs (candidate 12 8 1) μ := by - intro q hq - simp only [degreeQs112,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone112_1 - -abbrev degreeP112 := ResidualProperty 12 17 degreeQs112 [] - -lemma degreeCheck112_0_0 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 1 1 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_0_1 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 1 2 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_0_2 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 1 3 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_0_3 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 1 4 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_0_4 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 1 5 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_1_0 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 2 1 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_1_1 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 2 2 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_1_2 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 2 3 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_1_3 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 2 4 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_1_4 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 2 5 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_2_0 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 3 1 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_2_1 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 3 2 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_2_2 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 3 3 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_2_3 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 3 4 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_2_4 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 3 5 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_3_0 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 4 1 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_3_1 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 4 2 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_3_2 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 4 3 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_3_3 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 4 4 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_3_4 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 4 5 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_4_0 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 5 1 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_4_1 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 5 2 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_4_2 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 5 3 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_4_3 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 5 4 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112_4_4 : - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 5 5 (a+1) (c+1) degreeRows112_0 degreeP112 := by - decide +kernel - -lemma degreeCheck112 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, - residualCheck 112 12 17 (d+1) (e+1) (a+1) (c+1) degreeRows112_0 degreeP112 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck112_0_0 - · exact degreeCheck112_0_1 - · exact degreeCheck112_0_2 - · exact degreeCheck112_0_3 - · exact degreeCheck112_0_4 - · exact degreeCheck112_1_0 - · exact degreeCheck112_1_1 - · exact degreeCheck112_1_2 - · exact degreeCheck112_1_3 - · exact degreeCheck112_1_4 - · exact degreeCheck112_2_0 - · exact degreeCheck112_2_1 - · exact degreeCheck112_2_2 - · exact degreeCheck112_2_3 - · exact degreeCheck112_2_4 - · exact degreeCheck112_3_0 - · exact degreeCheck112_3_1 - · exact degreeCheck112_3_2 - · exact degreeCheck112_3_3 - · exact degreeCheck112_3_4 - · exact degreeCheck112_4_0 - · exact degreeCheck112_4_1 - · exact degreeCheck112_4_2 - · exact degreeCheck112_4_3 - · exact degreeCheck112_4_4 - -lemma degree_pos112 (μ : YoungDiagram) (hμ : μ.card = 112) : - 0 < kronecker (canonicalTableau (candidate 12 8 1) degreeCard112) - (canonicalTableau (candidate 12 8 1) degreeCard112) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 17) (by decide) (by decide) rfl (by decide) - degreeCard112 degreeRows112_0 (by decide) (by decide) - degreePlan112_0 (by decide) (by decide) (by decide) (by decide) degreeP112 ?_ - degreeCheck112 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard112 rfl degreeCones112 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 112. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard112 : (candidate 12 8 1).card = 112 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan112_0 : PackingPlan := (.join (.twoPaths 19 [11,11,10,10]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 9 3 [11,10])))))) +def degreeRows112_0 : List ℕ := [11,11,11,10,10,10,5,5,5,4,4,4,4,4,3,3,3,3,2] + +lemma degreeCone112_0 (μ : YoungDiagram) (hμ : μ.card = 112) + (hd : RowsDom μ.rowLens degreeRows112_0) : SquareOccurs (candidate 12 8 1) μ := by + exact candidate_cone (by decide) degreeCard112 degreePlan112_0 degreeRows112_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan112_1 : PackingPlan := (.join (.twoPaths 19 [11,11,10,10]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 9 2)))))) +def degreeRows112_1 : List ℕ := [18,11,11,10,10,5,5,5,4,4,4,4,3,3,3,3,2,2,2,2,1] + +lemma degreeCone112_1 (μ : YoungDiagram) (hμ : μ.card = 112) + (hd : RowsDom μ.rowLens degreeRows112_1) : SquareOccurs (candidate 12 8 1) μ := by + exact candidate_cone (by decide) degreeCard112 degreePlan112_1 degreeRows112_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs112 : List (List ℕ) := [degreeRows112_1] + +lemma degreeCones112 : ∀ q ∈ degreeQs112, ∀ μ : YoungDiagram, μ.card = 112 → + RowsDom μ.rowLens q → SquareOccurs (candidate 12 8 1) μ := by + intro q hq + simp only [degreeQs112,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone112_1 + +abbrev degreeP112 := ResidualProperty 12 17 degreeQs112 [] + +lemma degreeCheck112_0_0 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 1 1 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_0_1 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 1 2 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_0_2 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 1 3 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_0_3 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 1 4 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_0_4 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 1 5 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_1_0 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 2 1 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_1_1 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 2 2 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_1_2 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 2 3 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_1_3 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 2 4 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_1_4 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 2 5 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_2_0 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 3 1 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_2_1 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 3 2 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_2_2 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 3 3 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_2_3 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 3 4 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_2_4 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 3 5 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_3_0 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 4 1 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_3_1 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 4 2 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_3_2 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 4 3 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_3_3 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 4 4 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_3_4 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 4 5 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_4_0 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 5 1 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_4_1 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 5 2 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_4_2 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 5 3 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_4_3 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 5 4 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112_4_4 : + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 5 5 (a+1) (c+1) degreeRows112_0 degreeP112 := by + decide +kernel + +lemma degreeCheck112 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows112_0.length, ∀ c ∈ List.range degreeRows112_0.length, + residualCheck 112 12 17 (d+1) (e+1) (a+1) (c+1) degreeRows112_0 degreeP112 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck112_0_0 + · exact degreeCheck112_0_1 + · exact degreeCheck112_0_2 + · exact degreeCheck112_0_3 + · exact degreeCheck112_0_4 + · exact degreeCheck112_1_0 + · exact degreeCheck112_1_1 + · exact degreeCheck112_1_2 + · exact degreeCheck112_1_3 + · exact degreeCheck112_1_4 + · exact degreeCheck112_2_0 + · exact degreeCheck112_2_1 + · exact degreeCheck112_2_2 + · exact degreeCheck112_2_3 + · exact degreeCheck112_2_4 + · exact degreeCheck112_3_0 + · exact degreeCheck112_3_1 + · exact degreeCheck112_3_2 + · exact degreeCheck112_3_3 + · exact degreeCheck112_3_4 + · exact degreeCheck112_4_0 + · exact degreeCheck112_4_1 + · exact degreeCheck112_4_2 + · exact degreeCheck112_4_3 + · exact degreeCheck112_4_4 + +lemma degree_pos112 (μ : YoungDiagram) (hμ : μ.card = 112) : + 0 < kronecker (canonicalTableau (candidate 12 8 1) degreeCard112) + (canonicalTableau (candidate 12 8 1) degreeCard112) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 17) (by decide) (by decide) rfl (by decide) + degreeCard112 degreeRows112_0 (by decide) (by decide) + degreePlan112_0 (by decide) (by decide) (by decide) (by decide) degreeP112 ?_ + degreeCheck112 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard112 rfl degreeCones112 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree116.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree116.lean index da62a0bca1178eb94531b2da84cac020684a2342..b1f7dec1341fb1659ce3373629ecff1b45bd1f21 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree116.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree116.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks116 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof116 - -namespace OAI - -/-! Numerical Degree 116. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos116 (μ : YoungDiagram) (hμ : μ.card = 116) : - 0 < kronecker (canonicalTableau (candidate 12 9 1) degreeCard116) - (canonicalTableau (candidate 12 9 1) degreeCard116) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 19) (by decide) (by decide) rfl (by decide) - degreeCard116 degreeRows116_0 (by decide) (by decide) - degreePlan116_0 (by decide) (by decide) (by decide) (by decide) degreeP116 ?_ - degreeCheck116 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard116 rfl degreeCones116 - degreeTreeAll116 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks116 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof116 + +namespace OAI + +/-! Numerical Degree 116. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos116 (μ : YoungDiagram) (hμ : μ.card = 116) : + 0 < kronecker (canonicalTableau (candidate 12 9 1) degreeCard116) + (canonicalTableau (candidate 12 9 1) degreeCard116) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 19) (by decide) (by decide) rfl (by decide) + degreeCard116 degreeRows116_0 (by decide) (by decide) + degreePlan116_0 (by decide) (by decide) (by decide) (by decide) degreeP116 ?_ + degreeCheck116 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard116 rfl degreeCones116 + degreeTreeAll116 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree118.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree118.lean index 51dcbec373b8196d494e9a298ab5313df55639be..bd3d4a3a103188bd8feb36bcd6260cdcd5af45e8 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree118.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree118.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks118 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof118 - -namespace OAI - -/-! Numerical Degree 118. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos118 (μ : YoungDiagram) (hμ : μ.card = 118) : - 0 < kronecker (canonicalTableau (candidate 12 10 0) degreeCard118) - (canonicalTableau (candidate 12 10 0) degreeCard118) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 20) (by decide) (by decide) rfl (by decide) - degreeCard118 degreeRows118_0 (by decide) (by decide) - degreePlan118_0 (by decide) (by decide) (by decide) (by decide) degreeP118 ?_ - degreeCheck118 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard118 rfl degreeCones118 - degreeTreeAll118 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks118 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof118 + +namespace OAI + +/-! Numerical Degree 118. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos118 (μ : YoungDiagram) (hμ : μ.card = 118) : + 0 < kronecker (canonicalTableau (candidate 12 10 0) degreeCard118) + (canonicalTableau (candidate 12 10 0) degreeCard118) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 20) (by decide) (by decide) rfl (by decide) + degreeCard118 degreeRows118_0 (by decide) (by decide) + degreePlan118_0 (by decide) (by decide) (by decide) (by decide) degreeP118 ?_ + degreeCheck118 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard118 rfl degreeCones118 + degreeTreeAll118 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree12.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree12.lean index 657b25bedb0b9ff26645ae59e880455e9be47731..6b05963b2b0969128f961b0190808939aa44a282 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree12.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree12.lean @@ -1,218 +1,218 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.RowSquareTools - -namespace OAI - -/-! Numerical Degree 12. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard12 : (candidate 4 0 1).card = 12 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan12_0 : PackingPlan := (.join (.twoPaths 3 [3,3,2,2]) (.repeated 1 2)) -def degreeRows12_0 : List ℕ := [3,3,2,2,2] - -lemma degreeCone12_0 (μ : YoungDiagram) (hμ : μ.card = 12) - (hd : RowsDom μ.rowLens degreeRows12_0) : SquareOccurs (candidate 4 0 1) μ := by - exact candidate_cone (by decide) degreeCard12 degreePlan12_0 degreeRows12_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan12_1 : PackingPlan := (.join (.repeated 1 5) (.join (.neighbor 2 [2,1,1,1]) (.repeated 2 1))) -def degreeRows12_1 : List ℕ := [5,2,2,1,1,1] - -lemma degreeCone12_1 (μ : YoungDiagram) (hμ : μ.card = 12) - (hd : RowsDom μ.rowLens degreeRows12_1) : SquareOccurs (candidate 4 0 1) μ := by - exact candidate_cone (by decide) degreeCard12 degreePlan12_1 degreeRows12_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs12 : List (List ℕ) := [degreeRows12_1] - -lemma degreeCones12 : ∀ q ∈ degreeQs12, ∀ μ : YoungDiagram, μ.card = 12 → - RowsDom μ.rowLens q → SquareOccurs (candidate 4 0 1) μ := by - intro q hq - simp only [degreeQs12,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone12_1 - -abbrev degreeP12 := ResidualProperty 4 1 degreeQs12 [] - -lemma degreeCheck12_0_0 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 1 1 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_0_1 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 1 2 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_0_2 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 1 3 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_0_3 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 1 4 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_0_4 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 1 5 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_1_0 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 2 1 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_1_1 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 2 2 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_1_2 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 2 3 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_1_3 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 2 4 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_1_4 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 2 5 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_2_0 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 3 1 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_2_1 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 3 2 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_2_2 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 3 3 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_2_3 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 3 4 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_2_4 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 3 5 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_3_0 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 4 1 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_3_1 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 4 2 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_3_2 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 4 3 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_3_3 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 4 4 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_3_4 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 4 5 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_4_0 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 5 1 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_4_1 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 5 2 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_4_2 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 5 3 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_4_3 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 5 4 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12_4_4 : - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 5 5 (a+1) (c+1) degreeRows12_0 degreeP12 := by - decide +kernel - -lemma degreeCheck12 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, - residualCheck 12 4 1 (d+1) (e+1) (a+1) (c+1) degreeRows12_0 degreeP12 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck12_0_0 - · exact degreeCheck12_0_1 - · exact degreeCheck12_0_2 - · exact degreeCheck12_0_3 - · exact degreeCheck12_0_4 - · exact degreeCheck12_1_0 - · exact degreeCheck12_1_1 - · exact degreeCheck12_1_2 - · exact degreeCheck12_1_3 - · exact degreeCheck12_1_4 - · exact degreeCheck12_2_0 - · exact degreeCheck12_2_1 - · exact degreeCheck12_2_2 - · exact degreeCheck12_2_3 - · exact degreeCheck12_2_4 - · exact degreeCheck12_3_0 - · exact degreeCheck12_3_1 - · exact degreeCheck12_3_2 - · exact degreeCheck12_3_3 - · exact degreeCheck12_3_4 - · exact degreeCheck12_4_0 - · exact degreeCheck12_4_1 - · exact degreeCheck12_4_2 - · exact degreeCheck12_4_3 - · exact degreeCheck12_4_4 - -lemma degree_pos12 (μ : YoungDiagram) (hμ : μ.card = 12) : - 0 < kronecker (canonicalTableau (candidate 4 0 1) degreeCard12) - (canonicalTableau (candidate 4 0 1) degreeCard12) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) - degreeCard12 degreeRows12_0 (by decide) (by decide) - degreePlan12_0 (by decide) (by decide) (by decide) (by decide) degreeP12 ?_ - degreeCheck12 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard12 rfl degreeCones12 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.RowSquareTools + +namespace OAI + +/-! Numerical Degree 12. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard12 : (candidate 4 0 1).card = 12 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan12_0 : PackingPlan := (.join (.twoPaths 3 [3,3,2,2]) (.repeated 1 2)) +def degreeRows12_0 : List ℕ := [3,3,2,2,2] + +lemma degreeCone12_0 (μ : YoungDiagram) (hμ : μ.card = 12) + (hd : RowsDom μ.rowLens degreeRows12_0) : SquareOccurs (candidate 4 0 1) μ := by + exact candidate_cone (by decide) degreeCard12 degreePlan12_0 degreeRows12_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan12_1 : PackingPlan := (.join (.repeated 1 5) (.join (.neighbor 2 [2,1,1,1]) (.repeated 2 1))) +def degreeRows12_1 : List ℕ := [5,2,2,1,1,1] + +lemma degreeCone12_1 (μ : YoungDiagram) (hμ : μ.card = 12) + (hd : RowsDom μ.rowLens degreeRows12_1) : SquareOccurs (candidate 4 0 1) μ := by + exact candidate_cone (by decide) degreeCard12 degreePlan12_1 degreeRows12_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs12 : List (List ℕ) := [degreeRows12_1] + +lemma degreeCones12 : ∀ q ∈ degreeQs12, ∀ μ : YoungDiagram, μ.card = 12 → + RowsDom μ.rowLens q → SquareOccurs (candidate 4 0 1) μ := by + intro q hq + simp only [degreeQs12,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone12_1 + +abbrev degreeP12 := ResidualProperty 4 1 degreeQs12 [] + +lemma degreeCheck12_0_0 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 1 1 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_0_1 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 1 2 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_0_2 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 1 3 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_0_3 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 1 4 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_0_4 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 1 5 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_1_0 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 2 1 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_1_1 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 2 2 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_1_2 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 2 3 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_1_3 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 2 4 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_1_4 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 2 5 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_2_0 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 3 1 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_2_1 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 3 2 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_2_2 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 3 3 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_2_3 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 3 4 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_2_4 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 3 5 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_3_0 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 4 1 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_3_1 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 4 2 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_3_2 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 4 3 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_3_3 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 4 4 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_3_4 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 4 5 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_4_0 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 5 1 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_4_1 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 5 2 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_4_2 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 5 3 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_4_3 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 5 4 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12_4_4 : + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 5 5 (a+1) (c+1) degreeRows12_0 degreeP12 := by + decide +kernel + +lemma degreeCheck12 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows12_0.length, ∀ c ∈ List.range degreeRows12_0.length, + residualCheck 12 4 1 (d+1) (e+1) (a+1) (c+1) degreeRows12_0 degreeP12 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck12_0_0 + · exact degreeCheck12_0_1 + · exact degreeCheck12_0_2 + · exact degreeCheck12_0_3 + · exact degreeCheck12_0_4 + · exact degreeCheck12_1_0 + · exact degreeCheck12_1_1 + · exact degreeCheck12_1_2 + · exact degreeCheck12_1_3 + · exact degreeCheck12_1_4 + · exact degreeCheck12_2_0 + · exact degreeCheck12_2_1 + · exact degreeCheck12_2_2 + · exact degreeCheck12_2_3 + · exact degreeCheck12_2_4 + · exact degreeCheck12_3_0 + · exact degreeCheck12_3_1 + · exact degreeCheck12_3_2 + · exact degreeCheck12_3_3 + · exact degreeCheck12_3_4 + · exact degreeCheck12_4_0 + · exact degreeCheck12_4_1 + · exact degreeCheck12_4_2 + · exact degreeCheck12_4_3 + · exact degreeCheck12_4_4 + +lemma degree_pos12 (μ : YoungDiagram) (hμ : μ.card = 12) : + 0 < kronecker (canonicalTableau (candidate 4 0 1) degreeCard12) + (canonicalTableau (candidate 4 0 1) degreeCard12) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) + degreeCard12 degreeRows12_0 (by decide) (by decide) + degreePlan12_0 (by decide) (by decide) (by decide) (by decide) degreeP12 ?_ + degreeCheck12 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard12 rfl degreeCones12 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree13.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree13.lean index 40a9c40996e1dabfb74c2f8fe825ca72e0401306..82bd3b78061658ad8a1920a4a20896f031e07f08 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree13.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree13.lean @@ -1,101 +1,101 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.FiniteRowSquares -import OAI.RepresentationTheory.UniversalSquare.Finite.ChoiceCertificates13 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_1 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_2 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_3 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_4 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_5 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_6 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_7 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_8 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_9 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_10 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_11 -import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_12 - -namespace OAI - -/-! Numerical Degree 13. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallKeys13 : List (List ℕ) := [[13],[7,1,1,1,1,1,1],[6,3,1,1,1,1],[7,2,1,1,1,1],[8,1,1,1,1,1],[6,2,2,2,1],[5,3,3,1,1],[5,4,2,1,1],[6,3,2,1,1],[7,2,2,1,1],[5,5,1,1,1],[6,4,1,1,1],[7,3,1,1,1],[8,2,1,1,1],[9,1,1,1,1],[5,3,3,2],[5,4,2,2],[6,3,2,2],[7,2,2,2],[5,4,3,1],[6,3,3,1],[5,5,2,1],[6,4,2,1],[7,3,2,1],[8,2,2,1],[6,5,1,1],[7,4,1,1],[8,3,1,1],[9,2,1,1],[10,1,1,1],[7,3,3],[6,5,2],[7,4,2],[8,3,2],[9,2,2],[6,6,1],[7,5,1],[8,4,1],[9,3,1],[10,2,1],[11,1,1],[10,3],[12,1],[4,4,3,2],[4,4,4,1],[5,4,4],[5,5,3],[6,4,3],[7,6],[8,5],[9,4],[11,2]] -lemma smallCover13 : ∀ rs ∈ rowsWithin 13 [] [], - rs ∈ smallKeys13 ∨ transposeRows rs ∈ smallKeys13 := by - decide +kernel -lemma smallSupports13 : ∀ q ∈ smallKeys13, RowSquare [4,4,3,2] q := by - intro q hq - simp only [smallKeys13, List.mem_cons, List.not_mem_nil, or_false] at hq - rcases hq with rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl - · exact rowSquare_trivial _ (by decide) - · exact smallSupport13_0 - · exact smallSupport13_1 - · exact smallSupport13_2 - · exact smallSupport13_3 - · exact smallSupport13_4 - · exact smallSupport13_5 - · exact smallSupport13_6 - · exact smallSupport13_7 - · exact smallSupport13_8 - · exact smallSupport13_9 - · exact smallSupport13_10 - · exact smallSupport13_11 - · exact smallSupport13_12 - · exact smallSupport13_13 - · exact smallSupport13_14 - · exact smallSupport13_15 - · exact smallSupport13_16 - · exact smallSupport13_17 - · exact smallSupport13_18 - · exact smallSupport13_19 - · exact smallSupport13_20 - · exact smallSupport13_21 - · exact smallSupport13_22 - · exact smallSupport13_23 - · exact smallSupport13_24 - · exact smallSupport13_25 - · exact smallSupport13_26 - · exact smallSupport13_27 - · exact smallSupport13_28 - · exact smallSupport13_29 - · exact smallSupport13_30 - · exact smallSupport13_31 - · exact smallSupport13_32 - · exact smallSupport13_33 - · exact smallSupport13_34 - · exact smallSupport13_35 - · exact smallSupport13_36 - · exact smallSupport13_37 - · exact smallSupport13_38 - · exact smallSupport13_39 - · exact smallSupport13_40 - · exact smallSupport13_41 - · exact smallSupport13_42 - · exact smallSupport13_43 - · exact smallSupport13_44 - · exact smallSupport13_45 - · exact smallSupport13_46 - · exact smallSupport13_47 - · exact smallSupport13_48 - · exact smallSupport13_49 - · exact smallSupport13_50 - -lemma degreeCard13 : (rowDiagram [4,4,3,2]).card = 13 := rowDiagram_card _ - -lemma degree_pos13 (μ : YoungDiagram) (hμ : μ.card = 13) : - 0 < kronecker (canonicalTableau (rowDiagram [4,4,3,2]) degreeCard13) - (canonicalTableau (rowDiagram [4,4,3,2]) degreeCard13) (canonicalTableau μ hμ) := by - exact (rowSquare_of_exhaustion (by decide) (by decide) (by decide) - smallKeys13 smallSupports13 smallCover13 μ hμ).pos _ _ - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.FiniteRowSquares +import OAI.RepresentationTheory.UniversalSquare.Finite.ChoiceCertificates13 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_1 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_2 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_3 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_4 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_5 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_6 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_7 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_8 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_9 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_10 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_11 +import OAI.RepresentationTheory.UniversalSquare.Finite.SmallContracts13_12 + +namespace OAI + +/-! Numerical Degree 13. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallKeys13 : List (List ℕ) := [[13],[7,1,1,1,1,1,1],[6,3,1,1,1,1],[7,2,1,1,1,1],[8,1,1,1,1,1],[6,2,2,2,1],[5,3,3,1,1],[5,4,2,1,1],[6,3,2,1,1],[7,2,2,1,1],[5,5,1,1,1],[6,4,1,1,1],[7,3,1,1,1],[8,2,1,1,1],[9,1,1,1,1],[5,3,3,2],[5,4,2,2],[6,3,2,2],[7,2,2,2],[5,4,3,1],[6,3,3,1],[5,5,2,1],[6,4,2,1],[7,3,2,1],[8,2,2,1],[6,5,1,1],[7,4,1,1],[8,3,1,1],[9,2,1,1],[10,1,1,1],[7,3,3],[6,5,2],[7,4,2],[8,3,2],[9,2,2],[6,6,1],[7,5,1],[8,4,1],[9,3,1],[10,2,1],[11,1,1],[10,3],[12,1],[4,4,3,2],[4,4,4,1],[5,4,4],[5,5,3],[6,4,3],[7,6],[8,5],[9,4],[11,2]] +lemma smallCover13 : ∀ rs ∈ rowsWithin 13 [] [], + rs ∈ smallKeys13 ∨ transposeRows rs ∈ smallKeys13 := by + decide +kernel +lemma smallSupports13 : ∀ q ∈ smallKeys13, RowSquare [4,4,3,2] q := by + intro q hq + simp only [smallKeys13, List.mem_cons, List.not_mem_nil, or_false] at hq + rcases hq with rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl + · exact rowSquare_trivial _ (by decide) + · exact smallSupport13_0 + · exact smallSupport13_1 + · exact smallSupport13_2 + · exact smallSupport13_3 + · exact smallSupport13_4 + · exact smallSupport13_5 + · exact smallSupport13_6 + · exact smallSupport13_7 + · exact smallSupport13_8 + · exact smallSupport13_9 + · exact smallSupport13_10 + · exact smallSupport13_11 + · exact smallSupport13_12 + · exact smallSupport13_13 + · exact smallSupport13_14 + · exact smallSupport13_15 + · exact smallSupport13_16 + · exact smallSupport13_17 + · exact smallSupport13_18 + · exact smallSupport13_19 + · exact smallSupport13_20 + · exact smallSupport13_21 + · exact smallSupport13_22 + · exact smallSupport13_23 + · exact smallSupport13_24 + · exact smallSupport13_25 + · exact smallSupport13_26 + · exact smallSupport13_27 + · exact smallSupport13_28 + · exact smallSupport13_29 + · exact smallSupport13_30 + · exact smallSupport13_31 + · exact smallSupport13_32 + · exact smallSupport13_33 + · exact smallSupport13_34 + · exact smallSupport13_35 + · exact smallSupport13_36 + · exact smallSupport13_37 + · exact smallSupport13_38 + · exact smallSupport13_39 + · exact smallSupport13_40 + · exact smallSupport13_41 + · exact smallSupport13_42 + · exact smallSupport13_43 + · exact smallSupport13_44 + · exact smallSupport13_45 + · exact smallSupport13_46 + · exact smallSupport13_47 + · exact smallSupport13_48 + · exact smallSupport13_49 + · exact smallSupport13_50 + +lemma degreeCard13 : (rowDiagram [4,4,3,2]).card = 13 := rowDiagram_card _ + +lemma degree_pos13 (μ : YoungDiagram) (hμ : μ.card = 13) : + 0 < kronecker (canonicalTableau (rowDiagram [4,4,3,2]) degreeCard13) + (canonicalTableau (rowDiagram [4,4,3,2]) degreeCard13) (canonicalTableau μ hμ) := by + exact (rowSquare_of_exhaustion (by decide) (by decide) (by decide) + smallKeys13 smallSupports13 smallCover13 μ hμ).pos _ _ + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree14.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree14.lean index b3c4e28fc2c8bba0c0bab72ee3f6dbe3ca4b2a9e..10a7cdd20f0d2d9fdf2dffa22000c148f228ec65 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree14.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree14.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks14 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof14 - -namespace OAI - -/-! Numerical Degree 14. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos14 (μ : YoungDiagram) (hμ : μ.card = 14) : - 0 < kronecker (canonicalTableau (candidate 4 1 0) degreeCard14) - (canonicalTableau (candidate 4 1 0) degreeCard14) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 2) (by decide) (by decide) rfl (by decide) - degreeCard14 degreeRows14_0 (by decide) (by decide) - degreePlan14_0 (by decide) (by decide) (by decide) (by decide) degreeP14 ?_ - degreeCheck14 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard14 rfl degreeCones14 - degreeTreeAll14 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks14 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof14 + +namespace OAI + +/-! Numerical Degree 14. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos14 (μ : YoungDiagram) (hμ : μ.card = 14) : + 0 < kronecker (canonicalTableau (candidate 4 1 0) degreeCard14) + (canonicalTableau (candidate 4 1 0) degreeCard14) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 2) (by decide) (by decide) rfl (by decide) + degreeCard14 degreeRows14_0 (by decide) (by decide) + degreePlan14_0 (by decide) (by decide) (by decide) (by decide) degreeP14 ?_ + degreeCheck14 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard14 rfl degreeCones14 + degreeTreeAll14 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree151.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree151.lean index f638b50b33aad94c41ec09207a8c815c3093e8a8..3a6ae5a4d61b62b5fb7025c5aee572d4f25c6d90 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree151.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree151.lean @@ -1,218 +1,218 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 151. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard151 : (candidate 14 11 1).card = 151 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan151_0 : PackingPlan := (.join (.twoPaths 24 [13,13,13,13]) (.join (.neighbor 11 [6,6,6,5]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 12 3 [14,13]))))))) -def degreeRows151_0 : List ℕ := [14,13,13,13,13,13,6,6,6,5,5,5,5,4,4,4,4,4,3,3,3,3,2] - -lemma degreeCone151_0 (μ : YoungDiagram) (hμ : μ.card = 151) - (hd : RowsDom μ.rowLens degreeRows151_0) : SquareOccurs (candidate 14 11 1) μ := by - exact candidate_cone (by decide) degreeCard151 degreePlan151_0 degreeRows151_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan151_1 : PackingPlan := (.join (.twoPaths 24 [13,13,13,13]) (.join (.neighbor 11 [6,6,6,5]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 12 2))))))) -def degreeRows151_1 : List ℕ := [24,13,13,13,13,6,6,6,5,5,5,5,4,4,4,4,3,3,3,3,2,2,2,2,1] - -lemma degreeCone151_1 (μ : YoungDiagram) (hμ : μ.card = 151) - (hd : RowsDom μ.rowLens degreeRows151_1) : SquareOccurs (candidate 14 11 1) μ := by - exact candidate_cone (by decide) degreeCard151 degreePlan151_1 degreeRows151_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs151 : List (List ℕ) := [degreeRows151_1] - -lemma degreeCones151 : ∀ q ∈ degreeQs151, ∀ μ : YoungDiagram, μ.card = 151 → - RowsDom μ.rowLens q → SquareOccurs (candidate 14 11 1) μ := by - intro q hq - simp only [degreeQs151,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone151_1 - -abbrev degreeP151 := ResidualProperty 14 23 degreeQs151 [] - -lemma degreeCheck151_0_0 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 1 1 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_0_1 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 1 2 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_0_2 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 1 3 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_0_3 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 1 4 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_0_4 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 1 5 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_1_0 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 2 1 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_1_1 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 2 2 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_1_2 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 2 3 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_1_3 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 2 4 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_1_4 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 2 5 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_2_0 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 3 1 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_2_1 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 3 2 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_2_2 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 3 3 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_2_3 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 3 4 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_2_4 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 3 5 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_3_0 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 4 1 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_3_1 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 4 2 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_3_2 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 4 3 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_3_3 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 4 4 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_3_4 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 4 5 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_4_0 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 5 1 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_4_1 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 5 2 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_4_2 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 5 3 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_4_3 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 5 4 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151_4_4 : - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 5 5 (a+1) (c+1) degreeRows151_0 degreeP151 := by - decide +kernel - -lemma degreeCheck151 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, - residualCheck 151 14 23 (d+1) (e+1) (a+1) (c+1) degreeRows151_0 degreeP151 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck151_0_0 - · exact degreeCheck151_0_1 - · exact degreeCheck151_0_2 - · exact degreeCheck151_0_3 - · exact degreeCheck151_0_4 - · exact degreeCheck151_1_0 - · exact degreeCheck151_1_1 - · exact degreeCheck151_1_2 - · exact degreeCheck151_1_3 - · exact degreeCheck151_1_4 - · exact degreeCheck151_2_0 - · exact degreeCheck151_2_1 - · exact degreeCheck151_2_2 - · exact degreeCheck151_2_3 - · exact degreeCheck151_2_4 - · exact degreeCheck151_3_0 - · exact degreeCheck151_3_1 - · exact degreeCheck151_3_2 - · exact degreeCheck151_3_3 - · exact degreeCheck151_3_4 - · exact degreeCheck151_4_0 - · exact degreeCheck151_4_1 - · exact degreeCheck151_4_2 - · exact degreeCheck151_4_3 - · exact degreeCheck151_4_4 - -lemma degree_pos151 (μ : YoungDiagram) (hμ : μ.card = 151) : - 0 < kronecker (canonicalTableau (candidate 14 11 1) degreeCard151) - (canonicalTableau (candidate 14 11 1) degreeCard151) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 23) (by decide) (by decide) rfl (by decide) - degreeCard151 degreeRows151_0 (by decide) (by decide) - degreePlan151_0 (by decide) (by decide) (by decide) (by decide) degreeP151 ?_ - degreeCheck151 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard151 rfl degreeCones151 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 151. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard151 : (candidate 14 11 1).card = 151 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan151_0 : PackingPlan := (.join (.twoPaths 24 [13,13,13,13]) (.join (.neighbor 11 [6,6,6,5]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 12 3 [14,13]))))))) +def degreeRows151_0 : List ℕ := [14,13,13,13,13,13,6,6,6,5,5,5,5,4,4,4,4,4,3,3,3,3,2] + +lemma degreeCone151_0 (μ : YoungDiagram) (hμ : μ.card = 151) + (hd : RowsDom μ.rowLens degreeRows151_0) : SquareOccurs (candidate 14 11 1) μ := by + exact candidate_cone (by decide) degreeCard151 degreePlan151_0 degreeRows151_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan151_1 : PackingPlan := (.join (.twoPaths 24 [13,13,13,13]) (.join (.neighbor 11 [6,6,6,5]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 12 2))))))) +def degreeRows151_1 : List ℕ := [24,13,13,13,13,6,6,6,5,5,5,5,4,4,4,4,3,3,3,3,2,2,2,2,1] + +lemma degreeCone151_1 (μ : YoungDiagram) (hμ : μ.card = 151) + (hd : RowsDom μ.rowLens degreeRows151_1) : SquareOccurs (candidate 14 11 1) μ := by + exact candidate_cone (by decide) degreeCard151 degreePlan151_1 degreeRows151_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs151 : List (List ℕ) := [degreeRows151_1] + +lemma degreeCones151 : ∀ q ∈ degreeQs151, ∀ μ : YoungDiagram, μ.card = 151 → + RowsDom μ.rowLens q → SquareOccurs (candidate 14 11 1) μ := by + intro q hq + simp only [degreeQs151,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone151_1 + +abbrev degreeP151 := ResidualProperty 14 23 degreeQs151 [] + +lemma degreeCheck151_0_0 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 1 1 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_0_1 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 1 2 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_0_2 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 1 3 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_0_3 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 1 4 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_0_4 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 1 5 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_1_0 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 2 1 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_1_1 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 2 2 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_1_2 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 2 3 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_1_3 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 2 4 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_1_4 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 2 5 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_2_0 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 3 1 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_2_1 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 3 2 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_2_2 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 3 3 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_2_3 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 3 4 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_2_4 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 3 5 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_3_0 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 4 1 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_3_1 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 4 2 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_3_2 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 4 3 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_3_3 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 4 4 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_3_4 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 4 5 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_4_0 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 5 1 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_4_1 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 5 2 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_4_2 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 5 3 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_4_3 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 5 4 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151_4_4 : + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 5 5 (a+1) (c+1) degreeRows151_0 degreeP151 := by + decide +kernel + +lemma degreeCheck151 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows151_0.length, ∀ c ∈ List.range degreeRows151_0.length, + residualCheck 151 14 23 (d+1) (e+1) (a+1) (c+1) degreeRows151_0 degreeP151 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck151_0_0 + · exact degreeCheck151_0_1 + · exact degreeCheck151_0_2 + · exact degreeCheck151_0_3 + · exact degreeCheck151_0_4 + · exact degreeCheck151_1_0 + · exact degreeCheck151_1_1 + · exact degreeCheck151_1_2 + · exact degreeCheck151_1_3 + · exact degreeCheck151_1_4 + · exact degreeCheck151_2_0 + · exact degreeCheck151_2_1 + · exact degreeCheck151_2_2 + · exact degreeCheck151_2_3 + · exact degreeCheck151_2_4 + · exact degreeCheck151_3_0 + · exact degreeCheck151_3_1 + · exact degreeCheck151_3_2 + · exact degreeCheck151_3_3 + · exact degreeCheck151_3_4 + · exact degreeCheck151_4_0 + · exact degreeCheck151_4_1 + · exact degreeCheck151_4_2 + · exact degreeCheck151_4_3 + · exact degreeCheck151_4_4 + +lemma degree_pos151 (μ : YoungDiagram) (hμ : μ.card = 151) : + 0 < kronecker (canonicalTableau (candidate 14 11 1) degreeCard151) + (canonicalTableau (candidate 14 11 1) degreeCard151) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 23) (by decide) (by decide) rfl (by decide) + degreeCard151 degreeRows151_0 (by decide) (by decide) + degreePlan151_0 (by decide) (by decide) (by decide) (by decide) degreeP151 ?_ + degreeCheck151 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard151 rfl degreeCones151 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree16.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree16.lean index aa3c495a32e4486f51cca024ac1ef8d9d5ba86e8..c447b152cfdcc6b2dcf5b38031f228a038fa4fcf 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree16.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree16.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks16 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof16 - -namespace OAI - -/-! Numerical Degree 16. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos16 (μ : YoungDiagram) (hμ : μ.card = 16) : - 0 < kronecker (canonicalTableau (candidate 4 1 1) degreeCard16) - (canonicalTableau (candidate 4 1 1) degreeCard16) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 3) (by decide) (by decide) rfl (by decide) - degreeCard16 degreeRows16_0 (by decide) (by decide) - degreePlan16_0 (by decide) (by decide) (by decide) (by decide) degreeP16 ?_ - degreeCheck16 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard16 rfl degreeCones16 - degreeTreeAll16 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks16 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof16 + +namespace OAI + +/-! Numerical Degree 16. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos16 (μ : YoungDiagram) (hμ : μ.card = 16) : + 0 < kronecker (canonicalTableau (candidate 4 1 1) degreeCard16) + (canonicalTableau (candidate 4 1 1) degreeCard16) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 3) (by decide) (by decide) rfl (by decide) + degreeCard16 degreeRows16_0 (by decide) (by decide) + degreePlan16_0 (by decide) (by decide) (by decide) (by decide) degreeP16 ?_ + degreeCheck16 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard16 rfl degreeCones16 + degreeTreeAll16 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree17.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree17.lean index f1f786f864e66379f71b5dedbd315b7e6bb70dd4..2272d95fa9895b035452967c9fddaaeb2b0ad348 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree17.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree17.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 17. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard17 : (candidate 5 0 1).card = 17 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan17_0 : PackingPlan := (.join (.twoPaths 4 [3,3,3,3]) (.neighbor 2 [2,1,1,1])) -def degreeRows17_0 : List ℕ := [3,3,3,3,2,1,1,1] - -lemma degreeCone17_0 (μ : YoungDiagram) (hμ : μ.card = 17) - (hd : RowsDom μ.rowLens degreeRows17_0) : SquareOccurs (candidate 5 0 1) μ := by - exact candidate_cone (by decide) degreeCard17 degreePlan17_0 degreeRows17_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs17 : List (List ℕ) := [] - -lemma degreeCones17 : ∀ q ∈ degreeQs17, ∀ μ : YoungDiagram, μ.card = 17 → - RowsDom μ.rowLens q → SquareOccurs (candidate 5 0 1) μ := by - intro q hq - simp only [degreeQs17,List.not_mem_nil] at hq - -abbrev degreeP17 := ResidualProperty 5 1 degreeQs17 [] - -lemma degreeCheck17_0_0 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 1 1 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_0_1 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 1 2 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_0_2 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 1 3 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_0_3 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 1 4 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_0_4 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 1 5 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_1_0 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 2 1 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_1_1 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 2 2 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_1_2 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 2 3 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_1_3 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 2 4 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_1_4 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 2 5 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_2_0 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 3 1 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_2_1 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 3 2 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_2_2 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 3 3 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_2_3 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 3 4 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_2_4 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 3 5 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_3_0 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 4 1 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_3_1 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 4 2 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_3_2 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 4 3 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_3_3 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 4 4 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_3_4 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 4 5 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_4_0 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 5 1 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_4_1 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 5 2 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_4_2 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 5 3 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_4_3 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 5 4 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17_4_4 : - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 5 5 (a+1) (c+1) degreeRows17_0 degreeP17 := by - decide +kernel - -lemma degreeCheck17 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, - residualCheck 17 5 1 (d+1) (e+1) (a+1) (c+1) degreeRows17_0 degreeP17 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck17_0_0 - · exact degreeCheck17_0_1 - · exact degreeCheck17_0_2 - · exact degreeCheck17_0_3 - · exact degreeCheck17_0_4 - · exact degreeCheck17_1_0 - · exact degreeCheck17_1_1 - · exact degreeCheck17_1_2 - · exact degreeCheck17_1_3 - · exact degreeCheck17_1_4 - · exact degreeCheck17_2_0 - · exact degreeCheck17_2_1 - · exact degreeCheck17_2_2 - · exact degreeCheck17_2_3 - · exact degreeCheck17_2_4 - · exact degreeCheck17_3_0 - · exact degreeCheck17_3_1 - · exact degreeCheck17_3_2 - · exact degreeCheck17_3_3 - · exact degreeCheck17_3_4 - · exact degreeCheck17_4_0 - · exact degreeCheck17_4_1 - · exact degreeCheck17_4_2 - · exact degreeCheck17_4_3 - · exact degreeCheck17_4_4 - -lemma degree_pos17 (μ : YoungDiagram) (hμ : μ.card = 17) : - 0 < kronecker (canonicalTableau (candidate 5 0 1) degreeCard17) - (canonicalTableau (candidate 5 0 1) degreeCard17) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) - degreeCard17 degreeRows17_0 (by decide) (by decide) - degreePlan17_0 (by decide) (by decide) (by decide) (by decide) degreeP17 ?_ - degreeCheck17 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard17 rfl degreeCones17 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 17. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard17 : (candidate 5 0 1).card = 17 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan17_0 : PackingPlan := (.join (.twoPaths 4 [3,3,3,3]) (.neighbor 2 [2,1,1,1])) +def degreeRows17_0 : List ℕ := [3,3,3,3,2,1,1,1] + +lemma degreeCone17_0 (μ : YoungDiagram) (hμ : μ.card = 17) + (hd : RowsDom μ.rowLens degreeRows17_0) : SquareOccurs (candidate 5 0 1) μ := by + exact candidate_cone (by decide) degreeCard17 degreePlan17_0 degreeRows17_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs17 : List (List ℕ) := [] + +lemma degreeCones17 : ∀ q ∈ degreeQs17, ∀ μ : YoungDiagram, μ.card = 17 → + RowsDom μ.rowLens q → SquareOccurs (candidate 5 0 1) μ := by + intro q hq + simp only [degreeQs17,List.not_mem_nil] at hq + +abbrev degreeP17 := ResidualProperty 5 1 degreeQs17 [] + +lemma degreeCheck17_0_0 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 1 1 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_0_1 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 1 2 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_0_2 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 1 3 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_0_3 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 1 4 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_0_4 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 1 5 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_1_0 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 2 1 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_1_1 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 2 2 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_1_2 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 2 3 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_1_3 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 2 4 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_1_4 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 2 5 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_2_0 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 3 1 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_2_1 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 3 2 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_2_2 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 3 3 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_2_3 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 3 4 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_2_4 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 3 5 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_3_0 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 4 1 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_3_1 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 4 2 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_3_2 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 4 3 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_3_3 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 4 4 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_3_4 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 4 5 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_4_0 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 5 1 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_4_1 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 5 2 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_4_2 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 5 3 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_4_3 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 5 4 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17_4_4 : + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 5 5 (a+1) (c+1) degreeRows17_0 degreeP17 := by + decide +kernel + +lemma degreeCheck17 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows17_0.length, ∀ c ∈ List.range degreeRows17_0.length, + residualCheck 17 5 1 (d+1) (e+1) (a+1) (c+1) degreeRows17_0 degreeP17 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck17_0_0 + · exact degreeCheck17_0_1 + · exact degreeCheck17_0_2 + · exact degreeCheck17_0_3 + · exact degreeCheck17_0_4 + · exact degreeCheck17_1_0 + · exact degreeCheck17_1_1 + · exact degreeCheck17_1_2 + · exact degreeCheck17_1_3 + · exact degreeCheck17_1_4 + · exact degreeCheck17_2_0 + · exact degreeCheck17_2_1 + · exact degreeCheck17_2_2 + · exact degreeCheck17_2_3 + · exact degreeCheck17_2_4 + · exact degreeCheck17_3_0 + · exact degreeCheck17_3_1 + · exact degreeCheck17_3_2 + · exact degreeCheck17_3_3 + · exact degreeCheck17_3_4 + · exact degreeCheck17_4_0 + · exact degreeCheck17_4_1 + · exact degreeCheck17_4_2 + · exact degreeCheck17_4_3 + · exact degreeCheck17_4_4 + +lemma degree_pos17 (μ : YoungDiagram) (hμ : μ.card = 17) : + 0 < kronecker (canonicalTableau (candidate 5 0 1) degreeCard17) + (canonicalTableau (candidate 5 0 1) degreeCard17) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) + degreeCard17 degreeRows17_0 (by decide) (by decide) + degreePlan17_0 (by decide) (by decide) (by decide) (by decide) degreeP17 ?_ + degreeCheck17 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard17 rfl degreeCones17 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree18.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree18.lean index 4934ecf2df044bf275f534585ea83daf99a0ef4d..87ae053045e956e01061015d3713c7ec087c7481 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree18.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree18.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks18 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof18 - -namespace OAI - -/-! Numerical Degree 18. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos18 (μ : YoungDiagram) (hμ : μ.card = 18) : - 0 < kronecker (canonicalTableau (candidate 4 2 0) degreeCard18) - (canonicalTableau (candidate 4 2 0) degreeCard18) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 4) (by decide) (by decide) rfl (by decide) - degreeCard18 degreeRows18_0 (by decide) (by decide) - degreePlan18_0 (by decide) (by decide) (by decide) (by decide) degreeP18 ?_ - degreeCheck18 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard18 rfl degreeCones18 - degreeTreeAll18 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks18 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof18 + +namespace OAI + +/-! Numerical Degree 18. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos18 (μ : YoungDiagram) (hμ : μ.card = 18) : + 0 < kronecker (canonicalTableau (candidate 4 2 0) degreeCard18) + (canonicalTableau (candidate 4 2 0) degreeCard18) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 4) (by decide) (by decide) rfl (by decide) + degreeCard18 degreeRows18_0 (by decide) (by decide) + degreePlan18_0 (by decide) (by decide) (by decide) (by decide) degreeP18 ?_ + degreeCheck18 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard18 rfl degreeCones18 + degreeTreeAll18 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree19.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree19.lean index 9781c13f30bd1139c1fd6365721ea457d0eb0feb..6dbd4305340f995f763ebd5ab746078e763ab4ae 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree19.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree19.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks19 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof19 - -namespace OAI - -/-! Numerical Degree 19. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos19 (μ : YoungDiagram) (hμ : μ.card = 19) : - 0 < kronecker (canonicalTableau (candidate 5 1 0) degreeCard19) - (canonicalTableau (candidate 5 1 0) degreeCard19) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 2) (by decide) (by decide) rfl (by decide) - degreeCard19 degreeRows19_0 (by decide) (by decide) - degreePlan19_0 (by decide) (by decide) (by decide) (by decide) degreeP19 ?_ - degreeCheck19 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard19 rfl degreeCones19 - degreeTreeAll19 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks19 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof19 + +namespace OAI + +/-! Numerical Degree 19. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos19 (μ : YoungDiagram) (hμ : μ.card = 19) : + 0 < kronecker (canonicalTableau (candidate 5 1 0) degreeCard19) + (canonicalTableau (candidate 5 1 0) degreeCard19) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 2) (by decide) (by decide) rfl (by decide) + degreeCard19 degreeRows19_0 (by decide) (by decide) + degreePlan19_0 (by decide) (by decide) (by decide) (by decide) degreeP19 ?_ + degreeCheck19 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard19 rfl degreeCones19 + degreeTreeAll19 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree20.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree20.lean index d7491c2d502bf8d8a1e24b514c3ac5b5c3389716..04a5f22753e9e285afeaf1a75974625631ade144 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree20.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree20.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks20 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof20 - -namespace OAI - -/-! Numerical Degree 20. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos20 (μ : YoungDiagram) (hμ : μ.card = 20) : - 0 < kronecker (canonicalTableau (candidate 4 2 1) degreeCard20) - (canonicalTableau (candidate 4 2 1) degreeCard20) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 5) (by decide) (by decide) rfl (by decide) - degreeCard20 degreeRows20_0 (by decide) (by decide) - degreePlan20_0 (by decide) (by decide) (by decide) (by decide) degreeP20 ?_ - degreeCheck20 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard20 rfl degreeCones20 - degreeTreeAll20 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks20 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof20 + +namespace OAI + +/-! Numerical Degree 20. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos20 (μ : YoungDiagram) (hμ : μ.card = 20) : + 0 < kronecker (canonicalTableau (candidate 4 2 1) degreeCard20) + (canonicalTableau (candidate 4 2 1) degreeCard20) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 5) (by decide) (by decide) rfl (by decide) + degreeCard20 degreeRows20_0 (by decide) (by decide) + degreePlan20_0 (by decide) (by decide) (by decide) (by decide) degreeP20 ?_ + degreeCheck20 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard20 rfl degreeCones20 + degreeTreeAll20 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree22.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree22.lean index dd149cef1f3a753f34671e2d8517f7bf3b01b974..980f3f969ec60a785c5df3b40b24e08d33c3cf54 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree22.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree22.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks22 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof22 - -namespace OAI - -/-! Numerical Degree 22. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos22 (μ : YoungDiagram) (hμ : μ.card = 22) : - 0 < kronecker (canonicalTableau (candidate 4 3 0) degreeCard22) - (canonicalTableau (candidate 4 3 0) degreeCard22) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 6) (by decide) (by decide) rfl (by decide) - degreeCard22 degreeRows22_0 (by decide) (by decide) - degreePlan22_0 (by decide) (by decide) (by decide) (by decide) degreeP22 ?_ - degreeCheck22 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard22 rfl degreeCones22 - degreeTreeAll22 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks22 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof22 + +namespace OAI + +/-! Numerical Degree 22. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos22 (μ : YoungDiagram) (hμ : μ.card = 22) : + 0 < kronecker (canonicalTableau (candidate 4 3 0) degreeCard22) + (canonicalTableau (candidate 4 3 0) degreeCard22) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 6) (by decide) (by decide) rfl (by decide) + degreeCard22 degreeRows22_0 (by decide) (by decide) + degreePlan22_0 (by decide) (by decide) (by decide) (by decide) degreeP22 ?_ + degreeCheck22 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard22 rfl degreeCones22 + degreeTreeAll22 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree23.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree23.lean index cfdaf0cae2c0be137debbd8d4142a0913b2f22f8..51fda7e6ba5611792cea38ff00fd95d010a9cd37 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree23.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree23.lean @@ -1,218 +1,218 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 23. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard23 : (candidate 6 0 1).card = 23 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan23_0 : PackingPlan := (.join (.twoPaths 5 [4,4,3,3]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 1 2))) -def degreeRows23_0 : List ℕ := [4,4,3,3,2,2,2,2,1] - -lemma degreeCone23_0 (μ : YoungDiagram) (hμ : μ.card = 23) - (hd : RowsDom μ.rowLens degreeRows23_0) : SquareOccurs (candidate 6 0 1) μ := by - exact candidate_cone (by decide) degreeCard23 degreePlan23_0 degreeRows23_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan23_1 : PackingPlan := (.join (.repeated 1 7) (.join (.neighbor 4 [3,2,2,2]) (.join (.neighbor 2 [2,1,1,1]) (.repeated 2 1)))) -def degreeRows23_1 : List ℕ := [7,3,2,2,2,2,2,1,1,1] - -lemma degreeCone23_1 (μ : YoungDiagram) (hμ : μ.card = 23) - (hd : RowsDom μ.rowLens degreeRows23_1) : SquareOccurs (candidate 6 0 1) μ := by - exact candidate_cone (by decide) degreeCard23 degreePlan23_1 degreeRows23_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs23 : List (List ℕ) := [degreeRows23_1] - -lemma degreeCones23 : ∀ q ∈ degreeQs23, ∀ μ : YoungDiagram, μ.card = 23 → - RowsDom μ.rowLens q → SquareOccurs (candidate 6 0 1) μ := by - intro q hq - simp only [degreeQs23,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone23_1 - -abbrev degreeP23 := ResidualProperty 6 1 degreeQs23 [] - -lemma degreeCheck23_0_0 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 1 1 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_0_1 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 1 2 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_0_2 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 1 3 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_0_3 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 1 4 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_0_4 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 1 5 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_1_0 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 2 1 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_1_1 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 2 2 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_1_2 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 2 3 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_1_3 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 2 4 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_1_4 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 2 5 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_2_0 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 3 1 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_2_1 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 3 2 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_2_2 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 3 3 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_2_3 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 3 4 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_2_4 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 3 5 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_3_0 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 4 1 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_3_1 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 4 2 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_3_2 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 4 3 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_3_3 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 4 4 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_3_4 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 4 5 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_4_0 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 5 1 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_4_1 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 5 2 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_4_2 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 5 3 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_4_3 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 5 4 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23_4_4 : - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 5 5 (a+1) (c+1) degreeRows23_0 degreeP23 := by - decide +kernel - -lemma degreeCheck23 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, - residualCheck 23 6 1 (d+1) (e+1) (a+1) (c+1) degreeRows23_0 degreeP23 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck23_0_0 - · exact degreeCheck23_0_1 - · exact degreeCheck23_0_2 - · exact degreeCheck23_0_3 - · exact degreeCheck23_0_4 - · exact degreeCheck23_1_0 - · exact degreeCheck23_1_1 - · exact degreeCheck23_1_2 - · exact degreeCheck23_1_3 - · exact degreeCheck23_1_4 - · exact degreeCheck23_2_0 - · exact degreeCheck23_2_1 - · exact degreeCheck23_2_2 - · exact degreeCheck23_2_3 - · exact degreeCheck23_2_4 - · exact degreeCheck23_3_0 - · exact degreeCheck23_3_1 - · exact degreeCheck23_3_2 - · exact degreeCheck23_3_3 - · exact degreeCheck23_3_4 - · exact degreeCheck23_4_0 - · exact degreeCheck23_4_1 - · exact degreeCheck23_4_2 - · exact degreeCheck23_4_3 - · exact degreeCheck23_4_4 - -lemma degree_pos23 (μ : YoungDiagram) (hμ : μ.card = 23) : - 0 < kronecker (canonicalTableau (candidate 6 0 1) degreeCard23) - (canonicalTableau (candidate 6 0 1) degreeCard23) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) - degreeCard23 degreeRows23_0 (by decide) (by decide) - degreePlan23_0 (by decide) (by decide) (by decide) (by decide) degreeP23 ?_ - degreeCheck23 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard23 rfl degreeCones23 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 23. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard23 : (candidate 6 0 1).card = 23 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan23_0 : PackingPlan := (.join (.twoPaths 5 [4,4,3,3]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 1 2))) +def degreeRows23_0 : List ℕ := [4,4,3,3,2,2,2,2,1] + +lemma degreeCone23_0 (μ : YoungDiagram) (hμ : μ.card = 23) + (hd : RowsDom μ.rowLens degreeRows23_0) : SquareOccurs (candidate 6 0 1) μ := by + exact candidate_cone (by decide) degreeCard23 degreePlan23_0 degreeRows23_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan23_1 : PackingPlan := (.join (.repeated 1 7) (.join (.neighbor 4 [3,2,2,2]) (.join (.neighbor 2 [2,1,1,1]) (.repeated 2 1)))) +def degreeRows23_1 : List ℕ := [7,3,2,2,2,2,2,1,1,1] + +lemma degreeCone23_1 (μ : YoungDiagram) (hμ : μ.card = 23) + (hd : RowsDom μ.rowLens degreeRows23_1) : SquareOccurs (candidate 6 0 1) μ := by + exact candidate_cone (by decide) degreeCard23 degreePlan23_1 degreeRows23_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs23 : List (List ℕ) := [degreeRows23_1] + +lemma degreeCones23 : ∀ q ∈ degreeQs23, ∀ μ : YoungDiagram, μ.card = 23 → + RowsDom μ.rowLens q → SquareOccurs (candidate 6 0 1) μ := by + intro q hq + simp only [degreeQs23,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone23_1 + +abbrev degreeP23 := ResidualProperty 6 1 degreeQs23 [] + +lemma degreeCheck23_0_0 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 1 1 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_0_1 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 1 2 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_0_2 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 1 3 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_0_3 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 1 4 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_0_4 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 1 5 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_1_0 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 2 1 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_1_1 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 2 2 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_1_2 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 2 3 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_1_3 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 2 4 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_1_4 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 2 5 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_2_0 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 3 1 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_2_1 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 3 2 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_2_2 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 3 3 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_2_3 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 3 4 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_2_4 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 3 5 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_3_0 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 4 1 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_3_1 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 4 2 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_3_2 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 4 3 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_3_3 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 4 4 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_3_4 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 4 5 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_4_0 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 5 1 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_4_1 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 5 2 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_4_2 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 5 3 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_4_3 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 5 4 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23_4_4 : + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 5 5 (a+1) (c+1) degreeRows23_0 degreeP23 := by + decide +kernel + +lemma degreeCheck23 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows23_0.length, ∀ c ∈ List.range degreeRows23_0.length, + residualCheck 23 6 1 (d+1) (e+1) (a+1) (c+1) degreeRows23_0 degreeP23 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck23_0_0 + · exact degreeCheck23_0_1 + · exact degreeCheck23_0_2 + · exact degreeCheck23_0_3 + · exact degreeCheck23_0_4 + · exact degreeCheck23_1_0 + · exact degreeCheck23_1_1 + · exact degreeCheck23_1_2 + · exact degreeCheck23_1_3 + · exact degreeCheck23_1_4 + · exact degreeCheck23_2_0 + · exact degreeCheck23_2_1 + · exact degreeCheck23_2_2 + · exact degreeCheck23_2_3 + · exact degreeCheck23_2_4 + · exact degreeCheck23_3_0 + · exact degreeCheck23_3_1 + · exact degreeCheck23_3_2 + · exact degreeCheck23_3_3 + · exact degreeCheck23_3_4 + · exact degreeCheck23_4_0 + · exact degreeCheck23_4_1 + · exact degreeCheck23_4_2 + · exact degreeCheck23_4_3 + · exact degreeCheck23_4_4 + +lemma degree_pos23 (μ : YoungDiagram) (hμ : μ.card = 23) : + 0 < kronecker (canonicalTableau (candidate 6 0 1) degreeCard23) + (canonicalTableau (candidate 6 0 1) degreeCard23) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) + degreeCard23 degreeRows23_0 (by decide) (by decide) + degreePlan23_0 (by decide) (by decide) (by decide) (by decide) degreeP23 ?_ + degreeCheck23 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard23 rfl degreeCones23 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree24.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree24.lean index fdbe5c3c76cf57d0b1e261e74d59f5801aefc767..5660eae3c9f2fdae171af11da4211c1be3d3a650 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree24.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree24.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks24 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof24 - -namespace OAI - -/-! Numerical Degree 24. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos24 (μ : YoungDiagram) (hμ : μ.card = 24) : - 0 < kronecker (canonicalTableau (candidate 4 3 1) degreeCard24) - (canonicalTableau (candidate 4 3 1) degreeCard24) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 7) (by decide) (by decide) rfl (by decide) - degreeCard24 degreeRows24_0 (by decide) (by decide) - degreePlan24_0 (by decide) (by decide) (by decide) (by decide) degreeP24 ?_ - degreeCheck24 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard24 rfl degreeCones24 - degreeTreeAll24 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks24 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof24 + +namespace OAI + +/-! Numerical Degree 24. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos24 (μ : YoungDiagram) (hμ : μ.card = 24) : + 0 < kronecker (canonicalTableau (candidate 4 3 1) degreeCard24) + (canonicalTableau (candidate 4 3 1) degreeCard24) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 7) (by decide) (by decide) rfl (by decide) + degreeCard24 degreeRows24_0 (by decide) (by decide) + degreePlan24_0 (by decide) (by decide) (by decide) (by decide) degreeP24 ?_ + degreeCheck24 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard24 rfl degreeCones24 + degreeTreeAll24 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree25.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree25.lean index ac015abe1f4c20a37eccfc2fb7947a5a2fe9a3d9..5d2e9e6834238b5dc5f947b59bf4edef45ea51a4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree25.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree25.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 25. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard25 : (candidate 6 1 0).card = 25 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan25_0 : PackingPlan := (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 2 1 [3,2]))) -def degreeRows25_0 : List ℕ := [4,3,3,3,3,2,2,2,2,1] - -lemma degreeCone25_0 (μ : YoungDiagram) (hμ : μ.card = 25) - (hd : RowsDom μ.rowLens degreeRows25_0) : SquareOccurs (candidate 6 1 0) μ := by - exact candidate_cone (by decide) degreeCard25 degreePlan25_0 degreeRows25_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs25 : List (List ℕ) := [] - -lemma degreeCones25 : ∀ q ∈ degreeQs25, ∀ μ : YoungDiagram, μ.card = 25 → - RowsDom μ.rowLens q → SquareOccurs (candidate 6 1 0) μ := by - intro q hq - simp only [degreeQs25,List.not_mem_nil] at hq - -abbrev degreeP25 := ResidualProperty 6 2 degreeQs25 [] - -lemma degreeCheck25_0_0 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 1 1 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_0_1 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 1 2 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_0_2 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 1 3 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_0_3 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 1 4 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_0_4 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 1 5 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_1_0 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 2 1 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_1_1 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 2 2 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_1_2 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 2 3 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_1_3 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 2 4 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_1_4 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 2 5 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_2_0 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 3 1 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_2_1 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 3 2 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_2_2 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 3 3 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_2_3 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 3 4 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_2_4 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 3 5 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_3_0 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 4 1 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_3_1 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 4 2 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_3_2 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 4 3 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_3_3 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 4 4 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_3_4 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 4 5 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_4_0 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 5 1 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_4_1 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 5 2 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_4_2 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 5 3 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_4_3 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 5 4 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25_4_4 : - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 5 5 (a+1) (c+1) degreeRows25_0 degreeP25 := by - decide +kernel - -lemma degreeCheck25 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, - residualCheck 25 6 2 (d+1) (e+1) (a+1) (c+1) degreeRows25_0 degreeP25 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck25_0_0 - · exact degreeCheck25_0_1 - · exact degreeCheck25_0_2 - · exact degreeCheck25_0_3 - · exact degreeCheck25_0_4 - · exact degreeCheck25_1_0 - · exact degreeCheck25_1_1 - · exact degreeCheck25_1_2 - · exact degreeCheck25_1_3 - · exact degreeCheck25_1_4 - · exact degreeCheck25_2_0 - · exact degreeCheck25_2_1 - · exact degreeCheck25_2_2 - · exact degreeCheck25_2_3 - · exact degreeCheck25_2_4 - · exact degreeCheck25_3_0 - · exact degreeCheck25_3_1 - · exact degreeCheck25_3_2 - · exact degreeCheck25_3_3 - · exact degreeCheck25_3_4 - · exact degreeCheck25_4_0 - · exact degreeCheck25_4_1 - · exact degreeCheck25_4_2 - · exact degreeCheck25_4_3 - · exact degreeCheck25_4_4 - -lemma degree_pos25 (μ : YoungDiagram) (hμ : μ.card = 25) : - 0 < kronecker (canonicalTableau (candidate 6 1 0) degreeCard25) - (canonicalTableau (candidate 6 1 0) degreeCard25) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 2) (by decide) (by decide) rfl (by decide) - degreeCard25 degreeRows25_0 (by decide) (by decide) - degreePlan25_0 (by decide) (by decide) (by decide) (by decide) degreeP25 ?_ - degreeCheck25 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard25 rfl degreeCones25 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 25. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard25 : (candidate 6 1 0).card = 25 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan25_0 : PackingPlan := (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 2 1 [3,2]))) +def degreeRows25_0 : List ℕ := [4,3,3,3,3,2,2,2,2,1] + +lemma degreeCone25_0 (μ : YoungDiagram) (hμ : μ.card = 25) + (hd : RowsDom μ.rowLens degreeRows25_0) : SquareOccurs (candidate 6 1 0) μ := by + exact candidate_cone (by decide) degreeCard25 degreePlan25_0 degreeRows25_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs25 : List (List ℕ) := [] + +lemma degreeCones25 : ∀ q ∈ degreeQs25, ∀ μ : YoungDiagram, μ.card = 25 → + RowsDom μ.rowLens q → SquareOccurs (candidate 6 1 0) μ := by + intro q hq + simp only [degreeQs25,List.not_mem_nil] at hq + +abbrev degreeP25 := ResidualProperty 6 2 degreeQs25 [] + +lemma degreeCheck25_0_0 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 1 1 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_0_1 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 1 2 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_0_2 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 1 3 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_0_3 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 1 4 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_0_4 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 1 5 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_1_0 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 2 1 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_1_1 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 2 2 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_1_2 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 2 3 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_1_3 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 2 4 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_1_4 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 2 5 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_2_0 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 3 1 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_2_1 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 3 2 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_2_2 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 3 3 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_2_3 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 3 4 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_2_4 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 3 5 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_3_0 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 4 1 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_3_1 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 4 2 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_3_2 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 4 3 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_3_3 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 4 4 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_3_4 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 4 5 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_4_0 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 5 1 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_4_1 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 5 2 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_4_2 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 5 3 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_4_3 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 5 4 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25_4_4 : + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 5 5 (a+1) (c+1) degreeRows25_0 degreeP25 := by + decide +kernel + +lemma degreeCheck25 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows25_0.length, ∀ c ∈ List.range degreeRows25_0.length, + residualCheck 25 6 2 (d+1) (e+1) (a+1) (c+1) degreeRows25_0 degreeP25 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck25_0_0 + · exact degreeCheck25_0_1 + · exact degreeCheck25_0_2 + · exact degreeCheck25_0_3 + · exact degreeCheck25_0_4 + · exact degreeCheck25_1_0 + · exact degreeCheck25_1_1 + · exact degreeCheck25_1_2 + · exact degreeCheck25_1_3 + · exact degreeCheck25_1_4 + · exact degreeCheck25_2_0 + · exact degreeCheck25_2_1 + · exact degreeCheck25_2_2 + · exact degreeCheck25_2_3 + · exact degreeCheck25_2_4 + · exact degreeCheck25_3_0 + · exact degreeCheck25_3_1 + · exact degreeCheck25_3_2 + · exact degreeCheck25_3_3 + · exact degreeCheck25_3_4 + · exact degreeCheck25_4_0 + · exact degreeCheck25_4_1 + · exact degreeCheck25_4_2 + · exact degreeCheck25_4_3 + · exact degreeCheck25_4_4 + +lemma degree_pos25 (μ : YoungDiagram) (hμ : μ.card = 25) : + 0 < kronecker (canonicalTableau (candidate 6 1 0) degreeCard25) + (canonicalTableau (candidate 6 1 0) degreeCard25) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 2) (by decide) (by decide) rfl (by decide) + degreeCard25 degreeRows25_0 (by decide) (by decide) + degreePlan25_0 (by decide) (by decide) (by decide) (by decide) degreeP25 ?_ + degreeCheck25 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard25 rfl degreeCones25 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree26.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree26.lean index 943b3f6a29897bbb314971d894968b3bc713da8c..2195d06f75fb3d8459a53836318c8231484daff9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree26.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree26.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks26 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof26 - -namespace OAI - -/-! Numerical Degree 26. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos26 (μ : YoungDiagram) (hμ : μ.card = 26) : - 0 < kronecker (canonicalTableau (candidate 4 4 0) degreeCard26) - (canonicalTableau (candidate 4 4 0) degreeCard26) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 8) (by decide) (by decide) rfl (by decide) - degreeCard26 degreeRows26_0 (by decide) (by decide) - degreePlan26_0 (by decide) (by decide) (by decide) (by decide) degreeP26 ?_ - degreeCheck26 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard26 rfl degreeCones26 - degreeTreeAll26 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks26 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof26 + +namespace OAI + +/-! Numerical Degree 26. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos26 (μ : YoungDiagram) (hμ : μ.card = 26) : + 0 < kronecker (canonicalTableau (candidate 4 4 0) degreeCard26) + (canonicalTableau (candidate 4 4 0) degreeCard26) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 8) (by decide) (by decide) rfl (by decide) + degreeCard26 degreeRows26_0 (by decide) (by decide) + degreePlan26_0 (by decide) (by decide) (by decide) (by decide) degreeP26 ?_ + degreeCheck26 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard26 rfl degreeCones26 + degreeTreeAll26 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree27.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree27.lean index 158df20dc59176f21f8dee48f81032c6c9cab156..6b4e64cf5db66fd580e906cfd64b2546706375fc 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree27.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree27.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 27. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard27 : (candidate 6 1 1).card = 27 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan27_0 : PackingPlan := (.join (.twoPaths 6 [4,4,4,4]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 2 2))) -def degreeRows27_0 : List ℕ := [4,4,4,4,4,2,2,2,1] - -lemma degreeCone27_0 (μ : YoungDiagram) (hμ : μ.card = 27) - (hd : RowsDom μ.rowLens degreeRows27_0) : SquareOccurs (candidate 6 1 1) μ := by - exact candidate_cone (by decide) degreeCard27 degreePlan27_0 degreeRows27_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs27 : List (List ℕ) := [] - -lemma degreeCones27 : ∀ q ∈ degreeQs27, ∀ μ : YoungDiagram, μ.card = 27 → - RowsDom μ.rowLens q → SquareOccurs (candidate 6 1 1) μ := by - intro q hq - simp only [degreeQs27,List.not_mem_nil] at hq - -abbrev degreeP27 := ResidualProperty 6 3 degreeQs27 [] - -lemma degreeCheck27_0_0 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 1 1 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_0_1 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 1 2 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_0_2 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 1 3 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_0_3 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 1 4 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_0_4 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 1 5 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_1_0 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 2 1 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_1_1 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 2 2 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_1_2 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 2 3 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_1_3 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 2 4 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_1_4 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 2 5 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_2_0 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 3 1 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_2_1 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 3 2 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_2_2 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 3 3 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_2_3 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 3 4 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_2_4 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 3 5 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_3_0 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 4 1 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_3_1 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 4 2 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_3_2 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 4 3 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_3_3 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 4 4 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_3_4 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 4 5 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_4_0 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 5 1 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_4_1 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 5 2 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_4_2 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 5 3 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_4_3 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 5 4 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27_4_4 : - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 5 5 (a+1) (c+1) degreeRows27_0 degreeP27 := by - decide +kernel - -lemma degreeCheck27 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, - residualCheck 27 6 3 (d+1) (e+1) (a+1) (c+1) degreeRows27_0 degreeP27 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck27_0_0 - · exact degreeCheck27_0_1 - · exact degreeCheck27_0_2 - · exact degreeCheck27_0_3 - · exact degreeCheck27_0_4 - · exact degreeCheck27_1_0 - · exact degreeCheck27_1_1 - · exact degreeCheck27_1_2 - · exact degreeCheck27_1_3 - · exact degreeCheck27_1_4 - · exact degreeCheck27_2_0 - · exact degreeCheck27_2_1 - · exact degreeCheck27_2_2 - · exact degreeCheck27_2_3 - · exact degreeCheck27_2_4 - · exact degreeCheck27_3_0 - · exact degreeCheck27_3_1 - · exact degreeCheck27_3_2 - · exact degreeCheck27_3_3 - · exact degreeCheck27_3_4 - · exact degreeCheck27_4_0 - · exact degreeCheck27_4_1 - · exact degreeCheck27_4_2 - · exact degreeCheck27_4_3 - · exact degreeCheck27_4_4 - -lemma degree_pos27 (μ : YoungDiagram) (hμ : μ.card = 27) : - 0 < kronecker (canonicalTableau (candidate 6 1 1) degreeCard27) - (canonicalTableau (candidate 6 1 1) degreeCard27) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 3) (by decide) (by decide) rfl (by decide) - degreeCard27 degreeRows27_0 (by decide) (by decide) - degreePlan27_0 (by decide) (by decide) (by decide) (by decide) degreeP27 ?_ - degreeCheck27 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard27 rfl degreeCones27 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 27. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard27 : (candidate 6 1 1).card = 27 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan27_0 : PackingPlan := (.join (.twoPaths 6 [4,4,4,4]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 2 2))) +def degreeRows27_0 : List ℕ := [4,4,4,4,4,2,2,2,1] + +lemma degreeCone27_0 (μ : YoungDiagram) (hμ : μ.card = 27) + (hd : RowsDom μ.rowLens degreeRows27_0) : SquareOccurs (candidate 6 1 1) μ := by + exact candidate_cone (by decide) degreeCard27 degreePlan27_0 degreeRows27_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs27 : List (List ℕ) := [] + +lemma degreeCones27 : ∀ q ∈ degreeQs27, ∀ μ : YoungDiagram, μ.card = 27 → + RowsDom μ.rowLens q → SquareOccurs (candidate 6 1 1) μ := by + intro q hq + simp only [degreeQs27,List.not_mem_nil] at hq + +abbrev degreeP27 := ResidualProperty 6 3 degreeQs27 [] + +lemma degreeCheck27_0_0 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 1 1 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_0_1 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 1 2 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_0_2 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 1 3 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_0_3 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 1 4 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_0_4 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 1 5 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_1_0 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 2 1 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_1_1 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 2 2 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_1_2 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 2 3 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_1_3 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 2 4 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_1_4 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 2 5 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_2_0 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 3 1 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_2_1 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 3 2 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_2_2 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 3 3 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_2_3 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 3 4 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_2_4 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 3 5 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_3_0 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 4 1 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_3_1 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 4 2 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_3_2 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 4 3 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_3_3 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 4 4 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_3_4 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 4 5 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_4_0 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 5 1 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_4_1 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 5 2 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_4_2 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 5 3 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_4_3 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 5 4 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27_4_4 : + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 5 5 (a+1) (c+1) degreeRows27_0 degreeP27 := by + decide +kernel + +lemma degreeCheck27 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows27_0.length, ∀ c ∈ List.range degreeRows27_0.length, + residualCheck 27 6 3 (d+1) (e+1) (a+1) (c+1) degreeRows27_0 degreeP27 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck27_0_0 + · exact degreeCheck27_0_1 + · exact degreeCheck27_0_2 + · exact degreeCheck27_0_3 + · exact degreeCheck27_0_4 + · exact degreeCheck27_1_0 + · exact degreeCheck27_1_1 + · exact degreeCheck27_1_2 + · exact degreeCheck27_1_3 + · exact degreeCheck27_1_4 + · exact degreeCheck27_2_0 + · exact degreeCheck27_2_1 + · exact degreeCheck27_2_2 + · exact degreeCheck27_2_3 + · exact degreeCheck27_2_4 + · exact degreeCheck27_3_0 + · exact degreeCheck27_3_1 + · exact degreeCheck27_3_2 + · exact degreeCheck27_3_3 + · exact degreeCheck27_3_4 + · exact degreeCheck27_4_0 + · exact degreeCheck27_4_1 + · exact degreeCheck27_4_2 + · exact degreeCheck27_4_3 + · exact degreeCheck27_4_4 + +lemma degree_pos27 (μ : YoungDiagram) (hμ : μ.card = 27) : + 0 < kronecker (canonicalTableau (candidate 6 1 1) degreeCard27) + (canonicalTableau (candidate 6 1 1) degreeCard27) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 3) (by decide) (by decide) rfl (by decide) + degreeCard27 degreeRows27_0 (by decide) (by decide) + degreePlan27_0 (by decide) (by decide) (by decide) (by decide) degreeP27 ?_ + degreeCheck27 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard27 rfl degreeCones27 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree29.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree29.lean index 0748fe53c08bd885b836207ab2bd53937a34416a..99c0e0962b00088205c902c44a1b397db1646d06 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree29.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree29.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 29. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard29 : (candidate 6 2 0).card = 29 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan29_0 : PackingPlan := (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 3 1 [4,3]))) -def degreeRows29_0 : List ℕ := [4,4,4,4,3,3,2,2,2,1] - -lemma degreeCone29_0 (μ : YoungDiagram) (hμ : μ.card = 29) - (hd : RowsDom μ.rowLens degreeRows29_0) : SquareOccurs (candidate 6 2 0) μ := by - exact candidate_cone (by decide) degreeCard29 degreePlan29_0 degreeRows29_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs29 : List (List ℕ) := [] - -lemma degreeCones29 : ∀ q ∈ degreeQs29, ∀ μ : YoungDiagram, μ.card = 29 → - RowsDom μ.rowLens q → SquareOccurs (candidate 6 2 0) μ := by - intro q hq - simp only [degreeQs29,List.not_mem_nil] at hq - -abbrev degreeP29 := ResidualProperty 6 4 degreeQs29 [] - -lemma degreeCheck29_0_0 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 1 1 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_0_1 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 1 2 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_0_2 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 1 3 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_0_3 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 1 4 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_0_4 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 1 5 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_1_0 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 2 1 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_1_1 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 2 2 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_1_2 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 2 3 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_1_3 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 2 4 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_1_4 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 2 5 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_2_0 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 3 1 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_2_1 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 3 2 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_2_2 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 3 3 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_2_3 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 3 4 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_2_4 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 3 5 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_3_0 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 4 1 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_3_1 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 4 2 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_3_2 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 4 3 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_3_3 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 4 4 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_3_4 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 4 5 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_4_0 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 5 1 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_4_1 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 5 2 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_4_2 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 5 3 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_4_3 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 5 4 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29_4_4 : - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 5 5 (a+1) (c+1) degreeRows29_0 degreeP29 := by - decide +kernel - -lemma degreeCheck29 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, - residualCheck 29 6 4 (d+1) (e+1) (a+1) (c+1) degreeRows29_0 degreeP29 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck29_0_0 - · exact degreeCheck29_0_1 - · exact degreeCheck29_0_2 - · exact degreeCheck29_0_3 - · exact degreeCheck29_0_4 - · exact degreeCheck29_1_0 - · exact degreeCheck29_1_1 - · exact degreeCheck29_1_2 - · exact degreeCheck29_1_3 - · exact degreeCheck29_1_4 - · exact degreeCheck29_2_0 - · exact degreeCheck29_2_1 - · exact degreeCheck29_2_2 - · exact degreeCheck29_2_3 - · exact degreeCheck29_2_4 - · exact degreeCheck29_3_0 - · exact degreeCheck29_3_1 - · exact degreeCheck29_3_2 - · exact degreeCheck29_3_3 - · exact degreeCheck29_3_4 - · exact degreeCheck29_4_0 - · exact degreeCheck29_4_1 - · exact degreeCheck29_4_2 - · exact degreeCheck29_4_3 - · exact degreeCheck29_4_4 - -lemma degree_pos29 (μ : YoungDiagram) (hμ : μ.card = 29) : - 0 < kronecker (canonicalTableau (candidate 6 2 0) degreeCard29) - (canonicalTableau (candidate 6 2 0) degreeCard29) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 4) (by decide) (by decide) rfl (by decide) - degreeCard29 degreeRows29_0 (by decide) (by decide) - degreePlan29_0 (by decide) (by decide) (by decide) (by decide) degreeP29 ?_ - degreeCheck29 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard29 rfl degreeCones29 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 29. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard29 : (candidate 6 2 0).card = 29 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan29_0 : PackingPlan := (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 3 1 [4,3]))) +def degreeRows29_0 : List ℕ := [4,4,4,4,3,3,2,2,2,1] + +lemma degreeCone29_0 (μ : YoungDiagram) (hμ : μ.card = 29) + (hd : RowsDom μ.rowLens degreeRows29_0) : SquareOccurs (candidate 6 2 0) μ := by + exact candidate_cone (by decide) degreeCard29 degreePlan29_0 degreeRows29_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs29 : List (List ℕ) := [] + +lemma degreeCones29 : ∀ q ∈ degreeQs29, ∀ μ : YoungDiagram, μ.card = 29 → + RowsDom μ.rowLens q → SquareOccurs (candidate 6 2 0) μ := by + intro q hq + simp only [degreeQs29,List.not_mem_nil] at hq + +abbrev degreeP29 := ResidualProperty 6 4 degreeQs29 [] + +lemma degreeCheck29_0_0 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 1 1 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_0_1 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 1 2 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_0_2 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 1 3 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_0_3 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 1 4 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_0_4 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 1 5 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_1_0 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 2 1 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_1_1 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 2 2 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_1_2 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 2 3 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_1_3 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 2 4 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_1_4 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 2 5 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_2_0 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 3 1 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_2_1 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 3 2 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_2_2 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 3 3 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_2_3 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 3 4 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_2_4 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 3 5 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_3_0 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 4 1 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_3_1 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 4 2 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_3_2 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 4 3 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_3_3 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 4 4 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_3_4 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 4 5 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_4_0 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 5 1 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_4_1 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 5 2 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_4_2 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 5 3 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_4_3 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 5 4 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29_4_4 : + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 5 5 (a+1) (c+1) degreeRows29_0 degreeP29 := by + decide +kernel + +lemma degreeCheck29 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows29_0.length, ∀ c ∈ List.range degreeRows29_0.length, + residualCheck 29 6 4 (d+1) (e+1) (a+1) (c+1) degreeRows29_0 degreeP29 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck29_0_0 + · exact degreeCheck29_0_1 + · exact degreeCheck29_0_2 + · exact degreeCheck29_0_3 + · exact degreeCheck29_0_4 + · exact degreeCheck29_1_0 + · exact degreeCheck29_1_1 + · exact degreeCheck29_1_2 + · exact degreeCheck29_1_3 + · exact degreeCheck29_1_4 + · exact degreeCheck29_2_0 + · exact degreeCheck29_2_1 + · exact degreeCheck29_2_2 + · exact degreeCheck29_2_3 + · exact degreeCheck29_2_4 + · exact degreeCheck29_3_0 + · exact degreeCheck29_3_1 + · exact degreeCheck29_3_2 + · exact degreeCheck29_3_3 + · exact degreeCheck29_3_4 + · exact degreeCheck29_4_0 + · exact degreeCheck29_4_1 + · exact degreeCheck29_4_2 + · exact degreeCheck29_4_3 + · exact degreeCheck29_4_4 + +lemma degree_pos29 (μ : YoungDiagram) (hμ : μ.card = 29) : + 0 < kronecker (canonicalTableau (candidate 6 2 0) degreeCard29) + (canonicalTableau (candidate 6 2 0) degreeCard29) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 4) (by decide) (by decide) rfl (by decide) + degreeCard29 degreeRows29_0 (by decide) (by decide) + degreePlan29_0 (by decide) (by decide) (by decide) (by decide) degreeP29 ?_ + degreeCheck29 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard29 rfl degreeCones29 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree30.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree30.lean index 67cb76dda1466fc3dd2d2261ff07e1b810024c31..e0fa2fe4f5696f16012b665c6e9519fec7bbd4be 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree30.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree30.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 30. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard30 : (candidate 7 0 1).card = 30 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan30_0 : PackingPlan := (.join (.twoPaths 6 [4,4,4,4]) (.join (.neighbor 4 [3,2,2,2]) (.neighbor 2 [2,1,1,1]))) -def degreeRows30_0 : List ℕ := [4,4,4,4,3,2,2,2,2,1,1,1] - -lemma degreeCone30_0 (μ : YoungDiagram) (hμ : μ.card = 30) - (hd : RowsDom μ.rowLens degreeRows30_0) : SquareOccurs (candidate 7 0 1) μ := by - exact candidate_cone (by decide) degreeCard30 degreePlan30_0 degreeRows30_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs30 : List (List ℕ) := [] - -lemma degreeCones30 : ∀ q ∈ degreeQs30, ∀ μ : YoungDiagram, μ.card = 30 → - RowsDom μ.rowLens q → SquareOccurs (candidate 7 0 1) μ := by - intro q hq - simp only [degreeQs30,List.not_mem_nil] at hq - -abbrev degreeP30 := ResidualProperty 7 1 degreeQs30 [] - -lemma degreeCheck30_0_0 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 1 1 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_0_1 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 1 2 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_0_2 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 1 3 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_0_3 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 1 4 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_0_4 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 1 5 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_1_0 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 2 1 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_1_1 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 2 2 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_1_2 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 2 3 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_1_3 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 2 4 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_1_4 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 2 5 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_2_0 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 3 1 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_2_1 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 3 2 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_2_2 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 3 3 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_2_3 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 3 4 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_2_4 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 3 5 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_3_0 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 4 1 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_3_1 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 4 2 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_3_2 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 4 3 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_3_3 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 4 4 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_3_4 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 4 5 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_4_0 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 5 1 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_4_1 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 5 2 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_4_2 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 5 3 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_4_3 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 5 4 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30_4_4 : - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 5 5 (a+1) (c+1) degreeRows30_0 degreeP30 := by - decide +kernel - -lemma degreeCheck30 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, - residualCheck 30 7 1 (d+1) (e+1) (a+1) (c+1) degreeRows30_0 degreeP30 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck30_0_0 - · exact degreeCheck30_0_1 - · exact degreeCheck30_0_2 - · exact degreeCheck30_0_3 - · exact degreeCheck30_0_4 - · exact degreeCheck30_1_0 - · exact degreeCheck30_1_1 - · exact degreeCheck30_1_2 - · exact degreeCheck30_1_3 - · exact degreeCheck30_1_4 - · exact degreeCheck30_2_0 - · exact degreeCheck30_2_1 - · exact degreeCheck30_2_2 - · exact degreeCheck30_2_3 - · exact degreeCheck30_2_4 - · exact degreeCheck30_3_0 - · exact degreeCheck30_3_1 - · exact degreeCheck30_3_2 - · exact degreeCheck30_3_3 - · exact degreeCheck30_3_4 - · exact degreeCheck30_4_0 - · exact degreeCheck30_4_1 - · exact degreeCheck30_4_2 - · exact degreeCheck30_4_3 - · exact degreeCheck30_4_4 - -lemma degree_pos30 (μ : YoungDiagram) (hμ : μ.card = 30) : - 0 < kronecker (canonicalTableau (candidate 7 0 1) degreeCard30) - (canonicalTableau (candidate 7 0 1) degreeCard30) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) - degreeCard30 degreeRows30_0 (by decide) (by decide) - degreePlan30_0 (by decide) (by decide) (by decide) (by decide) degreeP30 ?_ - degreeCheck30 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard30 rfl degreeCones30 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 30. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard30 : (candidate 7 0 1).card = 30 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan30_0 : PackingPlan := (.join (.twoPaths 6 [4,4,4,4]) (.join (.neighbor 4 [3,2,2,2]) (.neighbor 2 [2,1,1,1]))) +def degreeRows30_0 : List ℕ := [4,4,4,4,3,2,2,2,2,1,1,1] + +lemma degreeCone30_0 (μ : YoungDiagram) (hμ : μ.card = 30) + (hd : RowsDom μ.rowLens degreeRows30_0) : SquareOccurs (candidate 7 0 1) μ := by + exact candidate_cone (by decide) degreeCard30 degreePlan30_0 degreeRows30_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs30 : List (List ℕ) := [] + +lemma degreeCones30 : ∀ q ∈ degreeQs30, ∀ μ : YoungDiagram, μ.card = 30 → + RowsDom μ.rowLens q → SquareOccurs (candidate 7 0 1) μ := by + intro q hq + simp only [degreeQs30,List.not_mem_nil] at hq + +abbrev degreeP30 := ResidualProperty 7 1 degreeQs30 [] + +lemma degreeCheck30_0_0 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 1 1 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_0_1 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 1 2 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_0_2 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 1 3 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_0_3 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 1 4 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_0_4 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 1 5 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_1_0 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 2 1 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_1_1 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 2 2 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_1_2 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 2 3 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_1_3 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 2 4 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_1_4 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 2 5 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_2_0 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 3 1 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_2_1 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 3 2 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_2_2 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 3 3 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_2_3 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 3 4 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_2_4 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 3 5 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_3_0 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 4 1 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_3_1 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 4 2 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_3_2 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 4 3 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_3_3 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 4 4 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_3_4 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 4 5 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_4_0 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 5 1 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_4_1 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 5 2 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_4_2 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 5 3 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_4_3 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 5 4 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30_4_4 : + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 5 5 (a+1) (c+1) degreeRows30_0 degreeP30 := by + decide +kernel + +lemma degreeCheck30 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows30_0.length, ∀ c ∈ List.range degreeRows30_0.length, + residualCheck 30 7 1 (d+1) (e+1) (a+1) (c+1) degreeRows30_0 degreeP30 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck30_0_0 + · exact degreeCheck30_0_1 + · exact degreeCheck30_0_2 + · exact degreeCheck30_0_3 + · exact degreeCheck30_0_4 + · exact degreeCheck30_1_0 + · exact degreeCheck30_1_1 + · exact degreeCheck30_1_2 + · exact degreeCheck30_1_3 + · exact degreeCheck30_1_4 + · exact degreeCheck30_2_0 + · exact degreeCheck30_2_1 + · exact degreeCheck30_2_2 + · exact degreeCheck30_2_3 + · exact degreeCheck30_2_4 + · exact degreeCheck30_3_0 + · exact degreeCheck30_3_1 + · exact degreeCheck30_3_2 + · exact degreeCheck30_3_3 + · exact degreeCheck30_3_4 + · exact degreeCheck30_4_0 + · exact degreeCheck30_4_1 + · exact degreeCheck30_4_2 + · exact degreeCheck30_4_3 + · exact degreeCheck30_4_4 + +lemma degree_pos30 (μ : YoungDiagram) (hμ : μ.card = 30) : + 0 < kronecker (canonicalTableau (candidate 7 0 1) degreeCard30) + (canonicalTableau (candidate 7 0 1) degreeCard30) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) + degreeCard30 degreeRows30_0 (by decide) (by decide) + degreePlan30_0 (by decide) (by decide) (by decide) (by decide) degreeP30 ?_ + degreeCheck30 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard30 rfl degreeCones30 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree31.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree31.lean index 39e2e9e6f2103f0a600c106ee28f65aac6cbd397..09c02c749ac6a6255a943c548f37c2c6c7e5308d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree31.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree31.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks31 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof31 - -namespace OAI - -/-! Numerical Degree 31. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos31 (μ : YoungDiagram) (hμ : μ.card = 31) : - 0 < kronecker (canonicalTableau (candidate 6 2 1) degreeCard31) - (canonicalTableau (candidate 6 2 1) degreeCard31) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 5) (by decide) (by decide) rfl (by decide) - degreeCard31 degreeRows31_0 (by decide) (by decide) - degreePlan31_0 (by decide) (by decide) (by decide) (by decide) degreeP31 ?_ - degreeCheck31 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard31 rfl degreeCones31 - degreeTreeAll31 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks31 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof31 + +namespace OAI + +/-! Numerical Degree 31. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos31 (μ : YoungDiagram) (hμ : μ.card = 31) : + 0 < kronecker (canonicalTableau (candidate 6 2 1) degreeCard31) + (canonicalTableau (candidate 6 2 1) degreeCard31) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 5) (by decide) (by decide) rfl (by decide) + degreeCard31 degreeRows31_0 (by decide) (by decide) + degreePlan31_0 (by decide) (by decide) (by decide) (by decide) degreeP31 ?_ + degreeCheck31 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard31 rfl degreeCones31 + degreeTreeAll31 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree32.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree32.lean index f38018398c989e5ab12fe9b64895c89a85230dca..6ab85ad7a146a8f0621e25a62738f0dcdef38be0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree32.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree32.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 32. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard32 : (candidate 7 1 0).card = 32 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan32_0 : PackingPlan := (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 4 [3,2,2,2]) (.join (.repeated 1 3) (.twosOdd 2 1 [3,2])))) -def degreeRows32_0 : List ℕ := [4,4,4,3,3,3,3,2,2,2,2] - -lemma degreeCone32_0 (μ : YoungDiagram) (hμ : μ.card = 32) - (hd : RowsDom μ.rowLens degreeRows32_0) : SquareOccurs (candidate 7 1 0) μ := by - exact candidate_cone (by decide) degreeCard32 degreePlan32_0 degreeRows32_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs32 : List (List ℕ) := [] - -lemma degreeCones32 : ∀ q ∈ degreeQs32, ∀ μ : YoungDiagram, μ.card = 32 → - RowsDom μ.rowLens q → SquareOccurs (candidate 7 1 0) μ := by - intro q hq - simp only [degreeQs32,List.not_mem_nil] at hq - -abbrev degreeP32 := ResidualProperty 7 2 degreeQs32 [] - -lemma degreeCheck32_0_0 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 1 1 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_0_1 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 1 2 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_0_2 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 1 3 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_0_3 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 1 4 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_0_4 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 1 5 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_1_0 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 2 1 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_1_1 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 2 2 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_1_2 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 2 3 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_1_3 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 2 4 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_1_4 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 2 5 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_2_0 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 3 1 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_2_1 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 3 2 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_2_2 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 3 3 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_2_3 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 3 4 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_2_4 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 3 5 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_3_0 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 4 1 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_3_1 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 4 2 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_3_2 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 4 3 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_3_3 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 4 4 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_3_4 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 4 5 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_4_0 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 5 1 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_4_1 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 5 2 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_4_2 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 5 3 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_4_3 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 5 4 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32_4_4 : - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 5 5 (a+1) (c+1) degreeRows32_0 degreeP32 := by - decide +kernel - -lemma degreeCheck32 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, - residualCheck 32 7 2 (d+1) (e+1) (a+1) (c+1) degreeRows32_0 degreeP32 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck32_0_0 - · exact degreeCheck32_0_1 - · exact degreeCheck32_0_2 - · exact degreeCheck32_0_3 - · exact degreeCheck32_0_4 - · exact degreeCheck32_1_0 - · exact degreeCheck32_1_1 - · exact degreeCheck32_1_2 - · exact degreeCheck32_1_3 - · exact degreeCheck32_1_4 - · exact degreeCheck32_2_0 - · exact degreeCheck32_2_1 - · exact degreeCheck32_2_2 - · exact degreeCheck32_2_3 - · exact degreeCheck32_2_4 - · exact degreeCheck32_3_0 - · exact degreeCheck32_3_1 - · exact degreeCheck32_3_2 - · exact degreeCheck32_3_3 - · exact degreeCheck32_3_4 - · exact degreeCheck32_4_0 - · exact degreeCheck32_4_1 - · exact degreeCheck32_4_2 - · exact degreeCheck32_4_3 - · exact degreeCheck32_4_4 - -lemma degree_pos32 (μ : YoungDiagram) (hμ : μ.card = 32) : - 0 < kronecker (canonicalTableau (candidate 7 1 0) degreeCard32) - (canonicalTableau (candidate 7 1 0) degreeCard32) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 2) (by decide) (by decide) rfl (by decide) - degreeCard32 degreeRows32_0 (by decide) (by decide) - degreePlan32_0 (by decide) (by decide) (by decide) (by decide) degreeP32 ?_ - degreeCheck32 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard32 rfl degreeCones32 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 32. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard32 : (candidate 7 1 0).card = 32 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan32_0 : PackingPlan := (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 4 [3,2,2,2]) (.join (.repeated 1 3) (.twosOdd 2 1 [3,2])))) +def degreeRows32_0 : List ℕ := [4,4,4,3,3,3,3,2,2,2,2] + +lemma degreeCone32_0 (μ : YoungDiagram) (hμ : μ.card = 32) + (hd : RowsDom μ.rowLens degreeRows32_0) : SquareOccurs (candidate 7 1 0) μ := by + exact candidate_cone (by decide) degreeCard32 degreePlan32_0 degreeRows32_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs32 : List (List ℕ) := [] + +lemma degreeCones32 : ∀ q ∈ degreeQs32, ∀ μ : YoungDiagram, μ.card = 32 → + RowsDom μ.rowLens q → SquareOccurs (candidate 7 1 0) μ := by + intro q hq + simp only [degreeQs32,List.not_mem_nil] at hq + +abbrev degreeP32 := ResidualProperty 7 2 degreeQs32 [] + +lemma degreeCheck32_0_0 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 1 1 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_0_1 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 1 2 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_0_2 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 1 3 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_0_3 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 1 4 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_0_4 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 1 5 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_1_0 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 2 1 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_1_1 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 2 2 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_1_2 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 2 3 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_1_3 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 2 4 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_1_4 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 2 5 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_2_0 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 3 1 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_2_1 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 3 2 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_2_2 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 3 3 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_2_3 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 3 4 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_2_4 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 3 5 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_3_0 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 4 1 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_3_1 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 4 2 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_3_2 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 4 3 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_3_3 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 4 4 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_3_4 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 4 5 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_4_0 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 5 1 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_4_1 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 5 2 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_4_2 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 5 3 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_4_3 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 5 4 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32_4_4 : + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 5 5 (a+1) (c+1) degreeRows32_0 degreeP32 := by + decide +kernel + +lemma degreeCheck32 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows32_0.length, ∀ c ∈ List.range degreeRows32_0.length, + residualCheck 32 7 2 (d+1) (e+1) (a+1) (c+1) degreeRows32_0 degreeP32 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck32_0_0 + · exact degreeCheck32_0_1 + · exact degreeCheck32_0_2 + · exact degreeCheck32_0_3 + · exact degreeCheck32_0_4 + · exact degreeCheck32_1_0 + · exact degreeCheck32_1_1 + · exact degreeCheck32_1_2 + · exact degreeCheck32_1_3 + · exact degreeCheck32_1_4 + · exact degreeCheck32_2_0 + · exact degreeCheck32_2_1 + · exact degreeCheck32_2_2 + · exact degreeCheck32_2_3 + · exact degreeCheck32_2_4 + · exact degreeCheck32_3_0 + · exact degreeCheck32_3_1 + · exact degreeCheck32_3_2 + · exact degreeCheck32_3_3 + · exact degreeCheck32_3_4 + · exact degreeCheck32_4_0 + · exact degreeCheck32_4_1 + · exact degreeCheck32_4_2 + · exact degreeCheck32_4_3 + · exact degreeCheck32_4_4 + +lemma degree_pos32 (μ : YoungDiagram) (hμ : μ.card = 32) : + 0 < kronecker (canonicalTableau (candidate 7 1 0) degreeCard32) + (canonicalTableau (candidate 7 1 0) degreeCard32) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 2) (by decide) (by decide) rfl (by decide) + degreeCard32 degreeRows32_0 (by decide) (by decide) + degreePlan32_0 (by decide) (by decide) (by decide) (by decide) degreeP32 ?_ + degreeCheck32 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard32 rfl degreeCones32 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree33.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree33.lean index dcaebbb5b3dc1da1a07eeb9362cd187e6e2e8b0c..953204800334059fdafd0b6ea77e62b8d18d53bf 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree33.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree33.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 33. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard33 : (candidate 6 3 0).card = 33 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan33_0 : PackingPlan := (.join (.neighbor 8 [5,4,4,4]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 4 1 [5,4]))) -def degreeRows33_0 : List ℕ := [5,5,4,4,4,4,2,2,2,1] - -lemma degreeCone33_0 (μ : YoungDiagram) (hμ : μ.card = 33) - (hd : RowsDom μ.rowLens degreeRows33_0) : SquareOccurs (candidate 6 3 0) μ := by - exact candidate_cone (by decide) degreeCard33 degreePlan33_0 degreeRows33_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs33 : List (List ℕ) := [] - -lemma degreeCones33 : ∀ q ∈ degreeQs33, ∀ μ : YoungDiagram, μ.card = 33 → - RowsDom μ.rowLens q → SquareOccurs (candidate 6 3 0) μ := by - intro q hq - simp only [degreeQs33,List.not_mem_nil] at hq - -abbrev degreeP33 := ResidualProperty 6 6 degreeQs33 [] - -lemma degreeCheck33_0_0 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 1 1 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_0_1 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 1 2 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_0_2 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 1 3 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_0_3 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 1 4 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_0_4 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 1 5 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_1_0 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 2 1 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_1_1 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 2 2 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_1_2 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 2 3 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_1_3 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 2 4 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_1_4 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 2 5 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_2_0 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 3 1 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_2_1 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 3 2 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_2_2 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 3 3 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_2_3 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 3 4 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_2_4 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 3 5 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_3_0 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 4 1 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_3_1 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 4 2 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_3_2 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 4 3 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_3_3 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 4 4 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_3_4 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 4 5 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_4_0 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 5 1 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_4_1 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 5 2 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_4_2 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 5 3 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_4_3 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 5 4 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33_4_4 : - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 5 5 (a+1) (c+1) degreeRows33_0 degreeP33 := by - decide +kernel - -lemma degreeCheck33 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, - residualCheck 33 6 6 (d+1) (e+1) (a+1) (c+1) degreeRows33_0 degreeP33 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck33_0_0 - · exact degreeCheck33_0_1 - · exact degreeCheck33_0_2 - · exact degreeCheck33_0_3 - · exact degreeCheck33_0_4 - · exact degreeCheck33_1_0 - · exact degreeCheck33_1_1 - · exact degreeCheck33_1_2 - · exact degreeCheck33_1_3 - · exact degreeCheck33_1_4 - · exact degreeCheck33_2_0 - · exact degreeCheck33_2_1 - · exact degreeCheck33_2_2 - · exact degreeCheck33_2_3 - · exact degreeCheck33_2_4 - · exact degreeCheck33_3_0 - · exact degreeCheck33_3_1 - · exact degreeCheck33_3_2 - · exact degreeCheck33_3_3 - · exact degreeCheck33_3_4 - · exact degreeCheck33_4_0 - · exact degreeCheck33_4_1 - · exact degreeCheck33_4_2 - · exact degreeCheck33_4_3 - · exact degreeCheck33_4_4 - -lemma degree_pos33 (μ : YoungDiagram) (hμ : μ.card = 33) : - 0 < kronecker (canonicalTableau (candidate 6 3 0) degreeCard33) - (canonicalTableau (candidate 6 3 0) degreeCard33) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 6) (by decide) (by decide) rfl (by decide) - degreeCard33 degreeRows33_0 (by decide) (by decide) - degreePlan33_0 (by decide) (by decide) (by decide) (by decide) degreeP33 ?_ - degreeCheck33 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard33 rfl degreeCones33 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 33. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard33 : (candidate 6 3 0).card = 33 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan33_0 : PackingPlan := (.join (.neighbor 8 [5,4,4,4]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 4 1 [5,4]))) +def degreeRows33_0 : List ℕ := [5,5,4,4,4,4,2,2,2,1] + +lemma degreeCone33_0 (μ : YoungDiagram) (hμ : μ.card = 33) + (hd : RowsDom μ.rowLens degreeRows33_0) : SquareOccurs (candidate 6 3 0) μ := by + exact candidate_cone (by decide) degreeCard33 degreePlan33_0 degreeRows33_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs33 : List (List ℕ) := [] + +lemma degreeCones33 : ∀ q ∈ degreeQs33, ∀ μ : YoungDiagram, μ.card = 33 → + RowsDom μ.rowLens q → SquareOccurs (candidate 6 3 0) μ := by + intro q hq + simp only [degreeQs33,List.not_mem_nil] at hq + +abbrev degreeP33 := ResidualProperty 6 6 degreeQs33 [] + +lemma degreeCheck33_0_0 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 1 1 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_0_1 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 1 2 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_0_2 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 1 3 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_0_3 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 1 4 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_0_4 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 1 5 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_1_0 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 2 1 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_1_1 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 2 2 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_1_2 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 2 3 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_1_3 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 2 4 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_1_4 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 2 5 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_2_0 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 3 1 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_2_1 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 3 2 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_2_2 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 3 3 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_2_3 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 3 4 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_2_4 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 3 5 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_3_0 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 4 1 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_3_1 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 4 2 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_3_2 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 4 3 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_3_3 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 4 4 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_3_4 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 4 5 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_4_0 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 5 1 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_4_1 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 5 2 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_4_2 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 5 3 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_4_3 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 5 4 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33_4_4 : + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 5 5 (a+1) (c+1) degreeRows33_0 degreeP33 := by + decide +kernel + +lemma degreeCheck33 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows33_0.length, ∀ c ∈ List.range degreeRows33_0.length, + residualCheck 33 6 6 (d+1) (e+1) (a+1) (c+1) degreeRows33_0 degreeP33 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck33_0_0 + · exact degreeCheck33_0_1 + · exact degreeCheck33_0_2 + · exact degreeCheck33_0_3 + · exact degreeCheck33_0_4 + · exact degreeCheck33_1_0 + · exact degreeCheck33_1_1 + · exact degreeCheck33_1_2 + · exact degreeCheck33_1_3 + · exact degreeCheck33_1_4 + · exact degreeCheck33_2_0 + · exact degreeCheck33_2_1 + · exact degreeCheck33_2_2 + · exact degreeCheck33_2_3 + · exact degreeCheck33_2_4 + · exact degreeCheck33_3_0 + · exact degreeCheck33_3_1 + · exact degreeCheck33_3_2 + · exact degreeCheck33_3_3 + · exact degreeCheck33_3_4 + · exact degreeCheck33_4_0 + · exact degreeCheck33_4_1 + · exact degreeCheck33_4_2 + · exact degreeCheck33_4_3 + · exact degreeCheck33_4_4 + +lemma degree_pos33 (μ : YoungDiagram) (hμ : μ.card = 33) : + 0 < kronecker (canonicalTableau (candidate 6 3 0) degreeCard33) + (canonicalTableau (candidate 6 3 0) degreeCard33) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 6) (by decide) (by decide) rfl (by decide) + degreeCard33 degreeRows33_0 (by decide) (by decide) + degreePlan33_0 (by decide) (by decide) (by decide) (by decide) degreeP33 ?_ + degreeCheck33 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard33 rfl degreeCones33 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree34.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree34.lean index e0946d0ed4cd9bd8715ef367ee2727ffa8eb327f..02ef42873a086036b9565339ed494edf0904e341 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree34.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree34.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 34. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard34 : (candidate 7 1 1).card = 34 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan34_0 : PackingPlan := (.join (.twoPaths 7 [5,5,4,4]) (.join (.neighbor 4 [3,2,2,2]) (.join (.repeated 1 3) (.repeated 2 2)))) -def degreeRows34_0 : List ℕ := [5,5,4,4,4,3,3,2,2,2] - -lemma degreeCone34_0 (μ : YoungDiagram) (hμ : μ.card = 34) - (hd : RowsDom μ.rowLens degreeRows34_0) : SquareOccurs (candidate 7 1 1) μ := by - exact candidate_cone (by decide) degreeCard34 degreePlan34_0 degreeRows34_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs34 : List (List ℕ) := [] - -lemma degreeCones34 : ∀ q ∈ degreeQs34, ∀ μ : YoungDiagram, μ.card = 34 → - RowsDom μ.rowLens q → SquareOccurs (candidate 7 1 1) μ := by - intro q hq - simp only [degreeQs34,List.not_mem_nil] at hq - -abbrev degreeP34 := ResidualProperty 7 3 degreeQs34 [] - -lemma degreeCheck34_0_0 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 1 1 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_0_1 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 1 2 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_0_2 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 1 3 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_0_3 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 1 4 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_0_4 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 1 5 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_1_0 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 2 1 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_1_1 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 2 2 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_1_2 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 2 3 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_1_3 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 2 4 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_1_4 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 2 5 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_2_0 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 3 1 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_2_1 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 3 2 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_2_2 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 3 3 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_2_3 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 3 4 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_2_4 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 3 5 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_3_0 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 4 1 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_3_1 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 4 2 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_3_2 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 4 3 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_3_3 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 4 4 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_3_4 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 4 5 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_4_0 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 5 1 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_4_1 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 5 2 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_4_2 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 5 3 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_4_3 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 5 4 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34_4_4 : - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 5 5 (a+1) (c+1) degreeRows34_0 degreeP34 := by - decide +kernel - -lemma degreeCheck34 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, - residualCheck 34 7 3 (d+1) (e+1) (a+1) (c+1) degreeRows34_0 degreeP34 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck34_0_0 - · exact degreeCheck34_0_1 - · exact degreeCheck34_0_2 - · exact degreeCheck34_0_3 - · exact degreeCheck34_0_4 - · exact degreeCheck34_1_0 - · exact degreeCheck34_1_1 - · exact degreeCheck34_1_2 - · exact degreeCheck34_1_3 - · exact degreeCheck34_1_4 - · exact degreeCheck34_2_0 - · exact degreeCheck34_2_1 - · exact degreeCheck34_2_2 - · exact degreeCheck34_2_3 - · exact degreeCheck34_2_4 - · exact degreeCheck34_3_0 - · exact degreeCheck34_3_1 - · exact degreeCheck34_3_2 - · exact degreeCheck34_3_3 - · exact degreeCheck34_3_4 - · exact degreeCheck34_4_0 - · exact degreeCheck34_4_1 - · exact degreeCheck34_4_2 - · exact degreeCheck34_4_3 - · exact degreeCheck34_4_4 - -lemma degree_pos34 (μ : YoungDiagram) (hμ : μ.card = 34) : - 0 < kronecker (canonicalTableau (candidate 7 1 1) degreeCard34) - (canonicalTableau (candidate 7 1 1) degreeCard34) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 3) (by decide) (by decide) rfl (by decide) - degreeCard34 degreeRows34_0 (by decide) (by decide) - degreePlan34_0 (by decide) (by decide) (by decide) (by decide) degreeP34 ?_ - degreeCheck34 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard34 rfl degreeCones34 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 34. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard34 : (candidate 7 1 1).card = 34 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan34_0 : PackingPlan := (.join (.twoPaths 7 [5,5,4,4]) (.join (.neighbor 4 [3,2,2,2]) (.join (.repeated 1 3) (.repeated 2 2)))) +def degreeRows34_0 : List ℕ := [5,5,4,4,4,3,3,2,2,2] + +lemma degreeCone34_0 (μ : YoungDiagram) (hμ : μ.card = 34) + (hd : RowsDom μ.rowLens degreeRows34_0) : SquareOccurs (candidate 7 1 1) μ := by + exact candidate_cone (by decide) degreeCard34 degreePlan34_0 degreeRows34_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs34 : List (List ℕ) := [] + +lemma degreeCones34 : ∀ q ∈ degreeQs34, ∀ μ : YoungDiagram, μ.card = 34 → + RowsDom μ.rowLens q → SquareOccurs (candidate 7 1 1) μ := by + intro q hq + simp only [degreeQs34,List.not_mem_nil] at hq + +abbrev degreeP34 := ResidualProperty 7 3 degreeQs34 [] + +lemma degreeCheck34_0_0 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 1 1 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_0_1 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 1 2 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_0_2 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 1 3 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_0_3 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 1 4 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_0_4 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 1 5 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_1_0 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 2 1 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_1_1 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 2 2 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_1_2 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 2 3 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_1_3 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 2 4 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_1_4 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 2 5 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_2_0 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 3 1 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_2_1 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 3 2 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_2_2 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 3 3 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_2_3 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 3 4 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_2_4 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 3 5 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_3_0 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 4 1 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_3_1 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 4 2 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_3_2 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 4 3 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_3_3 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 4 4 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_3_4 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 4 5 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_4_0 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 5 1 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_4_1 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 5 2 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_4_2 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 5 3 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_4_3 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 5 4 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34_4_4 : + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 5 5 (a+1) (c+1) degreeRows34_0 degreeP34 := by + decide +kernel + +lemma degreeCheck34 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows34_0.length, ∀ c ∈ List.range degreeRows34_0.length, + residualCheck 34 7 3 (d+1) (e+1) (a+1) (c+1) degreeRows34_0 degreeP34 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck34_0_0 + · exact degreeCheck34_0_1 + · exact degreeCheck34_0_2 + · exact degreeCheck34_0_3 + · exact degreeCheck34_0_4 + · exact degreeCheck34_1_0 + · exact degreeCheck34_1_1 + · exact degreeCheck34_1_2 + · exact degreeCheck34_1_3 + · exact degreeCheck34_1_4 + · exact degreeCheck34_2_0 + · exact degreeCheck34_2_1 + · exact degreeCheck34_2_2 + · exact degreeCheck34_2_3 + · exact degreeCheck34_2_4 + · exact degreeCheck34_3_0 + · exact degreeCheck34_3_1 + · exact degreeCheck34_3_2 + · exact degreeCheck34_3_3 + · exact degreeCheck34_3_4 + · exact degreeCheck34_4_0 + · exact degreeCheck34_4_1 + · exact degreeCheck34_4_2 + · exact degreeCheck34_4_3 + · exact degreeCheck34_4_4 + +lemma degree_pos34 (μ : YoungDiagram) (hμ : μ.card = 34) : + 0 < kronecker (canonicalTableau (candidate 7 1 1) degreeCard34) + (canonicalTableau (candidate 7 1 1) degreeCard34) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 3) (by decide) (by decide) rfl (by decide) + degreeCard34 degreeRows34_0 (by decide) (by decide) + degreePlan34_0 (by decide) (by decide) (by decide) (by decide) degreeP34 ?_ + degreeCheck34 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard34 rfl degreeCones34 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree35.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree35.lean index 4c9022d12315847982953f82f1bd623992ea6521..bb03db8e09e24b159d6d69a62635dddbc87c8f79 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree35.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree35.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks35 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof35 - -namespace OAI - -/-! Numerical Degree 35. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos35 (μ : YoungDiagram) (hμ : μ.card = 35) : - 0 < kronecker (canonicalTableau (candidate 6 3 1) degreeCard35) - (canonicalTableau (candidate 6 3 1) degreeCard35) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 7) (by decide) (by decide) rfl (by decide) - degreeCard35 degreeRows35_0 (by decide) (by decide) - degreePlan35_0 (by decide) (by decide) (by decide) (by decide) degreeP35 ?_ - degreeCheck35 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard35 rfl degreeCones35 - degreeTreeAll35 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks35 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof35 + +namespace OAI + +/-! Numerical Degree 35. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos35 (μ : YoungDiagram) (hμ : μ.card = 35) : + 0 < kronecker (canonicalTableau (candidate 6 3 1) degreeCard35) + (canonicalTableau (candidate 6 3 1) degreeCard35) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 7) (by decide) (by decide) rfl (by decide) + degreeCard35 degreeRows35_0 (by decide) (by decide) + degreePlan35_0 (by decide) (by decide) (by decide) (by decide) degreeP35 ?_ + degreeCheck35 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard35 rfl degreeCones35 + degreeTreeAll35 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree37.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree37.lean index 3986c24225abebf15cc6aeedbf74ce3f32dca007..bc2ec3c2e898e27b2031baf772d5fcf6a10200d3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree37.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree37.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks37 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof37 - -namespace OAI - -/-! Numerical Degree 37. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos37 (μ : YoungDiagram) (hμ : μ.card = 37) : - 0 < kronecker (canonicalTableau (candidate 6 4 0) degreeCard37) - (canonicalTableau (candidate 6 4 0) degreeCard37) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 8) (by decide) (by decide) rfl (by decide) - degreeCard37 degreeRows37_0 (by decide) (by decide) - degreePlan37_0 (by decide) (by decide) (by decide) (by decide) degreeP37 ?_ - degreeCheck37 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard37 rfl degreeCones37 - degreeTreeAll37 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks37 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof37 + +namespace OAI + +/-! Numerical Degree 37. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos37 (μ : YoungDiagram) (hμ : μ.card = 37) : + 0 < kronecker (canonicalTableau (candidate 6 4 0) degreeCard37) + (canonicalTableau (candidate 6 4 0) degreeCard37) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 8) (by decide) (by decide) rfl (by decide) + degreeCard37 degreeRows37_0 (by decide) (by decide) + degreePlan37_0 (by decide) (by decide) (by decide) (by decide) degreeP37 ?_ + degreeCheck37 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard37 rfl degreeCones37 + degreeTreeAll37 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree38.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree38.lean index ea95028c36fb630b2244de0d07c2e0031532d05d..c4b34f63e61b7f601b5305128c075b216c284aee 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree38.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree38.lean @@ -1,218 +1,218 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 38. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard38 : (candidate 8 0 1).card = 38 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan38_0 : PackingPlan := (.join (.twoPaths 7 [5,5,4,4]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 1 2)))) -def degreeRows38_0 : List ℕ := [5,5,4,4,3,3,3,2,2,2,2,2,1] - -lemma degreeCone38_0 (μ : YoungDiagram) (hμ : μ.card = 38) - (hd : RowsDom μ.rowLens degreeRows38_0) : SquareOccurs (candidate 8 0 1) μ := by - exact candidate_cone (by decide) degreeCard38 degreePlan38_0 degreeRows38_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan38_1 : PackingPlan := (.join (.repeated 1 9) (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 4 [3,2,2,2]) (.join (.neighbor 2 [2,1,1,1]) (.repeated 2 1))))) -def degreeRows38_1 : List ℕ := [9,4,3,3,3,3,2,2,2,2,2,1,1,1] - -lemma degreeCone38_1 (μ : YoungDiagram) (hμ : μ.card = 38) - (hd : RowsDom μ.rowLens degreeRows38_1) : SquareOccurs (candidate 8 0 1) μ := by - exact candidate_cone (by decide) degreeCard38 degreePlan38_1 degreeRows38_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs38 : List (List ℕ) := [degreeRows38_1] - -lemma degreeCones38 : ∀ q ∈ degreeQs38, ∀ μ : YoungDiagram, μ.card = 38 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 0 1) μ := by - intro q hq - simp only [degreeQs38,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone38_1 - -abbrev degreeP38 := ResidualProperty 8 1 degreeQs38 [] - -lemma degreeCheck38_0_0 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 1 1 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_0_1 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 1 2 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_0_2 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 1 3 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_0_3 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 1 4 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_0_4 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 1 5 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_1_0 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 2 1 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_1_1 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 2 2 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_1_2 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 2 3 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_1_3 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 2 4 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_1_4 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 2 5 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_2_0 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 3 1 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_2_1 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 3 2 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_2_2 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 3 3 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_2_3 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 3 4 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_2_4 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 3 5 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_3_0 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 4 1 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_3_1 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 4 2 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_3_2 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 4 3 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_3_3 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 4 4 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_3_4 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 4 5 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_4_0 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 5 1 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_4_1 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 5 2 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_4_2 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 5 3 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_4_3 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 5 4 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38_4_4 : - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 5 5 (a+1) (c+1) degreeRows38_0 degreeP38 := by - decide +kernel - -lemma degreeCheck38 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, - residualCheck 38 8 1 (d+1) (e+1) (a+1) (c+1) degreeRows38_0 degreeP38 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck38_0_0 - · exact degreeCheck38_0_1 - · exact degreeCheck38_0_2 - · exact degreeCheck38_0_3 - · exact degreeCheck38_0_4 - · exact degreeCheck38_1_0 - · exact degreeCheck38_1_1 - · exact degreeCheck38_1_2 - · exact degreeCheck38_1_3 - · exact degreeCheck38_1_4 - · exact degreeCheck38_2_0 - · exact degreeCheck38_2_1 - · exact degreeCheck38_2_2 - · exact degreeCheck38_2_3 - · exact degreeCheck38_2_4 - · exact degreeCheck38_3_0 - · exact degreeCheck38_3_1 - · exact degreeCheck38_3_2 - · exact degreeCheck38_3_3 - · exact degreeCheck38_3_4 - · exact degreeCheck38_4_0 - · exact degreeCheck38_4_1 - · exact degreeCheck38_4_2 - · exact degreeCheck38_4_3 - · exact degreeCheck38_4_4 - -lemma degree_pos38 (μ : YoungDiagram) (hμ : μ.card = 38) : - 0 < kronecker (canonicalTableau (candidate 8 0 1) degreeCard38) - (canonicalTableau (candidate 8 0 1) degreeCard38) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) - degreeCard38 degreeRows38_0 (by decide) (by decide) - degreePlan38_0 (by decide) (by decide) (by decide) (by decide) degreeP38 ?_ - degreeCheck38 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard38 rfl degreeCones38 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 38. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard38 : (candidate 8 0 1).card = 38 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan38_0 : PackingPlan := (.join (.twoPaths 7 [5,5,4,4]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 1 2)))) +def degreeRows38_0 : List ℕ := [5,5,4,4,3,3,3,2,2,2,2,2,1] + +lemma degreeCone38_0 (μ : YoungDiagram) (hμ : μ.card = 38) + (hd : RowsDom μ.rowLens degreeRows38_0) : SquareOccurs (candidate 8 0 1) μ := by + exact candidate_cone (by decide) degreeCard38 degreePlan38_0 degreeRows38_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan38_1 : PackingPlan := (.join (.repeated 1 9) (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 4 [3,2,2,2]) (.join (.neighbor 2 [2,1,1,1]) (.repeated 2 1))))) +def degreeRows38_1 : List ℕ := [9,4,3,3,3,3,2,2,2,2,2,1,1,1] + +lemma degreeCone38_1 (μ : YoungDiagram) (hμ : μ.card = 38) + (hd : RowsDom μ.rowLens degreeRows38_1) : SquareOccurs (candidate 8 0 1) μ := by + exact candidate_cone (by decide) degreeCard38 degreePlan38_1 degreeRows38_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs38 : List (List ℕ) := [degreeRows38_1] + +lemma degreeCones38 : ∀ q ∈ degreeQs38, ∀ μ : YoungDiagram, μ.card = 38 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 0 1) μ := by + intro q hq + simp only [degreeQs38,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone38_1 + +abbrev degreeP38 := ResidualProperty 8 1 degreeQs38 [] + +lemma degreeCheck38_0_0 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 1 1 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_0_1 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 1 2 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_0_2 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 1 3 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_0_3 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 1 4 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_0_4 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 1 5 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_1_0 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 2 1 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_1_1 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 2 2 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_1_2 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 2 3 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_1_3 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 2 4 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_1_4 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 2 5 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_2_0 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 3 1 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_2_1 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 3 2 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_2_2 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 3 3 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_2_3 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 3 4 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_2_4 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 3 5 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_3_0 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 4 1 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_3_1 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 4 2 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_3_2 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 4 3 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_3_3 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 4 4 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_3_4 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 4 5 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_4_0 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 5 1 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_4_1 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 5 2 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_4_2 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 5 3 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_4_3 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 5 4 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38_4_4 : + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 5 5 (a+1) (c+1) degreeRows38_0 degreeP38 := by + decide +kernel + +lemma degreeCheck38 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows38_0.length, ∀ c ∈ List.range degreeRows38_0.length, + residualCheck 38 8 1 (d+1) (e+1) (a+1) (c+1) degreeRows38_0 degreeP38 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck38_0_0 + · exact degreeCheck38_0_1 + · exact degreeCheck38_0_2 + · exact degreeCheck38_0_3 + · exact degreeCheck38_0_4 + · exact degreeCheck38_1_0 + · exact degreeCheck38_1_1 + · exact degreeCheck38_1_2 + · exact degreeCheck38_1_3 + · exact degreeCheck38_1_4 + · exact degreeCheck38_2_0 + · exact degreeCheck38_2_1 + · exact degreeCheck38_2_2 + · exact degreeCheck38_2_3 + · exact degreeCheck38_2_4 + · exact degreeCheck38_3_0 + · exact degreeCheck38_3_1 + · exact degreeCheck38_3_2 + · exact degreeCheck38_3_3 + · exact degreeCheck38_3_4 + · exact degreeCheck38_4_0 + · exact degreeCheck38_4_1 + · exact degreeCheck38_4_2 + · exact degreeCheck38_4_3 + · exact degreeCheck38_4_4 + +lemma degree_pos38 (μ : YoungDiagram) (hμ : μ.card = 38) : + 0 < kronecker (canonicalTableau (candidate 8 0 1) degreeCard38) + (canonicalTableau (candidate 8 0 1) degreeCard38) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) + degreeCard38 degreeRows38_0 (by decide) (by decide) + degreePlan38_0 (by decide) (by decide) (by decide) (by decide) degreeP38 ?_ + degreeCheck38 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard38 rfl degreeCones38 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree39.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree39.lean index d5ffb92573031a5dad9af4e932d6309179a5f43a..dc35d5f9041b263b299d59a7a39644b79cfb7c90 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree39.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree39.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks39 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof39 - -namespace OAI - -/-! Numerical Degree 39. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos39 (μ : YoungDiagram) (hμ : μ.card = 39) : - 0 < kronecker (canonicalTableau (candidate 6 4 1) degreeCard39) - (canonicalTableau (candidate 6 4 1) degreeCard39) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 9) (by decide) (by decide) rfl (by decide) - degreeCard39 degreeRows39_0 (by decide) (by decide) - degreePlan39_0 (by decide) (by decide) (by decide) (by decide) degreeP39 ?_ - degreeCheck39 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard39 rfl degreeCones39 - degreeTreeAll39 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks39 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof39 + +namespace OAI + +/-! Numerical Degree 39. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos39 (μ : YoungDiagram) (hμ : μ.card = 39) : + 0 < kronecker (canonicalTableau (candidate 6 4 1) degreeCard39) + (canonicalTableau (candidate 6 4 1) degreeCard39) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 9) (by decide) (by decide) rfl (by decide) + degreeCard39 degreeRows39_0 (by decide) (by decide) + degreePlan39_0 (by decide) (by decide) (by decide) (by decide) degreeP39 ?_ + degreeCheck39 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard39 rfl degreeCones39 + degreeTreeAll39 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree40.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree40.lean index be1d8d64591cee382e210fb61bd5e759e561f380..73c74b20cc3f1cc49c3b6c5ee41a089ba4921576 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree40.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree40.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 40. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard40 : (candidate 8 1 0).card = 40 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan40_0 : PackingPlan := (.join (.neighbor 8 [5,4,4,4]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 2 1 [3,2])))) -def degreeRows40_0 : List ℕ := [5,4,4,4,3,3,3,3,2,2,2,2,2,1] - -lemma degreeCone40_0 (μ : YoungDiagram) (hμ : μ.card = 40) - (hd : RowsDom μ.rowLens degreeRows40_0) : SquareOccurs (candidate 8 1 0) μ := by - exact candidate_cone (by decide) degreeCard40 degreePlan40_0 degreeRows40_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs40 : List (List ℕ) := [] - -lemma degreeCones40 : ∀ q ∈ degreeQs40, ∀ μ : YoungDiagram, μ.card = 40 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 1 0) μ := by - intro q hq - simp only [degreeQs40, List.not_mem_nil] at hq - -abbrev degreeP40 := ResidualProperty 8 2 degreeQs40 [] - -lemma degreeCheck40_0_0 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 1 1 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_0_1 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 1 2 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_0_2 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 1 3 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_0_3 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 1 4 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_0_4 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 1 5 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_1_0 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 2 1 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_1_1 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 2 2 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_1_2 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 2 3 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_1_3 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 2 4 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_1_4 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 2 5 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_2_0 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 3 1 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_2_1 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 3 2 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_2_2 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 3 3 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_2_3 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 3 4 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_2_4 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 3 5 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_3_0 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 4 1 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_3_1 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 4 2 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_3_2 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 4 3 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_3_3 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 4 4 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_3_4 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 4 5 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_4_0 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 5 1 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_4_1 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 5 2 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_4_2 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 5 3 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_4_3 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 5 4 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40_4_4 : - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 5 5 (a+1) (c+1) degreeRows40_0 degreeP40 := by - decide +kernel - -lemma degreeCheck40 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, - residualCheck 40 8 2 (d+1) (e+1) (a+1) (c+1) degreeRows40_0 degreeP40 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck40_0_0 - · exact degreeCheck40_0_1 - · exact degreeCheck40_0_2 - · exact degreeCheck40_0_3 - · exact degreeCheck40_0_4 - · exact degreeCheck40_1_0 - · exact degreeCheck40_1_1 - · exact degreeCheck40_1_2 - · exact degreeCheck40_1_3 - · exact degreeCheck40_1_4 - · exact degreeCheck40_2_0 - · exact degreeCheck40_2_1 - · exact degreeCheck40_2_2 - · exact degreeCheck40_2_3 - · exact degreeCheck40_2_4 - · exact degreeCheck40_3_0 - · exact degreeCheck40_3_1 - · exact degreeCheck40_3_2 - · exact degreeCheck40_3_3 - · exact degreeCheck40_3_4 - · exact degreeCheck40_4_0 - · exact degreeCheck40_4_1 - · exact degreeCheck40_4_2 - · exact degreeCheck40_4_3 - · exact degreeCheck40_4_4 - -lemma degree_pos40 (μ : YoungDiagram) (hμ : μ.card = 40) : - 0 < kronecker (canonicalTableau (candidate 8 1 0) degreeCard40) - (canonicalTableau (candidate 8 1 0) degreeCard40) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 2) (by decide) (by decide) rfl (by decide) - degreeCard40 degreeRows40_0 (by decide) (by decide) - degreePlan40_0 (by decide) (by decide) (by decide) (by decide) degreeP40 ?_ - degreeCheck40 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard40 rfl degreeCones40 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 40. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard40 : (candidate 8 1 0).card = 40 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan40_0 : PackingPlan := (.join (.neighbor 8 [5,4,4,4]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 2 1 [3,2])))) +def degreeRows40_0 : List ℕ := [5,4,4,4,3,3,3,3,2,2,2,2,2,1] + +lemma degreeCone40_0 (μ : YoungDiagram) (hμ : μ.card = 40) + (hd : RowsDom μ.rowLens degreeRows40_0) : SquareOccurs (candidate 8 1 0) μ := by + exact candidate_cone (by decide) degreeCard40 degreePlan40_0 degreeRows40_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs40 : List (List ℕ) := [] + +lemma degreeCones40 : ∀ q ∈ degreeQs40, ∀ μ : YoungDiagram, μ.card = 40 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 1 0) μ := by + intro q hq + simp only [degreeQs40, List.not_mem_nil] at hq + +abbrev degreeP40 := ResidualProperty 8 2 degreeQs40 [] + +lemma degreeCheck40_0_0 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 1 1 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_0_1 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 1 2 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_0_2 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 1 3 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_0_3 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 1 4 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_0_4 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 1 5 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_1_0 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 2 1 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_1_1 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 2 2 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_1_2 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 2 3 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_1_3 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 2 4 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_1_4 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 2 5 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_2_0 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 3 1 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_2_1 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 3 2 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_2_2 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 3 3 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_2_3 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 3 4 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_2_4 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 3 5 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_3_0 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 4 1 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_3_1 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 4 2 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_3_2 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 4 3 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_3_3 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 4 4 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_3_4 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 4 5 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_4_0 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 5 1 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_4_1 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 5 2 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_4_2 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 5 3 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_4_3 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 5 4 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40_4_4 : + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 5 5 (a+1) (c+1) degreeRows40_0 degreeP40 := by + decide +kernel + +lemma degreeCheck40 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows40_0.length, ∀ c ∈ List.range degreeRows40_0.length, + residualCheck 40 8 2 (d+1) (e+1) (a+1) (c+1) degreeRows40_0 degreeP40 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck40_0_0 + · exact degreeCheck40_0_1 + · exact degreeCheck40_0_2 + · exact degreeCheck40_0_3 + · exact degreeCheck40_0_4 + · exact degreeCheck40_1_0 + · exact degreeCheck40_1_1 + · exact degreeCheck40_1_2 + · exact degreeCheck40_1_3 + · exact degreeCheck40_1_4 + · exact degreeCheck40_2_0 + · exact degreeCheck40_2_1 + · exact degreeCheck40_2_2 + · exact degreeCheck40_2_3 + · exact degreeCheck40_2_4 + · exact degreeCheck40_3_0 + · exact degreeCheck40_3_1 + · exact degreeCheck40_3_2 + · exact degreeCheck40_3_3 + · exact degreeCheck40_3_4 + · exact degreeCheck40_4_0 + · exact degreeCheck40_4_1 + · exact degreeCheck40_4_2 + · exact degreeCheck40_4_3 + · exact degreeCheck40_4_4 + +lemma degree_pos40 (μ : YoungDiagram) (hμ : μ.card = 40) : + 0 < kronecker (canonicalTableau (candidate 8 1 0) degreeCard40) + (canonicalTableau (candidate 8 1 0) degreeCard40) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 2) (by decide) (by decide) rfl (by decide) + degreeCard40 degreeRows40_0 (by decide) (by decide) + degreePlan40_0 (by decide) (by decide) (by decide) (by decide) degreeP40 ?_ + degreeCheck40 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard40 rfl degreeCones40 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree41.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree41.lean index 583793e1981bf4f69e76c90081c365313d0ba58f..15622403f015db25a2220ba0ead4d8a34d4bebbc 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree41.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree41.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks41 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof41 - -namespace OAI - -/-! Numerical Degree 41. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos41 (μ : YoungDiagram) (hμ : μ.card = 41) : - 0 < kronecker (canonicalTableau (candidate 6 5 0) degreeCard41) - (canonicalTableau (candidate 6 5 0) degreeCard41) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 10) (by decide) (by decide) rfl (by decide) - degreeCard41 degreeRows41_0 (by decide) (by decide) - degreePlan41_0 (by decide) (by decide) (by decide) (by decide) degreeP41 ?_ - degreeCheck41 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard41 rfl degreeCones41 - degreeTreeAll41 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks41 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof41 + +namespace OAI + +/-! Numerical Degree 41. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos41 (μ : YoungDiagram) (hμ : μ.card = 41) : + 0 < kronecker (canonicalTableau (candidate 6 5 0) degreeCard41) + (canonicalTableau (candidate 6 5 0) degreeCard41) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 10) (by decide) (by decide) rfl (by decide) + degreeCard41 degreeRows41_0 (by decide) (by decide) + degreePlan41_0 (by decide) (by decide) (by decide) (by decide) degreeP41 ?_ + degreeCheck41 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard41 rfl degreeCones41 + degreeTreeAll41 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree42.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree42.lean index 5cd59b16e110c77b6e4904b9cff20b5b6d48f069..c6f723b67d54c7b9359d9eaf5d4547d29a2facb3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree42.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree42.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 42. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard42 : (candidate 8 1 1).card = 42 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan42_0 : PackingPlan := (.join (.twoPaths 8 [5,5,5,5]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 2 2)))) -def degreeRows42_0 : List ℕ := [5,5,5,5,4,3,3,3,2,2,2,2,1] - -lemma degreeCone42_0 (μ : YoungDiagram) (hμ : μ.card = 42) - (hd : RowsDom μ.rowLens degreeRows42_0) : SquareOccurs (candidate 8 1 1) μ := by - exact candidate_cone (by decide) degreeCard42 degreePlan42_0 degreeRows42_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs42 : List (List ℕ) := [] - -lemma degreeCones42 : ∀ q ∈ degreeQs42, ∀ μ : YoungDiagram, μ.card = 42 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 1 1) μ := by - intro q hq - simp only [degreeQs42,List.not_mem_nil] at hq - -abbrev degreeP42 := ResidualProperty 8 3 degreeQs42 [] - -lemma degreeCheck42_0_0 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 1 1 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_0_1 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 1 2 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_0_2 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 1 3 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_0_3 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 1 4 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_0_4 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 1 5 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_1_0 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 2 1 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_1_1 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 2 2 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_1_2 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 2 3 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_1_3 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 2 4 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_1_4 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 2 5 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_2_0 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 3 1 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_2_1 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 3 2 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_2_2 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 3 3 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_2_3 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 3 4 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_2_4 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 3 5 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_3_0 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 4 1 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_3_1 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 4 2 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_3_2 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 4 3 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_3_3 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 4 4 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_3_4 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 4 5 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_4_0 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 5 1 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_4_1 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 5 2 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_4_2 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 5 3 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_4_3 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 5 4 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42_4_4 : - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 5 5 (a+1) (c+1) degreeRows42_0 degreeP42 := by - decide +kernel - -lemma degreeCheck42 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, - residualCheck 42 8 3 (d+1) (e+1) (a+1) (c+1) degreeRows42_0 degreeP42 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck42_0_0 - · exact degreeCheck42_0_1 - · exact degreeCheck42_0_2 - · exact degreeCheck42_0_3 - · exact degreeCheck42_0_4 - · exact degreeCheck42_1_0 - · exact degreeCheck42_1_1 - · exact degreeCheck42_1_2 - · exact degreeCheck42_1_3 - · exact degreeCheck42_1_4 - · exact degreeCheck42_2_0 - · exact degreeCheck42_2_1 - · exact degreeCheck42_2_2 - · exact degreeCheck42_2_3 - · exact degreeCheck42_2_4 - · exact degreeCheck42_3_0 - · exact degreeCheck42_3_1 - · exact degreeCheck42_3_2 - · exact degreeCheck42_3_3 - · exact degreeCheck42_3_4 - · exact degreeCheck42_4_0 - · exact degreeCheck42_4_1 - · exact degreeCheck42_4_2 - · exact degreeCheck42_4_3 - · exact degreeCheck42_4_4 - -lemma degree_pos42 (μ : YoungDiagram) (hμ : μ.card = 42) : - 0 < kronecker (canonicalTableau (candidate 8 1 1) degreeCard42) - (canonicalTableau (candidate 8 1 1) degreeCard42) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 3) (by decide) (by decide) rfl (by decide) - degreeCard42 degreeRows42_0 (by decide) (by decide) - degreePlan42_0 (by decide) (by decide) (by decide) (by decide) degreeP42 ?_ - degreeCheck42 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard42 rfl degreeCones42 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 42. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard42 : (candidate 8 1 1).card = 42 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan42_0 : PackingPlan := (.join (.twoPaths 8 [5,5,5,5]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 2 2)))) +def degreeRows42_0 : List ℕ := [5,5,5,5,4,3,3,3,2,2,2,2,1] + +lemma degreeCone42_0 (μ : YoungDiagram) (hμ : μ.card = 42) + (hd : RowsDom μ.rowLens degreeRows42_0) : SquareOccurs (candidate 8 1 1) μ := by + exact candidate_cone (by decide) degreeCard42 degreePlan42_0 degreeRows42_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs42 : List (List ℕ) := [] + +lemma degreeCones42 : ∀ q ∈ degreeQs42, ∀ μ : YoungDiagram, μ.card = 42 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 1 1) μ := by + intro q hq + simp only [degreeQs42,List.not_mem_nil] at hq + +abbrev degreeP42 := ResidualProperty 8 3 degreeQs42 [] + +lemma degreeCheck42_0_0 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 1 1 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_0_1 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 1 2 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_0_2 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 1 3 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_0_3 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 1 4 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_0_4 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 1 5 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_1_0 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 2 1 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_1_1 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 2 2 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_1_2 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 2 3 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_1_3 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 2 4 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_1_4 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 2 5 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_2_0 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 3 1 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_2_1 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 3 2 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_2_2 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 3 3 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_2_3 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 3 4 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_2_4 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 3 5 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_3_0 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 4 1 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_3_1 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 4 2 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_3_2 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 4 3 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_3_3 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 4 4 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_3_4 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 4 5 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_4_0 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 5 1 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_4_1 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 5 2 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_4_2 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 5 3 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_4_3 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 5 4 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42_4_4 : + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 5 5 (a+1) (c+1) degreeRows42_0 degreeP42 := by + decide +kernel + +lemma degreeCheck42 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows42_0.length, ∀ c ∈ List.range degreeRows42_0.length, + residualCheck 42 8 3 (d+1) (e+1) (a+1) (c+1) degreeRows42_0 degreeP42 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck42_0_0 + · exact degreeCheck42_0_1 + · exact degreeCheck42_0_2 + · exact degreeCheck42_0_3 + · exact degreeCheck42_0_4 + · exact degreeCheck42_1_0 + · exact degreeCheck42_1_1 + · exact degreeCheck42_1_2 + · exact degreeCheck42_1_3 + · exact degreeCheck42_1_4 + · exact degreeCheck42_2_0 + · exact degreeCheck42_2_1 + · exact degreeCheck42_2_2 + · exact degreeCheck42_2_3 + · exact degreeCheck42_2_4 + · exact degreeCheck42_3_0 + · exact degreeCheck42_3_1 + · exact degreeCheck42_3_2 + · exact degreeCheck42_3_3 + · exact degreeCheck42_3_4 + · exact degreeCheck42_4_0 + · exact degreeCheck42_4_1 + · exact degreeCheck42_4_2 + · exact degreeCheck42_4_3 + · exact degreeCheck42_4_4 + +lemma degree_pos42 (μ : YoungDiagram) (hμ : μ.card = 42) : + 0 < kronecker (canonicalTableau (candidate 8 1 1) degreeCard42) + (canonicalTableau (candidate 8 1 1) degreeCard42) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 3) (by decide) (by decide) rfl (by decide) + degreeCard42 degreeRows42_0 (by decide) (by decide) + degreePlan42_0 (by decide) (by decide) (by decide) (by decide) degreeP42 ?_ + degreeCheck42 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard42 rfl degreeCones42 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree43.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree43.lean index 96471bd908da64ee9e6cada4699ec2b892b28bce..72b79231b0a9837fd9b1285edf60dd9323bc5990 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree43.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree43.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks43 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof43 - -namespace OAI - -/-! Numerical Degree 43. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos43 (μ : YoungDiagram) (hμ : μ.card = 43) : - 0 < kronecker (canonicalTableau (candidate 6 5 1) degreeCard43) - (canonicalTableau (candidate 6 5 1) degreeCard43) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 11) (by decide) (by decide) rfl (by decide) - degreeCard43 degreeRows43_0 (by decide) (by decide) - degreePlan43_0 (by decide) (by decide) (by decide) (by decide) degreeP43 ?_ - degreeCheck43 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard43 rfl degreeCones43 - degreeTreeAll43 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks43 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof43 + +namespace OAI + +/-! Numerical Degree 43. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos43 (μ : YoungDiagram) (hμ : μ.card = 43) : + 0 < kronecker (canonicalTableau (candidate 6 5 1) degreeCard43) + (canonicalTableau (candidate 6 5 1) degreeCard43) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 11) (by decide) (by decide) rfl (by decide) + degreeCard43 degreeRows43_0 (by decide) (by decide) + degreePlan43_0 (by decide) (by decide) (by decide) (by decide) degreeP43 ?_ + degreeCheck43 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard43 rfl degreeCones43 + degreeTreeAll43 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree44.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree44.lean index a71bc548b7e10b82f4dc8c8815cf7994f1601ce8..0b5be560445cafb6d471ac08850dcdac21dd01ed 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree44.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree44.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 44. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard44 : (candidate 8 2 0).card = 44 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan44_0 : PackingPlan := (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 3 1 [4,3])))) -def degreeRows44_0 : List ℕ := [5,5,5,4,4,3,3,3,3,2,2,2,2,1] - -lemma degreeCone44_0 (μ : YoungDiagram) (hμ : μ.card = 44) - (hd : RowsDom μ.rowLens degreeRows44_0) : SquareOccurs (candidate 8 2 0) μ := by - exact candidate_cone (by decide) degreeCard44 degreePlan44_0 degreeRows44_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs44 : List (List ℕ) := [] - -lemma degreeCones44 : ∀ q ∈ degreeQs44, ∀ μ : YoungDiagram, μ.card = 44 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 2 0) μ := by - intro q hq - simp only [degreeQs44,List.not_mem_nil] at hq - -abbrev degreeP44 := ResidualProperty 8 4 degreeQs44 [] - -lemma degreeCheck44_0_0 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 1 1 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_0_1 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 1 2 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_0_2 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 1 3 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_0_3 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 1 4 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_0_4 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 1 5 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_1_0 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 2 1 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_1_1 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 2 2 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_1_2 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 2 3 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_1_3 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 2 4 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_1_4 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 2 5 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_2_0 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 3 1 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_2_1 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 3 2 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_2_2 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 3 3 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_2_3 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 3 4 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_2_4 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 3 5 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_3_0 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 4 1 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_3_1 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 4 2 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_3_2 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 4 3 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_3_3 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 4 4 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_3_4 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 4 5 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_4_0 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 5 1 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_4_1 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 5 2 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_4_2 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 5 3 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_4_3 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 5 4 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44_4_4 : - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 5 5 (a+1) (c+1) degreeRows44_0 degreeP44 := by - decide +kernel - -lemma degreeCheck44 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, - residualCheck 44 8 4 (d+1) (e+1) (a+1) (c+1) degreeRows44_0 degreeP44 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck44_0_0 - · exact degreeCheck44_0_1 - · exact degreeCheck44_0_2 - · exact degreeCheck44_0_3 - · exact degreeCheck44_0_4 - · exact degreeCheck44_1_0 - · exact degreeCheck44_1_1 - · exact degreeCheck44_1_2 - · exact degreeCheck44_1_3 - · exact degreeCheck44_1_4 - · exact degreeCheck44_2_0 - · exact degreeCheck44_2_1 - · exact degreeCheck44_2_2 - · exact degreeCheck44_2_3 - · exact degreeCheck44_2_4 - · exact degreeCheck44_3_0 - · exact degreeCheck44_3_1 - · exact degreeCheck44_3_2 - · exact degreeCheck44_3_3 - · exact degreeCheck44_3_4 - · exact degreeCheck44_4_0 - · exact degreeCheck44_4_1 - · exact degreeCheck44_4_2 - · exact degreeCheck44_4_3 - · exact degreeCheck44_4_4 - -lemma degree_pos44 (μ : YoungDiagram) (hμ : μ.card = 44) : - 0 < kronecker (canonicalTableau (candidate 8 2 0) degreeCard44) - (canonicalTableau (candidate 8 2 0) degreeCard44) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 4) (by decide) (by decide) rfl (by decide) - degreeCard44 degreeRows44_0 (by decide) (by decide) - degreePlan44_0 (by decide) (by decide) (by decide) (by decide) degreeP44 ?_ - degreeCheck44 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard44 rfl degreeCones44 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 44. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard44 : (candidate 8 2 0).card = 44 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan44_0 : PackingPlan := (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 3 1 [4,3])))) +def degreeRows44_0 : List ℕ := [5,5,5,4,4,3,3,3,3,2,2,2,2,1] + +lemma degreeCone44_0 (μ : YoungDiagram) (hμ : μ.card = 44) + (hd : RowsDom μ.rowLens degreeRows44_0) : SquareOccurs (candidate 8 2 0) μ := by + exact candidate_cone (by decide) degreeCard44 degreePlan44_0 degreeRows44_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs44 : List (List ℕ) := [] + +lemma degreeCones44 : ∀ q ∈ degreeQs44, ∀ μ : YoungDiagram, μ.card = 44 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 2 0) μ := by + intro q hq + simp only [degreeQs44,List.not_mem_nil] at hq + +abbrev degreeP44 := ResidualProperty 8 4 degreeQs44 [] + +lemma degreeCheck44_0_0 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 1 1 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_0_1 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 1 2 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_0_2 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 1 3 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_0_3 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 1 4 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_0_4 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 1 5 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_1_0 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 2 1 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_1_1 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 2 2 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_1_2 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 2 3 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_1_3 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 2 4 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_1_4 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 2 5 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_2_0 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 3 1 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_2_1 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 3 2 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_2_2 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 3 3 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_2_3 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 3 4 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_2_4 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 3 5 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_3_0 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 4 1 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_3_1 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 4 2 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_3_2 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 4 3 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_3_3 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 4 4 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_3_4 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 4 5 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_4_0 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 5 1 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_4_1 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 5 2 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_4_2 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 5 3 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_4_3 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 5 4 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44_4_4 : + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 5 5 (a+1) (c+1) degreeRows44_0 degreeP44 := by + decide +kernel + +lemma degreeCheck44 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows44_0.length, ∀ c ∈ List.range degreeRows44_0.length, + residualCheck 44 8 4 (d+1) (e+1) (a+1) (c+1) degreeRows44_0 degreeP44 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck44_0_0 + · exact degreeCheck44_0_1 + · exact degreeCheck44_0_2 + · exact degreeCheck44_0_3 + · exact degreeCheck44_0_4 + · exact degreeCheck44_1_0 + · exact degreeCheck44_1_1 + · exact degreeCheck44_1_2 + · exact degreeCheck44_1_3 + · exact degreeCheck44_1_4 + · exact degreeCheck44_2_0 + · exact degreeCheck44_2_1 + · exact degreeCheck44_2_2 + · exact degreeCheck44_2_3 + · exact degreeCheck44_2_4 + · exact degreeCheck44_3_0 + · exact degreeCheck44_3_1 + · exact degreeCheck44_3_2 + · exact degreeCheck44_3_3 + · exact degreeCheck44_3_4 + · exact degreeCheck44_4_0 + · exact degreeCheck44_4_1 + · exact degreeCheck44_4_2 + · exact degreeCheck44_4_3 + · exact degreeCheck44_4_4 + +lemma degree_pos44 (μ : YoungDiagram) (hμ : μ.card = 44) : + 0 < kronecker (canonicalTableau (candidate 8 2 0) degreeCard44) + (canonicalTableau (candidate 8 2 0) degreeCard44) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 4) (by decide) (by decide) rfl (by decide) + degreeCard44 degreeRows44_0 (by decide) (by decide) + degreePlan44_0 (by decide) (by decide) (by decide) (by decide) degreeP44 ?_ + degreeCheck44 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard44 rfl degreeCones44 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree46.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree46.lean index e372dea936903a7b87da92f2e83e9847de5a1b24..9a31b7c9d67dc20918a9318f685782c960fd330c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree46.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree46.lean @@ -1,218 +1,218 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 46. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard46 : (candidate 8 2 1).card = 46 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan46_0 : PackingPlan := (.join (.twoPaths 9 [6,6,5,5]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 3 3 [5,4])))) -def degreeRows46_0 : List ℕ := [6,6,5,5,5,4,4,3,3,3,2] - -lemma degreeCone46_0 (μ : YoungDiagram) (hμ : μ.card = 46) - (hd : RowsDom μ.rowLens degreeRows46_0) : SquareOccurs (candidate 8 2 1) μ := by - exact candidate_cone (by decide) degreeCard46 degreePlan46_0 degreeRows46_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan46_1 : PackingPlan := (.join (.twoPaths 9 [6,6,5,5]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 3 2)))) -def degreeRows46_1 : List ℕ := [6,6,6,5,5,3,3,3,2,2,2,2,1] - -lemma degreeCone46_1 (μ : YoungDiagram) (hμ : μ.card = 46) - (hd : RowsDom μ.rowLens degreeRows46_1) : SquareOccurs (candidate 8 2 1) μ := by - exact candidate_cone (by decide) degreeCard46 degreePlan46_1 degreeRows46_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs46 : List (List ℕ) := [degreeRows46_1] - -lemma degreeCones46 : ∀ q ∈ degreeQs46, ∀ μ : YoungDiagram, μ.card = 46 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 2 1) μ := by - intro q hq - simp only [degreeQs46,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone46_1 - -abbrev degreeP46 := ResidualProperty 8 5 degreeQs46 [] - -lemma degreeCheck46_0_0 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 1 1 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_0_1 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 1 2 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_0_2 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 1 3 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_0_3 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 1 4 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_0_4 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 1 5 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_1_0 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 2 1 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_1_1 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 2 2 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_1_2 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 2 3 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_1_3 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 2 4 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_1_4 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 2 5 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_2_0 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 3 1 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_2_1 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 3 2 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_2_2 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 3 3 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_2_3 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 3 4 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_2_4 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 3 5 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_3_0 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 4 1 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_3_1 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 4 2 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_3_2 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 4 3 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_3_3 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 4 4 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_3_4 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 4 5 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_4_0 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 5 1 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_4_1 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 5 2 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_4_2 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 5 3 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_4_3 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 5 4 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46_4_4 : - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 5 5 (a+1) (c+1) degreeRows46_0 degreeP46 := by - decide +kernel - -lemma degreeCheck46 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, - residualCheck 46 8 5 (d+1) (e+1) (a+1) (c+1) degreeRows46_0 degreeP46 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck46_0_0 - · exact degreeCheck46_0_1 - · exact degreeCheck46_0_2 - · exact degreeCheck46_0_3 - · exact degreeCheck46_0_4 - · exact degreeCheck46_1_0 - · exact degreeCheck46_1_1 - · exact degreeCheck46_1_2 - · exact degreeCheck46_1_3 - · exact degreeCheck46_1_4 - · exact degreeCheck46_2_0 - · exact degreeCheck46_2_1 - · exact degreeCheck46_2_2 - · exact degreeCheck46_2_3 - · exact degreeCheck46_2_4 - · exact degreeCheck46_3_0 - · exact degreeCheck46_3_1 - · exact degreeCheck46_3_2 - · exact degreeCheck46_3_3 - · exact degreeCheck46_3_4 - · exact degreeCheck46_4_0 - · exact degreeCheck46_4_1 - · exact degreeCheck46_4_2 - · exact degreeCheck46_4_3 - · exact degreeCheck46_4_4 - -lemma degree_pos46 (μ : YoungDiagram) (hμ : μ.card = 46) : - 0 < kronecker (canonicalTableau (candidate 8 2 1) degreeCard46) - (canonicalTableau (candidate 8 2 1) degreeCard46) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 5) (by decide) (by decide) rfl (by decide) - degreeCard46 degreeRows46_0 (by decide) (by decide) - degreePlan46_0 (by decide) (by decide) (by decide) (by decide) degreeP46 ?_ - degreeCheck46 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard46 rfl degreeCones46 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 46. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard46 : (candidate 8 2 1).card = 46 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan46_0 : PackingPlan := (.join (.twoPaths 9 [6,6,5,5]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 3 3 [5,4])))) +def degreeRows46_0 : List ℕ := [6,6,5,5,5,4,4,3,3,3,2] + +lemma degreeCone46_0 (μ : YoungDiagram) (hμ : μ.card = 46) + (hd : RowsDom μ.rowLens degreeRows46_0) : SquareOccurs (candidate 8 2 1) μ := by + exact candidate_cone (by decide) degreeCard46 degreePlan46_0 degreeRows46_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan46_1 : PackingPlan := (.join (.twoPaths 9 [6,6,5,5]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 3 2)))) +def degreeRows46_1 : List ℕ := [6,6,6,5,5,3,3,3,2,2,2,2,1] + +lemma degreeCone46_1 (μ : YoungDiagram) (hμ : μ.card = 46) + (hd : RowsDom μ.rowLens degreeRows46_1) : SquareOccurs (candidate 8 2 1) μ := by + exact candidate_cone (by decide) degreeCard46 degreePlan46_1 degreeRows46_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs46 : List (List ℕ) := [degreeRows46_1] + +lemma degreeCones46 : ∀ q ∈ degreeQs46, ∀ μ : YoungDiagram, μ.card = 46 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 2 1) μ := by + intro q hq + simp only [degreeQs46,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone46_1 + +abbrev degreeP46 := ResidualProperty 8 5 degreeQs46 [] + +lemma degreeCheck46_0_0 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 1 1 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_0_1 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 1 2 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_0_2 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 1 3 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_0_3 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 1 4 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_0_4 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 1 5 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_1_0 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 2 1 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_1_1 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 2 2 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_1_2 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 2 3 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_1_3 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 2 4 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_1_4 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 2 5 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_2_0 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 3 1 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_2_1 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 3 2 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_2_2 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 3 3 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_2_3 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 3 4 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_2_4 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 3 5 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_3_0 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 4 1 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_3_1 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 4 2 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_3_2 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 4 3 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_3_3 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 4 4 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_3_4 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 4 5 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_4_0 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 5 1 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_4_1 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 5 2 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_4_2 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 5 3 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_4_3 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 5 4 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46_4_4 : + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 5 5 (a+1) (c+1) degreeRows46_0 degreeP46 := by + decide +kernel + +lemma degreeCheck46 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows46_0.length, ∀ c ∈ List.range degreeRows46_0.length, + residualCheck 46 8 5 (d+1) (e+1) (a+1) (c+1) degreeRows46_0 degreeP46 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck46_0_0 + · exact degreeCheck46_0_1 + · exact degreeCheck46_0_2 + · exact degreeCheck46_0_3 + · exact degreeCheck46_0_4 + · exact degreeCheck46_1_0 + · exact degreeCheck46_1_1 + · exact degreeCheck46_1_2 + · exact degreeCheck46_1_3 + · exact degreeCheck46_1_4 + · exact degreeCheck46_2_0 + · exact degreeCheck46_2_1 + · exact degreeCheck46_2_2 + · exact degreeCheck46_2_3 + · exact degreeCheck46_2_4 + · exact degreeCheck46_3_0 + · exact degreeCheck46_3_1 + · exact degreeCheck46_3_2 + · exact degreeCheck46_3_3 + · exact degreeCheck46_3_4 + · exact degreeCheck46_4_0 + · exact degreeCheck46_4_1 + · exact degreeCheck46_4_2 + · exact degreeCheck46_4_3 + · exact degreeCheck46_4_4 + +lemma degree_pos46 (μ : YoungDiagram) (hμ : μ.card = 46) : + 0 < kronecker (canonicalTableau (candidate 8 2 1) degreeCard46) + (canonicalTableau (candidate 8 2 1) degreeCard46) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 5) (by decide) (by decide) rfl (by decide) + degreeCard46 degreeRows46_0 (by decide) (by decide) + degreePlan46_0 (by decide) (by decide) (by decide) (by decide) degreeP46 ?_ + degreeCheck46 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard46 rfl degreeCones46 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree47.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree47.lean index 832a38cc32606b6b12be96e2d97e4884f032f7fd..4b3bcfb168b6f74baff0d1787d9a4f13c2bb57f3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree47.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree47.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 47. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard47 : (candidate 9 0 1).card = 47 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan47_0 : PackingPlan := (.join (.twoPaths 8 [5,5,5,5]) (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 4 [3,2,2,2]) (.neighbor 2 [2,1,1,1])))) -def degreeRows47_0 : List ℕ := [5,5,5,5,4,3,3,3,3,2,2,2,2,1,1,1] - -lemma degreeCone47_0 (μ : YoungDiagram) (hμ : μ.card = 47) - (hd : RowsDom μ.rowLens degreeRows47_0) : SquareOccurs (candidate 9 0 1) μ := by - exact candidate_cone (by decide) degreeCard47 degreePlan47_0 degreeRows47_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs47 : List (List ℕ) := [] - -lemma degreeCones47 : ∀ q ∈ degreeQs47, ∀ μ : YoungDiagram, μ.card = 47 → - RowsDom μ.rowLens q → SquareOccurs (candidate 9 0 1) μ := by - intro q hq - simp only [degreeQs47, List.not_mem_nil] at hq - -abbrev degreeP47 := ResidualProperty 9 1 degreeQs47 [] - -lemma degreeCheck47_0_0 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 1 1 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_0_1 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 1 2 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_0_2 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 1 3 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_0_3 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 1 4 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_0_4 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 1 5 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_1_0 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 2 1 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_1_1 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 2 2 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_1_2 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 2 3 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_1_3 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 2 4 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_1_4 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 2 5 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_2_0 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 3 1 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_2_1 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 3 2 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_2_2 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 3 3 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_2_3 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 3 4 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_2_4 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 3 5 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_3_0 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 4 1 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_3_1 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 4 2 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_3_2 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 4 3 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_3_3 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 4 4 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_3_4 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 4 5 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_4_0 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 5 1 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_4_1 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 5 2 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_4_2 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 5 3 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_4_3 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 5 4 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47_4_4 : - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 5 5 (a+1) (c+1) degreeRows47_0 degreeP47 := by - decide +kernel - -lemma degreeCheck47 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, - residualCheck 47 9 1 (d+1) (e+1) (a+1) (c+1) degreeRows47_0 degreeP47 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck47_0_0 - · exact degreeCheck47_0_1 - · exact degreeCheck47_0_2 - · exact degreeCheck47_0_3 - · exact degreeCheck47_0_4 - · exact degreeCheck47_1_0 - · exact degreeCheck47_1_1 - · exact degreeCheck47_1_2 - · exact degreeCheck47_1_3 - · exact degreeCheck47_1_4 - · exact degreeCheck47_2_0 - · exact degreeCheck47_2_1 - · exact degreeCheck47_2_2 - · exact degreeCheck47_2_3 - · exact degreeCheck47_2_4 - · exact degreeCheck47_3_0 - · exact degreeCheck47_3_1 - · exact degreeCheck47_3_2 - · exact degreeCheck47_3_3 - · exact degreeCheck47_3_4 - · exact degreeCheck47_4_0 - · exact degreeCheck47_4_1 - · exact degreeCheck47_4_2 - · exact degreeCheck47_4_3 - · exact degreeCheck47_4_4 - -lemma degree_pos47 (μ : YoungDiagram) (hμ : μ.card = 47) : - 0 < kronecker (canonicalTableau (candidate 9 0 1) degreeCard47) - (canonicalTableau (candidate 9 0 1) degreeCard47) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) - degreeCard47 degreeRows47_0 (by decide) (by decide) - degreePlan47_0 (by decide) (by decide) (by decide) (by decide) degreeP47 ?_ - degreeCheck47 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard47 rfl degreeCones47 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 47. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard47 : (candidate 9 0 1).card = 47 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan47_0 : PackingPlan := (.join (.twoPaths 8 [5,5,5,5]) (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 4 [3,2,2,2]) (.neighbor 2 [2,1,1,1])))) +def degreeRows47_0 : List ℕ := [5,5,5,5,4,3,3,3,3,2,2,2,2,1,1,1] + +lemma degreeCone47_0 (μ : YoungDiagram) (hμ : μ.card = 47) + (hd : RowsDom μ.rowLens degreeRows47_0) : SquareOccurs (candidate 9 0 1) μ := by + exact candidate_cone (by decide) degreeCard47 degreePlan47_0 degreeRows47_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs47 : List (List ℕ) := [] + +lemma degreeCones47 : ∀ q ∈ degreeQs47, ∀ μ : YoungDiagram, μ.card = 47 → + RowsDom μ.rowLens q → SquareOccurs (candidate 9 0 1) μ := by + intro q hq + simp only [degreeQs47, List.not_mem_nil] at hq + +abbrev degreeP47 := ResidualProperty 9 1 degreeQs47 [] + +lemma degreeCheck47_0_0 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 1 1 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_0_1 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 1 2 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_0_2 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 1 3 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_0_3 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 1 4 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_0_4 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 1 5 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_1_0 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 2 1 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_1_1 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 2 2 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_1_2 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 2 3 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_1_3 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 2 4 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_1_4 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 2 5 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_2_0 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 3 1 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_2_1 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 3 2 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_2_2 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 3 3 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_2_3 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 3 4 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_2_4 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 3 5 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_3_0 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 4 1 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_3_1 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 4 2 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_3_2 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 4 3 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_3_3 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 4 4 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_3_4 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 4 5 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_4_0 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 5 1 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_4_1 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 5 2 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_4_2 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 5 3 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_4_3 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 5 4 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47_4_4 : + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 5 5 (a+1) (c+1) degreeRows47_0 degreeP47 := by + decide +kernel + +lemma degreeCheck47 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows47_0.length, ∀ c ∈ List.range degreeRows47_0.length, + residualCheck 47 9 1 (d+1) (e+1) (a+1) (c+1) degreeRows47_0 degreeP47 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck47_0_0 + · exact degreeCheck47_0_1 + · exact degreeCheck47_0_2 + · exact degreeCheck47_0_3 + · exact degreeCheck47_0_4 + · exact degreeCheck47_1_0 + · exact degreeCheck47_1_1 + · exact degreeCheck47_1_2 + · exact degreeCheck47_1_3 + · exact degreeCheck47_1_4 + · exact degreeCheck47_2_0 + · exact degreeCheck47_2_1 + · exact degreeCheck47_2_2 + · exact degreeCheck47_2_3 + · exact degreeCheck47_2_4 + · exact degreeCheck47_3_0 + · exact degreeCheck47_3_1 + · exact degreeCheck47_3_2 + · exact degreeCheck47_3_3 + · exact degreeCheck47_3_4 + · exact degreeCheck47_4_0 + · exact degreeCheck47_4_1 + · exact degreeCheck47_4_2 + · exact degreeCheck47_4_3 + · exact degreeCheck47_4_4 + +lemma degree_pos47 (μ : YoungDiagram) (hμ : μ.card = 47) : + 0 < kronecker (canonicalTableau (candidate 9 0 1) degreeCard47) + (canonicalTableau (candidate 9 0 1) degreeCard47) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) + degreeCard47 degreeRows47_0 (by decide) (by decide) + degreePlan47_0 (by decide) (by decide) (by decide) (by decide) degreeP47 ?_ + degreeCheck47 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard47 rfl degreeCones47 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree48.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree48.lean index 293a1a94e452ac00d02efa7422c0177808a2a550..b43cbd0bc2742b8871962e2ee090cfc5c48da687 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree48.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree48.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 48. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard48 : (candidate 8 3 0).card = 48 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan48_0 : PackingPlan := (.join (.neighbor 10 [6,5,5,5]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 4 1 [5,4])))) -def degreeRows48_0 : List ℕ := [6,5,5,5,5,4,3,3,3,2,2,2,2,1] - -lemma degreeCone48_0 (μ : YoungDiagram) (hμ : μ.card = 48) - (hd : RowsDom μ.rowLens degreeRows48_0) : SquareOccurs (candidate 8 3 0) μ := by - exact candidate_cone (by decide) degreeCard48 degreePlan48_0 degreeRows48_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs48 : List (List ℕ) := [] - -lemma degreeCones48 : ∀ q ∈ degreeQs48, ∀ μ : YoungDiagram, μ.card = 48 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 3 0) μ := by - intro q hq - simp only [degreeQs48,List.not_mem_nil] at hq - -abbrev degreeP48 := ResidualProperty 8 6 degreeQs48 [] - -lemma degreeCheck48_0_0 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 1 1 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_0_1 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 1 2 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_0_2 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 1 3 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_0_3 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 1 4 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_0_4 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 1 5 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_1_0 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 2 1 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_1_1 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 2 2 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_1_2 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 2 3 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_1_3 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 2 4 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_1_4 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 2 5 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_2_0 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 3 1 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_2_1 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 3 2 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_2_2 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 3 3 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_2_3 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 3 4 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_2_4 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 3 5 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_3_0 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 4 1 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_3_1 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 4 2 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_3_2 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 4 3 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_3_3 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 4 4 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_3_4 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 4 5 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_4_0 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 5 1 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_4_1 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 5 2 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_4_2 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 5 3 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_4_3 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 5 4 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48_4_4 : - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 5 5 (a+1) (c+1) degreeRows48_0 degreeP48 := by - decide +kernel - -lemma degreeCheck48 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, - residualCheck 48 8 6 (d+1) (e+1) (a+1) (c+1) degreeRows48_0 degreeP48 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck48_0_0 - · exact degreeCheck48_0_1 - · exact degreeCheck48_0_2 - · exact degreeCheck48_0_3 - · exact degreeCheck48_0_4 - · exact degreeCheck48_1_0 - · exact degreeCheck48_1_1 - · exact degreeCheck48_1_2 - · exact degreeCheck48_1_3 - · exact degreeCheck48_1_4 - · exact degreeCheck48_2_0 - · exact degreeCheck48_2_1 - · exact degreeCheck48_2_2 - · exact degreeCheck48_2_3 - · exact degreeCheck48_2_4 - · exact degreeCheck48_3_0 - · exact degreeCheck48_3_1 - · exact degreeCheck48_3_2 - · exact degreeCheck48_3_3 - · exact degreeCheck48_3_4 - · exact degreeCheck48_4_0 - · exact degreeCheck48_4_1 - · exact degreeCheck48_4_2 - · exact degreeCheck48_4_3 - · exact degreeCheck48_4_4 - -lemma degree_pos48 (μ : YoungDiagram) (hμ : μ.card = 48) : - 0 < kronecker (canonicalTableau (candidate 8 3 0) degreeCard48) - (canonicalTableau (candidate 8 3 0) degreeCard48) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 6) (by decide) (by decide) rfl (by decide) - degreeCard48 degreeRows48_0 (by decide) (by decide) - degreePlan48_0 (by decide) (by decide) (by decide) (by decide) degreeP48 ?_ - degreeCheck48 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard48 rfl degreeCones48 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 48. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard48 : (candidate 8 3 0).card = 48 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan48_0 : PackingPlan := (.join (.neighbor 10 [6,5,5,5]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 4 1 [5,4])))) +def degreeRows48_0 : List ℕ := [6,5,5,5,5,4,3,3,3,2,2,2,2,1] + +lemma degreeCone48_0 (μ : YoungDiagram) (hμ : μ.card = 48) + (hd : RowsDom μ.rowLens degreeRows48_0) : SquareOccurs (candidate 8 3 0) μ := by + exact candidate_cone (by decide) degreeCard48 degreePlan48_0 degreeRows48_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs48 : List (List ℕ) := [] + +lemma degreeCones48 : ∀ q ∈ degreeQs48, ∀ μ : YoungDiagram, μ.card = 48 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 3 0) μ := by + intro q hq + simp only [degreeQs48,List.not_mem_nil] at hq + +abbrev degreeP48 := ResidualProperty 8 6 degreeQs48 [] + +lemma degreeCheck48_0_0 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 1 1 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_0_1 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 1 2 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_0_2 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 1 3 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_0_3 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 1 4 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_0_4 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 1 5 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_1_0 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 2 1 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_1_1 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 2 2 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_1_2 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 2 3 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_1_3 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 2 4 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_1_4 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 2 5 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_2_0 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 3 1 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_2_1 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 3 2 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_2_2 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 3 3 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_2_3 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 3 4 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_2_4 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 3 5 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_3_0 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 4 1 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_3_1 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 4 2 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_3_2 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 4 3 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_3_3 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 4 4 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_3_4 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 4 5 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_4_0 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 5 1 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_4_1 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 5 2 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_4_2 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 5 3 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_4_3 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 5 4 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48_4_4 : + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 5 5 (a+1) (c+1) degreeRows48_0 degreeP48 := by + decide +kernel + +lemma degreeCheck48 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows48_0.length, ∀ c ∈ List.range degreeRows48_0.length, + residualCheck 48 8 6 (d+1) (e+1) (a+1) (c+1) degreeRows48_0 degreeP48 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck48_0_0 + · exact degreeCheck48_0_1 + · exact degreeCheck48_0_2 + · exact degreeCheck48_0_3 + · exact degreeCheck48_0_4 + · exact degreeCheck48_1_0 + · exact degreeCheck48_1_1 + · exact degreeCheck48_1_2 + · exact degreeCheck48_1_3 + · exact degreeCheck48_1_4 + · exact degreeCheck48_2_0 + · exact degreeCheck48_2_1 + · exact degreeCheck48_2_2 + · exact degreeCheck48_2_3 + · exact degreeCheck48_2_4 + · exact degreeCheck48_3_0 + · exact degreeCheck48_3_1 + · exact degreeCheck48_3_2 + · exact degreeCheck48_3_3 + · exact degreeCheck48_3_4 + · exact degreeCheck48_4_0 + · exact degreeCheck48_4_1 + · exact degreeCheck48_4_2 + · exact degreeCheck48_4_3 + · exact degreeCheck48_4_4 + +lemma degree_pos48 (μ : YoungDiagram) (hμ : μ.card = 48) : + 0 < kronecker (canonicalTableau (candidate 8 3 0) degreeCard48) + (canonicalTableau (candidate 8 3 0) degreeCard48) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 6) (by decide) (by decide) rfl (by decide) + degreeCard48 degreeRows48_0 (by decide) (by decide) + degreePlan48_0 (by decide) (by decide) (by decide) (by decide) degreeP48 ?_ + degreeCheck48 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard48 rfl degreeCones48 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree49.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree49.lean index de6c1496e60370c261d64f9aa0b5e8a9ecf207c2..b5e0796d71cf1b48485c785ef06e6d6a59732ebc 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree49.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree49.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 49. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard49 : (candidate 9 1 0).card = 49 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan49_0 : PackingPlan := (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 4 [3,2,2,2]) (.join (.repeated 1 3) (.twosOdd 2 1 [3,2]))))) -def degreeRows49_0 : List ℕ := [5,5,5,4,4,3,3,3,3,3,3,2,2,2,2] - -lemma degreeCone49_0 (μ : YoungDiagram) (hμ : μ.card = 49) - (hd : RowsDom μ.rowLens degreeRows49_0) : SquareOccurs (candidate 9 1 0) μ := by - exact candidate_cone (by decide) degreeCard49 degreePlan49_0 degreeRows49_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs49 : List (List ℕ) := [] - -lemma degreeCones49 : ∀ q ∈ degreeQs49, ∀ μ : YoungDiagram, μ.card = 49 → - RowsDom μ.rowLens q → SquareOccurs (candidate 9 1 0) μ := by - intro q hq - simp only [degreeQs49,List.not_mem_nil] at hq - -abbrev degreeP49 := ResidualProperty 9 2 degreeQs49 [] - -lemma degreeCheck49_0_0 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 1 1 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_0_1 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 1 2 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_0_2 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 1 3 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_0_3 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 1 4 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_0_4 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 1 5 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_1_0 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 2 1 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_1_1 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 2 2 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_1_2 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 2 3 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_1_3 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 2 4 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_1_4 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 2 5 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_2_0 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 3 1 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_2_1 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 3 2 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_2_2 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 3 3 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_2_3 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 3 4 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_2_4 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 3 5 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_3_0 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 4 1 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_3_1 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 4 2 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_3_2 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 4 3 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_3_3 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 4 4 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_3_4 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 4 5 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_4_0 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 5 1 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_4_1 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 5 2 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_4_2 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 5 3 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_4_3 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 5 4 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49_4_4 : - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 5 5 (a+1) (c+1) degreeRows49_0 degreeP49 := by - decide +kernel - -lemma degreeCheck49 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, - residualCheck 49 9 2 (d+1) (e+1) (a+1) (c+1) degreeRows49_0 degreeP49 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck49_0_0 - · exact degreeCheck49_0_1 - · exact degreeCheck49_0_2 - · exact degreeCheck49_0_3 - · exact degreeCheck49_0_4 - · exact degreeCheck49_1_0 - · exact degreeCheck49_1_1 - · exact degreeCheck49_1_2 - · exact degreeCheck49_1_3 - · exact degreeCheck49_1_4 - · exact degreeCheck49_2_0 - · exact degreeCheck49_2_1 - · exact degreeCheck49_2_2 - · exact degreeCheck49_2_3 - · exact degreeCheck49_2_4 - · exact degreeCheck49_3_0 - · exact degreeCheck49_3_1 - · exact degreeCheck49_3_2 - · exact degreeCheck49_3_3 - · exact degreeCheck49_3_4 - · exact degreeCheck49_4_0 - · exact degreeCheck49_4_1 - · exact degreeCheck49_4_2 - · exact degreeCheck49_4_3 - · exact degreeCheck49_4_4 - -lemma degree_pos49 (μ : YoungDiagram) (hμ : μ.card = 49) : - 0 < kronecker (canonicalTableau (candidate 9 1 0) degreeCard49) - (canonicalTableau (candidate 9 1 0) degreeCard49) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 2) (by decide) (by decide) rfl (by decide) - degreeCard49 degreeRows49_0 (by decide) (by decide) - degreePlan49_0 (by decide) (by decide) (by decide) (by decide) degreeP49 ?_ - degreeCheck49 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard49 rfl degreeCones49 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 49. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard49 : (candidate 9 1 0).card = 49 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan49_0 : PackingPlan := (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 4 [3,2,2,2]) (.join (.repeated 1 3) (.twosOdd 2 1 [3,2]))))) +def degreeRows49_0 : List ℕ := [5,5,5,4,4,3,3,3,3,3,3,2,2,2,2] + +lemma degreeCone49_0 (μ : YoungDiagram) (hμ : μ.card = 49) + (hd : RowsDom μ.rowLens degreeRows49_0) : SquareOccurs (candidate 9 1 0) μ := by + exact candidate_cone (by decide) degreeCard49 degreePlan49_0 degreeRows49_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs49 : List (List ℕ) := [] + +lemma degreeCones49 : ∀ q ∈ degreeQs49, ∀ μ : YoungDiagram, μ.card = 49 → + RowsDom μ.rowLens q → SquareOccurs (candidate 9 1 0) μ := by + intro q hq + simp only [degreeQs49,List.not_mem_nil] at hq + +abbrev degreeP49 := ResidualProperty 9 2 degreeQs49 [] + +lemma degreeCheck49_0_0 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 1 1 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_0_1 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 1 2 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_0_2 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 1 3 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_0_3 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 1 4 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_0_4 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 1 5 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_1_0 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 2 1 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_1_1 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 2 2 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_1_2 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 2 3 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_1_3 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 2 4 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_1_4 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 2 5 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_2_0 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 3 1 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_2_1 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 3 2 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_2_2 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 3 3 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_2_3 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 3 4 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_2_4 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 3 5 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_3_0 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 4 1 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_3_1 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 4 2 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_3_2 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 4 3 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_3_3 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 4 4 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_3_4 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 4 5 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_4_0 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 5 1 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_4_1 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 5 2 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_4_2 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 5 3 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_4_3 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 5 4 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49_4_4 : + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 5 5 (a+1) (c+1) degreeRows49_0 degreeP49 := by + decide +kernel + +lemma degreeCheck49 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows49_0.length, ∀ c ∈ List.range degreeRows49_0.length, + residualCheck 49 9 2 (d+1) (e+1) (a+1) (c+1) degreeRows49_0 degreeP49 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck49_0_0 + · exact degreeCheck49_0_1 + · exact degreeCheck49_0_2 + · exact degreeCheck49_0_3 + · exact degreeCheck49_0_4 + · exact degreeCheck49_1_0 + · exact degreeCheck49_1_1 + · exact degreeCheck49_1_2 + · exact degreeCheck49_1_3 + · exact degreeCheck49_1_4 + · exact degreeCheck49_2_0 + · exact degreeCheck49_2_1 + · exact degreeCheck49_2_2 + · exact degreeCheck49_2_3 + · exact degreeCheck49_2_4 + · exact degreeCheck49_3_0 + · exact degreeCheck49_3_1 + · exact degreeCheck49_3_2 + · exact degreeCheck49_3_3 + · exact degreeCheck49_3_4 + · exact degreeCheck49_4_0 + · exact degreeCheck49_4_1 + · exact degreeCheck49_4_2 + · exact degreeCheck49_4_3 + · exact degreeCheck49_4_4 + +lemma degree_pos49 (μ : YoungDiagram) (hμ : μ.card = 49) : + 0 < kronecker (canonicalTableau (candidate 9 1 0) degreeCard49) + (canonicalTableau (candidate 9 1 0) degreeCard49) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 2) (by decide) (by decide) rfl (by decide) + degreeCard49 degreeRows49_0 (by decide) (by decide) + degreePlan49_0 (by decide) (by decide) (by decide) (by decide) degreeP49 ?_ + degreeCheck49 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard49 rfl degreeCones49 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree50.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree50.lean index c5ce9cb04e4d1c4759a9751f0787aa22fca9c79f..077e2c13d83013d7c4c8bc09b86c8b7f68773d0b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree50.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree50.lean @@ -1,218 +1,218 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 50. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard50 : (candidate 8 3 1).card = 50 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan50_0 : PackingPlan := (.join (.twoPaths 10 [6,6,6,6]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 4 3 [6,5])))) -def degreeRows50_0 : List ℕ := [6,6,6,6,6,5,4,3,3,3,2] - -lemma degreeCone50_0 (μ : YoungDiagram) (hμ : μ.card = 50) - (hd : RowsDom μ.rowLens degreeRows50_0) : SquareOccurs (candidate 8 3 1) μ := by - exact candidate_cone (by decide) degreeCard50 degreePlan50_0 degreeRows50_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan50_1 : PackingPlan := (.join (.twoPaths 10 [6,6,6,6]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 4 2)))) -def degreeRows50_1 : List ℕ := [8,6,6,6,6,3,3,3,2,2,2,2,1] - -lemma degreeCone50_1 (μ : YoungDiagram) (hμ : μ.card = 50) - (hd : RowsDom μ.rowLens degreeRows50_1) : SquareOccurs (candidate 8 3 1) μ := by - exact candidate_cone (by decide) degreeCard50 degreePlan50_1 degreeRows50_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs50 : List (List ℕ) := [degreeRows50_1] - -lemma degreeCones50 : ∀ q ∈ degreeQs50, ∀ μ : YoungDiagram, μ.card = 50 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 3 1) μ := by - intro q hq - simp only [degreeQs50,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone50_1 - -abbrev degreeP50 := ResidualProperty 8 7 degreeQs50 [] - -lemma degreeCheck50_0_0 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 1 1 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_0_1 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 1 2 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_0_2 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 1 3 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_0_3 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 1 4 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_0_4 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 1 5 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_1_0 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 2 1 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_1_1 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 2 2 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_1_2 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 2 3 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_1_3 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 2 4 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_1_4 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 2 5 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_2_0 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 3 1 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_2_1 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 3 2 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_2_2 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 3 3 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_2_3 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 3 4 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_2_4 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 3 5 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_3_0 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 4 1 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_3_1 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 4 2 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_3_2 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 4 3 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_3_3 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 4 4 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_3_4 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 4 5 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_4_0 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 5 1 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_4_1 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 5 2 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_4_2 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 5 3 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_4_3 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 5 4 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50_4_4 : - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 5 5 (a+1) (c+1) degreeRows50_0 degreeP50 := by - decide +kernel - -lemma degreeCheck50 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, - residualCheck 50 8 7 (d+1) (e+1) (a+1) (c+1) degreeRows50_0 degreeP50 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck50_0_0 - · exact degreeCheck50_0_1 - · exact degreeCheck50_0_2 - · exact degreeCheck50_0_3 - · exact degreeCheck50_0_4 - · exact degreeCheck50_1_0 - · exact degreeCheck50_1_1 - · exact degreeCheck50_1_2 - · exact degreeCheck50_1_3 - · exact degreeCheck50_1_4 - · exact degreeCheck50_2_0 - · exact degreeCheck50_2_1 - · exact degreeCheck50_2_2 - · exact degreeCheck50_2_3 - · exact degreeCheck50_2_4 - · exact degreeCheck50_3_0 - · exact degreeCheck50_3_1 - · exact degreeCheck50_3_2 - · exact degreeCheck50_3_3 - · exact degreeCheck50_3_4 - · exact degreeCheck50_4_0 - · exact degreeCheck50_4_1 - · exact degreeCheck50_4_2 - · exact degreeCheck50_4_3 - · exact degreeCheck50_4_4 - -lemma degree_pos50 (μ : YoungDiagram) (hμ : μ.card = 50) : - 0 < kronecker (canonicalTableau (candidate 8 3 1) degreeCard50) - (canonicalTableau (candidate 8 3 1) degreeCard50) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 7) (by decide) (by decide) rfl (by decide) - degreeCard50 degreeRows50_0 (by decide) (by decide) - degreePlan50_0 (by decide) (by decide) (by decide) (by decide) degreeP50 ?_ - degreeCheck50 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard50 rfl degreeCones50 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 50. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard50 : (candidate 8 3 1).card = 50 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan50_0 : PackingPlan := (.join (.twoPaths 10 [6,6,6,6]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 4 3 [6,5])))) +def degreeRows50_0 : List ℕ := [6,6,6,6,6,5,4,3,3,3,2] + +lemma degreeCone50_0 (μ : YoungDiagram) (hμ : μ.card = 50) + (hd : RowsDom μ.rowLens degreeRows50_0) : SquareOccurs (candidate 8 3 1) μ := by + exact candidate_cone (by decide) degreeCard50 degreePlan50_0 degreeRows50_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan50_1 : PackingPlan := (.join (.twoPaths 10 [6,6,6,6]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 4 2)))) +def degreeRows50_1 : List ℕ := [8,6,6,6,6,3,3,3,2,2,2,2,1] + +lemma degreeCone50_1 (μ : YoungDiagram) (hμ : μ.card = 50) + (hd : RowsDom μ.rowLens degreeRows50_1) : SquareOccurs (candidate 8 3 1) μ := by + exact candidate_cone (by decide) degreeCard50 degreePlan50_1 degreeRows50_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs50 : List (List ℕ) := [degreeRows50_1] + +lemma degreeCones50 : ∀ q ∈ degreeQs50, ∀ μ : YoungDiagram, μ.card = 50 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 3 1) μ := by + intro q hq + simp only [degreeQs50,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone50_1 + +abbrev degreeP50 := ResidualProperty 8 7 degreeQs50 [] + +lemma degreeCheck50_0_0 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 1 1 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_0_1 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 1 2 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_0_2 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 1 3 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_0_3 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 1 4 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_0_4 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 1 5 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_1_0 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 2 1 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_1_1 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 2 2 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_1_2 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 2 3 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_1_3 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 2 4 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_1_4 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 2 5 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_2_0 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 3 1 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_2_1 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 3 2 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_2_2 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 3 3 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_2_3 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 3 4 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_2_4 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 3 5 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_3_0 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 4 1 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_3_1 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 4 2 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_3_2 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 4 3 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_3_3 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 4 4 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_3_4 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 4 5 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_4_0 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 5 1 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_4_1 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 5 2 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_4_2 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 5 3 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_4_3 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 5 4 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50_4_4 : + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 5 5 (a+1) (c+1) degreeRows50_0 degreeP50 := by + decide +kernel + +lemma degreeCheck50 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows50_0.length, ∀ c ∈ List.range degreeRows50_0.length, + residualCheck 50 8 7 (d+1) (e+1) (a+1) (c+1) degreeRows50_0 degreeP50 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck50_0_0 + · exact degreeCheck50_0_1 + · exact degreeCheck50_0_2 + · exact degreeCheck50_0_3 + · exact degreeCheck50_0_4 + · exact degreeCheck50_1_0 + · exact degreeCheck50_1_1 + · exact degreeCheck50_1_2 + · exact degreeCheck50_1_3 + · exact degreeCheck50_1_4 + · exact degreeCheck50_2_0 + · exact degreeCheck50_2_1 + · exact degreeCheck50_2_2 + · exact degreeCheck50_2_3 + · exact degreeCheck50_2_4 + · exact degreeCheck50_3_0 + · exact degreeCheck50_3_1 + · exact degreeCheck50_3_2 + · exact degreeCheck50_3_3 + · exact degreeCheck50_3_4 + · exact degreeCheck50_4_0 + · exact degreeCheck50_4_1 + · exact degreeCheck50_4_2 + · exact degreeCheck50_4_3 + · exact degreeCheck50_4_4 + +lemma degree_pos50 (μ : YoungDiagram) (hμ : μ.card = 50) : + 0 < kronecker (canonicalTableau (candidate 8 3 1) degreeCard50) + (canonicalTableau (candidate 8 3 1) degreeCard50) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 7) (by decide) (by decide) rfl (by decide) + degreeCard50 degreeRows50_0 (by decide) (by decide) + degreePlan50_0 (by decide) (by decide) (by decide) (by decide) degreeP50 ?_ + degreeCheck50 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard50 rfl degreeCones50 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree51.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree51.lean index a497c5ae07c085b2ba476f7a39b93e68692dbb15..32caea665c21cab6be1be0f767cd0f9c5637b93d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree51.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree51.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 51. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard51 : (candidate 9 1 1).card = 51 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan51_0 : PackingPlan := (.join (.twoPaths 9 [6,6,5,5]) (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 4 [3,2,2,2]) (.join (.repeated 1 3) (.repeated 2 2))))) -def degreeRows51_0 : List ℕ := [6,6,5,5,4,4,3,3,3,3,3,2,2,2] - -lemma degreeCone51_0 (μ : YoungDiagram) (hμ : μ.card = 51) - (hd : RowsDom μ.rowLens degreeRows51_0) : SquareOccurs (candidate 9 1 1) μ := by - exact candidate_cone (by decide) degreeCard51 degreePlan51_0 degreeRows51_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs51 : List (List ℕ) := [] - -lemma degreeCones51 : ∀ q ∈ degreeQs51, ∀ μ : YoungDiagram, μ.card = 51 → - RowsDom μ.rowLens q → SquareOccurs (candidate 9 1 1) μ := by - intro q hq - simp only [degreeQs51,List.not_mem_nil] at hq - -abbrev degreeP51 := ResidualProperty 9 3 degreeQs51 [] - -lemma degreeCheck51_0_0 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 1 1 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_0_1 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 1 2 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_0_2 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 1 3 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_0_3 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 1 4 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_0_4 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 1 5 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_1_0 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 2 1 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_1_1 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 2 2 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_1_2 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 2 3 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_1_3 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 2 4 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_1_4 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 2 5 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_2_0 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 3 1 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_2_1 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 3 2 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_2_2 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 3 3 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_2_3 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 3 4 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_2_4 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 3 5 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_3_0 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 4 1 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_3_1 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 4 2 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_3_2 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 4 3 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_3_3 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 4 4 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_3_4 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 4 5 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_4_0 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 5 1 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_4_1 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 5 2 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_4_2 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 5 3 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_4_3 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 5 4 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51_4_4 : - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 5 5 (a+1) (c+1) degreeRows51_0 degreeP51 := by - decide +kernel - -lemma degreeCheck51 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, - residualCheck 51 9 3 (d+1) (e+1) (a+1) (c+1) degreeRows51_0 degreeP51 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck51_0_0 - · exact degreeCheck51_0_1 - · exact degreeCheck51_0_2 - · exact degreeCheck51_0_3 - · exact degreeCheck51_0_4 - · exact degreeCheck51_1_0 - · exact degreeCheck51_1_1 - · exact degreeCheck51_1_2 - · exact degreeCheck51_1_3 - · exact degreeCheck51_1_4 - · exact degreeCheck51_2_0 - · exact degreeCheck51_2_1 - · exact degreeCheck51_2_2 - · exact degreeCheck51_2_3 - · exact degreeCheck51_2_4 - · exact degreeCheck51_3_0 - · exact degreeCheck51_3_1 - · exact degreeCheck51_3_2 - · exact degreeCheck51_3_3 - · exact degreeCheck51_3_4 - · exact degreeCheck51_4_0 - · exact degreeCheck51_4_1 - · exact degreeCheck51_4_2 - · exact degreeCheck51_4_3 - · exact degreeCheck51_4_4 - -lemma degree_pos51 (μ : YoungDiagram) (hμ : μ.card = 51) : - 0 < kronecker (canonicalTableau (candidate 9 1 1) degreeCard51) - (canonicalTableau (candidate 9 1 1) degreeCard51) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 3) (by decide) (by decide) rfl (by decide) - degreeCard51 degreeRows51_0 (by decide) (by decide) - degreePlan51_0 (by decide) (by decide) (by decide) (by decide) degreeP51 ?_ - degreeCheck51 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard51 rfl degreeCones51 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 51. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard51 : (candidate 9 1 1).card = 51 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan51_0 : PackingPlan := (.join (.twoPaths 9 [6,6,5,5]) (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 4 [3,2,2,2]) (.join (.repeated 1 3) (.repeated 2 2))))) +def degreeRows51_0 : List ℕ := [6,6,5,5,4,4,3,3,3,3,3,2,2,2] + +lemma degreeCone51_0 (μ : YoungDiagram) (hμ : μ.card = 51) + (hd : RowsDom μ.rowLens degreeRows51_0) : SquareOccurs (candidate 9 1 1) μ := by + exact candidate_cone (by decide) degreeCard51 degreePlan51_0 degreeRows51_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs51 : List (List ℕ) := [] + +lemma degreeCones51 : ∀ q ∈ degreeQs51, ∀ μ : YoungDiagram, μ.card = 51 → + RowsDom μ.rowLens q → SquareOccurs (candidate 9 1 1) μ := by + intro q hq + simp only [degreeQs51,List.not_mem_nil] at hq + +abbrev degreeP51 := ResidualProperty 9 3 degreeQs51 [] + +lemma degreeCheck51_0_0 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 1 1 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_0_1 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 1 2 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_0_2 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 1 3 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_0_3 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 1 4 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_0_4 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 1 5 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_1_0 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 2 1 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_1_1 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 2 2 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_1_2 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 2 3 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_1_3 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 2 4 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_1_4 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 2 5 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_2_0 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 3 1 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_2_1 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 3 2 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_2_2 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 3 3 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_2_3 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 3 4 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_2_4 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 3 5 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_3_0 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 4 1 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_3_1 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 4 2 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_3_2 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 4 3 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_3_3 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 4 4 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_3_4 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 4 5 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_4_0 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 5 1 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_4_1 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 5 2 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_4_2 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 5 3 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_4_3 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 5 4 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51_4_4 : + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 5 5 (a+1) (c+1) degreeRows51_0 degreeP51 := by + decide +kernel + +lemma degreeCheck51 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows51_0.length, ∀ c ∈ List.range degreeRows51_0.length, + residualCheck 51 9 3 (d+1) (e+1) (a+1) (c+1) degreeRows51_0 degreeP51 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck51_0_0 + · exact degreeCheck51_0_1 + · exact degreeCheck51_0_2 + · exact degreeCheck51_0_3 + · exact degreeCheck51_0_4 + · exact degreeCheck51_1_0 + · exact degreeCheck51_1_1 + · exact degreeCheck51_1_2 + · exact degreeCheck51_1_3 + · exact degreeCheck51_1_4 + · exact degreeCheck51_2_0 + · exact degreeCheck51_2_1 + · exact degreeCheck51_2_2 + · exact degreeCheck51_2_3 + · exact degreeCheck51_2_4 + · exact degreeCheck51_3_0 + · exact degreeCheck51_3_1 + · exact degreeCheck51_3_2 + · exact degreeCheck51_3_3 + · exact degreeCheck51_3_4 + · exact degreeCheck51_4_0 + · exact degreeCheck51_4_1 + · exact degreeCheck51_4_2 + · exact degreeCheck51_4_3 + · exact degreeCheck51_4_4 + +lemma degree_pos51 (μ : YoungDiagram) (hμ : μ.card = 51) : + 0 < kronecker (canonicalTableau (candidate 9 1 1) degreeCard51) + (canonicalTableau (candidate 9 1 1) degreeCard51) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 3) (by decide) (by decide) rfl (by decide) + degreeCard51 degreeRows51_0 (by decide) (by decide) + degreePlan51_0 (by decide) (by decide) (by decide) (by decide) degreeP51 ?_ + degreeCheck51 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard51 rfl degreeCones51 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree52.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree52.lean index e8e27bb2f96862f3e74abcf87cb79ed5bde2279e..38dee3e784609724eaa8b63066e04838a4319813 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree52.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree52.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 52. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard52 : (candidate 8 4 0).card = 52 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan52_0 : PackingPlan := (.join (.neighbor 11 [6,6,6,5]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 5 1 [6,5])))) -def degreeRows52_0 : List ℕ := [6,6,6,6,5,5,3,3,3,2,2,2,2,1] - -lemma degreeCone52_0 (μ : YoungDiagram) (hμ : μ.card = 52) - (hd : RowsDom μ.rowLens degreeRows52_0) : SquareOccurs (candidate 8 4 0) μ := by - exact candidate_cone (by decide) degreeCard52 degreePlan52_0 degreeRows52_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs52 : List (List ℕ) := [] - -lemma degreeCones52 : ∀ q ∈ degreeQs52, ∀ μ : YoungDiagram, μ.card = 52 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 4 0) μ := by - intro q hq - simp only [degreeQs52, List.not_mem_nil] at hq - -abbrev degreeP52 := ResidualProperty 8 8 degreeQs52 [] - -lemma degreeCheck52_0_0 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 1 1 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_0_1 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 1 2 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_0_2 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 1 3 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_0_3 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 1 4 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_0_4 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 1 5 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_1_0 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 2 1 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_1_1 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 2 2 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_1_2 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 2 3 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_1_3 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 2 4 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_1_4 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 2 5 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_2_0 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 3 1 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_2_1 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 3 2 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_2_2 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 3 3 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_2_3 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 3 4 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_2_4 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 3 5 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_3_0 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 4 1 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_3_1 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 4 2 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_3_2 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 4 3 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_3_3 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 4 4 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_3_4 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 4 5 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_4_0 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 5 1 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_4_1 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 5 2 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_4_2 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 5 3 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_4_3 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 5 4 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52_4_4 : - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 5 5 (a+1) (c+1) degreeRows52_0 degreeP52 := by - decide +kernel - -lemma degreeCheck52 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, - residualCheck 52 8 8 (d+1) (e+1) (a+1) (c+1) degreeRows52_0 degreeP52 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck52_0_0 - · exact degreeCheck52_0_1 - · exact degreeCheck52_0_2 - · exact degreeCheck52_0_3 - · exact degreeCheck52_0_4 - · exact degreeCheck52_1_0 - · exact degreeCheck52_1_1 - · exact degreeCheck52_1_2 - · exact degreeCheck52_1_3 - · exact degreeCheck52_1_4 - · exact degreeCheck52_2_0 - · exact degreeCheck52_2_1 - · exact degreeCheck52_2_2 - · exact degreeCheck52_2_3 - · exact degreeCheck52_2_4 - · exact degreeCheck52_3_0 - · exact degreeCheck52_3_1 - · exact degreeCheck52_3_2 - · exact degreeCheck52_3_3 - · exact degreeCheck52_3_4 - · exact degreeCheck52_4_0 - · exact degreeCheck52_4_1 - · exact degreeCheck52_4_2 - · exact degreeCheck52_4_3 - · exact degreeCheck52_4_4 - -lemma degree_pos52 (μ : YoungDiagram) (hμ : μ.card = 52) : - 0 < kronecker (canonicalTableau (candidate 8 4 0) degreeCard52) - (canonicalTableau (candidate 8 4 0) degreeCard52) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 8) (by decide) (by decide) rfl (by decide) - degreeCard52 degreeRows52_0 (by decide) (by decide) - degreePlan52_0 (by decide) (by decide) (by decide) (by decide) degreeP52 ?_ - degreeCheck52 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard52 rfl degreeCones52 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 52. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard52 : (candidate 8 4 0).card = 52 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan52_0 : PackingPlan := (.join (.neighbor 11 [6,6,6,5]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 5 1 [6,5])))) +def degreeRows52_0 : List ℕ := [6,6,6,6,5,5,3,3,3,2,2,2,2,1] + +lemma degreeCone52_0 (μ : YoungDiagram) (hμ : μ.card = 52) + (hd : RowsDom μ.rowLens degreeRows52_0) : SquareOccurs (candidate 8 4 0) μ := by + exact candidate_cone (by decide) degreeCard52 degreePlan52_0 degreeRows52_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs52 : List (List ℕ) := [] + +lemma degreeCones52 : ∀ q ∈ degreeQs52, ∀ μ : YoungDiagram, μ.card = 52 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 4 0) μ := by + intro q hq + simp only [degreeQs52, List.not_mem_nil] at hq + +abbrev degreeP52 := ResidualProperty 8 8 degreeQs52 [] + +lemma degreeCheck52_0_0 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 1 1 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_0_1 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 1 2 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_0_2 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 1 3 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_0_3 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 1 4 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_0_4 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 1 5 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_1_0 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 2 1 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_1_1 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 2 2 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_1_2 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 2 3 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_1_3 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 2 4 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_1_4 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 2 5 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_2_0 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 3 1 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_2_1 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 3 2 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_2_2 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 3 3 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_2_3 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 3 4 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_2_4 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 3 5 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_3_0 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 4 1 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_3_1 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 4 2 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_3_2 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 4 3 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_3_3 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 4 4 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_3_4 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 4 5 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_4_0 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 5 1 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_4_1 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 5 2 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_4_2 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 5 3 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_4_3 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 5 4 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52_4_4 : + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 5 5 (a+1) (c+1) degreeRows52_0 degreeP52 := by + decide +kernel + +lemma degreeCheck52 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows52_0.length, ∀ c ∈ List.range degreeRows52_0.length, + residualCheck 52 8 8 (d+1) (e+1) (a+1) (c+1) degreeRows52_0 degreeP52 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck52_0_0 + · exact degreeCheck52_0_1 + · exact degreeCheck52_0_2 + · exact degreeCheck52_0_3 + · exact degreeCheck52_0_4 + · exact degreeCheck52_1_0 + · exact degreeCheck52_1_1 + · exact degreeCheck52_1_2 + · exact degreeCheck52_1_3 + · exact degreeCheck52_1_4 + · exact degreeCheck52_2_0 + · exact degreeCheck52_2_1 + · exact degreeCheck52_2_2 + · exact degreeCheck52_2_3 + · exact degreeCheck52_2_4 + · exact degreeCheck52_3_0 + · exact degreeCheck52_3_1 + · exact degreeCheck52_3_2 + · exact degreeCheck52_3_3 + · exact degreeCheck52_3_4 + · exact degreeCheck52_4_0 + · exact degreeCheck52_4_1 + · exact degreeCheck52_4_2 + · exact degreeCheck52_4_3 + · exact degreeCheck52_4_4 + +lemma degree_pos52 (μ : YoungDiagram) (hμ : μ.card = 52) : + 0 < kronecker (canonicalTableau (candidate 8 4 0) degreeCard52) + (canonicalTableau (candidate 8 4 0) degreeCard52) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 8) (by decide) (by decide) rfl (by decide) + degreeCard52 degreeRows52_0 (by decide) (by decide) + degreePlan52_0 (by decide) (by decide) (by decide) (by decide) degreeP52 ?_ + degreeCheck52 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard52 rfl degreeCones52 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree53.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree53.lean index 9c955b8adad50739d9ff9ae5dc998756fea1d309..ec9c24f491a1f954c4592557f3762136d379d3bb 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree53.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree53.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 53. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard53 : (candidate 9 2 0).card = 53 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan53_0 : PackingPlan := (.join (.neighbor 10 [6,5,5,5]) (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 4 [3,2,2,2]) (.join (.repeated 1 3) (.twosOdd 3 1 [4,3]))))) -def degreeRows53_0 : List ℕ := [6,5,5,5,4,4,3,3,3,3,3,3,2,2,2] - -lemma degreeCone53_0 (μ : YoungDiagram) (hμ : μ.card = 53) - (hd : RowsDom μ.rowLens degreeRows53_0) : SquareOccurs (candidate 9 2 0) μ := by - exact candidate_cone (by decide) degreeCard53 degreePlan53_0 degreeRows53_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs53 : List (List ℕ) := [] - -lemma degreeCones53 : ∀ q ∈ degreeQs53, ∀ μ : YoungDiagram, μ.card = 53 → - RowsDom μ.rowLens q → SquareOccurs (candidate 9 2 0) μ := by - intro q hq - simp only [degreeQs53,List.not_mem_nil] at hq - -abbrev degreeP53 := ResidualProperty 9 4 degreeQs53 [] - -lemma degreeCheck53_0_0 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 1 1 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_0_1 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 1 2 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_0_2 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 1 3 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_0_3 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 1 4 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_0_4 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 1 5 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_1_0 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 2 1 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_1_1 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 2 2 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_1_2 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 2 3 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_1_3 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 2 4 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_1_4 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 2 5 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_2_0 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 3 1 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_2_1 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 3 2 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_2_2 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 3 3 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_2_3 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 3 4 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_2_4 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 3 5 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_3_0 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 4 1 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_3_1 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 4 2 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_3_2 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 4 3 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_3_3 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 4 4 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_3_4 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 4 5 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_4_0 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 5 1 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_4_1 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 5 2 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_4_2 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 5 3 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_4_3 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 5 4 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53_4_4 : - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 5 5 (a+1) (c+1) degreeRows53_0 degreeP53 := by - decide +kernel - -lemma degreeCheck53 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, - residualCheck 53 9 4 (d+1) (e+1) (a+1) (c+1) degreeRows53_0 degreeP53 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck53_0_0 - · exact degreeCheck53_0_1 - · exact degreeCheck53_0_2 - · exact degreeCheck53_0_3 - · exact degreeCheck53_0_4 - · exact degreeCheck53_1_0 - · exact degreeCheck53_1_1 - · exact degreeCheck53_1_2 - · exact degreeCheck53_1_3 - · exact degreeCheck53_1_4 - · exact degreeCheck53_2_0 - · exact degreeCheck53_2_1 - · exact degreeCheck53_2_2 - · exact degreeCheck53_2_3 - · exact degreeCheck53_2_4 - · exact degreeCheck53_3_0 - · exact degreeCheck53_3_1 - · exact degreeCheck53_3_2 - · exact degreeCheck53_3_3 - · exact degreeCheck53_3_4 - · exact degreeCheck53_4_0 - · exact degreeCheck53_4_1 - · exact degreeCheck53_4_2 - · exact degreeCheck53_4_3 - · exact degreeCheck53_4_4 - -lemma degree_pos53 (μ : YoungDiagram) (hμ : μ.card = 53) : - 0 < kronecker (canonicalTableau (candidate 9 2 0) degreeCard53) - (canonicalTableau (candidate 9 2 0) degreeCard53) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 4) (by decide) (by decide) rfl (by decide) - degreeCard53 degreeRows53_0 (by decide) (by decide) - degreePlan53_0 (by decide) (by decide) (by decide) (by decide) degreeP53 ?_ - degreeCheck53 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard53 rfl degreeCones53 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 53. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard53 : (candidate 9 2 0).card = 53 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan53_0 : PackingPlan := (.join (.neighbor 10 [6,5,5,5]) (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 4 [3,2,2,2]) (.join (.repeated 1 3) (.twosOdd 3 1 [4,3]))))) +def degreeRows53_0 : List ℕ := [6,5,5,5,4,4,3,3,3,3,3,3,2,2,2] + +lemma degreeCone53_0 (μ : YoungDiagram) (hμ : μ.card = 53) + (hd : RowsDom μ.rowLens degreeRows53_0) : SquareOccurs (candidate 9 2 0) μ := by + exact candidate_cone (by decide) degreeCard53 degreePlan53_0 degreeRows53_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs53 : List (List ℕ) := [] + +lemma degreeCones53 : ∀ q ∈ degreeQs53, ∀ μ : YoungDiagram, μ.card = 53 → + RowsDom μ.rowLens q → SquareOccurs (candidate 9 2 0) μ := by + intro q hq + simp only [degreeQs53,List.not_mem_nil] at hq + +abbrev degreeP53 := ResidualProperty 9 4 degreeQs53 [] + +lemma degreeCheck53_0_0 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 1 1 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_0_1 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 1 2 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_0_2 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 1 3 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_0_3 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 1 4 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_0_4 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 1 5 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_1_0 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 2 1 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_1_1 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 2 2 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_1_2 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 2 3 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_1_3 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 2 4 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_1_4 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 2 5 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_2_0 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 3 1 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_2_1 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 3 2 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_2_2 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 3 3 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_2_3 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 3 4 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_2_4 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 3 5 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_3_0 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 4 1 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_3_1 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 4 2 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_3_2 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 4 3 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_3_3 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 4 4 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_3_4 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 4 5 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_4_0 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 5 1 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_4_1 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 5 2 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_4_2 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 5 3 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_4_3 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 5 4 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53_4_4 : + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 5 5 (a+1) (c+1) degreeRows53_0 degreeP53 := by + decide +kernel + +lemma degreeCheck53 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows53_0.length, ∀ c ∈ List.range degreeRows53_0.length, + residualCheck 53 9 4 (d+1) (e+1) (a+1) (c+1) degreeRows53_0 degreeP53 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck53_0_0 + · exact degreeCheck53_0_1 + · exact degreeCheck53_0_2 + · exact degreeCheck53_0_3 + · exact degreeCheck53_0_4 + · exact degreeCheck53_1_0 + · exact degreeCheck53_1_1 + · exact degreeCheck53_1_2 + · exact degreeCheck53_1_3 + · exact degreeCheck53_1_4 + · exact degreeCheck53_2_0 + · exact degreeCheck53_2_1 + · exact degreeCheck53_2_2 + · exact degreeCheck53_2_3 + · exact degreeCheck53_2_4 + · exact degreeCheck53_3_0 + · exact degreeCheck53_3_1 + · exact degreeCheck53_3_2 + · exact degreeCheck53_3_3 + · exact degreeCheck53_3_4 + · exact degreeCheck53_4_0 + · exact degreeCheck53_4_1 + · exact degreeCheck53_4_2 + · exact degreeCheck53_4_3 + · exact degreeCheck53_4_4 + +lemma degree_pos53 (μ : YoungDiagram) (hμ : μ.card = 53) : + 0 < kronecker (canonicalTableau (candidate 9 2 0) degreeCard53) + (canonicalTableau (candidate 9 2 0) degreeCard53) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 4) (by decide) (by decide) rfl (by decide) + degreeCard53 degreeRows53_0 (by decide) (by decide) + degreePlan53_0 (by decide) (by decide) (by decide) (by decide) degreeP53 ?_ + degreeCheck53 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard53 rfl degreeCones53 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree54.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree54.lean index 5042de129a50a1e8cbd2667add087e3205ea59df..8f27270cd18d7b9f901f07d384e5befb3ba6fb77 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree54.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree54.lean @@ -1,218 +1,218 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 54. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard54 : (candidate 8 4 1).card = 54 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan54_0 : PackingPlan := (.join (.twoPaths 11 [7,7,6,6]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 5 3 [7,6])))) -def degreeRows54_0 : List ℕ := [7,7,7,6,6,6,4,3,3,3,2] - -lemma degreeCone54_0 (μ : YoungDiagram) (hμ : μ.card = 54) - (hd : RowsDom μ.rowLens degreeRows54_0) : SquareOccurs (candidate 8 4 1) μ := by - exact candidate_cone (by decide) degreeCard54 degreePlan54_0 degreeRows54_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan54_1 : PackingPlan := (.join (.twoPaths 11 [7,7,6,6]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 5 2)))) -def degreeRows54_1 : List ℕ := [10,7,7,6,6,3,3,3,2,2,2,2,1] - -lemma degreeCone54_1 (μ : YoungDiagram) (hμ : μ.card = 54) - (hd : RowsDom μ.rowLens degreeRows54_1) : SquareOccurs (candidate 8 4 1) μ := by - exact candidate_cone (by decide) degreeCard54 degreePlan54_1 degreeRows54_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs54 : List (List ℕ) := [degreeRows54_1] - -lemma degreeCones54 : ∀ q ∈ degreeQs54, ∀ μ : YoungDiagram, μ.card = 54 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 4 1) μ := by - intro q hq - simp only [degreeQs54,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone54_1 - -abbrev degreeP54 := ResidualProperty 8 9 degreeQs54 [] - -lemma degreeCheck54_0_0 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 1 1 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_0_1 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 1 2 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_0_2 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 1 3 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_0_3 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 1 4 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_0_4 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 1 5 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_1_0 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 2 1 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_1_1 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 2 2 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_1_2 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 2 3 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_1_3 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 2 4 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_1_4 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 2 5 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_2_0 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 3 1 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_2_1 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 3 2 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_2_2 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 3 3 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_2_3 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 3 4 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_2_4 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 3 5 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_3_0 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 4 1 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_3_1 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 4 2 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_3_2 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 4 3 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_3_3 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 4 4 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_3_4 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 4 5 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_4_0 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 5 1 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_4_1 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 5 2 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_4_2 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 5 3 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_4_3 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 5 4 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54_4_4 : - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 5 5 (a+1) (c+1) degreeRows54_0 degreeP54 := by - decide +kernel - -lemma degreeCheck54 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, - residualCheck 54 8 9 (d+1) (e+1) (a+1) (c+1) degreeRows54_0 degreeP54 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck54_0_0 - · exact degreeCheck54_0_1 - · exact degreeCheck54_0_2 - · exact degreeCheck54_0_3 - · exact degreeCheck54_0_4 - · exact degreeCheck54_1_0 - · exact degreeCheck54_1_1 - · exact degreeCheck54_1_2 - · exact degreeCheck54_1_3 - · exact degreeCheck54_1_4 - · exact degreeCheck54_2_0 - · exact degreeCheck54_2_1 - · exact degreeCheck54_2_2 - · exact degreeCheck54_2_3 - · exact degreeCheck54_2_4 - · exact degreeCheck54_3_0 - · exact degreeCheck54_3_1 - · exact degreeCheck54_3_2 - · exact degreeCheck54_3_3 - · exact degreeCheck54_3_4 - · exact degreeCheck54_4_0 - · exact degreeCheck54_4_1 - · exact degreeCheck54_4_2 - · exact degreeCheck54_4_3 - · exact degreeCheck54_4_4 - -lemma degree_pos54 (μ : YoungDiagram) (hμ : μ.card = 54) : - 0 < kronecker (canonicalTableau (candidate 8 4 1) degreeCard54) - (canonicalTableau (candidate 8 4 1) degreeCard54) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 9) (by decide) (by decide) rfl (by decide) - degreeCard54 degreeRows54_0 (by decide) (by decide) - degreePlan54_0 (by decide) (by decide) (by decide) (by decide) degreeP54 ?_ - degreeCheck54 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard54 rfl degreeCones54 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 54. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard54 : (candidate 8 4 1).card = 54 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan54_0 : PackingPlan := (.join (.twoPaths 11 [7,7,6,6]) (.join (.neighbor 5 [3,3,3,2]) (.join (.repeated 1 4) (.twosOdd 5 3 [7,6])))) +def degreeRows54_0 : List ℕ := [7,7,7,6,6,6,4,3,3,3,2] + +lemma degreeCone54_0 (μ : YoungDiagram) (hμ : μ.card = 54) + (hd : RowsDom μ.rowLens degreeRows54_0) : SquareOccurs (candidate 8 4 1) μ := by + exact candidate_cone (by decide) degreeCard54 degreePlan54_0 degreeRows54_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan54_1 : PackingPlan := (.join (.twoPaths 11 [7,7,6,6]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 5 2)))) +def degreeRows54_1 : List ℕ := [10,7,7,6,6,3,3,3,2,2,2,2,1] + +lemma degreeCone54_1 (μ : YoungDiagram) (hμ : μ.card = 54) + (hd : RowsDom μ.rowLens degreeRows54_1) : SquareOccurs (candidate 8 4 1) μ := by + exact candidate_cone (by decide) degreeCard54 degreePlan54_1 degreeRows54_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs54 : List (List ℕ) := [degreeRows54_1] + +lemma degreeCones54 : ∀ q ∈ degreeQs54, ∀ μ : YoungDiagram, μ.card = 54 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 4 1) μ := by + intro q hq + simp only [degreeQs54,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone54_1 + +abbrev degreeP54 := ResidualProperty 8 9 degreeQs54 [] + +lemma degreeCheck54_0_0 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 1 1 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_0_1 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 1 2 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_0_2 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 1 3 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_0_3 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 1 4 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_0_4 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 1 5 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_1_0 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 2 1 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_1_1 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 2 2 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_1_2 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 2 3 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_1_3 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 2 4 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_1_4 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 2 5 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_2_0 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 3 1 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_2_1 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 3 2 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_2_2 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 3 3 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_2_3 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 3 4 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_2_4 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 3 5 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_3_0 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 4 1 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_3_1 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 4 2 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_3_2 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 4 3 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_3_3 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 4 4 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_3_4 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 4 5 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_4_0 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 5 1 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_4_1 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 5 2 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_4_2 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 5 3 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_4_3 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 5 4 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54_4_4 : + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 5 5 (a+1) (c+1) degreeRows54_0 degreeP54 := by + decide +kernel + +lemma degreeCheck54 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows54_0.length, ∀ c ∈ List.range degreeRows54_0.length, + residualCheck 54 8 9 (d+1) (e+1) (a+1) (c+1) degreeRows54_0 degreeP54 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck54_0_0 + · exact degreeCheck54_0_1 + · exact degreeCheck54_0_2 + · exact degreeCheck54_0_3 + · exact degreeCheck54_0_4 + · exact degreeCheck54_1_0 + · exact degreeCheck54_1_1 + · exact degreeCheck54_1_2 + · exact degreeCheck54_1_3 + · exact degreeCheck54_1_4 + · exact degreeCheck54_2_0 + · exact degreeCheck54_2_1 + · exact degreeCheck54_2_2 + · exact degreeCheck54_2_3 + · exact degreeCheck54_2_4 + · exact degreeCheck54_3_0 + · exact degreeCheck54_3_1 + · exact degreeCheck54_3_2 + · exact degreeCheck54_3_3 + · exact degreeCheck54_3_4 + · exact degreeCheck54_4_0 + · exact degreeCheck54_4_1 + · exact degreeCheck54_4_2 + · exact degreeCheck54_4_3 + · exact degreeCheck54_4_4 + +lemma degree_pos54 (μ : YoungDiagram) (hμ : μ.card = 54) : + 0 < kronecker (canonicalTableau (candidate 8 4 1) degreeCard54) + (canonicalTableau (candidate 8 4 1) degreeCard54) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 9) (by decide) (by decide) rfl (by decide) + degreeCard54 degreeRows54_0 (by decide) (by decide) + degreePlan54_0 (by decide) (by decide) (by decide) (by decide) degreeP54 ?_ + degreeCheck54 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard54 rfl degreeCones54 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree56.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree56.lean index 88e50c32008b2f6c833d84aa7ac50faed1e73c8f..0cda676540c09ba1f735094f8971f5f0a24763fc 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree56.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree56.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 56. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard56 : (candidate 8 5 0).card = 56 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan56_0 : PackingPlan := (.join (.neighbor 12 [7,6,6,6]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 6 1 [7,6])))) -def degreeRows56_0 : List ℕ := [7,7,6,6,6,6,3,3,3,2,2,2,2,1] - -lemma degreeCone56_0 (μ : YoungDiagram) (hμ : μ.card = 56) - (hd : RowsDom μ.rowLens degreeRows56_0) : SquareOccurs (candidate 8 5 0) μ := by - exact candidate_cone (by decide) degreeCard56 degreePlan56_0 degreeRows56_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs56 : List (List ℕ) := [] - -lemma degreeCones56 : ∀ q ∈ degreeQs56, ∀ μ : YoungDiagram, μ.card = 56 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 5 0) μ := by - intro q hq - simp only [degreeQs56,List.not_mem_nil] at hq - -abbrev degreeP56 := ResidualProperty 8 10 degreeQs56 [] - -lemma degreeCheck56_0_0 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 1 1 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_0_1 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 1 2 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_0_2 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 1 3 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_0_3 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 1 4 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_0_4 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 1 5 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_1_0 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 2 1 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_1_1 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 2 2 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_1_2 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 2 3 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_1_3 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 2 4 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_1_4 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 2 5 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_2_0 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 3 1 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_2_1 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 3 2 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_2_2 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 3 3 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_2_3 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 3 4 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_2_4 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 3 5 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_3_0 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 4 1 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_3_1 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 4 2 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_3_2 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 4 3 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_3_3 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 4 4 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_3_4 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 4 5 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_4_0 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 5 1 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_4_1 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 5 2 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_4_2 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 5 3 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_4_3 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 5 4 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56_4_4 : - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 5 5 (a+1) (c+1) degreeRows56_0 degreeP56 := by - decide +kernel - -lemma degreeCheck56 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, - residualCheck 56 8 10 (d+1) (e+1) (a+1) (c+1) degreeRows56_0 degreeP56 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck56_0_0 - · exact degreeCheck56_0_1 - · exact degreeCheck56_0_2 - · exact degreeCheck56_0_3 - · exact degreeCheck56_0_4 - · exact degreeCheck56_1_0 - · exact degreeCheck56_1_1 - · exact degreeCheck56_1_2 - · exact degreeCheck56_1_3 - · exact degreeCheck56_1_4 - · exact degreeCheck56_2_0 - · exact degreeCheck56_2_1 - · exact degreeCheck56_2_2 - · exact degreeCheck56_2_3 - · exact degreeCheck56_2_4 - · exact degreeCheck56_3_0 - · exact degreeCheck56_3_1 - · exact degreeCheck56_3_2 - · exact degreeCheck56_3_3 - · exact degreeCheck56_3_4 - · exact degreeCheck56_4_0 - · exact degreeCheck56_4_1 - · exact degreeCheck56_4_2 - · exact degreeCheck56_4_3 - · exact degreeCheck56_4_4 - -lemma degree_pos56 (μ : YoungDiagram) (hμ : μ.card = 56) : - 0 < kronecker (canonicalTableau (candidate 8 5 0) degreeCard56) - (canonicalTableau (candidate 8 5 0) degreeCard56) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 10) (by decide) (by decide) rfl (by decide) - degreeCard56 degreeRows56_0 (by decide) (by decide) - degreePlan56_0 (by decide) (by decide) (by decide) (by decide) degreeP56 ?_ - degreeCheck56 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard56 rfl degreeCones56 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 56. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard56 : (candidate 8 5 0).card = 56 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan56_0 : PackingPlan := (.join (.neighbor 12 [7,6,6,6]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 6 1 [7,6])))) +def degreeRows56_0 : List ℕ := [7,7,6,6,6,6,3,3,3,2,2,2,2,1] + +lemma degreeCone56_0 (μ : YoungDiagram) (hμ : μ.card = 56) + (hd : RowsDom μ.rowLens degreeRows56_0) : SquareOccurs (candidate 8 5 0) μ := by + exact candidate_cone (by decide) degreeCard56 degreePlan56_0 degreeRows56_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs56 : List (List ℕ) := [] + +lemma degreeCones56 : ∀ q ∈ degreeQs56, ∀ μ : YoungDiagram, μ.card = 56 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 5 0) μ := by + intro q hq + simp only [degreeQs56,List.not_mem_nil] at hq + +abbrev degreeP56 := ResidualProperty 8 10 degreeQs56 [] + +lemma degreeCheck56_0_0 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 1 1 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_0_1 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 1 2 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_0_2 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 1 3 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_0_3 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 1 4 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_0_4 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 1 5 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_1_0 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 2 1 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_1_1 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 2 2 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_1_2 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 2 3 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_1_3 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 2 4 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_1_4 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 2 5 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_2_0 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 3 1 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_2_1 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 3 2 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_2_2 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 3 3 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_2_3 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 3 4 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_2_4 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 3 5 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_3_0 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 4 1 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_3_1 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 4 2 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_3_2 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 4 3 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_3_3 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 4 4 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_3_4 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 4 5 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_4_0 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 5 1 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_4_1 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 5 2 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_4_2 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 5 3 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_4_3 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 5 4 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56_4_4 : + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 5 5 (a+1) (c+1) degreeRows56_0 degreeP56 := by + decide +kernel + +lemma degreeCheck56 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows56_0.length, ∀ c ∈ List.range degreeRows56_0.length, + residualCheck 56 8 10 (d+1) (e+1) (a+1) (c+1) degreeRows56_0 degreeP56 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck56_0_0 + · exact degreeCheck56_0_1 + · exact degreeCheck56_0_2 + · exact degreeCheck56_0_3 + · exact degreeCheck56_0_4 + · exact degreeCheck56_1_0 + · exact degreeCheck56_1_1 + · exact degreeCheck56_1_2 + · exact degreeCheck56_1_3 + · exact degreeCheck56_1_4 + · exact degreeCheck56_2_0 + · exact degreeCheck56_2_1 + · exact degreeCheck56_2_2 + · exact degreeCheck56_2_3 + · exact degreeCheck56_2_4 + · exact degreeCheck56_3_0 + · exact degreeCheck56_3_1 + · exact degreeCheck56_3_2 + · exact degreeCheck56_3_3 + · exact degreeCheck56_3_4 + · exact degreeCheck56_4_0 + · exact degreeCheck56_4_1 + · exact degreeCheck56_4_2 + · exact degreeCheck56_4_3 + · exact degreeCheck56_4_4 + +lemma degree_pos56 (μ : YoungDiagram) (hμ : μ.card = 56) : + 0 < kronecker (canonicalTableau (candidate 8 5 0) degreeCard56) + (canonicalTableau (candidate 8 5 0) degreeCard56) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 10) (by decide) (by decide) rfl (by decide) + degreeCard56 degreeRows56_0 (by decide) (by decide) + degreePlan56_0 (by decide) (by decide) (by decide) (by decide) degreeP56 ?_ + degreeCheck56 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard56 rfl degreeCones56 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree57.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree57.lean index e632faf81e54c64996d7de55a2086a7774f0f0b8..e61ae106c5887e86f7584b7a7f9504cc8466ecd4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree57.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree57.lean @@ -1,218 +1,218 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 57. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard57 : (candidate 10 0 1).card = 57 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan57_0 : PackingPlan := (.join (.twoPaths 9 [6,6,5,5]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 1 2))))) -def degreeRows57_0 : List ℕ := [6,6,5,5,4,4,4,3,3,3,3,2,2,2,2,2,1] - -lemma degreeCone57_0 (μ : YoungDiagram) (hμ : μ.card = 57) - (hd : RowsDom μ.rowLens degreeRows57_0) : SquareOccurs (candidate 10 0 1) μ := by - exact candidate_cone (by decide) degreeCard57 degreePlan57_0 degreeRows57_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreePlan57_1 : PackingPlan := (.join (.repeated 1 11) (.join (.neighbor 8 [5,4,4,4]) (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 4 [3,2,2,2]) (.join (.neighbor 2 [2,1,1,1]) (.repeated 2 1)))))) -def degreeRows57_1 : List ℕ := [11,5,4,4,4,4,3,3,3,3,2,2,2,2,2,1,1,1] - -lemma degreeCone57_1 (μ : YoungDiagram) (hμ : μ.card = 57) - (hd : RowsDom μ.rowLens degreeRows57_1) : SquareOccurs (candidate 10 0 1) μ := by - exact candidate_cone (by decide) degreeCard57 degreePlan57_1 degreeRows57_1 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs57 : List (List ℕ) := [degreeRows57_1] - -lemma degreeCones57 : ∀ q ∈ degreeQs57, ∀ μ : YoungDiagram, μ.card = 57 → - RowsDom μ.rowLens q → SquareOccurs (candidate 10 0 1) μ := by - intro q hq - simp only [degreeQs57,List.mem_cons,List.not_mem_nil,or_false] at hq - rcases hq with rfl - · exact degreeCone57_1 - -abbrev degreeP57 := ResidualProperty 10 1 degreeQs57 [] - -lemma degreeCheck57_0_0 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 1 1 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_0_1 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 1 2 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_0_2 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 1 3 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_0_3 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 1 4 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_0_4 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 1 5 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_1_0 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 2 1 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_1_1 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 2 2 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_1_2 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 2 3 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_1_3 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 2 4 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_1_4 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 2 5 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_2_0 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 3 1 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_2_1 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 3 2 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_2_2 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 3 3 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_2_3 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 3 4 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_2_4 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 3 5 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_3_0 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 4 1 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_3_1 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 4 2 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_3_2 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 4 3 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_3_3 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 4 4 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_3_4 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 4 5 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_4_0 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 5 1 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_4_1 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 5 2 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_4_2 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 5 3 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_4_3 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 5 4 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57_4_4 : - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 5 5 (a+1) (c+1) degreeRows57_0 degreeP57 := by - decide +kernel - -lemma degreeCheck57 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, - residualCheck 57 10 1 (d+1) (e+1) (a+1) (c+1) degreeRows57_0 degreeP57 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck57_0_0 - · exact degreeCheck57_0_1 - · exact degreeCheck57_0_2 - · exact degreeCheck57_0_3 - · exact degreeCheck57_0_4 - · exact degreeCheck57_1_0 - · exact degreeCheck57_1_1 - · exact degreeCheck57_1_2 - · exact degreeCheck57_1_3 - · exact degreeCheck57_1_4 - · exact degreeCheck57_2_0 - · exact degreeCheck57_2_1 - · exact degreeCheck57_2_2 - · exact degreeCheck57_2_3 - · exact degreeCheck57_2_4 - · exact degreeCheck57_3_0 - · exact degreeCheck57_3_1 - · exact degreeCheck57_3_2 - · exact degreeCheck57_3_3 - · exact degreeCheck57_3_4 - · exact degreeCheck57_4_0 - · exact degreeCheck57_4_1 - · exact degreeCheck57_4_2 - · exact degreeCheck57_4_3 - · exact degreeCheck57_4_4 - -lemma degree_pos57 (μ : YoungDiagram) (hμ : μ.card = 57) : - 0 < kronecker (canonicalTableau (candidate 10 0 1) degreeCard57) - (canonicalTableau (candidate 10 0 1) degreeCard57) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) - degreeCard57 degreeRows57_0 (by decide) (by decide) - degreePlan57_0 (by decide) (by decide) (by decide) (by decide) degreeP57 ?_ - degreeCheck57 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard57 rfl degreeCones57 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 57. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard57 : (candidate 10 0 1).card = 57 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan57_0 : PackingPlan := (.join (.twoPaths 9 [6,6,5,5]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 1 2))))) +def degreeRows57_0 : List ℕ := [6,6,5,5,4,4,4,3,3,3,3,2,2,2,2,2,1] + +lemma degreeCone57_0 (μ : YoungDiagram) (hμ : μ.card = 57) + (hd : RowsDom μ.rowLens degreeRows57_0) : SquareOccurs (candidate 10 0 1) μ := by + exact candidate_cone (by decide) degreeCard57 degreePlan57_0 degreeRows57_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreePlan57_1 : PackingPlan := (.join (.repeated 1 11) (.join (.neighbor 8 [5,4,4,4]) (.join (.neighbor 6 [4,3,3,3]) (.join (.neighbor 4 [3,2,2,2]) (.join (.neighbor 2 [2,1,1,1]) (.repeated 2 1)))))) +def degreeRows57_1 : List ℕ := [11,5,4,4,4,4,3,3,3,3,2,2,2,2,2,1,1,1] + +lemma degreeCone57_1 (μ : YoungDiagram) (hμ : μ.card = 57) + (hd : RowsDom μ.rowLens degreeRows57_1) : SquareOccurs (candidate 10 0 1) μ := by + exact candidate_cone (by decide) degreeCard57 degreePlan57_1 degreeRows57_1 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs57 : List (List ℕ) := [degreeRows57_1] + +lemma degreeCones57 : ∀ q ∈ degreeQs57, ∀ μ : YoungDiagram, μ.card = 57 → + RowsDom μ.rowLens q → SquareOccurs (candidate 10 0 1) μ := by + intro q hq + simp only [degreeQs57,List.mem_cons,List.not_mem_nil,or_false] at hq + rcases hq with rfl + · exact degreeCone57_1 + +abbrev degreeP57 := ResidualProperty 10 1 degreeQs57 [] + +lemma degreeCheck57_0_0 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 1 1 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_0_1 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 1 2 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_0_2 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 1 3 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_0_3 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 1 4 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_0_4 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 1 5 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_1_0 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 2 1 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_1_1 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 2 2 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_1_2 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 2 3 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_1_3 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 2 4 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_1_4 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 2 5 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_2_0 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 3 1 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_2_1 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 3 2 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_2_2 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 3 3 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_2_3 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 3 4 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_2_4 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 3 5 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_3_0 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 4 1 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_3_1 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 4 2 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_3_2 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 4 3 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_3_3 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 4 4 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_3_4 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 4 5 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_4_0 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 5 1 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_4_1 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 5 2 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_4_2 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 5 3 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_4_3 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 5 4 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57_4_4 : + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 5 5 (a+1) (c+1) degreeRows57_0 degreeP57 := by + decide +kernel + +lemma degreeCheck57 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows57_0.length, ∀ c ∈ List.range degreeRows57_0.length, + residualCheck 57 10 1 (d+1) (e+1) (a+1) (c+1) degreeRows57_0 degreeP57 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck57_0_0 + · exact degreeCheck57_0_1 + · exact degreeCheck57_0_2 + · exact degreeCheck57_0_3 + · exact degreeCheck57_0_4 + · exact degreeCheck57_1_0 + · exact degreeCheck57_1_1 + · exact degreeCheck57_1_2 + · exact degreeCheck57_1_3 + · exact degreeCheck57_1_4 + · exact degreeCheck57_2_0 + · exact degreeCheck57_2_1 + · exact degreeCheck57_2_2 + · exact degreeCheck57_2_3 + · exact degreeCheck57_2_4 + · exact degreeCheck57_3_0 + · exact degreeCheck57_3_1 + · exact degreeCheck57_3_2 + · exact degreeCheck57_3_3 + · exact degreeCheck57_3_4 + · exact degreeCheck57_4_0 + · exact degreeCheck57_4_1 + · exact degreeCheck57_4_2 + · exact degreeCheck57_4_3 + · exact degreeCheck57_4_4 + +lemma degree_pos57 (μ : YoungDiagram) (hμ : μ.card = 57) : + 0 < kronecker (canonicalTableau (candidate 10 0 1) degreeCard57) + (canonicalTableau (candidate 10 0 1) degreeCard57) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 1) (by decide) (by decide) rfl (by decide) + degreeCard57 degreeRows57_0 (by decide) (by decide) + degreePlan57_0 (by decide) (by decide) (by decide) (by decide) degreeP57 ?_ + degreeCheck57 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard57 rfl degreeCones57 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree58.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree58.lean index 166e9a3631526c3fe4631133ed9978237b8e1724..c252242181e80fe6abf98346d8dc45e05456174e 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree58.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree58.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks58 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof58 - -namespace OAI - -/-! Numerical Degree 58. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos58 (μ : YoungDiagram) (hμ : μ.card = 58) : - 0 < kronecker (canonicalTableau (candidate 8 5 1) degreeCard58) - (canonicalTableau (candidate 8 5 1) degreeCard58) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 11) (by decide) (by decide) rfl (by decide) - degreeCard58 degreeRows58_0 (by decide) (by decide) - degreePlan58_0 (by decide) (by decide) (by decide) (by decide) degreeP58 ?_ - degreeCheck58 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard58 rfl degreeCones58 - degreeTreeAll58 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks58 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof58 + +namespace OAI + +/-! Numerical Degree 58. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos58 (μ : YoungDiagram) (hμ : μ.card = 58) : + 0 < kronecker (canonicalTableau (candidate 8 5 1) degreeCard58) + (canonicalTableau (candidate 8 5 1) degreeCard58) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 11) (by decide) (by decide) rfl (by decide) + degreeCard58 degreeRows58_0 (by decide) (by decide) + degreePlan58_0 (by decide) (by decide) (by decide) (by decide) degreeP58 ?_ + degreeCheck58 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard58 rfl degreeCones58 + degreeTreeAll58 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree59.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree59.lean index 47c4758f236d6d082c5c7b292f4a506138535ffe..b38e8c16b7a5a6cc64151c31e0e14d74ca7c4fe9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree59.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree59.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 59. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard59 : (candidate 10 1 0).card = 59 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan59_0 : PackingPlan := (.join (.neighbor 10 [6,5,5,5]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 2 1 [3,2]))))) -def degreeRows59_0 : List ℕ := [6,5,5,5,4,4,4,3,3,3,3,3,2,2,2,2,2,1] - -lemma degreeCone59_0 (μ : YoungDiagram) (hμ : μ.card = 59) - (hd : RowsDom μ.rowLens degreeRows59_0) : SquareOccurs (candidate 10 1 0) μ := by - exact candidate_cone (by decide) degreeCard59 degreePlan59_0 degreeRows59_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs59 : List (List ℕ) := [] - -lemma degreeCones59 : ∀ q ∈ degreeQs59, ∀ μ : YoungDiagram, μ.card = 59 → - RowsDom μ.rowLens q → SquareOccurs (candidate 10 1 0) μ := by - intro q hq - simp only [degreeQs59,List.not_mem_nil] at hq - -abbrev degreeP59 := ResidualProperty 10 2 degreeQs59 [] - -lemma degreeCheck59_0_0 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 1 1 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_0_1 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 1 2 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_0_2 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 1 3 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_0_3 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 1 4 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_0_4 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 1 5 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_1_0 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 2 1 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_1_1 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 2 2 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_1_2 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 2 3 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_1_3 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 2 4 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_1_4 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 2 5 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_2_0 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 3 1 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_2_1 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 3 2 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_2_2 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 3 3 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_2_3 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 3 4 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_2_4 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 3 5 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_3_0 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 4 1 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_3_1 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 4 2 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_3_2 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 4 3 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_3_3 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 4 4 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_3_4 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 4 5 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_4_0 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 5 1 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_4_1 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 5 2 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_4_2 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 5 3 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_4_3 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 5 4 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59_4_4 : - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 5 5 (a+1) (c+1) degreeRows59_0 degreeP59 := by - decide +kernel - -lemma degreeCheck59 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, - residualCheck 59 10 2 (d+1) (e+1) (a+1) (c+1) degreeRows59_0 degreeP59 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck59_0_0 - · exact degreeCheck59_0_1 - · exact degreeCheck59_0_2 - · exact degreeCheck59_0_3 - · exact degreeCheck59_0_4 - · exact degreeCheck59_1_0 - · exact degreeCheck59_1_1 - · exact degreeCheck59_1_2 - · exact degreeCheck59_1_3 - · exact degreeCheck59_1_4 - · exact degreeCheck59_2_0 - · exact degreeCheck59_2_1 - · exact degreeCheck59_2_2 - · exact degreeCheck59_2_3 - · exact degreeCheck59_2_4 - · exact degreeCheck59_3_0 - · exact degreeCheck59_3_1 - · exact degreeCheck59_3_2 - · exact degreeCheck59_3_3 - · exact degreeCheck59_3_4 - · exact degreeCheck59_4_0 - · exact degreeCheck59_4_1 - · exact degreeCheck59_4_2 - · exact degreeCheck59_4_3 - · exact degreeCheck59_4_4 - -lemma degree_pos59 (μ : YoungDiagram) (hμ : μ.card = 59) : - 0 < kronecker (canonicalTableau (candidate 10 1 0) degreeCard59) - (canonicalTableau (candidate 10 1 0) degreeCard59) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 2) (by decide) (by decide) rfl (by decide) - degreeCard59 degreeRows59_0 (by decide) (by decide) - degreePlan59_0 (by decide) (by decide) (by decide) (by decide) degreeP59 ?_ - degreeCheck59 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard59 rfl degreeCones59 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 59. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard59 : (candidate 10 1 0).card = 59 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan59_0 : PackingPlan := (.join (.neighbor 10 [6,5,5,5]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 2 1 [3,2]))))) +def degreeRows59_0 : List ℕ := [6,5,5,5,4,4,4,3,3,3,3,3,2,2,2,2,2,1] + +lemma degreeCone59_0 (μ : YoungDiagram) (hμ : μ.card = 59) + (hd : RowsDom μ.rowLens degreeRows59_0) : SquareOccurs (candidate 10 1 0) μ := by + exact candidate_cone (by decide) degreeCard59 degreePlan59_0 degreeRows59_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs59 : List (List ℕ) := [] + +lemma degreeCones59 : ∀ q ∈ degreeQs59, ∀ μ : YoungDiagram, μ.card = 59 → + RowsDom μ.rowLens q → SquareOccurs (candidate 10 1 0) μ := by + intro q hq + simp only [degreeQs59,List.not_mem_nil] at hq + +abbrev degreeP59 := ResidualProperty 10 2 degreeQs59 [] + +lemma degreeCheck59_0_0 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 1 1 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_0_1 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 1 2 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_0_2 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 1 3 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_0_3 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 1 4 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_0_4 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 1 5 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_1_0 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 2 1 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_1_1 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 2 2 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_1_2 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 2 3 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_1_3 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 2 4 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_1_4 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 2 5 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_2_0 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 3 1 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_2_1 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 3 2 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_2_2 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 3 3 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_2_3 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 3 4 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_2_4 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 3 5 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_3_0 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 4 1 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_3_1 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 4 2 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_3_2 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 4 3 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_3_3 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 4 4 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_3_4 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 4 5 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_4_0 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 5 1 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_4_1 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 5 2 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_4_2 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 5 3 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_4_3 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 5 4 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59_4_4 : + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 5 5 (a+1) (c+1) degreeRows59_0 degreeP59 := by + decide +kernel + +lemma degreeCheck59 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows59_0.length, ∀ c ∈ List.range degreeRows59_0.length, + residualCheck 59 10 2 (d+1) (e+1) (a+1) (c+1) degreeRows59_0 degreeP59 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck59_0_0 + · exact degreeCheck59_0_1 + · exact degreeCheck59_0_2 + · exact degreeCheck59_0_3 + · exact degreeCheck59_0_4 + · exact degreeCheck59_1_0 + · exact degreeCheck59_1_1 + · exact degreeCheck59_1_2 + · exact degreeCheck59_1_3 + · exact degreeCheck59_1_4 + · exact degreeCheck59_2_0 + · exact degreeCheck59_2_1 + · exact degreeCheck59_2_2 + · exact degreeCheck59_2_3 + · exact degreeCheck59_2_4 + · exact degreeCheck59_3_0 + · exact degreeCheck59_3_1 + · exact degreeCheck59_3_2 + · exact degreeCheck59_3_3 + · exact degreeCheck59_3_4 + · exact degreeCheck59_4_0 + · exact degreeCheck59_4_1 + · exact degreeCheck59_4_2 + · exact degreeCheck59_4_3 + · exact degreeCheck59_4_4 + +lemma degree_pos59 (μ : YoungDiagram) (hμ : μ.card = 59) : + 0 < kronecker (canonicalTableau (candidate 10 1 0) degreeCard59) + (canonicalTableau (candidate 10 1 0) degreeCard59) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 2) (by decide) (by decide) rfl (by decide) + degreeCard59 degreeRows59_0 (by decide) (by decide) + degreePlan59_0 (by decide) (by decide) (by decide) (by decide) degreeP59 ?_ + degreeCheck59 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard59 rfl degreeCones59 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree60.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree60.lean index e25436daa91635abc3631e28bb80dc7800e64944..20ee7f6ec845ee0a4516f687210d1b98f3d33955 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree60.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree60.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 60. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard60 : (candidate 8 6 0).card = 60 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan60_0 : PackingPlan := (.join (.neighbor 13 [7,7,7,6]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 7 1 [8,7])))) -def degreeRows60_0 : List ℕ := [8,7,7,7,7,6,3,3,3,2,2,2,2,1] - -lemma degreeCone60_0 (μ : YoungDiagram) (hμ : μ.card = 60) - (hd : RowsDom μ.rowLens degreeRows60_0) : SquareOccurs (candidate 8 6 0) μ := by - exact candidate_cone (by decide) degreeCard60 degreePlan60_0 degreeRows60_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs60 : List (List ℕ) := [] - -lemma degreeCones60 : ∀ q ∈ degreeQs60, ∀ μ : YoungDiagram, μ.card = 60 → - RowsDom μ.rowLens q → SquareOccurs (candidate 8 6 0) μ := by - intro q hq - simp only [degreeQs60,List.not_mem_nil] at hq - -abbrev degreeP60 := ResidualProperty 8 12 degreeQs60 [] - -lemma degreeCheck60_0_0 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 1 1 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_0_1 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 1 2 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_0_2 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 1 3 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_0_3 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 1 4 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_0_4 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 1 5 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_1_0 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 2 1 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_1_1 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 2 2 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_1_2 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 2 3 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_1_3 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 2 4 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_1_4 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 2 5 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_2_0 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 3 1 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_2_1 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 3 2 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_2_2 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 3 3 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_2_3 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 3 4 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_2_4 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 3 5 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_3_0 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 4 1 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_3_1 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 4 2 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_3_2 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 4 3 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_3_3 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 4 4 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_3_4 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 4 5 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_4_0 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 5 1 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_4_1 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 5 2 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_4_2 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 5 3 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_4_3 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 5 4 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60_4_4 : - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 5 5 (a+1) (c+1) degreeRows60_0 degreeP60 := by - decide +kernel - -lemma degreeCheck60 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, - residualCheck 60 8 12 (d+1) (e+1) (a+1) (c+1) degreeRows60_0 degreeP60 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck60_0_0 - · exact degreeCheck60_0_1 - · exact degreeCheck60_0_2 - · exact degreeCheck60_0_3 - · exact degreeCheck60_0_4 - · exact degreeCheck60_1_0 - · exact degreeCheck60_1_1 - · exact degreeCheck60_1_2 - · exact degreeCheck60_1_3 - · exact degreeCheck60_1_4 - · exact degreeCheck60_2_0 - · exact degreeCheck60_2_1 - · exact degreeCheck60_2_2 - · exact degreeCheck60_2_3 - · exact degreeCheck60_2_4 - · exact degreeCheck60_3_0 - · exact degreeCheck60_3_1 - · exact degreeCheck60_3_2 - · exact degreeCheck60_3_3 - · exact degreeCheck60_3_4 - · exact degreeCheck60_4_0 - · exact degreeCheck60_4_1 - · exact degreeCheck60_4_2 - · exact degreeCheck60_4_3 - · exact degreeCheck60_4_4 - -lemma degree_pos60 (μ : YoungDiagram) (hμ : μ.card = 60) : - 0 < kronecker (canonicalTableau (candidate 8 6 0) degreeCard60) - (canonicalTableau (candidate 8 6 0) degreeCard60) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 12) (by decide) (by decide) rfl (by decide) - degreeCard60 degreeRows60_0 (by decide) (by decide) - degreePlan60_0 (by decide) (by decide) (by decide) (by decide) degreeP60 ?_ - degreeCheck60 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard60 rfl degreeCones60 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 60. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard60 : (candidate 8 6 0).card = 60 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan60_0 : PackingPlan := (.join (.neighbor 13 [7,7,7,6]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 7 1 [8,7])))) +def degreeRows60_0 : List ℕ := [8,7,7,7,7,6,3,3,3,2,2,2,2,1] + +lemma degreeCone60_0 (μ : YoungDiagram) (hμ : μ.card = 60) + (hd : RowsDom μ.rowLens degreeRows60_0) : SquareOccurs (candidate 8 6 0) μ := by + exact candidate_cone (by decide) degreeCard60 degreePlan60_0 degreeRows60_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs60 : List (List ℕ) := [] + +lemma degreeCones60 : ∀ q ∈ degreeQs60, ∀ μ : YoungDiagram, μ.card = 60 → + RowsDom μ.rowLens q → SquareOccurs (candidate 8 6 0) μ := by + intro q hq + simp only [degreeQs60,List.not_mem_nil] at hq + +abbrev degreeP60 := ResidualProperty 8 12 degreeQs60 [] + +lemma degreeCheck60_0_0 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 1 1 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_0_1 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 1 2 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_0_2 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 1 3 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_0_3 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 1 4 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_0_4 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 1 5 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_1_0 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 2 1 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_1_1 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 2 2 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_1_2 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 2 3 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_1_3 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 2 4 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_1_4 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 2 5 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_2_0 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 3 1 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_2_1 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 3 2 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_2_2 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 3 3 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_2_3 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 3 4 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_2_4 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 3 5 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_3_0 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 4 1 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_3_1 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 4 2 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_3_2 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 4 3 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_3_3 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 4 4 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_3_4 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 4 5 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_4_0 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 5 1 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_4_1 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 5 2 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_4_2 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 5 3 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_4_3 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 5 4 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60_4_4 : + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 5 5 (a+1) (c+1) degreeRows60_0 degreeP60 := by + decide +kernel + +lemma degreeCheck60 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows60_0.length, ∀ c ∈ List.range degreeRows60_0.length, + residualCheck 60 8 12 (d+1) (e+1) (a+1) (c+1) degreeRows60_0 degreeP60 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck60_0_0 + · exact degreeCheck60_0_1 + · exact degreeCheck60_0_2 + · exact degreeCheck60_0_3 + · exact degreeCheck60_0_4 + · exact degreeCheck60_1_0 + · exact degreeCheck60_1_1 + · exact degreeCheck60_1_2 + · exact degreeCheck60_1_3 + · exact degreeCheck60_1_4 + · exact degreeCheck60_2_0 + · exact degreeCheck60_2_1 + · exact degreeCheck60_2_2 + · exact degreeCheck60_2_3 + · exact degreeCheck60_2_4 + · exact degreeCheck60_3_0 + · exact degreeCheck60_3_1 + · exact degreeCheck60_3_2 + · exact degreeCheck60_3_3 + · exact degreeCheck60_3_4 + · exact degreeCheck60_4_0 + · exact degreeCheck60_4_1 + · exact degreeCheck60_4_2 + · exact degreeCheck60_4_3 + · exact degreeCheck60_4_4 + +lemma degree_pos60 (μ : YoungDiagram) (hμ : μ.card = 60) : + 0 < kronecker (canonicalTableau (candidate 8 6 0) degreeCard60) + (canonicalTableau (candidate 8 6 0) degreeCard60) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 12) (by decide) (by decide) rfl (by decide) + degreeCard60 degreeRows60_0 (by decide) (by decide) + degreePlan60_0 (by decide) (by decide) (by decide) (by decide) degreeP60 ?_ + degreeCheck60 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard60 rfl degreeCones60 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree61.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree61.lean index ab1b5cbc88996b0800cf42f64e3c402ae926f488..bed92ac10e0c1e181fda4a9768bad4d11fad6853 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree61.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree61.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 61. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard61 : (candidate 10 1 1).card = 61 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan61_0 : PackingPlan := (.join (.twoPaths 10 [6,6,6,6]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 2 2))))) -def degreeRows61_0 : List ℕ := [6,6,6,6,4,4,4,4,3,3,3,3,2,2,2,2,1] - -lemma degreeCone61_0 (μ : YoungDiagram) (hμ : μ.card = 61) - (hd : RowsDom μ.rowLens degreeRows61_0) : SquareOccurs (candidate 10 1 1) μ := by - exact candidate_cone (by decide) degreeCard61 degreePlan61_0 degreeRows61_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs61 : List (List ℕ) := [] - -lemma degreeCones61 : ∀ q ∈ degreeQs61, ∀ μ : YoungDiagram, μ.card = 61 → - RowsDom μ.rowLens q → SquareOccurs (candidate 10 1 1) μ := by - intro q hq - simp only [degreeQs61,List.not_mem_nil] at hq - -abbrev degreeP61 := ResidualProperty 10 3 degreeQs61 [] - -lemma degreeCheck61_0_0 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 1 1 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_0_1 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 1 2 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_0_2 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 1 3 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_0_3 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 1 4 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_0_4 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 1 5 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_1_0 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 2 1 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_1_1 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 2 2 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_1_2 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 2 3 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_1_3 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 2 4 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_1_4 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 2 5 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_2_0 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 3 1 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_2_1 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 3 2 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_2_2 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 3 3 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_2_3 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 3 4 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_2_4 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 3 5 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_3_0 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 4 1 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_3_1 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 4 2 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_3_2 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 4 3 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_3_3 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 4 4 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_3_4 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 4 5 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_4_0 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 5 1 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_4_1 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 5 2 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_4_2 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 5 3 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_4_3 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 5 4 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61_4_4 : - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 5 5 (a+1) (c+1) degreeRows61_0 degreeP61 := by - decide +kernel - -lemma degreeCheck61 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, - residualCheck 61 10 3 (d+1) (e+1) (a+1) (c+1) degreeRows61_0 degreeP61 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck61_0_0 - · exact degreeCheck61_0_1 - · exact degreeCheck61_0_2 - · exact degreeCheck61_0_3 - · exact degreeCheck61_0_4 - · exact degreeCheck61_1_0 - · exact degreeCheck61_1_1 - · exact degreeCheck61_1_2 - · exact degreeCheck61_1_3 - · exact degreeCheck61_1_4 - · exact degreeCheck61_2_0 - · exact degreeCheck61_2_1 - · exact degreeCheck61_2_2 - · exact degreeCheck61_2_3 - · exact degreeCheck61_2_4 - · exact degreeCheck61_3_0 - · exact degreeCheck61_3_1 - · exact degreeCheck61_3_2 - · exact degreeCheck61_3_3 - · exact degreeCheck61_3_4 - · exact degreeCheck61_4_0 - · exact degreeCheck61_4_1 - · exact degreeCheck61_4_2 - · exact degreeCheck61_4_3 - · exact degreeCheck61_4_4 - -lemma degree_pos61 (μ : YoungDiagram) (hμ : μ.card = 61) : - 0 < kronecker (canonicalTableau (candidate 10 1 1) degreeCard61) - (canonicalTableau (candidate 10 1 1) degreeCard61) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 3) (by decide) (by decide) rfl (by decide) - degreeCard61 degreeRows61_0 (by decide) (by decide) - degreePlan61_0 (by decide) (by decide) (by decide) (by decide) degreeP61 ?_ - degreeCheck61 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard61 rfl degreeCones61 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 61. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard61 : (candidate 10 1 1).card = 61 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan61_0 : PackingPlan := (.join (.twoPaths 10 [6,6,6,6]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.repeated 2 2))))) +def degreeRows61_0 : List ℕ := [6,6,6,6,4,4,4,4,3,3,3,3,2,2,2,2,1] + +lemma degreeCone61_0 (μ : YoungDiagram) (hμ : μ.card = 61) + (hd : RowsDom μ.rowLens degreeRows61_0) : SquareOccurs (candidate 10 1 1) μ := by + exact candidate_cone (by decide) degreeCard61 degreePlan61_0 degreeRows61_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs61 : List (List ℕ) := [] + +lemma degreeCones61 : ∀ q ∈ degreeQs61, ∀ μ : YoungDiagram, μ.card = 61 → + RowsDom μ.rowLens q → SquareOccurs (candidate 10 1 1) μ := by + intro q hq + simp only [degreeQs61,List.not_mem_nil] at hq + +abbrev degreeP61 := ResidualProperty 10 3 degreeQs61 [] + +lemma degreeCheck61_0_0 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 1 1 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_0_1 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 1 2 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_0_2 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 1 3 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_0_3 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 1 4 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_0_4 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 1 5 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_1_0 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 2 1 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_1_1 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 2 2 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_1_2 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 2 3 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_1_3 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 2 4 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_1_4 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 2 5 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_2_0 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 3 1 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_2_1 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 3 2 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_2_2 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 3 3 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_2_3 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 3 4 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_2_4 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 3 5 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_3_0 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 4 1 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_3_1 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 4 2 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_3_2 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 4 3 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_3_3 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 4 4 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_3_4 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 4 5 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_4_0 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 5 1 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_4_1 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 5 2 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_4_2 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 5 3 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_4_3 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 5 4 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61_4_4 : + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 5 5 (a+1) (c+1) degreeRows61_0 degreeP61 := by + decide +kernel + +lemma degreeCheck61 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows61_0.length, ∀ c ∈ List.range degreeRows61_0.length, + residualCheck 61 10 3 (d+1) (e+1) (a+1) (c+1) degreeRows61_0 degreeP61 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck61_0_0 + · exact degreeCheck61_0_1 + · exact degreeCheck61_0_2 + · exact degreeCheck61_0_3 + · exact degreeCheck61_0_4 + · exact degreeCheck61_1_0 + · exact degreeCheck61_1_1 + · exact degreeCheck61_1_2 + · exact degreeCheck61_1_3 + · exact degreeCheck61_1_4 + · exact degreeCheck61_2_0 + · exact degreeCheck61_2_1 + · exact degreeCheck61_2_2 + · exact degreeCheck61_2_3 + · exact degreeCheck61_2_4 + · exact degreeCheck61_3_0 + · exact degreeCheck61_3_1 + · exact degreeCheck61_3_2 + · exact degreeCheck61_3_3 + · exact degreeCheck61_3_4 + · exact degreeCheck61_4_0 + · exact degreeCheck61_4_1 + · exact degreeCheck61_4_2 + · exact degreeCheck61_4_3 + · exact degreeCheck61_4_4 + +lemma degree_pos61 (μ : YoungDiagram) (hμ : μ.card = 61) : + 0 < kronecker (canonicalTableau (candidate 10 1 1) degreeCard61) + (canonicalTableau (candidate 10 1 1) degreeCard61) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 3) (by decide) (by decide) rfl (by decide) + degreeCard61 degreeRows61_0 (by decide) (by decide) + degreePlan61_0 (by decide) (by decide) (by decide) (by decide) degreeP61 ?_ + degreeCheck61 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard61 rfl degreeCones61 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree62.lean index 0eb3b0bd9df66d56a605d7a4ee82f1cbe225a01c..16e4a35f1d0c3f45401fc55003225a0e7b8f8b5a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree62.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks62 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof62 - -namespace OAI - -/-! Numerical Degree 62. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos62 (μ : YoungDiagram) (hμ : μ.card = 62) : - 0 < kronecker (canonicalTableau (candidate 8 6 1) degreeCard62) - (canonicalTableau (candidate 8 6 1) degreeCard62) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 13) (by decide) (by decide) rfl (by decide) - degreeCard62 degreeRows62_0 (by decide) (by decide) - degreePlan62_0 (by decide) (by decide) (by decide) (by decide) degreeP62 ?_ - degreeCheck62 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard62 rfl degreeCones62 - degreeTreeAll62 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks62 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof62 + +namespace OAI + +/-! Numerical Degree 62. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos62 (μ : YoungDiagram) (hμ : μ.card = 62) : + 0 < kronecker (canonicalTableau (candidate 8 6 1) degreeCard62) + (canonicalTableau (candidate 8 6 1) degreeCard62) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 13) (by decide) (by decide) rfl (by decide) + degreeCard62 degreeRows62_0 (by decide) (by decide) + degreePlan62_0 (by decide) (by decide) (by decide) (by decide) degreeP62 ?_ + degreeCheck62 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard62 rfl degreeCones62 + degreeTreeAll62 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree63.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree63.lean index 3e3a578f4191d08ee9aa1d72a8b2c5994057270e..68c23ba2f7decbe9f8f338268c2f7e70864fc0e8 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree63.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree63.lean @@ -1,208 +1,208 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Numerical Degree 63. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degreeCard63 : (candidate 10 2 0).card = 63 := by - rw [candidate_card _ _ _ (by decide), staircase_card] - -def degreePlan63_0 : PackingPlan := (.join (.neighbor 11 [6,6,6,5]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 3 1 [4,3]))))) -def degreeRows63_0 : List ℕ := [6,6,6,5,4,4,4,4,3,3,3,3,3,2,2,2,2,1] - -lemma degreeCone63_0 (μ : YoungDiagram) (hμ : μ.card = 63) - (hd : RowsDom μ.rowLens degreeRows63_0) : SquareOccurs (candidate 10 2 0) μ := by - exact candidate_cone (by decide) degreeCard63 degreePlan63_0 degreeRows63_0 - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd - -def degreeQs63 : List (List ℕ) := [] - -lemma degreeCones63 : ∀ q ∈ degreeQs63, ∀ μ : YoungDiagram, μ.card = 63 → - RowsDom μ.rowLens q → SquareOccurs (candidate 10 2 0) μ := by - intro q hq - simp only [degreeQs63, List.not_mem_nil] at hq - -abbrev degreeP63 := ResidualProperty 10 4 degreeQs63 [] - -lemma degreeCheck63_0_0 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 1 1 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_0_1 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 1 2 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_0_2 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 1 3 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_0_3 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 1 4 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_0_4 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 1 5 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_1_0 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 2 1 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_1_1 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 2 2 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_1_2 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 2 3 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_1_3 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 2 4 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_1_4 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 2 5 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_2_0 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 3 1 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_2_1 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 3 2 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_2_2 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 3 3 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_2_3 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 3 4 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_2_4 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 3 5 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_3_0 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 4 1 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_3_1 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 4 2 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_3_2 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 4 3 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_3_3 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 4 4 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_3_4 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 4 5 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_4_0 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 5 1 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_4_1 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 5 2 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_4_2 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 5 3 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_4_3 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 5 4 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63_4_4 : - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 5 5 (a+1) (c+1) degreeRows63_0 degreeP63 := by - decide +kernel - -lemma degreeCheck63 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, - ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, - residualCheck 63 10 4 (d+1) (e+1) (a+1) (c+1) degreeRows63_0 degreeP63 := by - intro d hd e he - have hd' : d < 5 := List.mem_range.mp hd - have he' : e < 5 := List.mem_range.mp he - interval_cases d <;> interval_cases e - · exact degreeCheck63_0_0 - · exact degreeCheck63_0_1 - · exact degreeCheck63_0_2 - · exact degreeCheck63_0_3 - · exact degreeCheck63_0_4 - · exact degreeCheck63_1_0 - · exact degreeCheck63_1_1 - · exact degreeCheck63_1_2 - · exact degreeCheck63_1_3 - · exact degreeCheck63_1_4 - · exact degreeCheck63_2_0 - · exact degreeCheck63_2_1 - · exact degreeCheck63_2_2 - · exact degreeCheck63_2_3 - · exact degreeCheck63_2_4 - · exact degreeCheck63_3_0 - · exact degreeCheck63_3_1 - · exact degreeCheck63_3_2 - · exact degreeCheck63_3_3 - · exact degreeCheck63_3_4 - · exact degreeCheck63_4_0 - · exact degreeCheck63_4_1 - · exact degreeCheck63_4_2 - · exact degreeCheck63_4_3 - · exact degreeCheck63_4_4 - -lemma degree_pos63 (μ : YoungDiagram) (hμ : μ.card = 63) : - 0 < kronecker (canonicalTableau (candidate 10 2 0) degreeCard63) - (canonicalTableau (candidate 10 2 0) degreeCard63) (canonicalTableau μ hμ) := by - apply candidate_residual_pos (r := 4) (by decide) (by decide) rfl (by decide) - degreeCard63 degreeRows63_0 (by decide) (by decide) - degreePlan63_0 (by decide) (by decide) (by decide) (by decide) degreeP63 ?_ - degreeCheck63 μ hμ - intro rs hr hn hh - exact residualProperty_sound (by decide) (by decide) degreeCard63 rfl degreeCones63 - (by simp) hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Numerical Degree 63. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degreeCard63 : (candidate 10 2 0).card = 63 := by + rw [candidate_card _ _ _ (by decide), staircase_card] + +def degreePlan63_0 : PackingPlan := (.join (.neighbor 11 [6,6,6,5]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.join (.neighbor 3 [2,2,2,1]) (.twosOdd 3 1 [4,3]))))) +def degreeRows63_0 : List ℕ := [6,6,6,5,4,4,4,4,3,3,3,3,3,2,2,2,2,1] + +lemma degreeCone63_0 (μ : YoungDiagram) (hμ : μ.card = 63) + (hd : RowsDom μ.rowLens degreeRows63_0) : SquareOccurs (candidate 10 2 0) μ := by + exact candidate_cone (by decide) degreeCard63 degreePlan63_0 degreeRows63_0 + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) μ hμ hd + +def degreeQs63 : List (List ℕ) := [] + +lemma degreeCones63 : ∀ q ∈ degreeQs63, ∀ μ : YoungDiagram, μ.card = 63 → + RowsDom μ.rowLens q → SquareOccurs (candidate 10 2 0) μ := by + intro q hq + simp only [degreeQs63, List.not_mem_nil] at hq + +abbrev degreeP63 := ResidualProperty 10 4 degreeQs63 [] + +lemma degreeCheck63_0_0 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 1 1 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_0_1 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 1 2 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_0_2 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 1 3 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_0_3 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 1 4 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_0_4 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 1 5 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_1_0 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 2 1 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_1_1 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 2 2 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_1_2 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 2 3 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_1_3 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 2 4 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_1_4 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 2 5 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_2_0 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 3 1 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_2_1 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 3 2 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_2_2 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 3 3 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_2_3 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 3 4 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_2_4 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 3 5 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_3_0 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 4 1 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_3_1 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 4 2 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_3_2 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 4 3 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_3_3 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 4 4 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_3_4 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 4 5 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_4_0 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 5 1 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_4_1 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 5 2 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_4_2 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 5 3 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_4_3 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 5 4 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63_4_4 : + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 5 5 (a+1) (c+1) degreeRows63_0 degreeP63 := by + decide +kernel + +lemma degreeCheck63 : ∀ d ∈ List.range 5, ∀ e ∈ List.range 5, + ∀ a ∈ List.range degreeRows63_0.length, ∀ c ∈ List.range degreeRows63_0.length, + residualCheck 63 10 4 (d+1) (e+1) (a+1) (c+1) degreeRows63_0 degreeP63 := by + intro d hd e he + have hd' : d < 5 := List.mem_range.mp hd + have he' : e < 5 := List.mem_range.mp he + interval_cases d <;> interval_cases e + · exact degreeCheck63_0_0 + · exact degreeCheck63_0_1 + · exact degreeCheck63_0_2 + · exact degreeCheck63_0_3 + · exact degreeCheck63_0_4 + · exact degreeCheck63_1_0 + · exact degreeCheck63_1_1 + · exact degreeCheck63_1_2 + · exact degreeCheck63_1_3 + · exact degreeCheck63_1_4 + · exact degreeCheck63_2_0 + · exact degreeCheck63_2_1 + · exact degreeCheck63_2_2 + · exact degreeCheck63_2_3 + · exact degreeCheck63_2_4 + · exact degreeCheck63_3_0 + · exact degreeCheck63_3_1 + · exact degreeCheck63_3_2 + · exact degreeCheck63_3_3 + · exact degreeCheck63_3_4 + · exact degreeCheck63_4_0 + · exact degreeCheck63_4_1 + · exact degreeCheck63_4_2 + · exact degreeCheck63_4_3 + · exact degreeCheck63_4_4 + +lemma degree_pos63 (μ : YoungDiagram) (hμ : μ.card = 63) : + 0 < kronecker (canonicalTableau (candidate 10 2 0) degreeCard63) + (canonicalTableau (candidate 10 2 0) degreeCard63) (canonicalTableau μ hμ) := by + apply candidate_residual_pos (r := 4) (by decide) (by decide) rfl (by decide) + degreeCard63 degreeRows63_0 (by decide) (by decide) + degreePlan63_0 (by decide) (by decide) (by decide) (by decide) degreeP63 ?_ + degreeCheck63 μ hμ + intro rs hr hn hh + exact residualProperty_sound (by decide) (by decide) degreeCard63 rfl degreeCones63 + (by simp) hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree64.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree64.lean index 84299a14a7aaccff4f0700a104977c5424666f4a..a01a9239072d6c6c955e51d20cc845ecd440f940 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree64.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree64.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks64 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof64 - -namespace OAI - -/-! Numerical Degree 64. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos64 (μ : YoungDiagram) (hμ : μ.card = 64) : - 0 < kronecker (canonicalTableau (candidate 8 7 0) degreeCard64) - (canonicalTableau (candidate 8 7 0) degreeCard64) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 14) (by decide) (by decide) rfl (by decide) - degreeCard64 degreeRows64_0 (by decide) (by decide) - degreePlan64_0 (by decide) (by decide) (by decide) (by decide) degreeP64 ?_ - degreeCheck64 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard64 rfl degreeCones64 - degreeTreeAll64 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks64 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof64 + +namespace OAI + +/-! Numerical Degree 64. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos64 (μ : YoungDiagram) (hμ : μ.card = 64) : + 0 < kronecker (canonicalTableau (candidate 8 7 0) degreeCard64) + (canonicalTableau (candidate 8 7 0) degreeCard64) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 14) (by decide) (by decide) rfl (by decide) + degreeCard64 degreeRows64_0 (by decide) (by decide) + degreePlan64_0 (by decide) (by decide) (by decide) (by decide) degreeP64 ?_ + degreeCheck64 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard64 rfl degreeCones64 + degreeTreeAll64 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree89.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree89.lean index d3f3ded7a93aa103557b06805214d4272bb2adf7..233273ad7b2020d6cfcc81c363634e46d99615de 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree89.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/NumericalDegree89.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks89 -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof89 - -namespace OAI - -/-! Numerical Degree 89. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Balance Saxl.Columns - -lemma degree_pos89 (μ : YoungDiagram) (hμ : μ.card = 89) : - 0 < kronecker (canonicalTableau (candidate 10 8 1) degreeCard89) - (canonicalTableau (candidate 10 8 1) degreeCard89) (canonicalTableau μ hμ) := by - apply candidate_semantic_pos (r := 17) (by decide) (by decide) rfl (by decide) - degreeCard89 degreeRows89_0 (by decide) (by decide) - degreePlan89_0 (by decide) (by decide) (by decide) (by decide) degreeP89 ?_ - degreeCheck89 μ hμ - intro rs hr hn hh - exact treeResidual_sound (by decide) (by decide) degreeCard89 rfl degreeCones89 - degreeTreeAll89 hr hn hh - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeChecks89 +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeTreeProof89 + +namespace OAI + +/-! Numerical Degree 89. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Balance Saxl.Columns + +lemma degree_pos89 (μ : YoungDiagram) (hμ : μ.card = 89) : + 0 < kronecker (canonicalTableau (candidate 10 8 1) degreeCard89) + (canonicalTableau (candidate 10 8 1) degreeCard89) (canonicalTableau μ hμ) := by + apply candidate_semantic_pos (r := 17) (by decide) (by decide) rfl (by decide) + degreeCard89 degreeRows89_0 (by decide) (by decide) + degreePlan89_0 (by decide) (by decide) (by decide) (by decide) degreeP89 ?_ + degreeCheck89 μ hμ + intro rs hr hn hh + exact treeResidual_sound (by decide) (by decide) degreeCard89 rfl degreeCones89 + degreeTreeAll89 hr hn hh + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows116.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows116.lean index 079862b5bcc84efff50f581cf31958a6c43393c7..99b8fa627edbb7de8713e4f8ba1f20d28470bf33 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows116.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows116.lean @@ -1,49 +1,49 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.PieriCertificates - -namespace OAI - -/-! Pieri Rows 116. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def pieriLower116 : PackingPlan := - .join (.threeRows 10 2 [9,8,8] - [⟨[8,6,6],[8,8,6],[9,8,8]⟩,⟨[8,6,6],[9,7,6],[9,9,7]⟩,⟨[8,6,6],[8,8,6],[10,8,7]⟩,⟨[8,6,6],[9,7,6],[10,9,6]⟩,⟨[10,6,4],[10,7,5],[10,10,5]⟩,⟨[8,6,6],[9,7,6],[11,7,7]⟩,⟨[8,6,6],[8,8,6],[11,8,6]⟩,⟨[8,8,4],[9,8,5],[11,9,5]⟩,⟨[8,8,4],[10,8,4],[11,10,4]⟩,⟨[10,8,2],[11,8,3],[11,11,3]⟩,⟨[8,6,6],[9,7,6],[12,7,6]⟩,⟨[8,8,4],[9,8,5],[12,8,5]⟩,⟨[8,8,4],[10,8,4],[12,9,4]⟩,⟨[10,8,2],[10,9,3],[12,10,3]⟩,⟨[10,8,2],[11,9,2],[12,11,2]⟩,⟨[12,8],[12,9,1],[12,12,1]⟩,⟨[8,6,6],[10,6,6],[13,6,6]⟩,⟨[10,6,4],[10,7,5],[13,7,5]⟩,⟨[8,8,4],[10,8,4],[13,8,4]⟩,⟨[10,8,2],[10,9,3],[13,9,3]⟩,⟨[10,8,2],[10,10,2],[13,10,2]⟩,⟨[10,10],[11,10,1],[13,11,1]⟩,⟨[10,10],[12,10],[13,12]⟩,⟨[10,6,4],[11,6,5],[14,6,5]⟩,⟨[10,6,4],[11,7,4],[14,7,4]⟩,⟨[10,8,2],[11,8,3],[14,8,3]⟩,⟨[10,8,2],[11,9,2],[14,9,2]⟩,⟨[10,10],[11,10,1],[14,10,1]⟩,⟨[10,10],[12,10],[14,11]⟩,⟨[12,4,4],[13,5,4],[15,5,5]⟩,⟨[10,6,4],[12,6,4],[15,6,4]⟩,⟨[12,6,2],[12,7,3],[15,7,3]⟩,⟨[10,8,2],[12,8,2],[15,8,2]⟩,⟨[12,8],[12,9,1],[15,9,1]⟩,⟨[10,10],[12,10],[15,10]⟩,⟨[12,4,4],[13,5,4],[16,5,4]⟩,⟨[12,6,2],[13,6,3],[16,6,3]⟩,⟨[12,6,2],[13,7,2],[16,7,2]⟩,⟨[12,8],[13,8,1],[16,8,1]⟩,⟨[12,8],[13,9],[16,9]⟩,⟨[12,4,4],[14,4,4],[17,4,4]⟩,⟨[14,4,2],[14,5,3],[17,5,3]⟩,⟨[12,6,2],[14,6,2],[17,6,2]⟩,⟨[14,6],[14,7,1],[17,7,1]⟩,⟨[12,8],[14,8],[17,8]⟩,⟨[14,4,2],[15,4,3],[18,4,3]⟩,⟨[14,4,2],[15,5,2],[18,5,2]⟩,⟨[14,6],[15,6,1],[18,6,1]⟩,⟨[14,6],[15,7],[18,7]⟩,⟨[16,2,2],[17,3,2],[19,3,3]⟩,⟨[14,4,2],[16,4,2],[19,4,2]⟩,⟨[16,4],[16,5,1],[19,5,1]⟩,⟨[14,6],[16,6],[19,6]⟩,⟨[16,2,2],[17,3,2],[20,3,2]⟩,⟨[16,4],[17,4,1],[20,4,1]⟩,⟨[16,4],[17,5],[20,5]⟩,⟨[16,2,2],[18,2,2],[21,2,2]⟩,⟨[18,2],[18,3,1],[21,3,1]⟩,⟨[16,4],[18,4],[21,4]⟩,⟨[18,2],[19,2,1],[22,2,1]⟩,⟨[18,2],[19,3],[22,3]⟩,⟨[20],[21,1],[23,1,1]⟩,⟨[18,2],[20,2],[23,2]⟩,⟨[20],[21,1],[24,1]⟩,⟨[20],[22],[25]⟩]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.repeated 1 4)))) - -lemma pieriLowerValid116 : pieriLower116.Valid 22 := by decide +kernel - -lemma pieriSquare116_0 : RowSquare [22,20,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,1,1] [11,11,11,11,11,11,10,10,10,10,10] := by - exact rowSquare_pieri (rs := [11,11,11,9]) (cs := [[11,11,11,11,7],[11,11,11,11,11,4],[11,11,11,11,11,11,1],[11,11,11,11,11,11,6],[11,11,11,11,11,11,10,1],[11,11,11,11,11,11,10,6],[11,11,11,11,11,11,10,10],[11,11,11,11,11,11,10,10,4],[11,11,11,11,11,11,10,10,8],[11,11,11,11,11,11,10,10,10,2],[11,11,11,11,11,11,10,10,10,6],[11,11,11,11,11,11,10,10,10,9],[11,11,11,11,11,11,10,10,10,10,2],[11,11,11,11,11,11,10,10,10,10,5],[11,11,11,11,11,11,10,10,10,10,8],[11,11,11,11,11,11,10,10,10,10,10]]) pieriLower116 20 2 - (by decide) (by decide) (by decide) pieriLowerValid116 (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) - -lemma pieriSquare116_1 : RowSquare [22,20,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,1,1] [11,11,11,11,11,11,11,10,10,10,9] := by - exact rowSquare_pieri (rs := [11,11,11,9]) (cs := [[11,11,11,11,7],[11,11,11,11,11,4],[11,11,11,11,11,11,1],[11,11,11,11,11,11,6],[11,11,11,11,11,11,11],[11,11,11,11,11,11,11,5],[11,11,11,11,11,11,11,9],[11,11,11,11,11,11,11,10,3],[11,11,11,11,11,11,11,10,7],[11,11,11,11,11,11,11,10,10,1],[11,11,11,11,11,11,11,10,10,5],[11,11,11,11,11,11,11,10,10,8],[11,11,11,11,11,11,11,10,10,10,1],[11,11,11,11,11,11,11,10,10,10,4],[11,11,11,11,11,11,11,10,10,10,7],[11,11,11,11,11,11,11,10,10,10,9]]) pieriLower116 20 2 - (by decide) (by decide) (by decide) pieriLowerValid116 (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) - -lemma pieriSquare116_2 : RowSquare [22,20,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,1,1] [11,11,11,11,11,11,11,11,10,9,9] := by - exact rowSquare_pieri (rs := [11,11,11,9]) (cs := [[11,11,11,11,7],[11,11,11,11,11,4],[11,11,11,11,11,11,1],[11,11,11,11,11,11,6],[11,11,11,11,11,11,11],[11,11,11,11,11,11,11,5],[11,11,11,11,11,11,11,9],[11,11,11,11,11,11,11,11,2],[11,11,11,11,11,11,11,11,6],[11,11,11,11,11,11,11,11,10],[11,11,11,11,11,11,11,11,10,4],[11,11,11,11,11,11,11,11,10,7],[11,11,11,11,11,11,11,11,10,9,1],[11,11,11,11,11,11,11,11,10,9,4],[11,11,11,11,11,11,11,11,10,9,7],[11,11,11,11,11,11,11,11,10,9,9]]) pieriLower116 20 2 - (by decide) (by decide) (by decide) pieriLowerValid116 (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) - -lemma pieriSquare116_3 : RowSquare [22,20,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,1,1] [11,11,11,11,11,11,11,11,10,10,8] := by - exact rowSquare_pieri (rs := [11,11,11,9]) (cs := [[11,11,11,11,7],[11,11,11,11,11,4],[11,11,11,11,11,11,1],[11,11,11,11,11,11,6],[11,11,11,11,11,11,11],[11,11,11,11,11,11,11,5],[11,11,11,11,11,11,11,9],[11,11,11,11,11,11,11,11,2],[11,11,11,11,11,11,11,11,6],[11,11,11,11,11,11,11,11,10],[11,11,11,11,11,11,11,11,10,4],[11,11,11,11,11,11,11,11,10,7],[11,11,11,11,11,11,11,11,10,10],[11,11,11,11,11,11,11,11,10,10,3],[11,11,11,11,11,11,11,11,10,10,6],[11,11,11,11,11,11,11,11,10,10,8]]) pieriLower116 20 2 - (by decide) (by decide) (by decide) pieriLowerValid116 (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.PieriCertificates + +namespace OAI + +/-! Pieri Rows 116. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def pieriLower116 : PackingPlan := + .join (.threeRows 10 2 [9,8,8] + [⟨[8,6,6],[8,8,6],[9,8,8]⟩,⟨[8,6,6],[9,7,6],[9,9,7]⟩,⟨[8,6,6],[8,8,6],[10,8,7]⟩,⟨[8,6,6],[9,7,6],[10,9,6]⟩,⟨[10,6,4],[10,7,5],[10,10,5]⟩,⟨[8,6,6],[9,7,6],[11,7,7]⟩,⟨[8,6,6],[8,8,6],[11,8,6]⟩,⟨[8,8,4],[9,8,5],[11,9,5]⟩,⟨[8,8,4],[10,8,4],[11,10,4]⟩,⟨[10,8,2],[11,8,3],[11,11,3]⟩,⟨[8,6,6],[9,7,6],[12,7,6]⟩,⟨[8,8,4],[9,8,5],[12,8,5]⟩,⟨[8,8,4],[10,8,4],[12,9,4]⟩,⟨[10,8,2],[10,9,3],[12,10,3]⟩,⟨[10,8,2],[11,9,2],[12,11,2]⟩,⟨[12,8],[12,9,1],[12,12,1]⟩,⟨[8,6,6],[10,6,6],[13,6,6]⟩,⟨[10,6,4],[10,7,5],[13,7,5]⟩,⟨[8,8,4],[10,8,4],[13,8,4]⟩,⟨[10,8,2],[10,9,3],[13,9,3]⟩,⟨[10,8,2],[10,10,2],[13,10,2]⟩,⟨[10,10],[11,10,1],[13,11,1]⟩,⟨[10,10],[12,10],[13,12]⟩,⟨[10,6,4],[11,6,5],[14,6,5]⟩,⟨[10,6,4],[11,7,4],[14,7,4]⟩,⟨[10,8,2],[11,8,3],[14,8,3]⟩,⟨[10,8,2],[11,9,2],[14,9,2]⟩,⟨[10,10],[11,10,1],[14,10,1]⟩,⟨[10,10],[12,10],[14,11]⟩,⟨[12,4,4],[13,5,4],[15,5,5]⟩,⟨[10,6,4],[12,6,4],[15,6,4]⟩,⟨[12,6,2],[12,7,3],[15,7,3]⟩,⟨[10,8,2],[12,8,2],[15,8,2]⟩,⟨[12,8],[12,9,1],[15,9,1]⟩,⟨[10,10],[12,10],[15,10]⟩,⟨[12,4,4],[13,5,4],[16,5,4]⟩,⟨[12,6,2],[13,6,3],[16,6,3]⟩,⟨[12,6,2],[13,7,2],[16,7,2]⟩,⟨[12,8],[13,8,1],[16,8,1]⟩,⟨[12,8],[13,9],[16,9]⟩,⟨[12,4,4],[14,4,4],[17,4,4]⟩,⟨[14,4,2],[14,5,3],[17,5,3]⟩,⟨[12,6,2],[14,6,2],[17,6,2]⟩,⟨[14,6],[14,7,1],[17,7,1]⟩,⟨[12,8],[14,8],[17,8]⟩,⟨[14,4,2],[15,4,3],[18,4,3]⟩,⟨[14,4,2],[15,5,2],[18,5,2]⟩,⟨[14,6],[15,6,1],[18,6,1]⟩,⟨[14,6],[15,7],[18,7]⟩,⟨[16,2,2],[17,3,2],[19,3,3]⟩,⟨[14,4,2],[16,4,2],[19,4,2]⟩,⟨[16,4],[16,5,1],[19,5,1]⟩,⟨[14,6],[16,6],[19,6]⟩,⟨[16,2,2],[17,3,2],[20,3,2]⟩,⟨[16,4],[17,4,1],[20,4,1]⟩,⟨[16,4],[17,5],[20,5]⟩,⟨[16,2,2],[18,2,2],[21,2,2]⟩,⟨[18,2],[18,3,1],[21,3,1]⟩,⟨[16,4],[18,4],[21,4]⟩,⟨[18,2],[19,2,1],[22,2,1]⟩,⟨[18,2],[19,3],[22,3]⟩,⟨[20],[21,1],[23,1,1]⟩,⟨[18,2],[20,2],[23,2]⟩,⟨[20],[21,1],[24,1]⟩,⟨[20],[22],[25]⟩]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.repeated 1 4)))) + +lemma pieriLowerValid116 : pieriLower116.Valid 22 := by decide +kernel + +lemma pieriSquare116_0 : RowSquare [22,20,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,1,1] [11,11,11,11,11,11,10,10,10,10,10] := by + exact rowSquare_pieri (rs := [11,11,11,9]) (cs := [[11,11,11,11,7],[11,11,11,11,11,4],[11,11,11,11,11,11,1],[11,11,11,11,11,11,6],[11,11,11,11,11,11,10,1],[11,11,11,11,11,11,10,6],[11,11,11,11,11,11,10,10],[11,11,11,11,11,11,10,10,4],[11,11,11,11,11,11,10,10,8],[11,11,11,11,11,11,10,10,10,2],[11,11,11,11,11,11,10,10,10,6],[11,11,11,11,11,11,10,10,10,9],[11,11,11,11,11,11,10,10,10,10,2],[11,11,11,11,11,11,10,10,10,10,5],[11,11,11,11,11,11,10,10,10,10,8],[11,11,11,11,11,11,10,10,10,10,10]]) pieriLower116 20 2 + (by decide) (by decide) (by decide) pieriLowerValid116 (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) + +lemma pieriSquare116_1 : RowSquare [22,20,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,1,1] [11,11,11,11,11,11,11,10,10,10,9] := by + exact rowSquare_pieri (rs := [11,11,11,9]) (cs := [[11,11,11,11,7],[11,11,11,11,11,4],[11,11,11,11,11,11,1],[11,11,11,11,11,11,6],[11,11,11,11,11,11,11],[11,11,11,11,11,11,11,5],[11,11,11,11,11,11,11,9],[11,11,11,11,11,11,11,10,3],[11,11,11,11,11,11,11,10,7],[11,11,11,11,11,11,11,10,10,1],[11,11,11,11,11,11,11,10,10,5],[11,11,11,11,11,11,11,10,10,8],[11,11,11,11,11,11,11,10,10,10,1],[11,11,11,11,11,11,11,10,10,10,4],[11,11,11,11,11,11,11,10,10,10,7],[11,11,11,11,11,11,11,10,10,10,9]]) pieriLower116 20 2 + (by decide) (by decide) (by decide) pieriLowerValid116 (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) + +lemma pieriSquare116_2 : RowSquare [22,20,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,1,1] [11,11,11,11,11,11,11,11,10,9,9] := by + exact rowSquare_pieri (rs := [11,11,11,9]) (cs := [[11,11,11,11,7],[11,11,11,11,11,4],[11,11,11,11,11,11,1],[11,11,11,11,11,11,6],[11,11,11,11,11,11,11],[11,11,11,11,11,11,11,5],[11,11,11,11,11,11,11,9],[11,11,11,11,11,11,11,11,2],[11,11,11,11,11,11,11,11,6],[11,11,11,11,11,11,11,11,10],[11,11,11,11,11,11,11,11,10,4],[11,11,11,11,11,11,11,11,10,7],[11,11,11,11,11,11,11,11,10,9,1],[11,11,11,11,11,11,11,11,10,9,4],[11,11,11,11,11,11,11,11,10,9,7],[11,11,11,11,11,11,11,11,10,9,9]]) pieriLower116 20 2 + (by decide) (by decide) (by decide) pieriLowerValid116 (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) + +lemma pieriSquare116_3 : RowSquare [22,20,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,1,1] [11,11,11,11,11,11,11,11,10,10,8] := by + exact rowSquare_pieri (rs := [11,11,11,9]) (cs := [[11,11,11,11,7],[11,11,11,11,11,4],[11,11,11,11,11,11,1],[11,11,11,11,11,11,6],[11,11,11,11,11,11,11],[11,11,11,11,11,11,11,5],[11,11,11,11,11,11,11,9],[11,11,11,11,11,11,11,11,2],[11,11,11,11,11,11,11,11,6],[11,11,11,11,11,11,11,11,10],[11,11,11,11,11,11,11,11,10,4],[11,11,11,11,11,11,11,11,10,7],[11,11,11,11,11,11,11,11,10,10],[11,11,11,11,11,11,11,11,10,10,3],[11,11,11,11,11,11,11,11,10,10,6],[11,11,11,11,11,11,11,11,10,10,8]]) pieriLower116 20 2 + (by decide) (by decide) (by decide) pieriLowerValid116 (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows118.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows118.lean index 9cdd773d3246fb4119e9ac57117526602e5ff801..09f90d33f522e564ff88587e7322af2906587b21 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows118.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows118.lean @@ -1,37 +1,37 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.PieriCertificates - -namespace OAI - -/-! Pieri Rows 118. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def pieriLower118 : PackingPlan := - .join (.threeRows 11 1 [9,9,8] - [⟨[8,8,6],[9,8,6],[9,9,8]⟩,⟨[8,8,6],[8,8,7],[10,8,8]⟩,⟨[8,8,6],[9,8,6],[10,9,7]⟩,⟨[10,6,6],[10,7,6],[10,10,6]⟩,⟨[8,8,6],[8,8,7],[11,8,7]⟩,⟨[8,8,6],[9,8,6],[11,9,6]⟩,⟨[10,8,4],[10,8,5],[11,10,5]⟩,⟨[10,8,4],[11,8,4],[11,11,4]⟩,⟨[10,6,6],[10,7,6],[12,7,7]⟩,⟨[8,8,6],[9,8,6],[12,8,6]⟩,⟨[10,8,4],[10,8,5],[12,9,5]⟩,⟨[10,8,4],[10,9,4],[12,10,4]⟩,⟨[10,10,2],[11,10,2],[12,11,3]⟩,⟨[12,8,2],[12,9,2],[12,12,2]⟩,⟨[10,6,6],[10,7,6],[13,7,6]⟩,⟨[10,8,4],[10,8,5],[13,8,5]⟩,⟨[10,8,4],[10,9,4],[13,9,4]⟩,⟨[10,10,2],[10,10,3],[13,10,3]⟩,⟨[10,10,2],[11,10,2],[13,11,2]⟩,⟨[12,10],[12,10,1],[13,12,1]⟩,⟨[12,10],[13,10],[13,13]⟩,⟨[10,6,6],[11,6,6],[14,6,6]⟩,⟨[12,6,4],[12,6,5],[14,7,5]⟩,⟨[10,8,4],[11,8,4],[14,8,4]⟩,⟨[12,8,2],[12,8,3],[14,9,3]⟩,⟨[10,10,2],[11,10,2],[14,10,2]⟩,⟨[12,10],[12,10,1],[14,11,1]⟩,⟨[12,10],[12,11],[14,12]⟩,⟨[12,6,4],[12,6,5],[15,6,5]⟩,⟨[12,6,4],[12,7,4],[15,7,4]⟩,⟨[12,8,2],[12,8,3],[15,8,3]⟩,⟨[12,8,2],[12,9,2],[15,9,2]⟩,⟨[12,10],[12,10,1],[15,10,1]⟩,⟨[12,10],[12,11],[15,11]⟩,⟨[14,4,4],[14,5,4],[16,5,5]⟩,⟨[12,6,4],[13,6,4],[16,6,4]⟩,⟨[14,6,2],[14,6,3],[16,7,3]⟩,⟨[12,8,2],[13,8,2],[16,8,2]⟩,⟨[14,8],[14,8,1],[16,9,1]⟩,⟨[12,10],[13,10],[16,10]⟩,⟨[14,4,4],[14,5,4],[17,5,4]⟩,⟨[14,6,2],[14,6,3],[17,6,3]⟩,⟨[14,6,2],[14,7,2],[17,7,2]⟩,⟨[14,8],[14,8,1],[17,8,1]⟩,⟨[14,8],[14,9],[17,9]⟩,⟨[14,4,4],[15,4,4],[18,4,4]⟩,⟨[16,4,2],[16,4,3],[18,5,3]⟩,⟨[14,6,2],[15,6,2],[18,6,2]⟩,⟨[16,6],[16,6,1],[18,7,1]⟩,⟨[14,8],[15,8],[18,8]⟩,⟨[16,4,2],[16,4,3],[19,4,3]⟩,⟨[16,4,2],[16,5,2],[19,5,2]⟩,⟨[16,6],[16,6,1],[19,6,1]⟩,⟨[16,6],[16,7],[19,7]⟩,⟨[18,2,2],[18,3,2],[20,3,3]⟩,⟨[16,4,2],[17,4,2],[20,4,2]⟩,⟨[18,4],[18,4,1],[20,5,1]⟩,⟨[16,6],[17,6],[20,6]⟩,⟨[18,2,2],[18,3,2],[21,3,2]⟩,⟨[18,4],[18,4,1],[21,4,1]⟩,⟨[18,4],[18,5],[21,5]⟩,⟨[18,2,2],[19,2,2],[22,2,2]⟩,⟨[20,2],[20,2,1],[22,3,1]⟩,⟨[18,4],[19,4],[22,4]⟩,⟨[20,2],[20,2,1],[23,2,1]⟩,⟨[20,2],[20,3],[23,3]⟩,⟨[22],[22,1],[24,1,1]⟩,⟨[20,2],[21,2],[24,2]⟩,⟨[22],[22,1],[25,1]⟩,⟨[22],[23],[26]⟩]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.repeated 1 4)))) - -lemma pieriLowerValid118 : pieriLower118.Valid 22 := by decide +kernel - -lemma pieriSquare118_0 : RowSquare [22,21,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,2,1] [11,11,11,11,11,11,11,11,10,10,10] := by - exact rowSquare_pieri (rs := [11,11,11,10]) (cs := [[11,11,11,11,8],[11,11,11,11,11,6],[11,11,11,11,11,11,3],[11,11,11,11,11,11,8],[11,11,11,11,11,11,11,2],[11,11,11,11,11,11,11,7],[11,11,11,11,11,11,11,11],[11,11,11,11,11,11,11,11,4],[11,11,11,11,11,11,11,11,8],[11,11,11,11,11,11,11,11,10,2],[11,11,11,11,11,11,11,11,10,6],[11,11,11,11,11,11,11,11,10,9],[11,11,11,11,11,11,11,11,10,10,2],[11,11,11,11,11,11,11,11,10,10,5],[11,11,11,11,11,11,11,11,10,10,8],[11,11,11,11,11,11,11,11,10,10,10]]) pieriLower118 21 1 - (by decide) (by decide) (by decide) pieriLowerValid118 (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) - -lemma pieriSquare118_1 : RowSquare [22,21,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,2,1] [11,11,11,11,11,11,11,11,11,10,9] := by - exact rowSquare_pieri (rs := [11,11,11,10]) (cs := [[11,11,11,11,8],[11,11,11,11,11,6],[11,11,11,11,11,11,3],[11,11,11,11,11,11,8],[11,11,11,11,11,11,11,2],[11,11,11,11,11,11,11,7],[11,11,11,11,11,11,11,11],[11,11,11,11,11,11,11,11,4],[11,11,11,11,11,11,11,11,8],[11,11,11,11,11,11,11,11,11,1],[11,11,11,11,11,11,11,11,11,5],[11,11,11,11,11,11,11,11,11,8],[11,11,11,11,11,11,11,11,11,10,1],[11,11,11,11,11,11,11,11,11,10,4],[11,11,11,11,11,11,11,11,11,10,7],[11,11,11,11,11,11,11,11,11,10,9]]) pieriLower118 21 1 - (by decide) (by decide) (by decide) pieriLowerValid118 (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.PieriCertificates + +namespace OAI + +/-! Pieri Rows 118. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def pieriLower118 : PackingPlan := + .join (.threeRows 11 1 [9,9,8] + [⟨[8,8,6],[9,8,6],[9,9,8]⟩,⟨[8,8,6],[8,8,7],[10,8,8]⟩,⟨[8,8,6],[9,8,6],[10,9,7]⟩,⟨[10,6,6],[10,7,6],[10,10,6]⟩,⟨[8,8,6],[8,8,7],[11,8,7]⟩,⟨[8,8,6],[9,8,6],[11,9,6]⟩,⟨[10,8,4],[10,8,5],[11,10,5]⟩,⟨[10,8,4],[11,8,4],[11,11,4]⟩,⟨[10,6,6],[10,7,6],[12,7,7]⟩,⟨[8,8,6],[9,8,6],[12,8,6]⟩,⟨[10,8,4],[10,8,5],[12,9,5]⟩,⟨[10,8,4],[10,9,4],[12,10,4]⟩,⟨[10,10,2],[11,10,2],[12,11,3]⟩,⟨[12,8,2],[12,9,2],[12,12,2]⟩,⟨[10,6,6],[10,7,6],[13,7,6]⟩,⟨[10,8,4],[10,8,5],[13,8,5]⟩,⟨[10,8,4],[10,9,4],[13,9,4]⟩,⟨[10,10,2],[10,10,3],[13,10,3]⟩,⟨[10,10,2],[11,10,2],[13,11,2]⟩,⟨[12,10],[12,10,1],[13,12,1]⟩,⟨[12,10],[13,10],[13,13]⟩,⟨[10,6,6],[11,6,6],[14,6,6]⟩,⟨[12,6,4],[12,6,5],[14,7,5]⟩,⟨[10,8,4],[11,8,4],[14,8,4]⟩,⟨[12,8,2],[12,8,3],[14,9,3]⟩,⟨[10,10,2],[11,10,2],[14,10,2]⟩,⟨[12,10],[12,10,1],[14,11,1]⟩,⟨[12,10],[12,11],[14,12]⟩,⟨[12,6,4],[12,6,5],[15,6,5]⟩,⟨[12,6,4],[12,7,4],[15,7,4]⟩,⟨[12,8,2],[12,8,3],[15,8,3]⟩,⟨[12,8,2],[12,9,2],[15,9,2]⟩,⟨[12,10],[12,10,1],[15,10,1]⟩,⟨[12,10],[12,11],[15,11]⟩,⟨[14,4,4],[14,5,4],[16,5,5]⟩,⟨[12,6,4],[13,6,4],[16,6,4]⟩,⟨[14,6,2],[14,6,3],[16,7,3]⟩,⟨[12,8,2],[13,8,2],[16,8,2]⟩,⟨[14,8],[14,8,1],[16,9,1]⟩,⟨[12,10],[13,10],[16,10]⟩,⟨[14,4,4],[14,5,4],[17,5,4]⟩,⟨[14,6,2],[14,6,3],[17,6,3]⟩,⟨[14,6,2],[14,7,2],[17,7,2]⟩,⟨[14,8],[14,8,1],[17,8,1]⟩,⟨[14,8],[14,9],[17,9]⟩,⟨[14,4,4],[15,4,4],[18,4,4]⟩,⟨[16,4,2],[16,4,3],[18,5,3]⟩,⟨[14,6,2],[15,6,2],[18,6,2]⟩,⟨[16,6],[16,6,1],[18,7,1]⟩,⟨[14,8],[15,8],[18,8]⟩,⟨[16,4,2],[16,4,3],[19,4,3]⟩,⟨[16,4,2],[16,5,2],[19,5,2]⟩,⟨[16,6],[16,6,1],[19,6,1]⟩,⟨[16,6],[16,7],[19,7]⟩,⟨[18,2,2],[18,3,2],[20,3,3]⟩,⟨[16,4,2],[17,4,2],[20,4,2]⟩,⟨[18,4],[18,4,1],[20,5,1]⟩,⟨[16,6],[17,6],[20,6]⟩,⟨[18,2,2],[18,3,2],[21,3,2]⟩,⟨[18,4],[18,4,1],[21,4,1]⟩,⟨[18,4],[18,5],[21,5]⟩,⟨[18,2,2],[19,2,2],[22,2,2]⟩,⟨[20,2],[20,2,1],[22,3,1]⟩,⟨[18,4],[19,4],[22,4]⟩,⟨[20,2],[20,2,1],[23,2,1]⟩,⟨[20,2],[20,3],[23,3]⟩,⟨[22],[22,1],[24,1,1]⟩,⟨[20,2],[21,2],[24,2]⟩,⟨[22],[22,1],[25,1]⟩,⟨[22],[23],[26]⟩]) (.join (.neighbor 9 [5,5,5,4]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.repeated 1 4)))) + +lemma pieriLowerValid118 : pieriLower118.Valid 22 := by decide +kernel + +lemma pieriSquare118_0 : RowSquare [22,21,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,2,1] [11,11,11,11,11,11,11,11,10,10,10] := by + exact rowSquare_pieri (rs := [11,11,11,10]) (cs := [[11,11,11,11,8],[11,11,11,11,11,6],[11,11,11,11,11,11,3],[11,11,11,11,11,11,8],[11,11,11,11,11,11,11,2],[11,11,11,11,11,11,11,7],[11,11,11,11,11,11,11,11],[11,11,11,11,11,11,11,11,4],[11,11,11,11,11,11,11,11,8],[11,11,11,11,11,11,11,11,10,2],[11,11,11,11,11,11,11,11,10,6],[11,11,11,11,11,11,11,11,10,9],[11,11,11,11,11,11,11,11,10,10,2],[11,11,11,11,11,11,11,11,10,10,5],[11,11,11,11,11,11,11,11,10,10,8],[11,11,11,11,11,11,11,11,10,10,10]]) pieriLower118 21 1 + (by decide) (by decide) (by decide) pieriLowerValid118 (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) + +lemma pieriSquare118_1 : RowSquare [22,21,10,9,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,2,2,1] [11,11,11,11,11,11,11,11,11,10,9] := by + exact rowSquare_pieri (rs := [11,11,11,10]) (cs := [[11,11,11,11,8],[11,11,11,11,11,6],[11,11,11,11,11,11,3],[11,11,11,11,11,11,8],[11,11,11,11,11,11,11,2],[11,11,11,11,11,11,11,7],[11,11,11,11,11,11,11,11],[11,11,11,11,11,11,11,11,4],[11,11,11,11,11,11,11,11,8],[11,11,11,11,11,11,11,11,11,1],[11,11,11,11,11,11,11,11,11,5],[11,11,11,11,11,11,11,11,11,8],[11,11,11,11,11,11,11,11,11,10,1],[11,11,11,11,11,11,11,11,11,10,4],[11,11,11,11,11,11,11,11,11,10,7],[11,11,11,11,11,11,11,11,11,10,9]]) pieriLower118 21 1 + (by decide) (by decide) (by decide) pieriLowerValid118 (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows62.lean index b56064d7e4ef1ab5e733de373bc411fccf93dde3..9701819f90d87941a8131dd3227edb5b62dda7ea 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows62.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.PieriCertificates - -namespace OAI - -/-! Pieri Rows 62. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def pieriLower62 : PackingPlan := - .join (.threeRows 7 2 [7,6,6] - [⟨[6,4,4],[6,6,4],[7,6,6]⟩,⟨[6,4,4],[7,5,4],[7,7,5]⟩,⟨[6,4,4],[6,6,4],[8,6,5]⟩,⟨[6,4,4],[7,5,4],[8,7,4]⟩,⟨[8,4,2],[8,5,3],[8,8,3]⟩,⟨[6,4,4],[7,5,4],[9,5,5]⟩,⟨[6,4,4],[6,6,4],[9,6,4]⟩,⟨[6,6,2],[7,6,3],[9,7,3]⟩,⟨[6,6,2],[8,6,2],[9,8,2]⟩,⟨[8,6],[9,6,1],[9,9,1]⟩,⟨[6,4,4],[7,5,4],[10,5,4]⟩,⟨[6,6,2],[7,6,3],[10,6,3]⟩,⟨[6,6,2],[8,6,2],[10,7,2]⟩,⟨[8,6],[8,7,1],[10,8,1]⟩,⟨[8,6],[9,7],[10,9]⟩,⟨[6,4,4],[8,4,4],[11,4,4]⟩,⟨[8,4,2],[8,5,3],[11,5,3]⟩,⟨[6,6,2],[8,6,2],[11,6,2]⟩,⟨[8,6],[8,7,1],[11,7,1]⟩,⟨[8,6],[8,8],[11,8]⟩,⟨[8,4,2],[9,4,3],[12,4,3]⟩,⟨[8,4,2],[9,5,2],[12,5,2]⟩,⟨[8,6],[9,6,1],[12,6,1]⟩,⟨[8,6],[9,7],[12,7]⟩,⟨[10,2,2],[11,3,2],[13,3,3]⟩,⟨[8,4,2],[10,4,2],[13,4,2]⟩,⟨[10,4],[10,5,1],[13,5,1]⟩,⟨[8,6],[10,6],[13,6]⟩,⟨[10,2,2],[11,3,2],[14,3,2]⟩,⟨[10,4],[11,4,1],[14,4,1]⟩,⟨[10,4],[11,5],[14,5]⟩,⟨[10,2,2],[12,2,2],[15,2,2]⟩,⟨[12,2],[12,3,1],[15,3,1]⟩,⟨[10,4],[12,4],[15,4]⟩,⟨[12,2],[13,2,1],[16,2,1]⟩,⟨[12,2],[13,3],[16,3]⟩,⟨[14],[15,1],[17,1,1]⟩,⟨[12,2],[14,2],[17,2]⟩,⟨[14],[15,1],[18,1]⟩,⟨[14],[16],[19]⟩]) (.join (.neighbor 5 [3,3,3,2]) (.repeated 1 4)) - -lemma pieriLowerValid62 : pieriLower62.Valid 15 := by decide +kernel - -lemma pieriSquare62_0 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [8,8,8,8,8,8,7,7] := by - exact rowSquare_pieri (rs := [8,8,8,4]) (cs := [[8,8,8,8,3],[8,8,8,8,8,1],[8,8,8,8,8,7],[8,8,8,8,8,8,3],[8,8,8,8,8,8,6],[8,8,8,8,8,8,7,2],[8,8,8,8,8,8,7,5],[8,8,8,8,8,8,7,7]]) pieriLower62 13 2 - (by decide) (by decide) (by decide) pieriLowerValid62 (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.PieriCertificates + +namespace OAI + +/-! Pieri Rows 62. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def pieriLower62 : PackingPlan := + .join (.threeRows 7 2 [7,6,6] + [⟨[6,4,4],[6,6,4],[7,6,6]⟩,⟨[6,4,4],[7,5,4],[7,7,5]⟩,⟨[6,4,4],[6,6,4],[8,6,5]⟩,⟨[6,4,4],[7,5,4],[8,7,4]⟩,⟨[8,4,2],[8,5,3],[8,8,3]⟩,⟨[6,4,4],[7,5,4],[9,5,5]⟩,⟨[6,4,4],[6,6,4],[9,6,4]⟩,⟨[6,6,2],[7,6,3],[9,7,3]⟩,⟨[6,6,2],[8,6,2],[9,8,2]⟩,⟨[8,6],[9,6,1],[9,9,1]⟩,⟨[6,4,4],[7,5,4],[10,5,4]⟩,⟨[6,6,2],[7,6,3],[10,6,3]⟩,⟨[6,6,2],[8,6,2],[10,7,2]⟩,⟨[8,6],[8,7,1],[10,8,1]⟩,⟨[8,6],[9,7],[10,9]⟩,⟨[6,4,4],[8,4,4],[11,4,4]⟩,⟨[8,4,2],[8,5,3],[11,5,3]⟩,⟨[6,6,2],[8,6,2],[11,6,2]⟩,⟨[8,6],[8,7,1],[11,7,1]⟩,⟨[8,6],[8,8],[11,8]⟩,⟨[8,4,2],[9,4,3],[12,4,3]⟩,⟨[8,4,2],[9,5,2],[12,5,2]⟩,⟨[8,6],[9,6,1],[12,6,1]⟩,⟨[8,6],[9,7],[12,7]⟩,⟨[10,2,2],[11,3,2],[13,3,3]⟩,⟨[8,4,2],[10,4,2],[13,4,2]⟩,⟨[10,4],[10,5,1],[13,5,1]⟩,⟨[8,6],[10,6],[13,6]⟩,⟨[10,2,2],[11,3,2],[14,3,2]⟩,⟨[10,4],[11,4,1],[14,4,1]⟩,⟨[10,4],[11,5],[14,5]⟩,⟨[10,2,2],[12,2,2],[15,2,2]⟩,⟨[12,2],[12,3,1],[15,3,1]⟩,⟨[10,4],[12,4],[15,4]⟩,⟨[12,2],[13,2,1],[16,2,1]⟩,⟨[12,2],[13,3],[16,3]⟩,⟨[14],[15,1],[17,1,1]⟩,⟨[12,2],[14,2],[17,2]⟩,⟨[14],[15,1],[18,1]⟩,⟨[14],[16],[19]⟩]) (.join (.neighbor 5 [3,3,3,2]) (.repeated 1 4)) + +lemma pieriLowerValid62 : pieriLower62.Valid 15 := by decide +kernel + +lemma pieriSquare62_0 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [8,8,8,8,8,8,7,7] := by + exact rowSquare_pieri (rs := [8,8,8,4]) (cs := [[8,8,8,8,3],[8,8,8,8,8,1],[8,8,8,8,8,7],[8,8,8,8,8,8,3],[8,8,8,8,8,8,6],[8,8,8,8,8,8,7,2],[8,8,8,8,8,8,7,5],[8,8,8,8,8,8,7,7]]) pieriLower62 13 2 + (by decide) (by decide) (by decide) pieriLowerValid62 (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows64.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows64.lean index 9c7266fa53e8139b8c2cfe54361edb57d6172bfa..a482fe49c85f3b567707faeacce74e9a29c0dfa5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows64.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows64.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.PieriCertificates - -namespace OAI - -/-! Pieri Rows 64. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def pieriLower64 : PackingPlan := - .join (.threeRows 8 1 [7,7,6] - [⟨[6,6,4],[7,6,4],[7,7,6]⟩,⟨[6,6,4],[6,6,5],[8,6,6]⟩,⟨[6,6,4],[7,6,4],[8,7,5]⟩,⟨[8,4,4],[8,5,4],[8,8,4]⟩,⟨[6,6,4],[6,6,5],[9,6,5]⟩,⟨[6,6,4],[7,6,4],[9,7,4]⟩,⟨[8,6,2],[8,6,3],[9,8,3]⟩,⟨[8,6,2],[9,6,2],[9,9,2]⟩,⟨[8,4,4],[8,5,4],[10,5,5]⟩,⟨[6,6,4],[7,6,4],[10,6,4]⟩,⟨[8,6,2],[8,6,3],[10,7,3]⟩,⟨[8,6,2],[8,7,2],[10,8,2]⟩,⟨[8,8],[9,8],[10,9,1]⟩,⟨[10,6],[10,7],[10,10]⟩,⟨[8,4,4],[8,5,4],[11,5,4]⟩,⟨[8,6,2],[8,6,3],[11,6,3]⟩,⟨[8,6,2],[8,7,2],[11,7,2]⟩,⟨[8,8],[8,8,1],[11,8,1]⟩,⟨[8,8],[9,8],[11,9]⟩,⟨[8,4,4],[9,4,4],[12,4,4]⟩,⟨[10,4,2],[10,4,3],[12,5,3]⟩,⟨[8,6,2],[9,6,2],[12,6,2]⟩,⟨[10,6],[10,6,1],[12,7,1]⟩,⟨[8,8],[9,8],[12,8]⟩,⟨[10,4,2],[10,4,3],[13,4,3]⟩,⟨[10,4,2],[10,5,2],[13,5,2]⟩,⟨[10,6],[10,6,1],[13,6,1]⟩,⟨[10,6],[10,7],[13,7]⟩,⟨[12,2,2],[12,3,2],[14,3,3]⟩,⟨[10,4,2],[11,4,2],[14,4,2]⟩,⟨[12,4],[12,4,1],[14,5,1]⟩,⟨[10,6],[11,6],[14,6]⟩,⟨[12,2,2],[12,3,2],[15,3,2]⟩,⟨[12,4],[12,4,1],[15,4,1]⟩,⟨[12,4],[12,5],[15,5]⟩,⟨[12,2,2],[13,2,2],[16,2,2]⟩,⟨[14,2],[14,2,1],[16,3,1]⟩,⟨[12,4],[13,4],[16,4]⟩,⟨[14,2],[14,2,1],[17,2,1]⟩,⟨[14,2],[14,3],[17,3]⟩,⟨[16],[16,1],[18,1,1]⟩,⟨[14,2],[15,2],[18,2]⟩,⟨[16],[16,1],[19,1]⟩,⟨[16],[17],[20]⟩]) (.join (.neighbor 5 [3,3,3,2]) (.repeated 1 4)) - -lemma pieriLowerValid64 : pieriLower64.Valid 15 := by decide +kernel - -lemma pieriSquare64_0 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [8,8,8,8,8,8,8,8] := by - exact rowSquare_pieri (rs := [8,8,8,5]) (cs := [[8,8,8,8,4],[8,8,8,8,8,3],[8,8,8,8,8,8,1],[8,8,8,8,8,8,5],[8,8,8,8,8,8,8],[8,8,8,8,8,8,8,3],[8,8,8,8,8,8,8,6],[8,8,8,8,8,8,8,8]]) pieriLower64 14 1 - (by decide) (by decide) (by decide) pieriLowerValid64 (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.PieriCertificates + +namespace OAI + +/-! Pieri Rows 64. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def pieriLower64 : PackingPlan := + .join (.threeRows 8 1 [7,7,6] + [⟨[6,6,4],[7,6,4],[7,7,6]⟩,⟨[6,6,4],[6,6,5],[8,6,6]⟩,⟨[6,6,4],[7,6,4],[8,7,5]⟩,⟨[8,4,4],[8,5,4],[8,8,4]⟩,⟨[6,6,4],[6,6,5],[9,6,5]⟩,⟨[6,6,4],[7,6,4],[9,7,4]⟩,⟨[8,6,2],[8,6,3],[9,8,3]⟩,⟨[8,6,2],[9,6,2],[9,9,2]⟩,⟨[8,4,4],[8,5,4],[10,5,5]⟩,⟨[6,6,4],[7,6,4],[10,6,4]⟩,⟨[8,6,2],[8,6,3],[10,7,3]⟩,⟨[8,6,2],[8,7,2],[10,8,2]⟩,⟨[8,8],[9,8],[10,9,1]⟩,⟨[10,6],[10,7],[10,10]⟩,⟨[8,4,4],[8,5,4],[11,5,4]⟩,⟨[8,6,2],[8,6,3],[11,6,3]⟩,⟨[8,6,2],[8,7,2],[11,7,2]⟩,⟨[8,8],[8,8,1],[11,8,1]⟩,⟨[8,8],[9,8],[11,9]⟩,⟨[8,4,4],[9,4,4],[12,4,4]⟩,⟨[10,4,2],[10,4,3],[12,5,3]⟩,⟨[8,6,2],[9,6,2],[12,6,2]⟩,⟨[10,6],[10,6,1],[12,7,1]⟩,⟨[8,8],[9,8],[12,8]⟩,⟨[10,4,2],[10,4,3],[13,4,3]⟩,⟨[10,4,2],[10,5,2],[13,5,2]⟩,⟨[10,6],[10,6,1],[13,6,1]⟩,⟨[10,6],[10,7],[13,7]⟩,⟨[12,2,2],[12,3,2],[14,3,3]⟩,⟨[10,4,2],[11,4,2],[14,4,2]⟩,⟨[12,4],[12,4,1],[14,5,1]⟩,⟨[10,6],[11,6],[14,6]⟩,⟨[12,2,2],[12,3,2],[15,3,2]⟩,⟨[12,4],[12,4,1],[15,4,1]⟩,⟨[12,4],[12,5],[15,5]⟩,⟨[12,2,2],[13,2,2],[16,2,2]⟩,⟨[14,2],[14,2,1],[16,3,1]⟩,⟨[12,4],[13,4],[16,4]⟩,⟨[14,2],[14,2,1],[17,2,1]⟩,⟨[14,2],[14,3],[17,3]⟩,⟨[16],[16,1],[18,1,1]⟩,⟨[14,2],[15,2],[18,2]⟩,⟨[16],[16,1],[19,1]⟩,⟨[16],[17],[20]⟩]) (.join (.neighbor 5 [3,3,3,2]) (.repeated 1 4)) + +lemma pieriLowerValid64 : pieriLower64.Valid 15 := by decide +kernel + +lemma pieriSquare64_0 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [8,8,8,8,8,8,8,8] := by + exact rowSquare_pieri (rs := [8,8,8,5]) (cs := [[8,8,8,8,4],[8,8,8,8,8,3],[8,8,8,8,8,8,1],[8,8,8,8,8,8,5],[8,8,8,8,8,8,8],[8,8,8,8,8,8,8,3],[8,8,8,8,8,8,8,6],[8,8,8,8,8,8,8,8]]) pieriLower64 14 1 + (by decide) (by decide) (by decide) pieriLowerValid64 (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows89.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows89.lean index 0f0b227674d6814da438fa6c03a09a25f1982e13..ae7f4c3cb0d45435d0b32740bfc6f667fb76aee0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows89.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/PieriRows89.lean @@ -1,31 +1,31 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.PieriCertificates - -namespace OAI - -/-! Pieri Rows 89. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def pieriLower89 : PackingPlan := - .join (.threeRows 9 2 [8,8,7] - [⟨[8,6,4],[8,7,5],[8,8,7]⟩,⟨[8,6,4],[8,7,5],[9,7,7]⟩,⟨[6,6,6],[8,6,6],[9,8,6]⟩,⟨[8,6,4],[9,6,5],[9,9,5]⟩,⟨[6,6,6],[8,6,6],[10,7,6]⟩,⟨[8,6,4],[8,7,5],[10,8,5]⟩,⟨[8,6,4],[9,7,4],[10,9,4]⟩,⟨[10,6,2],[10,7,3],[10,10,3]⟩,⟨[6,6,6],[8,6,6],[11,6,6]⟩,⟨[8,6,4],[8,7,5],[11,7,5]⟩,⟨[8,6,4],[8,8,4],[11,8,4]⟩,⟨[8,8,2],[9,8,3],[11,9,3]⟩,⟨[8,8,2],[10,8,2],[11,10,2]⟩,⟨[10,8],[11,8,1],[11,11,1]⟩,⟨[8,6,4],[9,6,5],[12,6,5]⟩,⟨[8,6,4],[9,7,4],[12,7,4]⟩,⟨[8,8,2],[9,8,3],[12,8,3]⟩,⟨[8,8,2],[10,8,2],[12,9,2]⟩,⟨[10,8],[10,9,1],[12,10,1]⟩,⟨[10,8],[11,9],[12,11]⟩,⟨[10,4,4],[11,5,4],[13,5,5]⟩,⟨[8,6,4],[10,6,4],[13,6,4]⟩,⟨[10,6,2],[10,7,3],[13,7,3]⟩,⟨[8,8,2],[10,8,2],[13,8,2]⟩,⟨[10,8],[10,9,1],[13,9,1]⟩,⟨[10,8],[10,10],[13,10]⟩,⟨[10,4,4],[11,5,4],[14,5,4]⟩,⟨[10,6,2],[11,6,3],[14,6,3]⟩,⟨[10,6,2],[11,7,2],[14,7,2]⟩,⟨[10,8],[11,8,1],[14,8,1]⟩,⟨[10,8],[11,9],[14,9]⟩,⟨[10,4,4],[12,4,4],[15,4,4]⟩,⟨[12,4,2],[12,5,3],[15,5,3]⟩,⟨[10,6,2],[12,6,2],[15,6,2]⟩,⟨[12,6],[12,7,1],[15,7,1]⟩,⟨[10,8],[12,8],[15,8]⟩,⟨[12,4,2],[13,4,3],[16,4,3]⟩,⟨[12,4,2],[13,5,2],[16,5,2]⟩,⟨[12,6],[13,6,1],[16,6,1]⟩,⟨[12,6],[13,7],[16,7]⟩,⟨[14,2,2],[15,3,2],[17,3,3]⟩,⟨[12,4,2],[14,4,2],[17,4,2]⟩,⟨[14,4],[14,5,1],[17,5,1]⟩,⟨[12,6],[14,6],[17,6]⟩,⟨[14,2,2],[15,3,2],[18,3,2]⟩,⟨[14,4],[15,4,1],[18,4,1]⟩,⟨[14,4],[15,5],[18,5]⟩,⟨[14,2,2],[16,2,2],[19,2,2]⟩,⟨[16,2],[16,3,1],[19,3,1]⟩,⟨[14,4],[16,4],[19,4]⟩,⟨[16,2],[17,2,1],[20,2,1]⟩,⟨[16,2],[17,3],[20,3]⟩,⟨[18],[19,1],[21,1,1]⟩,⟨[16,2],[18,2],[21,2]⟩,⟨[18],[19,1],[22,1]⟩,⟨[18],[20],[23]⟩]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.repeated 1 4))) - -lemma pieriLowerValid89 : pieriLower89.Valid 19 := by decide +kernel - -lemma pieriSquare89_0 : RowSquare [19,17,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,10,10,10,9] := by - exact rowSquare_pieri (rs := [10,10,10,6]) (cs := [[10,10,10,10,4],[10,10,10,10,10,2],[10,10,10,10,10,9],[10,10,10,10,10,10,3],[10,10,10,10,10,10,7],[10,10,10,10,10,10,10,1],[10,10,10,10,10,10,10,5],[10,10,10,10,10,10,10,8],[10,10,10,10,10,10,10,10,1],[10,10,10,10,10,10,10,10,4],[10,10,10,10,10,10,10,10,7],[10,10,10,10,10,10,10,10,9]]) pieriLower89 17 2 - (by decide) (by decide) (by decide) pieriLowerValid89 (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.PieriCertificates + +namespace OAI + +/-! Pieri Rows 89. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def pieriLower89 : PackingPlan := + .join (.threeRows 9 2 [8,8,7] + [⟨[8,6,4],[8,7,5],[8,8,7]⟩,⟨[8,6,4],[8,7,5],[9,7,7]⟩,⟨[6,6,6],[8,6,6],[9,8,6]⟩,⟨[8,6,4],[9,6,5],[9,9,5]⟩,⟨[6,6,6],[8,6,6],[10,7,6]⟩,⟨[8,6,4],[8,7,5],[10,8,5]⟩,⟨[8,6,4],[9,7,4],[10,9,4]⟩,⟨[10,6,2],[10,7,3],[10,10,3]⟩,⟨[6,6,6],[8,6,6],[11,6,6]⟩,⟨[8,6,4],[8,7,5],[11,7,5]⟩,⟨[8,6,4],[8,8,4],[11,8,4]⟩,⟨[8,8,2],[9,8,3],[11,9,3]⟩,⟨[8,8,2],[10,8,2],[11,10,2]⟩,⟨[10,8],[11,8,1],[11,11,1]⟩,⟨[8,6,4],[9,6,5],[12,6,5]⟩,⟨[8,6,4],[9,7,4],[12,7,4]⟩,⟨[8,8,2],[9,8,3],[12,8,3]⟩,⟨[8,8,2],[10,8,2],[12,9,2]⟩,⟨[10,8],[10,9,1],[12,10,1]⟩,⟨[10,8],[11,9],[12,11]⟩,⟨[10,4,4],[11,5,4],[13,5,5]⟩,⟨[8,6,4],[10,6,4],[13,6,4]⟩,⟨[10,6,2],[10,7,3],[13,7,3]⟩,⟨[8,8,2],[10,8,2],[13,8,2]⟩,⟨[10,8],[10,9,1],[13,9,1]⟩,⟨[10,8],[10,10],[13,10]⟩,⟨[10,4,4],[11,5,4],[14,5,4]⟩,⟨[10,6,2],[11,6,3],[14,6,3]⟩,⟨[10,6,2],[11,7,2],[14,7,2]⟩,⟨[10,8],[11,8,1],[14,8,1]⟩,⟨[10,8],[11,9],[14,9]⟩,⟨[10,4,4],[12,4,4],[15,4,4]⟩,⟨[12,4,2],[12,5,3],[15,5,3]⟩,⟨[10,6,2],[12,6,2],[15,6,2]⟩,⟨[12,6],[12,7,1],[15,7,1]⟩,⟨[10,8],[12,8],[15,8]⟩,⟨[12,4,2],[13,4,3],[16,4,3]⟩,⟨[12,4,2],[13,5,2],[16,5,2]⟩,⟨[12,6],[13,6,1],[16,6,1]⟩,⟨[12,6],[13,7],[16,7]⟩,⟨[14,2,2],[15,3,2],[17,3,3]⟩,⟨[12,4,2],[14,4,2],[17,4,2]⟩,⟨[14,4],[14,5,1],[17,5,1]⟩,⟨[12,6],[14,6],[17,6]⟩,⟨[14,2,2],[15,3,2],[18,3,2]⟩,⟨[14,4],[15,4,1],[18,4,1]⟩,⟨[14,4],[15,5],[18,5]⟩,⟨[14,2,2],[16,2,2],[19,2,2]⟩,⟨[16,2],[16,3,1],[19,3,1]⟩,⟨[14,4],[16,4],[19,4]⟩,⟨[16,2],[17,2,1],[20,2,1]⟩,⟨[16,2],[17,3],[20,3]⟩,⟨[18],[19,1],[21,1,1]⟩,⟨[16,2],[18,2],[21,2]⟩,⟨[18],[19,1],[22,1]⟩,⟨[18],[20],[23]⟩]) (.join (.neighbor 7 [4,4,4,3]) (.join (.neighbor 5 [3,3,3,2]) (.repeated 1 4))) + +lemma pieriLowerValid89 : pieriLower89.Valid 19 := by decide +kernel + +lemma pieriSquare89_0 : RowSquare [19,17,8,7,6,5,4,3,2,2,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,10,10,10,9] := by + exact rowSquare_pieri (rs := [10,10,10,6]) (cs := [[10,10,10,10,4],[10,10,10,10,10,2],[10,10,10,10,10,9],[10,10,10,10,10,10,3],[10,10,10,10,10,10,7],[10,10,10,10,10,10,10,1],[10,10,10,10,10,10,10,5],[10,10,10,10,10,10,10,8],[10,10,10,10,10,10,10,10,1],[10,10,10,10,10,10,10,10,4],[10,10,10,10,10,10,10,10,7],[10,10,10,10,10,10,10,10,9]]) pieriLower89 17 2 + (by decide) (by decide) (by decide) pieriLowerValid89 (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_0.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_0.lean index 80fb83475db8ea36a8fa2e6e75fc6a0f9612c559..68ea4cce97c75612002f3839b8ede73764742c43 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_0.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_0.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 11 0. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB11_0 : Equiv.Perm (Fin 11) := Equiv.swap 7 0 * (Equiv.swap 7 4 * (Equiv.swap 4 9 * (Equiv.swap 4 1 * (Equiv.swap 4 5 * (Equiv.swap 2 8 * (Equiv.swap 1 6 * (Equiv.swap 0 10))))))) -def smallT11_0 : Equiv.Perm (Fin 11) := Equiv.swap 9 2 * (Equiv.swap 6 4 * (Equiv.swap 4 1 * (Equiv.swap 4 0 * (Equiv.swap 0 5 * (Equiv.swap 2 10 * (Equiv.swap 1 8 * (Equiv.swap 0 3))))))) -def smallFlag11_0 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(0,0,1),(1,1,1),(0,1,2),(2,2,0),(0,2,1),(4,2,2),(5,3,3)} - -def smallChoices11_0 : EdgeChoices := (.node 10 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => if _v = (3,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 7 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,1) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else if _v = (3,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 7 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (3,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (3,0,0) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))))))))))) -lemma smallCert11_0 : solveChoices smallChoices11_0 (.full [6,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [6,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_0 smallT11_0) smallFlag11_0 = 1 := by - decide +kernel - -lemma smallSupport11_0 : RowSquare [4,3,3,1] [6,1,1,1,1,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [6,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_0 smallT11_0 smallFlag11_0 smallChoices11_0 - change solveChoices smallChoices11_0 (.full [6,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [6,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_0 smallT11_0) smallFlag11_0 ≠ 0 - rw [smallCert11_0] - norm_num - -def smallB11_1 : Equiv.Perm (Fin 11) := Equiv.swap 7 8 * (Equiv.swap 8 0 * (Equiv.swap 7 6 * (Equiv.swap 6 1 * (Equiv.swap 0 10 * (Equiv.swap 0 3 * (Equiv.swap 3 5 * (Equiv.swap 1 9 * (Equiv.swap 0 4)))))))) -def smallT11_1 : Equiv.Perm (Fin 11) := Equiv.swap 7 5 * (Equiv.swap 7 4 * (Equiv.swap 5 1 * (Equiv.swap 4 9 * (Equiv.swap 1 10 * (Equiv.swap 1 3 * (Equiv.swap 0 2)))))) -def smallFlag11_1 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(4,0,2),(0,0,3),(1,1,0),(3,1,2),(0,2,1),(1,2,1),(0,2,2),(0,3,1)} - -def smallChoices11_1 : EdgeChoices := (.node 10 (fun _v => (.node 8 (fun _v => if _v = (1,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 6 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,0,0) then (.node 1 (fun _v => if _v = (4,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,2,1) then (.node 1 (fun _v => if _v = (4,0,2) then (.node 5 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (3,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,3) then (.node 3 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (3,1,2) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => if _v = (4,0,2) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 1 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => if _v = (4,0,2) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (4,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (4,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _ => .fallback)))))) -lemma smallCert11_1 : solveChoices smallChoices11_1 (.full [5,2,2,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [5,2,2,1,1] (Equiv.refl (Fin 11)) smallB11_1 smallT11_1) smallFlag11_1 = -10 := by - decide +kernel - -lemma smallSupport11_1 : RowSquare [4,3,3,1] [5,3,1,1,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [5,2,2,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_1 smallT11_1 smallFlag11_1 smallChoices11_1 - change solveChoices smallChoices11_1 (.full [5,2,2,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [5,2,2,1,1] (Equiv.refl (Fin 11)) smallB11_1 smallT11_1) smallFlag11_1 ≠ 0 - rw [smallCert11_1] - norm_num - -def smallB11_2 : Equiv.Perm (Fin 11) := Equiv.swap 4 9 * (Equiv.swap 5 7 * (Equiv.swap 5 2 * (Equiv.swap 4 1 * (Equiv.swap 1 8 * (Equiv.swap 2 6 * (Equiv.swap 1 3 * (Equiv.swap 0 10))))))) -def smallT11_2 : Equiv.Perm (Fin 11) := Equiv.swap 2 9 * (Equiv.swap 2 5 * (Equiv.swap 6 10 * (Equiv.swap 5 4 * (Equiv.swap 4 8 * (Equiv.swap 2 7 * (Equiv.swap 2 3)))))) -def smallFlag11_2 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,1),(0,1,2),(4,1,2),(1,1,3),(0,2,0),(2,2,0),(3,2,2),(0,3,1)} - -def smallChoices11_2 : EdgeChoices := (.node 10 (fun _v => if _v = (0,0,0) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,0,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 7 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (4,1,2) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (4,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (4,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert11_2 : solveChoices smallChoices11_2 (.full [5,2,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [5,2,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_2 smallT11_2) smallFlag11_2 = 12 := by - decide +kernel - -lemma smallSupport11_2 : RowSquare [4,3,3,1] [6,2,1,1,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [5,2,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_2 smallT11_2 smallFlag11_2 smallChoices11_2 - change solveChoices smallChoices11_2 (.full [5,2,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [5,2,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_2 smallT11_2) smallFlag11_2 ≠ 0 - rw [smallCert11_2] - norm_num - -def smallB11_3 : Equiv.Perm (Fin 11) := Equiv.swap 1 10 * (Equiv.swap 1 9 * (Equiv.swap 1 2 * (Equiv.swap 4 7 * (Equiv.swap 4 5 * (Equiv.swap 1 6 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 8)))))))) -def smallT11_3 : Equiv.Perm (Fin 11) := Equiv.swap 8 2 * (Equiv.swap 0 4 * (Equiv.swap 2 5 * (Equiv.swap 5 1 * (Equiv.swap 4 10 * (Equiv.swap 2 6 * (Equiv.swap 1 9 * (Equiv.swap 0 7))))))) -def smallFlag11_3 : Finset (ℕ × ℕ × ℕ) := {(4,0,0),(0,0,1),(1,1,0),(2,1,2),(0,1,3),(0,2,0),(0,2,2),(3,3,2)} - -def smallChoices11_3 : EdgeChoices := (.node 9 (fun _v => (.node 0 (fun _v => if _v = (4,0,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,3) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) -lemma smallCert11_3 : solveChoices smallChoices11_3 (.full [5,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [5,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_3 smallT11_3) smallFlag11_3 = -2 := by - decide +kernel - -lemma smallSupport11_3 : RowSquare [4,3,3,1] [7,1,1,1,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [5,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_3 smallT11_3 smallFlag11_3 smallChoices11_3 - change solveChoices smallChoices11_3 (.full [5,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [5,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_3 smallT11_3) smallFlag11_3 ≠ 0 - rw [smallCert11_3] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 11 0. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB11_0 : Equiv.Perm (Fin 11) := Equiv.swap 7 0 * (Equiv.swap 7 4 * (Equiv.swap 4 9 * (Equiv.swap 4 1 * (Equiv.swap 4 5 * (Equiv.swap 2 8 * (Equiv.swap 1 6 * (Equiv.swap 0 10))))))) +def smallT11_0 : Equiv.Perm (Fin 11) := Equiv.swap 9 2 * (Equiv.swap 6 4 * (Equiv.swap 4 1 * (Equiv.swap 4 0 * (Equiv.swap 0 5 * (Equiv.swap 2 10 * (Equiv.swap 1 8 * (Equiv.swap 0 3))))))) +def smallFlag11_0 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(0,0,1),(1,1,1),(0,1,2),(2,2,0),(0,2,1),(4,2,2),(5,3,3)} + +def smallChoices11_0 : EdgeChoices := (.node 10 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => if _v = (3,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 7 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,1) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else if _v = (3,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 7 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (3,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (3,0,0) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))))))))))) +lemma smallCert11_0 : solveChoices smallChoices11_0 (.full [6,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [6,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_0 smallT11_0) smallFlag11_0 = 1 := by + decide +kernel + +lemma smallSupport11_0 : RowSquare [4,3,3,1] [6,1,1,1,1,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [6,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_0 smallT11_0 smallFlag11_0 smallChoices11_0 + change solveChoices smallChoices11_0 (.full [6,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [6,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_0 smallT11_0) smallFlag11_0 ≠ 0 + rw [smallCert11_0] + norm_num + +def smallB11_1 : Equiv.Perm (Fin 11) := Equiv.swap 7 8 * (Equiv.swap 8 0 * (Equiv.swap 7 6 * (Equiv.swap 6 1 * (Equiv.swap 0 10 * (Equiv.swap 0 3 * (Equiv.swap 3 5 * (Equiv.swap 1 9 * (Equiv.swap 0 4)))))))) +def smallT11_1 : Equiv.Perm (Fin 11) := Equiv.swap 7 5 * (Equiv.swap 7 4 * (Equiv.swap 5 1 * (Equiv.swap 4 9 * (Equiv.swap 1 10 * (Equiv.swap 1 3 * (Equiv.swap 0 2)))))) +def smallFlag11_1 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(4,0,2),(0,0,3),(1,1,0),(3,1,2),(0,2,1),(1,2,1),(0,2,2),(0,3,1)} + +def smallChoices11_1 : EdgeChoices := (.node 10 (fun _v => (.node 8 (fun _v => if _v = (1,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 6 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,0,0) then (.node 1 (fun _v => if _v = (4,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,2,1) then (.node 1 (fun _v => if _v = (4,0,2) then (.node 5 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (3,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,3) then (.node 3 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (3,1,2) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => if _v = (4,0,2) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 1 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => if _v = (4,0,2) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (4,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (4,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _ => .fallback)))))) +lemma smallCert11_1 : solveChoices smallChoices11_1 (.full [5,2,2,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [5,2,2,1,1] (Equiv.refl (Fin 11)) smallB11_1 smallT11_1) smallFlag11_1 = -10 := by + decide +kernel + +lemma smallSupport11_1 : RowSquare [4,3,3,1] [5,3,1,1,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [5,2,2,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_1 smallT11_1 smallFlag11_1 smallChoices11_1 + change solveChoices smallChoices11_1 (.full [5,2,2,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [5,2,2,1,1] (Equiv.refl (Fin 11)) smallB11_1 smallT11_1) smallFlag11_1 ≠ 0 + rw [smallCert11_1] + norm_num + +def smallB11_2 : Equiv.Perm (Fin 11) := Equiv.swap 4 9 * (Equiv.swap 5 7 * (Equiv.swap 5 2 * (Equiv.swap 4 1 * (Equiv.swap 1 8 * (Equiv.swap 2 6 * (Equiv.swap 1 3 * (Equiv.swap 0 10))))))) +def smallT11_2 : Equiv.Perm (Fin 11) := Equiv.swap 2 9 * (Equiv.swap 2 5 * (Equiv.swap 6 10 * (Equiv.swap 5 4 * (Equiv.swap 4 8 * (Equiv.swap 2 7 * (Equiv.swap 2 3)))))) +def smallFlag11_2 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,1),(0,1,2),(4,1,2),(1,1,3),(0,2,0),(2,2,0),(3,2,2),(0,3,1)} + +def smallChoices11_2 : EdgeChoices := (.node 10 (fun _v => if _v = (0,0,0) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,0,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 7 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (4,1,2) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (4,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (4,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert11_2 : solveChoices smallChoices11_2 (.full [5,2,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [5,2,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_2 smallT11_2) smallFlag11_2 = 12 := by + decide +kernel + +lemma smallSupport11_2 : RowSquare [4,3,3,1] [6,2,1,1,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [5,2,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_2 smallT11_2 smallFlag11_2 smallChoices11_2 + change solveChoices smallChoices11_2 (.full [5,2,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [5,2,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_2 smallT11_2) smallFlag11_2 ≠ 0 + rw [smallCert11_2] + norm_num + +def smallB11_3 : Equiv.Perm (Fin 11) := Equiv.swap 1 10 * (Equiv.swap 1 9 * (Equiv.swap 1 2 * (Equiv.swap 4 7 * (Equiv.swap 4 5 * (Equiv.swap 1 6 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 8)))))))) +def smallT11_3 : Equiv.Perm (Fin 11) := Equiv.swap 8 2 * (Equiv.swap 0 4 * (Equiv.swap 2 5 * (Equiv.swap 5 1 * (Equiv.swap 4 10 * (Equiv.swap 2 6 * (Equiv.swap 1 9 * (Equiv.swap 0 7))))))) +def smallFlag11_3 : Finset (ℕ × ℕ × ℕ) := {(4,0,0),(0,0,1),(1,1,0),(2,1,2),(0,1,3),(0,2,0),(0,2,2),(3,3,2)} + +def smallChoices11_3 : EdgeChoices := (.node 9 (fun _v => (.node 0 (fun _v => if _v = (4,0,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,3) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) +lemma smallCert11_3 : solveChoices smallChoices11_3 (.full [5,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [5,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_3 smallT11_3) smallFlag11_3 = -2 := by + decide +kernel + +lemma smallSupport11_3 : RowSquare [4,3,3,1] [7,1,1,1,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [5,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_3 smallT11_3 smallFlag11_3 smallChoices11_3 + change solveChoices smallChoices11_3 (.full [5,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [5,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_3 smallT11_3) smallFlag11_3 ≠ 0 + rw [smallCert11_3] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_1.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_1.lean index 6c09ed6dd903ab764318eba2e30b64eeb4844723..835d70f824a1cbdeeae2e1578ed24960ea9d0072 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_1.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_1.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 11 1. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB11_4 : Equiv.Perm (Fin 11) := Equiv.swap 0 9 * (Equiv.swap 0 5 * (Equiv.swap 5 7 * (Equiv.swap 2 3 * (Equiv.swap 3 10 * (Equiv.swap 2 4 * (Equiv.swap 1 8 * (Equiv.swap 0 6))))))) -def smallT11_4 : Equiv.Perm (Fin 11) := Equiv.swap 9 4 * (Equiv.swap 4 0 * (Equiv.swap 5 6 * (Equiv.swap 4 3 * (Equiv.swap 3 2 * (Equiv.swap 2 8 * (Equiv.swap 0 10)))))) -def smallFlag11_4 : Finset (ℕ × ℕ × ℕ) := {(0,0,2),(3,0,2),(3,0,3),(2,1,0),(0,1,1),(1,1,1),(0,2,0),(1,2,1),(2,3,0)} - -def smallChoices11_4 : EdgeChoices := (.node 10 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 6 (fun _v => (.node 2 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 6 (fun _ => .fallback)) else (.node 6 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,1) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 6 (fun _v => (.node 2 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 6 (fun _ => .fallback)) else (.node 6 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,1) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) -lemma smallCert11_4 : solveChoices smallChoices11_4 (.full [4,4,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,4,1,1,1] (Equiv.refl (Fin 11)) smallB11_4 smallT11_4) smallFlag11_4 = -4 := by - decide +kernel - -lemma smallSupport11_4 : RowSquare [4,3,3,1] [5,2,2,2] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,4,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_4 smallT11_4 smallFlag11_4 smallChoices11_4 - change solveChoices smallChoices11_4 (.full [4,4,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,4,1,1,1] (Equiv.refl (Fin 11)) smallB11_4 smallT11_4) smallFlag11_4 ≠ 0 - rw [smallCert11_4] - norm_num - -def smallB11_5 : Equiv.Perm (Fin 11) := Equiv.swap 9 2 * (Equiv.swap 4 8 * (Equiv.swap 2 5 * (Equiv.swap 5 0 * (Equiv.swap 4 7 * (Equiv.swap 2 6 * (Equiv.swap 1 3 * (Equiv.swap 0 10))))))) -def smallT11_5 : Equiv.Perm (Fin 11) := Equiv.swap 1 9 * (Equiv.swap 5 10 * (Equiv.swap 5 7 * (Equiv.swap 5 6 * (Equiv.swap 3 4 * (Equiv.swap 1 8))))) -def smallFlag11_5 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(0,0,1),(1,0,2),(2,1,0),(1,1,3),(0,2,1),(1,2,2),(2,2,2),(0,3,1)} - -def smallChoices11_5 : EdgeChoices := (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (3,0,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 5 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => .fallback)) else if _v = (2,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,3) then (.node 7 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 6 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 7 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (1,1,3) then (.node 7 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 6 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (3,0,0) then (.node 6 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,2,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))))) else if _v = (0,2,1) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,1,0) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (2,1,0) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,1,0) then (.node 5 (fun _v => if _v = (1,1,3) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))) else if _v = (0,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,2,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))))) else if _v = (0,2,1) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,1,0) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (2,1,0) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,1,0) then (.node 5 (fun _v => if _v = (1,1,3) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (1,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,1,0) then (.node 2 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,1,0) then (.node 5 (fun _v => if _v = (1,1,3) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (2,1,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _v => if _v = (1,0,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,1,3) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 6 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => .fallback)) else if _v = (2,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => .fallback)) else if _v = (2,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))) else if _v = (1,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (3,0,0) then (.node 5 (fun _v => (.node 4 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 5 (fun _ => .fallback)) else if _v = (2,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => .fallback)) else if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _v => if _v = (1,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert11_5 : solveChoices smallChoices11_5 (.full [4,3,3,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,3,1] (Equiv.refl (Fin 11)) smallB11_5 smallT11_5) smallFlag11_5 = 5 := by - decide +kernel - -lemma smallSupport11_5 : RowSquare [4,3,3,1] [4,3,3,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,3,3,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_5 smallT11_5 smallFlag11_5 smallChoices11_5 - change solveChoices smallChoices11_5 (.full [4,3,3,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,3,1] (Equiv.refl (Fin 11)) smallB11_5 smallT11_5) smallFlag11_5 ≠ 0 - rw [smallCert11_5] - norm_num - -def smallB11_6 : Equiv.Perm (Fin 11) := Equiv.swap 4 0 * (Equiv.swap 0 3 * (Equiv.swap 3 10 * (Equiv.swap 4 9 * (Equiv.swap 3 6 * (Equiv.swap 0 8 * (Equiv.swap 1 5 * (Equiv.swap 0 2))))))) -def smallT11_6 : Equiv.Perm (Fin 11) := Equiv.swap 2 0 * (Equiv.swap 5 7 * (Equiv.swap 3 10 * (Equiv.swap 3 4 * (Equiv.swap 2 6 * (Equiv.swap 0 8))))) -def smallFlag11_6 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(1,0,2),(0,1,1),(1,1,1),(2,1,3),(0,2,0),(2,2,1),(0,3,2)} - -def smallChoices11_6 : EdgeChoices := (.node 6 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (1,0,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,2,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (3,0,0) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (1,0,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,2,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (2,1,3) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 6 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (3,0,0) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 5 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (1,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))) else if _v = (1,1,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,2) then (.node 6 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (1,0,2) then (.node 5 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (3,0,0) then (.node 5 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (1,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))) -lemma smallCert11_6 : solveChoices smallChoices11_6 (.full [4,3,2,2]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,2,2] (Equiv.refl (Fin 11)) smallB11_6 smallT11_6) smallFlag11_6 = 5 := by - decide +kernel - -lemma smallSupport11_6 : RowSquare [4,3,3,1] [4,4,2,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,3,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_6 smallT11_6 smallFlag11_6 smallChoices11_6 - change solveChoices smallChoices11_6 (.full [4,3,2,2]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,2,2] (Equiv.refl (Fin 11)) smallB11_6 smallT11_6) smallFlag11_6 ≠ 0 - rw [smallCert11_6] - norm_num - -def smallB11_7 : Equiv.Perm (Fin 11) := Equiv.swap 0 10 * (Equiv.swap 0 9 * (Equiv.swap 4 6 * (Equiv.swap 4 5 * (Equiv.swap 1 8 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 7))))))) -def smallT11_7 : Equiv.Perm (Fin 11) := Equiv.swap 8 3 * (Equiv.swap 3 4 * (Equiv.swap 2 0 * (Equiv.swap 4 9 * (Equiv.swap 3 1 * (Equiv.swap 2 5 * (Equiv.swap 1 7 * (Equiv.swap 0 10))))))) -def smallFlag11_7 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(0,0,1),(0,0,2),(3,1,1),(0,1,2),(1,2,0),(2,2,0),(1,2,3),(1,3,1)} - -def smallChoices11_7 : EdgeChoices := (.node 9 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (1,2,0) then (.node 7 (fun _v => if _v = (0,0,1) then (.node 7 (fun _ => (.node 6 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 5 (fun _ => (.node 5 (fun _ => .fallback)))) else (.node 5 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,3) then (.node 5 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 0 (fun _v => if _v = (3,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (2,0,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (2,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (3,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (2,0,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 2 (fun _v => if _v = (2,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 5 (fun _ => .fallback)))))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 8 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,0) then (.node 4 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (2,0,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 7 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,0,2) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (1,2,3) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => (.node 5 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,0,1) then (.node 8 (fun _v => (.node 7 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (3,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 6 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _ => (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))))))))) -lemma smallCert11_7 : solveChoices smallChoices11_7 (.full [4,3,2,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,2,1,1] (Equiv.refl (Fin 11)) smallB11_7 smallT11_7) smallFlag11_7 = 3 := by - decide +kernel - -lemma smallSupport11_7 : RowSquare [4,3,3,1] [5,3,2,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,3,2,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_7 smallT11_7 smallFlag11_7 smallChoices11_7 - change solveChoices smallChoices11_7 (.full [4,3,2,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,2,1,1] (Equiv.refl (Fin 11)) smallB11_7 smallT11_7) smallFlag11_7 ≠ 0 - rw [smallCert11_7] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 11 1. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB11_4 : Equiv.Perm (Fin 11) := Equiv.swap 0 9 * (Equiv.swap 0 5 * (Equiv.swap 5 7 * (Equiv.swap 2 3 * (Equiv.swap 3 10 * (Equiv.swap 2 4 * (Equiv.swap 1 8 * (Equiv.swap 0 6))))))) +def smallT11_4 : Equiv.Perm (Fin 11) := Equiv.swap 9 4 * (Equiv.swap 4 0 * (Equiv.swap 5 6 * (Equiv.swap 4 3 * (Equiv.swap 3 2 * (Equiv.swap 2 8 * (Equiv.swap 0 10)))))) +def smallFlag11_4 : Finset (ℕ × ℕ × ℕ) := {(0,0,2),(3,0,2),(3,0,3),(2,1,0),(0,1,1),(1,1,1),(0,2,0),(1,2,1),(2,3,0)} + +def smallChoices11_4 : EdgeChoices := (.node 10 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 6 (fun _v => (.node 2 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 6 (fun _ => .fallback)) else (.node 6 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,1) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 6 (fun _v => (.node 2 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 6 (fun _ => .fallback)) else (.node 6 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,1) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (3,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) +lemma smallCert11_4 : solveChoices smallChoices11_4 (.full [4,4,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,4,1,1,1] (Equiv.refl (Fin 11)) smallB11_4 smallT11_4) smallFlag11_4 = -4 := by + decide +kernel + +lemma smallSupport11_4 : RowSquare [4,3,3,1] [5,2,2,2] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,4,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_4 smallT11_4 smallFlag11_4 smallChoices11_4 + change solveChoices smallChoices11_4 (.full [4,4,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,4,1,1,1] (Equiv.refl (Fin 11)) smallB11_4 smallT11_4) smallFlag11_4 ≠ 0 + rw [smallCert11_4] + norm_num + +def smallB11_5 : Equiv.Perm (Fin 11) := Equiv.swap 9 2 * (Equiv.swap 4 8 * (Equiv.swap 2 5 * (Equiv.swap 5 0 * (Equiv.swap 4 7 * (Equiv.swap 2 6 * (Equiv.swap 1 3 * (Equiv.swap 0 10))))))) +def smallT11_5 : Equiv.Perm (Fin 11) := Equiv.swap 1 9 * (Equiv.swap 5 10 * (Equiv.swap 5 7 * (Equiv.swap 5 6 * (Equiv.swap 3 4 * (Equiv.swap 1 8))))) +def smallFlag11_5 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(0,0,1),(1,0,2),(2,1,0),(1,1,3),(0,2,1),(1,2,2),(2,2,2),(0,3,1)} + +def smallChoices11_5 : EdgeChoices := (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (3,0,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 5 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => .fallback)) else if _v = (2,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,3) then (.node 7 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 6 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 7 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (1,1,3) then (.node 7 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 6 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (3,0,0) then (.node 6 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,2,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))))) else if _v = (0,2,1) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,1,0) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (2,1,0) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,1,0) then (.node 5 (fun _v => if _v = (1,1,3) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))) else if _v = (0,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,2,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))))) else if _v = (0,2,1) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,1,0) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (2,1,0) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,1,0) then (.node 5 (fun _v => if _v = (1,1,3) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (1,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,1,0) then (.node 2 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,1,0) then (.node 5 (fun _v => if _v = (1,1,3) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (2,1,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _v => if _v = (1,0,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,1,3) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 6 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => .fallback)) else if _v = (2,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => .fallback)) else if _v = (2,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))) else if _v = (1,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (3,0,0) then (.node 5 (fun _v => (.node 4 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 5 (fun _ => .fallback)) else if _v = (2,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => .fallback)) else if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _v => if _v = (1,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert11_5 : solveChoices smallChoices11_5 (.full [4,3,3,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,3,1] (Equiv.refl (Fin 11)) smallB11_5 smallT11_5) smallFlag11_5 = 5 := by + decide +kernel + +lemma smallSupport11_5 : RowSquare [4,3,3,1] [4,3,3,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,3,3,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_5 smallT11_5 smallFlag11_5 smallChoices11_5 + change solveChoices smallChoices11_5 (.full [4,3,3,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,3,1] (Equiv.refl (Fin 11)) smallB11_5 smallT11_5) smallFlag11_5 ≠ 0 + rw [smallCert11_5] + norm_num + +def smallB11_6 : Equiv.Perm (Fin 11) := Equiv.swap 4 0 * (Equiv.swap 0 3 * (Equiv.swap 3 10 * (Equiv.swap 4 9 * (Equiv.swap 3 6 * (Equiv.swap 0 8 * (Equiv.swap 1 5 * (Equiv.swap 0 2))))))) +def smallT11_6 : Equiv.Perm (Fin 11) := Equiv.swap 2 0 * (Equiv.swap 5 7 * (Equiv.swap 3 10 * (Equiv.swap 3 4 * (Equiv.swap 2 6 * (Equiv.swap 0 8))))) +def smallFlag11_6 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(1,0,2),(0,1,1),(1,1,1),(2,1,3),(0,2,0),(2,2,1),(0,3,2)} + +def smallChoices11_6 : EdgeChoices := (.node 6 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (1,0,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,2,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (3,0,0) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (1,0,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,2,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (2,1,3) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 6 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (3,0,0) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 5 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (1,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))) else if _v = (1,1,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,2) then (.node 6 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (1,0,2) then (.node 5 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (3,0,0) then (.node 5 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (1,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))) +lemma smallCert11_6 : solveChoices smallChoices11_6 (.full [4,3,2,2]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,2,2] (Equiv.refl (Fin 11)) smallB11_6 smallT11_6) smallFlag11_6 = 5 := by + decide +kernel + +lemma smallSupport11_6 : RowSquare [4,3,3,1] [4,4,2,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,3,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_6 smallT11_6 smallFlag11_6 smallChoices11_6 + change solveChoices smallChoices11_6 (.full [4,3,2,2]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,2,2] (Equiv.refl (Fin 11)) smallB11_6 smallT11_6) smallFlag11_6 ≠ 0 + rw [smallCert11_6] + norm_num + +def smallB11_7 : Equiv.Perm (Fin 11) := Equiv.swap 0 10 * (Equiv.swap 0 9 * (Equiv.swap 4 6 * (Equiv.swap 4 5 * (Equiv.swap 1 8 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 7))))))) +def smallT11_7 : Equiv.Perm (Fin 11) := Equiv.swap 8 3 * (Equiv.swap 3 4 * (Equiv.swap 2 0 * (Equiv.swap 4 9 * (Equiv.swap 3 1 * (Equiv.swap 2 5 * (Equiv.swap 1 7 * (Equiv.swap 0 10))))))) +def smallFlag11_7 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(0,0,1),(0,0,2),(3,1,1),(0,1,2),(1,2,0),(2,2,0),(1,2,3),(1,3,1)} + +def smallChoices11_7 : EdgeChoices := (.node 9 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (1,2,0) then (.node 7 (fun _v => if _v = (0,0,1) then (.node 7 (fun _ => (.node 6 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 5 (fun _ => (.node 5 (fun _ => .fallback)))) else (.node 5 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,3) then (.node 5 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 0 (fun _v => if _v = (3,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (2,0,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (2,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (3,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (2,0,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 2 (fun _v => if _v = (2,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 5 (fun _ => .fallback)))))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 8 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,0) then (.node 4 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (2,0,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 7 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,0,2) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (1,2,3) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => (.node 5 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,0,1) then (.node 8 (fun _v => (.node 7 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (3,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 6 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _ => (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))))))))) +lemma smallCert11_7 : solveChoices smallChoices11_7 (.full [4,3,2,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,2,1,1] (Equiv.refl (Fin 11)) smallB11_7 smallT11_7) smallFlag11_7 = 3 := by + decide +kernel + +lemma smallSupport11_7 : RowSquare [4,3,3,1] [5,3,2,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,3,2,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_7 smallT11_7 smallFlag11_7 smallChoices11_7 + change solveChoices smallChoices11_7 (.full [4,3,2,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,2,1,1] (Equiv.refl (Fin 11)) smallB11_7 smallT11_7) smallFlag11_7 ≠ 0 + rw [smallCert11_7] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_2.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_2.lean index c3e1827d712532b1340556c2229a8cd98c3b26f6..aa0e9c4a2052657065a1485332c40018a95a0212 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_2.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_2.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 11 2. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB11_8 : Equiv.Perm (Fin 11) := Equiv.swap 7 8 * (Equiv.swap 4 9 * (Equiv.swap 5 0 * (Equiv.swap 4 6 * (Equiv.swap 0 10 * (Equiv.swap 0 3))))) -def smallT11_8 : Equiv.Perm (Fin 11) := Equiv.swap 4 1 * (Equiv.swap 1 10 * (Equiv.swap 1 3 * (Equiv.swap 4 9 * (Equiv.swap 4 5 * (Equiv.swap 3 0 * (Equiv.swap 1 6 * (Equiv.swap 0 7))))))) -def smallFlag11_8 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(1,0,2),(0,0,3),(0,1,0),(2,1,1),(1,2,0),(2,2,2),(3,2,2),(0,3,0)} - -def smallChoices11_8 : EdgeChoices := (.node 7 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (2,2,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 7 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,2,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (2,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert11_8 : solveChoices smallChoices11_8 (.full [4,3,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_8 smallT11_8) smallFlag11_8 = 2 := by - decide +kernel - -lemma smallSupport11_8 : RowSquare [4,3,3,1] [6,2,2,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,3,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_8 smallT11_8 smallFlag11_8 smallChoices11_8 - change solveChoices smallChoices11_8 (.full [4,3,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_8 smallT11_8) smallFlag11_8 ≠ 0 - rw [smallCert11_8] - norm_num - -def smallB11_9 : Equiv.Perm (Fin 11) := Equiv.swap 8 5 * (Equiv.swap 5 4 * (Equiv.swap 5 6 * (Equiv.swap 4 2 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 0 10 * (Equiv.swap 0 1))))))) -def smallT11_9 : Equiv.Perm (Fin 11) := Equiv.swap 9 3 * (Equiv.swap 7 4 * (Equiv.swap 4 1 * (Equiv.swap 1 8 * (Equiv.swap 4 6 * (Equiv.swap 3 10 * (Equiv.swap 1 5 * (Equiv.swap 1 2))))))) -def smallFlag11_9 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(1,0,1),(0,0,2),(0,0,3),(2,1,0),(1,1,1),(0,1,2),(1,2,0),(3,2,2),(0,3,0)} - -def smallChoices11_9 : EdgeChoices := (.node 1 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 6 (fun _v => (.node 7 (fun _v => (.node 0 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 6 (fun _v => if _v = (0,0,1) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 7 (fun _v => (.node 0 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 6 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,1,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,0,1) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 5 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 3 (fun _ => 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_v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 3 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert11_9 : solveChoices smallChoices11_9 (.full [4,2,2,2,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,2,2,2,1] (Equiv.refl (Fin 11)) smallB11_9 smallT11_9) smallFlag11_9 = -2 := by - decide +kernel - -lemma smallSupport11_9 : RowSquare [4,3,3,1] [5,4,1,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,2,2,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_9 smallT11_9 smallFlag11_9 smallChoices11_9 - change solveChoices smallChoices11_9 (.full [4,2,2,2,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,2,2,2,1] (Equiv.refl (Fin 11)) smallB11_9 smallT11_9) smallFlag11_9 ≠ 0 - rw [smallCert11_9] - norm_num - -def smallB11_10 : Equiv.Perm (Fin 11) := Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 4 0 * (Equiv.swap 4 5 * (Equiv.swap 1 7 * (Equiv.swap 2 9 * (Equiv.swap 1 3 * (Equiv.swap 0 10))))))) -def smallT11_10 : Equiv.Perm (Fin 11) := Equiv.swap 5 4 * (Equiv.swap 5 9 * (Equiv.swap 5 3 * (Equiv.swap 4 2 * (Equiv.swap 5 7 * (Equiv.swap 4 6 * (Equiv.swap 3 1 * (Equiv.swap 2 10 * (Equiv.swap 1 0 * (Equiv.swap 0 8))))))))) -def smallFlag11_10 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(0,0,1),(1,0,2),(1,1,0),(0,1,1),(0,1,3),(0,2,1),(0,2,2),(2,2,2),(1,3,0)} - -def smallChoices11_10 : EdgeChoices := (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,2,2) then (.node 6 (fun _v => (.node 3 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => (.node 5 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => .fallback)) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,0,0) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 7 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (1,1,0) then (.node 7 (fun _ => .fallback)) else if _v = (0,1,1) then (.node 4 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => if _v = (3,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (3,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert11_10 : solveChoices smallChoices11_10 (.full [4,2,2,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,2,2,1,1,1] (Equiv.refl (Fin 11)) smallB11_10 smallT11_10) smallFlag11_10 = 5 := by - decide +kernel - -lemma smallSupport11_10 : RowSquare [4,3,3,1] [6,3,1,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,2,2,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_10 smallT11_10 smallFlag11_10 smallChoices11_10 - change solveChoices smallChoices11_10 (.full [4,2,2,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,2,2,1,1,1] (Equiv.refl (Fin 11)) smallB11_10 smallT11_10) smallFlag11_10 ≠ 0 - rw [smallCert11_10] - norm_num - -def smallB11_11 : Equiv.Perm (Fin 11) := Equiv.swap 7 6 * (Equiv.swap 7 8 * (Equiv.swap 6 4 * (Equiv.swap 2 1 * (Equiv.swap 4 9 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 1 10 * (Equiv.swap 0 5)))))))) -def smallT11_11 : Equiv.Perm (Fin 11) := Equiv.swap 0 6 * (Equiv.swap 6 1 * (Equiv.swap 6 2 * (Equiv.swap 6 4 * (Equiv.swap 0 9 * (Equiv.swap 4 7 * (Equiv.swap 2 8 * (Equiv.swap 1 10 * (Equiv.swap 0 5)))))))) -def smallFlag11_11 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(2,0,1),(0,0,2),(0,1,0),(0,1,1),(1,1,2),(0,2,0),(0,2,3),(3,3,0)} - -def smallChoices11_11 : EdgeChoices := (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 8 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 4 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,2,0) then (.node 8 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 8 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 7 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 6 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 6 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 8 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 7 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) -lemma smallCert11_11 : solveChoices smallChoices11_11 (.full [4,2,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,2,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_11 smallT11_11) smallFlag11_11 = 3 := by - decide +kernel - -lemma smallSupport11_11 : RowSquare [4,3,3,1] [7,2,1,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,2,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_11 smallT11_11 smallFlag11_11 smallChoices11_11 - change solveChoices smallChoices11_11 (.full [4,2,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,2,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_11 smallT11_11) smallFlag11_11 ≠ 0 - rw [smallCert11_11] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 11 2. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB11_8 : Equiv.Perm (Fin 11) := Equiv.swap 7 8 * (Equiv.swap 4 9 * (Equiv.swap 5 0 * (Equiv.swap 4 6 * (Equiv.swap 0 10 * (Equiv.swap 0 3))))) +def smallT11_8 : Equiv.Perm (Fin 11) := Equiv.swap 4 1 * (Equiv.swap 1 10 * (Equiv.swap 1 3 * (Equiv.swap 4 9 * (Equiv.swap 4 5 * (Equiv.swap 3 0 * (Equiv.swap 1 6 * (Equiv.swap 0 7))))))) +def smallFlag11_8 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(1,0,2),(0,0,3),(0,1,0),(2,1,1),(1,2,0),(2,2,2),(3,2,2),(0,3,0)} + +def smallChoices11_8 : EdgeChoices := (.node 7 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (2,2,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 7 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,2,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (2,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert11_8 : solveChoices smallChoices11_8 (.full [4,3,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_8 smallT11_8) smallFlag11_8 = 2 := by + decide +kernel + +lemma smallSupport11_8 : RowSquare [4,3,3,1] [6,2,2,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,3,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_8 smallT11_8 smallFlag11_8 smallChoices11_8 + change solveChoices smallChoices11_8 (.full [4,3,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,3,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_8 smallT11_8) smallFlag11_8 ≠ 0 + rw [smallCert11_8] + norm_num + +def smallB11_9 : Equiv.Perm (Fin 11) := Equiv.swap 8 5 * (Equiv.swap 5 4 * (Equiv.swap 5 6 * (Equiv.swap 4 2 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 0 10 * (Equiv.swap 0 1))))))) +def smallT11_9 : Equiv.Perm (Fin 11) := Equiv.swap 9 3 * (Equiv.swap 7 4 * (Equiv.swap 4 1 * (Equiv.swap 1 8 * (Equiv.swap 4 6 * (Equiv.swap 3 10 * (Equiv.swap 1 5 * (Equiv.swap 1 2))))))) +def smallFlag11_9 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(1,0,1),(0,0,2),(0,0,3),(2,1,0),(1,1,1),(0,1,2),(1,2,0),(3,2,2),(0,3,0)} + +def smallChoices11_9 : EdgeChoices := (.node 1 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 6 (fun _v => (.node 7 (fun _v => (.node 0 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 6 (fun _v => if _v = (0,0,1) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 7 (fun _v => (.node 0 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 6 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,1,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,0,1) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 5 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 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(.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 6 (fun _v => if _v = (0,0,1) then (.node 7 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 3 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 3 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert11_9 : solveChoices smallChoices11_9 (.full [4,2,2,2,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,2,2,2,1] (Equiv.refl (Fin 11)) smallB11_9 smallT11_9) smallFlag11_9 = -2 := by + decide +kernel + +lemma smallSupport11_9 : RowSquare [4,3,3,1] [5,4,1,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,2,2,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_9 smallT11_9 smallFlag11_9 smallChoices11_9 + change solveChoices smallChoices11_9 (.full [4,2,2,2,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,2,2,2,1] (Equiv.refl (Fin 11)) smallB11_9 smallT11_9) smallFlag11_9 ≠ 0 + rw [smallCert11_9] + norm_num + +def smallB11_10 : Equiv.Perm (Fin 11) := Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 4 0 * (Equiv.swap 4 5 * (Equiv.swap 1 7 * (Equiv.swap 2 9 * (Equiv.swap 1 3 * (Equiv.swap 0 10))))))) +def smallT11_10 : Equiv.Perm (Fin 11) := Equiv.swap 5 4 * (Equiv.swap 5 9 * (Equiv.swap 5 3 * (Equiv.swap 4 2 * (Equiv.swap 5 7 * (Equiv.swap 4 6 * (Equiv.swap 3 1 * (Equiv.swap 2 10 * (Equiv.swap 1 0 * (Equiv.swap 0 8))))))))) +def smallFlag11_10 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(0,0,1),(1,0,2),(1,1,0),(0,1,1),(0,1,3),(0,2,1),(0,2,2),(2,2,2),(1,3,0)} + +def smallChoices11_10 : EdgeChoices := (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,2,2) then (.node 6 (fun _v => (.node 3 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => (.node 5 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => .fallback)) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,0,0) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 7 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (1,1,0) then (.node 7 (fun _ => .fallback)) else if _v = (0,1,1) then (.node 4 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => if _v = (3,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (3,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert11_10 : solveChoices smallChoices11_10 (.full [4,2,2,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,2,2,1,1,1] (Equiv.refl (Fin 11)) smallB11_10 smallT11_10) smallFlag11_10 = 5 := by + decide +kernel + +lemma smallSupport11_10 : RowSquare [4,3,3,1] [6,3,1,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,2,2,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_10 smallT11_10 smallFlag11_10 smallChoices11_10 + change solveChoices smallChoices11_10 (.full [4,2,2,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,2,2,1,1,1] (Equiv.refl (Fin 11)) smallB11_10 smallT11_10) smallFlag11_10 ≠ 0 + rw [smallCert11_10] + norm_num + +def smallB11_11 : Equiv.Perm (Fin 11) := Equiv.swap 7 6 * (Equiv.swap 7 8 * (Equiv.swap 6 4 * (Equiv.swap 2 1 * (Equiv.swap 4 9 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 1 10 * (Equiv.swap 0 5)))))))) +def smallT11_11 : Equiv.Perm (Fin 11) := Equiv.swap 0 6 * (Equiv.swap 6 1 * (Equiv.swap 6 2 * (Equiv.swap 6 4 * (Equiv.swap 0 9 * (Equiv.swap 4 7 * (Equiv.swap 2 8 * (Equiv.swap 1 10 * (Equiv.swap 0 5)))))))) +def smallFlag11_11 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(2,0,1),(0,0,2),(0,1,0),(0,1,1),(1,1,2),(0,2,0),(0,2,3),(3,3,0)} + +def smallChoices11_11 : EdgeChoices := (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 8 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 4 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,2,0) then (.node 8 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 8 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 7 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 6 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 6 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 8 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 7 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) +lemma smallCert11_11 : solveChoices smallChoices11_11 (.full [4,2,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,2,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_11 smallT11_11) smallFlag11_11 = 3 := by + decide +kernel + +lemma smallSupport11_11 : RowSquare [4,3,3,1] [7,2,1,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [4,2,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_11 smallT11_11 smallFlag11_11 smallChoices11_11 + change solveChoices smallChoices11_11 (.full [4,2,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,2,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_11 smallT11_11) smallFlag11_11 ≠ 0 + rw [smallCert11_11] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_3.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_3.lean index e146a983ff1e676d568c93630f4a93b4ab23e178..4201313e83039b6b266c8604d73360723c02a16d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_3.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_3.lean @@ -1,83 +1,83 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains - -namespace OAI - -/-! Small Contracts 11 3. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB11_12 : Equiv.Perm (Fin 11) := Equiv.swap 4 2 * (Equiv.swap 2 10 * (Equiv.swap 4 9 * (Equiv.swap 5 3 * (Equiv.swap 4 1 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 1 6 * (Equiv.swap 0 8)))))))) -def smallT11_12 : Equiv.Perm (Fin 11) := Equiv.swap 6 8 * (Equiv.swap 8 1 * (Equiv.swap 1 0 * (Equiv.swap 6 9 * (Equiv.swap 1 7 * (Equiv.swap 2 4 * (Equiv.swap 1 3 * (Equiv.swap 0 10))))))) -def smallFlag11_12 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(2,0,1),(1,1,0),(3,1,2),(0,1,3),(0,2,0),(0,2,2),(0,3,0)} -lemma smallCert11_12 : solveCompact 11 (.full [4,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_12 smallT11_12) smallFlag11_12 = -8 := by - decide +kernel - -lemma smallSupport11_12 : RowSquare [4,3,3,1] [8,1,1,1] := by - apply rowSquare_compact (n := 11) (cs := [4,3,3,1]) (ts := [4,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_12 smallT11_12 smallFlag11_12 - change solveCompact 11 (.full [4,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [4,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_12 smallT11_12) smallFlag11_12 ≠ 0 - rw [smallCert11_12] - norm_num - -def smallB11_13 : Equiv.Perm (Fin 11) := Equiv.swap 5 10 * (Equiv.swap 5 9 * (Equiv.swap 3 4 * (Equiv.swap 5 8 * (Equiv.swap 4 7 * (Equiv.swap 3 1 * (Equiv.swap 1 6 * (Equiv.swap 0 2))))))) -def smallT11_13 : Equiv.Perm (Fin 11) := Equiv.swap 8 5 * (Equiv.swap 5 10 * (Equiv.swap 6 1 * (Equiv.swap 5 3 * (Equiv.swap 1 0 * (Equiv.swap 3 7 * (Equiv.swap 1 4 * (Equiv.swap 1 2 * (Equiv.swap 0 9)))))))) -def smallFlag11_13 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,1),(0,0,2),(1,0,3),(0,1,1),(2,1,2),(0,2,0),(1,2,0),(1,3,1)} -lemma smallCert11_13 : solveCompact 11 (.full [3,3,3,2]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,3,2] (Equiv.refl (Fin 11)) smallB11_13 smallT11_13) smallFlag11_13 = 18 := by - decide +kernel - -lemma smallSupport11_13 : RowSquare [4,3,3,1] [4,4,3] := by - apply rowSquare_compact (n := 11) (cs := [4,3,3,1]) (ts := [3,3,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_13 smallT11_13 smallFlag11_13 - change solveCompact 11 (.full [3,3,3,2]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,3,2] (Equiv.refl (Fin 11)) smallB11_13 smallT11_13) smallFlag11_13 ≠ 0 - rw [smallCert11_13] - norm_num - -def smallB11_14 : Equiv.Perm (Fin 11) := Equiv.swap 8 5 * (Equiv.swap 8 6 * (Equiv.swap 5 3 * (Equiv.swap 6 9 * (Equiv.swap 5 7 * (Equiv.swap 3 0 * (Equiv.swap 3 4 * (Equiv.swap 0 10))))))) -def smallT11_14 : Equiv.Perm (Fin 11) := Equiv.swap 9 5 * (Equiv.swap 0 2 * (Equiv.swap 5 10 * (Equiv.swap 2 8 * (Equiv.swap 2 3 * (Equiv.swap 0 7))))) -def smallFlag11_14 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,3),(0,1,0),(1,1,1),(0,1,2),(2,2,1),(0,2,2),(2,3,0)} -lemma smallCert11_14 : solveCompact 11 (.full [3,3,3,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,3,1,1] (Equiv.refl (Fin 11)) smallB11_14 smallT11_14) smallFlag11_14 = 7 := by - decide +kernel - -lemma smallSupport11_14 : RowSquare [4,3,3,1] [5,3,3] := by - apply rowSquare_compact (n := 11) (cs := [4,3,3,1]) (ts := [3,3,3,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_14 smallT11_14 smallFlag11_14 - change solveCompact 11 (.full [3,3,3,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,3,1,1] (Equiv.refl (Fin 11)) smallB11_14 smallT11_14) smallFlag11_14 ≠ 0 - rw [smallCert11_14] - norm_num - -def smallB11_15 : Equiv.Perm (Fin 11) := Equiv.swap 3 7 * (Equiv.swap 7 2 * (Equiv.swap 7 8 * (Equiv.swap 3 9 * (Equiv.swap 3 5 * (Equiv.swap 2 10 * (Equiv.swap 0 6)))))) -def smallT11_15 : Equiv.Perm (Fin 11) := Equiv.swap 0 10 * (Equiv.swap 0 8 * (Equiv.swap 4 6 * (Equiv.swap 4 5 * (Equiv.swap 0 2 * (Equiv.swap 2 7 * (Equiv.swap 1 9 * (Equiv.swap 0 3))))))) -def smallFlag11_15 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(0,0,1),(0,0,2),(0,0,3),(1,1,1),(0,1,2),(1,2,0),(2,3,1)} -lemma smallCert11_15 : solveCompact 11 (.full [3,3,2,2,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,2,2,1] (Equiv.refl (Fin 11)) smallB11_15 smallT11_15) smallFlag11_15 = 2 := by - decide +kernel - -lemma smallSupport11_15 : RowSquare [4,3,3,1] [5,4,2] := by - apply rowSquare_compact (n := 11) (cs := [4,3,3,1]) (ts := [3,3,2,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_15 smallT11_15 smallFlag11_15 - change solveCompact 11 (.full [3,3,2,2,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,2,2,1] (Equiv.refl (Fin 11)) smallB11_15 smallT11_15) smallFlag11_15 ≠ 0 - rw [smallCert11_15] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains + +namespace OAI + +/-! Small Contracts 11 3. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB11_12 : Equiv.Perm (Fin 11) := Equiv.swap 4 2 * (Equiv.swap 2 10 * (Equiv.swap 4 9 * (Equiv.swap 5 3 * (Equiv.swap 4 1 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 1 6 * (Equiv.swap 0 8)))))))) +def smallT11_12 : Equiv.Perm (Fin 11) := Equiv.swap 6 8 * (Equiv.swap 8 1 * (Equiv.swap 1 0 * (Equiv.swap 6 9 * (Equiv.swap 1 7 * (Equiv.swap 2 4 * (Equiv.swap 1 3 * (Equiv.swap 0 10))))))) +def smallFlag11_12 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(2,0,1),(1,1,0),(3,1,2),(0,1,3),(0,2,0),(0,2,2),(0,3,0)} +lemma smallCert11_12 : solveCompact 11 (.full [4,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_12 smallT11_12) smallFlag11_12 = -8 := by + decide +kernel + +lemma smallSupport11_12 : RowSquare [4,3,3,1] [8,1,1,1] := by + apply rowSquare_compact (n := 11) (cs := [4,3,3,1]) (ts := [4,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_12 smallT11_12 smallFlag11_12 + change solveCompact 11 (.full [4,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [4,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_12 smallT11_12) smallFlag11_12 ≠ 0 + rw [smallCert11_12] + norm_num + +def smallB11_13 : Equiv.Perm (Fin 11) := Equiv.swap 5 10 * (Equiv.swap 5 9 * (Equiv.swap 3 4 * (Equiv.swap 5 8 * (Equiv.swap 4 7 * (Equiv.swap 3 1 * (Equiv.swap 1 6 * (Equiv.swap 0 2))))))) +def smallT11_13 : Equiv.Perm (Fin 11) := Equiv.swap 8 5 * (Equiv.swap 5 10 * (Equiv.swap 6 1 * (Equiv.swap 5 3 * (Equiv.swap 1 0 * (Equiv.swap 3 7 * (Equiv.swap 1 4 * (Equiv.swap 1 2 * (Equiv.swap 0 9)))))))) +def smallFlag11_13 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,1),(0,0,2),(1,0,3),(0,1,1),(2,1,2),(0,2,0),(1,2,0),(1,3,1)} +lemma smallCert11_13 : solveCompact 11 (.full [3,3,3,2]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,3,2] (Equiv.refl (Fin 11)) smallB11_13 smallT11_13) smallFlag11_13 = 18 := by + decide +kernel + +lemma smallSupport11_13 : RowSquare [4,3,3,1] [4,4,3] := by + apply rowSquare_compact (n := 11) (cs := [4,3,3,1]) (ts := [3,3,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_13 smallT11_13 smallFlag11_13 + change solveCompact 11 (.full [3,3,3,2]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,3,2] (Equiv.refl (Fin 11)) smallB11_13 smallT11_13) smallFlag11_13 ≠ 0 + rw [smallCert11_13] + norm_num + +def smallB11_14 : Equiv.Perm (Fin 11) := Equiv.swap 8 5 * (Equiv.swap 8 6 * (Equiv.swap 5 3 * (Equiv.swap 6 9 * (Equiv.swap 5 7 * (Equiv.swap 3 0 * (Equiv.swap 3 4 * (Equiv.swap 0 10))))))) +def smallT11_14 : Equiv.Perm (Fin 11) := Equiv.swap 9 5 * (Equiv.swap 0 2 * (Equiv.swap 5 10 * (Equiv.swap 2 8 * (Equiv.swap 2 3 * (Equiv.swap 0 7))))) +def smallFlag11_14 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,3),(0,1,0),(1,1,1),(0,1,2),(2,2,1),(0,2,2),(2,3,0)} +lemma smallCert11_14 : solveCompact 11 (.full [3,3,3,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,3,1,1] (Equiv.refl (Fin 11)) smallB11_14 smallT11_14) smallFlag11_14 = 7 := by + decide +kernel + +lemma smallSupport11_14 : RowSquare [4,3,3,1] [5,3,3] := by + apply rowSquare_compact (n := 11) (cs := [4,3,3,1]) (ts := [3,3,3,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_14 smallT11_14 smallFlag11_14 + change solveCompact 11 (.full [3,3,3,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,3,1,1] (Equiv.refl (Fin 11)) smallB11_14 smallT11_14) smallFlag11_14 ≠ 0 + rw [smallCert11_14] + norm_num + +def smallB11_15 : Equiv.Perm (Fin 11) := Equiv.swap 3 7 * (Equiv.swap 7 2 * (Equiv.swap 7 8 * (Equiv.swap 3 9 * (Equiv.swap 3 5 * (Equiv.swap 2 10 * (Equiv.swap 0 6)))))) +def smallT11_15 : Equiv.Perm (Fin 11) := Equiv.swap 0 10 * (Equiv.swap 0 8 * (Equiv.swap 4 6 * (Equiv.swap 4 5 * (Equiv.swap 0 2 * (Equiv.swap 2 7 * (Equiv.swap 1 9 * (Equiv.swap 0 3))))))) +def smallFlag11_15 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(0,0,1),(0,0,2),(0,0,3),(1,1,1),(0,1,2),(1,2,0),(2,3,1)} +lemma smallCert11_15 : solveCompact 11 (.full [3,3,2,2,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,2,2,1] (Equiv.refl (Fin 11)) smallB11_15 smallT11_15) smallFlag11_15 = 2 := by + decide +kernel + +lemma smallSupport11_15 : RowSquare [4,3,3,1] [5,4,2] := by + apply rowSquare_compact (n := 11) (cs := [4,3,3,1]) (ts := [3,3,2,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_15 smallT11_15 smallFlag11_15 + change solveCompact 11 (.full [3,3,2,2,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,2,2,1] (Equiv.refl (Fin 11)) smallB11_15 smallT11_15) smallFlag11_15 ≠ 0 + rw [smallCert11_15] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_4.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_4.lean index 7f345c8da0e7bc2cffa5bd259870a0a7a29e4dc4..b0596d1774bea2e719a8f410c51baac9cf038f98 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_4.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_4.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 11 4. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB11_16 : Equiv.Perm (Fin 11) := Equiv.swap 7 6 * (Equiv.swap 7 0 * (Equiv.swap 6 4 * (Equiv.swap 4 9 * (Equiv.swap 3 5 * (Equiv.swap 0 8 * (Equiv.swap 0 2)))))) -def smallT11_16 : Equiv.Perm (Fin 11) := Equiv.swap 3 6 * (Equiv.swap 5 0 * (Equiv.swap 6 2 * (Equiv.swap 5 7 * (Equiv.swap 2 10 * (Equiv.swap 3 8 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 9)))))))) -def smallFlag11_16 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,2),(1,1,1),(0,1,2),(1,1,3),(2,2,0),(1,2,1),(0,3,1)} - -def smallChoices11_16 : EdgeChoices := (.node 10 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (2,2,0) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (1,1,3) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => .fallback)) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))))) -lemma smallCert11_16 : solveChoices smallChoices11_16 (.full [3,3,2,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,2,1,1,1] (Equiv.refl (Fin 11)) smallB11_16 smallT11_16) smallFlag11_16 = -1 := by - decide +kernel - -lemma smallSupport11_16 : RowSquare [4,3,3,1] [6,3,2] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,3,2,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_16 smallT11_16 smallFlag11_16 smallChoices11_16 - change solveChoices smallChoices11_16 (.full [3,3,2,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,2,1,1,1] (Equiv.refl (Fin 11)) smallB11_16 smallT11_16) smallFlag11_16 ≠ 0 - rw [smallCert11_16] - norm_num - -def smallB11_17 : Equiv.Perm (Fin 11) := Equiv.swap 4 0 * (Equiv.swap 4 3 * (Equiv.swap 4 7 * (Equiv.swap 4 6 * (Equiv.swap 3 1 * (Equiv.swap 1 8 * (Equiv.swap 1 2 * (Equiv.swap 0 9))))))) -def smallT11_17 : Equiv.Perm (Fin 11) := Equiv.swap 4 6 * (Equiv.swap 6 0 * (Equiv.swap 5 8 * (Equiv.swap 4 2 * (Equiv.swap 2 9 * (Equiv.swap 1 3 * (Equiv.swap 0 10)))))) -def smallFlag11_17 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,2),(2,0,2),(0,0,3),(2,1,0),(0,1,1),(0,1,2),(0,2,0),(0,2,1),(1,3,1)} - -def smallChoices11_17 : EdgeChoices := (.node 10 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 7 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 4 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 3 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 7 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (2,0,2) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,2) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,2,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 4 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (2,0,2) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 3 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert11_17 : solveChoices smallChoices11_17 (.full [3,3,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_17 smallT11_17) smallFlag11_17 = 18 := by - decide +kernel - -lemma smallSupport11_17 : RowSquare [4,3,3,1] [7,2,2] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,3,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_17 smallT11_17 smallFlag11_17 smallChoices11_17 - change solveChoices smallChoices11_17 (.full [3,3,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_17 smallT11_17) smallFlag11_17 ≠ 0 - rw [smallCert11_17] - norm_num - -def smallB11_18 : Equiv.Perm (Fin 11) := Equiv.swap 7 2 * (Equiv.swap 7 0 * (Equiv.swap 2 10 * (Equiv.swap 2 6 * (Equiv.swap 1 9 * (Equiv.swap 2 4 * (Equiv.swap 1 3 * (Equiv.swap 0 8))))))) -def smallT11_18 : Equiv.Perm (Fin 11) := Equiv.swap 7 0 * (Equiv.swap 5 3 * (Equiv.swap 0 2 * (Equiv.swap 3 9 * (Equiv.swap 2 1 * (Equiv.swap 1 10 * (Equiv.swap 0 4)))))) -def smallFlag11_18 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(2,0,2),(0,1,1),(1,1,2),(1,1,3),(1,2,0),(0,2,1),(0,3,2)} - -def smallChoices11_18 : EdgeChoices := (.node 6 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 5 (fun _v => if _v = (2,0,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 6 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => (.node 1 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => (.node 6 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 6 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 8 (fun _ => (.node 7 (fun _ => (.node 6 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 6 (fun _ => .fallback)) else (.node 6 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 6 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 6 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert11_18 : solveChoices smallChoices11_18 (.full [3,2,2,2,2]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,2,2,2] (Equiv.refl (Fin 11)) smallB11_18 smallT11_18) smallFlag11_18 = -25 := by - decide +kernel - -lemma smallSupport11_18 : RowSquare [4,3,3,1] [5,5,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,2,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_18 smallT11_18 smallFlag11_18 smallChoices11_18 - change solveChoices smallChoices11_18 (.full [3,2,2,2,2]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,2,2,2] (Equiv.refl (Fin 11)) smallB11_18 smallT11_18) smallFlag11_18 ≠ 0 - rw [smallCert11_18] - norm_num - -def smallB11_19 : Equiv.Perm (Fin 11) := Equiv.swap 1 6 * (Equiv.swap 6 10 * (Equiv.swap 5 0 * (Equiv.swap 0 9 * (Equiv.swap 0 3 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))) -def smallT11_19 : Equiv.Perm (Fin 11) := Equiv.swap 8 4 * (Equiv.swap 4 3 * (Equiv.swap 5 9 * (Equiv.swap 4 2 * (Equiv.swap 3 1 * (Equiv.swap 2 6 * (Equiv.swap 1 10)))))) -def smallFlag11_19 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(1,0,1),(0,0,2),(0,1,0),(1,1,1),(0,2,0),(0,2,1),(1,2,3),(1,3,2)} - -def smallChoices11_19 : EdgeChoices := (.node 6 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _v => if _v = (2,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _v => if _v = (2,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (2,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (2,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))))))))))))))))) -lemma smallCert11_19 : solveChoices smallChoices11_19 (.full [3,2,2,2,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,2,2,1,1] (Equiv.refl (Fin 11)) smallB11_19 smallT11_19) smallFlag11_19 = -2 := by - decide +kernel - -lemma smallSupport11_19 : RowSquare [4,3,3,1] [6,4,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,2,2,2,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_19 smallT11_19 smallFlag11_19 smallChoices11_19 - change solveChoices smallChoices11_19 (.full [3,2,2,2,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,2,2,1,1] (Equiv.refl (Fin 11)) smallB11_19 smallT11_19) smallFlag11_19 ≠ 0 - rw [smallCert11_19] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 11 4. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB11_16 : Equiv.Perm (Fin 11) := Equiv.swap 7 6 * (Equiv.swap 7 0 * (Equiv.swap 6 4 * (Equiv.swap 4 9 * (Equiv.swap 3 5 * (Equiv.swap 0 8 * (Equiv.swap 0 2)))))) +def smallT11_16 : Equiv.Perm (Fin 11) := Equiv.swap 3 6 * (Equiv.swap 5 0 * (Equiv.swap 6 2 * (Equiv.swap 5 7 * (Equiv.swap 2 10 * (Equiv.swap 3 8 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 9)))))))) +def smallFlag11_16 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,2),(1,1,1),(0,1,2),(1,1,3),(2,2,0),(1,2,1),(0,3,1)} + +def smallChoices11_16 : EdgeChoices := (.node 10 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (2,2,0) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (1,1,3) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => .fallback)) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))))) +lemma smallCert11_16 : solveChoices smallChoices11_16 (.full [3,3,2,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,2,1,1,1] (Equiv.refl (Fin 11)) smallB11_16 smallT11_16) smallFlag11_16 = -1 := by + decide +kernel + +lemma smallSupport11_16 : RowSquare [4,3,3,1] [6,3,2] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,3,2,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_16 smallT11_16 smallFlag11_16 smallChoices11_16 + change solveChoices smallChoices11_16 (.full [3,3,2,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,2,1,1,1] (Equiv.refl (Fin 11)) smallB11_16 smallT11_16) smallFlag11_16 ≠ 0 + rw [smallCert11_16] + norm_num + +def smallB11_17 : Equiv.Perm (Fin 11) := Equiv.swap 4 0 * (Equiv.swap 4 3 * (Equiv.swap 4 7 * (Equiv.swap 4 6 * (Equiv.swap 3 1 * (Equiv.swap 1 8 * (Equiv.swap 1 2 * (Equiv.swap 0 9))))))) +def smallT11_17 : Equiv.Perm (Fin 11) := Equiv.swap 4 6 * (Equiv.swap 6 0 * (Equiv.swap 5 8 * (Equiv.swap 4 2 * (Equiv.swap 2 9 * (Equiv.swap 1 3 * (Equiv.swap 0 10)))))) +def smallFlag11_17 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,2),(2,0,2),(0,0,3),(2,1,0),(0,1,1),(0,1,2),(0,2,0),(0,2,1),(1,3,1)} + +def smallChoices11_17 : EdgeChoices := (.node 10 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 7 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 4 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 3 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 7 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (2,0,2) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,2) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,2,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 4 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (2,0,2) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 3 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert11_17 : solveChoices smallChoices11_17 (.full [3,3,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_17 smallT11_17) smallFlag11_17 = 18 := by + decide +kernel + +lemma smallSupport11_17 : RowSquare [4,3,3,1] [7,2,2] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,3,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_17 smallT11_17 smallFlag11_17 smallChoices11_17 + change solveChoices smallChoices11_17 (.full [3,3,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,3,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_17 smallT11_17) smallFlag11_17 ≠ 0 + rw [smallCert11_17] + norm_num + +def smallB11_18 : Equiv.Perm (Fin 11) := Equiv.swap 7 2 * (Equiv.swap 7 0 * (Equiv.swap 2 10 * (Equiv.swap 2 6 * (Equiv.swap 1 9 * (Equiv.swap 2 4 * (Equiv.swap 1 3 * (Equiv.swap 0 8))))))) +def smallT11_18 : Equiv.Perm (Fin 11) := Equiv.swap 7 0 * (Equiv.swap 5 3 * (Equiv.swap 0 2 * (Equiv.swap 3 9 * (Equiv.swap 2 1 * (Equiv.swap 1 10 * (Equiv.swap 0 4)))))) +def smallFlag11_18 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(2,0,2),(0,1,1),(1,1,2),(1,1,3),(1,2,0),(0,2,1),(0,3,2)} + +def smallChoices11_18 : EdgeChoices := (.node 6 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 5 (fun _v => if _v = (2,0,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 6 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => (.node 1 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => (.node 6 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 6 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 8 (fun _ => (.node 7 (fun _ => (.node 6 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 6 (fun _ => .fallback)) else (.node 6 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 6 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 6 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert11_18 : solveChoices smallChoices11_18 (.full [3,2,2,2,2]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,2,2,2] (Equiv.refl (Fin 11)) smallB11_18 smallT11_18) smallFlag11_18 = -25 := by + decide +kernel + +lemma smallSupport11_18 : RowSquare [4,3,3,1] [5,5,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,2,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_18 smallT11_18 smallFlag11_18 smallChoices11_18 + change solveChoices smallChoices11_18 (.full [3,2,2,2,2]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,2,2,2] (Equiv.refl (Fin 11)) smallB11_18 smallT11_18) smallFlag11_18 ≠ 0 + rw [smallCert11_18] + norm_num + +def smallB11_19 : Equiv.Perm (Fin 11) := Equiv.swap 1 6 * (Equiv.swap 6 10 * (Equiv.swap 5 0 * (Equiv.swap 0 9 * (Equiv.swap 0 3 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))) +def smallT11_19 : Equiv.Perm (Fin 11) := Equiv.swap 8 4 * (Equiv.swap 4 3 * (Equiv.swap 5 9 * (Equiv.swap 4 2 * (Equiv.swap 3 1 * (Equiv.swap 2 6 * (Equiv.swap 1 10)))))) +def smallFlag11_19 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(1,0,1),(0,0,2),(0,1,0),(1,1,1),(0,2,0),(0,2,1),(1,2,3),(1,3,2)} + +def smallChoices11_19 : EdgeChoices := (.node 6 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _v => if _v = (2,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _v => if _v = (2,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (2,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (2,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))))))))))))))))) +lemma smallCert11_19 : solveChoices smallChoices11_19 (.full [3,2,2,2,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,2,2,1,1] (Equiv.refl (Fin 11)) smallB11_19 smallT11_19) smallFlag11_19 = -2 := by + decide +kernel + +lemma smallSupport11_19 : RowSquare [4,3,3,1] [6,4,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,2,2,2,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_19 smallT11_19 smallFlag11_19 smallChoices11_19 + change solveChoices smallChoices11_19 (.full [3,2,2,2,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,2,2,1,1] (Equiv.refl (Fin 11)) smallB11_19 smallT11_19) smallFlag11_19 ≠ 0 + rw [smallCert11_19] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_5.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_5.lean index 8be0f8a418218546d5890d727dfe94632ce5c711..64552ed8a022e2dac155f1879af84a4e76afebb0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_5.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_5.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 11 5. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB11_20 : Equiv.Perm (Fin 11) := Equiv.swap 5 6 * (Equiv.swap 5 0 * (Equiv.swap 6 10 * (Equiv.swap 6 7 * (Equiv.swap 5 2 * (Equiv.swap 2 8 * (Equiv.swap 0 9 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 3))))))))) -def smallT11_20 : Equiv.Perm (Fin 11) := Equiv.swap 0 10 * (Equiv.swap 6 3 * (Equiv.swap 6 2 * (Equiv.swap 2 7 * (Equiv.swap 3 8 * (Equiv.swap 3 1 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 9)))))))) -def smallFlag11_20 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(0,0,3),(1,1,0),(0,1,2),(2,2,0),(0,2,1),(0,2,2),(1,3,2)} - -def smallChoices11_20 : EdgeChoices := (.node 7 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 6 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,1,0) then (.node 1 (fun _v => if _v = (2,2,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))))))))))) else (.node 6 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 6 (fun _v => if _v = (1,1,0) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 6 (fun _v => if _v = (1,1,0) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert11_20 : solveChoices smallChoices11_20 (.full [3,2,2,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,2,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_20 smallT11_20) smallFlag11_20 = 2 := by - decide +kernel - -lemma smallSupport11_20 : RowSquare [4,3,3,1] [7,3,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,2,2,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_20 smallT11_20 smallFlag11_20 smallChoices11_20 - change solveChoices smallChoices11_20 (.full [3,2,2,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,2,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_20 smallT11_20) smallFlag11_20 ≠ 0 - rw [smallCert11_20] - norm_num - -def smallB11_21 : Equiv.Perm (Fin 11) := Equiv.swap 1 0 * (Equiv.swap 1 8 * (Equiv.swap 1 7 * (Equiv.swap 1 6 * (Equiv.swap 1 3 * (Equiv.swap 3 2 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 10)))))))) -def smallT11_21 : Equiv.Perm (Fin 11) := Equiv.swap 8 7 * (Equiv.swap 7 10 * (Equiv.swap 5 2 * (Equiv.swap 2 1 * (Equiv.swap 0 6 * (Equiv.swap 2 4 * (Equiv.swap 1 9 * (Equiv.swap 0 3))))))) -def smallFlag11_21 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(1,0,3),(0,1,0),(2,1,2),(0,2,0),(1,2,1),(0,2,2),(0,3,2)} - -def smallChoices11_21 : EdgeChoices := (.node 10 (fun _v => if _v = (0,0,0) then (.node 8 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _ => .fallback)))))) -lemma smallCert11_21 : solveChoices smallChoices11_21 (.full [3,2,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_21 smallT11_21) smallFlag11_21 = -2 := by - decide +kernel - -lemma smallSupport11_21 : RowSquare [4,3,3,1] [8,2,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,2,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_21 smallT11_21 smallFlag11_21 smallChoices11_21 - change solveChoices smallChoices11_21 (.full [3,2,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_21 smallT11_21) smallFlag11_21 ≠ 0 - rw [smallCert11_21] - norm_num - -def smallB11_22 : Equiv.Perm (Fin 11) := Equiv.swap 5 3 * (Equiv.swap 4 7 * (Equiv.swap 3 8 * (Equiv.swap 0 1 * (Equiv.swap 1 10 * (Equiv.swap 0 2))))) -def smallT11_22 : Equiv.Perm (Fin 11) := Equiv.swap 6 10 * (Equiv.swap 4 8 * (Equiv.swap 6 9 * (Equiv.swap 4 7 * (Equiv.swap 1 5 * (Equiv.swap 1 2 * (Equiv.swap 0 3)))))) -def smallFlag11_22 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,2),(2,1,0),(0,1,1),(1,1,3),(0,2,1),(0,2,2),(0,3,1)} - -def smallChoices11_22 : EdgeChoices := (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 8 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,2) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert11_22 : solveChoices smallChoices11_22 (.full [3,1,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_22 smallT11_22) smallFlag11_22 = 8 := by - decide +kernel - -lemma smallSupport11_22 : RowSquare [4,3,3,1] [9,1,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,1,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_22 smallT11_22 smallFlag11_22 smallChoices11_22 - change solveChoices smallChoices11_22 (.full [3,1,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [3,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_22 smallT11_22) smallFlag11_22 ≠ 0 - rw [smallCert11_22] - norm_num - -def smallB11_23 : Equiv.Perm (Fin 11) := Equiv.swap 7 1 * (Equiv.swap 7 9 * (Equiv.swap 7 4 * (Equiv.swap 1 10 * (Equiv.swap 4 0 * (Equiv.swap 3 5 * (Equiv.swap 1 6 * (Equiv.swap 0 8))))))) -def smallT11_23 : Equiv.Perm (Fin 11) := Equiv.swap 3 10 * (Equiv.swap 3 1 * (Equiv.swap 2 9 * (Equiv.swap 3 6 * (Equiv.swap 2 5 * (Equiv.swap 1 0 * (Equiv.swap 0 7)))))) -def smallFlag11_23 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(0,1,2),(1,1,3),(1,2,0),(0,2,1),(1,2,2),(0,3,1)} - -def smallChoices11_23 : EdgeChoices := (.node 6 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,2) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,0,1) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => 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(fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,1) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,0,0) then (.node 7 (fun _v => if _v = (0,1,2) then (.node 6 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => 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(.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,2) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,0,0) then (.node 4 (fun _v => if _v = (0,1,2) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,0,0) then (.node 7 (fun _v => if _v = (0,0,0) then (.node 6 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 6 (fun _ => (.node 5 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 6 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 5 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,0,0) then (.node 5 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert11_23 : solveChoices smallChoices11_23 (.full [2,2,2,2,2,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,2,2,2,1] (Equiv.refl (Fin 11)) smallB11_23 smallT11_23) smallFlag11_23 = -3 := by - decide +kernel - -lemma smallSupport11_23 : RowSquare [4,3,3,1] [6,5] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [2,2,2,2,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_23 smallT11_23 smallFlag11_23 smallChoices11_23 - change solveChoices smallChoices11_23 (.full [2,2,2,2,2,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,2,2,2,1] (Equiv.refl (Fin 11)) smallB11_23 smallT11_23) smallFlag11_23 ≠ 0 - rw [smallCert11_23] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 11 5. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB11_20 : Equiv.Perm (Fin 11) := Equiv.swap 5 6 * (Equiv.swap 5 0 * (Equiv.swap 6 10 * (Equiv.swap 6 7 * (Equiv.swap 5 2 * (Equiv.swap 2 8 * (Equiv.swap 0 9 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 3))))))))) +def smallT11_20 : Equiv.Perm (Fin 11) := Equiv.swap 0 10 * (Equiv.swap 6 3 * (Equiv.swap 6 2 * (Equiv.swap 2 7 * (Equiv.swap 3 8 * (Equiv.swap 3 1 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 9)))))))) +def smallFlag11_20 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(0,0,3),(1,1,0),(0,1,2),(2,2,0),(0,2,1),(0,2,2),(1,3,2)} + +def smallChoices11_20 : EdgeChoices := (.node 7 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 6 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,1,0) then (.node 1 (fun _v => if _v = (2,2,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))))))))))) else (.node 6 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 6 (fun _v => if _v = (1,1,0) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 6 (fun _v => if _v = (1,1,0) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert11_20 : solveChoices smallChoices11_20 (.full [3,2,2,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,2,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_20 smallT11_20) smallFlag11_20 = 2 := by + decide +kernel + +lemma smallSupport11_20 : RowSquare [4,3,3,1] [7,3,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,2,2,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_20 smallT11_20 smallFlag11_20 smallChoices11_20 + change solveChoices smallChoices11_20 (.full [3,2,2,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,2,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_20 smallT11_20) smallFlag11_20 ≠ 0 + rw [smallCert11_20] + norm_num + +def smallB11_21 : Equiv.Perm (Fin 11) := Equiv.swap 1 0 * (Equiv.swap 1 8 * (Equiv.swap 1 7 * (Equiv.swap 1 6 * (Equiv.swap 1 3 * (Equiv.swap 3 2 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 10)))))))) +def smallT11_21 : Equiv.Perm (Fin 11) := Equiv.swap 8 7 * (Equiv.swap 7 10 * (Equiv.swap 5 2 * (Equiv.swap 2 1 * (Equiv.swap 0 6 * (Equiv.swap 2 4 * (Equiv.swap 1 9 * (Equiv.swap 0 3))))))) +def smallFlag11_21 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(1,0,3),(0,1,0),(2,1,2),(0,2,0),(1,2,1),(0,2,2),(0,3,2)} + +def smallChoices11_21 : EdgeChoices := (.node 10 (fun _v => if _v = (0,0,0) then (.node 8 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _ => .fallback)))))) +lemma smallCert11_21 : solveChoices smallChoices11_21 (.full [3,2,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_21 smallT11_21) smallFlag11_21 = -2 := by + decide +kernel + +lemma smallSupport11_21 : RowSquare [4,3,3,1] [8,2,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,2,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_21 smallT11_21 smallFlag11_21 smallChoices11_21 + change solveChoices smallChoices11_21 (.full [3,2,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,2,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_21 smallT11_21) smallFlag11_21 ≠ 0 + rw [smallCert11_21] + norm_num + +def smallB11_22 : Equiv.Perm (Fin 11) := Equiv.swap 5 3 * (Equiv.swap 4 7 * (Equiv.swap 3 8 * (Equiv.swap 0 1 * (Equiv.swap 1 10 * (Equiv.swap 0 2))))) +def smallT11_22 : Equiv.Perm (Fin 11) := Equiv.swap 6 10 * (Equiv.swap 4 8 * (Equiv.swap 6 9 * (Equiv.swap 4 7 * (Equiv.swap 1 5 * (Equiv.swap 1 2 * (Equiv.swap 0 3)))))) +def smallFlag11_22 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,2),(2,1,0),(0,1,1),(1,1,3),(0,2,1),(0,2,2),(0,3,1)} + +def smallChoices11_22 : EdgeChoices := (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 8 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,2) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert11_22 : solveChoices smallChoices11_22 (.full [3,1,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_22 smallT11_22) smallFlag11_22 = 8 := by + decide +kernel + +lemma smallSupport11_22 : RowSquare [4,3,3,1] [9,1,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [3,1,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_22 smallT11_22 smallFlag11_22 smallChoices11_22 + change solveChoices smallChoices11_22 (.full [3,1,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [3,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_22 smallT11_22) smallFlag11_22 ≠ 0 + rw [smallCert11_22] + norm_num + +def smallB11_23 : Equiv.Perm (Fin 11) := Equiv.swap 7 1 * (Equiv.swap 7 9 * (Equiv.swap 7 4 * (Equiv.swap 1 10 * (Equiv.swap 4 0 * (Equiv.swap 3 5 * (Equiv.swap 1 6 * (Equiv.swap 0 8))))))) +def smallT11_23 : Equiv.Perm (Fin 11) := Equiv.swap 3 10 * (Equiv.swap 3 1 * (Equiv.swap 2 9 * (Equiv.swap 3 6 * (Equiv.swap 2 5 * (Equiv.swap 1 0 * (Equiv.swap 0 7)))))) +def smallFlag11_23 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(0,1,2),(1,1,3),(1,2,0),(0,2,1),(1,2,2),(0,3,1)} + +def smallChoices11_23 : EdgeChoices := (.node 6 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,2) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,0,1) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,0,0) then (.node 7 (fun _v => if _v = (0,0,0) then (.node 6 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _ => (.node 5 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 6 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) 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(.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,2) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,0,0) then (.node 4 (fun _v => if _v = (0,1,2) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,0,0) then (.node 7 (fun _v => if _v = (0,0,0) then (.node 6 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 6 (fun _ => (.node 5 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 6 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 5 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,0,0) then (.node 5 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert11_23 : solveChoices smallChoices11_23 (.full [2,2,2,2,2,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,2,2,2,1] (Equiv.refl (Fin 11)) smallB11_23 smallT11_23) smallFlag11_23 = -3 := by + decide +kernel + +lemma smallSupport11_23 : RowSquare [4,3,3,1] [6,5] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [2,2,2,2,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_23 smallT11_23 smallFlag11_23 smallChoices11_23 + change solveChoices smallChoices11_23 (.full [2,2,2,2,2,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,2,2,2,1] (Equiv.refl (Fin 11)) smallB11_23 smallT11_23) smallFlag11_23 ≠ 0 + rw [smallCert11_23] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_6.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_6.lean index a45ec3205b918b2732128b74a18219c9ec66fea8..73e817b854f8da86f2a36097874c4daa18d2fa08 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_6.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts11_6.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 11 6. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB11_24 : Equiv.Perm (Fin 11) := Equiv.swap 7 1 * (Equiv.swap 7 4 * (Equiv.swap 1 0 * (Equiv.swap 1 6 * (Equiv.swap 4 8 * (Equiv.swap 3 2 * (Equiv.swap 2 10 * (Equiv.swap 1 5 * (Equiv.swap 0 9)))))))) -def smallT11_24 : Equiv.Perm (Fin 11) := Equiv.swap 2 0 * (Equiv.swap 0 10 * (Equiv.swap 2 9 * (Equiv.swap 5 8 * (Equiv.swap 2 3 * (Equiv.swap 3 6 * (Equiv.swap 2 4 * (Equiv.swap 0 7 * (Equiv.swap 0 1)))))))) -def smallFlag11_24 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(1,0,2),(0,0,3),(1,1,1),(0,1,2),(0,2,0),(0,3,2)} - -def smallChoices11_24 : EdgeChoices := (.node 2 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (0,1,2) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 5 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,2) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 5 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 5 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))))))))) -lemma smallCert11_24 : solveChoices smallChoices11_24 (.full [2,2,2,2,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,2,2,1,1,1] (Equiv.refl (Fin 11)) smallB11_24 smallT11_24) smallFlag11_24 = -1 := by - decide +kernel - -lemma smallSupport11_24 : RowSquare [4,3,3,1] [7,4] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [2,2,2,2,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_24 smallT11_24 smallFlag11_24 smallChoices11_24 - change solveChoices smallChoices11_24 (.full [2,2,2,2,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,2,2,1,1,1] (Equiv.refl (Fin 11)) smallB11_24 smallT11_24) smallFlag11_24 ≠ 0 - rw [smallCert11_24] - norm_num - -def smallB11_25 : Equiv.Perm (Fin 11) := Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 2 8 * (Equiv.swap 0 6))))) -def smallT11_25 : Equiv.Perm (Fin 11) := Equiv.swap 5 2 * (Equiv.swap 2 10 * (Equiv.swap 5 8 * (Equiv.swap 3 7 * (Equiv.swap 2 6 * (Equiv.swap 1 4))))) -def smallFlag11_25 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,2),(1,0,3),(0,1,0),(0,1,1),(0,2,1),(0,2,2),(0,3,0)} - -def smallChoices11_25 : EdgeChoices := (.node 10 (fun _v => (.node 5 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,1) then (.node 4 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert11_25 : solveChoices smallChoices11_25 (.full [2,2,2,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,2,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_25 smallT11_25) smallFlag11_25 = -8 := by - decide +kernel - -lemma smallSupport11_25 : RowSquare [4,3,3,1] [8,3] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [2,2,2,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_25 smallT11_25 smallFlag11_25 smallChoices11_25 - change solveChoices smallChoices11_25 (.full [2,2,2,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,2,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_25 smallT11_25) smallFlag11_25 ≠ 0 - rw [smallCert11_25] - norm_num - -def smallB11_26 : Equiv.Perm (Fin 11) := Equiv.swap 9 1 * (Equiv.swap 1 3 * (Equiv.swap 3 0 * (Equiv.swap 1 8 * (Equiv.swap 3 7 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 6 * (Equiv.swap 0 10)))))))) -def smallT11_26 : Equiv.Perm (Fin 11) := Equiv.swap 9 4 * (Equiv.swap 4 1 * (Equiv.swap 1 10 * (Equiv.swap 4 7 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 1 5 * (Equiv.swap 0 8))))))) -def smallFlag11_26 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,2),(0,1,1),(0,1,2),(0,1,3),(1,2,0),(0,2,1),(0,3,2)} - -def smallChoices11_26 : EdgeChoices := (.node 0 (fun _v => (.node 9 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (1,2,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 6 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (0,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 6 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 6 (fun _v => if _v = (0,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))))))))))))) -lemma smallCert11_26 : solveChoices smallChoices11_26 (.full [2,2,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_26 smallT11_26) smallFlag11_26 = -4 := by - decide +kernel - -lemma smallSupport11_26 : RowSquare [4,3,3,1] [9,2] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [2,2,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_26 smallT11_26 smallFlag11_26 smallChoices11_26 - change solveChoices smallChoices11_26 (.full [2,2,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_26 smallT11_26) smallFlag11_26 ≠ 0 - rw [smallCert11_26] - norm_num - -def smallB11_27 : Equiv.Perm (Fin 11) := Equiv.swap 1 4 * (Equiv.swap 4 6 * (Equiv.swap 6 10 * (Equiv.swap 4 3 * (Equiv.swap 4 0 * (Equiv.swap 3 8 * (Equiv.swap 1 9 * (Equiv.swap 0 5))))))) -def smallT11_27 : Equiv.Perm (Fin 11) := Equiv.swap 4 7 * (Equiv.swap 7 5 * (Equiv.swap 5 2 * (Equiv.swap 4 9 * (Equiv.swap 2 10 * (Equiv.swap 2 1 * (Equiv.swap 1 3)))))) -def smallFlag11_27 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(0,1,2),(0,1,3),(0,2,0),(1,2,2),(0,3,1)} - -def smallChoices11_27 : EdgeChoices := (.node 6 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,3) then (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert11_27 : solveChoices smallChoices11_27 (.full [2,1,1,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [2,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_27 smallT11_27) smallFlag11_27 = -24 := by - decide +kernel - -lemma smallSupport11_27 : RowSquare [4,3,3,1] [10,1] := by - apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [2,1,1,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB11_27 smallT11_27 smallFlag11_27 smallChoices11_27 - change solveChoices smallChoices11_27 (.full [2,1,1,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) - (certificateEdges [4,3,3,1] [4,3,3,1] [2,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_27 smallT11_27) smallFlag11_27 ≠ 0 - rw [smallCert11_27] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 11 6. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB11_24 : Equiv.Perm (Fin 11) := Equiv.swap 7 1 * (Equiv.swap 7 4 * (Equiv.swap 1 0 * (Equiv.swap 1 6 * (Equiv.swap 4 8 * (Equiv.swap 3 2 * (Equiv.swap 2 10 * (Equiv.swap 1 5 * (Equiv.swap 0 9)))))))) +def smallT11_24 : Equiv.Perm (Fin 11) := Equiv.swap 2 0 * (Equiv.swap 0 10 * (Equiv.swap 2 9 * (Equiv.swap 5 8 * (Equiv.swap 2 3 * (Equiv.swap 3 6 * (Equiv.swap 2 4 * (Equiv.swap 0 7 * (Equiv.swap 0 1)))))))) +def smallFlag11_24 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(1,0,2),(0,0,3),(1,1,1),(0,1,2),(0,2,0),(0,3,2)} + +def smallChoices11_24 : EdgeChoices := (.node 2 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (0,1,2) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 5 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,2) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 5 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 5 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))))))))) +lemma smallCert11_24 : solveChoices smallChoices11_24 (.full [2,2,2,2,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,2,2,1,1,1] (Equiv.refl (Fin 11)) smallB11_24 smallT11_24) smallFlag11_24 = -1 := by + decide +kernel + +lemma smallSupport11_24 : RowSquare [4,3,3,1] [7,4] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [2,2,2,2,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_24 smallT11_24 smallFlag11_24 smallChoices11_24 + change solveChoices smallChoices11_24 (.full [2,2,2,2,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,2,2,1,1,1] (Equiv.refl (Fin 11)) smallB11_24 smallT11_24) smallFlag11_24 ≠ 0 + rw [smallCert11_24] + norm_num + +def smallB11_25 : Equiv.Perm (Fin 11) := Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 2 8 * (Equiv.swap 0 6))))) +def smallT11_25 : Equiv.Perm (Fin 11) := Equiv.swap 5 2 * (Equiv.swap 2 10 * (Equiv.swap 5 8 * (Equiv.swap 3 7 * (Equiv.swap 2 6 * (Equiv.swap 1 4))))) +def smallFlag11_25 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,2),(1,0,3),(0,1,0),(0,1,1),(0,2,1),(0,2,2),(0,3,0)} + +def smallChoices11_25 : EdgeChoices := (.node 10 (fun _v => (.node 5 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,1) then (.node 4 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert11_25 : solveChoices smallChoices11_25 (.full [2,2,2,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,2,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_25 smallT11_25) smallFlag11_25 = -8 := by + decide +kernel + +lemma smallSupport11_25 : RowSquare [4,3,3,1] [8,3] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [2,2,2,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_25 smallT11_25 smallFlag11_25 smallChoices11_25 + change solveChoices smallChoices11_25 (.full [2,2,2,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,2,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_25 smallT11_25) smallFlag11_25 ≠ 0 + rw [smallCert11_25] + norm_num + +def smallB11_26 : Equiv.Perm (Fin 11) := Equiv.swap 9 1 * (Equiv.swap 1 3 * (Equiv.swap 3 0 * (Equiv.swap 1 8 * (Equiv.swap 3 7 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 6 * (Equiv.swap 0 10)))))))) +def smallT11_26 : Equiv.Perm (Fin 11) := Equiv.swap 9 4 * (Equiv.swap 4 1 * (Equiv.swap 1 10 * (Equiv.swap 4 7 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 1 5 * (Equiv.swap 0 8))))))) +def smallFlag11_26 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,2),(0,1,1),(0,1,2),(0,1,3),(1,2,0),(0,2,1),(0,3,2)} + +def smallChoices11_26 : EdgeChoices := (.node 0 (fun _v => (.node 9 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (1,2,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 6 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (0,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 6 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 6 (fun _v => if _v = (0,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))))))))))))) +lemma smallCert11_26 : solveChoices smallChoices11_26 (.full [2,2,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_26 smallT11_26) smallFlag11_26 = -4 := by + decide +kernel + +lemma smallSupport11_26 : RowSquare [4,3,3,1] [9,2] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [2,2,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_26 smallT11_26 smallFlag11_26 smallChoices11_26 + change solveChoices smallChoices11_26 (.full [2,2,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [2,2,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_26 smallT11_26) smallFlag11_26 ≠ 0 + rw [smallCert11_26] + norm_num + +def smallB11_27 : Equiv.Perm (Fin 11) := Equiv.swap 1 4 * (Equiv.swap 4 6 * (Equiv.swap 6 10 * (Equiv.swap 4 3 * (Equiv.swap 4 0 * (Equiv.swap 3 8 * (Equiv.swap 1 9 * (Equiv.swap 0 5))))))) +def smallT11_27 : Equiv.Perm (Fin 11) := Equiv.swap 4 7 * (Equiv.swap 7 5 * (Equiv.swap 5 2 * (Equiv.swap 4 9 * (Equiv.swap 2 10 * (Equiv.swap 2 1 * (Equiv.swap 1 3)))))) +def smallFlag11_27 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(0,1,2),(0,1,3),(0,2,0),(1,2,2),(0,3,1)} + +def smallChoices11_27 : EdgeChoices := (.node 6 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,3) then (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert11_27 : solveChoices smallChoices11_27 (.full [2,1,1,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [2,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_27 smallT11_27) smallFlag11_27 = -24 := by + decide +kernel + +lemma smallSupport11_27 : RowSquare [4,3,3,1] [10,1] := by + apply rowSquare_choices (n := 11) (cs := [4,3,3,1]) (ts := [2,1,1,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB11_27 smallT11_27 smallFlag11_27 smallChoices11_27 + change solveChoices smallChoices11_27 (.full [2,1,1,1,1,1,1,1,1,1]) (.full [4,3,3,1]) (.full [4,3,3,1]) + (certificateEdges [4,3,3,1] [4,3,3,1] [2,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 11)) smallB11_27 smallT11_27) smallFlag11_27 ≠ 0 + rw [smallCert11_27] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_1.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_1.lean index e6b3aede4f18887e20a745f8a14ef56a89e0683f..35396ae7833cc24fdbd0dadf4504b902d8998db2 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_1.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_1.lean @@ -1,83 +1,83 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains - -namespace OAI - -/-! Small Contracts 13 1. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_4 : Equiv.Perm (Fin 13) := Equiv.swap 5 10 * (Equiv.swap 1 3 * (Equiv.swap 5 9 * (Equiv.swap 5 2 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 1 7 * (Equiv.swap 0 11))))))) -def smallT13_4 : Equiv.Perm (Fin 13) := Equiv.swap 8 6 * (Equiv.swap 8 7 * (Equiv.swap 8 1 * (Equiv.swap 7 5 * (Equiv.swap 6 2 * (Equiv.swap 5 11 * (Equiv.swap 4 9 * (Equiv.swap 2 12 * (Equiv.swap 1 0 * (Equiv.swap 0 10))))))))) -def smallFlag13_4 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(3,1,1),(0,1,2),(4,1,2),(0,1,3),(2,2,1),(0,2,2),(3,3,0),(0,3,3)} -lemma smallCert13_4 : solveCompact 13 (.full [5,4,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,4,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_4 smallT13_4) smallFlag13_4 = -13 := by - decide +kernel - -lemma smallSupport13_4 : RowSquare [4,4,3,2] [6,2,2,2,1] := by - apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [5,4,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_4 smallT13_4 smallFlag13_4 - change solveCompact 13 (.full [5,4,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,4,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_4 smallT13_4) smallFlag13_4 ≠ 0 - rw [smallCert13_4] - norm_num - -def smallB13_5 : Equiv.Perm (Fin 13) := Equiv.swap 10 0 * (Equiv.swap 0 11 * (Equiv.swap 0 2 * (Equiv.swap 5 9 * (Equiv.swap 5 6 * (Equiv.swap 2 8 * (Equiv.swap 1 12 * (Equiv.swap 2 4 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))))))) -def smallT13_5 : Equiv.Perm (Fin 13) := Equiv.swap 10 4 * (Equiv.swap 10 2 * (Equiv.swap 7 6 * (Equiv.swap 6 9 * (Equiv.swap 4 12 * (Equiv.swap 4 0 * (Equiv.swap 0 1 * (Equiv.swap 2 11 * (Equiv.swap 1 5 * (Equiv.swap 0 3))))))))) -def smallFlag13_5 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,2),(3,0,3),(2,1,1),(0,1,2),(0,1,3),(0,2,0),(2,2,0),(1,2,1),(1,3,1),(1,3,2)} -lemma smallCert13_5 : solveCompact 13 (.full [5,3,3,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,3,1,1] (Equiv.refl (Fin 13)) smallB13_5 smallT13_5) smallFlag13_5 = 3 := by - decide +kernel - -lemma smallSupport13_5 : RowSquare [4,4,3,2] [5,3,3,1,1] := by - apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [5,3,3,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_5 smallT13_5 smallFlag13_5 - change solveCompact 13 (.full [5,3,3,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,3,1,1] (Equiv.refl (Fin 13)) smallB13_5 smallT13_5) smallFlag13_5 ≠ 0 - rw [smallCert13_5] - norm_num - -def smallB13_6 : Equiv.Perm (Fin 13) := Equiv.swap 6 4 * (Equiv.swap 6 1 * (Equiv.swap 7 10 * (Equiv.swap 7 0 * (Equiv.swap 6 2 * (Equiv.swap 4 12 * (Equiv.swap 4 5 * (Equiv.swap 2 9 * (Equiv.swap 1 11 * (Equiv.swap 0 8))))))))) -def smallT13_6 : Equiv.Perm (Fin 13) := Equiv.swap 10 11 * (Equiv.swap 7 0 * (Equiv.swap 7 3 * (Equiv.swap 0 2 * (Equiv.swap 2 9 * (Equiv.swap 3 8 * (Equiv.swap 2 4 * (Equiv.swap 0 5))))))) -def smallFlag13_6 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(0,0,2),(1,1,0),(2,1,1),(0,1,2),(4,2,1),(1,2,2),(1,2,3),(3,3,0),(0,3,3)} -lemma smallCert13_6 : solveCompact 13 (.full [5,3,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,2,2,1] (Equiv.refl (Fin 13)) smallB13_6 smallT13_6) smallFlag13_6 = 1 := by - decide +kernel - -lemma smallSupport13_6 : RowSquare [4,4,3,2] [5,4,2,1,1] := by - apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [5,3,2,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_6 smallT13_6 smallFlag13_6 - change solveCompact 13 (.full [5,3,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,2,2,1] (Equiv.refl (Fin 13)) smallB13_6 smallT13_6) smallFlag13_6 ≠ 0 - rw [smallCert13_6] - norm_num - -def smallB13_7 : Equiv.Perm (Fin 13) := Equiv.swap 10 1 * (Equiv.swap 10 7 * (Equiv.swap 7 8 * (Equiv.swap 8 6 * (Equiv.swap 7 2 * (Equiv.swap 6 5 * (Equiv.swap 5 11 * (Equiv.swap 3 4 * (Equiv.swap 2 9 * (Equiv.swap 1 0 * (Equiv.swap 0 12)))))))))) -def smallT13_7 : Equiv.Perm (Fin 13) := Equiv.swap 6 9 * (Equiv.swap 9 3 * (Equiv.swap 8 7 * (Equiv.swap 7 11 * (Equiv.swap 6 10 * (Equiv.swap 3 2 * (Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 2 12)))))))) -def smallFlag13_7 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(2,0,2),(0,0,3),(1,1,0),(2,1,0),(3,1,0),(1,1,2),(0,2,1),(1,2,3),(4,3,0),(0,3,2)} -lemma smallCert13_7 : solveCompact 13 (.full [5,3,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_7 smallT13_7) smallFlag13_7 = 2 := by - decide +kernel - -lemma smallSupport13_7 : RowSquare [4,4,3,2] [6,3,2,1,1] := by - apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [5,3,2,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_7 smallT13_7 smallFlag13_7 - change solveCompact 13 (.full [5,3,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_7 smallT13_7) smallFlag13_7 ≠ 0 - rw [smallCert13_7] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains + +namespace OAI + +/-! Small Contracts 13 1. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_4 : Equiv.Perm (Fin 13) := Equiv.swap 5 10 * (Equiv.swap 1 3 * (Equiv.swap 5 9 * (Equiv.swap 5 2 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 1 7 * (Equiv.swap 0 11))))))) +def smallT13_4 : Equiv.Perm (Fin 13) := Equiv.swap 8 6 * (Equiv.swap 8 7 * (Equiv.swap 8 1 * (Equiv.swap 7 5 * (Equiv.swap 6 2 * (Equiv.swap 5 11 * (Equiv.swap 4 9 * (Equiv.swap 2 12 * (Equiv.swap 1 0 * (Equiv.swap 0 10))))))))) +def smallFlag13_4 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(3,1,1),(0,1,2),(4,1,2),(0,1,3),(2,2,1),(0,2,2),(3,3,0),(0,3,3)} +lemma smallCert13_4 : solveCompact 13 (.full [5,4,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,4,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_4 smallT13_4) smallFlag13_4 = -13 := by + decide +kernel + +lemma smallSupport13_4 : RowSquare [4,4,3,2] [6,2,2,2,1] := by + apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [5,4,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_4 smallT13_4 smallFlag13_4 + change solveCompact 13 (.full [5,4,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,4,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_4 smallT13_4) smallFlag13_4 ≠ 0 + rw [smallCert13_4] + norm_num + +def smallB13_5 : Equiv.Perm (Fin 13) := Equiv.swap 10 0 * (Equiv.swap 0 11 * (Equiv.swap 0 2 * (Equiv.swap 5 9 * (Equiv.swap 5 6 * (Equiv.swap 2 8 * (Equiv.swap 1 12 * (Equiv.swap 2 4 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))))))) +def smallT13_5 : Equiv.Perm (Fin 13) := Equiv.swap 10 4 * (Equiv.swap 10 2 * (Equiv.swap 7 6 * (Equiv.swap 6 9 * (Equiv.swap 4 12 * (Equiv.swap 4 0 * (Equiv.swap 0 1 * (Equiv.swap 2 11 * (Equiv.swap 1 5 * (Equiv.swap 0 3))))))))) +def smallFlag13_5 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,2),(3,0,3),(2,1,1),(0,1,2),(0,1,3),(0,2,0),(2,2,0),(1,2,1),(1,3,1),(1,3,2)} +lemma smallCert13_5 : solveCompact 13 (.full [5,3,3,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,3,1,1] (Equiv.refl (Fin 13)) smallB13_5 smallT13_5) smallFlag13_5 = 3 := by + decide +kernel + +lemma smallSupport13_5 : RowSquare [4,4,3,2] [5,3,3,1,1] := by + apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [5,3,3,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_5 smallT13_5 smallFlag13_5 + change solveCompact 13 (.full [5,3,3,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,3,1,1] (Equiv.refl (Fin 13)) smallB13_5 smallT13_5) smallFlag13_5 ≠ 0 + rw [smallCert13_5] + norm_num + +def smallB13_6 : Equiv.Perm (Fin 13) := Equiv.swap 6 4 * (Equiv.swap 6 1 * (Equiv.swap 7 10 * (Equiv.swap 7 0 * (Equiv.swap 6 2 * (Equiv.swap 4 12 * (Equiv.swap 4 5 * (Equiv.swap 2 9 * (Equiv.swap 1 11 * (Equiv.swap 0 8))))))))) +def smallT13_6 : Equiv.Perm (Fin 13) := Equiv.swap 10 11 * (Equiv.swap 7 0 * (Equiv.swap 7 3 * (Equiv.swap 0 2 * (Equiv.swap 2 9 * (Equiv.swap 3 8 * (Equiv.swap 2 4 * (Equiv.swap 0 5))))))) +def smallFlag13_6 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(0,0,2),(1,1,0),(2,1,1),(0,1,2),(4,2,1),(1,2,2),(1,2,3),(3,3,0),(0,3,3)} +lemma smallCert13_6 : solveCompact 13 (.full [5,3,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,2,2,1] (Equiv.refl (Fin 13)) smallB13_6 smallT13_6) smallFlag13_6 = 1 := by + decide +kernel + +lemma smallSupport13_6 : RowSquare [4,4,3,2] [5,4,2,1,1] := by + apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [5,3,2,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_6 smallT13_6 smallFlag13_6 + change solveCompact 13 (.full [5,3,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,2,2,1] (Equiv.refl (Fin 13)) smallB13_6 smallT13_6) smallFlag13_6 ≠ 0 + rw [smallCert13_6] + norm_num + +def smallB13_7 : Equiv.Perm (Fin 13) := Equiv.swap 10 1 * (Equiv.swap 10 7 * (Equiv.swap 7 8 * (Equiv.swap 8 6 * (Equiv.swap 7 2 * (Equiv.swap 6 5 * (Equiv.swap 5 11 * (Equiv.swap 3 4 * (Equiv.swap 2 9 * (Equiv.swap 1 0 * (Equiv.swap 0 12)))))))))) +def smallT13_7 : Equiv.Perm (Fin 13) := Equiv.swap 6 9 * (Equiv.swap 9 3 * (Equiv.swap 8 7 * (Equiv.swap 7 11 * (Equiv.swap 6 10 * (Equiv.swap 3 2 * (Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 2 12)))))))) +def smallFlag13_7 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(2,0,2),(0,0,3),(1,1,0),(2,1,0),(3,1,0),(1,1,2),(0,2,1),(1,2,3),(4,3,0),(0,3,2)} +lemma smallCert13_7 : solveCompact 13 (.full [5,3,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_7 smallT13_7) smallFlag13_7 = 2 := by + decide +kernel + +lemma smallSupport13_7 : RowSquare [4,4,3,2] [6,3,2,1,1] := by + apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [5,3,2,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_7 smallT13_7 smallFlag13_7 + change solveCompact 13 (.full [5,3,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_7 smallT13_7) smallFlag13_7 ≠ 0 + rw [smallCert13_7] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_10.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_10.lean index 617396e9adb70473f6f46a57cc8f89d28077b6de..9522b9489cc773b377534e0d2af14d30b3d4e43f 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_10.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_10.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 13 10. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_40 : Equiv.Perm (Fin 13) := Equiv.swap 2 12 * (Equiv.swap 2 11 * (Equiv.swap 1 7 * (Equiv.swap 7 4 * (Equiv.swap 1 8 * (Equiv.swap 2 10 * (Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 2 5 * (Equiv.swap 1 6 * (Equiv.swap 0 9)))))))))) -def smallT13_40 : Equiv.Perm (Fin 13) := Equiv.swap 1 2 * (Equiv.swap 1 10 * (Equiv.swap 2 12 * (Equiv.swap 2 5 * (Equiv.swap 5 3 * (Equiv.swap 2 7 * (Equiv.swap 3 8 * (Equiv.swap 2 4 * (Equiv.swap 1 9)))))))) -def smallFlag13_40 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(0,0,3),(0,1,1),(0,1,2),(1,1,2),(0,2,0),(0,2,1),(0,3,0),(1,3,0)} - -def smallChoices13_40 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,1) then (.node 11 (fun _v => (.node 6 (fun _v => if _v = (1,1,2) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 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=> .fallback)))))) else if _v = (0,2,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => .fallback)) else if _v = (0,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 4 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 3 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => .fallback)) else if _v = (0,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_40 : solveChoices smallChoices13_40 (.full [2,2,2,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_40 smallT13_40) smallFlag13_40 = 10 := by - decide +kernel - -lemma smallSupport13_40 : RowSquare [4,4,3,2] [10,3] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [2,2,2,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_40 smallT13_40 smallFlag13_40 smallChoices13_40 - change solveChoices smallChoices13_40 (.full [2,2,2,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_40 smallT13_40) smallFlag13_40 ≠ 0 - rw [smallCert13_40] - norm_num - -def smallB13_41 : Equiv.Perm (Fin 13) := Equiv.swap 0 3 * (Equiv.swap 3 8 * (Equiv.swap 0 2 * (Equiv.swap 8 12 * (Equiv.swap 4 7 * (Equiv.swap 4 6 * (Equiv.swap 4 5 * (Equiv.swap 3 1 * (Equiv.swap 2 11 * (Equiv.swap 1 10 * (Equiv.swap 0 9)))))))))) -def smallT13_41 : Equiv.Perm (Fin 13) := Equiv.swap 6 9 * (Equiv.swap 9 5 * (Equiv.swap 9 10 * (Equiv.swap 6 0 * (Equiv.swap 6 1 * (Equiv.swap 6 7 * (Equiv.swap 5 12 * (Equiv.swap 1 8 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 11)))))))))) -def smallFlag13_41 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(0,0,3),(0,1,0),(0,1,2),(0,2,0),(0,2,3),(1,3,0),(0,3,1)} - -def smallChoices13_41 : EdgeChoices := (.node 8 (fun _v => if _v = (0,0,1) then (.node 11 (fun _v => (.node 6 (fun _v => if _v = (0,1,0) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,2) then (.node 8 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,1,0) then (.node 8 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,2) then (.node 8 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 8 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else if _v = (0,1,0) then (.node 11 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else (.node 11 (fun _v => (.node 6 (fun _v => if _v = (0,0,1) then (.node 5 (fun _v => if _v = (0,0,1) then (.node 8 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 8 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 8 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 8 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_41 : solveChoices smallChoices13_41 (.full [2,1,1,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [2,1,1,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_41 smallT13_41) smallFlag13_41 = 48 := by - decide +kernel - -lemma smallSupport13_41 : RowSquare [4,4,3,2] [12,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [2,1,1,1,1,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_41 smallT13_41 smallFlag13_41 smallChoices13_41 - change solveChoices smallChoices13_41 (.full [2,1,1,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [2,1,1,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_41 smallT13_41) smallFlag13_41 ≠ 0 - rw [smallCert13_41] - norm_num - -def smallB13_42 : Equiv.Perm (Fin 13) := Equiv.swap 4 6 * (Equiv.swap 4 9 * (Equiv.swap 9 11 * (Equiv.swap 4 5 * (Equiv.swap 6 2 * (Equiv.swap 5 10 * (Equiv.swap 4 7 * (Equiv.swap 1 8 * (Equiv.swap 2 12 * (Equiv.swap 1 0 * (Equiv.swap 0 3)))))))))) -def smallT13_42 : Equiv.Perm (Fin 13) := Equiv.swap 2 12 * (Equiv.swap 2 6 * (Equiv.swap 3 0 * (Equiv.swap 6 11 * (Equiv.swap 0 8 * (Equiv.swap 3 7 * (Equiv.swap 2 9 * (Equiv.swap 1 10 * (Equiv.swap 0 4)))))))) -def smallFlag13_42 : Finset (ℕ × ℕ × ℕ) := {(3,0,1),(1,0,2),(0,0,3),(2,1,0),(1,1,2),(1,2,1),(0,2,2),(3,3,0),(0,3,1)} - -def smallChoices13_42 : EdgeChoices := (.node 2 (fun _v => if _v = (2,1,0) then (.node 6 (fun _v => if _v = (3,0,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _v => if _v = (1,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,2,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,2,1) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,2,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,3) then (.node 1 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,1) then (.node 2 (fun _v => (.node 6 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _ => (.node 6 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _v => if _v = (1,0,2) then (.node 1 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 1 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 3 (fun _v => if _v = (1,2,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 5 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 3 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,2) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 1 (fun _v => if _v = (1,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (1,2,1) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 5 (fun _v => (.node 1 (fun _v => if _v = (1,0,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 3 (fun _v => if _v = (1,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (3,0,1) then (.node 4 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else if _v = (1,2,1) then (.node 6 (fun _v => (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,3) then (.node 6 (fun _v => (.node 2 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (0,2,2) then (.node 6 (fun _v => (.node 2 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _v => (.node 2 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 3 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 3 (fun _v => if _v = (0,0,3) then (.node 2 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else (.node 6 (fun _v => (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (1,0,2) then (.node 6 (fun _v => (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,2) then (.node 6 (fun _v => (.node 2 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 4 (fun _v => if _v = (3,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 6 (fun _v => (.node 2 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 6 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _v => if _v = (3,3,0) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) -lemma smallCert13_42 : solveChoices smallChoices13_42 (.full [4,4,3,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,3,2] (Equiv.refl (Fin 13)) smallB13_42 smallT13_42) smallFlag13_42 = 4 := by - decide +kernel - -lemma smallSupport13_42 : RowSquare [4,4,3,2] [4,4,3,2] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,4,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_42 smallT13_42 smallFlag13_42 smallChoices13_42 - change solveChoices smallChoices13_42 (.full [4,4,3,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,3,2] (Equiv.refl (Fin 13)) smallB13_42 smallT13_42) smallFlag13_42 ≠ 0 - rw [smallCert13_42] - norm_num - -def smallB13_43 : Equiv.Perm (Fin 13) := Equiv.swap 9 6 * (Equiv.swap 9 7 * (Equiv.swap 9 8 * (Equiv.swap 8 2 * (Equiv.swap 7 5 * (Equiv.swap 6 3 * (Equiv.swap 5 11 * (Equiv.swap 3 12 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 10)))))))))) -def smallT13_43 : Equiv.Perm (Fin 13) := Equiv.swap 10 12 * (Equiv.swap 10 9 * (Equiv.swap 9 8 * (Equiv.swap 8 3 * (Equiv.swap 3 4 * (Equiv.swap 4 1 * (Equiv.swap 3 7 * (Equiv.swap 1 11 * (Equiv.swap 1 0 * (Equiv.swap 0 2))))))))) -def smallFlag13_43 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(2,0,2),(3,0,2),(0,1,0),(1,1,0),(0,1,1),(1,2,0),(2,2,3),(0,3,1)} - -def smallChoices13_43 : EdgeChoices := (.node 11 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 8 (fun _v => if _v = (0,1,1) then (.node 7 (fun _v => (.node 1 (fun _v => if _v = (1,2,0) then (.node 6 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,1,0) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 6 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 7 (fun _v => (.node 1 (fun _v => if _v = (1,2,0) then (.node 6 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (1,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,1,0) then (.node 4 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => if 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.fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 7 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,1,0) then (.node 7 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 7 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (2,0,2) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,1,0) then (.node 1 (fun _ => (.node 5 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else if _v = (1,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 3 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,0) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _ => .fallback)))) else (.node 7 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (3,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _ => (.node 0 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 9 (fun _v => if _v = (2,0,2) then (.node 5 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 2 (fun _v => (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (3,0,2) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 2 (fun _v => (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (3,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 7 (fun _v => (.node 5 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,0) then (.node 7 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 7 (fun _v => (.node 5 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 5 (fun _ => (.node 4 (fun _ => .fallback)))))) else if _v = (1,1,0) then (.node 1 (fun _ => (.node 5 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,0) then (.node 8 (fun _v => (.node 0 (fun _v => (.node 3 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 8 (fun _v => (.node 0 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_43 : solveChoices smallChoices13_43 (.full [4,3,3,3]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,3,3] (Equiv.refl (Fin 13)) smallB13_43 smallT13_43) smallFlag13_43 = 6 := by - decide +kernel - -lemma smallSupport13_43 : RowSquare [4,4,3,2] [4,4,4,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,3,3,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_43 smallT13_43 smallFlag13_43 smallChoices13_43 - change solveChoices smallChoices13_43 (.full [4,3,3,3]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,3,3] (Equiv.refl (Fin 13)) smallB13_43 smallT13_43) smallFlag13_43 ≠ 0 - rw [smallCert13_43] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 13 10. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_40 : Equiv.Perm (Fin 13) := Equiv.swap 2 12 * (Equiv.swap 2 11 * (Equiv.swap 1 7 * (Equiv.swap 7 4 * (Equiv.swap 1 8 * (Equiv.swap 2 10 * (Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 2 5 * (Equiv.swap 1 6 * (Equiv.swap 0 9)))))))))) +def smallT13_40 : Equiv.Perm (Fin 13) := Equiv.swap 1 2 * (Equiv.swap 1 10 * (Equiv.swap 2 12 * (Equiv.swap 2 5 * (Equiv.swap 5 3 * (Equiv.swap 2 7 * (Equiv.swap 3 8 * (Equiv.swap 2 4 * (Equiv.swap 1 9)))))))) +def smallFlag13_40 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(0,0,3),(0,1,1),(0,1,2),(1,1,2),(0,2,0),(0,2,1),(0,3,0),(1,3,0)} + +def smallChoices13_40 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,1) then (.node 11 (fun _v => (.node 6 (fun _v => if _v = (1,1,2) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => 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(fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => 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then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = 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(fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_40 : solveChoices smallChoices13_40 (.full [2,2,2,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_40 smallT13_40) smallFlag13_40 = 10 := by + decide +kernel + +lemma smallSupport13_40 : RowSquare [4,4,3,2] [10,3] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [2,2,2,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_40 smallT13_40 smallFlag13_40 smallChoices13_40 + change solveChoices smallChoices13_40 (.full [2,2,2,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_40 smallT13_40) smallFlag13_40 ≠ 0 + rw [smallCert13_40] + norm_num + +def smallB13_41 : Equiv.Perm (Fin 13) := Equiv.swap 0 3 * (Equiv.swap 3 8 * (Equiv.swap 0 2 * (Equiv.swap 8 12 * (Equiv.swap 4 7 * (Equiv.swap 4 6 * (Equiv.swap 4 5 * (Equiv.swap 3 1 * (Equiv.swap 2 11 * (Equiv.swap 1 10 * (Equiv.swap 0 9)))))))))) +def smallT13_41 : Equiv.Perm (Fin 13) := Equiv.swap 6 9 * (Equiv.swap 9 5 * (Equiv.swap 9 10 * (Equiv.swap 6 0 * (Equiv.swap 6 1 * (Equiv.swap 6 7 * (Equiv.swap 5 12 * (Equiv.swap 1 8 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 11)))))))))) +def smallFlag13_41 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(0,0,3),(0,1,0),(0,1,2),(0,2,0),(0,2,3),(1,3,0),(0,3,1)} + +def smallChoices13_41 : EdgeChoices := (.node 8 (fun _v => if _v = (0,0,1) then (.node 11 (fun _v => (.node 6 (fun _v => if _v = (0,1,0) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,2) then (.node 8 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,1,0) then (.node 8 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,2) then (.node 8 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 8 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else if _v = (0,1,0) then (.node 11 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else (.node 11 (fun _v => (.node 6 (fun _v => if _v = (0,0,1) then (.node 5 (fun _v => if _v = (0,0,1) then (.node 8 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 8 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 8 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 8 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_41 : solveChoices smallChoices13_41 (.full [2,1,1,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [2,1,1,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_41 smallT13_41) smallFlag13_41 = 48 := by + decide +kernel + +lemma smallSupport13_41 : RowSquare [4,4,3,2] [12,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [2,1,1,1,1,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_41 smallT13_41 smallFlag13_41 smallChoices13_41 + change solveChoices smallChoices13_41 (.full [2,1,1,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [2,1,1,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_41 smallT13_41) smallFlag13_41 ≠ 0 + rw [smallCert13_41] + norm_num + +def smallB13_42 : Equiv.Perm (Fin 13) := Equiv.swap 4 6 * (Equiv.swap 4 9 * (Equiv.swap 9 11 * (Equiv.swap 4 5 * (Equiv.swap 6 2 * (Equiv.swap 5 10 * (Equiv.swap 4 7 * (Equiv.swap 1 8 * (Equiv.swap 2 12 * (Equiv.swap 1 0 * (Equiv.swap 0 3)))))))))) +def smallT13_42 : Equiv.Perm (Fin 13) := Equiv.swap 2 12 * (Equiv.swap 2 6 * (Equiv.swap 3 0 * (Equiv.swap 6 11 * (Equiv.swap 0 8 * (Equiv.swap 3 7 * (Equiv.swap 2 9 * (Equiv.swap 1 10 * (Equiv.swap 0 4)))))))) +def smallFlag13_42 : Finset (ℕ × ℕ × ℕ) := {(3,0,1),(1,0,2),(0,0,3),(2,1,0),(1,1,2),(1,2,1),(0,2,2),(3,3,0),(0,3,1)} + +def smallChoices13_42 : EdgeChoices := (.node 2 (fun _v => if _v = (2,1,0) then (.node 6 (fun _v => if _v = (3,0,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _v => if _v = (1,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,2,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,2,1) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,2,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,3) then (.node 1 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,1) then (.node 2 (fun _v => (.node 6 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _ => (.node 6 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _v => if _v = (1,0,2) then (.node 1 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 1 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 3 (fun _v => if _v = (1,2,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 5 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 3 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,2) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 1 (fun _v => if _v = (1,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (1,2,1) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 5 (fun _v => (.node 1 (fun _v => if _v = (1,0,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 3 (fun _v => if _v = (1,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (3,0,1) then (.node 4 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else if _v = (1,2,1) then (.node 6 (fun _v => (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,3) then (.node 6 (fun _v => (.node 2 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (0,2,2) then (.node 6 (fun _v => (.node 2 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _v => (.node 2 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 3 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 3 (fun _v => if _v = (0,0,3) then (.node 2 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else (.node 6 (fun _v => (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 3 (fun _v => if _v = (1,0,2) then (.node 6 (fun _v => (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,2) then (.node 6 (fun _v => (.node 2 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 4 (fun _v => if _v = (3,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 6 (fun _v => (.node 2 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (3,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 6 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _v => if _v = (3,3,0) then (.node 0 (fun _v => if _v = (3,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) +lemma smallCert13_42 : solveChoices smallChoices13_42 (.full [4,4,3,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,3,2] (Equiv.refl (Fin 13)) smallB13_42 smallT13_42) smallFlag13_42 = 4 := by + decide +kernel + +lemma smallSupport13_42 : RowSquare [4,4,3,2] [4,4,3,2] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,4,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_42 smallT13_42 smallFlag13_42 smallChoices13_42 + change solveChoices smallChoices13_42 (.full [4,4,3,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,3,2] (Equiv.refl (Fin 13)) smallB13_42 smallT13_42) smallFlag13_42 ≠ 0 + rw [smallCert13_42] + norm_num + +def smallB13_43 : Equiv.Perm (Fin 13) := Equiv.swap 9 6 * (Equiv.swap 9 7 * (Equiv.swap 9 8 * (Equiv.swap 8 2 * (Equiv.swap 7 5 * (Equiv.swap 6 3 * (Equiv.swap 5 11 * (Equiv.swap 3 12 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 10)))))))))) +def smallT13_43 : Equiv.Perm (Fin 13) := Equiv.swap 10 12 * (Equiv.swap 10 9 * (Equiv.swap 9 8 * (Equiv.swap 8 3 * (Equiv.swap 3 4 * (Equiv.swap 4 1 * (Equiv.swap 3 7 * (Equiv.swap 1 11 * (Equiv.swap 1 0 * (Equiv.swap 0 2))))))))) +def smallFlag13_43 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(2,0,2),(3,0,2),(0,1,0),(1,1,0),(0,1,1),(1,2,0),(2,2,3),(0,3,1)} + +def smallChoices13_43 : EdgeChoices := (.node 11 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 8 (fun _v => if _v = (0,1,1) then (.node 7 (fun _v => (.node 1 (fun _v => if _v = (1,2,0) then (.node 6 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,1,0) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 6 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 7 (fun _v => (.node 1 (fun _v => if _v = (1,2,0) then (.node 6 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (1,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,1,0) then (.node 4 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 6 (fun _ => .fallback)))))) else if _v = (1,1,0) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 7 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _ => .fallback)))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (1,0,1) then (.node 8 (fun _v => if _v = (0,1,1) then (.node 7 (fun _v => (.node 1 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 7 (fun _v => (.node 1 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,0) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (1,1,0) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (1,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 7 (fun _ => (.node 6 (fun _ => (.node 6 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (1,2,0) then (.node 5 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 5 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 6 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,0,2) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,0,2) then (.node 8 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => 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.fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else if _v = (1,1,0) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 7 (fun _ => (.node 6 (fun _ => (.node 6 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (1,2,0) then (.node 5 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 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(.node 5 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,0) then (.node 7 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 7 (fun _v => (.node 5 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 5 (fun _ => (.node 4 (fun _ => .fallback)))))) else if _v = (1,1,0) then (.node 1 (fun _ => (.node 5 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,0) then (.node 8 (fun _v => (.node 0 (fun _v => (.node 3 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 8 (fun _v => (.node 0 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_43 : solveChoices smallChoices13_43 (.full [4,3,3,3]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,3,3] (Equiv.refl (Fin 13)) smallB13_43 smallT13_43) smallFlag13_43 = 6 := by + decide +kernel + +lemma smallSupport13_43 : RowSquare [4,4,3,2] [4,4,4,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,3,3,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_43 smallT13_43 smallFlag13_43 smallChoices13_43 + change solveChoices smallChoices13_43 (.full [4,3,3,3]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,3,3] (Equiv.refl (Fin 13)) smallB13_43 smallT13_43) smallFlag13_43 ≠ 0 + rw [smallCert13_43] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_11.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_11.lean index 7b480504cf79c742ea8b28cf4014a67a441201a2..938418833ac3ce9fcb0fc6499c2633880e8c6a39 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_11.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_11.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 13 11. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_44 : Equiv.Perm (Fin 13) := Equiv.swap 8 9 * (Equiv.swap 9 3 * (Equiv.swap 8 0 * (Equiv.swap 2 1 * (Equiv.swap 2 6 * (Equiv.swap 3 12 * (Equiv.swap 2 4 * (Equiv.swap 1 11 * (Equiv.swap 0 10)))))))) -def smallT13_44 : Equiv.Perm (Fin 13) := Equiv.swap 9 5 * (Equiv.swap 5 7 * (Equiv.swap 7 10 * (Equiv.swap 6 3 * (Equiv.swap 5 4 * (Equiv.swap 4 8 * (Equiv.swap 3 1 * (Equiv.swap 2 0 * (Equiv.swap 1 12 * (Equiv.swap 0 11))))))))) -def smallFlag13_44 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,2),(0,1,0),(1,1,1),(2,1,3),(0,2,0),(0,2,1),(1,3,1),(1,3,3)} - -def smallChoices13_44 : EdgeChoices := (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 9 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,3,1) then (.node 6 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 6 (fun _v => (.node 3 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 6 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (1,3,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,3,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,3,1) then (.node 7 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 6 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) 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_ => .fallback)))))))))))))))))) else (.node 7 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 6 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,3,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (1,0,0) then 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(fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,3,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 6 (fun _v => 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=> .fallback)))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,2,0) then (.node 7 (fun _v => if 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.fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => (.node 6 (fun _v => if _v = (1,1,1) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 7 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 6 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,3,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (1,3,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,3,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 4 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => (.node 6 (fun _v => if _v = (1,1,1) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 7 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => (.node 6 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 6 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,3,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,3,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 6 (fun _v => (.node 4 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_44 : solveChoices smallChoices13_44 (.full [3,3,3,3,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,3,1] (Equiv.refl (Fin 13)) smallB13_44 smallT13_44) smallFlag13_44 = 6 := by - decide +kernel - -lemma smallSupport13_44 : RowSquare [4,4,3,2] [5,4,4] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,3,3,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_44 smallT13_44 smallFlag13_44 smallChoices13_44 - change solveChoices smallChoices13_44 (.full [3,3,3,3,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,3,1] (Equiv.refl (Fin 13)) smallB13_44 smallT13_44) smallFlag13_44 ≠ 0 - rw [smallCert13_44] - norm_num - -def smallB13_45 : Equiv.Perm (Fin 13) := Equiv.swap 8 1 * (Equiv.swap 9 11 * (Equiv.swap 8 5 * (Equiv.swap 5 3 * (Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 3 10 * (Equiv.swap 3 4 * (Equiv.swap 2 7 * (Equiv.swap 1 12 * (Equiv.swap 0 6)))))))))) -def smallT13_45 : Equiv.Perm (Fin 13) := Equiv.swap 11 10 * (Equiv.swap 10 7 * (Equiv.swap 7 4 * (Equiv.swap 5 9 * (Equiv.swap 4 2 * (Equiv.swap 2 12 * (Equiv.swap 1 0 * (Equiv.swap 0 8))))))) -def smallFlag13_45 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(2,0,2),(0,1,0),(2,1,0),(0,1,1),(1,2,1),(0,2,2),(1,2,3),(0,3,0),(1,3,3)} - -def smallChoices13_45 : EdgeChoices := (.node 11 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (2,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,1,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => if _v = (1,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,3) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (0,2,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => if _v = (1,2,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,3) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => if _v = (1,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,3) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (1,2,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => 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(fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 3 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,2,2) then (.node 3 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 4 (fun _v => if _v = (2,0,2) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => 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(fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))))) else if _v = (1,2,1) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 4 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,2,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))) -lemma smallCert13_45 : solveChoices smallChoices13_45 (.full [3,3,3,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,2,2] (Equiv.refl (Fin 13)) smallB13_45 smallT13_45) smallFlag13_45 = -4 := by - decide +kernel - -lemma smallSupport13_45 : RowSquare [4,4,3,2] [5,5,3] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,3,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_45 smallT13_45 smallFlag13_45 smallChoices13_45 - change solveChoices smallChoices13_45 (.full [3,3,3,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,2,2] (Equiv.refl (Fin 13)) smallB13_45 smallT13_45) smallFlag13_45 ≠ 0 - rw [smallCert13_45] - norm_num - -def smallB13_46 : Equiv.Perm (Fin 13) := Equiv.swap 6 5 * (Equiv.swap 6 11 * (Equiv.swap 6 0 * (Equiv.swap 5 3 * (Equiv.swap 4 9 * (Equiv.swap 3 12 * (Equiv.swap 2 8 * (Equiv.swap 0 10 * (Equiv.swap 0 1)))))))) -def smallT13_46 : Equiv.Perm (Fin 13) := Equiv.swap 11 10 * (Equiv.swap 10 0 * (Equiv.swap 0 12 * (Equiv.swap 0 3 * (Equiv.swap 0 6 * (Equiv.swap 6 8 * (Equiv.swap 3 2 * (Equiv.swap 0 7 * (Equiv.swap 3 5 * (Equiv.swap 2 9 * (Equiv.swap 0 4)))))))))) -def smallFlag13_46 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(0,0,2),(0,1,0),(0,1,2),(1,1,2),(2,1,3),(0,2,0),(2,2,0),(2,3,1),(0,3,3)} - -def smallChoices13_46 : EdgeChoices := (.node 12 (fun _v => 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=> (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,0) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun 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(fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))))))))))))))) -lemma smallCert13_46 : solveChoices smallChoices13_46 (.full [3,3,3,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,2,1,1] (Equiv.refl (Fin 13)) smallB13_46 smallT13_46) smallFlag13_46 = -8 := by - decide +kernel - -lemma smallSupport13_46 : RowSquare [4,4,3,2] [6,4,3] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,3,2,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_46 smallT13_46 smallFlag13_46 smallChoices13_46 - change solveChoices smallChoices13_46 (.full [3,3,3,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,2,1,1] (Equiv.refl (Fin 13)) smallB13_46 smallT13_46) smallFlag13_46 ≠ 0 - rw [smallCert13_46] - norm_num - -def smallB13_47 : Equiv.Perm (Fin 13) := Equiv.swap 5 10 * (Equiv.swap 10 0 * (Equiv.swap 0 1 * (Equiv.swap 0 7 * (Equiv.swap 5 4 * (Equiv.swap 4 11 * (Equiv.swap 1 12 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 6))))))))) -def smallT13_47 : Equiv.Perm (Fin 13) := Equiv.swap 11 8 * (Equiv.swap 8 5 * (Equiv.swap 8 4 * (Equiv.swap 5 6 * (Equiv.swap 6 3 * (Equiv.swap 5 0 * (Equiv.swap 4 10 * (Equiv.swap 3 12 * (Equiv.swap 0 1 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))))))) -def smallFlag13_47 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,2),(0,1,0),(1,1,1),(1,1,2),(1,2,0),(1,2,3),(0,3,1)} - -def smallChoices13_47 : EdgeChoices := (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 7 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,2,3) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => (.node 1 (fun _v => if _v = (1,1,1) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (1,2,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => (.node 1 (fun _v => if _v = (1,1,1) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 9 (fun _v => if _v = (0,1,0) then (.node 7 (fun _v => if _v = (1,1,1) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,3) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 7 (fun _v => if _v = (0,0,0) then (.node 7 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 7 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,3) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,3) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 7 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 7 (fun _ => .fallback)))))) else (.node 9 (fun _v => if _v = (0,0,0) then (.node 7 (fun _v => if _v = (1,1,1) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,3) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 7 (fun _ => .fallback)))) else (.node 7 (fun _v => if _v = (1,1,1) then (.node 7 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,3) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,3) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = 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(.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 7 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 7 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 7 (fun _ => .fallback)))))) else (.node 9 (fun _v => if _v = (0,0,0) then (.node 7 (fun _v => if _v = (1,1,1) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => 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.fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _ => .fallback)))) else (.node 7 (fun _v => if _v = (1,1,1) then (.node 7 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))))))))))) -lemma smallCert13_47 : solveChoices smallChoices13_47 (.full [2,2,2,2,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,2,2,2,1] (Equiv.refl (Fin 13)) smallB13_47 smallT13_47) smallFlag13_47 = -1 := by - decide +kernel - -lemma smallSupport13_47 : RowSquare [4,4,3,2] [7,6] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [2,2,2,2,2,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_47 smallT13_47 smallFlag13_47 smallChoices13_47 - change solveChoices smallChoices13_47 (.full [2,2,2,2,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,2,2,2,1] (Equiv.refl (Fin 13)) smallB13_47 smallT13_47) smallFlag13_47 ≠ 0 - rw [smallCert13_47] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 13 11. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_44 : Equiv.Perm (Fin 13) := Equiv.swap 8 9 * (Equiv.swap 9 3 * (Equiv.swap 8 0 * (Equiv.swap 2 1 * (Equiv.swap 2 6 * (Equiv.swap 3 12 * (Equiv.swap 2 4 * (Equiv.swap 1 11 * (Equiv.swap 0 10)))))))) +def smallT13_44 : Equiv.Perm (Fin 13) := Equiv.swap 9 5 * (Equiv.swap 5 7 * (Equiv.swap 7 10 * (Equiv.swap 6 3 * (Equiv.swap 5 4 * (Equiv.swap 4 8 * (Equiv.swap 3 1 * (Equiv.swap 2 0 * (Equiv.swap 1 12 * (Equiv.swap 0 11))))))))) +def smallFlag13_44 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,2),(0,1,0),(1,1,1),(2,1,3),(0,2,0),(0,2,1),(1,3,1),(1,3,3)} + +def smallChoices13_44 : EdgeChoices := (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 9 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,3,1) then (.node 6 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 6 (fun _v => (.node 3 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 6 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (1,3,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,3,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,3,1) then (.node 7 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 6 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) 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(.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_44 : solveChoices smallChoices13_44 (.full [3,3,3,3,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,3,1] (Equiv.refl (Fin 13)) smallB13_44 smallT13_44) smallFlag13_44 = 6 := by + decide +kernel + +lemma smallSupport13_44 : RowSquare [4,4,3,2] [5,4,4] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,3,3,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_44 smallT13_44 smallFlag13_44 smallChoices13_44 + change solveChoices smallChoices13_44 (.full [3,3,3,3,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,3,1] (Equiv.refl (Fin 13)) smallB13_44 smallT13_44) smallFlag13_44 ≠ 0 + rw [smallCert13_44] + norm_num + +def smallB13_45 : Equiv.Perm (Fin 13) := Equiv.swap 8 1 * (Equiv.swap 9 11 * (Equiv.swap 8 5 * (Equiv.swap 5 3 * (Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 3 10 * (Equiv.swap 3 4 * (Equiv.swap 2 7 * (Equiv.swap 1 12 * (Equiv.swap 0 6)))))))))) +def smallT13_45 : Equiv.Perm (Fin 13) := Equiv.swap 11 10 * (Equiv.swap 10 7 * (Equiv.swap 7 4 * (Equiv.swap 5 9 * (Equiv.swap 4 2 * (Equiv.swap 2 12 * (Equiv.swap 1 0 * (Equiv.swap 0 8))))))) +def smallFlag13_45 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(2,0,2),(0,1,0),(2,1,0),(0,1,1),(1,2,1),(0,2,2),(1,2,3),(0,3,0),(1,3,3)} + +def smallChoices13_45 : EdgeChoices := (.node 11 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (2,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,1,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => if _v = (1,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,3) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (0,2,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => if _v = (1,2,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,3) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => if _v = (1,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,3) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (1,2,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,1,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => if _v = (1,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,3) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 5 (fun _ => .fallback)))))) else if _v = (1,2,3) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (2,0,2) then (.node 5 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,3,0) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,1,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,2,2) then (.node 7 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 3 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if 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(fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 4 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,2,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))) +lemma smallCert13_45 : solveChoices smallChoices13_45 (.full [3,3,3,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,2,2] (Equiv.refl (Fin 13)) smallB13_45 smallT13_45) smallFlag13_45 = -4 := by + decide +kernel + +lemma smallSupport13_45 : RowSquare [4,4,3,2] [5,5,3] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,3,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_45 smallT13_45 smallFlag13_45 smallChoices13_45 + change solveChoices smallChoices13_45 (.full [3,3,3,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,2,2] (Equiv.refl (Fin 13)) smallB13_45 smallT13_45) smallFlag13_45 ≠ 0 + rw [smallCert13_45] + norm_num + +def smallB13_46 : Equiv.Perm (Fin 13) := Equiv.swap 6 5 * (Equiv.swap 6 11 * (Equiv.swap 6 0 * (Equiv.swap 5 3 * (Equiv.swap 4 9 * (Equiv.swap 3 12 * (Equiv.swap 2 8 * (Equiv.swap 0 10 * (Equiv.swap 0 1)))))))) +def smallT13_46 : Equiv.Perm (Fin 13) := Equiv.swap 11 10 * (Equiv.swap 10 0 * (Equiv.swap 0 12 * (Equiv.swap 0 3 * (Equiv.swap 0 6 * (Equiv.swap 6 8 * (Equiv.swap 3 2 * (Equiv.swap 0 7 * (Equiv.swap 3 5 * (Equiv.swap 2 9 * (Equiv.swap 0 4)))))))))) +def smallFlag13_46 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(0,0,2),(0,1,0),(0,1,2),(1,1,2),(2,1,3),(0,2,0),(2,2,0),(2,3,1),(0,3,3)} + +def smallChoices13_46 : EdgeChoices := (.node 12 (fun _v => if _v = (0,0,2) then (.node 11 (fun _ => (.node 9 (fun _ => .fallback)))) else if _v = (0,1,0) then (.node 9 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => (.node 7 (fun _v => if _v = (2,1,3) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,0) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,0) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,3) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (1,1,2) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,3) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,3) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (1,1,2) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,3) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => (.node 7 (fun _v => if _v = (2,1,3) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 7 (fun _v => if _v = (0,2,0) then (.node 3 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,0) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,3) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,2,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,2,0) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 7 (fun _v => if _v = (0,2,0) then (.node 3 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,3) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,2,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,3) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else (.node 11 (fun _v => (.node 9 (fun _v => if _v = (0,1,0) then (.node 8 (fun _v => if _v = (2,1,3) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 7 (fun _v => if _v = (0,2,0) then (.node 3 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,0) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,3) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,2,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,2,0) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => 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(fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 7 (fun _v => if _v = (2,1,3) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 3 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v 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(.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,3) then (.node 4 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (1,1,2) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => (.node 6 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,2,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (2,1,3) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,2,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))))))))))))))) +lemma smallCert13_46 : solveChoices smallChoices13_46 (.full [3,3,3,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,2,1,1] (Equiv.refl (Fin 13)) smallB13_46 smallT13_46) smallFlag13_46 = -8 := by + decide +kernel + +lemma smallSupport13_46 : RowSquare [4,4,3,2] [6,4,3] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,3,2,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_46 smallT13_46 smallFlag13_46 smallChoices13_46 + change solveChoices smallChoices13_46 (.full [3,3,3,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,2,1,1] (Equiv.refl (Fin 13)) smallB13_46 smallT13_46) smallFlag13_46 ≠ 0 + rw [smallCert13_46] + norm_num + +def smallB13_47 : Equiv.Perm (Fin 13) := Equiv.swap 5 10 * (Equiv.swap 10 0 * (Equiv.swap 0 1 * (Equiv.swap 0 7 * (Equiv.swap 5 4 * (Equiv.swap 4 11 * (Equiv.swap 1 12 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 6))))))))) +def smallT13_47 : Equiv.Perm (Fin 13) := Equiv.swap 11 8 * (Equiv.swap 8 5 * (Equiv.swap 8 4 * (Equiv.swap 5 6 * (Equiv.swap 6 3 * (Equiv.swap 5 0 * (Equiv.swap 4 10 * (Equiv.swap 3 12 * (Equiv.swap 0 1 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))))))) +def smallFlag13_47 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,2),(0,1,0),(1,1,1),(1,1,2),(1,2,0),(1,2,3),(0,3,1)} + +def smallChoices13_47 : EdgeChoices := (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 7 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,2,3) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => (.node 1 (fun _v => if _v = (1,1,1) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (1,2,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => (.node 1 (fun _v => if _v = (1,1,1) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 9 (fun _v => if _v = (0,1,0) then (.node 7 (fun _v => if _v = (1,1,1) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 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(0,0,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))))))))))) +lemma smallCert13_47 : solveChoices smallChoices13_47 (.full [2,2,2,2,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,2,2,2,1] (Equiv.refl (Fin 13)) smallB13_47 smallT13_47) smallFlag13_47 = -1 := by + decide +kernel + +lemma smallSupport13_47 : RowSquare [4,4,3,2] [7,6] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [2,2,2,2,2,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_47 smallT13_47 smallFlag13_47 smallChoices13_47 + change solveChoices smallChoices13_47 (.full [2,2,2,2,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,2,2,2,1] (Equiv.refl (Fin 13)) smallB13_47 smallT13_47) smallFlag13_47 ≠ 0 + rw [smallCert13_47] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_12.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_12.lean index 610795c84e9454a1ddfb6d021757b96f28edcd37..e2b6215ecad072854fb579c663e1e68c5f5558f4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_12.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_12.lean @@ -1,73 +1,73 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 13 12. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_48 : Equiv.Perm (Fin 13) := Equiv.swap 9 7 * (Equiv.swap 9 5 * (Equiv.swap 9 2 * (Equiv.swap 5 11 * (Equiv.swap 7 1 * (Equiv.swap 5 8 * (Equiv.swap 5 6 * (Equiv.swap 2 0 * (Equiv.swap 1 12 * (Equiv.swap 2 4 * (Equiv.swap 1 3 * (Equiv.swap 0 10))))))))))) -def smallT13_48 : Equiv.Perm (Fin 13) := Equiv.swap 10 1 * (Equiv.swap 1 3 * (Equiv.swap 1 5 * (Equiv.swap 1 8 * (Equiv.swap 3 11 * (Equiv.swap 5 9 * (Equiv.swap 1 7 * (Equiv.swap 3 6 * (Equiv.swap 1 4 * (Equiv.swap 0 2))))))))) -def smallFlag13_48 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,2),(0,0,3),(0,1,1),(1,1,2),(0,1,3),(0,2,0),(1,2,1),(0,3,1)} - -def smallChoices13_48 : EdgeChoices := (.node 12 (fun _v => if _v = (0,0,2) then (.node 11 (fun _v => if _v = (0,1,1) then (.node 6 (fun _v => if _v = (0,1,1) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (1,2,1) then (.node 6 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,1,3) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,3) then (.node 6 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 6 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 1 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 5 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,1) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (1,1,2) then (.node 5 (fun _v => (.node 4 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))))))) else (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 6 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,1,2) then (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,0) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (1,1,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then 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if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,2,1) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_48 : solveChoices smallChoices13_48 (.full [2,2,2,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_48 smallT13_48) smallFlag13_48 = -10 := by - decide +kernel - -lemma smallSupport13_48 : RowSquare [4,4,3,2] [8,5] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [2,2,2,2,2,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_48 smallT13_48 smallFlag13_48 smallChoices13_48 - change solveChoices smallChoices13_48 (.full [2,2,2,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_48 smallT13_48) smallFlag13_48 ≠ 0 - rw [smallCert13_48] - norm_num - -def smallB13_49 : Equiv.Perm (Fin 13) := Equiv.swap 4 12 * (Equiv.swap 4 7 * (Equiv.swap 7 9 * (Equiv.swap 6 0 * (Equiv.swap 4 8 * (Equiv.swap 4 5 * (Equiv.swap 2 1 * (Equiv.swap 2 3 * (Equiv.swap 1 11 * (Equiv.swap 0 10))))))))) -def smallT13_49 : Equiv.Perm (Fin 13) := Equiv.swap 6 3 * (Equiv.swap 6 0 * (Equiv.swap 6 9 * (Equiv.swap 7 1 * (Equiv.swap 6 2 * (Equiv.swap 3 11 * (Equiv.swap 3 5 * (Equiv.swap 2 8 * (Equiv.swap 1 12 * (Equiv.swap 0 10))))))))) -def smallFlag13_49 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(0,0,2),(0,0,3),(0,1,0),(1,1,0),(0,1,1),(0,2,0),(1,2,2),(0,2,3),(1,3,1)} - -def smallChoices13_49 : EdgeChoices := (.node 1 (fun _v => if _v = (0,0,1) then (.node 7 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,2,2) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 5 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,0) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => (.node 6 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => .fallback)) else if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => (.node 6 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 6 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => .fallback)) else if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => (.node 3 (fun _v => if 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.fallback)))))))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 7 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 0 (fun _v => if _v = 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=> if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 5 (fun _v => if _v = (1,2,2) then (.node 7 (fun _v => if _v = (0,0,1) then (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 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.fallback)))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_49 : solveChoices smallChoices13_49 (.full [2,2,2,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_49 smallT13_49) smallFlag13_49 = -3 := by - decide +kernel - -lemma smallSupport13_49 : RowSquare [4,4,3,2] [9,4] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [2,2,2,2,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_49 smallT13_49 smallFlag13_49 smallChoices13_49 - change solveChoices smallChoices13_49 (.full [2,2,2,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_49 smallT13_49) smallFlag13_49 ≠ 0 - rw [smallCert13_49] - norm_num - -def smallB13_50 : Equiv.Perm (Fin 13) := Equiv.swap 8 2 * (Equiv.swap 9 4 * (Equiv.swap 8 0 * (Equiv.swap 0 3 * (Equiv.swap 4 10 * (Equiv.swap 3 11 * (Equiv.swap 4 6 * (Equiv.swap 3 1 * (Equiv.swap 2 12 * (Equiv.swap 1 5 * (Equiv.swap 0 7)))))))))) -def smallT13_50 : Equiv.Perm (Fin 13) := Equiv.swap 11 5 * (Equiv.swap 7 6 * (Equiv.swap 5 3 * (Equiv.swap 7 0 * (Equiv.swap 6 10 * (Equiv.swap 5 8 * (Equiv.swap 0 2 * (Equiv.swap 3 12 * (Equiv.swap 2 9 * (Equiv.swap 0 4))))))))) -def smallFlag13_50 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,2),(0,0,3),(0,1,0),(1,1,1),(0,2,1),(0,2,2),(0,3,1),(0,3,3)} - -def smallChoices13_50 : EdgeChoices := (.node 12 (fun _v => if _v = (0,0,2) then (.node 11 (fun _v => (.node 10 (fun _v => if _v = (0,1,0) then (.node 6 (fun _v => if _v = (0,2,1) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 5 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,3,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 3 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 8 (fun _v => if _v = (0,1,0) then (.node 5 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,2,1) then (.node 3 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,3,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,2,1) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 3 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 6 (fun _v => (.node 8 (fun _v => (.node 5 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else (.node 11 (fun _v => if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 6 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,3,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,3,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,1,1) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,1,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,1) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,1) 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(fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => .fallback)))))))))))))))))) -lemma smallCert13_50 : solveChoices smallChoices13_50 (.full [2,2,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_50 smallT13_50) smallFlag13_50 = 12 := by - decide +kernel - -lemma smallSupport13_50 : RowSquare [4,4,3,2] [11,2] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [2,2,1,1,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_50 smallT13_50 smallFlag13_50 smallChoices13_50 - change solveChoices smallChoices13_50 (.full [2,2,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_50 smallT13_50) smallFlag13_50 ≠ 0 - rw [smallCert13_50] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 13 12. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_48 : Equiv.Perm (Fin 13) := Equiv.swap 9 7 * (Equiv.swap 9 5 * (Equiv.swap 9 2 * (Equiv.swap 5 11 * (Equiv.swap 7 1 * (Equiv.swap 5 8 * (Equiv.swap 5 6 * (Equiv.swap 2 0 * (Equiv.swap 1 12 * (Equiv.swap 2 4 * (Equiv.swap 1 3 * (Equiv.swap 0 10))))))))))) +def smallT13_48 : Equiv.Perm (Fin 13) := Equiv.swap 10 1 * (Equiv.swap 1 3 * (Equiv.swap 1 5 * (Equiv.swap 1 8 * (Equiv.swap 3 11 * (Equiv.swap 5 9 * (Equiv.swap 1 7 * (Equiv.swap 3 6 * (Equiv.swap 1 4 * (Equiv.swap 0 2))))))))) +def smallFlag13_48 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,2),(0,0,3),(0,1,1),(1,1,2),(0,1,3),(0,2,0),(1,2,1),(0,3,1)} + +def smallChoices13_48 : EdgeChoices := (.node 12 (fun _v => if _v = (0,0,2) then (.node 11 (fun _v => if _v = (0,1,1) then (.node 6 (fun _v => if _v = (0,1,1) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (1,2,1) then (.node 6 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,1,3) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,3) then (.node 6 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 6 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 1 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => .fallback)))) else if _v = (1,1,2) then (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 5 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun 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1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))))))) else (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 6 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,1,2) then (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,0) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (1,1,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then 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if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,2,1) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_48 : solveChoices smallChoices13_48 (.full [2,2,2,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_48 smallT13_48) smallFlag13_48 = -10 := by + decide +kernel + +lemma smallSupport13_48 : RowSquare [4,4,3,2] [8,5] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [2,2,2,2,2,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_48 smallT13_48 smallFlag13_48 smallChoices13_48 + change solveChoices smallChoices13_48 (.full [2,2,2,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_48 smallT13_48) smallFlag13_48 ≠ 0 + rw [smallCert13_48] + norm_num + +def smallB13_49 : Equiv.Perm (Fin 13) := Equiv.swap 4 12 * (Equiv.swap 4 7 * (Equiv.swap 7 9 * (Equiv.swap 6 0 * (Equiv.swap 4 8 * (Equiv.swap 4 5 * (Equiv.swap 2 1 * (Equiv.swap 2 3 * (Equiv.swap 1 11 * (Equiv.swap 0 10))))))))) +def smallT13_49 : Equiv.Perm (Fin 13) := Equiv.swap 6 3 * (Equiv.swap 6 0 * (Equiv.swap 6 9 * (Equiv.swap 7 1 * (Equiv.swap 6 2 * (Equiv.swap 3 11 * (Equiv.swap 3 5 * (Equiv.swap 2 8 * (Equiv.swap 1 12 * (Equiv.swap 0 10))))))))) +def smallFlag13_49 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(0,0,2),(0,0,3),(0,1,0),(1,1,0),(0,1,1),(0,2,0),(1,2,2),(0,2,3),(1,3,1)} + +def smallChoices13_49 : EdgeChoices := (.node 1 (fun _v => if _v = (0,0,1) then (.node 7 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,2,2) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 5 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,0) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => (.node 6 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => .fallback)) else if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => (.node 6 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 6 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => .fallback)) else if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => (.node 3 (fun _v => if 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.fallback)))))))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 7 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 0 (fun _v => if _v = 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=> if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 5 (fun _v => if _v = (1,2,2) then (.node 7 (fun _v => if _v = (0,0,1) then (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 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.fallback)))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _v => (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_49 : solveChoices smallChoices13_49 (.full [2,2,2,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_49 smallT13_49) smallFlag13_49 = -3 := by + decide +kernel + +lemma smallSupport13_49 : RowSquare [4,4,3,2] [9,4] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [2,2,2,2,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_49 smallT13_49 smallFlag13_49 smallChoices13_49 + change solveChoices smallChoices13_49 (.full [2,2,2,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,2,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_49 smallT13_49) smallFlag13_49 ≠ 0 + rw [smallCert13_49] + norm_num + +def smallB13_50 : Equiv.Perm (Fin 13) := Equiv.swap 8 2 * (Equiv.swap 9 4 * (Equiv.swap 8 0 * (Equiv.swap 0 3 * (Equiv.swap 4 10 * (Equiv.swap 3 11 * (Equiv.swap 4 6 * (Equiv.swap 3 1 * (Equiv.swap 2 12 * (Equiv.swap 1 5 * (Equiv.swap 0 7)))))))))) +def smallT13_50 : Equiv.Perm (Fin 13) := Equiv.swap 11 5 * (Equiv.swap 7 6 * (Equiv.swap 5 3 * (Equiv.swap 7 0 * (Equiv.swap 6 10 * (Equiv.swap 5 8 * (Equiv.swap 0 2 * (Equiv.swap 3 12 * (Equiv.swap 2 9 * (Equiv.swap 0 4))))))))) +def smallFlag13_50 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,2),(0,0,3),(0,1,0),(1,1,1),(0,2,1),(0,2,2),(0,3,1),(0,3,3)} + +def smallChoices13_50 : EdgeChoices := (.node 12 (fun _v => if _v = (0,0,2) then (.node 11 (fun _v => (.node 10 (fun _v => if _v = (0,1,0) then (.node 6 (fun _v => if _v = (0,2,1) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 5 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,3,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 3 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 8 (fun _v => if _v = (0,1,0) then (.node 5 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,2,1) then (.node 3 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,3,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,2,1) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 3 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 6 (fun _v => (.node 8 (fun _v => (.node 5 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else (.node 11 (fun _v => if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 6 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,3,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,3,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,1,1) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 4 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,1,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,1) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,1) 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(fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => .fallback)))))))))))))))))) +lemma smallCert13_50 : solveChoices smallChoices13_50 (.full [2,2,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_50 smallT13_50) smallFlag13_50 = 12 := by + decide +kernel + +lemma smallSupport13_50 : RowSquare [4,4,3,2] [11,2] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [2,2,1,1,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_50 smallT13_50 smallFlag13_50 smallChoices13_50 + change solveChoices smallChoices13_50 (.full [2,2,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [2,2,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_50 smallT13_50) smallFlag13_50 ≠ 0 + rw [smallCert13_50] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_2.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_2.lean index ee90d9926168b3b73e8673006370bac6a013437f..3a95c7d8c87e9cf8480aee12fc6e31a304832c4e 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_2.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_2.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 13 2. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_8 : Equiv.Perm (Fin 13) := Equiv.swap 7 5 * (Equiv.swap 7 6 * (Equiv.swap 5 4 * (Equiv.swap 7 10 * (Equiv.swap 6 11 * (Equiv.swap 5 9 * (Equiv.swap 4 3 * (Equiv.swap 3 12 * (Equiv.swap 2 0 * (Equiv.swap 0 8 * (Equiv.swap 0 1)))))))))) -def smallT13_8 : Equiv.Perm (Fin 13) := Equiv.swap 8 7 * (Equiv.swap 7 2 * (Equiv.swap 1 5 * (Equiv.swap 5 12 * (Equiv.swap 1 6 * (Equiv.swap 2 9 * (Equiv.swap 1 3 * (Equiv.swap 0 10))))))) -def smallFlag13_8 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(2,0,2),(4,0,3),(0,1,0),(3,1,0),(0,1,1),(1,1,3),(0,2,0),(0,2,2),(1,3,1),(2,3,2)} - -def smallChoices13_8 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 9 (fun _v => (.node 0 (fun _v => if _v = (4,0,3) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (3,1,0) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (1,3,1) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,1,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (4,0,3) then (.node 2 (fun _v => if _v = (3,1,0) then (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (3,1,0) then (.node 9 (fun _v => (.node 0 (fun _v => if _v = (4,0,3) then (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 9 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (4,0,3) then (.node 2 (fun _v => if _v = (3,1,0) then (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (4,0,3) then (.node 2 (fun _v => if _v = (3,1,0) then (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 9 (fun _v => (.node 0 (fun _v => if _v = (4,0,3) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (3,1,0) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (1,3,1) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,1,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (4,0,3) then (.node 2 (fun _v => if _v = (3,1,0) then (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 9 (fun _ => (.node 0 (fun _ => (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 9 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 8 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (3,1,0) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (1,3,1) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,1,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (3,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,1,3) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (3,1,0) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (1,3,1) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,1,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (3,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,1,3) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 9 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (4,0,3) then (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => .fallback)) else if _v = (3,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,0) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => .fallback)) else if _v = (3,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 9 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (3,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,1,3) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (3,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,1,3) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_8 : solveChoices smallChoices13_8 (.full [5,3,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_8 smallT13_8) smallFlag13_8 = 8 := by - decide +kernel - -lemma smallSupport13_8 : RowSquare [4,4,3,2] [7,2,2,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [5,3,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_8 smallT13_8 smallFlag13_8 smallChoices13_8 - change solveChoices smallChoices13_8 (.full [5,3,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_8 smallT13_8) smallFlag13_8 ≠ 0 - rw [smallCert13_8] - norm_num - -def smallB13_9 : Equiv.Perm (Fin 13) := Equiv.swap 5 8 * (Equiv.swap 8 4 * (Equiv.swap 4 0 * (Equiv.swap 4 7 * (Equiv.swap 5 1 * (Equiv.swap 4 6 * (Equiv.swap 3 11 * (Equiv.swap 1 10 * (Equiv.swap 1 2 * (Equiv.swap 0 12))))))))) -def smallT13_9 : Equiv.Perm (Fin 13) := Equiv.swap 11 8 * (Equiv.swap 8 0 * (Equiv.swap 0 7 * (Equiv.swap 8 10 * (Equiv.swap 7 3 * (Equiv.swap 0 2 * (Equiv.swap 3 12 * (Equiv.swap 2 9 * (Equiv.swap 0 4)))))))) -def smallFlag13_9 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,1),(2,0,2),(1,0,3),(0,1,1),(1,1,2),(0,2,0),(0,2,2),(1,2,3),(1,3,0),(3,3,0)} - -def smallChoices13_9 : EdgeChoices := (.node 3 (fun _v => if _v = (1,0,0) then (.node 8 (fun _v => (.node 0 (fun _v => (.node 9 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (1,3,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (4,0,1) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (4,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (0,1,1) then (.node 8 (fun _v => if _v = (1,0,0) then (.node 10 (fun _v => if _v = (0,1,1) then (.node 8 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => (.node 5 (fun _v => (.node 6 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,0,2) then (.node 0 (fun _v => if _v = (4,0,1) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else if _v = (4,0,1) then (.node 7 (fun _v => if _v = (0,2,2) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,0,3) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 1 (fun _v => if _v = (1,0,3) then (.node 1 (fun _v => if _v = (1,3,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (1,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (1,2,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else if _v = (1,0,3) then (.node 0 (fun _v => if _v = (1,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,2) then (.node 3 (fun _ => .fallback)) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else if _v = (1,0,3) then (.node 0 (fun _v => if _v = (1,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _ => .fallback)))))) else (.node 8 (fun _v => if _v = (0,1,1) then (.node 8 (fun _v => if _v = (1,0,3) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (4,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,0,2) then (.node 1 (fun _v => (.node 3 (fun _v => if _v = (1,2,3) then (.node 0 (fun _v => if _v = (1,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (1,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 3 (fun _v => if _v = (1,0,3) then (.node 0 (fun _v => if _v = (1,2,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (4,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))) else (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,3,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else if _v = (1,0,3) then (.node 0 (fun _v => if _v = (1,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (4,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (4,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else if _v = (1,0,3) then (.node 0 (fun _v => if _v = (1,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (4,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,2,0) then (.node 3 (fun _v => (.node 4 (fun _v => if _v = (1,0,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (4,0,1) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 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else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,3,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_9 : solveChoices smallChoices13_9 (.full [5,2,2,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,2,2,2] (Equiv.refl (Fin 13)) smallB13_9 smallT13_9) smallFlag13_9 = 28 := by - decide +kernel - -lemma smallSupport13_9 : RowSquare [4,4,3,2] [5,5,1,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [5,2,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_9 smallT13_9 smallFlag13_9 smallChoices13_9 - change solveChoices smallChoices13_9 (.full [5,2,2,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,2,2,2] (Equiv.refl (Fin 13)) smallB13_9 smallT13_9) smallFlag13_9 ≠ 0 - rw [smallCert13_9] - norm_num - -def smallB13_10 : Equiv.Perm (Fin 13) := Equiv.swap 0 6 * (Equiv.swap 6 4 * (Equiv.swap 4 12 * (Equiv.swap 0 2 * (Equiv.swap 6 10 * (Equiv.swap 5 3 * (Equiv.swap 4 8 * (Equiv.swap 3 1 * (Equiv.swap 2 11 * (Equiv.swap 1 9 * (Equiv.swap 0 7)))))))))) -def smallT13_10 : Equiv.Perm (Fin 13) := Equiv.swap 0 9 * (Equiv.swap 9 1 * (Equiv.swap 1 4 * (Equiv.swap 4 3 * (Equiv.swap 6 2 * (Equiv.swap 0 11 * (Equiv.swap 4 7 * (Equiv.swap 3 12 * (Equiv.swap 2 10 * (Equiv.swap 1 8 * (Equiv.swap 0 5)))))))))) -def smallFlag13_10 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,1),(0,0,2),(0,0,3),(0,1,0),(1,1,1),(0,1,3),(1,2,0),(2,2,2),(0,3,1),(3,3,2)} - -def smallChoices13_10 : EdgeChoices := (.node 2 (fun _v => if _v = (0,0,0) then (.node 8 (fun _v => (.node 8 (fun _v => if _v = (4,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else if _v = (0,1,3) then (.node 1 (fun _v => (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,1,3) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 5 (fun _v => if _v = (1,1,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 1 (fun _v => if _v = (0,1,3) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _ => (.node 6 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 7 (fun _ => .fallback)) else if _v = (0,1,3) then (.node 1 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => if _v = (0,0,2) then (.node 7 (fun _ => .fallback)) else (.node 7 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else if _v = (0,1,0) then (.node 8 (fun _v => (.node 8 (fun _v => if _v = (4,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else if _v = (0,1,3) then (.node 1 (fun _v => (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 5 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 5 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 8 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (4,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (4,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else if _v = (1,1,1) then (.node 5 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (4,0,1) then (.node 9 (fun _v => if _v = (0,1,0) then (.node 7 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (2,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (1,2,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => if _v = (1,2,0) then (.node 6 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 5 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else (.node 7 (fun _v => (.node 8 (fun _v => (.node 7 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => .fallback)) else (.node 4 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 3 (fun _v => if _v = (4,0,1) then (.node 7 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 7 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 6 (fun _v => if _v = (2,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (4,0,1) then (.node 0 (fun _ => (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 8 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (4,0,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (0,0,0) then (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (4,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 4 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (4,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))))))) else if _v = (1,2,0) then (.node 5 (fun _v => if _v = (4,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 5 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 5 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 5 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ 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(fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (1,1,1) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 7 (fun _ => .fallback)) else if _v = (4,0,1) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 6 (fun _v => if _v = (0,1,0) then (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => 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if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,0,2) then (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun _ => .fallback)))))))))) -lemma smallCert13_10 : solveChoices smallChoices13_10 (.full [5,2,2,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,2,2,1,1] (Equiv.refl (Fin 13)) smallB13_10 smallT13_10) smallFlag13_10 = -1 := by - decide +kernel - -lemma smallSupport13_10 : RowSquare [4,4,3,2] [6,4,1,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [5,2,2,2,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_10 smallT13_10 smallFlag13_10 smallChoices13_10 - change solveChoices smallChoices13_10 (.full [5,2,2,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,2,2,1,1] (Equiv.refl (Fin 13)) smallB13_10 smallT13_10) smallFlag13_10 ≠ 0 - rw [smallCert13_10] - norm_num - -def smallB13_11 : Equiv.Perm (Fin 13) := Equiv.swap 11 6 * (Equiv.swap 6 3 * (Equiv.swap 8 4 * (Equiv.swap 3 1 * (Equiv.swap 6 9 * (Equiv.swap 1 2 * (Equiv.swap 4 10 * (Equiv.swap 3 7 * (Equiv.swap 2 12 * (Equiv.swap 1 5))))))))) -def smallT13_11 : Equiv.Perm (Fin 13) := Equiv.swap 3 10 * (Equiv.swap 10 4 * (Equiv.swap 4 12 * (Equiv.swap 5 8 * (Equiv.swap 4 7 * (Equiv.swap 3 0 * (Equiv.swap 2 1 * (Equiv.swap 1 9 * (Equiv.swap 0 11)))))))) -def smallFlag13_11 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,2),(3,1,0),(0,1,1),(1,1,2),(2,1,3),(4,2,0),(1,2,1),(0,3,1),(0,3,3)} - -def smallChoices13_11 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (3,1,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 6 (fun _v => (.node 7 (fun _v => (.node 6 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (1,2,1) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,3,1) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,3,1) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = 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(.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,3,1) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_11 : solveChoices smallChoices13_11 (.full [5,2,2,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,2,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_11 smallT13_11) smallFlag13_11 = 1 := by - decide +kernel - -lemma smallSupport13_11 : RowSquare [4,4,3,2] [7,3,1,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [5,2,2,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_11 smallT13_11 smallFlag13_11 smallChoices13_11 - change solveChoices smallChoices13_11 (.full [5,2,2,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,2,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_11 smallT13_11) smallFlag13_11 ≠ 0 - rw [smallCert13_11] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 13 2. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_8 : Equiv.Perm (Fin 13) := Equiv.swap 7 5 * (Equiv.swap 7 6 * (Equiv.swap 5 4 * (Equiv.swap 7 10 * (Equiv.swap 6 11 * (Equiv.swap 5 9 * (Equiv.swap 4 3 * (Equiv.swap 3 12 * (Equiv.swap 2 0 * (Equiv.swap 0 8 * (Equiv.swap 0 1)))))))))) +def smallT13_8 : Equiv.Perm (Fin 13) := Equiv.swap 8 7 * (Equiv.swap 7 2 * (Equiv.swap 1 5 * (Equiv.swap 5 12 * (Equiv.swap 1 6 * (Equiv.swap 2 9 * (Equiv.swap 1 3 * (Equiv.swap 0 10))))))) +def smallFlag13_8 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(2,0,2),(4,0,3),(0,1,0),(3,1,0),(0,1,1),(1,1,3),(0,2,0),(0,2,2),(1,3,1),(2,3,2)} + +def smallChoices13_8 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 9 (fun _v => (.node 0 (fun _v => if _v = (4,0,3) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = 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=> (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ 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.fallback)))) else (.node 4 (fun _v => if _v = (4,0,3) then (.node 2 (fun _v => if _v = (3,1,0) then (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (2,0,2) then (.node 9 (fun _ => (.node 0 (fun _ => (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 9 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 8 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (3,1,0) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (1,3,1) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,1,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (3,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,1,3) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (3,1,0) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (1,3,1) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,1,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (3,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,1,3) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (2,0,2) then (.node 9 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (4,0,3) then (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => .fallback)) else if _v = (3,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,0) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => .fallback)) else if _v = (3,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 9 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (3,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,1,3) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 8 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (3,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,1,3) then (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 8 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_8 : solveChoices smallChoices13_8 (.full [5,3,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_8 smallT13_8) smallFlag13_8 = 8 := by + decide +kernel + +lemma smallSupport13_8 : RowSquare [4,4,3,2] [7,2,2,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [5,3,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_8 smallT13_8 smallFlag13_8 smallChoices13_8 + change solveChoices smallChoices13_8 (.full [5,3,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,3,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_8 smallT13_8) smallFlag13_8 ≠ 0 + rw [smallCert13_8] + norm_num + +def smallB13_9 : Equiv.Perm (Fin 13) := Equiv.swap 5 8 * (Equiv.swap 8 4 * (Equiv.swap 4 0 * (Equiv.swap 4 7 * (Equiv.swap 5 1 * (Equiv.swap 4 6 * (Equiv.swap 3 11 * (Equiv.swap 1 10 * (Equiv.swap 1 2 * (Equiv.swap 0 12))))))))) +def smallT13_9 : Equiv.Perm (Fin 13) := Equiv.swap 11 8 * (Equiv.swap 8 0 * (Equiv.swap 0 7 * (Equiv.swap 8 10 * (Equiv.swap 7 3 * (Equiv.swap 0 2 * (Equiv.swap 3 12 * (Equiv.swap 2 9 * (Equiv.swap 0 4)))))))) +def smallFlag13_9 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,1),(2,0,2),(1,0,3),(0,1,1),(1,1,2),(0,2,0),(0,2,2),(1,2,3),(1,3,0),(3,3,0)} + +def smallChoices13_9 : EdgeChoices := (.node 3 (fun _v => if _v = (1,0,0) then (.node 8 (fun _v => (.node 0 (fun _v => (.node 9 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (1,3,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (4,0,1) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (4,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (2,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (0,1,1) then (.node 8 (fun _v => if _v = (1,0,0) then (.node 10 (fun _v => if _v = (0,1,1) then (.node 8 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => (.node 5 (fun _v => (.node 6 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (2,0,2) then (.node 0 (fun _v => if _v = (4,0,1) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => .fallback)) else if _v = (4,0,1) then (.node 7 (fun _v => if _v = (0,2,2) then (.node 2 (fun _v => if _v = 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then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,3,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 9 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,0) then (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (4,0,1) then (.node 3 (fun _v => if _v = (1,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (4,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (4,0,1) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (4,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,3,0) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 6 (fun _v => (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (2,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,3,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,3,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_9 : solveChoices smallChoices13_9 (.full [5,2,2,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,2,2,2] (Equiv.refl (Fin 13)) smallB13_9 smallT13_9) smallFlag13_9 = 28 := by + decide +kernel + +lemma smallSupport13_9 : RowSquare [4,4,3,2] [5,5,1,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [5,2,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_9 smallT13_9 smallFlag13_9 smallChoices13_9 + change solveChoices smallChoices13_9 (.full [5,2,2,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,2,2,2] (Equiv.refl (Fin 13)) smallB13_9 smallT13_9) smallFlag13_9 ≠ 0 + rw [smallCert13_9] + norm_num + +def smallB13_10 : Equiv.Perm (Fin 13) := Equiv.swap 0 6 * (Equiv.swap 6 4 * (Equiv.swap 4 12 * (Equiv.swap 0 2 * (Equiv.swap 6 10 * (Equiv.swap 5 3 * (Equiv.swap 4 8 * (Equiv.swap 3 1 * (Equiv.swap 2 11 * (Equiv.swap 1 9 * (Equiv.swap 0 7)))))))))) +def smallT13_10 : Equiv.Perm (Fin 13) := Equiv.swap 0 9 * (Equiv.swap 9 1 * (Equiv.swap 1 4 * (Equiv.swap 4 3 * (Equiv.swap 6 2 * (Equiv.swap 0 11 * (Equiv.swap 4 7 * (Equiv.swap 3 12 * (Equiv.swap 2 10 * (Equiv.swap 1 8 * (Equiv.swap 0 5)))))))))) +def smallFlag13_10 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,1),(0,0,2),(0,0,3),(0,1,0),(1,1,1),(0,1,3),(1,2,0),(2,2,2),(0,3,1),(3,3,2)} + +def smallChoices13_10 : EdgeChoices := (.node 2 (fun _v => if _v = (0,0,0) then (.node 8 (fun _v => (.node 8 (fun _v => if _v = (4,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else if _v = (0,1,3) then (.node 1 (fun _v => (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,1,3) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 5 (fun _v => if _v = (1,1,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 1 (fun _v => if _v = (0,1,3) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _ => (.node 6 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 7 (fun _ => .fallback)) else if _v = (0,1,3) then (.node 1 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => if _v = (0,0,2) then (.node 7 (fun _ => .fallback)) else (.node 7 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else if _v = (0,1,0) then (.node 8 (fun _v => (.node 8 (fun _v => if _v = (4,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else if _v = (0,1,3) then (.node 1 (fun _v => (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 5 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 5 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 8 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (4,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (4,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else if _v = (1,1,1) then (.node 5 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (4,0,1) then (.node 9 (fun _v => if _v = (0,1,0) then (.node 7 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (2,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (1,2,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => if _v = (1,2,0) then (.node 6 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 5 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else (.node 7 (fun _v => (.node 8 (fun _v => (.node 7 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => .fallback)) else (.node 4 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if 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if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,0,2) then (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun _ => .fallback)))))))))) +lemma smallCert13_10 : solveChoices smallChoices13_10 (.full [5,2,2,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,2,2,1,1] (Equiv.refl (Fin 13)) smallB13_10 smallT13_10) smallFlag13_10 = -1 := by + decide +kernel + +lemma smallSupport13_10 : RowSquare [4,4,3,2] [6,4,1,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [5,2,2,2,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_10 smallT13_10 smallFlag13_10 smallChoices13_10 + change solveChoices smallChoices13_10 (.full [5,2,2,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,2,2,1,1] (Equiv.refl (Fin 13)) smallB13_10 smallT13_10) smallFlag13_10 ≠ 0 + rw [smallCert13_10] + norm_num + +def smallB13_11 : Equiv.Perm (Fin 13) := Equiv.swap 11 6 * (Equiv.swap 6 3 * (Equiv.swap 8 4 * (Equiv.swap 3 1 * (Equiv.swap 6 9 * (Equiv.swap 1 2 * (Equiv.swap 4 10 * (Equiv.swap 3 7 * (Equiv.swap 2 12 * (Equiv.swap 1 5))))))))) +def smallT13_11 : Equiv.Perm (Fin 13) := Equiv.swap 3 10 * (Equiv.swap 10 4 * (Equiv.swap 4 12 * (Equiv.swap 5 8 * (Equiv.swap 4 7 * (Equiv.swap 3 0 * (Equiv.swap 2 1 * (Equiv.swap 1 9 * (Equiv.swap 0 11)))))))) +def smallFlag13_11 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,2),(3,1,0),(0,1,1),(1,1,2),(2,1,3),(4,2,0),(1,2,1),(0,3,1),(0,3,3)} + +def smallChoices13_11 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (3,1,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 6 (fun _v => (.node 7 (fun _v => (.node 6 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (1,2,1) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,3,1) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,3,1) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,1,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 5 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,3,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 5 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,3,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => (.node 5 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,3,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => (.node 5 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,3,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 6 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))))) else (.node 9 (fun _v => if _v = (0,0,2) then (.node 8 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (3,1,0) then (.node 0 (fun _v => (.node 6 (fun _v => (.node 7 (fun _v => (.node 6 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 6 (fun _ => (.node 7 (fun _ => .fallback)))) else (.node 8 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,0,2) then (.node 0 (fun _v => if _v = (3,1,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (4,2,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 6 (fun _ => .fallback)))))) else (.node 4 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (1,2,1) then (.node 5 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,3,1) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,3,1) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 6 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))))) else (.node 9 (fun _v => if _v = (0,0,0) then (.node 8 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (3,1,0) then (.node 0 (fun _v => if _v = (4,2,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 6 (fun _ => .fallback)))))) else (.node 4 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 0 (fun _v => if _v = (3,1,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 6 (fun _ => .fallback)))))) else (.node 8 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _v => (.node 2 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 1 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (3,1,0) then (.node 6 (fun _v => (.node 7 (fun _v => (.node 6 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,3,1) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_11 : solveChoices smallChoices13_11 (.full [5,2,2,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,2,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_11 smallT13_11) smallFlag13_11 = 1 := by + decide +kernel + +lemma smallSupport13_11 : RowSquare [4,4,3,2] [7,3,1,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [5,2,2,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_11 smallT13_11 smallFlag13_11 smallChoices13_11 + change solveChoices smallChoices13_11 (.full [5,2,2,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,2,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_11 smallT13_11) smallFlag13_11 ≠ 0 + rw [smallCert13_11] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_3.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_3.lean index 22c14183616660cb87648a506d1d646ba0319668..20f0a844cbec2d9755cb0525f82d7687573c84b0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_3.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_3.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 13 3. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_12 : Equiv.Perm (Fin 13) := Equiv.swap 9 6 * (Equiv.swap 9 2 * (Equiv.swap 2 11 * (Equiv.swap 7 4 * (Equiv.swap 6 3 * (Equiv.swap 2 0 * (Equiv.swap 4 1 * (Equiv.swap 3 12 * (Equiv.swap 2 5 * (Equiv.swap 1 10 * (Equiv.swap 0 8)))))))))) -def smallT13_12 : Equiv.Perm (Fin 13) := Equiv.swap 2 11 * (Equiv.swap 9 0 * (Equiv.swap 6 8 * (Equiv.swap 0 12 * (Equiv.swap 2 10 * (Equiv.swap 3 7 * (Equiv.swap 2 4 * (Equiv.swap 0 5 * (Equiv.swap 0 1)))))))) -def smallFlag13_12 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,2),(0,1,0),(0,1,1),(0,1,2),(4,2,1),(0,2,3),(3,3,0),(0,3,1)} - -def smallChoices13_12 : EdgeChoices := (.node 3 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 9 (fun _v => if _v = (4,2,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 9 (fun _v => if _v = (4,2,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,2) then (.node 9 (fun _v => if _v = (4,2,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 9 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => if _v = (4,2,1) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 5 (fun _ => .fallback)))) else if _v = (0,1,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 5 (fun _v => (.node 9 (fun _v => if _v = (4,2,1) then (.node 8 (fun _v => (.node 0 (fun _v => if _v = (3,3,0) then (.node 6 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => .fallback)) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 5 (fun _v => (.node 6 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (4,2,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (4,2,1) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (3,3,0) then (.node 5 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 6 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 5 (fun _v => if _v = (0,0,1) then (.node 9 (fun _v => (.node 8 (fun _v => (.node 0 (fun _v => if _v = (4,2,1) then (.node 6 (fun _v => if _v = (1,0,0) then (.node 5 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (2,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 8 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (4,2,1) then (.node 6 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (4,2,1) then (.node 6 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 5 (fun _v => (.node 6 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (4,2,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (4,2,1) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (3,3,0) then (.node 5 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 6 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 9 (fun _v => if _v = (4,2,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 9 (fun _v => if _v = (4,2,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))))) else if _v = (0,1,2) then (.node 9 (fun _v => if _v = (4,2,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 9 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => (.node 6 (fun _v => if _v = (0,0,1) then (.node 8 (fun _v => if _v = (4,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 6 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 3 (fun _ => .fallback)))))))))))))))))) -lemma smallCert13_12 : solveChoices smallChoices13_12 (.full [5,2,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_12 smallT13_12) smallFlag13_12 = -6 := by - decide +kernel - -lemma smallSupport13_12 : RowSquare [4,4,3,2] [8,2,1,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [5,2,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_12 smallT13_12 smallFlag13_12 smallChoices13_12 - change solveChoices smallChoices13_12 (.full [5,2,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_12 smallT13_12) smallFlag13_12 ≠ 0 - rw [smallCert13_12] - norm_num - -def smallB13_13 : Equiv.Perm (Fin 13) := Equiv.swap 0 8 * (Equiv.swap 8 11 * (Equiv.swap 1 10 * (Equiv.swap 1 7 * (Equiv.swap 0 9 * (Equiv.swap 1 5 * (Equiv.swap 0 2)))))) -def smallT13_13 : Equiv.Perm (Fin 13) := Equiv.swap 2 8 * (Equiv.swap 7 6 * (Equiv.swap 8 3 * (Equiv.swap 7 4 * (Equiv.swap 6 5 * (Equiv.swap 5 1 * (Equiv.swap 4 9 * (Equiv.swap 3 12 * (Equiv.swap 2 10 * (Equiv.swap 1 11))))))))) -def smallFlag13_13 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(0,0,2),(0,1,0),(0,1,1),(2,1,1),(1,1,3),(0,2,1),(0,2,2),(4,3,2),(0,3,3)} - -def smallChoices13_13 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 8 (fun _v => (.node 2 (fun _v => if _v = (1,1,3) then (.node 4 (fun _v => if _v = (3,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 6 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 8 (fun _v => (.node 9 (fun _v => if _v = (2,1,1) then (.node 7 (fun _v => (.node 3 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 2 (fun _v => if _v = (2,1,1) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 8 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (1,1,3) then (.node 4 (fun _v => if _v = (3,0,0) then (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 6 (fun _ => (.node 6 (fun _ => (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))))))) else if _v = (3,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 8 (fun _v => if _v = (0,2,1) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (0,0,2) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 5 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (0,0,2) then (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) 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0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (3,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (3,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 8 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => if _v = (1,1,3) then (.node 4 (fun _v => if _v = (2,1,1) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 6 (fun _ => (.node 6 (fun _ => .fallback)))))) else if _v = (2,1,1) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 8 (fun _v => if _v = (0,2,1) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (0,0,2) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 4 (fun _v => 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(fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 5 (fun _ => .fallback)))))))) else (.node 8 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,0) then (.node 4 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 5 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,1,3) then (.node 4 (fun _v => if _v = (2,1,1) then (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 6 (fun _ => (.node 6 (fun _ => .fallback)))))))))))) -lemma smallCert13_13 : solveChoices smallChoices13_13 (.full [5,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_13 smallT13_13) smallFlag13_13 = -16 := by - decide +kernel - -lemma smallSupport13_13 : RowSquare [4,4,3,2] [9,1,1,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [5,1,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_13 smallT13_13 smallFlag13_13 smallChoices13_13 - change solveChoices smallChoices13_13 (.full [5,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [5,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_13 smallT13_13) smallFlag13_13 ≠ 0 - rw [smallCert13_13] - norm_num - -def smallB13_14 : Equiv.Perm (Fin 13) := Equiv.swap 2 12 * (Equiv.swap 7 0 * (Equiv.swap 3 1 * (Equiv.swap 3 5 * (Equiv.swap 2 8 * (Equiv.swap 1 10 * (Equiv.swap 0 9)))))) -def smallT13_14 : Equiv.Perm (Fin 13) := Equiv.swap 6 8 * (Equiv.swap 8 12 * (Equiv.swap 3 10 * (Equiv.swap 6 0 * (Equiv.swap 5 2 * (Equiv.swap 0 9 * (Equiv.swap 3 7 * (Equiv.swap 2 11 * (Equiv.swap 0 4)))))))) -def smallFlag13_14 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,1,1),(1,1,2),(2,1,2),(0,1,3),(0,2,0),(0,2,2),(3,2,3),(2,3,0),(3,3,1)} - -def smallChoices13_14 : EdgeChoices := (.node 8 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (2,1,1) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 7 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => (.node 6 (fun _v => if _v = (1,1,2) then (.node 4 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _v => if _v = (3,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _v => if _v = (3,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = 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(1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = 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0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 7 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => (.node 6 (fun _v => if _v = (1,1,2) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,1) then (.node 0 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,3) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,2) then (.node 0 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,3) then (.node 2 (fun _ => .fallback)) else 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then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => (.node 6 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,3) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else if _v = (1,1,2) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (3,2,3) then (.node 6 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))) else if _v = (1,1,2) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (1,1,2) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (3,2,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 6 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (1,1,2) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (3,2,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 6 (fun _v => if _v = (1,1,2) then (.node 5 (fun _v => if _v = (2,1,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,3) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 6 (fun _ => .fallback)))) else (.node 7 (fun _v => (.node 0 (fun _v => (.node 5 (fun _v => if _v = (2,1,2) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _v => if _v = (3,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_14 : solveChoices smallChoices13_14 (.full [4,4,3,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,3,1,1] (Equiv.refl (Fin 13)) smallB13_14 smallT13_14) smallFlag13_14 = 70 := by - decide +kernel - -lemma smallSupport13_14 : RowSquare [4,4,3,2] [5,3,3,2] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,4,3,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_14 smallT13_14 smallFlag13_14 smallChoices13_14 - change solveChoices smallChoices13_14 (.full [4,4,3,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,3,1,1] (Equiv.refl (Fin 13)) smallB13_14 smallT13_14) smallFlag13_14 ≠ 0 - rw [smallCert13_14] - norm_num - -def smallB13_15 : Equiv.Perm (Fin 13) := Equiv.swap 7 2 * (Equiv.swap 2 12 * (Equiv.swap 2 10 * (Equiv.swap 2 9 * (Equiv.swap 7 11 * (Equiv.swap 5 3 * (Equiv.swap 3 0 * (Equiv.swap 2 8 * (Equiv.swap 0 6 * (Equiv.swap 0 1))))))))) -def smallT13_15 : Equiv.Perm (Fin 13) := Equiv.swap 3 7 * (Equiv.swap 7 6 * (Equiv.swap 3 11 * (Equiv.swap 6 12 * (Equiv.swap 7 0 * (Equiv.swap 6 8 * (Equiv.swap 3 1 * (Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 1 9 * (Equiv.swap 0 10)))))))))) -def smallFlag13_15 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(3,0,2),(1,1,2),(1,1,3),(3,1,3),(2,2,0),(0,2,1),(2,2,1),(0,3,0)} - -def smallChoices13_15 : EdgeChoices := (.node 8 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,2,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,2,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,1,3) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else if _v = (1,1,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,1,2) 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(.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 4 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (3,0,2) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,1,3) then (.node 3 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (3,0,2) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 5 (fun _v => if _v = (3,1,3) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))))) -lemma smallCert13_15 : solveChoices smallChoices13_15 (.full [4,4,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,2,2,1] (Equiv.refl (Fin 13)) smallB13_15 smallT13_15) smallFlag13_15 = -1 := by - decide +kernel - -lemma smallSupport13_15 : RowSquare [4,4,3,2] [5,4,2,2] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,4,2,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_15 smallT13_15 smallFlag13_15 smallChoices13_15 - change solveChoices smallChoices13_15 (.full [4,4,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,2,2,1] (Equiv.refl (Fin 13)) smallB13_15 smallT13_15) smallFlag13_15 ≠ 0 - rw [smallCert13_15] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 13 3. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_12 : Equiv.Perm (Fin 13) := Equiv.swap 9 6 * (Equiv.swap 9 2 * (Equiv.swap 2 11 * (Equiv.swap 7 4 * (Equiv.swap 6 3 * (Equiv.swap 2 0 * (Equiv.swap 4 1 * (Equiv.swap 3 12 * (Equiv.swap 2 5 * (Equiv.swap 1 10 * (Equiv.swap 0 8)))))))))) +def smallT13_12 : Equiv.Perm (Fin 13) := Equiv.swap 2 11 * (Equiv.swap 9 0 * (Equiv.swap 6 8 * (Equiv.swap 0 12 * (Equiv.swap 2 10 * (Equiv.swap 3 7 * (Equiv.swap 2 4 * (Equiv.swap 0 5 * (Equiv.swap 0 1)))))))) +def smallFlag13_12 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,2),(0,1,0),(0,1,1),(0,1,2),(4,2,1),(0,2,3),(3,3,0),(0,3,1)} + +def smallChoices13_12 : EdgeChoices := (.node 3 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 9 (fun _v => if _v = (4,2,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) 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.fallback)))))))))))))))))))))) else (.node 5 (fun _ => .fallback)))) else if _v = (0,1,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 5 (fun _v => (.node 9 (fun _v => if _v = (4,2,1) then (.node 8 (fun _v => (.node 0 (fun _v => if _v = (3,3,0) then (.node 6 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => .fallback)) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 5 (fun _v => (.node 6 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (4,2,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (4,2,1) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (3,3,0) then (.node 5 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => 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3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 6 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 9 (fun _v => if _v = (4,2,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 9 (fun _v => if _v = (4,2,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))))) else if _v = (0,1,2) then (.node 9 (fun _v => if _v = (4,2,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 9 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => (.node 6 (fun _v => if _v = (0,0,1) then (.node 8 (fun _v => if _v = (4,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 6 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 3 (fun _ => .fallback)))))))))))))))))) +lemma smallCert13_12 : solveChoices smallChoices13_12 (.full [5,2,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_12 smallT13_12) smallFlag13_12 = -6 := by + decide +kernel + +lemma smallSupport13_12 : RowSquare [4,4,3,2] [8,2,1,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [5,2,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_12 smallT13_12 smallFlag13_12 smallChoices13_12 + change solveChoices smallChoices13_12 (.full [5,2,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,2,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_12 smallT13_12) smallFlag13_12 ≠ 0 + rw [smallCert13_12] + norm_num + +def smallB13_13 : Equiv.Perm (Fin 13) := Equiv.swap 0 8 * (Equiv.swap 8 11 * (Equiv.swap 1 10 * (Equiv.swap 1 7 * (Equiv.swap 0 9 * (Equiv.swap 1 5 * (Equiv.swap 0 2)))))) +def smallT13_13 : Equiv.Perm (Fin 13) := Equiv.swap 2 8 * (Equiv.swap 7 6 * (Equiv.swap 8 3 * (Equiv.swap 7 4 * (Equiv.swap 6 5 * (Equiv.swap 5 1 * (Equiv.swap 4 9 * (Equiv.swap 3 12 * (Equiv.swap 2 10 * (Equiv.swap 1 11))))))))) +def smallFlag13_13 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(0,0,2),(0,1,0),(0,1,1),(2,1,1),(1,1,3),(0,2,1),(0,2,2),(4,3,2),(0,3,3)} + +def smallChoices13_13 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 8 (fun _v => (.node 2 (fun _v => if _v = (1,1,3) then (.node 4 (fun _v => if _v = (3,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 6 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 8 (fun _v => (.node 9 (fun _v => if _v = (2,1,1) then (.node 7 (fun _v => (.node 3 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 2 (fun _v => if _v = (2,1,1) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 8 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (1,1,3) then (.node 4 (fun _v => if _v = (3,0,0) then (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 6 (fun _ => (.node 6 (fun _ => (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))))))) else if _v = (3,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 8 (fun _v => if _v = (0,2,1) then (.node 3 (fun 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(fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (0,0,2) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 5 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (0,0,2) then (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,2) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (0,0,2) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 8 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 4 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) 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.fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 6 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 8 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (3,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ 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if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 5 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 8 (fun _v => if _v = (0,2,1) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 5 (fun _ => .fallback)))))))) else (.node 8 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,0) then (.node 4 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 5 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,1,3) then (.node 4 (fun _v => if _v = (2,1,1) then (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 6 (fun _ => (.node 6 (fun _ => .fallback)))))))))))) +lemma smallCert13_13 : solveChoices smallChoices13_13 (.full [5,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_13 smallT13_13) smallFlag13_13 = -16 := by + decide +kernel + +lemma smallSupport13_13 : RowSquare [4,4,3,2] [9,1,1,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [5,1,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_13 smallT13_13 smallFlag13_13 smallChoices13_13 + change solveChoices smallChoices13_13 (.full [5,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [5,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_13 smallT13_13) smallFlag13_13 ≠ 0 + rw [smallCert13_13] + norm_num + +def smallB13_14 : Equiv.Perm (Fin 13) := Equiv.swap 2 12 * (Equiv.swap 7 0 * (Equiv.swap 3 1 * (Equiv.swap 3 5 * (Equiv.swap 2 8 * (Equiv.swap 1 10 * (Equiv.swap 0 9)))))) +def smallT13_14 : Equiv.Perm (Fin 13) := Equiv.swap 6 8 * (Equiv.swap 8 12 * (Equiv.swap 3 10 * (Equiv.swap 6 0 * (Equiv.swap 5 2 * (Equiv.swap 0 9 * (Equiv.swap 3 7 * (Equiv.swap 2 11 * (Equiv.swap 0 4)))))))) +def smallFlag13_14 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,1,1),(1,1,2),(2,1,2),(0,1,3),(0,2,0),(0,2,2),(3,2,3),(2,3,0),(3,3,1)} + +def smallChoices13_14 : EdgeChoices := (.node 8 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (2,1,1) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 7 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => (.node 6 (fun _v => if _v = (1,1,2) then (.node 4 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _v => if _v = (3,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _v => if _v = (3,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,0) then (.node 7 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => (.node 6 (fun _v => if _v = (1,1,2) then (.node 4 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _v => if _v = (3,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _v => if _v = (3,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 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(fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (1,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,3) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,1) then (.node 0 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,3) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = 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then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => (.node 6 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,3) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else if _v = (1,1,2) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (3,2,3) then (.node 6 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))) else if _v = (1,1,2) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (1,1,2) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (3,2,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 6 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (1,1,2) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (3,2,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 6 (fun _v => if _v = (1,1,2) then (.node 5 (fun _v => if _v = (2,1,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,3) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 6 (fun _ => .fallback)))) else (.node 7 (fun _v => (.node 0 (fun _v => (.node 5 (fun _v => if _v = (2,1,2) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _v => if _v = (3,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_14 : solveChoices smallChoices13_14 (.full [4,4,3,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,3,1,1] (Equiv.refl (Fin 13)) smallB13_14 smallT13_14) smallFlag13_14 = 70 := by + decide +kernel + +lemma smallSupport13_14 : RowSquare [4,4,3,2] [5,3,3,2] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,4,3,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_14 smallT13_14 smallFlag13_14 smallChoices13_14 + change solveChoices smallChoices13_14 (.full [4,4,3,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,3,1,1] (Equiv.refl (Fin 13)) smallB13_14 smallT13_14) smallFlag13_14 ≠ 0 + rw [smallCert13_14] + norm_num + +def smallB13_15 : Equiv.Perm (Fin 13) := Equiv.swap 7 2 * (Equiv.swap 2 12 * (Equiv.swap 2 10 * (Equiv.swap 2 9 * (Equiv.swap 7 11 * (Equiv.swap 5 3 * (Equiv.swap 3 0 * (Equiv.swap 2 8 * (Equiv.swap 0 6 * (Equiv.swap 0 1))))))))) +def smallT13_15 : Equiv.Perm (Fin 13) := Equiv.swap 3 7 * (Equiv.swap 7 6 * (Equiv.swap 3 11 * (Equiv.swap 6 12 * (Equiv.swap 7 0 * (Equiv.swap 6 8 * (Equiv.swap 3 1 * (Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 1 9 * (Equiv.swap 0 10)))))))))) +def smallFlag13_15 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(3,0,2),(1,1,2),(1,1,3),(3,1,3),(2,2,0),(0,2,1),(2,2,1),(0,3,0)} + +def smallChoices13_15 : EdgeChoices := (.node 8 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (2,2,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,2,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,1,3) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else if _v = (1,1,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,1,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,3) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (3,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (3,0,2) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,1,3) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (3,0,2) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,3) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (3,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,1,2) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (3,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (3,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 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4 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))))) else if _v = (1,1,3) then (.node 2 (fun _v => if _v = (2,2,0) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => (.node 4 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 7 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,2,0) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 5 (fun _v => if _v = (3,1,3) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (3,0,2) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => .fallback)) else if _v = (1,1,3) then (.node 0 (fun _ => .fallback)) else (.node 3 (fun _v => if _v = (1,1,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (3,0,2) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,1,3) then (.node 3 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,1,3) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 4 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (3,0,2) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (3,0,2) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (3,0,2) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,1,3) then (.node 3 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 4 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (3,0,2) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,1,3) then (.node 3 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (3,0,2) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 5 (fun _v => if _v = (3,1,3) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))))) +lemma smallCert13_15 : solveChoices smallChoices13_15 (.full [4,4,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,2,2,1] (Equiv.refl (Fin 13)) smallB13_15 smallT13_15) smallFlag13_15 = -1 := by + decide +kernel + +lemma smallSupport13_15 : RowSquare [4,4,3,2] [5,4,2,2] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,4,2,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_15 smallT13_15 smallFlag13_15 smallChoices13_15 + change solveChoices smallChoices13_15 (.full [4,4,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,2,2,1] (Equiv.refl (Fin 13)) smallB13_15 smallT13_15) smallFlag13_15 ≠ 0 + rw [smallCert13_15] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_4.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_4.lean index a1cc5f1325cd99c535853e73ce2e66bdf16560f5..5951a158fd397eb7c7d5703dd9e10d883223fc31 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_4.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_4.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 13 4. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_16 : Equiv.Perm (Fin 13) := Equiv.swap 3 9 * (Equiv.swap 9 11 * (Equiv.swap 3 6 * (Equiv.swap 6 5 * (Equiv.swap 6 2 * (Equiv.swap 5 0 * (Equiv.swap 3 8 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 0 10)))))))))) -def smallT13_16 : Equiv.Perm (Fin 13) := Equiv.swap 2 5 * (Equiv.swap 9 12 * (Equiv.swap 5 11 * (Equiv.swap 5 3 * (Equiv.swap 2 10 * (Equiv.swap 3 7 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 4)))))))) -def smallFlag13_16 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,2),(2,0,3),(0,1,0),(3,1,0),(1,1,1),(0,1,3),(1,2,1),(2,2,2),(3,3,0),(0,3,1)} - -def smallChoices13_16 : EdgeChoices := (.node 9 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => (.node 8 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (2,0,3) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => .fallback)) else if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (2,0,3) then (.node 0 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => .fallback)) else if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (2,2,2) then (.node 0 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else if _v = (2,2,2) then (.node 1 (fun _v => if _v = (3,3,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (2,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 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(.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (2,0,3) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (3,1,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (3,1,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (2,0,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 2 (fun _v => if _v = (3,1,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,3) then (.node 4 (fun _v => if _v = (3,3,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (2,0,3) then (.node 1 (fun _v => if _v = (3,3,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 3 (fun _ => .fallback)))) else if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,3) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if 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(.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (3,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 2 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (2,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (0,1,3) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 0 (fun _v => if _v = (2,0,3) then (.node 0 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (3,1,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (2,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (2,0,3) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,1) then (.node 0 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => .fallback)) else if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 4 (fun _v => if _v = (2,0,3) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (2,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => if _v = (3,3,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 4 (fun _v => if _v = (3,3,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (1,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 2 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (3,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else if _v = (0,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_16 : solveChoices smallChoices13_16 (.full [4,4,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_16 smallT13_16) smallFlag13_16 = 1 := by - decide +kernel - -lemma smallSupport13_16 : RowSquare [4,4,3,2] [6,3,2,2] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,4,2,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_16 smallT13_16 smallFlag13_16 smallChoices13_16 - change solveChoices smallChoices13_16 (.full [4,4,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_16 smallT13_16) smallFlag13_16 ≠ 0 - rw [smallCert13_16] - norm_num - -def smallB13_17 : Equiv.Perm (Fin 13) := Equiv.swap 5 9 * (Equiv.swap 5 11 * (Equiv.swap 9 3 * (Equiv.swap 3 1 * (Equiv.swap 3 0 * (Equiv.swap 5 10 * (Equiv.swap 3 6 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 12 * (Equiv.swap 0 8)))))))))) -def smallT13_17 : Equiv.Perm (Fin 13) := Equiv.swap 5 8 * (Equiv.swap 8 12 * (Equiv.swap 8 3 * (Equiv.swap 8 9 * (Equiv.swap 3 4 * (Equiv.swap 5 2 * (Equiv.swap 4 10 * (Equiv.swap 3 0 * (Equiv.swap 2 11 * (Equiv.swap 0 7))))))))) -def smallFlag13_17 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,1),(0,0,2),(1,1,1),(2,1,2),(3,1,3),(0,2,0),(2,2,0),(0,3,2),(0,3,3)} - -def smallChoices13_17 : EdgeChoices := (.node 10 (fun _v => if _v = (0,0,1) then (.node 10 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => if _v = (3,0,0) then (.node 6 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 5 (fun _v => if _v = (2,1,2) then (.node 0 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(.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 2 (fun _v => if _v = (3,0,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (3,1,3) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (2,1,2) then (.node 0 (fun _v => if _v = (3,0,0) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,3,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (2,1,2) then (.node 0 (fun _v => if _v = (3,0,0) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (2,1,2) then (.node 0 (fun _v => if _v = (3,0,0) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))))) -lemma smallCert13_17 : solveChoices smallChoices13_17 (.full [4,4,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_17 smallT13_17) smallFlag13_17 = -14 := by - decide +kernel - -lemma smallSupport13_17 : RowSquare [4,4,3,2] [7,2,2,2] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,4,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_17 smallT13_17 smallFlag13_17 smallChoices13_17 - change solveChoices smallChoices13_17 (.full [4,4,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_17 smallT13_17) smallFlag13_17 ≠ 0 - rw [smallCert13_17] - norm_num - -def smallB13_18 : Equiv.Perm (Fin 13) := Equiv.swap 9 1 * (Equiv.swap 1 4 * (Equiv.swap 0 3 * (Equiv.swap 0 7 * (Equiv.swap 1 8 * (Equiv.swap 4 12 * (Equiv.swap 3 2 * (Equiv.swap 2 11 * (Equiv.swap 1 5 * (Equiv.swap 0 6))))))))) -def smallT13_18 : Equiv.Perm (Fin 13) := Equiv.swap 0 3 * (Equiv.swap 0 8 * (Equiv.swap 0 10 * (Equiv.swap 8 1 * (Equiv.swap 0 2 * (Equiv.swap 2 9 * (Equiv.swap 1 11 * (Equiv.swap 3 12 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 7)))))))))) -def smallFlag13_18 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(1,0,1),(0,0,2),(2,1,0),(0,1,1),(1,2,0),(1,2,2),(2,2,3),(0,3,2),(2,3,3)} - -def smallChoices13_18 : EdgeChoices := (.node 3 (fun _v => if _v = (0,0,2) then (.node 11 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 4 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,2,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,2) then (.node 1 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 1 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (1,0,1) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 4 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 4 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))) else (.node 5 (fun _ => .fallback)))))) else (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 5 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (3,0,0) then (.node 5 (fun _v => (.node 2 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 4 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (0,3,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))))))) else (.node 5 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else if _v = (1,0,1) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 6 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (0,1,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (2,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else if _v = (0,1,1) then (.node 11 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))) else if _v = (1,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,2) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,2) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,3,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _ => .fallback)))))))) else if _v = (1,0,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 5 (fun _ => .fallback)))))) else (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) 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(fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))) else if _v = (1,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v 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(fun _v => (.node 1 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _ => .fallback)))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 5 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (3,0,0) then (.node 5 (fun _v => (.node 2 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _ => .fallback)))))))))))) -lemma smallCert13_18 : solveChoices smallChoices13_18 (.full [4,3,3,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,3,2,1] (Equiv.refl (Fin 13)) smallB13_18 smallT13_18) smallFlag13_18 = -19 := by - decide +kernel - -lemma smallSupport13_18 : RowSquare [4,4,3,2] [5,4,3,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,3,3,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_18 smallT13_18 smallFlag13_18 smallChoices13_18 - change solveChoices smallChoices13_18 (.full [4,3,3,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,3,2,1] (Equiv.refl (Fin 13)) smallB13_18 smallT13_18) smallFlag13_18 ≠ 0 - rw [smallCert13_18] - norm_num - -def smallB13_19 : Equiv.Perm (Fin 13) := Equiv.swap 4 1 * (Equiv.swap 8 0 * (Equiv.swap 1 11 * (Equiv.swap 4 9 * (Equiv.swap 4 5 * (Equiv.swap 1 6 * (Equiv.swap 2 12 * (Equiv.swap 1 3 * (Equiv.swap 0 10)))))))) -def smallT13_19 : Equiv.Perm (Fin 13) := Equiv.swap 4 8 * (Equiv.swap 8 1 * (Equiv.swap 8 5 * (Equiv.swap 5 2 * (Equiv.swap 2 0 * (Equiv.swap 5 7 * (Equiv.swap 4 11 * (Equiv.swap 1 12 * (Equiv.swap 2 6 * (Equiv.swap 1 3 * (Equiv.swap 0 9)))))))))) -def smallFlag13_19 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,2),(0,1,1),(1,1,1),(0,1,2),(3,1,3),(0,2,0),(2,2,1),(0,3,2),(2,3,3)} - -def smallChoices13_19 : EdgeChoices := (.node 10 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 4 (fun _v => if _v = (2,0,2) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 6 (fun _ => .fallback)) else if _v = (1,1,1) then (.node 6 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 6 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (3,1,3) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,2) then (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => (.node 5 (fun _v => (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,3,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _ => .fallback)))))))))) else if _v = (2,0,2) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 6 (fun _ => .fallback)) else if _v = (1,1,1) then (.node 6 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 6 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (3,1,3) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 6 (fun _ => .fallback)) else if 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.fallback)))))))))))))) else (.node 2 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (3,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 4 (fun _v => if _v = (0,1,2) then (.node 7 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else if _v = (0,1,2) then (.node 4 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v 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then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 4 (fun _v => if _v = (2,0,2) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,1,1) then (.node 6 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (3,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = 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(.node 0 (fun _v => if _v = (3,1,3) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,2) then (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,3,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _ => .fallback)))))))))) else if _v = (2,0,2) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,1,1) then (.node 6 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (3,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) 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(fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 4 (fun _v => if _v = (2,0,2) then (.node 5 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => 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(fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 5 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_19 : solveChoices smallChoices13_19 (.full [4,3,3,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,3,1,1,1] (Equiv.refl (Fin 13)) smallB13_19 smallT13_19) smallFlag13_19 = -22 := by - decide +kernel - -lemma smallSupport13_19 : RowSquare [4,4,3,2] [6,3,3,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,3,3,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_19 smallT13_19 smallFlag13_19 smallChoices13_19 - change solveChoices smallChoices13_19 (.full [4,3,3,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,3,1,1,1] (Equiv.refl (Fin 13)) smallB13_19 smallT13_19) smallFlag13_19 ≠ 0 - rw [smallCert13_19] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 13 4. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_16 : Equiv.Perm (Fin 13) := Equiv.swap 3 9 * (Equiv.swap 9 11 * (Equiv.swap 3 6 * (Equiv.swap 6 5 * (Equiv.swap 6 2 * (Equiv.swap 5 0 * (Equiv.swap 3 8 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 0 10)))))))))) +def smallT13_16 : Equiv.Perm (Fin 13) := Equiv.swap 2 5 * (Equiv.swap 9 12 * (Equiv.swap 5 11 * (Equiv.swap 5 3 * (Equiv.swap 2 10 * (Equiv.swap 3 7 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 4)))))))) +def smallFlag13_16 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,2),(2,0,3),(0,1,0),(3,1,0),(1,1,1),(0,1,3),(1,2,1),(2,2,2),(3,3,0),(0,3,1)} + +def smallChoices13_16 : EdgeChoices := (.node 9 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => (.node 8 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 4 (fun _v => if 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= (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 3 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (2,2,2) then (.node 0 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))) else if _v = (2,2,2) then (.node 1 (fun _v => if _v = (3,3,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (2,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,3) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,0,2) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => 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(fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,3) then (.node 4 (fun _v => if _v = (3,3,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,0,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (2,0,3) then (.node 1 (fun _v => if _v = (3,3,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 3 (fun _ => .fallback)))) else if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,3) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (3,3,0) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (3,1,0) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (3,1,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,1,0) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (3,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 2 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else if _v = (1,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (2,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 5 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (0,1,3) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _v => if _v = (2,0,3) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 0 (fun _v => if _v = (2,0,3) then (.node 0 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (3,1,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (1,2,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (2,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (2,0,3) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,1) then (.node 0 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => .fallback)) else if _v = (1,1,1) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 4 (fun _v => if _v = (2,0,3) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (2,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => if _v = (3,3,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 4 (fun _v => if _v = (3,3,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (1,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 2 (fun _v => if _v = (3,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (3,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else if _v = (0,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_16 : solveChoices smallChoices13_16 (.full [4,4,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_16 smallT13_16) smallFlag13_16 = 1 := by + decide +kernel + +lemma smallSupport13_16 : RowSquare [4,4,3,2] [6,3,2,2] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,4,2,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_16 smallT13_16 smallFlag13_16 smallChoices13_16 + change solveChoices smallChoices13_16 (.full [4,4,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_16 smallT13_16) smallFlag13_16 ≠ 0 + rw [smallCert13_16] + norm_num + +def smallB13_17 : Equiv.Perm (Fin 13) := Equiv.swap 5 9 * (Equiv.swap 5 11 * (Equiv.swap 9 3 * (Equiv.swap 3 1 * (Equiv.swap 3 0 * (Equiv.swap 5 10 * (Equiv.swap 3 6 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 12 * (Equiv.swap 0 8)))))))))) +def smallT13_17 : Equiv.Perm (Fin 13) := Equiv.swap 5 8 * (Equiv.swap 8 12 * (Equiv.swap 8 3 * (Equiv.swap 8 9 * (Equiv.swap 3 4 * (Equiv.swap 5 2 * (Equiv.swap 4 10 * (Equiv.swap 3 0 * (Equiv.swap 2 11 * (Equiv.swap 0 7))))))))) +def smallFlag13_17 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,1),(0,0,2),(1,1,1),(2,1,2),(3,1,3),(0,2,0),(2,2,0),(0,3,2),(0,3,3)} + +def smallChoices13_17 : EdgeChoices := (.node 10 (fun _v => if _v = (0,0,1) then (.node 10 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => if _v = (3,0,0) then (.node 6 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 5 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,3,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (3,1,3) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (1,1,1) then (.node 2 (fun _v => if _v = (3,1,3) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,2,0) then (.node 0 (fun _v => if _v = (0,3,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => .fallback)))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (3,0,0) then (.node 1 (fun _v => if _v = (3,1,3) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) 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= (1,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 2 (fun _v => if _v = (3,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (3,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _v => (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,3,2) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 2 (fun _v => if _v = (3,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (3,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (3,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (3,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (3,0,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (2,1,2) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 2 (fun _v => if _v = (3,1,3) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (3,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => .fallback)) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _v => if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,3,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,3,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (2,1,2) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 6 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (2,1,2) then (.node 3 (fun _v => (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,3,2) then (.node 1 (fun _v => if _v = (3,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => if _v = (2,1,2) then (.node 1 (fun _v => (.node 3 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,3,2) then (.node 1 (fun _v => if _v = (3,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 3 (fun _v => if _v = (3,1,3) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 2 (fun _v => if _v = (3,0,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (3,1,3) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (2,1,2) then (.node 0 (fun _v => if _v = (3,0,0) then (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,3,2) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (2,1,2) then (.node 0 (fun _v => if _v = (3,0,0) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else if _v = (2,1,2) then (.node 0 (fun _v => if _v = (3,0,0) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))))) +lemma smallCert13_17 : solveChoices smallChoices13_17 (.full [4,4,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_17 smallT13_17) smallFlag13_17 = -14 := by + decide +kernel + +lemma smallSupport13_17 : RowSquare [4,4,3,2] [7,2,2,2] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,4,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_17 smallT13_17 smallFlag13_17 smallChoices13_17 + change solveChoices smallChoices13_17 (.full [4,4,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,4,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_17 smallT13_17) smallFlag13_17 ≠ 0 + rw [smallCert13_17] + norm_num + +def smallB13_18 : Equiv.Perm (Fin 13) := Equiv.swap 9 1 * (Equiv.swap 1 4 * (Equiv.swap 0 3 * (Equiv.swap 0 7 * (Equiv.swap 1 8 * (Equiv.swap 4 12 * (Equiv.swap 3 2 * (Equiv.swap 2 11 * (Equiv.swap 1 5 * (Equiv.swap 0 6))))))))) +def smallT13_18 : Equiv.Perm (Fin 13) := Equiv.swap 0 3 * (Equiv.swap 0 8 * (Equiv.swap 0 10 * (Equiv.swap 8 1 * (Equiv.swap 0 2 * (Equiv.swap 2 9 * (Equiv.swap 1 11 * (Equiv.swap 3 12 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 7)))))))))) +def smallFlag13_18 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(1,0,1),(0,0,2),(2,1,0),(0,1,1),(1,2,0),(1,2,2),(2,2,3),(0,3,2),(2,3,3)} + +def smallChoices13_18 : EdgeChoices := (.node 3 (fun _v => if _v = (0,0,2) then (.node 11 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 4 (fun _v => if _v = (2,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,2,3) then 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(fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _ => .fallback)))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => if _v = (2,2,3) then (.node 4 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (2,1,0) then (.node 2 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))))))) else (.node 5 (fun _ => .fallback)))))))) else if _v = (1,0,1) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => (.node 0 (fun _v => if _v 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else (.node 1 (fun _v => if _v = (0,0,2) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))) else if _v = (2,1,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 3 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => .fallback)))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))))) else (.node 6 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 4 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (2,2,3) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 5 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 5 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => (.node 5 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))))) else if _v = (1,0,1) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,3,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,3,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 6 (fun _v => if _v = (2,2,3) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 5 (fun _ => (.node 3 (fun _ => .fallback)))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,3,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 5 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 5 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (3,0,0) then (.node 0 (fun _v => if _v = (2,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _ => (.node 5 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 4 (fun _v => (.node 5 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (1,0,0) then (.node 5 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (3,0,0) then (.node 5 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (2,1,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _ => .fallback)))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 5 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (3,0,0) then (.node 5 (fun _v => (.node 2 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _ => .fallback)))))))))))) +lemma smallCert13_18 : solveChoices smallChoices13_18 (.full [4,3,3,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,3,2,1] (Equiv.refl (Fin 13)) smallB13_18 smallT13_18) smallFlag13_18 = -19 := by + decide +kernel + +lemma smallSupport13_18 : RowSquare [4,4,3,2] [5,4,3,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,3,3,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_18 smallT13_18 smallFlag13_18 smallChoices13_18 + change solveChoices smallChoices13_18 (.full [4,3,3,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,3,2,1] (Equiv.refl (Fin 13)) smallB13_18 smallT13_18) smallFlag13_18 ≠ 0 + rw [smallCert13_18] + norm_num + +def smallB13_19 : Equiv.Perm (Fin 13) := Equiv.swap 4 1 * (Equiv.swap 8 0 * (Equiv.swap 1 11 * (Equiv.swap 4 9 * (Equiv.swap 4 5 * (Equiv.swap 1 6 * (Equiv.swap 2 12 * (Equiv.swap 1 3 * (Equiv.swap 0 10)))))))) +def smallT13_19 : Equiv.Perm (Fin 13) := Equiv.swap 4 8 * (Equiv.swap 8 1 * (Equiv.swap 8 5 * (Equiv.swap 5 2 * (Equiv.swap 2 0 * (Equiv.swap 5 7 * (Equiv.swap 4 11 * (Equiv.swap 1 12 * (Equiv.swap 2 6 * (Equiv.swap 1 3 * (Equiv.swap 0 9)))))))))) +def smallFlag13_19 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,2),(0,1,1),(1,1,1),(0,1,2),(3,1,3),(0,2,0),(2,2,1),(0,3,2),(2,3,3)} + +def smallChoices13_19 : EdgeChoices := (.node 10 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 4 (fun _v => if _v = (2,0,2) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 6 (fun _ => .fallback)) else if _v = (1,1,1) then (.node 6 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ 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(fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 4 (fun _v => if _v = (2,0,2) then (.node 5 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 6 (fun _v => if _v = (3,1,3) then (.node 7 (fun _v => if _v = (1,0,0) then (.node 6 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 6 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 5 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_19 : solveChoices smallChoices13_19 (.full [4,3,3,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,3,1,1,1] (Equiv.refl (Fin 13)) smallB13_19 smallT13_19) smallFlag13_19 = -22 := by + decide +kernel + +lemma smallSupport13_19 : RowSquare [4,4,3,2] [6,3,3,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,3,3,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_19 smallT13_19 smallFlag13_19 smallChoices13_19 + change solveChoices smallChoices13_19 (.full [4,3,3,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,3,1,1,1] (Equiv.refl (Fin 13)) smallB13_19 smallT13_19) smallFlag13_19 ≠ 0 + rw [smallCert13_19] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_5.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_5.lean index 40ac05ec6fdd7a6e60865cfdd22880bf8fd2d7b9..019d645be8554b24137cc9b8e6a06c29936da98c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_5.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_5.lean @@ -1,83 +1,83 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains - -namespace OAI - -/-! Small Contracts 13 5. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_20 : Equiv.Perm (Fin 13) := Equiv.swap 9 7 * (Equiv.swap 9 5 * (Equiv.swap 5 10 * (Equiv.swap 7 3 * (Equiv.swap 5 0 * (Equiv.swap 3 12 * (Equiv.swap 2 4 * (Equiv.swap 0 8))))))) -def smallT13_20 : Equiv.Perm (Fin 13) := Equiv.swap 6 9 * (Equiv.swap 9 11 * (Equiv.swap 6 2 * (Equiv.swap 5 8 * (Equiv.swap 4 12 * (Equiv.swap 2 10 * (Equiv.swap 2 3 * (Equiv.swap 1 7))))))) -def smallFlag13_20 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(1,0,2),(1,1,0),(0,1,1),(3,2,0),(2,2,2),(0,2,3),(1,3,1),(1,3,3)} -lemma smallCert13_20 : solveCompact 13 (.full [4,3,2,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,2,2,2] (Equiv.refl (Fin 13)) smallB13_20 smallT13_20) smallFlag13_20 = 144 := by - decide +kernel - -lemma smallSupport13_20 : RowSquare [4,4,3,2] [5,5,2,1] := by - apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [4,3,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_20 smallT13_20 smallFlag13_20 - change solveCompact 13 (.full [4,3,2,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,2,2,2] (Equiv.refl (Fin 13)) smallB13_20 smallT13_20) smallFlag13_20 ≠ 0 - rw [smallCert13_20] - norm_num - -def smallB13_21 : Equiv.Perm (Fin 13) := Equiv.swap 4 9 * (Equiv.swap 9 7 * (Equiv.swap 7 6 * (Equiv.swap 6 1 * (Equiv.swap 5 3 * (Equiv.swap 4 2 * (Equiv.swap 3 12 * (Equiv.swap 2 10 * (Equiv.swap 1 11)))))))) -def smallT13_21 : Equiv.Perm (Fin 13) := Equiv.swap 6 7 * (Equiv.swap 7 8 * (Equiv.swap 7 2 * (Equiv.swap 8 12 * (Equiv.swap 7 0 * (Equiv.swap 6 1 * (Equiv.swap 1 11 * (Equiv.swap 2 10 * (Equiv.swap 0 9 * (Equiv.swap 2 4 * (Equiv.swap 1 5 * (Equiv.swap 0 3))))))))))) -def smallFlag13_21 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(1,0,2),(1,1,0),(2,1,1),(0,1,3),(2,1,3),(1,2,1),(0,2,2),(0,3,1),(0,3,2)} -lemma smallCert13_21 : solveCompact 13 (.full [4,3,2,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,2,2,1,1] (Equiv.refl (Fin 13)) smallB13_21 smallT13_21) smallFlag13_21 = -24 := by - decide +kernel - -lemma smallSupport13_21 : RowSquare [4,4,3,2] [6,4,2,1] := by - apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [4,3,2,2,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_21 smallT13_21 smallFlag13_21 - change solveCompact 13 (.full [4,3,2,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,2,2,1,1] (Equiv.refl (Fin 13)) smallB13_21 smallT13_21) smallFlag13_21 ≠ 0 - rw [smallCert13_21] - norm_num - -def smallB13_22 : Equiv.Perm (Fin 13) := Equiv.swap 7 8 * (Equiv.swap 6 3 * (Equiv.swap 0 9 * (Equiv.swap 4 12 * (Equiv.swap 3 10 * (Equiv.swap 0 5 * (Equiv.swap 1 11 * (Equiv.swap 0 2))))))) -def smallT13_22 : Equiv.Perm (Fin 13) := Equiv.swap 11 2 * (Equiv.swap 2 12 * (Equiv.swap 3 4 * (Equiv.swap 6 5 * (Equiv.swap 5 8 * (Equiv.swap 4 10 * (Equiv.swap 3 1 * (Equiv.swap 2 0 * (Equiv.swap 1 7 * (Equiv.swap 0 9))))))))) -def smallFlag13_22 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(2,0,1),(0,0,2),(2,0,3),(0,1,0),(1,1,1),(0,2,1),(3,2,2),(1,2,3),(0,3,0),(1,3,2)} -lemma smallCert13_22 : solveCompact 13 (.full [4,3,2,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,2,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_22 smallT13_22) smallFlag13_22 = 11 := by - decide +kernel - -lemma smallSupport13_22 : RowSquare [4,4,3,2] [7,3,2,1] := by - apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [4,3,2,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_22 smallT13_22 smallFlag13_22 - change solveCompact 13 (.full [4,3,2,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,2,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_22 smallT13_22) smallFlag13_22 ≠ 0 - rw [smallCert13_22] - norm_num - -def smallB13_23 : Equiv.Perm (Fin 13) := Equiv.swap 7 12 * (Equiv.swap 2 11 * (Equiv.swap 7 10 * (Equiv.swap 7 5 * (Equiv.swap 5 1 * (Equiv.swap 5 3 * (Equiv.swap 1 8 * (Equiv.swap 3 0 * (Equiv.swap 2 9 * (Equiv.swap 1 4 * (Equiv.swap 0 6)))))))))) -def smallT13_23 : Equiv.Perm (Fin 13) := Equiv.swap 2 11 * (Equiv.swap 2 8 * (Equiv.swap 8 4 * (Equiv.swap 1 6 * (Equiv.swap 6 12 * (Equiv.swap 4 10 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 1 7 * (Equiv.swap 0 9))))))))) -def smallFlag13_23 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,2),(2,0,2),(0,1,0),(1,1,3),(0,2,1),(3,2,1),(0,3,0),(2,3,1)} -lemma smallCert13_23 : solveCompact 13 (.full [4,3,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_23 smallT13_23) smallFlag13_23 = 8 := by - decide +kernel - -lemma smallSupport13_23 : RowSquare [4,4,3,2] [8,2,2,1] := by - apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [4,3,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_23 smallT13_23 smallFlag13_23 - change solveCompact 13 (.full [4,3,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_23 smallT13_23) smallFlag13_23 ≠ 0 - rw [smallCert13_23] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains + +namespace OAI + +/-! Small Contracts 13 5. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_20 : Equiv.Perm (Fin 13) := Equiv.swap 9 7 * (Equiv.swap 9 5 * (Equiv.swap 5 10 * (Equiv.swap 7 3 * (Equiv.swap 5 0 * (Equiv.swap 3 12 * (Equiv.swap 2 4 * (Equiv.swap 0 8))))))) +def smallT13_20 : Equiv.Perm (Fin 13) := Equiv.swap 6 9 * (Equiv.swap 9 11 * (Equiv.swap 6 2 * (Equiv.swap 5 8 * (Equiv.swap 4 12 * (Equiv.swap 2 10 * (Equiv.swap 2 3 * (Equiv.swap 1 7))))))) +def smallFlag13_20 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(1,0,2),(1,1,0),(0,1,1),(3,2,0),(2,2,2),(0,2,3),(1,3,1),(1,3,3)} +lemma smallCert13_20 : solveCompact 13 (.full [4,3,2,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,2,2,2] (Equiv.refl (Fin 13)) smallB13_20 smallT13_20) smallFlag13_20 = 144 := by + decide +kernel + +lemma smallSupport13_20 : RowSquare [4,4,3,2] [5,5,2,1] := by + apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [4,3,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_20 smallT13_20 smallFlag13_20 + change solveCompact 13 (.full [4,3,2,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,2,2,2] (Equiv.refl (Fin 13)) smallB13_20 smallT13_20) smallFlag13_20 ≠ 0 + rw [smallCert13_20] + norm_num + +def smallB13_21 : Equiv.Perm (Fin 13) := Equiv.swap 4 9 * (Equiv.swap 9 7 * (Equiv.swap 7 6 * (Equiv.swap 6 1 * (Equiv.swap 5 3 * (Equiv.swap 4 2 * (Equiv.swap 3 12 * (Equiv.swap 2 10 * (Equiv.swap 1 11)))))))) +def smallT13_21 : Equiv.Perm (Fin 13) := Equiv.swap 6 7 * (Equiv.swap 7 8 * (Equiv.swap 7 2 * (Equiv.swap 8 12 * (Equiv.swap 7 0 * (Equiv.swap 6 1 * (Equiv.swap 1 11 * (Equiv.swap 2 10 * (Equiv.swap 0 9 * (Equiv.swap 2 4 * (Equiv.swap 1 5 * (Equiv.swap 0 3))))))))))) +def smallFlag13_21 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(1,0,2),(1,1,0),(2,1,1),(0,1,3),(2,1,3),(1,2,1),(0,2,2),(0,3,1),(0,3,2)} +lemma smallCert13_21 : solveCompact 13 (.full [4,3,2,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,2,2,1,1] (Equiv.refl (Fin 13)) smallB13_21 smallT13_21) smallFlag13_21 = -24 := by + decide +kernel + +lemma smallSupport13_21 : RowSquare [4,4,3,2] [6,4,2,1] := by + apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [4,3,2,2,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_21 smallT13_21 smallFlag13_21 + change solveCompact 13 (.full [4,3,2,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,2,2,1,1] (Equiv.refl (Fin 13)) smallB13_21 smallT13_21) smallFlag13_21 ≠ 0 + rw [smallCert13_21] + norm_num + +def smallB13_22 : Equiv.Perm (Fin 13) := Equiv.swap 7 8 * (Equiv.swap 6 3 * (Equiv.swap 0 9 * (Equiv.swap 4 12 * (Equiv.swap 3 10 * (Equiv.swap 0 5 * (Equiv.swap 1 11 * (Equiv.swap 0 2))))))) +def smallT13_22 : Equiv.Perm (Fin 13) := Equiv.swap 11 2 * (Equiv.swap 2 12 * (Equiv.swap 3 4 * (Equiv.swap 6 5 * (Equiv.swap 5 8 * (Equiv.swap 4 10 * (Equiv.swap 3 1 * (Equiv.swap 2 0 * (Equiv.swap 1 7 * (Equiv.swap 0 9))))))))) +def smallFlag13_22 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(2,0,1),(0,0,2),(2,0,3),(0,1,0),(1,1,1),(0,2,1),(3,2,2),(1,2,3),(0,3,0),(1,3,2)} +lemma smallCert13_22 : solveCompact 13 (.full [4,3,2,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,2,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_22 smallT13_22) smallFlag13_22 = 11 := by + decide +kernel + +lemma smallSupport13_22 : RowSquare [4,4,3,2] [7,3,2,1] := by + apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [4,3,2,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_22 smallT13_22 smallFlag13_22 + change solveCompact 13 (.full [4,3,2,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,2,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_22 smallT13_22) smallFlag13_22 ≠ 0 + rw [smallCert13_22] + norm_num + +def smallB13_23 : Equiv.Perm (Fin 13) := Equiv.swap 7 12 * (Equiv.swap 2 11 * (Equiv.swap 7 10 * (Equiv.swap 7 5 * (Equiv.swap 5 1 * (Equiv.swap 5 3 * (Equiv.swap 1 8 * (Equiv.swap 3 0 * (Equiv.swap 2 9 * (Equiv.swap 1 4 * (Equiv.swap 0 6)))))))))) +def smallT13_23 : Equiv.Perm (Fin 13) := Equiv.swap 2 11 * (Equiv.swap 2 8 * (Equiv.swap 8 4 * (Equiv.swap 1 6 * (Equiv.swap 6 12 * (Equiv.swap 4 10 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 1 7 * (Equiv.swap 0 9))))))))) +def smallFlag13_23 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,2),(2,0,2),(0,1,0),(1,1,3),(0,2,1),(3,2,1),(0,3,0),(2,3,1)} +lemma smallCert13_23 : solveCompact 13 (.full [4,3,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_23 smallT13_23) smallFlag13_23 = 8 := by + decide +kernel + +lemma smallSupport13_23 : RowSquare [4,4,3,2] [8,2,2,1] := by + apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [4,3,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_23 smallT13_23 smallFlag13_23 + change solveCompact 13 (.full [4,3,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,3,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_23 smallT13_23) smallFlag13_23 ≠ 0 + rw [smallCert13_23] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_6.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_6.lean index d9888cae5579314cf1f7cd95ec6e941a32da00e1..21a730b397ef7724f178b36a721e33a616a36810 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_6.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_6.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 13 6. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_24 : Equiv.Perm (Fin 13) := Equiv.swap 11 12 * (Equiv.swap 8 6 * (Equiv.swap 8 9 * (Equiv.swap 6 4 * (Equiv.swap 0 3 * (Equiv.swap 4 1 * (Equiv.swap 3 7 * (Equiv.swap 0 5 * (Equiv.swap 1 10 * (Equiv.swap 0 2))))))))) -def smallT13_24 : Equiv.Perm (Fin 13) := Equiv.swap 2 4 * (Equiv.swap 7 0 * (Equiv.swap 1 8 * (Equiv.swap 2 9 * (Equiv.swap 4 12 * (Equiv.swap 0 10 * (Equiv.swap 2 5 * (Equiv.swap 1 6 * (Equiv.swap 0 3)))))))) -def smallFlag13_24 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(1,0,1),(3,0,2),(2,1,0),(0,1,2),(1,1,3),(0,2,0),(1,2,0),(1,2,1),(0,3,0),(0,3,3)} - -def smallChoices13_24 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,1,2) then (.node 3 (fun _v => if _v = (1,1,3) then (.node 2 (fun _v => if _v = (0,2,0) then (.node 6 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,3,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,0) then (.node 4 (fun _v => if _v = (0,2,0) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 4 (fun _ => (.node 4 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _v => if _v = (1,1,3) then (.node 4 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => if _v = (0,3,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (1,1,3) then (.node 3 (fun _v => if _v = (0,1,2) then (.node 2 (fun _v => if _v = (0,2,0) then (.node 6 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,3,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,0) then (.node 4 (fun _v => if _v = (0,2,0) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 4 (fun _ => (.node 4 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,0) then (.node 2 (fun _v => (.node 4 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => if _v = (0,3,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _v => (.node 6 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,2,0) then (.node 0 (fun 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(.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (1,2,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,0,1) then (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (1,2,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => 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.fallback)))))))) else (.node 3 (fun _ => .fallback)))) else (.node 7 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,2) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 7 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,3,0) then (.node 3 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 1 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.fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,0,1) then (.node 3 (fun _v => if _v = (3,0,2) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_24 : solveChoices smallChoices13_24 (.full [4,2,2,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,2,2,2,1] (Equiv.refl (Fin 13)) smallB13_24 smallT13_24) smallFlag13_24 = -54 := by - decide +kernel - -lemma smallSupport13_24 : RowSquare [4,4,3,2] [6,5,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,2,2,2,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_24 smallT13_24 smallFlag13_24 smallChoices13_24 - change solveChoices smallChoices13_24 (.full [4,2,2,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,2,2,2,1] (Equiv.refl (Fin 13)) smallB13_24 smallT13_24) smallFlag13_24 ≠ 0 - rw [smallCert13_24] - norm_num - -def smallB13_25 : Equiv.Perm (Fin 13) := Equiv.swap 4 0 * (Equiv.swap 0 2 * (Equiv.swap 4 11 * (Equiv.swap 2 12 * (Equiv.swap 4 9 * (Equiv.swap 2 8 * (Equiv.swap 4 7 * (Equiv.swap 3 5 * (Equiv.swap 2 6 * (Equiv.swap 0 10))))))))) -def smallT13_25 : Equiv.Perm (Fin 13) := Equiv.swap 3 5 * (Equiv.swap 5 11 * (Equiv.swap 5 4 * (Equiv.swap 4 6 * (Equiv.swap 3 9 * (Equiv.swap 1 12 * (Equiv.swap 0 10)))))) -def smallFlag13_25 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,1),(0,0,2),(0,0,3),(1,1,0),(0,1,1),(0,1,3),(0,2,0),(0,2,2),(2,2,2),(1,3,1)} - -def smallChoices13_25 : EdgeChoices := (.node 8 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 6 (fun _v => if _v = (1,1,0) then (.node 4 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,2,2) then (.node 1 (fun _ => .fallback)) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 5 (fun _ => .fallback)) else (.node 6 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,2,2) 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(.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))))))))))) else (.node 6 (fun _v => if _v = (1,1,0) then (.node 1 (fun _v => if _v = (1,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (3,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (3,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))))))))))))))) -lemma smallCert13_25 : solveChoices smallChoices13_25 (.full [4,2,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_25 smallT13_25) smallFlag13_25 = -3 := by - decide +kernel - -lemma smallSupport13_25 : RowSquare [4,4,3,2] [7,4,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,2,2,2,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_25 smallT13_25 smallFlag13_25 smallChoices13_25 - change solveChoices smallChoices13_25 (.full [4,2,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_25 smallT13_25) smallFlag13_25 ≠ 0 - rw [smallCert13_25] - norm_num - -def smallB13_26 : Equiv.Perm (Fin 13) := Equiv.swap 6 5 * (Equiv.swap 6 11 * (Equiv.swap 6 4 * (Equiv.swap 5 12 * (Equiv.swap 4 9 * (Equiv.swap 3 2 * (Equiv.swap 2 7 * (Equiv.swap 1 8))))))) -def smallT13_26 : Equiv.Perm (Fin 13) := Equiv.swap 2 3 * (Equiv.swap 3 12 * (Equiv.swap 4 11 * (Equiv.swap 3 9 * (Equiv.swap 2 1 * (Equiv.swap 2 6 * (Equiv.swap 4 8 * (Equiv.swap 3 0 * (Equiv.swap 2 5 * (Equiv.swap 1 10 * (Equiv.swap 0 7)))))))))) -def smallFlag13_26 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(0,1,0),(0,1,1),(2,1,2),(1,2,0),(3,2,2),(1,2,3),(0,3,2),(0,3,3)} - -def smallChoices13_26 : EdgeChoices := (.node 8 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 7 (fun _v => if _v = (0,0,1) then (.node 8 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => (.node 3 (fun _v => if _v = (0,3,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,3,2) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => (.node 0 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,1) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (0,3,2) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,2,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => (.node 3 (fun _v => if _v = (0,3,2) then (.node 5 (fun _v => if _v = (1,2,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 8 (fun _v => (.node 5 (fun _v => (.node 3 (fun _v => if _v = (0,3,2) then (.node 5 (fun _v => if _v = (1,2,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 2 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,3,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 2 (fun _v => (.node 2 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (0,3,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,3,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (1,2,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (0,3,2) then (.node 5 (fun _v => if _v = (1,2,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (0,3,2) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,3,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,3,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,3,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 2 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 5 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,3,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 2 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,3,2) then (.node 5 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,3,2) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (1,2,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (0,3,2) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,3,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,3,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _v => (.node 3 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => 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.fallback)))))))))))))))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 2 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,3,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 2 (fun _v => (.node 2 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if 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(0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_26 : solveChoices smallChoices13_26 (.full [4,2,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_26 smallT13_26) smallFlag13_26 = 4 := by - decide +kernel - -lemma smallSupport13_26 : RowSquare [4,4,3,2] [8,3,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,2,2,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_26 smallT13_26 smallFlag13_26 smallChoices13_26 - change solveChoices smallChoices13_26 (.full [4,2,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_26 smallT13_26) smallFlag13_26 ≠ 0 - rw [smallCert13_26] - norm_num - -def smallB13_27 : Equiv.Perm (Fin 13) := Equiv.swap 10 8 * (Equiv.swap 8 7 * (Equiv.swap 7 11 * (Equiv.swap 3 1 * (Equiv.swap 3 4 * (Equiv.swap 2 6 * (Equiv.swap 1 9)))))) -def smallT13_27 : Equiv.Perm (Fin 13) := Equiv.swap 7 12 * (Equiv.swap 7 2 * (Equiv.swap 7 6 * (Equiv.swap 7 8 * (Equiv.swap 6 1 * (Equiv.swap 4 5 * (Equiv.swap 2 10 * (Equiv.swap 2 3 * (Equiv.swap 1 9 * (Equiv.swap 0 11))))))))) -def smallFlag13_27 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(0,0,2),(0,0,3),(0,1,1),(2,1,3),(0,2,0),(1,2,2),(3,2,2),(0,3,0)} - -def smallChoices13_27 : EdgeChoices := (.node 12 (fun _v => if _v = (0,0,0) then (.node 7 (fun _v => (.node 3 (fun _v => (.node 6 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,3) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,2,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if 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.fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 5 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => (.node 6 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 4 (fun _ => .fallback)) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,0,1) then (.node 9 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else if _v = (0,0,2) then (.node 7 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _v => if _v = (2,1,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => if _v = (2,1,3) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,1,1) then (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,2,0) 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.fallback)) else (.node 0 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,2,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,2) then (.node 5 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => (.node 4 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,2,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 5 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,2,2) then (.node 3 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (1,0,1) then (.node 6 (fun _v => (.node 1 (fun _v => if _v = (2,1,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,2) then (.node 5 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => (.node 6 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,2) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_27 : solveChoices smallChoices13_27 (.full [4,2,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_27 smallT13_27) smallFlag13_27 = -1 := by - decide +kernel - -lemma smallSupport13_27 : RowSquare [4,4,3,2] [9,2,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,2,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_27 smallT13_27 smallFlag13_27 smallChoices13_27 - change solveChoices smallChoices13_27 (.full [4,2,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_27 smallT13_27) smallFlag13_27 ≠ 0 - rw [smallCert13_27] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 13 6. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_24 : Equiv.Perm (Fin 13) := Equiv.swap 11 12 * (Equiv.swap 8 6 * (Equiv.swap 8 9 * (Equiv.swap 6 4 * (Equiv.swap 0 3 * (Equiv.swap 4 1 * (Equiv.swap 3 7 * (Equiv.swap 0 5 * (Equiv.swap 1 10 * (Equiv.swap 0 2))))))))) +def smallT13_24 : Equiv.Perm (Fin 13) := Equiv.swap 2 4 * (Equiv.swap 7 0 * (Equiv.swap 1 8 * (Equiv.swap 2 9 * (Equiv.swap 4 12 * (Equiv.swap 0 10 * (Equiv.swap 2 5 * (Equiv.swap 1 6 * (Equiv.swap 0 3)))))))) +def smallFlag13_24 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(1,0,1),(3,0,2),(2,1,0),(0,1,2),(1,1,3),(0,2,0),(1,2,0),(1,2,1),(0,3,0),(0,3,3)} + +def smallChoices13_24 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,1,2) then (.node 3 (fun _v => if _v = (1,1,3) then (.node 2 (fun _v => if _v = (0,2,0) then (.node 6 (fun _v => if 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_v = (1,2,1) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _v => if _v = (1,1,3) then (.node 4 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => if _v = (0,3,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (1,1,3) then (.node 3 (fun _v => if _v = (0,1,2) then (.node 2 (fun _v => if _v = (0,2,0) then (.node 6 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,3,0) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,0) then (.node 4 (fun _v => if _v = (0,2,0) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 4 (fun _ => (.node 4 (fun _ => .fallback)))) else if _v = (1,2,1) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,3) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,0) then (.node 2 (fun _v => (.node 4 (fun _v => if _v = (0,1,2) then (.node 5 (fun _v => if _v = (0,3,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _v => (.node 6 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,2,0) then (.node 0 (fun 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(.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 3 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 0 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,0,1) then (.node 3 (fun _v => if _v = (3,0,2) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_24 : solveChoices smallChoices13_24 (.full [4,2,2,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,2,2,2,1] (Equiv.refl (Fin 13)) smallB13_24 smallT13_24) smallFlag13_24 = -54 := by + decide +kernel + +lemma smallSupport13_24 : RowSquare [4,4,3,2] [6,5,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,2,2,2,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_24 smallT13_24 smallFlag13_24 smallChoices13_24 + change solveChoices smallChoices13_24 (.full [4,2,2,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,2,2,2,1] (Equiv.refl (Fin 13)) smallB13_24 smallT13_24) smallFlag13_24 ≠ 0 + rw [smallCert13_24] + norm_num + +def smallB13_25 : Equiv.Perm (Fin 13) := Equiv.swap 4 0 * (Equiv.swap 0 2 * (Equiv.swap 4 11 * (Equiv.swap 2 12 * (Equiv.swap 4 9 * (Equiv.swap 2 8 * (Equiv.swap 4 7 * (Equiv.swap 3 5 * (Equiv.swap 2 6 * (Equiv.swap 0 10))))))))) +def smallT13_25 : Equiv.Perm (Fin 13) := Equiv.swap 3 5 * (Equiv.swap 5 11 * (Equiv.swap 5 4 * (Equiv.swap 4 6 * (Equiv.swap 3 9 * (Equiv.swap 1 12 * (Equiv.swap 0 10)))))) +def smallFlag13_25 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,1),(0,0,2),(0,0,3),(1,1,0),(0,1,1),(0,1,3),(0,2,0),(0,2,2),(2,2,2),(1,3,1)} + +def smallChoices13_25 : EdgeChoices := (.node 8 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 6 (fun _v => if _v = (1,1,0) then (.node 4 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,2,2) then (.node 1 (fun _ => .fallback)) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 5 (fun _ => .fallback)) else (.node 6 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 5 (fun _ => .fallback)) else (.node 6 (fun _v => if _v = (0,2,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 3 (fun _ => .fallback)) else (.node 2 (fun _ => .fallback)))) else if _v = (0,2,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 3 (fun _ => .fallback)) else (.node 2 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 2 (fun _ => .fallback)) else if _v = (0,1,1) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))))) else (.node 4 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,2,2) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => if _v = (3,0,0) then (.node 7 (fun _v => if _v = (1,1,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 4 (fun _v => if _v = (0,1,3) then (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,1,3) then (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 7 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,0,3) then (.node 7 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,1,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,1,0) then (.node 7 (fun _v => if _v = (3,0,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 4 (fun _v => if _v = (0,1,3) then (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,1,3) then (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _ => .fallback)))) else (.node 7 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 6 (fun _v => if _v = (1,1,0) then (.node 1 (fun _v => if _v = (1,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,1,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))))))))))))) else if _v = (1,1,0) then (.node 0 (fun _v => (.node 8 (fun _v => if _v = (1,1,0) then (.node 2 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 5 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 2 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,2,2) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 5 (fun _v => if _v = (0,0,3) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,3) then (.node 5 (fun _v => if _v = (3,0,0) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,3) then (.node 5 (fun _v => if _v = (3,0,0) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (3,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))) else if _v = (0,0,3) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => (.node 6 (fun _v => if _v = (1,1,0) then (.node 1 (fun _v => if _v = (1,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (3,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (3,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 6 (fun _v => if _v = (1,1,0) then (.node 1 (fun _v => if _v = (1,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,1,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))))))))))) else (.node 6 (fun _v => if _v = (1,1,0) then (.node 1 (fun _v => if _v = (1,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (3,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (3,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))) else if _v = (0,0,2) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))))))))))))))) +lemma smallCert13_25 : solveChoices smallChoices13_25 (.full [4,2,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_25 smallT13_25) smallFlag13_25 = -3 := by + decide +kernel + +lemma smallSupport13_25 : RowSquare [4,4,3,2] [7,4,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,2,2,2,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_25 smallT13_25 smallFlag13_25 smallChoices13_25 + change solveChoices smallChoices13_25 (.full [4,2,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_25 smallT13_25) smallFlag13_25 ≠ 0 + rw [smallCert13_25] + norm_num + +def smallB13_26 : Equiv.Perm (Fin 13) := Equiv.swap 6 5 * (Equiv.swap 6 11 * (Equiv.swap 6 4 * (Equiv.swap 5 12 * (Equiv.swap 4 9 * (Equiv.swap 3 2 * (Equiv.swap 2 7 * (Equiv.swap 1 8))))))) +def smallT13_26 : Equiv.Perm (Fin 13) := Equiv.swap 2 3 * (Equiv.swap 3 12 * (Equiv.swap 4 11 * (Equiv.swap 3 9 * (Equiv.swap 2 1 * (Equiv.swap 2 6 * (Equiv.swap 4 8 * (Equiv.swap 3 0 * (Equiv.swap 2 5 * (Equiv.swap 1 10 * (Equiv.swap 0 7)))))))))) +def smallFlag13_26 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(0,1,0),(0,1,1),(2,1,2),(1,2,0),(3,2,2),(1,2,3),(0,3,2),(0,3,3)} + +def smallChoices13_26 : EdgeChoices := (.node 8 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 7 (fun _v => if _v = (0,0,1) then (.node 8 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => (.node 3 (fun _v => if _v = (0,3,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 1 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,3,2) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => (.node 0 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,1) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (0,3,2) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,2,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 5 (fun _v => (.node 3 (fun _v => if _v = (0,3,2) then (.node 5 (fun _v => if _v = (1,2,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 8 (fun _v => (.node 5 (fun _v => (.node 3 (fun _v => if _v = (0,3,2) then (.node 5 (fun _v => if _v = (1,2,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 2 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,3,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,1) then (.node 2 (fun _v => (.node 2 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (0,3,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,3,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (1,2,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _v => if _v = (0,3,2) then (.node 5 (fun _v => if _v = (1,2,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 4 (fun _v => if _v = (0,3,2) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,3,2) then (.node 1 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = 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(0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_26 : solveChoices smallChoices13_26 (.full [4,2,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_26 smallT13_26) smallFlag13_26 = 4 := by + decide +kernel + +lemma smallSupport13_26 : RowSquare [4,4,3,2] [8,3,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,2,2,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_26 smallT13_26 smallFlag13_26 smallChoices13_26 + change solveChoices smallChoices13_26 (.full [4,2,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_26 smallT13_26) smallFlag13_26 ≠ 0 + rw [smallCert13_26] + norm_num + +def smallB13_27 : Equiv.Perm (Fin 13) := Equiv.swap 10 8 * (Equiv.swap 8 7 * (Equiv.swap 7 11 * (Equiv.swap 3 1 * (Equiv.swap 3 4 * (Equiv.swap 2 6 * (Equiv.swap 1 9)))))) +def smallT13_27 : Equiv.Perm (Fin 13) := Equiv.swap 7 12 * (Equiv.swap 7 2 * (Equiv.swap 7 6 * (Equiv.swap 7 8 * (Equiv.swap 6 1 * (Equiv.swap 4 5 * (Equiv.swap 2 10 * (Equiv.swap 2 3 * (Equiv.swap 1 9 * (Equiv.swap 0 11))))))))) +def smallFlag13_27 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(0,0,2),(0,0,3),(0,1,1),(2,1,3),(0,2,0),(1,2,2),(3,2,2),(0,3,0)} + +def smallChoices13_27 : EdgeChoices := (.node 12 (fun _v => if _v = (0,0,0) then (.node 7 (fun _v => (.node 3 (fun _v => (.node 6 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,3) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (0,2,0) then (.node 5 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if 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(fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,0) then (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) 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(fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => (.node 4 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,2,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,2) then (.node 5 (fun _v => (.node 3 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 2 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,2,2) then (.node 3 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (1,0,1) then (.node 6 (fun _v => (.node 1 (fun _v => if _v = (2,1,3) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,2) then (.node 5 (fun _v => (.node 2 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 5 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 1 (fun _v => (.node 6 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,2) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_27 : solveChoices smallChoices13_27 (.full [4,2,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_27 smallT13_27) smallFlag13_27 = -1 := by + decide +kernel + +lemma smallSupport13_27 : RowSquare [4,4,3,2] [9,2,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,2,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_27 smallT13_27 smallFlag13_27 smallChoices13_27 + change solveChoices smallChoices13_27 (.full [4,2,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,2,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_27 smallT13_27) smallFlag13_27 ≠ 0 + rw [smallCert13_27] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_7.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_7.lean index 9a663566b17028a64e44cdb6f4f3fa2a8969bf61..d85a731bbb7525765b9fb2bbe63d144b979f3d5a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_7.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_7.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 13 7. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_28 : Equiv.Perm (Fin 13) := Equiv.swap 6 12 * (Equiv.swap 6 0 * (Equiv.swap 0 5 * (Equiv.swap 6 4 * (Equiv.swap 6 7 * (Equiv.swap 5 3 * (Equiv.swap 4 9 * (Equiv.swap 3 11 * (Equiv.swap 2 10 * (Equiv.swap 0 8 * (Equiv.swap 0 1)))))))))) -def smallT13_28 : Equiv.Perm (Fin 13) := Equiv.swap 6 10 * (Equiv.swap 10 3 * (Equiv.swap 6 11 * (Equiv.swap 7 1 * (Equiv.swap 6 8 * (Equiv.swap 1 2 * (Equiv.swap 3 12 * (Equiv.swap 2 9 * (Equiv.swap 1 5 * (Equiv.swap 0 4))))))))) -def smallFlag13_28 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(0,1,0),(0,1,2),(2,1,3),(0,2,2),(3,2,2),(0,2,3),(0,3,0),(1,3,0)} - -def smallChoices13_28 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 8 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,3,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,2) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun 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0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,2) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (3,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 3 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (3,2,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => 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=> (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 4 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 3 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,3) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,3,0) then (.node 3 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,2) then (.node 3 (fun _v => if _v = (3,2,2) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (3,2,2) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) -lemma smallCert13_28 : solveChoices smallChoices13_28 (.full [4,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_28 smallT13_28) smallFlag13_28 = -4 := by - decide +kernel - -lemma smallSupport13_28 : RowSquare [4,4,3,2] [10,1,1,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,1,1,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_28 smallT13_28 smallFlag13_28 smallChoices13_28 - change solveChoices smallChoices13_28 (.full [4,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [4,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_28 smallT13_28) smallFlag13_28 ≠ 0 - rw [smallCert13_28] - norm_num - -def smallB13_29 : Equiv.Perm (Fin 13) := Equiv.swap 2 7 * (Equiv.swap 0 9 * (Equiv.swap 7 4 * (Equiv.swap 0 5 * (Equiv.swap 5 3 * (Equiv.swap 4 12 * (Equiv.swap 3 8 * (Equiv.swap 2 11 * (Equiv.swap 0 6 * (Equiv.swap 0 1))))))))) -def smallT13_29 : Equiv.Perm (Fin 13) := Equiv.swap 5 12 * (Equiv.swap 5 11 * (Equiv.swap 5 9 * (Equiv.swap 1 8 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))) -def smallFlag13_29 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(0,0,3),(0,1,0),(0,1,2),(2,1,2),(0,1,3),(2,2,0),(0,2,1),(0,2,2),(0,3,0),(2,3,0)} - -def smallChoices13_29 : EdgeChoices := (.node 10 (fun _v => if _v = (0,1,0) then (.node 10 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 5 (fun _v => if _v = (0,1,2) then (.node 6 (fun _v => if _v = (2,2,0) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 4 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,1,2) then (.node 6 (fun _v => if _v = (0,0,3) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,2,2) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 4 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 6 (fun _v => if _v = (2,1,2) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 6 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => if _v = (2,1,2) then (.node 6 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _ => (.node 5 (fun _ => .fallback)))))) else if _v = (2,2,0) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 4 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (2,1,2) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (2,2,0) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 4 (fun _v => (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,1,3) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 4 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 4 (fun _v => (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,3,0) then (.node 4 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => .fallback)))) else if _v = (0,3,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 6 (fun _v => if _v = (2,2,0) then (.node 3 (fun _v => (.node 3 (fun _v => if _v = (0,3,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 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(fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,2,0) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))) else if _v = (0,3,0) then (.node 4 (fun _v => if _v = (2,1,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (1,0,1) then (.node 8 (fun _v => if _v = (2,2,0) then (.node 3 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 8 (fun _v => if _v = (1,0,1) then (.node 6 (fun _v => if _v = (2,1,2) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,2,0) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _ => (.node 4 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) -lemma smallCert13_29 : solveChoices smallChoices13_29 (.full [3,3,3,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_29 smallT13_29) smallFlag13_29 = 9 := by - decide +kernel - -lemma smallSupport13_29 : RowSquare [4,4,3,2] [7,3,3] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,3,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_29 smallT13_29 smallFlag13_29 smallChoices13_29 - change solveChoices smallChoices13_29 (.full [3,3,3,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_29 smallT13_29) smallFlag13_29 ≠ 0 - rw [smallCert13_29] - norm_num - -def smallB13_30 : Equiv.Perm (Fin 13) := Equiv.swap 1 12 * (Equiv.swap 8 6 * (Equiv.swap 3 11 * (Equiv.swap 6 10 * (Equiv.swap 1 4 * (Equiv.swap 4 9 * (Equiv.swap 3 7 * (Equiv.swap 1 5))))))) -def smallT13_30 : Equiv.Perm (Fin 13) := Equiv.swap 9 11 * (Equiv.swap 9 3 * (Equiv.swap 3 7 * (Equiv.swap 7 1 * (Equiv.swap 1 0 * (Equiv.swap 1 6 * (Equiv.swap 3 2 * (Equiv.swap 2 8 * (Equiv.swap 1 5 * (Equiv.swap 0 10))))))))) -def smallFlag13_30 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(1,0,2),(1,0,3),(0,1,0),(0,1,1),(2,1,1),(1,2,0),(0,2,2),(1,3,0),(2,3,3)} - -def smallChoices13_30 : EdgeChoices := (.node 12 (fun _v => if _v = (0,0,0) then (.node 11 (fun _v => (.node 2 (fun _v => if _v = (1,0,2) then (.node 8 (fun _ => .fallback)) else (.node 8 (fun _v => (.node 8 (fun _v => if _v = (1,0,1) then (.node 6 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => 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=> if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_30 : solveChoices smallChoices13_30 (.full [3,3,2,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,2,2,2,1] (Equiv.refl (Fin 13)) smallB13_30 smallT13_30) smallFlag13_30 = -20 := by - decide +kernel - -lemma smallSupport13_30 : RowSquare [4,4,3,2] [6,5,2] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,2,2,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_30 smallT13_30 smallFlag13_30 smallChoices13_30 - change solveChoices smallChoices13_30 (.full [3,3,2,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,2,2,2,1] (Equiv.refl (Fin 13)) smallB13_30 smallT13_30) smallFlag13_30 ≠ 0 - rw [smallCert13_30] - norm_num - -def smallB13_31 : Equiv.Perm (Fin 13) := Equiv.swap 6 12 * (Equiv.swap 6 9 * (Equiv.swap 4 11 * (Equiv.swap 6 3 * (Equiv.swap 4 2 * (Equiv.swap 4 1 * (Equiv.swap 3 0 * (Equiv.swap 2 7 * (Equiv.swap 1 5 * (Equiv.swap 0 8))))))))) -def smallT13_31 : Equiv.Perm (Fin 13) := Equiv.swap 7 11 * (Equiv.swap 3 2 * (Equiv.swap 7 6 * (Equiv.swap 6 9 * (Equiv.swap 2 0 * (Equiv.swap 0 10 * (Equiv.swap 3 1 * (Equiv.swap 2 5 * (Equiv.swap 1 8 * (Equiv.swap 0 4))))))))) -def smallFlag13_31 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,1),(0,1,1),(0,1,2),(0,2,2),(1,2,3),(2,2,3),(0,3,0),(1,3,0)} - -def smallChoices13_31 : EdgeChoices := (.node 9 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 10 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,1) then (.node 1 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (2,0,1) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (2,0,1) then (.node 1 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (0,1,1) then (.node 5 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else if _v = (0,1,2) then (.node 10 (fun _ => .fallback)) else (.node 10 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,1) then (.node 1 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (2,0,1) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (2,0,1) then (.node 1 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (0,1,1) then (.node 5 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 10 (fun _v => (.node 7 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,3,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (2,2,3) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,3,0) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,2,3) then (.node 4 (fun _v => if _v = (0,3,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (0,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (2,2,3) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,3,0) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 10 (fun _v => (.node 7 (fun _v => (.node 3 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,3) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else if _v = (2,0,1) then (.node 0 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))))))) else (.node 10 (fun _v => if _v = (1,0,0) then (.node 7 (fun _v => (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,2,3) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else if _v = (2,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,2,3) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else if _v = (2,0,1) then (.node 0 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,2,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => 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.fallback)))))))))) else if _v = (2,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (2,2,3) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,3,0) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))))))))))) -lemma smallCert13_31 : solveChoices smallChoices13_31 (.full [3,3,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_31 smallT13_31) smallFlag13_31 = -7 := by - decide +kernel - -lemma smallSupport13_31 : RowSquare [4,4,3,2] [7,4,2] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,2,2,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_31 smallT13_31 smallFlag13_31 smallChoices13_31 - change solveChoices smallChoices13_31 (.full [3,3,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_31 smallT13_31) smallFlag13_31 ≠ 0 - rw [smallCert13_31] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 13 7. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_28 : Equiv.Perm (Fin 13) := Equiv.swap 6 12 * (Equiv.swap 6 0 * (Equiv.swap 0 5 * (Equiv.swap 6 4 * (Equiv.swap 6 7 * (Equiv.swap 5 3 * (Equiv.swap 4 9 * (Equiv.swap 3 11 * (Equiv.swap 2 10 * (Equiv.swap 0 8 * (Equiv.swap 0 1)))))))))) +def smallT13_28 : Equiv.Perm (Fin 13) := Equiv.swap 6 10 * (Equiv.swap 10 3 * (Equiv.swap 6 11 * (Equiv.swap 7 1 * (Equiv.swap 6 8 * (Equiv.swap 1 2 * (Equiv.swap 3 12 * (Equiv.swap 2 9 * (Equiv.swap 1 5 * (Equiv.swap 0 4))))))))) +def smallFlag13_28 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(0,1,0),(0,1,2),(2,1,3),(0,2,2),(3,2,2),(0,2,3),(0,3,0),(1,3,0)} + +def smallChoices13_28 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (0,1,0) then (.node 8 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,3,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => .fallback)))))))))) else (.node 7 (fun _v => if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,2) then (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun 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else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 7 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,3,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 3 (fun _v => if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun 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.fallback)))))))))))) else (.node 1 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 6 (fun _v => (.node 2 (fun _v => if _v = (2,1,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 4 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,1,2) then (.node 7 (fun _v => if _v = (2,1,3) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if 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_v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (3,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (3,2,2) then (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) +lemma smallCert13_28 : solveChoices smallChoices13_28 (.full [4,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_28 smallT13_28) smallFlag13_28 = -4 := by + decide +kernel + +lemma smallSupport13_28 : RowSquare [4,4,3,2] [10,1,1,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [4,1,1,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_28 smallT13_28 smallFlag13_28 smallChoices13_28 + change solveChoices smallChoices13_28 (.full [4,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [4,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_28 smallT13_28) smallFlag13_28 ≠ 0 + rw [smallCert13_28] + norm_num + +def smallB13_29 : Equiv.Perm (Fin 13) := Equiv.swap 2 7 * (Equiv.swap 0 9 * (Equiv.swap 7 4 * (Equiv.swap 0 5 * (Equiv.swap 5 3 * (Equiv.swap 4 12 * (Equiv.swap 3 8 * (Equiv.swap 2 11 * (Equiv.swap 0 6 * (Equiv.swap 0 1))))))))) +def smallT13_29 : Equiv.Perm (Fin 13) := Equiv.swap 5 12 * (Equiv.swap 5 11 * (Equiv.swap 5 9 * (Equiv.swap 1 8 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))) +def smallFlag13_29 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(0,0,3),(0,1,0),(0,1,2),(2,1,2),(0,1,3),(2,2,0),(0,2,1),(0,2,2),(0,3,0),(2,3,0)} + +def smallChoices13_29 : EdgeChoices := (.node 10 (fun _v => if _v = (0,1,0) then (.node 10 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 5 (fun _v => if _v = (0,1,2) then (.node 6 (fun _v => if _v = (2,2,0) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 4 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (2,1,2) then (.node 6 (fun _v => if _v = (0,0,3) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,2,2) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 4 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 6 (fun _v => if _v = (2,1,2) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,1,2) then (.node 6 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => if _v = (2,1,2) then (.node 6 (fun _v => if _v = (0,0,3) then (.node 2 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _ => (.node 5 (fun _ => .fallback)))))) else if _v = (2,2,0) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 4 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))) else (.node 5 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (2,1,2) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => (.node 1 (fun _v => if _v = (2,2,0) then (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 4 (fun _v => (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else if _v = (0,1,3) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 4 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 4 (fun _v => (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (2,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 5 (fun _v => if _v = (0,3,0) then (.node 4 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 4 (fun _ => .fallback)))) else if _v = (0,3,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,2,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => (.node 4 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 6 (fun _v => if _v = (2,2,0) then (.node 3 (fun _v => (.node 3 (fun _v => if _v = (0,3,0) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => (.node 3 (fun _v => if _v = (2,2,0) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (2,1,2) then (.node 3 (fun _v => if _v = (2,1,2) then (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 3 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 6 (fun _v => if _v = (2,1,2) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,2,0) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (2,2,0) then (.node 4 (fun _v => (.node 5 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 5 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (1,0,1) then (.node 8 (fun _v => if _v = (2,2,0) then (.node 3 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 8 (fun _v => if _v = (1,0,1) then (.node 6 (fun _v => if _v = (2,1,2) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,2,0) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _ => (.node 4 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => 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=> .fallback)))) else (.node 1 (fun _ => .fallback)))))) else if _v = (2,2,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,3,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => .fallback)))))))))))))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun 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(.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (2,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,2,0) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))) else if _v = (0,3,0) then (.node 4 (fun _v => if _v = (2,1,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 4 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (1,0,1) then (.node 8 (fun _v => if _v = (2,2,0) then (.node 3 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 4 (fun _v => (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _v => if _v = (2,1,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => .fallback)))))))))) else (.node 8 (fun _v => if _v = (1,0,1) then (.node 6 (fun _v => if _v = (2,1,2) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,3,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (2,1,2) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,2,0) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,2,0) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,3,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 3 (fun _ => (.node 4 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) +lemma smallCert13_29 : solveChoices smallChoices13_29 (.full [3,3,3,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_29 smallT13_29) smallFlag13_29 = 9 := by + decide +kernel + +lemma smallSupport13_29 : RowSquare [4,4,3,2] [7,3,3] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,3,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_29 smallT13_29 smallFlag13_29 smallChoices13_29 + change solveChoices smallChoices13_29 (.full [3,3,3,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,3,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_29 smallT13_29) smallFlag13_29 ≠ 0 + rw [smallCert13_29] + norm_num + +def smallB13_30 : Equiv.Perm (Fin 13) := Equiv.swap 1 12 * (Equiv.swap 8 6 * (Equiv.swap 3 11 * (Equiv.swap 6 10 * (Equiv.swap 1 4 * (Equiv.swap 4 9 * (Equiv.swap 3 7 * (Equiv.swap 1 5))))))) +def smallT13_30 : Equiv.Perm (Fin 13) := Equiv.swap 9 11 * (Equiv.swap 9 3 * (Equiv.swap 3 7 * (Equiv.swap 7 1 * (Equiv.swap 1 0 * (Equiv.swap 1 6 * (Equiv.swap 3 2 * (Equiv.swap 2 8 * (Equiv.swap 1 5 * (Equiv.swap 0 10))))))))) +def smallFlag13_30 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(1,0,2),(1,0,3),(0,1,0),(0,1,1),(2,1,1),(1,2,0),(0,2,2),(1,3,0),(2,3,3)} + +def smallChoices13_30 : EdgeChoices := (.node 12 (fun _v => if _v = (0,0,0) then (.node 11 (fun _v => (.node 2 (fun _v => if _v = (1,0,2) then (.node 8 (fun _ => .fallback)) else (.node 8 (fun _v => (.node 8 (fun _v => if _v = (1,0,1) then (.node 6 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,1,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,1,1) then (.node 0 (fun _v => if _v = (1,3,0) then (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,3,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,1) then (.node 0 (fun _v => if _v = (1,3,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,3,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 2 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,3,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,0,2) then (.node 6 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 4 (fun _v => if _v = (0,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (2,1,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (2,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun 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=> (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (1,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,0,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,0) then (.node 7 (fun _v => if _v = (0,0,0) then (.node 6 (fun _v => if _v = (1,2,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,0,3) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,0,1) then (.node 6 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (2,1,1) then (.node 1 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,1,1) then (.node 2 (fun _ => (.node 4 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 7 (fun _v => if _v = (0,0,0) then (.node 6 (fun _v => if _v = (1,2,0) then (.node 3 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (1,0,2) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => .fallback)) else if _v = (1,0,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,0,1) then (.node 6 (fun _v => if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))) else if _v = (0,1,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 6 (fun _v => if _v = (0,1,0) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (1,0,1) then (.node 6 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 5 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => if _v = (2,1,1) then (.node 1 (fun _ => .fallback)) else if _v = (1,2,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,1) then (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (1,0,1) then (.node 3 (fun _v => (.node 2 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,0,2) then (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,0,3) then (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => (.node 1 (fun _v => if _v = (1,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 3 (fun _ => .fallback)))))))) else (.node 5 (fun _v => if _v = (0,0,0) then (.node 5 (fun _v => if _v = (2,1,1) then (.node 3 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 5 (fun _v => if _v = (1,0,1) then (.node 2 (fun _v => (.node 0 (fun _v => if _v = (1,2,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,2,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,2,0) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,1) then (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,1) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,2) then (.node 3 (fun _v => if _v = (0,0,0) then (.node 2 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 2 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_30 : solveChoices smallChoices13_30 (.full [3,3,2,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,2,2,2,1] (Equiv.refl (Fin 13)) smallB13_30 smallT13_30) smallFlag13_30 = -20 := by + decide +kernel + +lemma smallSupport13_30 : RowSquare [4,4,3,2] [6,5,2] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,2,2,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_30 smallT13_30 smallFlag13_30 smallChoices13_30 + change solveChoices smallChoices13_30 (.full [3,3,2,2,2,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,2,2,2,1] (Equiv.refl (Fin 13)) smallB13_30 smallT13_30) smallFlag13_30 ≠ 0 + rw [smallCert13_30] + norm_num + +def smallB13_31 : Equiv.Perm (Fin 13) := Equiv.swap 6 12 * (Equiv.swap 6 9 * (Equiv.swap 4 11 * (Equiv.swap 6 3 * (Equiv.swap 4 2 * (Equiv.swap 4 1 * (Equiv.swap 3 0 * (Equiv.swap 2 7 * (Equiv.swap 1 5 * (Equiv.swap 0 8))))))))) +def smallT13_31 : Equiv.Perm (Fin 13) := Equiv.swap 7 11 * (Equiv.swap 3 2 * (Equiv.swap 7 6 * (Equiv.swap 6 9 * (Equiv.swap 2 0 * (Equiv.swap 0 10 * (Equiv.swap 3 1 * (Equiv.swap 2 5 * (Equiv.swap 1 8 * (Equiv.swap 0 4))))))))) +def smallFlag13_31 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,1),(0,1,1),(0,1,2),(0,2,2),(1,2,3),(2,2,3),(0,3,0),(1,3,0)} + +def smallChoices13_31 : EdgeChoices := (.node 9 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,1) then (.node 10 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,1) then (.node 1 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (2,0,1) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (2,0,1) then (.node 1 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (0,1,1) then (.node 5 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else if _v = (0,1,2) then (.node 10 (fun _ => .fallback)) else (.node 10 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 0 (fun _v => (.node 1 (fun _v => if _v = (2,0,1) then (.node 1 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (2,0,1) then (.node 6 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (2,0,1) then (.node 1 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => 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.fallback)))))))))) else if _v = (2,0,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (2,2,3) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 1 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,3,0) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,0,1) then (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,3,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))))))))))))) +lemma smallCert13_31 : solveChoices smallChoices13_31 (.full [3,3,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_31 smallT13_31) smallFlag13_31 = -7 := by + decide +kernel + +lemma smallSupport13_31 : RowSquare [4,4,3,2] [7,4,2] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,2,2,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_31 smallT13_31 smallFlag13_31 smallChoices13_31 + change solveChoices smallChoices13_31 (.full [3,3,2,2,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,2,2,1,1,1] (Equiv.refl (Fin 13)) smallB13_31 smallT13_31) smallFlag13_31 ≠ 0 + rw [smallCert13_31] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_8.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_8.lean index d3d4d2cc1b24033892a82f23cbef6a5d36cce813..16adf639d3b5e24919f1551b06ea488f3cbc4756 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_8.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_8.lean @@ -1,91 +1,91 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions - -namespace OAI - -/-! Small Contracts 13 8. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_32 : Equiv.Perm (Fin 13) := Equiv.swap 10 6 * (Equiv.swap 6 11 * (Equiv.swap 5 12 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 0 4))))) -def smallT13_32 : Equiv.Perm (Fin 13) := Equiv.swap 1 5 * (Equiv.swap 1 3 * (Equiv.swap 5 7 * (Equiv.swap 7 12 * (Equiv.swap 3 11 * (Equiv.swap 5 0 * (Equiv.swap 4 2 * (Equiv.swap 3 6 * (Equiv.swap 2 9 * (Equiv.swap 1 10 * (Equiv.swap 0 8)))))))))) -def smallFlag13_32 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,2),(0,1,1),(1,1,1),(0,2,0),(0,2,2),(0,3,3)} - -def smallChoices13_32 : EdgeChoices := (.node 6 (fun _v => if _v = (0,0,0) then (.node 11 (fun _v => if _v = (0,1,1) then (.node 10 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 9 (fun _v => (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (0,2,2) then (.node 9 (fun _v => (.node 4 (fun _v => (.node 7 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 9 (fun _v => if _v = (0,2,0) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 4 (fun _v => (.node 7 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else if _v = (0,1,1) then (.node 11 (fun _v => if _v = (0,0,0) then (.node 10 (fun _ => .fallback)) else if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 9 (fun _v => (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (0,2,2) then (.node 9 (fun _v => (.node 4 (fun _v => (.node 7 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 9 (fun _v => if _v = (0,2,0) then (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => 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(.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => 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(fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else (.node 0 (fun 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=> (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => if _v = (0,2,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 5 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_32 : solveChoices smallChoices13_32 (.full [3,3,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_32 smallT13_32) smallFlag13_32 = 8 := by - decide +kernel - -lemma smallSupport13_32 : RowSquare [4,4,3,2] [8,3,2] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,2,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_32 smallT13_32 smallFlag13_32 smallChoices13_32 - change solveChoices smallChoices13_32 (.full [3,3,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_32 smallT13_32) smallFlag13_32 ≠ 0 - rw [smallCert13_32] - norm_num - -def smallB13_33 : Equiv.Perm (Fin 13) := Equiv.swap 9 2 * (Equiv.swap 9 10 * (Equiv.swap 3 12 * (Equiv.swap 2 1 * (Equiv.swap 3 0 * (Equiv.swap 0 7 * (Equiv.swap 3 5 * (Equiv.swap 2 6 * (Equiv.swap 1 11 * (Equiv.swap 0 4))))))))) -def smallT13_33 : Equiv.Perm (Fin 13) := Equiv.swap 2 10 * (Equiv.swap 10 12 * (Equiv.swap 2 7 * (Equiv.swap 7 11 * (Equiv.swap 2 3 * (Equiv.swap 3 1 * (Equiv.swap 1 8 * (Equiv.swap 3 0 * (Equiv.swap 2 6 * (Equiv.swap 1 4 * (Equiv.swap 0 5)))))))))) -def smallFlag13_33 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(0,0,1),(0,0,3),(1,1,0),(0,1,2),(2,1,3),(0,2,1),(0,2,2),(0,3,1)} - -def smallChoices13_33 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 7 (fun 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0 (fun _ => .fallback)) else (.node 6 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 6 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 6 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 6 (fun _ => (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))))))) else if _v = (0,2,1) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 4 (fun _ => .fallback)))))))) else if _v = (2,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 6 (fun _ => .fallback)))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 6 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 6 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 6 (fun _ => .fallback)) else if _v = (2,1,3) then (.node 6 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 (fun 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.fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => .fallback)) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else if _v = (1,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => .fallback)))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 5 (fun _v => if _v = (0,0,0) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (1,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,2) then (.node 5 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => (.node 1 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else if _v = (2,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 2 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,0,0) then (.node 3 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,2) then (.node 3 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => .fallback)) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else if _v = (1,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 7 (fun _v => if _v = (0,0,0) then (.node 1 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,0,1) then (.node 1 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,0,0) then (.node 3 (fun _v => if _v = (1,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,1,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,2) then (.node 3 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 3 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => .fallback)) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else if _v = (1,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _ => .fallback)))))))))))))))) else (.node 9 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 5 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,0,0) then (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,2,1) then (.node 5 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else if _v = (0,0,1) then (.node 3 (fun _v => if _v = (2,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,1,0) then (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => if _v = (2,0,0) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,0) then (.node 5 (fun _ => (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,0,0) then (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,2,1) then (.node 5 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else if _v = (0,0,1) then (.node 3 (fun _v => if _v = (2,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,1,0) then (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => if _v = (2,0,0) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) -lemma smallCert13_33 : solveChoices smallChoices13_33 (.full [3,3,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_33 smallT13_33) smallFlag13_33 = -24 := by - decide +kernel - -lemma smallSupport13_33 : RowSquare [4,4,3,2] [9,2,2] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_33 smallT13_33 smallFlag13_33 smallChoices13_33 - change solveChoices smallChoices13_33 (.full [3,3,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_33 smallT13_33) smallFlag13_33 ≠ 0 - rw [smallCert13_33] - norm_num - -def smallB13_34 : Equiv.Perm (Fin 13) := Equiv.swap 8 1 * (Equiv.swap 9 11 * (Equiv.swap 8 5 * (Equiv.swap 5 3 * (Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 3 10 * (Equiv.swap 3 4 * (Equiv.swap 2 7 * (Equiv.swap 1 12 * (Equiv.swap 0 6)))))))))) -def smallT13_34 : Equiv.Perm (Fin 13) := Equiv.swap 11 10 * (Equiv.swap 10 7 * (Equiv.swap 7 4 * (Equiv.swap 5 9 * (Equiv.swap 4 2 * (Equiv.swap 2 12 * (Equiv.swap 1 0 * (Equiv.swap 0 8))))))) -def smallFlag13_34 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(1,0,2),(2,0,2),(0,1,0),(0,1,1),(0,2,1),(1,2,2),(1,2,3),(0,3,0),(1,3,3)} - -def smallChoices13_34 : EdgeChoices := (.node 9 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 6 (fun _v => (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 6 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,3) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,3) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))))))))) else (.node 6 (fun _v => if _v = (1,2,2) then (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,3) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,3) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 6 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,3) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 5 (fun _v => (.node 0 (fun _v 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(fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (1,2,3) then (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,3,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))) else if _v = 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.fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,3) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => if _v = (1,0,2) then (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,2,2) then (.node 3 (fun _ => .fallback)) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))))))) else if _v = (1,0,2) then (.node 6 (fun _v => (.node 3 (fun _v => (.node 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then (.node 1 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))))))))))))) -lemma smallCert13_34 : solveChoices smallChoices13_34 (.full [3,2,2,2,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,2,2,2] (Equiv.refl (Fin 13)) smallB13_34 smallT13_34) smallFlag13_34 = -8 := by - decide +kernel - -lemma smallSupport13_34 : RowSquare [4,4,3,2] [6,6,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,2,2,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_34 smallT13_34 smallFlag13_34 smallChoices13_34 - change solveChoices smallChoices13_34 (.full [3,2,2,2,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,2,2,2] (Equiv.refl (Fin 13)) smallB13_34 smallT13_34) smallFlag13_34 ≠ 0 - rw [smallCert13_34] - norm_num - -def smallB13_35 : Equiv.Perm (Fin 13) := Equiv.swap 5 12 * (Equiv.swap 8 11 * (Equiv.swap 8 6 * (Equiv.swap 5 2 * (Equiv.swap 6 9 * (Equiv.swap 5 1 * (Equiv.swap 1 7 * (Equiv.swap 2 10 * (Equiv.swap 1 4 * (Equiv.swap 0 3))))))))) -def smallT13_35 : Equiv.Perm (Fin 13) := Equiv.swap 1 11 * (Equiv.swap 1 7 * (Equiv.swap 8 12 * (Equiv.swap 7 10 * (Equiv.swap 3 6 * (Equiv.swap 3 5 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 1 9 * (Equiv.swap 0 4))))))))) -def smallFlag13_35 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,2),(0,0,3),(1,0,3),(0,1,0),(1,1,1),(0,2,1),(0,2,2),(2,3,0),(1,3,2)} - -def smallChoices13_35 : EdgeChoices := (.node 10 (fun _v => if _v = (0,1,0) then (.node 11 (fun _v => (.node 10 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,0,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,3) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (1,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,0,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,0,3) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => 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then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))) else if _v = (0,2,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,2) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,1) then (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 8 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,2,1) then (.node 0 (fun 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=> (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,1,1) then (.node 1 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,1,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 3 (fun _v => if _v = (1,1,1) then (.node 3 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,3) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,3) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) -lemma smallCert13_35 : solveChoices smallChoices13_35 (.full [3,2,2,2,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,2,2,1,1] (Equiv.refl (Fin 13)) smallB13_35 smallT13_35) smallFlag13_35 = 16 := by - decide +kernel - -lemma smallSupport13_35 : RowSquare [4,4,3,2] [7,5,1] := by - apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,2,2,2,2,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_35 smallT13_35 smallFlag13_35 smallChoices13_35 - change solveChoices smallChoices13_35 (.full [3,2,2,2,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,2,2,1,1] (Equiv.refl (Fin 13)) smallB13_35 smallT13_35) smallFlag13_35 ≠ 0 - rw [smallCert13_35] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.ChoiceContractions + +namespace OAI + +/-! Small Contracts 13 8. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_32 : Equiv.Perm (Fin 13) := Equiv.swap 10 6 * (Equiv.swap 6 11 * (Equiv.swap 5 12 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 0 4))))) +def smallT13_32 : Equiv.Perm (Fin 13) := Equiv.swap 1 5 * (Equiv.swap 1 3 * (Equiv.swap 5 7 * (Equiv.swap 7 12 * (Equiv.swap 3 11 * (Equiv.swap 5 0 * (Equiv.swap 4 2 * (Equiv.swap 3 6 * (Equiv.swap 2 9 * (Equiv.swap 1 10 * (Equiv.swap 0 8)))))))))) +def smallFlag13_32 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,2),(0,1,1),(1,1,1),(0,2,0),(0,2,2),(0,3,3)} + +def smallChoices13_32 : EdgeChoices := (.node 6 (fun _v => if _v = (0,0,0) then (.node 11 (fun _v => if _v = (0,1,1) then (.node 10 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,2,0) then (.node 9 (fun _v => (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else if _v = (0,2,2) then (.node 9 (fun _v => (.node 4 (fun _v => (.node 7 (fun _v => if _v = (0,1,1) then (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 9 (fun _v => 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=> (.node 0 (fun _ => .fallback)))))))))))))) else (.node 1 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))) else if _v = (0,1,1) then (.node 11 (fun _v => if _v = (0,0,0) then (.node 10 (fun _ => .fallback)) else if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,0) then (.node 9 (fun _v => (.node 4 (fun _v => (.node 1 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => 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else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_32 : solveChoices smallChoices13_32 (.full [3,3,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_32 smallT13_32) smallFlag13_32 = 8 := by + decide +kernel + +lemma smallSupport13_32 : RowSquare [4,4,3,2] [8,3,2] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,2,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_32 smallT13_32 smallFlag13_32 smallChoices13_32 + change solveChoices smallChoices13_32 (.full [3,3,2,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,2,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_32 smallT13_32) smallFlag13_32 ≠ 0 + rw [smallCert13_32] + norm_num + +def smallB13_33 : Equiv.Perm (Fin 13) := Equiv.swap 9 2 * (Equiv.swap 9 10 * (Equiv.swap 3 12 * (Equiv.swap 2 1 * (Equiv.swap 3 0 * (Equiv.swap 0 7 * (Equiv.swap 3 5 * (Equiv.swap 2 6 * (Equiv.swap 1 11 * (Equiv.swap 0 4))))))))) +def smallT13_33 : Equiv.Perm (Fin 13) := Equiv.swap 2 10 * (Equiv.swap 10 12 * (Equiv.swap 2 7 * (Equiv.swap 7 11 * (Equiv.swap 2 3 * (Equiv.swap 3 1 * (Equiv.swap 1 8 * (Equiv.swap 3 0 * (Equiv.swap 2 6 * (Equiv.swap 1 4 * (Equiv.swap 0 5)))))))))) +def smallFlag13_33 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(0,0,1),(0,0,3),(1,1,0),(0,1,2),(2,1,3),(0,2,1),(0,2,2),(0,3,1)} + +def smallChoices13_33 : EdgeChoices := (.node 11 (fun _v => if _v = (0,0,0) then (.node 0 (fun _v => if _v = (1,1,0) then (.node 7 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,1) then (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (2,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => .fallback)) else (.node 6 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 6 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 6 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,1,2) then (.node 3 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 6 (fun _ => (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))))))) else if _v = (0,2,1) then (.node 4 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 3 (fun _ => (.node 4 (fun _ => .fallback)))))))) else if _v = (2,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 6 (fun _ => .fallback)))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 6 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 6 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 6 (fun _ => .fallback)) else if _v = (2,1,3) then (.node 6 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else if _v = (2,0,0) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _ => (.node 6 (fun _ => .fallback)))) else if _v = (0,2,1) then (.node 0 (fun _ => (.node 6 (fun _ => .fallback)))) else if _v = (0,2,2) then (.node 0 (fun _v => if _v = (2,1,3) then (.node 6 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,1,2) then (.node 6 (fun _ => .fallback)) else if _v = (2,1,3) then (.node 6 (fun _ => (.node 2 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 5 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (0,1,2) then (.node 0 (fun _v => if _v = (0,0,1) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (0,0,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,1,2) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (2,1,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))) else if _v = (0,1,2) then (.node 3 (fun _v => if _v = (2,0,0) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,0,1) then (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,3) then (.node 1 (fun _v => if _v = (1,1,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 2 (fun _ => .fallback)))) else (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,1,0) then (.node 1 (fun _v => if _v = (2,0,0) then (.node 1 (fun _v => (.node 4 (fun _v => if _v = (0,0,0) then (.node 6 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 3 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 4 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,0,0) then (.node 3 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else (.node 1 (fun _ => (.node 4 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 7 (fun _v => if _v = (0,0,0) then (.node 4 (fun _v => if _v = (0,0,1) then (.node 4 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,1) then (.node 4 (fun _v => (.node 3 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else if _v = (0,0,1) then (.node 0 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=> .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => (.node 1 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 3 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))))) else if _v = (0,0,1) then (.node 3 (fun _v => if _v = (2,0,0) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,1,0) then (.node 1 (fun _v => if _v = (2,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 5 (fun _v => if _v = (2,0,0) then (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 5 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))) +lemma smallCert13_33 : solveChoices smallChoices13_33 (.full [3,3,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_33 smallT13_33) smallFlag13_33 = -24 := by + decide +kernel + +lemma smallSupport13_33 : RowSquare [4,4,3,2] [9,2,2] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,3,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_33 smallT13_33 smallFlag13_33 smallChoices13_33 + change solveChoices smallChoices13_33 (.full [3,3,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,3,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_33 smallT13_33) smallFlag13_33 ≠ 0 + rw [smallCert13_33] + norm_num + +def smallB13_34 : Equiv.Perm (Fin 13) := Equiv.swap 8 1 * (Equiv.swap 9 11 * (Equiv.swap 8 5 * (Equiv.swap 5 3 * (Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 3 10 * (Equiv.swap 3 4 * (Equiv.swap 2 7 * (Equiv.swap 1 12 * (Equiv.swap 0 6)))))))))) +def smallT13_34 : Equiv.Perm (Fin 13) := Equiv.swap 11 10 * (Equiv.swap 10 7 * (Equiv.swap 7 4 * (Equiv.swap 5 9 * (Equiv.swap 4 2 * (Equiv.swap 2 12 * (Equiv.swap 1 0 * (Equiv.swap 0 8))))))) +def smallFlag13_34 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(1,0,2),(2,0,2),(0,1,0),(0,1,1),(0,2,1),(1,2,2),(1,2,3),(0,3,0),(1,3,3)} + +def smallChoices13_34 : EdgeChoices := (.node 9 (fun _v => if _v = (1,0,1) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 6 (fun _v => (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 6 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,3) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,3) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))))))))) else (.node 6 (fun _v => if _v = (1,2,2) then (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,3) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 4 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (0,1,0) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 2 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,3) then (.node 4 (fun _ => .fallback)) else (.node 4 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 4 (fun _ => .fallback)))))))))))) else (.node 6 (fun _v => (.node 3 (fun _v => if _v = (0,1,0) then (.node 6 (fun _v => if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,3) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,2,2) then (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))) else if _v = (1,2,3) then (.node 5 (fun _ => .fallback)) else (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 5 (fun _ => .fallback)))))))))))))) else if _v = (0,1,0) then (.node 4 (fun _v => if _v = (1,0,1) then (.node 6 (fun _v => if _v = (2,0,2) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 2 (fun _v => if _v = (1,2,3) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 5 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (1,0,1) then (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (1,2,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else if _v = (1,2,2) then (.node 7 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,3) then (.node 6 (fun _v => if _v = (0,1,0) then (.node 5 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 3 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,3,0) then (.node 6 (fun _v => (.node 0 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 6 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))) else if _v = (1,2,3) then (.node 6 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 6 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else if _v = (0,1,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 2 (fun _v => if _v = (1,0,2) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 7 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 6 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,2,2) then (.node 6 (fun _v => if _v = 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else if _v = (0,1,1) then (.node 6 (fun _ => (.node 5 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 4 (fun _v => (.node 1 (fun _v => if _v = (0,1,0) then (.node 4 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 4 (fun _v => (.node 1 (fun _v => if _v = (0,1,1) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))))))) else (.node 6 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (0,1,1) then (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))))))))) else (.node 6 (fun _v => (.node 3 (fun _v => if _v = 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(fun _v => (.node 3 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => if _v = (0,1,1) then (.node 1 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))))) else (.node 2 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,1) then (.node 0 (fun _v => (.node 5 (fun _v => if _v = (0,1,0) then (.node 4 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 4 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,1,0) then (.node 0 (fun _v => (.node 3 (fun _v => (.node 1 (fun _v => if _v = (1,0,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))))))))))))) +lemma smallCert13_34 : solveChoices smallChoices13_34 (.full [3,2,2,2,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,2,2,2] (Equiv.refl (Fin 13)) smallB13_34 smallT13_34) smallFlag13_34 = -8 := by + decide +kernel + +lemma smallSupport13_34 : RowSquare [4,4,3,2] [6,6,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,2,2,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_34 smallT13_34 smallFlag13_34 smallChoices13_34 + change solveChoices smallChoices13_34 (.full [3,2,2,2,2,2]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,2,2,2] (Equiv.refl (Fin 13)) smallB13_34 smallT13_34) smallFlag13_34 ≠ 0 + rw [smallCert13_34] + norm_num + +def smallB13_35 : Equiv.Perm (Fin 13) := Equiv.swap 5 12 * (Equiv.swap 8 11 * (Equiv.swap 8 6 * (Equiv.swap 5 2 * (Equiv.swap 6 9 * (Equiv.swap 5 1 * (Equiv.swap 1 7 * (Equiv.swap 2 10 * (Equiv.swap 1 4 * (Equiv.swap 0 3))))))))) +def smallT13_35 : Equiv.Perm (Fin 13) := Equiv.swap 1 11 * (Equiv.swap 1 7 * (Equiv.swap 8 12 * (Equiv.swap 7 10 * (Equiv.swap 3 6 * (Equiv.swap 3 5 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 1 9 * (Equiv.swap 0 4))))))))) +def smallFlag13_35 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,2),(0,0,3),(1,0,3),(0,1,0),(1,1,1),(0,2,1),(0,2,2),(2,3,0),(1,3,2)} + +def smallChoices13_35 : EdgeChoices := (.node 10 (fun _v => if _v = (0,1,0) then (.node 11 (fun _v => (.node 10 (fun _v => if _v = (0,0,2) then (.node 1 (fun _v => if _v = (1,0,0) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 0 (fun _v => (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 1 (fun _v => (.node 0 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (1,0,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,3) then (.node 0 (fun _ => .fallback)) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))) else if _v = (1,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))) else (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,0,3) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,2) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (1,0,3) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,0,3) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (1,1,1) then (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => (.node 1 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (1,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))))))))) else if _v = (1,0,3) then (.node 8 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 0 (fun _v => (.node 5 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 1 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (0,2,2) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,1,0) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else if _v = (0,2,1) then (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))))))) else if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,2,1) then (.node 2 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,1,0) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,3) then (.node 3 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 4 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => .fallback)))))) else if _v = (0,2,2) then (.node 0 (fun _v => (.node 1 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))) else if _v = (1,1,1) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,1,0) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _ => (.node 3 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,3) then (.node 0 (fun _v => if _v = (0,2,2) then (.node 0 (fun _ => .fallback)) else (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (0,0,3) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 2 (fun _v => if _v = (0,0,3) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => .fallback)))))))))))) else (.node 2 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (1,1,1) then (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,1,0) then (.node 0 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 1 (fun _ => .fallback)))))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,3) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 1 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))) else (.node 8 (fun _v => if _v = (1,0,0) then (.node 2 (fun _v => if _v = (0,0,2) then (.node 0 (fun _v => (.node 5 (fun _v => (.node 0 (fun _v => if _v = (0,0,3) then (.node 0 (fun _v => if _v = (1,1,1) then (.node 0 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))) else if _v = (0,2,1) then (.node 0 (fun _v => (.node 2 (fun 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.fallback)))))))) else (.node 0 (fun _ => (.node 2 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,3) then (.node 4 (fun _v => if _v = (0,1,0) then (.node 2 (fun _v => if _v = (1,0,0) then (.node 0 (fun _v => if _v = (0,2,1) then (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))) else (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _ => (.node 1 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 3 (fun _v => if _v = (0,0,2) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))) else if _v = (0,0,3) then (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 0 (fun _v => if _v = (1,0,0) then (.node 2 (fun _ => (.node 1 (fun _ => .fallback)))) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 1 (fun _v => (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else if _v = (1,0,3) then (.node 1 (fun _ => (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))) else (.node 1 (fun _v => if _v = (1,0,0) then (.node 3 (fun _v => (.node 0 (fun _v => if _v = (1,0,0) then (.node 0 (fun _ => .fallback)) else (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))) else (.node 3 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => (.node 0 (fun _ => .fallback)))))))))))))))))))))))))) +lemma smallCert13_35 : solveChoices smallChoices13_35 (.full [3,2,2,2,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,2,2,1,1] (Equiv.refl (Fin 13)) smallB13_35 smallT13_35) smallFlag13_35 = 16 := by + decide +kernel + +lemma smallSupport13_35 : RowSquare [4,4,3,2] [7,5,1] := by + apply rowSquare_choices (n := 13) (cs := [4,4,3,2]) (ts := [3,2,2,2,2,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_35 smallT13_35 smallFlag13_35 smallChoices13_35 + change solveChoices smallChoices13_35 (.full [3,2,2,2,2,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,2,2,1,1] (Equiv.refl (Fin 13)) smallB13_35 smallT13_35) smallFlag13_35 ≠ 0 + rw [smallCert13_35] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_9.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_9.lean index c46e8ec2e5b043788072d2b20a7734ab844102c1..453709dbaf47b94bb5edb8e718178444685dc2d7 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_9.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Finite/SmallContracts13_9.lean @@ -1,83 +1,83 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains - -namespace OAI - -/-! Small Contracts 13 9. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def smallB13_36 : Equiv.Perm (Fin 13) := Equiv.swap 7 6 * (Equiv.swap 7 3 * (Equiv.swap 1 11 * (Equiv.swap 7 9 * (Equiv.swap 6 5 * (Equiv.swap 5 2 * (Equiv.swap 3 10 * (Equiv.swap 2 12 * (Equiv.swap 1 8 * (Equiv.swap 0 4))))))))) -def smallT13_36 : Equiv.Perm (Fin 13) := Equiv.swap 2 9 * (Equiv.swap 9 11 * (Equiv.swap 8 12 * (Equiv.swap 2 10 * (Equiv.swap 3 1 * (Equiv.swap 2 4 * (Equiv.swap 1 5 * (Equiv.swap 0 7))))))) -def smallFlag13_36 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,1),(0,1,0),(0,1,2),(0,1,3),(1,1,3),(1,2,1),(0,2,2),(0,3,1),(1,3,2)} -lemma smallCert13_36 : solveCompact 13 (.full [3,2,2,2,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,2,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_36 smallT13_36) smallFlag13_36 = -7 := by - decide +kernel - -lemma smallSupport13_36 : RowSquare [4,4,3,2] [8,4,1] := by - apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [3,2,2,2,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_36 smallT13_36 smallFlag13_36 - change solveCompact 13 (.full [3,2,2,2,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,2,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_36 smallT13_36) smallFlag13_36 ≠ 0 - rw [smallCert13_36] - norm_num - -def smallB13_37 : Equiv.Perm (Fin 13) := Equiv.swap 10 8 * (Equiv.swap 10 7 * (Equiv.swap 7 4 * (Equiv.swap 8 12 * (Equiv.swap 7 1 * (Equiv.swap 4 11 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 1 9 * (Equiv.swap 0 5))))))))) -def smallT13_37 : Equiv.Perm (Fin 13) := Equiv.swap 1 10 * (Equiv.swap 10 7 * (Equiv.swap 7 5 * (Equiv.swap 7 4 * (Equiv.swap 5 0 * (Equiv.swap 5 6 * (Equiv.swap 4 8 * (Equiv.swap 0 12 * (Equiv.swap 1 11 * (Equiv.swap 1 2 * (Equiv.swap 0 3)))))))))) -def smallFlag13_37 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(0,1,0),(2,1,1),(1,1,2),(0,2,2),(0,2,3),(0,3,0),(1,3,1)} -lemma smallCert13_37 : solveCompact 13 (.full [3,2,2,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_37 smallT13_37) smallFlag13_37 = -4 := by - decide +kernel - -lemma smallSupport13_37 : RowSquare [4,4,3,2] [9,3,1] := by - apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [3,2,2,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_37 smallT13_37 smallFlag13_37 - change solveCompact 13 (.full [3,2,2,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_37 smallT13_37) smallFlag13_37 ≠ 0 - rw [smallCert13_37] - norm_num - -def smallB13_38 : Equiv.Perm (Fin 13) := Equiv.swap 3 6 * (Equiv.swap 3 1 * (Equiv.swap 1 2 * (Equiv.swap 6 12 * (Equiv.swap 6 4 * (Equiv.swap 4 0 * (Equiv.swap 3 10 * (Equiv.swap 2 11 * (Equiv.swap 1 9 * (Equiv.swap 0 8))))))))) -def smallT13_38 : Equiv.Perm (Fin 13) := Equiv.swap 1 2 * (Equiv.swap 1 10 * (Equiv.swap 4 12 * (Equiv.swap 4 8 * (Equiv.swap 4 5 * (Equiv.swap 2 11 * (Equiv.swap 2 3 * (Equiv.swap 1 9))))))) -def smallFlag13_38 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(1,0,2),(0,1,1),(0,1,2),(1,1,3),(0,2,0),(2,2,1),(0,3,2),(0,3,3)} -lemma smallCert13_38 : solveCompact 13 (.full [3,2,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_38 smallT13_38) smallFlag13_38 = -12 := by - decide +kernel - -lemma smallSupport13_38 : RowSquare [4,4,3,2] [10,2,1] := by - apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [3,2,1,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_38 smallT13_38 smallFlag13_38 - change solveCompact 13 (.full [3,2,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_38 smallT13_38) smallFlag13_38 ≠ 0 - rw [smallCert13_38] - norm_num - -def smallB13_39 : Equiv.Perm (Fin 13) := Equiv.swap 0 12 * (Equiv.swap 7 5 * (Equiv.swap 7 3 * (Equiv.swap 5 4 * (Equiv.swap 4 10 * (Equiv.swap 3 9 * (Equiv.swap 0 11 * (Equiv.swap 0 1))))))) -def smallT13_39 : Equiv.Perm (Fin 13) := Equiv.swap 10 4 * (Equiv.swap 10 3 * (Equiv.swap 3 2 * (Equiv.swap 2 11 * (Equiv.swap 2 8 * (Equiv.swap 3 9 * (Equiv.swap 4 1 * (Equiv.swap 3 5 * (Equiv.swap 2 7 * (Equiv.swap 1 12))))))))) -def smallFlag13_39 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(1,0,2),(0,1,0),(2,1,1),(0,2,2),(0,2,3),(0,3,1),(0,3,3)} -lemma smallCert13_39 : solveCompact 13 (.full [3,1,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,1,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_39 smallT13_39) smallFlag13_39 = 14 := by - decide +kernel - -lemma smallSupport13_39 : RowSquare [4,4,3,2] [11,1,1] := by - apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [3,1,1,1,1,1,1,1,1,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl smallB13_39 smallT13_39 smallFlag13_39 - change solveCompact 13 (.full [3,1,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) - (certificateEdges [4,4,3,2] [4,4,3,2] [3,1,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_39 smallT13_39) smallFlag13_39 ≠ 0 - rw [smallCert13_39] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains + +namespace OAI + +/-! Small Contracts 13 9. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def smallB13_36 : Equiv.Perm (Fin 13) := Equiv.swap 7 6 * (Equiv.swap 7 3 * (Equiv.swap 1 11 * (Equiv.swap 7 9 * (Equiv.swap 6 5 * (Equiv.swap 5 2 * (Equiv.swap 3 10 * (Equiv.swap 2 12 * (Equiv.swap 1 8 * (Equiv.swap 0 4))))))))) +def smallT13_36 : Equiv.Perm (Fin 13) := Equiv.swap 2 9 * (Equiv.swap 9 11 * (Equiv.swap 8 12 * (Equiv.swap 2 10 * (Equiv.swap 3 1 * (Equiv.swap 2 4 * (Equiv.swap 1 5 * (Equiv.swap 0 7))))))) +def smallFlag13_36 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,1),(0,1,0),(0,1,2),(0,1,3),(1,1,3),(1,2,1),(0,2,2),(0,3,1),(1,3,2)} +lemma smallCert13_36 : solveCompact 13 (.full [3,2,2,2,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,2,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_36 smallT13_36) smallFlag13_36 = -7 := by + decide +kernel + +lemma smallSupport13_36 : RowSquare [4,4,3,2] [8,4,1] := by + apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [3,2,2,2,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_36 smallT13_36 smallFlag13_36 + change solveCompact 13 (.full [3,2,2,2,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,2,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_36 smallT13_36) smallFlag13_36 ≠ 0 + rw [smallCert13_36] + norm_num + +def smallB13_37 : Equiv.Perm (Fin 13) := Equiv.swap 10 8 * (Equiv.swap 10 7 * (Equiv.swap 7 4 * (Equiv.swap 8 12 * (Equiv.swap 7 1 * (Equiv.swap 4 11 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 1 9 * (Equiv.swap 0 5))))))))) +def smallT13_37 : Equiv.Perm (Fin 13) := Equiv.swap 1 10 * (Equiv.swap 10 7 * (Equiv.swap 7 5 * (Equiv.swap 7 4 * (Equiv.swap 5 0 * (Equiv.swap 5 6 * (Equiv.swap 4 8 * (Equiv.swap 0 12 * (Equiv.swap 1 11 * (Equiv.swap 1 2 * (Equiv.swap 0 3)))))))))) +def smallFlag13_37 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(0,1,0),(2,1,1),(1,1,2),(0,2,2),(0,2,3),(0,3,0),(1,3,1)} +lemma smallCert13_37 : solveCompact 13 (.full [3,2,2,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_37 smallT13_37) smallFlag13_37 = -4 := by + decide +kernel + +lemma smallSupport13_37 : RowSquare [4,4,3,2] [9,3,1] := by + apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [3,2,2,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_37 smallT13_37 smallFlag13_37 + change solveCompact 13 (.full [3,2,2,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,2,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_37 smallT13_37) smallFlag13_37 ≠ 0 + rw [smallCert13_37] + norm_num + +def smallB13_38 : Equiv.Perm (Fin 13) := Equiv.swap 3 6 * (Equiv.swap 3 1 * (Equiv.swap 1 2 * (Equiv.swap 6 12 * (Equiv.swap 6 4 * (Equiv.swap 4 0 * (Equiv.swap 3 10 * (Equiv.swap 2 11 * (Equiv.swap 1 9 * (Equiv.swap 0 8))))))))) +def smallT13_38 : Equiv.Perm (Fin 13) := Equiv.swap 1 2 * (Equiv.swap 1 10 * (Equiv.swap 4 12 * (Equiv.swap 4 8 * (Equiv.swap 4 5 * (Equiv.swap 2 11 * (Equiv.swap 2 3 * (Equiv.swap 1 9))))))) +def smallFlag13_38 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(1,0,2),(0,1,1),(0,1,2),(1,1,3),(0,2,0),(2,2,1),(0,3,2),(0,3,3)} +lemma smallCert13_38 : solveCompact 13 (.full [3,2,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_38 smallT13_38) smallFlag13_38 = -12 := by + decide +kernel + +lemma smallSupport13_38 : RowSquare [4,4,3,2] [10,2,1] := by + apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [3,2,1,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_38 smallT13_38 smallFlag13_38 + change solveCompact 13 (.full [3,2,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,2,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_38 smallT13_38) smallFlag13_38 ≠ 0 + rw [smallCert13_38] + norm_num + +def smallB13_39 : Equiv.Perm (Fin 13) := Equiv.swap 0 12 * (Equiv.swap 7 5 * (Equiv.swap 7 3 * (Equiv.swap 5 4 * (Equiv.swap 4 10 * (Equiv.swap 3 9 * (Equiv.swap 0 11 * (Equiv.swap 0 1))))))) +def smallT13_39 : Equiv.Perm (Fin 13) := Equiv.swap 10 4 * (Equiv.swap 10 3 * (Equiv.swap 3 2 * (Equiv.swap 2 11 * (Equiv.swap 2 8 * (Equiv.swap 3 9 * (Equiv.swap 4 1 * (Equiv.swap 3 5 * (Equiv.swap 2 7 * (Equiv.swap 1 12))))))))) +def smallFlag13_39 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(1,0,2),(0,1,0),(2,1,1),(0,2,2),(0,2,3),(0,3,1),(0,3,3)} +lemma smallCert13_39 : solveCompact 13 (.full [3,1,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,1,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_39 smallT13_39) smallFlag13_39 = 14 := by + decide +kernel + +lemma smallSupport13_39 : RowSquare [4,4,3,2] [11,1,1] := by + apply rowSquare_compact (n := 13) (cs := [4,4,3,2]) (ts := [3,1,1,1,1,1,1,1,1,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl smallB13_39 smallT13_39 smallFlag13_39 + change solveCompact 13 (.full [3,1,1,1,1,1,1,1,1,1,1]) (.full [4,4,3,2]) (.full [4,4,3,2]) + (certificateEdges [4,4,3,2] [4,4,3,2] [3,1,1,1,1,1,1,1,1,1,1] (Equiv.refl (Fin 13)) smallB13_39 smallT13_39) smallFlag13_39 ≠ 0 + rw [smallCert13_39] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Main.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Main.lean index 4351352ea8f0d3810492774c4bb590249bbf23cd..60fd3a62e083b181c91758ae41f7f954107f69ac 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Main.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Main.lean @@ -1,221 +1,221 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Support.Asymptotic -import OAI.RepresentationTheory.UniversalSquare.Support.ExceptionalFourteen -import OAI.RepresentationTheory.UniversalSquare.Support.SmallDegrees -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree11 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree12 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree13 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree14 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree16 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree17 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree18 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree19 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree20 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree22 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree23 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree24 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree25 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree26 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree27 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree29 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree30 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree31 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree32 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree33 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree34 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree35 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree37 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree38 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree39 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree40 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree41 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree42 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree43 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree44 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree46 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree47 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree48 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree49 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree50 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree51 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree52 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree53 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree54 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree56 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree57 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree58 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree59 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree60 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree61 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree62 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree63 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree64 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree89 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree112 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree116 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree118 -import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree151 - -namespace OAI - -/-! Universal tensor squares. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl - -lemma universal_partition_le64 (n : ℕ) (hn : 0 < n) - (h2 : n ≠ 2) (h4 : n ≠ 4) (h9 : n ≠ 9) (hsmall : n ≤ 64) : - ∃ (lam : YoungDiagram) (hc : lam.card = n), - ∀ (μ : YoungDiagram) (hμ : μ.card = n), - 0 < kronecker (canonicalTableau lam hc) (canonicalTableau lam hc) - (canonicalTableau μ hμ) := by - by_cases hten : n ≤ 10 - · obtain ⟨lam,hc,hpos,_⟩ := universal_tensor_square_le_ten.{0} n hn h2 h4 h9 hten - exact ⟨lam,hc,hpos⟩ - have hlo : 11 ≤ n := by omega - interval_cases n - · exact ⟨_,degreeCard11,degree_pos11⟩ - · exact ⟨_,degreeCard12,degree_pos12⟩ - · exact ⟨_,degreeCard13,degree_pos13⟩ - · exact ⟨_,degreeCard14,degree_pos14⟩ - · exact ⟨staircase 5,staircase_card 5,saxl_kronecker_pos 5 (by decide)⟩ - · exact ⟨_,degreeCard16,degree_pos16⟩ - · exact ⟨_,degreeCard17,degree_pos17⟩ - · exact ⟨_,degreeCard18,degree_pos18⟩ - · exact ⟨_,degreeCard19,degree_pos19⟩ - · exact ⟨_,degreeCard20,degree_pos20⟩ - · exact ⟨staircase 6,staircase_card 6,saxl_kronecker_pos 6 (by decide)⟩ - · exact ⟨_,degreeCard22,degree_pos22⟩ - · exact ⟨_,degreeCard23,degree_pos23⟩ - · exact ⟨_,degreeCard24,degree_pos24⟩ - · exact ⟨_,degreeCard25,degree_pos25⟩ - · exact ⟨_,degreeCard26,degree_pos26⟩ - · exact ⟨_,degreeCard27,degree_pos27⟩ - · exact ⟨staircase 7,staircase_card 7,saxl_kronecker_pos 7 (by decide)⟩ - · exact ⟨_,degreeCard29,degree_pos29⟩ - · exact ⟨_,degreeCard30,degree_pos30⟩ - · exact ⟨_,degreeCard31,degree_pos31⟩ - · exact ⟨_,degreeCard32,degree_pos32⟩ - · exact ⟨_,degreeCard33,degree_pos33⟩ - · exact ⟨_,degreeCard34,degree_pos34⟩ - · exact ⟨_,degreeCard35,degree_pos35⟩ - · exact ⟨staircase 8,staircase_card 8,saxl_kronecker_pos 8 (by decide)⟩ - · exact ⟨_,degreeCard37,degree_pos37⟩ - · exact ⟨_,degreeCard38,degree_pos38⟩ - · exact ⟨_,degreeCard39,degree_pos39⟩ - · exact ⟨_,degreeCard40,degree_pos40⟩ - · exact ⟨_,degreeCard41,degree_pos41⟩ - · exact ⟨_,degreeCard42,degree_pos42⟩ - · exact ⟨_,degreeCard43,degree_pos43⟩ - · exact ⟨_,degreeCard44,degree_pos44⟩ - · exact ⟨staircase 9,staircase_card 9,saxl_kronecker_pos 9 (by decide)⟩ - · exact ⟨_,degreeCard46,degree_pos46⟩ - · exact ⟨_,degreeCard47,degree_pos47⟩ - · exact ⟨_,degreeCard48,degree_pos48⟩ - · exact ⟨_,degreeCard49,degree_pos49⟩ - · exact ⟨_,degreeCard50,degree_pos50⟩ - · exact ⟨_,degreeCard51,degree_pos51⟩ - · exact ⟨_,degreeCard52,degree_pos52⟩ - · exact ⟨_,degreeCard53,degree_pos53⟩ - · exact ⟨_,degreeCard54,degree_pos54⟩ - · exact ⟨staircase 10,staircase_card 10,saxl_kronecker_pos 10 (by decide)⟩ - · exact ⟨_,degreeCard56,degree_pos56⟩ - · exact ⟨_,degreeCard57,degree_pos57⟩ - · exact ⟨_,degreeCard58,degree_pos58⟩ - · exact ⟨_,degreeCard59,degree_pos59⟩ - · exact ⟨_,degreeCard60,degree_pos60⟩ - · exact ⟨_,degreeCard61,degree_pos61⟩ - · exact ⟨_,degreeCard62,degree_pos62⟩ - · exact ⟨_,degreeCard63,degree_pos63⟩ - · exact ⟨_,degreeCard64,degree_pos64⟩ - -lemma universal_partition_exceptional (n : ℕ) - (hexc : exceptionalPair (staircaseIndex n) (remainderPairs n)) : - ∃ (lam : YoungDiagram) (hc : lam.card = n), - ∀ (μ : YoungDiagram) (hμ : μ.card = n), - 0 < kronecker (canonicalTableau lam hc) (canonicalTableau lam hc) - (canonicalTableau μ hμ) := by - have he := degree_eq n - rw [staircase_card] at he - have hcases : n = 71 ∨ n = 73 ∨ n = 75 ∨ n = 77 ∨ n = 79 ∨ n = 81 ∨ n = 83 ∨ n = 85 ∨ n = 87 ∨ n = 89 ∨ n = 106 ∨ n = 108 ∨ n = 110 ∨ n = 112 ∨ n = 114 ∨ n = 116 ∨ n = 118 ∨ n = 149 ∨ n = 151 := by - unfold exceptionalPair at hexc - rcases hexc with ⟨hM,hr⟩ | ⟨hM,hr⟩ | ⟨hM,hr⟩ <;> - rw [hM] at he <;> norm_num at he <;> omega - rcases hcases with rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl - · exact ⟨_,exceptionalCard71,exceptional_pos71⟩ - · exact ⟨_,exceptionalCard73,exceptional_pos73⟩ - · exact ⟨_,exceptionalCard75,exceptional_pos75⟩ - · exact ⟨_,exceptionalCard77,exceptional_pos77⟩ - · exact ⟨_,exceptionalCard79,exceptional_pos79⟩ - · exact ⟨_,exceptionalCard81,exceptional_pos81⟩ - · exact ⟨_,exceptionalCard83,exceptional_pos83⟩ - · exact ⟨_,exceptionalCard85,exceptional_pos85⟩ - · exact ⟨_,exceptionalCard87,exceptional_pos87⟩ - · exact ⟨_,degreeCard89,degree_pos89⟩ - · exact ⟨_,exceptionalCard106,exceptional_pos106⟩ - · exact ⟨_,exceptionalCard108,exceptional_pos108⟩ - · exact ⟨_,exceptionalCard110,exceptional_pos110⟩ - · exact ⟨_,degreeCard112,degree_pos112⟩ - · exact ⟨_,exceptionalCard114,exceptional_pos114⟩ - · exact ⟨_,degreeCard116,degree_pos116⟩ - · exact ⟨_,degreeCard118,degree_pos118⟩ - · exact ⟨_,exceptionalCard149,exceptional_pos149⟩ - · exact ⟨_,degreeCard151,degree_pos151⟩ - -universe u - -theorem universal_tensor_square - (n : ℕ) (hn : 0 < n) (h2 : n ≠ 2) (h4 : n ≠ 4) (h9 : n ≠ 9) : - ∃ (lam : YoungDiagram) (hlam : lam.card = n), - (∀ (ν : YoungDiagram) (hν : ν.card = n), - 0 < Saxl.kronecker (Saxl.canonicalTableau lam hlam) - (Saxl.canonicalTableau lam hlam) (Saxl.canonicalTableau ν hν)) ∧ - Representation.IsIrreducible (Saxl.spechtRep (Saxl.canonicalTableau lam hlam)) ∧ - ∀ (V : Type u) [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) [Representation.IsIrreducible ρ], - ∃ F : Representation.IntertwiningMap ρ - ((Saxl.spechtRep (Saxl.canonicalTableau lam hlam)).tprod - (Saxl.spechtRep (Saxl.canonicalTableau lam hlam))), - Function.Injective F := by - have hex : ∃ (lam : YoungDiagram) (hc : lam.card = n), - ∀ (μ : YoungDiagram) (hμ : μ.card = n), - 0 < kronecker (canonicalTableau lam hc) (canonicalTableau lam hc) - (canonicalTableau μ hμ) := by - by_cases hsmall : n ≤ 64 - · exact universal_partition_le64 n hn h2 h4 h9 hsmall - · have hlarge : 64 < n := by omega - by_cases hexc : exceptionalPair (staircaseIndex n) (remainderPairs n) - · exact universal_partition_exceptional n hexc - · have hM := (fixedCandidate_large_degree n hlarge).1 - exact ⟨fixedCandidate n,fixedCandidate_card n (by omega), - fixedCandidate_nonexceptional_pos n hlarge hexc⟩ - obtain ⟨lam,hc,hpos⟩ := hex - exact ⟨lam,hc,hpos,irreducibles_of_kronecker_pos lam hc hpos⟩ - -end UniversalTensorSquare -end -end - -namespace UniversalTensorSquares -universe u -theorem universal_tensor_square - (n : ℕ) (hn : 0 < n) (h2 : n ≠ 2) (h4 : n ≠ 4) (h9 : n ≠ 9) : - ∃ (lam : YoungDiagram) (hlam : lam.card = n), - (∀ (ν : YoungDiagram) (hν : ν.card = n), - 0 < Saxl.kronecker (Saxl.canonicalTableau lam hlam) - (Saxl.canonicalTableau lam hlam) (Saxl.canonicalTableau ν hν)) ∧ - Representation.IsIrreducible (Saxl.spechtRep (Saxl.canonicalTableau lam hlam)) ∧ - ∀ (V : Type u) [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] - (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) [Representation.IsIrreducible ρ], - ∃ F : Representation.IntertwiningMap ρ - ((Saxl.spechtRep (Saxl.canonicalTableau lam hlam)).tprod - (Saxl.spechtRep (Saxl.canonicalTableau lam hlam))), - Function.Injective F := by - exact UniversalTensorSquare.universal_tensor_square n hn h2 h4 h9 -end UniversalTensorSquares - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Support.Asymptotic +import OAI.RepresentationTheory.UniversalSquare.Support.ExceptionalFourteen +import OAI.RepresentationTheory.UniversalSquare.Support.SmallDegrees +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree11 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree12 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree13 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree14 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree16 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree17 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree18 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree19 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree20 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree22 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree23 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree24 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree25 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree26 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree27 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree29 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree30 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree31 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree32 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree33 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree34 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree35 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree37 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree38 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree39 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree40 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree41 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree42 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree43 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree44 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree46 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree47 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree48 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree49 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree50 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree51 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree52 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree53 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree54 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree56 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree57 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree58 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree59 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree60 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree61 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree62 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree63 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree64 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree89 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree112 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree116 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree118 +import OAI.RepresentationTheory.UniversalSquare.Finite.NumericalDegree151 + +namespace OAI + +/-! Universal tensor squares. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl + +lemma universal_partition_le64 (n : ℕ) (hn : 0 < n) + (h2 : n ≠ 2) (h4 : n ≠ 4) (h9 : n ≠ 9) (hsmall : n ≤ 64) : + ∃ (lam : YoungDiagram) (hc : lam.card = n), + ∀ (μ : YoungDiagram) (hμ : μ.card = n), + 0 < kronecker (canonicalTableau lam hc) (canonicalTableau lam hc) + (canonicalTableau μ hμ) := by + by_cases hten : n ≤ 10 + · obtain ⟨lam,hc,hpos,_⟩ := universal_tensor_square_le_ten.{0} n hn h2 h4 h9 hten + exact ⟨lam,hc,hpos⟩ + have hlo : 11 ≤ n := by omega + interval_cases n + · exact ⟨_,degreeCard11,degree_pos11⟩ + · exact ⟨_,degreeCard12,degree_pos12⟩ + · exact ⟨_,degreeCard13,degree_pos13⟩ + · exact ⟨_,degreeCard14,degree_pos14⟩ + · exact ⟨staircase 5,staircase_card 5,saxl_kronecker_pos 5 (by decide)⟩ + · exact ⟨_,degreeCard16,degree_pos16⟩ + · exact ⟨_,degreeCard17,degree_pos17⟩ + · exact ⟨_,degreeCard18,degree_pos18⟩ + · exact ⟨_,degreeCard19,degree_pos19⟩ + · exact ⟨_,degreeCard20,degree_pos20⟩ + · exact ⟨staircase 6,staircase_card 6,saxl_kronecker_pos 6 (by decide)⟩ + · exact ⟨_,degreeCard22,degree_pos22⟩ + · exact ⟨_,degreeCard23,degree_pos23⟩ + · exact ⟨_,degreeCard24,degree_pos24⟩ + · exact ⟨_,degreeCard25,degree_pos25⟩ + · exact ⟨_,degreeCard26,degree_pos26⟩ + · exact ⟨_,degreeCard27,degree_pos27⟩ + · exact ⟨staircase 7,staircase_card 7,saxl_kronecker_pos 7 (by decide)⟩ + · exact ⟨_,degreeCard29,degree_pos29⟩ + · exact ⟨_,degreeCard30,degree_pos30⟩ + · exact ⟨_,degreeCard31,degree_pos31⟩ + · exact ⟨_,degreeCard32,degree_pos32⟩ + · exact ⟨_,degreeCard33,degree_pos33⟩ + · exact ⟨_,degreeCard34,degree_pos34⟩ + · exact ⟨_,degreeCard35,degree_pos35⟩ + · exact ⟨staircase 8,staircase_card 8,saxl_kronecker_pos 8 (by decide)⟩ + · exact ⟨_,degreeCard37,degree_pos37⟩ + · exact ⟨_,degreeCard38,degree_pos38⟩ + · exact ⟨_,degreeCard39,degree_pos39⟩ + · exact ⟨_,degreeCard40,degree_pos40⟩ + · exact ⟨_,degreeCard41,degree_pos41⟩ + · exact ⟨_,degreeCard42,degree_pos42⟩ + · exact ⟨_,degreeCard43,degree_pos43⟩ + · exact ⟨_,degreeCard44,degree_pos44⟩ + · exact ⟨staircase 9,staircase_card 9,saxl_kronecker_pos 9 (by decide)⟩ + · exact ⟨_,degreeCard46,degree_pos46⟩ + · exact ⟨_,degreeCard47,degree_pos47⟩ + · exact ⟨_,degreeCard48,degree_pos48⟩ + · exact ⟨_,degreeCard49,degree_pos49⟩ + · exact ⟨_,degreeCard50,degree_pos50⟩ + · exact ⟨_,degreeCard51,degree_pos51⟩ + · exact ⟨_,degreeCard52,degree_pos52⟩ + · exact ⟨_,degreeCard53,degree_pos53⟩ + · exact ⟨_,degreeCard54,degree_pos54⟩ + · exact ⟨staircase 10,staircase_card 10,saxl_kronecker_pos 10 (by decide)⟩ + · exact ⟨_,degreeCard56,degree_pos56⟩ + · exact ⟨_,degreeCard57,degree_pos57⟩ + · exact ⟨_,degreeCard58,degree_pos58⟩ + · exact ⟨_,degreeCard59,degree_pos59⟩ + · exact ⟨_,degreeCard60,degree_pos60⟩ + · exact ⟨_,degreeCard61,degree_pos61⟩ + · exact ⟨_,degreeCard62,degree_pos62⟩ + · exact ⟨_,degreeCard63,degree_pos63⟩ + · exact ⟨_,degreeCard64,degree_pos64⟩ + +lemma universal_partition_exceptional (n : ℕ) + (hexc : exceptionalPair (staircaseIndex n) (remainderPairs n)) : + ∃ (lam : YoungDiagram) (hc : lam.card = n), + ∀ (μ : YoungDiagram) (hμ : μ.card = n), + 0 < kronecker (canonicalTableau lam hc) (canonicalTableau lam hc) + (canonicalTableau μ hμ) := by + have he := degree_eq n + rw [staircase_card] at he + have hcases : n = 71 ∨ n = 73 ∨ n = 75 ∨ n = 77 ∨ n = 79 ∨ n = 81 ∨ n = 83 ∨ n = 85 ∨ n = 87 ∨ n = 89 ∨ n = 106 ∨ n = 108 ∨ n = 110 ∨ n = 112 ∨ n = 114 ∨ n = 116 ∨ n = 118 ∨ n = 149 ∨ n = 151 := by + unfold exceptionalPair at hexc + rcases hexc with ⟨hM,hr⟩ | ⟨hM,hr⟩ | ⟨hM,hr⟩ <;> + rw [hM] at he <;> norm_num at he <;> omega + rcases hcases with rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl + · exact ⟨_,exceptionalCard71,exceptional_pos71⟩ + · exact ⟨_,exceptionalCard73,exceptional_pos73⟩ + · exact ⟨_,exceptionalCard75,exceptional_pos75⟩ + · exact ⟨_,exceptionalCard77,exceptional_pos77⟩ + · exact ⟨_,exceptionalCard79,exceptional_pos79⟩ + · exact ⟨_,exceptionalCard81,exceptional_pos81⟩ + · exact ⟨_,exceptionalCard83,exceptional_pos83⟩ + · exact ⟨_,exceptionalCard85,exceptional_pos85⟩ + · exact ⟨_,exceptionalCard87,exceptional_pos87⟩ + · exact ⟨_,degreeCard89,degree_pos89⟩ + · exact ⟨_,exceptionalCard106,exceptional_pos106⟩ + · exact ⟨_,exceptionalCard108,exceptional_pos108⟩ + · exact ⟨_,exceptionalCard110,exceptional_pos110⟩ + · exact ⟨_,degreeCard112,degree_pos112⟩ + · exact ⟨_,exceptionalCard114,exceptional_pos114⟩ + · exact ⟨_,degreeCard116,degree_pos116⟩ + · exact ⟨_,degreeCard118,degree_pos118⟩ + · exact ⟨_,exceptionalCard149,exceptional_pos149⟩ + · exact ⟨_,degreeCard151,degree_pos151⟩ + +universe u + +theorem universal_tensor_square + (n : ℕ) (hn : 0 < n) (h2 : n ≠ 2) (h4 : n ≠ 4) (h9 : n ≠ 9) : + ∃ (lam : YoungDiagram) (hlam : lam.card = n), + (∀ (ν : YoungDiagram) (hν : ν.card = n), + 0 < Saxl.kronecker (Saxl.canonicalTableau lam hlam) + (Saxl.canonicalTableau lam hlam) (Saxl.canonicalTableau ν hν)) ∧ + Representation.IsIrreducible (Saxl.spechtRep (Saxl.canonicalTableau lam hlam)) ∧ + ∀ (V : Type u) [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) [Representation.IsIrreducible ρ], + ∃ F : Representation.IntertwiningMap ρ + ((Saxl.spechtRep (Saxl.canonicalTableau lam hlam)).tprod + (Saxl.spechtRep (Saxl.canonicalTableau lam hlam))), + Function.Injective F := by + have hex : ∃ (lam : YoungDiagram) (hc : lam.card = n), + ∀ (μ : YoungDiagram) (hμ : μ.card = n), + 0 < kronecker (canonicalTableau lam hc) (canonicalTableau lam hc) + (canonicalTableau μ hμ) := by + by_cases hsmall : n ≤ 64 + · exact universal_partition_le64 n hn h2 h4 h9 hsmall + · have hlarge : 64 < n := by omega + by_cases hexc : exceptionalPair (staircaseIndex n) (remainderPairs n) + · exact universal_partition_exceptional n hexc + · have hM := (fixedCandidate_large_degree n hlarge).1 + exact ⟨fixedCandidate n,fixedCandidate_card n (by omega), + fixedCandidate_nonexceptional_pos n hlarge hexc⟩ + obtain ⟨lam,hc,hpos⟩ := hex + exact ⟨lam,hc,hpos,irreducibles_of_kronecker_pos lam hc hpos⟩ + +end UniversalTensorSquare +end +end + +namespace UniversalTensorSquares +universe u +theorem universal_tensor_square + (n : ℕ) (hn : 0 < n) (h2 : n ≠ 2) (h4 : n ≠ 4) (h9 : n ≠ 9) : + ∃ (lam : YoungDiagram) (hlam : lam.card = n), + (∀ (ν : YoungDiagram) (hν : ν.card = n), + 0 < Saxl.kronecker (Saxl.canonicalTableau lam hlam) + (Saxl.canonicalTableau lam hlam) (Saxl.canonicalTableau ν hν)) ∧ + Representation.IsIrreducible (Saxl.spechtRep (Saxl.canonicalTableau lam hlam)) ∧ + ∀ (V : Type u) [AddCommGroup V] [Module ℂ V] [Module.Finite ℂ V] + (ρ : Representation ℂ (Equiv.Perm (Fin n)) V) [Representation.IsIrreducible ρ], + ∃ F : Representation.IntertwiningMap ρ + ((Saxl.spechtRep (Saxl.canonicalTableau lam hlam)).tprod + (Saxl.spechtRep (Saxl.canonicalTableau lam hlam))), + Function.Injective F := by + exact UniversalTensorSquare.universal_tensor_square n hn h2 h4 h9 +end UniversalTensorSquares + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves1.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves1.lean index d59abd50038f5b6de55c883d085635110b9dbd04..143a5a83ecbe6d6de38b28937859bcc20a9baba2 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves1.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves1.lean @@ -1,700 +1,700 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Semigroup Leaves 1. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB10 : Equiv.Perm (Fin 4) := Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 3)) -def sgT10 : Equiv.Perm (Fin 4) := Equiv.swap 1 3 * (Equiv.swap 1 0 * (Equiv.swap 0 2)) -def sgFlag10 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(0,1,0)} -lemma sgCert10 : solveCompact 4 (.full [2,2]) (.full [2,1,1]) (.full [2,1,1]) - (certificateEdges [2,1,1] [2,1,1] [2,2] (Equiv.refl (Fin 4)) sgB10 sgT10) sgFlag10 = -2 := by - decide +kernel - -lemma sg10 : RowSquare [2,1,1] [2,2] := by - apply rowSquare_compact (n := 4) (cs := [2,1,1]) (ts := [2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB10 sgT10 sgFlag10 - change solveCompact 4 (.full [2,2]) (.full [2,1,1]) (.full [2,1,1]) - (certificateEdges [2,1,1] [2,1,1] [2,2] (Equiv.refl (Fin 4)) sgB10 sgT10) sgFlag10 ≠ 0 - rw [sgCert10] - norm_num - -def sgB17 : Equiv.Perm (Fin 4) := Equiv.swap 0 3 * (Equiv.swap 0 1) -def sgT17 : Equiv.Perm (Fin 4) := Equiv.swap 2 3 -def sgFlag17 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,1),(1,1,0)} -lemma sgCert17 : solveCompact 4 (.full [2,2]) (.full [2,1,1]) (.full [2,1,1]) - (certificateEdges [2,1,1] [2,1,1] [2,2] (Equiv.refl (Fin 4)) sgB17 sgT17) sgFlag17 = -2 := by - decide +kernel - -lemma sg17 : RowSquare [3,1] [2,2] := by - apply rowSquare_compact (n := 4) (cs := [2,1,1]) (ts := [2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB17 sgT17 sgFlag17 - change solveCompact 4 (.full [2,2]) (.full [2,1,1]) (.full [2,1,1]) - (certificateEdges [2,1,1] [2,1,1] [2,2] (Equiv.refl (Fin 4)) sgB17 sgT17) sgFlag17 ≠ 0 - rw [sgCert17] - norm_num - -def sgB67 : Equiv.Perm (Fin 6) := Equiv.swap 1 2 * (Equiv.swap 1 0 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 4)))) -def sgT67 : Equiv.Perm (Fin 6) := Equiv.swap 3 5 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 4))) -def sgFlag67 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(3,0,1),(1,0,2),(0,1,0),(1,2,0)} -lemma sgCert67 : solveCompact 6 (.full [4,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) - (certificateEdges [3,1,1,1] [3,1,1,1] [4,2] (Equiv.refl (Fin 6)) sgB67 sgT67) sgFlag67 = -8 := by - decide +kernel - -lemma sg67 : RowSquare [3,1,1,1] [2,2,1,1] := by - apply rowSquare_compact (n := 6) (cs := [3,1,1,1]) (ts := [4,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB67 sgT67 sgFlag67 - change solveCompact 6 (.full [4,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) - (certificateEdges [3,1,1,1] [3,1,1,1] [4,2] (Equiv.refl (Fin 6)) sgB67 sgT67) sgFlag67 ≠ 0 - rw [sgCert67] - norm_num - -def sgB68 : Equiv.Perm (Fin 6) := Equiv.swap 2 5 * (Equiv.swap 0 1) -def sgT68 : Equiv.Perm (Fin 6) := Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 4)) -def sgFlag68 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(2,0,2),(2,1,0),(0,2,0)} -lemma sgCert68 : solveCompact 6 (.full [3,3]) (.full [3,1,1,1]) (.full [3,1,1,1]) - (certificateEdges [3,1,1,1] [3,1,1,1] [3,3] (Equiv.refl (Fin 6)) sgB68 sgT68) sgFlag68 = 6 := by - decide +kernel - -lemma sg68 : RowSquare [3,1,1,1] [2,2,2] := by - apply rowSquare_compact (n := 6) (cs := [3,1,1,1]) (ts := [3,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB68 sgT68 sgFlag68 - change solveCompact 6 (.full [3,3]) (.full [3,1,1,1]) (.full [3,1,1,1]) - (certificateEdges [3,1,1,1] [3,1,1,1] [3,3] (Equiv.refl (Fin 6)) sgB68 sgT68) sgFlag68 ≠ 0 - rw [sgCert68] - norm_num - -def sgB71 : Equiv.Perm (Fin 6) := Equiv.swap 1 5 * (Equiv.swap 1 4 * (Equiv.swap 0 3)) -def sgT71 : Equiv.Perm (Fin 6) := Equiv.swap 0 3 * (Equiv.swap 3 5 * (Equiv.swap 0 4)) -def sgFlag71 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,1),(1,1,0),(0,2,2)} -lemma sgCert71 : solveCompact 6 (.full [2,2,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) - (certificateEdges [3,1,1,1] [3,1,1,1] [2,2,2] (Equiv.refl (Fin 6)) sgB71 sgT71) sgFlag71 = 2 := by - decide +kernel - -lemma sg71 : RowSquare [3,1,1,1] [3,3] := by - apply rowSquare_compact (n := 6) (cs := [3,1,1,1]) (ts := [2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB71 sgT71 sgFlag71 - change solveCompact 6 (.full [2,2,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) - (certificateEdges [3,1,1,1] [3,1,1,1] [2,2,2] (Equiv.refl (Fin 6)) sgB71 sgT71) sgFlag71 ≠ 0 - rw [sgCert71] - norm_num - -def sgB88 : Equiv.Perm (Fin 6) := Equiv.swap 2 0 * (Equiv.swap 1 5 * (Equiv.swap 0 3)) -def sgT88 : Equiv.Perm (Fin 6) := Equiv.swap 0 2 -def sgFlag88 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(1,0,1),(3,0,2),(1,1,0),(0,2,0)} -lemma sgCert88 : solveCompact 6 (.full [4,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) - (certificateEdges [3,1,1,1] [3,1,1,1] [4,2] (Equiv.refl (Fin 6)) sgB88 sgT88) sgFlag88 = 8 := by - decide +kernel - -lemma sg88 : RowSquare [4,1,1] [2,2,1,1] := by - apply rowSquare_compact (n := 6) (cs := [3,1,1,1]) (ts := [4,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB88 sgT88 sgFlag88 - change solveCompact 6 (.full [4,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) - (certificateEdges [3,1,1,1] [3,1,1,1] [4,2] (Equiv.refl (Fin 6)) sgB88 sgT88) sgFlag88 ≠ 0 - rw [sgCert88] - norm_num - -def sgB89 : Equiv.Perm (Fin 6) := Equiv.swap 2 1 * (Equiv.swap 2 4 * (Equiv.swap 1 5)) -def sgT89 : Equiv.Perm (Fin 6) := Equiv.swap 1 3 * (Equiv.swap 3 5 * (Equiv.swap 1 4 * (Equiv.swap 1 0 * (Equiv.swap 0 2)))) -def sgFlag89 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(0,0,1),(1,0,2),(0,1,0),(1,2,0)} -lemma sgCert89 : solveCompact 6 (.full [3,3]) (.full [3,1,1,1]) (.full [3,1,1,1]) - (certificateEdges [3,1,1,1] [3,1,1,1] [3,3] (Equiv.refl (Fin 6)) sgB89 sgT89) sgFlag89 = 6 := by - decide +kernel - -lemma sg89 : RowSquare [4,1,1] [2,2,2] := by - apply rowSquare_compact (n := 6) (cs := [3,1,1,1]) (ts := [3,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB89 sgT89 sgFlag89 - change solveCompact 6 (.full [3,3]) (.full [3,1,1,1]) (.full [3,1,1,1]) - (certificateEdges [3,1,1,1] [3,1,1,1] [3,3] (Equiv.refl (Fin 6)) sgB89 sgT89) sgFlag89 ≠ 0 - rw [sgCert89] - norm_num - -def sgB92 : Equiv.Perm (Fin 6) := Equiv.swap 4 2 * (Equiv.swap 2 0 * (Equiv.swap 2 1 * (Equiv.swap 1 3 * (Equiv.swap 0 5)))) -def sgT92 : Equiv.Perm (Fin 6) := Equiv.swap 0 4 * (Equiv.swap 2 1 * (Equiv.swap 1 5 * (Equiv.swap 0 3))) -def sgFlag92 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,2),(1,1,0),(1,2,1)} -lemma sgCert92 : solveCompact 6 (.full [2,2,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) - (certificateEdges [3,1,1,1] [3,1,1,1] [2,2,2] (Equiv.refl (Fin 6)) sgB92 sgT92) sgFlag92 = 1 := by - decide +kernel - -lemma sg92 : RowSquare [4,1,1] [3,3] := by - apply rowSquare_compact (n := 6) (cs := [3,1,1,1]) (ts := [2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB92 sgT92 sgFlag92 - change solveCompact 6 (.full [2,2,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) - (certificateEdges [3,1,1,1] [3,1,1,1] [2,2,2] (Equiv.refl (Fin 6)) sgB92 sgT92) sgFlag92 ≠ 0 - rw [sgCert92] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB143 : Equiv.Perm (Fin 7) := Equiv.swap 0 6 * (Equiv.swap 3 2 * (Equiv.swap 2 5 * (Equiv.swap 0 4))) -def sgT143 : Equiv.Perm (Fin 7) := Equiv.swap 1 5 * (Equiv.swap 1 3 * (Equiv.swap 1 2)) -def sgFlag143 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(0,0,2),(4,1,0),(2,1,1),(3,2,0)} -lemma sgCert143 : solveCompact 7 (.full [5,2]) (.full [3,2,1,1]) (.full [3,2,1,1]) - (certificateEdges [3,2,1,1] [3,2,1,1] [5,2] (Equiv.refl (Fin 7)) sgB143 sgT143) sgFlag143 = 6 := by - decide +kernel - -lemma sg143 : RowSquare [3,2,1,1] [2,2,1,1,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,1,1]) (ts := [5,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB143 sgT143 sgFlag143 - change solveCompact 7 (.full [5,2]) (.full [3,2,1,1]) (.full [3,2,1,1]) - (certificateEdges [3,2,1,1] [3,2,1,1] [5,2] (Equiv.refl (Fin 7)) sgB143 sgT143) sgFlag143 ≠ 0 - rw [sgCert143] - norm_num - -def sgB144 : Equiv.Perm (Fin 7) := Equiv.swap 5 1 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 1 6 * (Equiv.swap 0 4)))) -def sgT144 : Equiv.Perm (Fin 7) := Equiv.swap 0 5 * (Equiv.swap 1 6 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 4)))) -def sgFlag144 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,2),(1,1,0),(2,1,0),(3,2,0)} -lemma sgCert144 : solveCompact 7 (.full [4,3]) (.full [3,2,1,1]) (.full [3,2,1,1]) - (certificateEdges [3,2,1,1] [3,2,1,1] [4,3] (Equiv.refl (Fin 7)) sgB144 sgT144) sgFlag144 = 2 := by - decide +kernel - -lemma sg144 : RowSquare [3,2,1,1] [2,2,2,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,1,1]) (ts := [4,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB144 sgT144 sgFlag144 - change solveCompact 7 (.full [4,3]) (.full [3,2,1,1]) (.full [3,2,1,1]) - (certificateEdges [3,2,1,1] [3,2,1,1] [4,3] (Equiv.refl (Fin 7)) sgB144 sgT144) sgFlag144 ≠ 0 - rw [sgCert144] - norm_num - -def sgB154 : Equiv.Perm (Fin 7) := Equiv.swap 4 5 * (Equiv.swap 0 2 * (Equiv.swap 2 6 * (Equiv.swap 0 3))) -def sgT154 : Equiv.Perm (Fin 7) := Equiv.swap 1 2 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 5))) -def sgFlag154 : Finset (ℕ × ℕ × ℕ) := {(5,0,0),(1,0,1),(3,0,2),(0,1,0),(2,1,0),(4,1,1),(0,2,1)} -lemma sgCert154 : solveCompact 7 (.full [6,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [6,1] (Equiv.refl (Fin 7)) sgB154 sgT154) sgFlag154 = 15 := by - decide +kernel - -lemma sg154 : RowSquare [3,2,2] [2,1,1,1,1,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [6,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB154 sgT154 sgFlag154 - change solveCompact 7 (.full [6,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [6,1] (Equiv.refl (Fin 7)) sgB154 sgT154) sgFlag154 ≠ 0 - rw [sgCert154] - norm_num - -def sgB155 : Equiv.Perm (Fin 7) := Equiv.swap 3 2 * (Equiv.swap 2 6 * (Equiv.swap 0 4 * (Equiv.swap 0 1))) -def sgT155 : Equiv.Perm (Fin 7) := Equiv.swap 4 2 * (Equiv.swap 2 5 * (Equiv.swap 2 0 * (Equiv.swap 0 3))) -def sgFlag155 : Finset (ℕ × ℕ × ℕ) := {(4,0,0),(3,0,1),(0,0,2),(1,1,0),(2,1,0),(1,1,1),(0,2,1)} -lemma sgCert155 : solveCompact 7 (.full [5,2]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [5,2] (Equiv.refl (Fin 7)) sgB155 sgT155) sgFlag155 = 12 := by - decide +kernel - -lemma sg155 : RowSquare [3,2,2] [2,2,1,1,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [5,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB155 sgT155 sgFlag155 - change solveCompact 7 (.full [5,2]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [5,2] (Equiv.refl (Fin 7)) sgB155 sgT155) sgFlag155 ≠ 0 - rw [sgCert155] - norm_num - -def sgB156 : Equiv.Perm (Fin 7) := Equiv.swap 4 0 * (Equiv.swap 4 1 * (Equiv.swap 1 5 * (Equiv.swap 0 6))) -def sgT156 : Equiv.Perm (Fin 7) := Equiv.swap 3 1 * (Equiv.swap 1 4) -def sgFlag156 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(0,1,0),(2,1,1),(3,1,1),(2,2,2)} -lemma sgCert156 : solveCompact 7 (.full [4,3]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [4,3] (Equiv.refl (Fin 7)) sgB156 sgT156) sgFlag156 = 12 := by - decide +kernel - -lemma sg156 : RowSquare [3,2,2] [2,2,2,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [4,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB156 sgT156 sgFlag156 - change solveCompact 7 (.full [4,3]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [4,3] (Equiv.refl (Fin 7)) sgB156 sgT156) sgFlag156 ≠ 0 - rw [sgCert156] - norm_num - -def sgB157 : Equiv.Perm (Fin 7) := Equiv.swap 2 6 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 2 3 * (Equiv.swap 0 5)))) -def sgT157 : Equiv.Perm (Fin 7) := Equiv.swap 2 0 * (Equiv.swap 0 6 * (Equiv.swap 2 5 * (Equiv.swap 2 3 * (Equiv.swap 0 4 * (Equiv.swap 0 1))))) -def sgFlag157 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(0,1,0),(4,1,1),(2,1,2),(3,2,0)} -lemma sgCert157 : solveCompact 7 (.full [5,1,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [5,1,1] (Equiv.refl (Fin 7)) sgB157 sgT157) sgFlag157 = 6 := by - decide +kernel - -lemma sg157 : RowSquare [3,2,2] [3,1,1,1,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [5,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB157 sgT157 sgFlag157 - change solveCompact 7 (.full [5,1,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [5,1,1] (Equiv.refl (Fin 7)) sgB157 sgT157) sgFlag157 ≠ 0 - rw [sgCert157] - norm_num - -def sgB158 : Equiv.Perm (Fin 7) := Equiv.swap 5 4 * (Equiv.swap 4 3 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 0 6 * (Equiv.swap 0 1))))) -def sgT158 : Equiv.Perm (Fin 7) := Equiv.swap 3 5 * (Equiv.swap 1 6 * (Equiv.swap 1 2)) -def sgFlag158 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(3,0,1),(1,0,2),(0,1,0),(1,1,0),(2,1,1),(0,2,0)} -lemma sgCert158 : solveCompact 7 (.full [4,2,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [4,2,1] (Equiv.refl (Fin 7)) sgB158 sgT158) sgFlag158 = 4 := by - decide +kernel - -lemma sg158 : RowSquare [3,2,2] [3,2,1,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [4,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB158 sgT158 sgFlag158 - change solveCompact 7 (.full [4,2,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [4,2,1] (Equiv.refl (Fin 7)) sgB158 sgT158) sgFlag158 ≠ 0 - rw [sgCert158] - norm_num - -def sgB160 : Equiv.Perm (Fin 7) := Equiv.swap 4 6 * (Equiv.swap 2 3 * (Equiv.swap 1 5)) -def sgT160 : Equiv.Perm (Fin 7) := Equiv.swap 5 2 * (Equiv.swap 2 3 * (Equiv.swap 3 6 * (Equiv.swap 2 0 * (Equiv.swap 0 4)))) -def sgFlag160 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(1,0,2),(1,1,0),(0,1,1),(0,2,0)} -lemma sgCert160 : solveCompact 7 (.full [3,2,2]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [3,2,2] (Equiv.refl (Fin 7)) sgB160 sgT160) sgFlag160 = -4 := by - decide +kernel - -lemma sg160 : RowSquare [3,2,2] [3,3,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [3,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB160 sgT160 sgFlag160 - change solveCompact 7 (.full [3,2,2]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [3,2,2] (Equiv.refl (Fin 7)) sgB160 sgT160) sgFlag160 ≠ 0 - rw [sgCert160] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB163 : Equiv.Perm (Fin 7) := Equiv.swap 2 1 * (Equiv.swap 1 6 * (Equiv.swap 0 5)) -def sgT163 : Equiv.Perm (Fin 7) := Equiv.swap 3 0 * (Equiv.swap 3 1 * (Equiv.swap 1 5 * (Equiv.swap 1 2 * (Equiv.swap 0 6)))) -def sgFlag163 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,1,1),(1,1,2),(1,2,1)} -lemma sgCert163 : solveCompact 7 (.full [2,2,2,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [2,2,2,1] (Equiv.refl (Fin 7)) sgB163 sgT163) sgFlag163 = -3 := by - decide +kernel - -lemma sg163 : RowSquare [3,2,2] [4,3] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [2,2,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB163 sgT163 sgFlag163 - change solveCompact 7 (.full [2,2,2,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [2,2,2,1] (Equiv.refl (Fin 7)) sgB163 sgT163) sgFlag163 ≠ 0 - rw [sgCert163] - norm_num - -def sgB165 : Equiv.Perm (Fin 7) := Equiv.swap 3 6 * (Equiv.swap 2 5 * (Equiv.swap 1 4)) -def sgT165 : Equiv.Perm (Fin 7) := Equiv.swap 1 6 * (Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 4))) -def sgFlag165 : Finset (ℕ × ℕ × ℕ) := {(4,0,0),(3,0,1),(5,0,2),(1,1,0),(0,1,1),(2,1,1),(0,2,0)} -lemma sgCert165 : solveCompact 7 (.full [6,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [6,1] (Equiv.refl (Fin 7)) sgB165 sgT165) sgFlag165 = 15 := by - decide +kernel - -lemma sg165 : RowSquare [3,3,1] [2,1,1,1,1,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [6,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB165 sgT165 sgFlag165 - change solveCompact 7 (.full [6,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [6,1] (Equiv.refl (Fin 7)) sgB165 sgT165) sgFlag165 ≠ 0 - rw [sgCert165] - norm_num - -def sgB166 : Equiv.Perm (Fin 7) := Equiv.swap 5 4 * (Equiv.swap 4 6 * (Equiv.swap 2 0 * (Equiv.swap 0 3 * (Equiv.swap 0 1)))) -def sgT166 : Equiv.Perm (Fin 7) := Equiv.swap 3 4 * (Equiv.swap 1 5 * (Equiv.swap 0 6)) -def sgFlag166 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(4,0,2),(0,1,0),(3,1,1),(2,2,0)} -lemma sgCert166 : solveCompact 7 (.full [5,2]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [5,2] (Equiv.refl (Fin 7)) sgB166 sgT166) sgFlag166 = 3 := by - decide +kernel - -lemma sg166 : RowSquare [3,3,1] [2,2,1,1,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [5,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB166 sgT166 sgFlag166 - change solveCompact 7 (.full [5,2]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [5,2] (Equiv.refl (Fin 7)) sgB166 sgT166) sgFlag166 ≠ 0 - rw [sgCert166] - norm_num - -def sgB167 : Equiv.Perm (Fin 7) := Equiv.swap 3 1 * (Equiv.swap 1 6 * (Equiv.swap 0 2)) -def sgT167 : Equiv.Perm (Fin 7) := Equiv.swap 2 0 * (Equiv.swap 2 5 * (Equiv.swap 0 6 * (Equiv.swap 2 4 * (Equiv.swap 0 3)))) -def sgFlag167 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,1),(3,0,2),(2,1,0),(1,1,1),(0,2,0)} -lemma sgCert167 : solveCompact 7 (.full [4,3]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [4,3] (Equiv.refl (Fin 7)) sgB167 sgT167) sgFlag167 = 12 := by - decide +kernel - -lemma sg167 : RowSquare [3,3,1] [2,2,2,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [4,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB167 sgT167 sgFlag167 - change solveCompact 7 (.full [4,3]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [4,3] (Equiv.refl (Fin 7)) sgB167 sgT167) sgFlag167 ≠ 0 - rw [sgCert167] - norm_num - -def sgB168 : Equiv.Perm (Fin 7) := Equiv.swap 1 0 * (Equiv.swap 1 4 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 5)))) -def sgT168 : Equiv.Perm (Fin 7) := Equiv.swap 1 6 * (Equiv.swap 1 4) -def sgFlag168 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(3,0,1),(0,1,0),(1,1,1),(4,1,2),(2,2,0)} -lemma sgCert168 : solveCompact 7 (.full [5,1,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [5,1,1] (Equiv.refl (Fin 7)) sgB168 sgT168) sgFlag168 = 6 := by - decide +kernel - -lemma sg168 : RowSquare [3,3,1] [3,1,1,1,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [5,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB168 sgT168 sgFlag168 - change solveCompact 7 (.full [5,1,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [5,1,1] (Equiv.refl (Fin 7)) sgB168 sgT168) sgFlag168 ≠ 0 - rw [sgCert168] - norm_num - -def sgB169 : Equiv.Perm (Fin 7) := Equiv.swap 2 1 * (Equiv.swap 1 6 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 4)))) -def sgT169 : Equiv.Perm (Fin 7) := Equiv.swap 4 2 * (Equiv.swap 2 1 * (Equiv.swap 2 3 * (Equiv.swap 1 6 * (Equiv.swap 0 5)))) -def sgFlag169 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(0,1,0),(2,1,1),(0,1,2),(3,2,0)} -lemma sgCert169 : solveCompact 7 (.full [4,2,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [4,2,1] (Equiv.refl (Fin 7)) sgB169 sgT169) sgFlag169 = 3 := by - decide +kernel - -lemma sg169 : RowSquare [3,3,1] [3,2,1,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [4,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB169 sgT169 sgFlag169 - change solveCompact 7 (.full [4,2,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [4,2,1] (Equiv.refl (Fin 7)) sgB169 sgT169) sgFlag169 ≠ 0 - rw [sgCert169] - norm_num - -def sgB171 : Equiv.Perm (Fin 7) := Equiv.swap 4 2 * (Equiv.swap 4 0 * (Equiv.swap 2 1 * (Equiv.swap 1 6 * (Equiv.swap 0 5)))) -def sgT171 : Equiv.Perm (Fin 7) := Equiv.swap 0 3 * (Equiv.swap 3 2 * (Equiv.swap 2 5 * (Equiv.swap 0 4))) -def sgFlag171 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(0,0,2),(0,1,0),(1,1,1),(0,2,1)} -lemma sgCert171 : solveCompact 7 (.full [3,2,2]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [3,2,2] (Equiv.refl (Fin 7)) sgB171 sgT171) sgFlag171 = -1 := by - decide +kernel - -lemma sg171 : RowSquare [3,3,1] [3,3,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [3,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB171 sgT171 sgFlag171 - change solveCompact 7 (.full [3,2,2]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [3,2,2] (Equiv.refl (Fin 7)) sgB171 sgT171) sgFlag171 ≠ 0 - rw [sgCert171] - norm_num - -def sgB174 : Equiv.Perm (Fin 7) := Equiv.swap 1 4 * (Equiv.swap 4 6 * (Equiv.swap 1 5 * (Equiv.swap 1 2))) -def sgT174 : Equiv.Perm (Fin 7) := Equiv.swap 5 0 * (Equiv.swap 0 3 * (Equiv.swap 3 6 * (Equiv.swap 0 4))) -def sgFlag174 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(1,1,1),(1,1,2),(0,2,0)} -lemma sgCert174 : solveCompact 7 (.full [2,2,2,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [2,2,2,1] (Equiv.refl (Fin 7)) sgB174 sgT174) sgFlag174 = 1 := by - decide +kernel - -lemma sg174 : RowSquare [3,3,1] [4,3] := by - apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [2,2,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB174 sgT174 sgFlag174 - change solveCompact 7 (.full [2,2,2,1]) (.full [3,2,2]) (.full [3,2,2]) - (certificateEdges [3,2,2] [3,2,2] [2,2,2,1] (Equiv.refl (Fin 7)) sgB174 sgT174) sgFlag174 ≠ 0 - rw [sgCert174] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB194 : Equiv.Perm (Fin 7) := Equiv.swap 1 3 * (Equiv.swap 3 5 * (Equiv.swap 2 6 * (Equiv.swap 1 4))) -def sgT194 : Equiv.Perm (Fin 7) := Equiv.swap 5 3 * (Equiv.swap 3 6 * (Equiv.swap 0 4 * (Equiv.swap 0 1))) -def sgFlag194 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,1),(0,0,2),(0,1,0),(4,1,1),(2,2,0)} -lemma sgCert194 : solveCompact 7 (.full [5,2]) (.full [3,2,1,1]) (.full [3,2,1,1]) - (certificateEdges [3,2,1,1] [3,2,1,1] [5,2] (Equiv.refl (Fin 7)) sgB194 sgT194) sgFlag194 = 17 := by - decide +kernel - -lemma sg194 : RowSquare [4,2,1] [2,2,1,1,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,1,1]) (ts := [5,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB194 sgT194 sgFlag194 - change solveCompact 7 (.full [5,2]) (.full [3,2,1,1]) (.full [3,2,1,1]) - (certificateEdges [3,2,1,1] [3,2,1,1] [5,2] (Equiv.refl (Fin 7)) sgB194 sgT194) sgFlag194 ≠ 0 - rw [sgCert194] - norm_num - -def sgB195 : Equiv.Perm (Fin 7) := Equiv.swap 2 1 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 1 6 * (Equiv.swap 0 5)))) -def sgT195 : Equiv.Perm (Fin 7) := Equiv.swap 5 3 * (Equiv.swap 3 6 * (Equiv.swap 3 0 * (Equiv.swap 0 4 * (Equiv.swap 0 1)))) -def sgFlag195 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(3,0,1),(1,0,2),(0,1,0),(2,1,0),(2,2,1)} -lemma sgCert195 : solveCompact 7 (.full [4,3]) (.full [3,2,1,1]) (.full [3,2,1,1]) - (certificateEdges [3,2,1,1] [3,2,1,1] [4,3] (Equiv.refl (Fin 7)) sgB195 sgT195) sgFlag195 = 3 := by - decide +kernel - -lemma sg195 : RowSquare [4,2,1] [2,2,2,1] := by - apply rowSquare_compact (n := 7) (cs := [3,2,1,1]) (ts := [4,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB195 sgT195 sgFlag195 - change solveCompact 7 (.full [4,3]) (.full [3,2,1,1]) (.full [3,2,1,1]) - (certificateEdges [3,2,1,1] [3,2,1,1] [4,3] (Equiv.refl (Fin 7)) sgB195 sgT195) sgFlag195 ≠ 0 - rw [sgCert195] - norm_num - -def sgB271 : Equiv.Perm (Fin 8) := Equiv.swap 5 4 * (Equiv.swap 4 7 * (Equiv.swap 2 6 * (Equiv.swap 0 1))) -def sgT271 : Equiv.Perm (Fin 8) := Equiv.swap 1 2 * (Equiv.swap 3 7 * (Equiv.swap 2 5 * (Equiv.swap 1 4))) -def sgFlag271 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,1),(1,0,1),(2,0,2),(0,1,0),(2,1,0),(1,2,0)} -lemma sgCert271 : solveCompact 8 (.full [4,4]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) - (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB271 sgT271) sgFlag271 = -4 := by - decide +kernel - -lemma sg271 : RowSquare [3,2,1,1,1] [2,2,2,2] := by - apply rowSquare_compact (n := 8) (cs := [3,2,1,1,1]) (ts := [4,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB271 sgT271 sgFlag271 - change solveCompact 8 (.full [4,4]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) - (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB271 sgT271) sgFlag271 ≠ 0 - rw [sgCert271] - norm_num - -def sgB275 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 1 * (Equiv.swap 1 6 * (Equiv.swap 1 3 * (Equiv.swap 1 0 * (Equiv.swap 0 2))))) -def sgT275 : Equiv.Perm (Fin 8) := Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 2 6 * (Equiv.swap 1 0 * (Equiv.swap 0 5)))) -def sgFlag275 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(2,0,1),(1,0,2),(0,1,0),(0,1,1),(0,2,0)} -lemma sgCert275 : solveCompact 8 (.full [4,2,2]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) - (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB275 sgT275) sgFlag275 = -1 := by - decide +kernel - -lemma sg275 : RowSquare [3,2,1,1,1] [3,3,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,2,1,1,1]) (ts := [4,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB275 sgT275 sgFlag275 - change solveCompact 8 (.full [4,2,2]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) - (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB275 sgT275) sgFlag275 ≠ 0 - rw [sgCert275] - norm_num - -def sgB285 : Equiv.Perm (Fin 8) := Equiv.swap 1 2 * (Equiv.swap 1 4 * (Equiv.swap 2 5 * (Equiv.swap 1 0 * (Equiv.swap 0 3)))) -def sgT285 : Equiv.Perm (Fin 8) := Equiv.swap 0 3 * (Equiv.swap 1 2 * (Equiv.swap 3 7 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))) -def sgFlag285 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(4,1,0),(3,1,1),(2,1,2),(5,2,0)} -lemma sgCert285 : solveCompact 8 (.full [6,2]) (.full [3,2,2,1]) (.full [3,2,2,1]) - (certificateEdges [3,2,2,1] [3,2,2,1] [6,2] (Equiv.refl (Fin 8)) sgB285 sgT285) sgFlag285 = 24 := by - decide +kernel - -lemma sg285 : RowSquare [3,2,2,1] [2,2,1,1,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,2,2,1]) (ts := [6,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB285 sgT285 sgFlag285 - change solveCompact 8 (.full [6,2]) (.full [3,2,2,1]) (.full [3,2,2,1]) - (certificateEdges [3,2,2,1] [3,2,2,1] [6,2] (Equiv.refl (Fin 8)) sgB285 sgT285) sgFlag285 ≠ 0 - rw [sgCert285] - norm_num - -def sgB286 : Equiv.Perm (Fin 8) := Equiv.swap 4 5 * (Equiv.swap 1 6 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 7)))) -def sgT286 : Equiv.Perm (Fin 8) := Equiv.swap 1 0 * (Equiv.swap 1 5 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 6)))) -def sgFlag286 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(0,0,1),(4,1,0),(1,1,1),(2,1,2),(3,2,0)} -lemma sgCert286 : solveCompact 8 (.full [5,3]) (.full [3,2,2,1]) (.full [3,2,2,1]) - (certificateEdges [3,2,2,1] [3,2,2,1] [5,3] (Equiv.refl (Fin 8)) sgB286 sgT286) sgFlag286 = -3 := by - decide +kernel - -lemma sg286 : RowSquare [3,2,2,1] [2,2,2,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,2,2,1]) (ts := [5,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB286 sgT286 sgFlag286 - change solveCompact 8 (.full [5,3]) (.full [3,2,2,1]) (.full [3,2,2,1]) - (certificateEdges [3,2,2,1] [3,2,2,1] [5,3] (Equiv.refl (Fin 8)) sgB286 sgT286) sgFlag286 ≠ 0 - rw [sgCert286] - norm_num - -def sgB287 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 2 0 * (Equiv.swap 1 6 * (Equiv.swap 0 3))) -def sgT287 : Equiv.Perm (Fin 8) := Equiv.swap 6 2 * (Equiv.swap 2 7 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 0 4 * (Equiv.swap 0 1))))) -def sgFlag287 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,0,2),(3,1,0),(0,1,1),(2,1,1),(3,2,0)} -lemma sgCert287 : solveCompact 8 (.full [4,4]) (.full [3,2,2,1]) (.full [3,2,2,1]) - (certificateEdges [3,2,2,1] [3,2,2,1] [4,4] (Equiv.refl (Fin 8)) sgB287 sgT287) sgFlag287 = 3 := by - decide +kernel - -lemma sg287 : RowSquare [3,2,2,1] [2,2,2,2] := by - apply rowSquare_compact (n := 8) (cs := [3,2,2,1]) (ts := [4,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB287 sgT287 sgFlag287 - change solveCompact 8 (.full [4,4]) (.full [3,2,2,1]) (.full [3,2,2,1]) - (certificateEdges [3,2,2,1] [3,2,2,1] [4,4] (Equiv.refl (Fin 8)) sgB287 sgT287) sgFlag287 ≠ 0 - rw [sgCert287] - norm_num - -def sgB295 : Equiv.Perm (Fin 8) := Equiv.swap 4 6 * (Equiv.swap 2 7 * (Equiv.swap 0 3)) -def sgT295 : Equiv.Perm (Fin 8) := Equiv.swap 6 2 * (Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 0 4 * (Equiv.swap 0 1))))) -def sgFlag295 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,0,2),(3,1,0),(4,1,1),(0,2,0),(5,2,2)} -lemma sgCert295 : solveCompact 8 (.full [6,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [6,2] (Equiv.refl (Fin 8)) sgB295 sgT295) sgFlag295 = 10 := by - decide +kernel - -lemma sg295 : RowSquare [3,3,1,1] [2,2,1,1,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [6,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB295 sgT295 sgFlag295 - change solveCompact 8 (.full [6,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [6,2] (Equiv.refl (Fin 8)) sgB295 sgT295) sgFlag295 ≠ 0 - rw [sgCert295] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB296 : Equiv.Perm (Fin 8) := Equiv.swap 4 0 * (Equiv.swap 3 1 * (Equiv.swap 0 7 * (Equiv.swap 1 5 * (Equiv.swap 0 2)))) -def sgT296 : Equiv.Perm (Fin 8) := Equiv.swap 4 2 * (Equiv.swap 2 0 * (Equiv.swap 4 6 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))) -def sgFlag296 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(1,0,1),(4,0,1),(2,0,2),(1,1,0),(3,1,2),(0,2,0)} -lemma sgCert296 : solveCompact 8 (.full [5,3]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [5,3] (Equiv.refl (Fin 8)) sgB296 sgT296) sgFlag296 = 6 := by - decide +kernel - -lemma sg296 : RowSquare [3,3,1,1] [2,2,2,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [5,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB296 sgT296 sgFlag296 - change solveCompact 8 (.full [5,3]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [5,3] (Equiv.refl (Fin 8)) sgB296 sgT296) sgFlag296 ≠ 0 - rw [sgCert296] - norm_num - -def sgB297 : Equiv.Perm (Fin 8) := Equiv.swap 1 6 * (Equiv.swap 0 4 * (Equiv.swap 0 3 * (Equiv.swap 1 5 * (Equiv.swap 0 2)))) -def sgT297 : Equiv.Perm (Fin 8) := Equiv.swap 0 2 * (Equiv.swap 2 7 * (Equiv.swap 0 6 * (Equiv.swap 2 5 * (Equiv.swap 0 3)))) -def sgFlag297 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,1),(3,0,2),(0,1,0),(1,1,2),(1,2,0),(3,2,0)} -lemma sgCert297 : solveCompact 8 (.full [4,4]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [4,4] (Equiv.refl (Fin 8)) sgB297 sgT297) sgFlag297 = -5 := by - decide +kernel - -lemma sg297 : RowSquare [3,3,1,1] [2,2,2,2] := by - apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [4,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB297 sgT297 sgFlag297 - change solveCompact 8 (.full [4,4]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [4,4] (Equiv.refl (Fin 8)) sgB297 sgT297) sgFlag297 ≠ 0 - rw [sgCert297] - norm_num - -def sgB300 : Equiv.Perm (Fin 8) := Equiv.swap 1 0 * (Equiv.swap 0 6 * (Equiv.swap 1 4 * (Equiv.swap 0 2))) -def sgT300 : Equiv.Perm (Fin 8) := Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 2 4 * (Equiv.swap 0 6))))) -def sgFlag300 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,0,2),(3,1,0),(1,1,1),(0,2,0),(0,2,2)} -lemma sgCert300 : solveCompact 8 (.full [4,2,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB300 sgT300) sgFlag300 = -1 := by - decide +kernel - -lemma sg300 : RowSquare [3,3,1,1] [3,3,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [4,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB300 sgT300 sgFlag300 - change solveCompact 8 (.full [4,2,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB300 sgT300) sgFlag300 ≠ 0 - rw [sgCert300] - norm_num - -def sgB301 : Equiv.Perm (Fin 8) := Equiv.swap 1 3 * (Equiv.swap 3 6 * (Equiv.swap 1 5 * (Equiv.swap 1 2))) -def sgT301 : Equiv.Perm (Fin 8) := Equiv.swap 6 3 * (Equiv.swap 3 4 * (Equiv.swap 4 1 * (Equiv.swap 3 5 * (Equiv.swap 1 7 * (Equiv.swap 0 2))))) -def sgFlag301 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(0,0,1),(1,1,1),(1,1,2),(1,2,0),(0,2,2)} -lemma sgCert301 : solveCompact 8 (.full [3,3,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB301 sgT301) sgFlag301 = 5 := by - decide +kernel - -lemma sg301 : RowSquare [3,3,1,1] [3,3,2] := by - apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [3,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB301 sgT301 sgFlag301 - change solveCompact 8 (.full [3,3,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB301 sgT301) sgFlag301 ≠ 0 - rw [sgCert301] - norm_num - -def sgB309 : Equiv.Perm (Fin 8) := Equiv.swap 4 2 * (Equiv.swap 4 3 * (Equiv.swap 4 0 * (Equiv.swap 3 6 * (Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 0 5)))))) -def sgT309 : Equiv.Perm (Fin 8) := Equiv.swap 0 7 * (Equiv.swap 2 4 * (Equiv.swap 0 5 * (Equiv.swap 0 1))) -def sgFlag309 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(1,0,2),(2,1,0),(0,1,1),(2,2,0),(4,2,1)} -lemma sgCert309 : solveCompact 8 (.full [5,3]) (.full [3,3,2]) (.full [3,3,2]) - (certificateEdges [3,3,2] [3,3,2] [5,3] (Equiv.refl (Fin 8)) sgB309 sgT309) sgFlag309 = -3 := by - decide +kernel - -lemma sg309 : RowSquare [3,3,2] [2,2,2,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,3,2]) (ts := [5,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB309 sgT309 sgFlag309 - change solveCompact 8 (.full [5,3]) (.full [3,3,2]) (.full [3,3,2]) - (certificateEdges [3,3,2] [3,3,2] [5,3] (Equiv.refl (Fin 8)) sgB309 sgT309) sgFlag309 ≠ 0 - rw [sgCert309] - norm_num - -def sgB310 : Equiv.Perm (Fin 8) := Equiv.swap 2 7 * (Equiv.swap 2 5 * (Equiv.swap 3 1 * (Equiv.swap 2 4 * (Equiv.swap 1 0 * (Equiv.swap 0 6))))) -def sgT310 : Equiv.Perm (Fin 8) := Equiv.swap 5 0 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 0 6 * (Equiv.swap 0 1)))) -def sgFlag310 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,1,0),(3,1,2),(0,2,1),(2,2,1)} -lemma sgCert310 : solveCompact 8 (.full [4,4]) (.full [3,3,2]) (.full [3,3,2]) - (certificateEdges [3,3,2] [3,3,2] [4,4] (Equiv.refl (Fin 8)) sgB310 sgT310) sgFlag310 = -2 := by - decide +kernel - -lemma sg310 : RowSquare [3,3,2] [2,2,2,2] := by - apply rowSquare_compact (n := 8) (cs := [3,3,2]) (ts := [4,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB310 sgT310 sgFlag310 - change solveCompact 8 (.full [4,4]) (.full [3,3,2]) (.full [3,3,2]) - (certificateEdges [3,3,2] [3,3,2] [4,4] (Equiv.refl (Fin 8)) sgB310 sgT310) sgFlag310 ≠ 0 - rw [sgCert310] - norm_num - -def sgB311 : Equiv.Perm (Fin 8) := Equiv.swap 1 0 * (Equiv.swap 0 2 * (Equiv.swap 3 7 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 0 4))))) -def sgT311 : Equiv.Perm (Fin 8) := Equiv.swap 5 0 * (Equiv.swap 5 3 * (Equiv.swap 0 7 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 6 * (Equiv.swap 0 4)))))) -def sgFlag311 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(1,1,0),(0,1,2),(1,1,2),(1,2,0)} -lemma sgCert311 : solveCompact 8 (.full [2,2,2,2]) (.full [3,3,2]) (.full [3,3,2]) - (certificateEdges [3,3,2] [3,3,2] [2,2,2,2] (Equiv.refl (Fin 8)) sgB311 sgT311) sgFlag311 = 6 := by - decide +kernel - -lemma sg311 : RowSquare [3,3,2] [4,4] := by - apply rowSquare_compact (n := 8) (cs := [3,3,2]) (ts := [2,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB311 sgT311 sgFlag311 - change solveCompact 8 (.full [2,2,2,2]) (.full [3,3,2]) (.full [3,3,2]) - (certificateEdges [3,3,2] [3,3,2] [2,2,2,2] (Equiv.refl (Fin 8)) sgB311 sgT311) sgFlag311 ≠ 0 - rw [sgCert311] - norm_num - -def sgB313 : Equiv.Perm (Fin 8) := Equiv.swap 5 2 * (Equiv.swap 2 3 * (Equiv.swap 3 0 * (Equiv.swap 2 4 * (Equiv.swap 0 6 * (Equiv.swap 0 1))))) -def sgT313 : Equiv.Perm (Fin 8) := Equiv.swap 2 1 * (Equiv.swap 1 3 * (Equiv.swap 0 7)) -def sgFlag313 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(5,0,2),(4,0,3),(3,1,0),(1,2,0),(2,3,0)} -lemma sgCert313 : solveCompact 8 (.full [6,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [6,2] (Equiv.refl (Fin 8)) sgB313 sgT313) sgFlag313 = 24 := by - decide +kernel - -lemma sg313 : RowSquare [4,1,1,1,1] [2,2,1,1,1,1] := by - apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [6,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB313 sgT313 sgFlag313 - change solveCompact 8 (.full [6,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [6,2] (Equiv.refl (Fin 8)) sgB313 sgT313) sgFlag313 ≠ 0 - rw [sgCert313] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Semigroup Leaves 1. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB10 : Equiv.Perm (Fin 4) := Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 3)) +def sgT10 : Equiv.Perm (Fin 4) := Equiv.swap 1 3 * (Equiv.swap 1 0 * (Equiv.swap 0 2)) +def sgFlag10 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(0,1,0)} +lemma sgCert10 : solveCompact 4 (.full [2,2]) (.full [2,1,1]) (.full [2,1,1]) + (certificateEdges [2,1,1] [2,1,1] [2,2] (Equiv.refl (Fin 4)) sgB10 sgT10) sgFlag10 = -2 := by + decide +kernel + +lemma sg10 : RowSquare [2,1,1] [2,2] := by + apply rowSquare_compact (n := 4) (cs := [2,1,1]) (ts := [2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB10 sgT10 sgFlag10 + change solveCompact 4 (.full [2,2]) (.full [2,1,1]) (.full [2,1,1]) + (certificateEdges [2,1,1] [2,1,1] [2,2] (Equiv.refl (Fin 4)) sgB10 sgT10) sgFlag10 ≠ 0 + rw [sgCert10] + norm_num + +def sgB17 : Equiv.Perm (Fin 4) := Equiv.swap 0 3 * (Equiv.swap 0 1) +def sgT17 : Equiv.Perm (Fin 4) := Equiv.swap 2 3 +def sgFlag17 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,1),(1,1,0)} +lemma sgCert17 : solveCompact 4 (.full [2,2]) (.full [2,1,1]) (.full [2,1,1]) + (certificateEdges [2,1,1] [2,1,1] [2,2] (Equiv.refl (Fin 4)) sgB17 sgT17) sgFlag17 = -2 := by + decide +kernel + +lemma sg17 : RowSquare [3,1] [2,2] := by + apply rowSquare_compact (n := 4) (cs := [2,1,1]) (ts := [2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB17 sgT17 sgFlag17 + change solveCompact 4 (.full [2,2]) (.full [2,1,1]) (.full [2,1,1]) + (certificateEdges [2,1,1] [2,1,1] [2,2] (Equiv.refl (Fin 4)) sgB17 sgT17) sgFlag17 ≠ 0 + rw [sgCert17] + norm_num + +def sgB67 : Equiv.Perm (Fin 6) := Equiv.swap 1 2 * (Equiv.swap 1 0 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 4)))) +def sgT67 : Equiv.Perm (Fin 6) := Equiv.swap 3 5 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 4))) +def sgFlag67 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(3,0,1),(1,0,2),(0,1,0),(1,2,0)} +lemma sgCert67 : solveCompact 6 (.full [4,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) + (certificateEdges [3,1,1,1] [3,1,1,1] [4,2] (Equiv.refl (Fin 6)) sgB67 sgT67) sgFlag67 = -8 := by + decide +kernel + +lemma sg67 : RowSquare [3,1,1,1] [2,2,1,1] := by + apply rowSquare_compact (n := 6) (cs := [3,1,1,1]) (ts := [4,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB67 sgT67 sgFlag67 + change solveCompact 6 (.full [4,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) + (certificateEdges [3,1,1,1] [3,1,1,1] [4,2] (Equiv.refl (Fin 6)) sgB67 sgT67) sgFlag67 ≠ 0 + rw [sgCert67] + norm_num + +def sgB68 : Equiv.Perm (Fin 6) := Equiv.swap 2 5 * (Equiv.swap 0 1) +def sgT68 : Equiv.Perm (Fin 6) := Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 4)) +def sgFlag68 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(2,0,2),(2,1,0),(0,2,0)} +lemma sgCert68 : solveCompact 6 (.full [3,3]) (.full [3,1,1,1]) (.full [3,1,1,1]) + (certificateEdges [3,1,1,1] [3,1,1,1] [3,3] (Equiv.refl (Fin 6)) sgB68 sgT68) sgFlag68 = 6 := by + decide +kernel + +lemma sg68 : RowSquare [3,1,1,1] [2,2,2] := by + apply rowSquare_compact (n := 6) (cs := [3,1,1,1]) (ts := [3,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB68 sgT68 sgFlag68 + change solveCompact 6 (.full [3,3]) (.full [3,1,1,1]) (.full [3,1,1,1]) + (certificateEdges [3,1,1,1] [3,1,1,1] [3,3] (Equiv.refl (Fin 6)) sgB68 sgT68) sgFlag68 ≠ 0 + rw [sgCert68] + norm_num + +def sgB71 : Equiv.Perm (Fin 6) := Equiv.swap 1 5 * (Equiv.swap 1 4 * (Equiv.swap 0 3)) +def sgT71 : Equiv.Perm (Fin 6) := Equiv.swap 0 3 * (Equiv.swap 3 5 * (Equiv.swap 0 4)) +def sgFlag71 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,1),(1,1,0),(0,2,2)} +lemma sgCert71 : solveCompact 6 (.full [2,2,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) + (certificateEdges [3,1,1,1] [3,1,1,1] [2,2,2] (Equiv.refl (Fin 6)) sgB71 sgT71) sgFlag71 = 2 := by + decide +kernel + +lemma sg71 : RowSquare [3,1,1,1] [3,3] := by + apply rowSquare_compact (n := 6) (cs := [3,1,1,1]) (ts := [2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB71 sgT71 sgFlag71 + change solveCompact 6 (.full [2,2,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) + (certificateEdges [3,1,1,1] [3,1,1,1] [2,2,2] (Equiv.refl (Fin 6)) sgB71 sgT71) sgFlag71 ≠ 0 + rw [sgCert71] + norm_num + +def sgB88 : Equiv.Perm (Fin 6) := Equiv.swap 2 0 * (Equiv.swap 1 5 * (Equiv.swap 0 3)) +def sgT88 : Equiv.Perm (Fin 6) := Equiv.swap 0 2 +def sgFlag88 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(1,0,1),(3,0,2),(1,1,0),(0,2,0)} +lemma sgCert88 : solveCompact 6 (.full [4,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) + (certificateEdges [3,1,1,1] [3,1,1,1] [4,2] (Equiv.refl (Fin 6)) sgB88 sgT88) sgFlag88 = 8 := by + decide +kernel + +lemma sg88 : RowSquare [4,1,1] [2,2,1,1] := by + apply rowSquare_compact (n := 6) (cs := [3,1,1,1]) (ts := [4,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB88 sgT88 sgFlag88 + change solveCompact 6 (.full [4,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) + (certificateEdges [3,1,1,1] [3,1,1,1] [4,2] (Equiv.refl (Fin 6)) sgB88 sgT88) sgFlag88 ≠ 0 + rw [sgCert88] + norm_num + +def sgB89 : Equiv.Perm (Fin 6) := Equiv.swap 2 1 * (Equiv.swap 2 4 * (Equiv.swap 1 5)) +def sgT89 : Equiv.Perm (Fin 6) := Equiv.swap 1 3 * (Equiv.swap 3 5 * (Equiv.swap 1 4 * (Equiv.swap 1 0 * (Equiv.swap 0 2)))) +def sgFlag89 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(0,0,1),(1,0,2),(0,1,0),(1,2,0)} +lemma sgCert89 : solveCompact 6 (.full [3,3]) (.full [3,1,1,1]) (.full [3,1,1,1]) + (certificateEdges [3,1,1,1] [3,1,1,1] [3,3] (Equiv.refl (Fin 6)) sgB89 sgT89) sgFlag89 = 6 := by + decide +kernel + +lemma sg89 : RowSquare [4,1,1] [2,2,2] := by + apply rowSquare_compact (n := 6) (cs := [3,1,1,1]) (ts := [3,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB89 sgT89 sgFlag89 + change solveCompact 6 (.full [3,3]) (.full [3,1,1,1]) (.full [3,1,1,1]) + (certificateEdges [3,1,1,1] [3,1,1,1] [3,3] (Equiv.refl (Fin 6)) sgB89 sgT89) sgFlag89 ≠ 0 + rw [sgCert89] + norm_num + +def sgB92 : Equiv.Perm (Fin 6) := Equiv.swap 4 2 * (Equiv.swap 2 0 * (Equiv.swap 2 1 * (Equiv.swap 1 3 * (Equiv.swap 0 5)))) +def sgT92 : Equiv.Perm (Fin 6) := Equiv.swap 0 4 * (Equiv.swap 2 1 * (Equiv.swap 1 5 * (Equiv.swap 0 3))) +def sgFlag92 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,2),(1,1,0),(1,2,1)} +lemma sgCert92 : solveCompact 6 (.full [2,2,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) + (certificateEdges [3,1,1,1] [3,1,1,1] [2,2,2] (Equiv.refl (Fin 6)) sgB92 sgT92) sgFlag92 = 1 := by + decide +kernel + +lemma sg92 : RowSquare [4,1,1] [3,3] := by + apply rowSquare_compact (n := 6) (cs := [3,1,1,1]) (ts := [2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB92 sgT92 sgFlag92 + change solveCompact 6 (.full [2,2,2]) (.full [3,1,1,1]) (.full [3,1,1,1]) + (certificateEdges [3,1,1,1] [3,1,1,1] [2,2,2] (Equiv.refl (Fin 6)) sgB92 sgT92) sgFlag92 ≠ 0 + rw [sgCert92] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB143 : Equiv.Perm (Fin 7) := Equiv.swap 0 6 * (Equiv.swap 3 2 * (Equiv.swap 2 5 * (Equiv.swap 0 4))) +def sgT143 : Equiv.Perm (Fin 7) := Equiv.swap 1 5 * (Equiv.swap 1 3 * (Equiv.swap 1 2)) +def sgFlag143 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(0,0,2),(4,1,0),(2,1,1),(3,2,0)} +lemma sgCert143 : solveCompact 7 (.full [5,2]) (.full [3,2,1,1]) (.full [3,2,1,1]) + (certificateEdges [3,2,1,1] [3,2,1,1] [5,2] (Equiv.refl (Fin 7)) sgB143 sgT143) sgFlag143 = 6 := by + decide +kernel + +lemma sg143 : RowSquare [3,2,1,1] [2,2,1,1,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,1,1]) (ts := [5,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB143 sgT143 sgFlag143 + change solveCompact 7 (.full [5,2]) (.full [3,2,1,1]) (.full [3,2,1,1]) + (certificateEdges [3,2,1,1] [3,2,1,1] [5,2] (Equiv.refl (Fin 7)) sgB143 sgT143) sgFlag143 ≠ 0 + rw [sgCert143] + norm_num + +def sgB144 : Equiv.Perm (Fin 7) := Equiv.swap 5 1 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 1 6 * (Equiv.swap 0 4)))) +def sgT144 : Equiv.Perm (Fin 7) := Equiv.swap 0 5 * (Equiv.swap 1 6 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 4)))) +def sgFlag144 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,2),(1,1,0),(2,1,0),(3,2,0)} +lemma sgCert144 : solveCompact 7 (.full [4,3]) (.full [3,2,1,1]) (.full [3,2,1,1]) + (certificateEdges [3,2,1,1] [3,2,1,1] [4,3] (Equiv.refl (Fin 7)) sgB144 sgT144) sgFlag144 = 2 := by + decide +kernel + +lemma sg144 : RowSquare [3,2,1,1] [2,2,2,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,1,1]) (ts := [4,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB144 sgT144 sgFlag144 + change solveCompact 7 (.full [4,3]) (.full [3,2,1,1]) (.full [3,2,1,1]) + (certificateEdges [3,2,1,1] [3,2,1,1] [4,3] (Equiv.refl (Fin 7)) sgB144 sgT144) sgFlag144 ≠ 0 + rw [sgCert144] + norm_num + +def sgB154 : Equiv.Perm (Fin 7) := Equiv.swap 4 5 * (Equiv.swap 0 2 * (Equiv.swap 2 6 * (Equiv.swap 0 3))) +def sgT154 : Equiv.Perm (Fin 7) := Equiv.swap 1 2 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 5))) +def sgFlag154 : Finset (ℕ × ℕ × ℕ) := {(5,0,0),(1,0,1),(3,0,2),(0,1,0),(2,1,0),(4,1,1),(0,2,1)} +lemma sgCert154 : solveCompact 7 (.full [6,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [6,1] (Equiv.refl (Fin 7)) sgB154 sgT154) sgFlag154 = 15 := by + decide +kernel + +lemma sg154 : RowSquare [3,2,2] [2,1,1,1,1,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [6,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB154 sgT154 sgFlag154 + change solveCompact 7 (.full [6,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [6,1] (Equiv.refl (Fin 7)) sgB154 sgT154) sgFlag154 ≠ 0 + rw [sgCert154] + norm_num + +def sgB155 : Equiv.Perm (Fin 7) := Equiv.swap 3 2 * (Equiv.swap 2 6 * (Equiv.swap 0 4 * (Equiv.swap 0 1))) +def sgT155 : Equiv.Perm (Fin 7) := Equiv.swap 4 2 * (Equiv.swap 2 5 * (Equiv.swap 2 0 * (Equiv.swap 0 3))) +def sgFlag155 : Finset (ℕ × ℕ × ℕ) := {(4,0,0),(3,0,1),(0,0,2),(1,1,0),(2,1,0),(1,1,1),(0,2,1)} +lemma sgCert155 : solveCompact 7 (.full [5,2]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [5,2] (Equiv.refl (Fin 7)) sgB155 sgT155) sgFlag155 = 12 := by + decide +kernel + +lemma sg155 : RowSquare [3,2,2] [2,2,1,1,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [5,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB155 sgT155 sgFlag155 + change solveCompact 7 (.full [5,2]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [5,2] (Equiv.refl (Fin 7)) sgB155 sgT155) sgFlag155 ≠ 0 + rw [sgCert155] + norm_num + +def sgB156 : Equiv.Perm (Fin 7) := Equiv.swap 4 0 * (Equiv.swap 4 1 * (Equiv.swap 1 5 * (Equiv.swap 0 6))) +def sgT156 : Equiv.Perm (Fin 7) := Equiv.swap 3 1 * (Equiv.swap 1 4) +def sgFlag156 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(0,1,0),(2,1,1),(3,1,1),(2,2,2)} +lemma sgCert156 : solveCompact 7 (.full [4,3]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [4,3] (Equiv.refl (Fin 7)) sgB156 sgT156) sgFlag156 = 12 := by + decide +kernel + +lemma sg156 : RowSquare [3,2,2] [2,2,2,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [4,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB156 sgT156 sgFlag156 + change solveCompact 7 (.full [4,3]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [4,3] (Equiv.refl (Fin 7)) sgB156 sgT156) sgFlag156 ≠ 0 + rw [sgCert156] + norm_num + +def sgB157 : Equiv.Perm (Fin 7) := Equiv.swap 2 6 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 2 3 * (Equiv.swap 0 5)))) +def sgT157 : Equiv.Perm (Fin 7) := Equiv.swap 2 0 * (Equiv.swap 0 6 * (Equiv.swap 2 5 * (Equiv.swap 2 3 * (Equiv.swap 0 4 * (Equiv.swap 0 1))))) +def sgFlag157 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(0,1,0),(4,1,1),(2,1,2),(3,2,0)} +lemma sgCert157 : solveCompact 7 (.full [5,1,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [5,1,1] (Equiv.refl (Fin 7)) sgB157 sgT157) sgFlag157 = 6 := by + decide +kernel + +lemma sg157 : RowSquare [3,2,2] [3,1,1,1,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [5,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB157 sgT157 sgFlag157 + change solveCompact 7 (.full [5,1,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [5,1,1] (Equiv.refl (Fin 7)) sgB157 sgT157) sgFlag157 ≠ 0 + rw [sgCert157] + norm_num + +def sgB158 : Equiv.Perm (Fin 7) := Equiv.swap 5 4 * (Equiv.swap 4 3 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 0 6 * (Equiv.swap 0 1))))) +def sgT158 : Equiv.Perm (Fin 7) := Equiv.swap 3 5 * (Equiv.swap 1 6 * (Equiv.swap 1 2)) +def sgFlag158 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(3,0,1),(1,0,2),(0,1,0),(1,1,0),(2,1,1),(0,2,0)} +lemma sgCert158 : solveCompact 7 (.full [4,2,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [4,2,1] (Equiv.refl (Fin 7)) sgB158 sgT158) sgFlag158 = 4 := by + decide +kernel + +lemma sg158 : RowSquare [3,2,2] [3,2,1,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [4,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB158 sgT158 sgFlag158 + change solveCompact 7 (.full [4,2,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [4,2,1] (Equiv.refl (Fin 7)) sgB158 sgT158) sgFlag158 ≠ 0 + rw [sgCert158] + norm_num + +def sgB160 : Equiv.Perm (Fin 7) := Equiv.swap 4 6 * (Equiv.swap 2 3 * (Equiv.swap 1 5)) +def sgT160 : Equiv.Perm (Fin 7) := Equiv.swap 5 2 * (Equiv.swap 2 3 * (Equiv.swap 3 6 * (Equiv.swap 2 0 * (Equiv.swap 0 4)))) +def sgFlag160 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(1,0,2),(1,1,0),(0,1,1),(0,2,0)} +lemma sgCert160 : solveCompact 7 (.full [3,2,2]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [3,2,2] (Equiv.refl (Fin 7)) sgB160 sgT160) sgFlag160 = -4 := by + decide +kernel + +lemma sg160 : RowSquare [3,2,2] [3,3,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [3,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB160 sgT160 sgFlag160 + change solveCompact 7 (.full [3,2,2]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [3,2,2] (Equiv.refl (Fin 7)) sgB160 sgT160) sgFlag160 ≠ 0 + rw [sgCert160] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB163 : Equiv.Perm (Fin 7) := Equiv.swap 2 1 * (Equiv.swap 1 6 * (Equiv.swap 0 5)) +def sgT163 : Equiv.Perm (Fin 7) := Equiv.swap 3 0 * (Equiv.swap 3 1 * (Equiv.swap 1 5 * (Equiv.swap 1 2 * (Equiv.swap 0 6)))) +def sgFlag163 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,1,1),(1,1,2),(1,2,1)} +lemma sgCert163 : solveCompact 7 (.full [2,2,2,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [2,2,2,1] (Equiv.refl (Fin 7)) sgB163 sgT163) sgFlag163 = -3 := by + decide +kernel + +lemma sg163 : RowSquare [3,2,2] [4,3] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [2,2,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB163 sgT163 sgFlag163 + change solveCompact 7 (.full [2,2,2,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [2,2,2,1] (Equiv.refl (Fin 7)) sgB163 sgT163) sgFlag163 ≠ 0 + rw [sgCert163] + norm_num + +def sgB165 : Equiv.Perm (Fin 7) := Equiv.swap 3 6 * (Equiv.swap 2 5 * (Equiv.swap 1 4)) +def sgT165 : Equiv.Perm (Fin 7) := Equiv.swap 1 6 * (Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 4))) +def sgFlag165 : Finset (ℕ × ℕ × ℕ) := {(4,0,0),(3,0,1),(5,0,2),(1,1,0),(0,1,1),(2,1,1),(0,2,0)} +lemma sgCert165 : solveCompact 7 (.full [6,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [6,1] (Equiv.refl (Fin 7)) sgB165 sgT165) sgFlag165 = 15 := by + decide +kernel + +lemma sg165 : RowSquare [3,3,1] [2,1,1,1,1,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [6,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB165 sgT165 sgFlag165 + change solveCompact 7 (.full [6,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [6,1] (Equiv.refl (Fin 7)) sgB165 sgT165) sgFlag165 ≠ 0 + rw [sgCert165] + norm_num + +def sgB166 : Equiv.Perm (Fin 7) := Equiv.swap 5 4 * (Equiv.swap 4 6 * (Equiv.swap 2 0 * (Equiv.swap 0 3 * (Equiv.swap 0 1)))) +def sgT166 : Equiv.Perm (Fin 7) := Equiv.swap 3 4 * (Equiv.swap 1 5 * (Equiv.swap 0 6)) +def sgFlag166 : Finset (ℕ × ℕ × ℕ) := {(1,0,1),(4,0,2),(0,1,0),(3,1,1),(2,2,0)} +lemma sgCert166 : solveCompact 7 (.full [5,2]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [5,2] (Equiv.refl (Fin 7)) sgB166 sgT166) sgFlag166 = 3 := by + decide +kernel + +lemma sg166 : RowSquare [3,3,1] [2,2,1,1,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [5,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB166 sgT166 sgFlag166 + change solveCompact 7 (.full [5,2]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [5,2] (Equiv.refl (Fin 7)) sgB166 sgT166) sgFlag166 ≠ 0 + rw [sgCert166] + norm_num + +def sgB167 : Equiv.Perm (Fin 7) := Equiv.swap 3 1 * (Equiv.swap 1 6 * (Equiv.swap 0 2)) +def sgT167 : Equiv.Perm (Fin 7) := Equiv.swap 2 0 * (Equiv.swap 2 5 * (Equiv.swap 0 6 * (Equiv.swap 2 4 * (Equiv.swap 0 3)))) +def sgFlag167 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,1),(3,0,2),(2,1,0),(1,1,1),(0,2,0)} +lemma sgCert167 : solveCompact 7 (.full [4,3]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [4,3] (Equiv.refl (Fin 7)) sgB167 sgT167) sgFlag167 = 12 := by + decide +kernel + +lemma sg167 : RowSquare [3,3,1] [2,2,2,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [4,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB167 sgT167 sgFlag167 + change solveCompact 7 (.full [4,3]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [4,3] (Equiv.refl (Fin 7)) sgB167 sgT167) sgFlag167 ≠ 0 + rw [sgCert167] + norm_num + +def sgB168 : Equiv.Perm (Fin 7) := Equiv.swap 1 0 * (Equiv.swap 1 4 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 5)))) +def sgT168 : Equiv.Perm (Fin 7) := Equiv.swap 1 6 * (Equiv.swap 1 4) +def sgFlag168 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(3,0,1),(0,1,0),(1,1,1),(4,1,2),(2,2,0)} +lemma sgCert168 : solveCompact 7 (.full [5,1,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [5,1,1] (Equiv.refl (Fin 7)) sgB168 sgT168) sgFlag168 = 6 := by + decide +kernel + +lemma sg168 : RowSquare [3,3,1] [3,1,1,1,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [5,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB168 sgT168 sgFlag168 + change solveCompact 7 (.full [5,1,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [5,1,1] (Equiv.refl (Fin 7)) sgB168 sgT168) sgFlag168 ≠ 0 + rw [sgCert168] + norm_num + +def sgB169 : Equiv.Perm (Fin 7) := Equiv.swap 2 1 * (Equiv.swap 1 6 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 4)))) +def sgT169 : Equiv.Perm (Fin 7) := Equiv.swap 4 2 * (Equiv.swap 2 1 * (Equiv.swap 2 3 * (Equiv.swap 1 6 * (Equiv.swap 0 5)))) +def sgFlag169 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(0,1,0),(2,1,1),(0,1,2),(3,2,0)} +lemma sgCert169 : solveCompact 7 (.full [4,2,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [4,2,1] (Equiv.refl (Fin 7)) sgB169 sgT169) sgFlag169 = 3 := by + decide +kernel + +lemma sg169 : RowSquare [3,3,1] [3,2,1,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [4,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB169 sgT169 sgFlag169 + change solveCompact 7 (.full [4,2,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [4,2,1] (Equiv.refl (Fin 7)) sgB169 sgT169) sgFlag169 ≠ 0 + rw [sgCert169] + norm_num + +def sgB171 : Equiv.Perm (Fin 7) := Equiv.swap 4 2 * (Equiv.swap 4 0 * (Equiv.swap 2 1 * (Equiv.swap 1 6 * (Equiv.swap 0 5)))) +def sgT171 : Equiv.Perm (Fin 7) := Equiv.swap 0 3 * (Equiv.swap 3 2 * (Equiv.swap 2 5 * (Equiv.swap 0 4))) +def sgFlag171 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(0,0,2),(0,1,0),(1,1,1),(0,2,1)} +lemma sgCert171 : solveCompact 7 (.full [3,2,2]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [3,2,2] (Equiv.refl (Fin 7)) sgB171 sgT171) sgFlag171 = -1 := by + decide +kernel + +lemma sg171 : RowSquare [3,3,1] [3,3,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [3,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB171 sgT171 sgFlag171 + change solveCompact 7 (.full [3,2,2]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [3,2,2] (Equiv.refl (Fin 7)) sgB171 sgT171) sgFlag171 ≠ 0 + rw [sgCert171] + norm_num + +def sgB174 : Equiv.Perm (Fin 7) := Equiv.swap 1 4 * (Equiv.swap 4 6 * (Equiv.swap 1 5 * (Equiv.swap 1 2))) +def sgT174 : Equiv.Perm (Fin 7) := Equiv.swap 5 0 * (Equiv.swap 0 3 * (Equiv.swap 3 6 * (Equiv.swap 0 4))) +def sgFlag174 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(1,1,1),(1,1,2),(0,2,0)} +lemma sgCert174 : solveCompact 7 (.full [2,2,2,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [2,2,2,1] (Equiv.refl (Fin 7)) sgB174 sgT174) sgFlag174 = 1 := by + decide +kernel + +lemma sg174 : RowSquare [3,3,1] [4,3] := by + apply rowSquare_compact (n := 7) (cs := [3,2,2]) (ts := [2,2,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB174 sgT174 sgFlag174 + change solveCompact 7 (.full [2,2,2,1]) (.full [3,2,2]) (.full [3,2,2]) + (certificateEdges [3,2,2] [3,2,2] [2,2,2,1] (Equiv.refl (Fin 7)) sgB174 sgT174) sgFlag174 ≠ 0 + rw [sgCert174] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB194 : Equiv.Perm (Fin 7) := Equiv.swap 1 3 * (Equiv.swap 3 5 * (Equiv.swap 2 6 * (Equiv.swap 1 4))) +def sgT194 : Equiv.Perm (Fin 7) := Equiv.swap 5 3 * (Equiv.swap 3 6 * (Equiv.swap 0 4 * (Equiv.swap 0 1))) +def sgFlag194 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,1),(0,0,2),(0,1,0),(4,1,1),(2,2,0)} +lemma sgCert194 : solveCompact 7 (.full [5,2]) (.full [3,2,1,1]) (.full [3,2,1,1]) + (certificateEdges [3,2,1,1] [3,2,1,1] [5,2] (Equiv.refl (Fin 7)) sgB194 sgT194) sgFlag194 = 17 := by + decide +kernel + +lemma sg194 : RowSquare [4,2,1] [2,2,1,1,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,1,1]) (ts := [5,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB194 sgT194 sgFlag194 + change solveCompact 7 (.full [5,2]) (.full [3,2,1,1]) (.full [3,2,1,1]) + (certificateEdges [3,2,1,1] [3,2,1,1] [5,2] (Equiv.refl (Fin 7)) sgB194 sgT194) sgFlag194 ≠ 0 + rw [sgCert194] + norm_num + +def sgB195 : Equiv.Perm (Fin 7) := Equiv.swap 2 1 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 1 6 * (Equiv.swap 0 5)))) +def sgT195 : Equiv.Perm (Fin 7) := Equiv.swap 5 3 * (Equiv.swap 3 6 * (Equiv.swap 3 0 * (Equiv.swap 0 4 * (Equiv.swap 0 1)))) +def sgFlag195 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(3,0,1),(1,0,2),(0,1,0),(2,1,0),(2,2,1)} +lemma sgCert195 : solveCompact 7 (.full [4,3]) (.full [3,2,1,1]) (.full [3,2,1,1]) + (certificateEdges [3,2,1,1] [3,2,1,1] [4,3] (Equiv.refl (Fin 7)) sgB195 sgT195) sgFlag195 = 3 := by + decide +kernel + +lemma sg195 : RowSquare [4,2,1] [2,2,2,1] := by + apply rowSquare_compact (n := 7) (cs := [3,2,1,1]) (ts := [4,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB195 sgT195 sgFlag195 + change solveCompact 7 (.full [4,3]) (.full [3,2,1,1]) (.full [3,2,1,1]) + (certificateEdges [3,2,1,1] [3,2,1,1] [4,3] (Equiv.refl (Fin 7)) sgB195 sgT195) sgFlag195 ≠ 0 + rw [sgCert195] + norm_num + +def sgB271 : Equiv.Perm (Fin 8) := Equiv.swap 5 4 * (Equiv.swap 4 7 * (Equiv.swap 2 6 * (Equiv.swap 0 1))) +def sgT271 : Equiv.Perm (Fin 8) := Equiv.swap 1 2 * (Equiv.swap 3 7 * (Equiv.swap 2 5 * (Equiv.swap 1 4))) +def sgFlag271 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,1),(1,0,1),(2,0,2),(0,1,0),(2,1,0),(1,2,0)} +lemma sgCert271 : solveCompact 8 (.full [4,4]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) + (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB271 sgT271) sgFlag271 = -4 := by + decide +kernel + +lemma sg271 : RowSquare [3,2,1,1,1] [2,2,2,2] := by + apply rowSquare_compact (n := 8) (cs := [3,2,1,1,1]) (ts := [4,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB271 sgT271 sgFlag271 + change solveCompact 8 (.full [4,4]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) + (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB271 sgT271) sgFlag271 ≠ 0 + rw [sgCert271] + norm_num + +def sgB275 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 1 * (Equiv.swap 1 6 * (Equiv.swap 1 3 * (Equiv.swap 1 0 * (Equiv.swap 0 2))))) +def sgT275 : Equiv.Perm (Fin 8) := Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 2 6 * (Equiv.swap 1 0 * (Equiv.swap 0 5)))) +def sgFlag275 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(2,0,1),(1,0,2),(0,1,0),(0,1,1),(0,2,0)} +lemma sgCert275 : solveCompact 8 (.full [4,2,2]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) + (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB275 sgT275) sgFlag275 = -1 := by + decide +kernel + +lemma sg275 : RowSquare [3,2,1,1,1] [3,3,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,2,1,1,1]) (ts := [4,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB275 sgT275 sgFlag275 + change solveCompact 8 (.full [4,2,2]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) + (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB275 sgT275) sgFlag275 ≠ 0 + rw [sgCert275] + norm_num + +def sgB285 : Equiv.Perm (Fin 8) := Equiv.swap 1 2 * (Equiv.swap 1 4 * (Equiv.swap 2 5 * (Equiv.swap 1 0 * (Equiv.swap 0 3)))) +def sgT285 : Equiv.Perm (Fin 8) := Equiv.swap 0 3 * (Equiv.swap 1 2 * (Equiv.swap 3 7 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))) +def sgFlag285 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(4,1,0),(3,1,1),(2,1,2),(5,2,0)} +lemma sgCert285 : solveCompact 8 (.full [6,2]) (.full [3,2,2,1]) (.full [3,2,2,1]) + (certificateEdges [3,2,2,1] [3,2,2,1] [6,2] (Equiv.refl (Fin 8)) sgB285 sgT285) sgFlag285 = 24 := by + decide +kernel + +lemma sg285 : RowSquare [3,2,2,1] [2,2,1,1,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,2,2,1]) (ts := [6,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB285 sgT285 sgFlag285 + change solveCompact 8 (.full [6,2]) (.full [3,2,2,1]) (.full [3,2,2,1]) + (certificateEdges [3,2,2,1] [3,2,2,1] [6,2] (Equiv.refl (Fin 8)) sgB285 sgT285) sgFlag285 ≠ 0 + rw [sgCert285] + norm_num + +def sgB286 : Equiv.Perm (Fin 8) := Equiv.swap 4 5 * (Equiv.swap 1 6 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 7)))) +def sgT286 : Equiv.Perm (Fin 8) := Equiv.swap 1 0 * (Equiv.swap 1 5 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 6)))) +def sgFlag286 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(0,0,1),(4,1,0),(1,1,1),(2,1,2),(3,2,0)} +lemma sgCert286 : solveCompact 8 (.full [5,3]) (.full [3,2,2,1]) (.full [3,2,2,1]) + (certificateEdges [3,2,2,1] [3,2,2,1] [5,3] (Equiv.refl (Fin 8)) sgB286 sgT286) sgFlag286 = -3 := by + decide +kernel + +lemma sg286 : RowSquare [3,2,2,1] [2,2,2,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,2,2,1]) (ts := [5,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB286 sgT286 sgFlag286 + change solveCompact 8 (.full [5,3]) (.full [3,2,2,1]) (.full [3,2,2,1]) + (certificateEdges [3,2,2,1] [3,2,2,1] [5,3] (Equiv.refl (Fin 8)) sgB286 sgT286) sgFlag286 ≠ 0 + rw [sgCert286] + norm_num + +def sgB287 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 2 0 * (Equiv.swap 1 6 * (Equiv.swap 0 3))) +def sgT287 : Equiv.Perm (Fin 8) := Equiv.swap 6 2 * (Equiv.swap 2 7 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 0 4 * (Equiv.swap 0 1))))) +def sgFlag287 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,0,2),(3,1,0),(0,1,1),(2,1,1),(3,2,0)} +lemma sgCert287 : solveCompact 8 (.full [4,4]) (.full [3,2,2,1]) (.full [3,2,2,1]) + (certificateEdges [3,2,2,1] [3,2,2,1] [4,4] (Equiv.refl (Fin 8)) sgB287 sgT287) sgFlag287 = 3 := by + decide +kernel + +lemma sg287 : RowSquare [3,2,2,1] [2,2,2,2] := by + apply rowSquare_compact (n := 8) (cs := [3,2,2,1]) (ts := [4,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB287 sgT287 sgFlag287 + change solveCompact 8 (.full [4,4]) (.full [3,2,2,1]) (.full [3,2,2,1]) + (certificateEdges [3,2,2,1] [3,2,2,1] [4,4] (Equiv.refl (Fin 8)) sgB287 sgT287) sgFlag287 ≠ 0 + rw [sgCert287] + norm_num + +def sgB295 : Equiv.Perm (Fin 8) := Equiv.swap 4 6 * (Equiv.swap 2 7 * (Equiv.swap 0 3)) +def sgT295 : Equiv.Perm (Fin 8) := Equiv.swap 6 2 * (Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 0 4 * (Equiv.swap 0 1))))) +def sgFlag295 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,0,2),(3,1,0),(4,1,1),(0,2,0),(5,2,2)} +lemma sgCert295 : solveCompact 8 (.full [6,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [6,2] (Equiv.refl (Fin 8)) sgB295 sgT295) sgFlag295 = 10 := by + decide +kernel + +lemma sg295 : RowSquare [3,3,1,1] [2,2,1,1,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [6,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB295 sgT295 sgFlag295 + change solveCompact 8 (.full [6,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [6,2] (Equiv.refl (Fin 8)) sgB295 sgT295) sgFlag295 ≠ 0 + rw [sgCert295] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB296 : Equiv.Perm (Fin 8) := Equiv.swap 4 0 * (Equiv.swap 3 1 * (Equiv.swap 0 7 * (Equiv.swap 1 5 * (Equiv.swap 0 2)))) +def sgT296 : Equiv.Perm (Fin 8) := Equiv.swap 4 2 * (Equiv.swap 2 0 * (Equiv.swap 4 6 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))) +def sgFlag296 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(1,0,1),(4,0,1),(2,0,2),(1,1,0),(3,1,2),(0,2,0)} +lemma sgCert296 : solveCompact 8 (.full [5,3]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [5,3] (Equiv.refl (Fin 8)) sgB296 sgT296) sgFlag296 = 6 := by + decide +kernel + +lemma sg296 : RowSquare [3,3,1,1] [2,2,2,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [5,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB296 sgT296 sgFlag296 + change solveCompact 8 (.full [5,3]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [5,3] (Equiv.refl (Fin 8)) sgB296 sgT296) sgFlag296 ≠ 0 + rw [sgCert296] + norm_num + +def sgB297 : Equiv.Perm (Fin 8) := Equiv.swap 1 6 * (Equiv.swap 0 4 * (Equiv.swap 0 3 * (Equiv.swap 1 5 * (Equiv.swap 0 2)))) +def sgT297 : Equiv.Perm (Fin 8) := Equiv.swap 0 2 * (Equiv.swap 2 7 * (Equiv.swap 0 6 * (Equiv.swap 2 5 * (Equiv.swap 0 3)))) +def sgFlag297 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,1),(3,0,2),(0,1,0),(1,1,2),(1,2,0),(3,2,0)} +lemma sgCert297 : solveCompact 8 (.full [4,4]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [4,4] (Equiv.refl (Fin 8)) sgB297 sgT297) sgFlag297 = -5 := by + decide +kernel + +lemma sg297 : RowSquare [3,3,1,1] [2,2,2,2] := by + apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [4,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB297 sgT297 sgFlag297 + change solveCompact 8 (.full [4,4]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [4,4] (Equiv.refl (Fin 8)) sgB297 sgT297) sgFlag297 ≠ 0 + rw [sgCert297] + norm_num + +def sgB300 : Equiv.Perm (Fin 8) := Equiv.swap 1 0 * (Equiv.swap 0 6 * (Equiv.swap 1 4 * (Equiv.swap 0 2))) +def sgT300 : Equiv.Perm (Fin 8) := Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 2 4 * (Equiv.swap 0 6))))) +def sgFlag300 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,0,2),(3,1,0),(1,1,1),(0,2,0),(0,2,2)} +lemma sgCert300 : solveCompact 8 (.full [4,2,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB300 sgT300) sgFlag300 = -1 := by + decide +kernel + +lemma sg300 : RowSquare [3,3,1,1] [3,3,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [4,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB300 sgT300 sgFlag300 + change solveCompact 8 (.full [4,2,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB300 sgT300) sgFlag300 ≠ 0 + rw [sgCert300] + norm_num + +def sgB301 : Equiv.Perm (Fin 8) := Equiv.swap 1 3 * (Equiv.swap 3 6 * (Equiv.swap 1 5 * (Equiv.swap 1 2))) +def sgT301 : Equiv.Perm (Fin 8) := Equiv.swap 6 3 * (Equiv.swap 3 4 * (Equiv.swap 4 1 * (Equiv.swap 3 5 * (Equiv.swap 1 7 * (Equiv.swap 0 2))))) +def sgFlag301 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(0,0,1),(1,1,1),(1,1,2),(1,2,0),(0,2,2)} +lemma sgCert301 : solveCompact 8 (.full [3,3,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB301 sgT301) sgFlag301 = 5 := by + decide +kernel + +lemma sg301 : RowSquare [3,3,1,1] [3,3,2] := by + apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [3,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB301 sgT301 sgFlag301 + change solveCompact 8 (.full [3,3,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB301 sgT301) sgFlag301 ≠ 0 + rw [sgCert301] + norm_num + +def sgB309 : Equiv.Perm (Fin 8) := Equiv.swap 4 2 * (Equiv.swap 4 3 * (Equiv.swap 4 0 * (Equiv.swap 3 6 * (Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 0 5)))))) +def sgT309 : Equiv.Perm (Fin 8) := Equiv.swap 0 7 * (Equiv.swap 2 4 * (Equiv.swap 0 5 * (Equiv.swap 0 1))) +def sgFlag309 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(1,0,2),(2,1,0),(0,1,1),(2,2,0),(4,2,1)} +lemma sgCert309 : solveCompact 8 (.full [5,3]) (.full [3,3,2]) (.full [3,3,2]) + (certificateEdges [3,3,2] [3,3,2] [5,3] (Equiv.refl (Fin 8)) sgB309 sgT309) sgFlag309 = -3 := by + decide +kernel + +lemma sg309 : RowSquare [3,3,2] [2,2,2,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,3,2]) (ts := [5,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB309 sgT309 sgFlag309 + change solveCompact 8 (.full [5,3]) (.full [3,3,2]) (.full [3,3,2]) + (certificateEdges [3,3,2] [3,3,2] [5,3] (Equiv.refl (Fin 8)) sgB309 sgT309) sgFlag309 ≠ 0 + rw [sgCert309] + norm_num + +def sgB310 : Equiv.Perm (Fin 8) := Equiv.swap 2 7 * (Equiv.swap 2 5 * (Equiv.swap 3 1 * (Equiv.swap 2 4 * (Equiv.swap 1 0 * (Equiv.swap 0 6))))) +def sgT310 : Equiv.Perm (Fin 8) := Equiv.swap 5 0 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 0 6 * (Equiv.swap 0 1)))) +def sgFlag310 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,1,0),(3,1,2),(0,2,1),(2,2,1)} +lemma sgCert310 : solveCompact 8 (.full [4,4]) (.full [3,3,2]) (.full [3,3,2]) + (certificateEdges [3,3,2] [3,3,2] [4,4] (Equiv.refl (Fin 8)) sgB310 sgT310) sgFlag310 = -2 := by + decide +kernel + +lemma sg310 : RowSquare [3,3,2] [2,2,2,2] := by + apply rowSquare_compact (n := 8) (cs := [3,3,2]) (ts := [4,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB310 sgT310 sgFlag310 + change solveCompact 8 (.full [4,4]) (.full [3,3,2]) (.full [3,3,2]) + (certificateEdges [3,3,2] [3,3,2] [4,4] (Equiv.refl (Fin 8)) sgB310 sgT310) sgFlag310 ≠ 0 + rw [sgCert310] + norm_num + +def sgB311 : Equiv.Perm (Fin 8) := Equiv.swap 1 0 * (Equiv.swap 0 2 * (Equiv.swap 3 7 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 0 4))))) +def sgT311 : Equiv.Perm (Fin 8) := Equiv.swap 5 0 * (Equiv.swap 5 3 * (Equiv.swap 0 7 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 6 * (Equiv.swap 0 4)))))) +def sgFlag311 : Finset (ℕ × ℕ × ℕ) := {(0,0,1),(1,1,0),(0,1,2),(1,1,2),(1,2,0)} +lemma sgCert311 : solveCompact 8 (.full [2,2,2,2]) (.full [3,3,2]) (.full [3,3,2]) + (certificateEdges [3,3,2] [3,3,2] [2,2,2,2] (Equiv.refl (Fin 8)) sgB311 sgT311) sgFlag311 = 6 := by + decide +kernel + +lemma sg311 : RowSquare [3,3,2] [4,4] := by + apply rowSquare_compact (n := 8) (cs := [3,3,2]) (ts := [2,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB311 sgT311 sgFlag311 + change solveCompact 8 (.full [2,2,2,2]) (.full [3,3,2]) (.full [3,3,2]) + (certificateEdges [3,3,2] [3,3,2] [2,2,2,2] (Equiv.refl (Fin 8)) sgB311 sgT311) sgFlag311 ≠ 0 + rw [sgCert311] + norm_num + +def sgB313 : Equiv.Perm (Fin 8) := Equiv.swap 5 2 * (Equiv.swap 2 3 * (Equiv.swap 3 0 * (Equiv.swap 2 4 * (Equiv.swap 0 6 * (Equiv.swap 0 1))))) +def sgT313 : Equiv.Perm (Fin 8) := Equiv.swap 2 1 * (Equiv.swap 1 3 * (Equiv.swap 0 7)) +def sgFlag313 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(5,0,2),(4,0,3),(3,1,0),(1,2,0),(2,3,0)} +lemma sgCert313 : solveCompact 8 (.full [6,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [6,2] (Equiv.refl (Fin 8)) sgB313 sgT313) sgFlag313 = 24 := by + decide +kernel + +lemma sg313 : RowSquare [4,1,1,1,1] [2,2,1,1,1,1] := by + apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [6,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB313 sgT313 sgFlag313 + change solveCompact 8 (.full [6,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [6,2] (Equiv.refl (Fin 8)) sgB313 sgT313) sgFlag313 ≠ 0 + rw [sgCert313] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves2.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves2.lean index 7161141fb7c7e30dd40a4020e06088ea9a4d089e..577e632623d67cb965f014aa7df6355d82f8e55d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves2.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves2.lean @@ -1,700 +1,700 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Semigroup Leaves 2. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB314 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 2 * (Equiv.swap 2 6 * (Equiv.swap 2 0 * (Equiv.swap 1 5 * (Equiv.swap 0 3))))) -def sgT314 : Equiv.Perm (Fin 8) := Equiv.swap 1 3 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 5))))) -def sgFlag314 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,1),(2,0,2),(0,0,3),(2,1,0),(0,2,0),(4,3,0)} -lemma sgCert314 : solveCompact 8 (.full [5,3]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [5,3] (Equiv.refl (Fin 8)) sgB314 sgT314) sgFlag314 = 20 := by - decide +kernel - -lemma sg314 : RowSquare [4,1,1,1,1] [2,2,2,1,1] := by - apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [5,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB314 sgT314 sgFlag314 - change solveCompact 8 (.full [5,3]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [5,3] (Equiv.refl (Fin 8)) sgB314 sgT314) sgFlag314 ≠ 0 - rw [sgCert314] - norm_num - -def sgB315 : Equiv.Perm (Fin 8) := Equiv.swap 5 2 * (Equiv.swap 5 6 * (Equiv.swap 2 1 * (Equiv.swap 2 4 * (Equiv.swap 1 7 * (Equiv.swap 0 3))))) -def sgT315 : Equiv.Perm (Fin 8) := Equiv.swap 3 7 * (Equiv.swap 3 5 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 0 6)))) -def sgFlag315 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(1,0,1),(0,0,2),(2,0,3),(1,1,0),(0,2,0),(2,3,0)} -lemma sgCert315 : solveCompact 8 (.full [4,4]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB315 sgT315) sgFlag315 = 24 := by - decide +kernel - -lemma sg315 : RowSquare [4,1,1,1,1] [2,2,2,2] := by - apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [4,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB315 sgT315 sgFlag315 - change solveCompact 8 (.full [4,4]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB315 sgT315) sgFlag315 ≠ 0 - rw [sgCert315] - norm_num - -def sgB319 : Equiv.Perm (Fin 8) := Equiv.swap 1 4 * (Equiv.swap 1 0 * (Equiv.swap 4 3 * (Equiv.swap 3 7 * (Equiv.swap 1 5 * (Equiv.swap 1 2 * (Equiv.swap 0 6)))))) -def sgT319 : Equiv.Perm (Fin 8) := Equiv.swap 0 2 * (Equiv.swap 2 7 * (Equiv.swap 2 5 * (Equiv.swap 2 4 * (Equiv.swap 0 6)))) -def sgFlag319 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,0),(0,0,1),(1,0,3),(1,1,2),(0,2,0),(3,3,0)} -lemma sgCert319 : solveCompact 8 (.full [4,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB319 sgT319) sgFlag319 = -2 := by - decide +kernel - -lemma sg319 : RowSquare [4,1,1,1,1] [3,3,1,1] := by - apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [4,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB319 sgT319 sgFlag319 - change solveCompact 8 (.full [4,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB319 sgT319) sgFlag319 ≠ 0 - rw [sgCert319] - norm_num - -def sgB320 : Equiv.Perm (Fin 8) := Equiv.swap 5 0 * (Equiv.swap 3 7 * (Equiv.swap 2 4 * (Equiv.swap 0 6))) -def sgT320 : Equiv.Perm (Fin 8) := Equiv.swap 3 4 * (Equiv.swap 4 7 * (Equiv.swap 4 5 * (Equiv.swap 3 6 * (Equiv.swap 0 1)))) -def sgFlag320 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,2),(0,0,3),(0,1,1),(2,2,0),(0,3,0)} -lemma sgCert320 : solveCompact 8 (.full [3,3,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB320 sgT320) sgFlag320 = 4 := by - decide +kernel - -lemma sg320 : RowSquare [4,1,1,1,1] [3,3,2] := by - apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [3,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB320 sgT320 sgFlag320 - change solveCompact 8 (.full [3,3,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB320 sgT320) sgFlag320 ≠ 0 - rw [sgCert320] - norm_num - -def sgB324 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 2 * (Equiv.swap 2 1 * (Equiv.swap 1 5 * (Equiv.swap 0 6)))) -def sgT324 : Equiv.Perm (Fin 8) := Equiv.swap 2 1 * (Equiv.swap 2 6 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 1 7 * (Equiv.swap 0 5))))) -def sgFlag324 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,2),(1,1,0),(0,2,1),(1,3,3)} -lemma sgCert324 : solveCompact 8 (.full [2,2,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [2,2,2,2] (Equiv.refl (Fin 8)) sgB324 sgT324) sgFlag324 = 4 := by - decide +kernel - -lemma sg324 : RowSquare [4,1,1,1,1] [4,4] := by - apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [2,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB324 sgT324 sgFlag324 - change solveCompact 8 (.full [2,2,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [2,2,2,2] (Equiv.refl (Fin 8)) sgB324 sgT324) sgFlag324 ≠ 0 - rw [sgCert324] - norm_num - -def sgB348 : Equiv.Perm (Fin 8) := Equiv.swap 5 3 * (Equiv.swap 5 6 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 0 * (Equiv.swap 0 7))))) -def sgT348 : Equiv.Perm (Fin 8) := Equiv.swap 2 7 * (Equiv.swap 0 1 * (Equiv.swap 0 4 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 0 3))))) -def sgFlag348 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(4,0,1),(2,0,2),(5,1,1),(1,1,2),(0,2,0)} -lemma sgCert348 : solveCompact 8 (.full [6,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [6,2] (Equiv.refl (Fin 8)) sgB348 sgT348) sgFlag348 = 6 := by - decide +kernel - -lemma sg348 : RowSquare [4,2,2] [2,2,1,1,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [6,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB348 sgT348 sgFlag348 - change solveCompact 8 (.full [6,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [6,2] (Equiv.refl (Fin 8)) sgB348 sgT348) sgFlag348 ≠ 0 - rw [sgCert348] - norm_num - -def sgB349 : Equiv.Perm (Fin 8) := Equiv.swap 2 6 * (Equiv.swap 2 4 * (Equiv.swap 2 3 * (Equiv.swap 1 0 * (Equiv.swap 0 5)))) -def sgT349 : Equiv.Perm (Fin 8) := Equiv.swap 5 3 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 0 * (Equiv.swap 1 7 * (Equiv.swap 0 6))))) -def sgFlag349 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,1),(0,0,2),(1,0,2),(2,1,0),(0,2,0),(3,2,1)} -lemma sgCert349 : solveCompact 8 (.full [5,3]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [5,3] (Equiv.refl (Fin 8)) sgB349 sgT349) sgFlag349 = -6 := by - decide +kernel - -lemma sg349 : RowSquare [4,2,2] [2,2,2,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [5,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB349 sgT349 sgFlag349 - change solveCompact 8 (.full [5,3]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [5,3] (Equiv.refl (Fin 8)) sgB349 sgT349) sgFlag349 ≠ 0 - rw [sgCert349] - norm_num - -def sgB350 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 6 * (Equiv.swap 2 3 * (Equiv.swap 0 1))) -def sgT350 : Equiv.Perm (Fin 8) := Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 4 7 * (Equiv.swap 1 5 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 6)))))) -def sgFlag350 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(1,0,2),(3,1,0),(0,2,0),(0,2,2)} -lemma sgCert350 : solveCompact 8 (.full [4,4]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [4,4] (Equiv.refl (Fin 8)) sgB350 sgT350) sgFlag350 = -5 := by - decide +kernel - -lemma sg350 : RowSquare [4,2,2] [2,2,2,2] := by - apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [4,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB350 sgT350 sgFlag350 - change solveCompact 8 (.full [4,4]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [4,4] (Equiv.refl (Fin 8)) sgB350 sgT350) sgFlag350 ≠ 0 - rw [sgCert350] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB352 : Equiv.Perm (Fin 8) := Equiv.swap 4 0 * (Equiv.swap 3 1 * (Equiv.swap 1 5 * (Equiv.swap 1 2 * (Equiv.swap 0 6)))) -def sgT352 : Equiv.Perm (Fin 8) := Equiv.swap 0 7 * (Equiv.swap 0 1 * (Equiv.swap 3 5 * (Equiv.swap 1 6 * (Equiv.swap 0 4)))) -def sgFlag352 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(1,1,0),(0,1,2),(3,2,0),(2,2,2)} -lemma sgCert352 : solveCompact 8 (.full [4,2,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB352 sgT352) sgFlag352 = 4 := by - decide +kernel - -lemma sg352 : RowSquare [4,2,2] [3,3,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [4,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB352 sgT352 sgFlag352 - change solveCompact 8 (.full [4,2,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB352 sgT352) sgFlag352 ≠ 0 - rw [sgCert352] - norm_num - -def sgB353 : Equiv.Perm (Fin 8) := Equiv.swap 3 6 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 5)))) -def sgT353 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 1 6 * (Equiv.swap 2 5 * (Equiv.swap 1 3))) -def sgFlag353 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,2),(1,1,0),(0,1,1),(2,2,0),(2,2,1)} -lemma sgCert353 : solveCompact 8 (.full [3,3,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB353 sgT353) sgFlag353 = 1 := by - decide +kernel - -lemma sg353 : RowSquare [4,2,2] [3,3,2] := by - apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [3,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB353 sgT353 sgFlag353 - change solveCompact 8 (.full [3,3,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) - (certificateEdges [3,3,1,1] [3,3,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB353 sgT353) sgFlag353 ≠ 0 - rw [sgCert353] - norm_num - -def sgB356 : Equiv.Perm (Fin 8) := Equiv.swap 4 2 * (Equiv.swap 4 5 * (Equiv.swap 0 1 * (Equiv.swap 2 7 * (Equiv.swap 1 6 * (Equiv.swap 0 3))))) -def sgT356 : Equiv.Perm (Fin 8) := Equiv.swap 1 2 * (Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 2 4 * (Equiv.swap 1 5)))) -def sgFlag356 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(2,0,2),(0,1,0),(3,1,0),(5,1,1),(4,2,0)} -lemma sgCert356 : solveCompact 8 (.full [6,2]) (.full [3,2,2,1]) (.full [3,2,2,1]) - (certificateEdges [3,2,2,1] [3,2,2,1] [6,2] (Equiv.refl (Fin 8)) sgB356 sgT356) sgFlag356 = 12 := by - decide +kernel - -lemma sg356 : RowSquare [4,3,1] [2,2,1,1,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,2,2,1]) (ts := [6,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB356 sgT356 sgFlag356 - change solveCompact 8 (.full [6,2]) (.full [3,2,2,1]) (.full [3,2,2,1]) - (certificateEdges [3,2,2,1] [3,2,2,1] [6,2] (Equiv.refl (Fin 8)) sgB356 sgT356) sgFlag356 ≠ 0 - rw [sgCert356] - norm_num - -def sgB357 : Equiv.Perm (Fin 8) := Equiv.swap 1 3 * (Equiv.swap 3 7 * (Equiv.swap 3 2 * (Equiv.swap 2 5 * (Equiv.swap 1 0 * (Equiv.swap 0 6))))) -def sgT357 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 3 * (Equiv.swap 4 0 * (Equiv.swap 3 6 * (Equiv.swap 0 5 * (Equiv.swap 0 2 * (Equiv.swap 0 1)))))) -def sgFlag357 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(1,0,1),(4,0,1),(1,0,2),(2,1,0),(0,1,1),(0,2,0)} -lemma sgCert357 : solveCompact 8 (.full [5,3]) (.full [3,2,2,1]) (.full [3,2,2,1]) - (certificateEdges [3,2,2,1] [3,2,2,1] [5,3] (Equiv.refl (Fin 8)) sgB357 sgT357) sgFlag357 = -4 := by - decide +kernel - -lemma sg357 : RowSquare [4,3,1] [2,2,2,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,2,2,1]) (ts := [5,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB357 sgT357 sgFlag357 - change solveCompact 8 (.full [5,3]) (.full [3,2,2,1]) (.full [3,2,2,1]) - (certificateEdges [3,2,2,1] [3,2,2,1] [5,3] (Equiv.refl (Fin 8)) sgB357 sgT357) sgFlag357 ≠ 0 - rw [sgCert357] - norm_num - -def sgB358 : Equiv.Perm (Fin 8) := Equiv.swap 2 4 * (Equiv.swap 4 6 * (Equiv.swap 2 0 * (Equiv.swap 1 7 * (Equiv.swap 0 5)))) -def sgT358 : Equiv.Perm (Fin 8) := Equiv.swap 6 7 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 5))) -def sgFlag358 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(3,1,0),(0,1,1),(3,1,2),(0,2,0)} -lemma sgCert358 : solveCompact 8 (.full [4,4]) (.full [3,2,2,1]) (.full [3,2,2,1]) - (certificateEdges [3,2,2,1] [3,2,2,1] [4,4] (Equiv.refl (Fin 8)) sgB358 sgT358) sgFlag358 = -2 := by - decide +kernel - -lemma sg358 : RowSquare [4,3,1] [2,2,2,2] := by - apply rowSquare_compact (n := 8) (cs := [3,2,2,1]) (ts := [4,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB358 sgT358 sgFlag358 - change solveCompact 8 (.full [4,4]) (.full [3,2,2,1]) (.full [3,2,2,1]) - (certificateEdges [3,2,2,1] [3,2,2,1] [4,4] (Equiv.refl (Fin 8)) sgB358 sgT358) sgFlag358 ≠ 0 - rw [sgCert358] - norm_num - -def sgB371 : Equiv.Perm (Fin 8) := Equiv.swap 1 2 * (Equiv.swap 2 7 * (Equiv.swap 2 5 * (Equiv.swap 2 4 * (Equiv.swap 1 6 * (Equiv.swap 0 3))))) -def sgT371 : Equiv.Perm (Fin 8) := Equiv.swap 3 1 * (Equiv.swap 4 7 * (Equiv.swap 3 5 * (Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 6))))) -def sgFlag371 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,1),(3,0,2),(0,0,3),(2,1,0),(0,2,0),(5,3,0)} -lemma sgCert371 : solveCompact 8 (.full [6,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [6,2] (Equiv.refl (Fin 8)) sgB371 sgT371) sgFlag371 = 24 := by - decide +kernel - -lemma sg371 : RowSquare [5,1,1,1] [2,2,1,1,1,1] := by - apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [6,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB371 sgT371 sgFlag371 - change solveCompact 8 (.full [6,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [6,2] (Equiv.refl (Fin 8)) sgB371 sgT371) sgFlag371 ≠ 0 - rw [sgCert371] - norm_num - -def sgB372 : Equiv.Perm (Fin 8) := Equiv.swap 5 6 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 0 4 * (Equiv.swap 0 1)))) -def sgT372 : Equiv.Perm (Fin 8) := Equiv.swap 1 3 * (Equiv.swap 3 7 * (Equiv.swap 2 5 * (Equiv.swap 1 4))) -def sgFlag372 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(0,0,1),(3,0,2),(1,0,3),(4,1,0),(0,2,0),(2,3,0)} -lemma sgCert372 : solveCompact 8 (.full [5,3]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [5,3] (Equiv.refl (Fin 8)) sgB372 sgT372) sgFlag372 = 20 := by - decide +kernel - -lemma sg372 : RowSquare [5,1,1,1] [2,2,2,1,1] := by - apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [5,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB372 sgT372 sgFlag372 - change solveCompact 8 (.full [5,3]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [5,3] (Equiv.refl (Fin 8)) sgB372 sgT372) sgFlag372 ≠ 0 - rw [sgCert372] - norm_num - -def sgB373 : Equiv.Perm (Fin 8) := Equiv.swap 6 2 * (Equiv.swap 2 7 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 3)))) -def sgT373 : Equiv.Perm (Fin 8) := Equiv.swap 0 6 * (Equiv.swap 0 5 * (Equiv.swap 3 7 * (Equiv.swap 0 4 * (Equiv.swap 0 2)))) -def sgFlag373 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(3,0,0),(1,0,1),(0,0,2),(2,0,3),(1,1,0),(0,2,0),(3,3,0)} -lemma sgCert373 : solveCompact 8 (.full [4,4]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB373 sgT373) sgFlag373 = 24 := by - decide +kernel - -lemma sg373 : RowSquare [5,1,1,1] [2,2,2,2] := by - apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [4,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB373 sgT373 sgFlag373 - change solveCompact 8 (.full [4,4]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB373 sgT373) sgFlag373 ≠ 0 - rw [sgCert373] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB377 : Equiv.Perm (Fin 8) := Equiv.swap 1 4 * (Equiv.swap 4 2 * (Equiv.swap 4 5 * (Equiv.swap 2 7 * (Equiv.swap 2 3 * (Equiv.swap 1 0 * (Equiv.swap 0 6)))))) -def sgT377 : Equiv.Perm (Fin 8) := Equiv.swap 2 7 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 6))) -def sgFlag377 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,1),(1,0,2),(0,1,0),(1,2,3),(3,3,0)} -lemma sgCert377 : solveCompact 8 (.full [4,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB377 sgT377) sgFlag377 = -4 := by - decide +kernel - -lemma sg377 : RowSquare [5,1,1,1] [3,3,1,1] := by - apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [4,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB377 sgT377 sgFlag377 - change solveCompact 8 (.full [4,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB377 sgT377) sgFlag377 ≠ 0 - rw [sgCert377] - norm_num - -def sgB378 : Equiv.Perm (Fin 8) := Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 0 4)))) -def sgT378 : Equiv.Perm (Fin 8) := Equiv.swap 2 7 * (Equiv.swap 2 0 * (Equiv.swap 3 1 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))) -def sgFlag378 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(2,0,2),(1,1,0),(2,2,0),(1,3,3)} -lemma sgCert378 : solveCompact 8 (.full [3,3,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB378 sgT378) sgFlag378 = 4 := by - decide +kernel - -lemma sg378 : RowSquare [5,1,1,1] [3,3,2] := by - apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [3,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB378 sgT378 sgFlag378 - change solveCompact 8 (.full [3,3,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB378 sgT378) sgFlag378 ≠ 0 - rw [sgCert378] - norm_num - -def sgB383 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 3 * (Equiv.swap 4 0 * (Equiv.swap 3 1 * (Equiv.swap 1 6 * (Equiv.swap 1 2 * (Equiv.swap 0 5)))))) -def sgT383 : Equiv.Perm (Fin 8) := Equiv.swap 0 7 * (Equiv.swap 0 2 * (Equiv.swap 2 1 * (Equiv.swap 2 3 * (Equiv.swap 1 5 * (Equiv.swap 0 4))))) -def sgFlag383 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,3),(1,1,2),(1,2,0),(1,3,1)} -lemma sgCert383 : solveCompact 8 (.full [2,2,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [2,2,2,2] (Equiv.refl (Fin 8)) sgB383 sgT383) sgFlag383 = 2 := by - decide +kernel - -lemma sg383 : RowSquare [5,1,1,1] [4,4] := by - apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [2,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB383 sgT383 sgFlag383 - change solveCompact 8 (.full [2,2,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) - (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [2,2,2,2] (Equiv.refl (Fin 8)) sgB383 sgT383) sgFlag383 ≠ 0 - rw [sgCert383] - norm_num - -def sgB390 : Equiv.Perm (Fin 8) := Equiv.swap 3 1 * (Equiv.swap 4 0 * (Equiv.swap 3 5 * (Equiv.swap 0 6 * (Equiv.swap 1 7 * (Equiv.swap 0 2))))) -def sgT390 : Equiv.Perm (Fin 8) := Equiv.swap 0 7 * (Equiv.swap 3 1 * (Equiv.swap 3 4 * (Equiv.swap 1 5 * (Equiv.swap 0 6)))) -def sgFlag390 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,1),(2,0,2),(1,1,0),(2,2,0)} -lemma sgCert390 : solveCompact 8 (.full [4,4]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) - (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB390 sgT390) sgFlag390 = 7 := by - decide +kernel - -lemma sg390 : RowSquare [5,2,1] [2,2,2,2] := by - apply rowSquare_compact (n := 8) (cs := [3,2,1,1,1]) (ts := [4,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB390 sgT390 sgFlag390 - change solveCompact 8 (.full [4,4]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) - (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB390 sgT390) sgFlag390 ≠ 0 - rw [sgCert390] - norm_num - -def sgB394 : Equiv.Perm (Fin 8) := Equiv.swap 5 4 * (Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 0 6 * (Equiv.swap 0 2)))) -def sgT394 : Equiv.Perm (Fin 8) := Equiv.swap 6 5 * (Equiv.swap 5 2 * (Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 0 3)))) -def sgFlag394 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,1),(3,0,2),(0,1,0),(1,1,1),(1,2,0)} -lemma sgCert394 : solveCompact 8 (.full [4,2,2]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) - (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB394 sgT394) sgFlag394 = 4 := by - decide +kernel - -lemma sg394 : RowSquare [5,2,1] [3,3,1,1] := by - apply rowSquare_compact (n := 8) (cs := [3,2,1,1,1]) (ts := [4,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB394 sgT394 sgFlag394 - change solveCompact 8 (.full [4,2,2]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) - (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB394 sgT394) sgFlag394 ≠ 0 - rw [sgCert394] - norm_num - -def sgB480 : Equiv.Perm (Fin 9) := Equiv.swap 3 8 * (Equiv.swap 2 0 * (Equiv.swap 3 5 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))) -def sgT480 : Equiv.Perm (Fin 9) := Equiv.swap 1 5 * (Equiv.swap 5 2 * (Equiv.swap 1 7 * (Equiv.swap 3 6 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 8)))))) -def sgFlag480 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(5,0,0),(2,0,1),(1,1,0),(4,1,1),(3,1,2),(0,2,1)} -lemma sgCert480 : solveCompact 9 (.full [6,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [6,3] (Equiv.refl (Fin 9)) sgB480 sgT480) sgFlag480 = 45 := by - decide +kernel - -lemma sg480 : RowSquare [3,2,2,2] [2,2,2,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [6,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB480 sgT480 sgFlag480 - change solveCompact 9 (.full [6,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [6,3] (Equiv.refl (Fin 9)) sgB480 sgT480) sgFlag480 ≠ 0 - rw [sgCert480] - norm_num - -def sgB481 : Equiv.Perm (Fin 9) := Equiv.swap 0 1 * (Equiv.swap 1 7 * (Equiv.swap 1 4 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 6))))) -def sgT481 : Equiv.Perm (Fin 9) := Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 2 6 * (Equiv.swap 3 0 * (Equiv.swap 2 4 * (Equiv.swap 0 5))))) -def sgFlag481 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(0,0,1),(1,1,0),(3,1,1),(1,1,2),(4,2,0)} -lemma sgCert481 : solveCompact 9 (.full [5,4]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [5,4] (Equiv.refl (Fin 9)) sgB481 sgT481) sgFlag481 = -12 := by - decide +kernel - -lemma sg481 : RowSquare [3,2,2,2] [2,2,2,2,1] := by - apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [5,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB481 sgT481 sgFlag481 - change solveCompact 9 (.full [5,4]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [5,4] (Equiv.refl (Fin 9)) sgB481 sgT481) sgFlag481 ≠ 0 - rw [sgCert481] - norm_num - -def sgB482 : Equiv.Perm (Fin 9) := Equiv.swap 4 2 * (Equiv.swap 4 7 * (Equiv.swap 2 8 * (Equiv.swap 4 6 * (Equiv.swap 2 5 * (Equiv.swap 0 3 * (Equiv.swap 0 1)))))) -def sgT482 : Equiv.Perm (Fin 9) := Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 2 6 * (Equiv.swap 1 4 * (Equiv.swap 0 8)))) -def sgFlag482 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,1),(2,0,2),(0,1,0),(4,1,0),(1,1,1),(2,1,1),(1,2,0)} -lemma sgCert482 : solveCompact 9 (.full [5,3,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [5,3,1] (Equiv.refl (Fin 9)) sgB482 sgT482) sgFlag482 = 4 := by - decide +kernel - -lemma sg482 : RowSquare [3,2,2,2] [3,2,2,1,1] := by - apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [5,3,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB482 sgT482 sgFlag482 - change solveCompact 9 (.full [5,3,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [5,3,1] (Equiv.refl (Fin 9)) sgB482 sgT482) sgFlag482 ≠ 0 - rw [sgCert482] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB483 : Equiv.Perm (Fin 9) := Equiv.swap 7 8 * (Equiv.swap 3 5 * (Equiv.swap 3 1 * (Equiv.swap 1 4 * (Equiv.swap 0 2)))) -def sgT483 : Equiv.Perm (Fin 9) := Equiv.swap 6 0 * (Equiv.swap 6 3 * (Equiv.swap 3 1 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 7 * (Equiv.swap 0 8)))))) -def sgFlag483 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(2,0,1),(1,0,2),(1,1,0),(0,1,1),(3,1,1),(4,2,0)} -lemma sgCert483 : solveCompact 9 (.full [5,2,2]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [5,2,2] (Equiv.refl (Fin 9)) sgB483 sgT483) sgFlag483 = -2 := by - decide +kernel - -lemma sg483 : RowSquare [3,2,2,2] [3,3,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [5,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB483 sgT483 sgFlag483 - change solveCompact 9 (.full [5,2,2]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [5,2,2] (Equiv.refl (Fin 9)) sgB483 sgT483) sgFlag483 ≠ 0 - rw [sgCert483] - norm_num - -def sgB484 : Equiv.Perm (Fin 9) := Equiv.swap 6 5 * (Equiv.swap 6 2 * (Equiv.swap 5 8 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 0 7 * (Equiv.swap 0 1)))))) -def sgT484 : Equiv.Perm (Fin 9) := Equiv.swap 1 0 * (Equiv.swap 1 4 * (Equiv.swap 0 8 * (Equiv.swap 1 3 * (Equiv.swap 0 2)))) -def sgFlag484 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,1,0),(1,1,1),(0,1,2),(2,2,1)} -lemma sgCert484 : solveCompact 9 (.full [3,3,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [3,3,3] (Equiv.refl (Fin 9)) sgB484 sgT484) sgFlag484 = 1 := by - decide +kernel - -lemma sg484 : RowSquare [3,2,2,2] [3,3,3] := by - apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [3,3,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB484 sgT484 sgFlag484 - change solveCompact 9 (.full [3,3,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [3,3,3] (Equiv.refl (Fin 9)) sgB484 sgT484) sgFlag484 ≠ 0 - rw [sgCert484] - norm_num - -def sgB487 : Equiv.Perm (Fin 9) := Equiv.swap 2 5 * (Equiv.swap 5 8 * (Equiv.swap 1 4 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 6))))) -def sgT487 : Equiv.Perm (Fin 9) := Equiv.swap 2 5 * (Equiv.swap 2 1 * (Equiv.swap 5 8 * (Equiv.swap 2 6 * (Equiv.swap 2 0 * (Equiv.swap 1 7 * (Equiv.swap 0 3)))))) -def sgFlag487 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(0,0,1),(1,1,0),(1,1,1),(2,1,2),(0,2,0)} -lemma sgCert487 : solveCompact 9 (.full [3,3,2,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [3,3,2,1] (Equiv.refl (Fin 9)) sgB487 sgT487) sgFlag487 = 2 := by - decide +kernel - -lemma sg487 : RowSquare [3,2,2,2] [4,3,2] := by - apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [3,3,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB487 sgT487 sgFlag487 - change solveCompact 9 (.full [3,3,2,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [3,3,2,1] (Equiv.refl (Fin 9)) sgB487 sgT487) sgFlag487 ≠ 0 - rw [sgCert487] - norm_num - -def sgB489 : Equiv.Perm (Fin 9) := Equiv.swap 7 0 * (Equiv.swap 0 4 * (Equiv.swap 0 6 * (Equiv.swap 4 3 * (Equiv.swap 3 2 * (Equiv.swap 2 8 * (Equiv.swap 0 5)))))) -def sgT489 : Equiv.Perm (Fin 9) := Equiv.swap 1 4 * (Equiv.swap 4 8 * (Equiv.swap 4 5 * (Equiv.swap 3 6 * (Equiv.swap 1 7)))) -def sgFlag489 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(3,0,1),(0,0,2),(5,1,0),(1,1,1),(2,2,0)} -lemma sgCert489 : solveCompact 9 (.full [6,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB489 sgT489) sgFlag489 = 9 := by - decide +kernel - -lemma sg489 : RowSquare [3,3,1,1,1] [2,2,2,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [6,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB489 sgT489 sgFlag489 - change solveCompact 9 (.full [6,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB489 sgT489) sgFlag489 ≠ 0 - rw [sgCert489] - norm_num - -def sgB490 : Equiv.Perm (Fin 9) := Equiv.swap 2 8 * (Equiv.swap 0 1 * (Equiv.swap 3 5 * (Equiv.swap 2 7 * (Equiv.swap 1 6 * (Equiv.swap 0 4))))) -def sgT490 : Equiv.Perm (Fin 9) := Equiv.swap 7 1 * (Equiv.swap 4 3 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 1 8 * (Equiv.swap 0 6))))) -def sgFlag490 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(1,0,1),(2,0,2),(3,1,0),(3,1,1),(0,2,0)} -lemma sgCert490 : solveCompact 9 (.full [5,4]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB490 sgT490) sgFlag490 = 2 := by - decide +kernel - -lemma sg490 : RowSquare [3,3,1,1,1] [2,2,2,2,1] := by - apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [5,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB490 sgT490 sgFlag490 - change solveCompact 9 (.full [5,4]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB490 sgT490) sgFlag490 ≠ 0 - rw [sgCert490] - norm_num - -def sgB495 : Equiv.Perm (Fin 9) := Equiv.swap 2 0 * (Equiv.swap 3 5 * (Equiv.swap 2 7 * (Equiv.swap 1 4 * (Equiv.swap 0 8)))) -def sgT495 : Equiv.Perm (Fin 9) := Equiv.swap 6 8 * (Equiv.swap 6 3 * (Equiv.swap 3 4 * (Equiv.swap 4 7 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 0 5)))))) -def sgFlag495 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(2,0,2),(0,1,1),(1,1,1),(0,2,0)} -lemma sgCert495 : solveCompact 9 (.full [4,3,2]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [4,3,2] (Equiv.refl (Fin 9)) sgB495 sgT495) sgFlag495 = 1 := by - decide +kernel - -lemma sg495 : RowSquare [3,3,1,1,1] [3,3,2,1] := by - apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [4,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB495 sgT495 sgFlag495 - change solveCompact 9 (.full [4,3,2]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [4,3,2] (Equiv.refl (Fin 9)) sgB495 sgT495) sgFlag495 ≠ 0 - rw [sgCert495] - norm_num - -def sgB496 : Equiv.Perm (Fin 9) := Equiv.swap 2 5 * (Equiv.swap 5 8 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))) -def sgT496 : Equiv.Perm (Fin 9) := Equiv.swap 5 7 * (Equiv.swap 3 1 * (Equiv.swap 2 4 * (Equiv.swap 1 8))) -def sgFlag496 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,0),(0,0,2),(2,1,1),(1,2,0)} -lemma sgCert496 : solveCompact 9 (.full [3,3,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [3,3,3] (Equiv.refl (Fin 9)) sgB496 sgT496) sgFlag496 = -1 := by - decide +kernel - -lemma sg496 : RowSquare [3,3,1,1,1] [3,3,3] := by - apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [3,3,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB496 sgT496 sgFlag496 - change solveCompact 9 (.full [3,3,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [3,3,3] (Equiv.refl (Fin 9)) sgB496 sgT496) sgFlag496 ≠ 0 - rw [sgCert496] - norm_num - -def sgB511 : Equiv.Perm (Fin 9) := Equiv.swap 3 6 * (Equiv.swap 6 2 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 2 8 * (Equiv.swap 1 5))))) -def sgT511 : Equiv.Perm (Fin 9) := Equiv.swap 5 4 * (Equiv.swap 4 0 * (Equiv.swap 0 2 * (Equiv.swap 2 7 * (Equiv.swap 0 3)))) -def sgFlag511 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(2,0,1),(6,0,2),(5,1,0),(0,1,1),(1,1,2),(0,2,0),(4,2,1)} -lemma sgCert511 : solveCompact 9 (.full [7,2]) (.full [3,3,2,1]) (.full [3,3,2,1]) - (certificateEdges [3,3,2,1] [3,3,2,1] [7,2] (Equiv.refl (Fin 9)) sgB511 sgT511) sgFlag511 = 120 := by - decide +kernel - -lemma sg511 : RowSquare [3,3,2,1] [2,2,1,1,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [3,3,2,1]) (ts := [7,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB511 sgT511 sgFlag511 - change solveCompact 9 (.full [7,2]) (.full [3,3,2,1]) (.full [3,3,2,1]) - (certificateEdges [3,3,2,1] [3,3,2,1] [7,2] (Equiv.refl (Fin 9)) sgB511 sgT511) sgFlag511 ≠ 0 - rw [sgCert511] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB513 : Equiv.Perm (Fin 9) := Equiv.swap 1 8 * (Equiv.swap 1 6 * (Equiv.swap 4 7 * (Equiv.swap 1 5 * (Equiv.swap 1 0 * (Equiv.swap 0 2))))) -def sgT513 : Equiv.Perm (Fin 9) := Equiv.swap 3 0 * (Equiv.swap 0 2 * (Equiv.swap 3 7 * (Equiv.swap 3 1 * (Equiv.swap 2 8 * (Equiv.swap 1 4 * (Equiv.swap 0 5)))))) -def sgFlag513 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,1),(0,0,2),(4,1,0),(0,1,1),(2,2,0),(1,2,2)} -lemma sgCert513 : solveCompact 9 (.full [5,2,2]) (.full [3,3,2,1]) (.full [3,3,2,1]) - (certificateEdges [3,3,2,1] [3,3,2,1] [5,2,2] (Equiv.refl (Fin 9)) sgB513 sgT513) sgFlag513 = 4 := by - decide +kernel - -lemma sg513 : RowSquare [3,3,2,1] [3,3,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [3,3,2,1]) (ts := [5,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB513 sgT513 sgFlag513 - change solveCompact 9 (.full [5,2,2]) (.full [3,3,2,1]) (.full [3,3,2,1]) - (certificateEdges [3,3,2,1] [3,3,2,1] [5,2,2] (Equiv.refl (Fin 9)) sgB513 sgT513) sgFlag513 ≠ 0 - rw [sgCert513] - norm_num - -def sgB535 : Equiv.Perm (Fin 9) := Equiv.swap 6 5 * (Equiv.swap 5 1 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 1 8 * (Equiv.swap 0 2))))) -def sgT535 : Equiv.Perm (Fin 9) := Equiv.swap 3 8 * (Equiv.swap 3 1 * (Equiv.swap 2 7 * (Equiv.swap 1 4 * (Equiv.swap 0 6)))) -def sgFlag535 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(0,0,1),(6,0,2),(2,0,3),(4,1,0),(5,1,1),(0,2,0),(1,3,0)} -lemma sgCert535 : solveCompact 9 (.full [7,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [7,2] (Equiv.refl (Fin 9)) sgB535 sgT535) sgFlag535 = 4 := by - decide +kernel - -lemma sg535 : RowSquare [4,2,1,1,1] [2,2,1,1,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [7,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB535 sgT535 sgFlag535 - change solveCompact 9 (.full [7,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [7,2] (Equiv.refl (Fin 9)) sgB535 sgT535) sgFlag535 ≠ 0 - rw [sgCert535] - norm_num - -def sgB536 : Equiv.Perm (Fin 9) := Equiv.swap 6 3 * (Equiv.swap 0 8 * (Equiv.swap 0 5 * (Equiv.swap 3 1 * (Equiv.swap 0 4 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))) -def sgT536 : Equiv.Perm (Fin 9) := Equiv.swap 1 4 * (Equiv.swap 4 0 * (Equiv.swap 0 8 * (Equiv.swap 0 3 * (Equiv.swap 1 6 * (Equiv.swap 0 2))))) -def sgFlag536 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,2),(4,0,3),(0,1,0),(5,1,0),(3,2,0),(2,3,1)} -lemma sgCert536 : solveCompact 9 (.full [6,3]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB536 sgT536) sgFlag536 = 10 := by - decide +kernel - -lemma sg536 : RowSquare [4,2,1,1,1] [2,2,2,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [6,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB536 sgT536 sgFlag536 - change solveCompact 9 (.full [6,3]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB536 sgT536) sgFlag536 ≠ 0 - rw [sgCert536] - norm_num - -def sgB537 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 2 7 * (Equiv.swap 2 0 * (Equiv.swap 2 5 * (Equiv.swap 2 4 * (Equiv.swap 1 8 * (Equiv.swap 0 6)))))) -def sgT537 : Equiv.Perm (Fin 9) := Equiv.swap 6 7 * (Equiv.swap 1 8 * (Equiv.swap 0 2)) -def sgFlag537 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(1,0,1),(4,0,1),(1,0,2),(0,1,0),(3,1,0),(0,2,0),(3,3,3)} -lemma sgCert537 : solveCompact 9 (.full [5,4]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB537 sgT537) sgFlag537 = 3 := by - decide +kernel - -lemma sg537 : RowSquare [4,2,1,1,1] [2,2,2,2,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [5,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB537 sgT537 sgFlag537 - change solveCompact 9 (.full [5,4]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB537 sgT537) sgFlag537 ≠ 0 - rw [sgCert537] - norm_num - -def sgB541 : Equiv.Perm (Fin 9) := Equiv.swap 2 5 * (Equiv.swap 2 7 * (Equiv.swap 5 0 * (Equiv.swap 2 6 * (Equiv.swap 2 4 * (Equiv.swap 1 3 * (Equiv.swap 0 8)))))) -def sgT541 : Equiv.Perm (Fin 9) := Equiv.swap 3 8 * (Equiv.swap 3 0 * (Equiv.swap 3 1 * (Equiv.swap 3 4 * (Equiv.swap 1 5 * (Equiv.swap 0 7))))) -def sgFlag541 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(3,0,2),(0,1,0),(0,1,3),(2,2,0),(4,3,1)} -lemma sgCert541 : solveCompact 9 (.full [5,2,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,2,2] (Equiv.refl (Fin 9)) sgB541 sgT541) sgFlag541 = 1 := by - decide +kernel - -lemma sg541 : RowSquare [4,2,1,1,1] [3,3,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [5,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB541 sgT541 sgFlag541 - change solveCompact 9 (.full [5,2,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,2,2] (Equiv.refl (Fin 9)) sgB541 sgT541) sgFlag541 ≠ 0 - rw [sgCert541] - norm_num - -def sgB548 : Equiv.Perm (Fin 9) := Equiv.swap 3 2 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 8 * (Equiv.swap 0 6))))) -def sgT548 : Equiv.Perm (Fin 9) := Equiv.swap 1 5 * (Equiv.swap 5 8 * (Equiv.swap 5 6 * (Equiv.swap 1 2 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 7)))))) -def sgFlag548 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(7,0,0),(2,0,1),(1,0,3),(4,1,0),(6,1,1),(5,1,2),(0,2,1),(3,3,0)} -lemma sgCert548 : solveCompact 9 (.full [8,1]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [8,1] (Equiv.refl (Fin 9)) sgB548 sgT548) sgFlag548 = 56 := by - decide +kernel - -lemma sg548 : RowSquare [4,2,2,1] [2,1,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [8,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB548 sgT548 sgFlag548 - change solveCompact 9 (.full [8,1]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [8,1] (Equiv.refl (Fin 9)) sgB548 sgT548) sgFlag548 ≠ 0 - rw [sgCert548] - norm_num - -def sgB549 : Equiv.Perm (Fin 9) := Equiv.swap 0 8 * (Equiv.swap 3 2 * (Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 6 * (Equiv.swap 0 7)))))) -def sgT549 : Equiv.Perm (Fin 9) := Equiv.swap 4 1 * (Equiv.swap 2 0 * (Equiv.swap 1 5 * (Equiv.swap 0 8))) -def sgFlag549 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(1,0,1),(6,0,3),(0,1,0),(5,1,0),(4,1,2),(0,2,1),(3,3,0)} -lemma sgCert549 : solveCompact 9 (.full [7,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [7,2] (Equiv.refl (Fin 9)) sgB549 sgT549) sgFlag549 = -8 := by - decide +kernel - -lemma sg549 : RowSquare [4,2,2,1] [2,2,1,1,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [7,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB549 sgT549 sgFlag549 - change solveCompact 9 (.full [7,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [7,2] (Equiv.refl (Fin 9)) sgB549 sgT549) sgFlag549 ≠ 0 - rw [sgCert549] - norm_num - -def sgB550 : Equiv.Perm (Fin 9) := Equiv.swap 1 4 * (Equiv.swap 4 8 * (Equiv.swap 4 6 * (Equiv.swap 4 2 * (Equiv.swap 1 0 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))))) -def sgT550 : Equiv.Perm (Fin 9) := Equiv.swap 5 6 * (Equiv.swap 3 7 * (Equiv.swap 0 2)) -def sgFlag550 : Finset (ℕ × ℕ × ℕ) := {(5,0,0),(2,0,1),(4,0,2),(0,1,0),(3,1,0),(1,1,3),(0,2,1),(1,3,0)} -lemma sgCert550 : solveCompact 9 (.full [6,3]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [6,3] (Equiv.refl (Fin 9)) sgB550 sgT550) sgFlag550 = 12 := by - decide +kernel - -lemma sg550 : RowSquare [4,2,2,1] [2,2,2,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [6,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB550 sgT550 sgFlag550 - change solveCompact 9 (.full [6,3]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [6,3] (Equiv.refl (Fin 9)) sgB550 sgT550) sgFlag550 ≠ 0 - rw [sgCert550] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Semigroup Leaves 2. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB314 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 2 * (Equiv.swap 2 6 * (Equiv.swap 2 0 * (Equiv.swap 1 5 * (Equiv.swap 0 3))))) +def sgT314 : Equiv.Perm (Fin 8) := Equiv.swap 1 3 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 5))))) +def sgFlag314 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,1),(2,0,2),(0,0,3),(2,1,0),(0,2,0),(4,3,0)} +lemma sgCert314 : solveCompact 8 (.full [5,3]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [5,3] (Equiv.refl (Fin 8)) sgB314 sgT314) sgFlag314 = 20 := by + decide +kernel + +lemma sg314 : RowSquare [4,1,1,1,1] [2,2,2,1,1] := by + apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [5,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB314 sgT314 sgFlag314 + change solveCompact 8 (.full [5,3]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [5,3] (Equiv.refl (Fin 8)) sgB314 sgT314) sgFlag314 ≠ 0 + rw [sgCert314] + norm_num + +def sgB315 : Equiv.Perm (Fin 8) := Equiv.swap 5 2 * (Equiv.swap 5 6 * (Equiv.swap 2 1 * (Equiv.swap 2 4 * (Equiv.swap 1 7 * (Equiv.swap 0 3))))) +def sgT315 : Equiv.Perm (Fin 8) := Equiv.swap 3 7 * (Equiv.swap 3 5 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 0 6)))) +def sgFlag315 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(1,0,1),(0,0,2),(2,0,3),(1,1,0),(0,2,0),(2,3,0)} +lemma sgCert315 : solveCompact 8 (.full [4,4]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB315 sgT315) sgFlag315 = 24 := by + decide +kernel + +lemma sg315 : RowSquare [4,1,1,1,1] [2,2,2,2] := by + apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [4,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB315 sgT315 sgFlag315 + change solveCompact 8 (.full [4,4]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB315 sgT315) sgFlag315 ≠ 0 + rw [sgCert315] + norm_num + +def sgB319 : Equiv.Perm (Fin 8) := Equiv.swap 1 4 * (Equiv.swap 1 0 * (Equiv.swap 4 3 * (Equiv.swap 3 7 * (Equiv.swap 1 5 * (Equiv.swap 1 2 * (Equiv.swap 0 6)))))) +def sgT319 : Equiv.Perm (Fin 8) := Equiv.swap 0 2 * (Equiv.swap 2 7 * (Equiv.swap 2 5 * (Equiv.swap 2 4 * (Equiv.swap 0 6)))) +def sgFlag319 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,0),(0,0,1),(1,0,3),(1,1,2),(0,2,0),(3,3,0)} +lemma sgCert319 : solveCompact 8 (.full [4,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB319 sgT319) sgFlag319 = -2 := by + decide +kernel + +lemma sg319 : RowSquare [4,1,1,1,1] [3,3,1,1] := by + apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [4,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB319 sgT319 sgFlag319 + change solveCompact 8 (.full [4,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB319 sgT319) sgFlag319 ≠ 0 + rw [sgCert319] + norm_num + +def sgB320 : Equiv.Perm (Fin 8) := Equiv.swap 5 0 * (Equiv.swap 3 7 * (Equiv.swap 2 4 * (Equiv.swap 0 6))) +def sgT320 : Equiv.Perm (Fin 8) := Equiv.swap 3 4 * (Equiv.swap 4 7 * (Equiv.swap 4 5 * (Equiv.swap 3 6 * (Equiv.swap 0 1)))) +def sgFlag320 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,2),(0,0,3),(0,1,1),(2,2,0),(0,3,0)} +lemma sgCert320 : solveCompact 8 (.full [3,3,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB320 sgT320) sgFlag320 = 4 := by + decide +kernel + +lemma sg320 : RowSquare [4,1,1,1,1] [3,3,2] := by + apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [3,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB320 sgT320 sgFlag320 + change solveCompact 8 (.full [3,3,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB320 sgT320) sgFlag320 ≠ 0 + rw [sgCert320] + norm_num + +def sgB324 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 2 * (Equiv.swap 2 1 * (Equiv.swap 1 5 * (Equiv.swap 0 6)))) +def sgT324 : Equiv.Perm (Fin 8) := Equiv.swap 2 1 * (Equiv.swap 2 6 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 1 7 * (Equiv.swap 0 5))))) +def sgFlag324 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,2),(1,1,0),(0,2,1),(1,3,3)} +lemma sgCert324 : solveCompact 8 (.full [2,2,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [2,2,2,2] (Equiv.refl (Fin 8)) sgB324 sgT324) sgFlag324 = 4 := by + decide +kernel + +lemma sg324 : RowSquare [4,1,1,1,1] [4,4] := by + apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [2,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB324 sgT324 sgFlag324 + change solveCompact 8 (.full [2,2,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [2,2,2,2] (Equiv.refl (Fin 8)) sgB324 sgT324) sgFlag324 ≠ 0 + rw [sgCert324] + norm_num + +def sgB348 : Equiv.Perm (Fin 8) := Equiv.swap 5 3 * (Equiv.swap 5 6 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 0 * (Equiv.swap 0 7))))) +def sgT348 : Equiv.Perm (Fin 8) := Equiv.swap 2 7 * (Equiv.swap 0 1 * (Equiv.swap 0 4 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 0 3))))) +def sgFlag348 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(4,0,1),(2,0,2),(5,1,1),(1,1,2),(0,2,0)} +lemma sgCert348 : solveCompact 8 (.full [6,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [6,2] (Equiv.refl (Fin 8)) sgB348 sgT348) sgFlag348 = 6 := by + decide +kernel + +lemma sg348 : RowSquare [4,2,2] [2,2,1,1,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [6,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB348 sgT348 sgFlag348 + change solveCompact 8 (.full [6,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [6,2] (Equiv.refl (Fin 8)) sgB348 sgT348) sgFlag348 ≠ 0 + rw [sgCert348] + norm_num + +def sgB349 : Equiv.Perm (Fin 8) := Equiv.swap 2 6 * (Equiv.swap 2 4 * (Equiv.swap 2 3 * (Equiv.swap 1 0 * (Equiv.swap 0 5)))) +def sgT349 : Equiv.Perm (Fin 8) := Equiv.swap 5 3 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 0 * (Equiv.swap 1 7 * (Equiv.swap 0 6))))) +def sgFlag349 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,1),(0,0,2),(1,0,2),(2,1,0),(0,2,0),(3,2,1)} +lemma sgCert349 : solveCompact 8 (.full [5,3]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [5,3] (Equiv.refl (Fin 8)) sgB349 sgT349) sgFlag349 = -6 := by + decide +kernel + +lemma sg349 : RowSquare [4,2,2] [2,2,2,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [5,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB349 sgT349 sgFlag349 + change solveCompact 8 (.full [5,3]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [5,3] (Equiv.refl (Fin 8)) sgB349 sgT349) sgFlag349 ≠ 0 + rw [sgCert349] + norm_num + +def sgB350 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 6 * (Equiv.swap 2 3 * (Equiv.swap 0 1))) +def sgT350 : Equiv.Perm (Fin 8) := Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 4 7 * (Equiv.swap 1 5 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 6)))))) +def sgFlag350 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(1,0,2),(3,1,0),(0,2,0),(0,2,2)} +lemma sgCert350 : solveCompact 8 (.full [4,4]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [4,4] (Equiv.refl (Fin 8)) sgB350 sgT350) sgFlag350 = -5 := by + decide +kernel + +lemma sg350 : RowSquare [4,2,2] [2,2,2,2] := by + apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [4,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB350 sgT350 sgFlag350 + change solveCompact 8 (.full [4,4]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [4,4] (Equiv.refl (Fin 8)) sgB350 sgT350) sgFlag350 ≠ 0 + rw [sgCert350] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB352 : Equiv.Perm (Fin 8) := Equiv.swap 4 0 * (Equiv.swap 3 1 * (Equiv.swap 1 5 * (Equiv.swap 1 2 * (Equiv.swap 0 6)))) +def sgT352 : Equiv.Perm (Fin 8) := Equiv.swap 0 7 * (Equiv.swap 0 1 * (Equiv.swap 3 5 * (Equiv.swap 1 6 * (Equiv.swap 0 4)))) +def sgFlag352 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(1,1,0),(0,1,2),(3,2,0),(2,2,2)} +lemma sgCert352 : solveCompact 8 (.full [4,2,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB352 sgT352) sgFlag352 = 4 := by + decide +kernel + +lemma sg352 : RowSquare [4,2,2] [3,3,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [4,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB352 sgT352 sgFlag352 + change solveCompact 8 (.full [4,2,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB352 sgT352) sgFlag352 ≠ 0 + rw [sgCert352] + norm_num + +def sgB353 : Equiv.Perm (Fin 8) := Equiv.swap 3 6 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 5)))) +def sgT353 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 1 6 * (Equiv.swap 2 5 * (Equiv.swap 1 3))) +def sgFlag353 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,2),(1,1,0),(0,1,1),(2,2,0),(2,2,1)} +lemma sgCert353 : solveCompact 8 (.full [3,3,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB353 sgT353) sgFlag353 = 1 := by + decide +kernel + +lemma sg353 : RowSquare [4,2,2] [3,3,2] := by + apply rowSquare_compact (n := 8) (cs := [3,3,1,1]) (ts := [3,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB353 sgT353 sgFlag353 + change solveCompact 8 (.full [3,3,2]) (.full [3,3,1,1]) (.full [3,3,1,1]) + (certificateEdges [3,3,1,1] [3,3,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB353 sgT353) sgFlag353 ≠ 0 + rw [sgCert353] + norm_num + +def sgB356 : Equiv.Perm (Fin 8) := Equiv.swap 4 2 * (Equiv.swap 4 5 * (Equiv.swap 0 1 * (Equiv.swap 2 7 * (Equiv.swap 1 6 * (Equiv.swap 0 3))))) +def sgT356 : Equiv.Perm (Fin 8) := Equiv.swap 1 2 * (Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 2 4 * (Equiv.swap 1 5)))) +def sgFlag356 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(2,0,2),(0,1,0),(3,1,0),(5,1,1),(4,2,0)} +lemma sgCert356 : solveCompact 8 (.full [6,2]) (.full [3,2,2,1]) (.full [3,2,2,1]) + (certificateEdges [3,2,2,1] [3,2,2,1] [6,2] (Equiv.refl (Fin 8)) sgB356 sgT356) sgFlag356 = 12 := by + decide +kernel + +lemma sg356 : RowSquare [4,3,1] [2,2,1,1,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,2,2,1]) (ts := [6,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB356 sgT356 sgFlag356 + change solveCompact 8 (.full [6,2]) (.full [3,2,2,1]) (.full [3,2,2,1]) + (certificateEdges [3,2,2,1] [3,2,2,1] [6,2] (Equiv.refl (Fin 8)) sgB356 sgT356) sgFlag356 ≠ 0 + rw [sgCert356] + norm_num + +def sgB357 : Equiv.Perm (Fin 8) := Equiv.swap 1 3 * (Equiv.swap 3 7 * (Equiv.swap 3 2 * (Equiv.swap 2 5 * (Equiv.swap 1 0 * (Equiv.swap 0 6))))) +def sgT357 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 3 * (Equiv.swap 4 0 * (Equiv.swap 3 6 * (Equiv.swap 0 5 * (Equiv.swap 0 2 * (Equiv.swap 0 1)))))) +def sgFlag357 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(1,0,1),(4,0,1),(1,0,2),(2,1,0),(0,1,1),(0,2,0)} +lemma sgCert357 : solveCompact 8 (.full [5,3]) (.full [3,2,2,1]) (.full [3,2,2,1]) + (certificateEdges [3,2,2,1] [3,2,2,1] [5,3] (Equiv.refl (Fin 8)) sgB357 sgT357) sgFlag357 = -4 := by + decide +kernel + +lemma sg357 : RowSquare [4,3,1] [2,2,2,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,2,2,1]) (ts := [5,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB357 sgT357 sgFlag357 + change solveCompact 8 (.full [5,3]) (.full [3,2,2,1]) (.full [3,2,2,1]) + (certificateEdges [3,2,2,1] [3,2,2,1] [5,3] (Equiv.refl (Fin 8)) sgB357 sgT357) sgFlag357 ≠ 0 + rw [sgCert357] + norm_num + +def sgB358 : Equiv.Perm (Fin 8) := Equiv.swap 2 4 * (Equiv.swap 4 6 * (Equiv.swap 2 0 * (Equiv.swap 1 7 * (Equiv.swap 0 5)))) +def sgT358 : Equiv.Perm (Fin 8) := Equiv.swap 6 7 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 5))) +def sgFlag358 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(3,1,0),(0,1,1),(3,1,2),(0,2,0)} +lemma sgCert358 : solveCompact 8 (.full [4,4]) (.full [3,2,2,1]) (.full [3,2,2,1]) + (certificateEdges [3,2,2,1] [3,2,2,1] [4,4] (Equiv.refl (Fin 8)) sgB358 sgT358) sgFlag358 = -2 := by + decide +kernel + +lemma sg358 : RowSquare [4,3,1] [2,2,2,2] := by + apply rowSquare_compact (n := 8) (cs := [3,2,2,1]) (ts := [4,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB358 sgT358 sgFlag358 + change solveCompact 8 (.full [4,4]) (.full [3,2,2,1]) (.full [3,2,2,1]) + (certificateEdges [3,2,2,1] [3,2,2,1] [4,4] (Equiv.refl (Fin 8)) sgB358 sgT358) sgFlag358 ≠ 0 + rw [sgCert358] + norm_num + +def sgB371 : Equiv.Perm (Fin 8) := Equiv.swap 1 2 * (Equiv.swap 2 7 * (Equiv.swap 2 5 * (Equiv.swap 2 4 * (Equiv.swap 1 6 * (Equiv.swap 0 3))))) +def sgT371 : Equiv.Perm (Fin 8) := Equiv.swap 3 1 * (Equiv.swap 4 7 * (Equiv.swap 3 5 * (Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 6))))) +def sgFlag371 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,1),(3,0,2),(0,0,3),(2,1,0),(0,2,0),(5,3,0)} +lemma sgCert371 : solveCompact 8 (.full [6,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [6,2] (Equiv.refl (Fin 8)) sgB371 sgT371) sgFlag371 = 24 := by + decide +kernel + +lemma sg371 : RowSquare [5,1,1,1] [2,2,1,1,1,1] := by + apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [6,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB371 sgT371 sgFlag371 + change solveCompact 8 (.full [6,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [6,2] (Equiv.refl (Fin 8)) sgB371 sgT371) sgFlag371 ≠ 0 + rw [sgCert371] + norm_num + +def sgB372 : Equiv.Perm (Fin 8) := Equiv.swap 5 6 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 0 4 * (Equiv.swap 0 1)))) +def sgT372 : Equiv.Perm (Fin 8) := Equiv.swap 1 3 * (Equiv.swap 3 7 * (Equiv.swap 2 5 * (Equiv.swap 1 4))) +def sgFlag372 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(0,0,1),(3,0,2),(1,0,3),(4,1,0),(0,2,0),(2,3,0)} +lemma sgCert372 : solveCompact 8 (.full [5,3]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [5,3] (Equiv.refl (Fin 8)) sgB372 sgT372) sgFlag372 = 20 := by + decide +kernel + +lemma sg372 : RowSquare [5,1,1,1] [2,2,2,1,1] := by + apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [5,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB372 sgT372 sgFlag372 + change solveCompact 8 (.full [5,3]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [5,3] (Equiv.refl (Fin 8)) sgB372 sgT372) sgFlag372 ≠ 0 + rw [sgCert372] + norm_num + +def sgB373 : Equiv.Perm (Fin 8) := Equiv.swap 6 2 * (Equiv.swap 2 7 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 3)))) +def sgT373 : Equiv.Perm (Fin 8) := Equiv.swap 0 6 * (Equiv.swap 0 5 * (Equiv.swap 3 7 * (Equiv.swap 0 4 * (Equiv.swap 0 2)))) +def sgFlag373 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(3,0,0),(1,0,1),(0,0,2),(2,0,3),(1,1,0),(0,2,0),(3,3,0)} +lemma sgCert373 : solveCompact 8 (.full [4,4]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB373 sgT373) sgFlag373 = 24 := by + decide +kernel + +lemma sg373 : RowSquare [5,1,1,1] [2,2,2,2] := by + apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [4,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB373 sgT373 sgFlag373 + change solveCompact 8 (.full [4,4]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB373 sgT373) sgFlag373 ≠ 0 + rw [sgCert373] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB377 : Equiv.Perm (Fin 8) := Equiv.swap 1 4 * (Equiv.swap 4 2 * (Equiv.swap 4 5 * (Equiv.swap 2 7 * (Equiv.swap 2 3 * (Equiv.swap 1 0 * (Equiv.swap 0 6)))))) +def sgT377 : Equiv.Perm (Fin 8) := Equiv.swap 2 7 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 6))) +def sgFlag377 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,1),(1,0,2),(0,1,0),(1,2,3),(3,3,0)} +lemma sgCert377 : solveCompact 8 (.full [4,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB377 sgT377) sgFlag377 = -4 := by + decide +kernel + +lemma sg377 : RowSquare [5,1,1,1] [3,3,1,1] := by + apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [4,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB377 sgT377 sgFlag377 + change solveCompact 8 (.full [4,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB377 sgT377) sgFlag377 ≠ 0 + rw [sgCert377] + norm_num + +def sgB378 : Equiv.Perm (Fin 8) := Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 0 4)))) +def sgT378 : Equiv.Perm (Fin 8) := Equiv.swap 2 7 * (Equiv.swap 2 0 * (Equiv.swap 3 1 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))) +def sgFlag378 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(2,0,2),(1,1,0),(2,2,0),(1,3,3)} +lemma sgCert378 : solveCompact 8 (.full [3,3,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB378 sgT378) sgFlag378 = 4 := by + decide +kernel + +lemma sg378 : RowSquare [5,1,1,1] [3,3,2] := by + apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [3,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB378 sgT378 sgFlag378 + change solveCompact 8 (.full [3,3,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [3,3,2] (Equiv.refl (Fin 8)) sgB378 sgT378) sgFlag378 ≠ 0 + rw [sgCert378] + norm_num + +def sgB383 : Equiv.Perm (Fin 8) := Equiv.swap 4 7 * (Equiv.swap 4 3 * (Equiv.swap 4 0 * (Equiv.swap 3 1 * (Equiv.swap 1 6 * (Equiv.swap 1 2 * (Equiv.swap 0 5)))))) +def sgT383 : Equiv.Perm (Fin 8) := Equiv.swap 0 7 * (Equiv.swap 0 2 * (Equiv.swap 2 1 * (Equiv.swap 2 3 * (Equiv.swap 1 5 * (Equiv.swap 0 4))))) +def sgFlag383 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,3),(1,1,2),(1,2,0),(1,3,1)} +lemma sgCert383 : solveCompact 8 (.full [2,2,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [2,2,2,2] (Equiv.refl (Fin 8)) sgB383 sgT383) sgFlag383 = 2 := by + decide +kernel + +lemma sg383 : RowSquare [5,1,1,1] [4,4] := by + apply rowSquare_compact (n := 8) (cs := [4,1,1,1,1]) (ts := [2,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB383 sgT383 sgFlag383 + change solveCompact 8 (.full [2,2,2,2]) (.full [4,1,1,1,1]) (.full [4,1,1,1,1]) + (certificateEdges [4,1,1,1,1] [4,1,1,1,1] [2,2,2,2] (Equiv.refl (Fin 8)) sgB383 sgT383) sgFlag383 ≠ 0 + rw [sgCert383] + norm_num + +def sgB390 : Equiv.Perm (Fin 8) := Equiv.swap 3 1 * (Equiv.swap 4 0 * (Equiv.swap 3 5 * (Equiv.swap 0 6 * (Equiv.swap 1 7 * (Equiv.swap 0 2))))) +def sgT390 : Equiv.Perm (Fin 8) := Equiv.swap 0 7 * (Equiv.swap 3 1 * (Equiv.swap 3 4 * (Equiv.swap 1 5 * (Equiv.swap 0 6)))) +def sgFlag390 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,1),(2,0,2),(1,1,0),(2,2,0)} +lemma sgCert390 : solveCompact 8 (.full [4,4]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) + (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB390 sgT390) sgFlag390 = 7 := by + decide +kernel + +lemma sg390 : RowSquare [5,2,1] [2,2,2,2] := by + apply rowSquare_compact (n := 8) (cs := [3,2,1,1,1]) (ts := [4,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB390 sgT390 sgFlag390 + change solveCompact 8 (.full [4,4]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) + (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,4] (Equiv.refl (Fin 8)) sgB390 sgT390) sgFlag390 ≠ 0 + rw [sgCert390] + norm_num + +def sgB394 : Equiv.Perm (Fin 8) := Equiv.swap 5 4 * (Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 0 6 * (Equiv.swap 0 2)))) +def sgT394 : Equiv.Perm (Fin 8) := Equiv.swap 6 5 * (Equiv.swap 5 2 * (Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 0 3)))) +def sgFlag394 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,1),(3,0,2),(0,1,0),(1,1,1),(1,2,0)} +lemma sgCert394 : solveCompact 8 (.full [4,2,2]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) + (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB394 sgT394) sgFlag394 = 4 := by + decide +kernel + +lemma sg394 : RowSquare [5,2,1] [3,3,1,1] := by + apply rowSquare_compact (n := 8) (cs := [3,2,1,1,1]) (ts := [4,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB394 sgT394 sgFlag394 + change solveCompact 8 (.full [4,2,2]) (.full [3,2,1,1,1]) (.full [3,2,1,1,1]) + (certificateEdges [3,2,1,1,1] [3,2,1,1,1] [4,2,2] (Equiv.refl (Fin 8)) sgB394 sgT394) sgFlag394 ≠ 0 + rw [sgCert394] + norm_num + +def sgB480 : Equiv.Perm (Fin 9) := Equiv.swap 3 8 * (Equiv.swap 2 0 * (Equiv.swap 3 5 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))) +def sgT480 : Equiv.Perm (Fin 9) := Equiv.swap 1 5 * (Equiv.swap 5 2 * (Equiv.swap 1 7 * (Equiv.swap 3 6 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 8)))))) +def sgFlag480 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(5,0,0),(2,0,1),(1,1,0),(4,1,1),(3,1,2),(0,2,1)} +lemma sgCert480 : solveCompact 9 (.full [6,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [6,3] (Equiv.refl (Fin 9)) sgB480 sgT480) sgFlag480 = 45 := by + decide +kernel + +lemma sg480 : RowSquare [3,2,2,2] [2,2,2,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [6,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB480 sgT480 sgFlag480 + change solveCompact 9 (.full [6,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [6,3] (Equiv.refl (Fin 9)) sgB480 sgT480) sgFlag480 ≠ 0 + rw [sgCert480] + norm_num + +def sgB481 : Equiv.Perm (Fin 9) := Equiv.swap 0 1 * (Equiv.swap 1 7 * (Equiv.swap 1 4 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 6))))) +def sgT481 : Equiv.Perm (Fin 9) := Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 2 6 * (Equiv.swap 3 0 * (Equiv.swap 2 4 * (Equiv.swap 0 5))))) +def sgFlag481 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(0,0,1),(1,1,0),(3,1,1),(1,1,2),(4,2,0)} +lemma sgCert481 : solveCompact 9 (.full [5,4]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [5,4] (Equiv.refl (Fin 9)) sgB481 sgT481) sgFlag481 = -12 := by + decide +kernel + +lemma sg481 : RowSquare [3,2,2,2] [2,2,2,2,1] := by + apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [5,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB481 sgT481 sgFlag481 + change solveCompact 9 (.full [5,4]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [5,4] (Equiv.refl (Fin 9)) sgB481 sgT481) sgFlag481 ≠ 0 + rw [sgCert481] + norm_num + +def sgB482 : Equiv.Perm (Fin 9) := Equiv.swap 4 2 * (Equiv.swap 4 7 * (Equiv.swap 2 8 * (Equiv.swap 4 6 * (Equiv.swap 2 5 * (Equiv.swap 0 3 * (Equiv.swap 0 1)))))) +def sgT482 : Equiv.Perm (Fin 9) := Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 2 6 * (Equiv.swap 1 4 * (Equiv.swap 0 8)))) +def sgFlag482 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,1),(2,0,2),(0,1,0),(4,1,0),(1,1,1),(2,1,1),(1,2,0)} +lemma sgCert482 : solveCompact 9 (.full [5,3,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [5,3,1] (Equiv.refl (Fin 9)) sgB482 sgT482) sgFlag482 = 4 := by + decide +kernel + +lemma sg482 : RowSquare [3,2,2,2] [3,2,2,1,1] := by + apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [5,3,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB482 sgT482 sgFlag482 + change solveCompact 9 (.full [5,3,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [5,3,1] (Equiv.refl (Fin 9)) sgB482 sgT482) sgFlag482 ≠ 0 + rw [sgCert482] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB483 : Equiv.Perm (Fin 9) := Equiv.swap 7 8 * (Equiv.swap 3 5 * (Equiv.swap 3 1 * (Equiv.swap 1 4 * (Equiv.swap 0 2)))) +def sgT483 : Equiv.Perm (Fin 9) := Equiv.swap 6 0 * (Equiv.swap 6 3 * (Equiv.swap 3 1 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 7 * (Equiv.swap 0 8)))))) +def sgFlag483 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(2,0,1),(1,0,2),(1,1,0),(0,1,1),(3,1,1),(4,2,0)} +lemma sgCert483 : solveCompact 9 (.full [5,2,2]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [5,2,2] (Equiv.refl (Fin 9)) sgB483 sgT483) sgFlag483 = -2 := by + decide +kernel + +lemma sg483 : RowSquare [3,2,2,2] [3,3,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [5,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB483 sgT483 sgFlag483 + change solveCompact 9 (.full [5,2,2]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [5,2,2] (Equiv.refl (Fin 9)) sgB483 sgT483) sgFlag483 ≠ 0 + rw [sgCert483] + norm_num + +def sgB484 : Equiv.Perm (Fin 9) := Equiv.swap 6 5 * (Equiv.swap 6 2 * (Equiv.swap 5 8 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 0 7 * (Equiv.swap 0 1)))))) +def sgT484 : Equiv.Perm (Fin 9) := Equiv.swap 1 0 * (Equiv.swap 1 4 * (Equiv.swap 0 8 * (Equiv.swap 1 3 * (Equiv.swap 0 2)))) +def sgFlag484 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,1,0),(1,1,1),(0,1,2),(2,2,1)} +lemma sgCert484 : solveCompact 9 (.full [3,3,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [3,3,3] (Equiv.refl (Fin 9)) sgB484 sgT484) sgFlag484 = 1 := by + decide +kernel + +lemma sg484 : RowSquare [3,2,2,2] [3,3,3] := by + apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [3,3,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB484 sgT484 sgFlag484 + change solveCompact 9 (.full [3,3,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [3,3,3] (Equiv.refl (Fin 9)) sgB484 sgT484) sgFlag484 ≠ 0 + rw [sgCert484] + norm_num + +def sgB487 : Equiv.Perm (Fin 9) := Equiv.swap 2 5 * (Equiv.swap 5 8 * (Equiv.swap 1 4 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 6))))) +def sgT487 : Equiv.Perm (Fin 9) := Equiv.swap 2 5 * (Equiv.swap 2 1 * (Equiv.swap 5 8 * (Equiv.swap 2 6 * (Equiv.swap 2 0 * (Equiv.swap 1 7 * (Equiv.swap 0 3)))))) +def sgFlag487 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(0,0,1),(1,1,0),(1,1,1),(2,1,2),(0,2,0)} +lemma sgCert487 : solveCompact 9 (.full [3,3,2,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [3,3,2,1] (Equiv.refl (Fin 9)) sgB487 sgT487) sgFlag487 = 2 := by + decide +kernel + +lemma sg487 : RowSquare [3,2,2,2] [4,3,2] := by + apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [3,3,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB487 sgT487 sgFlag487 + change solveCompact 9 (.full [3,3,2,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [3,3,2,1] (Equiv.refl (Fin 9)) sgB487 sgT487) sgFlag487 ≠ 0 + rw [sgCert487] + norm_num + +def sgB489 : Equiv.Perm (Fin 9) := Equiv.swap 7 0 * (Equiv.swap 0 4 * (Equiv.swap 0 6 * (Equiv.swap 4 3 * (Equiv.swap 3 2 * (Equiv.swap 2 8 * (Equiv.swap 0 5)))))) +def sgT489 : Equiv.Perm (Fin 9) := Equiv.swap 1 4 * (Equiv.swap 4 8 * (Equiv.swap 4 5 * (Equiv.swap 3 6 * (Equiv.swap 1 7)))) +def sgFlag489 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(3,0,1),(0,0,2),(5,1,0),(1,1,1),(2,2,0)} +lemma sgCert489 : solveCompact 9 (.full [6,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB489 sgT489) sgFlag489 = 9 := by + decide +kernel + +lemma sg489 : RowSquare [3,3,1,1,1] [2,2,2,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [6,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB489 sgT489 sgFlag489 + change solveCompact 9 (.full [6,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB489 sgT489) sgFlag489 ≠ 0 + rw [sgCert489] + norm_num + +def sgB490 : Equiv.Perm (Fin 9) := Equiv.swap 2 8 * (Equiv.swap 0 1 * (Equiv.swap 3 5 * (Equiv.swap 2 7 * (Equiv.swap 1 6 * (Equiv.swap 0 4))))) +def sgT490 : Equiv.Perm (Fin 9) := Equiv.swap 7 1 * (Equiv.swap 4 3 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 1 8 * (Equiv.swap 0 6))))) +def sgFlag490 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(1,0,1),(2,0,2),(3,1,0),(3,1,1),(0,2,0)} +lemma sgCert490 : solveCompact 9 (.full [5,4]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB490 sgT490) sgFlag490 = 2 := by + decide +kernel + +lemma sg490 : RowSquare [3,3,1,1,1] [2,2,2,2,1] := by + apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [5,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB490 sgT490 sgFlag490 + change solveCompact 9 (.full [5,4]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB490 sgT490) sgFlag490 ≠ 0 + rw [sgCert490] + norm_num + +def sgB495 : Equiv.Perm (Fin 9) := Equiv.swap 2 0 * (Equiv.swap 3 5 * (Equiv.swap 2 7 * (Equiv.swap 1 4 * (Equiv.swap 0 8)))) +def sgT495 : Equiv.Perm (Fin 9) := Equiv.swap 6 8 * (Equiv.swap 6 3 * (Equiv.swap 3 4 * (Equiv.swap 4 7 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 0 5)))))) +def sgFlag495 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(2,0,2),(0,1,1),(1,1,1),(0,2,0)} +lemma sgCert495 : solveCompact 9 (.full [4,3,2]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [4,3,2] (Equiv.refl (Fin 9)) sgB495 sgT495) sgFlag495 = 1 := by + decide +kernel + +lemma sg495 : RowSquare [3,3,1,1,1] [3,3,2,1] := by + apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [4,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB495 sgT495 sgFlag495 + change solveCompact 9 (.full [4,3,2]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [4,3,2] (Equiv.refl (Fin 9)) sgB495 sgT495) sgFlag495 ≠ 0 + rw [sgCert495] + norm_num + +def sgB496 : Equiv.Perm (Fin 9) := Equiv.swap 2 5 * (Equiv.swap 5 8 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))) +def sgT496 : Equiv.Perm (Fin 9) := Equiv.swap 5 7 * (Equiv.swap 3 1 * (Equiv.swap 2 4 * (Equiv.swap 1 8))) +def sgFlag496 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,0),(0,0,2),(2,1,1),(1,2,0)} +lemma sgCert496 : solveCompact 9 (.full [3,3,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [3,3,3] (Equiv.refl (Fin 9)) sgB496 sgT496) sgFlag496 = -1 := by + decide +kernel + +lemma sg496 : RowSquare [3,3,1,1,1] [3,3,3] := by + apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [3,3,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB496 sgT496 sgFlag496 + change solveCompact 9 (.full [3,3,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [3,3,3] (Equiv.refl (Fin 9)) sgB496 sgT496) sgFlag496 ≠ 0 + rw [sgCert496] + norm_num + +def sgB511 : Equiv.Perm (Fin 9) := Equiv.swap 3 6 * (Equiv.swap 6 2 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 2 8 * (Equiv.swap 1 5))))) +def sgT511 : Equiv.Perm (Fin 9) := Equiv.swap 5 4 * (Equiv.swap 4 0 * (Equiv.swap 0 2 * (Equiv.swap 2 7 * (Equiv.swap 0 3)))) +def sgFlag511 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(2,0,1),(6,0,2),(5,1,0),(0,1,1),(1,1,2),(0,2,0),(4,2,1)} +lemma sgCert511 : solveCompact 9 (.full [7,2]) (.full [3,3,2,1]) (.full [3,3,2,1]) + (certificateEdges [3,3,2,1] [3,3,2,1] [7,2] (Equiv.refl (Fin 9)) sgB511 sgT511) sgFlag511 = 120 := by + decide +kernel + +lemma sg511 : RowSquare [3,3,2,1] [2,2,1,1,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [3,3,2,1]) (ts := [7,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB511 sgT511 sgFlag511 + change solveCompact 9 (.full [7,2]) (.full [3,3,2,1]) (.full [3,3,2,1]) + (certificateEdges [3,3,2,1] [3,3,2,1] [7,2] (Equiv.refl (Fin 9)) sgB511 sgT511) sgFlag511 ≠ 0 + rw [sgCert511] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB513 : Equiv.Perm (Fin 9) := Equiv.swap 1 8 * (Equiv.swap 1 6 * (Equiv.swap 4 7 * (Equiv.swap 1 5 * (Equiv.swap 1 0 * (Equiv.swap 0 2))))) +def sgT513 : Equiv.Perm (Fin 9) := Equiv.swap 3 0 * (Equiv.swap 0 2 * (Equiv.swap 3 7 * (Equiv.swap 3 1 * (Equiv.swap 2 8 * (Equiv.swap 1 4 * (Equiv.swap 0 5)))))) +def sgFlag513 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,1),(0,0,2),(4,1,0),(0,1,1),(2,2,0),(1,2,2)} +lemma sgCert513 : solveCompact 9 (.full [5,2,2]) (.full [3,3,2,1]) (.full [3,3,2,1]) + (certificateEdges [3,3,2,1] [3,3,2,1] [5,2,2] (Equiv.refl (Fin 9)) sgB513 sgT513) sgFlag513 = 4 := by + decide +kernel + +lemma sg513 : RowSquare [3,3,2,1] [3,3,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [3,3,2,1]) (ts := [5,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB513 sgT513 sgFlag513 + change solveCompact 9 (.full [5,2,2]) (.full [3,3,2,1]) (.full [3,3,2,1]) + (certificateEdges [3,3,2,1] [3,3,2,1] [5,2,2] (Equiv.refl (Fin 9)) sgB513 sgT513) sgFlag513 ≠ 0 + rw [sgCert513] + norm_num + +def sgB535 : Equiv.Perm (Fin 9) := Equiv.swap 6 5 * (Equiv.swap 5 1 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 1 8 * (Equiv.swap 0 2))))) +def sgT535 : Equiv.Perm (Fin 9) := Equiv.swap 3 8 * (Equiv.swap 3 1 * (Equiv.swap 2 7 * (Equiv.swap 1 4 * (Equiv.swap 0 6)))) +def sgFlag535 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(0,0,1),(6,0,2),(2,0,3),(4,1,0),(5,1,1),(0,2,0),(1,3,0)} +lemma sgCert535 : solveCompact 9 (.full [7,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [7,2] (Equiv.refl (Fin 9)) sgB535 sgT535) sgFlag535 = 4 := by + decide +kernel + +lemma sg535 : RowSquare [4,2,1,1,1] [2,2,1,1,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [7,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB535 sgT535 sgFlag535 + change solveCompact 9 (.full [7,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [7,2] (Equiv.refl (Fin 9)) sgB535 sgT535) sgFlag535 ≠ 0 + rw [sgCert535] + norm_num + +def sgB536 : Equiv.Perm (Fin 9) := Equiv.swap 6 3 * (Equiv.swap 0 8 * (Equiv.swap 0 5 * (Equiv.swap 3 1 * (Equiv.swap 0 4 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))) +def sgT536 : Equiv.Perm (Fin 9) := Equiv.swap 1 4 * (Equiv.swap 4 0 * (Equiv.swap 0 8 * (Equiv.swap 0 3 * (Equiv.swap 1 6 * (Equiv.swap 0 2))))) +def sgFlag536 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,2),(4,0,3),(0,1,0),(5,1,0),(3,2,0),(2,3,1)} +lemma sgCert536 : solveCompact 9 (.full [6,3]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB536 sgT536) sgFlag536 = 10 := by + decide +kernel + +lemma sg536 : RowSquare [4,2,1,1,1] [2,2,2,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [6,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB536 sgT536 sgFlag536 + change solveCompact 9 (.full [6,3]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB536 sgT536) sgFlag536 ≠ 0 + rw [sgCert536] + norm_num + +def sgB537 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 2 7 * (Equiv.swap 2 0 * (Equiv.swap 2 5 * (Equiv.swap 2 4 * (Equiv.swap 1 8 * (Equiv.swap 0 6)))))) +def sgT537 : Equiv.Perm (Fin 9) := Equiv.swap 6 7 * (Equiv.swap 1 8 * (Equiv.swap 0 2)) +def sgFlag537 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(1,0,1),(4,0,1),(1,0,2),(0,1,0),(3,1,0),(0,2,0),(3,3,3)} +lemma sgCert537 : solveCompact 9 (.full [5,4]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB537 sgT537) sgFlag537 = 3 := by + decide +kernel + +lemma sg537 : RowSquare [4,2,1,1,1] [2,2,2,2,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [5,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB537 sgT537 sgFlag537 + change solveCompact 9 (.full [5,4]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB537 sgT537) sgFlag537 ≠ 0 + rw [sgCert537] + norm_num + +def sgB541 : Equiv.Perm (Fin 9) := Equiv.swap 2 5 * (Equiv.swap 2 7 * (Equiv.swap 5 0 * (Equiv.swap 2 6 * (Equiv.swap 2 4 * (Equiv.swap 1 3 * (Equiv.swap 0 8)))))) +def sgT541 : Equiv.Perm (Fin 9) := Equiv.swap 3 8 * (Equiv.swap 3 0 * (Equiv.swap 3 1 * (Equiv.swap 3 4 * (Equiv.swap 1 5 * (Equiv.swap 0 7))))) +def sgFlag541 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(3,0,2),(0,1,0),(0,1,3),(2,2,0),(4,3,1)} +lemma sgCert541 : solveCompact 9 (.full [5,2,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,2,2] (Equiv.refl (Fin 9)) sgB541 sgT541) sgFlag541 = 1 := by + decide +kernel + +lemma sg541 : RowSquare [4,2,1,1,1] [3,3,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [5,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB541 sgT541 sgFlag541 + change solveCompact 9 (.full [5,2,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,2,2] (Equiv.refl (Fin 9)) sgB541 sgT541) sgFlag541 ≠ 0 + rw [sgCert541] + norm_num + +def sgB548 : Equiv.Perm (Fin 9) := Equiv.swap 3 2 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 8 * (Equiv.swap 0 6))))) +def sgT548 : Equiv.Perm (Fin 9) := Equiv.swap 1 5 * (Equiv.swap 5 8 * (Equiv.swap 5 6 * (Equiv.swap 1 2 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 7)))))) +def sgFlag548 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(7,0,0),(2,0,1),(1,0,3),(4,1,0),(6,1,1),(5,1,2),(0,2,1),(3,3,0)} +lemma sgCert548 : solveCompact 9 (.full [8,1]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [8,1] (Equiv.refl (Fin 9)) sgB548 sgT548) sgFlag548 = 56 := by + decide +kernel + +lemma sg548 : RowSquare [4,2,2,1] [2,1,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [8,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB548 sgT548 sgFlag548 + change solveCompact 9 (.full [8,1]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [8,1] (Equiv.refl (Fin 9)) sgB548 sgT548) sgFlag548 ≠ 0 + rw [sgCert548] + norm_num + +def sgB549 : Equiv.Perm (Fin 9) := Equiv.swap 0 8 * (Equiv.swap 3 2 * (Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 6 * (Equiv.swap 0 7)))))) +def sgT549 : Equiv.Perm (Fin 9) := Equiv.swap 4 1 * (Equiv.swap 2 0 * (Equiv.swap 1 5 * (Equiv.swap 0 8))) +def sgFlag549 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(1,0,1),(6,0,3),(0,1,0),(5,1,0),(4,1,2),(0,2,1),(3,3,0)} +lemma sgCert549 : solveCompact 9 (.full [7,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [7,2] (Equiv.refl (Fin 9)) sgB549 sgT549) sgFlag549 = -8 := by + decide +kernel + +lemma sg549 : RowSquare [4,2,2,1] [2,2,1,1,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [7,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB549 sgT549 sgFlag549 + change solveCompact 9 (.full [7,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [7,2] (Equiv.refl (Fin 9)) sgB549 sgT549) sgFlag549 ≠ 0 + rw [sgCert549] + norm_num + +def sgB550 : Equiv.Perm (Fin 9) := Equiv.swap 1 4 * (Equiv.swap 4 8 * (Equiv.swap 4 6 * (Equiv.swap 4 2 * (Equiv.swap 1 0 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))))) +def sgT550 : Equiv.Perm (Fin 9) := Equiv.swap 5 6 * (Equiv.swap 3 7 * (Equiv.swap 0 2)) +def sgFlag550 : Finset (ℕ × ℕ × ℕ) := {(5,0,0),(2,0,1),(4,0,2),(0,1,0),(3,1,0),(1,1,3),(0,2,1),(1,3,0)} +lemma sgCert550 : solveCompact 9 (.full [6,3]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [6,3] (Equiv.refl (Fin 9)) sgB550 sgT550) sgFlag550 = 12 := by + decide +kernel + +lemma sg550 : RowSquare [4,2,2,1] [2,2,2,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [6,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB550 sgT550 sgFlag550 + change solveCompact 9 (.full [6,3]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [6,3] (Equiv.refl (Fin 9)) sgB550 sgT550) sgFlag550 ≠ 0 + rw [sgCert550] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves3.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves3.lean index 853477ac767a3567060337d67c2742402e1b0448..d20d50edfef81fa710067ca4207ed58bfd81af5d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves3.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves3.lean @@ -1,700 +1,700 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Semigroup Leaves 3. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB551 : Equiv.Perm (Fin 9) := Equiv.swap 6 2 * (Equiv.swap 4 8 * (Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 0 5)))))) -def sgT551 : Equiv.Perm (Fin 9) := Equiv.swap 3 1 * (Equiv.swap 1 0 * (Equiv.swap 2 7 * (Equiv.swap 3 6 * (Equiv.swap 2 4 * (Equiv.swap 1 5 * (Equiv.swap 0 8)))))) -def sgFlag551 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(3,0,1),(1,0,2),(2,0,3),(0,1,0),(2,1,0),(0,1,1),(4,2,1),(1,3,0)} -lemma sgCert551 : solveCompact 9 (.full [5,4]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [5,4] (Equiv.refl (Fin 9)) sgB551 sgT551) sgFlag551 = -3 := by - decide +kernel - -lemma sg551 : RowSquare [4,2,2,1] [2,2,2,2,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [5,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB551 sgT551 sgFlag551 - change solveCompact 9 (.full [5,4]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [5,4] (Equiv.refl (Fin 9)) sgB551 sgT551) sgFlag551 ≠ 0 - rw [sgCert551] - norm_num - -def sgB552 : Equiv.Perm (Fin 9) := Equiv.swap 0 2 * (Equiv.swap 0 1 * (Equiv.swap 1 7 * (Equiv.swap 2 8 * (Equiv.swap 2 4 * (Equiv.swap 1 5 * (Equiv.swap 0 6)))))) -def sgT552 : Equiv.Perm (Fin 9) := Equiv.swap 1 5 * (Equiv.swap 5 8 * (Equiv.swap 5 4 * (Equiv.swap 4 0 * (Equiv.swap 1 7 * (Equiv.swap 0 6))))) -def sgFlag552 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(0,1,1),(4,1,1),(0,1,2),(2,2,0),(3,3,3)} -lemma sgCert552 : solveCompact 9 (.full [5,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [5,2,2] (Equiv.refl (Fin 9)) sgB552 sgT552) sgFlag552 = -1 := by - decide +kernel - -lemma sg552 : RowSquare [4,2,2,1] [3,3,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [5,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB552 sgT552 sgFlag552 - change solveCompact 9 (.full [5,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [5,2,2] (Equiv.refl (Fin 9)) sgB552 sgT552) sgFlag552 ≠ 0 - rw [sgCert552] - norm_num - -def sgB553 : Equiv.Perm (Fin 9) := Equiv.swap 7 0 * (Equiv.swap 4 1 * (Equiv.swap 1 2 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 8))))) -def sgT553 : Equiv.Perm (Fin 9) := Equiv.swap 1 3 * (Equiv.swap 1 7 * (Equiv.swap 4 5 * (Equiv.swap 3 2 * (Equiv.swap 2 8 * (Equiv.swap 1 6))))) -def sgFlag553 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(0,1,0),(3,1,0),(2,1,3),(1,2,1),(2,3,2)} -lemma sgCert553 : solveCompact 9 (.full [4,3,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [4,3,2] (Equiv.refl (Fin 9)) sgB553 sgT553) sgFlag553 = 5 := by - decide +kernel - -lemma sg553 : RowSquare [4,2,2,1] [3,3,2,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [4,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB553 sgT553 sgFlag553 - change solveCompact 9 (.full [4,3,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [4,3,2] (Equiv.refl (Fin 9)) sgB553 sgT553) sgFlag553 ≠ 0 - rw [sgCert553] - norm_num - -def sgB559 : Equiv.Perm (Fin 9) := Equiv.swap 0 4 * (Equiv.swap 5 3 * (Equiv.swap 4 2 * (Equiv.swap 3 8 * (Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 0 6)))))) -def sgT559 : Equiv.Perm (Fin 9) := Equiv.swap 6 5 * (Equiv.swap 5 0 * (Equiv.swap 1 8 * (Equiv.swap 1 4 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))) -def sgFlag559 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(1,0,2),(1,1,0),(0,1,1),(0,1,3),(2,2,1),(1,3,0)} -lemma sgCert559 : solveCompact 9 (.full [3,2,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [3,2,2,2] (Equiv.refl (Fin 9)) sgB559 sgT559) sgFlag559 = 12 := by - decide +kernel - -lemma sg559 : RowSquare [4,2,2,1] [4,4,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [3,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB559 sgT559 sgFlag559 - change solveCompact 9 (.full [3,2,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [3,2,2,2] (Equiv.refl (Fin 9)) sgB559 sgT559) sgFlag559 ≠ 0 - rw [sgCert559] - norm_num - -def sgB561 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 1 8 * (Equiv.swap 2 4 * (Equiv.swap 4 0 * (Equiv.swap 1 6 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))))) -def sgT561 : Equiv.Perm (Fin 9) := Equiv.swap 6 4 * (Equiv.swap 4 0 * (Equiv.swap 2 1 * (Equiv.swap 1 5 * (Equiv.swap 0 8)))) -def sgFlag561 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,0),(0,0,1),(6,0,2),(2,1,0),(7,1,1),(5,1,3),(1,2,1),(3,3,0)} -lemma sgCert561 : solveCompact 9 (.full [8,1]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [8,1] (Equiv.refl (Fin 9)) sgB561 sgT561) sgFlag561 = 28 := by - decide +kernel - -lemma sg561 : RowSquare [4,3,1,1] [2,1,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [8,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB561 sgT561 sgFlag561 - change solveCompact 9 (.full [8,1]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [8,1] (Equiv.refl (Fin 9)) sgB561 sgT561) sgFlag561 ≠ 0 - rw [sgCert561] - norm_num - -def sgB562 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 1 8 * (Equiv.swap 1 5 * (Equiv.swap 2 6 * (Equiv.swap 2 3 * (Equiv.swap 1 4))))) -def sgT562 : Equiv.Perm (Fin 9) := Equiv.swap 3 0 * (Equiv.swap 4 5 * (Equiv.swap 3 6 * (Equiv.swap 1 8 * (Equiv.swap 0 7)))) -def sgFlag562 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(5,0,1),(1,0,2),(1,1,0),(4,1,0),(3,1,1),(2,2,3),(6,3,0)} -lemma sgCert562 : solveCompact 9 (.full [7,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [7,2] (Equiv.refl (Fin 9)) sgB562 sgT562) sgFlag562 = 3 := by - decide +kernel - -lemma sg562 : RowSquare [4,3,1,1] [2,2,1,1,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [7,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB562 sgT562 sgFlag562 - change solveCompact 9 (.full [7,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [7,2] (Equiv.refl (Fin 9)) sgB562 sgT562) sgFlag562 ≠ 0 - rw [sgCert562] - norm_num - -def sgB563 : Equiv.Perm (Fin 9) := Equiv.swap 3 8 * (Equiv.swap 3 5 * (Equiv.swap 5 2 * (Equiv.swap 2 7 * (Equiv.swap 3 0 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))))) -def sgT563 : Equiv.Perm (Fin 9) := Equiv.swap 3 6 * (Equiv.swap 6 1 * (Equiv.swap 3 4 * (Equiv.swap 4 7 * (Equiv.swap 3 5 * (Equiv.swap 1 8 * (Equiv.swap 1 0 * (Equiv.swap 0 2))))))) -def sgFlag563 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(1,0,1),(3,0,3),(0,1,0),(4,1,2),(2,2,1),(5,3,0)} -lemma sgCert563 : solveCompact 9 (.full [6,3]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [6,3] (Equiv.refl (Fin 9)) sgB563 sgT563) sgFlag563 = 9 := by - decide +kernel - -lemma sg563 : RowSquare [4,3,1,1] [2,2,2,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [6,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB563 sgT563 sgFlag563 - change solveCompact 9 (.full [6,3]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [6,3] (Equiv.refl (Fin 9)) sgB563 sgT563) sgFlag563 ≠ 0 - rw [sgCert563] - norm_num - -def sgB564 : Equiv.Perm (Fin 9) := Equiv.swap 5 8 * (Equiv.swap 3 2 * (Equiv.swap 3 0 * (Equiv.swap 2 6 * (Equiv.swap 1 7 * (Equiv.swap 0 4))))) -def sgT564 : Equiv.Perm (Fin 9) := Equiv.swap 5 1 * (Equiv.swap 3 4 * (Equiv.swap 1 8 * (Equiv.swap 1 2 * (Equiv.swap 0 6)))) -def sgFlag564 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(3,0,2),(0,0,3),(1,1,0),(2,1,1),(3,2,0),(4,3,0)} -lemma sgCert564 : solveCompact 9 (.full [5,4]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [5,4] (Equiv.refl (Fin 9)) sgB564 sgT564) sgFlag564 = 7 := by - decide +kernel - -lemma sg564 : RowSquare [4,3,1,1] [2,2,2,2,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [5,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB564 sgT564 sgFlag564 - change solveCompact 9 (.full [5,4]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [5,4] (Equiv.refl (Fin 9)) sgB564 sgT564) sgFlag564 ≠ 0 - rw [sgCert564] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB565 : Equiv.Perm (Fin 9) := Equiv.swap 1 0 * (Equiv.swap 0 8 * (Equiv.swap 1 7 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 6))))) -def sgT565 : Equiv.Perm (Fin 9) := Equiv.swap 3 6 * (Equiv.swap 6 5 * (Equiv.swap 5 4 * (Equiv.swap 4 8 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 7))))))) -def sgFlag565 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(5,0,0),(3,0,1),(6,1,0),(4,1,2),(0,1,3),(1,2,1),(2,3,1)} -lemma sgCert565 : solveCompact 9 (.full [7,1,1]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [7,1,1] (Equiv.refl (Fin 9)) sgB565 sgT565) sgFlag565 = 20 := by - decide +kernel - -lemma sg565 : RowSquare [4,3,1,1] [3,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [7,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB565 sgT565 sgFlag565 - change solveCompact 9 (.full [7,1,1]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [7,1,1] (Equiv.refl (Fin 9)) sgB565 sgT565) sgFlag565 ≠ 0 - rw [sgCert565] - norm_num - -def sgB569 : Equiv.Perm (Fin 9) := Equiv.swap 0 3 * (Equiv.swap 3 8 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 5 * (Equiv.swap 0 7))))) -def sgT569 : Equiv.Perm (Fin 9) := Equiv.swap 0 1 * (Equiv.swap 0 2 * (Equiv.swap 1 7 * (Equiv.swap 2 6 * (Equiv.swap 1 4 * (Equiv.swap 0 5))))) -def sgFlag569 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(0,0,2),(2,1,0),(4,1,1),(0,1,3),(1,2,1),(3,3,0)} -lemma sgCert569 : solveCompact 9 (.full [5,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [5,2,2] (Equiv.refl (Fin 9)) sgB569 sgT569) sgFlag569 = 10 := by - decide +kernel - -lemma sg569 : RowSquare [4,3,1,1] [3,3,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [5,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB569 sgT569 sgFlag569 - change solveCompact 9 (.full [5,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [5,2,2] (Equiv.refl (Fin 9)) sgB569 sgT569) sgFlag569 ≠ 0 - rw [sgCert569] - norm_num - -def sgB570 : Equiv.Perm (Fin 9) := Equiv.swap 4 1 * (Equiv.swap 3 7 * (Equiv.swap 1 5 * (Equiv.swap 1 2 * (Equiv.swap 0 8)))) -def sgT570 : Equiv.Perm (Fin 9) := Equiv.swap 5 3 * (Equiv.swap 3 0 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 0 6)))) -def sgFlag570 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(0,0,1),(3,1,0),(1,1,2),(0,1,3),(0,2,1),(2,3,1)} -lemma sgCert570 : solveCompact 9 (.full [4,3,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [4,3,2] (Equiv.refl (Fin 9)) sgB570 sgT570) sgFlag570 = -1 := by - decide +kernel - -lemma sg570 : RowSquare [4,3,1,1] [3,3,2,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [4,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB570 sgT570 sgFlag570 - change solveCompact 9 (.full [4,3,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [4,3,2] (Equiv.refl (Fin 9)) sgB570 sgT570) sgFlag570 ≠ 0 - rw [sgCert570] - norm_num - -def sgB575 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 1 8 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 1 5 * (Equiv.swap 0 6))))) -def sgT575 : Equiv.Perm (Fin 9) := Equiv.swap 3 2 * (Equiv.swap 2 7 * (Equiv.swap 0 8 * (Equiv.swap 3 6 * (Equiv.swap 2 1 * (Equiv.swap 1 5 * (Equiv.swap 0 4)))))) -def sgFlag575 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,0,2),(0,1,0),(0,1,1),(1,2,0),(1,3,3)} -lemma sgCert575 : solveCompact 9 (.full [3,2,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [3,2,2,2] (Equiv.refl (Fin 9)) sgB575 sgT575) sgFlag575 = 2 := by - decide +kernel - -lemma sg575 : RowSquare [4,3,1,1] [4,4,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [3,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB575 sgT575 sgFlag575 - change solveCompact 9 (.full [3,2,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) - (certificateEdges [4,2,2,1] [4,2,2,1] [3,2,2,2] (Equiv.refl (Fin 9)) sgB575 sgT575) sgFlag575 ≠ 0 - rw [sgCert575] - norm_num - -def sgB577 : Equiv.Perm (Fin 9) := Equiv.swap 6 5 * (Equiv.swap 5 3 * (Equiv.swap 3 0 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 0 8 * (Equiv.swap 0 1)))))) -def sgT577 : Equiv.Perm (Fin 9) := Equiv.swap 4 0 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 0 7 * (Equiv.swap 0 1)))) -def sgFlag577 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(1,0,1),(1,0,2),(2,0,2),(0,1,0),(4,1,1),(5,2,0),(6,2,1)} -lemma sgCert577 : solveCompact 9 (.full [7,2]) (.full [3,3,2,1]) (.full [3,3,2,1]) - (certificateEdges [3,3,2,1] [3,3,2,1] [7,2] (Equiv.refl (Fin 9)) sgB577 sgT577) sgFlag577 = 30 := by - decide +kernel - -lemma sg577 : RowSquare [4,3,2] [2,2,1,1,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [3,3,2,1]) (ts := [7,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB577 sgT577 sgFlag577 - change solveCompact 9 (.full [7,2]) (.full [3,3,2,1]) (.full [3,3,2,1]) - (certificateEdges [3,3,2,1] [3,3,2,1] [7,2] (Equiv.refl (Fin 9)) sgB577 sgT577) sgFlag577 ≠ 0 - rw [sgCert577] - norm_num - -def sgB578 : Equiv.Perm (Fin 9) := Equiv.swap 3 8 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 6 * (Equiv.swap 0 5)))) -def sgT578 : Equiv.Perm (Fin 9) := Equiv.swap 3 5 * (Equiv.swap 5 1 * (Equiv.swap 3 6 * (Equiv.swap 3 4 * (Equiv.swap 0 8 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))) -def sgFlag578 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,1),(2,0,2),(2,1,1),(3,1,1),(1,1,2),(1,2,0),(3,2,0)} -lemma sgCert578 : solveCompact 9 (.full [5,4]) (.full [3,3,2,1]) (.full [3,3,2,1]) - (certificateEdges [3,3,2,1] [3,3,2,1] [5,4] (Equiv.refl (Fin 9)) sgB578 sgT578) sgFlag578 = 11 := by - decide +kernel - -lemma sg578 : RowSquare [4,3,2] [2,2,2,2,1] := by - apply rowSquare_compact (n := 9) (cs := [3,3,2,1]) (ts := [5,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB578 sgT578 sgFlag578 - change solveCompact 9 (.full [5,4]) (.full [3,3,2,1]) (.full [3,3,2,1]) - (certificateEdges [3,3,2,1] [3,3,2,1] [5,4] (Equiv.refl (Fin 9)) sgB578 sgT578) sgFlag578 ≠ 0 - rw [sgCert578] - norm_num - -def sgB579 : Equiv.Perm (Fin 9) := Equiv.swap 6 4 * (Equiv.swap 4 7 * (Equiv.swap 4 5 * (Equiv.swap 2 1 * (Equiv.swap 2 0 * (Equiv.swap 1 8 * (Equiv.swap 0 3)))))) -def sgT579 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 2 3 * (Equiv.swap 1 8 * (Equiv.swap 0 6))))) -def sgFlag579 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(5,0,0),(1,0,1),(4,0,1),(0,1,0),(1,1,1),(2,1,1),(2,1,2),(3,2,0)} -lemma sgCert579 : solveCompact 9 (.full [6,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [6,3] (Equiv.refl (Fin 9)) sgB579 sgT579) sgFlag579 = 18 := by - decide +kernel - -lemma sg579 : RowSquare [4,4,1] [2,2,2,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [6,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB579 sgT579 sgFlag579 - change solveCompact 9 (.full [6,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [6,3] (Equiv.refl (Fin 9)) sgB579 sgT579) sgFlag579 ≠ 0 - rw [sgCert579] - norm_num - -def sgB580 : Equiv.Perm (Fin 9) := Equiv.swap 5 6 * (Equiv.swap 4 0 * (Equiv.swap 0 7 * (Equiv.swap 0 3 * (Equiv.swap 1 8 * (Equiv.swap 0 2))))) -def sgT580 : Equiv.Perm (Fin 9) := Equiv.swap 6 5 * (Equiv.swap 6 7 * (Equiv.swap 5 0 * (Equiv.swap 0 2 * (Equiv.swap 2 8 * (Equiv.swap 2 3 * (Equiv.swap 0 4)))))) -def sgFlag580 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,1),(4,0,2),(2,1,0),(1,1,1),(3,2,0)} -lemma sgCert580 : solveCompact 9 (.full [5,4]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [5,4] (Equiv.refl (Fin 9)) sgB580 sgT580) sgFlag580 = 6 := by - decide +kernel - -lemma sg580 : RowSquare [4,4,1] [2,2,2,2,1] := by - apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [5,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB580 sgT580 sgFlag580 - change solveCompact 9 (.full [5,4]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [5,4] (Equiv.refl (Fin 9)) sgB580 sgT580) sgFlag580 ≠ 0 - rw [sgCert580] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB581 : Equiv.Perm (Fin 9) := Equiv.swap 2 7 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 0 4))) -def sgT581 : Equiv.Perm (Fin 9) := Equiv.swap 0 4 * (Equiv.swap 0 3 * (Equiv.swap 3 7 * (Equiv.swap 4 8 * (Equiv.swap 3 5 * (Equiv.swap 0 1 * (Equiv.swap 1 6 * (Equiv.swap 0 2))))))) -def sgFlag581 : Finset (ℕ × ℕ × ℕ) := {(5,0,0),(1,0,1),(2,0,1),(4,0,2),(0,1,0),(3,1,0),(0,1,1),(1,2,1)} -lemma sgCert581 : solveCompact 9 (.full [6,2,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [6,2,1] (Equiv.refl (Fin 9)) sgB581 sgT581) sgFlag581 = 6 := by - decide +kernel - -lemma sg581 : RowSquare [4,4,1] [3,2,1,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [6,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB581 sgT581 sgFlag581 - change solveCompact 9 (.full [6,2,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [6,2,1] (Equiv.refl (Fin 9)) sgB581 sgT581) sgFlag581 ≠ 0 - rw [sgCert581] - norm_num - -def sgB582 : Equiv.Perm (Fin 9) := Equiv.swap 2 4 * (Equiv.swap 5 1 * (Equiv.swap 4 3 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 1 8 * (Equiv.swap 0 6)))))) -def sgT582 : Equiv.Perm (Fin 9) := Equiv.swap 1 3 * (Equiv.swap 3 8 * (Equiv.swap 3 2 * (Equiv.swap 2 5 * (Equiv.swap 1 7)))) -def sgFlag582 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(0,0,1),(3,0,2),(1,1,0),(4,1,0),(1,1,1),(2,1,1),(0,2,0)} -lemma sgCert582 : solveCompact 9 (.full [5,3,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [5,3,1] (Equiv.refl (Fin 9)) sgB582 sgT582) sgFlag582 = -2 := by - decide +kernel - -lemma sg582 : RowSquare [4,4,1] [3,2,2,1,1] := by - apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [5,3,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB582 sgT582 sgFlag582 - change solveCompact 9 (.full [5,3,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [5,3,1] (Equiv.refl (Fin 9)) sgB582 sgT582) sgFlag582 ≠ 0 - rw [sgCert582] - norm_num - -def sgB583 : Equiv.Perm (Fin 9) := Equiv.swap 4 8 * (Equiv.swap 4 5 * (Equiv.swap 5 0 * (Equiv.swap 4 6 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 7)))))) -def sgT583 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 1 8 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 4)))))) -def sgFlag583 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(0,0,1),(1,1,0),(1,1,1),(2,1,1),(3,1,2),(0,2,0)} -lemma sgCert583 : solveCompact 9 (.full [5,2,2]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [5,2,2] (Equiv.refl (Fin 9)) sgB583 sgT583) sgFlag583 = 4 := by - decide +kernel - -lemma sg583 : RowSquare [4,4,1] [3,3,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [5,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB583 sgT583 sgFlag583 - change solveCompact 9 (.full [5,2,2]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [5,2,2] (Equiv.refl (Fin 9)) sgB583 sgT583) sgFlag583 ≠ 0 - rw [sgCert583] - norm_num - -def sgB584 : Equiv.Perm (Fin 9) := Equiv.swap 7 5 * (Equiv.swap 5 4 * (Equiv.swap 5 2 * (Equiv.swap 4 8 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 6)))))) -def sgT584 : Equiv.Perm (Fin 9) := Equiv.swap 2 6 * (Equiv.swap 6 1 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 1 8 * (Equiv.swap 0 7))))) -def sgFlag584 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(2,0,2),(2,1,0),(1,1,1),(0,2,1)} -lemma sgCert584 : solveCompact 9 (.full [3,3,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [3,3,3] (Equiv.refl (Fin 9)) sgB584 sgT584) sgFlag584 = -5 := by - decide +kernel - -lemma sg584 : RowSquare [4,4,1] [3,3,3] := by - apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [3,3,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB584 sgT584 sgFlag584 - change solveCompact 9 (.full [3,3,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) - (certificateEdges [3,2,2,2] [3,2,2,2] [3,3,3] (Equiv.refl (Fin 9)) sgB584 sgT584) sgFlag584 ≠ 0 - rw [sgCert584] - norm_num - -def sgB614 : Equiv.Perm (Fin 9) := Equiv.swap 5 3 * (Equiv.swap 5 4 * (Equiv.swap 4 2 * (Equiv.swap 3 1 * (Equiv.swap 2 0 * (Equiv.swap 1 8 * (Equiv.swap 0 7)))))) -def sgT614 : Equiv.Perm (Fin 9) := Equiv.swap 6 2 * (Equiv.swap 6 7 * (Equiv.swap 4 5 * (Equiv.swap 2 8))) -def sgFlag614 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(6,0,1),(5,0,2),(2,0,3),(1,1,0),(4,1,0),(1,2,0),(3,3,1)} -lemma sgCert614 : solveCompact 9 (.full [7,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [7,2] (Equiv.refl (Fin 9)) sgB614 sgT614) sgFlag614 = -4 := by - decide +kernel - -lemma sg614 : RowSquare [5,2,1,1] [2,2,1,1,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [7,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB614 sgT614 sgFlag614 - change solveCompact 9 (.full [7,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [7,2] (Equiv.refl (Fin 9)) sgB614 sgT614) sgFlag614 ≠ 0 - rw [sgCert614] - norm_num - -def sgB615 : Equiv.Perm (Fin 9) := Equiv.swap 0 5 * (Equiv.swap 0 7 * (Equiv.swap 5 8 * (Equiv.swap 0 6 * (Equiv.swap 2 4 * (Equiv.swap 0 3))))) -def sgT615 : Equiv.Perm (Fin 9) := Equiv.swap 3 4 * (Equiv.swap 4 1 * (Equiv.swap 4 5 * (Equiv.swap 3 0 * (Equiv.swap 1 8 * (Equiv.swap 1 2 * (Equiv.swap 0 7)))))) -def sgFlag615 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(4,0,1),(5,0,2),(1,0,3),(1,1,0),(2,1,1),(2,2,0),(0,3,0)} -lemma sgCert615 : solveCompact 9 (.full [6,3]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB615 sgT615) sgFlag615 = 13 := by - decide +kernel - -lemma sg615 : RowSquare [5,2,1,1] [2,2,2,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [6,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB615 sgT615 sgFlag615 - change solveCompact 9 (.full [6,3]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB615 sgT615) sgFlag615 ≠ 0 - rw [sgCert615] - norm_num - -def sgB616 : Equiv.Perm (Fin 9) := Equiv.swap 2 7 * (Equiv.swap 5 8 * (Equiv.swap 2 1 * (Equiv.swap 2 4 * (Equiv.swap 2 0 * (Equiv.swap 1 6 * (Equiv.swap 0 3)))))) -def sgT616 : Equiv.Perm (Fin 9) := Equiv.swap 4 6 * (Equiv.swap 4 5 * (Equiv.swap 0 8 * (Equiv.swap 2 7 * (Equiv.swap 0 3 * (Equiv.swap 0 1))))) -def sgFlag616 : Finset (ℕ × ℕ × ℕ) := {(4,0,0),(0,0,1),(2,0,2),(1,0,3),(1,1,0),(3,1,0),(2,2,0),(3,3,0)} -lemma sgCert616 : solveCompact 9 (.full [5,4]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB616 sgT616) sgFlag616 = 12 := by - decide +kernel - -lemma sg616 : RowSquare [5,2,1,1] [2,2,2,2,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [5,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB616 sgT616 sgFlag616 - change solveCompact 9 (.full [5,4]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB616 sgT616) sgFlag616 ≠ 0 - rw [sgCert616] - norm_num - -def sgB621 : Equiv.Perm (Fin 9) := Equiv.swap 3 8 * (Equiv.swap 3 1 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 6 * (Equiv.swap 0 5))))) -def sgT621 : Equiv.Perm (Fin 9) := Equiv.swap 5 4 * (Equiv.swap 5 6 * (Equiv.swap 4 7 * (Equiv.swap 3 0 * (Equiv.swap 0 8 * (Equiv.swap 0 2 * (Equiv.swap 0 1)))))) -def sgFlag621 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,0),(0,0,1),(1,0,1),(3,0,3),(1,1,0),(2,1,0),(1,2,0),(0,3,2)} -lemma sgCert621 : solveCompact 9 (.full [5,2,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,2,2] (Equiv.refl (Fin 9)) sgB621 sgT621) sgFlag621 = -1 := by - decide +kernel - -lemma sg621 : RowSquare [5,2,1,1] [3,3,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [5,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB621 sgT621 sgFlag621 - change solveCompact 9 (.full [5,2,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) - (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,2,2] (Equiv.refl (Fin 9)) sgB621 sgT621) sgFlag621 ≠ 0 - rw [sgCert621] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB636 : Equiv.Perm (Fin 9) := Equiv.swap 5 1 * (Equiv.swap 5 7 * (Equiv.swap 5 6 * (Equiv.swap 1 0 * (Equiv.swap 0 8 * (Equiv.swap 1 4 * (Equiv.swap 0 2)))))) -def sgT636 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 3 7 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 8))))) -def sgFlag636 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(3,0,1),(2,0,2),(0,1,0),(4,1,1),(1,2,0),(5,2,0)} -lemma sgCert636 : solveCompact 9 (.full [6,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB636 sgT636) sgFlag636 = -6 := by - decide +kernel - -lemma sg636 : RowSquare [5,2,2] [2,2,2,1,1,1] := by - apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [6,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB636 sgT636 sgFlag636 - change solveCompact 9 (.full [6,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB636 sgT636) sgFlag636 ≠ 0 - rw [sgCert636] - norm_num - -def sgB637 : Equiv.Perm (Fin 9) := Equiv.swap 4 2 * (Equiv.swap 5 7 * (Equiv.swap 4 1 * (Equiv.swap 2 0 * (Equiv.swap 1 6 * (Equiv.swap 0 8))))) -def sgT637 : Equiv.Perm (Fin 9) := Equiv.swap 3 0 * (Equiv.swap 0 8 * (Equiv.swap 3 7 * (Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 0 6))))) -def sgFlag637 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(3,0,1),(0,0,2),(3,0,2),(1,1,0),(0,1,1),(2,2,0)} -lemma sgCert637 : solveCompact 9 (.full [5,4]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB637 sgT637) sgFlag637 = 24 := by - decide +kernel - -lemma sg637 : RowSquare [5,2,2] [2,2,2,2,1] := by - apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [5,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB637 sgT637 sgFlag637 - change solveCompact 9 (.full [5,4]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB637 sgT637) sgFlag637 ≠ 0 - rw [sgCert637] - norm_num - -def sgB640 : Equiv.Perm (Fin 9) := Equiv.swap 5 8 * (Equiv.swap 5 3 * (Equiv.swap 5 1 * (Equiv.swap 3 7 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 0 * (Equiv.swap 0 6))))))) -def sgT640 : Equiv.Perm (Fin 9) := Equiv.swap 6 0 * (Equiv.swap 5 7 * (Equiv.swap 0 8 * (Equiv.swap 2 3 * (Equiv.swap 0 4)))) -def sgFlag640 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,2),(1,1,0),(0,2,1),(3,2,1)} -lemma sgCert640 : solveCompact 9 (.full [4,3,2]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [4,3,2] (Equiv.refl (Fin 9)) sgB640 sgT640) sgFlag640 = -1 := by - decide +kernel - -lemma sg640 : RowSquare [5,2,2] [3,3,2,1] := by - apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [4,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB640 sgT640 sgFlag640 - change solveCompact 9 (.full [4,3,2]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [4,3,2] (Equiv.refl (Fin 9)) sgB640 sgT640) sgFlag640 ≠ 0 - rw [sgCert640] - norm_num - -def sgB641 : Equiv.Perm (Fin 9) := Equiv.swap 4 1 * (Equiv.swap 1 8 * (Equiv.swap 4 2 * (Equiv.swap 2 6 * (Equiv.swap 2 3 * (Equiv.swap 1 5))))) -def sgT641 : Equiv.Perm (Fin 9) := Equiv.swap 5 2 * (Equiv.swap 4 3 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 0 6 * (Equiv.swap 0 1))))) -def sgFlag641 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,1,2),(0,2,0),(2,2,0)} -lemma sgCert641 : solveCompact 9 (.full [3,3,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [3,3,3] (Equiv.refl (Fin 9)) sgB641 sgT641) sgFlag641 = 4 := by - decide +kernel - -lemma sg641 : RowSquare [5,2,2] [3,3,3] := by - apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [3,3,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB641 sgT641 sgFlag641 - change solveCompact 9 (.full [3,3,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) - (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [3,3,3] (Equiv.refl (Fin 9)) sgB641 sgT641) sgFlag641 ≠ 0 - rw [sgCert641] - norm_num - -def sgB759 : Equiv.Perm (Fin 10) := Equiv.swap 4 9 * (Equiv.swap 4 0 * (Equiv.swap 4 1 * (Equiv.swap 0 7 * (Equiv.swap 0 3 * (Equiv.swap 1 5 * (Equiv.swap 0 2)))))) -def sgT759 : Equiv.Perm (Fin 10) := Equiv.swap 4 9 * (Equiv.swap 6 2 * (Equiv.swap 2 8 * (Equiv.swap 4 7 * (Equiv.swap 2 5)))) -def sgFlag759 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(4,0,0),(4,0,1),(0,0,2),(1,1,0),(1,1,1),(2,1,1),(0,2,0)} -lemma sgCert759 : solveCompact 10 (.full [5,5]) (.full [3,2,2,2,1]) (.full [3,2,2,2,1]) - (certificateEdges [3,2,2,2,1] [3,2,2,2,1] [5,5] (Equiv.refl (Fin 10)) sgB759 sgT759) sgFlag759 = -9 := by - decide +kernel - -lemma sg759 : RowSquare [3,2,2,2,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [3,2,2,2,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB759 sgT759 sgFlag759 - change solveCompact 10 (.full [5,5]) (.full [3,2,2,2,1]) (.full [3,2,2,2,1]) - (certificateEdges [3,2,2,2,1] [3,2,2,2,1] [5,5] (Equiv.refl (Fin 10)) sgB759 sgT759) sgFlag759 ≠ 0 - rw [sgCert759] - norm_num - -def sgB765 : Equiv.Perm (Fin 10) := Equiv.swap 2 1 * (Equiv.swap 2 7 * (Equiv.swap 5 9 * (Equiv.swap 2 3 * (Equiv.swap 3 6 * (Equiv.swap 2 4 * (Equiv.swap 1 0 * (Equiv.swap 0 8))))))) -def sgT765 : Equiv.Perm (Fin 10) := Equiv.swap 4 1 * (Equiv.swap 0 3 * (Equiv.swap 4 6 * (Equiv.swap 3 9 * (Equiv.swap 0 5 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))) -def sgFlag765 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(4,0,1),(0,0,2),(0,1,0),(1,1,0),(3,2,0),(5,2,1)} -lemma sgCert765 : solveCompact 10 (.full [6,2,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) - (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB765 sgT765) sgFlag765 = 2 := by - decide +kernel - -lemma sg765 : RowSquare [3,3,1,1,1,1] [3,3,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [3,3,1,1,1,1]) (ts := [6,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB765 sgT765 sgFlag765 - change solveCompact 10 (.full [6,2,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) - (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB765 sgT765) sgFlag765 ≠ 0 - rw [sgCert765] - norm_num - -def sgB767 : Equiv.Perm (Fin 10) := Equiv.swap 6 5 * (Equiv.swap 6 1 * (Equiv.swap 5 3 * (Equiv.swap 3 0 * (Equiv.swap 0 9 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))) -def sgT767 : Equiv.Perm (Fin 10) := Equiv.swap 2 5 * (Equiv.swap 5 9 * (Equiv.swap 2 6 * (Equiv.swap 2 4 * (Equiv.swap 2 0 * (Equiv.swap 0 3))))) -def sgFlag767 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(1,0,1),(3,0,2),(1,1,0),(2,1,1),(0,2,0),(1,2,0)} -lemma sgCert767 : solveCompact 10 (.full [4,4,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) - (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB767 sgT767) sgFlag767 = 10 := by - decide +kernel - -lemma sg767 : RowSquare [3,3,1,1,1,1] [3,3,2,2] := by - apply rowSquare_compact (n := 10) (cs := [3,3,1,1,1,1]) (ts := [4,4,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB767 sgT767 sgFlag767 - change solveCompact 10 (.full [4,4,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) - (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB767 sgT767) sgFlag767 ≠ 0 - rw [sgCert767] - norm_num - -def sgB768 : Equiv.Perm (Fin 10) := Equiv.swap 4 6 * (Equiv.swap 6 2 * (Equiv.swap 6 7 * (Equiv.swap 2 0 * (Equiv.swap 4 1 * (Equiv.swap 2 5 * (Equiv.swap 2 3 * (Equiv.swap 1 8 * (Equiv.swap 0 9)))))))) -def sgT768 : Equiv.Perm (Fin 10) := Equiv.swap 8 6 * (Equiv.swap 6 9 * (Equiv.swap 0 7 * (Equiv.swap 0 4 * (Equiv.swap 1 2 * (Equiv.swap 0 3))))) -def sgFlag768 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(3,0,0),(1,0,1),(0,0,2),(2,1,0),(0,1,1),(1,2,0)} -lemma sgCert768 : solveCompact 10 (.full [4,3,3]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) - (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB768 sgT768) sgFlag768 = -16 := by - decide +kernel - -lemma sg768 : RowSquare [3,3,1,1,1,1] [3,3,3,1] := by - apply rowSquare_compact (n := 10) (cs := [3,3,1,1,1,1]) (ts := [4,3,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB768 sgT768 sgFlag768 - change solveCompact 10 (.full [4,3,3]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) - (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB768 sgT768) sgFlag768 ≠ 0 - rw [sgCert768] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB790 : Equiv.Perm (Fin 10) := Equiv.swap 3 6 * (Equiv.swap 6 4 * (Equiv.swap 5 0 * (Equiv.swap 4 2 * (Equiv.swap 3 7 * (Equiv.swap 2 8 * (Equiv.swap 0 9)))))) -def sgT790 : Equiv.Perm (Fin 10) := Equiv.swap 4 3 * (Equiv.swap 4 1 * (Equiv.swap 5 7 * (Equiv.swap 4 6 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 1 8 * (Equiv.swap 0 9))))))) -def sgFlag790 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(3,0,0),(1,0,1),(2,0,1),(4,0,2),(5,1,0),(1,1,1),(6,1,2),(0,2,0)} -lemma sgCert790 : solveCompact 10 (.full [7,3]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) - (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB790 sgT790) sgFlag790 = 24 := by - decide +kernel - -lemma sg790 : RowSquare [3,3,2,1,1] [2,2,2,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [3,3,2,1,1]) (ts := [7,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB790 sgT790 sgFlag790 - change solveCompact 10 (.full [7,3]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) - (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB790 sgT790) sgFlag790 ≠ 0 - rw [sgCert790] - norm_num - -def sgB791 : Equiv.Perm (Fin 10) := Equiv.swap 3 0 * (Equiv.swap 0 9 * (Equiv.swap 3 1 * (Equiv.swap 0 7 * (Equiv.swap 3 2 * (Equiv.swap 2 6 * (Equiv.swap 1 8 * (Equiv.swap 0 4))))))) -def sgT791 : Equiv.Perm (Fin 10) := Equiv.swap 3 2 * (Equiv.swap 3 6 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 8 * (Equiv.swap 0 5))))) -def sgFlag791 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(2,0,1),(5,0,1),(4,0,2),(1,1,0),(2,1,0),(0,1,1),(1,2,0),(0,2,2)} -lemma sgCert791 : solveCompact 10 (.full [6,4]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) - (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB791 sgT791) sgFlag791 = 33 := by - decide +kernel - -lemma sg791 : RowSquare [3,3,2,1,1] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [3,3,2,1,1]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB791 sgT791 sgFlag791 - change solveCompact 10 (.full [6,4]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) - (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB791 sgT791) sgFlag791 ≠ 0 - rw [sgCert791] - norm_num - -def sgB792 : Equiv.Perm (Fin 10) := Equiv.swap 3 8 * (Equiv.swap 6 4 * (Equiv.swap 4 0 * (Equiv.swap 4 5 * (Equiv.swap 3 7 * (Equiv.swap 0 9 * (Equiv.swap 0 2)))))) -def sgT792 : Equiv.Perm (Fin 10) := Equiv.swap 1 9 * (Equiv.swap 6 5 * (Equiv.swap 5 0 * (Equiv.swap 3 4 * (Equiv.swap 0 8 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))) -def sgFlag792 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(4,0,1),(2,0,2),(4,1,0),(2,1,1),(3,1,2),(0,2,0),(3,2,0)} -lemma sgCert792 : solveCompact 10 (.full [5,5]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) - (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB792 sgT792) sgFlag792 = -14 := by - decide +kernel - -lemma sg792 : RowSquare [3,3,2,1,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [3,3,2,1,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB792 sgT792 sgFlag792 - change solveCompact 10 (.full [5,5]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) - (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB792 sgT792) sgFlag792 ≠ 0 - rw [sgCert792] - norm_num - -def sgB796 : Equiv.Perm (Fin 10) := Equiv.swap 2 5 * (Equiv.swap 5 3 * (Equiv.swap 4 1 * (Equiv.swap 3 7 * (Equiv.swap 2 6 * (Equiv.swap 1 9 * (Equiv.swap 0 8)))))) -def sgT796 : Equiv.Perm (Fin 10) := Equiv.swap 5 9 * (Equiv.swap 6 4 * (Equiv.swap 5 2 * (Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 2 7 * (Equiv.swap 0 8 * (Equiv.swap 0 1))))))) -def sgFlag796 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(4,0,2),(0,1,1),(3,1,1),(4,1,2),(2,2,0)} -lemma sgCert796 : solveCompact 10 (.full [5,5]) (.full [3,3,2,2]) (.full [3,3,2,2]) - (certificateEdges [3,3,2,2] [3,3,2,2] [5,5] (Equiv.refl (Fin 10)) sgB796 sgT796) sgFlag796 = 15 := by - decide +kernel - -lemma sg796 : RowSquare [3,3,2,2] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [3,3,2,2]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB796 sgT796 sgFlag796 - change solveCompact 10 (.full [5,5]) (.full [3,3,2,2]) (.full [3,3,2,2]) - (certificateEdges [3,3,2,2] [3,3,2,2] [5,5] (Equiv.refl (Fin 10)) sgB796 sgT796) sgFlag796 ≠ 0 - rw [sgCert796] - norm_num - -def sgB808 : Equiv.Perm (Fin 10) := Equiv.swap 4 3 * (Equiv.swap 3 2 * (Equiv.swap 4 7 * (Equiv.swap 4 5 * (Equiv.swap 3 0 * (Equiv.swap 2 9 * (Equiv.swap 1 8 * (Equiv.swap 0 6))))))) -def sgT808 : Equiv.Perm (Fin 10) := Equiv.swap 5 3 * (Equiv.swap 5 7 * (Equiv.swap 3 8 * (Equiv.swap 3 1 * (Equiv.swap 2 6 * (Equiv.swap 1 4))))) -def sgFlag808 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(2,0,1),(5,0,1),(2,0,2),(3,0,3),(1,1,0),(4,1,0),(0,2,0),(1,3,0)} -lemma sgCert808 : solveCompact 10 (.full [6,4]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB808 sgT808) sgFlag808 = 216 := by - decide +kernel - -lemma sg808 : RowSquare [4,2,1,1,1,1] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB808 sgT808 sgFlag808 - change solveCompact 10 (.full [6,4]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB808 sgT808) sgFlag808 ≠ 0 - rw [sgCert808] - norm_num - -def sgB809 : Equiv.Perm (Fin 10) := Equiv.swap 1 5 * (Equiv.swap 5 9 * (Equiv.swap 2 7 * (Equiv.swap 2 4 * (Equiv.swap 1 6 * (Equiv.swap 0 3))))) -def sgT809 : Equiv.Perm (Fin 10) := Equiv.swap 5 9 * (Equiv.swap 6 0 * (Equiv.swap 5 1 * (Equiv.swap 1 3 * (Equiv.swap 3 2 * (Equiv.swap 2 8 * (Equiv.swap 1 4 * (Equiv.swap 0 7))))))) -def sgFlag809 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(4,0,0),(0,0,1),(1,0,2),(2,0,3),(1,1,0),(4,1,0),(3,2,0),(2,3,0)} -lemma sgCert809 : solveCompact 10 (.full [5,5]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB809 sgT809) sgFlag809 = -40 := by - decide +kernel - -lemma sg809 : RowSquare [4,2,1,1,1,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB809 sgT809 sgFlag809 - change solveCompact 10 (.full [5,5]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB809 sgT809) sgFlag809 ≠ 0 - rw [sgCert809] - norm_num - -def sgB814 : Equiv.Perm (Fin 10) := Equiv.swap 3 1 * (Equiv.swap 3 4 * (Equiv.swap 2 9 * (Equiv.swap 1 0 * (Equiv.swap 0 6)))) -def sgT814 : Equiv.Perm (Fin 10) := Equiv.swap 0 4 * (Equiv.swap 4 7 * (Equiv.swap 1 5 * (Equiv.swap 1 3 * (Equiv.swap 0 6)))) -def sgFlag814 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(1,0,2),(4,0,3),(3,1,0),(1,1,1),(2,2,0),(5,3,0)} -lemma sgCert814 : solveCompact 10 (.full [6,2,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB814 sgT814) sgFlag814 = -6 := by - decide +kernel - -lemma sg814 : RowSquare [4,2,1,1,1,1] [3,3,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [6,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB814 sgT814 sgFlag814 - change solveCompact 10 (.full [6,2,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB814 sgT814) sgFlag814 ≠ 0 - rw [sgCert814] - norm_num - -def sgB816 : Equiv.Perm (Fin 10) := Equiv.swap 8 0 * (Equiv.swap 4 7 * (Equiv.swap 4 3 * (Equiv.swap 3 5 * (Equiv.swap 2 6 * (Equiv.swap 0 9 * (Equiv.swap 0 1)))))) -def sgT816 : Equiv.Perm (Fin 10) := Equiv.swap 7 8 * (Equiv.swap 3 1 * (Equiv.swap 1 9 * (Equiv.swap 3 5 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))) -def sgFlag816 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(2,0,1),(0,0,2),(1,0,3),(0,1,0),(1,1,0),(2,2,0),(1,3,1)} -lemma sgCert816 : solveCompact 10 (.full [4,4,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB816 sgT816) sgFlag816 = 4 := by - decide +kernel - -lemma sg816 : RowSquare [4,2,1,1,1,1] [3,3,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [4,4,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB816 sgT816 sgFlag816 - change solveCompact 10 (.full [4,4,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB816 sgT816) sgFlag816 ≠ 0 - rw [sgCert816] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Semigroup Leaves 3. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB551 : Equiv.Perm (Fin 9) := Equiv.swap 6 2 * (Equiv.swap 4 8 * (Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 0 5)))))) +def sgT551 : Equiv.Perm (Fin 9) := Equiv.swap 3 1 * (Equiv.swap 1 0 * (Equiv.swap 2 7 * (Equiv.swap 3 6 * (Equiv.swap 2 4 * (Equiv.swap 1 5 * (Equiv.swap 0 8)))))) +def sgFlag551 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(3,0,1),(1,0,2),(2,0,3),(0,1,0),(2,1,0),(0,1,1),(4,2,1),(1,3,0)} +lemma sgCert551 : solveCompact 9 (.full [5,4]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [5,4] (Equiv.refl (Fin 9)) sgB551 sgT551) sgFlag551 = -3 := by + decide +kernel + +lemma sg551 : RowSquare [4,2,2,1] [2,2,2,2,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [5,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB551 sgT551 sgFlag551 + change solveCompact 9 (.full [5,4]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [5,4] (Equiv.refl (Fin 9)) sgB551 sgT551) sgFlag551 ≠ 0 + rw [sgCert551] + norm_num + +def sgB552 : Equiv.Perm (Fin 9) := Equiv.swap 0 2 * (Equiv.swap 0 1 * (Equiv.swap 1 7 * (Equiv.swap 2 8 * (Equiv.swap 2 4 * (Equiv.swap 1 5 * (Equiv.swap 0 6)))))) +def sgT552 : Equiv.Perm (Fin 9) := Equiv.swap 1 5 * (Equiv.swap 5 8 * (Equiv.swap 5 4 * (Equiv.swap 4 0 * (Equiv.swap 1 7 * (Equiv.swap 0 6))))) +def sgFlag552 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(0,1,1),(4,1,1),(0,1,2),(2,2,0),(3,3,3)} +lemma sgCert552 : solveCompact 9 (.full [5,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [5,2,2] (Equiv.refl (Fin 9)) sgB552 sgT552) sgFlag552 = -1 := by + decide +kernel + +lemma sg552 : RowSquare [4,2,2,1] [3,3,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [5,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB552 sgT552 sgFlag552 + change solveCompact 9 (.full [5,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [5,2,2] (Equiv.refl (Fin 9)) sgB552 sgT552) sgFlag552 ≠ 0 + rw [sgCert552] + norm_num + +def sgB553 : Equiv.Perm (Fin 9) := Equiv.swap 7 0 * (Equiv.swap 4 1 * (Equiv.swap 1 2 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 8))))) +def sgT553 : Equiv.Perm (Fin 9) := Equiv.swap 1 3 * (Equiv.swap 1 7 * (Equiv.swap 4 5 * (Equiv.swap 3 2 * (Equiv.swap 2 8 * (Equiv.swap 1 6))))) +def sgFlag553 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(0,1,0),(3,1,0),(2,1,3),(1,2,1),(2,3,2)} +lemma sgCert553 : solveCompact 9 (.full [4,3,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [4,3,2] (Equiv.refl (Fin 9)) sgB553 sgT553) sgFlag553 = 5 := by + decide +kernel + +lemma sg553 : RowSquare [4,2,2,1] [3,3,2,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [4,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB553 sgT553 sgFlag553 + change solveCompact 9 (.full [4,3,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [4,3,2] (Equiv.refl (Fin 9)) sgB553 sgT553) sgFlag553 ≠ 0 + rw [sgCert553] + norm_num + +def sgB559 : Equiv.Perm (Fin 9) := Equiv.swap 0 4 * (Equiv.swap 5 3 * (Equiv.swap 4 2 * (Equiv.swap 3 8 * (Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 0 6)))))) +def sgT559 : Equiv.Perm (Fin 9) := Equiv.swap 6 5 * (Equiv.swap 5 0 * (Equiv.swap 1 8 * (Equiv.swap 1 4 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))) +def sgFlag559 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(1,0,2),(1,1,0),(0,1,1),(0,1,3),(2,2,1),(1,3,0)} +lemma sgCert559 : solveCompact 9 (.full [3,2,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [3,2,2,2] (Equiv.refl (Fin 9)) sgB559 sgT559) sgFlag559 = 12 := by + decide +kernel + +lemma sg559 : RowSquare [4,2,2,1] [4,4,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [3,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB559 sgT559 sgFlag559 + change solveCompact 9 (.full [3,2,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [3,2,2,2] (Equiv.refl (Fin 9)) sgB559 sgT559) sgFlag559 ≠ 0 + rw [sgCert559] + norm_num + +def sgB561 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 1 8 * (Equiv.swap 2 4 * (Equiv.swap 4 0 * (Equiv.swap 1 6 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))))) +def sgT561 : Equiv.Perm (Fin 9) := Equiv.swap 6 4 * (Equiv.swap 4 0 * (Equiv.swap 2 1 * (Equiv.swap 1 5 * (Equiv.swap 0 8)))) +def sgFlag561 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,0),(0,0,1),(6,0,2),(2,1,0),(7,1,1),(5,1,3),(1,2,1),(3,3,0)} +lemma sgCert561 : solveCompact 9 (.full [8,1]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [8,1] (Equiv.refl (Fin 9)) sgB561 sgT561) sgFlag561 = 28 := by + decide +kernel + +lemma sg561 : RowSquare [4,3,1,1] [2,1,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [8,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB561 sgT561 sgFlag561 + change solveCompact 9 (.full [8,1]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [8,1] (Equiv.refl (Fin 9)) sgB561 sgT561) sgFlag561 ≠ 0 + rw [sgCert561] + norm_num + +def sgB562 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 1 8 * (Equiv.swap 1 5 * (Equiv.swap 2 6 * (Equiv.swap 2 3 * (Equiv.swap 1 4))))) +def sgT562 : Equiv.Perm (Fin 9) := Equiv.swap 3 0 * (Equiv.swap 4 5 * (Equiv.swap 3 6 * (Equiv.swap 1 8 * (Equiv.swap 0 7)))) +def sgFlag562 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(5,0,1),(1,0,2),(1,1,0),(4,1,0),(3,1,1),(2,2,3),(6,3,0)} +lemma sgCert562 : solveCompact 9 (.full [7,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [7,2] (Equiv.refl (Fin 9)) sgB562 sgT562) sgFlag562 = 3 := by + decide +kernel + +lemma sg562 : RowSquare [4,3,1,1] [2,2,1,1,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [7,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB562 sgT562 sgFlag562 + change solveCompact 9 (.full [7,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [7,2] (Equiv.refl (Fin 9)) sgB562 sgT562) sgFlag562 ≠ 0 + rw [sgCert562] + norm_num + +def sgB563 : Equiv.Perm (Fin 9) := Equiv.swap 3 8 * (Equiv.swap 3 5 * (Equiv.swap 5 2 * (Equiv.swap 2 7 * (Equiv.swap 3 0 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))))) +def sgT563 : Equiv.Perm (Fin 9) := Equiv.swap 3 6 * (Equiv.swap 6 1 * (Equiv.swap 3 4 * (Equiv.swap 4 7 * (Equiv.swap 3 5 * (Equiv.swap 1 8 * (Equiv.swap 1 0 * (Equiv.swap 0 2))))))) +def sgFlag563 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(1,0,1),(3,0,3),(0,1,0),(4,1,2),(2,2,1),(5,3,0)} +lemma sgCert563 : solveCompact 9 (.full [6,3]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [6,3] (Equiv.refl (Fin 9)) sgB563 sgT563) sgFlag563 = 9 := by + decide +kernel + +lemma sg563 : RowSquare [4,3,1,1] [2,2,2,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [6,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB563 sgT563 sgFlag563 + change solveCompact 9 (.full [6,3]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [6,3] (Equiv.refl (Fin 9)) sgB563 sgT563) sgFlag563 ≠ 0 + rw [sgCert563] + norm_num + +def sgB564 : Equiv.Perm (Fin 9) := Equiv.swap 5 8 * (Equiv.swap 3 2 * (Equiv.swap 3 0 * (Equiv.swap 2 6 * (Equiv.swap 1 7 * (Equiv.swap 0 4))))) +def sgT564 : Equiv.Perm (Fin 9) := Equiv.swap 5 1 * (Equiv.swap 3 4 * (Equiv.swap 1 8 * (Equiv.swap 1 2 * (Equiv.swap 0 6)))) +def sgFlag564 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(3,0,2),(0,0,3),(1,1,0),(2,1,1),(3,2,0),(4,3,0)} +lemma sgCert564 : solveCompact 9 (.full [5,4]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [5,4] (Equiv.refl (Fin 9)) sgB564 sgT564) sgFlag564 = 7 := by + decide +kernel + +lemma sg564 : RowSquare [4,3,1,1] [2,2,2,2,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [5,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB564 sgT564 sgFlag564 + change solveCompact 9 (.full [5,4]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [5,4] (Equiv.refl (Fin 9)) sgB564 sgT564) sgFlag564 ≠ 0 + rw [sgCert564] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB565 : Equiv.Perm (Fin 9) := Equiv.swap 1 0 * (Equiv.swap 0 8 * (Equiv.swap 1 7 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 6))))) +def sgT565 : Equiv.Perm (Fin 9) := Equiv.swap 3 6 * (Equiv.swap 6 5 * (Equiv.swap 5 4 * (Equiv.swap 4 8 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 7))))))) +def sgFlag565 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(5,0,0),(3,0,1),(6,1,0),(4,1,2),(0,1,3),(1,2,1),(2,3,1)} +lemma sgCert565 : solveCompact 9 (.full [7,1,1]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [7,1,1] (Equiv.refl (Fin 9)) sgB565 sgT565) sgFlag565 = 20 := by + decide +kernel + +lemma sg565 : RowSquare [4,3,1,1] [3,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [7,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB565 sgT565 sgFlag565 + change solveCompact 9 (.full [7,1,1]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [7,1,1] (Equiv.refl (Fin 9)) sgB565 sgT565) sgFlag565 ≠ 0 + rw [sgCert565] + norm_num + +def sgB569 : Equiv.Perm (Fin 9) := Equiv.swap 0 3 * (Equiv.swap 3 8 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 5 * (Equiv.swap 0 7))))) +def sgT569 : Equiv.Perm (Fin 9) := Equiv.swap 0 1 * (Equiv.swap 0 2 * (Equiv.swap 1 7 * (Equiv.swap 2 6 * (Equiv.swap 1 4 * (Equiv.swap 0 5))))) +def sgFlag569 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(0,0,2),(2,1,0),(4,1,1),(0,1,3),(1,2,1),(3,3,0)} +lemma sgCert569 : solveCompact 9 (.full [5,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [5,2,2] (Equiv.refl (Fin 9)) sgB569 sgT569) sgFlag569 = 10 := by + decide +kernel + +lemma sg569 : RowSquare [4,3,1,1] [3,3,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [5,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB569 sgT569 sgFlag569 + change solveCompact 9 (.full [5,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [5,2,2] (Equiv.refl (Fin 9)) sgB569 sgT569) sgFlag569 ≠ 0 + rw [sgCert569] + norm_num + +def sgB570 : Equiv.Perm (Fin 9) := Equiv.swap 4 1 * (Equiv.swap 3 7 * (Equiv.swap 1 5 * (Equiv.swap 1 2 * (Equiv.swap 0 8)))) +def sgT570 : Equiv.Perm (Fin 9) := Equiv.swap 5 3 * (Equiv.swap 3 0 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 0 6)))) +def sgFlag570 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(0,0,1),(3,1,0),(1,1,2),(0,1,3),(0,2,1),(2,3,1)} +lemma sgCert570 : solveCompact 9 (.full [4,3,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [4,3,2] (Equiv.refl (Fin 9)) sgB570 sgT570) sgFlag570 = -1 := by + decide +kernel + +lemma sg570 : RowSquare [4,3,1,1] [3,3,2,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [4,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB570 sgT570 sgFlag570 + change solveCompact 9 (.full [4,3,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [4,3,2] (Equiv.refl (Fin 9)) sgB570 sgT570) sgFlag570 ≠ 0 + rw [sgCert570] + norm_num + +def sgB575 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 1 8 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 1 5 * (Equiv.swap 0 6))))) +def sgT575 : Equiv.Perm (Fin 9) := Equiv.swap 3 2 * (Equiv.swap 2 7 * (Equiv.swap 0 8 * (Equiv.swap 3 6 * (Equiv.swap 2 1 * (Equiv.swap 1 5 * (Equiv.swap 0 4)))))) +def sgFlag575 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,0,2),(0,1,0),(0,1,1),(1,2,0),(1,3,3)} +lemma sgCert575 : solveCompact 9 (.full [3,2,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [3,2,2,2] (Equiv.refl (Fin 9)) sgB575 sgT575) sgFlag575 = 2 := by + decide +kernel + +lemma sg575 : RowSquare [4,3,1,1] [4,4,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,2,1]) (ts := [3,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB575 sgT575 sgFlag575 + change solveCompact 9 (.full [3,2,2,2]) (.full [4,2,2,1]) (.full [4,2,2,1]) + (certificateEdges [4,2,2,1] [4,2,2,1] [3,2,2,2] (Equiv.refl (Fin 9)) sgB575 sgT575) sgFlag575 ≠ 0 + rw [sgCert575] + norm_num + +def sgB577 : Equiv.Perm (Fin 9) := Equiv.swap 6 5 * (Equiv.swap 5 3 * (Equiv.swap 3 0 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 0 8 * (Equiv.swap 0 1)))))) +def sgT577 : Equiv.Perm (Fin 9) := Equiv.swap 4 0 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 0 7 * (Equiv.swap 0 1)))) +def sgFlag577 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(1,0,1),(1,0,2),(2,0,2),(0,1,0),(4,1,1),(5,2,0),(6,2,1)} +lemma sgCert577 : solveCompact 9 (.full [7,2]) (.full [3,3,2,1]) (.full [3,3,2,1]) + (certificateEdges [3,3,2,1] [3,3,2,1] [7,2] (Equiv.refl (Fin 9)) sgB577 sgT577) sgFlag577 = 30 := by + decide +kernel + +lemma sg577 : RowSquare [4,3,2] [2,2,1,1,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [3,3,2,1]) (ts := [7,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB577 sgT577 sgFlag577 + change solveCompact 9 (.full [7,2]) (.full [3,3,2,1]) (.full [3,3,2,1]) + (certificateEdges [3,3,2,1] [3,3,2,1] [7,2] (Equiv.refl (Fin 9)) sgB577 sgT577) sgFlag577 ≠ 0 + rw [sgCert577] + norm_num + +def sgB578 : Equiv.Perm (Fin 9) := Equiv.swap 3 8 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 6 * (Equiv.swap 0 5)))) +def sgT578 : Equiv.Perm (Fin 9) := Equiv.swap 3 5 * (Equiv.swap 5 1 * (Equiv.swap 3 6 * (Equiv.swap 3 4 * (Equiv.swap 0 8 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))) +def sgFlag578 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,1),(2,0,2),(2,1,1),(3,1,1),(1,1,2),(1,2,0),(3,2,0)} +lemma sgCert578 : solveCompact 9 (.full [5,4]) (.full [3,3,2,1]) (.full [3,3,2,1]) + (certificateEdges [3,3,2,1] [3,3,2,1] [5,4] (Equiv.refl (Fin 9)) sgB578 sgT578) sgFlag578 = 11 := by + decide +kernel + +lemma sg578 : RowSquare [4,3,2] [2,2,2,2,1] := by + apply rowSquare_compact (n := 9) (cs := [3,3,2,1]) (ts := [5,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB578 sgT578 sgFlag578 + change solveCompact 9 (.full [5,4]) (.full [3,3,2,1]) (.full [3,3,2,1]) + (certificateEdges [3,3,2,1] [3,3,2,1] [5,4] (Equiv.refl (Fin 9)) sgB578 sgT578) sgFlag578 ≠ 0 + rw [sgCert578] + norm_num + +def sgB579 : Equiv.Perm (Fin 9) := Equiv.swap 6 4 * (Equiv.swap 4 7 * (Equiv.swap 4 5 * (Equiv.swap 2 1 * (Equiv.swap 2 0 * (Equiv.swap 1 8 * (Equiv.swap 0 3)))))) +def sgT579 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 2 3 * (Equiv.swap 1 8 * (Equiv.swap 0 6))))) +def sgFlag579 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(5,0,0),(1,0,1),(4,0,1),(0,1,0),(1,1,1),(2,1,1),(2,1,2),(3,2,0)} +lemma sgCert579 : solveCompact 9 (.full [6,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [6,3] (Equiv.refl (Fin 9)) sgB579 sgT579) sgFlag579 = 18 := by + decide +kernel + +lemma sg579 : RowSquare [4,4,1] [2,2,2,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [6,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB579 sgT579 sgFlag579 + change solveCompact 9 (.full [6,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [6,3] (Equiv.refl (Fin 9)) sgB579 sgT579) sgFlag579 ≠ 0 + rw [sgCert579] + norm_num + +def sgB580 : Equiv.Perm (Fin 9) := Equiv.swap 5 6 * (Equiv.swap 4 0 * (Equiv.swap 0 7 * (Equiv.swap 0 3 * (Equiv.swap 1 8 * (Equiv.swap 0 2))))) +def sgT580 : Equiv.Perm (Fin 9) := Equiv.swap 6 5 * (Equiv.swap 6 7 * (Equiv.swap 5 0 * (Equiv.swap 0 2 * (Equiv.swap 2 8 * (Equiv.swap 2 3 * (Equiv.swap 0 4)))))) +def sgFlag580 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,1),(4,0,2),(2,1,0),(1,1,1),(3,2,0)} +lemma sgCert580 : solveCompact 9 (.full [5,4]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [5,4] (Equiv.refl (Fin 9)) sgB580 sgT580) sgFlag580 = 6 := by + decide +kernel + +lemma sg580 : RowSquare [4,4,1] [2,2,2,2,1] := by + apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [5,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB580 sgT580 sgFlag580 + change solveCompact 9 (.full [5,4]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [5,4] (Equiv.refl (Fin 9)) sgB580 sgT580) sgFlag580 ≠ 0 + rw [sgCert580] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB581 : Equiv.Perm (Fin 9) := Equiv.swap 2 7 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 0 4))) +def sgT581 : Equiv.Perm (Fin 9) := Equiv.swap 0 4 * (Equiv.swap 0 3 * (Equiv.swap 3 7 * (Equiv.swap 4 8 * (Equiv.swap 3 5 * (Equiv.swap 0 1 * (Equiv.swap 1 6 * (Equiv.swap 0 2))))))) +def sgFlag581 : Finset (ℕ × ℕ × ℕ) := {(5,0,0),(1,0,1),(2,0,1),(4,0,2),(0,1,0),(3,1,0),(0,1,1),(1,2,1)} +lemma sgCert581 : solveCompact 9 (.full [6,2,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [6,2,1] (Equiv.refl (Fin 9)) sgB581 sgT581) sgFlag581 = 6 := by + decide +kernel + +lemma sg581 : RowSquare [4,4,1] [3,2,1,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [6,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB581 sgT581 sgFlag581 + change solveCompact 9 (.full [6,2,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [6,2,1] (Equiv.refl (Fin 9)) sgB581 sgT581) sgFlag581 ≠ 0 + rw [sgCert581] + norm_num + +def sgB582 : Equiv.Perm (Fin 9) := Equiv.swap 2 4 * (Equiv.swap 5 1 * (Equiv.swap 4 3 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 1 8 * (Equiv.swap 0 6)))))) +def sgT582 : Equiv.Perm (Fin 9) := Equiv.swap 1 3 * (Equiv.swap 3 8 * (Equiv.swap 3 2 * (Equiv.swap 2 5 * (Equiv.swap 1 7)))) +def sgFlag582 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(0,0,1),(3,0,2),(1,1,0),(4,1,0),(1,1,1),(2,1,1),(0,2,0)} +lemma sgCert582 : solveCompact 9 (.full [5,3,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [5,3,1] (Equiv.refl (Fin 9)) sgB582 sgT582) sgFlag582 = -2 := by + decide +kernel + +lemma sg582 : RowSquare [4,4,1] [3,2,2,1,1] := by + apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [5,3,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB582 sgT582 sgFlag582 + change solveCompact 9 (.full [5,3,1]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [5,3,1] (Equiv.refl (Fin 9)) sgB582 sgT582) sgFlag582 ≠ 0 + rw [sgCert582] + norm_num + +def sgB583 : Equiv.Perm (Fin 9) := Equiv.swap 4 8 * (Equiv.swap 4 5 * (Equiv.swap 5 0 * (Equiv.swap 4 6 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 7)))))) +def sgT583 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 1 8 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 4)))))) +def sgFlag583 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(0,0,1),(1,1,0),(1,1,1),(2,1,1),(3,1,2),(0,2,0)} +lemma sgCert583 : solveCompact 9 (.full [5,2,2]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [5,2,2] (Equiv.refl (Fin 9)) sgB583 sgT583) sgFlag583 = 4 := by + decide +kernel + +lemma sg583 : RowSquare [4,4,1] [3,3,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [5,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB583 sgT583 sgFlag583 + change solveCompact 9 (.full [5,2,2]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [5,2,2] (Equiv.refl (Fin 9)) sgB583 sgT583) sgFlag583 ≠ 0 + rw [sgCert583] + norm_num + +def sgB584 : Equiv.Perm (Fin 9) := Equiv.swap 7 5 * (Equiv.swap 5 4 * (Equiv.swap 5 2 * (Equiv.swap 4 8 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 6)))))) +def sgT584 : Equiv.Perm (Fin 9) := Equiv.swap 2 6 * (Equiv.swap 6 1 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 1 8 * (Equiv.swap 0 7))))) +def sgFlag584 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(2,0,2),(2,1,0),(1,1,1),(0,2,1)} +lemma sgCert584 : solveCompact 9 (.full [3,3,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [3,3,3] (Equiv.refl (Fin 9)) sgB584 sgT584) sgFlag584 = -5 := by + decide +kernel + +lemma sg584 : RowSquare [4,4,1] [3,3,3] := by + apply rowSquare_compact (n := 9) (cs := [3,2,2,2]) (ts := [3,3,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB584 sgT584 sgFlag584 + change solveCompact 9 (.full [3,3,3]) (.full [3,2,2,2]) (.full [3,2,2,2]) + (certificateEdges [3,2,2,2] [3,2,2,2] [3,3,3] (Equiv.refl (Fin 9)) sgB584 sgT584) sgFlag584 ≠ 0 + rw [sgCert584] + norm_num + +def sgB614 : Equiv.Perm (Fin 9) := Equiv.swap 5 3 * (Equiv.swap 5 4 * (Equiv.swap 4 2 * (Equiv.swap 3 1 * (Equiv.swap 2 0 * (Equiv.swap 1 8 * (Equiv.swap 0 7)))))) +def sgT614 : Equiv.Perm (Fin 9) := Equiv.swap 6 2 * (Equiv.swap 6 7 * (Equiv.swap 4 5 * (Equiv.swap 2 8))) +def sgFlag614 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(6,0,1),(5,0,2),(2,0,3),(1,1,0),(4,1,0),(1,2,0),(3,3,1)} +lemma sgCert614 : solveCompact 9 (.full [7,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [7,2] (Equiv.refl (Fin 9)) sgB614 sgT614) sgFlag614 = -4 := by + decide +kernel + +lemma sg614 : RowSquare [5,2,1,1] [2,2,1,1,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [7,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB614 sgT614 sgFlag614 + change solveCompact 9 (.full [7,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [7,2] (Equiv.refl (Fin 9)) sgB614 sgT614) sgFlag614 ≠ 0 + rw [sgCert614] + norm_num + +def sgB615 : Equiv.Perm (Fin 9) := Equiv.swap 0 5 * (Equiv.swap 0 7 * (Equiv.swap 5 8 * (Equiv.swap 0 6 * (Equiv.swap 2 4 * (Equiv.swap 0 3))))) +def sgT615 : Equiv.Perm (Fin 9) := Equiv.swap 3 4 * (Equiv.swap 4 1 * (Equiv.swap 4 5 * (Equiv.swap 3 0 * (Equiv.swap 1 8 * (Equiv.swap 1 2 * (Equiv.swap 0 7)))))) +def sgFlag615 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(4,0,1),(5,0,2),(1,0,3),(1,1,0),(2,1,1),(2,2,0),(0,3,0)} +lemma sgCert615 : solveCompact 9 (.full [6,3]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB615 sgT615) sgFlag615 = 13 := by + decide +kernel + +lemma sg615 : RowSquare [5,2,1,1] [2,2,2,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [6,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB615 sgT615 sgFlag615 + change solveCompact 9 (.full [6,3]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB615 sgT615) sgFlag615 ≠ 0 + rw [sgCert615] + norm_num + +def sgB616 : Equiv.Perm (Fin 9) := Equiv.swap 2 7 * (Equiv.swap 5 8 * (Equiv.swap 2 1 * (Equiv.swap 2 4 * (Equiv.swap 2 0 * (Equiv.swap 1 6 * (Equiv.swap 0 3)))))) +def sgT616 : Equiv.Perm (Fin 9) := Equiv.swap 4 6 * (Equiv.swap 4 5 * (Equiv.swap 0 8 * (Equiv.swap 2 7 * (Equiv.swap 0 3 * (Equiv.swap 0 1))))) +def sgFlag616 : Finset (ℕ × ℕ × ℕ) := {(4,0,0),(0,0,1),(2,0,2),(1,0,3),(1,1,0),(3,1,0),(2,2,0),(3,3,0)} +lemma sgCert616 : solveCompact 9 (.full [5,4]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB616 sgT616) sgFlag616 = 12 := by + decide +kernel + +lemma sg616 : RowSquare [5,2,1,1] [2,2,2,2,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [5,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB616 sgT616 sgFlag616 + change solveCompact 9 (.full [5,4]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB616 sgT616) sgFlag616 ≠ 0 + rw [sgCert616] + norm_num + +def sgB621 : Equiv.Perm (Fin 9) := Equiv.swap 3 8 * (Equiv.swap 3 1 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 6 * (Equiv.swap 0 5))))) +def sgT621 : Equiv.Perm (Fin 9) := Equiv.swap 5 4 * (Equiv.swap 5 6 * (Equiv.swap 4 7 * (Equiv.swap 3 0 * (Equiv.swap 0 8 * (Equiv.swap 0 2 * (Equiv.swap 0 1)))))) +def sgFlag621 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,0),(0,0,1),(1,0,1),(3,0,3),(1,1,0),(2,1,0),(1,2,0),(0,3,2)} +lemma sgCert621 : solveCompact 9 (.full [5,2,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,2,2] (Equiv.refl (Fin 9)) sgB621 sgT621) sgFlag621 = -1 := by + decide +kernel + +lemma sg621 : RowSquare [5,2,1,1] [3,3,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [4,2,1,1,1]) (ts := [5,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB621 sgT621 sgFlag621 + change solveCompact 9 (.full [5,2,2]) (.full [4,2,1,1,1]) (.full [4,2,1,1,1]) + (certificateEdges [4,2,1,1,1] [4,2,1,1,1] [5,2,2] (Equiv.refl (Fin 9)) sgB621 sgT621) sgFlag621 ≠ 0 + rw [sgCert621] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB636 : Equiv.Perm (Fin 9) := Equiv.swap 5 1 * (Equiv.swap 5 7 * (Equiv.swap 5 6 * (Equiv.swap 1 0 * (Equiv.swap 0 8 * (Equiv.swap 1 4 * (Equiv.swap 0 2)))))) +def sgT636 : Equiv.Perm (Fin 9) := Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 3 7 * (Equiv.swap 2 5 * (Equiv.swap 1 4 * (Equiv.swap 0 8))))) +def sgFlag636 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(3,0,1),(2,0,2),(0,1,0),(4,1,1),(1,2,0),(5,2,0)} +lemma sgCert636 : solveCompact 9 (.full [6,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB636 sgT636) sgFlag636 = -6 := by + decide +kernel + +lemma sg636 : RowSquare [5,2,2] [2,2,2,1,1,1] := by + apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [6,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB636 sgT636 sgFlag636 + change solveCompact 9 (.full [6,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [6,3] (Equiv.refl (Fin 9)) sgB636 sgT636) sgFlag636 ≠ 0 + rw [sgCert636] + norm_num + +def sgB637 : Equiv.Perm (Fin 9) := Equiv.swap 4 2 * (Equiv.swap 5 7 * (Equiv.swap 4 1 * (Equiv.swap 2 0 * (Equiv.swap 1 6 * (Equiv.swap 0 8))))) +def sgT637 : Equiv.Perm (Fin 9) := Equiv.swap 3 0 * (Equiv.swap 0 8 * (Equiv.swap 3 7 * (Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 0 6))))) +def sgFlag637 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(3,0,1),(0,0,2),(3,0,2),(1,1,0),(0,1,1),(2,2,0)} +lemma sgCert637 : solveCompact 9 (.full [5,4]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB637 sgT637) sgFlag637 = 24 := by + decide +kernel + +lemma sg637 : RowSquare [5,2,2] [2,2,2,2,1] := by + apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [5,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB637 sgT637 sgFlag637 + change solveCompact 9 (.full [5,4]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [5,4] (Equiv.refl (Fin 9)) sgB637 sgT637) sgFlag637 ≠ 0 + rw [sgCert637] + norm_num + +def sgB640 : Equiv.Perm (Fin 9) := Equiv.swap 5 8 * (Equiv.swap 5 3 * (Equiv.swap 5 1 * (Equiv.swap 3 7 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 0 * (Equiv.swap 0 6))))))) +def sgT640 : Equiv.Perm (Fin 9) := Equiv.swap 6 0 * (Equiv.swap 5 7 * (Equiv.swap 0 8 * (Equiv.swap 2 3 * (Equiv.swap 0 4)))) +def sgFlag640 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,2),(1,1,0),(0,2,1),(3,2,1)} +lemma sgCert640 : solveCompact 9 (.full [4,3,2]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [4,3,2] (Equiv.refl (Fin 9)) sgB640 sgT640) sgFlag640 = -1 := by + decide +kernel + +lemma sg640 : RowSquare [5,2,2] [3,3,2,1] := by + apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [4,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB640 sgT640 sgFlag640 + change solveCompact 9 (.full [4,3,2]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [4,3,2] (Equiv.refl (Fin 9)) sgB640 sgT640) sgFlag640 ≠ 0 + rw [sgCert640] + norm_num + +def sgB641 : Equiv.Perm (Fin 9) := Equiv.swap 4 1 * (Equiv.swap 1 8 * (Equiv.swap 4 2 * (Equiv.swap 2 6 * (Equiv.swap 2 3 * (Equiv.swap 1 5))))) +def sgT641 : Equiv.Perm (Fin 9) := Equiv.swap 5 2 * (Equiv.swap 4 3 * (Equiv.swap 3 7 * (Equiv.swap 2 0 * (Equiv.swap 0 6 * (Equiv.swap 0 1))))) +def sgFlag641 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,1,2),(0,2,0),(2,2,0)} +lemma sgCert641 : solveCompact 9 (.full [3,3,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [3,3,3] (Equiv.refl (Fin 9)) sgB641 sgT641) sgFlag641 = 4 := by + decide +kernel + +lemma sg641 : RowSquare [5,2,2] [3,3,3] := by + apply rowSquare_compact (n := 9) (cs := [3,3,1,1,1]) (ts := [3,3,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB641 sgT641 sgFlag641 + change solveCompact 9 (.full [3,3,3]) (.full [3,3,1,1,1]) (.full [3,3,1,1,1]) + (certificateEdges [3,3,1,1,1] [3,3,1,1,1] [3,3,3] (Equiv.refl (Fin 9)) sgB641 sgT641) sgFlag641 ≠ 0 + rw [sgCert641] + norm_num + +def sgB759 : Equiv.Perm (Fin 10) := Equiv.swap 4 9 * (Equiv.swap 4 0 * (Equiv.swap 4 1 * (Equiv.swap 0 7 * (Equiv.swap 0 3 * (Equiv.swap 1 5 * (Equiv.swap 0 2)))))) +def sgT759 : Equiv.Perm (Fin 10) := Equiv.swap 4 9 * (Equiv.swap 6 2 * (Equiv.swap 2 8 * (Equiv.swap 4 7 * (Equiv.swap 2 5)))) +def sgFlag759 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(4,0,0),(4,0,1),(0,0,2),(1,1,0),(1,1,1),(2,1,1),(0,2,0)} +lemma sgCert759 : solveCompact 10 (.full [5,5]) (.full [3,2,2,2,1]) (.full [3,2,2,2,1]) + (certificateEdges [3,2,2,2,1] [3,2,2,2,1] [5,5] (Equiv.refl (Fin 10)) sgB759 sgT759) sgFlag759 = -9 := by + decide +kernel + +lemma sg759 : RowSquare [3,2,2,2,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [3,2,2,2,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB759 sgT759 sgFlag759 + change solveCompact 10 (.full [5,5]) (.full [3,2,2,2,1]) (.full [3,2,2,2,1]) + (certificateEdges [3,2,2,2,1] [3,2,2,2,1] [5,5] (Equiv.refl (Fin 10)) sgB759 sgT759) sgFlag759 ≠ 0 + rw [sgCert759] + norm_num + +def sgB765 : Equiv.Perm (Fin 10) := Equiv.swap 2 1 * (Equiv.swap 2 7 * (Equiv.swap 5 9 * (Equiv.swap 2 3 * (Equiv.swap 3 6 * (Equiv.swap 2 4 * (Equiv.swap 1 0 * (Equiv.swap 0 8))))))) +def sgT765 : Equiv.Perm (Fin 10) := Equiv.swap 4 1 * (Equiv.swap 0 3 * (Equiv.swap 4 6 * (Equiv.swap 3 9 * (Equiv.swap 0 5 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))) +def sgFlag765 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(4,0,1),(0,0,2),(0,1,0),(1,1,0),(3,2,0),(5,2,1)} +lemma sgCert765 : solveCompact 10 (.full [6,2,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) + (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB765 sgT765) sgFlag765 = 2 := by + decide +kernel + +lemma sg765 : RowSquare [3,3,1,1,1,1] [3,3,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [3,3,1,1,1,1]) (ts := [6,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB765 sgT765 sgFlag765 + change solveCompact 10 (.full [6,2,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) + (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB765 sgT765) sgFlag765 ≠ 0 + rw [sgCert765] + norm_num + +def sgB767 : Equiv.Perm (Fin 10) := Equiv.swap 6 5 * (Equiv.swap 6 1 * (Equiv.swap 5 3 * (Equiv.swap 3 0 * (Equiv.swap 0 9 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))) +def sgT767 : Equiv.Perm (Fin 10) := Equiv.swap 2 5 * (Equiv.swap 5 9 * (Equiv.swap 2 6 * (Equiv.swap 2 4 * (Equiv.swap 2 0 * (Equiv.swap 0 3))))) +def sgFlag767 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(1,0,1),(3,0,2),(1,1,0),(2,1,1),(0,2,0),(1,2,0)} +lemma sgCert767 : solveCompact 10 (.full [4,4,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) + (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB767 sgT767) sgFlag767 = 10 := by + decide +kernel + +lemma sg767 : RowSquare [3,3,1,1,1,1] [3,3,2,2] := by + apply rowSquare_compact (n := 10) (cs := [3,3,1,1,1,1]) (ts := [4,4,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB767 sgT767 sgFlag767 + change solveCompact 10 (.full [4,4,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) + (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB767 sgT767) sgFlag767 ≠ 0 + rw [sgCert767] + norm_num + +def sgB768 : Equiv.Perm (Fin 10) := Equiv.swap 4 6 * (Equiv.swap 6 2 * (Equiv.swap 6 7 * (Equiv.swap 2 0 * (Equiv.swap 4 1 * (Equiv.swap 2 5 * (Equiv.swap 2 3 * (Equiv.swap 1 8 * (Equiv.swap 0 9)))))))) +def sgT768 : Equiv.Perm (Fin 10) := Equiv.swap 8 6 * (Equiv.swap 6 9 * (Equiv.swap 0 7 * (Equiv.swap 0 4 * (Equiv.swap 1 2 * (Equiv.swap 0 3))))) +def sgFlag768 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(3,0,0),(1,0,1),(0,0,2),(2,1,0),(0,1,1),(1,2,0)} +lemma sgCert768 : solveCompact 10 (.full [4,3,3]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) + (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB768 sgT768) sgFlag768 = -16 := by + decide +kernel + +lemma sg768 : RowSquare [3,3,1,1,1,1] [3,3,3,1] := by + apply rowSquare_compact (n := 10) (cs := [3,3,1,1,1,1]) (ts := [4,3,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB768 sgT768 sgFlag768 + change solveCompact 10 (.full [4,3,3]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) + (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB768 sgT768) sgFlag768 ≠ 0 + rw [sgCert768] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB790 : Equiv.Perm (Fin 10) := Equiv.swap 3 6 * (Equiv.swap 6 4 * (Equiv.swap 5 0 * (Equiv.swap 4 2 * (Equiv.swap 3 7 * (Equiv.swap 2 8 * (Equiv.swap 0 9)))))) +def sgT790 : Equiv.Perm (Fin 10) := Equiv.swap 4 3 * (Equiv.swap 4 1 * (Equiv.swap 5 7 * (Equiv.swap 4 6 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 1 8 * (Equiv.swap 0 9))))))) +def sgFlag790 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(3,0,0),(1,0,1),(2,0,1),(4,0,2),(5,1,0),(1,1,1),(6,1,2),(0,2,0)} +lemma sgCert790 : solveCompact 10 (.full [7,3]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) + (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB790 sgT790) sgFlag790 = 24 := by + decide +kernel + +lemma sg790 : RowSquare [3,3,2,1,1] [2,2,2,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [3,3,2,1,1]) (ts := [7,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB790 sgT790 sgFlag790 + change solveCompact 10 (.full [7,3]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) + (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB790 sgT790) sgFlag790 ≠ 0 + rw [sgCert790] + norm_num + +def sgB791 : Equiv.Perm (Fin 10) := Equiv.swap 3 0 * (Equiv.swap 0 9 * (Equiv.swap 3 1 * (Equiv.swap 0 7 * (Equiv.swap 3 2 * (Equiv.swap 2 6 * (Equiv.swap 1 8 * (Equiv.swap 0 4))))))) +def sgT791 : Equiv.Perm (Fin 10) := Equiv.swap 3 2 * (Equiv.swap 3 6 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 8 * (Equiv.swap 0 5))))) +def sgFlag791 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(2,0,1),(5,0,1),(4,0,2),(1,1,0),(2,1,0),(0,1,1),(1,2,0),(0,2,2)} +lemma sgCert791 : solveCompact 10 (.full [6,4]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) + (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB791 sgT791) sgFlag791 = 33 := by + decide +kernel + +lemma sg791 : RowSquare [3,3,2,1,1] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [3,3,2,1,1]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB791 sgT791 sgFlag791 + change solveCompact 10 (.full [6,4]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) + (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB791 sgT791) sgFlag791 ≠ 0 + rw [sgCert791] + norm_num + +def sgB792 : Equiv.Perm (Fin 10) := Equiv.swap 3 8 * (Equiv.swap 6 4 * (Equiv.swap 4 0 * (Equiv.swap 4 5 * (Equiv.swap 3 7 * (Equiv.swap 0 9 * (Equiv.swap 0 2)))))) +def sgT792 : Equiv.Perm (Fin 10) := Equiv.swap 1 9 * (Equiv.swap 6 5 * (Equiv.swap 5 0 * (Equiv.swap 3 4 * (Equiv.swap 0 8 * (Equiv.swap 1 7 * (Equiv.swap 0 2)))))) +def sgFlag792 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(4,0,1),(2,0,2),(4,1,0),(2,1,1),(3,1,2),(0,2,0),(3,2,0)} +lemma sgCert792 : solveCompact 10 (.full [5,5]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) + (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB792 sgT792) sgFlag792 = -14 := by + decide +kernel + +lemma sg792 : RowSquare [3,3,2,1,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [3,3,2,1,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB792 sgT792 sgFlag792 + change solveCompact 10 (.full [5,5]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) + (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB792 sgT792) sgFlag792 ≠ 0 + rw [sgCert792] + norm_num + +def sgB796 : Equiv.Perm (Fin 10) := Equiv.swap 2 5 * (Equiv.swap 5 3 * (Equiv.swap 4 1 * (Equiv.swap 3 7 * (Equiv.swap 2 6 * (Equiv.swap 1 9 * (Equiv.swap 0 8)))))) +def sgT796 : Equiv.Perm (Fin 10) := Equiv.swap 5 9 * (Equiv.swap 6 4 * (Equiv.swap 5 2 * (Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 2 7 * (Equiv.swap 0 8 * (Equiv.swap 0 1))))))) +def sgFlag796 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(4,0,2),(0,1,1),(3,1,1),(4,1,2),(2,2,0)} +lemma sgCert796 : solveCompact 10 (.full [5,5]) (.full [3,3,2,2]) (.full [3,3,2,2]) + (certificateEdges [3,3,2,2] [3,3,2,2] [5,5] (Equiv.refl (Fin 10)) sgB796 sgT796) sgFlag796 = 15 := by + decide +kernel + +lemma sg796 : RowSquare [3,3,2,2] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [3,3,2,2]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB796 sgT796 sgFlag796 + change solveCompact 10 (.full [5,5]) (.full [3,3,2,2]) (.full [3,3,2,2]) + (certificateEdges [3,3,2,2] [3,3,2,2] [5,5] (Equiv.refl (Fin 10)) sgB796 sgT796) sgFlag796 ≠ 0 + rw [sgCert796] + norm_num + +def sgB808 : Equiv.Perm (Fin 10) := Equiv.swap 4 3 * (Equiv.swap 3 2 * (Equiv.swap 4 7 * (Equiv.swap 4 5 * (Equiv.swap 3 0 * (Equiv.swap 2 9 * (Equiv.swap 1 8 * (Equiv.swap 0 6))))))) +def sgT808 : Equiv.Perm (Fin 10) := Equiv.swap 5 3 * (Equiv.swap 5 7 * (Equiv.swap 3 8 * (Equiv.swap 3 1 * (Equiv.swap 2 6 * (Equiv.swap 1 4))))) +def sgFlag808 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(2,0,1),(5,0,1),(2,0,2),(3,0,3),(1,1,0),(4,1,0),(0,2,0),(1,3,0)} +lemma sgCert808 : solveCompact 10 (.full [6,4]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB808 sgT808) sgFlag808 = 216 := by + decide +kernel + +lemma sg808 : RowSquare [4,2,1,1,1,1] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB808 sgT808 sgFlag808 + change solveCompact 10 (.full [6,4]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB808 sgT808) sgFlag808 ≠ 0 + rw [sgCert808] + norm_num + +def sgB809 : Equiv.Perm (Fin 10) := Equiv.swap 1 5 * (Equiv.swap 5 9 * (Equiv.swap 2 7 * (Equiv.swap 2 4 * (Equiv.swap 1 6 * (Equiv.swap 0 3))))) +def sgT809 : Equiv.Perm (Fin 10) := Equiv.swap 5 9 * (Equiv.swap 6 0 * (Equiv.swap 5 1 * (Equiv.swap 1 3 * (Equiv.swap 3 2 * (Equiv.swap 2 8 * (Equiv.swap 1 4 * (Equiv.swap 0 7))))))) +def sgFlag809 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(4,0,0),(0,0,1),(1,0,2),(2,0,3),(1,1,0),(4,1,0),(3,2,0),(2,3,0)} +lemma sgCert809 : solveCompact 10 (.full [5,5]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB809 sgT809) sgFlag809 = -40 := by + decide +kernel + +lemma sg809 : RowSquare [4,2,1,1,1,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB809 sgT809 sgFlag809 + change solveCompact 10 (.full [5,5]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB809 sgT809) sgFlag809 ≠ 0 + rw [sgCert809] + norm_num + +def sgB814 : Equiv.Perm (Fin 10) := Equiv.swap 3 1 * (Equiv.swap 3 4 * (Equiv.swap 2 9 * (Equiv.swap 1 0 * (Equiv.swap 0 6)))) +def sgT814 : Equiv.Perm (Fin 10) := Equiv.swap 0 4 * (Equiv.swap 4 7 * (Equiv.swap 1 5 * (Equiv.swap 1 3 * (Equiv.swap 0 6)))) +def sgFlag814 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(1,0,2),(4,0,3),(3,1,0),(1,1,1),(2,2,0),(5,3,0)} +lemma sgCert814 : solveCompact 10 (.full [6,2,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB814 sgT814) sgFlag814 = -6 := by + decide +kernel + +lemma sg814 : RowSquare [4,2,1,1,1,1] [3,3,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [6,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB814 sgT814 sgFlag814 + change solveCompact 10 (.full [6,2,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB814 sgT814) sgFlag814 ≠ 0 + rw [sgCert814] + norm_num + +def sgB816 : Equiv.Perm (Fin 10) := Equiv.swap 8 0 * (Equiv.swap 4 7 * (Equiv.swap 4 3 * (Equiv.swap 3 5 * (Equiv.swap 2 6 * (Equiv.swap 0 9 * (Equiv.swap 0 1)))))) +def sgT816 : Equiv.Perm (Fin 10) := Equiv.swap 7 8 * (Equiv.swap 3 1 * (Equiv.swap 1 9 * (Equiv.swap 3 5 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))) +def sgFlag816 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(2,0,1),(0,0,2),(1,0,3),(0,1,0),(1,1,0),(2,2,0),(1,3,1)} +lemma sgCert816 : solveCompact 10 (.full [4,4,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB816 sgT816) sgFlag816 = 4 := by + decide +kernel + +lemma sg816 : RowSquare [4,2,1,1,1,1] [3,3,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [4,4,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB816 sgT816 sgFlag816 + change solveCompact 10 (.full [4,4,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB816 sgT816) sgFlag816 ≠ 0 + rw [sgCert816] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves4.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves4.lean index 4ad35a1efa9c6533316c4989bd041df834bda35f..65be3062703935cd8e41bef14e8edd06acca6de3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves4.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves4.lean @@ -1,700 +1,700 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Semigroup Leaves 4. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB826 : Equiv.Perm (Fin 10) := Equiv.swap 7 5 * (Equiv.swap 5 4 * (Equiv.swap 4 1 * (Equiv.swap 3 8 * (Equiv.swap 1 9 * (Equiv.swap 1 0 * (Equiv.swap 0 2)))))) -def sgT826 : Equiv.Perm (Fin 10) := Equiv.swap 3 6 * (Equiv.swap 6 0 * (Equiv.swap 0 4 * (Equiv.swap 4 8 * (Equiv.swap 3 7 * (Equiv.swap 2 1 * (Equiv.swap 1 9 * (Equiv.swap 0 5))))))) -def sgFlag826 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(2,0,1),(5,0,2),(3,0,3),(1,1,0),(4,1,0),(6,1,1),(1,2,0),(7,3,0)} -lemma sgCert826 : solveCompact 10 (.full [8,2]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [8,2] (Equiv.refl (Fin 10)) sgB826 sgT826) sgFlag826 = 24 := by - decide +kernel - -lemma sg826 : RowSquare [4,2,2,1,1] [2,2,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [8,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB826 sgT826 sgFlag826 - change solveCompact 10 (.full [8,2]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [8,2] (Equiv.refl (Fin 10)) sgB826 sgT826) sgFlag826 ≠ 0 - rw [sgCert826] - norm_num - -def sgB827 : Equiv.Perm (Fin 10) := Equiv.swap 8 1 * (Equiv.swap 1 5 * (Equiv.swap 5 3 * (Equiv.swap 5 6 * (Equiv.swap 1 0 * (Equiv.swap 3 9 * (Equiv.swap 1 4 * (Equiv.swap 1 2 * (Equiv.swap 0 7)))))))) -def sgT827 : Equiv.Perm (Fin 10) := Equiv.swap 7 3 * (Equiv.swap 3 9 * (Equiv.swap 3 5 * (Equiv.swap 0 4 * (Equiv.swap 0 1)))) -def sgFlag827 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(6,0,3),(2,1,0),(3,1,1),(4,1,2),(2,2,0),(5,3,0)} -lemma sgCert827 : solveCompact 10 (.full [7,3]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB827 sgT827) sgFlag827 = -8 := by - decide +kernel - -lemma sg827 : RowSquare [4,2,2,1,1] [2,2,2,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [7,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB827 sgT827 sgFlag827 - change solveCompact 10 (.full [7,3]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB827 sgT827) sgFlag827 ≠ 0 - rw [sgCert827] - norm_num - -def sgB828 : Equiv.Perm (Fin 10) := Equiv.swap 1 5 * (Equiv.swap 6 2 * (Equiv.swap 5 0 * (Equiv.swap 1 7 * (Equiv.swap 1 4 * (Equiv.swap 2 9 * (Equiv.swap 1 3 * (Equiv.swap 0 8))))))) -def sgT828 : Equiv.Perm (Fin 10) := Equiv.swap 7 3 * (Equiv.swap 0 4 * (Equiv.swap 4 1 * (Equiv.swap 3 8 * (Equiv.swap 2 5 * (Equiv.swap 1 9 * (Equiv.swap 0 6)))))) -def sgFlag828 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(4,0,2),(2,1,0),(3,1,1),(3,1,3),(5,2,0),(2,3,0)} -lemma sgCert828 : solveCompact 10 (.full [6,4]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB828 sgT828) sgFlag828 = 5 := by - decide +kernel - -lemma sg828 : RowSquare [4,2,2,1,1] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB828 sgT828 sgFlag828 - change solveCompact 10 (.full [6,4]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB828 sgT828) sgFlag828 ≠ 0 - rw [sgCert828] - norm_num - -def sgB829 : Equiv.Perm (Fin 10) := Equiv.swap 7 4 * (Equiv.swap 4 2 * (Equiv.swap 3 6 * (Equiv.swap 2 9 * (Equiv.swap 0 1)))) -def sgT829 : Equiv.Perm (Fin 10) := Equiv.swap 5 3 * (Equiv.swap 0 1 * (Equiv.swap 5 7 * (Equiv.swap 3 9 * (Equiv.swap 3 4 * (Equiv.swap 0 6 * (Equiv.swap 1 8 * (Equiv.swap 0 2))))))) -def sgFlag829 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(2,0,1),(4,0,2),(1,0,3),(3,1,0),(2,1,1),(1,2,0),(4,3,0)} -lemma sgCert829 : solveCompact 10 (.full [5,5]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB829 sgT829) sgFlag829 = 10 := by - decide +kernel - -lemma sg829 : RowSquare [4,2,2,1,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB829 sgT829 sgFlag829 - change solveCompact 10 (.full [5,5]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB829 sgT829) sgFlag829 ≠ 0 - rw [sgCert829] - norm_num - -def sgB832 : Equiv.Perm (Fin 10) := Equiv.swap 4 5 * (Equiv.swap 5 2 * (Equiv.swap 4 6 * (Equiv.swap 3 8 * (Equiv.swap 2 0 * (Equiv.swap 0 9 * (Equiv.swap 0 1)))))) -def sgT832 : Equiv.Perm (Fin 10) := Equiv.swap 2 7 * (Equiv.swap 7 3 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 4 6 * (Equiv.swap 3 1 * (Equiv.swap 2 5 * (Equiv.swap 1 9 * (Equiv.swap 0 8)))))))) -def sgFlag832 : Finset (ℕ × ℕ × ℕ) := {(6,0,0),(0,0,1),(1,0,1),(0,0,3),(2,1,0),(2,1,1),(3,1,1),(4,1,2),(5,2,0),(1,3,0)} -lemma sgCert832 : solveCompact 10 (.full [7,3]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [7,3] (Equiv.refl (Fin 10)) sgB832 sgT832) sgFlag832 = 36 := by - decide +kernel - -lemma sg832 : RowSquare [4,2,2,2] [2,2,2,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [7,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB832 sgT832 sgFlag832 - change solveCompact 10 (.full [7,3]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [7,3] (Equiv.refl (Fin 10)) sgB832 sgT832) sgFlag832 ≠ 0 - rw [sgCert832] - norm_num - -def sgB833 : Equiv.Perm (Fin 10) := Equiv.swap 2 4 * (Equiv.swap 2 7 * (Equiv.swap 4 8 * (Equiv.swap 3 5 * (Equiv.swap 2 6 * (Equiv.swap 0 1))))) -def sgT833 : Equiv.Perm (Fin 10) := Equiv.swap 6 3 * (Equiv.swap 6 1 * (Equiv.swap 5 9 * (Equiv.swap 3 8 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 0 * (Equiv.swap 0 7))))))) -def sgFlag833 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(1,0,1),(0,0,2),(0,1,0),(3,1,0),(5,1,1),(3,1,3),(4,2,0),(2,3,1)} -lemma sgCert833 : solveCompact 10 (.full [6,4]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [6,4] (Equiv.refl (Fin 10)) sgB833 sgT833) sgFlag833 = 6 := by - decide +kernel - -lemma sg833 : RowSquare [4,2,2,2] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB833 sgT833 sgFlag833 - change solveCompact 10 (.full [6,4]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [6,4] (Equiv.refl (Fin 10)) sgB833 sgT833) sgFlag833 ≠ 0 - rw [sgCert833] - norm_num - -def sgB834 : Equiv.Perm (Fin 10) := Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 5 9 * (Equiv.swap 4 2 * (Equiv.swap 3 6 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 8))))))) -def sgT834 : Equiv.Perm (Fin 10) := Equiv.swap 7 4 * (Equiv.swap 4 2 * (Equiv.swap 2 9 * (Equiv.swap 4 0 * (Equiv.swap 2 5 * (Equiv.swap 0 6))))) -def sgFlag834 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(3,0,1),(0,0,2),(1,1,0),(4,1,1),(2,1,3),(0,2,1),(3,3,0)} -lemma sgCert834 : solveCompact 10 (.full [5,5]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [5,5] (Equiv.refl (Fin 10)) sgB834 sgT834) sgFlag834 = 32 := by - decide +kernel - -lemma sg834 : RowSquare [4,2,2,2] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB834 sgT834 sgFlag834 - change solveCompact 10 (.full [5,5]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [5,5] (Equiv.refl (Fin 10)) sgB834 sgT834) sgFlag834 ≠ 0 - rw [sgCert834] - norm_num - -def sgB835 : Equiv.Perm (Fin 10) := Equiv.swap 2 9 * (Equiv.swap 5 0 * (Equiv.swap 5 6 * (Equiv.swap 1 4 * (Equiv.swap 2 8 * (Equiv.swap 1 3 * (Equiv.swap 0 7)))))) -def sgT835 : Equiv.Perm (Fin 10) := Equiv.swap 2 6 * (Equiv.swap 6 4 * (Equiv.swap 2 1 * (Equiv.swap 4 9 * (Equiv.swap 2 5 * (Equiv.swap 2 0 * (Equiv.swap 1 7 * (Equiv.swap 0 3))))))) -def sgFlag835 : Finset (ℕ × ℕ × ℕ) := {(4,0,0),(0,0,1),(3,0,1),(1,1,0),(6,1,1),(2,1,2),(7,1,3),(0,2,0),(5,3,0)} -lemma sgCert835 : solveCompact 10 (.full [8,1,1]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [8,1,1] (Equiv.refl (Fin 10)) sgB835 sgT835) sgFlag835 = -112 := by - decide +kernel - -lemma sg835 : RowSquare [4,2,2,2] [3,1,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [8,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB835 sgT835 sgFlag835 - change solveCompact 10 (.full [8,1,1]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [8,1,1] (Equiv.refl (Fin 10)) sgB835 sgT835) sgFlag835 ≠ 0 - rw [sgCert835] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB836 : Equiv.Perm (Fin 10) := Equiv.swap 4 7 * (Equiv.swap 3 0 * (Equiv.swap 4 6 * (Equiv.swap 3 1 * (Equiv.swap 1 5 * (Equiv.swap 1 2 * (Equiv.swap 0 8)))))) -def sgT836 : Equiv.Perm (Fin 10) := Equiv.swap 7 2 * (Equiv.swap 7 0 * (Equiv.swap 5 6 * (Equiv.swap 2 9 * (Equiv.swap 0 8 * (Equiv.swap 2 4 * (Equiv.swap 0 3 * (Equiv.swap 0 1))))))) -def sgFlag836 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(5,0,1),(2,0,3),(0,1,0),(1,1,1),(3,1,2),(4,2,1),(0,3,1)} -lemma sgCert836 : solveCompact 10 (.full [6,2,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [6,2,2] (Equiv.refl (Fin 10)) sgB836 sgT836) sgFlag836 = -8 := by - decide +kernel - -lemma sg836 : RowSquare [4,2,2,2] [3,3,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [6,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB836 sgT836 sgFlag836 - change solveCompact 10 (.full [6,2,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [6,2,2] (Equiv.refl (Fin 10)) sgB836 sgT836) sgFlag836 ≠ 0 - rw [sgCert836] - norm_num - -def sgB837 : Equiv.Perm (Fin 10) := Equiv.swap 0 1 * (Equiv.swap 0 7 * (Equiv.swap 0 6 * (Equiv.swap 0 2 * (Equiv.swap 2 5 * (Equiv.swap 2 3 * (Equiv.swap 1 8 * (Equiv.swap 0 4))))))) -def sgT837 : Equiv.Perm (Fin 10) := Equiv.swap 0 5 * (Equiv.swap 5 3 * (Equiv.swap 5 2 * (Equiv.swap 0 1 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 1 7 * (Equiv.swap 0 4))))))) -def sgFlag837 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,1),(1,0,2),(2,1,0),(3,1,0),(1,1,1),(2,2,3),(0,3,1)} -lemma sgCert837 : solveCompact 10 (.full [4,4,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [4,4,2] (Equiv.refl (Fin 10)) sgB837 sgT837) sgFlag837 = -6 := by - decide +kernel - -lemma sg837 : RowSquare [4,2,2,2] [3,3,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [4,4,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB837 sgT837 sgFlag837 - change solveCompact 10 (.full [4,4,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [4,4,2] (Equiv.refl (Fin 10)) sgB837 sgT837) sgFlag837 ≠ 0 - rw [sgCert837] - norm_num - -def sgB838 : Equiv.Perm (Fin 10) := Equiv.swap 2 5 * (Equiv.swap 5 1 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 2 8 * (Equiv.swap 1 9))))) -def sgT838 : Equiv.Perm (Fin 10) := Equiv.swap 7 6 * (Equiv.swap 7 1 * (Equiv.swap 6 4 * (Equiv.swap 1 8 * (Equiv.swap 4 0 * (Equiv.swap 0 9 * (Equiv.swap 1 5 * (Equiv.swap 0 2))))))) -def sgFlag838 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(6,0,1),(7,0,2),(1,0,3),(5,1,0),(0,1,1),(1,2,0),(4,2,2),(3,3,0)} -lemma sgCert838 : solveCompact 10 (.full [8,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB838 sgT838) sgFlag838 = -16 := by - decide +kernel - -lemma sg838 : RowSquare [4,3,1,1,1] [2,2,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [8,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB838 sgT838 sgFlag838 - change solveCompact 10 (.full [8,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB838 sgT838) sgFlag838 ≠ 0 - rw [sgCert838] - norm_num - -def sgB839 : Equiv.Perm (Fin 10) := Equiv.swap 6 9 * (Equiv.swap 6 0 * (Equiv.swap 1 8 * (Equiv.swap 1 3 * (Equiv.swap 3 5 * (Equiv.swap 1 4 * (Equiv.swap 1 2 * (Equiv.swap 0 7))))))) -def sgT839 : Equiv.Perm (Fin 10) := Equiv.swap 1 3 * (Equiv.swap 3 8 * (Equiv.swap 3 4 * (Equiv.swap 2 9 * (Equiv.swap 1 5 * (Equiv.swap 0 7))))) -def sgFlag839 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(2,0,2),(1,0,3),(3,1,0),(5,1,2),(2,2,0),(6,2,0),(4,3,1)} -lemma sgCert839 : solveCompact 10 (.full [7,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB839 sgT839) sgFlag839 = -3 := by - decide +kernel - -lemma sg839 : RowSquare [4,3,1,1,1] [2,2,2,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [7,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB839 sgT839 sgFlag839 - change solveCompact 10 (.full [7,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB839 sgT839) sgFlag839 ≠ 0 - rw [sgCert839] - norm_num - -def sgB840 : Equiv.Perm (Fin 10) := Equiv.swap 2 9 * (Equiv.swap 2 3 * (Equiv.swap 2 7 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 3 5 * (Equiv.swap 2 0 * (Equiv.swap 0 4))))))) -def sgT840 : Equiv.Perm (Fin 10) := Equiv.swap 6 9 * (Equiv.swap 6 2 * (Equiv.swap 4 0 * (Equiv.swap 0 7 * (Equiv.swap 2 8 * (Equiv.swap 0 3))))) -def sgFlag840 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,2),(4,0,3),(5,1,0),(1,1,1),(2,2,0),(1,3,1)} -lemma sgCert840 : solveCompact 10 (.full [6,4]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB840 sgT840) sgFlag840 = -2 := by - decide +kernel - -lemma sg840 : RowSquare [4,3,1,1,1] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB840 sgT840 sgFlag840 - change solveCompact 10 (.full [6,4]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB840 sgT840) sgFlag840 ≠ 0 - rw [sgCert840] - norm_num - -def sgB841 : Equiv.Perm (Fin 10) := Equiv.swap 6 1 * (Equiv.swap 6 4 * (Equiv.swap 4 0 * (Equiv.swap 4 5 * (Equiv.swap 0 7 * (Equiv.swap 0 3 * (Equiv.swap 1 8 * (Equiv.swap 0 2))))))) -def sgT841 : Equiv.Perm (Fin 10) := Equiv.swap 5 4 * (Equiv.swap 5 2 * (Equiv.swap 5 1 * (Equiv.swap 4 9 * (Equiv.swap 2 7 * (Equiv.swap 1 6 * (Equiv.swap 0 3)))))) -def sgFlag841 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,1),(3,0,2),(1,1,0),(2,2,0),(2,2,3),(0,3,0)} -lemma sgCert841 : solveCompact 10 (.full [5,5]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB841 sgT841) sgFlag841 = -2 := by - decide +kernel - -lemma sg841 : RowSquare [4,3,1,1,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB841 sgT841 sgFlag841 - change solveCompact 10 (.full [5,5]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB841 sgT841) sgFlag841 ≠ 0 - rw [sgCert841] - norm_num - -def sgB846 : Equiv.Perm (Fin 10) := Equiv.swap 1 5 * (Equiv.swap 5 9 * (Equiv.swap 5 7 * (Equiv.swap 1 8 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))))) -def sgT846 : Equiv.Perm (Fin 10) := Equiv.swap 1 0 * (Equiv.swap 1 8 * (Equiv.swap 5 4 * (Equiv.swap 4 3 * (Equiv.swap 3 2 * (Equiv.swap 2 6 * (Equiv.swap 1 7 * (Equiv.swap 0 9))))))) -def sgFlag846 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(0,0,1),(1,0,1),(1,0,2),(1,1,0),(4,1,0),(5,2,2),(0,2,3),(2,3,0)} -lemma sgCert846 : solveCompact 10 (.full [6,2,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB846 sgT846) sgFlag846 = 4 := by - decide +kernel - -lemma sg846 : RowSquare [4,3,1,1,1] [3,3,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [6,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB846 sgT846 sgFlag846 - change solveCompact 10 (.full [6,2,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB846 sgT846) sgFlag846 ≠ 0 - rw [sgCert846] - norm_num - -def sgB847 : Equiv.Perm (Fin 10) := Equiv.swap 8 0 * (Equiv.swap 0 5 * (Equiv.swap 5 4 * (Equiv.swap 4 9 * (Equiv.swap 1 7 * (Equiv.swap 1 3 * (Equiv.swap 0 6)))))) -def sgT847 : Equiv.Perm (Fin 10) := Equiv.swap 2 5 * (Equiv.swap 5 9 * (Equiv.swap 2 4 * (Equiv.swap 5 3 * (Equiv.swap 4 8 * (Equiv.swap 3 7 * (Equiv.swap 2 6)))))) -def sgFlag847 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(2,0,1),(0,0,2),(3,1,0),(1,1,3),(0,2,1),(2,2,2),(0,3,0)} -lemma sgCert847 : solveCompact 10 (.full [4,3,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB847 sgT847) sgFlag847 = 1 := by - decide +kernel - -lemma sg847 : RowSquare [4,3,1,1,1] [3,3,3,1] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [4,3,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB847 sgT847 sgFlag847 - change solveCompact 10 (.full [4,3,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB847 sgT847) sgFlag847 ≠ 0 - rw [sgCert847] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB873 : Equiv.Perm (Fin 10) := Equiv.swap 1 9 * (Equiv.swap 6 4 * (Equiv.swap 4 7 * (Equiv.swap 4 0 * (Equiv.swap 0 5 * (Equiv.swap 1 8 * (Equiv.swap 0 2)))))) -def sgT873 : Equiv.Perm (Fin 10) := Equiv.swap 6 1 * (Equiv.swap 2 0 * (Equiv.swap 4 8 * (Equiv.swap 1 9 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 7)))))) -def sgFlag873 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(1,0,1),(6,0,1),(7,0,2),(0,1,0),(2,1,0),(3,1,2),(4,2,0),(0,2,1),(5,2,2)} -lemma sgCert873 : solveCompact 10 (.full [8,2]) (.full [3,3,3,1]) (.full [3,3,3,1]) - (certificateEdges [3,3,3,1] [3,3,3,1] [8,2] (Equiv.refl (Fin 10)) sgB873 sgT873) sgFlag873 = -120 := by - decide +kernel - -lemma sg873 : RowSquare [4,3,3] [2,2,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [3,3,3,1]) (ts := [8,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB873 sgT873 sgFlag873 - change solveCompact 10 (.full [8,2]) (.full [3,3,3,1]) (.full [3,3,3,1]) - (certificateEdges [3,3,3,1] [3,3,3,1] [8,2] (Equiv.refl (Fin 10)) sgB873 sgT873) sgFlag873 ≠ 0 - rw [sgCert873] - norm_num - -def sgB874 : Equiv.Perm (Fin 10) := Equiv.swap 0 3 * (Equiv.swap 0 8 * (Equiv.swap 0 7 * (Equiv.swap 3 9 * (Equiv.swap 2 6 * (Equiv.swap 0 4 * (Equiv.swap 0 1)))))) -def sgT874 : Equiv.Perm (Fin 10) := Equiv.swap 3 9 * (Equiv.swap 0 8 * (Equiv.swap 4 5 * (Equiv.swap 3 2 * (Equiv.swap 2 7 * (Equiv.swap 0 6))))) -def sgFlag874 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(3,0,0),(6,0,1),(1,0,2),(1,1,1),(5,1,1),(2,1,2),(0,2,0),(4,2,2)} -lemma sgCert874 : solveCompact 10 (.full [7,3]) (.full [3,3,3,1]) (.full [3,3,3,1]) - (certificateEdges [3,3,3,1] [3,3,3,1] [7,3] (Equiv.refl (Fin 10)) sgB874 sgT874) sgFlag874 = 45 := by - decide +kernel - -lemma sg874 : RowSquare [4,3,3] [2,2,2,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [3,3,3,1]) (ts := [7,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB874 sgT874 sgFlag874 - change solveCompact 10 (.full [7,3]) (.full [3,3,3,1]) (.full [3,3,3,1]) - (certificateEdges [3,3,3,1] [3,3,3,1] [7,3] (Equiv.refl (Fin 10)) sgB874 sgT874) sgFlag874 ≠ 0 - rw [sgCert874] - norm_num - -def sgB875 : Equiv.Perm (Fin 10) := Equiv.swap 6 5 * (Equiv.swap 6 2 * (Equiv.swap 6 7 * (Equiv.swap 5 4 * (Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 2 8 * (Equiv.swap 0 9 * (Equiv.swap 0 1)))))))) -def sgT875 : Equiv.Perm (Fin 10) := Equiv.swap 4 9 * (Equiv.swap 4 5 * (Equiv.swap 4 7 * (Equiv.swap 5 8 * (Equiv.swap 4 0 * (Equiv.swap 0 1 * (Equiv.swap 0 3 * (Equiv.swap 1 6 * (Equiv.swap 0 2)))))))) -def sgFlag875 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(1,0,1),(2,0,1),(0,1,0),(5,1,2),(2,2,1),(3,2,2)} -lemma sgCert875 : solveCompact 10 (.full [6,4]) (.full [3,3,3,1]) (.full [3,3,3,1]) - (certificateEdges [3,3,3,1] [3,3,3,1] [6,4] (Equiv.refl (Fin 10)) sgB875 sgT875) sgFlag875 = -21 := by - decide +kernel - -lemma sg875 : RowSquare [4,3,3] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [3,3,3,1]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB875 sgT875 sgFlag875 - change solveCompact 10 (.full [6,4]) (.full [3,3,3,1]) (.full [3,3,3,1]) - (certificateEdges [3,3,3,1] [3,3,3,1] [6,4] (Equiv.refl (Fin 10)) sgB875 sgT875) sgFlag875 ≠ 0 - rw [sgCert875] - norm_num - -def sgB876 : Equiv.Perm (Fin 10) := Equiv.swap 4 7 * (Equiv.swap 7 6 * (Equiv.swap 6 2 * (Equiv.swap 4 8 * (Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 2 9 * (Equiv.swap 0 5 * (Equiv.swap 0 1)))))))) -def sgT876 : Equiv.Perm (Fin 10) := Equiv.swap 7 8 * (Equiv.swap 3 4 * (Equiv.swap 4 9 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 5))))) -def sgFlag876 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(0,0,1),(3,0,1),(6,0,2),(0,1,0),(5,1,2),(1,2,0),(7,2,1),(4,2,2)} -lemma sgCert876 : solveCompact 10 (.full [8,1,1]) (.full [3,3,3,1]) (.full [3,3,3,1]) - (certificateEdges [3,3,3,1] [3,3,3,1] [8,1,1] (Equiv.refl (Fin 10)) sgB876 sgT876) sgFlag876 = 60 := by - decide +kernel - -lemma sg876 : RowSquare [4,3,3] [3,1,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [3,3,3,1]) (ts := [8,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB876 sgT876 sgFlag876 - change solveCompact 10 (.full [8,1,1]) (.full [3,3,3,1]) (.full [3,3,3,1]) - (certificateEdges [3,3,3,1] [3,3,3,1] [8,1,1] (Equiv.refl (Fin 10)) sgB876 sgT876) sgFlag876 ≠ 0 - rw [sgCert876] - norm_num - -def sgB877 : Equiv.Perm (Fin 10) := Equiv.swap 7 9 * (Equiv.swap 7 8 * (Equiv.swap 0 4 * (Equiv.swap 1 6 * (Equiv.swap 1 2 * (Equiv.swap 0 3))))) -def sgT877 : Equiv.Perm (Fin 10) := Equiv.swap 7 3 * (Equiv.swap 3 1 * (Equiv.swap 4 5 * (Equiv.swap 3 2 * (Equiv.swap 2 6 * (Equiv.swap 1 9))))) -def sgFlag877 : Finset (ℕ × ℕ × ℕ) := {(5,0,0),(1,0,1),(0,0,3),(3,1,0),(0,1,1),(4,1,1),(2,1,2),(6,2,0),(2,3,0)} -lemma sgCert877 : solveCompact 10 (.full [7,3]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [7,3] (Equiv.refl (Fin 10)) sgB877 sgT877) sgFlag877 = 72 := by - decide +kernel - -lemma sg877 : RowSquare [4,4,1,1] [2,2,2,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [7,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB877 sgT877 sgFlag877 - change solveCompact 10 (.full [7,3]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [7,3] (Equiv.refl (Fin 10)) sgB877 sgT877) sgFlag877 ≠ 0 - rw [sgCert877] - norm_num - -def sgB878 : Equiv.Perm (Fin 10) := Equiv.swap 3 9 * (Equiv.swap 5 7 * (Equiv.swap 1 8 * (Equiv.swap 3 6 * (Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 4)))))) -def sgT878 : Equiv.Perm (Fin 10) := Equiv.swap 5 9 * (Equiv.swap 6 0 * (Equiv.swap 5 3 * (Equiv.swap 0 1 * (Equiv.swap 3 7 * (Equiv.swap 1 8 * (Equiv.swap 0 4)))))) -def sgFlag878 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(0,0,1),(3,1,1),(2,1,2),(5,1,3),(2,2,0),(1,3,0)} -lemma sgCert878 : solveCompact 10 (.full [6,4]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [6,4] (Equiv.refl (Fin 10)) sgB878 sgT878) sgFlag878 = 24 := by - decide +kernel - -lemma sg878 : RowSquare [4,4,1,1] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB878 sgT878 sgFlag878 - change solveCompact 10 (.full [6,4]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [6,4] (Equiv.refl (Fin 10)) sgB878 sgT878) sgFlag878 ≠ 0 - rw [sgCert878] - norm_num - -def sgB879 : Equiv.Perm (Fin 10) := Equiv.swap 7 8 * (Equiv.swap 4 2 * (Equiv.swap 3 6 * (Equiv.swap 2 0 * (Equiv.swap 1 9 * (Equiv.swap 0 5))))) -def sgT879 : Equiv.Perm (Fin 10) := Equiv.swap 1 7 * (Equiv.swap 7 4 * (Equiv.swap 4 9 * (Equiv.swap 4 5 * (Equiv.swap 3 6 * (Equiv.swap 1 8 * (Equiv.swap 0 2)))))) -def sgFlag879 : Finset (ℕ × ℕ × ℕ) := {(2,0,1),(0,0,2),(3,0,3),(4,1,0),(1,1,1),(3,1,1),(0,2,0),(1,3,0)} -lemma sgCert879 : solveCompact 10 (.full [5,5]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [5,5] (Equiv.refl (Fin 10)) sgB879 sgT879) sgFlag879 = -8 := by - decide +kernel - -lemma sg879 : RowSquare [4,4,1,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB879 sgT879 sgFlag879 - change solveCompact 10 (.full [5,5]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [5,5] (Equiv.refl (Fin 10)) sgB879 sgT879) sgFlag879 ≠ 0 - rw [sgCert879] - norm_num - -def sgB880 : Equiv.Perm (Fin 10) := Equiv.swap 6 2 * (Equiv.swap 5 0 * (Equiv.swap 2 1 * (Equiv.swap 0 7 * (Equiv.swap 2 4 * (Equiv.swap 1 9 * (Equiv.swap 0 3)))))) -def sgT880 : Equiv.Perm (Fin 10) := Equiv.swap 8 2 * (Equiv.swap 2 1 * (Equiv.swap 1 9 * (Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 2 4 * (Equiv.swap 1 0 * (Equiv.swap 0 5))))))) -def sgFlag880 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(3,0,1),(6,0,2),(5,0,3),(0,1,0),(0,1,1),(1,1,1),(4,2,0),(7,3,1)} -lemma sgCert880 : solveCompact 10 (.full [8,1,1]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [8,1,1] (Equiv.refl (Fin 10)) sgB880 sgT880) sgFlag880 = -112 := by - decide +kernel - -lemma sg880 : RowSquare [4,4,1,1] [3,1,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [8,1,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB880 sgT880 sgFlag880 - change solveCompact 10 (.full [8,1,1]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [8,1,1] (Equiv.refl (Fin 10)) sgB880 sgT880) sgFlag880 ≠ 0 - rw [sgCert880] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB881 : Equiv.Perm (Fin 10) := Equiv.swap 0 2 * (Equiv.swap 1 8 * (Equiv.swap 1 6 * (Equiv.swap 1 5 * (Equiv.swap 2 9 * (Equiv.swap 1 3 * (Equiv.swap 0 7)))))) -def sgT881 : Equiv.Perm (Fin 10) := Equiv.swap 4 0 * (Equiv.swap 3 7 * (Equiv.swap 1 5 * (Equiv.swap 0 6))) -def sgFlag881 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,0),(1,0,1),(6,0,1),(0,1,0),(1,1,0),(3,1,2),(5,1,3),(2,2,1),(0,3,1)} -lemma sgCert881 : solveCompact 10 (.full [7,2,1]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [7,2,1] (Equiv.refl (Fin 10)) sgB881 sgT881) sgFlag881 = -4 := by - decide +kernel - -lemma sg881 : RowSquare [4,4,1,1] [3,2,1,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [7,2,1]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB881 sgT881 sgFlag881 - change solveCompact 10 (.full [7,2,1]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [7,2,1] (Equiv.refl (Fin 10)) sgB881 sgT881) sgFlag881 ≠ 0 - rw [sgCert881] - norm_num - -def sgB884 : Equiv.Perm (Fin 10) := Equiv.swap 6 2 * (Equiv.swap 2 0 * (Equiv.swap 2 5 * (Equiv.swap 2 3 * (Equiv.swap 1 8 * (Equiv.swap 0 7))))) -def sgT884 : Equiv.Perm (Fin 10) := Equiv.swap 4 9 * (Equiv.swap 4 1 * (Equiv.swap 3 0 * (Equiv.swap 2 6 * (Equiv.swap 1 7 * (Equiv.swap 0 5))))) -def sgFlag884 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(5,0,1),(2,0,2),(1,1,0),(3,1,0),(4,1,1),(0,2,3),(0,3,1)} -lemma sgCert884 : solveCompact 10 (.full [6,2,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [6,2,2] (Equiv.refl (Fin 10)) sgB884 sgT884) sgFlag884 = 6 := by - decide +kernel - -lemma sg884 : RowSquare [4,4,1,1] [3,3,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [6,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB884 sgT884 sgFlag884 - change solveCompact 10 (.full [6,2,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [6,2,2] (Equiv.refl (Fin 10)) sgB884 sgT884) sgFlag884 ≠ 0 - rw [sgCert884] - norm_num - -def sgB885 : Equiv.Perm (Fin 10) := Equiv.swap 1 9 * (Equiv.swap 6 0 * (Equiv.swap 4 2 * (Equiv.swap 1 7 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 8)))))) -def sgT885 : Equiv.Perm (Fin 10) := Equiv.swap 5 8 * (Equiv.swap 5 6 * (Equiv.swap 3 7 * (Equiv.swap 2 1 * (Equiv.swap 1 4)))) -def sgFlag885 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,2),(1,1,0),(1,1,1),(3,1,1),(4,1,3),(1,2,1),(2,3,1)} -lemma sgCert885 : solveCompact 10 (.full [5,3,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [5,3,2] (Equiv.refl (Fin 10)) sgB885 sgT885) sgFlag885 = -1 := by - decide +kernel - -lemma sg885 : RowSquare [4,4,1,1] [3,3,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [5,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB885 sgT885 sgFlag885 - change solveCompact 10 (.full [5,3,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [5,3,2] (Equiv.refl (Fin 10)) sgB885 sgT885) sgFlag885 ≠ 0 - rw [sgCert885] - norm_num - -def sgB886 : Equiv.Perm (Fin 10) := Equiv.swap 2 0 * (Equiv.swap 0 9 * (Equiv.swap 2 7 * (Equiv.swap 2 5 * (Equiv.swap 0 6)))) -def sgT886 : Equiv.Perm (Fin 10) := Equiv.swap 8 7 * (Equiv.swap 7 3 * (Equiv.swap 3 0 * (Equiv.swap 3 5 * (Equiv.swap 3 1 * (Equiv.swap 1 4 * (Equiv.swap 0 9)))))) -def sgFlag886 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(2,0,1),(3,1,0),(0,1,1),(0,1,2),(2,2,1),(1,3,3)} -lemma sgCert886 : solveCompact 10 (.full [4,4,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [4,4,2] (Equiv.refl (Fin 10)) sgB886 sgT886) sgFlag886 = -1 := by - decide +kernel - -lemma sg886 : RowSquare [4,4,1,1] [3,3,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [4,4,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB886 sgT886 sgFlag886 - change solveCompact 10 (.full [4,4,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [4,4,2] (Equiv.refl (Fin 10)) sgB886 sgT886) sgFlag886 ≠ 0 - rw [sgCert886] - norm_num - -def sgB887 : Equiv.Perm (Fin 10) := Equiv.swap 6 1 * (Equiv.swap 6 4 * (Equiv.swap 4 3 * (Equiv.swap 3 7 * (Equiv.swap 2 8 * (Equiv.swap 1 9))))) -def sgT887 : Equiv.Perm (Fin 10) := Equiv.swap 0 3 * (Equiv.swap 3 1 * (Equiv.swap 0 8 * (Equiv.swap 3 2 * (Equiv.swap 2 7 * (Equiv.swap 1 9 * (Equiv.swap 0 4)))))) -def sgFlag887 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,2),(0,0,3),(0,1,0),(1,1,1),(1,2,0),(2,3,1)} -lemma sgCert887 : solveCompact 10 (.full [4,2,2,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [4,2,2,2] (Equiv.refl (Fin 10)) sgB887 sgT887) sgFlag887 = 1 := by - decide +kernel - -lemma sg887 : RowSquare [4,4,1,1] [4,4,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [4,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB887 sgT887 sgFlag887 - change solveCompact 10 (.full [4,2,2,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) - (certificateEdges [4,2,2,2] [4,2,2,2] [4,2,2,2] (Equiv.refl (Fin 10)) sgB887 sgT887) sgFlag887 ≠ 0 - rw [sgCert887] - norm_num - -def sgB889 : Equiv.Perm (Fin 10) := Equiv.swap 1 3 * (Equiv.swap 3 2 * (Equiv.swap 2 9 * (Equiv.swap 4 5 * (Equiv.swap 3 7 * (Equiv.swap 2 6 * (Equiv.swap 1 0 * (Equiv.swap 0 8))))))) -def sgT889 : Equiv.Perm (Fin 10) := Equiv.swap 2 0 * (Equiv.swap 0 9 * (Equiv.swap 4 5 * (Equiv.swap 0 6 * (Equiv.swap 2 8 * (Equiv.swap 0 3 * (Equiv.swap 0 1)))))) -def sgFlag889 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(7,0,2),(0,0,3),(4,0,4),(3,1,0),(0,2,0),(6,3,0),(5,4,0)} -lemma sgCert889 : solveCompact 10 (.full [8,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB889 sgT889) sgFlag889 = 1152 := by - decide +kernel - -lemma sg889 : RowSquare [5,1,1,1,1,1] [2,2,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [8,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB889 sgT889 sgFlag889 - change solveCompact 10 (.full [8,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB889 sgT889) sgFlag889 ≠ 0 - rw [sgCert889] - norm_num - -def sgB890 : Equiv.Perm (Fin 10) := Equiv.swap 1 2 * (Equiv.swap 5 3 * (Equiv.swap 4 0 * (Equiv.swap 3 8 * (Equiv.swap 2 9 * (Equiv.swap 1 6 * (Equiv.swap 0 7)))))) -def sgT890 : Equiv.Perm (Fin 10) := Equiv.swap 4 9 * (Equiv.swap 4 7 * (Equiv.swap 4 3 * (Equiv.swap 4 5 * (Equiv.swap 3 6 * (Equiv.swap 1 8))))) -def sgFlag890 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(4,0,1),(0,0,2),(3,0,3),(2,0,4),(1,1,0),(2,2,0),(6,3,0),(5,4,0)} -lemma sgCert890 : solveCompact 10 (.full [7,3]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB890 sgT890) sgFlag890 = -48 := by - decide +kernel - -lemma sg890 : RowSquare [5,1,1,1,1,1] [2,2,2,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [7,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB890 sgT890 sgFlag890 - change solveCompact 10 (.full [7,3]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB890 sgT890) sgFlag890 ≠ 0 - rw [sgCert890] - norm_num - -def sgB891 : Equiv.Perm (Fin 10) := Equiv.swap 4 6 * (Equiv.swap 6 3 * (Equiv.swap 4 8 * (Equiv.swap 3 9 * (Equiv.swap 1 5 * (Equiv.swap 0 2))))) -def sgT891 : Equiv.Perm (Fin 10) := Equiv.swap 1 9 * (Equiv.swap 1 3 * (Equiv.swap 1 4 * (Equiv.swap 4 7 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 1 5 * (Equiv.swap 0 8))))))) -def sgFlag891 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(4,0,1),(2,0,2),(0,0,3),(1,0,4),(5,1,0),(0,2,0),(2,3,0),(1,4,0)} -lemma sgCert891 : solveCompact 10 (.full [6,4]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB891 sgT891) sgFlag891 = 144 := by - decide +kernel - -lemma sg891 : RowSquare [5,1,1,1,1,1] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB891 sgT891 sgFlag891 - change solveCompact 10 (.full [6,4]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB891 sgT891) sgFlag891 ≠ 0 - rw [sgCert891] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB892 : Equiv.Perm (Fin 10) := Equiv.swap 2 1 * (Equiv.swap 2 3 * (Equiv.swap 1 4 * (Equiv.swap 4 9 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 0 7))))))) -def sgT892 : Equiv.Perm (Fin 10) := Equiv.swap 8 1 * (Equiv.swap 1 4 * (Equiv.swap 5 7 * (Equiv.swap 4 2 * (Equiv.swap 1 6 * (Equiv.swap 2 9 * (Equiv.swap 1 3)))))) -def sgFlag892 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(3,0,2),(4,0,3),(2,0,4),(3,1,0),(4,2,0),(1,3,0),(2,4,0)} -lemma sgCert892 : solveCompact 10 (.full [5,5]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB892 sgT892) sgFlag892 = 1440 := by - decide +kernel - -lemma sg892 : RowSquare [5,1,1,1,1,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB892 sgT892 sgFlag892 - change solveCompact 10 (.full [5,5]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB892 sgT892) sgFlag892 ≠ 0 - rw [sgCert892] - norm_num - -def sgB897 : Equiv.Perm (Fin 10) := Equiv.swap 5 4 * (Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 4 9 * (Equiv.swap 0 1 * (Equiv.swap 2 8 * (Equiv.swap 1 7 * (Equiv.swap 0 3))))))) -def sgT897 : Equiv.Perm (Fin 10) := Equiv.swap 6 7 * (Equiv.swap 5 9 * (Equiv.swap 4 1 * (Equiv.swap 1 8 * (Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 3)))))) -def sgFlag897 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(5,0,0),(0,0,2),(3,0,3),(4,0,4),(2,1,0),(0,2,0),(0,3,1),(1,4,0)} -lemma sgCert897 : solveCompact 10 (.full [6,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB897 sgT897) sgFlag897 = 12 := by - decide +kernel - -lemma sg897 : RowSquare [5,1,1,1,1,1] [3,3,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [6,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB897 sgT897 sgFlag897 - change solveCompact 10 (.full [6,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB897 sgT897) sgFlag897 ≠ 0 - rw [sgCert897] - norm_num - -def sgB898 : Equiv.Perm (Fin 10) := Equiv.swap 2 6 * (Equiv.swap 6 0 * (Equiv.swap 0 9 * (Equiv.swap 1 5 * (Equiv.swap 2 7 * (Equiv.swap 1 3 * (Equiv.swap 0 4)))))) -def sgT898 : Equiv.Perm (Fin 10) := Equiv.swap 5 8 * (Equiv.swap 5 7 * (Equiv.swap 5 2 * (Equiv.swap 2 1 * (Equiv.swap 2 0 * (Equiv.swap 1 6 * (Equiv.swap 0 3)))))) -def sgFlag898 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(2,0,1),(1,0,2),(3,0,4),(1,1,3),(0,2,0),(1,3,0),(4,4,0)} -lemma sgCert898 : solveCompact 10 (.full [5,3,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,3,2] (Equiv.refl (Fin 10)) sgB898 sgT898) sgFlag898 = -36 := by - decide +kernel - -lemma sg898 : RowSquare [5,1,1,1,1,1] [3,3,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [5,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB898 sgT898 sgFlag898 - change solveCompact 10 (.full [5,3,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,3,2] (Equiv.refl (Fin 10)) sgB898 sgT898) sgFlag898 ≠ 0 - rw [sgCert898] - norm_num - -def sgB899 : Equiv.Perm (Fin 10) := Equiv.swap 1 5 * (Equiv.swap 1 0 * (Equiv.swap 1 3 * (Equiv.swap 5 4 * (Equiv.swap 4 2 * (Equiv.swap 3 7 * (Equiv.swap 2 9 * (Equiv.swap 1 6 * (Equiv.swap 0 8)))))))) -def sgT899 : Equiv.Perm (Fin 10) := Equiv.swap 0 2 * (Equiv.swap 2 9 * (Equiv.swap 4 1 * (Equiv.swap 3 5 * (Equiv.swap 2 6 * (Equiv.swap 1 8 * (Equiv.swap 0 7)))))) -def sgFlag899 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(3,0,0),(0,0,1),(1,0,3),(3,0,4),(0,1,0),(2,2,0),(1,3,0),(1,4,2)} -lemma sgCert899 : solveCompact 10 (.full [4,4,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB899 sgT899) sgFlag899 = 36 := by - decide +kernel - -lemma sg899 : RowSquare [5,1,1,1,1,1] [3,3,2,2] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [4,4,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB899 sgT899 sgFlag899 - change solveCompact 10 (.full [4,4,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB899 sgT899) sgFlag899 ≠ 0 - rw [sgCert899] - norm_num - -def sgB902 : Equiv.Perm (Fin 10) := Equiv.swap 0 1 * (Equiv.swap 0 7 * (Equiv.swap 0 6 * (Equiv.swap 4 2 * (Equiv.swap 2 9 * (Equiv.swap 2 3 * (Equiv.swap 1 8 * (Equiv.swap 0 5))))))) -def sgT902 : Equiv.Perm (Fin 10) := Equiv.swap 2 8 * (Equiv.swap 5 7 * (Equiv.swap 4 9 * (Equiv.swap 2 6 * (Equiv.swap 2 0 * (Equiv.swap 0 3 * (Equiv.swap 0 1)))))) -def sgFlag902 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,0),(1,0,1),(0,0,4),(3,1,0),(0,2,3),(0,3,0),(1,4,2)} -lemma sgCert902 : solveCompact 10 (.full [4,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,2,2,2] (Equiv.refl (Fin 10)) sgB902 sgT902) sgFlag902 = 8 := by - decide +kernel - -lemma sg902 : RowSquare [5,1,1,1,1,1] [4,4,1,1] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [4,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB902 sgT902 sgFlag902 - change solveCompact 10 (.full [4,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,2,2,2] (Equiv.refl (Fin 10)) sgB902 sgT902) sgFlag902 ≠ 0 - rw [sgCert902] - norm_num - -def sgB903 : Equiv.Perm (Fin 10) := Equiv.swap 3 9 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 8 * (Equiv.swap 1 7 * (Equiv.swap 0 6))))) -def sgT903 : Equiv.Perm (Fin 10) := Equiv.swap 3 2 * (Equiv.swap 3 1 * (Equiv.swap 3 7 * (Equiv.swap 2 9 * (Equiv.swap 3 6 * (Equiv.swap 2 5 * (Equiv.swap 1 8 * (Equiv.swap 0 4))))))) -def sgFlag903 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(1,0,1),(0,0,3),(0,1,0),(2,2,0),(0,3,4),(0,4,2)} -lemma sgCert903 : solveCompact 10 (.full [3,3,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [3,3,2,2] (Equiv.refl (Fin 10)) sgB903 sgT903) sgFlag903 = 4 := by - decide +kernel - -lemma sg903 : RowSquare [5,1,1,1,1,1] [4,4,2] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [3,3,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB903 sgT903 sgFlag903 - change solveCompact 10 (.full [3,3,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [3,3,2,2] (Equiv.refl (Fin 10)) sgB903 sgT903) sgFlag903 ≠ 0 - rw [sgCert903] - norm_num - -def sgB909 : Equiv.Perm (Fin 10) := Equiv.swap 6 5 * (Equiv.swap 5 8 * (Equiv.swap 1 9 * (Equiv.swap 1 4 * (Equiv.swap 0 7)))) -def sgT909 : Equiv.Perm (Fin 10) := Equiv.swap 4 5 * (Equiv.swap 4 7 * (Equiv.swap 5 1 * (Equiv.swap 4 2 * (Equiv.swap 2 6 * (Equiv.swap 2 3 * (Equiv.swap 1 8)))))) -def sgFlag909 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(0,1,4),(1,2,2),(0,3,3),(0,4,0)} -lemma sgCert909 : solveCompact 10 (.full [2,2,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [2,2,2,2,2] (Equiv.refl (Fin 10)) sgB909 sgT909) sgFlag909 = 6 := by - decide +kernel - -lemma sg909 : RowSquare [5,1,1,1,1,1] [5,5] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [2,2,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB909 sgT909 sgFlag909 - change solveCompact 10 (.full [2,2,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [2,2,2,2,2] (Equiv.refl (Fin 10)) sgB909 sgT909) sgFlag909 ≠ 0 - rw [sgCert909] - norm_num - -def sgB915 : Equiv.Perm (Fin 10) := Equiv.swap 1 4 * (Equiv.swap 4 7 * (Equiv.swap 4 3 * (Equiv.swap 3 5 * (Equiv.swap 2 8 * (Equiv.swap 1 0 * (Equiv.swap 0 6)))))) -def sgT915 : Equiv.Perm (Fin 10) := Equiv.swap 5 9 * (Equiv.swap 5 3 * (Equiv.swap 5 1 * (Equiv.swap 5 4 * (Equiv.swap 4 6 * (Equiv.swap 3 0 * (Equiv.swap 1 7 * (Equiv.swap 1 2 * (Equiv.swap 0 8)))))))) -def sgFlag915 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,0),(3,0,1),(4,0,2),(2,1,0),(1,1,4),(2,2,0),(0,3,0),(1,4,3)} -lemma sgCert915 : solveCompact 10 (.full [5,5]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) - (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB915 sgT915) sgFlag915 = -6 := by - decide +kernel - -lemma sg915 : RowSquare [5,2,1,1,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [5,2,1,1,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB915 sgT915 sgFlag915 - change solveCompact 10 (.full [5,5]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) - (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB915 sgT915) sgFlag915 ≠ 0 - rw [sgCert915] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Semigroup Leaves 4. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB826 : Equiv.Perm (Fin 10) := Equiv.swap 7 5 * (Equiv.swap 5 4 * (Equiv.swap 4 1 * (Equiv.swap 3 8 * (Equiv.swap 1 9 * (Equiv.swap 1 0 * (Equiv.swap 0 2)))))) +def sgT826 : Equiv.Perm (Fin 10) := Equiv.swap 3 6 * (Equiv.swap 6 0 * (Equiv.swap 0 4 * (Equiv.swap 4 8 * (Equiv.swap 3 7 * (Equiv.swap 2 1 * (Equiv.swap 1 9 * (Equiv.swap 0 5))))))) +def sgFlag826 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(2,0,1),(5,0,2),(3,0,3),(1,1,0),(4,1,0),(6,1,1),(1,2,0),(7,3,0)} +lemma sgCert826 : solveCompact 10 (.full [8,2]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [8,2] (Equiv.refl (Fin 10)) sgB826 sgT826) sgFlag826 = 24 := by + decide +kernel + +lemma sg826 : RowSquare [4,2,2,1,1] [2,2,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [8,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB826 sgT826 sgFlag826 + change solveCompact 10 (.full [8,2]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [8,2] (Equiv.refl (Fin 10)) sgB826 sgT826) sgFlag826 ≠ 0 + rw [sgCert826] + norm_num + +def sgB827 : Equiv.Perm (Fin 10) := Equiv.swap 8 1 * (Equiv.swap 1 5 * (Equiv.swap 5 3 * (Equiv.swap 5 6 * (Equiv.swap 1 0 * (Equiv.swap 3 9 * (Equiv.swap 1 4 * (Equiv.swap 1 2 * (Equiv.swap 0 7)))))))) +def sgT827 : Equiv.Perm (Fin 10) := Equiv.swap 7 3 * (Equiv.swap 3 9 * (Equiv.swap 3 5 * (Equiv.swap 0 4 * (Equiv.swap 0 1)))) +def sgFlag827 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(6,0,3),(2,1,0),(3,1,1),(4,1,2),(2,2,0),(5,3,0)} +lemma sgCert827 : solveCompact 10 (.full [7,3]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB827 sgT827) sgFlag827 = -8 := by + decide +kernel + +lemma sg827 : RowSquare [4,2,2,1,1] [2,2,2,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [7,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB827 sgT827 sgFlag827 + change solveCompact 10 (.full [7,3]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB827 sgT827) sgFlag827 ≠ 0 + rw [sgCert827] + norm_num + +def sgB828 : Equiv.Perm (Fin 10) := Equiv.swap 1 5 * (Equiv.swap 6 2 * (Equiv.swap 5 0 * (Equiv.swap 1 7 * (Equiv.swap 1 4 * (Equiv.swap 2 9 * (Equiv.swap 1 3 * (Equiv.swap 0 8))))))) +def sgT828 : Equiv.Perm (Fin 10) := Equiv.swap 7 3 * (Equiv.swap 0 4 * (Equiv.swap 4 1 * (Equiv.swap 3 8 * (Equiv.swap 2 5 * (Equiv.swap 1 9 * (Equiv.swap 0 6)))))) +def sgFlag828 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(4,0,2),(2,1,0),(3,1,1),(3,1,3),(5,2,0),(2,3,0)} +lemma sgCert828 : solveCompact 10 (.full [6,4]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB828 sgT828) sgFlag828 = 5 := by + decide +kernel + +lemma sg828 : RowSquare [4,2,2,1,1] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB828 sgT828 sgFlag828 + change solveCompact 10 (.full [6,4]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB828 sgT828) sgFlag828 ≠ 0 + rw [sgCert828] + norm_num + +def sgB829 : Equiv.Perm (Fin 10) := Equiv.swap 7 4 * (Equiv.swap 4 2 * (Equiv.swap 3 6 * (Equiv.swap 2 9 * (Equiv.swap 0 1)))) +def sgT829 : Equiv.Perm (Fin 10) := Equiv.swap 5 3 * (Equiv.swap 0 1 * (Equiv.swap 5 7 * (Equiv.swap 3 9 * (Equiv.swap 3 4 * (Equiv.swap 0 6 * (Equiv.swap 1 8 * (Equiv.swap 0 2))))))) +def sgFlag829 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(2,0,1),(4,0,2),(1,0,3),(3,1,0),(2,1,1),(1,2,0),(4,3,0)} +lemma sgCert829 : solveCompact 10 (.full [5,5]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB829 sgT829) sgFlag829 = 10 := by + decide +kernel + +lemma sg829 : RowSquare [4,2,2,1,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB829 sgT829 sgFlag829 + change solveCompact 10 (.full [5,5]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB829 sgT829) sgFlag829 ≠ 0 + rw [sgCert829] + norm_num + +def sgB832 : Equiv.Perm (Fin 10) := Equiv.swap 4 5 * (Equiv.swap 5 2 * (Equiv.swap 4 6 * (Equiv.swap 3 8 * (Equiv.swap 2 0 * (Equiv.swap 0 9 * (Equiv.swap 0 1)))))) +def sgT832 : Equiv.Perm (Fin 10) := Equiv.swap 2 7 * (Equiv.swap 7 3 * (Equiv.swap 2 0 * (Equiv.swap 2 4 * (Equiv.swap 4 6 * (Equiv.swap 3 1 * (Equiv.swap 2 5 * (Equiv.swap 1 9 * (Equiv.swap 0 8)))))))) +def sgFlag832 : Finset (ℕ × ℕ × ℕ) := {(6,0,0),(0,0,1),(1,0,1),(0,0,3),(2,1,0),(2,1,1),(3,1,1),(4,1,2),(5,2,0),(1,3,0)} +lemma sgCert832 : solveCompact 10 (.full [7,3]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [7,3] (Equiv.refl (Fin 10)) sgB832 sgT832) sgFlag832 = 36 := by + decide +kernel + +lemma sg832 : RowSquare [4,2,2,2] [2,2,2,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [7,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB832 sgT832 sgFlag832 + change solveCompact 10 (.full [7,3]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [7,3] (Equiv.refl (Fin 10)) sgB832 sgT832) sgFlag832 ≠ 0 + rw [sgCert832] + norm_num + +def sgB833 : Equiv.Perm (Fin 10) := Equiv.swap 2 4 * (Equiv.swap 2 7 * (Equiv.swap 4 8 * (Equiv.swap 3 5 * (Equiv.swap 2 6 * (Equiv.swap 0 1))))) +def sgT833 : Equiv.Perm (Fin 10) := Equiv.swap 6 3 * (Equiv.swap 6 1 * (Equiv.swap 5 9 * (Equiv.swap 3 8 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 0 * (Equiv.swap 0 7))))))) +def sgFlag833 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(1,0,1),(0,0,2),(0,1,0),(3,1,0),(5,1,1),(3,1,3),(4,2,0),(2,3,1)} +lemma sgCert833 : solveCompact 10 (.full [6,4]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [6,4] (Equiv.refl (Fin 10)) sgB833 sgT833) sgFlag833 = 6 := by + decide +kernel + +lemma sg833 : RowSquare [4,2,2,2] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB833 sgT833 sgFlag833 + change solveCompact 10 (.full [6,4]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [6,4] (Equiv.refl (Fin 10)) sgB833 sgT833) sgFlag833 ≠ 0 + rw [sgCert833] + norm_num + +def sgB834 : Equiv.Perm (Fin 10) := Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 5 9 * (Equiv.swap 4 2 * (Equiv.swap 3 6 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 8))))))) +def sgT834 : Equiv.Perm (Fin 10) := Equiv.swap 7 4 * (Equiv.swap 4 2 * (Equiv.swap 2 9 * (Equiv.swap 4 0 * (Equiv.swap 2 5 * (Equiv.swap 0 6))))) +def sgFlag834 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(3,0,1),(0,0,2),(1,1,0),(4,1,1),(2,1,3),(0,2,1),(3,3,0)} +lemma sgCert834 : solveCompact 10 (.full [5,5]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [5,5] (Equiv.refl (Fin 10)) sgB834 sgT834) sgFlag834 = 32 := by + decide +kernel + +lemma sg834 : RowSquare [4,2,2,2] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB834 sgT834 sgFlag834 + change solveCompact 10 (.full [5,5]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [5,5] (Equiv.refl (Fin 10)) sgB834 sgT834) sgFlag834 ≠ 0 + rw [sgCert834] + norm_num + +def sgB835 : Equiv.Perm (Fin 10) := Equiv.swap 2 9 * (Equiv.swap 5 0 * (Equiv.swap 5 6 * (Equiv.swap 1 4 * (Equiv.swap 2 8 * (Equiv.swap 1 3 * (Equiv.swap 0 7)))))) +def sgT835 : Equiv.Perm (Fin 10) := Equiv.swap 2 6 * (Equiv.swap 6 4 * (Equiv.swap 2 1 * (Equiv.swap 4 9 * (Equiv.swap 2 5 * (Equiv.swap 2 0 * (Equiv.swap 1 7 * (Equiv.swap 0 3))))))) +def sgFlag835 : Finset (ℕ × ℕ × ℕ) := {(4,0,0),(0,0,1),(3,0,1),(1,1,0),(6,1,1),(2,1,2),(7,1,3),(0,2,0),(5,3,0)} +lemma sgCert835 : solveCompact 10 (.full [8,1,1]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [8,1,1] (Equiv.refl (Fin 10)) sgB835 sgT835) sgFlag835 = -112 := by + decide +kernel + +lemma sg835 : RowSquare [4,2,2,2] [3,1,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [8,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB835 sgT835 sgFlag835 + change solveCompact 10 (.full [8,1,1]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [8,1,1] (Equiv.refl (Fin 10)) sgB835 sgT835) sgFlag835 ≠ 0 + rw [sgCert835] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB836 : Equiv.Perm (Fin 10) := Equiv.swap 4 7 * (Equiv.swap 3 0 * (Equiv.swap 4 6 * (Equiv.swap 3 1 * (Equiv.swap 1 5 * (Equiv.swap 1 2 * (Equiv.swap 0 8)))))) +def sgT836 : Equiv.Perm (Fin 10) := Equiv.swap 7 2 * (Equiv.swap 7 0 * (Equiv.swap 5 6 * (Equiv.swap 2 9 * (Equiv.swap 0 8 * (Equiv.swap 2 4 * (Equiv.swap 0 3 * (Equiv.swap 0 1))))))) +def sgFlag836 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(5,0,1),(2,0,3),(0,1,0),(1,1,1),(3,1,2),(4,2,1),(0,3,1)} +lemma sgCert836 : solveCompact 10 (.full [6,2,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [6,2,2] (Equiv.refl (Fin 10)) sgB836 sgT836) sgFlag836 = -8 := by + decide +kernel + +lemma sg836 : RowSquare [4,2,2,2] [3,3,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [6,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB836 sgT836 sgFlag836 + change solveCompact 10 (.full [6,2,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [6,2,2] (Equiv.refl (Fin 10)) sgB836 sgT836) sgFlag836 ≠ 0 + rw [sgCert836] + norm_num + +def sgB837 : Equiv.Perm (Fin 10) := Equiv.swap 0 1 * (Equiv.swap 0 7 * (Equiv.swap 0 6 * (Equiv.swap 0 2 * (Equiv.swap 2 5 * (Equiv.swap 2 3 * (Equiv.swap 1 8 * (Equiv.swap 0 4))))))) +def sgT837 : Equiv.Perm (Fin 10) := Equiv.swap 0 5 * (Equiv.swap 5 3 * (Equiv.swap 5 2 * (Equiv.swap 0 1 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 1 7 * (Equiv.swap 0 4))))))) +def sgFlag837 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,1),(1,0,2),(2,1,0),(3,1,0),(1,1,1),(2,2,3),(0,3,1)} +lemma sgCert837 : solveCompact 10 (.full [4,4,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [4,4,2] (Equiv.refl (Fin 10)) sgB837 sgT837) sgFlag837 = -6 := by + decide +kernel + +lemma sg837 : RowSquare [4,2,2,2] [3,3,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [4,4,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB837 sgT837 sgFlag837 + change solveCompact 10 (.full [4,4,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [4,4,2] (Equiv.refl (Fin 10)) sgB837 sgT837) sgFlag837 ≠ 0 + rw [sgCert837] + norm_num + +def sgB838 : Equiv.Perm (Fin 10) := Equiv.swap 2 5 * (Equiv.swap 5 1 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 2 8 * (Equiv.swap 1 9))))) +def sgT838 : Equiv.Perm (Fin 10) := Equiv.swap 7 6 * (Equiv.swap 7 1 * (Equiv.swap 6 4 * (Equiv.swap 1 8 * (Equiv.swap 4 0 * (Equiv.swap 0 9 * (Equiv.swap 1 5 * (Equiv.swap 0 2))))))) +def sgFlag838 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(6,0,1),(7,0,2),(1,0,3),(5,1,0),(0,1,1),(1,2,0),(4,2,2),(3,3,0)} +lemma sgCert838 : solveCompact 10 (.full [8,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB838 sgT838) sgFlag838 = -16 := by + decide +kernel + +lemma sg838 : RowSquare [4,3,1,1,1] [2,2,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [8,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB838 sgT838 sgFlag838 + change solveCompact 10 (.full [8,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB838 sgT838) sgFlag838 ≠ 0 + rw [sgCert838] + norm_num + +def sgB839 : Equiv.Perm (Fin 10) := Equiv.swap 6 9 * (Equiv.swap 6 0 * (Equiv.swap 1 8 * (Equiv.swap 1 3 * (Equiv.swap 3 5 * (Equiv.swap 1 4 * (Equiv.swap 1 2 * (Equiv.swap 0 7))))))) +def sgT839 : Equiv.Perm (Fin 10) := Equiv.swap 1 3 * (Equiv.swap 3 8 * (Equiv.swap 3 4 * (Equiv.swap 2 9 * (Equiv.swap 1 5 * (Equiv.swap 0 7))))) +def sgFlag839 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(2,0,2),(1,0,3),(3,1,0),(5,1,2),(2,2,0),(6,2,0),(4,3,1)} +lemma sgCert839 : solveCompact 10 (.full [7,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB839 sgT839) sgFlag839 = -3 := by + decide +kernel + +lemma sg839 : RowSquare [4,3,1,1,1] [2,2,2,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [7,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB839 sgT839 sgFlag839 + change solveCompact 10 (.full [7,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB839 sgT839) sgFlag839 ≠ 0 + rw [sgCert839] + norm_num + +def sgB840 : Equiv.Perm (Fin 10) := Equiv.swap 2 9 * (Equiv.swap 2 3 * (Equiv.swap 2 7 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 3 5 * (Equiv.swap 2 0 * (Equiv.swap 0 4))))))) +def sgT840 : Equiv.Perm (Fin 10) := Equiv.swap 6 9 * (Equiv.swap 6 2 * (Equiv.swap 4 0 * (Equiv.swap 0 7 * (Equiv.swap 2 8 * (Equiv.swap 0 3))))) +def sgFlag840 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,2),(4,0,3),(5,1,0),(1,1,1),(2,2,0),(1,3,1)} +lemma sgCert840 : solveCompact 10 (.full [6,4]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB840 sgT840) sgFlag840 = -2 := by + decide +kernel + +lemma sg840 : RowSquare [4,3,1,1,1] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB840 sgT840 sgFlag840 + change solveCompact 10 (.full [6,4]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB840 sgT840) sgFlag840 ≠ 0 + rw [sgCert840] + norm_num + +def sgB841 : Equiv.Perm (Fin 10) := Equiv.swap 6 1 * (Equiv.swap 6 4 * (Equiv.swap 4 0 * (Equiv.swap 4 5 * (Equiv.swap 0 7 * (Equiv.swap 0 3 * (Equiv.swap 1 8 * (Equiv.swap 0 2))))))) +def sgT841 : Equiv.Perm (Fin 10) := Equiv.swap 5 4 * (Equiv.swap 5 2 * (Equiv.swap 5 1 * (Equiv.swap 4 9 * (Equiv.swap 2 7 * (Equiv.swap 1 6 * (Equiv.swap 0 3)))))) +def sgFlag841 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,1),(3,0,2),(1,1,0),(2,2,0),(2,2,3),(0,3,0)} +lemma sgCert841 : solveCompact 10 (.full [5,5]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB841 sgT841) sgFlag841 = -2 := by + decide +kernel + +lemma sg841 : RowSquare [4,3,1,1,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB841 sgT841 sgFlag841 + change solveCompact 10 (.full [5,5]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB841 sgT841) sgFlag841 ≠ 0 + rw [sgCert841] + norm_num + +def sgB846 : Equiv.Perm (Fin 10) := Equiv.swap 1 5 * (Equiv.swap 5 9 * (Equiv.swap 5 7 * (Equiv.swap 1 8 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))))) +def sgT846 : Equiv.Perm (Fin 10) := Equiv.swap 1 0 * (Equiv.swap 1 8 * (Equiv.swap 5 4 * (Equiv.swap 4 3 * (Equiv.swap 3 2 * (Equiv.swap 2 6 * (Equiv.swap 1 7 * (Equiv.swap 0 9))))))) +def sgFlag846 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(0,0,1),(1,0,1),(1,0,2),(1,1,0),(4,1,0),(5,2,2),(0,2,3),(2,3,0)} +lemma sgCert846 : solveCompact 10 (.full [6,2,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB846 sgT846) sgFlag846 = 4 := by + decide +kernel + +lemma sg846 : RowSquare [4,3,1,1,1] [3,3,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [6,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB846 sgT846 sgFlag846 + change solveCompact 10 (.full [6,2,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB846 sgT846) sgFlag846 ≠ 0 + rw [sgCert846] + norm_num + +def sgB847 : Equiv.Perm (Fin 10) := Equiv.swap 8 0 * (Equiv.swap 0 5 * (Equiv.swap 5 4 * (Equiv.swap 4 9 * (Equiv.swap 1 7 * (Equiv.swap 1 3 * (Equiv.swap 0 6)))))) +def sgT847 : Equiv.Perm (Fin 10) := Equiv.swap 2 5 * (Equiv.swap 5 9 * (Equiv.swap 2 4 * (Equiv.swap 5 3 * (Equiv.swap 4 8 * (Equiv.swap 3 7 * (Equiv.swap 2 6)))))) +def sgFlag847 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(2,0,1),(0,0,2),(3,1,0),(1,1,3),(0,2,1),(2,2,2),(0,3,0)} +lemma sgCert847 : solveCompact 10 (.full [4,3,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB847 sgT847) sgFlag847 = 1 := by + decide +kernel + +lemma sg847 : RowSquare [4,3,1,1,1] [3,3,3,1] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [4,3,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB847 sgT847 sgFlag847 + change solveCompact 10 (.full [4,3,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB847 sgT847) sgFlag847 ≠ 0 + rw [sgCert847] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB873 : Equiv.Perm (Fin 10) := Equiv.swap 1 9 * (Equiv.swap 6 4 * (Equiv.swap 4 7 * (Equiv.swap 4 0 * (Equiv.swap 0 5 * (Equiv.swap 1 8 * (Equiv.swap 0 2)))))) +def sgT873 : Equiv.Perm (Fin 10) := Equiv.swap 6 1 * (Equiv.swap 2 0 * (Equiv.swap 4 8 * (Equiv.swap 1 9 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 7)))))) +def sgFlag873 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(1,0,1),(6,0,1),(7,0,2),(0,1,0),(2,1,0),(3,1,2),(4,2,0),(0,2,1),(5,2,2)} +lemma sgCert873 : solveCompact 10 (.full [8,2]) (.full [3,3,3,1]) (.full [3,3,3,1]) + (certificateEdges [3,3,3,1] [3,3,3,1] [8,2] (Equiv.refl (Fin 10)) sgB873 sgT873) sgFlag873 = -120 := by + decide +kernel + +lemma sg873 : RowSquare [4,3,3] [2,2,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [3,3,3,1]) (ts := [8,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB873 sgT873 sgFlag873 + change solveCompact 10 (.full [8,2]) (.full [3,3,3,1]) (.full [3,3,3,1]) + (certificateEdges [3,3,3,1] [3,3,3,1] [8,2] (Equiv.refl (Fin 10)) sgB873 sgT873) sgFlag873 ≠ 0 + rw [sgCert873] + norm_num + +def sgB874 : Equiv.Perm (Fin 10) := Equiv.swap 0 3 * (Equiv.swap 0 8 * (Equiv.swap 0 7 * (Equiv.swap 3 9 * (Equiv.swap 2 6 * (Equiv.swap 0 4 * (Equiv.swap 0 1)))))) +def sgT874 : Equiv.Perm (Fin 10) := Equiv.swap 3 9 * (Equiv.swap 0 8 * (Equiv.swap 4 5 * (Equiv.swap 3 2 * (Equiv.swap 2 7 * (Equiv.swap 0 6))))) +def sgFlag874 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(3,0,0),(6,0,1),(1,0,2),(1,1,1),(5,1,1),(2,1,2),(0,2,0),(4,2,2)} +lemma sgCert874 : solveCompact 10 (.full [7,3]) (.full [3,3,3,1]) (.full [3,3,3,1]) + (certificateEdges [3,3,3,1] [3,3,3,1] [7,3] (Equiv.refl (Fin 10)) sgB874 sgT874) sgFlag874 = 45 := by + decide +kernel + +lemma sg874 : RowSquare [4,3,3] [2,2,2,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [3,3,3,1]) (ts := [7,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB874 sgT874 sgFlag874 + change solveCompact 10 (.full [7,3]) (.full [3,3,3,1]) (.full [3,3,3,1]) + (certificateEdges [3,3,3,1] [3,3,3,1] [7,3] (Equiv.refl (Fin 10)) sgB874 sgT874) sgFlag874 ≠ 0 + rw [sgCert874] + norm_num + +def sgB875 : Equiv.Perm (Fin 10) := Equiv.swap 6 5 * (Equiv.swap 6 2 * (Equiv.swap 6 7 * (Equiv.swap 5 4 * (Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 2 8 * (Equiv.swap 0 9 * (Equiv.swap 0 1)))))))) +def sgT875 : Equiv.Perm (Fin 10) := Equiv.swap 4 9 * (Equiv.swap 4 5 * (Equiv.swap 4 7 * (Equiv.swap 5 8 * (Equiv.swap 4 0 * (Equiv.swap 0 1 * (Equiv.swap 0 3 * (Equiv.swap 1 6 * (Equiv.swap 0 2)))))))) +def sgFlag875 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(1,0,1),(2,0,1),(0,1,0),(5,1,2),(2,2,1),(3,2,2)} +lemma sgCert875 : solveCompact 10 (.full [6,4]) (.full [3,3,3,1]) (.full [3,3,3,1]) + (certificateEdges [3,3,3,1] [3,3,3,1] [6,4] (Equiv.refl (Fin 10)) sgB875 sgT875) sgFlag875 = -21 := by + decide +kernel + +lemma sg875 : RowSquare [4,3,3] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [3,3,3,1]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB875 sgT875 sgFlag875 + change solveCompact 10 (.full [6,4]) (.full [3,3,3,1]) (.full [3,3,3,1]) + (certificateEdges [3,3,3,1] [3,3,3,1] [6,4] (Equiv.refl (Fin 10)) sgB875 sgT875) sgFlag875 ≠ 0 + rw [sgCert875] + norm_num + +def sgB876 : Equiv.Perm (Fin 10) := Equiv.swap 4 7 * (Equiv.swap 7 6 * (Equiv.swap 6 2 * (Equiv.swap 4 8 * (Equiv.swap 4 3 * (Equiv.swap 3 0 * (Equiv.swap 2 9 * (Equiv.swap 0 5 * (Equiv.swap 0 1)))))))) +def sgT876 : Equiv.Perm (Fin 10) := Equiv.swap 7 8 * (Equiv.swap 3 4 * (Equiv.swap 4 9 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 5))))) +def sgFlag876 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(0,0,1),(3,0,1),(6,0,2),(0,1,0),(5,1,2),(1,2,0),(7,2,1),(4,2,2)} +lemma sgCert876 : solveCompact 10 (.full [8,1,1]) (.full [3,3,3,1]) (.full [3,3,3,1]) + (certificateEdges [3,3,3,1] [3,3,3,1] [8,1,1] (Equiv.refl (Fin 10)) sgB876 sgT876) sgFlag876 = 60 := by + decide +kernel + +lemma sg876 : RowSquare [4,3,3] [3,1,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [3,3,3,1]) (ts := [8,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB876 sgT876 sgFlag876 + change solveCompact 10 (.full [8,1,1]) (.full [3,3,3,1]) (.full [3,3,3,1]) + (certificateEdges [3,3,3,1] [3,3,3,1] [8,1,1] (Equiv.refl (Fin 10)) sgB876 sgT876) sgFlag876 ≠ 0 + rw [sgCert876] + norm_num + +def sgB877 : Equiv.Perm (Fin 10) := Equiv.swap 7 9 * (Equiv.swap 7 8 * (Equiv.swap 0 4 * (Equiv.swap 1 6 * (Equiv.swap 1 2 * (Equiv.swap 0 3))))) +def sgT877 : Equiv.Perm (Fin 10) := Equiv.swap 7 3 * (Equiv.swap 3 1 * (Equiv.swap 4 5 * (Equiv.swap 3 2 * (Equiv.swap 2 6 * (Equiv.swap 1 9))))) +def sgFlag877 : Finset (ℕ × ℕ × ℕ) := {(5,0,0),(1,0,1),(0,0,3),(3,1,0),(0,1,1),(4,1,1),(2,1,2),(6,2,0),(2,3,0)} +lemma sgCert877 : solveCompact 10 (.full [7,3]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [7,3] (Equiv.refl (Fin 10)) sgB877 sgT877) sgFlag877 = 72 := by + decide +kernel + +lemma sg877 : RowSquare [4,4,1,1] [2,2,2,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [7,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB877 sgT877 sgFlag877 + change solveCompact 10 (.full [7,3]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [7,3] (Equiv.refl (Fin 10)) sgB877 sgT877) sgFlag877 ≠ 0 + rw [sgCert877] + norm_num + +def sgB878 : Equiv.Perm (Fin 10) := Equiv.swap 3 9 * (Equiv.swap 5 7 * (Equiv.swap 1 8 * (Equiv.swap 3 6 * (Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 4)))))) +def sgT878 : Equiv.Perm (Fin 10) := Equiv.swap 5 9 * (Equiv.swap 6 0 * (Equiv.swap 5 3 * (Equiv.swap 0 1 * (Equiv.swap 3 7 * (Equiv.swap 1 8 * (Equiv.swap 0 4)))))) +def sgFlag878 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(0,0,1),(3,1,1),(2,1,2),(5,1,3),(2,2,0),(1,3,0)} +lemma sgCert878 : solveCompact 10 (.full [6,4]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [6,4] (Equiv.refl (Fin 10)) sgB878 sgT878) sgFlag878 = 24 := by + decide +kernel + +lemma sg878 : RowSquare [4,4,1,1] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB878 sgT878 sgFlag878 + change solveCompact 10 (.full [6,4]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [6,4] (Equiv.refl (Fin 10)) sgB878 sgT878) sgFlag878 ≠ 0 + rw [sgCert878] + norm_num + +def sgB879 : Equiv.Perm (Fin 10) := Equiv.swap 7 8 * (Equiv.swap 4 2 * (Equiv.swap 3 6 * (Equiv.swap 2 0 * (Equiv.swap 1 9 * (Equiv.swap 0 5))))) +def sgT879 : Equiv.Perm (Fin 10) := Equiv.swap 1 7 * (Equiv.swap 7 4 * (Equiv.swap 4 9 * (Equiv.swap 4 5 * (Equiv.swap 3 6 * (Equiv.swap 1 8 * (Equiv.swap 0 2)))))) +def sgFlag879 : Finset (ℕ × ℕ × ℕ) := {(2,0,1),(0,0,2),(3,0,3),(4,1,0),(1,1,1),(3,1,1),(0,2,0),(1,3,0)} +lemma sgCert879 : solveCompact 10 (.full [5,5]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [5,5] (Equiv.refl (Fin 10)) sgB879 sgT879) sgFlag879 = -8 := by + decide +kernel + +lemma sg879 : RowSquare [4,4,1,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB879 sgT879 sgFlag879 + change solveCompact 10 (.full [5,5]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [5,5] (Equiv.refl (Fin 10)) sgB879 sgT879) sgFlag879 ≠ 0 + rw [sgCert879] + norm_num + +def sgB880 : Equiv.Perm (Fin 10) := Equiv.swap 6 2 * (Equiv.swap 5 0 * (Equiv.swap 2 1 * (Equiv.swap 0 7 * (Equiv.swap 2 4 * (Equiv.swap 1 9 * (Equiv.swap 0 3)))))) +def sgT880 : Equiv.Perm (Fin 10) := Equiv.swap 8 2 * (Equiv.swap 2 1 * (Equiv.swap 1 9 * (Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 2 4 * (Equiv.swap 1 0 * (Equiv.swap 0 5))))))) +def sgFlag880 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(3,0,1),(6,0,2),(5,0,3),(0,1,0),(0,1,1),(1,1,1),(4,2,0),(7,3,1)} +lemma sgCert880 : solveCompact 10 (.full [8,1,1]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [8,1,1] (Equiv.refl (Fin 10)) sgB880 sgT880) sgFlag880 = -112 := by + decide +kernel + +lemma sg880 : RowSquare [4,4,1,1] [3,1,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [8,1,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB880 sgT880 sgFlag880 + change solveCompact 10 (.full [8,1,1]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [8,1,1] (Equiv.refl (Fin 10)) sgB880 sgT880) sgFlag880 ≠ 0 + rw [sgCert880] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB881 : Equiv.Perm (Fin 10) := Equiv.swap 0 2 * (Equiv.swap 1 8 * (Equiv.swap 1 6 * (Equiv.swap 1 5 * (Equiv.swap 2 9 * (Equiv.swap 1 3 * (Equiv.swap 0 7)))))) +def sgT881 : Equiv.Perm (Fin 10) := Equiv.swap 4 0 * (Equiv.swap 3 7 * (Equiv.swap 1 5 * (Equiv.swap 0 6))) +def sgFlag881 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,0),(1,0,1),(6,0,1),(0,1,0),(1,1,0),(3,1,2),(5,1,3),(2,2,1),(0,3,1)} +lemma sgCert881 : solveCompact 10 (.full [7,2,1]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [7,2,1] (Equiv.refl (Fin 10)) sgB881 sgT881) sgFlag881 = -4 := by + decide +kernel + +lemma sg881 : RowSquare [4,4,1,1] [3,2,1,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [7,2,1]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB881 sgT881 sgFlag881 + change solveCompact 10 (.full [7,2,1]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [7,2,1] (Equiv.refl (Fin 10)) sgB881 sgT881) sgFlag881 ≠ 0 + rw [sgCert881] + norm_num + +def sgB884 : Equiv.Perm (Fin 10) := Equiv.swap 6 2 * (Equiv.swap 2 0 * (Equiv.swap 2 5 * (Equiv.swap 2 3 * (Equiv.swap 1 8 * (Equiv.swap 0 7))))) +def sgT884 : Equiv.Perm (Fin 10) := Equiv.swap 4 9 * (Equiv.swap 4 1 * (Equiv.swap 3 0 * (Equiv.swap 2 6 * (Equiv.swap 1 7 * (Equiv.swap 0 5))))) +def sgFlag884 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(5,0,1),(2,0,2),(1,1,0),(3,1,0),(4,1,1),(0,2,3),(0,3,1)} +lemma sgCert884 : solveCompact 10 (.full [6,2,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [6,2,2] (Equiv.refl (Fin 10)) sgB884 sgT884) sgFlag884 = 6 := by + decide +kernel + +lemma sg884 : RowSquare [4,4,1,1] [3,3,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [6,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB884 sgT884 sgFlag884 + change solveCompact 10 (.full [6,2,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [6,2,2] (Equiv.refl (Fin 10)) sgB884 sgT884) sgFlag884 ≠ 0 + rw [sgCert884] + norm_num + +def sgB885 : Equiv.Perm (Fin 10) := Equiv.swap 1 9 * (Equiv.swap 6 0 * (Equiv.swap 4 2 * (Equiv.swap 1 7 * (Equiv.swap 2 5 * (Equiv.swap 1 3 * (Equiv.swap 0 8)))))) +def sgT885 : Equiv.Perm (Fin 10) := Equiv.swap 5 8 * (Equiv.swap 5 6 * (Equiv.swap 3 7 * (Equiv.swap 2 1 * (Equiv.swap 1 4)))) +def sgFlag885 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,2),(1,1,0),(1,1,1),(3,1,1),(4,1,3),(1,2,1),(2,3,1)} +lemma sgCert885 : solveCompact 10 (.full [5,3,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [5,3,2] (Equiv.refl (Fin 10)) sgB885 sgT885) sgFlag885 = -1 := by + decide +kernel + +lemma sg885 : RowSquare [4,4,1,1] [3,3,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [5,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB885 sgT885 sgFlag885 + change solveCompact 10 (.full [5,3,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [5,3,2] (Equiv.refl (Fin 10)) sgB885 sgT885) sgFlag885 ≠ 0 + rw [sgCert885] + norm_num + +def sgB886 : Equiv.Perm (Fin 10) := Equiv.swap 2 0 * (Equiv.swap 0 9 * (Equiv.swap 2 7 * (Equiv.swap 2 5 * (Equiv.swap 0 6)))) +def sgT886 : Equiv.Perm (Fin 10) := Equiv.swap 8 7 * (Equiv.swap 7 3 * (Equiv.swap 3 0 * (Equiv.swap 3 5 * (Equiv.swap 3 1 * (Equiv.swap 1 4 * (Equiv.swap 0 9)))))) +def sgFlag886 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(2,0,1),(3,1,0),(0,1,1),(0,1,2),(2,2,1),(1,3,3)} +lemma sgCert886 : solveCompact 10 (.full [4,4,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [4,4,2] (Equiv.refl (Fin 10)) sgB886 sgT886) sgFlag886 = -1 := by + decide +kernel + +lemma sg886 : RowSquare [4,4,1,1] [3,3,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [4,4,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB886 sgT886 sgFlag886 + change solveCompact 10 (.full [4,4,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [4,4,2] (Equiv.refl (Fin 10)) sgB886 sgT886) sgFlag886 ≠ 0 + rw [sgCert886] + norm_num + +def sgB887 : Equiv.Perm (Fin 10) := Equiv.swap 6 1 * (Equiv.swap 6 4 * (Equiv.swap 4 3 * (Equiv.swap 3 7 * (Equiv.swap 2 8 * (Equiv.swap 1 9))))) +def sgT887 : Equiv.Perm (Fin 10) := Equiv.swap 0 3 * (Equiv.swap 3 1 * (Equiv.swap 0 8 * (Equiv.swap 3 2 * (Equiv.swap 2 7 * (Equiv.swap 1 9 * (Equiv.swap 0 4)))))) +def sgFlag887 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,2),(0,0,3),(0,1,0),(1,1,1),(1,2,0),(2,3,1)} +lemma sgCert887 : solveCompact 10 (.full [4,2,2,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [4,2,2,2] (Equiv.refl (Fin 10)) sgB887 sgT887) sgFlag887 = 1 := by + decide +kernel + +lemma sg887 : RowSquare [4,4,1,1] [4,4,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,2]) (ts := [4,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB887 sgT887 sgFlag887 + change solveCompact 10 (.full [4,2,2,2]) (.full [4,2,2,2]) (.full [4,2,2,2]) + (certificateEdges [4,2,2,2] [4,2,2,2] [4,2,2,2] (Equiv.refl (Fin 10)) sgB887 sgT887) sgFlag887 ≠ 0 + rw [sgCert887] + norm_num + +def sgB889 : Equiv.Perm (Fin 10) := Equiv.swap 1 3 * (Equiv.swap 3 2 * (Equiv.swap 2 9 * (Equiv.swap 4 5 * (Equiv.swap 3 7 * (Equiv.swap 2 6 * (Equiv.swap 1 0 * (Equiv.swap 0 8))))))) +def sgT889 : Equiv.Perm (Fin 10) := Equiv.swap 2 0 * (Equiv.swap 0 9 * (Equiv.swap 4 5 * (Equiv.swap 0 6 * (Equiv.swap 2 8 * (Equiv.swap 0 3 * (Equiv.swap 0 1)))))) +def sgFlag889 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(7,0,2),(0,0,3),(4,0,4),(3,1,0),(0,2,0),(6,3,0),(5,4,0)} +lemma sgCert889 : solveCompact 10 (.full [8,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB889 sgT889) sgFlag889 = 1152 := by + decide +kernel + +lemma sg889 : RowSquare [5,1,1,1,1,1] [2,2,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [8,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB889 sgT889 sgFlag889 + change solveCompact 10 (.full [8,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB889 sgT889) sgFlag889 ≠ 0 + rw [sgCert889] + norm_num + +def sgB890 : Equiv.Perm (Fin 10) := Equiv.swap 1 2 * (Equiv.swap 5 3 * (Equiv.swap 4 0 * (Equiv.swap 3 8 * (Equiv.swap 2 9 * (Equiv.swap 1 6 * (Equiv.swap 0 7)))))) +def sgT890 : Equiv.Perm (Fin 10) := Equiv.swap 4 9 * (Equiv.swap 4 7 * (Equiv.swap 4 3 * (Equiv.swap 4 5 * (Equiv.swap 3 6 * (Equiv.swap 1 8))))) +def sgFlag890 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(4,0,1),(0,0,2),(3,0,3),(2,0,4),(1,1,0),(2,2,0),(6,3,0),(5,4,0)} +lemma sgCert890 : solveCompact 10 (.full [7,3]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB890 sgT890) sgFlag890 = -48 := by + decide +kernel + +lemma sg890 : RowSquare [5,1,1,1,1,1] [2,2,2,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [7,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB890 sgT890 sgFlag890 + change solveCompact 10 (.full [7,3]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB890 sgT890) sgFlag890 ≠ 0 + rw [sgCert890] + norm_num + +def sgB891 : Equiv.Perm (Fin 10) := Equiv.swap 4 6 * (Equiv.swap 6 3 * (Equiv.swap 4 8 * (Equiv.swap 3 9 * (Equiv.swap 1 5 * (Equiv.swap 0 2))))) +def sgT891 : Equiv.Perm (Fin 10) := Equiv.swap 1 9 * (Equiv.swap 1 3 * (Equiv.swap 1 4 * (Equiv.swap 4 7 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 1 5 * (Equiv.swap 0 8))))))) +def sgFlag891 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(4,0,1),(2,0,2),(0,0,3),(1,0,4),(5,1,0),(0,2,0),(2,3,0),(1,4,0)} +lemma sgCert891 : solveCompact 10 (.full [6,4]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB891 sgT891) sgFlag891 = 144 := by + decide +kernel + +lemma sg891 : RowSquare [5,1,1,1,1,1] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB891 sgT891 sgFlag891 + change solveCompact 10 (.full [6,4]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB891 sgT891) sgFlag891 ≠ 0 + rw [sgCert891] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB892 : Equiv.Perm (Fin 10) := Equiv.swap 2 1 * (Equiv.swap 2 3 * (Equiv.swap 1 4 * (Equiv.swap 4 9 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 0 7))))))) +def sgT892 : Equiv.Perm (Fin 10) := Equiv.swap 8 1 * (Equiv.swap 1 4 * (Equiv.swap 5 7 * (Equiv.swap 4 2 * (Equiv.swap 1 6 * (Equiv.swap 2 9 * (Equiv.swap 1 3)))))) +def sgFlag892 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,1),(3,0,2),(4,0,3),(2,0,4),(3,1,0),(4,2,0),(1,3,0),(2,4,0)} +lemma sgCert892 : solveCompact 10 (.full [5,5]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB892 sgT892) sgFlag892 = 1440 := by + decide +kernel + +lemma sg892 : RowSquare [5,1,1,1,1,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB892 sgT892 sgFlag892 + change solveCompact 10 (.full [5,5]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB892 sgT892) sgFlag892 ≠ 0 + rw [sgCert892] + norm_num + +def sgB897 : Equiv.Perm (Fin 10) := Equiv.swap 5 4 * (Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 4 9 * (Equiv.swap 0 1 * (Equiv.swap 2 8 * (Equiv.swap 1 7 * (Equiv.swap 0 3))))))) +def sgT897 : Equiv.Perm (Fin 10) := Equiv.swap 6 7 * (Equiv.swap 5 9 * (Equiv.swap 4 1 * (Equiv.swap 1 8 * (Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 3)))))) +def sgFlag897 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(5,0,0),(0,0,2),(3,0,3),(4,0,4),(2,1,0),(0,2,0),(0,3,1),(1,4,0)} +lemma sgCert897 : solveCompact 10 (.full [6,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB897 sgT897) sgFlag897 = 12 := by + decide +kernel + +lemma sg897 : RowSquare [5,1,1,1,1,1] [3,3,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [6,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB897 sgT897 sgFlag897 + change solveCompact 10 (.full [6,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB897 sgT897) sgFlag897 ≠ 0 + rw [sgCert897] + norm_num + +def sgB898 : Equiv.Perm (Fin 10) := Equiv.swap 2 6 * (Equiv.swap 6 0 * (Equiv.swap 0 9 * (Equiv.swap 1 5 * (Equiv.swap 2 7 * (Equiv.swap 1 3 * (Equiv.swap 0 4)))))) +def sgT898 : Equiv.Perm (Fin 10) := Equiv.swap 5 8 * (Equiv.swap 5 7 * (Equiv.swap 5 2 * (Equiv.swap 2 1 * (Equiv.swap 2 0 * (Equiv.swap 1 6 * (Equiv.swap 0 3)))))) +def sgFlag898 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(2,0,1),(1,0,2),(3,0,4),(1,1,3),(0,2,0),(1,3,0),(4,4,0)} +lemma sgCert898 : solveCompact 10 (.full [5,3,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,3,2] (Equiv.refl (Fin 10)) sgB898 sgT898) sgFlag898 = -36 := by + decide +kernel + +lemma sg898 : RowSquare [5,1,1,1,1,1] [3,3,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [5,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB898 sgT898 sgFlag898 + change solveCompact 10 (.full [5,3,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,3,2] (Equiv.refl (Fin 10)) sgB898 sgT898) sgFlag898 ≠ 0 + rw [sgCert898] + norm_num + +def sgB899 : Equiv.Perm (Fin 10) := Equiv.swap 1 5 * (Equiv.swap 1 0 * (Equiv.swap 1 3 * (Equiv.swap 5 4 * (Equiv.swap 4 2 * (Equiv.swap 3 7 * (Equiv.swap 2 9 * (Equiv.swap 1 6 * (Equiv.swap 0 8)))))))) +def sgT899 : Equiv.Perm (Fin 10) := Equiv.swap 0 2 * (Equiv.swap 2 9 * (Equiv.swap 4 1 * (Equiv.swap 3 5 * (Equiv.swap 2 6 * (Equiv.swap 1 8 * (Equiv.swap 0 7)))))) +def sgFlag899 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(3,0,0),(0,0,1),(1,0,3),(3,0,4),(0,1,0),(2,2,0),(1,3,0),(1,4,2)} +lemma sgCert899 : solveCompact 10 (.full [4,4,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB899 sgT899) sgFlag899 = 36 := by + decide +kernel + +lemma sg899 : RowSquare [5,1,1,1,1,1] [3,3,2,2] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [4,4,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB899 sgT899 sgFlag899 + change solveCompact 10 (.full [4,4,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB899 sgT899) sgFlag899 ≠ 0 + rw [sgCert899] + norm_num + +def sgB902 : Equiv.Perm (Fin 10) := Equiv.swap 0 1 * (Equiv.swap 0 7 * (Equiv.swap 0 6 * (Equiv.swap 4 2 * (Equiv.swap 2 9 * (Equiv.swap 2 3 * (Equiv.swap 1 8 * (Equiv.swap 0 5))))))) +def sgT902 : Equiv.Perm (Fin 10) := Equiv.swap 2 8 * (Equiv.swap 5 7 * (Equiv.swap 4 9 * (Equiv.swap 2 6 * (Equiv.swap 2 0 * (Equiv.swap 0 3 * (Equiv.swap 0 1)))))) +def sgFlag902 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,0),(1,0,1),(0,0,4),(3,1,0),(0,2,3),(0,3,0),(1,4,2)} +lemma sgCert902 : solveCompact 10 (.full [4,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,2,2,2] (Equiv.refl (Fin 10)) sgB902 sgT902) sgFlag902 = 8 := by + decide +kernel + +lemma sg902 : RowSquare [5,1,1,1,1,1] [4,4,1,1] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [4,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB902 sgT902 sgFlag902 + change solveCompact 10 (.full [4,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,2,2,2] (Equiv.refl (Fin 10)) sgB902 sgT902) sgFlag902 ≠ 0 + rw [sgCert902] + norm_num + +def sgB903 : Equiv.Perm (Fin 10) := Equiv.swap 3 9 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 8 * (Equiv.swap 1 7 * (Equiv.swap 0 6))))) +def sgT903 : Equiv.Perm (Fin 10) := Equiv.swap 3 2 * (Equiv.swap 3 1 * (Equiv.swap 3 7 * (Equiv.swap 2 9 * (Equiv.swap 3 6 * (Equiv.swap 2 5 * (Equiv.swap 1 8 * (Equiv.swap 0 4))))))) +def sgFlag903 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,0),(1,0,1),(0,0,3),(0,1,0),(2,2,0),(0,3,4),(0,4,2)} +lemma sgCert903 : solveCompact 10 (.full [3,3,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [3,3,2,2] (Equiv.refl (Fin 10)) sgB903 sgT903) sgFlag903 = 4 := by + decide +kernel + +lemma sg903 : RowSquare [5,1,1,1,1,1] [4,4,2] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [3,3,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB903 sgT903 sgFlag903 + change solveCompact 10 (.full [3,3,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [3,3,2,2] (Equiv.refl (Fin 10)) sgB903 sgT903) sgFlag903 ≠ 0 + rw [sgCert903] + norm_num + +def sgB909 : Equiv.Perm (Fin 10) := Equiv.swap 6 5 * (Equiv.swap 5 8 * (Equiv.swap 1 9 * (Equiv.swap 1 4 * (Equiv.swap 0 7)))) +def sgT909 : Equiv.Perm (Fin 10) := Equiv.swap 4 5 * (Equiv.swap 4 7 * (Equiv.swap 5 1 * (Equiv.swap 4 2 * (Equiv.swap 2 6 * (Equiv.swap 2 3 * (Equiv.swap 1 8)))))) +def sgFlag909 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(0,1,4),(1,2,2),(0,3,3),(0,4,0)} +lemma sgCert909 : solveCompact 10 (.full [2,2,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [2,2,2,2,2] (Equiv.refl (Fin 10)) sgB909 sgT909) sgFlag909 = 6 := by + decide +kernel + +lemma sg909 : RowSquare [5,1,1,1,1,1] [5,5] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [2,2,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB909 sgT909 sgFlag909 + change solveCompact 10 (.full [2,2,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [2,2,2,2,2] (Equiv.refl (Fin 10)) sgB909 sgT909) sgFlag909 ≠ 0 + rw [sgCert909] + norm_num + +def sgB915 : Equiv.Perm (Fin 10) := Equiv.swap 1 4 * (Equiv.swap 4 7 * (Equiv.swap 4 3 * (Equiv.swap 3 5 * (Equiv.swap 2 8 * (Equiv.swap 1 0 * (Equiv.swap 0 6)))))) +def sgT915 : Equiv.Perm (Fin 10) := Equiv.swap 5 9 * (Equiv.swap 5 3 * (Equiv.swap 5 1 * (Equiv.swap 5 4 * (Equiv.swap 4 6 * (Equiv.swap 3 0 * (Equiv.swap 1 7 * (Equiv.swap 1 2 * (Equiv.swap 0 8)))))))) +def sgFlag915 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,0),(3,0,1),(4,0,2),(2,1,0),(1,1,4),(2,2,0),(0,3,0),(1,4,3)} +lemma sgCert915 : solveCompact 10 (.full [5,5]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) + (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB915 sgT915) sgFlag915 = -6 := by + decide +kernel + +lemma sg915 : RowSquare [5,2,1,1,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [5,2,1,1,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB915 sgT915 sgFlag915 + change solveCompact 10 (.full [5,5]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) + (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB915 sgT915) sgFlag915 ≠ 0 + rw [sgCert915] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves5.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves5.lean index b29d44ae6842396c807081fd637230b0d5812248..c55432871fc158aed8d26923cb6f52794a74c6e3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves5.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLeaves5.lean @@ -1,652 +1,652 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Semigroup Leaves 5. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB922 : Equiv.Perm (Fin 10) := Equiv.swap 8 0 * (Equiv.swap 0 9 * (Equiv.swap 3 7 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 5 * (Equiv.swap 0 6)))))) -def sgT922 : Equiv.Perm (Fin 10) := Equiv.swap 5 0 * (Equiv.swap 4 2 * (Equiv.swap 5 7 * (Equiv.swap 4 6 * (Equiv.swap 0 1 * (Equiv.swap 2 9 * (Equiv.swap 1 8 * (Equiv.swap 0 3))))))) -def sgFlag922 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(3,0,1),(0,0,3),(0,1,0),(2,1,0),(1,2,4),(1,3,2),(2,4,0)} -lemma sgCert922 : solveCompact 10 (.full [4,4,2]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) - (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB922 sgT922) sgFlag922 = 4 := by - decide +kernel - -lemma sg922 : RowSquare [5,2,1,1,1] [3,3,2,2] := by - apply rowSquare_compact (n := 10) (cs := [5,2,1,1,1]) (ts := [4,4,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB922 sgT922 sgFlag922 - change solveCompact 10 (.full [4,4,2]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) - (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB922 sgT922) sgFlag922 ≠ 0 - rw [sgCert922] - norm_num - -def sgB932 : Equiv.Perm (Fin 10) := Equiv.swap 3 7 * (Equiv.swap 7 1 * (Equiv.swap 3 2 * (Equiv.swap 3 6 * (Equiv.swap 1 9 * (Equiv.swap 3 5 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 8)))))))) -def sgT932 : Equiv.Perm (Fin 10) := Equiv.swap 4 6 * (Equiv.swap 6 0 * (Equiv.swap 6 1 * (Equiv.swap 1 7 * (Equiv.swap 4 8 * (Equiv.swap 0 2 * (Equiv.swap 2 9 * (Equiv.swap 1 5 * (Equiv.swap 0 3)))))))) -def sgFlag932 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(1,0,1),(1,0,3),(1,1,2),(2,1,4),(1,2,0),(2,3,0),(0,4,0)} -lemma sgCert932 : solveCompact 10 (.full [3,3,2,2]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) - (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [3,3,2,2] (Equiv.refl (Fin 10)) sgB932 sgT932) sgFlag932 = 1 := by - decide +kernel - -lemma sg932 : RowSquare [5,2,1,1,1] [4,4,2] := by - apply rowSquare_compact (n := 10) (cs := [5,2,1,1,1]) (ts := [3,3,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB932 sgT932 sgFlag932 - change solveCompact 10 (.full [3,3,2,2]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) - (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [3,3,2,2] (Equiv.refl (Fin 10)) sgB932 sgT932) sgFlag932 ≠ 0 - rw [sgCert932] - norm_num - -def sgB939 : Equiv.Perm (Fin 10) := Equiv.swap 1 7 * (Equiv.swap 7 3 * (Equiv.swap 3 9 * (Equiv.swap 1 0 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 0 8)))))))) -def sgT939 : Equiv.Perm (Fin 10) := Equiv.swap 8 0 * (Equiv.swap 1 7 * (Equiv.swap 0 9 * (Equiv.swap 2 6 * (Equiv.swap 1 4 * (Equiv.swap 0 3))))) -def sgFlag939 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,1),(1,0,3),(0,1,0),(0,2,1),(1,3,4),(1,4,2)} -lemma sgCert939 : solveCompact 10 (.full [2,2,2,2,2]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) - (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [2,2,2,2,2] (Equiv.refl (Fin 10)) sgB939 sgT939) sgFlag939 = 2 := by - decide +kernel - -lemma sg939 : RowSquare [5,2,1,1,1] [5,5] := by - apply rowSquare_compact (n := 10) (cs := [5,2,1,1,1]) (ts := [2,2,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB939 sgT939 sgFlag939 - change solveCompact 10 (.full [2,2,2,2,2]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) - (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [2,2,2,2,2] (Equiv.refl (Fin 10)) sgB939 sgT939) sgFlag939 ≠ 0 - rw [sgCert939] - norm_num - -def sgB940 : Equiv.Perm (Fin 10) := Equiv.swap 6 4 * (Equiv.swap 2 9 * (Equiv.swap 4 8 * (Equiv.swap 1 7 * (Equiv.swap 2 5 * (Equiv.swap 1 3))))) -def sgT940 : Equiv.Perm (Fin 10) := Equiv.swap 7 2 * (Equiv.swap 2 3 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 3 5 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 9))))))) -def sgFlag940 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(6,0,0),(2,0,1),(0,0,2),(7,0,2),(0,1,0),(4,1,3),(3,2,0),(1,2,1),(5,3,0)} -lemma sgCert940 : solveCompact 10 (.full [8,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB940 sgT940) sgFlag940 = 8 := by - decide +kernel - -lemma sg940 : RowSquare [5,2,2,1] [2,2,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [8,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB940 sgT940 sgFlag940 - change solveCompact 10 (.full [8,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB940 sgT940) sgFlag940 ≠ 0 - rw [sgCert940] - norm_num - -def sgB941 : Equiv.Perm (Fin 10) := Equiv.swap 6 4 * (Equiv.swap 4 0 * (Equiv.swap 3 8 * (Equiv.swap 1 9 * (Equiv.swap 0 7)))) -def sgT941 : Equiv.Perm (Fin 10) := Equiv.swap 7 3 * (Equiv.swap 5 9 * (Equiv.swap 5 6 * (Equiv.swap 3 8 * (Equiv.swap 3 2 * (Equiv.swap 2 4))))) -def sgFlag941 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(5,0,1),(3,0,2),(0,0,3),(1,1,0),(6,1,1),(2,2,0),(4,2,2),(2,3,0)} -lemma sgCert941 : solveCompact 10 (.full [7,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB941 sgT941) sgFlag941 = 18 := by - decide +kernel - -lemma sg941 : RowSquare [5,2,2,1] [2,2,2,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [7,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB941 sgT941 sgFlag941 - change solveCompact 10 (.full [7,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB941 sgT941) sgFlag941 ≠ 0 - rw [sgCert941] - norm_num - -def sgB942 : Equiv.Perm (Fin 10) := Equiv.swap 1 9 * (Equiv.swap 5 0 * (Equiv.swap 1 8 * (Equiv.swap 2 7 * (Equiv.swap 1 3 * (Equiv.swap 0 6))))) -def sgT942 : Equiv.Perm (Fin 10) := Equiv.swap 4 5 * (Equiv.swap 5 9 * (Equiv.swap 4 6 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 8))))) -def sgFlag942 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,1),(1,0,2),(2,0,2),(3,1,0),(2,1,3),(3,2,0),(5,2,1),(1,3,0)} -lemma sgCert942 : solveCompact 10 (.full [6,4]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB942 sgT942) sgFlag942 = 2 := by - decide +kernel - -lemma sg942 : RowSquare [5,2,2,1] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB942 sgT942 sgFlag942 - change solveCompact 10 (.full [6,4]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB942 sgT942) sgFlag942 ≠ 0 - rw [sgCert942] - norm_num - -def sgB943 : Equiv.Perm (Fin 10) := Equiv.swap 2 5 * (Equiv.swap 5 9 * (Equiv.swap 2 8 * (Equiv.swap 5 3 * (Equiv.swap 3 1 * (Equiv.swap 2 0 * (Equiv.swap 1 7 * (Equiv.swap 0 6))))))) -def sgT943 : Equiv.Perm (Fin 10) := Equiv.swap 7 6 * (Equiv.swap 6 3 * (Equiv.swap 3 2 * (Equiv.swap 3 0 * (Equiv.swap 2 8 * (Equiv.swap 1 4 * (Equiv.swap 0 5)))))) -def sgFlag943 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,0,2),(4,0,2),(4,1,0),(2,1,3),(3,2,0),(0,3,1)} -lemma sgCert943 : solveCompact 10 (.full [5,5]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB943 sgT943) sgFlag943 = 6 := by - decide +kernel - -lemma sg943 : RowSquare [5,2,2,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB943 sgT943 sgFlag943 - change solveCompact 10 (.full [5,5]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB943 sgT943) sgFlag943 ≠ 0 - rw [sgCert943] - norm_num - -def sgB948 : Equiv.Perm (Fin 10) := Equiv.swap 4 9 * (Equiv.swap 4 8 * (Equiv.swap 5 3 * (Equiv.swap 4 0 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 0 6))))))) -def sgT948 : Equiv.Perm (Fin 10) := Equiv.swap 0 2 * (Equiv.swap 0 3 * (Equiv.swap 3 8 * (Equiv.swap 3 4 * (Equiv.swap 2 9 * (Equiv.swap 1 7 * (Equiv.swap 0 6)))))) -def sgFlag948 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(1,0,1),(0,0,2),(1,1,0),(5,1,3),(3,2,0),(1,2,1),(4,3,2)} -lemma sgCert948 : solveCompact 10 (.full [6,2,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB948 sgT948) sgFlag948 = -4 := by - decide +kernel - -lemma sg948 : RowSquare [5,2,2,1] [3,3,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [6,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB948 sgT948 sgFlag948 - change solveCompact 10 (.full [6,2,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB948 sgT948) sgFlag948 ≠ 0 - rw [sgCert948] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB949 : Equiv.Perm (Fin 10) := Equiv.swap 7 5 * (Equiv.swap 5 9 * (Equiv.swap 5 6 * (Equiv.swap 2 0 * (Equiv.swap 0 4 * (Equiv.swap 0 1))))) -def sgT949 : Equiv.Perm (Fin 10) := Equiv.swap 8 0 * (Equiv.swap 0 5 * (Equiv.swap 0 1 * (Equiv.swap 5 3 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 9 * (Equiv.swap 1 7 * (Equiv.swap 0 6)))))))) -def sgFlag949 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(1,0,1),(2,0,2),(2,1,0),(3,1,2),(1,2,0),(4,3,3)} -lemma sgCert949 : solveCompact 10 (.full [5,3,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [5,3,2] (Equiv.refl (Fin 10)) sgB949 sgT949) sgFlag949 = 4 := by - decide +kernel - -lemma sg949 : RowSquare [5,2,2,1] [3,3,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [5,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB949 sgT949 sgFlag949 - change solveCompact 10 (.full [5,3,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [5,3,2] (Equiv.refl (Fin 10)) sgB949 sgT949) sgFlag949 ≠ 0 - rw [sgCert949] - norm_num - -def sgB950 : Equiv.Perm (Fin 10) := Equiv.swap 5 8 * (Equiv.swap 4 9 * (Equiv.swap 3 6 * (Equiv.swap 0 2 * (Equiv.swap 0 1)))) -def sgT950 : Equiv.Perm (Fin 10) := Equiv.swap 5 6 * (Equiv.swap 1 7 * (Equiv.swap 3 0 * (Equiv.swap 1 4 * (Equiv.swap 0 8)))) -def sgFlag950 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(0,0,1),(3,0,1),(2,1,0),(0,1,2),(2,2,0),(1,2,3),(0,3,2)} -lemma sgCert950 : solveCompact 10 (.full [4,4,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB950 sgT950) sgFlag950 = 2 := by - decide +kernel - -lemma sg950 : RowSquare [5,2,2,1] [3,3,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [4,4,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB950 sgT950 sgFlag950 - change solveCompact 10 (.full [4,4,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB950 sgT950) sgFlag950 ≠ 0 - rw [sgCert950] - norm_num - -def sgB951 : Equiv.Perm (Fin 10) := Equiv.swap 7 2 * (Equiv.swap 5 3 * (Equiv.swap 2 8 * (Equiv.swap 3 1 * (Equiv.swap 2 0 * (Equiv.swap 1 9 * (Equiv.swap 0 4)))))) -def sgT951 : Equiv.Perm (Fin 10) := Equiv.swap 0 7 * (Equiv.swap 7 9 * (Equiv.swap 0 1 * (Equiv.swap 0 6 * (Equiv.swap 0 5 * (Equiv.swap 1 8 * (Equiv.swap 0 3)))))) -def sgFlag951 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(0,0,1),(2,0,2),(1,1,0),(2,1,3),(2,2,0),(1,2,2),(1,3,1)} -lemma sgCert951 : solveCompact 10 (.full [4,3,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB951 sgT951) sgFlag951 = 4 := by - decide +kernel - -lemma sg951 : RowSquare [5,2,2,1] [3,3,3,1] := by - apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [4,3,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB951 sgT951 sgFlag951 - change solveCompact 10 (.full [4,3,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) - (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB951 sgT951) sgFlag951 ≠ 0 - rw [sgCert951] - norm_num - -def sgB958 : Equiv.Perm (Fin 10) := Equiv.swap 3 0 * (Equiv.swap 3 7 * (Equiv.swap 0 9 * (Equiv.swap 3 6 * (Equiv.swap 0 4 * (Equiv.swap 1 8 * (Equiv.swap 0 2)))))) -def sgT958 : Equiv.Perm (Fin 10) := Equiv.swap 6 5 * (Equiv.swap 5 4 * (Equiv.swap 6 8 * (Equiv.swap 5 7 * (Equiv.swap 4 9 * (Equiv.swap 0 3))))) -def sgFlag958 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(5,0,1),(3,0,2),(6,0,3),(1,1,0),(4,1,0),(7,1,1),(2,2,0),(0,3,0)} -lemma sgCert958 : solveCompact 10 (.full [8,2]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [8,2] (Equiv.refl (Fin 10)) sgB958 sgT958) sgFlag958 = -112 := by - decide +kernel - -lemma sg958 : RowSquare [5,3,1,1] [2,2,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [8,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB958 sgT958 sgFlag958 - change solveCompact 10 (.full [8,2]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [8,2] (Equiv.refl (Fin 10)) sgB958 sgT958) sgFlag958 ≠ 0 - rw [sgCert958] - norm_num - -def sgB959 : Equiv.Perm (Fin 10) := Equiv.swap 7 4 * (Equiv.swap 2 6 * (Equiv.swap 4 3 * (Equiv.swap 3 8 * (Equiv.swap 2 0 * (Equiv.swap 0 5 * (Equiv.swap 0 1)))))) -def sgT959 : Equiv.Perm (Fin 10) := Equiv.swap 8 0 * (Equiv.swap 0 2 * (Equiv.swap 3 6 * (Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 9 * (Equiv.swap 0 7))))))) -def sgFlag959 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(3,0,2),(5,0,3),(2,1,0),(6,1,0),(2,1,1),(1,2,0),(4,3,0)} -lemma sgCert959 : solveCompact 10 (.full [7,3]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB959 sgT959) sgFlag959 = -4 := by - decide +kernel - -lemma sg959 : RowSquare [5,3,1,1] [2,2,2,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [7,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB959 sgT959 sgFlag959 - change solveCompact 10 (.full [7,3]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB959 sgT959) sgFlag959 ≠ 0 - rw [sgCert959] - norm_num - -def sgB960 : Equiv.Perm (Fin 10) := Equiv.swap 8 7 * (Equiv.swap 7 1 * (Equiv.swap 1 9 * (Equiv.swap 3 4 * (Equiv.swap 1 6 * (Equiv.swap 0 2))))) -def sgT960 : Equiv.Perm (Fin 10) := Equiv.swap 7 2 * (Equiv.swap 3 5 * (Equiv.swap 5 8 * (Equiv.swap 3 0 * (Equiv.swap 2 9 * (Equiv.swap 0 6 * (Equiv.swap 0 1)))))) -def sgFlag960 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(5,0,0),(3,0,1),(1,0,2),(4,0,3),(0,1,0),(2,1,1),(3,2,0),(0,3,0)} -lemma sgCert960 : solveCompact 10 (.full [6,4]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB960 sgT960) sgFlag960 = 4 := by - decide +kernel - -lemma sg960 : RowSquare [5,3,1,1] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB960 sgT960 sgFlag960 - change solveCompact 10 (.full [6,4]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB960 sgT960) sgFlag960 ≠ 0 - rw [sgCert960] - norm_num - -def sgB961 : Equiv.Perm (Fin 10) := Equiv.swap 5 3 * (Equiv.swap 5 4 * (Equiv.swap 4 1 * (Equiv.swap 3 8 * (Equiv.swap 1 6 * (Equiv.swap 0 9))))) -def sgT961 : Equiv.Perm (Fin 10) := Equiv.swap 8 5 * (Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 5 6 * (Equiv.swap 0 1 * (Equiv.swap 2 9 * (Equiv.swap 1 7 * (Equiv.swap 0 3))))))) -def sgFlag961 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,1),(4,0,1),(0,0,3),(1,1,0),(2,1,0),(2,1,1),(4,2,2),(1,3,0)} -lemma sgCert961 : solveCompact 10 (.full [5,5]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB961 sgT961) sgFlag961 = 4 := by - decide +kernel - -lemma sg961 : RowSquare [5,3,1,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB961 sgT961 sgFlag961 - change solveCompact 10 (.full [5,5]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB961 sgT961) sgFlag961 ≠ 0 - rw [sgCert961] - norm_num - -def sgB964 : Equiv.Perm (Fin 10) := Equiv.swap 0 4 * (Equiv.swap 5 9 * (Equiv.swap 4 2 * (Equiv.swap 2 8 * (Equiv.swap 1 3 * (Equiv.swap 0 6))))) -def sgT964 : Equiv.Perm (Fin 10) := Equiv.swap 0 6 * (Equiv.swap 6 5 * (Equiv.swap 6 1 * (Equiv.swap 5 2 * (Equiv.swap 2 9 * (Equiv.swap 1 7 * (Equiv.swap 0 8)))))) -def sgFlag964 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,1),(4,0,2),(2,1,0),(5,1,1),(1,1,3),(1,2,0),(3,3,1)} -lemma sgCert964 : solveCompact 10 (.full [6,2,2]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB964 sgT964) sgFlag964 = 6 := by - decide +kernel - -lemma sg964 : RowSquare [5,3,1,1] [3,3,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [6,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB964 sgT964 sgFlag964 - change solveCompact 10 (.full [6,2,2]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) - (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB964 sgT964) sgFlag964 ≠ 0 - rw [sgCert964] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB975 : Equiv.Perm (Fin 10) := Equiv.swap 5 8 * (Equiv.swap 5 2 * (Equiv.swap 4 1 * (Equiv.swap 2 7 * (Equiv.swap 2 3 * (Equiv.swap 1 6))))) -def sgT975 : Equiv.Perm (Fin 10) := Equiv.swap 4 1 * (Equiv.swap 5 8 * (Equiv.swap 4 3 * (Equiv.swap 3 7 * (Equiv.swap 1 9 * (Equiv.swap 0 2))))) -def sgFlag975 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(4,0,0),(0,0,1),(6,0,1),(5,0,2),(1,1,0),(2,1,0),(3,1,1),(0,2,0),(1,2,2)} -lemma sgCert975 : solveCompact 10 (.full [7,3]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) - (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB975 sgT975) sgFlag975 = 6 := by - decide +kernel - -lemma sg975 : RowSquare [5,3,2] [2,2,2,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [3,3,2,1,1]) (ts := [7,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB975 sgT975 sgFlag975 - change solveCompact 10 (.full [7,3]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) - (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB975 sgT975) sgFlag975 ≠ 0 - rw [sgCert975] - norm_num - -def sgB976 : Equiv.Perm (Fin 10) := Equiv.swap 7 1 * (Equiv.swap 5 9 * (Equiv.swap 5 2 * (Equiv.swap 2 3 * (Equiv.swap 3 6 * (Equiv.swap 2 0 * (Equiv.swap 1 8 * (Equiv.swap 0 4))))))) -def sgT976 : Equiv.Perm (Fin 10) := Equiv.swap 8 7 * (Equiv.swap 7 1 * (Equiv.swap 1 4 * (Equiv.swap 1 2 * (Equiv.swap 4 9 * (Equiv.swap 1 0 * (Equiv.swap 2 6 * (Equiv.swap 1 3 * (Equiv.swap 0 5)))))))) -def sgFlag976 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,0),(1,0,1),(5,0,1),(2,0,2),(3,1,0),(1,1,1),(0,2,0),(2,2,2)} -lemma sgCert976 : solveCompact 10 (.full [6,4]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) - (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB976 sgT976) sgFlag976 = 4 := by - decide +kernel - -lemma sg976 : RowSquare [5,3,2] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [3,3,2,1,1]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB976 sgT976 sgFlag976 - change solveCompact 10 (.full [6,4]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) - (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB976 sgT976) sgFlag976 ≠ 0 - rw [sgCert976] - norm_num - -def sgB977 : Equiv.Perm (Fin 10) := Equiv.swap 7 6 * (Equiv.swap 7 1 * (Equiv.swap 6 9 * (Equiv.swap 1 0 * (Equiv.swap 1 3 * (Equiv.swap 3 5 * (Equiv.swap 0 8 * (Equiv.swap 1 4 * (Equiv.swap 0 2)))))))) -def sgT977 : Equiv.Perm (Fin 10) := Equiv.swap 7 3 * (Equiv.swap 3 9 * (Equiv.swap 0 4 * (Equiv.swap 4 2 * (Equiv.swap 3 6 * (Equiv.swap 2 8 * (Equiv.swap 0 5 * (Equiv.swap 0 1))))))) -def sgFlag977 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,0),(2,0,1),(1,0,2),(2,1,0),(0,1,1),(3,1,1),(3,2,0),(4,2,0)} -lemma sgCert977 : solveCompact 10 (.full [5,5]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) - (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB977 sgT977) sgFlag977 = 40 := by - decide +kernel - -lemma sg977 : RowSquare [5,3,2] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [3,3,2,1,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB977 sgT977 sgFlag977 - change solveCompact 10 (.full [5,5]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) - (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB977 sgT977) sgFlag977 ≠ 0 - rw [sgCert977] - norm_num - -def sgB982 : Equiv.Perm (Fin 10) := Equiv.swap 1 8 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 3 6 * (Equiv.swap 3 4 * (Equiv.swap 2 5 * (Equiv.swap 1 7 * (Equiv.swap 0 9))))))) -def sgT982 : Equiv.Perm (Fin 10) := Equiv.swap 1 7 * (Equiv.swap 7 9 * (Equiv.swap 3 6 * (Equiv.swap 3 4 * (Equiv.swap 1 8 * (Equiv.swap 0 5))))) -def sgFlag982 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,1),(1,0,2),(3,1,0),(1,1,1),(2,1,1),(2,2,0)} -lemma sgCert982 : solveCompact 10 (.full [5,5]) (.full [3,2,2,2,1]) (.full [3,2,2,2,1]) - (certificateEdges [3,2,2,2,1] [3,2,2,2,1] [5,5] (Equiv.refl (Fin 10)) sgB982 sgT982) sgFlag982 = 99 := by - decide +kernel - -lemma sg982 : RowSquare [5,4,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [3,2,2,2,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB982 sgT982 sgFlag982 - change solveCompact 10 (.full [5,5]) (.full [3,2,2,2,1]) (.full [3,2,2,2,1]) - (certificateEdges [3,2,2,2,1] [3,2,2,2,1] [5,5] (Equiv.refl (Fin 10)) sgB982 sgT982) sgFlag982 ≠ 0 - rw [sgCert982] - norm_num - -def sgB998 : Equiv.Perm (Fin 10) := Equiv.swap 2 5 * (Equiv.swap 5 4 * (Equiv.swap 4 9 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 1 7))))) -def sgT998 : Equiv.Perm (Fin 10) := Equiv.swap 8 9 * (Equiv.swap 3 7 * (Equiv.swap 3 6 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 0 4 * (Equiv.swap 0 1)))))) -def sgFlag998 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(7,0,0),(3,0,1),(0,0,2),(1,0,3),(5,0,4),(4,1,0),(0,2,0),(2,3,0),(6,4,0)} -lemma sgCert998 : solveCompact 10 (.full [8,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB998 sgT998) sgFlag998 = -288 := by - decide +kernel - -lemma sg998 : RowSquare [6,1,1,1,1] [2,2,1,1,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [8,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB998 sgT998 sgFlag998 - change solveCompact 10 (.full [8,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB998 sgT998) sgFlag998 ≠ 0 - rw [sgCert998] - norm_num - -def sgB999 : Equiv.Perm (Fin 10) := Equiv.swap 6 3 * (Equiv.swap 2 1 * (Equiv.swap 4 0 * (Equiv.swap 3 8 * (Equiv.swap 2 5 * (Equiv.swap 1 7 * (Equiv.swap 0 9)))))) -def sgT999 : Equiv.Perm (Fin 10) := Equiv.swap 5 6 * (Equiv.swap 6 1 * (Equiv.swap 5 7 * (Equiv.swap 2 4 * (Equiv.swap 1 8)))) -def sgFlag999 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(5,0,0),(0,0,1),(6,0,2),(1,0,3),(2,0,4),(1,1,0),(4,2,0),(3,3,0),(2,4,0)} -lemma sgCert999 : solveCompact 10 (.full [7,3]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB999 sgT999) sgFlag999 = -48 := by - decide +kernel - -lemma sg999 : RowSquare [6,1,1,1,1] [2,2,2,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [7,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB999 sgT999 sgFlag999 - change solveCompact 10 (.full [7,3]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB999 sgT999) sgFlag999 ≠ 0 - rw [sgCert999] - norm_num - -def sgB1000 : Equiv.Perm (Fin 10) := Equiv.swap 0 5 * (Equiv.swap 1 3 * (Equiv.swap 5 9 * (Equiv.swap 1 6 * (Equiv.swap 3 8 * (Equiv.swap 1 4 * (Equiv.swap 0 7)))))) -def sgT1000 : Equiv.Perm (Fin 10) := Equiv.swap 7 5 * (Equiv.swap 0 2 * (Equiv.swap 5 4 * (Equiv.swap 4 9 * (Equiv.swap 0 6 * (Equiv.swap 2 8 * (Equiv.swap 0 3 * (Equiv.swap 0 1))))))) -def sgFlag1000 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,3),(5,0,5),(3,1,4),(2,2,2),(0,3,0),(3,4,0),(4,5,0)} -lemma sgCert1000 : solveCompact 10 (.full [6,4]) (.full [6,1,1,1,1]) (.full [6,1,1,1,1]) - (certificateEdges [6,1,1,1,1] [6,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB1000 sgT1000) sgFlag1000 = 72 := by - decide +kernel - -lemma sg1000 : RowSquare [6,1,1,1,1] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [6,1,1,1,1]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1000 sgT1000 sgFlag1000 - change solveCompact 10 (.full [6,4]) (.full [6,1,1,1,1]) (.full [6,1,1,1,1]) - (certificateEdges [6,1,1,1,1] [6,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB1000 sgT1000) sgFlag1000 ≠ 0 - rw [sgCert1000] - norm_num - -def sgB1001 : Equiv.Perm (Fin 10) := Equiv.swap 8 2 * (Equiv.swap 2 4 * (Equiv.swap 4 9 * (Equiv.swap 3 6 * (Equiv.swap 2 5 * (Equiv.swap 0 1))))) -def sgT1001 : Equiv.Perm (Fin 10) := Equiv.swap 4 3 * (Equiv.swap 6 7 * (Equiv.swap 3 9 * (Equiv.swap 4 8 * (Equiv.swap 3 1 * (Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 5))))))) -def sgFlag1001 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(0,0,1),(3,0,2),(2,0,3),(4,0,4),(2,1,0),(0,2,0),(1,3,0),(3,4,0)} -lemma sgCert1001 : solveCompact 10 (.full [5,5]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB1001 sgT1001) sgFlag1001 = 240 := by - decide +kernel - -lemma sg1001 : RowSquare [6,1,1,1,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1001 sgT1001 sgFlag1001 - change solveCompact 10 (.full [5,5]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB1001 sgT1001) sgFlag1001 ≠ 0 - rw [sgCert1001] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB1006 : Equiv.Perm (Fin 10) := Equiv.swap 0 6 * (Equiv.swap 6 1 * (Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 2 5 * (Equiv.swap 1 9 * (Equiv.swap 0 8))))))) -def sgT1006 : Equiv.Perm (Fin 10) := Equiv.swap 1 0 * (Equiv.swap 1 8 * (Equiv.swap 1 7 * (Equiv.swap 1 4 * (Equiv.swap 4 6 * (Equiv.swap 0 9 * (Equiv.swap 0 3 * (Equiv.swap 1 5 * (Equiv.swap 0 2)))))))) -def sgFlag1006 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,0),(1,0,1),(0,0,2),(4,0,3),(5,1,0),(3,2,0),(1,3,4),(0,4,0)} -lemma sgCert1006 : solveCompact 10 (.full [6,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB1006 sgT1006) sgFlag1006 = -12 := by - decide +kernel - -lemma sg1006 : RowSquare [6,1,1,1,1] [3,3,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [6,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1006 sgT1006 sgFlag1006 - change solveCompact 10 (.full [6,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB1006 sgT1006) sgFlag1006 ≠ 0 - rw [sgCert1006] - norm_num - -def sgB1007 : Equiv.Perm (Fin 10) := Equiv.swap 2 4 * (Equiv.swap 5 3 * (Equiv.swap 4 9 * (Equiv.swap 3 7 * (Equiv.swap 2 8)))) -def sgT1007 : Equiv.Perm (Fin 10) := Equiv.swap 7 4 * (Equiv.swap 4 9 * (Equiv.swap 4 1 * (Equiv.swap 3 2 * (Equiv.swap 2 8 * (Equiv.swap 1 0 * (Equiv.swap 0 6)))))) -def sgFlag1007 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(2,0,2),(0,0,3),(3,0,4),(0,1,1),(0,2,0),(2,3,0),(1,4,0)} -lemma sgCert1007 : solveCompact 10 (.full [5,3,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,3,2] (Equiv.refl (Fin 10)) sgB1007 sgT1007) sgFlag1007 = 20 := by - decide +kernel - -lemma sg1007 : RowSquare [6,1,1,1,1] [3,3,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [5,3,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1007 sgT1007 sgFlag1007 - change solveCompact 10 (.full [5,3,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,3,2] (Equiv.refl (Fin 10)) sgB1007 sgT1007) sgFlag1007 ≠ 0 - rw [sgCert1007] - norm_num - -def sgB1008 : Equiv.Perm (Fin 10) := Equiv.swap 1 2 * (Equiv.swap 3 6 * (Equiv.swap 3 4 * (Equiv.swap 2 9 * (Equiv.swap 1 8 * (Equiv.swap 0 5))))) -def sgT1008 : Equiv.Perm (Fin 10) := Equiv.swap 0 4 * (Equiv.swap 6 9 * (Equiv.swap 0 3 * (Equiv.swap 4 8 * (Equiv.swap 3 1 * (Equiv.swap 1 7 * (Equiv.swap 1 2 * (Equiv.swap 0 5))))))) -def sgFlag1008 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(3,0,0),(2,0,1),(0,0,2),(1,0,3),(2,1,0),(3,2,0),(1,3,4),(0,4,0)} -lemma sgCert1008 : solveCompact 10 (.full [4,4,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB1008 sgT1008) sgFlag1008 = 4 := by - decide +kernel - -lemma sg1008 : RowSquare [6,1,1,1,1] [3,3,2,2] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [4,4,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1008 sgT1008 sgFlag1008 - change solveCompact 10 (.full [4,4,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB1008 sgT1008) sgFlag1008 ≠ 0 - rw [sgCert1008] - norm_num - -def sgB1015 : Equiv.Perm (Fin 10) := Equiv.swap 6 0 * (Equiv.swap 5 1 * (Equiv.swap 4 8 * (Equiv.swap 1 9 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))) -def sgT1015 : Equiv.Perm (Fin 10) := Equiv.swap 7 9 * (Equiv.swap 7 0 * (Equiv.swap 0 8 * (Equiv.swap 3 6 * (Equiv.swap 2 4 * (Equiv.swap 0 5))))) -def sgFlag1015 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(3,0,0),(0,0,1),(1,0,4),(1,1,3),(0,2,2),(0,3,0),(2,4,0)} -lemma sgCert1015 : solveCompact 10 (.full [4,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,2,2,2] (Equiv.refl (Fin 10)) sgB1015 sgT1015) sgFlag1015 = 4 := by - decide +kernel - -lemma sg1015 : RowSquare [6,1,1,1,1] [4,4,1,1] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [4,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1015 sgT1015 sgFlag1015 - change solveCompact 10 (.full [4,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,2,2,2] (Equiv.refl (Fin 10)) sgB1015 sgT1015) sgFlag1015 ≠ 0 - rw [sgCert1015] - norm_num - -def sgB1016 : Equiv.Perm (Fin 10) := Equiv.swap 3 2 * (Equiv.swap 3 5 * (Equiv.swap 5 0 * (Equiv.swap 2 9 * (Equiv.swap 3 6 * (Equiv.swap 2 4 * (Equiv.swap 0 8)))))) -def sgT1016 : Equiv.Perm (Fin 10) := Equiv.swap 7 6 * (Equiv.swap 6 3 * (Equiv.swap 5 0 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 9 * (Equiv.swap 0 8))))))) -def sgFlag1016 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,2),(1,0,3),(1,1,1),(1,2,4),(1,3,0),(2,4,0)} -lemma sgCert1016 : solveCompact 10 (.full [3,3,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [3,3,2,2] (Equiv.refl (Fin 10)) sgB1016 sgT1016) sgFlag1016 = 2 := by - decide +kernel - -lemma sg1016 : RowSquare [6,1,1,1,1] [4,4,2] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [3,3,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1016 sgT1016 sgFlag1016 - change solveCompact 10 (.full [3,3,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [3,3,2,2] (Equiv.refl (Fin 10)) sgB1016 sgT1016) sgFlag1016 ≠ 0 - rw [sgCert1016] - norm_num - -def sgB1023 : Equiv.Perm (Fin 10) := Equiv.swap 7 1 * (Equiv.swap 7 0 * (Equiv.swap 0 8 * (Equiv.swap 1 9 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))) -def sgT1023 : Equiv.Perm (Fin 10) := Equiv.swap 2 9 * (Equiv.swap 5 8 * (Equiv.swap 5 6 * (Equiv.swap 3 4 * (Equiv.swap 2 7)))) -def sgFlag1023 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(1,1,4),(1,2,2),(0,3,3),(1,4,0)} -lemma sgCert1023 : solveCompact 10 (.full [2,2,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [2,2,2,2,2] (Equiv.refl (Fin 10)) sgB1023 sgT1023) sgFlag1023 = -6 := by - decide +kernel - -lemma sg1023 : RowSquare [6,1,1,1,1] [5,5] := by - apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [2,2,2,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1023 sgT1023 sgFlag1023 - change solveCompact 10 (.full [2,2,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) - (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [2,2,2,2,2] (Equiv.refl (Fin 10)) sgB1023 sgT1023) sgFlag1023 ≠ 0 - rw [sgCert1023] - norm_num - -def sgB1032 : Equiv.Perm (Fin 10) := Equiv.swap 8 5 * (Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 1 7 * (Equiv.swap 0 6 * (Equiv.swap 2 9 * (Equiv.swap 1 4 * (Equiv.swap 0 3))))))) -def sgT1032 : Equiv.Perm (Fin 10) := Equiv.swap 1 3 * (Equiv.swap 3 9 * (Equiv.swap 5 8 * (Equiv.swap 3 0 * (Equiv.swap 1 7 * (Equiv.swap 0 6))))) -def sgFlag1032 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(3,0,1),(5,0,1),(3,0,2),(0,0,3),(1,1,0),(2,1,0),(2,2,0),(0,3,0)} -lemma sgCert1032 : solveCompact 10 (.full [6,4]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB1032 sgT1032) sgFlag1032 = 16 := by - decide +kernel - -lemma sg1032 : RowSquare [6,2,1,1] [2,2,2,2,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [6,4]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1032 sgT1032 sgFlag1032 - change solveCompact 10 (.full [6,4]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB1032 sgT1032) sgFlag1032 ≠ 0 - rw [sgCert1032] - norm_num - -def sgB1033 : Equiv.Perm (Fin 10) := Equiv.swap 8 5 * (Equiv.swap 1 7 * (Equiv.swap 5 9 * (Equiv.swap 1 2 * (Equiv.swap 2 6 * (Equiv.swap 1 4 * (Equiv.swap 0 3)))))) -def sgT1033 : Equiv.Perm (Fin 10) := Equiv.swap 2 4 * (Equiv.swap 4 9 * (Equiv.swap 2 8 * (Equiv.swap 4 6 * (Equiv.swap 1 7 * (Equiv.swap 2 5 * (Equiv.swap 1 0 * (Equiv.swap 0 3))))))) -def sgFlag1033 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(4,0,0),(1,0,1),(4,0,1),(1,0,2),(3,0,3),(0,1,0),(3,1,0),(0,2,0),(2,3,0)} -lemma sgCert1033 : solveCompact 10 (.full [5,5]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB1033 sgT1033) sgFlag1033 = -12 := by - decide +kernel - -lemma sg1033 : RowSquare [6,2,1,1] [2,2,2,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [5,5]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1033 sgT1033 sgFlag1033 - change solveCompact 10 (.full [5,5]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB1033 sgT1033) sgFlag1033 ≠ 0 - rw [sgCert1033] - norm_num - -end UniversalTensorSquare -end -end - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -def sgB1038 : Equiv.Perm (Fin 10) := Equiv.swap 8 5 * (Equiv.swap 5 2 * (Equiv.swap 2 3 * (Equiv.swap 5 7 * (Equiv.swap 3 9 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 6)))))))) -def sgT1038 : Equiv.Perm (Fin 10) := Equiv.swap 2 4 * (Equiv.swap 0 8 * (Equiv.swap 2 7 * (Equiv.swap 4 1 * (Equiv.swap 2 5 * (Equiv.swap 2 3 * (Equiv.swap 1 9 * (Equiv.swap 0 6))))))) -def sgFlag1038 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,0),(0,0,1),(4,0,2),(0,0,3),(1,1,0),(3,2,1),(5,3,0)} -lemma sgCert1038 : solveCompact 10 (.full [6,2,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB1038 sgT1038) sgFlag1038 = -2 := by - decide +kernel - -lemma sg1038 : RowSquare [6,2,1,1] [3,3,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [6,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1038 sgT1038 sgFlag1038 - change solveCompact 10 (.full [6,2,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB1038 sgT1038) sgFlag1038 ≠ 0 - rw [sgCert1038] - norm_num - -def sgB1040 : Equiv.Perm (Fin 10) := Equiv.swap 8 1 * (Equiv.swap 1 5 * (Equiv.swap 5 9 * (Equiv.swap 1 7 * (Equiv.swap 0 6 * (Equiv.swap 1 3 * (Equiv.swap 0 2)))))) -def sgT1040 : Equiv.Perm (Fin 10) := Equiv.swap 4 1 * (Equiv.swap 5 8 * (Equiv.swap 5 2 * (Equiv.swap 4 7 * (Equiv.swap 1 9 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 6))))))) -def sgFlag1040 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(1,0,1),(2,0,2),(2,1,0),(3,1,3),(0,2,0),(1,3,0)} -lemma sgCert1040 : solveCompact 10 (.full [4,4,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB1040 sgT1040) sgFlag1040 = 1 := by - decide +kernel - -lemma sg1040 : RowSquare [6,2,1,1] [3,3,2,2] := by - apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [4,4,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1040 sgT1040 sgFlag1040 - change solveCompact 10 (.full [4,4,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) - (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB1040 sgT1040) sgFlag1040 ≠ 0 - rw [sgCert1040] - norm_num - -def sgB1063 : Equiv.Perm (Fin 10) := Equiv.swap 7 2 * (Equiv.swap 2 1 * (Equiv.swap 2 6 * (Equiv.swap 4 3 * (Equiv.swap 3 9 * (Equiv.swap 2 5 * (Equiv.swap 1 8)))))) -def sgT1063 : Equiv.Perm (Fin 10) := Equiv.swap 7 4 * (Equiv.swap 3 9 * (Equiv.swap 4 8 * (Equiv.swap 3 0 * (Equiv.swap 0 6 * (Equiv.swap 0 1))))) -def sgFlag1063 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(3,0,1),(4,0,2),(0,1,0),(5,2,0),(2,2,2)} -lemma sgCert1063 : solveCompact 10 (.full [6,2,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) - (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB1063 sgT1063) sgFlag1063 = -16 := by - decide +kernel - -lemma sg1063 : RowSquare [6,2,2] [3,3,1,1,1,1] := by - apply rowSquare_compact (n := 10) (cs := [3,3,1,1,1,1]) (ts := [6,2,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1063 sgT1063 sgFlag1063 - change solveCompact 10 (.full [6,2,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) - (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB1063 sgT1063) sgFlag1063 ≠ 0 - rw [sgCert1063] - norm_num - -def sgB1064 : Equiv.Perm (Fin 10) := Equiv.swap 5 7 * (Equiv.swap 7 9 * (Equiv.swap 5 8 * (Equiv.swap 0 4 * (Equiv.swap 1 6 * (Equiv.swap 0 3))))) -def sgT1064 : Equiv.Perm (Fin 10) := Equiv.swap 7 9 * (Equiv.swap 5 8 * (Equiv.swap 4 2 * (Equiv.swap 2 6 * (Equiv.swap 0 3)))) -def sgFlag1064 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(0,0,1),(3,0,2),(1,1,0),(2,1,0),(0,2,0),(2,2,2)} -lemma sgCert1064 : solveCompact 10 (.full [4,4,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) - (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB1064 sgT1064) sgFlag1064 = -1 := by - decide +kernel - -lemma sg1064 : RowSquare [6,2,2] [3,3,2,2] := by - apply rowSquare_compact (n := 10) (cs := [3,3,1,1,1,1]) (ts := [4,4,2]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1064 sgT1064 sgFlag1064 - change solveCompact 10 (.full [4,4,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) - (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB1064 sgT1064) sgFlag1064 ≠ 0 - rw [sgCert1064] - norm_num - -def sgB1065 : Equiv.Perm (Fin 10) := Equiv.swap 3 4 * (Equiv.swap 3 0 * (Equiv.swap 5 9 * (Equiv.swap 4 1 * (Equiv.swap 3 2 * (Equiv.swap 2 6 * (Equiv.swap 1 8 * (Equiv.swap 0 7))))))) -def sgT1065 : Equiv.Perm (Fin 10) := Equiv.swap 2 9 * (Equiv.swap 2 8 * (Equiv.swap 2 7 * (Equiv.swap 2 0 * (Equiv.swap 0 6 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 3))))))) -def sgFlag1065 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(3,0,0),(1,0,1),(2,0,2),(0,1,0),(0,1,1),(1,2,0)} -lemma sgCert1065 : solveCompact 10 (.full [4,3,3]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) - (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB1065 sgT1065) sgFlag1065 = -4 := by - decide +kernel - -lemma sg1065 : RowSquare [6,2,2] [3,3,3,1] := by - apply rowSquare_compact (n := 10) (cs := [3,3,1,1,1,1]) (ts := [4,3,3]) - (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) - rfl rfl sgB1065 sgT1065 sgFlag1065 - change solveCompact 10 (.full [4,3,3]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) - (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB1065 sgT1065) sgFlag1065 ≠ 0 - rw [sgCert1065] - norm_num - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Contraction.CompactDomains +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Semigroup Leaves 5. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB922 : Equiv.Perm (Fin 10) := Equiv.swap 8 0 * (Equiv.swap 0 9 * (Equiv.swap 3 7 * (Equiv.swap 3 2 * (Equiv.swap 2 4 * (Equiv.swap 1 5 * (Equiv.swap 0 6)))))) +def sgT922 : Equiv.Perm (Fin 10) := Equiv.swap 5 0 * (Equiv.swap 4 2 * (Equiv.swap 5 7 * (Equiv.swap 4 6 * (Equiv.swap 0 1 * (Equiv.swap 2 9 * (Equiv.swap 1 8 * (Equiv.swap 0 3))))))) +def sgFlag922 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(3,0,1),(0,0,3),(0,1,0),(2,1,0),(1,2,4),(1,3,2),(2,4,0)} +lemma sgCert922 : solveCompact 10 (.full [4,4,2]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) + (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB922 sgT922) sgFlag922 = 4 := by + decide +kernel + +lemma sg922 : RowSquare [5,2,1,1,1] [3,3,2,2] := by + apply rowSquare_compact (n := 10) (cs := [5,2,1,1,1]) (ts := [4,4,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB922 sgT922 sgFlag922 + change solveCompact 10 (.full [4,4,2]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) + (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB922 sgT922) sgFlag922 ≠ 0 + rw [sgCert922] + norm_num + +def sgB932 : Equiv.Perm (Fin 10) := Equiv.swap 3 7 * (Equiv.swap 7 1 * (Equiv.swap 3 2 * (Equiv.swap 3 6 * (Equiv.swap 1 9 * (Equiv.swap 3 5 * (Equiv.swap 2 0 * (Equiv.swap 1 4 * (Equiv.swap 0 8)))))))) +def sgT932 : Equiv.Perm (Fin 10) := Equiv.swap 4 6 * (Equiv.swap 6 0 * (Equiv.swap 6 1 * (Equiv.swap 1 7 * (Equiv.swap 4 8 * (Equiv.swap 0 2 * (Equiv.swap 2 9 * (Equiv.swap 1 5 * (Equiv.swap 0 3)))))))) +def sgFlag932 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(1,0,1),(1,0,3),(1,1,2),(2,1,4),(1,2,0),(2,3,0),(0,4,0)} +lemma sgCert932 : solveCompact 10 (.full [3,3,2,2]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) + (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [3,3,2,2] (Equiv.refl (Fin 10)) sgB932 sgT932) sgFlag932 = 1 := by + decide +kernel + +lemma sg932 : RowSquare [5,2,1,1,1] [4,4,2] := by + apply rowSquare_compact (n := 10) (cs := [5,2,1,1,1]) (ts := [3,3,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB932 sgT932 sgFlag932 + change solveCompact 10 (.full [3,3,2,2]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) + (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [3,3,2,2] (Equiv.refl (Fin 10)) sgB932 sgT932) sgFlag932 ≠ 0 + rw [sgCert932] + norm_num + +def sgB939 : Equiv.Perm (Fin 10) := Equiv.swap 1 7 * (Equiv.swap 7 3 * (Equiv.swap 3 9 * (Equiv.swap 1 0 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 6 * (Equiv.swap 1 5 * (Equiv.swap 0 8)))))))) +def sgT939 : Equiv.Perm (Fin 10) := Equiv.swap 8 0 * (Equiv.swap 1 7 * (Equiv.swap 0 9 * (Equiv.swap 2 6 * (Equiv.swap 1 4 * (Equiv.swap 0 3))))) +def sgFlag939 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,1),(1,0,3),(0,1,0),(0,2,1),(1,3,4),(1,4,2)} +lemma sgCert939 : solveCompact 10 (.full [2,2,2,2,2]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) + (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [2,2,2,2,2] (Equiv.refl (Fin 10)) sgB939 sgT939) sgFlag939 = 2 := by + decide +kernel + +lemma sg939 : RowSquare [5,2,1,1,1] [5,5] := by + apply rowSquare_compact (n := 10) (cs := [5,2,1,1,1]) (ts := [2,2,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB939 sgT939 sgFlag939 + change solveCompact 10 (.full [2,2,2,2,2]) (.full [5,2,1,1,1]) (.full [5,2,1,1,1]) + (certificateEdges [5,2,1,1,1] [5,2,1,1,1] [2,2,2,2,2] (Equiv.refl (Fin 10)) sgB939 sgT939) sgFlag939 ≠ 0 + rw [sgCert939] + norm_num + +def sgB940 : Equiv.Perm (Fin 10) := Equiv.swap 6 4 * (Equiv.swap 2 9 * (Equiv.swap 4 8 * (Equiv.swap 1 7 * (Equiv.swap 2 5 * (Equiv.swap 1 3))))) +def sgT940 : Equiv.Perm (Fin 10) := Equiv.swap 7 2 * (Equiv.swap 2 3 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 3 5 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 9))))))) +def sgFlag940 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(6,0,0),(2,0,1),(0,0,2),(7,0,2),(0,1,0),(4,1,3),(3,2,0),(1,2,1),(5,3,0)} +lemma sgCert940 : solveCompact 10 (.full [8,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB940 sgT940) sgFlag940 = 8 := by + decide +kernel + +lemma sg940 : RowSquare [5,2,2,1] [2,2,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [8,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB940 sgT940 sgFlag940 + change solveCompact 10 (.full [8,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB940 sgT940) sgFlag940 ≠ 0 + rw [sgCert940] + norm_num + +def sgB941 : Equiv.Perm (Fin 10) := Equiv.swap 6 4 * (Equiv.swap 4 0 * (Equiv.swap 3 8 * (Equiv.swap 1 9 * (Equiv.swap 0 7)))) +def sgT941 : Equiv.Perm (Fin 10) := Equiv.swap 7 3 * (Equiv.swap 5 9 * (Equiv.swap 5 6 * (Equiv.swap 3 8 * (Equiv.swap 3 2 * (Equiv.swap 2 4))))) +def sgFlag941 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(5,0,1),(3,0,2),(0,0,3),(1,1,0),(6,1,1),(2,2,0),(4,2,2),(2,3,0)} +lemma sgCert941 : solveCompact 10 (.full [7,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB941 sgT941) sgFlag941 = 18 := by + decide +kernel + +lemma sg941 : RowSquare [5,2,2,1] [2,2,2,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [7,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB941 sgT941 sgFlag941 + change solveCompact 10 (.full [7,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB941 sgT941) sgFlag941 ≠ 0 + rw [sgCert941] + norm_num + +def sgB942 : Equiv.Perm (Fin 10) := Equiv.swap 1 9 * (Equiv.swap 5 0 * (Equiv.swap 1 8 * (Equiv.swap 2 7 * (Equiv.swap 1 3 * (Equiv.swap 0 6))))) +def sgT942 : Equiv.Perm (Fin 10) := Equiv.swap 4 5 * (Equiv.swap 5 9 * (Equiv.swap 4 6 * (Equiv.swap 1 3 * (Equiv.swap 1 2 * (Equiv.swap 0 8))))) +def sgFlag942 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,1),(1,0,2),(2,0,2),(3,1,0),(2,1,3),(3,2,0),(5,2,1),(1,3,0)} +lemma sgCert942 : solveCompact 10 (.full [6,4]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB942 sgT942) sgFlag942 = 2 := by + decide +kernel + +lemma sg942 : RowSquare [5,2,2,1] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB942 sgT942 sgFlag942 + change solveCompact 10 (.full [6,4]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB942 sgT942) sgFlag942 ≠ 0 + rw [sgCert942] + norm_num + +def sgB943 : Equiv.Perm (Fin 10) := Equiv.swap 2 5 * (Equiv.swap 5 9 * (Equiv.swap 2 8 * (Equiv.swap 5 3 * (Equiv.swap 3 1 * (Equiv.swap 2 0 * (Equiv.swap 1 7 * (Equiv.swap 0 6))))))) +def sgT943 : Equiv.Perm (Fin 10) := Equiv.swap 7 6 * (Equiv.swap 6 3 * (Equiv.swap 3 2 * (Equiv.swap 3 0 * (Equiv.swap 2 8 * (Equiv.swap 1 4 * (Equiv.swap 0 5)))))) +def sgFlag943 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(2,0,1),(0,0,2),(4,0,2),(4,1,0),(2,1,3),(3,2,0),(0,3,1)} +lemma sgCert943 : solveCompact 10 (.full [5,5]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB943 sgT943) sgFlag943 = 6 := by + decide +kernel + +lemma sg943 : RowSquare [5,2,2,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB943 sgT943 sgFlag943 + change solveCompact 10 (.full [5,5]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB943 sgT943) sgFlag943 ≠ 0 + rw [sgCert943] + norm_num + +def sgB948 : Equiv.Perm (Fin 10) := Equiv.swap 4 9 * (Equiv.swap 4 8 * (Equiv.swap 5 3 * (Equiv.swap 4 0 * (Equiv.swap 3 2 * (Equiv.swap 2 1 * (Equiv.swap 1 7 * (Equiv.swap 0 6))))))) +def sgT948 : Equiv.Perm (Fin 10) := Equiv.swap 0 2 * (Equiv.swap 0 3 * (Equiv.swap 3 8 * (Equiv.swap 3 4 * (Equiv.swap 2 9 * (Equiv.swap 1 7 * (Equiv.swap 0 6)))))) +def sgFlag948 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(1,0,1),(0,0,2),(1,1,0),(5,1,3),(3,2,0),(1,2,1),(4,3,2)} +lemma sgCert948 : solveCompact 10 (.full [6,2,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB948 sgT948) sgFlag948 = -4 := by + decide +kernel + +lemma sg948 : RowSquare [5,2,2,1] [3,3,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [6,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB948 sgT948 sgFlag948 + change solveCompact 10 (.full [6,2,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB948 sgT948) sgFlag948 ≠ 0 + rw [sgCert948] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB949 : Equiv.Perm (Fin 10) := Equiv.swap 7 5 * (Equiv.swap 5 9 * (Equiv.swap 5 6 * (Equiv.swap 2 0 * (Equiv.swap 0 4 * (Equiv.swap 0 1))))) +def sgT949 : Equiv.Perm (Fin 10) := Equiv.swap 8 0 * (Equiv.swap 0 5 * (Equiv.swap 0 1 * (Equiv.swap 5 3 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 9 * (Equiv.swap 1 7 * (Equiv.swap 0 6)))))))) +def sgFlag949 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(0,0,1),(1,0,1),(2,0,2),(2,1,0),(3,1,2),(1,2,0),(4,3,3)} +lemma sgCert949 : solveCompact 10 (.full [5,3,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [5,3,2] (Equiv.refl (Fin 10)) sgB949 sgT949) sgFlag949 = 4 := by + decide +kernel + +lemma sg949 : RowSquare [5,2,2,1] [3,3,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [5,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB949 sgT949 sgFlag949 + change solveCompact 10 (.full [5,3,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [5,3,2] (Equiv.refl (Fin 10)) sgB949 sgT949) sgFlag949 ≠ 0 + rw [sgCert949] + norm_num + +def sgB950 : Equiv.Perm (Fin 10) := Equiv.swap 5 8 * (Equiv.swap 4 9 * (Equiv.swap 3 6 * (Equiv.swap 0 2 * (Equiv.swap 0 1)))) +def sgT950 : Equiv.Perm (Fin 10) := Equiv.swap 5 6 * (Equiv.swap 1 7 * (Equiv.swap 3 0 * (Equiv.swap 1 4 * (Equiv.swap 0 8)))) +def sgFlag950 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(0,0,1),(3,0,1),(2,1,0),(0,1,2),(2,2,0),(1,2,3),(0,3,2)} +lemma sgCert950 : solveCompact 10 (.full [4,4,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB950 sgT950) sgFlag950 = 2 := by + decide +kernel + +lemma sg950 : RowSquare [5,2,2,1] [3,3,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [4,4,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB950 sgT950 sgFlag950 + change solveCompact 10 (.full [4,4,2]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB950 sgT950) sgFlag950 ≠ 0 + rw [sgCert950] + norm_num + +def sgB951 : Equiv.Perm (Fin 10) := Equiv.swap 7 2 * (Equiv.swap 5 3 * (Equiv.swap 2 8 * (Equiv.swap 3 1 * (Equiv.swap 2 0 * (Equiv.swap 1 9 * (Equiv.swap 0 4)))))) +def sgT951 : Equiv.Perm (Fin 10) := Equiv.swap 0 7 * (Equiv.swap 7 9 * (Equiv.swap 0 1 * (Equiv.swap 0 6 * (Equiv.swap 0 5 * (Equiv.swap 1 8 * (Equiv.swap 0 3)))))) +def sgFlag951 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(0,0,1),(2,0,2),(1,1,0),(2,1,3),(2,2,0),(1,2,2),(1,3,1)} +lemma sgCert951 : solveCompact 10 (.full [4,3,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB951 sgT951) sgFlag951 = 4 := by + decide +kernel + +lemma sg951 : RowSquare [5,2,2,1] [3,3,3,1] := by + apply rowSquare_compact (n := 10) (cs := [4,3,1,1,1]) (ts := [4,3,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB951 sgT951 sgFlag951 + change solveCompact 10 (.full [4,3,3]) (.full [4,3,1,1,1]) (.full [4,3,1,1,1]) + (certificateEdges [4,3,1,1,1] [4,3,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB951 sgT951) sgFlag951 ≠ 0 + rw [sgCert951] + norm_num + +def sgB958 : Equiv.Perm (Fin 10) := Equiv.swap 3 0 * (Equiv.swap 3 7 * (Equiv.swap 0 9 * (Equiv.swap 3 6 * (Equiv.swap 0 4 * (Equiv.swap 1 8 * (Equiv.swap 0 2)))))) +def sgT958 : Equiv.Perm (Fin 10) := Equiv.swap 6 5 * (Equiv.swap 5 4 * (Equiv.swap 6 8 * (Equiv.swap 5 7 * (Equiv.swap 4 9 * (Equiv.swap 0 3))))) +def sgFlag958 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(5,0,1),(3,0,2),(6,0,3),(1,1,0),(4,1,0),(7,1,1),(2,2,0),(0,3,0)} +lemma sgCert958 : solveCompact 10 (.full [8,2]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [8,2] (Equiv.refl (Fin 10)) sgB958 sgT958) sgFlag958 = -112 := by + decide +kernel + +lemma sg958 : RowSquare [5,3,1,1] [2,2,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [8,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB958 sgT958 sgFlag958 + change solveCompact 10 (.full [8,2]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [8,2] (Equiv.refl (Fin 10)) sgB958 sgT958) sgFlag958 ≠ 0 + rw [sgCert958] + norm_num + +def sgB959 : Equiv.Perm (Fin 10) := Equiv.swap 7 4 * (Equiv.swap 2 6 * (Equiv.swap 4 3 * (Equiv.swap 3 8 * (Equiv.swap 2 0 * (Equiv.swap 0 5 * (Equiv.swap 0 1)))))) +def sgT959 : Equiv.Perm (Fin 10) := Equiv.swap 8 0 * (Equiv.swap 0 2 * (Equiv.swap 3 6 * (Equiv.swap 3 5 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 9 * (Equiv.swap 0 7))))))) +def sgFlag959 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(3,0,2),(5,0,3),(2,1,0),(6,1,0),(2,1,1),(1,2,0),(4,3,0)} +lemma sgCert959 : solveCompact 10 (.full [7,3]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB959 sgT959) sgFlag959 = -4 := by + decide +kernel + +lemma sg959 : RowSquare [5,3,1,1] [2,2,2,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [7,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB959 sgT959 sgFlag959 + change solveCompact 10 (.full [7,3]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB959 sgT959) sgFlag959 ≠ 0 + rw [sgCert959] + norm_num + +def sgB960 : Equiv.Perm (Fin 10) := Equiv.swap 8 7 * (Equiv.swap 7 1 * (Equiv.swap 1 9 * (Equiv.swap 3 4 * (Equiv.swap 1 6 * (Equiv.swap 0 2))))) +def sgT960 : Equiv.Perm (Fin 10) := Equiv.swap 7 2 * (Equiv.swap 3 5 * (Equiv.swap 5 8 * (Equiv.swap 3 0 * (Equiv.swap 2 9 * (Equiv.swap 0 6 * (Equiv.swap 0 1)))))) +def sgFlag960 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(5,0,0),(3,0,1),(1,0,2),(4,0,3),(0,1,0),(2,1,1),(3,2,0),(0,3,0)} +lemma sgCert960 : solveCompact 10 (.full [6,4]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB960 sgT960) sgFlag960 = 4 := by + decide +kernel + +lemma sg960 : RowSquare [5,3,1,1] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB960 sgT960 sgFlag960 + change solveCompact 10 (.full [6,4]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB960 sgT960) sgFlag960 ≠ 0 + rw [sgCert960] + norm_num + +def sgB961 : Equiv.Perm (Fin 10) := Equiv.swap 5 3 * (Equiv.swap 5 4 * (Equiv.swap 4 1 * (Equiv.swap 3 8 * (Equiv.swap 1 6 * (Equiv.swap 0 9))))) +def sgT961 : Equiv.Perm (Fin 10) := Equiv.swap 8 5 * (Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 5 6 * (Equiv.swap 0 1 * (Equiv.swap 2 9 * (Equiv.swap 1 7 * (Equiv.swap 0 3))))))) +def sgFlag961 : Finset (ℕ × ℕ × ℕ) := {(3,0,0),(0,0,1),(4,0,1),(0,0,3),(1,1,0),(2,1,0),(2,1,1),(4,2,2),(1,3,0)} +lemma sgCert961 : solveCompact 10 (.full [5,5]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB961 sgT961) sgFlag961 = 4 := by + decide +kernel + +lemma sg961 : RowSquare [5,3,1,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB961 sgT961 sgFlag961 + change solveCompact 10 (.full [5,5]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB961 sgT961) sgFlag961 ≠ 0 + rw [sgCert961] + norm_num + +def sgB964 : Equiv.Perm (Fin 10) := Equiv.swap 0 4 * (Equiv.swap 5 9 * (Equiv.swap 4 2 * (Equiv.swap 2 8 * (Equiv.swap 1 3 * (Equiv.swap 0 6))))) +def sgT964 : Equiv.Perm (Fin 10) := Equiv.swap 0 6 * (Equiv.swap 6 5 * (Equiv.swap 6 1 * (Equiv.swap 5 2 * (Equiv.swap 2 9 * (Equiv.swap 1 7 * (Equiv.swap 0 8)))))) +def sgFlag964 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(0,0,1),(4,0,2),(2,1,0),(5,1,1),(1,1,3),(1,2,0),(3,3,1)} +lemma sgCert964 : solveCompact 10 (.full [6,2,2]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB964 sgT964) sgFlag964 = 6 := by + decide +kernel + +lemma sg964 : RowSquare [5,3,1,1] [3,3,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,2,1,1]) (ts := [6,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB964 sgT964 sgFlag964 + change solveCompact 10 (.full [6,2,2]) (.full [4,2,2,1,1]) (.full [4,2,2,1,1]) + (certificateEdges [4,2,2,1,1] [4,2,2,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB964 sgT964) sgFlag964 ≠ 0 + rw [sgCert964] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB975 : Equiv.Perm (Fin 10) := Equiv.swap 5 8 * (Equiv.swap 5 2 * (Equiv.swap 4 1 * (Equiv.swap 2 7 * (Equiv.swap 2 3 * (Equiv.swap 1 6))))) +def sgT975 : Equiv.Perm (Fin 10) := Equiv.swap 4 1 * (Equiv.swap 5 8 * (Equiv.swap 4 3 * (Equiv.swap 3 7 * (Equiv.swap 1 9 * (Equiv.swap 0 2))))) +def sgFlag975 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(4,0,0),(0,0,1),(6,0,1),(5,0,2),(1,1,0),(2,1,0),(3,1,1),(0,2,0),(1,2,2)} +lemma sgCert975 : solveCompact 10 (.full [7,3]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) + (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB975 sgT975) sgFlag975 = 6 := by + decide +kernel + +lemma sg975 : RowSquare [5,3,2] [2,2,2,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [3,3,2,1,1]) (ts := [7,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB975 sgT975 sgFlag975 + change solveCompact 10 (.full [7,3]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) + (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [7,3] (Equiv.refl (Fin 10)) sgB975 sgT975) sgFlag975 ≠ 0 + rw [sgCert975] + norm_num + +def sgB976 : Equiv.Perm (Fin 10) := Equiv.swap 7 1 * (Equiv.swap 5 9 * (Equiv.swap 5 2 * (Equiv.swap 2 3 * (Equiv.swap 3 6 * (Equiv.swap 2 0 * (Equiv.swap 1 8 * (Equiv.swap 0 4))))))) +def sgT976 : Equiv.Perm (Fin 10) := Equiv.swap 8 7 * (Equiv.swap 7 1 * (Equiv.swap 1 4 * (Equiv.swap 1 2 * (Equiv.swap 4 9 * (Equiv.swap 1 0 * (Equiv.swap 2 6 * (Equiv.swap 1 3 * (Equiv.swap 0 5)))))))) +def sgFlag976 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,0),(1,0,1),(5,0,1),(2,0,2),(3,1,0),(1,1,1),(0,2,0),(2,2,2)} +lemma sgCert976 : solveCompact 10 (.full [6,4]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) + (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB976 sgT976) sgFlag976 = 4 := by + decide +kernel + +lemma sg976 : RowSquare [5,3,2] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [3,3,2,1,1]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB976 sgT976 sgFlag976 + change solveCompact 10 (.full [6,4]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) + (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [6,4] (Equiv.refl (Fin 10)) sgB976 sgT976) sgFlag976 ≠ 0 + rw [sgCert976] + norm_num + +def sgB977 : Equiv.Perm (Fin 10) := Equiv.swap 7 6 * (Equiv.swap 7 1 * (Equiv.swap 6 9 * (Equiv.swap 1 0 * (Equiv.swap 1 3 * (Equiv.swap 3 5 * (Equiv.swap 0 8 * (Equiv.swap 1 4 * (Equiv.swap 0 2)))))))) +def sgT977 : Equiv.Perm (Fin 10) := Equiv.swap 7 3 * (Equiv.swap 3 9 * (Equiv.swap 0 4 * (Equiv.swap 4 2 * (Equiv.swap 3 6 * (Equiv.swap 2 8 * (Equiv.swap 0 5 * (Equiv.swap 0 1))))))) +def sgFlag977 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,0),(2,0,1),(1,0,2),(2,1,0),(0,1,1),(3,1,1),(3,2,0),(4,2,0)} +lemma sgCert977 : solveCompact 10 (.full [5,5]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) + (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB977 sgT977) sgFlag977 = 40 := by + decide +kernel + +lemma sg977 : RowSquare [5,3,2] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [3,3,2,1,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB977 sgT977 sgFlag977 + change solveCompact 10 (.full [5,5]) (.full [3,3,2,1,1]) (.full [3,3,2,1,1]) + (certificateEdges [3,3,2,1,1] [3,3,2,1,1] [5,5] (Equiv.refl (Fin 10)) sgB977 sgT977) sgFlag977 ≠ 0 + rw [sgCert977] + norm_num + +def sgB982 : Equiv.Perm (Fin 10) := Equiv.swap 1 8 * (Equiv.swap 2 0 * (Equiv.swap 2 3 * (Equiv.swap 3 6 * (Equiv.swap 3 4 * (Equiv.swap 2 5 * (Equiv.swap 1 7 * (Equiv.swap 0 9))))))) +def sgT982 : Equiv.Perm (Fin 10) := Equiv.swap 1 7 * (Equiv.swap 7 9 * (Equiv.swap 3 6 * (Equiv.swap 3 4 * (Equiv.swap 1 8 * (Equiv.swap 0 5))))) +def sgFlag982 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(4,0,1),(1,0,2),(3,1,0),(1,1,1),(2,1,1),(2,2,0)} +lemma sgCert982 : solveCompact 10 (.full [5,5]) (.full [3,2,2,2,1]) (.full [3,2,2,2,1]) + (certificateEdges [3,2,2,2,1] [3,2,2,2,1] [5,5] (Equiv.refl (Fin 10)) sgB982 sgT982) sgFlag982 = 99 := by + decide +kernel + +lemma sg982 : RowSquare [5,4,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [3,2,2,2,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB982 sgT982 sgFlag982 + change solveCompact 10 (.full [5,5]) (.full [3,2,2,2,1]) (.full [3,2,2,2,1]) + (certificateEdges [3,2,2,2,1] [3,2,2,2,1] [5,5] (Equiv.refl (Fin 10)) sgB982 sgT982) sgFlag982 ≠ 0 + rw [sgCert982] + norm_num + +def sgB998 : Equiv.Perm (Fin 10) := Equiv.swap 2 5 * (Equiv.swap 5 4 * (Equiv.swap 4 9 * (Equiv.swap 3 8 * (Equiv.swap 2 6 * (Equiv.swap 1 7))))) +def sgT998 : Equiv.Perm (Fin 10) := Equiv.swap 8 9 * (Equiv.swap 3 7 * (Equiv.swap 3 6 * (Equiv.swap 3 2 * (Equiv.swap 2 0 * (Equiv.swap 0 4 * (Equiv.swap 0 1)))))) +def sgFlag998 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(7,0,0),(3,0,1),(0,0,2),(1,0,3),(5,0,4),(4,1,0),(0,2,0),(2,3,0),(6,4,0)} +lemma sgCert998 : solveCompact 10 (.full [8,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB998 sgT998) sgFlag998 = -288 := by + decide +kernel + +lemma sg998 : RowSquare [6,1,1,1,1] [2,2,1,1,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [8,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB998 sgT998 sgFlag998 + change solveCompact 10 (.full [8,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [8,2] (Equiv.refl (Fin 10)) sgB998 sgT998) sgFlag998 ≠ 0 + rw [sgCert998] + norm_num + +def sgB999 : Equiv.Perm (Fin 10) := Equiv.swap 6 3 * (Equiv.swap 2 1 * (Equiv.swap 4 0 * (Equiv.swap 3 8 * (Equiv.swap 2 5 * (Equiv.swap 1 7 * (Equiv.swap 0 9)))))) +def sgT999 : Equiv.Perm (Fin 10) := Equiv.swap 5 6 * (Equiv.swap 6 1 * (Equiv.swap 5 7 * (Equiv.swap 2 4 * (Equiv.swap 1 8)))) +def sgFlag999 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(5,0,0),(0,0,1),(6,0,2),(1,0,3),(2,0,4),(1,1,0),(4,2,0),(3,3,0),(2,4,0)} +lemma sgCert999 : solveCompact 10 (.full [7,3]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB999 sgT999) sgFlag999 = -48 := by + decide +kernel + +lemma sg999 : RowSquare [6,1,1,1,1] [2,2,2,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [7,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB999 sgT999 sgFlag999 + change solveCompact 10 (.full [7,3]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [7,3] (Equiv.refl (Fin 10)) sgB999 sgT999) sgFlag999 ≠ 0 + rw [sgCert999] + norm_num + +def sgB1000 : Equiv.Perm (Fin 10) := Equiv.swap 0 5 * (Equiv.swap 1 3 * (Equiv.swap 5 9 * (Equiv.swap 1 6 * (Equiv.swap 3 8 * (Equiv.swap 1 4 * (Equiv.swap 0 7)))))) +def sgT1000 : Equiv.Perm (Fin 10) := Equiv.swap 7 5 * (Equiv.swap 0 2 * (Equiv.swap 5 4 * (Equiv.swap 4 9 * (Equiv.swap 0 6 * (Equiv.swap 2 8 * (Equiv.swap 0 3 * (Equiv.swap 0 1))))))) +def sgFlag1000 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(0,0,1),(2,0,3),(5,0,5),(3,1,4),(2,2,2),(0,3,0),(3,4,0),(4,5,0)} +lemma sgCert1000 : solveCompact 10 (.full [6,4]) (.full [6,1,1,1,1]) (.full [6,1,1,1,1]) + (certificateEdges [6,1,1,1,1] [6,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB1000 sgT1000) sgFlag1000 = 72 := by + decide +kernel + +lemma sg1000 : RowSquare [6,1,1,1,1] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [6,1,1,1,1]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1000 sgT1000 sgFlag1000 + change solveCompact 10 (.full [6,4]) (.full [6,1,1,1,1]) (.full [6,1,1,1,1]) + (certificateEdges [6,1,1,1,1] [6,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB1000 sgT1000) sgFlag1000 ≠ 0 + rw [sgCert1000] + norm_num + +def sgB1001 : Equiv.Perm (Fin 10) := Equiv.swap 8 2 * (Equiv.swap 2 4 * (Equiv.swap 4 9 * (Equiv.swap 3 6 * (Equiv.swap 2 5 * (Equiv.swap 0 1))))) +def sgT1001 : Equiv.Perm (Fin 10) := Equiv.swap 4 3 * (Equiv.swap 6 7 * (Equiv.swap 3 9 * (Equiv.swap 4 8 * (Equiv.swap 3 1 * (Equiv.swap 1 0 * (Equiv.swap 1 2 * (Equiv.swap 0 5))))))) +def sgFlag1001 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(0,0,1),(3,0,2),(2,0,3),(4,0,4),(2,1,0),(0,2,0),(1,3,0),(3,4,0)} +lemma sgCert1001 : solveCompact 10 (.full [5,5]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB1001 sgT1001) sgFlag1001 = 240 := by + decide +kernel + +lemma sg1001 : RowSquare [6,1,1,1,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1001 sgT1001 sgFlag1001 + change solveCompact 10 (.full [5,5]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB1001 sgT1001) sgFlag1001 ≠ 0 + rw [sgCert1001] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB1006 : Equiv.Perm (Fin 10) := Equiv.swap 0 6 * (Equiv.swap 6 1 * (Equiv.swap 2 3 * (Equiv.swap 3 7 * (Equiv.swap 3 4 * (Equiv.swap 2 5 * (Equiv.swap 1 9 * (Equiv.swap 0 8))))))) +def sgT1006 : Equiv.Perm (Fin 10) := Equiv.swap 1 0 * (Equiv.swap 1 8 * (Equiv.swap 1 7 * (Equiv.swap 1 4 * (Equiv.swap 4 6 * (Equiv.swap 0 9 * (Equiv.swap 0 3 * (Equiv.swap 1 5 * (Equiv.swap 0 2)))))))) +def sgFlag1006 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,0),(1,0,1),(0,0,2),(4,0,3),(5,1,0),(3,2,0),(1,3,4),(0,4,0)} +lemma sgCert1006 : solveCompact 10 (.full [6,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB1006 sgT1006) sgFlag1006 = -12 := by + decide +kernel + +lemma sg1006 : RowSquare [6,1,1,1,1] [3,3,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [6,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1006 sgT1006 sgFlag1006 + change solveCompact 10 (.full [6,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB1006 sgT1006) sgFlag1006 ≠ 0 + rw [sgCert1006] + norm_num + +def sgB1007 : Equiv.Perm (Fin 10) := Equiv.swap 2 4 * (Equiv.swap 5 3 * (Equiv.swap 4 9 * (Equiv.swap 3 7 * (Equiv.swap 2 8)))) +def sgT1007 : Equiv.Perm (Fin 10) := Equiv.swap 7 4 * (Equiv.swap 4 9 * (Equiv.swap 4 1 * (Equiv.swap 3 2 * (Equiv.swap 2 8 * (Equiv.swap 1 0 * (Equiv.swap 0 6)))))) +def sgFlag1007 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(2,0,2),(0,0,3),(3,0,4),(0,1,1),(0,2,0),(2,3,0),(1,4,0)} +lemma sgCert1007 : solveCompact 10 (.full [5,3,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,3,2] (Equiv.refl (Fin 10)) sgB1007 sgT1007) sgFlag1007 = 20 := by + decide +kernel + +lemma sg1007 : RowSquare [6,1,1,1,1] [3,3,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [5,3,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1007 sgT1007 sgFlag1007 + change solveCompact 10 (.full [5,3,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [5,3,2] (Equiv.refl (Fin 10)) sgB1007 sgT1007) sgFlag1007 ≠ 0 + rw [sgCert1007] + norm_num + +def sgB1008 : Equiv.Perm (Fin 10) := Equiv.swap 1 2 * (Equiv.swap 3 6 * (Equiv.swap 3 4 * (Equiv.swap 2 9 * (Equiv.swap 1 8 * (Equiv.swap 0 5))))) +def sgT1008 : Equiv.Perm (Fin 10) := Equiv.swap 0 4 * (Equiv.swap 6 9 * (Equiv.swap 0 3 * (Equiv.swap 4 8 * (Equiv.swap 3 1 * (Equiv.swap 1 7 * (Equiv.swap 1 2 * (Equiv.swap 0 5))))))) +def sgFlag1008 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(3,0,0),(2,0,1),(0,0,2),(1,0,3),(2,1,0),(3,2,0),(1,3,4),(0,4,0)} +lemma sgCert1008 : solveCompact 10 (.full [4,4,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB1008 sgT1008) sgFlag1008 = 4 := by + decide +kernel + +lemma sg1008 : RowSquare [6,1,1,1,1] [3,3,2,2] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [4,4,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1008 sgT1008 sgFlag1008 + change solveCompact 10 (.full [4,4,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB1008 sgT1008) sgFlag1008 ≠ 0 + rw [sgCert1008] + norm_num + +def sgB1015 : Equiv.Perm (Fin 10) := Equiv.swap 6 0 * (Equiv.swap 5 1 * (Equiv.swap 4 8 * (Equiv.swap 1 9 * (Equiv.swap 1 3 * (Equiv.swap 0 7))))) +def sgT1015 : Equiv.Perm (Fin 10) := Equiv.swap 7 9 * (Equiv.swap 7 0 * (Equiv.swap 0 8 * (Equiv.swap 3 6 * (Equiv.swap 2 4 * (Equiv.swap 0 5))))) +def sgFlag1015 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(3,0,0),(0,0,1),(1,0,4),(1,1,3),(0,2,2),(0,3,0),(2,4,0)} +lemma sgCert1015 : solveCompact 10 (.full [4,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,2,2,2] (Equiv.refl (Fin 10)) sgB1015 sgT1015) sgFlag1015 = 4 := by + decide +kernel + +lemma sg1015 : RowSquare [6,1,1,1,1] [4,4,1,1] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [4,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1015 sgT1015 sgFlag1015 + change solveCompact 10 (.full [4,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [4,2,2,2] (Equiv.refl (Fin 10)) sgB1015 sgT1015) sgFlag1015 ≠ 0 + rw [sgCert1015] + norm_num + +def sgB1016 : Equiv.Perm (Fin 10) := Equiv.swap 3 2 * (Equiv.swap 3 5 * (Equiv.swap 5 0 * (Equiv.swap 2 9 * (Equiv.swap 3 6 * (Equiv.swap 2 4 * (Equiv.swap 0 8)))))) +def sgT1016 : Equiv.Perm (Fin 10) := Equiv.swap 7 6 * (Equiv.swap 6 3 * (Equiv.swap 5 0 * (Equiv.swap 3 2 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 9 * (Equiv.swap 0 8))))))) +def sgFlag1016 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,2),(1,0,3),(1,1,1),(1,2,4),(1,3,0),(2,4,0)} +lemma sgCert1016 : solveCompact 10 (.full [3,3,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [3,3,2,2] (Equiv.refl (Fin 10)) sgB1016 sgT1016) sgFlag1016 = 2 := by + decide +kernel + +lemma sg1016 : RowSquare [6,1,1,1,1] [4,4,2] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [3,3,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1016 sgT1016 sgFlag1016 + change solveCompact 10 (.full [3,3,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [3,3,2,2] (Equiv.refl (Fin 10)) sgB1016 sgT1016) sgFlag1016 ≠ 0 + rw [sgCert1016] + norm_num + +def sgB1023 : Equiv.Perm (Fin 10) := Equiv.swap 7 1 * (Equiv.swap 7 0 * (Equiv.swap 0 8 * (Equiv.swap 1 9 * (Equiv.swap 1 4 * (Equiv.swap 0 6))))) +def sgT1023 : Equiv.Perm (Fin 10) := Equiv.swap 2 9 * (Equiv.swap 5 8 * (Equiv.swap 5 6 * (Equiv.swap 3 4 * (Equiv.swap 2 7)))) +def sgFlag1023 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(1,1,4),(1,2,2),(0,3,3),(1,4,0)} +lemma sgCert1023 : solveCompact 10 (.full [2,2,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [2,2,2,2,2] (Equiv.refl (Fin 10)) sgB1023 sgT1023) sgFlag1023 = -6 := by + decide +kernel + +lemma sg1023 : RowSquare [6,1,1,1,1] [5,5] := by + apply rowSquare_compact (n := 10) (cs := [5,1,1,1,1,1]) (ts := [2,2,2,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1023 sgT1023 sgFlag1023 + change solveCompact 10 (.full [2,2,2,2,2]) (.full [5,1,1,1,1,1]) (.full [5,1,1,1,1,1]) + (certificateEdges [5,1,1,1,1,1] [5,1,1,1,1,1] [2,2,2,2,2] (Equiv.refl (Fin 10)) sgB1023 sgT1023) sgFlag1023 ≠ 0 + rw [sgCert1023] + norm_num + +def sgB1032 : Equiv.Perm (Fin 10) := Equiv.swap 8 5 * (Equiv.swap 5 2 * (Equiv.swap 5 0 * (Equiv.swap 1 7 * (Equiv.swap 0 6 * (Equiv.swap 2 9 * (Equiv.swap 1 4 * (Equiv.swap 0 3))))))) +def sgT1032 : Equiv.Perm (Fin 10) := Equiv.swap 1 3 * (Equiv.swap 3 9 * (Equiv.swap 5 8 * (Equiv.swap 3 0 * (Equiv.swap 1 7 * (Equiv.swap 0 6))))) +def sgFlag1032 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(4,0,0),(3,0,1),(5,0,1),(3,0,2),(0,0,3),(1,1,0),(2,1,0),(2,2,0),(0,3,0)} +lemma sgCert1032 : solveCompact 10 (.full [6,4]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB1032 sgT1032) sgFlag1032 = 16 := by + decide +kernel + +lemma sg1032 : RowSquare [6,2,1,1] [2,2,2,2,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [6,4]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1032 sgT1032 sgFlag1032 + change solveCompact 10 (.full [6,4]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,4] (Equiv.refl (Fin 10)) sgB1032 sgT1032) sgFlag1032 ≠ 0 + rw [sgCert1032] + norm_num + +def sgB1033 : Equiv.Perm (Fin 10) := Equiv.swap 8 5 * (Equiv.swap 1 7 * (Equiv.swap 5 9 * (Equiv.swap 1 2 * (Equiv.swap 2 6 * (Equiv.swap 1 4 * (Equiv.swap 0 3)))))) +def sgT1033 : Equiv.Perm (Fin 10) := Equiv.swap 2 4 * (Equiv.swap 4 9 * (Equiv.swap 2 8 * (Equiv.swap 4 6 * (Equiv.swap 1 7 * (Equiv.swap 2 5 * (Equiv.swap 1 0 * (Equiv.swap 0 3))))))) +def sgFlag1033 : Finset (ℕ × ℕ × ℕ) := {(2,0,0),(4,0,0),(1,0,1),(4,0,1),(1,0,2),(3,0,3),(0,1,0),(3,1,0),(0,2,0),(2,3,0)} +lemma sgCert1033 : solveCompact 10 (.full [5,5]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB1033 sgT1033) sgFlag1033 = -12 := by + decide +kernel + +lemma sg1033 : RowSquare [6,2,1,1] [2,2,2,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [5,5]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1033 sgT1033 sgFlag1033 + change solveCompact 10 (.full [5,5]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [5,5] (Equiv.refl (Fin 10)) sgB1033 sgT1033) sgFlag1033 ≠ 0 + rw [sgCert1033] + norm_num + +end UniversalTensorSquare +end +end + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +def sgB1038 : Equiv.Perm (Fin 10) := Equiv.swap 8 5 * (Equiv.swap 5 2 * (Equiv.swap 2 3 * (Equiv.swap 5 7 * (Equiv.swap 3 9 * (Equiv.swap 3 4 * (Equiv.swap 2 1 * (Equiv.swap 1 0 * (Equiv.swap 0 6)))))))) +def sgT1038 : Equiv.Perm (Fin 10) := Equiv.swap 2 4 * (Equiv.swap 0 8 * (Equiv.swap 2 7 * (Equiv.swap 4 1 * (Equiv.swap 2 5 * (Equiv.swap 2 3 * (Equiv.swap 1 9 * (Equiv.swap 0 6))))))) +def sgFlag1038 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(2,0,0),(0,0,1),(4,0,2),(0,0,3),(1,1,0),(3,2,1),(5,3,0)} +lemma sgCert1038 : solveCompact 10 (.full [6,2,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB1038 sgT1038) sgFlag1038 = -2 := by + decide +kernel + +lemma sg1038 : RowSquare [6,2,1,1] [3,3,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [6,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1038 sgT1038 sgFlag1038 + change solveCompact 10 (.full [6,2,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB1038 sgT1038) sgFlag1038 ≠ 0 + rw [sgCert1038] + norm_num + +def sgB1040 : Equiv.Perm (Fin 10) := Equiv.swap 8 1 * (Equiv.swap 1 5 * (Equiv.swap 5 9 * (Equiv.swap 1 7 * (Equiv.swap 0 6 * (Equiv.swap 1 3 * (Equiv.swap 0 2)))))) +def sgT1040 : Equiv.Perm (Fin 10) := Equiv.swap 4 1 * (Equiv.swap 5 8 * (Equiv.swap 5 2 * (Equiv.swap 4 7 * (Equiv.swap 1 9 * (Equiv.swap 2 0 * (Equiv.swap 1 3 * (Equiv.swap 0 6))))))) +def sgFlag1040 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(3,0,0),(1,0,1),(2,0,2),(2,1,0),(3,1,3),(0,2,0),(1,3,0)} +lemma sgCert1040 : solveCompact 10 (.full [4,4,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB1040 sgT1040) sgFlag1040 = 1 := by + decide +kernel + +lemma sg1040 : RowSquare [6,2,1,1] [3,3,2,2] := by + apply rowSquare_compact (n := 10) (cs := [4,2,1,1,1,1]) (ts := [4,4,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1040 sgT1040 sgFlag1040 + change solveCompact 10 (.full [4,4,2]) (.full [4,2,1,1,1,1]) (.full [4,2,1,1,1,1]) + (certificateEdges [4,2,1,1,1,1] [4,2,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB1040 sgT1040) sgFlag1040 ≠ 0 + rw [sgCert1040] + norm_num + +def sgB1063 : Equiv.Perm (Fin 10) := Equiv.swap 7 2 * (Equiv.swap 2 1 * (Equiv.swap 2 6 * (Equiv.swap 4 3 * (Equiv.swap 3 9 * (Equiv.swap 2 5 * (Equiv.swap 1 8)))))) +def sgT1063 : Equiv.Perm (Fin 10) := Equiv.swap 7 4 * (Equiv.swap 3 9 * (Equiv.swap 4 8 * (Equiv.swap 3 0 * (Equiv.swap 0 6 * (Equiv.swap 0 1))))) +def sgFlag1063 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(1,0,0),(1,0,1),(3,0,1),(4,0,2),(0,1,0),(5,2,0),(2,2,2)} +lemma sgCert1063 : solveCompact 10 (.full [6,2,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) + (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB1063 sgT1063) sgFlag1063 = -16 := by + decide +kernel + +lemma sg1063 : RowSquare [6,2,2] [3,3,1,1,1,1] := by + apply rowSquare_compact (n := 10) (cs := [3,3,1,1,1,1]) (ts := [6,2,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1063 sgT1063 sgFlag1063 + change solveCompact 10 (.full [6,2,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) + (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [6,2,2] (Equiv.refl (Fin 10)) sgB1063 sgT1063) sgFlag1063 ≠ 0 + rw [sgCert1063] + norm_num + +def sgB1064 : Equiv.Perm (Fin 10) := Equiv.swap 5 7 * (Equiv.swap 7 9 * (Equiv.swap 5 8 * (Equiv.swap 0 4 * (Equiv.swap 1 6 * (Equiv.swap 0 3))))) +def sgT1064 : Equiv.Perm (Fin 10) := Equiv.swap 7 9 * (Equiv.swap 5 8 * (Equiv.swap 4 2 * (Equiv.swap 2 6 * (Equiv.swap 0 3)))) +def sgFlag1064 : Finset (ℕ × ℕ × ℕ) := {(1,0,0),(3,0,0),(0,0,1),(3,0,2),(1,1,0),(2,1,0),(0,2,0),(2,2,2)} +lemma sgCert1064 : solveCompact 10 (.full [4,4,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) + (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB1064 sgT1064) sgFlag1064 = -1 := by + decide +kernel + +lemma sg1064 : RowSquare [6,2,2] [3,3,2,2] := by + apply rowSquare_compact (n := 10) (cs := [3,3,1,1,1,1]) (ts := [4,4,2]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1064 sgT1064 sgFlag1064 + change solveCompact 10 (.full [4,4,2]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) + (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,4,2] (Equiv.refl (Fin 10)) sgB1064 sgT1064) sgFlag1064 ≠ 0 + rw [sgCert1064] + norm_num + +def sgB1065 : Equiv.Perm (Fin 10) := Equiv.swap 3 4 * (Equiv.swap 3 0 * (Equiv.swap 5 9 * (Equiv.swap 4 1 * (Equiv.swap 3 2 * (Equiv.swap 2 6 * (Equiv.swap 1 8 * (Equiv.swap 0 7))))))) +def sgT1065 : Equiv.Perm (Fin 10) := Equiv.swap 2 9 * (Equiv.swap 2 8 * (Equiv.swap 2 7 * (Equiv.swap 2 0 * (Equiv.swap 0 6 * (Equiv.swap 2 1 * (Equiv.swap 1 4 * (Equiv.swap 0 3))))))) +def sgFlag1065 : Finset (ℕ × ℕ × ℕ) := {(0,0,0),(2,0,0),(3,0,0),(1,0,1),(2,0,2),(0,1,0),(0,1,1),(1,2,0)} +lemma sgCert1065 : solveCompact 10 (.full [4,3,3]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) + (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB1065 sgT1065) sgFlag1065 = -4 := by + decide +kernel + +lemma sg1065 : RowSquare [6,2,2] [3,3,3,1] := by + apply rowSquare_compact (n := 10) (cs := [3,3,1,1,1,1]) (ts := [4,3,3]) + (by decide) (by decide) (by decide) (by decide) (by decide) (by decide) + rfl rfl sgB1065 sgT1065 sgFlag1065 + change solveCompact 10 (.full [4,3,3]) (.full [3,3,1,1,1,1]) (.full [3,3,1,1,1,1]) + (certificateEdges [3,3,1,1,1,1] [3,3,1,1,1,1] [4,3,3] (Equiv.refl (Fin 10)) sgB1065 sgT1065) sgFlag1065 ≠ 0 + rw [sgCert1065] + norm_num + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLocalLeaves.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLocalLeaves.lean index b432ffa6f51a252a110a3efe49374e15a00c1034..97f073ec2143ca2a7db8fa98310c9f6d2a9abfe5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLocalLeaves.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupLocalLeaves.lean @@ -1,1890 +1,1890 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeFive -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeSeven -import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeEight -import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees - -namespace OAI - -/-! Semigroup Local Leaves. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg0 : RowSquare [1] [1] := by - exact rowSquare_trivial _ (by decide) - -lemma sg1 : RowSquare [1,1] [2] := by - exact rowSquare_trivial _ (by decide) - -lemma sg2 : RowSquare [2] [2] := by - exact rowSquare_trivial _ (by decide) - -lemma sg3 : RowSquare [1,1,1] [3] := by - exact rowSquare_trivial _ (by decide) - -lemma sg4 : RowSquare [2,1] [1,1,1] := by - have he : rowDiagram [2,1] = (staircase 2) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [2,1]) (rowDiagram [1,1,1]) - have hh : SquareOccurs (staircase 2) (rowDiagram [1,1,1]) := - ⟨3,canonicalTableau _ (staircase_card 2),canonicalTableau _ (rowDiagram_card [1,1,1]), - saxl_kronecker_pos 2 (by decide) _ (rowDiagram_card [1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1])) he) hh - -lemma sg5 : RowSquare [2,1] [2,1] := by - have he : rowDiagram [2,1] = (staircase 2) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [2,1]) (rowDiagram [2,1]) - have hh : SquareOccurs (staircase 2) (rowDiagram [2,1]) := - ⟨3,canonicalTableau _ (staircase_card 2),canonicalTableau _ (rowDiagram_card [2,1]), - saxl_kronecker_pos 2 (by decide) _ (rowDiagram_card [2,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1])) he) hh - -lemma sg6 : RowSquare [2,1] [3] := by - exact rowSquare_trivial _ (by decide) - -lemma sg7 : RowSquare [3] [3] := by - exact rowSquare_trivial _ (by decide) - -lemma sg8 : RowSquare [1,1,1,1] [4] := by - exact rowSquare_trivial _ (by decide) - -lemma sg9 : RowSquare [2,1,1] [2,1,1] := by - exact rowSquare_short 1 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg11 : RowSquare [2,1,1] [3,1] := by - exact rowSquare_short 1 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg12 : RowSquare [2,1,1] [4] := by - exact rowSquare_trivial _ (by decide) - -lemma sg13 : RowSquare [2,2] [1,1,1,1] := by - exact rowSquare_target_transpose (q := [4]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg14 : RowSquare [2,2] [2,2] := by - exact rowSquare_even 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg15 : RowSquare [2,2] [4] := by - exact rowSquare_trivial _ (by decide) - -lemma sg16 : RowSquare [3,1] [2,1,1] := by - exact rowSquare_short 1 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg18 : RowSquare [3,1] [3,1] := by - exact rowSquare_short 1 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg19 : RowSquare [3,1] [4] := by - exact rowSquare_trivial _ (by decide) - -lemma sg20 : RowSquare [4] [4] := by - exact rowSquare_trivial _ (by decide) - -lemma sg21 : RowSquare [1,1,1,1,1] [5] := by - exact rowSquare_trivial _ (by decide) - -lemma sg25 : RowSquare [2,1,1,1] [5] := by - exact rowSquare_trivial _ (by decide) - -lemma sg26 : RowSquare [2,2,1] [2,1,1,1] := by - exact rowSquare_short 2 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg27 : RowSquare [2,2,1] [2,2,1] := by - exact rowSquare_short 2 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg28 : RowSquare [2,2,1] [3,1,1] := by - exact rowSquare_short 2 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg29 : RowSquare [2,2,1] [3,2] := by - exact rowSquare_short 2 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg30 : RowSquare [2,2,1] [4,1] := by - exact rowSquare_short 2 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg31 : RowSquare [2,2,1] [5] := by - exact rowSquare_trivial _ (by decide) - -lemma sg32 : RowSquare [3,1,1] [1,1,1,1,1] := by - have he : rowDiagram [3,1,1] = fiveWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,1,1]) (rowDiagram [1,1,1,1,1]) - have hh : SquareOccurs fiveWitness (rowDiagram [1,1,1,1,1]) := - ⟨5,canonicalTableau _ fiveWitness_card,canonicalTableau _ (rowDiagram_card [1,1,1,1,1]), - five_kronecker_pos _ (rowDiagram_card [1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1,1,1])) he) hh - -lemma sg33 : RowSquare [3,1,1] [2,1,1,1] := by - have he : rowDiagram [3,1,1] = fiveWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,1,1]) (rowDiagram [2,1,1,1]) - have hh : SquareOccurs fiveWitness (rowDiagram [2,1,1,1]) := - ⟨5,canonicalTableau _ fiveWitness_card,canonicalTableau _ (rowDiagram_card [2,1,1,1]), - five_kronecker_pos _ (rowDiagram_card [2,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1,1,1])) he) hh - -lemma sg34 : RowSquare [3,1,1] [2,2,1] := by - have he : rowDiagram [3,1,1] = fiveWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,1,1]) (rowDiagram [2,2,1]) - have hh : SquareOccurs fiveWitness (rowDiagram [2,2,1]) := - ⟨5,canonicalTableau _ fiveWitness_card,canonicalTableau _ (rowDiagram_card [2,2,1]), - five_kronecker_pos _ (rowDiagram_card [2,2,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,1])) he) hh - -lemma sg35 : RowSquare [3,1,1] [3,1,1] := by - have he : rowDiagram [3,1,1] = fiveWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,1,1]) (rowDiagram [3,1,1]) - have hh : SquareOccurs fiveWitness (rowDiagram [3,1,1]) := - ⟨5,canonicalTableau _ fiveWitness_card,canonicalTableau _ (rowDiagram_card [3,1,1]), - five_kronecker_pos _ (rowDiagram_card [3,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,1,1])) he) hh - -lemma sg36 : RowSquare [3,1,1] [3,2] := by - have he : rowDiagram [3,1,1] = fiveWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,1,1]) (rowDiagram [3,2]) - have hh : SquareOccurs fiveWitness (rowDiagram [3,2]) := - ⟨5,canonicalTableau _ fiveWitness_card,canonicalTableau _ (rowDiagram_card [3,2]), - five_kronecker_pos _ (rowDiagram_card [3,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2])) he) hh - -lemma sg37 : RowSquare [3,1,1] [4,1] := by - have he : rowDiagram [3,1,1] = fiveWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,1,1]) (rowDiagram [4,1]) - have hh : SquareOccurs fiveWitness (rowDiagram [4,1]) := - ⟨5,canonicalTableau _ fiveWitness_card,canonicalTableau _ (rowDiagram_card [4,1]), - five_kronecker_pos _ (rowDiagram_card [4,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,1])) he) hh - -lemma sg38 : RowSquare [3,1,1] [5] := by - exact rowSquare_trivial _ (by decide) - -lemma sg39 : RowSquare [3,2] [2,1,1,1] := by - exact rowSquare_short 2 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg40 : RowSquare [3,2] [2,2,1] := by - exact rowSquare_short 2 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg41 : RowSquare [3,2] [3,1,1] := by - exact rowSquare_short 2 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg42 : RowSquare [3,2] [3,2] := by - exact rowSquare_short 2 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg43 : RowSquare [3,2] [4,1] := by - exact rowSquare_short 2 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg44 : RowSquare [3,2] [5] := by - exact rowSquare_trivial _ (by decide) - -lemma sg48 : RowSquare [4,1] [5] := by - exact rowSquare_trivial _ (by decide) - -lemma sg49 : RowSquare [5] [5] := by - exact rowSquare_trivial _ (by decide) - -lemma sg50 : RowSquare [1,1,1,1,1,1] [6] := by - exact rowSquare_trivial _ (by decide) - -lemma sg54 : RowSquare [2,1,1,1,1] [6] := by - exact rowSquare_trivial _ (by decide) - -lemma sg55 : RowSquare [2,2,1,1] [2,2,2] := by - exact rowSquare_short 2 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg56 : RowSquare [2,2,1,1] [3,1,1,1] := by - exact rowSquare_short 2 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg57 : RowSquare [2,2,1,1] [3,2,1] := by - exact rowSquare_short 2 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg58 : RowSquare [2,2,1,1] [4,1,1] := by - exact rowSquare_short 2 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg59 : RowSquare [2,2,1,1] [4,2] := by - exact rowSquare_short 2 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg60 : RowSquare [2,2,1,1] [5,1] := by - exact rowSquare_short 2 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg61 : RowSquare [2,2,1,1] [6] := by - exact rowSquare_trivial _ (by decide) - -lemma sg62 : RowSquare [2,2,2] [2,2,2] := by - exact rowSquare_even 3 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg64 : RowSquare [2,2,2] [4,2] := by - exact rowSquare_even 3 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg65 : RowSquare [2,2,2] [6] := by - exact rowSquare_trivial _ (by decide) - -lemma sg74 : RowSquare [3,2,1] [1,1,1,1,1,1] := by - have he : rowDiagram [3,2,1] = (staircase 3) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [1,1,1,1,1,1]) - have hh : SquareOccurs (staircase 3) (rowDiagram [1,1,1,1,1,1]) := - ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [1,1,1,1,1,1]), - saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1,1,1,1])) he) hh - -lemma sg75 : RowSquare [3,2,1] [2,1,1,1,1] := by - have he : rowDiagram [3,2,1] = (staircase 3) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [2,1,1,1,1]) - have hh : SquareOccurs (staircase 3) (rowDiagram [2,1,1,1,1]) := - ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [2,1,1,1,1]), - saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [2,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1,1,1,1])) he) hh - -lemma sg76 : RowSquare [3,2,1] [2,2,1,1] := by - have he : rowDiagram [3,2,1] = (staircase 3) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [2,2,1,1]) - have hh : SquareOccurs (staircase 3) (rowDiagram [2,2,1,1]) := - ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [2,2,1,1]), - saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [2,2,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,1,1])) he) hh - -lemma sg77 : RowSquare [3,2,1] [2,2,2] := by - have he : rowDiagram [3,2,1] = (staircase 3) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [2,2,2]) - have hh : SquareOccurs (staircase 3) (rowDiagram [2,2,2]) := - ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [2,2,2]), - saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [2,2,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2])) he) hh - -lemma sg78 : RowSquare [3,2,1] [3,1,1,1] := by - have he : rowDiagram [3,2,1] = (staircase 3) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [3,1,1,1]) - have hh : SquareOccurs (staircase 3) (rowDiagram [3,1,1,1]) := - ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [3,1,1,1]), - saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [3,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,1,1,1])) he) hh - -lemma sg79 : RowSquare [3,2,1] [3,2,1] := by - have he : rowDiagram [3,2,1] = (staircase 3) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [3,2,1]) - have hh : SquareOccurs (staircase 3) (rowDiagram [3,2,1]) := - ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [3,2,1]), - saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [3,2,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,1])) he) hh - -lemma sg80 : RowSquare [3,2,1] [3,3] := by - have he : rowDiagram [3,2,1] = (staircase 3) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [3,3]) - have hh : SquareOccurs (staircase 3) (rowDiagram [3,3]) := - ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [3,3]), - saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [3,3])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3])) he) hh - -lemma sg81 : RowSquare [3,2,1] [4,2] := by - have he : rowDiagram [3,2,1] = (staircase 3) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [4,2]) - have hh : SquareOccurs (staircase 3) (rowDiagram [4,2]) := - ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [4,2]), - saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [4,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,2])) he) hh - -lemma sg82 : RowSquare [3,2,1] [5,1] := by - have he : rowDiagram [3,2,1] = (staircase 3) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [5,1]) - have hh : SquareOccurs (staircase 3) (rowDiagram [5,1]) := - ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [5,1]), - saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [5,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,1])) he) hh - -lemma sg83 : RowSquare [3,3] [2,2,2] := by - exact rowSquare_even 3 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg85 : RowSquare [3,3] [4,2] := by - exact rowSquare_even 3 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg86 : RowSquare [3,3] [6] := by - exact rowSquare_trivial _ (by decide) - -lemma sg96 : RowSquare [4,1,1] [6] := by - exact rowSquare_trivial _ (by decide) - -lemma sg97 : RowSquare [4,2] [2,2,2] := by - exact rowSquare_short 2 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg98 : RowSquare [4,2] [3,1,1,1] := by - exact rowSquare_short 2 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg99 : RowSquare [4,2] [3,2,1] := by - exact rowSquare_short 2 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg100 : RowSquare [4,2] [4,1,1] := by - exact rowSquare_short 2 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg101 : RowSquare [4,2] [4,2] := by - exact rowSquare_short 2 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg102 : RowSquare [4,2] [5,1] := by - exact rowSquare_short 2 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg103 : RowSquare [4,2] [6] := by - exact rowSquare_trivial _ (by decide) - -lemma sg107 : RowSquare [5,1] [6] := by - exact rowSquare_trivial _ (by decide) - -lemma sg108 : RowSquare [6] [6] := by - exact rowSquare_trivial _ (by decide) - -lemma sg109 : RowSquare [1,1,1,1,1,1,1] [7] := by - exact rowSquare_trivial _ (by decide) - -lemma sg113 : RowSquare [2,1,1,1,1,1] [7] := by - exact rowSquare_trivial _ (by decide) - -lemma sg122 : RowSquare [2,2,1,1,1] [7] := by - exact rowSquare_trivial _ (by decide) - -lemma sg123 : RowSquare [2,2,2,1] [2,2,2,1] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg124 : RowSquare [2,2,2,1] [3,2,2] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg125 : RowSquare [2,2,2,1] [3,3,1] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg126 : RowSquare [2,2,2,1] [4,1,1,1] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg127 : RowSquare [2,2,2,1] [4,2,1] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg128 : RowSquare [2,2,2,1] [4,3] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg129 : RowSquare [2,2,2,1] [5,1,1] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg130 : RowSquare [2,2,2,1] [5,2] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg131 : RowSquare [2,2,2,1] [7] := by - exact rowSquare_trivial _ (by decide) - -lemma sg141 : RowSquare [3,1,1,1,1] [7] := by - exact rowSquare_trivial _ (by decide) - -lemma sg178 : RowSquare [4,1,1,1] [1,1,1,1,1,1,1] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [1,1,1,1,1,1,1]) - have hh : SquareOccurs sevenWitness (rowDiagram [1,1,1,1,1,1,1]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [1,1,1,1,1,1,1]), - seven_kronecker_pos _ (rowDiagram_card [1,1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1,1,1,1,1])) he) hh - -lemma sg179 : RowSquare [4,1,1,1] [2,1,1,1,1,1] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [2,1,1,1,1,1]) - have hh : SquareOccurs sevenWitness (rowDiagram [2,1,1,1,1,1]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [2,1,1,1,1,1]), - seven_kronecker_pos _ (rowDiagram_card [2,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1,1,1,1,1])) he) hh - -lemma sg180 : RowSquare [4,1,1,1] [2,2,1,1,1] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [2,2,1,1,1]) - have hh : SquareOccurs sevenWitness (rowDiagram [2,2,1,1,1]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [2,2,1,1,1]), - seven_kronecker_pos _ (rowDiagram_card [2,2,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,1,1,1])) he) hh - -lemma sg181 : RowSquare [4,1,1,1] [2,2,2,1] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [2,2,2,1]) - have hh : SquareOccurs sevenWitness (rowDiagram [2,2,2,1]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [2,2,2,1]), - seven_kronecker_pos _ (rowDiagram_card [2,2,2,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,1])) he) hh - -lemma sg182 : RowSquare [4,1,1,1] [3,1,1,1,1] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [3,1,1,1,1]) - have hh : SquareOccurs sevenWitness (rowDiagram [3,1,1,1,1]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [3,1,1,1,1]), - seven_kronecker_pos _ (rowDiagram_card [3,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,1,1,1,1])) he) hh - -lemma sg183 : RowSquare [4,1,1,1] [3,2,1,1] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [3,2,1,1]) - have hh : SquareOccurs sevenWitness (rowDiagram [3,2,1,1]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [3,2,1,1]), - seven_kronecker_pos _ (rowDiagram_card [3,2,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,1,1])) he) hh - -lemma sg184 : RowSquare [4,1,1,1] [3,2,2] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [3,2,2]) - have hh : SquareOccurs sevenWitness (rowDiagram [3,2,2]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [3,2,2]), - seven_kronecker_pos _ (rowDiagram_card [3,2,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,2])) he) hh - -lemma sg185 : RowSquare [4,1,1,1] [3,3,1] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [3,3,1]) - have hh : SquareOccurs sevenWitness (rowDiagram [3,3,1]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [3,3,1]), - seven_kronecker_pos _ (rowDiagram_card [3,3,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,1])) he) hh - -lemma sg186 : RowSquare [4,1,1,1] [4,1,1,1] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [4,1,1,1]) - have hh : SquareOccurs sevenWitness (rowDiagram [4,1,1,1]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [4,1,1,1]), - seven_kronecker_pos _ (rowDiagram_card [4,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,1,1,1])) he) hh - -lemma sg187 : RowSquare [4,1,1,1] [4,2,1] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [4,2,1]) - have hh : SquareOccurs sevenWitness (rowDiagram [4,2,1]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [4,2,1]), - seven_kronecker_pos _ (rowDiagram_card [4,2,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,2,1])) he) hh - -lemma sg188 : RowSquare [4,1,1,1] [4,3] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [4,3]) - have hh : SquareOccurs sevenWitness (rowDiagram [4,3]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [4,3]), - seven_kronecker_pos _ (rowDiagram_card [4,3])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,3])) he) hh - -lemma sg189 : RowSquare [4,1,1,1] [5,1,1] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [5,1,1]) - have hh : SquareOccurs sevenWitness (rowDiagram [5,1,1]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [5,1,1]), - seven_kronecker_pos _ (rowDiagram_card [5,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,1,1])) he) hh - -lemma sg190 : RowSquare [4,1,1,1] [5,2] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [5,2]) - have hh : SquareOccurs sevenWitness (rowDiagram [5,2]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [5,2]), - seven_kronecker_pos _ (rowDiagram_card [5,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,2])) he) hh - -lemma sg191 : RowSquare [4,1,1,1] [6,1] := by - have he : rowDiagram [4,1,1,1] = sevenWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [6,1]) - have hh : SquareOccurs sevenWitness (rowDiagram [6,1]) := - ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [6,1]), - seven_kronecker_pos _ (rowDiagram_card [6,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [6,1])) he) hh - -lemma sg192 : RowSquare [4,1,1,1] [7] := by - exact rowSquare_trivial _ (by decide) - -lemma sg206 : RowSquare [4,2,1] [7] := by - exact rowSquare_trivial _ (by decide) - -lemma sg207 : RowSquare [4,3] [2,2,2,1] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg208 : RowSquare [4,3] [3,2,1,1] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg209 : RowSquare [4,3] [3,2,2] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg210 : RowSquare [4,3] [3,3,1] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg211 : RowSquare [4,3] [4,1,1,1] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg212 : RowSquare [4,3] [4,2,1] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg213 : RowSquare [4,3] [4,3] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg214 : RowSquare [4,3] [5,1,1] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg215 : RowSquare [4,3] [5,2] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg216 : RowSquare [4,3] [6,1] := by - exact rowSquare_short 3 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg217 : RowSquare [4,3] [7] := by - exact rowSquare_trivial _ (by decide) - -lemma sg226 : RowSquare [5,1,1] [7] := by - exact rowSquare_trivial _ (by decide) - -lemma sg234 : RowSquare [7] [7] := by - exact rowSquare_trivial _ (by decide) - -lemma sg235 : RowSquare [1,1,1,1,1,1,1,1] [8] := by - exact rowSquare_trivial _ (by decide) - -lemma sg238 : RowSquare [2,1,1,1,1,1,1] [8] := by - exact rowSquare_trivial _ (by decide) - -lemma sg248 : RowSquare [2,2,1,1,1,1] [8] := by - exact rowSquare_trivial _ (by decide) - -lemma sg249 : RowSquare [2,2,2,1,1] [3,2,2,1] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg251 : RowSquare [2,2,2,1,1] [3,3,2] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg253 : RowSquare [2,2,2,1,1] [6,2] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg256 : RowSquare [2,2,2,2] [4,2,2] := by - exact rowSquare_even 4 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg257 : RowSquare [2,2,2,2] [4,4] := by - exact rowSquare_even 4 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg259 : RowSquare [2,2,2,2] [6,2] := by - exact rowSquare_even 4 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg269 : RowSquare [3,1,1,1,1,1] [8] := by - exact rowSquare_trivial _ (by decide) - -lemma sg306 : RowSquare [3,3,2] [1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [8]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg330 : RowSquare [4,2,1,1] [1,1,1,1,1,1,1,1] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [1,1,1,1,1,1,1,1]) - have hh : SquareOccurs eightWitness (rowDiagram [1,1,1,1,1,1,1,1]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [1,1,1,1,1,1,1,1]), - eight_kronecker_pos _ (rowDiagram_card [1,1,1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1,1,1,1,1,1])) he) hh - -lemma sg331 : RowSquare [4,2,1,1] [2,1,1,1,1,1,1] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [2,1,1,1,1,1,1]) - have hh : SquareOccurs eightWitness (rowDiagram [2,1,1,1,1,1,1]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [2,1,1,1,1,1,1]), - eight_kronecker_pos _ (rowDiagram_card [2,1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1,1,1,1,1,1])) he) hh - -lemma sg332 : RowSquare [4,2,1,1] [2,2,1,1,1,1] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [2,2,1,1,1,1]) - have hh : SquareOccurs eightWitness (rowDiagram [2,2,1,1,1,1]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [2,2,1,1,1,1]), - eight_kronecker_pos _ (rowDiagram_card [2,2,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,1,1,1,1])) he) hh - -lemma sg333 : RowSquare [4,2,1,1] [2,2,2,1,1] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [2,2,2,1,1]) - have hh : SquareOccurs eightWitness (rowDiagram [2,2,2,1,1]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [2,2,2,1,1]), - eight_kronecker_pos _ (rowDiagram_card [2,2,2,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,1,1])) he) hh - -lemma sg334 : RowSquare [4,2,1,1] [2,2,2,2] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [2,2,2,2]) - have hh : SquareOccurs eightWitness (rowDiagram [2,2,2,2]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [2,2,2,2]), - eight_kronecker_pos _ (rowDiagram_card [2,2,2,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,2])) he) hh - -lemma sg335 : RowSquare [4,2,1,1] [3,1,1,1,1,1] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [3,1,1,1,1,1]) - have hh : SquareOccurs eightWitness (rowDiagram [3,1,1,1,1,1]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [3,1,1,1,1,1]), - eight_kronecker_pos _ (rowDiagram_card [3,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,1,1,1,1,1])) he) hh - -lemma sg336 : RowSquare [4,2,1,1] [3,2,1,1,1] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [3,2,1,1,1]) - have hh : SquareOccurs eightWitness (rowDiagram [3,2,1,1,1]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [3,2,1,1,1]), - eight_kronecker_pos _ (rowDiagram_card [3,2,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,1,1,1])) he) hh - -lemma sg337 : RowSquare [4,2,1,1] [3,2,2,1] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [3,2,2,1]) - have hh : SquareOccurs eightWitness (rowDiagram [3,2,2,1]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [3,2,2,1]), - eight_kronecker_pos _ (rowDiagram_card [3,2,2,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,2,1])) he) hh - -lemma sg338 : RowSquare [4,2,1,1] [3,3,1,1] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [3,3,1,1]) - have hh : SquareOccurs eightWitness (rowDiagram [3,3,1,1]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [3,3,1,1]), - eight_kronecker_pos _ (rowDiagram_card [3,3,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,1,1])) he) hh - -lemma sg339 : RowSquare [4,2,1,1] [3,3,2] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [3,3,2]) - have hh : SquareOccurs eightWitness (rowDiagram [3,3,2]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [3,3,2]), - eight_kronecker_pos _ (rowDiagram_card [3,3,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,2])) he) hh - -lemma sg340 : RowSquare [4,2,1,1] [4,2,2] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [4,2,2]) - have hh : SquareOccurs eightWitness (rowDiagram [4,2,2]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [4,2,2]), - eight_kronecker_pos _ (rowDiagram_card [4,2,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,2,2])) he) hh - -lemma sg341 : RowSquare [4,2,1,1] [4,3,1] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [4,3,1]) - have hh : SquareOccurs eightWitness (rowDiagram [4,3,1]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [4,3,1]), - eight_kronecker_pos _ (rowDiagram_card [4,3,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,3,1])) he) hh - -lemma sg342 : RowSquare [4,2,1,1] [4,4] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [4,4]) - have hh : SquareOccurs eightWitness (rowDiagram [4,4]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [4,4]), - eight_kronecker_pos _ (rowDiagram_card [4,4])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,4])) he) hh - -lemma sg343 : RowSquare [4,2,1,1] [5,1,1,1] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [5,1,1,1]) - have hh : SquareOccurs eightWitness (rowDiagram [5,1,1,1]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [5,1,1,1]), - eight_kronecker_pos _ (rowDiagram_card [5,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,1,1,1])) he) hh - -lemma sg344 : RowSquare [4,2,1,1] [5,2,1] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [5,2,1]) - have hh : SquareOccurs eightWitness (rowDiagram [5,2,1]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [5,2,1]), - eight_kronecker_pos _ (rowDiagram_card [5,2,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,2,1])) he) hh - -lemma sg345 : RowSquare [4,2,1,1] [5,3] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [5,3]) - have hh : SquareOccurs eightWitness (rowDiagram [5,3]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [5,3]), - eight_kronecker_pos _ (rowDiagram_card [5,3])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,3])) he) hh - -lemma sg346 : RowSquare [4,2,1,1] [6,2] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [6,2]) - have hh : SquareOccurs eightWitness (rowDiagram [6,2]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [6,2]), - eight_kronecker_pos _ (rowDiagram_card [6,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [6,2])) he) hh - -lemma sg347 : RowSquare [4,2,1,1] [7,1] := by - have he : rowDiagram [4,2,1,1] = eightWitness := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [7,1]) - have hh : SquareOccurs eightWitness (rowDiagram [7,1]) := - ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [7,1]), - eight_kronecker_pos _ (rowDiagram_card [7,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [7,1])) he) hh - -lemma sg366 : RowSquare [4,4] [4,2,2] := by - exact rowSquare_even 4 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg367 : RowSquare [4,4] [4,4] := by - exact rowSquare_even 4 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg369 : RowSquare [4,4] [6,2] := by - exact rowSquare_even 4 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg401 : RowSquare [5,3] [3,2,2,1] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg403 : RowSquare [5,3] [3,3,2] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg404 : RowSquare [5,3] [4,2,1,1] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg405 : RowSquare [5,3] [4,2,2] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg406 : RowSquare [5,3] [4,3,1] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg408 : RowSquare [5,3] [5,1,1,1] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg409 : RowSquare [5,3] [5,2,1] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg410 : RowSquare [5,3] [5,3] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg411 : RowSquare [5,3] [6,1,1] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg412 : RowSquare [5,3] [6,2] := by - exact rowSquare_short 3 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg421 : RowSquare [6,1,1] [8] := by - exact rowSquare_trivial _ (by decide) - -lemma sg426 : RowSquare [8] [8] := by - exact rowSquare_trivial _ (by decide) - -lemma sg427 : RowSquare [1,1,1,1,1,1,1,1,1] [9] := by - exact rowSquare_trivial _ (by decide) - -lemma sg431 : RowSquare [2,1,1,1,1,1,1,1] [9] := by - exact rowSquare_trivial _ (by decide) - -lemma sg445 : RowSquare [2,2,2,1,1,1] [9] := by - exact rowSquare_trivial _ (by decide) - -lemma sg446 : RowSquare [2,2,2,2,1] [3,3,3] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg454 : RowSquare [3,1,1,1,1,1,1] [9] := by - exact rowSquare_trivial _ (by decide) - -lemma sg474 : RowSquare [3,2,1,1,1,1] [9] := by - exact rowSquare_trivial _ (by decide) - -lemma sg509 : RowSquare [3,3,1,1,1] [9] := by - exact rowSquare_trivial _ (by decide) - -lemma sg516 : RowSquare [3,3,3] [1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [9]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg586 : RowSquare [5,1,1,1,1] [1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [9]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg656 : RowSquare [5,4] [3,2,2,2] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg657 : RowSquare [5,4] [3,3,2,1] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg658 : RowSquare [5,4] [3,3,3] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg659 : RowSquare [5,4] [4,2,2,1] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg660 : RowSquare [5,4] [4,3,1,1] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg661 : RowSquare [5,4] [4,3,2] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg662 : RowSquare [5,4] [4,4,1] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg663 : RowSquare [5,4] [5,2,1,1] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg664 : RowSquare [5,4] [5,2,2] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg665 : RowSquare [5,4] [5,3,1] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg666 : RowSquare [5,4] [5,4] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg667 : RowSquare [5,4] [6,1,1,1] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg668 : RowSquare [5,4] [6,2,1] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg669 : RowSquare [5,4] [6,3] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg670 : RowSquare [5,4] [7,2] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg671 : RowSquare [5,4] [8,1] := by - exact rowSquare_short 4 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg672 : RowSquare [5,4] [9] := by - exact rowSquare_trivial _ (by decide) - -lemma sg718 : RowSquare [1,1,1,1,1,1,1,1,1,1] [10] := by - exact rowSquare_trivial _ (by decide) - -lemma sg720 : RowSquare [2,1,1,1,1,1,1,1,1] [10] := by - exact rowSquare_trivial _ (by decide) - -lemma sg730 : RowSquare [2,2,2,2,1,1] [10] := by - exact rowSquare_trivial _ (by decide) - -lemma sg757 : RowSquare [3,2,2,1,1,1] [10] := by - exact rowSquare_trivial _ (by decide) - -lemma sg789 : RowSquare [3,3,1,1,1,1] [10] := by - exact rowSquare_trivial _ (by decide) - -lemma sg849 : RowSquare [4,3,2,1] [1,1,1,1,1,1,1,1,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [1,1,1,1,1,1,1,1,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [1,1,1,1,1,1,1,1,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [1,1,1,1,1,1,1,1,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [1,1,1,1,1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1,1,1,1,1,1,1,1])) he) hh - -lemma sg850 : RowSquare [4,3,2,1] [2,1,1,1,1,1,1,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [2,1,1,1,1,1,1,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [2,1,1,1,1,1,1,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [2,1,1,1,1,1,1,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [2,1,1,1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1,1,1,1,1,1,1,1])) he) hh - -lemma sg851 : RowSquare [4,3,2,1] [2,2,1,1,1,1,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [2,2,1,1,1,1,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [2,2,1,1,1,1,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [2,2,1,1,1,1,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [2,2,1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,1,1,1,1,1,1])) he) hh - -lemma sg852 : RowSquare [4,3,2,1] [2,2,2,1,1,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [2,2,2,1,1,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [2,2,2,1,1,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [2,2,2,1,1,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [2,2,2,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,1,1,1,1])) he) hh - -lemma sg853 : RowSquare [4,3,2,1] [2,2,2,2,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [2,2,2,2,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [2,2,2,2,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [2,2,2,2,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [2,2,2,2,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,2,1,1])) he) hh - -lemma sg854 : RowSquare [4,3,2,1] [2,2,2,2,2] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [2,2,2,2,2]) - have hh : SquareOccurs (staircase 4) (rowDiagram [2,2,2,2,2]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [2,2,2,2,2]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [2,2,2,2,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,2,2])) he) hh - -lemma sg855 : RowSquare [4,3,2,1] [3,1,1,1,1,1,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,1,1,1,1,1,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [3,1,1,1,1,1,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,1,1,1,1,1,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,1,1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,1,1,1,1,1,1,1])) he) hh - -lemma sg856 : RowSquare [4,3,2,1] [3,2,1,1,1,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,2,1,1,1,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [3,2,1,1,1,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,2,1,1,1,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,2,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,1,1,1,1,1])) he) hh - -lemma sg857 : RowSquare [4,3,2,1] [3,2,2,1,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,2,2,1,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [3,2,2,1,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,2,2,1,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,2,2,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,2,1,1,1])) he) hh - -lemma sg858 : RowSquare [4,3,2,1] [3,2,2,2,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,2,2,2,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [3,2,2,2,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,2,2,2,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,2,2,2,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,2,2,1])) he) hh - -lemma sg859 : RowSquare [4,3,2,1] [3,3,1,1,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,3,1,1,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [3,3,1,1,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,3,1,1,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,3,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,1,1,1,1])) he) hh - -lemma sg860 : RowSquare [4,3,2,1] [3,3,2,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,3,2,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [3,3,2,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,3,2,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,3,2,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,2,1,1])) he) hh - -lemma sg861 : RowSquare [4,3,2,1] [3,3,2,2] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,3,2,2]) - have hh : SquareOccurs (staircase 4) (rowDiagram [3,3,2,2]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,3,2,2]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,3,2,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,2,2])) he) hh - -lemma sg862 : RowSquare [4,3,2,1] [3,3,3,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,3,3,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [3,3,3,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,3,3,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,3,3,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,3,1])) he) hh - -lemma sg863 : RowSquare [4,3,2,1] [4,1,1,1,1,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,1,1,1,1,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [4,1,1,1,1,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,1,1,1,1,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,1,1,1,1,1,1])) he) hh - -lemma sg864 : RowSquare [4,3,2,1] [4,2,2,2] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,2,2,2]) - have hh : SquareOccurs (staircase 4) (rowDiagram [4,2,2,2]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,2,2,2]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,2,2,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,2,2,2])) he) hh - -lemma sg865 : RowSquare [4,3,2,1] [4,3,1,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,3,1,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [4,3,1,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,3,1,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,3,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,3,1,1,1])) he) hh - -lemma sg866 : RowSquare [4,3,2,1] [4,3,2,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,3,2,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [4,3,2,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,3,2,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,3,2,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,3,2,1])) he) hh - -lemma sg867 : RowSquare [4,3,2,1] [4,3,3] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,3,3]) - have hh : SquareOccurs (staircase 4) (rowDiagram [4,3,3]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,3,3]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,3,3])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,3,3])) he) hh - -lemma sg868 : RowSquare [4,3,2,1] [4,4,1,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,4,1,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [4,4,1,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,4,1,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,4,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,4,1,1])) he) hh - -lemma sg869 : RowSquare [4,3,2,1] [4,4,2] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,4,2]) - have hh : SquareOccurs (staircase 4) (rowDiagram [4,4,2]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,4,2]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,4,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,4,2])) he) hh - -lemma sg870 : RowSquare [4,3,2,1] [5,4,1] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [5,4,1]) - have hh : SquareOccurs (staircase 4) (rowDiagram [5,4,1]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [5,4,1]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [5,4,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,4,1])) he) hh - -lemma sg871 : RowSquare [4,3,2,1] [5,5] := by - have he : rowDiagram [4,3,2,1] = (staircase 4) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [5,5]) - have hh : SquareOccurs (staircase 4) (rowDiagram [5,5]) := - ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [5,5]), - saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [5,5])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,5])) he) hh - -lemma sg910 : RowSquare [5,2,1,1,1] [1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [10]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg996 : RowSquare [5,5] [4,4,2] := by - exact rowSquare_even 5 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg1075 : RowSquare [6,4] [3,3,3,1] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1076 : RowSquare [6,4] [4,2,2,2] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1077 : RowSquare [6,4] [4,3,3] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1078 : RowSquare [6,4] [4,4,2] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1079 : RowSquare [6,4] [5,2,2,1] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1080 : RowSquare [6,4] [5,3,1,1] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1081 : RowSquare [6,4] [5,3,2] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1082 : RowSquare [6,4] [5,4,1] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1083 : RowSquare [6,4] [6,2,1,1] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1084 : RowSquare [6,4] [6,2,2] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1085 : RowSquare [6,4] [6,3,1] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1086 : RowSquare [6,4] [6,4] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1087 : RowSquare [6,4] [7,1,1,1] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1088 : RowSquare [6,4] [7,2,1] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1089 : RowSquare [6,4] [7,3] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1090 : RowSquare [6,4] [9,1] := by - exact rowSquare_short 4 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1091 : RowSquare [6,4] [10] := by - exact rowSquare_trivial _ (by decide) - -lemma sg1131 : RowSquare [2,2,2,2,2,1] [3,3,3,2] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1132 : RowSquare [2,2,2,2,2,1] [4,3,2,2] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1133 : RowSquare [2,2,2,2,2,1] [4,3,3,1] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1134 : RowSquare [2,2,2,2,2,1] [4,4,2,1] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1135 : RowSquare [2,2,2,2,2,1] [4,4,3] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1177 : RowSquare [3,3,1,1,1,1,1] [11] := by - exact rowSquare_trivial _ (by decide) - -lemma sg1180 : RowSquare [3,3,2,1,1,1] [11] := by - exact rowSquare_trivial _ (by decide) - -lemma sg1232 : RowSquare [4,3,3,1] [1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [11]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg1327 : RowSquare [6,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [11]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg1478 : RowSquare [6,5] [3,3,3,2] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1479 : RowSquare [6,5] [4,3,2,2] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1480 : RowSquare [6,5] [4,3,3,1] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1481 : RowSquare [6,5] [4,4,2,1] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1482 : RowSquare [6,5] [4,4,3] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1483 : RowSquare [6,5] [5,2,2,2] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1484 : RowSquare [6,5] [5,3,2,1] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1485 : RowSquare [6,5] [5,3,3] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1486 : RowSquare [6,5] [5,4,1,1] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1487 : RowSquare [6,5] [5,4,2] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1488 : RowSquare [6,5] [5,5,1] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1489 : RowSquare [6,5] [6,2,2,1] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1490 : RowSquare [6,5] [6,3,1,1] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1491 : RowSquare [6,5] [6,3,2] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1492 : RowSquare [6,5] [6,4,1] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1493 : RowSquare [6,5] [6,5] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1494 : RowSquare [6,5] [7,2,1,1] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1495 : RowSquare [6,5] [7,2,2] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1496 : RowSquare [6,5] [7,3,1] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1497 : RowSquare [6,5] [7,4] := by - exact rowSquare_short 5 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1615 : RowSquare [3,3,2,1,1,1,1] [12] := by - exact rowSquare_trivial _ (by decide) - -lemma sg1650 : RowSquare [4,4,2,2] [1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [12]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg1682 : RowSquare [5,3,2,1,1] [1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [12]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg1734 : RowSquare [5,4,2,1] [12] := by - exact rowSquare_trivial _ (by decide) - -lemma sg1754 : RowSquare [6,2,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [12]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg1871 : RowSquare [6,6] [6,6] := by - exact rowSquare_even 6 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg1928 : RowSquare [7,5] [4,3,3,2] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1930 : RowSquare [7,5] [4,4,3,1] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1931 : RowSquare [7,5] [4,4,4] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1932 : RowSquare [7,5] [5,3,3,1] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1933 : RowSquare [7,5] [5,4,2,1] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1934 : RowSquare [7,5] [5,4,3] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1936 : RowSquare [7,5] [5,5,2] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1937 : RowSquare [7,5] [6,2,2,2] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1938 : RowSquare [7,5] [6,3,2,1] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1939 : RowSquare [7,5] [6,3,3] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1940 : RowSquare [7,5] [6,4,1,1] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1941 : RowSquare [7,5] [6,4,2] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg1942 : RowSquare [7,5] [6,5,1] := by - exact rowSquare_short 5 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg2015 : RowSquare [2,2,2,2,2,2,1] [7,6] := by - exact rowSquare_short 6 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg2016 : RowSquare [2,2,2,2,2,2,1] [8,5] := by - exact rowSquare_short 6 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg2017 : RowSquare [2,2,2,2,2,2,1] [9,4] := by - exact rowSquare_short 6 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg2018 : RowSquare [2,2,2,2,2,2,1] [10,3] := by - exact rowSquare_short 6 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg2019 : RowSquare [2,2,2,2,2,2,1] [11,2] := by - exact rowSquare_short 6 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg2072 : RowSquare [4,3,1,1,1,1,1,1] [13] := by - exact rowSquare_trivial _ (by decide) - -lemma sg2105 : RowSquare [4,4,1,1,1,1,1] [13] := by - exact rowSquare_trivial _ (by decide) - -lemma sg2107 : RowSquare [4,4,3,2] [1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [13]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg2137 : RowSquare [5,3,3,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [13]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg2251 : RowSquare [7,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [13]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg2364 : RowSquare [7,6] [4,4,4,1] := by - exact rowSquare_short 6 1 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg2488 : RowSquare [2,2,2,2,2,2,2] [8,6] := by - exact rowSquare_even 7 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg2489 : RowSquare [2,2,2,2,2,2,2] [10,4] := by - exact rowSquare_even 7 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) - -lemma sg2573 : RowSquare [4,4,1,1,1,1,1,1] [14] := by - exact rowSquare_trivial _ (by decide) - -lemma sg2596 : RowSquare [5,4,2,2,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [14]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg2626 : RowSquare [6,3,2,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [14]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg2702 : RowSquare [7,2,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [14]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg3106 : RowSquare [8,6] [4,4,4,2] := by - exact rowSquare_short 6 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg3239 : RowSquare [4,4,2,1,1,1,1,1] [15] := by - exact rowSquare_trivial _ (by decide) - -lemma sg3299 : RowSquare [5,4,3,2,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]) - have hh : SquareOccurs (staircase 5) (rowDiagram [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]) := - ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]), - saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1])) he) hh - -lemma sg3300 : RowSquare [5,4,3,2,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [2,1,1,1,1,1,1,1,1,1,1,1,1,1]) - have hh : SquareOccurs (staircase 5) (rowDiagram [2,1,1,1,1,1,1,1,1,1,1,1,1,1]) := - ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [2,1,1,1,1,1,1,1,1,1,1,1,1,1]), - saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [2,1,1,1,1,1,1,1,1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1,1,1,1,1,1,1,1,1,1,1,1,1])) he) hh - -lemma sg3301 : RowSquare [5,4,3,2,1] [2,2,1,1,1,1,1,1,1,1,1,1,1] := by - have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [2,2,1,1,1,1,1,1,1,1,1,1,1]) - have hh : SquareOccurs (staircase 5) (rowDiagram [2,2,1,1,1,1,1,1,1,1,1,1,1]) := - ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [2,2,1,1,1,1,1,1,1,1,1,1,1]), - saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [2,2,1,1,1,1,1,1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,1,1,1,1,1,1,1,1,1,1,1])) he) hh - -lemma sg3302 : RowSquare [5,4,3,2,1] [2,2,2,2,1,1,1,1,1,1,1] := by - have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [2,2,2,2,1,1,1,1,1,1,1]) - have hh : SquareOccurs (staircase 5) (rowDiagram [2,2,2,2,1,1,1,1,1,1,1]) := - ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [2,2,2,2,1,1,1,1,1,1,1]), - saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [2,2,2,2,1,1,1,1,1,1,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,2,1,1,1,1,1,1,1])) he) hh - -lemma sg3303 : RowSquare [5,4,3,2,1] [3,2,2,2,2,2,2] := by - have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [3,2,2,2,2,2,2]) - have hh : SquareOccurs (staircase 5) (rowDiagram [3,2,2,2,2,2,2]) := - ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [3,2,2,2,2,2,2]), - saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [3,2,2,2,2,2,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,2,2,2,2,2])) he) hh - -lemma sg3304 : RowSquare [5,4,3,2,1] [3,3,2,2,2,2,1] := by - have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [3,3,2,2,2,2,1]) - have hh : SquareOccurs (staircase 5) (rowDiagram [3,3,2,2,2,2,1]) := - ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [3,3,2,2,2,2,1]), - saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [3,3,2,2,2,2,1])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,2,2,2,2,1])) he) hh - -lemma sg3305 : RowSquare [5,4,3,2,1] [3,3,3,2,2,2] := by - have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [3,3,3,2,2,2]) - have hh : SquareOccurs (staircase 5) (rowDiagram [3,3,3,2,2,2]) := - ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [3,3,3,2,2,2]), - saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [3,3,3,2,2,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,3,2,2,2])) he) hh - -lemma sg3306 : RowSquare [5,4,3,2,1] [4,3,2,2,2,2] := by - have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by - rw [rowDiagram_eq _ (by decide)] - apply YoungDiagram.ext - decide - change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [4,3,2,2,2,2]) - have hh : SquareOccurs (staircase 5) (rowDiagram [4,3,2,2,2,2]) := - ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [4,3,2,2,2,2]), - saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [4,3,2,2,2,2])⟩ - exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,3,2,2,2,2])) he) hh - -lemma sg3521 : RowSquare [8,1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [15]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg3739 : RowSquare [2,2,2,2,2,2,2,1,1] [5,5,5,1] := by - exact rowSquare_short 7 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg3740 : RowSquare [2,2,2,2,2,2,2,1,1] [6,5,5] := by - exact rowSquare_short 7 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg3742 : RowSquare [2,2,2,2,2,2,2,1,1] [6,6,3,1] := by - exact rowSquare_short 7 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg3743 : RowSquare [2,2,2,2,2,2,2,1,1] [6,6,4] := by - exact rowSquare_short 7 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg3998 : RowSquare [5,5,2,2,2] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [16]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg4063 : RowSquare [6,4,2,2,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [16]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg4160 : RowSquare [7,3,2,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [16]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg4345 : RowSquare [8,2,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [16]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg4804 : RowSquare [5,4,4,3,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [17]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg4832 : RowSquare [5,5,3,2,2] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [17]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg4862 : RowSquare [6,4,3,2,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [17]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg4930 : RowSquare [9,1,1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [17]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg5011 : RowSquare [2,2,2,2,2,2,2,2,1,1] [5,5,5,3] := by - exact rowSquare_short 8 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg5012 : RowSquare [2,2,2,2,2,2,2,2,1,1] [6,4,4,4] := by - exact rowSquare_short 8 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg5013 : RowSquare [2,2,2,2,2,2,2,2,1,1] [6,5,4,3] := by - exact rowSquare_short 8 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg5014 : RowSquare [2,2,2,2,2,2,2,2,1,1] [6,5,5,2] := by - exact rowSquare_short 8 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg5015 : RowSquare [2,2,2,2,2,2,2,2,1,1] [6,6,4,2] := by - exact rowSquare_short 8 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg5016 : RowSquare [2,2,2,2,2,2,2,2,1,1] [6,6,5,1] := by - exact rowSquare_short 8 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg5017 : RowSquare [2,2,2,2,2,2,2,2,1,1] [6,6,6] := by - exact rowSquare_short 8 2 (by decide) (by decide) (by decide) - (by decide) (by decide) (by decide) (by decide) (by decide) - -lemma sg5672 : RowSquare [6,5,2,2,2,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [18]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg5735 : RowSquare [8,3,2,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [18]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg5757 : RowSquare [9,2,1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [18]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg6339 : RowSquare [5,5,4,3,2] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [19]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg6389 : RowSquare [6,4,4,3,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [19]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg6457 : RowSquare [6,5,3,2,2,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [19]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg6502 : RowSquare [10,1,1,1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [19]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg7812 : RowSquare [6,6,2,2,2,2] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [20]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg7998 : RowSquare [9,3,2,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [20]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg8008 : RowSquare [10,2,1,1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [20]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg8780 : RowSquare [6,6,3,2,2,2] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [21]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg10867 : RowSquare [7,6,2,2,2,2,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [22]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -lemma sg11531 : RowSquare [7,6,3,2,2,2,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_target_transpose (q := [23]) (by decide) (by decide) - (by decide) (rowSquare_trivial _ (by decide)) - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeFive +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeSeven +import OAI.RepresentationTheory.UniversalSquare.Finite.DegreeEight +import OAI.RepresentationTheory.UniversalSquare.Support.ResidualTrees + +namespace OAI + +/-! Semigroup Local Leaves. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg0 : RowSquare [1] [1] := by + exact rowSquare_trivial _ (by decide) + +lemma sg1 : RowSquare [1,1] [2] := by + exact rowSquare_trivial _ (by decide) + +lemma sg2 : RowSquare [2] [2] := by + exact rowSquare_trivial _ (by decide) + +lemma sg3 : RowSquare [1,1,1] [3] := by + exact rowSquare_trivial _ (by decide) + +lemma sg4 : RowSquare [2,1] [1,1,1] := by + have he : rowDiagram [2,1] = (staircase 2) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [2,1]) (rowDiagram [1,1,1]) + have hh : SquareOccurs (staircase 2) (rowDiagram [1,1,1]) := + ⟨3,canonicalTableau _ (staircase_card 2),canonicalTableau _ (rowDiagram_card [1,1,1]), + saxl_kronecker_pos 2 (by decide) _ (rowDiagram_card [1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1])) he) hh + +lemma sg5 : RowSquare [2,1] [2,1] := by + have he : rowDiagram [2,1] = (staircase 2) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [2,1]) (rowDiagram [2,1]) + have hh : SquareOccurs (staircase 2) (rowDiagram [2,1]) := + ⟨3,canonicalTableau _ (staircase_card 2),canonicalTableau _ (rowDiagram_card [2,1]), + saxl_kronecker_pos 2 (by decide) _ (rowDiagram_card [2,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1])) he) hh + +lemma sg6 : RowSquare [2,1] [3] := by + exact rowSquare_trivial _ (by decide) + +lemma sg7 : RowSquare [3] [3] := by + exact rowSquare_trivial _ (by decide) + +lemma sg8 : RowSquare [1,1,1,1] [4] := by + exact rowSquare_trivial _ (by decide) + +lemma sg9 : RowSquare [2,1,1] [2,1,1] := by + exact rowSquare_short 1 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg11 : RowSquare [2,1,1] [3,1] := by + exact rowSquare_short 1 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg12 : RowSquare [2,1,1] [4] := by + exact rowSquare_trivial _ (by decide) + +lemma sg13 : RowSquare [2,2] [1,1,1,1] := by + exact rowSquare_target_transpose (q := [4]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg14 : RowSquare [2,2] [2,2] := by + exact rowSquare_even 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg15 : RowSquare [2,2] [4] := by + exact rowSquare_trivial _ (by decide) + +lemma sg16 : RowSquare [3,1] [2,1,1] := by + exact rowSquare_short 1 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg18 : RowSquare [3,1] [3,1] := by + exact rowSquare_short 1 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg19 : RowSquare [3,1] [4] := by + exact rowSquare_trivial _ (by decide) + +lemma sg20 : RowSquare [4] [4] := by + exact rowSquare_trivial _ (by decide) + +lemma sg21 : RowSquare [1,1,1,1,1] [5] := by + exact rowSquare_trivial _ (by decide) + +lemma sg25 : RowSquare [2,1,1,1] [5] := by + exact rowSquare_trivial _ (by decide) + +lemma sg26 : RowSquare [2,2,1] [2,1,1,1] := by + exact rowSquare_short 2 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg27 : RowSquare [2,2,1] [2,2,1] := by + exact rowSquare_short 2 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg28 : RowSquare [2,2,1] [3,1,1] := by + exact rowSquare_short 2 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg29 : RowSquare [2,2,1] [3,2] := by + exact rowSquare_short 2 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg30 : RowSquare [2,2,1] [4,1] := by + exact rowSquare_short 2 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg31 : RowSquare [2,2,1] [5] := by + exact rowSquare_trivial _ (by decide) + +lemma sg32 : RowSquare [3,1,1] [1,1,1,1,1] := by + have he : rowDiagram [3,1,1] = fiveWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,1,1]) (rowDiagram [1,1,1,1,1]) + have hh : SquareOccurs fiveWitness (rowDiagram [1,1,1,1,1]) := + ⟨5,canonicalTableau _ fiveWitness_card,canonicalTableau _ (rowDiagram_card [1,1,1,1,1]), + five_kronecker_pos _ (rowDiagram_card [1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1,1,1])) he) hh + +lemma sg33 : RowSquare [3,1,1] [2,1,1,1] := by + have he : rowDiagram [3,1,1] = fiveWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,1,1]) (rowDiagram [2,1,1,1]) + have hh : SquareOccurs fiveWitness (rowDiagram [2,1,1,1]) := + ⟨5,canonicalTableau _ fiveWitness_card,canonicalTableau _ (rowDiagram_card [2,1,1,1]), + five_kronecker_pos _ (rowDiagram_card [2,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1,1,1])) he) hh + +lemma sg34 : RowSquare [3,1,1] [2,2,1] := by + have he : rowDiagram [3,1,1] = fiveWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,1,1]) (rowDiagram [2,2,1]) + have hh : SquareOccurs fiveWitness (rowDiagram [2,2,1]) := + ⟨5,canonicalTableau _ fiveWitness_card,canonicalTableau _ (rowDiagram_card [2,2,1]), + five_kronecker_pos _ (rowDiagram_card [2,2,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,1])) he) hh + +lemma sg35 : RowSquare [3,1,1] [3,1,1] := by + have he : rowDiagram [3,1,1] = fiveWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,1,1]) (rowDiagram [3,1,1]) + have hh : SquareOccurs fiveWitness (rowDiagram [3,1,1]) := + ⟨5,canonicalTableau _ fiveWitness_card,canonicalTableau _ (rowDiagram_card [3,1,1]), + five_kronecker_pos _ (rowDiagram_card [3,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,1,1])) he) hh + +lemma sg36 : RowSquare [3,1,1] [3,2] := by + have he : rowDiagram [3,1,1] = fiveWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,1,1]) (rowDiagram [3,2]) + have hh : SquareOccurs fiveWitness (rowDiagram [3,2]) := + ⟨5,canonicalTableau _ fiveWitness_card,canonicalTableau _ (rowDiagram_card [3,2]), + five_kronecker_pos _ (rowDiagram_card [3,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2])) he) hh + +lemma sg37 : RowSquare [3,1,1] [4,1] := by + have he : rowDiagram [3,1,1] = fiveWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,1,1]) (rowDiagram [4,1]) + have hh : SquareOccurs fiveWitness (rowDiagram [4,1]) := + ⟨5,canonicalTableau _ fiveWitness_card,canonicalTableau _ (rowDiagram_card [4,1]), + five_kronecker_pos _ (rowDiagram_card [4,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,1])) he) hh + +lemma sg38 : RowSquare [3,1,1] [5] := by + exact rowSquare_trivial _ (by decide) + +lemma sg39 : RowSquare [3,2] [2,1,1,1] := by + exact rowSquare_short 2 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg40 : RowSquare [3,2] [2,2,1] := by + exact rowSquare_short 2 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg41 : RowSquare [3,2] [3,1,1] := by + exact rowSquare_short 2 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg42 : RowSquare [3,2] [3,2] := by + exact rowSquare_short 2 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg43 : RowSquare [3,2] [4,1] := by + exact rowSquare_short 2 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg44 : RowSquare [3,2] [5] := by + exact rowSquare_trivial _ (by decide) + +lemma sg48 : RowSquare [4,1] [5] := by + exact rowSquare_trivial _ (by decide) + +lemma sg49 : RowSquare [5] [5] := by + exact rowSquare_trivial _ (by decide) + +lemma sg50 : RowSquare [1,1,1,1,1,1] [6] := by + exact rowSquare_trivial _ (by decide) + +lemma sg54 : RowSquare [2,1,1,1,1] [6] := by + exact rowSquare_trivial _ (by decide) + +lemma sg55 : RowSquare [2,2,1,1] [2,2,2] := by + exact rowSquare_short 2 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg56 : RowSquare [2,2,1,1] [3,1,1,1] := by + exact rowSquare_short 2 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg57 : RowSquare [2,2,1,1] [3,2,1] := by + exact rowSquare_short 2 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg58 : RowSquare [2,2,1,1] [4,1,1] := by + exact rowSquare_short 2 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg59 : RowSquare [2,2,1,1] [4,2] := by + exact rowSquare_short 2 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg60 : RowSquare [2,2,1,1] [5,1] := by + exact rowSquare_short 2 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg61 : RowSquare [2,2,1,1] [6] := by + exact rowSquare_trivial _ (by decide) + +lemma sg62 : RowSquare [2,2,2] [2,2,2] := by + exact rowSquare_even 3 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg64 : RowSquare [2,2,2] [4,2] := by + exact rowSquare_even 3 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg65 : RowSquare [2,2,2] [6] := by + exact rowSquare_trivial _ (by decide) + +lemma sg74 : RowSquare [3,2,1] [1,1,1,1,1,1] := by + have he : rowDiagram [3,2,1] = (staircase 3) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [1,1,1,1,1,1]) + have hh : SquareOccurs (staircase 3) (rowDiagram [1,1,1,1,1,1]) := + ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [1,1,1,1,1,1]), + saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1,1,1,1])) he) hh + +lemma sg75 : RowSquare [3,2,1] [2,1,1,1,1] := by + have he : rowDiagram [3,2,1] = (staircase 3) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [2,1,1,1,1]) + have hh : SquareOccurs (staircase 3) (rowDiagram [2,1,1,1,1]) := + ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [2,1,1,1,1]), + saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [2,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1,1,1,1])) he) hh + +lemma sg76 : RowSquare [3,2,1] [2,2,1,1] := by + have he : rowDiagram [3,2,1] = (staircase 3) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [2,2,1,1]) + have hh : SquareOccurs (staircase 3) (rowDiagram [2,2,1,1]) := + ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [2,2,1,1]), + saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [2,2,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,1,1])) he) hh + +lemma sg77 : RowSquare [3,2,1] [2,2,2] := by + have he : rowDiagram [3,2,1] = (staircase 3) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [2,2,2]) + have hh : SquareOccurs (staircase 3) (rowDiagram [2,2,2]) := + ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [2,2,2]), + saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [2,2,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2])) he) hh + +lemma sg78 : RowSquare [3,2,1] [3,1,1,1] := by + have he : rowDiagram [3,2,1] = (staircase 3) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [3,1,1,1]) + have hh : SquareOccurs (staircase 3) (rowDiagram [3,1,1,1]) := + ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [3,1,1,1]), + saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [3,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,1,1,1])) he) hh + +lemma sg79 : RowSquare [3,2,1] [3,2,1] := by + have he : rowDiagram [3,2,1] = (staircase 3) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [3,2,1]) + have hh : SquareOccurs (staircase 3) (rowDiagram [3,2,1]) := + ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [3,2,1]), + saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [3,2,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,1])) he) hh + +lemma sg80 : RowSquare [3,2,1] [3,3] := by + have he : rowDiagram [3,2,1] = (staircase 3) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [3,3]) + have hh : SquareOccurs (staircase 3) (rowDiagram [3,3]) := + ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [3,3]), + saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [3,3])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3])) he) hh + +lemma sg81 : RowSquare [3,2,1] [4,2] := by + have he : rowDiagram [3,2,1] = (staircase 3) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [4,2]) + have hh : SquareOccurs (staircase 3) (rowDiagram [4,2]) := + ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [4,2]), + saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [4,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,2])) he) hh + +lemma sg82 : RowSquare [3,2,1] [5,1] := by + have he : rowDiagram [3,2,1] = (staircase 3) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [3,2,1]) (rowDiagram [5,1]) + have hh : SquareOccurs (staircase 3) (rowDiagram [5,1]) := + ⟨6,canonicalTableau _ (staircase_card 3),canonicalTableau _ (rowDiagram_card [5,1]), + saxl_kronecker_pos 3 (by decide) _ (rowDiagram_card [5,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,1])) he) hh + +lemma sg83 : RowSquare [3,3] [2,2,2] := by + exact rowSquare_even 3 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg85 : RowSquare [3,3] [4,2] := by + exact rowSquare_even 3 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg86 : RowSquare [3,3] [6] := by + exact rowSquare_trivial _ (by decide) + +lemma sg96 : RowSquare [4,1,1] [6] := by + exact rowSquare_trivial _ (by decide) + +lemma sg97 : RowSquare [4,2] [2,2,2] := by + exact rowSquare_short 2 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg98 : RowSquare [4,2] [3,1,1,1] := by + exact rowSquare_short 2 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg99 : RowSquare [4,2] [3,2,1] := by + exact rowSquare_short 2 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg100 : RowSquare [4,2] [4,1,1] := by + exact rowSquare_short 2 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg101 : RowSquare [4,2] [4,2] := by + exact rowSquare_short 2 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg102 : RowSquare [4,2] [5,1] := by + exact rowSquare_short 2 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg103 : RowSquare [4,2] [6] := by + exact rowSquare_trivial _ (by decide) + +lemma sg107 : RowSquare [5,1] [6] := by + exact rowSquare_trivial _ (by decide) + +lemma sg108 : RowSquare [6] [6] := by + exact rowSquare_trivial _ (by decide) + +lemma sg109 : RowSquare [1,1,1,1,1,1,1] [7] := by + exact rowSquare_trivial _ (by decide) + +lemma sg113 : RowSquare [2,1,1,1,1,1] [7] := by + exact rowSquare_trivial _ (by decide) + +lemma sg122 : RowSquare [2,2,1,1,1] [7] := by + exact rowSquare_trivial _ (by decide) + +lemma sg123 : RowSquare [2,2,2,1] [2,2,2,1] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg124 : RowSquare [2,2,2,1] [3,2,2] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg125 : RowSquare [2,2,2,1] [3,3,1] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg126 : RowSquare [2,2,2,1] [4,1,1,1] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg127 : RowSquare [2,2,2,1] [4,2,1] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg128 : RowSquare [2,2,2,1] [4,3] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg129 : RowSquare [2,2,2,1] [5,1,1] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg130 : RowSquare [2,2,2,1] [5,2] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg131 : RowSquare [2,2,2,1] [7] := by + exact rowSquare_trivial _ (by decide) + +lemma sg141 : RowSquare [3,1,1,1,1] [7] := by + exact rowSquare_trivial _ (by decide) + +lemma sg178 : RowSquare [4,1,1,1] [1,1,1,1,1,1,1] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [1,1,1,1,1,1,1]) + have hh : SquareOccurs sevenWitness (rowDiagram [1,1,1,1,1,1,1]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [1,1,1,1,1,1,1]), + seven_kronecker_pos _ (rowDiagram_card [1,1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1,1,1,1,1])) he) hh + +lemma sg179 : RowSquare [4,1,1,1] [2,1,1,1,1,1] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [2,1,1,1,1,1]) + have hh : SquareOccurs sevenWitness (rowDiagram [2,1,1,1,1,1]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [2,1,1,1,1,1]), + seven_kronecker_pos _ (rowDiagram_card [2,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1,1,1,1,1])) he) hh + +lemma sg180 : RowSquare [4,1,1,1] [2,2,1,1,1] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [2,2,1,1,1]) + have hh : SquareOccurs sevenWitness (rowDiagram [2,2,1,1,1]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [2,2,1,1,1]), + seven_kronecker_pos _ (rowDiagram_card [2,2,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,1,1,1])) he) hh + +lemma sg181 : RowSquare [4,1,1,1] [2,2,2,1] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [2,2,2,1]) + have hh : SquareOccurs sevenWitness (rowDiagram [2,2,2,1]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [2,2,2,1]), + seven_kronecker_pos _ (rowDiagram_card [2,2,2,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,1])) he) hh + +lemma sg182 : RowSquare [4,1,1,1] [3,1,1,1,1] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [3,1,1,1,1]) + have hh : SquareOccurs sevenWitness (rowDiagram [3,1,1,1,1]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [3,1,1,1,1]), + seven_kronecker_pos _ (rowDiagram_card [3,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,1,1,1,1])) he) hh + +lemma sg183 : RowSquare [4,1,1,1] [3,2,1,1] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [3,2,1,1]) + have hh : SquareOccurs sevenWitness (rowDiagram [3,2,1,1]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [3,2,1,1]), + seven_kronecker_pos _ (rowDiagram_card [3,2,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,1,1])) he) hh + +lemma sg184 : RowSquare [4,1,1,1] [3,2,2] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [3,2,2]) + have hh : SquareOccurs sevenWitness (rowDiagram [3,2,2]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [3,2,2]), + seven_kronecker_pos _ (rowDiagram_card [3,2,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,2])) he) hh + +lemma sg185 : RowSquare [4,1,1,1] [3,3,1] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [3,3,1]) + have hh : SquareOccurs sevenWitness (rowDiagram [3,3,1]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [3,3,1]), + seven_kronecker_pos _ (rowDiagram_card [3,3,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,1])) he) hh + +lemma sg186 : RowSquare [4,1,1,1] [4,1,1,1] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [4,1,1,1]) + have hh : SquareOccurs sevenWitness (rowDiagram [4,1,1,1]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [4,1,1,1]), + seven_kronecker_pos _ (rowDiagram_card [4,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,1,1,1])) he) hh + +lemma sg187 : RowSquare [4,1,1,1] [4,2,1] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [4,2,1]) + have hh : SquareOccurs sevenWitness (rowDiagram [4,2,1]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [4,2,1]), + seven_kronecker_pos _ (rowDiagram_card [4,2,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,2,1])) he) hh + +lemma sg188 : RowSquare [4,1,1,1] [4,3] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [4,3]) + have hh : SquareOccurs sevenWitness (rowDiagram [4,3]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [4,3]), + seven_kronecker_pos _ (rowDiagram_card [4,3])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,3])) he) hh + +lemma sg189 : RowSquare [4,1,1,1] [5,1,1] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [5,1,1]) + have hh : SquareOccurs sevenWitness (rowDiagram [5,1,1]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [5,1,1]), + seven_kronecker_pos _ (rowDiagram_card [5,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,1,1])) he) hh + +lemma sg190 : RowSquare [4,1,1,1] [5,2] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [5,2]) + have hh : SquareOccurs sevenWitness (rowDiagram [5,2]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [5,2]), + seven_kronecker_pos _ (rowDiagram_card [5,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,2])) he) hh + +lemma sg191 : RowSquare [4,1,1,1] [6,1] := by + have he : rowDiagram [4,1,1,1] = sevenWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,1,1,1]) (rowDiagram [6,1]) + have hh : SquareOccurs sevenWitness (rowDiagram [6,1]) := + ⟨7,canonicalTableau _ sevenWitness_card,canonicalTableau _ (rowDiagram_card [6,1]), + seven_kronecker_pos _ (rowDiagram_card [6,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [6,1])) he) hh + +lemma sg192 : RowSquare [4,1,1,1] [7] := by + exact rowSquare_trivial _ (by decide) + +lemma sg206 : RowSquare [4,2,1] [7] := by + exact rowSquare_trivial _ (by decide) + +lemma sg207 : RowSquare [4,3] [2,2,2,1] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg208 : RowSquare [4,3] [3,2,1,1] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg209 : RowSquare [4,3] [3,2,2] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg210 : RowSquare [4,3] [3,3,1] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg211 : RowSquare [4,3] [4,1,1,1] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg212 : RowSquare [4,3] [4,2,1] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg213 : RowSquare [4,3] [4,3] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg214 : RowSquare [4,3] [5,1,1] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg215 : RowSquare [4,3] [5,2] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg216 : RowSquare [4,3] [6,1] := by + exact rowSquare_short 3 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg217 : RowSquare [4,3] [7] := by + exact rowSquare_trivial _ (by decide) + +lemma sg226 : RowSquare [5,1,1] [7] := by + exact rowSquare_trivial _ (by decide) + +lemma sg234 : RowSquare [7] [7] := by + exact rowSquare_trivial _ (by decide) + +lemma sg235 : RowSquare [1,1,1,1,1,1,1,1] [8] := by + exact rowSquare_trivial _ (by decide) + +lemma sg238 : RowSquare [2,1,1,1,1,1,1] [8] := by + exact rowSquare_trivial _ (by decide) + +lemma sg248 : RowSquare [2,2,1,1,1,1] [8] := by + exact rowSquare_trivial _ (by decide) + +lemma sg249 : RowSquare [2,2,2,1,1] [3,2,2,1] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg251 : RowSquare [2,2,2,1,1] [3,3,2] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg253 : RowSquare [2,2,2,1,1] [6,2] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg256 : RowSquare [2,2,2,2] [4,2,2] := by + exact rowSquare_even 4 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg257 : RowSquare [2,2,2,2] [4,4] := by + exact rowSquare_even 4 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg259 : RowSquare [2,2,2,2] [6,2] := by + exact rowSquare_even 4 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg269 : RowSquare [3,1,1,1,1,1] [8] := by + exact rowSquare_trivial _ (by decide) + +lemma sg306 : RowSquare [3,3,2] [1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [8]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg330 : RowSquare [4,2,1,1] [1,1,1,1,1,1,1,1] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [1,1,1,1,1,1,1,1]) + have hh : SquareOccurs eightWitness (rowDiagram [1,1,1,1,1,1,1,1]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [1,1,1,1,1,1,1,1]), + eight_kronecker_pos _ (rowDiagram_card [1,1,1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1,1,1,1,1,1])) he) hh + +lemma sg331 : RowSquare [4,2,1,1] [2,1,1,1,1,1,1] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [2,1,1,1,1,1,1]) + have hh : SquareOccurs eightWitness (rowDiagram [2,1,1,1,1,1,1]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [2,1,1,1,1,1,1]), + eight_kronecker_pos _ (rowDiagram_card [2,1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1,1,1,1,1,1])) he) hh + +lemma sg332 : RowSquare [4,2,1,1] [2,2,1,1,1,1] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [2,2,1,1,1,1]) + have hh : SquareOccurs eightWitness (rowDiagram [2,2,1,1,1,1]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [2,2,1,1,1,1]), + eight_kronecker_pos _ (rowDiagram_card [2,2,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,1,1,1,1])) he) hh + +lemma sg333 : RowSquare [4,2,1,1] [2,2,2,1,1] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [2,2,2,1,1]) + have hh : SquareOccurs eightWitness (rowDiagram [2,2,2,1,1]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [2,2,2,1,1]), + eight_kronecker_pos _ (rowDiagram_card [2,2,2,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,1,1])) he) hh + +lemma sg334 : RowSquare [4,2,1,1] [2,2,2,2] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [2,2,2,2]) + have hh : SquareOccurs eightWitness (rowDiagram [2,2,2,2]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [2,2,2,2]), + eight_kronecker_pos _ (rowDiagram_card [2,2,2,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,2])) he) hh + +lemma sg335 : RowSquare [4,2,1,1] [3,1,1,1,1,1] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [3,1,1,1,1,1]) + have hh : SquareOccurs eightWitness (rowDiagram [3,1,1,1,1,1]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [3,1,1,1,1,1]), + eight_kronecker_pos _ (rowDiagram_card [3,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,1,1,1,1,1])) he) hh + +lemma sg336 : RowSquare [4,2,1,1] [3,2,1,1,1] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [3,2,1,1,1]) + have hh : SquareOccurs eightWitness (rowDiagram [3,2,1,1,1]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [3,2,1,1,1]), + eight_kronecker_pos _ (rowDiagram_card [3,2,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,1,1,1])) he) hh + +lemma sg337 : RowSquare [4,2,1,1] [3,2,2,1] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [3,2,2,1]) + have hh : SquareOccurs eightWitness (rowDiagram [3,2,2,1]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [3,2,2,1]), + eight_kronecker_pos _ (rowDiagram_card [3,2,2,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,2,1])) he) hh + +lemma sg338 : RowSquare [4,2,1,1] [3,3,1,1] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [3,3,1,1]) + have hh : SquareOccurs eightWitness (rowDiagram [3,3,1,1]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [3,3,1,1]), + eight_kronecker_pos _ (rowDiagram_card [3,3,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,1,1])) he) hh + +lemma sg339 : RowSquare [4,2,1,1] [3,3,2] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [3,3,2]) + have hh : SquareOccurs eightWitness (rowDiagram [3,3,2]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [3,3,2]), + eight_kronecker_pos _ (rowDiagram_card [3,3,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,2])) he) hh + +lemma sg340 : RowSquare [4,2,1,1] [4,2,2] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [4,2,2]) + have hh : SquareOccurs eightWitness (rowDiagram [4,2,2]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [4,2,2]), + eight_kronecker_pos _ (rowDiagram_card [4,2,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,2,2])) he) hh + +lemma sg341 : RowSquare [4,2,1,1] [4,3,1] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [4,3,1]) + have hh : SquareOccurs eightWitness (rowDiagram [4,3,1]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [4,3,1]), + eight_kronecker_pos _ (rowDiagram_card [4,3,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,3,1])) he) hh + +lemma sg342 : RowSquare [4,2,1,1] [4,4] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [4,4]) + have hh : SquareOccurs eightWitness (rowDiagram [4,4]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [4,4]), + eight_kronecker_pos _ (rowDiagram_card [4,4])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,4])) he) hh + +lemma sg343 : RowSquare [4,2,1,1] [5,1,1,1] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [5,1,1,1]) + have hh : SquareOccurs eightWitness (rowDiagram [5,1,1,1]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [5,1,1,1]), + eight_kronecker_pos _ (rowDiagram_card [5,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,1,1,1])) he) hh + +lemma sg344 : RowSquare [4,2,1,1] [5,2,1] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [5,2,1]) + have hh : SquareOccurs eightWitness (rowDiagram [5,2,1]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [5,2,1]), + eight_kronecker_pos _ (rowDiagram_card [5,2,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,2,1])) he) hh + +lemma sg345 : RowSquare [4,2,1,1] [5,3] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [5,3]) + have hh : SquareOccurs eightWitness (rowDiagram [5,3]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [5,3]), + eight_kronecker_pos _ (rowDiagram_card [5,3])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,3])) he) hh + +lemma sg346 : RowSquare [4,2,1,1] [6,2] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [6,2]) + have hh : SquareOccurs eightWitness (rowDiagram [6,2]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [6,2]), + eight_kronecker_pos _ (rowDiagram_card [6,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [6,2])) he) hh + +lemma sg347 : RowSquare [4,2,1,1] [7,1] := by + have he : rowDiagram [4,2,1,1] = eightWitness := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,2,1,1]) (rowDiagram [7,1]) + have hh : SquareOccurs eightWitness (rowDiagram [7,1]) := + ⟨8,canonicalTableau _ eightWitness_card,canonicalTableau _ (rowDiagram_card [7,1]), + eight_kronecker_pos _ (rowDiagram_card [7,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [7,1])) he) hh + +lemma sg366 : RowSquare [4,4] [4,2,2] := by + exact rowSquare_even 4 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg367 : RowSquare [4,4] [4,4] := by + exact rowSquare_even 4 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg369 : RowSquare [4,4] [6,2] := by + exact rowSquare_even 4 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg401 : RowSquare [5,3] [3,2,2,1] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg403 : RowSquare [5,3] [3,3,2] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg404 : RowSquare [5,3] [4,2,1,1] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg405 : RowSquare [5,3] [4,2,2] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg406 : RowSquare [5,3] [4,3,1] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg408 : RowSquare [5,3] [5,1,1,1] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg409 : RowSquare [5,3] [5,2,1] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg410 : RowSquare [5,3] [5,3] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg411 : RowSquare [5,3] [6,1,1] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg412 : RowSquare [5,3] [6,2] := by + exact rowSquare_short 3 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg421 : RowSquare [6,1,1] [8] := by + exact rowSquare_trivial _ (by decide) + +lemma sg426 : RowSquare [8] [8] := by + exact rowSquare_trivial _ (by decide) + +lemma sg427 : RowSquare [1,1,1,1,1,1,1,1,1] [9] := by + exact rowSquare_trivial _ (by decide) + +lemma sg431 : RowSquare [2,1,1,1,1,1,1,1] [9] := by + exact rowSquare_trivial _ (by decide) + +lemma sg445 : RowSquare [2,2,2,1,1,1] [9] := by + exact rowSquare_trivial _ (by decide) + +lemma sg446 : RowSquare [2,2,2,2,1] [3,3,3] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg454 : RowSquare [3,1,1,1,1,1,1] [9] := by + exact rowSquare_trivial _ (by decide) + +lemma sg474 : RowSquare [3,2,1,1,1,1] [9] := by + exact rowSquare_trivial _ (by decide) + +lemma sg509 : RowSquare [3,3,1,1,1] [9] := by + exact rowSquare_trivial _ (by decide) + +lemma sg516 : RowSquare [3,3,3] [1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [9]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg586 : RowSquare [5,1,1,1,1] [1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [9]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg656 : RowSquare [5,4] [3,2,2,2] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg657 : RowSquare [5,4] [3,3,2,1] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg658 : RowSquare [5,4] [3,3,3] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg659 : RowSquare [5,4] [4,2,2,1] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg660 : RowSquare [5,4] [4,3,1,1] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg661 : RowSquare [5,4] [4,3,2] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg662 : RowSquare [5,4] [4,4,1] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg663 : RowSquare [5,4] [5,2,1,1] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg664 : RowSquare [5,4] [5,2,2] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg665 : RowSquare [5,4] [5,3,1] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg666 : RowSquare [5,4] [5,4] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg667 : RowSquare [5,4] [6,1,1,1] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg668 : RowSquare [5,4] [6,2,1] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg669 : RowSquare [5,4] [6,3] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg670 : RowSquare [5,4] [7,2] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg671 : RowSquare [5,4] [8,1] := by + exact rowSquare_short 4 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg672 : RowSquare [5,4] [9] := by + exact rowSquare_trivial _ (by decide) + +lemma sg718 : RowSquare [1,1,1,1,1,1,1,1,1,1] [10] := by + exact rowSquare_trivial _ (by decide) + +lemma sg720 : RowSquare [2,1,1,1,1,1,1,1,1] [10] := by + exact rowSquare_trivial _ (by decide) + +lemma sg730 : RowSquare [2,2,2,2,1,1] [10] := by + exact rowSquare_trivial _ (by decide) + +lemma sg757 : RowSquare [3,2,2,1,1,1] [10] := by + exact rowSquare_trivial _ (by decide) + +lemma sg789 : RowSquare [3,3,1,1,1,1] [10] := by + exact rowSquare_trivial _ (by decide) + +lemma sg849 : RowSquare [4,3,2,1] [1,1,1,1,1,1,1,1,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [1,1,1,1,1,1,1,1,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [1,1,1,1,1,1,1,1,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [1,1,1,1,1,1,1,1,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [1,1,1,1,1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1,1,1,1,1,1,1,1])) he) hh + +lemma sg850 : RowSquare [4,3,2,1] [2,1,1,1,1,1,1,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [2,1,1,1,1,1,1,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [2,1,1,1,1,1,1,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [2,1,1,1,1,1,1,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [2,1,1,1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1,1,1,1,1,1,1,1])) he) hh + +lemma sg851 : RowSquare [4,3,2,1] [2,2,1,1,1,1,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [2,2,1,1,1,1,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [2,2,1,1,1,1,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [2,2,1,1,1,1,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [2,2,1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,1,1,1,1,1,1])) he) hh + +lemma sg852 : RowSquare [4,3,2,1] [2,2,2,1,1,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [2,2,2,1,1,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [2,2,2,1,1,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [2,2,2,1,1,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [2,2,2,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,1,1,1,1])) he) hh + +lemma sg853 : RowSquare [4,3,2,1] [2,2,2,2,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [2,2,2,2,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [2,2,2,2,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [2,2,2,2,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [2,2,2,2,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,2,1,1])) he) hh + +lemma sg854 : RowSquare [4,3,2,1] [2,2,2,2,2] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [2,2,2,2,2]) + have hh : SquareOccurs (staircase 4) (rowDiagram [2,2,2,2,2]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [2,2,2,2,2]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [2,2,2,2,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,2,2])) he) hh + +lemma sg855 : RowSquare [4,3,2,1] [3,1,1,1,1,1,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,1,1,1,1,1,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [3,1,1,1,1,1,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,1,1,1,1,1,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,1,1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,1,1,1,1,1,1,1])) he) hh + +lemma sg856 : RowSquare [4,3,2,1] [3,2,1,1,1,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,2,1,1,1,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [3,2,1,1,1,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,2,1,1,1,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,2,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,1,1,1,1,1])) he) hh + +lemma sg857 : RowSquare [4,3,2,1] [3,2,2,1,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,2,2,1,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [3,2,2,1,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,2,2,1,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,2,2,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,2,1,1,1])) he) hh + +lemma sg858 : RowSquare [4,3,2,1] [3,2,2,2,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,2,2,2,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [3,2,2,2,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,2,2,2,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,2,2,2,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,2,2,1])) he) hh + +lemma sg859 : RowSquare [4,3,2,1] [3,3,1,1,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,3,1,1,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [3,3,1,1,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,3,1,1,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,3,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,1,1,1,1])) he) hh + +lemma sg860 : RowSquare [4,3,2,1] [3,3,2,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,3,2,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [3,3,2,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,3,2,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,3,2,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,2,1,1])) he) hh + +lemma sg861 : RowSquare [4,3,2,1] [3,3,2,2] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,3,2,2]) + have hh : SquareOccurs (staircase 4) (rowDiagram [3,3,2,2]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,3,2,2]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,3,2,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,2,2])) he) hh + +lemma sg862 : RowSquare [4,3,2,1] [3,3,3,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [3,3,3,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [3,3,3,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [3,3,3,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [3,3,3,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,3,1])) he) hh + +lemma sg863 : RowSquare [4,3,2,1] [4,1,1,1,1,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,1,1,1,1,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [4,1,1,1,1,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,1,1,1,1,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,1,1,1,1,1,1])) he) hh + +lemma sg864 : RowSquare [4,3,2,1] [4,2,2,2] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,2,2,2]) + have hh : SquareOccurs (staircase 4) (rowDiagram [4,2,2,2]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,2,2,2]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,2,2,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,2,2,2])) he) hh + +lemma sg865 : RowSquare [4,3,2,1] [4,3,1,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,3,1,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [4,3,1,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,3,1,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,3,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,3,1,1,1])) he) hh + +lemma sg866 : RowSquare [4,3,2,1] [4,3,2,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,3,2,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [4,3,2,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,3,2,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,3,2,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,3,2,1])) he) hh + +lemma sg867 : RowSquare [4,3,2,1] [4,3,3] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,3,3]) + have hh : SquareOccurs (staircase 4) (rowDiagram [4,3,3]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,3,3]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,3,3])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,3,3])) he) hh + +lemma sg868 : RowSquare [4,3,2,1] [4,4,1,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,4,1,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [4,4,1,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,4,1,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,4,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,4,1,1])) he) hh + +lemma sg869 : RowSquare [4,3,2,1] [4,4,2] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [4,4,2]) + have hh : SquareOccurs (staircase 4) (rowDiagram [4,4,2]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [4,4,2]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [4,4,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,4,2])) he) hh + +lemma sg870 : RowSquare [4,3,2,1] [5,4,1] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [5,4,1]) + have hh : SquareOccurs (staircase 4) (rowDiagram [5,4,1]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [5,4,1]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [5,4,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,4,1])) he) hh + +lemma sg871 : RowSquare [4,3,2,1] [5,5] := by + have he : rowDiagram [4,3,2,1] = (staircase 4) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [4,3,2,1]) (rowDiagram [5,5]) + have hh : SquareOccurs (staircase 4) (rowDiagram [5,5]) := + ⟨10,canonicalTableau _ (staircase_card 4),canonicalTableau _ (rowDiagram_card [5,5]), + saxl_kronecker_pos 4 (by decide) _ (rowDiagram_card [5,5])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [5,5])) he) hh + +lemma sg910 : RowSquare [5,2,1,1,1] [1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [10]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg996 : RowSquare [5,5] [4,4,2] := by + exact rowSquare_even 5 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg1075 : RowSquare [6,4] [3,3,3,1] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1076 : RowSquare [6,4] [4,2,2,2] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1077 : RowSquare [6,4] [4,3,3] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1078 : RowSquare [6,4] [4,4,2] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1079 : RowSquare [6,4] [5,2,2,1] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1080 : RowSquare [6,4] [5,3,1,1] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1081 : RowSquare [6,4] [5,3,2] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1082 : RowSquare [6,4] [5,4,1] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1083 : RowSquare [6,4] [6,2,1,1] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1084 : RowSquare [6,4] [6,2,2] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1085 : RowSquare [6,4] [6,3,1] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1086 : RowSquare [6,4] [6,4] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1087 : RowSquare [6,4] [7,1,1,1] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1088 : RowSquare [6,4] [7,2,1] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1089 : RowSquare [6,4] [7,3] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1090 : RowSquare [6,4] [9,1] := by + exact rowSquare_short 4 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1091 : RowSquare [6,4] [10] := by + exact rowSquare_trivial _ (by decide) + +lemma sg1131 : RowSquare [2,2,2,2,2,1] [3,3,3,2] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1132 : RowSquare [2,2,2,2,2,1] [4,3,2,2] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1133 : RowSquare [2,2,2,2,2,1] [4,3,3,1] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1134 : RowSquare [2,2,2,2,2,1] [4,4,2,1] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1135 : RowSquare [2,2,2,2,2,1] [4,4,3] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1177 : RowSquare [3,3,1,1,1,1,1] [11] := by + exact rowSquare_trivial _ (by decide) + +lemma sg1180 : RowSquare [3,3,2,1,1,1] [11] := by + exact rowSquare_trivial _ (by decide) + +lemma sg1232 : RowSquare [4,3,3,1] [1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [11]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg1327 : RowSquare [6,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [11]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg1478 : RowSquare [6,5] [3,3,3,2] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1479 : RowSquare [6,5] [4,3,2,2] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1480 : RowSquare [6,5] [4,3,3,1] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1481 : RowSquare [6,5] [4,4,2,1] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1482 : RowSquare [6,5] [4,4,3] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1483 : RowSquare [6,5] [5,2,2,2] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1484 : RowSquare [6,5] [5,3,2,1] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1485 : RowSquare [6,5] [5,3,3] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1486 : RowSquare [6,5] [5,4,1,1] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1487 : RowSquare [6,5] [5,4,2] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1488 : RowSquare [6,5] [5,5,1] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1489 : RowSquare [6,5] [6,2,2,1] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1490 : RowSquare [6,5] [6,3,1,1] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1491 : RowSquare [6,5] [6,3,2] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1492 : RowSquare [6,5] [6,4,1] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1493 : RowSquare [6,5] [6,5] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1494 : RowSquare [6,5] [7,2,1,1] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1495 : RowSquare [6,5] [7,2,2] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1496 : RowSquare [6,5] [7,3,1] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1497 : RowSquare [6,5] [7,4] := by + exact rowSquare_short 5 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1615 : RowSquare [3,3,2,1,1,1,1] [12] := by + exact rowSquare_trivial _ (by decide) + +lemma sg1650 : RowSquare [4,4,2,2] [1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [12]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg1682 : RowSquare [5,3,2,1,1] [1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [12]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg1734 : RowSquare [5,4,2,1] [12] := by + exact rowSquare_trivial _ (by decide) + +lemma sg1754 : RowSquare [6,2,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [12]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg1871 : RowSquare [6,6] [6,6] := by + exact rowSquare_even 6 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg1928 : RowSquare [7,5] [4,3,3,2] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1930 : RowSquare [7,5] [4,4,3,1] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1931 : RowSquare [7,5] [4,4,4] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1932 : RowSquare [7,5] [5,3,3,1] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1933 : RowSquare [7,5] [5,4,2,1] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1934 : RowSquare [7,5] [5,4,3] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1936 : RowSquare [7,5] [5,5,2] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1937 : RowSquare [7,5] [6,2,2,2] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1938 : RowSquare [7,5] [6,3,2,1] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1939 : RowSquare [7,5] [6,3,3] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1940 : RowSquare [7,5] [6,4,1,1] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1941 : RowSquare [7,5] [6,4,2] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg1942 : RowSquare [7,5] [6,5,1] := by + exact rowSquare_short 5 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg2015 : RowSquare [2,2,2,2,2,2,1] [7,6] := by + exact rowSquare_short 6 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg2016 : RowSquare [2,2,2,2,2,2,1] [8,5] := by + exact rowSquare_short 6 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg2017 : RowSquare [2,2,2,2,2,2,1] [9,4] := by + exact rowSquare_short 6 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg2018 : RowSquare [2,2,2,2,2,2,1] [10,3] := by + exact rowSquare_short 6 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg2019 : RowSquare [2,2,2,2,2,2,1] [11,2] := by + exact rowSquare_short 6 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg2072 : RowSquare [4,3,1,1,1,1,1,1] [13] := by + exact rowSquare_trivial _ (by decide) + +lemma sg2105 : RowSquare [4,4,1,1,1,1,1] [13] := by + exact rowSquare_trivial _ (by decide) + +lemma sg2107 : RowSquare [4,4,3,2] [1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [13]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg2137 : RowSquare [5,3,3,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [13]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg2251 : RowSquare [7,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [13]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg2364 : RowSquare [7,6] [4,4,4,1] := by + exact rowSquare_short 6 1 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg2488 : RowSquare [2,2,2,2,2,2,2] [8,6] := by + exact rowSquare_even 7 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg2489 : RowSquare [2,2,2,2,2,2,2] [10,4] := by + exact rowSquare_even 7 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) + +lemma sg2573 : RowSquare [4,4,1,1,1,1,1,1] [14] := by + exact rowSquare_trivial _ (by decide) + +lemma sg2596 : RowSquare [5,4,2,2,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [14]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg2626 : RowSquare [6,3,2,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [14]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg2702 : RowSquare [7,2,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [14]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg3106 : RowSquare [8,6] [4,4,4,2] := by + exact rowSquare_short 6 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg3239 : RowSquare [4,4,2,1,1,1,1,1] [15] := by + exact rowSquare_trivial _ (by decide) + +lemma sg3299 : RowSquare [5,4,3,2,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]) + have hh : SquareOccurs (staircase 5) (rowDiagram [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]) := + ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]), + saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1])) he) hh + +lemma sg3300 : RowSquare [5,4,3,2,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [2,1,1,1,1,1,1,1,1,1,1,1,1,1]) + have hh : SquareOccurs (staircase 5) (rowDiagram [2,1,1,1,1,1,1,1,1,1,1,1,1,1]) := + ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [2,1,1,1,1,1,1,1,1,1,1,1,1,1]), + saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [2,1,1,1,1,1,1,1,1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,1,1,1,1,1,1,1,1,1,1,1,1,1])) he) hh + +lemma sg3301 : RowSquare [5,4,3,2,1] [2,2,1,1,1,1,1,1,1,1,1,1,1] := by + have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [2,2,1,1,1,1,1,1,1,1,1,1,1]) + have hh : SquareOccurs (staircase 5) (rowDiagram [2,2,1,1,1,1,1,1,1,1,1,1,1]) := + ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [2,2,1,1,1,1,1,1,1,1,1,1,1]), + saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [2,2,1,1,1,1,1,1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,1,1,1,1,1,1,1,1,1,1,1])) he) hh + +lemma sg3302 : RowSquare [5,4,3,2,1] [2,2,2,2,1,1,1,1,1,1,1] := by + have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [2,2,2,2,1,1,1,1,1,1,1]) + have hh : SquareOccurs (staircase 5) (rowDiagram [2,2,2,2,1,1,1,1,1,1,1]) := + ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [2,2,2,2,1,1,1,1,1,1,1]), + saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [2,2,2,2,1,1,1,1,1,1,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [2,2,2,2,1,1,1,1,1,1,1])) he) hh + +lemma sg3303 : RowSquare [5,4,3,2,1] [3,2,2,2,2,2,2] := by + have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [3,2,2,2,2,2,2]) + have hh : SquareOccurs (staircase 5) (rowDiagram [3,2,2,2,2,2,2]) := + ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [3,2,2,2,2,2,2]), + saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [3,2,2,2,2,2,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,2,2,2,2,2,2])) he) hh + +lemma sg3304 : RowSquare [5,4,3,2,1] [3,3,2,2,2,2,1] := by + have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [3,3,2,2,2,2,1]) + have hh : SquareOccurs (staircase 5) (rowDiagram [3,3,2,2,2,2,1]) := + ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [3,3,2,2,2,2,1]), + saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [3,3,2,2,2,2,1])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,2,2,2,2,1])) he) hh + +lemma sg3305 : RowSquare [5,4,3,2,1] [3,3,3,2,2,2] := by + have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [3,3,3,2,2,2]) + have hh : SquareOccurs (staircase 5) (rowDiagram [3,3,3,2,2,2]) := + ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [3,3,3,2,2,2]), + saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [3,3,3,2,2,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [3,3,3,2,2,2])) he) hh + +lemma sg3306 : RowSquare [5,4,3,2,1] [4,3,2,2,2,2] := by + have he : rowDiagram [5,4,3,2,1] = (staircase 5) := by + rw [rowDiagram_eq _ (by decide)] + apply YoungDiagram.ext + decide + change SquareOccurs (rowDiagram [5,4,3,2,1]) (rowDiagram [4,3,2,2,2,2]) + have hh : SquareOccurs (staircase 5) (rowDiagram [4,3,2,2,2,2]) := + ⟨15,canonicalTableau _ (staircase_card 5),canonicalTableau _ (rowDiagram_card [4,3,2,2,2,2]), + saxl_kronecker_pos 5 (by decide) _ (rowDiagram_card [4,3,2,2,2,2])⟩ + exact Eq.mpr (congrArg (fun α => SquareOccurs α (rowDiagram [4,3,2,2,2,2])) he) hh + +lemma sg3521 : RowSquare [8,1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [15]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg3739 : RowSquare [2,2,2,2,2,2,2,1,1] [5,5,5,1] := by + exact rowSquare_short 7 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg3740 : RowSquare [2,2,2,2,2,2,2,1,1] [6,5,5] := by + exact rowSquare_short 7 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg3742 : RowSquare [2,2,2,2,2,2,2,1,1] [6,6,3,1] := by + exact rowSquare_short 7 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg3743 : RowSquare [2,2,2,2,2,2,2,1,1] [6,6,4] := by + exact rowSquare_short 7 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg3998 : RowSquare [5,5,2,2,2] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [16]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg4063 : RowSquare [6,4,2,2,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [16]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg4160 : RowSquare [7,3,2,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [16]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg4345 : RowSquare [8,2,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [16]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg4804 : RowSquare [5,4,4,3,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [17]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg4832 : RowSquare [5,5,3,2,2] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [17]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg4862 : RowSquare [6,4,3,2,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [17]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg4930 : RowSquare [9,1,1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [17]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg5011 : RowSquare [2,2,2,2,2,2,2,2,1,1] [5,5,5,3] := by + exact rowSquare_short 8 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg5012 : RowSquare [2,2,2,2,2,2,2,2,1,1] [6,4,4,4] := by + exact rowSquare_short 8 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg5013 : RowSquare [2,2,2,2,2,2,2,2,1,1] [6,5,4,3] := by + exact rowSquare_short 8 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg5014 : RowSquare [2,2,2,2,2,2,2,2,1,1] [6,5,5,2] := by + exact rowSquare_short 8 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg5015 : RowSquare [2,2,2,2,2,2,2,2,1,1] [6,6,4,2] := by + exact rowSquare_short 8 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg5016 : RowSquare [2,2,2,2,2,2,2,2,1,1] [6,6,5,1] := by + exact rowSquare_short 8 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg5017 : RowSquare [2,2,2,2,2,2,2,2,1,1] [6,6,6] := by + exact rowSquare_short 8 2 (by decide) (by decide) (by decide) + (by decide) (by decide) (by decide) (by decide) (by decide) + +lemma sg5672 : RowSquare [6,5,2,2,2,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [18]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg5735 : RowSquare [8,3,2,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [18]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg5757 : RowSquare [9,2,1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [18]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg6339 : RowSquare [5,5,4,3,2] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [19]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg6389 : RowSquare [6,4,4,3,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [19]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg6457 : RowSquare [6,5,3,2,2,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [19]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg6502 : RowSquare [10,1,1,1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [19]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg7812 : RowSquare [6,6,2,2,2,2] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [20]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg7998 : RowSquare [9,3,2,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [20]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg8008 : RowSquare [10,2,1,1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [20]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg8780 : RowSquare [6,6,3,2,2,2] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [21]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg10867 : RowSquare [7,6,2,2,2,2,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [22]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +lemma sg11531 : RowSquare [7,6,3,2,2,2,1] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_target_transpose (q := [23]) (by decide) (by decide) + (by decide) (rowSquare_trivial _ (by decide)) + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupMissingLeaves.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupMissingLeaves.lean index e1d968c29bc4290fcebd392b72b66d083db49301..8235276ab16497f35b42b1e4722dc3abfd3e26d3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupMissingLeaves.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupMissingLeaves.lean @@ -1,18 +1,18 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Finite.PieriRows62 -import OAI.RepresentationTheory.UniversalSquare.Finite.PieriRows64 - -namespace OAI - -/-! Semigroup Missing Leaves. -/ - -section - -namespace UniversalTensorSquare -lemma sg32006 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [8,8,8,8,8,8,7,7] := pieriSquare62_0 -lemma sg43233 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [8,8,8,8,8,8,8,8] := pieriSquare64_0 -end UniversalTensorSquare -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Finite.PieriRows62 +import OAI.RepresentationTheory.UniversalSquare.Finite.PieriRows64 + +namespace OAI + +/-! Semigroup Missing Leaves. -/ + +section + +namespace UniversalTensorSquare +lemma sg32006 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [8,8,8,8,8,8,7,7] := pieriSquare62_0 +lemma sg43233 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [8,8,8,8,8,8,8,8] := pieriSquare64_0 +end UniversalTensorSquare +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes0.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes0.lean index 404dee2f3233f51d00c0b6725af20bd1cdbe3bf7..4fa44ca9ee8a478909d91a7d42f075679f06e34c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes0.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes0.lean @@ -1,1221 +1,1221 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupLocalLeaves -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupLeaves1 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupLeaves2 - -namespace OAI - -/-! Semigroup Nodes 0. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg22 : RowSquare [2,1,1,1] [3,1,1] := by - exact rowSquare_join (by decide) sg2 sg4 - -lemma sg23 : RowSquare [2,1,1,1] [3,2] := by - exact rowSquare_join (by decide) sg0 sg17 - -lemma sg24 : RowSquare [2,1,1,1] [4,1] := by - exact rowSquare_join (by decide) sg2 sg5 - -lemma sg45 : RowSquare [4,1] [3,1,1] := by - exact rowSquare_join (by decide) sg2 sg4 - -lemma sg46 : RowSquare [4,1] [3,2] := by - exact rowSquare_join (by decide) sg0 sg17 - -lemma sg47 : RowSquare [4,1] [4,1] := by - exact rowSquare_join (by decide) sg2 sg5 - -lemma sg51 : RowSquare [2,1,1,1,1] [4,1,1] := by - exact rowSquare_join (by decide) sg4 sg7 - -lemma sg52 : RowSquare [2,1,1,1,1] [4,2] := by - exact rowSquare_join (by decide) sg2 sg17 - -lemma sg53 : RowSquare [2,1,1,1,1] [5,1] := by - exact rowSquare_join (by decide) sg5 sg7 - -lemma sg63 : RowSquare [2,2,2] [3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg13 - -lemma sg66 : RowSquare [3,1,1,1] [2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg32 - -lemma sg69 : RowSquare [3,1,1,1] [3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg33 - -lemma sg70 : RowSquare [3,1,1,1] [3,2,1] := by - exact rowSquare_join (by decide) sg0 sg34 - -lemma sg72 : RowSquare [3,1,1,1] [4,1,1] := by - exact rowSquare_join (by decide) sg0 sg22 - -lemma sg73 : RowSquare [3,1,1,1] [4,2] := by - exact rowSquare_join (by decide) sg0 sg23 - -lemma sg84 : RowSquare [3,3] [3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg13 - -lemma sg87 : RowSquare [4,1,1] [2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg32 - -lemma sg90 : RowSquare [4,1,1] [3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg33 - -lemma sg91 : RowSquare [4,1,1] [3,2,1] := by - exact rowSquare_join (by decide) sg0 sg34 - -lemma sg93 : RowSquare [4,1,1] [4,1,1] := by - exact rowSquare_join (by decide) sg2 sg9 - -lemma sg94 : RowSquare [4,1,1] [4,2] := by - exact rowSquare_join (by decide) sg2 sg10 - -lemma sg95 : RowSquare [4,1,1] [5,1] := by - exact rowSquare_join (by decide) sg2 sg11 - -lemma sg104 : RowSquare [5,1] [4,1,1] := by - exact rowSquare_join (by decide) sg4 sg7 - -lemma sg105 : RowSquare [5,1] [4,2] := by - exact rowSquare_join (by decide) sg2 sg17 - -lemma sg106 : RowSquare [5,1] [5,1] := by - exact rowSquare_join (by decide) sg5 sg7 - -lemma sg110 : RowSquare [2,1,1,1,1,1] [5,1,1] := by - exact rowSquare_join (by decide) sg4 sg20 - -lemma sg111 : RowSquare [2,1,1,1,1,1] [5,2] := by - exact rowSquare_join (by decide) sg7 sg17 - -lemma sg112 : RowSquare [2,1,1,1,1,1] [6,1] := by - exact rowSquare_join (by decide) sg5 sg20 - -lemma sg114 : RowSquare [2,2,1,1,1] [3,2,2] := by - exact rowSquare_join (by decide) sg4 sg16 - -lemma sg115 : RowSquare [2,2,1,1,1] [3,3,1] := by - exact rowSquare_join (by decide) sg4 sg17 - -lemma sg116 : RowSquare [2,2,1,1,1] [4,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg13 - -lemma sg117 : RowSquare [2,2,1,1,1] [4,2,1] := by - exact rowSquare_join (by decide) sg4 sg18 - -lemma sg118 : RowSquare [2,2,1,1,1] [4,3] := by - exact rowSquare_join (by decide) sg5 sg17 - -lemma sg119 : RowSquare [2,2,1,1,1] [5,1,1] := by - exact rowSquare_join (by decide) sg4 sg19 - -lemma sg120 : RowSquare [2,2,1,1,1] [5,2] := by - exact rowSquare_join (by decide) sg5 sg18 - -lemma sg121 : RowSquare [2,2,1,1,1] [6,1] := by - exact rowSquare_join (by decide) sg5 sg19 - -lemma sg132 : RowSquare [3,1,1,1,1] [3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg32 - -lemma sg133 : RowSquare [3,1,1,1,1] [3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg88 - -lemma sg134 : RowSquare [3,1,1,1,1] [3,2,2] := by - exact rowSquare_join (by decide) sg0 sg89 - -lemma sg135 : RowSquare [3,1,1,1,1] [4,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg33 - -lemma sg136 : RowSquare [3,1,1,1,1] [4,2,1] := by - exact rowSquare_join (by decide) sg2 sg34 - -lemma sg137 : RowSquare [3,1,1,1,1] [4,3] := by - exact rowSquare_join (by decide) sg0 sg92 - -lemma sg138 : RowSquare [3,1,1,1,1] [5,1,1] := by - exact rowSquare_join (by decide) sg0 sg51 - -lemma sg139 : RowSquare [3,1,1,1,1] [5,2] := by - exact rowSquare_join (by decide) sg0 sg52 - -lemma sg140 : RowSquare [3,1,1,1,1] [6,1] := by - exact rowSquare_join (by decide) sg0 sg53 - -lemma sg142 : RowSquare [3,2,1,1] [2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg74 - -lemma sg145 : RowSquare [3,2,1,1] [3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg32 - -lemma sg146 : RowSquare [3,2,1,1] [3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg76 - -lemma sg147 : RowSquare [3,2,1,1] [3,2,2] := by - exact rowSquare_join (by decide) sg0 sg55 - -lemma sg148 : RowSquare [3,2,1,1] [3,3,1] := by - exact rowSquare_join (by decide) sg4 sg10 - -lemma sg149 : RowSquare [3,2,1,1] [4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg56 - -lemma sg150 : RowSquare [3,2,1,1] [4,2,1] := by - exact rowSquare_join (by decide) sg0 sg57 - -lemma sg151 : RowSquare [3,2,1,1] [4,3] := by - exact rowSquare_join (by decide) sg5 sg10 - -lemma sg152 : RowSquare [3,2,1,1] [5,2] := by - exact rowSquare_join (by decide) sg1 sg23 - -lemma sg153 : RowSquare [3,2,1,1] [6,1] := by - exact rowSquare_join (by decide) sg5 sg8 - -lemma sg159 : RowSquare [3,2,2] [3,2,2] := by - exact rowSquare_join (by decide) sg0 sg62 - -lemma sg161 : RowSquare [3,2,2] [4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg63 - -lemma sg162 : RowSquare [3,2,2] [4,2,1] := by - exact rowSquare_join (by decide) sg1 sg27 - -lemma sg164 : RowSquare [3,2,2] [5,2] := by - exact rowSquare_join (by decide) sg3 sg10 - -lemma sg170 : RowSquare [3,3,1] [3,2,2] := by - exact rowSquare_join (by decide) sg0 sg62 - -lemma sg172 : RowSquare [3,3,1] [4,1,1,1] := by - exact rowSquare_join (by decide) sg3 sg13 - -lemma sg173 : RowSquare [3,3,1] [4,2,1] := by - exact rowSquare_join (by decide) sg1 sg27 - -lemma sg175 : RowSquare [3,3,1] [5,1,1] := by - exact rowSquare_join (by decide) sg1 sg28 - -lemma sg176 : RowSquare [3,3,1] [5,2] := by - exact rowSquare_join (by decide) sg3 sg14 - -lemma sg177 : RowSquare [3,3,1] [6,1] := by - exact rowSquare_join (by decide) sg1 sg30 - -lemma sg193 : RowSquare [4,2,1] [2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg74 - -lemma sg196 : RowSquare [4,2,1] [3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg32 - -lemma sg197 : RowSquare [4,2,1] [3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg76 - -lemma sg198 : RowSquare [4,2,1] [3,2,2] := by - exact rowSquare_join (by decide) sg4 sg9 - -lemma sg199 : RowSquare [4,2,1] [3,3,1] := by - exact rowSquare_join (by decide) sg4 sg10 - -lemma sg200 : RowSquare [4,2,1] [4,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg26 - -lemma sg201 : RowSquare [4,2,1] [4,2,1] := by - exact rowSquare_join (by decide) sg4 sg11 - -lemma sg202 : RowSquare [4,2,1] [4,3] := by - exact rowSquare_join (by decide) sg5 sg10 - -lemma sg203 : RowSquare [4,2,1] [5,1,1] := by - exact rowSquare_join (by decide) sg4 sg12 - -lemma sg204 : RowSquare [4,2,1] [5,2] := by - exact rowSquare_join (by decide) sg5 sg11 - -lemma sg205 : RowSquare [4,2,1] [6,1] := by - exact rowSquare_join (by decide) sg5 sg12 - -lemma sg218 : RowSquare [5,1,1] [3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg32 - -lemma sg219 : RowSquare [5,1,1] [3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg88 - -lemma sg220 : RowSquare [5,1,1] [3,2,2] := by - exact rowSquare_join (by decide) sg0 sg89 - -lemma sg221 : RowSquare [5,1,1] [4,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg33 - -lemma sg222 : RowSquare [5,1,1] [4,2,1] := by - exact rowSquare_join (by decide) sg2 sg34 - -lemma sg223 : RowSquare [5,1,1] [4,3] := by - exact rowSquare_join (by decide) sg0 sg92 - -lemma sg224 : RowSquare [5,1,1] [5,1,1] := by - exact rowSquare_join (by decide) sg7 sg9 - -lemma sg225 : RowSquare [5,1,1] [5,2] := by - exact rowSquare_join (by decide) sg7 sg10 - -lemma sg227 : RowSquare [5,2] [3,2,2] := by - exact rowSquare_join (by decide) sg4 sg16 - -lemma sg228 : RowSquare [5,2] [3,3,1] := by - exact rowSquare_join (by decide) sg4 sg17 - -lemma sg229 : RowSquare [5,2] [4,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg13 - -lemma sg230 : RowSquare [5,2] [4,3] := by - exact rowSquare_join (by decide) sg5 sg17 - -lemma sg231 : RowSquare [6,1] [5,1,1] := by - exact rowSquare_join (by decide) sg4 sg20 - -lemma sg232 : RowSquare [6,1] [5,2] := by - exact rowSquare_join (by decide) sg7 sg17 - -lemma sg233 : RowSquare [6,1] [6,1] := by - exact rowSquare_join (by decide) sg5 sg20 - -lemma sg236 : RowSquare [2,1,1,1,1,1,1] [6,2] := by - exact rowSquare_join (by decide) sg17 sg20 - -lemma sg237 : RowSquare [2,1,1,1,1,1,1] [7,1] := by - exact rowSquare_join (by decide) sg18 sg20 - -lemma sg239 : RowSquare [2,2,1,1,1,1] [4,2,2] := by - exact rowSquare_join (by decide) sg16 sg16 - -lemma sg240 : RowSquare [2,2,1,1,1,1] [4,3,1] := by - exact rowSquare_join (by decide) sg16 sg17 - -lemma sg241 : RowSquare [2,2,1,1,1,1] [4,4] := by - exact rowSquare_join (by decide) sg17 sg17 - -lemma sg242 : RowSquare [2,2,1,1,1,1] [5,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg20 - -lemma sg243 : RowSquare [2,2,1,1,1,1] [5,2,1] := by - exact rowSquare_join (by decide) sg16 sg18 - -lemma sg244 : RowSquare [2,2,1,1,1,1] [5,3] := by - exact rowSquare_join (by decide) sg17 sg18 - -lemma sg245 : RowSquare [2,2,1,1,1,1] [6,1,1] := by - exact rowSquare_join (by decide) sg16 sg19 - -lemma sg246 : RowSquare [2,2,1,1,1,1] [6,2] := by - exact rowSquare_join (by decide) sg17 sg19 - -lemma sg247 : RowSquare [2,2,1,1,1,1] [7,1] := by - exact rowSquare_join (by decide) sg18 sg19 - -lemma sg250 : RowSquare [2,2,2,1,1] [3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg17 - -lemma sg252 : RowSquare [2,2,2,1,1] [4,4] := by - exact rowSquare_join (by decide) sg17 sg14 - -lemma sg254 : RowSquare [2,2,2,2] [2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13 - -lemma sg255 : RowSquare [2,2,2,2] [3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14 - -lemma sg258 : RowSquare [2,2,2,2] [5,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg15 - -lemma sg260 : RowSquare [3,1,1,1,1,1] [4,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg32 - -lemma sg261 : RowSquare [3,1,1,1,1,1] [4,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg88 - -lemma sg262 : RowSquare [3,1,1,1,1,1] [4,2,2] := by - exact rowSquare_join (by decide) sg2 sg89 - -lemma sg263 : RowSquare [3,1,1,1,1,1] [5,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg33 - -lemma sg264 : RowSquare [3,1,1,1,1,1] [5,2,1] := by - exact rowSquare_join (by decide) sg7 sg34 - -lemma sg265 : RowSquare [3,1,1,1,1,1] [5,3] := by - exact rowSquare_join (by decide) sg2 sg92 - -lemma sg266 : RowSquare [3,1,1,1,1,1] [6,1,1] := by - exact rowSquare_join (by decide) sg0 sg110 - -lemma sg267 : RowSquare [3,1,1,1,1,1] [6,2] := by - exact rowSquare_join (by decide) sg0 sg111 - -lemma sg268 : RowSquare [3,1,1,1,1,1] [7,1] := by - exact rowSquare_join (by decide) sg0 sg112 - -lemma sg270 : RowSquare [3,2,1,1,1] [2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg32 - -lemma sg272 : RowSquare [3,2,1,1,1] [3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg74 - -lemma sg273 : RowSquare [3,2,1,1,1] [3,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg32 - -lemma sg274 : RowSquare [3,2,1,1,1] [3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg33 - -lemma sg276 : RowSquare [3,2,1,1,1] [3,3,2] := by - exact rowSquare_join (by decide) sg4 sg34 - -lemma sg277 : RowSquare [3,2,1,1,1] [4,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg32 - -lemma sg278 : RowSquare [3,2,1,1,1] [4,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg33 - -lemma sg279 : RowSquare [3,2,1,1,1] [4,2,2] := by - exact rowSquare_join (by decide) sg0 sg114 - -lemma sg280 : RowSquare [3,2,1,1,1] [4,3,1] := by - exact rowSquare_join (by decide) sg0 sg115 - -lemma sg281 : RowSquare [3,2,1,1,1] [4,4] := by - exact rowSquare_join (by decide) sg17 sg10 - -lemma sg282 : RowSquare [3,2,1,1,1] [5,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg116 - -lemma sg283 : RowSquare [3,2,1,1,1] [5,2,1] := by - exact rowSquare_join (by decide) sg0 sg117 - -lemma sg284 : RowSquare [3,2,1,1,1] [5,3] := by - exact rowSquare_join (by decide) sg0 sg118 - -lemma sg288 : RowSquare [3,2,2,1] [3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg74 - -lemma sg289 : RowSquare [3,2,2,1] [3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg166 - -lemma sg290 : RowSquare [3,2,2,1] [3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg123 - -lemma sg291 : RowSquare [3,2,2,1] [3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg10 - -lemma sg292 : RowSquare [3,2,2,1] [3,3,2] := by - exact rowSquare_join (by decide) sg4 sg27 - -lemma sg293 : RowSquare [3,2,2,1] [4,3,1] := by - exact rowSquare_join (by decide) sg0 sg125 - -lemma sg294 : RowSquare [3,2,2,1] [4,4] := by - exact rowSquare_join (by decide) sg14 sg10 - -lemma sg298 : RowSquare [3,3,1,1] [3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg154 - -lemma sg299 : RowSquare [3,3,1,1] [3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg155 - -lemma sg302 : RowSquare [3,3,1,1] [4,4] := by - exact rowSquare_join (by decide) sg10 sg10 - -lemma sg303 : RowSquare [3,3,1,1] [5,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg8 - -lemma sg304 : RowSquare [3,3,1,1] [5,2,1] := by - exact rowSquare_join (by decide) sg1 sg57 - -lemma sg305 : RowSquare [3,3,1,1] [5,3] := by - exact rowSquare_join (by decide) sg10 sg11 - -lemma sg307 : RowSquare [3,3,2] [2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3 sg30 - -lemma sg308 : RowSquare [3,3,2] [2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3 sg29 - -lemma sg312 : RowSquare [4,1,1,1,1] [2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg178 - -lemma sg316 : RowSquare [4,1,1,1,1] [3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg179 - -lemma sg317 : RowSquare [4,1,1,1,1] [3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg180 - -lemma sg318 : RowSquare [4,1,1,1,1] [3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg181 - -lemma sg321 : RowSquare [4,1,1,1,1] [4,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg132 - -lemma sg322 : RowSquare [4,1,1,1,1] [4,2,2] := by - exact rowSquare_join (by decide) sg0 sg134 - -lemma sg323 : RowSquare [4,1,1,1,1] [4,3,1] := by - exact rowSquare_join (by decide) sg0 sg185 - -lemma sg325 : RowSquare [4,1,1,1,1] [5,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg135 - -lemma sg326 : RowSquare [4,1,1,1,1] [5,2,1] := by - exact rowSquare_join (by decide) sg0 sg136 - -lemma sg327 : RowSquare [4,1,1,1,1] [5,3] := by - exact rowSquare_join (by decide) sg0 sg137 - -lemma sg328 : RowSquare [4,1,1,1,1] [6,1,1] := by - exact rowSquare_join (by decide) sg2 sg51 - -lemma sg329 : RowSquare [4,1,1,1,1] [6,2] := by - exact rowSquare_join (by decide) sg2 sg52 - -lemma sg351 : RowSquare [4,2,2] [3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg154 - -lemma sg354 : RowSquare [4,2,2] [4,4] := by - exact rowSquare_join (by decide) sg10 sg10 - -lemma sg355 : RowSquare [4,2,2] [5,3] := by - exact rowSquare_join (by decide) sg10 sg11 - -lemma sg359 : RowSquare [4,3,1] [3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg74 - -lemma sg360 : RowSquare [4,3,1] [3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg10 - -lemma sg361 : RowSquare [4,3,1] [3,3,2] := by - exact rowSquare_join (by decide) sg4 sg27 - -lemma sg362 : RowSquare [4,3,1] [4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg75 - -lemma sg363 : RowSquare [4,3,1] [4,4] := by - exact rowSquare_join (by decide) sg14 sg10 - -lemma sg364 : RowSquare [4,4] [2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13 - -lemma sg365 : RowSquare [4,4] [3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14 - -lemma sg368 : RowSquare [4,4] [5,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg15 - -lemma sg370 : RowSquare [5,1,1,1] [2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg178 - -lemma sg374 : RowSquare [5,1,1,1] [3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg179 - -lemma sg375 : RowSquare [5,1,1,1] [3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg180 - -lemma sg376 : RowSquare [5,1,1,1] [3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg181 - -lemma sg379 : RowSquare [5,1,1,1] [4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg66 - -lemma sg380 : RowSquare [5,1,1,1] [4,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg67 - -lemma sg381 : RowSquare [5,1,1,1] [4,2,2] := by - exact rowSquare_join (by decide) sg2 sg68 - -lemma sg382 : RowSquare [5,1,1,1] [4,3,1] := by - exact rowSquare_join (by decide) sg0 sg185 - -lemma sg384 : RowSquare [5,1,1,1] [5,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg69 - -lemma sg385 : RowSquare [5,1,1,1] [5,2,1] := by - exact rowSquare_join (by decide) sg2 sg70 - -lemma sg386 : RowSquare [5,1,1,1] [5,3] := by - exact rowSquare_join (by decide) sg2 sg71 - -lemma sg387 : RowSquare [5,1,1,1] [6,1,1] := by - exact rowSquare_join (by decide) sg7 sg22 - -lemma sg388 : RowSquare [5,1,1,1] [6,2] := by - exact rowSquare_join (by decide) sg7 sg23 - -lemma sg389 : RowSquare [5,2,1] [2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg32 - -lemma sg391 : RowSquare [5,2,1] [3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg74 - -lemma sg392 : RowSquare [5,2,1] [3,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg32 - -lemma sg393 : RowSquare [5,2,1] [3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg33 - -lemma sg395 : RowSquare [5,2,1] [3,3,2] := by - exact rowSquare_join (by decide) sg4 sg34 - -lemma sg396 : RowSquare [5,2,1] [4,4] := by - exact rowSquare_join (by decide) sg17 sg10 - -lemma sg397 : RowSquare [5,2,1] [5,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg26 - -lemma sg398 : RowSquare [5,2,1] [5,2,1] := by - exact rowSquare_join (by decide) sg16 sg11 - -lemma sg399 : RowSquare [5,2,1] [5,3] := by - exact rowSquare_join (by decide) sg17 sg11 - -lemma sg400 : RowSquare [5,2,1] [7,1] := by - exact rowSquare_join (by decide) sg18 sg12 - -lemma sg402 : RowSquare [5,3] [3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg17 - -lemma sg407 : RowSquare [5,3] [4,4] := by - exact rowSquare_join (by decide) sg17 sg14 - -lemma sg413 : RowSquare [6,1,1] [4,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg32 - -lemma sg414 : RowSquare [6,1,1] [4,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg88 - -lemma sg415 : RowSquare [6,1,1] [4,2,2] := by - exact rowSquare_join (by decide) sg2 sg89 - -lemma sg416 : RowSquare [6,1,1] [5,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg33 - -lemma sg417 : RowSquare [6,1,1] [5,2,1] := by - exact rowSquare_join (by decide) sg7 sg34 - -lemma sg418 : RowSquare [6,1,1] [5,3] := by - exact rowSquare_join (by decide) sg2 sg92 - -lemma sg419 : RowSquare [6,1,1] [6,1,1] := by - exact rowSquare_join (by decide) sg9 sg20 - -lemma sg420 : RowSquare [6,1,1] [6,2] := by - exact rowSquare_join (by decide) sg10 sg20 - -lemma sg422 : RowSquare [6,2] [4,2,2] := by - exact rowSquare_join (by decide) sg16 sg16 - -lemma sg423 : RowSquare [6,2] [4,3,1] := by - exact rowSquare_join (by decide) sg16 sg17 - -lemma sg424 : RowSquare [6,2] [4,4] := by - exact rowSquare_join (by decide) sg17 sg17 - -lemma sg425 : RowSquare [7,1] [6,2] := by - exact rowSquare_join (by decide) sg17 sg20 - -lemma sg428 : RowSquare [2,1,1,1,1,1,1,1] [7,1,1] := by - exact rowSquare_join (by decide) sg16 sg49 - -lemma sg429 : RowSquare [2,1,1,1,1,1,1,1] [7,2] := by - exact rowSquare_join (by decide) sg17 sg49 - -lemma sg430 : RowSquare [2,1,1,1,1,1,1,1] [8,1] := by - exact rowSquare_join (by decide) sg18 sg49 - -lemma sg432 : RowSquare [2,2,1,1,1,1,1] [5,2,2] := by - exact rowSquare_join (by decide) sg16 sg45 - -lemma sg433 : RowSquare [2,2,1,1,1,1,1] [5,3,1] := by - exact rowSquare_join (by decide) sg16 sg46 - -lemma sg434 : RowSquare [2,2,1,1,1,1,1] [5,4] := by - exact rowSquare_join (by decide) sg17 sg46 - -lemma sg435 : RowSquare [2,2,1,1,1,1,1] [6,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg49 - -lemma sg436 : RowSquare [2,2,1,1,1,1,1] [6,2,1] := by - exact rowSquare_join (by decide) sg16 sg47 - -lemma sg437 : RowSquare [2,2,1,1,1,1,1] [6,3] := by - exact rowSquare_join (by decide) sg17 sg47 - -lemma sg438 : RowSquare [2,2,1,1,1,1,1] [7,2] := by - exact rowSquare_join (by decide) sg17 sg48 - -lemma sg439 : RowSquare [2,2,1,1,1,1,1] [8,1] := by - exact rowSquare_join (by decide) sg18 sg48 - -lemma sg440 : RowSquare [2,2,2,1,1,1] [3,3,3] := by - exact rowSquare_join (by decide) sg4 sg97 - -lemma sg441 : RowSquare [2,2,2,1,1,1] [4,4,1] := by - exact rowSquare_join (by decide) sg17 sg40 - -lemma sg442 : RowSquare [2,2,2,1,1,1] [5,4] := by - exact rowSquare_join (by decide) sg17 sg42 - -lemma sg443 : RowSquare [2,2,2,1,1,1] [6,3] := by - exact rowSquare_join (by decide) sg17 sg43 - -lemma sg444 : RowSquare [2,2,2,1,1,1] [8,1] := by - exact rowSquare_join (by decide) sg18 sg44 - -lemma sg447 : RowSquare [3,1,1,1,1,1,1] [5,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg32 - -lemma sg448 : RowSquare [3,1,1,1,1,1,1] [5,2,1,1] := by - exact rowSquare_join (by decide) sg7 sg88 - -lemma sg449 : RowSquare [3,1,1,1,1,1,1] [5,2,2] := by - exact rowSquare_join (by decide) sg7 sg89 - -lemma sg450 : RowSquare [3,1,1,1,1,1,1] [6,2,1] := by - exact rowSquare_join (by decide) sg20 sg34 - -lemma sg451 : RowSquare [3,1,1,1,1,1,1] [6,3] := by - exact rowSquare_join (by decide) sg7 sg92 - -lemma sg452 : RowSquare [3,1,1,1,1,1,1] [7,2] := by - exact rowSquare_join (by decide) sg0 sg236 - -lemma sg453 : RowSquare [3,1,1,1,1,1,1] [8,1] := by - exact rowSquare_join (by decide) sg0 sg237 - -lemma sg455 : RowSquare [3,2,1,1,1,1] [3,2,2,1,1] := by - exact rowSquare_join (by decide) sg16 sg32 - -lemma sg456 : RowSquare [3,2,1,1,1,1] [3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg390 - -lemma sg457 : RowSquare [3,2,1,1,1,1] [3,3,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg32 - -lemma sg458 : RowSquare [3,2,1,1,1,1] [3,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg88 - -lemma sg459 : RowSquare [3,2,1,1,1,1] [3,3,3] := by - exact rowSquare_join (by decide) sg4 sg89 - -lemma sg460 : RowSquare [3,2,1,1,1,1] [4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg74 - -lemma sg461 : RowSquare [3,2,1,1,1,1] [4,2,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg32 - -lemma sg462 : RowSquare [3,2,1,1,1,1] [4,2,2,1] := by - exact rowSquare_join (by decide) sg16 sg33 - -lemma sg463 : RowSquare [3,2,1,1,1,1] [4,3,1,1] := by - exact rowSquare_join (by decide) sg17 sg33 - -lemma sg464 : RowSquare [3,2,1,1,1,1] [4,3,2] := by - exact rowSquare_join (by decide) sg16 sg34 - -lemma sg465 : RowSquare [3,2,1,1,1,1] [4,4,1] := by - exact rowSquare_join (by decide) sg17 sg34 - -lemma sg466 : RowSquare [3,2,1,1,1,1] [5,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg32 - -lemma sg467 : RowSquare [3,2,1,1,1,1] [5,2,1,1] := by - exact rowSquare_join (by decide) sg18 sg33 - -lemma sg468 : RowSquare [3,2,1,1,1,1] [5,2,2] := by - exact rowSquare_join (by decide) sg0 sg239 - -lemma sg469 : RowSquare [3,2,1,1,1,1] [5,3,1] := by - exact rowSquare_join (by decide) sg0 sg240 - -lemma sg470 : RowSquare [3,2,1,1,1,1] [5,4] := by - exact rowSquare_join (by decide) sg0 sg241 - -lemma sg471 : RowSquare [3,2,1,1,1,1] [6,3] := by - exact rowSquare_join (by decide) sg0 sg244 - -lemma sg472 : RowSquare [3,2,1,1,1,1] [7,2] := by - exact rowSquare_join (by decide) sg1 sg111 - -lemma sg473 : RowSquare [3,2,1,1,1,1] [8,1] := by - exact rowSquare_join (by decide) sg5 sg50 - -lemma sg475 : RowSquare [3,2,2,1,1] [2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg74 - -lemma sg476 : RowSquare [3,2,2,1,1] [2,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg32 - -lemma sg477 : RowSquare [3,2,2,1,1] [3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg33 - -lemma sg478 : RowSquare [3,2,2,1,1] [3,3,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg32 - -lemma sg479 : RowSquare [3,2,2,1,1] [3,3,3] := by - exact rowSquare_join (by decide) sg4 sg77 - -lemma sg485 : RowSquare [3,2,2,2] [4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg165 - -lemma sg486 : RowSquare [3,2,2,2] [4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg166 - -lemma sg488 : RowSquare [3,2,2,2] [4,4,1] := by - exact rowSquare_join (by decide) sg14 sg27 - -lemma sg491 : RowSquare [3,3,1,1,1] [3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg348 - -lemma sg492 : RowSquare [3,3,1,1,1] [3,2,2,1,1] := by - exact rowSquare_join (by decide) sg9 sg32 - -lemma sg493 : RowSquare [3,3,1,1,1] [3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg350 - -lemma sg494 : RowSquare [3,3,1,1,1] [3,3,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg32 - -lemma sg497 : RowSquare [3,3,1,1,1] [4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg154 - -lemma sg498 : RowSquare [3,3,1,1,1] [4,2,2,1] := by - exact rowSquare_join (by decide) sg9 sg33 - -lemma sg499 : RowSquare [3,3,1,1,1] [4,3,2] := by - exact rowSquare_join (by decide) sg9 sg34 - -lemma sg500 : RowSquare [3,3,1,1,1] [4,4,1] := by - exact rowSquare_join (by decide) sg10 sg34 - -lemma sg501 : RowSquare [3,3,1,1,1] [5,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg32 - -lemma sg502 : RowSquare [3,3,1,1,1] [5,2,2] := by - exact rowSquare_join (by decide) sg1 sg114 - -lemma sg503 : RowSquare [3,3,1,1,1] [5,4] := by - exact rowSquare_join (by decide) sg10 sg36 - -lemma sg504 : RowSquare [3,3,1,1,1] [6,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg21 - -lemma sg505 : RowSquare [3,3,1,1,1] [6,2,1] := by - exact rowSquare_join (by decide) sg1 sg117 - -lemma sg506 : RowSquare [3,3,1,1,1] [6,3] := by - exact rowSquare_join (by decide) sg1 sg118 - -lemma sg507 : RowSquare [3,3,1,1,1] [7,2] := by - exact rowSquare_join (by decide) sg14 sg21 - -lemma sg508 : RowSquare [3,3,1,1,1] [8,1] := by - exact rowSquare_join (by decide) sg1 sg121 - -lemma sg510 : RowSquare [3,3,2,1] [2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg306 - -lemma sg512 : RowSquare [3,3,2,1] [3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg307 - -lemma sg514 : RowSquare [3,3,2,1] [3,3,3] := by - exact rowSquare_join (by decide) sg4 sg62 - -lemma sg515 : RowSquare [3,3,2,1] [4,4,1] := by - exact rowSquare_join (by decide) sg10 sg27 - -lemma sg517 : RowSquare [4,1,1,1,1,1] [3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg178 - -lemma sg518 : RowSquare [4,1,1,1,1,1] [3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg371 - -lemma sg519 : RowSquare [4,1,1,1,1,1] [3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg372 - -lemma sg520 : RowSquare [4,1,1,1,1,1] [3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg373 - -lemma sg521 : RowSquare [4,1,1,1,1,1] [4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg179 - -lemma sg522 : RowSquare [4,1,1,1,1,1] [4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg180 - -lemma sg523 : RowSquare [4,1,1,1,1,1] [4,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg181 - -lemma sg524 : RowSquare [4,1,1,1,1,1] [4,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg377 - -lemma sg525 : RowSquare [4,1,1,1,1,1] [4,3,2] := by - exact rowSquare_join (by decide) sg0 sg378 - -lemma sg526 : RowSquare [4,1,1,1,1,1] [5,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg260 - -lemma sg527 : RowSquare [4,1,1,1,1,1] [5,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg261 - -lemma sg528 : RowSquare [4,1,1,1,1,1] [5,2,2] := by - exact rowSquare_join (by decide) sg0 sg262 - -lemma sg529 : RowSquare [4,1,1,1,1,1] [5,3,1] := by - exact rowSquare_join (by decide) sg2 sg185 - -lemma sg530 : RowSquare [4,1,1,1,1,1] [5,4] := by - exact rowSquare_join (by decide) sg0 sg383 - -lemma sg531 : RowSquare [4,1,1,1,1,1] [6,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg263 - -lemma sg532 : RowSquare [4,1,1,1,1,1] [6,2,1] := by - exact rowSquare_join (by decide) sg0 sg264 - -lemma sg533 : RowSquare [4,1,1,1,1,1] [6,3] := by - exact rowSquare_join (by decide) sg0 sg265 - -lemma sg534 : RowSquare [4,2,1,1,1] [2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg330 - -lemma sg538 : RowSquare [4,2,1,1,1] [3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg178 - -lemma sg539 : RowSquare [4,2,1,1,1] [3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg332 - -lemma sg540 : RowSquare [4,2,1,1,1] [3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg271 - -lemma sg542 : RowSquare [4,2,1,1,1] [3,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg67 - -lemma sg543 : RowSquare [4,2,1,1,1] [3,3,3] := by - exact rowSquare_join (by decide) sg4 sg68 - -lemma sg544 : RowSquare [4,2,1,1,1] [4,4,1] := by - exact rowSquare_join (by decide) sg4 sg71 - -lemma sg545 : RowSquare [4,2,1,1,1] [6,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg116 - -lemma sg546 : RowSquare [4,2,1,1,1] [6,2,1] := by - exact rowSquare_join (by decide) sg4 sg53 - -lemma sg547 : RowSquare [4,2,1,1,1] [6,3] := by - exact rowSquare_join (by decide) sg5 sg52 - -lemma sg554 : RowSquare [4,2,2,1] [3,3,3] := by - exact rowSquare_join (by decide) sg4 sg55 - -lemma sg555 : RowSquare [4,2,2,1] [4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg288 - -lemma sg556 : RowSquare [4,2,2,1] [4,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg123 - -lemma sg557 : RowSquare [4,2,2,1] [4,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg291 - -lemma sg558 : RowSquare [4,2,2,1] [4,3,2] := by - exact rowSquare_join (by decide) sg0 sg292 - -lemma sg560 : RowSquare [4,2,2,1] [5,4] := by - exact rowSquare_join (by decide) sg10 sg23 - -lemma sg566 : RowSquare [4,3,1,1] [3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg295 - -lemma sg567 : RowSquare [4,3,1,1] [3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg296 - -lemma sg568 : RowSquare [4,3,1,1] [3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg297 - -lemma sg571 : RowSquare [4,3,1,1] [3,3,3] := by - exact rowSquare_join (by decide) sg4 sg55 - -lemma sg572 : RowSquare [4,3,1,1] [4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg142 - -lemma sg573 : RowSquare [4,3,1,1] [4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg23 - -lemma sg574 : RowSquare [4,3,1,1] [4,3,2] := by - exact rowSquare_join (by decide) sg4 sg57 - -lemma sg576 : RowSquare [4,3,2] [2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg306 - -lemma sg585 : RowSquare [4,4,1] [4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg165 - -lemma sg587 : RowSquare [5,1,1,1,1] [2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg53 - -lemma sg588 : RowSquare [5,1,1,1,1] [2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg52 - -lemma sg589 : RowSquare [5,1,1,1,1] [2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg137 - -lemma sg590 : RowSquare [5,1,1,1,1] [2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg324 - -lemma sg591 : RowSquare [5,1,1,1,1] [3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg312 - -lemma sg592 : RowSquare [5,1,1,1,1] [3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg313 - -lemma sg593 : RowSquare [5,1,1,1,1] [3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg314 - -lemma sg594 : RowSquare [5,1,1,1,1] [3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg315 - -lemma sg595 : RowSquare [5,1,1,1,1] [3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg134 - -lemma sg596 : RowSquare [5,1,1,1,1] [3,3,2,1] := by - exact rowSquare_join (by decide) sg0 sg320 - -lemma sg597 : RowSquare [5,1,1,1,1] [4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg316 - -lemma sg598 : RowSquare [5,1,1,1,1] [4,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg317 - -lemma sg599 : RowSquare [5,1,1,1,1] [4,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg318 - -lemma sg600 : RowSquare [5,1,1,1,1] [4,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg319 - -lemma sg601 : RowSquare [5,1,1,1,1] [4,3,2] := by - exact rowSquare_join (by decide) sg0 sg320 - -lemma sg602 : RowSquare [5,1,1,1,1] [4,4,1] := by - exact rowSquare_join (by decide) sg0 sg315 - -lemma sg603 : RowSquare [5,1,1,1,1] [5,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg132 - -lemma sg604 : RowSquare [5,1,1,1,1] [5,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg133 - -lemma sg605 : RowSquare [5,1,1,1,1] [5,2,2] := by - exact rowSquare_join (by decide) sg2 sg134 - -lemma sg606 : RowSquare [5,1,1,1,1] [5,3,1] := by - exact rowSquare_join (by decide) sg0 sg323 - -lemma sg607 : RowSquare [5,1,1,1,1] [5,4] := by - exact rowSquare_join (by decide) sg0 sg324 - -lemma sg608 : RowSquare [5,1,1,1,1] [6,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg135 - -lemma sg609 : RowSquare [5,1,1,1,1] [6,2,1] := by - exact rowSquare_join (by decide) sg2 sg136 - -lemma sg610 : RowSquare [5,1,1,1,1] [6,3] := by - exact rowSquare_join (by decide) sg2 sg137 - -lemma sg611 : RowSquare [5,1,1,1,1] [7,1,1] := by - exact rowSquare_join (by decide) sg7 sg51 - -lemma sg612 : RowSquare [5,1,1,1,1] [7,2] := by - exact rowSquare_join (by decide) sg7 sg52 - -lemma sg613 : RowSquare [5,2,1,1] [2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg330 - -lemma sg617 : RowSquare [5,2,1,1] [3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg178 - -lemma sg618 : RowSquare [5,2,1,1] [3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg332 - -lemma sg619 : RowSquare [5,2,1,1] [3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg66 - -lemma sg620 : RowSquare [5,2,1,1] [3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg334 - -lemma sg622 : RowSquare [5,2,1,1] [3,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg67 - -lemma sg623 : RowSquare [5,2,1,1] [3,3,3] := by - exact rowSquare_join (by decide) sg4 sg68 - -lemma sg624 : RowSquare [5,2,1,1] [4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg142 - -lemma sg625 : RowSquare [5,2,1,1] [4,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg69 - -lemma sg626 : RowSquare [5,2,1,1] [4,3,1,1] := by - exact rowSquare_join (by decide) sg5 sg67 - -lemma sg627 : RowSquare [5,2,1,1] [4,3,2] := by - exact rowSquare_join (by decide) sg4 sg70 - -lemma sg628 : RowSquare [5,2,1,1] [4,4,1] := by - exact rowSquare_join (by decide) sg4 sg71 - -lemma sg629 : RowSquare [5,2,1,1] [5,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg66 - -lemma sg630 : RowSquare [5,2,1,1] [5,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg69 - -lemma sg631 : RowSquare [5,2,1,1] [5,2,2] := by - exact rowSquare_join (by decide) sg16 sg22 - -lemma sg632 : RowSquare [5,2,1,1] [5,4] := by - exact rowSquare_join (by decide) sg17 sg23 - -lemma sg633 : RowSquare [5,2,1,1] [6,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg56 - -lemma sg634 : RowSquare [5,2,1,1] [6,2,1] := by - exact rowSquare_join (by decide) sg16 sg24 - -lemma sg635 : RowSquare [5,2,1,1] [6,3] := by - exact rowSquare_join (by decide) sg17 sg24 - -lemma sg638 : RowSquare [5,2,2] [3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg350 - -lemma sg639 : RowSquare [5,2,2] [3,3,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg32 - -lemma sg642 : RowSquare [5,2,2] [5,4] := by - exact rowSquare_join (by decide) sg10 sg36 - -lemma sg643 : RowSquare [5,3,1] [2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg74 - -lemma sg644 : RowSquare [5,3,1] [2,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg32 - -lemma sg645 : RowSquare [5,3,1] [3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg74 - -lemma sg646 : RowSquare [5,3,1] [3,3,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg32 - -lemma sg647 : RowSquare [5,3,1] [3,3,3] := by - exact rowSquare_join (by decide) sg4 sg77 - -lemma sg648 : RowSquare [5,3,1] [4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg74 - -lemma sg649 : RowSquare [5,3,1] [4,3,2] := by - exact rowSquare_join (by decide) sg16 sg27 - -lemma sg650 : RowSquare [5,3,1] [4,4,1] := by - exact rowSquare_join (by decide) sg17 sg27 - -lemma sg651 : RowSquare [5,3,1] [5,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg32 - -lemma sg652 : RowSquare [5,3,1] [5,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg37 - -lemma sg653 : RowSquare [5,3,1] [5,2,2] := by - exact rowSquare_join (by decide) sg16 sg28 - -lemma sg654 : RowSquare [5,3,1] [5,3,1] := by - exact rowSquare_join (by decide) sg16 sg29 - -lemma sg655 : RowSquare [5,3,1] [5,4] := by - exact rowSquare_join (by decide) sg17 sg29 - -lemma sg673 : RowSquare [6,1,1,1] [3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg178 - -lemma sg674 : RowSquare [6,1,1,1] [3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg371 - -lemma sg675 : RowSquare [6,1,1,1] [3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg372 - -lemma sg676 : RowSquare [6,1,1,1] [3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg373 - -lemma sg677 : RowSquare [6,1,1,1] [4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg179 - -lemma sg678 : RowSquare [6,1,1,1] [4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg180 - -lemma sg679 : RowSquare [6,1,1,1] [4,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg181 - -lemma sg680 : RowSquare [6,1,1,1] [4,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg377 - -lemma sg681 : RowSquare [6,1,1,1] [4,3,2] := by - exact rowSquare_join (by decide) sg0 sg378 - -lemma sg682 : RowSquare [6,1,1,1] [5,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg66 - -lemma sg683 : RowSquare [6,1,1,1] [5,2,1,1] := by - exact rowSquare_join (by decide) sg7 sg67 - -lemma sg684 : RowSquare [6,1,1,1] [5,2,2] := by - exact rowSquare_join (by decide) sg7 sg68 - -lemma sg685 : RowSquare [6,1,1,1] [5,3,1] := by - exact rowSquare_join (by decide) sg2 sg185 - -lemma sg686 : RowSquare [6,1,1,1] [5,4] := by - exact rowSquare_join (by decide) sg0 sg383 - -lemma sg687 : RowSquare [6,1,1,1] [6,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg69 - -lemma sg688 : RowSquare [6,1,1,1] [6,2,1] := by - exact rowSquare_join (by decide) sg7 sg70 - -lemma sg689 : RowSquare [6,1,1,1] [6,3] := by - exact rowSquare_join (by decide) sg7 sg71 - -lemma sg690 : RowSquare [6,1,1,1] [7,1,1] := by - exact rowSquare_join (by decide) sg20 sg22 - -lemma sg691 : RowSquare [6,1,1,1] [7,2] := by - exact rowSquare_join (by decide) sg20 sg23 - -lemma sg692 : RowSquare [6,2,1] [3,2,2,1,1] := by - exact rowSquare_join (by decide) sg16 sg32 - -lemma sg693 : RowSquare [6,2,1] [3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg390 - -lemma sg694 : RowSquare [6,2,1] [3,3,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg32 - -lemma sg695 : RowSquare [6,2,1] [3,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg88 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupLocalLeaves +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupLeaves1 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupLeaves2 + +namespace OAI + +/-! Semigroup Nodes 0. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg22 : RowSquare [2,1,1,1] [3,1,1] := by + exact rowSquare_join (by decide) sg2 sg4 + +lemma sg23 : RowSquare [2,1,1,1] [3,2] := by + exact rowSquare_join (by decide) sg0 sg17 + +lemma sg24 : RowSquare [2,1,1,1] [4,1] := by + exact rowSquare_join (by decide) sg2 sg5 + +lemma sg45 : RowSquare [4,1] [3,1,1] := by + exact rowSquare_join (by decide) sg2 sg4 + +lemma sg46 : RowSquare [4,1] [3,2] := by + exact rowSquare_join (by decide) sg0 sg17 + +lemma sg47 : RowSquare [4,1] [4,1] := by + exact rowSquare_join (by decide) sg2 sg5 + +lemma sg51 : RowSquare [2,1,1,1,1] [4,1,1] := by + exact rowSquare_join (by decide) sg4 sg7 + +lemma sg52 : RowSquare [2,1,1,1,1] [4,2] := by + exact rowSquare_join (by decide) sg2 sg17 + +lemma sg53 : RowSquare [2,1,1,1,1] [5,1] := by + exact rowSquare_join (by decide) sg5 sg7 + +lemma sg63 : RowSquare [2,2,2] [3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg13 + +lemma sg66 : RowSquare [3,1,1,1] [2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg32 + +lemma sg69 : RowSquare [3,1,1,1] [3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg33 + +lemma sg70 : RowSquare [3,1,1,1] [3,2,1] := by + exact rowSquare_join (by decide) sg0 sg34 + +lemma sg72 : RowSquare [3,1,1,1] [4,1,1] := by + exact rowSquare_join (by decide) sg0 sg22 + +lemma sg73 : RowSquare [3,1,1,1] [4,2] := by + exact rowSquare_join (by decide) sg0 sg23 + +lemma sg84 : RowSquare [3,3] [3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg13 + +lemma sg87 : RowSquare [4,1,1] [2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg32 + +lemma sg90 : RowSquare [4,1,1] [3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg33 + +lemma sg91 : RowSquare [4,1,1] [3,2,1] := by + exact rowSquare_join (by decide) sg0 sg34 + +lemma sg93 : RowSquare [4,1,1] [4,1,1] := by + exact rowSquare_join (by decide) sg2 sg9 + +lemma sg94 : RowSquare [4,1,1] [4,2] := by + exact rowSquare_join (by decide) sg2 sg10 + +lemma sg95 : RowSquare [4,1,1] [5,1] := by + exact rowSquare_join (by decide) sg2 sg11 + +lemma sg104 : RowSquare [5,1] [4,1,1] := by + exact rowSquare_join (by decide) sg4 sg7 + +lemma sg105 : RowSquare [5,1] [4,2] := by + exact rowSquare_join (by decide) sg2 sg17 + +lemma sg106 : RowSquare [5,1] [5,1] := by + exact rowSquare_join (by decide) sg5 sg7 + +lemma sg110 : RowSquare [2,1,1,1,1,1] [5,1,1] := by + exact rowSquare_join (by decide) sg4 sg20 + +lemma sg111 : RowSquare [2,1,1,1,1,1] [5,2] := by + exact rowSquare_join (by decide) sg7 sg17 + +lemma sg112 : RowSquare [2,1,1,1,1,1] [6,1] := by + exact rowSquare_join (by decide) sg5 sg20 + +lemma sg114 : RowSquare [2,2,1,1,1] [3,2,2] := by + exact rowSquare_join (by decide) sg4 sg16 + +lemma sg115 : RowSquare [2,2,1,1,1] [3,3,1] := by + exact rowSquare_join (by decide) sg4 sg17 + +lemma sg116 : RowSquare [2,2,1,1,1] [4,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg13 + +lemma sg117 : RowSquare [2,2,1,1,1] [4,2,1] := by + exact rowSquare_join (by decide) sg4 sg18 + +lemma sg118 : RowSquare [2,2,1,1,1] [4,3] := by + exact rowSquare_join (by decide) sg5 sg17 + +lemma sg119 : RowSquare [2,2,1,1,1] [5,1,1] := by + exact rowSquare_join (by decide) sg4 sg19 + +lemma sg120 : RowSquare [2,2,1,1,1] [5,2] := by + exact rowSquare_join (by decide) sg5 sg18 + +lemma sg121 : RowSquare [2,2,1,1,1] [6,1] := by + exact rowSquare_join (by decide) sg5 sg19 + +lemma sg132 : RowSquare [3,1,1,1,1] [3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg32 + +lemma sg133 : RowSquare [3,1,1,1,1] [3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg88 + +lemma sg134 : RowSquare [3,1,1,1,1] [3,2,2] := by + exact rowSquare_join (by decide) sg0 sg89 + +lemma sg135 : RowSquare [3,1,1,1,1] [4,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg33 + +lemma sg136 : RowSquare [3,1,1,1,1] [4,2,1] := by + exact rowSquare_join (by decide) sg2 sg34 + +lemma sg137 : RowSquare [3,1,1,1,1] [4,3] := by + exact rowSquare_join (by decide) sg0 sg92 + +lemma sg138 : RowSquare [3,1,1,1,1] [5,1,1] := by + exact rowSquare_join (by decide) sg0 sg51 + +lemma sg139 : RowSquare [3,1,1,1,1] [5,2] := by + exact rowSquare_join (by decide) sg0 sg52 + +lemma sg140 : RowSquare [3,1,1,1,1] [6,1] := by + exact rowSquare_join (by decide) sg0 sg53 + +lemma sg142 : RowSquare [3,2,1,1] [2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg74 + +lemma sg145 : RowSquare [3,2,1,1] [3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg32 + +lemma sg146 : RowSquare [3,2,1,1] [3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg76 + +lemma sg147 : RowSquare [3,2,1,1] [3,2,2] := by + exact rowSquare_join (by decide) sg0 sg55 + +lemma sg148 : RowSquare [3,2,1,1] [3,3,1] := by + exact rowSquare_join (by decide) sg4 sg10 + +lemma sg149 : RowSquare [3,2,1,1] [4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg56 + +lemma sg150 : RowSquare [3,2,1,1] [4,2,1] := by + exact rowSquare_join (by decide) sg0 sg57 + +lemma sg151 : RowSquare [3,2,1,1] [4,3] := by + exact rowSquare_join (by decide) sg5 sg10 + +lemma sg152 : RowSquare [3,2,1,1] [5,2] := by + exact rowSquare_join (by decide) sg1 sg23 + +lemma sg153 : RowSquare [3,2,1,1] [6,1] := by + exact rowSquare_join (by decide) sg5 sg8 + +lemma sg159 : RowSquare [3,2,2] [3,2,2] := by + exact rowSquare_join (by decide) sg0 sg62 + +lemma sg161 : RowSquare [3,2,2] [4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg63 + +lemma sg162 : RowSquare [3,2,2] [4,2,1] := by + exact rowSquare_join (by decide) sg1 sg27 + +lemma sg164 : RowSquare [3,2,2] [5,2] := by + exact rowSquare_join (by decide) sg3 sg10 + +lemma sg170 : RowSquare [3,3,1] [3,2,2] := by + exact rowSquare_join (by decide) sg0 sg62 + +lemma sg172 : RowSquare [3,3,1] [4,1,1,1] := by + exact rowSquare_join (by decide) sg3 sg13 + +lemma sg173 : RowSquare [3,3,1] [4,2,1] := by + exact rowSquare_join (by decide) sg1 sg27 + +lemma sg175 : RowSquare [3,3,1] [5,1,1] := by + exact rowSquare_join (by decide) sg1 sg28 + +lemma sg176 : RowSquare [3,3,1] [5,2] := by + exact rowSquare_join (by decide) sg3 sg14 + +lemma sg177 : RowSquare [3,3,1] [6,1] := by + exact rowSquare_join (by decide) sg1 sg30 + +lemma sg193 : RowSquare [4,2,1] [2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg74 + +lemma sg196 : RowSquare [4,2,1] [3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg32 + +lemma sg197 : RowSquare [4,2,1] [3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg76 + +lemma sg198 : RowSquare [4,2,1] [3,2,2] := by + exact rowSquare_join (by decide) sg4 sg9 + +lemma sg199 : RowSquare [4,2,1] [3,3,1] := by + exact rowSquare_join (by decide) sg4 sg10 + +lemma sg200 : RowSquare [4,2,1] [4,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg26 + +lemma sg201 : RowSquare [4,2,1] [4,2,1] := by + exact rowSquare_join (by decide) sg4 sg11 + +lemma sg202 : RowSquare [4,2,1] [4,3] := by + exact rowSquare_join (by decide) sg5 sg10 + +lemma sg203 : RowSquare [4,2,1] [5,1,1] := by + exact rowSquare_join (by decide) sg4 sg12 + +lemma sg204 : RowSquare [4,2,1] [5,2] := by + exact rowSquare_join (by decide) sg5 sg11 + +lemma sg205 : RowSquare [4,2,1] [6,1] := by + exact rowSquare_join (by decide) sg5 sg12 + +lemma sg218 : RowSquare [5,1,1] [3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg32 + +lemma sg219 : RowSquare [5,1,1] [3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg88 + +lemma sg220 : RowSquare [5,1,1] [3,2,2] := by + exact rowSquare_join (by decide) sg0 sg89 + +lemma sg221 : RowSquare [5,1,1] [4,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg33 + +lemma sg222 : RowSquare [5,1,1] [4,2,1] := by + exact rowSquare_join (by decide) sg2 sg34 + +lemma sg223 : RowSquare [5,1,1] [4,3] := by + exact rowSquare_join (by decide) sg0 sg92 + +lemma sg224 : RowSquare [5,1,1] [5,1,1] := by + exact rowSquare_join (by decide) sg7 sg9 + +lemma sg225 : RowSquare [5,1,1] [5,2] := by + exact rowSquare_join (by decide) sg7 sg10 + +lemma sg227 : RowSquare [5,2] [3,2,2] := by + exact rowSquare_join (by decide) sg4 sg16 + +lemma sg228 : RowSquare [5,2] [3,3,1] := by + exact rowSquare_join (by decide) sg4 sg17 + +lemma sg229 : RowSquare [5,2] [4,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg13 + +lemma sg230 : RowSquare [5,2] [4,3] := by + exact rowSquare_join (by decide) sg5 sg17 + +lemma sg231 : RowSquare [6,1] [5,1,1] := by + exact rowSquare_join (by decide) sg4 sg20 + +lemma sg232 : RowSquare [6,1] [5,2] := by + exact rowSquare_join (by decide) sg7 sg17 + +lemma sg233 : RowSquare [6,1] [6,1] := by + exact rowSquare_join (by decide) sg5 sg20 + +lemma sg236 : RowSquare [2,1,1,1,1,1,1] [6,2] := by + exact rowSquare_join (by decide) sg17 sg20 + +lemma sg237 : RowSquare [2,1,1,1,1,1,1] [7,1] := by + exact rowSquare_join (by decide) sg18 sg20 + +lemma sg239 : RowSquare [2,2,1,1,1,1] [4,2,2] := by + exact rowSquare_join (by decide) sg16 sg16 + +lemma sg240 : RowSquare [2,2,1,1,1,1] [4,3,1] := by + exact rowSquare_join (by decide) sg16 sg17 + +lemma sg241 : RowSquare [2,2,1,1,1,1] [4,4] := by + exact rowSquare_join (by decide) sg17 sg17 + +lemma sg242 : RowSquare [2,2,1,1,1,1] [5,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg20 + +lemma sg243 : RowSquare [2,2,1,1,1,1] [5,2,1] := by + exact rowSquare_join (by decide) sg16 sg18 + +lemma sg244 : RowSquare [2,2,1,1,1,1] [5,3] := by + exact rowSquare_join (by decide) sg17 sg18 + +lemma sg245 : RowSquare [2,2,1,1,1,1] [6,1,1] := by + exact rowSquare_join (by decide) sg16 sg19 + +lemma sg246 : RowSquare [2,2,1,1,1,1] [6,2] := by + exact rowSquare_join (by decide) sg17 sg19 + +lemma sg247 : RowSquare [2,2,1,1,1,1] [7,1] := by + exact rowSquare_join (by decide) sg18 sg19 + +lemma sg250 : RowSquare [2,2,2,1,1] [3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg17 + +lemma sg252 : RowSquare [2,2,2,1,1] [4,4] := by + exact rowSquare_join (by decide) sg17 sg14 + +lemma sg254 : RowSquare [2,2,2,2] [2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13 + +lemma sg255 : RowSquare [2,2,2,2] [3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14 + +lemma sg258 : RowSquare [2,2,2,2] [5,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg15 + +lemma sg260 : RowSquare [3,1,1,1,1,1] [4,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg32 + +lemma sg261 : RowSquare [3,1,1,1,1,1] [4,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg88 + +lemma sg262 : RowSquare [3,1,1,1,1,1] [4,2,2] := by + exact rowSquare_join (by decide) sg2 sg89 + +lemma sg263 : RowSquare [3,1,1,1,1,1] [5,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg33 + +lemma sg264 : RowSquare [3,1,1,1,1,1] [5,2,1] := by + exact rowSquare_join (by decide) sg7 sg34 + +lemma sg265 : RowSquare [3,1,1,1,1,1] [5,3] := by + exact rowSquare_join (by decide) sg2 sg92 + +lemma sg266 : RowSquare [3,1,1,1,1,1] [6,1,1] := by + exact rowSquare_join (by decide) sg0 sg110 + +lemma sg267 : RowSquare [3,1,1,1,1,1] [6,2] := by + exact rowSquare_join (by decide) sg0 sg111 + +lemma sg268 : RowSquare [3,1,1,1,1,1] [7,1] := by + exact rowSquare_join (by decide) sg0 sg112 + +lemma sg270 : RowSquare [3,2,1,1,1] [2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg32 + +lemma sg272 : RowSquare [3,2,1,1,1] [3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg74 + +lemma sg273 : RowSquare [3,2,1,1,1] [3,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg32 + +lemma sg274 : RowSquare [3,2,1,1,1] [3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg33 + +lemma sg276 : RowSquare [3,2,1,1,1] [3,3,2] := by + exact rowSquare_join (by decide) sg4 sg34 + +lemma sg277 : RowSquare [3,2,1,1,1] [4,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg32 + +lemma sg278 : RowSquare [3,2,1,1,1] [4,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg33 + +lemma sg279 : RowSquare [3,2,1,1,1] [4,2,2] := by + exact rowSquare_join (by decide) sg0 sg114 + +lemma sg280 : RowSquare [3,2,1,1,1] [4,3,1] := by + exact rowSquare_join (by decide) sg0 sg115 + +lemma sg281 : RowSquare [3,2,1,1,1] [4,4] := by + exact rowSquare_join (by decide) sg17 sg10 + +lemma sg282 : RowSquare [3,2,1,1,1] [5,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg116 + +lemma sg283 : RowSquare [3,2,1,1,1] [5,2,1] := by + exact rowSquare_join (by decide) sg0 sg117 + +lemma sg284 : RowSquare [3,2,1,1,1] [5,3] := by + exact rowSquare_join (by decide) sg0 sg118 + +lemma sg288 : RowSquare [3,2,2,1] [3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg74 + +lemma sg289 : RowSquare [3,2,2,1] [3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg166 + +lemma sg290 : RowSquare [3,2,2,1] [3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg123 + +lemma sg291 : RowSquare [3,2,2,1] [3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg10 + +lemma sg292 : RowSquare [3,2,2,1] [3,3,2] := by + exact rowSquare_join (by decide) sg4 sg27 + +lemma sg293 : RowSquare [3,2,2,1] [4,3,1] := by + exact rowSquare_join (by decide) sg0 sg125 + +lemma sg294 : RowSquare [3,2,2,1] [4,4] := by + exact rowSquare_join (by decide) sg14 sg10 + +lemma sg298 : RowSquare [3,3,1,1] [3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg154 + +lemma sg299 : RowSquare [3,3,1,1] [3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg155 + +lemma sg302 : RowSquare [3,3,1,1] [4,4] := by + exact rowSquare_join (by decide) sg10 sg10 + +lemma sg303 : RowSquare [3,3,1,1] [5,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg8 + +lemma sg304 : RowSquare [3,3,1,1] [5,2,1] := by + exact rowSquare_join (by decide) sg1 sg57 + +lemma sg305 : RowSquare [3,3,1,1] [5,3] := by + exact rowSquare_join (by decide) sg10 sg11 + +lemma sg307 : RowSquare [3,3,2] [2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3 sg30 + +lemma sg308 : RowSquare [3,3,2] [2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3 sg29 + +lemma sg312 : RowSquare [4,1,1,1,1] [2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg178 + +lemma sg316 : RowSquare [4,1,1,1,1] [3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg179 + +lemma sg317 : RowSquare [4,1,1,1,1] [3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg180 + +lemma sg318 : RowSquare [4,1,1,1,1] [3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg181 + +lemma sg321 : RowSquare [4,1,1,1,1] [4,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg132 + +lemma sg322 : RowSquare [4,1,1,1,1] [4,2,2] := by + exact rowSquare_join (by decide) sg0 sg134 + +lemma sg323 : RowSquare [4,1,1,1,1] [4,3,1] := by + exact rowSquare_join (by decide) sg0 sg185 + +lemma sg325 : RowSquare [4,1,1,1,1] [5,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg135 + +lemma sg326 : RowSquare [4,1,1,1,1] [5,2,1] := by + exact rowSquare_join (by decide) sg0 sg136 + +lemma sg327 : RowSquare [4,1,1,1,1] [5,3] := by + exact rowSquare_join (by decide) sg0 sg137 + +lemma sg328 : RowSquare [4,1,1,1,1] [6,1,1] := by + exact rowSquare_join (by decide) sg2 sg51 + +lemma sg329 : RowSquare [4,1,1,1,1] [6,2] := by + exact rowSquare_join (by decide) sg2 sg52 + +lemma sg351 : RowSquare [4,2,2] [3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg154 + +lemma sg354 : RowSquare [4,2,2] [4,4] := by + exact rowSquare_join (by decide) sg10 sg10 + +lemma sg355 : RowSquare [4,2,2] [5,3] := by + exact rowSquare_join (by decide) sg10 sg11 + +lemma sg359 : RowSquare [4,3,1] [3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg74 + +lemma sg360 : RowSquare [4,3,1] [3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg10 + +lemma sg361 : RowSquare [4,3,1] [3,3,2] := by + exact rowSquare_join (by decide) sg4 sg27 + +lemma sg362 : RowSquare [4,3,1] [4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg75 + +lemma sg363 : RowSquare [4,3,1] [4,4] := by + exact rowSquare_join (by decide) sg14 sg10 + +lemma sg364 : RowSquare [4,4] [2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13 + +lemma sg365 : RowSquare [4,4] [3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14 + +lemma sg368 : RowSquare [4,4] [5,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg15 + +lemma sg370 : RowSquare [5,1,1,1] [2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg178 + +lemma sg374 : RowSquare [5,1,1,1] [3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg179 + +lemma sg375 : RowSquare [5,1,1,1] [3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg180 + +lemma sg376 : RowSquare [5,1,1,1] [3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg181 + +lemma sg379 : RowSquare [5,1,1,1] [4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg66 + +lemma sg380 : RowSquare [5,1,1,1] [4,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg67 + +lemma sg381 : RowSquare [5,1,1,1] [4,2,2] := by + exact rowSquare_join (by decide) sg2 sg68 + +lemma sg382 : RowSquare [5,1,1,1] [4,3,1] := by + exact rowSquare_join (by decide) sg0 sg185 + +lemma sg384 : RowSquare [5,1,1,1] [5,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg69 + +lemma sg385 : RowSquare [5,1,1,1] [5,2,1] := by + exact rowSquare_join (by decide) sg2 sg70 + +lemma sg386 : RowSquare [5,1,1,1] [5,3] := by + exact rowSquare_join (by decide) sg2 sg71 + +lemma sg387 : RowSquare [5,1,1,1] [6,1,1] := by + exact rowSquare_join (by decide) sg7 sg22 + +lemma sg388 : RowSquare [5,1,1,1] [6,2] := by + exact rowSquare_join (by decide) sg7 sg23 + +lemma sg389 : RowSquare [5,2,1] [2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg32 + +lemma sg391 : RowSquare [5,2,1] [3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg74 + +lemma sg392 : RowSquare [5,2,1] [3,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg32 + +lemma sg393 : RowSquare [5,2,1] [3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg33 + +lemma sg395 : RowSquare [5,2,1] [3,3,2] := by + exact rowSquare_join (by decide) sg4 sg34 + +lemma sg396 : RowSquare [5,2,1] [4,4] := by + exact rowSquare_join (by decide) sg17 sg10 + +lemma sg397 : RowSquare [5,2,1] [5,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg26 + +lemma sg398 : RowSquare [5,2,1] [5,2,1] := by + exact rowSquare_join (by decide) sg16 sg11 + +lemma sg399 : RowSquare [5,2,1] [5,3] := by + exact rowSquare_join (by decide) sg17 sg11 + +lemma sg400 : RowSquare [5,2,1] [7,1] := by + exact rowSquare_join (by decide) sg18 sg12 + +lemma sg402 : RowSquare [5,3] [3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg17 + +lemma sg407 : RowSquare [5,3] [4,4] := by + exact rowSquare_join (by decide) sg17 sg14 + +lemma sg413 : RowSquare [6,1,1] [4,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg32 + +lemma sg414 : RowSquare [6,1,1] [4,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg88 + +lemma sg415 : RowSquare [6,1,1] [4,2,2] := by + exact rowSquare_join (by decide) sg2 sg89 + +lemma sg416 : RowSquare [6,1,1] [5,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg33 + +lemma sg417 : RowSquare [6,1,1] [5,2,1] := by + exact rowSquare_join (by decide) sg7 sg34 + +lemma sg418 : RowSquare [6,1,1] [5,3] := by + exact rowSquare_join (by decide) sg2 sg92 + +lemma sg419 : RowSquare [6,1,1] [6,1,1] := by + exact rowSquare_join (by decide) sg9 sg20 + +lemma sg420 : RowSquare [6,1,1] [6,2] := by + exact rowSquare_join (by decide) sg10 sg20 + +lemma sg422 : RowSquare [6,2] [4,2,2] := by + exact rowSquare_join (by decide) sg16 sg16 + +lemma sg423 : RowSquare [6,2] [4,3,1] := by + exact rowSquare_join (by decide) sg16 sg17 + +lemma sg424 : RowSquare [6,2] [4,4] := by + exact rowSquare_join (by decide) sg17 sg17 + +lemma sg425 : RowSquare [7,1] [6,2] := by + exact rowSquare_join (by decide) sg17 sg20 + +lemma sg428 : RowSquare [2,1,1,1,1,1,1,1] [7,1,1] := by + exact rowSquare_join (by decide) sg16 sg49 + +lemma sg429 : RowSquare [2,1,1,1,1,1,1,1] [7,2] := by + exact rowSquare_join (by decide) sg17 sg49 + +lemma sg430 : RowSquare [2,1,1,1,1,1,1,1] [8,1] := by + exact rowSquare_join (by decide) sg18 sg49 + +lemma sg432 : RowSquare [2,2,1,1,1,1,1] [5,2,2] := by + exact rowSquare_join (by decide) sg16 sg45 + +lemma sg433 : RowSquare [2,2,1,1,1,1,1] [5,3,1] := by + exact rowSquare_join (by decide) sg16 sg46 + +lemma sg434 : RowSquare [2,2,1,1,1,1,1] [5,4] := by + exact rowSquare_join (by decide) sg17 sg46 + +lemma sg435 : RowSquare [2,2,1,1,1,1,1] [6,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg49 + +lemma sg436 : RowSquare [2,2,1,1,1,1,1] [6,2,1] := by + exact rowSquare_join (by decide) sg16 sg47 + +lemma sg437 : RowSquare [2,2,1,1,1,1,1] [6,3] := by + exact rowSquare_join (by decide) sg17 sg47 + +lemma sg438 : RowSquare [2,2,1,1,1,1,1] [7,2] := by + exact rowSquare_join (by decide) sg17 sg48 + +lemma sg439 : RowSquare [2,2,1,1,1,1,1] [8,1] := by + exact rowSquare_join (by decide) sg18 sg48 + +lemma sg440 : RowSquare [2,2,2,1,1,1] [3,3,3] := by + exact rowSquare_join (by decide) sg4 sg97 + +lemma sg441 : RowSquare [2,2,2,1,1,1] [4,4,1] := by + exact rowSquare_join (by decide) sg17 sg40 + +lemma sg442 : RowSquare [2,2,2,1,1,1] [5,4] := by + exact rowSquare_join (by decide) sg17 sg42 + +lemma sg443 : RowSquare [2,2,2,1,1,1] [6,3] := by + exact rowSquare_join (by decide) sg17 sg43 + +lemma sg444 : RowSquare [2,2,2,1,1,1] [8,1] := by + exact rowSquare_join (by decide) sg18 sg44 + +lemma sg447 : RowSquare [3,1,1,1,1,1,1] [5,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg32 + +lemma sg448 : RowSquare [3,1,1,1,1,1,1] [5,2,1,1] := by + exact rowSquare_join (by decide) sg7 sg88 + +lemma sg449 : RowSquare [3,1,1,1,1,1,1] [5,2,2] := by + exact rowSquare_join (by decide) sg7 sg89 + +lemma sg450 : RowSquare [3,1,1,1,1,1,1] [6,2,1] := by + exact rowSquare_join (by decide) sg20 sg34 + +lemma sg451 : RowSquare [3,1,1,1,1,1,1] [6,3] := by + exact rowSquare_join (by decide) sg7 sg92 + +lemma sg452 : RowSquare [3,1,1,1,1,1,1] [7,2] := by + exact rowSquare_join (by decide) sg0 sg236 + +lemma sg453 : RowSquare [3,1,1,1,1,1,1] [8,1] := by + exact rowSquare_join (by decide) sg0 sg237 + +lemma sg455 : RowSquare [3,2,1,1,1,1] [3,2,2,1,1] := by + exact rowSquare_join (by decide) sg16 sg32 + +lemma sg456 : RowSquare [3,2,1,1,1,1] [3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg390 + +lemma sg457 : RowSquare [3,2,1,1,1,1] [3,3,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg32 + +lemma sg458 : RowSquare [3,2,1,1,1,1] [3,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg88 + +lemma sg459 : RowSquare [3,2,1,1,1,1] [3,3,3] := by + exact rowSquare_join (by decide) sg4 sg89 + +lemma sg460 : RowSquare [3,2,1,1,1,1] [4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg74 + +lemma sg461 : RowSquare [3,2,1,1,1,1] [4,2,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg32 + +lemma sg462 : RowSquare [3,2,1,1,1,1] [4,2,2,1] := by + exact rowSquare_join (by decide) sg16 sg33 + +lemma sg463 : RowSquare [3,2,1,1,1,1] [4,3,1,1] := by + exact rowSquare_join (by decide) sg17 sg33 + +lemma sg464 : RowSquare [3,2,1,1,1,1] [4,3,2] := by + exact rowSquare_join (by decide) sg16 sg34 + +lemma sg465 : RowSquare [3,2,1,1,1,1] [4,4,1] := by + exact rowSquare_join (by decide) sg17 sg34 + +lemma sg466 : RowSquare [3,2,1,1,1,1] [5,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg32 + +lemma sg467 : RowSquare [3,2,1,1,1,1] [5,2,1,1] := by + exact rowSquare_join (by decide) sg18 sg33 + +lemma sg468 : RowSquare [3,2,1,1,1,1] [5,2,2] := by + exact rowSquare_join (by decide) sg0 sg239 + +lemma sg469 : RowSquare [3,2,1,1,1,1] [5,3,1] := by + exact rowSquare_join (by decide) sg0 sg240 + +lemma sg470 : RowSquare [3,2,1,1,1,1] [5,4] := by + exact rowSquare_join (by decide) sg0 sg241 + +lemma sg471 : RowSquare [3,2,1,1,1,1] [6,3] := by + exact rowSquare_join (by decide) sg0 sg244 + +lemma sg472 : RowSquare [3,2,1,1,1,1] [7,2] := by + exact rowSquare_join (by decide) sg1 sg111 + +lemma sg473 : RowSquare [3,2,1,1,1,1] [8,1] := by + exact rowSquare_join (by decide) sg5 sg50 + +lemma sg475 : RowSquare [3,2,2,1,1] [2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg74 + +lemma sg476 : RowSquare [3,2,2,1,1] [2,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg32 + +lemma sg477 : RowSquare [3,2,2,1,1] [3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg33 + +lemma sg478 : RowSquare [3,2,2,1,1] [3,3,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg32 + +lemma sg479 : RowSquare [3,2,2,1,1] [3,3,3] := by + exact rowSquare_join (by decide) sg4 sg77 + +lemma sg485 : RowSquare [3,2,2,2] [4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg165 + +lemma sg486 : RowSquare [3,2,2,2] [4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg166 + +lemma sg488 : RowSquare [3,2,2,2] [4,4,1] := by + exact rowSquare_join (by decide) sg14 sg27 + +lemma sg491 : RowSquare [3,3,1,1,1] [3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg348 + +lemma sg492 : RowSquare [3,3,1,1,1] [3,2,2,1,1] := by + exact rowSquare_join (by decide) sg9 sg32 + +lemma sg493 : RowSquare [3,3,1,1,1] [3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg350 + +lemma sg494 : RowSquare [3,3,1,1,1] [3,3,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg32 + +lemma sg497 : RowSquare [3,3,1,1,1] [4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg154 + +lemma sg498 : RowSquare [3,3,1,1,1] [4,2,2,1] := by + exact rowSquare_join (by decide) sg9 sg33 + +lemma sg499 : RowSquare [3,3,1,1,1] [4,3,2] := by + exact rowSquare_join (by decide) sg9 sg34 + +lemma sg500 : RowSquare [3,3,1,1,1] [4,4,1] := by + exact rowSquare_join (by decide) sg10 sg34 + +lemma sg501 : RowSquare [3,3,1,1,1] [5,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg32 + +lemma sg502 : RowSquare [3,3,1,1,1] [5,2,2] := by + exact rowSquare_join (by decide) sg1 sg114 + +lemma sg503 : RowSquare [3,3,1,1,1] [5,4] := by + exact rowSquare_join (by decide) sg10 sg36 + +lemma sg504 : RowSquare [3,3,1,1,1] [6,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg21 + +lemma sg505 : RowSquare [3,3,1,1,1] [6,2,1] := by + exact rowSquare_join (by decide) sg1 sg117 + +lemma sg506 : RowSquare [3,3,1,1,1] [6,3] := by + exact rowSquare_join (by decide) sg1 sg118 + +lemma sg507 : RowSquare [3,3,1,1,1] [7,2] := by + exact rowSquare_join (by decide) sg14 sg21 + +lemma sg508 : RowSquare [3,3,1,1,1] [8,1] := by + exact rowSquare_join (by decide) sg1 sg121 + +lemma sg510 : RowSquare [3,3,2,1] [2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg306 + +lemma sg512 : RowSquare [3,3,2,1] [3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg307 + +lemma sg514 : RowSquare [3,3,2,1] [3,3,3] := by + exact rowSquare_join (by decide) sg4 sg62 + +lemma sg515 : RowSquare [3,3,2,1] [4,4,1] := by + exact rowSquare_join (by decide) sg10 sg27 + +lemma sg517 : RowSquare [4,1,1,1,1,1] [3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg178 + +lemma sg518 : RowSquare [4,1,1,1,1,1] [3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg371 + +lemma sg519 : RowSquare [4,1,1,1,1,1] [3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg372 + +lemma sg520 : RowSquare [4,1,1,1,1,1] [3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg373 + +lemma sg521 : RowSquare [4,1,1,1,1,1] [4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg179 + +lemma sg522 : RowSquare [4,1,1,1,1,1] [4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg180 + +lemma sg523 : RowSquare [4,1,1,1,1,1] [4,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg181 + +lemma sg524 : RowSquare [4,1,1,1,1,1] [4,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg377 + +lemma sg525 : RowSquare [4,1,1,1,1,1] [4,3,2] := by + exact rowSquare_join (by decide) sg0 sg378 + +lemma sg526 : RowSquare [4,1,1,1,1,1] [5,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg260 + +lemma sg527 : RowSquare [4,1,1,1,1,1] [5,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg261 + +lemma sg528 : RowSquare [4,1,1,1,1,1] [5,2,2] := by + exact rowSquare_join (by decide) sg0 sg262 + +lemma sg529 : RowSquare [4,1,1,1,1,1] [5,3,1] := by + exact rowSquare_join (by decide) sg2 sg185 + +lemma sg530 : RowSquare [4,1,1,1,1,1] [5,4] := by + exact rowSquare_join (by decide) sg0 sg383 + +lemma sg531 : RowSquare [4,1,1,1,1,1] [6,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg263 + +lemma sg532 : RowSquare [4,1,1,1,1,1] [6,2,1] := by + exact rowSquare_join (by decide) sg0 sg264 + +lemma sg533 : RowSquare [4,1,1,1,1,1] [6,3] := by + exact rowSquare_join (by decide) sg0 sg265 + +lemma sg534 : RowSquare [4,2,1,1,1] [2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg330 + +lemma sg538 : RowSquare [4,2,1,1,1] [3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg178 + +lemma sg539 : RowSquare [4,2,1,1,1] [3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg332 + +lemma sg540 : RowSquare [4,2,1,1,1] [3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg271 + +lemma sg542 : RowSquare [4,2,1,1,1] [3,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg67 + +lemma sg543 : RowSquare [4,2,1,1,1] [3,3,3] := by + exact rowSquare_join (by decide) sg4 sg68 + +lemma sg544 : RowSquare [4,2,1,1,1] [4,4,1] := by + exact rowSquare_join (by decide) sg4 sg71 + +lemma sg545 : RowSquare [4,2,1,1,1] [6,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg116 + +lemma sg546 : RowSquare [4,2,1,1,1] [6,2,1] := by + exact rowSquare_join (by decide) sg4 sg53 + +lemma sg547 : RowSquare [4,2,1,1,1] [6,3] := by + exact rowSquare_join (by decide) sg5 sg52 + +lemma sg554 : RowSquare [4,2,2,1] [3,3,3] := by + exact rowSquare_join (by decide) sg4 sg55 + +lemma sg555 : RowSquare [4,2,2,1] [4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg288 + +lemma sg556 : RowSquare [4,2,2,1] [4,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg123 + +lemma sg557 : RowSquare [4,2,2,1] [4,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg291 + +lemma sg558 : RowSquare [4,2,2,1] [4,3,2] := by + exact rowSquare_join (by decide) sg0 sg292 + +lemma sg560 : RowSquare [4,2,2,1] [5,4] := by + exact rowSquare_join (by decide) sg10 sg23 + +lemma sg566 : RowSquare [4,3,1,1] [3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg295 + +lemma sg567 : RowSquare [4,3,1,1] [3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg296 + +lemma sg568 : RowSquare [4,3,1,1] [3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg297 + +lemma sg571 : RowSquare [4,3,1,1] [3,3,3] := by + exact rowSquare_join (by decide) sg4 sg55 + +lemma sg572 : RowSquare [4,3,1,1] [4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg142 + +lemma sg573 : RowSquare [4,3,1,1] [4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg23 + +lemma sg574 : RowSquare [4,3,1,1] [4,3,2] := by + exact rowSquare_join (by decide) sg4 sg57 + +lemma sg576 : RowSquare [4,3,2] [2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg306 + +lemma sg585 : RowSquare [4,4,1] [4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg165 + +lemma sg587 : RowSquare [5,1,1,1,1] [2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg53 + +lemma sg588 : RowSquare [5,1,1,1,1] [2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg52 + +lemma sg589 : RowSquare [5,1,1,1,1] [2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg137 + +lemma sg590 : RowSquare [5,1,1,1,1] [2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg324 + +lemma sg591 : RowSquare [5,1,1,1,1] [3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg312 + +lemma sg592 : RowSquare [5,1,1,1,1] [3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg313 + +lemma sg593 : RowSquare [5,1,1,1,1] [3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg314 + +lemma sg594 : RowSquare [5,1,1,1,1] [3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg315 + +lemma sg595 : RowSquare [5,1,1,1,1] [3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg134 + +lemma sg596 : RowSquare [5,1,1,1,1] [3,3,2,1] := by + exact rowSquare_join (by decide) sg0 sg320 + +lemma sg597 : RowSquare [5,1,1,1,1] [4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg316 + +lemma sg598 : RowSquare [5,1,1,1,1] [4,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg317 + +lemma sg599 : RowSquare [5,1,1,1,1] [4,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg318 + +lemma sg600 : RowSquare [5,1,1,1,1] [4,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg319 + +lemma sg601 : RowSquare [5,1,1,1,1] [4,3,2] := by + exact rowSquare_join (by decide) sg0 sg320 + +lemma sg602 : RowSquare [5,1,1,1,1] [4,4,1] := by + exact rowSquare_join (by decide) sg0 sg315 + +lemma sg603 : RowSquare [5,1,1,1,1] [5,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg132 + +lemma sg604 : RowSquare [5,1,1,1,1] [5,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg133 + +lemma sg605 : RowSquare [5,1,1,1,1] [5,2,2] := by + exact rowSquare_join (by decide) sg2 sg134 + +lemma sg606 : RowSquare [5,1,1,1,1] [5,3,1] := by + exact rowSquare_join (by decide) sg0 sg323 + +lemma sg607 : RowSquare [5,1,1,1,1] [5,4] := by + exact rowSquare_join (by decide) sg0 sg324 + +lemma sg608 : RowSquare [5,1,1,1,1] [6,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg135 + +lemma sg609 : RowSquare [5,1,1,1,1] [6,2,1] := by + exact rowSquare_join (by decide) sg2 sg136 + +lemma sg610 : RowSquare [5,1,1,1,1] [6,3] := by + exact rowSquare_join (by decide) sg2 sg137 + +lemma sg611 : RowSquare [5,1,1,1,1] [7,1,1] := by + exact rowSquare_join (by decide) sg7 sg51 + +lemma sg612 : RowSquare [5,1,1,1,1] [7,2] := by + exact rowSquare_join (by decide) sg7 sg52 + +lemma sg613 : RowSquare [5,2,1,1] [2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg330 + +lemma sg617 : RowSquare [5,2,1,1] [3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg178 + +lemma sg618 : RowSquare [5,2,1,1] [3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg332 + +lemma sg619 : RowSquare [5,2,1,1] [3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg66 + +lemma sg620 : RowSquare [5,2,1,1] [3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg334 + +lemma sg622 : RowSquare [5,2,1,1] [3,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg67 + +lemma sg623 : RowSquare [5,2,1,1] [3,3,3] := by + exact rowSquare_join (by decide) sg4 sg68 + +lemma sg624 : RowSquare [5,2,1,1] [4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg142 + +lemma sg625 : RowSquare [5,2,1,1] [4,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg69 + +lemma sg626 : RowSquare [5,2,1,1] [4,3,1,1] := by + exact rowSquare_join (by decide) sg5 sg67 + +lemma sg627 : RowSquare [5,2,1,1] [4,3,2] := by + exact rowSquare_join (by decide) sg4 sg70 + +lemma sg628 : RowSquare [5,2,1,1] [4,4,1] := by + exact rowSquare_join (by decide) sg4 sg71 + +lemma sg629 : RowSquare [5,2,1,1] [5,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg66 + +lemma sg630 : RowSquare [5,2,1,1] [5,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg69 + +lemma sg631 : RowSquare [5,2,1,1] [5,2,2] := by + exact rowSquare_join (by decide) sg16 sg22 + +lemma sg632 : RowSquare [5,2,1,1] [5,4] := by + exact rowSquare_join (by decide) sg17 sg23 + +lemma sg633 : RowSquare [5,2,1,1] [6,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg56 + +lemma sg634 : RowSquare [5,2,1,1] [6,2,1] := by + exact rowSquare_join (by decide) sg16 sg24 + +lemma sg635 : RowSquare [5,2,1,1] [6,3] := by + exact rowSquare_join (by decide) sg17 sg24 + +lemma sg638 : RowSquare [5,2,2] [3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg350 + +lemma sg639 : RowSquare [5,2,2] [3,3,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg32 + +lemma sg642 : RowSquare [5,2,2] [5,4] := by + exact rowSquare_join (by decide) sg10 sg36 + +lemma sg643 : RowSquare [5,3,1] [2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg74 + +lemma sg644 : RowSquare [5,3,1] [2,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg32 + +lemma sg645 : RowSquare [5,3,1] [3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg74 + +lemma sg646 : RowSquare [5,3,1] [3,3,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg32 + +lemma sg647 : RowSquare [5,3,1] [3,3,3] := by + exact rowSquare_join (by decide) sg4 sg77 + +lemma sg648 : RowSquare [5,3,1] [4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg74 + +lemma sg649 : RowSquare [5,3,1] [4,3,2] := by + exact rowSquare_join (by decide) sg16 sg27 + +lemma sg650 : RowSquare [5,3,1] [4,4,1] := by + exact rowSquare_join (by decide) sg17 sg27 + +lemma sg651 : RowSquare [5,3,1] [5,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg32 + +lemma sg652 : RowSquare [5,3,1] [5,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg37 + +lemma sg653 : RowSquare [5,3,1] [5,2,2] := by + exact rowSquare_join (by decide) sg16 sg28 + +lemma sg654 : RowSquare [5,3,1] [5,3,1] := by + exact rowSquare_join (by decide) sg16 sg29 + +lemma sg655 : RowSquare [5,3,1] [5,4] := by + exact rowSquare_join (by decide) sg17 sg29 + +lemma sg673 : RowSquare [6,1,1,1] [3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg178 + +lemma sg674 : RowSquare [6,1,1,1] [3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg371 + +lemma sg675 : RowSquare [6,1,1,1] [3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg372 + +lemma sg676 : RowSquare [6,1,1,1] [3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg373 + +lemma sg677 : RowSquare [6,1,1,1] [4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg179 + +lemma sg678 : RowSquare [6,1,1,1] [4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg180 + +lemma sg679 : RowSquare [6,1,1,1] [4,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg181 + +lemma sg680 : RowSquare [6,1,1,1] [4,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg377 + +lemma sg681 : RowSquare [6,1,1,1] [4,3,2] := by + exact rowSquare_join (by decide) sg0 sg378 + +lemma sg682 : RowSquare [6,1,1,1] [5,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg66 + +lemma sg683 : RowSquare [6,1,1,1] [5,2,1,1] := by + exact rowSquare_join (by decide) sg7 sg67 + +lemma sg684 : RowSquare [6,1,1,1] [5,2,2] := by + exact rowSquare_join (by decide) sg7 sg68 + +lemma sg685 : RowSquare [6,1,1,1] [5,3,1] := by + exact rowSquare_join (by decide) sg2 sg185 + +lemma sg686 : RowSquare [6,1,1,1] [5,4] := by + exact rowSquare_join (by decide) sg0 sg383 + +lemma sg687 : RowSquare [6,1,1,1] [6,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg69 + +lemma sg688 : RowSquare [6,1,1,1] [6,2,1] := by + exact rowSquare_join (by decide) sg7 sg70 + +lemma sg689 : RowSquare [6,1,1,1] [6,3] := by + exact rowSquare_join (by decide) sg7 sg71 + +lemma sg690 : RowSquare [6,1,1,1] [7,1,1] := by + exact rowSquare_join (by decide) sg20 sg22 + +lemma sg691 : RowSquare [6,1,1,1] [7,2] := by + exact rowSquare_join (by decide) sg20 sg23 + +lemma sg692 : RowSquare [6,2,1] [3,2,2,1,1] := by + exact rowSquare_join (by decide) sg16 sg32 + +lemma sg693 : RowSquare [6,2,1] [3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg390 + +lemma sg694 : RowSquare [6,2,1] [3,3,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg32 + +lemma sg695 : RowSquare [6,2,1] [3,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg88 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes1.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes1.lean index 9a3ef3806e4917eac9a0000c28d089530f45cbd9..808714d88788604166607c20c48e116ded23cff0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes1.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes1.lean @@ -1,1222 +1,1222 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupLeaves3 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupLeaves4 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupLeaves5 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes0 - -namespace OAI - -/-! Semigroup Nodes 1. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg696 : RowSquare [6,2,1] [3,3,3] := by - exact rowSquare_join (by decide) sg4 sg89 - -lemma sg697 : RowSquare [6,2,1] [4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg74 - -lemma sg698 : RowSquare [6,2,1] [4,2,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg32 - -lemma sg699 : RowSquare [6,2,1] [4,3,1,1] := by - exact rowSquare_join (by decide) sg17 sg33 - -lemma sg700 : RowSquare [6,2,1] [4,3,2] := by - exact rowSquare_join (by decide) sg16 sg34 - -lemma sg701 : RowSquare [6,2,1] [4,4,1] := by - exact rowSquare_join (by decide) sg17 sg34 - -lemma sg702 : RowSquare [6,2,1] [5,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg32 - -lemma sg703 : RowSquare [6,2,1] [5,4] := by - exact rowSquare_join (by decide) sg17 sg36 - -lemma sg704 : RowSquare [6,2,1] [6,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg26 - -lemma sg705 : RowSquare [6,2,1] [8,1] := by - exact rowSquare_join (by decide) sg18 sg38 - -lemma sg706 : RowSquare [6,3] [3,3,3] := by - exact rowSquare_join (by decide) sg4 sg97 - -lemma sg707 : RowSquare [6,3] [4,4,1] := by - exact rowSquare_join (by decide) sg17 sg40 - -lemma sg708 : RowSquare [7,1,1] [5,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg32 - -lemma sg709 : RowSquare [7,1,1] [5,2,1,1] := by - exact rowSquare_join (by decide) sg7 sg88 - -lemma sg710 : RowSquare [7,1,1] [5,2,2] := by - exact rowSquare_join (by decide) sg7 sg89 - -lemma sg711 : RowSquare [7,1,1] [6,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg33 - -lemma sg712 : RowSquare [7,1,1] [6,2,1] := by - exact rowSquare_join (by decide) sg20 sg34 - -lemma sg713 : RowSquare [7,1,1] [6,3] := by - exact rowSquare_join (by decide) sg7 sg92 - -lemma sg714 : RowSquare [7,2] [5,3,1] := by - exact rowSquare_join (by decide) sg16 sg46 - -lemma sg715 : RowSquare [7,2] [5,4] := by - exact rowSquare_join (by decide) sg17 sg46 - -lemma sg716 : RowSquare [8,1] [7,1,1] := by - exact rowSquare_join (by decide) sg16 sg49 - -lemma sg717 : RowSquare [8,1] [7,2] := by - exact rowSquare_join (by decide) sg17 sg49 - -lemma sg719 : RowSquare [2,1,1,1,1,1,1,1,1] [8,2] := by - exact rowSquare_join (by decide) sg46 sg49 - -lemma sg721 : RowSquare [2,2,1,1,1,1,1,1] [6,2,2] := by - exact rowSquare_join (by decide) sg45 sg45 - -lemma sg722 : RowSquare [2,2,1,1,1,1,1,1] [6,4] := by - exact rowSquare_join (by decide) sg46 sg46 - -lemma sg723 : RowSquare [2,2,1,1,1,1,1,1] [7,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg49 - -lemma sg724 : RowSquare [2,2,1,1,1,1,1,1] [7,3] := by - exact rowSquare_join (by decide) sg46 sg47 - -lemma sg725 : RowSquare [2,2,1,1,1,1,1,1] [8,2] := by - exact rowSquare_join (by decide) sg46 sg48 - -lemma sg726 : RowSquare [2,2,1,1,1,1,1,1] [9,1] := by - exact rowSquare_join (by decide) sg47 sg48 - -lemma sg727 : RowSquare [2,2,2,1,1,1,1] [6,4] := by - exact rowSquare_join (by decide) sg46 sg42 - -lemma sg728 : RowSquare [2,2,2,1,1,1,1] [7,3] := by - exact rowSquare_join (by decide) sg46 sg43 - -lemma sg729 : RowSquare [2,2,2,1,1,1,1] [8,2] := by - exact rowSquare_join (by decide) sg46 sg44 - -lemma sg731 : RowSquare [3,1,1,1,1,1,1,1] [6,2,2] := by - exact rowSquare_join (by decide) sg20 sg89 - -lemma sg732 : RowSquare [3,1,1,1,1,1,1,1] [7,2,1] := by - exact rowSquare_join (by decide) sg34 sg49 - -lemma sg733 : RowSquare [3,1,1,1,1,1,1,1] [7,3] := by - exact rowSquare_join (by decide) sg20 sg92 - -lemma sg734 : RowSquare [3,1,1,1,1,1,1,1] [8,2] := by - exact rowSquare_join (by decide) sg0 sg429 - -lemma sg735 : RowSquare [3,2,1,1,1,1,1] [4,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg45 - -lemma sg736 : RowSquare [3,2,1,1,1,1,1] [4,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg390 - -lemma sg737 : RowSquare [3,2,1,1,1,1,1] [4,3,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg46 - -lemma sg738 : RowSquare [3,2,1,1,1,1,1] [4,3,2,1] := by - exact rowSquare_join (by decide) sg16 sg88 - -lemma sg739 : RowSquare [3,2,1,1,1,1,1] [4,3,3] := by - exact rowSquare_join (by decide) sg16 sg89 - -lemma sg740 : RowSquare [3,2,1,1,1,1,1] [4,4,1,1] := by - exact rowSquare_join (by decide) sg17 sg88 - -lemma sg741 : RowSquare [3,2,1,1,1,1,1] [4,4,2] := by - exact rowSquare_join (by decide) sg17 sg89 - -lemma sg742 : RowSquare [3,2,1,1,1,1,1] [5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg74 - -lemma sg743 : RowSquare [3,2,1,1,1,1,1] [5,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg47 - -lemma sg744 : RowSquare [3,2,1,1,1,1,1] [5,2,2,1] := by - exact rowSquare_join (by decide) sg33 sg45 - -lemma sg745 : RowSquare [3,2,1,1,1,1,1] [5,3,1,1] := by - exact rowSquare_join (by decide) sg33 sg46 - -lemma sg746 : RowSquare [3,2,1,1,1,1,1] [5,3,2] := by - exact rowSquare_join (by decide) sg34 sg45 - -lemma sg747 : RowSquare [3,2,1,1,1,1,1] [5,4,1] := by - exact rowSquare_join (by decide) sg34 sg46 - -lemma sg748 : RowSquare [3,2,1,1,1,1,1] [5,5] := by - exact rowSquare_join (by decide) sg17 sg92 - -lemma sg749 : RowSquare [3,2,1,1,1,1,1] [6,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg48 - -lemma sg750 : RowSquare [3,2,1,1,1,1,1] [6,2,1,1] := by - exact rowSquare_join (by decide) sg33 sg47 - -lemma sg751 : RowSquare [3,2,2,1,1,1] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg39 - -lemma sg752 : RowSquare [3,2,2,1,1,1] [3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg74 - -lemma sg753 : RowSquare [3,2,2,1,1,1] [3,3,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg40 - -lemma sg754 : RowSquare [3,2,2,1,1,1] [3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg88 - -lemma sg755 : RowSquare [3,2,2,1,1,1] [3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg89 - -lemma sg756 : RowSquare [3,2,2,1,1,1] [4,3,3] := by - exact rowSquare_join (by decide) sg0 sg440 - -lemma sg758 : RowSquare [3,2,2,2,1] [2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg74 - -lemma sg760 : RowSquare [3,2,2,2,1] [3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg74 - -lemma sg761 : RowSquare [3,2,2,2,1] [5,5] := by - exact rowSquare_join (by decide) sg14 sg80 - -lemma sg762 : RowSquare [3,3,1,1,1,1] [2,2,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg32 - -lemma sg763 : RowSquare [3,3,1,1,1,1] [3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg636 - -lemma sg764 : RowSquare [3,3,1,1,1,1] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg33 - -lemma sg766 : RowSquare [3,3,1,1,1,1] [3,3,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg34 - -lemma sg769 : RowSquare [3,3,1,1,1,1] [4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg348 - -lemma sg770 : RowSquare [3,3,1,1,1,1] [4,2,2,2] := by - exact rowSquare_join (by decide) sg33 sg33 - -lemma sg771 : RowSquare [3,3,1,1,1,1] [4,3,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg36 - -lemma sg772 : RowSquare [3,3,1,1,1,1] [4,3,2,1] := by - exact rowSquare_join (by decide) sg33 sg34 - -lemma sg773 : RowSquare [3,3,1,1,1,1] [4,3,3] := by - exact rowSquare_join (by decide) sg9 sg89 - -lemma sg774 : RowSquare [3,3,1,1,1,1] [4,4,1,1] := by - exact rowSquare_join (by decide) sg10 sg88 - -lemma sg775 : RowSquare [3,3,1,1,1,1] [4,4,2] := by - exact rowSquare_join (by decide) sg34 sg34 - -lemma sg776 : RowSquare [3,3,1,1,1,1] [5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg154 - -lemma sg777 : RowSquare [3,3,1,1,1,1] [5,2,2,1] := by - exact rowSquare_join (by decide) sg33 sg35 - -lemma sg778 : RowSquare [3,3,1,1,1,1] [5,3,2] := by - exact rowSquare_join (by decide) sg34 sg35 - -lemma sg779 : RowSquare [3,3,1,1,1,1] [5,4,1] := by - exact rowSquare_join (by decide) sg34 sg36 - -lemma sg780 : RowSquare [3,3,1,1,1,1] [5,5] := by - exact rowSquare_join (by decide) sg10 sg92 - -lemma sg781 : RowSquare [3,3,1,1,1,1] [6,2,2] := by - exact rowSquare_join (by decide) sg1 sg239 - -lemma sg782 : RowSquare [3,3,1,1,1,1] [6,4] := by - exact rowSquare_join (by decide) sg1 sg241 - -lemma sg783 : RowSquare [3,3,1,1,1,1] [7,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg50 - -lemma sg784 : RowSquare [3,3,1,1,1,1] [7,2,1] := by - exact rowSquare_join (by decide) sg1 sg243 - -lemma sg785 : RowSquare [3,3,1,1,1,1] [7,3] := by - exact rowSquare_join (by decide) sg1 sg244 - -lemma sg786 : RowSquare [3,3,1,1,1,1] [8,1,1] := by - exact rowSquare_join (by decide) sg1 sg245 - -lemma sg787 : RowSquare [3,3,1,1,1,1] [8,2] := by - exact rowSquare_join (by decide) sg14 sg50 - -lemma sg788 : RowSquare [3,3,1,1,1,1] [9,1] := by - exact rowSquare_join (by decide) sg1 sg247 - -lemma sg793 : RowSquare [3,3,2,1,1] [3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg306 - -lemma sg794 : RowSquare [3,3,2,1,1] [3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg74 - -lemma sg795 : RowSquare [3,3,2,1,1] [3,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg156 - -lemma sg797 : RowSquare [3,3,2,2] [3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg306 - -lemma sg798 : RowSquare [3,3,3,1] [2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg516 - -lemma sg799 : RowSquare [4,1,1,1,1,1,1] [4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg178 - -lemma sg800 : RowSquare [4,1,1,1,1,1,1] [4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg371 - -lemma sg801 : RowSquare [4,1,1,1,1,1,1] [4,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg373 - -lemma sg802 : RowSquare [4,1,1,1,1,1,1] [5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg179 - -lemma sg803 : RowSquare [4,1,1,1,1,1,1] [5,2,2,1] := by - exact rowSquare_join (by decide) sg7 sg181 - -lemma sg804 : RowSquare [4,1,1,1,1,1,1] [5,3,2] := by - exact rowSquare_join (by decide) sg2 sg378 - -lemma sg805 : RowSquare [4,1,1,1,1,1,1] [6,3,1] := by - exact rowSquare_join (by decide) sg7 sg185 - -lemma sg806 : RowSquare [4,1,1,1,1,1,1] [6,4] := by - exact rowSquare_join (by decide) sg2 sg383 - -lemma sg807 : RowSquare [4,2,1,1,1,1] [2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg178 - -lemma sg810 : RowSquare [4,2,1,1,1,1] [3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg330 - -lemma sg811 : RowSquare [4,2,1,1,1,1] [3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg178 - -lemma sg812 : RowSquare [4,2,1,1,1,1] [3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg179 - -lemma sg813 : RowSquare [4,2,1,1,1,1] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg616 - -lemma sg815 : RowSquare [4,2,1,1,1,1] [3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg180 - -lemma sg817 : RowSquare [4,2,1,1,1,1] [3,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg181 - -lemma sg818 : RowSquare [4,2,1,1,1,1] [4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg178 - -lemma sg819 : RowSquare [4,2,1,1,1,1] [4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg179 - -lemma sg820 : RowSquare [4,2,1,1,1,1] [4,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg456 - -lemma sg821 : RowSquare [4,2,1,1,1,1] [4,3,3] := by - exact rowSquare_join (by decide) sg0 sg459 - -lemma sg822 : RowSquare [4,2,1,1,1,1] [4,4,1,1] := by - exact rowSquare_join (by decide) sg17 sg67 - -lemma sg823 : RowSquare [4,2,1,1,1,1] [4,4,2] := by - exact rowSquare_join (by decide) sg17 sg68 - -lemma sg824 : RowSquare [4,2,1,1,1,1] [5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg460 - -lemma sg825 : RowSquare [4,2,1,1,1,1] [5,5] := by - exact rowSquare_join (by decide) sg17 sg71 - -lemma sg830 : RowSquare [4,2,2,1,1] [3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg330 - -lemma sg831 : RowSquare [4,2,2,1,1] [3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg68 - -lemma sg842 : RowSquare [4,3,1,1,1] [3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg548 - -lemma sg843 : RowSquare [4,3,1,1,1] [3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg549 - -lemma sg844 : RowSquare [4,3,1,1,1] [3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg489 - -lemma sg845 : RowSquare [4,3,1,1,1] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg490 - -lemma sg848 : RowSquare [4,3,1,1,1] [4,3,3] := by - exact rowSquare_join (by decide) sg4 sg114 - -lemma sg872 : RowSquare [4,3,3] [2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg516 - -lemma sg882 : RowSquare [4,4,1,1] [3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg480 - -lemma sg883 : RowSquare [4,4,1,1] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg481 - -lemma sg888 : RowSquare [5,1,1,1,1,1] [2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg586 - -lemma sg893 : RowSquare [5,1,1,1,1,1] [3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg587 - -lemma sg894 : RowSquare [5,1,1,1,1,1] [3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg588 - -lemma sg895 : RowSquare [5,1,1,1,1,1] [3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg589 - -lemma sg896 : RowSquare [5,1,1,1,1,1] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg590 - -lemma sg900 : RowSquare [5,1,1,1,1,1] [4,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg595 - -lemma sg901 : RowSquare [5,1,1,1,1,1] [4,3,2,1] := by - exact rowSquare_join (by decide) sg0 sg596 - -lemma sg904 : RowSquare [5,1,1,1,1,1] [5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg521 - -lemma sg905 : RowSquare [5,1,1,1,1,1] [5,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg523 - -lemma sg906 : RowSquare [5,1,1,1,1,1] [5,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg524 - -lemma sg907 : RowSquare [5,1,1,1,1,1] [5,3,2] := by - exact rowSquare_join (by decide) sg0 sg525 - -lemma sg908 : RowSquare [5,1,1,1,1,1] [5,4,1] := by - exact rowSquare_join (by decide) sg0 sg602 - -lemma sg911 : RowSquare [5,2,1,1,1] [2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg47 sg21 - -lemma sg912 : RowSquare [5,2,1,1,1] [2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg21 - -lemma sg913 : RowSquare [5,2,1,1,1] [2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg53 - -lemma sg914 : RowSquare [5,2,1,1,1] [2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg52 - -lemma sg916 : RowSquare [5,2,1,1,1] [3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg534 - -lemma sg917 : RowSquare [5,2,1,1,1] [3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg535 - -lemma sg918 : RowSquare [5,2,1,1,1] [3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg536 - -lemma sg919 : RowSquare [5,2,1,1,1] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg537 - -lemma sg920 : RowSquare [5,2,1,1,1] [3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg51 - -lemma sg921 : RowSquare [5,2,1,1,1] [3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg136 - -lemma sg923 : RowSquare [5,2,1,1,1] [3,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg134 - -lemma sg924 : RowSquare [5,2,1,1,1] [4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg312 - -lemma sg925 : RowSquare [5,2,1,1,1] [4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg313 - -lemma sg926 : RowSquare [5,2,1,1,1] [4,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg132 - -lemma sg927 : RowSquare [5,2,1,1,1] [4,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg271 - -lemma sg928 : RowSquare [5,2,1,1,1] [4,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg541 - -lemma sg929 : RowSquare [5,2,1,1,1] [4,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg133 - -lemma sg930 : RowSquare [5,2,1,1,1] [4,3,3] := by - exact rowSquare_join (by decide) sg4 sg134 - -lemma sg931 : RowSquare [5,2,1,1,1] [4,4,1,1] := by - exact rowSquare_join (by decide) sg2 sg271 - -lemma sg933 : RowSquare [5,2,1,1,1] [5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg272 - -lemma sg934 : RowSquare [5,2,1,1,1] [5,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg132 - -lemma sg935 : RowSquare [5,2,1,1,1] [5,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg135 - -lemma sg936 : RowSquare [5,2,1,1,1] [5,3,1,1] := by - exact rowSquare_join (by decide) sg5 sg133 - -lemma sg937 : RowSquare [5,2,1,1,1] [5,3,2] := by - exact rowSquare_join (by decide) sg4 sg136 - -lemma sg938 : RowSquare [5,2,1,1,1] [5,4,1] := by - exact rowSquare_join (by decide) sg4 sg137 - -lemma sg944 : RowSquare [5,2,2,1] [3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg548 - -lemma sg945 : RowSquare [5,2,2,1] [3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg549 - -lemma sg946 : RowSquare [5,2,2,1] [3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg550 - -lemma sg947 : RowSquare [5,2,2,1] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg551 - -lemma sg952 : RowSquare [5,2,2,1] [4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3 sg178 - -lemma sg953 : RowSquare [5,2,2,1] [4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg285 - -lemma sg954 : RowSquare [5,2,2,1] [4,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg22 - -lemma sg955 : RowSquare [5,2,2,1] [4,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg287 - -lemma sg956 : RowSquare [5,2,2,1] [4,4,1,1] := by - exact rowSquare_join (by decide) sg10 sg67 - -lemma sg957 : RowSquare [5,2,2,1] [4,4,2] := by - exact rowSquare_join (by decide) sg10 sg68 - -lemma sg962 : RowSquare [5,3,1,1] [3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg330 - -lemma sg963 : RowSquare [5,3,1,1] [3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg562 - -lemma sg965 : RowSquare [5,3,1,1] [3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg67 - -lemma sg966 : RowSquare [5,3,1,1] [3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg68 - -lemma sg967 : RowSquare [5,3,1,1] [4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg331 - -lemma sg968 : RowSquare [5,3,1,1] [4,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg145 - -lemma sg969 : RowSquare [5,3,1,1] [4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg69 - -lemma sg970 : RowSquare [5,3,1,1] [4,3,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg66 - -lemma sg971 : RowSquare [5,3,1,1] [4,3,3] := by - exact rowSquare_join (by decide) sg16 sg55 - -lemma sg972 : RowSquare [5,3,1,1] [4,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg71 - -lemma sg973 : RowSquare [5,3,1,1] [5,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg145 - -lemma sg974 : RowSquare [5,3,1,1] [5,2,2,1] := by - exact rowSquare_join (by decide) sg39 sg22 - -lemma sg978 : RowSquare [5,3,2] [3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg306 - -lemma sg979 : RowSquare [5,3,2] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg26 - -lemma sg980 : RowSquare [5,3,2] [3,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg156 - -lemma sg981 : RowSquare [5,4,1] [2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg74 - -lemma sg983 : RowSquare [5,4,1] [3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg165 - -lemma sg984 : RowSquare [5,4,1] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg75 - -lemma sg985 : RowSquare [5,4,1] [3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg74 - -lemma sg986 : RowSquare [5,4,1] [3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg76 - -lemma sg987 : RowSquare [5,4,1] [4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg165 - -lemma sg988 : RowSquare [5,4,1] [4,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg168 - -lemma sg989 : RowSquare [5,4,1] [4,3,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg75 - -lemma sg990 : RowSquare [5,4,1] [4,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg80 - -lemma sg991 : RowSquare [5,4,1] [5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg74 - -lemma sg992 : RowSquare [5,4,1] [5,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg168 - -lemma sg993 : RowSquare [5,4,1] [5,5] := by - exact rowSquare_join (by decide) sg14 sg80 - -lemma sg994 : RowSquare [5,4,1] [6,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg75 - -lemma sg995 : RowSquare [5,5] [4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg84 - -lemma sg997 : RowSquare [6,1,1,1,1] [2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg586 - -lemma sg1002 : RowSquare [6,1,1,1,1] [3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg587 - -lemma sg1003 : RowSquare [6,1,1,1,1] [3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg588 - -lemma sg1004 : RowSquare [6,1,1,1,1] [3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg589 - -lemma sg1005 : RowSquare [6,1,1,1,1] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg590 - -lemma sg1009 : RowSquare [6,1,1,1,1] [4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg312 - -lemma sg1010 : RowSquare [6,1,1,1,1] [4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg313 - -lemma sg1011 : RowSquare [6,1,1,1,1] [4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg314 - -lemma sg1012 : RowSquare [6,1,1,1,1] [4,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg315 - -lemma sg1013 : RowSquare [6,1,1,1,1] [4,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg595 - -lemma sg1014 : RowSquare [6,1,1,1,1] [4,3,2,1] := by - exact rowSquare_join (by decide) sg0 sg596 - -lemma sg1017 : RowSquare [6,1,1,1,1] [5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg316 - -lemma sg1018 : RowSquare [6,1,1,1,1] [5,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg317 - -lemma sg1019 : RowSquare [6,1,1,1,1] [5,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg318 - -lemma sg1020 : RowSquare [6,1,1,1,1] [5,3,1,1] := by - exact rowSquare_join (by decide) sg2 sg319 - -lemma sg1021 : RowSquare [6,1,1,1,1] [5,3,2] := by - exact rowSquare_join (by decide) sg2 sg320 - -lemma sg1022 : RowSquare [6,1,1,1,1] [5,4,1] := by - exact rowSquare_join (by decide) sg0 sg602 - -lemma sg1024 : RowSquare [6,1,1,1,1] [6,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg132 - -lemma sg1025 : RowSquare [6,1,1,1,1] [6,2,1,1] := by - exact rowSquare_join (by decide) sg7 sg133 - -lemma sg1026 : RowSquare [6,1,1,1,1] [6,2,2] := by - exact rowSquare_join (by decide) sg7 sg134 - -lemma sg1027 : RowSquare [6,1,1,1,1] [6,3,1] := by - exact rowSquare_join (by decide) sg2 sg323 - -lemma sg1028 : RowSquare [6,1,1,1,1] [6,4] := by - exact rowSquare_join (by decide) sg2 sg324 - -lemma sg1029 : RowSquare [6,1,1,1,1] [7,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg135 - -lemma sg1030 : RowSquare [6,1,1,1,1] [7,3] := by - exact rowSquare_join (by decide) sg7 sg137 - -lemma sg1031 : RowSquare [6,2,1,1] [2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg178 - -lemma sg1034 : RowSquare [6,2,1,1] [3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg330 - -lemma sg1035 : RowSquare [6,2,1,1] [3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg178 - -lemma sg1036 : RowSquare [6,2,1,1] [3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg179 - -lemma sg1037 : RowSquare [6,2,1,1] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg616 - -lemma sg1039 : RowSquare [6,2,1,1] [3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg180 - -lemma sg1041 : RowSquare [6,2,1,1] [3,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg181 - -lemma sg1042 : RowSquare [6,2,1,1] [4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg178 - -lemma sg1043 : RowSquare [6,2,1,1] [4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg179 - -lemma sg1044 : RowSquare [6,2,1,1] [4,2,2,1,1] := by - exact rowSquare_join (by decide) sg16 sg66 - -lemma sg1045 : RowSquare [6,2,1,1] [4,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg334 - -lemma sg1046 : RowSquare [6,2,1,1] [4,3,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg66 - -lemma sg1047 : RowSquare [6,2,1,1] [4,3,3] := by - exact rowSquare_join (by decide) sg16 sg68 - -lemma sg1048 : RowSquare [6,2,1,1] [4,4,1,1] := by - exact rowSquare_join (by decide) sg17 sg67 - -lemma sg1049 : RowSquare [6,2,1,1] [4,4,2] := by - exact rowSquare_join (by decide) sg17 sg68 - -lemma sg1050 : RowSquare [6,2,1,1] [5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg142 - -lemma sg1051 : RowSquare [6,2,1,1] [5,2,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg66 - -lemma sg1052 : RowSquare [6,2,1,1] [5,2,2,1] := by - exact rowSquare_join (by decide) sg16 sg69 - -lemma sg1053 : RowSquare [6,2,1,1] [5,3,1,1] := by - exact rowSquare_join (by decide) sg17 sg69 - -lemma sg1054 : RowSquare [6,2,1,1] [5,3,2] := by - exact rowSquare_join (by decide) sg16 sg70 - -lemma sg1055 : RowSquare [6,2,1,1] [5,4,1] := by - exact rowSquare_join (by decide) sg16 sg71 - -lemma sg1056 : RowSquare [6,2,1,1] [5,5] := by - exact rowSquare_join (by decide) sg17 sg71 - -lemma sg1057 : RowSquare [6,2,1,1] [6,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg66 - -lemma sg1058 : RowSquare [6,2,1,1] [6,2,1,1] := by - exact rowSquare_join (by decide) sg18 sg69 - -lemma sg1059 : RowSquare [6,2,1,1] [6,2,2] := by - exact rowSquare_join (by decide) sg45 sg22 - -lemma sg1060 : RowSquare [6,2,1,1] [6,4] := by - exact rowSquare_join (by decide) sg46 sg23 - -lemma sg1061 : RowSquare [6,2,2] [2,2,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg32 - -lemma sg1062 : RowSquare [6,2,2] [3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg636 - -lemma sg1066 : RowSquare [6,2,2] [4,4,1,1] := by - exact rowSquare_join (by decide) sg10 sg88 - -lemma sg1067 : RowSquare [6,2,2] [5,5] := by - exact rowSquare_join (by decide) sg10 sg92 - -lemma sg1068 : RowSquare [6,3,1] [3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg74 - -lemma sg1069 : RowSquare [6,3,1] [3,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg39 - -lemma sg1070 : RowSquare [6,3,1] [3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg74 - -lemma sg1071 : RowSquare [6,3,1] [3,3,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg40 - -lemma sg1072 : RowSquare [6,3,1] [3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg88 - -lemma sg1073 : RowSquare [6,3,1] [3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg89 - -lemma sg1074 : RowSquare [6,3,1] [4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg74 - -lemma sg1092 : RowSquare [7,1,1,1] [4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg178 - -lemma sg1093 : RowSquare [7,1,1,1] [4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg371 - -lemma sg1094 : RowSquare [7,1,1,1] [4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg372 - -lemma sg1095 : RowSquare [7,1,1,1] [4,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg373 - -lemma sg1096 : RowSquare [7,1,1,1] [5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg179 - -lemma sg1097 : RowSquare [7,1,1,1] [5,2,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg180 - -lemma sg1098 : RowSquare [7,1,1,1] [5,2,2,1] := by - exact rowSquare_join (by decide) sg7 sg181 - -lemma sg1099 : RowSquare [7,1,1,1] [5,3,1,1] := by - exact rowSquare_join (by decide) sg2 sg377 - -lemma sg1100 : RowSquare [7,1,1,1] [5,3,2] := by - exact rowSquare_join (by decide) sg2 sg378 - -lemma sg1101 : RowSquare [7,1,1,1] [6,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg66 - -lemma sg1102 : RowSquare [7,1,1,1] [6,2,2] := by - exact rowSquare_join (by decide) sg20 sg68 - -lemma sg1103 : RowSquare [7,1,1,1] [6,4] := by - exact rowSquare_join (by decide) sg2 sg383 - -lemma sg1104 : RowSquare [7,2,1] [4,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg45 - -lemma sg1105 : RowSquare [7,2,1] [4,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg390 - -lemma sg1106 : RowSquare [7,2,1] [4,3,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg46 - -lemma sg1107 : RowSquare [7,2,1] [4,3,2,1] := by - exact rowSquare_join (by decide) sg16 sg88 - -lemma sg1108 : RowSquare [7,2,1] [4,3,3] := by - exact rowSquare_join (by decide) sg16 sg89 - -lemma sg1109 : RowSquare [7,2,1] [4,4,1,1] := by - exact rowSquare_join (by decide) sg17 sg88 - -lemma sg1110 : RowSquare [7,2,1] [4,4,2] := by - exact rowSquare_join (by decide) sg17 sg89 - -lemma sg1111 : RowSquare [7,2,1] [5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg74 - -lemma sg1112 : RowSquare [7,2,1] [5,5] := by - exact rowSquare_join (by decide) sg17 sg92 - -lemma sg1113 : RowSquare [7,2,1] [9,1] := by - exact rowSquare_join (by decide) sg47 sg38 - -lemma sg1114 : RowSquare [7,3] [4,3,3] := by - exact rowSquare_join (by decide) sg16 sg97 - -lemma sg1115 : RowSquare [7,3] [4,4,2] := by - exact rowSquare_join (by decide) sg17 sg97 - -lemma sg1116 : RowSquare [7,3] [5,2,2,1] := by - exact rowSquare_join (by decide) sg39 sg45 - -lemma sg1117 : RowSquare [7,3] [5,3,1,1] := by - exact rowSquare_join (by decide) sg39 sg46 - -lemma sg1118 : RowSquare [7,3] [5,3,2] := by - exact rowSquare_join (by decide) sg40 sg45 - -lemma sg1119 : RowSquare [7,3] [5,4,1] := by - exact rowSquare_join (by decide) sg40 sg46 - -lemma sg1120 : RowSquare [2,1,1,1,1,1,1,1,1,1] [9,2] := by - exact rowSquare_join (by decide) sg46 sg108 - -lemma sg1121 : RowSquare [2,2,1,1,1,1,1,1,1] [7,2,2] := by - exact rowSquare_join (by decide) sg45 sg104 - -lemma sg1122 : RowSquare [2,2,1,1,1,1,1,1,1] [7,4] := by - exact rowSquare_join (by decide) sg46 sg105 - -lemma sg1123 : RowSquare [2,2,1,1,1,1,1,1,1] [8,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg108 - -lemma sg1124 : RowSquare [2,2,1,1,1,1,1,1,1] [8,3] := by - exact rowSquare_join (by decide) sg46 sg106 - -lemma sg1125 : RowSquare [2,2,1,1,1,1,1,1,1] [9,2] := by - exact rowSquare_join (by decide) sg46 sg107 - -lemma sg1126 : RowSquare [2,2,1,1,1,1,1,1,1] [10,1] := by - exact rowSquare_join (by decide) sg47 sg107 - -lemma sg1127 : RowSquare [2,2,2,1,1,1,1,1] [6,5] := by - exact rowSquare_join (by decide) sg17 sg230 - -lemma sg1128 : RowSquare [2,2,2,1,1,1,1,1] [7,4] := by - exact rowSquare_join (by decide) sg46 sg101 - -lemma sg1129 : RowSquare [2,2,2,1,1,1,1,1] [9,2] := by - exact rowSquare_join (by decide) sg46 sg103 - -lemma sg1130 : RowSquare [2,2,2,2,1,1,1] [6,5] := by - exact rowSquare_join (by decide) sg17 sg213 - -lemma sg1136 : RowSquare [3,1,1,1,1,1,1,1,1] [8,3] := by - exact rowSquare_join (by decide) sg49 sg92 - -lemma sg1137 : RowSquare [3,2,1,1,1,1,1,1] [5,2,2,2] := by - exact rowSquare_join (by decide) sg7 sg390 - -lemma sg1138 : RowSquare [3,2,1,1,1,1,1,1] [5,3,3] := by - exact rowSquare_join (by decide) sg45 sg89 - -lemma sg1139 : RowSquare [3,2,1,1,1,1,1,1] [5,4,2] := by - exact rowSquare_join (by decide) sg46 sg89 - -lemma sg1140 : RowSquare [3,2,1,1,1,1,1,1] [6,4,1] := by - exact rowSquare_join (by decide) sg34 sg105 - -lemma sg1141 : RowSquare [3,2,1,1,1,1,1,1] [6,5] := by - exact rowSquare_join (by decide) sg46 sg92 - -lemma sg1142 : RowSquare [3,2,2,1,1,1,1] [4,4,3] := by - exact rowSquare_join (by decide) sg40 sg89 - -lemma sg1143 : RowSquare [3,2,2,1,1,1,1] [6,5] := by - exact rowSquare_join (by decide) sg46 sg80 - -lemma sg1144 : RowSquare [3,2,2,2,1,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg32 sg83 - -lemma sg1145 : RowSquare [3,2,2,2,1,1] [3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg195 - -lemma sg1146 : RowSquare [3,3,1,1,1,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg87 - -lemma sg1147 : RowSquare [3,3,1,1,1,1,1] [3,3,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg88 - -lemma sg1148 : RowSquare [3,3,1,1,1,1,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg32 sg89 - -lemma sg1149 : RowSquare [3,3,1,1,1,1,1] [4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg636 - -lemma sg1150 : RowSquare [3,3,1,1,1,1,1] [4,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg90 - -lemma sg1151 : RowSquare [3,3,1,1,1,1,1] [4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1063 - -lemma sg1152 : RowSquare [3,3,1,1,1,1,1] [4,3,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg91 - -lemma sg1153 : RowSquare [3,3,1,1,1,1,1] [4,3,2,2] := by - exact rowSquare_join (by decide) sg33 sg88 - -lemma sg1154 : RowSquare [3,3,1,1,1,1,1] [4,3,3,1] := by - exact rowSquare_join (by decide) sg33 sg89 - -lemma sg1155 : RowSquare [3,3,1,1,1,1,1] [4,4,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg92 - -lemma sg1156 : RowSquare [3,3,1,1,1,1,1] [4,4,2,1] := by - exact rowSquare_join (by decide) sg34 sg88 - -lemma sg1157 : RowSquare [3,3,1,1,1,1,1] [4,4,3] := by - exact rowSquare_join (by decide) sg34 sg89 - -lemma sg1158 : RowSquare [3,3,1,1,1,1,1] [5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg348 - -lemma sg1159 : RowSquare [3,3,1,1,1,1,1] [5,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg93 - -lemma sg1160 : RowSquare [3,3,1,1,1,1,1] [5,2,2,2] := by - exact rowSquare_join (by decide) sg33 sg90 - -lemma sg1161 : RowSquare [3,3,1,1,1,1,1] [5,3,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg94 - -lemma sg1162 : RowSquare [3,3,1,1,1,1,1] [5,3,3] := by - exact rowSquare_join (by decide) sg35 sg89 - -lemma sg1163 : RowSquare [3,3,1,1,1,1,1] [5,4,2] := by - exact rowSquare_join (by decide) sg34 sg91 - -lemma sg1164 : RowSquare [3,3,1,1,1,1,1] [5,5,1] := by - exact rowSquare_join (by decide) sg34 sg92 - -lemma sg1165 : RowSquare [3,3,1,1,1,1,1] [6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg154 - -lemma sg1166 : RowSquare [3,3,1,1,1,1,1] [6,2,2,1] := by - exact rowSquare_join (by decide) sg33 sg93 - -lemma sg1167 : RowSquare [3,3,1,1,1,1,1] [6,3,2] := by - exact rowSquare_join (by decide) sg34 sg93 - -lemma sg1168 : RowSquare [3,3,1,1,1,1,1] [6,4,1] := by - exact rowSquare_join (by decide) sg34 sg94 - -lemma sg1169 : RowSquare [3,3,1,1,1,1,1] [6,5] := by - exact rowSquare_join (by decide) sg36 sg92 - -lemma sg1170 : RowSquare [3,3,1,1,1,1,1] [7,2,2] := by - exact rowSquare_join (by decide) sg1 sg432 - -lemma sg1171 : RowSquare [3,3,1,1,1,1,1] [7,3,1] := by - exact rowSquare_join (by decide) sg1 sg433 - -lemma sg1172 : RowSquare [3,3,1,1,1,1,1] [7,4] := by - exact rowSquare_join (by decide) sg1 sg434 - -lemma sg1173 : RowSquare [3,3,1,1,1,1,1] [8,2,1] := by - exact rowSquare_join (by decide) sg1 sg436 - -lemma sg1174 : RowSquare [3,3,1,1,1,1,1] [8,3] := by - exact rowSquare_join (by decide) sg1 sg437 - -lemma sg1175 : RowSquare [3,3,1,1,1,1,1] [9,2] := by - exact rowSquare_join (by decide) sg14 sg109 - -lemma sg1176 : RowSquare [3,3,1,1,1,1,1] [10,1] := by - exact rowSquare_join (by decide) sg1 sg439 - -lemma sg1178 : RowSquare [3,3,2,1,1,1] [2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg74 - -lemma sg1179 : RowSquare [3,3,2,1,1,1] [3,3,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg76 - -lemma sg1181 : RowSquare [3,3,3,2] [3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg516 - -lemma sg1182 : RowSquare [4,1,1,1,1,1,1,1] [5,2,2,2] := by - exact rowSquare_join (by decide) sg7 sg373 - -lemma sg1183 : RowSquare [4,1,1,1,1,1,1,1] [6,3,2] := by - exact rowSquare_join (by decide) sg7 sg378 - -lemma sg1184 : RowSquare [4,1,1,1,1,1,1,1] [7,4] := by - exact rowSquare_join (by decide) sg7 sg383 - -lemma sg1185 : RowSquare [4,2,1,1,1,1,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg178 - -lemma sg1186 : RowSquare [4,2,1,1,1,1,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg1032 - -lemma sg1187 : RowSquare [4,2,1,1,1,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg1033 - -lemma sg1188 : RowSquare [4,2,1,1,1,1,1] [3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg178 - -lemma sg1189 : RowSquare [4,2,1,1,1,1,1] [3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg371 - -lemma sg1190 : RowSquare [4,2,1,1,1,1,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg372 - -lemma sg1191 : RowSquare [4,2,1,1,1,1,1] [3,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg373 - -lemma sg1192 : RowSquare [4,2,1,1,1,1,1] [4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg330 - -lemma sg1193 : RowSquare [4,2,1,1,1,1,1] [4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg179 - -lemma sg1194 : RowSquare [4,2,1,1,1,1,1] [4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg179 - -lemma sg1195 : RowSquare [4,2,2,1,1,1] [2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg330 - -lemma sg1196 : RowSquare [4,2,2,1,1,1] [2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg178 - -lemma sg1197 : RowSquare [4,2,2,1,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg961 - -lemma sg1198 : RowSquare [4,2,2,1,1,1] [3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg178 - -lemma sg1199 : RowSquare [4,2,2,1,1,1] [3,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg180 - -lemma sg1200 : RowSquare [4,2,2,1,1,1] [3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg181 - -lemma sg1201 : RowSquare [4,2,2,1,1,1] [4,4,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg143 - -lemma sg1202 : RowSquare [4,3,1,1,1,1] [3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg940 - -lemma sg1203 : RowSquare [4,3,1,1,1,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg178 - -lemma sg1204 : RowSquare [4,3,1,1,1,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg942 - -lemma sg1205 : RowSquare [4,3,1,1,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg762 - -lemma sg1206 : RowSquare [4,3,1,1,1,1] [3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg178 - -lemma sg1207 : RowSquare [4,3,1,1,1,1] [3,3,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg67 - -lemma sg1208 : RowSquare [4,3,1,1,1,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg32 sg68 - -lemma sg1209 : RowSquare [4,3,1,1,1,1] [4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg548 - -lemma sg1210 : RowSquare [4,3,1,1,1,1] [4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg11 sg178 - -lemma sg1211 : RowSquare [4,3,1,1,1,1] [4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg763 - -lemma sg1212 : RowSquare [4,3,1,1,1,1] [4,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg767 - -lemma sg1213 : RowSquare [4,3,1,1,1,1] [4,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg768 - -lemma sg1214 : RowSquare [4,3,1,1,1,1] [4,4,2,1] := by - exact rowSquare_join (by decide) sg34 sg67 - -lemma sg1215 : RowSquare [4,3,1,1,1,1] [4,4,3] := by - exact rowSquare_join (by decide) sg34 sg68 - -lemma sg1216 : RowSquare [4,3,1,1,1,1] [5,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg456 - -lemma sg1217 : RowSquare [4,3,1,1,1,1] [5,3,3] := by - exact rowSquare_join (by decide) sg4 sg239 - -lemma sg1218 : RowSquare [4,3,1,1,1,1] [5,5,1] := by - exact rowSquare_join (by decide) sg4 sg241 - -lemma sg1219 : RowSquare [4,3,1,1,1,1] [6,5] := by - exact rowSquare_join (by decide) sg5 sg241 - -lemma sg1220 : RowSquare [4,3,1,1,1,1] [7,2,2] := by - exact rowSquare_join (by decide) sg4 sg245 - -lemma sg1221 : RowSquare [4,3,1,1,1,1] [9,2] := by - exact rowSquare_join (by decide) sg42 sg50 - -lemma sg1222 : RowSquare [4,3,1,1,1,1] [10,1] := by - exact rowSquare_join (by decide) sg43 sg50 - -lemma sg1223 : RowSquare [4,3,2,1,1] [2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg849 - -lemma sg1224 : RowSquare [4,3,2,1,1] [3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg851 - -lemma sg1225 : RowSquare [4,3,2,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg792 - -lemma sg1226 : RowSquare [4,3,2,1,1] [3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg285 - -lemma sg1227 : RowSquare [4,3,2,1,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg32 sg55 - -lemma sg1228 : RowSquare [4,3,2,1,1] [4,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg249 - -lemma sg1229 : RowSquare [4,3,2,1,1] [4,4,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg143 - -lemma sg1230 : RowSquare [4,3,2,1,1] [4,4,3] := by - exact rowSquare_join (by decide) sg4 sg251 - -lemma sg1231 : RowSquare [4,3,2,1,1] [5,3,3] := by - exact rowSquare_join (by decide) sg9 sg114 - -lemma sg1233 : RowSquare [4,3,3,1] [2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg23 sg65 - -lemma sg1234 : RowSquare [4,3,3,1] [2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg10 sg128 - -lemma sg1235 : RowSquare [4,4,1,1,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg832 - -lemma sg1236 : RowSquare [4,4,1,1,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg833 - -lemma sg1237 : RowSquare [4,4,1,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg834 - -lemma sg1238 : RowSquare [4,4,2,1] [4,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg125 - -lemma sg1239 : RowSquare [4,4,3] [3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg516 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupLeaves3 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupLeaves4 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupLeaves5 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes0 + +namespace OAI + +/-! Semigroup Nodes 1. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg696 : RowSquare [6,2,1] [3,3,3] := by + exact rowSquare_join (by decide) sg4 sg89 + +lemma sg697 : RowSquare [6,2,1] [4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg74 + +lemma sg698 : RowSquare [6,2,1] [4,2,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg32 + +lemma sg699 : RowSquare [6,2,1] [4,3,1,1] := by + exact rowSquare_join (by decide) sg17 sg33 + +lemma sg700 : RowSquare [6,2,1] [4,3,2] := by + exact rowSquare_join (by decide) sg16 sg34 + +lemma sg701 : RowSquare [6,2,1] [4,4,1] := by + exact rowSquare_join (by decide) sg17 sg34 + +lemma sg702 : RowSquare [6,2,1] [5,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg32 + +lemma sg703 : RowSquare [6,2,1] [5,4] := by + exact rowSquare_join (by decide) sg17 sg36 + +lemma sg704 : RowSquare [6,2,1] [6,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg26 + +lemma sg705 : RowSquare [6,2,1] [8,1] := by + exact rowSquare_join (by decide) sg18 sg38 + +lemma sg706 : RowSquare [6,3] [3,3,3] := by + exact rowSquare_join (by decide) sg4 sg97 + +lemma sg707 : RowSquare [6,3] [4,4,1] := by + exact rowSquare_join (by decide) sg17 sg40 + +lemma sg708 : RowSquare [7,1,1] [5,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg32 + +lemma sg709 : RowSquare [7,1,1] [5,2,1,1] := by + exact rowSquare_join (by decide) sg7 sg88 + +lemma sg710 : RowSquare [7,1,1] [5,2,2] := by + exact rowSquare_join (by decide) sg7 sg89 + +lemma sg711 : RowSquare [7,1,1] [6,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg33 + +lemma sg712 : RowSquare [7,1,1] [6,2,1] := by + exact rowSquare_join (by decide) sg20 sg34 + +lemma sg713 : RowSquare [7,1,1] [6,3] := by + exact rowSquare_join (by decide) sg7 sg92 + +lemma sg714 : RowSquare [7,2] [5,3,1] := by + exact rowSquare_join (by decide) sg16 sg46 + +lemma sg715 : RowSquare [7,2] [5,4] := by + exact rowSquare_join (by decide) sg17 sg46 + +lemma sg716 : RowSquare [8,1] [7,1,1] := by + exact rowSquare_join (by decide) sg16 sg49 + +lemma sg717 : RowSquare [8,1] [7,2] := by + exact rowSquare_join (by decide) sg17 sg49 + +lemma sg719 : RowSquare [2,1,1,1,1,1,1,1,1] [8,2] := by + exact rowSquare_join (by decide) sg46 sg49 + +lemma sg721 : RowSquare [2,2,1,1,1,1,1,1] [6,2,2] := by + exact rowSquare_join (by decide) sg45 sg45 + +lemma sg722 : RowSquare [2,2,1,1,1,1,1,1] [6,4] := by + exact rowSquare_join (by decide) sg46 sg46 + +lemma sg723 : RowSquare [2,2,1,1,1,1,1,1] [7,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg49 + +lemma sg724 : RowSquare [2,2,1,1,1,1,1,1] [7,3] := by + exact rowSquare_join (by decide) sg46 sg47 + +lemma sg725 : RowSquare [2,2,1,1,1,1,1,1] [8,2] := by + exact rowSquare_join (by decide) sg46 sg48 + +lemma sg726 : RowSquare [2,2,1,1,1,1,1,1] [9,1] := by + exact rowSquare_join (by decide) sg47 sg48 + +lemma sg727 : RowSquare [2,2,2,1,1,1,1] [6,4] := by + exact rowSquare_join (by decide) sg46 sg42 + +lemma sg728 : RowSquare [2,2,2,1,1,1,1] [7,3] := by + exact rowSquare_join (by decide) sg46 sg43 + +lemma sg729 : RowSquare [2,2,2,1,1,1,1] [8,2] := by + exact rowSquare_join (by decide) sg46 sg44 + +lemma sg731 : RowSquare [3,1,1,1,1,1,1,1] [6,2,2] := by + exact rowSquare_join (by decide) sg20 sg89 + +lemma sg732 : RowSquare [3,1,1,1,1,1,1,1] [7,2,1] := by + exact rowSquare_join (by decide) sg34 sg49 + +lemma sg733 : RowSquare [3,1,1,1,1,1,1,1] [7,3] := by + exact rowSquare_join (by decide) sg20 sg92 + +lemma sg734 : RowSquare [3,1,1,1,1,1,1,1] [8,2] := by + exact rowSquare_join (by decide) sg0 sg429 + +lemma sg735 : RowSquare [3,2,1,1,1,1,1] [4,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg45 + +lemma sg736 : RowSquare [3,2,1,1,1,1,1] [4,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg390 + +lemma sg737 : RowSquare [3,2,1,1,1,1,1] [4,3,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg46 + +lemma sg738 : RowSquare [3,2,1,1,1,1,1] [4,3,2,1] := by + exact rowSquare_join (by decide) sg16 sg88 + +lemma sg739 : RowSquare [3,2,1,1,1,1,1] [4,3,3] := by + exact rowSquare_join (by decide) sg16 sg89 + +lemma sg740 : RowSquare [3,2,1,1,1,1,1] [4,4,1,1] := by + exact rowSquare_join (by decide) sg17 sg88 + +lemma sg741 : RowSquare [3,2,1,1,1,1,1] [4,4,2] := by + exact rowSquare_join (by decide) sg17 sg89 + +lemma sg742 : RowSquare [3,2,1,1,1,1,1] [5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg74 + +lemma sg743 : RowSquare [3,2,1,1,1,1,1] [5,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg47 + +lemma sg744 : RowSquare [3,2,1,1,1,1,1] [5,2,2,1] := by + exact rowSquare_join (by decide) sg33 sg45 + +lemma sg745 : RowSquare [3,2,1,1,1,1,1] [5,3,1,1] := by + exact rowSquare_join (by decide) sg33 sg46 + +lemma sg746 : RowSquare [3,2,1,1,1,1,1] [5,3,2] := by + exact rowSquare_join (by decide) sg34 sg45 + +lemma sg747 : RowSquare [3,2,1,1,1,1,1] [5,4,1] := by + exact rowSquare_join (by decide) sg34 sg46 + +lemma sg748 : RowSquare [3,2,1,1,1,1,1] [5,5] := by + exact rowSquare_join (by decide) sg17 sg92 + +lemma sg749 : RowSquare [3,2,1,1,1,1,1] [6,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg48 + +lemma sg750 : RowSquare [3,2,1,1,1,1,1] [6,2,1,1] := by + exact rowSquare_join (by decide) sg33 sg47 + +lemma sg751 : RowSquare [3,2,2,1,1,1] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg39 + +lemma sg752 : RowSquare [3,2,2,1,1,1] [3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg74 + +lemma sg753 : RowSquare [3,2,2,1,1,1] [3,3,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg40 + +lemma sg754 : RowSquare [3,2,2,1,1,1] [3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg88 + +lemma sg755 : RowSquare [3,2,2,1,1,1] [3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg89 + +lemma sg756 : RowSquare [3,2,2,1,1,1] [4,3,3] := by + exact rowSquare_join (by decide) sg0 sg440 + +lemma sg758 : RowSquare [3,2,2,2,1] [2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg74 + +lemma sg760 : RowSquare [3,2,2,2,1] [3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg74 + +lemma sg761 : RowSquare [3,2,2,2,1] [5,5] := by + exact rowSquare_join (by decide) sg14 sg80 + +lemma sg762 : RowSquare [3,3,1,1,1,1] [2,2,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg32 + +lemma sg763 : RowSquare [3,3,1,1,1,1] [3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg636 + +lemma sg764 : RowSquare [3,3,1,1,1,1] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg33 + +lemma sg766 : RowSquare [3,3,1,1,1,1] [3,3,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg34 + +lemma sg769 : RowSquare [3,3,1,1,1,1] [4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg348 + +lemma sg770 : RowSquare [3,3,1,1,1,1] [4,2,2,2] := by + exact rowSquare_join (by decide) sg33 sg33 + +lemma sg771 : RowSquare [3,3,1,1,1,1] [4,3,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg36 + +lemma sg772 : RowSquare [3,3,1,1,1,1] [4,3,2,1] := by + exact rowSquare_join (by decide) sg33 sg34 + +lemma sg773 : RowSquare [3,3,1,1,1,1] [4,3,3] := by + exact rowSquare_join (by decide) sg9 sg89 + +lemma sg774 : RowSquare [3,3,1,1,1,1] [4,4,1,1] := by + exact rowSquare_join (by decide) sg10 sg88 + +lemma sg775 : RowSquare [3,3,1,1,1,1] [4,4,2] := by + exact rowSquare_join (by decide) sg34 sg34 + +lemma sg776 : RowSquare [3,3,1,1,1,1] [5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg154 + +lemma sg777 : RowSquare [3,3,1,1,1,1] [5,2,2,1] := by + exact rowSquare_join (by decide) sg33 sg35 + +lemma sg778 : RowSquare [3,3,1,1,1,1] [5,3,2] := by + exact rowSquare_join (by decide) sg34 sg35 + +lemma sg779 : RowSquare [3,3,1,1,1,1] [5,4,1] := by + exact rowSquare_join (by decide) sg34 sg36 + +lemma sg780 : RowSquare [3,3,1,1,1,1] [5,5] := by + exact rowSquare_join (by decide) sg10 sg92 + +lemma sg781 : RowSquare [3,3,1,1,1,1] [6,2,2] := by + exact rowSquare_join (by decide) sg1 sg239 + +lemma sg782 : RowSquare [3,3,1,1,1,1] [6,4] := by + exact rowSquare_join (by decide) sg1 sg241 + +lemma sg783 : RowSquare [3,3,1,1,1,1] [7,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg50 + +lemma sg784 : RowSquare [3,3,1,1,1,1] [7,2,1] := by + exact rowSquare_join (by decide) sg1 sg243 + +lemma sg785 : RowSquare [3,3,1,1,1,1] [7,3] := by + exact rowSquare_join (by decide) sg1 sg244 + +lemma sg786 : RowSquare [3,3,1,1,1,1] [8,1,1] := by + exact rowSquare_join (by decide) sg1 sg245 + +lemma sg787 : RowSquare [3,3,1,1,1,1] [8,2] := by + exact rowSquare_join (by decide) sg14 sg50 + +lemma sg788 : RowSquare [3,3,1,1,1,1] [9,1] := by + exact rowSquare_join (by decide) sg1 sg247 + +lemma sg793 : RowSquare [3,3,2,1,1] [3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg306 + +lemma sg794 : RowSquare [3,3,2,1,1] [3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg74 + +lemma sg795 : RowSquare [3,3,2,1,1] [3,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg156 + +lemma sg797 : RowSquare [3,3,2,2] [3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg306 + +lemma sg798 : RowSquare [3,3,3,1] [2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg516 + +lemma sg799 : RowSquare [4,1,1,1,1,1,1] [4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg178 + +lemma sg800 : RowSquare [4,1,1,1,1,1,1] [4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg371 + +lemma sg801 : RowSquare [4,1,1,1,1,1,1] [4,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg373 + +lemma sg802 : RowSquare [4,1,1,1,1,1,1] [5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg179 + +lemma sg803 : RowSquare [4,1,1,1,1,1,1] [5,2,2,1] := by + exact rowSquare_join (by decide) sg7 sg181 + +lemma sg804 : RowSquare [4,1,1,1,1,1,1] [5,3,2] := by + exact rowSquare_join (by decide) sg2 sg378 + +lemma sg805 : RowSquare [4,1,1,1,1,1,1] [6,3,1] := by + exact rowSquare_join (by decide) sg7 sg185 + +lemma sg806 : RowSquare [4,1,1,1,1,1,1] [6,4] := by + exact rowSquare_join (by decide) sg2 sg383 + +lemma sg807 : RowSquare [4,2,1,1,1,1] [2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg178 + +lemma sg810 : RowSquare [4,2,1,1,1,1] [3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg330 + +lemma sg811 : RowSquare [4,2,1,1,1,1] [3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg178 + +lemma sg812 : RowSquare [4,2,1,1,1,1] [3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg179 + +lemma sg813 : RowSquare [4,2,1,1,1,1] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg616 + +lemma sg815 : RowSquare [4,2,1,1,1,1] [3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg180 + +lemma sg817 : RowSquare [4,2,1,1,1,1] [3,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg181 + +lemma sg818 : RowSquare [4,2,1,1,1,1] [4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg178 + +lemma sg819 : RowSquare [4,2,1,1,1,1] [4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg179 + +lemma sg820 : RowSquare [4,2,1,1,1,1] [4,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg456 + +lemma sg821 : RowSquare [4,2,1,1,1,1] [4,3,3] := by + exact rowSquare_join (by decide) sg0 sg459 + +lemma sg822 : RowSquare [4,2,1,1,1,1] [4,4,1,1] := by + exact rowSquare_join (by decide) sg17 sg67 + +lemma sg823 : RowSquare [4,2,1,1,1,1] [4,4,2] := by + exact rowSquare_join (by decide) sg17 sg68 + +lemma sg824 : RowSquare [4,2,1,1,1,1] [5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg460 + +lemma sg825 : RowSquare [4,2,1,1,1,1] [5,5] := by + exact rowSquare_join (by decide) sg17 sg71 + +lemma sg830 : RowSquare [4,2,2,1,1] [3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg330 + +lemma sg831 : RowSquare [4,2,2,1,1] [3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg68 + +lemma sg842 : RowSquare [4,3,1,1,1] [3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg548 + +lemma sg843 : RowSquare [4,3,1,1,1] [3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg549 + +lemma sg844 : RowSquare [4,3,1,1,1] [3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg489 + +lemma sg845 : RowSquare [4,3,1,1,1] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg490 + +lemma sg848 : RowSquare [4,3,1,1,1] [4,3,3] := by + exact rowSquare_join (by decide) sg4 sg114 + +lemma sg872 : RowSquare [4,3,3] [2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg516 + +lemma sg882 : RowSquare [4,4,1,1] [3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg480 + +lemma sg883 : RowSquare [4,4,1,1] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg481 + +lemma sg888 : RowSquare [5,1,1,1,1,1] [2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg586 + +lemma sg893 : RowSquare [5,1,1,1,1,1] [3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg587 + +lemma sg894 : RowSquare [5,1,1,1,1,1] [3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg588 + +lemma sg895 : RowSquare [5,1,1,1,1,1] [3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg589 + +lemma sg896 : RowSquare [5,1,1,1,1,1] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg590 + +lemma sg900 : RowSquare [5,1,1,1,1,1] [4,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg595 + +lemma sg901 : RowSquare [5,1,1,1,1,1] [4,3,2,1] := by + exact rowSquare_join (by decide) sg0 sg596 + +lemma sg904 : RowSquare [5,1,1,1,1,1] [5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg521 + +lemma sg905 : RowSquare [5,1,1,1,1,1] [5,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg523 + +lemma sg906 : RowSquare [5,1,1,1,1,1] [5,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg524 + +lemma sg907 : RowSquare [5,1,1,1,1,1] [5,3,2] := by + exact rowSquare_join (by decide) sg0 sg525 + +lemma sg908 : RowSquare [5,1,1,1,1,1] [5,4,1] := by + exact rowSquare_join (by decide) sg0 sg602 + +lemma sg911 : RowSquare [5,2,1,1,1] [2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg47 sg21 + +lemma sg912 : RowSquare [5,2,1,1,1] [2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg21 + +lemma sg913 : RowSquare [5,2,1,1,1] [2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg53 + +lemma sg914 : RowSquare [5,2,1,1,1] [2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg52 + +lemma sg916 : RowSquare [5,2,1,1,1] [3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg534 + +lemma sg917 : RowSquare [5,2,1,1,1] [3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg535 + +lemma sg918 : RowSquare [5,2,1,1,1] [3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg536 + +lemma sg919 : RowSquare [5,2,1,1,1] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg537 + +lemma sg920 : RowSquare [5,2,1,1,1] [3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg51 + +lemma sg921 : RowSquare [5,2,1,1,1] [3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg136 + +lemma sg923 : RowSquare [5,2,1,1,1] [3,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg134 + +lemma sg924 : RowSquare [5,2,1,1,1] [4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg312 + +lemma sg925 : RowSquare [5,2,1,1,1] [4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg313 + +lemma sg926 : RowSquare [5,2,1,1,1] [4,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg132 + +lemma sg927 : RowSquare [5,2,1,1,1] [4,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg271 + +lemma sg928 : RowSquare [5,2,1,1,1] [4,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg541 + +lemma sg929 : RowSquare [5,2,1,1,1] [4,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg133 + +lemma sg930 : RowSquare [5,2,1,1,1] [4,3,3] := by + exact rowSquare_join (by decide) sg4 sg134 + +lemma sg931 : RowSquare [5,2,1,1,1] [4,4,1,1] := by + exact rowSquare_join (by decide) sg2 sg271 + +lemma sg933 : RowSquare [5,2,1,1,1] [5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg272 + +lemma sg934 : RowSquare [5,2,1,1,1] [5,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg132 + +lemma sg935 : RowSquare [5,2,1,1,1] [5,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg135 + +lemma sg936 : RowSquare [5,2,1,1,1] [5,3,1,1] := by + exact rowSquare_join (by decide) sg5 sg133 + +lemma sg937 : RowSquare [5,2,1,1,1] [5,3,2] := by + exact rowSquare_join (by decide) sg4 sg136 + +lemma sg938 : RowSquare [5,2,1,1,1] [5,4,1] := by + exact rowSquare_join (by decide) sg4 sg137 + +lemma sg944 : RowSquare [5,2,2,1] [3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg548 + +lemma sg945 : RowSquare [5,2,2,1] [3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg549 + +lemma sg946 : RowSquare [5,2,2,1] [3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg550 + +lemma sg947 : RowSquare [5,2,2,1] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg551 + +lemma sg952 : RowSquare [5,2,2,1] [4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3 sg178 + +lemma sg953 : RowSquare [5,2,2,1] [4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg285 + +lemma sg954 : RowSquare [5,2,2,1] [4,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg22 + +lemma sg955 : RowSquare [5,2,2,1] [4,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg287 + +lemma sg956 : RowSquare [5,2,2,1] [4,4,1,1] := by + exact rowSquare_join (by decide) sg10 sg67 + +lemma sg957 : RowSquare [5,2,2,1] [4,4,2] := by + exact rowSquare_join (by decide) sg10 sg68 + +lemma sg962 : RowSquare [5,3,1,1] [3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg330 + +lemma sg963 : RowSquare [5,3,1,1] [3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg562 + +lemma sg965 : RowSquare [5,3,1,1] [3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg67 + +lemma sg966 : RowSquare [5,3,1,1] [3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg68 + +lemma sg967 : RowSquare [5,3,1,1] [4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg331 + +lemma sg968 : RowSquare [5,3,1,1] [4,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg145 + +lemma sg969 : RowSquare [5,3,1,1] [4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg69 + +lemma sg970 : RowSquare [5,3,1,1] [4,3,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg66 + +lemma sg971 : RowSquare [5,3,1,1] [4,3,3] := by + exact rowSquare_join (by decide) sg16 sg55 + +lemma sg972 : RowSquare [5,3,1,1] [4,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg71 + +lemma sg973 : RowSquare [5,3,1,1] [5,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg145 + +lemma sg974 : RowSquare [5,3,1,1] [5,2,2,1] := by + exact rowSquare_join (by decide) sg39 sg22 + +lemma sg978 : RowSquare [5,3,2] [3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg306 + +lemma sg979 : RowSquare [5,3,2] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg26 + +lemma sg980 : RowSquare [5,3,2] [3,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg156 + +lemma sg981 : RowSquare [5,4,1] [2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg74 + +lemma sg983 : RowSquare [5,4,1] [3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg165 + +lemma sg984 : RowSquare [5,4,1] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg75 + +lemma sg985 : RowSquare [5,4,1] [3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg74 + +lemma sg986 : RowSquare [5,4,1] [3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg76 + +lemma sg987 : RowSquare [5,4,1] [4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg165 + +lemma sg988 : RowSquare [5,4,1] [4,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg168 + +lemma sg989 : RowSquare [5,4,1] [4,3,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg75 + +lemma sg990 : RowSquare [5,4,1] [4,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg80 + +lemma sg991 : RowSquare [5,4,1] [5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg74 + +lemma sg992 : RowSquare [5,4,1] [5,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg168 + +lemma sg993 : RowSquare [5,4,1] [5,5] := by + exact rowSquare_join (by decide) sg14 sg80 + +lemma sg994 : RowSquare [5,4,1] [6,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg75 + +lemma sg995 : RowSquare [5,5] [4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg84 + +lemma sg997 : RowSquare [6,1,1,1,1] [2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg586 + +lemma sg1002 : RowSquare [6,1,1,1,1] [3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg587 + +lemma sg1003 : RowSquare [6,1,1,1,1] [3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg588 + +lemma sg1004 : RowSquare [6,1,1,1,1] [3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg589 + +lemma sg1005 : RowSquare [6,1,1,1,1] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg590 + +lemma sg1009 : RowSquare [6,1,1,1,1] [4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg312 + +lemma sg1010 : RowSquare [6,1,1,1,1] [4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg313 + +lemma sg1011 : RowSquare [6,1,1,1,1] [4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg314 + +lemma sg1012 : RowSquare [6,1,1,1,1] [4,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg315 + +lemma sg1013 : RowSquare [6,1,1,1,1] [4,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg595 + +lemma sg1014 : RowSquare [6,1,1,1,1] [4,3,2,1] := by + exact rowSquare_join (by decide) sg0 sg596 + +lemma sg1017 : RowSquare [6,1,1,1,1] [5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg316 + +lemma sg1018 : RowSquare [6,1,1,1,1] [5,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg317 + +lemma sg1019 : RowSquare [6,1,1,1,1] [5,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg318 + +lemma sg1020 : RowSquare [6,1,1,1,1] [5,3,1,1] := by + exact rowSquare_join (by decide) sg2 sg319 + +lemma sg1021 : RowSquare [6,1,1,1,1] [5,3,2] := by + exact rowSquare_join (by decide) sg2 sg320 + +lemma sg1022 : RowSquare [6,1,1,1,1] [5,4,1] := by + exact rowSquare_join (by decide) sg0 sg602 + +lemma sg1024 : RowSquare [6,1,1,1,1] [6,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg132 + +lemma sg1025 : RowSquare [6,1,1,1,1] [6,2,1,1] := by + exact rowSquare_join (by decide) sg7 sg133 + +lemma sg1026 : RowSquare [6,1,1,1,1] [6,2,2] := by + exact rowSquare_join (by decide) sg7 sg134 + +lemma sg1027 : RowSquare [6,1,1,1,1] [6,3,1] := by + exact rowSquare_join (by decide) sg2 sg323 + +lemma sg1028 : RowSquare [6,1,1,1,1] [6,4] := by + exact rowSquare_join (by decide) sg2 sg324 + +lemma sg1029 : RowSquare [6,1,1,1,1] [7,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg135 + +lemma sg1030 : RowSquare [6,1,1,1,1] [7,3] := by + exact rowSquare_join (by decide) sg7 sg137 + +lemma sg1031 : RowSquare [6,2,1,1] [2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg178 + +lemma sg1034 : RowSquare [6,2,1,1] [3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg330 + +lemma sg1035 : RowSquare [6,2,1,1] [3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg178 + +lemma sg1036 : RowSquare [6,2,1,1] [3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg179 + +lemma sg1037 : RowSquare [6,2,1,1] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg616 + +lemma sg1039 : RowSquare [6,2,1,1] [3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg180 + +lemma sg1041 : RowSquare [6,2,1,1] [3,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg181 + +lemma sg1042 : RowSquare [6,2,1,1] [4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg178 + +lemma sg1043 : RowSquare [6,2,1,1] [4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg179 + +lemma sg1044 : RowSquare [6,2,1,1] [4,2,2,1,1] := by + exact rowSquare_join (by decide) sg16 sg66 + +lemma sg1045 : RowSquare [6,2,1,1] [4,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg334 + +lemma sg1046 : RowSquare [6,2,1,1] [4,3,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg66 + +lemma sg1047 : RowSquare [6,2,1,1] [4,3,3] := by + exact rowSquare_join (by decide) sg16 sg68 + +lemma sg1048 : RowSquare [6,2,1,1] [4,4,1,1] := by + exact rowSquare_join (by decide) sg17 sg67 + +lemma sg1049 : RowSquare [6,2,1,1] [4,4,2] := by + exact rowSquare_join (by decide) sg17 sg68 + +lemma sg1050 : RowSquare [6,2,1,1] [5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg142 + +lemma sg1051 : RowSquare [6,2,1,1] [5,2,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg66 + +lemma sg1052 : RowSquare [6,2,1,1] [5,2,2,1] := by + exact rowSquare_join (by decide) sg16 sg69 + +lemma sg1053 : RowSquare [6,2,1,1] [5,3,1,1] := by + exact rowSquare_join (by decide) sg17 sg69 + +lemma sg1054 : RowSquare [6,2,1,1] [5,3,2] := by + exact rowSquare_join (by decide) sg16 sg70 + +lemma sg1055 : RowSquare [6,2,1,1] [5,4,1] := by + exact rowSquare_join (by decide) sg16 sg71 + +lemma sg1056 : RowSquare [6,2,1,1] [5,5] := by + exact rowSquare_join (by decide) sg17 sg71 + +lemma sg1057 : RowSquare [6,2,1,1] [6,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg66 + +lemma sg1058 : RowSquare [6,2,1,1] [6,2,1,1] := by + exact rowSquare_join (by decide) sg18 sg69 + +lemma sg1059 : RowSquare [6,2,1,1] [6,2,2] := by + exact rowSquare_join (by decide) sg45 sg22 + +lemma sg1060 : RowSquare [6,2,1,1] [6,4] := by + exact rowSquare_join (by decide) sg46 sg23 + +lemma sg1061 : RowSquare [6,2,2] [2,2,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg32 + +lemma sg1062 : RowSquare [6,2,2] [3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg636 + +lemma sg1066 : RowSquare [6,2,2] [4,4,1,1] := by + exact rowSquare_join (by decide) sg10 sg88 + +lemma sg1067 : RowSquare [6,2,2] [5,5] := by + exact rowSquare_join (by decide) sg10 sg92 + +lemma sg1068 : RowSquare [6,3,1] [3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg74 + +lemma sg1069 : RowSquare [6,3,1] [3,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg39 + +lemma sg1070 : RowSquare [6,3,1] [3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg74 + +lemma sg1071 : RowSquare [6,3,1] [3,3,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg40 + +lemma sg1072 : RowSquare [6,3,1] [3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg88 + +lemma sg1073 : RowSquare [6,3,1] [3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg89 + +lemma sg1074 : RowSquare [6,3,1] [4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg74 + +lemma sg1092 : RowSquare [7,1,1,1] [4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg178 + +lemma sg1093 : RowSquare [7,1,1,1] [4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg371 + +lemma sg1094 : RowSquare [7,1,1,1] [4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg372 + +lemma sg1095 : RowSquare [7,1,1,1] [4,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg373 + +lemma sg1096 : RowSquare [7,1,1,1] [5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg179 + +lemma sg1097 : RowSquare [7,1,1,1] [5,2,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg180 + +lemma sg1098 : RowSquare [7,1,1,1] [5,2,2,1] := by + exact rowSquare_join (by decide) sg7 sg181 + +lemma sg1099 : RowSquare [7,1,1,1] [5,3,1,1] := by + exact rowSquare_join (by decide) sg2 sg377 + +lemma sg1100 : RowSquare [7,1,1,1] [5,3,2] := by + exact rowSquare_join (by decide) sg2 sg378 + +lemma sg1101 : RowSquare [7,1,1,1] [6,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg66 + +lemma sg1102 : RowSquare [7,1,1,1] [6,2,2] := by + exact rowSquare_join (by decide) sg20 sg68 + +lemma sg1103 : RowSquare [7,1,1,1] [6,4] := by + exact rowSquare_join (by decide) sg2 sg383 + +lemma sg1104 : RowSquare [7,2,1] [4,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg45 + +lemma sg1105 : RowSquare [7,2,1] [4,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg390 + +lemma sg1106 : RowSquare [7,2,1] [4,3,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg46 + +lemma sg1107 : RowSquare [7,2,1] [4,3,2,1] := by + exact rowSquare_join (by decide) sg16 sg88 + +lemma sg1108 : RowSquare [7,2,1] [4,3,3] := by + exact rowSquare_join (by decide) sg16 sg89 + +lemma sg1109 : RowSquare [7,2,1] [4,4,1,1] := by + exact rowSquare_join (by decide) sg17 sg88 + +lemma sg1110 : RowSquare [7,2,1] [4,4,2] := by + exact rowSquare_join (by decide) sg17 sg89 + +lemma sg1111 : RowSquare [7,2,1] [5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg74 + +lemma sg1112 : RowSquare [7,2,1] [5,5] := by + exact rowSquare_join (by decide) sg17 sg92 + +lemma sg1113 : RowSquare [7,2,1] [9,1] := by + exact rowSquare_join (by decide) sg47 sg38 + +lemma sg1114 : RowSquare [7,3] [4,3,3] := by + exact rowSquare_join (by decide) sg16 sg97 + +lemma sg1115 : RowSquare [7,3] [4,4,2] := by + exact rowSquare_join (by decide) sg17 sg97 + +lemma sg1116 : RowSquare [7,3] [5,2,2,1] := by + exact rowSquare_join (by decide) sg39 sg45 + +lemma sg1117 : RowSquare [7,3] [5,3,1,1] := by + exact rowSquare_join (by decide) sg39 sg46 + +lemma sg1118 : RowSquare [7,3] [5,3,2] := by + exact rowSquare_join (by decide) sg40 sg45 + +lemma sg1119 : RowSquare [7,3] [5,4,1] := by + exact rowSquare_join (by decide) sg40 sg46 + +lemma sg1120 : RowSquare [2,1,1,1,1,1,1,1,1,1] [9,2] := by + exact rowSquare_join (by decide) sg46 sg108 + +lemma sg1121 : RowSquare [2,2,1,1,1,1,1,1,1] [7,2,2] := by + exact rowSquare_join (by decide) sg45 sg104 + +lemma sg1122 : RowSquare [2,2,1,1,1,1,1,1,1] [7,4] := by + exact rowSquare_join (by decide) sg46 sg105 + +lemma sg1123 : RowSquare [2,2,1,1,1,1,1,1,1] [8,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg108 + +lemma sg1124 : RowSquare [2,2,1,1,1,1,1,1,1] [8,3] := by + exact rowSquare_join (by decide) sg46 sg106 + +lemma sg1125 : RowSquare [2,2,1,1,1,1,1,1,1] [9,2] := by + exact rowSquare_join (by decide) sg46 sg107 + +lemma sg1126 : RowSquare [2,2,1,1,1,1,1,1,1] [10,1] := by + exact rowSquare_join (by decide) sg47 sg107 + +lemma sg1127 : RowSquare [2,2,2,1,1,1,1,1] [6,5] := by + exact rowSquare_join (by decide) sg17 sg230 + +lemma sg1128 : RowSquare [2,2,2,1,1,1,1,1] [7,4] := by + exact rowSquare_join (by decide) sg46 sg101 + +lemma sg1129 : RowSquare [2,2,2,1,1,1,1,1] [9,2] := by + exact rowSquare_join (by decide) sg46 sg103 + +lemma sg1130 : RowSquare [2,2,2,2,1,1,1] [6,5] := by + exact rowSquare_join (by decide) sg17 sg213 + +lemma sg1136 : RowSquare [3,1,1,1,1,1,1,1,1] [8,3] := by + exact rowSquare_join (by decide) sg49 sg92 + +lemma sg1137 : RowSquare [3,2,1,1,1,1,1,1] [5,2,2,2] := by + exact rowSquare_join (by decide) sg7 sg390 + +lemma sg1138 : RowSquare [3,2,1,1,1,1,1,1] [5,3,3] := by + exact rowSquare_join (by decide) sg45 sg89 + +lemma sg1139 : RowSquare [3,2,1,1,1,1,1,1] [5,4,2] := by + exact rowSquare_join (by decide) sg46 sg89 + +lemma sg1140 : RowSquare [3,2,1,1,1,1,1,1] [6,4,1] := by + exact rowSquare_join (by decide) sg34 sg105 + +lemma sg1141 : RowSquare [3,2,1,1,1,1,1,1] [6,5] := by + exact rowSquare_join (by decide) sg46 sg92 + +lemma sg1142 : RowSquare [3,2,2,1,1,1,1] [4,4,3] := by + exact rowSquare_join (by decide) sg40 sg89 + +lemma sg1143 : RowSquare [3,2,2,1,1,1,1] [6,5] := by + exact rowSquare_join (by decide) sg46 sg80 + +lemma sg1144 : RowSquare [3,2,2,2,1,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg32 sg83 + +lemma sg1145 : RowSquare [3,2,2,2,1,1] [3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg195 + +lemma sg1146 : RowSquare [3,3,1,1,1,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg87 + +lemma sg1147 : RowSquare [3,3,1,1,1,1,1] [3,3,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg88 + +lemma sg1148 : RowSquare [3,3,1,1,1,1,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg32 sg89 + +lemma sg1149 : RowSquare [3,3,1,1,1,1,1] [4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg636 + +lemma sg1150 : RowSquare [3,3,1,1,1,1,1] [4,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg90 + +lemma sg1151 : RowSquare [3,3,1,1,1,1,1] [4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1063 + +lemma sg1152 : RowSquare [3,3,1,1,1,1,1] [4,3,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg91 + +lemma sg1153 : RowSquare [3,3,1,1,1,1,1] [4,3,2,2] := by + exact rowSquare_join (by decide) sg33 sg88 + +lemma sg1154 : RowSquare [3,3,1,1,1,1,1] [4,3,3,1] := by + exact rowSquare_join (by decide) sg33 sg89 + +lemma sg1155 : RowSquare [3,3,1,1,1,1,1] [4,4,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg92 + +lemma sg1156 : RowSquare [3,3,1,1,1,1,1] [4,4,2,1] := by + exact rowSquare_join (by decide) sg34 sg88 + +lemma sg1157 : RowSquare [3,3,1,1,1,1,1] [4,4,3] := by + exact rowSquare_join (by decide) sg34 sg89 + +lemma sg1158 : RowSquare [3,3,1,1,1,1,1] [5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg348 + +lemma sg1159 : RowSquare [3,3,1,1,1,1,1] [5,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg93 + +lemma sg1160 : RowSquare [3,3,1,1,1,1,1] [5,2,2,2] := by + exact rowSquare_join (by decide) sg33 sg90 + +lemma sg1161 : RowSquare [3,3,1,1,1,1,1] [5,3,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg94 + +lemma sg1162 : RowSquare [3,3,1,1,1,1,1] [5,3,3] := by + exact rowSquare_join (by decide) sg35 sg89 + +lemma sg1163 : RowSquare [3,3,1,1,1,1,1] [5,4,2] := by + exact rowSquare_join (by decide) sg34 sg91 + +lemma sg1164 : RowSquare [3,3,1,1,1,1,1] [5,5,1] := by + exact rowSquare_join (by decide) sg34 sg92 + +lemma sg1165 : RowSquare [3,3,1,1,1,1,1] [6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg154 + +lemma sg1166 : RowSquare [3,3,1,1,1,1,1] [6,2,2,1] := by + exact rowSquare_join (by decide) sg33 sg93 + +lemma sg1167 : RowSquare [3,3,1,1,1,1,1] [6,3,2] := by + exact rowSquare_join (by decide) sg34 sg93 + +lemma sg1168 : RowSquare [3,3,1,1,1,1,1] [6,4,1] := by + exact rowSquare_join (by decide) sg34 sg94 + +lemma sg1169 : RowSquare [3,3,1,1,1,1,1] [6,5] := by + exact rowSquare_join (by decide) sg36 sg92 + +lemma sg1170 : RowSquare [3,3,1,1,1,1,1] [7,2,2] := by + exact rowSquare_join (by decide) sg1 sg432 + +lemma sg1171 : RowSquare [3,3,1,1,1,1,1] [7,3,1] := by + exact rowSquare_join (by decide) sg1 sg433 + +lemma sg1172 : RowSquare [3,3,1,1,1,1,1] [7,4] := by + exact rowSquare_join (by decide) sg1 sg434 + +lemma sg1173 : RowSquare [3,3,1,1,1,1,1] [8,2,1] := by + exact rowSquare_join (by decide) sg1 sg436 + +lemma sg1174 : RowSquare [3,3,1,1,1,1,1] [8,3] := by + exact rowSquare_join (by decide) sg1 sg437 + +lemma sg1175 : RowSquare [3,3,1,1,1,1,1] [9,2] := by + exact rowSquare_join (by decide) sg14 sg109 + +lemma sg1176 : RowSquare [3,3,1,1,1,1,1] [10,1] := by + exact rowSquare_join (by decide) sg1 sg439 + +lemma sg1178 : RowSquare [3,3,2,1,1,1] [2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg74 + +lemma sg1179 : RowSquare [3,3,2,1,1,1] [3,3,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg76 + +lemma sg1181 : RowSquare [3,3,3,2] [3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg516 + +lemma sg1182 : RowSquare [4,1,1,1,1,1,1,1] [5,2,2,2] := by + exact rowSquare_join (by decide) sg7 sg373 + +lemma sg1183 : RowSquare [4,1,1,1,1,1,1,1] [6,3,2] := by + exact rowSquare_join (by decide) sg7 sg378 + +lemma sg1184 : RowSquare [4,1,1,1,1,1,1,1] [7,4] := by + exact rowSquare_join (by decide) sg7 sg383 + +lemma sg1185 : RowSquare [4,2,1,1,1,1,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg178 + +lemma sg1186 : RowSquare [4,2,1,1,1,1,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg1032 + +lemma sg1187 : RowSquare [4,2,1,1,1,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg1033 + +lemma sg1188 : RowSquare [4,2,1,1,1,1,1] [3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg178 + +lemma sg1189 : RowSquare [4,2,1,1,1,1,1] [3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg371 + +lemma sg1190 : RowSquare [4,2,1,1,1,1,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg372 + +lemma sg1191 : RowSquare [4,2,1,1,1,1,1] [3,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg373 + +lemma sg1192 : RowSquare [4,2,1,1,1,1,1] [4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg330 + +lemma sg1193 : RowSquare [4,2,1,1,1,1,1] [4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg179 + +lemma sg1194 : RowSquare [4,2,1,1,1,1,1] [4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg179 + +lemma sg1195 : RowSquare [4,2,2,1,1,1] [2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg330 + +lemma sg1196 : RowSquare [4,2,2,1,1,1] [2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg178 + +lemma sg1197 : RowSquare [4,2,2,1,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg961 + +lemma sg1198 : RowSquare [4,2,2,1,1,1] [3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg178 + +lemma sg1199 : RowSquare [4,2,2,1,1,1] [3,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg180 + +lemma sg1200 : RowSquare [4,2,2,1,1,1] [3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg181 + +lemma sg1201 : RowSquare [4,2,2,1,1,1] [4,4,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg143 + +lemma sg1202 : RowSquare [4,3,1,1,1,1] [3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg940 + +lemma sg1203 : RowSquare [4,3,1,1,1,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg178 + +lemma sg1204 : RowSquare [4,3,1,1,1,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg942 + +lemma sg1205 : RowSquare [4,3,1,1,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg762 + +lemma sg1206 : RowSquare [4,3,1,1,1,1] [3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg178 + +lemma sg1207 : RowSquare [4,3,1,1,1,1] [3,3,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg67 + +lemma sg1208 : RowSquare [4,3,1,1,1,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg32 sg68 + +lemma sg1209 : RowSquare [4,3,1,1,1,1] [4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg548 + +lemma sg1210 : RowSquare [4,3,1,1,1,1] [4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg11 sg178 + +lemma sg1211 : RowSquare [4,3,1,1,1,1] [4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg763 + +lemma sg1212 : RowSquare [4,3,1,1,1,1] [4,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg767 + +lemma sg1213 : RowSquare [4,3,1,1,1,1] [4,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg768 + +lemma sg1214 : RowSquare [4,3,1,1,1,1] [4,4,2,1] := by + exact rowSquare_join (by decide) sg34 sg67 + +lemma sg1215 : RowSquare [4,3,1,1,1,1] [4,4,3] := by + exact rowSquare_join (by decide) sg34 sg68 + +lemma sg1216 : RowSquare [4,3,1,1,1,1] [5,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg456 + +lemma sg1217 : RowSquare [4,3,1,1,1,1] [5,3,3] := by + exact rowSquare_join (by decide) sg4 sg239 + +lemma sg1218 : RowSquare [4,3,1,1,1,1] [5,5,1] := by + exact rowSquare_join (by decide) sg4 sg241 + +lemma sg1219 : RowSquare [4,3,1,1,1,1] [6,5] := by + exact rowSquare_join (by decide) sg5 sg241 + +lemma sg1220 : RowSquare [4,3,1,1,1,1] [7,2,2] := by + exact rowSquare_join (by decide) sg4 sg245 + +lemma sg1221 : RowSquare [4,3,1,1,1,1] [9,2] := by + exact rowSquare_join (by decide) sg42 sg50 + +lemma sg1222 : RowSquare [4,3,1,1,1,1] [10,1] := by + exact rowSquare_join (by decide) sg43 sg50 + +lemma sg1223 : RowSquare [4,3,2,1,1] [2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg849 + +lemma sg1224 : RowSquare [4,3,2,1,1] [3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg851 + +lemma sg1225 : RowSquare [4,3,2,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg792 + +lemma sg1226 : RowSquare [4,3,2,1,1] [3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg285 + +lemma sg1227 : RowSquare [4,3,2,1,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg32 sg55 + +lemma sg1228 : RowSquare [4,3,2,1,1] [4,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg249 + +lemma sg1229 : RowSquare [4,3,2,1,1] [4,4,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg143 + +lemma sg1230 : RowSquare [4,3,2,1,1] [4,4,3] := by + exact rowSquare_join (by decide) sg4 sg251 + +lemma sg1231 : RowSquare [4,3,2,1,1] [5,3,3] := by + exact rowSquare_join (by decide) sg9 sg114 + +lemma sg1233 : RowSquare [4,3,3,1] [2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg23 sg65 + +lemma sg1234 : RowSquare [4,3,3,1] [2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg10 sg128 + +lemma sg1235 : RowSquare [4,4,1,1,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg832 + +lemma sg1236 : RowSquare [4,4,1,1,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg833 + +lemma sg1237 : RowSquare [4,4,1,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg834 + +lemma sg1238 : RowSquare [4,4,2,1] [4,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg125 + +lemma sg1239 : RowSquare [4,4,3] [3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg516 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes10.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes10.lean index cef090cbd08f6b04e4a6ee4fe0eab83cc177f4bb..135fffb80d96af4108ab01fb56897bb5aac2c7be 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes10.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes10.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes8 - -namespace OAI - -/-! Semigroup Nodes 10. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg4516 : RowSquare [10,1,1,1,1,1,1] [8,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg1751 - -lemma sg4517 : RowSquare [10,2,1,1,1,1] [5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg1331 - -lemma sg4518 : RowSquare [10,2,1,1,1,1] [5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg1331 - -lemma sg4519 : RowSquare [10,2,2,1,1] [4,3,3,3,3] := by - exact rowSquare_join (by decide) sg87 sg1001 - -lemma sg4520 : RowSquare [10,2,2,1,1] [4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg999 - -lemma sg4521 : RowSquare [10,2,2,2] [4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg371 - -lemma sg4522 : RowSquare [10,2,2,2] [4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg372 - -lemma sg4523 : RowSquare [10,2,2,2] [4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg371 sg373 - -lemma sg4524 : RowSquare [10,2,2,2] [4,4,4,2,2] := by - exact rowSquare_join (by decide) sg372 sg372 - -lemma sg4525 : RowSquare [10,2,2,2] [4,4,4,3,1] := by - exact rowSquare_join (by decide) sg372 sg373 - -lemma sg4526 : RowSquare [10,2,2,2] [4,4,4,4] := by - exact rowSquare_join (by decide) sg373 sg373 - -lemma sg4527 : RowSquare [10,2,2,2] [5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg371 sg377 - -lemma sg4528 : RowSquare [10,2,2,2] [5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg378 - -lemma sg4529 : RowSquare [10,2,2,2] [5,5,3,2,1] := by - exact rowSquare_join (by decide) sg372 sg377 - -lemma sg4530 : RowSquare [10,2,2,2] [5,5,3,3] := by - exact rowSquare_join (by decide) sg373 sg377 - -lemma sg4531 : RowSquare [10,2,2,2] [5,5,4,1,1] := by - exact rowSquare_join (by decide) sg372 sg378 - -lemma sg4532 : RowSquare [10,2,2,2] [5,5,4,2] := by - exact rowSquare_join (by decide) sg373 sg378 - -lemma sg4533 : RowSquare [10,3,1,1,1] [4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg998 - -lemma sg4534 : RowSquare [10,3,1,1,1] [4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg999 - -lemma sg4535 : RowSquare [10,3,1,1,1] [4,4,4,2,2] := by - exact rowSquare_join (by decide) sg97 sg1001 - -lemma sg4536 : RowSquare [10,3,2,1] [4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg371 sg390 - -lemma sg4537 : RowSquare [10,3,2,1] [4,4,3,3,2] := by - exact rowSquare_join (by decide) sg88 sg1033 - -lemma sg4538 : RowSquare [10,3,2,1] [4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg89 sg1032 - -lemma sg4539 : RowSquare [10,3,2,1] [4,4,4,4] := by - exact rowSquare_join (by decide) sg390 sg373 - -lemma sg4540 : RowSquare [10,3,3] [5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg88 sg1063 - -lemma sg4541 : RowSquare [10,3,3] [5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg1063 - -lemma sg4542 : RowSquare [10,3,3] [5,5,3,3] := by - exact rowSquare_join (by decide) sg88 sg1064 - -lemma sg4543 : RowSquare [10,4,2] [4,4,4,4] := by - exact rowSquare_join (by decide) sg390 sg390 - -lemma sg4544 : RowSquare [11,2,1,1,1] [6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg231 sg586 - -lemma sg4545 : RowSquare [11,2,1,1,1] [6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg232 sg586 - -lemma sg4546 : RowSquare [11,2,1,1,1] [6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg104 sg998 - -lemma sg4547 : RowSquare [11,2,1,1,1] [6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg104 sg1000 - -lemma sg4548 : RowSquare [11,2,1,1,1] [6,3,3,2,2] := by - exact rowSquare_join (by decide) sg104 sg1001 - -lemma sg4549 : RowSquare [11,2,1,1,1] [6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg105 sg998 - -lemma sg4550 : RowSquare [11,2,1,1,1] [6,4,2,2,2] := by - exact rowSquare_join (by decide) sg105 sg1001 - -lemma sg4551 : RowSquare [11,2,1,1,1] [7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg233 sg586 - -lemma sg4552 : RowSquare [11,2,1,1,1] [7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg231 sg587 - -lemma sg4553 : RowSquare [11,2,1,1,1] [7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg232 sg587 - -lemma sg4554 : RowSquare [3,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,2] := by - exact rowSquare_join (by decide) sg389 sg708 - -lemma sg4555 : RowSquare [3,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,1] := by - exact rowSquare_join (by decide) sg413 sg693 - -lemma sg4556 : RowSquare [3,3,2,1,1,1,1,1,1,1,1,1] [7,4,2,2,2] := by - exact rowSquare_join (by decide) sg413 sg694 - -lemma sg4557 : RowSquare [3,3,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,1] := by - exact rowSquare_join (by decide) sg389 sg709 - -lemma sg4558 : RowSquare [3,3,2,1,1,1,1,1,1,1,1,1] [7,4,3,3] := by - exact rowSquare_join (by decide) sg390 sg709 - -lemma sg4559 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg391 sg692 - -lemma sg4560 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg391 sg693 - -lemma sg4561 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [6,3,3,3,2] := by - exact rowSquare_join (by decide) sg413 sg644 - -lemma sg4562 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg391 sg697 - -lemma sg4563 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [8,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg306 sg716 - -lemma sg4564 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [8,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg391 sg702 - -lemma sg4565 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [8,3,3,3] := by - exact rowSquare_join (by decide) sg390 sg704 - -lemma sg4566 : RowSquare [3,3,2,2,2,2,2,1] [4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg306 sg656 - -lemma sg4567 : RowSquare [3,3,2,2,2,2,2,1] [4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg306 sg657 - -lemma sg4568 : RowSquare [3,3,2,2,2,2,2,1] [4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg306 sg658 - -lemma sg4569 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg193 sg1061 - -lemma sg4570 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg1533 - -lemma sg4571 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,4,3,3,3] := by - exact rowSquare_join (by decide) sg194 sg1061 - -lemma sg4572 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg389 sg636 - -lemma sg4573 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg390 sg636 - -lemma sg4574 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,4,4,3,2] := by - exact rowSquare_join (by decide) sg389 sg637 - -lemma sg4575 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,4,4,4,1] := by - exact rowSquare_join (by decide) sg390 sg637 - -lemma sg4576 : RowSquare [3,3,3,2,1,1,1,1,1,1] [5,4,4,4] := by - exact rowSquare_join (by decide) sg390 sg638 - -lemma sg4577 : RowSquare [3,3,3,2,1,1,1,1,1,1] [5,5,4,3] := by - exact rowSquare_join (by decide) sg390 sg640 - -lemma sg4578 : RowSquare [3,3,3,2,1,1,1,1,1,1] [7,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg348 sg703 - -lemma sg4579 : RowSquare [3,3,3,2,1,1,1,1,1,1] [7,7,1,1,1] := by - exact rowSquare_join (by decide) sg396 sg639 - -lemma sg4580 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg708 - -lemma sg4581 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg371 sg709 - -lemma sg4582 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg710 - -lemma sg4583 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [7,4,3,3] := by - exact rowSquare_join (by decide) sg373 sg709 - -lemma sg4584 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [8,3,3,3] := by - exact rowSquare_join (by decide) sg373 sg711 - -lemma sg4585 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [8,4,3,2] := by - exact rowSquare_join (by decide) sg373 sg712 - -lemma sg4586 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [8,5,2,2] := by - exact rowSquare_join (by decide) sg373 sg713 - -lemma sg4587 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg692 - -lemma sg4588 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg693 - -lemma sg4589 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg218 sg1032 - -lemma sg4590 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3] := by - exact rowSquare_join (by decide) sg218 sg1033 - -lemma sg4591 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg694 - -lemma sg4592 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg695 - -lemma sg4593 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg692 - -lemma sg4594 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg371 sg693 - -lemma sg4595 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,2] := by - exact rowSquare_join (by decide) sg219 sg1033 - -lemma sg4596 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg696 - -lemma sg4597 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg220 sg1032 - -lemma sg4598 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,4,2,2] := by - exact rowSquare_join (by decide) sg389 sg675 - -lemma sg4599 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,1] := by - exact rowSquare_join (by decide) sg389 sg676 - -lemma sg4600 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4] := by - exact rowSquare_join (by decide) sg390 sg676 - -lemma sg4601 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg1109 - -lemma sg4602 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg694 - -lemma sg4603 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg1110 - -lemma sg4604 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg371 sg695 - -lemma sg4605 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,3,2,2] := by - exact rowSquare_join (by decide) sg372 sg694 - -lemma sg4606 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,1] := by - exact rowSquare_join (by decide) sg373 sg694 - -lemma sg4607 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg696 - -lemma sg4608 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,4,2,1] := by - exact rowSquare_join (by decide) sg372 sg695 - -lemma sg4609 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3] := by - exact rowSquare_join (by decide) sg373 sg695 - -lemma sg4610 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,5,1,1] := by - exact rowSquare_join (by decide) sg372 sg696 - -lemma sg4611 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,5,2] := by - exact rowSquare_join (by decide) sg373 sg696 - -lemma sg4612 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg370 sg697 - -lemma sg4613 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg698 - -lemma sg4614 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg697 - -lemma sg4615 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg391 sg675 - -lemma sg4616 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg1112 - -lemma sg4617 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg701 - -lemma sg4618 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,6,3,1,1] := by - exact rowSquare_join (by decide) sg372 sg701 - -lemma sg4619 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,6,5] := by - exact rowSquare_join (by decide) sg378 sg696 - -lemma sg4620 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [7,7,1,1,1] := by - exact rowSquare_join (by decide) sg383 sg694 - -lemma sg4621 : RowSquare [4,3,2,2,1,1,1,1,1,1] [4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg693 - -lemma sg4622 : RowSquare [4,3,2,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg696 - -lemma sg4623 : RowSquare [4,3,2,2,1,1,1,1,1,1] [4,4,4,4,1] := by - exact rowSquare_join (by decide) sg390 sg616 - -lemma sg4624 : RowSquare [4,3,2,2,2,2,1,1] [3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg579 - -lemma sg4625 : RowSquare [4,3,2,2,2,2,1,1] [4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg849 - -lemma sg4626 : RowSquare [4,3,2,2,2,2,1,1] [4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg581 - -lemma sg4627 : RowSquare [4,3,2,2,2,2,1,1] [4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg849 - -lemma sg4628 : RowSquare [4,3,2,2,2,2,1,1] [4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg849 - -lemma sg4629 : RowSquare [4,3,2,2,2,2,1,1] [4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg583 - -lemma sg4630 : RowSquare [4,3,2,2,2,2,1,1] [4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg584 - -lemma sg4631 : RowSquare [4,3,2,2,2,2,1,1] [5,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg211 sg849 - -lemma sg4632 : RowSquare [4,3,2,2,2,2,1,1] [5,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg212 sg849 - -lemma sg4633 : RowSquare [4,3,2,2,2,2,1,1] [5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg213 sg849 - -lemma sg4634 : RowSquare [4,3,2,2,2,2,1,1] [6,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg214 sg849 - -lemma sg4635 : RowSquare [4,3,2,2,2,2,1,1] [6,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg215 sg849 - -lemma sg4636 : RowSquare [4,3,2,2,2,2,1,1] [7,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg216 sg849 - -lemma sg4637 : RowSquare [4,3,3,2,1,1,1,1,1] [4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg641 - -lemma sg4638 : RowSquare [4,3,3,2,1,1,1,1,1] [4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg980 - -lemma sg4639 : RowSquare [4,3,3,2,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg104 sg1232 - -lemma sg4640 : RowSquare [4,3,3,2,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg105 sg1232 - -lemma sg4641 : RowSquare [4,3,3,2,1,1,1,1,1] [5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg220 sg850 - -lemma sg4642 : RowSquare [4,3,3,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg106 sg1232 - -lemma sg4643 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg370 sg673 - -lemma sg4644 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg370 sg674 - -lemma sg4645 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg675 - -lemma sg4646 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg676 - -lemma sg4647 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg674 - -lemma sg4648 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg675 - -lemma sg4649 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg371 sg676 - -lemma sg4650 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,4,4,2,2] := by - exact rowSquare_join (by decide) sg372 sg675 - -lemma sg4651 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,4,4,3,1] := by - exact rowSquare_join (by decide) sg372 sg676 - -lemma sg4652 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,4,4,4] := by - exact rowSquare_join (by decide) sg373 sg676 - -lemma sg4653 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg370 sg677 - -lemma sg4654 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg678 - -lemma sg4655 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg677 - -lemma sg4656 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg374 sg675 - -lemma sg4657 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg374 sg676 - -lemma sg4658 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg681 - -lemma sg4659 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,5,3,2,1] := by - exact rowSquare_join (by decide) sg372 sg680 - -lemma sg4660 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,5,3,3] := by - exact rowSquare_join (by decide) sg373 sg680 - -lemma sg4661 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,5,4,1,1] := by - exact rowSquare_join (by decide) sg372 sg681 - -lemma sg4662 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,5,4,2] := by - exact rowSquare_join (by decide) sg373 sg681 - -lemma sg4663 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg682 - -lemma sg4664 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg374 sg677 - -lemma sg4665 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg682 - -lemma sg4666 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg684 - -lemma sg4667 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,3,3,2,2] := by - exact rowSquare_join (by decide) sg372 sg682 - -lemma sg4668 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg684 - -lemma sg4669 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,4,4,1,1] := by - exact rowSquare_join (by decide) sg372 sg684 - -lemma sg4670 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg686 - -lemma sg4671 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg686 - -lemma sg4672 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,6,2,1,1] := by - exact rowSquare_join (by decide) sg372 sg686 - -lemma sg4673 : RowSquare [4,4,2,1,1,1,1,1,1,1] [3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg1032 - -lemma sg4674 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg673 - -lemma sg4675 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg676 - -lemma sg4676 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg616 - -lemma sg4677 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg179 sg1032 - -lemma sg4678 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg179 sg1033 - -lemma sg4679 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,4,3,3,3] := by - exact rowSquare_join (by decide) sg180 sg1033 - -lemma sg4680 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg1041 - -lemma sg4681 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg372 sg615 - -lemma sg4682 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg373 sg615 - -lemma sg4683 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,4,4,3,2] := by - exact rowSquare_join (by decide) sg372 sg616 - -lemma sg4684 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,4,4,4,1] := by - exact rowSquare_join (by decide) sg373 sg616 - -lemma sg4685 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg677 - -lemma sg4686 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg370 sg617 - -lemma sg4687 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg678 - -lemma sg4688 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg370 sg618 - -lemma sg4689 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg679 - -lemma sg4690 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg374 sg615 - -lemma sg4691 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg376 sg615 - -lemma sg4692 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,5,5,1,1] := by - exact rowSquare_join (by decide) sg372 sg623 - -lemma sg4693 : RowSquare [4,4,2,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg685 - -lemma sg4694 : RowSquare [4,4,2,1,1,1,1,1,1,1] [6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg374 sg623 - -lemma sg4695 : RowSquare [4,4,2,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg686 - -lemma sg4696 : RowSquare [4,4,2,2,1,1,1,1,1] [3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg330 sg613 - -lemma sg4697 : RowSquare [4,4,2,2,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg1650 - -lemma sg4698 : RowSquare [4,4,2,2,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg1651 - -lemma sg4699 : RowSquare [4,4,2,2,2,2,1] [4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg1650 - -lemma sg4700 : RowSquare [4,4,2,2,2,2,1] [4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg1650 - -lemma sg4701 : RowSquare [4,4,2,2,2,2,1] [5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg1650 - -lemma sg4702 : RowSquare [4,4,2,2,2,2,1] [5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg1651 - -lemma sg4703 : RowSquare [4,4,2,2,2,2,1] [5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg1651 - -lemma sg4704 : RowSquare [4,4,2,2,2,2,1] [5,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg1655 - -lemma sg4705 : RowSquare [4,4,2,2,2,2,1] [5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg1656 - -lemma sg4706 : RowSquare [4,4,2,2,2,2,1] [5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg1653 - -lemma sg4707 : RowSquare [4,4,2,2,2,2,1] [5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg1652 - -lemma sg4708 : RowSquare [4,4,2,2,2,2,1] [5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg1656 - -lemma sg4709 : RowSquare [4,4,2,2,2,2,1] [6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg1650 - -lemma sg4710 : RowSquare [4,4,2,2,2,2,1] [6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg1651 - -lemma sg4711 : RowSquare [4,4,2,2,2,2,1] [6,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg1655 - -lemma sg4712 : RowSquare [4,4,2,2,2,2,1] [6,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg1655 - -lemma sg4713 : RowSquare [4,4,2,2,2,2,1] [6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg1657 - -lemma sg4714 : RowSquare [4,4,2,2,2,2,1] [6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg1656 - -lemma sg4715 : RowSquare [4,4,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg1651 - -lemma sg4716 : RowSquare [4,4,2,2,2,2,1] [7,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg1655 - -lemma sg4717 : RowSquare [4,4,2,2,2,2,1] [8,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg1655 - -lemma sg4718 : RowSquare [4,4,3,2,1,1,1,1] [2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg849 - -lemma sg4719 : RowSquare [4,4,3,2,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg2107 - -lemma sg4720 : RowSquare [4,4,3,2,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg2108 - -lemma sg4721 : RowSquare [4,4,3,2,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg2109 - -lemma sg4722 : RowSquare [4,4,3,2,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg2112 - -lemma sg4723 : RowSquare [4,4,3,2,1,1,1,1] [7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3 sg2504 - -lemma sg4724 : RowSquare [5,3,2,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg586 - -lemma sg4725 : RowSquare [5,3,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg391 sg586 - -lemma sg4726 : RowSquare [5,3,2,1,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg220 sg910 - -lemma sg4727 : RowSquare [5,3,2,1,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg394 sg586 - -lemma sg4728 : RowSquare [5,3,2,1,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg1682 - -lemma sg4729 : RowSquare [5,3,2,2,1,1,1,1,1] [4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg1682 - -lemma sg4730 : RowSquare [5,3,2,2,1,1,1,1,1] [4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg1682 - -lemma sg4731 : RowSquare [5,3,2,2,1,1,1,1,1] [5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg47 sg1682 - -lemma sg4732 : RowSquare [5,3,2,2,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg1683 - -lemma sg4733 : RowSquare [5,3,2,2,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg1683 - -lemma sg4734 : RowSquare [5,3,3,2,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg1682 - -lemma sg4735 : RowSquare [5,3,3,2,1,1,1,1] [3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg2137 - -lemma sg4736 : RowSquare [5,3,3,2,1,1,1,1] [3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg1682 - -lemma sg4737 : RowSquare [5,3,3,2,1,1,1,1] [3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg1683 - -lemma sg4738 : RowSquare [5,3,3,2,1,1,1,1] [4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg2137 - -lemma sg4739 : RowSquare [5,3,3,2,1,1,1,1] [8,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg3865 - -lemma sg4740 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg586 - -lemma sg4741 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg586 - -lemma sg4742 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg998 - -lemma sg4743 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg372 sg586 - -lemma sg4744 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg999 - -lemma sg4745 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg586 - -lemma sg4746 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg1000 - -lemma sg4747 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg178 sg1001 - -lemma sg4748 : RowSquare [5,4,1,1,1,1,1,1,1,1] [4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg179 sg1000 - -lemma sg4749 : RowSquare [5,4,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg588 - -lemma sg4750 : RowSquare [5,4,1,1,1,1,1,1,1,1] [4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg589 - -lemma sg4751 : RowSquare [5,4,1,1,1,1,1,1,1,1] [4,4,3,3,3] := by - exact rowSquare_join (by decide) sg180 sg1001 - -lemma sg4752 : RowSquare [5,4,1,1,1,1,1,1,1,1] [4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg373 sg589 - -lemma sg4753 : RowSquare [5,4,1,1,1,1,1,1,1,1] [4,4,4,4,1] := by - exact rowSquare_join (by decide) sg373 sg590 - -lemma sg4754 : RowSquare [5,4,1,1,1,1,1,1,1,1] [5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg376 sg589 - -lemma sg4755 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg384 sg586 - -lemma sg4756 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg379 sg587 - -lemma sg4757 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg3876 - -lemma sg4758 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg385 sg586 - -lemma sg4759 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg380 sg587 - -lemma sg4760 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg3877 - -lemma sg4761 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg3878 - -lemma sg4762 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg381 sg587 - -lemma sg4763 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg3879 - -lemma sg4764 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg3880 - -lemma sg4765 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg3881 - -lemma sg4766 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,3,3,2] := by - exact rowSquare_join (by decide) sg379 sg590 - -lemma sg4767 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg386 sg586 - -lemma sg4768 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg383 sg587 - -lemma sg4769 : RowSquare [5,4,1,1,1,1,1,1,1,1] [7,5,5] := by - exact rowSquare_join (by decide) sg4 sg2497 - -lemma sg4770 : RowSquare [5,4,1,1,1,1,1,1,1,1] [9,8] := by - exact rowSquare_join (by decide) sg0 sg3905 - -lemma sg4771 : RowSquare [5,4,1,1,1,1,1,1,1,1] [10,7] := by - exact rowSquare_join (by decide) sg14 sg2020 - -lemma sg4772 : RowSquare [5,4,1,1,1,1,1,1,1,1] [11,6] := by - exact rowSquare_join (by decide) sg42 sg1577 - -lemma sg4773 : RowSquare [5,4,1,1,1,1,1,1,1,1] [12,5] := by - exact rowSquare_join (by decide) sg42 sg1578 - -lemma sg4774 : RowSquare [5,4,1,1,1,1,1,1,1,1] [13,4] := by - exact rowSquare_join (by decide) sg85 sg1120 - -lemma sg4775 : RowSquare [5,4,1,1,1,1,1,1,1,1] [14,3] := by - exact rowSquare_join (by decide) sg213 sg718 - -lemma sg4776 : RowSquare [5,4,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg910 - -lemma sg4777 : RowSquare [5,4,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg586 - -lemma sg4778 : RowSquare [5,4,2,1,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg910 - -lemma sg4779 : RowSquare [5,4,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg330 sg587 - -lemma sg4780 : RowSquare [5,4,2,1,1,1,1,1,1] [3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg180 sg910 - -lemma sg4781 : RowSquare [5,4,2,1,1,1,1,1,1] [3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg181 sg910 - -lemma sg4782 : RowSquare [5,4,2,1,1,1,1,1,1] [3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg913 - -lemma sg4783 : RowSquare [5,4,2,1,1,1,1,1,1] [4,4,3,3,3] := by - exact rowSquare_join (by decide) sg180 sg915 - -lemma sg4784 : RowSquare [5,4,2,2,1,1,1,1] [3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg142 sg910 - -lemma sg4785 : RowSquare [5,4,2,2,1,1,1,1] [3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg143 sg910 - -lemma sg4786 : RowSquare [5,4,2,2,1,1,1,1] [3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg144 sg910 - -lemma sg4787 : RowSquare [5,4,2,2,1,1,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg2596 - -lemma sg4788 : RowSquare [5,4,2,2,1,1,1,1] [4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg910 - -lemma sg4789 : RowSquare [5,4,2,2,1,1,1,1] [4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg543 - -lemma sg4790 : RowSquare [5,4,2,2,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg2597 - -lemma sg4791 : RowSquare [5,4,2,2,1,1,1,1] [5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg2598 - -lemma sg4792 : RowSquare [5,4,2,2,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg2599 - -lemma sg4793 : RowSquare [5,4,2,2,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg3935 - -lemma sg4794 : RowSquare [5,4,2,2,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg2603 - -lemma sg4795 : RowSquare [5,4,2,2,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg3936 - -lemma sg4796 : RowSquare [5,4,2,2,1,1,1,1] [7,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3199 - -lemma sg4797 : RowSquare [5,4,2,2,2,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg2596 - -lemma sg4798 : RowSquare [5,4,2,2,2,1,1] [4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg2597 - -lemma sg4799 : RowSquare [5,4,2,2,2,1,1] [4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg2601 - -lemma sg4800 : RowSquare [5,4,2,2,2,1,1] [4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg2602 - -lemma sg4801 : RowSquare [5,4,2,2,2,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg2597 - -lemma sg4802 : RowSquare [5,4,2,2,2,1,1] [5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg2601 - -lemma sg4803 : RowSquare [5,4,2,2,2,1,1] [5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6 sg2602 - -lemma sg4805 : RowSquare [5,5,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg313 sg586 - -lemma sg4806 : RowSquare [5,5,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg312 sg587 - -lemma sg4807 : RowSquare [5,5,1,1,1,1,1,1,1] [4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg313 sg589 - -lemma sg4808 : RowSquare [5,5,1,1,1,1,1,1,1] [6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg3211 - -lemma sg4809 : RowSquare [5,5,1,1,1,1,1,1,1] [6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg3213 - -lemma sg4810 : RowSquare [5,5,1,1,1,1,1,1,1] [8,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg2028 - -lemma sg4811 : RowSquare [5,5,1,1,1,1,1,1,1] [8,5,2,2] := by - exact rowSquare_join (by decide) sg13 sg2029 - -lemma sg4812 : RowSquare [5,5,1,1,1,1,1,1,1] [8,5,3,1] := by - exact rowSquare_join (by decide) sg13 sg2030 - -lemma sg4813 : RowSquare [5,5,1,1,1,1,1,1,1] [9,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg2032 - -lemma sg4814 : RowSquare [5,5,1,1,1,1,1,1,1] [9,8] := by - exact rowSquare_join (by decide) sg14 sg2031 - -lemma sg4815 : RowSquare [5,5,1,1,1,1,1,1,1] [10,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg2034 - -lemma sg4816 : RowSquare [5,5,1,1,1,1,1,1,1] [10,3,3,1] := by - exact rowSquare_join (by decide) sg84 sg1121 - -lemma sg4817 : RowSquare [5,5,1,1,1,1,1,1,1] [10,7] := by - exact rowSquare_join (by decide) sg14 sg2033 - -lemma sg4818 : RowSquare [5,5,1,1,1,1,1,1,1] [11,6] := by - exact rowSquare_join (by decide) sg85 sg1122 - -lemma sg4819 : RowSquare [5,5,1,1,1,1,1,1,1] [12,5] := by - exact rowSquare_join (by decide) sg85 sg1124 - -lemma sg4820 : RowSquare [5,5,1,1,1,1,1,1,1] [13,4] := by - exact rowSquare_join (by decide) sg367 sg427 - -lemma sg4821 : RowSquare [5,5,1,1,1,1,1,1,1] [14,3] := by - exact rowSquare_join (by decide) sg85 sg1126 - -lemma sg4822 : RowSquare [5,5,2,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg132 sg910 - -lemma sg4823 : RowSquare [5,5,2,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg133 sg910 - -lemma sg4824 : RowSquare [5,5,2,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg134 sg910 - -lemma sg4825 : RowSquare [5,5,2,1,1,1,1,1] [4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg275 sg586 - -lemma sg4826 : RowSquare [5,5,2,1,1,1,1,1] [4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg276 sg586 - -lemma sg4827 : RowSquare [5,5,2,1,1,1,1,1] [5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg279 sg586 - -lemma sg4828 : RowSquare [5,5,2,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg137 sg910 - -lemma sg4829 : RowSquare [5,5,2,1,1,1,1,1] [5,4,4,4] := by - exact rowSquare_join (by decide) sg13 sg2035 - -lemma sg4830 : RowSquare [5,5,2,1,1,1,1,1] [5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg281 sg586 - -lemma sg4831 : RowSquare [5,5,2,1,1,1,1,1] [5,5,5,1,1] := by - exact rowSquare_join (by decide) sg314 sg543 - -lemma sg4833 : RowSquare [5,5,3,2,2] [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg253 sg509 - -lemma sg4834 : RowSquare [6,3,2,1,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg1754 - -lemma sg4835 : RowSquare [6,3,2,1,1,1,1,1,1] [2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg1327 - -lemma sg4836 : RowSquare [6,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg1328 - -lemma sg4837 : RowSquare [6,3,2,1,1,1,1,1,1] [3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg1755 - -lemma sg4838 : RowSquare [6,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg1329 - -lemma sg4839 : RowSquare [6,3,2,1,1,1,1,1,1] [3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg1757 - -lemma sg4840 : RowSquare [6,3,2,1,1,1,1,1,1] [3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg1331 - -lemma sg4841 : RowSquare [6,3,2,1,1,1,1,1,1] [3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg32 sg1758 - -lemma sg4842 : RowSquare [6,3,2,1,1,1,1,1,1] [3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg74 sg1332 - -lemma sg4843 : RowSquare [6,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg1338 - -lemma sg4844 : RowSquare [6,3,2,2,2,2] [4,4,3,3,3] := by - exact rowSquare_join (by decide) sg166 sg762 - -lemma sg4845 : RowSquare [6,4,1,1,1,1,1,1,1] [3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg66 sg1327 - -lemma sg4846 : RowSquare [6,4,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg889 - -lemma sg4847 : RowSquare [6,4,1,1,1,1,1,1,1] [3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg890 - -lemma sg4848 : RowSquare [6,4,1,1,1,1,1,1,1] [3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg178 sg892 - -lemma sg4849 : RowSquare [6,4,2,1,1,1,1,1] [4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg22 sg1754 - -lemma sg4850 : RowSquare [6,4,2,1,1,1,1,1] [4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg56 sg1327 - -lemma sg4851 : RowSquare [6,4,2,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3259 - -lemma sg4852 : RowSquare [6,4,2,1,1,1,1,1] [4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg3232 - -lemma sg4853 : RowSquare [6,4,2,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg3983 - -lemma sg4854 : RowSquare [6,4,2,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg3984 - -lemma sg4855 : RowSquare [6,4,2,1,1,1,1,1] [5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg1754 - -lemma sg4856 : RowSquare [6,4,2,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3261 - -lemma sg4857 : RowSquare [6,4,2,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3266 - -lemma sg4858 : RowSquare [6,4,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg60 sg1327 - -lemma sg4859 : RowSquare [6,4,2,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg2534 - -lemma sg4860 : RowSquare [6,4,2,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3267 - -lemma sg4861 : RowSquare [6,4,3,1,1,1,1] [3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg1628 - -lemma sg4863 : RowSquare [6,4,3,2,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg347 sg445 - -lemma sg4864 : RowSquare [6,4,3,2,1,1] [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg346 sg445 - -lemma sg4865 : RowSquare [6,4,3,2,1,1] [2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg345 sg445 - -lemma sg4866 : RowSquare [6,4,3,2,1,1] [2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg445 - -lemma sg4867 : RowSquare [6,4,3,2,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg444 - -lemma sg4868 : RowSquare [6,4,3,2,1,1] [2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg443 - -lemma sg4869 : RowSquare [6,4,3,2,1,1] [2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg342 sg442 - -lemma sg4870 : RowSquare [6,4,3,2,1,1] [3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg2545 - -lemma sg4871 : RowSquare [6,4,3,2,1,1] [3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg340 sg440 - -lemma sg4872 : RowSquare [6,4,3,2,1,1] [3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg1616 - -lemma sg4873 : RowSquare [6,5,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg51 sg1327 - -lemma sg4874 : RowSquare [6,5,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg52 sg1327 - -lemma sg4875 : RowSquare [7,3,3,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg355 sg454 - -lemma sg4876 : RowSquare [7,3,3,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg354 sg453 - -lemma sg4877 : RowSquare [7,3,3,1,1,1,1] [2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg354 sg451 - -lemma sg4878 : RowSquare [7,3,3,1,1,1,1] [2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg92 sg1143 - -lemma sg4879 : RowSquare [7,3,3,1,1,1,1] [3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg89 sg1142 - -lemma sg4880 : RowSquare [7,4,3,1,1,1] [4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg77 sg1195 - -lemma sg4881 : RowSquare [7,4,3,1,1,1] [4,4,4,4,1] := by - exact rowSquare_join (by decide) sg32 sg1587 - -lemma sg4882 : RowSquare [7,4,3,2,1] [3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg790 - -lemma sg4883 : RowSquare [7,4,3,2,1] [3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg178 sg792 - -lemma sg4884 : RowSquare [7,4,3,2,1] [4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg795 - -lemma sg4885 : RowSquare [7,4,3,2,1] [4,4,4,4,1] := by - exact rowSquare_join (by decide) sg334 sg476 - -lemma sg4886 : RowSquare [7,4,3,3] [3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg480 - -lemma sg4887 : RowSquare [7,4,3,3] [4,4,4,4,1] := by - exact rowSquare_join (by decide) sg334 sg481 - -lemma sg4888 : RowSquare [7,5,1,1,1,1,1] [5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg2128 - -lemma sg4889 : RowSquare [7,5,3,1,1] [3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg306 sg534 - -lemma sg4890 : RowSquare [8,3,1,1,1,1,1,1] [4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg2620 - -lemma sg4891 : RowSquare [8,3,1,1,1,1,1,1] [6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg2116 - -lemma sg4892 : RowSquare [8,3,1,1,1,1,1,1] [6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg2117 - -lemma sg4893 : RowSquare [8,3,1,1,1,1,1,1] [6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg2118 - -lemma sg4894 : RowSquare [8,3,2,1,1,1,1] [4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg1666 - -lemma sg4895 : RowSquare [8,3,2,1,1,1,1] [4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg1667 - -lemma sg4896 : RowSquare [8,3,2,2,1,1] [4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg2529 - -lemma sg4897 : RowSquare [8,3,3,1,1,1] [3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg62 sg1327 - -lemma sg4898 : RowSquare [8,3,3,2,1] [3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg286 sg586 - -lemma sg4899 : RowSquare [8,3,3,2,1] [4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg179 sg828 - -lemma sg4900 : RowSquare [8,4,1,1,1,1,1] [4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg2159 - -lemma sg4901 : RowSquare [8,4,1,1,1,1,1] [4,4,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg2160 - -lemma sg4902 : RowSquare [8,4,1,1,1,1,1] [5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg2161 - -lemma sg4903 : RowSquare [8,4,1,1,1,1,1] [5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg2162 - -lemma sg4904 : RowSquare [8,4,1,1,1,1,1] [5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg2163 - -lemma sg4905 : RowSquare [8,4,1,1,1,1,1] [5,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg2164 - -lemma sg4906 : RowSquare [8,4,1,1,1,1,1] [5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg1185 - -lemma sg4907 : RowSquare [8,4,1,1,1,1,1] [5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg2122 - -lemma sg4908 : RowSquare [8,4,1,1,1,1,1] [5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg17 sg2123 - -lemma sg4909 : RowSquare [8,4,1,1,1,1,1] [5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg1188 - -lemma sg4910 : RowSquare [8,4,1,1,1,1,1] [5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg2165 - -lemma sg4911 : RowSquare [8,4,1,1,1,1,1] [5,5,3,3,1] := by - exact rowSquare_join (by decide) sg17 sg2125 - -lemma sg4912 : RowSquare [8,4,1,1,1,1,1] [5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg1189 - -lemma sg4913 : RowSquare [8,4,1,1,1,1,1] [6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg2130 - -lemma sg4914 : RowSquare [8,4,1,1,1,1,1] [6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg1670 - -lemma sg4915 : RowSquare [8,4,1,1,1,1,1] [6,6,2,2,1] := by - exact rowSquare_join (by decide) sg17 sg2131 - -lemma sg4916 : RowSquare [8,4,1,1,1,1,1] [7,7,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg2133 - -lemma sg4917 : RowSquare [8,4,3,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg1682 - -lemma sg4918 : RowSquare [8,4,3,1,1] [2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg306 sg586 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes8 + +namespace OAI + +/-! Semigroup Nodes 10. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg4516 : RowSquare [10,1,1,1,1,1,1] [8,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg1751 + +lemma sg4517 : RowSquare [10,2,1,1,1,1] [5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg1331 + +lemma sg4518 : RowSquare [10,2,1,1,1,1] [5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg1331 + +lemma sg4519 : RowSquare [10,2,2,1,1] [4,3,3,3,3] := by + exact rowSquare_join (by decide) sg87 sg1001 + +lemma sg4520 : RowSquare [10,2,2,1,1] [4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg999 + +lemma sg4521 : RowSquare [10,2,2,2] [4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg371 + +lemma sg4522 : RowSquare [10,2,2,2] [4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg372 + +lemma sg4523 : RowSquare [10,2,2,2] [4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg371 sg373 + +lemma sg4524 : RowSquare [10,2,2,2] [4,4,4,2,2] := by + exact rowSquare_join (by decide) sg372 sg372 + +lemma sg4525 : RowSquare [10,2,2,2] [4,4,4,3,1] := by + exact rowSquare_join (by decide) sg372 sg373 + +lemma sg4526 : RowSquare [10,2,2,2] [4,4,4,4] := by + exact rowSquare_join (by decide) sg373 sg373 + +lemma sg4527 : RowSquare [10,2,2,2] [5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg371 sg377 + +lemma sg4528 : RowSquare [10,2,2,2] [5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg378 + +lemma sg4529 : RowSquare [10,2,2,2] [5,5,3,2,1] := by + exact rowSquare_join (by decide) sg372 sg377 + +lemma sg4530 : RowSquare [10,2,2,2] [5,5,3,3] := by + exact rowSquare_join (by decide) sg373 sg377 + +lemma sg4531 : RowSquare [10,2,2,2] [5,5,4,1,1] := by + exact rowSquare_join (by decide) sg372 sg378 + +lemma sg4532 : RowSquare [10,2,2,2] [5,5,4,2] := by + exact rowSquare_join (by decide) sg373 sg378 + +lemma sg4533 : RowSquare [10,3,1,1,1] [4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg998 + +lemma sg4534 : RowSquare [10,3,1,1,1] [4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg999 + +lemma sg4535 : RowSquare [10,3,1,1,1] [4,4,4,2,2] := by + exact rowSquare_join (by decide) sg97 sg1001 + +lemma sg4536 : RowSquare [10,3,2,1] [4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg371 sg390 + +lemma sg4537 : RowSquare [10,3,2,1] [4,4,3,3,2] := by + exact rowSquare_join (by decide) sg88 sg1033 + +lemma sg4538 : RowSquare [10,3,2,1] [4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg89 sg1032 + +lemma sg4539 : RowSquare [10,3,2,1] [4,4,4,4] := by + exact rowSquare_join (by decide) sg390 sg373 + +lemma sg4540 : RowSquare [10,3,3] [5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg88 sg1063 + +lemma sg4541 : RowSquare [10,3,3] [5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg1063 + +lemma sg4542 : RowSquare [10,3,3] [5,5,3,3] := by + exact rowSquare_join (by decide) sg88 sg1064 + +lemma sg4543 : RowSquare [10,4,2] [4,4,4,4] := by + exact rowSquare_join (by decide) sg390 sg390 + +lemma sg4544 : RowSquare [11,2,1,1,1] [6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg231 sg586 + +lemma sg4545 : RowSquare [11,2,1,1,1] [6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg232 sg586 + +lemma sg4546 : RowSquare [11,2,1,1,1] [6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg104 sg998 + +lemma sg4547 : RowSquare [11,2,1,1,1] [6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg104 sg1000 + +lemma sg4548 : RowSquare [11,2,1,1,1] [6,3,3,2,2] := by + exact rowSquare_join (by decide) sg104 sg1001 + +lemma sg4549 : RowSquare [11,2,1,1,1] [6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg105 sg998 + +lemma sg4550 : RowSquare [11,2,1,1,1] [6,4,2,2,2] := by + exact rowSquare_join (by decide) sg105 sg1001 + +lemma sg4551 : RowSquare [11,2,1,1,1] [7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg233 sg586 + +lemma sg4552 : RowSquare [11,2,1,1,1] [7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg231 sg587 + +lemma sg4553 : RowSquare [11,2,1,1,1] [7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg232 sg587 + +lemma sg4554 : RowSquare [3,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,2] := by + exact rowSquare_join (by decide) sg389 sg708 + +lemma sg4555 : RowSquare [3,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,1] := by + exact rowSquare_join (by decide) sg413 sg693 + +lemma sg4556 : RowSquare [3,3,2,1,1,1,1,1,1,1,1,1] [7,4,2,2,2] := by + exact rowSquare_join (by decide) sg413 sg694 + +lemma sg4557 : RowSquare [3,3,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,1] := by + exact rowSquare_join (by decide) sg389 sg709 + +lemma sg4558 : RowSquare [3,3,2,1,1,1,1,1,1,1,1,1] [7,4,3,3] := by + exact rowSquare_join (by decide) sg390 sg709 + +lemma sg4559 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg391 sg692 + +lemma sg4560 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg391 sg693 + +lemma sg4561 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [6,3,3,3,2] := by + exact rowSquare_join (by decide) sg413 sg644 + +lemma sg4562 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg391 sg697 + +lemma sg4563 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [8,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg306 sg716 + +lemma sg4564 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [8,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg391 sg702 + +lemma sg4565 : RowSquare [3,3,2,2,1,1,1,1,1,1,1] [8,3,3,3] := by + exact rowSquare_join (by decide) sg390 sg704 + +lemma sg4566 : RowSquare [3,3,2,2,2,2,2,1] [4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg306 sg656 + +lemma sg4567 : RowSquare [3,3,2,2,2,2,2,1] [4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg306 sg657 + +lemma sg4568 : RowSquare [3,3,2,2,2,2,2,1] [4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg306 sg658 + +lemma sg4569 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg193 sg1061 + +lemma sg4570 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg1533 + +lemma sg4571 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,4,3,3,3] := by + exact rowSquare_join (by decide) sg194 sg1061 + +lemma sg4572 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg389 sg636 + +lemma sg4573 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg390 sg636 + +lemma sg4574 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,4,4,3,2] := by + exact rowSquare_join (by decide) sg389 sg637 + +lemma sg4575 : RowSquare [3,3,3,2,1,1,1,1,1,1] [4,4,4,4,1] := by + exact rowSquare_join (by decide) sg390 sg637 + +lemma sg4576 : RowSquare [3,3,3,2,1,1,1,1,1,1] [5,4,4,4] := by + exact rowSquare_join (by decide) sg390 sg638 + +lemma sg4577 : RowSquare [3,3,3,2,1,1,1,1,1,1] [5,5,4,3] := by + exact rowSquare_join (by decide) sg390 sg640 + +lemma sg4578 : RowSquare [3,3,3,2,1,1,1,1,1,1] [7,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg348 sg703 + +lemma sg4579 : RowSquare [3,3,3,2,1,1,1,1,1,1] [7,7,1,1,1] := by + exact rowSquare_join (by decide) sg396 sg639 + +lemma sg4580 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg708 + +lemma sg4581 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg371 sg709 + +lemma sg4582 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg710 + +lemma sg4583 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [7,4,3,3] := by + exact rowSquare_join (by decide) sg373 sg709 + +lemma sg4584 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [8,3,3,3] := by + exact rowSquare_join (by decide) sg373 sg711 + +lemma sg4585 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [8,4,3,2] := by + exact rowSquare_join (by decide) sg373 sg712 + +lemma sg4586 : RowSquare [4,3,1,1,1,1,1,1,1,1,1,1] [8,5,2,2] := by + exact rowSquare_join (by decide) sg373 sg713 + +lemma sg4587 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg692 + +lemma sg4588 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg693 + +lemma sg4589 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg218 sg1032 + +lemma sg4590 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3] := by + exact rowSquare_join (by decide) sg218 sg1033 + +lemma sg4591 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg694 + +lemma sg4592 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg695 + +lemma sg4593 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg692 + +lemma sg4594 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg371 sg693 + +lemma sg4595 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,2] := by + exact rowSquare_join (by decide) sg219 sg1033 + +lemma sg4596 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg696 + +lemma sg4597 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg220 sg1032 + +lemma sg4598 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,4,2,2] := by + exact rowSquare_join (by decide) sg389 sg675 + +lemma sg4599 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,1] := by + exact rowSquare_join (by decide) sg389 sg676 + +lemma sg4600 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4] := by + exact rowSquare_join (by decide) sg390 sg676 + +lemma sg4601 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg1109 + +lemma sg4602 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg694 + +lemma sg4603 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg1110 + +lemma sg4604 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg371 sg695 + +lemma sg4605 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,3,2,2] := by + exact rowSquare_join (by decide) sg372 sg694 + +lemma sg4606 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,1] := by + exact rowSquare_join (by decide) sg373 sg694 + +lemma sg4607 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg696 + +lemma sg4608 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,4,2,1] := by + exact rowSquare_join (by decide) sg372 sg695 + +lemma sg4609 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3] := by + exact rowSquare_join (by decide) sg373 sg695 + +lemma sg4610 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,5,1,1] := by + exact rowSquare_join (by decide) sg372 sg696 + +lemma sg4611 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [5,5,5,2] := by + exact rowSquare_join (by decide) sg373 sg696 + +lemma sg4612 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg370 sg697 + +lemma sg4613 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg698 + +lemma sg4614 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg697 + +lemma sg4615 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg391 sg675 + +lemma sg4616 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg1112 + +lemma sg4617 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg701 + +lemma sg4618 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,6,3,1,1] := by + exact rowSquare_join (by decide) sg372 sg701 + +lemma sg4619 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [6,6,5] := by + exact rowSquare_join (by decide) sg378 sg696 + +lemma sg4620 : RowSquare [4,3,2,1,1,1,1,1,1,1,1] [7,7,1,1,1] := by + exact rowSquare_join (by decide) sg383 sg694 + +lemma sg4621 : RowSquare [4,3,2,2,1,1,1,1,1,1] [4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg693 + +lemma sg4622 : RowSquare [4,3,2,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg696 + +lemma sg4623 : RowSquare [4,3,2,2,1,1,1,1,1,1] [4,4,4,4,1] := by + exact rowSquare_join (by decide) sg390 sg616 + +lemma sg4624 : RowSquare [4,3,2,2,2,2,1,1] [3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg579 + +lemma sg4625 : RowSquare [4,3,2,2,2,2,1,1] [4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg849 + +lemma sg4626 : RowSquare [4,3,2,2,2,2,1,1] [4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg581 + +lemma sg4627 : RowSquare [4,3,2,2,2,2,1,1] [4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg849 + +lemma sg4628 : RowSquare [4,3,2,2,2,2,1,1] [4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg849 + +lemma sg4629 : RowSquare [4,3,2,2,2,2,1,1] [4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg583 + +lemma sg4630 : RowSquare [4,3,2,2,2,2,1,1] [4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg584 + +lemma sg4631 : RowSquare [4,3,2,2,2,2,1,1] [5,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg211 sg849 + +lemma sg4632 : RowSquare [4,3,2,2,2,2,1,1] [5,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg212 sg849 + +lemma sg4633 : RowSquare [4,3,2,2,2,2,1,1] [5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg213 sg849 + +lemma sg4634 : RowSquare [4,3,2,2,2,2,1,1] [6,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg214 sg849 + +lemma sg4635 : RowSquare [4,3,2,2,2,2,1,1] [6,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg215 sg849 + +lemma sg4636 : RowSquare [4,3,2,2,2,2,1,1] [7,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg216 sg849 + +lemma sg4637 : RowSquare [4,3,3,2,1,1,1,1,1] [4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg641 + +lemma sg4638 : RowSquare [4,3,3,2,1,1,1,1,1] [4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg980 + +lemma sg4639 : RowSquare [4,3,3,2,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg104 sg1232 + +lemma sg4640 : RowSquare [4,3,3,2,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg105 sg1232 + +lemma sg4641 : RowSquare [4,3,3,2,1,1,1,1,1] [5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg220 sg850 + +lemma sg4642 : RowSquare [4,3,3,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg106 sg1232 + +lemma sg4643 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg370 sg673 + +lemma sg4644 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg370 sg674 + +lemma sg4645 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg675 + +lemma sg4646 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg676 + +lemma sg4647 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg674 + +lemma sg4648 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg675 + +lemma sg4649 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg371 sg676 + +lemma sg4650 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,4,4,2,2] := by + exact rowSquare_join (by decide) sg372 sg675 + +lemma sg4651 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,4,4,3,1] := by + exact rowSquare_join (by decide) sg372 sg676 + +lemma sg4652 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [5,4,4,4] := by + exact rowSquare_join (by decide) sg373 sg676 + +lemma sg4653 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg370 sg677 + +lemma sg4654 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg678 + +lemma sg4655 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg677 + +lemma sg4656 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg374 sg675 + +lemma sg4657 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg374 sg676 + +lemma sg4658 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg681 + +lemma sg4659 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,5,3,2,1] := by + exact rowSquare_join (by decide) sg372 sg680 + +lemma sg4660 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,5,3,3] := by + exact rowSquare_join (by decide) sg373 sg680 + +lemma sg4661 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,5,4,1,1] := by + exact rowSquare_join (by decide) sg372 sg681 + +lemma sg4662 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [6,5,4,2] := by + exact rowSquare_join (by decide) sg373 sg681 + +lemma sg4663 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg682 + +lemma sg4664 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg374 sg677 + +lemma sg4665 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg682 + +lemma sg4666 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg684 + +lemma sg4667 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,3,3,2,2] := by + exact rowSquare_join (by decide) sg372 sg682 + +lemma sg4668 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg684 + +lemma sg4669 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,4,4,1,1] := by + exact rowSquare_join (by decide) sg372 sg684 + +lemma sg4670 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg686 + +lemma sg4671 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg686 + +lemma sg4672 : RowSquare [4,4,1,1,1,1,1,1,1,1,1] [7,6,2,1,1] := by + exact rowSquare_join (by decide) sg372 sg686 + +lemma sg4673 : RowSquare [4,4,2,1,1,1,1,1,1,1] [3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg1032 + +lemma sg4674 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg673 + +lemma sg4675 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg676 + +lemma sg4676 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg616 + +lemma sg4677 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg179 sg1032 + +lemma sg4678 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg179 sg1033 + +lemma sg4679 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,4,3,3,3] := by + exact rowSquare_join (by decide) sg180 sg1033 + +lemma sg4680 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg1041 + +lemma sg4681 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg372 sg615 + +lemma sg4682 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg373 sg615 + +lemma sg4683 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,4,4,3,2] := by + exact rowSquare_join (by decide) sg372 sg616 + +lemma sg4684 : RowSquare [4,4,2,1,1,1,1,1,1,1] [4,4,4,4,1] := by + exact rowSquare_join (by decide) sg373 sg616 + +lemma sg4685 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg677 + +lemma sg4686 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg370 sg617 + +lemma sg4687 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg678 + +lemma sg4688 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg370 sg618 + +lemma sg4689 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg679 + +lemma sg4690 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg374 sg615 + +lemma sg4691 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg376 sg615 + +lemma sg4692 : RowSquare [4,4,2,1,1,1,1,1,1,1] [5,5,5,1,1] := by + exact rowSquare_join (by decide) sg372 sg623 + +lemma sg4693 : RowSquare [4,4,2,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg685 + +lemma sg4694 : RowSquare [4,4,2,1,1,1,1,1,1,1] [6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg374 sg623 + +lemma sg4695 : RowSquare [4,4,2,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg686 + +lemma sg4696 : RowSquare [4,4,2,2,1,1,1,1,1] [3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg330 sg613 + +lemma sg4697 : RowSquare [4,4,2,2,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg1650 + +lemma sg4698 : RowSquare [4,4,2,2,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg1651 + +lemma sg4699 : RowSquare [4,4,2,2,2,2,1] [4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg1650 + +lemma sg4700 : RowSquare [4,4,2,2,2,2,1] [4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg1650 + +lemma sg4701 : RowSquare [4,4,2,2,2,2,1] [5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg1650 + +lemma sg4702 : RowSquare [4,4,2,2,2,2,1] [5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg1651 + +lemma sg4703 : RowSquare [4,4,2,2,2,2,1] [5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg1651 + +lemma sg4704 : RowSquare [4,4,2,2,2,2,1] [5,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg1655 + +lemma sg4705 : RowSquare [4,4,2,2,2,2,1] [5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg1656 + +lemma sg4706 : RowSquare [4,4,2,2,2,2,1] [5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg1653 + +lemma sg4707 : RowSquare [4,4,2,2,2,2,1] [5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg1652 + +lemma sg4708 : RowSquare [4,4,2,2,2,2,1] [5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg1656 + +lemma sg4709 : RowSquare [4,4,2,2,2,2,1] [6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg1650 + +lemma sg4710 : RowSquare [4,4,2,2,2,2,1] [6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg1651 + +lemma sg4711 : RowSquare [4,4,2,2,2,2,1] [6,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg1655 + +lemma sg4712 : RowSquare [4,4,2,2,2,2,1] [6,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg1655 + +lemma sg4713 : RowSquare [4,4,2,2,2,2,1] [6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg1657 + +lemma sg4714 : RowSquare [4,4,2,2,2,2,1] [6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg1656 + +lemma sg4715 : RowSquare [4,4,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg1651 + +lemma sg4716 : RowSquare [4,4,2,2,2,2,1] [7,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg1655 + +lemma sg4717 : RowSquare [4,4,2,2,2,2,1] [8,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg1655 + +lemma sg4718 : RowSquare [4,4,3,2,1,1,1,1] [2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg849 + +lemma sg4719 : RowSquare [4,4,3,2,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg2107 + +lemma sg4720 : RowSquare [4,4,3,2,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg2108 + +lemma sg4721 : RowSquare [4,4,3,2,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg2109 + +lemma sg4722 : RowSquare [4,4,3,2,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg2112 + +lemma sg4723 : RowSquare [4,4,3,2,1,1,1,1] [7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3 sg2504 + +lemma sg4724 : RowSquare [5,3,2,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg586 + +lemma sg4725 : RowSquare [5,3,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg391 sg586 + +lemma sg4726 : RowSquare [5,3,2,1,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg220 sg910 + +lemma sg4727 : RowSquare [5,3,2,1,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg394 sg586 + +lemma sg4728 : RowSquare [5,3,2,1,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg1682 + +lemma sg4729 : RowSquare [5,3,2,2,1,1,1,1,1] [4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg1682 + +lemma sg4730 : RowSquare [5,3,2,2,1,1,1,1,1] [4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg1682 + +lemma sg4731 : RowSquare [5,3,2,2,1,1,1,1,1] [5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg47 sg1682 + +lemma sg4732 : RowSquare [5,3,2,2,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg1683 + +lemma sg4733 : RowSquare [5,3,2,2,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg1683 + +lemma sg4734 : RowSquare [5,3,3,2,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg1682 + +lemma sg4735 : RowSquare [5,3,3,2,1,1,1,1] [3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg2137 + +lemma sg4736 : RowSquare [5,3,3,2,1,1,1,1] [3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg1682 + +lemma sg4737 : RowSquare [5,3,3,2,1,1,1,1] [3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg1683 + +lemma sg4738 : RowSquare [5,3,3,2,1,1,1,1] [4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg2137 + +lemma sg4739 : RowSquare [5,3,3,2,1,1,1,1] [8,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg3865 + +lemma sg4740 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg586 + +lemma sg4741 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg586 + +lemma sg4742 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg998 + +lemma sg4743 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg372 sg586 + +lemma sg4744 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg999 + +lemma sg4745 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg586 + +lemma sg4746 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg1000 + +lemma sg4747 : RowSquare [5,4,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg178 sg1001 + +lemma sg4748 : RowSquare [5,4,1,1,1,1,1,1,1,1] [4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg179 sg1000 + +lemma sg4749 : RowSquare [5,4,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg588 + +lemma sg4750 : RowSquare [5,4,1,1,1,1,1,1,1,1] [4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg589 + +lemma sg4751 : RowSquare [5,4,1,1,1,1,1,1,1,1] [4,4,3,3,3] := by + exact rowSquare_join (by decide) sg180 sg1001 + +lemma sg4752 : RowSquare [5,4,1,1,1,1,1,1,1,1] [4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg373 sg589 + +lemma sg4753 : RowSquare [5,4,1,1,1,1,1,1,1,1] [4,4,4,4,1] := by + exact rowSquare_join (by decide) sg373 sg590 + +lemma sg4754 : RowSquare [5,4,1,1,1,1,1,1,1,1] [5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg376 sg589 + +lemma sg4755 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg384 sg586 + +lemma sg4756 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg379 sg587 + +lemma sg4757 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg3876 + +lemma sg4758 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg385 sg586 + +lemma sg4759 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg380 sg587 + +lemma sg4760 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg3877 + +lemma sg4761 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg3878 + +lemma sg4762 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg381 sg587 + +lemma sg4763 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg3879 + +lemma sg4764 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg3880 + +lemma sg4765 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg3881 + +lemma sg4766 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,3,3,3,2] := by + exact rowSquare_join (by decide) sg379 sg590 + +lemma sg4767 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg386 sg586 + +lemma sg4768 : RowSquare [5,4,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg383 sg587 + +lemma sg4769 : RowSquare [5,4,1,1,1,1,1,1,1,1] [7,5,5] := by + exact rowSquare_join (by decide) sg4 sg2497 + +lemma sg4770 : RowSquare [5,4,1,1,1,1,1,1,1,1] [9,8] := by + exact rowSquare_join (by decide) sg0 sg3905 + +lemma sg4771 : RowSquare [5,4,1,1,1,1,1,1,1,1] [10,7] := by + exact rowSquare_join (by decide) sg14 sg2020 + +lemma sg4772 : RowSquare [5,4,1,1,1,1,1,1,1,1] [11,6] := by + exact rowSquare_join (by decide) sg42 sg1577 + +lemma sg4773 : RowSquare [5,4,1,1,1,1,1,1,1,1] [12,5] := by + exact rowSquare_join (by decide) sg42 sg1578 + +lemma sg4774 : RowSquare [5,4,1,1,1,1,1,1,1,1] [13,4] := by + exact rowSquare_join (by decide) sg85 sg1120 + +lemma sg4775 : RowSquare [5,4,1,1,1,1,1,1,1,1] [14,3] := by + exact rowSquare_join (by decide) sg213 sg718 + +lemma sg4776 : RowSquare [5,4,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg910 + +lemma sg4777 : RowSquare [5,4,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg586 + +lemma sg4778 : RowSquare [5,4,2,1,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg910 + +lemma sg4779 : RowSquare [5,4,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg330 sg587 + +lemma sg4780 : RowSquare [5,4,2,1,1,1,1,1,1] [3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg180 sg910 + +lemma sg4781 : RowSquare [5,4,2,1,1,1,1,1,1] [3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg181 sg910 + +lemma sg4782 : RowSquare [5,4,2,1,1,1,1,1,1] [3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg913 + +lemma sg4783 : RowSquare [5,4,2,1,1,1,1,1,1] [4,4,3,3,3] := by + exact rowSquare_join (by decide) sg180 sg915 + +lemma sg4784 : RowSquare [5,4,2,2,1,1,1,1] [3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg142 sg910 + +lemma sg4785 : RowSquare [5,4,2,2,1,1,1,1] [3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg143 sg910 + +lemma sg4786 : RowSquare [5,4,2,2,1,1,1,1] [3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg144 sg910 + +lemma sg4787 : RowSquare [5,4,2,2,1,1,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg2596 + +lemma sg4788 : RowSquare [5,4,2,2,1,1,1,1] [4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg910 + +lemma sg4789 : RowSquare [5,4,2,2,1,1,1,1] [4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg543 + +lemma sg4790 : RowSquare [5,4,2,2,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg2597 + +lemma sg4791 : RowSquare [5,4,2,2,1,1,1,1] [5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg2598 + +lemma sg4792 : RowSquare [5,4,2,2,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg2599 + +lemma sg4793 : RowSquare [5,4,2,2,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg3935 + +lemma sg4794 : RowSquare [5,4,2,2,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg2603 + +lemma sg4795 : RowSquare [5,4,2,2,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg3936 + +lemma sg4796 : RowSquare [5,4,2,2,1,1,1,1] [7,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3199 + +lemma sg4797 : RowSquare [5,4,2,2,2,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg2596 + +lemma sg4798 : RowSquare [5,4,2,2,2,1,1] [4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg2597 + +lemma sg4799 : RowSquare [5,4,2,2,2,1,1] [4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg2601 + +lemma sg4800 : RowSquare [5,4,2,2,2,1,1] [4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg2602 + +lemma sg4801 : RowSquare [5,4,2,2,2,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg2597 + +lemma sg4802 : RowSquare [5,4,2,2,2,1,1] [5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg2601 + +lemma sg4803 : RowSquare [5,4,2,2,2,1,1] [5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6 sg2602 + +lemma sg4805 : RowSquare [5,5,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg313 sg586 + +lemma sg4806 : RowSquare [5,5,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg312 sg587 + +lemma sg4807 : RowSquare [5,5,1,1,1,1,1,1,1] [4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg313 sg589 + +lemma sg4808 : RowSquare [5,5,1,1,1,1,1,1,1] [6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg3211 + +lemma sg4809 : RowSquare [5,5,1,1,1,1,1,1,1] [6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg3213 + +lemma sg4810 : RowSquare [5,5,1,1,1,1,1,1,1] [8,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg2028 + +lemma sg4811 : RowSquare [5,5,1,1,1,1,1,1,1] [8,5,2,2] := by + exact rowSquare_join (by decide) sg13 sg2029 + +lemma sg4812 : RowSquare [5,5,1,1,1,1,1,1,1] [8,5,3,1] := by + exact rowSquare_join (by decide) sg13 sg2030 + +lemma sg4813 : RowSquare [5,5,1,1,1,1,1,1,1] [9,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg2032 + +lemma sg4814 : RowSquare [5,5,1,1,1,1,1,1,1] [9,8] := by + exact rowSquare_join (by decide) sg14 sg2031 + +lemma sg4815 : RowSquare [5,5,1,1,1,1,1,1,1] [10,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg2034 + +lemma sg4816 : RowSquare [5,5,1,1,1,1,1,1,1] [10,3,3,1] := by + exact rowSquare_join (by decide) sg84 sg1121 + +lemma sg4817 : RowSquare [5,5,1,1,1,1,1,1,1] [10,7] := by + exact rowSquare_join (by decide) sg14 sg2033 + +lemma sg4818 : RowSquare [5,5,1,1,1,1,1,1,1] [11,6] := by + exact rowSquare_join (by decide) sg85 sg1122 + +lemma sg4819 : RowSquare [5,5,1,1,1,1,1,1,1] [12,5] := by + exact rowSquare_join (by decide) sg85 sg1124 + +lemma sg4820 : RowSquare [5,5,1,1,1,1,1,1,1] [13,4] := by + exact rowSquare_join (by decide) sg367 sg427 + +lemma sg4821 : RowSquare [5,5,1,1,1,1,1,1,1] [14,3] := by + exact rowSquare_join (by decide) sg85 sg1126 + +lemma sg4822 : RowSquare [5,5,2,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg132 sg910 + +lemma sg4823 : RowSquare [5,5,2,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg133 sg910 + +lemma sg4824 : RowSquare [5,5,2,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg134 sg910 + +lemma sg4825 : RowSquare [5,5,2,1,1,1,1,1] [4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg275 sg586 + +lemma sg4826 : RowSquare [5,5,2,1,1,1,1,1] [4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg276 sg586 + +lemma sg4827 : RowSquare [5,5,2,1,1,1,1,1] [5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg279 sg586 + +lemma sg4828 : RowSquare [5,5,2,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg137 sg910 + +lemma sg4829 : RowSquare [5,5,2,1,1,1,1,1] [5,4,4,4] := by + exact rowSquare_join (by decide) sg13 sg2035 + +lemma sg4830 : RowSquare [5,5,2,1,1,1,1,1] [5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg281 sg586 + +lemma sg4831 : RowSquare [5,5,2,1,1,1,1,1] [5,5,5,1,1] := by + exact rowSquare_join (by decide) sg314 sg543 + +lemma sg4833 : RowSquare [5,5,3,2,2] [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg253 sg509 + +lemma sg4834 : RowSquare [6,3,2,1,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg1754 + +lemma sg4835 : RowSquare [6,3,2,1,1,1,1,1,1] [2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg1327 + +lemma sg4836 : RowSquare [6,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg1328 + +lemma sg4837 : RowSquare [6,3,2,1,1,1,1,1,1] [3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg1755 + +lemma sg4838 : RowSquare [6,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg1329 + +lemma sg4839 : RowSquare [6,3,2,1,1,1,1,1,1] [3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg1757 + +lemma sg4840 : RowSquare [6,3,2,1,1,1,1,1,1] [3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg1331 + +lemma sg4841 : RowSquare [6,3,2,1,1,1,1,1,1] [3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg32 sg1758 + +lemma sg4842 : RowSquare [6,3,2,1,1,1,1,1,1] [3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg74 sg1332 + +lemma sg4843 : RowSquare [6,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg1338 + +lemma sg4844 : RowSquare [6,3,2,2,2,2] [4,4,3,3,3] := by + exact rowSquare_join (by decide) sg166 sg762 + +lemma sg4845 : RowSquare [6,4,1,1,1,1,1,1,1] [3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg66 sg1327 + +lemma sg4846 : RowSquare [6,4,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg889 + +lemma sg4847 : RowSquare [6,4,1,1,1,1,1,1,1] [3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg890 + +lemma sg4848 : RowSquare [6,4,1,1,1,1,1,1,1] [3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg178 sg892 + +lemma sg4849 : RowSquare [6,4,2,1,1,1,1,1] [4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg22 sg1754 + +lemma sg4850 : RowSquare [6,4,2,1,1,1,1,1] [4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg56 sg1327 + +lemma sg4851 : RowSquare [6,4,2,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3259 + +lemma sg4852 : RowSquare [6,4,2,1,1,1,1,1] [4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg3232 + +lemma sg4853 : RowSquare [6,4,2,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg3983 + +lemma sg4854 : RowSquare [6,4,2,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg3984 + +lemma sg4855 : RowSquare [6,4,2,1,1,1,1,1] [5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg1754 + +lemma sg4856 : RowSquare [6,4,2,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3261 + +lemma sg4857 : RowSquare [6,4,2,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3266 + +lemma sg4858 : RowSquare [6,4,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg60 sg1327 + +lemma sg4859 : RowSquare [6,4,2,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg2534 + +lemma sg4860 : RowSquare [6,4,2,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3267 + +lemma sg4861 : RowSquare [6,4,3,1,1,1,1] [3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg1628 + +lemma sg4863 : RowSquare [6,4,3,2,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg347 sg445 + +lemma sg4864 : RowSquare [6,4,3,2,1,1] [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg346 sg445 + +lemma sg4865 : RowSquare [6,4,3,2,1,1] [2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg345 sg445 + +lemma sg4866 : RowSquare [6,4,3,2,1,1] [2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg445 + +lemma sg4867 : RowSquare [6,4,3,2,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg444 + +lemma sg4868 : RowSquare [6,4,3,2,1,1] [2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg443 + +lemma sg4869 : RowSquare [6,4,3,2,1,1] [2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg342 sg442 + +lemma sg4870 : RowSquare [6,4,3,2,1,1] [3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg2545 + +lemma sg4871 : RowSquare [6,4,3,2,1,1] [3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg340 sg440 + +lemma sg4872 : RowSquare [6,4,3,2,1,1] [3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg1616 + +lemma sg4873 : RowSquare [6,5,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg51 sg1327 + +lemma sg4874 : RowSquare [6,5,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg52 sg1327 + +lemma sg4875 : RowSquare [7,3,3,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg355 sg454 + +lemma sg4876 : RowSquare [7,3,3,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg354 sg453 + +lemma sg4877 : RowSquare [7,3,3,1,1,1,1] [2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg354 sg451 + +lemma sg4878 : RowSquare [7,3,3,1,1,1,1] [2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg92 sg1143 + +lemma sg4879 : RowSquare [7,3,3,1,1,1,1] [3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg89 sg1142 + +lemma sg4880 : RowSquare [7,4,3,1,1,1] [4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg77 sg1195 + +lemma sg4881 : RowSquare [7,4,3,1,1,1] [4,4,4,4,1] := by + exact rowSquare_join (by decide) sg32 sg1587 + +lemma sg4882 : RowSquare [7,4,3,2,1] [3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg790 + +lemma sg4883 : RowSquare [7,4,3,2,1] [3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg178 sg792 + +lemma sg4884 : RowSquare [7,4,3,2,1] [4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg795 + +lemma sg4885 : RowSquare [7,4,3,2,1] [4,4,4,4,1] := by + exact rowSquare_join (by decide) sg334 sg476 + +lemma sg4886 : RowSquare [7,4,3,3] [3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg480 + +lemma sg4887 : RowSquare [7,4,3,3] [4,4,4,4,1] := by + exact rowSquare_join (by decide) sg334 sg481 + +lemma sg4888 : RowSquare [7,5,1,1,1,1,1] [5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg2128 + +lemma sg4889 : RowSquare [7,5,3,1,1] [3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg306 sg534 + +lemma sg4890 : RowSquare [8,3,1,1,1,1,1,1] [4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg2620 + +lemma sg4891 : RowSquare [8,3,1,1,1,1,1,1] [6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg2116 + +lemma sg4892 : RowSquare [8,3,1,1,1,1,1,1] [6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg2117 + +lemma sg4893 : RowSquare [8,3,1,1,1,1,1,1] [6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg2118 + +lemma sg4894 : RowSquare [8,3,2,1,1,1,1] [4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg1666 + +lemma sg4895 : RowSquare [8,3,2,1,1,1,1] [4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg1667 + +lemma sg4896 : RowSquare [8,3,2,2,1,1] [4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg2529 + +lemma sg4897 : RowSquare [8,3,3,1,1,1] [3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg62 sg1327 + +lemma sg4898 : RowSquare [8,3,3,2,1] [3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg286 sg586 + +lemma sg4899 : RowSquare [8,3,3,2,1] [4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg179 sg828 + +lemma sg4900 : RowSquare [8,4,1,1,1,1,1] [4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg2159 + +lemma sg4901 : RowSquare [8,4,1,1,1,1,1] [4,4,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg2160 + +lemma sg4902 : RowSquare [8,4,1,1,1,1,1] [5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg2161 + +lemma sg4903 : RowSquare [8,4,1,1,1,1,1] [5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg2162 + +lemma sg4904 : RowSquare [8,4,1,1,1,1,1] [5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg2163 + +lemma sg4905 : RowSquare [8,4,1,1,1,1,1] [5,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg2164 + +lemma sg4906 : RowSquare [8,4,1,1,1,1,1] [5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg1185 + +lemma sg4907 : RowSquare [8,4,1,1,1,1,1] [5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg2122 + +lemma sg4908 : RowSquare [8,4,1,1,1,1,1] [5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg17 sg2123 + +lemma sg4909 : RowSquare [8,4,1,1,1,1,1] [5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg1188 + +lemma sg4910 : RowSquare [8,4,1,1,1,1,1] [5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg2165 + +lemma sg4911 : RowSquare [8,4,1,1,1,1,1] [5,5,3,3,1] := by + exact rowSquare_join (by decide) sg17 sg2125 + +lemma sg4912 : RowSquare [8,4,1,1,1,1,1] [5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg1189 + +lemma sg4913 : RowSquare [8,4,1,1,1,1,1] [6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg2130 + +lemma sg4914 : RowSquare [8,4,1,1,1,1,1] [6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg1670 + +lemma sg4915 : RowSquare [8,4,1,1,1,1,1] [6,6,2,2,1] := by + exact rowSquare_join (by decide) sg17 sg2131 + +lemma sg4916 : RowSquare [8,4,1,1,1,1,1] [7,7,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg2133 + +lemma sg4917 : RowSquare [8,4,3,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg1682 + +lemma sg4918 : RowSquare [8,4,3,1,1] [2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg306 sg586 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes100.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes100.lean index 905fc32624dee78956cb8665c60169ccd5b2aaed..75fc2852471eba5cce7d3b6d8b538fc211402054 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes100.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes100.lean @@ -1,1230 +1,1230 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 - -namespace OAI - -/-! Semigroup Nodes 100. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg40541 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18693 - -lemma sg40542 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15996 - -lemma sg40543 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18693 - -lemma sg40544 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18693 - -lemma sg40545 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16527 - -lemma sg40546 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18694 - -lemma sg40547 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17684 - -lemma sg40548 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18694 - -lemma sg40549 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18694 - -lemma sg40550 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17685 - -lemma sg40551 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20702 sg16392 - -lemma sg40552 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15997 - -lemma sg40553 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20036 - -lemma sg40554 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18695 - -lemma sg40555 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17686 - -lemma sg40556 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18695 - -lemma sg40557 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18695 - -lemma sg40558 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18696 - -lemma sg40559 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18696 - -lemma sg40560 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18696 - -lemma sg40561 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17687 - -lemma sg40562 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17381 - -lemma sg40563 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17688 - -lemma sg40564 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17688 - -lemma sg40565 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17382 - -lemma sg40566 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg15978 - -lemma sg40567 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15822 - -lemma sg40568 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18233 - -lemma sg40569 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16529 - -lemma sg40570 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18697 - -lemma sg40571 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15999 - -lemma sg40572 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18697 - -lemma sg40573 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18697 - -lemma sg40574 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20857 sg15825 - -lemma sg40575 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18698 - -lemma sg40576 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17689 - -lemma sg40577 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18698 - -lemma sg40578 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18698 - -lemma sg40579 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17690 - -lemma sg40580 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18701 - -lemma sg40581 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18699 - -lemma sg40582 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15823 - -lemma sg40583 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18699 - -lemma sg40584 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18699 - -lemma sg40585 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18702 - -lemma sg40586 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16000 - -lemma sg40587 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20037 - -lemma sg40588 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18700 - -lemma sg40589 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17691 - -lemma sg40590 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18700 - -lemma sg40591 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18700 - -lemma sg40592 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18701 - -lemma sg40593 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18701 - -lemma sg40594 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18701 - -lemma sg40595 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17692 - -lemma sg40596 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17384 - -lemma sg40597 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16532 - -lemma sg40598 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20038 - -lemma sg40599 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16001 - -lemma sg40600 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15824 - -lemma sg40601 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18702 - -lemma sg40602 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18702 - -lemma sg40603 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18702 - -lemma sg40604 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17693 - -lemma sg40605 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17694 - -lemma sg40606 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17694 - -lemma sg40607 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17386 - -lemma sg40608 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16798 - -lemma sg40609 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20638 sg16798 - -lemma sg40610 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17387 - -lemma sg40611 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18704 - -lemma sg40612 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16002 - -lemma sg40613 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16531 - -lemma sg40614 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18703 - -lemma sg40615 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17695 - -lemma sg40616 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18703 - -lemma sg40617 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18703 - -lemma sg40618 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18705 - -lemma sg40619 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20039 - -lemma sg40620 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16003 - -lemma sg40621 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15826 - -lemma sg40622 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18704 - -lemma sg40623 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18704 - -lemma sg40624 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18704 - -lemma sg40625 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17696 - -lemma sg40626 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17697 - -lemma sg40627 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17697 - -lemma sg40628 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17389 - -lemma sg40629 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17870 - -lemma sg40630 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20315 sg18705 - -lemma sg40631 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18281 sg20413 - -lemma sg40632 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18705 - -lemma sg40633 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18282 sg20413 - -lemma sg40634 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18705 - -lemma sg40635 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18705 - -lemma sg40636 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16918 - -lemma sg40637 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17698 - -lemma sg40638 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19426 - -lemma sg40639 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17698 - -lemma sg40640 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17390 - -lemma sg40641 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16799 - -lemma sg40642 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20638 sg16799 - -lemma sg40643 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17391 - -lemma sg40644 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16910 - -lemma sg40645 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17699 - -lemma sg40646 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16004 - -lemma sg40647 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16919 - -lemma sg40648 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17699 - -lemma sg40649 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19575 sg19615 - -lemma sg40650 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17699 - -lemma sg40651 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16800 - -lemma sg40652 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20638 sg16800 - -lemma sg40653 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16911 - -lemma sg40654 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20886 sg15725 - -lemma sg40655 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,4,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16517 - -lemma sg40656 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18708 - -lemma sg40657 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18706 - -lemma sg40658 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15828 - -lemma sg40659 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18706 - -lemma sg40660 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18706 - -lemma sg40661 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16536 - -lemma sg40662 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16005 - -lemma sg40663 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20040 - -lemma sg40664 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18707 - -lemma sg40665 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17700 - -lemma sg40666 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18707 - -lemma sg40667 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18707 - -lemma sg40668 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18708 - -lemma sg40669 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18708 - -lemma sg40670 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18708 - -lemma sg40671 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17701 - -lemma sg40672 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17394 - -lemma sg40673 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18710 - -lemma sg40674 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16006 - -lemma sg40675 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16535 - -lemma sg40676 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18709 - -lemma sg40677 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17702 - -lemma sg40678 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18709 - -lemma sg40679 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18709 - -lemma sg40680 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18711 - -lemma sg40681 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20041 - -lemma sg40682 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16007 - -lemma sg40683 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15829 - -lemma sg40684 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18710 - -lemma sg40685 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18710 - -lemma sg40686 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18710 - -lemma sg40687 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17703 - -lemma sg40688 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17704 - -lemma sg40689 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17704 - -lemma sg40690 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17396 - -lemma sg40691 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17872 - -lemma sg40692 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20042 - -lemma sg40693 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20042 - -lemma sg40694 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18711 - -lemma sg40695 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20042 - -lemma sg40696 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18711 - -lemma sg40697 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18711 - -lemma sg40698 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16921 - -lemma sg40699 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17705 - -lemma sg40700 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19427 - -lemma sg40701 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17705 - -lemma sg40702 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17397 - -lemma sg40703 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16801 - -lemma sg40704 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20638 sg16801 - -lemma sg40705 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16695 - -lemma sg40706 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18712 - -lemma sg40707 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15831 - -lemma sg40708 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18713 - -lemma sg40709 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17873 - -lemma sg40710 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20043 - -lemma sg40711 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16008 - -lemma sg40712 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16394 - -lemma sg40713 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15831 - -lemma sg40714 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20043 - -lemma sg40715 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18712 - -lemma sg40716 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20043 - -lemma sg40717 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18712 - -lemma sg40718 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18712 - -lemma sg40719 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19428 - -lemma sg40720 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17706 - -lemma sg40721 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17874 - -lemma sg40722 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20044 - -lemma sg40723 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20044 - -lemma sg40724 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18713 - -lemma sg40725 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20044 - -lemma sg40726 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18713 - -lemma sg40727 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18713 - -lemma sg40728 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16922 - -lemma sg40729 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17707 - -lemma sg40730 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19429 - -lemma sg40731 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17707 - -lemma sg40732 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16802 - -lemma sg40733 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20638 sg16802 - -lemma sg40734 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17708 - -lemma sg40735 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16009 - -lemma sg40736 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16923 - -lemma sg40737 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17708 - -lemma sg40738 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19430 - -lemma sg40739 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17708 - -lemma sg40740 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16803 - -lemma sg40741 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20638 sg16803 - -lemma sg40742 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16696 - -lemma sg40743 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,7,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16397 - -lemma sg40744 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,7,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15833 - -lemma sg40745 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,7,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16804 - -lemma sg40746 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,7,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20638 sg16804 - -lemma sg40747 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,7,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16697 - -lemma sg40748 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20760 sg16314 - -lemma sg40749 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18714 - -lemma sg40750 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16924 - -lemma sg40751 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16538 - -lemma sg40752 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15834 - -lemma sg40753 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20831 sg16164 - -lemma sg40754 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20887 sg15730 - -lemma sg40755 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17875 - -lemma sg40756 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20045 - -lemma sg40757 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20045 - -lemma sg40758 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18714 - -lemma sg40759 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20045 - -lemma sg40760 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18714 - -lemma sg40761 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18714 - -lemma sg40762 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16924 - -lemma sg40763 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17709 - -lemma sg40764 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19431 - -lemma sg40765 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17709 - -lemma sg40766 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17710 - -lemma sg40767 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16010 - -lemma sg40768 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16925 - -lemma sg40769 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17710 - -lemma sg40770 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19432 - -lemma sg40771 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17710 - -lemma sg40772 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16805 - -lemma sg40773 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20638 sg16805 - -lemma sg40774 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16698 - -lemma sg40775 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16399 - -lemma sg40776 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15835 - -lemma sg40777 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16806 - -lemma sg40778 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,6,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20638 sg16806 - -lemma sg40779 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16699 - -lemma sg40780 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20761 sg16277 - -lemma sg40781 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20762 sg16277 - -lemma sg40782 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16700 - -lemma sg40783 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,8,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15618 sg21047 - -lemma sg40784 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,5,5,5,5,5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20840 sg16161 - -lemma sg40785 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,5,5,5,5,5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg20766 sg16268 - -lemma sg40786 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,5,5,5,5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18715 - -lemma sg40787 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,5,5,5,5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20873 sg15801 - -lemma sg40788 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,5,5,5,5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18715 - -lemma sg40789 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,5,5,5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18715 - -lemma sg40790 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,5,5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16011 - -lemma sg40791 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,5,5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18716 - -lemma sg40792 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,5,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17711 - -lemma sg40793 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,5,5,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20863 sg15810 - -lemma sg40794 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,5,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18716 - -lemma sg40795 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,5,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18716 - -lemma sg40796 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg15984 - -lemma sg40797 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16012 - -lemma sg40798 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19780 - -lemma sg40799 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18721 - -lemma sg40800 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18717 - -lemma sg40801 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18718 - -lemma sg40802 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18717 - -lemma sg40803 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18717 - -lemma sg40804 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18718 - -lemma sg40805 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18718 - -lemma sg40806 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20708 sg16388 - -lemma sg40807 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18719 - -lemma sg40808 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16013 - -lemma sg40809 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18719 - -lemma sg40810 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18719 - -lemma sg40811 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20046 - -lemma sg40812 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18720 - -lemma sg40813 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17712 - -lemma sg40814 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18720 - -lemma sg40815 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18720 - -lemma sg40816 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17713 - -lemma sg40817 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18721 - -lemma sg40818 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18721 - -lemma sg40819 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18721 - -lemma sg40820 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17714 - -lemma sg40821 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,5,5,5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16014 - -lemma sg40822 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,5,5,5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18722 - -lemma sg40823 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,5,5,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17715 - -lemma sg40824 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,5,5,5,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20867 sg15810 - -lemma sg40825 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,5,5,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18722 - -lemma sg40826 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,5,5,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18722 - -lemma sg40827 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg15986 - -lemma sg40828 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16015 - -lemma sg40829 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19783 - -lemma sg40830 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16542 - -lemma sg40831 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18723 - -lemma sg40832 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18724 - -lemma sg40833 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18723 - -lemma sg40834 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18723 - -lemma sg40835 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18724 - -lemma sg40836 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18724 - -lemma sg40837 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg15987 - -lemma sg40838 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18234 - -lemma sg40839 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18728 - -lemma sg40840 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18725 - -lemma sg40841 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16016 - -lemma sg40842 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18725 - -lemma sg40843 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18725 - -lemma sg40844 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16542 - -lemma sg40845 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18726 - -lemma sg40846 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17716 - -lemma sg40847 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18726 - -lemma sg40848 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18726 - -lemma sg40849 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17717 - -lemma sg40850 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20792 sg16184 - -lemma sg40851 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16017 - -lemma sg40852 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20047 - -lemma sg40853 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18727 - -lemma sg40854 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17718 - -lemma sg40855 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18727 - -lemma sg40856 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18727 - -lemma sg40857 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18728 - -lemma sg40858 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18728 - -lemma sg40859 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18728 - -lemma sg40860 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17719 - -lemma sg40861 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17720 - -lemma sg40862 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17720 - -lemma sg40863 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20863 sg15813 - -lemma sg40864 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg15989 - -lemma sg40865 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20864 sg15813 - -lemma sg40866 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16543 - -lemma sg40867 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18729 - -lemma sg40868 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16019 - -lemma sg40869 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18729 - -lemma sg40870 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18729 - -lemma sg40871 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20690 sg16523 - -lemma sg40872 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18730 - -lemma sg40873 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17721 - -lemma sg40874 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18730 - -lemma sg40875 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18730 - -lemma sg40876 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17722 - -lemma sg40877 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18733 - -lemma sg40878 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18731 - -lemma sg40879 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg15990 - -lemma sg40880 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18731 - -lemma sg40881 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18731 - -lemma sg40882 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18734 - -lemma sg40883 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16020 - -lemma sg40884 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20048 - -lemma sg40885 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18732 - -lemma sg40886 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17723 - -lemma sg40887 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18732 - -lemma sg40888 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18732 - -lemma sg40889 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18733 - -lemma sg40890 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18733 - -lemma sg40891 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18733 - -lemma sg40892 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17724 - -lemma sg40893 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16545 - -lemma sg40894 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20049 - -lemma sg40895 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16021 - -lemma sg40896 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19791 - -lemma sg40897 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18734 - -lemma sg40898 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18734 - -lemma sg40899 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18734 - -lemma sg40900 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17725 - -lemma sg40901 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17726 - -lemma sg40902 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17726 - -lemma sg40903 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18085 - -lemma sg40904 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16912 - -lemma sg40905 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18736 - -lemma sg40906 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16022 - -lemma sg40907 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16544 - -lemma sg40908 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18735 - -lemma sg40909 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17727 - -lemma sg40910 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18735 - -lemma sg40911 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18735 - -lemma sg40912 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18737 - -lemma sg40913 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20050 - -lemma sg40914 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16023 - -lemma sg40915 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19794 - -lemma sg40916 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18736 - -lemma sg40917 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18736 - -lemma sg40918 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18736 - -lemma sg40919 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17728 - -lemma sg40920 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17729 - -lemma sg40921 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17729 - -lemma sg40922 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17876 - -lemma sg40923 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20315 sg18737 - -lemma sg40924 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18281 sg20414 - -lemma sg40925 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18737 - -lemma sg40926 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18282 sg20414 - -lemma sg40927 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18737 - -lemma sg40928 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18737 - -lemma sg40929 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16929 - -lemma sg40930 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17730 - -lemma sg40931 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19433 - -lemma sg40932 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17730 - -lemma sg40933 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19092 - -lemma sg40934 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16913 - -lemma sg40935 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16796 - -lemma sg40936 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17731 - -lemma sg40937 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16024 - -lemma sg40938 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16930 - -lemma sg40939 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17731 - -lemma sg40940 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19434 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 + +namespace OAI + +/-! Semigroup Nodes 100. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg40541 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18693 + +lemma sg40542 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15996 + +lemma sg40543 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18693 + +lemma sg40544 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18693 + +lemma sg40545 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16527 + +lemma sg40546 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18694 + +lemma sg40547 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17684 + +lemma sg40548 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18694 + +lemma sg40549 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18694 + +lemma sg40550 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17685 + +lemma sg40551 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20702 sg16392 + +lemma sg40552 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15997 + +lemma sg40553 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20036 + +lemma sg40554 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18695 + +lemma sg40555 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17686 + +lemma sg40556 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18695 + +lemma sg40557 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18695 + +lemma sg40558 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18696 + +lemma sg40559 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18696 + +lemma sg40560 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18696 + +lemma sg40561 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17687 + +lemma sg40562 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17381 + +lemma sg40563 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17688 + +lemma sg40564 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17688 + +lemma sg40565 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,6,6,6,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17382 + +lemma sg40566 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg15978 + +lemma sg40567 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15822 + +lemma sg40568 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18233 + +lemma sg40569 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16529 + +lemma sg40570 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18697 + +lemma sg40571 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15999 + +lemma sg40572 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18697 + +lemma sg40573 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18697 + +lemma sg40574 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20857 sg15825 + +lemma sg40575 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18698 + +lemma sg40576 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17689 + +lemma sg40577 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18698 + +lemma sg40578 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18698 + +lemma sg40579 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,5,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17690 + +lemma sg40580 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18701 + +lemma sg40581 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18699 + +lemma sg40582 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15823 + +lemma sg40583 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18699 + +lemma sg40584 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18699 + +lemma sg40585 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18702 + +lemma sg40586 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16000 + +lemma sg40587 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20037 + +lemma sg40588 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18700 + +lemma sg40589 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17691 + +lemma sg40590 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18700 + +lemma sg40591 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18700 + +lemma sg40592 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18701 + +lemma sg40593 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18701 + +lemma sg40594 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18701 + +lemma sg40595 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17692 + +lemma sg40596 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17384 + +lemma sg40597 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16532 + +lemma sg40598 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20038 + +lemma sg40599 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16001 + +lemma sg40600 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15824 + +lemma sg40601 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18702 + +lemma sg40602 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18702 + +lemma sg40603 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18702 + +lemma sg40604 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17693 + +lemma sg40605 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17694 + +lemma sg40606 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17694 + +lemma sg40607 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17386 + +lemma sg40608 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16798 + +lemma sg40609 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20638 sg16798 + +lemma sg40610 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,6,6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17387 + +lemma sg40611 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18704 + +lemma sg40612 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16002 + +lemma sg40613 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16531 + +lemma sg40614 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18703 + +lemma sg40615 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17695 + +lemma sg40616 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18703 + +lemma sg40617 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18703 + +lemma sg40618 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18705 + +lemma sg40619 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20039 + +lemma sg40620 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16003 + +lemma sg40621 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15826 + +lemma sg40622 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18704 + +lemma sg40623 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18704 + +lemma sg40624 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18704 + +lemma sg40625 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17696 + +lemma sg40626 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17697 + +lemma sg40627 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17697 + +lemma sg40628 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17389 + +lemma sg40629 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17870 + +lemma sg40630 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20315 sg18705 + +lemma sg40631 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18281 sg20413 + +lemma sg40632 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18705 + +lemma sg40633 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18282 sg20413 + +lemma sg40634 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18705 + +lemma sg40635 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18705 + +lemma sg40636 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16918 + +lemma sg40637 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17698 + +lemma sg40638 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19426 + +lemma sg40639 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17698 + +lemma sg40640 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17390 + +lemma sg40641 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16799 + +lemma sg40642 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20638 sg16799 + +lemma sg40643 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17391 + +lemma sg40644 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16910 + +lemma sg40645 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17699 + +lemma sg40646 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16004 + +lemma sg40647 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16919 + +lemma sg40648 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17699 + +lemma sg40649 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19575 sg19615 + +lemma sg40650 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17699 + +lemma sg40651 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16800 + +lemma sg40652 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20638 sg16800 + +lemma sg40653 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,7,7,7,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16911 + +lemma sg40654 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20886 sg15725 + +lemma sg40655 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,4,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16517 + +lemma sg40656 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18708 + +lemma sg40657 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18706 + +lemma sg40658 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15828 + +lemma sg40659 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18706 + +lemma sg40660 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18706 + +lemma sg40661 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16536 + +lemma sg40662 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16005 + +lemma sg40663 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20040 + +lemma sg40664 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18707 + +lemma sg40665 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17700 + +lemma sg40666 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18707 + +lemma sg40667 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18707 + +lemma sg40668 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18708 + +lemma sg40669 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18708 + +lemma sg40670 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18708 + +lemma sg40671 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17701 + +lemma sg40672 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17394 + +lemma sg40673 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18710 + +lemma sg40674 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16006 + +lemma sg40675 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16535 + +lemma sg40676 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18709 + +lemma sg40677 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17702 + +lemma sg40678 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18709 + +lemma sg40679 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18709 + +lemma sg40680 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18711 + +lemma sg40681 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20041 + +lemma sg40682 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16007 + +lemma sg40683 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15829 + +lemma sg40684 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18710 + +lemma sg40685 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18710 + +lemma sg40686 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18710 + +lemma sg40687 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17703 + +lemma sg40688 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17704 + +lemma sg40689 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17704 + +lemma sg40690 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17396 + +lemma sg40691 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17872 + +lemma sg40692 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20042 + +lemma sg40693 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20042 + +lemma sg40694 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18711 + +lemma sg40695 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20042 + +lemma sg40696 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18711 + +lemma sg40697 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18711 + +lemma sg40698 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16921 + +lemma sg40699 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17705 + +lemma sg40700 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19427 + +lemma sg40701 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17705 + +lemma sg40702 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17397 + +lemma sg40703 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16801 + +lemma sg40704 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20638 sg16801 + +lemma sg40705 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16695 + +lemma sg40706 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18712 + +lemma sg40707 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15831 + +lemma sg40708 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18713 + +lemma sg40709 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17873 + +lemma sg40710 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20043 + +lemma sg40711 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16008 + +lemma sg40712 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16394 + +lemma sg40713 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15831 + +lemma sg40714 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20043 + +lemma sg40715 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18712 + +lemma sg40716 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20043 + +lemma sg40717 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18712 + +lemma sg40718 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18712 + +lemma sg40719 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19428 + +lemma sg40720 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17706 + +lemma sg40721 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17874 + +lemma sg40722 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20044 + +lemma sg40723 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20044 + +lemma sg40724 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18713 + +lemma sg40725 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20044 + +lemma sg40726 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18713 + +lemma sg40727 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18713 + +lemma sg40728 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16922 + +lemma sg40729 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17707 + +lemma sg40730 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19429 + +lemma sg40731 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17707 + +lemma sg40732 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16802 + +lemma sg40733 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20638 sg16802 + +lemma sg40734 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17708 + +lemma sg40735 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16009 + +lemma sg40736 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16923 + +lemma sg40737 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17708 + +lemma sg40738 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19430 + +lemma sg40739 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17708 + +lemma sg40740 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16803 + +lemma sg40741 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20638 sg16803 + +lemma sg40742 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16696 + +lemma sg40743 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,7,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16397 + +lemma sg40744 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,7,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15833 + +lemma sg40745 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,7,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16804 + +lemma sg40746 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,7,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20638 sg16804 + +lemma sg40747 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,7,7,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16697 + +lemma sg40748 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20760 sg16314 + +lemma sg40749 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18714 + +lemma sg40750 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16924 + +lemma sg40751 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16538 + +lemma sg40752 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15834 + +lemma sg40753 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20831 sg16164 + +lemma sg40754 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20887 sg15730 + +lemma sg40755 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17875 + +lemma sg40756 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20045 + +lemma sg40757 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20045 + +lemma sg40758 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18714 + +lemma sg40759 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20045 + +lemma sg40760 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18714 + +lemma sg40761 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18714 + +lemma sg40762 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16924 + +lemma sg40763 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17709 + +lemma sg40764 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19431 + +lemma sg40765 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17709 + +lemma sg40766 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17710 + +lemma sg40767 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16010 + +lemma sg40768 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16925 + +lemma sg40769 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17710 + +lemma sg40770 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19432 + +lemma sg40771 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17710 + +lemma sg40772 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16805 + +lemma sg40773 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20638 sg16805 + +lemma sg40774 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16698 + +lemma sg40775 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16399 + +lemma sg40776 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15835 + +lemma sg40777 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16806 + +lemma sg40778 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,6,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20638 sg16806 + +lemma sg40779 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16699 + +lemma sg40780 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20761 sg16277 + +lemma sg40781 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20762 sg16277 + +lemma sg40782 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16700 + +lemma sg40783 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,8,8,8,8,8,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15618 sg21047 + +lemma sg40784 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,5,5,5,5,5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20840 sg16161 + +lemma sg40785 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,5,5,5,5,5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg20766 sg16268 + +lemma sg40786 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,5,5,5,5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18715 + +lemma sg40787 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,5,5,5,5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20873 sg15801 + +lemma sg40788 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,5,5,5,5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18715 + +lemma sg40789 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,5,5,5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18715 + +lemma sg40790 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,5,5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16011 + +lemma sg40791 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,5,5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18716 + +lemma sg40792 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,5,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17711 + +lemma sg40793 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,5,5,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20863 sg15810 + +lemma sg40794 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,5,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18716 + +lemma sg40795 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,5,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18716 + +lemma sg40796 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg15984 + +lemma sg40797 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16012 + +lemma sg40798 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19780 + +lemma sg40799 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18721 + +lemma sg40800 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18717 + +lemma sg40801 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18718 + +lemma sg40802 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18717 + +lemma sg40803 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18717 + +lemma sg40804 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18718 + +lemma sg40805 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18718 + +lemma sg40806 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20708 sg16388 + +lemma sg40807 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18719 + +lemma sg40808 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16013 + +lemma sg40809 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18719 + +lemma sg40810 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18719 + +lemma sg40811 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20046 + +lemma sg40812 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18720 + +lemma sg40813 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17712 + +lemma sg40814 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18720 + +lemma sg40815 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18720 + +lemma sg40816 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17713 + +lemma sg40817 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18721 + +lemma sg40818 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18721 + +lemma sg40819 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18721 + +lemma sg40820 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,6,6,6,6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17714 + +lemma sg40821 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,5,5,5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16014 + +lemma sg40822 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,5,5,5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18722 + +lemma sg40823 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,5,5,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17715 + +lemma sg40824 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,5,5,5,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20867 sg15810 + +lemma sg40825 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,5,5,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18722 + +lemma sg40826 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,5,5,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18722 + +lemma sg40827 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg15986 + +lemma sg40828 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16015 + +lemma sg40829 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19783 + +lemma sg40830 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16542 + +lemma sg40831 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18723 + +lemma sg40832 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18724 + +lemma sg40833 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18723 + +lemma sg40834 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18723 + +lemma sg40835 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18724 + +lemma sg40836 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,5,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18724 + +lemma sg40837 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg15987 + +lemma sg40838 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18234 + +lemma sg40839 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18728 + +lemma sg40840 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18725 + +lemma sg40841 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16016 + +lemma sg40842 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18725 + +lemma sg40843 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18725 + +lemma sg40844 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16542 + +lemma sg40845 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18726 + +lemma sg40846 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17716 + +lemma sg40847 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18726 + +lemma sg40848 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18726 + +lemma sg40849 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17717 + +lemma sg40850 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20792 sg16184 + +lemma sg40851 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16017 + +lemma sg40852 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20047 + +lemma sg40853 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18727 + +lemma sg40854 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17718 + +lemma sg40855 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18727 + +lemma sg40856 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18727 + +lemma sg40857 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18728 + +lemma sg40858 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18728 + +lemma sg40859 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18728 + +lemma sg40860 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17719 + +lemma sg40861 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17720 + +lemma sg40862 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,6,6,6,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17720 + +lemma sg40863 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20863 sg15813 + +lemma sg40864 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg15989 + +lemma sg40865 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20864 sg15813 + +lemma sg40866 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16543 + +lemma sg40867 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18729 + +lemma sg40868 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16019 + +lemma sg40869 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18729 + +lemma sg40870 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18729 + +lemma sg40871 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20690 sg16523 + +lemma sg40872 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18730 + +lemma sg40873 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17721 + +lemma sg40874 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18730 + +lemma sg40875 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18730 + +lemma sg40876 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,5,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17722 + +lemma sg40877 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18733 + +lemma sg40878 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18731 + +lemma sg40879 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg15990 + +lemma sg40880 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18731 + +lemma sg40881 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18731 + +lemma sg40882 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18734 + +lemma sg40883 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16020 + +lemma sg40884 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20048 + +lemma sg40885 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18732 + +lemma sg40886 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17723 + +lemma sg40887 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18732 + +lemma sg40888 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18732 + +lemma sg40889 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18733 + +lemma sg40890 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18733 + +lemma sg40891 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18733 + +lemma sg40892 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17724 + +lemma sg40893 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16545 + +lemma sg40894 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20049 + +lemma sg40895 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16021 + +lemma sg40896 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19791 + +lemma sg40897 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18734 + +lemma sg40898 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18734 + +lemma sg40899 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18734 + +lemma sg40900 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17725 + +lemma sg40901 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17726 + +lemma sg40902 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17726 + +lemma sg40903 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18085 + +lemma sg40904 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,6,6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16912 + +lemma sg40905 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18736 + +lemma sg40906 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16022 + +lemma sg40907 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16544 + +lemma sg40908 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18735 + +lemma sg40909 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17727 + +lemma sg40910 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18735 + +lemma sg40911 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18735 + +lemma sg40912 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18737 + +lemma sg40913 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20050 + +lemma sg40914 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16023 + +lemma sg40915 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19794 + +lemma sg40916 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18736 + +lemma sg40917 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18736 + +lemma sg40918 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18736 + +lemma sg40919 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17728 + +lemma sg40920 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17729 + +lemma sg40921 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17729 + +lemma sg40922 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17876 + +lemma sg40923 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20315 sg18737 + +lemma sg40924 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18281 sg20414 + +lemma sg40925 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18737 + +lemma sg40926 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18282 sg20414 + +lemma sg40927 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18737 + +lemma sg40928 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18737 + +lemma sg40929 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16929 + +lemma sg40930 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17730 + +lemma sg40931 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19433 + +lemma sg40932 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17730 + +lemma sg40933 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19092 + +lemma sg40934 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16913 + +lemma sg40935 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16796 + +lemma sg40936 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17731 + +lemma sg40937 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16024 + +lemma sg40938 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16930 + +lemma sg40939 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17731 + +lemma sg40940 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19434 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes101.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes101.lean index 59ec004c439d60af3b67d17f444bce388ce374a1..7c9175bafd9860d9acf09ec73a2e8214c32555d5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes101.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes101.lean @@ -1,1231 +1,1231 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 - -namespace OAI - -/-! Semigroup Nodes 101. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg40941 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17731 - -lemma sg40942 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18086 - -lemma sg40943 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16797 - -lemma sg40944 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg15994 - -lemma sg40945 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16025 - -lemma sg40946 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19798 - -lemma sg40947 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20396 - -lemma sg40948 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18738 - -lemma sg40949 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18739 - -lemma sg40950 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18738 - -lemma sg40951 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18738 - -lemma sg40952 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18739 - -lemma sg40953 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18739 - -lemma sg40954 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg15986 - -lemma sg40955 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg15995 - -lemma sg40956 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18235 - -lemma sg40957 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16546 - -lemma sg40958 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18740 - -lemma sg40959 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16026 - -lemma sg40960 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18740 - -lemma sg40961 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18740 - -lemma sg40962 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20690 sg16527 - -lemma sg40963 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18741 - -lemma sg40964 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17732 - -lemma sg40965 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18741 - -lemma sg40966 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18741 - -lemma sg40967 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17733 - -lemma sg40968 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18744 - -lemma sg40969 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18742 - -lemma sg40970 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg15996 - -lemma sg40971 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18742 - -lemma sg40972 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18742 - -lemma sg40973 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18745 - -lemma sg40974 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16027 - -lemma sg40975 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20051 - -lemma sg40976 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18743 - -lemma sg40977 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17734 - -lemma sg40978 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18743 - -lemma sg40979 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18743 - -lemma sg40980 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18744 - -lemma sg40981 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18744 - -lemma sg40982 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18744 - -lemma sg40983 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17735 - -lemma sg40984 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20792 sg16185 - -lemma sg40985 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20052 - -lemma sg40986 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16028 - -lemma sg40987 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19802 - -lemma sg40988 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18745 - -lemma sg40989 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18745 - -lemma sg40990 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18745 - -lemma sg40991 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17736 - -lemma sg40992 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17737 - -lemma sg40993 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17737 - -lemma sg40994 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18087 - -lemma sg40995 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg15989 - -lemma sg40996 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,4,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16522 - -lemma sg40997 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18748 - -lemma sg40998 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18746 - -lemma sg40999 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg15999 - -lemma sg41000 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18746 - -lemma sg41001 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18746 - -lemma sg41002 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16548 - -lemma sg41003 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16029 - -lemma sg41004 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20053 - -lemma sg41005 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18747 - -lemma sg41006 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17738 - -lemma sg41007 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18747 - -lemma sg41008 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18747 - -lemma sg41009 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18748 - -lemma sg41010 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18748 - -lemma sg41011 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18748 - -lemma sg41012 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17739 - -lemma sg41013 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18750 - -lemma sg41014 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16030 - -lemma sg41015 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16547 - -lemma sg41016 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18749 - -lemma sg41017 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17740 - -lemma sg41018 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18749 - -lemma sg41019 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18749 - -lemma sg41020 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18751 - -lemma sg41021 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20054 - -lemma sg41022 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16031 - -lemma sg41023 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19806 - -lemma sg41024 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18750 - -lemma sg41025 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18750 - -lemma sg41026 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18750 - -lemma sg41027 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17741 - -lemma sg41028 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17742 - -lemma sg41029 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17742 - -lemma sg41030 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17877 - -lemma sg41031 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20055 - -lemma sg41032 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20055 - -lemma sg41033 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18751 - -lemma sg41034 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20055 - -lemma sg41035 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18751 - -lemma sg41036 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18751 - -lemma sg41037 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16933 - -lemma sg41038 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17743 - -lemma sg41039 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19435 - -lemma sg41040 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17743 - -lemma sg41041 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19093 - -lemma sg41042 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16912 - -lemma sg41043 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18752 - -lemma sg41044 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16002 - -lemma sg41045 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18753 - -lemma sg41046 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17878 - -lemma sg41047 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20056 - -lemma sg41048 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16032 - -lemma sg41049 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17695 - -lemma sg41050 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19810 - -lemma sg41051 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20056 - -lemma sg41052 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18752 - -lemma sg41053 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20056 - -lemma sg41054 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18752 - -lemma sg41055 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18752 - -lemma sg41056 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19436 - -lemma sg41057 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17744 - -lemma sg41058 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17879 - -lemma sg41059 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20057 - -lemma sg41060 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20057 - -lemma sg41061 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18753 - -lemma sg41062 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20057 - -lemma sg41063 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18753 - -lemma sg41064 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18753 - -lemma sg41065 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16934 - -lemma sg41066 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17745 - -lemma sg41067 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19437 - -lemma sg41068 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19094 - -lemma sg41069 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17746 - -lemma sg41070 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16033 - -lemma sg41071 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16935 - -lemma sg41072 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17746 - -lemma sg41073 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19438 - -lemma sg41074 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19095 - -lemma sg41075 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16913 - -lemma sg41076 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,7,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17699 - -lemma sg41077 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,7,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20321 sg18402 - -lemma sg41078 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,7,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18088 - -lemma sg41079 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,7,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16914 - -lemma sg41080 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16549 - -lemma sg41081 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,4,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18754 - -lemma sg41082 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,4,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20863 sg15828 - -lemma sg41083 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,4,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18754 - -lemma sg41084 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,4,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18754 - -lemma sg41085 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18756 - -lemma sg41086 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16034 - -lemma sg41087 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16549 - -lemma sg41088 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18755 - -lemma sg41089 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17747 - -lemma sg41090 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18755 - -lemma sg41091 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18755 - -lemma sg41092 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16550 - -lemma sg41093 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20058 - -lemma sg41094 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16035 - -lemma sg41095 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19814 - -lemma sg41096 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18756 - -lemma sg41097 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18756 - -lemma sg41098 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18756 - -lemma sg41099 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17748 - -lemma sg41100 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17749 - -lemma sg41101 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18757 - -lemma sg41102 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16006 - -lemma sg41103 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18758 - -lemma sg41104 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17880 - -lemma sg41105 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20059 - -lemma sg41106 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16036 - -lemma sg41107 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17702 - -lemma sg41108 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19816 - -lemma sg41109 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20059 - -lemma sg41110 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18757 - -lemma sg41111 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20059 - -lemma sg41112 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18757 - -lemma sg41113 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18757 - -lemma sg41114 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19439 - -lemma sg41115 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17881 - -lemma sg41116 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20060 - -lemma sg41117 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20060 - -lemma sg41118 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18758 - -lemma sg41119 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20060 - -lemma sg41120 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18758 - -lemma sg41121 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18758 - -lemma sg41122 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16937 - -lemma sg41123 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17750 - -lemma sg41124 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19440 - -lemma sg41125 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19096 - -lemma sg41126 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17751 - -lemma sg41127 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16037 - -lemma sg41128 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16938 - -lemma sg41129 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17751 - -lemma sg41130 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19441 - -lemma sg41131 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19097 - -lemma sg41132 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16801 - -lemma sg41133 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16628 - -lemma sg41134 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18759 - -lemma sg41135 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16939 - -lemma sg41136 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16551 - -lemma sg41137 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16008 - -lemma sg41138 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20709 sg16394 - -lemma sg41139 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20864 sg15831 - -lemma sg41140 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17882 - -lemma sg41141 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20061 - -lemma sg41142 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20061 - -lemma sg41143 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18759 - -lemma sg41144 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20061 - -lemma sg41145 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18759 - -lemma sg41146 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18759 - -lemma sg41147 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16939 - -lemma sg41148 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17752 - -lemma sg41149 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19442 - -lemma sg41150 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17753 - -lemma sg41151 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16038 - -lemma sg41152 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16940 - -lemma sg41153 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17753 - -lemma sg41154 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19443 - -lemma sg41155 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19098 - -lemma sg41156 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16802 - -lemma sg41157 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17708 - -lemma sg41158 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18284 sg20397 - -lemma sg41159 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18089 - -lemma sg41160 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16803 - -lemma sg41161 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16397 - -lemma sg41162 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16804 - -lemma sg41163 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17883 - -lemma sg41164 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18760 - -lemma sg41165 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17883 - -lemma sg41166 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20062 - -lemma sg41167 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20062 - -lemma sg41168 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18760 - -lemma sg41169 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20062 - -lemma sg41170 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18760 - -lemma sg41171 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18760 - -lemma sg41172 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17754 - -lemma sg41173 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16039 - -lemma sg41174 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16941 - -lemma sg41175 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17754 - -lemma sg41176 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19444 - -lemma sg41177 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18090 - -lemma sg41178 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17710 - -lemma sg41179 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18284 sg20398 - -lemma sg41180 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18091 - -lemma sg41181 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16805 - -lemma sg41182 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16399 - -lemma sg41183 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16806 - -lemma sg41184 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20763 sg16277 - -lemma sg41185 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,8,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15234 sg21188 - -lemma sg41186 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg15994 - -lemma sg41187 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15863 - -lemma sg41188 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18236 - -lemma sg41189 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20702 sg16417 - -lemma sg41190 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18761 - -lemma sg41191 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16040 - -lemma sg41192 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18761 - -lemma sg41193 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18761 - -lemma sg41194 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20854 sg15998 - -lemma sg41195 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18762 - -lemma sg41196 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17755 - -lemma sg41197 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18762 - -lemma sg41198 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18762 - -lemma sg41199 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg15995 - -lemma sg41200 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,4,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16525 - -lemma sg41201 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18765 - -lemma sg41202 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18763 - -lemma sg41203 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15864 - -lemma sg41204 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18763 - -lemma sg41205 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18763 - -lemma sg41206 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16554 - -lemma sg41207 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16041 - -lemma sg41208 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20063 - -lemma sg41209 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18764 - -lemma sg41210 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17756 - -lemma sg41211 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18764 - -lemma sg41212 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18764 - -lemma sg41213 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18765 - -lemma sg41214 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18765 - -lemma sg41215 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18765 - -lemma sg41216 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18767 - -lemma sg41217 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16042 - -lemma sg41218 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16553 - -lemma sg41219 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18766 - -lemma sg41220 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17757 - -lemma sg41221 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18766 - -lemma sg41222 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18766 - -lemma sg41223 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18768 - -lemma sg41224 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20064 - -lemma sg41225 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16043 - -lemma sg41226 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15865 - -lemma sg41227 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18767 - -lemma sg41228 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18767 - -lemma sg41229 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18767 - -lemma sg41230 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17758 - -lemma sg41231 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17884 - -lemma sg41232 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20065 - -lemma sg41233 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20065 - -lemma sg41234 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18768 - -lemma sg41235 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20065 - -lemma sg41236 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18768 - -lemma sg41237 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18768 - -lemma sg41238 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16942 - -lemma sg41239 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17759 - -lemma sg41240 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19445 - -lemma sg41241 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16821 - -lemma sg41242 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16915 - -lemma sg41243 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16555 - -lemma sg41244 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,4,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18769 - -lemma sg41245 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,4,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg15999 - -lemma sg41246 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,4,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18769 - -lemma sg41247 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,4,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18769 - -lemma sg41248 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18771 - -lemma sg41249 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16044 - -lemma sg41250 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16555 - -lemma sg41251 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18770 - -lemma sg41252 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17760 - -lemma sg41253 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18770 - -lemma sg41254 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18770 - -lemma sg41255 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16556 - -lemma sg41256 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20066 - -lemma sg41257 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16045 - -lemma sg41258 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15867 - -lemma sg41259 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18771 - -lemma sg41260 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18771 - -lemma sg41261 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18771 - -lemma sg41262 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17761 - -lemma sg41263 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18772 - -lemma sg41264 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15868 - -lemma sg41265 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18773 - -lemma sg41266 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17885 - -lemma sg41267 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20067 - -lemma sg41268 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16047 - -lemma sg41269 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16418 - -lemma sg41270 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15868 - -lemma sg41271 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20067 - -lemma sg41272 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18772 - -lemma sg41273 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20067 - -lemma sg41274 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18772 - -lemma sg41275 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19446 - -lemma sg41276 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17886 - -lemma sg41277 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20068 - -lemma sg41278 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20068 - -lemma sg41279 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18773 - -lemma sg41280 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20068 - -lemma sg41281 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18773 - -lemma sg41282 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16943 - -lemma sg41283 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17762 - -lemma sg41284 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19447 - -lemma sg41285 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16822 - -lemma sg41286 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17763 - -lemma sg41287 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16048 - -lemma sg41288 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16944 - -lemma sg41289 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17763 - -lemma sg41290 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19448 - -lemma sg41291 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16823 - -lemma sg41292 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16916 - -lemma sg41293 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20684 sg16560 - -lemma sg41294 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18774 - -lemma sg41295 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16945 - -lemma sg41296 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16557 - -lemma sg41297 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15870 - -lemma sg41298 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17695 - -lemma sg41299 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18237 - -lemma sg41300 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17887 - -lemma sg41301 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20069 - -lemma sg41302 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20069 - -lemma sg41303 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18774 - -lemma sg41304 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20069 - -lemma sg41305 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18774 - -lemma sg41306 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16945 - -lemma sg41307 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17764 - -lemma sg41308 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19449 - -lemma sg41309 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17765 - -lemma sg41310 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16049 - -lemma sg41311 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16946 - -lemma sg41312 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17765 - -lemma sg41313 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19450 - -lemma sg41314 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16824 - -lemma sg41315 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16917 - -lemma sg41316 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16421 - -lemma sg41317 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15871 - -lemma sg41318 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16825 - -lemma sg41319 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16918 - -lemma sg41320 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17699 - -lemma sg41321 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16919 - -lemma sg41322 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16558 - -lemma sg41323 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16050 - -lemma sg41324 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20856 sg15874 - -lemma sg41325 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20857 sg15874 - -lemma sg41326 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18775 - -lemma sg41327 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16947 - -lemma sg41328 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17766 - -lemma sg41329 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20070 - -lemma sg41330 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18775 - -lemma sg41331 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18775 - -lemma sg41332 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18776 - -lemma sg41333 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15872 - -lemma sg41334 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18777 - -lemma sg41335 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17888 - -lemma sg41336 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20071 - -lemma sg41337 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16051 - -lemma sg41338 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16422 - -lemma sg41339 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15872 - -lemma sg41340 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20071 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 + +namespace OAI + +/-! Semigroup Nodes 101. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg40941 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17731 + +lemma sg40942 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18086 + +lemma sg40943 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16797 + +lemma sg40944 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg15994 + +lemma sg40945 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16025 + +lemma sg40946 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19798 + +lemma sg40947 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20396 + +lemma sg40948 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18738 + +lemma sg40949 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18739 + +lemma sg40950 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18738 + +lemma sg40951 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18738 + +lemma sg40952 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18739 + +lemma sg40953 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,5,5,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18739 + +lemma sg40954 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg15986 + +lemma sg40955 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg15995 + +lemma sg40956 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18235 + +lemma sg40957 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16546 + +lemma sg40958 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18740 + +lemma sg40959 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16026 + +lemma sg40960 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18740 + +lemma sg40961 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18740 + +lemma sg40962 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20690 sg16527 + +lemma sg40963 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18741 + +lemma sg40964 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17732 + +lemma sg40965 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18741 + +lemma sg40966 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18741 + +lemma sg40967 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,5,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17733 + +lemma sg40968 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18744 + +lemma sg40969 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18742 + +lemma sg40970 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg15996 + +lemma sg40971 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18742 + +lemma sg40972 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18742 + +lemma sg40973 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18745 + +lemma sg40974 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16027 + +lemma sg40975 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20051 + +lemma sg40976 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18743 + +lemma sg40977 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17734 + +lemma sg40978 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18743 + +lemma sg40979 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18743 + +lemma sg40980 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18744 + +lemma sg40981 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18744 + +lemma sg40982 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18744 + +lemma sg40983 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17735 + +lemma sg40984 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20792 sg16185 + +lemma sg40985 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20052 + +lemma sg40986 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16028 + +lemma sg40987 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19802 + +lemma sg40988 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18745 + +lemma sg40989 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18745 + +lemma sg40990 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18745 + +lemma sg40991 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17736 + +lemma sg40992 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17737 + +lemma sg40993 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17737 + +lemma sg40994 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,6,6,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18087 + +lemma sg40995 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg15989 + +lemma sg40996 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,4,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16522 + +lemma sg40997 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18748 + +lemma sg40998 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18746 + +lemma sg40999 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg15999 + +lemma sg41000 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18746 + +lemma sg41001 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18746 + +lemma sg41002 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16548 + +lemma sg41003 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16029 + +lemma sg41004 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20053 + +lemma sg41005 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18747 + +lemma sg41006 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17738 + +lemma sg41007 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18747 + +lemma sg41008 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18747 + +lemma sg41009 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18748 + +lemma sg41010 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18748 + +lemma sg41011 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18748 + +lemma sg41012 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,5,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17739 + +lemma sg41013 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18750 + +lemma sg41014 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16030 + +lemma sg41015 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16547 + +lemma sg41016 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18749 + +lemma sg41017 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17740 + +lemma sg41018 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18749 + +lemma sg41019 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18749 + +lemma sg41020 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18751 + +lemma sg41021 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20054 + +lemma sg41022 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16031 + +lemma sg41023 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19806 + +lemma sg41024 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18750 + +lemma sg41025 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18750 + +lemma sg41026 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18750 + +lemma sg41027 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17741 + +lemma sg41028 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17742 + +lemma sg41029 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17742 + +lemma sg41030 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17877 + +lemma sg41031 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20055 + +lemma sg41032 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20055 + +lemma sg41033 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18751 + +lemma sg41034 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20055 + +lemma sg41035 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18751 + +lemma sg41036 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18751 + +lemma sg41037 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16933 + +lemma sg41038 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17743 + +lemma sg41039 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19435 + +lemma sg41040 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17743 + +lemma sg41041 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19093 + +lemma sg41042 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16912 + +lemma sg41043 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18752 + +lemma sg41044 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16002 + +lemma sg41045 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18753 + +lemma sg41046 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17878 + +lemma sg41047 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20056 + +lemma sg41048 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16032 + +lemma sg41049 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17695 + +lemma sg41050 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19810 + +lemma sg41051 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20056 + +lemma sg41052 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18752 + +lemma sg41053 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20056 + +lemma sg41054 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18752 + +lemma sg41055 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18752 + +lemma sg41056 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19436 + +lemma sg41057 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17744 + +lemma sg41058 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17879 + +lemma sg41059 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20057 + +lemma sg41060 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20057 + +lemma sg41061 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18753 + +lemma sg41062 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20057 + +lemma sg41063 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18753 + +lemma sg41064 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18753 + +lemma sg41065 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16934 + +lemma sg41066 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17745 + +lemma sg41067 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19437 + +lemma sg41068 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19094 + +lemma sg41069 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17746 + +lemma sg41070 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16033 + +lemma sg41071 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16935 + +lemma sg41072 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17746 + +lemma sg41073 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19438 + +lemma sg41074 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19095 + +lemma sg41075 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16913 + +lemma sg41076 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,7,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17699 + +lemma sg41077 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,7,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20321 sg18402 + +lemma sg41078 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,7,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18088 + +lemma sg41079 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,7,7,7,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16914 + +lemma sg41080 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16549 + +lemma sg41081 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,4,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18754 + +lemma sg41082 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,4,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20863 sg15828 + +lemma sg41083 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,4,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18754 + +lemma sg41084 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,4,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18754 + +lemma sg41085 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18756 + +lemma sg41086 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16034 + +lemma sg41087 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16549 + +lemma sg41088 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18755 + +lemma sg41089 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17747 + +lemma sg41090 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18755 + +lemma sg41091 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18755 + +lemma sg41092 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16550 + +lemma sg41093 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20058 + +lemma sg41094 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16035 + +lemma sg41095 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19814 + +lemma sg41096 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18756 + +lemma sg41097 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18756 + +lemma sg41098 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18756 + +lemma sg41099 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17748 + +lemma sg41100 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,5,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17749 + +lemma sg41101 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18757 + +lemma sg41102 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16006 + +lemma sg41103 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18758 + +lemma sg41104 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17880 + +lemma sg41105 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20059 + +lemma sg41106 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16036 + +lemma sg41107 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17702 + +lemma sg41108 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19816 + +lemma sg41109 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20059 + +lemma sg41110 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18757 + +lemma sg41111 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20059 + +lemma sg41112 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18757 + +lemma sg41113 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18757 + +lemma sg41114 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19439 + +lemma sg41115 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17881 + +lemma sg41116 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20060 + +lemma sg41117 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20060 + +lemma sg41118 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18758 + +lemma sg41119 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20060 + +lemma sg41120 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18758 + +lemma sg41121 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18758 + +lemma sg41122 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16937 + +lemma sg41123 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17750 + +lemma sg41124 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19440 + +lemma sg41125 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19096 + +lemma sg41126 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17751 + +lemma sg41127 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16037 + +lemma sg41128 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16938 + +lemma sg41129 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17751 + +lemma sg41130 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19441 + +lemma sg41131 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19097 + +lemma sg41132 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16801 + +lemma sg41133 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16628 + +lemma sg41134 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18759 + +lemma sg41135 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16939 + +lemma sg41136 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16551 + +lemma sg41137 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16008 + +lemma sg41138 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20709 sg16394 + +lemma sg41139 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20864 sg15831 + +lemma sg41140 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17882 + +lemma sg41141 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20061 + +lemma sg41142 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20061 + +lemma sg41143 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18759 + +lemma sg41144 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20061 + +lemma sg41145 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18759 + +lemma sg41146 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18759 + +lemma sg41147 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16939 + +lemma sg41148 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17752 + +lemma sg41149 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19442 + +lemma sg41150 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17753 + +lemma sg41151 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16038 + +lemma sg41152 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16940 + +lemma sg41153 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17753 + +lemma sg41154 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19443 + +lemma sg41155 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19098 + +lemma sg41156 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16802 + +lemma sg41157 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17708 + +lemma sg41158 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18284 sg20397 + +lemma sg41159 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18089 + +lemma sg41160 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16803 + +lemma sg41161 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16397 + +lemma sg41162 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16804 + +lemma sg41163 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17883 + +lemma sg41164 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18760 + +lemma sg41165 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17883 + +lemma sg41166 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20062 + +lemma sg41167 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20062 + +lemma sg41168 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18760 + +lemma sg41169 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20062 + +lemma sg41170 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18760 + +lemma sg41171 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18760 + +lemma sg41172 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17754 + +lemma sg41173 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16039 + +lemma sg41174 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16941 + +lemma sg41175 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17754 + +lemma sg41176 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19444 + +lemma sg41177 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18090 + +lemma sg41178 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17710 + +lemma sg41179 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18284 sg20398 + +lemma sg41180 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18091 + +lemma sg41181 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16805 + +lemma sg41182 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16399 + +lemma sg41183 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16806 + +lemma sg41184 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20763 sg16277 + +lemma sg41185 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,8,8,8,8,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15234 sg21188 + +lemma sg41186 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg15994 + +lemma sg41187 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15863 + +lemma sg41188 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18236 + +lemma sg41189 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20702 sg16417 + +lemma sg41190 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18761 + +lemma sg41191 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16040 + +lemma sg41192 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18761 + +lemma sg41193 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18761 + +lemma sg41194 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20854 sg15998 + +lemma sg41195 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18762 + +lemma sg41196 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17755 + +lemma sg41197 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18762 + +lemma sg41198 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,5,5,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18762 + +lemma sg41199 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg15995 + +lemma sg41200 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,4,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16525 + +lemma sg41201 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18765 + +lemma sg41202 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18763 + +lemma sg41203 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15864 + +lemma sg41204 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18763 + +lemma sg41205 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18763 + +lemma sg41206 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16554 + +lemma sg41207 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16041 + +lemma sg41208 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20063 + +lemma sg41209 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18764 + +lemma sg41210 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17756 + +lemma sg41211 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18764 + +lemma sg41212 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18764 + +lemma sg41213 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18765 + +lemma sg41214 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18765 + +lemma sg41215 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,5,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18765 + +lemma sg41216 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18767 + +lemma sg41217 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16042 + +lemma sg41218 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16553 + +lemma sg41219 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18766 + +lemma sg41220 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17757 + +lemma sg41221 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18766 + +lemma sg41222 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18766 + +lemma sg41223 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18768 + +lemma sg41224 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20064 + +lemma sg41225 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16043 + +lemma sg41226 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15865 + +lemma sg41227 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18767 + +lemma sg41228 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18767 + +lemma sg41229 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18767 + +lemma sg41230 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17758 + +lemma sg41231 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17884 + +lemma sg41232 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20065 + +lemma sg41233 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20065 + +lemma sg41234 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18768 + +lemma sg41235 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20065 + +lemma sg41236 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18768 + +lemma sg41237 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18768 + +lemma sg41238 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16942 + +lemma sg41239 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17759 + +lemma sg41240 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19445 + +lemma sg41241 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16821 + +lemma sg41242 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,6,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16915 + +lemma sg41243 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16555 + +lemma sg41244 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,4,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18769 + +lemma sg41245 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,4,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg15999 + +lemma sg41246 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,4,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18769 + +lemma sg41247 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,4,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18769 + +lemma sg41248 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18771 + +lemma sg41249 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16044 + +lemma sg41250 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16555 + +lemma sg41251 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18770 + +lemma sg41252 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17760 + +lemma sg41253 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18770 + +lemma sg41254 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18770 + +lemma sg41255 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16556 + +lemma sg41256 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20066 + +lemma sg41257 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16045 + +lemma sg41258 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15867 + +lemma sg41259 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18771 + +lemma sg41260 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18771 + +lemma sg41261 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18771 + +lemma sg41262 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,5,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17761 + +lemma sg41263 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18772 + +lemma sg41264 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15868 + +lemma sg41265 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18773 + +lemma sg41266 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17885 + +lemma sg41267 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20067 + +lemma sg41268 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16047 + +lemma sg41269 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16418 + +lemma sg41270 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15868 + +lemma sg41271 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20067 + +lemma sg41272 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18772 + +lemma sg41273 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20067 + +lemma sg41274 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18772 + +lemma sg41275 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19446 + +lemma sg41276 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17886 + +lemma sg41277 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20068 + +lemma sg41278 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20068 + +lemma sg41279 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18773 + +lemma sg41280 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20068 + +lemma sg41281 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18773 + +lemma sg41282 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16943 + +lemma sg41283 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17762 + +lemma sg41284 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19447 + +lemma sg41285 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16822 + +lemma sg41286 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17763 + +lemma sg41287 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16048 + +lemma sg41288 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16944 + +lemma sg41289 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17763 + +lemma sg41290 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19448 + +lemma sg41291 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16823 + +lemma sg41292 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16916 + +lemma sg41293 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20684 sg16560 + +lemma sg41294 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18774 + +lemma sg41295 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16945 + +lemma sg41296 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16557 + +lemma sg41297 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15870 + +lemma sg41298 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17695 + +lemma sg41299 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18237 + +lemma sg41300 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17887 + +lemma sg41301 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20069 + +lemma sg41302 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20069 + +lemma sg41303 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18774 + +lemma sg41304 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20069 + +lemma sg41305 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18774 + +lemma sg41306 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16945 + +lemma sg41307 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17764 + +lemma sg41308 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19449 + +lemma sg41309 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17765 + +lemma sg41310 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16049 + +lemma sg41311 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16946 + +lemma sg41312 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17765 + +lemma sg41313 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19450 + +lemma sg41314 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16824 + +lemma sg41315 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16917 + +lemma sg41316 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16421 + +lemma sg41317 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15871 + +lemma sg41318 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16825 + +lemma sg41319 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16918 + +lemma sg41320 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17699 + +lemma sg41321 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,7,7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16919 + +lemma sg41322 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16558 + +lemma sg41323 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16050 + +lemma sg41324 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20856 sg15874 + +lemma sg41325 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20857 sg15874 + +lemma sg41326 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18775 + +lemma sg41327 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16947 + +lemma sg41328 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17766 + +lemma sg41329 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20070 + +lemma sg41330 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18775 + +lemma sg41331 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,4,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18775 + +lemma sg41332 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18776 + +lemma sg41333 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15872 + +lemma sg41334 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18777 + +lemma sg41335 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17888 + +lemma sg41336 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20071 + +lemma sg41337 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16051 + +lemma sg41338 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16422 + +lemma sg41339 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15872 + +lemma sg41340 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20071 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes102.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes102.lean index 9cbaad04830651ddb10cafc7ec44def5b814c0e3..4ac7625c629adf6dceb2fdcb6eeb089bb6d66c35 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes102.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes102.lean @@ -1,1231 +1,1231 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes50 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 - -namespace OAI - -/-! Semigroup Nodes 102. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg41341 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18776 - -lemma sg41342 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20071 - -lemma sg41343 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18776 - -lemma sg41344 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19451 - -lemma sg41345 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17889 - -lemma sg41346 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20072 - -lemma sg41347 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20072 - -lemma sg41348 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18777 - -lemma sg41349 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20072 - -lemma sg41350 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18777 - -lemma sg41351 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16948 - -lemma sg41352 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17767 - -lemma sg41353 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19452 - -lemma sg41354 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16826 - -lemma sg41355 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16629 - -lemma sg41356 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18778 - -lemma sg41357 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16949 - -lemma sg41358 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16559 - -lemma sg41359 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15875 - -lemma sg41360 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17702 - -lemma sg41361 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18238 - -lemma sg41362 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17890 - -lemma sg41363 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20073 - -lemma sg41364 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20073 - -lemma sg41365 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18778 - -lemma sg41366 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20073 - -lemma sg41367 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18778 - -lemma sg41368 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16949 - -lemma sg41369 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17768 - -lemma sg41370 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19453 - -lemma sg41371 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17769 - -lemma sg41372 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16052 - -lemma sg41373 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16950 - -lemma sg41374 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17769 - -lemma sg41375 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19454 - -lemma sg41376 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16827 - -lemma sg41377 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16920 - -lemma sg41378 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16424 - -lemma sg41379 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15876 - -lemma sg41380 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16828 - -lemma sg41381 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16921 - -lemma sg41382 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17891 - -lemma sg41383 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18779 - -lemma sg41384 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17891 - -lemma sg41385 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20074 - -lemma sg41386 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20074 - -lemma sg41387 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18779 - -lemma sg41388 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20074 - -lemma sg41389 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18779 - -lemma sg41390 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17770 - -lemma sg41391 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16053 - -lemma sg41392 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16951 - -lemma sg41393 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17770 - -lemma sg41394 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19455 - -lemma sg41395 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16829 - -lemma sg41396 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16426 - -lemma sg41397 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15877 - -lemma sg41398 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16830 - -lemma sg41399 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16922 - -lemma sg41400 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17708 - -lemma sg41401 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16923 - -lemma sg41402 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17699 - -lemma sg41403 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16952 - -lemma sg41404 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16560 - -lemma sg41405 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17771 - -lemma sg41406 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16054 - -lemma sg41407 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16952 - -lemma sg41408 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17771 - -lemma sg41409 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19456 - -lemma sg41410 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16427 - -lemma sg41411 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15878 - -lemma sg41412 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16831 - -lemma sg41413 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16924 - -lemma sg41414 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17710 - -lemma sg41415 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16925 - -lemma sg41416 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20713 sg16399 - -lemma sg41417 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17699 - -lemma sg41418 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18780 - -lemma sg41419 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15879 - -lemma sg41420 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16562 - -lemma sg41421 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17892 - -lemma sg41422 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20075 - -lemma sg41423 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16055 - -lemma sg41424 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16428 - -lemma sg41425 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15879 - -lemma sg41426 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20075 - -lemma sg41427 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18780 - -lemma sg41428 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20075 - -lemma sg41429 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18780 - -lemma sg41430 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19457 - -lemma sg41431 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16630 - -lemma sg41432 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18781 - -lemma sg41433 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16953 - -lemma sg41434 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16561 - -lemma sg41435 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15880 - -lemma sg41436 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20831 sg16167 - -lemma sg41437 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20887 sg15750 - -lemma sg41438 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17893 - -lemma sg41439 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20076 - -lemma sg41440 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20076 - -lemma sg41441 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18781 - -lemma sg41442 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20076 - -lemma sg41443 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18781 - -lemma sg41444 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16953 - -lemma sg41445 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17772 - -lemma sg41446 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19458 - -lemma sg41447 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17773 - -lemma sg41448 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16056 - -lemma sg41449 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16954 - -lemma sg41450 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17773 - -lemma sg41451 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19459 - -lemma sg41452 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16833 - -lemma sg41453 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16724 - -lemma sg41454 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17894 - -lemma sg41455 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18782 - -lemma sg41456 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17894 - -lemma sg41457 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20077 - -lemma sg41458 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20077 - -lemma sg41459 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18782 - -lemma sg41460 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20077 - -lemma sg41461 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18782 - -lemma sg41462 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17774 - -lemma sg41463 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16057 - -lemma sg41464 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16955 - -lemma sg41465 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17774 - -lemma sg41466 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19460 - -lemma sg41467 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16834 - -lemma sg41468 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16431 - -lemma sg41469 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15881 - -lemma sg41470 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16835 - -lemma sg41471 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16726 - -lemma sg41472 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20761 sg16310 - -lemma sg41473 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16727 - -lemma sg41474 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16956 - -lemma sg41475 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16563 - -lemma sg41476 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17775 - -lemma sg41477 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16058 - -lemma sg41478 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16956 - -lemma sg41479 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17775 - -lemma sg41480 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19461 - -lemma sg41481 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16432 - -lemma sg41482 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15882 - -lemma sg41483 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16836 - -lemma sg41484 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16728 - -lemma sg41485 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20761 sg16312 - -lemma sg41486 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16729 - -lemma sg41487 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17708 - -lemma sg41488 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20719 sg16397 - -lemma sg41489 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20703 sg16433 - -lemma sg41490 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20858 sg15883 - -lemma sg41491 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16433 - -lemma sg41492 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20859 sg15883 - -lemma sg41493 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16837 - -lemma sg41494 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20761 sg16313 - -lemma sg41495 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16730 - -lemma sg41496 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17710 - -lemma sg41497 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17708 - -lemma sg41498 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,9,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20831 sg16168 - -lemma sg41499 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,9,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20887 sg15756 - -lemma sg41500 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,9,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20761 sg16314 - -lemma sg41501 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,9,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16731 - -lemma sg41502 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,9,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20769 sg16267 - -lemma sg41503 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,9,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17710 - -lemma sg41504 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,5,5,5,5,5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18783 - -lemma sg41505 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,5,5,5,5,5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20890 sg15718 - -lemma sg41506 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,5,5,5,5,5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18783 - -lemma sg41507 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,5,5,5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16059 - -lemma sg41508 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,5,5,5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18784 - -lemma sg41509 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,5,5,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17776 - -lemma sg41510 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,5,5,5,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20873 sg15810 - -lemma sg41511 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,5,5,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18784 - -lemma sg41512 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16011 - -lemma sg41513 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16060 - -lemma sg41514 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19823 - -lemma sg41515 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16564 - -lemma sg41516 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18785 - -lemma sg41517 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18786 - -lemma sg41518 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18785 - -lemma sg41519 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18786 - -lemma sg41520 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16012 - -lemma sg41521 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20864 sg15836 - -lemma sg41522 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18790 - -lemma sg41523 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18787 - -lemma sg41524 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16061 - -lemma sg41525 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18787 - -lemma sg41526 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16564 - -lemma sg41527 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18788 - -lemma sg41528 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17777 - -lemma sg41529 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18788 - -lemma sg41530 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20708 sg16403 - -lemma sg41531 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16062 - -lemma sg41532 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20078 - -lemma sg41533 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18789 - -lemma sg41534 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17778 - -lemma sg41535 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18789 - -lemma sg41536 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18790 - -lemma sg41537 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18790 - -lemma sg41538 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17779 - -lemma sg41539 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16014 - -lemma sg41540 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16064 - -lemma sg41541 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19827 - -lemma sg41542 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20399 - -lemma sg41543 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18791 - -lemma sg41544 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18792 - -lemma sg41545 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18791 - -lemma sg41546 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18792 - -lemma sg41547 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg16011 - -lemma sg41548 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16015 - -lemma sg41549 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18239 - -lemma sg41550 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16565 - -lemma sg41551 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18793 - -lemma sg41552 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16065 - -lemma sg41553 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18793 - -lemma sg41554 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20690 sg16542 - -lemma sg41555 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18794 - -lemma sg41556 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17780 - -lemma sg41557 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18794 - -lemma sg41558 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18797 - -lemma sg41559 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18795 - -lemma sg41560 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16016 - -lemma sg41561 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18795 - -lemma sg41562 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18798 - -lemma sg41563 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16066 - -lemma sg41564 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20079 - -lemma sg41565 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18796 - -lemma sg41566 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17781 - -lemma sg41567 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18796 - -lemma sg41568 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18797 - -lemma sg41569 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18797 - -lemma sg41570 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20792 sg16186 - -lemma sg41571 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20080 - -lemma sg41572 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16067 - -lemma sg41573 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19831 - -lemma sg41574 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18798 - -lemma sg41575 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18798 - -lemma sg41576 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17782 - -lemma sg41577 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18092 - -lemma sg41578 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20863 sg15841 - -lemma sg41579 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,4,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16540 - -lemma sg41580 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18801 - -lemma sg41581 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18799 - -lemma sg41582 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16019 - -lemma sg41583 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18799 - -lemma sg41584 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16567 - -lemma sg41585 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16068 - -lemma sg41586 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20081 - -lemma sg41587 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18800 - -lemma sg41588 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17783 - -lemma sg41589 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18800 - -lemma sg41590 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18801 - -lemma sg41591 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18801 - -lemma sg41592 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18803 - -lemma sg41593 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16069 - -lemma sg41594 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16566 - -lemma sg41595 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18802 - -lemma sg41596 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17784 - -lemma sg41597 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18802 - -lemma sg41598 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18804 - -lemma sg41599 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20082 - -lemma sg41600 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16070 - -lemma sg41601 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19835 - -lemma sg41602 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18803 - -lemma sg41603 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18803 - -lemma sg41604 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17785 - -lemma sg41605 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17895 - -lemma sg41606 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20083 - -lemma sg41607 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20083 - -lemma sg41608 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18804 - -lemma sg41609 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20083 - -lemma sg41610 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18804 - -lemma sg41611 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16960 - -lemma sg41612 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17786 - -lemma sg41613 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19462 - -lemma sg41614 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19099 - -lemma sg41615 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16807 - -lemma sg41616 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18805 - -lemma sg41617 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16022 - -lemma sg41618 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18806 - -lemma sg41619 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17896 - -lemma sg41620 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20084 - -lemma sg41621 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16071 - -lemma sg41622 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17727 - -lemma sg41623 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19839 - -lemma sg41624 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20084 - -lemma sg41625 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18805 - -lemma sg41626 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20084 - -lemma sg41627 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18805 - -lemma sg41628 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19463 - -lemma sg41629 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17897 - -lemma sg41630 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20085 - -lemma sg41631 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20085 - -lemma sg41632 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18806 - -lemma sg41633 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20085 - -lemma sg41634 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18806 - -lemma sg41635 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16961 - -lemma sg41636 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19464 - -lemma sg41637 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19100 - -lemma sg41638 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17787 - -lemma sg41639 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16072 - -lemma sg41640 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16962 - -lemma sg41641 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19465 - -lemma sg41642 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19101 - -lemma sg41643 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16808 - -lemma sg41644 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,7,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17731 - -lemma sg41645 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,7,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18093 - -lemma sg41646 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,7,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16809 - -lemma sg41647 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg16014 - -lemma sg41648 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16025 - -lemma sg41649 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18240 - -lemma sg41650 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20400 - -lemma sg41651 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18807 - -lemma sg41652 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16073 - -lemma sg41653 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18807 - -lemma sg41654 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20854 sg16018 - -lemma sg41655 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18808 - -lemma sg41656 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17788 - -lemma sg41657 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18808 - -lemma sg41658 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg16015 - -lemma sg41659 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,4,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16541 - -lemma sg41660 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18811 - -lemma sg41661 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18809 - -lemma sg41662 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16026 - -lemma sg41663 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18809 - -lemma sg41664 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16569 - -lemma sg41665 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16074 - -lemma sg41666 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20086 - -lemma sg41667 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18810 - -lemma sg41668 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17789 - -lemma sg41669 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18810 - -lemma sg41670 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18811 - -lemma sg41671 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18811 - -lemma sg41672 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18813 - -lemma sg41673 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16075 - -lemma sg41674 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16568 - -lemma sg41675 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18812 - -lemma sg41676 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17790 - -lemma sg41677 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18812 - -lemma sg41678 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18814 - -lemma sg41679 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20087 - -lemma sg41680 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16076 - -lemma sg41681 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19846 - -lemma sg41682 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18813 - -lemma sg41683 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18813 - -lemma sg41684 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17898 - -lemma sg41685 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20088 - -lemma sg41686 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20088 - -lemma sg41687 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18814 - -lemma sg41688 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20088 - -lemma sg41689 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18814 - -lemma sg41690 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16964 - -lemma sg41691 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19466 - -lemma sg41692 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19102 - -lemma sg41693 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16926 - -lemma sg41694 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16570 - -lemma sg41695 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,4,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18815 - -lemma sg41696 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,4,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg16019 - -lemma sg41697 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,4,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18815 - -lemma sg41698 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18817 - -lemma sg41699 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16077 - -lemma sg41700 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16570 - -lemma sg41701 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18816 - -lemma sg41702 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17791 - -lemma sg41703 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18816 - -lemma sg41704 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16571 - -lemma sg41705 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20089 - -lemma sg41706 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16078 - -lemma sg41707 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19850 - -lemma sg41708 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18817 - -lemma sg41709 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18817 - -lemma sg41710 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18818 - -lemma sg41711 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16030 - -lemma sg41712 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18819 - -lemma sg41713 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17899 - -lemma sg41714 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20090 - -lemma sg41715 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16079 - -lemma sg41716 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17740 - -lemma sg41717 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19852 - -lemma sg41718 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20090 - -lemma sg41719 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18818 - -lemma sg41720 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20090 - -lemma sg41721 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19467 - -lemma sg41722 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17900 - -lemma sg41723 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20091 - -lemma sg41724 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20091 - -lemma sg41725 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18819 - -lemma sg41726 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20091 - -lemma sg41727 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16966 - -lemma sg41728 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19468 - -lemma sg41729 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19103 - -lemma sg41730 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17792 - -lemma sg41731 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16080 - -lemma sg41732 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16967 - -lemma sg41733 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19469 - -lemma sg41734 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19104 - -lemma sg41735 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16927 - -lemma sg41736 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20684 sg16576 - -lemma sg41737 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18820 - -lemma sg41738 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16968 - -lemma sg41739 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16572 - -lemma sg41740 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16032 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes50 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 + +namespace OAI + +/-! Semigroup Nodes 102. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg41341 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18776 + +lemma sg41342 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20071 + +lemma sg41343 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18776 + +lemma sg41344 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19451 + +lemma sg41345 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17889 + +lemma sg41346 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20072 + +lemma sg41347 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20072 + +lemma sg41348 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18777 + +lemma sg41349 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20072 + +lemma sg41350 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18777 + +lemma sg41351 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16948 + +lemma sg41352 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17767 + +lemma sg41353 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19452 + +lemma sg41354 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,5,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16826 + +lemma sg41355 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16629 + +lemma sg41356 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18778 + +lemma sg41357 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16949 + +lemma sg41358 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16559 + +lemma sg41359 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15875 + +lemma sg41360 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17702 + +lemma sg41361 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18238 + +lemma sg41362 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17890 + +lemma sg41363 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20073 + +lemma sg41364 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20073 + +lemma sg41365 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18778 + +lemma sg41366 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20073 + +lemma sg41367 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18778 + +lemma sg41368 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16949 + +lemma sg41369 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17768 + +lemma sg41370 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19453 + +lemma sg41371 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17769 + +lemma sg41372 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16052 + +lemma sg41373 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16950 + +lemma sg41374 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17769 + +lemma sg41375 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19454 + +lemma sg41376 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16827 + +lemma sg41377 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16920 + +lemma sg41378 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16424 + +lemma sg41379 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15876 + +lemma sg41380 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16828 + +lemma sg41381 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,6,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16921 + +lemma sg41382 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17891 + +lemma sg41383 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18779 + +lemma sg41384 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17891 + +lemma sg41385 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20074 + +lemma sg41386 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20074 + +lemma sg41387 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18779 + +lemma sg41388 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20074 + +lemma sg41389 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18779 + +lemma sg41390 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17770 + +lemma sg41391 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16053 + +lemma sg41392 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16951 + +lemma sg41393 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17770 + +lemma sg41394 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19455 + +lemma sg41395 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16829 + +lemma sg41396 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16426 + +lemma sg41397 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15877 + +lemma sg41398 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16830 + +lemma sg41399 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16922 + +lemma sg41400 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17708 + +lemma sg41401 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16923 + +lemma sg41402 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,7,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17699 + +lemma sg41403 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16952 + +lemma sg41404 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16560 + +lemma sg41405 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17771 + +lemma sg41406 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16054 + +lemma sg41407 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16952 + +lemma sg41408 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17771 + +lemma sg41409 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19456 + +lemma sg41410 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16427 + +lemma sg41411 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15878 + +lemma sg41412 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16831 + +lemma sg41413 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16924 + +lemma sg41414 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17710 + +lemma sg41415 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16925 + +lemma sg41416 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20713 sg16399 + +lemma sg41417 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,8,8,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17699 + +lemma sg41418 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18780 + +lemma sg41419 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15879 + +lemma sg41420 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16562 + +lemma sg41421 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17892 + +lemma sg41422 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20075 + +lemma sg41423 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16055 + +lemma sg41424 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16428 + +lemma sg41425 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15879 + +lemma sg41426 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20075 + +lemma sg41427 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18780 + +lemma sg41428 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20075 + +lemma sg41429 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18780 + +lemma sg41430 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19457 + +lemma sg41431 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16630 + +lemma sg41432 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18781 + +lemma sg41433 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16953 + +lemma sg41434 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16561 + +lemma sg41435 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15880 + +lemma sg41436 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20831 sg16167 + +lemma sg41437 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20887 sg15750 + +lemma sg41438 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17893 + +lemma sg41439 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20076 + +lemma sg41440 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20076 + +lemma sg41441 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18781 + +lemma sg41442 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20076 + +lemma sg41443 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18781 + +lemma sg41444 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16953 + +lemma sg41445 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17772 + +lemma sg41446 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19458 + +lemma sg41447 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17773 + +lemma sg41448 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16056 + +lemma sg41449 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16954 + +lemma sg41450 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17773 + +lemma sg41451 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19459 + +lemma sg41452 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16833 + +lemma sg41453 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16724 + +lemma sg41454 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17894 + +lemma sg41455 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18782 + +lemma sg41456 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17894 + +lemma sg41457 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20077 + +lemma sg41458 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20077 + +lemma sg41459 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18782 + +lemma sg41460 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20077 + +lemma sg41461 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18782 + +lemma sg41462 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17774 + +lemma sg41463 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16057 + +lemma sg41464 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16955 + +lemma sg41465 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17774 + +lemma sg41466 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19460 + +lemma sg41467 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16834 + +lemma sg41468 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16431 + +lemma sg41469 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15881 + +lemma sg41470 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16835 + +lemma sg41471 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16726 + +lemma sg41472 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20761 sg16310 + +lemma sg41473 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16727 + +lemma sg41474 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16956 + +lemma sg41475 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16563 + +lemma sg41476 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17775 + +lemma sg41477 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16058 + +lemma sg41478 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16956 + +lemma sg41479 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17775 + +lemma sg41480 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19461 + +lemma sg41481 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16432 + +lemma sg41482 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15882 + +lemma sg41483 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16836 + +lemma sg41484 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16728 + +lemma sg41485 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20761 sg16312 + +lemma sg41486 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16729 + +lemma sg41487 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17708 + +lemma sg41488 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20719 sg16397 + +lemma sg41489 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20703 sg16433 + +lemma sg41490 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20858 sg15883 + +lemma sg41491 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16433 + +lemma sg41492 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20859 sg15883 + +lemma sg41493 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16837 + +lemma sg41494 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20761 sg16313 + +lemma sg41495 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16730 + +lemma sg41496 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17710 + +lemma sg41497 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,8,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17708 + +lemma sg41498 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,9,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20831 sg16168 + +lemma sg41499 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,9,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20887 sg15756 + +lemma sg41500 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,9,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20761 sg16314 + +lemma sg41501 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,9,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16731 + +lemma sg41502 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,9,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20769 sg16267 + +lemma sg41503 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,9,9,9,9,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17710 + +lemma sg41504 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,5,5,5,5,5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18783 + +lemma sg41505 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,5,5,5,5,5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20890 sg15718 + +lemma sg41506 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,5,5,5,5,5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18783 + +lemma sg41507 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,5,5,5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16059 + +lemma sg41508 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,5,5,5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18784 + +lemma sg41509 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,5,5,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17776 + +lemma sg41510 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,5,5,5,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20873 sg15810 + +lemma sg41511 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,5,5,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18784 + +lemma sg41512 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16011 + +lemma sg41513 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16060 + +lemma sg41514 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19823 + +lemma sg41515 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16564 + +lemma sg41516 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18785 + +lemma sg41517 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18786 + +lemma sg41518 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18785 + +lemma sg41519 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,5,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18786 + +lemma sg41520 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16012 + +lemma sg41521 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20864 sg15836 + +lemma sg41522 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18790 + +lemma sg41523 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18787 + +lemma sg41524 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16061 + +lemma sg41525 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18787 + +lemma sg41526 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16564 + +lemma sg41527 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18788 + +lemma sg41528 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17777 + +lemma sg41529 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18788 + +lemma sg41530 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20708 sg16403 + +lemma sg41531 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16062 + +lemma sg41532 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20078 + +lemma sg41533 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18789 + +lemma sg41534 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17778 + +lemma sg41535 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18789 + +lemma sg41536 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18790 + +lemma sg41537 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18790 + +lemma sg41538 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,6,6,6,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17779 + +lemma sg41539 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16014 + +lemma sg41540 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16064 + +lemma sg41541 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19827 + +lemma sg41542 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20399 + +lemma sg41543 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18791 + +lemma sg41544 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18792 + +lemma sg41545 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18791 + +lemma sg41546 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,5,5,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18792 + +lemma sg41547 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg16011 + +lemma sg41548 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16015 + +lemma sg41549 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18239 + +lemma sg41550 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16565 + +lemma sg41551 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18793 + +lemma sg41552 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16065 + +lemma sg41553 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18793 + +lemma sg41554 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20690 sg16542 + +lemma sg41555 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18794 + +lemma sg41556 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17780 + +lemma sg41557 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,5,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18794 + +lemma sg41558 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18797 + +lemma sg41559 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18795 + +lemma sg41560 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16016 + +lemma sg41561 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18795 + +lemma sg41562 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18798 + +lemma sg41563 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16066 + +lemma sg41564 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20079 + +lemma sg41565 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18796 + +lemma sg41566 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17781 + +lemma sg41567 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18796 + +lemma sg41568 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18797 + +lemma sg41569 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18797 + +lemma sg41570 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20792 sg16186 + +lemma sg41571 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20080 + +lemma sg41572 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16067 + +lemma sg41573 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19831 + +lemma sg41574 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18798 + +lemma sg41575 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18798 + +lemma sg41576 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17782 + +lemma sg41577 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,6,6,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18092 + +lemma sg41578 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20863 sg15841 + +lemma sg41579 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,4,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16540 + +lemma sg41580 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18801 + +lemma sg41581 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18799 + +lemma sg41582 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16019 + +lemma sg41583 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18799 + +lemma sg41584 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16567 + +lemma sg41585 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16068 + +lemma sg41586 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20081 + +lemma sg41587 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18800 + +lemma sg41588 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17783 + +lemma sg41589 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18800 + +lemma sg41590 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18801 + +lemma sg41591 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,5,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18801 + +lemma sg41592 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18803 + +lemma sg41593 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16069 + +lemma sg41594 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16566 + +lemma sg41595 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18802 + +lemma sg41596 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17784 + +lemma sg41597 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18802 + +lemma sg41598 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18804 + +lemma sg41599 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20082 + +lemma sg41600 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16070 + +lemma sg41601 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19835 + +lemma sg41602 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18803 + +lemma sg41603 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18803 + +lemma sg41604 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17785 + +lemma sg41605 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17895 + +lemma sg41606 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20083 + +lemma sg41607 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20083 + +lemma sg41608 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18804 + +lemma sg41609 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20083 + +lemma sg41610 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18804 + +lemma sg41611 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16960 + +lemma sg41612 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17786 + +lemma sg41613 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19462 + +lemma sg41614 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19099 + +lemma sg41615 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16807 + +lemma sg41616 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18805 + +lemma sg41617 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16022 + +lemma sg41618 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18806 + +lemma sg41619 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17896 + +lemma sg41620 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20084 + +lemma sg41621 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16071 + +lemma sg41622 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17727 + +lemma sg41623 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19839 + +lemma sg41624 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20084 + +lemma sg41625 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18805 + +lemma sg41626 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20084 + +lemma sg41627 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18805 + +lemma sg41628 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19463 + +lemma sg41629 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17897 + +lemma sg41630 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20085 + +lemma sg41631 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20085 + +lemma sg41632 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18806 + +lemma sg41633 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20085 + +lemma sg41634 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18806 + +lemma sg41635 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16961 + +lemma sg41636 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19464 + +lemma sg41637 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19100 + +lemma sg41638 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17787 + +lemma sg41639 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16072 + +lemma sg41640 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16962 + +lemma sg41641 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19465 + +lemma sg41642 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19101 + +lemma sg41643 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16808 + +lemma sg41644 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,7,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17731 + +lemma sg41645 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,7,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18093 + +lemma sg41646 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,7,7,7,7,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16809 + +lemma sg41647 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg16014 + +lemma sg41648 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16025 + +lemma sg41649 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18240 + +lemma sg41650 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20400 + +lemma sg41651 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18807 + +lemma sg41652 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16073 + +lemma sg41653 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18807 + +lemma sg41654 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20854 sg16018 + +lemma sg41655 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18808 + +lemma sg41656 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17788 + +lemma sg41657 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,5,5,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18808 + +lemma sg41658 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg16015 + +lemma sg41659 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,4,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16541 + +lemma sg41660 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18811 + +lemma sg41661 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18809 + +lemma sg41662 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16026 + +lemma sg41663 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18809 + +lemma sg41664 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16569 + +lemma sg41665 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16074 + +lemma sg41666 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20086 + +lemma sg41667 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18810 + +lemma sg41668 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17789 + +lemma sg41669 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18810 + +lemma sg41670 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18811 + +lemma sg41671 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,5,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18811 + +lemma sg41672 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18813 + +lemma sg41673 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16075 + +lemma sg41674 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16568 + +lemma sg41675 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18812 + +lemma sg41676 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17790 + +lemma sg41677 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18812 + +lemma sg41678 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18814 + +lemma sg41679 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20087 + +lemma sg41680 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16076 + +lemma sg41681 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19846 + +lemma sg41682 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18813 + +lemma sg41683 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18813 + +lemma sg41684 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17898 + +lemma sg41685 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20088 + +lemma sg41686 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20088 + +lemma sg41687 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18814 + +lemma sg41688 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20088 + +lemma sg41689 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18814 + +lemma sg41690 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16964 + +lemma sg41691 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19466 + +lemma sg41692 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19102 + +lemma sg41693 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,6,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16926 + +lemma sg41694 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16570 + +lemma sg41695 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,4,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18815 + +lemma sg41696 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,4,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg16019 + +lemma sg41697 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,4,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18815 + +lemma sg41698 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18817 + +lemma sg41699 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16077 + +lemma sg41700 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16570 + +lemma sg41701 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18816 + +lemma sg41702 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17791 + +lemma sg41703 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18816 + +lemma sg41704 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16571 + +lemma sg41705 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20089 + +lemma sg41706 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16078 + +lemma sg41707 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19850 + +lemma sg41708 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18817 + +lemma sg41709 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,5,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18817 + +lemma sg41710 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18818 + +lemma sg41711 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16030 + +lemma sg41712 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18819 + +lemma sg41713 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17899 + +lemma sg41714 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20090 + +lemma sg41715 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16079 + +lemma sg41716 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17740 + +lemma sg41717 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19852 + +lemma sg41718 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20090 + +lemma sg41719 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18818 + +lemma sg41720 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20090 + +lemma sg41721 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19467 + +lemma sg41722 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17900 + +lemma sg41723 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20091 + +lemma sg41724 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20091 + +lemma sg41725 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18819 + +lemma sg41726 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20091 + +lemma sg41727 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16966 + +lemma sg41728 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19468 + +lemma sg41729 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19103 + +lemma sg41730 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17792 + +lemma sg41731 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16080 + +lemma sg41732 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16967 + +lemma sg41733 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19469 + +lemma sg41734 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19104 + +lemma sg41735 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16927 + +lemma sg41736 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20684 sg16576 + +lemma sg41737 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18820 + +lemma sg41738 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16968 + +lemma sg41739 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16572 + +lemma sg41740 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16032 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes103.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes103.lean index a9a66a2fe562ae5408081768d892e52109067304..0860b85ee438354451c074d5757d7ea97ee60c33 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes103.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes103.lean @@ -1,1231 +1,1231 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes50 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 - -namespace OAI - -/-! Semigroup Nodes 103. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg41741 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17727 - -lemma sg41742 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18241 - -lemma sg41743 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17901 - -lemma sg41744 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20092 - -lemma sg41745 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20092 - -lemma sg41746 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18820 - -lemma sg41747 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20092 - -lemma sg41748 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16968 - -lemma sg41749 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19470 - -lemma sg41750 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17794 - -lemma sg41751 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16081 - -lemma sg41752 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16969 - -lemma sg41753 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19471 - -lemma sg41754 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19105 - -lemma sg41755 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16928 - -lemma sg41756 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17746 - -lemma sg41757 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18094 - -lemma sg41758 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16929 - -lemma sg41759 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17731 - -lemma sg41760 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16930 - -lemma sg41761 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16574 - -lemma sg41762 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16082 - -lemma sg41763 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16549 - -lemma sg41764 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20690 sg16549 - -lemma sg41765 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18821 - -lemma sg41766 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16970 - -lemma sg41767 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17795 - -lemma sg41768 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20093 - -lemma sg41769 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18821 - -lemma sg41770 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18822 - -lemma sg41771 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16034 - -lemma sg41772 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18823 - -lemma sg41773 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17902 - -lemma sg41774 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20094 - -lemma sg41775 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16083 - -lemma sg41776 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17747 - -lemma sg41777 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19858 - -lemma sg41778 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20094 - -lemma sg41779 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18822 - -lemma sg41780 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20094 - -lemma sg41781 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19472 - -lemma sg41782 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17903 - -lemma sg41783 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20095 - -lemma sg41784 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20095 - -lemma sg41785 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18823 - -lemma sg41786 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20095 - -lemma sg41787 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16971 - -lemma sg41788 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19473 - -lemma sg41789 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19106 - -lemma sg41790 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16632 - -lemma sg41791 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18824 - -lemma sg41792 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16972 - -lemma sg41793 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16575 - -lemma sg41794 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16036 - -lemma sg41795 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20709 sg16410 - -lemma sg41796 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20864 sg15858 - -lemma sg41797 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17904 - -lemma sg41798 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20096 - -lemma sg41799 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20096 - -lemma sg41800 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18824 - -lemma sg41801 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20096 - -lemma sg41802 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16972 - -lemma sg41803 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19474 - -lemma sg41804 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17797 - -lemma sg41805 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16084 - -lemma sg41806 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16973 - -lemma sg41807 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19475 - -lemma sg41808 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19107 - -lemma sg41809 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16815 - -lemma sg41810 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17751 - -lemma sg41811 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18095 - -lemma sg41812 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16816 - -lemma sg41813 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17905 - -lemma sg41814 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18825 - -lemma sg41815 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17905 - -lemma sg41816 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20097 - -lemma sg41817 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20097 - -lemma sg41818 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18825 - -lemma sg41819 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20097 - -lemma sg41820 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17798 - -lemma sg41821 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16085 - -lemma sg41822 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16974 - -lemma sg41823 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19476 - -lemma sg41824 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19108 - -lemma sg41825 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17753 - -lemma sg41826 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19109 - -lemma sg41827 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16817 - -lemma sg41828 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16414 - -lemma sg41829 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16818 - -lemma sg41830 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17731 - -lemma sg41831 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16975 - -lemma sg41832 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16576 - -lemma sg41833 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17799 - -lemma sg41834 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16086 - -lemma sg41835 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16975 - -lemma sg41836 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19477 - -lemma sg41837 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17754 - -lemma sg41838 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18096 - -lemma sg41839 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16819 - -lemma sg41840 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16416 - -lemma sg41841 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16820 - -lemma sg41842 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20536 sg17406 - -lemma sg41843 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17731 - -lemma sg41844 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,4,4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20867 sg15846 - -lemma sg41845 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg16025 - -lemma sg41846 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,4,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20869 sg15846 - -lemma sg41847 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18828 - -lemma sg41848 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18826 - -lemma sg41849 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16040 - -lemma sg41850 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18826 - -lemma sg41851 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20402 - -lemma sg41852 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16087 - -lemma sg41853 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20098 - -lemma sg41854 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18827 - -lemma sg41855 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17800 - -lemma sg41856 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18828 - -lemma sg41857 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16577 - -lemma sg41858 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,4,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18829 - -lemma sg41859 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,4,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg16026 - -lemma sg41860 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,4,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18829 - -lemma sg41861 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18831 - -lemma sg41862 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16088 - -lemma sg41863 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16577 - -lemma sg41864 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18830 - -lemma sg41865 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17801 - -lemma sg41866 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16578 - -lemma sg41867 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20099 - -lemma sg41868 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16089 - -lemma sg41869 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19869 - -lemma sg41870 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18831 - -lemma sg41871 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18832 - -lemma sg41872 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16042 - -lemma sg41873 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18833 - -lemma sg41874 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17906 - -lemma sg41875 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20100 - -lemma sg41876 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16090 - -lemma sg41877 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17757 - -lemma sg41878 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20100 - -lemma sg41879 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18832 - -lemma sg41880 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20100 - -lemma sg41881 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19478 - -lemma sg41882 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17907 - -lemma sg41883 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20101 - -lemma sg41884 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20101 - -lemma sg41885 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18833 - -lemma sg41886 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20101 - -lemma sg41887 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16976 - -lemma sg41888 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19479 - -lemma sg41889 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19110 - -lemma sg41890 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17802 - -lemma sg41891 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16091 - -lemma sg41892 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16977 - -lemma sg41893 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19480 - -lemma sg41894 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19111 - -lemma sg41895 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16931 - -lemma sg41896 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16579 - -lemma sg41897 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16092 - -lemma sg41898 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16555 - -lemma sg41899 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20690 sg16555 - -lemma sg41900 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18834 - -lemma sg41901 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16978 - -lemma sg41902 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17803 - -lemma sg41903 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20102 - -lemma sg41904 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18835 - -lemma sg41905 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16044 - -lemma sg41906 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18836 - -lemma sg41907 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17908 - -lemma sg41908 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20103 - -lemma sg41909 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16093 - -lemma sg41910 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17760 - -lemma sg41911 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20103 - -lemma sg41912 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18835 - -lemma sg41913 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20103 - -lemma sg41914 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19481 - -lemma sg41915 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17909 - -lemma sg41916 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20104 - -lemma sg41917 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20104 - -lemma sg41918 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18836 - -lemma sg41919 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20104 - -lemma sg41920 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16979 - -lemma sg41921 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19482 - -lemma sg41922 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19112 - -lemma sg41923 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16633 - -lemma sg41924 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18837 - -lemma sg41925 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16980 - -lemma sg41926 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16580 - -lemma sg41927 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16047 - -lemma sg41928 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17740 - -lemma sg41929 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17910 - -lemma sg41930 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20105 - -lemma sg41931 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20105 - -lemma sg41932 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18837 - -lemma sg41933 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20105 - -lemma sg41934 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16980 - -lemma sg41935 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19483 - -lemma sg41936 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17805 - -lemma sg41937 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16094 - -lemma sg41938 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16981 - -lemma sg41939 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19484 - -lemma sg41940 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19113 - -lemma sg41941 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16932 - -lemma sg41942 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17763 - -lemma sg41943 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18097 - -lemma sg41944 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16933 - -lemma sg41945 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17911 - -lemma sg41946 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18838 - -lemma sg41947 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17911 - -lemma sg41948 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20106 - -lemma sg41949 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20106 - -lemma sg41950 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18838 - -lemma sg41951 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20106 - -lemma sg41952 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17806 - -lemma sg41953 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16095 - -lemma sg41954 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16982 - -lemma sg41955 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19485 - -lemma sg41956 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19114 - -lemma sg41957 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17765 - -lemma sg41958 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19115 - -lemma sg41959 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16934 - -lemma sg41960 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17746 - -lemma sg41961 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16935 - -lemma sg41962 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20713 sg16409 - -lemma sg41963 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18839 - -lemma sg41964 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16050 - -lemma sg41965 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16582 - -lemma sg41966 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17912 - -lemma sg41967 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20107 - -lemma sg41968 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16096 - -lemma sg41969 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17766 - -lemma sg41970 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20107 - -lemma sg41971 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18839 - -lemma sg41972 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20107 - -lemma sg41973 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19486 - -lemma sg41974 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16634 - -lemma sg41975 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18840 - -lemma sg41976 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16983 - -lemma sg41977 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16581 - -lemma sg41978 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16051 - -lemma sg41979 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17747 - -lemma sg41980 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17913 - -lemma sg41981 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20108 - -lemma sg41982 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20108 - -lemma sg41983 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18840 - -lemma sg41984 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20108 - -lemma sg41985 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16983 - -lemma sg41986 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19487 - -lemma sg41987 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17808 - -lemma sg41988 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16097 - -lemma sg41989 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16984 - -lemma sg41990 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19488 - -lemma sg41991 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19116 - -lemma sg41992 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16936 - -lemma sg41993 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17914 - -lemma sg41994 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18841 - -lemma sg41995 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17914 - -lemma sg41996 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20109 - -lemma sg41997 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20109 - -lemma sg41998 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18841 - -lemma sg41999 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20109 - -lemma sg42000 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17809 - -lemma sg42001 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16098 - -lemma sg42002 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16985 - -lemma sg42003 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19489 - -lemma sg42004 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19117 - -lemma sg42005 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17769 - -lemma sg42006 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19118 - -lemma sg42007 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16937 - -lemma sg42008 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17751 - -lemma sg42009 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16938 - -lemma sg42010 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16986 - -lemma sg42011 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16583 - -lemma sg42012 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17810 - -lemma sg42013 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16099 - -lemma sg42014 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16986 - -lemma sg42015 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19490 - -lemma sg42016 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17770 - -lemma sg42017 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19119 - -lemma sg42018 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16939 - -lemma sg42019 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17753 - -lemma sg42020 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16940 - -lemma sg42021 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17746 - -lemma sg42022 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20719 sg16409 - -lemma sg42023 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17771 - -lemma sg42024 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16054 - -lemma sg42025 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17771 - -lemma sg42026 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18098 - -lemma sg42027 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17754 - -lemma sg42028 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16941 - -lemma sg42029 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20713 sg16416 - -lemma sg42030 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17746 - -lemma sg42031 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16584 - -lemma sg42032 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20863 sg15879 - -lemma sg42033 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16635 - -lemma sg42034 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18842 - -lemma sg42035 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16987 - -lemma sg42036 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16584 - -lemma sg42037 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16055 - -lemma sg42038 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20709 sg16428 - -lemma sg42039 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17915 - -lemma sg42040 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20110 - -lemma sg42041 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20110 - -lemma sg42042 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18842 - -lemma sg42043 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20110 - -lemma sg42044 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16987 - -lemma sg42045 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19491 - -lemma sg42046 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17916 - -lemma sg42047 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18843 - -lemma sg42048 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17916 - -lemma sg42049 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20111 - -lemma sg42050 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20111 - -lemma sg42051 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18843 - -lemma sg42052 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20111 - -lemma sg42053 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17812 - -lemma sg42054 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16100 - -lemma sg42055 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16988 - -lemma sg42056 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19492 - -lemma sg42057 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19120 - -lemma sg42058 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17773 - -lemma sg42059 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19121 - -lemma sg42060 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16833 - -lemma sg42061 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16989 - -lemma sg42062 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16585 - -lemma sg42063 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17813 - -lemma sg42064 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16101 - -lemma sg42065 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16989 - -lemma sg42066 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19493 - -lemma sg42067 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17774 - -lemma sg42068 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19122 - -lemma sg42069 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16834 - -lemma sg42070 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16431 - -lemma sg42071 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16835 - -lemma sg42072 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17751 - -lemma sg42073 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17775 - -lemma sg42074 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16058 - -lemma sg42075 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17775 - -lemma sg42076 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19123 - -lemma sg42077 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16432 - -lemma sg42078 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16836 - -lemma sg42079 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17753 - -lemma sg42080 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17751 - -lemma sg42081 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,8,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20709 sg16433 - -lemma sg42082 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,8,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16433 - -lemma sg42083 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,8,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16837 - -lemma sg42084 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,8,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17754 - -lemma sg42085 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,8,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17753 - -lemma sg42086 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,9,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20837 sg16168 - -lemma sg42087 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,9,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20763 sg16314 - -lemma sg42088 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,9,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17754 - -lemma sg42089 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,5,5,5,5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16102 - -lemma sg42090 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,5,5,5,5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18844 - -lemma sg42091 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,5,5,5,5,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20840 sg16165 - -lemma sg42092 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,5,5,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16059 - -lemma sg42093 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,5,5,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16103 - -lemma sg42094 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,5,5,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20403 - -lemma sg42095 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,5,5,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18845 - -lemma sg42096 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,5,5,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18846 - -lemma sg42097 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20863 sg15884 - -lemma sg42098 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,5,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16060 - -lemma sg42099 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,5,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16586 - -lemma sg42100 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,5,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18847 - -lemma sg42101 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,5,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16104 - -lemma sg42102 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,5,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20690 sg16564 - -lemma sg42103 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,5,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18848 - -lemma sg42104 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18851 - -lemma sg42105 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18849 - -lemma sg42106 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16061 - -lemma sg42107 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18852 - -lemma sg42108 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16105 - -lemma sg42109 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20112 - -lemma sg42110 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18850 - -lemma sg42111 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18851 - -lemma sg42112 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20708 sg16441 - -lemma sg42113 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20113 - -lemma sg42114 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16106 - -lemma sg42115 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18852 - -lemma sg42116 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18099 - -lemma sg42117 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg16059 - -lemma sg42118 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,5,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16064 - -lemma sg42119 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,5,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20404 - -lemma sg42120 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,5,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18853 - -lemma sg42121 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,5,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16107 - -lemma sg42122 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,5,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20854 sg16063 - -lemma sg42123 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,5,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18854 - -lemma sg42124 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg16060 - -lemma sg42125 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18857 - -lemma sg42126 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18855 - -lemma sg42127 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16065 - -lemma sg42128 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16588 - -lemma sg42129 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16108 - -lemma sg42130 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20114 - -lemma sg42131 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18856 - -lemma sg42132 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18857 - -lemma sg42133 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18859 - -lemma sg42134 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16109 - -lemma sg42135 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16587 - -lemma sg42136 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18858 - -lemma sg42137 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18860 - -lemma sg42138 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20115 - -lemma sg42139 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16110 - -lemma sg42140 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18859 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes50 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 + +namespace OAI + +/-! Semigroup Nodes 103. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg41741 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17727 + +lemma sg41742 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18241 + +lemma sg41743 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17901 + +lemma sg41744 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20092 + +lemma sg41745 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20092 + +lemma sg41746 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18820 + +lemma sg41747 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20092 + +lemma sg41748 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16968 + +lemma sg41749 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19470 + +lemma sg41750 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17794 + +lemma sg41751 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16081 + +lemma sg41752 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16969 + +lemma sg41753 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19471 + +lemma sg41754 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19105 + +lemma sg41755 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16928 + +lemma sg41756 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17746 + +lemma sg41757 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18094 + +lemma sg41758 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16929 + +lemma sg41759 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17731 + +lemma sg41760 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,7,7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16930 + +lemma sg41761 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16574 + +lemma sg41762 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16082 + +lemma sg41763 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16549 + +lemma sg41764 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20690 sg16549 + +lemma sg41765 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18821 + +lemma sg41766 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16970 + +lemma sg41767 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17795 + +lemma sg41768 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20093 + +lemma sg41769 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,4,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18821 + +lemma sg41770 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18822 + +lemma sg41771 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16034 + +lemma sg41772 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18823 + +lemma sg41773 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17902 + +lemma sg41774 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20094 + +lemma sg41775 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16083 + +lemma sg41776 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17747 + +lemma sg41777 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19858 + +lemma sg41778 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20094 + +lemma sg41779 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18822 + +lemma sg41780 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20094 + +lemma sg41781 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19472 + +lemma sg41782 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17903 + +lemma sg41783 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20095 + +lemma sg41784 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20095 + +lemma sg41785 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18823 + +lemma sg41786 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20095 + +lemma sg41787 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16971 + +lemma sg41788 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19473 + +lemma sg41789 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,5,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19106 + +lemma sg41790 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16632 + +lemma sg41791 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18824 + +lemma sg41792 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16972 + +lemma sg41793 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16575 + +lemma sg41794 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16036 + +lemma sg41795 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20709 sg16410 + +lemma sg41796 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20864 sg15858 + +lemma sg41797 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17904 + +lemma sg41798 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20096 + +lemma sg41799 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20096 + +lemma sg41800 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18824 + +lemma sg41801 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20096 + +lemma sg41802 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16972 + +lemma sg41803 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19474 + +lemma sg41804 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17797 + +lemma sg41805 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16084 + +lemma sg41806 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16973 + +lemma sg41807 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19475 + +lemma sg41808 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19107 + +lemma sg41809 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16815 + +lemma sg41810 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17751 + +lemma sg41811 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18095 + +lemma sg41812 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,6,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16816 + +lemma sg41813 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17905 + +lemma sg41814 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18825 + +lemma sg41815 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17905 + +lemma sg41816 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20097 + +lemma sg41817 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20097 + +lemma sg41818 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18825 + +lemma sg41819 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20097 + +lemma sg41820 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17798 + +lemma sg41821 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16085 + +lemma sg41822 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16974 + +lemma sg41823 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19476 + +lemma sg41824 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19108 + +lemma sg41825 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17753 + +lemma sg41826 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19109 + +lemma sg41827 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16817 + +lemma sg41828 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16414 + +lemma sg41829 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16818 + +lemma sg41830 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,7,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17731 + +lemma sg41831 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16975 + +lemma sg41832 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16576 + +lemma sg41833 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17799 + +lemma sg41834 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16086 + +lemma sg41835 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16975 + +lemma sg41836 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19477 + +lemma sg41837 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17754 + +lemma sg41838 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18096 + +lemma sg41839 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16819 + +lemma sg41840 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16416 + +lemma sg41841 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16820 + +lemma sg41842 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20536 sg17406 + +lemma sg41843 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,8,8,8,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17731 + +lemma sg41844 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,4,4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20867 sg15846 + +lemma sg41845 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg16025 + +lemma sg41846 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,4,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20869 sg15846 + +lemma sg41847 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18828 + +lemma sg41848 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18826 + +lemma sg41849 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16040 + +lemma sg41850 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18826 + +lemma sg41851 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20402 + +lemma sg41852 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16087 + +lemma sg41853 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20098 + +lemma sg41854 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18827 + +lemma sg41855 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17800 + +lemma sg41856 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,5,5,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18828 + +lemma sg41857 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16577 + +lemma sg41858 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,4,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18829 + +lemma sg41859 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,4,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg16026 + +lemma sg41860 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,4,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18829 + +lemma sg41861 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18831 + +lemma sg41862 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16088 + +lemma sg41863 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16577 + +lemma sg41864 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18830 + +lemma sg41865 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17801 + +lemma sg41866 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16578 + +lemma sg41867 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20099 + +lemma sg41868 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16089 + +lemma sg41869 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19869 + +lemma sg41870 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,5,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18831 + +lemma sg41871 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18832 + +lemma sg41872 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16042 + +lemma sg41873 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18833 + +lemma sg41874 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17906 + +lemma sg41875 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20100 + +lemma sg41876 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16090 + +lemma sg41877 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17757 + +lemma sg41878 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20100 + +lemma sg41879 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18832 + +lemma sg41880 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20100 + +lemma sg41881 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19478 + +lemma sg41882 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17907 + +lemma sg41883 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20101 + +lemma sg41884 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20101 + +lemma sg41885 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18833 + +lemma sg41886 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20101 + +lemma sg41887 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16976 + +lemma sg41888 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19479 + +lemma sg41889 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19110 + +lemma sg41890 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17802 + +lemma sg41891 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16091 + +lemma sg41892 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16977 + +lemma sg41893 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19480 + +lemma sg41894 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19111 + +lemma sg41895 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,6,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16931 + +lemma sg41896 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16579 + +lemma sg41897 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16092 + +lemma sg41898 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16555 + +lemma sg41899 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20690 sg16555 + +lemma sg41900 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18834 + +lemma sg41901 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16978 + +lemma sg41902 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17803 + +lemma sg41903 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20102 + +lemma sg41904 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18835 + +lemma sg41905 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16044 + +lemma sg41906 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18836 + +lemma sg41907 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17908 + +lemma sg41908 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20103 + +lemma sg41909 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16093 + +lemma sg41910 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17760 + +lemma sg41911 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20103 + +lemma sg41912 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18835 + +lemma sg41913 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20103 + +lemma sg41914 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19481 + +lemma sg41915 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17909 + +lemma sg41916 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20104 + +lemma sg41917 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20104 + +lemma sg41918 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18836 + +lemma sg41919 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20104 + +lemma sg41920 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16979 + +lemma sg41921 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19482 + +lemma sg41922 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,5,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19112 + +lemma sg41923 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16633 + +lemma sg41924 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18837 + +lemma sg41925 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16980 + +lemma sg41926 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16580 + +lemma sg41927 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16047 + +lemma sg41928 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17740 + +lemma sg41929 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17910 + +lemma sg41930 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20105 + +lemma sg41931 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20105 + +lemma sg41932 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18837 + +lemma sg41933 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20105 + +lemma sg41934 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16980 + +lemma sg41935 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19483 + +lemma sg41936 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17805 + +lemma sg41937 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16094 + +lemma sg41938 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16981 + +lemma sg41939 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19484 + +lemma sg41940 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19113 + +lemma sg41941 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16932 + +lemma sg41942 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17763 + +lemma sg41943 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18097 + +lemma sg41944 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,6,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16933 + +lemma sg41945 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17911 + +lemma sg41946 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18838 + +lemma sg41947 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17911 + +lemma sg41948 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20106 + +lemma sg41949 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20106 + +lemma sg41950 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18838 + +lemma sg41951 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20106 + +lemma sg41952 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17806 + +lemma sg41953 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16095 + +lemma sg41954 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16982 + +lemma sg41955 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19485 + +lemma sg41956 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19114 + +lemma sg41957 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17765 + +lemma sg41958 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19115 + +lemma sg41959 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16934 + +lemma sg41960 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17746 + +lemma sg41961 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16935 + +lemma sg41962 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,7,7,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20713 sg16409 + +lemma sg41963 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18839 + +lemma sg41964 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16050 + +lemma sg41965 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16582 + +lemma sg41966 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17912 + +lemma sg41967 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20107 + +lemma sg41968 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16096 + +lemma sg41969 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17766 + +lemma sg41970 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20107 + +lemma sg41971 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18839 + +lemma sg41972 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20107 + +lemma sg41973 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19486 + +lemma sg41974 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16634 + +lemma sg41975 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18840 + +lemma sg41976 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16983 + +lemma sg41977 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16581 + +lemma sg41978 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16051 + +lemma sg41979 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17747 + +lemma sg41980 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17913 + +lemma sg41981 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20108 + +lemma sg41982 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20108 + +lemma sg41983 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18840 + +lemma sg41984 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20108 + +lemma sg41985 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16983 + +lemma sg41986 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19487 + +lemma sg41987 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17808 + +lemma sg41988 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16097 + +lemma sg41989 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16984 + +lemma sg41990 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19488 + +lemma sg41991 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19116 + +lemma sg41992 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16936 + +lemma sg41993 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17914 + +lemma sg41994 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18841 + +lemma sg41995 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17914 + +lemma sg41996 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20109 + +lemma sg41997 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20109 + +lemma sg41998 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18841 + +lemma sg41999 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20109 + +lemma sg42000 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17809 + +lemma sg42001 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16098 + +lemma sg42002 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16985 + +lemma sg42003 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19489 + +lemma sg42004 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19117 + +lemma sg42005 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17769 + +lemma sg42006 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19118 + +lemma sg42007 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16937 + +lemma sg42008 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17751 + +lemma sg42009 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16938 + +lemma sg42010 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16986 + +lemma sg42011 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16583 + +lemma sg42012 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17810 + +lemma sg42013 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16099 + +lemma sg42014 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16986 + +lemma sg42015 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19490 + +lemma sg42016 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17770 + +lemma sg42017 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19119 + +lemma sg42018 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16939 + +lemma sg42019 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17753 + +lemma sg42020 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16940 + +lemma sg42021 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17746 + +lemma sg42022 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20719 sg16409 + +lemma sg42023 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17771 + +lemma sg42024 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16054 + +lemma sg42025 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17771 + +lemma sg42026 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18098 + +lemma sg42027 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17754 + +lemma sg42028 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16941 + +lemma sg42029 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20713 sg16416 + +lemma sg42030 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,8,8,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17746 + +lemma sg42031 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16584 + +lemma sg42032 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20863 sg15879 + +lemma sg42033 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16635 + +lemma sg42034 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18842 + +lemma sg42035 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16987 + +lemma sg42036 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16584 + +lemma sg42037 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16055 + +lemma sg42038 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20709 sg16428 + +lemma sg42039 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17915 + +lemma sg42040 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20110 + +lemma sg42041 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20110 + +lemma sg42042 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18842 + +lemma sg42043 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20110 + +lemma sg42044 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16987 + +lemma sg42045 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19491 + +lemma sg42046 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17916 + +lemma sg42047 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18843 + +lemma sg42048 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17916 + +lemma sg42049 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20111 + +lemma sg42050 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20111 + +lemma sg42051 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18843 + +lemma sg42052 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20111 + +lemma sg42053 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17812 + +lemma sg42054 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16100 + +lemma sg42055 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16988 + +lemma sg42056 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19492 + +lemma sg42057 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19120 + +lemma sg42058 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17773 + +lemma sg42059 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19121 + +lemma sg42060 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16833 + +lemma sg42061 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16989 + +lemma sg42062 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16585 + +lemma sg42063 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17813 + +lemma sg42064 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16101 + +lemma sg42065 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16989 + +lemma sg42066 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19493 + +lemma sg42067 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17774 + +lemma sg42068 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19122 + +lemma sg42069 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16834 + +lemma sg42070 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16431 + +lemma sg42071 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16835 + +lemma sg42072 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,6,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17751 + +lemma sg42073 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17775 + +lemma sg42074 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16058 + +lemma sg42075 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17775 + +lemma sg42076 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19123 + +lemma sg42077 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16432 + +lemma sg42078 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16836 + +lemma sg42079 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17753 + +lemma sg42080 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,7,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17751 + +lemma sg42081 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,8,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20709 sg16433 + +lemma sg42082 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,8,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16433 + +lemma sg42083 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,8,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16837 + +lemma sg42084 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,8,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17754 + +lemma sg42085 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,8,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17753 + +lemma sg42086 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,9,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20837 sg16168 + +lemma sg42087 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,9,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20763 sg16314 + +lemma sg42088 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,10,9,9,9,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17754 + +lemma sg42089 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,5,5,5,5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16102 + +lemma sg42090 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,5,5,5,5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18844 + +lemma sg42091 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,5,5,5,5,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20840 sg16165 + +lemma sg42092 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,5,5,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16059 + +lemma sg42093 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,5,5,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16103 + +lemma sg42094 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,5,5,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20403 + +lemma sg42095 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,5,5,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18845 + +lemma sg42096 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,5,5,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18846 + +lemma sg42097 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20863 sg15884 + +lemma sg42098 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,5,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16060 + +lemma sg42099 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,5,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16586 + +lemma sg42100 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,5,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18847 + +lemma sg42101 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,5,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16104 + +lemma sg42102 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,5,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20690 sg16564 + +lemma sg42103 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,5,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18848 + +lemma sg42104 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18851 + +lemma sg42105 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18849 + +lemma sg42106 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16061 + +lemma sg42107 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18852 + +lemma sg42108 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16105 + +lemma sg42109 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20112 + +lemma sg42110 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18850 + +lemma sg42111 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18851 + +lemma sg42112 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20708 sg16441 + +lemma sg42113 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20113 + +lemma sg42114 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16106 + +lemma sg42115 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18852 + +lemma sg42116 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,6,6,6,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18099 + +lemma sg42117 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg16059 + +lemma sg42118 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,5,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16064 + +lemma sg42119 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,5,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20404 + +lemma sg42120 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,5,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18853 + +lemma sg42121 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,5,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16107 + +lemma sg42122 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,5,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20854 sg16063 + +lemma sg42123 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,5,5,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18854 + +lemma sg42124 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg16060 + +lemma sg42125 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18857 + +lemma sg42126 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18855 + +lemma sg42127 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16065 + +lemma sg42128 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16588 + +lemma sg42129 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16108 + +lemma sg42130 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20114 + +lemma sg42131 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18856 + +lemma sg42132 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,5,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18857 + +lemma sg42133 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18859 + +lemma sg42134 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16109 + +lemma sg42135 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16587 + +lemma sg42136 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18858 + +lemma sg42137 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18860 + +lemma sg42138 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20115 + +lemma sg42139 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16110 + +lemma sg42140 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18859 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes104.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes104.lean index 069e844ecaed7fc727a05e52d5d9c978bb2d1ce2..16557f57619418ed6d0b35d58371da5bb1b91784 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes104.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes104.lean @@ -1,1231 +1,1231 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes50 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 - -namespace OAI - -/-! Semigroup Nodes 104. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg42141 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17917 - -lemma sg42142 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20116 - -lemma sg42143 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20116 - -lemma sg42144 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18860 - -lemma sg42145 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20116 - -lemma sg42146 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16991 - -lemma sg42147 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19494 - -lemma sg42148 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19124 - -lemma sg42149 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16957 - -lemma sg42150 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16589 - -lemma sg42151 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,4,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18861 - -lemma sg42152 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,4,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20863 sg15892 - -lemma sg42153 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18863 - -lemma sg42154 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16111 - -lemma sg42155 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16589 - -lemma sg42156 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18862 - -lemma sg42157 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16590 - -lemma sg42158 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20117 - -lemma sg42159 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16112 - -lemma sg42160 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18863 - -lemma sg42161 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18864 - -lemma sg42162 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16069 - -lemma sg42163 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18865 - -lemma sg42164 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17918 - -lemma sg42165 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20118 - -lemma sg42166 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16113 - -lemma sg42167 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17784 - -lemma sg42168 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20118 - -lemma sg42169 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20118 - -lemma sg42170 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19495 - -lemma sg42171 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17919 - -lemma sg42172 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20119 - -lemma sg42173 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20119 - -lemma sg42174 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20119 - -lemma sg42175 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16992 - -lemma sg42176 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19496 - -lemma sg42177 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19125 - -lemma sg42178 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17816 - -lemma sg42179 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16993 - -lemma sg42180 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19497 - -lemma sg42181 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19126 - -lemma sg42182 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16839 - -lemma sg42183 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20688 sg16576 - -lemma sg42184 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18866 - -lemma sg42185 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16994 - -lemma sg42186 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16591 - -lemma sg42187 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16071 - -lemma sg42188 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20709 sg16438 - -lemma sg42189 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17920 - -lemma sg42190 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20120 - -lemma sg42191 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20120 - -lemma sg42192 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20120 - -lemma sg42193 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16994 - -lemma sg42194 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19498 - -lemma sg42195 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17818 - -lemma sg42196 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16995 - -lemma sg42197 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19499 - -lemma sg42198 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19127 - -lemma sg42199 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16840 - -lemma sg42200 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17787 - -lemma sg42201 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18100 - -lemma sg42202 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16841 - -lemma sg42203 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16441 - -lemma sg42204 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16842 - -lemma sg42205 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,4,4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20867 sg15887 - -lemma sg42206 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg16064 - -lemma sg42207 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18869 - -lemma sg42208 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18867 - -lemma sg42209 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16073 - -lemma sg42210 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20406 - -lemma sg42211 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16114 - -lemma sg42212 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20121 - -lemma sg42213 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18868 - -lemma sg42214 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16592 - -lemma sg42215 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,4,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18870 - -lemma sg42216 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,4,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg16065 - -lemma sg42217 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18872 - -lemma sg42218 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16115 - -lemma sg42219 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16592 - -lemma sg42220 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18871 - -lemma sg42221 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16593 - -lemma sg42222 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20122 - -lemma sg42223 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16116 - -lemma sg42224 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18873 - -lemma sg42225 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16075 - -lemma sg42226 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18874 - -lemma sg42227 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17921 - -lemma sg42228 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20123 - -lemma sg42229 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17790 - -lemma sg42230 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20123 - -lemma sg42231 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20123 - -lemma sg42232 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19500 - -lemma sg42233 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17922 - -lemma sg42234 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20124 - -lemma sg42235 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20124 - -lemma sg42236 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20124 - -lemma sg42237 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16996 - -lemma sg42238 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19501 - -lemma sg42239 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19128 - -lemma sg42240 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17819 - -lemma sg42241 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16997 - -lemma sg42242 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19502 - -lemma sg42243 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19129 - -lemma sg42244 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16958 - -lemma sg42245 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16594 - -lemma sg42246 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16117 - -lemma sg42247 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16570 - -lemma sg42248 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20690 sg16570 - -lemma sg42249 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18875 - -lemma sg42250 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16998 - -lemma sg42251 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20125 - -lemma sg42252 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18876 - -lemma sg42253 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16077 - -lemma sg42254 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18877 - -lemma sg42255 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17923 - -lemma sg42256 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20126 - -lemma sg42257 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17791 - -lemma sg42258 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20126 - -lemma sg42259 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20126 - -lemma sg42260 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19503 - -lemma sg42261 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17924 - -lemma sg42262 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20127 - -lemma sg42263 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20127 - -lemma sg42264 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20127 - -lemma sg42265 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16999 - -lemma sg42266 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19504 - -lemma sg42267 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19130 - -lemma sg42268 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16636 - -lemma sg42269 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18878 - -lemma sg42270 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17000 - -lemma sg42271 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16595 - -lemma sg42272 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17784 - -lemma sg42273 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17925 - -lemma sg42274 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20128 - -lemma sg42275 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20128 - -lemma sg42276 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20128 - -lemma sg42277 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17000 - -lemma sg42278 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19505 - -lemma sg42279 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17821 - -lemma sg42280 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17001 - -lemma sg42281 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19506 - -lemma sg42282 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19131 - -lemma sg42283 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16959 - -lemma sg42284 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17792 - -lemma sg42285 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19132 - -lemma sg42286 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16960 - -lemma sg42287 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17926 - -lemma sg42288 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18879 - -lemma sg42289 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17926 - -lemma sg42290 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20129 - -lemma sg42291 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20129 - -lemma sg42292 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20129 - -lemma sg42293 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17822 - -lemma sg42294 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17002 - -lemma sg42295 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19507 - -lemma sg42296 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19133 - -lemma sg42297 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17794 - -lemma sg42298 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19134 - -lemma sg42299 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16961 - -lemma sg42300 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17787 - -lemma sg42301 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16962 - -lemma sg42302 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20713 sg16441 - -lemma sg42303 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18880 - -lemma sg42304 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg16082 - -lemma sg42305 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16597 - -lemma sg42306 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17927 - -lemma sg42307 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20130 - -lemma sg42308 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17795 - -lemma sg42309 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20130 - -lemma sg42310 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20130 - -lemma sg42311 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19508 - -lemma sg42312 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16637 - -lemma sg42313 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18881 - -lemma sg42314 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17003 - -lemma sg42315 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16596 - -lemma sg42316 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20709 sg16447 - -lemma sg42317 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17928 - -lemma sg42318 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20131 - -lemma sg42319 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20131 - -lemma sg42320 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20131 - -lemma sg42321 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17003 - -lemma sg42322 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19509 - -lemma sg42323 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17824 - -lemma sg42324 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17004 - -lemma sg42325 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19510 - -lemma sg42326 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19135 - -lemma sg42327 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16848 - -lemma sg42328 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17929 - -lemma sg42329 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18882 - -lemma sg42330 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17929 - -lemma sg42331 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20132 - -lemma sg42332 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20132 - -lemma sg42333 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20132 - -lemma sg42334 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17825 - -lemma sg42335 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17005 - -lemma sg42336 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19511 - -lemma sg42337 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19136 - -lemma sg42338 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17797 - -lemma sg42339 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19137 - -lemma sg42340 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16849 - -lemma sg42341 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16450 - -lemma sg42342 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16850 - -lemma sg42343 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17006 - -lemma sg42344 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16598 - -lemma sg42345 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17826 - -lemma sg42346 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17006 - -lemma sg42347 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19512 - -lemma sg42348 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17798 - -lemma sg42349 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19138 - -lemma sg42350 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16851 - -lemma sg42351 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16452 - -lemma sg42352 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16852 - -lemma sg42353 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17787 - -lemma sg42354 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20719 sg16441 - -lemma sg42355 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17799 - -lemma sg42356 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17799 - -lemma sg42357 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18101 - -lemma sg42358 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16453 - -lemma sg42359 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16853 - -lemma sg42360 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20536 sg17451 - -lemma sg42361 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17787 - -lemma sg42362 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,4,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20867 sg15898 - -lemma sg42363 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16599 - -lemma sg42364 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,4,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18883 - -lemma sg42365 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18884 - -lemma sg42366 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,5,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16118 - -lemma sg42367 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,5,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16599 - -lemma sg42368 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,5,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20407 - -lemma sg42369 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,5,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20133 - -lemma sg42370 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16600 - -lemma sg42371 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,4,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg16119 - -lemma sg42372 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16577 - -lemma sg42373 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20690 sg16577 - -lemma sg42374 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17007 - -lemma sg42375 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20134 - -lemma sg42376 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18885 - -lemma sg42377 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18886 - -lemma sg42378 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17930 - -lemma sg42379 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20135 - -lemma sg42380 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17801 - -lemma sg42381 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20135 - -lemma sg42382 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20135 - -lemma sg42383 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19513 - -lemma sg42384 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17931 - -lemma sg42385 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20136 - -lemma sg42386 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20136 - -lemma sg42387 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20136 - -lemma sg42388 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17008 - -lemma sg42389 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19514 - -lemma sg42390 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19139 - -lemma sg42391 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20684 sg16604 - -lemma sg42392 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18887 - -lemma sg42393 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17009 - -lemma sg42394 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16601 - -lemma sg42395 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17790 - -lemma sg42396 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17932 - -lemma sg42397 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20137 - -lemma sg42398 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20137 - -lemma sg42399 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20137 - -lemma sg42400 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17009 - -lemma sg42401 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19515 - -lemma sg42402 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17828 - -lemma sg42403 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17010 - -lemma sg42404 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19516 - -lemma sg42405 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19140 - -lemma sg42406 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16963 - -lemma sg42407 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17802 - -lemma sg42408 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19141 - -lemma sg42409 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16964 - -lemma sg42410 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18888 - -lemma sg42411 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16603 - -lemma sg42412 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17933 - -lemma sg42413 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20138 - -lemma sg42414 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17803 - -lemma sg42415 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20138 - -lemma sg42416 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20138 - -lemma sg42417 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19517 - -lemma sg42418 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16638 - -lemma sg42419 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18889 - -lemma sg42420 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17011 - -lemma sg42421 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16602 - -lemma sg42422 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17791 - -lemma sg42423 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17934 - -lemma sg42424 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20139 - -lemma sg42425 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20139 - -lemma sg42426 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20139 - -lemma sg42427 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17011 - -lemma sg42428 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19518 - -lemma sg42429 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17830 - -lemma sg42430 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17012 - -lemma sg42431 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19519 - -lemma sg42432 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19142 - -lemma sg42433 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16965 - -lemma sg42434 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17935 - -lemma sg42435 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18890 - -lemma sg42436 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17935 - -lemma sg42437 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20140 - -lemma sg42438 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20140 - -lemma sg42439 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20140 - -lemma sg42440 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17831 - -lemma sg42441 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17013 - -lemma sg42442 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19520 - -lemma sg42443 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19143 - -lemma sg42444 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17805 - -lemma sg42445 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19144 - -lemma sg42446 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16966 - -lemma sg42447 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17792 - -lemma sg42448 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16967 - -lemma sg42449 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17014 - -lemma sg42450 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16604 - -lemma sg42451 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17832 - -lemma sg42452 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17014 - -lemma sg42453 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19521 - -lemma sg42454 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17806 - -lemma sg42455 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19145 - -lemma sg42456 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16968 - -lemma sg42457 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17794 - -lemma sg42458 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16969 - -lemma sg42459 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20713 sg16446 - -lemma sg42460 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20735 sg16409 - -lemma sg42461 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16605 - -lemma sg42462 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16639 - -lemma sg42463 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18891 - -lemma sg42464 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17015 - -lemma sg42465 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16605 - -lemma sg42466 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17795 - -lemma sg42467 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17936 - -lemma sg42468 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20141 - -lemma sg42469 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20141 - -lemma sg42470 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20141 - -lemma sg42471 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17015 - -lemma sg42472 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19522 - -lemma sg42473 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17937 - -lemma sg42474 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18892 - -lemma sg42475 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17937 - -lemma sg42476 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20142 - -lemma sg42477 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20142 - -lemma sg42478 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20142 - -lemma sg42479 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17834 - -lemma sg42480 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17016 - -lemma sg42481 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19523 - -lemma sg42482 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19146 - -lemma sg42483 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17808 - -lemma sg42484 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19147 - -lemma sg42485 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16971 - -lemma sg42486 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17017 - -lemma sg42487 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16606 - -lemma sg42488 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17835 - -lemma sg42489 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17017 - -lemma sg42490 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19524 - -lemma sg42491 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17809 - -lemma sg42492 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19148 - -lemma sg42493 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16972 - -lemma sg42494 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17797 - -lemma sg42495 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16973 - -lemma sg42496 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17792 - -lemma sg42497 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17810 - -lemma sg42498 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17810 - -lemma sg42499 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19149 - -lemma sg42500 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17798 - -lemma sg42501 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16974 - -lemma sg42502 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17794 - -lemma sg42503 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17792 - -lemma sg42504 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,8,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17799 - -lemma sg42505 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,8,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17799 - -lemma sg42506 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,8,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16975 - -lemma sg42507 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,8,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20713 sg16453 - -lemma sg42508 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,8,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17794 - -lemma sg42509 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16640 - -lemma sg42510 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16607 - -lemma sg42511 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16584 - -lemma sg42512 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20690 sg16584 - -lemma sg42513 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16573 - -lemma sg42514 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17938 - -lemma sg42515 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18893 - -lemma sg42516 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17938 - -lemma sg42517 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20143 - -lemma sg42518 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20143 - -lemma sg42519 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20143 - -lemma sg42520 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17836 - -lemma sg42521 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17018 - -lemma sg42522 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19525 - -lemma sg42523 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19150 - -lemma sg42524 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17019 - -lemma sg42525 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16608 - -lemma sg42526 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17837 - -lemma sg42527 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17019 - -lemma sg42528 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19526 - -lemma sg42529 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17812 - -lemma sg42530 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19151 - -lemma sg42531 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16867 - -lemma sg42532 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16466 - -lemma sg42533 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16868 - -lemma sg42534 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17813 - -lemma sg42535 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17813 - -lemma sg42536 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19152 - -lemma sg42537 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16467 - -lemma sg42538 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16869 - -lemma sg42539 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17797 - -lemma sg42540 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20719 sg16450 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes50 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 + +namespace OAI + +/-! Semigroup Nodes 104. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg42141 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17917 + +lemma sg42142 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20116 + +lemma sg42143 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20116 + +lemma sg42144 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18860 + +lemma sg42145 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20116 + +lemma sg42146 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16991 + +lemma sg42147 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19494 + +lemma sg42148 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19124 + +lemma sg42149 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,6,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16957 + +lemma sg42150 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16589 + +lemma sg42151 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,4,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18861 + +lemma sg42152 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,4,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20863 sg15892 + +lemma sg42153 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18863 + +lemma sg42154 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16111 + +lemma sg42155 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16589 + +lemma sg42156 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18862 + +lemma sg42157 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16590 + +lemma sg42158 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20117 + +lemma sg42159 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16112 + +lemma sg42160 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,5,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18863 + +lemma sg42161 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18864 + +lemma sg42162 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16069 + +lemma sg42163 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18865 + +lemma sg42164 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17918 + +lemma sg42165 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20118 + +lemma sg42166 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16113 + +lemma sg42167 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17784 + +lemma sg42168 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20118 + +lemma sg42169 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20118 + +lemma sg42170 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19495 + +lemma sg42171 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17919 + +lemma sg42172 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20119 + +lemma sg42173 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20119 + +lemma sg42174 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20119 + +lemma sg42175 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16992 + +lemma sg42176 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19496 + +lemma sg42177 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19125 + +lemma sg42178 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17816 + +lemma sg42179 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16993 + +lemma sg42180 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19497 + +lemma sg42181 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19126 + +lemma sg42182 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16839 + +lemma sg42183 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20688 sg16576 + +lemma sg42184 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18866 + +lemma sg42185 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16994 + +lemma sg42186 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16591 + +lemma sg42187 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16071 + +lemma sg42188 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20709 sg16438 + +lemma sg42189 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17920 + +lemma sg42190 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20120 + +lemma sg42191 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20120 + +lemma sg42192 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20120 + +lemma sg42193 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16994 + +lemma sg42194 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19498 + +lemma sg42195 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17818 + +lemma sg42196 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16995 + +lemma sg42197 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19499 + +lemma sg42198 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19127 + +lemma sg42199 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16840 + +lemma sg42200 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17787 + +lemma sg42201 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18100 + +lemma sg42202 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16841 + +lemma sg42203 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16441 + +lemma sg42204 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,7,7,7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16842 + +lemma sg42205 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,4,4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20867 sg15887 + +lemma sg42206 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg16064 + +lemma sg42207 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18869 + +lemma sg42208 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18867 + +lemma sg42209 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16073 + +lemma sg42210 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20406 + +lemma sg42211 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16114 + +lemma sg42212 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20121 + +lemma sg42213 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,5,5,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18868 + +lemma sg42214 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16592 + +lemma sg42215 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,4,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18870 + +lemma sg42216 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,4,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg16065 + +lemma sg42217 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18872 + +lemma sg42218 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16115 + +lemma sg42219 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16592 + +lemma sg42220 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18871 + +lemma sg42221 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16593 + +lemma sg42222 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20122 + +lemma sg42223 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,5,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16116 + +lemma sg42224 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18873 + +lemma sg42225 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16075 + +lemma sg42226 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18874 + +lemma sg42227 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17921 + +lemma sg42228 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20123 + +lemma sg42229 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17790 + +lemma sg42230 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20123 + +lemma sg42231 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20123 + +lemma sg42232 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19500 + +lemma sg42233 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17922 + +lemma sg42234 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20124 + +lemma sg42235 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20124 + +lemma sg42236 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20124 + +lemma sg42237 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16996 + +lemma sg42238 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19501 + +lemma sg42239 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19128 + +lemma sg42240 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17819 + +lemma sg42241 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16997 + +lemma sg42242 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19502 + +lemma sg42243 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19129 + +lemma sg42244 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,6,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16958 + +lemma sg42245 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16594 + +lemma sg42246 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16117 + +lemma sg42247 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16570 + +lemma sg42248 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20690 sg16570 + +lemma sg42249 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18875 + +lemma sg42250 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16998 + +lemma sg42251 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20125 + +lemma sg42252 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18876 + +lemma sg42253 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16077 + +lemma sg42254 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18877 + +lemma sg42255 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17923 + +lemma sg42256 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20126 + +lemma sg42257 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17791 + +lemma sg42258 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20126 + +lemma sg42259 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20126 + +lemma sg42260 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19503 + +lemma sg42261 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17924 + +lemma sg42262 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20127 + +lemma sg42263 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20127 + +lemma sg42264 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20127 + +lemma sg42265 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16999 + +lemma sg42266 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19504 + +lemma sg42267 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,5,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19130 + +lemma sg42268 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16636 + +lemma sg42269 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18878 + +lemma sg42270 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17000 + +lemma sg42271 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16595 + +lemma sg42272 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17784 + +lemma sg42273 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17925 + +lemma sg42274 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20128 + +lemma sg42275 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20128 + +lemma sg42276 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20128 + +lemma sg42277 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17000 + +lemma sg42278 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19505 + +lemma sg42279 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17821 + +lemma sg42280 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17001 + +lemma sg42281 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19506 + +lemma sg42282 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19131 + +lemma sg42283 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16959 + +lemma sg42284 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17792 + +lemma sg42285 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19132 + +lemma sg42286 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,6,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16960 + +lemma sg42287 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17926 + +lemma sg42288 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18879 + +lemma sg42289 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17926 + +lemma sg42290 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20129 + +lemma sg42291 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20129 + +lemma sg42292 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20129 + +lemma sg42293 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17822 + +lemma sg42294 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17002 + +lemma sg42295 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19507 + +lemma sg42296 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19133 + +lemma sg42297 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17794 + +lemma sg42298 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19134 + +lemma sg42299 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16961 + +lemma sg42300 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17787 + +lemma sg42301 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16962 + +lemma sg42302 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,7,7,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20713 sg16441 + +lemma sg42303 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18880 + +lemma sg42304 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg16082 + +lemma sg42305 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16597 + +lemma sg42306 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17927 + +lemma sg42307 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20130 + +lemma sg42308 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17795 + +lemma sg42309 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20130 + +lemma sg42310 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20130 + +lemma sg42311 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19508 + +lemma sg42312 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16637 + +lemma sg42313 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18881 + +lemma sg42314 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17003 + +lemma sg42315 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16596 + +lemma sg42316 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20709 sg16447 + +lemma sg42317 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17928 + +lemma sg42318 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20131 + +lemma sg42319 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20131 + +lemma sg42320 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20131 + +lemma sg42321 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17003 + +lemma sg42322 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19509 + +lemma sg42323 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17824 + +lemma sg42324 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17004 + +lemma sg42325 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19510 + +lemma sg42326 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19135 + +lemma sg42327 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16848 + +lemma sg42328 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17929 + +lemma sg42329 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18882 + +lemma sg42330 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17929 + +lemma sg42331 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20132 + +lemma sg42332 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20132 + +lemma sg42333 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20132 + +lemma sg42334 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17825 + +lemma sg42335 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17005 + +lemma sg42336 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19511 + +lemma sg42337 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19136 + +lemma sg42338 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17797 + +lemma sg42339 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19137 + +lemma sg42340 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16849 + +lemma sg42341 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16450 + +lemma sg42342 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16850 + +lemma sg42343 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17006 + +lemma sg42344 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16598 + +lemma sg42345 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17826 + +lemma sg42346 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17006 + +lemma sg42347 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19512 + +lemma sg42348 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17798 + +lemma sg42349 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19138 + +lemma sg42350 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16851 + +lemma sg42351 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16452 + +lemma sg42352 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16852 + +lemma sg42353 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17787 + +lemma sg42354 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20719 sg16441 + +lemma sg42355 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17799 + +lemma sg42356 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17799 + +lemma sg42357 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18101 + +lemma sg42358 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16453 + +lemma sg42359 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16853 + +lemma sg42360 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20536 sg17451 + +lemma sg42361 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,8,8,8,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17787 + +lemma sg42362 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,4,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20867 sg15898 + +lemma sg42363 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16599 + +lemma sg42364 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,4,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18883 + +lemma sg42365 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18884 + +lemma sg42366 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,5,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16118 + +lemma sg42367 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,5,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16599 + +lemma sg42368 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,5,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20407 + +lemma sg42369 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,5,5,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20133 + +lemma sg42370 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16600 + +lemma sg42371 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,4,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg16119 + +lemma sg42372 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16577 + +lemma sg42373 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20690 sg16577 + +lemma sg42374 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17007 + +lemma sg42375 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20134 + +lemma sg42376 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18885 + +lemma sg42377 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18886 + +lemma sg42378 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17930 + +lemma sg42379 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20135 + +lemma sg42380 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17801 + +lemma sg42381 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20135 + +lemma sg42382 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20135 + +lemma sg42383 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19513 + +lemma sg42384 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17931 + +lemma sg42385 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20136 + +lemma sg42386 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20136 + +lemma sg42387 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20136 + +lemma sg42388 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17008 + +lemma sg42389 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19514 + +lemma sg42390 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,5,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19139 + +lemma sg42391 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20684 sg16604 + +lemma sg42392 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18887 + +lemma sg42393 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17009 + +lemma sg42394 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16601 + +lemma sg42395 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17790 + +lemma sg42396 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17932 + +lemma sg42397 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20137 + +lemma sg42398 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20137 + +lemma sg42399 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20137 + +lemma sg42400 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17009 + +lemma sg42401 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19515 + +lemma sg42402 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17828 + +lemma sg42403 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17010 + +lemma sg42404 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19516 + +lemma sg42405 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19140 + +lemma sg42406 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16963 + +lemma sg42407 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17802 + +lemma sg42408 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19141 + +lemma sg42409 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,6,6,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16964 + +lemma sg42410 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18888 + +lemma sg42411 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16603 + +lemma sg42412 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17933 + +lemma sg42413 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20138 + +lemma sg42414 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17803 + +lemma sg42415 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20138 + +lemma sg42416 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20138 + +lemma sg42417 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19517 + +lemma sg42418 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16638 + +lemma sg42419 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18889 + +lemma sg42420 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17011 + +lemma sg42421 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16602 + +lemma sg42422 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17791 + +lemma sg42423 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17934 + +lemma sg42424 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20139 + +lemma sg42425 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20139 + +lemma sg42426 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20139 + +lemma sg42427 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17011 + +lemma sg42428 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19518 + +lemma sg42429 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17830 + +lemma sg42430 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17012 + +lemma sg42431 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19519 + +lemma sg42432 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19142 + +lemma sg42433 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16965 + +lemma sg42434 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17935 + +lemma sg42435 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18890 + +lemma sg42436 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17935 + +lemma sg42437 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20140 + +lemma sg42438 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20140 + +lemma sg42439 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20140 + +lemma sg42440 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17831 + +lemma sg42441 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17013 + +lemma sg42442 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19520 + +lemma sg42443 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19143 + +lemma sg42444 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17805 + +lemma sg42445 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19144 + +lemma sg42446 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16966 + +lemma sg42447 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17792 + +lemma sg42448 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16967 + +lemma sg42449 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17014 + +lemma sg42450 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16604 + +lemma sg42451 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17832 + +lemma sg42452 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17014 + +lemma sg42453 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19521 + +lemma sg42454 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17806 + +lemma sg42455 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19145 + +lemma sg42456 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16968 + +lemma sg42457 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17794 + +lemma sg42458 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16969 + +lemma sg42459 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20713 sg16446 + +lemma sg42460 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,7,7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20735 sg16409 + +lemma sg42461 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16605 + +lemma sg42462 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16639 + +lemma sg42463 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18891 + +lemma sg42464 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17015 + +lemma sg42465 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16605 + +lemma sg42466 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17795 + +lemma sg42467 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17936 + +lemma sg42468 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20141 + +lemma sg42469 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20141 + +lemma sg42470 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20141 + +lemma sg42471 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17015 + +lemma sg42472 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19522 + +lemma sg42473 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17937 + +lemma sg42474 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18892 + +lemma sg42475 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17937 + +lemma sg42476 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20142 + +lemma sg42477 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20142 + +lemma sg42478 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20142 + +lemma sg42479 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17834 + +lemma sg42480 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17016 + +lemma sg42481 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19523 + +lemma sg42482 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19146 + +lemma sg42483 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17808 + +lemma sg42484 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19147 + +lemma sg42485 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16971 + +lemma sg42486 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17017 + +lemma sg42487 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16606 + +lemma sg42488 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17835 + +lemma sg42489 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17017 + +lemma sg42490 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19524 + +lemma sg42491 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17809 + +lemma sg42492 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19148 + +lemma sg42493 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16972 + +lemma sg42494 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17797 + +lemma sg42495 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16973 + +lemma sg42496 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,6,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17792 + +lemma sg42497 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17810 + +lemma sg42498 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17810 + +lemma sg42499 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19149 + +lemma sg42500 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17798 + +lemma sg42501 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16974 + +lemma sg42502 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17794 + +lemma sg42503 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,7,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17792 + +lemma sg42504 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,8,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17799 + +lemma sg42505 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,8,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17799 + +lemma sg42506 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,8,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16975 + +lemma sg42507 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,8,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20713 sg16453 + +lemma sg42508 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,8,8,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17794 + +lemma sg42509 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16640 + +lemma sg42510 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16607 + +lemma sg42511 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16584 + +lemma sg42512 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20690 sg16584 + +lemma sg42513 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16573 + +lemma sg42514 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17938 + +lemma sg42515 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18893 + +lemma sg42516 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17938 + +lemma sg42517 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20143 + +lemma sg42518 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20143 + +lemma sg42519 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20143 + +lemma sg42520 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17836 + +lemma sg42521 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17018 + +lemma sg42522 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19525 + +lemma sg42523 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19150 + +lemma sg42524 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17019 + +lemma sg42525 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16608 + +lemma sg42526 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17837 + +lemma sg42527 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17019 + +lemma sg42528 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19526 + +lemma sg42529 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17812 + +lemma sg42530 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19151 + +lemma sg42531 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16867 + +lemma sg42532 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16466 + +lemma sg42533 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16868 + +lemma sg42534 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17813 + +lemma sg42535 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17813 + +lemma sg42536 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19152 + +lemma sg42537 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16467 + +lemma sg42538 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16869 + +lemma sg42539 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17797 + +lemma sg42540 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20719 sg16450 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes105.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes105.lean index 3f2fdba4488ad36fd0ab0d0e0785c067c380040c..1872748e891eb0ac505c017a8cd0e8a50d6c648d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes105.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes105.lean @@ -1,1231 +1,1231 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 - -namespace OAI - -/-! Semigroup Nodes 105. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg42541 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20709 sg16468 - -lemma sg42542 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,7,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16468 - -lemma sg42543 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,7,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16870 - -lemma sg42544 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,7,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17798 - -lemma sg42545 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,7,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17797 - -lemma sg42546 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,8,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16576 - -lemma sg42547 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,8,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17799 - -lemma sg42548 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,8,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17798 - -lemma sg42549 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,9,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17799 - -lemma sg42550 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,9,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17799 - -lemma sg42551 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,5,5,5,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20708 sg16478 - -lemma sg42552 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,5,5,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20408 - -lemma sg42553 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,5,5,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20862 sg15934 - -lemma sg42554 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18894 - -lemma sg42555 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16615 - -lemma sg42556 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20144 - -lemma sg42557 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18895 - -lemma sg42558 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16614 - -lemma sg42559 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18896 - -lemma sg42560 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20145 - -lemma sg42561 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17939 - -lemma sg42562 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20146 - -lemma sg42563 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20146 - -lemma sg42564 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20146 - -lemma sg42565 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17021 - -lemma sg42566 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19527 - -lemma sg42567 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19153 - -lemma sg42568 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16873 - -lemma sg42569 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,5,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18897 - -lemma sg42570 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,5,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20409 - -lemma sg42571 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,5,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20147 - -lemma sg42572 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16616 - -lemma sg42573 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18898 - -lemma sg42574 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,5,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16616 - -lemma sg42575 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,5,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16617 - -lemma sg42576 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,5,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg20148 - -lemma sg42577 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18899 - -lemma sg42578 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18900 - -lemma sg42579 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17940 - -lemma sg42580 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17814 - -lemma sg42581 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20149 - -lemma sg42582 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20149 - -lemma sg42583 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19528 - -lemma sg42584 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17941 - -lemma sg42585 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20150 - -lemma sg42586 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20150 - -lemma sg42587 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17022 - -lemma sg42588 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19529 - -lemma sg42589 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19154 - -lemma sg42590 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17849 - -lemma sg42591 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17023 - -lemma sg42592 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19530 - -lemma sg42593 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19155 - -lemma sg42594 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16990 - -lemma sg42595 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16618 - -lemma sg42596 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16589 - -lemma sg42597 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20690 sg16589 - -lemma sg42598 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17024 - -lemma sg42599 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20151 - -lemma sg42600 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18901 - -lemma sg42601 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18902 - -lemma sg42602 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17942 - -lemma sg42603 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17815 - -lemma sg42604 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20152 - -lemma sg42605 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20152 - -lemma sg42606 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19531 - -lemma sg42607 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17943 - -lemma sg42608 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20153 - -lemma sg42609 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20153 - -lemma sg42610 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17025 - -lemma sg42611 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19532 - -lemma sg42612 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19156 - -lemma sg42613 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16641 - -lemma sg42614 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18903 - -lemma sg42615 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17026 - -lemma sg42616 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20709 sg16480 - -lemma sg42617 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17944 - -lemma sg42618 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20154 - -lemma sg42619 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20154 - -lemma sg42620 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17026 - -lemma sg42621 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19533 - -lemma sg42622 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17853 - -lemma sg42623 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17027 - -lemma sg42624 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19534 - -lemma sg42625 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19157 - -lemma sg42626 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16880 - -lemma sg42627 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17816 - -lemma sg42628 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19158 - -lemma sg42629 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16881 - -lemma sg42630 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17945 - -lemma sg42631 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18904 - -lemma sg42632 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17945 - -lemma sg42633 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20155 - -lemma sg42634 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20155 - -lemma sg42635 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17854 - -lemma sg42636 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17028 - -lemma sg42637 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19535 - -lemma sg42638 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19159 - -lemma sg42639 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17818 - -lemma sg42640 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19160 - -lemma sg42641 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16883 - -lemma sg42642 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16484 - -lemma sg42643 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16884 - -lemma sg42644 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20536 sg17503 - -lemma sg42645 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20765 sg16315 - -lemma sg42646 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20731 sg16471 - -lemma sg42647 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20156 - -lemma sg42648 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20723 sg16478 - -lemma sg42649 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20765 sg16316 - -lemma sg42650 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20157 - -lemma sg42651 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15608 sg21064 - -lemma sg42652 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,4,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20725 sg16472 - -lemma sg42653 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18905 - -lemma sg42654 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20158 - -lemma sg42655 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20410 - -lemma sg42656 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17946 - -lemma sg42657 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17838 - -lemma sg42658 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20159 - -lemma sg42659 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20160 - -lemma sg42660 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20160 - -lemma sg42661 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19161 - -lemma sg42662 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20700 sg16609 - -lemma sg42663 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,4,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20161 - -lemma sg42664 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18906 - -lemma sg42665 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16614 - -lemma sg42666 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20725 sg16475 - -lemma sg42667 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20162 - -lemma sg42668 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18920 sg20020 - -lemma sg42669 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17947 - -lemma sg42670 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17840 - -lemma sg42671 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20163 - -lemma sg42672 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20163 - -lemma sg42673 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15608 sg21065 - -lemma sg42674 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20725 sg16478 - -lemma sg42675 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19162 - -lemma sg42676 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18907 - -lemma sg42677 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17948 - -lemma sg42678 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17841 - -lemma sg42679 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20164 - -lemma sg42680 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20164 - -lemma sg42681 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20728 sg16476 - -lemma sg42682 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17949 - -lemma sg42683 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20165 - -lemma sg42684 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20165 - -lemma sg42685 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17843 - -lemma sg42686 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19163 - -lemma sg42687 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19164 - -lemma sg42688 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15607 sg21066 - -lemma sg42689 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17844 - -lemma sg42690 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15608 sg21066 - -lemma sg42691 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19165 - -lemma sg42692 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20536 sg17570 - -lemma sg42693 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,4,4,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20817 sg16176 - -lemma sg42694 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20411 - -lemma sg42695 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,4,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20166 - -lemma sg42696 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18908 - -lemma sg42697 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20853 sg16120 - -lemma sg42698 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17838 - -lemma sg42699 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20167 - -lemma sg42700 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17950 - -lemma sg42701 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17845 - -lemma sg42702 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20168 - -lemma sg42703 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20168 - -lemma sg42704 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17839 - -lemma sg42705 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20875 sg15934 - -lemma sg42706 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19166 - -lemma sg42707 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18283 sg20412 - -lemma sg42708 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16616 - -lemma sg42709 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16610 - -lemma sg42710 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20169 - -lemma sg42711 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17951 - -lemma sg42712 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17846 - -lemma sg42713 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20170 - -lemma sg42714 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20170 - -lemma sg42715 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16611 - -lemma sg42716 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17952 - -lemma sg42717 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20171 - -lemma sg42718 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20171 - -lemma sg42719 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17847 - -lemma sg42720 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19167 - -lemma sg42721 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19168 - -lemma sg42722 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20688 sg16620 - -lemma sg42723 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20723 sg16489 - -lemma sg42724 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17841 - -lemma sg42725 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17953 - -lemma sg42726 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20172 - -lemma sg42727 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20172 - -lemma sg42728 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17843 - -lemma sg42729 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19169 - -lemma sg42730 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17849 - -lemma sg42731 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17848 - -lemma sg42732 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17842 - -lemma sg42733 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19170 - -lemma sg42734 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg17020 - -lemma sg42735 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17849 - -lemma sg42736 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19171 - -lemma sg42737 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg17021 - -lemma sg42738 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17954 - -lemma sg42739 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17850 - -lemma sg42740 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20173 - -lemma sg42741 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20173 - -lemma sg42742 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15608 sg21067 - -lemma sg42743 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16642 - -lemma sg42744 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16619 - -lemma sg42745 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16612 - -lemma sg42746 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17955 - -lemma sg42747 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20174 - -lemma sg42748 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20174 - -lemma sg42749 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16614 - -lemma sg42750 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19172 - -lemma sg42751 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15607 sg21068 - -lemma sg42752 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17851 - -lemma sg42753 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15608 sg21068 - -lemma sg42754 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19173 - -lemma sg42755 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20736 sg16478 - -lemma sg42756 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17956 - -lemma sg42757 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17956 - -lemma sg42758 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20175 - -lemma sg42759 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20175 - -lemma sg42760 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17853 - -lemma sg42761 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17852 - -lemma sg42762 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16613 - -lemma sg42763 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19174 - -lemma sg42764 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17853 - -lemma sg42765 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19175 - -lemma sg42766 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17843 - -lemma sg42767 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15644 sg20990 - -lemma sg42768 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17844 - -lemma sg42769 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20723 sg16495 - -lemma sg42770 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17854 - -lemma sg42771 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20765 sg16333 - -lemma sg42772 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20728 sg16483 - -lemma sg42773 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17854 - -lemma sg42774 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18102 - -lemma sg42775 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17843 - -lemma sg42776 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20728 sg16484 - -lemma sg42777 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20536 sg17585 - -lemma sg42778 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20536 sg17586 - -lemma sg42779 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15646 sg20989 - -lemma sg42780 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,5,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20848 sg16160 - -lemma sg42781 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,6,5,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20176 - -lemma sg42782 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,6,6,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17029 - -lemma sg42783 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,6,6,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20177 - -lemma sg42784 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,6,6,6,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20178 - -lemma sg42785 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,6,6,6,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18282 sg20415 - -lemma sg42786 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,6,6,6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19536 - -lemma sg42787 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,5,5,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20849 sg16160 - -lemma sg42788 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,5,5,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20179 - -lemma sg42789 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,5,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17030 - -lemma sg42790 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,5,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20180 - -lemma sg42791 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17855 - -lemma sg42792 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20181 - -lemma sg42793 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20182 - -lemma sg42794 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20893 sg15717 - -lemma sg42795 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,6,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17031 - -lemma sg42796 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,6,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20183 - -lemma sg42797 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,6,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19537 - -lemma sg42798 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,5,5,5,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20184 - -lemma sg42799 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,5,5,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17032 - -lemma sg42800 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,5,5,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20185 - -lemma sg42801 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16516 - -lemma sg42802 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20186 - -lemma sg42803 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20187 - -lemma sg42804 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20188 - -lemma sg42805 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17957 - -lemma sg42806 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17033 - -lemma sg42807 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20189 - -lemma sg42808 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19538 - -lemma sg42809 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20190 - -lemma sg42810 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20190 - -lemma sg42811 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19539 - -lemma sg42812 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,5,5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16517 - -lemma sg42813 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,5,5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20191 - -lemma sg42814 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,5,5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20192 - -lemma sg42815 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20831 sg16174 - -lemma sg42816 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20193 - -lemma sg42817 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17036 - -lemma sg42818 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17034 - -lemma sg42819 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20194 - -lemma sg42820 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19540 - -lemma sg42821 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17958 - -lemma sg42822 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17035 - -lemma sg42823 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20195 - -lemma sg42824 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20196 - -lemma sg42825 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20196 - -lemma sg42826 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19541 - -lemma sg42827 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17036 - -lemma sg42828 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19542 - -lemma sg42829 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20197 - -lemma sg42830 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17959 - -lemma sg42831 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17037 - -lemma sg42832 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20198 - -lemma sg42833 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20199 - -lemma sg42834 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20199 - -lemma sg42835 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19543 - -lemma sg42836 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17960 - -lemma sg42837 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16518 - -lemma sg42838 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20200 - -lemma sg42839 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20200 - -lemma sg42840 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19544 - -lemma sg42841 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17038 - -lemma sg42842 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19545 - -lemma sg42843 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16910 - -lemma sg42844 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17961 - -lemma sg42845 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17860 - -lemma sg42846 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18112 sg20495 - -lemma sg42847 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17039 - -lemma sg42848 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19546 - -lemma sg42849 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16911 - -lemma sg42850 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20654 sg16795 - -lemma sg42851 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,5,5,5,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20850 sg16160 - -lemma sg42852 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,5,5,5,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20201 - -lemma sg42853 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,5,5,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17040 - -lemma sg42854 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,5,5,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20202 - -lemma sg42855 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17856 - -lemma sg42856 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20203 - -lemma sg42857 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20204 - -lemma sg42858 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20205 - -lemma sg42859 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17962 - -lemma sg42860 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17041 - -lemma sg42861 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20206 - -lemma sg42862 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19547 - -lemma sg42863 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20207 - -lemma sg42864 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20207 - -lemma sg42865 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19548 - -lemma sg42866 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,5,5,5,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17042 - -lemma sg42867 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,5,5,5,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20208 - -lemma sg42868 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,5,5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17857 - -lemma sg42869 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,5,5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20209 - -lemma sg42870 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,5,5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20210 - -lemma sg42871 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17856 - -lemma sg42872 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20211 - -lemma sg42873 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17045 - -lemma sg42874 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17043 - -lemma sg42875 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20212 - -lemma sg42876 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19549 - -lemma sg42877 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17963 - -lemma sg42878 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17044 - -lemma sg42879 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20213 - -lemma sg42880 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20214 - -lemma sg42881 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20214 - -lemma sg42882 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19550 - -lemma sg42883 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17045 - -lemma sg42884 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19551 - -lemma sg42885 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,5,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20709 sg16517 - -lemma sg42886 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,5,5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20215 - -lemma sg42887 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,5,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16622 - -lemma sg42888 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,5,5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17046 - -lemma sg42889 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,5,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20216 - -lemma sg42890 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,5,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19552 - -lemma sg42891 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20217 - -lemma sg42892 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17964 - -lemma sg42893 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17047 - -lemma sg42894 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20218 - -lemma sg42895 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20219 - -lemma sg42896 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20219 - -lemma sg42897 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19553 - -lemma sg42898 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17965 - -lemma sg42899 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17858 - -lemma sg42900 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20220 - -lemma sg42901 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20220 - -lemma sg42902 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19554 - -lemma sg42903 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17048 - -lemma sg42904 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19555 - -lemma sg42905 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18103 - -lemma sg42906 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17050 - -lemma sg42907 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17049 - -lemma sg42908 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20221 - -lemma sg42909 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17966 - -lemma sg42910 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17859 - -lemma sg42911 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20222 - -lemma sg42912 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20222 - -lemma sg42913 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19556 - -lemma sg42914 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17050 - -lemma sg42915 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19557 - -lemma sg42916 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17967 - -lemma sg42917 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20223 - -lemma sg42918 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20223 - -lemma sg42919 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17051 - -lemma sg42920 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19558 - -lemma sg42921 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg19176 - -lemma sg42922 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,7,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17866 - -lemma sg42923 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,7,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17052 - -lemma sg42924 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,7,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19559 - -lemma sg42925 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,5,5,5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16525 - -lemma sg42926 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,5,5,5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20224 - -lemma sg42927 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,5,5,5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20225 - -lemma sg42928 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,5,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17857 - -lemma sg42929 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,5,5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20226 - -lemma sg42930 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,5,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20856 sg15998 - -lemma sg42931 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,5,5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17053 - -lemma sg42932 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,5,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20227 - -lemma sg42933 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,5,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19560 - -lemma sg42934 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20228 - -lemma sg42935 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17968 - -lemma sg42936 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17054 - -lemma sg42937 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20229 - -lemma sg42938 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20230 - -lemma sg42939 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20230 - -lemma sg42940 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19561 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 + +namespace OAI + +/-! Semigroup Nodes 105. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg42541 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20709 sg16468 + +lemma sg42542 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,7,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16468 + +lemma sg42543 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,7,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16870 + +lemma sg42544 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,7,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17798 + +lemma sg42545 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,7,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17797 + +lemma sg42546 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,8,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16576 + +lemma sg42547 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,8,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17799 + +lemma sg42548 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,8,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17798 + +lemma sg42549 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,9,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17799 + +lemma sg42550 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,11,9,9,9,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17799 + +lemma sg42551 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,5,5,5,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20708 sg16478 + +lemma sg42552 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,5,5,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20408 + +lemma sg42553 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,5,5,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20862 sg15934 + +lemma sg42554 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18894 + +lemma sg42555 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16615 + +lemma sg42556 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20144 + +lemma sg42557 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18895 + +lemma sg42558 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16614 + +lemma sg42559 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18896 + +lemma sg42560 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20145 + +lemma sg42561 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17939 + +lemma sg42562 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20146 + +lemma sg42563 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20146 + +lemma sg42564 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20146 + +lemma sg42565 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17021 + +lemma sg42566 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19527 + +lemma sg42567 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19153 + +lemma sg42568 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,6,6,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16873 + +lemma sg42569 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,5,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18897 + +lemma sg42570 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,5,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20409 + +lemma sg42571 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,5,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20147 + +lemma sg42572 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16616 + +lemma sg42573 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18898 + +lemma sg42574 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,5,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16616 + +lemma sg42575 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,5,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16617 + +lemma sg42576 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,5,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg20148 + +lemma sg42577 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18899 + +lemma sg42578 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18900 + +lemma sg42579 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17940 + +lemma sg42580 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17814 + +lemma sg42581 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20149 + +lemma sg42582 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20149 + +lemma sg42583 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19528 + +lemma sg42584 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17941 + +lemma sg42585 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20150 + +lemma sg42586 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20150 + +lemma sg42587 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17022 + +lemma sg42588 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19529 + +lemma sg42589 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19154 + +lemma sg42590 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17849 + +lemma sg42591 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17023 + +lemma sg42592 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19530 + +lemma sg42593 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19155 + +lemma sg42594 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,6,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16990 + +lemma sg42595 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16618 + +lemma sg42596 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16589 + +lemma sg42597 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20690 sg16589 + +lemma sg42598 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17024 + +lemma sg42599 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20151 + +lemma sg42600 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18901 + +lemma sg42601 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18902 + +lemma sg42602 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17942 + +lemma sg42603 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17815 + +lemma sg42604 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20152 + +lemma sg42605 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20152 + +lemma sg42606 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19531 + +lemma sg42607 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17943 + +lemma sg42608 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20153 + +lemma sg42609 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20153 + +lemma sg42610 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17025 + +lemma sg42611 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19532 + +lemma sg42612 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,5,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19156 + +lemma sg42613 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16641 + +lemma sg42614 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18903 + +lemma sg42615 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17026 + +lemma sg42616 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20709 sg16480 + +lemma sg42617 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17944 + +lemma sg42618 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20154 + +lemma sg42619 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20154 + +lemma sg42620 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17026 + +lemma sg42621 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19533 + +lemma sg42622 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17853 + +lemma sg42623 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17027 + +lemma sg42624 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19534 + +lemma sg42625 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19157 + +lemma sg42626 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16880 + +lemma sg42627 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17816 + +lemma sg42628 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19158 + +lemma sg42629 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,6,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16881 + +lemma sg42630 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17945 + +lemma sg42631 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18904 + +lemma sg42632 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17945 + +lemma sg42633 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20155 + +lemma sg42634 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20155 + +lemma sg42635 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17854 + +lemma sg42636 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17028 + +lemma sg42637 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19535 + +lemma sg42638 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19159 + +lemma sg42639 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17818 + +lemma sg42640 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19160 + +lemma sg42641 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16883 + +lemma sg42642 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16484 + +lemma sg42643 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16884 + +lemma sg42644 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,12,7,7,7,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20536 sg17503 + +lemma sg42645 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20765 sg16315 + +lemma sg42646 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20731 sg16471 + +lemma sg42647 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20156 + +lemma sg42648 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20723 sg16478 + +lemma sg42649 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20765 sg16316 + +lemma sg42650 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20157 + +lemma sg42651 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,5,5,5,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15608 sg21064 + +lemma sg42652 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,4,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20725 sg16472 + +lemma sg42653 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18905 + +lemma sg42654 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20158 + +lemma sg42655 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20410 + +lemma sg42656 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17946 + +lemma sg42657 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17838 + +lemma sg42658 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20159 + +lemma sg42659 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20160 + +lemma sg42660 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20160 + +lemma sg42661 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,5,5,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19161 + +lemma sg42662 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20700 sg16609 + +lemma sg42663 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,4,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20161 + +lemma sg42664 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18906 + +lemma sg42665 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16614 + +lemma sg42666 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20725 sg16475 + +lemma sg42667 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20162 + +lemma sg42668 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18920 sg20020 + +lemma sg42669 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17947 + +lemma sg42670 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17840 + +lemma sg42671 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20163 + +lemma sg42672 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20163 + +lemma sg42673 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15608 sg21065 + +lemma sg42674 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20725 sg16478 + +lemma sg42675 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,5,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19162 + +lemma sg42676 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18907 + +lemma sg42677 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17948 + +lemma sg42678 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17841 + +lemma sg42679 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20164 + +lemma sg42680 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20164 + +lemma sg42681 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20728 sg16476 + +lemma sg42682 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17949 + +lemma sg42683 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20165 + +lemma sg42684 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20165 + +lemma sg42685 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17843 + +lemma sg42686 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19163 + +lemma sg42687 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19164 + +lemma sg42688 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15607 sg21066 + +lemma sg42689 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17844 + +lemma sg42690 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15608 sg21066 + +lemma sg42691 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19165 + +lemma sg42692 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,6,6,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20536 sg17570 + +lemma sg42693 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,4,4,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20817 sg16176 + +lemma sg42694 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20411 + +lemma sg42695 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,4,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20166 + +lemma sg42696 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18908 + +lemma sg42697 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20853 sg16120 + +lemma sg42698 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17838 + +lemma sg42699 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20167 + +lemma sg42700 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17950 + +lemma sg42701 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17845 + +lemma sg42702 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20168 + +lemma sg42703 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20168 + +lemma sg42704 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17839 + +lemma sg42705 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20875 sg15934 + +lemma sg42706 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,5,5,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19166 + +lemma sg42707 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18283 sg20412 + +lemma sg42708 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16616 + +lemma sg42709 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16610 + +lemma sg42710 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20169 + +lemma sg42711 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17951 + +lemma sg42712 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17846 + +lemma sg42713 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20170 + +lemma sg42714 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20170 + +lemma sg42715 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16611 + +lemma sg42716 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17952 + +lemma sg42717 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20171 + +lemma sg42718 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20171 + +lemma sg42719 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17847 + +lemma sg42720 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19167 + +lemma sg42721 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,5,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19168 + +lemma sg42722 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20688 sg16620 + +lemma sg42723 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20723 sg16489 + +lemma sg42724 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17841 + +lemma sg42725 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17953 + +lemma sg42726 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20172 + +lemma sg42727 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20172 + +lemma sg42728 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17843 + +lemma sg42729 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19169 + +lemma sg42730 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17849 + +lemma sg42731 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17848 + +lemma sg42732 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17842 + +lemma sg42733 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19170 + +lemma sg42734 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg17020 + +lemma sg42735 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17849 + +lemma sg42736 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19171 + +lemma sg42737 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,6,6,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg17021 + +lemma sg42738 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17954 + +lemma sg42739 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17850 + +lemma sg42740 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20173 + +lemma sg42741 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20173 + +lemma sg42742 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15608 sg21067 + +lemma sg42743 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16642 + +lemma sg42744 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16619 + +lemma sg42745 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16612 + +lemma sg42746 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17955 + +lemma sg42747 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20174 + +lemma sg42748 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20174 + +lemma sg42749 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16614 + +lemma sg42750 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19172 + +lemma sg42751 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15607 sg21068 + +lemma sg42752 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17851 + +lemma sg42753 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15608 sg21068 + +lemma sg42754 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19173 + +lemma sg42755 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20736 sg16478 + +lemma sg42756 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17956 + +lemma sg42757 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17956 + +lemma sg42758 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20175 + +lemma sg42759 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20175 + +lemma sg42760 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17853 + +lemma sg42761 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17852 + +lemma sg42762 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16613 + +lemma sg42763 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19174 + +lemma sg42764 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17853 + +lemma sg42765 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19175 + +lemma sg42766 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17843 + +lemma sg42767 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15644 sg20990 + +lemma sg42768 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17844 + +lemma sg42769 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20723 sg16495 + +lemma sg42770 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17854 + +lemma sg42771 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20765 sg16333 + +lemma sg42772 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20728 sg16483 + +lemma sg42773 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17854 + +lemma sg42774 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18102 + +lemma sg42775 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17843 + +lemma sg42776 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20728 sg16484 + +lemma sg42777 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20536 sg17585 + +lemma sg42778 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20536 sg17586 + +lemma sg42779 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [13,13,7,7,7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15646 sg20989 + +lemma sg42780 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,5,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20848 sg16160 + +lemma sg42781 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,6,5,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20176 + +lemma sg42782 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,6,6,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17029 + +lemma sg42783 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,6,6,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20177 + +lemma sg42784 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,6,6,6,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20178 + +lemma sg42785 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,6,6,6,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18282 sg20415 + +lemma sg42786 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,6,6,6,6,6,6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19536 + +lemma sg42787 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,5,5,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20849 sg16160 + +lemma sg42788 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,5,5,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20179 + +lemma sg42789 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,5,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17030 + +lemma sg42790 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,5,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20180 + +lemma sg42791 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17855 + +lemma sg42792 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20181 + +lemma sg42793 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20182 + +lemma sg42794 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20893 sg15717 + +lemma sg42795 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,6,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17031 + +lemma sg42796 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,6,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20183 + +lemma sg42797 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,6,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19537 + +lemma sg42798 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,5,5,5,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20184 + +lemma sg42799 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,5,5,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17032 + +lemma sg42800 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,5,5,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20185 + +lemma sg42801 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16516 + +lemma sg42802 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20186 + +lemma sg42803 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20187 + +lemma sg42804 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20188 + +lemma sg42805 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17957 + +lemma sg42806 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17033 + +lemma sg42807 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20189 + +lemma sg42808 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19538 + +lemma sg42809 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20190 + +lemma sg42810 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20190 + +lemma sg42811 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19539 + +lemma sg42812 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,5,5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16517 + +lemma sg42813 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,5,5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20191 + +lemma sg42814 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,5,5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20192 + +lemma sg42815 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20831 sg16174 + +lemma sg42816 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20193 + +lemma sg42817 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17036 + +lemma sg42818 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17034 + +lemma sg42819 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20194 + +lemma sg42820 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19540 + +lemma sg42821 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17958 + +lemma sg42822 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17035 + +lemma sg42823 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20195 + +lemma sg42824 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20196 + +lemma sg42825 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20196 + +lemma sg42826 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19541 + +lemma sg42827 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17036 + +lemma sg42828 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19542 + +lemma sg42829 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20197 + +lemma sg42830 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17959 + +lemma sg42831 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17037 + +lemma sg42832 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20198 + +lemma sg42833 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20199 + +lemma sg42834 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20199 + +lemma sg42835 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19543 + +lemma sg42836 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17960 + +lemma sg42837 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16518 + +lemma sg42838 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20200 + +lemma sg42839 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20200 + +lemma sg42840 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19544 + +lemma sg42841 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17038 + +lemma sg42842 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19545 + +lemma sg42843 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16910 + +lemma sg42844 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17961 + +lemma sg42845 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17860 + +lemma sg42846 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18112 sg20495 + +lemma sg42847 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17039 + +lemma sg42848 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19546 + +lemma sg42849 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16911 + +lemma sg42850 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,7,7,7,7,7,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20654 sg16795 + +lemma sg42851 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,5,5,5,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20850 sg16160 + +lemma sg42852 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,5,5,5,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20201 + +lemma sg42853 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,5,5,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17040 + +lemma sg42854 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,5,5,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20202 + +lemma sg42855 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17856 + +lemma sg42856 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20203 + +lemma sg42857 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20204 + +lemma sg42858 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20205 + +lemma sg42859 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17962 + +lemma sg42860 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17041 + +lemma sg42861 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20206 + +lemma sg42862 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19547 + +lemma sg42863 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20207 + +lemma sg42864 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20207 + +lemma sg42865 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,6,6,6,6,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19548 + +lemma sg42866 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,5,5,5,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17042 + +lemma sg42867 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,5,5,5,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20208 + +lemma sg42868 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,5,5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17857 + +lemma sg42869 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,5,5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20209 + +lemma sg42870 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,5,5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20210 + +lemma sg42871 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17856 + +lemma sg42872 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20211 + +lemma sg42873 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17045 + +lemma sg42874 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17043 + +lemma sg42875 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20212 + +lemma sg42876 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19549 + +lemma sg42877 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17963 + +lemma sg42878 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17044 + +lemma sg42879 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20213 + +lemma sg42880 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20214 + +lemma sg42881 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20214 + +lemma sg42882 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19550 + +lemma sg42883 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17045 + +lemma sg42884 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,6,6,6,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19551 + +lemma sg42885 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,5,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20709 sg16517 + +lemma sg42886 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,5,5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20215 + +lemma sg42887 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,5,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16622 + +lemma sg42888 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,5,5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17046 + +lemma sg42889 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,5,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20216 + +lemma sg42890 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,5,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19552 + +lemma sg42891 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20217 + +lemma sg42892 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17964 + +lemma sg42893 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17047 + +lemma sg42894 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20218 + +lemma sg42895 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20219 + +lemma sg42896 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20219 + +lemma sg42897 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19553 + +lemma sg42898 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17965 + +lemma sg42899 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17858 + +lemma sg42900 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20220 + +lemma sg42901 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20220 + +lemma sg42902 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19554 + +lemma sg42903 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17048 + +lemma sg42904 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19555 + +lemma sg42905 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,6,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18103 + +lemma sg42906 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17050 + +lemma sg42907 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17049 + +lemma sg42908 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20221 + +lemma sg42909 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17966 + +lemma sg42910 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17859 + +lemma sg42911 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20222 + +lemma sg42912 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20222 + +lemma sg42913 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19556 + +lemma sg42914 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17050 + +lemma sg42915 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19557 + +lemma sg42916 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17967 + +lemma sg42917 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20223 + +lemma sg42918 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20223 + +lemma sg42919 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17051 + +lemma sg42920 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19558 + +lemma sg42921 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg19176 + +lemma sg42922 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,7,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17866 + +lemma sg42923 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,7,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17052 + +lemma sg42924 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,7,7,7,7,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19559 + +lemma sg42925 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,5,5,5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16525 + +lemma sg42926 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,5,5,5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20224 + +lemma sg42927 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,5,5,5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20225 + +lemma sg42928 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,5,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17857 + +lemma sg42929 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,5,5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20226 + +lemma sg42930 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,5,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20856 sg15998 + +lemma sg42931 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,5,5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17053 + +lemma sg42932 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,5,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20227 + +lemma sg42933 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,5,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19560 + +lemma sg42934 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20228 + +lemma sg42935 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17968 + +lemma sg42936 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17054 + +lemma sg42937 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20229 + +lemma sg42938 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20230 + +lemma sg42939 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20230 + +lemma sg42940 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19561 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes106.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes106.lean index 3be6b1cff223ad98a727736f2d5b4da890a89d78..9432cc7e3af697498e5f4bbf5f47b2ba943200bd 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes106.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes106.lean @@ -1,945 +1,945 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 - -namespace OAI - -/-! Semigroup Nodes 106. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg42941 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17969 - -lemma sg42942 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16526 - -lemma sg42943 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20231 - -lemma sg42944 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20231 - -lemma sg42945 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19562 - -lemma sg42946 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17055 - -lemma sg42947 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19563 - -lemma sg42948 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,4,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16621 - -lemma sg42949 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20232 - -lemma sg42950 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17970 - -lemma sg42951 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17056 - -lemma sg42952 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20233 - -lemma sg42953 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20234 - -lemma sg42954 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20234 - -lemma sg42955 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19564 - -lemma sg42956 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17058 - -lemma sg42957 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17057 - -lemma sg42958 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20235 - -lemma sg42959 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17971 - -lemma sg42960 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16528 - -lemma sg42961 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20236 - -lemma sg42962 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20236 - -lemma sg42963 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19565 - -lemma sg42964 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17058 - -lemma sg42965 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19566 - -lemma sg42966 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17972 - -lemma sg42967 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20237 - -lemma sg42968 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20237 - -lemma sg42969 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17059 - -lemma sg42970 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19567 - -lemma sg42971 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17973 - -lemma sg42972 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16530 - -lemma sg42973 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20238 - -lemma sg42974 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20238 - -lemma sg42975 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19568 - -lemma sg42976 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17974 - -lemma sg42977 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20239 - -lemma sg42978 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20239 - -lemma sg42979 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17060 - -lemma sg42980 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17870 - -lemma sg42981 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17061 - -lemma sg42982 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,7,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16532 - -lemma sg42983 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,4,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20240 - -lemma sg42984 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17063 - -lemma sg42985 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17062 - -lemma sg42986 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20241 - -lemma sg42987 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17975 - -lemma sg42988 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16533 - -lemma sg42989 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20242 - -lemma sg42990 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20242 - -lemma sg42991 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19569 - -lemma sg42992 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17063 - -lemma sg42993 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17976 - -lemma sg42994 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16534 - -lemma sg42995 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20243 - -lemma sg42996 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20243 - -lemma sg42997 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17977 - -lemma sg42998 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20244 - -lemma sg42999 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20244 - -lemma sg43000 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17064 - -lemma sg43001 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17872 - -lemma sg43002 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17065 - -lemma sg43003 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16643 - -lemma sg43004 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17066 - -lemma sg43005 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20831 sg16175 - -lemma sg43006 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17978 - -lemma sg43007 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20245 - -lemma sg43008 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20245 - -lemma sg43009 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17066 - -lemma sg43010 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17874 - -lemma sg43011 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17067 - -lemma sg43012 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16537 - -lemma sg43013 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17979 - -lemma sg43014 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17979 - -lemma sg43015 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20246 - -lemma sg43016 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20246 - -lemma sg43017 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17875 - -lemma sg43018 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17068 - -lemma sg43019 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16539 - -lemma sg43020 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,5,5,5,5,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20247 - -lemma sg43021 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,5,5,5,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17069 - -lemma sg43022 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,5,5,5,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20248 - -lemma sg43023 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,5,5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17861 - -lemma sg43024 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,5,5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20249 - -lemma sg43025 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,5,5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20250 - -lemma sg43026 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20709 sg16521 - -lemma sg43027 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20251 - -lemma sg43028 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17072 - -lemma sg43029 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17070 - -lemma sg43030 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20252 - -lemma sg43031 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,6,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17980 - -lemma sg43032 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,6,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17071 - -lemma sg43033 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,6,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20253 - -lemma sg43034 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,6,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20254 - -lemma sg43035 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,6,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20254 - -lemma sg43036 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,6,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17072 - -lemma sg43037 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,5,5,5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17862 - -lemma sg43038 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,5,5,5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20255 - -lemma sg43039 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,5,5,5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20256 - -lemma sg43040 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,5,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17861 - -lemma sg43041 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,5,5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20257 - -lemma sg43042 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,5,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16625 - -lemma sg43043 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,5,5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17073 - -lemma sg43044 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,5,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20258 - -lemma sg43045 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20259 - -lemma sg43046 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17981 - -lemma sg43047 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17074 - -lemma sg43048 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20260 - -lemma sg43049 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20261 - -lemma sg43050 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20261 - -lemma sg43051 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17982 - -lemma sg43052 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17863 - -lemma sg43053 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20262 - -lemma sg43054 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20262 - -lemma sg43055 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17075 - -lemma sg43056 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,4,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16623 - -lemma sg43057 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,5,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20263 - -lemma sg43058 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,5,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17983 - -lemma sg43059 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,5,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17076 - -lemma sg43060 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,5,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20264 - -lemma sg43061 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,5,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20265 - -lemma sg43062 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,5,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20265 - -lemma sg43063 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17078 - -lemma sg43064 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17077 - -lemma sg43065 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20266 - -lemma sg43066 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17984 - -lemma sg43067 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17864 - -lemma sg43068 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20267 - -lemma sg43069 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20267 - -lemma sg43070 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17078 - -lemma sg43071 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17985 - -lemma sg43072 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20268 - -lemma sg43073 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20268 - -lemma sg43074 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17079 - -lemma sg43075 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17986 - -lemma sg43076 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17865 - -lemma sg43077 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20269 - -lemma sg43078 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20269 - -lemma sg43079 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17987 - -lemma sg43080 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20270 - -lemma sg43081 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20270 - -lemma sg43082 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17876 - -lemma sg43083 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,5,5,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17862 - -lemma sg43084 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,5,5,5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20271 - -lemma sg43085 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,5,5,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20853 sg16121 - -lemma sg43086 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,5,5,5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17080 - -lemma sg43087 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,5,5,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20272 - -lemma sg43088 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,4,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16624 - -lemma sg43089 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,5,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20273 - -lemma sg43090 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,5,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17988 - -lemma sg43091 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,5,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17081 - -lemma sg43092 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,5,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20274 - -lemma sg43093 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,5,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20275 - -lemma sg43094 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,5,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20275 - -lemma sg43095 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17083 - -lemma sg43096 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17082 - -lemma sg43097 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20276 - -lemma sg43098 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17989 - -lemma sg43099 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17867 - -lemma sg43100 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20277 - -lemma sg43101 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20277 - -lemma sg43102 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17990 - -lemma sg43103 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20278 - -lemma sg43104 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20278 - -lemma sg43105 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,4,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20279 - -lemma sg43106 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17085 - -lemma sg43107 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17084 - -lemma sg43108 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20280 - -lemma sg43109 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17991 - -lemma sg43110 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17868 - -lemma sg43111 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20281 - -lemma sg43112 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20281 - -lemma sg43113 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17992 - -lemma sg43114 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,6,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17869 - -lemma sg43115 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20282 - -lemma sg43116 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17993 - -lemma sg43117 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20283 - -lemma sg43118 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17877 - -lemma sg43119 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,7,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20684 sg16628 - -lemma sg43120 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,7,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17086 - -lemma sg43121 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,7,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17865 - -lemma sg43122 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,7,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17994 - -lemma sg43123 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,7,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20284 - -lemma sg43124 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,7,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17879 - -lemma sg43125 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16626 - -lemma sg43126 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17087 - -lemma sg43127 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20285 - -lemma sg43128 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17995 - -lemma sg43129 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17871 - -lemma sg43130 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20286 - -lemma sg43131 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17996 - -lemma sg43132 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20287 - -lemma sg43133 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16644 - -lemma sg43134 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,6,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17088 - -lemma sg43135 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,6,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20709 sg16534 - -lemma sg43136 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17997 - -lemma sg43137 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,6,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20288 - -lemma sg43138 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,6,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17881 - -lemma sg43139 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17998 - -lemma sg43140 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,7,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17998 - -lemma sg43141 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,7,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20289 - -lemma sg43142 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,7,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17882 - -lemma sg43143 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,8,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17089 - -lemma sg43144 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,8,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17883 - -lemma sg43145 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,5,4,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20868 sg15994 - -lemma sg43146 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,5,5,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20290 - -lemma sg43147 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,5,5,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17999 - -lemma sg43148 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,5,5,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17090 - -lemma sg43149 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,5,5,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20291 - -lemma sg43150 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,4,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg20292 - -lemma sg43151 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,5,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17092 - -lemma sg43152 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,5,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17091 - -lemma sg43153 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,5,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18000 - -lemma sg43154 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,5,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16552 - -lemma sg43155 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,5,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20293 - -lemma sg43156 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18001 - -lemma sg43157 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20294 - -lemma sg43158 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18002 - -lemma sg43159 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20295 - -lemma sg43160 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17884 - -lemma sg43161 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20856 sg16046 - -lemma sg43162 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg17093 - -lemma sg43163 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18003 - -lemma sg43164 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20296 - -lemma sg43165 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18004 - -lemma sg43166 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20297 - -lemma sg43167 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16645 - -lemma sg43168 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,6,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17094 - -lemma sg43169 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18005 - -lemma sg43170 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,6,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20298 - -lemma sg43171 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,6,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17886 - -lemma sg43172 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg18006 - -lemma sg43173 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,7,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18006 - -lemma sg43174 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,7,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20299 - -lemma sg43175 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,7,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17887 - -lemma sg43176 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18007 - -lemma sg43177 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20300 - -lemma sg43178 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16646 - -lemma sg43179 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,5,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17095 - -lemma sg43180 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18008 - -lemma sg43181 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20301 - -lemma sg43182 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17889 - -lemma sg43183 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,6,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg18009 - -lemma sg43184 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,6,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18009 - -lemma sg43185 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,6,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20302 - -lemma sg43186 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,6,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17890 - -lemma sg43187 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,7,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17096 - -lemma sg43188 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,7,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17891 - -lemma sg43189 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,8,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20703 sg16560 - -lemma sg43190 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16647 - -lemma sg43191 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17097 - -lemma sg43192 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18010 - -lemma sg43193 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20303 - -lemma sg43194 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg18011 - -lemma sg43195 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18011 - -lemma sg43196 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,5,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20304 - -lemma sg43197 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,5,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17893 - -lemma sg43198 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,6,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17098 - -lemma sg43199 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,6,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17894 - -lemma sg43200 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,7,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20703 sg16563 - -lemma sg43201 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,6,6,5,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16627 - -lemma sg43202 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,6,6,6,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18012 - -lemma sg43203 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,6,6,6,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20305 - -lemma sg43204 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,6,6,6,6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18013 - -lemma sg43205 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,6,6,6,6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20306 - -lemma sg43206 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,5,5,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20853 sg16122 - -lemma sg43207 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,5,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18014 - -lemma sg43208 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,5,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20307 - -lemma sg43209 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,6,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17099 - -lemma sg43210 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,6,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18015 - -lemma sg43211 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,6,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20308 - -lemma sg43212 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18016 - -lemma sg43213 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20309 - -lemma sg43214 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,5,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17100 - -lemma sg43215 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,5,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18017 - -lemma sg43216 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,5,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg20310 - -lemma sg43217 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18018 - -lemma sg43218 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18019 - -lemma sg43219 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,7,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20688 sg16628 - -lemma sg43220 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,7,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17101 - -lemma sg43221 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,7,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18020 - -lemma sg43222 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,6,5,5,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20861 sg16063 - -lemma sg43223 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,6,6,5,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18021 - -lemma sg43224 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,6,6,6,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17102 - -lemma sg43225 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,6,6,6,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18022 - -lemma sg43226 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,6,6,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18023 - -lemma sg43227 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,7,5,5,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18024 - -lemma sg43228 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,7,6,5,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg17103 - -lemma sg43229 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,7,6,5,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg18025 - -lemma sg43230 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,7,7,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20689 sg16631 - -lemma sg43231 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,7,7,6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16648 - -lemma sg43232 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,7,7,7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg18026 - -lemma sg43234 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [11,11,11,10,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20911 - -lemma sg43235 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [11,11,11,11,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20912 - -lemma sg43236 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [12,11,10,10,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20913 - -lemma sg43237 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [12,11,11,9,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20914 - -lemma sg43238 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [12,11,11,10,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20915 - -lemma sg43239 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,10,10,10,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20916 - -lemma sg43240 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,11,10,9,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20917 - -lemma sg43241 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,11,10,10,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20918 - -lemma sg43242 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,11,11,8,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20919 - -lemma sg43243 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,11,11,9,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20920 - -lemma sg43244 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,12,9,9,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20921 - -lemma sg43245 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,13,9,8,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20922 - -lemma sg43246 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,13,9,9,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20923 - -lemma sg43247 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [14,11,9,9,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg21092 sg20924 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 + +namespace OAI + +/-! Semigroup Nodes 106. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg42941 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17969 + +lemma sg42942 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16526 + +lemma sg42943 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20231 + +lemma sg42944 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20231 + +lemma sg42945 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19562 + +lemma sg42946 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17055 + +lemma sg42947 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,6,6,6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19563 + +lemma sg42948 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,4,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16621 + +lemma sg42949 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20232 + +lemma sg42950 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17970 + +lemma sg42951 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17056 + +lemma sg42952 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20233 + +lemma sg42953 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20234 + +lemma sg42954 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20234 + +lemma sg42955 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,5,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19564 + +lemma sg42956 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17058 + +lemma sg42957 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17057 + +lemma sg42958 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20235 + +lemma sg42959 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17971 + +lemma sg42960 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16528 + +lemma sg42961 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20236 + +lemma sg42962 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20236 + +lemma sg42963 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19565 + +lemma sg42964 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17058 + +lemma sg42965 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19566 + +lemma sg42966 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17972 + +lemma sg42967 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20237 + +lemma sg42968 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20237 + +lemma sg42969 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17059 + +lemma sg42970 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,6,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19567 + +lemma sg42971 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17973 + +lemma sg42972 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16530 + +lemma sg42973 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20238 + +lemma sg42974 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20238 + +lemma sg42975 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19568 + +lemma sg42976 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17974 + +lemma sg42977 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20239 + +lemma sg42978 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20239 + +lemma sg42979 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17060 + +lemma sg42980 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17870 + +lemma sg42981 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17061 + +lemma sg42982 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,7,7,7,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16532 + +lemma sg42983 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,4,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20240 + +lemma sg42984 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17063 + +lemma sg42985 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17062 + +lemma sg42986 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20241 + +lemma sg42987 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17975 + +lemma sg42988 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16533 + +lemma sg42989 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20242 + +lemma sg42990 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20242 + +lemma sg42991 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19569 + +lemma sg42992 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,5,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17063 + +lemma sg42993 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17976 + +lemma sg42994 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16534 + +lemma sg42995 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20243 + +lemma sg42996 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20243 + +lemma sg42997 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17977 + +lemma sg42998 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20244 + +lemma sg42999 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20244 + +lemma sg43000 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17064 + +lemma sg43001 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17872 + +lemma sg43002 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,6,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17065 + +lemma sg43003 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16643 + +lemma sg43004 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17066 + +lemma sg43005 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20831 sg16175 + +lemma sg43006 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17978 + +lemma sg43007 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20245 + +lemma sg43008 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20245 + +lemma sg43009 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17066 + +lemma sg43010 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17874 + +lemma sg43011 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17067 + +lemma sg43012 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,7,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16537 + +lemma sg43013 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17979 + +lemma sg43014 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17979 + +lemma sg43015 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20246 + +lemma sg43016 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20246 + +lemma sg43017 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17875 + +lemma sg43018 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17068 + +lemma sg43019 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,8,8,8,8,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16539 + +lemma sg43020 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,5,5,5,5,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20247 + +lemma sg43021 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,5,5,5,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17069 + +lemma sg43022 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,5,5,5,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20248 + +lemma sg43023 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,5,5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17861 + +lemma sg43024 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,5,5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20249 + +lemma sg43025 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,5,5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20250 + +lemma sg43026 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20709 sg16521 + +lemma sg43027 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20251 + +lemma sg43028 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17072 + +lemma sg43029 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17070 + +lemma sg43030 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20252 + +lemma sg43031 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,6,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17980 + +lemma sg43032 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,6,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17071 + +lemma sg43033 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,6,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20253 + +lemma sg43034 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,6,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20254 + +lemma sg43035 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,6,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20254 + +lemma sg43036 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,6,6,6,6,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17072 + +lemma sg43037 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,5,5,5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17862 + +lemma sg43038 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,5,5,5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20255 + +lemma sg43039 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,5,5,5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20256 + +lemma sg43040 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,5,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17861 + +lemma sg43041 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,5,5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20257 + +lemma sg43042 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,5,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16625 + +lemma sg43043 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,5,5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17073 + +lemma sg43044 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,5,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20258 + +lemma sg43045 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20259 + +lemma sg43046 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17981 + +lemma sg43047 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17074 + +lemma sg43048 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20260 + +lemma sg43049 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20261 + +lemma sg43050 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20261 + +lemma sg43051 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17982 + +lemma sg43052 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17863 + +lemma sg43053 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20262 + +lemma sg43054 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20262 + +lemma sg43055 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,6,6,6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17075 + +lemma sg43056 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,4,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16623 + +lemma sg43057 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,5,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20263 + +lemma sg43058 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,5,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17983 + +lemma sg43059 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,5,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17076 + +lemma sg43060 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,5,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20264 + +lemma sg43061 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,5,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20265 + +lemma sg43062 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,5,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20265 + +lemma sg43063 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17078 + +lemma sg43064 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17077 + +lemma sg43065 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20266 + +lemma sg43066 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17984 + +lemma sg43067 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17864 + +lemma sg43068 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20267 + +lemma sg43069 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20267 + +lemma sg43070 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17078 + +lemma sg43071 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17985 + +lemma sg43072 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20268 + +lemma sg43073 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20268 + +lemma sg43074 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17079 + +lemma sg43075 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17986 + +lemma sg43076 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17865 + +lemma sg43077 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20269 + +lemma sg43078 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20269 + +lemma sg43079 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17987 + +lemma sg43080 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20270 + +lemma sg43081 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20270 + +lemma sg43082 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,7,7,7,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17876 + +lemma sg43083 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,5,5,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17862 + +lemma sg43084 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,5,5,5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20271 + +lemma sg43085 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,5,5,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20853 sg16121 + +lemma sg43086 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,5,5,5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17080 + +lemma sg43087 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,5,5,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20272 + +lemma sg43088 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,4,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16624 + +lemma sg43089 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,5,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20273 + +lemma sg43090 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,5,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17988 + +lemma sg43091 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,5,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17081 + +lemma sg43092 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,5,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20274 + +lemma sg43093 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,5,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20275 + +lemma sg43094 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,5,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20275 + +lemma sg43095 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17083 + +lemma sg43096 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17082 + +lemma sg43097 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20276 + +lemma sg43098 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17989 + +lemma sg43099 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17867 + +lemma sg43100 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20277 + +lemma sg43101 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20277 + +lemma sg43102 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17990 + +lemma sg43103 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20278 + +lemma sg43104 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,6,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20278 + +lemma sg43105 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,4,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20279 + +lemma sg43106 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17085 + +lemma sg43107 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17084 + +lemma sg43108 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20280 + +lemma sg43109 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17991 + +lemma sg43110 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17868 + +lemma sg43111 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20281 + +lemma sg43112 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,5,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20281 + +lemma sg43113 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17992 + +lemma sg43114 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,6,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17869 + +lemma sg43115 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20282 + +lemma sg43116 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17993 + +lemma sg43117 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20283 + +lemma sg43118 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17877 + +lemma sg43119 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,7,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20684 sg16628 + +lemma sg43120 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,7,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17086 + +lemma sg43121 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,7,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17865 + +lemma sg43122 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,7,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17994 + +lemma sg43123 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,7,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20284 + +lemma sg43124 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,7,7,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17879 + +lemma sg43125 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16626 + +lemma sg43126 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17087 + +lemma sg43127 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20285 + +lemma sg43128 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17995 + +lemma sg43129 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17871 + +lemma sg43130 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20286 + +lemma sg43131 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17996 + +lemma sg43132 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20287 + +lemma sg43133 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16644 + +lemma sg43134 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,6,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17088 + +lemma sg43135 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,6,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20709 sg16534 + +lemma sg43136 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17997 + +lemma sg43137 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,6,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20288 + +lemma sg43138 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,6,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17881 + +lemma sg43139 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17998 + +lemma sg43140 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,7,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17998 + +lemma sg43141 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,7,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20289 + +lemma sg43142 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,7,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17882 + +lemma sg43143 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,8,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17089 + +lemma sg43144 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,8,8,8,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17883 + +lemma sg43145 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,5,4,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20868 sg15994 + +lemma sg43146 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,5,5,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20290 + +lemma sg43147 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,5,5,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17999 + +lemma sg43148 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,5,5,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17090 + +lemma sg43149 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,5,5,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20291 + +lemma sg43150 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,4,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg20292 + +lemma sg43151 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,5,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17092 + +lemma sg43152 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,5,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17091 + +lemma sg43153 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,5,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18000 + +lemma sg43154 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,5,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16552 + +lemma sg43155 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,5,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20293 + +lemma sg43156 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18001 + +lemma sg43157 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20294 + +lemma sg43158 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18002 + +lemma sg43159 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20295 + +lemma sg43160 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,6,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17884 + +lemma sg43161 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20856 sg16046 + +lemma sg43162 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg17093 + +lemma sg43163 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18003 + +lemma sg43164 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20296 + +lemma sg43165 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18004 + +lemma sg43166 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20297 + +lemma sg43167 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16645 + +lemma sg43168 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,6,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17094 + +lemma sg43169 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18005 + +lemma sg43170 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,6,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20298 + +lemma sg43171 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,6,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17886 + +lemma sg43172 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg18006 + +lemma sg43173 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,7,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18006 + +lemma sg43174 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,7,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20299 + +lemma sg43175 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,7,7,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17887 + +lemma sg43176 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18007 + +lemma sg43177 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20300 + +lemma sg43178 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16646 + +lemma sg43179 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,5,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17095 + +lemma sg43180 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18008 + +lemma sg43181 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20301 + +lemma sg43182 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17889 + +lemma sg43183 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,6,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg18009 + +lemma sg43184 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,6,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18009 + +lemma sg43185 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,6,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20302 + +lemma sg43186 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,6,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17890 + +lemma sg43187 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,7,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17096 + +lemma sg43188 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,7,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17891 + +lemma sg43189 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,8,8,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20703 sg16560 + +lemma sg43190 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16647 + +lemma sg43191 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17097 + +lemma sg43192 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18010 + +lemma sg43193 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20303 + +lemma sg43194 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg18011 + +lemma sg43195 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18011 + +lemma sg43196 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,5,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20304 + +lemma sg43197 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,5,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17893 + +lemma sg43198 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,6,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17098 + +lemma sg43199 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,6,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17894 + +lemma sg43200 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,9,9,9,7,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20703 sg16563 + +lemma sg43201 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,6,6,5,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16627 + +lemma sg43202 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,6,6,6,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18012 + +lemma sg43203 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,6,6,6,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20305 + +lemma sg43204 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,6,6,6,6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18013 + +lemma sg43205 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,6,6,6,6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20306 + +lemma sg43206 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,5,5,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20853 sg16122 + +lemma sg43207 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,5,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18014 + +lemma sg43208 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,5,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20307 + +lemma sg43209 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,6,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17099 + +lemma sg43210 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,6,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18015 + +lemma sg43211 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,6,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20308 + +lemma sg43212 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18016 + +lemma sg43213 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,6,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20309 + +lemma sg43214 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,5,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17100 + +lemma sg43215 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,5,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18017 + +lemma sg43216 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,5,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg20310 + +lemma sg43217 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18018 + +lemma sg43218 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18019 + +lemma sg43219 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,7,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20688 sg16628 + +lemma sg43220 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,7,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17101 + +lemma sg43221 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,10,7,7,7,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18020 + +lemma sg43222 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,6,5,5,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20861 sg16063 + +lemma sg43223 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,6,6,5,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18021 + +lemma sg43224 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,6,6,6,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17102 + +lemma sg43225 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,6,6,6,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18022 + +lemma sg43226 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,6,6,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18023 + +lemma sg43227 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,7,5,5,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18024 + +lemma sg43228 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,7,6,5,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg17103 + +lemma sg43229 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,7,6,5,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg18025 + +lemma sg43230 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,7,7,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20689 sg16631 + +lemma sg43231 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,7,7,6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16648 + +lemma sg43232 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [14,11,7,7,7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg18026 + +lemma sg43234 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [11,11,11,10,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20911 + +lemma sg43235 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [11,11,11,11,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20912 + +lemma sg43236 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [12,11,10,10,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20913 + +lemma sg43237 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [12,11,11,9,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20914 + +lemma sg43238 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [12,11,11,10,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20915 + +lemma sg43239 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,10,10,10,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20916 + +lemma sg43240 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,11,10,9,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20917 + +lemma sg43241 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,11,10,10,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20918 + +lemma sg43242 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,11,11,8,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20919 + +lemma sg43243 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,11,11,9,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20920 + +lemma sg43244 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,12,9,9,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20921 + +lemma sg43245 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,13,9,8,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20922 + +lemma sg43246 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [13,13,9,9,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20923 + +lemma sg43247 : RowSquare [15,14,6,5,4,3,2,2,2,2,2,2,2,2,1] [14,11,9,9,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg21092 sg20924 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes11.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes11.lean index f446fdec67188fd5f0a46b1468aa5ec5f902b33c..f50785daf7828eccdd303f1c4f9126af45c3001b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes11.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes11.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes5 - -namespace OAI - -/-! Semigroup Nodes 11. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg4919 : RowSquare [8,4,3,1,1] [3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg307 sg586 - -lemma sg4920 : RowSquare [8,4,3,1,1] [3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg306 sg587 - -lemma sg4921 : RowSquare [8,4,3,1,1] [3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg306 sg589 - -lemma sg4922 : RowSquare [8,4,3,1,1] [3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg310 sg586 - -lemma sg4923 : RowSquare [8,4,3,1,1] [3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg32 sg1687 - -lemma sg4924 : RowSquare [8,4,3,1,1] [3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg1688 - -lemma sg4925 : RowSquare [8,4,3,1,1] [4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg307 sg588 - -lemma sg4926 : RowSquare [8,4,3,2] [3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg330 sg548 - -lemma sg4927 : RowSquare [8,4,3,2] [3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg178 sg854 - -lemma sg4928 : RowSquare [8,4,4,1] [3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg516 - -lemma sg4929 : RowSquare [8,6,2,1] [3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg849 - -lemma sg4931 : RowSquare [9,1,1,1,1,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg108 sg1136 - -lemma sg4932 : RowSquare [9,1,1,1,1,1,1,1,1] [2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg1620 - -lemma sg4933 : RowSquare [9,1,1,1,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg2114 - -lemma sg4934 : RowSquare [9,2,2,2,1,1] [5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg518 - -lemma sg4935 : RowSquare [9,3,1,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg2702 - -lemma sg4936 : RowSquare [9,3,1,1,1,1,1] [2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg2251 - -lemma sg4937 : RowSquare [9,3,1,1,1,1,1] [3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg2708 - -lemma sg4938 : RowSquare [9,3,1,1,1,1,1] [3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg2256 - -lemma sg4939 : RowSquare [9,3,1,1,1,1,1] [4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg2256 - -lemma sg4940 : RowSquare [9,3,1,1,1,1,1] [4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg2713 - -lemma sg4941 : RowSquare [9,3,2,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg1754 - -lemma sg4942 : RowSquare [9,3,2,1,1,1] [3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg1328 - -lemma sg4943 : RowSquare [9,3,2,1,1,1] [3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg1329 - -lemma sg4944 : RowSquare [9,3,2,1,1,1] [3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg77 sg1327 - -lemma sg4945 : RowSquare [9,3,2,1,1,1] [3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg1330 - -lemma sg4946 : RowSquare [9,3,2,1,1,1] [3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg1757 - -lemma sg4947 : RowSquare [9,3,2,1,1,1] [3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg1331 - -lemma sg4948 : RowSquare [9,3,2,1,1,1] [3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg32 sg1758 - -lemma sg4949 : RowSquare [9,3,2,1,1,1] [3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg74 sg1332 - -lemma sg4950 : RowSquare [9,3,2,1,1,1] [4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg75 sg1330 - -lemma sg4951 : RowSquare [9,3,2,1,1,1] [4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg1757 - -lemma sg4952 : RowSquare [9,3,2,1,1,1] [4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg75 sg1331 - -lemma sg4953 : RowSquare [9,3,2,1,1,1] [4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg76 sg1329 - -lemma sg4954 : RowSquare [9,3,2,1,1,1] [4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg1338 - -lemma sg4955 : RowSquare [9,3,2,1,1,1] [4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg194 sg890 - -lemma sg4956 : RowSquare [9,3,2,1,1,1] [4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg1339 - -lemma sg4957 : RowSquare [9,3,2,1,1,1] [4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg76 sg1331 - -lemma sg4958 : RowSquare [9,3,2,1,1,1] [4,4,3,3,3] := by - exact rowSquare_join (by decide) sg194 sg892 - -lemma sg4959 : RowSquare [9,3,2,1,1,1] [4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg77 sg1330 - -lemma sg4960 : RowSquare [9,3,2,1,1,1] [4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg77 sg1332 - -lemma sg4961 : RowSquare [9,3,2,1,1,1] [4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg195 sg891 - -lemma sg4962 : RowSquare [9,3,2,1,1,1] [4,4,4,3,2] := by - exact rowSquare_join (by decide) sg195 sg892 - -lemma sg4963 : RowSquare [9,3,2,1,1,1] [5,5,5,1,1] := by - exact rowSquare_join (by decide) sg89 sg1262 - -lemma sg4964 : RowSquare [9,3,2,2,1] [2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg910 - -lemma sg4965 : RowSquare [9,3,2,2,1] [2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg586 - -lemma sg4966 : RowSquare [9,3,2,2,1] [3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg330 sg587 - -lemma sg4967 : RowSquare [9,3,2,2,1] [3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg178 sg915 - -lemma sg4968 : RowSquare [9,3,2,2,1] [4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg179 sg915 - -lemma sg4969 : RowSquare [9,3,3,1,1] [3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg350 sg586 - -lemma sg4970 : RowSquare [9,3,3,1,1] [4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg350 sg588 - -lemma sg4971 : RowSquare [9,3,3,1,1] [4,4,3,3,3] := by - exact rowSquare_join (by decide) sg155 sg1001 - -lemma sg4972 : RowSquare [9,3,3,1,1] [4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg156 sg999 - -lemma sg4973 : RowSquare [9,3,3,1,1] [4,4,4,4,1] := by - exact rowSquare_join (by decide) sg350 sg590 - -lemma sg4974 : RowSquare [9,3,3,1,1] [5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg354 sg586 - -lemma sg4975 : RowSquare [9,3,3,1,1] [6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg354 sg588 - -lemma sg4976 : RowSquare [9,3,3,2] [3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg178 sg943 - -lemma sg4977 : RowSquare [9,3,3,2] [4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg179 sg943 - -lemma sg4978 : RowSquare [9,3,3,2] [4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg550 - -lemma sg4979 : RowSquare [9,3,3,2] [4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg371 sg551 - -lemma sg4980 : RowSquare [9,3,3,2] [4,4,3,3,3] := by - exact rowSquare_join (by decide) sg180 sg943 - -lemma sg4981 : RowSquare [9,4,1,1,1,1] [4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg1329 - -lemma sg4982 : RowSquare [9,4,1,1,1,1] [4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg1758 - -lemma sg4983 : RowSquare [9,4,1,1,1,1] [4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg1330 - -lemma sg4984 : RowSquare [9,4,1,1,1,1] [4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg83 sg1332 - -lemma sg4985 : RowSquare [9,4,1,1,1,1] [5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg40 sg1762 - -lemma sg4986 : RowSquare [9,4,2,1,1] [4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg534 - -lemma sg4987 : RowSquare [9,4,2,1,1] [4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg356 sg588 - -lemma sg4988 : RowSquare [9,4,2,1,1] [4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg535 - -lemma sg4989 : RowSquare [9,4,2,1,1] [4,4,3,3,3] := by - exact rowSquare_join (by decide) sg194 sg915 - -lemma sg4990 : RowSquare [9,4,3,1] [3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg636 - -lemma sg4991 : RowSquare [10,2,1,1,1,1,1] [5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg2263 - -lemma sg4992 : RowSquare [10,2,2,2,1] [3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg586 - -lemma sg4993 : RowSquare [10,2,2,2,1] [4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg179 sg1001 - -lemma sg4994 : RowSquare [10,2,2,2,1] [4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg589 - -lemma sg4995 : RowSquare [10,2,2,2,1] [4,4,3,3,3] := by - exact rowSquare_join (by decide) sg180 sg1001 - -lemma sg4996 : RowSquare [10,2,2,2,1] [4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg372 sg589 - -lemma sg4997 : RowSquare [10,3,2,1,1] [3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg586 - -lemma sg4998 : RowSquare [10,3,2,1,1] [4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg588 - -lemma sg4999 : RowSquare [10,3,2,1,1] [4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg195 sg999 - -lemma sg5000 : RowSquare [10,3,2,1,1] [4,4,4,4,1] := by - exact rowSquare_join (by decide) sg390 sg590 - -lemma sg5001 : RowSquare [10,3,2,1,1] [5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg396 sg586 - -lemma sg5002 : RowSquare [10,3,2,2] [3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg1032 - -lemma sg5003 : RowSquare [10,3,2,2] [3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg178 sg1033 - -lemma sg5004 : RowSquare [10,3,2,2] [4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg179 sg1032 - -lemma sg5005 : RowSquare [10,3,3,1] [4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg179 sg1061 - -lemma sg5006 : RowSquare [10,3,3,1] [4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg1063 - -lemma sg5007 : RowSquare [10,3,3,1] [4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg636 - -lemma sg5008 : RowSquare [10,3,3,1] [4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg1064 - -lemma sg5009 : RowSquare [10,3,3,1] [4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg1065 - -lemma sg5010 : RowSquare [10,3,3,1] [4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg373 sg636 - -lemma sg5018 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2] := by - exact rowSquare_join (by decide) sg692 sg692 - -lemma sg5019 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,1] := by - exact rowSquare_join (by decide) sg692 sg693 - -lemma sg5020 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,4] := by - exact rowSquare_join (by decide) sg693 sg693 - -lemma sg5021 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2] := by - exact rowSquare_join (by decide) sg692 sg694 - -lemma sg5022 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,1] := by - exact rowSquare_join (by decide) sg694 sg693 - -lemma sg5023 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,5,4,3] := by - exact rowSquare_join (by decide) sg693 sg695 - -lemma sg5024 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,2] := by - exact rowSquare_join (by decide) sg693 sg696 - -lemma sg5025 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2] := by - exact rowSquare_join (by decide) sg694 sg694 - -lemma sg5026 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,6,3,3] := by - exact rowSquare_join (by decide) sg390 sg1109 - -lemma sg5027 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg643 sg708 - -lemma sg5028 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg697 sg693 - -lemma sg5029 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,2] := by - exact rowSquare_join (by decide) sg644 sg708 - -lemma sg5030 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg697 sg694 - -lemma sg5031 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg643 sg709 - -lemma sg5032 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,2] := by - exact rowSquare_join (by decide) sg692 sg698 - -lemma sg5033 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,1] := by - exact rowSquare_join (by decide) sg644 sg709 - -lemma sg5034 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg391 sg1109 - -lemma sg5035 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,2] := by - exact rowSquare_join (by decide) sg694 sg698 - -lemma sg5036 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg636 sg714 - -lemma sg5037 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,5,3,2,1] := by - exact rowSquare_join (by decide) sg637 sg714 - -lemma sg5038 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,5,3,3] := by - exact rowSquare_join (by decide) sg693 sg699 - -lemma sg5039 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,7,1,1,1,1] := by - exact rowSquare_join (by decide) sg424 sg1063 - -lemma sg5040 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [8,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg697 sg697 - -lemma sg5041 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [8,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg645 sg708 - -lemma sg5042 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [8,3,3,2,2] := by - exact rowSquare_join (by decide) sg692 sg702 - -lemma sg5043 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [8,3,3,3,1] := by - exact rowSquare_join (by decide) sg644 sg711 - -lemma sg5044 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [8,4,2,2,2] := by - exact rowSquare_join (by decide) sg694 sg702 - -lemma sg5045 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [8,7,1,1,1] := by - exact rowSquare_join (by decide) sg694 sg703 - -lemma sg5046 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [9,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg576 sg716 - -lemma sg5047 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [9,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg576 sg717 - -lemma sg5048 : RowSquare [4,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg673 sg706 - -lemma sg5049 : RowSquare [4,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg422 sg1032 - -lemma sg5050 : RowSquare [4,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2] := by - exact rowSquare_join (by decide) sg422 sg1033 - -lemma sg5051 : RowSquare [4,2,2,2,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg424 sg1031 - -lemma sg5052 : RowSquare [4,2,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg424 sg1032 - -lemma sg5053 : RowSquare [4,2,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2] := by - exact rowSquare_join (by decide) sg424 sg1033 - -lemma sg5054 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg673 sg692 - -lemma sg5055 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg673 sg693 - -lemma sg5056 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg413 sg1032 - -lemma sg5057 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3] := by - exact rowSquare_join (by decide) sg413 sg1033 - -lemma sg5058 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg673 sg694 - -lemma sg5059 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg673 sg695 - -lemma sg5060 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg674 sg692 - -lemma sg5061 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg674 sg693 - -lemma sg5062 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,2] := by - exact rowSquare_join (by decide) sg414 sg1033 - -lemma sg5063 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg673 sg696 - -lemma sg5064 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg415 sg1032 - -lemma sg5065 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,2] := by - exact rowSquare_join (by decide) sg692 sg675 - -lemma sg5066 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,1] := by - exact rowSquare_join (by decide) sg692 sg676 - -lemma sg5067 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,4] := by - exact rowSquare_join (by decide) sg693 sg676 - -lemma sg5068 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg1109 - -lemma sg5069 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg674 sg694 - -lemma sg5070 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg1110 - -lemma sg5071 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg674 sg695 - -lemma sg5072 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2] := by - exact rowSquare_join (by decide) sg675 sg694 - -lemma sg5073 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,1] := by - exact rowSquare_join (by decide) sg694 sg676 - -lemma sg5074 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg696 - -lemma sg5075 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,1] := by - exact rowSquare_join (by decide) sg675 sg695 - -lemma sg5076 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,3] := by - exact rowSquare_join (by decide) sg676 sg695 - -lemma sg5077 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,1,1] := by - exact rowSquare_join (by decide) sg675 sg696 - -lemma sg5078 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,2] := by - exact rowSquare_join (by decide) sg676 sg696 - -lemma sg5079 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg371 sg1109 - -lemma sg5080 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg1110 - -lemma sg5081 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,1] := by - exact rowSquare_join (by decide) sg372 sg1109 - -lemma sg5082 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,6,3,3] := by - exact rowSquare_join (by decide) sg373 sg1109 - -lemma sg5083 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,1,1] := by - exact rowSquare_join (by decide) sg372 sg1110 - -lemma sg5084 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,2] := by - exact rowSquare_join (by decide) sg373 sg1110 - -lemma sg5085 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg674 sg697 - -lemma sg5086 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg615 sg708 - -lemma sg5087 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg697 sg676 - -lemma sg5088 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,2] := by - exact rowSquare_join (by decide) sg616 sg708 - -lemma sg5089 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg674 sg698 - -lemma sg5090 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg615 sg709 - -lemma sg5091 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,2] := by - exact rowSquare_join (by decide) sg692 sg678 - -lemma sg5092 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,1] := by - exact rowSquare_join (by decide) sg616 sg709 - -lemma sg5093 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg674 sg699 - -lemma sg5094 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,2] := by - exact rowSquare_join (by decide) sg694 sg678 - -lemma sg5095 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg700 - -lemma sg5096 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,5,3,2,1] := by - exact rowSquare_join (by decide) sg692 sg680 - -lemma sg5097 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,5,3,3] := by - exact rowSquare_join (by decide) sg693 sg680 - -lemma sg5098 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg1112 - -lemma sg5099 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg697 sg677 - -lemma sg5100 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [8,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg615 sg711 - -lemma sg5101 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg389 sg1031 - -lemma sg5102 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg1031 - -lemma sg5103 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg389 sg1032 - -lemma sg5104 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [4,4,4,3,3] := by - exact rowSquare_join (by decide) sg389 sg1033 - -lemma sg5105 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg390 sg1032 - -lemma sg5106 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,2] := by - exact rowSquare_join (by decide) sg390 sg1033 - -lemma sg5107 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg692 - -lemma sg5108 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg693 - -lemma sg5109 : RowSquare [4,3,2,2,2,2,2,1] [4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg561 sg579 - -lemma sg5110 : RowSquare [4,3,2,2,2,2,2,1] [5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg561 sg581 - -lemma sg5111 : RowSquare [4,3,2,2,2,2,2,1] [5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg366 sg849 - -lemma sg5112 : RowSquare [4,3,2,2,2,2,2,1] [5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg561 sg582 - -lemma sg5113 : RowSquare [4,3,2,2,2,2,2,1] [5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg849 - -lemma sg5114 : RowSquare [4,3,2,2,2,2,2,1] [5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg365 sg851 - -lemma sg5115 : RowSquare [4,3,2,2,2,2,2,1] [5,5,4,4] := by - exact rowSquare_join (by decide) sg364 sg861 - -lemma sg5116 : RowSquare [4,3,2,2,2,2,2,1] [6,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg368 sg849 - -lemma sg5117 : RowSquare [4,3,2,2,2,2,2,1] [6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg561 sg585 - -lemma sg5118 : RowSquare [4,3,2,2,2,2,2,1] [7,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg369 sg849 - -lemma sg5119 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg1063 - -lemma sg5120 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1064 - -lemma sg5121 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg348 sg1032 - -lemma sg5122 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1065 - -lemma sg5123 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg389 sg941 - -lemma sg5124 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg636 sg615 - -lemma sg5125 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg941 - -lemma sg5126 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,4,3,3] := by - exact rowSquare_join (by decide) sg389 sg943 - -lemma sg5127 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,4,4,2] := by - exact rowSquare_join (by decide) sg637 sg616 - -lemma sg5128 : RowSquare [4,3,3,2,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg413 sg849 - -lemma sg5129 : RowSquare [4,3,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg576 sg673 - -lemma sg5130 : RowSquare [4,3,3,2,1,1,1,1,1,1] [5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1066 - -lemma sg5131 : RowSquare [4,3,3,2,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg231 sg1232 - -lemma sg5132 : RowSquare [4,3,3,2,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg232 sg1232 - -lemma sg5133 : RowSquare [4,3,3,2,1,1,1,1,1,1] [6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1067 - -lemma sg5134 : RowSquare [4,3,3,2,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg233 sg1232 - -lemma sg5135 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg673 sg673 - -lemma sg5136 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg673 sg674 - -lemma sg5137 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg673 sg675 - -lemma sg5138 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg673 sg676 - -lemma sg5139 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg674 sg674 - -lemma sg5140 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg674 sg675 - -lemma sg5141 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg674 sg676 - -lemma sg5142 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2] := by - exact rowSquare_join (by decide) sg675 sg675 - -lemma sg5143 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,1] := by - exact rowSquare_join (by decide) sg675 sg676 - -lemma sg5144 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,4,4,4] := by - exact rowSquare_join (by decide) sg676 sg676 - -lemma sg5145 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg673 sg677 - -lemma sg5146 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg673 sg678 - -lemma sg5147 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg674 sg677 - -lemma sg5148 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg673 sg679 - -lemma sg5149 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg677 sg675 - -lemma sg5150 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg677 sg676 - -lemma sg5151 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg673 sg680 - -lemma sg5152 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg674 sg678 - -lemma sg5153 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg673 sg681 - -lemma sg5154 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg674 sg679 - -lemma sg5155 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2] := by - exact rowSquare_join (by decide) sg675 sg678 - -lemma sg5156 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,1] := by - exact rowSquare_join (by decide) sg678 sg676 - -lemma sg5157 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,1] := by - exact rowSquare_join (by decide) sg675 sg679 - -lemma sg5158 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,4,3] := by - exact rowSquare_join (by decide) sg676 sg679 - -lemma sg5159 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg674 sg680 - -lemma sg5160 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg681 - -lemma sg5161 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,1] := by - exact rowSquare_join (by decide) sg675 sg680 - -lemma sg5162 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,5,3,3] := by - exact rowSquare_join (by decide) sg676 sg680 - -lemma sg5163 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,5,4,1,1] := by - exact rowSquare_join (by decide) sg675 sg681 - -lemma sg5164 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,5,4,2] := by - exact rowSquare_join (by decide) sg676 sg681 - -lemma sg5165 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg677 sg677 - -lemma sg5166 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg674 sg682 - -lemma sg5167 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg677 sg679 - -lemma sg5168 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2] := by - exact rowSquare_join (by decide) sg675 sg682 - -lemma sg5169 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,1] := by - exact rowSquare_join (by decide) sg682 sg676 - -lemma sg5170 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg674 sg683 - -lemma sg5171 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2] := by - exact rowSquare_join (by decide) sg678 sg678 - -lemma sg5172 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg684 - -lemma sg5173 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,1] := by - exact rowSquare_join (by decide) sg675 sg683 - -lemma sg5174 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,4,3,3] := by - exact rowSquare_join (by decide) sg676 sg683 - -lemma sg5175 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,4,4,2] := by - exact rowSquare_join (by decide) sg676 sg684 - -lemma sg5176 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg685 - -lemma sg5177 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,1] := by - exact rowSquare_join (by decide) sg678 sg680 - -lemma sg5178 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,5,3,1,1] := by - exact rowSquare_join (by decide) sg675 sg685 - -lemma sg5179 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,5,3,2] := by - exact rowSquare_join (by decide) sg676 sg685 - -lemma sg5180 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg686 - -lemma sg5181 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,6,2,2] := by - exact rowSquare_join (by decide) sg676 sg686 - -lemma sg5182 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg677 sg682 - -lemma sg5183 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg674 sg687 - -lemma sg5184 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,2] := by - exact rowSquare_join (by decide) sg678 sg682 - -lemma sg5185 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg677 sg684 - -lemma sg5186 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,3,3,2,1] := by - exact rowSquare_join (by decide) sg675 sg687 - -lemma sg5187 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,3,3,3] := by - exact rowSquare_join (by decide) sg676 sg687 - -lemma sg5188 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg688 - -lemma sg5189 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,4,3,2] := by - exact rowSquare_join (by decide) sg676 sg688 - -lemma sg5190 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg689 - -lemma sg5191 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,5,2,2] := by - exact rowSquare_join (by decide) sg676 sg689 - -lemma sg5192 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,7,1,1] := by - exact rowSquare_join (by decide) sg680 sg686 - -lemma sg5193 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [10,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg677 sg687 - -lemma sg5194 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [10,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg690 - -lemma sg5195 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [10,3,3,2] := by - exact rowSquare_join (by decide) sg676 sg690 - -lemma sg5196 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [10,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg691 - -lemma sg5197 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg370 sg1031 - -lemma sg5198 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg370 sg1032 - -lemma sg5199 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg370 sg1033 - -lemma sg5200 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg1520 - -lemma sg5201 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg1031 - -lemma sg5202 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg371 sg1032 - -lemma sg5203 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg371 sg1033 - -lemma sg5204 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg372 sg1031 - -lemma sg5205 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg1031 - -lemma sg5206 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg372 sg1032 - -lemma sg5207 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,3] := by - exact rowSquare_join (by decide) sg372 sg1033 - -lemma sg5208 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg373 sg1032 - -lemma sg5209 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,4,4,2] := by - exact rowSquare_join (by decide) sg373 sg1033 - -lemma sg5210 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg613 sg673 - -lemma sg5211 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg674 - -lemma sg5212 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg614 sg673 - -lemma sg5213 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg675 - -lemma sg5214 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg673 sg615 - -lemma sg5215 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg676 - -lemma sg5216 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg673 sg616 - -lemma sg5217 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg374 sg1032 - -lemma sg5218 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg374 sg1033 - -lemma sg5219 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg614 sg674 - -lemma sg5220 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg614 sg675 - -lemma sg5221 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg674 - -lemma sg5222 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg614 sg676 - -lemma sg5223 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg674 sg616 - -lemma sg5224 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,3] := by - exact rowSquare_join (by decide) sg375 sg1033 - -lemma sg5225 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg1041 - -lemma sg5226 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg615 sg675 - -lemma sg5227 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg615 sg676 - -lemma sg5228 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg1527 - -lemma sg5229 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg1038 - -lemma sg5230 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg377 sg1031 - -lemma sg5231 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg1039 - -lemma sg5232 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg371 sg1040 - -lemma sg5233 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg378 sg1031 - -lemma sg5234 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg371 sg1041 - -lemma sg5235 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,4,2,2] := by - exact rowSquare_join (by decide) sg372 sg1039 - -lemma sg5236 : RowSquare [4,4,2,2,1,1,1,1,1,1] [3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg1031 - -lemma sg5237 : RowSquare [4,4,2,2,1,1,1,1,1,1] [3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg1032 - -lemma sg5238 : RowSquare [4,4,2,2,1,1,1,1,1,1] [3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg1417 - -lemma sg5239 : RowSquare [4,4,2,2,1,1,1,1,1,1] [3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1033 - -lemma sg5240 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg613 sg613 - -lemma sg5241 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg615 - -lemma sg5242 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg1038 - -lemma sg5243 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg614 sg614 - -lemma sg5244 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1039 - -lemma sg5245 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg614 sg615 - -lemma sg5246 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1040 - -lemma sg5247 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg614 sg616 - -lemma sg5248 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg371 sg960 - -lemma sg5249 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg371 sg961 - -lemma sg5250 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1041 - -lemma sg5251 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg372 sg959 - -lemma sg5252 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg615 - -lemma sg5253 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg959 - -lemma sg5254 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg615 sg616 - -lemma sg5255 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,3,3] := by - exact rowSquare_join (by decide) sg372 sg961 - -lemma sg5256 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg373 sg960 - -lemma sg5257 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,4,2] := by - exact rowSquare_join (by decide) sg616 sg616 - -lemma sg5258 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg613 sg617 - -lemma sg5259 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg620 - -lemma sg5260 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,4,3,3,3] := by - exact rowSquare_join (by decide) sg375 sg961 - -lemma sg5261 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg623 - -lemma sg5262 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg614 sg621 - -lemma sg5263 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg964 - -lemma sg5264 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1049 - -lemma sg5265 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,3,3,2] := by - exact rowSquare_join (by decide) sg616 sg621 - -lemma sg5266 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg614 sg623 - -lemma sg5267 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,4,4] := by - exact rowSquare_join (by decide) sg373 sg965 - -lemma sg5268 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg615 sg623 - -lemma sg5269 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,5,2,1] := by - exact rowSquare_join (by decide) sg616 sg623 - -lemma sg5270 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,5,3] := by - exact rowSquare_join (by decide) sg373 sg966 - -lemma sg5271 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg624 - -lemma sg5272 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg673 sg565 - -lemma sg5273 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg625 - -lemma sg5274 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,3,3,3,3] := by - exact rowSquare_join (by decide) sg379 sg961 - -lemma sg5275 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg626 - -lemma sg5276 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg627 - -lemma sg5277 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,6,6] := by - exact rowSquare_join (by decide) sg623 sg623 - -lemma sg5278 : RowSquare [4,4,2,2,2,2,1,1] [3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg1650 - -lemma sg5279 : RowSquare [4,4,2,2,2,2,1,1] [3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg878 - -lemma sg5280 : RowSquare [4,4,2,2,2,2,1,1] [4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg1650 - -lemma sg5281 : RowSquare [4,4,2,2,2,2,1,1] [4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg561 sg561 - -lemma sg5282 : RowSquare [4,4,2,2,2,2,1,1] [4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg99 sg1650 - -lemma sg5283 : RowSquare [4,4,2,2,2,2,1,1] [4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg1651 - -lemma sg5284 : RowSquare [4,4,2,2,2,2,1,1] [4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg1652 - -lemma sg5285 : RowSquare [4,4,2,2,2,2,1,1] [4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg885 - -lemma sg5286 : RowSquare [4,4,2,2,2,2,1,1] [4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg563 sg563 - -lemma sg5287 : RowSquare [4,4,2,2,2,2,1,1] [5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg100 sg1650 - -lemma sg5288 : RowSquare [4,4,2,2,2,2,1,1] [5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg1651 - -lemma sg5289 : RowSquare [4,4,2,2,2,2,1,1] [5,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg1650 - -lemma sg5290 : RowSquare [4,4,2,2,2,2,1,1] [5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg99 sg1651 - -lemma sg5291 : RowSquare [4,4,2,2,2,2,1,1] [6,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg102 sg1650 - -lemma sg5292 : RowSquare [4,4,2,2,2,2,1,1] [7,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg103 sg1650 - -lemma sg5293 : RowSquare [4,4,2,2,2,2,2] [6,6,6] := by - exact rowSquare_join (by decide) sg83 sg1658 - -lemma sg5294 : RowSquare [4,4,3,2,1,1,1,1,1] [4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg390 sg833 - -lemma sg5295 : RowSquare [4,4,3,2,1,1,1,1,1] [4,4,4,4,2] := by - exact rowSquare_join (by decide) sg616 sg551 - -lemma sg5296 : RowSquare [4,4,3,2,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg381 sg849 - -lemma sg5297 : RowSquare [4,4,3,2,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg383 sg849 - -lemma sg5298 : RowSquare [4,4,3,2,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg2107 - -lemma sg5299 : RowSquare [4,4,3,2,1,1,1,1,1] [6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg555 - -lemma sg5300 : RowSquare [4,4,3,2,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg2108 - -lemma sg5301 : RowSquare [4,4,3,2,2,2,1] [3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg1654 - -lemma sg5302 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg708 - -lemma sg5303 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg413 sg998 - -lemma sg5304 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg710 - -lemma sg5305 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3] := by - exact rowSquare_join (by decide) sg413 sg1001 - -lemma sg5306 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg415 sg998 - -lemma sg5307 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg414 sg1000 - -lemma sg5308 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2] := by - exact rowSquare_join (by decide) sg414 sg1001 - -lemma sg5309 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg415 sg999 - -lemma sg5310 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg415 sg1000 - -lemma sg5311 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2] := by - exact rowSquare_join (by decide) sg415 sg1001 - -lemma sg5312 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg711 - -lemma sg5313 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg708 - -lemma sg5314 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg712 - -lemma sg5315 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg709 - -lemma sg5316 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg708 - -lemma sg5317 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg710 - -lemma sg5318 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg416 sg999 - -lemma sg5319 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg589 sg708 - -lemma sg5320 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg416 sg1000 - -lemma sg5321 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,2] := by - exact rowSquare_join (by decide) sg590 sg708 - -lemma sg5322 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg713 - -lemma sg5323 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg417 sg998 - -lemma sg5324 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg709 - -lemma sg5325 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg413 sg1006 - -lemma sg5326 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg710 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes5 + +namespace OAI + +/-! Semigroup Nodes 11. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg4919 : RowSquare [8,4,3,1,1] [3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg307 sg586 + +lemma sg4920 : RowSquare [8,4,3,1,1] [3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg306 sg587 + +lemma sg4921 : RowSquare [8,4,3,1,1] [3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg306 sg589 + +lemma sg4922 : RowSquare [8,4,3,1,1] [3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg310 sg586 + +lemma sg4923 : RowSquare [8,4,3,1,1] [3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg32 sg1687 + +lemma sg4924 : RowSquare [8,4,3,1,1] [3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg1688 + +lemma sg4925 : RowSquare [8,4,3,1,1] [4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg307 sg588 + +lemma sg4926 : RowSquare [8,4,3,2] [3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg330 sg548 + +lemma sg4927 : RowSquare [8,4,3,2] [3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg178 sg854 + +lemma sg4928 : RowSquare [8,4,4,1] [3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg516 + +lemma sg4929 : RowSquare [8,6,2,1] [3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg849 + +lemma sg4931 : RowSquare [9,1,1,1,1,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg108 sg1136 + +lemma sg4932 : RowSquare [9,1,1,1,1,1,1,1,1] [2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg1620 + +lemma sg4933 : RowSquare [9,1,1,1,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg2114 + +lemma sg4934 : RowSquare [9,2,2,2,1,1] [5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg518 + +lemma sg4935 : RowSquare [9,3,1,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg2702 + +lemma sg4936 : RowSquare [9,3,1,1,1,1,1] [2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg2251 + +lemma sg4937 : RowSquare [9,3,1,1,1,1,1] [3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg2708 + +lemma sg4938 : RowSquare [9,3,1,1,1,1,1] [3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg2256 + +lemma sg4939 : RowSquare [9,3,1,1,1,1,1] [4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg2256 + +lemma sg4940 : RowSquare [9,3,1,1,1,1,1] [4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg2713 + +lemma sg4941 : RowSquare [9,3,2,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg1754 + +lemma sg4942 : RowSquare [9,3,2,1,1,1] [3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg1328 + +lemma sg4943 : RowSquare [9,3,2,1,1,1] [3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg1329 + +lemma sg4944 : RowSquare [9,3,2,1,1,1] [3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg77 sg1327 + +lemma sg4945 : RowSquare [9,3,2,1,1,1] [3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg1330 + +lemma sg4946 : RowSquare [9,3,2,1,1,1] [3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg1757 + +lemma sg4947 : RowSquare [9,3,2,1,1,1] [3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg1331 + +lemma sg4948 : RowSquare [9,3,2,1,1,1] [3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg32 sg1758 + +lemma sg4949 : RowSquare [9,3,2,1,1,1] [3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg74 sg1332 + +lemma sg4950 : RowSquare [9,3,2,1,1,1] [4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg75 sg1330 + +lemma sg4951 : RowSquare [9,3,2,1,1,1] [4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg1757 + +lemma sg4952 : RowSquare [9,3,2,1,1,1] [4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg75 sg1331 + +lemma sg4953 : RowSquare [9,3,2,1,1,1] [4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg76 sg1329 + +lemma sg4954 : RowSquare [9,3,2,1,1,1] [4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg1338 + +lemma sg4955 : RowSquare [9,3,2,1,1,1] [4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg194 sg890 + +lemma sg4956 : RowSquare [9,3,2,1,1,1] [4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg1339 + +lemma sg4957 : RowSquare [9,3,2,1,1,1] [4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg76 sg1331 + +lemma sg4958 : RowSquare [9,3,2,1,1,1] [4,4,3,3,3] := by + exact rowSquare_join (by decide) sg194 sg892 + +lemma sg4959 : RowSquare [9,3,2,1,1,1] [4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg77 sg1330 + +lemma sg4960 : RowSquare [9,3,2,1,1,1] [4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg77 sg1332 + +lemma sg4961 : RowSquare [9,3,2,1,1,1] [4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg195 sg891 + +lemma sg4962 : RowSquare [9,3,2,1,1,1] [4,4,4,3,2] := by + exact rowSquare_join (by decide) sg195 sg892 + +lemma sg4963 : RowSquare [9,3,2,1,1,1] [5,5,5,1,1] := by + exact rowSquare_join (by decide) sg89 sg1262 + +lemma sg4964 : RowSquare [9,3,2,2,1] [2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg910 + +lemma sg4965 : RowSquare [9,3,2,2,1] [2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg586 + +lemma sg4966 : RowSquare [9,3,2,2,1] [3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg330 sg587 + +lemma sg4967 : RowSquare [9,3,2,2,1] [3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg178 sg915 + +lemma sg4968 : RowSquare [9,3,2,2,1] [4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg179 sg915 + +lemma sg4969 : RowSquare [9,3,3,1,1] [3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg350 sg586 + +lemma sg4970 : RowSquare [9,3,3,1,1] [4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg350 sg588 + +lemma sg4971 : RowSquare [9,3,3,1,1] [4,4,3,3,3] := by + exact rowSquare_join (by decide) sg155 sg1001 + +lemma sg4972 : RowSquare [9,3,3,1,1] [4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg156 sg999 + +lemma sg4973 : RowSquare [9,3,3,1,1] [4,4,4,4,1] := by + exact rowSquare_join (by decide) sg350 sg590 + +lemma sg4974 : RowSquare [9,3,3,1,1] [5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg354 sg586 + +lemma sg4975 : RowSquare [9,3,3,1,1] [6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg354 sg588 + +lemma sg4976 : RowSquare [9,3,3,2] [3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg178 sg943 + +lemma sg4977 : RowSquare [9,3,3,2] [4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg179 sg943 + +lemma sg4978 : RowSquare [9,3,3,2] [4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg550 + +lemma sg4979 : RowSquare [9,3,3,2] [4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg371 sg551 + +lemma sg4980 : RowSquare [9,3,3,2] [4,4,3,3,3] := by + exact rowSquare_join (by decide) sg180 sg943 + +lemma sg4981 : RowSquare [9,4,1,1,1,1] [4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg1329 + +lemma sg4982 : RowSquare [9,4,1,1,1,1] [4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg1758 + +lemma sg4983 : RowSquare [9,4,1,1,1,1] [4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg1330 + +lemma sg4984 : RowSquare [9,4,1,1,1,1] [4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg83 sg1332 + +lemma sg4985 : RowSquare [9,4,1,1,1,1] [5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg40 sg1762 + +lemma sg4986 : RowSquare [9,4,2,1,1] [4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg534 + +lemma sg4987 : RowSquare [9,4,2,1,1] [4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg356 sg588 + +lemma sg4988 : RowSquare [9,4,2,1,1] [4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg535 + +lemma sg4989 : RowSquare [9,4,2,1,1] [4,4,3,3,3] := by + exact rowSquare_join (by decide) sg194 sg915 + +lemma sg4990 : RowSquare [9,4,3,1] [3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg636 + +lemma sg4991 : RowSquare [10,2,1,1,1,1,1] [5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg2263 + +lemma sg4992 : RowSquare [10,2,2,2,1] [3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg586 + +lemma sg4993 : RowSquare [10,2,2,2,1] [4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg179 sg1001 + +lemma sg4994 : RowSquare [10,2,2,2,1] [4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg589 + +lemma sg4995 : RowSquare [10,2,2,2,1] [4,4,3,3,3] := by + exact rowSquare_join (by decide) sg180 sg1001 + +lemma sg4996 : RowSquare [10,2,2,2,1] [4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg372 sg589 + +lemma sg4997 : RowSquare [10,3,2,1,1] [3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg586 + +lemma sg4998 : RowSquare [10,3,2,1,1] [4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg588 + +lemma sg4999 : RowSquare [10,3,2,1,1] [4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg195 sg999 + +lemma sg5000 : RowSquare [10,3,2,1,1] [4,4,4,4,1] := by + exact rowSquare_join (by decide) sg390 sg590 + +lemma sg5001 : RowSquare [10,3,2,1,1] [5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg396 sg586 + +lemma sg5002 : RowSquare [10,3,2,2] [3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg1032 + +lemma sg5003 : RowSquare [10,3,2,2] [3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg178 sg1033 + +lemma sg5004 : RowSquare [10,3,2,2] [4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg179 sg1032 + +lemma sg5005 : RowSquare [10,3,3,1] [4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg179 sg1061 + +lemma sg5006 : RowSquare [10,3,3,1] [4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg1063 + +lemma sg5007 : RowSquare [10,3,3,1] [4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg636 + +lemma sg5008 : RowSquare [10,3,3,1] [4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg1064 + +lemma sg5009 : RowSquare [10,3,3,1] [4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg1065 + +lemma sg5010 : RowSquare [10,3,3,1] [4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg373 sg636 + +lemma sg5018 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2] := by + exact rowSquare_join (by decide) sg692 sg692 + +lemma sg5019 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,1] := by + exact rowSquare_join (by decide) sg692 sg693 + +lemma sg5020 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,4] := by + exact rowSquare_join (by decide) sg693 sg693 + +lemma sg5021 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2] := by + exact rowSquare_join (by decide) sg692 sg694 + +lemma sg5022 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,1] := by + exact rowSquare_join (by decide) sg694 sg693 + +lemma sg5023 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,5,4,3] := by + exact rowSquare_join (by decide) sg693 sg695 + +lemma sg5024 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,2] := by + exact rowSquare_join (by decide) sg693 sg696 + +lemma sg5025 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2] := by + exact rowSquare_join (by decide) sg694 sg694 + +lemma sg5026 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [6,6,3,3] := by + exact rowSquare_join (by decide) sg390 sg1109 + +lemma sg5027 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg643 sg708 + +lemma sg5028 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg697 sg693 + +lemma sg5029 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,2] := by + exact rowSquare_join (by decide) sg644 sg708 + +lemma sg5030 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg697 sg694 + +lemma sg5031 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg643 sg709 + +lemma sg5032 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,2] := by + exact rowSquare_join (by decide) sg692 sg698 + +lemma sg5033 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,1] := by + exact rowSquare_join (by decide) sg644 sg709 + +lemma sg5034 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg391 sg1109 + +lemma sg5035 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,2] := by + exact rowSquare_join (by decide) sg694 sg698 + +lemma sg5036 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg636 sg714 + +lemma sg5037 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,5,3,2,1] := by + exact rowSquare_join (by decide) sg637 sg714 + +lemma sg5038 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,5,3,3] := by + exact rowSquare_join (by decide) sg693 sg699 + +lemma sg5039 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [7,7,1,1,1,1] := by + exact rowSquare_join (by decide) sg424 sg1063 + +lemma sg5040 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [8,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg697 sg697 + +lemma sg5041 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [8,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg645 sg708 + +lemma sg5042 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [8,3,3,2,2] := by + exact rowSquare_join (by decide) sg692 sg702 + +lemma sg5043 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [8,3,3,3,1] := by + exact rowSquare_join (by decide) sg644 sg711 + +lemma sg5044 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [8,4,2,2,2] := by + exact rowSquare_join (by decide) sg694 sg702 + +lemma sg5045 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [8,7,1,1,1] := by + exact rowSquare_join (by decide) sg694 sg703 + +lemma sg5046 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [9,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg576 sg716 + +lemma sg5047 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1] [9,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg576 sg717 + +lemma sg5048 : RowSquare [4,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg673 sg706 + +lemma sg5049 : RowSquare [4,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg422 sg1032 + +lemma sg5050 : RowSquare [4,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2] := by + exact rowSquare_join (by decide) sg422 sg1033 + +lemma sg5051 : RowSquare [4,2,2,2,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg424 sg1031 + +lemma sg5052 : RowSquare [4,2,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg424 sg1032 + +lemma sg5053 : RowSquare [4,2,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2] := by + exact rowSquare_join (by decide) sg424 sg1033 + +lemma sg5054 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg673 sg692 + +lemma sg5055 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg673 sg693 + +lemma sg5056 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg413 sg1032 + +lemma sg5057 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3] := by + exact rowSquare_join (by decide) sg413 sg1033 + +lemma sg5058 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg673 sg694 + +lemma sg5059 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg673 sg695 + +lemma sg5060 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg674 sg692 + +lemma sg5061 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg674 sg693 + +lemma sg5062 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,2] := by + exact rowSquare_join (by decide) sg414 sg1033 + +lemma sg5063 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg673 sg696 + +lemma sg5064 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg415 sg1032 + +lemma sg5065 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,2] := by + exact rowSquare_join (by decide) sg692 sg675 + +lemma sg5066 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,1] := by + exact rowSquare_join (by decide) sg692 sg676 + +lemma sg5067 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,4] := by + exact rowSquare_join (by decide) sg693 sg676 + +lemma sg5068 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg1109 + +lemma sg5069 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg674 sg694 + +lemma sg5070 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg1110 + +lemma sg5071 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg674 sg695 + +lemma sg5072 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2] := by + exact rowSquare_join (by decide) sg675 sg694 + +lemma sg5073 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,1] := by + exact rowSquare_join (by decide) sg694 sg676 + +lemma sg5074 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg696 + +lemma sg5075 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,1] := by + exact rowSquare_join (by decide) sg675 sg695 + +lemma sg5076 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,3] := by + exact rowSquare_join (by decide) sg676 sg695 + +lemma sg5077 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,1,1] := by + exact rowSquare_join (by decide) sg675 sg696 + +lemma sg5078 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,2] := by + exact rowSquare_join (by decide) sg676 sg696 + +lemma sg5079 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg371 sg1109 + +lemma sg5080 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg1110 + +lemma sg5081 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,1] := by + exact rowSquare_join (by decide) sg372 sg1109 + +lemma sg5082 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,6,3,3] := by + exact rowSquare_join (by decide) sg373 sg1109 + +lemma sg5083 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,1,1] := by + exact rowSquare_join (by decide) sg372 sg1110 + +lemma sg5084 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,2] := by + exact rowSquare_join (by decide) sg373 sg1110 + +lemma sg5085 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg674 sg697 + +lemma sg5086 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg615 sg708 + +lemma sg5087 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg697 sg676 + +lemma sg5088 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,2] := by + exact rowSquare_join (by decide) sg616 sg708 + +lemma sg5089 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg674 sg698 + +lemma sg5090 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg615 sg709 + +lemma sg5091 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,2] := by + exact rowSquare_join (by decide) sg692 sg678 + +lemma sg5092 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,1] := by + exact rowSquare_join (by decide) sg616 sg709 + +lemma sg5093 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg674 sg699 + +lemma sg5094 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,2] := by + exact rowSquare_join (by decide) sg694 sg678 + +lemma sg5095 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg700 + +lemma sg5096 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,5,3,2,1] := by + exact rowSquare_join (by decide) sg692 sg680 + +lemma sg5097 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,5,3,3] := by + exact rowSquare_join (by decide) sg693 sg680 + +lemma sg5098 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg1112 + +lemma sg5099 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg697 sg677 + +lemma sg5100 : RowSquare [4,3,2,1,1,1,1,1,1,1,1,1] [8,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg615 sg711 + +lemma sg5101 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg389 sg1031 + +lemma sg5102 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg1031 + +lemma sg5103 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg389 sg1032 + +lemma sg5104 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [4,4,4,3,3] := by + exact rowSquare_join (by decide) sg389 sg1033 + +lemma sg5105 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg390 sg1032 + +lemma sg5106 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,2] := by + exact rowSquare_join (by decide) sg390 sg1033 + +lemma sg5107 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg692 + +lemma sg5108 : RowSquare [4,3,2,2,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg693 + +lemma sg5109 : RowSquare [4,3,2,2,2,2,2,1] [4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg561 sg579 + +lemma sg5110 : RowSquare [4,3,2,2,2,2,2,1] [5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg561 sg581 + +lemma sg5111 : RowSquare [4,3,2,2,2,2,2,1] [5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg366 sg849 + +lemma sg5112 : RowSquare [4,3,2,2,2,2,2,1] [5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg561 sg582 + +lemma sg5113 : RowSquare [4,3,2,2,2,2,2,1] [5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg849 + +lemma sg5114 : RowSquare [4,3,2,2,2,2,2,1] [5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg365 sg851 + +lemma sg5115 : RowSquare [4,3,2,2,2,2,2,1] [5,5,4,4] := by + exact rowSquare_join (by decide) sg364 sg861 + +lemma sg5116 : RowSquare [4,3,2,2,2,2,2,1] [6,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg368 sg849 + +lemma sg5117 : RowSquare [4,3,2,2,2,2,2,1] [6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg561 sg585 + +lemma sg5118 : RowSquare [4,3,2,2,2,2,2,1] [7,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg369 sg849 + +lemma sg5119 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg1063 + +lemma sg5120 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1064 + +lemma sg5121 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg348 sg1032 + +lemma sg5122 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1065 + +lemma sg5123 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg389 sg941 + +lemma sg5124 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg636 sg615 + +lemma sg5125 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg941 + +lemma sg5126 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,4,3,3] := by + exact rowSquare_join (by decide) sg389 sg943 + +lemma sg5127 : RowSquare [4,3,3,2,1,1,1,1,1,1] [4,4,4,4,2] := by + exact rowSquare_join (by decide) sg637 sg616 + +lemma sg5128 : RowSquare [4,3,3,2,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg413 sg849 + +lemma sg5129 : RowSquare [4,3,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg576 sg673 + +lemma sg5130 : RowSquare [4,3,3,2,1,1,1,1,1,1] [5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1066 + +lemma sg5131 : RowSquare [4,3,3,2,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg231 sg1232 + +lemma sg5132 : RowSquare [4,3,3,2,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg232 sg1232 + +lemma sg5133 : RowSquare [4,3,3,2,1,1,1,1,1,1] [6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1067 + +lemma sg5134 : RowSquare [4,3,3,2,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg233 sg1232 + +lemma sg5135 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg673 sg673 + +lemma sg5136 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg673 sg674 + +lemma sg5137 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg673 sg675 + +lemma sg5138 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg673 sg676 + +lemma sg5139 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg674 sg674 + +lemma sg5140 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg674 sg675 + +lemma sg5141 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg674 sg676 + +lemma sg5142 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2] := by + exact rowSquare_join (by decide) sg675 sg675 + +lemma sg5143 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,1] := by + exact rowSquare_join (by decide) sg675 sg676 + +lemma sg5144 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [6,4,4,4] := by + exact rowSquare_join (by decide) sg676 sg676 + +lemma sg5145 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg673 sg677 + +lemma sg5146 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg673 sg678 + +lemma sg5147 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg674 sg677 + +lemma sg5148 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg673 sg679 + +lemma sg5149 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg677 sg675 + +lemma sg5150 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg677 sg676 + +lemma sg5151 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg673 sg680 + +lemma sg5152 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg674 sg678 + +lemma sg5153 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg673 sg681 + +lemma sg5154 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg674 sg679 + +lemma sg5155 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2] := by + exact rowSquare_join (by decide) sg675 sg678 + +lemma sg5156 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,1] := by + exact rowSquare_join (by decide) sg678 sg676 + +lemma sg5157 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,1] := by + exact rowSquare_join (by decide) sg675 sg679 + +lemma sg5158 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,4,4,3] := by + exact rowSquare_join (by decide) sg676 sg679 + +lemma sg5159 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg674 sg680 + +lemma sg5160 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg681 + +lemma sg5161 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,1] := by + exact rowSquare_join (by decide) sg675 sg680 + +lemma sg5162 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,5,3,3] := by + exact rowSquare_join (by decide) sg676 sg680 + +lemma sg5163 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,5,4,1,1] := by + exact rowSquare_join (by decide) sg675 sg681 + +lemma sg5164 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [7,5,4,2] := by + exact rowSquare_join (by decide) sg676 sg681 + +lemma sg5165 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg677 sg677 + +lemma sg5166 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg674 sg682 + +lemma sg5167 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg677 sg679 + +lemma sg5168 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2] := by + exact rowSquare_join (by decide) sg675 sg682 + +lemma sg5169 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,1] := by + exact rowSquare_join (by decide) sg682 sg676 + +lemma sg5170 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg674 sg683 + +lemma sg5171 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2] := by + exact rowSquare_join (by decide) sg678 sg678 + +lemma sg5172 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg684 + +lemma sg5173 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,1] := by + exact rowSquare_join (by decide) sg675 sg683 + +lemma sg5174 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,4,3,3] := by + exact rowSquare_join (by decide) sg676 sg683 + +lemma sg5175 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,4,4,2] := by + exact rowSquare_join (by decide) sg676 sg684 + +lemma sg5176 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg685 + +lemma sg5177 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,1] := by + exact rowSquare_join (by decide) sg678 sg680 + +lemma sg5178 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,5,3,1,1] := by + exact rowSquare_join (by decide) sg675 sg685 + +lemma sg5179 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,5,3,2] := by + exact rowSquare_join (by decide) sg676 sg685 + +lemma sg5180 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg686 + +lemma sg5181 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [8,6,2,2] := by + exact rowSquare_join (by decide) sg676 sg686 + +lemma sg5182 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg677 sg682 + +lemma sg5183 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg674 sg687 + +lemma sg5184 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,2] := by + exact rowSquare_join (by decide) sg678 sg682 + +lemma sg5185 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg677 sg684 + +lemma sg5186 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,3,3,2,1] := by + exact rowSquare_join (by decide) sg675 sg687 + +lemma sg5187 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,3,3,3] := by + exact rowSquare_join (by decide) sg676 sg687 + +lemma sg5188 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg688 + +lemma sg5189 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,4,3,2] := by + exact rowSquare_join (by decide) sg676 sg688 + +lemma sg5190 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg689 + +lemma sg5191 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,5,2,2] := by + exact rowSquare_join (by decide) sg676 sg689 + +lemma sg5192 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [9,7,1,1] := by + exact rowSquare_join (by decide) sg680 sg686 + +lemma sg5193 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [10,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg677 sg687 + +lemma sg5194 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [10,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg690 + +lemma sg5195 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [10,3,3,2] := by + exact rowSquare_join (by decide) sg676 sg690 + +lemma sg5196 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1] [10,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg691 + +lemma sg5197 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg370 sg1031 + +lemma sg5198 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg370 sg1032 + +lemma sg5199 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg370 sg1033 + +lemma sg5200 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg1520 + +lemma sg5201 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg1031 + +lemma sg5202 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg371 sg1032 + +lemma sg5203 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg371 sg1033 + +lemma sg5204 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg372 sg1031 + +lemma sg5205 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg1031 + +lemma sg5206 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg372 sg1032 + +lemma sg5207 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,3] := by + exact rowSquare_join (by decide) sg372 sg1033 + +lemma sg5208 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg373 sg1032 + +lemma sg5209 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [4,4,4,4,2] := by + exact rowSquare_join (by decide) sg373 sg1033 + +lemma sg5210 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg613 sg673 + +lemma sg5211 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg674 + +lemma sg5212 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg614 sg673 + +lemma sg5213 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg675 + +lemma sg5214 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg673 sg615 + +lemma sg5215 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg676 + +lemma sg5216 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg673 sg616 + +lemma sg5217 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg374 sg1032 + +lemma sg5218 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg374 sg1033 + +lemma sg5219 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg614 sg674 + +lemma sg5220 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg614 sg675 + +lemma sg5221 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg674 + +lemma sg5222 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg614 sg676 + +lemma sg5223 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg674 sg616 + +lemma sg5224 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,3] := by + exact rowSquare_join (by decide) sg375 sg1033 + +lemma sg5225 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg1041 + +lemma sg5226 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg615 sg675 + +lemma sg5227 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg615 sg676 + +lemma sg5228 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg1527 + +lemma sg5229 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg1038 + +lemma sg5230 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg377 sg1031 + +lemma sg5231 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg1039 + +lemma sg5232 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg371 sg1040 + +lemma sg5233 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg378 sg1031 + +lemma sg5234 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg371 sg1041 + +lemma sg5235 : RowSquare [4,4,2,1,1,1,1,1,1,1,1] [5,5,4,2,2] := by + exact rowSquare_join (by decide) sg372 sg1039 + +lemma sg5236 : RowSquare [4,4,2,2,1,1,1,1,1,1] [3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg1031 + +lemma sg5237 : RowSquare [4,4,2,2,1,1,1,1,1,1] [3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg1032 + +lemma sg5238 : RowSquare [4,4,2,2,1,1,1,1,1,1] [3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg1417 + +lemma sg5239 : RowSquare [4,4,2,2,1,1,1,1,1,1] [3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1033 + +lemma sg5240 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg613 sg613 + +lemma sg5241 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg615 + +lemma sg5242 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg1038 + +lemma sg5243 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg614 sg614 + +lemma sg5244 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1039 + +lemma sg5245 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg614 sg615 + +lemma sg5246 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1040 + +lemma sg5247 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg614 sg616 + +lemma sg5248 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg371 sg960 + +lemma sg5249 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg371 sg961 + +lemma sg5250 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1041 + +lemma sg5251 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg372 sg959 + +lemma sg5252 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg615 + +lemma sg5253 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg959 + +lemma sg5254 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg615 sg616 + +lemma sg5255 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,3,3] := by + exact rowSquare_join (by decide) sg372 sg961 + +lemma sg5256 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg373 sg960 + +lemma sg5257 : RowSquare [4,4,2,2,1,1,1,1,1,1] [4,4,4,4,2] := by + exact rowSquare_join (by decide) sg616 sg616 + +lemma sg5258 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg613 sg617 + +lemma sg5259 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg620 + +lemma sg5260 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,4,3,3,3] := by + exact rowSquare_join (by decide) sg375 sg961 + +lemma sg5261 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg623 + +lemma sg5262 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg614 sg621 + +lemma sg5263 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg964 + +lemma sg5264 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1049 + +lemma sg5265 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,3,3,2] := by + exact rowSquare_join (by decide) sg616 sg621 + +lemma sg5266 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg614 sg623 + +lemma sg5267 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,4,4] := by + exact rowSquare_join (by decide) sg373 sg965 + +lemma sg5268 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg615 sg623 + +lemma sg5269 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,5,2,1] := by + exact rowSquare_join (by decide) sg616 sg623 + +lemma sg5270 : RowSquare [4,4,2,2,1,1,1,1,1,1] [5,5,5,3] := by + exact rowSquare_join (by decide) sg373 sg966 + +lemma sg5271 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg624 + +lemma sg5272 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg673 sg565 + +lemma sg5273 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg625 + +lemma sg5274 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,3,3,3,3] := by + exact rowSquare_join (by decide) sg379 sg961 + +lemma sg5275 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg626 + +lemma sg5276 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg627 + +lemma sg5277 : RowSquare [4,4,2,2,1,1,1,1,1,1] [6,6,6] := by + exact rowSquare_join (by decide) sg623 sg623 + +lemma sg5278 : RowSquare [4,4,2,2,2,2,1,1] [3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg1650 + +lemma sg5279 : RowSquare [4,4,2,2,2,2,1,1] [3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg878 + +lemma sg5280 : RowSquare [4,4,2,2,2,2,1,1] [4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg1650 + +lemma sg5281 : RowSquare [4,4,2,2,2,2,1,1] [4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg561 sg561 + +lemma sg5282 : RowSquare [4,4,2,2,2,2,1,1] [4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg99 sg1650 + +lemma sg5283 : RowSquare [4,4,2,2,2,2,1,1] [4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg1651 + +lemma sg5284 : RowSquare [4,4,2,2,2,2,1,1] [4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg1652 + +lemma sg5285 : RowSquare [4,4,2,2,2,2,1,1] [4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg885 + +lemma sg5286 : RowSquare [4,4,2,2,2,2,1,1] [4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg563 sg563 + +lemma sg5287 : RowSquare [4,4,2,2,2,2,1,1] [5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg100 sg1650 + +lemma sg5288 : RowSquare [4,4,2,2,2,2,1,1] [5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg1651 + +lemma sg5289 : RowSquare [4,4,2,2,2,2,1,1] [5,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg1650 + +lemma sg5290 : RowSquare [4,4,2,2,2,2,1,1] [5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg99 sg1651 + +lemma sg5291 : RowSquare [4,4,2,2,2,2,1,1] [6,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg102 sg1650 + +lemma sg5292 : RowSquare [4,4,2,2,2,2,1,1] [7,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg103 sg1650 + +lemma sg5293 : RowSquare [4,4,2,2,2,2,2] [6,6,6] := by + exact rowSquare_join (by decide) sg83 sg1658 + +lemma sg5294 : RowSquare [4,4,3,2,1,1,1,1,1] [4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg390 sg833 + +lemma sg5295 : RowSquare [4,4,3,2,1,1,1,1,1] [4,4,4,4,2] := by + exact rowSquare_join (by decide) sg616 sg551 + +lemma sg5296 : RowSquare [4,4,3,2,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg381 sg849 + +lemma sg5297 : RowSquare [4,4,3,2,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg383 sg849 + +lemma sg5298 : RowSquare [4,4,3,2,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg2107 + +lemma sg5299 : RowSquare [4,4,3,2,1,1,1,1,1] [6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg555 + +lemma sg5300 : RowSquare [4,4,3,2,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg2108 + +lemma sg5301 : RowSquare [4,4,3,2,2,2,1] [3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg1654 + +lemma sg5302 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg708 + +lemma sg5303 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg413 sg998 + +lemma sg5304 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg710 + +lemma sg5305 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3] := by + exact rowSquare_join (by decide) sg413 sg1001 + +lemma sg5306 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg415 sg998 + +lemma sg5307 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg414 sg1000 + +lemma sg5308 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2] := by + exact rowSquare_join (by decide) sg414 sg1001 + +lemma sg5309 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg415 sg999 + +lemma sg5310 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg415 sg1000 + +lemma sg5311 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2] := by + exact rowSquare_join (by decide) sg415 sg1001 + +lemma sg5312 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg711 + +lemma sg5313 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg708 + +lemma sg5314 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg712 + +lemma sg5315 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg709 + +lemma sg5316 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg708 + +lemma sg5317 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg710 + +lemma sg5318 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg416 sg999 + +lemma sg5319 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg589 sg708 + +lemma sg5320 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg416 sg1000 + +lemma sg5321 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,2] := by + exact rowSquare_join (by decide) sg590 sg708 + +lemma sg5322 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg713 + +lemma sg5323 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg417 sg998 + +lemma sg5324 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg709 + +lemma sg5325 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg413 sg1006 + +lemma sg5326 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg710 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes12.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes12.lean index d01b584c9ab5ec8b493b49c309d09fc33b4584bb..6701667a063da6e3d13172dbb1cb745d8f884716 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes12.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes12.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes10 - -namespace OAI - -/-! Semigroup Nodes 12. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg5327 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg589 sg709 - -lemma sg5328 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2] := by - exact rowSquare_join (by decide) sg413 sg1007 - -lemma sg5329 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,1] := by - exact rowSquare_join (by decide) sg590 sg709 - -lemma sg5330 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg710 - -lemma sg5331 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,1] := by - exact rowSquare_join (by decide) sg590 sg710 - -lemma sg5332 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg418 sg998 - -lemma sg5333 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg418 sg999 - -lemma sg5334 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg414 sg1006 - -lemma sg5335 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,2] := by - exact rowSquare_join (by decide) sg418 sg1001 - -lemma sg5336 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg415 sg1006 - -lemma sg5337 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,1] := by - exact rowSquare_join (by decide) sg414 sg1007 - -lemma sg5338 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,3,3] := by - exact rowSquare_join (by decide) sg414 sg1008 - -lemma sg5339 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,4,1,1] := by - exact rowSquare_join (by decide) sg415 sg1007 - -lemma sg5340 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,4,2] := by - exact rowSquare_join (by decide) sg415 sg1008 - -lemma sg5341 : RowSquare [5,3,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg389 sg998 - -lemma sg5342 : RowSquare [5,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg998 - -lemma sg5343 : RowSquare [5,3,2,1,1,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg696 - -lemma sg5344 : RowSquare [5,3,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg413 sg910 - -lemma sg5345 : RowSquare [5,3,2,1,1,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg414 sg910 - -lemma sg5346 : RowSquare [5,3,2,1,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg415 sg910 - -lemma sg5347 : RowSquare [5,3,2,2,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg389 sg910 - -lemma sg5348 : RowSquare [5,3,2,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg910 - -lemma sg5349 : RowSquare [5,3,2,2,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg646 - -lemma sg5350 : RowSquare [5,3,2,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg647 - -lemma sg5351 : RowSquare [5,3,2,2,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg104 sg1682 - -lemma sg5352 : RowSquare [5,3,2,2,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg105 sg1682 - -lemma sg5353 : RowSquare [5,3,2,2,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg649 - -lemma sg5354 : RowSquare [5,3,2,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg396 sg910 - -lemma sg5355 : RowSquare [5,3,2,2,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg650 - -lemma sg5356 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg106 sg1682 - -lemma sg5357 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg397 sg910 - -lemma sg5358 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg651 - -lemma sg5359 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg398 sg910 - -lemma sg5360 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg652 - -lemma sg5361 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg653 - -lemma sg5362 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg399 sg910 - -lemma sg5363 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg654 - -lemma sg5364 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg655 - -lemma sg5365 : RowSquare [5,3,3,2,1,1,1,1,1] [4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg2137 - -lemma sg5366 : RowSquare [5,3,3,2,1,1,1,1,1] [4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg2137 - -lemma sg5367 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg673 - -lemma sg5368 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg674 - -lemma sg5369 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg370 sg998 - -lemma sg5370 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg675 - -lemma sg5371 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg676 - -lemma sg5372 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg370 sg1000 - -lemma sg5373 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg370 sg1001 - -lemma sg5374 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg371 sg998 - -lemma sg5375 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg372 sg998 - -lemma sg5376 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg998 - -lemma sg5377 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg371 sg1000 - -lemma sg5378 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg371 sg1001 - -lemma sg5379 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg372 sg1000 - -lemma sg5380 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,4,3,3] := by - exact rowSquare_join (by decide) sg372 sg1001 - -lemma sg5381 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg373 sg1000 - -lemma sg5382 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,4,4,2] := by - exact rowSquare_join (by decide) sg373 sg1001 - -lemma sg5383 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg677 - -lemma sg5384 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg587 sg673 - -lemma sg5385 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg678 - -lemma sg5386 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg674 - -lemma sg5387 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg679 - -lemma sg5388 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg675 - -lemma sg5389 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg676 - -lemma sg5390 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg374 sg1000 - -lemma sg5391 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg374 sg1001 - -lemma sg5392 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg680 - -lemma sg5393 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg375 sg998 - -lemma sg5394 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg681 - -lemma sg5395 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg376 sg998 - -lemma sg5396 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,4,3,3,3] := by - exact rowSquare_join (by decide) sg375 sg1001 - -lemma sg5397 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg377 sg998 - -lemma sg5398 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg1006 - -lemma sg5399 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg682 - -lemma sg5400 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg677 - -lemma sg5401 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg683 - -lemma sg5402 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg678 - -lemma sg5403 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg684 - -lemma sg5404 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg679 - -lemma sg5405 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,3,3,3,3] := by - exact rowSquare_join (by decide) sg379 sg1001 - -lemma sg5406 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg685 - -lemma sg5407 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg680 - -lemma sg5408 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg681 - -lemma sg5409 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg686 - -lemma sg5410 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg382 sg998 - -lemma sg5411 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg383 sg998 - -lemma sg5412 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,6,2,2,2] := by - exact rowSquare_join (by decide) sg383 sg1001 - -lemma sg5413 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [10,4,4] := by - exact rowSquare_join (by decide) sg4 sg3162 - -lemma sg5414 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg910 - -lemma sg5415 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg613 - -lemma sg5416 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg910 - -lemma sg5417 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg330 sg998 - -lemma sg5418 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg372 sg910 - -lemma sg5419 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg615 - -lemma sg5420 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg999 - -lemma sg5421 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg910 - -lemma sg5422 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg1000 - -lemma sg5423 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1001 - -lemma sg5424 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg374 sg910 - -lemma sg5425 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg617 - -lemma sg5426 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg376 sg910 - -lemma sg5427 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg589 - -lemma sg5428 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg378 sg910 - -lemma sg5429 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg623 - -lemma sg5430 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg589 - -lemma sg5431 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg379 sg910 - -lemma sg5432 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg624 - -lemma sg5433 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg4674 - -lemma sg5434 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg380 sg910 - -lemma sg5435 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg381 sg910 - -lemma sg5436 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg4675 - -lemma sg5437 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg4676 - -lemma sg5438 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg4677 - -lemma sg5439 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg4678 - -lemma sg5440 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,4,4,4,1] := by - exact rowSquare_join (by decide) sg0 sg4684 - -lemma sg5441 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg383 sg910 - -lemma sg5442 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg628 - -lemma sg5443 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg920 - -lemma sg5444 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1016 - -lemma sg5445 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg623 - -lemma sg5446 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg615 sg596 - -lemma sg5447 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,4,4] := by - exact rowSquare_join (by decide) sg373 sg922 - -lemma sg5448 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg623 - -lemma sg5449 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,5,2,1] := by - exact rowSquare_join (by decide) sg590 sg623 - -lemma sg5450 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,5,3] := by - exact rowSquare_join (by decide) sg373 sg923 - -lemma sg5451 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg384 sg910 - -lemma sg5452 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg629 - -lemma sg5453 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg4685 - -lemma sg5454 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg4686 - -lemma sg5455 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg385 sg910 - -lemma sg5456 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg630 - -lemma sg5457 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg4687 - -lemma sg5458 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg4688 - -lemma sg5459 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg631 - -lemma sg5460 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg4689 - -lemma sg5461 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg3832 - -lemma sg5462 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg4690 - -lemma sg5463 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3833 - -lemma sg5464 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg3834 - -lemma sg5465 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg3835 - -lemma sg5466 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg386 sg910 - -lemma sg5467 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg3839 - -lemma sg5468 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg632 - -lemma sg5469 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,5,4,2,1] := by - exact rowSquare_join (by decide) sg4 sg3165 - -lemma sg5470 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,5,4,3] := by - exact rowSquare_join (by decide) sg4 sg3166 - -lemma sg5471 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,5,5,1,1] := by - exact rowSquare_join (by decide) sg4 sg3167 - -lemma sg5472 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,5,5,2] := by - exact rowSquare_join (by decide) sg4 sg3168 - -lemma sg5473 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1023 - -lemma sg5474 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg371 sg931 - -lemma sg5475 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,2,2,2] := by - exact rowSquare_join (by decide) sg621 sg595 - -lemma sg5476 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg615 sg602 - -lemma sg5477 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg3169 - -lemma sg5478 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,3,3] := by - exact rowSquare_join (by decide) sg373 sg931 - -lemma sg5479 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,4,1,1] := by - exact rowSquare_join (by decide) sg4 sg3170 - -lemma sg5480 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,4,2] := by - exact rowSquare_join (by decide) sg4 sg3171 - -lemma sg5481 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,5,1] := by - exact rowSquare_join (by decide) sg4 sg3172 - -lemma sg5482 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,6] := by - exact rowSquare_join (by decide) sg4 sg3173 - -lemma sg5483 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg387 sg910 - -lemma sg5484 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg633 - -lemma sg5485 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3840 - -lemma sg5486 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg388 sg910 - -lemma sg5487 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg634 - -lemma sg5488 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3841 - -lemma sg5489 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg3842 - -lemma sg5490 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3843 - -lemma sg5491 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg3174 - -lemma sg5492 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg3844 - -lemma sg5493 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg3845 - -lemma sg5494 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg635 - -lemma sg5495 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg4693 - -lemma sg5496 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg3846 - -lemma sg5497 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg3175 - -lemma sg5498 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,4,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg3176 - -lemma sg5499 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg3177 - -lemma sg5500 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg4695 - -lemma sg5501 : RowSquare [5,4,2,1,1,1,1,1,1,1] [9,9] := by - exact rowSquare_join (by decide) sg14 sg2490 - -lemma sg5502 : RowSquare [5,4,2,1,1,1,1,1,1,1] [10,8] := by - exact rowSquare_join (by decide) sg42 sg2014 - -lemma sg5503 : RowSquare [5,4,2,1,1,1,1,1,1,1] [11,7] := by - exact rowSquare_join (by decide) sg80 sg1577 - -lemma sg5504 : RowSquare [5,4,2,1,1,1,1,1,1,1] [12,6] := by - exact rowSquare_join (by decide) sg80 sg1578 - -lemma sg5505 : RowSquare [5,4,2,1,1,1,1,1,1,1] [13,5] := by - exact rowSquare_join (by decide) sg174 sg1120 - -lemma sg5506 : RowSquare [5,4,2,1,1,1,1,1,1,1] [14,4] := by - exact rowSquare_join (by decide) sg363 sg718 - -lemma sg5507 : RowSquare [5,4,2,2,1,1,1,1,1] [2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg910 - -lemma sg5508 : RowSquare [5,4,2,2,1,1,1,1,1] [3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg330 sg912 - -lemma sg5509 : RowSquare [5,4,2,2,1,1,1,1,1] [3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg915 - -lemma sg5510 : RowSquare [5,4,2,2,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg2596 - -lemma sg5511 : RowSquare [5,4,2,2,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg2597 - -lemma sg5512 : RowSquare [5,4,2,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg2598 - -lemma sg5513 : RowSquare [5,4,2,2,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg4697 - -lemma sg5514 : RowSquare [5,4,2,2,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg4698 - -lemma sg5515 : RowSquare [5,4,2,2,2,2,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg2596 - -lemma sg5516 : RowSquare [5,4,2,2,2,2,1] [5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg2603 - -lemma sg5517 : RowSquare [5,4,2,2,2,2,1] [5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg2607 - -lemma sg5518 : RowSquare [5,4,2,2,2,2,1] [5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg2608 - -lemma sg5519 : RowSquare [5,4,2,2,2,2,1] [6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg2597 - -lemma sg5520 : RowSquare [5,4,2,2,2,2,1] [6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg2601 - -lemma sg5521 : RowSquare [5,4,2,2,2,2,1] [6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg2602 - -lemma sg5522 : RowSquare [5,4,2,2,2,2,1] [6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg2611 - -lemma sg5523 : RowSquare [5,4,2,2,2,2,1] [6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg302 sg838 - -lemma sg5524 : RowSquare [5,4,3,2,1,1,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg3299 - -lemma sg5525 : RowSquare [5,5,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg586 - -lemma sg5526 : RowSquare [5,5,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg587 - -lemma sg5527 : RowSquare [5,5,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg588 - -lemma sg5528 : RowSquare [5,5,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg589 - -lemma sg5529 : RowSquare [5,5,1,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg590 - -lemma sg5530 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg591 - -lemma sg5531 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg587 - -lemma sg5532 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg593 - -lemma sg5533 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg312 sg999 - -lemma sg5534 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg594 - -lemma sg5535 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg312 sg1000 - -lemma sg5536 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg595 - -lemma sg5537 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg313 sg998 - -lemma sg5538 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg588 - -lemma sg5539 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg596 - -lemma sg5540 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg314 sg998 - -lemma sg5541 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg588 sg589 - -lemma sg5542 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg315 sg998 - -lemma sg5543 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg590 - -lemma sg5544 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg313 sg1000 - -lemma sg5545 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg313 sg1001 - -lemma sg5546 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg314 sg999 - -lemma sg5547 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg589 sg589 - -lemma sg5548 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg315 sg999 - -lemma sg5549 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg589 sg590 - -lemma sg5550 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,3,3] := by - exact rowSquare_join (by decide) sg314 sg1001 - -lemma sg5551 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg315 sg1000 - -lemma sg5552 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,4,2] := by - exact rowSquare_join (by decide) sg590 sg590 - -lemma sg5553 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg597 - -lemma sg5554 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg587 sg591 - -lemma sg5555 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg592 - -lemma sg5556 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg591 - -lemma sg5557 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg591 sg589 - -lemma sg5558 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg594 - -lemma sg5559 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg316 sg1000 - -lemma sg5560 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg316 sg1001 - -lemma sg5561 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg588 sg592 - -lemma sg5562 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg601 - -lemma sg5563 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg589 sg592 - -lemma sg5564 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg594 - -lemma sg5565 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,4,4,4,1] := by - exact rowSquare_join (by decide) sg590 sg594 - -lemma sg5566 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg602 - -lemma sg5567 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg319 sg998 - -lemma sg5568 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg595 - -lemma sg5569 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg313 sg1006 - -lemma sg5570 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg320 sg998 - -lemma sg5571 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg596 - -lemma sg5572 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg313 sg1008 - -lemma sg5573 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,3,3,2] := by - exact rowSquare_join (by decide) sg590 sg595 - -lemma sg5574 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg320 sg999 - -lemma sg5575 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg589 sg596 - -lemma sg5576 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,4,2,2] := by - exact rowSquare_join (by decide) sg314 sg1007 - -lemma sg5577 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,4,4] := by - exact rowSquare_join (by decide) sg315 sg1008 - -lemma sg5578 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg603 - -lemma sg5579 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg597 - -lemma sg5580 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg3866 - -lemma sg5581 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3869 - -lemma sg5582 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg3875 - -lemma sg5583 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg324 sg998 - -lemma sg5584 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg313 sg1015 - -lemma sg5585 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,6,2,2,2] := by - exact rowSquare_join (by decide) sg595 sg595 - -lemma sg5586 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,6,3,3] := by - exact rowSquare_join (by decide) sg315 sg1015 - -lemma sg5587 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,6,4,1,1] := by - exact rowSquare_join (by decide) sg314 sg1016 - -lemma sg5588 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg608 - -lemma sg5589 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg603 - -lemma sg5590 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg3876 - -lemma sg5591 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,5,5,1] := by - exact rowSquare_join (by decide) sg13 sg2497 - -lemma sg5592 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,7,1,1,1,1] := by - exact rowSquare_join (by decide) sg313 sg1023 - -lemma sg5593 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,7,2,2] := by - exact rowSquare_join (by decide) sg315 sg1023 - -lemma sg5594 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,7,4] := by - exact rowSquare_join (by decide) sg320 sg1016 - -lemma sg5595 : RowSquare [5,5,1,1,1,1,1,1,1,1] [8,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg611 - -lemma sg5596 : RowSquare [5,5,1,1,1,1,1,1,1,1] [8,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg608 - -lemma sg5597 : RowSquare [5,5,1,1,1,1,1,1,1,1] [8,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg3896 - -lemma sg5598 : RowSquare [5,5,1,1,1,1,1,1,1,1] [8,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg3897 - -lemma sg5599 : RowSquare [5,5,1,1,1,1,1,1,1,1] [8,8,1,1] := by - exact rowSquare_join (by decide) sg319 sg1023 - -lemma sg5600 : RowSquare [5,5,1,1,1,1,1,1,1,1] [9,9] := by - exact rowSquare_join (by decide) sg324 sg1023 - -lemma sg5601 : RowSquare [5,5,2,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg313 sg910 - -lemma sg5602 : RowSquare [5,5,2,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg314 sg910 - -lemma sg5603 : RowSquare [5,5,2,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg536 - -lemma sg5604 : RowSquare [5,5,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg315 sg910 - -lemma sg5605 : RowSquare [5,5,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg534 - -lemma sg5606 : RowSquare [5,5,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg324 sg910 - -lemma sg5607 : RowSquare [5,5,2,2,2,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg3999 - -lemma sg5608 : RowSquare [5,5,2,2,2,1,1] [4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg4002 - -lemma sg5609 : RowSquare [5,5,2,2,2,1,1] [4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg4003 - -lemma sg5610 : RowSquare [5,5,2,2,2,1,1] [4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg4004 - -lemma sg5611 : RowSquare [5,5,2,2,2,1,1] [4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg4005 - -lemma sg5612 : RowSquare [5,5,2,2,2,1,1] [5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg4009 - -lemma sg5613 : RowSquare [5,5,2,2,2,1,1] [5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg4010 - -lemma sg5614 : RowSquare [5,5,2,2,2,1,1] [5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg4011 - -lemma sg5615 : RowSquare [6,4,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg1327 - -lemma sg5616 : RowSquare [6,4,1,1,1,1,1,1,1,1] [3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg181 sg1327 - -lemma sg5617 : RowSquare [6,4,1,1,1,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg182 sg1327 - -lemma sg5618 : RowSquare [6,4,1,1,1,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg183 sg1327 - -lemma sg5619 : RowSquare [6,4,1,1,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg184 sg1327 - -lemma sg5620 : RowSquare [6,4,1,1,1,1,1,1,1,1] [4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg179 sg1332 - -lemma sg5621 : RowSquare [6,4,1,1,1,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg186 sg1327 - -lemma sg5622 : RowSquare [6,4,1,1,1,1,1,1,1,1] [5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg187 sg1327 - -lemma sg5623 : RowSquare [6,4,1,1,1,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg188 sg1327 - -lemma sg5624 : RowSquare [6,4,1,1,1,1,1,1,1,1] [6,5,5,1,1] := by - exact rowSquare_join (by decide) sg4 sg3187 - -lemma sg5625 : RowSquare [6,4,1,1,1,1,1,1,1,1] [6,5,5,2] := by - exact rowSquare_join (by decide) sg4 sg3188 - -lemma sg5626 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,5,5,1] := by - exact rowSquare_join (by decide) sg4 sg3190 - -lemma sg5627 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,6,4,1] := by - exact rowSquare_join (by decide) sg4 sg3191 - -lemma sg5628 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,6,5] := by - exact rowSquare_join (by decide) sg4 sg3192 - -lemma sg5629 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,7,1,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg909 - -lemma sg5630 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,7,2,1,1] := by - exact rowSquare_join (by decide) sg372 sg909 - -lemma sg5631 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,7,2,2] := by - exact rowSquare_join (by decide) sg373 sg909 - -lemma sg5632 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,7,3,1] := by - exact rowSquare_join (by decide) sg377 sg903 - -lemma sg5633 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,7,4] := by - exact rowSquare_join (by decide) sg378 sg903 - -lemma sg5634 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg191 sg1328 - -lemma sg5635 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3945 - -lemma sg5636 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg2511 - -lemma sg5637 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6 sg3186 - -lemma sg5638 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg3897 - -lemma sg5639 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3946 - -lemma sg5640 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg3193 - -lemma sg5641 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg2512 - -lemma sg5642 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg3189 - -lemma sg5643 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg3194 - -lemma sg5644 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg2513 - -lemma sg5645 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,3,2,2] := by - exact rowSquare_join (by decide) sg16 sg2495 - -lemma sg5646 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg2514 - -lemma sg5647 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3947 - -lemma sg5648 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg2508 - -lemma sg5649 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg2515 - -lemma sg5650 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg2495 - -lemma sg5651 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg3195 - -lemma sg5652 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg2516 - -lemma sg5653 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg2517 - -lemma sg5654 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,4,1,1] := by - exact rowSquare_join (by decide) sg16 sg2496 - -lemma sg5655 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,4,2] := by - exact rowSquare_join (by decide) sg13 sg2518 - -lemma sg5656 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg2509 - -lemma sg5657 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg2510 - -lemma sg5658 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg2519 - -lemma sg5659 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,5,3,1,1] := by - exact rowSquare_join (by decide) sg17 sg2496 - -lemma sg5660 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,5,5] := by - exact rowSquare_join (by decide) sg16 sg2497 - -lemma sg5661 : RowSquare [6,4,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg330 sg889 - -lemma sg5662 : RowSquare [6,4,2,1,1,1,1,1,1] [3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg890 - -lemma sg5663 : RowSquare [6,4,2,1,1,1,1,1,1] [3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg892 - -lemma sg5664 : RowSquare [6,4,2,1,1,1,1,1,1] [4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg71 sg1754 - -lemma sg5665 : RowSquare [6,4,2,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3957 - -lemma sg5666 : RowSquare [6,4,2,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg153 sg1327 - -lemma sg5667 : RowSquare [6,4,2,1,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg3198 - -lemma sg5668 : RowSquare [6,4,2,1,1,1,1,1,1] [7,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3958 - -lemma sg5669 : RowSquare [6,4,3,1,1,1,1,1] [3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg1196 - -lemma sg5670 : RowSquare [6,4,3,2,2,1] [3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg1616 - -lemma sg5671 : RowSquare [6,5,1,1,1,1,1,1,1] [8,5,5] := by - exact rowSquare_join (by decide) sg83 sg1583 - -lemma sg5673 : RowSquare [6,5,2,2,2,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg508 sg474 - -lemma sg5674 : RowSquare [6,5,2,2,2,1] [2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg506 sg474 - -lemma sg5675 : RowSquare [6,5,2,2,2,1] [2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg503 sg473 - -lemma sg5676 : RowSquare [6,5,2,2,2,1] [2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg503 sg472 - -lemma sg5677 : RowSquare [6,5,2,2,2,1] [2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg503 sg471 - -lemma sg5678 : RowSquare [6,5,2,2,2,1] [2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg503 sg470 - -lemma sg5679 : RowSquare [6,5,2,2,2,1] [2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg281 sg780 - -lemma sg5680 : RowSquare [6,5,2,2,2,1] [3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg505 sg474 - -lemma sg5681 : RowSquare [6,5,2,2,2,1] [3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg500 sg473 - -lemma sg5682 : RowSquare [6,5,2,2,2,1] [3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg500 sg472 - -lemma sg5683 : RowSquare [6,5,2,2,2,1] [3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg500 sg471 - -lemma sg5684 : RowSquare [6,5,2,2,2,1] [3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg500 sg470 - -lemma sg5685 : RowSquare [6,5,2,2,2,1] [3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg502 sg474 - -lemma sg5686 : RowSquare [6,5,2,2,2,1] [3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg499 sg474 - -lemma sg5687 : RowSquare [6,5,2,2,2,1] [3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg499 sg472 - -lemma sg5688 : RowSquare [6,5,2,2,2,1] [3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg499 sg471 - -lemma sg5689 : RowSquare [6,5,2,2,2,1] [3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg499 sg470 - -lemma sg5690 : RowSquare [6,5,2,2,2,1] [3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg500 sg465 - -lemma sg5691 : RowSquare [6,5,2,2,2,1] [3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg496 sg472 - -lemma sg5692 : RowSquare [6,5,2,2,2,1] [3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg496 sg471 - -lemma sg5693 : RowSquare [6,5,2,2,2,1] [3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg496 sg470 - -lemma sg5694 : RowSquare [6,5,2,2,2,1] [3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg496 sg468 - -lemma sg5695 : RowSquare [6,5,2,2,2,1] [3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg496 sg464 - -lemma sg5696 : RowSquare [6,5,2,2,2,1] [3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg496 sg459 - -lemma sg5697 : RowSquare [6,5,2,2,2,1] [4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg498 sg474 - -lemma sg5698 : RowSquare [6,5,2,2,2,1] [4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg495 sg473 - -lemma sg5699 : RowSquare [6,5,2,2,2,1] [4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg495 sg472 - -lemma sg5700 : RowSquare [6,5,2,2,2,1] [4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg495 sg471 - -lemma sg5701 : RowSquare [6,5,2,2,2,1] [4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg495 sg470 - -lemma sg5702 : RowSquare [6,5,2,2,2,1] [4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg493 sg474 - -lemma sg5703 : RowSquare [6,5,2,2,2,1] [4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg493 sg473 - -lemma sg5704 : RowSquare [6,5,2,2,2,1] [4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg493 sg470 - -lemma sg5705 : RowSquare [6,5,2,2,2,1] [4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg493 sg469 - -lemma sg5706 : RowSquare [6,5,2,2,2,1] [5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg490 sg474 - -lemma sg5707 : RowSquare [6,5,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg3243 - -lemma sg5708 : RowSquare [6,5,2,2,2,1] [7,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg3244 - -lemma sg5709 : RowSquare [6,5,2,2,2,1] [7,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg3246 - -lemma sg5710 : RowSquare [6,5,2,2,2,1] [7,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg2544 - -lemma sg5711 : RowSquare [6,5,2,2,2,1] [7,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg3989 - -lemma sg5712 : RowSquare [6,5,2,2,2,1] [7,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg3990 - -lemma sg5713 : RowSquare [6,5,2,2,2,1] [7,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg2543 - -lemma sg5714 : RowSquare [6,5,2,2,2,1] [7,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg3247 - -lemma sg5715 : RowSquare [6,5,2,2,2,1] [7,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg838 - -lemma sg5716 : RowSquare [6,5,2,2,2,1] [7,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg3991 - -lemma sg5717 : RowSquare [6,5,2,2,2,1] [7,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg842 - -lemma sg5718 : RowSquare [6,5,2,2,2,1] [7,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg839 - -lemma sg5719 : RowSquare [6,5,2,2,2,1] [7,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg3245 - -lemma sg5720 : RowSquare [6,5,2,2,2,1] [7,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg842 - -lemma sg5721 : RowSquare [6,5,2,2,2,1] [7,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg116 sg1206 - -lemma sg5722 : RowSquare [6,5,2,2,2,1] [7,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg842 - -lemma sg5723 : RowSquare [6,5,2,2,2,1] [8,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg3244 - -lemma sg5724 : RowSquare [6,5,2,2,2,1] [8,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg3246 - -lemma sg5725 : RowSquare [6,5,2,2,2,1] [8,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg3248 - -lemma sg5726 : RowSquare [6,5,2,2,2,1] [8,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg842 - -lemma sg5727 : RowSquare [6,5,2,2,2,1] [8,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg2544 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes10 + +namespace OAI + +/-! Semigroup Nodes 12. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg5327 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg589 sg709 + +lemma sg5328 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2] := by + exact rowSquare_join (by decide) sg413 sg1007 + +lemma sg5329 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,1] := by + exact rowSquare_join (by decide) sg590 sg709 + +lemma sg5330 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg710 + +lemma sg5331 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,1] := by + exact rowSquare_join (by decide) sg590 sg710 + +lemma sg5332 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg418 sg998 + +lemma sg5333 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg418 sg999 + +lemma sg5334 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg414 sg1006 + +lemma sg5335 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,2] := by + exact rowSquare_join (by decide) sg418 sg1001 + +lemma sg5336 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg415 sg1006 + +lemma sg5337 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,1] := by + exact rowSquare_join (by decide) sg414 sg1007 + +lemma sg5338 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,3,3] := by + exact rowSquare_join (by decide) sg414 sg1008 + +lemma sg5339 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,4,1,1] := by + exact rowSquare_join (by decide) sg415 sg1007 + +lemma sg5340 : RowSquare [5,3,1,1,1,1,1,1,1,1,1,1] [7,5,4,2] := by + exact rowSquare_join (by decide) sg415 sg1008 + +lemma sg5341 : RowSquare [5,3,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg389 sg998 + +lemma sg5342 : RowSquare [5,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg998 + +lemma sg5343 : RowSquare [5,3,2,1,1,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg696 + +lemma sg5344 : RowSquare [5,3,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg413 sg910 + +lemma sg5345 : RowSquare [5,3,2,1,1,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg414 sg910 + +lemma sg5346 : RowSquare [5,3,2,1,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg415 sg910 + +lemma sg5347 : RowSquare [5,3,2,2,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg389 sg910 + +lemma sg5348 : RowSquare [5,3,2,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg910 + +lemma sg5349 : RowSquare [5,3,2,2,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg646 + +lemma sg5350 : RowSquare [5,3,2,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg647 + +lemma sg5351 : RowSquare [5,3,2,2,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg104 sg1682 + +lemma sg5352 : RowSquare [5,3,2,2,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg105 sg1682 + +lemma sg5353 : RowSquare [5,3,2,2,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg649 + +lemma sg5354 : RowSquare [5,3,2,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg396 sg910 + +lemma sg5355 : RowSquare [5,3,2,2,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg650 + +lemma sg5356 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg106 sg1682 + +lemma sg5357 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg397 sg910 + +lemma sg5358 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg651 + +lemma sg5359 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg398 sg910 + +lemma sg5360 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg652 + +lemma sg5361 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg653 + +lemma sg5362 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg399 sg910 + +lemma sg5363 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg654 + +lemma sg5364 : RowSquare [5,3,2,2,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg655 + +lemma sg5365 : RowSquare [5,3,3,2,1,1,1,1,1] [4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg2137 + +lemma sg5366 : RowSquare [5,3,3,2,1,1,1,1,1] [4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg2137 + +lemma sg5367 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg673 + +lemma sg5368 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg674 + +lemma sg5369 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg370 sg998 + +lemma sg5370 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg675 + +lemma sg5371 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg676 + +lemma sg5372 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg370 sg1000 + +lemma sg5373 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg370 sg1001 + +lemma sg5374 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg371 sg998 + +lemma sg5375 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg372 sg998 + +lemma sg5376 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg998 + +lemma sg5377 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg371 sg1000 + +lemma sg5378 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg371 sg1001 + +lemma sg5379 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg372 sg1000 + +lemma sg5380 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,4,3,3] := by + exact rowSquare_join (by decide) sg372 sg1001 + +lemma sg5381 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg373 sg1000 + +lemma sg5382 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [4,4,4,4,2] := by + exact rowSquare_join (by decide) sg373 sg1001 + +lemma sg5383 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg677 + +lemma sg5384 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg587 sg673 + +lemma sg5385 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg678 + +lemma sg5386 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg674 + +lemma sg5387 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg679 + +lemma sg5388 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg675 + +lemma sg5389 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg676 + +lemma sg5390 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg374 sg1000 + +lemma sg5391 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg374 sg1001 + +lemma sg5392 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg680 + +lemma sg5393 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg375 sg998 + +lemma sg5394 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg681 + +lemma sg5395 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg376 sg998 + +lemma sg5396 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,4,3,3,3] := by + exact rowSquare_join (by decide) sg375 sg1001 + +lemma sg5397 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg377 sg998 + +lemma sg5398 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg1006 + +lemma sg5399 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg682 + +lemma sg5400 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg677 + +lemma sg5401 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg683 + +lemma sg5402 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg678 + +lemma sg5403 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg684 + +lemma sg5404 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg679 + +lemma sg5405 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,3,3,3,3] := by + exact rowSquare_join (by decide) sg379 sg1001 + +lemma sg5406 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg685 + +lemma sg5407 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg680 + +lemma sg5408 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg681 + +lemma sg5409 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg686 + +lemma sg5410 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg382 sg998 + +lemma sg5411 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg383 sg998 + +lemma sg5412 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [6,6,2,2,2] := by + exact rowSquare_join (by decide) sg383 sg1001 + +lemma sg5413 : RowSquare [5,4,1,1,1,1,1,1,1,1,1] [10,4,4] := by + exact rowSquare_join (by decide) sg4 sg3162 + +lemma sg5414 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg910 + +lemma sg5415 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg613 + +lemma sg5416 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg910 + +lemma sg5417 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg330 sg998 + +lemma sg5418 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg372 sg910 + +lemma sg5419 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg615 + +lemma sg5420 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg999 + +lemma sg5421 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg910 + +lemma sg5422 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg1000 + +lemma sg5423 : RowSquare [5,4,2,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1001 + +lemma sg5424 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg374 sg910 + +lemma sg5425 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg617 + +lemma sg5426 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg376 sg910 + +lemma sg5427 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg589 + +lemma sg5428 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg378 sg910 + +lemma sg5429 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg623 + +lemma sg5430 : RowSquare [5,4,2,1,1,1,1,1,1,1] [4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg589 + +lemma sg5431 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg379 sg910 + +lemma sg5432 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg624 + +lemma sg5433 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg4674 + +lemma sg5434 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg380 sg910 + +lemma sg5435 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg381 sg910 + +lemma sg5436 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg4675 + +lemma sg5437 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg4676 + +lemma sg5438 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg4677 + +lemma sg5439 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg4678 + +lemma sg5440 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,4,4,4,1] := by + exact rowSquare_join (by decide) sg0 sg4684 + +lemma sg5441 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg383 sg910 + +lemma sg5442 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg628 + +lemma sg5443 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg920 + +lemma sg5444 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1016 + +lemma sg5445 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg623 + +lemma sg5446 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg615 sg596 + +lemma sg5447 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,4,4] := by + exact rowSquare_join (by decide) sg373 sg922 + +lemma sg5448 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg623 + +lemma sg5449 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,5,2,1] := by + exact rowSquare_join (by decide) sg590 sg623 + +lemma sg5450 : RowSquare [5,4,2,1,1,1,1,1,1,1] [5,5,5,3] := by + exact rowSquare_join (by decide) sg373 sg923 + +lemma sg5451 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg384 sg910 + +lemma sg5452 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg629 + +lemma sg5453 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg4685 + +lemma sg5454 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg4686 + +lemma sg5455 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg385 sg910 + +lemma sg5456 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg630 + +lemma sg5457 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg4687 + +lemma sg5458 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg4688 + +lemma sg5459 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg631 + +lemma sg5460 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg4689 + +lemma sg5461 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg3832 + +lemma sg5462 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg4690 + +lemma sg5463 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3833 + +lemma sg5464 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg3834 + +lemma sg5465 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,3,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg3835 + +lemma sg5466 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg386 sg910 + +lemma sg5467 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg3839 + +lemma sg5468 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg632 + +lemma sg5469 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,5,4,2,1] := by + exact rowSquare_join (by decide) sg4 sg3165 + +lemma sg5470 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,5,4,3] := by + exact rowSquare_join (by decide) sg4 sg3166 + +lemma sg5471 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,5,5,1,1] := by + exact rowSquare_join (by decide) sg4 sg3167 + +lemma sg5472 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,5,5,2] := by + exact rowSquare_join (by decide) sg4 sg3168 + +lemma sg5473 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1023 + +lemma sg5474 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg371 sg931 + +lemma sg5475 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,2,2,2] := by + exact rowSquare_join (by decide) sg621 sg595 + +lemma sg5476 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg615 sg602 + +lemma sg5477 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg3169 + +lemma sg5478 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,3,3] := by + exact rowSquare_join (by decide) sg373 sg931 + +lemma sg5479 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,4,1,1] := by + exact rowSquare_join (by decide) sg4 sg3170 + +lemma sg5480 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,4,2] := by + exact rowSquare_join (by decide) sg4 sg3171 + +lemma sg5481 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,5,1] := by + exact rowSquare_join (by decide) sg4 sg3172 + +lemma sg5482 : RowSquare [5,4,2,1,1,1,1,1,1,1] [6,6,6] := by + exact rowSquare_join (by decide) sg4 sg3173 + +lemma sg5483 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg387 sg910 + +lemma sg5484 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg633 + +lemma sg5485 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3840 + +lemma sg5486 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg388 sg910 + +lemma sg5487 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg634 + +lemma sg5488 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3841 + +lemma sg5489 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg3842 + +lemma sg5490 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3843 + +lemma sg5491 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg3174 + +lemma sg5492 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg3844 + +lemma sg5493 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg3845 + +lemma sg5494 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg635 + +lemma sg5495 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg4693 + +lemma sg5496 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg3846 + +lemma sg5497 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg3175 + +lemma sg5498 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,4,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg3176 + +lemma sg5499 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg3177 + +lemma sg5500 : RowSquare [5,4,2,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg4695 + +lemma sg5501 : RowSquare [5,4,2,1,1,1,1,1,1,1] [9,9] := by + exact rowSquare_join (by decide) sg14 sg2490 + +lemma sg5502 : RowSquare [5,4,2,1,1,1,1,1,1,1] [10,8] := by + exact rowSquare_join (by decide) sg42 sg2014 + +lemma sg5503 : RowSquare [5,4,2,1,1,1,1,1,1,1] [11,7] := by + exact rowSquare_join (by decide) sg80 sg1577 + +lemma sg5504 : RowSquare [5,4,2,1,1,1,1,1,1,1] [12,6] := by + exact rowSquare_join (by decide) sg80 sg1578 + +lemma sg5505 : RowSquare [5,4,2,1,1,1,1,1,1,1] [13,5] := by + exact rowSquare_join (by decide) sg174 sg1120 + +lemma sg5506 : RowSquare [5,4,2,1,1,1,1,1,1,1] [14,4] := by + exact rowSquare_join (by decide) sg363 sg718 + +lemma sg5507 : RowSquare [5,4,2,2,1,1,1,1,1] [2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg910 + +lemma sg5508 : RowSquare [5,4,2,2,1,1,1,1,1] [3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg330 sg912 + +lemma sg5509 : RowSquare [5,4,2,2,1,1,1,1,1] [3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg915 + +lemma sg5510 : RowSquare [5,4,2,2,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg2596 + +lemma sg5511 : RowSquare [5,4,2,2,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg2597 + +lemma sg5512 : RowSquare [5,4,2,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg2598 + +lemma sg5513 : RowSquare [5,4,2,2,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg4697 + +lemma sg5514 : RowSquare [5,4,2,2,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg4698 + +lemma sg5515 : RowSquare [5,4,2,2,2,2,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg2596 + +lemma sg5516 : RowSquare [5,4,2,2,2,2,1] [5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg2603 + +lemma sg5517 : RowSquare [5,4,2,2,2,2,1] [5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg2607 + +lemma sg5518 : RowSquare [5,4,2,2,2,2,1] [5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg2608 + +lemma sg5519 : RowSquare [5,4,2,2,2,2,1] [6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg2597 + +lemma sg5520 : RowSquare [5,4,2,2,2,2,1] [6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg2601 + +lemma sg5521 : RowSquare [5,4,2,2,2,2,1] [6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg2602 + +lemma sg5522 : RowSquare [5,4,2,2,2,2,1] [6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg2611 + +lemma sg5523 : RowSquare [5,4,2,2,2,2,1] [6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg302 sg838 + +lemma sg5524 : RowSquare [5,4,3,2,1,1,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg3299 + +lemma sg5525 : RowSquare [5,5,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg586 + +lemma sg5526 : RowSquare [5,5,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg587 + +lemma sg5527 : RowSquare [5,5,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg588 + +lemma sg5528 : RowSquare [5,5,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg589 + +lemma sg5529 : RowSquare [5,5,1,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg590 + +lemma sg5530 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg591 + +lemma sg5531 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg587 + +lemma sg5532 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg593 + +lemma sg5533 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg312 sg999 + +lemma sg5534 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg594 + +lemma sg5535 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg312 sg1000 + +lemma sg5536 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg595 + +lemma sg5537 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg313 sg998 + +lemma sg5538 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg588 + +lemma sg5539 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg596 + +lemma sg5540 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg314 sg998 + +lemma sg5541 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg588 sg589 + +lemma sg5542 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg315 sg998 + +lemma sg5543 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg590 + +lemma sg5544 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg313 sg1000 + +lemma sg5545 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg313 sg1001 + +lemma sg5546 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg314 sg999 + +lemma sg5547 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg589 sg589 + +lemma sg5548 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg315 sg999 + +lemma sg5549 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg589 sg590 + +lemma sg5550 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,3,3] := by + exact rowSquare_join (by decide) sg314 sg1001 + +lemma sg5551 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg315 sg1000 + +lemma sg5552 : RowSquare [5,5,1,1,1,1,1,1,1,1] [4,4,4,4,2] := by + exact rowSquare_join (by decide) sg590 sg590 + +lemma sg5553 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg597 + +lemma sg5554 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg587 sg591 + +lemma sg5555 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg592 + +lemma sg5556 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg591 + +lemma sg5557 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg591 sg589 + +lemma sg5558 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg594 + +lemma sg5559 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg316 sg1000 + +lemma sg5560 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg316 sg1001 + +lemma sg5561 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg588 sg592 + +lemma sg5562 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg601 + +lemma sg5563 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg589 sg592 + +lemma sg5564 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg594 + +lemma sg5565 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,4,4,4,1] := by + exact rowSquare_join (by decide) sg590 sg594 + +lemma sg5566 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg602 + +lemma sg5567 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg319 sg998 + +lemma sg5568 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg595 + +lemma sg5569 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg313 sg1006 + +lemma sg5570 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg320 sg998 + +lemma sg5571 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg596 + +lemma sg5572 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg313 sg1008 + +lemma sg5573 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,3,3,2] := by + exact rowSquare_join (by decide) sg590 sg595 + +lemma sg5574 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg320 sg999 + +lemma sg5575 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg589 sg596 + +lemma sg5576 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,4,2,2] := by + exact rowSquare_join (by decide) sg314 sg1007 + +lemma sg5577 : RowSquare [5,5,1,1,1,1,1,1,1,1] [5,5,4,4] := by + exact rowSquare_join (by decide) sg315 sg1008 + +lemma sg5578 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg603 + +lemma sg5579 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg597 + +lemma sg5580 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg3866 + +lemma sg5581 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3869 + +lemma sg5582 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg3875 + +lemma sg5583 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg324 sg998 + +lemma sg5584 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg313 sg1015 + +lemma sg5585 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,6,2,2,2] := by + exact rowSquare_join (by decide) sg595 sg595 + +lemma sg5586 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,6,3,3] := by + exact rowSquare_join (by decide) sg315 sg1015 + +lemma sg5587 : RowSquare [5,5,1,1,1,1,1,1,1,1] [6,6,4,1,1] := by + exact rowSquare_join (by decide) sg314 sg1016 + +lemma sg5588 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg608 + +lemma sg5589 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg603 + +lemma sg5590 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg3876 + +lemma sg5591 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,5,5,1] := by + exact rowSquare_join (by decide) sg13 sg2497 + +lemma sg5592 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,7,1,1,1,1] := by + exact rowSquare_join (by decide) sg313 sg1023 + +lemma sg5593 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,7,2,2] := by + exact rowSquare_join (by decide) sg315 sg1023 + +lemma sg5594 : RowSquare [5,5,1,1,1,1,1,1,1,1] [7,7,4] := by + exact rowSquare_join (by decide) sg320 sg1016 + +lemma sg5595 : RowSquare [5,5,1,1,1,1,1,1,1,1] [8,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg611 + +lemma sg5596 : RowSquare [5,5,1,1,1,1,1,1,1,1] [8,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg608 + +lemma sg5597 : RowSquare [5,5,1,1,1,1,1,1,1,1] [8,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg3896 + +lemma sg5598 : RowSquare [5,5,1,1,1,1,1,1,1,1] [8,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg3897 + +lemma sg5599 : RowSquare [5,5,1,1,1,1,1,1,1,1] [8,8,1,1] := by + exact rowSquare_join (by decide) sg319 sg1023 + +lemma sg5600 : RowSquare [5,5,1,1,1,1,1,1,1,1] [9,9] := by + exact rowSquare_join (by decide) sg324 sg1023 + +lemma sg5601 : RowSquare [5,5,2,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg313 sg910 + +lemma sg5602 : RowSquare [5,5,2,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg314 sg910 + +lemma sg5603 : RowSquare [5,5,2,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg536 + +lemma sg5604 : RowSquare [5,5,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg315 sg910 + +lemma sg5605 : RowSquare [5,5,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg534 + +lemma sg5606 : RowSquare [5,5,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg324 sg910 + +lemma sg5607 : RowSquare [5,5,2,2,2,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg3999 + +lemma sg5608 : RowSquare [5,5,2,2,2,1,1] [4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg4002 + +lemma sg5609 : RowSquare [5,5,2,2,2,1,1] [4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg4003 + +lemma sg5610 : RowSquare [5,5,2,2,2,1,1] [4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg4004 + +lemma sg5611 : RowSquare [5,5,2,2,2,1,1] [4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg4005 + +lemma sg5612 : RowSquare [5,5,2,2,2,1,1] [5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg4009 + +lemma sg5613 : RowSquare [5,5,2,2,2,1,1] [5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg4010 + +lemma sg5614 : RowSquare [5,5,2,2,2,1,1] [5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg4011 + +lemma sg5615 : RowSquare [6,4,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg1327 + +lemma sg5616 : RowSquare [6,4,1,1,1,1,1,1,1,1] [3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg181 sg1327 + +lemma sg5617 : RowSquare [6,4,1,1,1,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg182 sg1327 + +lemma sg5618 : RowSquare [6,4,1,1,1,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg183 sg1327 + +lemma sg5619 : RowSquare [6,4,1,1,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg184 sg1327 + +lemma sg5620 : RowSquare [6,4,1,1,1,1,1,1,1,1] [4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg179 sg1332 + +lemma sg5621 : RowSquare [6,4,1,1,1,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg186 sg1327 + +lemma sg5622 : RowSquare [6,4,1,1,1,1,1,1,1,1] [5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg187 sg1327 + +lemma sg5623 : RowSquare [6,4,1,1,1,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg188 sg1327 + +lemma sg5624 : RowSquare [6,4,1,1,1,1,1,1,1,1] [6,5,5,1,1] := by + exact rowSquare_join (by decide) sg4 sg3187 + +lemma sg5625 : RowSquare [6,4,1,1,1,1,1,1,1,1] [6,5,5,2] := by + exact rowSquare_join (by decide) sg4 sg3188 + +lemma sg5626 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,5,5,1] := by + exact rowSquare_join (by decide) sg4 sg3190 + +lemma sg5627 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,6,4,1] := by + exact rowSquare_join (by decide) sg4 sg3191 + +lemma sg5628 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,6,5] := by + exact rowSquare_join (by decide) sg4 sg3192 + +lemma sg5629 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,7,1,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg909 + +lemma sg5630 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,7,2,1,1] := by + exact rowSquare_join (by decide) sg372 sg909 + +lemma sg5631 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,7,2,2] := by + exact rowSquare_join (by decide) sg373 sg909 + +lemma sg5632 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,7,3,1] := by + exact rowSquare_join (by decide) sg377 sg903 + +lemma sg5633 : RowSquare [6,4,1,1,1,1,1,1,1,1] [7,7,4] := by + exact rowSquare_join (by decide) sg378 sg903 + +lemma sg5634 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg191 sg1328 + +lemma sg5635 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3945 + +lemma sg5636 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg2511 + +lemma sg5637 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6 sg3186 + +lemma sg5638 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg3897 + +lemma sg5639 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3946 + +lemma sg5640 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg3193 + +lemma sg5641 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg2512 + +lemma sg5642 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg3189 + +lemma sg5643 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg3194 + +lemma sg5644 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg2513 + +lemma sg5645 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,3,2,2] := by + exact rowSquare_join (by decide) sg16 sg2495 + +lemma sg5646 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg2514 + +lemma sg5647 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3947 + +lemma sg5648 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg2508 + +lemma sg5649 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg2515 + +lemma sg5650 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg2495 + +lemma sg5651 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg3195 + +lemma sg5652 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg2516 + +lemma sg5653 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg2517 + +lemma sg5654 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,4,1,1] := by + exact rowSquare_join (by decide) sg16 sg2496 + +lemma sg5655 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,4,4,2] := by + exact rowSquare_join (by decide) sg13 sg2518 + +lemma sg5656 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg2509 + +lemma sg5657 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg2510 + +lemma sg5658 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg2519 + +lemma sg5659 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,5,3,1,1] := by + exact rowSquare_join (by decide) sg17 sg2496 + +lemma sg5660 : RowSquare [6,4,1,1,1,1,1,1,1,1] [8,5,5] := by + exact rowSquare_join (by decide) sg16 sg2497 + +lemma sg5661 : RowSquare [6,4,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg330 sg889 + +lemma sg5662 : RowSquare [6,4,2,1,1,1,1,1,1] [3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg890 + +lemma sg5663 : RowSquare [6,4,2,1,1,1,1,1,1] [3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg892 + +lemma sg5664 : RowSquare [6,4,2,1,1,1,1,1,1] [4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg71 sg1754 + +lemma sg5665 : RowSquare [6,4,2,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3957 + +lemma sg5666 : RowSquare [6,4,2,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg153 sg1327 + +lemma sg5667 : RowSquare [6,4,2,1,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg3198 + +lemma sg5668 : RowSquare [6,4,2,1,1,1,1,1,1] [7,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3958 + +lemma sg5669 : RowSquare [6,4,3,1,1,1,1,1] [3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg1196 + +lemma sg5670 : RowSquare [6,4,3,2,2,1] [3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg1616 + +lemma sg5671 : RowSquare [6,5,1,1,1,1,1,1,1] [8,5,5] := by + exact rowSquare_join (by decide) sg83 sg1583 + +lemma sg5673 : RowSquare [6,5,2,2,2,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg508 sg474 + +lemma sg5674 : RowSquare [6,5,2,2,2,1] [2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg506 sg474 + +lemma sg5675 : RowSquare [6,5,2,2,2,1] [2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg503 sg473 + +lemma sg5676 : RowSquare [6,5,2,2,2,1] [2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg503 sg472 + +lemma sg5677 : RowSquare [6,5,2,2,2,1] [2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg503 sg471 + +lemma sg5678 : RowSquare [6,5,2,2,2,1] [2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg503 sg470 + +lemma sg5679 : RowSquare [6,5,2,2,2,1] [2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg281 sg780 + +lemma sg5680 : RowSquare [6,5,2,2,2,1] [3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg505 sg474 + +lemma sg5681 : RowSquare [6,5,2,2,2,1] [3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg500 sg473 + +lemma sg5682 : RowSquare [6,5,2,2,2,1] [3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg500 sg472 + +lemma sg5683 : RowSquare [6,5,2,2,2,1] [3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg500 sg471 + +lemma sg5684 : RowSquare [6,5,2,2,2,1] [3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg500 sg470 + +lemma sg5685 : RowSquare [6,5,2,2,2,1] [3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg502 sg474 + +lemma sg5686 : RowSquare [6,5,2,2,2,1] [3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg499 sg474 + +lemma sg5687 : RowSquare [6,5,2,2,2,1] [3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg499 sg472 + +lemma sg5688 : RowSquare [6,5,2,2,2,1] [3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg499 sg471 + +lemma sg5689 : RowSquare [6,5,2,2,2,1] [3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg499 sg470 + +lemma sg5690 : RowSquare [6,5,2,2,2,1] [3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg500 sg465 + +lemma sg5691 : RowSquare [6,5,2,2,2,1] [3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg496 sg472 + +lemma sg5692 : RowSquare [6,5,2,2,2,1] [3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg496 sg471 + +lemma sg5693 : RowSquare [6,5,2,2,2,1] [3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg496 sg470 + +lemma sg5694 : RowSquare [6,5,2,2,2,1] [3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg496 sg468 + +lemma sg5695 : RowSquare [6,5,2,2,2,1] [3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg496 sg464 + +lemma sg5696 : RowSquare [6,5,2,2,2,1] [3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg496 sg459 + +lemma sg5697 : RowSquare [6,5,2,2,2,1] [4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg498 sg474 + +lemma sg5698 : RowSquare [6,5,2,2,2,1] [4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg495 sg473 + +lemma sg5699 : RowSquare [6,5,2,2,2,1] [4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg495 sg472 + +lemma sg5700 : RowSquare [6,5,2,2,2,1] [4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg495 sg471 + +lemma sg5701 : RowSquare [6,5,2,2,2,1] [4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg495 sg470 + +lemma sg5702 : RowSquare [6,5,2,2,2,1] [4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg493 sg474 + +lemma sg5703 : RowSquare [6,5,2,2,2,1] [4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg493 sg473 + +lemma sg5704 : RowSquare [6,5,2,2,2,1] [4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg493 sg470 + +lemma sg5705 : RowSquare [6,5,2,2,2,1] [4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg493 sg469 + +lemma sg5706 : RowSquare [6,5,2,2,2,1] [5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg490 sg474 + +lemma sg5707 : RowSquare [6,5,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg3243 + +lemma sg5708 : RowSquare [6,5,2,2,2,1] [7,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg3244 + +lemma sg5709 : RowSquare [6,5,2,2,2,1] [7,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg3246 + +lemma sg5710 : RowSquare [6,5,2,2,2,1] [7,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg2544 + +lemma sg5711 : RowSquare [6,5,2,2,2,1] [7,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg3989 + +lemma sg5712 : RowSquare [6,5,2,2,2,1] [7,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg3990 + +lemma sg5713 : RowSquare [6,5,2,2,2,1] [7,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg2543 + +lemma sg5714 : RowSquare [6,5,2,2,2,1] [7,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg3247 + +lemma sg5715 : RowSquare [6,5,2,2,2,1] [7,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg838 + +lemma sg5716 : RowSquare [6,5,2,2,2,1] [7,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg3991 + +lemma sg5717 : RowSquare [6,5,2,2,2,1] [7,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg842 + +lemma sg5718 : RowSquare [6,5,2,2,2,1] [7,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg839 + +lemma sg5719 : RowSquare [6,5,2,2,2,1] [7,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg3245 + +lemma sg5720 : RowSquare [6,5,2,2,2,1] [7,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg842 + +lemma sg5721 : RowSquare [6,5,2,2,2,1] [7,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg116 sg1206 + +lemma sg5722 : RowSquare [6,5,2,2,2,1] [7,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg842 + +lemma sg5723 : RowSquare [6,5,2,2,2,1] [8,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg3244 + +lemma sg5724 : RowSquare [6,5,2,2,2,1] [8,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg3246 + +lemma sg5725 : RowSquare [6,5,2,2,2,1] [8,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg3248 + +lemma sg5726 : RowSquare [6,5,2,2,2,1] [8,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg842 + +lemma sg5727 : RowSquare [6,5,2,2,2,1] [8,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg2544 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes13.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes13.lean index a51f8ae5639f727bae7feab2ec3f97b796e83c47..95739332ca8e944c4eba34d73049b14687e2802b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes13.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes13.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes10 - -namespace OAI - -/-! Semigroup Nodes 13. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg5728 : RowSquare [6,5,2,2,2,1] [8,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg243 sg842 - -lemma sg5729 : RowSquare [6,5,2,2,2,1] [9,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg2543 - -lemma sg5730 : RowSquare [6,5,2,2,2,1] [9,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg3248 - -lemma sg5731 : RowSquare [6,5,3,2,1,1] [3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg1616 - -lemma sg5732 : RowSquare [6,6,1,1,1,1,1,1] [3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg2546 - -lemma sg5733 : RowSquare [7,5,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg21 sg2251 - -lemma sg5734 : RowSquare [7,5,3,1,1,1] [4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg306 sg810 - -lemma sg5736 : RowSquare [8,3,2,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg705 sg431 - -lemma sg5737 : RowSquare [8,3,2,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg703 sg430 - -lemma sg5738 : RowSquare [8,3,2,1,1,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg703 sg429 - -lemma sg5739 : RowSquare [8,3,2,1,1,1,1,1] [2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg396 sg733 - -lemma sg5740 : RowSquare [8,3,2,1,1,1,1,1] [2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg223 sg1141 - -lemma sg5741 : RowSquare [8,3,2,1,1,1,1,1] [2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg92 sg1625 - -lemma sg5742 : RowSquare [8,3,2,1,1,1,1,1] [3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg220 sg1140 - -lemma sg5743 : RowSquare [8,3,2,1,1,1,1,1] [3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg89 sg1624 - -lemma sg5744 : RowSquare [8,3,2,1,1,1,1,1] [3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg89 sg1623 - -lemma sg5745 : RowSquare [8,3,2,1,1,1,1,1] [3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg220 sg1138 - -lemma sg5746 : RowSquare [8,3,2,1,1,1,1,1] [3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg89 sg1621 - -lemma sg5747 : RowSquare [8,3,2,1,1,1,1,1] [4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg88 sg1623 - -lemma sg5748 : RowSquare [8,3,2,1,1,1,1,1] [5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg1622 - -lemma sg5749 : RowSquare [8,3,3,1,1,1,1] [3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg2120 - -lemma sg5750 : RowSquare [8,4,2,1,1,1,1] [4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg2123 - -lemma sg5751 : RowSquare [8,4,3,1,1,1] [4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg306 sg893 - -lemma sg5752 : RowSquare [8,4,3,2,1] [4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg513 - -lemma sg5753 : RowSquare [8,4,3,3] [4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg330 sg835 - -lemma sg5754 : RowSquare [8,5,3,1,1] [3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg306 sg912 - -lemma sg5755 : RowSquare [8,5,3,1,1] [3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg1688 - -lemma sg5756 : RowSquare [8,7,2,1] [3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg849 - -lemma sg5758 : RowSquare [9,2,1,1,1,1,1,1,1] [2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg425 sg719 - -lemma sg5759 : RowSquare [9,2,1,1,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg232 sg1136 - -lemma sg5760 : RowSquare [9,2,1,1,1,1,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg105 sg1620 - -lemma sg5761 : RowSquare [9,2,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg2114 - -lemma sg5762 : RowSquare [9,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg2618 - -lemma sg5763 : RowSquare [9,3,2,2,1,1] [4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg142 sg1332 - -lemma sg5764 : RowSquare [9,3,3,1,1,1] [4,4,4,3,3] := by - exact rowSquare_join (by decide) sg349 sg892 - -lemma sg5765 : RowSquare [9,3,3,1,1,1] [4,4,4,4,2] := by - exact rowSquare_join (by decide) sg350 sg892 - -lemma sg5766 : RowSquare [9,3,3,2,1] [4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg373 sg828 - -lemma sg5767 : RowSquare [9,3,3,2,1] [4,4,4,4,2] := by - exact rowSquare_join (by decide) sg551 sg590 - -lemma sg5768 : RowSquare [9,4,2,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg1754 - -lemma sg5769 : RowSquare [9,4,2,1,1,1] [4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg357 sg889 - -lemma sg5770 : RowSquare [9,4,2,1,1,1] [4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg356 sg892 - -lemma sg5771 : RowSquare [9,4,2,1,1,1] [4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg390 sg808 - -lemma sg5772 : RowSquare [9,4,3,2] [3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg943 - -lemma sg5773 : RowSquare [9,4,3,2] [4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg371 sg853 - -lemma sg5774 : RowSquare [9,4,3,2] [4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg550 - -lemma sg5775 : RowSquare [9,4,3,2] [4,4,4,4,2] := by - exact rowSquare_join (by decide) sg616 sg551 - -lemma sg5776 : RowSquare [10,2,2,2,2] [2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg586 - -lemma sg5777 : RowSquare [10,3,2,1,1,1] [4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg195 sg1330 - -lemma sg5778 : RowSquare [10,3,2,2,1] [3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg330 sg998 - -lemma sg5779 : RowSquare [10,3,2,2,1] [3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg616 - -lemma sg5780 : RowSquare [10,3,2,2,1] [3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg1000 - -lemma sg5781 : RowSquare [10,3,2,2,1] [4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg371 sg914 - -lemma sg5782 : RowSquare [10,3,2,2,1] [4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg371 sg915 - -lemma sg5783 : RowSquare [10,3,2,2,1] [4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg589 - -lemma sg5784 : RowSquare [10,3,2,2,1] [4,4,4,3,3] := by - exact rowSquare_join (by decide) sg372 sg915 - -lemma sg5785 : RowSquare [10,3,2,2,1] [4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg373 sg914 - -lemma sg5786 : RowSquare [10,3,2,2,1] [5,5,4,4] := by - exact rowSquare_join (by decide) sg373 sg922 - -lemma sg5787 : RowSquare [10,3,3,1,1] [4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg348 sg1000 - -lemma sg5788 : RowSquare [10,3,3,1,1] [4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg636 sg589 - -lemma sg5789 : RowSquare [10,3,3,1,1] [4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg350 sg1000 - -lemma sg5790 : RowSquare [10,4,2,2] [4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg615 - -lemma sg5791 : RowSquare [10,4,3,1] [4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg636 sg615 - -lemma sg5792 : RowSquare [11,3,2,2] [4,4,4,3,3] := by - exact rowSquare_join (by decide) sg372 sg1033 - -lemma sg5793 : RowSquare [11,3,2,2] [5,5,4,4] := by - exact rowSquare_join (by decide) sg373 sg1040 - -lemma sg5794 : RowSquare [3,3,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,3] := by - exact rowSquare_join (by decide) sg692 sg1061 - -lemma sg5795 : RowSquare [3,3,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,2] := by - exact rowSquare_join (by decide) sg693 sg1061 - -lemma sg5796 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg692 sg1031 - -lemma sg5797 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg693 sg1031 - -lemma sg5798 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg692 sg1032 - -lemma sg5799 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3] := by - exact rowSquare_join (by decide) sg692 sg1033 - -lemma sg5800 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg693 sg1032 - -lemma sg5801 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2] := by - exact rowSquare_join (by decide) sg693 sg1033 - -lemma sg5802 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg1520 - -lemma sg5803 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg694 sg1032 - -lemma sg5804 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3] := by - exact rowSquare_join (by decide) sg694 sg1033 - -lemma sg5805 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg673 sg1068 - -lemma sg5806 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg673 sg1069 - -lemma sg5807 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg697 sg1032 - -lemma sg5808 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg697 sg1033 - -lemma sg5809 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg673 sg1070 - -lemma sg5810 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg614 sg1104 - -lemma sg5811 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg643 sg1093 - -lemma sg5812 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg614 sg1105 - -lemma sg5813 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg674 sg1069 - -lemma sg5814 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,3] := by - exact rowSquare_join (by decide) sg698 sg1033 - -lemma sg5815 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg643 sg1094 - -lemma sg5816 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,1] := by - exact rowSquare_join (by decide) sg644 sg1095 - -lemma sg5817 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg614 sg1106 - -lemma sg5818 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg674 sg1070 - -lemma sg5819 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg694 sg1038 - -lemma sg5820 : RowSquare [4,3,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg374 sg1455 - -lemma sg5821 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg673 sg1092 - -lemma sg5822 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg673 sg1093 - -lemma sg5823 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg673 sg1094 - -lemma sg5824 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg673 sg1095 - -lemma sg5825 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg674 sg1093 - -lemma sg5826 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg674 sg1094 - -lemma sg5827 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg674 sg1095 - -lemma sg5828 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2] := by - exact rowSquare_join (by decide) sg675 sg1094 - -lemma sg5829 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,1] := by - exact rowSquare_join (by decide) sg675 sg1095 - -lemma sg5830 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,4] := by - exact rowSquare_join (by decide) sg676 sg1095 - -lemma sg5831 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg673 sg1031 - -lemma sg5832 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg673 sg1032 - -lemma sg5833 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg673 sg1033 - -lemma sg5834 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg370 sg1520 - -lemma sg5835 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg674 sg1031 - -lemma sg5836 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg674 sg1032 - -lemma sg5837 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg674 sg1033 - -lemma sg5838 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg675 sg1031 - -lemma sg5839 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg676 sg1031 - -lemma sg5840 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg675 sg1032 - -lemma sg5841 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3] := by - exact rowSquare_join (by decide) sg675 sg1033 - -lemma sg5842 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg676 sg1032 - -lemma sg5843 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2] := by - exact rowSquare_join (by decide) sg676 sg1033 - -lemma sg5844 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg1520 - -lemma sg5845 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg372 sg1520 - -lemma sg5846 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg1521 - -lemma sg5847 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg1520 - -lemma sg5848 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg1522 - -lemma sg5849 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg371 sg1523 - -lemma sg5850 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2] := by - exact rowSquare_join (by decide) sg372 sg1522 - -lemma sg5851 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,1] := by - exact rowSquare_join (by decide) sg372 sg1523 - -lemma sg5852 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,5,4] := by - exact rowSquare_join (by decide) sg373 sg1523 - -lemma sg5853 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg613 sg1092 - -lemma sg5854 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg1093 - -lemma sg5855 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg614 sg1092 - -lemma sg5856 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1094 - -lemma sg5857 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg673 sg1036 - -lemma sg5858 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1095 - -lemma sg5859 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg677 sg1032 - -lemma sg5860 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg677 sg1033 - -lemma sg5861 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg614 sg1093 - -lemma sg5862 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg614 sg1094 - -lemma sg5863 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg1093 - -lemma sg5864 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3] := by - exact rowSquare_join (by decide) sg678 sg1033 - -lemma sg5865 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg615 sg1094 - -lemma sg5866 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg1527 - -lemma sg5867 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg674 sg1038 - -lemma sg5868 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg674 sg1039 - -lemma sg5869 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg674 sg1040 - -lemma sg5870 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg681 sg1031 - -lemma sg5871 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg674 sg1041 - -lemma sg5872 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,2] := by - exact rowSquare_join (by decide) sg675 sg1039 - -lemma sg5873 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,1] := by - exact rowSquare_join (by decide) sg675 sg1040 - -lemma sg5874 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,4,4] := by - exact rowSquare_join (by decide) sg676 sg1040 - -lemma sg5875 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg377 sg1520 - -lemma sg5876 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg1527 - -lemma sg5877 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg378 sg1520 - -lemma sg5878 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg371 sg1528 - -lemma sg5879 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,2] := by - exact rowSquare_join (by decide) sg372 sg1527 - -lemma sg5880 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,1] := by - exact rowSquare_join (by decide) sg373 sg1527 - -lemma sg5881 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg1529 - -lemma sg5882 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,4,2,1] := by - exact rowSquare_join (by decide) sg372 sg1528 - -lemma sg5883 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,4,3] := by - exact rowSquare_join (by decide) sg373 sg1528 - -lemma sg5884 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,5,1,1] := by - exact rowSquare_join (by decide) sg372 sg1529 - -lemma sg5885 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,5,2] := by - exact rowSquare_join (by decide) sg373 sg1529 - -lemma sg5886 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg1096 - -lemma sg5887 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3] := by - exact rowSquare_join (by decide) sg682 sg1033 - -lemma sg5888 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [7,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg674 sg1048 - -lemma sg5889 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg383 sg1520 - -lemma sg5890 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg613 sg1031 - -lemma sg5891 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg1032 - -lemma sg5892 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg370 sg1417 - -lemma sg5893 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1033 - -lemma sg5894 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1522 - -lemma sg5895 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg615 sg1031 - -lemma sg5896 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1523 - -lemma sg5897 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg616 sg1031 - -lemma sg5898 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg615 sg1032 - -lemma sg5899 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg615 sg1033 - -lemma sg5900 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg1417 - -lemma sg5901 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg616 sg1032 - -lemma sg5902 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,3] := by - exact rowSquare_join (by decide) sg616 sg1033 - -lemma sg5903 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg613 sg1034 - -lemma sg5904 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg1036 - -lemma sg5905 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg673 sg959 - -lemma sg5906 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1037 - -lemma sg5907 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg673 sg960 - -lemma sg5908 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg673 sg961 - -lemma sg5909 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1041 - -lemma sg5910 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg1036 - -lemma sg5911 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,4,4,3,3] := by - exact rowSquare_join (by decide) sg675 sg961 - -lemma sg5912 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1527 - -lemma sg5913 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg614 sg1038 - -lemma sg5914 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg623 sg1031 - -lemma sg5915 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1045 - -lemma sg5916 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg677 sg961 - -lemma sg5917 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [6,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg615 sg1044 - -lemma sg5918 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg674 sg964 - -lemma sg5919 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [6,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg614 sg1048 - -lemma sg5920 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg621 sg1038 - -lemma sg5921 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [7,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg1050 - -lemma sg5922 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [7,3,3,3,3] := by - exact rowSquare_join (by decide) sg682 sg961 - -lemma sg5923 : RowSquare [4,4,2,2,2,2,2,1] [4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg1650 - -lemma sg5924 : RowSquare [4,4,2,2,2,2,2,1] [4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg1650 - -lemma sg5925 : RowSquare [4,4,2,2,2,2,2,1] [4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg561 sg877 - -lemma sg5926 : RowSquare [4,4,2,2,2,2,2,1] [4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg561 sg879 - -lemma sg5927 : RowSquare [4,4,2,2,2,2,2,1] [4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg1650 - -lemma sg5928 : RowSquare [4,4,2,2,2,2,2,1] [5,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg211 sg1650 - -lemma sg5929 : RowSquare [4,4,2,2,2,2,2,1] [5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg561 sg880 - -lemma sg5930 : RowSquare [4,4,2,2,2,2,2,1] [5,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg212 sg1650 - -lemma sg5931 : RowSquare [4,4,2,2,2,2,2,1] [5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg1651 - -lemma sg5932 : RowSquare [4,4,2,2,2,2,2,1] [5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg1651 - -lemma sg5933 : RowSquare [4,4,2,2,2,2,2,1] [5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg561 sg882 - -lemma sg5934 : RowSquare [4,4,2,2,2,2,2,1] [5,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg213 sg1650 - -lemma sg5935 : RowSquare [4,4,2,2,2,2,2,1] [5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg1651 - -lemma sg5936 : RowSquare [4,4,2,2,2,2,2,1] [5,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg1652 - -lemma sg5937 : RowSquare [4,4,2,2,2,2,2,1] [5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg1652 - -lemma sg5938 : RowSquare [4,4,2,2,2,2,2,1] [5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg1652 - -lemma sg5939 : RowSquare [4,4,2,2,2,2,2,1] [6,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg214 sg1650 - -lemma sg5940 : RowSquare [4,4,2,2,2,2,2,1] [6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg211 sg1651 - -lemma sg5941 : RowSquare [4,4,2,2,2,2,2,1] [6,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg215 sg1650 - -lemma sg5942 : RowSquare [4,4,2,2,2,2,2,1] [6,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg212 sg1651 - -lemma sg5943 : RowSquare [4,4,2,2,2,2,2,1] [6,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg1655 - -lemma sg5944 : RowSquare [4,4,2,2,2,2,2,1] [6,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg1655 - -lemma sg5945 : RowSquare [4,4,2,2,2,2,2,1] [6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg213 sg1651 - -lemma sg5946 : RowSquare [4,4,2,2,2,2,2,1] [6,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg1655 - -lemma sg5947 : RowSquare [4,4,2,2,2,2,2,1] [6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg213 sg1652 - -lemma sg5948 : RowSquare [4,4,2,2,2,2,2,1] [7,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg216 sg1650 - -lemma sg5949 : RowSquare [4,4,2,2,2,2,2,1] [7,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg214 sg1651 - -lemma sg5950 : RowSquare [4,4,2,2,2,2,2,1] [7,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg211 sg1655 - -lemma sg5951 : RowSquare [4,4,2,2,2,2,2,1] [7,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg215 sg1651 - -lemma sg5952 : RowSquare [4,4,2,2,2,2,2,1] [7,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg212 sg1655 - -lemma sg5953 : RowSquare [4,4,2,2,2,2,2,1] [7,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg213 sg1655 - -lemma sg5954 : RowSquare [4,4,2,2,2,2,2,1] [8,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg217 sg1650 - -lemma sg5955 : RowSquare [4,4,2,2,2,2,2,1] [8,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg216 sg1651 - -lemma sg5956 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg673 sg849 - -lemma sg5957 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg849 - -lemma sg5958 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg675 sg849 - -lemma sg5959 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg676 sg849 - -lemma sg5960 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg178 sg1796 - -lemma sg5961 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg615 sg940 - -lemma sg5962 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg614 sg941 - -lemma sg5963 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg616 sg940 - -lemma sg5964 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg614 sg943 - -lemma sg5965 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1413 - -lemma sg5966 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg615 sg941 - -lemma sg5967 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg616 sg941 - -lemma sg5968 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg615 sg942 - -lemma sg5969 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg615 sg943 - -lemma sg5970 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg616 sg942 - -lemma sg5971 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,4,3] := by - exact rowSquare_join (by decide) sg616 sg943 - -lemma sg5972 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg677 sg849 - -lemma sg5973 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg673 sg850 - -lemma sg5974 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg613 sg944 - -lemma sg5975 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg678 sg849 - -lemma sg5976 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg850 - -lemma sg5977 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg613 sg945 - -lemma sg5978 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg679 sg849 - -lemma sg5979 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg946 - -lemma sg5980 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg676 sg850 - -lemma sg5981 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg673 sg853 - -lemma sg5982 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg179 sg1796 - -lemma sg5983 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg680 sg849 - -lemma sg5984 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg948 - -lemma sg5985 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg681 sg849 - -lemma sg5986 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg950 - -lemma sg5987 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg614 sg947 - -lemma sg5988 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg674 sg853 - -lemma sg5989 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg951 - -lemma sg5990 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg946 - -lemma sg5991 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg693 sg832 - -lemma sg5992 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg693 sg833 - -lemma sg5993 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,4,4,2] := by - exact rowSquare_join (by decide) sg616 sg947 - -lemma sg5994 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg622 sg940 - -lemma sg5995 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg948 - -lemma sg5996 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg614 sg950 - -lemma sg5997 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg623 sg940 - -lemma sg5998 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg614 sg951 - -lemma sg5999 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg615 sg950 - -lemma sg6000 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,4,3,2] := by - exact rowSquare_join (by decide) sg616 sg949 - -lemma sg6001 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,4,4,1] := by - exact rowSquare_join (by decide) sg616 sg950 - -lemma sg6002 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg696 sg832 - -lemma sg6003 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg615 sg951 - -lemma sg6004 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,5,2,2] := by - exact rowSquare_join (by decide) sg696 sg834 - -lemma sg6005 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,5,3,1] := by - exact rowSquare_join (by decide) sg616 sg951 - -lemma sg6006 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,5,4] := by - exact rowSquare_join (by decide) sg373 sg1294 - -lemma sg6007 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg682 sg849 - -lemma sg6008 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg613 sg952 - -lemma sg6009 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg614 sg952 - -lemma sg6010 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg955 - -lemma sg6011 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg673 sg858 - -lemma sg6012 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg614 sg955 - -lemma sg6013 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,4,4,4,1] := by - exact rowSquare_join (by decide) sg1 sg4575 - -lemma sg6014 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg674 sg859 - -lemma sg6015 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,5,4,4] := by - exact rowSquare_join (by decide) sg693 sg837 - -lemma sg6016 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg694 sg836 - -lemma sg6017 : RowSquare [5,3,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1109 - -lemma sg6018 : RowSquare [5,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg696 sg998 - -lemma sg6019 : RowSquare [5,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg696 sg999 - -lemma sg6020 : RowSquare [5,3,2,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1112 - -lemma sg6021 : RowSquare [5,3,2,2,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg695 sg910 - -lemma sg6022 : RowSquare [5,3,2,2,1,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg696 sg910 - -lemma sg6023 : RowSquare [5,3,3,2,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg104 sg2137 - -lemma sg6024 : RowSquare [5,3,3,2,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg218 sg1683 - -lemma sg6025 : RowSquare [5,3,3,2,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg105 sg2137 - -lemma sg6026 : RowSquare [5,3,3,2,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg219 sg1683 - -lemma sg6027 : RowSquare [5,3,3,2,1,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg106 sg2137 - -lemma sg6028 : RowSquare [5,3,3,2,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg221 sg1683 - -lemma sg6029 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg1092 - -lemma sg6030 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg673 sg998 - -lemma sg6031 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1094 - -lemma sg6032 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg673 sg999 - -lemma sg6033 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1095 - -lemma sg6034 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg673 sg1000 - -lemma sg6035 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg673 sg1001 - -lemma sg6036 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg674 sg998 - -lemma sg6037 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg675 sg998 - -lemma sg6038 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg674 sg999 - -lemma sg6039 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg676 sg998 - -lemma sg6040 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg675 sg999 - -lemma sg6041 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg676 sg999 - -lemma sg6042 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg675 sg1000 - -lemma sg6043 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3] := by - exact rowSquare_join (by decide) sg675 sg1001 - -lemma sg6044 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg676 sg1000 - -lemma sg6045 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2] := by - exact rowSquare_join (by decide) sg676 sg1001 - -lemma sg6046 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1096 - -lemma sg6047 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg587 sg1092 - -lemma sg6048 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg1093 - -lemma sg6049 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg677 sg1000 - -lemma sg6050 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg677 sg1001 - -lemma sg6051 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1100 - -lemma sg6052 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg589 sg1094 - -lemma sg6053 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,1] := by - exact rowSquare_join (by decide) sg590 sg1095 - -lemma sg6054 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg681 sg998 - -lemma sg6055 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg680 sg999 - -lemma sg6056 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg674 sg1007 - -lemma sg6057 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg674 sg1008 - -lemma sg6058 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,2] := by - exact rowSquare_join (by decide) sg680 sg1001 - -lemma sg6059 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg681 sg999 - -lemma sg6060 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg681 sg1000 - -lemma sg6061 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2] := by - exact rowSquare_join (by decide) sg675 sg1007 - -lemma sg6062 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,1] := by - exact rowSquare_join (by decide) sg675 sg1008 - -lemma sg6063 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,4,4] := by - exact rowSquare_join (by decide) sg676 sg1008 - -lemma sg6064 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1101 - -lemma sg6065 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg1096 - -lemma sg6066 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1097 - -lemma sg6067 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1102 - -lemma sg6068 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg589 sg1096 - -lemma sg6069 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3] := by - exact rowSquare_join (by decide) sg682 sg1001 - -lemma sg6070 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1100 - -lemma sg6071 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg684 sg999 - -lemma sg6072 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1103 - -lemma sg6073 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg1100 - -lemma sg6074 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg686 sg998 - -lemma sg6075 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg686 sg999 - -lemma sg6076 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg674 sg1015 - -lemma sg6077 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2] := by - exact rowSquare_join (by decide) sg686 sg1001 - -lemma sg6078 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg674 sg1016 - -lemma sg6079 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,1] := by - exact rowSquare_join (by decide) sg675 sg1015 - -lemma sg6080 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,3,3] := by - exact rowSquare_join (by decide) sg676 sg1015 - -lemma sg6081 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg613 sg998 - -lemma sg6082 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg613 sg999 - -lemma sg6083 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg1000 - -lemma sg6084 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1001 - -lemma sg6085 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg614 sg998 - -lemma sg6086 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg615 sg998 - -lemma sg6087 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg614 sg999 - -lemma sg6088 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg616 sg998 - -lemma sg6089 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg614 sg1000 - -lemma sg6090 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg614 sg1001 - -lemma sg6091 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1041 - -lemma sg6092 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg615 sg999 - -lemma sg6093 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg616 sg999 - -lemma sg6094 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg615 sg1000 - -lemma sg6095 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg615 sg1001 - -lemma sg6096 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg616 sg1000 - -lemma sg6097 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,4,3] := by - exact rowSquare_join (by decide) sg616 sg1001 - -lemma sg6098 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg613 sg1002 - -lemma sg6099 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg613 sg1003 - -lemma sg6100 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg1004 - -lemma sg6101 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1005 - -lemma sg6102 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg1006 - -lemma sg6103 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg681 sg910 - -lemma sg6104 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg614 sg1005 - -lemma sg6105 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1041 - -lemma sg6106 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg1004 - -lemma sg6107 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg621 sg998 - -lemma sg6108 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg614 sg1006 - -lemma sg6109 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg622 sg998 - -lemma sg6110 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg1006 - -lemma sg6111 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg614 sg1008 - -lemma sg6112 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg616 sg1006 - -lemma sg6113 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,3] := by - exact rowSquare_join (by decide) sg621 sg1001 - -lemma sg6114 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg623 sg998 - -lemma sg6115 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,4,4,1] := by - exact rowSquare_join (by decide) sg616 sg1008 - -lemma sg6116 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg685 sg910 - -lemma sg6117 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg686 sg910 - -lemma sg6118 : RowSquare [5,4,2,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg910 - -lemma sg6119 : RowSquare [5,4,2,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg623 sg910 - -lemma sg6120 : RowSquare [5,4,2,2,1,1,1,1,1,1] [4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1378 - -lemma sg6121 : RowSquare [5,4,2,2,1,1,1,1,1,1] [4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1379 - -lemma sg6122 : RowSquare [5,4,2,2,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg628 sg910 - -lemma sg6123 : RowSquare [5,4,2,2,1,1,1,1,1,1] [5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg623 sg913 - -lemma sg6124 : RowSquare [5,4,2,2,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg2596 - -lemma sg6125 : RowSquare [5,4,2,2,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg2597 - -lemma sg6126 : RowSquare [5,4,2,2,2,2,1,1] [4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg2596 - -lemma sg6127 : RowSquare [5,4,2,2,2,2,1,1] [4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg2597 - -lemma sg6128 : RowSquare [5,4,2,2,2,2,1,1] [4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg2596 - -lemma sg6129 : RowSquare [5,4,2,2,2,2,1,1] [4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg2597 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes10 + +namespace OAI + +/-! Semigroup Nodes 13. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg5728 : RowSquare [6,5,2,2,2,1] [8,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg243 sg842 + +lemma sg5729 : RowSquare [6,5,2,2,2,1] [9,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg2543 + +lemma sg5730 : RowSquare [6,5,2,2,2,1] [9,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg3248 + +lemma sg5731 : RowSquare [6,5,3,2,1,1] [3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg1616 + +lemma sg5732 : RowSquare [6,6,1,1,1,1,1,1] [3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg2546 + +lemma sg5733 : RowSquare [7,5,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg21 sg2251 + +lemma sg5734 : RowSquare [7,5,3,1,1,1] [4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg306 sg810 + +lemma sg5736 : RowSquare [8,3,2,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg705 sg431 + +lemma sg5737 : RowSquare [8,3,2,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg703 sg430 + +lemma sg5738 : RowSquare [8,3,2,1,1,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg703 sg429 + +lemma sg5739 : RowSquare [8,3,2,1,1,1,1,1] [2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg396 sg733 + +lemma sg5740 : RowSquare [8,3,2,1,1,1,1,1] [2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg223 sg1141 + +lemma sg5741 : RowSquare [8,3,2,1,1,1,1,1] [2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg92 sg1625 + +lemma sg5742 : RowSquare [8,3,2,1,1,1,1,1] [3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg220 sg1140 + +lemma sg5743 : RowSquare [8,3,2,1,1,1,1,1] [3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg89 sg1624 + +lemma sg5744 : RowSquare [8,3,2,1,1,1,1,1] [3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg89 sg1623 + +lemma sg5745 : RowSquare [8,3,2,1,1,1,1,1] [3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg220 sg1138 + +lemma sg5746 : RowSquare [8,3,2,1,1,1,1,1] [3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg89 sg1621 + +lemma sg5747 : RowSquare [8,3,2,1,1,1,1,1] [4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg88 sg1623 + +lemma sg5748 : RowSquare [8,3,2,1,1,1,1,1] [5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg1622 + +lemma sg5749 : RowSquare [8,3,3,1,1,1,1] [3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg2120 + +lemma sg5750 : RowSquare [8,4,2,1,1,1,1] [4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg2123 + +lemma sg5751 : RowSquare [8,4,3,1,1,1] [4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg306 sg893 + +lemma sg5752 : RowSquare [8,4,3,2,1] [4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg513 + +lemma sg5753 : RowSquare [8,4,3,3] [4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg330 sg835 + +lemma sg5754 : RowSquare [8,5,3,1,1] [3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg306 sg912 + +lemma sg5755 : RowSquare [8,5,3,1,1] [3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg1688 + +lemma sg5756 : RowSquare [8,7,2,1] [3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg849 + +lemma sg5758 : RowSquare [9,2,1,1,1,1,1,1,1] [2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg425 sg719 + +lemma sg5759 : RowSquare [9,2,1,1,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg232 sg1136 + +lemma sg5760 : RowSquare [9,2,1,1,1,1,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg105 sg1620 + +lemma sg5761 : RowSquare [9,2,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg2114 + +lemma sg5762 : RowSquare [9,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg2618 + +lemma sg5763 : RowSquare [9,3,2,2,1,1] [4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg142 sg1332 + +lemma sg5764 : RowSquare [9,3,3,1,1,1] [4,4,4,3,3] := by + exact rowSquare_join (by decide) sg349 sg892 + +lemma sg5765 : RowSquare [9,3,3,1,1,1] [4,4,4,4,2] := by + exact rowSquare_join (by decide) sg350 sg892 + +lemma sg5766 : RowSquare [9,3,3,2,1] [4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg373 sg828 + +lemma sg5767 : RowSquare [9,3,3,2,1] [4,4,4,4,2] := by + exact rowSquare_join (by decide) sg551 sg590 + +lemma sg5768 : RowSquare [9,4,2,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg1754 + +lemma sg5769 : RowSquare [9,4,2,1,1,1] [4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg357 sg889 + +lemma sg5770 : RowSquare [9,4,2,1,1,1] [4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg356 sg892 + +lemma sg5771 : RowSquare [9,4,2,1,1,1] [4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg390 sg808 + +lemma sg5772 : RowSquare [9,4,3,2] [3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg943 + +lemma sg5773 : RowSquare [9,4,3,2] [4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg371 sg853 + +lemma sg5774 : RowSquare [9,4,3,2] [4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg550 + +lemma sg5775 : RowSquare [9,4,3,2] [4,4,4,4,2] := by + exact rowSquare_join (by decide) sg616 sg551 + +lemma sg5776 : RowSquare [10,2,2,2,2] [2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg586 + +lemma sg5777 : RowSquare [10,3,2,1,1,1] [4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg195 sg1330 + +lemma sg5778 : RowSquare [10,3,2,2,1] [3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg330 sg998 + +lemma sg5779 : RowSquare [10,3,2,2,1] [3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg616 + +lemma sg5780 : RowSquare [10,3,2,2,1] [3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg1000 + +lemma sg5781 : RowSquare [10,3,2,2,1] [4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg371 sg914 + +lemma sg5782 : RowSquare [10,3,2,2,1] [4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg371 sg915 + +lemma sg5783 : RowSquare [10,3,2,2,1] [4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg589 + +lemma sg5784 : RowSquare [10,3,2,2,1] [4,4,4,3,3] := by + exact rowSquare_join (by decide) sg372 sg915 + +lemma sg5785 : RowSquare [10,3,2,2,1] [4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg373 sg914 + +lemma sg5786 : RowSquare [10,3,2,2,1] [5,5,4,4] := by + exact rowSquare_join (by decide) sg373 sg922 + +lemma sg5787 : RowSquare [10,3,3,1,1] [4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg348 sg1000 + +lemma sg5788 : RowSquare [10,3,3,1,1] [4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg636 sg589 + +lemma sg5789 : RowSquare [10,3,3,1,1] [4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg350 sg1000 + +lemma sg5790 : RowSquare [10,4,2,2] [4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg615 + +lemma sg5791 : RowSquare [10,4,3,1] [4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg636 sg615 + +lemma sg5792 : RowSquare [11,3,2,2] [4,4,4,3,3] := by + exact rowSquare_join (by decide) sg372 sg1033 + +lemma sg5793 : RowSquare [11,3,2,2] [5,5,4,4] := by + exact rowSquare_join (by decide) sg373 sg1040 + +lemma sg5794 : RowSquare [3,3,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,3] := by + exact rowSquare_join (by decide) sg692 sg1061 + +lemma sg5795 : RowSquare [3,3,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,2] := by + exact rowSquare_join (by decide) sg693 sg1061 + +lemma sg5796 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg692 sg1031 + +lemma sg5797 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg693 sg1031 + +lemma sg5798 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg692 sg1032 + +lemma sg5799 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3] := by + exact rowSquare_join (by decide) sg692 sg1033 + +lemma sg5800 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg693 sg1032 + +lemma sg5801 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2] := by + exact rowSquare_join (by decide) sg693 sg1033 + +lemma sg5802 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg1520 + +lemma sg5803 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg694 sg1032 + +lemma sg5804 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3] := by + exact rowSquare_join (by decide) sg694 sg1033 + +lemma sg5805 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg673 sg1068 + +lemma sg5806 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg673 sg1069 + +lemma sg5807 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg697 sg1032 + +lemma sg5808 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg697 sg1033 + +lemma sg5809 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg673 sg1070 + +lemma sg5810 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg614 sg1104 + +lemma sg5811 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg643 sg1093 + +lemma sg5812 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg614 sg1105 + +lemma sg5813 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg674 sg1069 + +lemma sg5814 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,3] := by + exact rowSquare_join (by decide) sg698 sg1033 + +lemma sg5815 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg643 sg1094 + +lemma sg5816 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,1] := by + exact rowSquare_join (by decide) sg644 sg1095 + +lemma sg5817 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg614 sg1106 + +lemma sg5818 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg674 sg1070 + +lemma sg5819 : RowSquare [4,3,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg694 sg1038 + +lemma sg5820 : RowSquare [4,3,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg374 sg1455 + +lemma sg5821 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg673 sg1092 + +lemma sg5822 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg673 sg1093 + +lemma sg5823 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg673 sg1094 + +lemma sg5824 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg673 sg1095 + +lemma sg5825 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg674 sg1093 + +lemma sg5826 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg674 sg1094 + +lemma sg5827 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg674 sg1095 + +lemma sg5828 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2] := by + exact rowSquare_join (by decide) sg675 sg1094 + +lemma sg5829 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,1] := by + exact rowSquare_join (by decide) sg675 sg1095 + +lemma sg5830 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,4] := by + exact rowSquare_join (by decide) sg676 sg1095 + +lemma sg5831 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg673 sg1031 + +lemma sg5832 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg673 sg1032 + +lemma sg5833 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg673 sg1033 + +lemma sg5834 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg370 sg1520 + +lemma sg5835 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg674 sg1031 + +lemma sg5836 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg674 sg1032 + +lemma sg5837 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg674 sg1033 + +lemma sg5838 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg675 sg1031 + +lemma sg5839 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg676 sg1031 + +lemma sg5840 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg675 sg1032 + +lemma sg5841 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3] := by + exact rowSquare_join (by decide) sg675 sg1033 + +lemma sg5842 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg676 sg1032 + +lemma sg5843 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2] := by + exact rowSquare_join (by decide) sg676 sg1033 + +lemma sg5844 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg1520 + +lemma sg5845 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg372 sg1520 + +lemma sg5846 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg1521 + +lemma sg5847 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg1520 + +lemma sg5848 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg1522 + +lemma sg5849 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg371 sg1523 + +lemma sg5850 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2] := by + exact rowSquare_join (by decide) sg372 sg1522 + +lemma sg5851 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,1] := by + exact rowSquare_join (by decide) sg372 sg1523 + +lemma sg5852 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [5,5,5,4] := by + exact rowSquare_join (by decide) sg373 sg1523 + +lemma sg5853 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg613 sg1092 + +lemma sg5854 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg1093 + +lemma sg5855 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg614 sg1092 + +lemma sg5856 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1094 + +lemma sg5857 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg673 sg1036 + +lemma sg5858 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1095 + +lemma sg5859 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg677 sg1032 + +lemma sg5860 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg677 sg1033 + +lemma sg5861 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg614 sg1093 + +lemma sg5862 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg614 sg1094 + +lemma sg5863 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg1093 + +lemma sg5864 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3] := by + exact rowSquare_join (by decide) sg678 sg1033 + +lemma sg5865 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg615 sg1094 + +lemma sg5866 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg1527 + +lemma sg5867 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg674 sg1038 + +lemma sg5868 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg674 sg1039 + +lemma sg5869 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg674 sg1040 + +lemma sg5870 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg681 sg1031 + +lemma sg5871 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg674 sg1041 + +lemma sg5872 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,2] := by + exact rowSquare_join (by decide) sg675 sg1039 + +lemma sg5873 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,1] := by + exact rowSquare_join (by decide) sg675 sg1040 + +lemma sg5874 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,5,4,4] := by + exact rowSquare_join (by decide) sg676 sg1040 + +lemma sg5875 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg377 sg1520 + +lemma sg5876 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg1527 + +lemma sg5877 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg378 sg1520 + +lemma sg5878 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg371 sg1528 + +lemma sg5879 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,2] := by + exact rowSquare_join (by decide) sg372 sg1527 + +lemma sg5880 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,1] := by + exact rowSquare_join (by decide) sg373 sg1527 + +lemma sg5881 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg1529 + +lemma sg5882 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,4,2,1] := by + exact rowSquare_join (by decide) sg372 sg1528 + +lemma sg5883 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,4,3] := by + exact rowSquare_join (by decide) sg373 sg1528 + +lemma sg5884 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,5,1,1] := by + exact rowSquare_join (by decide) sg372 sg1529 + +lemma sg5885 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [6,6,5,2] := by + exact rowSquare_join (by decide) sg373 sg1529 + +lemma sg5886 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg1096 + +lemma sg5887 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3] := by + exact rowSquare_join (by decide) sg682 sg1033 + +lemma sg5888 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [7,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg674 sg1048 + +lemma sg5889 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg383 sg1520 + +lemma sg5890 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg613 sg1031 + +lemma sg5891 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg1032 + +lemma sg5892 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg370 sg1417 + +lemma sg5893 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1033 + +lemma sg5894 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1522 + +lemma sg5895 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg615 sg1031 + +lemma sg5896 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1523 + +lemma sg5897 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg616 sg1031 + +lemma sg5898 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg615 sg1032 + +lemma sg5899 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg615 sg1033 + +lemma sg5900 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg1417 + +lemma sg5901 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg616 sg1032 + +lemma sg5902 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,3] := by + exact rowSquare_join (by decide) sg616 sg1033 + +lemma sg5903 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg613 sg1034 + +lemma sg5904 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg1036 + +lemma sg5905 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg673 sg959 + +lemma sg5906 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1037 + +lemma sg5907 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg673 sg960 + +lemma sg5908 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg673 sg961 + +lemma sg5909 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1041 + +lemma sg5910 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg1036 + +lemma sg5911 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,4,4,3,3] := by + exact rowSquare_join (by decide) sg675 sg961 + +lemma sg5912 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1527 + +lemma sg5913 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg614 sg1038 + +lemma sg5914 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg623 sg1031 + +lemma sg5915 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1045 + +lemma sg5916 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg677 sg961 + +lemma sg5917 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [6,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg615 sg1044 + +lemma sg5918 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg674 sg964 + +lemma sg5919 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [6,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg614 sg1048 + +lemma sg5920 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg621 sg1038 + +lemma sg5921 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [7,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg1050 + +lemma sg5922 : RowSquare [4,4,2,2,1,1,1,1,1,1,1] [7,3,3,3,3] := by + exact rowSquare_join (by decide) sg682 sg961 + +lemma sg5923 : RowSquare [4,4,2,2,2,2,2,1] [4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg1650 + +lemma sg5924 : RowSquare [4,4,2,2,2,2,2,1] [4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg1650 + +lemma sg5925 : RowSquare [4,4,2,2,2,2,2,1] [4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg561 sg877 + +lemma sg5926 : RowSquare [4,4,2,2,2,2,2,1] [4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg561 sg879 + +lemma sg5927 : RowSquare [4,4,2,2,2,2,2,1] [4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg1650 + +lemma sg5928 : RowSquare [4,4,2,2,2,2,2,1] [5,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg211 sg1650 + +lemma sg5929 : RowSquare [4,4,2,2,2,2,2,1] [5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg561 sg880 + +lemma sg5930 : RowSquare [4,4,2,2,2,2,2,1] [5,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg212 sg1650 + +lemma sg5931 : RowSquare [4,4,2,2,2,2,2,1] [5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg1651 + +lemma sg5932 : RowSquare [4,4,2,2,2,2,2,1] [5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg1651 + +lemma sg5933 : RowSquare [4,4,2,2,2,2,2,1] [5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg561 sg882 + +lemma sg5934 : RowSquare [4,4,2,2,2,2,2,1] [5,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg213 sg1650 + +lemma sg5935 : RowSquare [4,4,2,2,2,2,2,1] [5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg1651 + +lemma sg5936 : RowSquare [4,4,2,2,2,2,2,1] [5,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg1652 + +lemma sg5937 : RowSquare [4,4,2,2,2,2,2,1] [5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg1652 + +lemma sg5938 : RowSquare [4,4,2,2,2,2,2,1] [5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg1652 + +lemma sg5939 : RowSquare [4,4,2,2,2,2,2,1] [6,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg214 sg1650 + +lemma sg5940 : RowSquare [4,4,2,2,2,2,2,1] [6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg211 sg1651 + +lemma sg5941 : RowSquare [4,4,2,2,2,2,2,1] [6,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg215 sg1650 + +lemma sg5942 : RowSquare [4,4,2,2,2,2,2,1] [6,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg212 sg1651 + +lemma sg5943 : RowSquare [4,4,2,2,2,2,2,1] [6,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg1655 + +lemma sg5944 : RowSquare [4,4,2,2,2,2,2,1] [6,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg1655 + +lemma sg5945 : RowSquare [4,4,2,2,2,2,2,1] [6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg213 sg1651 + +lemma sg5946 : RowSquare [4,4,2,2,2,2,2,1] [6,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg1655 + +lemma sg5947 : RowSquare [4,4,2,2,2,2,2,1] [6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg213 sg1652 + +lemma sg5948 : RowSquare [4,4,2,2,2,2,2,1] [7,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg216 sg1650 + +lemma sg5949 : RowSquare [4,4,2,2,2,2,2,1] [7,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg214 sg1651 + +lemma sg5950 : RowSquare [4,4,2,2,2,2,2,1] [7,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg211 sg1655 + +lemma sg5951 : RowSquare [4,4,2,2,2,2,2,1] [7,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg215 sg1651 + +lemma sg5952 : RowSquare [4,4,2,2,2,2,2,1] [7,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg212 sg1655 + +lemma sg5953 : RowSquare [4,4,2,2,2,2,2,1] [7,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg213 sg1655 + +lemma sg5954 : RowSquare [4,4,2,2,2,2,2,1] [8,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg217 sg1650 + +lemma sg5955 : RowSquare [4,4,2,2,2,2,2,1] [8,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg216 sg1651 + +lemma sg5956 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg673 sg849 + +lemma sg5957 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg849 + +lemma sg5958 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg675 sg849 + +lemma sg5959 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg676 sg849 + +lemma sg5960 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg178 sg1796 + +lemma sg5961 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg615 sg940 + +lemma sg5962 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg614 sg941 + +lemma sg5963 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg616 sg940 + +lemma sg5964 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg614 sg943 + +lemma sg5965 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1413 + +lemma sg5966 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg615 sg941 + +lemma sg5967 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg616 sg941 + +lemma sg5968 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg615 sg942 + +lemma sg5969 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg615 sg943 + +lemma sg5970 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg616 sg942 + +lemma sg5971 : RowSquare [4,4,3,2,1,1,1,1,1,1] [4,4,4,4,3] := by + exact rowSquare_join (by decide) sg616 sg943 + +lemma sg5972 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg677 sg849 + +lemma sg5973 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg673 sg850 + +lemma sg5974 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg613 sg944 + +lemma sg5975 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg678 sg849 + +lemma sg5976 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg850 + +lemma sg5977 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg613 sg945 + +lemma sg5978 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg679 sg849 + +lemma sg5979 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg946 + +lemma sg5980 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg676 sg850 + +lemma sg5981 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg673 sg853 + +lemma sg5982 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg179 sg1796 + +lemma sg5983 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg680 sg849 + +lemma sg5984 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg948 + +lemma sg5985 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg681 sg849 + +lemma sg5986 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg950 + +lemma sg5987 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg614 sg947 + +lemma sg5988 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg674 sg853 + +lemma sg5989 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg951 + +lemma sg5990 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg946 + +lemma sg5991 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg693 sg832 + +lemma sg5992 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg693 sg833 + +lemma sg5993 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,4,4,4,2] := by + exact rowSquare_join (by decide) sg616 sg947 + +lemma sg5994 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg622 sg940 + +lemma sg5995 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg948 + +lemma sg5996 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg614 sg950 + +lemma sg5997 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg623 sg940 + +lemma sg5998 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg614 sg951 + +lemma sg5999 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg615 sg950 + +lemma sg6000 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,4,3,2] := by + exact rowSquare_join (by decide) sg616 sg949 + +lemma sg6001 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,4,4,1] := by + exact rowSquare_join (by decide) sg616 sg950 + +lemma sg6002 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg696 sg832 + +lemma sg6003 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg615 sg951 + +lemma sg6004 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,5,2,2] := by + exact rowSquare_join (by decide) sg696 sg834 + +lemma sg6005 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,5,3,1] := by + exact rowSquare_join (by decide) sg616 sg951 + +lemma sg6006 : RowSquare [4,4,3,2,1,1,1,1,1,1] [5,5,5,4] := by + exact rowSquare_join (by decide) sg373 sg1294 + +lemma sg6007 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg682 sg849 + +lemma sg6008 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg613 sg952 + +lemma sg6009 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg614 sg952 + +lemma sg6010 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg955 + +lemma sg6011 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg673 sg858 + +lemma sg6012 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg614 sg955 + +lemma sg6013 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,4,4,4,1] := by + exact rowSquare_join (by decide) sg1 sg4575 + +lemma sg6014 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg674 sg859 + +lemma sg6015 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,5,4,4] := by + exact rowSquare_join (by decide) sg693 sg837 + +lemma sg6016 : RowSquare [4,4,3,2,1,1,1,1,1,1] [6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg694 sg836 + +lemma sg6017 : RowSquare [5,3,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1109 + +lemma sg6018 : RowSquare [5,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg696 sg998 + +lemma sg6019 : RowSquare [5,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg696 sg999 + +lemma sg6020 : RowSquare [5,3,2,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1112 + +lemma sg6021 : RowSquare [5,3,2,2,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg695 sg910 + +lemma sg6022 : RowSquare [5,3,2,2,1,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg696 sg910 + +lemma sg6023 : RowSquare [5,3,3,2,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg104 sg2137 + +lemma sg6024 : RowSquare [5,3,3,2,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg218 sg1683 + +lemma sg6025 : RowSquare [5,3,3,2,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg105 sg2137 + +lemma sg6026 : RowSquare [5,3,3,2,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg219 sg1683 + +lemma sg6027 : RowSquare [5,3,3,2,1,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg106 sg2137 + +lemma sg6028 : RowSquare [5,3,3,2,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg221 sg1683 + +lemma sg6029 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg1092 + +lemma sg6030 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg673 sg998 + +lemma sg6031 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1094 + +lemma sg6032 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg673 sg999 + +lemma sg6033 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1095 + +lemma sg6034 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg673 sg1000 + +lemma sg6035 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg673 sg1001 + +lemma sg6036 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg674 sg998 + +lemma sg6037 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg675 sg998 + +lemma sg6038 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg674 sg999 + +lemma sg6039 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg676 sg998 + +lemma sg6040 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg675 sg999 + +lemma sg6041 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg676 sg999 + +lemma sg6042 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg675 sg1000 + +lemma sg6043 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3] := by + exact rowSquare_join (by decide) sg675 sg1001 + +lemma sg6044 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg676 sg1000 + +lemma sg6045 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2] := by + exact rowSquare_join (by decide) sg676 sg1001 + +lemma sg6046 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1096 + +lemma sg6047 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg587 sg1092 + +lemma sg6048 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg1093 + +lemma sg6049 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg677 sg1000 + +lemma sg6050 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg677 sg1001 + +lemma sg6051 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1100 + +lemma sg6052 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg589 sg1094 + +lemma sg6053 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,1] := by + exact rowSquare_join (by decide) sg590 sg1095 + +lemma sg6054 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg681 sg998 + +lemma sg6055 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg680 sg999 + +lemma sg6056 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg674 sg1007 + +lemma sg6057 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg674 sg1008 + +lemma sg6058 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,2] := by + exact rowSquare_join (by decide) sg680 sg1001 + +lemma sg6059 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg681 sg999 + +lemma sg6060 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg681 sg1000 + +lemma sg6061 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2] := by + exact rowSquare_join (by decide) sg675 sg1007 + +lemma sg6062 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,1] := by + exact rowSquare_join (by decide) sg675 sg1008 + +lemma sg6063 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [6,5,4,4] := by + exact rowSquare_join (by decide) sg676 sg1008 + +lemma sg6064 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1101 + +lemma sg6065 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg1096 + +lemma sg6066 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1097 + +lemma sg6067 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1102 + +lemma sg6068 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg589 sg1096 + +lemma sg6069 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3] := by + exact rowSquare_join (by decide) sg682 sg1001 + +lemma sg6070 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1100 + +lemma sg6071 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg684 sg999 + +lemma sg6072 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1103 + +lemma sg6073 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg1100 + +lemma sg6074 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg686 sg998 + +lemma sg6075 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg686 sg999 + +lemma sg6076 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg674 sg1015 + +lemma sg6077 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2] := by + exact rowSquare_join (by decide) sg686 sg1001 + +lemma sg6078 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg674 sg1016 + +lemma sg6079 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,1] := by + exact rowSquare_join (by decide) sg675 sg1015 + +lemma sg6080 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1] [7,6,3,3] := by + exact rowSquare_join (by decide) sg676 sg1015 + +lemma sg6081 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg613 sg998 + +lemma sg6082 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg613 sg999 + +lemma sg6083 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg1000 + +lemma sg6084 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1001 + +lemma sg6085 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg614 sg998 + +lemma sg6086 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg615 sg998 + +lemma sg6087 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg614 sg999 + +lemma sg6088 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg616 sg998 + +lemma sg6089 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg614 sg1000 + +lemma sg6090 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg614 sg1001 + +lemma sg6091 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1041 + +lemma sg6092 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg615 sg999 + +lemma sg6093 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg616 sg999 + +lemma sg6094 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg615 sg1000 + +lemma sg6095 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg615 sg1001 + +lemma sg6096 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg616 sg1000 + +lemma sg6097 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [4,4,4,4,3] := by + exact rowSquare_join (by decide) sg616 sg1001 + +lemma sg6098 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg613 sg1002 + +lemma sg6099 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg613 sg1003 + +lemma sg6100 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg1004 + +lemma sg6101 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1005 + +lemma sg6102 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg1006 + +lemma sg6103 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg681 sg910 + +lemma sg6104 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg614 sg1005 + +lemma sg6105 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1041 + +lemma sg6106 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg1004 + +lemma sg6107 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg621 sg998 + +lemma sg6108 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg614 sg1006 + +lemma sg6109 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg622 sg998 + +lemma sg6110 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg1006 + +lemma sg6111 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg614 sg1008 + +lemma sg6112 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg616 sg1006 + +lemma sg6113 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,3] := by + exact rowSquare_join (by decide) sg621 sg1001 + +lemma sg6114 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg623 sg998 + +lemma sg6115 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [5,5,4,4,1] := by + exact rowSquare_join (by decide) sg616 sg1008 + +lemma sg6116 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg685 sg910 + +lemma sg6117 : RowSquare [5,4,2,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg686 sg910 + +lemma sg6118 : RowSquare [5,4,2,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg910 + +lemma sg6119 : RowSquare [5,4,2,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg623 sg910 + +lemma sg6120 : RowSquare [5,4,2,2,1,1,1,1,1,1] [4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1378 + +lemma sg6121 : RowSquare [5,4,2,2,1,1,1,1,1,1] [4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1379 + +lemma sg6122 : RowSquare [5,4,2,2,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg628 sg910 + +lemma sg6123 : RowSquare [5,4,2,2,1,1,1,1,1,1] [5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg623 sg913 + +lemma sg6124 : RowSquare [5,4,2,2,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg2596 + +lemma sg6125 : RowSquare [5,4,2,2,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg2597 + +lemma sg6126 : RowSquare [5,4,2,2,2,2,1,1] [4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg2596 + +lemma sg6127 : RowSquare [5,4,2,2,2,2,1,1] [4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg2597 + +lemma sg6128 : RowSquare [5,4,2,2,2,2,1,1] [4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg2596 + +lemma sg6129 : RowSquare [5,4,2,2,2,2,1,1] [4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg2597 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes14.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes14.lean index 57b53bbffba1ad51d9462592eb9077ce6a986830..4354d64c5269595974c4a402f3a9f0e079bbdb06 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes14.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes14.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes12 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes11 - -namespace OAI - -/-! Semigroup Nodes 14. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg6130 : RowSquare [5,4,2,2,2,2,1,1] [4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg2598 - -lemma sg6131 : RowSquare [5,4,2,2,2,2,1,1] [4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg561 sg838 - -lemma sg6132 : RowSquare [5,4,2,2,2,2,1,1] [4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg2599 - -lemma sg6133 : RowSquare [5,4,2,2,2,2,1,1] [4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg2600 - -lemma sg6134 : RowSquare [5,4,2,2,2,2,1,1] [4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg2598 - -lemma sg6135 : RowSquare [5,4,2,2,2,2,1,1] [4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg562 sg838 - -lemma sg6136 : RowSquare [5,4,2,2,2,2,1,1] [4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg2599 - -lemma sg6137 : RowSquare [5,4,2,2,2,2,1,1] [5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg2596 - -lemma sg6138 : RowSquare [5,4,2,2,2,2,1,1] [5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg2597 - -lemma sg6139 : RowSquare [5,4,2,2,2,2,1,1] [5,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg2597 - -lemma sg6140 : RowSquare [5,4,2,2,2,2,1,1] [5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg2603 - -lemma sg6141 : RowSquare [5,4,2,2,2,2,1,1] [5,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg2598 - -lemma sg6142 : RowSquare [5,4,2,2,2,2,1,1] [5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg2603 - -lemma sg6143 : RowSquare [5,4,2,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg2596 - -lemma sg6144 : RowSquare [5,4,2,2,2,2,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg2597 - -lemma sg6145 : RowSquare [5,4,2,2,2,2,1,1] [6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg2603 - -lemma sg6146 : RowSquare [5,4,2,2,2,2,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg2597 - -lemma sg6147 : RowSquare [5,4,3,2,1,1,1,1,1] [2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg1682 - -lemma sg6148 : RowSquare [5,4,3,2,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg849 - -lemma sg6149 : RowSquare [5,4,3,2,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg1682 - -lemma sg6150 : RowSquare [5,4,3,2,1,1,1,1,1] [3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg1683 - -lemma sg6151 : RowSquare [5,4,3,2,1,1,1,1,1] [3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg850 - -lemma sg6152 : RowSquare [5,4,3,2,1,1,1,1,1] [3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg180 sg1682 - -lemma sg6153 : RowSquare [5,4,3,2,1,1,1,1,1] [3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg181 sg1682 - -lemma sg6154 : RowSquare [5,4,3,2,1,1,1,1,1] [3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg1686 - -lemma sg6155 : RowSquare [5,4,3,2,1,1,1,1,1] [3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg178 sg1688 - -lemma sg6156 : RowSquare [5,4,3,2,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg182 sg1682 - -lemma sg6157 : RowSquare [5,4,3,2,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg1683 - -lemma sg6158 : RowSquare [5,4,3,2,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg183 sg1682 - -lemma sg6159 : RowSquare [5,4,3,2,1,1,1,1,1] [4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg180 sg1683 - -lemma sg6160 : RowSquare [5,4,3,2,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg184 sg1682 - -lemma sg6161 : RowSquare [5,4,3,2,1,1,1,1,1] [4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg181 sg1683 - -lemma sg6162 : RowSquare [5,4,3,2,1,1,1,1,1] [4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg179 sg1688 - -lemma sg6163 : RowSquare [5,4,3,2,1,1,1,1,1] [4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg862 - -lemma sg6164 : RowSquare [5,4,3,2,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg3299 - -lemma sg6165 : RowSquare [5,4,3,2,1,1,1,1,1] [5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg868 - -lemma sg6166 : RowSquare [5,4,3,2,1,1,1,1,1] [5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg869 - -lemma sg6167 : RowSquare [5,4,3,2,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg3300 - -lemma sg6168 : RowSquare [5,4,3,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg3301 - -lemma sg6169 : RowSquare [5,4,3,2,1,1,1,1,1] [6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg871 - -lemma sg6170 : RowSquare [5,4,3,2,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5298 - -lemma sg6171 : RowSquare [5,4,3,2,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg191 sg1682 - -lemma sg6172 : RowSquare [5,4,3,2,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4639 - -lemma sg6173 : RowSquare [5,4,3,2,1,1,1,1,1] [7,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4640 - -lemma sg6174 : RowSquare [5,4,3,2,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5300 - -lemma sg6175 : RowSquare [5,4,3,2,1,1,1,1,1] [8,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4642 - -lemma sg6176 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg997 - -lemma sg6177 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg998 - -lemma sg6178 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1000 - -lemma sg6179 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1001 - -lemma sg6180 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg1002 - -lemma sg6181 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg1003 - -lemma sg6182 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg998 - -lemma sg6183 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1004 - -lemma sg6184 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg587 sg999 - -lemma sg6185 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1005 - -lemma sg6186 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg1000 - -lemma sg6187 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1001 - -lemma sg6188 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1006 - -lemma sg6189 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg588 sg998 - -lemma sg6190 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1007 - -lemma sg6191 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg589 sg998 - -lemma sg6192 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg999 - -lemma sg6193 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1008 - -lemma sg6194 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg998 - -lemma sg6195 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg588 sg1000 - -lemma sg6196 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg588 sg1001 - -lemma sg6197 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg589 sg999 - -lemma sg6198 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg590 sg999 - -lemma sg6199 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg589 sg1000 - -lemma sg6200 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg589 sg1001 - -lemma sg6201 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg590 sg1000 - -lemma sg6202 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,4,4,3] := by - exact rowSquare_join (by decide) sg590 sg1001 - -lemma sg6203 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg1002 - -lemma sg6204 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg1004 - -lemma sg6205 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1012 - -lemma sg6206 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1005 - -lemma sg6207 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg591 sg1000 - -lemma sg6208 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg591 sg1001 - -lemma sg6209 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1013 - -lemma sg6210 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg1003 - -lemma sg6211 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1014 - -lemma sg6212 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1008 - -lemma sg6213 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg1005 - -lemma sg6214 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg593 sg999 - -lemma sg6215 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg589 sg1004 - -lemma sg6216 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg594 sg999 - -lemma sg6217 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg589 sg1005 - -lemma sg6218 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,3] := by - exact rowSquare_join (by decide) sg593 sg1001 - -lemma sg6219 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg594 sg1000 - -lemma sg6220 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,4,2] := by - exact rowSquare_join (by decide) sg590 sg1005 - -lemma sg6221 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1015 - -lemma sg6222 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg595 sg998 - -lemma sg6223 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg588 sg1006 - -lemma sg6224 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1016 - -lemma sg6225 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg998 - -lemma sg6226 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg1007 - -lemma sg6227 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg589 sg1006 - -lemma sg6228 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg1008 - -lemma sg6229 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg590 sg1006 - -lemma sg6230 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,3] := by - exact rowSquare_join (by decide) sg595 sg1001 - -lemma sg6231 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg999 - -lemma sg6232 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,4,3,2] := by - exact rowSquare_join (by decide) sg590 sg1007 - -lemma sg6233 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,4,4,1] := by - exact rowSquare_join (by decide) sg590 sg1008 - -lemma sg6234 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1017 - -lemma sg6235 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg587 sg1009 - -lemma sg6236 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1018 - -lemma sg6237 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg1010 - -lemma sg6238 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg1009 - -lemma sg6239 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1019 - -lemma sg6240 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1011 - -lemma sg6241 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg591 sg1004 - -lemma sg6242 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1012 - -lemma sg6243 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg591 sg1005 - -lemma sg6244 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg597 sg1000 - -lemma sg6245 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg597 sg1001 - -lemma sg6246 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1020 - -lemma sg6247 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1013 - -lemma sg6248 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg588 sg1010 - -lemma sg6249 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1021 - -lemma sg6250 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1014 - -lemma sg6251 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg1011 - -lemma sg6252 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg589 sg1010 - -lemma sg6253 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg1012 - -lemma sg6254 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg592 sg1005 - -lemma sg6255 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,3] := by - exact rowSquare_join (by decide) sg598 sg1001 - -lemma sg6256 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg599 sg999 - -lemma sg6257 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg589 sg1011 - -lemma sg6258 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg589 sg1012 - -lemma sg6259 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,4,3,2] := by - exact rowSquare_join (by decide) sg590 sg1011 - -lemma sg6260 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,4,4,1] := by - exact rowSquare_join (by decide) sg590 sg1012 - -lemma sg6261 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1022 - -lemma sg6262 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1015 - -lemma sg6263 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg1013 - -lemma sg6264 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg592 sg1006 - -lemma sg6265 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1016 - -lemma sg6266 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg1014 - -lemma sg6267 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg589 sg1013 - -lemma sg6268 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg592 sg1008 - -lemma sg6269 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,3,3,2] := by - exact rowSquare_join (by decide) sg590 sg1013 - -lemma sg6270 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg601 sg999 - -lemma sg6271 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg589 sg1014 - -lemma sg6272 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,4,2,2] := by - exact rowSquare_join (by decide) sg593 sg1007 - -lemma sg6273 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,4,3,1] := by - exact rowSquare_join (by decide) sg590 sg1014 - -lemma sg6274 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,4,4] := by - exact rowSquare_join (by decide) sg594 sg1008 - -lemma sg6275 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1023 - -lemma sg6276 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg998 - -lemma sg6277 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg1015 - -lemma sg6278 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg595 sg1006 - -lemma sg6279 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg1016 - -lemma sg6280 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg589 sg1015 - -lemma sg6281 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,3,2,2] := by - exact rowSquare_join (by decide) sg595 sg1007 - -lemma sg6282 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,3,3,1] := by - exact rowSquare_join (by decide) sg590 sg1015 - -lemma sg6283 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg4643 - -lemma sg6284 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1026 - -lemma sg6285 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg4647 - -lemma sg6286 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg1023 - -lemma sg6287 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [7,7,2,2,1] := by - exact rowSquare_join (by decide) sg590 sg1023 - -lemma sg6288 : RowSquare [5,5,2,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg910 - -lemma sg6289 : RowSquare [5,5,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg910 - -lemma sg6290 : RowSquare [5,5,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg911 - -lemma sg6291 : RowSquare [5,5,2,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg910 - -lemma sg6292 : RowSquare [5,5,2,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg915 - -lemma sg6293 : RowSquare [5,5,2,1,1,1,1,1,1,1] [4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg589 sg914 - -lemma sg6294 : RowSquare [5,5,2,1,1,1,1,1,1,1] [6,6,6,1] := by - exact rowSquare_join (by decide) sg13 sg3173 - -lemma sg6295 : RowSquare [5,5,2,2,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg534 sg910 - -lemma sg6296 : RowSquare [5,5,2,2,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg535 sg910 - -lemma sg6297 : RowSquare [5,5,2,2,1,1,1,1,1] [3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg838 - -lemma sg6298 : RowSquare [5,5,2,2,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg536 sg910 - -lemma sg6299 : RowSquare [5,5,2,2,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg537 sg910 - -lemma sg6300 : RowSquare [5,5,2,2,1,1,1,1,1] [3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg840 - -lemma sg6301 : RowSquare [5,5,2,2,1,1,1,1,1] [3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg841 - -lemma sg6302 : RowSquare [5,5,2,2,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg538 sg910 - -lemma sg6303 : RowSquare [5,5,2,2,1,1,1,1,1] [4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg842 - -lemma sg6304 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg539 sg910 - -lemma sg6305 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg838 - -lemma sg6306 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg844 - -lemma sg6307 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg540 sg910 - -lemma sg6308 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg845 - -lemma sg6309 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg840 - -lemma sg6310 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg841 - -lemma sg6311 : RowSquare [5,5,2,2,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg541 sg910 - -lemma sg6312 : RowSquare [5,5,2,2,1,1,1,1,1] [4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg846 - -lemma sg6313 : RowSquare [5,5,2,2,1,1,1,1,1] [4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg588 sg838 - -lemma sg6314 : RowSquare [5,5,2,2,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg542 sg910 - -lemma sg6315 : RowSquare [5,5,2,2,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg543 sg910 - -lemma sg6316 : RowSquare [5,5,2,2,1,1,1,1,1] [4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg847 - -lemma sg6317 : RowSquare [5,5,2,2,2,2,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg3998 - -lemma sg6318 : RowSquare [5,5,2,2,2,2,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg3999 - -lemma sg6319 : RowSquare [5,5,2,2,2,2,1] [5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg4002 - -lemma sg6320 : RowSquare [5,5,2,2,2,2,1] [5,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg4003 - -lemma sg6321 : RowSquare [5,5,2,2,2,2,1] [5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6 sg4004 - -lemma sg6322 : RowSquare [5,5,2,2,2,2,1] [5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6 sg4005 - -lemma sg6323 : RowSquare [5,5,2,2,2,2,1] [5,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg4007 - -lemma sg6324 : RowSquare [5,5,2,2,2,2,1] [5,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg4009 - -lemma sg6325 : RowSquare [5,5,2,2,2,2,1] [5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg4010 - -lemma sg6326 : RowSquare [5,5,2,2,2,2,1] [5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg4011 - -lemma sg6327 : RowSquare [5,5,2,2,2,2,1] [5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg4015 - -lemma sg6328 : RowSquare [5,5,2,2,2,2,1] [5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg4016 - -lemma sg6329 : RowSquare [5,5,2,2,2,2,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg4006 - -lemma sg6330 : RowSquare [5,5,2,2,2,2,1] [6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg4018 - -lemma sg6331 : RowSquare [5,5,2,2,2,2,1] [6,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg4009 - -lemma sg6332 : RowSquare [5,5,2,2,2,2,1] [6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg4010 - -lemma sg6333 : RowSquare [5,5,2,2,2,2,1] [6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6 sg4011 - -lemma sg6334 : RowSquare [5,5,2,2,2,2,1] [6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg4019 - -lemma sg6335 : RowSquare [5,5,2,2,2,2,1] [6,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg4020 - -lemma sg6336 : RowSquare [5,5,2,2,2,2,1] [6,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4022 - -lemma sg6337 : RowSquare [5,5,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg4018 - -lemma sg6338 : RowSquare [5,5,2,2,2,2,1] [7,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg4019 - -lemma sg6340 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg1327 - -lemma sg6341 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg372 sg1327 - -lemma sg6342 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg1327 - -lemma sg6343 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg1329 - -lemma sg6344 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg370 sg1330 - -lemma sg6345 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg1329 - -lemma sg6346 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg1331 - -lemma sg6347 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg374 sg1328 - -lemma sg6348 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg383 sg1327 - -lemma sg6349 : RowSquare [6,4,2,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg1754 - -lemma sg6350 : RowSquare [6,4,2,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1327 - -lemma sg6351 : RowSquare [6,4,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg1754 - -lemma sg6352 : RowSquare [6,4,2,1,1,1,1,1,1,1] [3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg180 sg1754 - -lemma sg6353 : RowSquare [6,4,2,1,1,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg182 sg1754 - -lemma sg6354 : RowSquare [6,4,2,1,1,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg183 sg1754 - -lemma sg6355 : RowSquare [6,4,2,1,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg184 sg1754 - -lemma sg6356 : RowSquare [6,4,2,1,1,1,1,1,1,1] [4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg185 sg1754 - -lemma sg6357 : RowSquare [6,4,2,1,1,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg186 sg1754 - -lemma sg6358 : RowSquare [6,4,2,1,1,1,1,1,1,1] [5,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg187 sg1754 - -lemma sg6359 : RowSquare [6,4,2,1,1,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg188 sg1754 - -lemma sg6360 : RowSquare [6,4,2,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg1327 - -lemma sg6361 : RowSquare [6,4,2,1,1,1,1,1,1,1] [6,6,6,1] := by - exact rowSquare_join (by decide) sg4 sg3848 - -lemma sg6362 : RowSquare [6,4,2,1,1,1,1,1,1,1] [7,6,6] := by - exact rowSquare_join (by decide) sg16 sg3173 - -lemma sg6363 : RowSquare [6,4,2,1,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4728 - -lemma sg6364 : RowSquare [6,4,2,2,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg142 sg1754 - -lemma sg6365 : RowSquare [6,4,2,2,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg5507 - -lemma sg6366 : RowSquare [6,4,2,2,1,1,1,1,1] [3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg143 sg1754 - -lemma sg6367 : RowSquare [6,4,2,2,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg295 sg1327 - -lemma sg6368 : RowSquare [6,4,2,2,1,1,1,1,1] [3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg144 sg1754 - -lemma sg6369 : RowSquare [6,4,2,2,1,1,1,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg4063 - -lemma sg6370 : RowSquare [6,4,2,2,1,1,1,1,1] [4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg1754 - -lemma sg6371 : RowSquare [6,4,2,2,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg143 sg1755 - -lemma sg6372 : RowSquare [6,4,2,2,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg144 sg1755 - -lemma sg6373 : RowSquare [6,4,2,2,1,1,1,1,1] [4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg295 sg1332 - -lemma sg6374 : RowSquare [6,4,2,2,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg4064 - -lemma sg6375 : RowSquare [6,4,2,2,1,1,1,1,1] [5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg4065 - -lemma sg6376 : RowSquare [6,4,2,2,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg4066 - -lemma sg6377 : RowSquare [6,4,2,2,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg1755 - -lemma sg6378 : RowSquare [6,4,2,2,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5510 - -lemma sg6379 : RowSquare [6,4,2,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg4071 - -lemma sg6380 : RowSquare [6,4,2,2,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4729 - -lemma sg6381 : RowSquare [6,4,2,2,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg303 sg1327 - -lemma sg6382 : RowSquare [6,4,2,2,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4730 - -lemma sg6383 : RowSquare [6,4,2,2,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg304 sg1327 - -lemma sg6384 : RowSquare [6,4,2,2,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg305 sg1327 - -lemma sg6385 : RowSquare [6,4,2,2,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5511 - -lemma sg6386 : RowSquare [6,4,2,2,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4731 - -lemma sg6387 : RowSquare [6,4,2,2,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4732 - -lemma sg6388 : RowSquare [6,4,2,2,1,1,1,1,1] [7,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4733 - -lemma sg6390 : RowSquare [6,4,4,3,1,1] [2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg560 sg730 - -lemma sg6391 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg312 sg1327 - -lemma sg6392 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg5525 - -lemma sg6393 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg313 sg1327 - -lemma sg6394 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg889 - -lemma sg6395 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg314 sg1327 - -lemma sg6396 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg890 - -lemma sg6397 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg315 sg1327 - -lemma sg6398 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg892 - -lemma sg6399 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg312 sg1328 - -lemma sg6400 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg5526 - -lemma sg6401 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg889 - -lemma sg6402 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg588 sg889 - -lemma sg6403 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg313 sg1332 - -lemma sg6404 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg589 sg890 - -lemma sg6405 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg589 sg891 - -lemma sg6406 : RowSquare [6,5,2,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg270 sg1327 - -lemma sg6407 : RowSquare [6,5,2,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg807 - -lemma sg6408 : RowSquare [6,5,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg271 sg1327 - -lemma sg6409 : RowSquare [6,5,2,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg808 - -lemma sg6410 : RowSquare [6,5,2,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg809 - -lemma sg6411 : RowSquare [6,5,2,1,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg132 sg1754 - -lemma sg6412 : RowSquare [6,5,2,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg272 sg1327 - -lemma sg6413 : RowSquare [6,5,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4776 - -lemma sg6414 : RowSquare [6,5,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg4777 - -lemma sg6415 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg133 sg1754 - -lemma sg6416 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg273 sg1327 - -lemma sg6417 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5601 - -lemma sg6418 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg534 sg889 - -lemma sg6419 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg134 sg1754 - -lemma sg6420 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg274 sg1327 - -lemma sg6421 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5602 - -lemma sg6422 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5603 - -lemma sg6423 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg3911 - -lemma sg6424 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5604 - -lemma sg6425 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg808 - -lemma sg6426 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg809 - -lemma sg6427 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg275 sg1327 - -lemma sg6428 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg814 - -lemma sg6429 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg535 sg889 - -lemma sg6430 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg276 sg1327 - -lemma sg6431 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg815 - -lemma sg6432 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg3912 - -lemma sg6433 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg816 - -lemma sg6434 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg537 sg889 - -lemma sg6435 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg817 - -lemma sg6436 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg3913 - -lemma sg6437 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg3914 - -lemma sg6438 : RowSquare [6,5,2,1,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg135 sg1754 - -lemma sg6439 : RowSquare [6,5,2,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4778 - -lemma sg6440 : RowSquare [6,5,2,1,1,1,1,1,1] [5,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg136 sg1754 - -lemma sg6441 : RowSquare [6,5,2,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4780 - -lemma sg6442 : RowSquare [6,5,2,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4781 - -lemma sg6443 : RowSquare [6,5,2,1,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg137 sg1754 - -lemma sg6444 : RowSquare [6,5,2,1,1,1,1,1,1] [5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg280 sg1327 - -lemma sg6445 : RowSquare [6,5,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg281 sg1327 - -lemma sg6446 : RowSquare [6,5,2,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg822 - -lemma sg6447 : RowSquare [6,5,2,1,1,1,1,1,1] [5,5,5,4] := by - exact rowSquare_join (by decide) sg13 sg3197 - -lemma sg6448 : RowSquare [6,5,2,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg138 sg1754 - -lemma sg6449 : RowSquare [6,5,2,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg282 sg1327 - -lemma sg6450 : RowSquare [6,5,2,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg139 sg1754 - -lemma sg6451 : RowSquare [6,5,2,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg283 sg1327 - -lemma sg6452 : RowSquare [6,5,2,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg284 sg1327 - -lemma sg6453 : RowSquare [6,5,2,2,2,1,1] [5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5698 - -lemma sg6454 : RowSquare [6,5,2,2,2,1,1] [5,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5699 - -lemma sg6455 : RowSquare [6,5,2,2,2,1,1] [5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5700 - -lemma sg6456 : RowSquare [6,5,2,2,2,1,1] [5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg5701 - -lemma sg6458 : RowSquare [6,5,3,2,2,1] [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg507 sg757 - -lemma sg6459 : RowSquare [6,5,3,2,2,1] [3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg496 sg756 - -lemma sg6460 : RowSquare [6,5,3,2,2,1] [4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg2036 - -lemma sg6461 : RowSquare [6,5,3,2,2,1] [8,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg466 sg793 - -lemma sg6462 : RowSquare [6,5,3,2,2,1] [8,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg467 sg793 - -lemma sg6463 : RowSquare [6,5,3,2,2,1] [8,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg468 sg793 - -lemma sg6464 : RowSquare [6,6,1,1,1,1,1,1,1] [4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg3210 - -lemma sg6465 : RowSquare [6,6,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg260 sg1327 - -lemma sg6466 : RowSquare [6,6,1,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg261 sg1327 - -lemma sg6467 : RowSquare [6,6,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg262 sg1327 - -lemma sg6468 : RowSquare [7,4,3,2,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg632 sg729 - -lemma sg6469 : RowSquare [7,4,3,2,1,1,1] [2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg632 sg728 - -lemma sg6470 : RowSquare [7,4,3,2,1,1,1] [2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg632 sg727 - -lemma sg6471 : RowSquare [7,4,3,2,1,1,1] [2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg560 sg748 - -lemma sg6472 : RowSquare [7,5,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg3964 - -lemma sg6473 : RowSquare [7,5,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg3964 - -lemma sg6474 : RowSquare [7,5,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg3965 - -lemma sg6475 : RowSquare [7,5,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg3966 - -lemma sg6476 : RowSquare [7,5,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg3255 - -lemma sg6477 : RowSquare [7,5,1,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg3257 - -lemma sg6478 : RowSquare [7,5,1,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg51 sg2251 - -lemma sg6479 : RowSquare [7,5,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg4845 - -lemma sg6480 : RowSquare [7,5,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6 sg3964 - -lemma sg6481 : RowSquare [7,5,1,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg52 sg2251 - -lemma sg6482 : RowSquare [7,5,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg3966 - -lemma sg6483 : RowSquare [7,5,1,1,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg53 sg2251 - -lemma sg6484 : RowSquare [7,5,1,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg54 sg2251 - -lemma sg6485 : RowSquare [7,5,2,1,1,1,1,1] [3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg32 sg2546 - -lemma sg6486 : RowSquare [8,3,2,2,2,1,1] [3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg32 sg2546 - -lemma sg6487 : RowSquare [8,3,3,1,1,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg642 sg734 - -lemma sg6488 : RowSquare [8,3,3,1,1,1,1,1] [3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg220 sg1586 - -lemma sg6489 : RowSquare [8,3,3,1,1,1,1,1] [4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg89 sg2038 - -lemma sg6490 : RowSquare [8,4,4,3] [4,4,4,4,3] := by - exact rowSquare_join (by decide) sg551 sg834 - -lemma sg6491 : RowSquare [9,3,3,2,1,1] [5,5,5,4] := by - exact rowSquare_join (by decide) sg373 sg1200 - -lemma sg6492 : RowSquare [9,4,3,1,1,1] [2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg306 sg1327 - -lemma sg6493 : RowSquare [9,4,3,1,1,1] [3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg306 sg1330 - -lemma sg6494 : RowSquare [9,4,3,1,1,1] [3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg306 sg1331 - -lemma sg6495 : RowSquare [9,4,3,1,1,1] [4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg1196 - -lemma sg6496 : RowSquare [9,4,3,1,1,1] [5,5,5,4] := by - exact rowSquare_join (by decide) sg390 sg1200 - -lemma sg6497 : RowSquare [9,4,3,2,1] [2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg849 - -lemma sg6498 : RowSquare [9,4,3,2,1] [3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg178 sg1688 - -lemma sg6499 : RowSquare [9,4,3,2,1] [4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg179 sg1688 - -lemma sg6500 : RowSquare [9,4,4,1,1] [3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg516 sg1001 - -lemma sg6501 : RowSquare [9,5,3,1,1] [4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg577 sg912 - -lemma sg6503 : RowSquare [10,3,2,1,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg2251 - -lemma sg6504 : RowSquare [10,3,2,2,1,1] [2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg1754 - -lemma sg6505 : RowSquare [10,3,2,2,1,1] [4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg332 sg1332 - -lemma sg6506 : RowSquare [10,3,2,2,1,1] [4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg615 sg891 - -lemma sg6507 : RowSquare [10,3,2,2,1,1] [4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg334 sg1331 - -lemma sg6508 : RowSquare [10,3,2,2,2] [4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg913 - -lemma sg6509 : RowSquare [10,3,3,1,1,1] [4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg348 sg1332 - -lemma sg6510 : RowSquare [10,3,3,1,1,1] [4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg350 sg1330 - -lemma sg6511 : RowSquare [10,3,3,1,1,1] [4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg350 sg1331 - -lemma sg6512 : RowSquare [10,3,3,1,1,1] [4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg637 sg891 - -lemma sg6513 : RowSquare [10,3,3,2,1] [4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg550 sg1000 - -lemma sg6514 : RowSquare [10,3,3,2,1] [4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg550 sg1001 - -lemma sg6515 : RowSquare [10,3,3,2,1] [4,4,4,4,3] := by - exact rowSquare_join (by decide) sg551 sg1001 - -lemma sg6516 : RowSquare [10,3,3,2,1] [5,5,3,3,3] := by - exact rowSquare_join (by decide) sg552 sg1001 - -lemma sg6517 : RowSquare [10,3,3,2,1] [5,5,5,4] := by - exact rowSquare_join (by decide) sg373 sg1272 - -lemma sg6518 : RowSquare [10,4,2,1,1,1] [3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg358 sg1327 - -lemma sg6519 : RowSquare [10,4,2,1,1,1] [4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg358 sg1329 - -lemma sg6520 : RowSquare [3,2,2,2,2,2,1,1,1,1,1,1,1] [7,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg1068 sg1115 - -lemma sg6521 : RowSquare [3,2,2,2,2,2,1,1,1,1,1,1,1] [7,6,4,2,1] := by - exact rowSquare_join (by decide) sg1069 sg1115 - -lemma sg6522 : RowSquare [3,2,2,2,2,2,1,1,1,1,1,1,1] [7,6,4,3] := by - exact rowSquare_join (by decide) sg693 sg1549 - -lemma sg6523 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,2] := by - exact rowSquare_join (by decide) sg1061 sg1114 - -lemma sg6524 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,1] := by - exact rowSquare_join (by decide) sg692 sg1539 - -lemma sg6525 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,5,4] := by - exact rowSquare_join (by decide) sg693 sg1539 - -lemma sg6526 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,4,2,2] := by - exact rowSquare_join (by decide) sg1061 sg1115 - -lemma sg6527 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,4,3,1] := by - exact rowSquare_join (by decide) sg694 sg1539 - -lemma sg6528 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,4,4] := by - exact rowSquare_join (by decide) sg390 sg1980 - -lemma sg6529 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,5,2,1] := by - exact rowSquare_join (by decide) sg695 sg1538 - -lemma sg6530 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,5,3] := by - exact rowSquare_join (by decide) sg695 sg1539 - -lemma sg6531 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1068 sg1104 - -lemma sg6532 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1068 sg1105 - -lemma sg6533 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,2] := by - exact rowSquare_join (by decide) sg1061 sg1116 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes12 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes11 + +namespace OAI + +/-! Semigroup Nodes 14. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg6130 : RowSquare [5,4,2,2,2,2,1,1] [4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg2598 + +lemma sg6131 : RowSquare [5,4,2,2,2,2,1,1] [4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg561 sg838 + +lemma sg6132 : RowSquare [5,4,2,2,2,2,1,1] [4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg2599 + +lemma sg6133 : RowSquare [5,4,2,2,2,2,1,1] [4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg2600 + +lemma sg6134 : RowSquare [5,4,2,2,2,2,1,1] [4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg2598 + +lemma sg6135 : RowSquare [5,4,2,2,2,2,1,1] [4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg562 sg838 + +lemma sg6136 : RowSquare [5,4,2,2,2,2,1,1] [4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg2599 + +lemma sg6137 : RowSquare [5,4,2,2,2,2,1,1] [5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg2596 + +lemma sg6138 : RowSquare [5,4,2,2,2,2,1,1] [5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg2597 + +lemma sg6139 : RowSquare [5,4,2,2,2,2,1,1] [5,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg2597 + +lemma sg6140 : RowSquare [5,4,2,2,2,2,1,1] [5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg2603 + +lemma sg6141 : RowSquare [5,4,2,2,2,2,1,1] [5,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg2598 + +lemma sg6142 : RowSquare [5,4,2,2,2,2,1,1] [5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg2603 + +lemma sg6143 : RowSquare [5,4,2,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg2596 + +lemma sg6144 : RowSquare [5,4,2,2,2,2,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg2597 + +lemma sg6145 : RowSquare [5,4,2,2,2,2,1,1] [6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg2603 + +lemma sg6146 : RowSquare [5,4,2,2,2,2,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg2597 + +lemma sg6147 : RowSquare [5,4,3,2,1,1,1,1,1] [2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg1682 + +lemma sg6148 : RowSquare [5,4,3,2,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg849 + +lemma sg6149 : RowSquare [5,4,3,2,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg1682 + +lemma sg6150 : RowSquare [5,4,3,2,1,1,1,1,1] [3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg1683 + +lemma sg6151 : RowSquare [5,4,3,2,1,1,1,1,1] [3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg850 + +lemma sg6152 : RowSquare [5,4,3,2,1,1,1,1,1] [3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg180 sg1682 + +lemma sg6153 : RowSquare [5,4,3,2,1,1,1,1,1] [3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg181 sg1682 + +lemma sg6154 : RowSquare [5,4,3,2,1,1,1,1,1] [3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg1686 + +lemma sg6155 : RowSquare [5,4,3,2,1,1,1,1,1] [3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg178 sg1688 + +lemma sg6156 : RowSquare [5,4,3,2,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg182 sg1682 + +lemma sg6157 : RowSquare [5,4,3,2,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg1683 + +lemma sg6158 : RowSquare [5,4,3,2,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg183 sg1682 + +lemma sg6159 : RowSquare [5,4,3,2,1,1,1,1,1] [4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg180 sg1683 + +lemma sg6160 : RowSquare [5,4,3,2,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg184 sg1682 + +lemma sg6161 : RowSquare [5,4,3,2,1,1,1,1,1] [4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg181 sg1683 + +lemma sg6162 : RowSquare [5,4,3,2,1,1,1,1,1] [4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg179 sg1688 + +lemma sg6163 : RowSquare [5,4,3,2,1,1,1,1,1] [4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg862 + +lemma sg6164 : RowSquare [5,4,3,2,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg3299 + +lemma sg6165 : RowSquare [5,4,3,2,1,1,1,1,1] [5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg868 + +lemma sg6166 : RowSquare [5,4,3,2,1,1,1,1,1] [5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg869 + +lemma sg6167 : RowSquare [5,4,3,2,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg3300 + +lemma sg6168 : RowSquare [5,4,3,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg3301 + +lemma sg6169 : RowSquare [5,4,3,2,1,1,1,1,1] [6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg871 + +lemma sg6170 : RowSquare [5,4,3,2,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5298 + +lemma sg6171 : RowSquare [5,4,3,2,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg191 sg1682 + +lemma sg6172 : RowSquare [5,4,3,2,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4639 + +lemma sg6173 : RowSquare [5,4,3,2,1,1,1,1,1] [7,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4640 + +lemma sg6174 : RowSquare [5,4,3,2,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5300 + +lemma sg6175 : RowSquare [5,4,3,2,1,1,1,1,1] [8,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4642 + +lemma sg6176 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg997 + +lemma sg6177 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg998 + +lemma sg6178 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1000 + +lemma sg6179 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1001 + +lemma sg6180 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg1002 + +lemma sg6181 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg1003 + +lemma sg6182 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg998 + +lemma sg6183 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1004 + +lemma sg6184 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg587 sg999 + +lemma sg6185 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1005 + +lemma sg6186 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg1000 + +lemma sg6187 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1001 + +lemma sg6188 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1006 + +lemma sg6189 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg588 sg998 + +lemma sg6190 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1007 + +lemma sg6191 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg589 sg998 + +lemma sg6192 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg999 + +lemma sg6193 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1008 + +lemma sg6194 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg998 + +lemma sg6195 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg588 sg1000 + +lemma sg6196 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg588 sg1001 + +lemma sg6197 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg589 sg999 + +lemma sg6198 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg590 sg999 + +lemma sg6199 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg589 sg1000 + +lemma sg6200 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg589 sg1001 + +lemma sg6201 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg590 sg1000 + +lemma sg6202 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [4,4,4,4,3] := by + exact rowSquare_join (by decide) sg590 sg1001 + +lemma sg6203 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg1002 + +lemma sg6204 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg1004 + +lemma sg6205 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1012 + +lemma sg6206 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1005 + +lemma sg6207 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg591 sg1000 + +lemma sg6208 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg591 sg1001 + +lemma sg6209 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1013 + +lemma sg6210 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg1003 + +lemma sg6211 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1014 + +lemma sg6212 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1008 + +lemma sg6213 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg1005 + +lemma sg6214 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg593 sg999 + +lemma sg6215 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg589 sg1004 + +lemma sg6216 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg594 sg999 + +lemma sg6217 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg589 sg1005 + +lemma sg6218 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,3] := by + exact rowSquare_join (by decide) sg593 sg1001 + +lemma sg6219 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg594 sg1000 + +lemma sg6220 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,4,4,4,2] := by + exact rowSquare_join (by decide) sg590 sg1005 + +lemma sg6221 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1015 + +lemma sg6222 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg595 sg998 + +lemma sg6223 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg588 sg1006 + +lemma sg6224 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1016 + +lemma sg6225 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg998 + +lemma sg6226 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg1007 + +lemma sg6227 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg589 sg1006 + +lemma sg6228 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg1008 + +lemma sg6229 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg590 sg1006 + +lemma sg6230 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,3] := by + exact rowSquare_join (by decide) sg595 sg1001 + +lemma sg6231 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg999 + +lemma sg6232 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,4,3,2] := by + exact rowSquare_join (by decide) sg590 sg1007 + +lemma sg6233 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [5,5,4,4,1] := by + exact rowSquare_join (by decide) sg590 sg1008 + +lemma sg6234 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1017 + +lemma sg6235 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg587 sg1009 + +lemma sg6236 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1018 + +lemma sg6237 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg1010 + +lemma sg6238 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg1009 + +lemma sg6239 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1019 + +lemma sg6240 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1011 + +lemma sg6241 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg591 sg1004 + +lemma sg6242 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1012 + +lemma sg6243 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg591 sg1005 + +lemma sg6244 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg597 sg1000 + +lemma sg6245 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg597 sg1001 + +lemma sg6246 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1020 + +lemma sg6247 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1013 + +lemma sg6248 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg588 sg1010 + +lemma sg6249 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1021 + +lemma sg6250 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1014 + +lemma sg6251 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg1011 + +lemma sg6252 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg589 sg1010 + +lemma sg6253 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg1012 + +lemma sg6254 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg592 sg1005 + +lemma sg6255 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,3] := by + exact rowSquare_join (by decide) sg598 sg1001 + +lemma sg6256 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg599 sg999 + +lemma sg6257 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg589 sg1011 + +lemma sg6258 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg589 sg1012 + +lemma sg6259 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,4,3,2] := by + exact rowSquare_join (by decide) sg590 sg1011 + +lemma sg6260 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,4,4,4,1] := by + exact rowSquare_join (by decide) sg590 sg1012 + +lemma sg6261 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1022 + +lemma sg6262 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1015 + +lemma sg6263 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg1013 + +lemma sg6264 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg592 sg1006 + +lemma sg6265 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1016 + +lemma sg6266 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg1014 + +lemma sg6267 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg589 sg1013 + +lemma sg6268 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg592 sg1008 + +lemma sg6269 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,3,3,2] := by + exact rowSquare_join (by decide) sg590 sg1013 + +lemma sg6270 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg601 sg999 + +lemma sg6271 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg589 sg1014 + +lemma sg6272 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,4,2,2] := by + exact rowSquare_join (by decide) sg593 sg1007 + +lemma sg6273 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,4,3,1] := by + exact rowSquare_join (by decide) sg590 sg1014 + +lemma sg6274 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,5,4,4] := by + exact rowSquare_join (by decide) sg594 sg1008 + +lemma sg6275 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1023 + +lemma sg6276 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg998 + +lemma sg6277 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg1015 + +lemma sg6278 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg595 sg1006 + +lemma sg6279 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg1016 + +lemma sg6280 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg589 sg1015 + +lemma sg6281 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,3,2,2] := by + exact rowSquare_join (by decide) sg595 sg1007 + +lemma sg6282 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [6,6,3,3,1] := by + exact rowSquare_join (by decide) sg590 sg1015 + +lemma sg6283 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg4643 + +lemma sg6284 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1026 + +lemma sg6285 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg4647 + +lemma sg6286 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg1023 + +lemma sg6287 : RowSquare [5,5,1,1,1,1,1,1,1,1,1] [7,7,2,2,1] := by + exact rowSquare_join (by decide) sg590 sg1023 + +lemma sg6288 : RowSquare [5,5,2,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg910 + +lemma sg6289 : RowSquare [5,5,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg910 + +lemma sg6290 : RowSquare [5,5,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg911 + +lemma sg6291 : RowSquare [5,5,2,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg910 + +lemma sg6292 : RowSquare [5,5,2,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg915 + +lemma sg6293 : RowSquare [5,5,2,1,1,1,1,1,1,1] [4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg589 sg914 + +lemma sg6294 : RowSquare [5,5,2,1,1,1,1,1,1,1] [6,6,6,1] := by + exact rowSquare_join (by decide) sg13 sg3173 + +lemma sg6295 : RowSquare [5,5,2,2,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg534 sg910 + +lemma sg6296 : RowSquare [5,5,2,2,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg535 sg910 + +lemma sg6297 : RowSquare [5,5,2,2,1,1,1,1,1] [3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg838 + +lemma sg6298 : RowSquare [5,5,2,2,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg536 sg910 + +lemma sg6299 : RowSquare [5,5,2,2,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg537 sg910 + +lemma sg6300 : RowSquare [5,5,2,2,1,1,1,1,1] [3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg840 + +lemma sg6301 : RowSquare [5,5,2,2,1,1,1,1,1] [3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg841 + +lemma sg6302 : RowSquare [5,5,2,2,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg538 sg910 + +lemma sg6303 : RowSquare [5,5,2,2,1,1,1,1,1] [4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg842 + +lemma sg6304 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg539 sg910 + +lemma sg6305 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg838 + +lemma sg6306 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg844 + +lemma sg6307 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg540 sg910 + +lemma sg6308 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg845 + +lemma sg6309 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg840 + +lemma sg6310 : RowSquare [5,5,2,2,1,1,1,1,1] [4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg841 + +lemma sg6311 : RowSquare [5,5,2,2,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg541 sg910 + +lemma sg6312 : RowSquare [5,5,2,2,1,1,1,1,1] [4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg846 + +lemma sg6313 : RowSquare [5,5,2,2,1,1,1,1,1] [4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg588 sg838 + +lemma sg6314 : RowSquare [5,5,2,2,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg542 sg910 + +lemma sg6315 : RowSquare [5,5,2,2,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg543 sg910 + +lemma sg6316 : RowSquare [5,5,2,2,1,1,1,1,1] [4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg847 + +lemma sg6317 : RowSquare [5,5,2,2,2,2,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg3998 + +lemma sg6318 : RowSquare [5,5,2,2,2,2,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg3999 + +lemma sg6319 : RowSquare [5,5,2,2,2,2,1] [5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg4002 + +lemma sg6320 : RowSquare [5,5,2,2,2,2,1] [5,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg4003 + +lemma sg6321 : RowSquare [5,5,2,2,2,2,1] [5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6 sg4004 + +lemma sg6322 : RowSquare [5,5,2,2,2,2,1] [5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6 sg4005 + +lemma sg6323 : RowSquare [5,5,2,2,2,2,1] [5,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg4007 + +lemma sg6324 : RowSquare [5,5,2,2,2,2,1] [5,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg4009 + +lemma sg6325 : RowSquare [5,5,2,2,2,2,1] [5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg4010 + +lemma sg6326 : RowSquare [5,5,2,2,2,2,1] [5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg4011 + +lemma sg6327 : RowSquare [5,5,2,2,2,2,1] [5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg4015 + +lemma sg6328 : RowSquare [5,5,2,2,2,2,1] [5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg4016 + +lemma sg6329 : RowSquare [5,5,2,2,2,2,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg4006 + +lemma sg6330 : RowSquare [5,5,2,2,2,2,1] [6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg4018 + +lemma sg6331 : RowSquare [5,5,2,2,2,2,1] [6,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg4009 + +lemma sg6332 : RowSquare [5,5,2,2,2,2,1] [6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg4010 + +lemma sg6333 : RowSquare [5,5,2,2,2,2,1] [6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6 sg4011 + +lemma sg6334 : RowSquare [5,5,2,2,2,2,1] [6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg4019 + +lemma sg6335 : RowSquare [5,5,2,2,2,2,1] [6,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg4020 + +lemma sg6336 : RowSquare [5,5,2,2,2,2,1] [6,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4022 + +lemma sg6337 : RowSquare [5,5,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg4018 + +lemma sg6338 : RowSquare [5,5,2,2,2,2,1] [7,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg4019 + +lemma sg6340 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg1327 + +lemma sg6341 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg372 sg1327 + +lemma sg6342 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg1327 + +lemma sg6343 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg1329 + +lemma sg6344 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg370 sg1330 + +lemma sg6345 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg1329 + +lemma sg6346 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg1331 + +lemma sg6347 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg374 sg1328 + +lemma sg6348 : RowSquare [6,4,1,1,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg383 sg1327 + +lemma sg6349 : RowSquare [6,4,2,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg1754 + +lemma sg6350 : RowSquare [6,4,2,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1327 + +lemma sg6351 : RowSquare [6,4,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg1754 + +lemma sg6352 : RowSquare [6,4,2,1,1,1,1,1,1,1] [3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg180 sg1754 + +lemma sg6353 : RowSquare [6,4,2,1,1,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg182 sg1754 + +lemma sg6354 : RowSquare [6,4,2,1,1,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg183 sg1754 + +lemma sg6355 : RowSquare [6,4,2,1,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg184 sg1754 + +lemma sg6356 : RowSquare [6,4,2,1,1,1,1,1,1,1] [4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg185 sg1754 + +lemma sg6357 : RowSquare [6,4,2,1,1,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg186 sg1754 + +lemma sg6358 : RowSquare [6,4,2,1,1,1,1,1,1,1] [5,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg187 sg1754 + +lemma sg6359 : RowSquare [6,4,2,1,1,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg188 sg1754 + +lemma sg6360 : RowSquare [6,4,2,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg1327 + +lemma sg6361 : RowSquare [6,4,2,1,1,1,1,1,1,1] [6,6,6,1] := by + exact rowSquare_join (by decide) sg4 sg3848 + +lemma sg6362 : RowSquare [6,4,2,1,1,1,1,1,1,1] [7,6,6] := by + exact rowSquare_join (by decide) sg16 sg3173 + +lemma sg6363 : RowSquare [6,4,2,1,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4728 + +lemma sg6364 : RowSquare [6,4,2,2,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg142 sg1754 + +lemma sg6365 : RowSquare [6,4,2,2,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg5507 + +lemma sg6366 : RowSquare [6,4,2,2,1,1,1,1,1] [3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg143 sg1754 + +lemma sg6367 : RowSquare [6,4,2,2,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg295 sg1327 + +lemma sg6368 : RowSquare [6,4,2,2,1,1,1,1,1] [3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg144 sg1754 + +lemma sg6369 : RowSquare [6,4,2,2,1,1,1,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg4063 + +lemma sg6370 : RowSquare [6,4,2,2,1,1,1,1,1] [4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg1754 + +lemma sg6371 : RowSquare [6,4,2,2,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg143 sg1755 + +lemma sg6372 : RowSquare [6,4,2,2,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg144 sg1755 + +lemma sg6373 : RowSquare [6,4,2,2,1,1,1,1,1] [4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg295 sg1332 + +lemma sg6374 : RowSquare [6,4,2,2,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg4064 + +lemma sg6375 : RowSquare [6,4,2,2,1,1,1,1,1] [5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg4065 + +lemma sg6376 : RowSquare [6,4,2,2,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg4066 + +lemma sg6377 : RowSquare [6,4,2,2,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg1755 + +lemma sg6378 : RowSquare [6,4,2,2,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5510 + +lemma sg6379 : RowSquare [6,4,2,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg4071 + +lemma sg6380 : RowSquare [6,4,2,2,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4729 + +lemma sg6381 : RowSquare [6,4,2,2,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg303 sg1327 + +lemma sg6382 : RowSquare [6,4,2,2,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4730 + +lemma sg6383 : RowSquare [6,4,2,2,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg304 sg1327 + +lemma sg6384 : RowSquare [6,4,2,2,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg305 sg1327 + +lemma sg6385 : RowSquare [6,4,2,2,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5511 + +lemma sg6386 : RowSquare [6,4,2,2,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4731 + +lemma sg6387 : RowSquare [6,4,2,2,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4732 + +lemma sg6388 : RowSquare [6,4,2,2,1,1,1,1,1] [7,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4733 + +lemma sg6390 : RowSquare [6,4,4,3,1,1] [2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg560 sg730 + +lemma sg6391 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg312 sg1327 + +lemma sg6392 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg5525 + +lemma sg6393 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg313 sg1327 + +lemma sg6394 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg889 + +lemma sg6395 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg314 sg1327 + +lemma sg6396 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg890 + +lemma sg6397 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg315 sg1327 + +lemma sg6398 : RowSquare [6,5,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg892 + +lemma sg6399 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg312 sg1328 + +lemma sg6400 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg5526 + +lemma sg6401 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg889 + +lemma sg6402 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg588 sg889 + +lemma sg6403 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg313 sg1332 + +lemma sg6404 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg589 sg890 + +lemma sg6405 : RowSquare [6,5,1,1,1,1,1,1,1,1] [4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg589 sg891 + +lemma sg6406 : RowSquare [6,5,2,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg270 sg1327 + +lemma sg6407 : RowSquare [6,5,2,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg807 + +lemma sg6408 : RowSquare [6,5,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg271 sg1327 + +lemma sg6409 : RowSquare [6,5,2,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg808 + +lemma sg6410 : RowSquare [6,5,2,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg809 + +lemma sg6411 : RowSquare [6,5,2,1,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg132 sg1754 + +lemma sg6412 : RowSquare [6,5,2,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg272 sg1327 + +lemma sg6413 : RowSquare [6,5,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4776 + +lemma sg6414 : RowSquare [6,5,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg4777 + +lemma sg6415 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg133 sg1754 + +lemma sg6416 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg273 sg1327 + +lemma sg6417 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5601 + +lemma sg6418 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg534 sg889 + +lemma sg6419 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg134 sg1754 + +lemma sg6420 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg274 sg1327 + +lemma sg6421 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5602 + +lemma sg6422 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5603 + +lemma sg6423 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg3911 + +lemma sg6424 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5604 + +lemma sg6425 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg808 + +lemma sg6426 : RowSquare [6,5,2,1,1,1,1,1,1] [4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg809 + +lemma sg6427 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg275 sg1327 + +lemma sg6428 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg814 + +lemma sg6429 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg535 sg889 + +lemma sg6430 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg276 sg1327 + +lemma sg6431 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg815 + +lemma sg6432 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg3912 + +lemma sg6433 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg816 + +lemma sg6434 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg537 sg889 + +lemma sg6435 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg817 + +lemma sg6436 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg3913 + +lemma sg6437 : RowSquare [6,5,2,1,1,1,1,1,1] [4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg3914 + +lemma sg6438 : RowSquare [6,5,2,1,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg135 sg1754 + +lemma sg6439 : RowSquare [6,5,2,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4778 + +lemma sg6440 : RowSquare [6,5,2,1,1,1,1,1,1] [5,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg136 sg1754 + +lemma sg6441 : RowSquare [6,5,2,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4780 + +lemma sg6442 : RowSquare [6,5,2,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4781 + +lemma sg6443 : RowSquare [6,5,2,1,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg137 sg1754 + +lemma sg6444 : RowSquare [6,5,2,1,1,1,1,1,1] [5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg280 sg1327 + +lemma sg6445 : RowSquare [6,5,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg281 sg1327 + +lemma sg6446 : RowSquare [6,5,2,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg822 + +lemma sg6447 : RowSquare [6,5,2,1,1,1,1,1,1] [5,5,5,4] := by + exact rowSquare_join (by decide) sg13 sg3197 + +lemma sg6448 : RowSquare [6,5,2,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg138 sg1754 + +lemma sg6449 : RowSquare [6,5,2,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg282 sg1327 + +lemma sg6450 : RowSquare [6,5,2,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg139 sg1754 + +lemma sg6451 : RowSquare [6,5,2,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg283 sg1327 + +lemma sg6452 : RowSquare [6,5,2,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg284 sg1327 + +lemma sg6453 : RowSquare [6,5,2,2,2,1,1] [5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5698 + +lemma sg6454 : RowSquare [6,5,2,2,2,1,1] [5,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5699 + +lemma sg6455 : RowSquare [6,5,2,2,2,1,1] [5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5700 + +lemma sg6456 : RowSquare [6,5,2,2,2,1,1] [5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg5701 + +lemma sg6458 : RowSquare [6,5,3,2,2,1] [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg507 sg757 + +lemma sg6459 : RowSquare [6,5,3,2,2,1] [3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg496 sg756 + +lemma sg6460 : RowSquare [6,5,3,2,2,1] [4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg2036 + +lemma sg6461 : RowSquare [6,5,3,2,2,1] [8,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg466 sg793 + +lemma sg6462 : RowSquare [6,5,3,2,2,1] [8,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg467 sg793 + +lemma sg6463 : RowSquare [6,5,3,2,2,1] [8,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg468 sg793 + +lemma sg6464 : RowSquare [6,6,1,1,1,1,1,1,1] [4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg3210 + +lemma sg6465 : RowSquare [6,6,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg260 sg1327 + +lemma sg6466 : RowSquare [6,6,1,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg261 sg1327 + +lemma sg6467 : RowSquare [6,6,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg262 sg1327 + +lemma sg6468 : RowSquare [7,4,3,2,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg632 sg729 + +lemma sg6469 : RowSquare [7,4,3,2,1,1,1] [2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg632 sg728 + +lemma sg6470 : RowSquare [7,4,3,2,1,1,1] [2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg632 sg727 + +lemma sg6471 : RowSquare [7,4,3,2,1,1,1] [2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg560 sg748 + +lemma sg6472 : RowSquare [7,5,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg3964 + +lemma sg6473 : RowSquare [7,5,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg3964 + +lemma sg6474 : RowSquare [7,5,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg3965 + +lemma sg6475 : RowSquare [7,5,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg3966 + +lemma sg6476 : RowSquare [7,5,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg3255 + +lemma sg6477 : RowSquare [7,5,1,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg3257 + +lemma sg6478 : RowSquare [7,5,1,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg51 sg2251 + +lemma sg6479 : RowSquare [7,5,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg4845 + +lemma sg6480 : RowSquare [7,5,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6 sg3964 + +lemma sg6481 : RowSquare [7,5,1,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg52 sg2251 + +lemma sg6482 : RowSquare [7,5,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg3966 + +lemma sg6483 : RowSquare [7,5,1,1,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg53 sg2251 + +lemma sg6484 : RowSquare [7,5,1,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg54 sg2251 + +lemma sg6485 : RowSquare [7,5,2,1,1,1,1,1] [3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg32 sg2546 + +lemma sg6486 : RowSquare [8,3,2,2,2,1,1] [3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg32 sg2546 + +lemma sg6487 : RowSquare [8,3,3,1,1,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg642 sg734 + +lemma sg6488 : RowSquare [8,3,3,1,1,1,1,1] [3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg220 sg1586 + +lemma sg6489 : RowSquare [8,3,3,1,1,1,1,1] [4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg89 sg2038 + +lemma sg6490 : RowSquare [8,4,4,3] [4,4,4,4,3] := by + exact rowSquare_join (by decide) sg551 sg834 + +lemma sg6491 : RowSquare [9,3,3,2,1,1] [5,5,5,4] := by + exact rowSquare_join (by decide) sg373 sg1200 + +lemma sg6492 : RowSquare [9,4,3,1,1,1] [2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg306 sg1327 + +lemma sg6493 : RowSquare [9,4,3,1,1,1] [3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg306 sg1330 + +lemma sg6494 : RowSquare [9,4,3,1,1,1] [3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg306 sg1331 + +lemma sg6495 : RowSquare [9,4,3,1,1,1] [4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg1196 + +lemma sg6496 : RowSquare [9,4,3,1,1,1] [5,5,5,4] := by + exact rowSquare_join (by decide) sg390 sg1200 + +lemma sg6497 : RowSquare [9,4,3,2,1] [2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg849 + +lemma sg6498 : RowSquare [9,4,3,2,1] [3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg178 sg1688 + +lemma sg6499 : RowSquare [9,4,3,2,1] [4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg179 sg1688 + +lemma sg6500 : RowSquare [9,4,4,1,1] [3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg516 sg1001 + +lemma sg6501 : RowSquare [9,5,3,1,1] [4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg577 sg912 + +lemma sg6503 : RowSquare [10,3,2,1,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg2251 + +lemma sg6504 : RowSquare [10,3,2,2,1,1] [2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg1754 + +lemma sg6505 : RowSquare [10,3,2,2,1,1] [4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg332 sg1332 + +lemma sg6506 : RowSquare [10,3,2,2,1,1] [4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg615 sg891 + +lemma sg6507 : RowSquare [10,3,2,2,1,1] [4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg334 sg1331 + +lemma sg6508 : RowSquare [10,3,2,2,2] [4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg913 + +lemma sg6509 : RowSquare [10,3,3,1,1,1] [4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg348 sg1332 + +lemma sg6510 : RowSquare [10,3,3,1,1,1] [4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg350 sg1330 + +lemma sg6511 : RowSquare [10,3,3,1,1,1] [4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg350 sg1331 + +lemma sg6512 : RowSquare [10,3,3,1,1,1] [4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg637 sg891 + +lemma sg6513 : RowSquare [10,3,3,2,1] [4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg550 sg1000 + +lemma sg6514 : RowSquare [10,3,3,2,1] [4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg550 sg1001 + +lemma sg6515 : RowSquare [10,3,3,2,1] [4,4,4,4,3] := by + exact rowSquare_join (by decide) sg551 sg1001 + +lemma sg6516 : RowSquare [10,3,3,2,1] [5,5,3,3,3] := by + exact rowSquare_join (by decide) sg552 sg1001 + +lemma sg6517 : RowSquare [10,3,3,2,1] [5,5,5,4] := by + exact rowSquare_join (by decide) sg373 sg1272 + +lemma sg6518 : RowSquare [10,4,2,1,1,1] [3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg358 sg1327 + +lemma sg6519 : RowSquare [10,4,2,1,1,1] [4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg358 sg1329 + +lemma sg6520 : RowSquare [3,2,2,2,2,2,1,1,1,1,1,1,1] [7,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg1068 sg1115 + +lemma sg6521 : RowSquare [3,2,2,2,2,2,1,1,1,1,1,1,1] [7,6,4,2,1] := by + exact rowSquare_join (by decide) sg1069 sg1115 + +lemma sg6522 : RowSquare [3,2,2,2,2,2,1,1,1,1,1,1,1] [7,6,4,3] := by + exact rowSquare_join (by decide) sg693 sg1549 + +lemma sg6523 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,2] := by + exact rowSquare_join (by decide) sg1061 sg1114 + +lemma sg6524 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,1] := by + exact rowSquare_join (by decide) sg692 sg1539 + +lemma sg6525 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,5,4] := by + exact rowSquare_join (by decide) sg693 sg1539 + +lemma sg6526 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,4,2,2] := by + exact rowSquare_join (by decide) sg1061 sg1115 + +lemma sg6527 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,4,3,1] := by + exact rowSquare_join (by decide) sg694 sg1539 + +lemma sg6528 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,4,4] := by + exact rowSquare_join (by decide) sg390 sg1980 + +lemma sg6529 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,5,2,1] := by + exact rowSquare_join (by decide) sg695 sg1538 + +lemma sg6530 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,5,3] := by + exact rowSquare_join (by decide) sg695 sg1539 + +lemma sg6531 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1068 sg1104 + +lemma sg6532 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1068 sg1105 + +lemma sg6533 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,2] := by + exact rowSquare_join (by decide) sg1061 sg1116 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes15.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes15.lean index c0be9e8249f4a23be85b75fc170cda6881335d5e..1f985178ab28dd084a49fd386feb11b3755c30a2 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes15.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes15.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes13 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes11 - -namespace OAI - -/-! Semigroup Nodes 15. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg6534 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,4,4,1] := by - exact rowSquare_join (by decide) sg1069 sg1105 - -lemma sg6535 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg1068 sg1106 - -lemma sg6536 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg1070 sg1105 - -lemma sg6537 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,2] := by - exact rowSquare_join (by decide) sg1061 sg1117 - -lemma sg6538 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg1068 sg1107 - -lemma sg6539 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,2] := by - exact rowSquare_join (by decide) sg1061 sg1118 - -lemma sg6540 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,1] := by - exact rowSquare_join (by decide) sg1069 sg1107 - -lemma sg6541 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,4,4] := by - exact rowSquare_join (by decide) sg1072 sg1105 - -lemma sg6542 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg1068 sg1108 - -lemma sg6543 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,5,2,1] := by - exact rowSquare_join (by decide) sg1069 sg1108 - -lemma sg6544 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,5,3] := by - exact rowSquare_join (by decide) sg1105 sg1073 - -lemma sg6545 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg1070 sg1106 - -lemma sg6546 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg1068 sg1109 - -lemma sg6547 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,2] := by - exact rowSquare_join (by decide) sg1061 sg1119 - -lemma sg6548 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,1] := by - exact rowSquare_join (by decide) sg1069 sg1109 - -lemma sg6549 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg1068 sg1110 - -lemma sg6550 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,4,2,1] := by - exact rowSquare_join (by decide) sg1069 sg1110 - -lemma sg6551 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,4,3] := by - exact rowSquare_join (by decide) sg1072 sg1107 - -lemma sg6552 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,1,1] := by - exact rowSquare_join (by decide) sg1070 sg1109 - -lemma sg6553 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,2] := by - exact rowSquare_join (by decide) sg694 sg1545 - -lemma sg6554 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,7,3,1,1,1] := by - exact rowSquare_join (by decide) sg1070 sg1110 - -lemma sg6555 : RowSquare [4,3,2,2,2,2,2,2,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg982 sg879 - -lemma sg6556 : RowSquare [4,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1031 sg1061 - -lemma sg6557 : RowSquare [4,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg390 sg1891 - -lemma sg6558 : RowSquare [4,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1032 sg1061 - -lemma sg6559 : RowSquare [4,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1061 sg1033 - -lemma sg6560 : RowSquare [4,3,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,3] := by - exact rowSquare_join (by decide) sg1061 sg1037 - -lemma sg6561 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1031 sg1092 - -lemma sg6562 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg673 sg1520 - -lemma sg6563 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1031 sg1031 - -lemma sg6564 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1031 sg1032 - -lemma sg6565 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1031 sg1033 - -lemma sg6566 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1032 sg1032 - -lemma sg6567 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1032 sg1033 - -lemma sg6568 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1033 sg1033 - -lemma sg6569 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg673 sg1417 - -lemma sg6570 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1034 sg1033 - -lemma sg6571 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg613 sg1520 - -lemma sg6572 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg1521 - -lemma sg6573 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1031 sg1035 - -lemma sg6574 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1035 sg1032 - -lemma sg6575 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1035 sg1033 - -lemma sg6576 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1522 - -lemma sg6577 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1031 sg1036 - -lemma sg6578 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1523 - -lemma sg6579 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1031 sg1037 - -lemma sg6580 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg1036 - -lemma sg6581 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1036 sg1033 - -lemma sg6582 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg676 sg1417 - -lemma sg6583 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg1032 sg1037 - -lemma sg6584 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,3] := by - exact rowSquare_join (by decide) sg1033 sg1037 - -lemma sg6585 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg1961 - -lemma sg6586 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg614 sg1520 - -lemma sg6587 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1962 - -lemma sg6588 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1031 sg1038 - -lemma sg6589 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1963 - -lemma sg6590 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg616 sg1520 - -lemma sg6591 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg1038 - -lemma sg6592 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1038 sg1033 - -lemma sg6593 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1031 sg1039 - -lemma sg6594 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg1521 - -lemma sg6595 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1031 sg1040 - -lemma sg6596 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg1032 sg1039 - -lemma sg6597 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,3] := by - exact rowSquare_join (by decide) sg1033 sg1039 - -lemma sg6598 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1032 sg1040 - -lemma sg6599 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2] := by - exact rowSquare_join (by decide) sg1033 sg1040 - -lemma sg6600 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg1031 sg1041 - -lemma sg6601 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg615 sg1522 - -lemma sg6602 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg1032 sg1041 - -lemma sg6603 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,2] := by - exact rowSquare_join (by decide) sg1033 sg1041 - -lemma sg6604 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,1] := by - exact rowSquare_join (by decide) sg616 sg1523 - -lemma sg6605 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,5] := by - exact rowSquare_join (by decide) sg373 sg1908 - -lemma sg6606 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg1095 - -lemma sg6607 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg1043 - -lemma sg6608 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1093 sg961 - -lemma sg6609 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1036 sg1036 - -lemma sg6610 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,3] := by - exact rowSquare_join (by decide) sg1033 sg1044 - -lemma sg6611 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1528 - -lemma sg6612 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg1036 sg1038 - -lemma sg6613 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,3] := by - exact rowSquare_join (by decide) sg1033 sg1046 - -lemma sg6614 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg1036 sg1039 - -lemma sg6615 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1968 - -lemma sg6616 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg1038 sg1038 - -lemma sg6617 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg1038 sg1039 - -lemma sg6618 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1034 sg1045 - -lemma sg6619 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1096 sg961 - -lemma sg6620 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg1098 - -lemma sg6621 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1036 sg1043 - -lemma sg6622 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,3] := by - exact rowSquare_join (by decide) sg1033 sg1051 - -lemma sg6623 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1036 sg1044 - -lemma sg6624 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg1099 - -lemma sg6625 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg1100 - -lemma sg6626 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1969 - -lemma sg6627 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [8,3,3,3,3] := by - exact rowSquare_join (by decide) sg1033 sg1057 - -lemma sg6628 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg1891 - -lemma sg6629 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg178 sg2311 - -lemma sg6630 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg1892 - -lemma sg6631 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg1893 - -lemma sg6632 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg331 sg1891 - -lemma sg6633 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg178 sg2314 - -lemma sg6634 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg2316 - -lemma sg6635 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg332 sg1891 - -lemma sg6636 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1031 sg941 - -lemma sg6637 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1896 - -lemma sg6638 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1031 sg943 - -lemma sg6639 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg334 sg1891 - -lemma sg6640 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1032 sg942 - -lemma sg6641 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1032 sg943 - -lemma sg6642 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1033 sg943 - -lemma sg6643 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg1092 - -lemma sg6644 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg1093 - -lemma sg6645 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg940 sg1034 - -lemma sg6646 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg1094 - -lemma sg6647 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1034 sg941 - -lemma sg6648 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg1095 - -lemma sg6649 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1034 sg942 - -lemma sg6650 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg370 sg1795 - -lemma sg6651 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1034 sg943 - -lemma sg6652 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg370 sg1796 - -lemma sg6653 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg179 sg2314 - -lemma sg6654 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg940 sg1035 - -lemma sg6655 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg940 sg1036 - -lemma sg6656 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1031 sg945 - -lemma sg6657 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg940 sg1037 - -lemma sg6658 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1035 sg942 - -lemma sg6659 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1035 sg943 - -lemma sg6660 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg371 sg1796 - -lemma sg6661 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1413 - -lemma sg6662 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1031 sg946 - -lemma sg6663 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg548 sg1523 - -lemma sg6664 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1031 sg947 - -lemma sg6665 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg946 - -lemma sg6666 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1036 sg943 - -lemma sg6667 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg1795 - -lemma sg6668 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg1032 sg947 - -lemma sg6669 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,4,3] := by - exact rowSquare_join (by decide) sg1033 sg947 - -lemma sg6670 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg940 sg1038 - -lemma sg6671 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg614 sg1411 - -lemma sg6672 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg940 sg1039 - -lemma sg6673 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1031 sg948 - -lemma sg6674 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg940 sg1040 - -lemma sg6675 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg614 sg1412 - -lemma sg6676 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg948 - -lemma sg6677 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1038 sg943 - -lemma sg6678 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1031 sg949 - -lemma sg6679 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg550 sg1521 - -lemma sg6680 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1031 sg950 - -lemma sg6681 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg1032 sg949 - -lemma sg6682 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,3,3] := by - exact rowSquare_join (by decide) sg1033 sg949 - -lemma sg6683 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1032 sg950 - -lemma sg6684 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,4,2] := by - exact rowSquare_join (by decide) sg1033 sg950 - -lemma sg6685 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1900 - -lemma sg6686 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg1031 sg951 - -lemma sg6687 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg615 sg1413 - -lemma sg6688 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg1032 sg951 - -lemma sg6689 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,5,3,2] := by - exact rowSquare_join (by decide) sg1033 sg951 - -lemma sg6690 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,5,4,1] := by - exact rowSquare_join (by decide) sg551 sg1523 - -lemma sg6691 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1031 sg952 - -lemma sg6692 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1092 sg853 - -lemma sg6693 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1092 sg854 - -lemma sg6694 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg374 sg1796 - -lemma sg6695 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1035 sg945 - -lemma sg6696 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1031 sg953 - -lemma sg6697 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1035 sg947 - -lemma sg6698 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg953 - -lemma sg6699 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1093 sg854 - -lemma sg6700 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1031 sg954 - -lemma sg6701 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1032 sg955 - -lemma sg6702 : RowSquare [5,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1108 - -lemma sg6703 : RowSquare [5,3,3,2,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1064 - -lemma sg6704 : RowSquare [5,3,3,2,1,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1065 - -lemma sg6705 : RowSquare [5,3,3,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg978 - -lemma sg6706 : RowSquare [5,3,3,2,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg979 - -lemma sg6707 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1092 - -lemma sg6708 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1093 - -lemma sg6709 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1092 - -lemma sg6710 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1094 - -lemma sg6711 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg1092 - -lemma sg6712 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1095 - -lemma sg6713 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1092 sg1000 - -lemma sg6714 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1092 sg1001 - -lemma sg6715 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1093 - -lemma sg6716 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1093 - -lemma sg6717 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg1000 sg1093 - -lemma sg6718 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1093 sg1001 - -lemma sg6719 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1096 - -lemma sg6720 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1002 sg1092 - -lemma sg6721 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1097 - -lemma sg6722 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1003 sg1092 - -lemma sg6723 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1098 - -lemma sg6724 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1099 - -lemma sg6725 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1100 - -lemma sg6726 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1031 - -lemma sg6727 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1032 - -lemma sg6728 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1033 - -lemma sg6729 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg1520 - -lemma sg6730 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1521 - -lemma sg6731 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1031 - -lemma sg6732 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1032 - -lemma sg6733 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1033 - -lemma sg6734 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1522 - -lemma sg6735 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1523 - -lemma sg6736 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1032 sg1000 - -lemma sg6737 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1032 sg1001 - -lemma sg6738 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1033 sg1001 - -lemma sg6739 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1092 - -lemma sg6740 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg1034 - -lemma sg6741 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1093 - -lemma sg6742 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1035 - -lemma sg6743 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg1034 - -lemma sg6744 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1094 - -lemma sg6745 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1036 - -lemma sg6746 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1095 - -lemma sg6747 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1037 - -lemma sg6748 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1034 sg1000 - -lemma sg6749 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1034 sg1001 - -lemma sg6750 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1038 - -lemma sg6751 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1035 - -lemma sg6752 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1039 - -lemma sg6753 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1040 - -lemma sg6754 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1037 - -lemma sg6755 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1041 - -lemma sg6756 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1522 - -lemma sg6757 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1523 - -lemma sg6758 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1527 - -lemma sg6759 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1038 - -lemma sg6760 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1528 - -lemma sg6761 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1039 - -lemma sg6762 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1040 - -lemma sg6763 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1529 - -lemma sg6764 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1041 - -lemma sg6765 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1100 - -lemma sg6766 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1032 - -lemma sg6767 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg910 sg1034 - -lemma sg6768 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg1416 - -lemma sg6769 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg587 sg1417 - -lemma sg6770 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg1422 - -lemma sg6771 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg958 sg998 - -lemma sg6772 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1423 - -lemma sg6773 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg958 sg999 - -lemma sg6774 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1424 - -lemma sg6775 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg958 sg1000 - -lemma sg6776 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg1417 - -lemma sg6777 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg1001 - -lemma sg6778 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1425 - -lemma sg6779 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg589 sg1416 - -lemma sg6780 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1031 sg913 - -lemma sg6781 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1426 - -lemma sg6782 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg1416 - -lemma sg6783 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1031 sg914 - -lemma sg6784 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1031 sg915 - -lemma sg6785 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg590 sg1417 - -lemma sg6786 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1032 sg914 - -lemma sg6787 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1032 sg915 - -lemma sg6788 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1033 sg915 - -lemma sg6789 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg962 - -lemma sg6790 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg958 sg1002 - -lemma sg6791 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg5890 - -lemma sg6792 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1045 - -lemma sg6793 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg5891 - -lemma sg6794 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg5892 - -lemma sg6795 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5893 - -lemma sg6796 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1047 - -lemma sg6797 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5894 - -lemma sg6798 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg5895 - -lemma sg6799 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5896 - -lemma sg6800 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg5897 - -lemma sg6801 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg5898 - -lemma sg6802 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg5899 - -lemma sg6803 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5900 - -lemma sg6804 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg0 sg5901 - -lemma sg6805 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,4,3] := by - exact rowSquare_join (by decide) sg0 sg5902 - -lemma sg6806 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1435 - -lemma sg6807 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg1422 - -lemma sg6808 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1049 - -lemma sg6809 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1436 - -lemma sg6810 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg1008 - -lemma sg6811 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg1424 - -lemma sg6812 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg920 - -lemma sg6813 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1038 sg915 - -lemma sg6814 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1437 - -lemma sg6815 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg1377 - -lemma sg6816 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg1032 sg921 - -lemma sg6817 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,4,3,3] := by - exact rowSquare_join (by decide) sg1033 sg921 - -lemma sg6818 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1032 sg922 - -lemma sg6819 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,4,4,2] := by - exact rowSquare_join (by decide) sg1033 sg922 - -lemma sg6820 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg1031 sg923 - -lemma sg6821 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg615 sg1378 - -lemma sg6822 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg1032 sg923 - -lemma sg6823 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,5,3,2] := by - exact rowSquare_join (by decide) sg1033 sg923 - -lemma sg6824 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,5,4,1] := by - exact rowSquare_join (by decide) sg616 sg1379 - -lemma sg6825 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,5,5] := by - exact rowSquare_join (by decide) sg373 sg1782 - -lemma sg6826 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1050 - -lemma sg6827 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg5903 - -lemma sg6828 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1051 - -lemma sg6829 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1052 - -lemma sg6830 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg968 - -lemma sg6831 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg5904 - -lemma sg6832 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg5905 - -lemma sg6833 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg969 - -lemma sg6834 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5906 - -lemma sg6835 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg5907 - -lemma sg6836 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg5908 - -lemma sg6837 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1053 - -lemma sg6838 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg970 - -lemma sg6839 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1054 - -lemma sg6840 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg971 - -lemma sg6841 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5909 - -lemma sg6842 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg5101 - -lemma sg6843 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg5910 - -lemma sg6844 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5102 - -lemma sg6845 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg5103 - -lemma sg6846 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,3,3] := by - exact rowSquare_join (by decide) sg1 sg5104 - -lemma sg6847 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1 sg5105 - -lemma sg6848 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,4,2] := by - exact rowSquare_join (by decide) sg1 sg5106 - -lemma sg6849 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1055 - -lemma sg6850 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg972 - -lemma sg6851 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5912 - -lemma sg6852 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg5914 - -lemma sg6853 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1056 - -lemma sg6854 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1447 - -lemma sg6855 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg108 sg2596 - -lemma sg6856 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1057 - -lemma sg6857 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1058 - -lemma sg6858 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg973 - -lemma sg6859 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1059 - -lemma sg6860 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg974 - -lemma sg6861 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5107 - -lemma sg6862 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5108 - -lemma sg6863 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1060 - -lemma sg6864 : RowSquare [5,4,2,2,2,2,2,1] [4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg2596 - -lemma sg6865 : RowSquare [5,4,2,2,2,2,2,1] [4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg2597 - -lemma sg6866 : RowSquare [5,4,2,2,2,2,2,1] [5,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg2597 - -lemma sg6867 : RowSquare [5,4,2,2,2,2,2,1] [5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg85 sg2596 - -lemma sg6868 : RowSquare [5,4,2,2,2,2,2,1] [5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg838 sg880 - -lemma sg6869 : RowSquare [5,4,2,2,2,2,2,1] [5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg2603 - -lemma sg6870 : RowSquare [5,4,2,2,2,2,2,1] [5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg882 - -lemma sg6871 : RowSquare [5,4,2,2,2,2,2,1] [5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg2604 - -lemma sg6872 : RowSquare [5,4,2,2,2,2,2,1] [5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg884 - -lemma sg6873 : RowSquare [5,4,2,2,2,2,2,1] [5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg2607 - -lemma sg6874 : RowSquare [5,4,2,2,2,2,2,1] [5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg885 - -lemma sg6875 : RowSquare [5,4,2,2,2,2,2,1] [6,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg85 sg2597 - -lemma sg6876 : RowSquare [5,4,2,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg86 sg2596 - -lemma sg6877 : RowSquare [5,4,2,2,2,2,2,1] [8,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg86 sg2597 - -lemma sg6878 : RowSquare [5,4,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg849 sg997 - -lemma sg6879 : RowSquare [5,4,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg1682 - -lemma sg6880 : RowSquare [5,4,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg849 sg998 - -lemma sg6881 : RowSquare [5,4,3,2,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg999 - -lemma sg6882 : RowSquare [5,4,3,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg1682 - -lemma sg6883 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg374 sg1682 - -lemma sg6884 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg1683 - -lemma sg6885 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg849 sg1002 - -lemma sg6886 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg850 sg997 - -lemma sg6887 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg1683 - -lemma sg6888 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg1003 - -lemma sg6889 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg850 sg998 - -lemma sg6890 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg370 sg1688 - -lemma sg6891 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg377 sg1682 - -lemma sg6892 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg378 sg1682 - -lemma sg6893 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg371 sg1688 - -lemma sg6894 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg374 sg1683 - -lemma sg6895 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg375 sg1683 - -lemma sg6896 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg376 sg1683 - -lemma sg6897 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg374 sg1688 - -lemma sg6898 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg377 sg1683 - -lemma sg6899 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg378 sg1683 - -lemma sg6900 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg383 sg1682 - -lemma sg6901 : RowSquare [5,4,3,2,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg3299 - -lemma sg6902 : RowSquare [5,4,3,2,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg383 sg1683 - -lemma sg6903 : RowSquare [5,4,3,2,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg3300 - -lemma sg6904 : RowSquare [5,4,3,2,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg3301 - -lemma sg6905 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg997 sg997 - -lemma sg6906 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg998 - -lemma sg6907 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg999 - -lemma sg6908 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1000 - -lemma sg6909 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1001 - -lemma sg6910 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg998 - -lemma sg6911 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg999 - -lemma sg6912 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1000 - -lemma sg6913 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1001 - -lemma sg6914 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg999 - -lemma sg6915 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1000 - -lemma sg6916 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg999 sg1001 - -lemma sg6917 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1000 sg1000 - -lemma sg6918 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1000 sg1001 - -lemma sg6919 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1001 sg1001 - -lemma sg6920 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg1002 - -lemma sg6921 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1003 - -lemma sg6922 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg1002 - -lemma sg6923 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1004 - -lemma sg6924 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1002 sg999 - -lemma sg6925 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1005 - -lemma sg6926 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1000 - -lemma sg6927 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1001 - -lemma sg6928 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1006 - -lemma sg6929 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1003 - -lemma sg6930 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1007 - -lemma sg6931 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1004 - -lemma sg6932 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg1003 - -lemma sg6933 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1008 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes13 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes11 + +namespace OAI + +/-! Semigroup Nodes 15. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg6534 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,4,4,1] := by + exact rowSquare_join (by decide) sg1069 sg1105 + +lemma sg6535 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg1068 sg1106 + +lemma sg6536 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg1070 sg1105 + +lemma sg6537 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,2] := by + exact rowSquare_join (by decide) sg1061 sg1117 + +lemma sg6538 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg1068 sg1107 + +lemma sg6539 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,2] := by + exact rowSquare_join (by decide) sg1061 sg1118 + +lemma sg6540 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,1] := by + exact rowSquare_join (by decide) sg1069 sg1107 + +lemma sg6541 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,4,4] := by + exact rowSquare_join (by decide) sg1072 sg1105 + +lemma sg6542 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg1068 sg1108 + +lemma sg6543 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,5,2,1] := by + exact rowSquare_join (by decide) sg1069 sg1108 + +lemma sg6544 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,5,3] := by + exact rowSquare_join (by decide) sg1105 sg1073 + +lemma sg6545 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg1070 sg1106 + +lemma sg6546 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg1068 sg1109 + +lemma sg6547 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,2] := by + exact rowSquare_join (by decide) sg1061 sg1119 + +lemma sg6548 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,1] := by + exact rowSquare_join (by decide) sg1069 sg1109 + +lemma sg6549 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg1068 sg1110 + +lemma sg6550 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,4,2,1] := by + exact rowSquare_join (by decide) sg1069 sg1110 + +lemma sg6551 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,4,3] := by + exact rowSquare_join (by decide) sg1072 sg1107 + +lemma sg6552 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,1,1] := by + exact rowSquare_join (by decide) sg1070 sg1109 + +lemma sg6553 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,2] := by + exact rowSquare_join (by decide) sg694 sg1545 + +lemma sg6554 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1] [7,7,3,1,1,1] := by + exact rowSquare_join (by decide) sg1070 sg1110 + +lemma sg6555 : RowSquare [4,3,2,2,2,2,2,2,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg982 sg879 + +lemma sg6556 : RowSquare [4,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1031 sg1061 + +lemma sg6557 : RowSquare [4,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg390 sg1891 + +lemma sg6558 : RowSquare [4,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1032 sg1061 + +lemma sg6559 : RowSquare [4,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1061 sg1033 + +lemma sg6560 : RowSquare [4,3,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,3] := by + exact rowSquare_join (by decide) sg1061 sg1037 + +lemma sg6561 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1031 sg1092 + +lemma sg6562 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg673 sg1520 + +lemma sg6563 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1031 sg1031 + +lemma sg6564 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1031 sg1032 + +lemma sg6565 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1031 sg1033 + +lemma sg6566 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1032 sg1032 + +lemma sg6567 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1032 sg1033 + +lemma sg6568 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1033 sg1033 + +lemma sg6569 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg673 sg1417 + +lemma sg6570 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1034 sg1033 + +lemma sg6571 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg613 sg1520 + +lemma sg6572 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg1521 + +lemma sg6573 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1031 sg1035 + +lemma sg6574 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1035 sg1032 + +lemma sg6575 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1035 sg1033 + +lemma sg6576 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1522 + +lemma sg6577 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1031 sg1036 + +lemma sg6578 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1523 + +lemma sg6579 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1031 sg1037 + +lemma sg6580 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg1036 + +lemma sg6581 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1036 sg1033 + +lemma sg6582 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg676 sg1417 + +lemma sg6583 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg1032 sg1037 + +lemma sg6584 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,3] := by + exact rowSquare_join (by decide) sg1033 sg1037 + +lemma sg6585 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg1961 + +lemma sg6586 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg614 sg1520 + +lemma sg6587 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1962 + +lemma sg6588 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1031 sg1038 + +lemma sg6589 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1963 + +lemma sg6590 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg616 sg1520 + +lemma sg6591 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg1038 + +lemma sg6592 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1038 sg1033 + +lemma sg6593 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1031 sg1039 + +lemma sg6594 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg1521 + +lemma sg6595 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1031 sg1040 + +lemma sg6596 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg1032 sg1039 + +lemma sg6597 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,3] := by + exact rowSquare_join (by decide) sg1033 sg1039 + +lemma sg6598 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1032 sg1040 + +lemma sg6599 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2] := by + exact rowSquare_join (by decide) sg1033 sg1040 + +lemma sg6600 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg1031 sg1041 + +lemma sg6601 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg615 sg1522 + +lemma sg6602 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg1032 sg1041 + +lemma sg6603 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,2] := by + exact rowSquare_join (by decide) sg1033 sg1041 + +lemma sg6604 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,1] := by + exact rowSquare_join (by decide) sg616 sg1523 + +lemma sg6605 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,5] := by + exact rowSquare_join (by decide) sg373 sg1908 + +lemma sg6606 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg1095 + +lemma sg6607 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg1043 + +lemma sg6608 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1093 sg961 + +lemma sg6609 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1036 sg1036 + +lemma sg6610 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,3] := by + exact rowSquare_join (by decide) sg1033 sg1044 + +lemma sg6611 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1528 + +lemma sg6612 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg1036 sg1038 + +lemma sg6613 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,3] := by + exact rowSquare_join (by decide) sg1033 sg1046 + +lemma sg6614 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg1036 sg1039 + +lemma sg6615 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1968 + +lemma sg6616 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg1038 sg1038 + +lemma sg6617 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg1038 sg1039 + +lemma sg6618 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1034 sg1045 + +lemma sg6619 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1096 sg961 + +lemma sg6620 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg1098 + +lemma sg6621 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1036 sg1043 + +lemma sg6622 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,3] := by + exact rowSquare_join (by decide) sg1033 sg1051 + +lemma sg6623 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1036 sg1044 + +lemma sg6624 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg1099 + +lemma sg6625 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg1100 + +lemma sg6626 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1969 + +lemma sg6627 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1] [8,3,3,3,3] := by + exact rowSquare_join (by decide) sg1033 sg1057 + +lemma sg6628 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg1891 + +lemma sg6629 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg178 sg2311 + +lemma sg6630 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg1892 + +lemma sg6631 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg1893 + +lemma sg6632 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg331 sg1891 + +lemma sg6633 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg178 sg2314 + +lemma sg6634 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg2316 + +lemma sg6635 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg332 sg1891 + +lemma sg6636 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1031 sg941 + +lemma sg6637 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1896 + +lemma sg6638 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1031 sg943 + +lemma sg6639 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg334 sg1891 + +lemma sg6640 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1032 sg942 + +lemma sg6641 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1032 sg943 + +lemma sg6642 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1033 sg943 + +lemma sg6643 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg1092 + +lemma sg6644 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg1093 + +lemma sg6645 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg940 sg1034 + +lemma sg6646 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg1094 + +lemma sg6647 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1034 sg941 + +lemma sg6648 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg1095 + +lemma sg6649 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1034 sg942 + +lemma sg6650 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg370 sg1795 + +lemma sg6651 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1034 sg943 + +lemma sg6652 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg370 sg1796 + +lemma sg6653 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg179 sg2314 + +lemma sg6654 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg940 sg1035 + +lemma sg6655 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg940 sg1036 + +lemma sg6656 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1031 sg945 + +lemma sg6657 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg940 sg1037 + +lemma sg6658 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1035 sg942 + +lemma sg6659 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1035 sg943 + +lemma sg6660 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg371 sg1796 + +lemma sg6661 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1413 + +lemma sg6662 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1031 sg946 + +lemma sg6663 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg548 sg1523 + +lemma sg6664 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1031 sg947 + +lemma sg6665 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg946 + +lemma sg6666 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1036 sg943 + +lemma sg6667 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg1795 + +lemma sg6668 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg1032 sg947 + +lemma sg6669 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,4,4,4,3] := by + exact rowSquare_join (by decide) sg1033 sg947 + +lemma sg6670 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg940 sg1038 + +lemma sg6671 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg614 sg1411 + +lemma sg6672 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg940 sg1039 + +lemma sg6673 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1031 sg948 + +lemma sg6674 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg940 sg1040 + +lemma sg6675 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg614 sg1412 + +lemma sg6676 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg948 + +lemma sg6677 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1038 sg943 + +lemma sg6678 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1031 sg949 + +lemma sg6679 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg550 sg1521 + +lemma sg6680 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1031 sg950 + +lemma sg6681 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg1032 sg949 + +lemma sg6682 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,3,3] := by + exact rowSquare_join (by decide) sg1033 sg949 + +lemma sg6683 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1032 sg950 + +lemma sg6684 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,4,4,2] := by + exact rowSquare_join (by decide) sg1033 sg950 + +lemma sg6685 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1900 + +lemma sg6686 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg1031 sg951 + +lemma sg6687 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg615 sg1413 + +lemma sg6688 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg1032 sg951 + +lemma sg6689 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,5,3,2] := by + exact rowSquare_join (by decide) sg1033 sg951 + +lemma sg6690 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [5,5,5,4,1] := by + exact rowSquare_join (by decide) sg551 sg1523 + +lemma sg6691 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1031 sg952 + +lemma sg6692 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1092 sg853 + +lemma sg6693 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1092 sg854 + +lemma sg6694 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg374 sg1796 + +lemma sg6695 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1035 sg945 + +lemma sg6696 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1031 sg953 + +lemma sg6697 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1035 sg947 + +lemma sg6698 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg953 + +lemma sg6699 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1093 sg854 + +lemma sg6700 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1031 sg954 + +lemma sg6701 : RowSquare [4,4,3,2,1,1,1,1,1,1,1] [6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1032 sg955 + +lemma sg6702 : RowSquare [5,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1108 + +lemma sg6703 : RowSquare [5,3,3,2,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1064 + +lemma sg6704 : RowSquare [5,3,3,2,1,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1065 + +lemma sg6705 : RowSquare [5,3,3,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg978 + +lemma sg6706 : RowSquare [5,3,3,2,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg979 + +lemma sg6707 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1092 + +lemma sg6708 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1093 + +lemma sg6709 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1092 + +lemma sg6710 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1094 + +lemma sg6711 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg1092 + +lemma sg6712 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1095 + +lemma sg6713 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1092 sg1000 + +lemma sg6714 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1092 sg1001 + +lemma sg6715 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1093 + +lemma sg6716 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1093 + +lemma sg6717 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg1000 sg1093 + +lemma sg6718 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1093 sg1001 + +lemma sg6719 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1096 + +lemma sg6720 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1002 sg1092 + +lemma sg6721 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1097 + +lemma sg6722 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1003 sg1092 + +lemma sg6723 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1098 + +lemma sg6724 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1099 + +lemma sg6725 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1100 + +lemma sg6726 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1031 + +lemma sg6727 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1032 + +lemma sg6728 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1033 + +lemma sg6729 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg1520 + +lemma sg6730 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1521 + +lemma sg6731 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1031 + +lemma sg6732 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1032 + +lemma sg6733 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1033 + +lemma sg6734 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1522 + +lemma sg6735 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1523 + +lemma sg6736 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1032 sg1000 + +lemma sg6737 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1032 sg1001 + +lemma sg6738 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1033 sg1001 + +lemma sg6739 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1092 + +lemma sg6740 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg1034 + +lemma sg6741 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1093 + +lemma sg6742 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1035 + +lemma sg6743 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg1034 + +lemma sg6744 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1094 + +lemma sg6745 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1036 + +lemma sg6746 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1095 + +lemma sg6747 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1037 + +lemma sg6748 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1034 sg1000 + +lemma sg6749 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1034 sg1001 + +lemma sg6750 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1038 + +lemma sg6751 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1035 + +lemma sg6752 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1039 + +lemma sg6753 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1040 + +lemma sg6754 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1037 + +lemma sg6755 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1041 + +lemma sg6756 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1522 + +lemma sg6757 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1523 + +lemma sg6758 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1527 + +lemma sg6759 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1038 + +lemma sg6760 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1528 + +lemma sg6761 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1039 + +lemma sg6762 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1040 + +lemma sg6763 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1529 + +lemma sg6764 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1041 + +lemma sg6765 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1100 + +lemma sg6766 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1032 + +lemma sg6767 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg910 sg1034 + +lemma sg6768 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg1416 + +lemma sg6769 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg587 sg1417 + +lemma sg6770 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg1422 + +lemma sg6771 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg958 sg998 + +lemma sg6772 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1423 + +lemma sg6773 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg958 sg999 + +lemma sg6774 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1424 + +lemma sg6775 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg958 sg1000 + +lemma sg6776 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg1417 + +lemma sg6777 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg1001 + +lemma sg6778 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1425 + +lemma sg6779 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg589 sg1416 + +lemma sg6780 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1031 sg913 + +lemma sg6781 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1426 + +lemma sg6782 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg1416 + +lemma sg6783 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1031 sg914 + +lemma sg6784 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1031 sg915 + +lemma sg6785 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg590 sg1417 + +lemma sg6786 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1032 sg914 + +lemma sg6787 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1032 sg915 + +lemma sg6788 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1033 sg915 + +lemma sg6789 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg962 + +lemma sg6790 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg958 sg1002 + +lemma sg6791 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg5890 + +lemma sg6792 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1045 + +lemma sg6793 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg5891 + +lemma sg6794 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg5892 + +lemma sg6795 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5893 + +lemma sg6796 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1047 + +lemma sg6797 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5894 + +lemma sg6798 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg5895 + +lemma sg6799 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5896 + +lemma sg6800 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg5897 + +lemma sg6801 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg5898 + +lemma sg6802 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg5899 + +lemma sg6803 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5900 + +lemma sg6804 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg0 sg5901 + +lemma sg6805 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,4,4,4,3] := by + exact rowSquare_join (by decide) sg0 sg5902 + +lemma sg6806 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1435 + +lemma sg6807 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg1422 + +lemma sg6808 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1049 + +lemma sg6809 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1436 + +lemma sg6810 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg1008 + +lemma sg6811 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg1424 + +lemma sg6812 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg920 + +lemma sg6813 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1038 sg915 + +lemma sg6814 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1437 + +lemma sg6815 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg1377 + +lemma sg6816 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg1032 sg921 + +lemma sg6817 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,4,3,3] := by + exact rowSquare_join (by decide) sg1033 sg921 + +lemma sg6818 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1032 sg922 + +lemma sg6819 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,4,4,2] := by + exact rowSquare_join (by decide) sg1033 sg922 + +lemma sg6820 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg1031 sg923 + +lemma sg6821 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg615 sg1378 + +lemma sg6822 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg1032 sg923 + +lemma sg6823 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,5,3,2] := by + exact rowSquare_join (by decide) sg1033 sg923 + +lemma sg6824 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,5,4,1] := by + exact rowSquare_join (by decide) sg616 sg1379 + +lemma sg6825 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [5,5,5,5] := by + exact rowSquare_join (by decide) sg373 sg1782 + +lemma sg6826 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1050 + +lemma sg6827 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg5903 + +lemma sg6828 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1051 + +lemma sg6829 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1052 + +lemma sg6830 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg968 + +lemma sg6831 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg5904 + +lemma sg6832 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg5905 + +lemma sg6833 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg969 + +lemma sg6834 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5906 + +lemma sg6835 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg5907 + +lemma sg6836 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg5908 + +lemma sg6837 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1053 + +lemma sg6838 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg970 + +lemma sg6839 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1054 + +lemma sg6840 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg971 + +lemma sg6841 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5909 + +lemma sg6842 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg5101 + +lemma sg6843 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg5910 + +lemma sg6844 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5102 + +lemma sg6845 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg5103 + +lemma sg6846 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,3,3] := by + exact rowSquare_join (by decide) sg1 sg5104 + +lemma sg6847 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1 sg5105 + +lemma sg6848 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,4,4,4,2] := by + exact rowSquare_join (by decide) sg1 sg5106 + +lemma sg6849 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1055 + +lemma sg6850 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg972 + +lemma sg6851 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5912 + +lemma sg6852 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg5914 + +lemma sg6853 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1056 + +lemma sg6854 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1447 + +lemma sg6855 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg108 sg2596 + +lemma sg6856 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1057 + +lemma sg6857 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1058 + +lemma sg6858 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg973 + +lemma sg6859 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1059 + +lemma sg6860 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg974 + +lemma sg6861 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5107 + +lemma sg6862 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5108 + +lemma sg6863 : RowSquare [5,4,2,2,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1060 + +lemma sg6864 : RowSquare [5,4,2,2,2,2,2,1] [4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg2596 + +lemma sg6865 : RowSquare [5,4,2,2,2,2,2,1] [4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg2597 + +lemma sg6866 : RowSquare [5,4,2,2,2,2,2,1] [5,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg2597 + +lemma sg6867 : RowSquare [5,4,2,2,2,2,2,1] [5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg85 sg2596 + +lemma sg6868 : RowSquare [5,4,2,2,2,2,2,1] [5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg838 sg880 + +lemma sg6869 : RowSquare [5,4,2,2,2,2,2,1] [5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg2603 + +lemma sg6870 : RowSquare [5,4,2,2,2,2,2,1] [5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg882 + +lemma sg6871 : RowSquare [5,4,2,2,2,2,2,1] [5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg2604 + +lemma sg6872 : RowSquare [5,4,2,2,2,2,2,1] [5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg884 + +lemma sg6873 : RowSquare [5,4,2,2,2,2,2,1] [5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg2607 + +lemma sg6874 : RowSquare [5,4,2,2,2,2,2,1] [5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg885 + +lemma sg6875 : RowSquare [5,4,2,2,2,2,2,1] [6,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg85 sg2597 + +lemma sg6876 : RowSquare [5,4,2,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg86 sg2596 + +lemma sg6877 : RowSquare [5,4,2,2,2,2,2,1] [8,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg86 sg2597 + +lemma sg6878 : RowSquare [5,4,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg849 sg997 + +lemma sg6879 : RowSquare [5,4,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg1682 + +lemma sg6880 : RowSquare [5,4,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg849 sg998 + +lemma sg6881 : RowSquare [5,4,3,2,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg999 + +lemma sg6882 : RowSquare [5,4,3,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg1682 + +lemma sg6883 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg374 sg1682 + +lemma sg6884 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg1683 + +lemma sg6885 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg849 sg1002 + +lemma sg6886 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg850 sg997 + +lemma sg6887 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg1683 + +lemma sg6888 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg1003 + +lemma sg6889 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg850 sg998 + +lemma sg6890 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg370 sg1688 + +lemma sg6891 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg377 sg1682 + +lemma sg6892 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg378 sg1682 + +lemma sg6893 : RowSquare [5,4,3,2,1,1,1,1,1,1] [4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg371 sg1688 + +lemma sg6894 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg374 sg1683 + +lemma sg6895 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg375 sg1683 + +lemma sg6896 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg376 sg1683 + +lemma sg6897 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg374 sg1688 + +lemma sg6898 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg377 sg1683 + +lemma sg6899 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg378 sg1683 + +lemma sg6900 : RowSquare [5,4,3,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg383 sg1682 + +lemma sg6901 : RowSquare [5,4,3,2,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg3299 + +lemma sg6902 : RowSquare [5,4,3,2,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg383 sg1683 + +lemma sg6903 : RowSquare [5,4,3,2,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg3300 + +lemma sg6904 : RowSquare [5,4,3,2,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg3301 + +lemma sg6905 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg997 sg997 + +lemma sg6906 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg998 + +lemma sg6907 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg999 + +lemma sg6908 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1000 + +lemma sg6909 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1001 + +lemma sg6910 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg998 + +lemma sg6911 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg999 + +lemma sg6912 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1000 + +lemma sg6913 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1001 + +lemma sg6914 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg999 + +lemma sg6915 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1000 + +lemma sg6916 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg999 sg1001 + +lemma sg6917 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1000 sg1000 + +lemma sg6918 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1000 sg1001 + +lemma sg6919 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1001 sg1001 + +lemma sg6920 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg1002 + +lemma sg6921 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1003 + +lemma sg6922 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg1002 + +lemma sg6923 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1004 + +lemma sg6924 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1002 sg999 + +lemma sg6925 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1005 + +lemma sg6926 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1000 + +lemma sg6927 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1001 + +lemma sg6928 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1006 + +lemma sg6929 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1003 + +lemma sg6930 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1007 + +lemma sg6931 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1004 + +lemma sg6932 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg1003 + +lemma sg6933 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1008 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes16.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes16.lean index b8828342257c1dc05200d84c3ab55ee135662d30..c45fba0d1389e77611c73b8c06c16685260898b1 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes16.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes16.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes13 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes11 - -namespace OAI - -/-! Semigroup Nodes 16. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg6934 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1005 - -lemma sg6935 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1003 sg1000 - -lemma sg6936 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1003 sg1001 - -lemma sg6937 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1004 - -lemma sg6938 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg1005 - -lemma sg6939 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg1000 sg1004 - -lemma sg6940 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1004 sg1001 - -lemma sg6941 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1005 - -lemma sg6942 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3] := by - exact rowSquare_join (by decide) sg1001 sg1005 - -lemma sg6943 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1006 - -lemma sg6944 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1007 - -lemma sg6945 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1006 - -lemma sg6946 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1008 - -lemma sg6947 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg1000 sg1006 - -lemma sg6948 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1006 sg1001 - -lemma sg6949 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg1007 - -lemma sg6950 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1008 - -lemma sg6951 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1007 - -lemma sg6952 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,3] := by - exact rowSquare_join (by decide) sg1001 sg1007 - -lemma sg6953 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1008 - -lemma sg6954 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,2] := by - exact rowSquare_join (by decide) sg1001 sg1008 - -lemma sg6955 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1009 - -lemma sg6956 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1002 sg1002 - -lemma sg6957 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1010 - -lemma sg6958 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1009 - -lemma sg6959 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1011 - -lemma sg6960 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1004 - -lemma sg6961 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg1009 - -lemma sg6962 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1012 - -lemma sg6963 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1005 - -lemma sg6964 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1009 sg1001 - -lemma sg6965 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1013 - -lemma sg6966 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1010 - -lemma sg6967 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1003 sg1003 - -lemma sg6968 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1014 - -lemma sg6969 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1011 - -lemma sg6970 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1010 - -lemma sg6971 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1012 - -lemma sg6972 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1003 sg1005 - -lemma sg6973 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1010 sg1001 - -lemma sg6974 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg1011 - -lemma sg6975 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1004 sg1004 - -lemma sg6976 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1012 - -lemma sg6977 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1011 - -lemma sg6978 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3] := by - exact rowSquare_join (by decide) sg1001 sg1011 - -lemma sg6979 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1012 - -lemma sg6980 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,2] := by - exact rowSquare_join (by decide) sg1001 sg1012 - -lemma sg6981 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1015 - -lemma sg6982 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1013 - -lemma sg6983 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1003 sg1006 - -lemma sg6984 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1016 - -lemma sg6985 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1014 - -lemma sg6986 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg1004 sg1006 - -lemma sg6987 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1003 sg1008 - -lemma sg6988 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3] := by - exact rowSquare_join (by decide) sg1001 sg1013 - -lemma sg6989 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1014 - -lemma sg6990 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg1004 sg1007 - -lemma sg6991 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1014 - -lemma sg6992 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,2] := by - exact rowSquare_join (by decide) sg1001 sg1014 - -lemma sg6993 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,1] := by - exact rowSquare_join (by decide) sg1005 sg1008 - -lemma sg6994 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1015 - -lemma sg6995 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg1006 sg1006 - -lemma sg6996 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1016 - -lemma sg6997 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1015 - -lemma sg6998 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg1006 sg1007 - -lemma sg6999 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1015 - -lemma sg7000 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,2] := by - exact rowSquare_join (by decide) sg1001 sg1015 - -lemma sg7001 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1016 - -lemma sg7002 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,1] := by - exact rowSquare_join (by decide) sg1007 sg1008 - -lemma sg7003 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,4,4] := by - exact rowSquare_join (by decide) sg1008 sg1008 - -lemma sg7004 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1012 - -lemma sg7005 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1017 sg1001 - -lemma sg7006 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1019 - -lemma sg7007 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1004 sg1010 - -lemma sg7008 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3] := by - exact rowSquare_join (by decide) sg1001 sg1018 - -lemma sg7009 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1004 sg1011 - -lemma sg7010 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1020 - -lemma sg7011 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1021 - -lemma sg7012 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2] := by - exact rowSquare_join (by decide) sg1001 sg1021 - -lemma sg7013 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1022 - -lemma sg7014 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,1] := by - exact rowSquare_join (by decide) sg1005 sg1015 - -lemma sg7015 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg1004 sg1016 - -lemma sg7016 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1023 - -lemma sg7017 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2] := by - exact rowSquare_join (by decide) sg1001 sg1023 - -lemma sg7018 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1019 - -lemma sg7019 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1004 sg1017 - -lemma sg7020 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3] := by - exact rowSquare_join (by decide) sg1001 sg1024 - -lemma sg7021 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [8,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1028 - -lemma sg7022 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1029 - -lemma sg7023 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [9,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1026 - -lemma sg7024 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [9,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1030 - -lemma sg7025 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg910 sg997 - -lemma sg7026 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1000 - -lemma sg7027 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1001 - -lemma sg7028 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg910 sg1002 - -lemma sg7029 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg997 sg911 - -lemma sg7030 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg912 - -lemma sg7031 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1004 - -lemma sg7032 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg913 - -lemma sg7033 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1005 - -lemma sg7034 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg914 - -lemma sg7035 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg915 - -lemma sg7036 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg912 - -lemma sg7037 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1378 - -lemma sg7038 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg913 - -lemma sg7039 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1379 - -lemma sg7040 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg914 - -lemma sg7041 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg999 sg915 - -lemma sg7042 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1000 sg914 - -lemma sg7043 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1000 sg915 - -lemma sg7044 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1001 sg915 - -lemma sg7045 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1009 - -lemma sg7046 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg916 - -lemma sg7047 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1010 - -lemma sg7048 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg917 - -lemma sg7049 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg916 - -lemma sg7050 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1011 - -lemma sg7051 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg918 - -lemma sg7052 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1002 sg913 - -lemma sg7053 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1012 - -lemma sg7054 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg919 - -lemma sg7055 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1002 sg914 - -lemma sg7056 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg915 - -lemma sg7057 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1013 - -lemma sg7058 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg920 - -lemma sg7059 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg917 - -lemma sg7060 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1014 - -lemma sg7061 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg921 - -lemma sg7062 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg918 - -lemma sg7063 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg917 - -lemma sg7064 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg922 - -lemma sg7065 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg919 - -lemma sg7066 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1003 sg914 - -lemma sg7067 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1003 sg915 - -lemma sg7068 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg923 - -lemma sg7069 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1378 - -lemma sg7070 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg918 - -lemma sg7071 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1379 - -lemma sg7072 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg919 - -lemma sg7073 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg1000 sg918 - -lemma sg7074 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1004 sg915 - -lemma sg7075 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg1000 sg919 - -lemma sg7076 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,4,3] := by - exact rowSquare_join (by decide) sg1001 sg919 - -lemma sg7077 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1015 - -lemma sg7078 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg920 - -lemma sg7079 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1016 - -lemma sg7080 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1388 - -lemma sg7081 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg921 - -lemma sg7082 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg920 - -lemma sg7083 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg922 - -lemma sg7084 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg1000 sg920 - -lemma sg7085 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1006 sg915 - -lemma sg7086 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1389 - -lemma sg7087 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg923 - -lemma sg7088 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg921 - -lemma sg7089 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg589 sg1377 - -lemma sg7090 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg922 - -lemma sg7091 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg1000 sg921 - -lemma sg7092 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,3,3] := by - exact rowSquare_join (by decide) sg1001 sg921 - -lemma sg7093 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1000 sg922 - -lemma sg7094 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,4,2] := by - exact rowSquare_join (by decide) sg1001 sg922 - -lemma sg7095 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg923 - -lemma sg7096 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg589 sg1378 - -lemma sg7097 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg1000 sg923 - -lemma sg7098 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,5,3,2] := by - exact rowSquare_join (by decide) sg1001 sg923 - -lemma sg7099 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,5,4,1] := by - exact rowSquare_join (by decide) sg590 sg1379 - -lemma sg7100 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1017 - -lemma sg7101 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg924 - -lemma sg7102 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1002 sg916 - -lemma sg7103 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1018 - -lemma sg7104 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg925 - -lemma sg7105 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg924 - -lemma sg7106 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1019 - -lemma sg7107 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg926 - -lemma sg7108 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1002 sg918 - -lemma sg7109 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg5197 - -lemma sg7110 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg927 - -lemma sg7111 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg919 - -lemma sg7112 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg5198 - -lemma sg7113 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg5199 - -lemma sg7114 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1020 - -lemma sg7115 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg928 - -lemma sg7116 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg925 - -lemma sg7117 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg5200 - -lemma sg7118 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1021 - -lemma sg7119 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg929 - -lemma sg7120 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg926 - -lemma sg7121 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg5201 - -lemma sg7122 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg927 - -lemma sg7123 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1003 sg919 - -lemma sg7124 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg5202 - -lemma sg7125 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg5203 - -lemma sg7126 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg930 - -lemma sg7127 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg923 - -lemma sg7128 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg5204 - -lemma sg7129 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1004 sg918 - -lemma sg7130 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5205 - -lemma sg7131 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg5206 - -lemma sg7132 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,3,3] := by - exact rowSquare_join (by decide) sg1 sg5207 - -lemma sg7133 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1 sg5208 - -lemma sg7134 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,4,2] := by - exact rowSquare_join (by decide) sg1 sg5209 - -lemma sg7135 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1022 - -lemma sg7136 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg931 - -lemma sg7137 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg928 - -lemma sg7138 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1003 sg920 - -lemma sg7139 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg932 - -lemma sg7140 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg929 - -lemma sg7141 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg928 - -lemma sg7142 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg1004 sg920 - -lemma sg7143 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1003 sg922 - -lemma sg7144 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg1000 sg928 - -lemma sg7145 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,3,3] := by - exact rowSquare_join (by decide) sg1001 sg928 - -lemma sg7146 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg930 - -lemma sg7147 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg929 - -lemma sg7148 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg1004 sg921 - -lemma sg7149 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg1000 sg929 - -lemma sg7150 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,4,3,2] := by - exact rowSquare_join (by decide) sg1001 sg929 - -lemma sg7151 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,4,4,1] := by - exact rowSquare_join (by decide) sg1005 sg922 - -lemma sg7152 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg930 - -lemma sg7153 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg1000 sg930 - -lemma sg7154 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,5,2,2] := by - exact rowSquare_join (by decide) sg1001 sg930 - -lemma sg7155 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,5,3,1] := by - exact rowSquare_join (by decide) sg1005 sg923 - -lemma sg7156 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,5,4] := by - exact rowSquare_join (by decide) sg594 sg1379 - -lemma sg7157 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1023 - -lemma sg7158 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1399 - -lemma sg7159 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg931 - -lemma sg7160 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg1006 sg920 - -lemma sg7161 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg932 - -lemma sg7162 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg931 - -lemma sg7163 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg1006 sg921 - -lemma sg7164 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg1000 sg931 - -lemma sg7165 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,3,3,2] := by - exact rowSquare_join (by decide) sg1001 sg931 - -lemma sg7166 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg932 - -lemma sg7167 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg1000 sg932 - -lemma sg7168 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,4,2,2] := by - exact rowSquare_join (by decide) sg1001 sg932 - -lemma sg7169 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,4,3,1] := by - exact rowSquare_join (by decide) sg1007 sg922 - -lemma sg7170 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,4,4] := by - exact rowSquare_join (by decide) sg1008 sg922 - -lemma sg7171 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg1389 - -lemma sg7172 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,5,2,1] := by - exact rowSquare_join (by decide) sg1007 sg923 - -lemma sg7173 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,5,3] := by - exact rowSquare_join (by decide) sg1008 sg923 - -lemma sg7174 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1024 - -lemma sg7175 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg933 - -lemma sg7176 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg5210 - -lemma sg7177 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1025 - -lemma sg7178 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg934 - -lemma sg7179 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg5211 - -lemma sg7180 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg5212 - -lemma sg7181 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1026 - -lemma sg7182 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg935 - -lemma sg7183 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5213 - -lemma sg7184 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg5214 - -lemma sg7185 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5215 - -lemma sg7186 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg5216 - -lemma sg7187 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg5217 - -lemma sg7188 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg5218 - -lemma sg7189 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1027 - -lemma sg7190 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg936 - -lemma sg7191 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg934 - -lemma sg7192 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg5219 - -lemma sg7193 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg937 - -lemma sg7194 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg935 - -lemma sg7195 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg5220 - -lemma sg7196 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg5221 - -lemma sg7197 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5222 - -lemma sg7198 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg5223 - -lemma sg7199 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg5224 - -lemma sg7200 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg930 - -lemma sg7201 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5225 - -lemma sg7202 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg5226 - -lemma sg7203 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg5227 - -lemma sg7204 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg3757 - -lemma sg7205 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg3758 - -lemma sg7206 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1028 - -lemma sg7207 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg938 - -lemma sg7208 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg936 - -lemma sg7209 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg5228 - -lemma sg7210 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg5229 - -lemma sg7211 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg937 - -lemma sg7212 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5230 - -lemma sg7213 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg5231 - -lemma sg7214 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg5232 - -lemma sg7215 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg3759 - -lemma sg7216 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5233 - -lemma sg7217 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg5234 - -lemma sg7218 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg5235 - -lemma sg7219 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg3760 - -lemma sg7220 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,4,4] := by - exact rowSquare_join (by decide) sg13 sg3761 - -lemma sg7221 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg1004 sg930 - -lemma sg7222 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,5,2,1] := by - exact rowSquare_join (by decide) sg13 sg3762 - -lemma sg7223 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,5,3] := by - exact rowSquare_join (by decide) sg13 sg3763 - -lemma sg7224 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg939 - -lemma sg7225 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg938 - -lemma sg7226 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1003 sg931 - -lemma sg7227 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg1006 sg928 - -lemma sg7228 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg938 - -lemma sg7229 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg1000 sg938 - -lemma sg7230 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,3,2,2] := by - exact rowSquare_join (by decide) sg1001 sg938 - -lemma sg7231 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg1004 sg932 - -lemma sg7232 : RowSquare [5,5,2,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg910 sg910 - -lemma sg7233 : RowSquare [5,5,2,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg910 sg911 - -lemma sg7234 : RowSquare [5,5,2,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg910 sg912 - -lemma sg7235 : RowSquare [5,5,2,2,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg915 - -lemma sg7236 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg910 sg916 - -lemma sg7237 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg911 sg911 - -lemma sg7238 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg838 - -lemma sg7239 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg920 - -lemma sg7240 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg838 - -lemma sg7241 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg921 - -lemma sg7242 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg922 - -lemma sg7243 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg840 - -lemma sg7244 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg841 - -lemma sg7245 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg923 - -lemma sg7246 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1000 sg840 - -lemma sg7247 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1001 sg841 - -lemma sg7248 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg842 - -lemma sg7249 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg931 - -lemma sg7250 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg846 - -lemma sg7251 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg932 - -lemma sg7252 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1006 sg841 - -lemma sg7253 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg536 sg1377 - -lemma sg7254 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,5,5,5] := by - exact rowSquare_join (by decide) sg13 sg3768 - -lemma sg7255 : RowSquare [5,5,2,2,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg939 - -lemma sg7256 : RowSquare [5,5,2,2,2,2,1,1] [4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg3998 - -lemma sg7257 : RowSquare [5,5,2,2,2,2,1,1] [4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg3999 - -lemma sg7258 : RowSquare [5,5,2,2,2,2,1,1] [4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg3999 - -lemma sg7259 : RowSquare [5,5,2,2,2,2,1,1] [4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg4001 - -lemma sg7260 : RowSquare [5,5,2,2,2,2,1,1] [4,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg4002 - -lemma sg7261 : RowSquare [5,5,2,2,2,2,1,1] [4,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg4003 - -lemma sg7262 : RowSquare [5,5,2,2,2,2,1,1] [4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg16 sg4004 - -lemma sg7263 : RowSquare [5,5,2,2,2,2,1,1] [4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg4000 - -lemma sg7264 : RowSquare [5,5,2,2,2,2,1,1] [4,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg4001 - -lemma sg7265 : RowSquare [5,5,2,2,2,2,1,1] [4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg4002 - -lemma sg7266 : RowSquare [5,5,2,2,2,2,1,1] [4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg4003 - -lemma sg7267 : RowSquare [5,5,2,2,2,2,1,1] [4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg4004 - -lemma sg7268 : RowSquare [5,5,2,2,2,2,1,1] [4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg838 sg838 - -lemma sg7269 : RowSquare [5,5,2,2,2,2,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg3998 - -lemma sg7270 : RowSquare [5,5,2,2,2,2,1,1] [5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg3999 - -lemma sg7271 : RowSquare [5,5,2,2,2,2,1,1] [5,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg4002 - -lemma sg7272 : RowSquare [5,5,2,2,2,2,1,1] [5,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg4003 - -lemma sg7273 : RowSquare [5,5,2,2,2,2,1,1] [5,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18 sg4004 - -lemma sg7274 : RowSquare [5,5,2,2,2,2,1,1] [5,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg4009 - -lemma sg7275 : RowSquare [5,5,2,2,2,2,1,1] [5,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg4007 - -lemma sg7276 : RowSquare [5,5,2,2,2,2,1,1] [5,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg4009 - -lemma sg7277 : RowSquare [5,5,2,2,2,2,1,1] [5,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg4012 - -lemma sg7278 : RowSquare [5,5,2,2,2,2,1,1] [5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg4013 - -lemma sg7279 : RowSquare [5,5,2,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg3999 - -lemma sg7280 : RowSquare [5,5,2,2,2,2,1,1] [6,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg4002 - -lemma sg7281 : RowSquare [5,5,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg4003 - -lemma sg7282 : RowSquare [5,5,2,2,2,2,1,1] [6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg19 sg4004 - -lemma sg7283 : RowSquare [5,5,2,2,2,2,1,1] [6,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg4009 - -lemma sg7284 : RowSquare [5,5,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg4021 - -lemma sg7285 : RowSquare [5,5,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg4009 - -lemma sg7286 : RowSquare [5,5,3,2,1,1,1,1,1] [4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg313 sg1688 - -lemma sg7287 : RowSquare [5,5,3,2,1,1,1,1,1] [5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg316 sg1688 - -lemma sg7288 : RowSquare [5,5,3,2,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg324 sg1682 - -lemma sg7289 : RowSquare [5,5,3,2,1,1,1,1,1] [7,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg325 sg1683 - -lemma sg7290 : RowSquare [5,5,3,2,1,1,1,1,1] [7,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg326 sg1683 - -lemma sg7291 : RowSquare [5,5,3,2,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg327 sg1683 - -lemma sg7292 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg682 sg1327 - -lemma sg7293 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg677 sg1328 - -lemma sg7294 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg683 sg1327 - -lemma sg7295 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg678 sg1328 - -lemma sg7296 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg684 sg1327 - -lemma sg7297 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg679 sg1328 - -lemma sg7298 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg677 sg1332 - -lemma sg7299 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg685 sg1327 - -lemma sg7300 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg680 sg1328 - -lemma sg7301 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg681 sg1328 - -lemma sg7302 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg686 sg1327 - -lemma sg7303 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg1332 - -lemma sg7304 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg370 sg1758 - -lemma sg7305 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg372 sg1755 - -lemma sg7306 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg1755 - -lemma sg7307 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg1033 - -lemma sg7308 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg614 sg1332 - -lemma sg7309 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg372 sg1756 - -lemma sg7310 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1031 sg890 - -lemma sg7311 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg1756 - -lemma sg7312 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1031 sg892 - -lemma sg7313 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg615 sg1332 - -lemma sg7314 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg373 sg1757 - -lemma sg7315 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1033 sg892 - -lemma sg7316 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6081 - -lemma sg7317 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6082 - -lemma sg7318 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6083 - -lemma sg7319 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg617 sg1331 - -lemma sg7320 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6084 - -lemma sg7321 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg617 sg1332 - -lemma sg7322 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6085 - -lemma sg7323 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6086 - -lemma sg7324 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6087 - -lemma sg7325 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6088 - -lemma sg7326 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6089 - -lemma sg7327 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg6090 - -lemma sg7328 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg618 sg1332 - -lemma sg7329 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg623 sg1328 - -lemma sg7330 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6091 - -lemma sg7331 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg619 sg1330 - -lemma sg7332 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6092 - -lemma sg7333 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg620 sg1330 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes13 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes11 + +namespace OAI + +/-! Semigroup Nodes 16. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg6934 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1005 + +lemma sg6935 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1003 sg1000 + +lemma sg6936 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1003 sg1001 + +lemma sg6937 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1004 + +lemma sg6938 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg1005 + +lemma sg6939 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg1000 sg1004 + +lemma sg6940 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1004 sg1001 + +lemma sg6941 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1005 + +lemma sg6942 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3] := by + exact rowSquare_join (by decide) sg1001 sg1005 + +lemma sg6943 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1006 + +lemma sg6944 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1007 + +lemma sg6945 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1006 + +lemma sg6946 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1008 + +lemma sg6947 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg1000 sg1006 + +lemma sg6948 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1006 sg1001 + +lemma sg6949 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg1007 + +lemma sg6950 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1008 + +lemma sg6951 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1007 + +lemma sg6952 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,3] := by + exact rowSquare_join (by decide) sg1001 sg1007 + +lemma sg6953 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1008 + +lemma sg6954 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,2] := by + exact rowSquare_join (by decide) sg1001 sg1008 + +lemma sg6955 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1009 + +lemma sg6956 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1002 sg1002 + +lemma sg6957 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1010 + +lemma sg6958 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1009 + +lemma sg6959 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1011 + +lemma sg6960 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1004 + +lemma sg6961 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg1009 + +lemma sg6962 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1012 + +lemma sg6963 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1005 + +lemma sg6964 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1009 sg1001 + +lemma sg6965 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1013 + +lemma sg6966 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1010 + +lemma sg6967 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1003 sg1003 + +lemma sg6968 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1014 + +lemma sg6969 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1011 + +lemma sg6970 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1010 + +lemma sg6971 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1012 + +lemma sg6972 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1003 sg1005 + +lemma sg6973 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1010 sg1001 + +lemma sg6974 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg1011 + +lemma sg6975 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1004 sg1004 + +lemma sg6976 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1012 + +lemma sg6977 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1011 + +lemma sg6978 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3] := by + exact rowSquare_join (by decide) sg1001 sg1011 + +lemma sg6979 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1012 + +lemma sg6980 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,2] := by + exact rowSquare_join (by decide) sg1001 sg1012 + +lemma sg6981 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1015 + +lemma sg6982 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1013 + +lemma sg6983 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1003 sg1006 + +lemma sg6984 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1016 + +lemma sg6985 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1014 + +lemma sg6986 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg1004 sg1006 + +lemma sg6987 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1003 sg1008 + +lemma sg6988 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3] := by + exact rowSquare_join (by decide) sg1001 sg1013 + +lemma sg6989 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1014 + +lemma sg6990 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg1004 sg1007 + +lemma sg6991 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1014 + +lemma sg6992 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,2] := by + exact rowSquare_join (by decide) sg1001 sg1014 + +lemma sg6993 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,1] := by + exact rowSquare_join (by decide) sg1005 sg1008 + +lemma sg6994 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1015 + +lemma sg6995 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg1006 sg1006 + +lemma sg6996 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1016 + +lemma sg6997 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1015 + +lemma sg6998 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg1006 sg1007 + +lemma sg6999 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1015 + +lemma sg7000 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,2] := by + exact rowSquare_join (by decide) sg1001 sg1015 + +lemma sg7001 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1016 + +lemma sg7002 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,1] := by + exact rowSquare_join (by decide) sg1007 sg1008 + +lemma sg7003 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [6,6,4,4] := by + exact rowSquare_join (by decide) sg1008 sg1008 + +lemma sg7004 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1012 + +lemma sg7005 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1017 sg1001 + +lemma sg7006 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1019 + +lemma sg7007 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1004 sg1010 + +lemma sg7008 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3] := by + exact rowSquare_join (by decide) sg1001 sg1018 + +lemma sg7009 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1004 sg1011 + +lemma sg7010 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1020 + +lemma sg7011 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1021 + +lemma sg7012 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2] := by + exact rowSquare_join (by decide) sg1001 sg1021 + +lemma sg7013 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1022 + +lemma sg7014 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,1] := by + exact rowSquare_join (by decide) sg1005 sg1015 + +lemma sg7015 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg1004 sg1016 + +lemma sg7016 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1023 + +lemma sg7017 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2] := by + exact rowSquare_join (by decide) sg1001 sg1023 + +lemma sg7018 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1019 + +lemma sg7019 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1004 sg1017 + +lemma sg7020 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3] := by + exact rowSquare_join (by decide) sg1001 sg1024 + +lemma sg7021 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [8,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1028 + +lemma sg7022 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1029 + +lemma sg7023 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [9,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1026 + +lemma sg7024 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1] [9,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1030 + +lemma sg7025 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg910 sg997 + +lemma sg7026 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1000 + +lemma sg7027 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1001 + +lemma sg7028 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg910 sg1002 + +lemma sg7029 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg997 sg911 + +lemma sg7030 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg912 + +lemma sg7031 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1004 + +lemma sg7032 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg913 + +lemma sg7033 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1005 + +lemma sg7034 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg914 + +lemma sg7035 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg915 + +lemma sg7036 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg912 + +lemma sg7037 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1378 + +lemma sg7038 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg913 + +lemma sg7039 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1379 + +lemma sg7040 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg914 + +lemma sg7041 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg999 sg915 + +lemma sg7042 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1000 sg914 + +lemma sg7043 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1000 sg915 + +lemma sg7044 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1001 sg915 + +lemma sg7045 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1009 + +lemma sg7046 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg916 + +lemma sg7047 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1010 + +lemma sg7048 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg917 + +lemma sg7049 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg916 + +lemma sg7050 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1011 + +lemma sg7051 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg918 + +lemma sg7052 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1002 sg913 + +lemma sg7053 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1012 + +lemma sg7054 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg919 + +lemma sg7055 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1002 sg914 + +lemma sg7056 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg915 + +lemma sg7057 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1013 + +lemma sg7058 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg920 + +lemma sg7059 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg917 + +lemma sg7060 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1014 + +lemma sg7061 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg921 + +lemma sg7062 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg918 + +lemma sg7063 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg917 + +lemma sg7064 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg922 + +lemma sg7065 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg919 + +lemma sg7066 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1003 sg914 + +lemma sg7067 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1003 sg915 + +lemma sg7068 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg923 + +lemma sg7069 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1378 + +lemma sg7070 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg918 + +lemma sg7071 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1379 + +lemma sg7072 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg919 + +lemma sg7073 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg1000 sg918 + +lemma sg7074 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1004 sg915 + +lemma sg7075 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg1000 sg919 + +lemma sg7076 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,4,4,4,3] := by + exact rowSquare_join (by decide) sg1001 sg919 + +lemma sg7077 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1015 + +lemma sg7078 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg920 + +lemma sg7079 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1016 + +lemma sg7080 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1388 + +lemma sg7081 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg921 + +lemma sg7082 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg920 + +lemma sg7083 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg922 + +lemma sg7084 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg1000 sg920 + +lemma sg7085 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1006 sg915 + +lemma sg7086 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1389 + +lemma sg7087 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg923 + +lemma sg7088 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg921 + +lemma sg7089 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg589 sg1377 + +lemma sg7090 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg922 + +lemma sg7091 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg1000 sg921 + +lemma sg7092 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,3,3] := by + exact rowSquare_join (by decide) sg1001 sg921 + +lemma sg7093 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1000 sg922 + +lemma sg7094 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,4,4,2] := by + exact rowSquare_join (by decide) sg1001 sg922 + +lemma sg7095 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg923 + +lemma sg7096 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg589 sg1378 + +lemma sg7097 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg1000 sg923 + +lemma sg7098 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,5,3,2] := by + exact rowSquare_join (by decide) sg1001 sg923 + +lemma sg7099 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [5,5,5,4,1] := by + exact rowSquare_join (by decide) sg590 sg1379 + +lemma sg7100 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1017 + +lemma sg7101 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg924 + +lemma sg7102 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1002 sg916 + +lemma sg7103 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1018 + +lemma sg7104 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg925 + +lemma sg7105 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg924 + +lemma sg7106 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1019 + +lemma sg7107 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg926 + +lemma sg7108 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1002 sg918 + +lemma sg7109 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg5197 + +lemma sg7110 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg927 + +lemma sg7111 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg919 + +lemma sg7112 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg5198 + +lemma sg7113 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg5199 + +lemma sg7114 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1020 + +lemma sg7115 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg928 + +lemma sg7116 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg925 + +lemma sg7117 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg5200 + +lemma sg7118 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1021 + +lemma sg7119 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg929 + +lemma sg7120 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg926 + +lemma sg7121 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg5201 + +lemma sg7122 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg927 + +lemma sg7123 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1003 sg919 + +lemma sg7124 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg5202 + +lemma sg7125 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg5203 + +lemma sg7126 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg930 + +lemma sg7127 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg923 + +lemma sg7128 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg5204 + +lemma sg7129 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1004 sg918 + +lemma sg7130 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5205 + +lemma sg7131 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg5206 + +lemma sg7132 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,3,3] := by + exact rowSquare_join (by decide) sg1 sg5207 + +lemma sg7133 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1 sg5208 + +lemma sg7134 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,4,4,4,2] := by + exact rowSquare_join (by decide) sg1 sg5209 + +lemma sg7135 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1022 + +lemma sg7136 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg931 + +lemma sg7137 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg928 + +lemma sg7138 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1003 sg920 + +lemma sg7139 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg932 + +lemma sg7140 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg929 + +lemma sg7141 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg928 + +lemma sg7142 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg1004 sg920 + +lemma sg7143 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1003 sg922 + +lemma sg7144 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg1000 sg928 + +lemma sg7145 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,3,3,3] := by + exact rowSquare_join (by decide) sg1001 sg928 + +lemma sg7146 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg930 + +lemma sg7147 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg929 + +lemma sg7148 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg1004 sg921 + +lemma sg7149 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg1000 sg929 + +lemma sg7150 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,4,3,2] := by + exact rowSquare_join (by decide) sg1001 sg929 + +lemma sg7151 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,4,4,1] := by + exact rowSquare_join (by decide) sg1005 sg922 + +lemma sg7152 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg930 + +lemma sg7153 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg1000 sg930 + +lemma sg7154 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,5,2,2] := by + exact rowSquare_join (by decide) sg1001 sg930 + +lemma sg7155 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,5,3,1] := by + exact rowSquare_join (by decide) sg1005 sg923 + +lemma sg7156 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,5,5,4] := by + exact rowSquare_join (by decide) sg594 sg1379 + +lemma sg7157 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1023 + +lemma sg7158 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1399 + +lemma sg7159 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg931 + +lemma sg7160 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg1006 sg920 + +lemma sg7161 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg932 + +lemma sg7162 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg931 + +lemma sg7163 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg1006 sg921 + +lemma sg7164 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg1000 sg931 + +lemma sg7165 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,3,3,2] := by + exact rowSquare_join (by decide) sg1001 sg931 + +lemma sg7166 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg932 + +lemma sg7167 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg1000 sg932 + +lemma sg7168 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,4,2,2] := by + exact rowSquare_join (by decide) sg1001 sg932 + +lemma sg7169 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,4,3,1] := by + exact rowSquare_join (by decide) sg1007 sg922 + +lemma sg7170 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,4,4] := by + exact rowSquare_join (by decide) sg1008 sg922 + +lemma sg7171 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg1389 + +lemma sg7172 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,5,2,1] := by + exact rowSquare_join (by decide) sg1007 sg923 + +lemma sg7173 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [6,6,5,3] := by + exact rowSquare_join (by decide) sg1008 sg923 + +lemma sg7174 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1024 + +lemma sg7175 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg933 + +lemma sg7176 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg5210 + +lemma sg7177 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1025 + +lemma sg7178 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg934 + +lemma sg7179 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg5211 + +lemma sg7180 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg5212 + +lemma sg7181 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1026 + +lemma sg7182 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg935 + +lemma sg7183 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5213 + +lemma sg7184 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg5214 + +lemma sg7185 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5215 + +lemma sg7186 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg5216 + +lemma sg7187 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg5217 + +lemma sg7188 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg5218 + +lemma sg7189 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1027 + +lemma sg7190 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg936 + +lemma sg7191 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg934 + +lemma sg7192 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg5219 + +lemma sg7193 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg937 + +lemma sg7194 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg935 + +lemma sg7195 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg5220 + +lemma sg7196 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg5221 + +lemma sg7197 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5222 + +lemma sg7198 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg5223 + +lemma sg7199 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg5224 + +lemma sg7200 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg930 + +lemma sg7201 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5225 + +lemma sg7202 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg5226 + +lemma sg7203 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg5227 + +lemma sg7204 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg3757 + +lemma sg7205 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,4,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg3758 + +lemma sg7206 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1028 + +lemma sg7207 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg938 + +lemma sg7208 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg936 + +lemma sg7209 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg5228 + +lemma sg7210 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg5229 + +lemma sg7211 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg937 + +lemma sg7212 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5230 + +lemma sg7213 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg5231 + +lemma sg7214 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg5232 + +lemma sg7215 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg3759 + +lemma sg7216 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5233 + +lemma sg7217 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg5234 + +lemma sg7218 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg5235 + +lemma sg7219 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg3760 + +lemma sg7220 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,4,4] := by + exact rowSquare_join (by decide) sg13 sg3761 + +lemma sg7221 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg1004 sg930 + +lemma sg7222 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,5,2,1] := by + exact rowSquare_join (by decide) sg13 sg3762 + +lemma sg7223 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,5,5,3] := by + exact rowSquare_join (by decide) sg13 sg3763 + +lemma sg7224 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg939 + +lemma sg7225 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg938 + +lemma sg7226 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1003 sg931 + +lemma sg7227 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg1006 sg928 + +lemma sg7228 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg938 + +lemma sg7229 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg1000 sg938 + +lemma sg7230 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,3,2,2] := by + exact rowSquare_join (by decide) sg1001 sg938 + +lemma sg7231 : RowSquare [5,5,2,1,1,1,1,1,1,1,1] [7,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg1004 sg932 + +lemma sg7232 : RowSquare [5,5,2,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg910 sg910 + +lemma sg7233 : RowSquare [5,5,2,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg910 sg911 + +lemma sg7234 : RowSquare [5,5,2,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg910 sg912 + +lemma sg7235 : RowSquare [5,5,2,2,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg915 + +lemma sg7236 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg910 sg916 + +lemma sg7237 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg911 sg911 + +lemma sg7238 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg838 + +lemma sg7239 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg920 + +lemma sg7240 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg838 + +lemma sg7241 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg921 + +lemma sg7242 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg922 + +lemma sg7243 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg840 + +lemma sg7244 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg841 + +lemma sg7245 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg923 + +lemma sg7246 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1000 sg840 + +lemma sg7247 : RowSquare [5,5,2,2,1,1,1,1,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1001 sg841 + +lemma sg7248 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg842 + +lemma sg7249 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg931 + +lemma sg7250 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg846 + +lemma sg7251 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg932 + +lemma sg7252 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1006 sg841 + +lemma sg7253 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg536 sg1377 + +lemma sg7254 : RowSquare [5,5,2,2,1,1,1,1,1,1] [5,5,5,5] := by + exact rowSquare_join (by decide) sg13 sg3768 + +lemma sg7255 : RowSquare [5,5,2,2,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg939 + +lemma sg7256 : RowSquare [5,5,2,2,2,2,1,1] [4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg3998 + +lemma sg7257 : RowSquare [5,5,2,2,2,2,1,1] [4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg3999 + +lemma sg7258 : RowSquare [5,5,2,2,2,2,1,1] [4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg3999 + +lemma sg7259 : RowSquare [5,5,2,2,2,2,1,1] [4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg4001 + +lemma sg7260 : RowSquare [5,5,2,2,2,2,1,1] [4,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg4002 + +lemma sg7261 : RowSquare [5,5,2,2,2,2,1,1] [4,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg4003 + +lemma sg7262 : RowSquare [5,5,2,2,2,2,1,1] [4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg16 sg4004 + +lemma sg7263 : RowSquare [5,5,2,2,2,2,1,1] [4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg4000 + +lemma sg7264 : RowSquare [5,5,2,2,2,2,1,1] [4,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg4001 + +lemma sg7265 : RowSquare [5,5,2,2,2,2,1,1] [4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg4002 + +lemma sg7266 : RowSquare [5,5,2,2,2,2,1,1] [4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg4003 + +lemma sg7267 : RowSquare [5,5,2,2,2,2,1,1] [4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg4004 + +lemma sg7268 : RowSquare [5,5,2,2,2,2,1,1] [4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg838 sg838 + +lemma sg7269 : RowSquare [5,5,2,2,2,2,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg3998 + +lemma sg7270 : RowSquare [5,5,2,2,2,2,1,1] [5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg3999 + +lemma sg7271 : RowSquare [5,5,2,2,2,2,1,1] [5,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg4002 + +lemma sg7272 : RowSquare [5,5,2,2,2,2,1,1] [5,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg4003 + +lemma sg7273 : RowSquare [5,5,2,2,2,2,1,1] [5,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18 sg4004 + +lemma sg7274 : RowSquare [5,5,2,2,2,2,1,1] [5,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg4009 + +lemma sg7275 : RowSquare [5,5,2,2,2,2,1,1] [5,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg4007 + +lemma sg7276 : RowSquare [5,5,2,2,2,2,1,1] [5,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg4009 + +lemma sg7277 : RowSquare [5,5,2,2,2,2,1,1] [5,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg4012 + +lemma sg7278 : RowSquare [5,5,2,2,2,2,1,1] [5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg4013 + +lemma sg7279 : RowSquare [5,5,2,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg3999 + +lemma sg7280 : RowSquare [5,5,2,2,2,2,1,1] [6,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg4002 + +lemma sg7281 : RowSquare [5,5,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg4003 + +lemma sg7282 : RowSquare [5,5,2,2,2,2,1,1] [6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg19 sg4004 + +lemma sg7283 : RowSquare [5,5,2,2,2,2,1,1] [6,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg4009 + +lemma sg7284 : RowSquare [5,5,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg4021 + +lemma sg7285 : RowSquare [5,5,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg4009 + +lemma sg7286 : RowSquare [5,5,3,2,1,1,1,1,1] [4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg313 sg1688 + +lemma sg7287 : RowSquare [5,5,3,2,1,1,1,1,1] [5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg316 sg1688 + +lemma sg7288 : RowSquare [5,5,3,2,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg324 sg1682 + +lemma sg7289 : RowSquare [5,5,3,2,1,1,1,1,1] [7,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg325 sg1683 + +lemma sg7290 : RowSquare [5,5,3,2,1,1,1,1,1] [7,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg326 sg1683 + +lemma sg7291 : RowSquare [5,5,3,2,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg327 sg1683 + +lemma sg7292 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg682 sg1327 + +lemma sg7293 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg677 sg1328 + +lemma sg7294 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg683 sg1327 + +lemma sg7295 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg678 sg1328 + +lemma sg7296 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg684 sg1327 + +lemma sg7297 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg679 sg1328 + +lemma sg7298 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg677 sg1332 + +lemma sg7299 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg685 sg1327 + +lemma sg7300 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg680 sg1328 + +lemma sg7301 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg681 sg1328 + +lemma sg7302 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg686 sg1327 + +lemma sg7303 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg1332 + +lemma sg7304 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg370 sg1758 + +lemma sg7305 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg372 sg1755 + +lemma sg7306 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg1755 + +lemma sg7307 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg1033 + +lemma sg7308 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg614 sg1332 + +lemma sg7309 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg372 sg1756 + +lemma sg7310 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1031 sg890 + +lemma sg7311 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg1756 + +lemma sg7312 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1031 sg892 + +lemma sg7313 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg615 sg1332 + +lemma sg7314 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg373 sg1757 + +lemma sg7315 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1033 sg892 + +lemma sg7316 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6081 + +lemma sg7317 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6082 + +lemma sg7318 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6083 + +lemma sg7319 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg617 sg1331 + +lemma sg7320 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6084 + +lemma sg7321 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg617 sg1332 + +lemma sg7322 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6085 + +lemma sg7323 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6086 + +lemma sg7324 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6087 + +lemma sg7325 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6088 + +lemma sg7326 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6089 + +lemma sg7327 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg6090 + +lemma sg7328 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg618 sg1332 + +lemma sg7329 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg623 sg1328 + +lemma sg7330 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6091 + +lemma sg7331 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg619 sg1330 + +lemma sg7332 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6092 + +lemma sg7333 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg620 sg1330 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes17.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes17.lean index ef581a569addb323cde041c0465c64a8bb49f009..a3d96e771c3c46dab61a7eb4bbef76f2a4425415 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes17.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes17.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes13 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes14 - -namespace OAI - -/-! Semigroup Nodes 17. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg7334 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6093 - -lemma sg7335 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg6094 - -lemma sg7336 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg6095 - -lemma sg7337 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg620 sg1331 - -lemma sg7338 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg0 sg6096 - -lemma sg7339 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,4,3] := by - exact rowSquare_join (by decide) sg0 sg6097 - -lemma sg7340 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg621 sg1329 - -lemma sg7341 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg889 sg1038 - -lemma sg7342 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg614 sg1338 - -lemma sg7343 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg378 sg1755 - -lemma sg7344 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg622 sg1329 - -lemma sg7345 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg1039 - -lemma sg7346 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1031 sg897 - -lemma sg7347 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg1040 - -lemma sg7348 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg614 sg1340 - -lemma sg7349 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg897 - -lemma sg7350 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1038 sg892 - -lemma sg7351 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg623 sg1329 - -lemma sg7352 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg1041 - -lemma sg7353 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1031 sg898 - -lemma sg7354 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg1339 - -lemma sg7355 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1031 sg899 - -lemma sg7356 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg1032 sg898 - -lemma sg7357 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,3,3] := by - exact rowSquare_join (by decide) sg1033 sg898 - -lemma sg7358 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1032 sg899 - -lemma sg7359 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,4,2] := by - exact rowSquare_join (by decide) sg1033 sg899 - -lemma sg7360 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg623 sg1330 - -lemma sg7361 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg890 sg1041 - -lemma sg7362 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg623 sg1332 - -lemma sg7363 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg891 sg1041 - -lemma sg7364 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,5,3,2] := by - exact rowSquare_join (by decide) sg892 sg1041 - -lemma sg7365 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,5,4,1] := by - exact rowSquare_join (by decide) sg373 sg1767 - -lemma sg7366 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6098 - -lemma sg7367 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6099 - -lemma sg7368 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6100 - -lemma sg7369 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg5197 - -lemma sg7370 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6101 - -lemma sg7371 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg5198 - -lemma sg7372 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2 sg5199 - -lemma sg7373 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg624 sg1332 - -lemma sg7374 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6102 - -lemma sg7375 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg5200 - -lemma sg7376 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6103 - -lemma sg7377 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5341 - -lemma sg7378 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg5201 - -lemma sg7379 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5342 - -lemma sg7380 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6104 - -lemma sg7381 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2 sg5202 - -lemma sg7382 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg2 sg5203 - -lemma sg7383 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5343 - -lemma sg7384 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6105 - -lemma sg7385 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg4587 - -lemma sg7386 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6106 - -lemma sg7387 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4588 - -lemma sg7388 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg4589 - -lemma sg7389 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,3,3] := by - exact rowSquare_join (by decide) sg4 sg4590 - -lemma sg7390 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2 sg5208 - -lemma sg7391 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,4,2] := by - exact rowSquare_join (by decide) sg2 sg5209 - -lemma sg7392 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg628 sg1328 - -lemma sg7393 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6107 - -lemma sg7394 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6108 - -lemma sg7395 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6109 - -lemma sg7396 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg4591 - -lemma sg7397 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6110 - -lemma sg7398 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6111 - -lemma sg7399 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg0 sg6112 - -lemma sg7400 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg6113 - -lemma sg7401 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6114 - -lemma sg7402 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4592 - -lemma sg7403 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg4593 - -lemma sg7404 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg4594 - -lemma sg7405 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,4,3,2] := by - exact rowSquare_join (by decide) sg4 sg4595 - -lemma sg7406 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,4,4,1] := by - exact rowSquare_join (by decide) sg0 sg6115 - -lemma sg7407 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4596 - -lemma sg7408 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg4597 - -lemma sg7409 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,5,2,2] := by - exact rowSquare_join (by decide) sg4 sg4598 - -lemma sg7410 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,5,3,1] := by - exact rowSquare_join (by decide) sg4 sg4599 - -lemma sg7411 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,5,4] := by - exact rowSquare_join (by decide) sg4 sg4600 - -lemma sg7412 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg383 sg1755 - -lemma sg7413 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg628 sg1329 - -lemma sg7414 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg1048 - -lemma sg7415 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg614 sg1348 - -lemma sg7416 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg1038 sg897 - -lemma sg7417 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg1049 - -lemma sg7418 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4601 - -lemma sg7419 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg4602 - -lemma sg7420 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg1032 sg902 - -lemma sg7421 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,3,3,2] := by - exact rowSquare_join (by decide) sg1033 sg902 - -lemma sg7422 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4603 - -lemma sg7423 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg4604 - -lemma sg7424 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,4,2,2] := by - exact rowSquare_join (by decide) sg4 sg4605 - -lemma sg7425 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,4,3,1] := by - exact rowSquare_join (by decide) sg4 sg4606 - -lemma sg7426 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,4,4] := by - exact rowSquare_join (by decide) sg1040 sg899 - -lemma sg7427 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4607 - -lemma sg7428 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,5,2,1] := by - exact rowSquare_join (by decide) sg4 sg4608 - -lemma sg7429 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,5,3] := by - exact rowSquare_join (by decide) sg4 sg4609 - -lemma sg7430 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,6,1,1] := by - exact rowSquare_join (by decide) sg4 sg4610 - -lemma sg7431 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,6,2] := by - exact rowSquare_join (by decide) sg4 sg4611 - -lemma sg7432 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5344 - -lemma sg7433 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5345 - -lemma sg7434 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg5212 - -lemma sg7435 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5346 - -lemma sg7436 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg4612 - -lemma sg7437 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg5216 - -lemma sg7438 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2 sg5217 - -lemma sg7439 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2 sg5218 - -lemma sg7440 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6116 - -lemma sg7441 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg5219 - -lemma sg7442 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg4613 - -lemma sg7443 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg4614 - -lemma sg7444 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg4588 - -lemma sg7445 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg5 sg4589 - -lemma sg7446 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,3,3,3] := by - exact rowSquare_join (by decide) sg5 sg4590 - -lemma sg7447 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg3797 - -lemma sg7448 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg4615 - -lemma sg7449 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6117 - -lemma sg7450 : RowSquare [6,4,2,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg1754 - -lemma sg7451 : RowSquare [6,4,2,2,1,1,1,1,1,1] [3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg1758 - -lemma sg7452 : RowSquare [6,4,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg332 sg1755 - -lemma sg7453 : RowSquare [6,4,2,2,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg334 sg1756 - -lemma sg7454 : RowSquare [6,4,2,2,1,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg4063 - -lemma sg7455 : RowSquare [6,4,2,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg1754 - -lemma sg7456 : RowSquare [6,4,2,2,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg4064 - -lemma sg7457 : RowSquare [6,4,2,2,1,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg4065 - -lemma sg7458 : RowSquare [6,4,2,2,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6124 - -lemma sg7459 : RowSquare [6,4,2,2,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg4071 - -lemma sg7460 : RowSquare [6,4,2,2,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6125 - -lemma sg7461 : RowSquare [6,4,2,2,1,1,1,1,1,1] [8,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5356 - -lemma sg7462 : RowSquare [6,4,2,2,2,2,1,1] [4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg4078 - -lemma sg7463 : RowSquare [6,4,2,2,2,2,1,1] [4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg878 sg808 - -lemma sg7464 : RowSquare [6,4,2,2,2,2,1,1] [4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg960 sg762 - -lemma sg7465 : RowSquare [6,4,2,2,2,2,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg4063 - -lemma sg7466 : RowSquare [6,4,2,2,2,2,1,1] [5,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg4071 - -lemma sg7467 : RowSquare [6,4,2,2,2,2,1,1] [5,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg4080 - -lemma sg7468 : RowSquare [6,4,2,2,2,2,1,1] [5,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg4072 - -lemma sg7469 : RowSquare [6,4,2,2,2,2,1,1] [5,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg4073 - -lemma sg7470 : RowSquare [6,4,2,2,2,2,1,1] [5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg4074 - -lemma sg7471 : RowSquare [6,4,2,2,2,2,1,1] [5,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg4081 - -lemma sg7472 : RowSquare [6,4,2,2,2,2,1,1] [5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg958 sg765 - -lemma sg7473 : RowSquare [6,4,2,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg4064 - -lemma sg7474 : RowSquare [6,4,2,2,2,2,1,1] [6,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg4067 - -lemma sg7475 : RowSquare [6,4,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg4068 - -lemma sg7476 : RowSquare [6,4,2,2,2,2,1,1] [6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg15 sg4069 - -lemma sg7477 : RowSquare [6,4,2,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg4080 - -lemma sg7478 : RowSquare [6,4,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg4081 - -lemma sg7479 : RowSquare [6,4,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg4072 - -lemma sg7480 : RowSquare [6,4,3,2,1,1,1,1,1] [3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg66 sg2626 - -lemma sg7481 : RowSquare [6,4,3,2,1,1,1,1,1] [3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg67 sg2626 - -lemma sg7482 : RowSquare [6,4,3,2,1,1,1,1,1] [3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg2626 - -lemma sg7483 : RowSquare [6,4,3,2,1,1,1,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg4862 - -lemma sg7484 : RowSquare [6,4,3,2,1,1,1,1,1] [4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg69 sg2626 - -lemma sg7485 : RowSquare [6,4,3,2,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg66 sg2627 - -lemma sg7486 : RowSquare [6,4,3,2,1,1,1,1,1] [4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg6155 - -lemma sg7487 : RowSquare [6,4,3,2,1,1,1,1,1] [4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg71 sg2626 - -lemma sg7488 : RowSquare [6,4,3,2,1,1,1,1,1] [5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg4864 - -lemma sg7489 : RowSquare [6,4,3,2,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg72 sg2626 - -lemma sg7490 : RowSquare [6,4,3,2,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg69 sg2627 - -lemma sg7491 : RowSquare [6,4,3,2,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg73 sg2626 - -lemma sg7492 : RowSquare [6,4,3,2,1,1,1,1,1] [5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg6162 - -lemma sg7493 : RowSquare [6,4,3,2,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg71 sg2627 - -lemma sg7494 : RowSquare [6,4,3,2,1,1,1,1,1] [5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6163 - -lemma sg7495 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg514 sg1329 - -lemma sg7496 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4637 - -lemma sg7497 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4638 - -lemma sg7498 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg2491 - -lemma sg7499 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg74 sg2492 - -lemma sg7500 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,3,2] := by - exact rowSquare_join (by decide) sg32 sg3179 - -lemma sg7501 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,4,1] := by - exact rowSquare_join (by decide) sg32 sg3180 - -lemma sg7502 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,5] := by - exact rowSquare_join (by decide) sg390 sg1631 - -lemma sg7503 : RowSquare [6,4,3,2,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5366 - -lemma sg7504 : RowSquare [6,4,3,2,1,1,1,1,1] [6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4641 - -lemma sg7505 : RowSquare [6,4,3,2,1,1,1,1,1] [6,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg55 sg2520 - -lemma sg7506 : RowSquare [6,4,3,2,1,1,1,1,1] [6,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg2493 - -lemma sg7507 : RowSquare [6,4,3,2,1,1,1,1,1] [6,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg2494 - -lemma sg7508 : RowSquare [6,4,3,2,1,1,1,1,1] [6,6,5,2,1] := by - exact rowSquare_join (by decide) sg76 sg2491 - -lemma sg7509 : RowSquare [6,4,3,2,1,1,1,1,1] [6,6,5,3] := by - exact rowSquare_join (by decide) sg76 sg2492 - -lemma sg7510 : RowSquare [6,4,3,2,1,1,1,1,1] [6,6,6,1,1] := by - exact rowSquare_join (by decide) sg77 sg2491 - -lemma sg7511 : RowSquare [6,4,3,2,1,1,1,1,1] [6,6,6,2] := by - exact rowSquare_join (by decide) sg77 sg2492 - -lemma sg7512 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg1327 - -lemma sg7513 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1327 - -lemma sg7514 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg1329 - -lemma sg7515 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg1327 - -lemma sg7516 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg1327 - -lemma sg7517 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg1331 - -lemma sg7518 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1332 - -lemma sg7519 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg591 sg1327 - -lemma sg7520 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg592 sg1327 - -lemma sg7521 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg593 sg1327 - -lemma sg7522 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg1330 - -lemma sg7523 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg594 sg1327 - -lemma sg7524 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg587 sg1331 - -lemma sg7525 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg1332 - -lemma sg7526 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg595 sg1327 - -lemma sg7527 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg1338 - -lemma sg7528 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg889 - -lemma sg7529 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg1327 - -lemma sg7530 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1339 - -lemma sg7531 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1340 - -lemma sg7532 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg1331 - -lemma sg7533 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg588 sg1332 - -lemma sg7534 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg589 sg1330 - -lemma sg7535 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg1330 - -lemma sg7536 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg589 sg1332 - -lemma sg7537 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg590 sg1331 - -lemma sg7538 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1001 sg892 - -lemma sg7539 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg597 sg1327 - -lemma sg7540 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6180 - -lemma sg7541 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg598 sg1327 - -lemma sg7542 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6181 - -lemma sg7543 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6182 - -lemma sg7544 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg599 sg1327 - -lemma sg7545 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6183 - -lemma sg7546 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6184 - -lemma sg7547 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6185 - -lemma sg7548 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6186 - -lemma sg7549 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg591 sg1331 - -lemma sg7550 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6187 - -lemma sg7551 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg591 sg1332 - -lemma sg7552 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg600 sg1327 - -lemma sg7553 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6188 - -lemma sg7554 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6189 - -lemma sg7555 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg601 sg1327 - -lemma sg7556 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6190 - -lemma sg7557 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6191 - -lemma sg7558 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6192 - -lemma sg7559 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6193 - -lemma sg7560 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6194 - -lemma sg7561 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6195 - -lemma sg7562 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg6196 - -lemma sg7563 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg592 sg1332 - -lemma sg7564 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg593 sg1330 - -lemma sg7565 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6197 - -lemma sg7566 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg594 sg1330 - -lemma sg7567 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6198 - -lemma sg7568 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg6199 - -lemma sg7569 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg6200 - -lemma sg7570 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg594 sg1331 - -lemma sg7571 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg0 sg6201 - -lemma sg7572 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,4,3] := by - exact rowSquare_join (by decide) sg0 sg6202 - -lemma sg7573 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg1327 - -lemma sg7574 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1348 - -lemma sg7575 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg897 - -lemma sg7576 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg1338 - -lemma sg7577 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1349 - -lemma sg7578 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg898 - -lemma sg7579 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg897 - -lemma sg7580 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg899 - -lemma sg7581 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg1340 - -lemma sg7582 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg1000 sg897 - -lemma sg7583 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1006 sg892 - -lemma sg7584 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg1330 - -lemma sg7585 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg898 - -lemma sg7586 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg589 sg1339 - -lemma sg7587 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg899 - -lemma sg7588 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg1000 sg898 - -lemma sg7589 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,3,3] := by - exact rowSquare_join (by decide) sg1001 sg898 - -lemma sg7590 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1000 sg899 - -lemma sg7591 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,4,2] := by - exact rowSquare_join (by decide) sg1001 sg899 - -lemma sg7592 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg603 sg1327 - -lemma sg7593 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg5367 - -lemma sg7594 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6203 - -lemma sg7595 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg604 sg1327 - -lemma sg7596 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5368 - -lemma sg7597 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg5369 - -lemma sg7598 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg605 sg1327 - -lemma sg7599 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5370 - -lemma sg7600 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6204 - -lemma sg7601 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg4643 - -lemma sg7602 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5371 - -lemma sg7603 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6206 - -lemma sg7604 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg5372 - -lemma sg7605 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg5373 - -lemma sg7606 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg597 sg1332 - -lemma sg7607 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6209 - -lemma sg7608 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg5374 - -lemma sg7609 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6210 - -lemma sg7610 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6211 - -lemma sg7611 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5375 - -lemma sg7612 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg4644 - -lemma sg7613 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5376 - -lemma sg7614 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6213 - -lemma sg7615 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg5377 - -lemma sg7616 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg5378 - -lemma sg7617 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg599 sg1330 - -lemma sg7618 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg4645 - -lemma sg7619 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6215 - -lemma sg7620 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4646 - -lemma sg7621 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg5379 - -lemma sg7622 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,3,3] := by - exact rowSquare_join (by decide) sg1 sg5380 - -lemma sg7623 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1 sg5381 - -lemma sg7624 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,4,2] := by - exact rowSquare_join (by decide) sg1 sg5382 - -lemma sg7625 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg607 sg1327 - -lemma sg7626 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6221 - -lemma sg7627 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6222 - -lemma sg7628 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6223 - -lemma sg7629 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6224 - -lemma sg7630 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6225 - -lemma sg7631 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6226 - -lemma sg7632 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg4647 - -lemma sg7633 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6228 - -lemma sg7634 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg0 sg6229 - -lemma sg7635 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg6230 - -lemma sg7636 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg601 sg1330 - -lemma sg7637 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6231 - -lemma sg7638 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg4648 - -lemma sg7639 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg4649 - -lemma sg7640 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,4,3,2] := by - exact rowSquare_join (by decide) sg0 sg6232 - -lemma sg7641 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,4,4,1] := by - exact rowSquare_join (by decide) sg0 sg6233 - -lemma sg7642 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,5,2,2] := by - exact rowSquare_join (by decide) sg4 sg4650 - -lemma sg7643 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,5,3,1] := by - exact rowSquare_join (by decide) sg4 sg4651 - -lemma sg7644 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,5,4] := by - exact rowSquare_join (by decide) sg4 sg4652 - -lemma sg7645 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1358 - -lemma sg7646 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg902 - -lemma sg7647 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg1348 - -lemma sg7648 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg1006 sg897 - -lemma sg7649 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg903 - -lemma sg7650 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg902 - -lemma sg7651 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg1006 sg898 - -lemma sg7652 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg1000 sg902 - -lemma sg7653 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,3,3,2] := by - exact rowSquare_join (by decide) sg1001 sg902 - -lemma sg7654 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg903 - -lemma sg7655 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg1000 sg903 - -lemma sg7656 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,4,2,2] := by - exact rowSquare_join (by decide) sg1001 sg903 - -lemma sg7657 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,4,3,1] := by - exact rowSquare_join (by decide) sg1007 sg899 - -lemma sg7658 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,4,4] := by - exact rowSquare_join (by decide) sg1008 sg899 - -lemma sg7659 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg608 sg1327 - -lemma sg7660 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg603 sg1328 - -lemma sg7661 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5383 - -lemma sg7662 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg5384 - -lemma sg7663 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg609 sg1327 - -lemma sg7664 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg604 sg1328 - -lemma sg7665 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5385 - -lemma sg7666 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg5386 - -lemma sg7667 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg4643 - -lemma sg7668 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg605 sg1328 - -lemma sg7669 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5387 - -lemma sg7670 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5388 - -lemma sg7671 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg4653 - -lemma sg7672 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5389 - -lemma sg7673 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg3803 - -lemma sg7674 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg5390 - -lemma sg7675 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg5391 - -lemma sg7676 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg610 sg1327 - -lemma sg7677 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg606 sg1328 - -lemma sg7678 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5392 - -lemma sg7679 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5393 - -lemma sg7680 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg4644 - -lemma sg7681 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5394 - -lemma sg7682 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5395 - -lemma sg7683 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg4654 - -lemma sg7684 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg4655 - -lemma sg7685 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg3804 - -lemma sg7686 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg3805 - -lemma sg7687 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg5396 - -lemma sg7688 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg605 sg1330 - -lemma sg7689 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg3806 - -lemma sg7690 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg4656 - -lemma sg7691 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg4657 - -lemma sg7692 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg3807 - -lemma sg7693 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg3808 - -lemma sg7694 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg607 sg1328 - -lemma sg7695 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6261 - -lemma sg7696 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5397 - -lemma sg7697 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6263 - -lemma sg7698 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg4647 - -lemma sg7699 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,4,4] := by - exact rowSquare_join (by decide) sg13 sg3810 - -lemma sg7700 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,5,2,1] := by - exact rowSquare_join (by decide) sg13 sg3811 - -lemma sg7701 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,5,3] := by - exact rowSquare_join (by decide) sg13 sg3812 - -lemma sg7702 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6275 - -lemma sg7703 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6276 - -lemma sg7704 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6277 - -lemma sg7705 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6278 - -lemma sg7706 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4658 - -lemma sg7707 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,4,2,1] := by - exact rowSquare_join (by decide) sg4 sg4659 - -lemma sg7708 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,4,3] := by - exact rowSquare_join (by decide) sg4 sg4660 - -lemma sg7709 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,5,1,1] := by - exact rowSquare_join (by decide) sg4 sg4661 - -lemma sg7710 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,5,2] := by - exact rowSquare_join (by decide) sg4 sg4662 - -lemma sg7711 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg909 - -lemma sg7712 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg909 - -lemma sg7713 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,2,2,1,1] := by - exact rowSquare_join (by decide) sg1000 sg909 - -lemma sg7714 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,2,2,2] := by - exact rowSquare_join (by decide) sg1001 sg909 - -lemma sg7715 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,3,1,1,1] := by - exact rowSquare_join (by decide) sg1006 sg903 - -lemma sg7716 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,3,2,1] := by - exact rowSquare_join (by decide) sg1007 sg902 - -lemma sg7717 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,3,3] := by - exact rowSquare_join (by decide) sg1008 sg902 - -lemma sg7718 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,4,1,1] := by - exact rowSquare_join (by decide) sg1007 sg903 - -lemma sg7719 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,4,2] := by - exact rowSquare_join (by decide) sg1008 sg903 - -lemma sg7720 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg611 sg1327 - -lemma sg7721 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg608 sg1328 - -lemma sg7722 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5399 - -lemma sg7723 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg5400 - -lemma sg7724 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6 sg4643 - -lemma sg7725 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg612 sg1327 - -lemma sg7726 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg609 sg1328 - -lemma sg7727 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5401 - -lemma sg7728 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5402 - -lemma sg7729 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg4653 - -lemma sg7730 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5403 - -lemma sg7731 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5404 - -lemma sg7732 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg4663 - -lemma sg7733 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg4664 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes13 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes14 + +namespace OAI + +/-! Semigroup Nodes 17. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg7334 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6093 + +lemma sg7335 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg6094 + +lemma sg7336 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg6095 + +lemma sg7337 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg620 sg1331 + +lemma sg7338 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg0 sg6096 + +lemma sg7339 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,4,4,4,3] := by + exact rowSquare_join (by decide) sg0 sg6097 + +lemma sg7340 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg621 sg1329 + +lemma sg7341 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg889 sg1038 + +lemma sg7342 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg614 sg1338 + +lemma sg7343 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg378 sg1755 + +lemma sg7344 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg622 sg1329 + +lemma sg7345 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg1039 + +lemma sg7346 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1031 sg897 + +lemma sg7347 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg1040 + +lemma sg7348 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg614 sg1340 + +lemma sg7349 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg897 + +lemma sg7350 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1038 sg892 + +lemma sg7351 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg623 sg1329 + +lemma sg7352 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg1041 + +lemma sg7353 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1031 sg898 + +lemma sg7354 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg1339 + +lemma sg7355 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1031 sg899 + +lemma sg7356 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg1032 sg898 + +lemma sg7357 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,3,3] := by + exact rowSquare_join (by decide) sg1033 sg898 + +lemma sg7358 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1032 sg899 + +lemma sg7359 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,4,4,2] := by + exact rowSquare_join (by decide) sg1033 sg899 + +lemma sg7360 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg623 sg1330 + +lemma sg7361 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg890 sg1041 + +lemma sg7362 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg623 sg1332 + +lemma sg7363 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg891 sg1041 + +lemma sg7364 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,5,3,2] := by + exact rowSquare_join (by decide) sg892 sg1041 + +lemma sg7365 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [5,5,5,4,1] := by + exact rowSquare_join (by decide) sg373 sg1767 + +lemma sg7366 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6098 + +lemma sg7367 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6099 + +lemma sg7368 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6100 + +lemma sg7369 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg5197 + +lemma sg7370 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6101 + +lemma sg7371 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg5198 + +lemma sg7372 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2 sg5199 + +lemma sg7373 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg624 sg1332 + +lemma sg7374 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6102 + +lemma sg7375 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg5200 + +lemma sg7376 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6103 + +lemma sg7377 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5341 + +lemma sg7378 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg5201 + +lemma sg7379 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5342 + +lemma sg7380 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6104 + +lemma sg7381 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2 sg5202 + +lemma sg7382 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg2 sg5203 + +lemma sg7383 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5343 + +lemma sg7384 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6105 + +lemma sg7385 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg4587 + +lemma sg7386 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6106 + +lemma sg7387 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4588 + +lemma sg7388 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg4589 + +lemma sg7389 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,3,3] := by + exact rowSquare_join (by decide) sg4 sg4590 + +lemma sg7390 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2 sg5208 + +lemma sg7391 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,4,4,4,2] := by + exact rowSquare_join (by decide) sg2 sg5209 + +lemma sg7392 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg628 sg1328 + +lemma sg7393 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6107 + +lemma sg7394 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6108 + +lemma sg7395 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6109 + +lemma sg7396 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg4591 + +lemma sg7397 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6110 + +lemma sg7398 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6111 + +lemma sg7399 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg0 sg6112 + +lemma sg7400 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg6113 + +lemma sg7401 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6114 + +lemma sg7402 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4592 + +lemma sg7403 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg4593 + +lemma sg7404 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg4594 + +lemma sg7405 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,4,3,2] := by + exact rowSquare_join (by decide) sg4 sg4595 + +lemma sg7406 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,4,4,1] := by + exact rowSquare_join (by decide) sg0 sg6115 + +lemma sg7407 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4596 + +lemma sg7408 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg4597 + +lemma sg7409 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,5,2,2] := by + exact rowSquare_join (by decide) sg4 sg4598 + +lemma sg7410 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,5,3,1] := by + exact rowSquare_join (by decide) sg4 sg4599 + +lemma sg7411 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,5,5,4] := by + exact rowSquare_join (by decide) sg4 sg4600 + +lemma sg7412 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg383 sg1755 + +lemma sg7413 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg628 sg1329 + +lemma sg7414 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg1048 + +lemma sg7415 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg614 sg1348 + +lemma sg7416 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg1038 sg897 + +lemma sg7417 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg1049 + +lemma sg7418 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4601 + +lemma sg7419 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg4602 + +lemma sg7420 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg1032 sg902 + +lemma sg7421 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,3,3,2] := by + exact rowSquare_join (by decide) sg1033 sg902 + +lemma sg7422 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4603 + +lemma sg7423 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg4604 + +lemma sg7424 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,4,2,2] := by + exact rowSquare_join (by decide) sg4 sg4605 + +lemma sg7425 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,4,3,1] := by + exact rowSquare_join (by decide) sg4 sg4606 + +lemma sg7426 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,4,4] := by + exact rowSquare_join (by decide) sg1040 sg899 + +lemma sg7427 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4607 + +lemma sg7428 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,5,2,1] := by + exact rowSquare_join (by decide) sg4 sg4608 + +lemma sg7429 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,5,3] := by + exact rowSquare_join (by decide) sg4 sg4609 + +lemma sg7430 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,6,1,1] := by + exact rowSquare_join (by decide) sg4 sg4610 + +lemma sg7431 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [6,6,6,2] := by + exact rowSquare_join (by decide) sg4 sg4611 + +lemma sg7432 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5344 + +lemma sg7433 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5345 + +lemma sg7434 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg5212 + +lemma sg7435 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5346 + +lemma sg7436 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg4612 + +lemma sg7437 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg5216 + +lemma sg7438 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2 sg5217 + +lemma sg7439 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2 sg5218 + +lemma sg7440 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6116 + +lemma sg7441 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg5219 + +lemma sg7442 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg4613 + +lemma sg7443 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg4614 + +lemma sg7444 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg4588 + +lemma sg7445 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg5 sg4589 + +lemma sg7446 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,3,3,3] := by + exact rowSquare_join (by decide) sg5 sg4590 + +lemma sg7447 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg3797 + +lemma sg7448 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg4615 + +lemma sg7449 : RowSquare [6,4,2,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6117 + +lemma sg7450 : RowSquare [6,4,2,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg1754 + +lemma sg7451 : RowSquare [6,4,2,2,1,1,1,1,1,1] [3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg1758 + +lemma sg7452 : RowSquare [6,4,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg332 sg1755 + +lemma sg7453 : RowSquare [6,4,2,2,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg334 sg1756 + +lemma sg7454 : RowSquare [6,4,2,2,1,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg4063 + +lemma sg7455 : RowSquare [6,4,2,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg1754 + +lemma sg7456 : RowSquare [6,4,2,2,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg4064 + +lemma sg7457 : RowSquare [6,4,2,2,1,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg4065 + +lemma sg7458 : RowSquare [6,4,2,2,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6124 + +lemma sg7459 : RowSquare [6,4,2,2,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg4071 + +lemma sg7460 : RowSquare [6,4,2,2,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6125 + +lemma sg7461 : RowSquare [6,4,2,2,1,1,1,1,1,1] [8,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5356 + +lemma sg7462 : RowSquare [6,4,2,2,2,2,1,1] [4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg4078 + +lemma sg7463 : RowSquare [6,4,2,2,2,2,1,1] [4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg878 sg808 + +lemma sg7464 : RowSquare [6,4,2,2,2,2,1,1] [4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg960 sg762 + +lemma sg7465 : RowSquare [6,4,2,2,2,2,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg4063 + +lemma sg7466 : RowSquare [6,4,2,2,2,2,1,1] [5,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg4071 + +lemma sg7467 : RowSquare [6,4,2,2,2,2,1,1] [5,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg4080 + +lemma sg7468 : RowSquare [6,4,2,2,2,2,1,1] [5,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg4072 + +lemma sg7469 : RowSquare [6,4,2,2,2,2,1,1] [5,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg4073 + +lemma sg7470 : RowSquare [6,4,2,2,2,2,1,1] [5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg4074 + +lemma sg7471 : RowSquare [6,4,2,2,2,2,1,1] [5,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg4081 + +lemma sg7472 : RowSquare [6,4,2,2,2,2,1,1] [5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg958 sg765 + +lemma sg7473 : RowSquare [6,4,2,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg4064 + +lemma sg7474 : RowSquare [6,4,2,2,2,2,1,1] [6,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg4067 + +lemma sg7475 : RowSquare [6,4,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg4068 + +lemma sg7476 : RowSquare [6,4,2,2,2,2,1,1] [6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg15 sg4069 + +lemma sg7477 : RowSquare [6,4,2,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg4080 + +lemma sg7478 : RowSquare [6,4,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg4081 + +lemma sg7479 : RowSquare [6,4,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg4072 + +lemma sg7480 : RowSquare [6,4,3,2,1,1,1,1,1] [3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg66 sg2626 + +lemma sg7481 : RowSquare [6,4,3,2,1,1,1,1,1] [3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg67 sg2626 + +lemma sg7482 : RowSquare [6,4,3,2,1,1,1,1,1] [3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg2626 + +lemma sg7483 : RowSquare [6,4,3,2,1,1,1,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg4862 + +lemma sg7484 : RowSquare [6,4,3,2,1,1,1,1,1] [4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg69 sg2626 + +lemma sg7485 : RowSquare [6,4,3,2,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg66 sg2627 + +lemma sg7486 : RowSquare [6,4,3,2,1,1,1,1,1] [4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg6155 + +lemma sg7487 : RowSquare [6,4,3,2,1,1,1,1,1] [4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg71 sg2626 + +lemma sg7488 : RowSquare [6,4,3,2,1,1,1,1,1] [5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg4864 + +lemma sg7489 : RowSquare [6,4,3,2,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg72 sg2626 + +lemma sg7490 : RowSquare [6,4,3,2,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg69 sg2627 + +lemma sg7491 : RowSquare [6,4,3,2,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg73 sg2626 + +lemma sg7492 : RowSquare [6,4,3,2,1,1,1,1,1] [5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg6162 + +lemma sg7493 : RowSquare [6,4,3,2,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg71 sg2627 + +lemma sg7494 : RowSquare [6,4,3,2,1,1,1,1,1] [5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6163 + +lemma sg7495 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg514 sg1329 + +lemma sg7496 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4637 + +lemma sg7497 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4638 + +lemma sg7498 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg2491 + +lemma sg7499 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg74 sg2492 + +lemma sg7500 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,3,2] := by + exact rowSquare_join (by decide) sg32 sg3179 + +lemma sg7501 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,4,1] := by + exact rowSquare_join (by decide) sg32 sg3180 + +lemma sg7502 : RowSquare [6,4,3,2,1,1,1,1,1] [5,5,5,5] := by + exact rowSquare_join (by decide) sg390 sg1631 + +lemma sg7503 : RowSquare [6,4,3,2,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5366 + +lemma sg7504 : RowSquare [6,4,3,2,1,1,1,1,1] [6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4641 + +lemma sg7505 : RowSquare [6,4,3,2,1,1,1,1,1] [6,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg55 sg2520 + +lemma sg7506 : RowSquare [6,4,3,2,1,1,1,1,1] [6,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg2493 + +lemma sg7507 : RowSquare [6,4,3,2,1,1,1,1,1] [6,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg2494 + +lemma sg7508 : RowSquare [6,4,3,2,1,1,1,1,1] [6,6,5,2,1] := by + exact rowSquare_join (by decide) sg76 sg2491 + +lemma sg7509 : RowSquare [6,4,3,2,1,1,1,1,1] [6,6,5,3] := by + exact rowSquare_join (by decide) sg76 sg2492 + +lemma sg7510 : RowSquare [6,4,3,2,1,1,1,1,1] [6,6,6,1,1] := by + exact rowSquare_join (by decide) sg77 sg2491 + +lemma sg7511 : RowSquare [6,4,3,2,1,1,1,1,1] [6,6,6,2] := by + exact rowSquare_join (by decide) sg77 sg2492 + +lemma sg7512 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg1327 + +lemma sg7513 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1327 + +lemma sg7514 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg1329 + +lemma sg7515 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg1327 + +lemma sg7516 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg1327 + +lemma sg7517 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg1331 + +lemma sg7518 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1332 + +lemma sg7519 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg591 sg1327 + +lemma sg7520 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg592 sg1327 + +lemma sg7521 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg593 sg1327 + +lemma sg7522 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg1330 + +lemma sg7523 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg594 sg1327 + +lemma sg7524 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg587 sg1331 + +lemma sg7525 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg1332 + +lemma sg7526 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg595 sg1327 + +lemma sg7527 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg1338 + +lemma sg7528 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg889 + +lemma sg7529 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg1327 + +lemma sg7530 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1339 + +lemma sg7531 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1340 + +lemma sg7532 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg1331 + +lemma sg7533 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg588 sg1332 + +lemma sg7534 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg589 sg1330 + +lemma sg7535 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg1330 + +lemma sg7536 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg589 sg1332 + +lemma sg7537 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg590 sg1331 + +lemma sg7538 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1001 sg892 + +lemma sg7539 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg597 sg1327 + +lemma sg7540 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6180 + +lemma sg7541 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg598 sg1327 + +lemma sg7542 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6181 + +lemma sg7543 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6182 + +lemma sg7544 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg599 sg1327 + +lemma sg7545 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6183 + +lemma sg7546 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6184 + +lemma sg7547 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6185 + +lemma sg7548 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6186 + +lemma sg7549 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg591 sg1331 + +lemma sg7550 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6187 + +lemma sg7551 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg591 sg1332 + +lemma sg7552 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg600 sg1327 + +lemma sg7553 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6188 + +lemma sg7554 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6189 + +lemma sg7555 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg601 sg1327 + +lemma sg7556 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6190 + +lemma sg7557 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6191 + +lemma sg7558 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6192 + +lemma sg7559 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6193 + +lemma sg7560 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6194 + +lemma sg7561 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6195 + +lemma sg7562 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg6196 + +lemma sg7563 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg592 sg1332 + +lemma sg7564 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg593 sg1330 + +lemma sg7565 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6197 + +lemma sg7566 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg594 sg1330 + +lemma sg7567 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6198 + +lemma sg7568 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg6199 + +lemma sg7569 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg6200 + +lemma sg7570 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg594 sg1331 + +lemma sg7571 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg0 sg6201 + +lemma sg7572 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,4,4,4,3] := by + exact rowSquare_join (by decide) sg0 sg6202 + +lemma sg7573 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg1327 + +lemma sg7574 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1348 + +lemma sg7575 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg897 + +lemma sg7576 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg1338 + +lemma sg7577 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1349 + +lemma sg7578 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg898 + +lemma sg7579 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg897 + +lemma sg7580 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg899 + +lemma sg7581 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg1340 + +lemma sg7582 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg1000 sg897 + +lemma sg7583 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1006 sg892 + +lemma sg7584 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg1330 + +lemma sg7585 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg898 + +lemma sg7586 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg589 sg1339 + +lemma sg7587 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg899 + +lemma sg7588 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg1000 sg898 + +lemma sg7589 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,3,3] := by + exact rowSquare_join (by decide) sg1001 sg898 + +lemma sg7590 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1000 sg899 + +lemma sg7591 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [5,5,4,4,2] := by + exact rowSquare_join (by decide) sg1001 sg899 + +lemma sg7592 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg603 sg1327 + +lemma sg7593 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg5367 + +lemma sg7594 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6203 + +lemma sg7595 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg604 sg1327 + +lemma sg7596 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5368 + +lemma sg7597 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg5369 + +lemma sg7598 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg605 sg1327 + +lemma sg7599 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5370 + +lemma sg7600 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6204 + +lemma sg7601 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg4643 + +lemma sg7602 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5371 + +lemma sg7603 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6206 + +lemma sg7604 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg5372 + +lemma sg7605 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg5373 + +lemma sg7606 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg597 sg1332 + +lemma sg7607 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6209 + +lemma sg7608 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg5374 + +lemma sg7609 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6210 + +lemma sg7610 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6211 + +lemma sg7611 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5375 + +lemma sg7612 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg4644 + +lemma sg7613 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5376 + +lemma sg7614 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6213 + +lemma sg7615 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg5377 + +lemma sg7616 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg5378 + +lemma sg7617 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg599 sg1330 + +lemma sg7618 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg4645 + +lemma sg7619 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6215 + +lemma sg7620 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4646 + +lemma sg7621 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg5379 + +lemma sg7622 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,3,3] := by + exact rowSquare_join (by decide) sg1 sg5380 + +lemma sg7623 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1 sg5381 + +lemma sg7624 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,4,4,4,2] := by + exact rowSquare_join (by decide) sg1 sg5382 + +lemma sg7625 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg607 sg1327 + +lemma sg7626 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6221 + +lemma sg7627 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6222 + +lemma sg7628 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6223 + +lemma sg7629 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6224 + +lemma sg7630 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6225 + +lemma sg7631 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6226 + +lemma sg7632 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg4647 + +lemma sg7633 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6228 + +lemma sg7634 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg0 sg6229 + +lemma sg7635 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg6230 + +lemma sg7636 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg601 sg1330 + +lemma sg7637 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6231 + +lemma sg7638 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg4648 + +lemma sg7639 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg4649 + +lemma sg7640 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,4,3,2] := by + exact rowSquare_join (by decide) sg0 sg6232 + +lemma sg7641 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,4,4,1] := by + exact rowSquare_join (by decide) sg0 sg6233 + +lemma sg7642 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,5,2,2] := by + exact rowSquare_join (by decide) sg4 sg4650 + +lemma sg7643 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,5,3,1] := by + exact rowSquare_join (by decide) sg4 sg4651 + +lemma sg7644 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,5,5,4] := by + exact rowSquare_join (by decide) sg4 sg4652 + +lemma sg7645 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1358 + +lemma sg7646 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg902 + +lemma sg7647 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg1348 + +lemma sg7648 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg1006 sg897 + +lemma sg7649 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg903 + +lemma sg7650 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg902 + +lemma sg7651 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg1006 sg898 + +lemma sg7652 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg1000 sg902 + +lemma sg7653 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,3,3,2] := by + exact rowSquare_join (by decide) sg1001 sg902 + +lemma sg7654 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg903 + +lemma sg7655 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg1000 sg903 + +lemma sg7656 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,4,2,2] := by + exact rowSquare_join (by decide) sg1001 sg903 + +lemma sg7657 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,4,3,1] := by + exact rowSquare_join (by decide) sg1007 sg899 + +lemma sg7658 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [6,6,4,4] := by + exact rowSquare_join (by decide) sg1008 sg899 + +lemma sg7659 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg608 sg1327 + +lemma sg7660 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg603 sg1328 + +lemma sg7661 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5383 + +lemma sg7662 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg5384 + +lemma sg7663 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg609 sg1327 + +lemma sg7664 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg604 sg1328 + +lemma sg7665 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5385 + +lemma sg7666 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg5386 + +lemma sg7667 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg4643 + +lemma sg7668 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg605 sg1328 + +lemma sg7669 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5387 + +lemma sg7670 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5388 + +lemma sg7671 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg4653 + +lemma sg7672 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5389 + +lemma sg7673 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg3803 + +lemma sg7674 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg5390 + +lemma sg7675 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg5391 + +lemma sg7676 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg610 sg1327 + +lemma sg7677 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg606 sg1328 + +lemma sg7678 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5392 + +lemma sg7679 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5393 + +lemma sg7680 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg4644 + +lemma sg7681 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5394 + +lemma sg7682 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5395 + +lemma sg7683 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg4654 + +lemma sg7684 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg4655 + +lemma sg7685 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg3804 + +lemma sg7686 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg3805 + +lemma sg7687 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg5396 + +lemma sg7688 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg605 sg1330 + +lemma sg7689 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg3806 + +lemma sg7690 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg4656 + +lemma sg7691 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg4657 + +lemma sg7692 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg3807 + +lemma sg7693 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,4,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg3808 + +lemma sg7694 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg607 sg1328 + +lemma sg7695 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6261 + +lemma sg7696 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5397 + +lemma sg7697 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6263 + +lemma sg7698 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg4647 + +lemma sg7699 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,4,4] := by + exact rowSquare_join (by decide) sg13 sg3810 + +lemma sg7700 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,5,2,1] := by + exact rowSquare_join (by decide) sg13 sg3811 + +lemma sg7701 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,5,5,3] := by + exact rowSquare_join (by decide) sg13 sg3812 + +lemma sg7702 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6275 + +lemma sg7703 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6276 + +lemma sg7704 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6277 + +lemma sg7705 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6278 + +lemma sg7706 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4658 + +lemma sg7707 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,4,2,1] := by + exact rowSquare_join (by decide) sg4 sg4659 + +lemma sg7708 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,4,3] := by + exact rowSquare_join (by decide) sg4 sg4660 + +lemma sg7709 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,5,1,1] := by + exact rowSquare_join (by decide) sg4 sg4661 + +lemma sg7710 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,6,5,2] := by + exact rowSquare_join (by decide) sg4 sg4662 + +lemma sg7711 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg909 + +lemma sg7712 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg909 + +lemma sg7713 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,2,2,1,1] := by + exact rowSquare_join (by decide) sg1000 sg909 + +lemma sg7714 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,2,2,2] := by + exact rowSquare_join (by decide) sg1001 sg909 + +lemma sg7715 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,3,1,1,1] := by + exact rowSquare_join (by decide) sg1006 sg903 + +lemma sg7716 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,3,2,1] := by + exact rowSquare_join (by decide) sg1007 sg902 + +lemma sg7717 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,3,3] := by + exact rowSquare_join (by decide) sg1008 sg902 + +lemma sg7718 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,4,1,1] := by + exact rowSquare_join (by decide) sg1007 sg903 + +lemma sg7719 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [7,7,4,2] := by + exact rowSquare_join (by decide) sg1008 sg903 + +lemma sg7720 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg611 sg1327 + +lemma sg7721 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg608 sg1328 + +lemma sg7722 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5399 + +lemma sg7723 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg5400 + +lemma sg7724 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6 sg4643 + +lemma sg7725 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg612 sg1327 + +lemma sg7726 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg609 sg1328 + +lemma sg7727 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5401 + +lemma sg7728 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5402 + +lemma sg7729 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg4653 + +lemma sg7730 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5403 + +lemma sg7731 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5404 + +lemma sg7732 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg4663 + +lemma sg7733 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg4664 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes18.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes18.lean index da7e52399d67fc25948c6278a87b9d9657abb61e..dce26e49df3bb0daf0f02dd62efb3cf7ccb86b52 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes18.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes18.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes14 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes7 - -namespace OAI - -/-! Semigroup Nodes 18. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg7734 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg3813 - -lemma sg7735 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg3814 - -lemma sg7736 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg5405 - -lemma sg7737 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg610 sg1328 - -lemma sg7738 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5406 - -lemma sg7739 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5407 - -lemma sg7740 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg3803 - -lemma sg7741 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg4655 - -lemma sg7742 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5408 - -lemma sg7743 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg3815 - -lemma sg7744 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg4665 - -lemma sg7745 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg3816 - -lemma sg7746 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg3817 - -lemma sg7747 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4666 - -lemma sg7748 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg3818 - -lemma sg7749 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,4,2,2] := by - exact rowSquare_join (by decide) sg4 sg4667 - -lemma sg7750 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg3819 - -lemma sg7751 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,4,4] := by - exact rowSquare_join (by decide) sg13 sg3820 - -lemma sg7752 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5409 - -lemma sg7753 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5410 - -lemma sg7754 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg3821 - -lemma sg7755 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg3805 - -lemma sg7756 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg3806 - -lemma sg7757 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg3822 - -lemma sg7758 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg3807 - -lemma sg7759 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg3823 - -lemma sg7760 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4668 - -lemma sg7761 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg3824 - -lemma sg7762 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg3825 - -lemma sg7763 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,5,1,1] := by - exact rowSquare_join (by decide) sg4 sg4669 - -lemma sg7764 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,5,2] := by - exact rowSquare_join (by decide) sg13 sg3826 - -lemma sg7765 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5411 - -lemma sg7766 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4670 - -lemma sg7767 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg3827 - -lemma sg7768 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg5412 - -lemma sg7769 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg3809 - -lemma sg7770 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg3828 - -lemma sg7771 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,3,3] := by - exact rowSquare_join (by decide) sg13 sg3829 - -lemma sg7772 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,4,1,1] := by - exact rowSquare_join (by decide) sg14 sg3811 - -lemma sg7773 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,4,2] := by - exact rowSquare_join (by decide) sg13 sg3830 - -lemma sg7774 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,5,1] := by - exact rowSquare_join (by decide) sg13 sg3831 - -lemma sg7775 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,7,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6286 - -lemma sg7776 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,7,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4671 - -lemma sg7777 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,7,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6287 - -lemma sg7778 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,7,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg4672 - -lemma sg7779 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg312 sg1754 - -lemma sg7780 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg313 sg1754 - -lemma sg7781 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg535 sg1327 - -lemma sg7782 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg910 sg889 - -lemma sg7783 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg314 sg1754 - -lemma sg7784 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg536 sg1327 - -lemma sg7785 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg890 - -lemma sg7786 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg315 sg1754 - -lemma sg7787 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg537 sg1327 - -lemma sg7788 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg891 - -lemma sg7789 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg892 - -lemma sg7790 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg316 sg1754 - -lemma sg7791 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg319 sg1754 - -lemma sg7792 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg541 sg1327 - -lemma sg7793 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg543 sg1327 - -lemma sg7794 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg315 sg1757 - -lemma sg7795 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1000 sg808 - -lemma sg7796 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1001 sg809 - -lemma sg7797 : RowSquare [6,5,2,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg321 sg1754 - -lemma sg7798 : RowSquare [6,5,2,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg324 sg1754 - -lemma sg7799 : RowSquare [6,5,2,1,1,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg328 sg1754 - -lemma sg7800 : RowSquare [6,5,2,1,1,1,1,1,1,1] [7,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg329 sg1754 - -lemma sg7801 : RowSquare [6,5,2,2,2,2,1] [5,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5681 - -lemma sg7802 : RowSquare [6,5,2,2,2,2,1] [5,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5682 - -lemma sg7803 : RowSquare [6,5,2,2,2,2,1] [5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5683 - -lemma sg7804 : RowSquare [6,5,2,2,2,2,1] [5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg5684 - -lemma sg7805 : RowSquare [6,6,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg518 sg1327 - -lemma sg7806 : RowSquare [6,6,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg889 sg889 - -lemma sg7807 : RowSquare [6,6,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg892 sg892 - -lemma sg7808 : RowSquare [6,6,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg521 sg1327 - -lemma sg7809 : RowSquare [6,6,1,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg895 sg892 - -lemma sg7810 : RowSquare [6,6,1,1,1,1,1,1,1,1] [5,5,5,5] := by - exact rowSquare_join (by decide) sg13 sg3875 - -lemma sg7811 : RowSquare [6,6,2,1,1,1,1,1,1] [5,5,5,5] := by - exact rowSquare_join (by decide) sg13 sg3916 - -lemma sg7813 : RowSquare [6,6,2,2,2,2] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg788 sg789 - -lemma sg7814 : RowSquare [6,6,2,2,2,2] [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg787 sg789 - -lemma sg7815 : RowSquare [6,6,2,2,2,2] [2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg785 sg789 - -lemma sg7816 : RowSquare [6,6,2,2,2,2] [2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg780 sg789 - -lemma sg7817 : RowSquare [6,6,2,2,2,2] [2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg780 sg788 - -lemma sg7818 : RowSquare [6,6,2,2,2,2] [2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg780 sg787 - -lemma sg7819 : RowSquare [6,6,2,2,2,2] [2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg780 sg785 - -lemma sg7820 : RowSquare [6,6,2,2,2,2] [2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg780 sg782 - -lemma sg7821 : RowSquare [6,6,2,2,2,2] [2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg780 sg780 - -lemma sg7822 : RowSquare [6,6,2,2,2,2] [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg786 sg789 - -lemma sg7823 : RowSquare [6,6,2,2,2,2] [3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg784 sg789 - -lemma sg7824 : RowSquare [6,6,2,2,2,2] [3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg779 sg788 - -lemma sg7825 : RowSquare [6,6,2,2,2,2] [3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg779 sg787 - -lemma sg7826 : RowSquare [6,6,2,2,2,2] [3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg779 sg785 - -lemma sg7827 : RowSquare [6,6,2,2,2,2] [3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg779 sg782 - -lemma sg7828 : RowSquare [6,6,2,2,2,2] [3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg779 sg780 - -lemma sg7829 : RowSquare [6,6,2,2,2,2] [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg781 sg789 - -lemma sg7830 : RowSquare [6,6,2,2,2,2] [3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg778 sg789 - -lemma sg7831 : RowSquare [6,6,2,2,2,2] [3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg775 sg788 - -lemma sg7832 : RowSquare [6,6,2,2,2,2] [3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg775 sg787 - -lemma sg7833 : RowSquare [6,6,2,2,2,2] [3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg775 sg785 - -lemma sg7834 : RowSquare [6,6,2,2,2,2] [3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg775 sg782 - -lemma sg7835 : RowSquare [6,6,2,2,2,2] [3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg775 sg780 - -lemma sg7836 : RowSquare [6,6,2,2,2,2] [3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg773 sg787 - -lemma sg7837 : RowSquare [6,6,2,2,2,2] [3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg773 sg781 - -lemma sg7838 : RowSquare [6,6,2,2,2,2] [3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg773 sg778 - -lemma sg7839 : RowSquare [6,6,2,2,2,2] [3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg773 sg775 - -lemma sg7840 : RowSquare [6,6,2,2,2,2] [3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg773 sg773 - -lemma sg7841 : RowSquare [6,6,2,2,2,2] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg783 sg789 - -lemma sg7842 : RowSquare [6,6,2,2,2,2] [4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg774 sg788 - -lemma sg7843 : RowSquare [6,6,2,2,2,2] [4,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg774 sg787 - -lemma sg7844 : RowSquare [6,6,2,2,2,2] [4,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg774 sg785 - -lemma sg7845 : RowSquare [6,6,2,2,2,2] [4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg774 sg782 - -lemma sg7846 : RowSquare [6,6,2,2,2,2] [4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg774 sg780 - -lemma sg7847 : RowSquare [6,6,2,2,2,2] [4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg777 sg789 - -lemma sg7848 : RowSquare [6,6,2,2,2,2] [4,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg772 sg787 - -lemma sg7849 : RowSquare [6,6,2,2,2,2] [4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg772 sg785 - -lemma sg7850 : RowSquare [6,6,2,2,2,2] [4,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg772 sg782 - -lemma sg7851 : RowSquare [6,6,2,2,2,2] [4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg772 sg780 - -lemma sg7852 : RowSquare [6,6,2,2,2,2] [4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg768 sg778 - -lemma sg7853 : RowSquare [6,6,2,2,2,2] [5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg771 sg789 - -lemma sg7854 : RowSquare [6,6,2,2,2,2] [5,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg771 sg787 - -lemma sg7855 : RowSquare [6,6,2,2,2,2] [5,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg771 sg785 - -lemma sg7856 : RowSquare [6,6,2,2,2,2] [5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg771 sg782 - -lemma sg7857 : RowSquare [6,6,2,2,2,2] [5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg771 sg780 - -lemma sg7858 : RowSquare [6,6,2,2,2,2] [5,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg766 sg784 - -lemma sg7859 : RowSquare [7,5,2,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg51 sg2702 - -lemma sg7860 : RowSquare [7,5,2,1,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg53 sg2702 - -lemma sg7861 : RowSquare [7,5,2,2,2,1,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg13 sg3959 - -lemma sg7862 : RowSquare [7,5,2,2,2,1,1] [5,4,4,4,3] := by - exact rowSquare_join (by decide) sg537 sg1146 - -lemma sg7863 : RowSquare [7,5,2,2,2,1,1] [5,5,4,3,3] := by - exact rowSquare_join (by decide) sg270 sg1636 - -lemma sg7864 : RowSquare [7,5,2,2,2,1,1] [5,5,4,4,2] := by - exact rowSquare_join (by decide) sg537 sg1147 - -lemma sg7865 : RowSquare [7,5,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg5607 - -lemma sg7866 : RowSquare [7,5,2,2,2,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg4797 - -lemma sg7867 : RowSquare [7,5,2,2,2,1,1] [6,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4801 - -lemma sg7868 : RowSquare [7,5,2,2,2,1,1] [6,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg3960 - -lemma sg7869 : RowSquare [7,5,2,2,2,1,1] [6,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg5608 - -lemma sg7870 : RowSquare [7,5,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg5609 - -lemma sg7871 : RowSquare [7,5,2,2,2,1,1] [6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg5610 - -lemma sg7872 : RowSquare [7,5,2,2,2,1,1] [6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg5611 - -lemma sg7873 : RowSquare [7,5,2,2,2,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg4798 - -lemma sg7874 : RowSquare [7,5,2,2,2,1,1] [6,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg3937 - -lemma sg7875 : RowSquare [7,5,2,2,2,1,1] [6,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6453 - -lemma sg7876 : RowSquare [7,5,2,2,2,1,1] [6,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6454 - -lemma sg7877 : RowSquare [7,5,2,2,2,1,1] [6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6455 - -lemma sg7878 : RowSquare [7,5,2,2,2,1,1] [6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6456 - -lemma sg7879 : RowSquare [7,5,2,2,2,1,1] [6,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg3938 - -lemma sg7880 : RowSquare [7,5,2,2,2,1,1] [6,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg3200 - -lemma sg7881 : RowSquare [7,5,2,2,2,1,1] [6,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg4802 - -lemma sg7882 : RowSquare [7,5,2,2,2,1,1] [6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg534 sg1149 - -lemma sg7883 : RowSquare [7,5,2,2,2,1,1] [6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg4803 - -lemma sg7884 : RowSquare [7,5,2,2,2,1,1] [6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg3201 - -lemma sg7885 : RowSquare [7,5,2,2,2,1,1] [6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg534 sg1150 - -lemma sg7886 : RowSquare [7,5,2,2,2,1,1] [6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg272 sg1633 - -lemma sg7887 : RowSquare [7,5,2,2,2,1,1] [6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg538 sg1146 - -lemma sg7888 : RowSquare [7,5,2,2,2,1,1] [6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg272 sg1634 - -lemma sg7889 : RowSquare [7,5,2,2,2,1,1] [6,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg3937 - -lemma sg7890 : RowSquare [7,5,2,2,2,1,1] [6,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg3939 - -lemma sg7891 : RowSquare [7,5,2,2,2,1,1] [6,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg3202 - -lemma sg7892 : RowSquare [7,5,2,2,2,1,1] [6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg4799 - -lemma sg7893 : RowSquare [7,5,2,2,2,1,1] [6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg534 sg1151 - -lemma sg7894 : RowSquare [7,5,2,2,2,1,1] [6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg4800 - -lemma sg7895 : RowSquare [7,5,2,2,2,1,1] [6,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg3200 - -lemma sg7896 : RowSquare [7,5,2,2,2,1,1] [6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg3203 - -lemma sg7897 : RowSquare [7,5,2,2,2,1,1] [6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg735 - -lemma sg7898 : RowSquare [7,5,2,2,2,1,1] [6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg535 sg1149 - -lemma sg7899 : RowSquare [7,5,2,2,2,1,1] [6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg736 - -lemma sg7900 : RowSquare [7,5,2,2,2,1,1] [6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg535 sg1150 - -lemma sg7901 : RowSquare [7,5,2,2,2,1,1] [6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg491 sg1186 - -lemma sg7902 : RowSquare [7,5,2,2,2,1,1] [6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg539 sg1146 - -lemma sg7903 : RowSquare [7,5,2,2,2,1,1] [6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg114 sg2121 - -lemma sg7904 : RowSquare [7,5,2,2,2,1,1] [6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg534 sg1154 - -lemma sg7905 : RowSquare [7,5,2,2,2,1,1] [6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg839 sg735 - -lemma sg7906 : RowSquare [7,5,2,2,2,1,1] [6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg536 sg1149 - -lemma sg7907 : RowSquare [7,5,2,2,2,1,1] [6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg839 sg736 - -lemma sg7908 : RowSquare [7,5,2,2,2,1,1] [6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg840 sg735 - -lemma sg7909 : RowSquare [7,5,2,2,2,1,1] [6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg840 sg736 - -lemma sg7910 : RowSquare [7,5,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg3939 - -lemma sg7911 : RowSquare [7,5,2,2,2,1,1] [6,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg3202 - -lemma sg7912 : RowSquare [7,5,2,2,2,1,1] [6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg3961 - -lemma sg7913 : RowSquare [7,5,2,2,2,1,1] [6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg737 - -lemma sg7914 : RowSquare [7,5,2,2,2,1,1] [6,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg535 sg1151 - -lemma sg7915 : RowSquare [7,5,2,2,2,1,1] [6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg114 sg2122 - -lemma sg7916 : RowSquare [7,5,2,2,2,1,1] [6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg738 - -lemma sg7917 : RowSquare [7,5,2,2,2,1,1] [6,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg839 sg737 - -lemma sg7918 : RowSquare [7,5,2,2,2,1,1] [6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg536 sg1151 - -lemma sg7919 : RowSquare [7,5,2,2,2,1,1] [6,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg535 sg1153 - -lemma sg7920 : RowSquare [7,5,2,2,2,1,1] [6,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg840 sg737 - -lemma sg7921 : RowSquare [7,5,2,2,2,1,1] [6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg739 - -lemma sg7922 : RowSquare [7,5,2,2,2,1,1] [6,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg839 sg738 - -lemma sg7923 : RowSquare [7,5,2,2,2,1,1] [6,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg839 sg739 - -lemma sg7924 : RowSquare [7,5,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg3940 - -lemma sg7925 : RowSquare [7,5,2,2,2,1,1] [6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg115 sg2122 - -lemma sg7926 : RowSquare [7,5,2,2,2,1,1] [6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg740 - -lemma sg7927 : RowSquare [7,5,2,2,2,1,1] [6,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg535 sg1155 - -lemma sg7928 : RowSquare [7,5,2,2,2,1,1] [6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg3941 - -lemma sg7929 : RowSquare [7,5,2,2,2,1,1] [6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg741 - -lemma sg7930 : RowSquare [7,5,2,2,2,1,1] [6,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg839 sg740 - -lemma sg7931 : RowSquare [7,5,2,2,2,1,1] [6,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg839 sg741 - -lemma sg7932 : RowSquare [7,5,2,2,2,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg4797 - -lemma sg7933 : RowSquare [7,5,2,2,2,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg4801 - -lemma sg7934 : RowSquare [7,5,2,2,2,1,1] [7,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg3942 - -lemma sg7935 : RowSquare [7,5,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg3962 - -lemma sg7936 : RowSquare [7,5,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg5612 - -lemma sg7937 : RowSquare [7,5,2,2,2,1,1] [7,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg5613 - -lemma sg7938 : RowSquare [7,5,2,2,2,1,1] [7,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg5614 - -lemma sg7939 : RowSquare [7,5,2,2,2,1,1] [7,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg3942 - -lemma sg7940 : RowSquare [7,5,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg3943 - -lemma sg7941 : RowSquare [7,5,2,2,2,1,1] [7,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg3204 - -lemma sg7942 : RowSquare [7,5,2,2,2,1,1] [7,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg4802 - -lemma sg7943 : RowSquare [7,5,2,2,2,1,1] [7,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg742 - -lemma sg7944 : RowSquare [7,5,2,2,2,1,1] [7,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg4803 - -lemma sg7945 : RowSquare [7,5,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg3200 - -lemma sg7946 : RowSquare [7,5,2,2,2,1,1] [7,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg116 sg2121 - -lemma sg7947 : RowSquare [7,5,2,2,2,1,1] [7,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg842 sg735 - -lemma sg7948 : RowSquare [7,5,2,2,2,1,1] [7,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg839 sg742 - -lemma sg7949 : RowSquare [7,5,2,2,2,1,1] [7,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg842 sg736 - -lemma sg7950 : RowSquare [7,5,2,2,2,1,1] [7,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg538 sg1150 - -lemma sg7951 : RowSquare [7,5,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg3943 - -lemma sg7952 : RowSquare [7,5,2,2,2,1,1] [7,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg3204 - -lemma sg7953 : RowSquare [7,5,2,2,2,1,1] [7,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg116 sg2122 - -lemma sg7954 : RowSquare [7,5,2,2,2,1,1] [7,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg743 - -lemma sg7955 : RowSquare [7,5,2,2,2,1,1] [7,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg535 sg1158 - -lemma sg7956 : RowSquare [7,5,2,2,2,1,1] [7,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg114 sg2126 - -lemma sg7957 : RowSquare [7,5,2,2,2,1,1] [7,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg744 - -lemma sg7958 : RowSquare [7,5,2,2,2,1,1] [7,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg839 sg743 - -lemma sg7959 : RowSquare [7,5,2,2,2,1,1] [7,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg843 sg736 - -lemma sg7960 : RowSquare [7,5,2,2,2,1,1] [7,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg842 sg739 - -lemma sg7961 : RowSquare [7,5,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg3202 - -lemma sg7962 : RowSquare [7,5,2,2,2,1,1] [7,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg115 sg2126 - -lemma sg7963 : RowSquare [7,5,2,2,2,1,1] [7,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg745 - -lemma sg7964 : RowSquare [7,5,2,2,2,1,1] [7,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg843 sg737 - -lemma sg7965 : RowSquare [7,5,2,2,2,1,1] [7,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg746 - -lemma sg7966 : RowSquare [7,5,2,2,2,1,1] [7,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg118 sg2122 - -lemma sg7967 : RowSquare [7,5,2,2,2,1,1] [7,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg747 - -lemma sg7968 : RowSquare [7,5,2,2,2,1,1] [7,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg748 - -lemma sg7969 : RowSquare [7,5,2,2,2,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg4801 - -lemma sg7970 : RowSquare [7,5,2,2,2,1,1] [8,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg3942 - -lemma sg7971 : RowSquare [7,5,2,2,2,1,1] [8,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg3944 - -lemma sg7972 : RowSquare [7,5,2,2,2,1,1] [8,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg3205 - -lemma sg7973 : RowSquare [7,5,2,2,2,1,1] [8,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg4802 - -lemma sg7974 : RowSquare [7,5,2,2,2,1,1] [8,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg842 sg742 - -lemma sg7975 : RowSquare [7,5,2,2,2,1,1] [8,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg3944 - -lemma sg7976 : RowSquare [7,5,2,2,2,1,1] [8,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg3205 - -lemma sg7977 : RowSquare [7,5,2,2,2,1,1] [8,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg116 sg2126 - -lemma sg7978 : RowSquare [7,5,2,2,2,1,1] [8,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg749 - -lemma sg7979 : RowSquare [7,5,2,2,2,1,1] [8,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg114 sg2132 - -lemma sg7980 : RowSquare [7,5,2,2,2,1,1] [8,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg842 sg744 - -lemma sg7981 : RowSquare [7,5,2,2,2,1,1] [8,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg3204 - -lemma sg7982 : RowSquare [7,5,2,2,2,1,1] [8,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg115 sg2132 - -lemma sg7983 : RowSquare [7,5,2,2,2,1,1] [8,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg750 - -lemma sg7984 : RowSquare [7,5,2,2,2,1,1] [8,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg118 sg2126 - -lemma sg7985 : RowSquare [7,5,2,2,2,1,1] [9,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg3942 - -lemma sg7986 : RowSquare [7,5,2,2,2,1,1] [9,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg3944 - -lemma sg7987 : RowSquare [7,5,2,2,2,1,1] [9,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg3205 - -lemma sg7988 : RowSquare [7,5,2,2,2,1,1] [9,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg116 sg2132 - -lemma sg7989 : RowSquare [7,5,2,2,2,1,1] [9,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg3205 - -lemma sg7990 : RowSquare [7,5,2,2,2,1,1] [9,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg117 sg2132 - -lemma sg7991 : RowSquare [7,5,2,2,2,1,1] [10,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg21 sg3349 - -lemma sg7992 : RowSquare [7,5,2,2,2,1,1] [10,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg3205 - -lemma sg7993 : RowSquare [7,6,2,1,1,1,1,1] [3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg74 sg2546 - -lemma sg7994 : RowSquare [7,6,2,1,1,1,1,1] [4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg2547 - -lemma sg7995 : RowSquare [8,3,2,2,2,2,1] [3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg74 sg2546 - -lemma sg7996 : RowSquare [8,3,2,2,2,2,1] [4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg2547 - -lemma sg7997 : RowSquare [8,3,2,2,2,2,1] [5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg2550 - -lemma sg7999 : RowSquare [9,3,2,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1113 sg720 - -lemma sg8000 : RowSquare [9,3,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg396 sg1620 - -lemma sg8001 : RowSquare [9,4,3,2,2] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1001 sg792 - -lemma sg8002 : RowSquare [9,4,4,1,1,1] [5,5,5,5] := by - exact rowSquare_join (by decide) sg350 sg1675 - -lemma sg8003 : RowSquare [9,4,4,3] [4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg942 sg833 - -lemma sg8004 : RowSquare [9,4,4,3] [4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg942 sg834 - -lemma sg8005 : RowSquare [9,4,4,3] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg943 sg834 - -lemma sg8006 : RowSquare [9,5,4,1,1] [3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg875 - -lemma sg8007 : RowSquare [9,7,4] [3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg306 sg1844 - -lemma sg8009 : RowSquare [10,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg232 sg2037 - -lemma sg8010 : RowSquare [10,2,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg105 sg2575 - -lemma sg8011 : RowSquare [10,3,3,2,1,1] [4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg942 sg891 - -lemma sg8012 : RowSquare [10,3,3,3,1] [4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg833 sg1000 - -lemma sg8013 : RowSquare [10,3,3,3,1] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg834 sg1001 - -lemma sg8014 : RowSquare [10,3,3,3,1] [5,5,5,5] := by - exact rowSquare_join (by decide) sg373 sg1677 - -lemma sg8015 : RowSquare [10,4,3,1,1,1] [5,5,5,5] := by - exact rowSquare_join (by decide) sg390 sg1675 - -lemma sg8016 : RowSquare [11,3,2,2,2] [4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg913 - -lemma sg8017 : RowSquare [11,3,2,2,2] [4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1000 sg915 - -lemma sg8018 : RowSquare [11,3,2,2,2] [4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1001 sg915 - -lemma sg8019 : RowSquare [3,2,2,2,2,2,2,2,2,1,1] [5,5,5,5,1] := by - exact rowSquare_join (by decide) sg644 sg1868 - -lemma sg8020 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,2,2] := by - exact rowSquare_join (by decide) sg1061 sg1575 - -lemma sg8021 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,1] := by - exact rowSquare_join (by decide) sg1104 sg1562 - -lemma sg8022 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,4] := by - exact rowSquare_join (by decide) sg1105 sg1562 - -lemma sg8023 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] [9,6,2,2,2] := by - exact rowSquare_join (by decide) sg1061 sg1576 - -lemma sg8024 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg1068 sg1538 - -lemma sg8025 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg1068 sg1539 - -lemma sg8026 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,5,5,3,2] := by - exact rowSquare_join (by decide) sg1061 sg1548 - -lemma sg8027 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,5,5,4,1] := by - exact rowSquare_join (by decide) sg1069 sg1539 - -lemma sg8028 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,5,5,5] := by - exact rowSquare_join (by decide) sg693 sg1926 - -lemma sg8029 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg1070 sg1538 - -lemma sg8030 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,4,3,2] := by - exact rowSquare_join (by decide) sg1061 sg1549 - -lemma sg8031 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,4,4,1] := by - exact rowSquare_join (by decide) sg644 sg1980 - -lemma sg8032 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,5,2,2] := by - exact rowSquare_join (by decide) sg1061 sg1550 - -lemma sg8033 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,5,3,1] := by - exact rowSquare_join (by decide) sg1071 sg1539 - -lemma sg8034 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,5,4] := by - exact rowSquare_join (by decide) sg1072 sg1539 - -lemma sg8035 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg643 sg1982 - -lemma sg8036 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,6,2,1] := by - exact rowSquare_join (by decide) sg1075 sg1534 - -lemma sg8037 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,6,3] := by - exact rowSquare_join (by decide) sg1073 sg1539 - -lemma sg8038 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1068 sg1540 - -lemma sg8039 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg981 sg1561 - -lemma sg8040 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,4,4,3,3] := by - exact rowSquare_join (by decide) sg982 sg1561 - -lemma sg8041 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg981 sg1562 - -lemma sg8042 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,4,4,4,2] := by - exact rowSquare_join (by decide) sg982 sg1562 - -lemma sg8043 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg1068 sg1542 - -lemma sg8044 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg981 sg1563 - -lemma sg8045 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,3,3,3] := by - exact rowSquare_join (by decide) sg982 sg1563 - -lemma sg8046 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg1068 sg1543 - -lemma sg8047 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,4,3,2] := by - exact rowSquare_join (by decide) sg982 sg1564 - -lemma sg8048 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,4,4,1] := by - exact rowSquare_join (by decide) sg1069 sg1544 - -lemma sg8049 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg975 sg1570 - -lemma sg8050 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg981 sg1565 - -lemma sg8051 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg1070 sg1542 - -lemma sg8052 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg1068 sg1545 - -lemma sg8053 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg981 sg1566 - -lemma sg8054 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,3,3,2] := by - exact rowSquare_join (by decide) sg982 sg1566 - -lemma sg8055 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg975 sg1571 - -lemma sg8056 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg981 sg1567 - -lemma sg8057 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg1068 sg1546 - -lemma sg8058 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,7,2,2,2,1] := by - exact rowSquare_join (by decide) sg1070 sg1545 - -lemma sg8059 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,7,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg975 sg1572 - -lemma sg8060 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,7,3,2,1,1] := by - exact rowSquare_join (by decide) sg976 sg1572 - -lemma sg8061 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,7,3,2,2] := by - exact rowSquare_join (by decide) sg1061 sg1551 - -lemma sg8062 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,7,3,3,1] := by - exact rowSquare_join (by decide) sg1072 sg1545 - -lemma sg8063 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg981 sg1568 - -lemma sg8064 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1111 sg1461 - -lemma sg8065 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1068 sg1547 - -lemma sg8066 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg981 sg1569 - -lemma sg8067 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,4,3,3,3] := by - exact rowSquare_join (by decide) sg982 sg1569 - -lemma sg8068 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg978 sg1570 - -lemma sg8069 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1070 sg1547 - -lemma sg8070 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg978 sg1571 - -lemma sg8071 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg978 sg1572 - -lemma sg8072 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg975 sg1573 - -lemma sg8073 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,7,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg975 sg1574 - -lemma sg8074 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,8,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg577 sg2011 - -lemma sg8075 : RowSquare [3,3,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1] := by - exact rowSquare_join (by decide) sg390 sg2433 - -lemma sg8076 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,3] := by - exact rowSquare_join (by decide) sg1033 sg1538 - -lemma sg8077 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,2] := by - exact rowSquare_join (by decide) sg1033 sg1539 - -lemma sg8078 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1068 sg1519 - -lemma sg8079 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1105 sg1417 - -lemma sg8080 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,3] := by - exact rowSquare_join (by decide) sg1033 sg1541 - -lemma sg8081 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1069 sg1520 - -lemma sg8082 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1070 sg1519 - -lemma sg8083 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg1068 sg1521 - -lemma sg8084 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,3] := by - exact rowSquare_join (by decide) sg1033 sg1543 - -lemma sg8085 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,2] := by - exact rowSquare_join (by decide) sg1033 sg1544 - -lemma sg8086 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,5,5] := by - exact rowSquare_join (by decide) sg693 sg1908 - -lemma sg8087 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1070 sg1520 - -lemma sg8088 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg1070 sg1521 - -lemma sg8089 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1072 sg1520 - -lemma sg8090 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,3] := by - exact rowSquare_join (by decide) sg1033 sg1545 - -lemma sg8091 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1034 sg1540 - -lemma sg8092 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1034 sg1541 - -lemma sg8093 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1092 sg1460 - -lemma sg8094 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1092 sg1461 - -lemma sg8095 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1034 sg1542 - -lemma sg8096 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1031 sg1547 - -lemma sg8097 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1035 sg1541 - -lemma sg8098 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg981 sg1553 - -lemma sg8099 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1074 sg1519 - -lemma sg8100 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1035 sg1542 - -lemma sg8101 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1035 sg1544 - -lemma sg8102 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1035 sg1545 - -lemma sg8103 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1109 sg1422 - -lemma sg8104 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [8,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1092 sg1466 - -lemma sg8105 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1092 sg1552 - -lemma sg8106 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1092 sg1553 - -lemma sg8107 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1092 sg1554 - -lemma sg8108 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1092 sg1555 - -lemma sg8109 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1093 sg1553 - -lemma sg8110 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1093 sg1554 - -lemma sg8111 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1093 sg1555 - -lemma sg8112 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,2,2] := by - exact rowSquare_join (by decide) sg1094 sg1554 - -lemma sg8113 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,1] := by - exact rowSquare_join (by decide) sg1094 sg1555 - -lemma sg8114 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,4] := by - exact rowSquare_join (by decide) sg1095 sg1555 - -lemma sg8115 : RowSquare [4,4,2,2,2,2,2,2,1] [5,4,4,4,4] := by - exact rowSquare_join (by decide) sg879 sg1304 - -lemma sg8116 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg613 sg1891 - -lemma sg8117 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg370 sg2311 - -lemma sg8118 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg2391 - -lemma sg8119 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg2392 - -lemma sg8120 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg614 sg1891 - -lemma sg8121 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg371 sg2311 - -lemma sg8122 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg2393 - -lemma sg8123 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg3006 - -lemma sg8124 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg2394 - -lemma sg8125 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg615 sg1891 - -lemma sg8126 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg2395 - -lemma sg8127 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg373 sg2311 - -lemma sg8128 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg616 sg1891 - -lemma sg8129 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg613 sg1892 - -lemma sg8130 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg613 sg1893 - -lemma sg8131 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg617 sg1891 - -lemma sg8132 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg370 sg2314 - -lemma sg8133 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg940 sg1517 - -lemma sg8134 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg940 sg1518 - -lemma sg8135 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg614 sg1892 - -lemma sg8136 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg940 sg1519 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes14 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes7 + +namespace OAI + +/-! Semigroup Nodes 18. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg7734 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg3813 + +lemma sg7735 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg3814 + +lemma sg7736 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,3,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg5405 + +lemma sg7737 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg610 sg1328 + +lemma sg7738 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5406 + +lemma sg7739 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5407 + +lemma sg7740 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg3803 + +lemma sg7741 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg4655 + +lemma sg7742 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5408 + +lemma sg7743 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg3815 + +lemma sg7744 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg4665 + +lemma sg7745 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg3816 + +lemma sg7746 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg3817 + +lemma sg7747 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4666 + +lemma sg7748 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg3818 + +lemma sg7749 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,4,2,2] := by + exact rowSquare_join (by decide) sg4 sg4667 + +lemma sg7750 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg3819 + +lemma sg7751 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,4,4,4] := by + exact rowSquare_join (by decide) sg13 sg3820 + +lemma sg7752 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5409 + +lemma sg7753 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5410 + +lemma sg7754 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg3821 + +lemma sg7755 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg3805 + +lemma sg7756 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg3806 + +lemma sg7757 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg3822 + +lemma sg7758 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg3807 + +lemma sg7759 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg3823 + +lemma sg7760 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4668 + +lemma sg7761 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg3824 + +lemma sg7762 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg3825 + +lemma sg7763 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,5,1,1] := by + exact rowSquare_join (by decide) sg4 sg4669 + +lemma sg7764 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,5,5,2] := by + exact rowSquare_join (by decide) sg13 sg3826 + +lemma sg7765 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5411 + +lemma sg7766 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4670 + +lemma sg7767 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg3827 + +lemma sg7768 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg5412 + +lemma sg7769 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg3809 + +lemma sg7770 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg3828 + +lemma sg7771 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,3,3] := by + exact rowSquare_join (by decide) sg13 sg3829 + +lemma sg7772 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,4,1,1] := by + exact rowSquare_join (by decide) sg14 sg3811 + +lemma sg7773 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,4,2] := by + exact rowSquare_join (by decide) sg13 sg3830 + +lemma sg7774 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,6,5,1] := by + exact rowSquare_join (by decide) sg13 sg3831 + +lemma sg7775 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,7,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6286 + +lemma sg7776 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,7,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4671 + +lemma sg7777 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,7,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6287 + +lemma sg7778 : RowSquare [6,5,1,1,1,1,1,1,1,1,1] [8,7,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg4672 + +lemma sg7779 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg312 sg1754 + +lemma sg7780 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg313 sg1754 + +lemma sg7781 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg535 sg1327 + +lemma sg7782 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg910 sg889 + +lemma sg7783 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg314 sg1754 + +lemma sg7784 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg536 sg1327 + +lemma sg7785 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg890 + +lemma sg7786 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg315 sg1754 + +lemma sg7787 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg537 sg1327 + +lemma sg7788 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg891 + +lemma sg7789 : RowSquare [6,5,2,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg892 + +lemma sg7790 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg316 sg1754 + +lemma sg7791 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg319 sg1754 + +lemma sg7792 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg541 sg1327 + +lemma sg7793 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg543 sg1327 + +lemma sg7794 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg315 sg1757 + +lemma sg7795 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1000 sg808 + +lemma sg7796 : RowSquare [6,5,2,1,1,1,1,1,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1001 sg809 + +lemma sg7797 : RowSquare [6,5,2,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg321 sg1754 + +lemma sg7798 : RowSquare [6,5,2,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg324 sg1754 + +lemma sg7799 : RowSquare [6,5,2,1,1,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg328 sg1754 + +lemma sg7800 : RowSquare [6,5,2,1,1,1,1,1,1,1] [7,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg329 sg1754 + +lemma sg7801 : RowSquare [6,5,2,2,2,2,1] [5,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5681 + +lemma sg7802 : RowSquare [6,5,2,2,2,2,1] [5,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5682 + +lemma sg7803 : RowSquare [6,5,2,2,2,2,1] [5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5683 + +lemma sg7804 : RowSquare [6,5,2,2,2,2,1] [5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg5684 + +lemma sg7805 : RowSquare [6,6,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg518 sg1327 + +lemma sg7806 : RowSquare [6,6,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg889 sg889 + +lemma sg7807 : RowSquare [6,6,1,1,1,1,1,1,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg892 sg892 + +lemma sg7808 : RowSquare [6,6,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg521 sg1327 + +lemma sg7809 : RowSquare [6,6,1,1,1,1,1,1,1,1] [5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg895 sg892 + +lemma sg7810 : RowSquare [6,6,1,1,1,1,1,1,1,1] [5,5,5,5] := by + exact rowSquare_join (by decide) sg13 sg3875 + +lemma sg7811 : RowSquare [6,6,2,1,1,1,1,1,1] [5,5,5,5] := by + exact rowSquare_join (by decide) sg13 sg3916 + +lemma sg7813 : RowSquare [6,6,2,2,2,2] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg788 sg789 + +lemma sg7814 : RowSquare [6,6,2,2,2,2] [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg787 sg789 + +lemma sg7815 : RowSquare [6,6,2,2,2,2] [2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg785 sg789 + +lemma sg7816 : RowSquare [6,6,2,2,2,2] [2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg780 sg789 + +lemma sg7817 : RowSquare [6,6,2,2,2,2] [2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg780 sg788 + +lemma sg7818 : RowSquare [6,6,2,2,2,2] [2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg780 sg787 + +lemma sg7819 : RowSquare [6,6,2,2,2,2] [2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg780 sg785 + +lemma sg7820 : RowSquare [6,6,2,2,2,2] [2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg780 sg782 + +lemma sg7821 : RowSquare [6,6,2,2,2,2] [2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg780 sg780 + +lemma sg7822 : RowSquare [6,6,2,2,2,2] [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg786 sg789 + +lemma sg7823 : RowSquare [6,6,2,2,2,2] [3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg784 sg789 + +lemma sg7824 : RowSquare [6,6,2,2,2,2] [3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg779 sg788 + +lemma sg7825 : RowSquare [6,6,2,2,2,2] [3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg779 sg787 + +lemma sg7826 : RowSquare [6,6,2,2,2,2] [3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg779 sg785 + +lemma sg7827 : RowSquare [6,6,2,2,2,2] [3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg779 sg782 + +lemma sg7828 : RowSquare [6,6,2,2,2,2] [3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg779 sg780 + +lemma sg7829 : RowSquare [6,6,2,2,2,2] [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg781 sg789 + +lemma sg7830 : RowSquare [6,6,2,2,2,2] [3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg778 sg789 + +lemma sg7831 : RowSquare [6,6,2,2,2,2] [3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg775 sg788 + +lemma sg7832 : RowSquare [6,6,2,2,2,2] [3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg775 sg787 + +lemma sg7833 : RowSquare [6,6,2,2,2,2] [3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg775 sg785 + +lemma sg7834 : RowSquare [6,6,2,2,2,2] [3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg775 sg782 + +lemma sg7835 : RowSquare [6,6,2,2,2,2] [3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg775 sg780 + +lemma sg7836 : RowSquare [6,6,2,2,2,2] [3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg773 sg787 + +lemma sg7837 : RowSquare [6,6,2,2,2,2] [3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg773 sg781 + +lemma sg7838 : RowSquare [6,6,2,2,2,2] [3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg773 sg778 + +lemma sg7839 : RowSquare [6,6,2,2,2,2] [3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg773 sg775 + +lemma sg7840 : RowSquare [6,6,2,2,2,2] [3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg773 sg773 + +lemma sg7841 : RowSquare [6,6,2,2,2,2] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg783 sg789 + +lemma sg7842 : RowSquare [6,6,2,2,2,2] [4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg774 sg788 + +lemma sg7843 : RowSquare [6,6,2,2,2,2] [4,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg774 sg787 + +lemma sg7844 : RowSquare [6,6,2,2,2,2] [4,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg774 sg785 + +lemma sg7845 : RowSquare [6,6,2,2,2,2] [4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg774 sg782 + +lemma sg7846 : RowSquare [6,6,2,2,2,2] [4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg774 sg780 + +lemma sg7847 : RowSquare [6,6,2,2,2,2] [4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg777 sg789 + +lemma sg7848 : RowSquare [6,6,2,2,2,2] [4,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg772 sg787 + +lemma sg7849 : RowSquare [6,6,2,2,2,2] [4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg772 sg785 + +lemma sg7850 : RowSquare [6,6,2,2,2,2] [4,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg772 sg782 + +lemma sg7851 : RowSquare [6,6,2,2,2,2] [4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg772 sg780 + +lemma sg7852 : RowSquare [6,6,2,2,2,2] [4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg768 sg778 + +lemma sg7853 : RowSquare [6,6,2,2,2,2] [5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg771 sg789 + +lemma sg7854 : RowSquare [6,6,2,2,2,2] [5,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg771 sg787 + +lemma sg7855 : RowSquare [6,6,2,2,2,2] [5,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg771 sg785 + +lemma sg7856 : RowSquare [6,6,2,2,2,2] [5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg771 sg782 + +lemma sg7857 : RowSquare [6,6,2,2,2,2] [5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg771 sg780 + +lemma sg7858 : RowSquare [6,6,2,2,2,2] [5,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg766 sg784 + +lemma sg7859 : RowSquare [7,5,2,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg51 sg2702 + +lemma sg7860 : RowSquare [7,5,2,1,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg53 sg2702 + +lemma sg7861 : RowSquare [7,5,2,2,2,1,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg13 sg3959 + +lemma sg7862 : RowSquare [7,5,2,2,2,1,1] [5,4,4,4,3] := by + exact rowSquare_join (by decide) sg537 sg1146 + +lemma sg7863 : RowSquare [7,5,2,2,2,1,1] [5,5,4,3,3] := by + exact rowSquare_join (by decide) sg270 sg1636 + +lemma sg7864 : RowSquare [7,5,2,2,2,1,1] [5,5,4,4,2] := by + exact rowSquare_join (by decide) sg537 sg1147 + +lemma sg7865 : RowSquare [7,5,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg5607 + +lemma sg7866 : RowSquare [7,5,2,2,2,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg4797 + +lemma sg7867 : RowSquare [7,5,2,2,2,1,1] [6,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4801 + +lemma sg7868 : RowSquare [7,5,2,2,2,1,1] [6,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg3960 + +lemma sg7869 : RowSquare [7,5,2,2,2,1,1] [6,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg5608 + +lemma sg7870 : RowSquare [7,5,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg5609 + +lemma sg7871 : RowSquare [7,5,2,2,2,1,1] [6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg5610 + +lemma sg7872 : RowSquare [7,5,2,2,2,1,1] [6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg5611 + +lemma sg7873 : RowSquare [7,5,2,2,2,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg4798 + +lemma sg7874 : RowSquare [7,5,2,2,2,1,1] [6,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg3937 + +lemma sg7875 : RowSquare [7,5,2,2,2,1,1] [6,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6453 + +lemma sg7876 : RowSquare [7,5,2,2,2,1,1] [6,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6454 + +lemma sg7877 : RowSquare [7,5,2,2,2,1,1] [6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6455 + +lemma sg7878 : RowSquare [7,5,2,2,2,1,1] [6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6456 + +lemma sg7879 : RowSquare [7,5,2,2,2,1,1] [6,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg3938 + +lemma sg7880 : RowSquare [7,5,2,2,2,1,1] [6,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg3200 + +lemma sg7881 : RowSquare [7,5,2,2,2,1,1] [6,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg4802 + +lemma sg7882 : RowSquare [7,5,2,2,2,1,1] [6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg534 sg1149 + +lemma sg7883 : RowSquare [7,5,2,2,2,1,1] [6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg4803 + +lemma sg7884 : RowSquare [7,5,2,2,2,1,1] [6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg3201 + +lemma sg7885 : RowSquare [7,5,2,2,2,1,1] [6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg534 sg1150 + +lemma sg7886 : RowSquare [7,5,2,2,2,1,1] [6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg272 sg1633 + +lemma sg7887 : RowSquare [7,5,2,2,2,1,1] [6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg538 sg1146 + +lemma sg7888 : RowSquare [7,5,2,2,2,1,1] [6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg272 sg1634 + +lemma sg7889 : RowSquare [7,5,2,2,2,1,1] [6,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg3937 + +lemma sg7890 : RowSquare [7,5,2,2,2,1,1] [6,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg3939 + +lemma sg7891 : RowSquare [7,5,2,2,2,1,1] [6,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg3202 + +lemma sg7892 : RowSquare [7,5,2,2,2,1,1] [6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg4799 + +lemma sg7893 : RowSquare [7,5,2,2,2,1,1] [6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg534 sg1151 + +lemma sg7894 : RowSquare [7,5,2,2,2,1,1] [6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg4800 + +lemma sg7895 : RowSquare [7,5,2,2,2,1,1] [6,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg3200 + +lemma sg7896 : RowSquare [7,5,2,2,2,1,1] [6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg3203 + +lemma sg7897 : RowSquare [7,5,2,2,2,1,1] [6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg735 + +lemma sg7898 : RowSquare [7,5,2,2,2,1,1] [6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg535 sg1149 + +lemma sg7899 : RowSquare [7,5,2,2,2,1,1] [6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg736 + +lemma sg7900 : RowSquare [7,5,2,2,2,1,1] [6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg535 sg1150 + +lemma sg7901 : RowSquare [7,5,2,2,2,1,1] [6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg491 sg1186 + +lemma sg7902 : RowSquare [7,5,2,2,2,1,1] [6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg539 sg1146 + +lemma sg7903 : RowSquare [7,5,2,2,2,1,1] [6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg114 sg2121 + +lemma sg7904 : RowSquare [7,5,2,2,2,1,1] [6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg534 sg1154 + +lemma sg7905 : RowSquare [7,5,2,2,2,1,1] [6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg839 sg735 + +lemma sg7906 : RowSquare [7,5,2,2,2,1,1] [6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg536 sg1149 + +lemma sg7907 : RowSquare [7,5,2,2,2,1,1] [6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg839 sg736 + +lemma sg7908 : RowSquare [7,5,2,2,2,1,1] [6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg840 sg735 + +lemma sg7909 : RowSquare [7,5,2,2,2,1,1] [6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg840 sg736 + +lemma sg7910 : RowSquare [7,5,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg3939 + +lemma sg7911 : RowSquare [7,5,2,2,2,1,1] [6,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg3202 + +lemma sg7912 : RowSquare [7,5,2,2,2,1,1] [6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg3961 + +lemma sg7913 : RowSquare [7,5,2,2,2,1,1] [6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg737 + +lemma sg7914 : RowSquare [7,5,2,2,2,1,1] [6,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg535 sg1151 + +lemma sg7915 : RowSquare [7,5,2,2,2,1,1] [6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg114 sg2122 + +lemma sg7916 : RowSquare [7,5,2,2,2,1,1] [6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg738 + +lemma sg7917 : RowSquare [7,5,2,2,2,1,1] [6,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg839 sg737 + +lemma sg7918 : RowSquare [7,5,2,2,2,1,1] [6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg536 sg1151 + +lemma sg7919 : RowSquare [7,5,2,2,2,1,1] [6,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg535 sg1153 + +lemma sg7920 : RowSquare [7,5,2,2,2,1,1] [6,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg840 sg737 + +lemma sg7921 : RowSquare [7,5,2,2,2,1,1] [6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg739 + +lemma sg7922 : RowSquare [7,5,2,2,2,1,1] [6,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg839 sg738 + +lemma sg7923 : RowSquare [7,5,2,2,2,1,1] [6,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg839 sg739 + +lemma sg7924 : RowSquare [7,5,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg3940 + +lemma sg7925 : RowSquare [7,5,2,2,2,1,1] [6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg115 sg2122 + +lemma sg7926 : RowSquare [7,5,2,2,2,1,1] [6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg740 + +lemma sg7927 : RowSquare [7,5,2,2,2,1,1] [6,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg535 sg1155 + +lemma sg7928 : RowSquare [7,5,2,2,2,1,1] [6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg3941 + +lemma sg7929 : RowSquare [7,5,2,2,2,1,1] [6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg741 + +lemma sg7930 : RowSquare [7,5,2,2,2,1,1] [6,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg839 sg740 + +lemma sg7931 : RowSquare [7,5,2,2,2,1,1] [6,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg839 sg741 + +lemma sg7932 : RowSquare [7,5,2,2,2,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg4797 + +lemma sg7933 : RowSquare [7,5,2,2,2,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg4801 + +lemma sg7934 : RowSquare [7,5,2,2,2,1,1] [7,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg3942 + +lemma sg7935 : RowSquare [7,5,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg3962 + +lemma sg7936 : RowSquare [7,5,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg5612 + +lemma sg7937 : RowSquare [7,5,2,2,2,1,1] [7,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg5613 + +lemma sg7938 : RowSquare [7,5,2,2,2,1,1] [7,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg5614 + +lemma sg7939 : RowSquare [7,5,2,2,2,1,1] [7,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg3942 + +lemma sg7940 : RowSquare [7,5,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg3943 + +lemma sg7941 : RowSquare [7,5,2,2,2,1,1] [7,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg3204 + +lemma sg7942 : RowSquare [7,5,2,2,2,1,1] [7,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg4802 + +lemma sg7943 : RowSquare [7,5,2,2,2,1,1] [7,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg742 + +lemma sg7944 : RowSquare [7,5,2,2,2,1,1] [7,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg4803 + +lemma sg7945 : RowSquare [7,5,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg3200 + +lemma sg7946 : RowSquare [7,5,2,2,2,1,1] [7,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg116 sg2121 + +lemma sg7947 : RowSquare [7,5,2,2,2,1,1] [7,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg842 sg735 + +lemma sg7948 : RowSquare [7,5,2,2,2,1,1] [7,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg839 sg742 + +lemma sg7949 : RowSquare [7,5,2,2,2,1,1] [7,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg842 sg736 + +lemma sg7950 : RowSquare [7,5,2,2,2,1,1] [7,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg538 sg1150 + +lemma sg7951 : RowSquare [7,5,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg3943 + +lemma sg7952 : RowSquare [7,5,2,2,2,1,1] [7,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg3204 + +lemma sg7953 : RowSquare [7,5,2,2,2,1,1] [7,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg116 sg2122 + +lemma sg7954 : RowSquare [7,5,2,2,2,1,1] [7,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg743 + +lemma sg7955 : RowSquare [7,5,2,2,2,1,1] [7,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg535 sg1158 + +lemma sg7956 : RowSquare [7,5,2,2,2,1,1] [7,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg114 sg2126 + +lemma sg7957 : RowSquare [7,5,2,2,2,1,1] [7,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg744 + +lemma sg7958 : RowSquare [7,5,2,2,2,1,1] [7,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg839 sg743 + +lemma sg7959 : RowSquare [7,5,2,2,2,1,1] [7,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg843 sg736 + +lemma sg7960 : RowSquare [7,5,2,2,2,1,1] [7,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg842 sg739 + +lemma sg7961 : RowSquare [7,5,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg3202 + +lemma sg7962 : RowSquare [7,5,2,2,2,1,1] [7,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg115 sg2126 + +lemma sg7963 : RowSquare [7,5,2,2,2,1,1] [7,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg745 + +lemma sg7964 : RowSquare [7,5,2,2,2,1,1] [7,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg843 sg737 + +lemma sg7965 : RowSquare [7,5,2,2,2,1,1] [7,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg746 + +lemma sg7966 : RowSquare [7,5,2,2,2,1,1] [7,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg118 sg2122 + +lemma sg7967 : RowSquare [7,5,2,2,2,1,1] [7,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg747 + +lemma sg7968 : RowSquare [7,5,2,2,2,1,1] [7,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg748 + +lemma sg7969 : RowSquare [7,5,2,2,2,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg4801 + +lemma sg7970 : RowSquare [7,5,2,2,2,1,1] [8,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg3942 + +lemma sg7971 : RowSquare [7,5,2,2,2,1,1] [8,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg3944 + +lemma sg7972 : RowSquare [7,5,2,2,2,1,1] [8,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg3205 + +lemma sg7973 : RowSquare [7,5,2,2,2,1,1] [8,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg4802 + +lemma sg7974 : RowSquare [7,5,2,2,2,1,1] [8,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg842 sg742 + +lemma sg7975 : RowSquare [7,5,2,2,2,1,1] [8,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg3944 + +lemma sg7976 : RowSquare [7,5,2,2,2,1,1] [8,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg3205 + +lemma sg7977 : RowSquare [7,5,2,2,2,1,1] [8,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg116 sg2126 + +lemma sg7978 : RowSquare [7,5,2,2,2,1,1] [8,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg749 + +lemma sg7979 : RowSquare [7,5,2,2,2,1,1] [8,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg114 sg2132 + +lemma sg7980 : RowSquare [7,5,2,2,2,1,1] [8,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg842 sg744 + +lemma sg7981 : RowSquare [7,5,2,2,2,1,1] [8,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg3204 + +lemma sg7982 : RowSquare [7,5,2,2,2,1,1] [8,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg115 sg2132 + +lemma sg7983 : RowSquare [7,5,2,2,2,1,1] [8,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg750 + +lemma sg7984 : RowSquare [7,5,2,2,2,1,1] [8,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg118 sg2126 + +lemma sg7985 : RowSquare [7,5,2,2,2,1,1] [9,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg3942 + +lemma sg7986 : RowSquare [7,5,2,2,2,1,1] [9,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg3944 + +lemma sg7987 : RowSquare [7,5,2,2,2,1,1] [9,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg3205 + +lemma sg7988 : RowSquare [7,5,2,2,2,1,1] [9,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg116 sg2132 + +lemma sg7989 : RowSquare [7,5,2,2,2,1,1] [9,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg3205 + +lemma sg7990 : RowSquare [7,5,2,2,2,1,1] [9,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg117 sg2132 + +lemma sg7991 : RowSquare [7,5,2,2,2,1,1] [10,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg21 sg3349 + +lemma sg7992 : RowSquare [7,5,2,2,2,1,1] [10,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg3205 + +lemma sg7993 : RowSquare [7,6,2,1,1,1,1,1] [3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg74 sg2546 + +lemma sg7994 : RowSquare [7,6,2,1,1,1,1,1] [4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg2547 + +lemma sg7995 : RowSquare [8,3,2,2,2,2,1] [3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg74 sg2546 + +lemma sg7996 : RowSquare [8,3,2,2,2,2,1] [4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg2547 + +lemma sg7997 : RowSquare [8,3,2,2,2,2,1] [5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg2550 + +lemma sg7999 : RowSquare [9,3,2,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1113 sg720 + +lemma sg8000 : RowSquare [9,3,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg396 sg1620 + +lemma sg8001 : RowSquare [9,4,3,2,2] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1001 sg792 + +lemma sg8002 : RowSquare [9,4,4,1,1,1] [5,5,5,5] := by + exact rowSquare_join (by decide) sg350 sg1675 + +lemma sg8003 : RowSquare [9,4,4,3] [4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg942 sg833 + +lemma sg8004 : RowSquare [9,4,4,3] [4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg942 sg834 + +lemma sg8005 : RowSquare [9,4,4,3] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg943 sg834 + +lemma sg8006 : RowSquare [9,5,4,1,1] [3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg875 + +lemma sg8007 : RowSquare [9,7,4] [3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg306 sg1844 + +lemma sg8009 : RowSquare [10,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg232 sg2037 + +lemma sg8010 : RowSquare [10,2,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg105 sg2575 + +lemma sg8011 : RowSquare [10,3,3,2,1,1] [4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg942 sg891 + +lemma sg8012 : RowSquare [10,3,3,3,1] [4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg833 sg1000 + +lemma sg8013 : RowSquare [10,3,3,3,1] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg834 sg1001 + +lemma sg8014 : RowSquare [10,3,3,3,1] [5,5,5,5] := by + exact rowSquare_join (by decide) sg373 sg1677 + +lemma sg8015 : RowSquare [10,4,3,1,1,1] [5,5,5,5] := by + exact rowSquare_join (by decide) sg390 sg1675 + +lemma sg8016 : RowSquare [11,3,2,2,2] [4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg913 + +lemma sg8017 : RowSquare [11,3,2,2,2] [4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1000 sg915 + +lemma sg8018 : RowSquare [11,3,2,2,2] [4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1001 sg915 + +lemma sg8019 : RowSquare [3,2,2,2,2,2,2,2,2,1,1] [5,5,5,5,1] := by + exact rowSquare_join (by decide) sg644 sg1868 + +lemma sg8020 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,2,2] := by + exact rowSquare_join (by decide) sg1061 sg1575 + +lemma sg8021 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,1] := by + exact rowSquare_join (by decide) sg1104 sg1562 + +lemma sg8022 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,4] := by + exact rowSquare_join (by decide) sg1105 sg1562 + +lemma sg8023 : RowSquare [3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] [9,6,2,2,2] := by + exact rowSquare_join (by decide) sg1061 sg1576 + +lemma sg8024 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg1068 sg1538 + +lemma sg8025 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg1068 sg1539 + +lemma sg8026 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,5,5,3,2] := by + exact rowSquare_join (by decide) sg1061 sg1548 + +lemma sg8027 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,5,5,4,1] := by + exact rowSquare_join (by decide) sg1069 sg1539 + +lemma sg8028 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,5,5,5] := by + exact rowSquare_join (by decide) sg693 sg1926 + +lemma sg8029 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg1070 sg1538 + +lemma sg8030 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,4,3,2] := by + exact rowSquare_join (by decide) sg1061 sg1549 + +lemma sg8031 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,4,4,1] := by + exact rowSquare_join (by decide) sg644 sg1980 + +lemma sg8032 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,5,2,2] := by + exact rowSquare_join (by decide) sg1061 sg1550 + +lemma sg8033 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,5,3,1] := by + exact rowSquare_join (by decide) sg1071 sg1539 + +lemma sg8034 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,5,4] := by + exact rowSquare_join (by decide) sg1072 sg1539 + +lemma sg8035 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg643 sg1982 + +lemma sg8036 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,6,2,1] := by + exact rowSquare_join (by decide) sg1075 sg1534 + +lemma sg8037 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,6,3] := by + exact rowSquare_join (by decide) sg1073 sg1539 + +lemma sg8038 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1068 sg1540 + +lemma sg8039 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg981 sg1561 + +lemma sg8040 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,4,4,3,3] := by + exact rowSquare_join (by decide) sg982 sg1561 + +lemma sg8041 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg981 sg1562 + +lemma sg8042 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,4,4,4,2] := by + exact rowSquare_join (by decide) sg982 sg1562 + +lemma sg8043 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg1068 sg1542 + +lemma sg8044 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg981 sg1563 + +lemma sg8045 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,3,3,3] := by + exact rowSquare_join (by decide) sg982 sg1563 + +lemma sg8046 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg1068 sg1543 + +lemma sg8047 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,4,3,2] := by + exact rowSquare_join (by decide) sg982 sg1564 + +lemma sg8048 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,4,4,1] := by + exact rowSquare_join (by decide) sg1069 sg1544 + +lemma sg8049 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg975 sg1570 + +lemma sg8050 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg981 sg1565 + +lemma sg8051 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg1070 sg1542 + +lemma sg8052 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg1068 sg1545 + +lemma sg8053 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg981 sg1566 + +lemma sg8054 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,3,3,2] := by + exact rowSquare_join (by decide) sg982 sg1566 + +lemma sg8055 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg975 sg1571 + +lemma sg8056 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg981 sg1567 + +lemma sg8057 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg1068 sg1546 + +lemma sg8058 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,7,2,2,2,1] := by + exact rowSquare_join (by decide) sg1070 sg1545 + +lemma sg8059 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,7,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg975 sg1572 + +lemma sg8060 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,7,3,2,1,1] := by + exact rowSquare_join (by decide) sg976 sg1572 + +lemma sg8061 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,7,3,2,2] := by + exact rowSquare_join (by decide) sg1061 sg1551 + +lemma sg8062 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [7,7,3,3,1] := by + exact rowSquare_join (by decide) sg1072 sg1545 + +lemma sg8063 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg981 sg1568 + +lemma sg8064 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1111 sg1461 + +lemma sg8065 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1068 sg1547 + +lemma sg8066 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg981 sg1569 + +lemma sg8067 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,4,3,3,3] := by + exact rowSquare_join (by decide) sg982 sg1569 + +lemma sg8068 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg978 sg1570 + +lemma sg8069 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1070 sg1547 + +lemma sg8070 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg978 sg1571 + +lemma sg8071 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg978 sg1572 + +lemma sg8072 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg975 sg1573 + +lemma sg8073 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,7,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg975 sg1574 + +lemma sg8074 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1] [8,8,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg577 sg2011 + +lemma sg8075 : RowSquare [3,3,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1] := by + exact rowSquare_join (by decide) sg390 sg2433 + +lemma sg8076 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,3] := by + exact rowSquare_join (by decide) sg1033 sg1538 + +lemma sg8077 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,2] := by + exact rowSquare_join (by decide) sg1033 sg1539 + +lemma sg8078 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1068 sg1519 + +lemma sg8079 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1105 sg1417 + +lemma sg8080 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,3] := by + exact rowSquare_join (by decide) sg1033 sg1541 + +lemma sg8081 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1069 sg1520 + +lemma sg8082 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1070 sg1519 + +lemma sg8083 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg1068 sg1521 + +lemma sg8084 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,3] := by + exact rowSquare_join (by decide) sg1033 sg1543 + +lemma sg8085 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,2] := by + exact rowSquare_join (by decide) sg1033 sg1544 + +lemma sg8086 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,5,5,5] := by + exact rowSquare_join (by decide) sg693 sg1908 + +lemma sg8087 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1070 sg1520 + +lemma sg8088 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg1070 sg1521 + +lemma sg8089 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1072 sg1520 + +lemma sg8090 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,3] := by + exact rowSquare_join (by decide) sg1033 sg1545 + +lemma sg8091 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1034 sg1540 + +lemma sg8092 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1034 sg1541 + +lemma sg8093 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1092 sg1460 + +lemma sg8094 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1092 sg1461 + +lemma sg8095 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1034 sg1542 + +lemma sg8096 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1031 sg1547 + +lemma sg8097 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1035 sg1541 + +lemma sg8098 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg981 sg1553 + +lemma sg8099 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1074 sg1519 + +lemma sg8100 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1035 sg1542 + +lemma sg8101 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1035 sg1544 + +lemma sg8102 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1035 sg1545 + +lemma sg8103 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1109 sg1422 + +lemma sg8104 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1] [8,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1092 sg1466 + +lemma sg8105 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1092 sg1552 + +lemma sg8106 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1092 sg1553 + +lemma sg8107 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1092 sg1554 + +lemma sg8108 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1092 sg1555 + +lemma sg8109 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1093 sg1553 + +lemma sg8110 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1093 sg1554 + +lemma sg8111 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1093 sg1555 + +lemma sg8112 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,2,2] := by + exact rowSquare_join (by decide) sg1094 sg1554 + +lemma sg8113 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,1] := by + exact rowSquare_join (by decide) sg1094 sg1555 + +lemma sg8114 : RowSquare [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,4] := by + exact rowSquare_join (by decide) sg1095 sg1555 + +lemma sg8115 : RowSquare [4,4,2,2,2,2,2,2,1] [5,4,4,4,4] := by + exact rowSquare_join (by decide) sg879 sg1304 + +lemma sg8116 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg613 sg1891 + +lemma sg8117 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg370 sg2311 + +lemma sg8118 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg2391 + +lemma sg8119 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg2392 + +lemma sg8120 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg614 sg1891 + +lemma sg8121 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg371 sg2311 + +lemma sg8122 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg2393 + +lemma sg8123 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg3006 + +lemma sg8124 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg2394 + +lemma sg8125 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg615 sg1891 + +lemma sg8126 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg2395 + +lemma sg8127 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg373 sg2311 + +lemma sg8128 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg616 sg1891 + +lemma sg8129 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg613 sg1892 + +lemma sg8130 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg613 sg1893 + +lemma sg8131 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg617 sg1891 + +lemma sg8132 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg370 sg2314 + +lemma sg8133 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg940 sg1517 + +lemma sg8134 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg940 sg1518 + +lemma sg8135 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg614 sg1892 + +lemma sg8136 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg940 sg1519 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes19.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes19.lean index d0f8bb8776f1385ad8ca323767d29f4409fdee90..b70787b689002ee8627ddb8de33c17fff0150690 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes19.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes19.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes12 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes15 - -namespace OAI - -/-! Semigroup Nodes 19. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg8137 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg614 sg1893 - -lemma sg8138 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg371 sg2314 - -lemma sg8139 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg2397 - -lemma sg8140 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1031 sg1409 - -lemma sg8141 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg1896 - -lemma sg8142 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1031 sg1410 - -lemma sg8143 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg615 sg1893 - -lemma sg8144 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg2398 - -lemma sg8145 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1032 sg1410 - -lemma sg8146 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg940 sg1520 - -lemma sg8147 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg940 sg1521 - -lemma sg8148 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1031 sg1411 - -lemma sg8149 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg2401 - -lemma sg8150 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1032 sg1411 - -lemma sg8151 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1033 sg1411 - -lemma sg8152 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg371 sg2317 - -lemma sg8153 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg940 sg1522 - -lemma sg8154 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg941 sg1521 - -lemma sg8155 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg940 sg1523 - -lemma sg8156 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1031 sg1412 - -lemma sg8157 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg942 sg1521 - -lemma sg8158 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg943 sg1521 - -lemma sg8159 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg2285 - -lemma sg8160 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg1032 sg1412 - -lemma sg8161 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,3] := by - exact rowSquare_join (by decide) sg1033 sg1412 - -lemma sg8162 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg2402 - -lemma sg8163 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg1031 sg1413 - -lemma sg8164 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg941 sg1523 - -lemma sg8165 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg1032 sg1413 - -lemma sg8166 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg942 sg1523 - -lemma sg8167 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,1] := by - exact rowSquare_join (by decide) sg373 sg2319 - -lemma sg8168 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1032 sg1414 - -lemma sg8169 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg1032 sg1415 - -lemma sg8170 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,4,1] := by - exact rowSquare_join (by decide) sg947 sg1523 - -lemma sg8171 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,5] := by - exact rowSquare_join (by decide) sg373 sg2323 - -lemma sg8172 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [8,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg940 sg1531 - -lemma sg8173 : RowSquare [5,3,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1533 - -lemma sg8174 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4] := by - exact rowSquare_join (by decide) sg1033 sg1502 - -lemma sg8175 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg1524 - -lemma sg8176 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1034 sg1500 - -lemma sg8177 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1003 sg1520 - -lemma sg8178 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1034 sg1503 - -lemma sg8179 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1520 - -lemma sg8180 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1521 - -lemma sg8181 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg1416 - -lemma sg8182 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1417 - -lemma sg8183 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1522 - -lemma sg8184 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1416 - -lemma sg8185 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1523 - -lemma sg8186 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1416 - -lemma sg8187 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg1417 - -lemma sg8188 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1416 - -lemma sg8189 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1908 - -lemma sg8190 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1417 - -lemma sg8191 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1417 - -lemma sg8192 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1003 sg1417 - -lemma sg8193 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1526 - -lemma sg8194 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1908 - -lemma sg8195 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1005 sg1417 - -lemma sg8196 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg1422 - -lemma sg8197 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1422 - -lemma sg8198 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1422 - -lemma sg8199 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1529 - -lemma sg8200 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1031 sg1377 - -lemma sg8201 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg1424 - -lemma sg8202 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg1377 - -lemma sg8203 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg1033 sg1377 - -lemma sg8204 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1008 sg1417 - -lemma sg8205 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1424 - -lemma sg8206 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3] := by - exact rowSquare_join (by decide) sg1001 sg1424 - -lemma sg8207 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg1878 - -lemma sg8208 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1] := by - exact rowSquare_join (by decide) sg590 sg1908 - -lemma sg8209 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1006 sg1422 - -lemma sg8210 : RowSquare [5,4,3,2,1,1,1,1,1,1,1] [5,4,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg6642 - -lemma sg8211 : RowSquare [5,4,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg6653 - -lemma sg8212 : RowSquare [5,4,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg5820 - -lemma sg8213 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4] := by - exact rowSquare_join (by decide) sg1001 sg1502 - -lemma sg8214 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg1503 - -lemma sg8215 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1002 sg1500 - -lemma sg8216 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1002 sg1503 - -lemma sg8217 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1510 - -lemma sg8218 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1003 sg1504 - -lemma sg8219 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg1874 - -lemma sg8220 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg910 sg1498 - -lemma sg8221 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg910 sg1499 - -lemma sg8222 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg1875 - -lemma sg8223 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1500 - -lemma sg8224 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg1876 - -lemma sg8225 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1501 - -lemma sg8226 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1502 - -lemma sg8227 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg1877 - -lemma sg8228 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1878 - -lemma sg8229 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1879 - -lemma sg8230 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg910 sg1503 - -lemma sg8231 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg997 sg1372 - -lemma sg8232 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1504 - -lemma sg8233 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg1373 - -lemma sg8234 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1505 - -lemma sg8235 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg1876 - -lemma sg8236 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1506 - -lemma sg8237 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1507 - -lemma sg8238 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg1373 - -lemma sg8239 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1508 - -lemma sg8240 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1509 - -lemma sg8241 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1882 - -lemma sg8242 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg587 sg1878 - -lemma sg8243 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg1374 - -lemma sg8244 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1379 - -lemma sg8245 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1879 - -lemma sg8246 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1883 - -lemma sg8247 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1884 - -lemma sg8248 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1377 - -lemma sg8249 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1885 - -lemma sg8250 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1886 - -lemma sg8251 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1378 - -lemma sg8252 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1379 - -lemma sg8253 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg1879 - -lemma sg8254 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg1378 - -lemma sg8255 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg589 sg1878 - -lemma sg8256 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1379 - -lemma sg8257 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1378 - -lemma sg8258 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3] := by - exact rowSquare_join (by decide) sg1001 sg1378 - -lemma sg8259 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1379 - -lemma sg8260 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2] := by - exact rowSquare_join (by decide) sg1001 sg1379 - -lemma sg8261 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1512 - -lemma sg8262 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1513 - -lemma sg8263 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1514 - -lemma sg8264 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1515 - -lemma sg8265 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,1] := by - exact rowSquare_join (by decide) sg1005 sg1379 - -lemma sg8266 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1888 - -lemma sg8267 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1889 - -lemma sg8268 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1388 - -lemma sg8269 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1389 - -lemma sg8270 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1516 - -lemma sg8271 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg910 sg1371 - -lemma sg8272 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg1778 - -lemma sg8273 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [5,5,5,5,1] := by - exact rowSquare_join (by decide) sg590 sg1782 - -lemma sg8274 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [6,4,4,4,3] := by - exact rowSquare_join (by decide) sg1 sg5902 - -lemma sg8275 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1399 - -lemma sg8276 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg5910 - -lemma sg8277 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg4559 - -lemma sg8278 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,4,4,3,3] := by - exact rowSquare_join (by decide) sg1 sg5911 - -lemma sg8279 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg4560 - -lemma sg8280 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,4,4,4,2] := by - exact rowSquare_join (by decide) sg13 sg4561 - -lemma sg8281 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1793 - -lemma sg8282 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1287 - -lemma sg8283 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,7,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg1791 - -lemma sg8284 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,7,2,2,2,1] := by - exact rowSquare_join (by decide) sg595 sg1785 - -lemma sg8285 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [8,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg5915 - -lemma sg8286 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [8,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg4562 - -lemma sg8287 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [8,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg5916 - -lemma sg8288 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [8,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg5917 - -lemma sg8289 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [8,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg5918 - -lemma sg8290 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [9,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg4563 - -lemma sg8291 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [9,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg5921 - -lemma sg8292 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [9,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg4564 - -lemma sg8293 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [9,3,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg5922 - -lemma sg8294 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [9,4,4,4] := by - exact rowSquare_join (by decide) sg13 sg4565 - -lemma sg8295 : RowSquare [5,5,2,2,2,2,2,1] [4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg3998 - -lemma sg8296 : RowSquare [5,5,2,2,2,2,2,1] [4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg3998 - -lemma sg8297 : RowSquare [5,5,2,2,2,2,2,1] [5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg3998 - -lemma sg8298 : RowSquare [5,5,2,2,2,2,2,1] [5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg3999 - -lemma sg8299 : RowSquare [5,5,2,2,2,2,2,1] [5,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg3999 - -lemma sg8300 : RowSquare [5,5,2,2,2,2,2,1] [5,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4006 - -lemma sg8301 : RowSquare [5,5,2,2,2,2,2,1] [5,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4007 - -lemma sg8302 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg4001 - -lemma sg8303 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg4002 - -lemma sg8304 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg4003 - -lemma sg8305 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg41 sg4004 - -lemma sg8306 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4008 - -lemma sg8307 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4009 - -lemma sg8308 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4010 - -lemma sg8309 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg39 sg4011 - -lemma sg8310 : RowSquare [5,5,2,2,2,2,2,1] [5,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4000 - -lemma sg8311 : RowSquare [5,5,2,2,2,2,2,1] [5,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4007 - -lemma sg8312 : RowSquare [5,5,2,2,2,2,2,1] [5,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4002 - -lemma sg8313 : RowSquare [5,5,2,2,2,2,2,1] [5,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4003 - -lemma sg8314 : RowSquare [5,5,2,2,2,2,2,1] [5,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg42 sg4004 - -lemma sg8315 : RowSquare [5,5,2,2,2,2,2,1] [5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg42 sg4005 - -lemma sg8316 : RowSquare [5,5,2,2,2,2,2,1] [5,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4009 - -lemma sg8317 : RowSquare [5,5,2,2,2,2,2,1] [5,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4014 - -lemma sg8318 : RowSquare [5,5,2,2,2,2,2,1] [5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4017 - -lemma sg8319 : RowSquare [5,5,2,2,2,2,2,1] [5,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4013 - -lemma sg8320 : RowSquare [5,5,2,2,2,2,2,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg3998 - -lemma sg8321 : RowSquare [5,5,2,2,2,2,2,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg3999 - -lemma sg8322 : RowSquare [5,5,2,2,2,2,2,1] [6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg4006 - -lemma sg8323 : RowSquare [5,5,2,2,2,2,2,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4006 - -lemma sg8324 : RowSquare [5,5,2,2,2,2,2,1] [6,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4018 - -lemma sg8325 : RowSquare [5,5,2,2,2,2,2,1] [6,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg4002 - -lemma sg8326 : RowSquare [5,5,2,2,2,2,2,1] [6,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg4003 - -lemma sg8327 : RowSquare [5,5,2,2,2,2,2,1] [6,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg43 sg4004 - -lemma sg8328 : RowSquare [5,5,2,2,2,2,2,1] [6,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg4009 - -lemma sg8329 : RowSquare [5,5,2,2,2,2,2,1] [6,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4007 - -lemma sg8330 : RowSquare [5,5,2,2,2,2,2,1] [6,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4009 - -lemma sg8331 : RowSquare [5,5,2,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg3999 - -lemma sg8332 : RowSquare [5,5,2,2,2,2,2,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg4006 - -lemma sg8333 : RowSquare [5,5,2,2,2,2,2,1] [7,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg4018 - -lemma sg8334 : RowSquare [5,5,2,2,2,2,2,1] [7,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg4002 - -lemma sg8335 : RowSquare [5,5,2,2,2,2,2,1] [7,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg4003 - -lemma sg8336 : RowSquare [5,5,2,2,2,2,2,1] [7,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg44 sg4004 - -lemma sg8337 : RowSquare [5,5,2,2,2,2,2,1] [7,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4018 - -lemma sg8338 : RowSquare [5,5,2,2,2,2,2,1] [7,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg4009 - -lemma sg8339 : RowSquare [5,5,2,2,2,2,2,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg4006 - -lemma sg8340 : RowSquare [5,5,2,2,2,2,2,1] [8,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg4018 - -lemma sg8341 : RowSquare [5,5,2,2,2,2,2,1] [8,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg4009 - -lemma sg8342 : RowSquare [5,5,2,2,2,2,2,1] [9,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg4018 - -lemma sg8343 : RowSquare [5,5,3,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1682 - -lemma sg8344 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1682 - -lemma sg8345 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg1683 - -lemma sg8346 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg1682 - -lemma sg8347 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg1684 - -lemma sg8348 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg1682 - -lemma sg8349 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg1682 - -lemma sg8350 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg1686 - -lemma sg8351 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg1687 - -lemma sg8352 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1688 - -lemma sg8353 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1683 - -lemma sg8354 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg1223 - -lemma sg8355 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg592 sg1682 - -lemma sg8356 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg910 sg1267 - -lemma sg8357 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg593 sg1682 - -lemma sg8358 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1268 - -lemma sg8359 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg594 sg1682 - -lemma sg8360 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1269 - -lemma sg8361 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg1686 - -lemma sg8362 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1270 - -lemma sg8363 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1690 - -lemma sg8364 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg587 sg1687 - -lemma sg8365 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg587 sg1688 - -lemma sg8366 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg595 sg1682 - -lemma sg8367 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg1684 - -lemma sg8368 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg1691 - -lemma sg8369 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg1682 - -lemma sg8370 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg1684 - -lemma sg8371 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1693 - -lemma sg8372 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg588 sg1688 - -lemma sg8373 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1271 - -lemma sg8374 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1272 - -lemma sg8375 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg589 sg1687 - -lemma sg8376 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg589 sg1688 - -lemma sg8377 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg1686 - -lemma sg8378 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg590 sg1687 - -lemma sg8379 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg590 sg1688 - -lemma sg8380 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg597 sg1682 - -lemma sg8381 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg910 sg1273 - -lemma sg8382 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg591 sg1688 - -lemma sg8383 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg601 sg1682 - -lemma sg8384 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg592 sg1688 - -lemma sg8385 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,4,4,4,4] := by - exact rowSquare_join (by decide) sg1001 sg1225 - -lemma sg8386 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg1682 - -lemma sg8387 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg595 sg1684 - -lemma sg8388 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1695 - -lemma sg8389 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg588 sg1691 - -lemma sg8390 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg1691 - -lemma sg8391 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg588 sg1692 - -lemma sg8392 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg588 sg1693 - -lemma sg8393 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg595 sg1688 - -lemma sg8394 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1226 - -lemma sg8395 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg1001 sg1226 - -lemma sg8396 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,4,4,3] := by - exact rowSquare_join (by decide) sg13 sg4571 - -lemma sg8397 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg1696 - -lemma sg8398 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg589 sg1694 - -lemma sg8399 : RowSquare [5,5,3,2,1,1,1,1,1,1] [6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg597 sg1688 - -lemma sg8400 : RowSquare [5,5,3,2,1,1,1,1,1,1] [6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1229 - -lemma sg8401 : RowSquare [5,5,3,2,1,1,1,1,1,1] [6,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg588 sg1695 - -lemma sg8402 : RowSquare [5,5,3,2,1,1,1,1,1,1] [6,6,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg4571 - -lemma sg8403 : RowSquare [5,5,3,2,1,1,1,1,1,1] [7,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3 sg5240 - -lemma sg8404 : RowSquare [5,5,3,2,1,1,1,1,1,1] [8,8,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg1697 - -lemma sg8405 : RowSquare [5,5,3,2,1,1,1,1,1,1] [8,8,2,1,1,1] := by - exact rowSquare_join (by decide) sg27 sg3786 - -lemma sg8406 : RowSquare [5,5,3,2,1,1,1,1,1,1] [8,8,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg4579 - -lemma sg8407 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg1093 sg1332 - -lemma sg8408 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1096 sg1332 - -lemma sg8409 : RowSquare [6,4,2,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg613 sg1757 - -lemma sg8410 : RowSquare [6,4,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg613 sg1758 - -lemma sg8411 : RowSquare [6,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg616 sg1757 - -lemma sg8412 : RowSquare [6,4,2,2,1,1,1,1,1,1,1] [5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg623 sg1756 - -lemma sg8413 : RowSquare [6,4,2,2,1,1,1,1,1,1,1] [5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg615 sg1766 - -lemma sg8414 : RowSquare [6,4,3,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg2626 - -lemma sg8415 : RowSquare [6,4,3,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg849 sg1327 - -lemma sg8416 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg2626 - -lemma sg8417 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg2627 - -lemma sg8418 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg850 sg1327 - -lemma sg8419 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg849 sg1328 - -lemma sg8420 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg180 sg2626 - -lemma sg8421 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg549 sg1754 - -lemma sg8422 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg851 sg1327 - -lemma sg8423 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg849 sg1329 - -lemma sg8424 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg181 sg2626 - -lemma sg8425 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg849 sg1330 - -lemma sg8426 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg551 sg1754 - -lemma sg8427 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg1331 - -lemma sg8428 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg854 sg1327 - -lemma sg8429 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg1332 - -lemma sg8430 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg2631 - -lemma sg8431 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg178 sg2632 - -lemma sg8432 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg178 sg2633 - -lemma sg8433 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg182 sg2626 - -lemma sg8434 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg2627 - -lemma sg8435 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg855 sg1327 - -lemma sg8436 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6878 - -lemma sg8437 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg183 sg2626 - -lemma sg8438 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg180 sg2627 - -lemma sg8439 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6879 - -lemma sg8440 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg856 sg1327 - -lemma sg8441 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6880 - -lemma sg8442 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg850 sg1329 - -lemma sg8443 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg184 sg2626 - -lemma sg8444 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg181 sg2627 - -lemma sg8445 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg857 sg1327 - -lemma sg8446 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6881 - -lemma sg8447 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg850 sg1330 - -lemma sg8448 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg850 sg1331 - -lemma sg8449 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg548 sg1757 - -lemma sg8450 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg548 sg1758 - -lemma sg8451 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg179 sg2632 - -lemma sg8452 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg178 sg2636 - -lemma sg8453 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg185 sg2626 - -lemma sg8454 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg552 sg1754 - -lemma sg8455 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg859 sg1327 - -lemma sg8456 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg1338 - -lemma sg8457 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg851 sg1329 - -lemma sg8458 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg553 sg1754 - -lemma sg8459 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg851 sg1330 - -lemma sg8460 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg853 sg1329 - -lemma sg8461 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg854 sg1329 - -lemma sg8462 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg178 sg2640 - -lemma sg8463 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg554 sg1754 - -lemma sg8464 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg862 sg1327 - -lemma sg8465 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg550 sg1756 - -lemma sg8466 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg181 sg2630 - -lemma sg8467 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg551 sg1756 - -lemma sg8468 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg4862 - -lemma sg8469 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg186 sg2626 - -lemma sg8470 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg182 sg2627 - -lemma sg8471 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6883 - -lemma sg8472 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6884 - -lemma sg8473 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6885 - -lemma sg8474 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6886 - -lemma sg8475 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg187 sg2626 - -lemma sg8476 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg183 sg2627 - -lemma sg8477 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6887 - -lemma sg8478 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6888 - -lemma sg8479 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6889 - -lemma sg8480 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg184 sg2627 - -lemma sg8481 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg6890 - -lemma sg8482 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg188 sg2626 - -lemma sg8483 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg185 sg2627 - -lemma sg8484 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg6893 - -lemma sg8485 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg868 sg1327 - -lemma sg8486 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg869 sg1327 - -lemma sg8487 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg554 sg1755 - -lemma sg8488 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg554 sg1756 - -lemma sg8489 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5124 - -lemma sg8490 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg4863 - -lemma sg8491 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg4864 - -lemma sg8492 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg189 sg2626 - -lemma sg8493 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg186 sg2627 - -lemma sg8494 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6894 - -lemma sg8495 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg5956 - -lemma sg8496 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg190 sg2626 - -lemma sg8497 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg187 sg2627 - -lemma sg8498 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6895 - -lemma sg8499 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6896 - -lemma sg8500 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg6897 - -lemma sg8501 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg188 sg2627 - -lemma sg8502 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6898 - -lemma sg8503 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6899 - -lemma sg8504 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg870 sg1327 - -lemma sg8505 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,5,5,5] := by - exact rowSquare_join (by decide) sg33 sg3768 - -lemma sg8506 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg871 sg1327 - -lemma sg8507 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg3160 - -lemma sg8508 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6901 - -lemma sg8509 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg191 sg2626 - -lemma sg8510 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6023 - -lemma sg8511 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6024 - -lemma sg8512 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6025 - -lemma sg8513 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6026 - -lemma sg8514 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5131 - -lemma sg8515 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5132 - -lemma sg8516 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6902 - -lemma sg8517 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg6903 - -lemma sg8518 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6027 - -lemma sg8519 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3 sg5351 - -lemma sg8520 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6028 - -lemma sg8521 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3 sg5352 - -lemma sg8522 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5134 - -lemma sg8523 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg5132 - -lemma sg8524 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1327 - -lemma sg8525 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1327 - -lemma sg8526 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1327 - -lemma sg8527 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1327 - -lemma sg8528 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1327 - -lemma sg8529 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1327 - -lemma sg8530 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg1328 - -lemma sg8531 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1003 sg1327 - -lemma sg8532 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1328 - -lemma sg8533 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg997 sg1329 - -lemma sg8534 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1004 sg1327 - -lemma sg8535 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1328 - -lemma sg8536 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg1330 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes12 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes15 + +namespace OAI + +/-! Semigroup Nodes 19. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg8137 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg614 sg1893 + +lemma sg8138 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg371 sg2314 + +lemma sg8139 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg2397 + +lemma sg8140 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1031 sg1409 + +lemma sg8141 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg1896 + +lemma sg8142 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1031 sg1410 + +lemma sg8143 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg615 sg1893 + +lemma sg8144 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg2398 + +lemma sg8145 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1032 sg1410 + +lemma sg8146 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg940 sg1520 + +lemma sg8147 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg940 sg1521 + +lemma sg8148 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1031 sg1411 + +lemma sg8149 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg2401 + +lemma sg8150 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1032 sg1411 + +lemma sg8151 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1033 sg1411 + +lemma sg8152 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg371 sg2317 + +lemma sg8153 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg940 sg1522 + +lemma sg8154 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg941 sg1521 + +lemma sg8155 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg940 sg1523 + +lemma sg8156 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1031 sg1412 + +lemma sg8157 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg942 sg1521 + +lemma sg8158 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg943 sg1521 + +lemma sg8159 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg2285 + +lemma sg8160 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg1032 sg1412 + +lemma sg8161 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,3] := by + exact rowSquare_join (by decide) sg1033 sg1412 + +lemma sg8162 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg2402 + +lemma sg8163 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg1031 sg1413 + +lemma sg8164 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg941 sg1523 + +lemma sg8165 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg1032 sg1413 + +lemma sg8166 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg942 sg1523 + +lemma sg8167 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,1] := by + exact rowSquare_join (by decide) sg373 sg2319 + +lemma sg8168 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1032 sg1414 + +lemma sg8169 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg1032 sg1415 + +lemma sg8170 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,4,1] := by + exact rowSquare_join (by decide) sg947 sg1523 + +lemma sg8171 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,5] := by + exact rowSquare_join (by decide) sg373 sg2323 + +lemma sg8172 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1] [8,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg940 sg1531 + +lemma sg8173 : RowSquare [5,3,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1533 + +lemma sg8174 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4] := by + exact rowSquare_join (by decide) sg1033 sg1502 + +lemma sg8175 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg1524 + +lemma sg8176 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1034 sg1500 + +lemma sg8177 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1003 sg1520 + +lemma sg8178 : RowSquare [5,4,2,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1034 sg1503 + +lemma sg8179 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1520 + +lemma sg8180 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1521 + +lemma sg8181 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg1416 + +lemma sg8182 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1417 + +lemma sg8183 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1522 + +lemma sg8184 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1416 + +lemma sg8185 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1523 + +lemma sg8186 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1416 + +lemma sg8187 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg1417 + +lemma sg8188 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1416 + +lemma sg8189 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1908 + +lemma sg8190 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1417 + +lemma sg8191 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1417 + +lemma sg8192 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1003 sg1417 + +lemma sg8193 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1526 + +lemma sg8194 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1908 + +lemma sg8195 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1005 sg1417 + +lemma sg8196 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg1422 + +lemma sg8197 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1422 + +lemma sg8198 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1422 + +lemma sg8199 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1529 + +lemma sg8200 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1031 sg1377 + +lemma sg8201 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg1424 + +lemma sg8202 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg1377 + +lemma sg8203 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg1033 sg1377 + +lemma sg8204 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1008 sg1417 + +lemma sg8205 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1424 + +lemma sg8206 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3] := by + exact rowSquare_join (by decide) sg1001 sg1424 + +lemma sg8207 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg1878 + +lemma sg8208 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1] := by + exact rowSquare_join (by decide) sg590 sg1908 + +lemma sg8209 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1006 sg1422 + +lemma sg8210 : RowSquare [5,4,3,2,1,1,1,1,1,1,1] [5,4,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg6642 + +lemma sg8211 : RowSquare [5,4,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg6653 + +lemma sg8212 : RowSquare [5,4,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg5820 + +lemma sg8213 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4] := by + exact rowSquare_join (by decide) sg1001 sg1502 + +lemma sg8214 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg1503 + +lemma sg8215 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1002 sg1500 + +lemma sg8216 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1002 sg1503 + +lemma sg8217 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1510 + +lemma sg8218 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1003 sg1504 + +lemma sg8219 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg1874 + +lemma sg8220 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg910 sg1498 + +lemma sg8221 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg910 sg1499 + +lemma sg8222 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg1875 + +lemma sg8223 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1500 + +lemma sg8224 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg1876 + +lemma sg8225 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1501 + +lemma sg8226 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1502 + +lemma sg8227 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg1877 + +lemma sg8228 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1878 + +lemma sg8229 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1879 + +lemma sg8230 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg910 sg1503 + +lemma sg8231 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg997 sg1372 + +lemma sg8232 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1504 + +lemma sg8233 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg1373 + +lemma sg8234 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1505 + +lemma sg8235 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg1876 + +lemma sg8236 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1506 + +lemma sg8237 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1507 + +lemma sg8238 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg1373 + +lemma sg8239 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1508 + +lemma sg8240 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1509 + +lemma sg8241 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1882 + +lemma sg8242 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg587 sg1878 + +lemma sg8243 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg1374 + +lemma sg8244 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1379 + +lemma sg8245 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1879 + +lemma sg8246 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1883 + +lemma sg8247 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1884 + +lemma sg8248 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1377 + +lemma sg8249 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1885 + +lemma sg8250 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1886 + +lemma sg8251 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1378 + +lemma sg8252 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1379 + +lemma sg8253 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg1879 + +lemma sg8254 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg1378 + +lemma sg8255 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg589 sg1878 + +lemma sg8256 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1379 + +lemma sg8257 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1378 + +lemma sg8258 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3] := by + exact rowSquare_join (by decide) sg1001 sg1378 + +lemma sg8259 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1379 + +lemma sg8260 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2] := by + exact rowSquare_join (by decide) sg1001 sg1379 + +lemma sg8261 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1512 + +lemma sg8262 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1513 + +lemma sg8263 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1514 + +lemma sg8264 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1515 + +lemma sg8265 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,1] := by + exact rowSquare_join (by decide) sg1005 sg1379 + +lemma sg8266 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1888 + +lemma sg8267 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1889 + +lemma sg8268 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1388 + +lemma sg8269 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1389 + +lemma sg8270 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1516 + +lemma sg8271 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg910 sg1371 + +lemma sg8272 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg1778 + +lemma sg8273 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [5,5,5,5,1] := by + exact rowSquare_join (by decide) sg590 sg1782 + +lemma sg8274 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [6,4,4,4,3] := by + exact rowSquare_join (by decide) sg1 sg5902 + +lemma sg8275 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1399 + +lemma sg8276 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg5910 + +lemma sg8277 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg4559 + +lemma sg8278 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,4,4,3,3] := by + exact rowSquare_join (by decide) sg1 sg5911 + +lemma sg8279 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg4560 + +lemma sg8280 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,4,4,4,2] := by + exact rowSquare_join (by decide) sg13 sg4561 + +lemma sg8281 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1793 + +lemma sg8282 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1287 + +lemma sg8283 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,7,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg1791 + +lemma sg8284 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [7,7,2,2,2,1] := by + exact rowSquare_join (by decide) sg595 sg1785 + +lemma sg8285 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [8,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg5915 + +lemma sg8286 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [8,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg4562 + +lemma sg8287 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [8,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg5916 + +lemma sg8288 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [8,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg5917 + +lemma sg8289 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [8,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg5918 + +lemma sg8290 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [9,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg4563 + +lemma sg8291 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [9,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg5921 + +lemma sg8292 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [9,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg4564 + +lemma sg8293 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [9,3,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg5922 + +lemma sg8294 : RowSquare [5,5,2,2,1,1,1,1,1,1,1] [9,4,4,4] := by + exact rowSquare_join (by decide) sg13 sg4565 + +lemma sg8295 : RowSquare [5,5,2,2,2,2,2,1] [4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg3998 + +lemma sg8296 : RowSquare [5,5,2,2,2,2,2,1] [4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg3998 + +lemma sg8297 : RowSquare [5,5,2,2,2,2,2,1] [5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg3998 + +lemma sg8298 : RowSquare [5,5,2,2,2,2,2,1] [5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg3999 + +lemma sg8299 : RowSquare [5,5,2,2,2,2,2,1] [5,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg3999 + +lemma sg8300 : RowSquare [5,5,2,2,2,2,2,1] [5,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4006 + +lemma sg8301 : RowSquare [5,5,2,2,2,2,2,1] [5,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4007 + +lemma sg8302 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg4001 + +lemma sg8303 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg4002 + +lemma sg8304 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg4003 + +lemma sg8305 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg41 sg4004 + +lemma sg8306 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4008 + +lemma sg8307 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4009 + +lemma sg8308 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4010 + +lemma sg8309 : RowSquare [5,5,2,2,2,2,2,1] [5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg39 sg4011 + +lemma sg8310 : RowSquare [5,5,2,2,2,2,2,1] [5,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4000 + +lemma sg8311 : RowSquare [5,5,2,2,2,2,2,1] [5,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4007 + +lemma sg8312 : RowSquare [5,5,2,2,2,2,2,1] [5,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4002 + +lemma sg8313 : RowSquare [5,5,2,2,2,2,2,1] [5,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4003 + +lemma sg8314 : RowSquare [5,5,2,2,2,2,2,1] [5,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg42 sg4004 + +lemma sg8315 : RowSquare [5,5,2,2,2,2,2,1] [5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg42 sg4005 + +lemma sg8316 : RowSquare [5,5,2,2,2,2,2,1] [5,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4009 + +lemma sg8317 : RowSquare [5,5,2,2,2,2,2,1] [5,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4014 + +lemma sg8318 : RowSquare [5,5,2,2,2,2,2,1] [5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4017 + +lemma sg8319 : RowSquare [5,5,2,2,2,2,2,1] [5,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4013 + +lemma sg8320 : RowSquare [5,5,2,2,2,2,2,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg3998 + +lemma sg8321 : RowSquare [5,5,2,2,2,2,2,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg3999 + +lemma sg8322 : RowSquare [5,5,2,2,2,2,2,1] [6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg4006 + +lemma sg8323 : RowSquare [5,5,2,2,2,2,2,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4006 + +lemma sg8324 : RowSquare [5,5,2,2,2,2,2,1] [6,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4018 + +lemma sg8325 : RowSquare [5,5,2,2,2,2,2,1] [6,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg4002 + +lemma sg8326 : RowSquare [5,5,2,2,2,2,2,1] [6,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg4003 + +lemma sg8327 : RowSquare [5,5,2,2,2,2,2,1] [6,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg43 sg4004 + +lemma sg8328 : RowSquare [5,5,2,2,2,2,2,1] [6,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg4009 + +lemma sg8329 : RowSquare [5,5,2,2,2,2,2,1] [6,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4007 + +lemma sg8330 : RowSquare [5,5,2,2,2,2,2,1] [6,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4009 + +lemma sg8331 : RowSquare [5,5,2,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg3999 + +lemma sg8332 : RowSquare [5,5,2,2,2,2,2,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg4006 + +lemma sg8333 : RowSquare [5,5,2,2,2,2,2,1] [7,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg4018 + +lemma sg8334 : RowSquare [5,5,2,2,2,2,2,1] [7,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg4002 + +lemma sg8335 : RowSquare [5,5,2,2,2,2,2,1] [7,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg4003 + +lemma sg8336 : RowSquare [5,5,2,2,2,2,2,1] [7,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg44 sg4004 + +lemma sg8337 : RowSquare [5,5,2,2,2,2,2,1] [7,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4018 + +lemma sg8338 : RowSquare [5,5,2,2,2,2,2,1] [7,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg4009 + +lemma sg8339 : RowSquare [5,5,2,2,2,2,2,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg4006 + +lemma sg8340 : RowSquare [5,5,2,2,2,2,2,1] [8,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg4018 + +lemma sg8341 : RowSquare [5,5,2,2,2,2,2,1] [8,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg4009 + +lemma sg8342 : RowSquare [5,5,2,2,2,2,2,1] [9,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg4018 + +lemma sg8343 : RowSquare [5,5,3,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1682 + +lemma sg8344 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1682 + +lemma sg8345 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg1683 + +lemma sg8346 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg1682 + +lemma sg8347 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg1684 + +lemma sg8348 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg1682 + +lemma sg8349 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg1682 + +lemma sg8350 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg1686 + +lemma sg8351 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg1687 + +lemma sg8352 : RowSquare [5,5,3,2,1,1,1,1,1,1] [3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1688 + +lemma sg8353 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1683 + +lemma sg8354 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg1223 + +lemma sg8355 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg592 sg1682 + +lemma sg8356 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg910 sg1267 + +lemma sg8357 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg593 sg1682 + +lemma sg8358 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1268 + +lemma sg8359 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg594 sg1682 + +lemma sg8360 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1269 + +lemma sg8361 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg1686 + +lemma sg8362 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1270 + +lemma sg8363 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1690 + +lemma sg8364 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg587 sg1687 + +lemma sg8365 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg587 sg1688 + +lemma sg8366 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg595 sg1682 + +lemma sg8367 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg1684 + +lemma sg8368 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg1691 + +lemma sg8369 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg1682 + +lemma sg8370 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg1684 + +lemma sg8371 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1693 + +lemma sg8372 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg588 sg1688 + +lemma sg8373 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1271 + +lemma sg8374 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1272 + +lemma sg8375 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg589 sg1687 + +lemma sg8376 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg589 sg1688 + +lemma sg8377 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg1686 + +lemma sg8378 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg590 sg1687 + +lemma sg8379 : RowSquare [5,5,3,2,1,1,1,1,1,1] [4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg590 sg1688 + +lemma sg8380 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg597 sg1682 + +lemma sg8381 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg910 sg1273 + +lemma sg8382 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg591 sg1688 + +lemma sg8383 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg601 sg1682 + +lemma sg8384 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg592 sg1688 + +lemma sg8385 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,4,4,4,4] := by + exact rowSquare_join (by decide) sg1001 sg1225 + +lemma sg8386 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg1682 + +lemma sg8387 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg595 sg1684 + +lemma sg8388 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1695 + +lemma sg8389 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg588 sg1691 + +lemma sg8390 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg1691 + +lemma sg8391 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg588 sg1692 + +lemma sg8392 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg588 sg1693 + +lemma sg8393 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg595 sg1688 + +lemma sg8394 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1226 + +lemma sg8395 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg1001 sg1226 + +lemma sg8396 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,4,4,3] := by + exact rowSquare_join (by decide) sg13 sg4571 + +lemma sg8397 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg1696 + +lemma sg8398 : RowSquare [5,5,3,2,1,1,1,1,1,1] [5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg589 sg1694 + +lemma sg8399 : RowSquare [5,5,3,2,1,1,1,1,1,1] [6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg597 sg1688 + +lemma sg8400 : RowSquare [5,5,3,2,1,1,1,1,1,1] [6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1229 + +lemma sg8401 : RowSquare [5,5,3,2,1,1,1,1,1,1] [6,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg588 sg1695 + +lemma sg8402 : RowSquare [5,5,3,2,1,1,1,1,1,1] [6,6,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg4571 + +lemma sg8403 : RowSquare [5,5,3,2,1,1,1,1,1,1] [7,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3 sg5240 + +lemma sg8404 : RowSquare [5,5,3,2,1,1,1,1,1,1] [8,8,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg1697 + +lemma sg8405 : RowSquare [5,5,3,2,1,1,1,1,1,1] [8,8,2,1,1,1] := by + exact rowSquare_join (by decide) sg27 sg3786 + +lemma sg8406 : RowSquare [5,5,3,2,1,1,1,1,1,1] [8,8,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg4579 + +lemma sg8407 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg1093 sg1332 + +lemma sg8408 : RowSquare [6,4,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1096 sg1332 + +lemma sg8409 : RowSquare [6,4,2,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg613 sg1757 + +lemma sg8410 : RowSquare [6,4,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg613 sg1758 + +lemma sg8411 : RowSquare [6,4,2,2,1,1,1,1,1,1,1] [4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg616 sg1757 + +lemma sg8412 : RowSquare [6,4,2,2,1,1,1,1,1,1,1] [5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg623 sg1756 + +lemma sg8413 : RowSquare [6,4,2,2,1,1,1,1,1,1,1] [5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg615 sg1766 + +lemma sg8414 : RowSquare [6,4,3,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg2626 + +lemma sg8415 : RowSquare [6,4,3,2,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg849 sg1327 + +lemma sg8416 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg2626 + +lemma sg8417 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg2627 + +lemma sg8418 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg850 sg1327 + +lemma sg8419 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg849 sg1328 + +lemma sg8420 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg180 sg2626 + +lemma sg8421 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg549 sg1754 + +lemma sg8422 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg851 sg1327 + +lemma sg8423 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg849 sg1329 + +lemma sg8424 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg181 sg2626 + +lemma sg8425 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg849 sg1330 + +lemma sg8426 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg551 sg1754 + +lemma sg8427 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg1331 + +lemma sg8428 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg854 sg1327 + +lemma sg8429 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg1332 + +lemma sg8430 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg2631 + +lemma sg8431 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg178 sg2632 + +lemma sg8432 : RowSquare [6,4,3,2,1,1,1,1,1,1] [3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg178 sg2633 + +lemma sg8433 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg182 sg2626 + +lemma sg8434 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg2627 + +lemma sg8435 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg855 sg1327 + +lemma sg8436 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6878 + +lemma sg8437 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg183 sg2626 + +lemma sg8438 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg180 sg2627 + +lemma sg8439 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6879 + +lemma sg8440 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg856 sg1327 + +lemma sg8441 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6880 + +lemma sg8442 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg850 sg1329 + +lemma sg8443 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg184 sg2626 + +lemma sg8444 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg181 sg2627 + +lemma sg8445 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg857 sg1327 + +lemma sg8446 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6881 + +lemma sg8447 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg850 sg1330 + +lemma sg8448 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg850 sg1331 + +lemma sg8449 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg548 sg1757 + +lemma sg8450 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg548 sg1758 + +lemma sg8451 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg179 sg2632 + +lemma sg8452 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg178 sg2636 + +lemma sg8453 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg185 sg2626 + +lemma sg8454 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg552 sg1754 + +lemma sg8455 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg859 sg1327 + +lemma sg8456 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg1338 + +lemma sg8457 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg851 sg1329 + +lemma sg8458 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg553 sg1754 + +lemma sg8459 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg851 sg1330 + +lemma sg8460 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg853 sg1329 + +lemma sg8461 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg854 sg1329 + +lemma sg8462 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg178 sg2640 + +lemma sg8463 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg554 sg1754 + +lemma sg8464 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg862 sg1327 + +lemma sg8465 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg550 sg1756 + +lemma sg8466 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg181 sg2630 + +lemma sg8467 : RowSquare [6,4,3,2,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg551 sg1756 + +lemma sg8468 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg4862 + +lemma sg8469 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg186 sg2626 + +lemma sg8470 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg182 sg2627 + +lemma sg8471 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6883 + +lemma sg8472 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6884 + +lemma sg8473 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6885 + +lemma sg8474 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6886 + +lemma sg8475 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg187 sg2626 + +lemma sg8476 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg183 sg2627 + +lemma sg8477 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6887 + +lemma sg8478 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6888 + +lemma sg8479 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6889 + +lemma sg8480 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg184 sg2627 + +lemma sg8481 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg6890 + +lemma sg8482 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg188 sg2626 + +lemma sg8483 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg185 sg2627 + +lemma sg8484 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg6893 + +lemma sg8485 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg868 sg1327 + +lemma sg8486 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg869 sg1327 + +lemma sg8487 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg554 sg1755 + +lemma sg8488 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg554 sg1756 + +lemma sg8489 : RowSquare [6,4,3,2,1,1,1,1,1,1] [5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5124 + +lemma sg8490 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg4863 + +lemma sg8491 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg4864 + +lemma sg8492 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg189 sg2626 + +lemma sg8493 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg186 sg2627 + +lemma sg8494 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6894 + +lemma sg8495 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg5956 + +lemma sg8496 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg190 sg2626 + +lemma sg8497 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg187 sg2627 + +lemma sg8498 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6895 + +lemma sg8499 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6896 + +lemma sg8500 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg6897 + +lemma sg8501 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg188 sg2627 + +lemma sg8502 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6898 + +lemma sg8503 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6899 + +lemma sg8504 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg870 sg1327 + +lemma sg8505 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,5,5,5] := by + exact rowSquare_join (by decide) sg33 sg3768 + +lemma sg8506 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg871 sg1327 + +lemma sg8507 : RowSquare [6,4,3,2,1,1,1,1,1,1] [6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg3160 + +lemma sg8508 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6901 + +lemma sg8509 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg191 sg2626 + +lemma sg8510 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6023 + +lemma sg8511 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6024 + +lemma sg8512 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6025 + +lemma sg8513 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6026 + +lemma sg8514 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5131 + +lemma sg8515 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5132 + +lemma sg8516 : RowSquare [6,4,3,2,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6902 + +lemma sg8517 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg6903 + +lemma sg8518 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6027 + +lemma sg8519 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3 sg5351 + +lemma sg8520 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6028 + +lemma sg8521 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3 sg5352 + +lemma sg8522 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5134 + +lemma sg8523 : RowSquare [6,4,3,2,1,1,1,1,1,1] [8,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg5132 + +lemma sg8524 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1327 + +lemma sg8525 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1327 + +lemma sg8526 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1327 + +lemma sg8527 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1327 + +lemma sg8528 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1327 + +lemma sg8529 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1327 + +lemma sg8530 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg1328 + +lemma sg8531 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1003 sg1327 + +lemma sg8532 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1328 + +lemma sg8533 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg997 sg1329 + +lemma sg8534 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1004 sg1327 + +lemma sg8535 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1328 + +lemma sg8536 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg1330 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes2.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes2.lean index 46184f2a0f20509079da444553357072ad7af090..0e61fff202c67bb3b264f67d4cc448fbaa9f5094 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes2.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes2.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes1 - -namespace OAI - -/-! Semigroup Nodes 2. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg1240 : RowSquare [5,1,1,1,1,1,1] [3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg586 - -lemma sg1241 : RowSquare [5,1,1,1,1,1,1] [3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg998 - -lemma sg1242 : RowSquare [5,1,1,1,1,1,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg999 - -lemma sg1243 : RowSquare [5,1,1,1,1,1,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg1000 - -lemma sg1244 : RowSquare [5,1,1,1,1,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg1001 - -lemma sg1245 : RowSquare [5,1,1,1,1,1,1] [4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg587 - -lemma sg1246 : RowSquare [5,1,1,1,1,1,1] [4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg588 - -lemma sg1247 : RowSquare [5,1,1,1,1,1,1] [4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg589 - -lemma sg1248 : RowSquare [5,1,1,1,1,1,1] [4,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg590 - -lemma sg1249 : RowSquare [5,1,1,1,1,1,1] [4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1006 - -lemma sg1250 : RowSquare [5,1,1,1,1,1,1] [4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg1007 - -lemma sg1251 : RowSquare [5,1,1,1,1,1,1] [4,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg1008 - -lemma sg1252 : RowSquare [5,1,1,1,1,1,1] [5,3,2,1] := by - exact rowSquare_join (by decide) sg2 sg596 - -lemma sg1253 : RowSquare [5,1,1,1,1,1,1] [5,4,1,1] := by - exact rowSquare_join (by decide) sg0 sg1015 - -lemma sg1254 : RowSquare [5,1,1,1,1,1,1] [5,4,2] := by - exact rowSquare_join (by decide) sg0 sg1016 - -lemma sg1255 : RowSquare [5,1,1,1,1,1,1] [6,4,1] := by - exact rowSquare_join (by decide) sg2 sg602 - -lemma sg1256 : RowSquare [5,1,1,1,1,1,1] [6,5] := by - exact rowSquare_join (by decide) sg0 sg1023 - -lemma sg1257 : RowSquare [5,2,1,1,1,1] [2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg910 - -lemma sg1258 : RowSquare [5,2,1,1,1,1] [3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg586 - -lemma sg1259 : RowSquare [5,2,1,1,1,1] [3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg912 - -lemma sg1260 : RowSquare [5,2,1,1,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg809 - -lemma sg1261 : RowSquare [5,2,1,1,1,1] [3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg313 - -lemma sg1262 : RowSquare [5,2,1,1,1,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg314 - -lemma sg1263 : RowSquare [5,2,1,1,1,1] [3,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg315 - -lemma sg1264 : RowSquare [5,2,1,1,1,1] [4,4,2,1] := by - exact rowSquare_join (by decide) sg4 sg319 - -lemma sg1265 : RowSquare [5,2,1,1,1,1] [4,4,3] := by - exact rowSquare_join (by decide) sg4 sg320 - -lemma sg1266 : RowSquare [5,2,1,1,1,1] [5,5,1] := by - exact rowSquare_join (by decide) sg4 sg324 - -lemma sg1267 : RowSquare [5,2,2,1,1] [3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg826 - -lemma sg1268 : RowSquare [5,2,2,1,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg827 - -lemma sg1269 : RowSquare [5,2,2,1,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg828 - -lemma sg1270 : RowSquare [5,2,2,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg829 - -lemma sg1271 : RowSquare [5,2,2,1,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg270 - -lemma sg1272 : RowSquare [5,2,2,1,1] [3,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg271 - -lemma sg1273 : RowSquare [5,2,2,1,1] [4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg830 - -lemma sg1274 : RowSquare [5,3,1,1,1] [3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg838 - -lemma sg1275 : RowSquare [5,3,1,1,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg839 - -lemma sg1276 : RowSquare [5,3,1,1,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg840 - -lemma sg1277 : RowSquare [5,3,1,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg841 - -lemma sg1278 : RowSquare [5,3,1,1,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg270 - -lemma sg1279 : RowSquare [5,3,1,1,1] [3,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg271 - -lemma sg1280 : RowSquare [5,3,1,1,1] [4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg534 - -lemma sg1281 : RowSquare [5,3,1,1,1] [4,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg132 - -lemma sg1282 : RowSquare [5,3,1,1,1] [4,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg273 - -lemma sg1283 : RowSquare [5,3,1,1,1] [4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg133 - -lemma sg1284 : RowSquare [5,3,1,1,1] [4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg134 - -lemma sg1285 : RowSquare [5,3,1,1,1] [4,4,2,1] := by - exact rowSquare_join (by decide) sg4 sg275 - -lemma sg1286 : RowSquare [5,3,1,1,1] [4,4,3] := by - exact rowSquare_join (by decide) sg4 sg276 - -lemma sg1287 : RowSquare [5,3,1,1,1] [5,5,1] := by - exact rowSquare_join (by decide) sg17 sg115 - -lemma sg1288 : RowSquare [5,3,2,1] [2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg849 - -lemma sg1289 : RowSquare [5,3,2,1] [3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg850 - -lemma sg1290 : RowSquare [5,3,2,1] [3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg851 - -lemma sg1291 : RowSquare [5,3,2,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg852 - -lemma sg1292 : RowSquare [5,3,2,1] [3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg285 - -lemma sg1293 : RowSquare [5,3,2,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg32 sg55 - -lemma sg1294 : RowSquare [5,3,2,1] [3,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg287 - -lemma sg1295 : RowSquare [5,3,2,1] [4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg511 - -lemma sg1296 : RowSquare [5,3,2,1] [4,3,3,1] := by - exact rowSquare_join (by decide) sg33 sg55 - -lemma sg1297 : RowSquare [5,3,2,1] [4,4,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg143 - -lemma sg1298 : RowSquare [5,3,2,1] [4,4,2,1] := by - exact rowSquare_join (by decide) sg27 sg67 - -lemma sg1299 : RowSquare [5,3,2,1] [4,4,3] := by - exact rowSquare_join (by decide) sg34 sg55 - -lemma sg1300 : RowSquare [5,3,3] [3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg516 - -lemma sg1301 : RowSquare [5,3,3] [4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg876 - -lemma sg1302 : RowSquare [5,4,1,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg877 - -lemma sg1303 : RowSquare [5,4,1,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg142 - -lemma sg1304 : RowSquare [5,4,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg879 - -lemma sg1305 : RowSquare [5,4,1,1] [3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg295 - -lemma sg1306 : RowSquare [5,4,1,1] [3,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg143 - -lemma sg1307 : RowSquare [5,4,1,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg296 - -lemma sg1308 : RowSquare [5,4,1,1] [3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg144 - -lemma sg1309 : RowSquare [5,4,1,1] [4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg561 - -lemma sg1310 : RowSquare [5,4,1,1] [4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg562 - -lemma sg1311 : RowSquare [5,4,1,1] [4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg298 - -lemma sg1312 : RowSquare [5,4,1,1] [4,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg145 - -lemma sg1313 : RowSquare [5,4,1,1] [4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg142 - -lemma sg1314 : RowSquare [5,4,1,1] [4,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg299 - -lemma sg1315 : RowSquare [5,4,1,1] [4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg146 - -lemma sg1316 : RowSquare [5,4,1,1] [4,3,3,1] := by - exact rowSquare_join (by decide) sg39 sg55 - -lemma sg1317 : RowSquare [5,4,1,1] [4,4,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg143 - -lemma sg1318 : RowSquare [5,4,1,1] [4,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg148 - -lemma sg1319 : RowSquare [5,4,1,1] [4,4,3] := by - exact rowSquare_join (by decide) sg40 sg55 - -lemma sg1320 : RowSquare [5,4,1,1] [5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg565 - -lemma sg1321 : RowSquare [5,4,1,1] [5,3,3] := by - exact rowSquare_join (by decide) sg41 sg55 - -lemma sg1322 : RowSquare [5,4,1,1] [5,5,1] := by - exact rowSquare_join (by decide) sg14 sg148 - -lemma sg1323 : RowSquare [5,4,2] [2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg306 - -lemma sg1324 : RowSquare [5,5,1] [3,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg166 - -lemma sg1325 : RowSquare [5,5,1] [4,4,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg166 - -lemma sg1326 : RowSquare [5,5,1] [5,5,1] := by - exact rowSquare_join (by decide) sg14 sg171 - -lemma sg1328 : RowSquare [6,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg112 - -lemma sg1329 : RowSquare [6,1,1,1,1,1] [2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg111 - -lemma sg1330 : RowSquare [6,1,1,1,1,1] [2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg265 - -lemma sg1331 : RowSquare [6,1,1,1,1,1] [2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg530 - -lemma sg1332 : RowSquare [6,1,1,1,1,1] [2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg909 - -lemma sg1333 : RowSquare [6,1,1,1,1,1] [3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg888 - -lemma sg1334 : RowSquare [6,1,1,1,1,1] [3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg889 - -lemma sg1335 : RowSquare [6,1,1,1,1,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg890 - -lemma sg1336 : RowSquare [6,1,1,1,1,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg891 - -lemma sg1337 : RowSquare [6,1,1,1,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg892 - -lemma sg1338 : RowSquare [6,1,1,1,1,1] [3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg262 - -lemma sg1339 : RowSquare [6,1,1,1,1,1] [3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg525 - -lemma sg1340 : RowSquare [6,1,1,1,1,1] [3,3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg903 - -lemma sg1341 : RowSquare [6,1,1,1,1,1] [4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg893 - -lemma sg1342 : RowSquare [6,1,1,1,1,1] [4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg894 - -lemma sg1343 : RowSquare [6,1,1,1,1,1] [4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg895 - -lemma sg1344 : RowSquare [6,1,1,1,1,1] [4,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg896 - -lemma sg1345 : RowSquare [6,1,1,1,1,1] [4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg897 - -lemma sg1346 : RowSquare [6,1,1,1,1,1] [4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg898 - -lemma sg1347 : RowSquare [6,1,1,1,1,1] [4,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg899 - -lemma sg1348 : RowSquare [6,1,1,1,1,1] [4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg520 - -lemma sg1349 : RowSquare [6,1,1,1,1,1] [4,4,2,1] := by - exact rowSquare_join (by decide) sg0 sg899 - -lemma sg1350 : RowSquare [6,1,1,1,1,1] [5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg517 - -lemma sg1351 : RowSquare [6,1,1,1,1,1] [5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg518 - -lemma sg1352 : RowSquare [6,1,1,1,1,1] [5,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg519 - -lemma sg1353 : RowSquare [6,1,1,1,1,1] [5,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg520 - -lemma sg1354 : RowSquare [6,1,1,1,1,1] [5,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg900 - -lemma sg1355 : RowSquare [6,1,1,1,1,1] [5,3,2,1] := by - exact rowSquare_join (by decide) sg0 sg901 - -lemma sg1356 : RowSquare [6,1,1,1,1,1] [5,4,1,1] := by - exact rowSquare_join (by decide) sg0 sg902 - -lemma sg1357 : RowSquare [6,1,1,1,1,1] [5,4,2] := by - exact rowSquare_join (by decide) sg0 sg903 - -lemma sg1358 : RowSquare [6,1,1,1,1,1] [5,5,1] := by - exact rowSquare_join (by decide) sg0 sg892 - -lemma sg1359 : RowSquare [6,1,1,1,1,1] [6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg521 - -lemma sg1360 : RowSquare [6,1,1,1,1,1] [6,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg522 - -lemma sg1361 : RowSquare [6,1,1,1,1,1] [6,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg523 - -lemma sg1362 : RowSquare [6,1,1,1,1,1] [6,3,1,1] := by - exact rowSquare_join (by decide) sg2 sg524 - -lemma sg1363 : RowSquare [6,1,1,1,1,1] [6,3,2] := by - exact rowSquare_join (by decide) sg2 sg525 - -lemma sg1364 : RowSquare [6,1,1,1,1,1] [6,4,1] := by - exact rowSquare_join (by decide) sg0 sg908 - -lemma sg1365 : RowSquare [6,1,1,1,1,1] [6,5] := by - exact rowSquare_join (by decide) sg0 sg909 - -lemma sg1366 : RowSquare [6,1,1,1,1,1] [7,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg260 - -lemma sg1367 : RowSquare [6,1,1,1,1,1] [7,2,1,1] := by - exact rowSquare_join (by decide) sg7 sg261 - -lemma sg1368 : RowSquare [6,1,1,1,1,1] [7,2,2] := by - exact rowSquare_join (by decide) sg7 sg262 - -lemma sg1369 : RowSquare [6,1,1,1,1,1] [7,3,1] := by - exact rowSquare_join (by decide) sg2 sg529 - -lemma sg1370 : RowSquare [6,1,1,1,1,1] [7,4] := by - exact rowSquare_join (by decide) sg2 sg530 - -lemma sg1371 : RowSquare [6,2,1,1,1] [2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg910 - -lemma sg1372 : RowSquare [6,2,1,1,1] [3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg586 - -lemma sg1373 : RowSquare [6,2,1,1,1] [3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg912 - -lemma sg1374 : RowSquare [6,2,1,1,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg312 - -lemma sg1375 : RowSquare [6,2,1,1,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg914 - -lemma sg1376 : RowSquare [6,2,1,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg915 - -lemma sg1377 : RowSquare [6,2,1,1,1] [3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg313 - -lemma sg1378 : RowSquare [6,2,1,1,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg314 - -lemma sg1379 : RowSquare [6,2,1,1,1] [3,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg315 - -lemma sg1380 : RowSquare [6,2,1,1,1] [4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg534 - -lemma sg1381 : RowSquare [6,2,1,1,1] [4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg312 - -lemma sg1382 : RowSquare [6,2,1,1,1] [4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg316 - -lemma sg1383 : RowSquare [6,2,1,1,1] [4,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg537 - -lemma sg1384 : RowSquare [6,2,1,1,1] [4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg313 - -lemma sg1385 : RowSquare [6,2,1,1,1] [4,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg317 - -lemma sg1386 : RowSquare [6,2,1,1,1] [4,3,2,2] := by - exact rowSquare_join (by decide) sg5 sg315 - -lemma sg1387 : RowSquare [6,2,1,1,1] [4,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg318 - -lemma sg1388 : RowSquare [6,2,1,1,1] [4,4,2,1] := by - exact rowSquare_join (by decide) sg4 sg319 - -lemma sg1389 : RowSquare [6,2,1,1,1] [4,4,3] := by - exact rowSquare_join (by decide) sg4 sg320 - -lemma sg1390 : RowSquare [6,2,1,1,1] [5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg312 - -lemma sg1391 : RowSquare [6,2,1,1,1] [5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg316 - -lemma sg1392 : RowSquare [6,2,1,1,1] [5,2,2,1,1] := by - exact rowSquare_join (by decide) sg16 sg132 - -lemma sg1393 : RowSquare [6,2,1,1,1] [5,2,2,2] := by - exact rowSquare_join (by decide) sg7 sg271 - -lemma sg1394 : RowSquare [6,2,1,1,1] [5,3,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg132 - -lemma sg1395 : RowSquare [6,2,1,1,1] [5,3,2,1] := by - exact rowSquare_join (by decide) sg16 sg133 - -lemma sg1396 : RowSquare [6,2,1,1,1] [5,3,3] := by - exact rowSquare_join (by decide) sg16 sg134 - -lemma sg1397 : RowSquare [6,2,1,1,1] [5,4,1,1] := by - exact rowSquare_join (by decide) sg17 sg133 - -lemma sg1398 : RowSquare [6,2,1,1,1] [5,4,2] := by - exact rowSquare_join (by decide) sg17 sg134 - -lemma sg1399 : RowSquare [6,2,1,1,1] [5,5,1] := by - exact rowSquare_join (by decide) sg4 sg324 - -lemma sg1400 : RowSquare [6,2,1,1,1] [6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg272 - -lemma sg1401 : RowSquare [6,2,1,1,1] [6,2,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg132 - -lemma sg1402 : RowSquare [6,2,1,1,1] [6,2,2,1] := by - exact rowSquare_join (by decide) sg16 sg135 - -lemma sg1403 : RowSquare [6,2,1,1,1] [6,3,1,1] := by - exact rowSquare_join (by decide) sg17 sg135 - -lemma sg1404 : RowSquare [6,2,1,1,1] [6,3,2] := by - exact rowSquare_join (by decide) sg16 sg136 - -lemma sg1405 : RowSquare [6,2,1,1,1] [6,4,1] := by - exact rowSquare_join (by decide) sg16 sg137 - -lemma sg1406 : RowSquare [6,2,1,1,1] [6,5] := by - exact rowSquare_join (by decide) sg17 sg137 - -lemma sg1407 : RowSquare [6,2,1,1,1] [7,4] := by - exact rowSquare_join (by decide) sg46 sg52 - -lemma sg1408 : RowSquare [6,2,2,1] [3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg940 - -lemma sg1409 : RowSquare [6,2,2,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg178 - -lemma sg1410 : RowSquare [6,2,2,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg942 - -lemma sg1411 : RowSquare [6,2,2,1] [3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg178 - -lemma sg1412 : RowSquare [6,2,2,1] [3,3,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg67 - -lemma sg1413 : RowSquare [6,2,2,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg32 sg68 - -lemma sg1414 : RowSquare [6,2,2,1] [4,3,2,2] := by - exact rowSquare_join (by decide) sg33 sg67 - -lemma sg1415 : RowSquare [6,2,2,1] [4,3,3,1] := by - exact rowSquare_join (by decide) sg33 sg68 - -lemma sg1416 : RowSquare [6,3,1,1] [2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg330 - -lemma sg1417 : RowSquare [6,3,1,1] [2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg178 - -lemma sg1418 : RowSquare [6,3,1,1] [3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg330 - -lemma sg1419 : RowSquare [6,3,1,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg331 - -lemma sg1420 : RowSquare [6,3,1,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg179 - -lemma sg1421 : RowSquare [6,3,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg961 - -lemma sg1422 : RowSquare [6,3,1,1] [3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg178 - -lemma sg1423 : RowSquare [6,3,1,1] [3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg332 - -lemma sg1424 : RowSquare [6,3,1,1] [3,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg180 - -lemma sg1425 : RowSquare [6,3,1,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg333 - -lemma sg1426 : RowSquare [6,3,1,1] [3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg181 - -lemma sg1427 : RowSquare [6,3,1,1] [4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg330 - -lemma sg1428 : RowSquare [6,3,1,1] [4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg331 - -lemma sg1429 : RowSquare [6,3,1,1] [4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg142 - -lemma sg1430 : RowSquare [6,3,1,1] [4,2,2,2,1] := by - exact rowSquare_join (by decide) sg39 sg66 - -lemma sg1431 : RowSquare [6,3,1,1] [4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg142 - -lemma sg1432 : RowSquare [6,3,1,1] [4,3,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg66 - -lemma sg1433 : RowSquare [6,3,1,1] [4,3,2,2] := by - exact rowSquare_join (by decide) sg39 sg67 - -lemma sg1434 : RowSquare [6,3,1,1] [4,3,3,1] := by - exact rowSquare_join (by decide) sg39 sg68 - -lemma sg1435 : RowSquare [6,3,1,1] [4,4,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg143 - -lemma sg1436 : RowSquare [6,3,1,1] [4,4,2,1] := by - exact rowSquare_join (by decide) sg40 sg67 - -lemma sg1437 : RowSquare [6,3,1,1] [4,4,3] := by - exact rowSquare_join (by decide) sg40 sg68 - -lemma sg1438 : RowSquare [6,3,1,1] [5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg178 - -lemma sg1439 : RowSquare [6,3,1,1] [5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg142 - -lemma sg1440 : RowSquare [6,3,1,1] [5,2,2,1,1] := by - exact rowSquare_join (by decide) sg41 sg66 - -lemma sg1441 : RowSquare [6,3,1,1] [5,2,2,2] := by - exact rowSquare_join (by decide) sg39 sg69 - -lemma sg1442 : RowSquare [6,3,1,1] [5,3,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg66 - -lemma sg1443 : RowSquare [6,3,1,1] [5,3,2,1] := by - exact rowSquare_join (by decide) sg39 sg70 - -lemma sg1444 : RowSquare [6,3,1,1] [5,3,3] := by - exact rowSquare_join (by decide) sg45 sg55 - -lemma sg1445 : RowSquare [6,3,1,1] [5,4,1,1] := by - exact rowSquare_join (by decide) sg39 sg71 - -lemma sg1446 : RowSquare [6,3,1,1] [5,4,2] := by - exact rowSquare_join (by decide) sg40 sg70 - -lemma sg1447 : RowSquare [6,3,1,1] [5,5,1] := by - exact rowSquare_join (by decide) sg40 sg71 - -lemma sg1448 : RowSquare [6,3,1,1] [6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg142 - -lemma sg1449 : RowSquare [6,3,1,1] [6,2,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg66 - -lemma sg1450 : RowSquare [6,3,1,1] [6,2,2,1] := by - exact rowSquare_join (by decide) sg39 sg72 - -lemma sg1451 : RowSquare [6,3,1,1] [6,3,1,1] := by - exact rowSquare_join (by decide) sg39 sg73 - -lemma sg1452 : RowSquare [6,3,1,1] [6,3,2] := by - exact rowSquare_join (by decide) sg40 sg72 - -lemma sg1453 : RowSquare [6,3,1,1] [6,4,1] := by - exact rowSquare_join (by decide) sg40 sg73 - -lemma sg1454 : RowSquare [6,3,1,1] [6,5] := by - exact rowSquare_join (by decide) sg42 sg71 - -lemma sg1455 : RowSquare [6,3,2] [2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg74 - -lemma sg1456 : RowSquare [6,3,2] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg975 - -lemma sg1457 : RowSquare [6,3,2] [3,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg350 - -lemma sg1458 : RowSquare [6,3,2] [4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg577 - -lemma sg1459 : RowSquare [6,3,2] [5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg307 - -lemma sg1460 : RowSquare [6,4,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg74 - -lemma sg1461 : RowSquare [6,4,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg982 - -lemma sg1462 : RowSquare [6,4,1] [3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg74 - -lemma sg1463 : RowSquare [6,4,1] [3,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg194 - -lemma sg1464 : RowSquare [6,4,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg32 sg83 - -lemma sg1465 : RowSquare [6,4,1] [4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg74 - -lemma sg1466 : RowSquare [6,4,1] [4,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg84 - -lemma sg1467 : RowSquare [6,4,1] [4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg74 - -lemma sg1468 : RowSquare [6,4,1] [4,4,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg166 - -lemma sg1469 : RowSquare [6,4,1] [4,4,3] := by - exact rowSquare_join (by decide) sg40 sg77 - -lemma sg1470 : RowSquare [6,4,1] [5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg74 - -lemma sg1471 : RowSquare [6,4,1] [5,2,2,1,1] := by - exact rowSquare_join (by decide) sg41 sg75 - -lemma sg1472 : RowSquare [6,4,1] [5,3,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg85 - -lemma sg1473 : RowSquare [6,4,1] [5,5,1] := by - exact rowSquare_join (by decide) sg40 sg80 - -lemma sg1474 : RowSquare [6,4,1] [6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg74 - -lemma sg1475 : RowSquare [6,4,1] [6,2,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg75 - -lemma sg1476 : RowSquare [6,4,1] [6,5] := by - exact rowSquare_join (by decide) sg42 sg80 - -lemma sg1477 : RowSquare [6,4,1] [7,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg86 - -lemma sg1498 : RowSquare [7,1,1,1,1] [3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg586 - -lemma sg1499 : RowSquare [7,1,1,1,1] [3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg998 - -lemma sg1500 : RowSquare [7,1,1,1,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg999 - -lemma sg1501 : RowSquare [7,1,1,1,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg1000 - -lemma sg1502 : RowSquare [7,1,1,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg1001 - -lemma sg1503 : RowSquare [7,1,1,1,1] [4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg587 - -lemma sg1504 : RowSquare [7,1,1,1,1] [4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg588 - -lemma sg1505 : RowSquare [7,1,1,1,1] [4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg589 - -lemma sg1506 : RowSquare [7,1,1,1,1] [4,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg590 - -lemma sg1507 : RowSquare [7,1,1,1,1] [4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1006 - -lemma sg1508 : RowSquare [7,1,1,1,1] [4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg1007 - -lemma sg1509 : RowSquare [7,1,1,1,1] [4,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg1008 - -lemma sg1510 : RowSquare [7,1,1,1,1] [5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg312 - -lemma sg1511 : RowSquare [7,1,1,1,1] [5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg313 - -lemma sg1512 : RowSquare [7,1,1,1,1] [5,3,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg595 - -lemma sg1513 : RowSquare [7,1,1,1,1] [5,3,2,1] := by - exact rowSquare_join (by decide) sg2 sg596 - -lemma sg1514 : RowSquare [7,1,1,1,1] [5,4,1,1] := by - exact rowSquare_join (by decide) sg0 sg1015 - -lemma sg1515 : RowSquare [7,1,1,1,1] [5,4,2] := by - exact rowSquare_join (by decide) sg0 sg1016 - -lemma sg1516 : RowSquare [7,1,1,1,1] [6,5] := by - exact rowSquare_join (by decide) sg0 sg1023 - -lemma sg1517 : RowSquare [7,2,1,1] [3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg178 - -lemma sg1518 : RowSquare [7,2,1,1] [3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg1032 - -lemma sg1519 : RowSquare [7,2,1,1] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg1033 - -lemma sg1520 : RowSquare [7,2,1,1] [3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg178 - -lemma sg1521 : RowSquare [7,2,1,1] [3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg371 - -lemma sg1522 : RowSquare [7,2,1,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg372 - -lemma sg1523 : RowSquare [7,2,1,1] [3,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg373 - -lemma sg1524 : RowSquare [7,2,1,1] [4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg330 - -lemma sg1525 : RowSquare [7,2,1,1] [4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg178 - -lemma sg1526 : RowSquare [7,2,1,1] [4,3,3,1] := by - exact rowSquare_join (by decide) sg16 sg181 - -lemma sg1527 : RowSquare [7,2,1,1] [4,4,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg180 - -lemma sg1528 : RowSquare [7,2,1,1] [4,4,2,1] := by - exact rowSquare_join (by decide) sg17 sg181 - -lemma sg1529 : RowSquare [7,2,1,1] [4,4,3] := by - exact rowSquare_join (by decide) sg4 sg378 - -lemma sg1530 : RowSquare [7,2,1,1] [5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg178 - -lemma sg1531 : RowSquare [7,2,1,1] [6,5] := by - exact rowSquare_join (by decide) sg46 sg71 - -lemma sg1532 : RowSquare [7,2,2] [3,2,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg87 - -lemma sg1533 : RowSquare [7,2,2] [3,3,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg88 - -lemma sg1534 : RowSquare [7,2,2] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg32 sg89 - -lemma sg1535 : RowSquare [7,2,2] [4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg636 - -lemma sg1536 : RowSquare [7,2,2] [4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1063 - -lemma sg1537 : RowSquare [7,2,2] [4,4,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg92 - -lemma sg1538 : RowSquare [7,3,1] [3,3,3,1,1] := by - exact rowSquare_join (by decide) sg32 sg97 - -lemma sg1539 : RowSquare [7,3,1] [3,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg390 - -lemma sg1540 : RowSquare [7,3,1] [4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg74 - -lemma sg1541 : RowSquare [7,3,1] [4,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg98 - -lemma sg1542 : RowSquare [7,3,1] [4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg74 - -lemma sg1543 : RowSquare [7,3,1] [4,3,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg99 - -lemma sg1544 : RowSquare [7,3,1] [4,3,2,2] := by - exact rowSquare_join (by decide) sg39 sg88 - -lemma sg1545 : RowSquare [7,3,1] [4,4,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg194 - -lemma sg1546 : RowSquare [7,3,1] [4,4,3] := by - exact rowSquare_join (by decide) sg40 sg89 - -lemma sg1547 : RowSquare [7,3,1] [5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg47 sg74 - -lemma sg1548 : RowSquare [7,4] [4,3,3,1] := by - exact rowSquare_join (by decide) sg39 sg97 - -lemma sg1549 : RowSquare [7,4] [4,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg228 - -lemma sg1550 : RowSquare [7,4] [4,4,3] := by - exact rowSquare_join (by decide) sg40 sg97 - -lemma sg1551 : RowSquare [7,4] [5,5,1] := by - exact rowSquare_join (by decide) sg17 sg210 - -lemma sg1552 : RowSquare [8,1,1,1] [5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg178 - -lemma sg1553 : RowSquare [8,1,1,1] [5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg371 - -lemma sg1554 : RowSquare [8,1,1,1] [5,2,2,1,1] := by - exact rowSquare_join (by decide) sg7 sg372 - -lemma sg1555 : RowSquare [8,1,1,1] [5,2,2,2] := by - exact rowSquare_join (by decide) sg7 sg373 - -lemma sg1556 : RowSquare [8,1,1,1] [6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg179 - -lemma sg1557 : RowSquare [8,1,1,1] [6,2,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg180 - -lemma sg1558 : RowSquare [8,1,1,1] [6,2,2,1] := by - exact rowSquare_join (by decide) sg20 sg181 - -lemma sg1559 : RowSquare [8,1,1,1] [6,3,1,1] := by - exact rowSquare_join (by decide) sg7 sg377 - -lemma sg1560 : RowSquare [8,1,1,1] [6,3,2] := by - exact rowSquare_join (by decide) sg7 sg378 - -lemma sg1561 : RowSquare [8,2,1] [5,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg104 - -lemma sg1562 : RowSquare [8,2,1] [5,2,2,2] := by - exact rowSquare_join (by decide) sg7 sg390 - -lemma sg1563 : RowSquare [8,2,1] [5,3,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg105 - -lemma sg1564 : RowSquare [8,2,1] [5,3,2,1] := by - exact rowSquare_join (by decide) sg45 sg88 - -lemma sg1565 : RowSquare [8,2,1] [5,3,3] := by - exact rowSquare_join (by decide) sg45 sg89 - -lemma sg1566 : RowSquare [8,2,1] [5,4,1,1] := by - exact rowSquare_join (by decide) sg46 sg88 - -lemma sg1567 : RowSquare [8,2,1] [5,4,2] := by - exact rowSquare_join (by decide) sg46 sg89 - -lemma sg1568 : RowSquare [8,2,1] [6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg74 - -lemma sg1569 : RowSquare [8,2,1] [6,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg106 - -lemma sg1570 : RowSquare [8,3] [5,3,3] := by - exact rowSquare_join (by decide) sg45 sg97 - -lemma sg1571 : RowSquare [8,3] [5,4,2] := by - exact rowSquare_join (by decide) sg46 sg97 - -lemma sg1572 : RowSquare [8,3] [5,5,1] := by - exact rowSquare_join (by decide) sg17 sg228 - -lemma sg1573 : RowSquare [8,3] [6,4,1] := by - exact rowSquare_join (by decide) sg40 sg105 - -lemma sg1574 : RowSquare [8,3] [6,5] := by - exact rowSquare_join (by decide) sg17 sg230 - -lemma sg1575 : RowSquare [9,2] [7,2,2] := by - exact rowSquare_join (by decide) sg45 sg104 - -lemma sg1576 : RowSquare [9,2] [7,4] := by - exact rowSquare_join (by decide) sg46 sg105 - -lemma sg1577 : RowSquare [2,2,1,1,1,1,1,1,1,1] [8,4] := by - exact rowSquare_join (by decide) sg105 sg105 - -lemma sg1578 : RowSquare [2,2,1,1,1,1,1,1,1,1] [9,3] := by - exact rowSquare_join (by decide) sg105 sg106 - -lemma sg1579 : RowSquare [2,2,1,1,1,1,1,1,1,1] [10,2] := by - exact rowSquare_join (by decide) sg105 sg107 - -lemma sg1580 : RowSquare [2,2,1,1,1,1,1,1,1,1] [11,1] := by - exact rowSquare_join (by decide) sg106 sg107 - -lemma sg1581 : RowSquare [2,2,2,1,1,1,1,1,1] [6,6] := by - exact rowSquare_join (by decide) sg17 sg424 - -lemma sg1582 : RowSquare [2,2,2,1,1,1,1,1,1] [7,5] := by - exact rowSquare_join (by decide) sg46 sg230 - -lemma sg1583 : RowSquare [3,2,1,1,1,1,1,1,1] [6,3,3] := by - exact rowSquare_join (by decide) sg89 sg104 - -lemma sg1584 : RowSquare [3,2,1,1,1,1,1,1,1] [7,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg108 - -lemma sg1585 : RowSquare [3,2,1,1,1,1,1,1,1] [7,2,1,1,1] := by - exact rowSquare_join (by decide) sg87 sg106 - -lemma sg1586 : RowSquare [3,2,2,1,1,1,1,1] [4,4,4] := by - exact rowSquare_join (by decide) sg97 sg89 - -lemma sg1587 : RowSquare [3,2,2,2,1,1,1] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg390 - -lemma sg1588 : RowSquare [3,2,2,2,2,1] [3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg356 - -lemma sg1589 : RowSquare [3,2,2,2,2,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg83 - -lemma sg1590 : RowSquare [3,2,2,2,2,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg357 - -lemma sg1591 : RowSquare [3,2,2,2,2,1] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg358 - -lemma sg1592 : RowSquare [3,3,1,1,1,1,1,1] [4,2,2,2,2] := by - exact rowSquare_join (by decide) sg87 sg87 - -lemma sg1593 : RowSquare [3,3,1,1,1,1,1,1] [4,3,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg88 - -lemma sg1594 : RowSquare [3,3,1,1,1,1,1,1] [4,3,3,1,1] := by - exact rowSquare_join (by decide) sg87 sg89 - -lemma sg1595 : RowSquare [3,3,1,1,1,1,1,1] [4,4,2,2] := by - exact rowSquare_join (by decide) sg88 sg88 - -lemma sg1596 : RowSquare [3,3,1,1,1,1,1,1] [4,4,3,1] := by - exact rowSquare_join (by decide) sg88 sg89 - -lemma sg1597 : RowSquare [3,3,1,1,1,1,1,1] [4,4,4] := by - exact rowSquare_join (by decide) sg89 sg89 - -lemma sg1598 : RowSquare [3,3,1,1,1,1,1,1] [5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg636 - -lemma sg1599 : RowSquare [3,3,1,1,1,1,1,1] [5,2,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg90 - -lemma sg1600 : RowSquare [3,3,1,1,1,1,1,1] [5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1063 - -lemma sg1601 : RowSquare [3,3,1,1,1,1,1,1] [5,3,2,1,1] := by - exact rowSquare_join (by decide) sg87 sg91 - -lemma sg1602 : RowSquare [3,3,1,1,1,1,1,1] [5,3,2,2] := by - exact rowSquare_join (by decide) sg88 sg90 - -lemma sg1603 : RowSquare [3,3,1,1,1,1,1,1] [5,4,1,1,1] := by - exact rowSquare_join (by decide) sg87 sg92 - -lemma sg1604 : RowSquare [3,3,1,1,1,1,1,1] [6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg348 - -lemma sg1605 : RowSquare [3,3,1,1,1,1,1,1] [6,3,1,1,1] := by - exact rowSquare_join (by decide) sg87 sg94 - -lemma sg1606 : RowSquare [3,3,1,1,1,1,1,1] [6,6] := by - exact rowSquare_join (by decide) sg92 sg92 - -lemma sg1607 : RowSquare [3,3,1,1,1,1,1,1] [7,2,1,1,1] := by - exact rowSquare_join (by decide) sg87 sg95 - -lemma sg1608 : RowSquare [3,3,1,1,1,1,1,1] [8,1,1,1,1] := by - exact rowSquare_join (by decide) sg87 sg96 - -lemma sg1609 : RowSquare [3,3,2,1,1,1,1] [5,5,2] := by - exact rowSquare_join (by decide) sg89 sg80 - -lemma sg1610 : RowSquare [3,3,2,1,1,1,1] [6,2,2,2] := by - exact rowSquare_join (by decide) sg90 sg78 - -lemma sg1611 : RowSquare [3,3,2,1,1,1,1] [6,6] := by - exact rowSquare_join (by decide) sg92 sg80 - -lemma sg1612 : RowSquare [3,3,2,1,1,1,1] [7,5] := by - exact rowSquare_join (by decide) sg92 sg81 - -lemma sg1613 : RowSquare [3,3,2,1,1,1,1] [8,2,2] := by - exact rowSquare_join (by decide) sg3 sg432 - -lemma sg1614 : RowSquare [3,3,2,1,1,1,1] [9,3] := by - exact rowSquare_join (by decide) sg3 sg437 - -lemma sg1616 : RowSquare [3,3,2,2,1,1] [2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg74 - -lemma sg1617 : RowSquare [3,3,2,2,2] [6,6] := by - exact rowSquare_join (by decide) sg14 sg311 - -lemma sg1618 : RowSquare [3,3,3,1,1,1] [3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg154 - -lemma sg1619 : RowSquare [3,3,3,2,1] [2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg516 - -lemma sg1620 : RowSquare [4,1,1,1,1,1,1,1,1] [8,4] := by - exact rowSquare_join (by decide) sg20 sg383 - -lemma sg1621 : RowSquare [4,2,1,1,1,1,1,1] [5,4,3] := by - exact rowSquare_join (by decide) sg16 sg378 - -lemma sg1622 : RowSquare [4,2,1,1,1,1,1,1] [5,5,1,1] := by - exact rowSquare_join (by decide) sg17 sg377 - -lemma sg1623 : RowSquare [4,2,1,1,1,1,1,1] [5,5,2] := by - exact rowSquare_join (by decide) sg17 sg378 - -lemma sg1624 : RowSquare [4,2,1,1,1,1,1,1] [6,5,1] := by - exact rowSquare_join (by decide) sg46 sg185 - -lemma sg1625 : RowSquare [4,2,1,1,1,1,1,1] [6,6] := by - exact rowSquare_join (by decide) sg17 sg383 - -lemma sg1626 : RowSquare [4,2,2,1,1,1,1] [3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg330 - -lemma sg1627 : RowSquare [4,2,2,1,1,1,1] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg373 - -lemma sg1628 : RowSquare [4,2,2,2,1,1] [2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg330 - -lemma sg1629 : RowSquare [4,2,2,2,1,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg563 - -lemma sg1630 : RowSquare [4,2,2,2,1,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg333 - -lemma sg1631 : RowSquare [4,2,2,2,1,1] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg334 - -lemma sg1632 : RowSquare [4,3,1,1,1,1,1] [2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg178 - -lemma sg1633 : RowSquare [4,3,1,1,1,1,1] [3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg178 - -lemma sg1634 : RowSquare [4,3,1,1,1,1,1] [3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg179 - -lemma sg1635 : RowSquare [4,3,1,1,1,1,1] [3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg34 sg178 - -lemma sg1636 : RowSquare [4,3,1,1,1,1,1] [3,3,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg180 - -lemma sg1637 : RowSquare [4,3,1,1,1,1,1] [4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg940 - -lemma sg1638 : RowSquare [4,3,1,1,1,1,1] [4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg35 sg178 - -lemma sg1639 : RowSquare [4,3,1,1,1,1,1] [4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg36 sg178 - -lemma sg1640 : RowSquare [4,3,1,1,1,1,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg371 - -lemma sg1641 : RowSquare [4,3,1,1,1,1,1] [4,4,4] := by - exact rowSquare_join (by decide) sg89 sg68 - -lemma sg1642 : RowSquare [4,3,1,1,1,1,1] [5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg548 - -lemma sg1643 : RowSquare [4,3,1,1,1,1,1] [5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg37 sg178 - -lemma sg1644 : RowSquare [4,3,1,1,1,1,1] [6,6] := by - exact rowSquare_join (by decide) sg92 sg71 - -lemma sg1645 : RowSquare [4,3,2,1,1,1] [3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg178 - -lemma sg1646 : RowSquare [4,3,2,1,1,1] [3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg330 - -lemma sg1647 : RowSquare [4,3,2,1,1,1] [3,3,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg143 - -lemma sg1648 : RowSquare [4,3,3,1,1] [3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1233 - -lemma sg1649 : RowSquare [4,4,1,1,1,1] [4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg23 sg178 - -lemma sg1651 : RowSquare [4,4,2,2] [2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg60 sg61 - -lemma sg1652 : RowSquare [4,4,2,2] [2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg59 sg61 - -lemma sg1653 : RowSquare [4,4,2,2] [2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg59 sg60 - -lemma sg1654 : RowSquare [4,4,2,2] [2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg257 - -lemma sg1655 : RowSquare [4,4,2,2] [3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg58 sg61 - -lemma sg1656 : RowSquare [4,4,2,2] [3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg57 sg61 - -lemma sg1657 : RowSquare [4,4,2,2] [4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg56 sg61 - -lemma sg1658 : RowSquare [4,4,2,2] [4,4,4] := by - exact rowSquare_join (by decide) sg55 sg55 - -lemma sg1659 : RowSquare [5,1,1,1,1,1,1,1] [4,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg1001 - -lemma sg1660 : RowSquare [5,1,1,1,1,1,1,1] [5,3,2,2] := by - exact rowSquare_join (by decide) sg2 sg1008 - -lemma sg1661 : RowSquare [5,1,1,1,1,1,1,1] [6,4,2] := by - exact rowSquare_join (by decide) sg2 sg1016 - -lemma sg1662 : RowSquare [5,1,1,1,1,1,1,1] [7,5] := by - exact rowSquare_join (by decide) sg2 sg1023 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes1 + +namespace OAI + +/-! Semigroup Nodes 2. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg1240 : RowSquare [5,1,1,1,1,1,1] [3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg586 + +lemma sg1241 : RowSquare [5,1,1,1,1,1,1] [3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg998 + +lemma sg1242 : RowSquare [5,1,1,1,1,1,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg999 + +lemma sg1243 : RowSquare [5,1,1,1,1,1,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg1000 + +lemma sg1244 : RowSquare [5,1,1,1,1,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg1001 + +lemma sg1245 : RowSquare [5,1,1,1,1,1,1] [4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg587 + +lemma sg1246 : RowSquare [5,1,1,1,1,1,1] [4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg588 + +lemma sg1247 : RowSquare [5,1,1,1,1,1,1] [4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg589 + +lemma sg1248 : RowSquare [5,1,1,1,1,1,1] [4,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg590 + +lemma sg1249 : RowSquare [5,1,1,1,1,1,1] [4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1006 + +lemma sg1250 : RowSquare [5,1,1,1,1,1,1] [4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg1007 + +lemma sg1251 : RowSquare [5,1,1,1,1,1,1] [4,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg1008 + +lemma sg1252 : RowSquare [5,1,1,1,1,1,1] [5,3,2,1] := by + exact rowSquare_join (by decide) sg2 sg596 + +lemma sg1253 : RowSquare [5,1,1,1,1,1,1] [5,4,1,1] := by + exact rowSquare_join (by decide) sg0 sg1015 + +lemma sg1254 : RowSquare [5,1,1,1,1,1,1] [5,4,2] := by + exact rowSquare_join (by decide) sg0 sg1016 + +lemma sg1255 : RowSquare [5,1,1,1,1,1,1] [6,4,1] := by + exact rowSquare_join (by decide) sg2 sg602 + +lemma sg1256 : RowSquare [5,1,1,1,1,1,1] [6,5] := by + exact rowSquare_join (by decide) sg0 sg1023 + +lemma sg1257 : RowSquare [5,2,1,1,1,1] [2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg910 + +lemma sg1258 : RowSquare [5,2,1,1,1,1] [3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg586 + +lemma sg1259 : RowSquare [5,2,1,1,1,1] [3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg912 + +lemma sg1260 : RowSquare [5,2,1,1,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg809 + +lemma sg1261 : RowSquare [5,2,1,1,1,1] [3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg313 + +lemma sg1262 : RowSquare [5,2,1,1,1,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg314 + +lemma sg1263 : RowSquare [5,2,1,1,1,1] [3,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg315 + +lemma sg1264 : RowSquare [5,2,1,1,1,1] [4,4,2,1] := by + exact rowSquare_join (by decide) sg4 sg319 + +lemma sg1265 : RowSquare [5,2,1,1,1,1] [4,4,3] := by + exact rowSquare_join (by decide) sg4 sg320 + +lemma sg1266 : RowSquare [5,2,1,1,1,1] [5,5,1] := by + exact rowSquare_join (by decide) sg4 sg324 + +lemma sg1267 : RowSquare [5,2,2,1,1] [3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg826 + +lemma sg1268 : RowSquare [5,2,2,1,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg827 + +lemma sg1269 : RowSquare [5,2,2,1,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg828 + +lemma sg1270 : RowSquare [5,2,2,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg829 + +lemma sg1271 : RowSquare [5,2,2,1,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg270 + +lemma sg1272 : RowSquare [5,2,2,1,1] [3,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg271 + +lemma sg1273 : RowSquare [5,2,2,1,1] [4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg830 + +lemma sg1274 : RowSquare [5,3,1,1,1] [3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg838 + +lemma sg1275 : RowSquare [5,3,1,1,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg839 + +lemma sg1276 : RowSquare [5,3,1,1,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg840 + +lemma sg1277 : RowSquare [5,3,1,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg841 + +lemma sg1278 : RowSquare [5,3,1,1,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg270 + +lemma sg1279 : RowSquare [5,3,1,1,1] [3,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg271 + +lemma sg1280 : RowSquare [5,3,1,1,1] [4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg534 + +lemma sg1281 : RowSquare [5,3,1,1,1] [4,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg132 + +lemma sg1282 : RowSquare [5,3,1,1,1] [4,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg273 + +lemma sg1283 : RowSquare [5,3,1,1,1] [4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg133 + +lemma sg1284 : RowSquare [5,3,1,1,1] [4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg134 + +lemma sg1285 : RowSquare [5,3,1,1,1] [4,4,2,1] := by + exact rowSquare_join (by decide) sg4 sg275 + +lemma sg1286 : RowSquare [5,3,1,1,1] [4,4,3] := by + exact rowSquare_join (by decide) sg4 sg276 + +lemma sg1287 : RowSquare [5,3,1,1,1] [5,5,1] := by + exact rowSquare_join (by decide) sg17 sg115 + +lemma sg1288 : RowSquare [5,3,2,1] [2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg849 + +lemma sg1289 : RowSquare [5,3,2,1] [3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg850 + +lemma sg1290 : RowSquare [5,3,2,1] [3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg851 + +lemma sg1291 : RowSquare [5,3,2,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg852 + +lemma sg1292 : RowSquare [5,3,2,1] [3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg285 + +lemma sg1293 : RowSquare [5,3,2,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg32 sg55 + +lemma sg1294 : RowSquare [5,3,2,1] [3,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg287 + +lemma sg1295 : RowSquare [5,3,2,1] [4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg511 + +lemma sg1296 : RowSquare [5,3,2,1] [4,3,3,1] := by + exact rowSquare_join (by decide) sg33 sg55 + +lemma sg1297 : RowSquare [5,3,2,1] [4,4,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg143 + +lemma sg1298 : RowSquare [5,3,2,1] [4,4,2,1] := by + exact rowSquare_join (by decide) sg27 sg67 + +lemma sg1299 : RowSquare [5,3,2,1] [4,4,3] := by + exact rowSquare_join (by decide) sg34 sg55 + +lemma sg1300 : RowSquare [5,3,3] [3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg516 + +lemma sg1301 : RowSquare [5,3,3] [4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg876 + +lemma sg1302 : RowSquare [5,4,1,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg877 + +lemma sg1303 : RowSquare [5,4,1,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg142 + +lemma sg1304 : RowSquare [5,4,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg879 + +lemma sg1305 : RowSquare [5,4,1,1] [3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg295 + +lemma sg1306 : RowSquare [5,4,1,1] [3,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg143 + +lemma sg1307 : RowSquare [5,4,1,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg296 + +lemma sg1308 : RowSquare [5,4,1,1] [3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg144 + +lemma sg1309 : RowSquare [5,4,1,1] [4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg561 + +lemma sg1310 : RowSquare [5,4,1,1] [4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg562 + +lemma sg1311 : RowSquare [5,4,1,1] [4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg298 + +lemma sg1312 : RowSquare [5,4,1,1] [4,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg145 + +lemma sg1313 : RowSquare [5,4,1,1] [4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg142 + +lemma sg1314 : RowSquare [5,4,1,1] [4,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg299 + +lemma sg1315 : RowSquare [5,4,1,1] [4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg146 + +lemma sg1316 : RowSquare [5,4,1,1] [4,3,3,1] := by + exact rowSquare_join (by decide) sg39 sg55 + +lemma sg1317 : RowSquare [5,4,1,1] [4,4,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg143 + +lemma sg1318 : RowSquare [5,4,1,1] [4,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg148 + +lemma sg1319 : RowSquare [5,4,1,1] [4,4,3] := by + exact rowSquare_join (by decide) sg40 sg55 + +lemma sg1320 : RowSquare [5,4,1,1] [5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg565 + +lemma sg1321 : RowSquare [5,4,1,1] [5,3,3] := by + exact rowSquare_join (by decide) sg41 sg55 + +lemma sg1322 : RowSquare [5,4,1,1] [5,5,1] := by + exact rowSquare_join (by decide) sg14 sg148 + +lemma sg1323 : RowSquare [5,4,2] [2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg306 + +lemma sg1324 : RowSquare [5,5,1] [3,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg166 + +lemma sg1325 : RowSquare [5,5,1] [4,4,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg166 + +lemma sg1326 : RowSquare [5,5,1] [5,5,1] := by + exact rowSquare_join (by decide) sg14 sg171 + +lemma sg1328 : RowSquare [6,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg112 + +lemma sg1329 : RowSquare [6,1,1,1,1,1] [2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg111 + +lemma sg1330 : RowSquare [6,1,1,1,1,1] [2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg265 + +lemma sg1331 : RowSquare [6,1,1,1,1,1] [2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg530 + +lemma sg1332 : RowSquare [6,1,1,1,1,1] [2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg909 + +lemma sg1333 : RowSquare [6,1,1,1,1,1] [3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg888 + +lemma sg1334 : RowSquare [6,1,1,1,1,1] [3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg889 + +lemma sg1335 : RowSquare [6,1,1,1,1,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg890 + +lemma sg1336 : RowSquare [6,1,1,1,1,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg891 + +lemma sg1337 : RowSquare [6,1,1,1,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg892 + +lemma sg1338 : RowSquare [6,1,1,1,1,1] [3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg262 + +lemma sg1339 : RowSquare [6,1,1,1,1,1] [3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg525 + +lemma sg1340 : RowSquare [6,1,1,1,1,1] [3,3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg903 + +lemma sg1341 : RowSquare [6,1,1,1,1,1] [4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg893 + +lemma sg1342 : RowSquare [6,1,1,1,1,1] [4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg894 + +lemma sg1343 : RowSquare [6,1,1,1,1,1] [4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg895 + +lemma sg1344 : RowSquare [6,1,1,1,1,1] [4,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg896 + +lemma sg1345 : RowSquare [6,1,1,1,1,1] [4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg897 + +lemma sg1346 : RowSquare [6,1,1,1,1,1] [4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg898 + +lemma sg1347 : RowSquare [6,1,1,1,1,1] [4,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg899 + +lemma sg1348 : RowSquare [6,1,1,1,1,1] [4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg520 + +lemma sg1349 : RowSquare [6,1,1,1,1,1] [4,4,2,1] := by + exact rowSquare_join (by decide) sg0 sg899 + +lemma sg1350 : RowSquare [6,1,1,1,1,1] [5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg517 + +lemma sg1351 : RowSquare [6,1,1,1,1,1] [5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg518 + +lemma sg1352 : RowSquare [6,1,1,1,1,1] [5,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg519 + +lemma sg1353 : RowSquare [6,1,1,1,1,1] [5,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg520 + +lemma sg1354 : RowSquare [6,1,1,1,1,1] [5,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg900 + +lemma sg1355 : RowSquare [6,1,1,1,1,1] [5,3,2,1] := by + exact rowSquare_join (by decide) sg0 sg901 + +lemma sg1356 : RowSquare [6,1,1,1,1,1] [5,4,1,1] := by + exact rowSquare_join (by decide) sg0 sg902 + +lemma sg1357 : RowSquare [6,1,1,1,1,1] [5,4,2] := by + exact rowSquare_join (by decide) sg0 sg903 + +lemma sg1358 : RowSquare [6,1,1,1,1,1] [5,5,1] := by + exact rowSquare_join (by decide) sg0 sg892 + +lemma sg1359 : RowSquare [6,1,1,1,1,1] [6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg521 + +lemma sg1360 : RowSquare [6,1,1,1,1,1] [6,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg522 + +lemma sg1361 : RowSquare [6,1,1,1,1,1] [6,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg523 + +lemma sg1362 : RowSquare [6,1,1,1,1,1] [6,3,1,1] := by + exact rowSquare_join (by decide) sg2 sg524 + +lemma sg1363 : RowSquare [6,1,1,1,1,1] [6,3,2] := by + exact rowSquare_join (by decide) sg2 sg525 + +lemma sg1364 : RowSquare [6,1,1,1,1,1] [6,4,1] := by + exact rowSquare_join (by decide) sg0 sg908 + +lemma sg1365 : RowSquare [6,1,1,1,1,1] [6,5] := by + exact rowSquare_join (by decide) sg0 sg909 + +lemma sg1366 : RowSquare [6,1,1,1,1,1] [7,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg260 + +lemma sg1367 : RowSquare [6,1,1,1,1,1] [7,2,1,1] := by + exact rowSquare_join (by decide) sg7 sg261 + +lemma sg1368 : RowSquare [6,1,1,1,1,1] [7,2,2] := by + exact rowSquare_join (by decide) sg7 sg262 + +lemma sg1369 : RowSquare [6,1,1,1,1,1] [7,3,1] := by + exact rowSquare_join (by decide) sg2 sg529 + +lemma sg1370 : RowSquare [6,1,1,1,1,1] [7,4] := by + exact rowSquare_join (by decide) sg2 sg530 + +lemma sg1371 : RowSquare [6,2,1,1,1] [2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg910 + +lemma sg1372 : RowSquare [6,2,1,1,1] [3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg586 + +lemma sg1373 : RowSquare [6,2,1,1,1] [3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg912 + +lemma sg1374 : RowSquare [6,2,1,1,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg312 + +lemma sg1375 : RowSquare [6,2,1,1,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg914 + +lemma sg1376 : RowSquare [6,2,1,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg915 + +lemma sg1377 : RowSquare [6,2,1,1,1] [3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg313 + +lemma sg1378 : RowSquare [6,2,1,1,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg314 + +lemma sg1379 : RowSquare [6,2,1,1,1] [3,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg315 + +lemma sg1380 : RowSquare [6,2,1,1,1] [4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg534 + +lemma sg1381 : RowSquare [6,2,1,1,1] [4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg312 + +lemma sg1382 : RowSquare [6,2,1,1,1] [4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg316 + +lemma sg1383 : RowSquare [6,2,1,1,1] [4,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg537 + +lemma sg1384 : RowSquare [6,2,1,1,1] [4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg313 + +lemma sg1385 : RowSquare [6,2,1,1,1] [4,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg317 + +lemma sg1386 : RowSquare [6,2,1,1,1] [4,3,2,2] := by + exact rowSquare_join (by decide) sg5 sg315 + +lemma sg1387 : RowSquare [6,2,1,1,1] [4,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg318 + +lemma sg1388 : RowSquare [6,2,1,1,1] [4,4,2,1] := by + exact rowSquare_join (by decide) sg4 sg319 + +lemma sg1389 : RowSquare [6,2,1,1,1] [4,4,3] := by + exact rowSquare_join (by decide) sg4 sg320 + +lemma sg1390 : RowSquare [6,2,1,1,1] [5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg312 + +lemma sg1391 : RowSquare [6,2,1,1,1] [5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg316 + +lemma sg1392 : RowSquare [6,2,1,1,1] [5,2,2,1,1] := by + exact rowSquare_join (by decide) sg16 sg132 + +lemma sg1393 : RowSquare [6,2,1,1,1] [5,2,2,2] := by + exact rowSquare_join (by decide) sg7 sg271 + +lemma sg1394 : RowSquare [6,2,1,1,1] [5,3,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg132 + +lemma sg1395 : RowSquare [6,2,1,1,1] [5,3,2,1] := by + exact rowSquare_join (by decide) sg16 sg133 + +lemma sg1396 : RowSquare [6,2,1,1,1] [5,3,3] := by + exact rowSquare_join (by decide) sg16 sg134 + +lemma sg1397 : RowSquare [6,2,1,1,1] [5,4,1,1] := by + exact rowSquare_join (by decide) sg17 sg133 + +lemma sg1398 : RowSquare [6,2,1,1,1] [5,4,2] := by + exact rowSquare_join (by decide) sg17 sg134 + +lemma sg1399 : RowSquare [6,2,1,1,1] [5,5,1] := by + exact rowSquare_join (by decide) sg4 sg324 + +lemma sg1400 : RowSquare [6,2,1,1,1] [6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg272 + +lemma sg1401 : RowSquare [6,2,1,1,1] [6,2,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg132 + +lemma sg1402 : RowSquare [6,2,1,1,1] [6,2,2,1] := by + exact rowSquare_join (by decide) sg16 sg135 + +lemma sg1403 : RowSquare [6,2,1,1,1] [6,3,1,1] := by + exact rowSquare_join (by decide) sg17 sg135 + +lemma sg1404 : RowSquare [6,2,1,1,1] [6,3,2] := by + exact rowSquare_join (by decide) sg16 sg136 + +lemma sg1405 : RowSquare [6,2,1,1,1] [6,4,1] := by + exact rowSquare_join (by decide) sg16 sg137 + +lemma sg1406 : RowSquare [6,2,1,1,1] [6,5] := by + exact rowSquare_join (by decide) sg17 sg137 + +lemma sg1407 : RowSquare [6,2,1,1,1] [7,4] := by + exact rowSquare_join (by decide) sg46 sg52 + +lemma sg1408 : RowSquare [6,2,2,1] [3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg940 + +lemma sg1409 : RowSquare [6,2,2,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg178 + +lemma sg1410 : RowSquare [6,2,2,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg942 + +lemma sg1411 : RowSquare [6,2,2,1] [3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg178 + +lemma sg1412 : RowSquare [6,2,2,1] [3,3,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg67 + +lemma sg1413 : RowSquare [6,2,2,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg32 sg68 + +lemma sg1414 : RowSquare [6,2,2,1] [4,3,2,2] := by + exact rowSquare_join (by decide) sg33 sg67 + +lemma sg1415 : RowSquare [6,2,2,1] [4,3,3,1] := by + exact rowSquare_join (by decide) sg33 sg68 + +lemma sg1416 : RowSquare [6,3,1,1] [2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg330 + +lemma sg1417 : RowSquare [6,3,1,1] [2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg178 + +lemma sg1418 : RowSquare [6,3,1,1] [3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg330 + +lemma sg1419 : RowSquare [6,3,1,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg331 + +lemma sg1420 : RowSquare [6,3,1,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg179 + +lemma sg1421 : RowSquare [6,3,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg961 + +lemma sg1422 : RowSquare [6,3,1,1] [3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg178 + +lemma sg1423 : RowSquare [6,3,1,1] [3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg332 + +lemma sg1424 : RowSquare [6,3,1,1] [3,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg180 + +lemma sg1425 : RowSquare [6,3,1,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg333 + +lemma sg1426 : RowSquare [6,3,1,1] [3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg181 + +lemma sg1427 : RowSquare [6,3,1,1] [4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg330 + +lemma sg1428 : RowSquare [6,3,1,1] [4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg331 + +lemma sg1429 : RowSquare [6,3,1,1] [4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg142 + +lemma sg1430 : RowSquare [6,3,1,1] [4,2,2,2,1] := by + exact rowSquare_join (by decide) sg39 sg66 + +lemma sg1431 : RowSquare [6,3,1,1] [4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg142 + +lemma sg1432 : RowSquare [6,3,1,1] [4,3,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg66 + +lemma sg1433 : RowSquare [6,3,1,1] [4,3,2,2] := by + exact rowSquare_join (by decide) sg39 sg67 + +lemma sg1434 : RowSquare [6,3,1,1] [4,3,3,1] := by + exact rowSquare_join (by decide) sg39 sg68 + +lemma sg1435 : RowSquare [6,3,1,1] [4,4,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg143 + +lemma sg1436 : RowSquare [6,3,1,1] [4,4,2,1] := by + exact rowSquare_join (by decide) sg40 sg67 + +lemma sg1437 : RowSquare [6,3,1,1] [4,4,3] := by + exact rowSquare_join (by decide) sg40 sg68 + +lemma sg1438 : RowSquare [6,3,1,1] [5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg178 + +lemma sg1439 : RowSquare [6,3,1,1] [5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg142 + +lemma sg1440 : RowSquare [6,3,1,1] [5,2,2,1,1] := by + exact rowSquare_join (by decide) sg41 sg66 + +lemma sg1441 : RowSquare [6,3,1,1] [5,2,2,2] := by + exact rowSquare_join (by decide) sg39 sg69 + +lemma sg1442 : RowSquare [6,3,1,1] [5,3,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg66 + +lemma sg1443 : RowSquare [6,3,1,1] [5,3,2,1] := by + exact rowSquare_join (by decide) sg39 sg70 + +lemma sg1444 : RowSquare [6,3,1,1] [5,3,3] := by + exact rowSquare_join (by decide) sg45 sg55 + +lemma sg1445 : RowSquare [6,3,1,1] [5,4,1,1] := by + exact rowSquare_join (by decide) sg39 sg71 + +lemma sg1446 : RowSquare [6,3,1,1] [5,4,2] := by + exact rowSquare_join (by decide) sg40 sg70 + +lemma sg1447 : RowSquare [6,3,1,1] [5,5,1] := by + exact rowSquare_join (by decide) sg40 sg71 + +lemma sg1448 : RowSquare [6,3,1,1] [6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg142 + +lemma sg1449 : RowSquare [6,3,1,1] [6,2,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg66 + +lemma sg1450 : RowSquare [6,3,1,1] [6,2,2,1] := by + exact rowSquare_join (by decide) sg39 sg72 + +lemma sg1451 : RowSquare [6,3,1,1] [6,3,1,1] := by + exact rowSquare_join (by decide) sg39 sg73 + +lemma sg1452 : RowSquare [6,3,1,1] [6,3,2] := by + exact rowSquare_join (by decide) sg40 sg72 + +lemma sg1453 : RowSquare [6,3,1,1] [6,4,1] := by + exact rowSquare_join (by decide) sg40 sg73 + +lemma sg1454 : RowSquare [6,3,1,1] [6,5] := by + exact rowSquare_join (by decide) sg42 sg71 + +lemma sg1455 : RowSquare [6,3,2] [2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg74 + +lemma sg1456 : RowSquare [6,3,2] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg975 + +lemma sg1457 : RowSquare [6,3,2] [3,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg350 + +lemma sg1458 : RowSquare [6,3,2] [4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg577 + +lemma sg1459 : RowSquare [6,3,2] [5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg307 + +lemma sg1460 : RowSquare [6,4,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg74 + +lemma sg1461 : RowSquare [6,4,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg982 + +lemma sg1462 : RowSquare [6,4,1] [3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg74 + +lemma sg1463 : RowSquare [6,4,1] [3,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg194 + +lemma sg1464 : RowSquare [6,4,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg32 sg83 + +lemma sg1465 : RowSquare [6,4,1] [4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg74 + +lemma sg1466 : RowSquare [6,4,1] [4,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg84 + +lemma sg1467 : RowSquare [6,4,1] [4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg74 + +lemma sg1468 : RowSquare [6,4,1] [4,4,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg166 + +lemma sg1469 : RowSquare [6,4,1] [4,4,3] := by + exact rowSquare_join (by decide) sg40 sg77 + +lemma sg1470 : RowSquare [6,4,1] [5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg74 + +lemma sg1471 : RowSquare [6,4,1] [5,2,2,1,1] := by + exact rowSquare_join (by decide) sg41 sg75 + +lemma sg1472 : RowSquare [6,4,1] [5,3,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg85 + +lemma sg1473 : RowSquare [6,4,1] [5,5,1] := by + exact rowSquare_join (by decide) sg40 sg80 + +lemma sg1474 : RowSquare [6,4,1] [6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg74 + +lemma sg1475 : RowSquare [6,4,1] [6,2,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg75 + +lemma sg1476 : RowSquare [6,4,1] [6,5] := by + exact rowSquare_join (by decide) sg42 sg80 + +lemma sg1477 : RowSquare [6,4,1] [7,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg86 + +lemma sg1498 : RowSquare [7,1,1,1,1] [3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg586 + +lemma sg1499 : RowSquare [7,1,1,1,1] [3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg998 + +lemma sg1500 : RowSquare [7,1,1,1,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg999 + +lemma sg1501 : RowSquare [7,1,1,1,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg1000 + +lemma sg1502 : RowSquare [7,1,1,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg1001 + +lemma sg1503 : RowSquare [7,1,1,1,1] [4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg587 + +lemma sg1504 : RowSquare [7,1,1,1,1] [4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg588 + +lemma sg1505 : RowSquare [7,1,1,1,1] [4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg589 + +lemma sg1506 : RowSquare [7,1,1,1,1] [4,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg590 + +lemma sg1507 : RowSquare [7,1,1,1,1] [4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1006 + +lemma sg1508 : RowSquare [7,1,1,1,1] [4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg1007 + +lemma sg1509 : RowSquare [7,1,1,1,1] [4,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg1008 + +lemma sg1510 : RowSquare [7,1,1,1,1] [5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg312 + +lemma sg1511 : RowSquare [7,1,1,1,1] [5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg313 + +lemma sg1512 : RowSquare [7,1,1,1,1] [5,3,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg595 + +lemma sg1513 : RowSquare [7,1,1,1,1] [5,3,2,1] := by + exact rowSquare_join (by decide) sg2 sg596 + +lemma sg1514 : RowSquare [7,1,1,1,1] [5,4,1,1] := by + exact rowSquare_join (by decide) sg0 sg1015 + +lemma sg1515 : RowSquare [7,1,1,1,1] [5,4,2] := by + exact rowSquare_join (by decide) sg0 sg1016 + +lemma sg1516 : RowSquare [7,1,1,1,1] [6,5] := by + exact rowSquare_join (by decide) sg0 sg1023 + +lemma sg1517 : RowSquare [7,2,1,1] [3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg178 + +lemma sg1518 : RowSquare [7,2,1,1] [3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg1032 + +lemma sg1519 : RowSquare [7,2,1,1] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg1033 + +lemma sg1520 : RowSquare [7,2,1,1] [3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg178 + +lemma sg1521 : RowSquare [7,2,1,1] [3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg371 + +lemma sg1522 : RowSquare [7,2,1,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg372 + +lemma sg1523 : RowSquare [7,2,1,1] [3,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg373 + +lemma sg1524 : RowSquare [7,2,1,1] [4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg330 + +lemma sg1525 : RowSquare [7,2,1,1] [4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg178 + +lemma sg1526 : RowSquare [7,2,1,1] [4,3,3,1] := by + exact rowSquare_join (by decide) sg16 sg181 + +lemma sg1527 : RowSquare [7,2,1,1] [4,4,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg180 + +lemma sg1528 : RowSquare [7,2,1,1] [4,4,2,1] := by + exact rowSquare_join (by decide) sg17 sg181 + +lemma sg1529 : RowSquare [7,2,1,1] [4,4,3] := by + exact rowSquare_join (by decide) sg4 sg378 + +lemma sg1530 : RowSquare [7,2,1,1] [5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg178 + +lemma sg1531 : RowSquare [7,2,1,1] [6,5] := by + exact rowSquare_join (by decide) sg46 sg71 + +lemma sg1532 : RowSquare [7,2,2] [3,2,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg87 + +lemma sg1533 : RowSquare [7,2,2] [3,3,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg88 + +lemma sg1534 : RowSquare [7,2,2] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg32 sg89 + +lemma sg1535 : RowSquare [7,2,2] [4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg636 + +lemma sg1536 : RowSquare [7,2,2] [4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1063 + +lemma sg1537 : RowSquare [7,2,2] [4,4,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg92 + +lemma sg1538 : RowSquare [7,3,1] [3,3,3,1,1] := by + exact rowSquare_join (by decide) sg32 sg97 + +lemma sg1539 : RowSquare [7,3,1] [3,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg390 + +lemma sg1540 : RowSquare [7,3,1] [4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg74 + +lemma sg1541 : RowSquare [7,3,1] [4,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg98 + +lemma sg1542 : RowSquare [7,3,1] [4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg74 + +lemma sg1543 : RowSquare [7,3,1] [4,3,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg99 + +lemma sg1544 : RowSquare [7,3,1] [4,3,2,2] := by + exact rowSquare_join (by decide) sg39 sg88 + +lemma sg1545 : RowSquare [7,3,1] [4,4,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg194 + +lemma sg1546 : RowSquare [7,3,1] [4,4,3] := by + exact rowSquare_join (by decide) sg40 sg89 + +lemma sg1547 : RowSquare [7,3,1] [5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg47 sg74 + +lemma sg1548 : RowSquare [7,4] [4,3,3,1] := by + exact rowSquare_join (by decide) sg39 sg97 + +lemma sg1549 : RowSquare [7,4] [4,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg228 + +lemma sg1550 : RowSquare [7,4] [4,4,3] := by + exact rowSquare_join (by decide) sg40 sg97 + +lemma sg1551 : RowSquare [7,4] [5,5,1] := by + exact rowSquare_join (by decide) sg17 sg210 + +lemma sg1552 : RowSquare [8,1,1,1] [5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg178 + +lemma sg1553 : RowSquare [8,1,1,1] [5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg371 + +lemma sg1554 : RowSquare [8,1,1,1] [5,2,2,1,1] := by + exact rowSquare_join (by decide) sg7 sg372 + +lemma sg1555 : RowSquare [8,1,1,1] [5,2,2,2] := by + exact rowSquare_join (by decide) sg7 sg373 + +lemma sg1556 : RowSquare [8,1,1,1] [6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg179 + +lemma sg1557 : RowSquare [8,1,1,1] [6,2,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg180 + +lemma sg1558 : RowSquare [8,1,1,1] [6,2,2,1] := by + exact rowSquare_join (by decide) sg20 sg181 + +lemma sg1559 : RowSquare [8,1,1,1] [6,3,1,1] := by + exact rowSquare_join (by decide) sg7 sg377 + +lemma sg1560 : RowSquare [8,1,1,1] [6,3,2] := by + exact rowSquare_join (by decide) sg7 sg378 + +lemma sg1561 : RowSquare [8,2,1] [5,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg104 + +lemma sg1562 : RowSquare [8,2,1] [5,2,2,2] := by + exact rowSquare_join (by decide) sg7 sg390 + +lemma sg1563 : RowSquare [8,2,1] [5,3,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg105 + +lemma sg1564 : RowSquare [8,2,1] [5,3,2,1] := by + exact rowSquare_join (by decide) sg45 sg88 + +lemma sg1565 : RowSquare [8,2,1] [5,3,3] := by + exact rowSquare_join (by decide) sg45 sg89 + +lemma sg1566 : RowSquare [8,2,1] [5,4,1,1] := by + exact rowSquare_join (by decide) sg46 sg88 + +lemma sg1567 : RowSquare [8,2,1] [5,4,2] := by + exact rowSquare_join (by decide) sg46 sg89 + +lemma sg1568 : RowSquare [8,2,1] [6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg74 + +lemma sg1569 : RowSquare [8,2,1] [6,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg106 + +lemma sg1570 : RowSquare [8,3] [5,3,3] := by + exact rowSquare_join (by decide) sg45 sg97 + +lemma sg1571 : RowSquare [8,3] [5,4,2] := by + exact rowSquare_join (by decide) sg46 sg97 + +lemma sg1572 : RowSquare [8,3] [5,5,1] := by + exact rowSquare_join (by decide) sg17 sg228 + +lemma sg1573 : RowSquare [8,3] [6,4,1] := by + exact rowSquare_join (by decide) sg40 sg105 + +lemma sg1574 : RowSquare [8,3] [6,5] := by + exact rowSquare_join (by decide) sg17 sg230 + +lemma sg1575 : RowSquare [9,2] [7,2,2] := by + exact rowSquare_join (by decide) sg45 sg104 + +lemma sg1576 : RowSquare [9,2] [7,4] := by + exact rowSquare_join (by decide) sg46 sg105 + +lemma sg1577 : RowSquare [2,2,1,1,1,1,1,1,1,1] [8,4] := by + exact rowSquare_join (by decide) sg105 sg105 + +lemma sg1578 : RowSquare [2,2,1,1,1,1,1,1,1,1] [9,3] := by + exact rowSquare_join (by decide) sg105 sg106 + +lemma sg1579 : RowSquare [2,2,1,1,1,1,1,1,1,1] [10,2] := by + exact rowSquare_join (by decide) sg105 sg107 + +lemma sg1580 : RowSquare [2,2,1,1,1,1,1,1,1,1] [11,1] := by + exact rowSquare_join (by decide) sg106 sg107 + +lemma sg1581 : RowSquare [2,2,2,1,1,1,1,1,1] [6,6] := by + exact rowSquare_join (by decide) sg17 sg424 + +lemma sg1582 : RowSquare [2,2,2,1,1,1,1,1,1] [7,5] := by + exact rowSquare_join (by decide) sg46 sg230 + +lemma sg1583 : RowSquare [3,2,1,1,1,1,1,1,1] [6,3,3] := by + exact rowSquare_join (by decide) sg89 sg104 + +lemma sg1584 : RowSquare [3,2,1,1,1,1,1,1,1] [7,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg108 + +lemma sg1585 : RowSquare [3,2,1,1,1,1,1,1,1] [7,2,1,1,1] := by + exact rowSquare_join (by decide) sg87 sg106 + +lemma sg1586 : RowSquare [3,2,2,1,1,1,1,1] [4,4,4] := by + exact rowSquare_join (by decide) sg97 sg89 + +lemma sg1587 : RowSquare [3,2,2,2,1,1,1] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg390 + +lemma sg1588 : RowSquare [3,2,2,2,2,1] [3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg356 + +lemma sg1589 : RowSquare [3,2,2,2,2,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg83 + +lemma sg1590 : RowSquare [3,2,2,2,2,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg357 + +lemma sg1591 : RowSquare [3,2,2,2,2,1] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg358 + +lemma sg1592 : RowSquare [3,3,1,1,1,1,1,1] [4,2,2,2,2] := by + exact rowSquare_join (by decide) sg87 sg87 + +lemma sg1593 : RowSquare [3,3,1,1,1,1,1,1] [4,3,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg88 + +lemma sg1594 : RowSquare [3,3,1,1,1,1,1,1] [4,3,3,1,1] := by + exact rowSquare_join (by decide) sg87 sg89 + +lemma sg1595 : RowSquare [3,3,1,1,1,1,1,1] [4,4,2,2] := by + exact rowSquare_join (by decide) sg88 sg88 + +lemma sg1596 : RowSquare [3,3,1,1,1,1,1,1] [4,4,3,1] := by + exact rowSquare_join (by decide) sg88 sg89 + +lemma sg1597 : RowSquare [3,3,1,1,1,1,1,1] [4,4,4] := by + exact rowSquare_join (by decide) sg89 sg89 + +lemma sg1598 : RowSquare [3,3,1,1,1,1,1,1] [5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg636 + +lemma sg1599 : RowSquare [3,3,1,1,1,1,1,1] [5,2,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg90 + +lemma sg1600 : RowSquare [3,3,1,1,1,1,1,1] [5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1063 + +lemma sg1601 : RowSquare [3,3,1,1,1,1,1,1] [5,3,2,1,1] := by + exact rowSquare_join (by decide) sg87 sg91 + +lemma sg1602 : RowSquare [3,3,1,1,1,1,1,1] [5,3,2,2] := by + exact rowSquare_join (by decide) sg88 sg90 + +lemma sg1603 : RowSquare [3,3,1,1,1,1,1,1] [5,4,1,1,1] := by + exact rowSquare_join (by decide) sg87 sg92 + +lemma sg1604 : RowSquare [3,3,1,1,1,1,1,1] [6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg348 + +lemma sg1605 : RowSquare [3,3,1,1,1,1,1,1] [6,3,1,1,1] := by + exact rowSquare_join (by decide) sg87 sg94 + +lemma sg1606 : RowSquare [3,3,1,1,1,1,1,1] [6,6] := by + exact rowSquare_join (by decide) sg92 sg92 + +lemma sg1607 : RowSquare [3,3,1,1,1,1,1,1] [7,2,1,1,1] := by + exact rowSquare_join (by decide) sg87 sg95 + +lemma sg1608 : RowSquare [3,3,1,1,1,1,1,1] [8,1,1,1,1] := by + exact rowSquare_join (by decide) sg87 sg96 + +lemma sg1609 : RowSquare [3,3,2,1,1,1,1] [5,5,2] := by + exact rowSquare_join (by decide) sg89 sg80 + +lemma sg1610 : RowSquare [3,3,2,1,1,1,1] [6,2,2,2] := by + exact rowSquare_join (by decide) sg90 sg78 + +lemma sg1611 : RowSquare [3,3,2,1,1,1,1] [6,6] := by + exact rowSquare_join (by decide) sg92 sg80 + +lemma sg1612 : RowSquare [3,3,2,1,1,1,1] [7,5] := by + exact rowSquare_join (by decide) sg92 sg81 + +lemma sg1613 : RowSquare [3,3,2,1,1,1,1] [8,2,2] := by + exact rowSquare_join (by decide) sg3 sg432 + +lemma sg1614 : RowSquare [3,3,2,1,1,1,1] [9,3] := by + exact rowSquare_join (by decide) sg3 sg437 + +lemma sg1616 : RowSquare [3,3,2,2,1,1] [2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg74 + +lemma sg1617 : RowSquare [3,3,2,2,2] [6,6] := by + exact rowSquare_join (by decide) sg14 sg311 + +lemma sg1618 : RowSquare [3,3,3,1,1,1] [3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg154 + +lemma sg1619 : RowSquare [3,3,3,2,1] [2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg516 + +lemma sg1620 : RowSquare [4,1,1,1,1,1,1,1,1] [8,4] := by + exact rowSquare_join (by decide) sg20 sg383 + +lemma sg1621 : RowSquare [4,2,1,1,1,1,1,1] [5,4,3] := by + exact rowSquare_join (by decide) sg16 sg378 + +lemma sg1622 : RowSquare [4,2,1,1,1,1,1,1] [5,5,1,1] := by + exact rowSquare_join (by decide) sg17 sg377 + +lemma sg1623 : RowSquare [4,2,1,1,1,1,1,1] [5,5,2] := by + exact rowSquare_join (by decide) sg17 sg378 + +lemma sg1624 : RowSquare [4,2,1,1,1,1,1,1] [6,5,1] := by + exact rowSquare_join (by decide) sg46 sg185 + +lemma sg1625 : RowSquare [4,2,1,1,1,1,1,1] [6,6] := by + exact rowSquare_join (by decide) sg17 sg383 + +lemma sg1626 : RowSquare [4,2,2,1,1,1,1] [3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg330 + +lemma sg1627 : RowSquare [4,2,2,1,1,1,1] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg373 + +lemma sg1628 : RowSquare [4,2,2,2,1,1] [2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg330 + +lemma sg1629 : RowSquare [4,2,2,2,1,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg563 + +lemma sg1630 : RowSquare [4,2,2,2,1,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg333 + +lemma sg1631 : RowSquare [4,2,2,2,1,1] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg334 + +lemma sg1632 : RowSquare [4,3,1,1,1,1,1] [2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg178 + +lemma sg1633 : RowSquare [4,3,1,1,1,1,1] [3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg178 + +lemma sg1634 : RowSquare [4,3,1,1,1,1,1] [3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg179 + +lemma sg1635 : RowSquare [4,3,1,1,1,1,1] [3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg34 sg178 + +lemma sg1636 : RowSquare [4,3,1,1,1,1,1] [3,3,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg180 + +lemma sg1637 : RowSquare [4,3,1,1,1,1,1] [4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg940 + +lemma sg1638 : RowSquare [4,3,1,1,1,1,1] [4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg35 sg178 + +lemma sg1639 : RowSquare [4,3,1,1,1,1,1] [4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg36 sg178 + +lemma sg1640 : RowSquare [4,3,1,1,1,1,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg371 + +lemma sg1641 : RowSquare [4,3,1,1,1,1,1] [4,4,4] := by + exact rowSquare_join (by decide) sg89 sg68 + +lemma sg1642 : RowSquare [4,3,1,1,1,1,1] [5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg548 + +lemma sg1643 : RowSquare [4,3,1,1,1,1,1] [5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg37 sg178 + +lemma sg1644 : RowSquare [4,3,1,1,1,1,1] [6,6] := by + exact rowSquare_join (by decide) sg92 sg71 + +lemma sg1645 : RowSquare [4,3,2,1,1,1] [3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg178 + +lemma sg1646 : RowSquare [4,3,2,1,1,1] [3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg330 + +lemma sg1647 : RowSquare [4,3,2,1,1,1] [3,3,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg143 + +lemma sg1648 : RowSquare [4,3,3,1,1] [3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1233 + +lemma sg1649 : RowSquare [4,4,1,1,1,1] [4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg23 sg178 + +lemma sg1651 : RowSquare [4,4,2,2] [2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg60 sg61 + +lemma sg1652 : RowSquare [4,4,2,2] [2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg59 sg61 + +lemma sg1653 : RowSquare [4,4,2,2] [2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg59 sg60 + +lemma sg1654 : RowSquare [4,4,2,2] [2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg257 + +lemma sg1655 : RowSquare [4,4,2,2] [3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg58 sg61 + +lemma sg1656 : RowSquare [4,4,2,2] [3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg57 sg61 + +lemma sg1657 : RowSquare [4,4,2,2] [4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg56 sg61 + +lemma sg1658 : RowSquare [4,4,2,2] [4,4,4] := by + exact rowSquare_join (by decide) sg55 sg55 + +lemma sg1659 : RowSquare [5,1,1,1,1,1,1,1] [4,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg1001 + +lemma sg1660 : RowSquare [5,1,1,1,1,1,1,1] [5,3,2,2] := by + exact rowSquare_join (by decide) sg2 sg1008 + +lemma sg1661 : RowSquare [5,1,1,1,1,1,1,1] [6,4,2] := by + exact rowSquare_join (by decide) sg2 sg1016 + +lemma sg1662 : RowSquare [5,1,1,1,1,1,1,1] [7,5] := by + exact rowSquare_join (by decide) sg2 sg1023 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes20.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes20.lean index bd067ae2a31883885430fce09405f57287f0dc40..352144024c4fac66a5d231fa9489c206fb2def5f 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes20.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes20.lean @@ -1,1221 +1,1221 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes18 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes15 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes16 - -namespace OAI - -/-! Semigroup Nodes 20. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg8537 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1005 sg1327 - -lemma sg8538 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1328 - -lemma sg8539 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1331 - -lemma sg8540 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1328 - -lemma sg8541 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1332 - -lemma sg8542 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1006 sg1327 - -lemma sg8543 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1329 - -lemma sg8544 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1007 sg1327 - -lemma sg8545 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg1329 - -lemma sg8546 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg1330 - -lemma sg8547 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1008 sg1327 - -lemma sg8548 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1329 - -lemma sg8549 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1331 - -lemma sg8550 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1332 - -lemma sg8551 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1330 - -lemma sg8552 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1330 - -lemma sg8553 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg1331 - -lemma sg8554 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1330 - -lemma sg8555 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg999 sg1332 - -lemma sg8556 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1331 - -lemma sg8557 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1331 - -lemma sg8558 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg1000 sg1332 - -lemma sg8559 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg1001 sg1332 - -lemma sg8560 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1009 sg1327 - -lemma sg8561 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1328 - -lemma sg8562 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6905 - -lemma sg8563 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1003 sg1328 - -lemma sg8564 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg6906 - -lemma sg8565 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1004 sg1328 - -lemma sg8566 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg6907 - -lemma sg8567 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1002 sg1330 - -lemma sg8568 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1005 sg1328 - -lemma sg8569 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1002 sg1331 - -lemma sg8570 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1332 - -lemma sg8571 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1338 - -lemma sg8572 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6910 - -lemma sg8573 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1008 sg1328 - -lemma sg8574 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1003 sg1331 - -lemma sg8575 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1003 sg1332 - -lemma sg8576 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1004 sg1330 - -lemma sg8577 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1005 sg1330 - -lemma sg8578 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg1004 sg1332 - -lemma sg8579 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1005 sg1331 - -lemma sg8580 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg0 sg6917 - -lemma sg8581 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg0 sg6918 - -lemma sg8582 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg6919 - -lemma sg8583 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1015 sg1327 - -lemma sg8584 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1006 sg1329 - -lemma sg8585 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1338 - -lemma sg8586 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1016 sg1327 - -lemma sg8587 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1007 sg1329 - -lemma sg8588 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1339 - -lemma sg8589 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg1338 - -lemma sg8590 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1008 sg1329 - -lemma sg8591 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1340 - -lemma sg8592 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1338 - -lemma sg8593 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1338 - -lemma sg8594 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg1006 sg1332 - -lemma sg8595 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1008 sg1330 - -lemma sg8596 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg1000 sg1339 - -lemma sg8597 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1008 sg1331 - -lemma sg8598 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1340 - -lemma sg8599 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,3] := by - exact rowSquare_join (by decide) sg1001 sg1340 - -lemma sg8600 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1009 sg1328 - -lemma sg8601 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1012 sg1330 - -lemma sg8602 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1006 sg1338 - -lemma sg8603 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1016 sg1329 - -lemma sg8604 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg1006 sg1339 - -lemma sg8605 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3] := by - exact rowSquare_join (by decide) sg1001 sg1348 - -lemma sg8606 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,1] := by - exact rowSquare_join (by decide) sg1008 sg1340 - -lemma sg8607 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1022 sg1328 - -lemma sg8608 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1023 sg1328 - -lemma sg8609 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1003 sg1348 - -lemma sg8610 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg6995 - -lemma sg8611 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1023 sg1329 - -lemma sg8612 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1015 sg1338 - -lemma sg8613 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,1] := by - exact rowSquare_join (by decide) sg1006 sg1348 - -lemma sg8614 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,1] := by - exact rowSquare_join (by decide) sg1008 sg1348 - -lemma sg8615 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg910 sg1327 - -lemma sg8616 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg1754 - -lemma sg8617 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg1754 - -lemma sg8618 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg1754 - -lemma sg8619 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg914 sg1327 - -lemma sg8620 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg591 sg1754 - -lemma sg8621 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg592 sg1754 - -lemma sg8622 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg593 sg1754 - -lemma sg8623 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg594 sg1754 - -lemma sg8624 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg595 sg1754 - -lemma sg8625 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg1754 - -lemma sg8626 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg915 sg1332 - -lemma sg8627 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg597 sg1754 - -lemma sg8628 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg598 sg1754 - -lemma sg8629 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg599 sg1754 - -lemma sg8630 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg600 sg1754 - -lemma sg8631 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg601 sg1754 - -lemma sg8632 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg930 sg1327 - -lemma sg8633 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg923 sg1328 - -lemma sg8634 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg1754 - -lemma sg8635 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg931 sg1327 - -lemma sg8636 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg932 sg1327 - -lemma sg8637 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg923 sg1330 - -lemma sg8638 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg939 sg1327 - -lemma sg8639 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [7,7,6,1] := by - exact rowSquare_join (by decide) sg13 sg4619 - -lemma sg8640 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,6,6,1] := by - exact rowSquare_join (by decide) sg39 sg3764 - -lemma sg8641 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,7,5,1] := by - exact rowSquare_join (by decide) sg39 sg3765 - -lemma sg8642 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,7,6] := by - exact rowSquare_join (by decide) sg40 sg3764 - -lemma sg8643 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,8,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg4616 - -lemma sg8644 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,8,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg4617 - -lemma sg8645 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,8,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg4620 - -lemma sg8646 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,8,3,1,1] := by - exact rowSquare_join (by decide) sg14 sg4618 - -lemma sg8647 : RowSquare [6,5,2,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg534 sg1754 - -lemma sg8648 : RowSquare [6,5,2,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg7232 - -lemma sg8649 : RowSquare [6,5,2,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg535 sg1754 - -lemma sg8650 : RowSquare [6,5,2,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg1327 - -lemma sg8651 : RowSquare [6,5,2,2,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg536 sg1754 - -lemma sg8652 : RowSquare [6,5,2,2,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg537 sg1754 - -lemma sg8653 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg7233 - -lemma sg8654 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg7234 - -lemma sg8655 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg534 sg1757 - -lemma sg8656 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg534 sg1758 - -lemma sg8657 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg541 sg1754 - -lemma sg8658 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg535 sg1755 - -lemma sg8659 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg838 sg1329 - -lemma sg8660 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg542 sg1754 - -lemma sg8661 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1261 - -lemma sg8662 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg838 sg1330 - -lemma sg8663 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg537 sg1755 - -lemma sg8664 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg838 sg1331 - -lemma sg8665 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg1332 - -lemma sg8666 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg543 sg1754 - -lemma sg8667 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg847 sg1327 - -lemma sg8668 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1262 - -lemma sg8669 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg536 sg1756 - -lemma sg8670 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1263 - -lemma sg8671 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg537 sg1756 - -lemma sg8672 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg537 sg1757 - -lemma sg8673 : RowSquare [6,5,2,2,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg848 sg1327 - -lemma sg8674 : RowSquare [6,5,2,2,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg544 sg1754 - -lemma sg8675 : RowSquare [6,5,2,2,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg541 sg1755 - -lemma sg8676 : RowSquare [6,5,2,2,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1264 - -lemma sg8677 : RowSquare [6,5,2,2,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1265 - -lemma sg8678 : RowSquare [6,5,2,2,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1266 - -lemma sg8679 : RowSquare [6,5,2,2,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg545 sg1754 - -lemma sg8680 : RowSquare [6,5,2,2,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg546 sg1754 - -lemma sg8681 : RowSquare [6,5,2,2,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg547 sg1754 - -lemma sg8682 : RowSquare [6,5,2,2,2,2,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg5672 - -lemma sg8683 : RowSquare [6,5,2,2,2,2,1,1] [4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg5673 - -lemma sg8684 : RowSquare [6,5,2,2,2,2,1,1] [4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg5675 - -lemma sg8685 : RowSquare [6,5,2,2,2,2,1,1] [4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg5676 - -lemma sg8686 : RowSquare [6,5,2,2,2,2,1,1] [4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg5677 - -lemma sg8687 : RowSquare [6,5,2,2,2,2,1,1] [4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg5678 - -lemma sg8688 : RowSquare [6,5,2,2,2,2,1,1] [4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg5679 - -lemma sg8689 : RowSquare [6,5,2,2,2,2,1,1] [4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg5695 - -lemma sg8690 : RowSquare [6,5,2,2,2,2,1,1] [4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg5696 - -lemma sg8691 : RowSquare [6,5,2,2,2,2,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg5673 - -lemma sg8692 : RowSquare [6,5,2,2,2,2,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg5675 - -lemma sg8693 : RowSquare [6,5,2,2,2,2,1,1] [5,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg5676 - -lemma sg8694 : RowSquare [6,5,2,2,2,2,1,1] [5,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg5677 - -lemma sg8695 : RowSquare [6,5,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6 sg5678 - -lemma sg8696 : RowSquare [6,5,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6 sg5679 - -lemma sg8697 : RowSquare [6,5,2,2,2,2,1,1] [5,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg5681 - -lemma sg8698 : RowSquare [6,5,2,2,2,2,1,1] [5,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg5682 - -lemma sg8699 : RowSquare [6,5,2,2,2,2,1,1] [5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg5683 - -lemma sg8700 : RowSquare [6,5,2,2,2,2,1,1] [5,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg5684 - -lemma sg8701 : RowSquare [6,5,2,2,2,2,1,1] [5,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5699 - -lemma sg8702 : RowSquare [6,5,2,2,2,2,1,1] [5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg5 sg5696 - -lemma sg8703 : RowSquare [6,5,2,2,2,2,1,1] [6,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg5681 - -lemma sg8704 : RowSquare [6,5,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg5682 - -lemma sg8705 : RowSquare [6,5,2,2,2,2,1,1] [6,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg5683 - -lemma sg8706 : RowSquare [6,5,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6 sg5684 - -lemma sg8707 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg889 sg1338 - -lemma sg8708 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg892 sg1338 - -lemma sg8709 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg905 sg1327 - -lemma sg8710 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg906 sg1327 - -lemma sg8711 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg900 sg1328 - -lemma sg8712 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg907 sg1327 - -lemma sg8713 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg908 sg1327 - -lemma sg8714 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg902 sg1328 - -lemma sg8715 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg903 sg1328 - -lemma sg8716 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,5,5,5] := by - exact rowSquare_join (by decide) sg13 sg4652 - -lemma sg8717 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg909 sg1327 - -lemma sg8718 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg1348 - -lemma sg8719 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg904 sg1332 - -lemma sg8720 : RowSquare [6,6,2,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg807 sg1327 - -lemma sg8721 : RowSquare [6,6,2,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg808 sg1327 - -lemma sg8722 : RowSquare [6,6,2,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg809 sg1327 - -lemma sg8723 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg517 sg1754 - -lemma sg8724 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg810 sg1327 - -lemma sg8725 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6288 - -lemma sg8726 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg518 sg1754 - -lemma sg8727 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg811 sg1327 - -lemma sg8728 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg889 sg1257 - -lemma sg8729 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg519 sg1754 - -lemma sg8730 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg812 sg1327 - -lemma sg8731 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg890 sg1257 - -lemma sg8732 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg520 sg1754 - -lemma sg8733 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg813 sg1327 - -lemma sg8734 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg891 sg1257 - -lemma sg8735 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg892 sg1257 - -lemma sg8736 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg814 sg1327 - -lemma sg8737 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg815 sg1327 - -lemma sg8738 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg807 sg1329 - -lemma sg8739 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg816 sg1327 - -lemma sg8740 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg808 sg1329 - -lemma sg8741 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg809 sg1329 - -lemma sg8742 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg817 sg1327 - -lemma sg8743 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg807 sg1330 - -lemma sg8744 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg808 sg1330 - -lemma sg8745 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg809 sg1330 - -lemma sg8746 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg4673 - -lemma sg8747 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg808 sg1332 - -lemma sg8748 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg809 sg1332 - -lemma sg8749 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg521 sg1754 - -lemma sg8750 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg818 sg1327 - -lemma sg8751 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6289 - -lemma sg8752 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3 sg5525 - -lemma sg8753 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg819 sg1327 - -lemma sg8754 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6291 - -lemma sg8755 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg523 sg1754 - -lemma sg8756 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg820 sg1327 - -lemma sg8757 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg1260 - -lemma sg8758 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg821 sg1327 - -lemma sg8759 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg817 sg1328 - -lemma sg8760 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg4675 - -lemma sg8761 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg4677 - -lemma sg8762 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,4,4,4,4] := by - exact rowSquare_join (by decide) sg892 sg1260 - -lemma sg8763 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg822 sg1327 - -lemma sg8764 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg814 sg1329 - -lemma sg8765 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg816 sg1329 - -lemma sg8766 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg814 sg1332 - -lemma sg8767 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,4,4,3] := by - exact rowSquare_join (by decide) sg13 sg4679 - -lemma sg8768 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,5,3,3] := by - exact rowSquare_join (by decide) sg892 sg1262 - -lemma sg8769 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg4682 - -lemma sg8770 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,5,5,1] := by - exact rowSquare_join (by decide) sg13 sg4684 - -lemma sg8771 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg526 sg1754 - -lemma sg8772 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg824 sg1327 - -lemma sg8773 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg821 sg1328 - -lemma sg8774 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg530 sg1754 - -lemma sg8775 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg4691 - -lemma sg8776 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,5,5,5] := by - exact rowSquare_join (by decide) sg26 sg3875 - -lemma sg8777 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg825 sg1327 - -lemma sg8778 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,6,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg4679 - -lemma sg8779 : RowSquare [6,6,2,1,1,1,1,1,1,1] [7,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg4694 - -lemma sg8781 : RowSquare [6,6,3,2,2,2] [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg787 sg1180 - -lemma sg8782 : RowSquare [6,6,3,2,2,2] [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg781 sg1180 - -lemma sg8783 : RowSquare [6,6,3,2,2,2] [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg770 sg1180 - -lemma sg8784 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg316 sg2251 - -lemma sg8785 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg317 sg2251 - -lemma sg8786 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [4,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg318 sg2251 - -lemma sg8787 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg319 sg2251 - -lemma sg8788 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg320 sg2251 - -lemma sg8789 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg322 sg2251 - -lemma sg8790 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg324 sg2251 - -lemma sg8791 : RowSquare [7,5,2,1,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg270 sg2251 - -lemma sg8792 : RowSquare [7,5,2,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg1663 - -lemma sg8793 : RowSquare [7,5,2,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg271 sg2251 - -lemma sg8794 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg132 sg2702 - -lemma sg8795 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg272 sg2251 - -lemma sg8796 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6349 - -lemma sg8797 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6350 - -lemma sg8798 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg6288 - -lemma sg8799 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg133 sg2702 - -lemma sg8800 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg273 sg2251 - -lemma sg8801 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg7780 - -lemma sg8802 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg7781 - -lemma sg8803 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg7782 - -lemma sg8804 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg1664 - -lemma sg8805 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg134 sg2702 - -lemma sg8806 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg274 sg2251 - -lemma sg8807 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg7783 - -lemma sg8808 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg7784 - -lemma sg8809 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5414 - -lemma sg8810 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5415 - -lemma sg8811 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg7786 - -lemma sg8812 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg7787 - -lemma sg8813 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg7788 - -lemma sg8814 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg7789 - -lemma sg8815 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg275 sg2251 - -lemma sg8816 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg276 sg2251 - -lemma sg8817 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg270 sg2253 - -lemma sg8818 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5416 - -lemma sg8819 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg271 sg2253 - -lemma sg8820 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5418 - -lemma sg8821 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5419 - -lemma sg8822 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5420 - -lemma sg8823 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5421 - -lemma sg8824 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5422 - -lemma sg8825 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5423 - -lemma sg8826 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg4724 - -lemma sg8827 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg135 sg2702 - -lemma sg8828 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6351 - -lemma sg8829 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg6289 - -lemma sg8830 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg6290 - -lemma sg8831 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg136 sg2702 - -lemma sg8832 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6352 - -lemma sg8833 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg279 sg2251 - -lemma sg8834 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg4725 - -lemma sg8835 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg6292 - -lemma sg8836 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg137 sg2702 - -lemma sg8837 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg280 sg2251 - -lemma sg8838 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg7793 - -lemma sg8839 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg4726 - -lemma sg8840 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5427 - -lemma sg8841 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,4,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg7796 - -lemma sg8842 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg281 sg2251 - -lemma sg8843 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg275 sg2253 - -lemma sg8844 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg4741 - -lemma sg8845 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg276 sg2253 - -lemma sg8846 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg4727 - -lemma sg8847 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5428 - -lemma sg8848 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5430 - -lemma sg8849 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg138 sg2702 - -lemma sg8850 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg282 sg2251 - -lemma sg8851 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6353 - -lemma sg8852 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg139 sg2702 - -lemma sg8853 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg283 sg2251 - -lemma sg8854 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6354 - -lemma sg8855 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6355 - -lemma sg8856 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg284 sg2251 - -lemma sg8857 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6356 - -lemma sg8858 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg7798 - -lemma sg8859 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg281 sg2253 - -lemma sg8860 : RowSquare [7,6,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5525 - -lemma sg8861 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg5525 - -lemma sg8862 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5526 - -lemma sg8863 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg4740 - -lemma sg8864 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5527 - -lemma sg8865 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg4741 - -lemma sg8866 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg4742 - -lemma sg8867 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5528 - -lemma sg8868 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg4743 - -lemma sg8869 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg4744 - -lemma sg8870 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg4745 - -lemma sg8871 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg260 sg2251 - -lemma sg8872 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6391 - -lemma sg8873 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6 sg5525 - -lemma sg8874 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg261 sg2251 - -lemma sg8875 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6393 - -lemma sg8876 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg5526 - -lemma sg8877 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg262 sg2251 - -lemma sg8878 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6395 - -lemma sg8879 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5530 - -lemma sg8880 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6397 - -lemma sg8881 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6398 - -lemma sg8882 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,4,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg7807 - -lemma sg8883 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,5,4,4,3] := by - exact rowSquare_join (by decide) sg13 sg4751 - -lemma sg8884 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,5,5,3,3] := by - exact rowSquare_join (by decide) sg4 sg5550 - -lemma sg8885 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg4752 - -lemma sg8886 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,5,5,5,1] := by - exact rowSquare_join (by decide) sg13 sg4753 - -lemma sg8887 : RowSquare [7,6,1,1,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg263 sg2251 - -lemma sg8888 : RowSquare [7,6,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6399 - -lemma sg8889 : RowSquare [7,6,1,1,1,1,1,1,1,1] [6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg4754 - -lemma sg8890 : RowSquare [8,3,2,2,2,2,2] [6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg165 sg2550 - -lemma sg8891 : RowSquare [8,4,3,2,1,1,1,1] [2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1056 sg1129 - -lemma sg8892 : RowSquare [8,4,3,2,1,1,1,1] [2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1056 sg1128 - -lemma sg8893 : RowSquare [9,3,2,2,2,2,1] [4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg3209 - -lemma sg8894 : RowSquare [9,3,2,2,2,2,1] [5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg3213 - -lemma sg8895 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4] := by - exact rowSquare_join (by decide) sg1105 sg1980 - -lemma sg8896 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1416 sg1538 - -lemma sg8897 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1416 sg1539 - -lemma sg8898 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1032 sg1926 - -lemma sg8899 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1033 sg1926 - -lemma sg8900 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1417 sg1541 - -lemma sg8901 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1460 sg1518 - -lemma sg8902 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1417 sg1542 - -lemma sg8903 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,5,5] := by - exact rowSquare_join (by decide) sg1072 sg1908 - -lemma sg8904 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,6,4] := by - exact rowSquare_join (by decide) sg1539 sg1426 - -lemma sg8905 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [7,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1524 sg1460 - -lemma sg8906 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [7,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1417 sg1547 - -lemma sg8907 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [8,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg1570 - -lemma sg8908 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [8,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg1572 - -lemma sg8909 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1517 sg1552 - -lemma sg8910 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1552 sg1518 - -lemma sg8911 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] [9,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1524 sg1552 - -lemma sg8912 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1416 sg1517 - -lemma sg8913 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1417 sg1517 - -lemma sg8914 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1417 sg1518 - -lemma sg8915 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1416 sg1520 - -lemma sg8916 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1032 sg1903 - -lemma sg8917 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1417 sg1520 - -lemma sg8918 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1031 sg1904 - -lemma sg8919 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1032 sg1905 - -lemma sg8920 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1033 sg1905 - -lemma sg8921 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1032 sg1908 - -lemma sg8922 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1033 sg1908 - -lemma sg8923 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1416 sg1524 - -lemma sg8924 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1524 sg1417 - -lemma sg8925 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1034 sg1903 - -lemma sg8926 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1416 sg1525 - -lemma sg8927 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1417 sg1525 - -lemma sg8928 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1517 sg1419 - -lemma sg8929 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1418 sg1520 - -lemma sg8930 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1517 sg1422 - -lemma sg8931 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1520 sg1422 - -lemma sg8932 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg1032 sg1913 - -lemma sg8933 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,5,5] := by - exact rowSquare_join (by decide) sg1040 sg1908 - -lemma sg8934 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1418 sg1524 - -lemma sg8935 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1416 sg1530 - -lemma sg8936 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1417 sg1530 - -lemma sg8937 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1418 sg1525 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes18 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes15 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes16 + +namespace OAI + +/-! Semigroup Nodes 20. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg8537 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1005 sg1327 + +lemma sg8538 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1328 + +lemma sg8539 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1331 + +lemma sg8540 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1328 + +lemma sg8541 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1332 + +lemma sg8542 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1006 sg1327 + +lemma sg8543 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1329 + +lemma sg8544 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1007 sg1327 + +lemma sg8545 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg1329 + +lemma sg8546 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg1330 + +lemma sg8547 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1008 sg1327 + +lemma sg8548 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1329 + +lemma sg8549 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1331 + +lemma sg8550 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1332 + +lemma sg8551 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1330 + +lemma sg8552 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1330 + +lemma sg8553 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg1331 + +lemma sg8554 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1330 + +lemma sg8555 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg999 sg1332 + +lemma sg8556 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1331 + +lemma sg8557 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1331 + +lemma sg8558 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg1000 sg1332 + +lemma sg8559 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg1001 sg1332 + +lemma sg8560 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1009 sg1327 + +lemma sg8561 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1328 + +lemma sg8562 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6905 + +lemma sg8563 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1003 sg1328 + +lemma sg8564 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg6906 + +lemma sg8565 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1004 sg1328 + +lemma sg8566 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg6907 + +lemma sg8567 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1002 sg1330 + +lemma sg8568 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1005 sg1328 + +lemma sg8569 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1002 sg1331 + +lemma sg8570 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1332 + +lemma sg8571 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1338 + +lemma sg8572 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6910 + +lemma sg8573 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1008 sg1328 + +lemma sg8574 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1003 sg1331 + +lemma sg8575 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1003 sg1332 + +lemma sg8576 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1004 sg1330 + +lemma sg8577 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1005 sg1330 + +lemma sg8578 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg1004 sg1332 + +lemma sg8579 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1005 sg1331 + +lemma sg8580 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg0 sg6917 + +lemma sg8581 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg0 sg6918 + +lemma sg8582 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg6919 + +lemma sg8583 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1015 sg1327 + +lemma sg8584 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1006 sg1329 + +lemma sg8585 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1338 + +lemma sg8586 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1016 sg1327 + +lemma sg8587 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1007 sg1329 + +lemma sg8588 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1339 + +lemma sg8589 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg1338 + +lemma sg8590 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1008 sg1329 + +lemma sg8591 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1340 + +lemma sg8592 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1338 + +lemma sg8593 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1338 + +lemma sg8594 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg1006 sg1332 + +lemma sg8595 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1008 sg1330 + +lemma sg8596 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg1000 sg1339 + +lemma sg8597 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1008 sg1331 + +lemma sg8598 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1340 + +lemma sg8599 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,3] := by + exact rowSquare_join (by decide) sg1001 sg1340 + +lemma sg8600 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1009 sg1328 + +lemma sg8601 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1012 sg1330 + +lemma sg8602 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1006 sg1338 + +lemma sg8603 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1016 sg1329 + +lemma sg8604 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg1006 sg1339 + +lemma sg8605 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3] := by + exact rowSquare_join (by decide) sg1001 sg1348 + +lemma sg8606 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,1] := by + exact rowSquare_join (by decide) sg1008 sg1340 + +lemma sg8607 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1022 sg1328 + +lemma sg8608 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1023 sg1328 + +lemma sg8609 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1003 sg1348 + +lemma sg8610 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg6995 + +lemma sg8611 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1023 sg1329 + +lemma sg8612 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1015 sg1338 + +lemma sg8613 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,1] := by + exact rowSquare_join (by decide) sg1006 sg1348 + +lemma sg8614 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,1] := by + exact rowSquare_join (by decide) sg1008 sg1348 + +lemma sg8615 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg910 sg1327 + +lemma sg8616 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg1754 + +lemma sg8617 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg1754 + +lemma sg8618 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg1754 + +lemma sg8619 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg914 sg1327 + +lemma sg8620 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg591 sg1754 + +lemma sg8621 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg592 sg1754 + +lemma sg8622 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg593 sg1754 + +lemma sg8623 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg594 sg1754 + +lemma sg8624 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg595 sg1754 + +lemma sg8625 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg1754 + +lemma sg8626 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg915 sg1332 + +lemma sg8627 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg597 sg1754 + +lemma sg8628 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg598 sg1754 + +lemma sg8629 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg599 sg1754 + +lemma sg8630 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg600 sg1754 + +lemma sg8631 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg601 sg1754 + +lemma sg8632 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg930 sg1327 + +lemma sg8633 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg923 sg1328 + +lemma sg8634 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg1754 + +lemma sg8635 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg931 sg1327 + +lemma sg8636 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg932 sg1327 + +lemma sg8637 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg923 sg1330 + +lemma sg8638 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg939 sg1327 + +lemma sg8639 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [7,7,6,1] := by + exact rowSquare_join (by decide) sg13 sg4619 + +lemma sg8640 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,6,6,1] := by + exact rowSquare_join (by decide) sg39 sg3764 + +lemma sg8641 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,7,5,1] := by + exact rowSquare_join (by decide) sg39 sg3765 + +lemma sg8642 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,7,6] := by + exact rowSquare_join (by decide) sg40 sg3764 + +lemma sg8643 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,8,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg4616 + +lemma sg8644 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,8,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg4617 + +lemma sg8645 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,8,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg4620 + +lemma sg8646 : RowSquare [6,5,2,1,1,1,1,1,1,1,1] [8,8,3,1,1] := by + exact rowSquare_join (by decide) sg14 sg4618 + +lemma sg8647 : RowSquare [6,5,2,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg534 sg1754 + +lemma sg8648 : RowSquare [6,5,2,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg7232 + +lemma sg8649 : RowSquare [6,5,2,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg535 sg1754 + +lemma sg8650 : RowSquare [6,5,2,2,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg1327 + +lemma sg8651 : RowSquare [6,5,2,2,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg536 sg1754 + +lemma sg8652 : RowSquare [6,5,2,2,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg537 sg1754 + +lemma sg8653 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg7233 + +lemma sg8654 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg7234 + +lemma sg8655 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg534 sg1757 + +lemma sg8656 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg534 sg1758 + +lemma sg8657 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg541 sg1754 + +lemma sg8658 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg535 sg1755 + +lemma sg8659 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg838 sg1329 + +lemma sg8660 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg542 sg1754 + +lemma sg8661 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1261 + +lemma sg8662 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg838 sg1330 + +lemma sg8663 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg537 sg1755 + +lemma sg8664 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg838 sg1331 + +lemma sg8665 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg1332 + +lemma sg8666 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg543 sg1754 + +lemma sg8667 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg847 sg1327 + +lemma sg8668 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1262 + +lemma sg8669 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg536 sg1756 + +lemma sg8670 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1263 + +lemma sg8671 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg537 sg1756 + +lemma sg8672 : RowSquare [6,5,2,2,1,1,1,1,1,1] [4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg537 sg1757 + +lemma sg8673 : RowSquare [6,5,2,2,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg848 sg1327 + +lemma sg8674 : RowSquare [6,5,2,2,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg544 sg1754 + +lemma sg8675 : RowSquare [6,5,2,2,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg541 sg1755 + +lemma sg8676 : RowSquare [6,5,2,2,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1264 + +lemma sg8677 : RowSquare [6,5,2,2,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1265 + +lemma sg8678 : RowSquare [6,5,2,2,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1266 + +lemma sg8679 : RowSquare [6,5,2,2,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg545 sg1754 + +lemma sg8680 : RowSquare [6,5,2,2,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg546 sg1754 + +lemma sg8681 : RowSquare [6,5,2,2,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg547 sg1754 + +lemma sg8682 : RowSquare [6,5,2,2,2,2,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg5672 + +lemma sg8683 : RowSquare [6,5,2,2,2,2,1,1] [4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg5673 + +lemma sg8684 : RowSquare [6,5,2,2,2,2,1,1] [4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg5675 + +lemma sg8685 : RowSquare [6,5,2,2,2,2,1,1] [4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg5676 + +lemma sg8686 : RowSquare [6,5,2,2,2,2,1,1] [4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg5677 + +lemma sg8687 : RowSquare [6,5,2,2,2,2,1,1] [4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg5678 + +lemma sg8688 : RowSquare [6,5,2,2,2,2,1,1] [4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg5679 + +lemma sg8689 : RowSquare [6,5,2,2,2,2,1,1] [4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg5695 + +lemma sg8690 : RowSquare [6,5,2,2,2,2,1,1] [4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg5696 + +lemma sg8691 : RowSquare [6,5,2,2,2,2,1,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg5673 + +lemma sg8692 : RowSquare [6,5,2,2,2,2,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg5675 + +lemma sg8693 : RowSquare [6,5,2,2,2,2,1,1] [5,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg5676 + +lemma sg8694 : RowSquare [6,5,2,2,2,2,1,1] [5,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg5677 + +lemma sg8695 : RowSquare [6,5,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6 sg5678 + +lemma sg8696 : RowSquare [6,5,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6 sg5679 + +lemma sg8697 : RowSquare [6,5,2,2,2,2,1,1] [5,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg5681 + +lemma sg8698 : RowSquare [6,5,2,2,2,2,1,1] [5,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg5682 + +lemma sg8699 : RowSquare [6,5,2,2,2,2,1,1] [5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg5683 + +lemma sg8700 : RowSquare [6,5,2,2,2,2,1,1] [5,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg5684 + +lemma sg8701 : RowSquare [6,5,2,2,2,2,1,1] [5,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5699 + +lemma sg8702 : RowSquare [6,5,2,2,2,2,1,1] [5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg5 sg5696 + +lemma sg8703 : RowSquare [6,5,2,2,2,2,1,1] [6,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg5681 + +lemma sg8704 : RowSquare [6,5,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg5682 + +lemma sg8705 : RowSquare [6,5,2,2,2,2,1,1] [6,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg5683 + +lemma sg8706 : RowSquare [6,5,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6 sg5684 + +lemma sg8707 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg889 sg1338 + +lemma sg8708 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg892 sg1338 + +lemma sg8709 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg905 sg1327 + +lemma sg8710 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg906 sg1327 + +lemma sg8711 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg900 sg1328 + +lemma sg8712 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg907 sg1327 + +lemma sg8713 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg908 sg1327 + +lemma sg8714 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg902 sg1328 + +lemma sg8715 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg903 sg1328 + +lemma sg8716 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,5,5,5] := by + exact rowSquare_join (by decide) sg13 sg4652 + +lemma sg8717 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg909 sg1327 + +lemma sg8718 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg1348 + +lemma sg8719 : RowSquare [6,6,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg904 sg1332 + +lemma sg8720 : RowSquare [6,6,2,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg807 sg1327 + +lemma sg8721 : RowSquare [6,6,2,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg808 sg1327 + +lemma sg8722 : RowSquare [6,6,2,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg809 sg1327 + +lemma sg8723 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg517 sg1754 + +lemma sg8724 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg810 sg1327 + +lemma sg8725 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6288 + +lemma sg8726 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg518 sg1754 + +lemma sg8727 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg811 sg1327 + +lemma sg8728 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg889 sg1257 + +lemma sg8729 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg519 sg1754 + +lemma sg8730 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg812 sg1327 + +lemma sg8731 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg890 sg1257 + +lemma sg8732 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg520 sg1754 + +lemma sg8733 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg813 sg1327 + +lemma sg8734 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg891 sg1257 + +lemma sg8735 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg892 sg1257 + +lemma sg8736 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg814 sg1327 + +lemma sg8737 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg815 sg1327 + +lemma sg8738 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg807 sg1329 + +lemma sg8739 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg816 sg1327 + +lemma sg8740 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg808 sg1329 + +lemma sg8741 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg809 sg1329 + +lemma sg8742 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg817 sg1327 + +lemma sg8743 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg807 sg1330 + +lemma sg8744 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg808 sg1330 + +lemma sg8745 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg809 sg1330 + +lemma sg8746 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg4673 + +lemma sg8747 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg808 sg1332 + +lemma sg8748 : RowSquare [6,6,2,1,1,1,1,1,1,1] [4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg809 sg1332 + +lemma sg8749 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg521 sg1754 + +lemma sg8750 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg818 sg1327 + +lemma sg8751 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6289 + +lemma sg8752 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3 sg5525 + +lemma sg8753 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg819 sg1327 + +lemma sg8754 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6291 + +lemma sg8755 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg523 sg1754 + +lemma sg8756 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg820 sg1327 + +lemma sg8757 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg1260 + +lemma sg8758 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg821 sg1327 + +lemma sg8759 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg817 sg1328 + +lemma sg8760 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg4675 + +lemma sg8761 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg4677 + +lemma sg8762 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,4,4,4,4] := by + exact rowSquare_join (by decide) sg892 sg1260 + +lemma sg8763 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg822 sg1327 + +lemma sg8764 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg814 sg1329 + +lemma sg8765 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg816 sg1329 + +lemma sg8766 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg814 sg1332 + +lemma sg8767 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,4,4,3] := by + exact rowSquare_join (by decide) sg13 sg4679 + +lemma sg8768 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,5,3,3] := by + exact rowSquare_join (by decide) sg892 sg1262 + +lemma sg8769 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg4682 + +lemma sg8770 : RowSquare [6,6,2,1,1,1,1,1,1,1] [5,5,5,5,1] := by + exact rowSquare_join (by decide) sg13 sg4684 + +lemma sg8771 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg526 sg1754 + +lemma sg8772 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg824 sg1327 + +lemma sg8773 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg821 sg1328 + +lemma sg8774 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg530 sg1754 + +lemma sg8775 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg4691 + +lemma sg8776 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,5,5,5] := by + exact rowSquare_join (by decide) sg26 sg3875 + +lemma sg8777 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg825 sg1327 + +lemma sg8778 : RowSquare [6,6,2,1,1,1,1,1,1,1] [6,6,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg4679 + +lemma sg8779 : RowSquare [6,6,2,1,1,1,1,1,1,1] [7,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg4694 + +lemma sg8781 : RowSquare [6,6,3,2,2,2] [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg787 sg1180 + +lemma sg8782 : RowSquare [6,6,3,2,2,2] [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg781 sg1180 + +lemma sg8783 : RowSquare [6,6,3,2,2,2] [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg770 sg1180 + +lemma sg8784 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg316 sg2251 + +lemma sg8785 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg317 sg2251 + +lemma sg8786 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [4,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg318 sg2251 + +lemma sg8787 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg319 sg2251 + +lemma sg8788 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg320 sg2251 + +lemma sg8789 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg322 sg2251 + +lemma sg8790 : RowSquare [7,5,1,1,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg324 sg2251 + +lemma sg8791 : RowSquare [7,5,2,1,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg270 sg2251 + +lemma sg8792 : RowSquare [7,5,2,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg1663 + +lemma sg8793 : RowSquare [7,5,2,1,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg271 sg2251 + +lemma sg8794 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg132 sg2702 + +lemma sg8795 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg272 sg2251 + +lemma sg8796 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6349 + +lemma sg8797 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6350 + +lemma sg8798 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg6288 + +lemma sg8799 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg133 sg2702 + +lemma sg8800 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg273 sg2251 + +lemma sg8801 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg7780 + +lemma sg8802 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg7781 + +lemma sg8803 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg7782 + +lemma sg8804 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg1664 + +lemma sg8805 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg134 sg2702 + +lemma sg8806 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg274 sg2251 + +lemma sg8807 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg7783 + +lemma sg8808 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg7784 + +lemma sg8809 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5414 + +lemma sg8810 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5415 + +lemma sg8811 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg7786 + +lemma sg8812 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg7787 + +lemma sg8813 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg7788 + +lemma sg8814 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg7789 + +lemma sg8815 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg275 sg2251 + +lemma sg8816 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg276 sg2251 + +lemma sg8817 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg270 sg2253 + +lemma sg8818 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5416 + +lemma sg8819 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg271 sg2253 + +lemma sg8820 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5418 + +lemma sg8821 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5419 + +lemma sg8822 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5420 + +lemma sg8823 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5421 + +lemma sg8824 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5422 + +lemma sg8825 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5423 + +lemma sg8826 : RowSquare [7,5,2,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg4724 + +lemma sg8827 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg135 sg2702 + +lemma sg8828 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6351 + +lemma sg8829 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg6289 + +lemma sg8830 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg6290 + +lemma sg8831 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg136 sg2702 + +lemma sg8832 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6352 + +lemma sg8833 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg279 sg2251 + +lemma sg8834 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg4725 + +lemma sg8835 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg6292 + +lemma sg8836 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg137 sg2702 + +lemma sg8837 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg280 sg2251 + +lemma sg8838 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg7793 + +lemma sg8839 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg4726 + +lemma sg8840 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5427 + +lemma sg8841 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,4,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg7796 + +lemma sg8842 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg281 sg2251 + +lemma sg8843 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg275 sg2253 + +lemma sg8844 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg4741 + +lemma sg8845 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg276 sg2253 + +lemma sg8846 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg4727 + +lemma sg8847 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5428 + +lemma sg8848 : RowSquare [7,5,2,1,1,1,1,1,1,1] [5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5430 + +lemma sg8849 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg138 sg2702 + +lemma sg8850 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg282 sg2251 + +lemma sg8851 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6353 + +lemma sg8852 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg139 sg2702 + +lemma sg8853 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg283 sg2251 + +lemma sg8854 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6354 + +lemma sg8855 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6355 + +lemma sg8856 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg284 sg2251 + +lemma sg8857 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6356 + +lemma sg8858 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg7798 + +lemma sg8859 : RowSquare [7,5,2,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg281 sg2253 + +lemma sg8860 : RowSquare [7,6,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5525 + +lemma sg8861 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg5525 + +lemma sg8862 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5526 + +lemma sg8863 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg4740 + +lemma sg8864 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5527 + +lemma sg8865 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg4741 + +lemma sg8866 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg4742 + +lemma sg8867 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5528 + +lemma sg8868 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg4743 + +lemma sg8869 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg4744 + +lemma sg8870 : RowSquare [7,6,1,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg4745 + +lemma sg8871 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg260 sg2251 + +lemma sg8872 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6391 + +lemma sg8873 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6 sg5525 + +lemma sg8874 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg261 sg2251 + +lemma sg8875 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6393 + +lemma sg8876 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg5526 + +lemma sg8877 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg262 sg2251 + +lemma sg8878 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6395 + +lemma sg8879 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5530 + +lemma sg8880 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6397 + +lemma sg8881 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6398 + +lemma sg8882 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,4,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg7807 + +lemma sg8883 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,5,4,4,3] := by + exact rowSquare_join (by decide) sg13 sg4751 + +lemma sg8884 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,5,5,3,3] := by + exact rowSquare_join (by decide) sg4 sg5550 + +lemma sg8885 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg4752 + +lemma sg8886 : RowSquare [7,6,1,1,1,1,1,1,1,1] [5,5,5,5,1] := by + exact rowSquare_join (by decide) sg13 sg4753 + +lemma sg8887 : RowSquare [7,6,1,1,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg263 sg2251 + +lemma sg8888 : RowSquare [7,6,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6399 + +lemma sg8889 : RowSquare [7,6,1,1,1,1,1,1,1,1] [6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg4754 + +lemma sg8890 : RowSquare [8,3,2,2,2,2,2] [6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg165 sg2550 + +lemma sg8891 : RowSquare [8,4,3,2,1,1,1,1] [2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1056 sg1129 + +lemma sg8892 : RowSquare [8,4,3,2,1,1,1,1] [2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1056 sg1128 + +lemma sg8893 : RowSquare [9,3,2,2,2,2,1] [4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg3209 + +lemma sg8894 : RowSquare [9,3,2,2,2,2,1] [5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg3213 + +lemma sg8895 : RowSquare [3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4] := by + exact rowSquare_join (by decide) sg1105 sg1980 + +lemma sg8896 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1416 sg1538 + +lemma sg8897 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1416 sg1539 + +lemma sg8898 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1032 sg1926 + +lemma sg8899 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1033 sg1926 + +lemma sg8900 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1417 sg1541 + +lemma sg8901 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1460 sg1518 + +lemma sg8902 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1417 sg1542 + +lemma sg8903 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,5,5] := by + exact rowSquare_join (by decide) sg1072 sg1908 + +lemma sg8904 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [6,6,6,4] := by + exact rowSquare_join (by decide) sg1539 sg1426 + +lemma sg8905 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [7,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1524 sg1460 + +lemma sg8906 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [7,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1417 sg1547 + +lemma sg8907 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [8,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg1570 + +lemma sg8908 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1] [8,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg1572 + +lemma sg8909 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1517 sg1552 + +lemma sg8910 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1552 sg1518 + +lemma sg8911 : RowSquare [4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] [9,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1524 sg1552 + +lemma sg8912 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1416 sg1517 + +lemma sg8913 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1417 sg1517 + +lemma sg8914 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1417 sg1518 + +lemma sg8915 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1416 sg1520 + +lemma sg8916 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1032 sg1903 + +lemma sg8917 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1417 sg1520 + +lemma sg8918 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1031 sg1904 + +lemma sg8919 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1032 sg1905 + +lemma sg8920 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1033 sg1905 + +lemma sg8921 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1032 sg1908 + +lemma sg8922 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1033 sg1908 + +lemma sg8923 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1416 sg1524 + +lemma sg8924 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1524 sg1417 + +lemma sg8925 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1034 sg1903 + +lemma sg8926 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1416 sg1525 + +lemma sg8927 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1417 sg1525 + +lemma sg8928 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1517 sg1419 + +lemma sg8929 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1418 sg1520 + +lemma sg8930 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1517 sg1422 + +lemma sg8931 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1520 sg1422 + +lemma sg8932 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg1032 sg1913 + +lemma sg8933 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,5,5] := by + exact rowSquare_join (by decide) sg1040 sg1908 + +lemma sg8934 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1418 sg1524 + +lemma sg8935 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1416 sg1530 + +lemma sg8936 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1417 sg1530 + +lemma sg8937 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1418 sg1525 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes21.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes21.lean index cb5a90a96c757e091a459878374901bc3cf7af2d..40f455af41dafe3435ee20a1f2c6f32107ea4f54 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes21.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes21.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes18 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes19 - -namespace OAI - -/-! Semigroup Nodes 21. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg8938 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1517 sg1428 - -lemma sg8939 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1520 sg1428 - -lemma sg8940 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1552 - -lemma sg8941 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1553 - -lemma sg8942 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1499 sg1552 - -lemma sg8943 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1554 - -lemma sg8944 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1500 sg1552 - -lemma sg8945 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1555 - -lemma sg8946 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1552 sg1501 - -lemma sg8947 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1552 sg1502 - -lemma sg8948 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1500 sg1553 - -lemma sg8949 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg1501 sg1553 - -lemma sg8950 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1553 sg1502 - -lemma sg8951 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1500 sg1554 - -lemma sg8952 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1500 sg1555 - -lemma sg8953 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1501 sg1554 - -lemma sg8954 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3] := by - exact rowSquare_join (by decide) sg1502 sg1554 - -lemma sg8955 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1501 sg1555 - -lemma sg8956 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,2] := by - exact rowSquare_join (by decide) sg1502 sg1555 - -lemma sg8957 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1556 - -lemma sg8958 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1503 sg1552 - -lemma sg8959 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1557 - -lemma sg8960 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1499 sg1556 - -lemma sg8961 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1504 sg1552 - -lemma sg8962 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1558 - -lemma sg8963 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1503 sg1554 - -lemma sg8964 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1500 sg1556 - -lemma sg8965 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1503 sg1555 - -lemma sg8966 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1501 sg1556 - -lemma sg8967 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1556 sg1502 - -lemma sg8968 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1559 - -lemma sg8969 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1499 sg1557 - -lemma sg8970 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1504 sg1553 - -lemma sg8971 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1560 - -lemma sg8972 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1499 sg1558 - -lemma sg8973 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1500 sg1557 - -lemma sg8974 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1505 sg1553 - -lemma sg8975 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1504 sg1555 - -lemma sg8976 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,3] := by - exact rowSquare_join (by decide) sg1502 sg1557 - -lemma sg8977 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1500 sg1558 - -lemma sg8978 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1505 sg1554 - -lemma sg8979 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1501 sg1558 - -lemma sg8980 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1507 sg1553 - -lemma sg8981 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1891 - -lemma sg8982 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg2310 - -lemma sg8983 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg2311 - -lemma sg8984 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg2312 - -lemma sg8985 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg911 sg1891 - -lemma sg8986 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg2310 - -lemma sg8987 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2314 - -lemma sg8988 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg587 sg2311 - -lemma sg8989 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1894 - -lemma sg8990 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg2316 - -lemma sg8991 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1895 - -lemma sg8992 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2317 - -lemma sg8993 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg912 sg1891 - -lemma sg8994 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg588 sg2311 - -lemma sg8995 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg941 sg1874 - -lemma sg8996 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg589 sg2310 - -lemma sg8997 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg913 sg1891 - -lemma sg8998 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg589 sg2311 - -lemma sg8999 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2319 - -lemma sg9000 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg2310 - -lemma sg9001 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg914 sg1891 - -lemma sg9002 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg915 sg1891 - -lemma sg9003 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1092 sg1682 - -lemma sg9004 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1288 sg1498 - -lemma sg9005 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1093 sg1682 - -lemma sg9006 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1094 sg1682 - -lemma sg9007 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg1500 - -lemma sg9008 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg1794 - -lemma sg9009 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1095 sg1682 - -lemma sg9010 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1795 - -lemma sg9011 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg2312 - -lemma sg9012 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg1502 - -lemma sg9013 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1796 - -lemma sg9014 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8116 - -lemma sg9015 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg587 sg2314 - -lemma sg9016 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg0 sg8117 - -lemma sg9017 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg1797 - -lemma sg9018 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1798 - -lemma sg9019 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg940 sg1876 - -lemma sg9020 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1799 - -lemma sg9021 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8118 - -lemma sg9022 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1800 - -lemma sg9023 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8119 - -lemma sg9024 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg8120 - -lemma sg9025 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg8121 - -lemma sg9026 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1801 - -lemma sg9027 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8122 - -lemma sg9028 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1802 - -lemma sg9029 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg942 sg1876 - -lemma sg9030 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8123 - -lemma sg9031 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8124 - -lemma sg9032 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg0 sg8125 - -lemma sg9033 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg589 sg2314 - -lemma sg9034 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2323 - -lemma sg9035 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8126 - -lemma sg9036 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8127 - -lemma sg9037 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg8128 - -lemma sg9038 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg1000 sg1796 - -lemma sg9039 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg1001 sg1796 - -lemma sg9040 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1898 - -lemma sg9041 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg2324 - -lemma sg9042 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg1797 - -lemma sg9043 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg948 sg1874 - -lemma sg9044 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg940 sg1877 - -lemma sg9045 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1899 - -lemma sg9046 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2325 - -lemma sg9047 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1799 - -lemma sg9048 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg2316 - -lemma sg9049 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1800 - -lemma sg9050 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg920 sg1891 - -lemma sg9051 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg371 sg2746 - -lemma sg9052 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg949 sg1874 - -lemma sg9053 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg940 sg1878 - -lemma sg9054 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg941 sg1877 - -lemma sg9055 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg950 sg1874 - -lemma sg9056 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg940 sg1879 - -lemma sg9057 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1799 - -lemma sg9058 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg999 sg1800 - -lemma sg9059 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg615 sg2281 - -lemma sg9060 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg2921 - -lemma sg9061 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg922 sg1891 - -lemma sg9062 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1000 sg1799 - -lemma sg9063 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1000 sg1800 - -lemma sg9064 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,4] := by - exact rowSquare_join (by decide) sg1001 sg1800 - -lemma sg9065 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1900 - -lemma sg9066 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg951 sg1874 - -lemma sg9067 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg2922 - -lemma sg9068 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg941 sg1878 - -lemma sg9069 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg2923 - -lemma sg9070 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg941 sg1879 - -lemma sg9071 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg942 sg1878 - -lemma sg9072 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg943 sg1878 - -lemma sg9073 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg315 sg3006 - -lemma sg9074 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg942 sg1879 - -lemma sg9075 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,4,3] := by - exact rowSquare_join (by decide) sg943 sg1879 - -lemma sg9076 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg373 sg2748 - -lemma sg9077 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,2] := by - exact rowSquare_join (by decide) sg616 sg2282 - -lemma sg9078 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1289 sg1498 - -lemma sg9079 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1289 sg1499 - -lemma sg9080 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1289 sg1500 - -lemma sg9081 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg944 sg1876 - -lemma sg9082 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg1501 - -lemma sg9083 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8129 - -lemma sg9084 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg1502 - -lemma sg9085 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8130 - -lemma sg9086 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg8131 - -lemma sg9087 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg8132 - -lemma sg9088 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1372 sg1411 - -lemma sg9089 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1408 sg1373 - -lemma sg9090 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1292 - -lemma sg9091 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8133 - -lemma sg9092 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1372 sg1412 - -lemma sg9093 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8134 - -lemma sg9094 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8135 - -lemma sg9095 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8136 - -lemma sg9096 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg0 sg8137 - -lemma sg9097 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg8138 - -lemma sg9098 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1293 - -lemma sg9099 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8139 - -lemma sg9100 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8140 - -lemma sg9101 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1294 - -lemma sg9102 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8141 - -lemma sg9103 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8142 - -lemma sg9104 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg6556 - -lemma sg9105 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg0 sg8143 - -lemma sg9106 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8144 - -lemma sg9107 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6557 - -lemma sg9108 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg0 sg8145 - -lemma sg9109 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg6558 - -lemma sg9110 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg6559 - -lemma sg9111 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1804 - -lemma sg9112 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8146 - -lemma sg9113 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1805 - -lemma sg9114 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8147 - -lemma sg9115 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8148 - -lemma sg9116 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1806 - -lemma sg9117 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8149 - -lemma sg9118 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8150 - -lemma sg9119 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg8151 - -lemma sg9120 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg0 sg8152 - -lemma sg9121 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1807 - -lemma sg9122 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8153 - -lemma sg9123 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8154 - -lemma sg9124 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8155 - -lemma sg9125 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8156 - -lemma sg9126 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg8157 - -lemma sg9127 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg8158 - -lemma sg9128 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8159 - -lemma sg9129 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg0 sg8160 - -lemma sg9130 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,4,3] := by - exact rowSquare_join (by decide) sg0 sg8161 - -lemma sg9131 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1808 - -lemma sg9132 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8162 - -lemma sg9133 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8163 - -lemma sg9134 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg946 sg1878 - -lemma sg9135 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8164 - -lemma sg9136 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg0 sg8165 - -lemma sg9137 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,3,3] := by - exact rowSquare_join (by decide) sg4 sg5794 - -lemma sg9138 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg0 sg8166 - -lemma sg9139 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,4,2] := by - exact rowSquare_join (by decide) sg4 sg5795 - -lemma sg9140 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,1] := by - exact rowSquare_join (by decide) sg0 sg8167 - -lemma sg9141 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2328 - -lemma sg9142 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg940 sg1883 - -lemma sg9143 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg614 sg2283 - -lemma sg9144 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg956 sg1874 - -lemma sg9145 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg940 sg1884 - -lemma sg9146 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1411 sg1377 - -lemma sg9147 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg940 sg1885 - -lemma sg9148 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg931 sg1891 - -lemma sg9149 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg1774 - -lemma sg9150 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg1006 sg1800 - -lemma sg9151 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg957 sg1874 - -lemma sg9152 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg940 sg1886 - -lemma sg9153 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1520 sg1271 - -lemma sg9154 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1808 - -lemma sg9155 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [7,4,4,4,3] := by - exact rowSquare_join (by decide) sg1 sg6560 - -lemma sg9156 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg234 sg3299 - -lemma sg9157 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg910 sg1874 - -lemma sg9158 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg2288 - -lemma sg9159 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1371 sg1371 - -lemma sg9160 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg911 sg1874 - -lemma sg9161 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg2290 - -lemma sg9162 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg2291 - -lemma sg9163 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1877 - -lemma sg9164 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg912 sg1874 - -lemma sg9165 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg2293 - -lemma sg9166 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1878 - -lemma sg9167 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg913 sg1874 - -lemma sg9168 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1879 - -lemma sg9169 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg914 sg1874 - -lemma sg9170 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg915 sg1874 - -lemma sg9171 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2297 - -lemma sg9172 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1371 sg1372 - -lemma sg9173 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1373 - -lemma sg9174 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg911 sg1875 - -lemma sg9175 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg997 sg1776 - -lemma sg9176 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1375 - -lemma sg9177 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1777 - -lemma sg9178 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg2290 - -lemma sg9179 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1376 - -lemma sg9180 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1881 - -lemma sg9181 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg912 sg1875 - -lemma sg9182 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1377 - -lemma sg9183 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1778 - -lemma sg9184 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg1776 - -lemma sg9185 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1777 - -lemma sg9186 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1378 - -lemma sg9187 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1780 - -lemma sg9188 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1776 - -lemma sg9189 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1379 - -lemma sg9190 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1781 - -lemma sg9191 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1776 - -lemma sg9192 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg1777 - -lemma sg9193 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1776 - -lemma sg9194 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1782 - -lemma sg9195 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg2297 - -lemma sg9196 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1777 - -lemma sg9197 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1777 - -lemma sg9198 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1883 - -lemma sg9199 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg2305 - -lemma sg9200 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1884 - -lemma sg9201 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg920 sg1874 - -lemma sg9202 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1778 - -lemma sg9203 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1885 - -lemma sg9204 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2307 - -lemma sg9205 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1779 - -lemma sg9206 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg2293 - -lemma sg9207 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1886 - -lemma sg9208 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg921 sg1874 - -lemma sg9209 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1780 - -lemma sg9210 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg1778 - -lemma sg9211 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg922 sg1874 - -lemma sg9212 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1781 - -lemma sg9213 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1779 - -lemma sg9214 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1778 - -lemma sg9215 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1782 - -lemma sg9216 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg2297 - -lemma sg9217 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1000 sg1779 - -lemma sg9218 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1001 sg1779 - -lemma sg9219 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg923 sg1874 - -lemma sg9220 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1780 - -lemma sg9221 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg1781 - -lemma sg9222 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg1000 sg1780 - -lemma sg9223 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg1001 sg1780 - -lemma sg9224 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1782 - -lemma sg9225 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1781 - -lemma sg9226 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,3] := by - exact rowSquare_join (by decide) sg1001 sg1781 - -lemma sg9227 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1782 - -lemma sg9228 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1001 sg1782 - -lemma sg9229 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1380 - -lemma sg9230 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1372 sg1372 - -lemma sg9231 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1498 sg1274 - -lemma sg9232 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1382 - -lemma sg9233 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1275 - -lemma sg9234 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1002 sg1776 - -lemma sg9235 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1383 - -lemma sg9236 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1276 - -lemma sg9237 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1002 sg1777 - -lemma sg9238 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1277 - -lemma sg9239 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1384 - -lemma sg9240 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1499 sg1274 - -lemma sg9241 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1385 - -lemma sg9242 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1372 sg1377 - -lemma sg9243 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1386 - -lemma sg9244 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1784 - -lemma sg9245 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1499 sg1276 - -lemma sg9246 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1003 sg1777 - -lemma sg9247 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1499 sg1277 - -lemma sg9248 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1387 - -lemma sg9249 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1278 - -lemma sg9250 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1780 - -lemma sg9251 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6563 - -lemma sg9252 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1279 - -lemma sg9253 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1781 - -lemma sg9254 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6564 - -lemma sg9255 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg6565 - -lemma sg9256 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1782 - -lemma sg9257 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1005 sg1777 - -lemma sg9258 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg6566 - -lemma sg9259 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg6567 - -lemma sg9260 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg6568 - -lemma sg9261 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1887 - -lemma sg9262 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1785 - -lemma sg9263 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1783 - -lemma sg9264 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1388 - -lemma sg9265 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1786 - -lemma sg9266 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1373 sg1377 - -lemma sg9267 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg1783 - -lemma sg9268 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1787 - -lemma sg9269 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1784 - -lemma sg9270 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1003 sg1779 - -lemma sg9271 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1783 - -lemma sg9272 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1389 - -lemma sg9273 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1788 - -lemma sg9274 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1499 sg1278 - -lemma sg9275 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1374 sg1377 - -lemma sg9276 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1499 sg1279 - -lemma sg9277 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg1784 - -lemma sg9278 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg1375 sg1377 - -lemma sg9279 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg1377 sg1376 - -lemma sg9280 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1003 sg1782 - -lemma sg9281 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1784 - -lemma sg9282 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,3] := by - exact rowSquare_join (by decide) sg1001 sg1784 - -lemma sg9283 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1789 - -lemma sg9284 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg923 sg1876 - -lemma sg9285 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg1500 sg1278 - -lemma sg9286 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg1004 sg1780 - -lemma sg9287 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg1500 sg1279 - -lemma sg9288 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg1501 sg1278 - -lemma sg9289 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,3] := by - exact rowSquare_join (by decide) sg1502 sg1278 - -lemma sg9290 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg1501 sg1279 - -lemma sg9291 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,2] := by - exact rowSquare_join (by decide) sg1502 sg1279 - -lemma sg9292 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,1] := by - exact rowSquare_join (by decide) sg1005 sg1782 - -lemma sg9293 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1888 - -lemma sg9294 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2309 - -lemma sg9295 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1785 - -lemma sg9296 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg2305 - -lemma sg9297 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1889 - -lemma sg9298 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg931 sg1874 - -lemma sg9299 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1786 - -lemma sg9300 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1785 - -lemma sg9301 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1787 - -lemma sg9302 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg2307 - -lemma sg9303 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg1000 sg1785 - -lemma sg9304 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg1001 sg1785 - -lemma sg9305 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg932 sg1874 - -lemma sg9306 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1788 - -lemma sg9307 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg1377 sg1377 - -lemma sg9308 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1786 - -lemma sg9309 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,3,3] := by - exact rowSquare_join (by decide) sg1001 sg1786 - -lemma sg9310 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1787 - -lemma sg9311 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,2] := by - exact rowSquare_join (by decide) sg1001 sg1787 - -lemma sg9312 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1789 - -lemma sg9313 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1788 - -lemma sg9314 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg1377 sg1378 - -lemma sg9315 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg1377 sg1379 - -lemma sg9316 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,3,2] := by - exact rowSquare_join (by decide) sg1001 sg1788 - -lemma sg9317 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,4,1] := by - exact rowSquare_join (by decide) sg1007 sg1782 - -lemma sg9318 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,5] := by - exact rowSquare_join (by decide) sg1008 sg1782 - -lemma sg9319 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1789 - -lemma sg9320 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1789 - -lemma sg9321 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,6,2,2] := by - exact rowSquare_join (by decide) sg1378 sg1378 - -lemma sg9322 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,6,3,1] := by - exact rowSquare_join (by decide) sg1378 sg1379 - -lemma sg9323 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,6,4] := by - exact rowSquare_join (by decide) sg1379 sg1379 - -lemma sg9324 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1498 sg1280 - -lemma sg9325 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1499 sg1280 - -lemma sg9326 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1392 - -lemma sg9327 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1393 - -lemma sg9328 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1281 - -lemma sg9329 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6570 - -lemma sg9330 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1394 - -lemma sg9331 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1395 - -lemma sg9332 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1282 - -lemma sg9333 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1283 - -lemma sg9334 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1499 sg1281 - -lemma sg9335 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1396 - -lemma sg9336 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1284 - -lemma sg9337 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6576 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes18 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes19 + +namespace OAI + +/-! Semigroup Nodes 21. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg8938 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1517 sg1428 + +lemma sg8939 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1520 sg1428 + +lemma sg8940 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1552 + +lemma sg8941 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1553 + +lemma sg8942 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1499 sg1552 + +lemma sg8943 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1554 + +lemma sg8944 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1500 sg1552 + +lemma sg8945 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1555 + +lemma sg8946 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1552 sg1501 + +lemma sg8947 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1552 sg1502 + +lemma sg8948 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1500 sg1553 + +lemma sg8949 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg1501 sg1553 + +lemma sg8950 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1553 sg1502 + +lemma sg8951 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1500 sg1554 + +lemma sg8952 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1500 sg1555 + +lemma sg8953 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1501 sg1554 + +lemma sg8954 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3] := by + exact rowSquare_join (by decide) sg1502 sg1554 + +lemma sg8955 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1501 sg1555 + +lemma sg8956 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,2] := by + exact rowSquare_join (by decide) sg1502 sg1555 + +lemma sg8957 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1556 + +lemma sg8958 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1503 sg1552 + +lemma sg8959 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1557 + +lemma sg8960 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1499 sg1556 + +lemma sg8961 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1504 sg1552 + +lemma sg8962 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1558 + +lemma sg8963 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1503 sg1554 + +lemma sg8964 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1500 sg1556 + +lemma sg8965 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1503 sg1555 + +lemma sg8966 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1501 sg1556 + +lemma sg8967 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1556 sg1502 + +lemma sg8968 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1559 + +lemma sg8969 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1499 sg1557 + +lemma sg8970 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1504 sg1553 + +lemma sg8971 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1560 + +lemma sg8972 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1499 sg1558 + +lemma sg8973 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1500 sg1557 + +lemma sg8974 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1505 sg1553 + +lemma sg8975 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1504 sg1555 + +lemma sg8976 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,3] := by + exact rowSquare_join (by decide) sg1502 sg1557 + +lemma sg8977 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1500 sg1558 + +lemma sg8978 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1505 sg1554 + +lemma sg8979 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1501 sg1558 + +lemma sg8980 : RowSquare [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1507 sg1553 + +lemma sg8981 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1891 + +lemma sg8982 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg2310 + +lemma sg8983 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg2311 + +lemma sg8984 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg2312 + +lemma sg8985 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg911 sg1891 + +lemma sg8986 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg2310 + +lemma sg8987 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2314 + +lemma sg8988 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg587 sg2311 + +lemma sg8989 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1894 + +lemma sg8990 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg2316 + +lemma sg8991 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1895 + +lemma sg8992 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2317 + +lemma sg8993 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg912 sg1891 + +lemma sg8994 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg588 sg2311 + +lemma sg8995 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg941 sg1874 + +lemma sg8996 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg589 sg2310 + +lemma sg8997 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg913 sg1891 + +lemma sg8998 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg589 sg2311 + +lemma sg8999 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2319 + +lemma sg9000 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg2310 + +lemma sg9001 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg914 sg1891 + +lemma sg9002 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg915 sg1891 + +lemma sg9003 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1092 sg1682 + +lemma sg9004 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1288 sg1498 + +lemma sg9005 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1093 sg1682 + +lemma sg9006 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1094 sg1682 + +lemma sg9007 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg1500 + +lemma sg9008 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg1794 + +lemma sg9009 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1095 sg1682 + +lemma sg9010 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1795 + +lemma sg9011 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg2312 + +lemma sg9012 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg1502 + +lemma sg9013 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1796 + +lemma sg9014 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8116 + +lemma sg9015 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg587 sg2314 + +lemma sg9016 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg0 sg8117 + +lemma sg9017 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg1797 + +lemma sg9018 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1798 + +lemma sg9019 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg940 sg1876 + +lemma sg9020 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1799 + +lemma sg9021 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8118 + +lemma sg9022 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1800 + +lemma sg9023 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8119 + +lemma sg9024 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg8120 + +lemma sg9025 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg8121 + +lemma sg9026 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1801 + +lemma sg9027 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8122 + +lemma sg9028 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1802 + +lemma sg9029 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg942 sg1876 + +lemma sg9030 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8123 + +lemma sg9031 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8124 + +lemma sg9032 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg0 sg8125 + +lemma sg9033 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg589 sg2314 + +lemma sg9034 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2323 + +lemma sg9035 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8126 + +lemma sg9036 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8127 + +lemma sg9037 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg8128 + +lemma sg9038 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg1000 sg1796 + +lemma sg9039 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg1001 sg1796 + +lemma sg9040 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1898 + +lemma sg9041 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg2324 + +lemma sg9042 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg1797 + +lemma sg9043 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg948 sg1874 + +lemma sg9044 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg940 sg1877 + +lemma sg9045 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1899 + +lemma sg9046 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2325 + +lemma sg9047 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1799 + +lemma sg9048 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg2316 + +lemma sg9049 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1800 + +lemma sg9050 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg920 sg1891 + +lemma sg9051 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg371 sg2746 + +lemma sg9052 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg949 sg1874 + +lemma sg9053 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg940 sg1878 + +lemma sg9054 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg941 sg1877 + +lemma sg9055 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg950 sg1874 + +lemma sg9056 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg940 sg1879 + +lemma sg9057 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1799 + +lemma sg9058 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg999 sg1800 + +lemma sg9059 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg615 sg2281 + +lemma sg9060 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg2921 + +lemma sg9061 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg922 sg1891 + +lemma sg9062 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1000 sg1799 + +lemma sg9063 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1000 sg1800 + +lemma sg9064 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,4,4,4] := by + exact rowSquare_join (by decide) sg1001 sg1800 + +lemma sg9065 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1900 + +lemma sg9066 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg951 sg1874 + +lemma sg9067 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg2922 + +lemma sg9068 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg941 sg1878 + +lemma sg9069 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg2923 + +lemma sg9070 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg941 sg1879 + +lemma sg9071 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg942 sg1878 + +lemma sg9072 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg943 sg1878 + +lemma sg9073 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg315 sg3006 + +lemma sg9074 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg942 sg1879 + +lemma sg9075 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,4,3] := by + exact rowSquare_join (by decide) sg943 sg1879 + +lemma sg9076 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg373 sg2748 + +lemma sg9077 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,2] := by + exact rowSquare_join (by decide) sg616 sg2282 + +lemma sg9078 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1289 sg1498 + +lemma sg9079 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1289 sg1499 + +lemma sg9080 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1289 sg1500 + +lemma sg9081 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg944 sg1876 + +lemma sg9082 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg1501 + +lemma sg9083 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8129 + +lemma sg9084 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg1502 + +lemma sg9085 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8130 + +lemma sg9086 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg8131 + +lemma sg9087 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg8132 + +lemma sg9088 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1372 sg1411 + +lemma sg9089 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1408 sg1373 + +lemma sg9090 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1292 + +lemma sg9091 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8133 + +lemma sg9092 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1372 sg1412 + +lemma sg9093 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8134 + +lemma sg9094 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8135 + +lemma sg9095 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8136 + +lemma sg9096 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg0 sg8137 + +lemma sg9097 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg8138 + +lemma sg9098 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1293 + +lemma sg9099 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8139 + +lemma sg9100 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8140 + +lemma sg9101 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1294 + +lemma sg9102 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8141 + +lemma sg9103 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8142 + +lemma sg9104 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg6556 + +lemma sg9105 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg0 sg8143 + +lemma sg9106 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8144 + +lemma sg9107 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6557 + +lemma sg9108 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg0 sg8145 + +lemma sg9109 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg6558 + +lemma sg9110 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,4,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg6559 + +lemma sg9111 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1804 + +lemma sg9112 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8146 + +lemma sg9113 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1805 + +lemma sg9114 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8147 + +lemma sg9115 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8148 + +lemma sg9116 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1806 + +lemma sg9117 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8149 + +lemma sg9118 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8150 + +lemma sg9119 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg8151 + +lemma sg9120 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg0 sg8152 + +lemma sg9121 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1807 + +lemma sg9122 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8153 + +lemma sg9123 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8154 + +lemma sg9124 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8155 + +lemma sg9125 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8156 + +lemma sg9126 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg8157 + +lemma sg9127 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg8158 + +lemma sg9128 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8159 + +lemma sg9129 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg0 sg8160 + +lemma sg9130 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,4,4,3] := by + exact rowSquare_join (by decide) sg0 sg8161 + +lemma sg9131 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1808 + +lemma sg9132 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8162 + +lemma sg9133 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8163 + +lemma sg9134 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg946 sg1878 + +lemma sg9135 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8164 + +lemma sg9136 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg0 sg8165 + +lemma sg9137 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,3,3] := by + exact rowSquare_join (by decide) sg4 sg5794 + +lemma sg9138 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg0 sg8166 + +lemma sg9139 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,4,2] := by + exact rowSquare_join (by decide) sg4 sg5795 + +lemma sg9140 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,1] := by + exact rowSquare_join (by decide) sg0 sg8167 + +lemma sg9141 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2328 + +lemma sg9142 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg940 sg1883 + +lemma sg9143 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg614 sg2283 + +lemma sg9144 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg956 sg1874 + +lemma sg9145 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg940 sg1884 + +lemma sg9146 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1411 sg1377 + +lemma sg9147 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg940 sg1885 + +lemma sg9148 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg931 sg1891 + +lemma sg9149 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg1774 + +lemma sg9150 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg1006 sg1800 + +lemma sg9151 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg957 sg1874 + +lemma sg9152 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg940 sg1886 + +lemma sg9153 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1520 sg1271 + +lemma sg9154 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1808 + +lemma sg9155 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [7,4,4,4,3] := by + exact rowSquare_join (by decide) sg1 sg6560 + +lemma sg9156 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg234 sg3299 + +lemma sg9157 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg910 sg1874 + +lemma sg9158 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg2288 + +lemma sg9159 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1371 sg1371 + +lemma sg9160 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg911 sg1874 + +lemma sg9161 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg2290 + +lemma sg9162 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg2291 + +lemma sg9163 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1877 + +lemma sg9164 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg912 sg1874 + +lemma sg9165 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg2293 + +lemma sg9166 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1878 + +lemma sg9167 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg913 sg1874 + +lemma sg9168 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1879 + +lemma sg9169 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg914 sg1874 + +lemma sg9170 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg915 sg1874 + +lemma sg9171 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2297 + +lemma sg9172 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1371 sg1372 + +lemma sg9173 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1373 + +lemma sg9174 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg911 sg1875 + +lemma sg9175 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg997 sg1776 + +lemma sg9176 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1375 + +lemma sg9177 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1777 + +lemma sg9178 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg2290 + +lemma sg9179 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1376 + +lemma sg9180 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1881 + +lemma sg9181 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg912 sg1875 + +lemma sg9182 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1377 + +lemma sg9183 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1778 + +lemma sg9184 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg1776 + +lemma sg9185 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1777 + +lemma sg9186 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1378 + +lemma sg9187 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1780 + +lemma sg9188 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1776 + +lemma sg9189 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1379 + +lemma sg9190 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1781 + +lemma sg9191 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1776 + +lemma sg9192 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg1777 + +lemma sg9193 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1776 + +lemma sg9194 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1782 + +lemma sg9195 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg2297 + +lemma sg9196 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1777 + +lemma sg9197 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1777 + +lemma sg9198 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1883 + +lemma sg9199 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg2305 + +lemma sg9200 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1884 + +lemma sg9201 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg920 sg1874 + +lemma sg9202 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1778 + +lemma sg9203 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1885 + +lemma sg9204 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2307 + +lemma sg9205 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1779 + +lemma sg9206 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg2293 + +lemma sg9207 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1886 + +lemma sg9208 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg921 sg1874 + +lemma sg9209 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1780 + +lemma sg9210 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg1778 + +lemma sg9211 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg922 sg1874 + +lemma sg9212 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1781 + +lemma sg9213 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1779 + +lemma sg9214 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1778 + +lemma sg9215 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1782 + +lemma sg9216 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg2297 + +lemma sg9217 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1000 sg1779 + +lemma sg9218 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1001 sg1779 + +lemma sg9219 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg923 sg1874 + +lemma sg9220 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1780 + +lemma sg9221 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg1781 + +lemma sg9222 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg1000 sg1780 + +lemma sg9223 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg1001 sg1780 + +lemma sg9224 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1782 + +lemma sg9225 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1781 + +lemma sg9226 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,3] := by + exact rowSquare_join (by decide) sg1001 sg1781 + +lemma sg9227 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1782 + +lemma sg9228 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1001 sg1782 + +lemma sg9229 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1380 + +lemma sg9230 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1372 sg1372 + +lemma sg9231 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1498 sg1274 + +lemma sg9232 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1382 + +lemma sg9233 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1275 + +lemma sg9234 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1002 sg1776 + +lemma sg9235 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1383 + +lemma sg9236 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1276 + +lemma sg9237 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1002 sg1777 + +lemma sg9238 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1277 + +lemma sg9239 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1384 + +lemma sg9240 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1499 sg1274 + +lemma sg9241 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1385 + +lemma sg9242 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1372 sg1377 + +lemma sg9243 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1386 + +lemma sg9244 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1784 + +lemma sg9245 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1499 sg1276 + +lemma sg9246 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1003 sg1777 + +lemma sg9247 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1499 sg1277 + +lemma sg9248 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1387 + +lemma sg9249 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1278 + +lemma sg9250 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1780 + +lemma sg9251 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6563 + +lemma sg9252 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1279 + +lemma sg9253 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1781 + +lemma sg9254 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6564 + +lemma sg9255 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg6565 + +lemma sg9256 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1782 + +lemma sg9257 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1005 sg1777 + +lemma sg9258 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg6566 + +lemma sg9259 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg6567 + +lemma sg9260 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg6568 + +lemma sg9261 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1887 + +lemma sg9262 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1785 + +lemma sg9263 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1783 + +lemma sg9264 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1388 + +lemma sg9265 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1786 + +lemma sg9266 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1373 sg1377 + +lemma sg9267 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg1783 + +lemma sg9268 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1787 + +lemma sg9269 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1784 + +lemma sg9270 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1003 sg1779 + +lemma sg9271 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1783 + +lemma sg9272 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1389 + +lemma sg9273 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1788 + +lemma sg9274 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1499 sg1278 + +lemma sg9275 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1374 sg1377 + +lemma sg9276 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1499 sg1279 + +lemma sg9277 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg1784 + +lemma sg9278 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg1375 sg1377 + +lemma sg9279 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg1377 sg1376 + +lemma sg9280 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1003 sg1782 + +lemma sg9281 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1784 + +lemma sg9282 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,3] := by + exact rowSquare_join (by decide) sg1001 sg1784 + +lemma sg9283 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1789 + +lemma sg9284 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg923 sg1876 + +lemma sg9285 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg1500 sg1278 + +lemma sg9286 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg1004 sg1780 + +lemma sg9287 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg1500 sg1279 + +lemma sg9288 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg1501 sg1278 + +lemma sg9289 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,3] := by + exact rowSquare_join (by decide) sg1502 sg1278 + +lemma sg9290 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg1501 sg1279 + +lemma sg9291 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,2] := by + exact rowSquare_join (by decide) sg1502 sg1279 + +lemma sg9292 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,1] := by + exact rowSquare_join (by decide) sg1005 sg1782 + +lemma sg9293 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1888 + +lemma sg9294 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2309 + +lemma sg9295 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1785 + +lemma sg9296 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg2305 + +lemma sg9297 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1889 + +lemma sg9298 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg931 sg1874 + +lemma sg9299 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1786 + +lemma sg9300 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1785 + +lemma sg9301 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1787 + +lemma sg9302 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg2307 + +lemma sg9303 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg1000 sg1785 + +lemma sg9304 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg1001 sg1785 + +lemma sg9305 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg932 sg1874 + +lemma sg9306 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1788 + +lemma sg9307 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg1377 sg1377 + +lemma sg9308 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1786 + +lemma sg9309 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,3,3] := by + exact rowSquare_join (by decide) sg1001 sg1786 + +lemma sg9310 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1787 + +lemma sg9311 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,2] := by + exact rowSquare_join (by decide) sg1001 sg1787 + +lemma sg9312 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1789 + +lemma sg9313 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1788 + +lemma sg9314 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg1377 sg1378 + +lemma sg9315 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg1377 sg1379 + +lemma sg9316 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,3,2] := by + exact rowSquare_join (by decide) sg1001 sg1788 + +lemma sg9317 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,4,1] := by + exact rowSquare_join (by decide) sg1007 sg1782 + +lemma sg9318 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,5,5] := by + exact rowSquare_join (by decide) sg1008 sg1782 + +lemma sg9319 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1789 + +lemma sg9320 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1789 + +lemma sg9321 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,6,2,2] := by + exact rowSquare_join (by decide) sg1378 sg1378 + +lemma sg9322 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,6,3,1] := by + exact rowSquare_join (by decide) sg1378 sg1379 + +lemma sg9323 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [6,6,6,4] := by + exact rowSquare_join (by decide) sg1379 sg1379 + +lemma sg9324 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1498 sg1280 + +lemma sg9325 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1499 sg1280 + +lemma sg9326 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1392 + +lemma sg9327 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1393 + +lemma sg9328 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1281 + +lemma sg9329 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6570 + +lemma sg9330 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1394 + +lemma sg9331 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1395 + +lemma sg9332 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1282 + +lemma sg9333 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1283 + +lemma sg9334 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1499 sg1281 + +lemma sg9335 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1396 + +lemma sg9336 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1284 + +lemma sg9337 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6576 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes22.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes22.lean index e35213d420144149094da7ab43dca00fc812075d..53fc9e2b2dc2e6f73d2bed324e7139547bbb79fd 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes22.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes22.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes19 - -namespace OAI - -/-! Semigroup Nodes 22. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg9338 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6578 - -lemma sg9339 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg6580 - -lemma sg9340 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg6581 - -lemma sg9341 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg1 sg6583 - -lemma sg9342 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,4,3] := by - exact rowSquare_join (by decide) sg1 sg6584 - -lemma sg9343 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1397 - -lemma sg9344 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1790 - -lemma sg9345 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1398 - -lemma sg9346 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1285 - -lemma sg9347 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6587 - -lemma sg9348 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6589 - -lemma sg9349 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg6591 - -lemma sg9350 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg6592 - -lemma sg9351 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1286 - -lemma sg9352 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1499 sg1284 - -lemma sg9353 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6593 - -lemma sg9354 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6594 - -lemma sg9355 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6595 - -lemma sg9356 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg6596 - -lemma sg9357 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,3] := by - exact rowSquare_join (by decide) sg1 sg6597 - -lemma sg9358 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1 sg6598 - -lemma sg9359 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,2] := by - exact rowSquare_join (by decide) sg1 sg6599 - -lemma sg9360 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg1789 - -lemma sg9361 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6600 - -lemma sg9362 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg5018 - -lemma sg9363 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg5019 - -lemma sg9364 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,5,5] := by - exact rowSquare_join (by decide) sg13 sg5020 - -lemma sg9365 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1399 - -lemma sg9366 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1791 - -lemma sg9367 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1790 - -lemma sg9368 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1003 sg1785 - -lemma sg9369 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg1792 - -lemma sg9370 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1499 sg1285 - -lemma sg9371 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg1790 - -lemma sg9372 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg1377 sg1384 - -lemma sg9373 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1003 sg1787 - -lemma sg9374 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1790 - -lemma sg9375 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,3] := by - exact rowSquare_join (by decide) sg1001 sg1790 - -lemma sg9376 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg1377 sg1385 - -lemma sg9377 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg1501 sg1285 - -lemma sg9378 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg5021 - -lemma sg9379 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg5022 - -lemma sg9380 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1890 - -lemma sg9381 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg939 sg1874 - -lemma sg9382 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1791 - -lemma sg9383 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg2309 - -lemma sg9384 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,2,2] := by - exact rowSquare_join (by decide) sg1006 sg1785 - -lemma sg9385 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1792 - -lemma sg9386 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1791 - -lemma sg9387 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,3,2,2,1] := by - exact rowSquare_join (by decide) sg1006 sg1786 - -lemma sg9388 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,3,3,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1791 - -lemma sg9389 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg5025 - -lemma sg9390 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1402 - -lemma sg9391 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1403 - -lemma sg9392 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1404 - -lemma sg9393 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6606 - -lemma sg9394 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg6607 - -lemma sg9395 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg6608 - -lemma sg9396 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6609 - -lemma sg9397 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5027 - -lemma sg9398 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,4,3,3] := by - exact rowSquare_join (by decide) sg1 sg6610 - -lemma sg9399 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg5028 - -lemma sg9400 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,4,4,2] := by - exact rowSquare_join (by decide) sg13 sg5029 - -lemma sg9401 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1405 - -lemma sg9402 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6611 - -lemma sg9403 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6612 - -lemma sg9404 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5030 - -lemma sg9405 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg6613 - -lemma sg9406 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6614 - -lemma sg9407 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5031 - -lemma sg9408 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg5032 - -lemma sg9409 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg5033 - -lemma sg9410 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1406 - -lemma sg9411 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6615 - -lemma sg9412 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6616 - -lemma sg9413 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6617 - -lemma sg9414 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5034 - -lemma sg9415 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg5035 - -lemma sg9416 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5036 - -lemma sg9417 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,4,2,2] := by - exact rowSquare_join (by decide) sg14 sg5018 - -lemma sg9418 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg5037 - -lemma sg9419 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,4,4] := by - exact rowSquare_join (by decide) sg13 sg5038 - -lemma sg9420 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,7,2,2,2,1] := by - exact rowSquare_join (by decide) sg1006 sg1790 - -lemma sg9421 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,8,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5039 - -lemma sg9422 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,8,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg5025 - -lemma sg9423 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6618 - -lemma sg9424 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg5040 - -lemma sg9425 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg6619 - -lemma sg9426 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6620 - -lemma sg9427 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6621 - -lemma sg9428 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5041 - -lemma sg9429 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg6622 - -lemma sg9430 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6623 - -lemma sg9431 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg5042 - -lemma sg9432 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg5043 - -lemma sg9433 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1407 - -lemma sg9434 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6624 - -lemma sg9435 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6625 - -lemma sg9436 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,5,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg5044 - -lemma sg9437 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6626 - -lemma sg9438 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [10,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5046 - -lemma sg9439 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [10,3,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg6627 - -lemma sg9440 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [10,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5047 - -lemma sg9441 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1416 - -lemma sg9442 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1032 sg1754 - -lemma sg9443 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1417 - -lemma sg9444 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1033 sg1754 - -lemma sg9445 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1419 - -lemma sg9446 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1416 - -lemma sg9447 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1420 - -lemma sg9448 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1421 - -lemma sg9449 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1038 sg1754 - -lemma sg9450 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1422 - -lemma sg9451 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1039 sg1754 - -lemma sg9452 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1423 - -lemma sg9453 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1040 sg1754 - -lemma sg9454 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1424 - -lemma sg9455 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1032 sg1755 - -lemma sg9456 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1033 sg1755 - -lemma sg9457 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1425 - -lemma sg9458 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1416 sg1330 - -lemma sg9459 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1426 - -lemma sg9460 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1416 sg1331 - -lemma sg9461 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1033 sg1756 - -lemma sg9462 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1416 sg1332 - -lemma sg9463 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg1031 sg1758 - -lemma sg9464 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1032 sg1757 - -lemma sg9465 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1417 sg1331 - -lemma sg9466 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1033 sg1757 - -lemma sg9467 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1417 sg1332 - -lemma sg9468 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1033 sg1758 - -lemma sg9469 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1427 - -lemma sg9470 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1428 - -lemma sg9471 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1429 - -lemma sg9472 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1045 sg1754 - -lemma sg9473 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1430 - -lemma sg9474 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1034 sg1758 - -lemma sg9475 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1431 - -lemma sg9476 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1432 - -lemma sg9477 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1433 - -lemma sg9478 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1418 sg1332 - -lemma sg9479 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1035 sg1758 - -lemma sg9480 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1047 sg1754 - -lemma sg9481 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1434 - -lemma sg9482 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8183 - -lemma sg9483 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8184 - -lemma sg9484 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8185 - -lemma sg9485 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8186 - -lemma sg9486 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8187 - -lemma sg9487 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8188 - -lemma sg9488 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg1419 sg1332 - -lemma sg9489 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1037 sg1757 - -lemma sg9490 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8190 - -lemma sg9491 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg8191 - -lemma sg9492 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1420 - -lemma sg9493 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg1332 sg1421 - -lemma sg9494 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1048 sg1754 - -lemma sg9495 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1435 - -lemma sg9496 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1038 sg1755 - -lemma sg9497 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1422 - -lemma sg9498 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg889 sg1903 - -lemma sg9499 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1049 sg1754 - -lemma sg9500 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1436 - -lemma sg9501 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1039 sg1755 - -lemma sg9502 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1423 - -lemma sg9503 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1040 sg1755 - -lemma sg9504 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1424 - -lemma sg9505 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1417 sg1338 - -lemma sg9506 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1033 sg1763 - -lemma sg9507 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1422 sg1332 - -lemma sg9508 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1437 - -lemma sg9509 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1041 sg1755 - -lemma sg9510 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1425 - -lemma sg9511 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1031 sg1764 - -lemma sg9512 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1426 - -lemma sg9513 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1417 sg1339 - -lemma sg9514 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1033 sg1764 - -lemma sg9515 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1423 - -lemma sg9516 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1417 sg1340 - -lemma sg9517 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1032 sg1765 - -lemma sg9518 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1332 sg1424 - -lemma sg9519 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1041 sg1756 - -lemma sg9520 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1425 - -lemma sg9521 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg1031 sg1766 - -lemma sg9522 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1426 - -lemma sg9523 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1425 - -lemma sg9524 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg1766 - -lemma sg9525 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg1332 sg1425 - -lemma sg9526 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1426 - -lemma sg9527 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg1332 sg1426 - -lemma sg9528 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,3] := by - exact rowSquare_join (by decide) sg1033 sg1767 - -lemma sg9529 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg891 sg1908 - -lemma sg9530 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,2] := by - exact rowSquare_join (by decide) sg892 sg1908 - -lemma sg9531 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1050 sg1754 - -lemma sg9532 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1438 - -lemma sg9533 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1051 sg1754 - -lemma sg9534 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1439 - -lemma sg9535 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1052 sg1754 - -lemma sg9536 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1440 - -lemma sg9537 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1441 - -lemma sg9538 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1427 sg1332 - -lemma sg9539 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1042 sg1758 - -lemma sg9540 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1053 sg1754 - -lemma sg9541 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1442 - -lemma sg9542 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1054 sg1754 - -lemma sg9543 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1443 - -lemma sg9544 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8192 - -lemma sg9545 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1428 sg1332 - -lemma sg9546 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1444 - -lemma sg9547 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8193 - -lemma sg9548 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg6563 - -lemma sg9549 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg6564 - -lemma sg9550 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg2 sg6565 - -lemma sg9551 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1429 - -lemma sg9552 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8195 - -lemma sg9553 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2 sg6566 - -lemma sg9554 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2 sg6567 - -lemma sg9555 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,4] := by - exact rowSquare_join (by decide) sg2 sg6568 - -lemma sg9556 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1055 sg1754 - -lemma sg9557 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1445 - -lemma sg9558 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1446 - -lemma sg9559 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8196 - -lemma sg9560 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8197 - -lemma sg9561 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg8198 - -lemma sg9562 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1431 - -lemma sg9563 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8199 - -lemma sg9564 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8200 - -lemma sg9565 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8201 - -lemma sg9566 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg8202 - -lemma sg9567 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg8203 - -lemma sg9568 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8204 - -lemma sg9569 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg0 sg8205 - -lemma sg9570 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,3] := by - exact rowSquare_join (by decide) sg0 sg8206 - -lemma sg9571 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1434 - -lemma sg9572 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5796 - -lemma sg9573 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8207 - -lemma sg9574 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5797 - -lemma sg9575 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg5798 - -lemma sg9576 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,3] := by - exact rowSquare_join (by decide) sg4 sg5799 - -lemma sg9577 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg4 sg5800 - -lemma sg9578 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,2] := by - exact rowSquare_join (by decide) sg4 sg5801 - -lemma sg9579 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,1] := by - exact rowSquare_join (by decide) sg0 sg8208 - -lemma sg9580 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1056 sg1754 - -lemma sg9581 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1447 - -lemma sg9582 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1048 sg1755 - -lemma sg9583 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1435 - -lemma sg9584 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1422 sg1338 - -lemma sg9585 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1049 sg1755 - -lemma sg9586 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1436 - -lemma sg9587 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1520 sg1261 - -lemma sg9588 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1417 sg1348 - -lemma sg9589 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg1770 - -lemma sg9590 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg1332 sg1435 - -lemma sg9591 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1437 - -lemma sg9592 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg1521 sg1261 - -lemma sg9593 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,4,3,3] := by - exact rowSquare_join (by decide) sg4 sg5804 - -lemma sg9594 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg108 sg4063 - -lemma sg9595 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1448 - -lemma sg9596 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1449 - -lemma sg9597 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1450 - -lemma sg9598 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg6569 - -lemma sg9599 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1438 sg1332 - -lemma sg9600 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1451 - -lemma sg9601 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1452 - -lemma sg9602 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg6573 - -lemma sg9603 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg6574 - -lemma sg9604 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2 sg6575 - -lemma sg9605 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1439 - -lemma sg9606 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6702 - -lemma sg9607 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5805 - -lemma sg9608 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5806 - -lemma sg9609 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg5807 - -lemma sg9610 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg5808 - -lemma sg9611 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg6582 - -lemma sg9612 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2 sg6583 - -lemma sg9613 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,4,3] := by - exact rowSquare_join (by decide) sg2 sg6584 - -lemma sg9614 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1453 - -lemma sg9615 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg6586 - -lemma sg9616 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5809 - -lemma sg9617 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg6590 - -lemma sg9618 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg2 sg6591 - -lemma sg9619 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg2 sg6592 - -lemma sg9620 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5810 - -lemma sg9621 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5811 - -lemma sg9622 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5812 - -lemma sg9623 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg5813 - -lemma sg9624 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,3] := by - exact rowSquare_join (by decide) sg4 sg5814 - -lemma sg9625 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg5 sg5800 - -lemma sg9626 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,2] := by - exact rowSquare_join (by decide) sg5 sg5801 - -lemma sg9627 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5048 - -lemma sg9628 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5815 - -lemma sg9629 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5049 - -lemma sg9630 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg5050 - -lemma sg9631 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,5,4,1] := by - exact rowSquare_join (by decide) sg4 sg5816 - -lemma sg9632 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,5,5] := by - exact rowSquare_join (by decide) sg2 sg6605 - -lemma sg9633 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1454 - -lemma sg9634 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8209 - -lemma sg9635 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5817 - -lemma sg9636 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5818 - -lemma sg9637 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg5802 - -lemma sg9638 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg5 sg5803 - -lemma sg9639 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,3] := by - exact rowSquare_join (by decide) sg5 sg5804 - -lemma sg9640 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1056 sg1755 - -lemma sg9641 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1447 - -lemma sg9642 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1422 sg1348 - -lemma sg9643 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,2,2] := by - exact rowSquare_join (by decide) sg1038 sg1770 - -lemma sg9644 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5051 - -lemma sg9645 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5819 - -lemma sg9646 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5052 - -lemma sg9647 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg5053 - -lemma sg9648 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [8,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1448 - -lemma sg9649 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [8,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg5 sg5807 - -lemma sg9650 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg5 sg5808 - -lemma sg9651 : RowSquare [6,4,3,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg374 sg2626 - -lemma sg9652 : RowSquare [6,4,3,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg370 sg2633 - -lemma sg9653 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1501 - -lemma sg9654 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg1332 sg1502 - -lemma sg9655 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1507 - -lemma sg9656 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1511 - -lemma sg9657 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1327 sg1371 - -lemma sg9658 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1371 sg1328 - -lemma sg9659 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1330 - -lemma sg9660 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1331 - -lemma sg9661 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg997 sg1758 - -lemma sg9662 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1755 - -lemma sg9663 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1007 sg1754 - -lemma sg9664 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1377 - -lemma sg9665 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg1755 - -lemma sg9666 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1756 - -lemma sg9667 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1008 sg1754 - -lemma sg9668 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1755 - -lemma sg9669 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg1757 - -lemma sg9670 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1755 - -lemma sg9671 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1758 - -lemma sg9672 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1378 - -lemma sg9673 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg999 sg1756 - -lemma sg9674 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1379 - -lemma sg9675 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1756 - -lemma sg9676 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1757 - -lemma sg9677 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1756 - -lemma sg9678 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg999 sg1758 - -lemma sg9679 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1000 sg1757 - -lemma sg9680 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1757 - -lemma sg9681 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1000 sg1758 - -lemma sg9682 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1758 - -lemma sg9683 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1380 - -lemma sg9684 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8220 - -lemma sg9685 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1381 - -lemma sg9686 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8221 - -lemma sg9687 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8222 - -lemma sg9688 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1382 - -lemma sg9689 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8223 - -lemma sg9690 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8224 - -lemma sg9691 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1383 - -lemma sg9692 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8225 - -lemma sg9693 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1372 sg1331 - -lemma sg9694 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1002 sg1757 - -lemma sg9695 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8226 - -lemma sg9696 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1372 sg1332 - -lemma sg9697 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1002 sg1758 - -lemma sg9698 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1384 - -lemma sg9699 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1338 - -lemma sg9700 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1329 sg1373 - -lemma sg9701 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1014 sg1754 - -lemma sg9702 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1385 - -lemma sg9703 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1339 - -lemma sg9704 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8227 - -lemma sg9705 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1330 sg1373 - -lemma sg9706 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1386 - -lemma sg9707 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1340 - -lemma sg9708 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1375 - -lemma sg9709 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1373 sg1331 - -lemma sg9710 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1376 - -lemma sg9711 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1373 sg1332 - -lemma sg9712 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1003 sg1758 - -lemma sg9713 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1387 - -lemma sg9714 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1378 - -lemma sg9715 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8228 - -lemma sg9716 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1330 sg1374 - -lemma sg9717 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1379 - -lemma sg9718 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8229 - -lemma sg9719 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1375 - -lemma sg9720 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1331 sg1374 - -lemma sg9721 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1376 - -lemma sg9722 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg1374 sg1332 - -lemma sg9723 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1005 sg1757 - -lemma sg9724 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1331 sg1375 - -lemma sg9725 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1376 - -lemma sg9726 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1375 - -lemma sg9727 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg1332 sg1376 - -lemma sg9728 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1015 sg1754 - -lemma sg9729 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1006 sg1755 - -lemma sg9730 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg1763 - -lemma sg9731 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1016 sg1754 - -lemma sg9732 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1388 - -lemma sg9733 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1007 sg1755 - -lemma sg9734 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1377 - -lemma sg9735 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg1764 - -lemma sg9736 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1008 sg1755 - -lemma sg9737 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1765 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes19 + +namespace OAI + +/-! Semigroup Nodes 22. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg9338 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6578 + +lemma sg9339 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg6580 + +lemma sg9340 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg6581 + +lemma sg9341 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg1 sg6583 + +lemma sg9342 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,4,4,4,3] := by + exact rowSquare_join (by decide) sg1 sg6584 + +lemma sg9343 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1397 + +lemma sg9344 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1790 + +lemma sg9345 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1398 + +lemma sg9346 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1285 + +lemma sg9347 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6587 + +lemma sg9348 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6589 + +lemma sg9349 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg6591 + +lemma sg9350 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg6592 + +lemma sg9351 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1286 + +lemma sg9352 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1499 sg1284 + +lemma sg9353 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6593 + +lemma sg9354 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6594 + +lemma sg9355 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6595 + +lemma sg9356 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg6596 + +lemma sg9357 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,3] := by + exact rowSquare_join (by decide) sg1 sg6597 + +lemma sg9358 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1 sg6598 + +lemma sg9359 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,2] := by + exact rowSquare_join (by decide) sg1 sg6599 + +lemma sg9360 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg1789 + +lemma sg9361 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6600 + +lemma sg9362 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg5018 + +lemma sg9363 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg5019 + +lemma sg9364 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,5,5,5] := by + exact rowSquare_join (by decide) sg13 sg5020 + +lemma sg9365 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1399 + +lemma sg9366 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1791 + +lemma sg9367 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1790 + +lemma sg9368 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1003 sg1785 + +lemma sg9369 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg1792 + +lemma sg9370 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1499 sg1285 + +lemma sg9371 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg1790 + +lemma sg9372 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg1377 sg1384 + +lemma sg9373 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1003 sg1787 + +lemma sg9374 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1790 + +lemma sg9375 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,3] := by + exact rowSquare_join (by decide) sg1001 sg1790 + +lemma sg9376 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg1377 sg1385 + +lemma sg9377 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg1501 sg1285 + +lemma sg9378 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg5021 + +lemma sg9379 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,6,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg5022 + +lemma sg9380 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1890 + +lemma sg9381 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg939 sg1874 + +lemma sg9382 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1791 + +lemma sg9383 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg2309 + +lemma sg9384 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,2,2] := by + exact rowSquare_join (by decide) sg1006 sg1785 + +lemma sg9385 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1792 + +lemma sg9386 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1791 + +lemma sg9387 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,3,2,2,1] := by + exact rowSquare_join (by decide) sg1006 sg1786 + +lemma sg9388 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,3,3,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1791 + +lemma sg9389 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [7,7,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg5025 + +lemma sg9390 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1402 + +lemma sg9391 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1403 + +lemma sg9392 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1404 + +lemma sg9393 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6606 + +lemma sg9394 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg6607 + +lemma sg9395 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg6608 + +lemma sg9396 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6609 + +lemma sg9397 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5027 + +lemma sg9398 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,4,3,3] := by + exact rowSquare_join (by decide) sg1 sg6610 + +lemma sg9399 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg5028 + +lemma sg9400 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,4,4,4,2] := by + exact rowSquare_join (by decide) sg13 sg5029 + +lemma sg9401 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1405 + +lemma sg9402 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6611 + +lemma sg9403 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6612 + +lemma sg9404 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5030 + +lemma sg9405 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg6613 + +lemma sg9406 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6614 + +lemma sg9407 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5031 + +lemma sg9408 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg5032 + +lemma sg9409 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,5,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg5033 + +lemma sg9410 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1406 + +lemma sg9411 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6615 + +lemma sg9412 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6616 + +lemma sg9413 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6617 + +lemma sg9414 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5034 + +lemma sg9415 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg5035 + +lemma sg9416 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5036 + +lemma sg9417 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,4,2,2] := by + exact rowSquare_join (by decide) sg14 sg5018 + +lemma sg9418 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg5037 + +lemma sg9419 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,6,4,4] := by + exact rowSquare_join (by decide) sg13 sg5038 + +lemma sg9420 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,7,2,2,2,1] := by + exact rowSquare_join (by decide) sg1006 sg1790 + +lemma sg9421 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,8,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5039 + +lemma sg9422 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [8,8,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg5025 + +lemma sg9423 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6618 + +lemma sg9424 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg5040 + +lemma sg9425 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg6619 + +lemma sg9426 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6620 + +lemma sg9427 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6621 + +lemma sg9428 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5041 + +lemma sg9429 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg6622 + +lemma sg9430 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6623 + +lemma sg9431 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg5042 + +lemma sg9432 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,4,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg5043 + +lemma sg9433 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1407 + +lemma sg9434 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6624 + +lemma sg9435 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6625 + +lemma sg9436 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,5,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg5044 + +lemma sg9437 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [9,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6626 + +lemma sg9438 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [10,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5046 + +lemma sg9439 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [10,3,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg6627 + +lemma sg9440 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1] [10,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5047 + +lemma sg9441 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1416 + +lemma sg9442 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1032 sg1754 + +lemma sg9443 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1417 + +lemma sg9444 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1033 sg1754 + +lemma sg9445 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1419 + +lemma sg9446 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1416 + +lemma sg9447 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1420 + +lemma sg9448 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1421 + +lemma sg9449 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1038 sg1754 + +lemma sg9450 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1422 + +lemma sg9451 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1039 sg1754 + +lemma sg9452 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1423 + +lemma sg9453 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1040 sg1754 + +lemma sg9454 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1424 + +lemma sg9455 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1032 sg1755 + +lemma sg9456 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1033 sg1755 + +lemma sg9457 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1425 + +lemma sg9458 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1416 sg1330 + +lemma sg9459 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1426 + +lemma sg9460 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1416 sg1331 + +lemma sg9461 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1033 sg1756 + +lemma sg9462 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1416 sg1332 + +lemma sg9463 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg1031 sg1758 + +lemma sg9464 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1032 sg1757 + +lemma sg9465 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1417 sg1331 + +lemma sg9466 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1033 sg1757 + +lemma sg9467 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1417 sg1332 + +lemma sg9468 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1033 sg1758 + +lemma sg9469 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1427 + +lemma sg9470 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1428 + +lemma sg9471 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1429 + +lemma sg9472 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1045 sg1754 + +lemma sg9473 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1430 + +lemma sg9474 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1034 sg1758 + +lemma sg9475 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1431 + +lemma sg9476 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1432 + +lemma sg9477 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1433 + +lemma sg9478 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1418 sg1332 + +lemma sg9479 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1035 sg1758 + +lemma sg9480 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1047 sg1754 + +lemma sg9481 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1434 + +lemma sg9482 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8183 + +lemma sg9483 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8184 + +lemma sg9484 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8185 + +lemma sg9485 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8186 + +lemma sg9486 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8187 + +lemma sg9487 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8188 + +lemma sg9488 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg1419 sg1332 + +lemma sg9489 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1037 sg1757 + +lemma sg9490 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8190 + +lemma sg9491 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg8191 + +lemma sg9492 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1420 + +lemma sg9493 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg1332 sg1421 + +lemma sg9494 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1048 sg1754 + +lemma sg9495 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1435 + +lemma sg9496 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1038 sg1755 + +lemma sg9497 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1422 + +lemma sg9498 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg889 sg1903 + +lemma sg9499 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1049 sg1754 + +lemma sg9500 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1436 + +lemma sg9501 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1039 sg1755 + +lemma sg9502 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1423 + +lemma sg9503 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1040 sg1755 + +lemma sg9504 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1424 + +lemma sg9505 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1417 sg1338 + +lemma sg9506 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1033 sg1763 + +lemma sg9507 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1422 sg1332 + +lemma sg9508 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1437 + +lemma sg9509 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1041 sg1755 + +lemma sg9510 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1425 + +lemma sg9511 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1031 sg1764 + +lemma sg9512 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1426 + +lemma sg9513 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1417 sg1339 + +lemma sg9514 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1033 sg1764 + +lemma sg9515 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1423 + +lemma sg9516 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1417 sg1340 + +lemma sg9517 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1032 sg1765 + +lemma sg9518 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1332 sg1424 + +lemma sg9519 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1041 sg1756 + +lemma sg9520 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1425 + +lemma sg9521 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg1031 sg1766 + +lemma sg9522 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1426 + +lemma sg9523 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1425 + +lemma sg9524 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg1766 + +lemma sg9525 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg1332 sg1425 + +lemma sg9526 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1426 + +lemma sg9527 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg1332 sg1426 + +lemma sg9528 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,3] := by + exact rowSquare_join (by decide) sg1033 sg1767 + +lemma sg9529 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg891 sg1908 + +lemma sg9530 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,2] := by + exact rowSquare_join (by decide) sg892 sg1908 + +lemma sg9531 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1050 sg1754 + +lemma sg9532 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1438 + +lemma sg9533 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1051 sg1754 + +lemma sg9534 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1439 + +lemma sg9535 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1052 sg1754 + +lemma sg9536 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1440 + +lemma sg9537 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1441 + +lemma sg9538 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1427 sg1332 + +lemma sg9539 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1042 sg1758 + +lemma sg9540 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1053 sg1754 + +lemma sg9541 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1442 + +lemma sg9542 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1054 sg1754 + +lemma sg9543 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1443 + +lemma sg9544 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8192 + +lemma sg9545 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1428 sg1332 + +lemma sg9546 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1444 + +lemma sg9547 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8193 + +lemma sg9548 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg6563 + +lemma sg9549 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg6564 + +lemma sg9550 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg2 sg6565 + +lemma sg9551 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1429 + +lemma sg9552 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8195 + +lemma sg9553 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2 sg6566 + +lemma sg9554 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2 sg6567 + +lemma sg9555 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,4] := by + exact rowSquare_join (by decide) sg2 sg6568 + +lemma sg9556 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1055 sg1754 + +lemma sg9557 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1445 + +lemma sg9558 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1446 + +lemma sg9559 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8196 + +lemma sg9560 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8197 + +lemma sg9561 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg8198 + +lemma sg9562 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1431 + +lemma sg9563 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8199 + +lemma sg9564 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8200 + +lemma sg9565 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8201 + +lemma sg9566 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg8202 + +lemma sg9567 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg8203 + +lemma sg9568 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8204 + +lemma sg9569 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg0 sg8205 + +lemma sg9570 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,3] := by + exact rowSquare_join (by decide) sg0 sg8206 + +lemma sg9571 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1434 + +lemma sg9572 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5796 + +lemma sg9573 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8207 + +lemma sg9574 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5797 + +lemma sg9575 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg5798 + +lemma sg9576 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,3,3] := by + exact rowSquare_join (by decide) sg4 sg5799 + +lemma sg9577 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg4 sg5800 + +lemma sg9578 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,2] := by + exact rowSquare_join (by decide) sg4 sg5801 + +lemma sg9579 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,1] := by + exact rowSquare_join (by decide) sg0 sg8208 + +lemma sg9580 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1056 sg1754 + +lemma sg9581 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1447 + +lemma sg9582 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1048 sg1755 + +lemma sg9583 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1435 + +lemma sg9584 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1422 sg1338 + +lemma sg9585 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1049 sg1755 + +lemma sg9586 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1436 + +lemma sg9587 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1520 sg1261 + +lemma sg9588 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1417 sg1348 + +lemma sg9589 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg1770 + +lemma sg9590 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg1332 sg1435 + +lemma sg9591 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1437 + +lemma sg9592 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg1521 sg1261 + +lemma sg9593 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [6,6,4,3,3] := by + exact rowSquare_join (by decide) sg4 sg5804 + +lemma sg9594 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg108 sg4063 + +lemma sg9595 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1448 + +lemma sg9596 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1449 + +lemma sg9597 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1450 + +lemma sg9598 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg6569 + +lemma sg9599 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1438 sg1332 + +lemma sg9600 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1451 + +lemma sg9601 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1452 + +lemma sg9602 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg6573 + +lemma sg9603 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg6574 + +lemma sg9604 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2 sg6575 + +lemma sg9605 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1439 + +lemma sg9606 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6702 + +lemma sg9607 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5805 + +lemma sg9608 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5806 + +lemma sg9609 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg5807 + +lemma sg9610 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg5808 + +lemma sg9611 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg6582 + +lemma sg9612 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2 sg6583 + +lemma sg9613 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,4,4,4,3] := by + exact rowSquare_join (by decide) sg2 sg6584 + +lemma sg9614 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1453 + +lemma sg9615 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg6586 + +lemma sg9616 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5809 + +lemma sg9617 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg6590 + +lemma sg9618 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg2 sg6591 + +lemma sg9619 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg2 sg6592 + +lemma sg9620 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5810 + +lemma sg9621 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5811 + +lemma sg9622 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5812 + +lemma sg9623 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg5813 + +lemma sg9624 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,3,3] := by + exact rowSquare_join (by decide) sg4 sg5814 + +lemma sg9625 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg5 sg5800 + +lemma sg9626 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,2] := by + exact rowSquare_join (by decide) sg5 sg5801 + +lemma sg9627 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5048 + +lemma sg9628 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5815 + +lemma sg9629 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5049 + +lemma sg9630 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg5050 + +lemma sg9631 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,5,4,1] := by + exact rowSquare_join (by decide) sg4 sg5816 + +lemma sg9632 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,5,5,5] := by + exact rowSquare_join (by decide) sg2 sg6605 + +lemma sg9633 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1454 + +lemma sg9634 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8209 + +lemma sg9635 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5817 + +lemma sg9636 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5818 + +lemma sg9637 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg5802 + +lemma sg9638 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg5 sg5803 + +lemma sg9639 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,6,3,3,3] := by + exact rowSquare_join (by decide) sg5 sg5804 + +lemma sg9640 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1056 sg1755 + +lemma sg9641 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1447 + +lemma sg9642 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1422 sg1348 + +lemma sg9643 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,2,2,2,2] := by + exact rowSquare_join (by decide) sg1038 sg1770 + +lemma sg9644 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5051 + +lemma sg9645 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5819 + +lemma sg9646 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5052 + +lemma sg9647 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [7,7,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg5053 + +lemma sg9648 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [8,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1448 + +lemma sg9649 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [8,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg5 sg5807 + +lemma sg9650 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1] [8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg5 sg5808 + +lemma sg9651 : RowSquare [6,4,3,2,1,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg374 sg2626 + +lemma sg9652 : RowSquare [6,4,3,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg370 sg2633 + +lemma sg9653 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1501 + +lemma sg9654 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg1332 sg1502 + +lemma sg9655 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1507 + +lemma sg9656 : RowSquare [6,5,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1511 + +lemma sg9657 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1327 sg1371 + +lemma sg9658 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1371 sg1328 + +lemma sg9659 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1330 + +lemma sg9660 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1331 + +lemma sg9661 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg997 sg1758 + +lemma sg9662 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1755 + +lemma sg9663 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1007 sg1754 + +lemma sg9664 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1377 + +lemma sg9665 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg1755 + +lemma sg9666 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1756 + +lemma sg9667 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1008 sg1754 + +lemma sg9668 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1755 + +lemma sg9669 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg1757 + +lemma sg9670 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1755 + +lemma sg9671 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1758 + +lemma sg9672 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1378 + +lemma sg9673 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg999 sg1756 + +lemma sg9674 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1379 + +lemma sg9675 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1756 + +lemma sg9676 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1757 + +lemma sg9677 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1756 + +lemma sg9678 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg999 sg1758 + +lemma sg9679 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1000 sg1757 + +lemma sg9680 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1757 + +lemma sg9681 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1000 sg1758 + +lemma sg9682 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1758 + +lemma sg9683 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1380 + +lemma sg9684 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8220 + +lemma sg9685 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1381 + +lemma sg9686 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8221 + +lemma sg9687 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8222 + +lemma sg9688 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1382 + +lemma sg9689 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8223 + +lemma sg9690 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8224 + +lemma sg9691 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1383 + +lemma sg9692 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8225 + +lemma sg9693 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1372 sg1331 + +lemma sg9694 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1002 sg1757 + +lemma sg9695 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8226 + +lemma sg9696 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1372 sg1332 + +lemma sg9697 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1002 sg1758 + +lemma sg9698 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1384 + +lemma sg9699 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1338 + +lemma sg9700 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1329 sg1373 + +lemma sg9701 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1014 sg1754 + +lemma sg9702 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1385 + +lemma sg9703 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1339 + +lemma sg9704 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8227 + +lemma sg9705 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1330 sg1373 + +lemma sg9706 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1386 + +lemma sg9707 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1340 + +lemma sg9708 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1375 + +lemma sg9709 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1373 sg1331 + +lemma sg9710 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1376 + +lemma sg9711 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1373 sg1332 + +lemma sg9712 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1003 sg1758 + +lemma sg9713 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1387 + +lemma sg9714 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1378 + +lemma sg9715 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8228 + +lemma sg9716 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1330 sg1374 + +lemma sg9717 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1379 + +lemma sg9718 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8229 + +lemma sg9719 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1375 + +lemma sg9720 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1331 sg1374 + +lemma sg9721 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1376 + +lemma sg9722 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg1374 sg1332 + +lemma sg9723 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1005 sg1757 + +lemma sg9724 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1331 sg1375 + +lemma sg9725 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1376 + +lemma sg9726 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1375 + +lemma sg9727 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg1332 sg1376 + +lemma sg9728 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1015 sg1754 + +lemma sg9729 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1006 sg1755 + +lemma sg9730 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg1763 + +lemma sg9731 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1016 sg1754 + +lemma sg9732 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1388 + +lemma sg9733 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1007 sg1755 + +lemma sg9734 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1377 + +lemma sg9735 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg1764 + +lemma sg9736 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1008 sg1755 + +lemma sg9737 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1765 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes23.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes23.lean index 5a2e554f75b3d68df4e1801dc28802ecb04622a5..55bcbba754bb59da9a42b967ce6939e4d0357192 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes23.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes23.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes19 - -namespace OAI - -/-! Semigroup Nodes 23. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg9738 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1763 - -lemma sg9739 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1006 sg1758 - -lemma sg9740 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1389 - -lemma sg9741 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1378 - -lemma sg9742 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1377 - -lemma sg9743 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg1764 - -lemma sg9744 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1379 - -lemma sg9745 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1767 - -lemma sg9746 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1331 sg1377 - -lemma sg9747 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1001 sg1764 - -lemma sg9748 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1377 - -lemma sg9749 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1008 sg1757 - -lemma sg9750 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1008 sg1758 - -lemma sg9751 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1000 sg1765 - -lemma sg9752 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1001 sg1765 - -lemma sg9753 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1378 - -lemma sg9754 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg999 sg1766 - -lemma sg9755 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1379 - -lemma sg9756 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1378 - -lemma sg9757 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg1000 sg1766 - -lemma sg9758 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg1332 sg1378 - -lemma sg9759 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1379 - -lemma sg9760 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg1332 sg1379 - -lemma sg9761 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3] := by - exact rowSquare_join (by decide) sg1001 sg1767 - -lemma sg9762 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1390 - -lemma sg9763 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8230 - -lemma sg9764 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8231 - -lemma sg9765 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1018 sg1754 - -lemma sg9766 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1391 - -lemma sg9767 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8232 - -lemma sg9768 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8233 - -lemma sg9769 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1392 - -lemma sg9770 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8234 - -lemma sg9771 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6726 - -lemma sg9772 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8235 - -lemma sg9773 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1393 - -lemma sg9774 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8236 - -lemma sg9775 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6727 - -lemma sg9776 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1380 sg1331 - -lemma sg9777 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6728 - -lemma sg9778 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1380 sg1332 - -lemma sg9779 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1009 sg1758 - -lemma sg9780 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1394 - -lemma sg9781 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8237 - -lemma sg9782 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6729 - -lemma sg9783 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8238 - -lemma sg9784 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1021 sg1754 - -lemma sg9785 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1395 - -lemma sg9786 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8239 - -lemma sg9787 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6730 - -lemma sg9788 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6731 - -lemma sg9789 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8240 - -lemma sg9790 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8241 - -lemma sg9791 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6732 - -lemma sg9792 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1331 sg1381 - -lemma sg9793 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6733 - -lemma sg9794 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1381 sg1332 - -lemma sg9795 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1396 - -lemma sg9796 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1387 - -lemma sg9797 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6734 - -lemma sg9798 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8242 - -lemma sg9799 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5831 - -lemma sg9800 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6735 - -lemma sg9801 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8245 - -lemma sg9802 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5832 - -lemma sg9803 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg5833 - -lemma sg9804 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1382 - -lemma sg9805 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1012 sg1757 - -lemma sg9806 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1383 - -lemma sg9807 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg6736 - -lemma sg9808 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg6737 - -lemma sg9809 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg6738 - -lemma sg9810 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1022 sg1754 - -lemma sg9811 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1397 - -lemma sg9812 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1348 - -lemma sg9813 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8246 - -lemma sg9814 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1373 sg1338 - -lemma sg9815 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1398 - -lemma sg9816 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1349 - -lemma sg9817 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8247 - -lemma sg9818 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8248 - -lemma sg9819 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5834 - -lemma sg9820 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8249 - -lemma sg9821 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1373 sg1340 - -lemma sg9822 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1331 sg1384 - -lemma sg9823 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1338 sg1376 - -lemma sg9824 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1384 - -lemma sg9825 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1389 - -lemma sg9826 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8250 - -lemma sg9827 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8251 - -lemma sg9828 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5835 - -lemma sg9829 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8252 - -lemma sg9830 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8253 - -lemma sg9831 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg5836 - -lemma sg9832 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg5837 - -lemma sg9833 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1386 - -lemma sg9834 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg1332 sg1386 - -lemma sg9835 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,3] := by - exact rowSquare_join (by decide) sg1376 sg1340 - -lemma sg9836 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1387 - -lemma sg9837 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5838 - -lemma sg9838 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8255 - -lemma sg9839 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5839 - -lemma sg9840 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg5840 - -lemma sg9841 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3] := by - exact rowSquare_join (by decide) sg4 sg5841 - -lemma sg9842 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg4 sg5842 - -lemma sg9843 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,2] := by - exact rowSquare_join (by decide) sg4 sg5843 - -lemma sg9844 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1023 sg1754 - -lemma sg9845 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1399 - -lemma sg9846 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1015 sg1755 - -lemma sg9847 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg998 sg1770 - -lemma sg9848 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1016 sg1755 - -lemma sg9849 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1388 - -lemma sg9850 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1771 - -lemma sg9851 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5844 - -lemma sg9852 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg1885 - -lemma sg9853 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1015 sg1758 - -lemma sg9854 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg1000 sg1770 - -lemma sg9855 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg1001 sg1770 - -lemma sg9856 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1389 - -lemma sg9857 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1388 - -lemma sg9858 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5845 - -lemma sg9859 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5846 - -lemma sg9860 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5847 - -lemma sg9861 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg1332 sg1388 - -lemma sg9862 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3] := by - exact rowSquare_join (by decide) sg1001 sg1771 - -lemma sg9863 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg891 sg1885 - -lemma sg9864 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,2] := by - exact rowSquare_join (by decide) sg892 sg1885 - -lemma sg9865 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1389 - -lemma sg9866 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1389 - -lemma sg9867 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5848 - -lemma sg9868 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg5849 - -lemma sg9869 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,2] := by - exact rowSquare_join (by decide) sg1340 sg1378 - -lemma sg9870 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,1] := by - exact rowSquare_join (by decide) sg1340 sg1379 - -lemma sg9871 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2] := by - exact rowSquare_join (by decide) sg4 sg5850 - -lemma sg9872 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,1] := by - exact rowSquare_join (by decide) sg4 sg5851 - -lemma sg9873 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,6,4] := by - exact rowSquare_join (by decide) sg4 sg5852 - -lemma sg9874 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1024 sg1754 - -lemma sg9875 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1400 - -lemma sg9876 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6739 - -lemma sg9877 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6740 - -lemma sg9878 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1025 sg1754 - -lemma sg9879 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1401 - -lemma sg9880 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6741 - -lemma sg9881 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6742 - -lemma sg9882 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6743 - -lemma sg9883 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1026 sg1754 - -lemma sg9884 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1402 - -lemma sg9885 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6744 - -lemma sg9886 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6745 - -lemma sg9887 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5853 - -lemma sg9888 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6746 - -lemma sg9889 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6747 - -lemma sg9890 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6748 - -lemma sg9891 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1331 sg1390 - -lemma sg9892 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6749 - -lemma sg9893 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1390 sg1332 - -lemma sg9894 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1027 sg1754 - -lemma sg9895 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1403 - -lemma sg9896 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8261 - -lemma sg9897 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6750 - -lemma sg9898 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6751 - -lemma sg9899 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1404 - -lemma sg9900 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8262 - -lemma sg9901 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6752 - -lemma sg9902 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5854 - -lemma sg9903 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5855 - -lemma sg9904 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6753 - -lemma sg9905 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6754 - -lemma sg9906 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg5832 - -lemma sg9907 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg5 sg5833 - -lemma sg9908 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1391 - -lemma sg9909 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1396 - -lemma sg9910 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6755 - -lemma sg9911 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5856 - -lemma sg9912 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5857 - -lemma sg9913 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5858 - -lemma sg9914 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5054 - -lemma sg9915 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg5859 - -lemma sg9916 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg5860 - -lemma sg9917 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5055 - -lemma sg9918 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg5056 - -lemma sg9919 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3] := by - exact rowSquare_join (by decide) sg13 sg5057 - -lemma sg9920 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1028 sg1754 - -lemma sg9921 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1405 - -lemma sg9922 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8263 - -lemma sg9923 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6758 - -lemma sg9924 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6759 - -lemma sg9925 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg5834 - -lemma sg9926 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8264 - -lemma sg9927 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6760 - -lemma sg9928 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6761 - -lemma sg9929 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5861 - -lemma sg9930 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6762 - -lemma sg9931 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5058 - -lemma sg9932 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg5 sg5836 - -lemma sg9933 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg5 sg5837 - -lemma sg9934 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6763 - -lemma sg9935 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6764 - -lemma sg9936 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5862 - -lemma sg9937 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5863 - -lemma sg9938 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5059 - -lemma sg9939 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5060 - -lemma sg9940 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3] := by - exact rowSquare_join (by decide) sg4 sg5864 - -lemma sg9941 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg5061 - -lemma sg9942 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,2] := by - exact rowSquare_join (by decide) sg13 sg5062 - -lemma sg9943 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1396 - -lemma sg9944 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5063 - -lemma sg9945 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5865 - -lemma sg9946 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5064 - -lemma sg9947 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg5065 - -lemma sg9948 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg5066 - -lemma sg9949 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,5] := by - exact rowSquare_join (by decide) sg13 sg5067 - -lemma sg9950 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1406 - -lemma sg9951 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1358 - -lemma sg9952 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8266 - -lemma sg9953 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1373 sg1348 - -lemma sg9954 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg5844 - -lemma sg9955 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8267 - -lemma sg9956 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8268 - -lemma sg9957 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg5866 - -lemma sg9958 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5867 - -lemma sg9959 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5068 - -lemma sg9960 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5069 - -lemma sg9961 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3] := by - exact rowSquare_join (by decide) sg1376 sg1348 - -lemma sg9962 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8269 - -lemma sg9963 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5070 - -lemma sg9964 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5868 - -lemma sg9965 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5071 - -lemma sg9966 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg5072 - -lemma sg9967 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg5073 - -lemma sg9968 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5870 - -lemma sg9969 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5074 - -lemma sg9970 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,5,2,2] := by - exact rowSquare_join (by decide) sg4 sg5872 - -lemma sg9971 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,1] := by - exact rowSquare_join (by decide) sg13 sg5075 - -lemma sg9972 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,5,4] := by - exact rowSquare_join (by decide) sg13 sg5076 - -lemma sg9973 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,6,2,1] := by - exact rowSquare_join (by decide) sg13 sg5077 - -lemma sg9974 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,6,3] := by - exact rowSquare_join (by decide) sg13 sg5078 - -lemma sg9975 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1023 sg1755 - -lemma sg9976 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1399 - -lemma sg9977 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg1773 - -lemma sg9978 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1023 sg1758 - -lemma sg9979 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2] := by - exact rowSquare_join (by decide) sg1006 sg1770 - -lemma sg9980 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1399 - -lemma sg9981 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5875 - -lemma sg9982 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5876 - -lemma sg9983 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5079 - -lemma sg9984 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,2] := by - exact rowSquare_join (by decide) sg1001 sg1773 - -lemma sg9985 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5877 - -lemma sg9986 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5080 - -lemma sg9987 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,4,2,2] := by - exact rowSquare_join (by decide) sg4 sg5879 - -lemma sg9988 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg5081 - -lemma sg9989 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,4,4] := by - exact rowSquare_join (by decide) sg13 sg5082 - -lemma sg9990 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,5,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5881 - -lemma sg9991 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,1] := by - exact rowSquare_join (by decide) sg13 sg5083 - -lemma sg9992 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,5,3] := by - exact rowSquare_join (by decide) sg13 sg5084 - -lemma sg9993 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,6,1,1] := by - exact rowSquare_join (by decide) sg4 sg5884 - -lemma sg9994 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,6,2] := by - exact rowSquare_join (by decide) sg4 sg5885 - -lemma sg9995 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1400 - -lemma sg9996 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6765 - -lemma sg9997 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg5085 - -lemma sg9998 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg5 sg5860 - -lemma sg9999 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5886 - -lemma sg10000 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5086 - -lemma sg10001 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3] := by - exact rowSquare_join (by decide) sg4 sg5887 - -lemma sg10002 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg5087 - -lemma sg10003 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2] := by - exact rowSquare_join (by decide) sg13 sg5088 - -lemma sg10004 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg9 sg5139 - -lemma sg10005 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5089 - -lemma sg10006 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg5057 - -lemma sg10007 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg9 sg5140 - -lemma sg10008 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5090 - -lemma sg10009 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg5091 - -lemma sg10010 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg5092 - -lemma sg10011 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8270 - -lemma sg10012 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg10 sg5139 - -lemma sg10013 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg5060 - -lemma sg10014 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5093 - -lemma sg10015 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg5094 - -lemma sg10016 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5095 - -lemma sg10017 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,4,2,2] := by - exact rowSquare_join (by decide) sg14 sg5065 - -lemma sg10018 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg5096 - -lemma sg10019 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,4,4] := by - exact rowSquare_join (by decide) sg13 sg5097 - -lemma sg10020 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg5069 - -lemma sg10021 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5098 - -lemma sg10022 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2] := by - exact rowSquare_join (by decide) sg892 sg1890 - -lemma sg10023 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg5099 - -lemma sg10024 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg3745 - -lemma sg10025 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg9 sg5147 - -lemma sg10026 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg3746 - -lemma sg10027 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3] := by - exact rowSquare_join (by decide) sg5 sg5887 - -lemma sg10028 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg3747 - -lemma sg10029 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5100 - -lemma sg10030 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,2] := by - exact rowSquare_join (by decide) sg39 sg4554 - -lemma sg10031 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,1] := by - exact rowSquare_join (by decide) sg39 sg4555 - -lemma sg10032 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg5085 - -lemma sg10033 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg27 sg4580 - -lemma sg10034 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg74 sg3748 - -lemma sg10035 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,2] := by - exact rowSquare_join (by decide) sg39 sg4556 - -lemma sg10036 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg3749 - -lemma sg10037 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,4,2,2] := by - exact rowSquare_join (by decide) sg40 sg4554 - -lemma sg10038 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,1] := by - exact rowSquare_join (by decide) sg39 sg4557 - -lemma sg10039 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,4,4] := by - exact rowSquare_join (by decide) sg39 sg4558 - -lemma sg10040 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg5089 - -lemma sg10041 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg27 sg4581 - -lemma sg10042 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,6,3,2,2] := by - exact rowSquare_join (by decide) sg40 sg4556 - -lemma sg10043 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg27 sg4582 - -lemma sg10044 : RowSquare [6,5,2,2,2,2,2,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg5672 - -lemma sg10045 : RowSquare [6,5,2,2,2,2,2,1] [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5680 - -lemma sg10046 : RowSquare [6,5,2,2,2,2,2,1] [5,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5681 - -lemma sg10047 : RowSquare [6,5,2,2,2,2,2,1] [5,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5682 - -lemma sg10048 : RowSquare [6,5,2,2,2,2,2,1] [5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5683 - -lemma sg10049 : RowSquare [6,5,2,2,2,2,2,1] [5,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg5684 - -lemma sg10050 : RowSquare [6,5,2,2,2,2,2,1] [5,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5685 - -lemma sg10051 : RowSquare [6,5,2,2,2,2,2,1] [5,5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5686 - -lemma sg10052 : RowSquare [6,5,2,2,2,2,2,1] [5,5,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5687 - -lemma sg10053 : RowSquare [6,5,2,2,2,2,2,1] [5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5688 - -lemma sg10054 : RowSquare [6,5,2,2,2,2,2,1] [5,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg5689 - -lemma sg10055 : RowSquare [6,5,2,2,2,2,2,1] [5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg5690 - -lemma sg10056 : RowSquare [6,5,2,2,2,2,2,1] [5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5691 - -lemma sg10057 : RowSquare [6,5,2,2,2,2,2,1] [5,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5692 - -lemma sg10058 : RowSquare [6,5,2,2,2,2,2,1] [5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg5693 - -lemma sg10059 : RowSquare [6,5,2,2,2,2,2,1] [5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5694 - -lemma sg10060 : RowSquare [6,5,2,2,2,2,2,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg5673 - -lemma sg10061 : RowSquare [6,5,2,2,2,2,2,1] [6,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg5675 - -lemma sg10062 : RowSquare [6,5,2,2,2,2,2,1] [6,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg5676 - -lemma sg10063 : RowSquare [6,5,2,2,2,2,2,1] [6,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg5677 - -lemma sg10064 : RowSquare [6,5,2,2,2,2,2,1] [6,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg15 sg5678 - -lemma sg10065 : RowSquare [6,5,2,2,2,2,2,1] [6,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg5679 - -lemma sg10066 : RowSquare [6,5,2,2,2,2,2,1] [6,5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5697 - -lemma sg10067 : RowSquare [6,5,2,2,2,2,2,1] [6,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5706 - -lemma sg10068 : RowSquare [6,5,2,2,2,2,2,1] [6,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5699 - -lemma sg10069 : RowSquare [6,5,2,2,2,2,2,1] [6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg838 sg1649 - -lemma sg10070 : RowSquare [6,5,2,2,2,2,2,1] [6,6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5702 - -lemma sg10071 : RowSquare [6,5,2,2,2,2,2,1] [6,6,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5703 - -lemma sg10072 : RowSquare [6,5,2,2,2,2,2,1] [6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg5704 - -lemma sg10073 : RowSquare [6,5,2,2,2,2,2,1] [6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5705 - -lemma sg10074 : RowSquare [6,5,2,2,2,2,2,1] [7,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg5681 - -lemma sg10075 : RowSquare [6,5,2,2,2,2,2,1] [7,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg5682 - -lemma sg10076 : RowSquare [6,5,2,2,2,2,2,1] [7,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg5683 - -lemma sg10077 : RowSquare [6,5,2,2,2,2,2,1] [7,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg15 sg5684 - -lemma sg10078 : RowSquare [6,5,2,2,2,2,2,1] [7,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5706 - -lemma sg10079 : RowSquare [6,5,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg313 sg2626 - -lemma sg10080 : RowSquare [6,5,3,2,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg314 sg2626 - -lemma sg10081 : RowSquare [6,5,3,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg315 sg2626 - -lemma sg10082 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg314 sg2627 - -lemma sg10083 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg315 sg2627 - -lemma sg10084 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8352 - -lemma sg10085 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg312 sg2632 - -lemma sg10086 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg312 sg2633 - -lemma sg10087 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg319 sg2626 - -lemma sg10088 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg320 sg2626 - -lemma sg10089 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg826 sg1757 - -lemma sg10090 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg889 sg1688 - -lemma sg10091 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg313 sg2633 - -lemma sg10092 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1673 - -lemma sg10093 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1674 - -lemma sg10094 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg890 sg1688 - -lemma sg10095 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1675 - -lemma sg10096 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2136 - -lemma sg10097 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg828 sg1757 - -lemma sg10098 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg891 sg1688 - -lemma sg10099 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg8365 - -lemma sg10100 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg312 sg2636 - -lemma sg10101 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg320 sg2627 - -lemma sg10102 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg8372 - -lemma sg10103 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1228 - -lemma sg10104 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg8376 - -lemma sg10105 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg324 sg2626 - -lemma sg10106 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg1646 - -lemma sg10107 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5119 - -lemma sg10108 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg897 sg1688 - -lemma sg10109 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1230 - -lemma sg10110 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1227 - -lemma sg10111 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg5962 - -lemma sg10112 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg5964 - -lemma sg10113 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5120 - -lemma sg10114 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg5121 - -lemma sg10115 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,4,4] := by - exact rowSquare_join (by decide) sg1001 sg1647 - -lemma sg10116 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg1676 - -lemma sg10117 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg831 sg1756 - -lemma sg10118 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg5965 - -lemma sg10119 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg5966 - -lemma sg10120 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5122 - -lemma sg10121 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5123 - -lemma sg10122 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg5124 - -lemma sg10123 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg3766 - -lemma sg10124 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5125 - -lemma sg10125 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg74 sg3767 - -lemma sg10126 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg5126 - -lemma sg10127 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg74 sg3768 - -lemma sg10128 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,5,2] := by - exact rowSquare_join (by decide) sg13 sg5127 - -lemma sg10129 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg6890 - -lemma sg10130 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg6893 - -lemma sg10131 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1231 - -lemma sg10132 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg324 sg2627 - -lemma sg10133 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8397 - -lemma sg10134 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg4622 - -lemma sg10135 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg3774 - -lemma sg10136 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,5,5,5,1] := by - exact rowSquare_join (by decide) sg75 sg3768 - -lemma sg10137 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg5119 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes19 + +namespace OAI + +/-! Semigroup Nodes 23. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg9738 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1763 + +lemma sg9739 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1006 sg1758 + +lemma sg9740 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1389 + +lemma sg9741 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1378 + +lemma sg9742 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1377 + +lemma sg9743 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg1764 + +lemma sg9744 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1379 + +lemma sg9745 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1767 + +lemma sg9746 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1331 sg1377 + +lemma sg9747 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1001 sg1764 + +lemma sg9748 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1377 + +lemma sg9749 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1008 sg1757 + +lemma sg9750 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1008 sg1758 + +lemma sg9751 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1000 sg1765 + +lemma sg9752 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1001 sg1765 + +lemma sg9753 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1378 + +lemma sg9754 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg999 sg1766 + +lemma sg9755 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1379 + +lemma sg9756 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1378 + +lemma sg9757 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg1000 sg1766 + +lemma sg9758 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg1332 sg1378 + +lemma sg9759 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1379 + +lemma sg9760 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg1332 sg1379 + +lemma sg9761 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3] := by + exact rowSquare_join (by decide) sg1001 sg1767 + +lemma sg9762 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1390 + +lemma sg9763 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8230 + +lemma sg9764 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8231 + +lemma sg9765 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1018 sg1754 + +lemma sg9766 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1391 + +lemma sg9767 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8232 + +lemma sg9768 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8233 + +lemma sg9769 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1392 + +lemma sg9770 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8234 + +lemma sg9771 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6726 + +lemma sg9772 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8235 + +lemma sg9773 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1393 + +lemma sg9774 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8236 + +lemma sg9775 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6727 + +lemma sg9776 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1380 sg1331 + +lemma sg9777 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6728 + +lemma sg9778 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1380 sg1332 + +lemma sg9779 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1009 sg1758 + +lemma sg9780 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1394 + +lemma sg9781 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8237 + +lemma sg9782 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6729 + +lemma sg9783 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8238 + +lemma sg9784 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1021 sg1754 + +lemma sg9785 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1395 + +lemma sg9786 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8239 + +lemma sg9787 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6730 + +lemma sg9788 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6731 + +lemma sg9789 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8240 + +lemma sg9790 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8241 + +lemma sg9791 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6732 + +lemma sg9792 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1331 sg1381 + +lemma sg9793 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6733 + +lemma sg9794 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1381 sg1332 + +lemma sg9795 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1396 + +lemma sg9796 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1387 + +lemma sg9797 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6734 + +lemma sg9798 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8242 + +lemma sg9799 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5831 + +lemma sg9800 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6735 + +lemma sg9801 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8245 + +lemma sg9802 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5832 + +lemma sg9803 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg5833 + +lemma sg9804 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1382 + +lemma sg9805 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1012 sg1757 + +lemma sg9806 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1383 + +lemma sg9807 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg6736 + +lemma sg9808 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg6737 + +lemma sg9809 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg6738 + +lemma sg9810 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1022 sg1754 + +lemma sg9811 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1397 + +lemma sg9812 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1348 + +lemma sg9813 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8246 + +lemma sg9814 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1373 sg1338 + +lemma sg9815 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1398 + +lemma sg9816 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1349 + +lemma sg9817 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8247 + +lemma sg9818 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8248 + +lemma sg9819 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5834 + +lemma sg9820 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8249 + +lemma sg9821 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1373 sg1340 + +lemma sg9822 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1331 sg1384 + +lemma sg9823 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1338 sg1376 + +lemma sg9824 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1384 + +lemma sg9825 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1389 + +lemma sg9826 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8250 + +lemma sg9827 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8251 + +lemma sg9828 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5835 + +lemma sg9829 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8252 + +lemma sg9830 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8253 + +lemma sg9831 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg5836 + +lemma sg9832 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg5837 + +lemma sg9833 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1386 + +lemma sg9834 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg1332 sg1386 + +lemma sg9835 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,3] := by + exact rowSquare_join (by decide) sg1376 sg1340 + +lemma sg9836 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1387 + +lemma sg9837 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5838 + +lemma sg9838 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8255 + +lemma sg9839 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5839 + +lemma sg9840 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg5840 + +lemma sg9841 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3] := by + exact rowSquare_join (by decide) sg4 sg5841 + +lemma sg9842 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg4 sg5842 + +lemma sg9843 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,2] := by + exact rowSquare_join (by decide) sg4 sg5843 + +lemma sg9844 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1023 sg1754 + +lemma sg9845 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1399 + +lemma sg9846 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1015 sg1755 + +lemma sg9847 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg998 sg1770 + +lemma sg9848 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1016 sg1755 + +lemma sg9849 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1388 + +lemma sg9850 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1771 + +lemma sg9851 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5844 + +lemma sg9852 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg1885 + +lemma sg9853 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1015 sg1758 + +lemma sg9854 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg1000 sg1770 + +lemma sg9855 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg1001 sg1770 + +lemma sg9856 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1389 + +lemma sg9857 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1388 + +lemma sg9858 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5845 + +lemma sg9859 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5846 + +lemma sg9860 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5847 + +lemma sg9861 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg1332 sg1388 + +lemma sg9862 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3] := by + exact rowSquare_join (by decide) sg1001 sg1771 + +lemma sg9863 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg891 sg1885 + +lemma sg9864 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,2] := by + exact rowSquare_join (by decide) sg892 sg1885 + +lemma sg9865 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1389 + +lemma sg9866 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1389 + +lemma sg9867 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5848 + +lemma sg9868 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg5849 + +lemma sg9869 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,2] := by + exact rowSquare_join (by decide) sg1340 sg1378 + +lemma sg9870 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,1] := by + exact rowSquare_join (by decide) sg1340 sg1379 + +lemma sg9871 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2] := by + exact rowSquare_join (by decide) sg4 sg5850 + +lemma sg9872 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,1] := by + exact rowSquare_join (by decide) sg4 sg5851 + +lemma sg9873 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [6,6,6,4] := by + exact rowSquare_join (by decide) sg4 sg5852 + +lemma sg9874 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1024 sg1754 + +lemma sg9875 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1400 + +lemma sg9876 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6739 + +lemma sg9877 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6740 + +lemma sg9878 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1025 sg1754 + +lemma sg9879 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1401 + +lemma sg9880 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6741 + +lemma sg9881 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6742 + +lemma sg9882 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6743 + +lemma sg9883 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1026 sg1754 + +lemma sg9884 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1402 + +lemma sg9885 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6744 + +lemma sg9886 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6745 + +lemma sg9887 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5853 + +lemma sg9888 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6746 + +lemma sg9889 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6747 + +lemma sg9890 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6748 + +lemma sg9891 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1331 sg1390 + +lemma sg9892 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6749 + +lemma sg9893 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1390 sg1332 + +lemma sg9894 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1027 sg1754 + +lemma sg9895 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1403 + +lemma sg9896 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8261 + +lemma sg9897 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6750 + +lemma sg9898 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6751 + +lemma sg9899 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1404 + +lemma sg9900 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8262 + +lemma sg9901 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6752 + +lemma sg9902 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5854 + +lemma sg9903 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5855 + +lemma sg9904 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6753 + +lemma sg9905 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6754 + +lemma sg9906 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg5832 + +lemma sg9907 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg5 sg5833 + +lemma sg9908 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1391 + +lemma sg9909 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1396 + +lemma sg9910 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6755 + +lemma sg9911 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5856 + +lemma sg9912 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5857 + +lemma sg9913 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5858 + +lemma sg9914 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5054 + +lemma sg9915 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg5859 + +lemma sg9916 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg5860 + +lemma sg9917 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5055 + +lemma sg9918 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg5056 + +lemma sg9919 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3] := by + exact rowSquare_join (by decide) sg13 sg5057 + +lemma sg9920 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1028 sg1754 + +lemma sg9921 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1405 + +lemma sg9922 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8263 + +lemma sg9923 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6758 + +lemma sg9924 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6759 + +lemma sg9925 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg5834 + +lemma sg9926 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8264 + +lemma sg9927 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6760 + +lemma sg9928 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6761 + +lemma sg9929 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5861 + +lemma sg9930 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6762 + +lemma sg9931 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5058 + +lemma sg9932 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg5 sg5836 + +lemma sg9933 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg5 sg5837 + +lemma sg9934 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6763 + +lemma sg9935 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6764 + +lemma sg9936 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5862 + +lemma sg9937 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5863 + +lemma sg9938 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5059 + +lemma sg9939 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5060 + +lemma sg9940 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3] := by + exact rowSquare_join (by decide) sg4 sg5864 + +lemma sg9941 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg5061 + +lemma sg9942 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,2] := by + exact rowSquare_join (by decide) sg13 sg5062 + +lemma sg9943 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1396 + +lemma sg9944 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5063 + +lemma sg9945 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5865 + +lemma sg9946 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5064 + +lemma sg9947 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg5065 + +lemma sg9948 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg5066 + +lemma sg9949 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,5,5,5] := by + exact rowSquare_join (by decide) sg13 sg5067 + +lemma sg9950 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1406 + +lemma sg9951 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1358 + +lemma sg9952 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8266 + +lemma sg9953 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1373 sg1348 + +lemma sg9954 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg5844 + +lemma sg9955 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8267 + +lemma sg9956 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8268 + +lemma sg9957 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg5866 + +lemma sg9958 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5867 + +lemma sg9959 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5068 + +lemma sg9960 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5069 + +lemma sg9961 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3] := by + exact rowSquare_join (by decide) sg1376 sg1348 + +lemma sg9962 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8269 + +lemma sg9963 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5070 + +lemma sg9964 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5868 + +lemma sg9965 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5071 + +lemma sg9966 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg5072 + +lemma sg9967 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg5073 + +lemma sg9968 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5870 + +lemma sg9969 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5074 + +lemma sg9970 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,5,2,2] := by + exact rowSquare_join (by decide) sg4 sg5872 + +lemma sg9971 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,1] := by + exact rowSquare_join (by decide) sg13 sg5075 + +lemma sg9972 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,5,4] := by + exact rowSquare_join (by decide) sg13 sg5076 + +lemma sg9973 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,6,2,1] := by + exact rowSquare_join (by decide) sg13 sg5077 + +lemma sg9974 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,6,6,3] := by + exact rowSquare_join (by decide) sg13 sg5078 + +lemma sg9975 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1023 sg1755 + +lemma sg9976 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1399 + +lemma sg9977 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg1773 + +lemma sg9978 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1023 sg1758 + +lemma sg9979 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2] := by + exact rowSquare_join (by decide) sg1006 sg1770 + +lemma sg9980 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1399 + +lemma sg9981 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5875 + +lemma sg9982 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5876 + +lemma sg9983 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5079 + +lemma sg9984 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,2] := by + exact rowSquare_join (by decide) sg1001 sg1773 + +lemma sg9985 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5877 + +lemma sg9986 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5080 + +lemma sg9987 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,4,2,2] := by + exact rowSquare_join (by decide) sg4 sg5879 + +lemma sg9988 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg5081 + +lemma sg9989 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,4,4] := by + exact rowSquare_join (by decide) sg13 sg5082 + +lemma sg9990 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,5,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5881 + +lemma sg9991 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,1] := by + exact rowSquare_join (by decide) sg13 sg5083 + +lemma sg9992 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,5,3] := by + exact rowSquare_join (by decide) sg13 sg5084 + +lemma sg9993 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,6,1,1] := by + exact rowSquare_join (by decide) sg4 sg5884 + +lemma sg9994 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [7,7,6,2] := by + exact rowSquare_join (by decide) sg4 sg5885 + +lemma sg9995 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1400 + +lemma sg9996 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6765 + +lemma sg9997 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg5085 + +lemma sg9998 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg5 sg5860 + +lemma sg9999 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5886 + +lemma sg10000 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5086 + +lemma sg10001 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3] := by + exact rowSquare_join (by decide) sg4 sg5887 + +lemma sg10002 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg5087 + +lemma sg10003 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2] := by + exact rowSquare_join (by decide) sg13 sg5088 + +lemma sg10004 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg9 sg5139 + +lemma sg10005 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5089 + +lemma sg10006 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg5057 + +lemma sg10007 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg9 sg5140 + +lemma sg10008 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5090 + +lemma sg10009 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg5091 + +lemma sg10010 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg5092 + +lemma sg10011 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8270 + +lemma sg10012 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg10 sg5139 + +lemma sg10013 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg5060 + +lemma sg10014 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5093 + +lemma sg10015 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg5094 + +lemma sg10016 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5095 + +lemma sg10017 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,4,2,2] := by + exact rowSquare_join (by decide) sg14 sg5065 + +lemma sg10018 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg5096 + +lemma sg10019 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,6,4,4] := by + exact rowSquare_join (by decide) sg13 sg5097 + +lemma sg10020 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg5069 + +lemma sg10021 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5098 + +lemma sg10022 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2] := by + exact rowSquare_join (by decide) sg892 sg1890 + +lemma sg10023 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg5099 + +lemma sg10024 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg3745 + +lemma sg10025 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg9 sg5147 + +lemma sg10026 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg3746 + +lemma sg10027 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3] := by + exact rowSquare_join (by decide) sg5 sg5887 + +lemma sg10028 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg3747 + +lemma sg10029 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5100 + +lemma sg10030 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,2] := by + exact rowSquare_join (by decide) sg39 sg4554 + +lemma sg10031 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,1] := by + exact rowSquare_join (by decide) sg39 sg4555 + +lemma sg10032 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg5085 + +lemma sg10033 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg27 sg4580 + +lemma sg10034 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg74 sg3748 + +lemma sg10035 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,2] := by + exact rowSquare_join (by decide) sg39 sg4556 + +lemma sg10036 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg3749 + +lemma sg10037 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,4,2,2] := by + exact rowSquare_join (by decide) sg40 sg4554 + +lemma sg10038 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,1] := by + exact rowSquare_join (by decide) sg39 sg4557 + +lemma sg10039 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,5,4,4] := by + exact rowSquare_join (by decide) sg39 sg4558 + +lemma sg10040 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg5089 + +lemma sg10041 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg27 sg4581 + +lemma sg10042 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,6,3,2,2] := by + exact rowSquare_join (by decide) sg40 sg4556 + +lemma sg10043 : RowSquare [6,5,2,1,1,1,1,1,1,1,1,1] [9,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg27 sg4582 + +lemma sg10044 : RowSquare [6,5,2,2,2,2,2,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg5672 + +lemma sg10045 : RowSquare [6,5,2,2,2,2,2,1] [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5680 + +lemma sg10046 : RowSquare [6,5,2,2,2,2,2,1] [5,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5681 + +lemma sg10047 : RowSquare [6,5,2,2,2,2,2,1] [5,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5682 + +lemma sg10048 : RowSquare [6,5,2,2,2,2,2,1] [5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5683 + +lemma sg10049 : RowSquare [6,5,2,2,2,2,2,1] [5,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg5684 + +lemma sg10050 : RowSquare [6,5,2,2,2,2,2,1] [5,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5685 + +lemma sg10051 : RowSquare [6,5,2,2,2,2,2,1] [5,5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5686 + +lemma sg10052 : RowSquare [6,5,2,2,2,2,2,1] [5,5,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5687 + +lemma sg10053 : RowSquare [6,5,2,2,2,2,2,1] [5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5688 + +lemma sg10054 : RowSquare [6,5,2,2,2,2,2,1] [5,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg5689 + +lemma sg10055 : RowSquare [6,5,2,2,2,2,2,1] [5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg5690 + +lemma sg10056 : RowSquare [6,5,2,2,2,2,2,1] [5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5691 + +lemma sg10057 : RowSquare [6,5,2,2,2,2,2,1] [5,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5692 + +lemma sg10058 : RowSquare [6,5,2,2,2,2,2,1] [5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg5693 + +lemma sg10059 : RowSquare [6,5,2,2,2,2,2,1] [5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5694 + +lemma sg10060 : RowSquare [6,5,2,2,2,2,2,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg5673 + +lemma sg10061 : RowSquare [6,5,2,2,2,2,2,1] [6,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg5675 + +lemma sg10062 : RowSquare [6,5,2,2,2,2,2,1] [6,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg5676 + +lemma sg10063 : RowSquare [6,5,2,2,2,2,2,1] [6,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg5677 + +lemma sg10064 : RowSquare [6,5,2,2,2,2,2,1] [6,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg15 sg5678 + +lemma sg10065 : RowSquare [6,5,2,2,2,2,2,1] [6,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg5679 + +lemma sg10066 : RowSquare [6,5,2,2,2,2,2,1] [6,5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5697 + +lemma sg10067 : RowSquare [6,5,2,2,2,2,2,1] [6,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5706 + +lemma sg10068 : RowSquare [6,5,2,2,2,2,2,1] [6,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5699 + +lemma sg10069 : RowSquare [6,5,2,2,2,2,2,1] [6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg838 sg1649 + +lemma sg10070 : RowSquare [6,5,2,2,2,2,2,1] [6,6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5702 + +lemma sg10071 : RowSquare [6,5,2,2,2,2,2,1] [6,6,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5703 + +lemma sg10072 : RowSquare [6,5,2,2,2,2,2,1] [6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg5704 + +lemma sg10073 : RowSquare [6,5,2,2,2,2,2,1] [6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5705 + +lemma sg10074 : RowSquare [6,5,2,2,2,2,2,1] [7,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg5681 + +lemma sg10075 : RowSquare [6,5,2,2,2,2,2,1] [7,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg5682 + +lemma sg10076 : RowSquare [6,5,2,2,2,2,2,1] [7,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg5683 + +lemma sg10077 : RowSquare [6,5,2,2,2,2,2,1] [7,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg15 sg5684 + +lemma sg10078 : RowSquare [6,5,2,2,2,2,2,1] [7,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5706 + +lemma sg10079 : RowSquare [6,5,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg313 sg2626 + +lemma sg10080 : RowSquare [6,5,3,2,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg314 sg2626 + +lemma sg10081 : RowSquare [6,5,3,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg315 sg2626 + +lemma sg10082 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg314 sg2627 + +lemma sg10083 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg315 sg2627 + +lemma sg10084 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8352 + +lemma sg10085 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg312 sg2632 + +lemma sg10086 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg312 sg2633 + +lemma sg10087 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg319 sg2626 + +lemma sg10088 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg320 sg2626 + +lemma sg10089 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg826 sg1757 + +lemma sg10090 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg889 sg1688 + +lemma sg10091 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg313 sg2633 + +lemma sg10092 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1673 + +lemma sg10093 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1674 + +lemma sg10094 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg890 sg1688 + +lemma sg10095 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1675 + +lemma sg10096 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2136 + +lemma sg10097 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg828 sg1757 + +lemma sg10098 : RowSquare [6,5,3,2,1,1,1,1,1,1] [4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg891 sg1688 + +lemma sg10099 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg8365 + +lemma sg10100 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg312 sg2636 + +lemma sg10101 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg320 sg2627 + +lemma sg10102 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg8372 + +lemma sg10103 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1228 + +lemma sg10104 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg8376 + +lemma sg10105 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg324 sg2626 + +lemma sg10106 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg1646 + +lemma sg10107 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5119 + +lemma sg10108 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg897 sg1688 + +lemma sg10109 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1230 + +lemma sg10110 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1227 + +lemma sg10111 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg5962 + +lemma sg10112 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg5964 + +lemma sg10113 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5120 + +lemma sg10114 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg5121 + +lemma sg10115 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,4,4,4] := by + exact rowSquare_join (by decide) sg1001 sg1647 + +lemma sg10116 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg1676 + +lemma sg10117 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg831 sg1756 + +lemma sg10118 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg5965 + +lemma sg10119 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg5966 + +lemma sg10120 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5122 + +lemma sg10121 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5123 + +lemma sg10122 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg5124 + +lemma sg10123 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg3766 + +lemma sg10124 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5125 + +lemma sg10125 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg74 sg3767 + +lemma sg10126 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg5126 + +lemma sg10127 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg74 sg3768 + +lemma sg10128 : RowSquare [6,5,3,2,1,1,1,1,1,1] [5,5,5,5,2] := by + exact rowSquare_join (by decide) sg13 sg5127 + +lemma sg10129 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg6890 + +lemma sg10130 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg6893 + +lemma sg10131 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1231 + +lemma sg10132 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg324 sg2627 + +lemma sg10133 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8397 + +lemma sg10134 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg4622 + +lemma sg10135 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg3774 + +lemma sg10136 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,5,5,5,1] := by + exact rowSquare_join (by decide) sg75 sg3768 + +lemma sg10137 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg5119 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes24.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes24.lean index ce78e3d2f23846c79da1325e82a7a8a860dce0cd..8b9810af70fc89e47cc12ff34eaf322601ca534f 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes24.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes24.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes15 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes16 - -namespace OAI - -/-! Semigroup Nodes 24. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg10138 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5130 - -lemma sg10139 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg74 sg3777 - -lemma sg10140 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1230 - -lemma sg10141 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg55 sg3836 - -lemma sg10142 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,4,3,3] := by - exact rowSquare_join (by decide) sg40 sg4571 - -lemma sg10143 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg74 sg3781 - -lemma sg10144 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg27 sg4622 - -lemma sg10145 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg55 sg3837 - -lemma sg10146 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg3782 - -lemma sg10147 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg74 sg3783 - -lemma sg10148 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,3,2] := by - exact rowSquare_join (by decide) sg76 sg3766 - -lemma sg10149 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,4,1] := by - exact rowSquare_join (by decide) sg76 sg3767 - -lemma sg10150 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,5] := by - exact rowSquare_join (by decide) sg76 sg3768 - -lemma sg10151 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg55 sg3838 - -lemma sg10152 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg3784 - -lemma sg10153 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,6,2,2] := by - exact rowSquare_join (by decide) sg77 sg3766 - -lemma sg10154 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,6,3,1] := by - exact rowSquare_join (by decide) sg77 sg3767 - -lemma sg10155 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,6,4] := by - exact rowSquare_join (by decide) sg77 sg3768 - -lemma sg10156 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg3785 - -lemma sg10157 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg55 sg3843 - -lemma sg10158 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg165 sg3160 - -lemma sg10159 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,6,6,2,1] := by - exact rowSquare_join (by decide) sg167 sg3157 - -lemma sg10160 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,6,6,3] := by - exact rowSquare_join (by decide) sg167 sg3158 - -lemma sg10161 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5133 - -lemma sg10162 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,7,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg3786 - -lemma sg10163 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,7,3,3,1,1] := by - exact rowSquare_join (by decide) sg74 sg3787 - -lemma sg10164 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,7,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg55 sg3847 - -lemma sg10165 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,7,4,2,2] := by - exact rowSquare_join (by decide) sg166 sg3159 - -lemma sg10166 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,7,4,4] := by - exact rowSquare_join (by decide) sg76 sg3781 - -lemma sg10167 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1327 sg1327 - -lemma sg10168 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1327 sg1328 - -lemma sg10169 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1329 - -lemma sg10170 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1330 - -lemma sg10171 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1331 - -lemma sg10172 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1332 - -lemma sg10173 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1333 - -lemma sg10174 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1328 sg1328 - -lemma sg10175 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1334 - -lemma sg10176 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1328 sg1329 - -lemma sg10177 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1335 - -lemma sg10178 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1330 - -lemma sg10179 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1336 - -lemma sg10180 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1331 - -lemma sg10181 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1337 - -lemma sg10182 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1332 - -lemma sg10183 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1338 - -lemma sg10184 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1329 sg1329 - -lemma sg10185 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1339 - -lemma sg10186 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1329 sg1330 - -lemma sg10187 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1340 - -lemma sg10188 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1331 - -lemma sg10189 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1332 - -lemma sg10190 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1330 sg1330 - -lemma sg10191 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1330 sg1331 - -lemma sg10192 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1332 - -lemma sg10193 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1331 sg1331 - -lemma sg10194 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1331 sg1332 - -lemma sg10195 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg1332 sg1332 - -lemma sg10196 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1341 - -lemma sg10197 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1328 sg1333 - -lemma sg10198 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1342 - -lemma sg10199 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1334 - -lemma sg10200 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1329 sg1333 - -lemma sg10201 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1343 - -lemma sg10202 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1335 - -lemma sg10203 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1333 sg1330 - -lemma sg10204 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1344 - -lemma sg10205 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1336 - -lemma sg10206 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1333 sg1331 - -lemma sg10207 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1337 - -lemma sg10208 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1333 sg1332 - -lemma sg10209 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1345 - -lemma sg10210 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1338 - -lemma sg10211 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1329 sg1334 - -lemma sg10212 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1346 - -lemma sg10213 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1339 - -lemma sg10214 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1335 - -lemma sg10215 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1330 sg1334 - -lemma sg10216 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1347 - -lemma sg10217 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1340 - -lemma sg10218 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1336 - -lemma sg10219 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1334 sg1331 - -lemma sg10220 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1337 - -lemma sg10221 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1334 sg1332 - -lemma sg10222 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1330 sg1335 - -lemma sg10223 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1336 - -lemma sg10224 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1331 sg1335 - -lemma sg10225 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1337 - -lemma sg10226 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg1335 sg1332 - -lemma sg10227 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1331 sg1336 - -lemma sg10228 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1337 - -lemma sg10229 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1336 - -lemma sg10230 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg1332 sg1337 - -lemma sg10231 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1348 - -lemma sg10232 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1338 - -lemma sg10233 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1349 - -lemma sg10234 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1339 - -lemma sg10235 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1330 sg1338 - -lemma sg10236 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1340 - -lemma sg10237 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1331 sg1338 - -lemma sg10238 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1338 sg1332 - -lemma sg10239 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1339 - -lemma sg10240 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1340 - -lemma sg10241 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1331 sg1339 - -lemma sg10242 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1339 - -lemma sg10243 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1340 - -lemma sg10244 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1332 sg1340 - -lemma sg10245 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1350 - -lemma sg10246 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1341 - -lemma sg10247 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6905 - -lemma sg10248 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1351 - -lemma sg10249 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1342 - -lemma sg10250 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6906 - -lemma sg10251 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1352 - -lemma sg10252 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1343 - -lemma sg10253 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6907 - -lemma sg10254 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1330 sg1341 - -lemma sg10255 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1353 - -lemma sg10256 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1344 - -lemma sg10257 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6908 - -lemma sg10258 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1341 sg1331 - -lemma sg10259 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6909 - -lemma sg10260 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1341 sg1332 - -lemma sg10261 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1354 - -lemma sg10262 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1345 - -lemma sg10263 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1342 - -lemma sg10264 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6910 - -lemma sg10265 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1355 - -lemma sg10266 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1346 - -lemma sg10267 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1343 - -lemma sg10268 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6911 - -lemma sg10269 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1347 - -lemma sg10270 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1344 - -lemma sg10271 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6912 - -lemma sg10272 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1331 sg1342 - -lemma sg10273 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6913 - -lemma sg10274 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1342 sg1332 - -lemma sg10275 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1343 - -lemma sg10276 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6914 - -lemma sg10277 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1344 - -lemma sg10278 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6915 - -lemma sg10279 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg6916 - -lemma sg10280 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1343 - -lemma sg10281 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1344 - -lemma sg10282 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg6917 - -lemma sg10283 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg6918 - -lemma sg10284 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg6919 - -lemma sg10285 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1356 - -lemma sg10286 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1348 - -lemma sg10287 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1345 - -lemma sg10288 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1334 sg1338 - -lemma sg10289 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1357 - -lemma sg10290 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1349 - -lemma sg10291 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1346 - -lemma sg10292 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1345 - -lemma sg10293 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1335 sg1338 - -lemma sg10294 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1347 - -lemma sg10295 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1334 sg1340 - -lemma sg10296 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1331 sg1345 - -lemma sg10297 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1338 sg1337 - -lemma sg10298 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1345 - -lemma sg10299 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1346 - -lemma sg10300 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1335 sg1339 - -lemma sg10301 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1347 - -lemma sg10302 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1346 - -lemma sg10303 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg1336 sg1339 - -lemma sg10304 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg1332 sg1346 - -lemma sg10305 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1347 - -lemma sg10306 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg1332 sg1347 - -lemma sg10307 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,3] := by - exact rowSquare_join (by decide) sg1337 sg1340 - -lemma sg10308 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1358 - -lemma sg10309 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1348 - -lemma sg10310 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1338 sg1338 - -lemma sg10311 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1349 - -lemma sg10312 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1348 - -lemma sg10313 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1338 sg1339 - -lemma sg10314 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1348 - -lemma sg10315 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg1332 sg1348 - -lemma sg10316 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1349 - -lemma sg10317 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg1339 sg1339 - -lemma sg10318 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1349 - -lemma sg10319 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg1332 sg1349 - -lemma sg10320 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2] := by - exact rowSquare_join (by decide) sg1340 sg1340 - -lemma sg10321 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1359 - -lemma sg10322 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1350 - -lemma sg10323 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6920 - -lemma sg10324 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1360 - -lemma sg10325 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1351 - -lemma sg10326 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6921 - -lemma sg10327 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6922 - -lemma sg10328 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1361 - -lemma sg10329 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1352 - -lemma sg10330 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6923 - -lemma sg10331 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6924 - -lemma sg10332 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1353 - -lemma sg10333 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6925 - -lemma sg10334 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6926 - -lemma sg10335 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg5135 - -lemma sg10336 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6927 - -lemma sg10337 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1350 sg1332 - -lemma sg10338 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1362 - -lemma sg10339 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1354 - -lemma sg10340 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6928 - -lemma sg10341 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6929 - -lemma sg10342 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1363 - -lemma sg10343 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1355 - -lemma sg10344 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6930 - -lemma sg10345 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6931 - -lemma sg10346 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6932 - -lemma sg10347 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6933 - -lemma sg10348 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6934 - -lemma sg10349 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg5136 - -lemma sg10350 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg6936 - -lemma sg10351 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1351 - -lemma sg10352 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1352 - -lemma sg10353 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6937 - -lemma sg10354 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1353 - -lemma sg10355 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5137 - -lemma sg10356 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg6939 - -lemma sg10357 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg6940 - -lemma sg10358 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5138 - -lemma sg10359 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg1 sg6941 - -lemma sg10360 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3] := by - exact rowSquare_join (by decide) sg1 sg6942 - -lemma sg10361 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1364 - -lemma sg10362 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1356 - -lemma sg10363 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1354 - -lemma sg10364 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6943 - -lemma sg10365 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1338 sg1342 - -lemma sg10366 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1357 - -lemma sg10367 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1355 - -lemma sg10368 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6944 - -lemma sg10369 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6945 - -lemma sg10370 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6946 - -lemma sg10371 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1354 - -lemma sg10372 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg5139 - -lemma sg10373 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg6948 - -lemma sg10374 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1355 - -lemma sg10375 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6949 - -lemma sg10376 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg1339 sg1343 - -lemma sg10377 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6950 - -lemma sg10378 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5140 - -lemma sg10379 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3] := by - exact rowSquare_join (by decide) sg1 sg6952 - -lemma sg10380 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg5141 - -lemma sg10381 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,2] := by - exact rowSquare_join (by decide) sg1 sg6954 - -lemma sg10382 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg5142 - -lemma sg10383 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg5143 - -lemma sg10384 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,5,5] := by - exact rowSquare_join (by decide) sg13 sg5144 - -lemma sg10385 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1365 - -lemma sg10386 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1358 - -lemma sg10387 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1356 - -lemma sg10388 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1334 sg1348 - -lemma sg10389 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1338 sg1345 - -lemma sg10390 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1357 - -lemma sg10391 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1356 - -lemma sg10392 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1335 sg1348 - -lemma sg10393 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg1339 sg1345 - -lemma sg10394 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1356 - -lemma sg10395 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg1332 sg1356 - -lemma sg10396 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3] := by - exact rowSquare_join (by decide) sg1337 sg1348 - -lemma sg10397 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1357 - -lemma sg10398 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1357 - -lemma sg10399 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg1332 sg1357 - -lemma sg10400 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg1336 sg1349 - -lemma sg10401 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,2] := by - exact rowSquare_join (by decide) sg1337 sg1349 - -lemma sg10402 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,1] := by - exact rowSquare_join (by decide) sg1340 sg1347 - -lemma sg10403 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1358 - -lemma sg10404 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1338 sg1348 - -lemma sg10405 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1358 - -lemma sg10406 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1358 - -lemma sg10407 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,1] := by - exact rowSquare_join (by decide) sg1332 sg1358 - -lemma sg10408 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2] := by - exact rowSquare_join (by decide) sg1340 sg1348 - -lemma sg10409 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,4,2,1,1] := by - exact rowSquare_join (by decide) sg1339 sg1349 - -lemma sg10410 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,1] := by - exact rowSquare_join (by decide) sg1340 sg1349 - -lemma sg10411 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1366 - -lemma sg10412 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1359 - -lemma sg10413 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6955 - -lemma sg10414 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6956 - -lemma sg10415 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1367 - -lemma sg10416 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1360 - -lemma sg10417 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6957 - -lemma sg10418 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6958 - -lemma sg10419 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1368 - -lemma sg10420 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1361 - -lemma sg10421 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6959 - -lemma sg10422 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6960 - -lemma sg10423 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6961 - -lemma sg10424 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6962 - -lemma sg10425 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6963 - -lemma sg10426 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg5145 - -lemma sg10427 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg6964 - -lemma sg10428 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1359 - -lemma sg10429 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1369 - -lemma sg10430 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1362 - -lemma sg10431 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6965 - -lemma sg10432 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6966 - -lemma sg10433 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg5135 - -lemma sg10434 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1363 - -lemma sg10435 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6968 - -lemma sg10436 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6969 - -lemma sg10437 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6970 - -lemma sg10438 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6971 - -lemma sg10439 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5146 - -lemma sg10440 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg5147 - -lemma sg10441 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg6973 - -lemma sg10442 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1361 - -lemma sg10443 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg6974 - -lemma sg10444 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6975 - -lemma sg10445 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5148 - -lemma sg10446 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5149 - -lemma sg10447 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3] := by - exact rowSquare_join (by decide) sg1 sg6978 - -lemma sg10448 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg5150 - -lemma sg10449 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,2] := by - exact rowSquare_join (by decide) sg1 sg6980 - -lemma sg10450 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1370 - -lemma sg10451 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1364 - -lemma sg10452 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6981 - -lemma sg10453 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6982 - -lemma sg10454 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg5136 - -lemma sg10455 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6984 - -lemma sg10456 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6985 - -lemma sg10457 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg5137 - -lemma sg10458 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg6986 - -lemma sg10459 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5151 - -lemma sg10460 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5152 - -lemma sg10461 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg6988 - -lemma sg10462 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1363 - -lemma sg10463 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5153 - -lemma sg10464 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg6990 - -lemma sg10465 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5154 - -lemma sg10466 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg5155 - -lemma sg10467 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg5156 - -lemma sg10468 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,1] := by - exact rowSquare_join (by decide) sg13 sg5157 - -lemma sg10469 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,5,4] := by - exact rowSquare_join (by decide) sg13 sg5158 - -lemma sg10470 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1365 - -lemma sg10471 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1364 - -lemma sg10472 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6994 - -lemma sg10473 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1338 sg1354 - -lemma sg10474 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg5139 - -lemma sg10475 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6996 - -lemma sg10476 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg6997 - -lemma sg10477 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg5140 - -lemma sg10478 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5159 - -lemma sg10479 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg7000 - -lemma sg10480 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7001 - -lemma sg10481 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5160 - -lemma sg10482 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,2] := by - exact rowSquare_join (by decide) sg14 sg5142 - -lemma sg10483 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg5161 - -lemma sg10484 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,4,4] := by - exact rowSquare_join (by decide) sg13 sg5162 - -lemma sg10485 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,5,2,1] := by - exact rowSquare_join (by decide) sg13 sg5163 - -lemma sg10486 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,5,3] := by - exact rowSquare_join (by decide) sg13 sg5164 - -lemma sg10487 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1365 - -lemma sg10488 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1365 - -lemma sg10489 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1365 - -lemma sg10490 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,1] := by - exact rowSquare_join (by decide) sg1332 sg1365 - -lemma sg10491 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1335 sg1358 - -lemma sg10492 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,3,2,1,1] := by - exact rowSquare_join (by decide) sg1336 sg1358 - -lemma sg10493 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,3,2,2] := by - exact rowSquare_join (by decide) sg1337 sg1358 - -lemma sg10494 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,1] := by - exact rowSquare_join (by decide) sg1340 sg1356 - -lemma sg10495 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,4,1,1,1] := by - exact rowSquare_join (by decide) sg1339 sg1357 - -lemma sg10496 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,4,2,1] := by - exact rowSquare_join (by decide) sg1340 sg1357 - -lemma sg10497 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,4,3] := by - exact rowSquare_join (by decide) sg1347 sg1349 - -lemma sg10498 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,8,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1338 sg1358 - -lemma sg10499 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2] := by - exact rowSquare_join (by decide) sg1348 sg1348 - -lemma sg10500 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,8,3,1,1,1] := by - exact rowSquare_join (by decide) sg1339 sg1358 - -lemma sg10501 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,8,3,2,1] := by - exact rowSquare_join (by decide) sg1340 sg1358 - -lemma sg10502 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,8,4,2] := by - exact rowSquare_join (by decide) sg1349 sg1349 - -lemma sg10503 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7004 - -lemma sg10504 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg5165 - -lemma sg10505 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg7005 - -lemma sg10506 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7006 - -lemma sg10507 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg7007 - -lemma sg10508 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5166 - -lemma sg10509 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg7008 - -lemma sg10510 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg7009 - -lemma sg10511 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5167 - -lemma sg10512 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg5168 - -lemma sg10513 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg5169 - -lemma sg10514 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7010 - -lemma sg10515 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg5147 - -lemma sg10516 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7011 - -lemma sg10517 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg5149 - -lemma sg10518 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5170 - -lemma sg10519 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg5171 - -lemma sg10520 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5172 - -lemma sg10521 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg7012 - -lemma sg10522 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg5173 - -lemma sg10523 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,4,4] := by - exact rowSquare_join (by decide) sg13 sg5174 - -lemma sg10524 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,5,3] := by - exact rowSquare_join (by decide) sg13 sg5175 - -lemma sg10525 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg5152 - -lemma sg10526 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5176 - -lemma sg10527 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg5155 - -lemma sg10528 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg5177 - -lemma sg10529 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7015 - -lemma sg10530 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg5178 - -lemma sg10531 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,4,3] := by - exact rowSquare_join (by decide) sg13 sg5179 - -lemma sg10532 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7016 - -lemma sg10533 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,7,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5180 - -lemma sg10534 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,7,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg7017 - -lemma sg10535 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,7,3,3] := by - exact rowSquare_join (by decide) sg13 sg5181 - -lemma sg10536 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,8,2,1,1,1] := by - exact rowSquare_join (by decide) sg1339 sg1365 - -lemma sg10537 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,8,2,2,1] := by - exact rowSquare_join (by decide) sg1340 sg1365 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes15 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes16 + +namespace OAI + +/-! Semigroup Nodes 24. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg10138 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5130 + +lemma sg10139 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg74 sg3777 + +lemma sg10140 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1230 + +lemma sg10141 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg55 sg3836 + +lemma sg10142 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,4,3,3] := by + exact rowSquare_join (by decide) sg40 sg4571 + +lemma sg10143 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg74 sg3781 + +lemma sg10144 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg27 sg4622 + +lemma sg10145 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg55 sg3837 + +lemma sg10146 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg3782 + +lemma sg10147 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg74 sg3783 + +lemma sg10148 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,3,2] := by + exact rowSquare_join (by decide) sg76 sg3766 + +lemma sg10149 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,4,1] := by + exact rowSquare_join (by decide) sg76 sg3767 + +lemma sg10150 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,5,5] := by + exact rowSquare_join (by decide) sg76 sg3768 + +lemma sg10151 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg55 sg3838 + +lemma sg10152 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg3784 + +lemma sg10153 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,6,2,2] := by + exact rowSquare_join (by decide) sg77 sg3766 + +lemma sg10154 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,6,3,1] := by + exact rowSquare_join (by decide) sg77 sg3767 + +lemma sg10155 : RowSquare [6,5,3,2,1,1,1,1,1,1] [6,6,6,4] := by + exact rowSquare_join (by decide) sg77 sg3768 + +lemma sg10156 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg3785 + +lemma sg10157 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg55 sg3843 + +lemma sg10158 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg165 sg3160 + +lemma sg10159 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,6,6,2,1] := by + exact rowSquare_join (by decide) sg167 sg3157 + +lemma sg10160 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,6,6,3] := by + exact rowSquare_join (by decide) sg167 sg3158 + +lemma sg10161 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5133 + +lemma sg10162 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,7,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg3786 + +lemma sg10163 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,7,3,3,1,1] := by + exact rowSquare_join (by decide) sg74 sg3787 + +lemma sg10164 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,7,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg55 sg3847 + +lemma sg10165 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,7,4,2,2] := by + exact rowSquare_join (by decide) sg166 sg3159 + +lemma sg10166 : RowSquare [6,5,3,2,1,1,1,1,1,1] [7,7,4,4] := by + exact rowSquare_join (by decide) sg76 sg3781 + +lemma sg10167 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1327 sg1327 + +lemma sg10168 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1327 sg1328 + +lemma sg10169 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1329 + +lemma sg10170 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1330 + +lemma sg10171 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1331 + +lemma sg10172 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1332 + +lemma sg10173 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1333 + +lemma sg10174 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1328 sg1328 + +lemma sg10175 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1334 + +lemma sg10176 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1328 sg1329 + +lemma sg10177 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1335 + +lemma sg10178 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1330 + +lemma sg10179 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1336 + +lemma sg10180 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1331 + +lemma sg10181 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1337 + +lemma sg10182 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1332 + +lemma sg10183 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1338 + +lemma sg10184 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1329 sg1329 + +lemma sg10185 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1339 + +lemma sg10186 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1329 sg1330 + +lemma sg10187 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1340 + +lemma sg10188 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1331 + +lemma sg10189 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1332 + +lemma sg10190 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1330 sg1330 + +lemma sg10191 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1330 sg1331 + +lemma sg10192 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1332 + +lemma sg10193 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1331 sg1331 + +lemma sg10194 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1331 sg1332 + +lemma sg10195 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg1332 sg1332 + +lemma sg10196 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1341 + +lemma sg10197 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1328 sg1333 + +lemma sg10198 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1342 + +lemma sg10199 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1334 + +lemma sg10200 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1329 sg1333 + +lemma sg10201 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1343 + +lemma sg10202 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1335 + +lemma sg10203 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1333 sg1330 + +lemma sg10204 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1344 + +lemma sg10205 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1336 + +lemma sg10206 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1333 sg1331 + +lemma sg10207 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1337 + +lemma sg10208 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1333 sg1332 + +lemma sg10209 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1345 + +lemma sg10210 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1338 + +lemma sg10211 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1329 sg1334 + +lemma sg10212 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1346 + +lemma sg10213 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1339 + +lemma sg10214 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1335 + +lemma sg10215 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1330 sg1334 + +lemma sg10216 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1347 + +lemma sg10217 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1340 + +lemma sg10218 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1336 + +lemma sg10219 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1334 sg1331 + +lemma sg10220 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1337 + +lemma sg10221 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1334 sg1332 + +lemma sg10222 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1330 sg1335 + +lemma sg10223 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1336 + +lemma sg10224 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1331 sg1335 + +lemma sg10225 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1337 + +lemma sg10226 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg1335 sg1332 + +lemma sg10227 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1331 sg1336 + +lemma sg10228 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1337 + +lemma sg10229 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1336 + +lemma sg10230 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg1332 sg1337 + +lemma sg10231 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1348 + +lemma sg10232 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1338 + +lemma sg10233 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1349 + +lemma sg10234 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1339 + +lemma sg10235 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1330 sg1338 + +lemma sg10236 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1340 + +lemma sg10237 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1331 sg1338 + +lemma sg10238 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1338 sg1332 + +lemma sg10239 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1339 + +lemma sg10240 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1340 + +lemma sg10241 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1331 sg1339 + +lemma sg10242 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1339 + +lemma sg10243 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1340 + +lemma sg10244 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1332 sg1340 + +lemma sg10245 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1350 + +lemma sg10246 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1341 + +lemma sg10247 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6905 + +lemma sg10248 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1351 + +lemma sg10249 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1342 + +lemma sg10250 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6906 + +lemma sg10251 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1352 + +lemma sg10252 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1343 + +lemma sg10253 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6907 + +lemma sg10254 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1330 sg1341 + +lemma sg10255 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1353 + +lemma sg10256 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1344 + +lemma sg10257 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6908 + +lemma sg10258 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1341 sg1331 + +lemma sg10259 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6909 + +lemma sg10260 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1341 sg1332 + +lemma sg10261 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1354 + +lemma sg10262 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1345 + +lemma sg10263 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1342 + +lemma sg10264 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6910 + +lemma sg10265 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1355 + +lemma sg10266 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1346 + +lemma sg10267 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1343 + +lemma sg10268 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6911 + +lemma sg10269 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1347 + +lemma sg10270 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1344 + +lemma sg10271 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6912 + +lemma sg10272 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1331 sg1342 + +lemma sg10273 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6913 + +lemma sg10274 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1342 sg1332 + +lemma sg10275 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1343 + +lemma sg10276 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6914 + +lemma sg10277 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1344 + +lemma sg10278 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6915 + +lemma sg10279 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg6916 + +lemma sg10280 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1343 + +lemma sg10281 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1344 + +lemma sg10282 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg6917 + +lemma sg10283 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg6918 + +lemma sg10284 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg6919 + +lemma sg10285 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1356 + +lemma sg10286 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1348 + +lemma sg10287 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1345 + +lemma sg10288 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1334 sg1338 + +lemma sg10289 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1357 + +lemma sg10290 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1349 + +lemma sg10291 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1346 + +lemma sg10292 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1345 + +lemma sg10293 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1335 sg1338 + +lemma sg10294 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1347 + +lemma sg10295 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1334 sg1340 + +lemma sg10296 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1331 sg1345 + +lemma sg10297 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1338 sg1337 + +lemma sg10298 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1345 + +lemma sg10299 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1346 + +lemma sg10300 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1335 sg1339 + +lemma sg10301 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1347 + +lemma sg10302 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1346 + +lemma sg10303 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg1336 sg1339 + +lemma sg10304 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg1332 sg1346 + +lemma sg10305 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1347 + +lemma sg10306 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg1332 sg1347 + +lemma sg10307 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,3] := by + exact rowSquare_join (by decide) sg1337 sg1340 + +lemma sg10308 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1358 + +lemma sg10309 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1348 + +lemma sg10310 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1338 sg1338 + +lemma sg10311 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1349 + +lemma sg10312 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1348 + +lemma sg10313 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1338 sg1339 + +lemma sg10314 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1348 + +lemma sg10315 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg1332 sg1348 + +lemma sg10316 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1349 + +lemma sg10317 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg1339 sg1339 + +lemma sg10318 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1349 + +lemma sg10319 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg1332 sg1349 + +lemma sg10320 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2] := by + exact rowSquare_join (by decide) sg1340 sg1340 + +lemma sg10321 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1359 + +lemma sg10322 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1350 + +lemma sg10323 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6920 + +lemma sg10324 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1360 + +lemma sg10325 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1351 + +lemma sg10326 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6921 + +lemma sg10327 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6922 + +lemma sg10328 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1361 + +lemma sg10329 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1352 + +lemma sg10330 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6923 + +lemma sg10331 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6924 + +lemma sg10332 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1353 + +lemma sg10333 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6925 + +lemma sg10334 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6926 + +lemma sg10335 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg5135 + +lemma sg10336 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6927 + +lemma sg10337 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1350 sg1332 + +lemma sg10338 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1362 + +lemma sg10339 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1354 + +lemma sg10340 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6928 + +lemma sg10341 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6929 + +lemma sg10342 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1363 + +lemma sg10343 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1355 + +lemma sg10344 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6930 + +lemma sg10345 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6931 + +lemma sg10346 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6932 + +lemma sg10347 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6933 + +lemma sg10348 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6934 + +lemma sg10349 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg5136 + +lemma sg10350 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg6936 + +lemma sg10351 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1351 + +lemma sg10352 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1352 + +lemma sg10353 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6937 + +lemma sg10354 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1353 + +lemma sg10355 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5137 + +lemma sg10356 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg6939 + +lemma sg10357 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg6940 + +lemma sg10358 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5138 + +lemma sg10359 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg1 sg6941 + +lemma sg10360 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3] := by + exact rowSquare_join (by decide) sg1 sg6942 + +lemma sg10361 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1364 + +lemma sg10362 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1356 + +lemma sg10363 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1354 + +lemma sg10364 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6943 + +lemma sg10365 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1338 sg1342 + +lemma sg10366 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1357 + +lemma sg10367 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1355 + +lemma sg10368 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6944 + +lemma sg10369 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6945 + +lemma sg10370 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6946 + +lemma sg10371 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1354 + +lemma sg10372 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg5139 + +lemma sg10373 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg6948 + +lemma sg10374 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1355 + +lemma sg10375 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6949 + +lemma sg10376 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg1339 sg1343 + +lemma sg10377 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6950 + +lemma sg10378 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5140 + +lemma sg10379 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3] := by + exact rowSquare_join (by decide) sg1 sg6952 + +lemma sg10380 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg5141 + +lemma sg10381 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,2] := by + exact rowSquare_join (by decide) sg1 sg6954 + +lemma sg10382 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg5142 + +lemma sg10383 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg5143 + +lemma sg10384 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,5,5,5] := by + exact rowSquare_join (by decide) sg13 sg5144 + +lemma sg10385 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1365 + +lemma sg10386 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1358 + +lemma sg10387 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1356 + +lemma sg10388 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1334 sg1348 + +lemma sg10389 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1338 sg1345 + +lemma sg10390 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1357 + +lemma sg10391 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1356 + +lemma sg10392 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1335 sg1348 + +lemma sg10393 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg1339 sg1345 + +lemma sg10394 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1356 + +lemma sg10395 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg1332 sg1356 + +lemma sg10396 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3] := by + exact rowSquare_join (by decide) sg1337 sg1348 + +lemma sg10397 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1357 + +lemma sg10398 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1357 + +lemma sg10399 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg1332 sg1357 + +lemma sg10400 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg1336 sg1349 + +lemma sg10401 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,2] := by + exact rowSquare_join (by decide) sg1337 sg1349 + +lemma sg10402 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,1] := by + exact rowSquare_join (by decide) sg1340 sg1347 + +lemma sg10403 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1358 + +lemma sg10404 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1338 sg1348 + +lemma sg10405 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1358 + +lemma sg10406 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1358 + +lemma sg10407 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,1] := by + exact rowSquare_join (by decide) sg1332 sg1358 + +lemma sg10408 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2] := by + exact rowSquare_join (by decide) sg1340 sg1348 + +lemma sg10409 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,4,2,1,1] := by + exact rowSquare_join (by decide) sg1339 sg1349 + +lemma sg10410 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,1] := by + exact rowSquare_join (by decide) sg1340 sg1349 + +lemma sg10411 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1366 + +lemma sg10412 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1359 + +lemma sg10413 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6955 + +lemma sg10414 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6956 + +lemma sg10415 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1367 + +lemma sg10416 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1360 + +lemma sg10417 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6957 + +lemma sg10418 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6958 + +lemma sg10419 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1368 + +lemma sg10420 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1361 + +lemma sg10421 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6959 + +lemma sg10422 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6960 + +lemma sg10423 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6961 + +lemma sg10424 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6962 + +lemma sg10425 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6963 + +lemma sg10426 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg5145 + +lemma sg10427 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg6964 + +lemma sg10428 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1359 + +lemma sg10429 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1369 + +lemma sg10430 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1362 + +lemma sg10431 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6965 + +lemma sg10432 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6966 + +lemma sg10433 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg5135 + +lemma sg10434 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1363 + +lemma sg10435 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6968 + +lemma sg10436 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6969 + +lemma sg10437 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6970 + +lemma sg10438 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6971 + +lemma sg10439 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5146 + +lemma sg10440 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg5147 + +lemma sg10441 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg6973 + +lemma sg10442 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1361 + +lemma sg10443 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg6974 + +lemma sg10444 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6975 + +lemma sg10445 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5148 + +lemma sg10446 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5149 + +lemma sg10447 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3] := by + exact rowSquare_join (by decide) sg1 sg6978 + +lemma sg10448 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg5150 + +lemma sg10449 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,2] := by + exact rowSquare_join (by decide) sg1 sg6980 + +lemma sg10450 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1370 + +lemma sg10451 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1364 + +lemma sg10452 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6981 + +lemma sg10453 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6982 + +lemma sg10454 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg5136 + +lemma sg10455 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6984 + +lemma sg10456 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6985 + +lemma sg10457 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg5137 + +lemma sg10458 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg6986 + +lemma sg10459 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5151 + +lemma sg10460 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5152 + +lemma sg10461 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg6988 + +lemma sg10462 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1363 + +lemma sg10463 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5153 + +lemma sg10464 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg6990 + +lemma sg10465 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5154 + +lemma sg10466 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg5155 + +lemma sg10467 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg5156 + +lemma sg10468 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,1] := by + exact rowSquare_join (by decide) sg13 sg5157 + +lemma sg10469 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,5,5,4] := by + exact rowSquare_join (by decide) sg13 sg5158 + +lemma sg10470 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1365 + +lemma sg10471 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1364 + +lemma sg10472 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6994 + +lemma sg10473 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1338 sg1354 + +lemma sg10474 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg5139 + +lemma sg10475 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6996 + +lemma sg10476 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg6997 + +lemma sg10477 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg5140 + +lemma sg10478 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5159 + +lemma sg10479 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg7000 + +lemma sg10480 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7001 + +lemma sg10481 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5160 + +lemma sg10482 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,2] := by + exact rowSquare_join (by decide) sg14 sg5142 + +lemma sg10483 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg5161 + +lemma sg10484 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,4,4] := by + exact rowSquare_join (by decide) sg13 sg5162 + +lemma sg10485 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,5,2,1] := by + exact rowSquare_join (by decide) sg13 sg5163 + +lemma sg10486 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,6,5,3] := by + exact rowSquare_join (by decide) sg13 sg5164 + +lemma sg10487 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1365 + +lemma sg10488 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1365 + +lemma sg10489 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1365 + +lemma sg10490 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,1] := by + exact rowSquare_join (by decide) sg1332 sg1365 + +lemma sg10491 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1335 sg1358 + +lemma sg10492 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,3,2,1,1] := by + exact rowSquare_join (by decide) sg1336 sg1358 + +lemma sg10493 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,3,2,2] := by + exact rowSquare_join (by decide) sg1337 sg1358 + +lemma sg10494 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,1] := by + exact rowSquare_join (by decide) sg1340 sg1356 + +lemma sg10495 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,4,1,1,1] := by + exact rowSquare_join (by decide) sg1339 sg1357 + +lemma sg10496 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,4,2,1] := by + exact rowSquare_join (by decide) sg1340 sg1357 + +lemma sg10497 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,7,4,3] := by + exact rowSquare_join (by decide) sg1347 sg1349 + +lemma sg10498 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,8,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1338 sg1358 + +lemma sg10499 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2] := by + exact rowSquare_join (by decide) sg1348 sg1348 + +lemma sg10500 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,8,3,1,1,1] := by + exact rowSquare_join (by decide) sg1339 sg1358 + +lemma sg10501 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,8,3,2,1] := by + exact rowSquare_join (by decide) sg1340 sg1358 + +lemma sg10502 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [8,8,4,2] := by + exact rowSquare_join (by decide) sg1349 sg1349 + +lemma sg10503 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7004 + +lemma sg10504 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg5165 + +lemma sg10505 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg7005 + +lemma sg10506 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7006 + +lemma sg10507 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg7007 + +lemma sg10508 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5166 + +lemma sg10509 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg7008 + +lemma sg10510 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg7009 + +lemma sg10511 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5167 + +lemma sg10512 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg5168 + +lemma sg10513 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg5169 + +lemma sg10514 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7010 + +lemma sg10515 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg5147 + +lemma sg10516 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7011 + +lemma sg10517 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg5149 + +lemma sg10518 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5170 + +lemma sg10519 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg5171 + +lemma sg10520 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5172 + +lemma sg10521 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg7012 + +lemma sg10522 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg5173 + +lemma sg10523 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,4,4] := by + exact rowSquare_join (by decide) sg13 sg5174 + +lemma sg10524 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,5,5,3] := by + exact rowSquare_join (by decide) sg13 sg5175 + +lemma sg10525 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg5152 + +lemma sg10526 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5176 + +lemma sg10527 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg5155 + +lemma sg10528 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg5177 + +lemma sg10529 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7015 + +lemma sg10530 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg5178 + +lemma sg10531 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,6,4,3] := by + exact rowSquare_join (by decide) sg13 sg5179 + +lemma sg10532 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7016 + +lemma sg10533 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,7,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5180 + +lemma sg10534 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,7,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg7017 + +lemma sg10535 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,7,3,3] := by + exact rowSquare_join (by decide) sg13 sg5181 + +lemma sg10536 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,8,2,1,1,1] := by + exact rowSquare_join (by decide) sg1339 sg1365 + +lemma sg10537 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [9,8,2,2,1] := by + exact rowSquare_join (by decide) sg1340 sg1365 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes25.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes25.lean index 2cbf34ef54f94b08b1d67501b7840b96aa9801cc..2d8d7effc874bc937a59529d81dd4729afed6bc0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes25.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes25.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes17 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes20 - -namespace OAI - -/-! Semigroup Nodes 25. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg10538 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7018 - -lemma sg10539 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg7019 - -lemma sg10540 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5182 - -lemma sg10541 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,3,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg7020 - -lemma sg10542 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg5165 - -lemma sg10543 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg15 sg5140 - -lemma sg10544 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5183 - -lemma sg10545 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg5184 - -lemma sg10546 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5185 - -lemma sg10547 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,4,2,2] := by - exact rowSquare_join (by decide) sg83 sg3745 - -lemma sg10548 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg5186 - -lemma sg10549 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,4,4] := by - exact rowSquare_join (by decide) sg13 sg5187 - -lemma sg10550 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg5166 - -lemma sg10551 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5188 - -lemma sg10552 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg5189 - -lemma sg10553 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7021 - -lemma sg10554 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5190 - -lemma sg10555 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,6,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg5171 - -lemma sg10556 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,6,3,3] := by - exact rowSquare_join (by decide) sg13 sg5191 - -lemma sg10557 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,6,4,2] := by - exact rowSquare_join (by decide) sg83 sg3748 - -lemma sg10558 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,8,2,2] := by - exact rowSquare_join (by decide) sg13 sg5192 - -lemma sg10559 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7022 - -lemma sg10560 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg5147 - -lemma sg10561 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7023 - -lemma sg10562 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg15 sg5149 - -lemma sg10563 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5193 - -lemma sg10564 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,3,3,3,2] := by - exact rowSquare_join (by decide) sg84 sg3745 - -lemma sg10565 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg5182 - -lemma sg10566 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5194 - -lemma sg10567 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,4,3,2,2] := by - exact rowSquare_join (by decide) sg15 sg5155 - -lemma sg10568 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg3750 - -lemma sg10569 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,4,4,3] := by - exact rowSquare_join (by decide) sg13 sg5195 - -lemma sg10570 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7024 - -lemma sg10571 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,5,3,3] := by - exact rowSquare_join (by decide) sg84 sg3748 - -lemma sg10572 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,7,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5190 - -lemma sg10573 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [12,4,3,3] := by - exact rowSquare_join (by decide) sg84 sg3751 - -lemma sg10574 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [12,4,4,2] := by - exact rowSquare_join (by decide) sg364 sg2485 - -lemma sg10575 : RowSquare [6,6,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg5208 - -lemma sg10576 : RowSquare [6,6,2,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg905 sg1754 - -lemma sg10577 : RowSquare [6,6,2,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg906 sg1754 - -lemma sg10578 : RowSquare [6,6,2,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg907 sg1754 - -lemma sg10579 : RowSquare [6,6,2,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg908 sg1754 - -lemma sg10580 : RowSquare [6,6,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg909 sg1754 - -lemma sg10581 : RowSquare [6,6,2,2,2,2,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg7813 - -lemma sg10582 : RowSquare [6,6,2,2,2,2,1,1] [4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg7816 - -lemma sg10583 : RowSquare [6,6,2,2,2,2,1,1] [4,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg7817 - -lemma sg10584 : RowSquare [6,6,2,2,2,2,1,1] [4,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg7818 - -lemma sg10585 : RowSquare [6,6,2,2,2,2,1,1] [4,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg7819 - -lemma sg10586 : RowSquare [6,6,2,2,2,2,1,1] [4,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg7820 - -lemma sg10587 : RowSquare [6,6,2,2,2,2,1,1] [4,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg7821 - -lemma sg10588 : RowSquare [6,6,2,2,2,2,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg7824 - -lemma sg10589 : RowSquare [6,6,2,2,2,2,1,1] [5,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg7825 - -lemma sg10590 : RowSquare [6,6,2,2,2,2,1,1] [5,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg7826 - -lemma sg10591 : RowSquare [6,6,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg7827 - -lemma sg10592 : RowSquare [6,6,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg7828 - -lemma sg10593 : RowSquare [6,6,2,2,2,2,1,1] [5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg7837 - -lemma sg10594 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2251 - -lemma sg10595 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg2251 - -lemma sg10596 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2252 - -lemma sg10597 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg2251 - -lemma sg10598 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg2251 - -lemma sg10599 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg2251 - -lemma sg10600 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg594 sg2251 - -lemma sg10601 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg2256 - -lemma sg10602 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg595 sg2251 - -lemma sg10603 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg2251 - -lemma sg10604 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg2253 - -lemma sg10605 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg2254 - -lemma sg10606 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg2254 - -lemma sg10607 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg2254 - -lemma sg10608 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg2255 - -lemma sg10609 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg589 sg2256 - -lemma sg10610 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg2255 - -lemma sg10611 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg597 sg2251 - -lemma sg10612 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg591 sg2252 - -lemma sg10613 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg592 sg2252 - -lemma sg10614 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8539 - -lemma sg10615 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg587 sg2259 - -lemma sg10616 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8541 - -lemma sg10617 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg587 sg2260 - -lemma sg10618 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg600 sg2251 - -lemma sg10619 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg2257 - -lemma sg10620 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg601 sg2251 - -lemma sg10621 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg2257 - -lemma sg10622 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8546 - -lemma sg10623 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8549 - -lemma sg10624 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8550 - -lemma sg10625 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg588 sg2260 - -lemma sg10626 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg593 sg2254 - -lemma sg10627 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg2258 - -lemma sg10628 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8551 - -lemma sg10629 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg594 sg2254 - -lemma sg10630 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg2258 - -lemma sg10631 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8552 - -lemma sg10632 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8553 - -lemma sg10633 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8554 - -lemma sg10634 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg0 sg8555 - -lemma sg10635 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg594 sg2255 - -lemma sg10636 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg2259 - -lemma sg10637 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8556 - -lemma sg10638 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg8557 - -lemma sg10639 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg0 sg8558 - -lemma sg10640 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg0 sg8559 - -lemma sg10641 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg2251 - -lemma sg10642 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg586 sg2267 - -lemma sg10643 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg595 sg2254 - -lemma sg10644 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg588 sg2262 - -lemma sg10645 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg2261 - -lemma sg10646 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg588 sg2263 - -lemma sg10647 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg595 sg2256 - -lemma sg10648 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg2254 - -lemma sg10649 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg589 sg2262 - -lemma sg10650 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg2255 - -lemma sg10651 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg2262 - -lemma sg10652 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg589 sg2263 - -lemma sg10653 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg590 sg2263 - -lemma sg10654 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg603 sg2251 - -lemma sg10655 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg597 sg2252 - -lemma sg10656 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg605 sg2251 - -lemma sg10657 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8567 - -lemma sg10658 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8569 - -lemma sg10659 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8570 - -lemma sg10660 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg591 sg2260 - -lemma sg10661 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg606 sg2251 - -lemma sg10662 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg6910 - -lemma sg10663 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg6030 - -lemma sg10664 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg6912 - -lemma sg10665 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8574 - -lemma sg10666 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg6913 - -lemma sg10667 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg0 sg8575 - -lemma sg10668 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg599 sg2254 - -lemma sg10669 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6031 - -lemma sg10670 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8576 - -lemma sg10671 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg6032 - -lemma sg10672 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6033 - -lemma sg10673 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8577 - -lemma sg10674 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg6034 - -lemma sg10675 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg6035 - -lemma sg10676 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg0 sg8578 - -lemma sg10677 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg594 sg2259 - -lemma sg10678 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8579 - -lemma sg10679 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2 sg6917 - -lemma sg10680 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2 sg6918 - -lemma sg10681 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,4] := by - exact rowSquare_join (by decide) sg2 sg6919 - -lemma sg10682 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg607 sg2251 - -lemma sg10683 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8585 - -lemma sg10684 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg6036 - -lemma sg10685 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg8589 - -lemma sg10686 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8591 - -lemma sg10687 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8592 - -lemma sg10688 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg8593 - -lemma sg10689 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg0 sg8594 - -lemma sg10690 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg601 sg2254 - -lemma sg10691 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg2258 - -lemma sg10692 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6037 - -lemma sg10693 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg6038 - -lemma sg10694 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6039 - -lemma sg10695 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg6040 - -lemma sg10696 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6041 - -lemma sg10697 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg6042 - -lemma sg10698 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,3] := by - exact rowSquare_join (by decide) sg4 sg6043 - -lemma sg10699 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg4 sg6044 - -lemma sg10700 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,2] := by - exact rowSquare_join (by decide) sg4 sg6045 - -lemma sg10701 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg2269 - -lemma sg10702 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg2254 - -lemma sg10703 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg608 sg2251 - -lemma sg10704 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg609 sg2251 - -lemma sg10705 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg610 sg2251 - -lemma sg10706 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg605 sg2254 - -lemma sg10707 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5304 - -lemma sg10708 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6051 - -lemma sg10709 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg5307 - -lemma sg10710 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,2] := by - exact rowSquare_join (by decide) sg13 sg5308 - -lemma sg10711 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5309 - -lemma sg10712 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg6052 - -lemma sg10713 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5310 - -lemma sg10714 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg5311 - -lemma sg10715 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,1] := by - exact rowSquare_join (by decide) sg4 sg6053 - -lemma sg10716 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6054 - -lemma sg10717 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6055 - -lemma sg10718 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg6056 - -lemma sg10719 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg6057 - -lemma sg10720 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,2] := by - exact rowSquare_join (by decide) sg4 sg6058 - -lemma sg10721 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,1] := by - exact rowSquare_join (by decide) sg0 sg8606 - -lemma sg10722 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6059 - -lemma sg10723 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg6060 - -lemma sg10724 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,5,2,2] := by - exact rowSquare_join (by decide) sg4 sg6061 - -lemma sg10725 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,1] := by - exact rowSquare_join (by decide) sg4 sg6062 - -lemma sg10726 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,5,4] := by - exact rowSquare_join (by decide) sg4 sg6063 - -lemma sg10727 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg2261 - -lemma sg10728 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg588 sg2269 - -lemma sg10729 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg2262 - -lemma sg10730 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg2267 - -lemma sg10731 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,1] := by - exact rowSquare_join (by decide) sg589 sg2269 - -lemma sg10732 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2] := by - exact rowSquare_join (by decide) sg590 sg2269 - -lemma sg10733 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,4,2,1,1] := by - exact rowSquare_join (by decide) sg596 sg2268 - -lemma sg10734 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg611 sg2251 - -lemma sg10735 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg608 sg2252 - -lemma sg10736 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7292 - -lemma sg10737 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7293 - -lemma sg10738 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6 sg6029 - -lemma sg10739 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg6956 - -lemma sg10740 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg612 sg2251 - -lemma sg10741 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg609 sg2252 - -lemma sg10742 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7294 - -lemma sg10743 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7295 - -lemma sg10744 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6046 - -lemma sg10745 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg6047 - -lemma sg10746 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7296 - -lemma sg10747 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7297 - -lemma sg10748 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6064 - -lemma sg10749 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg6065 - -lemma sg10750 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg16 sg5135 - -lemma sg10751 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5312 - -lemma sg10752 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5313 - -lemma sg10753 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6 sg6034 - -lemma sg10754 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6 sg6035 - -lemma sg10755 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg7298 - -lemma sg10756 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg610 sg2252 - -lemma sg10757 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7299 - -lemma sg10758 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7300 - -lemma sg10759 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5302 - -lemma sg10760 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg6048 - -lemma sg10761 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg5135 - -lemma sg10762 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7301 - -lemma sg10763 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5314 - -lemma sg10764 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6066 - -lemma sg10765 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg16 sg5136 - -lemma sg10766 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5315 - -lemma sg10767 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5316 - -lemma sg10768 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg5 sg6049 - -lemma sg10769 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg5 sg6050 - -lemma sg10770 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6067 - -lemma sg10771 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5317 - -lemma sg10772 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg16 sg5137 - -lemma sg10773 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg6068 - -lemma sg10774 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5318 - -lemma sg10775 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5319 - -lemma sg10776 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3] := by - exact rowSquare_join (by decide) sg4 sg6069 - -lemma sg10777 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg5320 - -lemma sg10778 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,2] := by - exact rowSquare_join (by decide) sg13 sg5321 - -lemma sg10779 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7302 - -lemma sg10780 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8607 - -lemma sg10781 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5322 - -lemma sg10782 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5303 - -lemma sg10783 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg17 sg5136 - -lemma sg10784 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5304 - -lemma sg10785 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5323 - -lemma sg10786 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg5137 - -lemma sg10787 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg16 sg5139 - -lemma sg10788 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5324 - -lemma sg10789 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg5325 - -lemma sg10790 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg5305 - -lemma sg10791 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6070 - -lemma sg10792 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5326 - -lemma sg10793 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg16 sg5140 - -lemma sg10794 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5327 - -lemma sg10795 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg5328 - -lemma sg10796 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg5329 - -lemma sg10797 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6071 - -lemma sg10798 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5330 - -lemma sg10799 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,5,2,2] := by - exact rowSquare_join (by decide) sg16 sg5142 - -lemma sg10800 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,1] := by - exact rowSquare_join (by decide) sg13 sg5331 - -lemma sg10801 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,5,4] := by - exact rowSquare_join (by decide) sg16 sg5144 - -lemma sg10802 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8608 - -lemma sg10803 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6072 - -lemma sg10804 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5332 - -lemma sg10805 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg8609 - -lemma sg10806 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg5139 - -lemma sg10807 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5306 - -lemma sg10808 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5333 - -lemma sg10809 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg17 sg5140 - -lemma sg10810 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5334 - -lemma sg10811 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg5335 - -lemma sg10812 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5309 - -lemma sg10813 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5336 - -lemma sg10814 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,2] := by - exact rowSquare_join (by decide) sg17 sg5142 - -lemma sg10815 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg5337 - -lemma sg10816 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,4,4] := by - exact rowSquare_join (by decide) sg13 sg5338 - -lemma sg10817 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6073 - -lemma sg10818 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,5,2,1] := by - exact rowSquare_join (by decide) sg13 sg5339 - -lemma sg10819 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,5,3] := by - exact rowSquare_join (by decide) sg13 sg5340 - -lemma sg10820 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8611 - -lemma sg10821 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6074 - -lemma sg10822 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg8612 - -lemma sg10823 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg8613 - -lemma sg10824 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6075 - -lemma sg10825 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg6076 - -lemma sg10826 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg6077 - -lemma sg10827 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg8614 - -lemma sg10828 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,4,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6078 - -lemma sg10829 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,4,2,1] := by - exact rowSquare_join (by decide) sg4 sg6079 - -lemma sg10830 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,4,3] := by - exact rowSquare_join (by decide) sg4 sg6080 - -lemma sg10831 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,8,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg2267 - -lemma sg10832 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2] := by - exact rowSquare_join (by decide) sg595 sg2269 - -lemma sg10833 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,8,3,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg2268 - -lemma sg10834 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,8,3,2,1] := by - exact rowSquare_join (by decide) sg596 sg2269 - -lemma sg10835 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [9,5,4,4] := by - exact rowSquare_join (by decide) sg39 sg4583 - -lemma sg10836 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [9,6,4,3] := by - exact rowSquare_join (by decide) sg40 sg4583 - -lemma sg10837 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [10,4,4,4] := by - exact rowSquare_join (by decide) sg39 sg4584 - -lemma sg10838 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [10,5,4,3] := by - exact rowSquare_join (by decide) sg39 sg4585 - -lemma sg10839 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [10,6,3,3] := by - exact rowSquare_join (by decide) sg39 sg4586 - -lemma sg10840 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [10,6,4,2] := by - exact rowSquare_join (by decide) sg97 sg3748 - -lemma sg10841 : RowSquare [7,5,2,1,1,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg543 sg2251 - -lemma sg10842 : RowSquare [7,5,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg316 sg2708 - -lemma sg10843 : RowSquare [7,5,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg312 sg2710 - -lemma sg10844 : RowSquare [7,5,2,2,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg270 sg2702 - -lemma sg10845 : RowSquare [7,5,2,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg271 sg2702 - -lemma sg10846 : RowSquare [7,5,2,2,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg272 sg2702 - -lemma sg10847 : RowSquare [7,5,2,2,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg276 sg2702 - -lemma sg10848 : RowSquare [7,5,2,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg496 sg2251 - -lemma sg10849 : RowSquare [7,5,2,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg281 sg2702 - -lemma sg10850 : RowSquare [7,5,2,2,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg496 sg2253 - -lemma sg10851 : RowSquare [7,5,2,2,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7454 - -lemma sg10852 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg457 sg2251 - -lemma sg10853 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg5417 - -lemma sg10854 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg459 sg2251 - -lemma sg10855 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1191 - -lemma sg10856 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg5420 - -lemma sg10857 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5421 - -lemma sg10858 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5422 - -lemma sg10859 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg74 sg3866 - -lemma sg10860 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg3867 - -lemma sg10861 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg465 sg2251 - -lemma sg10862 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg3870 - -lemma sg10863 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg459 sg2254 - -lemma sg10864 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5429 - -lemma sg10865 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg74 sg3875 - -lemma sg10866 : RowSquare [7,6,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg3876 - -lemma sg10868 : RowSquare [7,6,2,2,2,2,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1222 sg1177 - -lemma sg10869 : RowSquare [7,6,2,2,2,2,1] [2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1219 sg1177 - -lemma sg10870 : RowSquare [7,6,2,2,2,2,1] [2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1219 sg1176 - -lemma sg10871 : RowSquare [7,6,2,2,2,2,1] [2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1219 sg1174 - -lemma sg10872 : RowSquare [7,6,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1219 sg1172 - -lemma sg10873 : RowSquare [7,6,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1219 sg1169 - -lemma sg10874 : RowSquare [7,6,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg780 sg1644 - -lemma sg10875 : RowSquare [7,6,2,2,2,2,1] [3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1218 sg1177 - -lemma sg10876 : RowSquare [7,6,2,2,2,2,1] [3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1218 sg1176 - -lemma sg10877 : RowSquare [7,6,2,2,2,2,1] [3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1218 sg1175 - -lemma sg10878 : RowSquare [7,6,2,2,2,2,1] [3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1218 sg1174 - -lemma sg10879 : RowSquare [7,6,2,2,2,2,1] [3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1218 sg1172 - -lemma sg10880 : RowSquare [7,6,2,2,2,2,1] [3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1218 sg1169 - -lemma sg10881 : RowSquare [7,6,2,2,2,2,1] [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1220 sg1177 - -lemma sg10882 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1217 sg1170 - -lemma sg10883 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1215 sg1170 - -lemma sg10884 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1215 sg1167 - -lemma sg10885 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1215 sg1163 - -lemma sg10886 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1217 sg1162 - -lemma sg10887 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1215 sg1162 - -lemma sg10888 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1215 sg1157 - -lemma sg10889 : RowSquare [7,6,2,2,2,2,1] [4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1214 sg1177 - -lemma sg10890 : RowSquare [7,6,2,2,2,2,1] [4,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1214 sg1176 - -lemma sg10891 : RowSquare [7,6,2,2,2,2,1] [4,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1214 sg1175 - -lemma sg10892 : RowSquare [7,6,2,2,2,2,1] [4,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1214 sg1174 - -lemma sg10893 : RowSquare [7,6,2,2,2,2,1] [4,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1214 sg1172 - -lemma sg10894 : RowSquare [7,6,2,2,2,2,1] [4,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1214 sg1169 - -lemma sg10895 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1213 sg1173 - -lemma sg10896 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1213 sg1171 - -lemma sg10897 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1213 sg1168 - -lemma sg10898 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1213 sg1164 - -lemma sg10899 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1213 sg1170 - -lemma sg10900 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1213 sg1167 - -lemma sg10901 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1213 sg1163 - -lemma sg10902 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1214 sg1157 - -lemma sg10903 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1213 sg1162 - -lemma sg10904 : RowSquare [7,6,2,2,2,2,1] [4,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1212 sg1170 - -lemma sg10905 : RowSquare [7,6,2,2,2,2,1] [4,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1212 sg1167 - -lemma sg10906 : RowSquare [7,6,2,2,2,2,1] [4,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1212 sg1163 - -lemma sg10907 : RowSquare [7,6,2,2,2,2,1] [4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1216 sg1162 - -lemma sg10908 : RowSquare [7,6,2,2,2,2,1] [4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1213 sg1154 - -lemma sg10909 : RowSquare [7,6,2,2,2,2,1] [4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1212 sg1166 - -lemma sg10910 : RowSquare [7,6,2,2,2,2,1] [5,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1207 sg1170 - -lemma sg10911 : RowSquare [7,6,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg6317 - -lemma sg10912 : RowSquare [7,6,2,2,2,2,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6318 - -lemma sg10913 : RowSquare [7,6,2,2,2,2,1] [7,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6329 - -lemma sg10914 : RowSquare [7,6,2,2,2,2,1] [7,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5519 - -lemma sg10915 : RowSquare [7,6,2,2,2,2,1] [7,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7801 - -lemma sg10916 : RowSquare [7,6,2,2,2,2,1] [7,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7802 - -lemma sg10917 : RowSquare [7,6,2,2,2,2,1] [7,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg7803 - -lemma sg10918 : RowSquare [7,6,2,2,2,2,1] [7,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg7804 - -lemma sg10919 : RowSquare [7,6,2,2,2,2,1] [7,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5515 - -lemma sg10920 : RowSquare [7,6,2,2,2,2,1] [7,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6330 - -lemma sg10921 : RowSquare [7,6,2,2,2,2,1] [7,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4701 - -lemma sg10922 : RowSquare [7,6,2,2,2,2,1] [7,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6319 - -lemma sg10923 : RowSquare [7,6,2,2,2,2,1] [7,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6320 - -lemma sg10924 : RowSquare [7,6,2,2,2,2,1] [7,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg6321 - -lemma sg10925 : RowSquare [7,6,2,2,2,2,1] [7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg6322 - -lemma sg10926 : RowSquare [7,6,2,2,2,2,1] [7,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg4699 - -lemma sg10927 : RowSquare [7,6,2,2,2,2,1] [7,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4702 - -lemma sg10928 : RowSquare [7,6,2,2,2,2,1] [7,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6331 - -lemma sg10929 : RowSquare [7,6,2,2,2,2,1] [7,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6332 - -lemma sg10930 : RowSquare [7,6,2,2,2,2,1] [7,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg6333 - -lemma sg10931 : RowSquare [7,6,2,2,2,2,1] [7,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg3859 - -lemma sg10932 : RowSquare [7,6,2,2,2,2,1] [7,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5520 - -lemma sg10933 : RowSquare [7,6,2,2,2,2,1] [7,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg3860 - -lemma sg10934 : RowSquare [7,6,2,2,2,2,1] [7,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg5521 - -lemma sg10935 : RowSquare [7,6,2,2,2,2,1] [7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1209 sg1146 - -lemma sg10936 : RowSquare [7,6,2,2,2,2,1] [7,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg776 sg1632 - -lemma sg10937 : RowSquare [7,6,2,2,2,2,1] [7,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6323 - -lemma sg10938 : RowSquare [7,6,2,2,2,2,1] [7,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4701 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes17 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes20 + +namespace OAI + +/-! Semigroup Nodes 25. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg10538 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7018 + +lemma sg10539 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg7019 + +lemma sg10540 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5182 + +lemma sg10541 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,3,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg7020 + +lemma sg10542 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg5165 + +lemma sg10543 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg15 sg5140 + +lemma sg10544 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5183 + +lemma sg10545 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg5184 + +lemma sg10546 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5185 + +lemma sg10547 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,4,2,2] := by + exact rowSquare_join (by decide) sg83 sg3745 + +lemma sg10548 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg5186 + +lemma sg10549 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,4,4,4] := by + exact rowSquare_join (by decide) sg13 sg5187 + +lemma sg10550 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg5166 + +lemma sg10551 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5188 + +lemma sg10552 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg5189 + +lemma sg10553 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7021 + +lemma sg10554 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5190 + +lemma sg10555 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,6,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg5171 + +lemma sg10556 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,6,3,3] := by + exact rowSquare_join (by decide) sg13 sg5191 + +lemma sg10557 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,6,4,2] := by + exact rowSquare_join (by decide) sg83 sg3748 + +lemma sg10558 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [10,8,2,2] := by + exact rowSquare_join (by decide) sg13 sg5192 + +lemma sg10559 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7022 + +lemma sg10560 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg5147 + +lemma sg10561 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7023 + +lemma sg10562 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg15 sg5149 + +lemma sg10563 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5193 + +lemma sg10564 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,3,3,3,2] := by + exact rowSquare_join (by decide) sg84 sg3745 + +lemma sg10565 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg5182 + +lemma sg10566 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5194 + +lemma sg10567 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,4,3,2,2] := by + exact rowSquare_join (by decide) sg15 sg5155 + +lemma sg10568 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg3750 + +lemma sg10569 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,4,4,3] := by + exact rowSquare_join (by decide) sg13 sg5195 + +lemma sg10570 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7024 + +lemma sg10571 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,5,3,3] := by + exact rowSquare_join (by decide) sg84 sg3748 + +lemma sg10572 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [11,7,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5190 + +lemma sg10573 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [12,4,3,3] := by + exact rowSquare_join (by decide) sg84 sg3751 + +lemma sg10574 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1] [12,4,4,2] := by + exact rowSquare_join (by decide) sg364 sg2485 + +lemma sg10575 : RowSquare [6,6,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg5208 + +lemma sg10576 : RowSquare [6,6,2,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg905 sg1754 + +lemma sg10577 : RowSquare [6,6,2,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg906 sg1754 + +lemma sg10578 : RowSquare [6,6,2,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg907 sg1754 + +lemma sg10579 : RowSquare [6,6,2,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg908 sg1754 + +lemma sg10580 : RowSquare [6,6,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg909 sg1754 + +lemma sg10581 : RowSquare [6,6,2,2,2,2,1,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg7813 + +lemma sg10582 : RowSquare [6,6,2,2,2,2,1,1] [4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg7816 + +lemma sg10583 : RowSquare [6,6,2,2,2,2,1,1] [4,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg7817 + +lemma sg10584 : RowSquare [6,6,2,2,2,2,1,1] [4,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg7818 + +lemma sg10585 : RowSquare [6,6,2,2,2,2,1,1] [4,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg7819 + +lemma sg10586 : RowSquare [6,6,2,2,2,2,1,1] [4,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg7820 + +lemma sg10587 : RowSquare [6,6,2,2,2,2,1,1] [4,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg7821 + +lemma sg10588 : RowSquare [6,6,2,2,2,2,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg7824 + +lemma sg10589 : RowSquare [6,6,2,2,2,2,1,1] [5,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg7825 + +lemma sg10590 : RowSquare [6,6,2,2,2,2,1,1] [5,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg7826 + +lemma sg10591 : RowSquare [6,6,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg7827 + +lemma sg10592 : RowSquare [6,6,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg7828 + +lemma sg10593 : RowSquare [6,6,2,2,2,2,1,1] [5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg7837 + +lemma sg10594 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2251 + +lemma sg10595 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg2251 + +lemma sg10596 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2252 + +lemma sg10597 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg2251 + +lemma sg10598 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg2251 + +lemma sg10599 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg2251 + +lemma sg10600 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg594 sg2251 + +lemma sg10601 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg2256 + +lemma sg10602 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg595 sg2251 + +lemma sg10603 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg2251 + +lemma sg10604 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg2253 + +lemma sg10605 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg2254 + +lemma sg10606 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg2254 + +lemma sg10607 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg2254 + +lemma sg10608 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg2255 + +lemma sg10609 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg589 sg2256 + +lemma sg10610 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg2255 + +lemma sg10611 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg597 sg2251 + +lemma sg10612 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg591 sg2252 + +lemma sg10613 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg592 sg2252 + +lemma sg10614 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8539 + +lemma sg10615 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg587 sg2259 + +lemma sg10616 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8541 + +lemma sg10617 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg587 sg2260 + +lemma sg10618 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg600 sg2251 + +lemma sg10619 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg2257 + +lemma sg10620 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg601 sg2251 + +lemma sg10621 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg2257 + +lemma sg10622 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8546 + +lemma sg10623 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8549 + +lemma sg10624 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8550 + +lemma sg10625 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg588 sg2260 + +lemma sg10626 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg593 sg2254 + +lemma sg10627 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg2258 + +lemma sg10628 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8551 + +lemma sg10629 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg594 sg2254 + +lemma sg10630 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg2258 + +lemma sg10631 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8552 + +lemma sg10632 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8553 + +lemma sg10633 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8554 + +lemma sg10634 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg0 sg8555 + +lemma sg10635 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg594 sg2255 + +lemma sg10636 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg2259 + +lemma sg10637 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8556 + +lemma sg10638 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg8557 + +lemma sg10639 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg0 sg8558 + +lemma sg10640 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg0 sg8559 + +lemma sg10641 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg2251 + +lemma sg10642 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg586 sg2267 + +lemma sg10643 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg595 sg2254 + +lemma sg10644 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg588 sg2262 + +lemma sg10645 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg2261 + +lemma sg10646 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg588 sg2263 + +lemma sg10647 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg595 sg2256 + +lemma sg10648 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg2254 + +lemma sg10649 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg589 sg2262 + +lemma sg10650 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg2255 + +lemma sg10651 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg2262 + +lemma sg10652 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg589 sg2263 + +lemma sg10653 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg590 sg2263 + +lemma sg10654 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg603 sg2251 + +lemma sg10655 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg597 sg2252 + +lemma sg10656 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg605 sg2251 + +lemma sg10657 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8567 + +lemma sg10658 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8569 + +lemma sg10659 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8570 + +lemma sg10660 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg591 sg2260 + +lemma sg10661 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg606 sg2251 + +lemma sg10662 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg6910 + +lemma sg10663 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg6030 + +lemma sg10664 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg6912 + +lemma sg10665 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8574 + +lemma sg10666 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg6913 + +lemma sg10667 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg0 sg8575 + +lemma sg10668 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg599 sg2254 + +lemma sg10669 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6031 + +lemma sg10670 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8576 + +lemma sg10671 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg6032 + +lemma sg10672 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6033 + +lemma sg10673 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8577 + +lemma sg10674 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg6034 + +lemma sg10675 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg6035 + +lemma sg10676 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg0 sg8578 + +lemma sg10677 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg594 sg2259 + +lemma sg10678 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8579 + +lemma sg10679 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2 sg6917 + +lemma sg10680 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2 sg6918 + +lemma sg10681 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,4] := by + exact rowSquare_join (by decide) sg2 sg6919 + +lemma sg10682 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg607 sg2251 + +lemma sg10683 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8585 + +lemma sg10684 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg6036 + +lemma sg10685 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg8589 + +lemma sg10686 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8591 + +lemma sg10687 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8592 + +lemma sg10688 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg8593 + +lemma sg10689 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg0 sg8594 + +lemma sg10690 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg601 sg2254 + +lemma sg10691 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg2258 + +lemma sg10692 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6037 + +lemma sg10693 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg6038 + +lemma sg10694 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6039 + +lemma sg10695 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg6040 + +lemma sg10696 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6041 + +lemma sg10697 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg6042 + +lemma sg10698 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,3] := by + exact rowSquare_join (by decide) sg4 sg6043 + +lemma sg10699 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg4 sg6044 + +lemma sg10700 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,2] := by + exact rowSquare_join (by decide) sg4 sg6045 + +lemma sg10701 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg2269 + +lemma sg10702 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg2254 + +lemma sg10703 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg608 sg2251 + +lemma sg10704 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg609 sg2251 + +lemma sg10705 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg610 sg2251 + +lemma sg10706 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg605 sg2254 + +lemma sg10707 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5304 + +lemma sg10708 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6051 + +lemma sg10709 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg5307 + +lemma sg10710 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,2] := by + exact rowSquare_join (by decide) sg13 sg5308 + +lemma sg10711 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5309 + +lemma sg10712 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg6052 + +lemma sg10713 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5310 + +lemma sg10714 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg5311 + +lemma sg10715 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,1] := by + exact rowSquare_join (by decide) sg4 sg6053 + +lemma sg10716 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6054 + +lemma sg10717 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6055 + +lemma sg10718 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg6056 + +lemma sg10719 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg6057 + +lemma sg10720 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,2] := by + exact rowSquare_join (by decide) sg4 sg6058 + +lemma sg10721 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,1] := by + exact rowSquare_join (by decide) sg0 sg8606 + +lemma sg10722 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6059 + +lemma sg10723 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg6060 + +lemma sg10724 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,5,2,2] := by + exact rowSquare_join (by decide) sg4 sg6061 + +lemma sg10725 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,1] := by + exact rowSquare_join (by decide) sg4 sg6062 + +lemma sg10726 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,6,5,4] := by + exact rowSquare_join (by decide) sg4 sg6063 + +lemma sg10727 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg2261 + +lemma sg10728 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg588 sg2269 + +lemma sg10729 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg2262 + +lemma sg10730 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg2267 + +lemma sg10731 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,1] := by + exact rowSquare_join (by decide) sg589 sg2269 + +lemma sg10732 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2] := by + exact rowSquare_join (by decide) sg590 sg2269 + +lemma sg10733 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [7,7,4,2,1,1] := by + exact rowSquare_join (by decide) sg596 sg2268 + +lemma sg10734 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg611 sg2251 + +lemma sg10735 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg608 sg2252 + +lemma sg10736 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7292 + +lemma sg10737 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7293 + +lemma sg10738 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6 sg6029 + +lemma sg10739 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg6956 + +lemma sg10740 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg612 sg2251 + +lemma sg10741 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg609 sg2252 + +lemma sg10742 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7294 + +lemma sg10743 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7295 + +lemma sg10744 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6046 + +lemma sg10745 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg6047 + +lemma sg10746 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7296 + +lemma sg10747 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7297 + +lemma sg10748 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6064 + +lemma sg10749 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg6065 + +lemma sg10750 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg16 sg5135 + +lemma sg10751 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5312 + +lemma sg10752 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5313 + +lemma sg10753 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6 sg6034 + +lemma sg10754 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6 sg6035 + +lemma sg10755 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg7298 + +lemma sg10756 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg610 sg2252 + +lemma sg10757 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7299 + +lemma sg10758 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7300 + +lemma sg10759 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5302 + +lemma sg10760 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg6048 + +lemma sg10761 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg5135 + +lemma sg10762 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7301 + +lemma sg10763 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5314 + +lemma sg10764 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6066 + +lemma sg10765 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg16 sg5136 + +lemma sg10766 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5315 + +lemma sg10767 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5316 + +lemma sg10768 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg5 sg6049 + +lemma sg10769 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg5 sg6050 + +lemma sg10770 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6067 + +lemma sg10771 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5317 + +lemma sg10772 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg16 sg5137 + +lemma sg10773 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg6068 + +lemma sg10774 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5318 + +lemma sg10775 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5319 + +lemma sg10776 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3] := by + exact rowSquare_join (by decide) sg4 sg6069 + +lemma sg10777 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg5320 + +lemma sg10778 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,2] := by + exact rowSquare_join (by decide) sg13 sg5321 + +lemma sg10779 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7302 + +lemma sg10780 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8607 + +lemma sg10781 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5322 + +lemma sg10782 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5303 + +lemma sg10783 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg17 sg5136 + +lemma sg10784 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5304 + +lemma sg10785 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5323 + +lemma sg10786 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg5137 + +lemma sg10787 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg16 sg5139 + +lemma sg10788 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5324 + +lemma sg10789 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg5325 + +lemma sg10790 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg5305 + +lemma sg10791 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6070 + +lemma sg10792 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5326 + +lemma sg10793 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg16 sg5140 + +lemma sg10794 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5327 + +lemma sg10795 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg5328 + +lemma sg10796 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg5329 + +lemma sg10797 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6071 + +lemma sg10798 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5330 + +lemma sg10799 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,5,2,2] := by + exact rowSquare_join (by decide) sg16 sg5142 + +lemma sg10800 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,1] := by + exact rowSquare_join (by decide) sg13 sg5331 + +lemma sg10801 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,5,5,4] := by + exact rowSquare_join (by decide) sg16 sg5144 + +lemma sg10802 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8608 + +lemma sg10803 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6072 + +lemma sg10804 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5332 + +lemma sg10805 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg8609 + +lemma sg10806 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg5139 + +lemma sg10807 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5306 + +lemma sg10808 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5333 + +lemma sg10809 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg17 sg5140 + +lemma sg10810 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5334 + +lemma sg10811 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg5335 + +lemma sg10812 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5309 + +lemma sg10813 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5336 + +lemma sg10814 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,2] := by + exact rowSquare_join (by decide) sg17 sg5142 + +lemma sg10815 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg5337 + +lemma sg10816 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,4,4] := by + exact rowSquare_join (by decide) sg13 sg5338 + +lemma sg10817 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6073 + +lemma sg10818 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,5,2,1] := by + exact rowSquare_join (by decide) sg13 sg5339 + +lemma sg10819 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,6,5,3] := by + exact rowSquare_join (by decide) sg13 sg5340 + +lemma sg10820 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8611 + +lemma sg10821 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6074 + +lemma sg10822 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg8612 + +lemma sg10823 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg8613 + +lemma sg10824 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6075 + +lemma sg10825 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg6076 + +lemma sg10826 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg6077 + +lemma sg10827 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg8614 + +lemma sg10828 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,4,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6078 + +lemma sg10829 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,4,2,1] := by + exact rowSquare_join (by decide) sg4 sg6079 + +lemma sg10830 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,7,4,3] := by + exact rowSquare_join (by decide) sg4 sg6080 + +lemma sg10831 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,8,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg2267 + +lemma sg10832 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2] := by + exact rowSquare_join (by decide) sg595 sg2269 + +lemma sg10833 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,8,3,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg2268 + +lemma sg10834 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [8,8,3,2,1] := by + exact rowSquare_join (by decide) sg596 sg2269 + +lemma sg10835 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [9,5,4,4] := by + exact rowSquare_join (by decide) sg39 sg4583 + +lemma sg10836 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [9,6,4,3] := by + exact rowSquare_join (by decide) sg40 sg4583 + +lemma sg10837 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [10,4,4,4] := by + exact rowSquare_join (by decide) sg39 sg4584 + +lemma sg10838 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [10,5,4,3] := by + exact rowSquare_join (by decide) sg39 sg4585 + +lemma sg10839 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [10,6,3,3] := by + exact rowSquare_join (by decide) sg39 sg4586 + +lemma sg10840 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1] [10,6,4,2] := by + exact rowSquare_join (by decide) sg97 sg3748 + +lemma sg10841 : RowSquare [7,5,2,1,1,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg543 sg2251 + +lemma sg10842 : RowSquare [7,5,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg316 sg2708 + +lemma sg10843 : RowSquare [7,5,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg312 sg2710 + +lemma sg10844 : RowSquare [7,5,2,2,1,1,1,1,1,1] [3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg270 sg2702 + +lemma sg10845 : RowSquare [7,5,2,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg271 sg2702 + +lemma sg10846 : RowSquare [7,5,2,2,1,1,1,1,1,1] [4,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg272 sg2702 + +lemma sg10847 : RowSquare [7,5,2,2,1,1,1,1,1,1] [4,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg276 sg2702 + +lemma sg10848 : RowSquare [7,5,2,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg496 sg2251 + +lemma sg10849 : RowSquare [7,5,2,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg281 sg2702 + +lemma sg10850 : RowSquare [7,5,2,2,1,1,1,1,1,1] [5,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg496 sg2253 + +lemma sg10851 : RowSquare [7,5,2,2,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7454 + +lemma sg10852 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg457 sg2251 + +lemma sg10853 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg5417 + +lemma sg10854 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg459 sg2251 + +lemma sg10855 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1191 + +lemma sg10856 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg5420 + +lemma sg10857 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5421 + +lemma sg10858 : RowSquare [7,6,2,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5422 + +lemma sg10859 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg74 sg3866 + +lemma sg10860 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg3867 + +lemma sg10861 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg465 sg2251 + +lemma sg10862 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg3870 + +lemma sg10863 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg459 sg2254 + +lemma sg10864 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5429 + +lemma sg10865 : RowSquare [7,6,2,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg74 sg3875 + +lemma sg10866 : RowSquare [7,6,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg3876 + +lemma sg10868 : RowSquare [7,6,2,2,2,2,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1222 sg1177 + +lemma sg10869 : RowSquare [7,6,2,2,2,2,1] [2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1219 sg1177 + +lemma sg10870 : RowSquare [7,6,2,2,2,2,1] [2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1219 sg1176 + +lemma sg10871 : RowSquare [7,6,2,2,2,2,1] [2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1219 sg1174 + +lemma sg10872 : RowSquare [7,6,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1219 sg1172 + +lemma sg10873 : RowSquare [7,6,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1219 sg1169 + +lemma sg10874 : RowSquare [7,6,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg780 sg1644 + +lemma sg10875 : RowSquare [7,6,2,2,2,2,1] [3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1218 sg1177 + +lemma sg10876 : RowSquare [7,6,2,2,2,2,1] [3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1218 sg1176 + +lemma sg10877 : RowSquare [7,6,2,2,2,2,1] [3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1218 sg1175 + +lemma sg10878 : RowSquare [7,6,2,2,2,2,1] [3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1218 sg1174 + +lemma sg10879 : RowSquare [7,6,2,2,2,2,1] [3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1218 sg1172 + +lemma sg10880 : RowSquare [7,6,2,2,2,2,1] [3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1218 sg1169 + +lemma sg10881 : RowSquare [7,6,2,2,2,2,1] [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1220 sg1177 + +lemma sg10882 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1217 sg1170 + +lemma sg10883 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1215 sg1170 + +lemma sg10884 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1215 sg1167 + +lemma sg10885 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1215 sg1163 + +lemma sg10886 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1217 sg1162 + +lemma sg10887 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1215 sg1162 + +lemma sg10888 : RowSquare [7,6,2,2,2,2,1] [3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1215 sg1157 + +lemma sg10889 : RowSquare [7,6,2,2,2,2,1] [4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1214 sg1177 + +lemma sg10890 : RowSquare [7,6,2,2,2,2,1] [4,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1214 sg1176 + +lemma sg10891 : RowSquare [7,6,2,2,2,2,1] [4,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1214 sg1175 + +lemma sg10892 : RowSquare [7,6,2,2,2,2,1] [4,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1214 sg1174 + +lemma sg10893 : RowSquare [7,6,2,2,2,2,1] [4,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1214 sg1172 + +lemma sg10894 : RowSquare [7,6,2,2,2,2,1] [4,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1214 sg1169 + +lemma sg10895 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1213 sg1173 + +lemma sg10896 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1213 sg1171 + +lemma sg10897 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1213 sg1168 + +lemma sg10898 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1213 sg1164 + +lemma sg10899 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1213 sg1170 + +lemma sg10900 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1213 sg1167 + +lemma sg10901 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1213 sg1163 + +lemma sg10902 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1214 sg1157 + +lemma sg10903 : RowSquare [7,6,2,2,2,2,1] [4,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1213 sg1162 + +lemma sg10904 : RowSquare [7,6,2,2,2,2,1] [4,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1212 sg1170 + +lemma sg10905 : RowSquare [7,6,2,2,2,2,1] [4,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1212 sg1167 + +lemma sg10906 : RowSquare [7,6,2,2,2,2,1] [4,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1212 sg1163 + +lemma sg10907 : RowSquare [7,6,2,2,2,2,1] [4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1216 sg1162 + +lemma sg10908 : RowSquare [7,6,2,2,2,2,1] [4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1213 sg1154 + +lemma sg10909 : RowSquare [7,6,2,2,2,2,1] [4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1212 sg1166 + +lemma sg10910 : RowSquare [7,6,2,2,2,2,1] [5,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1207 sg1170 + +lemma sg10911 : RowSquare [7,6,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg6317 + +lemma sg10912 : RowSquare [7,6,2,2,2,2,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6318 + +lemma sg10913 : RowSquare [7,6,2,2,2,2,1] [7,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6329 + +lemma sg10914 : RowSquare [7,6,2,2,2,2,1] [7,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5519 + +lemma sg10915 : RowSquare [7,6,2,2,2,2,1] [7,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7801 + +lemma sg10916 : RowSquare [7,6,2,2,2,2,1] [7,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7802 + +lemma sg10917 : RowSquare [7,6,2,2,2,2,1] [7,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg7803 + +lemma sg10918 : RowSquare [7,6,2,2,2,2,1] [7,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg7804 + +lemma sg10919 : RowSquare [7,6,2,2,2,2,1] [7,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5515 + +lemma sg10920 : RowSquare [7,6,2,2,2,2,1] [7,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6330 + +lemma sg10921 : RowSquare [7,6,2,2,2,2,1] [7,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4701 + +lemma sg10922 : RowSquare [7,6,2,2,2,2,1] [7,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6319 + +lemma sg10923 : RowSquare [7,6,2,2,2,2,1] [7,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6320 + +lemma sg10924 : RowSquare [7,6,2,2,2,2,1] [7,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg6321 + +lemma sg10925 : RowSquare [7,6,2,2,2,2,1] [7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg6322 + +lemma sg10926 : RowSquare [7,6,2,2,2,2,1] [7,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg4699 + +lemma sg10927 : RowSquare [7,6,2,2,2,2,1] [7,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4702 + +lemma sg10928 : RowSquare [7,6,2,2,2,2,1] [7,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6331 + +lemma sg10929 : RowSquare [7,6,2,2,2,2,1] [7,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6332 + +lemma sg10930 : RowSquare [7,6,2,2,2,2,1] [7,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg6333 + +lemma sg10931 : RowSquare [7,6,2,2,2,2,1] [7,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg3859 + +lemma sg10932 : RowSquare [7,6,2,2,2,2,1] [7,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5520 + +lemma sg10933 : RowSquare [7,6,2,2,2,2,1] [7,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg3860 + +lemma sg10934 : RowSquare [7,6,2,2,2,2,1] [7,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg5521 + +lemma sg10935 : RowSquare [7,6,2,2,2,2,1] [7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1209 sg1146 + +lemma sg10936 : RowSquare [7,6,2,2,2,2,1] [7,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg776 sg1632 + +lemma sg10937 : RowSquare [7,6,2,2,2,2,1] [7,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6323 + +lemma sg10938 : RowSquare [7,6,2,2,2,2,1] [7,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4701 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes26.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes26.lean index f13488214e79e9ada743e94042098ab76377046f..28c6dfbe116bb92aa26c202278762df408b34366 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes26.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes26.lean @@ -1,1221 +1,1221 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes14 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes7 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes15 - -namespace OAI - -/-! Semigroup Nodes 26. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg10939 : RowSquare [7,6,2,2,2,2,1] [7,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4703 - -lemma sg10940 : RowSquare [7,6,2,2,2,2,1] [7,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6324 - -lemma sg10941 : RowSquare [7,6,2,2,2,2,1] [7,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6325 - -lemma sg10942 : RowSquare [7,6,2,2,2,2,1] [7,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg6326 - -lemma sg10943 : RowSquare [7,6,2,2,2,2,1] [7,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4702 - -lemma sg10944 : RowSquare [7,6,2,2,2,2,1] [7,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4704 - -lemma sg10945 : RowSquare [7,6,2,2,2,2,1] [7,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6334 - -lemma sg10946 : RowSquare [7,6,2,2,2,2,1] [7,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1149 - -lemma sg10947 : RowSquare [7,6,2,2,2,2,1] [7,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg6335 - -lemma sg10948 : RowSquare [7,6,2,2,2,2,1] [7,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4705 - -lemma sg10949 : RowSquare [7,6,2,2,2,2,1] [7,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1150 - -lemma sg10950 : RowSquare [7,6,2,2,2,2,1] [7,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg769 sg1633 - -lemma sg10951 : RowSquare [7,6,2,2,2,2,1] [7,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1210 sg1146 - -lemma sg10952 : RowSquare [7,6,2,2,2,2,1] [7,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6336 - -lemma sg10953 : RowSquare [7,6,2,2,2,2,1] [7,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg3861 - -lemma sg10954 : RowSquare [7,6,2,2,2,2,1] [7,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1209 sg1148 - -lemma sg10955 : RowSquare [7,6,2,2,2,2,1] [7,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1203 sg1149 - -lemma sg10956 : RowSquare [7,6,2,2,2,2,1] [7,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg3185 - -lemma sg10957 : RowSquare [7,6,2,2,2,2,1] [7,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1203 sg1150 - -lemma sg10958 : RowSquare [7,6,2,2,2,2,1] [7,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg770 sg1633 - -lemma sg10959 : RowSquare [7,6,2,2,2,2,1] [7,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4700 - -lemma sg10960 : RowSquare [7,6,2,2,2,2,1] [7,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4703 - -lemma sg10961 : RowSquare [7,6,2,2,2,2,1] [7,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4707 - -lemma sg10962 : RowSquare [7,6,2,2,2,2,1] [7,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6327 - -lemma sg10963 : RowSquare [7,6,2,2,2,2,1] [7,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1151 - -lemma sg10964 : RowSquare [7,6,2,2,2,2,1] [7,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg6328 - -lemma sg10965 : RowSquare [7,6,2,2,2,2,1] [7,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg3863 - -lemma sg10966 : RowSquare [7,6,2,2,2,2,1] [7,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4708 - -lemma sg10967 : RowSquare [7,6,2,2,2,2,1] [7,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1152 - -lemma sg10968 : RowSquare [7,6,2,2,2,2,1] [7,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1203 sg1151 - -lemma sg10969 : RowSquare [7,6,2,2,2,2,1] [7,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1153 - -lemma sg10970 : RowSquare [7,6,2,2,2,2,1] [7,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1206 sg1150 - -lemma sg10971 : RowSquare [7,6,2,2,2,2,1] [7,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4706 - -lemma sg10972 : RowSquare [7,6,2,2,2,2,1] [7,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1154 - -lemma sg10973 : RowSquare [7,6,2,2,2,2,1] [7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg3183 - -lemma sg10974 : RowSquare [7,6,2,2,2,2,1] [7,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5516 - -lemma sg10975 : RowSquare [7,6,2,2,2,2,1] [7,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4707 - -lemma sg10976 : RowSquare [7,6,2,2,2,2,1] [7,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5522 - -lemma sg10977 : RowSquare [7,6,2,2,2,2,1] [7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1155 - -lemma sg10978 : RowSquare [7,6,2,2,2,2,1] [7,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1206 sg1151 - -lemma sg10979 : RowSquare [7,6,2,2,2,2,1] [7,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4708 - -lemma sg10980 : RowSquare [7,6,2,2,2,2,1] [7,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1156 - -lemma sg10981 : RowSquare [7,6,2,2,2,2,1] [7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1157 - -lemma sg10982 : RowSquare [7,6,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5517 - -lemma sg10983 : RowSquare [7,6,2,2,2,2,1] [7,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5518 - -lemma sg10984 : RowSquare [7,6,2,2,2,2,1] [7,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg5523 - -lemma sg10985 : RowSquare [7,6,2,2,2,2,1] [7,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg3184 - -lemma sg10986 : RowSquare [7,6,2,2,2,2,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg6318 - -lemma sg10987 : RowSquare [7,6,2,2,2,2,1] [8,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6329 - -lemma sg10988 : RowSquare [7,6,2,2,2,2,1] [8,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6337 - -lemma sg10989 : RowSquare [7,6,2,2,2,2,1] [8,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4709 - -lemma sg10990 : RowSquare [7,6,2,2,2,2,1] [8,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg6319 - -lemma sg10991 : RowSquare [7,6,2,2,2,2,1] [8,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg6320 - -lemma sg10992 : RowSquare [7,6,2,2,2,2,1] [8,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6 sg6321 - -lemma sg10993 : RowSquare [7,6,2,2,2,2,1] [8,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6 sg6322 - -lemma sg10994 : RowSquare [7,6,2,2,2,2,1] [8,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5519 - -lemma sg10995 : RowSquare [7,6,2,2,2,2,1] [8,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4709 - -lemma sg10996 : RowSquare [7,6,2,2,2,2,1] [8,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4710 - -lemma sg10997 : RowSquare [7,6,2,2,2,2,1] [8,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6331 - -lemma sg10998 : RowSquare [7,6,2,2,2,2,1] [8,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6332 - -lemma sg10999 : RowSquare [7,6,2,2,2,2,1] [8,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg6333 - -lemma sg11000 : RowSquare [7,6,2,2,2,2,1] [8,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg4702 - -lemma sg11001 : RowSquare [7,6,2,2,2,2,1] [8,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4711 - -lemma sg11002 : RowSquare [7,6,2,2,2,2,1] [8,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg6338 - -lemma sg11003 : RowSquare [7,6,2,2,2,2,1] [8,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1209 sg1149 - -lemma sg11004 : RowSquare [7,6,2,2,2,2,1] [8,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg3862 - -lemma sg11005 : RowSquare [7,6,2,2,2,2,1] [8,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1209 sg1150 - -lemma sg11006 : RowSquare [7,6,2,2,2,2,1] [8,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4701 - -lemma sg11007 : RowSquare [7,6,2,2,2,2,1] [8,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4710 - -lemma sg11008 : RowSquare [7,6,2,2,2,2,1] [8,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg3863 - -lemma sg11009 : RowSquare [7,6,2,2,2,2,1] [8,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5520 - -lemma sg11010 : RowSquare [7,6,2,2,2,2,1] [8,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1158 - -lemma sg11011 : RowSquare [7,6,2,2,2,2,1] [8,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4711 - -lemma sg11012 : RowSquare [7,6,2,2,2,2,1] [8,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4713 - -lemma sg11013 : RowSquare [7,6,2,2,2,2,1] [8,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1159 - -lemma sg11014 : RowSquare [7,6,2,2,2,2,1] [8,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1160 - -lemma sg11015 : RowSquare [7,6,2,2,2,2,1] [8,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg2592 - -lemma sg11016 : RowSquare [7,6,2,2,2,2,1] [8,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4703 - -lemma sg11017 : RowSquare [7,6,2,2,2,2,1] [8,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4712 - -lemma sg11018 : RowSquare [7,6,2,2,2,2,1] [8,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4714 - -lemma sg11019 : RowSquare [7,6,2,2,2,2,1] [8,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg1161 - -lemma sg11020 : RowSquare [7,6,2,2,2,2,1] [8,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg2593 - -lemma sg11021 : RowSquare [7,6,2,2,2,2,1] [8,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4707 - -lemma sg11022 : RowSquare [7,6,2,2,2,2,1] [8,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg2593 - -lemma sg11023 : RowSquare [7,6,2,2,2,2,1] [8,7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg2593 - -lemma sg11024 : RowSquare [7,6,2,2,2,2,1] [9,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg5515 - -lemma sg11025 : RowSquare [7,6,2,2,2,2,1] [9,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6337 - -lemma sg11026 : RowSquare [7,6,2,2,2,2,1] [9,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg4709 - -lemma sg11027 : RowSquare [7,6,2,2,2,2,1] [9,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4715 - -lemma sg11028 : RowSquare [7,6,2,2,2,2,1] [9,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg6331 - -lemma sg11029 : RowSquare [7,6,2,2,2,2,1] [9,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg6332 - -lemma sg11030 : RowSquare [7,6,2,2,2,2,1] [9,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4709 - -lemma sg11031 : RowSquare [7,6,2,2,2,2,1] [9,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4715 - -lemma sg11032 : RowSquare [7,6,2,2,2,2,1] [9,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg4716 - -lemma sg11033 : RowSquare [7,6,2,2,2,2,1] [9,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg6338 - -lemma sg11034 : RowSquare [7,6,2,2,2,2,1] [9,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg3864 - -lemma sg11035 : RowSquare [7,6,2,2,2,2,1] [9,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg2592 - -lemma sg11036 : RowSquare [7,6,2,2,2,2,1] [9,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4710 - -lemma sg11037 : RowSquare [7,6,2,2,2,2,1] [9,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4716 - -lemma sg11038 : RowSquare [7,6,2,2,2,2,1] [9,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg2593 - -lemma sg11039 : RowSquare [7,6,2,2,2,2,1] [9,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg85 sg3863 - -lemma sg11040 : RowSquare [7,6,2,2,2,2,1] [10,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg5519 - -lemma sg11041 : RowSquare [7,6,2,2,2,2,1] [10,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg4709 - -lemma sg11042 : RowSquare [7,6,2,2,2,2,1] [10,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg4715 - -lemma sg11043 : RowSquare [7,6,2,2,2,2,1] [10,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg3864 - -lemma sg11044 : RowSquare [7,6,2,2,2,2,1] [10,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg4715 - -lemma sg11045 : RowSquare [7,6,2,2,2,2,1] [10,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg4717 - -lemma sg11046 : RowSquare [7,6,2,2,2,2,1] [11,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg4709 - -lemma sg11047 : RowSquare [7,6,2,2,2,2,1] [11,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg4715 - -lemma sg11048 : RowSquare [7,7,1,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg5551 - -lemma sg11049 : RowSquare [7,7,1,1,1,1,1,1,1,1] [5,5,5,5,2] := by - exact rowSquare_join (by decide) sg13 sg5552 - -lemma sg11050 : RowSquare [8,3,2,2,2,2,2,1] [5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg3995 - -lemma sg11051 : RowSquare [8,4,3,2,2,2,1] [4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg287 sg2546 - -lemma sg11052 : RowSquare [8,6,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg6396 - -lemma sg11053 : RowSquare [8,6,1,1,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg110 sg3521 - -lemma sg11054 : RowSquare [8,6,1,1,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg111 sg3521 - -lemma sg11055 : RowSquare [8,6,1,1,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg112 sg3521 - -lemma sg11056 : RowSquare [9,3,2,2,2,2,1,1] [4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg74 sg3967 - -lemma sg11057 : RowSquare [9,3,2,2,2,2,1,1] [5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg3968 - -lemma sg11058 : RowSquare [9,3,2,2,2,2,2] [6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg165 sg3213 - -lemma sg11059 : RowSquare [9,7,3,2,1] [4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg878 sg1688 - -lemma sg11060 : RowSquare [10,3,2,2,2,2,1] [5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg3870 - -lemma sg11061 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4] := by - exact rowSquare_join (by decide) sg1539 sg1978 - -lemma sg11062 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg1455 sg2008 - -lemma sg11063 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg1540 sg1978 - -lemma sg11064 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2] := by - exact rowSquare_join (by decide) sg1532 sg1993 - -lemma sg11065 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,1] := by - exact rowSquare_join (by decide) sg1541 sg1978 - -lemma sg11066 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5] := by - exact rowSquare_join (by decide) sg1562 sg1926 - -lemma sg11067 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg1455 sg2009 - -lemma sg11068 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg1540 sg1980 - -lemma sg11069 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2] := by - exact rowSquare_join (by decide) sg1532 sg1994 - -lemma sg11070 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,1] := by - exact rowSquare_join (by decide) sg1541 sg1980 - -lemma sg11071 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg1540 sg1981 - -lemma sg11072 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2] := by - exact rowSquare_join (by decide) sg1532 sg1995 - -lemma sg11073 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,1] := by - exact rowSquare_join (by decide) sg1533 sg1993 - -lemma sg11074 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4] := by - exact rowSquare_join (by decide) sg1539 sg1987 - -lemma sg11075 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3] := by - exact rowSquare_join (by decide) sg1539 sg1988 - -lemma sg11076 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,2,2,1] := by - exact rowSquare_join (by decide) sg1455 sg2010 - -lemma sg11077 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,1,1] := by - exact rowSquare_join (by decide) sg1542 sg1980 - -lemma sg11078 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2] := by - exact rowSquare_join (by decide) sg1532 sg1996 - -lemma sg11079 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4] := by - exact rowSquare_join (by decide) sg1544 sg1980 - -lemma sg11080 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,1] := by - exact rowSquare_join (by decide) sg1455 sg2011 - -lemma sg11081 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,1,1] := by - exact rowSquare_join (by decide) sg1572 sg1915 - -lemma sg11082 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2] := by - exact rowSquare_join (by decide) sg1545 sg1979 - -lemma sg11083 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,1] := by - exact rowSquare_join (by decide) sg1533 sg1996 - -lemma sg11084 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3] := by - exact rowSquare_join (by decide) sg1539 sg1991 - -lemma sg11085 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1540 sg1983 - -lemma sg11086 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1455 sg2012 - -lemma sg11087 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3] := by - exact rowSquare_join (by decide) sg1461 sg2002 - -lemma sg11088 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1460 sg2003 - -lemma sg11089 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2] := by - exact rowSquare_join (by decide) sg1461 sg2003 - -lemma sg11090 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg1540 sg1985 - -lemma sg11091 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg1455 sg2013 - -lemma sg11092 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3] := by - exact rowSquare_join (by decide) sg1461 sg2004 - -lemma sg11093 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg1542 sg1985 - -lemma sg11094 : RowSquare [3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3] := by - exact rowSquare_join (by decide) sg1532 sg1979 - -lemma sg11095 : RowSquare [3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,2] := by - exact rowSquare_join (by decide) sg1532 sg1980 - -lemma sg11096 : RowSquare [3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5] := by - exact rowSquare_join (by decide) sg693 sg3152 - -lemma sg11097 : RowSquare [3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3] := by - exact rowSquare_join (by decide) sg1061 sg2479 - -lemma sg11098 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg1517 sg1977 - -lemma sg11099 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3] := by - exact rowSquare_join (by decide) sg1519 sg1977 - -lemma sg11100 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1517 sg1979 - -lemma sg11101 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1517 sg1980 - -lemma sg11102 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg1518 sg1979 - -lemma sg11103 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3] := by - exact rowSquare_join (by decide) sg1519 sg1979 - -lemma sg11104 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg1518 sg1980 - -lemma sg11105 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,2] := by - exact rowSquare_join (by decide) sg1519 sg1980 - -lemma sg11106 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1520 sg1979 - -lemma sg11107 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3] := by - exact rowSquare_join (by decide) sg1033 sg2479 - -lemma sg11108 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1416 sg2003 - -lemma sg11109 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1417 sg2003 - -lemma sg11110 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1517 sg1985 - -lemma sg11111 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1524 sg1980 - -lemma sg11112 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1417 sg2004 - -lemma sg11113 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg1518 sg1985 - -lemma sg11114 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1542 sg1956 - -lemma sg11115 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1416 sg2005 - -lemma sg11116 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg1521 sg1983 - -lemma sg11117 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1417 sg2005 - -lemma sg11118 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1518 sg1987 - -lemma sg11119 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,2] := by - exact rowSquare_join (by decide) sg1519 sg1987 - -lemma sg11120 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1520 sg1985 - -lemma sg11121 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1416 sg2006 - -lemma sg11122 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1517 sg1989 - -lemma sg11123 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg1521 sg1985 - -lemma sg11124 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1417 sg2006 - -lemma sg11125 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg1518 sg1989 - -lemma sg11126 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3] := by - exact rowSquare_join (by decide) sg1519 sg1989 - -lemma sg11127 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1416 sg2007 - -lemma sg11128 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1417 sg2007 - -lemma sg11129 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg1521 sg1986 - -lemma sg11130 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg1518 sg1990 - -lemma sg11131 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,2] := by - exact rowSquare_join (by decide) sg1519 sg1990 - -lemma sg11132 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,1] := by - exact rowSquare_join (by decide) sg1541 sg1963 - -lemma sg11133 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1566 sg1903 - -lemma sg11134 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1520 sg1989 - -lemma sg11135 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,2] := by - exact rowSquare_join (by decide) sg1542 sg1961 - -lemma sg11136 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1520 sg1991 - -lemma sg11137 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,1] := by - exact rowSquare_join (by decide) sg1545 sg1961 - -lemma sg11138 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1520 sg1992 - -lemma sg11139 : RowSquare [4,3,2,2,2,2,2,2,2,1,1] [5,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg2364 - -lemma sg11140 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1517 sg1954 - -lemma sg11141 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1517 sg1955 - -lemma sg11142 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1517 sg1956 - -lemma sg11143 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1517 sg1957 - -lemma sg11144 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1520 sg1955 - -lemma sg11145 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1517 sg1958 - -lemma sg11146 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1520 sg1957 - -lemma sg11147 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1517 sg1961 - -lemma sg11148 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1520 sg1961 - -lemma sg11149 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1520 sg1963 - -lemma sg11150 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1417 sg1902 - -lemma sg11151 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1416 sg1903 - -lemma sg11152 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1416 sg1908 - -lemma sg11153 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg1417 sg1908 - -lemma sg11154 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1524 sg1811 - -lemma sg11155 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1416 sg1909 - -lemma sg11156 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1418 sg1902 - -lemma sg11157 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1418 sg1903 - -lemma sg11158 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1520 sg1814 - -lemma sg11159 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1520 sg1815 - -lemma sg11160 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1417 sg1913 - -lemma sg11161 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,6,6,5] := by - exact rowSquare_join (by decide) sg1523 sg1819 - -lemma sg11162 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1032 sg2311 - -lemma sg11163 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1038 sg2311 - -lemma sg11164 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1032 sg2316 - -lemma sg11165 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg3637 - -lemma sg11166 : RowSquare [5,3,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,5] := by - exact rowSquare_join (by decide) sg390 sg3630 - -lemma sg11167 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1416 sg1874 - -lemma sg11168 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1032 sg2288 - -lemma sg11169 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1033 sg2288 - -lemma sg11170 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1498 sg1811 - -lemma sg11171 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1416 sg1875 - -lemma sg11172 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1417 sg1875 - -lemma sg11173 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1419 sg1874 - -lemma sg11174 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1420 sg1874 - -lemma sg11175 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1421 sg1874 - -lemma sg11176 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg2337 - -lemma sg11177 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg958 sg2370 - -lemma sg11178 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1422 sg1874 - -lemma sg11179 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1032 sg2291 - -lemma sg11180 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1033 sg2291 - -lemma sg11181 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1423 sg1874 - -lemma sg11182 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1424 sg1874 - -lemma sg11183 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1040 sg2288 - -lemma sg11184 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1425 sg1874 - -lemma sg11185 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1426 sg1874 - -lemma sg11186 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg1032 sg2297 - -lemma sg11187 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,3] := by - exact rowSquare_join (by decide) sg1033 sg2297 - -lemma sg11188 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1498 sg1812 - -lemma sg11189 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1813 - -lemma sg11190 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1498 sg1814 - -lemma sg11191 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1816 - -lemma sg11192 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1421 sg1875 - -lemma sg11193 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1819 - -lemma sg11194 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1422 sg1875 - -lemma sg11195 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1435 sg1874 - -lemma sg11196 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1040 sg2291 - -lemma sg11197 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1436 sg1874 - -lemma sg11198 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,1] := by - exact rowSquare_join (by decide) sg1040 sg2297 - -lemma sg11199 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg1522 sg1780 - -lemma sg11200 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,6,4,1] := by - exact rowSquare_join (by decide) sg1522 sg1782 - -lemma sg11201 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,6,5] := by - exact rowSquare_join (by decide) sg1523 sg1782 - -lemma sg11202 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1498 sg1944 - -lemma sg11203 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1498 sg1945 - -lemma sg11204 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1946 - -lemma sg11205 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1947 - -lemma sg11206 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1948 - -lemma sg11207 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1499 sg1945 - -lemma sg11208 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1499 sg1946 - -lemma sg11209 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1499 sg1947 - -lemma sg11210 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1499 sg1948 - -lemma sg11211 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1500 sg1946 - -lemma sg11212 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1500 sg1947 - -lemma sg11213 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1500 sg1948 - -lemma sg11214 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1501 sg1947 - -lemma sg11215 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1501 sg1948 - -lemma sg11216 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4] := by - exact rowSquare_join (by decide) sg1502 sg1948 - -lemma sg11217 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1498 sg1949 - -lemma sg11218 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1498 sg1950 - -lemma sg11219 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1499 sg1949 - -lemma sg11220 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1503 sg1946 - -lemma sg11221 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1503 sg1947 - -lemma sg11222 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1503 sg1948 - -lemma sg11223 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1500 sg1950 - -lemma sg11224 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1504 sg1947 - -lemma sg11225 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1504 sg1948 - -lemma sg11226 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1500 sg1951 - -lemma sg11227 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg1501 sg1951 - -lemma sg11228 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1507 sg1948 - -lemma sg11229 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1500 sg1952 - -lemma sg11230 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1500 sg1953 - -lemma sg11231 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg1501 sg1952 - -lemma sg11232 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3] := by - exact rowSquare_join (by decide) sg1502 sg1952 - -lemma sg11233 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1501 sg1953 - -lemma sg11234 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,2] := by - exact rowSquare_join (by decide) sg1502 sg1953 - -lemma sg11235 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1503 sg1949 - -lemma sg11236 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1504 sg1950 - -lemma sg11237 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1523 sg1754 - -lemma sg11238 : RowSquare [6,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg676 sg2626 - -lemma sg11239 : RowSquare [6,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg889 sg2310 - -lemma sg11240 : RowSquare [6,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg889 sg2311 - -lemma sg11241 : RowSquare [6,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg892 sg2310 - -lemma sg11242 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1754 - -lemma sg11243 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1371 sg1757 - -lemma sg11244 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1782 - -lemma sg11245 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg891 sg2288 - -lemma sg11246 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg892 sg2288 - -lemma sg11247 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1782 - -lemma sg11248 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1782 - -lemma sg11249 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg6563 - -lemma sg11250 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1379 sg1756 - -lemma sg11251 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg4 sg6566 - -lemma sg11252 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,4] := by - exact rowSquare_join (by decide) sg4 sg6568 - -lemma sg11253 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1782 - -lemma sg11254 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,3] := by - exact rowSquare_join (by decide) sg892 sg2297 - -lemma sg11255 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1327 sg1872 - -lemma sg11256 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1327 sg1754 - -lemma sg11257 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1754 - -lemma sg11258 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1754 - -lemma sg11259 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1754 - -lemma sg11260 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1332 sg1754 - -lemma sg11261 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1333 sg1754 - -lemma sg11262 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1334 sg1754 - -lemma sg11263 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1335 sg1754 - -lemma sg11264 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1328 sg1756 - -lemma sg11265 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1336 sg1754 - -lemma sg11266 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1757 - -lemma sg11267 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1337 sg1754 - -lemma sg11268 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1758 - -lemma sg11269 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1338 sg1754 - -lemma sg11270 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1329 sg1755 - -lemma sg11271 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1339 sg1754 - -lemma sg11272 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1329 sg1756 - -lemma sg11273 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1340 sg1754 - -lemma sg11274 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1329 sg1757 - -lemma sg11275 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1332 sg1755 - -lemma sg11276 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1758 - -lemma sg11277 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1766 - -lemma sg11278 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1330 sg1756 - -lemma sg11279 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1767 - -lemma sg11280 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1756 - -lemma sg11281 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1330 sg1757 - -lemma sg11282 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1332 sg1756 - -lemma sg11283 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1331 sg1757 - -lemma sg11284 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1332 sg1757 - -lemma sg11285 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg1331 sg1758 - -lemma sg11286 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg1332 sg1758 - -lemma sg11287 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1341 sg1754 - -lemma sg11288 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1342 sg1754 - -lemma sg11289 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1343 sg1754 - -lemma sg11290 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1344 sg1754 - -lemma sg11291 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1333 sg1757 - -lemma sg11292 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1333 sg1758 - -lemma sg11293 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1345 sg1754 - -lemma sg11294 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1763 - -lemma sg11295 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1346 sg1754 - -lemma sg11296 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1764 - -lemma sg11297 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1347 sg1754 - -lemma sg11298 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1765 - -lemma sg11299 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1334 sg1757 - -lemma sg11300 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1337 sg1755 - -lemma sg11301 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1334 sg1758 - -lemma sg11302 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1768 - -lemma sg11303 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1766 - -lemma sg11304 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1335 sg1756 - -lemma sg11305 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1769 - -lemma sg11306 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg1767 - -lemma sg11307 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1336 sg1756 - -lemma sg11308 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1337 sg1756 - -lemma sg11309 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg1335 sg1758 - -lemma sg11310 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1336 sg1757 - -lemma sg11311 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1337 sg1757 - -lemma sg11312 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1337 sg1758 - -lemma sg11313 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1348 sg1754 - -lemma sg11314 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1770 - -lemma sg11315 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1338 sg1755 - -lemma sg11316 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1329 sg1763 - -lemma sg11317 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1349 sg1754 - -lemma sg11318 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1771 - -lemma sg11319 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1339 sg1755 - -lemma sg11320 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1764 - -lemma sg11321 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1330 sg1763 - -lemma sg11322 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1340 sg1755 - -lemma sg11323 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1765 - -lemma sg11324 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1331 sg1763 - -lemma sg11325 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1332 sg1763 - -lemma sg11326 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1338 sg1758 - -lemma sg11327 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg1772 - -lemma sg11328 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1766 - -lemma sg11329 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1330 sg1764 - -lemma sg11330 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg1767 - -lemma sg11331 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1765 - -lemma sg11332 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1331 sg1764 - -lemma sg11333 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg2277 - -lemma sg11334 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg1332 sg1764 - -lemma sg11335 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1340 sg1757 - -lemma sg11336 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1331 sg1765 - -lemma sg11337 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1340 sg1758 - -lemma sg11338 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1765 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes14 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes7 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes15 + +namespace OAI + +/-! Semigroup Nodes 26. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg10939 : RowSquare [7,6,2,2,2,2,1] [7,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4703 + +lemma sg10940 : RowSquare [7,6,2,2,2,2,1] [7,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6324 + +lemma sg10941 : RowSquare [7,6,2,2,2,2,1] [7,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6325 + +lemma sg10942 : RowSquare [7,6,2,2,2,2,1] [7,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg6326 + +lemma sg10943 : RowSquare [7,6,2,2,2,2,1] [7,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4702 + +lemma sg10944 : RowSquare [7,6,2,2,2,2,1] [7,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4704 + +lemma sg10945 : RowSquare [7,6,2,2,2,2,1] [7,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6334 + +lemma sg10946 : RowSquare [7,6,2,2,2,2,1] [7,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1149 + +lemma sg10947 : RowSquare [7,6,2,2,2,2,1] [7,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg6335 + +lemma sg10948 : RowSquare [7,6,2,2,2,2,1] [7,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4705 + +lemma sg10949 : RowSquare [7,6,2,2,2,2,1] [7,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1150 + +lemma sg10950 : RowSquare [7,6,2,2,2,2,1] [7,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg769 sg1633 + +lemma sg10951 : RowSquare [7,6,2,2,2,2,1] [7,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1210 sg1146 + +lemma sg10952 : RowSquare [7,6,2,2,2,2,1] [7,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6336 + +lemma sg10953 : RowSquare [7,6,2,2,2,2,1] [7,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg3861 + +lemma sg10954 : RowSquare [7,6,2,2,2,2,1] [7,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1209 sg1148 + +lemma sg10955 : RowSquare [7,6,2,2,2,2,1] [7,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1203 sg1149 + +lemma sg10956 : RowSquare [7,6,2,2,2,2,1] [7,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg3185 + +lemma sg10957 : RowSquare [7,6,2,2,2,2,1] [7,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1203 sg1150 + +lemma sg10958 : RowSquare [7,6,2,2,2,2,1] [7,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg770 sg1633 + +lemma sg10959 : RowSquare [7,6,2,2,2,2,1] [7,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4700 + +lemma sg10960 : RowSquare [7,6,2,2,2,2,1] [7,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4703 + +lemma sg10961 : RowSquare [7,6,2,2,2,2,1] [7,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4707 + +lemma sg10962 : RowSquare [7,6,2,2,2,2,1] [7,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6327 + +lemma sg10963 : RowSquare [7,6,2,2,2,2,1] [7,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1151 + +lemma sg10964 : RowSquare [7,6,2,2,2,2,1] [7,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg6328 + +lemma sg10965 : RowSquare [7,6,2,2,2,2,1] [7,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg3863 + +lemma sg10966 : RowSquare [7,6,2,2,2,2,1] [7,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4708 + +lemma sg10967 : RowSquare [7,6,2,2,2,2,1] [7,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1152 + +lemma sg10968 : RowSquare [7,6,2,2,2,2,1] [7,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1203 sg1151 + +lemma sg10969 : RowSquare [7,6,2,2,2,2,1] [7,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1153 + +lemma sg10970 : RowSquare [7,6,2,2,2,2,1] [7,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1206 sg1150 + +lemma sg10971 : RowSquare [7,6,2,2,2,2,1] [7,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4706 + +lemma sg10972 : RowSquare [7,6,2,2,2,2,1] [7,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1154 + +lemma sg10973 : RowSquare [7,6,2,2,2,2,1] [7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg3183 + +lemma sg10974 : RowSquare [7,6,2,2,2,2,1] [7,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5516 + +lemma sg10975 : RowSquare [7,6,2,2,2,2,1] [7,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4707 + +lemma sg10976 : RowSquare [7,6,2,2,2,2,1] [7,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5522 + +lemma sg10977 : RowSquare [7,6,2,2,2,2,1] [7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1155 + +lemma sg10978 : RowSquare [7,6,2,2,2,2,1] [7,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1206 sg1151 + +lemma sg10979 : RowSquare [7,6,2,2,2,2,1] [7,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4708 + +lemma sg10980 : RowSquare [7,6,2,2,2,2,1] [7,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1156 + +lemma sg10981 : RowSquare [7,6,2,2,2,2,1] [7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1157 + +lemma sg10982 : RowSquare [7,6,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5517 + +lemma sg10983 : RowSquare [7,6,2,2,2,2,1] [7,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5518 + +lemma sg10984 : RowSquare [7,6,2,2,2,2,1] [7,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg5523 + +lemma sg10985 : RowSquare [7,6,2,2,2,2,1] [7,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg3184 + +lemma sg10986 : RowSquare [7,6,2,2,2,2,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg6318 + +lemma sg10987 : RowSquare [7,6,2,2,2,2,1] [8,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6329 + +lemma sg10988 : RowSquare [7,6,2,2,2,2,1] [8,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6337 + +lemma sg10989 : RowSquare [7,6,2,2,2,2,1] [8,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4709 + +lemma sg10990 : RowSquare [7,6,2,2,2,2,1] [8,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg6319 + +lemma sg10991 : RowSquare [7,6,2,2,2,2,1] [8,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg6320 + +lemma sg10992 : RowSquare [7,6,2,2,2,2,1] [8,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6 sg6321 + +lemma sg10993 : RowSquare [7,6,2,2,2,2,1] [8,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6 sg6322 + +lemma sg10994 : RowSquare [7,6,2,2,2,2,1] [8,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5519 + +lemma sg10995 : RowSquare [7,6,2,2,2,2,1] [8,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4709 + +lemma sg10996 : RowSquare [7,6,2,2,2,2,1] [8,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4710 + +lemma sg10997 : RowSquare [7,6,2,2,2,2,1] [8,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6331 + +lemma sg10998 : RowSquare [7,6,2,2,2,2,1] [8,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6332 + +lemma sg10999 : RowSquare [7,6,2,2,2,2,1] [8,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg6333 + +lemma sg11000 : RowSquare [7,6,2,2,2,2,1] [8,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg4702 + +lemma sg11001 : RowSquare [7,6,2,2,2,2,1] [8,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4711 + +lemma sg11002 : RowSquare [7,6,2,2,2,2,1] [8,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg6338 + +lemma sg11003 : RowSquare [7,6,2,2,2,2,1] [8,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1209 sg1149 + +lemma sg11004 : RowSquare [7,6,2,2,2,2,1] [8,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg3862 + +lemma sg11005 : RowSquare [7,6,2,2,2,2,1] [8,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1209 sg1150 + +lemma sg11006 : RowSquare [7,6,2,2,2,2,1] [8,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4701 + +lemma sg11007 : RowSquare [7,6,2,2,2,2,1] [8,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4710 + +lemma sg11008 : RowSquare [7,6,2,2,2,2,1] [8,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg3863 + +lemma sg11009 : RowSquare [7,6,2,2,2,2,1] [8,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5520 + +lemma sg11010 : RowSquare [7,6,2,2,2,2,1] [8,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1158 + +lemma sg11011 : RowSquare [7,6,2,2,2,2,1] [8,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4711 + +lemma sg11012 : RowSquare [7,6,2,2,2,2,1] [8,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4713 + +lemma sg11013 : RowSquare [7,6,2,2,2,2,1] [8,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1159 + +lemma sg11014 : RowSquare [7,6,2,2,2,2,1] [8,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1160 + +lemma sg11015 : RowSquare [7,6,2,2,2,2,1] [8,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg2592 + +lemma sg11016 : RowSquare [7,6,2,2,2,2,1] [8,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4703 + +lemma sg11017 : RowSquare [7,6,2,2,2,2,1] [8,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4712 + +lemma sg11018 : RowSquare [7,6,2,2,2,2,1] [8,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4714 + +lemma sg11019 : RowSquare [7,6,2,2,2,2,1] [8,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg1161 + +lemma sg11020 : RowSquare [7,6,2,2,2,2,1] [8,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg2593 + +lemma sg11021 : RowSquare [7,6,2,2,2,2,1] [8,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4707 + +lemma sg11022 : RowSquare [7,6,2,2,2,2,1] [8,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg2593 + +lemma sg11023 : RowSquare [7,6,2,2,2,2,1] [8,7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg2593 + +lemma sg11024 : RowSquare [7,6,2,2,2,2,1] [9,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg5515 + +lemma sg11025 : RowSquare [7,6,2,2,2,2,1] [9,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6337 + +lemma sg11026 : RowSquare [7,6,2,2,2,2,1] [9,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg4709 + +lemma sg11027 : RowSquare [7,6,2,2,2,2,1] [9,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4715 + +lemma sg11028 : RowSquare [7,6,2,2,2,2,1] [9,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg6331 + +lemma sg11029 : RowSquare [7,6,2,2,2,2,1] [9,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg6332 + +lemma sg11030 : RowSquare [7,6,2,2,2,2,1] [9,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4709 + +lemma sg11031 : RowSquare [7,6,2,2,2,2,1] [9,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4715 + +lemma sg11032 : RowSquare [7,6,2,2,2,2,1] [9,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg4716 + +lemma sg11033 : RowSquare [7,6,2,2,2,2,1] [9,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg6338 + +lemma sg11034 : RowSquare [7,6,2,2,2,2,1] [9,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg3864 + +lemma sg11035 : RowSquare [7,6,2,2,2,2,1] [9,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg2592 + +lemma sg11036 : RowSquare [7,6,2,2,2,2,1] [9,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4710 + +lemma sg11037 : RowSquare [7,6,2,2,2,2,1] [9,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4716 + +lemma sg11038 : RowSquare [7,6,2,2,2,2,1] [9,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg2593 + +lemma sg11039 : RowSquare [7,6,2,2,2,2,1] [9,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg85 sg3863 + +lemma sg11040 : RowSquare [7,6,2,2,2,2,1] [10,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg5519 + +lemma sg11041 : RowSquare [7,6,2,2,2,2,1] [10,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg4709 + +lemma sg11042 : RowSquare [7,6,2,2,2,2,1] [10,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg4715 + +lemma sg11043 : RowSquare [7,6,2,2,2,2,1] [10,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg3864 + +lemma sg11044 : RowSquare [7,6,2,2,2,2,1] [10,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg4715 + +lemma sg11045 : RowSquare [7,6,2,2,2,2,1] [10,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg4717 + +lemma sg11046 : RowSquare [7,6,2,2,2,2,1] [11,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg4709 + +lemma sg11047 : RowSquare [7,6,2,2,2,2,1] [11,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg4715 + +lemma sg11048 : RowSquare [7,7,1,1,1,1,1,1,1,1] [5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg5551 + +lemma sg11049 : RowSquare [7,7,1,1,1,1,1,1,1,1] [5,5,5,5,2] := by + exact rowSquare_join (by decide) sg13 sg5552 + +lemma sg11050 : RowSquare [8,3,2,2,2,2,2,1] [5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg3995 + +lemma sg11051 : RowSquare [8,4,3,2,2,2,1] [4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg287 sg2546 + +lemma sg11052 : RowSquare [8,6,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg6396 + +lemma sg11053 : RowSquare [8,6,1,1,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg110 sg3521 + +lemma sg11054 : RowSquare [8,6,1,1,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg111 sg3521 + +lemma sg11055 : RowSquare [8,6,1,1,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg112 sg3521 + +lemma sg11056 : RowSquare [9,3,2,2,2,2,1,1] [4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg74 sg3967 + +lemma sg11057 : RowSquare [9,3,2,2,2,2,1,1] [5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg3968 + +lemma sg11058 : RowSquare [9,3,2,2,2,2,2] [6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg165 sg3213 + +lemma sg11059 : RowSquare [9,7,3,2,1] [4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg878 sg1688 + +lemma sg11060 : RowSquare [10,3,2,2,2,2,1] [5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg3870 + +lemma sg11061 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4] := by + exact rowSquare_join (by decide) sg1539 sg1978 + +lemma sg11062 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg1455 sg2008 + +lemma sg11063 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg1540 sg1978 + +lemma sg11064 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2] := by + exact rowSquare_join (by decide) sg1532 sg1993 + +lemma sg11065 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,1] := by + exact rowSquare_join (by decide) sg1541 sg1978 + +lemma sg11066 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5] := by + exact rowSquare_join (by decide) sg1562 sg1926 + +lemma sg11067 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg1455 sg2009 + +lemma sg11068 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg1540 sg1980 + +lemma sg11069 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2] := by + exact rowSquare_join (by decide) sg1532 sg1994 + +lemma sg11070 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,1] := by + exact rowSquare_join (by decide) sg1541 sg1980 + +lemma sg11071 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg1540 sg1981 + +lemma sg11072 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2] := by + exact rowSquare_join (by decide) sg1532 sg1995 + +lemma sg11073 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,1] := by + exact rowSquare_join (by decide) sg1533 sg1993 + +lemma sg11074 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4] := by + exact rowSquare_join (by decide) sg1539 sg1987 + +lemma sg11075 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3] := by + exact rowSquare_join (by decide) sg1539 sg1988 + +lemma sg11076 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,2,2,1] := by + exact rowSquare_join (by decide) sg1455 sg2010 + +lemma sg11077 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,1,1] := by + exact rowSquare_join (by decide) sg1542 sg1980 + +lemma sg11078 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2] := by + exact rowSquare_join (by decide) sg1532 sg1996 + +lemma sg11079 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4] := by + exact rowSquare_join (by decide) sg1544 sg1980 + +lemma sg11080 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,1] := by + exact rowSquare_join (by decide) sg1455 sg2011 + +lemma sg11081 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,1,1] := by + exact rowSquare_join (by decide) sg1572 sg1915 + +lemma sg11082 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2] := by + exact rowSquare_join (by decide) sg1545 sg1979 + +lemma sg11083 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,1] := by + exact rowSquare_join (by decide) sg1533 sg1996 + +lemma sg11084 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3] := by + exact rowSquare_join (by decide) sg1539 sg1991 + +lemma sg11085 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1540 sg1983 + +lemma sg11086 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1455 sg2012 + +lemma sg11087 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3] := by + exact rowSquare_join (by decide) sg1461 sg2002 + +lemma sg11088 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1460 sg2003 + +lemma sg11089 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2] := by + exact rowSquare_join (by decide) sg1461 sg2003 + +lemma sg11090 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg1540 sg1985 + +lemma sg11091 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg1455 sg2013 + +lemma sg11092 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3] := by + exact rowSquare_join (by decide) sg1461 sg2004 + +lemma sg11093 : RowSquare [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg1542 sg1985 + +lemma sg11094 : RowSquare [3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3] := by + exact rowSquare_join (by decide) sg1532 sg1979 + +lemma sg11095 : RowSquare [3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,2] := by + exact rowSquare_join (by decide) sg1532 sg1980 + +lemma sg11096 : RowSquare [3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5] := by + exact rowSquare_join (by decide) sg693 sg3152 + +lemma sg11097 : RowSquare [3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3] := by + exact rowSquare_join (by decide) sg1061 sg2479 + +lemma sg11098 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg1517 sg1977 + +lemma sg11099 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3] := by + exact rowSquare_join (by decide) sg1519 sg1977 + +lemma sg11100 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1517 sg1979 + +lemma sg11101 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1517 sg1980 + +lemma sg11102 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg1518 sg1979 + +lemma sg11103 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3] := by + exact rowSquare_join (by decide) sg1519 sg1979 + +lemma sg11104 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg1518 sg1980 + +lemma sg11105 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,2] := by + exact rowSquare_join (by decide) sg1519 sg1980 + +lemma sg11106 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1520 sg1979 + +lemma sg11107 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3] := by + exact rowSquare_join (by decide) sg1033 sg2479 + +lemma sg11108 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1416 sg2003 + +lemma sg11109 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1417 sg2003 + +lemma sg11110 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1517 sg1985 + +lemma sg11111 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1524 sg1980 + +lemma sg11112 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1417 sg2004 + +lemma sg11113 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg1518 sg1985 + +lemma sg11114 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1542 sg1956 + +lemma sg11115 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1416 sg2005 + +lemma sg11116 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg1521 sg1983 + +lemma sg11117 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1417 sg2005 + +lemma sg11118 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1518 sg1987 + +lemma sg11119 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,2] := by + exact rowSquare_join (by decide) sg1519 sg1987 + +lemma sg11120 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1520 sg1985 + +lemma sg11121 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1416 sg2006 + +lemma sg11122 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1517 sg1989 + +lemma sg11123 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg1521 sg1985 + +lemma sg11124 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1417 sg2006 + +lemma sg11125 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg1518 sg1989 + +lemma sg11126 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3] := by + exact rowSquare_join (by decide) sg1519 sg1989 + +lemma sg11127 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1416 sg2007 + +lemma sg11128 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1417 sg2007 + +lemma sg11129 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg1521 sg1986 + +lemma sg11130 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg1518 sg1990 + +lemma sg11131 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,2] := by + exact rowSquare_join (by decide) sg1519 sg1990 + +lemma sg11132 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,1] := by + exact rowSquare_join (by decide) sg1541 sg1963 + +lemma sg11133 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1566 sg1903 + +lemma sg11134 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1520 sg1989 + +lemma sg11135 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,2] := by + exact rowSquare_join (by decide) sg1542 sg1961 + +lemma sg11136 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1520 sg1991 + +lemma sg11137 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,1] := by + exact rowSquare_join (by decide) sg1545 sg1961 + +lemma sg11138 : RowSquare [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1520 sg1992 + +lemma sg11139 : RowSquare [4,3,2,2,2,2,2,2,2,1,1] [5,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg2364 + +lemma sg11140 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1517 sg1954 + +lemma sg11141 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1517 sg1955 + +lemma sg11142 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1517 sg1956 + +lemma sg11143 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1517 sg1957 + +lemma sg11144 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1520 sg1955 + +lemma sg11145 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1517 sg1958 + +lemma sg11146 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1520 sg1957 + +lemma sg11147 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1517 sg1961 + +lemma sg11148 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1520 sg1961 + +lemma sg11149 : RowSquare [4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1520 sg1963 + +lemma sg11150 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1417 sg1902 + +lemma sg11151 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1416 sg1903 + +lemma sg11152 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1416 sg1908 + +lemma sg11153 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg1417 sg1908 + +lemma sg11154 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1524 sg1811 + +lemma sg11155 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1416 sg1909 + +lemma sg11156 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1418 sg1902 + +lemma sg11157 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1418 sg1903 + +lemma sg11158 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1520 sg1814 + +lemma sg11159 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1520 sg1815 + +lemma sg11160 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1417 sg1913 + +lemma sg11161 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1] [6,6,6,5] := by + exact rowSquare_join (by decide) sg1523 sg1819 + +lemma sg11162 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1032 sg2311 + +lemma sg11163 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1038 sg2311 + +lemma sg11164 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1032 sg2316 + +lemma sg11165 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg3637 + +lemma sg11166 : RowSquare [5,3,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,5] := by + exact rowSquare_join (by decide) sg390 sg3630 + +lemma sg11167 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1416 sg1874 + +lemma sg11168 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1032 sg2288 + +lemma sg11169 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1033 sg2288 + +lemma sg11170 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1498 sg1811 + +lemma sg11171 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1416 sg1875 + +lemma sg11172 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1417 sg1875 + +lemma sg11173 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1419 sg1874 + +lemma sg11174 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1420 sg1874 + +lemma sg11175 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1421 sg1874 + +lemma sg11176 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg2337 + +lemma sg11177 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg958 sg2370 + +lemma sg11178 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1422 sg1874 + +lemma sg11179 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1032 sg2291 + +lemma sg11180 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1033 sg2291 + +lemma sg11181 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1423 sg1874 + +lemma sg11182 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1424 sg1874 + +lemma sg11183 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1040 sg2288 + +lemma sg11184 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1425 sg1874 + +lemma sg11185 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1426 sg1874 + +lemma sg11186 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg1032 sg2297 + +lemma sg11187 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,3] := by + exact rowSquare_join (by decide) sg1033 sg2297 + +lemma sg11188 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1498 sg1812 + +lemma sg11189 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1813 + +lemma sg11190 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1498 sg1814 + +lemma sg11191 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1816 + +lemma sg11192 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1421 sg1875 + +lemma sg11193 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1819 + +lemma sg11194 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1422 sg1875 + +lemma sg11195 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1435 sg1874 + +lemma sg11196 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1040 sg2291 + +lemma sg11197 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1436 sg1874 + +lemma sg11198 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,1] := by + exact rowSquare_join (by decide) sg1040 sg2297 + +lemma sg11199 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg1522 sg1780 + +lemma sg11200 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,6,4,1] := by + exact rowSquare_join (by decide) sg1522 sg1782 + +lemma sg11201 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1] [6,6,6,5] := by + exact rowSquare_join (by decide) sg1523 sg1782 + +lemma sg11202 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1498 sg1944 + +lemma sg11203 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1498 sg1945 + +lemma sg11204 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1946 + +lemma sg11205 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1947 + +lemma sg11206 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1948 + +lemma sg11207 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1499 sg1945 + +lemma sg11208 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1499 sg1946 + +lemma sg11209 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1499 sg1947 + +lemma sg11210 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1499 sg1948 + +lemma sg11211 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1500 sg1946 + +lemma sg11212 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1500 sg1947 + +lemma sg11213 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1500 sg1948 + +lemma sg11214 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1501 sg1947 + +lemma sg11215 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1501 sg1948 + +lemma sg11216 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4] := by + exact rowSquare_join (by decide) sg1502 sg1948 + +lemma sg11217 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1498 sg1949 + +lemma sg11218 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1498 sg1950 + +lemma sg11219 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1499 sg1949 + +lemma sg11220 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1503 sg1946 + +lemma sg11221 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1503 sg1947 + +lemma sg11222 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1503 sg1948 + +lemma sg11223 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1500 sg1950 + +lemma sg11224 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1504 sg1947 + +lemma sg11225 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1504 sg1948 + +lemma sg11226 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1500 sg1951 + +lemma sg11227 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg1501 sg1951 + +lemma sg11228 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1507 sg1948 + +lemma sg11229 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1500 sg1952 + +lemma sg11230 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1500 sg1953 + +lemma sg11231 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg1501 sg1952 + +lemma sg11232 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3] := by + exact rowSquare_join (by decide) sg1502 sg1952 + +lemma sg11233 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1501 sg1953 + +lemma sg11234 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,2] := by + exact rowSquare_join (by decide) sg1502 sg1953 + +lemma sg11235 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1503 sg1949 + +lemma sg11236 : RowSquare [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] [9,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1504 sg1950 + +lemma sg11237 : RowSquare [6,4,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1523 sg1754 + +lemma sg11238 : RowSquare [6,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg676 sg2626 + +lemma sg11239 : RowSquare [6,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg889 sg2310 + +lemma sg11240 : RowSquare [6,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg889 sg2311 + +lemma sg11241 : RowSquare [6,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg892 sg2310 + +lemma sg11242 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1754 + +lemma sg11243 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1371 sg1757 + +lemma sg11244 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1782 + +lemma sg11245 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg891 sg2288 + +lemma sg11246 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg892 sg2288 + +lemma sg11247 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1782 + +lemma sg11248 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1782 + +lemma sg11249 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg6563 + +lemma sg11250 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1379 sg1756 + +lemma sg11251 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg4 sg6566 + +lemma sg11252 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,4] := by + exact rowSquare_join (by decide) sg4 sg6568 + +lemma sg11253 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1782 + +lemma sg11254 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,3] := by + exact rowSquare_join (by decide) sg892 sg2297 + +lemma sg11255 : RowSquare [6,6,1,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1327 sg1872 + +lemma sg11256 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1327 sg1754 + +lemma sg11257 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1754 + +lemma sg11258 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1754 + +lemma sg11259 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1754 + +lemma sg11260 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1332 sg1754 + +lemma sg11261 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1333 sg1754 + +lemma sg11262 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1334 sg1754 + +lemma sg11263 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1335 sg1754 + +lemma sg11264 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1328 sg1756 + +lemma sg11265 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1336 sg1754 + +lemma sg11266 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1757 + +lemma sg11267 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1337 sg1754 + +lemma sg11268 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1758 + +lemma sg11269 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1338 sg1754 + +lemma sg11270 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1329 sg1755 + +lemma sg11271 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1339 sg1754 + +lemma sg11272 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1329 sg1756 + +lemma sg11273 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1340 sg1754 + +lemma sg11274 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1329 sg1757 + +lemma sg11275 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1332 sg1755 + +lemma sg11276 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1758 + +lemma sg11277 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1766 + +lemma sg11278 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1330 sg1756 + +lemma sg11279 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1767 + +lemma sg11280 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1756 + +lemma sg11281 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1330 sg1757 + +lemma sg11282 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1332 sg1756 + +lemma sg11283 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1331 sg1757 + +lemma sg11284 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1332 sg1757 + +lemma sg11285 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg1331 sg1758 + +lemma sg11286 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg1332 sg1758 + +lemma sg11287 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1341 sg1754 + +lemma sg11288 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1342 sg1754 + +lemma sg11289 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1343 sg1754 + +lemma sg11290 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1344 sg1754 + +lemma sg11291 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1333 sg1757 + +lemma sg11292 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1333 sg1758 + +lemma sg11293 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1345 sg1754 + +lemma sg11294 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1763 + +lemma sg11295 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1346 sg1754 + +lemma sg11296 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1764 + +lemma sg11297 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1347 sg1754 + +lemma sg11298 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1765 + +lemma sg11299 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1334 sg1757 + +lemma sg11300 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1337 sg1755 + +lemma sg11301 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1334 sg1758 + +lemma sg11302 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1768 + +lemma sg11303 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1766 + +lemma sg11304 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1335 sg1756 + +lemma sg11305 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1769 + +lemma sg11306 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg1767 + +lemma sg11307 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1336 sg1756 + +lemma sg11308 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1337 sg1756 + +lemma sg11309 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg1335 sg1758 + +lemma sg11310 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1336 sg1757 + +lemma sg11311 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1337 sg1757 + +lemma sg11312 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1337 sg1758 + +lemma sg11313 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1348 sg1754 + +lemma sg11314 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1770 + +lemma sg11315 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1338 sg1755 + +lemma sg11316 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1329 sg1763 + +lemma sg11317 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1349 sg1754 + +lemma sg11318 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1771 + +lemma sg11319 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1339 sg1755 + +lemma sg11320 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1764 + +lemma sg11321 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1330 sg1763 + +lemma sg11322 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1340 sg1755 + +lemma sg11323 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1765 + +lemma sg11324 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1331 sg1763 + +lemma sg11325 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1332 sg1763 + +lemma sg11326 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1338 sg1758 + +lemma sg11327 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg1772 + +lemma sg11328 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1766 + +lemma sg11329 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1330 sg1764 + +lemma sg11330 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg1767 + +lemma sg11331 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1765 + +lemma sg11332 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1331 sg1764 + +lemma sg11333 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg2277 + +lemma sg11334 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg1332 sg1764 + +lemma sg11335 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1340 sg1757 + +lemma sg11336 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1331 sg1765 + +lemma sg11337 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1340 sg1758 + +lemma sg11338 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1765 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes27.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes27.lean index 2d7eae51a65511b5ebc07c83b5ff6eb3486ec689..c9565228bf09ac8566cbdaefe90833a866b62cf9 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes27.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes27.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes25 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes9 - -namespace OAI - -/-! Semigroup Nodes 27. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg11339 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1766 - -lemma sg11340 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg890 sg2275 - -lemma sg11341 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg1767 - -lemma sg11342 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg1331 sg1766 - -lemma sg11343 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg890 sg2277 - -lemma sg11344 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg1332 sg1766 - -lemma sg11345 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg1331 sg1767 - -lemma sg11346 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg891 sg2276 - -lemma sg11347 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg1332 sg1767 - -lemma sg11348 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4] := by - exact rowSquare_join (by decide) sg892 sg2277 - -lemma sg11349 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg5842 - -lemma sg11350 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg5849 - -lemma sg11351 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [6,6,6,5] := by - exact rowSquare_join (by decide) sg13 sg5852 - -lemma sg11352 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg5869 - -lemma sg11353 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5871 - -lemma sg11354 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg5873 - -lemma sg11355 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,6,5,5] := by - exact rowSquare_join (by decide) sg13 sg5874 - -lemma sg11356 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5878 - -lemma sg11357 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg5880 - -lemma sg11358 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg5881 - -lemma sg11359 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,1] := by - exact rowSquare_join (by decide) sg13 sg5882 - -lemma sg11360 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,7,5,4] := by - exact rowSquare_join (by decide) sg13 sg5883 - -lemma sg11361 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg5888 - -lemma sg11362 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [9,8,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1365 sg1763 - -lemma sg11363 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [9,9,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg5889 - -lemma sg11364 : RowSquare [6,6,2,2,2,2,2,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7812 - -lemma sg11365 : RowSquare [6,6,2,2,2,2,2,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7813 - -lemma sg11366 : RowSquare [6,6,2,2,2,2,2,1] [5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7816 - -lemma sg11367 : RowSquare [6,6,2,2,2,2,2,1] [5,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7817 - -lemma sg11368 : RowSquare [6,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7818 - -lemma sg11369 : RowSquare [6,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7819 - -lemma sg11370 : RowSquare [6,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6 sg7820 - -lemma sg11371 : RowSquare [6,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6 sg7821 - -lemma sg11372 : RowSquare [6,6,2,2,2,2,2,1] [5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7823 - -lemma sg11373 : RowSquare [6,6,2,2,2,2,2,1] [5,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7824 - -lemma sg11374 : RowSquare [6,6,2,2,2,2,2,1] [5,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7825 - -lemma sg11375 : RowSquare [6,6,2,2,2,2,2,1] [5,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7826 - -lemma sg11376 : RowSquare [6,6,2,2,2,2,2,1] [5,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7827 - -lemma sg11377 : RowSquare [6,6,2,2,2,2,2,1] [5,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg7828 - -lemma sg11378 : RowSquare [6,6,2,2,2,2,2,1] [5,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7831 - -lemma sg11379 : RowSquare [6,6,2,2,2,2,2,1] [5,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7832 - -lemma sg11380 : RowSquare [6,6,2,2,2,2,2,1] [5,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7833 - -lemma sg11381 : RowSquare [6,6,2,2,2,2,2,1] [5,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg7834 - -lemma sg11382 : RowSquare [6,6,2,2,2,2,2,1] [5,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg7835 - -lemma sg11383 : RowSquare [6,6,2,2,2,2,2,1] [5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7837 - -lemma sg11384 : RowSquare [6,6,2,2,2,2,2,1] [5,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg5 sg7840 - -lemma sg11385 : RowSquare [6,6,2,2,2,2,2,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7822 - -lemma sg11386 : RowSquare [6,6,2,2,2,2,2,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7841 - -lemma sg11387 : RowSquare [6,6,2,2,2,2,2,1] [6,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7824 - -lemma sg11388 : RowSquare [6,6,2,2,2,2,2,1] [6,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7825 - -lemma sg11389 : RowSquare [6,6,2,2,2,2,2,1] [6,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7826 - -lemma sg11390 : RowSquare [6,6,2,2,2,2,2,1] [6,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7827 - -lemma sg11391 : RowSquare [6,6,2,2,2,2,2,1] [6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6 sg7828 - -lemma sg11392 : RowSquare [6,6,2,2,2,2,2,1] [6,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7842 - -lemma sg11393 : RowSquare [6,6,2,2,2,2,2,1] [6,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7843 - -lemma sg11394 : RowSquare [6,6,2,2,2,2,2,1] [6,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7844 - -lemma sg11395 : RowSquare [6,6,2,2,2,2,2,1] [6,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg7845 - -lemma sg11396 : RowSquare [6,6,2,2,2,2,2,1] [6,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg7846 - -lemma sg11397 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg7853 - -lemma sg11398 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg7854 - -lemma sg11399 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg7855 - -lemma sg11400 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg7856 - -lemma sg11401 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg7857 - -lemma sg11402 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7837 - -lemma sg11403 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6 sg7839 - -lemma sg11404 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6 sg7840 - -lemma sg11405 : RowSquare [6,6,2,2,2,2,2,1] [6,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7848 - -lemma sg11406 : RowSquare [6,6,2,2,2,2,2,1] [6,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7849 - -lemma sg11407 : RowSquare [6,6,2,2,2,2,2,1] [6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7850 - -lemma sg11408 : RowSquare [6,6,2,2,2,2,2,1] [6,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg7851 - -lemma sg11409 : RowSquare [6,6,2,2,2,2,2,1] [6,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg7852 - -lemma sg11410 : RowSquare [6,6,2,2,2,2,2,1] [6,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg7858 - -lemma sg11411 : RowSquare [6,6,2,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7841 - -lemma sg11412 : RowSquare [6,6,2,2,2,2,2,1] [7,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7842 - -lemma sg11413 : RowSquare [6,6,2,2,2,2,2,1] [7,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7843 - -lemma sg11414 : RowSquare [6,6,2,2,2,2,2,1] [7,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7844 - -lemma sg11415 : RowSquare [6,6,2,2,2,2,2,1] [7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6 sg7845 - -lemma sg11416 : RowSquare [6,6,2,2,2,2,2,1] [7,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6 sg7846 - -lemma sg11417 : RowSquare [6,6,2,2,2,2,2,1] [7,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7854 - -lemma sg11418 : RowSquare [6,6,2,2,2,2,2,1] [7,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7855 - -lemma sg11419 : RowSquare [6,6,2,2,2,2,2,1] [7,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg7856 - -lemma sg11420 : RowSquare [6,6,2,2,2,2,2,1] [7,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg7857 - -lemma sg11421 : RowSquare [6,6,2,2,2,2,2,1] [8,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7854 - -lemma sg11422 : RowSquare [6,6,2,2,2,2,2,1] [8,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7855 - -lemma sg11423 : RowSquare [6,6,2,2,2,2,2,1] [8,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg7856 - -lemma sg11424 : RowSquare [6,6,2,2,2,2,2,1] [8,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6 sg7857 - -lemma sg11425 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg997 sg2251 - -lemma sg11426 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg2251 - -lemma sg11427 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg999 sg2251 - -lemma sg11428 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1000 sg2251 - -lemma sg11429 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1001 sg2251 - -lemma sg11430 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1002 sg2251 - -lemma sg11431 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg587 sg2702 - -lemma sg11432 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg2702 - -lemma sg11433 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg2702 - -lemma sg11434 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg2702 - -lemma sg11435 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg915 sg2251 - -lemma sg11436 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg910 sg2256 - -lemma sg11437 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg2707 - -lemma sg11438 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg2708 - -lemma sg11439 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg587 sg2708 - -lemma sg11440 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg595 sg2702 - -lemma sg11441 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg920 sg2251 - -lemma sg11442 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg2702 - -lemma sg11443 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg921 sg2251 - -lemma sg11444 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg588 sg2708 - -lemma sg11445 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg2713 - -lemma sg11446 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg589 sg2708 - -lemma sg11447 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg2706 - -lemma sg11448 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg915 sg2256 - -lemma sg11449 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg2702 - -lemma sg11450 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg931 sg2251 - -lemma sg11451 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg923 sg2257 - -lemma sg11452 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg930 sg2254 - -lemma sg11453 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg939 sg2251 - -lemma sg11454 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg931 sg2253 - -lemma sg11455 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg2269 - -lemma sg11456 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg920 sg2261 - -lemma sg11457 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg932 sg2253 - -lemma sg11458 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg931 sg2254 - -lemma sg11459 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg6017 - -lemma sg11460 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg932 sg2254 - -lemma sg11461 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg6018 - -lemma sg11462 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg6019 - -lemma sg11463 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg939 sg2253 - -lemma sg11464 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg939 sg2254 - -lemma sg11465 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg6020 - -lemma sg11466 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [8,8,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg6020 - -lemma sg11467 : RowSquare [7,5,3,2,1,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg132 sg4160 - -lemma sg11468 : RowSquare [7,5,3,2,1,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg133 sg4160 - -lemma sg11469 : RowSquare [7,5,3,2,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg134 sg4160 - -lemma sg11470 : RowSquare [7,5,3,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg479 sg2702 - -lemma sg11471 : RowSquare [7,5,3,2,1,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg135 sg4160 - -lemma sg11472 : RowSquare [7,5,3,2,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg132 sg4161 - -lemma sg11473 : RowSquare [7,5,3,2,1,1,1,1,1,1] [5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg136 sg4160 - -lemma sg11474 : RowSquare [7,5,3,2,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg133 sg4161 - -lemma sg11475 : RowSquare [7,5,3,2,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg134 sg4161 - -lemma sg11476 : RowSquare [7,5,3,2,1,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg137 sg4160 - -lemma sg11477 : RowSquare [7,5,3,2,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg135 sg4161 - -lemma sg11478 : RowSquare [7,5,3,2,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg139 sg4160 - -lemma sg11479 : RowSquare [7,5,3,2,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg136 sg4161 - -lemma sg11480 : RowSquare [7,5,3,2,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg137 sg4161 - -lemma sg11481 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg888 sg2251 - -lemma sg11482 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg2251 - -lemma sg11483 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg890 sg2251 - -lemma sg11484 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg891 sg2251 - -lemma sg11485 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg892 sg2251 - -lemma sg11486 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg893 sg2251 - -lemma sg11487 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg894 sg2251 - -lemma sg11488 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg895 sg2251 - -lemma sg11489 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg896 sg2251 - -lemma sg11490 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg888 sg2255 - -lemma sg11491 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg892 sg2252 - -lemma sg11492 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg888 sg2256 - -lemma sg11493 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg897 sg2251 - -lemma sg11494 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg898 sg2251 - -lemma sg11495 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg899 sg2251 - -lemma sg11496 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg889 sg2256 - -lemma sg11497 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg890 sg2254 - -lemma sg11498 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg891 sg2254 - -lemma sg11499 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg892 sg2254 - -lemma sg11500 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg891 sg2255 - -lemma sg11501 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg892 sg2255 - -lemma sg11502 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg892 sg2256 - -lemma sg11503 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg902 sg2251 - -lemma sg11504 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg903 sg2251 - -lemma sg11505 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg909 sg2251 - -lemma sg11506 : RowSquare [7,6,2,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg525 sg2702 - -lemma sg11507 : RowSquare [7,6,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg825 sg2251 - -lemma sg11508 : RowSquare [7,6,2,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg459 sg2702 - -lemma sg11509 : RowSquare [7,6,2,2,2,2,1,1] [5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10889 - -lemma sg11510 : RowSquare [7,6,2,2,2,2,1,1] [5,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10890 - -lemma sg11511 : RowSquare [7,6,2,2,2,2,1,1] [5,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10891 - -lemma sg11512 : RowSquare [7,6,2,2,2,2,1,1] [5,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10892 - -lemma sg11513 : RowSquare [7,6,2,2,2,2,1,1] [5,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10893 - -lemma sg11514 : RowSquare [7,6,2,2,2,2,1,1] [5,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg10894 - -lemma sg11515 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10895 - -lemma sg11516 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10896 - -lemma sg11517 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10897 - -lemma sg11518 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg10898 - -lemma sg11519 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10899 - -lemma sg11520 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10900 - -lemma sg11521 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg10901 - -lemma sg11522 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg10902 - -lemma sg11523 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10903 - -lemma sg11524 : RowSquare [7,6,2,2,2,2,1,1] [5,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10904 - -lemma sg11525 : RowSquare [7,6,2,2,2,2,1,1] [5,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10905 - -lemma sg11526 : RowSquare [7,6,2,2,2,2,1,1] [5,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg10906 - -lemma sg11527 : RowSquare [7,6,2,2,2,2,1,1] [5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10907 - -lemma sg11528 : RowSquare [7,6,2,2,2,2,1,1] [5,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg10908 - -lemma sg11529 : RowSquare [7,6,2,2,2,2,1,1] [5,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10909 - -lemma sg11530 : RowSquare [7,6,2,2,2,2,1,1] [6,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg10910 - -lemma sg11532 : RowSquare [7,6,3,2,2,2,1] [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1221 sg1615 - -lemma sg11533 : RowSquare [7,6,3,2,2,2,1] [2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1219 sg1614 - -lemma sg11534 : RowSquare [7,6,3,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1219 sg1612 - -lemma sg11535 : RowSquare [8,3,2,2,2,2,2,1,1] [5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg358 sg3279 - -lemma sg11536 : RowSquare [8,3,2,2,2,2,2,2] [6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg579 sg2550 - -lemma sg11537 : RowSquare [8,6,1,1,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg262 sg3521 - -lemma sg11538 : RowSquare [8,6,1,1,1,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg263 sg3521 - -lemma sg11539 : RowSquare [8,6,1,1,1,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg265 sg3521 - -lemma sg11540 : RowSquare [8,6,2,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg3521 - -lemma sg11541 : RowSquare [8,6,2,1,1,1,1,1,1,1] [5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg3521 - -lemma sg11542 : RowSquare [8,6,2,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg3521 - -lemma sg11543 : RowSquare [8,6,2,1,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg111 sg4345 - -lemma sg11544 : RowSquare [9,3,2,2,2,2,2,1] [4,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg4805 - -lemma sg11545 : RowSquare [9,3,2,2,2,2,2,1] [5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg356 sg3209 - -lemma sg11546 : RowSquare [9,3,2,2,2,2,2,1] [5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg4807 - -lemma sg11547 : RowSquare [9,3,2,2,2,2,2,1] [6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg165 sg3968 - -lemma sg11548 : RowSquare [9,4,2,2,2,2,2] [5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg295 sg3209 - -lemma sg11549 : RowSquare [10,3,2,2,2,2,1,1] [4,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg4741 - -lemma sg11550 : RowSquare [10,3,2,2,2,2,1,1] [5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg74 sg4748 - -lemma sg11551 : RowSquare [10,3,2,2,2,2,1,1] [5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg4749 - -lemma sg11552 : RowSquare [10,3,2,2,2,2,1,1] [5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg4750 - -lemma sg11553 : RowSquare [10,3,2,2,2,2,2] [6,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg165 sg3870 - -lemma sg11554 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6] := by - exact rowSquare_join (by decide) sg390 sg4543 - -lemma sg11555 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg1914 sg1977 - -lemma sg11556 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg1914 sg1978 - -lemma sg11557 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3] := by - exact rowSquare_join (by decide) sg1970 sg1925 - -lemma sg11558 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1105 sg3102 - -lemma sg11559 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2] := by - exact rowSquare_join (by decide) sg1970 sg1926 - -lemma sg11560 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,1] := by - exact rowSquare_join (by decide) sg1914 sg1979 - -lemma sg11561 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg1914 sg1980 - -lemma sg11562 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3] := by - exact rowSquare_join (by decide) sg1532 sg2452 - -lemma sg11563 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,1] := by - exact rowSquare_join (by decide) sg1914 sg1981 - -lemma sg11564 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3] := by - exact rowSquare_join (by decide) sg1916 sg1977 - -lemma sg11565 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg1915 sg1978 - -lemma sg11566 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2] := by - exact rowSquare_join (by decide) sg1916 sg1978 - -lemma sg11567 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,1] := by - exact rowSquare_join (by decide) sg1971 sg1926 - -lemma sg11568 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5] := by - exact rowSquare_join (by decide) sg1539 sg2439 - -lemma sg11569 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,1] := by - exact rowSquare_join (by decide) sg1455 sg2479 - -lemma sg11570 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,1] := by - exact rowSquare_join (by decide) sg1915 sg1979 - -lemma sg11571 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3] := by - exact rowSquare_join (by decide) sg1916 sg1979 - -lemma sg11572 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,1,1] := by - exact rowSquare_join (by decide) sg1915 sg1980 - -lemma sg11573 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2] := by - exact rowSquare_join (by decide) sg1916 sg1980 - -lemma sg11574 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,1] := by - exact rowSquare_join (by decide) sg1917 sg1979 - -lemma sg11575 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,1,1] := by - exact rowSquare_join (by decide) sg1915 sg1981 - -lemma sg11576 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2] := by - exact rowSquare_join (by decide) sg1916 sg1981 - -lemma sg11577 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,1] := by - exact rowSquare_join (by decide) sg1925 sg1973 - -lemma sg11578 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5] := by - exact rowSquare_join (by decide) sg1926 sg1973 - -lemma sg11579 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg1844 sg2002 - -lemma sg11580 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1844 sg2003 - -lemma sg11581 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1914 sg1984 - -lemma sg11582 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4] := by - exact rowSquare_join (by decide) sg1927 sg1970 - -lemma sg11583 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4] := by - exact rowSquare_join (by decide) sg1926 sg1976 - -lemma sg11584 : RowSquare [3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4] := by - exact rowSquare_join (by decide) sg1532 sg2432 - -lemma sg11585 : RowSquare [3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4] := by - exact rowSquare_join (by decide) sg1061 sg3151 - -lemma sg11586 : RowSquare [3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg1914 sg1970 - -lemma sg11587 : RowSquare [3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4] := by - exact rowSquare_join (by decide) sg1916 sg1970 - -lemma sg11588 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [5,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg636 sg3657 - -lemma sg11589 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1300 sg2433 - -lemma sg11590 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [6,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg1062 sg2838 - -lemma sg11591 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [6,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg872 sg3152 - -lemma sg11592 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [6,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg1063 sg2838 - -lemma sg11593 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1735 sg1975 - -lemma sg11594 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1810 sg1914 - -lemma sg11595 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1957 sg1924 - -lemma sg11596 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1891 sg1994 - -lemma sg11597 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1902 sg1980 - -lemma sg11598 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2] := by - exact rowSquare_join (by decide) sg1032 sg3154 - -lemma sg11599 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1954 sg1927 - -lemma sg11600 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1891 sg1997 - -lemma sg11601 : RowSquare [4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1] := by - exact rowSquare_join (by decide) sg1032 sg3152 - -lemma sg11602 : RowSquare [4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6] := by - exact rowSquare_join (by decide) sg390 sg4539 - -lemma sg11603 : RowSquare [4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1903 sg1976 - -lemma sg11604 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1517 sg2405 - -lemma sg11605 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg1517 sg2406 - -lemma sg11606 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg1517 sg2407 - -lemma sg11607 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg1518 sg2406 - -lemma sg11608 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg1518 sg2407 - -lemma sg11609 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4] := by - exact rowSquare_join (by decide) sg1519 sg2407 - -lemma sg11610 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1520 sg2405 - -lemma sg11611 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1520 sg2406 - -lemma sg11612 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1520 sg2407 - -lemma sg11613 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,2] := by - exact rowSquare_join (by decide) sg1032 sg3148 - -lemma sg11614 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,1] := by - exact rowSquare_join (by decide) sg1032 sg3149 - -lemma sg11615 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4] := by - exact rowSquare_join (by decide) sg1033 sg3149 - -lemma sg11616 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg1521 sg2405 - -lemma sg11617 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,2,2] := by - exact rowSquare_join (by decide) sg1521 sg2406 - -lemma sg11618 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,1] := by - exact rowSquare_join (by decide) sg1521 sg2407 - -lemma sg11619 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg1522 sg2405 - -lemma sg11620 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg1523 sg2405 - -lemma sg11621 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,1] := by - exact rowSquare_join (by decide) sg1522 sg2406 - -lemma sg11622 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,3] := by - exact rowSquare_join (by decide) sg1522 sg2407 - -lemma sg11623 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,1,1] := by - exact rowSquare_join (by decide) sg1523 sg2406 - -lemma sg11624 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,2] := by - exact rowSquare_join (by decide) sg1523 sg2407 - -lemma sg11625 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1901 sg1954 - -lemma sg11626 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1901 sg1955 - -lemma sg11627 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1901 sg1956 - -lemma sg11628 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1902 sg1955 - -lemma sg11629 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1902 sg1956 - -lemma sg11630 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1901 sg1957 - -lemma sg11631 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1903 sg1955 - -lemma sg11632 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1902 sg1957 - -lemma sg11633 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1903 sg1956 - -lemma sg11634 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1901 sg1958 - -lemma sg11635 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1904 sg1954 - -lemma sg11636 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1902 sg1958 - -lemma sg11637 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1904 sg1956 - -lemma sg11638 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1905 sg1955 - -lemma sg11639 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1905 sg1956 - -lemma sg11640 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4] := by - exact rowSquare_join (by decide) sg1519 sg2413 - -lemma sg11641 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1901 sg1959 - -lemma sg11642 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg1954 sg1906 - -lemma sg11643 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1901 sg1960 - -lemma sg11644 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg1902 sg1959 - -lemma sg11645 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg1955 sg1906 - -lemma sg11646 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg1906 sg1956 - -lemma sg11647 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg1902 sg1960 - -lemma sg11648 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg1955 sg1907 - -lemma sg11649 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,3] := by - exact rowSquare_join (by decide) sg1956 sg1907 - -lemma sg11650 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1955 sg1908 - -lemma sg11651 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,2] := by - exact rowSquare_join (by decide) sg1956 sg1908 - -lemma sg11652 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1903 sg1957 - -lemma sg11653 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1901 sg1961 - -lemma sg11654 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1904 sg1957 - -lemma sg11655 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1902 sg1961 - -lemma sg11656 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1520 sg2413 - -lemma sg11657 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1901 sg1962 - -lemma sg11658 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1904 sg1958 - -lemma sg11659 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1901 sg1963 - -lemma sg11660 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1902 sg1962 - -lemma sg11661 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg1905 sg1958 - -lemma sg11662 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,1] := by - exact rowSquare_join (by decide) sg1521 sg2413 - -lemma sg11663 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1902 sg1963 - -lemma sg11664 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg1518 sg2419 - -lemma sg11665 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,3] := by - exact rowSquare_join (by decide) sg1519 sg2419 - -lemma sg11666 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg1904 sg1959 - -lemma sg11667 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg1906 sg1958 - -lemma sg11668 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg1904 sg1960 - -lemma sg11669 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,1] := by - exact rowSquare_join (by decide) sg1905 sg1959 - -lemma sg11670 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,3] := by - exact rowSquare_join (by decide) sg1519 sg2420 - -lemma sg11671 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg1905 sg1960 - -lemma sg11672 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,2] := by - exact rowSquare_join (by decide) sg1519 sg2421 - -lemma sg11673 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1903 sg1961 - -lemma sg11674 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1520 sg2417 - -lemma sg11675 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1903 sg1962 - -lemma sg11676 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1904 sg1961 - -lemma sg11677 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1903 sg1963 - -lemma sg11678 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1520 sg2419 - -lemma sg11679 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2] := by - exact rowSquare_join (by decide) sg1905 sg1961 - -lemma sg11680 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,1] := by - exact rowSquare_join (by decide) sg1038 sg3149 - -lemma sg11681 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1904 sg1962 - -lemma sg11682 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,2,2,2] := by - exact rowSquare_join (by decide) sg1906 sg1961 - -lemma sg11683 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1904 sg1963 - -lemma sg11684 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,1] := by - exact rowSquare_join (by decide) sg1905 sg1962 - -lemma sg11685 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,3] := by - exact rowSquare_join (by decide) sg1527 sg2407 - -lemma sg11686 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,1,1] := by - exact rowSquare_join (by decide) sg1905 sg1963 - -lemma sg11687 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,2] := by - exact rowSquare_join (by decide) sg1033 sg3150 - -lemma sg11688 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg1520 sg2422 - -lemma sg11689 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,1] := by - exact rowSquare_join (by decide) sg1906 sg1962 - -lemma sg11690 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,3,1,1] := by - exact rowSquare_join (by decide) sg1906 sg1963 - -lemma sg11691 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,3,2] := by - exact rowSquare_join (by decide) sg1907 sg1962 - -lemma sg11692 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,4,1] := by - exact rowSquare_join (by decide) sg1907 sg1963 - -lemma sg11693 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5] := by - exact rowSquare_join (by decide) sg1908 sg1963 - -lemma sg11694 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1901 sg1964 - -lemma sg11695 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1811 sg1998 - -lemma sg11696 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1903 sg1964 - -lemma sg11697 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1901 sg1965 - -lemma sg11698 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1811 sg1999 - -lemma sg11699 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1902 sg1965 - -lemma sg11700 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1909 sg1956 - -lemma sg11701 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1901 sg1966 - -lemma sg11702 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1811 sg2000 - -lemma sg11703 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1811 sg2001 - -lemma sg11704 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1957 sg1911 - -lemma sg11705 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1904 sg1967 - -lemma sg11706 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg1961 sg1910 - -lemma sg11707 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg1906 sg1967 - -lemma sg11708 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1957 sg1912 - -lemma sg11709 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1903 sg1968 - -lemma sg11710 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2] := by - exact rowSquare_join (by decide) sg1961 sg1912 - -lemma sg11711 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,1,1] := by - exact rowSquare_join (by decide) sg1905 sg1968 - -lemma sg11712 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,1] := by - exact rowSquare_join (by decide) sg1523 sg2395 - -lemma sg11713 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6] := by - exact rowSquare_join (by decide) sg390 sg4526 - -lemma sg11714 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1520 sg2399 - -lemma sg11715 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg330 sg4506 - -lemma sg11716 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1] [5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg4508 - -lemma sg11717 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1] [6,6,6,6] := by - exact rowSquare_join (by decide) sg390 sg4419 - -lemma sg11718 : RowSquare [5,3,3,3,2,1,1,1,1,1,1,1,1] [6,6,6,6] := by - exact rowSquare_join (by decide) sg390 sg4405 - -lemma sg11719 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [6,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1517 sg2372 - -lemma sg11720 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1520 sg2372 - -lemma sg11721 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg1521 sg2372 - -lemma sg11722 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg1954 sg1878 - -lemma sg11723 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg1878 sg1958 - -lemma sg11724 : RowSquare [5,4,2,2,2,2,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1875 sg1811 - -lemma sg11725 : RowSquare [5,4,2,2,2,2,1,1,1,1,1,1,1] [5,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1417 sg2291 - -lemma sg11726 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg998 sg3115 - -lemma sg11727 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg3650 - -lemma sg11728 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1372 sg2288 - -lemma sg11729 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg911 sg2958 - -lemma sg11730 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,4] := by - exact rowSquare_join (by decide) sg1001 sg2784 - -lemma sg11731 : RowSquare [5,5,2,2,2,2,2,2,1,1] [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg411 sg3999 - -lemma sg11732 : RowSquare [5,5,2,2,2,2,2,2,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg412 sg3999 - -lemma sg11733 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg1874 - -lemma sg11734 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg1878 - -lemma sg11735 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg998 sg2633 - -lemma sg11736 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1001 sg2633 - -lemma sg11737 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1002 sg2633 - -lemma sg11738 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1754 sg1872 - -lemma sg11739 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1754 sg1754 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes25 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes9 + +namespace OAI + +/-! Semigroup Nodes 27. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg11339 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1766 + +lemma sg11340 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg890 sg2275 + +lemma sg11341 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg1767 + +lemma sg11342 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg1331 sg1766 + +lemma sg11343 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg890 sg2277 + +lemma sg11344 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg1332 sg1766 + +lemma sg11345 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg1331 sg1767 + +lemma sg11346 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg891 sg2276 + +lemma sg11347 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg1332 sg1767 + +lemma sg11348 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4] := by + exact rowSquare_join (by decide) sg892 sg2277 + +lemma sg11349 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg5842 + +lemma sg11350 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg5849 + +lemma sg11351 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [6,6,6,5] := by + exact rowSquare_join (by decide) sg13 sg5852 + +lemma sg11352 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg5869 + +lemma sg11353 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5871 + +lemma sg11354 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg5873 + +lemma sg11355 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,6,5,5] := by + exact rowSquare_join (by decide) sg13 sg5874 + +lemma sg11356 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5878 + +lemma sg11357 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg5880 + +lemma sg11358 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg5881 + +lemma sg11359 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,1] := by + exact rowSquare_join (by decide) sg13 sg5882 + +lemma sg11360 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [7,7,5,4] := by + exact rowSquare_join (by decide) sg13 sg5883 + +lemma sg11361 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg5888 + +lemma sg11362 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [9,8,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1365 sg1763 + +lemma sg11363 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1] [9,9,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg5889 + +lemma sg11364 : RowSquare [6,6,2,2,2,2,2,1] [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7812 + +lemma sg11365 : RowSquare [6,6,2,2,2,2,2,1] [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7813 + +lemma sg11366 : RowSquare [6,6,2,2,2,2,2,1] [5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7816 + +lemma sg11367 : RowSquare [6,6,2,2,2,2,2,1] [5,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7817 + +lemma sg11368 : RowSquare [6,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7818 + +lemma sg11369 : RowSquare [6,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7819 + +lemma sg11370 : RowSquare [6,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6 sg7820 + +lemma sg11371 : RowSquare [6,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6 sg7821 + +lemma sg11372 : RowSquare [6,6,2,2,2,2,2,1] [5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7823 + +lemma sg11373 : RowSquare [6,6,2,2,2,2,2,1] [5,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7824 + +lemma sg11374 : RowSquare [6,6,2,2,2,2,2,1] [5,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7825 + +lemma sg11375 : RowSquare [6,6,2,2,2,2,2,1] [5,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7826 + +lemma sg11376 : RowSquare [6,6,2,2,2,2,2,1] [5,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7827 + +lemma sg11377 : RowSquare [6,6,2,2,2,2,2,1] [5,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg7828 + +lemma sg11378 : RowSquare [6,6,2,2,2,2,2,1] [5,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7831 + +lemma sg11379 : RowSquare [6,6,2,2,2,2,2,1] [5,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7832 + +lemma sg11380 : RowSquare [6,6,2,2,2,2,2,1] [5,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7833 + +lemma sg11381 : RowSquare [6,6,2,2,2,2,2,1] [5,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg7834 + +lemma sg11382 : RowSquare [6,6,2,2,2,2,2,1] [5,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg7835 + +lemma sg11383 : RowSquare [6,6,2,2,2,2,2,1] [5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7837 + +lemma sg11384 : RowSquare [6,6,2,2,2,2,2,1] [5,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg5 sg7840 + +lemma sg11385 : RowSquare [6,6,2,2,2,2,2,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7822 + +lemma sg11386 : RowSquare [6,6,2,2,2,2,2,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7841 + +lemma sg11387 : RowSquare [6,6,2,2,2,2,2,1] [6,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7824 + +lemma sg11388 : RowSquare [6,6,2,2,2,2,2,1] [6,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7825 + +lemma sg11389 : RowSquare [6,6,2,2,2,2,2,1] [6,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7826 + +lemma sg11390 : RowSquare [6,6,2,2,2,2,2,1] [6,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7827 + +lemma sg11391 : RowSquare [6,6,2,2,2,2,2,1] [6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6 sg7828 + +lemma sg11392 : RowSquare [6,6,2,2,2,2,2,1] [6,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7842 + +lemma sg11393 : RowSquare [6,6,2,2,2,2,2,1] [6,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7843 + +lemma sg11394 : RowSquare [6,6,2,2,2,2,2,1] [6,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7844 + +lemma sg11395 : RowSquare [6,6,2,2,2,2,2,1] [6,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg7845 + +lemma sg11396 : RowSquare [6,6,2,2,2,2,2,1] [6,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg7846 + +lemma sg11397 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg7853 + +lemma sg11398 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg7854 + +lemma sg11399 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg7855 + +lemma sg11400 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg7856 + +lemma sg11401 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg7857 + +lemma sg11402 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7837 + +lemma sg11403 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6 sg7839 + +lemma sg11404 : RowSquare [6,6,2,2,2,2,2,1] [6,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6 sg7840 + +lemma sg11405 : RowSquare [6,6,2,2,2,2,2,1] [6,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7848 + +lemma sg11406 : RowSquare [6,6,2,2,2,2,2,1] [6,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7849 + +lemma sg11407 : RowSquare [6,6,2,2,2,2,2,1] [6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7850 + +lemma sg11408 : RowSquare [6,6,2,2,2,2,2,1] [6,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg7851 + +lemma sg11409 : RowSquare [6,6,2,2,2,2,2,1] [6,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg7852 + +lemma sg11410 : RowSquare [6,6,2,2,2,2,2,1] [6,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg7858 + +lemma sg11411 : RowSquare [6,6,2,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7841 + +lemma sg11412 : RowSquare [6,6,2,2,2,2,2,1] [7,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7842 + +lemma sg11413 : RowSquare [6,6,2,2,2,2,2,1] [7,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7843 + +lemma sg11414 : RowSquare [6,6,2,2,2,2,2,1] [7,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7844 + +lemma sg11415 : RowSquare [6,6,2,2,2,2,2,1] [7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6 sg7845 + +lemma sg11416 : RowSquare [6,6,2,2,2,2,2,1] [7,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6 sg7846 + +lemma sg11417 : RowSquare [6,6,2,2,2,2,2,1] [7,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7854 + +lemma sg11418 : RowSquare [6,6,2,2,2,2,2,1] [7,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7855 + +lemma sg11419 : RowSquare [6,6,2,2,2,2,2,1] [7,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg7856 + +lemma sg11420 : RowSquare [6,6,2,2,2,2,2,1] [7,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg7857 + +lemma sg11421 : RowSquare [6,6,2,2,2,2,2,1] [8,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7854 + +lemma sg11422 : RowSquare [6,6,2,2,2,2,2,1] [8,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7855 + +lemma sg11423 : RowSquare [6,6,2,2,2,2,2,1] [8,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg7856 + +lemma sg11424 : RowSquare [6,6,2,2,2,2,2,1] [8,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6 sg7857 + +lemma sg11425 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg997 sg2251 + +lemma sg11426 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg2251 + +lemma sg11427 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg999 sg2251 + +lemma sg11428 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1000 sg2251 + +lemma sg11429 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1001 sg2251 + +lemma sg11430 : RowSquare [7,5,1,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1002 sg2251 + +lemma sg11431 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg587 sg2702 + +lemma sg11432 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg2702 + +lemma sg11433 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg2702 + +lemma sg11434 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg2702 + +lemma sg11435 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg915 sg2251 + +lemma sg11436 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg910 sg2256 + +lemma sg11437 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg2707 + +lemma sg11438 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg2708 + +lemma sg11439 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg587 sg2708 + +lemma sg11440 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg595 sg2702 + +lemma sg11441 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg920 sg2251 + +lemma sg11442 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg2702 + +lemma sg11443 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg921 sg2251 + +lemma sg11444 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg588 sg2708 + +lemma sg11445 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg2713 + +lemma sg11446 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg589 sg2708 + +lemma sg11447 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg2706 + +lemma sg11448 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg915 sg2256 + +lemma sg11449 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg2702 + +lemma sg11450 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg931 sg2251 + +lemma sg11451 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg923 sg2257 + +lemma sg11452 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg930 sg2254 + +lemma sg11453 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg939 sg2251 + +lemma sg11454 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg931 sg2253 + +lemma sg11455 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg2269 + +lemma sg11456 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg920 sg2261 + +lemma sg11457 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg932 sg2253 + +lemma sg11458 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg931 sg2254 + +lemma sg11459 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg6017 + +lemma sg11460 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg932 sg2254 + +lemma sg11461 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg6018 + +lemma sg11462 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg6019 + +lemma sg11463 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [7,7,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg939 sg2253 + +lemma sg11464 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [7,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg939 sg2254 + +lemma sg11465 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg6020 + +lemma sg11466 : RowSquare [7,5,2,1,1,1,1,1,1,1,1,1] [8,8,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg6020 + +lemma sg11467 : RowSquare [7,5,3,2,1,1,1,1,1,1] [4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg132 sg4160 + +lemma sg11468 : RowSquare [7,5,3,2,1,1,1,1,1,1] [4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg133 sg4160 + +lemma sg11469 : RowSquare [7,5,3,2,1,1,1,1,1,1] [4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg134 sg4160 + +lemma sg11470 : RowSquare [7,5,3,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg479 sg2702 + +lemma sg11471 : RowSquare [7,5,3,2,1,1,1,1,1,1] [5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg135 sg4160 + +lemma sg11472 : RowSquare [7,5,3,2,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg132 sg4161 + +lemma sg11473 : RowSquare [7,5,3,2,1,1,1,1,1,1] [5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg136 sg4160 + +lemma sg11474 : RowSquare [7,5,3,2,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg133 sg4161 + +lemma sg11475 : RowSquare [7,5,3,2,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg134 sg4161 + +lemma sg11476 : RowSquare [7,5,3,2,1,1,1,1,1,1] [5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg137 sg4160 + +lemma sg11477 : RowSquare [7,5,3,2,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg135 sg4161 + +lemma sg11478 : RowSquare [7,5,3,2,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg139 sg4160 + +lemma sg11479 : RowSquare [7,5,3,2,1,1,1,1,1,1] [6,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg136 sg4161 + +lemma sg11480 : RowSquare [7,5,3,2,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg137 sg4161 + +lemma sg11481 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg888 sg2251 + +lemma sg11482 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg2251 + +lemma sg11483 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg890 sg2251 + +lemma sg11484 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg891 sg2251 + +lemma sg11485 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg892 sg2251 + +lemma sg11486 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg893 sg2251 + +lemma sg11487 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg894 sg2251 + +lemma sg11488 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg895 sg2251 + +lemma sg11489 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg896 sg2251 + +lemma sg11490 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg888 sg2255 + +lemma sg11491 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg892 sg2252 + +lemma sg11492 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg888 sg2256 + +lemma sg11493 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg897 sg2251 + +lemma sg11494 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg898 sg2251 + +lemma sg11495 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg899 sg2251 + +lemma sg11496 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg889 sg2256 + +lemma sg11497 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg890 sg2254 + +lemma sg11498 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg891 sg2254 + +lemma sg11499 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg892 sg2254 + +lemma sg11500 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg891 sg2255 + +lemma sg11501 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg892 sg2255 + +lemma sg11502 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg892 sg2256 + +lemma sg11503 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg902 sg2251 + +lemma sg11504 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg903 sg2251 + +lemma sg11505 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg909 sg2251 + +lemma sg11506 : RowSquare [7,6,2,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg525 sg2702 + +lemma sg11507 : RowSquare [7,6,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg825 sg2251 + +lemma sg11508 : RowSquare [7,6,2,2,1,1,1,1,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg459 sg2702 + +lemma sg11509 : RowSquare [7,6,2,2,2,2,1,1] [5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10889 + +lemma sg11510 : RowSquare [7,6,2,2,2,2,1,1] [5,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10890 + +lemma sg11511 : RowSquare [7,6,2,2,2,2,1,1] [5,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10891 + +lemma sg11512 : RowSquare [7,6,2,2,2,2,1,1] [5,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10892 + +lemma sg11513 : RowSquare [7,6,2,2,2,2,1,1] [5,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10893 + +lemma sg11514 : RowSquare [7,6,2,2,2,2,1,1] [5,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg10894 + +lemma sg11515 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10895 + +lemma sg11516 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10896 + +lemma sg11517 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10897 + +lemma sg11518 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg10898 + +lemma sg11519 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10899 + +lemma sg11520 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10900 + +lemma sg11521 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg10901 + +lemma sg11522 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg10902 + +lemma sg11523 : RowSquare [7,6,2,2,2,2,1,1] [5,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10903 + +lemma sg11524 : RowSquare [7,6,2,2,2,2,1,1] [5,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10904 + +lemma sg11525 : RowSquare [7,6,2,2,2,2,1,1] [5,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10905 + +lemma sg11526 : RowSquare [7,6,2,2,2,2,1,1] [5,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg10906 + +lemma sg11527 : RowSquare [7,6,2,2,2,2,1,1] [5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10907 + +lemma sg11528 : RowSquare [7,6,2,2,2,2,1,1] [5,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg10908 + +lemma sg11529 : RowSquare [7,6,2,2,2,2,1,1] [5,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10909 + +lemma sg11530 : RowSquare [7,6,2,2,2,2,1,1] [6,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg10910 + +lemma sg11532 : RowSquare [7,6,3,2,2,2,1] [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1221 sg1615 + +lemma sg11533 : RowSquare [7,6,3,2,2,2,1] [2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1219 sg1614 + +lemma sg11534 : RowSquare [7,6,3,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1219 sg1612 + +lemma sg11535 : RowSquare [8,3,2,2,2,2,2,1,1] [5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg358 sg3279 + +lemma sg11536 : RowSquare [8,3,2,2,2,2,2,2] [6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg579 sg2550 + +lemma sg11537 : RowSquare [8,6,1,1,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg262 sg3521 + +lemma sg11538 : RowSquare [8,6,1,1,1,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg263 sg3521 + +lemma sg11539 : RowSquare [8,6,1,1,1,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg265 sg3521 + +lemma sg11540 : RowSquare [8,6,2,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg3521 + +lemma sg11541 : RowSquare [8,6,2,1,1,1,1,1,1,1] [5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg3521 + +lemma sg11542 : RowSquare [8,6,2,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg3521 + +lemma sg11543 : RowSquare [8,6,2,1,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg111 sg4345 + +lemma sg11544 : RowSquare [9,3,2,2,2,2,2,1] [4,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg4805 + +lemma sg11545 : RowSquare [9,3,2,2,2,2,2,1] [5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg356 sg3209 + +lemma sg11546 : RowSquare [9,3,2,2,2,2,2,1] [5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg4807 + +lemma sg11547 : RowSquare [9,3,2,2,2,2,2,1] [6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg165 sg3968 + +lemma sg11548 : RowSquare [9,4,2,2,2,2,2] [5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg295 sg3209 + +lemma sg11549 : RowSquare [10,3,2,2,2,2,1,1] [4,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg4741 + +lemma sg11550 : RowSquare [10,3,2,2,2,2,1,1] [5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg74 sg4748 + +lemma sg11551 : RowSquare [10,3,2,2,2,2,1,1] [5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg4749 + +lemma sg11552 : RowSquare [10,3,2,2,2,2,1,1] [5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg4750 + +lemma sg11553 : RowSquare [10,3,2,2,2,2,2] [6,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg165 sg3870 + +lemma sg11554 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6] := by + exact rowSquare_join (by decide) sg390 sg4543 + +lemma sg11555 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg1914 sg1977 + +lemma sg11556 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg1914 sg1978 + +lemma sg11557 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3] := by + exact rowSquare_join (by decide) sg1970 sg1925 + +lemma sg11558 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1105 sg3102 + +lemma sg11559 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2] := by + exact rowSquare_join (by decide) sg1970 sg1926 + +lemma sg11560 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,1] := by + exact rowSquare_join (by decide) sg1914 sg1979 + +lemma sg11561 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg1914 sg1980 + +lemma sg11562 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3] := by + exact rowSquare_join (by decide) sg1532 sg2452 + +lemma sg11563 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,1] := by + exact rowSquare_join (by decide) sg1914 sg1981 + +lemma sg11564 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3] := by + exact rowSquare_join (by decide) sg1916 sg1977 + +lemma sg11565 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg1915 sg1978 + +lemma sg11566 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2] := by + exact rowSquare_join (by decide) sg1916 sg1978 + +lemma sg11567 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,1] := by + exact rowSquare_join (by decide) sg1971 sg1926 + +lemma sg11568 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5] := by + exact rowSquare_join (by decide) sg1539 sg2439 + +lemma sg11569 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,1] := by + exact rowSquare_join (by decide) sg1455 sg2479 + +lemma sg11570 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,1] := by + exact rowSquare_join (by decide) sg1915 sg1979 + +lemma sg11571 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3] := by + exact rowSquare_join (by decide) sg1916 sg1979 + +lemma sg11572 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,1,1] := by + exact rowSquare_join (by decide) sg1915 sg1980 + +lemma sg11573 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2] := by + exact rowSquare_join (by decide) sg1916 sg1980 + +lemma sg11574 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,1] := by + exact rowSquare_join (by decide) sg1917 sg1979 + +lemma sg11575 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,1,1] := by + exact rowSquare_join (by decide) sg1915 sg1981 + +lemma sg11576 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2] := by + exact rowSquare_join (by decide) sg1916 sg1981 + +lemma sg11577 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,1] := by + exact rowSquare_join (by decide) sg1925 sg1973 + +lemma sg11578 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5] := by + exact rowSquare_join (by decide) sg1926 sg1973 + +lemma sg11579 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg1844 sg2002 + +lemma sg11580 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1844 sg2003 + +lemma sg11581 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1914 sg1984 + +lemma sg11582 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4] := by + exact rowSquare_join (by decide) sg1927 sg1970 + +lemma sg11583 : RowSquare [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4] := by + exact rowSquare_join (by decide) sg1926 sg1976 + +lemma sg11584 : RowSquare [3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4] := by + exact rowSquare_join (by decide) sg1532 sg2432 + +lemma sg11585 : RowSquare [3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4] := by + exact rowSquare_join (by decide) sg1061 sg3151 + +lemma sg11586 : RowSquare [3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg1914 sg1970 + +lemma sg11587 : RowSquare [3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4] := by + exact rowSquare_join (by decide) sg1916 sg1970 + +lemma sg11588 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [5,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg636 sg3657 + +lemma sg11589 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1300 sg2433 + +lemma sg11590 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [6,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg1062 sg2838 + +lemma sg11591 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [6,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg872 sg3152 + +lemma sg11592 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [6,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg1063 sg2838 + +lemma sg11593 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1735 sg1975 + +lemma sg11594 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1810 sg1914 + +lemma sg11595 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1957 sg1924 + +lemma sg11596 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1891 sg1994 + +lemma sg11597 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1902 sg1980 + +lemma sg11598 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2] := by + exact rowSquare_join (by decide) sg1032 sg3154 + +lemma sg11599 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1954 sg1927 + +lemma sg11600 : RowSquare [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1891 sg1997 + +lemma sg11601 : RowSquare [4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1] := by + exact rowSquare_join (by decide) sg1032 sg3152 + +lemma sg11602 : RowSquare [4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6] := by + exact rowSquare_join (by decide) sg390 sg4539 + +lemma sg11603 : RowSquare [4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1903 sg1976 + +lemma sg11604 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1517 sg2405 + +lemma sg11605 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg1517 sg2406 + +lemma sg11606 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg1517 sg2407 + +lemma sg11607 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg1518 sg2406 + +lemma sg11608 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg1518 sg2407 + +lemma sg11609 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4] := by + exact rowSquare_join (by decide) sg1519 sg2407 + +lemma sg11610 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1520 sg2405 + +lemma sg11611 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1520 sg2406 + +lemma sg11612 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1520 sg2407 + +lemma sg11613 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,2] := by + exact rowSquare_join (by decide) sg1032 sg3148 + +lemma sg11614 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,1] := by + exact rowSquare_join (by decide) sg1032 sg3149 + +lemma sg11615 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4] := by + exact rowSquare_join (by decide) sg1033 sg3149 + +lemma sg11616 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg1521 sg2405 + +lemma sg11617 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,2,2] := by + exact rowSquare_join (by decide) sg1521 sg2406 + +lemma sg11618 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,1] := by + exact rowSquare_join (by decide) sg1521 sg2407 + +lemma sg11619 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg1522 sg2405 + +lemma sg11620 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg1523 sg2405 + +lemma sg11621 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,1] := by + exact rowSquare_join (by decide) sg1522 sg2406 + +lemma sg11622 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,3] := by + exact rowSquare_join (by decide) sg1522 sg2407 + +lemma sg11623 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,1,1] := by + exact rowSquare_join (by decide) sg1523 sg2406 + +lemma sg11624 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,2] := by + exact rowSquare_join (by decide) sg1523 sg2407 + +lemma sg11625 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1901 sg1954 + +lemma sg11626 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1901 sg1955 + +lemma sg11627 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1901 sg1956 + +lemma sg11628 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1902 sg1955 + +lemma sg11629 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1902 sg1956 + +lemma sg11630 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1901 sg1957 + +lemma sg11631 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1903 sg1955 + +lemma sg11632 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1902 sg1957 + +lemma sg11633 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1903 sg1956 + +lemma sg11634 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1901 sg1958 + +lemma sg11635 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1904 sg1954 + +lemma sg11636 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1902 sg1958 + +lemma sg11637 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1904 sg1956 + +lemma sg11638 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1905 sg1955 + +lemma sg11639 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1905 sg1956 + +lemma sg11640 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4] := by + exact rowSquare_join (by decide) sg1519 sg2413 + +lemma sg11641 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1901 sg1959 + +lemma sg11642 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg1954 sg1906 + +lemma sg11643 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1901 sg1960 + +lemma sg11644 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg1902 sg1959 + +lemma sg11645 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg1955 sg1906 + +lemma sg11646 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg1906 sg1956 + +lemma sg11647 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg1902 sg1960 + +lemma sg11648 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg1955 sg1907 + +lemma sg11649 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,3] := by + exact rowSquare_join (by decide) sg1956 sg1907 + +lemma sg11650 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1955 sg1908 + +lemma sg11651 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,2] := by + exact rowSquare_join (by decide) sg1956 sg1908 + +lemma sg11652 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1903 sg1957 + +lemma sg11653 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1901 sg1961 + +lemma sg11654 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1904 sg1957 + +lemma sg11655 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1902 sg1961 + +lemma sg11656 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1520 sg2413 + +lemma sg11657 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1901 sg1962 + +lemma sg11658 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1904 sg1958 + +lemma sg11659 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1901 sg1963 + +lemma sg11660 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1902 sg1962 + +lemma sg11661 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg1905 sg1958 + +lemma sg11662 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,1] := by + exact rowSquare_join (by decide) sg1521 sg2413 + +lemma sg11663 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1902 sg1963 + +lemma sg11664 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg1518 sg2419 + +lemma sg11665 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,3] := by + exact rowSquare_join (by decide) sg1519 sg2419 + +lemma sg11666 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg1904 sg1959 + +lemma sg11667 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg1906 sg1958 + +lemma sg11668 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg1904 sg1960 + +lemma sg11669 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,1] := by + exact rowSquare_join (by decide) sg1905 sg1959 + +lemma sg11670 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,3] := by + exact rowSquare_join (by decide) sg1519 sg2420 + +lemma sg11671 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg1905 sg1960 + +lemma sg11672 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,2] := by + exact rowSquare_join (by decide) sg1519 sg2421 + +lemma sg11673 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1903 sg1961 + +lemma sg11674 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1520 sg2417 + +lemma sg11675 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1903 sg1962 + +lemma sg11676 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1904 sg1961 + +lemma sg11677 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1903 sg1963 + +lemma sg11678 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1520 sg2419 + +lemma sg11679 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2] := by + exact rowSquare_join (by decide) sg1905 sg1961 + +lemma sg11680 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,1] := by + exact rowSquare_join (by decide) sg1038 sg3149 + +lemma sg11681 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1904 sg1962 + +lemma sg11682 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,2,2,2] := by + exact rowSquare_join (by decide) sg1906 sg1961 + +lemma sg11683 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1904 sg1963 + +lemma sg11684 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,1] := by + exact rowSquare_join (by decide) sg1905 sg1962 + +lemma sg11685 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,3] := by + exact rowSquare_join (by decide) sg1527 sg2407 + +lemma sg11686 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,1,1] := by + exact rowSquare_join (by decide) sg1905 sg1963 + +lemma sg11687 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,2] := by + exact rowSquare_join (by decide) sg1033 sg3150 + +lemma sg11688 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg1520 sg2422 + +lemma sg11689 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,1] := by + exact rowSquare_join (by decide) sg1906 sg1962 + +lemma sg11690 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,3,1,1] := by + exact rowSquare_join (by decide) sg1906 sg1963 + +lemma sg11691 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,3,2] := by + exact rowSquare_join (by decide) sg1907 sg1962 + +lemma sg11692 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,4,1] := by + exact rowSquare_join (by decide) sg1907 sg1963 + +lemma sg11693 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5] := by + exact rowSquare_join (by decide) sg1908 sg1963 + +lemma sg11694 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1901 sg1964 + +lemma sg11695 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1811 sg1998 + +lemma sg11696 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1903 sg1964 + +lemma sg11697 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1901 sg1965 + +lemma sg11698 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1811 sg1999 + +lemma sg11699 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1902 sg1965 + +lemma sg11700 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1909 sg1956 + +lemma sg11701 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1901 sg1966 + +lemma sg11702 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1811 sg2000 + +lemma sg11703 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1811 sg2001 + +lemma sg11704 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1957 sg1911 + +lemma sg11705 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1904 sg1967 + +lemma sg11706 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg1961 sg1910 + +lemma sg11707 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg1906 sg1967 + +lemma sg11708 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1957 sg1912 + +lemma sg11709 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1903 sg1968 + +lemma sg11710 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2] := by + exact rowSquare_join (by decide) sg1961 sg1912 + +lemma sg11711 : RowSquare [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,1,1] := by + exact rowSquare_join (by decide) sg1905 sg1968 + +lemma sg11712 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,1] := by + exact rowSquare_join (by decide) sg1523 sg2395 + +lemma sg11713 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6] := by + exact rowSquare_join (by decide) sg390 sg4526 + +lemma sg11714 : RowSquare [4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1520 sg2399 + +lemma sg11715 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg330 sg4506 + +lemma sg11716 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1] [5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg4508 + +lemma sg11717 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1] [6,6,6,6] := by + exact rowSquare_join (by decide) sg390 sg4419 + +lemma sg11718 : RowSquare [5,3,3,3,2,1,1,1,1,1,1,1,1] [6,6,6,6] := by + exact rowSquare_join (by decide) sg390 sg4405 + +lemma sg11719 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [6,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1517 sg2372 + +lemma sg11720 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1520 sg2372 + +lemma sg11721 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg1521 sg2372 + +lemma sg11722 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg1954 sg1878 + +lemma sg11723 : RowSquare [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg1878 sg1958 + +lemma sg11724 : RowSquare [5,4,2,2,2,2,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1875 sg1811 + +lemma sg11725 : RowSquare [5,4,2,2,2,2,1,1,1,1,1,1,1] [5,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1417 sg2291 + +lemma sg11726 : RowSquare [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg998 sg3115 + +lemma sg11727 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg3650 + +lemma sg11728 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1372 sg2288 + +lemma sg11729 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg911 sg2958 + +lemma sg11730 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,4] := by + exact rowSquare_join (by decide) sg1001 sg2784 + +lemma sg11731 : RowSquare [5,5,2,2,2,2,2,2,1,1] [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg411 sg3999 + +lemma sg11732 : RowSquare [5,5,2,2,2,2,2,2,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg412 sg3999 + +lemma sg11733 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg1874 + +lemma sg11734 : RowSquare [6,5,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg1878 + +lemma sg11735 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg998 sg2633 + +lemma sg11736 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1001 sg2633 + +lemma sg11737 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1002 sg2633 + +lemma sg11738 : RowSquare [6,6,2,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1754 sg1872 + +lemma sg11739 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1754 sg1754 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes28.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes28.lean index 35f3a6b279aabc38b14effa5f2b7f163844cf903..44257ae3f21084d8657669836bf36d502a6ea803 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes28.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes28.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes27 - -namespace OAI - -/-! Semigroup Nodes 28. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg11740 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg1757 - -lemma sg11741 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg1758 - -lemma sg11742 : RowSquare [7,5,2,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg910 sg2702 - -lemma sg11743 : RowSquare [7,5,3,2,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg321 sg4160 - -lemma sg11744 : RowSquare [7,5,3,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg316 sg4161 - -lemma sg11745 : RowSquare [7,5,3,2,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg324 sg4160 - -lemma sg11746 : RowSquare [7,5,3,2,1,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg327 sg4160 - -lemma sg11747 : RowSquare [7,5,3,2,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg324 sg4161 - -lemma sg11748 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1327 sg2251 - -lemma sg11749 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1328 sg2251 - -lemma sg11750 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1327 sg2252 - -lemma sg11751 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg2251 - -lemma sg11752 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1327 sg2253 - -lemma sg11753 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg2251 - -lemma sg11754 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg2251 - -lemma sg11755 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1332 sg2251 - -lemma sg11756 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1328 sg2252 - -lemma sg11757 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1257 sg2251 - -lemma sg11758 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg893 sg2702 - -lemma sg11759 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg894 sg2702 - -lemma sg11760 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg895 sg2702 - -lemma sg11761 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg896 sg2702 - -lemma sg11762 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg897 sg2702 - -lemma sg11763 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg898 sg2702 - -lemma sg11764 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1261 sg2251 - -lemma sg11765 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg899 sg2702 - -lemma sg11766 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1262 sg2251 - -lemma sg11767 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1263 sg2251 - -lemma sg11768 : RowSquare [7,6,2,2,2,2,2,1] [5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg10875 - -lemma sg11769 : RowSquare [7,6,2,2,2,2,2,1] [5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg10876 - -lemma sg11770 : RowSquare [7,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg10877 - -lemma sg11771 : RowSquare [7,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg10878 - -lemma sg11772 : RowSquare [7,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg10879 - -lemma sg11773 : RowSquare [7,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg10880 - -lemma sg11774 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg10882 - -lemma sg11775 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg10883 - -lemma sg11776 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg10884 - -lemma sg11777 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg10885 - -lemma sg11778 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg10886 - -lemma sg11779 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg10887 - -lemma sg11780 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg10888 - -lemma sg11781 : RowSquare [7,6,2,2,2,2,2,1] [6,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg10899 - -lemma sg11782 : RowSquare [7,6,2,2,2,2,2,1] [6,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg10900 - -lemma sg11783 : RowSquare [7,6,2,2,2,2,2,1] [6,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg10901 - -lemma sg11784 : RowSquare [7,6,2,2,2,2,2,1] [6,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg10902 - -lemma sg11785 : RowSquare [7,6,2,2,2,2,2,1] [6,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg10903 - -lemma sg11786 : RowSquare [7,6,3,2,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg263 sg4160 - -lemma sg11787 : RowSquare [7,6,3,2,1,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg266 sg4160 - -lemma sg11788 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1245 sg2251 - -lemma sg11789 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1246 sg2251 - -lemma sg11790 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1247 sg2251 - -lemma sg11791 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1248 sg2251 - -lemma sg11792 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1249 sg2251 - -lemma sg11793 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1250 sg2251 - -lemma sg11794 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1251 sg2251 - -lemma sg11795 : RowSquare [7,7,2,2,2,2,2] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1176 sg2105 - -lemma sg11796 : RowSquare [7,7,2,2,2,2,2] [2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1169 sg2105 - -lemma sg11797 : RowSquare [7,7,2,2,2,2,2] [2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1169 sg2104 - -lemma sg11798 : RowSquare [7,7,2,2,2,2,2] [2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1169 sg2103 - -lemma sg11799 : RowSquare [7,7,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1169 sg2101 - -lemma sg11800 : RowSquare [7,7,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1169 sg2097 - -lemma sg11801 : RowSquare [7,7,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg367 sg3789 - -lemma sg11802 : RowSquare [7,7,2,2,2,2,2] [3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1173 sg2105 - -lemma sg11803 : RowSquare [7,7,2,2,2,2,2] [3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1164 sg2105 - -lemma sg11804 : RowSquare [7,7,2,2,2,2,2] [3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1164 sg2104 - -lemma sg11805 : RowSquare [7,7,2,2,2,2,2] [3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1164 sg2102 - -lemma sg11806 : RowSquare [7,7,2,2,2,2,2] [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1170 sg2105 - -lemma sg11807 : RowSquare [7,7,2,2,2,2,2] [3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1167 sg2105 - -lemma sg11808 : RowSquare [7,7,2,2,2,2,2] [3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1163 sg2104 - -lemma sg11809 : RowSquare [7,7,2,2,2,2,2] [3,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1163 sg2099 - -lemma sg11810 : RowSquare [7,7,2,2,2,2,2] [3,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1164 sg2092 - -lemma sg11811 : RowSquare [7,7,2,2,2,2,2] [3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg83 sg5293 - -lemma sg11812 : RowSquare [7,7,2,2,2,2,2] [4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1166 sg2105 - -lemma sg11813 : RowSquare [7,7,2,2,2,2,2] [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1156 sg2104 - -lemma sg11814 : RowSquare [7,7,2,2,2,2,2] [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1160 sg2105 - -lemma sg11815 : RowSquare [7,7,2,2,2,2,2] [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1153 sg2103 - -lemma sg11816 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1147 sg2100 - -lemma sg11817 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1147 sg2098 - -lemma sg11818 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1147 sg2095 - -lemma sg11819 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1147 sg2091 - -lemma sg11820 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1150 sg2094 - -lemma sg11821 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1147 sg2094 - -lemma sg11822 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1147 sg2090 - -lemma sg11823 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1147 sg2089 - -lemma sg11824 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1150 sg2088 - -lemma sg11825 : RowSquare [7,7,2,2,2,2,2] [5,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1147 sg2087 - -lemma sg11826 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg517 sg3521 - -lemma sg11827 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg518 sg3521 - -lemma sg11828 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg519 sg3521 - -lemma sg11829 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg520 sg3521 - -lemma sg11830 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg521 sg3521 - -lemma sg11831 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg522 sg3521 - -lemma sg11832 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg523 sg3521 - -lemma sg11833 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg524 sg3521 - -lemma sg11834 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg525 sg3521 - -lemma sg11835 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg527 sg3521 - -lemma sg11836 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg528 sg3521 - -lemma sg11837 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg529 sg3521 - -lemma sg11838 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg530 sg3521 - -lemma sg11839 : RowSquare [8,6,2,2,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg4345 - -lemma sg11840 : RowSquare [8,6,2,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg4345 - -lemma sg11841 : RowSquare [8,6,2,2,2,2,1,1] [4,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg807 sg2546 - -lemma sg11842 : RowSquare [8,6,2,2,2,2,1,1] [4,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg808 sg2546 - -lemma sg11843 : RowSquare [8,6,2,2,2,2,1,1] [4,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg809 sg2546 - -lemma sg11844 : RowSquare [8,6,2,2,2,2,1,1] [4,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg656 sg3161 - -lemma sg11845 : RowSquare [8,6,2,2,2,2,1,1] [4,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg364 sg3802 - -lemma sg11846 : RowSquare [8,6,2,2,2,2,1,1] [5,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg811 sg2546 - -lemma sg11847 : RowSquare [8,6,2,2,2,2,1,1] [5,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg807 sg2547 - -lemma sg11848 : RowSquare [8,6,2,2,2,2,1,1] [5,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg813 sg2546 - -lemma sg11849 : RowSquare [8,6,2,2,2,2,1,1] [5,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg808 sg2547 - -lemma sg11850 : RowSquare [8,6,2,2,2,2,1,1] [5,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg809 sg2547 - -lemma sg11851 : RowSquare [8,6,2,2,2,2,1,1] [5,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg364 sg3801 - -lemma sg11852 : RowSquare [8,6,2,2,2,2,1,1] [5,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg814 sg2546 - -lemma sg11853 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg807 sg2548 - -lemma sg11854 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1205 sg2058 - -lemma sg11855 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg816 sg2546 - -lemma sg11856 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg808 sg2548 - -lemma sg11857 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg1208 sg2044 - -lemma sg11858 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg809 sg2548 - -lemma sg11859 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg1207 sg2044 - -lemma sg11860 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg807 sg2549 - -lemma sg11861 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg8689 - -lemma sg11862 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg8690 - -lemma sg11863 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg808 sg2549 - -lemma sg11864 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg809 sg2549 - -lemma sg11865 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,4,3,2] := by - exact rowSquare_join (by decide) sg1207 sg2043 - -lemma sg11866 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg762 sg2581 - -lemma sg11867 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg7462 - -lemma sg11868 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg13 sg7463 - -lemma sg11869 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg13 sg7464 - -lemma sg11870 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,5,4] := by - exact rowSquare_join (by decide) sg762 sg2582 - -lemma sg11871 : RowSquare [8,6,2,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg10581 - -lemma sg11872 : RowSquare [8,6,2,2,2,2,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8682 - -lemma sg11873 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg8691 - -lemma sg11874 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7465 - -lemma sg11875 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg10582 - -lemma sg11876 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg10583 - -lemma sg11877 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg10584 - -lemma sg11878 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg10585 - -lemma sg11879 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg10586 - -lemma sg11880 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg10587 - -lemma sg11881 : RowSquare [8,6,2,2,2,2,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8683 - -lemma sg11882 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7256 - -lemma sg11883 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11509 - -lemma sg11884 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11510 - -lemma sg11885 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11511 - -lemma sg11886 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11512 - -lemma sg11887 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11513 - -lemma sg11888 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg11514 - -lemma sg11889 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7257 - -lemma sg11890 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6126 - -lemma sg11891 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg8692 - -lemma sg11892 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg8693 - -lemma sg11893 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg8694 - -lemma sg11894 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg8695 - -lemma sg11895 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg8696 - -lemma sg11896 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6127 - -lemma sg11897 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11515 - -lemma sg11898 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11516 - -lemma sg11899 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11517 - -lemma sg11900 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg11518 - -lemma sg11901 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11519 - -lemma sg11902 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11520 - -lemma sg11903 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg11521 - -lemma sg11904 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg11522 - -lemma sg11905 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11523 - -lemma sg11906 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg810 sg2547 - -lemma sg11907 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg818 sg2546 - -lemma sg11908 : RowSquare [8,6,2,2,2,2,1,1] [6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7256 - -lemma sg11909 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7258 - -lemma sg11910 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6128 - -lemma sg11911 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8684 - -lemma sg11912 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8685 - -lemma sg11913 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8686 - -lemma sg11914 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg8687 - -lemma sg11915 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg8688 - -lemma sg11916 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6126 - -lemma sg11917 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6129 - -lemma sg11918 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg8697 - -lemma sg11919 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg8698 - -lemma sg11920 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg8699 - -lemma sg11921 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg8700 - -lemma sg11922 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6130 - -lemma sg11923 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11524 - -lemma sg11924 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11525 - -lemma sg11925 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg11526 - -lemma sg11926 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg39 sg6131 - -lemma sg11927 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11527 - -lemma sg11928 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg769 sg2576 - -lemma sg11929 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1202 sg2039 - -lemma sg11930 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg11528 - -lemma sg11931 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg811 sg2547 - -lemma sg11932 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7259 - -lemma sg11933 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg5278 - -lemma sg11934 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7260 - -lemma sg11935 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7261 - -lemma sg11936 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg16 sg7262 - -lemma sg11937 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg97 sg5281 - -lemma sg11938 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6132 - -lemma sg11939 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11529 - -lemma sg11940 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg763 sg2577 - -lemma sg11941 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg810 sg2549 - -lemma sg11942 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg762 sg2583 - -lemma sg11943 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg763 sg2578 - -lemma sg11944 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg1203 sg2039 - -lemma sg11945 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg807 sg2550 - -lemma sg11946 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6133 - -lemma sg11947 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg764 sg2577 - -lemma sg11948 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg98 sg5279 - -lemma sg11949 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg820 sg2546 - -lemma sg11950 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg762 sg2584 - -lemma sg11951 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1204 sg2039 - -lemma sg11952 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg808 sg2550 - -lemma sg11953 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1205 sg2039 - -lemma sg11954 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg809 sg2550 - -lemma sg11955 : RowSquare [8,6,2,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7258 - -lemma sg11956 : RowSquare [8,6,2,2,2,2,1,1] [6,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6128 - -lemma sg11957 : RowSquare [8,6,2,2,2,2,1,1] [6,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7466 - -lemma sg11958 : RowSquare [8,6,2,2,2,2,1,1] [6,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1681 sg1608 - -lemma sg11959 : RowSquare [8,6,2,2,2,2,1,1] [6,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1681 sg1607 - -lemma sg11960 : RowSquare [8,6,2,2,2,2,1,1] [6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1681 sg1605 - -lemma sg11961 : RowSquare [8,6,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1681 sg1603 - -lemma sg11962 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6129 - -lemma sg11963 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6134 - -lemma sg11964 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7265 - -lemma sg11965 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7266 - -lemma sg11966 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg16 sg7267 - -lemma sg11967 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg40 sg6131 - -lemma sg11968 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7467 - -lemma sg11969 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7468 - -lemma sg11970 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg765 sg2577 - -lemma sg11971 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1202 sg2040 - -lemma sg11972 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg762 sg2585 - -lemma sg11973 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2041 - -lemma sg11974 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1206 sg2039 - -lemma sg11975 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg814 sg2547 - -lemma sg11976 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg5282 - -lemma sg11977 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6136 - -lemma sg11978 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg8701 - -lemma sg11979 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg763 sg2579 - -lemma sg11980 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1202 sg2042 - -lemma sg11981 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg4625 - -lemma sg11982 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg764 sg2579 - -lemma sg11983 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg207 sg4626 - -lemma sg11984 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1203 sg2040 - -lemma sg11985 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2043 - -lemma sg11986 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg1203 sg2041 - -lemma sg11987 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg8702 - -lemma sg11988 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg767 sg2577 - -lemma sg11989 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2044 - -lemma sg11990 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1204 sg2040 - -lemma sg11991 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1205 sg2040 - -lemma sg11992 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg1204 sg2041 - -lemma sg11993 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg1205 sg2041 - -lemma sg11994 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg5283 - -lemma sg11995 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg4627 - -lemma sg11996 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg773 sg2576 - -lemma sg11997 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg209 sg4624 - -lemma sg11998 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1203 sg2042 - -lemma sg11999 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg768 sg2577 - -lemma sg12000 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg768 sg2578 - -lemma sg12001 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg1204 sg2042 - -lemma sg12002 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg1203 sg2043 - -lemma sg12003 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg763 sg2581 - -lemma sg12004 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg3798 - -lemma sg12005 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg1203 sg2044 - -lemma sg12006 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg808 sg2552 - -lemma sg12007 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg1204 sg2043 - -lemma sg12008 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg456 sg3279 - -lemma sg12009 : RowSquare [8,6,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7263 - -lemma sg12010 : RowSquare [8,6,2,2,2,2,1,1] [6,6,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7264 - -lemma sg12011 : RowSquare [8,6,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7469 - -lemma sg12012 : RowSquare [8,6,2,2,2,2,1,1] [6,6,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7265 - -lemma sg12013 : RowSquare [8,6,2,2,2,2,1,1] [6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7266 - -lemma sg12014 : RowSquare [8,6,2,2,2,2,1,1] [6,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg7267 - -lemma sg12015 : RowSquare [8,6,2,2,2,2,1,1] [6,6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg7268 - -lemma sg12016 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6134 - -lemma sg12017 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7470 - -lemma sg12018 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1680 sg1604 - -lemma sg12019 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg765 sg2579 - -lemma sg12020 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg40 sg6135 - -lemma sg12021 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7471 - -lemma sg12022 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg774 sg2576 - -lemma sg12023 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg7472 - -lemma sg12024 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1206 sg2040 - -lemma sg12025 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg762 sg2586 - -lemma sg12026 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1206 sg2041 - -lemma sg12027 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg97 sg5286 - -lemma sg12028 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6136 - -lemma sg12029 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg4628 - -lemma sg12030 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg766 sg2579 - -lemma sg12031 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg210 sg4624 - -lemma sg12032 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1206 sg2042 - -lemma sg12033 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg767 sg2579 - -lemma sg12034 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg4629 - -lemma sg12035 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg807 sg2556 - -lemma sg12036 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1206 sg2043 - -lemma sg12037 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,3,3,2] := by - exact rowSquare_join (by decide) sg765 sg2581 - -lemma sg12038 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg3799 - -lemma sg12039 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1206 sg2044 - -lemma sg12040 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,4,2,2] := by - exact rowSquare_join (by decide) sg808 sg2556 - -lemma sg12041 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg5284 - -lemma sg12042 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg768 sg2579 - -lemma sg12043 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg5285 - -lemma sg12044 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg807 sg2558 - -lemma sg12045 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg3800 - -lemma sg12046 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg1207 sg2042 - -lemma sg12047 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg807 sg2559 - -lemma sg12048 : RowSquare [8,6,2,2,2,2,1,1] [6,6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg459 sg3278 - -lemma sg12049 : RowSquare [8,6,2,2,2,2,1,1] [6,6,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg4630 - -lemma sg12050 : RowSquare [8,6,2,2,2,2,1,1] [6,6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg1208 sg2042 - -lemma sg12051 : RowSquare [8,6,2,2,2,2,1,1] [6,6,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg807 sg2561 - -lemma sg12052 : RowSquare [8,6,2,2,2,2,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg8682 - -lemma sg12053 : RowSquare [8,6,2,2,2,2,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8691 - -lemma sg12054 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7269 - -lemma sg12055 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7473 - -lemma sg12056 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg10588 - -lemma sg12057 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg10589 - -lemma sg12058 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg10590 - -lemma sg12059 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg10591 - -lemma sg12060 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg10592 - -lemma sg12061 : RowSquare [8,6,2,2,2,2,1,1] [7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7269 - -lemma sg12062 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7270 - -lemma sg12063 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6137 - -lemma sg12064 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8692 - -lemma sg12065 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8693 - -lemma sg12066 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8694 - -lemma sg12067 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg8695 - -lemma sg12068 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg8696 - -lemma sg12069 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg6126 - -lemma sg12070 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6138 - -lemma sg12071 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg8703 - -lemma sg12072 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg8704 - -lemma sg12073 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg8705 - -lemma sg12074 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg8706 - -lemma sg12075 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg5280 - -lemma sg12076 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7474 - -lemma sg12077 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7475 - -lemma sg12078 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg7476 - -lemma sg12079 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg98 sg5281 - -lemma sg12080 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg10593 - -lemma sg12081 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg776 sg2576 - -lemma sg12082 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1209 sg2039 - -lemma sg12083 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg810 sg2550 - -lemma sg12084 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg818 sg2547 - -lemma sg12085 : RowSquare [8,6,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7270 - -lemma sg12086 : RowSquare [8,6,2,2,2,2,1,1] [7,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6137 - -lemma sg12087 : RowSquare [8,6,2,2,2,2,1,1] [7,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6139 - -lemma sg12088 : RowSquare [8,6,2,2,2,2,1,1] [7,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8697 - -lemma sg12089 : RowSquare [8,6,2,2,2,2,1,1] [7,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8698 - -lemma sg12090 : RowSquare [8,6,2,2,2,2,1,1] [7,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8699 - -lemma sg12091 : RowSquare [8,6,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg8700 - -lemma sg12092 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6138 - -lemma sg12093 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg5282 - -lemma sg12094 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7271 - -lemma sg12095 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7272 - -lemma sg12096 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg16 sg7273 - -lemma sg12097 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg99 sg5281 - -lemma sg12098 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6140 - -lemma sg12099 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11530 - -lemma sg12100 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg769 sg2577 - -lemma sg12101 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1202 sg2045 - -lemma sg12102 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg762 sg2587 - -lemma sg12103 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2046 - -lemma sg12104 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1210 sg2039 - -lemma sg12105 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg811 sg2550 - -lemma sg12106 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg5287 - -lemma sg12107 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg5283 - -lemma sg12108 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7274 - -lemma sg12109 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg763 sg2583 - -lemma sg12110 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1209 sg2042 - -lemma sg12111 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg4631 - -lemma sg12112 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg764 sg2583 - -lemma sg12113 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg810 sg2552 - -lemma sg12114 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1203 sg2045 - -lemma sg12115 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1209 sg2043 - -lemma sg12116 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg1203 sg2046 - -lemma sg12117 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg770 sg2577 - -lemma sg12118 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1209 sg2044 - -lemma sg12119 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1204 sg2045 - -lemma sg12120 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1205 sg2045 - -lemma sg12121 : RowSquare [8,6,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg6128 - -lemma sg12122 : RowSquare [8,6,2,2,2,2,1,1] [7,5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6139 - -lemma sg12123 : RowSquare [8,6,2,2,2,2,1,1] [7,5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6141 - -lemma sg12124 : RowSquare [8,6,2,2,2,2,1,1] [7,5,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7271 - -lemma sg12125 : RowSquare [8,6,2,2,2,2,1,1] [7,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7272 - -lemma sg12126 : RowSquare [8,6,2,2,2,2,1,1] [7,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg7273 - -lemma sg12127 : RowSquare [8,6,2,2,2,2,1,1] [7,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg42 sg6131 - -lemma sg12128 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg5289 - -lemma sg12129 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6142 - -lemma sg12130 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7276 - -lemma sg12131 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg763 sg2585 - -lemma sg12132 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1202 sg2047 - -lemma sg12133 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg4625 - -lemma sg12134 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg764 sg2585 - -lemma sg12135 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2048 - -lemma sg12136 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1206 sg2045 - -lemma sg12137 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2049 - -lemma sg12138 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1206 sg2046 - -lemma sg12139 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg5290 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes27 + +namespace OAI + +/-! Semigroup Nodes 28. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg11740 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg1757 + +lemma sg11741 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg1758 + +lemma sg11742 : RowSquare [7,5,2,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg910 sg2702 + +lemma sg11743 : RowSquare [7,5,3,2,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg321 sg4160 + +lemma sg11744 : RowSquare [7,5,3,2,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg316 sg4161 + +lemma sg11745 : RowSquare [7,5,3,2,1,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg324 sg4160 + +lemma sg11746 : RowSquare [7,5,3,2,1,1,1,1,1,1,1] [6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg327 sg4160 + +lemma sg11747 : RowSquare [7,5,3,2,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg324 sg4161 + +lemma sg11748 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1327 sg2251 + +lemma sg11749 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1328 sg2251 + +lemma sg11750 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1327 sg2252 + +lemma sg11751 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg2251 + +lemma sg11752 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1327 sg2253 + +lemma sg11753 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg2251 + +lemma sg11754 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg2251 + +lemma sg11755 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1332 sg2251 + +lemma sg11756 : RowSquare [7,6,1,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1328 sg2252 + +lemma sg11757 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1257 sg2251 + +lemma sg11758 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg893 sg2702 + +lemma sg11759 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg894 sg2702 + +lemma sg11760 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg895 sg2702 + +lemma sg11761 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg896 sg2702 + +lemma sg11762 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg897 sg2702 + +lemma sg11763 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg898 sg2702 + +lemma sg11764 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1261 sg2251 + +lemma sg11765 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg899 sg2702 + +lemma sg11766 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1262 sg2251 + +lemma sg11767 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1263 sg2251 + +lemma sg11768 : RowSquare [7,6,2,2,2,2,2,1] [5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg10875 + +lemma sg11769 : RowSquare [7,6,2,2,2,2,2,1] [5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg10876 + +lemma sg11770 : RowSquare [7,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg10877 + +lemma sg11771 : RowSquare [7,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg10878 + +lemma sg11772 : RowSquare [7,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg10879 + +lemma sg11773 : RowSquare [7,6,2,2,2,2,2,1] [5,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg10880 + +lemma sg11774 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg10882 + +lemma sg11775 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg10883 + +lemma sg11776 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg10884 + +lemma sg11777 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg10885 + +lemma sg11778 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg10886 + +lemma sg11779 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg10887 + +lemma sg11780 : RowSquare [7,6,2,2,2,2,2,1] [5,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg10888 + +lemma sg11781 : RowSquare [7,6,2,2,2,2,2,1] [6,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg10899 + +lemma sg11782 : RowSquare [7,6,2,2,2,2,2,1] [6,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg10900 + +lemma sg11783 : RowSquare [7,6,2,2,2,2,2,1] [6,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg10901 + +lemma sg11784 : RowSquare [7,6,2,2,2,2,2,1] [6,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg10902 + +lemma sg11785 : RowSquare [7,6,2,2,2,2,2,1] [6,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg10903 + +lemma sg11786 : RowSquare [7,6,3,2,1,1,1,1,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg263 sg4160 + +lemma sg11787 : RowSquare [7,6,3,2,1,1,1,1,1,1] [7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg266 sg4160 + +lemma sg11788 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1245 sg2251 + +lemma sg11789 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1246 sg2251 + +lemma sg11790 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1247 sg2251 + +lemma sg11791 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1248 sg2251 + +lemma sg11792 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1249 sg2251 + +lemma sg11793 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1250 sg2251 + +lemma sg11794 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1251 sg2251 + +lemma sg11795 : RowSquare [7,7,2,2,2,2,2] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1176 sg2105 + +lemma sg11796 : RowSquare [7,7,2,2,2,2,2] [2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1169 sg2105 + +lemma sg11797 : RowSquare [7,7,2,2,2,2,2] [2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1169 sg2104 + +lemma sg11798 : RowSquare [7,7,2,2,2,2,2] [2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1169 sg2103 + +lemma sg11799 : RowSquare [7,7,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1169 sg2101 + +lemma sg11800 : RowSquare [7,7,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1169 sg2097 + +lemma sg11801 : RowSquare [7,7,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg367 sg3789 + +lemma sg11802 : RowSquare [7,7,2,2,2,2,2] [3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1173 sg2105 + +lemma sg11803 : RowSquare [7,7,2,2,2,2,2] [3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1164 sg2105 + +lemma sg11804 : RowSquare [7,7,2,2,2,2,2] [3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1164 sg2104 + +lemma sg11805 : RowSquare [7,7,2,2,2,2,2] [3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1164 sg2102 + +lemma sg11806 : RowSquare [7,7,2,2,2,2,2] [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1170 sg2105 + +lemma sg11807 : RowSquare [7,7,2,2,2,2,2] [3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1167 sg2105 + +lemma sg11808 : RowSquare [7,7,2,2,2,2,2] [3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1163 sg2104 + +lemma sg11809 : RowSquare [7,7,2,2,2,2,2] [3,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1163 sg2099 + +lemma sg11810 : RowSquare [7,7,2,2,2,2,2] [3,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1164 sg2092 + +lemma sg11811 : RowSquare [7,7,2,2,2,2,2] [3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg83 sg5293 + +lemma sg11812 : RowSquare [7,7,2,2,2,2,2] [4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1166 sg2105 + +lemma sg11813 : RowSquare [7,7,2,2,2,2,2] [4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1156 sg2104 + +lemma sg11814 : RowSquare [7,7,2,2,2,2,2] [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1160 sg2105 + +lemma sg11815 : RowSquare [7,7,2,2,2,2,2] [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1153 sg2103 + +lemma sg11816 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1147 sg2100 + +lemma sg11817 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1147 sg2098 + +lemma sg11818 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1147 sg2095 + +lemma sg11819 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1147 sg2091 + +lemma sg11820 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1150 sg2094 + +lemma sg11821 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1147 sg2094 + +lemma sg11822 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1147 sg2090 + +lemma sg11823 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1147 sg2089 + +lemma sg11824 : RowSquare [7,7,2,2,2,2,2] [5,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1150 sg2088 + +lemma sg11825 : RowSquare [7,7,2,2,2,2,2] [5,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1147 sg2087 + +lemma sg11826 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg517 sg3521 + +lemma sg11827 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg518 sg3521 + +lemma sg11828 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg519 sg3521 + +lemma sg11829 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg520 sg3521 + +lemma sg11830 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg521 sg3521 + +lemma sg11831 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg522 sg3521 + +lemma sg11832 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg523 sg3521 + +lemma sg11833 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg524 sg3521 + +lemma sg11834 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg525 sg3521 + +lemma sg11835 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg527 sg3521 + +lemma sg11836 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg528 sg3521 + +lemma sg11837 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg529 sg3521 + +lemma sg11838 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg530 sg3521 + +lemma sg11839 : RowSquare [8,6,2,2,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg4345 + +lemma sg11840 : RowSquare [8,6,2,2,1,1,1,1,1,1] [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg4345 + +lemma sg11841 : RowSquare [8,6,2,2,2,2,1,1] [4,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg807 sg2546 + +lemma sg11842 : RowSquare [8,6,2,2,2,2,1,1] [4,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg808 sg2546 + +lemma sg11843 : RowSquare [8,6,2,2,2,2,1,1] [4,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg809 sg2546 + +lemma sg11844 : RowSquare [8,6,2,2,2,2,1,1] [4,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg656 sg3161 + +lemma sg11845 : RowSquare [8,6,2,2,2,2,1,1] [4,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg364 sg3802 + +lemma sg11846 : RowSquare [8,6,2,2,2,2,1,1] [5,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg811 sg2546 + +lemma sg11847 : RowSquare [8,6,2,2,2,2,1,1] [5,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg807 sg2547 + +lemma sg11848 : RowSquare [8,6,2,2,2,2,1,1] [5,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg813 sg2546 + +lemma sg11849 : RowSquare [8,6,2,2,2,2,1,1] [5,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg808 sg2547 + +lemma sg11850 : RowSquare [8,6,2,2,2,2,1,1] [5,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg809 sg2547 + +lemma sg11851 : RowSquare [8,6,2,2,2,2,1,1] [5,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg364 sg3801 + +lemma sg11852 : RowSquare [8,6,2,2,2,2,1,1] [5,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg814 sg2546 + +lemma sg11853 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg807 sg2548 + +lemma sg11854 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1205 sg2058 + +lemma sg11855 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg816 sg2546 + +lemma sg11856 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg808 sg2548 + +lemma sg11857 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg1208 sg2044 + +lemma sg11858 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg809 sg2548 + +lemma sg11859 : RowSquare [8,6,2,2,2,2,1,1] [5,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg1207 sg2044 + +lemma sg11860 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg807 sg2549 + +lemma sg11861 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg8689 + +lemma sg11862 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg8690 + +lemma sg11863 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg808 sg2549 + +lemma sg11864 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg809 sg2549 + +lemma sg11865 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,4,3,2] := by + exact rowSquare_join (by decide) sg1207 sg2043 + +lemma sg11866 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg762 sg2581 + +lemma sg11867 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg7462 + +lemma sg11868 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg13 sg7463 + +lemma sg11869 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg13 sg7464 + +lemma sg11870 : RowSquare [8,6,2,2,2,2,1,1] [5,5,5,5,4] := by + exact rowSquare_join (by decide) sg762 sg2582 + +lemma sg11871 : RowSquare [8,6,2,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg10581 + +lemma sg11872 : RowSquare [8,6,2,2,2,2,1,1] [6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8682 + +lemma sg11873 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg8691 + +lemma sg11874 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7465 + +lemma sg11875 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg10582 + +lemma sg11876 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg10583 + +lemma sg11877 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg10584 + +lemma sg11878 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg10585 + +lemma sg11879 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg10586 + +lemma sg11880 : RowSquare [8,6,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg10587 + +lemma sg11881 : RowSquare [8,6,2,2,2,2,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8683 + +lemma sg11882 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7256 + +lemma sg11883 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11509 + +lemma sg11884 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11510 + +lemma sg11885 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11511 + +lemma sg11886 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11512 + +lemma sg11887 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11513 + +lemma sg11888 : RowSquare [8,6,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg11514 + +lemma sg11889 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7257 + +lemma sg11890 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6126 + +lemma sg11891 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg8692 + +lemma sg11892 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg8693 + +lemma sg11893 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg8694 + +lemma sg11894 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg8695 + +lemma sg11895 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg8696 + +lemma sg11896 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6127 + +lemma sg11897 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11515 + +lemma sg11898 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11516 + +lemma sg11899 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11517 + +lemma sg11900 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg11518 + +lemma sg11901 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11519 + +lemma sg11902 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11520 + +lemma sg11903 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg11521 + +lemma sg11904 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg11522 + +lemma sg11905 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11523 + +lemma sg11906 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg810 sg2547 + +lemma sg11907 : RowSquare [8,6,2,2,2,2,1,1] [6,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg818 sg2546 + +lemma sg11908 : RowSquare [8,6,2,2,2,2,1,1] [6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7256 + +lemma sg11909 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7258 + +lemma sg11910 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6128 + +lemma sg11911 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8684 + +lemma sg11912 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8685 + +lemma sg11913 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8686 + +lemma sg11914 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg8687 + +lemma sg11915 : RowSquare [8,6,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg8688 + +lemma sg11916 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6126 + +lemma sg11917 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6129 + +lemma sg11918 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg8697 + +lemma sg11919 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg8698 + +lemma sg11920 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg8699 + +lemma sg11921 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg8700 + +lemma sg11922 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6130 + +lemma sg11923 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11524 + +lemma sg11924 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11525 + +lemma sg11925 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg11526 + +lemma sg11926 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg39 sg6131 + +lemma sg11927 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11527 + +lemma sg11928 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg769 sg2576 + +lemma sg11929 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1202 sg2039 + +lemma sg11930 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg11528 + +lemma sg11931 : RowSquare [8,6,2,2,2,2,1,1] [6,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg811 sg2547 + +lemma sg11932 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7259 + +lemma sg11933 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg5278 + +lemma sg11934 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7260 + +lemma sg11935 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7261 + +lemma sg11936 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg16 sg7262 + +lemma sg11937 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg97 sg5281 + +lemma sg11938 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6132 + +lemma sg11939 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11529 + +lemma sg11940 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg763 sg2577 + +lemma sg11941 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg810 sg2549 + +lemma sg11942 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg762 sg2583 + +lemma sg11943 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg763 sg2578 + +lemma sg11944 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg1203 sg2039 + +lemma sg11945 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg807 sg2550 + +lemma sg11946 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6133 + +lemma sg11947 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg764 sg2577 + +lemma sg11948 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg98 sg5279 + +lemma sg11949 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg820 sg2546 + +lemma sg11950 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg762 sg2584 + +lemma sg11951 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1204 sg2039 + +lemma sg11952 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg808 sg2550 + +lemma sg11953 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1205 sg2039 + +lemma sg11954 : RowSquare [8,6,2,2,2,2,1,1] [6,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg809 sg2550 + +lemma sg11955 : RowSquare [8,6,2,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7258 + +lemma sg11956 : RowSquare [8,6,2,2,2,2,1,1] [6,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6128 + +lemma sg11957 : RowSquare [8,6,2,2,2,2,1,1] [6,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7466 + +lemma sg11958 : RowSquare [8,6,2,2,2,2,1,1] [6,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1681 sg1608 + +lemma sg11959 : RowSquare [8,6,2,2,2,2,1,1] [6,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1681 sg1607 + +lemma sg11960 : RowSquare [8,6,2,2,2,2,1,1] [6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1681 sg1605 + +lemma sg11961 : RowSquare [8,6,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1681 sg1603 + +lemma sg11962 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6129 + +lemma sg11963 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6134 + +lemma sg11964 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7265 + +lemma sg11965 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7266 + +lemma sg11966 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg16 sg7267 + +lemma sg11967 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg40 sg6131 + +lemma sg11968 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7467 + +lemma sg11969 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7468 + +lemma sg11970 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg765 sg2577 + +lemma sg11971 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1202 sg2040 + +lemma sg11972 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg762 sg2585 + +lemma sg11973 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2041 + +lemma sg11974 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1206 sg2039 + +lemma sg11975 : RowSquare [8,6,2,2,2,2,1,1] [6,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg814 sg2547 + +lemma sg11976 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg5282 + +lemma sg11977 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6136 + +lemma sg11978 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg8701 + +lemma sg11979 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg763 sg2579 + +lemma sg11980 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1202 sg2042 + +lemma sg11981 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg4625 + +lemma sg11982 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg764 sg2579 + +lemma sg11983 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg207 sg4626 + +lemma sg11984 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1203 sg2040 + +lemma sg11985 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2043 + +lemma sg11986 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg1203 sg2041 + +lemma sg11987 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg8702 + +lemma sg11988 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg767 sg2577 + +lemma sg11989 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2044 + +lemma sg11990 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1204 sg2040 + +lemma sg11991 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1205 sg2040 + +lemma sg11992 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg1204 sg2041 + +lemma sg11993 : RowSquare [8,6,2,2,2,2,1,1] [6,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg1205 sg2041 + +lemma sg11994 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg5283 + +lemma sg11995 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg4627 + +lemma sg11996 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg773 sg2576 + +lemma sg11997 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg209 sg4624 + +lemma sg11998 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1203 sg2042 + +lemma sg11999 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg768 sg2577 + +lemma sg12000 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg768 sg2578 + +lemma sg12001 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg1204 sg2042 + +lemma sg12002 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg1203 sg2043 + +lemma sg12003 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg763 sg2581 + +lemma sg12004 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg3798 + +lemma sg12005 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg1203 sg2044 + +lemma sg12006 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg808 sg2552 + +lemma sg12007 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg1204 sg2043 + +lemma sg12008 : RowSquare [8,6,2,2,2,2,1,1] [6,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg456 sg3279 + +lemma sg12009 : RowSquare [8,6,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7263 + +lemma sg12010 : RowSquare [8,6,2,2,2,2,1,1] [6,6,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7264 + +lemma sg12011 : RowSquare [8,6,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7469 + +lemma sg12012 : RowSquare [8,6,2,2,2,2,1,1] [6,6,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7265 + +lemma sg12013 : RowSquare [8,6,2,2,2,2,1,1] [6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7266 + +lemma sg12014 : RowSquare [8,6,2,2,2,2,1,1] [6,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg7267 + +lemma sg12015 : RowSquare [8,6,2,2,2,2,1,1] [6,6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg7268 + +lemma sg12016 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6134 + +lemma sg12017 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7470 + +lemma sg12018 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1680 sg1604 + +lemma sg12019 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg765 sg2579 + +lemma sg12020 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg40 sg6135 + +lemma sg12021 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7471 + +lemma sg12022 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg774 sg2576 + +lemma sg12023 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg7472 + +lemma sg12024 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1206 sg2040 + +lemma sg12025 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg762 sg2586 + +lemma sg12026 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1206 sg2041 + +lemma sg12027 : RowSquare [8,6,2,2,2,2,1,1] [6,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg97 sg5286 + +lemma sg12028 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6136 + +lemma sg12029 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg4628 + +lemma sg12030 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg766 sg2579 + +lemma sg12031 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg210 sg4624 + +lemma sg12032 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1206 sg2042 + +lemma sg12033 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg767 sg2579 + +lemma sg12034 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg4629 + +lemma sg12035 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg807 sg2556 + +lemma sg12036 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1206 sg2043 + +lemma sg12037 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,3,3,2] := by + exact rowSquare_join (by decide) sg765 sg2581 + +lemma sg12038 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg3799 + +lemma sg12039 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1206 sg2044 + +lemma sg12040 : RowSquare [8,6,2,2,2,2,1,1] [6,6,4,4,2,2] := by + exact rowSquare_join (by decide) sg808 sg2556 + +lemma sg12041 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg5284 + +lemma sg12042 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg768 sg2579 + +lemma sg12043 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg5285 + +lemma sg12044 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg807 sg2558 + +lemma sg12045 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg3800 + +lemma sg12046 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg1207 sg2042 + +lemma sg12047 : RowSquare [8,6,2,2,2,2,1,1] [6,6,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg807 sg2559 + +lemma sg12048 : RowSquare [8,6,2,2,2,2,1,1] [6,6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg459 sg3278 + +lemma sg12049 : RowSquare [8,6,2,2,2,2,1,1] [6,6,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg4630 + +lemma sg12050 : RowSquare [8,6,2,2,2,2,1,1] [6,6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg1208 sg2042 + +lemma sg12051 : RowSquare [8,6,2,2,2,2,1,1] [6,6,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg807 sg2561 + +lemma sg12052 : RowSquare [8,6,2,2,2,2,1,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg8682 + +lemma sg12053 : RowSquare [8,6,2,2,2,2,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8691 + +lemma sg12054 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7269 + +lemma sg12055 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7473 + +lemma sg12056 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg10588 + +lemma sg12057 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg10589 + +lemma sg12058 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg10590 + +lemma sg12059 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg10591 + +lemma sg12060 : RowSquare [8,6,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg10592 + +lemma sg12061 : RowSquare [8,6,2,2,2,2,1,1] [7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7269 + +lemma sg12062 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7270 + +lemma sg12063 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6137 + +lemma sg12064 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8692 + +lemma sg12065 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8693 + +lemma sg12066 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8694 + +lemma sg12067 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg8695 + +lemma sg12068 : RowSquare [8,6,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg8696 + +lemma sg12069 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg6126 + +lemma sg12070 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6138 + +lemma sg12071 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg8703 + +lemma sg12072 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg8704 + +lemma sg12073 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg8705 + +lemma sg12074 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg8706 + +lemma sg12075 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg5280 + +lemma sg12076 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7474 + +lemma sg12077 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7475 + +lemma sg12078 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg7476 + +lemma sg12079 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg98 sg5281 + +lemma sg12080 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg10593 + +lemma sg12081 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg776 sg2576 + +lemma sg12082 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1209 sg2039 + +lemma sg12083 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg810 sg2550 + +lemma sg12084 : RowSquare [8,6,2,2,2,2,1,1] [7,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg818 sg2547 + +lemma sg12085 : RowSquare [8,6,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7270 + +lemma sg12086 : RowSquare [8,6,2,2,2,2,1,1] [7,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6137 + +lemma sg12087 : RowSquare [8,6,2,2,2,2,1,1] [7,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6139 + +lemma sg12088 : RowSquare [8,6,2,2,2,2,1,1] [7,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8697 + +lemma sg12089 : RowSquare [8,6,2,2,2,2,1,1] [7,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8698 + +lemma sg12090 : RowSquare [8,6,2,2,2,2,1,1] [7,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8699 + +lemma sg12091 : RowSquare [8,6,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg8700 + +lemma sg12092 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6138 + +lemma sg12093 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg5282 + +lemma sg12094 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7271 + +lemma sg12095 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7272 + +lemma sg12096 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg16 sg7273 + +lemma sg12097 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg99 sg5281 + +lemma sg12098 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6140 + +lemma sg12099 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11530 + +lemma sg12100 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg769 sg2577 + +lemma sg12101 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1202 sg2045 + +lemma sg12102 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg762 sg2587 + +lemma sg12103 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2046 + +lemma sg12104 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1210 sg2039 + +lemma sg12105 : RowSquare [8,6,2,2,2,2,1,1] [7,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg811 sg2550 + +lemma sg12106 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg5287 + +lemma sg12107 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg5283 + +lemma sg12108 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7274 + +lemma sg12109 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg763 sg2583 + +lemma sg12110 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1209 sg2042 + +lemma sg12111 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg4631 + +lemma sg12112 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg764 sg2583 + +lemma sg12113 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg810 sg2552 + +lemma sg12114 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1203 sg2045 + +lemma sg12115 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1209 sg2043 + +lemma sg12116 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg1203 sg2046 + +lemma sg12117 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg770 sg2577 + +lemma sg12118 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1209 sg2044 + +lemma sg12119 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1204 sg2045 + +lemma sg12120 : RowSquare [8,6,2,2,2,2,1,1] [7,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1205 sg2045 + +lemma sg12121 : RowSquare [8,6,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg6128 + +lemma sg12122 : RowSquare [8,6,2,2,2,2,1,1] [7,5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6139 + +lemma sg12123 : RowSquare [8,6,2,2,2,2,1,1] [7,5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6141 + +lemma sg12124 : RowSquare [8,6,2,2,2,2,1,1] [7,5,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7271 + +lemma sg12125 : RowSquare [8,6,2,2,2,2,1,1] [7,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7272 + +lemma sg12126 : RowSquare [8,6,2,2,2,2,1,1] [7,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg7273 + +lemma sg12127 : RowSquare [8,6,2,2,2,2,1,1] [7,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg42 sg6131 + +lemma sg12128 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg5289 + +lemma sg12129 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6142 + +lemma sg12130 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7276 + +lemma sg12131 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg763 sg2585 + +lemma sg12132 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1202 sg2047 + +lemma sg12133 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg4625 + +lemma sg12134 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg764 sg2585 + +lemma sg12135 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2048 + +lemma sg12136 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1206 sg2045 + +lemma sg12137 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2049 + +lemma sg12138 : RowSquare [8,6,2,2,2,2,1,1] [7,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1206 sg2046 + +lemma sg12139 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg5290 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes29.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes29.lean index f1f9e58f7f443a3e0a514dad872cba8ec2a62e9b..023c90cc7e4f70251377c10d8738b4fe68bdb5d1 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes29.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes29.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes17 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes20 - -namespace OAI - -/-! Semigroup Nodes 29. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg12140 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg4632 - -lemma sg12141 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg766 sg2583 - -lemma sg12142 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2050 - -lemma sg12143 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1203 sg2047 - -lemma sg12144 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg767 sg2583 - -lemma sg12145 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2051 - -lemma sg12146 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1203 sg2048 - -lemma sg12147 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1203 sg2049 - -lemma sg12148 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2052 - -lemma sg12149 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1210 sg2044 - -lemma sg12150 : RowSquare [8,6,2,2,2,2,1,1] [7,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg4627 - -lemma sg12151 : RowSquare [8,6,2,2,2,2,1,1] [7,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg768 sg2583 - -lemma sg12152 : RowSquare [8,6,2,2,2,2,1,1] [7,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg810 sg2560 - -lemma sg12153 : RowSquare [8,6,2,2,2,2,1,1] [7,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg1203 sg2050 - -lemma sg12154 : RowSquare [8,6,2,2,2,2,1,1] [7,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg810 sg2561 - -lemma sg12155 : RowSquare [8,6,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7275 - -lemma sg12156 : RowSquare [8,6,2,2,2,2,1,1] [7,6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6141 - -lemma sg12157 : RowSquare [8,6,2,2,2,2,1,1] [7,6,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7477 - -lemma sg12158 : RowSquare [8,6,2,2,2,2,1,1] [7,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7276 - -lemma sg12159 : RowSquare [8,6,2,2,2,2,1,1] [7,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg765 sg2585 - -lemma sg12160 : RowSquare [8,6,2,2,2,2,1,1] [7,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1202 sg2053 - -lemma sg12161 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6142 - -lemma sg12162 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg4633 - -lemma sg12163 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg766 sg2585 - -lemma sg12164 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2054 - -lemma sg12165 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1203 sg2053 - -lemma sg12166 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg767 sg2585 - -lemma sg12167 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2055 - -lemma sg12168 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1206 sg2048 - -lemma sg12169 : RowSquare [8,6,2,2,2,2,1,1] [7,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg4628 - -lemma sg12170 : RowSquare [8,6,2,2,2,2,1,1] [7,6,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg768 sg2585 - -lemma sg12171 : RowSquare [8,6,2,2,2,2,1,1] [7,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2056 - -lemma sg12172 : RowSquare [8,6,2,2,2,2,1,1] [7,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2057 - -lemma sg12173 : RowSquare [8,6,2,2,2,2,1,1] [7,6,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg773 sg2579 - -lemma sg12174 : RowSquare [8,6,2,2,2,2,1,1] [7,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2058 - -lemma sg12175 : RowSquare [8,6,2,2,2,2,1,1] [7,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg459 sg3285 - -lemma sg12176 : RowSquare [8,6,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7277 - -lemma sg12177 : RowSquare [8,6,2,2,2,2,1,1] [7,7,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7278 - -lemma sg12178 : RowSquare [8,6,2,2,2,2,1,1] [7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7478 - -lemma sg12179 : RowSquare [8,6,2,2,2,2,1,1] [7,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg780 sg2576 - -lemma sg12180 : RowSquare [8,6,2,2,2,2,1,1] [7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg765 sg2586 - -lemma sg12181 : RowSquare [8,6,2,2,2,2,1,1] [7,7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1206 sg2053 - -lemma sg12182 : RowSquare [8,6,2,2,2,2,1,1] [7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg4628 - -lemma sg12183 : RowSquare [8,6,2,2,2,2,1,1] [7,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg774 sg2579 - -lemma sg12184 : RowSquare [8,6,2,2,2,2,1,1] [7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg766 sg2586 - -lemma sg12185 : RowSquare [8,6,2,2,2,2,1,1] [7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg767 sg2586 - -lemma sg12186 : RowSquare [8,6,2,2,2,2,1,1] [7,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg775 sg2579 - -lemma sg12187 : RowSquare [8,6,2,2,2,2,1,1] [7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg768 sg2586 - -lemma sg12188 : RowSquare [8,6,2,2,2,2,1,1] [7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg403 sg3788 - -lemma sg12189 : RowSquare [8,6,2,2,2,2,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg8691 - -lemma sg12190 : RowSquare [8,6,2,2,2,2,1,1] [8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg7269 - -lemma sg12191 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7279 - -lemma sg12192 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6143 - -lemma sg12193 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg8692 - -lemma sg12194 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg8693 - -lemma sg12195 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg8694 - -lemma sg12196 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6 sg8695 - -lemma sg12197 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6 sg8696 - -lemma sg12198 : RowSquare [8,6,2,2,2,2,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7279 - -lemma sg12199 : RowSquare [8,6,2,2,2,2,1,1] [8,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6143 - -lemma sg12200 : RowSquare [8,6,2,2,2,2,1,1] [8,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6144 - -lemma sg12201 : RowSquare [8,6,2,2,2,2,1,1] [8,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8703 - -lemma sg12202 : RowSquare [8,6,2,2,2,2,1,1] [8,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8704 - -lemma sg12203 : RowSquare [8,6,2,2,2,2,1,1] [8,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg8705 - -lemma sg12204 : RowSquare [8,6,2,2,2,2,1,1] [8,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg8706 - -lemma sg12205 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg6138 - -lemma sg12206 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg5287 - -lemma sg12207 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7280 - -lemma sg12208 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7281 - -lemma sg12209 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg16 sg7282 - -lemma sg12210 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg100 sg5281 - -lemma sg12211 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg5288 - -lemma sg12212 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg7479 - -lemma sg12213 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg776 sg2577 - -lemma sg12214 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1209 sg2045 - -lemma sg12215 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1678 sg1592 - -lemma sg12216 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1209 sg2046 - -lemma sg12217 : RowSquare [8,6,2,2,2,2,1,1] [8,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg6137 - -lemma sg12218 : RowSquare [8,6,2,2,2,2,1,1] [8,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6144 - -lemma sg12219 : RowSquare [8,6,2,2,2,2,1,1] [8,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg5289 - -lemma sg12220 : RowSquare [8,6,2,2,2,2,1,1] [8,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7280 - -lemma sg12221 : RowSquare [8,6,2,2,2,2,1,1] [8,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7281 - -lemma sg12222 : RowSquare [8,6,2,2,2,2,1,1] [8,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg7282 - -lemma sg12223 : RowSquare [8,6,2,2,2,2,1,1] [8,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1202 sg2059 - -lemma sg12224 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg5291 - -lemma sg12225 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg5290 - -lemma sg12226 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7283 - -lemma sg12227 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg763 sg2587 - -lemma sg12228 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1202 sg2060 - -lemma sg12229 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg4631 - -lemma sg12230 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1678 sg1593 - -lemma sg12231 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2061 - -lemma sg12232 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1679 sg1592 - -lemma sg12233 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg4050 - -lemma sg12234 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg4634 - -lemma sg12235 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1678 sg1594 - -lemma sg12236 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1209 sg2050 - -lemma sg12237 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg770 sg2583 - -lemma sg12238 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1209 sg2051 - -lemma sg12239 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1209 sg2052 - -lemma sg12240 : RowSquare [8,6,2,2,2,2,1,1] [8,5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg6139 - -lemma sg12241 : RowSquare [8,6,2,2,2,2,1,1] [8,5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg99 sg5289 - -lemma sg12242 : RowSquare [8,6,2,2,2,2,1,1] [8,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6145 - -lemma sg12243 : RowSquare [8,6,2,2,2,2,1,1] [8,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7283 - -lemma sg12244 : RowSquare [8,6,2,2,2,2,1,1] [8,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg765 sg2587 - -lemma sg12245 : RowSquare [8,6,2,2,2,2,1,1] [8,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1202 sg2062 - -lemma sg12246 : RowSquare [8,6,2,2,2,2,1,1] [8,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg4052 - -lemma sg12247 : RowSquare [8,6,2,2,2,2,1,1] [8,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg4635 - -lemma sg12248 : RowSquare [8,6,2,2,2,2,1,1] [8,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg766 sg2587 - -lemma sg12249 : RowSquare [8,6,2,2,2,2,1,1] [8,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2063 - -lemma sg12250 : RowSquare [8,6,2,2,2,2,1,1] [8,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1678 sg1595 - -lemma sg12251 : RowSquare [8,6,2,2,2,2,1,1] [8,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1679 sg1593 - -lemma sg12252 : RowSquare [8,6,2,2,2,2,1,1] [8,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg4632 - -lemma sg12253 : RowSquare [8,6,2,2,2,2,1,1] [8,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1678 sg1596 - -lemma sg12254 : RowSquare [8,6,2,2,2,2,1,1] [8,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1678 sg1597 - -lemma sg12255 : RowSquare [8,6,2,2,2,2,1,1] [8,6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg6141 - -lemma sg12256 : RowSquare [8,6,2,2,2,2,1,1] [8,6,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg4052 - -lemma sg12257 : RowSquare [8,6,2,2,2,2,1,1] [8,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg4633 - -lemma sg12258 : RowSquare [8,6,2,2,2,2,1,1] [8,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg771 sg2585 - -lemma sg12259 : RowSquare [8,6,2,2,2,2,1,1] [8,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg2064 - -lemma sg12260 : RowSquare [8,6,2,2,2,2,1,1] [8,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg4633 - -lemma sg12261 : RowSquare [8,6,2,2,2,2,1,1] [8,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg772 sg2585 - -lemma sg12262 : RowSquare [8,6,2,2,2,2,1,1] [8,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg773 sg2585 - -lemma sg12263 : RowSquare [8,6,2,2,2,2,1,1] [8,7,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg4052 - -lemma sg12264 : RowSquare [8,6,2,2,2,2,1,1] [8,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg4633 - -lemma sg12265 : RowSquare [8,6,2,2,2,2,1,1] [8,7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg774 sg2585 - -lemma sg12266 : RowSquare [8,6,2,2,2,2,1,1] [8,7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg775 sg2585 - -lemma sg12267 : RowSquare [8,6,2,2,2,2,1,1] [8,8,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7284 - -lemma sg12268 : RowSquare [8,6,2,2,2,2,1,1] [8,8,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg780 sg2579 - -lemma sg12269 : RowSquare [8,6,2,2,2,2,1,1] [9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg7269 - -lemma sg12270 : RowSquare [8,6,2,2,2,2,1,1] [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg7279 - -lemma sg12271 : RowSquare [8,6,2,2,2,2,1,1] [9,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg6143 - -lemma sg12272 : RowSquare [8,6,2,2,2,2,1,1] [9,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg6146 - -lemma sg12273 : RowSquare [8,6,2,2,2,2,1,1] [9,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg8703 - -lemma sg12274 : RowSquare [8,6,2,2,2,2,1,1] [9,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg8704 - -lemma sg12275 : RowSquare [8,6,2,2,2,2,1,1] [9,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg8705 - -lemma sg12276 : RowSquare [8,6,2,2,2,2,1,1] [9,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6 sg8706 - -lemma sg12277 : RowSquare [8,6,2,2,2,2,1,1] [9,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg6143 - -lemma sg12278 : RowSquare [8,6,2,2,2,2,1,1] [9,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg6146 - -lemma sg12279 : RowSquare [8,6,2,2,2,2,1,1] [9,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg5291 - -lemma sg12280 : RowSquare [8,6,2,2,2,2,1,1] [9,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg7280 - -lemma sg12281 : RowSquare [8,6,2,2,2,2,1,1] [9,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg7281 - -lemma sg12282 : RowSquare [8,6,2,2,2,2,1,1] [9,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18 sg7282 - -lemma sg12283 : RowSquare [8,6,2,2,2,2,1,1] [9,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg5292 - -lemma sg12284 : RowSquare [8,6,2,2,2,2,1,1] [9,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg4050 - -lemma sg12285 : RowSquare [8,6,2,2,2,2,1,1] [9,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg7285 - -lemma sg12286 : RowSquare [8,6,2,2,2,2,1,1] [9,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1678 sg1598 - -lemma sg12287 : RowSquare [8,6,2,2,2,2,1,1] [9,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg211 sg4631 - -lemma sg12288 : RowSquare [8,6,2,2,2,2,1,1] [9,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1678 sg1599 - -lemma sg12289 : RowSquare [8,6,2,2,2,2,1,1] [9,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg6144 - -lemma sg12290 : RowSquare [8,6,2,2,2,2,1,1] [9,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg99 sg5291 - -lemma sg12291 : RowSquare [8,6,2,2,2,2,1,1] [9,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg4052 - -lemma sg12292 : RowSquare [8,6,2,2,2,2,1,1] [9,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg7285 - -lemma sg12293 : RowSquare [8,6,2,2,2,2,1,1] [9,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1678 sg1600 - -lemma sg12294 : RowSquare [8,6,2,2,2,2,1,1] [9,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg4054 - -lemma sg12295 : RowSquare [8,6,2,2,2,2,1,1] [9,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg4636 - -lemma sg12296 : RowSquare [8,6,2,2,2,2,1,1] [9,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1678 sg1601 - -lemma sg12297 : RowSquare [8,6,2,2,2,2,1,1] [9,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1678 sg1602 - -lemma sg12298 : RowSquare [8,6,2,2,2,2,1,1] [9,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg4055 - -lemma sg12299 : RowSquare [8,6,2,2,2,2,1,1] [9,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg5289 - -lemma sg12300 : RowSquare [8,6,2,2,2,2,1,1] [9,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg4054 - -lemma sg12301 : RowSquare [8,6,2,2,2,2,1,1] [9,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg4635 - -lemma sg12302 : RowSquare [8,6,2,2,2,2,1,1] [9,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1678 sg1603 - -lemma sg12303 : RowSquare [8,6,2,2,2,2,1,1] [9,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg4056 - -lemma sg12304 : RowSquare [8,6,2,2,2,2,1,1] [9,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg4054 - -lemma sg12305 : RowSquare [8,6,2,2,2,2,1,1] [9,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg4056 - -lemma sg12306 : RowSquare [8,6,2,2,2,2,1,1] [9,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg4056 - -lemma sg12307 : RowSquare [8,6,2,2,2,2,1,1] [10,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg7279 - -lemma sg12308 : RowSquare [8,6,2,2,2,2,1,1] [10,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg6143 - -lemma sg12309 : RowSquare [8,6,2,2,2,2,1,1] [10,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg6146 - -lemma sg12310 : RowSquare [8,6,2,2,2,2,1,1] [10,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg5292 - -lemma sg12311 : RowSquare [8,6,2,2,2,2,1,1] [10,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg7280 - -lemma sg12312 : RowSquare [8,6,2,2,2,2,1,1] [10,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg7281 - -lemma sg12313 : RowSquare [8,6,2,2,2,2,1,1] [10,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg6146 - -lemma sg12314 : RowSquare [8,6,2,2,2,2,1,1] [10,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg99 sg5292 - -lemma sg12315 : RowSquare [8,6,2,2,2,2,1,1] [10,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg4054 - -lemma sg12316 : RowSquare [8,6,2,2,2,2,1,1] [10,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg7285 - -lemma sg12317 : RowSquare [8,6,2,2,2,2,1,1] [10,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg4058 - -lemma sg12318 : RowSquare [8,6,2,2,2,2,1,1] [10,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg4055 - -lemma sg12319 : RowSquare [8,6,2,2,2,2,1,1] [10,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg5291 - -lemma sg12320 : RowSquare [8,6,2,2,2,2,1,1] [10,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg4058 - -lemma sg12321 : RowSquare [8,6,2,2,2,2,1,1] [10,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg4056 - -lemma sg12322 : RowSquare [8,6,2,2,2,2,1,1] [10,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg4058 - -lemma sg12323 : RowSquare [8,6,2,2,2,2,1,1] [11,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg6143 - -lemma sg12324 : RowSquare [8,6,2,2,2,2,1,1] [11,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg6146 - -lemma sg12325 : RowSquare [8,6,2,2,2,2,1,1] [11,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg100 sg5292 - -lemma sg12326 : RowSquare [8,6,2,2,2,2,1,1] [11,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg4058 - -lemma sg12327 : RowSquare [8,6,2,2,2,2,1,1] [11,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg5292 - -lemma sg12328 : RowSquare [8,6,2,2,2,2,1,1] [11,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg243 sg4058 - -lemma sg12329 : RowSquare [8,6,2,2,2,2,1,1] [12,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg50 sg5733 - -lemma sg12330 : RowSquare [8,6,2,2,2,2,1,1] [12,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg102 sg5292 - -lemma sg12331 : RowSquare [9,3,2,2,2,2,2,2] [5,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg579 sg3209 - -lemma sg12332 : RowSquare [9,3,2,2,2,2,2,2] [6,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg579 sg3213 - -lemma sg12333 : RowSquare [10,3,2,2,2,2,2,1] [4,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg5528 - -lemma sg12334 : RowSquare [10,3,2,2,2,2,2,1] [5,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg74 sg5538 - -lemma sg12335 : RowSquare [10,3,2,2,2,2,2,1] [5,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg74 sg5544 - -lemma sg12336 : RowSquare [10,3,2,2,2,2,2,1] [5,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg5547 - -lemma sg12337 : RowSquare [10,3,2,2,2,2,2,1] [6,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg165 sg4748 - -lemma sg12338 : RowSquare [10,3,2,2,2,2,2,1] [6,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg356 sg3870 - -lemma sg12339 : RowSquare [10,4,2,2,2,2,2] [6,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg295 sg3870 - -lemma sg12340 : RowSquare [11,3,2,2,2,2,1,1] [6,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg5398 - -lemma sg12341 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg1914 sg2432 - -lemma sg12342 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg1914 sg2433 - -lemma sg12343 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4] := by - exact rowSquare_join (by decide) sg1532 sg3103 - -lemma sg12344 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1] := by - exact rowSquare_join (by decide) sg1455 sg3151 - -lemma sg12345 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1] := by - exact rowSquare_join (by decide) sg1915 sg2432 - -lemma sg12346 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4] := by - exact rowSquare_join (by decide) sg1916 sg2432 - -lemma sg12347 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1] := by - exact rowSquare_join (by decide) sg1915 sg2433 - -lemma sg12348 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3] := by - exact rowSquare_join (by decide) sg1916 sg2433 - -lemma sg12349 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1] := by - exact rowSquare_join (by decide) sg1917 sg2432 - -lemma sg12350 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,1] := by - exact rowSquare_join (by decide) sg1917 sg2433 - -lemma sg12351 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3] := by - exact rowSquare_join (by decide) sg1918 sg2432 - -lemma sg12352 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1] := by - exact rowSquare_join (by decide) sg636 sg4543 - -lemma sg12353 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2] := by - exact rowSquare_join (by decide) sg1918 sg2433 - -lemma sg12354 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1] := by - exact rowSquare_join (by decide) sg637 sg4543 - -lemma sg12355 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg1844 sg2461 - -lemma sg12356 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg1844 sg2462 - -lemma sg12357 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg1914 sg2436 - -lemma sg12358 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg1919 sg2432 - -lemma sg12359 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg1844 sg2463 - -lemma sg12360 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg1919 sg2433 - -lemma sg12361 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg1535 sg3102 - -lemma sg12362 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg1914 sg2438 - -lemma sg12363 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4] := by - exact rowSquare_join (by decide) sg1970 sg2343 - -lemma sg12364 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg1914 sg2439 - -lemma sg12365 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3] := by - exact rowSquare_join (by decide) sg1970 sg2344 - -lemma sg12366 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1456 sg3151 - -lemma sg12367 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2] := by - exact rowSquare_join (by decide) sg1914 sg2440 - -lemma sg12368 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2] := by - exact rowSquare_join (by decide) sg1844 sg2464 - -lemma sg12369 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,1] := by - exact rowSquare_join (by decide) sg1914 sg2441 - -lemma sg12370 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4] := by - exact rowSquare_join (by decide) sg1916 sg2436 - -lemma sg12371 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg1971 sg2341 - -lemma sg12372 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,2] := by - exact rowSquare_join (by decide) sg1844 sg2465 - -lemma sg12373 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,1] := by - exact rowSquare_join (by decide) sg1914 sg2442 - -lemma sg12374 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg1456 sg3152 - -lemma sg12375 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,1] := by - exact rowSquare_join (by decide) sg1914 sg2443 - -lemma sg12376 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3] := by - exact rowSquare_join (by decide) sg1916 sg2438 - -lemma sg12377 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,1,1] := by - exact rowSquare_join (by decide) sg1915 sg2439 - -lemma sg12378 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2] := by - exact rowSquare_join (by decide) sg1916 sg2439 - -lemma sg12379 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2] := by - exact rowSquare_join (by decide) sg1455 sg3153 - -lemma sg12380 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1533 sg3104 - -lemma sg12381 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,2] := by - exact rowSquare_join (by decide) sg1915 sg2440 - -lemma sg12382 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,1] := by - exact rowSquare_join (by decide) sg1920 sg2432 - -lemma sg12383 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,1] := by - exact rowSquare_join (by decide) sg1915 sg2441 - -lemma sg12384 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3] := by - exact rowSquare_join (by decide) sg1916 sg2441 - -lemma sg12385 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg1534 sg3104 - -lemma sg12386 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,2] := by - exact rowSquare_join (by decide) sg1917 sg2440 - -lemma sg12387 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg1973 sg2341 - -lemma sg12388 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2,1] := by - exact rowSquare_join (by decide) sg1915 sg2442 - -lemma sg12389 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,3] := by - exact rowSquare_join (by decide) sg1916 sg2442 - -lemma sg12390 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,1,1] := by - exact rowSquare_join (by decide) sg1915 sg2443 - -lemma sg12391 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,2] := by - exact rowSquare_join (by decide) sg1916 sg2443 - -lemma sg12392 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,1] := by - exact rowSquare_join (by decide) sg1980 sg2330 - -lemma sg12393 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg1919 sg2434 - -lemma sg12394 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg1844 sg2466 - -lemma sg12395 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg1844 sg2467 - -lemma sg12396 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg1914 sg2446 - -lemma sg12397 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg1844 sg2468 - -lemma sg12398 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1919 sg2435 - -lemma sg12399 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1846 sg2461 - -lemma sg12400 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg1844 sg2469 - -lemma sg12401 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1922 sg2433 - -lemma sg12402 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1844 sg2470 - -lemma sg12403 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1914 sg2447 - -lemma sg12404 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4] := by - exact rowSquare_join (by decide) sg1916 sg2446 - -lemma sg12405 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg1919 sg2437 - -lemma sg12406 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg1919 sg2438 - -lemma sg12407 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg1844 sg2471 - -lemma sg12408 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg1919 sg2439 - -lemma sg12409 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1970 sg2350 - -lemma sg12410 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg1844 sg2472 - -lemma sg12411 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1919 sg2440 - -lemma sg12412 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1846 sg2462 - -lemma sg12413 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg1844 sg2473 - -lemma sg12414 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1458 sg3152 - -lemma sg12415 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg1846 sg2463 - -lemma sg12416 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg1844 sg2474 - -lemma sg12417 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg1919 sg2443 - -lemma sg12418 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1456 sg3153 - -lemma sg12419 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1971 sg2350 - -lemma sg12420 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2] := by - exact rowSquare_join (by decide) sg1844 sg2475 - -lemma sg12421 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1972 sg2350 - -lemma sg12422 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2] := by - exact rowSquare_join (by decide) sg1844 sg2476 - -lemma sg12423 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1846 sg2464 - -lemma sg12424 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1537 sg3104 - -lemma sg12425 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2] := by - exact rowSquare_join (by decide) sg1920 sg2440 - -lemma sg12426 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1973 sg2350 - -lemma sg12427 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,1] := by - exact rowSquare_join (by decide) sg1915 sg2449 - -lemma sg12428 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1922 sg2434 - -lemma sg12429 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg1844 sg2477 - -lemma sg12430 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1735 sg2480 - -lemma sg12431 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1919 sg2444 - -lemma sg12432 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1735 sg2481 - -lemma sg12433 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1919 sg2445 - -lemma sg12434 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1919 sg2446 - -lemma sg12435 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1923 sg2433 - -lemma sg12436 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1735 sg2482 - -lemma sg12437 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1810 sg2478 - -lemma sg12438 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1922 sg2435 - -lemma sg12439 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1735 sg2483 - -lemma sg12440 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1735 sg2484 - -lemma sg12441 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,5] := by - exact rowSquare_join (by decide) sg1061 sg3658 - -lemma sg12442 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg1891 sg2451 - -lemma sg12443 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1891 sg2452 - -lemma sg12444 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg1926 sg2391 - -lemma sg12445 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1891 sg2453 - -lemma sg12446 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1919 sg2405 - -lemma sg12447 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg1902 sg2439 - -lemma sg12448 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1520 sg3104 - -lemma sg12449 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg1844 sg2392 - -lemma sg12450 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1892 sg2339 - -lemma sg12451 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1923 sg2311 - -lemma sg12452 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1891 sg2212 - -lemma sg12453 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1735 sg2390 - -lemma sg12454 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1519 sg2664 - -lemma sg12455 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1891 sg2214 - -lemma sg12456 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1891 sg2215 - -lemma sg12457 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [5,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1891 sg2216 - -lemma sg12458 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [5,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1735 sg2392 - -lemma sg12459 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1810 sg2310 - -lemma sg12460 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1810 sg2311 - -lemma sg12461 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1736 sg2390 - -lemma sg12462 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1300 sg3004 - -lemma sg12463 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg1809 sg2314 - -lemma sg12464 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1736 sg2392 - -lemma sg12465 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg3736 - -lemma sg12466 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1810 sg2313 - -lemma sg12467 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1810 sg2314 - -lemma sg12468 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [7,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1736 sg2396 - -lemma sg12469 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg1902 sg2405 - -lemma sg12470 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg1902 sg2406 - -lemma sg12471 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg1902 sg2407 - -lemma sg12472 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg1518 sg3099 - -lemma sg12473 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg1518 sg3100 - -lemma sg12474 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4] := by - exact rowSquare_join (by decide) sg1519 sg3100 - -lemma sg12475 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1903 sg2405 - -lemma sg12476 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1903 sg2406 - -lemma sg12477 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1417 sg3147 - -lemma sg12478 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1903 sg2407 - -lemma sg12479 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1417 sg3148 - -lemma sg12480 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1417 sg3149 - -lemma sg12481 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1904 sg2405 - -lemma sg12482 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg1904 sg2406 - -lemma sg12483 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg1904 sg2407 - -lemma sg12484 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2] := by - exact rowSquare_join (by decide) sg1905 sg2406 - -lemma sg12485 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1] := by - exact rowSquare_join (by decide) sg1905 sg2407 - -lemma sg12486 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4] := by - exact rowSquare_join (by decide) sg1033 sg3737 - -lemma sg12487 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg1907 sg2405 - -lemma sg12488 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2] := by - exact rowSquare_join (by decide) sg1906 sg2406 - -lemma sg12489 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg1908 sg2405 - -lemma sg12490 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1902 sg2413 - -lemma sg12491 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg1902 sg2416 - -lemma sg12492 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1902 sg2419 - -lemma sg12493 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4] := by - exact rowSquare_join (by decide) sg1519 sg3101 - -lemma sg12494 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1903 sg2417 - -lemma sg12495 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1520 sg3101 - -lemma sg12496 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1908 sg2417 - -lemma sg12497 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1902 sg2424 - -lemma sg12498 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1902 sg2425 - -lemma sg12499 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1902 sg2426 - -lemma sg12500 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1902 sg2427 - -lemma sg12501 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1904 sg2424 - -lemma sg12502 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1904 sg2427 - -lemma sg12503 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1902 sg2429 - -lemma sg12504 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1957 sg2338 - -lemma sg12505 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1961 sg2338 - -lemma sg12506 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg1891 sg2405 - -lemma sg12507 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg1539 sg2925 - -lemma sg12508 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg1891 sg2406 - -lemma sg12509 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1891 sg2407 - -lemma sg12510 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg1032 sg3724 - -lemma sg12511 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg1033 sg3724 - -lemma sg12512 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2] := by - exact rowSquare_join (by decide) sg1032 sg3725 - -lemma sg12513 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1] := by - exact rowSquare_join (by decide) sg1032 sg3726 - -lemma sg12514 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5] := by - exact rowSquare_join (by decide) sg1033 sg3726 - -lemma sg12515 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1901 sg2390 - -lemma sg12516 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1034 sg3724 - -lemma sg12517 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1955 sg2310 - -lemma sg12518 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1956 sg2310 - -lemma sg12519 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1903 sg2390 - -lemma sg12520 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1519 sg3002 - -lemma sg12521 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg1518 sg3004 - -lemma sg12522 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1901 sg2395 - -lemma sg12523 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg613 sg4539 - -lemma sg12524 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg1891 sg2416 - -lemma sg12525 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4] := by - exact rowSquare_join (by decide) sg1519 sg3009 - -lemma sg12526 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1961 sg2311 - -lemma sg12527 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1903 sg2394 - -lemma sg12528 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3] := by - exact rowSquare_join (by decide) sg1521 sg3004 - -lemma sg12529 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1903 sg2395 - -lemma sg12530 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1891 sg2419 - -lemma sg12531 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1416 sg3128 - -lemma sg12532 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg1908 sg2391 - -lemma sg12533 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1964 sg2310 - -lemma sg12534 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1524 sg3002 - -lemma sg12535 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg1955 sg2314 - -lemma sg12536 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2406 - -lemma sg12537 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2407 - -lemma sg12538 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1874 sg2408 - -lemma sg12539 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1874 sg2410 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes17 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes20 + +namespace OAI + +/-! Semigroup Nodes 29. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg12140 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg4632 + +lemma sg12141 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg766 sg2583 + +lemma sg12142 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2050 + +lemma sg12143 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1203 sg2047 + +lemma sg12144 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg767 sg2583 + +lemma sg12145 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2051 + +lemma sg12146 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1203 sg2048 + +lemma sg12147 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1203 sg2049 + +lemma sg12148 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2052 + +lemma sg12149 : RowSquare [8,6,2,2,2,2,1,1] [7,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1210 sg2044 + +lemma sg12150 : RowSquare [8,6,2,2,2,2,1,1] [7,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg4627 + +lemma sg12151 : RowSquare [8,6,2,2,2,2,1,1] [7,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg768 sg2583 + +lemma sg12152 : RowSquare [8,6,2,2,2,2,1,1] [7,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg810 sg2560 + +lemma sg12153 : RowSquare [8,6,2,2,2,2,1,1] [7,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg1203 sg2050 + +lemma sg12154 : RowSquare [8,6,2,2,2,2,1,1] [7,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg810 sg2561 + +lemma sg12155 : RowSquare [8,6,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7275 + +lemma sg12156 : RowSquare [8,6,2,2,2,2,1,1] [7,6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6141 + +lemma sg12157 : RowSquare [8,6,2,2,2,2,1,1] [7,6,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7477 + +lemma sg12158 : RowSquare [8,6,2,2,2,2,1,1] [7,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7276 + +lemma sg12159 : RowSquare [8,6,2,2,2,2,1,1] [7,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg765 sg2585 + +lemma sg12160 : RowSquare [8,6,2,2,2,2,1,1] [7,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1202 sg2053 + +lemma sg12161 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6142 + +lemma sg12162 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg4633 + +lemma sg12163 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg766 sg2585 + +lemma sg12164 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2054 + +lemma sg12165 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1203 sg2053 + +lemma sg12166 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg767 sg2585 + +lemma sg12167 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2055 + +lemma sg12168 : RowSquare [8,6,2,2,2,2,1,1] [7,6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1206 sg2048 + +lemma sg12169 : RowSquare [8,6,2,2,2,2,1,1] [7,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg4628 + +lemma sg12170 : RowSquare [8,6,2,2,2,2,1,1] [7,6,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg768 sg2585 + +lemma sg12171 : RowSquare [8,6,2,2,2,2,1,1] [7,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2056 + +lemma sg12172 : RowSquare [8,6,2,2,2,2,1,1] [7,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2057 + +lemma sg12173 : RowSquare [8,6,2,2,2,2,1,1] [7,6,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg773 sg2579 + +lemma sg12174 : RowSquare [8,6,2,2,2,2,1,1] [7,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2058 + +lemma sg12175 : RowSquare [8,6,2,2,2,2,1,1] [7,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg459 sg3285 + +lemma sg12176 : RowSquare [8,6,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7277 + +lemma sg12177 : RowSquare [8,6,2,2,2,2,1,1] [7,7,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7278 + +lemma sg12178 : RowSquare [8,6,2,2,2,2,1,1] [7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7478 + +lemma sg12179 : RowSquare [8,6,2,2,2,2,1,1] [7,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg780 sg2576 + +lemma sg12180 : RowSquare [8,6,2,2,2,2,1,1] [7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg765 sg2586 + +lemma sg12181 : RowSquare [8,6,2,2,2,2,1,1] [7,7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1206 sg2053 + +lemma sg12182 : RowSquare [8,6,2,2,2,2,1,1] [7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg4628 + +lemma sg12183 : RowSquare [8,6,2,2,2,2,1,1] [7,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg774 sg2579 + +lemma sg12184 : RowSquare [8,6,2,2,2,2,1,1] [7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg766 sg2586 + +lemma sg12185 : RowSquare [8,6,2,2,2,2,1,1] [7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg767 sg2586 + +lemma sg12186 : RowSquare [8,6,2,2,2,2,1,1] [7,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg775 sg2579 + +lemma sg12187 : RowSquare [8,6,2,2,2,2,1,1] [7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg768 sg2586 + +lemma sg12188 : RowSquare [8,6,2,2,2,2,1,1] [7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg403 sg3788 + +lemma sg12189 : RowSquare [8,6,2,2,2,2,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg8691 + +lemma sg12190 : RowSquare [8,6,2,2,2,2,1,1] [8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg7269 + +lemma sg12191 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7279 + +lemma sg12192 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6143 + +lemma sg12193 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg8692 + +lemma sg12194 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg8693 + +lemma sg12195 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg8694 + +lemma sg12196 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6 sg8695 + +lemma sg12197 : RowSquare [8,6,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6 sg8696 + +lemma sg12198 : RowSquare [8,6,2,2,2,2,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7279 + +lemma sg12199 : RowSquare [8,6,2,2,2,2,1,1] [8,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6143 + +lemma sg12200 : RowSquare [8,6,2,2,2,2,1,1] [8,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6144 + +lemma sg12201 : RowSquare [8,6,2,2,2,2,1,1] [8,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8703 + +lemma sg12202 : RowSquare [8,6,2,2,2,2,1,1] [8,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8704 + +lemma sg12203 : RowSquare [8,6,2,2,2,2,1,1] [8,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg8705 + +lemma sg12204 : RowSquare [8,6,2,2,2,2,1,1] [8,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg8706 + +lemma sg12205 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg6138 + +lemma sg12206 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg5287 + +lemma sg12207 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7280 + +lemma sg12208 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7281 + +lemma sg12209 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg16 sg7282 + +lemma sg12210 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg100 sg5281 + +lemma sg12211 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg5288 + +lemma sg12212 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg7479 + +lemma sg12213 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg776 sg2577 + +lemma sg12214 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1209 sg2045 + +lemma sg12215 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1678 sg1592 + +lemma sg12216 : RowSquare [8,6,2,2,2,2,1,1] [8,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1209 sg2046 + +lemma sg12217 : RowSquare [8,6,2,2,2,2,1,1] [8,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg6137 + +lemma sg12218 : RowSquare [8,6,2,2,2,2,1,1] [8,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6144 + +lemma sg12219 : RowSquare [8,6,2,2,2,2,1,1] [8,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg5289 + +lemma sg12220 : RowSquare [8,6,2,2,2,2,1,1] [8,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7280 + +lemma sg12221 : RowSquare [8,6,2,2,2,2,1,1] [8,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7281 + +lemma sg12222 : RowSquare [8,6,2,2,2,2,1,1] [8,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg7282 + +lemma sg12223 : RowSquare [8,6,2,2,2,2,1,1] [8,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1202 sg2059 + +lemma sg12224 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg5291 + +lemma sg12225 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg5290 + +lemma sg12226 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7283 + +lemma sg12227 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg763 sg2587 + +lemma sg12228 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1202 sg2060 + +lemma sg12229 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg4631 + +lemma sg12230 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1678 sg1593 + +lemma sg12231 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2061 + +lemma sg12232 : RowSquare [8,6,2,2,2,2,1,1] [8,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1679 sg1592 + +lemma sg12233 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg4050 + +lemma sg12234 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg4634 + +lemma sg12235 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1678 sg1594 + +lemma sg12236 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1209 sg2050 + +lemma sg12237 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg770 sg2583 + +lemma sg12238 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1209 sg2051 + +lemma sg12239 : RowSquare [8,6,2,2,2,2,1,1] [8,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1209 sg2052 + +lemma sg12240 : RowSquare [8,6,2,2,2,2,1,1] [8,5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg6139 + +lemma sg12241 : RowSquare [8,6,2,2,2,2,1,1] [8,5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg99 sg5289 + +lemma sg12242 : RowSquare [8,6,2,2,2,2,1,1] [8,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6145 + +lemma sg12243 : RowSquare [8,6,2,2,2,2,1,1] [8,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7283 + +lemma sg12244 : RowSquare [8,6,2,2,2,2,1,1] [8,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg765 sg2587 + +lemma sg12245 : RowSquare [8,6,2,2,2,2,1,1] [8,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1202 sg2062 + +lemma sg12246 : RowSquare [8,6,2,2,2,2,1,1] [8,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg4052 + +lemma sg12247 : RowSquare [8,6,2,2,2,2,1,1] [8,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg4635 + +lemma sg12248 : RowSquare [8,6,2,2,2,2,1,1] [8,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg766 sg2587 + +lemma sg12249 : RowSquare [8,6,2,2,2,2,1,1] [8,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2063 + +lemma sg12250 : RowSquare [8,6,2,2,2,2,1,1] [8,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1678 sg1595 + +lemma sg12251 : RowSquare [8,6,2,2,2,2,1,1] [8,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1679 sg1593 + +lemma sg12252 : RowSquare [8,6,2,2,2,2,1,1] [8,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg4632 + +lemma sg12253 : RowSquare [8,6,2,2,2,2,1,1] [8,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1678 sg1596 + +lemma sg12254 : RowSquare [8,6,2,2,2,2,1,1] [8,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1678 sg1597 + +lemma sg12255 : RowSquare [8,6,2,2,2,2,1,1] [8,6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg6141 + +lemma sg12256 : RowSquare [8,6,2,2,2,2,1,1] [8,6,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg4052 + +lemma sg12257 : RowSquare [8,6,2,2,2,2,1,1] [8,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg4633 + +lemma sg12258 : RowSquare [8,6,2,2,2,2,1,1] [8,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg771 sg2585 + +lemma sg12259 : RowSquare [8,6,2,2,2,2,1,1] [8,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg2064 + +lemma sg12260 : RowSquare [8,6,2,2,2,2,1,1] [8,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg4633 + +lemma sg12261 : RowSquare [8,6,2,2,2,2,1,1] [8,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg772 sg2585 + +lemma sg12262 : RowSquare [8,6,2,2,2,2,1,1] [8,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg773 sg2585 + +lemma sg12263 : RowSquare [8,6,2,2,2,2,1,1] [8,7,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg4052 + +lemma sg12264 : RowSquare [8,6,2,2,2,2,1,1] [8,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg4633 + +lemma sg12265 : RowSquare [8,6,2,2,2,2,1,1] [8,7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg774 sg2585 + +lemma sg12266 : RowSquare [8,6,2,2,2,2,1,1] [8,7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg775 sg2585 + +lemma sg12267 : RowSquare [8,6,2,2,2,2,1,1] [8,8,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7284 + +lemma sg12268 : RowSquare [8,6,2,2,2,2,1,1] [8,8,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg780 sg2579 + +lemma sg12269 : RowSquare [8,6,2,2,2,2,1,1] [9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg7269 + +lemma sg12270 : RowSquare [8,6,2,2,2,2,1,1] [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg7279 + +lemma sg12271 : RowSquare [8,6,2,2,2,2,1,1] [9,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg6143 + +lemma sg12272 : RowSquare [8,6,2,2,2,2,1,1] [9,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg6146 + +lemma sg12273 : RowSquare [8,6,2,2,2,2,1,1] [9,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg8703 + +lemma sg12274 : RowSquare [8,6,2,2,2,2,1,1] [9,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg8704 + +lemma sg12275 : RowSquare [8,6,2,2,2,2,1,1] [9,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg8705 + +lemma sg12276 : RowSquare [8,6,2,2,2,2,1,1] [9,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6 sg8706 + +lemma sg12277 : RowSquare [8,6,2,2,2,2,1,1] [9,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg6143 + +lemma sg12278 : RowSquare [8,6,2,2,2,2,1,1] [9,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg6146 + +lemma sg12279 : RowSquare [8,6,2,2,2,2,1,1] [9,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg5291 + +lemma sg12280 : RowSquare [8,6,2,2,2,2,1,1] [9,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg7280 + +lemma sg12281 : RowSquare [8,6,2,2,2,2,1,1] [9,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg7281 + +lemma sg12282 : RowSquare [8,6,2,2,2,2,1,1] [9,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18 sg7282 + +lemma sg12283 : RowSquare [8,6,2,2,2,2,1,1] [9,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg5292 + +lemma sg12284 : RowSquare [8,6,2,2,2,2,1,1] [9,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg4050 + +lemma sg12285 : RowSquare [8,6,2,2,2,2,1,1] [9,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg7285 + +lemma sg12286 : RowSquare [8,6,2,2,2,2,1,1] [9,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1678 sg1598 + +lemma sg12287 : RowSquare [8,6,2,2,2,2,1,1] [9,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg211 sg4631 + +lemma sg12288 : RowSquare [8,6,2,2,2,2,1,1] [9,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1678 sg1599 + +lemma sg12289 : RowSquare [8,6,2,2,2,2,1,1] [9,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg6144 + +lemma sg12290 : RowSquare [8,6,2,2,2,2,1,1] [9,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg99 sg5291 + +lemma sg12291 : RowSquare [8,6,2,2,2,2,1,1] [9,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg4052 + +lemma sg12292 : RowSquare [8,6,2,2,2,2,1,1] [9,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg7285 + +lemma sg12293 : RowSquare [8,6,2,2,2,2,1,1] [9,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1678 sg1600 + +lemma sg12294 : RowSquare [8,6,2,2,2,2,1,1] [9,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg4054 + +lemma sg12295 : RowSquare [8,6,2,2,2,2,1,1] [9,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg4636 + +lemma sg12296 : RowSquare [8,6,2,2,2,2,1,1] [9,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1678 sg1601 + +lemma sg12297 : RowSquare [8,6,2,2,2,2,1,1] [9,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1678 sg1602 + +lemma sg12298 : RowSquare [8,6,2,2,2,2,1,1] [9,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg4055 + +lemma sg12299 : RowSquare [8,6,2,2,2,2,1,1] [9,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg5289 + +lemma sg12300 : RowSquare [8,6,2,2,2,2,1,1] [9,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg4054 + +lemma sg12301 : RowSquare [8,6,2,2,2,2,1,1] [9,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg4635 + +lemma sg12302 : RowSquare [8,6,2,2,2,2,1,1] [9,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1678 sg1603 + +lemma sg12303 : RowSquare [8,6,2,2,2,2,1,1] [9,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg4056 + +lemma sg12304 : RowSquare [8,6,2,2,2,2,1,1] [9,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg4054 + +lemma sg12305 : RowSquare [8,6,2,2,2,2,1,1] [9,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg4056 + +lemma sg12306 : RowSquare [8,6,2,2,2,2,1,1] [9,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg4056 + +lemma sg12307 : RowSquare [8,6,2,2,2,2,1,1] [10,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg7279 + +lemma sg12308 : RowSquare [8,6,2,2,2,2,1,1] [10,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg6143 + +lemma sg12309 : RowSquare [8,6,2,2,2,2,1,1] [10,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg6146 + +lemma sg12310 : RowSquare [8,6,2,2,2,2,1,1] [10,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg5292 + +lemma sg12311 : RowSquare [8,6,2,2,2,2,1,1] [10,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg7280 + +lemma sg12312 : RowSquare [8,6,2,2,2,2,1,1] [10,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg7281 + +lemma sg12313 : RowSquare [8,6,2,2,2,2,1,1] [10,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg6146 + +lemma sg12314 : RowSquare [8,6,2,2,2,2,1,1] [10,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg99 sg5292 + +lemma sg12315 : RowSquare [8,6,2,2,2,2,1,1] [10,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg4054 + +lemma sg12316 : RowSquare [8,6,2,2,2,2,1,1] [10,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg7285 + +lemma sg12317 : RowSquare [8,6,2,2,2,2,1,1] [10,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg4058 + +lemma sg12318 : RowSquare [8,6,2,2,2,2,1,1] [10,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg4055 + +lemma sg12319 : RowSquare [8,6,2,2,2,2,1,1] [10,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg5291 + +lemma sg12320 : RowSquare [8,6,2,2,2,2,1,1] [10,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg4058 + +lemma sg12321 : RowSquare [8,6,2,2,2,2,1,1] [10,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg4056 + +lemma sg12322 : RowSquare [8,6,2,2,2,2,1,1] [10,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg4058 + +lemma sg12323 : RowSquare [8,6,2,2,2,2,1,1] [11,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg6143 + +lemma sg12324 : RowSquare [8,6,2,2,2,2,1,1] [11,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg6146 + +lemma sg12325 : RowSquare [8,6,2,2,2,2,1,1] [11,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg100 sg5292 + +lemma sg12326 : RowSquare [8,6,2,2,2,2,1,1] [11,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg4058 + +lemma sg12327 : RowSquare [8,6,2,2,2,2,1,1] [11,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg5292 + +lemma sg12328 : RowSquare [8,6,2,2,2,2,1,1] [11,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg243 sg4058 + +lemma sg12329 : RowSquare [8,6,2,2,2,2,1,1] [12,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg50 sg5733 + +lemma sg12330 : RowSquare [8,6,2,2,2,2,1,1] [12,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg102 sg5292 + +lemma sg12331 : RowSquare [9,3,2,2,2,2,2,2] [5,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg579 sg3209 + +lemma sg12332 : RowSquare [9,3,2,2,2,2,2,2] [6,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg579 sg3213 + +lemma sg12333 : RowSquare [10,3,2,2,2,2,2,1] [4,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg5528 + +lemma sg12334 : RowSquare [10,3,2,2,2,2,2,1] [5,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg74 sg5538 + +lemma sg12335 : RowSquare [10,3,2,2,2,2,2,1] [5,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg74 sg5544 + +lemma sg12336 : RowSquare [10,3,2,2,2,2,2,1] [5,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg5547 + +lemma sg12337 : RowSquare [10,3,2,2,2,2,2,1] [6,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg165 sg4748 + +lemma sg12338 : RowSquare [10,3,2,2,2,2,2,1] [6,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg356 sg3870 + +lemma sg12339 : RowSquare [10,4,2,2,2,2,2] [6,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg295 sg3870 + +lemma sg12340 : RowSquare [11,3,2,2,2,2,1,1] [6,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg5398 + +lemma sg12341 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg1914 sg2432 + +lemma sg12342 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg1914 sg2433 + +lemma sg12343 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4] := by + exact rowSquare_join (by decide) sg1532 sg3103 + +lemma sg12344 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1] := by + exact rowSquare_join (by decide) sg1455 sg3151 + +lemma sg12345 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1] := by + exact rowSquare_join (by decide) sg1915 sg2432 + +lemma sg12346 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4] := by + exact rowSquare_join (by decide) sg1916 sg2432 + +lemma sg12347 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1] := by + exact rowSquare_join (by decide) sg1915 sg2433 + +lemma sg12348 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3] := by + exact rowSquare_join (by decide) sg1916 sg2433 + +lemma sg12349 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1] := by + exact rowSquare_join (by decide) sg1917 sg2432 + +lemma sg12350 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,1] := by + exact rowSquare_join (by decide) sg1917 sg2433 + +lemma sg12351 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3] := by + exact rowSquare_join (by decide) sg1918 sg2432 + +lemma sg12352 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1] := by + exact rowSquare_join (by decide) sg636 sg4543 + +lemma sg12353 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2] := by + exact rowSquare_join (by decide) sg1918 sg2433 + +lemma sg12354 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1] := by + exact rowSquare_join (by decide) sg637 sg4543 + +lemma sg12355 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg1844 sg2461 + +lemma sg12356 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg1844 sg2462 + +lemma sg12357 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg1914 sg2436 + +lemma sg12358 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg1919 sg2432 + +lemma sg12359 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg1844 sg2463 + +lemma sg12360 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg1919 sg2433 + +lemma sg12361 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg1535 sg3102 + +lemma sg12362 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg1914 sg2438 + +lemma sg12363 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4] := by + exact rowSquare_join (by decide) sg1970 sg2343 + +lemma sg12364 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg1914 sg2439 + +lemma sg12365 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3] := by + exact rowSquare_join (by decide) sg1970 sg2344 + +lemma sg12366 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1456 sg3151 + +lemma sg12367 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2] := by + exact rowSquare_join (by decide) sg1914 sg2440 + +lemma sg12368 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2] := by + exact rowSquare_join (by decide) sg1844 sg2464 + +lemma sg12369 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,1] := by + exact rowSquare_join (by decide) sg1914 sg2441 + +lemma sg12370 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4] := by + exact rowSquare_join (by decide) sg1916 sg2436 + +lemma sg12371 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg1971 sg2341 + +lemma sg12372 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,2] := by + exact rowSquare_join (by decide) sg1844 sg2465 + +lemma sg12373 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,1] := by + exact rowSquare_join (by decide) sg1914 sg2442 + +lemma sg12374 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg1456 sg3152 + +lemma sg12375 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,1] := by + exact rowSquare_join (by decide) sg1914 sg2443 + +lemma sg12376 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3] := by + exact rowSquare_join (by decide) sg1916 sg2438 + +lemma sg12377 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,1,1] := by + exact rowSquare_join (by decide) sg1915 sg2439 + +lemma sg12378 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2] := by + exact rowSquare_join (by decide) sg1916 sg2439 + +lemma sg12379 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2] := by + exact rowSquare_join (by decide) sg1455 sg3153 + +lemma sg12380 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1533 sg3104 + +lemma sg12381 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,2] := by + exact rowSquare_join (by decide) sg1915 sg2440 + +lemma sg12382 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,1] := by + exact rowSquare_join (by decide) sg1920 sg2432 + +lemma sg12383 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,1] := by + exact rowSquare_join (by decide) sg1915 sg2441 + +lemma sg12384 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3] := by + exact rowSquare_join (by decide) sg1916 sg2441 + +lemma sg12385 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg1534 sg3104 + +lemma sg12386 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,2] := by + exact rowSquare_join (by decide) sg1917 sg2440 + +lemma sg12387 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg1973 sg2341 + +lemma sg12388 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2,1] := by + exact rowSquare_join (by decide) sg1915 sg2442 + +lemma sg12389 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,3] := by + exact rowSquare_join (by decide) sg1916 sg2442 + +lemma sg12390 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,1,1] := by + exact rowSquare_join (by decide) sg1915 sg2443 + +lemma sg12391 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,2] := by + exact rowSquare_join (by decide) sg1916 sg2443 + +lemma sg12392 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,1] := by + exact rowSquare_join (by decide) sg1980 sg2330 + +lemma sg12393 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg1919 sg2434 + +lemma sg12394 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg1844 sg2466 + +lemma sg12395 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg1844 sg2467 + +lemma sg12396 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg1914 sg2446 + +lemma sg12397 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg1844 sg2468 + +lemma sg12398 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1919 sg2435 + +lemma sg12399 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1846 sg2461 + +lemma sg12400 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg1844 sg2469 + +lemma sg12401 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1922 sg2433 + +lemma sg12402 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1844 sg2470 + +lemma sg12403 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1914 sg2447 + +lemma sg12404 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4] := by + exact rowSquare_join (by decide) sg1916 sg2446 + +lemma sg12405 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg1919 sg2437 + +lemma sg12406 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg1919 sg2438 + +lemma sg12407 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg1844 sg2471 + +lemma sg12408 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg1919 sg2439 + +lemma sg12409 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1970 sg2350 + +lemma sg12410 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg1844 sg2472 + +lemma sg12411 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1919 sg2440 + +lemma sg12412 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1846 sg2462 + +lemma sg12413 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg1844 sg2473 + +lemma sg12414 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1458 sg3152 + +lemma sg12415 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg1846 sg2463 + +lemma sg12416 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg1844 sg2474 + +lemma sg12417 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg1919 sg2443 + +lemma sg12418 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1456 sg3153 + +lemma sg12419 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1971 sg2350 + +lemma sg12420 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2] := by + exact rowSquare_join (by decide) sg1844 sg2475 + +lemma sg12421 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1972 sg2350 + +lemma sg12422 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2] := by + exact rowSquare_join (by decide) sg1844 sg2476 + +lemma sg12423 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1846 sg2464 + +lemma sg12424 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1537 sg3104 + +lemma sg12425 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2] := by + exact rowSquare_join (by decide) sg1920 sg2440 + +lemma sg12426 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1973 sg2350 + +lemma sg12427 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,1] := by + exact rowSquare_join (by decide) sg1915 sg2449 + +lemma sg12428 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1922 sg2434 + +lemma sg12429 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg1844 sg2477 + +lemma sg12430 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1735 sg2480 + +lemma sg12431 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1919 sg2444 + +lemma sg12432 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1735 sg2481 + +lemma sg12433 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1919 sg2445 + +lemma sg12434 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1919 sg2446 + +lemma sg12435 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1923 sg2433 + +lemma sg12436 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1735 sg2482 + +lemma sg12437 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1810 sg2478 + +lemma sg12438 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1922 sg2435 + +lemma sg12439 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1735 sg2483 + +lemma sg12440 : RowSquare [3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1735 sg2484 + +lemma sg12441 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,5] := by + exact rowSquare_join (by decide) sg1061 sg3658 + +lemma sg12442 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg1891 sg2451 + +lemma sg12443 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1891 sg2452 + +lemma sg12444 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg1926 sg2391 + +lemma sg12445 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1891 sg2453 + +lemma sg12446 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1919 sg2405 + +lemma sg12447 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg1902 sg2439 + +lemma sg12448 : RowSquare [4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1520 sg3104 + +lemma sg12449 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg1844 sg2392 + +lemma sg12450 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1892 sg2339 + +lemma sg12451 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1923 sg2311 + +lemma sg12452 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1891 sg2212 + +lemma sg12453 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1735 sg2390 + +lemma sg12454 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1519 sg2664 + +lemma sg12455 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1891 sg2214 + +lemma sg12456 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1891 sg2215 + +lemma sg12457 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [5,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1891 sg2216 + +lemma sg12458 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [5,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1735 sg2392 + +lemma sg12459 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1810 sg2310 + +lemma sg12460 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1810 sg2311 + +lemma sg12461 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1736 sg2390 + +lemma sg12462 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1300 sg3004 + +lemma sg12463 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg1809 sg2314 + +lemma sg12464 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1736 sg2392 + +lemma sg12465 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg3736 + +lemma sg12466 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1810 sg2313 + +lemma sg12467 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1810 sg2314 + +lemma sg12468 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1] [7,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1736 sg2396 + +lemma sg12469 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg1902 sg2405 + +lemma sg12470 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg1902 sg2406 + +lemma sg12471 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg1902 sg2407 + +lemma sg12472 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg1518 sg3099 + +lemma sg12473 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg1518 sg3100 + +lemma sg12474 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4] := by + exact rowSquare_join (by decide) sg1519 sg3100 + +lemma sg12475 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1903 sg2405 + +lemma sg12476 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1903 sg2406 + +lemma sg12477 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1417 sg3147 + +lemma sg12478 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1903 sg2407 + +lemma sg12479 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1417 sg3148 + +lemma sg12480 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1417 sg3149 + +lemma sg12481 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1904 sg2405 + +lemma sg12482 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg1904 sg2406 + +lemma sg12483 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg1904 sg2407 + +lemma sg12484 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2] := by + exact rowSquare_join (by decide) sg1905 sg2406 + +lemma sg12485 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1] := by + exact rowSquare_join (by decide) sg1905 sg2407 + +lemma sg12486 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4] := by + exact rowSquare_join (by decide) sg1033 sg3737 + +lemma sg12487 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg1907 sg2405 + +lemma sg12488 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2] := by + exact rowSquare_join (by decide) sg1906 sg2406 + +lemma sg12489 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg1908 sg2405 + +lemma sg12490 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1902 sg2413 + +lemma sg12491 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg1902 sg2416 + +lemma sg12492 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1902 sg2419 + +lemma sg12493 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4] := by + exact rowSquare_join (by decide) sg1519 sg3101 + +lemma sg12494 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1903 sg2417 + +lemma sg12495 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1520 sg3101 + +lemma sg12496 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1908 sg2417 + +lemma sg12497 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1902 sg2424 + +lemma sg12498 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1902 sg2425 + +lemma sg12499 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1902 sg2426 + +lemma sg12500 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1902 sg2427 + +lemma sg12501 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1904 sg2424 + +lemma sg12502 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1904 sg2427 + +lemma sg12503 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1902 sg2429 + +lemma sg12504 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1957 sg2338 + +lemma sg12505 : RowSquare [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1961 sg2338 + +lemma sg12506 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg1891 sg2405 + +lemma sg12507 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg1539 sg2925 + +lemma sg12508 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg1891 sg2406 + +lemma sg12509 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1891 sg2407 + +lemma sg12510 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg1032 sg3724 + +lemma sg12511 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg1033 sg3724 + +lemma sg12512 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2] := by + exact rowSquare_join (by decide) sg1032 sg3725 + +lemma sg12513 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1] := by + exact rowSquare_join (by decide) sg1032 sg3726 + +lemma sg12514 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5] := by + exact rowSquare_join (by decide) sg1033 sg3726 + +lemma sg12515 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1901 sg2390 + +lemma sg12516 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1034 sg3724 + +lemma sg12517 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1955 sg2310 + +lemma sg12518 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1956 sg2310 + +lemma sg12519 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1903 sg2390 + +lemma sg12520 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1519 sg3002 + +lemma sg12521 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg1518 sg3004 + +lemma sg12522 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1901 sg2395 + +lemma sg12523 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg613 sg4539 + +lemma sg12524 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg1891 sg2416 + +lemma sg12525 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4] := by + exact rowSquare_join (by decide) sg1519 sg3009 + +lemma sg12526 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1961 sg2311 + +lemma sg12527 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1903 sg2394 + +lemma sg12528 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3] := by + exact rowSquare_join (by decide) sg1521 sg3004 + +lemma sg12529 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1903 sg2395 + +lemma sg12530 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1891 sg2419 + +lemma sg12531 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1416 sg3128 + +lemma sg12532 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg1908 sg2391 + +lemma sg12533 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1964 sg2310 + +lemma sg12534 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1524 sg3002 + +lemma sg12535 : RowSquare [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg1955 sg2314 + +lemma sg12536 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2406 + +lemma sg12537 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2407 + +lemma sg12538 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1874 sg2408 + +lemma sg12539 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1874 sg2410 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes3.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes3.lean index 4d92588429bc950778edf06bd3dd65c95166b36e..bb3fdc6c0a403368ceebcb7e39ac8d48f9b2559a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes3.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes3.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes2 - -namespace OAI - -/-! Semigroup Nodes 3. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg1663 : RowSquare [5,2,1,1,1,1,1] [2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg586 - -lemma sg1664 : RowSquare [5,2,1,1,1,1,1] [3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg586 - -lemma sg1665 : RowSquare [5,2,1,1,1,1,1] [3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg587 - -lemma sg1666 : RowSquare [5,2,1,1,1,1,1] [3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg588 - -lemma sg1667 : RowSquare [5,2,1,1,1,1,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg589 - -lemma sg1668 : RowSquare [5,2,1,1,1,1,1] [4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg586 - -lemma sg1669 : RowSquare [5,2,1,1,1,1,1] [4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg587 - -lemma sg1670 : RowSquare [5,2,1,1,1,1,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg313 - -lemma sg1671 : RowSquare [5,2,1,1,1,1,1] [5,5,1,1] := by - exact rowSquare_join (by decide) sg17 sg319 - -lemma sg1672 : RowSquare [5,2,1,1,1,1,1] [6,6] := by - exact rowSquare_join (by decide) sg17 sg324 - -lemma sg1673 : RowSquare [5,2,2,1,1,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg536 - -lemma sg1674 : RowSquare [5,2,2,1,1,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg314 - -lemma sg1675 : RowSquare [5,2,2,1,1,1] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg315 - -lemma sg1676 : RowSquare [5,2,2,1,1,1] [4,4,4] := by - exact rowSquare_join (by decide) sg4 sg543 - -lemma sg1677 : RowSquare [5,2,2,2,1] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg271 - -lemma sg1678 : RowSquare [5,3,1,1,1,1] [4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3 sg586 - -lemma sg1679 : RowSquare [5,3,1,1,1,1] [4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1202 - -lemma sg1680 : RowSquare [5,3,1,1,1,1] [4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg313 - -lemma sg1681 : RowSquare [5,3,1,1,1,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg313 - -lemma sg1683 : RowSquare [5,3,2,1,1] [2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg82 sg54 - -lemma sg1684 : RowSquare [5,3,2,1,1] [2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg81 sg54 - -lemma sg1685 : RowSquare [5,3,2,1,1] [2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg54 - -lemma sg1686 : RowSquare [5,3,2,1,1] [2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg53 - -lemma sg1687 : RowSquare [5,3,2,1,1] [2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg80 sg52 - -lemma sg1688 : RowSquare [5,3,2,1,1] [2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg252 - -lemma sg1689 : RowSquare [5,3,2,1,1] [3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg79 sg54 - -lemma sg1690 : RowSquare [5,3,2,1,1] [3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg34 sg118 - -lemma sg1691 : RowSquare [5,3,2,1,1] [3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg77 sg54 - -lemma sg1692 : RowSquare [5,3,2,1,1] [3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg77 sg52 - -lemma sg1693 : RowSquare [5,3,2,1,1] [3,3,2,2,2] := by - exact rowSquare_join (by decide) sg34 sg115 - -lemma sg1694 : RowSquare [5,3,2,1,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg475 - -lemma sg1695 : RowSquare [5,3,2,1,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg116 - -lemma sg1696 : RowSquare [5,3,2,1,1] [4,4,4] := by - exact rowSquare_join (by decide) sg4 sg479 - -lemma sg1697 : RowSquare [5,3,2,1,1] [6,6] := by - exact rowSquare_join (by decide) sg17 sg252 - -lemma sg1698 : RowSquare [5,3,3,1] [2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1232 - -lemma sg1699 : RowSquare [5,3,3,1] [3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1233 - -lemma sg1700 : RowSquare [5,3,3,1] [3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg1234 - -lemma sg1701 : RowSquare [5,3,3,1] [4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg798 - -lemma sg1702 : RowSquare [5,4,2,1] [3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg849 - -lemma sg1703 : RowSquare [5,4,2,1] [3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg510 - -lemma sg1704 : RowSquare [5,4,2,1] [3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg511 - -lemma sg1705 : RowSquare [5,4,2,1] [3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg285 - -lemma sg1706 : RowSquare [5,4,2,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg55 - -lemma sg1707 : RowSquare [5,4,2,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg286 - -lemma sg1708 : RowSquare [5,4,2,1] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg287 - -lemma sg1709 : RowSquare [5,4,2,1] [4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg850 - -lemma sg1710 : RowSquare [5,4,2,1] [4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg510 - -lemma sg1711 : RowSquare [5,4,2,1] [4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg512 - -lemma sg1712 : RowSquare [5,4,2,1] [4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg56 - -lemma sg1713 : RowSquare [5,4,2,1] [4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg854 - -lemma sg1714 : RowSquare [5,4,2,1] [4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg511 - -lemma sg1715 : RowSquare [5,4,2,1] [4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg57 - -lemma sg1716 : RowSquare [5,4,2,1] [4,3,2,2,1] := by - exact rowSquare_join (by decide) sg26 sg143 - -lemma sg1717 : RowSquare [5,4,2,1] [4,3,3,1,1] := by - exact rowSquare_join (by decide) sg75 sg55 - -lemma sg1718 : RowSquare [5,4,2,1] [4,3,3,2] := by - exact rowSquare_join (by decide) sg39 sg123 - -lemma sg1719 : RowSquare [5,4,2,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg285 - -lemma sg1720 : RowSquare [5,4,2,1] [4,4,2,1,1] := by - exact rowSquare_join (by decide) sg27 sg143 - -lemma sg1721 : RowSquare [5,4,2,1] [4,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg291 - -lemma sg1722 : RowSquare [5,4,2,1] [4,4,3,1] := by - exact rowSquare_join (by decide) sg76 sg55 - -lemma sg1723 : RowSquare [5,4,2,1] [4,4,4] := by - exact rowSquare_join (by decide) sg77 sg55 - -lemma sg1724 : RowSquare [5,4,2,1] [5,3,3,1] := by - exact rowSquare_join (by decide) sg78 sg55 - -lemma sg1725 : RowSquare [5,4,2,1] [5,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg294 - -lemma sg1726 : RowSquare [5,4,2,1] [5,5,2] := by - exact rowSquare_join (by decide) sg55 sg80 - -lemma sg1727 : RowSquare [5,4,2,1] [6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg512 - -lemma sg1728 : RowSquare [5,4,2,1] [6,6] := by - exact rowSquare_join (by decide) sg14 sg294 - -lemma sg1729 : RowSquare [5,4,2,1] [7,5] := by - exact rowSquare_join (by decide) sg80 sg59 - -lemma sg1730 : RowSquare [5,4,2,1] [8,4] := by - exact rowSquare_join (by decide) sg80 sg60 - -lemma sg1731 : RowSquare [5,4,2,1] [9,3] := by - exact rowSquare_join (by decide) sg80 sg61 - -lemma sg1732 : RowSquare [5,4,2,1] [10,2] := by - exact rowSquare_join (by decide) sg81 sg61 - -lemma sg1733 : RowSquare [5,4,2,1] [11,1] := by - exact rowSquare_join (by decide) sg82 sg61 - -lemma sg1735 : RowSquare [5,4,3] [2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg516 - -lemma sg1736 : RowSquare [5,4,3] [3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg516 - -lemma sg1737 : RowSquare [5,4,3] [4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg516 - -lemma sg1738 : RowSquare [5,4,3] [4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg11 sg306 - -lemma sg1739 : RowSquare [5,4,3] [4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg307 - -lemma sg1740 : RowSquare [5,4,3] [4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg307 - -lemma sg1741 : RowSquare [5,4,3] [5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg306 - -lemma sg1742 : RowSquare [5,4,3] [5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg11 sg307 - -lemma sg1743 : RowSquare [5,4,3] [6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg307 - -lemma sg1744 : RowSquare [5,5,1,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg295 - -lemma sg1745 : RowSquare [5,5,1,1] [4,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg300 - -lemma sg1746 : RowSquare [5,5,1,1] [5,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg302 - -lemma sg1747 : RowSquare [5,5,2] [3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg306 - -lemma sg1748 : RowSquare [6,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1327 - -lemma sg1749 : RowSquare [6,1,1,1,1,1,1] [3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1331 - -lemma sg1750 : RowSquare [6,1,1,1,1,1,1] [3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg1332 - -lemma sg1751 : RowSquare [6,1,1,1,1,1,1] [4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1338 - -lemma sg1752 : RowSquare [6,1,1,1,1,1,1] [5,4,2,1] := by - exact rowSquare_join (by decide) sg0 sg1349 - -lemma sg1753 : RowSquare [6,1,1,1,1,1,1] [6,5,1] := by - exact rowSquare_join (by decide) sg0 sg1358 - -lemma sg1755 : RowSquare [6,2,1,1,1,1] [2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg105 sg50 - -lemma sg1756 : RowSquare [6,2,1,1,1,1] [2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg112 - -lemma sg1757 : RowSquare [6,2,1,1,1,1] [2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg111 - -lemma sg1758 : RowSquare [6,2,1,1,1,1] [2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg265 - -lemma sg1759 : RowSquare [6,2,1,1,1,1] [3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg112 - -lemma sg1760 : RowSquare [6,2,1,1,1,1] [3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg111 - -lemma sg1761 : RowSquare [6,2,1,1,1,1] [3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg265 - -lemma sg1762 : RowSquare [6,2,1,1,1,1] [3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg530 - -lemma sg1763 : RowSquare [6,2,1,1,1,1] [3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg110 - -lemma sg1764 : RowSquare [6,2,1,1,1,1] [3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg264 - -lemma sg1765 : RowSquare [6,2,1,1,1,1] [3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg262 - -lemma sg1766 : RowSquare [6,2,1,1,1,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg262 - -lemma sg1767 : RowSquare [6,2,1,1,1,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg525 - -lemma sg1768 : RowSquare [6,2,1,1,1,1] [4,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg519 - -lemma sg1769 : RowSquare [6,2,1,1,1,1] [4,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg520 - -lemma sg1770 : RowSquare [6,2,1,1,1,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg456 - -lemma sg1771 : RowSquare [6,2,1,1,1,1] [4,4,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg520 - -lemma sg1772 : RowSquare [6,2,1,1,1,1] [4,4,3,1] := by - exact rowSquare_join (by decide) sg4 sg520 - -lemma sg1773 : RowSquare [6,2,1,1,1,1] [5,5,1,1] := by - exact rowSquare_join (by decide) sg2 sg809 - -lemma sg1774 : RowSquare [6,2,2,1,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg313 - -lemma sg1775 : RowSquare [6,2,2,1,1] [4,4,4] := by - exact rowSquare_join (by decide) sg4 sg459 - -lemma sg1776 : RowSquare [6,3,1,1,1] [3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg534 - -lemma sg1777 : RowSquare [6,3,1,1,1] [3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg312 - -lemma sg1778 : RowSquare [6,3,1,1,1] [3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg535 - -lemma sg1779 : RowSquare [6,3,1,1,1] [3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg313 - -lemma sg1780 : RowSquare [6,3,1,1,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg536 - -lemma sg1781 : RowSquare [6,3,1,1,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg314 - -lemma sg1782 : RowSquare [6,3,1,1,1] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg315 - -lemma sg1783 : RowSquare [6,3,1,1,1] [4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg312 - -lemma sg1784 : RowSquare [6,3,1,1,1] [4,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg317 - -lemma sg1785 : RowSquare [6,3,1,1,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg313 - -lemma sg1786 : RowSquare [6,3,1,1,1] [4,4,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg270 - -lemma sg1787 : RowSquare [6,3,1,1,1] [4,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg319 - -lemma sg1788 : RowSquare [6,3,1,1,1] [4,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg320 - -lemma sg1789 : RowSquare [6,3,1,1,1] [4,4,4] := by - exact rowSquare_join (by decide) sg4 sg543 - -lemma sg1790 : RowSquare [6,3,1,1,1] [5,4,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg273 - -lemma sg1791 : RowSquare [6,3,1,1,1] [5,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg324 - -lemma sg1792 : RowSquare [6,3,1,1,1] [5,5,2] := by - exact rowSquare_join (by decide) sg17 sg276 - -lemma sg1793 : RowSquare [6,3,1,1,1] [6,6] := by - exact rowSquare_join (by decide) sg17 sg281 - -lemma sg1794 : RowSquare [6,3,2,1] [3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg330 - -lemma sg1795 : RowSquare [6,3,2,1] [3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg178 - -lemma sg1796 : RowSquare [6,3,2,1] [3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg66 - -lemma sg1797 : RowSquare [6,3,2,1] [3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg330 - -lemma sg1798 : RowSquare [6,3,2,1] [3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg27 sg178 - -lemma sg1799 : RowSquare [6,3,2,1] [3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg67 - -lemma sg1800 : RowSquare [6,3,2,1] [3,3,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg143 - -lemma sg1801 : RowSquare [6,3,2,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg68 - -lemma sg1802 : RowSquare [6,3,2,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg32 sg144 - -lemma sg1803 : RowSquare [6,3,2,1] [4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg850 - -lemma sg1804 : RowSquare [6,3,2,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg71 - -lemma sg1805 : RowSquare [6,3,2,1] [4,4,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg148 - -lemma sg1806 : RowSquare [6,3,2,1] [4,4,2,2] := by - exact rowSquare_join (by decide) sg76 sg67 - -lemma sg1807 : RowSquare [6,3,2,1] [4,4,3,1] := by - exact rowSquare_join (by decide) sg88 sg55 - -lemma sg1808 : RowSquare [6,3,2,1] [4,4,4] := by - exact rowSquare_join (by decide) sg89 sg55 - -lemma sg1809 : RowSquare [6,3,3] [3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg154 - -lemma sg1810 : RowSquare [6,3,3] [4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg516 - -lemma sg1811 : RowSquare [6,4,1,1] [2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg330 - -lemma sg1812 : RowSquare [6,4,1,1] [3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg561 - -lemma sg1813 : RowSquare [6,4,1,1] [3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg331 - -lemma sg1814 : RowSquare [6,4,1,1] [3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg330 - -lemma sg1815 : RowSquare [6,4,1,1] [3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg562 - -lemma sg1816 : RowSquare [6,4,1,1] [3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg332 - -lemma sg1817 : RowSquare [6,4,1,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg563 - -lemma sg1818 : RowSquare [6,4,1,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg333 - -lemma sg1819 : RowSquare [6,4,1,1] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg334 - -lemma sg1820 : RowSquare [6,4,1,1] [4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg565 - -lemma sg1821 : RowSquare [6,4,1,1] [4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg142 - -lemma sg1822 : RowSquare [6,4,1,1] [4,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg879 - -lemma sg1823 : RowSquare [6,4,1,1] [4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg331 - -lemma sg1824 : RowSquare [6,4,1,1] [4,3,2,2,1] := by - exact rowSquare_join (by decide) sg39 sg143 - -lemma sg1825 : RowSquare [6,4,1,1] [4,3,3,1,1] := by - exact rowSquare_join (by decide) sg66 sg83 - -lemma sg1826 : RowSquare [6,4,1,1] [4,3,3,2] := by - exact rowSquare_join (by decide) sg39 sg144 - -lemma sg1827 : RowSquare [6,4,1,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg295 - -lemma sg1828 : RowSquare [6,4,1,1] [4,4,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg143 - -lemma sg1829 : RowSquare [6,4,1,1] [4,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg338 - -lemma sg1830 : RowSquare [6,4,1,1] [4,4,3,1] := by - exact rowSquare_join (by decide) sg67 sg83 - -lemma sg1831 : RowSquare [6,4,1,1] [4,4,4] := by - exact rowSquare_join (by decide) sg97 sg55 - -lemma sg1832 : RowSquare [6,4,1,1] [5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg330 - -lemma sg1833 : RowSquare [6,4,1,1] [5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg565 - -lemma sg1834 : RowSquare [6,4,1,1] [5,2,2,2,1] := by - exact rowSquare_join (by decide) sg66 sg84 - -lemma sg1835 : RowSquare [6,4,1,1] [5,3,3,1] := by - exact rowSquare_join (by decide) sg98 sg55 - -lemma sg1836 : RowSquare [6,4,1,1] [5,4,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg143 - -lemma sg1837 : RowSquare [6,4,1,1] [5,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg342 - -lemma sg1838 : RowSquare [6,4,1,1] [5,5,2] := by - exact rowSquare_join (by decide) sg83 sg71 - -lemma sg1839 : RowSquare [6,4,1,1] [6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg331 - -lemma sg1840 : RowSquare [6,4,1,1] [6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg142 - -lemma sg1841 : RowSquare [6,4,1,1] [6,6] := by - exact rowSquare_join (by decide) sg17 sg302 - -lemma sg1842 : RowSquare [6,4,1,1] [7,5] := by - exact rowSquare_join (by decide) sg71 sg85 - -lemma sg1843 : RowSquare [6,4,1,1] [9,3] := by - exact rowSquare_join (by decide) sg71 sg86 - -lemma sg1844 : RowSquare [6,4,2] [2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg74 - -lemma sg1845 : RowSquare [6,4,2] [3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg75 - -lemma sg1846 : RowSquare [6,4,2] [3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg577 - -lemma sg1847 : RowSquare [6,4,2] [3,3,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg166 - -lemma sg1848 : RowSquare [6,4,2] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg350 - -lemma sg1849 : RowSquare [6,5,1] [3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg356 - -lemma sg1850 : RowSquare [6,5,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg83 - -lemma sg1851 : RowSquare [6,5,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg357 - -lemma sg1852 : RowSquare [6,5,1] [4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg982 - -lemma sg1853 : RowSquare [6,5,1] [4,3,3,1,1] := by - exact rowSquare_join (by decide) sg75 sg83 - -lemma sg1854 : RowSquare [6,5,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg356 - -lemma sg1855 : RowSquare [6,5,1] [4,4,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg166 - -lemma sg1856 : RowSquare [6,5,1] [4,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg360 - -lemma sg1857 : RowSquare [6,5,1] [4,4,4] := by - exact rowSquare_join (by decide) sg83 sg77 - -lemma sg1858 : RowSquare [6,5,1] [5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg165 - -lemma sg1859 : RowSquare [6,5,1] [5,2,2,2,1] := by - exact rowSquare_join (by decide) sg75 sg84 - -lemma sg1860 : RowSquare [6,5,1] [5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg85 - -lemma sg1861 : RowSquare [6,5,1] [5,3,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg168 - -lemma sg1862 : RowSquare [6,5,1] [5,4,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg166 - -lemma sg1863 : RowSquare [6,5,1] [5,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg363 - -lemma sg1864 : RowSquare [6,5,1] [6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg165 - -lemma sg1865 : RowSquare [6,5,1] [6,2,2,1,1] := by - exact rowSquare_join (by decide) sg41 sg168 - -lemma sg1866 : RowSquare [6,5,1] [6,3,1,1,1] := by - exact rowSquare_join (by decide) sg75 sg85 - -lemma sg1867 : RowSquare [6,5,1] [6,6] := by - exact rowSquare_join (by decide) sg14 sg363 - -lemma sg1868 : RowSquare [6,6] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg364 - -lemma sg1869 : RowSquare [6,6] [4,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg365 - -lemma sg1870 : RowSquare [6,6] [5,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg367 - -lemma sg1872 : RowSquare [7,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1327 - -lemma sg1873 : RowSquare [7,1,1,1,1,1] [3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg1332 - -lemma sg1874 : RowSquare [7,2,1,1,1] [2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg586 - -lemma sg1875 : RowSquare [7,2,1,1,1] [3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg586 - -lemma sg1876 : RowSquare [7,2,1,1,1] [3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg587 - -lemma sg1877 : RowSquare [7,2,1,1,1] [3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg588 - -lemma sg1878 : RowSquare [7,2,1,1,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg589 - -lemma sg1879 : RowSquare [7,2,1,1,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg590 - -lemma sg1880 : RowSquare [7,2,1,1,1] [4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg586 - -lemma sg1881 : RowSquare [7,2,1,1,1] [4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg312 - -lemma sg1882 : RowSquare [7,2,1,1,1] [4,3,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg590 - -lemma sg1883 : RowSquare [7,2,1,1,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg313 - -lemma sg1884 : RowSquare [7,2,1,1,1] [4,4,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg314 - -lemma sg1885 : RowSquare [7,2,1,1,1] [4,4,2,2] := by - exact rowSquare_join (by decide) sg17 sg315 - -lemma sg1886 : RowSquare [7,2,1,1,1] [4,4,3,1] := by - exact rowSquare_join (by decide) sg4 sg596 - -lemma sg1887 : RowSquare [7,2,1,1,1] [5,4,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg317 - -lemma sg1888 : RowSquare [7,2,1,1,1] [5,5,1,1] := by - exact rowSquare_join (by decide) sg17 sg319 - -lemma sg1889 : RowSquare [7,2,1,1,1] [5,5,2] := by - exact rowSquare_join (by decide) sg17 sg320 - -lemma sg1890 : RowSquare [7,2,1,1,1] [6,6] := by - exact rowSquare_join (by decide) sg17 sg324 - -lemma sg1891 : RowSquare [7,2,2,1] [2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg178 - -lemma sg1892 : RowSquare [7,2,2,1] [3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg178 - -lemma sg1893 : RowSquare [7,2,2,1] [3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg179 - -lemma sg1894 : RowSquare [7,2,2,1] [3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg34 sg178 - -lemma sg1895 : RowSquare [7,2,2,1] [3,3,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg180 - -lemma sg1896 : RowSquare [7,2,2,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg32 sg181 - -lemma sg1897 : RowSquare [7,2,2,1] [4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg940 - -lemma sg1898 : RowSquare [7,2,2,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg371 - -lemma sg1899 : RowSquare [7,2,2,1] [4,4,2,2] := by - exact rowSquare_join (by decide) sg88 sg67 - -lemma sg1900 : RowSquare [7,2,2,1] [4,4,4] := by - exact rowSquare_join (by decide) sg89 sg68 - -lemma sg1901 : RowSquare [7,3,1,1] [3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg330 - -lemma sg1902 : RowSquare [7,3,1,1] [3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg178 - -lemma sg1903 : RowSquare [7,3,1,1] [3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg330 - -lemma sg1904 : RowSquare [7,3,1,1] [3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg178 - -lemma sg1905 : RowSquare [7,3,1,1] [3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg371 - -lemma sg1906 : RowSquare [7,3,1,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg615 - -lemma sg1907 : RowSquare [7,3,1,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg372 - -lemma sg1908 : RowSquare [7,3,1,1] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg373 - -lemma sg1909 : RowSquare [7,3,1,1] [4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg330 - -lemma sg1910 : RowSquare [7,3,1,1] [4,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg961 - -lemma sg1911 : RowSquare [7,3,1,1] [4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg178 - -lemma sg1912 : RowSquare [7,3,1,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg332 - -lemma sg1913 : RowSquare [7,3,1,1] [4,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg377 - -lemma sg1914 : RowSquare [7,3,2] [3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg87 - -lemma sg1915 : RowSquare [7,3,2] [3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg88 - -lemma sg1916 : RowSquare [7,3,2] [3,3,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg194 - -lemma sg1917 : RowSquare [7,3,2] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg89 - -lemma sg1918 : RowSquare [7,3,2] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg32 sg195 - -lemma sg1919 : RowSquare [7,3,2] [4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg975 - -lemma sg1920 : RowSquare [7,3,2] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg92 - -lemma sg1921 : RowSquare [7,3,2] [5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg306 - -lemma sg1922 : RowSquare [7,3,2] [5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg577 - -lemma sg1923 : RowSquare [7,3,2] [6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg307 - -lemma sg1924 : RowSquare [7,4,1] [3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg97 - -lemma sg1925 : RowSquare [7,4,1] [3,3,3,2,1] := by - exact rowSquare_join (by decide) sg32 sg207 - -lemma sg1926 : RowSquare [7,4,1] [3,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg390 - -lemma sg1927 : RowSquare [7,4,1] [4,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg982 - -lemma sg1929 : RowSquare [7,5] [4,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg402 - -lemma sg1935 : RowSquare [7,5] [5,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg407 - -lemma sg1943 : RowSquare [7,5] [6,6] := by - exact rowSquare_join (by decide) sg17 sg367 - -lemma sg1944 : RowSquare [8,1,1,1,1] [4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg586 - -lemma sg1945 : RowSquare [8,1,1,1,1] [4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg998 - -lemma sg1946 : RowSquare [8,1,1,1,1] [4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg999 - -lemma sg1947 : RowSquare [8,1,1,1,1] [4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg1000 - -lemma sg1948 : RowSquare [8,1,1,1,1] [4,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg1001 - -lemma sg1949 : RowSquare [8,1,1,1,1] [5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg587 - -lemma sg1950 : RowSquare [8,1,1,1,1] [5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg588 - -lemma sg1951 : RowSquare [8,1,1,1,1] [5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1006 - -lemma sg1952 : RowSquare [8,1,1,1,1] [5,3,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg1007 - -lemma sg1953 : RowSquare [8,1,1,1,1] [5,3,2,2] := by - exact rowSquare_join (by decide) sg2 sg1008 - -lemma sg1954 : RowSquare [8,2,1,1] [4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg178 - -lemma sg1955 : RowSquare [8,2,1,1] [4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg1032 - -lemma sg1956 : RowSquare [8,2,1,1] [4,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg1033 - -lemma sg1957 : RowSquare [8,2,1,1] [4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg178 - -lemma sg1958 : RowSquare [8,2,1,1] [4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg371 - -lemma sg1959 : RowSquare [8,2,1,1] [4,3,3,1,1] := by - exact rowSquare_join (by decide) sg16 sg372 - -lemma sg1960 : RowSquare [8,2,1,1] [4,3,3,2] := by - exact rowSquare_join (by decide) sg16 sg373 - -lemma sg1961 : RowSquare [8,2,1,1] [4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg371 - -lemma sg1962 : RowSquare [8,2,1,1] [4,4,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg372 - -lemma sg1963 : RowSquare [8,2,1,1] [4,4,2,2] := by - exact rowSquare_join (by decide) sg17 sg373 - -lemma sg1964 : RowSquare [8,2,1,1] [5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg330 - -lemma sg1965 : RowSquare [8,2,1,1] [5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg47 sg178 - -lemma sg1966 : RowSquare [8,2,1,1] [5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg179 - -lemma sg1967 : RowSquare [8,2,1,1] [5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg179 - -lemma sg1968 : RowSquare [8,2,1,1] [5,5,1,1] := by - exact rowSquare_join (by decide) sg17 sg377 - -lemma sg1969 : RowSquare [8,2,1,1] [6,6] := by - exact rowSquare_join (by decide) sg17 sg383 - -lemma sg1970 : RowSquare [8,2,2] [4,2,2,2,2] := by - exact rowSquare_join (by decide) sg87 sg87 - -lemma sg1971 : RowSquare [8,2,2] [4,3,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg88 - -lemma sg1972 : RowSquare [8,2,2] [4,3,3,1,1] := by - exact rowSquare_join (by decide) sg87 sg89 - -lemma sg1973 : RowSquare [8,2,2] [4,4,2,2] := by - exact rowSquare_join (by decide) sg88 sg88 - -lemma sg1974 : RowSquare [8,2,2] [4,4,3,1] := by - exact rowSquare_join (by decide) sg88 sg89 - -lemma sg1975 : RowSquare [8,2,2] [4,4,4] := by - exact rowSquare_join (by decide) sg89 sg89 - -lemma sg1976 : RowSquare [8,2,2] [5,5,1,1] := by - exact rowSquare_join (by decide) sg88 sg92 - -lemma sg1977 : RowSquare [8,3,1] [4,3,3,1,1] := by - exact rowSquare_join (by decide) sg87 sg97 - -lemma sg1978 : RowSquare [8,3,1] [4,3,3,2] := by - exact rowSquare_join (by decide) sg16 sg390 - -lemma sg1979 : RowSquare [8,3,1] [4,4,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg228 - -lemma sg1980 : RowSquare [8,3,1] [4,4,2,2] := by - exact rowSquare_join (by decide) sg17 sg390 - -lemma sg1981 : RowSquare [8,3,1] [4,4,3,1] := by - exact rowSquare_join (by decide) sg88 sg97 - -lemma sg1982 : RowSquare [8,3,1] [4,4,4] := by - exact rowSquare_join (by decide) sg97 sg89 - -lemma sg1983 : RowSquare [8,3,1] [5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg104 - -lemma sg1984 : RowSquare [8,3,1] [5,2,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg98 - -lemma sg1985 : RowSquare [8,3,1] [5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg105 - -lemma sg1986 : RowSquare [8,3,1] [5,3,2,1,1] := by - exact rowSquare_join (by decide) sg87 sg99 - -lemma sg1987 : RowSquare [8,3,1] [5,3,2,2] := by - exact rowSquare_join (by decide) sg88 sg98 - -lemma sg1988 : RowSquare [8,3,1] [5,3,3,1] := by - exact rowSquare_join (by decide) sg98 sg89 - -lemma sg1989 : RowSquare [8,3,1] [5,4,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg230 - -lemma sg1990 : RowSquare [8,3,1] [5,4,2,1] := by - exact rowSquare_join (by decide) sg88 sg99 - -lemma sg1991 : RowSquare [8,3,1] [5,5,1,1] := by - exact rowSquare_join (by decide) sg17 sg394 - -lemma sg1992 : RowSquare [8,3,1] [6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg106 - -lemma sg1993 : RowSquare [8,4] [5,3,3,1] := by - exact rowSquare_join (by decide) sg98 sg97 - -lemma sg1994 : RowSquare [8,4] [5,4,2,1] := by - exact rowSquare_join (by decide) sg39 sg228 - -lemma sg1995 : RowSquare [8,4] [5,4,3] := by - exact rowSquare_join (by decide) sg97 sg99 - -lemma sg1996 : RowSquare [8,4] [5,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg424 - -lemma sg1997 : RowSquare [8,4] [6,2,2,2] := by - exact rowSquare_join (by decide) sg98 sg98 - -lemma sg1998 : RowSquare [9,1,1,1] [6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg178 - -lemma sg1999 : RowSquare [9,1,1,1] [6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg371 - -lemma sg2000 : RowSquare [9,1,1,1] [6,2,2,1,1] := by - exact rowSquare_join (by decide) sg20 sg372 - -lemma sg2001 : RowSquare [9,1,1,1] [6,2,2,2] := by - exact rowSquare_join (by decide) sg20 sg373 - -lemma sg2002 : RowSquare [9,2,1] [6,2,2,1,1] := by - exact rowSquare_join (by decide) sg87 sg104 - -lemma sg2003 : RowSquare [9,2,1] [6,2,2,2] := by - exact rowSquare_join (by decide) sg20 sg390 - -lemma sg2004 : RowSquare [9,2,1] [6,3,1,1,1] := by - exact rowSquare_join (by decide) sg87 sg105 - -lemma sg2005 : RowSquare [9,2,1] [6,3,2,1] := by - exact rowSquare_join (by decide) sg88 sg104 - -lemma sg2006 : RowSquare [9,2,1] [6,4,1,1] := by - exact rowSquare_join (by decide) sg88 sg105 - -lemma sg2007 : RowSquare [9,2,1] [6,4,2] := by - exact rowSquare_join (by decide) sg89 sg105 - -lemma sg2008 : RowSquare [9,3] [6,3,3] := by - exact rowSquare_join (by decide) sg97 sg104 - -lemma sg2009 : RowSquare [9,3] [6,4,2] := by - exact rowSquare_join (by decide) sg97 sg105 - -lemma sg2010 : RowSquare [9,3] [6,5,1] := by - exact rowSquare_join (by decide) sg46 sg228 - -lemma sg2011 : RowSquare [9,3] [6,6] := by - exact rowSquare_join (by decide) sg17 sg424 - -lemma sg2012 : RowSquare [9,3] [7,2,2,1] := by - exact rowSquare_join (by decide) sg98 sg104 - -lemma sg2013 : RowSquare [9,3] [7,3,1,1] := by - exact rowSquare_join (by decide) sg98 sg105 - -lemma sg2014 : RowSquare [2,2,2,1,1,1,1,1,1,1] [7,6] := by - exact rowSquare_join (by decide) sg46 sg424 - -lemma sg2020 : RowSquare [3,2,1,1,1,1,1,1,1,1] [8,5] := by - exact rowSquare_join (by decide) sg92 sg232 - -lemma sg2021 : RowSquare [3,3,1,1,1,1,1,1,1] [5,2,2,2,2] := by - exact rowSquare_join (by decide) sg87 sg218 - -lemma sg2022 : RowSquare [3,3,1,1,1,1,1,1,1] [5,3,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg219 - -lemma sg2023 : RowSquare [3,3,1,1,1,1,1,1,1] [5,3,3,1,1] := by - exact rowSquare_join (by decide) sg87 sg220 - -lemma sg2024 : RowSquare [3,3,1,1,1,1,1,1,1] [5,4,2,2] := by - exact rowSquare_join (by decide) sg88 sg219 - -lemma sg2025 : RowSquare [3,3,1,1,1,1,1,1,1] [6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg1063 - -lemma sg2026 : RowSquare [3,3,1,1,1,1,1,1,1] [7,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg348 - -lemma sg2027 : RowSquare [3,3,1,1,1,1,1,1,1] [7,2,2,1,1] := by - exact rowSquare_join (by decide) sg87 sg224 - -lemma sg2028 : RowSquare [3,3,1,1,1,1,1,1,1] [7,2,2,2] := by - exact rowSquare_join (by decide) sg90 sg221 - -lemma sg2029 : RowSquare [3,3,1,1,1,1,1,1,1] [7,4,1,1] := by - exact rowSquare_join (by decide) sg88 sg225 - -lemma sg2030 : RowSquare [3,3,1,1,1,1,1,1,1] [7,4,2] := by - exact rowSquare_join (by decide) sg89 sg225 - -lemma sg2031 : RowSquare [3,3,1,1,1,1,1,1,1] [7,6] := by - exact rowSquare_join (by decide) sg92 sg223 - -lemma sg2032 : RowSquare [3,3,1,1,1,1,1,1,1] [8,2,2,1] := by - exact rowSquare_join (by decide) sg90 sg224 - -lemma sg2033 : RowSquare [3,3,1,1,1,1,1,1,1] [8,5] := by - exact rowSquare_join (by decide) sg92 sg225 - -lemma sg2034 : RowSquare [3,3,1,1,1,1,1,1,1] [9,2,1,1] := by - exact rowSquare_join (by decide) sg88 sg226 - -lemma sg2035 : RowSquare [3,3,2,1,1,1,1,1] [4,3,3,3] := by - exact rowSquare_join (by decide) sg33 sg390 - -lemma sg2036 : RowSquare [3,3,2,2,2,1] [3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg165 - -lemma sg2037 : RowSquare [4,1,1,1,1,1,1,1,1,1] [9,4] := by - exact rowSquare_join (by decide) sg49 sg383 - -lemma sg2038 : RowSquare [4,2,2,1,1,1,1,1] [4,4,4,1] := by - exact rowSquare_join (by decide) sg97 sg181 - -lemma sg2039 : RowSquare [4,3,1,1,1,1,1,1] [3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg87 sg178 - -lemma sg2040 : RowSquare [4,3,1,1,1,1,1,1] [3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg88 sg178 - -lemma sg2041 : RowSquare [4,3,1,1,1,1,1,1] [3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg371 - -lemma sg2042 : RowSquare [4,3,1,1,1,1,1,1] [3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg178 - -lemma sg2043 : RowSquare [4,3,1,1,1,1,1,1] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg32 sg372 - -lemma sg2044 : RowSquare [4,3,1,1,1,1,1,1] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg373 - -lemma sg2045 : RowSquare [4,3,1,1,1,1,1,1] [4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg90 sg178 - -lemma sg2046 : RowSquare [4,3,1,1,1,1,1,1] [4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg179 - -lemma sg2047 : RowSquare [4,3,1,1,1,1,1,1] [4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg91 sg178 - -lemma sg2048 : RowSquare [4,3,1,1,1,1,1,1] [4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg88 sg179 - -lemma sg2049 : RowSquare [4,3,1,1,1,1,1,1] [4,3,2,2,2] := by - exact rowSquare_join (by decide) sg87 sg180 - -lemma sg2050 : RowSquare [4,3,1,1,1,1,1,1] [4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg179 - -lemma sg2051 : RowSquare [4,3,1,1,1,1,1,1] [4,3,3,2,1] := by - exact rowSquare_join (by decide) sg87 sg181 - -lemma sg2052 : RowSquare [4,3,1,1,1,1,1,1] [4,3,3,3] := by - exact rowSquare_join (by decide) sg33 sg373 - -lemma sg2053 : RowSquare [4,3,1,1,1,1,1,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg178 - -lemma sg2054 : RowSquare [4,3,1,1,1,1,1,1] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg34 sg371 - -lemma sg2055 : RowSquare [4,3,1,1,1,1,1,1] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg88 sg180 - -lemma sg2056 : RowSquare [4,3,1,1,1,1,1,1] [4,4,3,1,1] := by - exact rowSquare_join (by decide) sg89 sg180 - -lemma sg2057 : RowSquare [4,3,1,1,1,1,1,1] [4,4,3,2] := by - exact rowSquare_join (by decide) sg88 sg181 - -lemma sg2058 : RowSquare [4,3,1,1,1,1,1,1] [4,4,4,1] := by - exact rowSquare_join (by decide) sg89 sg181 - -lemma sg2059 : RowSquare [4,3,1,1,1,1,1,1] [5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg940 - -lemma sg2060 : RowSquare [4,3,1,1,1,1,1,1] [5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg93 sg178 - -lemma sg2061 : RowSquare [4,3,1,1,1,1,1,1] [5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg90 sg179 - -lemma sg2062 : RowSquare [4,3,1,1,1,1,1,1] [5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg94 sg178 - -lemma sg2063 : RowSquare [4,3,1,1,1,1,1,1] [5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg91 sg179 - -lemma sg2064 : RowSquare [4,3,1,1,1,1,1,1] [5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg179 - -lemma sg2065 : RowSquare [4,3,1,1,1,1,1,1] [5,4,4] := by - exact rowSquare_join (by decide) sg0 sg1597 - -lemma sg2066 : RowSquare [4,3,1,1,1,1,1,1] [7,6] := by - exact rowSquare_join (by decide) sg0 sg1606 - -lemma sg2067 : RowSquare [4,3,1,1,1,1,1,1] [8,5] := by - exact rowSquare_join (by decide) sg5 sg722 - -lemma sg2068 : RowSquare [4,3,1,1,1,1,1,1] [9,4] := by - exact rowSquare_join (by decide) sg14 sg429 - -lemma sg2069 : RowSquare [4,3,1,1,1,1,1,1] [10,3] := by - exact rowSquare_join (by decide) sg14 sg430 - -lemma sg2070 : RowSquare [4,3,1,1,1,1,1,1] [11,2] := by - exact rowSquare_join (by decide) sg42 sg235 - -lemma sg2071 : RowSquare [4,3,1,1,1,1,1,1] [12,1] := by - exact rowSquare_join (by decide) sg43 sg235 - -lemma sg2073 : RowSquare [4,3,2,1,1,1,1] [2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg330 - -lemma sg2074 : RowSquare [4,3,2,1,1,1,1] [2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg178 - -lemma sg2075 : RowSquare [4,3,2,1,1,1,1] [3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg179 - -lemma sg2076 : RowSquare [4,3,2,1,1,1,1] [3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg180 - -lemma sg2077 : RowSquare [4,3,2,1,1,1,1] [4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg849 - -lemma sg2078 : RowSquare [4,3,2,1,1,1,1] [4,3,3,3] := by - exact rowSquare_join (by decide) sg33 sg334 - -lemma sg2079 : RowSquare [4,3,2,2,1,1] [4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg849 - -lemma sg2080 : RowSquare [4,3,2,2,1,1] [4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg850 - -lemma sg2081 : RowSquare [4,3,2,2,1,1] [5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg850 - -lemma sg2082 : RowSquare [4,4,1,1,1,1,1] [3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg66 sg178 - -lemma sg2083 : RowSquare [4,4,1,1,1,1,1] [3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg67 sg178 - -lemma sg2084 : RowSquare [4,4,1,1,1,1,1] [3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg178 - -lemma sg2085 : RowSquare [4,4,1,1,1,1,1] [4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg69 sg178 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes2 + +namespace OAI + +/-! Semigroup Nodes 3. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg1663 : RowSquare [5,2,1,1,1,1,1] [2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg586 + +lemma sg1664 : RowSquare [5,2,1,1,1,1,1] [3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg586 + +lemma sg1665 : RowSquare [5,2,1,1,1,1,1] [3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg587 + +lemma sg1666 : RowSquare [5,2,1,1,1,1,1] [3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg588 + +lemma sg1667 : RowSquare [5,2,1,1,1,1,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg589 + +lemma sg1668 : RowSquare [5,2,1,1,1,1,1] [4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg586 + +lemma sg1669 : RowSquare [5,2,1,1,1,1,1] [4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg587 + +lemma sg1670 : RowSquare [5,2,1,1,1,1,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg313 + +lemma sg1671 : RowSquare [5,2,1,1,1,1,1] [5,5,1,1] := by + exact rowSquare_join (by decide) sg17 sg319 + +lemma sg1672 : RowSquare [5,2,1,1,1,1,1] [6,6] := by + exact rowSquare_join (by decide) sg17 sg324 + +lemma sg1673 : RowSquare [5,2,2,1,1,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg536 + +lemma sg1674 : RowSquare [5,2,2,1,1,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg314 + +lemma sg1675 : RowSquare [5,2,2,1,1,1] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg315 + +lemma sg1676 : RowSquare [5,2,2,1,1,1] [4,4,4] := by + exact rowSquare_join (by decide) sg4 sg543 + +lemma sg1677 : RowSquare [5,2,2,2,1] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg271 + +lemma sg1678 : RowSquare [5,3,1,1,1,1] [4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3 sg586 + +lemma sg1679 : RowSquare [5,3,1,1,1,1] [4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1202 + +lemma sg1680 : RowSquare [5,3,1,1,1,1] [4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg313 + +lemma sg1681 : RowSquare [5,3,1,1,1,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg313 + +lemma sg1683 : RowSquare [5,3,2,1,1] [2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg82 sg54 + +lemma sg1684 : RowSquare [5,3,2,1,1] [2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg81 sg54 + +lemma sg1685 : RowSquare [5,3,2,1,1] [2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg54 + +lemma sg1686 : RowSquare [5,3,2,1,1] [2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg53 + +lemma sg1687 : RowSquare [5,3,2,1,1] [2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg80 sg52 + +lemma sg1688 : RowSquare [5,3,2,1,1] [2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg252 + +lemma sg1689 : RowSquare [5,3,2,1,1] [3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg79 sg54 + +lemma sg1690 : RowSquare [5,3,2,1,1] [3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg34 sg118 + +lemma sg1691 : RowSquare [5,3,2,1,1] [3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg77 sg54 + +lemma sg1692 : RowSquare [5,3,2,1,1] [3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg77 sg52 + +lemma sg1693 : RowSquare [5,3,2,1,1] [3,3,2,2,2] := by + exact rowSquare_join (by decide) sg34 sg115 + +lemma sg1694 : RowSquare [5,3,2,1,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg475 + +lemma sg1695 : RowSquare [5,3,2,1,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg116 + +lemma sg1696 : RowSquare [5,3,2,1,1] [4,4,4] := by + exact rowSquare_join (by decide) sg4 sg479 + +lemma sg1697 : RowSquare [5,3,2,1,1] [6,6] := by + exact rowSquare_join (by decide) sg17 sg252 + +lemma sg1698 : RowSquare [5,3,3,1] [2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1232 + +lemma sg1699 : RowSquare [5,3,3,1] [3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1233 + +lemma sg1700 : RowSquare [5,3,3,1] [3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg1234 + +lemma sg1701 : RowSquare [5,3,3,1] [4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg798 + +lemma sg1702 : RowSquare [5,4,2,1] [3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg849 + +lemma sg1703 : RowSquare [5,4,2,1] [3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg510 + +lemma sg1704 : RowSquare [5,4,2,1] [3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg511 + +lemma sg1705 : RowSquare [5,4,2,1] [3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg285 + +lemma sg1706 : RowSquare [5,4,2,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg55 + +lemma sg1707 : RowSquare [5,4,2,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg286 + +lemma sg1708 : RowSquare [5,4,2,1] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg287 + +lemma sg1709 : RowSquare [5,4,2,1] [4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg850 + +lemma sg1710 : RowSquare [5,4,2,1] [4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg510 + +lemma sg1711 : RowSquare [5,4,2,1] [4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg512 + +lemma sg1712 : RowSquare [5,4,2,1] [4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg56 + +lemma sg1713 : RowSquare [5,4,2,1] [4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg854 + +lemma sg1714 : RowSquare [5,4,2,1] [4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg511 + +lemma sg1715 : RowSquare [5,4,2,1] [4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg57 + +lemma sg1716 : RowSquare [5,4,2,1] [4,3,2,2,1] := by + exact rowSquare_join (by decide) sg26 sg143 + +lemma sg1717 : RowSquare [5,4,2,1] [4,3,3,1,1] := by + exact rowSquare_join (by decide) sg75 sg55 + +lemma sg1718 : RowSquare [5,4,2,1] [4,3,3,2] := by + exact rowSquare_join (by decide) sg39 sg123 + +lemma sg1719 : RowSquare [5,4,2,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg285 + +lemma sg1720 : RowSquare [5,4,2,1] [4,4,2,1,1] := by + exact rowSquare_join (by decide) sg27 sg143 + +lemma sg1721 : RowSquare [5,4,2,1] [4,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg291 + +lemma sg1722 : RowSquare [5,4,2,1] [4,4,3,1] := by + exact rowSquare_join (by decide) sg76 sg55 + +lemma sg1723 : RowSquare [5,4,2,1] [4,4,4] := by + exact rowSquare_join (by decide) sg77 sg55 + +lemma sg1724 : RowSquare [5,4,2,1] [5,3,3,1] := by + exact rowSquare_join (by decide) sg78 sg55 + +lemma sg1725 : RowSquare [5,4,2,1] [5,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg294 + +lemma sg1726 : RowSquare [5,4,2,1] [5,5,2] := by + exact rowSquare_join (by decide) sg55 sg80 + +lemma sg1727 : RowSquare [5,4,2,1] [6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg512 + +lemma sg1728 : RowSquare [5,4,2,1] [6,6] := by + exact rowSquare_join (by decide) sg14 sg294 + +lemma sg1729 : RowSquare [5,4,2,1] [7,5] := by + exact rowSquare_join (by decide) sg80 sg59 + +lemma sg1730 : RowSquare [5,4,2,1] [8,4] := by + exact rowSquare_join (by decide) sg80 sg60 + +lemma sg1731 : RowSquare [5,4,2,1] [9,3] := by + exact rowSquare_join (by decide) sg80 sg61 + +lemma sg1732 : RowSquare [5,4,2,1] [10,2] := by + exact rowSquare_join (by decide) sg81 sg61 + +lemma sg1733 : RowSquare [5,4,2,1] [11,1] := by + exact rowSquare_join (by decide) sg82 sg61 + +lemma sg1735 : RowSquare [5,4,3] [2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg516 + +lemma sg1736 : RowSquare [5,4,3] [3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg516 + +lemma sg1737 : RowSquare [5,4,3] [4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg516 + +lemma sg1738 : RowSquare [5,4,3] [4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg11 sg306 + +lemma sg1739 : RowSquare [5,4,3] [4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg307 + +lemma sg1740 : RowSquare [5,4,3] [4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg307 + +lemma sg1741 : RowSquare [5,4,3] [5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg306 + +lemma sg1742 : RowSquare [5,4,3] [5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg11 sg307 + +lemma sg1743 : RowSquare [5,4,3] [6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg307 + +lemma sg1744 : RowSquare [5,5,1,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg295 + +lemma sg1745 : RowSquare [5,5,1,1] [4,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg300 + +lemma sg1746 : RowSquare [5,5,1,1] [5,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg302 + +lemma sg1747 : RowSquare [5,5,2] [3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg306 + +lemma sg1748 : RowSquare [6,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1327 + +lemma sg1749 : RowSquare [6,1,1,1,1,1,1] [3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1331 + +lemma sg1750 : RowSquare [6,1,1,1,1,1,1] [3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg1332 + +lemma sg1751 : RowSquare [6,1,1,1,1,1,1] [4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1338 + +lemma sg1752 : RowSquare [6,1,1,1,1,1,1] [5,4,2,1] := by + exact rowSquare_join (by decide) sg0 sg1349 + +lemma sg1753 : RowSquare [6,1,1,1,1,1,1] [6,5,1] := by + exact rowSquare_join (by decide) sg0 sg1358 + +lemma sg1755 : RowSquare [6,2,1,1,1,1] [2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg105 sg50 + +lemma sg1756 : RowSquare [6,2,1,1,1,1] [2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg112 + +lemma sg1757 : RowSquare [6,2,1,1,1,1] [2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg111 + +lemma sg1758 : RowSquare [6,2,1,1,1,1] [2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg265 + +lemma sg1759 : RowSquare [6,2,1,1,1,1] [3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg112 + +lemma sg1760 : RowSquare [6,2,1,1,1,1] [3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg111 + +lemma sg1761 : RowSquare [6,2,1,1,1,1] [3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg265 + +lemma sg1762 : RowSquare [6,2,1,1,1,1] [3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg530 + +lemma sg1763 : RowSquare [6,2,1,1,1,1] [3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg110 + +lemma sg1764 : RowSquare [6,2,1,1,1,1] [3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg264 + +lemma sg1765 : RowSquare [6,2,1,1,1,1] [3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg262 + +lemma sg1766 : RowSquare [6,2,1,1,1,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg262 + +lemma sg1767 : RowSquare [6,2,1,1,1,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg525 + +lemma sg1768 : RowSquare [6,2,1,1,1,1] [4,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg519 + +lemma sg1769 : RowSquare [6,2,1,1,1,1] [4,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg520 + +lemma sg1770 : RowSquare [6,2,1,1,1,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg456 + +lemma sg1771 : RowSquare [6,2,1,1,1,1] [4,4,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg520 + +lemma sg1772 : RowSquare [6,2,1,1,1,1] [4,4,3,1] := by + exact rowSquare_join (by decide) sg4 sg520 + +lemma sg1773 : RowSquare [6,2,1,1,1,1] [5,5,1,1] := by + exact rowSquare_join (by decide) sg2 sg809 + +lemma sg1774 : RowSquare [6,2,2,1,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg313 + +lemma sg1775 : RowSquare [6,2,2,1,1] [4,4,4] := by + exact rowSquare_join (by decide) sg4 sg459 + +lemma sg1776 : RowSquare [6,3,1,1,1] [3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg534 + +lemma sg1777 : RowSquare [6,3,1,1,1] [3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg312 + +lemma sg1778 : RowSquare [6,3,1,1,1] [3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg535 + +lemma sg1779 : RowSquare [6,3,1,1,1] [3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg313 + +lemma sg1780 : RowSquare [6,3,1,1,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg536 + +lemma sg1781 : RowSquare [6,3,1,1,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg314 + +lemma sg1782 : RowSquare [6,3,1,1,1] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg315 + +lemma sg1783 : RowSquare [6,3,1,1,1] [4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg312 + +lemma sg1784 : RowSquare [6,3,1,1,1] [4,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg317 + +lemma sg1785 : RowSquare [6,3,1,1,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg313 + +lemma sg1786 : RowSquare [6,3,1,1,1] [4,4,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg270 + +lemma sg1787 : RowSquare [6,3,1,1,1] [4,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg319 + +lemma sg1788 : RowSquare [6,3,1,1,1] [4,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg320 + +lemma sg1789 : RowSquare [6,3,1,1,1] [4,4,4] := by + exact rowSquare_join (by decide) sg4 sg543 + +lemma sg1790 : RowSquare [6,3,1,1,1] [5,4,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg273 + +lemma sg1791 : RowSquare [6,3,1,1,1] [5,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg324 + +lemma sg1792 : RowSquare [6,3,1,1,1] [5,5,2] := by + exact rowSquare_join (by decide) sg17 sg276 + +lemma sg1793 : RowSquare [6,3,1,1,1] [6,6] := by + exact rowSquare_join (by decide) sg17 sg281 + +lemma sg1794 : RowSquare [6,3,2,1] [3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg330 + +lemma sg1795 : RowSquare [6,3,2,1] [3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg178 + +lemma sg1796 : RowSquare [6,3,2,1] [3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg66 + +lemma sg1797 : RowSquare [6,3,2,1] [3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg330 + +lemma sg1798 : RowSquare [6,3,2,1] [3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg27 sg178 + +lemma sg1799 : RowSquare [6,3,2,1] [3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg67 + +lemma sg1800 : RowSquare [6,3,2,1] [3,3,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg143 + +lemma sg1801 : RowSquare [6,3,2,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg68 + +lemma sg1802 : RowSquare [6,3,2,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg32 sg144 + +lemma sg1803 : RowSquare [6,3,2,1] [4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg850 + +lemma sg1804 : RowSquare [6,3,2,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg71 + +lemma sg1805 : RowSquare [6,3,2,1] [4,4,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg148 + +lemma sg1806 : RowSquare [6,3,2,1] [4,4,2,2] := by + exact rowSquare_join (by decide) sg76 sg67 + +lemma sg1807 : RowSquare [6,3,2,1] [4,4,3,1] := by + exact rowSquare_join (by decide) sg88 sg55 + +lemma sg1808 : RowSquare [6,3,2,1] [4,4,4] := by + exact rowSquare_join (by decide) sg89 sg55 + +lemma sg1809 : RowSquare [6,3,3] [3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg154 + +lemma sg1810 : RowSquare [6,3,3] [4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg516 + +lemma sg1811 : RowSquare [6,4,1,1] [2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg330 + +lemma sg1812 : RowSquare [6,4,1,1] [3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg561 + +lemma sg1813 : RowSquare [6,4,1,1] [3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg331 + +lemma sg1814 : RowSquare [6,4,1,1] [3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg330 + +lemma sg1815 : RowSquare [6,4,1,1] [3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg562 + +lemma sg1816 : RowSquare [6,4,1,1] [3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg332 + +lemma sg1817 : RowSquare [6,4,1,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg563 + +lemma sg1818 : RowSquare [6,4,1,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg333 + +lemma sg1819 : RowSquare [6,4,1,1] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg334 + +lemma sg1820 : RowSquare [6,4,1,1] [4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg565 + +lemma sg1821 : RowSquare [6,4,1,1] [4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg142 + +lemma sg1822 : RowSquare [6,4,1,1] [4,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg879 + +lemma sg1823 : RowSquare [6,4,1,1] [4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg331 + +lemma sg1824 : RowSquare [6,4,1,1] [4,3,2,2,1] := by + exact rowSquare_join (by decide) sg39 sg143 + +lemma sg1825 : RowSquare [6,4,1,1] [4,3,3,1,1] := by + exact rowSquare_join (by decide) sg66 sg83 + +lemma sg1826 : RowSquare [6,4,1,1] [4,3,3,2] := by + exact rowSquare_join (by decide) sg39 sg144 + +lemma sg1827 : RowSquare [6,4,1,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg295 + +lemma sg1828 : RowSquare [6,4,1,1] [4,4,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg143 + +lemma sg1829 : RowSquare [6,4,1,1] [4,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg338 + +lemma sg1830 : RowSquare [6,4,1,1] [4,4,3,1] := by + exact rowSquare_join (by decide) sg67 sg83 + +lemma sg1831 : RowSquare [6,4,1,1] [4,4,4] := by + exact rowSquare_join (by decide) sg97 sg55 + +lemma sg1832 : RowSquare [6,4,1,1] [5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg330 + +lemma sg1833 : RowSquare [6,4,1,1] [5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg565 + +lemma sg1834 : RowSquare [6,4,1,1] [5,2,2,2,1] := by + exact rowSquare_join (by decide) sg66 sg84 + +lemma sg1835 : RowSquare [6,4,1,1] [5,3,3,1] := by + exact rowSquare_join (by decide) sg98 sg55 + +lemma sg1836 : RowSquare [6,4,1,1] [5,4,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg143 + +lemma sg1837 : RowSquare [6,4,1,1] [5,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg342 + +lemma sg1838 : RowSquare [6,4,1,1] [5,5,2] := by + exact rowSquare_join (by decide) sg83 sg71 + +lemma sg1839 : RowSquare [6,4,1,1] [6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg331 + +lemma sg1840 : RowSquare [6,4,1,1] [6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg142 + +lemma sg1841 : RowSquare [6,4,1,1] [6,6] := by + exact rowSquare_join (by decide) sg17 sg302 + +lemma sg1842 : RowSquare [6,4,1,1] [7,5] := by + exact rowSquare_join (by decide) sg71 sg85 + +lemma sg1843 : RowSquare [6,4,1,1] [9,3] := by + exact rowSquare_join (by decide) sg71 sg86 + +lemma sg1844 : RowSquare [6,4,2] [2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg74 + +lemma sg1845 : RowSquare [6,4,2] [3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg75 + +lemma sg1846 : RowSquare [6,4,2] [3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg577 + +lemma sg1847 : RowSquare [6,4,2] [3,3,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg166 + +lemma sg1848 : RowSquare [6,4,2] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg350 + +lemma sg1849 : RowSquare [6,5,1] [3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg356 + +lemma sg1850 : RowSquare [6,5,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg83 + +lemma sg1851 : RowSquare [6,5,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg357 + +lemma sg1852 : RowSquare [6,5,1] [4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg982 + +lemma sg1853 : RowSquare [6,5,1] [4,3,3,1,1] := by + exact rowSquare_join (by decide) sg75 sg83 + +lemma sg1854 : RowSquare [6,5,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg356 + +lemma sg1855 : RowSquare [6,5,1] [4,4,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg166 + +lemma sg1856 : RowSquare [6,5,1] [4,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg360 + +lemma sg1857 : RowSquare [6,5,1] [4,4,4] := by + exact rowSquare_join (by decide) sg83 sg77 + +lemma sg1858 : RowSquare [6,5,1] [5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg165 + +lemma sg1859 : RowSquare [6,5,1] [5,2,2,2,1] := by + exact rowSquare_join (by decide) sg75 sg84 + +lemma sg1860 : RowSquare [6,5,1] [5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg85 + +lemma sg1861 : RowSquare [6,5,1] [5,3,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg168 + +lemma sg1862 : RowSquare [6,5,1] [5,4,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg166 + +lemma sg1863 : RowSquare [6,5,1] [5,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg363 + +lemma sg1864 : RowSquare [6,5,1] [6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg165 + +lemma sg1865 : RowSquare [6,5,1] [6,2,2,1,1] := by + exact rowSquare_join (by decide) sg41 sg168 + +lemma sg1866 : RowSquare [6,5,1] [6,3,1,1,1] := by + exact rowSquare_join (by decide) sg75 sg85 + +lemma sg1867 : RowSquare [6,5,1] [6,6] := by + exact rowSquare_join (by decide) sg14 sg363 + +lemma sg1868 : RowSquare [6,6] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg364 + +lemma sg1869 : RowSquare [6,6] [4,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg365 + +lemma sg1870 : RowSquare [6,6] [5,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg367 + +lemma sg1872 : RowSquare [7,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1327 + +lemma sg1873 : RowSquare [7,1,1,1,1,1] [3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg1332 + +lemma sg1874 : RowSquare [7,2,1,1,1] [2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg586 + +lemma sg1875 : RowSquare [7,2,1,1,1] [3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg586 + +lemma sg1876 : RowSquare [7,2,1,1,1] [3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg587 + +lemma sg1877 : RowSquare [7,2,1,1,1] [3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg588 + +lemma sg1878 : RowSquare [7,2,1,1,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg589 + +lemma sg1879 : RowSquare [7,2,1,1,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg590 + +lemma sg1880 : RowSquare [7,2,1,1,1] [4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg586 + +lemma sg1881 : RowSquare [7,2,1,1,1] [4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg312 + +lemma sg1882 : RowSquare [7,2,1,1,1] [4,3,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg590 + +lemma sg1883 : RowSquare [7,2,1,1,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg313 + +lemma sg1884 : RowSquare [7,2,1,1,1] [4,4,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg314 + +lemma sg1885 : RowSquare [7,2,1,1,1] [4,4,2,2] := by + exact rowSquare_join (by decide) sg17 sg315 + +lemma sg1886 : RowSquare [7,2,1,1,1] [4,4,3,1] := by + exact rowSquare_join (by decide) sg4 sg596 + +lemma sg1887 : RowSquare [7,2,1,1,1] [5,4,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg317 + +lemma sg1888 : RowSquare [7,2,1,1,1] [5,5,1,1] := by + exact rowSquare_join (by decide) sg17 sg319 + +lemma sg1889 : RowSquare [7,2,1,1,1] [5,5,2] := by + exact rowSquare_join (by decide) sg17 sg320 + +lemma sg1890 : RowSquare [7,2,1,1,1] [6,6] := by + exact rowSquare_join (by decide) sg17 sg324 + +lemma sg1891 : RowSquare [7,2,2,1] [2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg178 + +lemma sg1892 : RowSquare [7,2,2,1] [3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg178 + +lemma sg1893 : RowSquare [7,2,2,1] [3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg179 + +lemma sg1894 : RowSquare [7,2,2,1] [3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg34 sg178 + +lemma sg1895 : RowSquare [7,2,2,1] [3,3,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg180 + +lemma sg1896 : RowSquare [7,2,2,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg32 sg181 + +lemma sg1897 : RowSquare [7,2,2,1] [4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg940 + +lemma sg1898 : RowSquare [7,2,2,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg371 + +lemma sg1899 : RowSquare [7,2,2,1] [4,4,2,2] := by + exact rowSquare_join (by decide) sg88 sg67 + +lemma sg1900 : RowSquare [7,2,2,1] [4,4,4] := by + exact rowSquare_join (by decide) sg89 sg68 + +lemma sg1901 : RowSquare [7,3,1,1] [3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg330 + +lemma sg1902 : RowSquare [7,3,1,1] [3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg178 + +lemma sg1903 : RowSquare [7,3,1,1] [3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg330 + +lemma sg1904 : RowSquare [7,3,1,1] [3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg178 + +lemma sg1905 : RowSquare [7,3,1,1] [3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg371 + +lemma sg1906 : RowSquare [7,3,1,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg615 + +lemma sg1907 : RowSquare [7,3,1,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg372 + +lemma sg1908 : RowSquare [7,3,1,1] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg373 + +lemma sg1909 : RowSquare [7,3,1,1] [4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg330 + +lemma sg1910 : RowSquare [7,3,1,1] [4,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg961 + +lemma sg1911 : RowSquare [7,3,1,1] [4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg178 + +lemma sg1912 : RowSquare [7,3,1,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg332 + +lemma sg1913 : RowSquare [7,3,1,1] [4,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg377 + +lemma sg1914 : RowSquare [7,3,2] [3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg87 + +lemma sg1915 : RowSquare [7,3,2] [3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg88 + +lemma sg1916 : RowSquare [7,3,2] [3,3,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg194 + +lemma sg1917 : RowSquare [7,3,2] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg89 + +lemma sg1918 : RowSquare [7,3,2] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg32 sg195 + +lemma sg1919 : RowSquare [7,3,2] [4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg975 + +lemma sg1920 : RowSquare [7,3,2] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg92 + +lemma sg1921 : RowSquare [7,3,2] [5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg306 + +lemma sg1922 : RowSquare [7,3,2] [5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg577 + +lemma sg1923 : RowSquare [7,3,2] [6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg307 + +lemma sg1924 : RowSquare [7,4,1] [3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg97 + +lemma sg1925 : RowSquare [7,4,1] [3,3,3,2,1] := by + exact rowSquare_join (by decide) sg32 sg207 + +lemma sg1926 : RowSquare [7,4,1] [3,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg390 + +lemma sg1927 : RowSquare [7,4,1] [4,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg982 + +lemma sg1929 : RowSquare [7,5] [4,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg402 + +lemma sg1935 : RowSquare [7,5] [5,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg407 + +lemma sg1943 : RowSquare [7,5] [6,6] := by + exact rowSquare_join (by decide) sg17 sg367 + +lemma sg1944 : RowSquare [8,1,1,1,1] [4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg586 + +lemma sg1945 : RowSquare [8,1,1,1,1] [4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg998 + +lemma sg1946 : RowSquare [8,1,1,1,1] [4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg999 + +lemma sg1947 : RowSquare [8,1,1,1,1] [4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg1000 + +lemma sg1948 : RowSquare [8,1,1,1,1] [4,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg1001 + +lemma sg1949 : RowSquare [8,1,1,1,1] [5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg587 + +lemma sg1950 : RowSquare [8,1,1,1,1] [5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg588 + +lemma sg1951 : RowSquare [8,1,1,1,1] [5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1006 + +lemma sg1952 : RowSquare [8,1,1,1,1] [5,3,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg1007 + +lemma sg1953 : RowSquare [8,1,1,1,1] [5,3,2,2] := by + exact rowSquare_join (by decide) sg2 sg1008 + +lemma sg1954 : RowSquare [8,2,1,1] [4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg178 + +lemma sg1955 : RowSquare [8,2,1,1] [4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg1032 + +lemma sg1956 : RowSquare [8,2,1,1] [4,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg1033 + +lemma sg1957 : RowSquare [8,2,1,1] [4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg178 + +lemma sg1958 : RowSquare [8,2,1,1] [4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg371 + +lemma sg1959 : RowSquare [8,2,1,1] [4,3,3,1,1] := by + exact rowSquare_join (by decide) sg16 sg372 + +lemma sg1960 : RowSquare [8,2,1,1] [4,3,3,2] := by + exact rowSquare_join (by decide) sg16 sg373 + +lemma sg1961 : RowSquare [8,2,1,1] [4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg371 + +lemma sg1962 : RowSquare [8,2,1,1] [4,4,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg372 + +lemma sg1963 : RowSquare [8,2,1,1] [4,4,2,2] := by + exact rowSquare_join (by decide) sg17 sg373 + +lemma sg1964 : RowSquare [8,2,1,1] [5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg330 + +lemma sg1965 : RowSquare [8,2,1,1] [5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg47 sg178 + +lemma sg1966 : RowSquare [8,2,1,1] [5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg179 + +lemma sg1967 : RowSquare [8,2,1,1] [5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg179 + +lemma sg1968 : RowSquare [8,2,1,1] [5,5,1,1] := by + exact rowSquare_join (by decide) sg17 sg377 + +lemma sg1969 : RowSquare [8,2,1,1] [6,6] := by + exact rowSquare_join (by decide) sg17 sg383 + +lemma sg1970 : RowSquare [8,2,2] [4,2,2,2,2] := by + exact rowSquare_join (by decide) sg87 sg87 + +lemma sg1971 : RowSquare [8,2,2] [4,3,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg88 + +lemma sg1972 : RowSquare [8,2,2] [4,3,3,1,1] := by + exact rowSquare_join (by decide) sg87 sg89 + +lemma sg1973 : RowSquare [8,2,2] [4,4,2,2] := by + exact rowSquare_join (by decide) sg88 sg88 + +lemma sg1974 : RowSquare [8,2,2] [4,4,3,1] := by + exact rowSquare_join (by decide) sg88 sg89 + +lemma sg1975 : RowSquare [8,2,2] [4,4,4] := by + exact rowSquare_join (by decide) sg89 sg89 + +lemma sg1976 : RowSquare [8,2,2] [5,5,1,1] := by + exact rowSquare_join (by decide) sg88 sg92 + +lemma sg1977 : RowSquare [8,3,1] [4,3,3,1,1] := by + exact rowSquare_join (by decide) sg87 sg97 + +lemma sg1978 : RowSquare [8,3,1] [4,3,3,2] := by + exact rowSquare_join (by decide) sg16 sg390 + +lemma sg1979 : RowSquare [8,3,1] [4,4,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg228 + +lemma sg1980 : RowSquare [8,3,1] [4,4,2,2] := by + exact rowSquare_join (by decide) sg17 sg390 + +lemma sg1981 : RowSquare [8,3,1] [4,4,3,1] := by + exact rowSquare_join (by decide) sg88 sg97 + +lemma sg1982 : RowSquare [8,3,1] [4,4,4] := by + exact rowSquare_join (by decide) sg97 sg89 + +lemma sg1983 : RowSquare [8,3,1] [5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg104 + +lemma sg1984 : RowSquare [8,3,1] [5,2,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg98 + +lemma sg1985 : RowSquare [8,3,1] [5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg105 + +lemma sg1986 : RowSquare [8,3,1] [5,3,2,1,1] := by + exact rowSquare_join (by decide) sg87 sg99 + +lemma sg1987 : RowSquare [8,3,1] [5,3,2,2] := by + exact rowSquare_join (by decide) sg88 sg98 + +lemma sg1988 : RowSquare [8,3,1] [5,3,3,1] := by + exact rowSquare_join (by decide) sg98 sg89 + +lemma sg1989 : RowSquare [8,3,1] [5,4,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg230 + +lemma sg1990 : RowSquare [8,3,1] [5,4,2,1] := by + exact rowSquare_join (by decide) sg88 sg99 + +lemma sg1991 : RowSquare [8,3,1] [5,5,1,1] := by + exact rowSquare_join (by decide) sg17 sg394 + +lemma sg1992 : RowSquare [8,3,1] [6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg106 + +lemma sg1993 : RowSquare [8,4] [5,3,3,1] := by + exact rowSquare_join (by decide) sg98 sg97 + +lemma sg1994 : RowSquare [8,4] [5,4,2,1] := by + exact rowSquare_join (by decide) sg39 sg228 + +lemma sg1995 : RowSquare [8,4] [5,4,3] := by + exact rowSquare_join (by decide) sg97 sg99 + +lemma sg1996 : RowSquare [8,4] [5,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg424 + +lemma sg1997 : RowSquare [8,4] [6,2,2,2] := by + exact rowSquare_join (by decide) sg98 sg98 + +lemma sg1998 : RowSquare [9,1,1,1] [6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg178 + +lemma sg1999 : RowSquare [9,1,1,1] [6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg371 + +lemma sg2000 : RowSquare [9,1,1,1] [6,2,2,1,1] := by + exact rowSquare_join (by decide) sg20 sg372 + +lemma sg2001 : RowSquare [9,1,1,1] [6,2,2,2] := by + exact rowSquare_join (by decide) sg20 sg373 + +lemma sg2002 : RowSquare [9,2,1] [6,2,2,1,1] := by + exact rowSquare_join (by decide) sg87 sg104 + +lemma sg2003 : RowSquare [9,2,1] [6,2,2,2] := by + exact rowSquare_join (by decide) sg20 sg390 + +lemma sg2004 : RowSquare [9,2,1] [6,3,1,1,1] := by + exact rowSquare_join (by decide) sg87 sg105 + +lemma sg2005 : RowSquare [9,2,1] [6,3,2,1] := by + exact rowSquare_join (by decide) sg88 sg104 + +lemma sg2006 : RowSquare [9,2,1] [6,4,1,1] := by + exact rowSquare_join (by decide) sg88 sg105 + +lemma sg2007 : RowSquare [9,2,1] [6,4,2] := by + exact rowSquare_join (by decide) sg89 sg105 + +lemma sg2008 : RowSquare [9,3] [6,3,3] := by + exact rowSquare_join (by decide) sg97 sg104 + +lemma sg2009 : RowSquare [9,3] [6,4,2] := by + exact rowSquare_join (by decide) sg97 sg105 + +lemma sg2010 : RowSquare [9,3] [6,5,1] := by + exact rowSquare_join (by decide) sg46 sg228 + +lemma sg2011 : RowSquare [9,3] [6,6] := by + exact rowSquare_join (by decide) sg17 sg424 + +lemma sg2012 : RowSquare [9,3] [7,2,2,1] := by + exact rowSquare_join (by decide) sg98 sg104 + +lemma sg2013 : RowSquare [9,3] [7,3,1,1] := by + exact rowSquare_join (by decide) sg98 sg105 + +lemma sg2014 : RowSquare [2,2,2,1,1,1,1,1,1,1] [7,6] := by + exact rowSquare_join (by decide) sg46 sg424 + +lemma sg2020 : RowSquare [3,2,1,1,1,1,1,1,1,1] [8,5] := by + exact rowSquare_join (by decide) sg92 sg232 + +lemma sg2021 : RowSquare [3,3,1,1,1,1,1,1,1] [5,2,2,2,2] := by + exact rowSquare_join (by decide) sg87 sg218 + +lemma sg2022 : RowSquare [3,3,1,1,1,1,1,1,1] [5,3,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg219 + +lemma sg2023 : RowSquare [3,3,1,1,1,1,1,1,1] [5,3,3,1,1] := by + exact rowSquare_join (by decide) sg87 sg220 + +lemma sg2024 : RowSquare [3,3,1,1,1,1,1,1,1] [5,4,2,2] := by + exact rowSquare_join (by decide) sg88 sg219 + +lemma sg2025 : RowSquare [3,3,1,1,1,1,1,1,1] [6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg1063 + +lemma sg2026 : RowSquare [3,3,1,1,1,1,1,1,1] [7,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg348 + +lemma sg2027 : RowSquare [3,3,1,1,1,1,1,1,1] [7,2,2,1,1] := by + exact rowSquare_join (by decide) sg87 sg224 + +lemma sg2028 : RowSquare [3,3,1,1,1,1,1,1,1] [7,2,2,2] := by + exact rowSquare_join (by decide) sg90 sg221 + +lemma sg2029 : RowSquare [3,3,1,1,1,1,1,1,1] [7,4,1,1] := by + exact rowSquare_join (by decide) sg88 sg225 + +lemma sg2030 : RowSquare [3,3,1,1,1,1,1,1,1] [7,4,2] := by + exact rowSquare_join (by decide) sg89 sg225 + +lemma sg2031 : RowSquare [3,3,1,1,1,1,1,1,1] [7,6] := by + exact rowSquare_join (by decide) sg92 sg223 + +lemma sg2032 : RowSquare [3,3,1,1,1,1,1,1,1] [8,2,2,1] := by + exact rowSquare_join (by decide) sg90 sg224 + +lemma sg2033 : RowSquare [3,3,1,1,1,1,1,1,1] [8,5] := by + exact rowSquare_join (by decide) sg92 sg225 + +lemma sg2034 : RowSquare [3,3,1,1,1,1,1,1,1] [9,2,1,1] := by + exact rowSquare_join (by decide) sg88 sg226 + +lemma sg2035 : RowSquare [3,3,2,1,1,1,1,1] [4,3,3,3] := by + exact rowSquare_join (by decide) sg33 sg390 + +lemma sg2036 : RowSquare [3,3,2,2,2,1] [3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg165 + +lemma sg2037 : RowSquare [4,1,1,1,1,1,1,1,1,1] [9,4] := by + exact rowSquare_join (by decide) sg49 sg383 + +lemma sg2038 : RowSquare [4,2,2,1,1,1,1,1] [4,4,4,1] := by + exact rowSquare_join (by decide) sg97 sg181 + +lemma sg2039 : RowSquare [4,3,1,1,1,1,1,1] [3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg87 sg178 + +lemma sg2040 : RowSquare [4,3,1,1,1,1,1,1] [3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg88 sg178 + +lemma sg2041 : RowSquare [4,3,1,1,1,1,1,1] [3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg371 + +lemma sg2042 : RowSquare [4,3,1,1,1,1,1,1] [3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg178 + +lemma sg2043 : RowSquare [4,3,1,1,1,1,1,1] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg32 sg372 + +lemma sg2044 : RowSquare [4,3,1,1,1,1,1,1] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg373 + +lemma sg2045 : RowSquare [4,3,1,1,1,1,1,1] [4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg90 sg178 + +lemma sg2046 : RowSquare [4,3,1,1,1,1,1,1] [4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg179 + +lemma sg2047 : RowSquare [4,3,1,1,1,1,1,1] [4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg91 sg178 + +lemma sg2048 : RowSquare [4,3,1,1,1,1,1,1] [4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg88 sg179 + +lemma sg2049 : RowSquare [4,3,1,1,1,1,1,1] [4,3,2,2,2] := by + exact rowSquare_join (by decide) sg87 sg180 + +lemma sg2050 : RowSquare [4,3,1,1,1,1,1,1] [4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg179 + +lemma sg2051 : RowSquare [4,3,1,1,1,1,1,1] [4,3,3,2,1] := by + exact rowSquare_join (by decide) sg87 sg181 + +lemma sg2052 : RowSquare [4,3,1,1,1,1,1,1] [4,3,3,3] := by + exact rowSquare_join (by decide) sg33 sg373 + +lemma sg2053 : RowSquare [4,3,1,1,1,1,1,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg178 + +lemma sg2054 : RowSquare [4,3,1,1,1,1,1,1] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg34 sg371 + +lemma sg2055 : RowSquare [4,3,1,1,1,1,1,1] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg88 sg180 + +lemma sg2056 : RowSquare [4,3,1,1,1,1,1,1] [4,4,3,1,1] := by + exact rowSquare_join (by decide) sg89 sg180 + +lemma sg2057 : RowSquare [4,3,1,1,1,1,1,1] [4,4,3,2] := by + exact rowSquare_join (by decide) sg88 sg181 + +lemma sg2058 : RowSquare [4,3,1,1,1,1,1,1] [4,4,4,1] := by + exact rowSquare_join (by decide) sg89 sg181 + +lemma sg2059 : RowSquare [4,3,1,1,1,1,1,1] [5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg940 + +lemma sg2060 : RowSquare [4,3,1,1,1,1,1,1] [5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg93 sg178 + +lemma sg2061 : RowSquare [4,3,1,1,1,1,1,1] [5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg90 sg179 + +lemma sg2062 : RowSquare [4,3,1,1,1,1,1,1] [5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg94 sg178 + +lemma sg2063 : RowSquare [4,3,1,1,1,1,1,1] [5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg91 sg179 + +lemma sg2064 : RowSquare [4,3,1,1,1,1,1,1] [5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg179 + +lemma sg2065 : RowSquare [4,3,1,1,1,1,1,1] [5,4,4] := by + exact rowSquare_join (by decide) sg0 sg1597 + +lemma sg2066 : RowSquare [4,3,1,1,1,1,1,1] [7,6] := by + exact rowSquare_join (by decide) sg0 sg1606 + +lemma sg2067 : RowSquare [4,3,1,1,1,1,1,1] [8,5] := by + exact rowSquare_join (by decide) sg5 sg722 + +lemma sg2068 : RowSquare [4,3,1,1,1,1,1,1] [9,4] := by + exact rowSquare_join (by decide) sg14 sg429 + +lemma sg2069 : RowSquare [4,3,1,1,1,1,1,1] [10,3] := by + exact rowSquare_join (by decide) sg14 sg430 + +lemma sg2070 : RowSquare [4,3,1,1,1,1,1,1] [11,2] := by + exact rowSquare_join (by decide) sg42 sg235 + +lemma sg2071 : RowSquare [4,3,1,1,1,1,1,1] [12,1] := by + exact rowSquare_join (by decide) sg43 sg235 + +lemma sg2073 : RowSquare [4,3,2,1,1,1,1] [2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg330 + +lemma sg2074 : RowSquare [4,3,2,1,1,1,1] [2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg178 + +lemma sg2075 : RowSquare [4,3,2,1,1,1,1] [3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg179 + +lemma sg2076 : RowSquare [4,3,2,1,1,1,1] [3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg180 + +lemma sg2077 : RowSquare [4,3,2,1,1,1,1] [4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg849 + +lemma sg2078 : RowSquare [4,3,2,1,1,1,1] [4,3,3,3] := by + exact rowSquare_join (by decide) sg33 sg334 + +lemma sg2079 : RowSquare [4,3,2,2,1,1] [4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg849 + +lemma sg2080 : RowSquare [4,3,2,2,1,1] [4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg850 + +lemma sg2081 : RowSquare [4,3,2,2,1,1] [5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg850 + +lemma sg2082 : RowSquare [4,4,1,1,1,1,1] [3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg66 sg178 + +lemma sg2083 : RowSquare [4,4,1,1,1,1,1] [3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg67 sg178 + +lemma sg2084 : RowSquare [4,4,1,1,1,1,1] [3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg178 + +lemma sg2085 : RowSquare [4,4,1,1,1,1,1] [4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg69 sg178 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes30.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes30.lean index 672ff367c0f1f7f45dd19571c72286ff4ba93a91..cca0f4126569f0202c0ff2899c912aac4b3f1786 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes30.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes30.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes28 - -namespace OAI - -/-! Semigroup Nodes 30. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg12540 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1902 sg2370 - -lemma sg12541 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2411 - -lemma sg12542 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1901 sg2371 - -lemma sg12543 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2412 - -lemma sg12544 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2413 - -lemma sg12545 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2414 - -lemma sg12546 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2415 - -lemma sg12547 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2416 - -lemma sg12548 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1903 sg2370 - -lemma sg12549 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2417 - -lemma sg12550 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1903 sg2371 - -lemma sg12551 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1905 sg2370 - -lemma sg12552 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1417 sg3115 - -lemma sg12553 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2418 - -lemma sg12554 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2419 - -lemma sg12555 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1908 sg2370 - -lemma sg12556 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1417 sg3116 - -lemma sg12557 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1417 sg3117 - -lemma sg12558 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2420 - -lemma sg12559 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2421 - -lemma sg12560 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1907 sg2371 - -lemma sg12561 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1908 sg2371 - -lemma sg12562 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4] := by - exact rowSquare_join (by decide) sg1033 sg3722 - -lemma sg12563 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2422 - -lemma sg12564 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg1906 sg2372 - -lemma sg12565 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2] := by - exact rowSquare_join (by decide) sg1906 sg2373 - -lemma sg12566 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1] := by - exact rowSquare_join (by decide) sg1906 sg2374 - -lemma sg12567 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1874 sg2423 - -lemma sg12568 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2424 - -lemma sg12569 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1901 sg2376 - -lemma sg12570 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2426 - -lemma sg12571 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1875 sg2410 - -lemma sg12572 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2427 - -lemma sg12573 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1901 sg2377 - -lemma sg12574 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1875 sg2413 - -lemma sg12575 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2428 - -lemma sg12576 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1901 sg2378 - -lemma sg12577 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1901 sg2380 - -lemma sg12578 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1875 sg2417 - -lemma sg12579 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1903 sg2377 - -lemma sg12580 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2429 - -lemma sg12581 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1901 sg2382 - -lemma sg12582 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1875 sg2419 - -lemma sg12583 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1903 sg2380 - -lemma sg12584 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2430 - -lemma sg12585 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg2431 - -lemma sg12586 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1968 sg2291 - -lemma sg12587 : RowSquare [5,4,2,2,2,2,2,2,2,1,1] [7,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1492 sg2596 - -lemma sg12588 : RowSquare [5,4,2,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1493 sg2596 - -lemma sg12589 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg4539 - -lemma sg12590 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5] := by - exact rowSquare_join (by decide) sg1033 sg3691 - -lemma sg12591 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1] [5,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1688 sg2314 - -lemma sg12592 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1877 sg2382 - -lemma sg12593 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5] := by - exact rowSquare_join (by decide) sg1001 sg3476 - -lemma sg12594 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2287 - -lemma sg12595 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2288 - -lemma sg12596 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2291 - -lemma sg12597 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2167 - -lemma sg12598 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1754 sg2270 - -lemma sg12599 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2271 - -lemma sg12600 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2275 - -lemma sg12601 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2276 - -lemma sg12602 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2277 - -lemma sg12603 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg2626 - -lemma sg12604 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1327 sg2627 - -lemma sg12605 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1332 sg2626 - -lemma sg12606 : RowSquare [7,5,2,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1372 sg2702 - -lemma sg12607 : RowSquare [7,5,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1378 sg2702 - -lemma sg12608 : RowSquare [7,5,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1780 sg2251 - -lemma sg12609 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg4160 - -lemma sg12610 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1682 sg2251 - -lemma sg12611 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg586 sg4161 - -lemma sg12612 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg4160 - -lemma sg12613 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg589 sg4160 - -lemma sg12614 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg590 sg4160 - -lemma sg12615 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1687 sg2251 - -lemma sg12616 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg586 sg4165 - -lemma sg12617 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg591 sg4160 - -lemma sg12618 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg594 sg4160 - -lemma sg12619 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg587 sg4167 - -lemma sg12620 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg595 sg4160 - -lemma sg12621 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg4160 - -lemma sg12622 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg588 sg4165 - -lemma sg12623 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg588 sg4167 - -lemma sg12624 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg589 sg4167 - -lemma sg12625 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg597 sg4160 - -lemma sg12626 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg599 sg4160 - -lemma sg12627 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg587 sg4168 - -lemma sg12628 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg601 sg4160 - -lemma sg12629 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg596 sg4161 - -lemma sg12630 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg4160 - -lemma sg12631 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg601 sg4161 - -lemma sg12632 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg607 sg4160 - -lemma sg12633 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg602 sg4161 - -lemma sg12634 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg607 sg4161 - -lemma sg12635 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1327 sg2702 - -lemma sg12636 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1754 sg2251 - -lemma sg12637 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg2702 - -lemma sg12638 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1755 sg2251 - -lemma sg12639 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg2702 - -lemma sg12640 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1756 sg2251 - -lemma sg12641 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2254 - -lemma sg12642 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1327 sg2705 - -lemma sg12643 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2255 - -lemma sg12644 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1332 sg2702 - -lemma sg12645 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1758 sg2251 - -lemma sg12646 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2256 - -lemma sg12647 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1766 sg2251 - -lemma sg12648 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1257 sg2702 - -lemma sg12649 : RowSquare [7,6,4,3,2,2,1] [2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1728 sg2019 - -lemma sg12650 : RowSquare [7,6,4,3,2,2,1] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1728 sg2018 - -lemma sg12651 : RowSquare [7,6,4,3,2,2,1] [2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1728 sg2017 - -lemma sg12652 : RowSquare [7,6,4,3,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1728 sg2016 - -lemma sg12653 : RowSquare [7,6,4,3,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1728 sg2015 - -lemma sg12654 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1247 sg2702 - -lemma sg12655 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1248 sg2702 - -lemma sg12656 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1249 sg2702 - -lemma sg12657 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1250 sg2702 - -lemma sg12658 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1251 sg2702 - -lemma sg12659 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11816 - -lemma sg12660 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11817 - -lemma sg12661 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11818 - -lemma sg12662 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg11819 - -lemma sg12663 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11820 - -lemma sg12664 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11821 - -lemma sg12665 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg11822 - -lemma sg12666 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg11823 - -lemma sg12667 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg11824 - -lemma sg12668 : RowSquare [7,7,2,2,2,2,2,1] [6,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg11825 - -lemma sg12669 : RowSquare [7,7,3,2,2,2,2] [2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1611 sg2104 - -lemma sg12670 : RowSquare [7,7,3,2,2,2,2] [2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1611 sg2103 - -lemma sg12671 : RowSquare [7,7,3,2,2,2,2] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1611 sg2102 - -lemma sg12672 : RowSquare [7,7,3,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1611 sg2101 - -lemma sg12673 : RowSquare [7,7,3,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1611 sg2099 - -lemma sg12674 : RowSquare [7,7,3,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1611 sg2097 - -lemma sg12675 : RowSquare [7,7,3,2,2,2,2] [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1613 sg2105 - -lemma sg12676 : RowSquare [7,7,3,2,2,2,2] [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1609 sg2104 - -lemma sg12677 : RowSquare [7,7,3,2,2,2,2] [3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1609 sg2102 - -lemma sg12678 : RowSquare [7,7,3,2,2,2,2] [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1610 sg2105 - -lemma sg12679 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg888 sg3522 - -lemma sg12680 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg807 sg3521 - -lemma sg12681 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg809 sg3521 - -lemma sg12682 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg517 sg4345 - -lemma sg12683 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg519 sg4345 - -lemma sg12684 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg520 sg4345 - -lemma sg12685 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg814 sg3521 - -lemma sg12686 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg815 sg3521 - -lemma sg12687 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg816 sg3521 - -lemma sg12688 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg817 sg3521 - -lemma sg12689 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg523 sg4345 - -lemma sg12690 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg525 sg4345 - -lemma sg12691 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg821 sg3521 - -lemma sg12692 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg822 sg3521 - -lemma sg12693 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg823 sg3521 - -lemma sg12694 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg528 sg4345 - -lemma sg12695 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg825 sg3521 - -lemma sg12696 : RowSquare [8,6,2,2,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg767 sg3521 - -lemma sg12697 : RowSquare [8,6,3,2,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg110 sg5735 - -lemma sg12698 : RowSquare [8,6,3,2,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg111 sg5735 - -lemma sg12699 : RowSquare [8,6,3,2,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg112 sg5735 - -lemma sg12700 : RowSquare [8,6,3,2,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg113 sg5735 - -lemma sg12701 : RowSquare [8,7,2,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg740 sg3521 - -lemma sg12702 : RowSquare [9,7,2,1,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg109 sg5757 - -lemma sg12703 : RowSquare [10,3,2,2,2,2,2,1,1] [5,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg356 sg4746 - -lemma sg12704 : RowSquare [10,3,2,2,2,2,2,1,1] [5,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg74 sg6403 - -lemma sg12705 : RowSquare [10,3,2,2,2,2,2,1,1] [5,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg6404 - -lemma sg12706 : RowSquare [10,3,2,2,2,2,2,1,1] [5,5,5,4,3,3] := by - exact rowSquare_join (by decide) sg74 sg6405 - -lemma sg12707 : RowSquare [10,3,2,2,2,2,2,1,1] [5,5,5,5,5] := by - exact rowSquare_join (by decide) sg32 sg7807 - -lemma sg12708 : RowSquare [10,3,2,2,2,2,2,1,1] [6,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg165 sg5620 - -lemma sg12709 : RowSquare [10,3,2,2,2,2,2,1,1] [6,6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg356 sg4749 - -lemma sg12710 : RowSquare [10,3,2,2,2,2,2,2] [6,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg165 sg5538 - -lemma sg12711 : RowSquare [10,3,2,2,2,2,2,2] [6,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg165 sg5544 - -lemma sg12712 : RowSquare [10,3,2,2,2,2,2,2] [6,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg165 sg5545 - -lemma sg12713 : RowSquare [10,3,2,2,2,2,2,2] [6,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg165 sg5547 - -lemma sg12714 : RowSquare [10,3,2,2,2,2,2,2] [6,6,4,3,3,3] := by - exact rowSquare_join (by decide) sg579 sg3870 - -lemma sg12715 : RowSquare [10,3,2,2,2,2,2,2] [6,6,5,3,3,2] := by - exact rowSquare_join (by decide) sg579 sg3871 - -lemma sg12716 : RowSquare [10,3,2,2,2,2,2,2] [7,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg165 sg5559 - -lemma sg12717 : RowSquare [10,3,2,2,2,2,2,2] [7,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg165 sg5560 - -lemma sg12718 : RowSquare [10,3,2,2,2,2,2,2] [7,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg581 sg3870 - -lemma sg12719 : RowSquare [10,3,3,2,2,2,2,1] [5,5,5,4,3,3] := by - exact rowSquare_join (by decide) sg74 sg6293 - -lemma sg12720 : RowSquare [11,3,2,2,2,2,2,1] [5,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg6197 - -lemma sg12721 : RowSquare [11,3,2,2,2,2,2,1] [5,5,5,4,3,3] := by - exact rowSquare_join (by decide) sg74 sg6199 - -lemma sg12722 : RowSquare [12,3,2,2,2,2,2] [6,6,5,4,4] := by - exact rowSquare_join (by decide) sg27 sg6919 - -lemma sg12723 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg1455 sg3732 - -lemma sg12724 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1456 sg3732 - -lemma sg12725 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2] := by - exact rowSquare_join (by decide) sg1914 sg3068 - -lemma sg12726 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1] := by - exact rowSquare_join (by decide) sg1914 sg3069 - -lemma sg12727 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5] := by - exact rowSquare_join (by decide) sg1532 sg3658 - -lemma sg12728 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2] := by - exact rowSquare_join (by decide) sg1455 sg3733 - -lemma sg12729 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg1533 sg3656 - -lemma sg12730 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,2] := by - exact rowSquare_join (by decide) sg1915 sg3068 - -lemma sg12731 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1] := by - exact rowSquare_join (by decide) sg2329 sg2432 - -lemma sg12732 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1] := by - exact rowSquare_join (by decide) sg2329 sg2433 - -lemma sg12733 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4] := by - exact rowSquare_join (by decide) sg1916 sg3069 - -lemma sg12734 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3] := by - exact rowSquare_join (by decide) sg2432 sg2330 - -lemma sg12735 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2] := by - exact rowSquare_join (by decide) sg2433 sg2330 - -lemma sg12736 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1970 sg2837 - -lemma sg12737 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg1535 sg3657 - -lemma sg12738 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg1919 sg3069 - -lemma sg12739 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4] := by - exact rowSquare_join (by decide) sg1970 sg2841 - -lemma sg12740 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,3] := by - exact rowSquare_join (by decide) sg1536 sg3657 - -lemma sg12741 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1971 sg2837 - -lemma sg12742 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg1456 sg3734 - -lemma sg12743 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg1972 sg2837 - -lemma sg12744 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg1456 sg3735 - -lemma sg12745 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,2] := by - exact rowSquare_join (by decide) sg1915 sg3071 - -lemma sg12746 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4] := by - exact rowSquare_join (by decide) sg2432 sg2331 - -lemma sg12747 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,3] := by - exact rowSquare_join (by decide) sg2436 sg2330 - -lemma sg12748 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3] := by - exact rowSquare_join (by decide) sg1063 sg4509 - -lemma sg12749 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg975 sg4540 - -lemma sg12750 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1537 sg3656 - -lemma sg12751 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1973 sg2837 - -lemma sg12752 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,2] := by - exact rowSquare_join (by decide) sg1915 sg3074 - -lemma sg12753 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4] := by - exact rowSquare_join (by decide) sg1916 sg3075 - -lemma sg12754 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg975 sg4541 - -lemma sg12755 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg1974 sg2837 - -lemma sg12756 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2,2] := by - exact rowSquare_join (by decide) sg1915 sg3076 - -lemma sg12757 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg975 sg4542 - -lemma sg12758 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,3] := by - exact rowSquare_join (by decide) sg2432 sg2334 - -lemma sg12759 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1] := by - exact rowSquare_join (by decide) sg1915 sg3078 - -lemma sg12760 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2] := by - exact rowSquare_join (by decide) sg2433 sg2334 - -lemma sg12761 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3] := by - exact rowSquare_join (by decide) sg2461 sg2219 - -lemma sg12762 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3] := by - exact rowSquare_join (by decide) sg2432 sg2336 - -lemma sg12763 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2] := by - exact rowSquare_join (by decide) sg2436 sg2332 - -lemma sg12764 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3] := by - exact rowSquare_join (by decide) sg2436 sg2334 - -lemma sg12765 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg2432 - -lemma sg12766 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg2311 sg2432 - -lemma sg12767 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg2433 - -lemma sg12768 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg2433 - -lemma sg12769 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg1891 sg3103 - -lemma sg12770 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg1455 sg3725 - -lemma sg12771 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg1455 sg3726 - -lemma sg12772 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2311 sg2434 - -lemma sg12773 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg2435 - -lemma sg12774 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2311 sg2436 - -lemma sg12775 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg2339 sg2392 - -lemma sg12776 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2341 - -lemma sg12777 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg2437 - -lemma sg12778 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg1456 sg3724 - -lemma sg12779 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2343 - -lemma sg12780 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg2439 - -lemma sg12781 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2344 - -lemma sg12782 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg1891 sg3104 - -lemma sg12783 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg2440 - -lemma sg12784 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg2441 - -lemma sg12785 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3] := by - exact rowSquare_join (by decide) sg1844 sg3125 - -lemma sg12786 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1891 sg3105 - -lemma sg12787 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2] := by - exact rowSquare_join (by decide) sg2340 sg2392 - -lemma sg12788 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2341 - -lemma sg12789 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2343 - -lemma sg12790 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2344 - -lemma sg12791 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg2444 - -lemma sg12792 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg2445 - -lemma sg12793 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2311 sg2446 - -lemma sg12794 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2347 - -lemma sg12795 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1458 sg3724 - -lemma sg12796 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2348 - -lemma sg12797 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2350 - -lemma sg12798 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg2448 - -lemma sg12799 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2347 - -lemma sg12800 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2351 - -lemma sg12801 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg2450 - -lemma sg12802 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2213 sg2456 - -lemma sg12803 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2213 sg2457 - -lemma sg12804 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2214 sg2456 - -lemma sg12805 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2326 sg2433 - -lemma sg12806 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1459 sg3724 - -lemma sg12807 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2213 sg2458 - -lemma sg12808 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2216 sg2457 - -lemma sg12809 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2214 sg2458 - -lemma sg12810 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg2462 - -lemma sg12811 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2353 - -lemma sg12812 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1803 sg3152 - -lemma sg12813 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2213 sg2459 - -lemma sg12814 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2213 sg2460 - -lemma sg12815 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2355 - -lemma sg12816 : RowSquare [4,4,2,2,2,2,2,2,2,2,1,1] [5,5,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1650 sg3106 - -lemma sg12817 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg2405 - -lemma sg12818 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg1926 sg2925 - -lemma sg12819 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg2409 - -lemma sg12820 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1927 sg2925 - -lemma sg12821 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg2417 - -lemma sg12822 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg1891 sg3009 - -lemma sg12823 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg1919 sg2925 - -lemma sg12824 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg2314 sg2392 - -lemma sg12825 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,3] := by - exact rowSquare_join (by decide) sg1032 sg4504 - -lemma sg12826 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg2399 - -lemma sg12827 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3] := by - exact rowSquare_join (by decide) sg976 sg4521 - -lemma sg12828 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2] := by - exact rowSquare_join (by decide) sg2392 sg2317 - -lemma sg12829 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1922 sg2925 - -lemma sg12830 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg2314 sg2396 - -lemma sg12831 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1923 sg2925 - -lemma sg12832 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg2314 sg2314 - -lemma sg12833 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1033 sg4341 - -lemma sg12834 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1300 sg3632 - -lemma sg12835 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1033 sg4342 - -lemma sg12836 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg2212 sg2284 - -lemma sg12837 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1300 sg3633 - -lemma sg12838 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1737 sg2925 - -lemma sg12839 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1301 sg3632 - -lemma sg12840 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2169 sg2310 - -lemma sg12841 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2169 sg2311 - -lemma sg12842 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1738 sg2925 - -lemma sg12843 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg1739 sg2925 - -lemma sg12844 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg3648 - -lemma sg12845 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2214 sg2284 - -lemma sg12846 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2311 sg2170 - -lemma sg12847 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1699 sg3004 - -lemma sg12848 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1740 sg2925 - -lemma sg12849 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg2314 sg2168 - -lemma sg12850 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1233 sg3730 - -lemma sg12851 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg2171 - -lemma sg12852 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2172 sg2310 - -lemma sg12853 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2172 sg2311 - -lemma sg12854 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1741 sg2925 - -lemma sg12855 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [7,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2169 sg2314 - -lemma sg12856 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [7,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1742 sg2925 - -lemma sg12857 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [7,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg2215 sg2286 - -lemma sg12858 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [8,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2221 sg2284 - -lemma sg12859 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [8,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2172 sg2314 - -lemma sg12860 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [8,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1743 sg2925 - -lemma sg12861 : RowSquare [5,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2407 - -lemma sg12862 : RowSquare [5,4,3,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1493 sg3299 - -lemma sg12863 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg2311 sg2167 - -lemma sg12864 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1] [5,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg1688 sg3004 - -lemma sg12865 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1] [6,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg2314 sg2167 - -lemma sg12866 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2288 sg2375 - -lemma sg12867 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2369 sg2289 - -lemma sg12868 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2369 sg2291 - -lemma sg12869 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2290 sg2371 - -lemma sg12870 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2379 - -lemma sg12871 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2380 - -lemma sg12872 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2381 - -lemma sg12873 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2290 sg2373 - -lemma sg12874 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg2290 sg2374 - -lemma sg12875 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2370 sg2291 - -lemma sg12876 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2382 - -lemma sg12877 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2371 sg2292 - -lemma sg12878 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2383 - -lemma sg12879 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2371 sg2293 - -lemma sg12880 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2296 - -lemma sg12881 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2384 - -lemma sg12882 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2385 - -lemma sg12883 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2386 - -lemma sg12884 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2371 sg2297 - -lemma sg12885 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg2293 sg2373 - -lemma sg12886 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg2293 sg2374 - -lemma sg12887 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1] := by - exact rowSquare_join (by decide) sg2373 sg2297 - -lemma sg12888 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,3] := by - exact rowSquare_join (by decide) sg2374 sg2297 - -lemma sg12889 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2369 sg2298 - -lemma sg12890 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2290 sg2376 - -lemma sg12891 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2370 sg2298 - -lemma sg12892 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2387 - -lemma sg12893 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2290 sg2381 - -lemma sg12894 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2370 sg2301 - -lemma sg12895 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2302 - -lemma sg12896 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2290 sg2384 - -lemma sg12897 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg2293 sg2381 - -lemma sg12898 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,1] := by - exact rowSquare_join (by decide) sg2379 sg2297 - -lemma sg12899 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,3] := by - exact rowSquare_join (by decide) sg2380 sg2297 - -lemma sg12900 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2305 - -lemma sg12901 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2306 - -lemma sg12902 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2388 - -lemma sg12903 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1779 sg3115 - -lemma sg12904 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2293 sg2382 - -lemma sg12905 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2389 - -lemma sg12906 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2371 sg2307 - -lemma sg12907 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1782 sg3115 - -lemma sg12908 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg2293 sg2384 - -lemma sg12909 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2309 - -lemma sg12910 : RowSquare [5,5,2,2,2,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1086 sg3998 - -lemma sg12911 : RowSquare [5,5,2,2,2,2,2,2,2,1,1] [7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1082 sg3999 - -lemma sg12912 : RowSquare [5,5,2,2,2,2,2,2,2,1,1] [8,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1084 sg3999 - -lemma sg12913 : RowSquare [5,5,2,2,2,2,2,2,2,1,1] [8,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1086 sg3999 - -lemma sg12914 : RowSquare [5,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1] := by - exact rowSquare_join (by decide) sg1000 sg4496 - -lemma sg12915 : RowSquare [5,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,2] := by - exact rowSquare_join (by decide) sg1001 sg4496 - -lemma sg12916 : RowSquare [5,5,3,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1682 sg2902 - -lemma sg12917 : RowSquare [5,5,3,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg586 sg4918 - -lemma sg12918 : RowSquare [5,5,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg586 sg4922 - -lemma sg12919 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1] [5,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg1688 sg2746 - -lemma sg12920 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2746 - -lemma sg12921 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2702 - -lemma sg12922 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1756 sg2702 - -lemma sg12923 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1754 sg2705 - -lemma sg12924 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1757 sg2702 - -lemma sg12925 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2706 - -lemma sg12926 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2707 - -lemma sg12927 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg2708 - -lemma sg12928 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1759 sg2702 - -lemma sg12929 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg888 sg4160 - -lemma sg12930 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2251 sg2134 - -lemma sg12931 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg892 sg4165 - -lemma sg12932 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg892 sg4167 - -lemma sg12933 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1748 sg2702 - -lemma sg12934 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2251 sg2156 - -lemma sg12935 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg891 sg4348 - -lemma sg12936 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg892 sg4348 - -lemma sg12937 : RowSquare [8,6,2,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg807 sg4345 - -lemma sg12938 : RowSquare [8,6,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg809 sg4345 - -lemma sg12939 : RowSquare [8,6,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg817 sg4345 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes28 + +namespace OAI + +/-! Semigroup Nodes 30. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg12540 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1902 sg2370 + +lemma sg12541 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2411 + +lemma sg12542 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1901 sg2371 + +lemma sg12543 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2412 + +lemma sg12544 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2413 + +lemma sg12545 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2414 + +lemma sg12546 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2415 + +lemma sg12547 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2416 + +lemma sg12548 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1903 sg2370 + +lemma sg12549 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2417 + +lemma sg12550 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1903 sg2371 + +lemma sg12551 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1905 sg2370 + +lemma sg12552 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1417 sg3115 + +lemma sg12553 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2418 + +lemma sg12554 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2419 + +lemma sg12555 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1908 sg2370 + +lemma sg12556 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1417 sg3116 + +lemma sg12557 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1417 sg3117 + +lemma sg12558 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2420 + +lemma sg12559 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2421 + +lemma sg12560 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1907 sg2371 + +lemma sg12561 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1908 sg2371 + +lemma sg12562 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4] := by + exact rowSquare_join (by decide) sg1033 sg3722 + +lemma sg12563 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2422 + +lemma sg12564 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg1906 sg2372 + +lemma sg12565 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2] := by + exact rowSquare_join (by decide) sg1906 sg2373 + +lemma sg12566 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1] := by + exact rowSquare_join (by decide) sg1906 sg2374 + +lemma sg12567 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1874 sg2423 + +lemma sg12568 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2424 + +lemma sg12569 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1901 sg2376 + +lemma sg12570 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2426 + +lemma sg12571 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1875 sg2410 + +lemma sg12572 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2427 + +lemma sg12573 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1901 sg2377 + +lemma sg12574 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1875 sg2413 + +lemma sg12575 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2428 + +lemma sg12576 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1901 sg2378 + +lemma sg12577 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1901 sg2380 + +lemma sg12578 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1875 sg2417 + +lemma sg12579 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1903 sg2377 + +lemma sg12580 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2429 + +lemma sg12581 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1901 sg2382 + +lemma sg12582 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1875 sg2419 + +lemma sg12583 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1903 sg2380 + +lemma sg12584 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2430 + +lemma sg12585 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg2431 + +lemma sg12586 : RowSquare [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1968 sg2291 + +lemma sg12587 : RowSquare [5,4,2,2,2,2,2,2,2,1,1] [7,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1492 sg2596 + +lemma sg12588 : RowSquare [5,4,2,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1493 sg2596 + +lemma sg12589 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg4539 + +lemma sg12590 : RowSquare [5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5] := by + exact rowSquare_join (by decide) sg1033 sg3691 + +lemma sg12591 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1] [5,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1688 sg2314 + +lemma sg12592 : RowSquare [5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1877 sg2382 + +lemma sg12593 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5] := by + exact rowSquare_join (by decide) sg1001 sg3476 + +lemma sg12594 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2287 + +lemma sg12595 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2288 + +lemma sg12596 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2291 + +lemma sg12597 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2167 + +lemma sg12598 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1754 sg2270 + +lemma sg12599 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2271 + +lemma sg12600 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2275 + +lemma sg12601 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2276 + +lemma sg12602 : RowSquare [6,6,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2277 + +lemma sg12603 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg2626 + +lemma sg12604 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1327 sg2627 + +lemma sg12605 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1332 sg2626 + +lemma sg12606 : RowSquare [7,5,2,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1372 sg2702 + +lemma sg12607 : RowSquare [7,5,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1378 sg2702 + +lemma sg12608 : RowSquare [7,5,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1780 sg2251 + +lemma sg12609 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg4160 + +lemma sg12610 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1682 sg2251 + +lemma sg12611 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg586 sg4161 + +lemma sg12612 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg4160 + +lemma sg12613 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg589 sg4160 + +lemma sg12614 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg590 sg4160 + +lemma sg12615 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1687 sg2251 + +lemma sg12616 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg586 sg4165 + +lemma sg12617 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg591 sg4160 + +lemma sg12618 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg594 sg4160 + +lemma sg12619 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg587 sg4167 + +lemma sg12620 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg595 sg4160 + +lemma sg12621 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg4160 + +lemma sg12622 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg588 sg4165 + +lemma sg12623 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg588 sg4167 + +lemma sg12624 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg589 sg4167 + +lemma sg12625 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg597 sg4160 + +lemma sg12626 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg599 sg4160 + +lemma sg12627 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg587 sg4168 + +lemma sg12628 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg601 sg4160 + +lemma sg12629 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg596 sg4161 + +lemma sg12630 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg4160 + +lemma sg12631 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg601 sg4161 + +lemma sg12632 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg607 sg4160 + +lemma sg12633 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg602 sg4161 + +lemma sg12634 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg607 sg4161 + +lemma sg12635 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1327 sg2702 + +lemma sg12636 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1754 sg2251 + +lemma sg12637 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg2702 + +lemma sg12638 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1755 sg2251 + +lemma sg12639 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg2702 + +lemma sg12640 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1756 sg2251 + +lemma sg12641 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2254 + +lemma sg12642 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1327 sg2705 + +lemma sg12643 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2255 + +lemma sg12644 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1332 sg2702 + +lemma sg12645 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1758 sg2251 + +lemma sg12646 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2256 + +lemma sg12647 : RowSquare [7,6,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1766 sg2251 + +lemma sg12648 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1257 sg2702 + +lemma sg12649 : RowSquare [7,6,4,3,2,2,1] [2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1728 sg2019 + +lemma sg12650 : RowSquare [7,6,4,3,2,2,1] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1728 sg2018 + +lemma sg12651 : RowSquare [7,6,4,3,2,2,1] [2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1728 sg2017 + +lemma sg12652 : RowSquare [7,6,4,3,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1728 sg2016 + +lemma sg12653 : RowSquare [7,6,4,3,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1728 sg2015 + +lemma sg12654 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1247 sg2702 + +lemma sg12655 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1248 sg2702 + +lemma sg12656 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1249 sg2702 + +lemma sg12657 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1250 sg2702 + +lemma sg12658 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1251 sg2702 + +lemma sg12659 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11816 + +lemma sg12660 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11817 + +lemma sg12661 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11818 + +lemma sg12662 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg11819 + +lemma sg12663 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11820 + +lemma sg12664 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11821 + +lemma sg12665 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg11822 + +lemma sg12666 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg11823 + +lemma sg12667 : RowSquare [7,7,2,2,2,2,2,1] [6,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg11824 + +lemma sg12668 : RowSquare [7,7,2,2,2,2,2,1] [6,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg11825 + +lemma sg12669 : RowSquare [7,7,3,2,2,2,2] [2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1611 sg2104 + +lemma sg12670 : RowSquare [7,7,3,2,2,2,2] [2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1611 sg2103 + +lemma sg12671 : RowSquare [7,7,3,2,2,2,2] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1611 sg2102 + +lemma sg12672 : RowSquare [7,7,3,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1611 sg2101 + +lemma sg12673 : RowSquare [7,7,3,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1611 sg2099 + +lemma sg12674 : RowSquare [7,7,3,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1611 sg2097 + +lemma sg12675 : RowSquare [7,7,3,2,2,2,2] [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1613 sg2105 + +lemma sg12676 : RowSquare [7,7,3,2,2,2,2] [3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1609 sg2104 + +lemma sg12677 : RowSquare [7,7,3,2,2,2,2] [3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1609 sg2102 + +lemma sg12678 : RowSquare [7,7,3,2,2,2,2] [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1610 sg2105 + +lemma sg12679 : RowSquare [8,6,1,1,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg888 sg3522 + +lemma sg12680 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg807 sg3521 + +lemma sg12681 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg809 sg3521 + +lemma sg12682 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg517 sg4345 + +lemma sg12683 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg519 sg4345 + +lemma sg12684 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg520 sg4345 + +lemma sg12685 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg814 sg3521 + +lemma sg12686 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg815 sg3521 + +lemma sg12687 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg816 sg3521 + +lemma sg12688 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg817 sg3521 + +lemma sg12689 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg523 sg4345 + +lemma sg12690 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg525 sg4345 + +lemma sg12691 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg821 sg3521 + +lemma sg12692 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg822 sg3521 + +lemma sg12693 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg823 sg3521 + +lemma sg12694 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg528 sg4345 + +lemma sg12695 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg825 sg3521 + +lemma sg12696 : RowSquare [8,6,2,2,1,1,1,1,1,1,1] [4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg767 sg3521 + +lemma sg12697 : RowSquare [8,6,3,2,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg110 sg5735 + +lemma sg12698 : RowSquare [8,6,3,2,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg111 sg5735 + +lemma sg12699 : RowSquare [8,6,3,2,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg112 sg5735 + +lemma sg12700 : RowSquare [8,6,3,2,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg113 sg5735 + +lemma sg12701 : RowSquare [8,7,2,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg740 sg3521 + +lemma sg12702 : RowSquare [9,7,2,1,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg109 sg5757 + +lemma sg12703 : RowSquare [10,3,2,2,2,2,2,1,1] [5,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg356 sg4746 + +lemma sg12704 : RowSquare [10,3,2,2,2,2,2,1,1] [5,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg74 sg6403 + +lemma sg12705 : RowSquare [10,3,2,2,2,2,2,1,1] [5,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg6404 + +lemma sg12706 : RowSquare [10,3,2,2,2,2,2,1,1] [5,5,5,4,3,3] := by + exact rowSquare_join (by decide) sg74 sg6405 + +lemma sg12707 : RowSquare [10,3,2,2,2,2,2,1,1] [5,5,5,5,5] := by + exact rowSquare_join (by decide) sg32 sg7807 + +lemma sg12708 : RowSquare [10,3,2,2,2,2,2,1,1] [6,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg165 sg5620 + +lemma sg12709 : RowSquare [10,3,2,2,2,2,2,1,1] [6,6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg356 sg4749 + +lemma sg12710 : RowSquare [10,3,2,2,2,2,2,2] [6,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg165 sg5538 + +lemma sg12711 : RowSquare [10,3,2,2,2,2,2,2] [6,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg165 sg5544 + +lemma sg12712 : RowSquare [10,3,2,2,2,2,2,2] [6,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg165 sg5545 + +lemma sg12713 : RowSquare [10,3,2,2,2,2,2,2] [6,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg165 sg5547 + +lemma sg12714 : RowSquare [10,3,2,2,2,2,2,2] [6,6,4,3,3,3] := by + exact rowSquare_join (by decide) sg579 sg3870 + +lemma sg12715 : RowSquare [10,3,2,2,2,2,2,2] [6,6,5,3,3,2] := by + exact rowSquare_join (by decide) sg579 sg3871 + +lemma sg12716 : RowSquare [10,3,2,2,2,2,2,2] [7,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg165 sg5559 + +lemma sg12717 : RowSquare [10,3,2,2,2,2,2,2] [7,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg165 sg5560 + +lemma sg12718 : RowSquare [10,3,2,2,2,2,2,2] [7,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg581 sg3870 + +lemma sg12719 : RowSquare [10,3,3,2,2,2,2,1] [5,5,5,4,3,3] := by + exact rowSquare_join (by decide) sg74 sg6293 + +lemma sg12720 : RowSquare [11,3,2,2,2,2,2,1] [5,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg6197 + +lemma sg12721 : RowSquare [11,3,2,2,2,2,2,1] [5,5,5,4,3,3] := by + exact rowSquare_join (by decide) sg74 sg6199 + +lemma sg12722 : RowSquare [12,3,2,2,2,2,2] [6,6,5,4,4] := by + exact rowSquare_join (by decide) sg27 sg6919 + +lemma sg12723 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg1455 sg3732 + +lemma sg12724 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1456 sg3732 + +lemma sg12725 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2] := by + exact rowSquare_join (by decide) sg1914 sg3068 + +lemma sg12726 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1] := by + exact rowSquare_join (by decide) sg1914 sg3069 + +lemma sg12727 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5] := by + exact rowSquare_join (by decide) sg1532 sg3658 + +lemma sg12728 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2] := by + exact rowSquare_join (by decide) sg1455 sg3733 + +lemma sg12729 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg1533 sg3656 + +lemma sg12730 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,2] := by + exact rowSquare_join (by decide) sg1915 sg3068 + +lemma sg12731 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1] := by + exact rowSquare_join (by decide) sg2329 sg2432 + +lemma sg12732 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1] := by + exact rowSquare_join (by decide) sg2329 sg2433 + +lemma sg12733 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4] := by + exact rowSquare_join (by decide) sg1916 sg3069 + +lemma sg12734 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3] := by + exact rowSquare_join (by decide) sg2432 sg2330 + +lemma sg12735 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2] := by + exact rowSquare_join (by decide) sg2433 sg2330 + +lemma sg12736 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1970 sg2837 + +lemma sg12737 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg1535 sg3657 + +lemma sg12738 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg1919 sg3069 + +lemma sg12739 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4] := by + exact rowSquare_join (by decide) sg1970 sg2841 + +lemma sg12740 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,3] := by + exact rowSquare_join (by decide) sg1536 sg3657 + +lemma sg12741 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1971 sg2837 + +lemma sg12742 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg1456 sg3734 + +lemma sg12743 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg1972 sg2837 + +lemma sg12744 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg1456 sg3735 + +lemma sg12745 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,2] := by + exact rowSquare_join (by decide) sg1915 sg3071 + +lemma sg12746 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4] := by + exact rowSquare_join (by decide) sg2432 sg2331 + +lemma sg12747 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,3] := by + exact rowSquare_join (by decide) sg2436 sg2330 + +lemma sg12748 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3] := by + exact rowSquare_join (by decide) sg1063 sg4509 + +lemma sg12749 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg975 sg4540 + +lemma sg12750 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1537 sg3656 + +lemma sg12751 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1973 sg2837 + +lemma sg12752 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,2] := by + exact rowSquare_join (by decide) sg1915 sg3074 + +lemma sg12753 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4] := by + exact rowSquare_join (by decide) sg1916 sg3075 + +lemma sg12754 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg975 sg4541 + +lemma sg12755 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg1974 sg2837 + +lemma sg12756 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2,2] := by + exact rowSquare_join (by decide) sg1915 sg3076 + +lemma sg12757 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg975 sg4542 + +lemma sg12758 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,3] := by + exact rowSquare_join (by decide) sg2432 sg2334 + +lemma sg12759 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1] := by + exact rowSquare_join (by decide) sg1915 sg3078 + +lemma sg12760 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2] := by + exact rowSquare_join (by decide) sg2433 sg2334 + +lemma sg12761 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3] := by + exact rowSquare_join (by decide) sg2461 sg2219 + +lemma sg12762 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3] := by + exact rowSquare_join (by decide) sg2432 sg2336 + +lemma sg12763 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2] := by + exact rowSquare_join (by decide) sg2436 sg2332 + +lemma sg12764 : RowSquare [3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3] := by + exact rowSquare_join (by decide) sg2436 sg2334 + +lemma sg12765 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg2432 + +lemma sg12766 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg2311 sg2432 + +lemma sg12767 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg2433 + +lemma sg12768 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg2433 + +lemma sg12769 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg1891 sg3103 + +lemma sg12770 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg1455 sg3725 + +lemma sg12771 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg1455 sg3726 + +lemma sg12772 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2311 sg2434 + +lemma sg12773 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg2435 + +lemma sg12774 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2311 sg2436 + +lemma sg12775 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg2339 sg2392 + +lemma sg12776 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2341 + +lemma sg12777 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg2437 + +lemma sg12778 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg1456 sg3724 + +lemma sg12779 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2343 + +lemma sg12780 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg2439 + +lemma sg12781 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2344 + +lemma sg12782 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg1891 sg3104 + +lemma sg12783 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg2440 + +lemma sg12784 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg2441 + +lemma sg12785 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3] := by + exact rowSquare_join (by decide) sg1844 sg3125 + +lemma sg12786 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1891 sg3105 + +lemma sg12787 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2] := by + exact rowSquare_join (by decide) sg2340 sg2392 + +lemma sg12788 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2341 + +lemma sg12789 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2343 + +lemma sg12790 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2344 + +lemma sg12791 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg2444 + +lemma sg12792 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg2445 + +lemma sg12793 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2311 sg2446 + +lemma sg12794 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2347 + +lemma sg12795 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1458 sg3724 + +lemma sg12796 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2348 + +lemma sg12797 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2350 + +lemma sg12798 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg2448 + +lemma sg12799 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2347 + +lemma sg12800 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2351 + +lemma sg12801 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg2450 + +lemma sg12802 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2213 sg2456 + +lemma sg12803 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2213 sg2457 + +lemma sg12804 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2214 sg2456 + +lemma sg12805 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2326 sg2433 + +lemma sg12806 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1459 sg3724 + +lemma sg12807 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2213 sg2458 + +lemma sg12808 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2216 sg2457 + +lemma sg12809 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2214 sg2458 + +lemma sg12810 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg2462 + +lemma sg12811 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2353 + +lemma sg12812 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1803 sg3152 + +lemma sg12813 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2213 sg2459 + +lemma sg12814 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2213 sg2460 + +lemma sg12815 : RowSquare [4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2355 + +lemma sg12816 : RowSquare [4,4,2,2,2,2,2,2,2,2,1,1] [5,5,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1650 sg3106 + +lemma sg12817 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg2405 + +lemma sg12818 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg1926 sg2925 + +lemma sg12819 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg2409 + +lemma sg12820 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1927 sg2925 + +lemma sg12821 : RowSquare [4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg2417 + +lemma sg12822 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg1891 sg3009 + +lemma sg12823 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg1919 sg2925 + +lemma sg12824 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg2314 sg2392 + +lemma sg12825 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,3] := by + exact rowSquare_join (by decide) sg1032 sg4504 + +lemma sg12826 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg2399 + +lemma sg12827 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3] := by + exact rowSquare_join (by decide) sg976 sg4521 + +lemma sg12828 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2] := by + exact rowSquare_join (by decide) sg2392 sg2317 + +lemma sg12829 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1922 sg2925 + +lemma sg12830 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg2314 sg2396 + +lemma sg12831 : RowSquare [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1923 sg2925 + +lemma sg12832 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg2314 sg2314 + +lemma sg12833 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1033 sg4341 + +lemma sg12834 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1300 sg3632 + +lemma sg12835 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1033 sg4342 + +lemma sg12836 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg2212 sg2284 + +lemma sg12837 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1300 sg3633 + +lemma sg12838 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1737 sg2925 + +lemma sg12839 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1301 sg3632 + +lemma sg12840 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2169 sg2310 + +lemma sg12841 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2169 sg2311 + +lemma sg12842 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1738 sg2925 + +lemma sg12843 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg1739 sg2925 + +lemma sg12844 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg3648 + +lemma sg12845 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2214 sg2284 + +lemma sg12846 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2311 sg2170 + +lemma sg12847 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1699 sg3004 + +lemma sg12848 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1740 sg2925 + +lemma sg12849 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg2314 sg2168 + +lemma sg12850 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1233 sg3730 + +lemma sg12851 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [6,6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg2171 + +lemma sg12852 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2172 sg2310 + +lemma sg12853 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2172 sg2311 + +lemma sg12854 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1741 sg2925 + +lemma sg12855 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [7,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2169 sg2314 + +lemma sg12856 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [7,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1742 sg2925 + +lemma sg12857 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [7,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg2215 sg2286 + +lemma sg12858 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [8,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2221 sg2284 + +lemma sg12859 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [8,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2172 sg2314 + +lemma sg12860 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1] [8,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1743 sg2925 + +lemma sg12861 : RowSquare [5,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2407 + +lemma sg12862 : RowSquare [5,4,3,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1493 sg3299 + +lemma sg12863 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg2311 sg2167 + +lemma sg12864 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1] [5,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg1688 sg3004 + +lemma sg12865 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1] [6,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg2314 sg2167 + +lemma sg12866 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2288 sg2375 + +lemma sg12867 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2369 sg2289 + +lemma sg12868 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2369 sg2291 + +lemma sg12869 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2290 sg2371 + +lemma sg12870 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2379 + +lemma sg12871 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2380 + +lemma sg12872 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2381 + +lemma sg12873 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2290 sg2373 + +lemma sg12874 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg2290 sg2374 + +lemma sg12875 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2370 sg2291 + +lemma sg12876 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2382 + +lemma sg12877 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2371 sg2292 + +lemma sg12878 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2383 + +lemma sg12879 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2371 sg2293 + +lemma sg12880 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2296 + +lemma sg12881 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2384 + +lemma sg12882 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2385 + +lemma sg12883 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2386 + +lemma sg12884 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2371 sg2297 + +lemma sg12885 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg2293 sg2373 + +lemma sg12886 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg2293 sg2374 + +lemma sg12887 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1] := by + exact rowSquare_join (by decide) sg2373 sg2297 + +lemma sg12888 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,3] := by + exact rowSquare_join (by decide) sg2374 sg2297 + +lemma sg12889 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2369 sg2298 + +lemma sg12890 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2290 sg2376 + +lemma sg12891 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2370 sg2298 + +lemma sg12892 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2387 + +lemma sg12893 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2290 sg2381 + +lemma sg12894 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2370 sg2301 + +lemma sg12895 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2302 + +lemma sg12896 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2290 sg2384 + +lemma sg12897 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg2293 sg2381 + +lemma sg12898 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,1] := by + exact rowSquare_join (by decide) sg2379 sg2297 + +lemma sg12899 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,3] := by + exact rowSquare_join (by decide) sg2380 sg2297 + +lemma sg12900 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2305 + +lemma sg12901 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2306 + +lemma sg12902 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2388 + +lemma sg12903 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1779 sg3115 + +lemma sg12904 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2293 sg2382 + +lemma sg12905 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2389 + +lemma sg12906 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2371 sg2307 + +lemma sg12907 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1782 sg3115 + +lemma sg12908 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg2293 sg2384 + +lemma sg12909 : RowSquare [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2309 + +lemma sg12910 : RowSquare [5,5,2,2,2,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1086 sg3998 + +lemma sg12911 : RowSquare [5,5,2,2,2,2,2,2,2,1,1] [7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1082 sg3999 + +lemma sg12912 : RowSquare [5,5,2,2,2,2,2,2,2,1,1] [8,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1084 sg3999 + +lemma sg12913 : RowSquare [5,5,2,2,2,2,2,2,2,1,1] [8,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1086 sg3999 + +lemma sg12914 : RowSquare [5,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1] := by + exact rowSquare_join (by decide) sg1000 sg4496 + +lemma sg12915 : RowSquare [5,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,2] := by + exact rowSquare_join (by decide) sg1001 sg4496 + +lemma sg12916 : RowSquare [5,5,3,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1682 sg2902 + +lemma sg12917 : RowSquare [5,5,3,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg586 sg4918 + +lemma sg12918 : RowSquare [5,5,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg586 sg4922 + +lemma sg12919 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1] [5,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg1688 sg2746 + +lemma sg12920 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2746 + +lemma sg12921 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2702 + +lemma sg12922 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1756 sg2702 + +lemma sg12923 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1754 sg2705 + +lemma sg12924 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1757 sg2702 + +lemma sg12925 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2706 + +lemma sg12926 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2707 + +lemma sg12927 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg2708 + +lemma sg12928 : RowSquare [7,6,2,2,1,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1759 sg2702 + +lemma sg12929 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg888 sg4160 + +lemma sg12930 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2251 sg2134 + +lemma sg12931 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg892 sg4165 + +lemma sg12932 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg892 sg4167 + +lemma sg12933 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1748 sg2702 + +lemma sg12934 : RowSquare [7,7,2,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2251 sg2156 + +lemma sg12935 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg891 sg4348 + +lemma sg12936 : RowSquare [8,6,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg892 sg4348 + +lemma sg12937 : RowSquare [8,6,2,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg807 sg4345 + +lemma sg12938 : RowSquare [8,6,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg809 sg4345 + +lemma sg12939 : RowSquare [8,6,2,2,1,1,1,1,1,1,1,1] [4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg817 sg4345 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes31.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes31.lean index 99138fe9f41bcf9c6b5232a6b6fed6526c83067a..7a246c5b44c4f428d0b183557ee2a072e5ebacb2 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes31.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes31.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes23 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes30 - -namespace OAI - -/-! Semigroup Nodes 31. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg12940 : RowSquare [8,6,2,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg821 sg4345 - -lemma sg12941 : RowSquare [8,6,3,2,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg260 sg5735 - -lemma sg12942 : RowSquare [8,6,3,2,1,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg261 sg5735 - -lemma sg12943 : RowSquare [8,6,3,2,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg262 sg5735 - -lemma sg12944 : RowSquare [8,7,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1189 sg3521 - -lemma sg12945 : RowSquare [8,7,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1190 sg3521 - -lemma sg12946 : RowSquare [8,7,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1191 sg3521 - -lemma sg12947 : RowSquare [8,7,2,2,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg740 sg4345 - -lemma sg12948 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2099 sg2072 - -lemma sg12949 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2072 - -lemma sg12950 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2071 - -lemma sg12951 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2070 - -lemma sg12952 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2069 - -lemma sg12953 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2068 - -lemma sg12954 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2067 - -lemma sg12955 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2066 - -lemma sg12956 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1644 sg2566 - -lemma sg12957 : RowSquare [8,7,2,2,2,2,2,1] [3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2096 sg2072 - -lemma sg12958 : RowSquare [8,7,2,2,2,2,2,1] [3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2092 sg2072 - -lemma sg12959 : RowSquare [8,7,2,2,2,2,2,1] [3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2092 sg2071 - -lemma sg12960 : RowSquare [8,7,2,2,2,2,2,1] [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2100 sg2072 - -lemma sg12961 : RowSquare [8,7,2,2,2,2,2,1] [3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2091 sg2072 - -lemma sg12962 : RowSquare [8,7,2,2,2,2,2,1] [3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2091 sg2070 - -lemma sg12963 : RowSquare [8,7,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2091 sg2068 - -lemma sg12964 : RowSquare [8,7,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2091 sg2066 - -lemma sg12965 : RowSquare [8,7,2,2,2,2,2,1] [3,3,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2088 sg2065 - -lemma sg12966 : RowSquare [8,7,2,2,2,2,2,1] [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2093 sg2072 - -lemma sg12967 : RowSquare [8,7,2,2,2,2,2,1] [4,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg995 sg3744 - -lemma sg12968 : RowSquare [8,7,2,2,2,2,2,1] [4,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg364 sg5115 - -lemma sg12969 : RowSquare [8,7,2,2,2,2,2,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2086 sg2072 - -lemma sg12970 : RowSquare [8,7,2,2,2,2,2,1] [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2086 sg2070 - -lemma sg12971 : RowSquare [8,7,2,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg11364 - -lemma sg12972 : RowSquare [8,7,2,2,2,2,2,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11365 - -lemma sg12973 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11385 - -lemma sg12974 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10060 - -lemma sg12975 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg11768 - -lemma sg12976 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg11769 - -lemma sg12977 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg11770 - -lemma sg12978 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg11771 - -lemma sg12979 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg11772 - -lemma sg12980 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg11773 - -lemma sg12981 : RowSquare [8,7,2,2,2,2,2,1] [7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10044 - -lemma sg12982 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11386 - -lemma sg12983 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8297 - -lemma sg12984 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11366 - -lemma sg12985 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11367 - -lemma sg12986 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11368 - -lemma sg12987 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11369 - -lemma sg12988 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg11370 - -lemma sg12989 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg11371 - -lemma sg12990 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg8295 - -lemma sg12991 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8298 - -lemma sg12992 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11387 - -lemma sg12993 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11388 - -lemma sg12994 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11389 - -lemma sg12995 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11390 - -lemma sg12996 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg11391 - -lemma sg12997 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg6864 - -lemma sg12998 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10061 - -lemma sg12999 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10062 - -lemma sg13000 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10063 - -lemma sg13001 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg10064 - -lemma sg13002 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg10065 - -lemma sg13003 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg11774 - -lemma sg13004 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg11775 - -lemma sg13005 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg11776 - -lemma sg13006 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg11777 - -lemma sg13007 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg11778 - -lemma sg13008 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg11779 - -lemma sg13009 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg11780 - -lemma sg13010 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1642 sg2546 - -lemma sg13011 : RowSquare [8,7,2,2,2,2,2,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11372 - -lemma sg13012 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8297 - -lemma sg13013 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8299 - -lemma sg13014 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11373 - -lemma sg13015 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11374 - -lemma sg13016 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11375 - -lemma sg13017 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11376 - -lemma sg13018 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg11377 - -lemma sg13019 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8298 - -lemma sg13020 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8300 - -lemma sg13021 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11392 - -lemma sg13022 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11393 - -lemma sg13023 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11394 - -lemma sg13024 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg11395 - -lemma sg13025 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg11396 - -lemma sg13026 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8301 - -lemma sg13027 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg12659 - -lemma sg13028 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg12660 - -lemma sg13029 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg12661 - -lemma sg13030 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg12662 - -lemma sg13031 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg12663 - -lemma sg13032 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg12664 - -lemma sg13033 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg12665 - -lemma sg13034 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg12666 - -lemma sg13035 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg12667 - -lemma sg13036 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1637 sg2547 - -lemma sg13037 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1643 sg2546 - -lemma sg13038 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11397 - -lemma sg13039 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg6865 - -lemma sg13040 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11398 - -lemma sg13041 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11399 - -lemma sg13042 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11400 - -lemma sg13043 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg11401 - -lemma sg13044 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5928 - -lemma sg13045 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8303 - -lemma sg13046 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8304 - -lemma sg13047 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg8305 - -lemma sg13048 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg207 sg5929 - -lemma sg13049 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11402 - -lemma sg13050 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1149 sg3274 - -lemma sg13051 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg11403 - -lemma sg13052 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg11404 - -lemma sg13053 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg1638 sg2547 - -lemma sg13054 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8306 - -lemma sg13055 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8307 - -lemma sg13056 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8308 - -lemma sg13057 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg39 sg8309 - -lemma sg13058 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1146 sg3280 - -lemma sg13059 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg12668 - -lemma sg13060 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2082 sg2045 - -lemma sg13061 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1633 sg2550 - -lemma sg13062 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1146 sg3281 - -lemma sg13063 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2082 sg2046 - -lemma sg13064 : RowSquare [8,7,2,2,2,2,2,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8296 - -lemma sg13065 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8299 - -lemma sg13066 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8310 - -lemma sg13067 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11378 - -lemma sg13068 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11379 - -lemma sg13069 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11380 - -lemma sg13070 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg11381 - -lemma sg13071 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg11382 - -lemma sg13072 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg6867 - -lemma sg13073 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8311 - -lemma sg13074 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11405 - -lemma sg13075 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11406 - -lemma sg13076 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11407 - -lemma sg13077 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg11408 - -lemma sg13078 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5923 - -lemma sg13079 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8312 - -lemma sg13080 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8313 - -lemma sg13081 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg8314 - -lemma sg13082 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg39 sg8315 - -lemma sg13083 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11383 - -lemma sg13084 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1151 sg3274 - -lemma sg13085 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1637 sg2548 - -lemma sg13086 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg5 sg11384 - -lemma sg13087 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1639 sg2547 - -lemma sg13088 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8302 - -lemma sg13089 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5930 - -lemma sg13090 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8303 - -lemma sg13091 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8304 - -lemma sg13092 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg8305 - -lemma sg13093 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg83 sg6868 - -lemma sg13094 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5931 - -lemma sg13095 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8316 - -lemma sg13096 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1149 sg3276 - -lemma sg13097 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1637 sg2549 - -lemma sg13098 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1146 sg3282 - -lemma sg13099 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg11409 - -lemma sg13100 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2082 sg2047 - -lemma sg13101 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1635 sg2550 - -lemma sg13102 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8317 - -lemma sg13103 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1147 sg3280 - -lemma sg13104 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg364 sg5110 - -lemma sg13105 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2083 sg2045 - -lemma sg13106 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1146 sg3283 - -lemma sg13107 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg2082 sg2048 - -lemma sg13108 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2082 sg2049 - -lemma sg13109 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5924 - -lemma sg13110 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5932 - -lemma sg13111 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11410 - -lemma sg13112 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1149 sg3278 - -lemma sg13113 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg209 sg5925 - -lemma sg13114 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg5111 - -lemma sg13115 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1150 sg3278 - -lemma sg13116 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg207 sg5933 - -lemma sg13117 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg2085 sg2042 - -lemma sg13118 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1146 sg3285 - -lemma sg13119 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg2082 sg2050 - -lemma sg13120 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8318 - -lemma sg13121 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg5112 - -lemma sg13122 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg1633 sg2552 - -lemma sg13123 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg2082 sg2051 - -lemma sg13124 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg656 sg4566 - -lemma sg13125 : RowSquare [8,7,2,2,2,2,2,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10045 - -lemma sg13126 : RowSquare [8,7,2,2,2,2,2,1] [7,6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8310 - -lemma sg13127 : RowSquare [8,7,2,2,2,2,2,1] [7,6,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10066 - -lemma sg13128 : RowSquare [8,7,2,2,2,2,2,1] [7,6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10046 - -lemma sg13129 : RowSquare [8,7,2,2,2,2,2,1] [7,6,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10047 - -lemma sg13130 : RowSquare [8,7,2,2,2,2,2,1] [7,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10048 - -lemma sg13131 : RowSquare [8,7,2,2,2,2,2,1] [7,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg10049 - -lemma sg13132 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8311 - -lemma sg13133 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5934 - -lemma sg13134 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8312 - -lemma sg13135 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8313 - -lemma sg13136 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg8314 - -lemma sg13137 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg40 sg8315 - -lemma sg13138 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10067 - -lemma sg13139 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10068 - -lemma sg13140 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1151 sg3276 - -lemma sg13141 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg10069 - -lemma sg13142 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1146 sg3287 - -lemma sg13143 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2084 sg2063 - -lemma sg13144 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2082 sg2053 - -lemma sg13145 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1640 sg2547 - -lemma sg13146 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5927 - -lemma sg13147 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5935 - -lemma sg13148 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8316 - -lemma sg13149 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1151 sg3278 - -lemma sg13150 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg210 sg5925 - -lemma sg13151 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5936 - -lemma sg13152 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1147 sg3282 - -lemma sg13153 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg365 sg5109 - -lemma sg13154 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg2083 sg2047 - -lemma sg13155 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg5926 - -lemma sg13156 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg2082 sg2054 - -lemma sg13157 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1153 sg3276 - -lemma sg13158 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1147 sg3283 - -lemma sg13159 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg2083 sg2048 - -lemma sg13160 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg6869 - -lemma sg13161 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5937 - -lemma sg13162 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1148 sg3282 - -lemma sg13163 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg83 sg6870 - -lemma sg13164 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg2084 sg2047 - -lemma sg13165 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1153 sg3278 - -lemma sg13166 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1147 sg3285 - -lemma sg13167 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg656 sg4567 - -lemma sg13168 : RowSquare [8,7,2,2,2,2,2,1] [7,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg6871 - -lemma sg13169 : RowSquare [8,7,2,2,2,2,2,1] [7,6,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1154 sg3278 - -lemma sg13170 : RowSquare [8,7,2,2,2,2,2,1] [7,6,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1148 sg3285 - -lemma sg13171 : RowSquare [8,7,2,2,2,2,2,1] [7,6,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg656 sg4568 - -lemma sg13172 : RowSquare [8,7,2,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10050 - -lemma sg13173 : RowSquare [8,7,2,2,2,2,2,1] [7,7,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10051 - -lemma sg13174 : RowSquare [8,7,2,2,2,2,2,1] [7,7,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10070 - -lemma sg13175 : RowSquare [8,7,2,2,2,2,2,1] [7,7,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10052 - -lemma sg13176 : RowSquare [8,7,2,2,2,2,2,1] [7,7,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10053 - -lemma sg13177 : RowSquare [8,7,2,2,2,2,2,1] [7,7,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg10054 - -lemma sg13178 : RowSquare [8,7,2,2,2,2,2,1] [7,7,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg10055 - -lemma sg13179 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg5927 - -lemma sg13180 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10071 - -lemma sg13181 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10056 - -lemma sg13182 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10057 - -lemma sg13183 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg10058 - -lemma sg13184 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg5113 - -lemma sg13185 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1147 sg3287 - -lemma sg13186 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg10072 - -lemma sg13187 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2083 sg2053 - -lemma sg13188 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10059 - -lemma sg13189 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8319 - -lemma sg13190 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5938 - -lemma sg13191 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1148 sg3287 - -lemma sg13192 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg83 sg6872 - -lemma sg13193 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1156 sg3276 - -lemma sg13194 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10073 - -lemma sg13195 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg5114 - -lemma sg13196 : RowSquare [8,7,2,2,2,2,2,1] [7,7,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg6873 - -lemma sg13197 : RowSquare [8,7,2,2,2,2,2,1] [7,7,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1156 sg3278 - -lemma sg13198 : RowSquare [8,7,2,2,2,2,2,1] [7,7,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg6874 - -lemma sg13199 : RowSquare [8,7,2,2,2,2,2,1] [7,7,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg657 sg4567 - -lemma sg13200 : RowSquare [8,7,2,2,2,2,2,1] [7,7,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1157 sg3278 - -lemma sg13201 : RowSquare [8,7,2,2,2,2,2,1] [7,7,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg657 sg4568 - -lemma sg13202 : RowSquare [8,7,2,2,2,2,2,1] [7,7,7,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg658 sg4568 - -lemma sg13203 : RowSquare [8,7,2,2,2,2,2,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg11365 - -lemma sg13204 : RowSquare [8,7,2,2,2,2,2,1] [8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11385 - -lemma sg13205 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11411 - -lemma sg13206 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8320 - -lemma sg13207 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg11366 - -lemma sg13208 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg11367 - -lemma sg13209 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg11368 - -lemma sg13210 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg11369 - -lemma sg13211 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6 sg11370 - -lemma sg13212 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6 sg11371 - -lemma sg13213 : RowSquare [8,7,2,2,2,2,2,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10060 - -lemma sg13214 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8320 - -lemma sg13215 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8321 - -lemma sg13216 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11387 - -lemma sg13217 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11388 - -lemma sg13218 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11389 - -lemma sg13219 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11390 - -lemma sg13220 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg11391 - -lemma sg13221 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg8298 - -lemma sg13222 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8322 - -lemma sg13223 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11412 - -lemma sg13224 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11413 - -lemma sg13225 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11414 - -lemma sg13226 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg11415 - -lemma sg13227 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg11416 - -lemma sg13228 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg6866 - -lemma sg13229 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10074 - -lemma sg13230 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10075 - -lemma sg13231 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10076 - -lemma sg13232 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg10077 - -lemma sg13233 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg11781 - -lemma sg13234 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg11782 - -lemma sg13235 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg11783 - -lemma sg13236 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg11784 - -lemma sg13237 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg11785 - -lemma sg13238 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1642 sg2547 - -lemma sg13239 : RowSquare [8,7,2,2,2,2,2,1] [8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8297 - -lemma sg13240 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8321 - -lemma sg13241 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg6867 - -lemma sg13242 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10061 - -lemma sg13243 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10062 - -lemma sg13244 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10063 - -lemma sg13245 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg10064 - -lemma sg13246 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg10065 - -lemma sg13247 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8322 - -lemma sg13248 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8324 - -lemma sg13249 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11417 - -lemma sg13250 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11418 - -lemma sg13251 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11419 - -lemma sg13252 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg11420 - -lemma sg13253 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5928 - -lemma sg13254 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8325 - -lemma sg13255 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8326 - -lemma sg13256 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg8327 - -lemma sg13257 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg208 sg5929 - -lemma sg13258 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11402 - -lemma sg13259 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1158 sg3274 - -lemma sg13260 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2059 sg2082 - -lemma sg13261 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1637 sg2550 - -lemma sg13262 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg8302 - -lemma sg13263 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5939 - -lemma sg13264 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg8303 - -lemma sg13265 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg8304 - -lemma sg13266 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg41 sg8305 - -lemma sg13267 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg209 sg5929 - -lemma sg13268 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5940 - -lemma sg13269 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8328 - -lemma sg13270 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1149 sg3280 - -lemma sg13271 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1642 sg2549 - -lemma sg13272 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1592 sg2592 - -lemma sg13273 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1149 sg3281 - -lemma sg13274 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg5116 - -lemma sg13275 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1150 sg3280 - -lemma sg13276 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg364 sg5117 - -lemma sg13277 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1146 sg3289 - -lemma sg13278 : RowSquare [8,7,2,2,2,2,2,1] [8,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8299 - -lemma sg13279 : RowSquare [8,7,2,2,2,2,2,1] [8,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8323 - -lemma sg13280 : RowSquare [8,7,2,2,2,2,2,1] [8,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8329 - -lemma sg13281 : RowSquare [8,7,2,2,2,2,2,1] [8,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11405 - -lemma sg13282 : RowSquare [8,7,2,2,2,2,2,1] [8,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11406 - -lemma sg13283 : RowSquare [8,7,2,2,2,2,2,1] [8,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11407 - -lemma sg13284 : RowSquare [8,7,2,2,2,2,2,1] [8,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg11408 - -lemma sg13285 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg6875 - -lemma sg13286 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5941 - -lemma sg13287 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8325 - -lemma sg13288 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8326 - -lemma sg13289 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg8327 - -lemma sg13290 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg210 sg5929 - -lemma sg13291 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5931 - -lemma sg13292 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8330 - -lemma sg13293 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1151 sg3280 - -lemma sg13294 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2059 sg2083 - -lemma sg13295 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1592 sg2593 - -lemma sg13296 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1637 sg2551 - -lemma sg13297 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5930 - -lemma sg13298 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5942 - -lemma sg13299 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8328 - -lemma sg13300 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1149 sg3282 - -lemma sg13301 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2059 sg2084 - -lemma sg13302 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5943 - -lemma sg13303 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1593 sg2592 - -lemma sg13304 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1637 sg2552 - -lemma sg13305 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1637 sg2553 - -lemma sg13306 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1153 sg3280 - -lemma sg13307 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1637 sg2554 - -lemma sg13308 : RowSquare [8,7,2,2,2,2,2,1] [8,5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5932 - -lemma sg13309 : RowSquare [8,7,2,2,2,2,2,1] [8,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5944 - -lemma sg13310 : RowSquare [8,7,2,2,2,2,2,1] [8,5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1594 sg2592 - -lemma sg13311 : RowSquare [8,7,2,2,2,2,2,1] [8,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1149 sg3285 - -lemma sg13312 : RowSquare [8,7,2,2,2,2,2,1] [8,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1160 sg3278 - -lemma sg13313 : RowSquare [8,7,2,2,2,2,2,1] [8,6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8310 - -lemma sg13314 : RowSquare [8,7,2,2,2,2,2,1] [8,6,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8329 - -lemma sg13315 : RowSquare [8,7,2,2,2,2,2,1] [8,6,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5934 - -lemma sg13316 : RowSquare [8,7,2,2,2,2,2,1] [8,6,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8312 - -lemma sg13317 : RowSquare [8,7,2,2,2,2,2,1] [8,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8313 - -lemma sg13318 : RowSquare [8,7,2,2,2,2,2,1] [8,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg42 sg8314 - -lemma sg13319 : RowSquare [8,7,2,2,2,2,2,1] [8,6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg42 sg8315 - -lemma sg13320 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5934 - -lemma sg13321 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5945 - -lemma sg13322 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8330 - -lemma sg13323 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1149 sg3287 - -lemma sg13324 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1637 sg2555 - -lemma sg13325 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5936 - -lemma sg13326 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1593 sg2593 - -lemma sg13327 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1637 sg2556 - -lemma sg13328 : RowSquare [8,7,2,2,2,2,2,1] [8,6,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5935 - -lemma sg13329 : RowSquare [8,7,2,2,2,2,2,1] [8,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg365 sg5111 - -lemma sg13330 : RowSquare [8,7,2,2,2,2,2,1] [8,6,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1594 sg2593 - -lemma sg13331 : RowSquare [8,7,2,2,2,2,2,1] [8,6,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1595 sg2592 - -lemma sg13332 : RowSquare [8,7,2,2,2,2,2,1] [8,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5937 - -lemma sg13333 : RowSquare [8,7,2,2,2,2,2,1] [8,6,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1596 sg2592 - -lemma sg13334 : RowSquare [8,7,2,2,2,2,2,1] [8,6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1597 sg2592 - -lemma sg13335 : RowSquare [8,7,2,2,2,2,2,1] [8,7,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10066 - -lemma sg13336 : RowSquare [8,7,2,2,2,2,2,1] [8,7,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg5934 - -lemma sg13337 : RowSquare [8,7,2,2,2,2,2,1] [8,7,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg10078 - -lemma sg13338 : RowSquare [8,7,2,2,2,2,2,1] [8,7,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10068 - -lemma sg13339 : RowSquare [8,7,2,2,2,2,2,1] [8,7,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1151 sg3287 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes23 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes30 + +namespace OAI + +/-! Semigroup Nodes 31. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg12940 : RowSquare [8,6,2,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg821 sg4345 + +lemma sg12941 : RowSquare [8,6,3,2,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg260 sg5735 + +lemma sg12942 : RowSquare [8,6,3,2,1,1,1,1,1,1,1] [5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg261 sg5735 + +lemma sg12943 : RowSquare [8,6,3,2,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg262 sg5735 + +lemma sg12944 : RowSquare [8,7,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1189 sg3521 + +lemma sg12945 : RowSquare [8,7,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1190 sg3521 + +lemma sg12946 : RowSquare [8,7,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1191 sg3521 + +lemma sg12947 : RowSquare [8,7,2,2,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg740 sg4345 + +lemma sg12948 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2099 sg2072 + +lemma sg12949 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2072 + +lemma sg12950 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2071 + +lemma sg12951 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2070 + +lemma sg12952 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2069 + +lemma sg12953 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2068 + +lemma sg12954 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2067 + +lemma sg12955 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2066 + +lemma sg12956 : RowSquare [8,7,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1644 sg2566 + +lemma sg12957 : RowSquare [8,7,2,2,2,2,2,1] [3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2096 sg2072 + +lemma sg12958 : RowSquare [8,7,2,2,2,2,2,1] [3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2092 sg2072 + +lemma sg12959 : RowSquare [8,7,2,2,2,2,2,1] [3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2092 sg2071 + +lemma sg12960 : RowSquare [8,7,2,2,2,2,2,1] [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2100 sg2072 + +lemma sg12961 : RowSquare [8,7,2,2,2,2,2,1] [3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2091 sg2072 + +lemma sg12962 : RowSquare [8,7,2,2,2,2,2,1] [3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2091 sg2070 + +lemma sg12963 : RowSquare [8,7,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2091 sg2068 + +lemma sg12964 : RowSquare [8,7,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2091 sg2066 + +lemma sg12965 : RowSquare [8,7,2,2,2,2,2,1] [3,3,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2088 sg2065 + +lemma sg12966 : RowSquare [8,7,2,2,2,2,2,1] [4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2093 sg2072 + +lemma sg12967 : RowSquare [8,7,2,2,2,2,2,1] [4,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg995 sg3744 + +lemma sg12968 : RowSquare [8,7,2,2,2,2,2,1] [4,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg364 sg5115 + +lemma sg12969 : RowSquare [8,7,2,2,2,2,2,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2086 sg2072 + +lemma sg12970 : RowSquare [8,7,2,2,2,2,2,1] [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2086 sg2070 + +lemma sg12971 : RowSquare [8,7,2,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg11364 + +lemma sg12972 : RowSquare [8,7,2,2,2,2,2,1] [7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11365 + +lemma sg12973 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11385 + +lemma sg12974 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10060 + +lemma sg12975 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg11768 + +lemma sg12976 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg11769 + +lemma sg12977 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg11770 + +lemma sg12978 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg11771 + +lemma sg12979 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg11772 + +lemma sg12980 : RowSquare [8,7,2,2,2,2,2,1] [7,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg11773 + +lemma sg12981 : RowSquare [8,7,2,2,2,2,2,1] [7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10044 + +lemma sg12982 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11386 + +lemma sg12983 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8297 + +lemma sg12984 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11366 + +lemma sg12985 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11367 + +lemma sg12986 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11368 + +lemma sg12987 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11369 + +lemma sg12988 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg11370 + +lemma sg12989 : RowSquare [8,7,2,2,2,2,2,1] [7,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg11371 + +lemma sg12990 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg8295 + +lemma sg12991 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8298 + +lemma sg12992 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11387 + +lemma sg12993 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11388 + +lemma sg12994 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11389 + +lemma sg12995 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11390 + +lemma sg12996 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg11391 + +lemma sg12997 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg6864 + +lemma sg12998 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10061 + +lemma sg12999 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10062 + +lemma sg13000 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10063 + +lemma sg13001 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg10064 + +lemma sg13002 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg10065 + +lemma sg13003 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg11774 + +lemma sg13004 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg11775 + +lemma sg13005 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg11776 + +lemma sg13006 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg11777 + +lemma sg13007 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg11778 + +lemma sg13008 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg11779 + +lemma sg13009 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg11780 + +lemma sg13010 : RowSquare [8,7,2,2,2,2,2,1] [7,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1642 sg2546 + +lemma sg13011 : RowSquare [8,7,2,2,2,2,2,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11372 + +lemma sg13012 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8297 + +lemma sg13013 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8299 + +lemma sg13014 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11373 + +lemma sg13015 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11374 + +lemma sg13016 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11375 + +lemma sg13017 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11376 + +lemma sg13018 : RowSquare [8,7,2,2,2,2,2,1] [7,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg11377 + +lemma sg13019 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8298 + +lemma sg13020 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8300 + +lemma sg13021 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11392 + +lemma sg13022 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11393 + +lemma sg13023 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11394 + +lemma sg13024 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg11395 + +lemma sg13025 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg11396 + +lemma sg13026 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8301 + +lemma sg13027 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg12659 + +lemma sg13028 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg12660 + +lemma sg13029 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg12661 + +lemma sg13030 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg12662 + +lemma sg13031 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg12663 + +lemma sg13032 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg12664 + +lemma sg13033 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg12665 + +lemma sg13034 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg12666 + +lemma sg13035 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg12667 + +lemma sg13036 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1637 sg2547 + +lemma sg13037 : RowSquare [8,7,2,2,2,2,2,1] [7,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1643 sg2546 + +lemma sg13038 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11397 + +lemma sg13039 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg6865 + +lemma sg13040 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11398 + +lemma sg13041 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11399 + +lemma sg13042 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11400 + +lemma sg13043 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg11401 + +lemma sg13044 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5928 + +lemma sg13045 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8303 + +lemma sg13046 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8304 + +lemma sg13047 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg8305 + +lemma sg13048 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg207 sg5929 + +lemma sg13049 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11402 + +lemma sg13050 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1149 sg3274 + +lemma sg13051 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg11403 + +lemma sg13052 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg11404 + +lemma sg13053 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg1638 sg2547 + +lemma sg13054 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8306 + +lemma sg13055 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8307 + +lemma sg13056 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8308 + +lemma sg13057 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg39 sg8309 + +lemma sg13058 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1146 sg3280 + +lemma sg13059 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg12668 + +lemma sg13060 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2082 sg2045 + +lemma sg13061 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1633 sg2550 + +lemma sg13062 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1146 sg3281 + +lemma sg13063 : RowSquare [8,7,2,2,2,2,2,1] [7,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2082 sg2046 + +lemma sg13064 : RowSquare [8,7,2,2,2,2,2,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8296 + +lemma sg13065 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8299 + +lemma sg13066 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8310 + +lemma sg13067 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11378 + +lemma sg13068 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11379 + +lemma sg13069 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11380 + +lemma sg13070 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg11381 + +lemma sg13071 : RowSquare [8,7,2,2,2,2,2,1] [7,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg11382 + +lemma sg13072 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg6867 + +lemma sg13073 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8311 + +lemma sg13074 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11405 + +lemma sg13075 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11406 + +lemma sg13076 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11407 + +lemma sg13077 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg11408 + +lemma sg13078 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5923 + +lemma sg13079 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8312 + +lemma sg13080 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8313 + +lemma sg13081 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg8314 + +lemma sg13082 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg39 sg8315 + +lemma sg13083 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11383 + +lemma sg13084 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1151 sg3274 + +lemma sg13085 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1637 sg2548 + +lemma sg13086 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg5 sg11384 + +lemma sg13087 : RowSquare [8,7,2,2,2,2,2,1] [7,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1639 sg2547 + +lemma sg13088 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8302 + +lemma sg13089 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5930 + +lemma sg13090 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8303 + +lemma sg13091 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8304 + +lemma sg13092 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg8305 + +lemma sg13093 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg83 sg6868 + +lemma sg13094 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5931 + +lemma sg13095 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8316 + +lemma sg13096 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1149 sg3276 + +lemma sg13097 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1637 sg2549 + +lemma sg13098 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1146 sg3282 + +lemma sg13099 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg11409 + +lemma sg13100 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2082 sg2047 + +lemma sg13101 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1635 sg2550 + +lemma sg13102 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8317 + +lemma sg13103 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1147 sg3280 + +lemma sg13104 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg364 sg5110 + +lemma sg13105 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2083 sg2045 + +lemma sg13106 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1146 sg3283 + +lemma sg13107 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg2082 sg2048 + +lemma sg13108 : RowSquare [8,7,2,2,2,2,2,1] [7,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2082 sg2049 + +lemma sg13109 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5924 + +lemma sg13110 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5932 + +lemma sg13111 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11410 + +lemma sg13112 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1149 sg3278 + +lemma sg13113 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg209 sg5925 + +lemma sg13114 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg5111 + +lemma sg13115 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1150 sg3278 + +lemma sg13116 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg207 sg5933 + +lemma sg13117 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg2085 sg2042 + +lemma sg13118 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1146 sg3285 + +lemma sg13119 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg2082 sg2050 + +lemma sg13120 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8318 + +lemma sg13121 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg5112 + +lemma sg13122 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg1633 sg2552 + +lemma sg13123 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg2082 sg2051 + +lemma sg13124 : RowSquare [8,7,2,2,2,2,2,1] [7,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg656 sg4566 + +lemma sg13125 : RowSquare [8,7,2,2,2,2,2,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10045 + +lemma sg13126 : RowSquare [8,7,2,2,2,2,2,1] [7,6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8310 + +lemma sg13127 : RowSquare [8,7,2,2,2,2,2,1] [7,6,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10066 + +lemma sg13128 : RowSquare [8,7,2,2,2,2,2,1] [7,6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10046 + +lemma sg13129 : RowSquare [8,7,2,2,2,2,2,1] [7,6,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10047 + +lemma sg13130 : RowSquare [8,7,2,2,2,2,2,1] [7,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10048 + +lemma sg13131 : RowSquare [8,7,2,2,2,2,2,1] [7,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg10049 + +lemma sg13132 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8311 + +lemma sg13133 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5934 + +lemma sg13134 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8312 + +lemma sg13135 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8313 + +lemma sg13136 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg8314 + +lemma sg13137 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg40 sg8315 + +lemma sg13138 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10067 + +lemma sg13139 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10068 + +lemma sg13140 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1151 sg3276 + +lemma sg13141 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg10069 + +lemma sg13142 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1146 sg3287 + +lemma sg13143 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2084 sg2063 + +lemma sg13144 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2082 sg2053 + +lemma sg13145 : RowSquare [8,7,2,2,2,2,2,1] [7,6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1640 sg2547 + +lemma sg13146 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5927 + +lemma sg13147 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5935 + +lemma sg13148 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8316 + +lemma sg13149 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1151 sg3278 + +lemma sg13150 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg210 sg5925 + +lemma sg13151 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5936 + +lemma sg13152 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1147 sg3282 + +lemma sg13153 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg365 sg5109 + +lemma sg13154 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg2083 sg2047 + +lemma sg13155 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg5926 + +lemma sg13156 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg2082 sg2054 + +lemma sg13157 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1153 sg3276 + +lemma sg13158 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1147 sg3283 + +lemma sg13159 : RowSquare [8,7,2,2,2,2,2,1] [7,6,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg2083 sg2048 + +lemma sg13160 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg6869 + +lemma sg13161 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5937 + +lemma sg13162 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1148 sg3282 + +lemma sg13163 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg83 sg6870 + +lemma sg13164 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg2084 sg2047 + +lemma sg13165 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1153 sg3278 + +lemma sg13166 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1147 sg3285 + +lemma sg13167 : RowSquare [8,7,2,2,2,2,2,1] [7,6,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg656 sg4567 + +lemma sg13168 : RowSquare [8,7,2,2,2,2,2,1] [7,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg6871 + +lemma sg13169 : RowSquare [8,7,2,2,2,2,2,1] [7,6,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1154 sg3278 + +lemma sg13170 : RowSquare [8,7,2,2,2,2,2,1] [7,6,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1148 sg3285 + +lemma sg13171 : RowSquare [8,7,2,2,2,2,2,1] [7,6,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg656 sg4568 + +lemma sg13172 : RowSquare [8,7,2,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10050 + +lemma sg13173 : RowSquare [8,7,2,2,2,2,2,1] [7,7,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10051 + +lemma sg13174 : RowSquare [8,7,2,2,2,2,2,1] [7,7,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10070 + +lemma sg13175 : RowSquare [8,7,2,2,2,2,2,1] [7,7,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10052 + +lemma sg13176 : RowSquare [8,7,2,2,2,2,2,1] [7,7,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10053 + +lemma sg13177 : RowSquare [8,7,2,2,2,2,2,1] [7,7,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg10054 + +lemma sg13178 : RowSquare [8,7,2,2,2,2,2,1] [7,7,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg10055 + +lemma sg13179 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg5927 + +lemma sg13180 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10071 + +lemma sg13181 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10056 + +lemma sg13182 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10057 + +lemma sg13183 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg10058 + +lemma sg13184 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg5113 + +lemma sg13185 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1147 sg3287 + +lemma sg13186 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg10072 + +lemma sg13187 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2083 sg2053 + +lemma sg13188 : RowSquare [8,7,2,2,2,2,2,1] [7,7,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10059 + +lemma sg13189 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8319 + +lemma sg13190 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5938 + +lemma sg13191 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1148 sg3287 + +lemma sg13192 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg83 sg6872 + +lemma sg13193 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1156 sg3276 + +lemma sg13194 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10073 + +lemma sg13195 : RowSquare [8,7,2,2,2,2,2,1] [7,7,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg5114 + +lemma sg13196 : RowSquare [8,7,2,2,2,2,2,1] [7,7,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg6873 + +lemma sg13197 : RowSquare [8,7,2,2,2,2,2,1] [7,7,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1156 sg3278 + +lemma sg13198 : RowSquare [8,7,2,2,2,2,2,1] [7,7,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg6874 + +lemma sg13199 : RowSquare [8,7,2,2,2,2,2,1] [7,7,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg657 sg4567 + +lemma sg13200 : RowSquare [8,7,2,2,2,2,2,1] [7,7,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1157 sg3278 + +lemma sg13201 : RowSquare [8,7,2,2,2,2,2,1] [7,7,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg657 sg4568 + +lemma sg13202 : RowSquare [8,7,2,2,2,2,2,1] [7,7,7,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg658 sg4568 + +lemma sg13203 : RowSquare [8,7,2,2,2,2,2,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg11365 + +lemma sg13204 : RowSquare [8,7,2,2,2,2,2,1] [8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11385 + +lemma sg13205 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11411 + +lemma sg13206 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8320 + +lemma sg13207 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg11366 + +lemma sg13208 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg11367 + +lemma sg13209 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg11368 + +lemma sg13210 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg11369 + +lemma sg13211 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6 sg11370 + +lemma sg13212 : RowSquare [8,7,2,2,2,2,2,1] [8,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6 sg11371 + +lemma sg13213 : RowSquare [8,7,2,2,2,2,2,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10060 + +lemma sg13214 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8320 + +lemma sg13215 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8321 + +lemma sg13216 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11387 + +lemma sg13217 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11388 + +lemma sg13218 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11389 + +lemma sg13219 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11390 + +lemma sg13220 : RowSquare [8,7,2,2,2,2,2,1] [8,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg11391 + +lemma sg13221 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg8298 + +lemma sg13222 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8322 + +lemma sg13223 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11412 + +lemma sg13224 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11413 + +lemma sg13225 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11414 + +lemma sg13226 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg11415 + +lemma sg13227 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg11416 + +lemma sg13228 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg6866 + +lemma sg13229 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10074 + +lemma sg13230 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10075 + +lemma sg13231 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10076 + +lemma sg13232 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg10077 + +lemma sg13233 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg11781 + +lemma sg13234 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg11782 + +lemma sg13235 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg11783 + +lemma sg13236 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg11784 + +lemma sg13237 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg11785 + +lemma sg13238 : RowSquare [8,7,2,2,2,2,2,1] [8,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1642 sg2547 + +lemma sg13239 : RowSquare [8,7,2,2,2,2,2,1] [8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8297 + +lemma sg13240 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8321 + +lemma sg13241 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg6867 + +lemma sg13242 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10061 + +lemma sg13243 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10062 + +lemma sg13244 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10063 + +lemma sg13245 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg10064 + +lemma sg13246 : RowSquare [8,7,2,2,2,2,2,1] [8,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg10065 + +lemma sg13247 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8322 + +lemma sg13248 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8324 + +lemma sg13249 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11417 + +lemma sg13250 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11418 + +lemma sg13251 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11419 + +lemma sg13252 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg11420 + +lemma sg13253 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5928 + +lemma sg13254 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8325 + +lemma sg13255 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8326 + +lemma sg13256 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg8327 + +lemma sg13257 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg208 sg5929 + +lemma sg13258 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11402 + +lemma sg13259 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1158 sg3274 + +lemma sg13260 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2059 sg2082 + +lemma sg13261 : RowSquare [8,7,2,2,2,2,2,1] [8,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1637 sg2550 + +lemma sg13262 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg8302 + +lemma sg13263 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5939 + +lemma sg13264 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg8303 + +lemma sg13265 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg8304 + +lemma sg13266 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg41 sg8305 + +lemma sg13267 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg209 sg5929 + +lemma sg13268 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5940 + +lemma sg13269 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8328 + +lemma sg13270 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1149 sg3280 + +lemma sg13271 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1642 sg2549 + +lemma sg13272 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1592 sg2592 + +lemma sg13273 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1149 sg3281 + +lemma sg13274 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg5116 + +lemma sg13275 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1150 sg3280 + +lemma sg13276 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg364 sg5117 + +lemma sg13277 : RowSquare [8,7,2,2,2,2,2,1] [8,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1146 sg3289 + +lemma sg13278 : RowSquare [8,7,2,2,2,2,2,1] [8,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8299 + +lemma sg13279 : RowSquare [8,7,2,2,2,2,2,1] [8,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8323 + +lemma sg13280 : RowSquare [8,7,2,2,2,2,2,1] [8,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8329 + +lemma sg13281 : RowSquare [8,7,2,2,2,2,2,1] [8,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11405 + +lemma sg13282 : RowSquare [8,7,2,2,2,2,2,1] [8,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11406 + +lemma sg13283 : RowSquare [8,7,2,2,2,2,2,1] [8,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11407 + +lemma sg13284 : RowSquare [8,7,2,2,2,2,2,1] [8,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg11408 + +lemma sg13285 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg6875 + +lemma sg13286 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5941 + +lemma sg13287 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8325 + +lemma sg13288 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8326 + +lemma sg13289 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg8327 + +lemma sg13290 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg210 sg5929 + +lemma sg13291 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5931 + +lemma sg13292 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8330 + +lemma sg13293 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1151 sg3280 + +lemma sg13294 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2059 sg2083 + +lemma sg13295 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1592 sg2593 + +lemma sg13296 : RowSquare [8,7,2,2,2,2,2,1] [8,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1637 sg2551 + +lemma sg13297 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5930 + +lemma sg13298 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5942 + +lemma sg13299 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8328 + +lemma sg13300 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1149 sg3282 + +lemma sg13301 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2059 sg2084 + +lemma sg13302 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5943 + +lemma sg13303 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1593 sg2592 + +lemma sg13304 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1637 sg2552 + +lemma sg13305 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1637 sg2553 + +lemma sg13306 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1153 sg3280 + +lemma sg13307 : RowSquare [8,7,2,2,2,2,2,1] [8,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1637 sg2554 + +lemma sg13308 : RowSquare [8,7,2,2,2,2,2,1] [8,5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5932 + +lemma sg13309 : RowSquare [8,7,2,2,2,2,2,1] [8,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5944 + +lemma sg13310 : RowSquare [8,7,2,2,2,2,2,1] [8,5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1594 sg2592 + +lemma sg13311 : RowSquare [8,7,2,2,2,2,2,1] [8,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1149 sg3285 + +lemma sg13312 : RowSquare [8,7,2,2,2,2,2,1] [8,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1160 sg3278 + +lemma sg13313 : RowSquare [8,7,2,2,2,2,2,1] [8,6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8310 + +lemma sg13314 : RowSquare [8,7,2,2,2,2,2,1] [8,6,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8329 + +lemma sg13315 : RowSquare [8,7,2,2,2,2,2,1] [8,6,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5934 + +lemma sg13316 : RowSquare [8,7,2,2,2,2,2,1] [8,6,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8312 + +lemma sg13317 : RowSquare [8,7,2,2,2,2,2,1] [8,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8313 + +lemma sg13318 : RowSquare [8,7,2,2,2,2,2,1] [8,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg42 sg8314 + +lemma sg13319 : RowSquare [8,7,2,2,2,2,2,1] [8,6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg42 sg8315 + +lemma sg13320 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5934 + +lemma sg13321 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5945 + +lemma sg13322 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8330 + +lemma sg13323 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1149 sg3287 + +lemma sg13324 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1637 sg2555 + +lemma sg13325 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5936 + +lemma sg13326 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1593 sg2593 + +lemma sg13327 : RowSquare [8,7,2,2,2,2,2,1] [8,6,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1637 sg2556 + +lemma sg13328 : RowSquare [8,7,2,2,2,2,2,1] [8,6,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5935 + +lemma sg13329 : RowSquare [8,7,2,2,2,2,2,1] [8,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg365 sg5111 + +lemma sg13330 : RowSquare [8,7,2,2,2,2,2,1] [8,6,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1594 sg2593 + +lemma sg13331 : RowSquare [8,7,2,2,2,2,2,1] [8,6,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1595 sg2592 + +lemma sg13332 : RowSquare [8,7,2,2,2,2,2,1] [8,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5937 + +lemma sg13333 : RowSquare [8,7,2,2,2,2,2,1] [8,6,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1596 sg2592 + +lemma sg13334 : RowSquare [8,7,2,2,2,2,2,1] [8,6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1597 sg2592 + +lemma sg13335 : RowSquare [8,7,2,2,2,2,2,1] [8,7,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10066 + +lemma sg13336 : RowSquare [8,7,2,2,2,2,2,1] [8,7,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg5934 + +lemma sg13337 : RowSquare [8,7,2,2,2,2,2,1] [8,7,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg10078 + +lemma sg13338 : RowSquare [8,7,2,2,2,2,2,1] [8,7,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10068 + +lemma sg13339 : RowSquare [8,7,2,2,2,2,2,1] [8,7,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1151 sg3287 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes32.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes32.lean index 5b9b591f45d13b15137ba78fae258bdbf74d89e0..cd5e167f8cae1b13b59c786dc076d41ce214aaa2 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes32.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes32.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes27 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes23 - -namespace OAI - -/-! Semigroup Nodes 32. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg13340 : RowSquare [8,7,2,2,2,2,2,1] [8,7,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg10069 - -lemma sg13341 : RowSquare [8,7,2,2,2,2,2,1] [8,7,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg5935 - -lemma sg13342 : RowSquare [8,7,2,2,2,2,2,1] [8,7,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5947 - -lemma sg13343 : RowSquare [8,7,2,2,2,2,2,1] [8,7,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1152 sg3287 - -lemma sg13344 : RowSquare [8,7,2,2,2,2,2,1] [8,7,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1595 sg2593 - -lemma sg13345 : RowSquare [8,7,2,2,2,2,2,1] [8,7,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5938 - -lemma sg13346 : RowSquare [8,7,2,2,2,2,2,1] [8,7,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1596 sg2593 - -lemma sg13347 : RowSquare [8,7,2,2,2,2,2,1] [8,7,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1597 sg2593 - -lemma sg13348 : RowSquare [8,7,2,2,2,2,2,1] [8,8,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10070 - -lemma sg13349 : RowSquare [8,7,2,2,2,2,2,1] [8,8,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10071 - -lemma sg13350 : RowSquare [8,7,2,2,2,2,2,1] [8,8,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg365 sg5113 - -lemma sg13351 : RowSquare [8,7,2,2,2,2,2,1] [8,8,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1155 sg3287 - -lemma sg13352 : RowSquare [8,7,2,2,2,2,2,1] [8,8,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg5938 - -lemma sg13353 : RowSquare [8,7,2,2,2,2,2,1] [8,8,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1156 sg3287 - -lemma sg13354 : RowSquare [8,7,2,2,2,2,2,1] [8,8,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1157 sg3287 - -lemma sg13355 : RowSquare [8,7,2,2,2,2,2,1] [9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg10044 - -lemma sg13356 : RowSquare [8,7,2,2,2,2,2,1] [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11411 - -lemma sg13357 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg8320 - -lemma sg13358 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8331 - -lemma sg13359 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg11387 - -lemma sg13360 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg11388 - -lemma sg13361 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg11389 - -lemma sg13362 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg11390 - -lemma sg13363 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6 sg11391 - -lemma sg13364 : RowSquare [8,7,2,2,2,2,2,1] [9,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8320 - -lemma sg13365 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8331 - -lemma sg13366 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8332 - -lemma sg13367 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11412 - -lemma sg13368 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11413 - -lemma sg13369 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11414 - -lemma sg13370 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg11415 - -lemma sg13371 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg11416 - -lemma sg13372 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg6876 - -lemma sg13373 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8333 - -lemma sg13374 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11421 - -lemma sg13375 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11422 - -lemma sg13376 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg11423 - -lemma sg13377 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg11424 - -lemma sg13378 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg211 sg5928 - -lemma sg13379 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8334 - -lemma sg13380 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8335 - -lemma sg13381 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg8336 - -lemma sg13382 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg11402 - -lemma sg13383 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1165 sg3274 - -lemma sg13384 : RowSquare [8,7,2,2,2,2,2,1] [9,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8321 - -lemma sg13385 : RowSquare [8,7,2,2,2,2,2,1] [9,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8332 - -lemma sg13386 : RowSquare [8,7,2,2,2,2,2,1] [9,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg6875 - -lemma sg13387 : RowSquare [8,7,2,2,2,2,2,1] [9,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10074 - -lemma sg13388 : RowSquare [8,7,2,2,2,2,2,1] [9,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10075 - -lemma sg13389 : RowSquare [8,7,2,2,2,2,2,1] [9,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10076 - -lemma sg13390 : RowSquare [8,7,2,2,2,2,2,1] [9,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg10077 - -lemma sg13391 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8333 - -lemma sg13392 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5948 - -lemma sg13393 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8334 - -lemma sg13394 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8335 - -lemma sg13395 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg8336 - -lemma sg13396 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5940 - -lemma sg13397 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8338 - -lemma sg13398 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1158 sg3280 - -lemma sg13399 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1592 sg2594 - -lemma sg13400 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5939 - -lemma sg13401 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5949 - -lemma sg13402 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg8328 - -lemma sg13403 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1598 sg2592 - -lemma sg13404 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5950 - -lemma sg13405 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1599 sg2592 - -lemma sg13406 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1160 sg3280 - -lemma sg13407 : RowSquare [8,7,2,2,2,2,2,1] [9,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg85 sg6867 - -lemma sg13408 : RowSquare [8,7,2,2,2,2,2,1] [9,5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8337 - -lemma sg13409 : RowSquare [8,7,2,2,2,2,2,1] [9,5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5941 - -lemma sg13410 : RowSquare [8,7,2,2,2,2,2,1] [9,5,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8325 - -lemma sg13411 : RowSquare [8,7,2,2,2,2,2,1] [9,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8326 - -lemma sg13412 : RowSquare [8,7,2,2,2,2,2,1] [9,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg42 sg8327 - -lemma sg13413 : RowSquare [8,7,2,2,2,2,2,1] [9,5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5941 - -lemma sg13414 : RowSquare [8,7,2,2,2,2,2,1] [9,5,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5951 - -lemma sg13415 : RowSquare [8,7,2,2,2,2,2,1] [9,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8338 - -lemma sg13416 : RowSquare [8,7,2,2,2,2,2,1] [9,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1598 sg2593 - -lemma sg13417 : RowSquare [8,7,2,2,2,2,2,1] [9,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg5118 - -lemma sg13418 : RowSquare [8,7,2,2,2,2,2,1] [9,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1593 sg2594 - -lemma sg13419 : RowSquare [8,7,2,2,2,2,2,1] [9,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5942 - -lemma sg13420 : RowSquare [8,7,2,2,2,2,2,1] [9,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5952 - -lemma sg13421 : RowSquare [8,7,2,2,2,2,2,1] [9,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg366 sg5111 - -lemma sg13422 : RowSquare [8,7,2,2,2,2,2,1] [9,6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8329 - -lemma sg13423 : RowSquare [8,7,2,2,2,2,2,1] [9,6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg5941 - -lemma sg13424 : RowSquare [8,7,2,2,2,2,2,1] [9,6,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5945 - -lemma sg13425 : RowSquare [8,7,2,2,2,2,2,1] [9,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8330 - -lemma sg13426 : RowSquare [8,7,2,2,2,2,2,1] [9,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1600 sg2593 - -lemma sg13427 : RowSquare [8,7,2,2,2,2,2,1] [9,6,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5945 - -lemma sg13428 : RowSquare [8,7,2,2,2,2,2,1] [9,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5953 - -lemma sg13429 : RowSquare [8,7,2,2,2,2,2,1] [9,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5946 - -lemma sg13430 : RowSquare [8,7,2,2,2,2,2,1] [9,7,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg213 sg5934 - -lemma sg13431 : RowSquare [8,7,2,2,2,2,2,1] [9,7,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg5945 - -lemma sg13432 : RowSquare [8,7,2,2,2,2,2,1] [9,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5947 - -lemma sg13433 : RowSquare [8,7,2,2,2,2,2,1] [9,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg366 sg5113 - -lemma sg13434 : RowSquare [8,7,2,2,2,2,2,1] [9,8,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg10078 - -lemma sg13435 : RowSquare [8,7,2,2,2,2,2,1] [9,8,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg5947 - -lemma sg13436 : RowSquare [8,7,2,2,2,2,2,1] [9,9,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg5113 - -lemma sg13437 : RowSquare [8,7,2,2,2,2,2,1] [10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg10060 - -lemma sg13438 : RowSquare [8,7,2,2,2,2,2,1] [10,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg8320 - -lemma sg13439 : RowSquare [8,7,2,2,2,2,2,1] [10,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg8331 - -lemma sg13440 : RowSquare [8,7,2,2,2,2,2,1] [10,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg6876 - -lemma sg13441 : RowSquare [8,7,2,2,2,2,2,1] [10,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg10061 - -lemma sg13442 : RowSquare [8,7,2,2,2,2,2,1] [10,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg10062 - -lemma sg13443 : RowSquare [8,7,2,2,2,2,2,1] [10,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg10063 - -lemma sg13444 : RowSquare [8,7,2,2,2,2,2,1] [10,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg15 sg10064 - -lemma sg13445 : RowSquare [8,7,2,2,2,2,2,1] [10,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8331 - -lemma sg13446 : RowSquare [8,7,2,2,2,2,2,1] [10,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8339 - -lemma sg13447 : RowSquare [8,7,2,2,2,2,2,1] [10,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8340 - -lemma sg13448 : RowSquare [8,7,2,2,2,2,2,1] [10,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11421 - -lemma sg13449 : RowSquare [8,7,2,2,2,2,2,1] [10,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11422 - -lemma sg13450 : RowSquare [8,7,2,2,2,2,2,1] [10,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg11423 - -lemma sg13451 : RowSquare [8,7,2,2,2,2,2,1] [10,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg6877 - -lemma sg13452 : RowSquare [8,7,2,2,2,2,2,1] [10,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5954 - -lemma sg13453 : RowSquare [8,7,2,2,2,2,2,1] [10,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg8334 - -lemma sg13454 : RowSquare [8,7,2,2,2,2,2,1] [10,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg8335 - -lemma sg13455 : RowSquare [8,7,2,2,2,2,2,1] [10,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg211 sg5940 - -lemma sg13456 : RowSquare [8,7,2,2,2,2,2,1] [10,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg8341 - -lemma sg13457 : RowSquare [8,7,2,2,2,2,2,1] [10,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8332 - -lemma sg13458 : RowSquare [8,7,2,2,2,2,2,1] [10,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8340 - -lemma sg13459 : RowSquare [8,7,2,2,2,2,2,1] [10,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5948 - -lemma sg13460 : RowSquare [8,7,2,2,2,2,2,1] [10,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8334 - -lemma sg13461 : RowSquare [8,7,2,2,2,2,2,1] [10,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8335 - -lemma sg13462 : RowSquare [8,7,2,2,2,2,2,1] [10,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5948 - -lemma sg13463 : RowSquare [8,7,2,2,2,2,2,1] [10,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg5955 - -lemma sg13464 : RowSquare [8,7,2,2,2,2,2,1] [10,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8341 - -lemma sg13465 : RowSquare [8,7,2,2,2,2,2,1] [10,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5950 - -lemma sg13466 : RowSquare [8,7,2,2,2,2,2,1] [10,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg432 sg4873 - -lemma sg13467 : RowSquare [8,7,2,2,2,2,2,1] [10,5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg85 sg6875 - -lemma sg13468 : RowSquare [8,7,2,2,2,2,2,1] [10,5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg5948 - -lemma sg13469 : RowSquare [8,7,2,2,2,2,2,1] [10,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5951 - -lemma sg13470 : RowSquare [8,7,2,2,2,2,2,1] [10,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8338 - -lemma sg13471 : RowSquare [8,7,2,2,2,2,2,1] [10,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg432 sg4874 - -lemma sg13472 : RowSquare [8,7,2,2,2,2,2,1] [10,6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg213 sg5941 - -lemma sg13473 : RowSquare [8,7,2,2,2,2,2,1] [10,6,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg433 sg4874 - -lemma sg13474 : RowSquare [8,7,2,2,2,2,2,1] [10,7,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg434 sg4874 - -lemma sg13475 : RowSquare [8,7,2,2,2,2,2,1] [11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg8320 - -lemma sg13476 : RowSquare [8,7,2,2,2,2,2,1] [11,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg8331 - -lemma sg13477 : RowSquare [8,7,2,2,2,2,2,1] [11,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg8339 - -lemma sg13478 : RowSquare [8,7,2,2,2,2,2,1] [11,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg6877 - -lemma sg13479 : RowSquare [8,7,2,2,2,2,2,1] [11,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg10074 - -lemma sg13480 : RowSquare [8,7,2,2,2,2,2,1] [11,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg10075 - -lemma sg13481 : RowSquare [8,7,2,2,2,2,2,1] [11,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg85 sg6876 - -lemma sg13482 : RowSquare [8,7,2,2,2,2,2,1] [11,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg8342 - -lemma sg13483 : RowSquare [8,7,2,2,2,2,2,1] [11,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg5954 - -lemma sg13484 : RowSquare [8,7,2,2,2,2,2,1] [11,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg8334 - -lemma sg13485 : RowSquare [8,7,2,2,2,2,2,1] [11,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg5954 - -lemma sg13486 : RowSquare [8,7,2,2,2,2,2,1] [11,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg435 sg4873 - -lemma sg13487 : RowSquare [8,7,2,2,2,2,2,1] [11,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg8340 - -lemma sg13488 : RowSquare [8,7,2,2,2,2,2,1] [11,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg5954 - -lemma sg13489 : RowSquare [8,7,2,2,2,2,2,1] [11,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg435 sg4874 - -lemma sg13490 : RowSquare [8,7,2,2,2,2,2,1] [11,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg213 sg5948 - -lemma sg13491 : RowSquare [8,7,2,2,2,2,2,1] [12,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg8331 - -lemma sg13492 : RowSquare [8,7,2,2,2,2,2,1] [12,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg8339 - -lemma sg13493 : RowSquare [8,7,2,2,2,2,2,1] [12,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg8342 - -lemma sg13494 : RowSquare [8,7,2,2,2,2,2,1] [12,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg211 sg5954 - -lemma sg13495 : RowSquare [8,7,2,2,2,2,2,1] [12,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg85 sg6877 - -lemma sg13496 : RowSquare [8,7,2,2,2,2,2,1] [12,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg212 sg5954 - -lemma sg13497 : RowSquare [8,7,2,2,2,2,2,1] [13,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg86 sg6876 - -lemma sg13498 : RowSquare [8,7,2,2,2,2,2,1] [13,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg8342 - -lemma sg13499 : RowSquare [9,7,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg447 sg4930 - -lemma sg13500 : RowSquare [9,7,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg448 sg4930 - -lemma sg13501 : RowSquare [9,7,1,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg449 sg4930 - -lemma sg13502 : RowSquare [9,7,1,1,1,1,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg450 sg4930 - -lemma sg13503 : RowSquare [9,7,1,1,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg451 sg4930 - -lemma sg13504 : RowSquare [12,3,2,2,2,2,2,1] [5,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg74 sg6917 - -lemma sg13505 : RowSquare [12,3,2,2,2,2,2,1] [5,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg74 sg6918 - -lemma sg13506 : RowSquare [12,3,2,2,2,2,2,1] [5,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg74 sg6919 - -lemma sg13507 : RowSquare [12,3,2,2,2,2,2,1] [6,5,5,5,5] := by - exact rowSquare_join (by decide) sg75 sg6919 - -lemma sg13508 : RowSquare [12,3,2,2,2,2,2,1] [6,6,4,4,3,3] := by - exact rowSquare_join (by decide) sg74 sg6947 - -lemma sg13509 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3068 - -lemma sg13510 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1891 sg3656 - -lemma sg13511 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3068 - -lemma sg13512 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3069 - -lemma sg13513 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3069 - -lemma sg13514 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1891 sg3658 - -lemma sg13515 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2837 - -lemma sg13516 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3070 - -lemma sg13517 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg1456 sg4503 - -lemma sg13518 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3071 - -lemma sg13519 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg1891 sg3659 - -lemma sg13520 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3071 - -lemma sg13521 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2212 sg3123 - -lemma sg13522 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3072 - -lemma sg13523 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg2314 sg3068 - -lemma sg13524 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg2212 sg3124 - -lemma sg13525 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3073 - -lemma sg13526 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2841 - -lemma sg13527 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg2314 sg3069 - -lemma sg13528 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg975 sg5006 - -lemma sg13529 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg2212 sg3125 - -lemma sg13530 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2837 - -lemma sg13531 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3074 - -lemma sg13532 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3075 - -lemma sg13533 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3075 - -lemma sg13534 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3] := by - exact rowSquare_join (by decide) sg2329 sg3004 - -lemma sg13535 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg2393 sg2837 - -lemma sg13536 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3076 - -lemma sg13537 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg975 sg5008 - -lemma sg13538 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg2212 sg3127 - -lemma sg13539 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3077 - -lemma sg13540 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,3] := by - exact rowSquare_join (by decide) sg976 sg5007 - -lemma sg13541 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg2432 sg2770 - -lemma sg13542 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2] := by - exact rowSquare_join (by decide) sg2329 sg3007 - -lemma sg13543 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg2212 sg3128 - -lemma sg13544 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3078 - -lemma sg13545 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2841 - -lemma sg13546 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2] := by - exact rowSquare_join (by decide) sg2329 sg3008 - -lemma sg13547 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1] := by - exact rowSquare_join (by decide) sg2329 sg3009 - -lemma sg13548 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5] := by - exact rowSquare_join (by decide) sg1916 sg3648 - -lemma sg13549 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2393 sg2839 - -lemma sg13550 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1065 sg4990 - -lemma sg13551 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg975 sg5009 - -lemma sg13552 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2212 sg3129 - -lemma sg13553 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3079 - -lemma sg13554 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3] := by - exact rowSquare_join (by decide) sg636 sg5791 - -lemma sg13555 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2212 sg3130 - -lemma sg13556 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3080 - -lemma sg13557 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg2393 sg2841 - -lemma sg13558 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2] := by - exact rowSquare_join (by decide) sg2318 sg3068 - -lemma sg13559 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1] := by - exact rowSquare_join (by decide) sg2432 sg2772 - -lemma sg13560 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg2433 sg2771 - -lemma sg13561 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by - exact rowSquare_join (by decide) sg976 sg5010 - -lemma sg13562 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1] := by - exact rowSquare_join (by decide) sg2318 sg3069 - -lemma sg13563 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4] := by - exact rowSquare_join (by decide) sg2432 sg2773 - -lemma sg13564 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1] := by - exact rowSquare_join (by decide) sg2330 sg3008 - -lemma sg13565 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3] := by - exact rowSquare_join (by decide) sg2433 sg2773 - -lemma sg13566 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2457 sg2664 - -lemma sg13567 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2214 sg3119 - -lemma sg13568 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3081 - -lemma sg13569 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg1919 sg3647 - -lemma sg13570 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1956 sg3512 - -lemma sg13571 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2214 sg3120 - -lemma sg13572 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3082 - -lemma sg13573 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3083 - -lemma sg13574 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg2215 sg3121 - -lemma sg13575 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2213 sg3123 - -lemma sg13576 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg2214 sg3122 - -lemma sg13577 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3084 - -lemma sg13578 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2213 sg3124 - -lemma sg13579 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg1892 sg3659 - -lemma sg13580 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3] := by - exact rowSquare_join (by decide) sg2314 sg3071 - -lemma sg13581 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1300 sg4539 - -lemma sg13582 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3085 - -lemma sg13583 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg2214 sg3124 - -lemma sg13584 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,2] := by - exact rowSquare_join (by decide) sg2215 sg3124 - -lemma sg13585 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1536 sg4420 - -lemma sg13586 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2849 - -lemma sg13587 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3086 - -lemma sg13588 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2216 sg3124 - -lemma sg13589 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2845 - -lemma sg13590 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3087 - -lemma sg13591 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,3] := by - exact rowSquare_join (by decide) sg2215 sg3125 - -lemma sg13592 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2850 - -lemma sg13593 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2847 - -lemma sg13594 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3] := by - exact rowSquare_join (by decide) sg2215 sg3126 - -lemma sg13595 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3088 - -lemma sg13596 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg2214 sg3128 - -lemma sg13597 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2] := by - exact rowSquare_join (by decide) sg2215 sg3128 - -lemma sg13598 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg2217 sg3122 - -lemma sg13599 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2212 sg3144 - -lemma sg13600 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2399 sg2837 - -lemma sg13601 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3089 - -lemma sg13602 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2849 - -lemma sg13603 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,3] := by - exact rowSquare_join (by decide) sg2333 sg3004 - -lemma sg13604 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3090 - -lemma sg13605 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2850 - -lemma sg13606 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,2] := by - exact rowSquare_join (by decide) sg2329 sg3022 - -lemma sg13607 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,1] := by - exact rowSquare_join (by decide) sg2329 sg3023 - -lemma sg13608 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg2393 sg2849 - -lemma sg13609 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3091 - -lemma sg13610 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2851 - -lemma sg13611 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,2,2] := by - exact rowSquare_join (by decide) sg2218 sg3125 - -lemma sg13612 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2852 - -lemma sg13613 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,1] := by - exact rowSquare_join (by decide) sg2329 sg3026 - -lemma sg13614 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3] := by - exact rowSquare_join (by decide) sg2433 sg2777 - -lemma sg13615 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1] := by - exact rowSquare_join (by decide) sg2433 sg2779 - -lemma sg13616 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3] := by - exact rowSquare_join (by decide) sg2432 sg2780 - -lemma sg13617 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2] := by - exact rowSquare_join (by decide) sg2432 sg2781 - -lemma sg13618 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1] := by - exact rowSquare_join (by decide) sg2433 sg2781 - -lemma sg13619 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6] := by - exact rowSquare_join (by decide) sg1457 sg4505 - -lemma sg13620 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2213 sg3132 - -lemma sg13621 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3092 - -lemma sg13622 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2335 sg3008 - -lemma sg13623 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2335 sg3009 - -lemma sg13624 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2214 sg3131 - -lemma sg13625 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3093 - -lemma sg13626 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg2215 sg3132 - -lemma sg13627 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1922 sg3647 - -lemma sg13628 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2214 sg3133 - -lemma sg13629 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3094 - -lemma sg13630 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2854 - -lemma sg13631 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg2215 sg3134 - -lemma sg13632 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2213 sg3136 - -lemma sg13633 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg2220 sg3122 - -lemma sg13634 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3095 - -lemma sg13635 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg2214 sg3138 - -lemma sg13636 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg2215 sg3138 - -lemma sg13637 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2214 sg3139 - -lemma sg13638 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3096 - -lemma sg13639 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2856 - -lemma sg13640 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2216 sg3138 - -lemma sg13641 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3097 - -lemma sg13642 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg2217 sg3133 - -lemma sg13643 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2859 - -lemma sg13644 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2860 - -lemma sg13645 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg2217 sg3139 - -lemma sg13646 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2399 sg2849 - -lemma sg13647 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3098 - -lemma sg13648 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2399 sg2850 - -lemma sg13649 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2220 sg3131 - -lemma sg13650 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2863 - -lemma sg13651 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3] := by - exact rowSquare_join (by decide) sg2449 sg2777 - -lemma sg13652 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2310 sg3000 - -lemma sg13653 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg2310 sg3001 - -lemma sg13654 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg2311 sg3001 - -lemma sg13655 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg2310 sg3003 - -lemma sg13656 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3004 - -lemma sg13657 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3003 - -lemma sg13658 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg2311 sg3004 - -lemma sg13659 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2310 sg3005 - -lemma sg13660 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3005 - -lemma sg13661 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg2341 sg2925 - -lemma sg13662 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3006 - -lemma sg13663 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3007 - -lemma sg13664 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg2343 sg2925 - -lemma sg13665 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3007 - -lemma sg13666 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3008 - -lemma sg13667 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg2344 sg2925 - -lemma sg13668 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3008 - -lemma sg13669 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3009 - -lemma sg13670 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3009 - -lemma sg13671 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1891 sg3655 - -lemma sg13672 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1535 sg4418 - -lemma sg13673 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2345 sg2925 - -lemma sg13674 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg2310 sg3010 - -lemma sg13675 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg2312 sg3001 - -lemma sg13676 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg2310 sg3011 - -lemma sg13677 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3012 - -lemma sg13678 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3011 - -lemma sg13679 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg2311 sg3012 - -lemma sg13680 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1536 sg4418 - -lemma sg13681 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2346 sg2925 - -lemma sg13682 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2310 sg3013 - -lemma sg13683 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2315 sg3001 - -lemma sg13684 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg2347 sg2925 - -lemma sg13685 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3014 - -lemma sg13686 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3015 - -lemma sg13687 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2801 - -lemma sg13688 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3015 - -lemma sg13689 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg2314 sg3004 - -lemma sg13690 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2312 sg3005 - -lemma sg13691 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2310 sg3016 - -lemma sg13692 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2314 sg3005 - -lemma sg13693 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3016 - -lemma sg13694 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg2312 sg3006 - -lemma sg13695 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3017 - -lemma sg13696 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2804 - -lemma sg13697 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3017 - -lemma sg13698 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3018 - -lemma sg13699 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3018 - -lemma sg13700 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg2314 sg3007 - -lemma sg13701 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg2312 sg3008 - -lemma sg13702 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg2349 sg2925 - -lemma sg13703 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3019 - -lemma sg13704 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3019 - -lemma sg13705 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg2314 sg3008 - -lemma sg13706 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2807 - -lemma sg13707 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg2314 sg3009 - -lemma sg13708 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg1893 sg3655 - -lemma sg13709 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2310 sg3020 - -lemma sg13710 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3020 - -lemma sg13711 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2350 sg2925 - -lemma sg13712 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2315 sg3002 - -lemma sg13713 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2310 sg3021 - -lemma sg13714 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2315 sg3004 - -lemma sg13715 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3021 - -lemma sg13716 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg2391 sg2800 - -lemma sg13717 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3022 - -lemma sg13718 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2801 - -lemma sg13719 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3022 - -lemma sg13720 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3023 - -lemma sg13721 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3023 - -lemma sg13722 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3] := by - exact rowSquare_join (by decide) sg2392 sg2802 - -lemma sg13723 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2315 sg3005 - -lemma sg13724 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3024 - -lemma sg13725 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg2341 sg2927 - -lemma sg13726 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3024 - -lemma sg13727 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2315 sg3008 - -lemma sg13728 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2804 - -lemma sg13729 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3025 - -lemma sg13730 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3025 - -lemma sg13731 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,3] := by - exact rowSquare_join (by decide) sg2318 sg3004 - -lemma sg13732 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg2432 sg2761 - -lemma sg13733 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2] := by - exact rowSquare_join (by decide) sg2392 sg2805 - -lemma sg13734 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3026 - -lemma sg13735 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3026 - -lemma sg13736 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2807 - -lemma sg13737 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2] := by - exact rowSquare_join (by decide) sg2392 sg2806 - -lemma sg13738 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1] := by - exact rowSquare_join (by decide) sg2392 sg2807 - -lemma sg13739 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5] := by - exact rowSquare_join (by decide) sg1895 sg3655 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes27 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes23 + +namespace OAI + +/-! Semigroup Nodes 32. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg13340 : RowSquare [8,7,2,2,2,2,2,1] [8,7,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg10069 + +lemma sg13341 : RowSquare [8,7,2,2,2,2,2,1] [8,7,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg5935 + +lemma sg13342 : RowSquare [8,7,2,2,2,2,2,1] [8,7,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5947 + +lemma sg13343 : RowSquare [8,7,2,2,2,2,2,1] [8,7,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1152 sg3287 + +lemma sg13344 : RowSquare [8,7,2,2,2,2,2,1] [8,7,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1595 sg2593 + +lemma sg13345 : RowSquare [8,7,2,2,2,2,2,1] [8,7,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5938 + +lemma sg13346 : RowSquare [8,7,2,2,2,2,2,1] [8,7,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1596 sg2593 + +lemma sg13347 : RowSquare [8,7,2,2,2,2,2,1] [8,7,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1597 sg2593 + +lemma sg13348 : RowSquare [8,7,2,2,2,2,2,1] [8,8,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10070 + +lemma sg13349 : RowSquare [8,7,2,2,2,2,2,1] [8,8,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10071 + +lemma sg13350 : RowSquare [8,7,2,2,2,2,2,1] [8,8,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg365 sg5113 + +lemma sg13351 : RowSquare [8,7,2,2,2,2,2,1] [8,8,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1155 sg3287 + +lemma sg13352 : RowSquare [8,7,2,2,2,2,2,1] [8,8,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg5938 + +lemma sg13353 : RowSquare [8,7,2,2,2,2,2,1] [8,8,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1156 sg3287 + +lemma sg13354 : RowSquare [8,7,2,2,2,2,2,1] [8,8,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1157 sg3287 + +lemma sg13355 : RowSquare [8,7,2,2,2,2,2,1] [9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg10044 + +lemma sg13356 : RowSquare [8,7,2,2,2,2,2,1] [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11411 + +lemma sg13357 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg8320 + +lemma sg13358 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8331 + +lemma sg13359 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg11387 + +lemma sg13360 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg11388 + +lemma sg13361 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg11389 + +lemma sg13362 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg11390 + +lemma sg13363 : RowSquare [8,7,2,2,2,2,2,1] [9,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6 sg11391 + +lemma sg13364 : RowSquare [8,7,2,2,2,2,2,1] [9,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8320 + +lemma sg13365 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8331 + +lemma sg13366 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8332 + +lemma sg13367 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11412 + +lemma sg13368 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11413 + +lemma sg13369 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11414 + +lemma sg13370 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg11415 + +lemma sg13371 : RowSquare [8,7,2,2,2,2,2,1] [9,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg11416 + +lemma sg13372 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg6876 + +lemma sg13373 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8333 + +lemma sg13374 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11421 + +lemma sg13375 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11422 + +lemma sg13376 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg11423 + +lemma sg13377 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg11424 + +lemma sg13378 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg211 sg5928 + +lemma sg13379 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8334 + +lemma sg13380 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8335 + +lemma sg13381 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg8336 + +lemma sg13382 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg11402 + +lemma sg13383 : RowSquare [8,7,2,2,2,2,2,1] [9,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1165 sg3274 + +lemma sg13384 : RowSquare [8,7,2,2,2,2,2,1] [9,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8321 + +lemma sg13385 : RowSquare [8,7,2,2,2,2,2,1] [9,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8332 + +lemma sg13386 : RowSquare [8,7,2,2,2,2,2,1] [9,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg6875 + +lemma sg13387 : RowSquare [8,7,2,2,2,2,2,1] [9,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10074 + +lemma sg13388 : RowSquare [8,7,2,2,2,2,2,1] [9,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10075 + +lemma sg13389 : RowSquare [8,7,2,2,2,2,2,1] [9,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10076 + +lemma sg13390 : RowSquare [8,7,2,2,2,2,2,1] [9,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg10077 + +lemma sg13391 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8333 + +lemma sg13392 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5948 + +lemma sg13393 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8334 + +lemma sg13394 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8335 + +lemma sg13395 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg8336 + +lemma sg13396 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5940 + +lemma sg13397 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8338 + +lemma sg13398 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1158 sg3280 + +lemma sg13399 : RowSquare [8,7,2,2,2,2,2,1] [9,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1592 sg2594 + +lemma sg13400 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5939 + +lemma sg13401 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5949 + +lemma sg13402 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg8328 + +lemma sg13403 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1598 sg2592 + +lemma sg13404 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5950 + +lemma sg13405 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1599 sg2592 + +lemma sg13406 : RowSquare [8,7,2,2,2,2,2,1] [9,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1160 sg3280 + +lemma sg13407 : RowSquare [8,7,2,2,2,2,2,1] [9,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg85 sg6867 + +lemma sg13408 : RowSquare [8,7,2,2,2,2,2,1] [9,5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8337 + +lemma sg13409 : RowSquare [8,7,2,2,2,2,2,1] [9,5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5941 + +lemma sg13410 : RowSquare [8,7,2,2,2,2,2,1] [9,5,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8325 + +lemma sg13411 : RowSquare [8,7,2,2,2,2,2,1] [9,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8326 + +lemma sg13412 : RowSquare [8,7,2,2,2,2,2,1] [9,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg42 sg8327 + +lemma sg13413 : RowSquare [8,7,2,2,2,2,2,1] [9,5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5941 + +lemma sg13414 : RowSquare [8,7,2,2,2,2,2,1] [9,5,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5951 + +lemma sg13415 : RowSquare [8,7,2,2,2,2,2,1] [9,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8338 + +lemma sg13416 : RowSquare [8,7,2,2,2,2,2,1] [9,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1598 sg2593 + +lemma sg13417 : RowSquare [8,7,2,2,2,2,2,1] [9,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg5118 + +lemma sg13418 : RowSquare [8,7,2,2,2,2,2,1] [9,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1593 sg2594 + +lemma sg13419 : RowSquare [8,7,2,2,2,2,2,1] [9,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5942 + +lemma sg13420 : RowSquare [8,7,2,2,2,2,2,1] [9,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5952 + +lemma sg13421 : RowSquare [8,7,2,2,2,2,2,1] [9,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg366 sg5111 + +lemma sg13422 : RowSquare [8,7,2,2,2,2,2,1] [9,6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8329 + +lemma sg13423 : RowSquare [8,7,2,2,2,2,2,1] [9,6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg5941 + +lemma sg13424 : RowSquare [8,7,2,2,2,2,2,1] [9,6,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5945 + +lemma sg13425 : RowSquare [8,7,2,2,2,2,2,1] [9,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8330 + +lemma sg13426 : RowSquare [8,7,2,2,2,2,2,1] [9,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1600 sg2593 + +lemma sg13427 : RowSquare [8,7,2,2,2,2,2,1] [9,6,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5945 + +lemma sg13428 : RowSquare [8,7,2,2,2,2,2,1] [9,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5953 + +lemma sg13429 : RowSquare [8,7,2,2,2,2,2,1] [9,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5946 + +lemma sg13430 : RowSquare [8,7,2,2,2,2,2,1] [9,7,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg213 sg5934 + +lemma sg13431 : RowSquare [8,7,2,2,2,2,2,1] [9,7,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg5945 + +lemma sg13432 : RowSquare [8,7,2,2,2,2,2,1] [9,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5947 + +lemma sg13433 : RowSquare [8,7,2,2,2,2,2,1] [9,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg366 sg5113 + +lemma sg13434 : RowSquare [8,7,2,2,2,2,2,1] [9,8,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg10078 + +lemma sg13435 : RowSquare [8,7,2,2,2,2,2,1] [9,8,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg5947 + +lemma sg13436 : RowSquare [8,7,2,2,2,2,2,1] [9,9,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg5113 + +lemma sg13437 : RowSquare [8,7,2,2,2,2,2,1] [10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg10060 + +lemma sg13438 : RowSquare [8,7,2,2,2,2,2,1] [10,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg8320 + +lemma sg13439 : RowSquare [8,7,2,2,2,2,2,1] [10,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg8331 + +lemma sg13440 : RowSquare [8,7,2,2,2,2,2,1] [10,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg6876 + +lemma sg13441 : RowSquare [8,7,2,2,2,2,2,1] [10,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg10061 + +lemma sg13442 : RowSquare [8,7,2,2,2,2,2,1] [10,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg10062 + +lemma sg13443 : RowSquare [8,7,2,2,2,2,2,1] [10,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg10063 + +lemma sg13444 : RowSquare [8,7,2,2,2,2,2,1] [10,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg15 sg10064 + +lemma sg13445 : RowSquare [8,7,2,2,2,2,2,1] [10,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8331 + +lemma sg13446 : RowSquare [8,7,2,2,2,2,2,1] [10,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8339 + +lemma sg13447 : RowSquare [8,7,2,2,2,2,2,1] [10,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8340 + +lemma sg13448 : RowSquare [8,7,2,2,2,2,2,1] [10,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11421 + +lemma sg13449 : RowSquare [8,7,2,2,2,2,2,1] [10,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11422 + +lemma sg13450 : RowSquare [8,7,2,2,2,2,2,1] [10,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg11423 + +lemma sg13451 : RowSquare [8,7,2,2,2,2,2,1] [10,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg6877 + +lemma sg13452 : RowSquare [8,7,2,2,2,2,2,1] [10,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5954 + +lemma sg13453 : RowSquare [8,7,2,2,2,2,2,1] [10,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg8334 + +lemma sg13454 : RowSquare [8,7,2,2,2,2,2,1] [10,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg8335 + +lemma sg13455 : RowSquare [8,7,2,2,2,2,2,1] [10,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg211 sg5940 + +lemma sg13456 : RowSquare [8,7,2,2,2,2,2,1] [10,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg8341 + +lemma sg13457 : RowSquare [8,7,2,2,2,2,2,1] [10,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8332 + +lemma sg13458 : RowSquare [8,7,2,2,2,2,2,1] [10,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8340 + +lemma sg13459 : RowSquare [8,7,2,2,2,2,2,1] [10,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5948 + +lemma sg13460 : RowSquare [8,7,2,2,2,2,2,1] [10,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8334 + +lemma sg13461 : RowSquare [8,7,2,2,2,2,2,1] [10,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8335 + +lemma sg13462 : RowSquare [8,7,2,2,2,2,2,1] [10,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5948 + +lemma sg13463 : RowSquare [8,7,2,2,2,2,2,1] [10,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg5955 + +lemma sg13464 : RowSquare [8,7,2,2,2,2,2,1] [10,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8341 + +lemma sg13465 : RowSquare [8,7,2,2,2,2,2,1] [10,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5950 + +lemma sg13466 : RowSquare [8,7,2,2,2,2,2,1] [10,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg432 sg4873 + +lemma sg13467 : RowSquare [8,7,2,2,2,2,2,1] [10,5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg85 sg6875 + +lemma sg13468 : RowSquare [8,7,2,2,2,2,2,1] [10,5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg5948 + +lemma sg13469 : RowSquare [8,7,2,2,2,2,2,1] [10,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5951 + +lemma sg13470 : RowSquare [8,7,2,2,2,2,2,1] [10,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8338 + +lemma sg13471 : RowSquare [8,7,2,2,2,2,2,1] [10,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg432 sg4874 + +lemma sg13472 : RowSquare [8,7,2,2,2,2,2,1] [10,6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg213 sg5941 + +lemma sg13473 : RowSquare [8,7,2,2,2,2,2,1] [10,6,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg433 sg4874 + +lemma sg13474 : RowSquare [8,7,2,2,2,2,2,1] [10,7,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg434 sg4874 + +lemma sg13475 : RowSquare [8,7,2,2,2,2,2,1] [11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg8320 + +lemma sg13476 : RowSquare [8,7,2,2,2,2,2,1] [11,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg8331 + +lemma sg13477 : RowSquare [8,7,2,2,2,2,2,1] [11,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg8339 + +lemma sg13478 : RowSquare [8,7,2,2,2,2,2,1] [11,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg6877 + +lemma sg13479 : RowSquare [8,7,2,2,2,2,2,1] [11,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg10074 + +lemma sg13480 : RowSquare [8,7,2,2,2,2,2,1] [11,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg10075 + +lemma sg13481 : RowSquare [8,7,2,2,2,2,2,1] [11,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg85 sg6876 + +lemma sg13482 : RowSquare [8,7,2,2,2,2,2,1] [11,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg8342 + +lemma sg13483 : RowSquare [8,7,2,2,2,2,2,1] [11,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg5954 + +lemma sg13484 : RowSquare [8,7,2,2,2,2,2,1] [11,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg8334 + +lemma sg13485 : RowSquare [8,7,2,2,2,2,2,1] [11,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg5954 + +lemma sg13486 : RowSquare [8,7,2,2,2,2,2,1] [11,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg435 sg4873 + +lemma sg13487 : RowSquare [8,7,2,2,2,2,2,1] [11,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg8340 + +lemma sg13488 : RowSquare [8,7,2,2,2,2,2,1] [11,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg5954 + +lemma sg13489 : RowSquare [8,7,2,2,2,2,2,1] [11,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg435 sg4874 + +lemma sg13490 : RowSquare [8,7,2,2,2,2,2,1] [11,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg213 sg5948 + +lemma sg13491 : RowSquare [8,7,2,2,2,2,2,1] [12,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg8331 + +lemma sg13492 : RowSquare [8,7,2,2,2,2,2,1] [12,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg8339 + +lemma sg13493 : RowSquare [8,7,2,2,2,2,2,1] [12,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg8342 + +lemma sg13494 : RowSquare [8,7,2,2,2,2,2,1] [12,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg211 sg5954 + +lemma sg13495 : RowSquare [8,7,2,2,2,2,2,1] [12,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg85 sg6877 + +lemma sg13496 : RowSquare [8,7,2,2,2,2,2,1] [12,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg212 sg5954 + +lemma sg13497 : RowSquare [8,7,2,2,2,2,2,1] [13,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg86 sg6876 + +lemma sg13498 : RowSquare [8,7,2,2,2,2,2,1] [13,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg8342 + +lemma sg13499 : RowSquare [9,7,1,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg447 sg4930 + +lemma sg13500 : RowSquare [9,7,1,1,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg448 sg4930 + +lemma sg13501 : RowSquare [9,7,1,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg449 sg4930 + +lemma sg13502 : RowSquare [9,7,1,1,1,1,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg450 sg4930 + +lemma sg13503 : RowSquare [9,7,1,1,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg451 sg4930 + +lemma sg13504 : RowSquare [12,3,2,2,2,2,2,1] [5,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg74 sg6917 + +lemma sg13505 : RowSquare [12,3,2,2,2,2,2,1] [5,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg74 sg6918 + +lemma sg13506 : RowSquare [12,3,2,2,2,2,2,1] [5,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg74 sg6919 + +lemma sg13507 : RowSquare [12,3,2,2,2,2,2,1] [6,5,5,5,5] := by + exact rowSquare_join (by decide) sg75 sg6919 + +lemma sg13508 : RowSquare [12,3,2,2,2,2,2,1] [6,6,4,4,3,3] := by + exact rowSquare_join (by decide) sg74 sg6947 + +lemma sg13509 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3068 + +lemma sg13510 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1891 sg3656 + +lemma sg13511 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3068 + +lemma sg13512 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3069 + +lemma sg13513 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3069 + +lemma sg13514 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1891 sg3658 + +lemma sg13515 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2837 + +lemma sg13516 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3070 + +lemma sg13517 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg1456 sg4503 + +lemma sg13518 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3071 + +lemma sg13519 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg1891 sg3659 + +lemma sg13520 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3071 + +lemma sg13521 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2212 sg3123 + +lemma sg13522 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3072 + +lemma sg13523 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg2314 sg3068 + +lemma sg13524 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg2212 sg3124 + +lemma sg13525 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3073 + +lemma sg13526 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2841 + +lemma sg13527 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg2314 sg3069 + +lemma sg13528 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg975 sg5006 + +lemma sg13529 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg2212 sg3125 + +lemma sg13530 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2837 + +lemma sg13531 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3074 + +lemma sg13532 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3075 + +lemma sg13533 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3075 + +lemma sg13534 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3] := by + exact rowSquare_join (by decide) sg2329 sg3004 + +lemma sg13535 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg2393 sg2837 + +lemma sg13536 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3076 + +lemma sg13537 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg975 sg5008 + +lemma sg13538 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg2212 sg3127 + +lemma sg13539 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3077 + +lemma sg13540 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,3] := by + exact rowSquare_join (by decide) sg976 sg5007 + +lemma sg13541 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg2432 sg2770 + +lemma sg13542 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2] := by + exact rowSquare_join (by decide) sg2329 sg3007 + +lemma sg13543 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg2212 sg3128 + +lemma sg13544 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3078 + +lemma sg13545 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2841 + +lemma sg13546 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2] := by + exact rowSquare_join (by decide) sg2329 sg3008 + +lemma sg13547 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1] := by + exact rowSquare_join (by decide) sg2329 sg3009 + +lemma sg13548 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5] := by + exact rowSquare_join (by decide) sg1916 sg3648 + +lemma sg13549 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2393 sg2839 + +lemma sg13550 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1065 sg4990 + +lemma sg13551 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg975 sg5009 + +lemma sg13552 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2212 sg3129 + +lemma sg13553 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3079 + +lemma sg13554 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3] := by + exact rowSquare_join (by decide) sg636 sg5791 + +lemma sg13555 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2212 sg3130 + +lemma sg13556 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3080 + +lemma sg13557 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg2393 sg2841 + +lemma sg13558 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2] := by + exact rowSquare_join (by decide) sg2318 sg3068 + +lemma sg13559 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1] := by + exact rowSquare_join (by decide) sg2432 sg2772 + +lemma sg13560 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg2433 sg2771 + +lemma sg13561 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by + exact rowSquare_join (by decide) sg976 sg5010 + +lemma sg13562 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1] := by + exact rowSquare_join (by decide) sg2318 sg3069 + +lemma sg13563 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4] := by + exact rowSquare_join (by decide) sg2432 sg2773 + +lemma sg13564 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1] := by + exact rowSquare_join (by decide) sg2330 sg3008 + +lemma sg13565 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3] := by + exact rowSquare_join (by decide) sg2433 sg2773 + +lemma sg13566 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2457 sg2664 + +lemma sg13567 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2214 sg3119 + +lemma sg13568 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3081 + +lemma sg13569 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg1919 sg3647 + +lemma sg13570 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1956 sg3512 + +lemma sg13571 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2214 sg3120 + +lemma sg13572 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3082 + +lemma sg13573 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3083 + +lemma sg13574 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg2215 sg3121 + +lemma sg13575 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2213 sg3123 + +lemma sg13576 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg2214 sg3122 + +lemma sg13577 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3084 + +lemma sg13578 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2213 sg3124 + +lemma sg13579 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg1892 sg3659 + +lemma sg13580 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3] := by + exact rowSquare_join (by decide) sg2314 sg3071 + +lemma sg13581 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1300 sg4539 + +lemma sg13582 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3085 + +lemma sg13583 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg2214 sg3124 + +lemma sg13584 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,2] := by + exact rowSquare_join (by decide) sg2215 sg3124 + +lemma sg13585 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1536 sg4420 + +lemma sg13586 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2849 + +lemma sg13587 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3086 + +lemma sg13588 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2216 sg3124 + +lemma sg13589 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2845 + +lemma sg13590 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3087 + +lemma sg13591 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,3] := by + exact rowSquare_join (by decide) sg2215 sg3125 + +lemma sg13592 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2850 + +lemma sg13593 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2847 + +lemma sg13594 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3] := by + exact rowSquare_join (by decide) sg2215 sg3126 + +lemma sg13595 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3088 + +lemma sg13596 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg2214 sg3128 + +lemma sg13597 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2] := by + exact rowSquare_join (by decide) sg2215 sg3128 + +lemma sg13598 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg2217 sg3122 + +lemma sg13599 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2212 sg3144 + +lemma sg13600 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2399 sg2837 + +lemma sg13601 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3089 + +lemma sg13602 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2849 + +lemma sg13603 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,3] := by + exact rowSquare_join (by decide) sg2333 sg3004 + +lemma sg13604 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3090 + +lemma sg13605 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2850 + +lemma sg13606 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,2] := by + exact rowSquare_join (by decide) sg2329 sg3022 + +lemma sg13607 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,1] := by + exact rowSquare_join (by decide) sg2329 sg3023 + +lemma sg13608 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg2393 sg2849 + +lemma sg13609 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3091 + +lemma sg13610 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2851 + +lemma sg13611 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,2,2] := by + exact rowSquare_join (by decide) sg2218 sg3125 + +lemma sg13612 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2852 + +lemma sg13613 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,1] := by + exact rowSquare_join (by decide) sg2329 sg3026 + +lemma sg13614 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3] := by + exact rowSquare_join (by decide) sg2433 sg2777 + +lemma sg13615 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1] := by + exact rowSquare_join (by decide) sg2433 sg2779 + +lemma sg13616 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3] := by + exact rowSquare_join (by decide) sg2432 sg2780 + +lemma sg13617 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2] := by + exact rowSquare_join (by decide) sg2432 sg2781 + +lemma sg13618 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1] := by + exact rowSquare_join (by decide) sg2433 sg2781 + +lemma sg13619 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6] := by + exact rowSquare_join (by decide) sg1457 sg4505 + +lemma sg13620 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2213 sg3132 + +lemma sg13621 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3092 + +lemma sg13622 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2335 sg3008 + +lemma sg13623 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2335 sg3009 + +lemma sg13624 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2214 sg3131 + +lemma sg13625 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3093 + +lemma sg13626 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg2215 sg3132 + +lemma sg13627 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1922 sg3647 + +lemma sg13628 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2214 sg3133 + +lemma sg13629 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3094 + +lemma sg13630 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2854 + +lemma sg13631 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg2215 sg3134 + +lemma sg13632 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2213 sg3136 + +lemma sg13633 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg2220 sg3122 + +lemma sg13634 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3095 + +lemma sg13635 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg2214 sg3138 + +lemma sg13636 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg2215 sg3138 + +lemma sg13637 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2214 sg3139 + +lemma sg13638 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3096 + +lemma sg13639 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2856 + +lemma sg13640 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2216 sg3138 + +lemma sg13641 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3097 + +lemma sg13642 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg2217 sg3133 + +lemma sg13643 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2859 + +lemma sg13644 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2860 + +lemma sg13645 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg2217 sg3139 + +lemma sg13646 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2399 sg2849 + +lemma sg13647 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3098 + +lemma sg13648 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2399 sg2850 + +lemma sg13649 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2220 sg3131 + +lemma sg13650 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2863 + +lemma sg13651 : RowSquare [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3] := by + exact rowSquare_join (by decide) sg2449 sg2777 + +lemma sg13652 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2310 sg3000 + +lemma sg13653 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg2310 sg3001 + +lemma sg13654 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg2311 sg3001 + +lemma sg13655 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg2310 sg3003 + +lemma sg13656 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3004 + +lemma sg13657 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3003 + +lemma sg13658 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg2311 sg3004 + +lemma sg13659 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2310 sg3005 + +lemma sg13660 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3005 + +lemma sg13661 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg2341 sg2925 + +lemma sg13662 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3006 + +lemma sg13663 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3007 + +lemma sg13664 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg2343 sg2925 + +lemma sg13665 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3007 + +lemma sg13666 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3008 + +lemma sg13667 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg2344 sg2925 + +lemma sg13668 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3008 + +lemma sg13669 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3009 + +lemma sg13670 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3009 + +lemma sg13671 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1891 sg3655 + +lemma sg13672 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1535 sg4418 + +lemma sg13673 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2345 sg2925 + +lemma sg13674 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg2310 sg3010 + +lemma sg13675 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg2312 sg3001 + +lemma sg13676 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg2310 sg3011 + +lemma sg13677 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3012 + +lemma sg13678 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3011 + +lemma sg13679 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg2311 sg3012 + +lemma sg13680 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1536 sg4418 + +lemma sg13681 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2346 sg2925 + +lemma sg13682 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2310 sg3013 + +lemma sg13683 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2315 sg3001 + +lemma sg13684 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg2347 sg2925 + +lemma sg13685 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3014 + +lemma sg13686 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3015 + +lemma sg13687 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2801 + +lemma sg13688 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3015 + +lemma sg13689 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg2314 sg3004 + +lemma sg13690 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2312 sg3005 + +lemma sg13691 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2310 sg3016 + +lemma sg13692 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2314 sg3005 + +lemma sg13693 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3016 + +lemma sg13694 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg2312 sg3006 + +lemma sg13695 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3017 + +lemma sg13696 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2804 + +lemma sg13697 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3017 + +lemma sg13698 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3018 + +lemma sg13699 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3018 + +lemma sg13700 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg2314 sg3007 + +lemma sg13701 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg2312 sg3008 + +lemma sg13702 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg2349 sg2925 + +lemma sg13703 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3019 + +lemma sg13704 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3019 + +lemma sg13705 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg2314 sg3008 + +lemma sg13706 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2807 + +lemma sg13707 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg2314 sg3009 + +lemma sg13708 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg1893 sg3655 + +lemma sg13709 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2310 sg3020 + +lemma sg13710 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3020 + +lemma sg13711 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2350 sg2925 + +lemma sg13712 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2315 sg3002 + +lemma sg13713 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2310 sg3021 + +lemma sg13714 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2315 sg3004 + +lemma sg13715 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3021 + +lemma sg13716 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg2391 sg2800 + +lemma sg13717 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3022 + +lemma sg13718 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2801 + +lemma sg13719 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3022 + +lemma sg13720 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3023 + +lemma sg13721 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3023 + +lemma sg13722 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3] := by + exact rowSquare_join (by decide) sg2392 sg2802 + +lemma sg13723 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2315 sg3005 + +lemma sg13724 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3024 + +lemma sg13725 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg2341 sg2927 + +lemma sg13726 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3024 + +lemma sg13727 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2315 sg3008 + +lemma sg13728 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2804 + +lemma sg13729 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3025 + +lemma sg13730 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3025 + +lemma sg13731 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,3] := by + exact rowSquare_join (by decide) sg2318 sg3004 + +lemma sg13732 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg2432 sg2761 + +lemma sg13733 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2] := by + exact rowSquare_join (by decide) sg2392 sg2805 + +lemma sg13734 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3026 + +lemma sg13735 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3026 + +lemma sg13736 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2807 + +lemma sg13737 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2] := by + exact rowSquare_join (by decide) sg2392 sg2806 + +lemma sg13738 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1] := by + exact rowSquare_join (by decide) sg2392 sg2807 + +lemma sg13739 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5] := by + exact rowSquare_join (by decide) sg1895 sg3655 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes33.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes33.lean index 8b91e9b6032d2a5c00d997cdf9b8d747e6dc2b17..90731602622bfeef4db5a0b88a78821826984126 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes33.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes33.lean @@ -1,1221 +1,1221 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes13 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes11 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes9 - -namespace OAI - -/-! Semigroup Nodes 33. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg13740 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2393 sg2803 - -lemma sg13741 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2318 sg3005 - -lemma sg13742 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg2341 sg2928 - -lemma sg13743 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3027 - -lemma sg13744 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3027 - -lemma sg13745 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3] := by - exact rowSquare_join (by decide) sg636 sg5790 - -lemma sg13746 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3028 - -lemma sg13747 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3028 - -lemma sg13748 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg2405 sg2773 - -lemma sg13749 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2] := by - exact rowSquare_join (by decide) sg2406 sg2772 - -lemma sg13750 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1] := by - exact rowSquare_join (by decide) sg2407 sg2772 - -lemma sg13751 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg1323 sg4526 - -lemma sg13752 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg2433 sg2763 - -lemma sg13753 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by - exact rowSquare_join (by decide) sg2318 sg3008 - -lemma sg13754 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1] := by - exact rowSquare_join (by decide) sg2406 sg2773 - -lemma sg13755 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4] := by - exact rowSquare_join (by decide) sg2407 sg2773 - -lemma sg13756 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg1848 sg3703 - -lemma sg13757 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1] := by - exact rowSquare_join (by decide) sg2395 sg2806 - -lemma sg13758 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3] := by - exact rowSquare_join (by decide) sg2395 sg2807 - -lemma sg13759 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1921 sg3632 - -lemma sg13760 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2403 sg2798 - -lemma sg13761 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2352 sg2925 - -lemma sg13762 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3119 - -lemma sg13763 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2310 sg3029 - -lemma sg13764 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2345 sg2926 - -lemma sg13765 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg2353 sg2925 - -lemma sg13766 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1803 sg3724 - -lemma sg13767 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg2312 sg3010 - -lemma sg13768 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1803 sg3725 - -lemma sg13769 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg2310 sg3030 - -lemma sg13770 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg2312 sg3012 - -lemma sg13771 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3030 - -lemma sg13772 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1803 sg3726 - -lemma sg13773 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3031 - -lemma sg13774 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2809 - -lemma sg13775 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3031 - -lemma sg13776 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg2339 sg2930 - -lemma sg13777 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2810 - -lemma sg13778 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2310 sg3032 - -lemma sg13779 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2346 sg2926 - -lemma sg13780 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2355 sg2925 - -lemma sg13781 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3120 - -lemma sg13782 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2312 sg3013 - -lemma sg13783 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3121 - -lemma sg13784 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2310 sg3033 - -lemma sg13785 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2315 sg3012 - -lemma sg13786 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3033 - -lemma sg13787 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg4536 - -lemma sg13788 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg2312 sg3014 - -lemma sg13789 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg4537 - -lemma sg13790 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3034 - -lemma sg13791 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2811 - -lemma sg13792 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3034 - -lemma sg13793 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3035 - -lemma sg13794 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3035 - -lemma sg13795 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg2339 sg2931 - -lemma sg13796 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3122 - -lemma sg13797 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2320 sg3005 - -lemma sg13798 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg4538 - -lemma sg13799 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2312 sg3016 - -lemma sg13800 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3123 - -lemma sg13801 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3036 - -lemma sg13802 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2812 - -lemma sg13803 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3036 - -lemma sg13804 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3124 - -lemma sg13805 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2312 sg3017 - -lemma sg13806 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg2409 sg2771 - -lemma sg13807 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3037 - -lemma sg13808 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3037 - -lemma sg13809 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3] := by - exact rowSquare_join (by decide) sg2339 sg2932 - -lemma sg13810 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2813 - -lemma sg13811 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,2] := by - exact rowSquare_join (by decide) sg2339 sg2933 - -lemma sg13812 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg4539 - -lemma sg13813 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3038 - -lemma sg13814 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3038 - -lemma sg13815 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2814 - -lemma sg13816 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,2] := by - exact rowSquare_join (by decide) sg2339 sg2934 - -lemma sg13817 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,1] := by - exact rowSquare_join (by decide) sg2396 sg2807 - -lemma sg13818 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5] := by - exact rowSquare_join (by decide) sg1956 sg3505 - -lemma sg13819 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2810 - -lemma sg13820 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2312 sg3020 - -lemma sg13821 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2392 sg2810 - -lemma sg13822 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2310 sg3039 - -lemma sg13823 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2321 sg3004 - -lemma sg13824 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3039 - -lemma sg13825 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2393 sg2810 - -lemma sg13826 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2315 sg3013 - -lemma sg13827 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3125 - -lemma sg13828 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2312 sg3021 - -lemma sg13829 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2394 sg2810 - -lemma sg13830 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3040 - -lemma sg13831 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2816 - -lemma sg13832 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3040 - -lemma sg13833 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2395 sg2810 - -lemma sg13834 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2312 sg3022 - -lemma sg13835 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2811 - -lemma sg13836 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3041 - -lemma sg13837 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3041 - -lemma sg13838 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,3] := by - exact rowSquare_join (by decide) sg2339 sg2936 - -lemma sg13839 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2817 - -lemma sg13840 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,2] := by - exact rowSquare_join (by decide) sg2339 sg2937 - -lemma sg13841 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3126 - -lemma sg13842 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2315 sg3016 - -lemma sg13843 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3127 - -lemma sg13844 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2312 sg3024 - -lemma sg13845 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2812 - -lemma sg13846 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3042 - -lemma sg13847 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3042 - -lemma sg13848 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3] := by - exact rowSquare_join (by decide) sg2339 sg2938 - -lemma sg13849 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3128 - -lemma sg13850 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3043 - -lemma sg13851 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3043 - -lemma sg13852 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2819 - -lemma sg13853 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,2] := by - exact rowSquare_join (by decide) sg2339 sg2939 - -lemma sg13854 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,1] := by - exact rowSquare_join (by decide) sg2340 sg2933 - -lemma sg13855 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg2312 sg3026 - -lemma sg13856 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2820 - -lemma sg13857 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2] := by - exact rowSquare_join (by decide) sg2339 sg2940 - -lemma sg13858 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,1] := by - exact rowSquare_join (by decide) sg2340 sg2934 - -lemma sg13859 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4] := by - exact rowSquare_join (by decide) sg2413 sg2773 - -lemma sg13860 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3130 - -lemma sg13861 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg2439 sg2763 - -lemma sg13862 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,1] := by - exact rowSquare_join (by decide) sg2342 sg2934 - -lemma sg13863 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3] := by - exact rowSquare_join (by decide) sg2432 sg2764 - -lemma sg13864 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,1,1] := by - exact rowSquare_join (by decide) sg2398 sg2806 - -lemma sg13865 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2] := by - exact rowSquare_join (by decide) sg2433 sg2764 - -lemma sg13866 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1961 sg3503 - -lemma sg13867 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2315 sg3020 - -lemma sg13868 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1963 sg3503 - -lemma sg13869 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2391 sg2815 - -lemma sg13870 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3044 - -lemma sg13871 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2350 sg2927 - -lemma sg13872 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3044 - -lemma sg13873 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2315 sg3021 - -lemma sg13874 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2315 sg3022 - -lemma sg13875 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2816 - -lemma sg13876 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3045 - -lemma sg13877 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3045 - -lemma sg13878 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,3] := by - exact rowSquare_join (by decide) sg2400 sg2802 - -lemma sg13879 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3046 - -lemma sg13880 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3046 - -lemma sg13881 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2817 - -lemma sg13882 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,2] := by - exact rowSquare_join (by decide) sg2340 sg2936 - -lemma sg13883 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,1] := by - exact rowSquare_join (by decide) sg2340 sg2937 - -lemma sg13884 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3047 - -lemma sg13885 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,3,2] := by - exact rowSquare_join (by decide) sg2340 sg2938 - -lemma sg13886 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2315 sg3026 - -lemma sg13887 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2819 - -lemma sg13888 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,2,2] := by - exact rowSquare_join (by decide) sg2342 sg2936 - -lemma sg13889 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,3,1] := by - exact rowSquare_join (by decide) sg2340 sg2939 - -lemma sg13890 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4] := by - exact rowSquare_join (by decide) sg2432 sg2766 - -lemma sg13891 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2820 - -lemma sg13892 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,1] := by - exact rowSquare_join (by decide) sg2340 sg2940 - -lemma sg13893 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3] := by - exact rowSquare_join (by decide) sg2433 sg2766 - -lemma sg13894 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2822 - -lemma sg13895 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,1,1] := by - exact rowSquare_join (by decide) sg2342 sg2940 - -lemma sg13896 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2] := by - exact rowSquare_join (by decide) sg2432 sg2767 - -lemma sg13897 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1] := by - exact rowSquare_join (by decide) sg2433 sg2767 - -lemma sg13898 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6] := by - exact rowSquare_join (by decide) sg1848 sg3712 - -lemma sg13899 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2326 sg3001 - -lemma sg13900 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2404 sg2798 - -lemma sg13901 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2356 sg2925 - -lemma sg13902 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2186 sg3119 - -lemma sg13903 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2310 sg3049 - -lemma sg13904 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2326 sg3004 - -lemma sg13905 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2352 sg2926 - -lemma sg13906 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2357 sg2925 - -lemma sg13907 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3131 - -lemma sg13908 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2312 sg3029 - -lemma sg13909 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3132 - -lemma sg13910 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2310 sg3050 - -lemma sg13911 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2345 sg2930 - -lemma sg13912 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3050 - -lemma sg13913 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2326 sg3008 - -lemma sg13914 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg2312 sg3030 - -lemma sg13915 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2326 sg3009 - -lemma sg13916 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3051 - -lemma sg13917 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2824 - -lemma sg13918 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3051 - -lemma sg13919 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3052 - -lemma sg13920 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3052 - -lemma sg13921 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg2339 sg2943 - -lemma sg13922 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2186 sg3120 - -lemma sg13923 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2312 sg3032 - -lemma sg13924 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2186 sg3121 - -lemma sg13925 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2310 sg3053 - -lemma sg13926 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2346 sg2930 - -lemma sg13927 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3053 - -lemma sg13928 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3133 - -lemma sg13929 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2315 sg3029 - -lemma sg13930 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3134 - -lemma sg13931 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2312 sg3033 - -lemma sg13932 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3135 - -lemma sg13933 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3054 - -lemma sg13934 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2825 - -lemma sg13935 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3054 - -lemma sg13936 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2186 sg3124 - -lemma sg13937 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2312 sg3034 - -lemma sg13938 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2391 sg2824 - -lemma sg13939 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3055 - -lemma sg13940 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg2339 sg2944 - -lemma sg13941 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2826 - -lemma sg13942 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg2339 sg2945 - -lemma sg13943 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3136 - -lemma sg13944 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3137 - -lemma sg13945 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3056 - -lemma sg13946 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg2339 sg2946 - -lemma sg13947 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3138 - -lemma sg13948 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2] := by - exact rowSquare_join (by decide) sg2339 sg2947 - -lemma sg13949 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2827 - -lemma sg13950 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3139 - -lemma sg13951 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2186 sg3125 - -lemma sg13952 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2169 sg3149 - -lemma sg13953 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2828 - -lemma sg13954 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3057 - -lemma sg13955 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3140 - -lemma sg13956 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3141 - -lemma sg13957 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3] := by - exact rowSquare_join (by decide) sg2339 sg2948 - -lemma sg13958 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2186 sg3128 - -lemma sg13959 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2] := by - exact rowSquare_join (by decide) sg2339 sg2949 - -lemma sg13960 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3142 - -lemma sg13961 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3143 - -lemma sg13962 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2829 - -lemma sg13963 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2827 - -lemma sg13964 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2401 sg2810 - -lemma sg13965 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3] := by - exact rowSquare_join (by decide) sg2339 sg2951 - -lemma sg13966 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2] := by - exact rowSquare_join (by decide) sg2339 sg2952 - -lemma sg13967 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2830 - -lemma sg13968 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2] := by - exact rowSquare_join (by decide) sg2339 sg2953 - -lemma sg13969 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,1] := by - exact rowSquare_join (by decide) sg2340 sg2949 - -lemma sg13970 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4] := by - exact rowSquare_join (by decide) sg2436 sg2766 - -lemma sg13971 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2829 - -lemma sg13972 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,1] := by - exact rowSquare_join (by decide) sg2340 sg2950 - -lemma sg13973 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3] := by - exact rowSquare_join (by decide) sg2432 sg2768 - -lemma sg13974 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,1,1] := by - exact rowSquare_join (by decide) sg2435 sg2767 - -lemma sg13975 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2] := by - exact rowSquare_join (by decide) sg2436 sg2767 - -lemma sg13976 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1961 sg3508 - -lemma sg13977 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1962 sg3508 - -lemma sg13978 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2350 sg2935 - -lemma sg13979 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1963 sg3508 - -lemma sg13980 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3058 - -lemma sg13981 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2350 sg2937 - -lemma sg13982 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2] := by - exact rowSquare_join (by decide) sg2340 sg2951 - -lemma sg13983 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2326 sg3012 - -lemma sg13984 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2358 sg2925 - -lemma sg13985 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2186 sg3132 - -lemma sg13986 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3059 - -lemma sg13987 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3145 - -lemma sg13988 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg3146 - -lemma sg13989 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2832 - -lemma sg13990 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3060 - -lemma sg13991 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2326 sg3019 - -lemma sg13992 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg2339 sg2954 - -lemma sg13993 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2833 - -lemma sg13994 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2834 - -lemma sg13995 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3061 - -lemma sg13996 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3062 - -lemma sg13997 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg2339 sg2955 - -lemma sg13998 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3063 - -lemma sg13999 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg2339 sg2956 - -lemma sg14000 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2390 sg2835 - -lemma sg14001 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3064 - -lemma sg14002 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2350 sg2952 - -lemma sg14003 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2391 sg2835 - -lemma sg14004 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3] := by - exact rowSquare_join (by decide) sg2479 sg2657 - -lemma sg14005 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2311 sg3065 - -lemma sg14006 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2836 - -lemma sg14007 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3066 - -lemma sg14008 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3067 - -lemma sg14009 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1891 sg3505 - -lemma sg14010 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg2311 sg2925 - -lemma sg14011 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg2313 sg2925 - -lemma sg14012 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg2311 sg2926 - -lemma sg14013 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1033 sg4976 - -lemma sg14014 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg2311 sg2930 - -lemma sg14015 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg2322 sg2925 - -lemma sg14016 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg1032 sg4977 - -lemma sg14017 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg1033 sg4977 - -lemma sg14018 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2324 sg2925 - -lemma sg14019 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2] := by - exact rowSquare_join (by decide) sg1033 sg4978 - -lemma sg14020 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2] := by - exact rowSquare_join (by decide) sg1032 sg4979 - -lemma sg14021 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1] := by - exact rowSquare_join (by decide) sg1032 sg4980 - -lemma sg14022 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5] := by - exact rowSquare_join (by decide) sg1033 sg4980 - -lemma sg14023 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg2314 sg2930 - -lemma sg14024 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2327 sg2925 - -lemma sg14025 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2399 sg2761 - -lemma sg14026 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg2951 - -lemma sg14027 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1033 sg4927 - -lemma sg14028 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2209 sg2925 - -lemma sg14029 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2390 sg2661 - -lemma sg14030 : RowSquare [4,4,4,3,3,2,1,1,1,1,1,1,1] [6,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2149 sg2925 - -lemma sg14031 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg976 sg4997 - -lemma sg14032 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg3069 - -lemma sg14033 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg1844 sg3690 - -lemma sg14034 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1844 sg3691 - -lemma sg14035 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2348 sg2902 - -lemma sg14036 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg2339 sg2907 - -lemma sg14037 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg3073 - -lemma sg14038 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg1844 sg3694 - -lemma sg14039 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2837 - -lemma sg14040 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2212 sg3117 - -lemma sg14041 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3] := by - exact rowSquare_join (by decide) sg1844 sg3697 - -lemma sg14042 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg3077 - -lemma sg14043 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2371 sg2840 - -lemma sg14044 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg975 sg4998 - -lemma sg14045 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,3] := by - exact rowSquare_join (by decide) sg2373 sg2838 - -lemma sg14046 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg3078 - -lemma sg14047 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg2330 sg2959 - -lemma sg14048 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg2293 sg3069 - -lemma sg14049 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2] := by - exact rowSquare_join (by decide) sg2329 sg2961 - -lemma sg14050 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1] := by - exact rowSquare_join (by decide) sg2340 sg2908 - -lemma sg14051 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5] := by - exact rowSquare_join (by decide) sg1916 sg3622 - -lemma sg14052 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg3660 - -lemma sg14053 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2372 sg2839 - -lemma sg14054 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg3079 - -lemma sg14055 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2373 sg2839 - -lemma sg14056 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg975 sg4999 - -lemma sg14057 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2374 sg2839 - -lemma sg14058 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg2341 sg2907 - -lemma sg14059 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3] := by - exact rowSquare_join (by decide) sg1844 sg3699 - -lemma sg14060 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg3080 - -lemma sg14061 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg2372 sg2840 - -lemma sg14062 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg2341 sg2908 - -lemma sg14063 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2] := by - exact rowSquare_join (by decide) sg2342 sg2907 - -lemma sg14064 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1] := by - exact rowSquare_join (by decide) sg2432 sg2747 - -lemma sg14065 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg2330 sg2960 - -lemma sg14066 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by - exact rowSquare_join (by decide) sg2373 sg2840 - -lemma sg14067 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1] := by - exact rowSquare_join (by decide) sg2342 sg2908 - -lemma sg14068 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4] := by - exact rowSquare_join (by decide) sg2432 sg2749 - -lemma sg14069 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1] := by - exact rowSquare_join (by decide) sg2433 sg2748 - -lemma sg14070 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3] := by - exact rowSquare_join (by decide) sg2433 sg2749 - -lemma sg14071 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2213 sg3110 - -lemma sg14072 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2354 sg2902 - -lemma sg14073 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2213 sg3111 - -lemma sg14074 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg3083 - -lemma sg14075 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2216 sg3111 - -lemma sg14076 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg3087 - -lemma sg14077 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2153 sg3155 - -lemma sg14078 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2213 sg3118 - -lemma sg14079 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2153 sg3156 - -lemma sg14080 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2216 sg3118 - -lemma sg14081 : RowSquare [5,3,3,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1688 sg3732 - -lemma sg14082 : RowSquare [5,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2288 sg3011 - -lemma sg14083 : RowSquare [5,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg3012 - -lemma sg14084 : RowSquare [5,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1910 sg3614 - -lemma sg14085 : RowSquare [5,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg1926 sg3565 - -lemma sg14086 : RowSquare [5,4,3,2,2,2,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1871 sg3299 - -lemma sg14087 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1891 sg3476 - -lemma sg14088 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1688 sg3726 - -lemma sg14089 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg872 sg4965 - -lemma sg14090 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1239 sg4439 - -lemma sg14091 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg872 sg4966 - -lemma sg14092 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1699 sg3614 - -lemma sg14093 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg873 sg4966 - -lemma sg14094 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2147 sg2902 - -lemma sg14095 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2310 sg2646 - -lemma sg14096 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1700 sg3614 - -lemma sg14097 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg2310 sg2647 - -lemma sg14098 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg2311 sg2647 - -lemma sg14099 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2140 sg3004 - -lemma sg14100 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg2141 sg3003 - -lemma sg14101 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg2141 sg3004 - -lemma sg14102 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1688 sg3648 - -lemma sg14103 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1701 sg3614 - -lemma sg14104 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg876 sg4966 - -lemma sg14105 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2148 sg2902 - -lemma sg14106 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2310 sg2651 - -lemma sg14107 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg2311 sg2650 - -lemma sg14108 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg2311 sg2651 - -lemma sg14109 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg2144 sg3004 - -lemma sg14110 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,6,5,5,5] := by - exact rowSquare_join (by decide) sg1916 sg3337 - -lemma sg14111 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2150 sg2902 - -lemma sg14112 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [7,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg2314 sg2651 - -lemma sg14113 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [7,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2213 sg2718 - -lemma sg14114 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2216 sg2718 - -lemma sg14115 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [7,7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2138 sg3044 - -lemma sg14116 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [8,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2139 sg3048 - -lemma sg14117 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [8,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2213 sg2719 - -lemma sg14118 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [8,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2216 sg2719 - -lemma sg14119 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [8,8,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2138 sg3058 - -lemma sg14120 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1682 sg3632 - -lemma sg14121 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2288 sg2957 - -lemma sg14122 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2288 sg2958 - -lemma sg14123 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1874 sg3650 - -lemma sg14124 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2962 - -lemma sg14125 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2288 sg2963 - -lemma sg14126 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2288 sg2965 - -lemma sg14127 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2289 sg2958 - -lemma sg14128 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2291 sg2958 - -lemma sg14129 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2294 sg2958 - -lemma sg14130 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2296 sg2958 - -lemma sg14131 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2977 - -lemma sg14132 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg2297 sg2959 - -lemma sg14133 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg2293 sg2961 - -lemma sg14134 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg2293 sg2962 - -lemma sg14135 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1874 sg3652 - -lemma sg14136 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2978 - -lemma sg14137 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg2372 sg2783 - -lemma sg14138 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg2372 sg2784 - -lemma sg14139 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg2297 sg2960 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes13 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes11 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes9 + +namespace OAI + +/-! Semigroup Nodes 33. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg13740 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2393 sg2803 + +lemma sg13741 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2318 sg3005 + +lemma sg13742 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg2341 sg2928 + +lemma sg13743 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3027 + +lemma sg13744 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3027 + +lemma sg13745 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3] := by + exact rowSquare_join (by decide) sg636 sg5790 + +lemma sg13746 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3028 + +lemma sg13747 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3028 + +lemma sg13748 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg2405 sg2773 + +lemma sg13749 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2] := by + exact rowSquare_join (by decide) sg2406 sg2772 + +lemma sg13750 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1] := by + exact rowSquare_join (by decide) sg2407 sg2772 + +lemma sg13751 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg1323 sg4526 + +lemma sg13752 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg2433 sg2763 + +lemma sg13753 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by + exact rowSquare_join (by decide) sg2318 sg3008 + +lemma sg13754 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1] := by + exact rowSquare_join (by decide) sg2406 sg2773 + +lemma sg13755 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4] := by + exact rowSquare_join (by decide) sg2407 sg2773 + +lemma sg13756 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg1848 sg3703 + +lemma sg13757 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1] := by + exact rowSquare_join (by decide) sg2395 sg2806 + +lemma sg13758 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3] := by + exact rowSquare_join (by decide) sg2395 sg2807 + +lemma sg13759 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1921 sg3632 + +lemma sg13760 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2403 sg2798 + +lemma sg13761 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2352 sg2925 + +lemma sg13762 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3119 + +lemma sg13763 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2310 sg3029 + +lemma sg13764 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2345 sg2926 + +lemma sg13765 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg2353 sg2925 + +lemma sg13766 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1803 sg3724 + +lemma sg13767 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg2312 sg3010 + +lemma sg13768 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1803 sg3725 + +lemma sg13769 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg2310 sg3030 + +lemma sg13770 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg2312 sg3012 + +lemma sg13771 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3030 + +lemma sg13772 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1803 sg3726 + +lemma sg13773 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3031 + +lemma sg13774 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2809 + +lemma sg13775 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3031 + +lemma sg13776 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg2339 sg2930 + +lemma sg13777 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2810 + +lemma sg13778 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2310 sg3032 + +lemma sg13779 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2346 sg2926 + +lemma sg13780 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2355 sg2925 + +lemma sg13781 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3120 + +lemma sg13782 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2312 sg3013 + +lemma sg13783 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3121 + +lemma sg13784 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2310 sg3033 + +lemma sg13785 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2315 sg3012 + +lemma sg13786 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3033 + +lemma sg13787 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg4536 + +lemma sg13788 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg2312 sg3014 + +lemma sg13789 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg4537 + +lemma sg13790 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3034 + +lemma sg13791 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2811 + +lemma sg13792 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3034 + +lemma sg13793 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3035 + +lemma sg13794 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3035 + +lemma sg13795 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg2339 sg2931 + +lemma sg13796 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3122 + +lemma sg13797 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2320 sg3005 + +lemma sg13798 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg4538 + +lemma sg13799 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2312 sg3016 + +lemma sg13800 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3123 + +lemma sg13801 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3036 + +lemma sg13802 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2812 + +lemma sg13803 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3036 + +lemma sg13804 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3124 + +lemma sg13805 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2312 sg3017 + +lemma sg13806 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg2409 sg2771 + +lemma sg13807 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3037 + +lemma sg13808 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3037 + +lemma sg13809 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3] := by + exact rowSquare_join (by decide) sg2339 sg2932 + +lemma sg13810 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2813 + +lemma sg13811 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,2] := by + exact rowSquare_join (by decide) sg2339 sg2933 + +lemma sg13812 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg4539 + +lemma sg13813 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3038 + +lemma sg13814 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3038 + +lemma sg13815 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2814 + +lemma sg13816 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,2] := by + exact rowSquare_join (by decide) sg2339 sg2934 + +lemma sg13817 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,1] := by + exact rowSquare_join (by decide) sg2396 sg2807 + +lemma sg13818 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5] := by + exact rowSquare_join (by decide) sg1956 sg3505 + +lemma sg13819 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2810 + +lemma sg13820 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2312 sg3020 + +lemma sg13821 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2392 sg2810 + +lemma sg13822 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2310 sg3039 + +lemma sg13823 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2321 sg3004 + +lemma sg13824 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3039 + +lemma sg13825 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2393 sg2810 + +lemma sg13826 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2315 sg3013 + +lemma sg13827 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3125 + +lemma sg13828 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2312 sg3021 + +lemma sg13829 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2394 sg2810 + +lemma sg13830 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3040 + +lemma sg13831 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2816 + +lemma sg13832 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3040 + +lemma sg13833 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2395 sg2810 + +lemma sg13834 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2312 sg3022 + +lemma sg13835 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2811 + +lemma sg13836 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3041 + +lemma sg13837 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3041 + +lemma sg13838 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,3] := by + exact rowSquare_join (by decide) sg2339 sg2936 + +lemma sg13839 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2817 + +lemma sg13840 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,2] := by + exact rowSquare_join (by decide) sg2339 sg2937 + +lemma sg13841 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3126 + +lemma sg13842 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2315 sg3016 + +lemma sg13843 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3127 + +lemma sg13844 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2312 sg3024 + +lemma sg13845 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2812 + +lemma sg13846 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3042 + +lemma sg13847 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3042 + +lemma sg13848 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3] := by + exact rowSquare_join (by decide) sg2339 sg2938 + +lemma sg13849 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3128 + +lemma sg13850 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3043 + +lemma sg13851 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3043 + +lemma sg13852 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2819 + +lemma sg13853 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,2] := by + exact rowSquare_join (by decide) sg2339 sg2939 + +lemma sg13854 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,1] := by + exact rowSquare_join (by decide) sg2340 sg2933 + +lemma sg13855 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg2312 sg3026 + +lemma sg13856 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2820 + +lemma sg13857 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2] := by + exact rowSquare_join (by decide) sg2339 sg2940 + +lemma sg13858 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,1] := by + exact rowSquare_join (by decide) sg2340 sg2934 + +lemma sg13859 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4] := by + exact rowSquare_join (by decide) sg2413 sg2773 + +lemma sg13860 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3130 + +lemma sg13861 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg2439 sg2763 + +lemma sg13862 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,1] := by + exact rowSquare_join (by decide) sg2342 sg2934 + +lemma sg13863 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3] := by + exact rowSquare_join (by decide) sg2432 sg2764 + +lemma sg13864 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,1,1] := by + exact rowSquare_join (by decide) sg2398 sg2806 + +lemma sg13865 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2] := by + exact rowSquare_join (by decide) sg2433 sg2764 + +lemma sg13866 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1961 sg3503 + +lemma sg13867 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2315 sg3020 + +lemma sg13868 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1963 sg3503 + +lemma sg13869 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2391 sg2815 + +lemma sg13870 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3044 + +lemma sg13871 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2350 sg2927 + +lemma sg13872 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3044 + +lemma sg13873 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2315 sg3021 + +lemma sg13874 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2315 sg3022 + +lemma sg13875 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2816 + +lemma sg13876 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3045 + +lemma sg13877 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3045 + +lemma sg13878 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,3] := by + exact rowSquare_join (by decide) sg2400 sg2802 + +lemma sg13879 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3046 + +lemma sg13880 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3046 + +lemma sg13881 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2817 + +lemma sg13882 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,2] := by + exact rowSquare_join (by decide) sg2340 sg2936 + +lemma sg13883 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,1] := by + exact rowSquare_join (by decide) sg2340 sg2937 + +lemma sg13884 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3047 + +lemma sg13885 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,3,2] := by + exact rowSquare_join (by decide) sg2340 sg2938 + +lemma sg13886 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2315 sg3026 + +lemma sg13887 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2819 + +lemma sg13888 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,2,2] := by + exact rowSquare_join (by decide) sg2342 sg2936 + +lemma sg13889 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,3,1] := by + exact rowSquare_join (by decide) sg2340 sg2939 + +lemma sg13890 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4] := by + exact rowSquare_join (by decide) sg2432 sg2766 + +lemma sg13891 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2820 + +lemma sg13892 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,1] := by + exact rowSquare_join (by decide) sg2340 sg2940 + +lemma sg13893 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3] := by + exact rowSquare_join (by decide) sg2433 sg2766 + +lemma sg13894 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2822 + +lemma sg13895 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,1,1] := by + exact rowSquare_join (by decide) sg2342 sg2940 + +lemma sg13896 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2] := by + exact rowSquare_join (by decide) sg2432 sg2767 + +lemma sg13897 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1] := by + exact rowSquare_join (by decide) sg2433 sg2767 + +lemma sg13898 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6] := by + exact rowSquare_join (by decide) sg1848 sg3712 + +lemma sg13899 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2326 sg3001 + +lemma sg13900 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2404 sg2798 + +lemma sg13901 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2356 sg2925 + +lemma sg13902 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2186 sg3119 + +lemma sg13903 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2310 sg3049 + +lemma sg13904 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2326 sg3004 + +lemma sg13905 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2352 sg2926 + +lemma sg13906 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2357 sg2925 + +lemma sg13907 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3131 + +lemma sg13908 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2312 sg3029 + +lemma sg13909 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3132 + +lemma sg13910 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2310 sg3050 + +lemma sg13911 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2345 sg2930 + +lemma sg13912 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3050 + +lemma sg13913 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2326 sg3008 + +lemma sg13914 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg2312 sg3030 + +lemma sg13915 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2326 sg3009 + +lemma sg13916 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3051 + +lemma sg13917 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2824 + +lemma sg13918 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3051 + +lemma sg13919 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3052 + +lemma sg13920 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3052 + +lemma sg13921 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg2339 sg2943 + +lemma sg13922 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2186 sg3120 + +lemma sg13923 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2312 sg3032 + +lemma sg13924 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2186 sg3121 + +lemma sg13925 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2310 sg3053 + +lemma sg13926 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2346 sg2930 + +lemma sg13927 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3053 + +lemma sg13928 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3133 + +lemma sg13929 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2315 sg3029 + +lemma sg13930 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3134 + +lemma sg13931 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2312 sg3033 + +lemma sg13932 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3135 + +lemma sg13933 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3054 + +lemma sg13934 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2825 + +lemma sg13935 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3054 + +lemma sg13936 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2186 sg3124 + +lemma sg13937 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2312 sg3034 + +lemma sg13938 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2391 sg2824 + +lemma sg13939 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3055 + +lemma sg13940 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg2339 sg2944 + +lemma sg13941 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2826 + +lemma sg13942 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg2339 sg2945 + +lemma sg13943 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3136 + +lemma sg13944 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3137 + +lemma sg13945 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3056 + +lemma sg13946 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg2339 sg2946 + +lemma sg13947 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3138 + +lemma sg13948 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2] := by + exact rowSquare_join (by decide) sg2339 sg2947 + +lemma sg13949 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2827 + +lemma sg13950 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3139 + +lemma sg13951 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2186 sg3125 + +lemma sg13952 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2169 sg3149 + +lemma sg13953 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2828 + +lemma sg13954 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3057 + +lemma sg13955 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3140 + +lemma sg13956 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3141 + +lemma sg13957 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3] := by + exact rowSquare_join (by decide) sg2339 sg2948 + +lemma sg13958 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2186 sg3128 + +lemma sg13959 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2] := by + exact rowSquare_join (by decide) sg2339 sg2949 + +lemma sg13960 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3142 + +lemma sg13961 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3143 + +lemma sg13962 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2829 + +lemma sg13963 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2827 + +lemma sg13964 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2401 sg2810 + +lemma sg13965 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3] := by + exact rowSquare_join (by decide) sg2339 sg2951 + +lemma sg13966 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2] := by + exact rowSquare_join (by decide) sg2339 sg2952 + +lemma sg13967 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2830 + +lemma sg13968 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2] := by + exact rowSquare_join (by decide) sg2339 sg2953 + +lemma sg13969 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,1] := by + exact rowSquare_join (by decide) sg2340 sg2949 + +lemma sg13970 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4] := by + exact rowSquare_join (by decide) sg2436 sg2766 + +lemma sg13971 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2829 + +lemma sg13972 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,1] := by + exact rowSquare_join (by decide) sg2340 sg2950 + +lemma sg13973 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3] := by + exact rowSquare_join (by decide) sg2432 sg2768 + +lemma sg13974 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,1,1] := by + exact rowSquare_join (by decide) sg2435 sg2767 + +lemma sg13975 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2] := by + exact rowSquare_join (by decide) sg2436 sg2767 + +lemma sg13976 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1961 sg3508 + +lemma sg13977 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1962 sg3508 + +lemma sg13978 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2350 sg2935 + +lemma sg13979 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1963 sg3508 + +lemma sg13980 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3058 + +lemma sg13981 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2350 sg2937 + +lemma sg13982 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2] := by + exact rowSquare_join (by decide) sg2340 sg2951 + +lemma sg13983 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2326 sg3012 + +lemma sg13984 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2358 sg2925 + +lemma sg13985 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2186 sg3132 + +lemma sg13986 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3059 + +lemma sg13987 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3145 + +lemma sg13988 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg3146 + +lemma sg13989 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2832 + +lemma sg13990 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3060 + +lemma sg13991 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2326 sg3019 + +lemma sg13992 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg2339 sg2954 + +lemma sg13993 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2833 + +lemma sg13994 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2834 + +lemma sg13995 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3061 + +lemma sg13996 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3062 + +lemma sg13997 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg2339 sg2955 + +lemma sg13998 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3063 + +lemma sg13999 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg2339 sg2956 + +lemma sg14000 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2390 sg2835 + +lemma sg14001 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3064 + +lemma sg14002 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2350 sg2952 + +lemma sg14003 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2391 sg2835 + +lemma sg14004 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3] := by + exact rowSquare_join (by decide) sg2479 sg2657 + +lemma sg14005 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2311 sg3065 + +lemma sg14006 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2836 + +lemma sg14007 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3066 + +lemma sg14008 : RowSquare [4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3067 + +lemma sg14009 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1891 sg3505 + +lemma sg14010 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg2311 sg2925 + +lemma sg14011 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg2313 sg2925 + +lemma sg14012 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg2311 sg2926 + +lemma sg14013 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1033 sg4976 + +lemma sg14014 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg2311 sg2930 + +lemma sg14015 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg2322 sg2925 + +lemma sg14016 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg1032 sg4977 + +lemma sg14017 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg1033 sg4977 + +lemma sg14018 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2324 sg2925 + +lemma sg14019 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2] := by + exact rowSquare_join (by decide) sg1033 sg4978 + +lemma sg14020 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2] := by + exact rowSquare_join (by decide) sg1032 sg4979 + +lemma sg14021 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1] := by + exact rowSquare_join (by decide) sg1032 sg4980 + +lemma sg14022 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5] := by + exact rowSquare_join (by decide) sg1033 sg4980 + +lemma sg14023 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg2314 sg2930 + +lemma sg14024 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2327 sg2925 + +lemma sg14025 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2399 sg2761 + +lemma sg14026 : RowSquare [4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg2951 + +lemma sg14027 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1033 sg4927 + +lemma sg14028 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2209 sg2925 + +lemma sg14029 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2390 sg2661 + +lemma sg14030 : RowSquare [4,4,4,3,3,2,1,1,1,1,1,1,1] [6,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2149 sg2925 + +lemma sg14031 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg976 sg4997 + +lemma sg14032 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg3069 + +lemma sg14033 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg1844 sg3690 + +lemma sg14034 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1844 sg3691 + +lemma sg14035 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2348 sg2902 + +lemma sg14036 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg2339 sg2907 + +lemma sg14037 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg3073 + +lemma sg14038 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg1844 sg3694 + +lemma sg14039 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2837 + +lemma sg14040 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2212 sg3117 + +lemma sg14041 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3] := by + exact rowSquare_join (by decide) sg1844 sg3697 + +lemma sg14042 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg3077 + +lemma sg14043 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2371 sg2840 + +lemma sg14044 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg975 sg4998 + +lemma sg14045 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,3] := by + exact rowSquare_join (by decide) sg2373 sg2838 + +lemma sg14046 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg3078 + +lemma sg14047 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg2330 sg2959 + +lemma sg14048 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg2293 sg3069 + +lemma sg14049 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2] := by + exact rowSquare_join (by decide) sg2329 sg2961 + +lemma sg14050 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1] := by + exact rowSquare_join (by decide) sg2340 sg2908 + +lemma sg14051 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5] := by + exact rowSquare_join (by decide) sg1916 sg3622 + +lemma sg14052 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg3660 + +lemma sg14053 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2372 sg2839 + +lemma sg14054 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg3079 + +lemma sg14055 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2373 sg2839 + +lemma sg14056 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg975 sg4999 + +lemma sg14057 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2374 sg2839 + +lemma sg14058 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg2341 sg2907 + +lemma sg14059 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3] := by + exact rowSquare_join (by decide) sg1844 sg3699 + +lemma sg14060 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg3080 + +lemma sg14061 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg2372 sg2840 + +lemma sg14062 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg2341 sg2908 + +lemma sg14063 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2] := by + exact rowSquare_join (by decide) sg2342 sg2907 + +lemma sg14064 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1] := by + exact rowSquare_join (by decide) sg2432 sg2747 + +lemma sg14065 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg2330 sg2960 + +lemma sg14066 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by + exact rowSquare_join (by decide) sg2373 sg2840 + +lemma sg14067 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1] := by + exact rowSquare_join (by decide) sg2342 sg2908 + +lemma sg14068 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4] := by + exact rowSquare_join (by decide) sg2432 sg2749 + +lemma sg14069 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1] := by + exact rowSquare_join (by decide) sg2433 sg2748 + +lemma sg14070 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3] := by + exact rowSquare_join (by decide) sg2433 sg2749 + +lemma sg14071 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2213 sg3110 + +lemma sg14072 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2354 sg2902 + +lemma sg14073 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2213 sg3111 + +lemma sg14074 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg3083 + +lemma sg14075 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2216 sg3111 + +lemma sg14076 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg3087 + +lemma sg14077 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2153 sg3155 + +lemma sg14078 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2213 sg3118 + +lemma sg14079 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2153 sg3156 + +lemma sg14080 : RowSquare [5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2216 sg3118 + +lemma sg14081 : RowSquare [5,3,3,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1688 sg3732 + +lemma sg14082 : RowSquare [5,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2288 sg3011 + +lemma sg14083 : RowSquare [5,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg3012 + +lemma sg14084 : RowSquare [5,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1910 sg3614 + +lemma sg14085 : RowSquare [5,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg1926 sg3565 + +lemma sg14086 : RowSquare [5,4,3,2,2,2,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1871 sg3299 + +lemma sg14087 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1891 sg3476 + +lemma sg14088 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1688 sg3726 + +lemma sg14089 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg872 sg4965 + +lemma sg14090 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1239 sg4439 + +lemma sg14091 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg872 sg4966 + +lemma sg14092 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1699 sg3614 + +lemma sg14093 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg873 sg4966 + +lemma sg14094 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2147 sg2902 + +lemma sg14095 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2310 sg2646 + +lemma sg14096 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1700 sg3614 + +lemma sg14097 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg2310 sg2647 + +lemma sg14098 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg2311 sg2647 + +lemma sg14099 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2140 sg3004 + +lemma sg14100 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg2141 sg3003 + +lemma sg14101 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg2141 sg3004 + +lemma sg14102 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1688 sg3648 + +lemma sg14103 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1701 sg3614 + +lemma sg14104 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg876 sg4966 + +lemma sg14105 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2148 sg2902 + +lemma sg14106 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2310 sg2651 + +lemma sg14107 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg2311 sg2650 + +lemma sg14108 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg2311 sg2651 + +lemma sg14109 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg2144 sg3004 + +lemma sg14110 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [6,6,5,5,5] := by + exact rowSquare_join (by decide) sg1916 sg3337 + +lemma sg14111 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [7,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2150 sg2902 + +lemma sg14112 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [7,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg2314 sg2651 + +lemma sg14113 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [7,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2213 sg2718 + +lemma sg14114 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2216 sg2718 + +lemma sg14115 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [7,7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2138 sg3044 + +lemma sg14116 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [8,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2139 sg3048 + +lemma sg14117 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [8,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2213 sg2719 + +lemma sg14118 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [8,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2216 sg2719 + +lemma sg14119 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1] [8,8,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2138 sg3058 + +lemma sg14120 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1682 sg3632 + +lemma sg14121 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2288 sg2957 + +lemma sg14122 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2288 sg2958 + +lemma sg14123 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1874 sg3650 + +lemma sg14124 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2962 + +lemma sg14125 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2288 sg2963 + +lemma sg14126 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2288 sg2965 + +lemma sg14127 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2289 sg2958 + +lemma sg14128 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2291 sg2958 + +lemma sg14129 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2294 sg2958 + +lemma sg14130 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2296 sg2958 + +lemma sg14131 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2977 + +lemma sg14132 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg2297 sg2959 + +lemma sg14133 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg2293 sg2961 + +lemma sg14134 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg2293 sg2962 + +lemma sg14135 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1874 sg3652 + +lemma sg14136 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2978 + +lemma sg14137 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg2372 sg2783 + +lemma sg14138 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg2372 sg2784 + +lemma sg14139 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg2297 sg2960 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes34.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes34.lean index 13e4382b9a3bce7801f742240dfa07a084a7a279..d772c0a41916fb8cb69301895d452d3884dad1b0 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes34.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes34.lean @@ -1,1221 +1,1221 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes13 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes14 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes9 - -namespace OAI - -/-! Semigroup Nodes 34. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg14140 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by - exact rowSquare_join (by decide) sg2373 sg2783 - -lemma sg14141 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1] := by - exact rowSquare_join (by decide) sg2373 sg2784 - -lemma sg14142 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4] := by - exact rowSquare_join (by decide) sg2374 sg2784 - -lemma sg14143 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1] := by - exact rowSquare_join (by decide) sg2297 sg2961 - -lemma sg14144 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3] := by - exact rowSquare_join (by decide) sg2297 sg2962 - -lemma sg14145 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2288 sg2979 - -lemma sg14146 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2289 sg2963 - -lemma sg14147 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2288 sg2980 - -lemma sg14148 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2981 - -lemma sg14149 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg2290 sg2964 - -lemma sg14150 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2369 sg2785 - -lemma sg14151 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2288 sg2982 - -lemma sg14152 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2369 sg2786 - -lemma sg14153 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2983 - -lemma sg14154 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2290 sg2966 - -lemma sg14155 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2984 - -lemma sg14156 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg2290 sg2967 - -lemma sg14157 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2985 - -lemma sg14158 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2369 sg2787 - -lemma sg14159 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1876 sg3651 - -lemma sg14160 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2986 - -lemma sg14161 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2290 sg2968 - -lemma sg14162 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2369 sg2788 - -lemma sg14163 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2987 - -lemma sg14164 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2290 sg2969 - -lemma sg14165 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg2300 sg2960 - -lemma sg14166 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2988 - -lemma sg14167 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg2300 sg2961 - -lemma sg14168 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg2300 sg2962 - -lemma sg14169 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2370 sg2785 - -lemma sg14170 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2989 - -lemma sg14171 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2369 sg2791 - -lemma sg14172 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2990 - -lemma sg14173 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2369 sg2793 - -lemma sg14174 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2991 - -lemma sg14175 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2293 sg2967 - -lemma sg14176 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2369 sg2794 - -lemma sg14177 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2992 - -lemma sg14178 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg2293 sg2968 - -lemma sg14179 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2993 - -lemma sg14180 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg2293 sg2969 - -lemma sg14181 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg2293 sg2970 - -lemma sg14182 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg2293 sg2971 - -lemma sg14183 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2] := by - exact rowSquare_join (by decide) sg2379 sg2783 - -lemma sg14184 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,1] := by - exact rowSquare_join (by decide) sg2379 sg2784 - -lemma sg14185 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4] := by - exact rowSquare_join (by decide) sg2380 sg2784 - -lemma sg14186 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2791 - -lemma sg14187 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2371 sg2790 - -lemma sg14188 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2994 - -lemma sg14189 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2793 - -lemma sg14190 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2794 - -lemma sg14191 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2995 - -lemma sg14192 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2371 sg2793 - -lemma sg14193 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2996 - -lemma sg14194 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2796 - -lemma sg14195 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2997 - -lemma sg14196 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2293 sg2981 - -lemma sg14197 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg2300 sg2971 - -lemma sg14198 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg2293 sg2987 - -lemma sg14199 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2293 sg2988 - -lemma sg14200 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,1] := by - exact rowSquare_join (by decide) sg2379 sg2789 - -lemma sg14201 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3] := by - exact rowSquare_join (by decide) sg2380 sg2789 - -lemma sg14202 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2293 sg2989 - -lemma sg14203 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2382 sg2790 - -lemma sg14204 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2371 sg2797 - -lemma sg14205 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2382 sg2791 - -lemma sg14206 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2384 sg2790 - -lemma sg14207 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2293 sg2994 - -lemma sg14208 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2382 sg2793 - -lemma sg14209 : RowSquare [5,5,2,2,2,2,2,2,2,2,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1488 sg3998 - -lemma sg14210 : RowSquare [5,5,2,2,2,2,2,2,2,2,1] [7,7,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1488 sg4000 - -lemma sg14211 : RowSquare [5,5,2,2,2,2,2,2,2,2,1] [7,7,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1488 sg4001 - -lemma sg14212 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1874 sg3614 - -lemma sg14213 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1880 sg3614 - -lemma sg14214 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1876 sg3615 - -lemma sg14215 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1499 sg4415 - -lemma sg14216 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2371 sg2742 - -lemma sg14217 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2371 sg2743 - -lemma sg14218 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1499 sg4417 - -lemma sg14219 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1876 sg3620 - -lemma sg14220 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg2279 sg2960 - -lemma sg14221 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg2373 sg2743 - -lemma sg14222 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2374 sg2742 - -lemma sg14223 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg2374 sg2743 - -lemma sg14224 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg1000 sg4986 - -lemma sg14225 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg2290 sg2908 - -lemma sg14226 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg2279 sg2961 - -lemma sg14227 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg1501 sg4416 - -lemma sg14228 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg2279 sg2962 - -lemma sg14229 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg1501 sg4417 - -lemma sg14230 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg1502 sg4417 - -lemma sg14231 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg998 sg4988 - -lemma sg14232 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg2281 sg2959 - -lemma sg14233 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2293 sg2906 - -lemma sg14234 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1000 sg4987 - -lemma sg14235 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg998 sg4989 - -lemma sg14236 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg1001 sg4987 - -lemma sg14237 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg2372 sg2745 - -lemma sg14238 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg2372 sg2746 - -lemma sg14239 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg999 sg4988 - -lemma sg14240 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg2293 sg2907 - -lemma sg14241 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,3] := by - exact rowSquare_join (by decide) sg2373 sg2746 - -lemma sg14242 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg2374 sg2745 - -lemma sg14243 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2] := by - exact rowSquare_join (by decide) sg2374 sg2746 - -lemma sg14244 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg2282 sg2959 - -lemma sg14245 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg1000 sg4988 - -lemma sg14246 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg2293 sg2908 - -lemma sg14247 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2] := by - exact rowSquare_join (by decide) sg2281 sg2961 - -lemma sg14248 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1] := by - exact rowSquare_join (by decide) sg2281 sg2962 - -lemma sg14249 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5] := by - exact rowSquare_join (by decide) sg1001 sg4989 - -lemma sg14250 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3] := by - exact rowSquare_join (by decide) sg1878 sg3620 - -lemma sg14251 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg2282 sg2960 - -lemma sg14252 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by - exact rowSquare_join (by decide) sg2373 sg2748 - -lemma sg14253 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1] := by - exact rowSquare_join (by decide) sg2373 sg2749 - -lemma sg14254 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,4] := by - exact rowSquare_join (by decide) sg2374 sg2749 - -lemma sg14255 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1] := by - exact rowSquare_join (by decide) sg2282 sg2961 - -lemma sg14256 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,3] := by - exact rowSquare_join (by decide) sg2297 sg2908 - -lemma sg14257 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1945 sg3470 - -lemma sg14258 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2376 sg2742 - -lemma sg14259 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2369 sg2752 - -lemma sg14260 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2376 sg2743 - -lemma sg14261 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg2290 sg2910 - -lemma sg14262 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg2290 sg2911 - -lemma sg14263 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1947 sg3470 - -lemma sg14264 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1948 sg3470 - -lemma sg14265 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2377 sg2742 - -lemma sg14266 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2752 - -lemma sg14267 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2377 sg2743 - -lemma sg14268 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2371 sg2751 - -lemma sg14269 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2371 sg2752 - -lemma sg14270 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg2378 sg2743 - -lemma sg14271 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg2290 sg2914 - -lemma sg14272 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg2290 sg2915 - -lemma sg14273 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2279 sg2967 - -lemma sg14274 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg2379 sg2743 - -lemma sg14275 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2380 sg2742 - -lemma sg14276 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2380 sg2743 - -lemma sg14277 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1876 sg3624 - -lemma sg14278 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg2290 sg2916 - -lemma sg14279 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2290 sg2917 - -lemma sg14280 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2377 sg2745 - -lemma sg14281 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2377 sg2746 - -lemma sg14282 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2382 sg2743 - -lemma sg14283 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2371 sg2754 - -lemma sg14284 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2279 sg2973 - -lemma sg14285 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2290 sg2918 - -lemma sg14286 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg2290 sg2919 - -lemma sg14287 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg2279 sg2974 - -lemma sg14288 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2279 sg2975 - -lemma sg14289 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg2290 sg2921 - -lemma sg14290 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg2279 sg2977 - -lemma sg14291 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2] := by - exact rowSquare_join (by decide) sg2379 sg2748 - -lemma sg14292 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,1] := by - exact rowSquare_join (by decide) sg2281 sg2971 - -lemma sg14293 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,4] := by - exact rowSquare_join (by decide) sg2380 sg2749 - -lemma sg14294 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2382 sg2746 - -lemma sg14295 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2371 sg2755 - -lemma sg14296 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,3] := by - exact rowSquare_join (by decide) sg2383 sg2746 - -lemma sg14297 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2297 sg2917 - -lemma sg14298 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg2293 sg2918 - -lemma sg14299 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2293 sg2919 - -lemma sg14300 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2371 sg2756 - -lemma sg14301 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg2293 sg2920 - -lemma sg14302 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2293 sg2921 - -lemma sg14303 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,1] := by - exact rowSquare_join (by decide) sg2281 sg2977 - -lemma sg14304 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,3] := by - exact rowSquare_join (by decide) sg2297 sg2919 - -lemma sg14305 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2377 sg2755 - -lemma sg14306 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2293 sg2924 - -lemma sg14307 : RowSquare [5,5,3,2,2,2,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1084 sg4832 - -lemma sg14308 : RowSquare [5,5,3,2,2,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1086 sg4832 - -lemma sg14309 : RowSquare [5,5,3,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1476 sg3998 - -lemma sg14310 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1688 sg3614 - -lemma sg14311 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1688 sg3615 - -lemma sg14312 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1] [5,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg1688 sg3617 - -lemma sg14313 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1] [5,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg1688 sg3620 - -lemma sg14314 : RowSquare [6,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg1908 sg3577 - -lemma sg14315 : RowSquare [6,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1758 sg3738 - -lemma sg14316 : RowSquare [6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3] := by - exact rowSquare_join (by decide) sg1332 sg4507 - -lemma sg14317 : RowSquare [6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg1757 sg3731 - -lemma sg14318 : RowSquare [6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg4508 - -lemma sg14319 : RowSquare [6,4,3,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg3501 - -lemma sg14320 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2289 sg2891 - -lemma sg14321 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg2273 sg2962 - -lemma sg14322 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2291 sg2891 - -lemma sg14323 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1782 sg3671 - -lemma sg14324 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2894 - -lemma sg14325 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1758 sg3722 - -lemma sg14326 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2297 sg2889 - -lemma sg14327 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg2372 sg2723 - -lemma sg14328 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg2372 sg2724 - -lemma sg14329 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2] := by - exact rowSquare_join (by decide) sg2295 sg2891 - -lemma sg14330 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1] := by - exact rowSquare_join (by decide) sg2296 sg2891 - -lemma sg14331 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg2297 sg2890 - -lemma sg14332 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by - exact rowSquare_join (by decide) sg2373 sg2723 - -lemma sg14333 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1] := by - exact rowSquare_join (by decide) sg2373 sg2724 - -lemma sg14334 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,4] := by - exact rowSquare_join (by decide) sg2374 sg2724 - -lemma sg14335 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2369 sg2726 - -lemma sg14336 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2898 - -lemma sg14337 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2726 - -lemma sg14338 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2289 sg2893 - -lemma sg14339 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2371 sg2726 - -lemma sg14340 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2299 sg2891 - -lemma sg14341 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg2273 sg2968 - -lemma sg14342 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg2273 sg2970 - -lemma sg14343 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,2] := by - exact rowSquare_join (by decide) sg2368 sg2783 - -lemma sg14344 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,1] := by - exact rowSquare_join (by decide) sg2368 sg2784 - -lemma sg14345 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2291 sg2893 - -lemma sg14346 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2273 sg2972 - -lemma sg14347 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2292 sg2893 - -lemma sg14348 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2273 sg2973 - -lemma sg14349 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2273 sg2975 - -lemma sg14350 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg2273 sg2976 - -lemma sg14351 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,2] := by - exact rowSquare_join (by decide) sg2295 sg2893 - -lemma sg14352 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,1] := by - exact rowSquare_join (by decide) sg2296 sg2893 - -lemma sg14353 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2] := by - exact rowSquare_join (by decide) sg2379 sg2723 - -lemma sg14354 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,1] := by - exact rowSquare_join (by decide) sg2379 sg2724 - -lemma sg14355 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,4] := by - exact rowSquare_join (by decide) sg2380 sg2724 - -lemma sg14356 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,2] := by - exact rowSquare_join (by decide) sg2303 sg2891 - -lemma sg14357 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg2304 sg2890 - -lemma sg14358 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1883 sg3572 - -lemma sg14359 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2900 - -lemma sg14360 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2733 - -lemma sg14361 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg2305 sg2891 - -lemma sg14362 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg1782 sg3678 - -lemma sg14363 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,1] := by - exact rowSquare_join (by decide) sg2297 sg2894 - -lemma sg14364 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,3] := by - exact rowSquare_join (by decide) sg2297 sg2895 - -lemma sg14365 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg2372 sg2735 - -lemma sg14366 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,1,1] := by - exact rowSquare_join (by decide) sg2373 sg2735 - -lemma sg14367 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,2] := by - exact rowSquare_join (by decide) sg2374 sg2735 - -lemma sg14368 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2308 sg2889 - -lemma sg14369 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2375 sg2726 - -lemma sg14370 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2376 sg2726 - -lemma sg14371 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg2290 sg2897 - -lemma sg14372 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg2290 sg2898 - -lemma sg14373 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2273 sg2981 - -lemma sg14374 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2737 - -lemma sg14375 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2377 sg2726 - -lemma sg14376 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2273 sg2983 - -lemma sg14377 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2293 sg2897 - -lemma sg14378 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg2273 sg2984 - -lemma sg14379 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2273 sg2985 - -lemma sg14380 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg2272 sg2988 - -lemma sg14381 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg2273 sg2988 - -lemma sg14382 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2301 sg2893 - -lemma sg14383 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2273 sg2989 - -lemma sg14384 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg2273 sg2990 - -lemma sg14385 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2] := by - exact rowSquare_join (by decide) sg2368 sg2792 - -lemma sg14386 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,1] := by - exact rowSquare_join (by decide) sg2368 sg2793 - -lemma sg14387 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2] := by - exact rowSquare_join (by decide) sg2368 sg2794 - -lemma sg14388 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2367 sg2795 - -lemma sg14389 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2377 sg2731 - -lemma sg14390 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2377 sg2733 - -lemma sg14391 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2273 sg2994 - -lemma sg14392 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2] := by - exact rowSquare_join (by decide) sg2306 sg2893 - -lemma sg14393 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2370 sg2739 - -lemma sg14394 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2382 sg2731 - -lemma sg14395 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2293 sg2900 - -lemma sg14396 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2382 sg2733 - -lemma sg14397 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2] := by - exact rowSquare_join (by decide) sg1883 sg3589 - -lemma sg14398 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2300 sg2897 - -lemma sg14399 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2273 sg2998 - -lemma sg14400 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2273 sg2999 - -lemma sg14401 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,2] := by - exact rowSquare_join (by decide) sg2368 sg2797 - -lemma sg14402 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg2901 - -lemma sg14403 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2388 sg2731 - -lemma sg14404 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2382 sg2739 - -lemma sg14405 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg656 sg5672 - -lemma sg14406 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg663 sg5672 - -lemma sg14407 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg664 sg5672 - -lemma sg14408 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg665 sg5672 - -lemma sg14409 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg666 sg5672 - -lemma sg14410 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg667 sg5672 - -lemma sg14411 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg668 sg5672 - -lemma sg14412 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg663 sg5673 - -lemma sg14413 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg664 sg5673 - -lemma sg14414 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg669 sg5672 - -lemma sg14415 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg665 sg5673 - -lemma sg14416 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg666 sg5673 - -lemma sg14417 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1758 sg3689 - -lemma sg14418 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1332 sg4487 - -lemma sg14419 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg1331 sg4488 - -lemma sg14420 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg1758 sg3690 - -lemma sg14421 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg1332 sg4488 - -lemma sg14422 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1758 sg3691 - -lemma sg14423 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1332 sg4489 - -lemma sg14424 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg1873 sg3620 - -lemma sg14425 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg1331 sg4490 - -lemma sg14426 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg1758 sg3697 - -lemma sg14427 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3] := by - exact rowSquare_join (by decide) sg1332 sg4492 - -lemma sg14428 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg4496 - -lemma sg14429 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg1757 sg3698 - -lemma sg14430 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg1331 sg4493 - -lemma sg14431 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg1758 sg3698 - -lemma sg14432 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2] := by - exact rowSquare_join (by decide) sg1765 sg3690 - -lemma sg14433 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1] := by - exact rowSquare_join (by decide) sg1765 sg3691 - -lemma sg14434 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5] := by - exact rowSquare_join (by decide) sg1001 sg4958 - -lemma sg14435 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg4496 - -lemma sg14436 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by - exact rowSquare_join (by decide) sg1000 sg4961 - -lemma sg14437 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg4496 - -lemma sg14438 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1] := by - exact rowSquare_join (by decide) sg1332 sg4496 - -lemma sg14439 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,3] := by - exact rowSquare_join (by decide) sg892 sg5000 - -lemma sg14440 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2454 sg2633 - -lemma sg14441 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg2455 sg2633 - -lemma sg14442 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg2368 sg2746 - -lemma sg14443 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1338 sg4492 - -lemma sg14444 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,1] := by - exact rowSquare_join (by decide) sg1340 sg4496 - -lemma sg14445 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg2167 sg3108 - -lemma sg14446 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg1332 sg4378 - -lemma sg14447 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1332 sg4379 - -lemma sg14448 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg4303 - -lemma sg14449 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1675 sg3571 - -lemma sg14450 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg1332 sg4303 - -lemma sg14451 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1332 sg4304 - -lemma sg14452 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg2135 sg2891 - -lemma sg14453 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1329 sg4308 - -lemma sg14454 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,4,3] := by - exact rowSquare_join (by decide) sg1332 sg4308 - -lemma sg14455 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1675 sg3573 - -lemma sg14456 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg2135 sg2893 - -lemma sg14457 : RowSquare [7,5,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2167 sg2708 - -lemma sg14458 : RowSquare [7,5,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg390 sg6486 - -lemma sg14459 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2251 sg2626 - -lemma sg14460 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2251 sg2627 - -lemma sg14461 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2253 sg2626 - -lemma sg14462 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2251 sg2628 - -lemma sg14463 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2254 sg2626 - -lemma sg14464 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2255 sg2626 - -lemma sg14465 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg2630 - -lemma sg14466 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1327 sg4163 - -lemma sg14467 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2256 sg2626 - -lemma sg14468 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg2631 - -lemma sg14469 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1327 sg4164 - -lemma sg14470 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg2632 - -lemma sg14471 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg2633 - -lemma sg14472 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg2634 - -lemma sg14473 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg2635 - -lemma sg14474 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2252 sg2633 - -lemma sg14475 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2261 sg2626 - -lemma sg14476 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg2637 - -lemma sg14477 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2253 sg2628 - -lemma sg14478 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2263 sg2626 - -lemma sg14479 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg2638 - -lemma sg14480 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2255 sg2628 - -lemma sg14481 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2256 sg2628 - -lemma sg14482 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg2640 - -lemma sg14483 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2166 sg2702 - -lemma sg14484 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1330 sg4163 - -lemma sg14485 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg2642 - -lemma sg14486 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg4163 - -lemma sg14487 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg2643 - -lemma sg14488 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1332 sg4163 - -lemma sg14489 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2251 sg2879 - -lemma sg14490 : RowSquare [7,7,2,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2156 sg2707 - -lemma sg14491 : RowSquare [7,7,2,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2158 sg2702 - -lemma sg14492 : RowSquare [7,7,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2160 sg2702 - -lemma sg14493 : RowSquare [7,7,4,3,2,2,2] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2507 - -lemma sg14494 : RowSquare [7,7,4,3,2,2,2] [2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2152 sg2489 - -lemma sg14495 : RowSquare [7,7,4,3,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2506 - -lemma sg14496 : RowSquare [7,7,4,3,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2152 sg2488 - -lemma sg14497 : RowSquare [7,7,4,3,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2097 sg2505 - -lemma sg14498 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1195 sg4345 - -lemma sg14499 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg519 sg5735 - -lemma sg14500 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg520 sg5735 - -lemma sg14501 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1645 sg3521 - -lemma sg14502 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1200 sg4345 - -lemma sg14503 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1196 sg4350 - -lemma sg14504 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg521 sg5735 - -lemma sg14505 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg522 sg5735 - -lemma sg14506 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg523 sg5735 - -lemma sg14507 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg519 sg5736 - -lemma sg14508 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg520 sg5736 - -lemma sg14509 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg524 sg5735 - -lemma sg14510 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg525 sg5735 - -lemma sg14511 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg526 sg5735 - -lemma sg14512 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg521 sg5736 - -lemma sg14513 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg527 sg5735 - -lemma sg14514 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg522 sg5736 - -lemma sg14515 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg528 sg5735 - -lemma sg14516 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg523 sg5736 - -lemma sg14517 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg529 sg5735 - -lemma sg14518 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg524 sg5736 - -lemma sg14519 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg525 sg5736 - -lemma sg14520 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg530 sg5735 - -lemma sg14521 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg531 sg5735 - -lemma sg14522 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg532 sg5735 - -lemma sg14523 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg533 sg5735 - -lemma sg14524 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg530 sg5736 - -lemma sg14525 : RowSquare [8,7,2,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1663 sg3522 - -lemma sg14526 : RowSquare [8,7,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1663 sg3524 - -lemma sg14527 : RowSquare [8,7,3,2,2,2,2,1] [2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2541 - -lemma sg14528 : RowSquare [8,7,3,2,2,2,2,1] [2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2540 - -lemma sg14529 : RowSquare [8,7,3,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2539 - -lemma sg14530 : RowSquare [8,7,3,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2537 - -lemma sg14531 : RowSquare [8,7,3,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2097 sg2536 - -lemma sg14532 : RowSquare [8,7,3,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2097 sg2535 - -lemma sg14533 : RowSquare [8,7,3,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2091 sg2538 - -lemma sg14534 : RowSquare [8,7,3,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2091 sg2537 - -lemma sg14535 : RowSquare [8,7,3,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2091 sg2536 - -lemma sg14536 : RowSquare [8,7,3,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2091 sg2535 - -lemma sg14537 : RowSquare [8,7,3,2,2,2,2,1] [4,4,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2078 sg2564 - -lemma sg14538 : RowSquare [8,7,3,2,2,2,2,1] [4,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2078 sg2562 - -lemma sg14539 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg737 sg4930 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes13 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes14 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes9 + +namespace OAI + +/-! Semigroup Nodes 34. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg14140 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by + exact rowSquare_join (by decide) sg2373 sg2783 + +lemma sg14141 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1] := by + exact rowSquare_join (by decide) sg2373 sg2784 + +lemma sg14142 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4] := by + exact rowSquare_join (by decide) sg2374 sg2784 + +lemma sg14143 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1] := by + exact rowSquare_join (by decide) sg2297 sg2961 + +lemma sg14144 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3] := by + exact rowSquare_join (by decide) sg2297 sg2962 + +lemma sg14145 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2288 sg2979 + +lemma sg14146 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2289 sg2963 + +lemma sg14147 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2288 sg2980 + +lemma sg14148 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2981 + +lemma sg14149 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg2290 sg2964 + +lemma sg14150 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2369 sg2785 + +lemma sg14151 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2288 sg2982 + +lemma sg14152 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2369 sg2786 + +lemma sg14153 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2983 + +lemma sg14154 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2290 sg2966 + +lemma sg14155 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2984 + +lemma sg14156 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg2290 sg2967 + +lemma sg14157 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2985 + +lemma sg14158 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2369 sg2787 + +lemma sg14159 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1876 sg3651 + +lemma sg14160 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2986 + +lemma sg14161 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2290 sg2968 + +lemma sg14162 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2369 sg2788 + +lemma sg14163 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2987 + +lemma sg14164 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2290 sg2969 + +lemma sg14165 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg2300 sg2960 + +lemma sg14166 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2988 + +lemma sg14167 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg2300 sg2961 + +lemma sg14168 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg2300 sg2962 + +lemma sg14169 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2370 sg2785 + +lemma sg14170 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2989 + +lemma sg14171 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2369 sg2791 + +lemma sg14172 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2990 + +lemma sg14173 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2369 sg2793 + +lemma sg14174 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2991 + +lemma sg14175 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2293 sg2967 + +lemma sg14176 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2369 sg2794 + +lemma sg14177 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2992 + +lemma sg14178 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg2293 sg2968 + +lemma sg14179 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2993 + +lemma sg14180 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg2293 sg2969 + +lemma sg14181 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg2293 sg2970 + +lemma sg14182 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg2293 sg2971 + +lemma sg14183 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2] := by + exact rowSquare_join (by decide) sg2379 sg2783 + +lemma sg14184 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,1] := by + exact rowSquare_join (by decide) sg2379 sg2784 + +lemma sg14185 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4] := by + exact rowSquare_join (by decide) sg2380 sg2784 + +lemma sg14186 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2791 + +lemma sg14187 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2371 sg2790 + +lemma sg14188 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2994 + +lemma sg14189 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2793 + +lemma sg14190 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2794 + +lemma sg14191 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2995 + +lemma sg14192 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2371 sg2793 + +lemma sg14193 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2996 + +lemma sg14194 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2796 + +lemma sg14195 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2997 + +lemma sg14196 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2293 sg2981 + +lemma sg14197 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg2300 sg2971 + +lemma sg14198 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg2293 sg2987 + +lemma sg14199 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2293 sg2988 + +lemma sg14200 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,1] := by + exact rowSquare_join (by decide) sg2379 sg2789 + +lemma sg14201 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3] := by + exact rowSquare_join (by decide) sg2380 sg2789 + +lemma sg14202 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2293 sg2989 + +lemma sg14203 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2382 sg2790 + +lemma sg14204 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2371 sg2797 + +lemma sg14205 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2382 sg2791 + +lemma sg14206 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2384 sg2790 + +lemma sg14207 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2293 sg2994 + +lemma sg14208 : RowSquare [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2382 sg2793 + +lemma sg14209 : RowSquare [5,5,2,2,2,2,2,2,2,2,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1488 sg3998 + +lemma sg14210 : RowSquare [5,5,2,2,2,2,2,2,2,2,1] [7,7,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1488 sg4000 + +lemma sg14211 : RowSquare [5,5,2,2,2,2,2,2,2,2,1] [7,7,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1488 sg4001 + +lemma sg14212 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1874 sg3614 + +lemma sg14213 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1880 sg3614 + +lemma sg14214 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1876 sg3615 + +lemma sg14215 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1499 sg4415 + +lemma sg14216 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2371 sg2742 + +lemma sg14217 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2371 sg2743 + +lemma sg14218 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1499 sg4417 + +lemma sg14219 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1876 sg3620 + +lemma sg14220 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg2279 sg2960 + +lemma sg14221 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg2373 sg2743 + +lemma sg14222 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2374 sg2742 + +lemma sg14223 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg2374 sg2743 + +lemma sg14224 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg1000 sg4986 + +lemma sg14225 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg2290 sg2908 + +lemma sg14226 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg2279 sg2961 + +lemma sg14227 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg1501 sg4416 + +lemma sg14228 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg2279 sg2962 + +lemma sg14229 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg1501 sg4417 + +lemma sg14230 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg1502 sg4417 + +lemma sg14231 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg998 sg4988 + +lemma sg14232 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg2281 sg2959 + +lemma sg14233 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2293 sg2906 + +lemma sg14234 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1000 sg4987 + +lemma sg14235 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg998 sg4989 + +lemma sg14236 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg1001 sg4987 + +lemma sg14237 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg2372 sg2745 + +lemma sg14238 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg2372 sg2746 + +lemma sg14239 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg999 sg4988 + +lemma sg14240 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg2293 sg2907 + +lemma sg14241 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,3] := by + exact rowSquare_join (by decide) sg2373 sg2746 + +lemma sg14242 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg2374 sg2745 + +lemma sg14243 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2] := by + exact rowSquare_join (by decide) sg2374 sg2746 + +lemma sg14244 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg2282 sg2959 + +lemma sg14245 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg1000 sg4988 + +lemma sg14246 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg2293 sg2908 + +lemma sg14247 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2] := by + exact rowSquare_join (by decide) sg2281 sg2961 + +lemma sg14248 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1] := by + exact rowSquare_join (by decide) sg2281 sg2962 + +lemma sg14249 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5] := by + exact rowSquare_join (by decide) sg1001 sg4989 + +lemma sg14250 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3] := by + exact rowSquare_join (by decide) sg1878 sg3620 + +lemma sg14251 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg2282 sg2960 + +lemma sg14252 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by + exact rowSquare_join (by decide) sg2373 sg2748 + +lemma sg14253 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1] := by + exact rowSquare_join (by decide) sg2373 sg2749 + +lemma sg14254 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,4] := by + exact rowSquare_join (by decide) sg2374 sg2749 + +lemma sg14255 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1] := by + exact rowSquare_join (by decide) sg2282 sg2961 + +lemma sg14256 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,3] := by + exact rowSquare_join (by decide) sg2297 sg2908 + +lemma sg14257 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1945 sg3470 + +lemma sg14258 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2376 sg2742 + +lemma sg14259 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2369 sg2752 + +lemma sg14260 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2376 sg2743 + +lemma sg14261 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg2290 sg2910 + +lemma sg14262 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg2290 sg2911 + +lemma sg14263 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1947 sg3470 + +lemma sg14264 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1948 sg3470 + +lemma sg14265 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2377 sg2742 + +lemma sg14266 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2752 + +lemma sg14267 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2377 sg2743 + +lemma sg14268 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2371 sg2751 + +lemma sg14269 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2371 sg2752 + +lemma sg14270 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg2378 sg2743 + +lemma sg14271 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg2290 sg2914 + +lemma sg14272 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg2290 sg2915 + +lemma sg14273 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2279 sg2967 + +lemma sg14274 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg2379 sg2743 + +lemma sg14275 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2380 sg2742 + +lemma sg14276 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2380 sg2743 + +lemma sg14277 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1876 sg3624 + +lemma sg14278 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg2290 sg2916 + +lemma sg14279 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2290 sg2917 + +lemma sg14280 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2377 sg2745 + +lemma sg14281 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2377 sg2746 + +lemma sg14282 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2382 sg2743 + +lemma sg14283 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2371 sg2754 + +lemma sg14284 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2279 sg2973 + +lemma sg14285 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2290 sg2918 + +lemma sg14286 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg2290 sg2919 + +lemma sg14287 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg2279 sg2974 + +lemma sg14288 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2279 sg2975 + +lemma sg14289 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg2290 sg2921 + +lemma sg14290 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg2279 sg2977 + +lemma sg14291 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2] := by + exact rowSquare_join (by decide) sg2379 sg2748 + +lemma sg14292 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,1] := by + exact rowSquare_join (by decide) sg2281 sg2971 + +lemma sg14293 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,4] := by + exact rowSquare_join (by decide) sg2380 sg2749 + +lemma sg14294 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2382 sg2746 + +lemma sg14295 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2371 sg2755 + +lemma sg14296 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,3] := by + exact rowSquare_join (by decide) sg2383 sg2746 + +lemma sg14297 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2297 sg2917 + +lemma sg14298 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg2293 sg2918 + +lemma sg14299 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2293 sg2919 + +lemma sg14300 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2371 sg2756 + +lemma sg14301 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg2293 sg2920 + +lemma sg14302 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2293 sg2921 + +lemma sg14303 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,1] := by + exact rowSquare_join (by decide) sg2281 sg2977 + +lemma sg14304 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,3] := by + exact rowSquare_join (by decide) sg2297 sg2919 + +lemma sg14305 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2377 sg2755 + +lemma sg14306 : RowSquare [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2293 sg2924 + +lemma sg14307 : RowSquare [5,5,3,2,2,2,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1084 sg4832 + +lemma sg14308 : RowSquare [5,5,3,2,2,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1086 sg4832 + +lemma sg14309 : RowSquare [5,5,3,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1476 sg3998 + +lemma sg14310 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1688 sg3614 + +lemma sg14311 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1688 sg3615 + +lemma sg14312 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1] [5,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg1688 sg3617 + +lemma sg14313 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1] [5,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg1688 sg3620 + +lemma sg14314 : RowSquare [6,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg1908 sg3577 + +lemma sg14315 : RowSquare [6,4,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1758 sg3738 + +lemma sg14316 : RowSquare [6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3] := by + exact rowSquare_join (by decide) sg1332 sg4507 + +lemma sg14317 : RowSquare [6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg1757 sg3731 + +lemma sg14318 : RowSquare [6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg4508 + +lemma sg14319 : RowSquare [6,4,3,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg3501 + +lemma sg14320 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2289 sg2891 + +lemma sg14321 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg2273 sg2962 + +lemma sg14322 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2291 sg2891 + +lemma sg14323 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1782 sg3671 + +lemma sg14324 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2894 + +lemma sg14325 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1758 sg3722 + +lemma sg14326 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2297 sg2889 + +lemma sg14327 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg2372 sg2723 + +lemma sg14328 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg2372 sg2724 + +lemma sg14329 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2] := by + exact rowSquare_join (by decide) sg2295 sg2891 + +lemma sg14330 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1] := by + exact rowSquare_join (by decide) sg2296 sg2891 + +lemma sg14331 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg2297 sg2890 + +lemma sg14332 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by + exact rowSquare_join (by decide) sg2373 sg2723 + +lemma sg14333 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1] := by + exact rowSquare_join (by decide) sg2373 sg2724 + +lemma sg14334 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,4] := by + exact rowSquare_join (by decide) sg2374 sg2724 + +lemma sg14335 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2369 sg2726 + +lemma sg14336 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2898 + +lemma sg14337 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2726 + +lemma sg14338 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2289 sg2893 + +lemma sg14339 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2371 sg2726 + +lemma sg14340 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2299 sg2891 + +lemma sg14341 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg2273 sg2968 + +lemma sg14342 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg2273 sg2970 + +lemma sg14343 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,2] := by + exact rowSquare_join (by decide) sg2368 sg2783 + +lemma sg14344 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,1] := by + exact rowSquare_join (by decide) sg2368 sg2784 + +lemma sg14345 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2291 sg2893 + +lemma sg14346 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2273 sg2972 + +lemma sg14347 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2292 sg2893 + +lemma sg14348 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2273 sg2973 + +lemma sg14349 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2273 sg2975 + +lemma sg14350 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg2273 sg2976 + +lemma sg14351 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,2] := by + exact rowSquare_join (by decide) sg2295 sg2893 + +lemma sg14352 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,1] := by + exact rowSquare_join (by decide) sg2296 sg2893 + +lemma sg14353 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2] := by + exact rowSquare_join (by decide) sg2379 sg2723 + +lemma sg14354 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,1] := by + exact rowSquare_join (by decide) sg2379 sg2724 + +lemma sg14355 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,4] := by + exact rowSquare_join (by decide) sg2380 sg2724 + +lemma sg14356 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,2] := by + exact rowSquare_join (by decide) sg2303 sg2891 + +lemma sg14357 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg2304 sg2890 + +lemma sg14358 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1883 sg3572 + +lemma sg14359 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2900 + +lemma sg14360 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2733 + +lemma sg14361 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg2305 sg2891 + +lemma sg14362 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg1782 sg3678 + +lemma sg14363 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,1] := by + exact rowSquare_join (by decide) sg2297 sg2894 + +lemma sg14364 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,3] := by + exact rowSquare_join (by decide) sg2297 sg2895 + +lemma sg14365 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg2372 sg2735 + +lemma sg14366 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,1,1] := by + exact rowSquare_join (by decide) sg2373 sg2735 + +lemma sg14367 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,2] := by + exact rowSquare_join (by decide) sg2374 sg2735 + +lemma sg14368 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2308 sg2889 + +lemma sg14369 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2375 sg2726 + +lemma sg14370 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2376 sg2726 + +lemma sg14371 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg2290 sg2897 + +lemma sg14372 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg2290 sg2898 + +lemma sg14373 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2273 sg2981 + +lemma sg14374 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2737 + +lemma sg14375 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2377 sg2726 + +lemma sg14376 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2273 sg2983 + +lemma sg14377 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2293 sg2897 + +lemma sg14378 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg2273 sg2984 + +lemma sg14379 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2273 sg2985 + +lemma sg14380 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg2272 sg2988 + +lemma sg14381 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg2273 sg2988 + +lemma sg14382 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2301 sg2893 + +lemma sg14383 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2273 sg2989 + +lemma sg14384 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg2273 sg2990 + +lemma sg14385 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2] := by + exact rowSquare_join (by decide) sg2368 sg2792 + +lemma sg14386 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,1] := by + exact rowSquare_join (by decide) sg2368 sg2793 + +lemma sg14387 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2] := by + exact rowSquare_join (by decide) sg2368 sg2794 + +lemma sg14388 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2367 sg2795 + +lemma sg14389 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2377 sg2731 + +lemma sg14390 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2377 sg2733 + +lemma sg14391 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2273 sg2994 + +lemma sg14392 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2] := by + exact rowSquare_join (by decide) sg2306 sg2893 + +lemma sg14393 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2370 sg2739 + +lemma sg14394 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2382 sg2731 + +lemma sg14395 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2293 sg2900 + +lemma sg14396 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2382 sg2733 + +lemma sg14397 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2] := by + exact rowSquare_join (by decide) sg1883 sg3589 + +lemma sg14398 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2300 sg2897 + +lemma sg14399 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2273 sg2998 + +lemma sg14400 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2273 sg2999 + +lemma sg14401 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,2] := by + exact rowSquare_join (by decide) sg2368 sg2797 + +lemma sg14402 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg2901 + +lemma sg14403 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2388 sg2731 + +lemma sg14404 : RowSquare [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2382 sg2739 + +lemma sg14405 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg656 sg5672 + +lemma sg14406 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg663 sg5672 + +lemma sg14407 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg664 sg5672 + +lemma sg14408 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg665 sg5672 + +lemma sg14409 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg666 sg5672 + +lemma sg14410 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg667 sg5672 + +lemma sg14411 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg668 sg5672 + +lemma sg14412 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg663 sg5673 + +lemma sg14413 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg664 sg5673 + +lemma sg14414 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg669 sg5672 + +lemma sg14415 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg665 sg5673 + +lemma sg14416 : RowSquare [6,5,2,2,2,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg666 sg5673 + +lemma sg14417 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1758 sg3689 + +lemma sg14418 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1332 sg4487 + +lemma sg14419 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg1331 sg4488 + +lemma sg14420 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg1758 sg3690 + +lemma sg14421 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg1332 sg4488 + +lemma sg14422 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1758 sg3691 + +lemma sg14423 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1332 sg4489 + +lemma sg14424 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg1873 sg3620 + +lemma sg14425 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg1331 sg4490 + +lemma sg14426 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg1758 sg3697 + +lemma sg14427 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3] := by + exact rowSquare_join (by decide) sg1332 sg4492 + +lemma sg14428 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg4496 + +lemma sg14429 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg1757 sg3698 + +lemma sg14430 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg1331 sg4493 + +lemma sg14431 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg1758 sg3698 + +lemma sg14432 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2] := by + exact rowSquare_join (by decide) sg1765 sg3690 + +lemma sg14433 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1] := by + exact rowSquare_join (by decide) sg1765 sg3691 + +lemma sg14434 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5] := by + exact rowSquare_join (by decide) sg1001 sg4958 + +lemma sg14435 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg4496 + +lemma sg14436 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2] := by + exact rowSquare_join (by decide) sg1000 sg4961 + +lemma sg14437 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg4496 + +lemma sg14438 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1] := by + exact rowSquare_join (by decide) sg1332 sg4496 + +lemma sg14439 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,3] := by + exact rowSquare_join (by decide) sg892 sg5000 + +lemma sg14440 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2454 sg2633 + +lemma sg14441 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg2455 sg2633 + +lemma sg14442 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg2368 sg2746 + +lemma sg14443 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1338 sg4492 + +lemma sg14444 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,1] := by + exact rowSquare_join (by decide) sg1340 sg4496 + +lemma sg14445 : RowSquare [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg2167 sg3108 + +lemma sg14446 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg1332 sg4378 + +lemma sg14447 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1332 sg4379 + +lemma sg14448 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg4303 + +lemma sg14449 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1675 sg3571 + +lemma sg14450 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg1332 sg4303 + +lemma sg14451 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1332 sg4304 + +lemma sg14452 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg2135 sg2891 + +lemma sg14453 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1329 sg4308 + +lemma sg14454 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,4,3] := by + exact rowSquare_join (by decide) sg1332 sg4308 + +lemma sg14455 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1675 sg3573 + +lemma sg14456 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg2135 sg2893 + +lemma sg14457 : RowSquare [7,5,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2167 sg2708 + +lemma sg14458 : RowSquare [7,5,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg390 sg6486 + +lemma sg14459 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2251 sg2626 + +lemma sg14460 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2251 sg2627 + +lemma sg14461 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2253 sg2626 + +lemma sg14462 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2251 sg2628 + +lemma sg14463 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2254 sg2626 + +lemma sg14464 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2255 sg2626 + +lemma sg14465 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg2630 + +lemma sg14466 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1327 sg4163 + +lemma sg14467 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2256 sg2626 + +lemma sg14468 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg2631 + +lemma sg14469 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1327 sg4164 + +lemma sg14470 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg2632 + +lemma sg14471 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg2633 + +lemma sg14472 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg2634 + +lemma sg14473 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg2635 + +lemma sg14474 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2252 sg2633 + +lemma sg14475 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2261 sg2626 + +lemma sg14476 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg2637 + +lemma sg14477 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2253 sg2628 + +lemma sg14478 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2263 sg2626 + +lemma sg14479 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg2638 + +lemma sg14480 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2255 sg2628 + +lemma sg14481 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2256 sg2628 + +lemma sg14482 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg2640 + +lemma sg14483 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2166 sg2702 + +lemma sg14484 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1330 sg4163 + +lemma sg14485 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg2642 + +lemma sg14486 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg4163 + +lemma sg14487 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg2643 + +lemma sg14488 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1332 sg4163 + +lemma sg14489 : RowSquare [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2251 sg2879 + +lemma sg14490 : RowSquare [7,7,2,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2156 sg2707 + +lemma sg14491 : RowSquare [7,7,2,2,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2158 sg2702 + +lemma sg14492 : RowSquare [7,7,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2160 sg2702 + +lemma sg14493 : RowSquare [7,7,4,3,2,2,2] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2507 + +lemma sg14494 : RowSquare [7,7,4,3,2,2,2] [2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2152 sg2489 + +lemma sg14495 : RowSquare [7,7,4,3,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2506 + +lemma sg14496 : RowSquare [7,7,4,3,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2152 sg2488 + +lemma sg14497 : RowSquare [7,7,4,3,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2097 sg2505 + +lemma sg14498 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1195 sg4345 + +lemma sg14499 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg519 sg5735 + +lemma sg14500 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg520 sg5735 + +lemma sg14501 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1645 sg3521 + +lemma sg14502 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1200 sg4345 + +lemma sg14503 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1196 sg4350 + +lemma sg14504 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg521 sg5735 + +lemma sg14505 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg522 sg5735 + +lemma sg14506 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg523 sg5735 + +lemma sg14507 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg519 sg5736 + +lemma sg14508 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg520 sg5736 + +lemma sg14509 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg524 sg5735 + +lemma sg14510 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg525 sg5735 + +lemma sg14511 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg526 sg5735 + +lemma sg14512 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg521 sg5736 + +lemma sg14513 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg527 sg5735 + +lemma sg14514 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg522 sg5736 + +lemma sg14515 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg528 sg5735 + +lemma sg14516 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg523 sg5736 + +lemma sg14517 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg529 sg5735 + +lemma sg14518 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg524 sg5736 + +lemma sg14519 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg525 sg5736 + +lemma sg14520 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg530 sg5735 + +lemma sg14521 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg531 sg5735 + +lemma sg14522 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg532 sg5735 + +lemma sg14523 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg533 sg5735 + +lemma sg14524 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg530 sg5736 + +lemma sg14525 : RowSquare [8,7,2,1,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1663 sg3522 + +lemma sg14526 : RowSquare [8,7,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1663 sg3524 + +lemma sg14527 : RowSquare [8,7,3,2,2,2,2,1] [2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2541 + +lemma sg14528 : RowSquare [8,7,3,2,2,2,2,1] [2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2540 + +lemma sg14529 : RowSquare [8,7,3,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2539 + +lemma sg14530 : RowSquare [8,7,3,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2537 + +lemma sg14531 : RowSquare [8,7,3,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2097 sg2536 + +lemma sg14532 : RowSquare [8,7,3,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2097 sg2535 + +lemma sg14533 : RowSquare [8,7,3,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2091 sg2538 + +lemma sg14534 : RowSquare [8,7,3,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2091 sg2537 + +lemma sg14535 : RowSquare [8,7,3,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2091 sg2536 + +lemma sg14536 : RowSquare [8,7,3,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2091 sg2535 + +lemma sg14537 : RowSquare [8,7,3,2,2,2,2,1] [4,4,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2078 sg2564 + +lemma sg14538 : RowSquare [8,7,3,2,2,2,2,1] [4,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2078 sg2562 + +lemma sg14539 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg737 sg4930 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes35.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes35.lean index 403de97c45fd8ffbd9cc182a31bab1bb5e9dd3a5..d1023c97369ea574ce4c04779a8655c5d2f349c1 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes35.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes35.lean @@ -1,1223 +1,1223 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes18 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes16 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes17 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes26 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes34 - -namespace OAI - -/-! Semigroup Nodes 35. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg14540 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg738 sg4930 - -lemma sg14541 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg739 sg4930 - -lemma sg14542 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg740 sg4930 - -lemma sg14543 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg741 sg4930 - -lemma sg14544 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg747 sg4930 - -lemma sg14545 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg748 sg4930 - -lemma sg14546 : RowSquare [9,7,3,2,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg109 sg7998 - -lemma sg14547 : RowSquare [9,7,3,2,1,1,1,1,1,1] [9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg109 sg7999 - -lemma sg14548 : RowSquare [11,3,2,2,2,2,2,2,1] [6,6,5,5,5] := by - exact rowSquare_join (by decide) sg166 sg7538 - -lemma sg14549 : RowSquare [11,3,3,2,2,2,2,1,1] [5,5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg306 sg6346 - -lemma sg14550 : RowSquare [11,3,3,2,2,2,2,2] [5,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg310 sg6178 - -lemma sg14551 : RowSquare [12,4,2,2,2,2,2,1] [6,6,5,5,5] := by - exact rowSquare_join (by decide) sg143 sg6919 - -lemma sg14552 : RowSquare [12,4,2,2,2,2,2,1] [7,7,4,4,4,1] := by - exact rowSquare_join (by decide) sg143 sg6948 - -lemma sg14553 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2837 - -lemma sg14554 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg2925 sg2838 - -lemma sg14555 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2839 sg2925 - -lemma sg14556 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg2925 sg2840 - -lemma sg14557 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3648 - -lemma sg14558 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3648 - -lemma sg14559 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2843 - -lemma sg14560 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg2925 sg2844 - -lemma sg14561 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2845 - -lemma sg14562 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg2925 sg2846 - -lemma sg14563 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg2769 sg3004 - -lemma sg14564 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2847 - -lemma sg14565 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2394 sg3502 - -lemma sg14566 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg3000 sg2772 - -lemma sg14567 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg2925 sg2848 - -lemma sg14568 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg3001 sg2772 - -lemma sg14569 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1698 sg4539 - -lemma sg14570 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1518 sg4928 - -lemma sg14571 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2395 sg3502 - -lemma sg14572 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg2390 sg3505 - -lemma sg14573 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg2314 sg3648 - -lemma sg14574 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2849 - -lemma sg14575 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2662 sg3128 - -lemma sg14576 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2212 sg3709 - -lemma sg14577 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg3003 sg2772 - -lemma sg14578 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg3004 sg2772 - -lemma sg14579 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3005 sg2772 - -lemma sg14580 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg2925 sg2853 - -lemma sg14581 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3649 - -lemma sg14582 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg2393 sg3505 - -lemma sg14583 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2] := by - exact rowSquare_join (by decide) sg3007 sg2772 - -lemma sg14584 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1735 sg4526 - -lemma sg14585 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5] := by - exact rowSquare_join (by decide) sg2432 sg3420 - -lemma sg14586 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2854 - -lemma sg14587 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg2925 sg2855 - -lemma sg14588 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg3001 sg2774 - -lemma sg14589 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2856 - -lemma sg14590 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2925 sg2857 - -lemma sg14591 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg3001 sg2775 - -lemma sg14592 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg2838 sg2930 - -lemma sg14593 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg2925 sg2858 - -lemma sg14594 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg3012 sg2772 - -lemma sg14595 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2860 - -lemma sg14596 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg2925 sg2861 - -lemma sg14597 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg3001 sg2778 - -lemma sg14598 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2842 sg2930 - -lemma sg14599 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2862 - -lemma sg14600 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2326 sg3648 - -lemma sg14601 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg2844 sg2930 - -lemma sg14602 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2863 - -lemma sg14603 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg2925 sg2864 - -lemma sg14604 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg2925 sg2865 - -lemma sg14605 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg3001 sg2782 - -lemma sg14606 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2216 sg3720 - -lemma sg14607 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3020 sg2776 - -lemma sg14608 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2866 - -lemma sg14609 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg2925 sg2799 - -lemma sg14610 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2801 - -lemma sg14611 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg2925 sg2802 - -lemma sg14612 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg5792 - -lemma sg14613 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg2925 sg2805 - -lemma sg14614 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg2925 sg2806 - -lemma sg14615 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg2925 sg2807 - -lemma sg14616 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg1033 sg5772 - -lemma sg14617 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2809 - -lemma sg14618 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2811 - -lemma sg14619 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg2925 sg2818 - -lemma sg14620 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg2925 sg2819 - -lemma sg14621 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg2928 sg2802 - -lemma sg14622 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg2925 sg2820 - -lemma sg14623 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg1032 sg5773 - -lemma sg14624 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3005 sg2762 - -lemma sg14625 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3005 sg2763 - -lemma sg14626 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2798 sg2941 - -lemma sg14627 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg2925 sg2821 - -lemma sg14628 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3644 - -lemma sg14629 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2798 sg2942 - -lemma sg14630 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg2925 sg2822 - -lemma sg14631 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg2762 sg3009 - -lemma sg14632 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg2928 sg2805 - -lemma sg14633 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,3] := by - exact rowSquare_join (by decide) sg1032 sg5774 - -lemma sg14634 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg2405 sg3420 - -lemma sg14635 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3645 - -lemma sg14636 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg2928 sg2806 - -lemma sg14637 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg2928 sg2807 - -lemma sg14638 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5] := by - exact rowSquare_join (by decide) sg2407 sg3420 - -lemma sg14639 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg2395 sg3500 - -lemma sg14640 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4] := by - exact rowSquare_join (by decide) sg1033 sg5775 - -lemma sg14641 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg2824 - -lemma sg14642 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg850 sg5793 - -lemma sg14643 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2831 sg2925 - -lemma sg14644 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg2925 sg2615 - -lemma sg14645 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1] [5,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg2111 sg3702 - -lemma sg14646 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1] [6,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg2111 sg3704 - -lemma sg14647 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3622 - -lemma sg14648 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg2311 sg3622 - -lemma sg14649 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1289 sg4997 - -lemma sg14650 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2902 sg2810 - -lemma sg14651 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg2314 sg3620 - -lemma sg14652 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg2314 sg3622 - -lemma sg14653 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg3004 sg2746 - -lemma sg14654 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg3004 sg2747 - -lemma sg14655 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg3004 sg2748 - -lemma sg14656 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2173 sg3699 - -lemma sg14657 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2341 sg3563 - -lemma sg14658 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg2821 - -lemma sg14659 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2798 sg2922 - -lemma sg14660 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg2341 sg3564 - -lemma sg14661 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg2311 sg3629 - -lemma sg14662 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg2405 sg3411 - -lemma sg14663 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2] := by - exact rowSquare_join (by decide) sg3007 sg2747 - -lemma sg14664 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg2310 sg3630 - -lemma sg14665 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5] := by - exact rowSquare_join (by decide) sg2407 sg3411 - -lemma sg14666 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg1686 sg4539 - -lemma sg14667 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2] := by - exact rowSquare_join (by decide) sg3008 sg2748 - -lemma sg14668 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2326 sg3614 - -lemma sg14669 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2902 sg2823 - -lemma sg14670 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2903 sg2808 - -lemma sg14671 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2903 sg2810 - -lemma sg14672 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2663 sg3110 - -lemma sg14673 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg2826 - -lemma sg14674 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2663 sg3111 - -lemma sg14675 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2370 sg3508 - -lemma sg14676 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2902 sg2831 - -lemma sg14677 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2808 sg2909 - -lemma sg14678 : RowSquare [5,4,3,3,2,2,2,2,2,2,1] [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2250 sg3299 - -lemma sg14679 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1] [7,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg3004 sg2651 - -lemma sg14680 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1931 sg3998 - -lemma sg14681 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1934 sg3998 - -lemma sg14682 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [6,5,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1930 sg3999 - -lemma sg14683 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [6,5,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1931 sg3999 - -lemma sg14684 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1935 sg3998 - -lemma sg14685 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1936 sg3998 - -lemma sg14686 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1937 sg3998 - -lemma sg14687 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1938 sg3998 - -lemma sg14688 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1939 sg3998 - -lemma sg14689 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1940 sg3998 - -lemma sg14690 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1941 sg3998 - -lemma sg14691 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1942 sg3998 - -lemma sg14692 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1935 sg3999 - -lemma sg14693 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1936 sg3999 - -lemma sg14694 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1943 sg3998 - -lemma sg14695 : RowSquare [5,5,3,2,2,2,2,2,2,2,1] [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1854 sg3998 - -lemma sg14696 : RowSquare [5,5,3,2,2,2,2,2,2,2,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1488 sg4832 - -lemma sg14697 : RowSquare [5,5,3,2,2,2,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1867 sg3998 - -lemma sg14698 : RowSquare [5,5,3,3,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1476 sg4832 - -lemma sg14699 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2144 sg3614 - -lemma sg14700 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1] [5,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg2141 sg3620 - -lemma sg14701 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2144 sg3615 - -lemma sg14702 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1] [6,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg2144 sg3620 - -lemma sg14703 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1] [7,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg2746 sg2651 - -lemma sg14704 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1] [8,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg2752 sg2651 - -lemma sg14705 : RowSquare [6,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg4508 - -lemma sg14706 : RowSquare [6,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1757 sg4506 - -lemma sg14707 : RowSquare [6,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg1757 sg4508 - -lemma sg14708 : RowSquare [6,5,2,2,2,2,2,2,2,2,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg996 sg5672 - -lemma sg14709 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg1757 sg4493 - -lemma sg14710 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg1765 sg4488 - -lemma sg14711 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg1757 sg4496 - -lemma sg14712 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2] := by - exact rowSquare_join (by decide) sg1000 sg5771 - -lemma sg14713 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg2721 sg2921 - -lemma sg14714 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg991 sg5672 - -lemma sg14715 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg663 sg6457 - -lemma sg14716 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg992 sg5672 - -lemma sg14717 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg664 sg6457 - -lemma sg14718 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg666 sg6457 - -lemma sg14719 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg993 sg5672 - -lemma sg14720 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg667 sg6457 - -lemma sg14721 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg994 sg5672 - -lemma sg14722 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg668 sg6457 - -lemma sg14723 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg669 sg6457 - -lemma sg14724 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg14310 - -lemma sg14725 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1] [5,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg1688 sg4377 - -lemma sg14726 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1] [5,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg1688 sg4378 - -lemma sg14727 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg2273 sg3578 - -lemma sg14728 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2887 sg2736 - -lemma sg14729 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1330 sg4983 - -lemma sg14730 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1330 sg4984 - -lemma sg14731 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg2277 sg3576 - -lemma sg14732 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2] := by - exact rowSquare_join (by decide) sg1332 sg4984 - -lemma sg14733 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2273 sg3581 - -lemma sg14734 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2725 sg2891 - -lemma sg14735 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg2278 sg3578 - -lemma sg14736 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2273 sg3589 - -lemma sg14737 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,2] := by - exact rowSquare_join (by decide) sg1762 sg4466 - -lemma sg14738 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2889 sg2736 - -lemma sg14739 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2892 sg2726 - -lemma sg14740 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2888 sg2737 - -lemma sg14741 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2726 sg2893 - -lemma sg14742 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2889 sg2737 - -lemma sg14743 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2] := by - exact rowSquare_join (by decide) sg2891 sg2737 - -lemma sg14744 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2] := by - exact rowSquare_join (by decide) sg2278 sg3589 - -lemma sg14745 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg2892 sg2734 - -lemma sg14746 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1] := by - exact rowSquare_join (by decide) sg2891 sg2738 - -lemma sg14747 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,2] := by - exact rowSquare_join (by decide) sg2891 sg2740 - -lemma sg14748 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg408 sg7813 - -lemma sg14749 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg409 sg7813 - -lemma sg14750 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg410 sg7813 - -lemma sg14751 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg7829 - -lemma sg14752 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [7,7,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg7830 - -lemma sg14753 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg411 sg7813 - -lemma sg14754 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg412 sg7813 - -lemma sg14755 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [8,7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg7847 - -lemma sg14756 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg1758 sg4438 - -lemma sg14757 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg1332 sg4949 - -lemma sg14758 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1873 sg4379 - -lemma sg14759 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg1332 sg4956 - -lemma sg14760 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg3107 sg2633 - -lemma sg14761 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg1873 sg4384 - -lemma sg14762 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg2633 sg3109 - -lemma sg14763 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg2640 sg3108 - -lemma sg14764 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg3617 - -lemma sg14765 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg3620 - -lemma sg14766 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1754 sg4163 - -lemma sg14767 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2626 sg2707 - -lemma sg14768 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1754 sg4164 - -lemma sg14769 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2626 sg2708 - -lemma sg14770 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg4167 - -lemma sg14771 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2627 sg2703 - -lemma sg14772 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg2710 sg2640 - -lemma sg14773 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg74 sg11060 - -lemma sg14774 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [8,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg391 sg7997 - -lemma sg14775 : RowSquare [7,7,2,2,1,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2702 sg2702 - -lemma sg14776 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1] [6,6,6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg3351 - -lemma sg14777 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2251 sg3311 - -lemma sg14778 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2251 sg3312 - -lemma sg14779 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg3313 - -lemma sg14780 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg3314 - -lemma sg14781 : RowSquare [8,7,1,1,1,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2251 sg3523 - -lemma sg14782 : RowSquare [8,7,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2705 sg2619 - -lemma sg14783 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2879 sg2546 - -lemma sg14784 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2073 sg3522 - -lemma sg14785 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2252 sg3259 - -lemma sg14786 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2074 sg3522 - -lemma sg14787 : RowSquare [8,8,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2115 sg3524 - -lemma sg14788 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2566 sg2573 - -lemma sg14789 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2566 sg2572 - -lemma sg14790 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2566 sg2571 - -lemma sg14791 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2566 sg2570 - -lemma sg14792 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2566 sg2569 - -lemma sg14793 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2566 sg2568 - -lemma sg14794 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2566 sg2566 - -lemma sg14795 : RowSquare [8,8,2,2,2,2,2,2] [3,3,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2563 sg2563 - -lemma sg14796 : RowSquare [8,8,2,2,2,2,2,2] [4,4,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2562 sg2565 - -lemma sg14797 : RowSquare [8,8,2,2,2,2,2,2] [4,4,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2559 sg2567 - -lemma sg14798 : RowSquare [8,8,2,2,2,2,2,2] [4,4,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2562 sg2562 - -lemma sg14799 : RowSquare [8,8,2,2,2,2,2,2] [4,4,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg2559 sg2562 - -lemma sg14800 : RowSquare [8,8,2,2,2,2,2,2] [5,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2554 sg2562 - -lemma sg14801 : RowSquare [8,8,2,2,2,2,2,2] [5,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2554 sg2559 - -lemma sg14802 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1147 sg4930 - -lemma sg14803 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg737 sg5757 - -lemma sg14804 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg739 sg5757 - -lemma sg14805 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg740 sg5757 - -lemma sg14806 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg741 sg5757 - -lemma sg14807 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg748 sg5757 - -lemma sg14808 : RowSquare [9,7,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2595 sg2527 - -lemma sg14809 : RowSquare [9,7,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2595 sg2526 - -lemma sg14810 : RowSquare [9,7,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2595 sg2525 - -lemma sg14811 : RowSquare [9,7,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2595 sg2524 - -lemma sg14812 : RowSquare [11,4,2,2,2,2,2,2,1] [6,6,6,5,5] := by - exact rowSquare_join (by decide) sg879 sg5380 - -lemma sg14813 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg2925 sg3362 - -lemma sg14814 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2759 sg3420 - -lemma sg14815 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg2926 sg3362 - -lemma sg14816 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1] [6,6,6,6,5] := by - exact rowSquare_join (by decide) sg1033 sg6490 - -lemma sg14817 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg2929 sg3362 - -lemma sg14818 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg2930 sg3362 - -lemma sg14819 : RowSquare [5,4,3,3,2,2,2,2,2,2,1,1] [4,4,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2596 sg3520 - -lemma sg14820 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2137 sg4539 - -lemma sg14821 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3505 - -lemma sg14822 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg1891 sg4923 - -lemma sg14823 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg1891 sg4924 - -lemma sg14824 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1736 sg4992 - -lemma sg14825 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2213 sg4442 - -lemma sg14826 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg1688 sg5005 - -lemma sg14827 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2663 sg3686 - -lemma sg14828 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2663 sg3688 - -lemma sg14829 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2902 sg3509 - -lemma sg14830 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2903 sg3506 - -lemma sg14831 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3510 - -lemma sg14832 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2902 sg3511 - -lemma sg14833 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2903 sg3507 - -lemma sg14834 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2842 sg3563 - -lemma sg14835 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2903 sg3508 - -lemma sg14836 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2663 sg3693 - -lemma sg14837 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2903 sg3509 - -lemma sg14838 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2903 sg3511 - -lemma sg14839 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2663 sg3700 - -lemma sg14840 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,3,2] := by - exact rowSquare_join (by decide) sg2925 sg3475 - -lemma sg14841 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg1688 sg5002 - -lemma sg14842 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg2925 sg3476 - -lemma sg14843 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg1688 sg5003 - -lemma sg14844 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg1688 sg5004 - -lemma sg14845 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2288 sg4410 - -lemma sg14846 : RowSquare [5,4,4,3,2,2,2,2,2,2,1] [5,5,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2107 sg4343 - -lemma sg14847 : RowSquare [5,4,4,3,2,2,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1871 sg4804 - -lemma sg14848 : RowSquare [5,4,4,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3362 - -lemma sg14849 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1928 sg4832 - -lemma sg14850 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1929 sg4832 - -lemma sg14851 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1930 sg4832 - -lemma sg14852 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1931 sg4832 - -lemma sg14853 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [6,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1932 sg4832 - -lemma sg14854 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1933 sg4832 - -lemma sg14855 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1934 sg4832 - -lemma sg14856 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1935 sg4832 - -lemma sg14857 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1936 sg4832 - -lemma sg14858 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1937 sg4832 - -lemma sg14859 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1938 sg4832 - -lemma sg14860 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1939 sg4832 - -lemma sg14861 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1940 sg4832 - -lemma sg14862 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1941 sg4832 - -lemma sg14863 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1942 sg4832 - -lemma sg14864 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1943 sg4832 - -lemma sg14865 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2746 sg3614 - -lemma sg14866 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1875 sg4919 - -lemma sg14867 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2750 sg3614 - -lemma sg14868 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1876 sg4920 - -lemma sg14869 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2902 sg3477 - -lemma sg14870 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3478 - -lemma sg14871 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2904 sg3470 - -lemma sg14872 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2752 sg3614 - -lemma sg14873 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2743 sg3615 - -lemma sg14874 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2753 sg3614 - -lemma sg14875 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1499 sg5754 - -lemma sg14876 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2902 sg3479 - -lemma sg14877 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1874 sg4925 - -lemma sg14878 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2371 sg4317 - -lemma sg14879 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2741 sg3616 - -lemma sg14880 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2903 sg3472 - -lemma sg14881 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3480 - -lemma sg14882 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2904 sg3471 - -lemma sg14883 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3481 - -lemma sg14884 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg2904 sg3472 - -lemma sg14885 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2746 sg3615 - -lemma sg14886 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg2743 sg3617 - -lemma sg14887 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2957 sg3409 - -lemma sg14888 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2743 sg3618 - -lemma sg14889 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1876 sg4921 - -lemma sg14890 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2372 sg4317 - -lemma sg14891 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2903 sg3474 - -lemma sg14892 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3482 - -lemma sg14893 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg2904 sg3473 - -lemma sg14894 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2904 sg3474 - -lemma sg14895 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg2743 sg3619 - -lemma sg14896 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg2743 sg3620 - -lemma sg14897 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg2167 sg4488 - -lemma sg14898 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2904 sg3476 - -lemma sg14899 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg2743 sg3622 - -lemma sg14900 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg2167 sg4489 - -lemma sg14901 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2291 sg4403 - -lemma sg14902 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg998 sg6501 - -lemma sg14903 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2744 sg3616 - -lemma sg14904 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2905 sg3472 - -lemma sg14905 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2746 sg3616 - -lemma sg14906 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3483 - -lemma sg14907 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2958 sg3409 - -lemma sg14908 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3484 - -lemma sg14909 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2140 sg4533 - -lemma sg14910 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2905 sg3474 - -lemma sg14911 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2371 sg4318 - -lemma sg14912 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg975 sg6508 - -lemma sg14913 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3485 - -lemma sg14914 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg2907 sg3471 - -lemma sg14915 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg2906 sg3473 - -lemma sg14916 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg2906 sg3474 - -lemma sg14917 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg2746 sg3620 - -lemma sg14918 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg2906 sg3476 - -lemma sg14919 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg2746 sg3622 - -lemma sg14920 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3486 - -lemma sg14921 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2140 sg4534 - -lemma sg14922 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1878 sg4921 - -lemma sg14923 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg2141 sg4534 - -lemma sg14924 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2140 sg4535 - -lemma sg14925 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg2907 sg3473 - -lemma sg14926 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3] := by - exact rowSquare_join (by decide) sg2907 sg3474 - -lemma sg14927 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,1] := by - exact rowSquare_join (by decide) sg2907 sg3476 - -lemma sg14928 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1880 sg4919 - -lemma sg14929 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2757 sg3614 - -lemma sg14930 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1945 sg4889 - -lemma sg14931 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2902 sg3487 - -lemma sg14932 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2369 sg4322 - -lemma sg14933 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2376 sg4317 - -lemma sg14934 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3488 - -lemma sg14935 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3489 - -lemma sg14936 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2752 sg3615 - -lemma sg14937 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2902 sg3490 - -lemma sg14938 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2370 sg4322 - -lemma sg14939 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2958 sg3412 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes18 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes16 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes17 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes26 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes34 + +namespace OAI + +/-! Semigroup Nodes 35. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg14540 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg738 sg4930 + +lemma sg14541 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg739 sg4930 + +lemma sg14542 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg740 sg4930 + +lemma sg14543 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg741 sg4930 + +lemma sg14544 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg747 sg4930 + +lemma sg14545 : RowSquare [9,7,2,1,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg748 sg4930 + +lemma sg14546 : RowSquare [9,7,3,2,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg109 sg7998 + +lemma sg14547 : RowSquare [9,7,3,2,1,1,1,1,1,1] [9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg109 sg7999 + +lemma sg14548 : RowSquare [11,3,2,2,2,2,2,2,1] [6,6,5,5,5] := by + exact rowSquare_join (by decide) sg166 sg7538 + +lemma sg14549 : RowSquare [11,3,3,2,2,2,2,1,1] [5,5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg306 sg6346 + +lemma sg14550 : RowSquare [11,3,3,2,2,2,2,2] [5,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg310 sg6178 + +lemma sg14551 : RowSquare [12,4,2,2,2,2,2,1] [6,6,5,5,5] := by + exact rowSquare_join (by decide) sg143 sg6919 + +lemma sg14552 : RowSquare [12,4,2,2,2,2,2,1] [7,7,4,4,4,1] := by + exact rowSquare_join (by decide) sg143 sg6948 + +lemma sg14553 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2837 + +lemma sg14554 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg2925 sg2838 + +lemma sg14555 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2839 sg2925 + +lemma sg14556 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg2925 sg2840 + +lemma sg14557 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3648 + +lemma sg14558 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3648 + +lemma sg14559 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2843 + +lemma sg14560 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg2925 sg2844 + +lemma sg14561 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2845 + +lemma sg14562 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg2925 sg2846 + +lemma sg14563 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg2769 sg3004 + +lemma sg14564 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2847 + +lemma sg14565 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2394 sg3502 + +lemma sg14566 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg3000 sg2772 + +lemma sg14567 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg2925 sg2848 + +lemma sg14568 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg3001 sg2772 + +lemma sg14569 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1698 sg4539 + +lemma sg14570 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1518 sg4928 + +lemma sg14571 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2395 sg3502 + +lemma sg14572 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg2390 sg3505 + +lemma sg14573 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg2314 sg3648 + +lemma sg14574 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2849 + +lemma sg14575 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2662 sg3128 + +lemma sg14576 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2212 sg3709 + +lemma sg14577 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg3003 sg2772 + +lemma sg14578 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg3004 sg2772 + +lemma sg14579 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3005 sg2772 + +lemma sg14580 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg2925 sg2853 + +lemma sg14581 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3649 + +lemma sg14582 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg2393 sg3505 + +lemma sg14583 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2] := by + exact rowSquare_join (by decide) sg3007 sg2772 + +lemma sg14584 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1735 sg4526 + +lemma sg14585 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5] := by + exact rowSquare_join (by decide) sg2432 sg3420 + +lemma sg14586 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2854 + +lemma sg14587 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg2925 sg2855 + +lemma sg14588 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg3001 sg2774 + +lemma sg14589 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2856 + +lemma sg14590 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2925 sg2857 + +lemma sg14591 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg3001 sg2775 + +lemma sg14592 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg2838 sg2930 + +lemma sg14593 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg2925 sg2858 + +lemma sg14594 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg3012 sg2772 + +lemma sg14595 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2860 + +lemma sg14596 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg2925 sg2861 + +lemma sg14597 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg3001 sg2778 + +lemma sg14598 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2842 sg2930 + +lemma sg14599 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2862 + +lemma sg14600 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2326 sg3648 + +lemma sg14601 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg2844 sg2930 + +lemma sg14602 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2863 + +lemma sg14603 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg2925 sg2864 + +lemma sg14604 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg2925 sg2865 + +lemma sg14605 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg3001 sg2782 + +lemma sg14606 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2216 sg3720 + +lemma sg14607 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3020 sg2776 + +lemma sg14608 : RowSquare [4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2866 + +lemma sg14609 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg2925 sg2799 + +lemma sg14610 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2801 + +lemma sg14611 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg2925 sg2802 + +lemma sg14612 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg5792 + +lemma sg14613 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg2925 sg2805 + +lemma sg14614 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg2925 sg2806 + +lemma sg14615 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg2925 sg2807 + +lemma sg14616 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg1033 sg5772 + +lemma sg14617 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2809 + +lemma sg14618 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2811 + +lemma sg14619 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg2925 sg2818 + +lemma sg14620 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg2925 sg2819 + +lemma sg14621 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg2928 sg2802 + +lemma sg14622 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg2925 sg2820 + +lemma sg14623 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg1032 sg5773 + +lemma sg14624 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3005 sg2762 + +lemma sg14625 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3005 sg2763 + +lemma sg14626 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2798 sg2941 + +lemma sg14627 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg2925 sg2821 + +lemma sg14628 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3644 + +lemma sg14629 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2798 sg2942 + +lemma sg14630 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg2925 sg2822 + +lemma sg14631 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg2762 sg3009 + +lemma sg14632 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg2928 sg2805 + +lemma sg14633 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,3] := by + exact rowSquare_join (by decide) sg1032 sg5774 + +lemma sg14634 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg2405 sg3420 + +lemma sg14635 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3645 + +lemma sg14636 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg2928 sg2806 + +lemma sg14637 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg2928 sg2807 + +lemma sg14638 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5] := by + exact rowSquare_join (by decide) sg2407 sg3420 + +lemma sg14639 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg2395 sg3500 + +lemma sg14640 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4] := by + exact rowSquare_join (by decide) sg1033 sg5775 + +lemma sg14641 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg2824 + +lemma sg14642 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg850 sg5793 + +lemma sg14643 : RowSquare [4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2831 sg2925 + +lemma sg14644 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg2925 sg2615 + +lemma sg14645 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1] [5,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg2111 sg3702 + +lemma sg14646 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1] [6,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg2111 sg3704 + +lemma sg14647 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3622 + +lemma sg14648 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg2311 sg3622 + +lemma sg14649 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1289 sg4997 + +lemma sg14650 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2902 sg2810 + +lemma sg14651 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg2314 sg3620 + +lemma sg14652 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg2314 sg3622 + +lemma sg14653 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg3004 sg2746 + +lemma sg14654 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg3004 sg2747 + +lemma sg14655 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg3004 sg2748 + +lemma sg14656 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2173 sg3699 + +lemma sg14657 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2341 sg3563 + +lemma sg14658 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg2821 + +lemma sg14659 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2798 sg2922 + +lemma sg14660 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg2341 sg3564 + +lemma sg14661 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg2311 sg3629 + +lemma sg14662 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg2405 sg3411 + +lemma sg14663 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2] := by + exact rowSquare_join (by decide) sg3007 sg2747 + +lemma sg14664 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg2310 sg3630 + +lemma sg14665 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5] := by + exact rowSquare_join (by decide) sg2407 sg3411 + +lemma sg14666 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg1686 sg4539 + +lemma sg14667 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2] := by + exact rowSquare_join (by decide) sg3008 sg2748 + +lemma sg14668 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2326 sg3614 + +lemma sg14669 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2902 sg2823 + +lemma sg14670 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2903 sg2808 + +lemma sg14671 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2903 sg2810 + +lemma sg14672 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2663 sg3110 + +lemma sg14673 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg2826 + +lemma sg14674 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2663 sg3111 + +lemma sg14675 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2370 sg3508 + +lemma sg14676 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2902 sg2831 + +lemma sg14677 : RowSquare [5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2808 sg2909 + +lemma sg14678 : RowSquare [5,4,3,3,2,2,2,2,2,2,1] [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2250 sg3299 + +lemma sg14679 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1] [7,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg3004 sg2651 + +lemma sg14680 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1931 sg3998 + +lemma sg14681 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1934 sg3998 + +lemma sg14682 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [6,5,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1930 sg3999 + +lemma sg14683 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [6,5,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1931 sg3999 + +lemma sg14684 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1935 sg3998 + +lemma sg14685 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1936 sg3998 + +lemma sg14686 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1937 sg3998 + +lemma sg14687 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1938 sg3998 + +lemma sg14688 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1939 sg3998 + +lemma sg14689 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1940 sg3998 + +lemma sg14690 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1941 sg3998 + +lemma sg14691 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1942 sg3998 + +lemma sg14692 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1935 sg3999 + +lemma sg14693 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1936 sg3999 + +lemma sg14694 : RowSquare [5,5,2,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1943 sg3998 + +lemma sg14695 : RowSquare [5,5,3,2,2,2,2,2,2,2,1] [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1854 sg3998 + +lemma sg14696 : RowSquare [5,5,3,2,2,2,2,2,2,2,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1488 sg4832 + +lemma sg14697 : RowSquare [5,5,3,2,2,2,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1867 sg3998 + +lemma sg14698 : RowSquare [5,5,3,3,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1476 sg4832 + +lemma sg14699 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2144 sg3614 + +lemma sg14700 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1] [5,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg2141 sg3620 + +lemma sg14701 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2144 sg3615 + +lemma sg14702 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1] [6,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg2144 sg3620 + +lemma sg14703 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1] [7,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg2746 sg2651 + +lemma sg14704 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1] [8,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg2752 sg2651 + +lemma sg14705 : RowSquare [6,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg4508 + +lemma sg14706 : RowSquare [6,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1757 sg4506 + +lemma sg14707 : RowSquare [6,4,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg1757 sg4508 + +lemma sg14708 : RowSquare [6,5,2,2,2,2,2,2,2,2,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg996 sg5672 + +lemma sg14709 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg1757 sg4493 + +lemma sg14710 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg1765 sg4488 + +lemma sg14711 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg1757 sg4496 + +lemma sg14712 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2] := by + exact rowSquare_join (by decide) sg1000 sg5771 + +lemma sg14713 : RowSquare [6,5,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg2721 sg2921 + +lemma sg14714 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg991 sg5672 + +lemma sg14715 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg663 sg6457 + +lemma sg14716 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg992 sg5672 + +lemma sg14717 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg664 sg6457 + +lemma sg14718 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg666 sg6457 + +lemma sg14719 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg993 sg5672 + +lemma sg14720 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg667 sg6457 + +lemma sg14721 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg994 sg5672 + +lemma sg14722 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg668 sg6457 + +lemma sg14723 : RowSquare [6,5,3,2,2,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg669 sg6457 + +lemma sg14724 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg14310 + +lemma sg14725 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1] [5,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg1688 sg4377 + +lemma sg14726 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1] [5,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg1688 sg4378 + +lemma sg14727 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg2273 sg3578 + +lemma sg14728 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2887 sg2736 + +lemma sg14729 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1330 sg4983 + +lemma sg14730 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1330 sg4984 + +lemma sg14731 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg2277 sg3576 + +lemma sg14732 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2] := by + exact rowSquare_join (by decide) sg1332 sg4984 + +lemma sg14733 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2273 sg3581 + +lemma sg14734 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2725 sg2891 + +lemma sg14735 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg2278 sg3578 + +lemma sg14736 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2273 sg3589 + +lemma sg14737 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,2] := by + exact rowSquare_join (by decide) sg1762 sg4466 + +lemma sg14738 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2889 sg2736 + +lemma sg14739 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2892 sg2726 + +lemma sg14740 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2888 sg2737 + +lemma sg14741 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2726 sg2893 + +lemma sg14742 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2889 sg2737 + +lemma sg14743 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2] := by + exact rowSquare_join (by decide) sg2891 sg2737 + +lemma sg14744 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2] := by + exact rowSquare_join (by decide) sg2278 sg3589 + +lemma sg14745 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg2892 sg2734 + +lemma sg14746 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1] := by + exact rowSquare_join (by decide) sg2891 sg2738 + +lemma sg14747 : RowSquare [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,2] := by + exact rowSquare_join (by decide) sg2891 sg2740 + +lemma sg14748 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg408 sg7813 + +lemma sg14749 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg409 sg7813 + +lemma sg14750 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg410 sg7813 + +lemma sg14751 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg7829 + +lemma sg14752 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [7,7,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg7830 + +lemma sg14753 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg411 sg7813 + +lemma sg14754 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg412 sg7813 + +lemma sg14755 : RowSquare [6,6,2,2,2,2,2,2,2,1,1] [8,7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg7847 + +lemma sg14756 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg1758 sg4438 + +lemma sg14757 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg1332 sg4949 + +lemma sg14758 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1873 sg4379 + +lemma sg14759 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg1332 sg4956 + +lemma sg14760 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg3107 sg2633 + +lemma sg14761 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg1873 sg4384 + +lemma sg14762 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg2633 sg3109 + +lemma sg14763 : RowSquare [6,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg2640 sg3108 + +lemma sg14764 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg3617 + +lemma sg14765 : RowSquare [7,5,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg3620 + +lemma sg14766 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1754 sg4163 + +lemma sg14767 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2626 sg2707 + +lemma sg14768 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1754 sg4164 + +lemma sg14769 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2626 sg2708 + +lemma sg14770 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg4167 + +lemma sg14771 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2627 sg2703 + +lemma sg14772 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg2710 sg2640 + +lemma sg14773 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg74 sg11060 + +lemma sg14774 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1] [8,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg391 sg7997 + +lemma sg14775 : RowSquare [7,7,2,2,1,1,1,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2702 sg2702 + +lemma sg14776 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1] [6,6,6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg3351 + +lemma sg14777 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2251 sg3311 + +lemma sg14778 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2251 sg3312 + +lemma sg14779 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg3313 + +lemma sg14780 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg3314 + +lemma sg14781 : RowSquare [8,7,1,1,1,1,1,1,1,1,1,1,1,1,1] [3,3,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2251 sg3523 + +lemma sg14782 : RowSquare [8,7,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2705 sg2619 + +lemma sg14783 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2879 sg2546 + +lemma sg14784 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2073 sg3522 + +lemma sg14785 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2252 sg3259 + +lemma sg14786 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2074 sg3522 + +lemma sg14787 : RowSquare [8,8,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2115 sg3524 + +lemma sg14788 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2566 sg2573 + +lemma sg14789 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2566 sg2572 + +lemma sg14790 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2566 sg2571 + +lemma sg14791 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2566 sg2570 + +lemma sg14792 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2566 sg2569 + +lemma sg14793 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2566 sg2568 + +lemma sg14794 : RowSquare [8,8,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2566 sg2566 + +lemma sg14795 : RowSquare [8,8,2,2,2,2,2,2] [3,3,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2563 sg2563 + +lemma sg14796 : RowSquare [8,8,2,2,2,2,2,2] [4,4,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2562 sg2565 + +lemma sg14797 : RowSquare [8,8,2,2,2,2,2,2] [4,4,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2559 sg2567 + +lemma sg14798 : RowSquare [8,8,2,2,2,2,2,2] [4,4,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2562 sg2562 + +lemma sg14799 : RowSquare [8,8,2,2,2,2,2,2] [4,4,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg2559 sg2562 + +lemma sg14800 : RowSquare [8,8,2,2,2,2,2,2] [5,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2554 sg2562 + +lemma sg14801 : RowSquare [8,8,2,2,2,2,2,2] [5,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2554 sg2559 + +lemma sg14802 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1147 sg4930 + +lemma sg14803 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1] [5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg737 sg5757 + +lemma sg14804 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1] [5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg739 sg5757 + +lemma sg14805 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg740 sg5757 + +lemma sg14806 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg741 sg5757 + +lemma sg14807 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg748 sg5757 + +lemma sg14808 : RowSquare [9,7,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2595 sg2527 + +lemma sg14809 : RowSquare [9,7,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2595 sg2526 + +lemma sg14810 : RowSquare [9,7,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2595 sg2525 + +lemma sg14811 : RowSquare [9,7,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2595 sg2524 + +lemma sg14812 : RowSquare [11,4,2,2,2,2,2,2,1] [6,6,6,5,5] := by + exact rowSquare_join (by decide) sg879 sg5380 + +lemma sg14813 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg2925 sg3362 + +lemma sg14814 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2759 sg3420 + +lemma sg14815 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg2926 sg3362 + +lemma sg14816 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1] [6,6,6,6,5] := by + exact rowSquare_join (by decide) sg1033 sg6490 + +lemma sg14817 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg2929 sg3362 + +lemma sg14818 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg2930 sg3362 + +lemma sg14819 : RowSquare [5,4,3,3,2,2,2,2,2,2,1,1] [4,4,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2596 sg3520 + +lemma sg14820 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2137 sg4539 + +lemma sg14821 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3505 + +lemma sg14822 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg1891 sg4923 + +lemma sg14823 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg1891 sg4924 + +lemma sg14824 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1736 sg4992 + +lemma sg14825 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2213 sg4442 + +lemma sg14826 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg1688 sg5005 + +lemma sg14827 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2663 sg3686 + +lemma sg14828 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2663 sg3688 + +lemma sg14829 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2902 sg3509 + +lemma sg14830 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2903 sg3506 + +lemma sg14831 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3510 + +lemma sg14832 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2902 sg3511 + +lemma sg14833 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2903 sg3507 + +lemma sg14834 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2842 sg3563 + +lemma sg14835 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2903 sg3508 + +lemma sg14836 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2663 sg3693 + +lemma sg14837 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2903 sg3509 + +lemma sg14838 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2903 sg3511 + +lemma sg14839 : RowSquare [5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2663 sg3700 + +lemma sg14840 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,3,2] := by + exact rowSquare_join (by decide) sg2925 sg3475 + +lemma sg14841 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg1688 sg5002 + +lemma sg14842 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg2925 sg3476 + +lemma sg14843 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg1688 sg5003 + +lemma sg14844 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg1688 sg5004 + +lemma sg14845 : RowSquare [5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2288 sg4410 + +lemma sg14846 : RowSquare [5,4,4,3,2,2,2,2,2,2,1] [5,5,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2107 sg4343 + +lemma sg14847 : RowSquare [5,4,4,3,2,2,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1871 sg4804 + +lemma sg14848 : RowSquare [5,4,4,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3362 + +lemma sg14849 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1928 sg4832 + +lemma sg14850 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1929 sg4832 + +lemma sg14851 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1930 sg4832 + +lemma sg14852 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1931 sg4832 + +lemma sg14853 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [6,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1932 sg4832 + +lemma sg14854 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1933 sg4832 + +lemma sg14855 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1934 sg4832 + +lemma sg14856 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1935 sg4832 + +lemma sg14857 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1936 sg4832 + +lemma sg14858 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1937 sg4832 + +lemma sg14859 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1938 sg4832 + +lemma sg14860 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1939 sg4832 + +lemma sg14861 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1940 sg4832 + +lemma sg14862 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1941 sg4832 + +lemma sg14863 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1942 sg4832 + +lemma sg14864 : RowSquare [5,5,3,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1943 sg4832 + +lemma sg14865 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2746 sg3614 + +lemma sg14866 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1875 sg4919 + +lemma sg14867 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2750 sg3614 + +lemma sg14868 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1876 sg4920 + +lemma sg14869 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2902 sg3477 + +lemma sg14870 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3478 + +lemma sg14871 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2904 sg3470 + +lemma sg14872 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2752 sg3614 + +lemma sg14873 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2743 sg3615 + +lemma sg14874 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2753 sg3614 + +lemma sg14875 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1499 sg5754 + +lemma sg14876 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2902 sg3479 + +lemma sg14877 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1874 sg4925 + +lemma sg14878 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2371 sg4317 + +lemma sg14879 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2741 sg3616 + +lemma sg14880 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2903 sg3472 + +lemma sg14881 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3480 + +lemma sg14882 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2904 sg3471 + +lemma sg14883 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3481 + +lemma sg14884 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg2904 sg3472 + +lemma sg14885 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2746 sg3615 + +lemma sg14886 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg2743 sg3617 + +lemma sg14887 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2957 sg3409 + +lemma sg14888 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2743 sg3618 + +lemma sg14889 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1876 sg4921 + +lemma sg14890 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2372 sg4317 + +lemma sg14891 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2903 sg3474 + +lemma sg14892 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3482 + +lemma sg14893 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg2904 sg3473 + +lemma sg14894 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2904 sg3474 + +lemma sg14895 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg2743 sg3619 + +lemma sg14896 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg2743 sg3620 + +lemma sg14897 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg2167 sg4488 + +lemma sg14898 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2904 sg3476 + +lemma sg14899 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg2743 sg3622 + +lemma sg14900 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg2167 sg4489 + +lemma sg14901 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2291 sg4403 + +lemma sg14902 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg998 sg6501 + +lemma sg14903 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2744 sg3616 + +lemma sg14904 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2905 sg3472 + +lemma sg14905 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2746 sg3616 + +lemma sg14906 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3483 + +lemma sg14907 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2958 sg3409 + +lemma sg14908 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3484 + +lemma sg14909 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2140 sg4533 + +lemma sg14910 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2905 sg3474 + +lemma sg14911 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2371 sg4318 + +lemma sg14912 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg975 sg6508 + +lemma sg14913 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3485 + +lemma sg14914 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg2907 sg3471 + +lemma sg14915 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg2906 sg3473 + +lemma sg14916 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg2906 sg3474 + +lemma sg14917 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg2746 sg3620 + +lemma sg14918 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg2906 sg3476 + +lemma sg14919 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg2746 sg3622 + +lemma sg14920 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3486 + +lemma sg14921 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2140 sg4534 + +lemma sg14922 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1878 sg4921 + +lemma sg14923 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg2141 sg4534 + +lemma sg14924 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2140 sg4535 + +lemma sg14925 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg2907 sg3473 + +lemma sg14926 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3] := by + exact rowSquare_join (by decide) sg2907 sg3474 + +lemma sg14927 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,1] := by + exact rowSquare_join (by decide) sg2907 sg3476 + +lemma sg14928 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1880 sg4919 + +lemma sg14929 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2757 sg3614 + +lemma sg14930 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1945 sg4889 + +lemma sg14931 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2902 sg3487 + +lemma sg14932 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2369 sg4322 + +lemma sg14933 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2376 sg4317 + +lemma sg14934 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3488 + +lemma sg14935 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3489 + +lemma sg14936 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2752 sg3615 + +lemma sg14937 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2902 sg3490 + +lemma sg14938 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2370 sg4322 + +lemma sg14939 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2958 sg3412 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes36.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes36.lean index b6c036dcb0b1958f1d4936f21168812f1f336442..21c7bbbfb4ae090bcde729a14e0b5b4484b6be45 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes36.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes36.lean @@ -1,1223 +1,1223 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes29 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes30 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes22 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes35 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes33 - -namespace OAI - -/-! Semigroup Nodes 36. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg14940 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2913 sg3470 - -lemma sg14941 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2371 sg4322 - -lemma sg14942 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3491 - -lemma sg14943 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3492 - -lemma sg14944 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3110 sg3358 - -lemma sg14945 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3493 - -lemma sg14946 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg2752 sg3620 - -lemma sg14947 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg2752 sg3622 - -lemma sg14948 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2741 sg3626 - -lemma sg14949 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2912 sg3472 - -lemma sg14950 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2905 sg3479 - -lemma sg14951 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2958 sg3413 - -lemma sg14952 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3494 - -lemma sg14953 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2904 sg3484 - -lemma sg14954 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3112 sg3358 - -lemma sg14955 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg2743 sg3627 - -lemma sg14956 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2904 sg3485 - -lemma sg14957 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg2743 sg3628 - -lemma sg14958 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg2746 sg3625 - -lemma sg14959 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,1] := by - exact rowSquare_join (by decide) sg2915 sg3476 - -lemma sg14960 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2968 sg3409 - -lemma sg14961 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3495 - -lemma sg14962 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg3113 sg3357 - -lemma sg14963 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg2743 sg3629 - -lemma sg14964 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg3113 sg3359 - -lemma sg14965 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5] := by - exact rowSquare_join (by decide) sg3114 sg3359 - -lemma sg14966 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2744 sg3626 - -lemma sg14967 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2746 sg3626 - -lemma sg14968 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2958 sg3414 - -lemma sg14969 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,3] := by - exact rowSquare_join (by decide) sg2746 sg3629 - -lemma sg14970 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2758 sg3614 - -lemma sg14971 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2902 sg3496 - -lemma sg14972 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3497 - -lemma sg14973 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2958 sg3416 - -lemma sg14974 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3498 - -lemma sg14975 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3499 - -lemma sg14976 : RowSquare [5,5,3,3,2,2,2,2,2,2,1] [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1854 sg4833 - -lemma sg14977 : RowSquare [5,5,3,3,2,2,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1867 sg4832 - -lemma sg14978 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg3359 - -lemma sg14979 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg2144 sg4488 - -lemma sg14980 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2904 sg3359 - -lemma sg14981 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg2743 sg3411 - -lemma sg14982 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg2144 sg4489 - -lemma sg14983 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [6,6,6,6,5] := by - exact rowSquare_join (by decide) sg13 sg12441 - -lemma sg14984 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1 sg14009 - -lemma sg14985 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg2752 sg3411 - -lemma sg14986 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg2745 sg3560 - -lemma sg14987 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg2743 sg3562 - -lemma sg14988 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg2167 sg4443 - -lemma sg14989 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg1687 sg4993 - -lemma sg14990 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg1688 sg4993 - -lemma sg14991 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg1688 sg4994 - -lemma sg14992 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1687 sg4995 - -lemma sg14993 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg1688 sg4995 - -lemma sg14994 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3] := by - exact rowSquare_join (by decide) sg1688 sg4996 - -lemma sg14995 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg2743 sg3567 - -lemma sg14996 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg2167 sg4446 - -lemma sg14997 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2605 sg3691 - -lemma sg14998 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg2606 sg3691 - -lemma sg14999 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg1688 sg4968 - -lemma sg15000 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,5] := by - exact rowSquare_join (by decide) sg2962 sg3337 - -lemma sg15001 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1 sg14027 - -lemma sg15002 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg2610 sg3691 - -lemma sg15003 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1] [6,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg1688 sg4899 - -lemma sg15004 : RowSquare [6,4,3,2,2,2,2,2,2,2,1,1] [4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1868 sg4862 - -lemma sg15005 : RowSquare [6,4,3,3,3,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1 sg14081 - -lemma sg15006 : RowSquare [6,4,3,3,3,2,1,1,1,1,1,1,1,1] [8,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg14679 - -lemma sg15007 : RowSquare [6,4,4,3,2,2,1,1,1,1,1,1,1,1] [10,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2 sg14028 - -lemma sg15008 : RowSquare [6,4,4,3,2,2,1,1,1,1,1,1,1,1] [10,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg9 sg12451 - -lemma sg15009 : RowSquare [6,4,4,3,2,2,1,1,1,1,1,1,1,1] [10,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2 sg14029 - -lemma sg15010 : RowSquare [6,4,4,3,2,2,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg12 sg12450 - -lemma sg15011 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1478 sg5672 - -lemma sg15012 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1480 sg5672 - -lemma sg15013 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1481 sg5672 - -lemma sg15014 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1482 sg5672 - -lemma sg15015 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1483 sg5672 - -lemma sg15016 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1485 sg5672 - -lemma sg15017 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1480 sg5673 - -lemma sg15018 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1487 sg5672 - -lemma sg15019 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1481 sg5673 - -lemma sg15020 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1482 sg5673 - -lemma sg15021 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1480 sg5674 - -lemma sg15022 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1488 sg5672 - -lemma sg15023 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1482 sg5674 - -lemma sg15024 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1489 sg5672 - -lemma sg15025 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1483 sg5673 - -lemma sg15026 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1490 sg5672 - -lemma sg15027 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1491 sg5672 - -lemma sg15028 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1484 sg5673 - -lemma sg15029 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1485 sg5673 - -lemma sg15030 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1492 sg5672 - -lemma sg15031 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1486 sg5673 - -lemma sg15032 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1487 sg5673 - -lemma sg15033 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1493 sg5672 - -lemma sg15034 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1488 sg5673 - -lemma sg15035 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,7,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1488 sg5674 - -lemma sg15036 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1494 sg5672 - -lemma sg15037 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1495 sg5672 - -lemma sg15038 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1489 sg5673 - -lemma sg15039 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1496 sg5672 - -lemma sg15040 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1490 sg5673 - -lemma sg15041 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1491 sg5673 - -lemma sg15042 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1497 sg5672 - -lemma sg15043 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1492 sg5673 - -lemma sg15044 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1493 sg5673 - -lemma sg15045 : RowSquare [6,5,3,2,2,2,2,2,2,2,1] [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1325 sg5672 - -lemma sg15046 : RowSquare [6,5,3,2,2,2,2,2,2,2,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg996 sg6457 - -lemma sg15047 : RowSquare [6,5,3,2,2,2,2,2,2,2,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1326 sg5672 - -lemma sg15048 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,4] := by - exact rowSquare_join (by decide) sg1688 sg4949 - -lemma sg15049 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1 sg14087 - -lemma sg15050 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1 sg14088 - -lemma sg15051 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1] [8,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg5 sg12832 - -lemma sg15052 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1] [9,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg6 sg12832 - -lemma sg15053 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1] [9,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg15 sg12449 - -lemma sg15054 : RowSquare [6,5,3,3,2,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg991 sg6457 - -lemma sg15055 : RowSquare [6,5,3,3,2,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg993 sg6457 - -lemma sg15056 : RowSquare [6,5,3,3,2,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg994 sg6457 - -lemma sg15057 : RowSquare [6,5,3,3,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg993 sg6458 - -lemma sg15058 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1] [7,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg2633 sg3415 - -lemma sg15059 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2720 sg3576 - -lemma sg15060 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2720 sg3578 - -lemma sg15061 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg2272 sg4412 - -lemma sg15062 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg2273 sg4412 - -lemma sg15063 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1756 sg4981 - -lemma sg15064 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1756 sg4982 - -lemma sg15065 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg2721 sg3576 - -lemma sg15066 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1758 sg4982 - -lemma sg15067 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg2721 sg3578 - -lemma sg15068 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1756 sg4983 - -lemma sg15069 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1756 sg4984 - -lemma sg15070 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1758 sg4983 - -lemma sg15071 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1757 sg4984 - -lemma sg15072 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg2722 sg3576 - -lemma sg15073 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg1758 sg4984 - -lemma sg15074 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,2,1] := by - exact rowSquare_join (by decide) sg2722 sg3578 - -lemma sg15075 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg2724 sg3576 - -lemma sg15076 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2] := by - exact rowSquare_join (by decide) sg2723 sg3578 - -lemma sg15077 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,1] := by - exact rowSquare_join (by decide) sg2724 sg3578 - -lemma sg15078 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg2726 sg3576 - -lemma sg15079 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg2726 sg3577 - -lemma sg15080 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg2726 sg3578 - -lemma sg15081 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2273 sg4413 - -lemma sg15082 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg2722 sg3581 - -lemma sg15083 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg1758 sg4985 - -lemma sg15084 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg2728 sg3578 - -lemma sg15085 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg2724 sg3581 - -lemma sg15086 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg2729 sg3576 - -lemma sg15087 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg2722 sg3584 - -lemma sg15088 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg2730 sg3576 - -lemma sg15089 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2] := by - exact rowSquare_join (by decide) sg1762 sg4984 - -lemma sg15090 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2] := by - exact rowSquare_join (by decide) sg2891 sg3457 - -lemma sg15091 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,1] := by - exact rowSquare_join (by decide) sg2891 sg3458 - -lemma sg15092 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg2732 sg3576 - -lemma sg15093 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg2722 sg3589 - -lemma sg15094 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg2733 sg3576 - -lemma sg15095 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2] := by - exact rowSquare_join (by decide) sg2723 sg3589 - -lemma sg15096 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,1] := by - exact rowSquare_join (by decide) sg2724 sg3589 - -lemma sg15097 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg2891 sg3459 - -lemma sg15098 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,2] := by - exact rowSquare_join (by decide) sg2891 sg3460 - -lemma sg15099 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,1] := by - exact rowSquare_join (by decide) sg2891 sg3461 - -lemma sg15100 : RowSquare [6,6,2,2,2,2,2,2,2,2,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg662 sg7812 - -lemma sg15101 : RowSquare [6,6,2,2,2,2,2,2,2,2,1] [5,5,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg658 sg7821 - -lemma sg15102 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg4949 - -lemma sg15103 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg1758 sg4948 - -lemma sg15104 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg1758 sg4949 - -lemma sg15105 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg2273 sg4375 - -lemma sg15106 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2888 sg3403 - -lemma sg15107 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1759 sg4949 - -lemma sg15108 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg2273 sg4376 - -lemma sg15109 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2632 sg3673 - -lemma sg15110 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2889 sg3403 - -lemma sg15111 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg2633 sg3674 - -lemma sg15112 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1760 sg4948 - -lemma sg15113 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2632 sg3675 - -lemma sg15114 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg2633 sg3675 - -lemma sg15115 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg1761 sg4947 - -lemma sg15116 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg1758 sg4952 - -lemma sg15117 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg2273 sg4378 - -lemma sg15118 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg2273 sg4379 - -lemma sg15119 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg1762 sg4949 - -lemma sg15120 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2633 sg3676 - -lemma sg15121 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2633 sg3677 - -lemma sg15122 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg2633 sg3678 - -lemma sg15123 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1763 sg4948 - -lemma sg15124 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2632 sg3679 - -lemma sg15125 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg2633 sg3679 - -lemma sg15126 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1330 sg5769 - -lemma sg15127 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1756 sg4956 - -lemma sg15128 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2274 sg4377 - -lemma sg15129 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg2274 sg4379 - -lemma sg15130 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1758 sg4955 - -lemma sg15131 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1758 sg4956 - -lemma sg15132 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,3] := by - exact rowSquare_join (by decide) sg1765 sg4949 - -lemma sg15133 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1758 sg4958 - -lemma sg15134 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg1332 sg5770 - -lemma sg15135 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1766 sg4945 - -lemma sg15136 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3] := by - exact rowSquare_join (by decide) sg1766 sg4949 - -lemma sg15137 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg2636 sg3675 - -lemma sg15138 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg2368 sg4303 - -lemma sg15139 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg2892 sg3404 - -lemma sg15140 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg2368 sg4304 - -lemma sg15141 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2636 sg3679 - -lemma sg15142 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg2640 sg3675 - -lemma sg15143 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3] := by - exact rowSquare_join (by decide) sg2640 sg3679 - -lemma sg15144 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2896 sg3403 - -lemma sg15145 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg2633 sg3682 - -lemma sg15146 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg2635 sg3680 - -lemma sg15147 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2632 sg3683 - -lemma sg15148 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg2633 sg3683 - -lemma sg15149 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2899 sg3403 - -lemma sg15150 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg2633 sg3684 - -lemma sg15151 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2636 sg3681 - -lemma sg15152 : RowSquare [6,6,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg648 sg7813 - -lemma sg15153 : RowSquare [6,6,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg651 sg7813 - -lemma sg15154 : RowSquare [6,6,3,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg8782 - -lemma sg15155 : RowSquare [6,6,3,2,2,2,2,2,2,1,1] [8,8,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg8783 - -lemma sg15156 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1] [6,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg1618 sg4949 - -lemma sg15157 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1] [7,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg2644 sg3332 - -lemma sg15158 : RowSquare [7,5,3,3,3,2,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1682 sg4879 - -lemma sg15159 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2707 sg3579 - -lemma sg15160 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2707 sg3580 - -lemma sg15161 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2707 sg3584 - -lemma sg15162 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg2710 sg3576 - -lemma sg15163 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg3577 - -lemma sg15164 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2707 sg3586 - -lemma sg15165 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg2260 sg4412 - -lemma sg15166 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg2710 sg3578 - -lemma sg15167 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2707 sg3587 - -lemma sg15168 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2707 sg3589 - -lemma sg15169 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2707 sg3592 - -lemma sg15170 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2725 sg3534 - -lemma sg15171 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2707 sg3594 - -lemma sg15172 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2720 sg3537 - -lemma sg15173 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg2708 sg3594 - -lemma sg15174 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg2707 sg3595 - -lemma sg15175 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg2708 sg3595 - -lemma sg15176 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2707 sg3596 - -lemma sg15177 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg2727 sg3534 - -lemma sg15178 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2710 sg3580 - -lemma sg15179 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2708 sg3597 - -lemma sg15180 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg2881 sg3456 - -lemma sg15181 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg2708 sg3598 - -lemma sg15182 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2707 sg3599 - -lemma sg15183 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg2709 sg3581 - -lemma sg15184 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2708 sg3599 - -lemma sg15185 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg2710 sg3581 - -lemma sg15186 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2709 sg3582 - -lemma sg15187 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2708 sg3600 - -lemma sg15188 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg2708 sg3601 - -lemma sg15189 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg3583 - -lemma sg15190 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg2708 sg3602 - -lemma sg15191 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg2710 sg3584 - -lemma sg15192 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg3585 - -lemma sg15193 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg2881 sg3458 - -lemma sg15194 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2707 sg3603 - -lemma sg15195 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2710 sg3587 - -lemma sg15196 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2708 sg3603 - -lemma sg15197 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2708 sg3604 - -lemma sg15198 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg2708 sg3605 - -lemma sg15199 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg3588 - -lemma sg15200 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2707 sg3606 - -lemma sg15201 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg2708 sg3606 - -lemma sg15202 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2710 sg3589 - -lemma sg15203 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2708 sg3607 - -lemma sg15204 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg3590 - -lemma sg15205 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg3591 - -lemma sg15206 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg3593 - -lemma sg15207 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg2256 sg4414 - -lemma sg15208 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg2708 sg3608 - -lemma sg15209 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2708 sg3609 - -lemma sg15210 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg2710 sg3595 - -lemma sg15211 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg3598 - -lemma sg15212 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2710 sg3599 - -lemma sg15213 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg3604 - -lemma sg15214 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg3605 - -lemma sg15215 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg3608 - -lemma sg15216 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg3609 - -lemma sg15217 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3] := by - exact rowSquare_join (by decide) sg227 sg11060 - -lemma sg15218 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg424 sg8893 - -lemma sg15219 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3] := by - exact rowSquare_join (by decide) sg228 sg11060 - -lemma sg15220 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2710 sg3610 - -lemma sg15221 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg3611 - -lemma sg15222 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg3612 - -lemma sg15223 : RowSquare [7,6,2,2,2,2,2,2,2,1,1] [9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg217 sg10869 - -lemma sg15224 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg4377 - -lemma sg15225 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg4378 - -lemma sg15226 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg4388 - -lemma sg15227 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2366 sg4167 - -lemma sg15228 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg2367 sg4167 - -lemma sg15229 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1] [5,5,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg643 sg7995 - -lemma sg15230 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1] [6,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg643 sg7996 - -lemma sg15231 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1] [6,6,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg356 sg8893 - -lemma sg15232 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1] [7,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg643 sg7997 - -lemma sg15233 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1] [7,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg356 sg8894 - -lemma sg15234 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1] [8,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg645 sg7997 - -lemma sg15235 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2881 sg3316 - -lemma sg15236 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg1 sg14446 - -lemma sg15237 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1 sg14447 - -lemma sg15238 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2156 sg4167 - -lemma sg15239 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2879 sg3294 - -lemma sg15240 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg2710 sg3314 - -lemma sg15241 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2708 sg3317 - -lemma sg15242 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [7,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg74 sg11553 - -lemma sg15243 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [8,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg193 sg11058 - -lemma sg15244 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [9,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg391 sg8890 - -lemma sg15245 : RowSquare [7,7,3,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg12673 - -lemma sg15246 : RowSquare [7,7,3,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19 sg12674 - -lemma sg15247 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1332 sg5738 - -lemma sg15248 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg11549 - -lemma sg15249 : RowSquare [8,7,2,1,1,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2710 sg3522 - -lemma sg15250 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2879 sg3275 - -lemma sg15251 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2879 sg3260 - -lemma sg15252 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2588 sg3522 - -lemma sg15253 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg3263 - -lemma sg15254 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2074 sg4348 - -lemma sg15255 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1] [5,4,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg12597 - -lemma sg15256 : RowSquare [8,8,2,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2576 sg3522 - -lemma sg15257 : RowSquare [8,8,2,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2546 sg3522 - -lemma sg15258 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg12605 - -lemma sg15259 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2529 sg3522 - -lemma sg15260 : RowSquare [8,8,3,2,2,2,2,2] [2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2566 sg3239 - -lemma sg15261 : RowSquare [8,8,3,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2566 sg3238 - -lemma sg15262 : RowSquare [8,8,3,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2566 sg3237 - -lemma sg15263 : RowSquare [8,8,3,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2566 sg3236 - -lemma sg15264 : RowSquare [8,8,3,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2566 sg3235 - -lemma sg15265 : RowSquare [8,8,3,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2566 sg3234 - -lemma sg15266 : RowSquare [8,8,3,2,2,2,2,2] [4,4,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2562 sg3233 - -lemma sg15267 : RowSquare [9,7,2,2,2,1,1,1,1,1,1,1] [4,4,4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg3258 - -lemma sg15268 : RowSquare [9,7,2,2,2,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg14783 - -lemma sg15269 : RowSquare [9,7,2,2,2,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2252 sg3966 - -lemma sg15270 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg12615 - -lemma sg15271 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg11740 - -lemma sg15272 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg3953 - -lemma sg15273 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg11741 - -lemma sg15274 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg14784 - -lemma sg15275 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg75 sg11242 - -lemma sg15276 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg14786 - -lemma sg15277 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg165 sg9442 - -lemma sg15278 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg165 sg9444 - -lemma sg15279 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg451 sg7998 - -lemma sg15280 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg452 sg7998 - -lemma sg15281 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg453 sg7998 - -lemma sg15282 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [9,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg452 sg7999 - -lemma sg15283 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2699 sg3258 - -lemma sg15284 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2700 sg3258 - -lemma sg15285 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg11484 - -lemma sg15286 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg11485 - -lemma sg15287 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg168 sg10594 - -lemma sg15288 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg165 sg10595 - -lemma sg15289 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg165 sg10596 - -lemma sg15290 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg75 sg11485 - -lemma sg15291 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg11491 - -lemma sg15292 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg722 sg6502 - -lemma sg15293 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg430 sg8008 - -lemma sg15294 : RowSquare [12,3,2,2,2,2,2,2,1,1] [4,4,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg11484 - -lemma sg15295 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg2925 sg4331 - -lemma sg15296 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg3634 sg3418 - -lemma sg15297 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg4335 - -lemma sg15298 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg3636 sg3420 - -lemma sg15299 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2] := by - exact rowSquare_join (by decide) sg3724 sg3338 - -lemma sg15300 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg2656 sg4501 - -lemma sg15301 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3] := by - exact rowSquare_join (by decide) sg1032 sg8003 - -lemma sg15302 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,2] := by - exact rowSquare_join (by decide) sg1032 sg8004 - -lemma sg15303 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1] := by - exact rowSquare_join (by decide) sg1032 sg8005 - -lemma sg15304 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by - exact rowSquare_join (by decide) sg1033 sg8005 - -lemma sg15305 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg3633 sg3421 - -lemma sg15306 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg3633 sg3422 - -lemma sg15307 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg3635 sg3421 - -lemma sg15308 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3423 - -lemma sg15309 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3633 sg3424 - -lemma sg15310 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg3421 sg3636 - -lemma sg15311 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg3701 sg3365 - -lemma sg15312 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3425 - -lemma sg15313 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3426 - -lemma sg15314 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3427 - -lemma sg15315 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg2930 sg4328 - -lemma sg15316 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg3638 sg3420 - -lemma sg15317 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg2930 sg4329 - -lemma sg15318 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg3635 sg3422 - -lemma sg15319 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2614 sg4521 - -lemma sg15320 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3428 - -lemma sg15321 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3635 sg3424 - -lemma sg15322 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg3701 sg3367 - -lemma sg15323 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg3636 sg3422 - -lemma sg15324 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2614 sg4522 - -lemma sg15325 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3429 - -lemma sg15326 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3430 - -lemma sg15327 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg3360 sg3704 - -lemma sg15328 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2614 sg4523 - -lemma sg15329 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3431 - -lemma sg15330 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3427 - -lemma sg15331 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,3] := by - exact rowSquare_join (by decide) sg3704 sg3361 - -lemma sg15332 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg3704 sg3362 - -lemma sg15333 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3636 sg3424 - -lemma sg15334 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3432 - -lemma sg15335 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2614 sg4524 - -lemma sg15336 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3433 - -lemma sg15337 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3640 sg3420 - -lemma sg15338 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,3] := by - exact rowSquare_join (by decide) sg3360 sg3705 - -lemma sg15339 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2614 sg4525 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes29 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes30 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes22 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes35 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes33 + +namespace OAI + +/-! Semigroup Nodes 36. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg14940 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2913 sg3470 + +lemma sg14941 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2371 sg4322 + +lemma sg14942 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3491 + +lemma sg14943 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3492 + +lemma sg14944 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3110 sg3358 + +lemma sg14945 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3493 + +lemma sg14946 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg2752 sg3620 + +lemma sg14947 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg2752 sg3622 + +lemma sg14948 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2741 sg3626 + +lemma sg14949 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2912 sg3472 + +lemma sg14950 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2905 sg3479 + +lemma sg14951 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2958 sg3413 + +lemma sg14952 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3494 + +lemma sg14953 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2904 sg3484 + +lemma sg14954 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3112 sg3358 + +lemma sg14955 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg2743 sg3627 + +lemma sg14956 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2904 sg3485 + +lemma sg14957 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg2743 sg3628 + +lemma sg14958 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg2746 sg3625 + +lemma sg14959 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,1] := by + exact rowSquare_join (by decide) sg2915 sg3476 + +lemma sg14960 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2968 sg3409 + +lemma sg14961 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3495 + +lemma sg14962 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg3113 sg3357 + +lemma sg14963 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg2743 sg3629 + +lemma sg14964 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg3113 sg3359 + +lemma sg14965 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5] := by + exact rowSquare_join (by decide) sg3114 sg3359 + +lemma sg14966 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2744 sg3626 + +lemma sg14967 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2746 sg3626 + +lemma sg14968 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2958 sg3414 + +lemma sg14969 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,3] := by + exact rowSquare_join (by decide) sg2746 sg3629 + +lemma sg14970 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2758 sg3614 + +lemma sg14971 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2902 sg3496 + +lemma sg14972 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3497 + +lemma sg14973 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2958 sg3416 + +lemma sg14974 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3498 + +lemma sg14975 : RowSquare [5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3499 + +lemma sg14976 : RowSquare [5,5,3,3,2,2,2,2,2,2,1] [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1854 sg4833 + +lemma sg14977 : RowSquare [5,5,3,3,2,2,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1867 sg4832 + +lemma sg14978 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg3359 + +lemma sg14979 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg2144 sg4488 + +lemma sg14980 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2904 sg3359 + +lemma sg14981 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg2743 sg3411 + +lemma sg14982 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg2144 sg4489 + +lemma sg14983 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [6,6,6,6,5] := by + exact rowSquare_join (by decide) sg13 sg12441 + +lemma sg14984 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1 sg14009 + +lemma sg14985 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg2752 sg3411 + +lemma sg14986 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg2745 sg3560 + +lemma sg14987 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg2743 sg3562 + +lemma sg14988 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg2167 sg4443 + +lemma sg14989 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg1687 sg4993 + +lemma sg14990 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg1688 sg4993 + +lemma sg14991 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg1688 sg4994 + +lemma sg14992 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1687 sg4995 + +lemma sg14993 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg1688 sg4995 + +lemma sg14994 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3] := by + exact rowSquare_join (by decide) sg1688 sg4996 + +lemma sg14995 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg2743 sg3567 + +lemma sg14996 : RowSquare [5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg2167 sg4446 + +lemma sg14997 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2605 sg3691 + +lemma sg14998 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg2606 sg3691 + +lemma sg14999 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg1688 sg4968 + +lemma sg15000 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,5] := by + exact rowSquare_join (by decide) sg2962 sg3337 + +lemma sg15001 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1 sg14027 + +lemma sg15002 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg2610 sg3691 + +lemma sg15003 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1] [6,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg1688 sg4899 + +lemma sg15004 : RowSquare [6,4,3,2,2,2,2,2,2,2,1,1] [4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1868 sg4862 + +lemma sg15005 : RowSquare [6,4,3,3,3,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1 sg14081 + +lemma sg15006 : RowSquare [6,4,3,3,3,2,1,1,1,1,1,1,1,1] [8,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg14679 + +lemma sg15007 : RowSquare [6,4,4,3,2,2,1,1,1,1,1,1,1,1] [10,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2 sg14028 + +lemma sg15008 : RowSquare [6,4,4,3,2,2,1,1,1,1,1,1,1,1] [10,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg9 sg12451 + +lemma sg15009 : RowSquare [6,4,4,3,2,2,1,1,1,1,1,1,1,1] [10,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2 sg14029 + +lemma sg15010 : RowSquare [6,4,4,3,2,2,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg12 sg12450 + +lemma sg15011 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1478 sg5672 + +lemma sg15012 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1480 sg5672 + +lemma sg15013 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1481 sg5672 + +lemma sg15014 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1482 sg5672 + +lemma sg15015 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1483 sg5672 + +lemma sg15016 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1485 sg5672 + +lemma sg15017 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1480 sg5673 + +lemma sg15018 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1487 sg5672 + +lemma sg15019 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1481 sg5673 + +lemma sg15020 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1482 sg5673 + +lemma sg15021 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1480 sg5674 + +lemma sg15022 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1488 sg5672 + +lemma sg15023 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1482 sg5674 + +lemma sg15024 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1489 sg5672 + +lemma sg15025 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1483 sg5673 + +lemma sg15026 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1490 sg5672 + +lemma sg15027 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1491 sg5672 + +lemma sg15028 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1484 sg5673 + +lemma sg15029 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1485 sg5673 + +lemma sg15030 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1492 sg5672 + +lemma sg15031 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1486 sg5673 + +lemma sg15032 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1487 sg5673 + +lemma sg15033 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1493 sg5672 + +lemma sg15034 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1488 sg5673 + +lemma sg15035 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [7,7,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1488 sg5674 + +lemma sg15036 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1494 sg5672 + +lemma sg15037 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1495 sg5672 + +lemma sg15038 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1489 sg5673 + +lemma sg15039 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1496 sg5672 + +lemma sg15040 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1490 sg5673 + +lemma sg15041 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1491 sg5673 + +lemma sg15042 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1497 sg5672 + +lemma sg15043 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1492 sg5673 + +lemma sg15044 : RowSquare [6,5,2,2,2,2,2,2,2,2,1,1] [8,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1493 sg5673 + +lemma sg15045 : RowSquare [6,5,3,2,2,2,2,2,2,2,1] [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1325 sg5672 + +lemma sg15046 : RowSquare [6,5,3,2,2,2,2,2,2,2,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg996 sg6457 + +lemma sg15047 : RowSquare [6,5,3,2,2,2,2,2,2,2,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1326 sg5672 + +lemma sg15048 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,4] := by + exact rowSquare_join (by decide) sg1688 sg4949 + +lemma sg15049 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1 sg14087 + +lemma sg15050 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1 sg14088 + +lemma sg15051 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1] [8,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg5 sg12832 + +lemma sg15052 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1] [9,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg6 sg12832 + +lemma sg15053 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1] [9,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg15 sg12449 + +lemma sg15054 : RowSquare [6,5,3,3,2,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg991 sg6457 + +lemma sg15055 : RowSquare [6,5,3,3,2,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg993 sg6457 + +lemma sg15056 : RowSquare [6,5,3,3,2,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg994 sg6457 + +lemma sg15057 : RowSquare [6,5,3,3,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg993 sg6458 + +lemma sg15058 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1] [7,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg2633 sg3415 + +lemma sg15059 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2720 sg3576 + +lemma sg15060 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2720 sg3578 + +lemma sg15061 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg2272 sg4412 + +lemma sg15062 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg2273 sg4412 + +lemma sg15063 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1756 sg4981 + +lemma sg15064 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1756 sg4982 + +lemma sg15065 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg2721 sg3576 + +lemma sg15066 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1758 sg4982 + +lemma sg15067 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg2721 sg3578 + +lemma sg15068 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1756 sg4983 + +lemma sg15069 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1756 sg4984 + +lemma sg15070 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1758 sg4983 + +lemma sg15071 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1757 sg4984 + +lemma sg15072 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg2722 sg3576 + +lemma sg15073 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg1758 sg4984 + +lemma sg15074 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,2,1] := by + exact rowSquare_join (by decide) sg2722 sg3578 + +lemma sg15075 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg2724 sg3576 + +lemma sg15076 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2] := by + exact rowSquare_join (by decide) sg2723 sg3578 + +lemma sg15077 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,1] := by + exact rowSquare_join (by decide) sg2724 sg3578 + +lemma sg15078 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg2726 sg3576 + +lemma sg15079 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg2726 sg3577 + +lemma sg15080 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg2726 sg3578 + +lemma sg15081 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2273 sg4413 + +lemma sg15082 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg2722 sg3581 + +lemma sg15083 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg1758 sg4985 + +lemma sg15084 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg2728 sg3578 + +lemma sg15085 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg2724 sg3581 + +lemma sg15086 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg2729 sg3576 + +lemma sg15087 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg2722 sg3584 + +lemma sg15088 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg2730 sg3576 + +lemma sg15089 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2] := by + exact rowSquare_join (by decide) sg1762 sg4984 + +lemma sg15090 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2] := by + exact rowSquare_join (by decide) sg2891 sg3457 + +lemma sg15091 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,1] := by + exact rowSquare_join (by decide) sg2891 sg3458 + +lemma sg15092 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg2732 sg3576 + +lemma sg15093 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg2722 sg3589 + +lemma sg15094 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg2733 sg3576 + +lemma sg15095 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2] := by + exact rowSquare_join (by decide) sg2723 sg3589 + +lemma sg15096 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,1] := by + exact rowSquare_join (by decide) sg2724 sg3589 + +lemma sg15097 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg2891 sg3459 + +lemma sg15098 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,2] := by + exact rowSquare_join (by decide) sg2891 sg3460 + +lemma sg15099 : RowSquare [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,1] := by + exact rowSquare_join (by decide) sg2891 sg3461 + +lemma sg15100 : RowSquare [6,6,2,2,2,2,2,2,2,2,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg662 sg7812 + +lemma sg15101 : RowSquare [6,6,2,2,2,2,2,2,2,2,1] [5,5,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg658 sg7821 + +lemma sg15102 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg4949 + +lemma sg15103 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg1758 sg4948 + +lemma sg15104 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg1758 sg4949 + +lemma sg15105 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg2273 sg4375 + +lemma sg15106 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2888 sg3403 + +lemma sg15107 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1759 sg4949 + +lemma sg15108 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg2273 sg4376 + +lemma sg15109 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2632 sg3673 + +lemma sg15110 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2889 sg3403 + +lemma sg15111 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg2633 sg3674 + +lemma sg15112 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1760 sg4948 + +lemma sg15113 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2632 sg3675 + +lemma sg15114 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg2633 sg3675 + +lemma sg15115 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg1761 sg4947 + +lemma sg15116 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg1758 sg4952 + +lemma sg15117 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg2273 sg4378 + +lemma sg15118 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg2273 sg4379 + +lemma sg15119 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg1762 sg4949 + +lemma sg15120 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2633 sg3676 + +lemma sg15121 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2633 sg3677 + +lemma sg15122 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg2633 sg3678 + +lemma sg15123 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1763 sg4948 + +lemma sg15124 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2632 sg3679 + +lemma sg15125 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg2633 sg3679 + +lemma sg15126 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1330 sg5769 + +lemma sg15127 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1756 sg4956 + +lemma sg15128 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2274 sg4377 + +lemma sg15129 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg2274 sg4379 + +lemma sg15130 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1758 sg4955 + +lemma sg15131 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1758 sg4956 + +lemma sg15132 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,3] := by + exact rowSquare_join (by decide) sg1765 sg4949 + +lemma sg15133 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1758 sg4958 + +lemma sg15134 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg1332 sg5770 + +lemma sg15135 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1766 sg4945 + +lemma sg15136 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3] := by + exact rowSquare_join (by decide) sg1766 sg4949 + +lemma sg15137 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg2636 sg3675 + +lemma sg15138 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg2368 sg4303 + +lemma sg15139 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg2892 sg3404 + +lemma sg15140 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg2368 sg4304 + +lemma sg15141 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2636 sg3679 + +lemma sg15142 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg2640 sg3675 + +lemma sg15143 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3] := by + exact rowSquare_join (by decide) sg2640 sg3679 + +lemma sg15144 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2896 sg3403 + +lemma sg15145 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg2633 sg3682 + +lemma sg15146 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg2635 sg3680 + +lemma sg15147 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2632 sg3683 + +lemma sg15148 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg2633 sg3683 + +lemma sg15149 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2899 sg3403 + +lemma sg15150 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg2633 sg3684 + +lemma sg15151 : RowSquare [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2636 sg3681 + +lemma sg15152 : RowSquare [6,6,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg648 sg7813 + +lemma sg15153 : RowSquare [6,6,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg651 sg7813 + +lemma sg15154 : RowSquare [6,6,3,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg8782 + +lemma sg15155 : RowSquare [6,6,3,2,2,2,2,2,2,1,1] [8,8,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg8783 + +lemma sg15156 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1] [6,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg1618 sg4949 + +lemma sg15157 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1] [7,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg2644 sg3332 + +lemma sg15158 : RowSquare [7,5,3,3,3,2,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1682 sg4879 + +lemma sg15159 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2707 sg3579 + +lemma sg15160 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2707 sg3580 + +lemma sg15161 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2707 sg3584 + +lemma sg15162 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg2710 sg3576 + +lemma sg15163 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg3577 + +lemma sg15164 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2707 sg3586 + +lemma sg15165 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg2260 sg4412 + +lemma sg15166 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg2710 sg3578 + +lemma sg15167 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2707 sg3587 + +lemma sg15168 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2707 sg3589 + +lemma sg15169 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2707 sg3592 + +lemma sg15170 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2725 sg3534 + +lemma sg15171 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2707 sg3594 + +lemma sg15172 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2720 sg3537 + +lemma sg15173 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg2708 sg3594 + +lemma sg15174 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg2707 sg3595 + +lemma sg15175 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg2708 sg3595 + +lemma sg15176 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2707 sg3596 + +lemma sg15177 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg2727 sg3534 + +lemma sg15178 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2710 sg3580 + +lemma sg15179 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2708 sg3597 + +lemma sg15180 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg2881 sg3456 + +lemma sg15181 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg2708 sg3598 + +lemma sg15182 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2707 sg3599 + +lemma sg15183 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg2709 sg3581 + +lemma sg15184 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2708 sg3599 + +lemma sg15185 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg2710 sg3581 + +lemma sg15186 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2709 sg3582 + +lemma sg15187 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2708 sg3600 + +lemma sg15188 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg2708 sg3601 + +lemma sg15189 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg3583 + +lemma sg15190 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg2708 sg3602 + +lemma sg15191 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg2710 sg3584 + +lemma sg15192 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg3585 + +lemma sg15193 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg2881 sg3458 + +lemma sg15194 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2707 sg3603 + +lemma sg15195 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2710 sg3587 + +lemma sg15196 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2708 sg3603 + +lemma sg15197 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2708 sg3604 + +lemma sg15198 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg2708 sg3605 + +lemma sg15199 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg3588 + +lemma sg15200 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2707 sg3606 + +lemma sg15201 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg2708 sg3606 + +lemma sg15202 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2710 sg3589 + +lemma sg15203 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2708 sg3607 + +lemma sg15204 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg3590 + +lemma sg15205 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg3591 + +lemma sg15206 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg3593 + +lemma sg15207 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg2256 sg4414 + +lemma sg15208 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg2708 sg3608 + +lemma sg15209 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2708 sg3609 + +lemma sg15210 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg2710 sg3595 + +lemma sg15211 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg3598 + +lemma sg15212 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2710 sg3599 + +lemma sg15213 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg3604 + +lemma sg15214 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg3605 + +lemma sg15215 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg3608 + +lemma sg15216 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg3609 + +lemma sg15217 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3] := by + exact rowSquare_join (by decide) sg227 sg11060 + +lemma sg15218 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg424 sg8893 + +lemma sg15219 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3] := by + exact rowSquare_join (by decide) sg228 sg11060 + +lemma sg15220 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2710 sg3610 + +lemma sg15221 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg3611 + +lemma sg15222 : RowSquare [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg3612 + +lemma sg15223 : RowSquare [7,6,2,2,2,2,2,2,2,1,1] [9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg217 sg10869 + +lemma sg15224 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg4377 + +lemma sg15225 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg4378 + +lemma sg15226 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg4388 + +lemma sg15227 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2366 sg4167 + +lemma sg15228 : RowSquare [7,6,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg2367 sg4167 + +lemma sg15229 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1] [5,5,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg643 sg7995 + +lemma sg15230 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1] [6,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg643 sg7996 + +lemma sg15231 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1] [6,6,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg356 sg8893 + +lemma sg15232 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1] [7,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg643 sg7997 + +lemma sg15233 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1] [7,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg356 sg8894 + +lemma sg15234 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1] [8,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg645 sg7997 + +lemma sg15235 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2881 sg3316 + +lemma sg15236 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg1 sg14446 + +lemma sg15237 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1 sg14447 + +lemma sg15238 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2156 sg4167 + +lemma sg15239 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2879 sg3294 + +lemma sg15240 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg2710 sg3314 + +lemma sg15241 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2708 sg3317 + +lemma sg15242 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [7,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg74 sg11553 + +lemma sg15243 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [8,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg193 sg11058 + +lemma sg15244 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1] [9,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg391 sg8890 + +lemma sg15245 : RowSquare [7,7,3,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg12673 + +lemma sg15246 : RowSquare [7,7,3,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19 sg12674 + +lemma sg15247 : RowSquare [8,6,3,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1332 sg5738 + +lemma sg15248 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg11549 + +lemma sg15249 : RowSquare [8,7,2,1,1,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2710 sg3522 + +lemma sg15250 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2879 sg3275 + +lemma sg15251 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2879 sg3260 + +lemma sg15252 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2588 sg3522 + +lemma sg15253 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg3263 + +lemma sg15254 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2074 sg4348 + +lemma sg15255 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1] [5,4,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg12597 + +lemma sg15256 : RowSquare [8,8,2,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2576 sg3522 + +lemma sg15257 : RowSquare [8,8,2,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2546 sg3522 + +lemma sg15258 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg12605 + +lemma sg15259 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2529 sg3522 + +lemma sg15260 : RowSquare [8,8,3,2,2,2,2,2] [2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2566 sg3239 + +lemma sg15261 : RowSquare [8,8,3,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2566 sg3238 + +lemma sg15262 : RowSquare [8,8,3,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2566 sg3237 + +lemma sg15263 : RowSquare [8,8,3,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2566 sg3236 + +lemma sg15264 : RowSquare [8,8,3,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2566 sg3235 + +lemma sg15265 : RowSquare [8,8,3,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2566 sg3234 + +lemma sg15266 : RowSquare [8,8,3,2,2,2,2,2] [4,4,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2562 sg3233 + +lemma sg15267 : RowSquare [9,7,2,2,2,1,1,1,1,1,1,1] [4,4,4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg3258 + +lemma sg15268 : RowSquare [9,7,2,2,2,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg14783 + +lemma sg15269 : RowSquare [9,7,2,2,2,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2252 sg3966 + +lemma sg15270 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg12615 + +lemma sg15271 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg11740 + +lemma sg15272 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg3953 + +lemma sg15273 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg11741 + +lemma sg15274 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg14784 + +lemma sg15275 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg75 sg11242 + +lemma sg15276 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg14786 + +lemma sg15277 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg165 sg9442 + +lemma sg15278 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg165 sg9444 + +lemma sg15279 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg451 sg7998 + +lemma sg15280 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg452 sg7998 + +lemma sg15281 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg453 sg7998 + +lemma sg15282 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1] [9,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg452 sg7999 + +lemma sg15283 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2699 sg3258 + +lemma sg15284 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1] [6,4,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2700 sg3258 + +lemma sg15285 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg11484 + +lemma sg15286 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg11485 + +lemma sg15287 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg168 sg10594 + +lemma sg15288 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg165 sg10595 + +lemma sg15289 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg165 sg10596 + +lemma sg15290 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg75 sg11485 + +lemma sg15291 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg11491 + +lemma sg15292 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg722 sg6502 + +lemma sg15293 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1] [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg430 sg8008 + +lemma sg15294 : RowSquare [12,3,2,2,2,2,2,2,1,1] [4,4,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg11484 + +lemma sg15295 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg2925 sg4331 + +lemma sg15296 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg3634 sg3418 + +lemma sg15297 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg4335 + +lemma sg15298 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg3636 sg3420 + +lemma sg15299 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2] := by + exact rowSquare_join (by decide) sg3724 sg3338 + +lemma sg15300 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg2656 sg4501 + +lemma sg15301 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3] := by + exact rowSquare_join (by decide) sg1032 sg8003 + +lemma sg15302 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,2] := by + exact rowSquare_join (by decide) sg1032 sg8004 + +lemma sg15303 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1] := by + exact rowSquare_join (by decide) sg1032 sg8005 + +lemma sg15304 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by + exact rowSquare_join (by decide) sg1033 sg8005 + +lemma sg15305 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg3633 sg3421 + +lemma sg15306 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg3633 sg3422 + +lemma sg15307 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg3635 sg3421 + +lemma sg15308 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3423 + +lemma sg15309 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3633 sg3424 + +lemma sg15310 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg3421 sg3636 + +lemma sg15311 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg3701 sg3365 + +lemma sg15312 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3425 + +lemma sg15313 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3426 + +lemma sg15314 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3427 + +lemma sg15315 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg2930 sg4328 + +lemma sg15316 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg3638 sg3420 + +lemma sg15317 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg2930 sg4329 + +lemma sg15318 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg3635 sg3422 + +lemma sg15319 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2614 sg4521 + +lemma sg15320 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3428 + +lemma sg15321 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3635 sg3424 + +lemma sg15322 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg3701 sg3367 + +lemma sg15323 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg3636 sg3422 + +lemma sg15324 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2614 sg4522 + +lemma sg15325 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3429 + +lemma sg15326 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3430 + +lemma sg15327 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg3360 sg3704 + +lemma sg15328 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2614 sg4523 + +lemma sg15329 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3431 + +lemma sg15330 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3427 + +lemma sg15331 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,3] := by + exact rowSquare_join (by decide) sg3704 sg3361 + +lemma sg15332 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg3704 sg3362 + +lemma sg15333 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3636 sg3424 + +lemma sg15334 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3432 + +lemma sg15335 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2614 sg4524 + +lemma sg15336 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3433 + +lemma sg15337 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3640 sg3420 + +lemma sg15338 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,3] := by + exact rowSquare_join (by decide) sg3360 sg3705 + +lemma sg15339 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2614 sg4525 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes37.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes37.lean index 80af7660cfff9eea0a0788cbad835b39da45a7ae..c1d8ebdae8b4464337694334909ebc8b11ce1662 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes37.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes37.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes31 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes36 - -namespace OAI - -/-! Semigroup Nodes 37. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg15340 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3434 - -lemma sg15341 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg3701 sg3368 - -lemma sg15342 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg3636 sg3427 - -lemma sg15343 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,3] := by - exact rowSquare_join (by decide) sg3360 sg3706 - -lemma sg15344 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,2] := by - exact rowSquare_join (by decide) sg3725 sg3339 - -lemma sg15345 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2614 sg4526 - -lemma sg15346 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg3000 sg4238 - -lemma sg15347 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,2] := by - exact rowSquare_join (by decide) sg3725 sg3340 - -lemma sg15348 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1] := by - exact rowSquare_join (by decide) sg3725 sg3341 - -lemma sg15349 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5] := by - exact rowSquare_join (by decide) sg3726 sg3341 - -lemma sg15350 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg4340 - -lemma sg15351 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg2760 sg4407 - -lemma sg15352 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg2760 sg4408 - -lemma sg15353 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3428 - -lemma sg15354 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2760 sg4409 - -lemma sg15355 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2762 sg4408 - -lemma sg15356 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3429 - -lemma sg15357 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3430 - -lemma sg15358 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,3] := by - exact rowSquare_join (by decide) sg3360 sg3707 - -lemma sg15359 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg3002 sg4236 - -lemma sg15360 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3431 - -lemma sg15361 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,3] := by - exact rowSquare_join (by decide) sg3004 sg4236 - -lemma sg15362 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,2] := by - exact rowSquare_join (by decide) sg3419 sg3642 - -lemma sg15363 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2762 sg4409 - -lemma sg15364 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3432 - -lemma sg15365 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg3636 sg3429 - -lemma sg15366 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3433 - -lemma sg15367 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,3] := by - exact rowSquare_join (by decide) sg3360 sg3708 - -lemma sg15368 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,2] := by - exact rowSquare_join (by decide) sg3360 sg3709 - -lemma sg15369 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3434 - -lemma sg15370 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,2] := by - exact rowSquare_join (by decide) sg3360 sg3710 - -lemma sg15371 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1] := by - exact rowSquare_join (by decide) sg3419 sg3643 - -lemma sg15372 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5] := by - exact rowSquare_join (by decide) sg3420 sg3643 - -lemma sg15373 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg3002 sg4238 - -lemma sg15374 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2] := by - exact rowSquare_join (by decide) sg3004 sg4238 - -lemma sg15375 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1] := by - exact rowSquare_join (by decide) sg3725 sg3342 - -lemma sg15376 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,4] := by - exact rowSquare_join (by decide) sg3726 sg3342 - -lemma sg15377 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1897 sg5753 - -lemma sg15378 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg3633 sg3435 - -lemma sg15379 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg3638 sg3421 - -lemma sg15380 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg2930 sg4330 - -lemma sg15381 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3436 - -lemma sg15382 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3633 sg3437 - -lemma sg15383 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg3635 sg3435 - -lemma sg15384 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3363 sg3704 - -lemma sg15385 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2931 sg4330 - -lemma sg15386 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3438 - -lemma sg15387 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3638 sg3424 - -lemma sg15388 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2930 sg4333 - -lemma sg15389 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg3701 sg3369 - -lemma sg15390 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg3636 sg3435 - -lemma sg15391 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3363 sg3705 - -lemma sg15392 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3439 - -lemma sg15393 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2933 sg4330 - -lemma sg15394 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg3360 sg3713 - -lemma sg15395 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3363 sg3706 - -lemma sg15396 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2934 sg4330 - -lemma sg15397 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3441 - -lemma sg15398 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg3713 sg3361 - -lemma sg15399 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg3713 sg3362 - -lemma sg15400 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3633 sg3442 - -lemma sg15401 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3635 sg3437 - -lemma sg15402 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2616 sg4521 - -lemma sg15403 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg3701 sg3370 - -lemma sg15404 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg3639 sg3422 - -lemma sg15405 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3363 sg3707 - -lemma sg15406 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3443 - -lemma sg15407 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2937 sg4330 - -lemma sg15408 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3444 - -lemma sg15409 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg3704 sg3364 - -lemma sg15410 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3636 sg3437 - -lemma sg15411 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2616 sg4522 - -lemma sg15412 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3445 - -lemma sg15413 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3363 sg3708 - -lemma sg15414 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3363 sg3709 - -lemma sg15415 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3446 - -lemma sg15416 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3440 - -lemma sg15417 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg3360 sg3714 - -lemma sg15418 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3363 sg3710 - -lemma sg15419 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3447 - -lemma sg15420 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3441 - -lemma sg15421 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg3728 sg3340 - -lemma sg15422 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,2] := by - exact rowSquare_join (by decide) sg3728 sg3341 - -lemma sg15423 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3640 sg3424 - -lemma sg15424 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2932 sg4333 - -lemma sg15425 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2616 sg4524 - -lemma sg15426 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3448 - -lemma sg15427 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3363 sg3711 - -lemma sg15428 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3449 - -lemma sg15429 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg3701 sg3371 - -lemma sg15430 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg3727 sg3343 - -lemma sg15431 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,3] := by - exact rowSquare_join (by decide) sg3360 sg3715 - -lemma sg15432 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3363 sg3712 - -lemma sg15433 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg3727 sg3344 - -lemma sg15434 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,2] := by - exact rowSquare_join (by decide) sg3360 sg3716 - -lemma sg15435 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg3010 sg4238 - -lemma sg15436 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,2] := by - exact rowSquare_join (by decide) sg3729 sg3340 - -lemma sg15437 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,1] := by - exact rowSquare_join (by decide) sg3725 sg3345 - -lemma sg15438 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,4] := by - exact rowSquare_join (by decide) sg3726 sg3345 - -lemma sg15439 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3635 sg3442 - -lemma sg15440 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2617 sg4521 - -lemma sg15441 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg3701 sg3372 - -lemma sg15442 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3636 sg3442 - -lemma sg15443 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2617 sg4522 - -lemma sg15444 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3451 - -lemma sg15445 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2614 sg4527 - -lemma sg15446 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2937 sg4332 - -lemma sg15447 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3452 - -lemma sg15448 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3444 - -lemma sg15449 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,3] := by - exact rowSquare_join (by decide) sg3704 sg3366 - -lemma sg15450 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3424 sg3641 - -lemma sg15451 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2614 sg4528 - -lemma sg15452 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2617 sg4524 - -lemma sg15453 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3453 - -lemma sg15454 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2614 sg4529 - -lemma sg15455 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3454 - -lemma sg15456 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3446 - -lemma sg15457 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,3] := by - exact rowSquare_join (by decide) sg3360 sg3717 - -lemma sg15458 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2614 sg4530 - -lemma sg15459 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3447 - -lemma sg15460 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,2] := by - exact rowSquare_join (by decide) sg3728 sg3342 - -lemma sg15461 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2938 sg4333 - -lemma sg15462 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2614 sg4531 - -lemma sg15463 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg3633 sg3455 - -lemma sg15464 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3448 - -lemma sg15465 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3] := by - exact rowSquare_join (by decide) sg3360 sg3718 - -lemma sg15466 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2614 sg4532 - -lemma sg15467 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3449 - -lemma sg15468 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg3636 sg3447 - -lemma sg15469 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,2] := by - exact rowSquare_join (by decide) sg3360 sg3719 - -lemma sg15470 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,1] := by - exact rowSquare_join (by decide) sg3725 sg3346 - -lemma sg15471 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,3] := by - exact rowSquare_join (by decide) sg3726 sg3346 - -lemma sg15472 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2760 sg4411 - -lemma sg15473 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2765 sg4408 - -lemma sg15474 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2762 sg4411 - -lemma sg15475 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3451 - -lemma sg15476 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg3002 sg4245 - -lemma sg15477 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg3452 - -lemma sg15478 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg3636 sg3451 - -lemma sg15479 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg3701 sg3373 - -lemma sg15480 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg3701 sg3374 - -lemma sg15481 : RowSquare [5,5,3,3,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2361 sg4832 - -lemma sg15482 : RowSquare [5,5,3,3,2,2,2,2,2,2,1,1] [5,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2362 sg4832 - -lemma sg15483 : RowSquare [5,5,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2363 sg4832 - -lemma sg15484 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1736 sg5776 - -lemma sg15485 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2282 sg4917 - -lemma sg15486 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1737 sg5776 - -lemma sg15487 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg3413 - -lemma sg15488 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg2647 sg4488 - -lemma sg15489 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg3359 - -lemma sg15490 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,4] := by - exact rowSquare_join (by decide) sg1688 sg5787 - -lemma sg15491 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3] := by - exact rowSquare_join (by decide) sg2281 sg4924 - -lemma sg15492 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg1688 sg5788 - -lemma sg15493 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg4324 - -lemma sg15494 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg1686 sg5789 - -lemma sg15495 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3] := by - exact rowSquare_join (by decide) sg1688 sg5789 - -lemma sg15496 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by - exact rowSquare_join (by decide) sg3691 sg3359 - -lemma sg15497 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg2651 sg4488 - -lemma sg15498 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2139 sg5001 - -lemma sg15499 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3409 sg3626 - -lemma sg15500 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3695 sg3359 - -lemma sg15501 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,4] := by - exact rowSquare_join (by decide) sg2838 sg4360 - -lemma sg15502 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg8018 - -lemma sg15503 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg3562 sg3475 - -lemma sg15504 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,4] := by - exact rowSquare_join (by decide) sg1688 sg5781 - -lemma sg15505 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg3562 sg3476 - -lemma sg15506 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3] := by - exact rowSquare_join (by decide) sg1688 sg5782 - -lemma sg15507 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg1688 sg5783 - -lemma sg15508 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,3] := by - exact rowSquare_join (by decide) sg3356 sg3690 - -lemma sg15509 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg2798 sg4361 - -lemma sg15510 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3] := by - exact rowSquare_join (by decide) sg1688 sg5785 - -lemma sg15511 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by - exact rowSquare_join (by decide) sg1033 sg8001 - -lemma sg15512 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1478 sg6457 - -lemma sg15513 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1852 sg5672 - -lemma sg15514 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1479 sg6457 - -lemma sg15515 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1480 sg6457 - -lemma sg15516 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1854 sg5672 - -lemma sg15517 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1481 sg6457 - -lemma sg15518 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1855 sg5672 - -lemma sg15519 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1856 sg5672 - -lemma sg15520 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1482 sg6457 - -lemma sg15521 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1857 sg5672 - -lemma sg15522 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1858 sg5672 - -lemma sg15523 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1483 sg6457 - -lemma sg15524 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1859 sg5672 - -lemma sg15525 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1852 sg5673 - -lemma sg15526 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1860 sg5672 - -lemma sg15527 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1484 sg6457 - -lemma sg15528 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1861 sg5672 - -lemma sg15529 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1485 sg6457 - -lemma sg15530 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1853 sg5673 - -lemma sg15531 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1486 sg6457 - -lemma sg15532 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1862 sg5672 - -lemma sg15533 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1854 sg5673 - -lemma sg15534 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1487 sg6457 - -lemma sg15535 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1855 sg5673 - -lemma sg15536 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1488 sg6457 - -lemma sg15537 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1863 sg5672 - -lemma sg15538 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1864 sg5672 - -lemma sg15539 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1489 sg6457 - -lemma sg15540 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1865 sg5672 - -lemma sg15541 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1858 sg5673 - -lemma sg15542 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1859 sg5673 - -lemma sg15543 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1490 sg6457 - -lemma sg15544 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1866 sg5672 - -lemma sg15545 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1860 sg5673 - -lemma sg15546 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1491 sg6457 - -lemma sg15547 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1492 sg6457 - -lemma sg15548 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1862 sg5673 - -lemma sg15549 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1493 sg6457 - -lemma sg15550 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1867 sg5672 - -lemma sg15551 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,4] := by - exact rowSquare_join (by decide) sg2167 sg4949 - -lemma sg15552 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,4] := by - exact rowSquare_join (by decide) sg2746 sg4378 - -lemma sg15553 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3] := by - exact rowSquare_join (by decide) sg2746 sg4379 - -lemma sg15554 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2] := by - exact rowSquare_join (by decide) sg2633 sg4496 - -lemma sg15555 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by - exact rowSquare_join (by decide) sg3691 sg3353 - -lemma sg15556 : RowSquare [6,5,3,3,2,2,2,2,2,2,1] [5,5,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1747 sg5674 - -lemma sg15557 : RowSquare [6,5,3,3,2,2,2,2,2,2,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1326 sg6457 - -lemma sg15558 : RowSquare [6,5,3,3,2,2,2,2,2,2,1] [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1325 sg6458 - -lemma sg15559 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by - exact rowSquare_join (by decide) sg3691 sg3298 - -lemma sg15560 : RowSquare [6,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2] := by - exact rowSquare_join (by decide) sg2633 sg4455 - -lemma sg15561 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1075 sg7812 - -lemma sg15562 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1076 sg7812 - -lemma sg15563 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1077 sg7812 - -lemma sg15564 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1078 sg7812 - -lemma sg15565 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [5,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1075 sg7815 - -lemma sg15566 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1079 sg7812 - -lemma sg15567 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1076 sg7813 - -lemma sg15568 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1080 sg7812 - -lemma sg15569 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1081 sg7812 - -lemma sg15570 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1077 sg7813 - -lemma sg15571 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1082 sg7812 - -lemma sg15572 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1077 sg7815 - -lemma sg15573 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1077 sg7816 - -lemma sg15574 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1078 sg7815 - -lemma sg15575 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,6,6,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1075 sg7836 - -lemma sg15576 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1083 sg7812 - -lemma sg15577 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1084 sg7812 - -lemma sg15578 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1079 sg7813 - -lemma sg15579 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1085 sg7812 - -lemma sg15580 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1080 sg7813 - -lemma sg15581 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1081 sg7813 - -lemma sg15582 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1077 sg7822 - -lemma sg15583 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1086 sg7812 - -lemma sg15584 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1082 sg7813 - -lemma sg15585 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1077 sg7823 - -lemma sg15586 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1087 sg7812 - -lemma sg15587 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1088 sg7812 - -lemma sg15588 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1083 sg7813 - -lemma sg15589 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1084 sg7813 - -lemma sg15590 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1089 sg7812 - -lemma sg15591 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1085 sg7813 - -lemma sg15592 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1077 sg7841 - -lemma sg15593 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1086 sg7813 - -lemma sg15594 : RowSquare [6,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1754 sg5768 - -lemma sg15595 : RowSquare [6,6,3,2,2,2,2,2,2,2,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg662 sg8780 - -lemma sg15596 : RowSquare [6,6,3,2,2,2,2,2,2,2,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg993 sg7812 - -lemma sg15597 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg3325 sg3403 - -lemma sg15598 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,6,6] := by - exact rowSquare_join (by decide) sg3556 sg3298 - -lemma sg15599 : RowSquare [7,5,3,3,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg4918 - -lemma sg15600 : RowSquare [7,5,3,3,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2256 sg4917 - -lemma sg15601 : RowSquare [7,6,2,2,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg10872 - -lemma sg15602 : RowSquare [7,6,2,2,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg367 sg10874 - -lemma sg15603 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2708 sg4376 - -lemma sg15604 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg2708 sg4378 - -lemma sg15605 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2708 sg4388 - -lemma sg15606 : RowSquare [7,6,3,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg363 sg10881 - -lemma sg15607 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2626 sg4165 - -lemma sg15608 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2626 sg4167 - -lemma sg15609 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2627 sg4167 - -lemma sg15610 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2628 sg4165 - -lemma sg15611 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2628 sg4167 - -lemma sg15612 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [5,5,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg2632 sg4173 - -lemma sg15613 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [6,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg4 sg14313 - -lemma sg15614 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [6,6,6,6,2,2,2] := by - exact rowSquare_join (by decide) sg390 sg11051 - -lemma sg15615 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [6,6,6,6,6] := by - exact rowSquare_join (by decide) sg3404 sg3316 - -lemma sg15616 : RowSquare [7,6,4,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1327 sg6469 - -lemma sg15617 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4366 - -lemma sg15618 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4369 - -lemma sg15619 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2708 sg4368 - -lemma sg15620 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2708 sg4369 - -lemma sg15621 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2709 sg4368 - -lemma sg15622 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg2710 sg4369 - -lemma sg15623 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg4371 - -lemma sg15624 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2881 sg4295 - -lemma sg15625 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg4372 - -lemma sg15626 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2708 sg4373 - -lemma sg15627 : RowSquare [7,7,2,2,2,2,2,2,2,1,1] [5,5,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg97 sg11811 - -lemma sg15628 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2879 sg4167 - -lemma sg15629 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2880 sg4167 - -lemma sg15630 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2879 sg4169 - -lemma sg15631 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2885 sg4167 - -lemma sg15632 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2883 sg4168 - -lemma sg15633 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg2882 sg4169 - -lemma sg15634 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg2884 sg4169 - -lemma sg15635 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2886 sg4169 - -lemma sg15636 : RowSquare [7,7,3,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2156 sg4878 - -lemma sg15637 : RowSquare [7,7,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg4861 - -lemma sg15638 : RowSquare [7,7,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg12917 - -lemma sg15639 : RowSquare [7,7,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg12918 - -lemma sg15640 : RowSquare [8,6,3,2,2,2,1,1,1,1,1,1,1] [6,6,6,6,6] := by - exact rowSquare_join (by decide) sg3404 sg3309 - -lemma sg15641 : RowSquare [8,6,3,3,2,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by - exact rowSquare_join (by decide) sg3556 sg3265 - -lemma sg15642 : RowSquare [8,7,2,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2706 sg4348 - -lemma sg15643 : RowSquare [8,7,2,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2708 sg4348 - -lemma sg15644 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4024 - -lemma sg15645 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4026 - -lemma sg15646 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4030 - -lemma sg15647 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg12920 - -lemma sg15648 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg12333 - -lemma sg15649 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,4,4] := by - exact rowSquare_join (by decide) sg74 sg12335 - -lemma sg15650 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg74 sg12336 - -lemma sg15651 : RowSquare [8,7,3,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg14531 - -lemma sg15652 : RowSquare [8,7,3,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6 sg14532 - -lemma sg15653 : RowSquare [8,7,3,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg12954 - -lemma sg15654 : RowSquare [8,7,3,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg12 sg12955 - -lemma sg15655 : RowSquare [8,7,3,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg12 sg12956 - -lemma sg15656 : RowSquare [8,8,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2576 sg4348 - -lemma sg15657 : RowSquare [8,8,2,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3275 - -lemma sg15658 : RowSquare [8,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2578 sg4348 - -lemma sg15659 : RowSquare [8,8,2,2,2,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg3275 sg3532 - -lemma sg15660 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3259 - -lemma sg15661 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3260 - -lemma sg15662 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3523 sg3260 - -lemma sg15663 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3262 - -lemma sg15664 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3263 - -lemma sg15665 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2251 sg4834 - -lemma sg15666 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg4837 - -lemma sg15667 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2254 sg4834 - -lemma sg15668 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg11733 - -lemma sg15669 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg4839 - -lemma sg15670 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg4841 - -lemma sg15671 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2256 sg4834 - -lemma sg15672 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg4842 - -lemma sg15673 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg11734 - -lemma sg15674 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by - exact rowSquare_join (by decide) sg32 sg12707 - -lemma sg15675 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg12921 - -lemma sg15676 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg12924 - -lemma sg15677 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg12925 - -lemma sg15678 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg12926 - -lemma sg15679 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg12927 - -lemma sg15680 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3256 - -lemma sg15681 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg11733 - -lemma sg15682 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3524 sg3258 - -lemma sg15683 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3525 sg3258 - -lemma sg15684 : RowSquare [9,8,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3292 sg3231 - -lemma sg15685 : RowSquare [9,8,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3292 sg3230 - -lemma sg15686 : RowSquare [9,8,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3292 sg3229 - -lemma sg15687 : RowSquare [9,8,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3292 sg3228 - -lemma sg15688 : RowSquare [9,8,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3292 sg3226 - -lemma sg15689 : RowSquare [9,8,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2566 sg3982 - -lemma sg15690 : RowSquare [9,8,2,2,2,2,2,2,1] [4,4,4,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3288 sg3227 - -lemma sg15691 : RowSquare [9,8,2,2,2,2,2,2,1] [4,4,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3290 sg3225 - -lemma sg15692 : RowSquare [9,8,2,2,2,2,2,2,1] [5,5,5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3286 sg3222 - -lemma sg15693 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg11755 - -lemma sg15694 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14526 - -lemma sg15695 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg12935 - -lemma sg15696 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg12936 - -lemma sg15697 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg2925 sg4882 - -lemma sg15698 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg3362 sg4439 - -lemma sg15699 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg2925 sg4883 - -lemma sg15700 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2614 sg4992 - -lemma sg15701 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg3417 sg4397 - -lemma sg15702 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg3420 sg4396 - -lemma sg15703 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg3420 sg4397 - -lemma sg15704 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3563 sg4327 - -lemma sg15705 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg3632 sg4222 - -lemma sg15706 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3688 sg4124 - -lemma sg15707 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,3,3] := by - exact rowSquare_join (by decide) sg2925 sg4884 - -lemma sg15708 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3613 sg4237 - -lemma sg15709 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg3632 sg4224 - -lemma sg15710 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg3420 sg4398 - -lemma sg15711 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3302 sg4526 - -lemma sg15712 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg3632 sg4226 - -lemma sg15713 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg4887 - -lemma sg15714 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2717 sg4926 - -lemma sg15715 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3363 sg4440 - -lemma sg15716 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg3559 sg4330 - -lemma sg15717 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg15295 - -lemma sg15718 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2718 sg4926 - -lemma sg15719 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3559 sg4332 - -lemma sg15720 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3559 sg4333 - -lemma sg15721 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3363 sg4442 - -lemma sg15722 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3559 sg4334 - -lemma sg15723 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg3421 sg4398 - -lemma sg15724 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4239 - -lemma sg15725 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3692 sg4124 - -lemma sg15726 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg3421 sg4399 - -lemma sg15727 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4240 - -lemma sg15728 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15296 - -lemma sg15729 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4241 - -lemma sg15730 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4125 - -lemma sg15731 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3561 sg4332 - -lemma sg15732 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg3422 sg4399 - -lemma sg15733 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4127 - -lemma sg15734 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by - exact rowSquare_join (by decide) sg3704 sg4119 - -lemma sg15735 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by - exact rowSquare_join (by decide) sg3704 sg4120 - -lemma sg15736 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3563 sg4333 - -lemma sg15737 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3563 sg4334 - -lemma sg15738 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3424 sg4398 - -lemma sg15739 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4242 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes31 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes36 + +namespace OAI + +/-! Semigroup Nodes 37. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg15340 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3434 + +lemma sg15341 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg3701 sg3368 + +lemma sg15342 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg3636 sg3427 + +lemma sg15343 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,3] := by + exact rowSquare_join (by decide) sg3360 sg3706 + +lemma sg15344 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,2] := by + exact rowSquare_join (by decide) sg3725 sg3339 + +lemma sg15345 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2614 sg4526 + +lemma sg15346 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg3000 sg4238 + +lemma sg15347 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,2] := by + exact rowSquare_join (by decide) sg3725 sg3340 + +lemma sg15348 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1] := by + exact rowSquare_join (by decide) sg3725 sg3341 + +lemma sg15349 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5] := by + exact rowSquare_join (by decide) sg3726 sg3341 + +lemma sg15350 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg4340 + +lemma sg15351 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg2760 sg4407 + +lemma sg15352 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg2760 sg4408 + +lemma sg15353 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3428 + +lemma sg15354 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2760 sg4409 + +lemma sg15355 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2762 sg4408 + +lemma sg15356 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3429 + +lemma sg15357 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3430 + +lemma sg15358 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,3] := by + exact rowSquare_join (by decide) sg3360 sg3707 + +lemma sg15359 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg3002 sg4236 + +lemma sg15360 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3431 + +lemma sg15361 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,3] := by + exact rowSquare_join (by decide) sg3004 sg4236 + +lemma sg15362 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,2] := by + exact rowSquare_join (by decide) sg3419 sg3642 + +lemma sg15363 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2762 sg4409 + +lemma sg15364 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3432 + +lemma sg15365 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg3636 sg3429 + +lemma sg15366 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3433 + +lemma sg15367 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,3] := by + exact rowSquare_join (by decide) sg3360 sg3708 + +lemma sg15368 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,2] := by + exact rowSquare_join (by decide) sg3360 sg3709 + +lemma sg15369 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3434 + +lemma sg15370 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,2] := by + exact rowSquare_join (by decide) sg3360 sg3710 + +lemma sg15371 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1] := by + exact rowSquare_join (by decide) sg3419 sg3643 + +lemma sg15372 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5] := by + exact rowSquare_join (by decide) sg3420 sg3643 + +lemma sg15373 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg3002 sg4238 + +lemma sg15374 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2] := by + exact rowSquare_join (by decide) sg3004 sg4238 + +lemma sg15375 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1] := by + exact rowSquare_join (by decide) sg3725 sg3342 + +lemma sg15376 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,4] := by + exact rowSquare_join (by decide) sg3726 sg3342 + +lemma sg15377 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1897 sg5753 + +lemma sg15378 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg3633 sg3435 + +lemma sg15379 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg3638 sg3421 + +lemma sg15380 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg2930 sg4330 + +lemma sg15381 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3436 + +lemma sg15382 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3633 sg3437 + +lemma sg15383 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg3635 sg3435 + +lemma sg15384 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3363 sg3704 + +lemma sg15385 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2931 sg4330 + +lemma sg15386 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3438 + +lemma sg15387 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3638 sg3424 + +lemma sg15388 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2930 sg4333 + +lemma sg15389 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg3701 sg3369 + +lemma sg15390 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg3636 sg3435 + +lemma sg15391 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3363 sg3705 + +lemma sg15392 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3439 + +lemma sg15393 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2933 sg4330 + +lemma sg15394 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg3360 sg3713 + +lemma sg15395 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3363 sg3706 + +lemma sg15396 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2934 sg4330 + +lemma sg15397 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3441 + +lemma sg15398 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg3713 sg3361 + +lemma sg15399 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg3713 sg3362 + +lemma sg15400 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3633 sg3442 + +lemma sg15401 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3635 sg3437 + +lemma sg15402 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2616 sg4521 + +lemma sg15403 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg3701 sg3370 + +lemma sg15404 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg3639 sg3422 + +lemma sg15405 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3363 sg3707 + +lemma sg15406 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3443 + +lemma sg15407 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2937 sg4330 + +lemma sg15408 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3444 + +lemma sg15409 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg3704 sg3364 + +lemma sg15410 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3636 sg3437 + +lemma sg15411 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2616 sg4522 + +lemma sg15412 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3445 + +lemma sg15413 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3363 sg3708 + +lemma sg15414 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3363 sg3709 + +lemma sg15415 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3446 + +lemma sg15416 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3440 + +lemma sg15417 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg3360 sg3714 + +lemma sg15418 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3363 sg3710 + +lemma sg15419 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3447 + +lemma sg15420 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3441 + +lemma sg15421 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg3728 sg3340 + +lemma sg15422 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,2] := by + exact rowSquare_join (by decide) sg3728 sg3341 + +lemma sg15423 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3640 sg3424 + +lemma sg15424 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2932 sg4333 + +lemma sg15425 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2616 sg4524 + +lemma sg15426 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3448 + +lemma sg15427 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3363 sg3711 + +lemma sg15428 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3449 + +lemma sg15429 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg3701 sg3371 + +lemma sg15430 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg3727 sg3343 + +lemma sg15431 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,3] := by + exact rowSquare_join (by decide) sg3360 sg3715 + +lemma sg15432 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3363 sg3712 + +lemma sg15433 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg3727 sg3344 + +lemma sg15434 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,2] := by + exact rowSquare_join (by decide) sg3360 sg3716 + +lemma sg15435 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg3010 sg4238 + +lemma sg15436 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,2] := by + exact rowSquare_join (by decide) sg3729 sg3340 + +lemma sg15437 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,1] := by + exact rowSquare_join (by decide) sg3725 sg3345 + +lemma sg15438 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,4] := by + exact rowSquare_join (by decide) sg3726 sg3345 + +lemma sg15439 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3635 sg3442 + +lemma sg15440 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2617 sg4521 + +lemma sg15441 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg3701 sg3372 + +lemma sg15442 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3636 sg3442 + +lemma sg15443 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2617 sg4522 + +lemma sg15444 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3451 + +lemma sg15445 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2614 sg4527 + +lemma sg15446 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2937 sg4332 + +lemma sg15447 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3452 + +lemma sg15448 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3444 + +lemma sg15449 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,3] := by + exact rowSquare_join (by decide) sg3704 sg3366 + +lemma sg15450 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3424 sg3641 + +lemma sg15451 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2614 sg4528 + +lemma sg15452 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2617 sg4524 + +lemma sg15453 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3453 + +lemma sg15454 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2614 sg4529 + +lemma sg15455 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3454 + +lemma sg15456 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3446 + +lemma sg15457 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,3] := by + exact rowSquare_join (by decide) sg3360 sg3717 + +lemma sg15458 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2614 sg4530 + +lemma sg15459 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3447 + +lemma sg15460 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,2] := by + exact rowSquare_join (by decide) sg3728 sg3342 + +lemma sg15461 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2938 sg4333 + +lemma sg15462 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2614 sg4531 + +lemma sg15463 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg3633 sg3455 + +lemma sg15464 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3448 + +lemma sg15465 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3] := by + exact rowSquare_join (by decide) sg3360 sg3718 + +lemma sg15466 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2614 sg4532 + +lemma sg15467 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3449 + +lemma sg15468 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg3636 sg3447 + +lemma sg15469 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,2] := by + exact rowSquare_join (by decide) sg3360 sg3719 + +lemma sg15470 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,1] := by + exact rowSquare_join (by decide) sg3725 sg3346 + +lemma sg15471 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,3] := by + exact rowSquare_join (by decide) sg3726 sg3346 + +lemma sg15472 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2760 sg4411 + +lemma sg15473 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2765 sg4408 + +lemma sg15474 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2762 sg4411 + +lemma sg15475 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3451 + +lemma sg15476 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg3002 sg4245 + +lemma sg15477 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg3452 + +lemma sg15478 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg3636 sg3451 + +lemma sg15479 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg3701 sg3373 + +lemma sg15480 : RowSquare [4,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg3701 sg3374 + +lemma sg15481 : RowSquare [5,5,3,3,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2361 sg4832 + +lemma sg15482 : RowSquare [5,5,3,3,2,2,2,2,2,2,1,1] [5,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2362 sg4832 + +lemma sg15483 : RowSquare [5,5,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2363 sg4832 + +lemma sg15484 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1736 sg5776 + +lemma sg15485 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2282 sg4917 + +lemma sg15486 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1737 sg5776 + +lemma sg15487 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg3413 + +lemma sg15488 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg2647 sg4488 + +lemma sg15489 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg3359 + +lemma sg15490 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,4] := by + exact rowSquare_join (by decide) sg1688 sg5787 + +lemma sg15491 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3] := by + exact rowSquare_join (by decide) sg2281 sg4924 + +lemma sg15492 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg1688 sg5788 + +lemma sg15493 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg4324 + +lemma sg15494 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg1686 sg5789 + +lemma sg15495 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3] := by + exact rowSquare_join (by decide) sg1688 sg5789 + +lemma sg15496 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by + exact rowSquare_join (by decide) sg3691 sg3359 + +lemma sg15497 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg2651 sg4488 + +lemma sg15498 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2139 sg5001 + +lemma sg15499 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3409 sg3626 + +lemma sg15500 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3695 sg3359 + +lemma sg15501 : RowSquare [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,4] := by + exact rowSquare_join (by decide) sg2838 sg4360 + +lemma sg15502 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg8018 + +lemma sg15503 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg3562 sg3475 + +lemma sg15504 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,4] := by + exact rowSquare_join (by decide) sg1688 sg5781 + +lemma sg15505 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg3562 sg3476 + +lemma sg15506 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3] := by + exact rowSquare_join (by decide) sg1688 sg5782 + +lemma sg15507 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg1688 sg5783 + +lemma sg15508 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,3] := by + exact rowSquare_join (by decide) sg3356 sg3690 + +lemma sg15509 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg2798 sg4361 + +lemma sg15510 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3] := by + exact rowSquare_join (by decide) sg1688 sg5785 + +lemma sg15511 : RowSquare [5,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by + exact rowSquare_join (by decide) sg1033 sg8001 + +lemma sg15512 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1478 sg6457 + +lemma sg15513 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1852 sg5672 + +lemma sg15514 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1479 sg6457 + +lemma sg15515 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1480 sg6457 + +lemma sg15516 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1854 sg5672 + +lemma sg15517 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1481 sg6457 + +lemma sg15518 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1855 sg5672 + +lemma sg15519 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1856 sg5672 + +lemma sg15520 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1482 sg6457 + +lemma sg15521 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1857 sg5672 + +lemma sg15522 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1858 sg5672 + +lemma sg15523 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1483 sg6457 + +lemma sg15524 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1859 sg5672 + +lemma sg15525 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1852 sg5673 + +lemma sg15526 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1860 sg5672 + +lemma sg15527 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1484 sg6457 + +lemma sg15528 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1861 sg5672 + +lemma sg15529 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1485 sg6457 + +lemma sg15530 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1853 sg5673 + +lemma sg15531 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1486 sg6457 + +lemma sg15532 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1862 sg5672 + +lemma sg15533 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1854 sg5673 + +lemma sg15534 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1487 sg6457 + +lemma sg15535 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1855 sg5673 + +lemma sg15536 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1488 sg6457 + +lemma sg15537 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1863 sg5672 + +lemma sg15538 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1864 sg5672 + +lemma sg15539 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1489 sg6457 + +lemma sg15540 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1865 sg5672 + +lemma sg15541 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1858 sg5673 + +lemma sg15542 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1859 sg5673 + +lemma sg15543 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1490 sg6457 + +lemma sg15544 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1866 sg5672 + +lemma sg15545 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1860 sg5673 + +lemma sg15546 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1491 sg6457 + +lemma sg15547 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1492 sg6457 + +lemma sg15548 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1862 sg5673 + +lemma sg15549 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1493 sg6457 + +lemma sg15550 : RowSquare [6,5,3,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1867 sg5672 + +lemma sg15551 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,4] := by + exact rowSquare_join (by decide) sg2167 sg4949 + +lemma sg15552 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,4] := by + exact rowSquare_join (by decide) sg2746 sg4378 + +lemma sg15553 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3] := by + exact rowSquare_join (by decide) sg2746 sg4379 + +lemma sg15554 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2] := by + exact rowSquare_join (by decide) sg2633 sg4496 + +lemma sg15555 : RowSquare [6,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by + exact rowSquare_join (by decide) sg3691 sg3353 + +lemma sg15556 : RowSquare [6,5,3,3,2,2,2,2,2,2,1] [5,5,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1747 sg5674 + +lemma sg15557 : RowSquare [6,5,3,3,2,2,2,2,2,2,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1326 sg6457 + +lemma sg15558 : RowSquare [6,5,3,3,2,2,2,2,2,2,1] [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1325 sg6458 + +lemma sg15559 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by + exact rowSquare_join (by decide) sg3691 sg3298 + +lemma sg15560 : RowSquare [6,5,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2] := by + exact rowSquare_join (by decide) sg2633 sg4455 + +lemma sg15561 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1075 sg7812 + +lemma sg15562 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1076 sg7812 + +lemma sg15563 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1077 sg7812 + +lemma sg15564 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1078 sg7812 + +lemma sg15565 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [5,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1075 sg7815 + +lemma sg15566 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1079 sg7812 + +lemma sg15567 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1076 sg7813 + +lemma sg15568 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1080 sg7812 + +lemma sg15569 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1081 sg7812 + +lemma sg15570 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1077 sg7813 + +lemma sg15571 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1082 sg7812 + +lemma sg15572 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1077 sg7815 + +lemma sg15573 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1077 sg7816 + +lemma sg15574 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1078 sg7815 + +lemma sg15575 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [6,6,6,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1075 sg7836 + +lemma sg15576 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1083 sg7812 + +lemma sg15577 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1084 sg7812 + +lemma sg15578 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1079 sg7813 + +lemma sg15579 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1085 sg7812 + +lemma sg15580 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1080 sg7813 + +lemma sg15581 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1081 sg7813 + +lemma sg15582 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1077 sg7822 + +lemma sg15583 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1086 sg7812 + +lemma sg15584 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1082 sg7813 + +lemma sg15585 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [7,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1077 sg7823 + +lemma sg15586 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1087 sg7812 + +lemma sg15587 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1088 sg7812 + +lemma sg15588 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1083 sg7813 + +lemma sg15589 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1084 sg7813 + +lemma sg15590 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1089 sg7812 + +lemma sg15591 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1085 sg7813 + +lemma sg15592 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1077 sg7841 + +lemma sg15593 : RowSquare [6,6,2,2,2,2,2,2,2,2,1,1] [8,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1086 sg7813 + +lemma sg15594 : RowSquare [6,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1754 sg5768 + +lemma sg15595 : RowSquare [6,6,3,2,2,2,2,2,2,2,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg662 sg8780 + +lemma sg15596 : RowSquare [6,6,3,2,2,2,2,2,2,2,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg993 sg7812 + +lemma sg15597 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg3325 sg3403 + +lemma sg15598 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,6,6] := by + exact rowSquare_join (by decide) sg3556 sg3298 + +lemma sg15599 : RowSquare [7,5,3,3,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg4918 + +lemma sg15600 : RowSquare [7,5,3,3,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2256 sg4917 + +lemma sg15601 : RowSquare [7,6,2,2,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg10872 + +lemma sg15602 : RowSquare [7,6,2,2,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg367 sg10874 + +lemma sg15603 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2708 sg4376 + +lemma sg15604 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg2708 sg4378 + +lemma sg15605 : RowSquare [7,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2708 sg4388 + +lemma sg15606 : RowSquare [7,6,3,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg363 sg10881 + +lemma sg15607 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2626 sg4165 + +lemma sg15608 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2626 sg4167 + +lemma sg15609 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2627 sg4167 + +lemma sg15610 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2628 sg4165 + +lemma sg15611 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2628 sg4167 + +lemma sg15612 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [5,5,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg2632 sg4173 + +lemma sg15613 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [6,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg4 sg14313 + +lemma sg15614 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [6,6,6,6,2,2,2] := by + exact rowSquare_join (by decide) sg390 sg11051 + +lemma sg15615 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1] [6,6,6,6,6] := by + exact rowSquare_join (by decide) sg3404 sg3316 + +lemma sg15616 : RowSquare [7,6,4,3,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1327 sg6469 + +lemma sg15617 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4366 + +lemma sg15618 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4369 + +lemma sg15619 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2708 sg4368 + +lemma sg15620 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2708 sg4369 + +lemma sg15621 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2709 sg4368 + +lemma sg15622 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg2710 sg4369 + +lemma sg15623 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg4371 + +lemma sg15624 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2881 sg4295 + +lemma sg15625 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg4372 + +lemma sg15626 : RowSquare [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2708 sg4373 + +lemma sg15627 : RowSquare [7,7,2,2,2,2,2,2,2,1,1] [5,5,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg97 sg11811 + +lemma sg15628 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2879 sg4167 + +lemma sg15629 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2880 sg4167 + +lemma sg15630 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2879 sg4169 + +lemma sg15631 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2885 sg4167 + +lemma sg15632 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2883 sg4168 + +lemma sg15633 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg2882 sg4169 + +lemma sg15634 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg2884 sg4169 + +lemma sg15635 : RowSquare [7,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2886 sg4169 + +lemma sg15636 : RowSquare [7,7,3,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2156 sg4878 + +lemma sg15637 : RowSquare [7,7,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg4861 + +lemma sg15638 : RowSquare [7,7,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg12917 + +lemma sg15639 : RowSquare [7,7,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg12918 + +lemma sg15640 : RowSquare [8,6,3,2,2,2,1,1,1,1,1,1,1] [6,6,6,6,6] := by + exact rowSquare_join (by decide) sg3404 sg3309 + +lemma sg15641 : RowSquare [8,6,3,3,2,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by + exact rowSquare_join (by decide) sg3556 sg3265 + +lemma sg15642 : RowSquare [8,7,2,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2706 sg4348 + +lemma sg15643 : RowSquare [8,7,2,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2708 sg4348 + +lemma sg15644 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4024 + +lemma sg15645 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4026 + +lemma sg15646 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4030 + +lemma sg15647 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg12920 + +lemma sg15648 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg12333 + +lemma sg15649 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,4,4] := by + exact rowSquare_join (by decide) sg74 sg12335 + +lemma sg15650 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg74 sg12336 + +lemma sg15651 : RowSquare [8,7,3,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg14531 + +lemma sg15652 : RowSquare [8,7,3,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6 sg14532 + +lemma sg15653 : RowSquare [8,7,3,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg12954 + +lemma sg15654 : RowSquare [8,7,3,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg12 sg12955 + +lemma sg15655 : RowSquare [8,7,3,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg12 sg12956 + +lemma sg15656 : RowSquare [8,8,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2576 sg4348 + +lemma sg15657 : RowSquare [8,8,2,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3275 + +lemma sg15658 : RowSquare [8,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2578 sg4348 + +lemma sg15659 : RowSquare [8,8,2,2,2,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg3275 sg3532 + +lemma sg15660 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3259 + +lemma sg15661 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3260 + +lemma sg15662 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3523 sg3260 + +lemma sg15663 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3262 + +lemma sg15664 : RowSquare [8,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3263 + +lemma sg15665 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2251 sg4834 + +lemma sg15666 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg4837 + +lemma sg15667 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2254 sg4834 + +lemma sg15668 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg11733 + +lemma sg15669 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg4839 + +lemma sg15670 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg4841 + +lemma sg15671 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2256 sg4834 + +lemma sg15672 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg4842 + +lemma sg15673 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg11734 + +lemma sg15674 : RowSquare [9,7,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6] := by + exact rowSquare_join (by decide) sg32 sg12707 + +lemma sg15675 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg12921 + +lemma sg15676 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg12924 + +lemma sg15677 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg12925 + +lemma sg15678 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg12926 + +lemma sg15679 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg12927 + +lemma sg15680 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3256 + +lemma sg15681 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg11733 + +lemma sg15682 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3524 sg3258 + +lemma sg15683 : RowSquare [9,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3525 sg3258 + +lemma sg15684 : RowSquare [9,8,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3292 sg3231 + +lemma sg15685 : RowSquare [9,8,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3292 sg3230 + +lemma sg15686 : RowSquare [9,8,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3292 sg3229 + +lemma sg15687 : RowSquare [9,8,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3292 sg3228 + +lemma sg15688 : RowSquare [9,8,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3292 sg3226 + +lemma sg15689 : RowSquare [9,8,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2566 sg3982 + +lemma sg15690 : RowSquare [9,8,2,2,2,2,2,2,1] [4,4,4,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3288 sg3227 + +lemma sg15691 : RowSquare [9,8,2,2,2,2,2,2,1] [4,4,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3290 sg3225 + +lemma sg15692 : RowSquare [9,8,2,2,2,2,2,2,1] [5,5,5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3286 sg3222 + +lemma sg15693 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg11755 + +lemma sg15694 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14526 + +lemma sg15695 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg12935 + +lemma sg15696 : RowSquare [10,8,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg12936 + +lemma sg15697 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg2925 sg4882 + +lemma sg15698 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg3362 sg4439 + +lemma sg15699 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg2925 sg4883 + +lemma sg15700 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2614 sg4992 + +lemma sg15701 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg3417 sg4397 + +lemma sg15702 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg3420 sg4396 + +lemma sg15703 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg3420 sg4397 + +lemma sg15704 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3563 sg4327 + +lemma sg15705 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg3632 sg4222 + +lemma sg15706 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3688 sg4124 + +lemma sg15707 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,3,3] := by + exact rowSquare_join (by decide) sg2925 sg4884 + +lemma sg15708 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3613 sg4237 + +lemma sg15709 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg3632 sg4224 + +lemma sg15710 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg3420 sg4398 + +lemma sg15711 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3302 sg4526 + +lemma sg15712 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg3632 sg4226 + +lemma sg15713 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg4887 + +lemma sg15714 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2717 sg4926 + +lemma sg15715 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3363 sg4440 + +lemma sg15716 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg3559 sg4330 + +lemma sg15717 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg15295 + +lemma sg15718 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2718 sg4926 + +lemma sg15719 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3559 sg4332 + +lemma sg15720 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3559 sg4333 + +lemma sg15721 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3363 sg4442 + +lemma sg15722 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3559 sg4334 + +lemma sg15723 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg3421 sg4398 + +lemma sg15724 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4239 + +lemma sg15725 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3692 sg4124 + +lemma sg15726 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg3421 sg4399 + +lemma sg15727 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4240 + +lemma sg15728 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15296 + +lemma sg15729 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4241 + +lemma sg15730 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4125 + +lemma sg15731 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3561 sg4332 + +lemma sg15732 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg3422 sg4399 + +lemma sg15733 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4127 + +lemma sg15734 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by + exact rowSquare_join (by decide) sg3704 sg4119 + +lemma sg15735 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by + exact rowSquare_join (by decide) sg3704 sg4120 + +lemma sg15736 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3563 sg4333 + +lemma sg15737 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3563 sg4334 + +lemma sg15738 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3424 sg4398 + +lemma sg15739 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4242 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes38.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes38.lean index 42a0c53d5dbc91098d7e91736fdb7aa7fde3c5bc..fd16c6e237332a723a55f1a9ac026fd1d2a74be5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes38.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes38.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 - -namespace OAI - -/-! Semigroup Nodes 38. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg15740 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15297 - -lemma sg15741 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg3636 sg4217 - -lemma sg15742 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4243 - -lemma sg15743 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4128 - -lemma sg15744 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg3360 sg4446 - -lemma sg15745 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4244 - -lemma sg15746 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4129 - -lemma sg15747 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15298 - -lemma sg15748 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by - exact rowSquare_join (by decide) sg3360 sg4447 - -lemma sg15749 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by - exact rowSquare_join (by decide) sg3360 sg4448 - -lemma sg15750 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4130 - -lemma sg15751 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15299 - -lemma sg15752 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15300 - -lemma sg15753 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by - exact rowSquare_join (by decide) sg0 sg15301 - -lemma sg15754 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by - exact rowSquare_join (by decide) sg0 sg15302 - -lemma sg15755 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by - exact rowSquare_join (by decide) sg0 sg15303 - -lemma sg15756 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg0 sg15304 - -lemma sg15757 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg3568 sg4325 - -lemma sg15758 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3568 sg4326 - -lemma sg15759 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2917 sg4886 - -lemma sg15760 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3686 sg4126 - -lemma sg15761 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg3635 sg4219 - -lemma sg15762 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by - exact rowSquare_join (by decide) sg3360 sg4449 - -lemma sg15763 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4127 - -lemma sg15764 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by - exact rowSquare_join (by decide) sg3419 sg4400 - -lemma sg15765 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by - exact rowSquare_join (by decide) sg3707 sg4120 - -lemma sg15766 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg3636 sg4221 - -lemma sg15767 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by - exact rowSquare_join (by decide) sg3360 sg4450 - -lemma sg15768 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by - exact rowSquare_join (by decide) sg3360 sg4451 - -lemma sg15769 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by - exact rowSquare_join (by decide) sg3420 sg4401 - -lemma sg15770 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4130 - -lemma sg15771 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg4226 - -lemma sg15772 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by - exact rowSquare_join (by decide) sg3725 sg4040 - -lemma sg15773 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by - exact rowSquare_join (by decide) sg3725 sg4041 - -lemma sg15774 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by - exact rowSquare_join (by decide) sg3726 sg4041 - -lemma sg15775 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4246 - -lemma sg15776 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3688 sg4128 - -lemma sg15777 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3432 sg4398 - -lemma sg15778 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,2] := by - exact rowSquare_join (by decide) sg3723 sg4042 - -lemma sg15779 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3688 sg4129 - -lemma sg15780 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg3636 sg4223 - -lemma sg15781 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,2] := by - exact rowSquare_join (by decide) sg3724 sg4042 - -lemma sg15782 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg3636 sg4224 - -lemma sg15783 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by - exact rowSquare_join (by decide) sg3360 sg4452 - -lemma sg15784 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by - exact rowSquare_join (by decide) sg3723 sg4043 - -lemma sg15785 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by - exact rowSquare_join (by decide) sg3360 sg4453 - -lemma sg15786 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3688 sg4130 - -lemma sg15787 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg3636 sg4225 - -lemma sg15788 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by - exact rowSquare_join (by decide) sg3723 sg4044 - -lemma sg15789 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by - exact rowSquare_join (by decide) sg3360 sg4454 - -lemma sg15790 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by - exact rowSquare_join (by decide) sg3725 sg4043 - -lemma sg15791 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg3726 sg4043 - -lemma sg15792 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg3636 sg4226 - -lemma sg15793 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by - exact rowSquare_join (by decide) sg3723 sg4045 - -lemma sg15794 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by - exact rowSquare_join (by decide) sg3360 sg4455 - -lemma sg15795 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by - exact rowSquare_join (by decide) sg3725 sg4044 - -lemma sg15796 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by - exact rowSquare_join (by decide) sg3726 sg4044 - -lemma sg15797 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by - exact rowSquare_join (by decide) sg3724 sg4045 - -lemma sg15798 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by - exact rowSquare_join (by decide) sg3725 sg4045 - -lemma sg15799 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by - exact rowSquare_join (by decide) sg3726 sg4045 - -lemma sg15800 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2660 sg4965 - -lemma sg15801 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2719 sg4926 - -lemma sg15802 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3251 sg4544 - -lemma sg15803 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2658 sg4966 - -lemma sg15804 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3559 sg4336 - -lemma sg15805 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg3614 sg4247 - -lemma sg15806 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg3685 sg4131 - -lemma sg15807 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg15305 - -lemma sg15808 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4248 - -lemma sg15809 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3251 sg4545 - -lemma sg15810 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2659 sg4966 - -lemma sg15811 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3559 sg4337 - -lemma sg15812 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg3251 sg4546 - -lemma sg15813 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3561 sg4336 - -lemma sg15814 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3685 sg4132 - -lemma sg15815 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg15306 - -lemma sg15816 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15307 - -lemma sg15817 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4249 - -lemma sg15818 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg0 sg15308 - -lemma sg15819 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3363 sg4444 - -lemma sg15820 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3685 sg4133 - -lemma sg15821 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg15309 - -lemma sg15822 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3363 sg4445 - -lemma sg15823 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15310 - -lemma sg15824 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3251 sg4547 - -lemma sg15825 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15311 - -lemma sg15826 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg3251 sg4548 - -lemma sg15827 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15312 - -lemma sg15828 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg3435 sg4399 - -lemma sg15829 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4250 - -lemma sg15830 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15313 - -lemma sg15831 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4134 - -lemma sg15832 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15314 - -lemma sg15833 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg0 sg15315 - -lemma sg15834 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15316 - -lemma sg15835 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg0 sg15317 - -lemma sg15836 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3559 sg4338 - -lemma sg15837 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg3251 sg4549 - -lemma sg15838 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3561 sg4337 - -lemma sg15839 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3559 sg4339 - -lemma sg15840 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3633 sg4227 - -lemma sg15841 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3686 sg4132 - -lemma sg15842 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15318 - -lemma sg15843 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15319 - -lemma sg15844 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg3251 sg4550 - -lemma sg15845 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15320 - -lemma sg15846 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3563 sg4337 - -lemma sg15847 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3686 sg4133 - -lemma sg15848 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15321 - -lemma sg15849 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4251 - -lemma sg15850 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15322 - -lemma sg15851 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15323 - -lemma sg15852 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15324 - -lemma sg15853 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15325 - -lemma sg15854 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4135 - -lemma sg15855 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15326 - -lemma sg15856 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg15327 - -lemma sg15857 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15328 - -lemma sg15858 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4136 - -lemma sg15859 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15329 - -lemma sg15860 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15330 - -lemma sg15861 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by - exact rowSquare_join (by decide) sg0 sg15331 - -lemma sg15862 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg0 sg15332 - -lemma sg15863 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3688 sg4133 - -lemma sg15864 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15333 - -lemma sg15865 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4252 - -lemma sg15866 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15334 - -lemma sg15867 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4253 - -lemma sg15868 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15335 - -lemma sg15869 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15336 - -lemma sg15870 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15337 - -lemma sg15871 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by - exact rowSquare_join (by decide) sg0 sg15338 - -lemma sg15872 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15339 - -lemma sg15873 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15340 - -lemma sg15874 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15341 - -lemma sg15875 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15342 - -lemma sg15876 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by - exact rowSquare_join (by decide) sg0 sg15343 - -lemma sg15877 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by - exact rowSquare_join (by decide) sg0 sg15344 - -lemma sg15878 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by - exact rowSquare_join (by decide) sg22 sg12723 - -lemma sg15879 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15345 - -lemma sg15880 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15346 - -lemma sg15881 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by - exact rowSquare_join (by decide) sg0 sg15347 - -lemma sg15882 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by - exact rowSquare_join (by decide) sg0 sg15348 - -lemma sg15883 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by - exact rowSquare_join (by decide) sg0 sg15349 - -lemma sg15884 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3561 sg4338 - -lemma sg15885 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3685 sg4138 - -lemma sg15886 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3633 sg4228 - -lemma sg15887 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3563 sg4338 - -lemma sg15888 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3561 sg4339 - -lemma sg15889 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3635 sg4227 - -lemma sg15890 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4254 - -lemma sg15891 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15350 - -lemma sg15892 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15351 - -lemma sg15893 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4255 - -lemma sg15894 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15352 - -lemma sg15895 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4139 - -lemma sg15896 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15353 - -lemma sg15897 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by - exact rowSquare_join (by decide) sg3704 sg4123 - -lemma sg15898 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3563 sg4339 - -lemma sg15899 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15354 - -lemma sg15900 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4256 - -lemma sg15901 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15355 - -lemma sg15902 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4257 - -lemma sg15903 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4140 - -lemma sg15904 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15356 - -lemma sg15905 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15357 - -lemma sg15906 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by - exact rowSquare_join (by decide) sg0 sg15358 - -lemma sg15907 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4141 - -lemma sg15908 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15359 - -lemma sg15909 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15360 - -lemma sg15910 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by - exact rowSquare_join (by decide) sg0 sg15361 - -lemma sg15911 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by - exact rowSquare_join (by decide) sg0 sg15362 - -lemma sg15912 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by - exact rowSquare_join (by decide) sg23 sg12723 - -lemma sg15913 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15363 - -lemma sg15914 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4258 - -lemma sg15915 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4142 - -lemma sg15916 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15364 - -lemma sg15917 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4143 - -lemma sg15918 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15365 - -lemma sg15919 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15366 - -lemma sg15920 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by - exact rowSquare_join (by decide) sg0 sg15367 - -lemma sg15921 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by - exact rowSquare_join (by decide) sg0 sg15368 - -lemma sg15922 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4137 - -lemma sg15923 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15369 - -lemma sg15924 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by - exact rowSquare_join (by decide) sg0 sg15370 - -lemma sg15925 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by - exact rowSquare_join (by decide) sg0 sg15371 - -lemma sg15926 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by - exact rowSquare_join (by decide) sg0 sg15372 - -lemma sg15927 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15373 - -lemma sg15928 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by - exact rowSquare_join (by decide) sg0 sg15374 - -lemma sg15929 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by - exact rowSquare_join (by decide) sg0 sg15375 - -lemma sg15930 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by - exact rowSquare_join (by decide) sg0 sg15376 - -lemma sg15931 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3686 sg4138 - -lemma sg15932 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3635 sg4228 - -lemma sg15933 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4259 - -lemma sg15934 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg3450 sg4397 - -lemma sg15935 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3688 sg4138 - -lemma sg15936 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3636 sg4228 - -lemma sg15937 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4260 - -lemma sg15938 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3641 sg4219 - -lemma sg15939 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4261 - -lemma sg15940 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4139 - -lemma sg15941 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg3635 sg4229 - -lemma sg15942 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg4230 - -lemma sg15943 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by - exact rowSquare_join (by decide) sg3707 sg4123 - -lemma sg15944 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3641 sg4220 - -lemma sg15945 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4262 - -lemma sg15946 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3688 sg4139 - -lemma sg15947 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3635 sg4231 - -lemma sg15948 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4140 - -lemma sg15949 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg3636 sg4229 - -lemma sg15950 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg4232 - -lemma sg15951 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,3] := by - exact rowSquare_join (by decide) sg3360 sg4458 - -lemma sg15952 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,2] := by - exact rowSquare_join (by decide) sg3360 sg4459 - -lemma sg15953 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4141 - -lemma sg15954 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg4233 - -lemma sg15955 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,2] := by - exact rowSquare_join (by decide) sg3725 sg4046 - -lemma sg15956 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,4,1] := by - exact rowSquare_join (by decide) sg3725 sg4047 - -lemma sg15957 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,5] := by - exact rowSquare_join (by decide) sg3726 sg4047 - -lemma sg15958 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4263 - -lemma sg15959 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4142 - -lemma sg15960 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg3636 sg4231 - -lemma sg15961 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg4234 - -lemma sg15962 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,3] := by - exact rowSquare_join (by decide) sg3360 sg4460 - -lemma sg15963 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4143 - -lemma sg15964 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg3635 sg4235 - -lemma sg15965 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,2] := by - exact rowSquare_join (by decide) sg3360 sg4461 - -lemma sg15966 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,4,1] := by - exact rowSquare_join (by decide) sg3730 sg4043 - -lemma sg15967 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg3636 sg4233 - -lemma sg15968 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,2] := by - exact rowSquare_join (by decide) sg3360 sg4462 - -lemma sg15969 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,3,1] := by - exact rowSquare_join (by decide) sg3725 sg4048 - -lemma sg15970 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,4] := by - exact rowSquare_join (by decide) sg3726 sg4048 - -lemma sg15971 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by - exact rowSquare_join (by decide) sg3725 sg4049 - -lemma sg15972 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,3] := by - exact rowSquare_join (by decide) sg3726 sg4049 - -lemma sg15973 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2660 sg4966 - -lemma sg15974 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3251 sg4551 - -lemma sg15975 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15377 - -lemma sg15976 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3252 sg4544 - -lemma sg15977 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg3251 sg4552 - -lemma sg15978 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3363 sg4456 - -lemma sg15979 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3685 sg4144 - -lemma sg15980 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg15378 - -lemma sg15981 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15379 - -lemma sg15982 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15380 - -lemma sg15983 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg0 sg15381 - -lemma sg15984 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3252 sg4545 - -lemma sg15985 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg3251 sg4553 - -lemma sg15986 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3253 sg4544 - -lemma sg15987 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3252 sg4546 - -lemma sg15988 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg15382 - -lemma sg15989 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3686 sg4144 - -lemma sg15990 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15383 - -lemma sg15991 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15384 - -lemma sg15992 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15385 - -lemma sg15993 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15386 - -lemma sg15994 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3254 sg4544 - -lemma sg15995 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3363 sg4457 - -lemma sg15996 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15387 - -lemma sg15997 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15388 - -lemma sg15998 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15389 - -lemma sg15999 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15390 - -lemma sg16000 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15391 - -lemma sg16001 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15392 - -lemma sg16002 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15393 - -lemma sg16003 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8 sg13509 - -lemma sg16004 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg15394 - -lemma sg16005 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15395 - -lemma sg16006 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15396 - -lemma sg16007 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15397 - -lemma sg16008 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg8 sg13512 - -lemma sg16009 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg0 sg15398 - -lemma sg16010 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg0 sg15399 - -lemma sg16011 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3253 sg4545 - -lemma sg16012 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3252 sg4549 - -lemma sg16013 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg15400 - -lemma sg16014 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3254 sg4545 - -lemma sg16015 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3253 sg4546 - -lemma sg16016 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15401 - -lemma sg16017 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15402 - -lemma sg16018 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15403 - -lemma sg16019 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15404 - -lemma sg16020 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15405 - -lemma sg16021 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15406 - -lemma sg16022 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15407 - -lemma sg16023 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15408 - -lemma sg16024 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg15409 - -lemma sg16025 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3254 sg4546 - -lemma sg16026 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15410 - -lemma sg16027 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15411 - -lemma sg16028 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15412 - -lemma sg16029 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15413 - -lemma sg16030 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15414 - -lemma sg16031 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15415 - -lemma sg16032 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15416 - -lemma sg16033 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg0 sg15417 - -lemma sg16034 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15418 - -lemma sg16035 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15419 - -lemma sg16036 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15420 - -lemma sg16037 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg0 sg15421 - -lemma sg16038 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by - exact rowSquare_join (by decide) sg0 sg15422 - -lemma sg16039 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by - exact rowSquare_join (by decide) sg24 sg12723 - -lemma sg16040 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15423 - -lemma sg16041 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15424 - -lemma sg16042 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15425 - -lemma sg16043 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15426 - -lemma sg16044 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15427 - -lemma sg16045 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15428 - -lemma sg16046 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15429 - -lemma sg16047 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15430 - -lemma sg16048 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by - exact rowSquare_join (by decide) sg0 sg15431 - -lemma sg16049 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by - exact rowSquare_join (by decide) sg22 sg12725 - -lemma sg16050 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15432 - -lemma sg16051 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15433 - -lemma sg16052 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by - exact rowSquare_join (by decide) sg0 sg15434 - -lemma sg16053 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by - exact rowSquare_join (by decide) sg22 sg12726 - -lemma sg16054 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by - exact rowSquare_join (by decide) sg22 sg12727 - -lemma sg16055 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15435 - -lemma sg16056 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by - exact rowSquare_join (by decide) sg0 sg15436 - -lemma sg16057 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by - exact rowSquare_join (by decide) sg0 sg15437 - -lemma sg16058 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by - exact rowSquare_join (by decide) sg0 sg15438 - -lemma sg16059 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3566 sg4338 - -lemma sg16060 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3253 sg4549 - -lemma sg16061 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15439 - -lemma sg16062 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15440 - -lemma sg16063 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15441 - -lemma sg16064 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3254 sg4549 - -lemma sg16065 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15442 - -lemma sg16066 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15443 - -lemma sg16067 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15444 - -lemma sg16068 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15445 - -lemma sg16069 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15446 - -lemma sg16070 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15447 - -lemma sg16071 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15448 - -lemma sg16072 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by - exact rowSquare_join (by decide) sg0 sg15449 - -lemma sg16073 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15450 - -lemma sg16074 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15451 - -lemma sg16075 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15452 - -lemma sg16076 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15453 - -lemma sg16077 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15454 - -lemma sg16078 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15455 - -lemma sg16079 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15456 - -lemma sg16080 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by - exact rowSquare_join (by decide) sg0 sg15457 - -lemma sg16081 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by - exact rowSquare_join (by decide) sg22 sg12728 - -lemma sg16082 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15458 - -lemma sg16083 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15459 - -lemma sg16084 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by - exact rowSquare_join (by decide) sg0 sg15460 - -lemma sg16085 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by - exact rowSquare_join (by decide) sg23 sg12726 - -lemma sg16086 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by - exact rowSquare_join (by decide) sg23 sg12727 - -lemma sg16087 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15461 - -lemma sg16088 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15462 - -lemma sg16089 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15463 - -lemma sg16090 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15464 - -lemma sg16091 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15465 - -lemma sg16092 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15466 - -lemma sg16093 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15467 - -lemma sg16094 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by - exact rowSquare_join (by decide) sg22 sg12730 - -lemma sg16095 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by - exact rowSquare_join (by decide) sg22 sg12731 - -lemma sg16096 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15468 - -lemma sg16097 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by - exact rowSquare_join (by decide) sg0 sg15469 - -lemma sg16098 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by - exact rowSquare_join (by decide) sg22 sg12732 - -lemma sg16099 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by - exact rowSquare_join (by decide) sg22 sg12733 - -lemma sg16100 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by - exact rowSquare_join (by decide) sg0 sg15470 - -lemma sg16101 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by - exact rowSquare_join (by decide) sg0 sg15471 - -lemma sg16102 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3568 sg4338 - -lemma sg16103 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3693 sg4138 - -lemma sg16104 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15472 - -lemma sg16105 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4264 - -lemma sg16106 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15473 - -lemma sg16107 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15474 - -lemma sg16108 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4265 - -lemma sg16109 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4147 - -lemma sg16110 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15475 - -lemma sg16111 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4148 - -lemma sg16112 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15476 - -lemma sg16113 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15477 - -lemma sg16114 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4266 - -lemma sg16115 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4149 - -lemma sg16116 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15478 - -lemma sg16117 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4145 - -lemma sg16118 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4150 - -lemma sg16119 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4146 - -lemma sg16120 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3646 sg4218 - -lemma sg16121 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15479 - -lemma sg16122 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [10,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15480 - -lemma sg16123 : RowSquare [5,5,4,3,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1943 sg6339 - -lemma sg16124 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1232 sg8016 - -lemma sg16125 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2137 sg5784 - -lemma sg16126 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2137 sg5785 - -lemma sg16127 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2139 sg5779 - -lemma sg16128 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1682 sg6515 - -lemma sg16129 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1232 sg8017 - -lemma sg16130 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1232 sg8018 - -lemma sg16131 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg3359 sg4439 - -lemma sg16132 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2148 sg5776 - -lemma sg16133 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2645 sg4966 - -lemma sg16134 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2652 sg4965 - -lemma sg16135 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3302 sg4519 - -lemma sg16136 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg2144 sg5780 - -lemma sg16137 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg2654 sg4965 - -lemma sg16138 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2146 sg5778 - -lemma sg16139 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1682 sg6516 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 + +namespace OAI + +/-! Semigroup Nodes 38. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg15740 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15297 + +lemma sg15741 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg3636 sg4217 + +lemma sg15742 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4243 + +lemma sg15743 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4128 + +lemma sg15744 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg3360 sg4446 + +lemma sg15745 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4244 + +lemma sg15746 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4129 + +lemma sg15747 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15298 + +lemma sg15748 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by + exact rowSquare_join (by decide) sg3360 sg4447 + +lemma sg15749 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by + exact rowSquare_join (by decide) sg3360 sg4448 + +lemma sg15750 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4130 + +lemma sg15751 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15299 + +lemma sg15752 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15300 + +lemma sg15753 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by + exact rowSquare_join (by decide) sg0 sg15301 + +lemma sg15754 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by + exact rowSquare_join (by decide) sg0 sg15302 + +lemma sg15755 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by + exact rowSquare_join (by decide) sg0 sg15303 + +lemma sg15756 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg0 sg15304 + +lemma sg15757 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg3568 sg4325 + +lemma sg15758 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3568 sg4326 + +lemma sg15759 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2917 sg4886 + +lemma sg15760 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3686 sg4126 + +lemma sg15761 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg3635 sg4219 + +lemma sg15762 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by + exact rowSquare_join (by decide) sg3360 sg4449 + +lemma sg15763 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4127 + +lemma sg15764 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by + exact rowSquare_join (by decide) sg3419 sg4400 + +lemma sg15765 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by + exact rowSquare_join (by decide) sg3707 sg4120 + +lemma sg15766 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg3636 sg4221 + +lemma sg15767 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by + exact rowSquare_join (by decide) sg3360 sg4450 + +lemma sg15768 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by + exact rowSquare_join (by decide) sg3360 sg4451 + +lemma sg15769 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by + exact rowSquare_join (by decide) sg3420 sg4401 + +lemma sg15770 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4130 + +lemma sg15771 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg4226 + +lemma sg15772 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by + exact rowSquare_join (by decide) sg3725 sg4040 + +lemma sg15773 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by + exact rowSquare_join (by decide) sg3725 sg4041 + +lemma sg15774 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by + exact rowSquare_join (by decide) sg3726 sg4041 + +lemma sg15775 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4246 + +lemma sg15776 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3688 sg4128 + +lemma sg15777 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3432 sg4398 + +lemma sg15778 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,2] := by + exact rowSquare_join (by decide) sg3723 sg4042 + +lemma sg15779 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3688 sg4129 + +lemma sg15780 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg3636 sg4223 + +lemma sg15781 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,2] := by + exact rowSquare_join (by decide) sg3724 sg4042 + +lemma sg15782 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg3636 sg4224 + +lemma sg15783 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by + exact rowSquare_join (by decide) sg3360 sg4452 + +lemma sg15784 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by + exact rowSquare_join (by decide) sg3723 sg4043 + +lemma sg15785 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by + exact rowSquare_join (by decide) sg3360 sg4453 + +lemma sg15786 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3688 sg4130 + +lemma sg15787 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg3636 sg4225 + +lemma sg15788 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by + exact rowSquare_join (by decide) sg3723 sg4044 + +lemma sg15789 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by + exact rowSquare_join (by decide) sg3360 sg4454 + +lemma sg15790 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by + exact rowSquare_join (by decide) sg3725 sg4043 + +lemma sg15791 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg3726 sg4043 + +lemma sg15792 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg3636 sg4226 + +lemma sg15793 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by + exact rowSquare_join (by decide) sg3723 sg4045 + +lemma sg15794 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by + exact rowSquare_join (by decide) sg3360 sg4455 + +lemma sg15795 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by + exact rowSquare_join (by decide) sg3725 sg4044 + +lemma sg15796 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by + exact rowSquare_join (by decide) sg3726 sg4044 + +lemma sg15797 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by + exact rowSquare_join (by decide) sg3724 sg4045 + +lemma sg15798 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by + exact rowSquare_join (by decide) sg3725 sg4045 + +lemma sg15799 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by + exact rowSquare_join (by decide) sg3726 sg4045 + +lemma sg15800 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2660 sg4965 + +lemma sg15801 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2719 sg4926 + +lemma sg15802 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3251 sg4544 + +lemma sg15803 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2658 sg4966 + +lemma sg15804 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3559 sg4336 + +lemma sg15805 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg3614 sg4247 + +lemma sg15806 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg3685 sg4131 + +lemma sg15807 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg15305 + +lemma sg15808 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4248 + +lemma sg15809 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3251 sg4545 + +lemma sg15810 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2659 sg4966 + +lemma sg15811 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3559 sg4337 + +lemma sg15812 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg3251 sg4546 + +lemma sg15813 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3561 sg4336 + +lemma sg15814 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3685 sg4132 + +lemma sg15815 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg15306 + +lemma sg15816 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15307 + +lemma sg15817 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4249 + +lemma sg15818 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg0 sg15308 + +lemma sg15819 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3363 sg4444 + +lemma sg15820 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3685 sg4133 + +lemma sg15821 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg15309 + +lemma sg15822 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3363 sg4445 + +lemma sg15823 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15310 + +lemma sg15824 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3251 sg4547 + +lemma sg15825 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15311 + +lemma sg15826 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg3251 sg4548 + +lemma sg15827 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15312 + +lemma sg15828 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg3435 sg4399 + +lemma sg15829 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4250 + +lemma sg15830 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15313 + +lemma sg15831 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4134 + +lemma sg15832 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15314 + +lemma sg15833 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg0 sg15315 + +lemma sg15834 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15316 + +lemma sg15835 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg0 sg15317 + +lemma sg15836 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3559 sg4338 + +lemma sg15837 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg3251 sg4549 + +lemma sg15838 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3561 sg4337 + +lemma sg15839 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3559 sg4339 + +lemma sg15840 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3633 sg4227 + +lemma sg15841 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3686 sg4132 + +lemma sg15842 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15318 + +lemma sg15843 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15319 + +lemma sg15844 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg3251 sg4550 + +lemma sg15845 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15320 + +lemma sg15846 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3563 sg4337 + +lemma sg15847 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3686 sg4133 + +lemma sg15848 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15321 + +lemma sg15849 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4251 + +lemma sg15850 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15322 + +lemma sg15851 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15323 + +lemma sg15852 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15324 + +lemma sg15853 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15325 + +lemma sg15854 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4135 + +lemma sg15855 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15326 + +lemma sg15856 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg15327 + +lemma sg15857 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15328 + +lemma sg15858 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4136 + +lemma sg15859 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15329 + +lemma sg15860 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15330 + +lemma sg15861 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by + exact rowSquare_join (by decide) sg0 sg15331 + +lemma sg15862 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg0 sg15332 + +lemma sg15863 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3688 sg4133 + +lemma sg15864 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15333 + +lemma sg15865 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4252 + +lemma sg15866 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15334 + +lemma sg15867 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4253 + +lemma sg15868 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15335 + +lemma sg15869 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15336 + +lemma sg15870 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15337 + +lemma sg15871 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by + exact rowSquare_join (by decide) sg0 sg15338 + +lemma sg15872 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15339 + +lemma sg15873 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15340 + +lemma sg15874 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15341 + +lemma sg15875 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15342 + +lemma sg15876 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by + exact rowSquare_join (by decide) sg0 sg15343 + +lemma sg15877 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by + exact rowSquare_join (by decide) sg0 sg15344 + +lemma sg15878 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by + exact rowSquare_join (by decide) sg22 sg12723 + +lemma sg15879 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15345 + +lemma sg15880 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15346 + +lemma sg15881 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by + exact rowSquare_join (by decide) sg0 sg15347 + +lemma sg15882 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by + exact rowSquare_join (by decide) sg0 sg15348 + +lemma sg15883 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by + exact rowSquare_join (by decide) sg0 sg15349 + +lemma sg15884 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3561 sg4338 + +lemma sg15885 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3685 sg4138 + +lemma sg15886 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3633 sg4228 + +lemma sg15887 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3563 sg4338 + +lemma sg15888 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3561 sg4339 + +lemma sg15889 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3635 sg4227 + +lemma sg15890 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4254 + +lemma sg15891 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15350 + +lemma sg15892 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15351 + +lemma sg15893 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4255 + +lemma sg15894 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15352 + +lemma sg15895 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4139 + +lemma sg15896 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15353 + +lemma sg15897 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by + exact rowSquare_join (by decide) sg3704 sg4123 + +lemma sg15898 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3563 sg4339 + +lemma sg15899 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15354 + +lemma sg15900 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4256 + +lemma sg15901 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15355 + +lemma sg15902 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4257 + +lemma sg15903 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4140 + +lemma sg15904 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15356 + +lemma sg15905 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15357 + +lemma sg15906 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by + exact rowSquare_join (by decide) sg0 sg15358 + +lemma sg15907 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4141 + +lemma sg15908 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15359 + +lemma sg15909 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15360 + +lemma sg15910 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by + exact rowSquare_join (by decide) sg0 sg15361 + +lemma sg15911 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by + exact rowSquare_join (by decide) sg0 sg15362 + +lemma sg15912 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by + exact rowSquare_join (by decide) sg23 sg12723 + +lemma sg15913 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15363 + +lemma sg15914 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4258 + +lemma sg15915 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4142 + +lemma sg15916 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15364 + +lemma sg15917 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4143 + +lemma sg15918 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15365 + +lemma sg15919 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15366 + +lemma sg15920 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by + exact rowSquare_join (by decide) sg0 sg15367 + +lemma sg15921 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by + exact rowSquare_join (by decide) sg0 sg15368 + +lemma sg15922 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4137 + +lemma sg15923 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15369 + +lemma sg15924 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by + exact rowSquare_join (by decide) sg0 sg15370 + +lemma sg15925 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by + exact rowSquare_join (by decide) sg0 sg15371 + +lemma sg15926 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by + exact rowSquare_join (by decide) sg0 sg15372 + +lemma sg15927 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15373 + +lemma sg15928 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by + exact rowSquare_join (by decide) sg0 sg15374 + +lemma sg15929 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by + exact rowSquare_join (by decide) sg0 sg15375 + +lemma sg15930 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by + exact rowSquare_join (by decide) sg0 sg15376 + +lemma sg15931 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3686 sg4138 + +lemma sg15932 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3635 sg4228 + +lemma sg15933 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4259 + +lemma sg15934 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg3450 sg4397 + +lemma sg15935 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3688 sg4138 + +lemma sg15936 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3636 sg4228 + +lemma sg15937 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4260 + +lemma sg15938 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3641 sg4219 + +lemma sg15939 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4261 + +lemma sg15940 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4139 + +lemma sg15941 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg3635 sg4229 + +lemma sg15942 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg4230 + +lemma sg15943 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by + exact rowSquare_join (by decide) sg3707 sg4123 + +lemma sg15944 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3641 sg4220 + +lemma sg15945 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4262 + +lemma sg15946 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3688 sg4139 + +lemma sg15947 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3635 sg4231 + +lemma sg15948 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4140 + +lemma sg15949 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg3636 sg4229 + +lemma sg15950 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg4232 + +lemma sg15951 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,3] := by + exact rowSquare_join (by decide) sg3360 sg4458 + +lemma sg15952 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,2] := by + exact rowSquare_join (by decide) sg3360 sg4459 + +lemma sg15953 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4141 + +lemma sg15954 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg4233 + +lemma sg15955 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,2] := by + exact rowSquare_join (by decide) sg3725 sg4046 + +lemma sg15956 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,4,1] := by + exact rowSquare_join (by decide) sg3725 sg4047 + +lemma sg15957 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,5] := by + exact rowSquare_join (by decide) sg3726 sg4047 + +lemma sg15958 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4263 + +lemma sg15959 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4142 + +lemma sg15960 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg3636 sg4231 + +lemma sg15961 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg4234 + +lemma sg15962 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,3] := by + exact rowSquare_join (by decide) sg3360 sg4460 + +lemma sg15963 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4143 + +lemma sg15964 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg3635 sg4235 + +lemma sg15965 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,2] := by + exact rowSquare_join (by decide) sg3360 sg4461 + +lemma sg15966 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,4,1] := by + exact rowSquare_join (by decide) sg3730 sg4043 + +lemma sg15967 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg3636 sg4233 + +lemma sg15968 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,2] := by + exact rowSquare_join (by decide) sg3360 sg4462 + +lemma sg15969 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,3,1] := by + exact rowSquare_join (by decide) sg3725 sg4048 + +lemma sg15970 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,4] := by + exact rowSquare_join (by decide) sg3726 sg4048 + +lemma sg15971 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by + exact rowSquare_join (by decide) sg3725 sg4049 + +lemma sg15972 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,3] := by + exact rowSquare_join (by decide) sg3726 sg4049 + +lemma sg15973 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2660 sg4966 + +lemma sg15974 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3251 sg4551 + +lemma sg15975 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15377 + +lemma sg15976 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3252 sg4544 + +lemma sg15977 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg3251 sg4552 + +lemma sg15978 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3363 sg4456 + +lemma sg15979 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3685 sg4144 + +lemma sg15980 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg15378 + +lemma sg15981 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15379 + +lemma sg15982 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15380 + +lemma sg15983 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg0 sg15381 + +lemma sg15984 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3252 sg4545 + +lemma sg15985 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg3251 sg4553 + +lemma sg15986 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3253 sg4544 + +lemma sg15987 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3252 sg4546 + +lemma sg15988 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg15382 + +lemma sg15989 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3686 sg4144 + +lemma sg15990 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15383 + +lemma sg15991 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15384 + +lemma sg15992 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15385 + +lemma sg15993 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15386 + +lemma sg15994 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3254 sg4544 + +lemma sg15995 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3363 sg4457 + +lemma sg15996 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15387 + +lemma sg15997 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15388 + +lemma sg15998 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15389 + +lemma sg15999 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15390 + +lemma sg16000 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15391 + +lemma sg16001 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15392 + +lemma sg16002 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15393 + +lemma sg16003 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8 sg13509 + +lemma sg16004 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg15394 + +lemma sg16005 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15395 + +lemma sg16006 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15396 + +lemma sg16007 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15397 + +lemma sg16008 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg8 sg13512 + +lemma sg16009 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg0 sg15398 + +lemma sg16010 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg0 sg15399 + +lemma sg16011 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3253 sg4545 + +lemma sg16012 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3252 sg4549 + +lemma sg16013 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg15400 + +lemma sg16014 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3254 sg4545 + +lemma sg16015 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3253 sg4546 + +lemma sg16016 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15401 + +lemma sg16017 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15402 + +lemma sg16018 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15403 + +lemma sg16019 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15404 + +lemma sg16020 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15405 + +lemma sg16021 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15406 + +lemma sg16022 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15407 + +lemma sg16023 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15408 + +lemma sg16024 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg15409 + +lemma sg16025 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3254 sg4546 + +lemma sg16026 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15410 + +lemma sg16027 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15411 + +lemma sg16028 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15412 + +lemma sg16029 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15413 + +lemma sg16030 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15414 + +lemma sg16031 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15415 + +lemma sg16032 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15416 + +lemma sg16033 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg0 sg15417 + +lemma sg16034 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15418 + +lemma sg16035 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15419 + +lemma sg16036 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15420 + +lemma sg16037 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg0 sg15421 + +lemma sg16038 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by + exact rowSquare_join (by decide) sg0 sg15422 + +lemma sg16039 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by + exact rowSquare_join (by decide) sg24 sg12723 + +lemma sg16040 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15423 + +lemma sg16041 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15424 + +lemma sg16042 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15425 + +lemma sg16043 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15426 + +lemma sg16044 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15427 + +lemma sg16045 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15428 + +lemma sg16046 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15429 + +lemma sg16047 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15430 + +lemma sg16048 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by + exact rowSquare_join (by decide) sg0 sg15431 + +lemma sg16049 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by + exact rowSquare_join (by decide) sg22 sg12725 + +lemma sg16050 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15432 + +lemma sg16051 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15433 + +lemma sg16052 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by + exact rowSquare_join (by decide) sg0 sg15434 + +lemma sg16053 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by + exact rowSquare_join (by decide) sg22 sg12726 + +lemma sg16054 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by + exact rowSquare_join (by decide) sg22 sg12727 + +lemma sg16055 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15435 + +lemma sg16056 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by + exact rowSquare_join (by decide) sg0 sg15436 + +lemma sg16057 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by + exact rowSquare_join (by decide) sg0 sg15437 + +lemma sg16058 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by + exact rowSquare_join (by decide) sg0 sg15438 + +lemma sg16059 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3566 sg4338 + +lemma sg16060 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3253 sg4549 + +lemma sg16061 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15439 + +lemma sg16062 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15440 + +lemma sg16063 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15441 + +lemma sg16064 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3254 sg4549 + +lemma sg16065 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15442 + +lemma sg16066 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15443 + +lemma sg16067 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15444 + +lemma sg16068 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15445 + +lemma sg16069 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15446 + +lemma sg16070 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15447 + +lemma sg16071 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15448 + +lemma sg16072 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by + exact rowSquare_join (by decide) sg0 sg15449 + +lemma sg16073 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15450 + +lemma sg16074 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15451 + +lemma sg16075 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15452 + +lemma sg16076 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15453 + +lemma sg16077 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15454 + +lemma sg16078 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15455 + +lemma sg16079 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15456 + +lemma sg16080 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by + exact rowSquare_join (by decide) sg0 sg15457 + +lemma sg16081 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by + exact rowSquare_join (by decide) sg22 sg12728 + +lemma sg16082 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15458 + +lemma sg16083 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15459 + +lemma sg16084 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by + exact rowSquare_join (by decide) sg0 sg15460 + +lemma sg16085 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by + exact rowSquare_join (by decide) sg23 sg12726 + +lemma sg16086 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by + exact rowSquare_join (by decide) sg23 sg12727 + +lemma sg16087 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15461 + +lemma sg16088 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15462 + +lemma sg16089 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15463 + +lemma sg16090 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15464 + +lemma sg16091 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15465 + +lemma sg16092 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15466 + +lemma sg16093 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15467 + +lemma sg16094 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by + exact rowSquare_join (by decide) sg22 sg12730 + +lemma sg16095 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by + exact rowSquare_join (by decide) sg22 sg12731 + +lemma sg16096 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15468 + +lemma sg16097 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by + exact rowSquare_join (by decide) sg0 sg15469 + +lemma sg16098 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by + exact rowSquare_join (by decide) sg22 sg12732 + +lemma sg16099 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by + exact rowSquare_join (by decide) sg22 sg12733 + +lemma sg16100 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by + exact rowSquare_join (by decide) sg0 sg15470 + +lemma sg16101 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by + exact rowSquare_join (by decide) sg0 sg15471 + +lemma sg16102 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3568 sg4338 + +lemma sg16103 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3693 sg4138 + +lemma sg16104 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15472 + +lemma sg16105 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4264 + +lemma sg16106 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15473 + +lemma sg16107 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15474 + +lemma sg16108 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4265 + +lemma sg16109 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4147 + +lemma sg16110 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15475 + +lemma sg16111 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4148 + +lemma sg16112 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15476 + +lemma sg16113 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15477 + +lemma sg16114 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4266 + +lemma sg16115 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4149 + +lemma sg16116 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15478 + +lemma sg16117 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4145 + +lemma sg16118 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4150 + +lemma sg16119 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4146 + +lemma sg16120 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3646 sg4218 + +lemma sg16121 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15479 + +lemma sg16122 : RowSquare [5,4,4,4,3,2,1,1,1,1,1,1,1,1,1] [10,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15480 + +lemma sg16123 : RowSquare [5,5,4,3,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1943 sg6339 + +lemma sg16124 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1232 sg8016 + +lemma sg16125 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2137 sg5784 + +lemma sg16126 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2137 sg5785 + +lemma sg16127 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2139 sg5779 + +lemma sg16128 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1682 sg6515 + +lemma sg16129 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1232 sg8017 + +lemma sg16130 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1232 sg8018 + +lemma sg16131 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg3359 sg4439 + +lemma sg16132 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2148 sg5776 + +lemma sg16133 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2645 sg4966 + +lemma sg16134 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2652 sg4965 + +lemma sg16135 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3302 sg4519 + +lemma sg16136 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg2144 sg5780 + +lemma sg16137 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg2654 sg4965 + +lemma sg16138 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2146 sg5778 + +lemma sg16139 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1682 sg6516 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes39.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes39.lean index f07d3b5eb3d013613fde3d0eae3bde74cf0ea818..c9e4d4160482e98f2d448ad91125039ef3485b7d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes39.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes39.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 - -namespace OAI - -/-! Semigroup Nodes 39. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg16140 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2137 sg5786 - -lemma sg16141 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg3411 sg4395 - -lemma sg16142 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg3411 sg4397 - -lemma sg16143 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg3562 sg4321 - -lemma sg16144 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3569 sg4316 - -lemma sg16145 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3302 sg4520 - -lemma sg16146 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3618 sg4214 - -lemma sg16147 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3570 sg4316 - -lemma sg16148 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,4,1] := by - exact rowSquare_join (by decide) sg3620 sg4215 - -lemma sg16149 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1682 sg6517 - -lemma sg16150 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by - exact rowSquare_join (by decide) sg1688 sg6513 - -lemma sg16151 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,3] := by - exact rowSquare_join (by decide) sg1688 sg6514 - -lemma sg16152 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4226 - -lemma sg16153 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg3501 sg4361 - -lemma sg16154 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg4885 - -lemma sg16155 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1] := by - exact rowSquare_join (by decide) sg3565 sg4320 - -lemma sg16156 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by - exact rowSquare_join (by decide) sg3690 sg4119 - -lemma sg16157 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by - exact rowSquare_join (by decide) sg3622 sg4216 - -lemma sg16158 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by - exact rowSquare_join (by decide) sg3690 sg4120 - -lemma sg16159 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by - exact rowSquare_join (by decide) sg3691 sg4120 - -lemma sg16160 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2150 sg5776 - -lemma sg16161 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2655 sg4965 - -lemma sg16162 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg2649 sg4966 - -lemma sg16163 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2653 sg4966 - -lemma sg16164 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg3685 sg4121 - -lemma sg16165 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2654 sg4966 - -lemma sg16166 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by - exact rowSquare_join (by decide) sg3567 sg4321 - -lemma sg16167 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3502 sg4361 - -lemma sg16168 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg3691 sg4121 - -lemma sg16169 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2280 sg5752 - -lemma sg16170 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3503 sg4360 - -lemma sg16171 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg3617 sg4218 - -lemma sg16172 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg3504 sg4360 - -lemma sg16173 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3688 sg4122 - -lemma sg16174 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3502 sg4362 - -lemma sg16175 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3502 sg4364 - -lemma sg16176 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3695 sg4122 - -lemma sg16177 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [7,4,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg3303 sg4359 - -lemma sg16178 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg3 sg14644 - -lemma sg16179 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg3 sg14645 - -lemma sg16180 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg3250 sg4446 - -lemma sg16181 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg3304 sg4363 - -lemma sg16182 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg3305 sg4363 - -lemma sg16183 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by - exact rowSquare_join (by decide) sg3306 sg4360 - -lemma sg16184 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg3 sg14646 - -lemma sg16185 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg3305 sg4365 - -lemma sg16186 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg3306 sg4363 - -lemma sg16187 : RowSquare [6,4,4,3,2,2,2,2,2,2,1,1] [5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1869 sg6389 - -lemma sg16188 : RowSquare [6,4,4,3,2,2,2,2,2,2,1,1] [5,5,5,5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1868 sg6390 - -lemma sg16189 : RowSquare [6,4,4,3,2,2,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1870 sg6389 - -lemma sg16190 : RowSquare [6,4,4,3,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1871 sg6389 - -lemma sg16191 : RowSquare [6,4,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3362 sg4434 - -lemma sg16192 : RowSquare [6,4,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg3331 sg4501 - -lemma sg16193 : RowSquare [6,4,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3322 sg4502 - -lemma sg16194 : RowSquare [6,4,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by - exact rowSquare_join (by decide) sg32 sg12723 - -lemma sg16195 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2248 sg5672 - -lemma sg16196 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1852 sg6457 - -lemma sg16197 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [5,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2247 sg5673 - -lemma sg16198 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1854 sg6457 - -lemma sg16199 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1855 sg6457 - -lemma sg16200 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1850 sg6458 - -lemma sg16201 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1857 sg6457 - -lemma sg16202 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [6,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1859 sg6457 - -lemma sg16203 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1860 sg6457 - -lemma sg16204 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [6,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1861 sg6457 - -lemma sg16205 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1862 sg6457 - -lemma sg16206 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1863 sg6457 - -lemma sg16207 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1854 sg6458 - -lemma sg16208 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1867 sg6457 - -lemma sg16209 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3321 sg4489 - -lemma sg16210 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1682 sg6511 - -lemma sg16211 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2630 sg4969 - -lemma sg16212 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1682 sg6512 - -lemma sg16213 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2631 sg4969 - -lemma sg16214 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1331 sg8006 - -lemma sg16215 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2633 sg4969 - -lemma sg16216 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2648 sg4941 - -lemma sg16217 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3359 sg4434 - -lemma sg16218 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3323 sg4489 - -lemma sg16219 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg1758 sg6500 - -lemma sg16220 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15484 - -lemma sg16221 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15485 - -lemma sg16222 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg2646 sg4946 - -lemma sg16223 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg3326 sg4488 - -lemma sg16224 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,2] := by - exact rowSquare_join (by decide) sg3327 sg4488 - -lemma sg16225 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg3325 sg4491 - -lemma sg16226 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3,2] := by - exact rowSquare_join (by decide) sg3327 sg4489 - -lemma sg16227 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,4,1] := by - exact rowSquare_join (by decide) sg2647 sg4949 - -lemma sg16228 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg4 sg14554 - -lemma sg16229 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg3616 sg4191 - -lemma sg16230 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg3553 sg4319 - -lemma sg16231 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg2633 sg4970 - -lemma sg16232 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg3329 sg4488 - -lemma sg16233 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg3359 sg4435 - -lemma sg16234 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg3687 sg4111 - -lemma sg16235 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg2633 sg4971 - -lemma sg16236 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg3329 sg4489 - -lemma sg16237 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,4] := by - exact rowSquare_join (by decide) sg1688 sg6509 - -lemma sg16238 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1775 sg6492 - -lemma sg16239 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3322 sg4494 - -lemma sg16240 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3321 sg4495 - -lemma sg16241 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg14555 - -lemma sg16242 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3333 sg4486 - -lemma sg16243 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg2140 sg5777 - -lemma sg16244 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,3,3] := by - exact rowSquare_join (by decide) sg2633 sg4972 - -lemma sg16245 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,4,1] := by - exact rowSquare_join (by decide) sg3332 sg4487 - -lemma sg16246 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1686 sg6510 - -lemma sg16247 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg14556 - -lemma sg16248 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13509 - -lemma sg16249 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg13510 - -lemma sg16250 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg13511 - -lemma sg16251 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by - exact rowSquare_join (by decide) sg3332 sg4488 - -lemma sg16252 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14557 - -lemma sg16253 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,2,1] := by - exact rowSquare_join (by decide) sg4 sg14558 - -lemma sg16254 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,3] := by - exact rowSquare_join (by decide) sg3358 sg4438 - -lemma sg16255 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3322 sg4496 - -lemma sg16256 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4496 - -lemma sg16257 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg3325 sg4496 - -lemma sg16258 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2902 sg4881 - -lemma sg16259 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg3555 sg4319 - -lemma sg16260 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,2] := by - exact rowSquare_join (by decide) sg2633 sg4973 - -lemma sg16261 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1] := by - exact rowSquare_join (by decide) sg3333 sg4488 - -lemma sg16262 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13512 - -lemma sg16263 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg13513 - -lemma sg16264 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by - exact rowSquare_join (by decide) sg3410 sg4378 - -lemma sg16265 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg13514 - -lemma sg16266 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by - exact rowSquare_join (by decide) sg3690 sg4111 - -lemma sg16267 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by - exact rowSquare_join (by decide) sg3732 sg4031 - -lemma sg16268 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15486 - -lemma sg16269 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15487 - -lemma sg16270 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg3403 sg4404 - -lemma sg16271 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg4 sg14559 - -lemma sg16272 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg4 sg14560 - -lemma sg16273 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg0 sg15488 - -lemma sg16274 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14821 - -lemma sg16275 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg1 sg14822 - -lemma sg16276 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg1 sg14823 - -lemma sg16277 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,4] := by - exact rowSquare_join (by decide) sg2651 sg4949 - -lemma sg16278 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg5 sg14553 - -lemma sg16279 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg5 sg14554 - -lemma sg16280 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg4 sg14562 - -lemma sg16281 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg4 sg14563 - -lemma sg16282 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15489 - -lemma sg16283 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg13515 - -lemma sg16284 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg13516 - -lemma sg16285 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by - exact rowSquare_join (by decide) sg0 sg15490 - -lemma sg16286 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg5 sg14558 - -lemma sg16287 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by - exact rowSquare_join (by decide) sg0 sg15491 - -lemma sg16288 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg14564 - -lemma sg16289 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14565 - -lemma sg16290 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg14566 - -lemma sg16291 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2,2] := by - exact rowSquare_join (by decide) sg4 sg14567 - -lemma sg16292 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,3,1] := by - exact rowSquare_join (by decide) sg4 sg14568 - -lemma sg16293 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg15492 - -lemma sg16294 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14569 - -lemma sg16295 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14570 - -lemma sg16296 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14571 - -lemma sg16297 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13518 - -lemma sg16298 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13519 - -lemma sg16299 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13520 - -lemma sg16300 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13521 - -lemma sg16301 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg13522 - -lemma sg16302 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg13523 - -lemma sg16303 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by - exact rowSquare_join (by decide) sg4 sg14572 - -lemma sg16304 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by - exact rowSquare_join (by decide) sg4 sg14573 - -lemma sg16305 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15493 - -lemma sg16306 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15494 - -lemma sg16307 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,2] := by - exact rowSquare_join (by decide) sg3403 sg4405 - -lemma sg16308 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13524 - -lemma sg16309 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13525 - -lemma sg16310 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by - exact rowSquare_join (by decide) sg0 sg15495 - -lemma sg16311 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg13526 - -lemma sg16312 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by - exact rowSquare_join (by decide) sg13 sg13527 - -lemma sg16313 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by - exact rowSquare_join (by decide) sg39 sg12723 - -lemma sg16314 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg0 sg15496 - -lemma sg16315 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3335 sg4485 - -lemma sg16316 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2633 sg4974 - -lemma sg16317 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg3687 sg4112 - -lemma sg16318 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg3617 sg4195 - -lemma sg16319 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg3329 sg4492 - -lemma sg16320 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg14574 - -lemma sg16321 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg14 sg13510 - -lemma sg16322 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg14 sg13511 - -lemma sg16323 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by - exact rowSquare_join (by decide) sg3332 sg4492 - -lemma sg16324 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3322 sg4497 - -lemma sg16325 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4209 - -lemma sg16326 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4114 - -lemma sg16327 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13529 - -lemma sg16328 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13530 - -lemma sg16329 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13531 - -lemma sg16330 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13532 - -lemma sg16331 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg13533 - -lemma sg16332 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg13534 - -lemma sg16333 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg14 sg13514 - -lemma sg16334 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by - exact rowSquare_join (by decide) sg3733 sg4031 - -lemma sg16335 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14575 - -lemma sg16336 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13535 - -lemma sg16337 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13536 - -lemma sg16338 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14576 - -lemma sg16339 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg4 sg14577 - -lemma sg16340 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,3] := by - exact rowSquare_join (by decide) sg4 sg14578 - -lemma sg16341 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13537 - -lemma sg16342 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13538 - -lemma sg16343 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13539 - -lemma sg16344 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by - exact rowSquare_join (by decide) sg13 sg13540 - -lemma sg16345 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg13541 - -lemma sg16346 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by - exact rowSquare_join (by decide) sg13 sg13542 - -lemma sg16347 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by - exact rowSquare_join (by decide) sg40 sg12723 - -lemma sg16348 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3328 sg4496 - -lemma sg16349 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13543 - -lemma sg16350 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13544 - -lemma sg16351 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13545 - -lemma sg16352 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by - exact rowSquare_join (by decide) sg13 sg13546 - -lemma sg16353 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by - exact rowSquare_join (by decide) sg13 sg13547 - -lemma sg16354 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by - exact rowSquare_join (by decide) sg13 sg13548 - -lemma sg16355 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3336 sg4486 - -lemma sg16356 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3688 sg4115 - -lemma sg16357 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1775 sg6493 - -lemma sg16358 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4212 - -lemma sg16359 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13549 - -lemma sg16360 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg14579 - -lemma sg16361 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg14580 - -lemma sg16362 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg14581 - -lemma sg16363 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13550 - -lemma sg16364 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13551 - -lemma sg16365 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13552 - -lemma sg16366 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13553 - -lemma sg16367 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg13554 - -lemma sg16368 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by - exact rowSquare_join (by decide) sg4 sg14582 - -lemma sg16369 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by - exact rowSquare_join (by decide) sg4 sg14583 - -lemma sg16370 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14584 - -lemma sg16371 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13555 - -lemma sg16372 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13556 - -lemma sg16373 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13557 - -lemma sg16374 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg13558 - -lemma sg16375 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg13559 - -lemma sg16376 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg4 sg14585 - -lemma sg16377 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg3331 sg4496 - -lemma sg16378 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13560 - -lemma sg16379 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg13561 - -lemma sg16380 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by - exact rowSquare_join (by decide) sg13 sg13562 - -lemma sg16381 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by - exact rowSquare_join (by decide) sg13 sg13563 - -lemma sg16382 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by - exact rowSquare_join (by decide) sg3333 sg4496 - -lemma sg16383 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by - exact rowSquare_join (by decide) sg13 sg13564 - -lemma sg16384 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by - exact rowSquare_join (by decide) sg13 sg13565 - -lemma sg16385 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg3403 sg4406 - -lemma sg16386 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14824 - -lemma sg16387 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg5 sg14559 - -lemma sg16388 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg5 sg14560 - -lemma sg16389 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14825 - -lemma sg16390 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg14586 - -lemma sg16391 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg4 sg14587 - -lemma sg16392 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg4 sg14588 - -lemma sg16393 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg6 sg14556 - -lemma sg16394 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13566 - -lemma sg16395 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg13567 - -lemma sg16396 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg13568 - -lemma sg16397 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg0 sg15497 - -lemma sg16398 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg6 sg14558 - -lemma sg16399 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg1 sg14826 - -lemma sg16400 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14827 - -lemma sg16401 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg5 sg14561 - -lemma sg16402 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg5 sg14562 - -lemma sg16403 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg5 sg14563 - -lemma sg16404 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14828 - -lemma sg16405 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg14589 - -lemma sg16406 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg13569 - -lemma sg16407 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg4 sg14590 - -lemma sg16408 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg4 sg14591 - -lemma sg16409 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg4 sg14592 - -lemma sg16410 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13570 - -lemma sg16411 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13571 - -lemma sg16412 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13572 - -lemma sg16413 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg13573 - -lemma sg16414 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg13574 - -lemma sg16415 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg5 sg14572 - -lemma sg16416 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg5 sg14573 - -lemma sg16417 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg14593 - -lemma sg16418 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13575 - -lemma sg16419 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13576 - -lemma sg16420 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13577 - -lemma sg16421 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by - exact rowSquare_join (by decide) sg4 sg14594 - -lemma sg16422 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13578 - -lemma sg16423 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13579 - -lemma sg16424 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by - exact rowSquare_join (by decide) sg13 sg13580 - -lemma sg16425 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg39 sg12724 - -lemma sg16426 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by - exact rowSquare_join (by decide) sg39 sg12725 - -lemma sg16427 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by - exact rowSquare_join (by decide) sg41 sg12723 - -lemma sg16428 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13581 - -lemma sg16429 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13582 - -lemma sg16430 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13583 - -lemma sg16431 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by - exact rowSquare_join (by decide) sg13 sg13584 - -lemma sg16432 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by - exact rowSquare_join (by decide) sg39 sg12726 - -lemma sg16433 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by - exact rowSquare_join (by decide) sg39 sg12727 - -lemma sg16434 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15498 - -lemma sg16435 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15499 - -lemma sg16436 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg14595 - -lemma sg16437 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg13585 - -lemma sg16438 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15500 - -lemma sg16439 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg14 sg13515 - -lemma sg16440 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg14 sg13516 - -lemma sg16441 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg15501 - -lemma sg16442 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg13517 - -lemma sg16443 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13586 - -lemma sg16444 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13587 - -lemma sg16445 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg14 sg13522 - -lemma sg16446 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by - exact rowSquare_join (by decide) sg14 sg13523 - -lemma sg16447 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13588 - -lemma sg16448 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13589 - -lemma sg16449 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13590 - -lemma sg16450 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by - exact rowSquare_join (by decide) sg13 sg13591 - -lemma sg16451 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg13592 - -lemma sg16452 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by - exact rowSquare_join (by decide) sg39 sg12728 - -lemma sg16453 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by - exact rowSquare_join (by decide) sg42 sg12723 - -lemma sg16454 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg14596 - -lemma sg16455 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg14597 - -lemma sg16456 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13593 - -lemma sg16457 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg13594 - -lemma sg16458 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg40 sg12724 - -lemma sg16459 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by - exact rowSquare_join (by decide) sg40 sg12725 - -lemma sg16460 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13595 - -lemma sg16461 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg39 sg12729 - -lemma sg16462 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by - exact rowSquare_join (by decide) sg39 sg12730 - -lemma sg16463 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by - exact rowSquare_join (by decide) sg39 sg12731 - -lemma sg16464 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by - exact rowSquare_join (by decide) sg40 sg12727 - -lemma sg16465 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13596 - -lemma sg16466 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg13597 - -lemma sg16467 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by - exact rowSquare_join (by decide) sg39 sg12732 - -lemma sg16468 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by - exact rowSquare_join (by decide) sg39 sg12733 - -lemma sg16469 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,7,6,3] := by - exact rowSquare_join (by decide) sg39 sg12734 - -lemma sg16470 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,7,7,2] := by - exact rowSquare_join (by decide) sg39 sg12735 - -lemma sg16471 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3320 sg4498 - -lemma sg16472 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3558 sg4323 - -lemma sg16473 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3320 sg4499 - -lemma sg16474 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3322 sg4498 - -lemma sg16475 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg3626 sg4195 - -lemma sg16476 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3687 sg4116 - -lemma sg16477 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4213 - -lemma sg16478 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg2633 sg4975 - -lemma sg16479 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg13528 - -lemma sg16480 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4118 - -lemma sg16481 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13600 - -lemma sg16482 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13601 - -lemma sg16483 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg13532 - -lemma sg16484 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by - exact rowSquare_join (by decide) sg14 sg13534 - -lemma sg16485 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg13535 - -lemma sg16486 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg14 sg13536 - -lemma sg16487 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13602 - -lemma sg16488 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg13603 - -lemma sg16489 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg14 sg13541 - -lemma sg16490 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,2] := by - exact rowSquare_join (by decide) sg40 sg12728 - -lemma sg16491 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13604 - -lemma sg16492 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13605 - -lemma sg16493 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg13606 - -lemma sg16494 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg13607 - -lemma sg16495 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,5] := by - exact rowSquare_join (by decide) sg14 sg13548 - -lemma sg16496 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13608 - -lemma sg16497 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg13554 - -lemma sg16498 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13609 - -lemma sg16499 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg40 sg12729 - -lemma sg16500 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,2] := by - exact rowSquare_join (by decide) sg40 sg12730 - -lemma sg16501 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,4,1] := by - exact rowSquare_join (by decide) sg40 sg12731 - -lemma sg16502 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13610 - -lemma sg16503 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,2] := by - exact rowSquare_join (by decide) sg13 sg13611 - -lemma sg16504 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,3,1] := by - exact rowSquare_join (by decide) sg40 sg12732 - -lemma sg16505 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,4] := by - exact rowSquare_join (by decide) sg40 sg12733 - -lemma sg16506 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13612 - -lemma sg16507 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by - exact rowSquare_join (by decide) sg13 sg13613 - -lemma sg16508 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,3] := by - exact rowSquare_join (by decide) sg13 sg13614 - -lemma sg16509 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,7,5,3] := by - exact rowSquare_join (by decide) sg40 sg12734 - -lemma sg16510 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,7,6,2] := by - exact rowSquare_join (by decide) sg40 sg12735 - -lemma sg16511 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,7,7,1] := by - exact rowSquare_join (by decide) sg13 sg13615 - -lemma sg16512 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,4,3] := by - exact rowSquare_join (by decide) sg13 sg13616 - -lemma sg16513 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,5,2] := by - exact rowSquare_join (by decide) sg13 sg13617 - -lemma sg16514 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,6,1] := by - exact rowSquare_join (by decide) sg13 sg13618 - -lemma sg16515 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,7] := by - exact rowSquare_join (by decide) sg13 sg13619 - -lemma sg16516 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14829 - -lemma sg16517 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14830 - -lemma sg16518 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14831 - -lemma sg16519 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg6 sg14559 - -lemma sg16520 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg6 sg14560 - -lemma sg16521 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14832 - -lemma sg16522 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14833 - -lemma sg16523 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg5 sg14586 - -lemma sg16524 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg5 sg14588 - -lemma sg16525 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14834 - -lemma sg16526 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14598 - -lemma sg16527 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg14599 - -lemma sg16528 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13620 - -lemma sg16529 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg13621 - -lemma sg16530 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14600 - -lemma sg16531 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg15 sg13510 - -lemma sg16532 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg4 sg14601 - -lemma sg16533 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13622 - -lemma sg16534 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13623 - -lemma sg16535 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13624 - -lemma sg16536 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13625 - -lemma sg16537 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg13626 - -lemma sg16538 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg15 sg13514 - -lemma sg16539 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg6 sg14573 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 + +namespace OAI + +/-! Semigroup Nodes 39. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg16140 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2137 sg5786 + +lemma sg16141 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg3411 sg4395 + +lemma sg16142 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg3411 sg4397 + +lemma sg16143 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg3562 sg4321 + +lemma sg16144 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3569 sg4316 + +lemma sg16145 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3302 sg4520 + +lemma sg16146 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3618 sg4214 + +lemma sg16147 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3570 sg4316 + +lemma sg16148 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,4,1] := by + exact rowSquare_join (by decide) sg3620 sg4215 + +lemma sg16149 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1682 sg6517 + +lemma sg16150 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by + exact rowSquare_join (by decide) sg1688 sg6513 + +lemma sg16151 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,3] := by + exact rowSquare_join (by decide) sg1688 sg6514 + +lemma sg16152 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4226 + +lemma sg16153 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg3501 sg4361 + +lemma sg16154 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg4885 + +lemma sg16155 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1] := by + exact rowSquare_join (by decide) sg3565 sg4320 + +lemma sg16156 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by + exact rowSquare_join (by decide) sg3690 sg4119 + +lemma sg16157 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by + exact rowSquare_join (by decide) sg3622 sg4216 + +lemma sg16158 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by + exact rowSquare_join (by decide) sg3690 sg4120 + +lemma sg16159 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by + exact rowSquare_join (by decide) sg3691 sg4120 + +lemma sg16160 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2150 sg5776 + +lemma sg16161 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2655 sg4965 + +lemma sg16162 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg2649 sg4966 + +lemma sg16163 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2653 sg4966 + +lemma sg16164 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg3685 sg4121 + +lemma sg16165 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2654 sg4966 + +lemma sg16166 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by + exact rowSquare_join (by decide) sg3567 sg4321 + +lemma sg16167 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3502 sg4361 + +lemma sg16168 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg3691 sg4121 + +lemma sg16169 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2280 sg5752 + +lemma sg16170 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3503 sg4360 + +lemma sg16171 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg3617 sg4218 + +lemma sg16172 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg3504 sg4360 + +lemma sg16173 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3688 sg4122 + +lemma sg16174 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3502 sg4362 + +lemma sg16175 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3502 sg4364 + +lemma sg16176 : RowSquare [5,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3695 sg4122 + +lemma sg16177 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [7,4,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg3303 sg4359 + +lemma sg16178 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg3 sg14644 + +lemma sg16179 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg3 sg14645 + +lemma sg16180 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg3250 sg4446 + +lemma sg16181 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg3304 sg4363 + +lemma sg16182 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg3305 sg4363 + +lemma sg16183 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by + exact rowSquare_join (by decide) sg3306 sg4360 + +lemma sg16184 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg3 sg14646 + +lemma sg16185 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg3305 sg4365 + +lemma sg16186 : RowSquare [5,5,5,4,3,2,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg3306 sg4363 + +lemma sg16187 : RowSquare [6,4,4,3,2,2,2,2,2,2,1,1] [5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1869 sg6389 + +lemma sg16188 : RowSquare [6,4,4,3,2,2,2,2,2,2,1,1] [5,5,5,5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1868 sg6390 + +lemma sg16189 : RowSquare [6,4,4,3,2,2,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1870 sg6389 + +lemma sg16190 : RowSquare [6,4,4,3,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1871 sg6389 + +lemma sg16191 : RowSquare [6,4,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3362 sg4434 + +lemma sg16192 : RowSquare [6,4,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg3331 sg4501 + +lemma sg16193 : RowSquare [6,4,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3322 sg4502 + +lemma sg16194 : RowSquare [6,4,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by + exact rowSquare_join (by decide) sg32 sg12723 + +lemma sg16195 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2248 sg5672 + +lemma sg16196 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1852 sg6457 + +lemma sg16197 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [5,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2247 sg5673 + +lemma sg16198 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1854 sg6457 + +lemma sg16199 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1855 sg6457 + +lemma sg16200 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1850 sg6458 + +lemma sg16201 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1857 sg6457 + +lemma sg16202 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [6,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1859 sg6457 + +lemma sg16203 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1860 sg6457 + +lemma sg16204 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [6,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1861 sg6457 + +lemma sg16205 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1862 sg6457 + +lemma sg16206 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1863 sg6457 + +lemma sg16207 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1854 sg6458 + +lemma sg16208 : RowSquare [6,5,3,3,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1867 sg6457 + +lemma sg16209 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3321 sg4489 + +lemma sg16210 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1682 sg6511 + +lemma sg16211 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2630 sg4969 + +lemma sg16212 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1682 sg6512 + +lemma sg16213 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2631 sg4969 + +lemma sg16214 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1331 sg8006 + +lemma sg16215 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2633 sg4969 + +lemma sg16216 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2648 sg4941 + +lemma sg16217 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3359 sg4434 + +lemma sg16218 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3323 sg4489 + +lemma sg16219 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg1758 sg6500 + +lemma sg16220 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15484 + +lemma sg16221 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15485 + +lemma sg16222 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg2646 sg4946 + +lemma sg16223 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg3326 sg4488 + +lemma sg16224 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,2] := by + exact rowSquare_join (by decide) sg3327 sg4488 + +lemma sg16225 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg3325 sg4491 + +lemma sg16226 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3,2] := by + exact rowSquare_join (by decide) sg3327 sg4489 + +lemma sg16227 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,4,1] := by + exact rowSquare_join (by decide) sg2647 sg4949 + +lemma sg16228 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg4 sg14554 + +lemma sg16229 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg3616 sg4191 + +lemma sg16230 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg3553 sg4319 + +lemma sg16231 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg2633 sg4970 + +lemma sg16232 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg3329 sg4488 + +lemma sg16233 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg3359 sg4435 + +lemma sg16234 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg3687 sg4111 + +lemma sg16235 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg2633 sg4971 + +lemma sg16236 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg3329 sg4489 + +lemma sg16237 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,4] := by + exact rowSquare_join (by decide) sg1688 sg6509 + +lemma sg16238 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1775 sg6492 + +lemma sg16239 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3322 sg4494 + +lemma sg16240 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3321 sg4495 + +lemma sg16241 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg14555 + +lemma sg16242 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3333 sg4486 + +lemma sg16243 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg2140 sg5777 + +lemma sg16244 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,3,3] := by + exact rowSquare_join (by decide) sg2633 sg4972 + +lemma sg16245 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,4,1] := by + exact rowSquare_join (by decide) sg3332 sg4487 + +lemma sg16246 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1686 sg6510 + +lemma sg16247 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg14556 + +lemma sg16248 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13509 + +lemma sg16249 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg13510 + +lemma sg16250 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg13511 + +lemma sg16251 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by + exact rowSquare_join (by decide) sg3332 sg4488 + +lemma sg16252 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14557 + +lemma sg16253 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,2,1] := by + exact rowSquare_join (by decide) sg4 sg14558 + +lemma sg16254 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,3] := by + exact rowSquare_join (by decide) sg3358 sg4438 + +lemma sg16255 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3322 sg4496 + +lemma sg16256 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4496 + +lemma sg16257 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg3325 sg4496 + +lemma sg16258 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2902 sg4881 + +lemma sg16259 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg3555 sg4319 + +lemma sg16260 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,2] := by + exact rowSquare_join (by decide) sg2633 sg4973 + +lemma sg16261 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1] := by + exact rowSquare_join (by decide) sg3333 sg4488 + +lemma sg16262 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13512 + +lemma sg16263 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg13513 + +lemma sg16264 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by + exact rowSquare_join (by decide) sg3410 sg4378 + +lemma sg16265 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg13514 + +lemma sg16266 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by + exact rowSquare_join (by decide) sg3690 sg4111 + +lemma sg16267 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by + exact rowSquare_join (by decide) sg3732 sg4031 + +lemma sg16268 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15486 + +lemma sg16269 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15487 + +lemma sg16270 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg3403 sg4404 + +lemma sg16271 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg4 sg14559 + +lemma sg16272 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg4 sg14560 + +lemma sg16273 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg0 sg15488 + +lemma sg16274 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14821 + +lemma sg16275 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg1 sg14822 + +lemma sg16276 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg1 sg14823 + +lemma sg16277 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,4] := by + exact rowSquare_join (by decide) sg2651 sg4949 + +lemma sg16278 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg5 sg14553 + +lemma sg16279 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg5 sg14554 + +lemma sg16280 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg4 sg14562 + +lemma sg16281 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg4 sg14563 + +lemma sg16282 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15489 + +lemma sg16283 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg13515 + +lemma sg16284 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg13516 + +lemma sg16285 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by + exact rowSquare_join (by decide) sg0 sg15490 + +lemma sg16286 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg5 sg14558 + +lemma sg16287 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by + exact rowSquare_join (by decide) sg0 sg15491 + +lemma sg16288 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg14564 + +lemma sg16289 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14565 + +lemma sg16290 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg14566 + +lemma sg16291 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2,2] := by + exact rowSquare_join (by decide) sg4 sg14567 + +lemma sg16292 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,3,1] := by + exact rowSquare_join (by decide) sg4 sg14568 + +lemma sg16293 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg15492 + +lemma sg16294 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14569 + +lemma sg16295 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14570 + +lemma sg16296 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14571 + +lemma sg16297 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13518 + +lemma sg16298 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13519 + +lemma sg16299 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13520 + +lemma sg16300 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13521 + +lemma sg16301 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg13522 + +lemma sg16302 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg13523 + +lemma sg16303 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by + exact rowSquare_join (by decide) sg4 sg14572 + +lemma sg16304 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by + exact rowSquare_join (by decide) sg4 sg14573 + +lemma sg16305 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15493 + +lemma sg16306 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15494 + +lemma sg16307 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,2] := by + exact rowSquare_join (by decide) sg3403 sg4405 + +lemma sg16308 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13524 + +lemma sg16309 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13525 + +lemma sg16310 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by + exact rowSquare_join (by decide) sg0 sg15495 + +lemma sg16311 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg13526 + +lemma sg16312 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by + exact rowSquare_join (by decide) sg13 sg13527 + +lemma sg16313 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by + exact rowSquare_join (by decide) sg39 sg12723 + +lemma sg16314 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg0 sg15496 + +lemma sg16315 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3335 sg4485 + +lemma sg16316 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2633 sg4974 + +lemma sg16317 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg3687 sg4112 + +lemma sg16318 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg3617 sg4195 + +lemma sg16319 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg3329 sg4492 + +lemma sg16320 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg14574 + +lemma sg16321 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg14 sg13510 + +lemma sg16322 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg14 sg13511 + +lemma sg16323 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by + exact rowSquare_join (by decide) sg3332 sg4492 + +lemma sg16324 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3322 sg4497 + +lemma sg16325 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4209 + +lemma sg16326 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4114 + +lemma sg16327 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13529 + +lemma sg16328 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13530 + +lemma sg16329 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13531 + +lemma sg16330 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13532 + +lemma sg16331 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg13533 + +lemma sg16332 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg13534 + +lemma sg16333 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg14 sg13514 + +lemma sg16334 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by + exact rowSquare_join (by decide) sg3733 sg4031 + +lemma sg16335 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14575 + +lemma sg16336 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13535 + +lemma sg16337 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13536 + +lemma sg16338 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14576 + +lemma sg16339 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg4 sg14577 + +lemma sg16340 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,3] := by + exact rowSquare_join (by decide) sg4 sg14578 + +lemma sg16341 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13537 + +lemma sg16342 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13538 + +lemma sg16343 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13539 + +lemma sg16344 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by + exact rowSquare_join (by decide) sg13 sg13540 + +lemma sg16345 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg13541 + +lemma sg16346 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by + exact rowSquare_join (by decide) sg13 sg13542 + +lemma sg16347 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by + exact rowSquare_join (by decide) sg40 sg12723 + +lemma sg16348 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3328 sg4496 + +lemma sg16349 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13543 + +lemma sg16350 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13544 + +lemma sg16351 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13545 + +lemma sg16352 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by + exact rowSquare_join (by decide) sg13 sg13546 + +lemma sg16353 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by + exact rowSquare_join (by decide) sg13 sg13547 + +lemma sg16354 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by + exact rowSquare_join (by decide) sg13 sg13548 + +lemma sg16355 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3336 sg4486 + +lemma sg16356 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3688 sg4115 + +lemma sg16357 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1775 sg6493 + +lemma sg16358 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4212 + +lemma sg16359 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13549 + +lemma sg16360 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg14579 + +lemma sg16361 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg14580 + +lemma sg16362 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg14581 + +lemma sg16363 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13550 + +lemma sg16364 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13551 + +lemma sg16365 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13552 + +lemma sg16366 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13553 + +lemma sg16367 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg13554 + +lemma sg16368 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by + exact rowSquare_join (by decide) sg4 sg14582 + +lemma sg16369 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by + exact rowSquare_join (by decide) sg4 sg14583 + +lemma sg16370 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14584 + +lemma sg16371 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13555 + +lemma sg16372 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13556 + +lemma sg16373 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13557 + +lemma sg16374 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg13558 + +lemma sg16375 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg13559 + +lemma sg16376 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg4 sg14585 + +lemma sg16377 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg3331 sg4496 + +lemma sg16378 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13560 + +lemma sg16379 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg13561 + +lemma sg16380 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by + exact rowSquare_join (by decide) sg13 sg13562 + +lemma sg16381 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by + exact rowSquare_join (by decide) sg13 sg13563 + +lemma sg16382 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by + exact rowSquare_join (by decide) sg3333 sg4496 + +lemma sg16383 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by + exact rowSquare_join (by decide) sg13 sg13564 + +lemma sg16384 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by + exact rowSquare_join (by decide) sg13 sg13565 + +lemma sg16385 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg3403 sg4406 + +lemma sg16386 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14824 + +lemma sg16387 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg5 sg14559 + +lemma sg16388 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg5 sg14560 + +lemma sg16389 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14825 + +lemma sg16390 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg14586 + +lemma sg16391 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg4 sg14587 + +lemma sg16392 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg4 sg14588 + +lemma sg16393 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg6 sg14556 + +lemma sg16394 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13566 + +lemma sg16395 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg13567 + +lemma sg16396 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg13568 + +lemma sg16397 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg0 sg15497 + +lemma sg16398 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg6 sg14558 + +lemma sg16399 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg1 sg14826 + +lemma sg16400 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14827 + +lemma sg16401 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg5 sg14561 + +lemma sg16402 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg5 sg14562 + +lemma sg16403 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg5 sg14563 + +lemma sg16404 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14828 + +lemma sg16405 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg14589 + +lemma sg16406 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg13569 + +lemma sg16407 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg4 sg14590 + +lemma sg16408 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg4 sg14591 + +lemma sg16409 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg4 sg14592 + +lemma sg16410 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13570 + +lemma sg16411 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13571 + +lemma sg16412 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13572 + +lemma sg16413 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg13573 + +lemma sg16414 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg13574 + +lemma sg16415 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg5 sg14572 + +lemma sg16416 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg5 sg14573 + +lemma sg16417 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg14593 + +lemma sg16418 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13575 + +lemma sg16419 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13576 + +lemma sg16420 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13577 + +lemma sg16421 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by + exact rowSquare_join (by decide) sg4 sg14594 + +lemma sg16422 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13578 + +lemma sg16423 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13579 + +lemma sg16424 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by + exact rowSquare_join (by decide) sg13 sg13580 + +lemma sg16425 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg39 sg12724 + +lemma sg16426 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by + exact rowSquare_join (by decide) sg39 sg12725 + +lemma sg16427 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by + exact rowSquare_join (by decide) sg41 sg12723 + +lemma sg16428 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13581 + +lemma sg16429 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13582 + +lemma sg16430 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13583 + +lemma sg16431 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by + exact rowSquare_join (by decide) sg13 sg13584 + +lemma sg16432 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by + exact rowSquare_join (by decide) sg39 sg12726 + +lemma sg16433 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by + exact rowSquare_join (by decide) sg39 sg12727 + +lemma sg16434 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15498 + +lemma sg16435 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15499 + +lemma sg16436 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg14595 + +lemma sg16437 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg13585 + +lemma sg16438 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15500 + +lemma sg16439 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg14 sg13515 + +lemma sg16440 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg14 sg13516 + +lemma sg16441 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg15501 + +lemma sg16442 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg13517 + +lemma sg16443 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13586 + +lemma sg16444 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13587 + +lemma sg16445 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg14 sg13522 + +lemma sg16446 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by + exact rowSquare_join (by decide) sg14 sg13523 + +lemma sg16447 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13588 + +lemma sg16448 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13589 + +lemma sg16449 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13590 + +lemma sg16450 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by + exact rowSquare_join (by decide) sg13 sg13591 + +lemma sg16451 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg13592 + +lemma sg16452 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by + exact rowSquare_join (by decide) sg39 sg12728 + +lemma sg16453 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by + exact rowSquare_join (by decide) sg42 sg12723 + +lemma sg16454 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg14596 + +lemma sg16455 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg14597 + +lemma sg16456 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13593 + +lemma sg16457 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg13594 + +lemma sg16458 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg40 sg12724 + +lemma sg16459 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by + exact rowSquare_join (by decide) sg40 sg12725 + +lemma sg16460 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13595 + +lemma sg16461 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg39 sg12729 + +lemma sg16462 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by + exact rowSquare_join (by decide) sg39 sg12730 + +lemma sg16463 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by + exact rowSquare_join (by decide) sg39 sg12731 + +lemma sg16464 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by + exact rowSquare_join (by decide) sg40 sg12727 + +lemma sg16465 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13596 + +lemma sg16466 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg13597 + +lemma sg16467 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by + exact rowSquare_join (by decide) sg39 sg12732 + +lemma sg16468 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by + exact rowSquare_join (by decide) sg39 sg12733 + +lemma sg16469 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,7,6,3] := by + exact rowSquare_join (by decide) sg39 sg12734 + +lemma sg16470 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,7,7,7,2] := by + exact rowSquare_join (by decide) sg39 sg12735 + +lemma sg16471 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3320 sg4498 + +lemma sg16472 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3558 sg4323 + +lemma sg16473 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3320 sg4499 + +lemma sg16474 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3322 sg4498 + +lemma sg16475 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg3626 sg4195 + +lemma sg16476 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3687 sg4116 + +lemma sg16477 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4213 + +lemma sg16478 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg2633 sg4975 + +lemma sg16479 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg13528 + +lemma sg16480 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4118 + +lemma sg16481 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13600 + +lemma sg16482 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13601 + +lemma sg16483 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg13532 + +lemma sg16484 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by + exact rowSquare_join (by decide) sg14 sg13534 + +lemma sg16485 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg13535 + +lemma sg16486 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg14 sg13536 + +lemma sg16487 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13602 + +lemma sg16488 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg13603 + +lemma sg16489 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg14 sg13541 + +lemma sg16490 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,2] := by + exact rowSquare_join (by decide) sg40 sg12728 + +lemma sg16491 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13604 + +lemma sg16492 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13605 + +lemma sg16493 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg13606 + +lemma sg16494 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg13607 + +lemma sg16495 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,5] := by + exact rowSquare_join (by decide) sg14 sg13548 + +lemma sg16496 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13608 + +lemma sg16497 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg13554 + +lemma sg16498 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13609 + +lemma sg16499 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg40 sg12729 + +lemma sg16500 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,2] := by + exact rowSquare_join (by decide) sg40 sg12730 + +lemma sg16501 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,4,1] := by + exact rowSquare_join (by decide) sg40 sg12731 + +lemma sg16502 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13610 + +lemma sg16503 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,2] := by + exact rowSquare_join (by decide) sg13 sg13611 + +lemma sg16504 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,3,1] := by + exact rowSquare_join (by decide) sg40 sg12732 + +lemma sg16505 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,4] := by + exact rowSquare_join (by decide) sg40 sg12733 + +lemma sg16506 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13612 + +lemma sg16507 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by + exact rowSquare_join (by decide) sg13 sg13613 + +lemma sg16508 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,3] := by + exact rowSquare_join (by decide) sg13 sg13614 + +lemma sg16509 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,7,5,3] := by + exact rowSquare_join (by decide) sg40 sg12734 + +lemma sg16510 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,7,6,2] := by + exact rowSquare_join (by decide) sg40 sg12735 + +lemma sg16511 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,7,7,1] := by + exact rowSquare_join (by decide) sg13 sg13615 + +lemma sg16512 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,4,3] := by + exact rowSquare_join (by decide) sg13 sg13616 + +lemma sg16513 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,5,2] := by + exact rowSquare_join (by decide) sg13 sg13617 + +lemma sg16514 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,6,1] := by + exact rowSquare_join (by decide) sg13 sg13618 + +lemma sg16515 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,7] := by + exact rowSquare_join (by decide) sg13 sg13619 + +lemma sg16516 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14829 + +lemma sg16517 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14830 + +lemma sg16518 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14831 + +lemma sg16519 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg6 sg14559 + +lemma sg16520 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg6 sg14560 + +lemma sg16521 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14832 + +lemma sg16522 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14833 + +lemma sg16523 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg5 sg14586 + +lemma sg16524 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg5 sg14588 + +lemma sg16525 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14834 + +lemma sg16526 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14598 + +lemma sg16527 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg14599 + +lemma sg16528 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13620 + +lemma sg16529 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg13621 + +lemma sg16530 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14600 + +lemma sg16531 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg15 sg13510 + +lemma sg16532 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg4 sg14601 + +lemma sg16533 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13622 + +lemma sg16534 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13623 + +lemma sg16535 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13624 + +lemma sg16536 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13625 + +lemma sg16537 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg13626 + +lemma sg16538 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg15 sg13514 + +lemma sg16539 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg6 sg14573 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes4.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes4.lean index 143afe5bf81cad88e9ea5fba353854095233c653..bfb5d8f8ea759bc7ca6a33ee07c9811f0fd3bb0a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes4.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes4.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes3 - -namespace OAI - -/-! Semigroup Nodes 4. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg2086 : RowSquare [4,4,1,1,1,1,1] [4,3,2,2,2] := by - exact rowSquare_join (by decide) sg66 sg180 - -lemma sg2087 : RowSquare [4,4,1,1,1,1,1] [5,3,3,2] := by - exact rowSquare_join (by decide) sg69 sg181 - -lemma sg2088 : RowSquare [4,4,1,1,1,1,1] [5,4,4] := by - exact rowSquare_join (by decide) sg68 sg184 - -lemma sg2089 : RowSquare [4,4,1,1,1,1,1] [5,5,3] := by - exact rowSquare_join (by decide) sg68 sg185 - -lemma sg2090 : RowSquare [4,4,1,1,1,1,1] [6,4,3] := by - exact rowSquare_join (by decide) sg1 sg1157 - -lemma sg2091 : RowSquare [4,4,1,1,1,1,1] [6,5,2] := by - exact rowSquare_join (by decide) sg68 sg188 - -lemma sg2092 : RowSquare [4,4,1,1,1,1,1] [6,6,1] := by - exact rowSquare_join (by decide) sg71 sg185 - -lemma sg2093 : RowSquare [4,4,1,1,1,1,1] [7,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg435 - -lemma sg2094 : RowSquare [4,4,1,1,1,1,1] [7,3,3] := by - exact rowSquare_join (by decide) sg1 sg1162 - -lemma sg2095 : RowSquare [4,4,1,1,1,1,1] [7,4,2] := by - exact rowSquare_join (by decide) sg14 sg432 - -lemma sg2096 : RowSquare [4,4,1,1,1,1,1] [7,5,1] := by - exact rowSquare_join (by decide) sg14 sg433 - -lemma sg2097 : RowSquare [4,4,1,1,1,1,1] [7,6] := by - exact rowSquare_join (by decide) sg14 sg434 - -lemma sg2098 : RowSquare [4,4,1,1,1,1,1] [8,3,2] := by - exact rowSquare_join (by decide) sg1 sg1167 - -lemma sg2099 : RowSquare [4,4,1,1,1,1,1] [8,5] := by - exact rowSquare_join (by decide) sg14 sg437 - -lemma sg2100 : RowSquare [4,4,1,1,1,1,1] [9,2,2] := by - exact rowSquare_join (by decide) sg83 sg109 - -lemma sg2101 : RowSquare [4,4,1,1,1,1,1] [9,4] := by - exact rowSquare_join (by decide) sg14 sg438 - -lemma sg2102 : RowSquare [4,4,1,1,1,1,1] [10,3] := by - exact rowSquare_join (by decide) sg14 sg439 - -lemma sg2103 : RowSquare [4,4,1,1,1,1,1] [11,2] := by - exact rowSquare_join (by decide) sg85 sg109 - -lemma sg2104 : RowSquare [4,4,1,1,1,1,1] [12,1] := by - exact rowSquare_join (by decide) sg15 sg439 - -lemma sg2106 : RowSquare [4,4,2,2,1] [3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg1654 - -lemma sg2108 : RowSquare [4,4,3,2] [2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg60 sg131 - -lemma sg2109 : RowSquare [4,4,3,2] [2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg59 sg131 - -lemma sg2110 : RowSquare [4,4,3,2] [2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg59 sg130 - -lemma sg2111 : RowSquare [4,4,3,2] [2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg29 sg257 - -lemma sg2112 : RowSquare [4,4,3,2] [3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg58 sg131 - -lemma sg2113 : RowSquare [4,4,3,2] [3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg55 sg131 - -lemma sg2114 : RowSquare [5,1,1,1,1,1,1,1,1] [8,5] := by - exact rowSquare_join (by decide) sg7 sg1023 - -lemma sg2115 : RowSquare [5,2,1,1,1,1,1,1] [3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg999 - -lemma sg2116 : RowSquare [5,2,1,1,1,1,1,1] [4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg1000 - -lemma sg2117 : RowSquare [5,2,1,1,1,1,1,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg588 - -lemma sg2118 : RowSquare [5,2,1,1,1,1,1,1] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg589 - -lemma sg2119 : RowSquare [5,2,2,1,1,1,1] [2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg910 - -lemma sg2120 : RowSquare [5,2,2,1,1,1,1] [2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg586 - -lemma sg2121 : RowSquare [5,3,1,1,1,1,1] [3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg586 - -lemma sg2122 : RowSquare [5,3,1,1,1,1,1] [3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg586 - -lemma sg2123 : RowSquare [5,3,1,1,1,1,1] [3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg313 - -lemma sg2124 : RowSquare [5,3,1,1,1,1,1] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg32 sg314 - -lemma sg2125 : RowSquare [5,3,1,1,1,1,1] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg315 - -lemma sg2126 : RowSquare [5,3,1,1,1,1,1] [4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg11 sg586 - -lemma sg2127 : RowSquare [5,3,1,1,1,1,1] [4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg587 - -lemma sg2128 : RowSquare [5,3,1,1,1,1,1] [4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg587 - -lemma sg2129 : RowSquare [5,3,1,1,1,1,1] [4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg589 - -lemma sg2130 : RowSquare [5,3,1,1,1,1,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg588 - -lemma sg2131 : RowSquare [5,3,1,1,1,1,1] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg319 - -lemma sg2132 : RowSquare [5,3,1,1,1,1,1] [5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg586 - -lemma sg2133 : RowSquare [5,3,1,1,1,1,1] [5,5,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg324 - -lemma sg2134 : RowSquare [5,3,2,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1682 - -lemma sg2135 : RowSquare [5,3,2,1,1,1] [3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg1688 - -lemma sg2136 : RowSquare [5,3,2,1,1,1] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg271 - -lemma sg2138 : RowSquare [5,3,3,1,1] [2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg64 sg141 - -lemma sg2139 : RowSquare [5,3,3,1,1] [2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg64 sg139 - -lemma sg2140 : RowSquare [5,3,3,1,1] [2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg64 sg137 - -lemma sg2141 : RowSquare [5,3,3,1,1] [2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg36 sg252 - -lemma sg2142 : RowSquare [5,3,3,1,1] [3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg51 sg163 - -lemma sg2143 : RowSquare [5,3,3,1,1] [3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg52 sg160 - -lemma sg2144 : RowSquare [5,3,3,1,1] [3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg34 sg252 - -lemma sg2145 : RowSquare [5,3,3,1,1] [3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg62 sg141 - -lemma sg2146 : RowSquare [5,3,3,1,1] [3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg62 sg140 - -lemma sg2147 : RowSquare [5,4,3,1] [3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg798 - -lemma sg2148 : RowSquare [5,4,3,1] [4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg798 - -lemma sg2149 : RowSquare [5,4,3,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg511 - -lemma sg2150 : RowSquare [5,4,3,1] [5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg798 - -lemma sg2151 : RowSquare [5,5,2,1] [5,5,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg513 - -lemma sg2152 : RowSquare [5,5,2,1] [7,6] := by - exact rowSquare_join (by decide) sg29 sg302 - -lemma sg2153 : RowSquare [5,5,3] [2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg516 - -lemma sg2154 : RowSquare [6,1,1,1,1,1,1,1] [5,3,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg1340 - -lemma sg2155 : RowSquare [6,1,1,1,1,1,1,1] [7,5,1] := by - exact rowSquare_join (by decide) sg2 sg1358 - -lemma sg2156 : RowSquare [6,2,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1754 - -lemma sg2157 : RowSquare [6,2,1,1,1,1,1] [3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1757 - -lemma sg2158 : RowSquare [6,2,1,1,1,1,1] [3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg889 - -lemma sg2159 : RowSquare [6,2,1,1,1,1,1] [3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg891 - -lemma sg2160 : RowSquare [6,2,1,1,1,1,1] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg892 - -lemma sg2161 : RowSquare [6,2,1,1,1,1,1] [4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg1331 - -lemma sg2162 : RowSquare [6,2,1,1,1,1,1] [4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg1332 - -lemma sg2163 : RowSquare [6,2,1,1,1,1,1] [4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg891 - -lemma sg2164 : RowSquare [6,2,1,1,1,1,1] [4,3,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg892 - -lemma sg2165 : RowSquare [6,2,1,1,1,1,1] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg897 - -lemma sg2166 : RowSquare [6,2,2,1,1,1] [3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg808 - -lemma sg2167 : RowSquare [6,3,2,1,1] [3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg1688 - -lemma sg2168 : RowSquare [6,3,3,1] [3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg285 - -lemma sg2169 : RowSquare [6,3,3,1] [4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1233 - -lemma sg2170 : RowSquare [6,3,3,1] [4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg66 sg154 - -lemma sg2171 : RowSquare [6,3,3,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg549 - -lemma sg2172 : RowSquare [6,3,3,1] [5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg798 - -lemma sg2173 : RowSquare [6,4,2,1] [2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg849 - -lemma sg2174 : RowSquare [6,4,2,1] [3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg849 - -lemma sg2175 : RowSquare [6,4,2,1] [3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg850 - -lemma sg2176 : RowSquare [6,4,2,1] [3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg330 - -lemma sg2177 : RowSquare [6,4,2,1] [3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg142 - -lemma sg2178 : RowSquare [6,4,2,1] [3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg27 sg330 - -lemma sg2179 : RowSquare [6,4,2,1] [3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg549 - -lemma sg2180 : RowSquare [6,4,2,1] [3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg143 - -lemma sg2181 : RowSquare [6,4,2,1] [3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg852 - -lemma sg2182 : RowSquare [6,4,2,1] [3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg144 - -lemma sg2183 : RowSquare [6,4,2,1] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg32 sg296 - -lemma sg2184 : RowSquare [6,4,2,1] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg297 - -lemma sg2185 : RowSquare [6,4,2,1] [4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg849 - -lemma sg2186 : RowSquare [6,4,2,1] [4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg850 - -lemma sg2187 : RowSquare [6,4,2,1] [4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg331 - -lemma sg2188 : RowSquare [6,4,2,1] [4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg145 - -lemma sg2189 : RowSquare [6,4,2,1] [4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg146 - -lemma sg2190 : RowSquare [6,4,2,1] [4,3,2,2,2] := by - exact rowSquare_join (by decide) sg75 sg143 - -lemma sg2191 : RowSquare [6,4,2,1] [4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg147 - -lemma sg2192 : RowSquare [6,4,2,1] [4,3,3,2,1] := by - exact rowSquare_join (by decide) sg75 sg144 - -lemma sg2193 : RowSquare [6,4,2,1] [4,3,3,3] := by - exact rowSquare_join (by decide) sg39 sg287 - -lemma sg2194 : RowSquare [6,4,2,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg511 - -lemma sg2195 : RowSquare [6,4,2,1] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg148 - -lemma sg2196 : RowSquare [6,4,2,1] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg76 sg143 - -lemma sg2197 : RowSquare [6,4,2,1] [4,4,3,1,1] := by - exact rowSquare_join (by decide) sg77 sg143 - -lemma sg2198 : RowSquare [6,4,2,1] [4,4,3,2] := by - exact rowSquare_join (by decide) sg76 sg144 - -lemma sg2199 : RowSquare [6,4,2,1] [4,4,4,1] := by - exact rowSquare_join (by decide) sg97 sg123 - -lemma sg2200 : RowSquare [6,4,2,1] [5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg850 - -lemma sg2201 : RowSquare [6,4,2,1] [5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg149 - -lemma sg2202 : RowSquare [6,4,2,1] [5,2,2,2,2] := by - exact rowSquare_join (by decide) sg75 sg145 - -lemma sg2203 : RowSquare [6,4,2,1] [5,3,3,1,1] := by - exact rowSquare_join (by decide) sg75 sg147 - -lemma sg2204 : RowSquare [6,4,2,1] [5,3,3,2] := by - exact rowSquare_join (by decide) sg98 sg123 - -lemma sg2205 : RowSquare [6,4,2,1] [5,4,4] := by - exact rowSquare_join (by decide) sg97 sg124 - -lemma sg2206 : RowSquare [6,4,2,1] [5,5,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg143 - -lemma sg2207 : RowSquare [6,4,2,1] [5,5,2,1] := by - exact rowSquare_join (by decide) sg76 sg148 - -lemma sg2208 : RowSquare [6,4,2,1] [5,5,3] := by - exact rowSquare_join (by decide) sg97 sg125 - -lemma sg2209 : RowSquare [6,4,2,1] [6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg30 sg331 - -lemma sg2210 : RowSquare [6,4,2,1] [6,5,1,1] := by - exact rowSquare_join (by decide) sg76 sg151 - -lemma sg2211 : RowSquare [6,4,2,1] [6,6,1] := by - exact rowSquare_join (by decide) sg80 sg148 - -lemma sg2212 : RowSquare [6,4,3] [2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg306 - -lemma sg2213 : RowSquare [6,4,3] [3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg516 - -lemma sg2214 : RowSquare [6,4,3] [3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg307 - -lemma sg2215 : RowSquare [6,4,3] [3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg154 - -lemma sg2216 : RowSquare [6,4,3] [3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg516 - -lemma sg2217 : RowSquare [6,4,3] [3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg874 - -lemma sg2218 : RowSquare [6,4,3] [3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg156 - -lemma sg2219 : RowSquare [6,4,3] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg310 - -lemma sg2220 : RowSquare [6,4,3] [4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg307 - -lemma sg2221 : RowSquare [6,4,3] [5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg516 - -lemma sg2222 : RowSquare [6,5,1,1] [3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg561 - -lemma sg2223 : RowSquare [6,5,1,1] [3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg562 - -lemma sg2224 : RowSquare [6,5,1,1] [3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg877 - -lemma sg2225 : RowSquare [6,5,1,1] [3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg563 - -lemma sg2226 : RowSquare [6,5,1,1] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg879 - -lemma sg2227 : RowSquare [6,5,1,1] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg564 - -lemma sg2228 : RowSquare [6,5,1,1] [4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg880 - -lemma sg2229 : RowSquare [6,5,1,1] [4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg565 - -lemma sg2230 : RowSquare [6,5,1,1] [4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg561 - -lemma sg2231 : RowSquare [6,5,1,1] [4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg881 - -lemma sg2232 : RowSquare [6,5,1,1] [4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg295 - -lemma sg2233 : RowSquare [6,5,1,1] [4,3,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg879 - -lemma sg2234 : RowSquare [6,5,1,1] [4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg142 - -lemma sg2235 : RowSquare [6,5,1,1] [4,3,3,2,1] := by - exact rowSquare_join (by decide) sg39 sg296 - -lemma sg2236 : RowSquare [6,5,1,1] [4,3,3,3] := by - exact rowSquare_join (by decide) sg39 sg297 - -lemma sg2237 : RowSquare [6,5,1,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg562 - -lemma sg2238 : RowSquare [6,5,1,1] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg295 - -lemma sg2239 : RowSquare [6,5,1,1] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg569 - -lemma sg2240 : RowSquare [6,5,1,1] [4,4,3,1,1] := by - exact rowSquare_join (by decide) sg83 sg143 - -lemma sg2241 : RowSquare [6,5,1,1] [4,4,3,2] := by - exact rowSquare_join (by decide) sg40 sg297 - -lemma sg2242 : RowSquare [6,5,1,1] [4,4,4,1] := by - exact rowSquare_join (by decide) sg83 sg144 - -lemma sg2243 : RowSquare [6,5,1,1] [5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg880 - -lemma sg2244 : RowSquare [6,5,1,1] [5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg142 - -lemma sg2245 : RowSquare [6,5,1,1] [5,2,2,2,2] := by - exact rowSquare_join (by decide) sg6 sg879 - -lemma sg2246 : RowSquare [6,5,1,1] [5,5,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg569 - -lemma sg2247 : RowSquare [6,5,2] [3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg165 - -lemma sg2248 : RowSquare [6,5,2] [3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg306 - -lemma sg2249 : RowSquare [6,6,1] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg579 - -lemma sg2250 : RowSquare [6,6,1] [5,5,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg583 - -lemma sg2252 : RowSquare [7,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg237 - -lemma sg2253 : RowSquare [7,1,1,1,1,1,1] [2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg236 - -lemma sg2254 : RowSquare [7,1,1,1,1,1,1] [2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg451 - -lemma sg2255 : RowSquare [7,1,1,1,1,1,1] [2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg806 - -lemma sg2256 : RowSquare [7,1,1,1,1,1,1] [2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1256 - -lemma sg2257 : RowSquare [7,1,1,1,1,1,1] [3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg450 - -lemma sg2258 : RowSquare [7,1,1,1,1,1,1] [3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg805 - -lemma sg2259 : RowSquare [7,1,1,1,1,1,1] [3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1255 - -lemma sg2260 : RowSquare [7,1,1,1,1,1,1] [3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg1753 - -lemma sg2261 : RowSquare [7,1,1,1,1,1,1] [3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg449 - -lemma sg2262 : RowSquare [7,1,1,1,1,1,1] [3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg804 - -lemma sg2263 : RowSquare [7,1,1,1,1,1,1] [3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1254 - -lemma sg2264 : RowSquare [7,1,1,1,1,1,1] [4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg803 - -lemma sg2265 : RowSquare [7,1,1,1,1,1,1] [4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1252 - -lemma sg2266 : RowSquare [7,1,1,1,1,1,1] [4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg1752 - -lemma sg2267 : RowSquare [7,1,1,1,1,1,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg801 - -lemma sg2268 : RowSquare [7,1,1,1,1,1,1] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1251 - -lemma sg2269 : RowSquare [7,1,1,1,1,1,1] [5,5,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1244 - -lemma sg2270 : RowSquare [7,2,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1754 - -lemma sg2271 : RowSquare [7,2,1,1,1,1] [3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1755 - -lemma sg2272 : RowSquare [7,2,1,1,1,1] [3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg1757 - -lemma sg2273 : RowSquare [7,2,1,1,1,1] [3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg1758 - -lemma sg2274 : RowSquare [7,2,1,1,1,1] [3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg889 - -lemma sg2275 : RowSquare [7,2,1,1,1,1] [3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg890 - -lemma sg2276 : RowSquare [7,2,1,1,1,1] [3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg891 - -lemma sg2277 : RowSquare [7,2,1,1,1,1] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg892 - -lemma sg2278 : RowSquare [7,2,1,1,1,1] [4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg1332 - -lemma sg2279 : RowSquare [7,2,2,1,1] [3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg312 - -lemma sg2280 : RowSquare [7,2,2,1,1] [3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg586 - -lemma sg2281 : RowSquare [7,2,2,1,1] [3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg313 - -lemma sg2282 : RowSquare [7,2,2,1,1] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg315 - -lemma sg2283 : RowSquare [7,2,2,1,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg588 - -lemma sg2284 : RowSquare [7,2,2,2] [3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg66 sg178 - -lemma sg2285 : RowSquare [7,2,2,2] [3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg67 sg178 - -lemma sg2286 : RowSquare [7,2,2,2] [4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg66 sg179 - -lemma sg2287 : RowSquare [7,3,1,1,1] [2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg910 - -lemma sg2288 : RowSquare [7,3,1,1,1] [2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg586 - -lemma sg2289 : RowSquare [7,3,1,1,1] [3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg911 - -lemma sg2290 : RowSquare [7,3,1,1,1] [3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg587 - -lemma sg2291 : RowSquare [7,3,1,1,1] [3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg586 - -lemma sg2292 : RowSquare [7,3,1,1,1] [3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg912 - -lemma sg2293 : RowSquare [7,3,1,1,1] [3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg588 - -lemma sg2294 : RowSquare [7,3,1,1,1] [3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg913 - -lemma sg2295 : RowSquare [7,3,1,1,1] [3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg589 - -lemma sg2296 : RowSquare [7,3,1,1,1] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg915 - -lemma sg2297 : RowSquare [7,3,1,1,1] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg590 - -lemma sg2298 : RowSquare [7,3,1,1,1] [4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg911 - -lemma sg2299 : RowSquare [7,3,1,1,1] [4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg534 - -lemma sg2300 : RowSquare [7,3,1,1,1] [4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg312 - -lemma sg2301 : RowSquare [7,3,1,1,1] [4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg534 - -lemma sg2302 : RowSquare [7,3,1,1,1] [4,3,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg915 - -lemma sg2303 : RowSquare [7,3,1,1,1] [4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg536 - -lemma sg2304 : RowSquare [7,3,1,1,1] [4,3,3,3] := by - exact rowSquare_join (by decide) sg39 sg315 - -lemma sg2305 : RowSquare [7,3,1,1,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg535 - -lemma sg2306 : RowSquare [7,3,1,1,1] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg313 - -lemma sg2307 : RowSquare [7,3,1,1,1] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg595 - -lemma sg2308 : RowSquare [7,3,1,1,1] [4,4,4,1] := by - exact rowSquare_join (by decide) sg4 sg923 - -lemma sg2309 : RowSquare [7,3,1,1,1] [5,5,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg541 - -lemma sg2310 : RowSquare [7,3,2,1] [2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg330 - -lemma sg2311 : RowSquare [7,3,2,1] [2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg178 - -lemma sg2312 : RowSquare [7,3,2,1] [3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg330 - -lemma sg2313 : RowSquare [7,3,2,1] [3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg75 sg178 - -lemma sg2314 : RowSquare [7,3,2,1] [3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg179 - -lemma sg2315 : RowSquare [7,3,2,1] [3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg34 sg330 - -lemma sg2316 : RowSquare [7,3,2,1] [3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg76 sg178 - -lemma sg2317 : RowSquare [7,3,2,1] [3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg180 - -lemma sg2318 : RowSquare [7,3,2,1] [3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg181 - -lemma sg2319 : RowSquare [7,3,2,1] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg334 - -lemma sg2320 : RowSquare [7,3,2,1] [4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg35 sg330 - -lemma sg2321 : RowSquare [7,3,2,1] [4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg36 sg330 - -lemma sg2322 : RowSquare [7,3,2,1] [4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg79 sg178 - -lemma sg2323 : RowSquare [7,3,2,1] [4,3,3,3] := by - exact rowSquare_join (by decide) sg33 sg334 - -lemma sg2324 : RowSquare [7,3,2,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg178 - -lemma sg2325 : RowSquare [7,3,2,1] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg88 sg143 - -lemma sg2326 : RowSquare [7,3,2,1] [5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg850 - -lemma sg2327 : RowSquare [7,3,2,1] [5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg81 sg178 - -lemma sg2328 : RowSquare [7,3,2,1] [5,5,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg143 - -lemma sg2329 : RowSquare [7,3,3] [3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg348 - -lemma sg2330 : RowSquare [7,3,3] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg350 - -lemma sg2331 : RowSquare [7,3,3] [4,3,2,2,2] := by - exact rowSquare_join (by decide) sg87 sg155 - -lemma sg2332 : RowSquare [7,3,3] [4,3,3,3] := by - exact rowSquare_join (by decide) sg33 sg350 - -lemma sg2333 : RowSquare [7,3,3] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg34 sg348 - -lemma sg2334 : RowSquare [7,3,3] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg88 sg155 - -lemma sg2335 : RowSquare [7,3,3] [5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg516 - -lemma sg2336 : RowSquare [7,3,3] [5,3,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg158 - -lemma sg2337 : RowSquare [7,4,1,1] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg616 - -lemma sg2338 : RowSquare [7,4,1,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg562 - -lemma sg2339 : RowSquare [7,4,2] [3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg193 - -lemma sg2340 : RowSquare [7,4,2] [3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg194 - -lemma sg2341 : RowSquare [7,4,2] [3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg975 - -lemma sg2342 : RowSquare [7,4,2] [3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg195 - -lemma sg2343 : RowSquare [7,4,2] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg32 sg357 - -lemma sg2344 : RowSquare [7,4,2] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg358 - -lemma sg2345 : RowSquare [7,4,2] [4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg306 - -lemma sg2346 : RowSquare [7,4,2] [4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg306 - -lemma sg2347 : RowSquare [7,4,2] [4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg577 - -lemma sg2348 : RowSquare [7,4,2] [4,3,2,2,2] := by - exact rowSquare_join (by decide) sg87 sg166 - -lemma sg2349 : RowSquare [7,4,2] [4,3,3,3] := by - exact rowSquare_join (by decide) sg39 sg350 - -lemma sg2350 : RowSquare [7,4,2] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg577 - -lemma sg2351 : RowSquare [7,4,2] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg88 sg166 - -lemma sg2352 : RowSquare [7,4,2] [5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg47 sg306 - -lemma sg2353 : RowSquare [7,4,2] [5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg307 - -lemma sg2354 : RowSquare [7,4,2] [5,2,2,2,2] := by - exact rowSquare_join (by decide) sg87 sg168 - -lemma sg2355 : RowSquare [7,4,2] [5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg307 - -lemma sg2356 : RowSquare [7,4,2] [6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg48 sg306 - -lemma sg2357 : RowSquare [7,4,2] [6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg47 sg307 - -lemma sg2358 : RowSquare [7,4,2] [7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg48 sg307 - -lemma sg2359 : RowSquare [7,5,1] [3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg207 - -lemma sg2360 : RowSquare [7,5,1] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg982 - -lemma sg2361 : RowSquare [7,5,1] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg210 - -lemma sg2362 : RowSquare [7,5,1] [4,4,3,1,1] := by - exact rowSquare_join (by decide) sg97 sg166 - -lemma sg2363 : RowSquare [7,5,1] [5,5,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg367 - -lemma sg2365 : RowSquare [8,1,1,1,1,1] [3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1327 - -lemma sg2366 : RowSquare [8,1,1,1,1,1] [4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1330 - -lemma sg2367 : RowSquare [8,1,1,1,1,1] [4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1331 - -lemma sg2368 : RowSquare [8,1,1,1,1,1] [4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg1332 - -lemma sg2369 : RowSquare [8,2,1,1,1] [3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg586 - -lemma sg2370 : RowSquare [8,2,1,1,1] [3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg586 - -lemma sg2371 : RowSquare [8,2,1,1,1] [3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg998 - -lemma sg2372 : RowSquare [8,2,1,1,1] [3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg999 - -lemma sg2373 : RowSquare [8,2,1,1,1] [3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg1000 - -lemma sg2374 : RowSquare [8,2,1,1,1] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg1001 - -lemma sg2375 : RowSquare [8,2,1,1,1] [4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg586 - -lemma sg2376 : RowSquare [8,2,1,1,1] [4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg587 - -lemma sg2377 : RowSquare [8,2,1,1,1] [4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg587 - -lemma sg2378 : RowSquare [8,2,1,1,1] [4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg588 - -lemma sg2379 : RowSquare [8,2,1,1,1] [4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg1000 - -lemma sg2380 : RowSquare [8,2,1,1,1] [4,3,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg1001 - -lemma sg2381 : RowSquare [8,2,1,1,1] [4,3,3,2,1] := by - exact rowSquare_join (by decide) sg16 sg590 - -lemma sg2382 : RowSquare [8,2,1,1,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg588 - -lemma sg2383 : RowSquare [8,2,1,1,1] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg589 - -lemma sg2384 : RowSquare [8,2,1,1,1] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg17 sg590 - -lemma sg2385 : RowSquare [8,2,1,1,1] [4,4,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg1007 - -lemma sg2386 : RowSquare [8,2,1,1,1] [4,4,3,2] := by - exact rowSquare_join (by decide) sg4 sg1008 - -lemma sg2387 : RowSquare [8,2,1,1,1] [5,3,2,2,1] := by - exact rowSquare_join (by decide) sg18 sg590 - -lemma sg2388 : RowSquare [8,2,1,1,1] [5,5,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg595 - -lemma sg2389 : RowSquare [8,2,1,1,1] [5,5,2,1] := by - exact rowSquare_join (by decide) sg17 sg596 - -lemma sg2390 : RowSquare [8,2,2,1] [3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg87 sg178 - -lemma sg2391 : RowSquare [8,2,2,1] [3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg88 sg178 - -lemma sg2392 : RowSquare [8,2,2,1] [3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg371 - -lemma sg2393 : RowSquare [8,2,2,1] [3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg178 - -lemma sg2394 : RowSquare [8,2,2,1] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg32 sg372 - -lemma sg2395 : RowSquare [8,2,2,1] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg373 - -lemma sg2396 : RowSquare [8,2,2,1] [4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg179 - -lemma sg2397 : RowSquare [8,2,2,1] [4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg179 - -lemma sg2398 : RowSquare [8,2,2,1] [4,3,3,3] := by - exact rowSquare_join (by decide) sg33 sg373 - -lemma sg2399 : RowSquare [8,2,2,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg178 - -lemma sg2400 : RowSquare [8,2,2,1] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg34 sg371 - -lemma sg2401 : RowSquare [8,2,2,1] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg88 sg180 - -lemma sg2402 : RowSquare [8,2,2,1] [4,4,4,1] := by - exact rowSquare_join (by decide) sg89 sg181 - -lemma sg2403 : RowSquare [8,2,2,1] [5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg940 - -lemma sg2404 : RowSquare [8,2,2,1] [6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg548 - -lemma sg2405 : RowSquare [8,3,1,1] [3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg178 - -lemma sg2406 : RowSquare [8,3,1,1] [3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg1032 - -lemma sg2407 : RowSquare [8,3,1,1] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg1033 - -lemma sg2408 : RowSquare [8,3,1,1] [4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg330 - -lemma sg2409 : RowSquare [8,3,1,1] [4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg178 - -lemma sg2410 : RowSquare [8,3,1,1] [4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg330 - -lemma sg2411 : RowSquare [8,3,1,1] [4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg99 sg178 - -lemma sg2412 : RowSquare [8,3,1,1] [4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg371 - -lemma sg2413 : RowSquare [8,3,1,1] [4,3,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg1033 - -lemma sg2414 : RowSquare [8,3,1,1] [4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg179 - -lemma sg2415 : RowSquare [8,3,1,1] [4,3,3,2,1] := by - exact rowSquare_join (by decide) sg39 sg372 - -lemma sg2416 : RowSquare [8,3,1,1] [4,3,3,3] := by - exact rowSquare_join (by decide) sg39 sg373 - -lemma sg2417 : RowSquare [8,3,1,1] [4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg614 - -lemma sg2418 : RowSquare [8,3,1,1] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg371 - -lemma sg2419 : RowSquare [8,3,1,1] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg17 sg616 - -lemma sg2420 : RowSquare [8,3,1,1] [4,4,3,1,1] := by - exact rowSquare_join (by decide) sg97 sg180 - -lemma sg2421 : RowSquare [8,3,1,1] [4,4,3,2] := by - exact rowSquare_join (by decide) sg40 sg373 - -lemma sg2422 : RowSquare [8,3,1,1] [4,4,4,1] := by - exact rowSquare_join (by decide) sg97 sg181 - -lemma sg2423 : RowSquare [8,3,1,1] [5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg47 sg330 - -lemma sg2424 : RowSquare [8,3,1,1] [5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg100 sg178 - -lemma sg2425 : RowSquare [8,3,1,1] [5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg98 sg179 - -lemma sg2426 : RowSquare [8,3,1,1] [5,2,2,2,2] := by - exact rowSquare_join (by decide) sg7 sg961 - -lemma sg2427 : RowSquare [8,3,1,1] [5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg178 - -lemma sg2428 : RowSquare [8,3,1,1] [5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg99 sg179 - -lemma sg2429 : RowSquare [8,3,1,1] [5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg332 - -lemma sg2430 : RowSquare [8,3,1,1] [5,4,2,1,1] := by - exact rowSquare_join (by decide) sg66 sg228 - -lemma sg2431 : RowSquare [8,3,1,1] [5,4,2,2] := by - exact rowSquare_join (by decide) sg39 sg377 - -lemma sg2432 : RowSquare [8,3,2] [3,3,3,2,2] := by - exact rowSquare_join (by decide) sg32 sg389 - -lemma sg2433 : RowSquare [8,3,2] [3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg390 - -lemma sg2434 : RowSquare [8,3,2] [4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg218 - -lemma sg2435 : RowSquare [8,3,2] [4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg219 - -lemma sg2436 : RowSquare [8,3,2] [4,3,2,2,2] := by - exact rowSquare_join (by decide) sg87 sg194 - -lemma sg2437 : RowSquare [8,3,2] [4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg220 - -lemma sg2438 : RowSquare [8,3,2] [4,3,3,2,1] := by - exact rowSquare_join (by decide) sg87 sg195 - -lemma sg2439 : RowSquare [8,3,2] [4,3,3,3] := by - exact rowSquare_join (by decide) sg33 sg390 - -lemma sg2440 : RowSquare [8,3,2] [4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg636 - -lemma sg2441 : RowSquare [8,3,2] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg88 sg194 - -lemma sg2442 : RowSquare [8,3,2] [4,4,3,1,1] := by - exact rowSquare_join (by decide) sg89 sg194 - -lemma sg2443 : RowSquare [8,3,2] [4,4,3,2] := by - exact rowSquare_join (by decide) sg88 sg195 - -lemma sg2444 : RowSquare [8,3,2] [5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg975 - -lemma sg2445 : RowSquare [8,3,2] [5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg221 - -lemma sg2446 : RowSquare [8,3,2] [5,2,2,2,2] := by - exact rowSquare_join (by decide) sg87 sg196 - -lemma sg2447 : RowSquare [8,3,2] [5,3,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg197 - -lemma sg2448 : RowSquare [8,3,2] [5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg223 - -lemma sg2449 : RowSquare [8,3,2] [5,5,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg194 - -lemma sg2450 : RowSquare [8,3,2] [6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg577 - -lemma sg2451 : RowSquare [8,4,1] [4,3,3,3] := by - exact rowSquare_join (by decide) sg39 sg390 - -lemma sg2452 : RowSquare [8,4,1] [4,4,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg402 - -lemma sg2453 : RowSquare [8,4,1] [5,2,2,2,2] := by - exact rowSquare_join (by decide) sg7 sg982 - -lemma sg2454 : RowSquare [9,1,1,1,1] [5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg998 - -lemma sg2455 : RowSquare [9,1,1,1,1] [5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg999 - -lemma sg2456 : RowSquare [9,2,1,1] [5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg104 sg178 - -lemma sg2457 : RowSquare [9,2,1,1] [5,2,2,2,2] := by - exact rowSquare_join (by decide) sg7 sg1033 - -lemma sg2458 : RowSquare [9,2,1,1] [5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg105 sg178 - -lemma sg2459 : RowSquare [9,2,1,1] [5,3,3,1,1] := by - exact rowSquare_join (by decide) sg45 sg372 - -lemma sg2460 : RowSquare [9,2,1,1] [5,3,3,2] := by - exact rowSquare_join (by decide) sg45 sg373 - -lemma sg2461 : RowSquare [9,2,2] [5,2,2,2,2] := by - exact rowSquare_join (by decide) sg87 sg218 - -lemma sg2462 : RowSquare [9,2,2] [5,3,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg219 - -lemma sg2463 : RowSquare [9,2,2] [5,3,3,1,1] := by - exact rowSquare_join (by decide) sg87 sg220 - -lemma sg2464 : RowSquare [9,2,2] [5,4,2,2] := by - exact rowSquare_join (by decide) sg88 sg219 - -lemma sg2465 : RowSquare [9,2,2] [5,4,3,1] := by - exact rowSquare_join (by decide) sg88 sg220 - -lemma sg2466 : RowSquare [9,2,2] [6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg636 - -lemma sg2467 : RowSquare [9,2,2] [6,2,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg221 - -lemma sg2468 : RowSquare [9,2,2] [6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg1063 - -lemma sg2469 : RowSquare [9,2,2] [6,3,2,1,1] := by - exact rowSquare_join (by decide) sg87 sg222 - -lemma sg2470 : RowSquare [9,2,2] [6,3,2,2] := by - exact rowSquare_join (by decide) sg88 sg221 - -lemma sg2471 : RowSquare [9,2,2] [6,3,3,1] := by - exact rowSquare_join (by decide) sg90 sg220 - -lemma sg2472 : RowSquare [9,2,2] [6,4,1,1,1] := by - exact rowSquare_join (by decide) sg87 sg223 - -lemma sg2473 : RowSquare [9,2,2] [6,4,2,1] := by - exact rowSquare_join (by decide) sg88 sg222 - -lemma sg2474 : RowSquare [9,2,2] [6,4,3] := by - exact rowSquare_join (by decide) sg89 sg222 - -lemma sg2475 : RowSquare [9,2,2] [6,5,1,1] := by - exact rowSquare_join (by decide) sg88 sg223 - -lemma sg2476 : RowSquare [9,2,2] [6,5,2] := by - exact rowSquare_join (by decide) sg89 sg223 - -lemma sg2477 : RowSquare [9,2,2] [7,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg348 - -lemma sg2478 : RowSquare [9,3,1] [5,4,2,2] := by - exact rowSquare_join (by decide) sg46 sg390 - -lemma sg2479 : RowSquare [9,3,1] [5,5,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg424 - -lemma sg2480 : RowSquare [10,2,1] [7,2,2,1,1] := by - exact rowSquare_join (by decide) sg87 sg231 - -lemma sg2481 : RowSquare [10,2,1] [7,2,2,2] := by - exact rowSquare_join (by decide) sg49 sg390 - -lemma sg2482 : RowSquare [10,2,1] [7,3,1,1,1] := by - exact rowSquare_join (by decide) sg87 sg232 - -lemma sg2483 : RowSquare [10,2,1] [7,3,2,1] := by - exact rowSquare_join (by decide) sg88 sg231 - -lemma sg2484 : RowSquare [10,2,1] [7,3,3] := by - exact rowSquare_join (by decide) sg89 sg231 - -lemma sg2485 : RowSquare [2,2,1,1,1,1,1,1,1,1,1,1] [10,2,2] := by - exact rowSquare_join (by decide) sg227 sg234 - -lemma sg2486 : RowSquare [2,2,2,2,1,1,1,1,1,1] [7,5,1,1] := by - exact rowSquare_join (by decide) sg98 sg424 - -lemma sg2487 : RowSquare [2,2,2,2,1,1,1,1,1,1] [7,6,1] := by - exact rowSquare_join (by decide) sg228 sg230 - -lemma sg2490 : RowSquare [3,2,2,1,1,1,1,1,1,1] [7,7] := by - exact rowSquare_join (by decide) sg92 sg424 - -lemma sg2491 : RowSquare [3,2,2,2,1,1,1,1,1] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg97 sg389 - -lemma sg2492 : RowSquare [3,2,2,2,1,1,1,1,1] [4,4,4,2] := by - exact rowSquare_join (by decide) sg97 sg390 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes3 + +namespace OAI + +/-! Semigroup Nodes 4. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg2086 : RowSquare [4,4,1,1,1,1,1] [4,3,2,2,2] := by + exact rowSquare_join (by decide) sg66 sg180 + +lemma sg2087 : RowSquare [4,4,1,1,1,1,1] [5,3,3,2] := by + exact rowSquare_join (by decide) sg69 sg181 + +lemma sg2088 : RowSquare [4,4,1,1,1,1,1] [5,4,4] := by + exact rowSquare_join (by decide) sg68 sg184 + +lemma sg2089 : RowSquare [4,4,1,1,1,1,1] [5,5,3] := by + exact rowSquare_join (by decide) sg68 sg185 + +lemma sg2090 : RowSquare [4,4,1,1,1,1,1] [6,4,3] := by + exact rowSquare_join (by decide) sg1 sg1157 + +lemma sg2091 : RowSquare [4,4,1,1,1,1,1] [6,5,2] := by + exact rowSquare_join (by decide) sg68 sg188 + +lemma sg2092 : RowSquare [4,4,1,1,1,1,1] [6,6,1] := by + exact rowSquare_join (by decide) sg71 sg185 + +lemma sg2093 : RowSquare [4,4,1,1,1,1,1] [7,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg435 + +lemma sg2094 : RowSquare [4,4,1,1,1,1,1] [7,3,3] := by + exact rowSquare_join (by decide) sg1 sg1162 + +lemma sg2095 : RowSquare [4,4,1,1,1,1,1] [7,4,2] := by + exact rowSquare_join (by decide) sg14 sg432 + +lemma sg2096 : RowSquare [4,4,1,1,1,1,1] [7,5,1] := by + exact rowSquare_join (by decide) sg14 sg433 + +lemma sg2097 : RowSquare [4,4,1,1,1,1,1] [7,6] := by + exact rowSquare_join (by decide) sg14 sg434 + +lemma sg2098 : RowSquare [4,4,1,1,1,1,1] [8,3,2] := by + exact rowSquare_join (by decide) sg1 sg1167 + +lemma sg2099 : RowSquare [4,4,1,1,1,1,1] [8,5] := by + exact rowSquare_join (by decide) sg14 sg437 + +lemma sg2100 : RowSquare [4,4,1,1,1,1,1] [9,2,2] := by + exact rowSquare_join (by decide) sg83 sg109 + +lemma sg2101 : RowSquare [4,4,1,1,1,1,1] [9,4] := by + exact rowSquare_join (by decide) sg14 sg438 + +lemma sg2102 : RowSquare [4,4,1,1,1,1,1] [10,3] := by + exact rowSquare_join (by decide) sg14 sg439 + +lemma sg2103 : RowSquare [4,4,1,1,1,1,1] [11,2] := by + exact rowSquare_join (by decide) sg85 sg109 + +lemma sg2104 : RowSquare [4,4,1,1,1,1,1] [12,1] := by + exact rowSquare_join (by decide) sg15 sg439 + +lemma sg2106 : RowSquare [4,4,2,2,1] [3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg1654 + +lemma sg2108 : RowSquare [4,4,3,2] [2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg60 sg131 + +lemma sg2109 : RowSquare [4,4,3,2] [2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg59 sg131 + +lemma sg2110 : RowSquare [4,4,3,2] [2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg59 sg130 + +lemma sg2111 : RowSquare [4,4,3,2] [2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg29 sg257 + +lemma sg2112 : RowSquare [4,4,3,2] [3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg58 sg131 + +lemma sg2113 : RowSquare [4,4,3,2] [3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg55 sg131 + +lemma sg2114 : RowSquare [5,1,1,1,1,1,1,1,1] [8,5] := by + exact rowSquare_join (by decide) sg7 sg1023 + +lemma sg2115 : RowSquare [5,2,1,1,1,1,1,1] [3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg999 + +lemma sg2116 : RowSquare [5,2,1,1,1,1,1,1] [4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg1000 + +lemma sg2117 : RowSquare [5,2,1,1,1,1,1,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg588 + +lemma sg2118 : RowSquare [5,2,1,1,1,1,1,1] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg589 + +lemma sg2119 : RowSquare [5,2,2,1,1,1,1] [2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg910 + +lemma sg2120 : RowSquare [5,2,2,1,1,1,1] [2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg586 + +lemma sg2121 : RowSquare [5,3,1,1,1,1,1] [3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg586 + +lemma sg2122 : RowSquare [5,3,1,1,1,1,1] [3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg586 + +lemma sg2123 : RowSquare [5,3,1,1,1,1,1] [3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg313 + +lemma sg2124 : RowSquare [5,3,1,1,1,1,1] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg32 sg314 + +lemma sg2125 : RowSquare [5,3,1,1,1,1,1] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg315 + +lemma sg2126 : RowSquare [5,3,1,1,1,1,1] [4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg11 sg586 + +lemma sg2127 : RowSquare [5,3,1,1,1,1,1] [4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg587 + +lemma sg2128 : RowSquare [5,3,1,1,1,1,1] [4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg587 + +lemma sg2129 : RowSquare [5,3,1,1,1,1,1] [4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg589 + +lemma sg2130 : RowSquare [5,3,1,1,1,1,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg588 + +lemma sg2131 : RowSquare [5,3,1,1,1,1,1] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg319 + +lemma sg2132 : RowSquare [5,3,1,1,1,1,1] [5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg586 + +lemma sg2133 : RowSquare [5,3,1,1,1,1,1] [5,5,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg324 + +lemma sg2134 : RowSquare [5,3,2,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1682 + +lemma sg2135 : RowSquare [5,3,2,1,1,1] [3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg1688 + +lemma sg2136 : RowSquare [5,3,2,1,1,1] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg271 + +lemma sg2138 : RowSquare [5,3,3,1,1] [2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg64 sg141 + +lemma sg2139 : RowSquare [5,3,3,1,1] [2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg64 sg139 + +lemma sg2140 : RowSquare [5,3,3,1,1] [2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg64 sg137 + +lemma sg2141 : RowSquare [5,3,3,1,1] [2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg36 sg252 + +lemma sg2142 : RowSquare [5,3,3,1,1] [3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg51 sg163 + +lemma sg2143 : RowSquare [5,3,3,1,1] [3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg52 sg160 + +lemma sg2144 : RowSquare [5,3,3,1,1] [3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg34 sg252 + +lemma sg2145 : RowSquare [5,3,3,1,1] [3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg62 sg141 + +lemma sg2146 : RowSquare [5,3,3,1,1] [3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg62 sg140 + +lemma sg2147 : RowSquare [5,4,3,1] [3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg798 + +lemma sg2148 : RowSquare [5,4,3,1] [4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg798 + +lemma sg2149 : RowSquare [5,4,3,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg511 + +lemma sg2150 : RowSquare [5,4,3,1] [5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg798 + +lemma sg2151 : RowSquare [5,5,2,1] [5,5,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg513 + +lemma sg2152 : RowSquare [5,5,2,1] [7,6] := by + exact rowSquare_join (by decide) sg29 sg302 + +lemma sg2153 : RowSquare [5,5,3] [2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg516 + +lemma sg2154 : RowSquare [6,1,1,1,1,1,1,1] [5,3,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg1340 + +lemma sg2155 : RowSquare [6,1,1,1,1,1,1,1] [7,5,1] := by + exact rowSquare_join (by decide) sg2 sg1358 + +lemma sg2156 : RowSquare [6,2,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1754 + +lemma sg2157 : RowSquare [6,2,1,1,1,1,1] [3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1757 + +lemma sg2158 : RowSquare [6,2,1,1,1,1,1] [3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg889 + +lemma sg2159 : RowSquare [6,2,1,1,1,1,1] [3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg891 + +lemma sg2160 : RowSquare [6,2,1,1,1,1,1] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg892 + +lemma sg2161 : RowSquare [6,2,1,1,1,1,1] [4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg1331 + +lemma sg2162 : RowSquare [6,2,1,1,1,1,1] [4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg1332 + +lemma sg2163 : RowSquare [6,2,1,1,1,1,1] [4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg891 + +lemma sg2164 : RowSquare [6,2,1,1,1,1,1] [4,3,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg892 + +lemma sg2165 : RowSquare [6,2,1,1,1,1,1] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg897 + +lemma sg2166 : RowSquare [6,2,2,1,1,1] [3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg808 + +lemma sg2167 : RowSquare [6,3,2,1,1] [3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg1688 + +lemma sg2168 : RowSquare [6,3,3,1] [3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg285 + +lemma sg2169 : RowSquare [6,3,3,1] [4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1233 + +lemma sg2170 : RowSquare [6,3,3,1] [4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg66 sg154 + +lemma sg2171 : RowSquare [6,3,3,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg549 + +lemma sg2172 : RowSquare [6,3,3,1] [5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg798 + +lemma sg2173 : RowSquare [6,4,2,1] [2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg849 + +lemma sg2174 : RowSquare [6,4,2,1] [3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg849 + +lemma sg2175 : RowSquare [6,4,2,1] [3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg850 + +lemma sg2176 : RowSquare [6,4,2,1] [3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg330 + +lemma sg2177 : RowSquare [6,4,2,1] [3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg142 + +lemma sg2178 : RowSquare [6,4,2,1] [3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg27 sg330 + +lemma sg2179 : RowSquare [6,4,2,1] [3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg549 + +lemma sg2180 : RowSquare [6,4,2,1] [3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg143 + +lemma sg2181 : RowSquare [6,4,2,1] [3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg852 + +lemma sg2182 : RowSquare [6,4,2,1] [3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg144 + +lemma sg2183 : RowSquare [6,4,2,1] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg32 sg296 + +lemma sg2184 : RowSquare [6,4,2,1] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg297 + +lemma sg2185 : RowSquare [6,4,2,1] [4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg849 + +lemma sg2186 : RowSquare [6,4,2,1] [4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg850 + +lemma sg2187 : RowSquare [6,4,2,1] [4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg331 + +lemma sg2188 : RowSquare [6,4,2,1] [4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg145 + +lemma sg2189 : RowSquare [6,4,2,1] [4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg146 + +lemma sg2190 : RowSquare [6,4,2,1] [4,3,2,2,2] := by + exact rowSquare_join (by decide) sg75 sg143 + +lemma sg2191 : RowSquare [6,4,2,1] [4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg147 + +lemma sg2192 : RowSquare [6,4,2,1] [4,3,3,2,1] := by + exact rowSquare_join (by decide) sg75 sg144 + +lemma sg2193 : RowSquare [6,4,2,1] [4,3,3,3] := by + exact rowSquare_join (by decide) sg39 sg287 + +lemma sg2194 : RowSquare [6,4,2,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg511 + +lemma sg2195 : RowSquare [6,4,2,1] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg148 + +lemma sg2196 : RowSquare [6,4,2,1] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg76 sg143 + +lemma sg2197 : RowSquare [6,4,2,1] [4,4,3,1,1] := by + exact rowSquare_join (by decide) sg77 sg143 + +lemma sg2198 : RowSquare [6,4,2,1] [4,4,3,2] := by + exact rowSquare_join (by decide) sg76 sg144 + +lemma sg2199 : RowSquare [6,4,2,1] [4,4,4,1] := by + exact rowSquare_join (by decide) sg97 sg123 + +lemma sg2200 : RowSquare [6,4,2,1] [5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg850 + +lemma sg2201 : RowSquare [6,4,2,1] [5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg149 + +lemma sg2202 : RowSquare [6,4,2,1] [5,2,2,2,2] := by + exact rowSquare_join (by decide) sg75 sg145 + +lemma sg2203 : RowSquare [6,4,2,1] [5,3,3,1,1] := by + exact rowSquare_join (by decide) sg75 sg147 + +lemma sg2204 : RowSquare [6,4,2,1] [5,3,3,2] := by + exact rowSquare_join (by decide) sg98 sg123 + +lemma sg2205 : RowSquare [6,4,2,1] [5,4,4] := by + exact rowSquare_join (by decide) sg97 sg124 + +lemma sg2206 : RowSquare [6,4,2,1] [5,5,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg143 + +lemma sg2207 : RowSquare [6,4,2,1] [5,5,2,1] := by + exact rowSquare_join (by decide) sg76 sg148 + +lemma sg2208 : RowSquare [6,4,2,1] [5,5,3] := by + exact rowSquare_join (by decide) sg97 sg125 + +lemma sg2209 : RowSquare [6,4,2,1] [6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg30 sg331 + +lemma sg2210 : RowSquare [6,4,2,1] [6,5,1,1] := by + exact rowSquare_join (by decide) sg76 sg151 + +lemma sg2211 : RowSquare [6,4,2,1] [6,6,1] := by + exact rowSquare_join (by decide) sg80 sg148 + +lemma sg2212 : RowSquare [6,4,3] [2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg306 + +lemma sg2213 : RowSquare [6,4,3] [3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg516 + +lemma sg2214 : RowSquare [6,4,3] [3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg307 + +lemma sg2215 : RowSquare [6,4,3] [3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg154 + +lemma sg2216 : RowSquare [6,4,3] [3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg516 + +lemma sg2217 : RowSquare [6,4,3] [3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg874 + +lemma sg2218 : RowSquare [6,4,3] [3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg156 + +lemma sg2219 : RowSquare [6,4,3] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg310 + +lemma sg2220 : RowSquare [6,4,3] [4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg307 + +lemma sg2221 : RowSquare [6,4,3] [5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg516 + +lemma sg2222 : RowSquare [6,5,1,1] [3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg561 + +lemma sg2223 : RowSquare [6,5,1,1] [3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg562 + +lemma sg2224 : RowSquare [6,5,1,1] [3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg877 + +lemma sg2225 : RowSquare [6,5,1,1] [3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg563 + +lemma sg2226 : RowSquare [6,5,1,1] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg879 + +lemma sg2227 : RowSquare [6,5,1,1] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg564 + +lemma sg2228 : RowSquare [6,5,1,1] [4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg880 + +lemma sg2229 : RowSquare [6,5,1,1] [4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg565 + +lemma sg2230 : RowSquare [6,5,1,1] [4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg561 + +lemma sg2231 : RowSquare [6,5,1,1] [4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg881 + +lemma sg2232 : RowSquare [6,5,1,1] [4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg295 + +lemma sg2233 : RowSquare [6,5,1,1] [4,3,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg879 + +lemma sg2234 : RowSquare [6,5,1,1] [4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg142 + +lemma sg2235 : RowSquare [6,5,1,1] [4,3,3,2,1] := by + exact rowSquare_join (by decide) sg39 sg296 + +lemma sg2236 : RowSquare [6,5,1,1] [4,3,3,3] := by + exact rowSquare_join (by decide) sg39 sg297 + +lemma sg2237 : RowSquare [6,5,1,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg562 + +lemma sg2238 : RowSquare [6,5,1,1] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg295 + +lemma sg2239 : RowSquare [6,5,1,1] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg569 + +lemma sg2240 : RowSquare [6,5,1,1] [4,4,3,1,1] := by + exact rowSquare_join (by decide) sg83 sg143 + +lemma sg2241 : RowSquare [6,5,1,1] [4,4,3,2] := by + exact rowSquare_join (by decide) sg40 sg297 + +lemma sg2242 : RowSquare [6,5,1,1] [4,4,4,1] := by + exact rowSquare_join (by decide) sg83 sg144 + +lemma sg2243 : RowSquare [6,5,1,1] [5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg880 + +lemma sg2244 : RowSquare [6,5,1,1] [5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg142 + +lemma sg2245 : RowSquare [6,5,1,1] [5,2,2,2,2] := by + exact rowSquare_join (by decide) sg6 sg879 + +lemma sg2246 : RowSquare [6,5,1,1] [5,5,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg569 + +lemma sg2247 : RowSquare [6,5,2] [3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg165 + +lemma sg2248 : RowSquare [6,5,2] [3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg306 + +lemma sg2249 : RowSquare [6,6,1] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg579 + +lemma sg2250 : RowSquare [6,6,1] [5,5,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg583 + +lemma sg2252 : RowSquare [7,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg237 + +lemma sg2253 : RowSquare [7,1,1,1,1,1,1] [2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg236 + +lemma sg2254 : RowSquare [7,1,1,1,1,1,1] [2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg451 + +lemma sg2255 : RowSquare [7,1,1,1,1,1,1] [2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg806 + +lemma sg2256 : RowSquare [7,1,1,1,1,1,1] [2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1256 + +lemma sg2257 : RowSquare [7,1,1,1,1,1,1] [3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg450 + +lemma sg2258 : RowSquare [7,1,1,1,1,1,1] [3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg805 + +lemma sg2259 : RowSquare [7,1,1,1,1,1,1] [3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1255 + +lemma sg2260 : RowSquare [7,1,1,1,1,1,1] [3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg1753 + +lemma sg2261 : RowSquare [7,1,1,1,1,1,1] [3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg449 + +lemma sg2262 : RowSquare [7,1,1,1,1,1,1] [3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg804 + +lemma sg2263 : RowSquare [7,1,1,1,1,1,1] [3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1254 + +lemma sg2264 : RowSquare [7,1,1,1,1,1,1] [4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg803 + +lemma sg2265 : RowSquare [7,1,1,1,1,1,1] [4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1252 + +lemma sg2266 : RowSquare [7,1,1,1,1,1,1] [4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg1752 + +lemma sg2267 : RowSquare [7,1,1,1,1,1,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg801 + +lemma sg2268 : RowSquare [7,1,1,1,1,1,1] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1251 + +lemma sg2269 : RowSquare [7,1,1,1,1,1,1] [5,5,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1244 + +lemma sg2270 : RowSquare [7,2,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1754 + +lemma sg2271 : RowSquare [7,2,1,1,1,1] [3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1755 + +lemma sg2272 : RowSquare [7,2,1,1,1,1] [3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg1757 + +lemma sg2273 : RowSquare [7,2,1,1,1,1] [3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg1758 + +lemma sg2274 : RowSquare [7,2,1,1,1,1] [3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg889 + +lemma sg2275 : RowSquare [7,2,1,1,1,1] [3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg890 + +lemma sg2276 : RowSquare [7,2,1,1,1,1] [3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg891 + +lemma sg2277 : RowSquare [7,2,1,1,1,1] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg892 + +lemma sg2278 : RowSquare [7,2,1,1,1,1] [4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg1332 + +lemma sg2279 : RowSquare [7,2,2,1,1] [3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg312 + +lemma sg2280 : RowSquare [7,2,2,1,1] [3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg586 + +lemma sg2281 : RowSquare [7,2,2,1,1] [3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg313 + +lemma sg2282 : RowSquare [7,2,2,1,1] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg315 + +lemma sg2283 : RowSquare [7,2,2,1,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg588 + +lemma sg2284 : RowSquare [7,2,2,2] [3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg66 sg178 + +lemma sg2285 : RowSquare [7,2,2,2] [3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg67 sg178 + +lemma sg2286 : RowSquare [7,2,2,2] [4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg66 sg179 + +lemma sg2287 : RowSquare [7,3,1,1,1] [2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg910 + +lemma sg2288 : RowSquare [7,3,1,1,1] [2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg586 + +lemma sg2289 : RowSquare [7,3,1,1,1] [3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg911 + +lemma sg2290 : RowSquare [7,3,1,1,1] [3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg587 + +lemma sg2291 : RowSquare [7,3,1,1,1] [3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg586 + +lemma sg2292 : RowSquare [7,3,1,1,1] [3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg912 + +lemma sg2293 : RowSquare [7,3,1,1,1] [3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg588 + +lemma sg2294 : RowSquare [7,3,1,1,1] [3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg913 + +lemma sg2295 : RowSquare [7,3,1,1,1] [3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg589 + +lemma sg2296 : RowSquare [7,3,1,1,1] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg915 + +lemma sg2297 : RowSquare [7,3,1,1,1] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg590 + +lemma sg2298 : RowSquare [7,3,1,1,1] [4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg911 + +lemma sg2299 : RowSquare [7,3,1,1,1] [4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg534 + +lemma sg2300 : RowSquare [7,3,1,1,1] [4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg312 + +lemma sg2301 : RowSquare [7,3,1,1,1] [4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg534 + +lemma sg2302 : RowSquare [7,3,1,1,1] [4,3,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg915 + +lemma sg2303 : RowSquare [7,3,1,1,1] [4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg536 + +lemma sg2304 : RowSquare [7,3,1,1,1] [4,3,3,3] := by + exact rowSquare_join (by decide) sg39 sg315 + +lemma sg2305 : RowSquare [7,3,1,1,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg535 + +lemma sg2306 : RowSquare [7,3,1,1,1] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg313 + +lemma sg2307 : RowSquare [7,3,1,1,1] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg595 + +lemma sg2308 : RowSquare [7,3,1,1,1] [4,4,4,1] := by + exact rowSquare_join (by decide) sg4 sg923 + +lemma sg2309 : RowSquare [7,3,1,1,1] [5,5,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg541 + +lemma sg2310 : RowSquare [7,3,2,1] [2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg330 + +lemma sg2311 : RowSquare [7,3,2,1] [2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg178 + +lemma sg2312 : RowSquare [7,3,2,1] [3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg330 + +lemma sg2313 : RowSquare [7,3,2,1] [3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg75 sg178 + +lemma sg2314 : RowSquare [7,3,2,1] [3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg179 + +lemma sg2315 : RowSquare [7,3,2,1] [3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg34 sg330 + +lemma sg2316 : RowSquare [7,3,2,1] [3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg76 sg178 + +lemma sg2317 : RowSquare [7,3,2,1] [3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg180 + +lemma sg2318 : RowSquare [7,3,2,1] [3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg181 + +lemma sg2319 : RowSquare [7,3,2,1] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg334 + +lemma sg2320 : RowSquare [7,3,2,1] [4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg35 sg330 + +lemma sg2321 : RowSquare [7,3,2,1] [4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg36 sg330 + +lemma sg2322 : RowSquare [7,3,2,1] [4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg79 sg178 + +lemma sg2323 : RowSquare [7,3,2,1] [4,3,3,3] := by + exact rowSquare_join (by decide) sg33 sg334 + +lemma sg2324 : RowSquare [7,3,2,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg178 + +lemma sg2325 : RowSquare [7,3,2,1] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg88 sg143 + +lemma sg2326 : RowSquare [7,3,2,1] [5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg850 + +lemma sg2327 : RowSquare [7,3,2,1] [5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg81 sg178 + +lemma sg2328 : RowSquare [7,3,2,1] [5,5,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg143 + +lemma sg2329 : RowSquare [7,3,3] [3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg348 + +lemma sg2330 : RowSquare [7,3,3] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg350 + +lemma sg2331 : RowSquare [7,3,3] [4,3,2,2,2] := by + exact rowSquare_join (by decide) sg87 sg155 + +lemma sg2332 : RowSquare [7,3,3] [4,3,3,3] := by + exact rowSquare_join (by decide) sg33 sg350 + +lemma sg2333 : RowSquare [7,3,3] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg34 sg348 + +lemma sg2334 : RowSquare [7,3,3] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg88 sg155 + +lemma sg2335 : RowSquare [7,3,3] [5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg516 + +lemma sg2336 : RowSquare [7,3,3] [5,3,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg158 + +lemma sg2337 : RowSquare [7,4,1,1] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg616 + +lemma sg2338 : RowSquare [7,4,1,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg562 + +lemma sg2339 : RowSquare [7,4,2] [3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg193 + +lemma sg2340 : RowSquare [7,4,2] [3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg194 + +lemma sg2341 : RowSquare [7,4,2] [3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg975 + +lemma sg2342 : RowSquare [7,4,2] [3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg195 + +lemma sg2343 : RowSquare [7,4,2] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg32 sg357 + +lemma sg2344 : RowSquare [7,4,2] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg358 + +lemma sg2345 : RowSquare [7,4,2] [4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg306 + +lemma sg2346 : RowSquare [7,4,2] [4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg306 + +lemma sg2347 : RowSquare [7,4,2] [4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg577 + +lemma sg2348 : RowSquare [7,4,2] [4,3,2,2,2] := by + exact rowSquare_join (by decide) sg87 sg166 + +lemma sg2349 : RowSquare [7,4,2] [4,3,3,3] := by + exact rowSquare_join (by decide) sg39 sg350 + +lemma sg2350 : RowSquare [7,4,2] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg577 + +lemma sg2351 : RowSquare [7,4,2] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg88 sg166 + +lemma sg2352 : RowSquare [7,4,2] [5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg47 sg306 + +lemma sg2353 : RowSquare [7,4,2] [5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg307 + +lemma sg2354 : RowSquare [7,4,2] [5,2,2,2,2] := by + exact rowSquare_join (by decide) sg87 sg168 + +lemma sg2355 : RowSquare [7,4,2] [5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg307 + +lemma sg2356 : RowSquare [7,4,2] [6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg48 sg306 + +lemma sg2357 : RowSquare [7,4,2] [6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg47 sg307 + +lemma sg2358 : RowSquare [7,4,2] [7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg48 sg307 + +lemma sg2359 : RowSquare [7,5,1] [3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg207 + +lemma sg2360 : RowSquare [7,5,1] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg982 + +lemma sg2361 : RowSquare [7,5,1] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg210 + +lemma sg2362 : RowSquare [7,5,1] [4,4,3,1,1] := by + exact rowSquare_join (by decide) sg97 sg166 + +lemma sg2363 : RowSquare [7,5,1] [5,5,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg367 + +lemma sg2365 : RowSquare [8,1,1,1,1,1] [3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1327 + +lemma sg2366 : RowSquare [8,1,1,1,1,1] [4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1330 + +lemma sg2367 : RowSquare [8,1,1,1,1,1] [4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1331 + +lemma sg2368 : RowSquare [8,1,1,1,1,1] [4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg1332 + +lemma sg2369 : RowSquare [8,2,1,1,1] [3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg586 + +lemma sg2370 : RowSquare [8,2,1,1,1] [3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg586 + +lemma sg2371 : RowSquare [8,2,1,1,1] [3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg998 + +lemma sg2372 : RowSquare [8,2,1,1,1] [3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg999 + +lemma sg2373 : RowSquare [8,2,1,1,1] [3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg1000 + +lemma sg2374 : RowSquare [8,2,1,1,1] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg1001 + +lemma sg2375 : RowSquare [8,2,1,1,1] [4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg586 + +lemma sg2376 : RowSquare [8,2,1,1,1] [4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg587 + +lemma sg2377 : RowSquare [8,2,1,1,1] [4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg587 + +lemma sg2378 : RowSquare [8,2,1,1,1] [4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg588 + +lemma sg2379 : RowSquare [8,2,1,1,1] [4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg1000 + +lemma sg2380 : RowSquare [8,2,1,1,1] [4,3,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg1001 + +lemma sg2381 : RowSquare [8,2,1,1,1] [4,3,3,2,1] := by + exact rowSquare_join (by decide) sg16 sg590 + +lemma sg2382 : RowSquare [8,2,1,1,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg588 + +lemma sg2383 : RowSquare [8,2,1,1,1] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg589 + +lemma sg2384 : RowSquare [8,2,1,1,1] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg17 sg590 + +lemma sg2385 : RowSquare [8,2,1,1,1] [4,4,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg1007 + +lemma sg2386 : RowSquare [8,2,1,1,1] [4,4,3,2] := by + exact rowSquare_join (by decide) sg4 sg1008 + +lemma sg2387 : RowSquare [8,2,1,1,1] [5,3,2,2,1] := by + exact rowSquare_join (by decide) sg18 sg590 + +lemma sg2388 : RowSquare [8,2,1,1,1] [5,5,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg595 + +lemma sg2389 : RowSquare [8,2,1,1,1] [5,5,2,1] := by + exact rowSquare_join (by decide) sg17 sg596 + +lemma sg2390 : RowSquare [8,2,2,1] [3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg87 sg178 + +lemma sg2391 : RowSquare [8,2,2,1] [3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg88 sg178 + +lemma sg2392 : RowSquare [8,2,2,1] [3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg371 + +lemma sg2393 : RowSquare [8,2,2,1] [3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg178 + +lemma sg2394 : RowSquare [8,2,2,1] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg32 sg372 + +lemma sg2395 : RowSquare [8,2,2,1] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg373 + +lemma sg2396 : RowSquare [8,2,2,1] [4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg179 + +lemma sg2397 : RowSquare [8,2,2,1] [4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg179 + +lemma sg2398 : RowSquare [8,2,2,1] [4,3,3,3] := by + exact rowSquare_join (by decide) sg33 sg373 + +lemma sg2399 : RowSquare [8,2,2,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg178 + +lemma sg2400 : RowSquare [8,2,2,1] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg34 sg371 + +lemma sg2401 : RowSquare [8,2,2,1] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg88 sg180 + +lemma sg2402 : RowSquare [8,2,2,1] [4,4,4,1] := by + exact rowSquare_join (by decide) sg89 sg181 + +lemma sg2403 : RowSquare [8,2,2,1] [5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg940 + +lemma sg2404 : RowSquare [8,2,2,1] [6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg548 + +lemma sg2405 : RowSquare [8,3,1,1] [3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg178 + +lemma sg2406 : RowSquare [8,3,1,1] [3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg1032 + +lemma sg2407 : RowSquare [8,3,1,1] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg1033 + +lemma sg2408 : RowSquare [8,3,1,1] [4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg330 + +lemma sg2409 : RowSquare [8,3,1,1] [4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg178 + +lemma sg2410 : RowSquare [8,3,1,1] [4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg330 + +lemma sg2411 : RowSquare [8,3,1,1] [4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg99 sg178 + +lemma sg2412 : RowSquare [8,3,1,1] [4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg371 + +lemma sg2413 : RowSquare [8,3,1,1] [4,3,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg1033 + +lemma sg2414 : RowSquare [8,3,1,1] [4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg179 + +lemma sg2415 : RowSquare [8,3,1,1] [4,3,3,2,1] := by + exact rowSquare_join (by decide) sg39 sg372 + +lemma sg2416 : RowSquare [8,3,1,1] [4,3,3,3] := by + exact rowSquare_join (by decide) sg39 sg373 + +lemma sg2417 : RowSquare [8,3,1,1] [4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg614 + +lemma sg2418 : RowSquare [8,3,1,1] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg371 + +lemma sg2419 : RowSquare [8,3,1,1] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg17 sg616 + +lemma sg2420 : RowSquare [8,3,1,1] [4,4,3,1,1] := by + exact rowSquare_join (by decide) sg97 sg180 + +lemma sg2421 : RowSquare [8,3,1,1] [4,4,3,2] := by + exact rowSquare_join (by decide) sg40 sg373 + +lemma sg2422 : RowSquare [8,3,1,1] [4,4,4,1] := by + exact rowSquare_join (by decide) sg97 sg181 + +lemma sg2423 : RowSquare [8,3,1,1] [5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg47 sg330 + +lemma sg2424 : RowSquare [8,3,1,1] [5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg100 sg178 + +lemma sg2425 : RowSquare [8,3,1,1] [5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg98 sg179 + +lemma sg2426 : RowSquare [8,3,1,1] [5,2,2,2,2] := by + exact rowSquare_join (by decide) sg7 sg961 + +lemma sg2427 : RowSquare [8,3,1,1] [5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg178 + +lemma sg2428 : RowSquare [8,3,1,1] [5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg99 sg179 + +lemma sg2429 : RowSquare [8,3,1,1] [5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg332 + +lemma sg2430 : RowSquare [8,3,1,1] [5,4,2,1,1] := by + exact rowSquare_join (by decide) sg66 sg228 + +lemma sg2431 : RowSquare [8,3,1,1] [5,4,2,2] := by + exact rowSquare_join (by decide) sg39 sg377 + +lemma sg2432 : RowSquare [8,3,2] [3,3,3,2,2] := by + exact rowSquare_join (by decide) sg32 sg389 + +lemma sg2433 : RowSquare [8,3,2] [3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg390 + +lemma sg2434 : RowSquare [8,3,2] [4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg218 + +lemma sg2435 : RowSquare [8,3,2] [4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg219 + +lemma sg2436 : RowSquare [8,3,2] [4,3,2,2,2] := by + exact rowSquare_join (by decide) sg87 sg194 + +lemma sg2437 : RowSquare [8,3,2] [4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg220 + +lemma sg2438 : RowSquare [8,3,2] [4,3,3,2,1] := by + exact rowSquare_join (by decide) sg87 sg195 + +lemma sg2439 : RowSquare [8,3,2] [4,3,3,3] := by + exact rowSquare_join (by decide) sg33 sg390 + +lemma sg2440 : RowSquare [8,3,2] [4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg636 + +lemma sg2441 : RowSquare [8,3,2] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg88 sg194 + +lemma sg2442 : RowSquare [8,3,2] [4,4,3,1,1] := by + exact rowSquare_join (by decide) sg89 sg194 + +lemma sg2443 : RowSquare [8,3,2] [4,4,3,2] := by + exact rowSquare_join (by decide) sg88 sg195 + +lemma sg2444 : RowSquare [8,3,2] [5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg975 + +lemma sg2445 : RowSquare [8,3,2] [5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg221 + +lemma sg2446 : RowSquare [8,3,2] [5,2,2,2,2] := by + exact rowSquare_join (by decide) sg87 sg196 + +lemma sg2447 : RowSquare [8,3,2] [5,3,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg197 + +lemma sg2448 : RowSquare [8,3,2] [5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg223 + +lemma sg2449 : RowSquare [8,3,2] [5,5,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg194 + +lemma sg2450 : RowSquare [8,3,2] [6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg577 + +lemma sg2451 : RowSquare [8,4,1] [4,3,3,3] := by + exact rowSquare_join (by decide) sg39 sg390 + +lemma sg2452 : RowSquare [8,4,1] [4,4,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg402 + +lemma sg2453 : RowSquare [8,4,1] [5,2,2,2,2] := by + exact rowSquare_join (by decide) sg7 sg982 + +lemma sg2454 : RowSquare [9,1,1,1,1] [5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg998 + +lemma sg2455 : RowSquare [9,1,1,1,1] [5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg999 + +lemma sg2456 : RowSquare [9,2,1,1] [5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg104 sg178 + +lemma sg2457 : RowSquare [9,2,1,1] [5,2,2,2,2] := by + exact rowSquare_join (by decide) sg7 sg1033 + +lemma sg2458 : RowSquare [9,2,1,1] [5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg105 sg178 + +lemma sg2459 : RowSquare [9,2,1,1] [5,3,3,1,1] := by + exact rowSquare_join (by decide) sg45 sg372 + +lemma sg2460 : RowSquare [9,2,1,1] [5,3,3,2] := by + exact rowSquare_join (by decide) sg45 sg373 + +lemma sg2461 : RowSquare [9,2,2] [5,2,2,2,2] := by + exact rowSquare_join (by decide) sg87 sg218 + +lemma sg2462 : RowSquare [9,2,2] [5,3,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg219 + +lemma sg2463 : RowSquare [9,2,2] [5,3,3,1,1] := by + exact rowSquare_join (by decide) sg87 sg220 + +lemma sg2464 : RowSquare [9,2,2] [5,4,2,2] := by + exact rowSquare_join (by decide) sg88 sg219 + +lemma sg2465 : RowSquare [9,2,2] [5,4,3,1] := by + exact rowSquare_join (by decide) sg88 sg220 + +lemma sg2466 : RowSquare [9,2,2] [6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg636 + +lemma sg2467 : RowSquare [9,2,2] [6,2,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg221 + +lemma sg2468 : RowSquare [9,2,2] [6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg1063 + +lemma sg2469 : RowSquare [9,2,2] [6,3,2,1,1] := by + exact rowSquare_join (by decide) sg87 sg222 + +lemma sg2470 : RowSquare [9,2,2] [6,3,2,2] := by + exact rowSquare_join (by decide) sg88 sg221 + +lemma sg2471 : RowSquare [9,2,2] [6,3,3,1] := by + exact rowSquare_join (by decide) sg90 sg220 + +lemma sg2472 : RowSquare [9,2,2] [6,4,1,1,1] := by + exact rowSquare_join (by decide) sg87 sg223 + +lemma sg2473 : RowSquare [9,2,2] [6,4,2,1] := by + exact rowSquare_join (by decide) sg88 sg222 + +lemma sg2474 : RowSquare [9,2,2] [6,4,3] := by + exact rowSquare_join (by decide) sg89 sg222 + +lemma sg2475 : RowSquare [9,2,2] [6,5,1,1] := by + exact rowSquare_join (by decide) sg88 sg223 + +lemma sg2476 : RowSquare [9,2,2] [6,5,2] := by + exact rowSquare_join (by decide) sg89 sg223 + +lemma sg2477 : RowSquare [9,2,2] [7,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg348 + +lemma sg2478 : RowSquare [9,3,1] [5,4,2,2] := by + exact rowSquare_join (by decide) sg46 sg390 + +lemma sg2479 : RowSquare [9,3,1] [5,5,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg424 + +lemma sg2480 : RowSquare [10,2,1] [7,2,2,1,1] := by + exact rowSquare_join (by decide) sg87 sg231 + +lemma sg2481 : RowSquare [10,2,1] [7,2,2,2] := by + exact rowSquare_join (by decide) sg49 sg390 + +lemma sg2482 : RowSquare [10,2,1] [7,3,1,1,1] := by + exact rowSquare_join (by decide) sg87 sg232 + +lemma sg2483 : RowSquare [10,2,1] [7,3,2,1] := by + exact rowSquare_join (by decide) sg88 sg231 + +lemma sg2484 : RowSquare [10,2,1] [7,3,3] := by + exact rowSquare_join (by decide) sg89 sg231 + +lemma sg2485 : RowSquare [2,2,1,1,1,1,1,1,1,1,1,1] [10,2,2] := by + exact rowSquare_join (by decide) sg227 sg234 + +lemma sg2486 : RowSquare [2,2,2,2,1,1,1,1,1,1] [7,5,1,1] := by + exact rowSquare_join (by decide) sg98 sg424 + +lemma sg2487 : RowSquare [2,2,2,2,1,1,1,1,1,1] [7,6,1] := by + exact rowSquare_join (by decide) sg228 sg230 + +lemma sg2490 : RowSquare [3,2,2,1,1,1,1,1,1,1] [7,7] := by + exact rowSquare_join (by decide) sg92 sg424 + +lemma sg2491 : RowSquare [3,2,2,2,1,1,1,1,1] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg97 sg389 + +lemma sg2492 : RowSquare [3,2,2,2,1,1,1,1,1] [4,4,4,2] := by + exact rowSquare_join (by decide) sg97 sg390 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes40.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes40.lean index a22b541514362b7219c815be77ccea8ab17a2fa3..dc96694302f90094b33ecdf67e7a71a53813616f 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes40.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes40.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 - -namespace OAI - -/-! Semigroup Nodes 40. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg16540 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14835 - -lemma sg16541 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14836 - -lemma sg16542 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg14602 - -lemma sg16543 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg13627 - -lemma sg16544 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg14 sg13567 - -lemma sg16545 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg5 sg14592 - -lemma sg16546 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg14603 - -lemma sg16547 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13628 - -lemma sg16548 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13629 - -lemma sg16549 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13630 - -lemma sg16550 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg13 sg13631 - -lemma sg16551 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg39 sg12736 - -lemma sg16552 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13632 - -lemma sg16553 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg14604 - -lemma sg16554 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg14605 - -lemma sg16555 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13633 - -lemma sg16556 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by - exact rowSquare_join (by decide) sg39 sg12737 - -lemma sg16557 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg41 sg12724 - -lemma sg16558 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13634 - -lemma sg16559 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg39 sg12738 - -lemma sg16560 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by - exact rowSquare_join (by decide) sg41 sg12727 - -lemma sg16561 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13635 - -lemma sg16562 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg13636 - -lemma sg16563 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by - exact rowSquare_join (by decide) sg39 sg12739 - -lemma sg16564 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg5 sg14595 - -lemma sg16565 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg13569 - -lemma sg16566 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13637 - -lemma sg16567 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13638 - -lemma sg16568 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg13576 - -lemma sg16569 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg14 sg13577 - -lemma sg16570 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13639 - -lemma sg16571 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by - exact rowSquare_join (by decide) sg39 sg12740 - -lemma sg16572 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg40 sg12736 - -lemma sg16573 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13640 - -lemma sg16574 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13641 - -lemma sg16575 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg39 sg12741 - -lemma sg16576 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by - exact rowSquare_join (by decide) sg42 sg12727 - -lemma sg16577 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13642 - -lemma sg16578 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by - exact rowSquare_join (by decide) sg40 sg12737 - -lemma sg16579 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg39 sg12742 - -lemma sg16580 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg39 sg12743 - -lemma sg16581 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg12744 - -lemma sg16582 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by - exact rowSquare_join (by decide) sg39 sg12745 - -lemma sg16583 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by - exact rowSquare_join (by decide) sg39 sg12746 - -lemma sg16584 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13643 - -lemma sg16585 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by - exact rowSquare_join (by decide) sg39 sg12747 - -lemma sg16586 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg13585 - -lemma sg16587 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg13586 - -lemma sg16588 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg14 sg13587 - -lemma sg16589 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13644 - -lemma sg16590 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by - exact rowSquare_join (by decide) sg39 sg12748 - -lemma sg16591 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg14 sg13592 - -lemma sg16592 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13645 - -lemma sg16593 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,3] := by - exact rowSquare_join (by decide) sg40 sg12740 - -lemma sg16594 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg39 sg12749 - -lemma sg16595 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg39 sg12750 - -lemma sg16596 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg12751 - -lemma sg16597 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,2] := by - exact rowSquare_join (by decide) sg39 sg12752 - -lemma sg16598 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,4] := by - exact rowSquare_join (by decide) sg39 sg12753 - -lemma sg16599 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg13598 - -lemma sg16600 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg39 sg12754 - -lemma sg16601 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg40 sg12743 - -lemma sg16602 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg12755 - -lemma sg16603 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,2] := by - exact rowSquare_join (by decide) sg39 sg12756 - -lemma sg16604 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,4] := by - exact rowSquare_join (by decide) sg40 sg12746 - -lemma sg16605 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12757 - -lemma sg16606 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,3] := by - exact rowSquare_join (by decide) sg39 sg12758 - -lemma sg16607 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,6,1,1] := by - exact rowSquare_join (by decide) sg39 sg12759 - -lemma sg16608 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,6,2] := by - exact rowSquare_join (by decide) sg39 sg12760 - -lemma sg16609 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3320 sg4500 - -lemma sg16610 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg14606 - -lemma sg16611 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14607 - -lemma sg16612 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3695 sg4118 - -lemma sg16613 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg13599 - -lemma sg16614 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg13600 - -lemma sg16615 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg14 sg13601 - -lemma sg16616 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13646 - -lemma sg16617 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by - exact rowSquare_join (by decide) sg40 sg12748 - -lemma sg16618 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13647 - -lemma sg16619 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13648 - -lemma sg16620 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,5,4,4] := by - exact rowSquare_join (by decide) sg40 sg12753 - -lemma sg16621 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14837 - -lemma sg16622 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg6 sg14586 - -lemma sg16623 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14838 - -lemma sg16624 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14839 - -lemma sg16625 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg14608 - -lemma sg16626 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13649 - -lemma sg16627 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg5 sg14602 - -lemma sg16628 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,5] := by - exact rowSquare_join (by decide) sg43 sg12727 - -lemma sg16629 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,4] := by - exact rowSquare_join (by decide) sg51 sg12474 - -lemma sg16630 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,6,6,6,3] := by - exact rowSquare_join (by decide) sg39 sg12761 - -lemma sg16631 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,7,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13650 - -lemma sg16632 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,7,5,5,4] := by - exact rowSquare_join (by decide) sg52 sg12474 - -lemma sg16633 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,7,6,4,4] := by - exact rowSquare_join (by decide) sg51 sg12486 - -lemma sg16634 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,7,6,5,3] := by - exact rowSquare_join (by decide) sg39 sg12762 - -lemma sg16635 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,7,6,6,2] := by - exact rowSquare_join (by decide) sg39 sg12763 - -lemma sg16636 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,5,4,4] := by - exact rowSquare_join (by decide) sg52 sg12486 - -lemma sg16637 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,5,5,3] := by - exact rowSquare_join (by decide) sg39 sg12764 - -lemma sg16638 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,6,4,3] := by - exact rowSquare_join (by decide) sg270 sg11069 - -lemma sg16639 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,6,5,2] := by - exact rowSquare_join (by decide) sg270 sg11070 - -lemma sg16640 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,6,6,1] := by - exact rowSquare_join (by decide) sg271 sg11070 - -lemma sg16641 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,9,4,4,4] := by - exact rowSquare_join (by decide) sg42 sg12753 - -lemma sg16642 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,10,4,4,3] := by - exact rowSquare_join (by decide) sg13 sg13651 - -lemma sg16643 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [11,5,5,5,5] := by - exact rowSquare_join (by decide) sg44 sg12727 - -lemma sg16644 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [11,6,5,5,4] := by - exact rowSquare_join (by decide) sg53 sg12474 - -lemma sg16645 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [11,6,6,4,4] := by - exact rowSquare_join (by decide) sg270 sg11087 - -lemma sg16646 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [11,6,6,5,3] := by - exact rowSquare_join (by decide) sg270 sg11089 - -lemma sg16647 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [11,6,6,6,2] := by - exact rowSquare_join (by decide) sg271 sg11089 - -lemma sg16648 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [11,8,4,4,4] := by - exact rowSquare_join (by decide) sg111 sg11615 - -lemma sg16649 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1682 sg6504 - -lemma sg16650 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1754 sg6497 - -lemma sg16651 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2633 sg4964 - -lemma sg16652 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3691 sg4067 - -lemma sg16653 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3691 sg4068 - -lemma sg16654 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg3691 sg4070 - -lemma sg16655 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg2633 sg4967 - -lemma sg16656 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg1758 sg6498 - -lemma sg16657 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,3,3] := by - exact rowSquare_join (by decide) sg3355 sg4437 - -lemma sg16658 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,2] := by - exact rowSquare_join (by decide) sg3560 sg4303 - -lemma sg16659 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15502 - -lemma sg16660 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3,2] := by - exact rowSquare_join (by decide) sg3560 sg4304 - -lemma sg16661 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,4,1] := by - exact rowSquare_join (by decide) sg1758 sg6499 - -lemma sg16662 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3691 sg4074 - -lemma sg16663 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg4 sg14611 - -lemma sg16664 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg3352 sg4441 - -lemma sg16665 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,3,2] := by - exact rowSquare_join (by decide) sg3653 sg4157 - -lemma sg16666 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg3562 sg4303 - -lemma sg16667 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg3691 sg4075 - -lemma sg16668 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg3691 sg4076 - -lemma sg16669 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg3562 sg4304 - -lemma sg16670 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,4] := by - exact rowSquare_join (by decide) sg1688 sg6505 - -lemma sg16671 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14612 - -lemma sg16672 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3,2] := by - exact rowSquare_join (by decide) sg4 sg14613 - -lemma sg16673 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,4,1] := by - exact rowSquare_join (by decide) sg3620 sg4185 - -lemma sg16674 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg14614 - -lemma sg16675 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,2,2] := by - exact rowSquare_join (by decide) sg4 sg14615 - -lemma sg16676 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,3,1] := by - exact rowSquare_join (by decide) sg3689 sg4079 - -lemma sg16677 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by - exact rowSquare_join (by decide) sg1688 sg6506 - -lemma sg16678 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14616 - -lemma sg16679 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,2,1] := by - exact rowSquare_join (by decide) sg3723 sg4031 - -lemma sg16680 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,3] := by - exact rowSquare_join (by decide) sg3356 sg4438 - -lemma sg16681 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3571 sg4226 - -lemma sg16682 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3613 sg4188 - -lemma sg16683 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,2] := by - exact rowSquare_join (by decide) sg3654 sg4157 - -lemma sg16684 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1] := by - exact rowSquare_join (by decide) sg3565 sg4303 - -lemma sg16685 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg3691 sg4077 - -lemma sg16686 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,2,1] := by - exact rowSquare_join (by decide) sg3724 sg4031 - -lemma sg16687 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by - exact rowSquare_join (by decide) sg3690 sg4079 - -lemma sg16688 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by - exact rowSquare_join (by decide) sg3655 sg4157 - -lemma sg16689 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by - exact rowSquare_join (by decide) sg3725 sg4031 - -lemma sg16690 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by - exact rowSquare_join (by decide) sg3726 sg4031 - -lemma sg16691 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg3560 sg4305 - -lemma sg16692 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg5 sg14609 - -lemma sg16693 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg4 sg14617 - -lemma sg16694 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg9 sg13654 - -lemma sg16695 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg3560 sg4306 - -lemma sg16696 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,3,2] := by - exact rowSquare_join (by decide) sg1 sg14840 - -lemma sg16697 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg1 sg14841 - -lemma sg16698 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg1 sg14842 - -lemma sg16699 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg1 sg14843 - -lemma sg16700 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,4] := by - exact rowSquare_join (by decide) sg2167 sg5763 - -lemma sg16701 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg5 sg14610 - -lemma sg16702 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg10 sg13654 - -lemma sg16703 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg9 sg13657 - -lemma sg16704 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg9 sg13658 - -lemma sg16705 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg5 sg14614 - -lemma sg16706 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg5 sg14615 - -lemma sg16707 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg0 sg15503 - -lemma sg16708 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by - exact rowSquare_join (by decide) sg0 sg15504 - -lemma sg16709 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg0 sg15505 - -lemma sg16710 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by - exact rowSquare_join (by decide) sg0 sg15506 - -lemma sg16711 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg9 sg13661 - -lemma sg16712 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,3,2] := by - exact rowSquare_join (by decide) sg9 sg13662 - -lemma sg16713 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2,2] := by - exact rowSquare_join (by decide) sg9 sg13664 - -lemma sg16714 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,3,1] := by - exact rowSquare_join (by decide) sg9 sg13665 - -lemma sg16715 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg15507 - -lemma sg16716 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2,2] := by - exact rowSquare_join (by decide) sg9 sg13667 - -lemma sg16717 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,3,1] := by - exact rowSquare_join (by decide) sg9 sg13668 - -lemma sg16718 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg12765 - -lemma sg16719 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,2,1] := by - exact rowSquare_join (by decide) sg26 sg12766 - -lemma sg16720 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by - exact rowSquare_join (by decide) sg0 sg15508 - -lemma sg16721 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by - exact rowSquare_join (by decide) sg9 sg13671 - -lemma sg16722 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by - exact rowSquare_join (by decide) sg74 sg12341 - -lemma sg16723 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg15509 - -lemma sg16724 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,2] := by - exact rowSquare_join (by decide) sg3560 sg4311 - -lemma sg16725 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg12767 - -lemma sg16726 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,2,1] := by - exact rowSquare_join (by decide) sg26 sg12768 - -lemma sg16727 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by - exact rowSquare_join (by decide) sg0 sg15510 - -lemma sg16728 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by - exact rowSquare_join (by decide) sg26 sg12769 - -lemma sg16729 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by - exact rowSquare_join (by decide) sg74 sg12342 - -lemma sg16730 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by - exact rowSquare_join (by decide) sg74 sg12343 - -lemma sg16731 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg0 sg15511 - -lemma sg16732 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg3696 sg4076 - -lemma sg16733 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg10 sg13657 - -lemma sg16734 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg10 sg13658 - -lemma sg16735 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg10 sg13662 - -lemma sg16736 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg10 sg13664 - -lemma sg16737 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg10 sg13665 - -lemma sg16738 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by - exact rowSquare_join (by decide) sg2746 sg4896 - -lemma sg16739 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg10 sg13667 - -lemma sg16740 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg10 sg13668 - -lemma sg16741 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg10 sg13670 - -lemma sg16742 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by - exact rowSquare_join (by decide) sg3725 sg4032 - -lemma sg16743 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg10 sg13671 - -lemma sg16744 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by - exact rowSquare_join (by decide) sg74 sg12344 - -lemma sg16745 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg14619 - -lemma sg16746 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg14620 - -lemma sg16747 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg14621 - -lemma sg16748 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg27 sg12766 - -lemma sg16749 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,3] := by - exact rowSquare_join (by decide) sg3620 sg4187 - -lemma sg16750 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4082 - -lemma sg16751 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14622 - -lemma sg16752 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,2,1] := by - exact rowSquare_join (by decide) sg27 sg12768 - -lemma sg16753 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by - exact rowSquare_join (by decide) sg4 sg14623 - -lemma sg16754 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg27 sg12769 - -lemma sg16755 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by - exact rowSquare_join (by decide) sg74 sg12345 - -lemma sg16756 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by - exact rowSquare_join (by decide) sg74 sg12346 - -lemma sg16757 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4083 - -lemma sg16758 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg3687 sg4083 - -lemma sg16759 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg3617 sg4188 - -lemma sg16760 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg3724 sg4033 - -lemma sg16761 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by - exact rowSquare_join (by decide) sg74 sg12347 - -lemma sg16762 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by - exact rowSquare_join (by decide) sg74 sg12348 - -lemma sg16763 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by - exact rowSquare_join (by decide) sg3726 sg4033 - -lemma sg16764 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3721 sg4037 - -lemma sg16765 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14624 - -lemma sg16766 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3614 sg4189 - -lemma sg16767 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg14625 - -lemma sg16768 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3721 sg4038 - -lemma sg16769 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg14626 - -lemma sg16770 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg14627 - -lemma sg16771 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg14628 - -lemma sg16772 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3721 sg4039 - -lemma sg16773 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg14629 - -lemma sg16774 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14630 - -lemma sg16775 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14631 - -lemma sg16776 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg14632 - -lemma sg16777 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by - exact rowSquare_join (by decide) sg4 sg14633 - -lemma sg16778 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by - exact rowSquare_join (by decide) sg4 sg14634 - -lemma sg16779 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by - exact rowSquare_join (by decide) sg74 sg12349 - -lemma sg16780 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3688 sg4083 - -lemma sg16781 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14635 - -lemma sg16782 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg14636 - -lemma sg16783 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg14637 - -lemma sg16784 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by - exact rowSquare_join (by decide) sg74 sg12350 - -lemma sg16785 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by - exact rowSquare_join (by decide) sg74 sg12351 - -lemma sg16786 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg4 sg14638 - -lemma sg16787 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg3575 sg4226 - -lemma sg16788 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg14639 - -lemma sg16789 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by - exact rowSquare_join (by decide) sg74 sg12352 - -lemma sg16790 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by - exact rowSquare_join (by decide) sg74 sg12353 - -lemma sg16791 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by - exact rowSquare_join (by decide) sg4 sg14640 - -lemma sg16792 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by - exact rowSquare_join (by decide) sg3565 sg4311 - -lemma sg16793 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by - exact rowSquare_join (by decide) sg74 sg12354 - -lemma sg16794 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by - exact rowSquare_join (by decide) sg3691 sg4083 - -lemma sg16795 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg6 sg14609 - -lemma sg16796 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg5 sg14617 - -lemma sg16797 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg11 sg13654 - -lemma sg16798 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg14641 - -lemma sg16799 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg9 sg13678 - -lemma sg16800 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg9 sg13679 - -lemma sg16801 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg6 sg14614 - -lemma sg16802 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg6 sg14615 - -lemma sg16803 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg26 sg12772 - -lemma sg16804 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg1 sg14844 - -lemma sg16805 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg3 sg14648 - -lemma sg16806 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg74 sg12355 - -lemma sg16807 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg5 sg14618 - -lemma sg16808 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg10 sg13678 - -lemma sg16809 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg10 sg13679 - -lemma sg16810 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg9 sg13684 - -lemma sg16811 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg9 sg13685 - -lemma sg16812 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg9 sg13687 - -lemma sg16813 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg27 sg12772 - -lemma sg16814 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg9 sg13689 - -lemma sg16815 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg11 sg13667 - -lemma sg16816 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg26 sg12773 - -lemma sg16817 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg26 sg12774 - -lemma sg16818 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by - exact rowSquare_join (by decide) sg74 sg12356 - -lemma sg16819 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg11 sg13671 - -lemma sg16820 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg74 sg12357 - -lemma sg16821 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg22 sg12817 - -lemma sg16822 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg26 sg12776 - -lemma sg16823 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,3,1] := by - exact rowSquare_join (by decide) sg26 sg12777 - -lemma sg16824 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg74 sg12358 - -lemma sg16825 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by - exact rowSquare_join (by decide) sg74 sg12359 - -lemma sg16826 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg26 sg12778 - -lemma sg16827 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg12360 - -lemma sg16828 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by - exact rowSquare_join (by decide) sg74 sg12361 - -lemma sg16829 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg26 sg12779 - -lemma sg16830 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by - exact rowSquare_join (by decide) sg74 sg12362 - -lemma sg16831 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by - exact rowSquare_join (by decide) sg74 sg12363 - -lemma sg16832 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14845 - -lemma sg16833 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg26 sg12780 - -lemma sg16834 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg26 sg12781 - -lemma sg16835 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by - exact rowSquare_join (by decide) sg74 sg12364 - -lemma sg16836 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by - exact rowSquare_join (by decide) sg74 sg12365 - -lemma sg16837 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by - exact rowSquare_join (by decide) sg75 sg12343 - -lemma sg16838 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg9 sg13711 - -lemma sg16839 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg10 sg13685 - -lemma sg16840 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg10 sg13687 - -lemma sg16841 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg10 sg13688 - -lemma sg16842 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by - exact rowSquare_join (by decide) sg10 sg13689 - -lemma sg16843 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg23 sg12817 - -lemma sg16844 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg26 sg12782 - -lemma sg16845 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg26 sg12783 - -lemma sg16846 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg74 sg12366 - -lemma sg16847 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by - exact rowSquare_join (by decide) sg74 sg12367 - -lemma sg16848 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg23 sg12818 - -lemma sg16849 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg26 sg12784 - -lemma sg16850 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by - exact rowSquare_join (by decide) sg74 sg12368 - -lemma sg16851 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg26 sg12786 - -lemma sg16852 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by - exact rowSquare_join (by decide) sg74 sg12369 - -lemma sg16853 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by - exact rowSquare_join (by decide) sg74 sg12370 - -lemma sg16854 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg27 sg12776 - -lemma sg16855 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg27 sg12777 - -lemma sg16856 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg26 sg12788 - -lemma sg16857 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg12371 - -lemma sg16858 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by - exact rowSquare_join (by decide) sg74 sg12372 - -lemma sg16859 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg27 sg12779 - -lemma sg16860 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by - exact rowSquare_join (by decide) sg74 sg12373 - -lemma sg16861 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14642 - -lemma sg16862 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg12374 - -lemma sg16863 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg26 sg12789 - -lemma sg16864 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by - exact rowSquare_join (by decide) sg74 sg12375 - -lemma sg16865 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by - exact rowSquare_join (by decide) sg74 sg12376 - -lemma sg16866 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by - exact rowSquare_join (by decide) sg75 sg12346 - -lemma sg16867 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg26 sg12790 - -lemma sg16868 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by - exact rowSquare_join (by decide) sg74 sg12377 - -lemma sg16869 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by - exact rowSquare_join (by decide) sg74 sg12378 - -lemma sg16870 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by - exact rowSquare_join (by decide) sg75 sg12348 - -lemma sg16871 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg10 sg13709 - -lemma sg16872 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg10 sg13710 - -lemma sg16873 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg10 sg13711 - -lemma sg16874 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg10 sg13712 - -lemma sg16875 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg10 sg13713 - -lemma sg16876 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg10 sg13714 - -lemma sg16877 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg10 sg13715 - -lemma sg16878 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg10 sg13716 - -lemma sg16879 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg10 sg13717 - -lemma sg16880 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg10 sg13718 - -lemma sg16881 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg10 sg13719 - -lemma sg16882 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg13720 - -lemma sg16883 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg10 sg13721 - -lemma sg16884 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by - exact rowSquare_join (by decide) sg74 sg12379 - -lemma sg16885 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg27 sg12783 - -lemma sg16886 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg12380 - -lemma sg16887 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,3] := by - exact rowSquare_join (by decide) sg74 sg12381 - -lemma sg16888 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg27 sg12786 - -lemma sg16889 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,2] := by - exact rowSquare_join (by decide) sg74 sg12382 - -lemma sg16890 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4084 - -lemma sg16891 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg10 sg13735 - -lemma sg16892 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg10 sg13736 - -lemma sg16893 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,2] := by - exact rowSquare_join (by decide) sg74 sg12383 - -lemma sg16894 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,4,1] := by - exact rowSquare_join (by decide) sg74 sg12384 - -lemma sg16895 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,5] := by - exact rowSquare_join (by decide) sg10 sg13739 - -lemma sg16896 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg12385 - -lemma sg16897 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg12386 - -lemma sg16898 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4085 - -lemma sg16899 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg12387 - -lemma sg16900 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg55 sg12443 - -lemma sg16901 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,2] := by - exact rowSquare_join (by decide) sg74 sg12388 - -lemma sg16902 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,4,1] := by - exact rowSquare_join (by decide) sg74 sg12389 - -lemma sg16903 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg27 sg12790 - -lemma sg16904 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,2] := by - exact rowSquare_join (by decide) sg74 sg12390 - -lemma sg16905 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,3,1] := by - exact rowSquare_join (by decide) sg74 sg12391 - -lemma sg16906 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,4] := by - exact rowSquare_join (by decide) sg76 sg12346 - -lemma sg16907 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg13756 - -lemma sg16908 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by - exact rowSquare_join (by decide) sg74 sg12392 - -lemma sg16909 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,3] := by - exact rowSquare_join (by decide) sg76 sg12348 - -lemma sg16910 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg6 sg14617 - -lemma sg16911 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg12 sg13654 - -lemma sg16912 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg5 sg14641 - -lemma sg16913 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg11 sg13678 - -lemma sg16914 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg11 sg13679 - -lemma sg16915 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg9 sg13765 - -lemma sg16916 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg26 sg12791 - -lemma sg16917 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg22 sg12820 - -lemma sg16918 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg74 sg12393 - -lemma sg16919 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg74 sg12394 - -lemma sg16920 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg12 sg13667 - -lemma sg16921 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg26 sg12792 - -lemma sg16922 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg26 sg12793 - -lemma sg16923 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg74 sg12395 - -lemma sg16924 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg12 sg13671 - -lemma sg16925 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg74 sg12396 - -lemma sg16926 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg9 sg13780 - -lemma sg16927 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg23 sg12819 - -lemma sg16928 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg23 sg12820 - -lemma sg16929 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg29 sg12772 - -lemma sg16930 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg74 sg12397 - -lemma sg16931 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg27 sg12791 - -lemma sg16932 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg26 sg12794 - -lemma sg16933 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg12398 - -lemma sg16934 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg74 sg12399 - -lemma sg16935 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg74 sg12400 - -lemma sg16936 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg26 sg12795 - -lemma sg16937 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg12401 - -lemma sg16938 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg74 sg12402 - -lemma sg16939 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg26 sg12796 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 + +namespace OAI + +/-! Semigroup Nodes 40. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg16540 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14835 + +lemma sg16541 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14836 + +lemma sg16542 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg14602 + +lemma sg16543 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg13627 + +lemma sg16544 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg14 sg13567 + +lemma sg16545 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg5 sg14592 + +lemma sg16546 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg14603 + +lemma sg16547 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13628 + +lemma sg16548 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13629 + +lemma sg16549 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13630 + +lemma sg16550 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg13 sg13631 + +lemma sg16551 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg39 sg12736 + +lemma sg16552 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13632 + +lemma sg16553 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg14604 + +lemma sg16554 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg14605 + +lemma sg16555 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13633 + +lemma sg16556 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by + exact rowSquare_join (by decide) sg39 sg12737 + +lemma sg16557 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg41 sg12724 + +lemma sg16558 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13634 + +lemma sg16559 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg39 sg12738 + +lemma sg16560 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by + exact rowSquare_join (by decide) sg41 sg12727 + +lemma sg16561 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13635 + +lemma sg16562 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg13636 + +lemma sg16563 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by + exact rowSquare_join (by decide) sg39 sg12739 + +lemma sg16564 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg5 sg14595 + +lemma sg16565 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg13569 + +lemma sg16566 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13637 + +lemma sg16567 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13638 + +lemma sg16568 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg13576 + +lemma sg16569 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg14 sg13577 + +lemma sg16570 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13639 + +lemma sg16571 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by + exact rowSquare_join (by decide) sg39 sg12740 + +lemma sg16572 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg40 sg12736 + +lemma sg16573 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13640 + +lemma sg16574 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13641 + +lemma sg16575 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg39 sg12741 + +lemma sg16576 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by + exact rowSquare_join (by decide) sg42 sg12727 + +lemma sg16577 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13642 + +lemma sg16578 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by + exact rowSquare_join (by decide) sg40 sg12737 + +lemma sg16579 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg39 sg12742 + +lemma sg16580 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg39 sg12743 + +lemma sg16581 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg12744 + +lemma sg16582 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by + exact rowSquare_join (by decide) sg39 sg12745 + +lemma sg16583 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by + exact rowSquare_join (by decide) sg39 sg12746 + +lemma sg16584 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13643 + +lemma sg16585 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by + exact rowSquare_join (by decide) sg39 sg12747 + +lemma sg16586 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg13585 + +lemma sg16587 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg13586 + +lemma sg16588 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg14 sg13587 + +lemma sg16589 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13644 + +lemma sg16590 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by + exact rowSquare_join (by decide) sg39 sg12748 + +lemma sg16591 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg14 sg13592 + +lemma sg16592 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13645 + +lemma sg16593 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,3] := by + exact rowSquare_join (by decide) sg40 sg12740 + +lemma sg16594 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg39 sg12749 + +lemma sg16595 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg39 sg12750 + +lemma sg16596 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg12751 + +lemma sg16597 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,2] := by + exact rowSquare_join (by decide) sg39 sg12752 + +lemma sg16598 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,4] := by + exact rowSquare_join (by decide) sg39 sg12753 + +lemma sg16599 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg13598 + +lemma sg16600 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg39 sg12754 + +lemma sg16601 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg40 sg12743 + +lemma sg16602 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg12755 + +lemma sg16603 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,2] := by + exact rowSquare_join (by decide) sg39 sg12756 + +lemma sg16604 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,4] := by + exact rowSquare_join (by decide) sg40 sg12746 + +lemma sg16605 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12757 + +lemma sg16606 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,3] := by + exact rowSquare_join (by decide) sg39 sg12758 + +lemma sg16607 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,6,1,1] := by + exact rowSquare_join (by decide) sg39 sg12759 + +lemma sg16608 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,6,6,2] := by + exact rowSquare_join (by decide) sg39 sg12760 + +lemma sg16609 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3320 sg4500 + +lemma sg16610 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg14606 + +lemma sg16611 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14607 + +lemma sg16612 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3695 sg4118 + +lemma sg16613 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg13599 + +lemma sg16614 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg13600 + +lemma sg16615 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg14 sg13601 + +lemma sg16616 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13646 + +lemma sg16617 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by + exact rowSquare_join (by decide) sg40 sg12748 + +lemma sg16618 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13647 + +lemma sg16619 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13648 + +lemma sg16620 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [9,9,5,4,4] := by + exact rowSquare_join (by decide) sg40 sg12753 + +lemma sg16621 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14837 + +lemma sg16622 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg6 sg14586 + +lemma sg16623 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14838 + +lemma sg16624 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14839 + +lemma sg16625 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg14608 + +lemma sg16626 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13649 + +lemma sg16627 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg5 sg14602 + +lemma sg16628 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,5] := by + exact rowSquare_join (by decide) sg43 sg12727 + +lemma sg16629 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,4] := by + exact rowSquare_join (by decide) sg51 sg12474 + +lemma sg16630 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,6,6,6,3] := by + exact rowSquare_join (by decide) sg39 sg12761 + +lemma sg16631 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,7,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13650 + +lemma sg16632 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,7,5,5,4] := by + exact rowSquare_join (by decide) sg52 sg12474 + +lemma sg16633 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,7,6,4,4] := by + exact rowSquare_join (by decide) sg51 sg12486 + +lemma sg16634 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,7,6,5,3] := by + exact rowSquare_join (by decide) sg39 sg12762 + +lemma sg16635 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,7,6,6,2] := by + exact rowSquare_join (by decide) sg39 sg12763 + +lemma sg16636 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,5,4,4] := by + exact rowSquare_join (by decide) sg52 sg12486 + +lemma sg16637 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,5,5,3] := by + exact rowSquare_join (by decide) sg39 sg12764 + +lemma sg16638 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,6,4,3] := by + exact rowSquare_join (by decide) sg270 sg11069 + +lemma sg16639 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,6,5,2] := by + exact rowSquare_join (by decide) sg270 sg11070 + +lemma sg16640 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,6,6,1] := by + exact rowSquare_join (by decide) sg271 sg11070 + +lemma sg16641 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,9,4,4,4] := by + exact rowSquare_join (by decide) sg42 sg12753 + +lemma sg16642 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [10,10,4,4,3] := by + exact rowSquare_join (by decide) sg13 sg13651 + +lemma sg16643 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [11,5,5,5,5] := by + exact rowSquare_join (by decide) sg44 sg12727 + +lemma sg16644 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [11,6,5,5,4] := by + exact rowSquare_join (by decide) sg53 sg12474 + +lemma sg16645 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [11,6,6,4,4] := by + exact rowSquare_join (by decide) sg270 sg11087 + +lemma sg16646 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [11,6,6,5,3] := by + exact rowSquare_join (by decide) sg270 sg11089 + +lemma sg16647 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [11,6,6,6,2] := by + exact rowSquare_join (by decide) sg271 sg11089 + +lemma sg16648 : RowSquare [6,5,3,3,3,2,1,1,1,1,1,1,1,1,1] [11,8,4,4,4] := by + exact rowSquare_join (by decide) sg111 sg11615 + +lemma sg16649 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1682 sg6504 + +lemma sg16650 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1754 sg6497 + +lemma sg16651 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2633 sg4964 + +lemma sg16652 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3691 sg4067 + +lemma sg16653 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3691 sg4068 + +lemma sg16654 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg3691 sg4070 + +lemma sg16655 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg2633 sg4967 + +lemma sg16656 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg1758 sg6498 + +lemma sg16657 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,3,3] := by + exact rowSquare_join (by decide) sg3355 sg4437 + +lemma sg16658 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,2] := by + exact rowSquare_join (by decide) sg3560 sg4303 + +lemma sg16659 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15502 + +lemma sg16660 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3,2] := by + exact rowSquare_join (by decide) sg3560 sg4304 + +lemma sg16661 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,4,1] := by + exact rowSquare_join (by decide) sg1758 sg6499 + +lemma sg16662 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3691 sg4074 + +lemma sg16663 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg4 sg14611 + +lemma sg16664 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg3352 sg4441 + +lemma sg16665 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,3,2] := by + exact rowSquare_join (by decide) sg3653 sg4157 + +lemma sg16666 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg3562 sg4303 + +lemma sg16667 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg3691 sg4075 + +lemma sg16668 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg3691 sg4076 + +lemma sg16669 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg3562 sg4304 + +lemma sg16670 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,4] := by + exact rowSquare_join (by decide) sg1688 sg6505 + +lemma sg16671 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14612 + +lemma sg16672 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3,2] := by + exact rowSquare_join (by decide) sg4 sg14613 + +lemma sg16673 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,4,1] := by + exact rowSquare_join (by decide) sg3620 sg4185 + +lemma sg16674 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg14614 + +lemma sg16675 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,2,2] := by + exact rowSquare_join (by decide) sg4 sg14615 + +lemma sg16676 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,3,1] := by + exact rowSquare_join (by decide) sg3689 sg4079 + +lemma sg16677 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by + exact rowSquare_join (by decide) sg1688 sg6506 + +lemma sg16678 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14616 + +lemma sg16679 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,2,1] := by + exact rowSquare_join (by decide) sg3723 sg4031 + +lemma sg16680 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,3] := by + exact rowSquare_join (by decide) sg3356 sg4438 + +lemma sg16681 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3571 sg4226 + +lemma sg16682 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3613 sg4188 + +lemma sg16683 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,2] := by + exact rowSquare_join (by decide) sg3654 sg4157 + +lemma sg16684 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1] := by + exact rowSquare_join (by decide) sg3565 sg4303 + +lemma sg16685 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg3691 sg4077 + +lemma sg16686 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,2,1] := by + exact rowSquare_join (by decide) sg3724 sg4031 + +lemma sg16687 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by + exact rowSquare_join (by decide) sg3690 sg4079 + +lemma sg16688 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by + exact rowSquare_join (by decide) sg3655 sg4157 + +lemma sg16689 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by + exact rowSquare_join (by decide) sg3725 sg4031 + +lemma sg16690 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by + exact rowSquare_join (by decide) sg3726 sg4031 + +lemma sg16691 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg3560 sg4305 + +lemma sg16692 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg5 sg14609 + +lemma sg16693 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg4 sg14617 + +lemma sg16694 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg9 sg13654 + +lemma sg16695 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg3560 sg4306 + +lemma sg16696 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,3,2] := by + exact rowSquare_join (by decide) sg1 sg14840 + +lemma sg16697 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg1 sg14841 + +lemma sg16698 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg1 sg14842 + +lemma sg16699 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg1 sg14843 + +lemma sg16700 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,4] := by + exact rowSquare_join (by decide) sg2167 sg5763 + +lemma sg16701 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg5 sg14610 + +lemma sg16702 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg10 sg13654 + +lemma sg16703 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg9 sg13657 + +lemma sg16704 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg9 sg13658 + +lemma sg16705 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg5 sg14614 + +lemma sg16706 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg5 sg14615 + +lemma sg16707 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg0 sg15503 + +lemma sg16708 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by + exact rowSquare_join (by decide) sg0 sg15504 + +lemma sg16709 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg0 sg15505 + +lemma sg16710 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by + exact rowSquare_join (by decide) sg0 sg15506 + +lemma sg16711 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg9 sg13661 + +lemma sg16712 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,3,2] := by + exact rowSquare_join (by decide) sg9 sg13662 + +lemma sg16713 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2,2] := by + exact rowSquare_join (by decide) sg9 sg13664 + +lemma sg16714 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,3,1] := by + exact rowSquare_join (by decide) sg9 sg13665 + +lemma sg16715 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg15507 + +lemma sg16716 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2,2] := by + exact rowSquare_join (by decide) sg9 sg13667 + +lemma sg16717 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,3,1] := by + exact rowSquare_join (by decide) sg9 sg13668 + +lemma sg16718 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg12765 + +lemma sg16719 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,2,1] := by + exact rowSquare_join (by decide) sg26 sg12766 + +lemma sg16720 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by + exact rowSquare_join (by decide) sg0 sg15508 + +lemma sg16721 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by + exact rowSquare_join (by decide) sg9 sg13671 + +lemma sg16722 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by + exact rowSquare_join (by decide) sg74 sg12341 + +lemma sg16723 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg15509 + +lemma sg16724 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,2] := by + exact rowSquare_join (by decide) sg3560 sg4311 + +lemma sg16725 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg12767 + +lemma sg16726 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,2,1] := by + exact rowSquare_join (by decide) sg26 sg12768 + +lemma sg16727 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by + exact rowSquare_join (by decide) sg0 sg15510 + +lemma sg16728 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by + exact rowSquare_join (by decide) sg26 sg12769 + +lemma sg16729 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by + exact rowSquare_join (by decide) sg74 sg12342 + +lemma sg16730 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by + exact rowSquare_join (by decide) sg74 sg12343 + +lemma sg16731 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg0 sg15511 + +lemma sg16732 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg3696 sg4076 + +lemma sg16733 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg10 sg13657 + +lemma sg16734 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg10 sg13658 + +lemma sg16735 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg10 sg13662 + +lemma sg16736 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg10 sg13664 + +lemma sg16737 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg10 sg13665 + +lemma sg16738 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by + exact rowSquare_join (by decide) sg2746 sg4896 + +lemma sg16739 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg10 sg13667 + +lemma sg16740 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg10 sg13668 + +lemma sg16741 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg10 sg13670 + +lemma sg16742 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by + exact rowSquare_join (by decide) sg3725 sg4032 + +lemma sg16743 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg10 sg13671 + +lemma sg16744 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by + exact rowSquare_join (by decide) sg74 sg12344 + +lemma sg16745 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg14619 + +lemma sg16746 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg14620 + +lemma sg16747 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg14621 + +lemma sg16748 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg27 sg12766 + +lemma sg16749 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,3] := by + exact rowSquare_join (by decide) sg3620 sg4187 + +lemma sg16750 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4082 + +lemma sg16751 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14622 + +lemma sg16752 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,2,1] := by + exact rowSquare_join (by decide) sg27 sg12768 + +lemma sg16753 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by + exact rowSquare_join (by decide) sg4 sg14623 + +lemma sg16754 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg27 sg12769 + +lemma sg16755 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by + exact rowSquare_join (by decide) sg74 sg12345 + +lemma sg16756 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by + exact rowSquare_join (by decide) sg74 sg12346 + +lemma sg16757 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4083 + +lemma sg16758 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg3687 sg4083 + +lemma sg16759 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg3617 sg4188 + +lemma sg16760 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg3724 sg4033 + +lemma sg16761 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by + exact rowSquare_join (by decide) sg74 sg12347 + +lemma sg16762 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by + exact rowSquare_join (by decide) sg74 sg12348 + +lemma sg16763 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by + exact rowSquare_join (by decide) sg3726 sg4033 + +lemma sg16764 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3721 sg4037 + +lemma sg16765 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14624 + +lemma sg16766 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3614 sg4189 + +lemma sg16767 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg14625 + +lemma sg16768 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3721 sg4038 + +lemma sg16769 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg14626 + +lemma sg16770 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg14627 + +lemma sg16771 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg14628 + +lemma sg16772 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3721 sg4039 + +lemma sg16773 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg14629 + +lemma sg16774 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14630 + +lemma sg16775 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14631 + +lemma sg16776 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg14632 + +lemma sg16777 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by + exact rowSquare_join (by decide) sg4 sg14633 + +lemma sg16778 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by + exact rowSquare_join (by decide) sg4 sg14634 + +lemma sg16779 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by + exact rowSquare_join (by decide) sg74 sg12349 + +lemma sg16780 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3688 sg4083 + +lemma sg16781 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14635 + +lemma sg16782 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg14636 + +lemma sg16783 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg14637 + +lemma sg16784 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by + exact rowSquare_join (by decide) sg74 sg12350 + +lemma sg16785 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by + exact rowSquare_join (by decide) sg74 sg12351 + +lemma sg16786 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg4 sg14638 + +lemma sg16787 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg3575 sg4226 + +lemma sg16788 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg14639 + +lemma sg16789 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by + exact rowSquare_join (by decide) sg74 sg12352 + +lemma sg16790 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by + exact rowSquare_join (by decide) sg74 sg12353 + +lemma sg16791 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by + exact rowSquare_join (by decide) sg4 sg14640 + +lemma sg16792 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by + exact rowSquare_join (by decide) sg3565 sg4311 + +lemma sg16793 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by + exact rowSquare_join (by decide) sg74 sg12354 + +lemma sg16794 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by + exact rowSquare_join (by decide) sg3691 sg4083 + +lemma sg16795 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg6 sg14609 + +lemma sg16796 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg5 sg14617 + +lemma sg16797 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg11 sg13654 + +lemma sg16798 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg14641 + +lemma sg16799 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg9 sg13678 + +lemma sg16800 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg9 sg13679 + +lemma sg16801 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg6 sg14614 + +lemma sg16802 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg6 sg14615 + +lemma sg16803 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg26 sg12772 + +lemma sg16804 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg1 sg14844 + +lemma sg16805 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg3 sg14648 + +lemma sg16806 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg74 sg12355 + +lemma sg16807 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg5 sg14618 + +lemma sg16808 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg10 sg13678 + +lemma sg16809 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg10 sg13679 + +lemma sg16810 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg9 sg13684 + +lemma sg16811 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg9 sg13685 + +lemma sg16812 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg9 sg13687 + +lemma sg16813 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg27 sg12772 + +lemma sg16814 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg9 sg13689 + +lemma sg16815 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg11 sg13667 + +lemma sg16816 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg26 sg12773 + +lemma sg16817 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg26 sg12774 + +lemma sg16818 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by + exact rowSquare_join (by decide) sg74 sg12356 + +lemma sg16819 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg11 sg13671 + +lemma sg16820 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg74 sg12357 + +lemma sg16821 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg22 sg12817 + +lemma sg16822 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg26 sg12776 + +lemma sg16823 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,3,1] := by + exact rowSquare_join (by decide) sg26 sg12777 + +lemma sg16824 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg74 sg12358 + +lemma sg16825 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by + exact rowSquare_join (by decide) sg74 sg12359 + +lemma sg16826 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg26 sg12778 + +lemma sg16827 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg12360 + +lemma sg16828 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by + exact rowSquare_join (by decide) sg74 sg12361 + +lemma sg16829 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg26 sg12779 + +lemma sg16830 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by + exact rowSquare_join (by decide) sg74 sg12362 + +lemma sg16831 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by + exact rowSquare_join (by decide) sg74 sg12363 + +lemma sg16832 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14845 + +lemma sg16833 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg26 sg12780 + +lemma sg16834 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg26 sg12781 + +lemma sg16835 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by + exact rowSquare_join (by decide) sg74 sg12364 + +lemma sg16836 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by + exact rowSquare_join (by decide) sg74 sg12365 + +lemma sg16837 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by + exact rowSquare_join (by decide) sg75 sg12343 + +lemma sg16838 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg9 sg13711 + +lemma sg16839 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg10 sg13685 + +lemma sg16840 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg10 sg13687 + +lemma sg16841 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg10 sg13688 + +lemma sg16842 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by + exact rowSquare_join (by decide) sg10 sg13689 + +lemma sg16843 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg23 sg12817 + +lemma sg16844 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg26 sg12782 + +lemma sg16845 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg26 sg12783 + +lemma sg16846 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg74 sg12366 + +lemma sg16847 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by + exact rowSquare_join (by decide) sg74 sg12367 + +lemma sg16848 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg23 sg12818 + +lemma sg16849 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg26 sg12784 + +lemma sg16850 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by + exact rowSquare_join (by decide) sg74 sg12368 + +lemma sg16851 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg26 sg12786 + +lemma sg16852 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by + exact rowSquare_join (by decide) sg74 sg12369 + +lemma sg16853 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by + exact rowSquare_join (by decide) sg74 sg12370 + +lemma sg16854 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg27 sg12776 + +lemma sg16855 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg27 sg12777 + +lemma sg16856 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg26 sg12788 + +lemma sg16857 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg12371 + +lemma sg16858 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by + exact rowSquare_join (by decide) sg74 sg12372 + +lemma sg16859 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg27 sg12779 + +lemma sg16860 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by + exact rowSquare_join (by decide) sg74 sg12373 + +lemma sg16861 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14642 + +lemma sg16862 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg12374 + +lemma sg16863 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg26 sg12789 + +lemma sg16864 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by + exact rowSquare_join (by decide) sg74 sg12375 + +lemma sg16865 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by + exact rowSquare_join (by decide) sg74 sg12376 + +lemma sg16866 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by + exact rowSquare_join (by decide) sg75 sg12346 + +lemma sg16867 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg26 sg12790 + +lemma sg16868 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by + exact rowSquare_join (by decide) sg74 sg12377 + +lemma sg16869 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by + exact rowSquare_join (by decide) sg74 sg12378 + +lemma sg16870 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by + exact rowSquare_join (by decide) sg75 sg12348 + +lemma sg16871 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg10 sg13709 + +lemma sg16872 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg10 sg13710 + +lemma sg16873 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg10 sg13711 + +lemma sg16874 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg10 sg13712 + +lemma sg16875 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg10 sg13713 + +lemma sg16876 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg10 sg13714 + +lemma sg16877 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg10 sg13715 + +lemma sg16878 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg10 sg13716 + +lemma sg16879 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg10 sg13717 + +lemma sg16880 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg10 sg13718 + +lemma sg16881 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg10 sg13719 + +lemma sg16882 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg13720 + +lemma sg16883 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg10 sg13721 + +lemma sg16884 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by + exact rowSquare_join (by decide) sg74 sg12379 + +lemma sg16885 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg27 sg12783 + +lemma sg16886 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg12380 + +lemma sg16887 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,3] := by + exact rowSquare_join (by decide) sg74 sg12381 + +lemma sg16888 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg27 sg12786 + +lemma sg16889 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,2] := by + exact rowSquare_join (by decide) sg74 sg12382 + +lemma sg16890 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4084 + +lemma sg16891 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg10 sg13735 + +lemma sg16892 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg10 sg13736 + +lemma sg16893 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,2] := by + exact rowSquare_join (by decide) sg74 sg12383 + +lemma sg16894 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,4,1] := by + exact rowSquare_join (by decide) sg74 sg12384 + +lemma sg16895 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,5] := by + exact rowSquare_join (by decide) sg10 sg13739 + +lemma sg16896 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg12385 + +lemma sg16897 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg12386 + +lemma sg16898 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4085 + +lemma sg16899 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg12387 + +lemma sg16900 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg55 sg12443 + +lemma sg16901 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,2] := by + exact rowSquare_join (by decide) sg74 sg12388 + +lemma sg16902 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,4,1] := by + exact rowSquare_join (by decide) sg74 sg12389 + +lemma sg16903 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg27 sg12790 + +lemma sg16904 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,2] := by + exact rowSquare_join (by decide) sg74 sg12390 + +lemma sg16905 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,3,1] := by + exact rowSquare_join (by decide) sg74 sg12391 + +lemma sg16906 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,4] := by + exact rowSquare_join (by decide) sg76 sg12346 + +lemma sg16907 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg13756 + +lemma sg16908 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by + exact rowSquare_join (by decide) sg74 sg12392 + +lemma sg16909 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,3] := by + exact rowSquare_join (by decide) sg76 sg12348 + +lemma sg16910 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg6 sg14617 + +lemma sg16911 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg12 sg13654 + +lemma sg16912 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg5 sg14641 + +lemma sg16913 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg11 sg13678 + +lemma sg16914 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg11 sg13679 + +lemma sg16915 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg9 sg13765 + +lemma sg16916 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg26 sg12791 + +lemma sg16917 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg22 sg12820 + +lemma sg16918 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg74 sg12393 + +lemma sg16919 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg74 sg12394 + +lemma sg16920 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg12 sg13667 + +lemma sg16921 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg26 sg12792 + +lemma sg16922 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg26 sg12793 + +lemma sg16923 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg74 sg12395 + +lemma sg16924 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg12 sg13671 + +lemma sg16925 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg74 sg12396 + +lemma sg16926 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg9 sg13780 + +lemma sg16927 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg23 sg12819 + +lemma sg16928 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg23 sg12820 + +lemma sg16929 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg29 sg12772 + +lemma sg16930 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg74 sg12397 + +lemma sg16931 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg27 sg12791 + +lemma sg16932 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg26 sg12794 + +lemma sg16933 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg12398 + +lemma sg16934 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg74 sg12399 + +lemma sg16935 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg74 sg12400 + +lemma sg16936 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg26 sg12795 + +lemma sg16937 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg12401 + +lemma sg16938 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg74 sg12402 + +lemma sg16939 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg26 sg12796 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes41.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes41.lean index de62bb39b6669f9ddc68b2959ffae2d601e1270d..4d764ff75d0d3cad923a87fccdd9035755332c5d 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes41.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes41.lean @@ -1,1223 +1,1223 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes29 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes30 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes35 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes33 - -namespace OAI - -/-! Semigroup Nodes 41. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg16940 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by - exact rowSquare_join (by decide) sg74 sg12403 - -lemma sg16941 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by - exact rowSquare_join (by decide) sg74 sg12404 - -lemma sg16942 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg12405 - -lemma sg16943 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg12406 - -lemma sg16944 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by - exact rowSquare_join (by decide) sg74 sg12407 - -lemma sg16945 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg75 sg12358 - -lemma sg16946 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by - exact rowSquare_join (by decide) sg142 sg11555 - -lemma sg16947 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg13812 - -lemma sg16948 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg12408 - -lemma sg16949 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg75 sg12360 - -lemma sg16950 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by - exact rowSquare_join (by decide) sg142 sg11556 - -lemma sg16951 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by - exact rowSquare_join (by decide) sg142 sg11557 - -lemma sg16952 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by - exact rowSquare_join (by decide) sg75 sg12363 - -lemma sg16953 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg56 sg12442 - -lemma sg16954 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by - exact rowSquare_join (by decide) sg142 sg11558 - -lemma sg16955 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by - exact rowSquare_join (by decide) sg142 sg11559 - -lemma sg16956 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by - exact rowSquare_join (by decide) sg75 sg12365 - -lemma sg16957 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg10 sg13780 - -lemma sg16958 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg22 sg12821 - -lemma sg16959 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg26 sg12797 - -lemma sg16960 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg26 sg12798 - -lemma sg16961 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg74 sg12409 - -lemma sg16962 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by - exact rowSquare_join (by decide) sg74 sg12410 - -lemma sg16963 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg27 sg12794 - -lemma sg16964 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg12411 - -lemma sg16965 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg26 sg12799 - -lemma sg16966 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg12412 - -lemma sg16967 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by - exact rowSquare_join (by decide) sg74 sg12413 - -lemma sg16968 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg75 sg12366 - -lemma sg16969 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by - exact rowSquare_join (by decide) sg142 sg11560 - -lemma sg16970 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg13812 - -lemma sg16971 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg12414 - -lemma sg16972 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg56 sg12443 - -lemma sg16973 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by - exact rowSquare_join (by decide) sg142 sg11561 - -lemma sg16974 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by - exact rowSquare_join (by decide) sg142 sg11562 - -lemma sg16975 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by - exact rowSquare_join (by decide) sg75 sg12370 - -lemma sg16976 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg12415 - -lemma sg16977 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg12416 - -lemma sg16978 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg13849 - -lemma sg16979 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg12417 - -lemma sg16980 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg75 sg12371 - -lemma sg16981 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by - exact rowSquare_join (by decide) sg142 sg11563 - -lemma sg16982 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by - exact rowSquare_join (by decide) sg142 sg11564 - -lemma sg16983 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg75 sg12374 - -lemma sg16984 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by - exact rowSquare_join (by decide) sg142 sg11565 - -lemma sg16985 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by - exact rowSquare_join (by decide) sg142 sg11566 - -lemma sg16986 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by - exact rowSquare_join (by decide) sg143 sg11557 - -lemma sg16987 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg56 sg12444 - -lemma sg16988 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by - exact rowSquare_join (by decide) sg142 sg11567 - -lemma sg16989 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by - exact rowSquare_join (by decide) sg143 sg11559 - -lemma sg16990 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg23 sg12821 - -lemma sg16991 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg12418 - -lemma sg16992 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg12419 - -lemma sg16993 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by - exact rowSquare_join (by decide) sg74 sg12420 - -lemma sg16994 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg29 sg12786 - -lemma sg16995 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,2] := by - exact rowSquare_join (by decide) sg142 sg11569 - -lemma sg16996 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg12421 - -lemma sg16997 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg12422 - -lemma sg16998 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg13849 - -lemma sg16999 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg12423 - -lemma sg17000 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg75 sg12380 - -lemma sg17001 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,2] := by - exact rowSquare_join (by decide) sg142 sg11570 - -lemma sg17002 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,4,1] := by - exact rowSquare_join (by decide) sg142 sg11571 - -lemma sg17003 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg26 sg12800 - -lemma sg17004 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,2] := by - exact rowSquare_join (by decide) sg142 sg11572 - -lemma sg17005 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,3,1] := by - exact rowSquare_join (by decide) sg142 sg11573 - -lemma sg17006 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,4] := by - exact rowSquare_join (by decide) sg143 sg11562 - -lemma sg17007 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg13860 - -lemma sg17008 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg123 sg11595 - -lemma sg17009 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg75 sg12385 - -lemma sg17010 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,2] := by - exact rowSquare_join (by decide) sg142 sg11574 - -lemma sg17011 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg123 sg11596 - -lemma sg17012 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,2] := by - exact rowSquare_join (by decide) sg142 sg11575 - -lemma sg17013 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,3,1] := by - exact rowSquare_join (by decide) sg142 sg11576 - -lemma sg17014 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,4] := by - exact rowSquare_join (by decide) sg143 sg11564 - -lemma sg17015 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg123 sg11597 - -lemma sg17016 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,2,1] := by - exact rowSquare_join (by decide) sg142 sg11577 - -lemma sg17017 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,3] := by - exact rowSquare_join (by decide) sg143 sg11566 - -lemma sg17018 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,6,1,1] := by - exact rowSquare_join (by decide) sg142 sg11578 - -lemma sg17019 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,6,2] := by - exact rowSquare_join (by decide) sg143 sg11567 - -lemma sg17020 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg10 sg13871 - -lemma sg17021 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg10 sg13872 - -lemma sg17022 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg12424 - -lemma sg17023 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by - exact rowSquare_join (by decide) sg74 sg12425 - -lemma sg17024 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3686 sg4102 - -lemma sg17025 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg12426 - -lemma sg17026 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg10 sg13881 - -lemma sg17027 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,2] := by - exact rowSquare_join (by decide) sg74 sg12427 - -lemma sg17028 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,4,1] := by - exact rowSquare_join (by decide) sg143 sg11569 - -lemma sg17029 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3 sg14668 - -lemma sg17030 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3 sg14669 - -lemma sg17031 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg5 sg14643 - -lemma sg17032 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3 sg14670 - -lemma sg17033 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg9 sg13899 - -lemma sg17034 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8 sg14082 - -lemma sg17035 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8 sg14083 - -lemma sg17036 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg6 sg14641 - -lemma sg17037 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8 sg14084 - -lemma sg17038 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg12 sg13678 - -lemma sg17039 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg12 sg13679 - -lemma sg17040 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3 sg14671 - -lemma sg17041 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg10 sg13899 - -lemma sg17042 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3 sg14672 - -lemma sg17043 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg9 sg13902 - -lemma sg17044 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg13904 - -lemma sg17045 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg9 sg13906 - -lemma sg17046 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg11 sg13766 - -lemma sg17047 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg11 sg13768 - -lemma sg17048 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg26 sg12801 - -lemma sg17049 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg11 sg13772 - -lemma sg17050 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg24 sg12820 - -lemma sg17051 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg74 sg12428 - -lemma sg17052 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg74 sg12429 - -lemma sg17053 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg26 sg12802 - -lemma sg17054 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg12430 - -lemma sg17055 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg74 sg12431 - -lemma sg17056 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg12432 - -lemma sg17057 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg12803 - -lemma sg17058 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg26 sg12804 - -lemma sg17059 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg12433 - -lemma sg17060 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg74 sg12434 - -lemma sg17061 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg142 sg11579 - -lemma sg17062 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg12805 - -lemma sg17063 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg26 sg12806 - -lemma sg17064 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg12435 - -lemma sg17065 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg142 sg11580 - -lemma sg17066 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg56 sg12445 - -lemma sg17067 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg142 sg11581 - -lemma sg17068 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg142 sg11582 - -lemma sg17069 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3 sg14674 - -lemma sg17070 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg10 sg13902 - -lemma sg17071 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg13904 - -lemma sg17072 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg10 sg13906 - -lemma sg17073 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg26 sg12807 - -lemma sg17074 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg12436 - -lemma sg17075 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg27 sg12801 - -lemma sg17076 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg12437 - -lemma sg17077 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg12808 - -lemma sg17078 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg26 sg12809 - -lemma sg17079 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg12438 - -lemma sg17080 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg27 sg12802 - -lemma sg17081 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg12439 - -lemma sg17082 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg27 sg12803 - -lemma sg17083 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg27 sg12804 - -lemma sg17084 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg12810 - -lemma sg17085 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg26 sg12811 - -lemma sg17086 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg75 sg12399 - -lemma sg17087 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg12812 - -lemma sg17088 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg75 sg12401 - -lemma sg17089 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,5] := by - exact rowSquare_join (by decide) sg143 sg11582 - -lemma sg17090 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg12440 - -lemma sg17091 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg12813 - -lemma sg17092 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg56 sg12446 - -lemma sg17093 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg12814 - -lemma sg17094 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg123 sg11599 - -lemma sg17095 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg123 sg11600 - -lemma sg17096 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,4] := by - exact rowSquare_join (by decide) sg145 sg11557 - -lemma sg17097 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg56 sg12447 - -lemma sg17098 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,6,3] := by - exact rowSquare_join (by decide) sg145 sg11559 - -lemma sg17099 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg27 sg12809 - -lemma sg17100 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg26 sg12815 - -lemma sg17101 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg75 sg12409 - -lemma sg17102 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg29 sg12797 - -lemma sg17103 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg56 sg12448 - -lemma sg17104 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1461 sg7812 - -lemma sg17105 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1075 sg8780 - -lemma sg17106 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1464 sg7812 - -lemma sg17107 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1076 sg8780 - -lemma sg17108 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1461 sg7813 - -lemma sg17109 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1077 sg8780 - -lemma sg17110 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1468 sg7812 - -lemma sg17111 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1078 sg8780 - -lemma sg17112 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1469 sg7812 - -lemma sg17113 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1464 sg7815 - -lemma sg17114 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1470 sg7812 - -lemma sg17115 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1079 sg8780 - -lemma sg17116 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1471 sg7812 - -lemma sg17117 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1465 sg7813 - -lemma sg17118 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1080 sg8780 - -lemma sg17119 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1472 sg7812 - -lemma sg17120 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1467 sg7813 - -lemma sg17121 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1081 sg8780 - -lemma sg17122 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1082 sg8780 - -lemma sg17123 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1468 sg7813 - -lemma sg17124 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1473 sg7812 - -lemma sg17125 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1468 sg7814 - -lemma sg17126 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1078 sg8781 - -lemma sg17127 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1468 sg7815 - -lemma sg17128 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1474 sg7812 - -lemma sg17129 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1083 sg8780 - -lemma sg17130 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1475 sg7812 - -lemma sg17131 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1470 sg7813 - -lemma sg17132 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1084 sg8780 - -lemma sg17133 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1471 sg7813 - -lemma sg17134 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1085 sg8780 - -lemma sg17135 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1472 sg7813 - -lemma sg17136 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1086 sg8780 - -lemma sg17137 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1476 sg7812 - -lemma sg17138 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1468 sg7823 - -lemma sg17139 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1087 sg8780 - -lemma sg17140 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1477 sg7812 - -lemma sg17141 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1474 sg7813 - -lemma sg17142 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1088 sg8780 - -lemma sg17143 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1475 sg7813 - -lemma sg17144 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1089 sg8780 - -lemma sg17145 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [10,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1090 sg8780 - -lemma sg17146 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1091 sg8780 - -lemma sg17147 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1754 sg6492 - -lemma sg17148 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2626 sg4947 - -lemma sg17149 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1754 sg6494 - -lemma sg17150 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2626 sg4949 - -lemma sg17151 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3325 sg4463 - -lemma sg17152 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg2632 sg4945 - -lemma sg17153 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2630 sg4949 - -lemma sg17154 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg2632 sg4947 - -lemma sg17155 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg2633 sg4947 - -lemma sg17156 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3353 sg4434 - -lemma sg17157 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg2631 sg4949 - -lemma sg17158 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg2633 sg4948 - -lemma sg17159 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg2632 sg4949 - -lemma sg17160 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg2633 sg4949 - -lemma sg17161 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2640 sg4942 - -lemma sg17162 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg3402 sg4376 - -lemma sg17163 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg3402 sg4377 - -lemma sg17164 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg3403 sg4377 - -lemma sg17165 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3401 sg4378 - -lemma sg17166 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg2632 sg4951 - -lemma sg17167 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg3325 sg4464 - -lemma sg17168 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13652 - -lemma sg17169 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13653 - -lemma sg17170 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg3402 sg4378 - -lemma sg17171 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,2] := by - exact rowSquare_join (by decide) sg13 sg13654 - -lemma sg17172 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3404 sg4374 - -lemma sg17173 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg3552 sg4304 - -lemma sg17174 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg2635 sg4948 - -lemma sg17175 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg3402 sg4379 - -lemma sg17176 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3,2] := by - exact rowSquare_join (by decide) sg3403 sg4379 - -lemma sg17177 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,4,1] := by - exact rowSquare_join (by decide) sg2636 sg4949 - -lemma sg17178 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2640 sg4943 - -lemma sg17179 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2632 sg4954 - -lemma sg17180 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg2633 sg4954 - -lemma sg17181 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg2632 sg4956 - -lemma sg17182 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg2633 sg4956 - -lemma sg17183 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg2633 sg4957 - -lemma sg17184 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13656 - -lemma sg17185 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg13658 - -lemma sg17186 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg3353 sg4435 - -lemma sg17187 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg3553 sg4304 - -lemma sg17188 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg2633 sg4958 - -lemma sg17189 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg2639 sg4949 - -lemma sg17190 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,4] := by - exact rowSquare_join (by decide) sg2640 sg4949 - -lemma sg17191 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg13661 - -lemma sg17192 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3323 sg4468 - -lemma sg17193 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4468 - -lemma sg17194 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2632 sg4960 - -lemma sg17195 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3,2] := by - exact rowSquare_join (by decide) sg3554 sg4302 - -lemma sg17196 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg13662 - -lemma sg17197 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2631 sg4962 - -lemma sg17198 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13663 - -lemma sg17199 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg13664 - -lemma sg17200 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg3353 sg4436 - -lemma sg17201 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,2,1] := by - exact rowSquare_join (by decide) sg3554 sg4304 - -lemma sg17202 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,3] := by - exact rowSquare_join (by decide) sg2641 sg4949 - -lemma sg17203 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1675 sg6518 - -lemma sg17204 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg1757 sg6495 - -lemma sg17205 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13666 - -lemma sg17206 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13667 - -lemma sg17207 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13668 - -lemma sg17208 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13669 - -lemma sg17209 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg13670 - -lemma sg17210 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by - exact rowSquare_join (by decide) sg3555 sg4303 - -lemma sg17211 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg13671 - -lemma sg17212 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by - exact rowSquare_join (by decide) sg3555 sg4304 - -lemma sg17213 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by - exact rowSquare_join (by decide) sg3556 sg4304 - -lemma sg17214 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2365 sg5734 - -lemma sg17215 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg2272 sg5751 - -lemma sg17216 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg2273 sg5751 - -lemma sg17217 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg2644 sg4942 - -lemma sg17218 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg3402 sg4380 - -lemma sg17219 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg3402 sg4381 - -lemma sg17220 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg3403 sg4381 - -lemma sg17221 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14865 - -lemma sg17222 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg3402 sg4382 - -lemma sg17223 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg3403 sg4382 - -lemma sg17224 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg3325 sg4469 - -lemma sg17225 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13672 - -lemma sg17226 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13673 - -lemma sg17227 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg2635 sg4950 - -lemma sg17228 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg3325 sg4470 - -lemma sg17229 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg3403 sg4383 - -lemma sg17230 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg3402 sg4384 - -lemma sg17231 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg3403 sg4384 - -lemma sg17232 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13674 - -lemma sg17233 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13675 - -lemma sg17234 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg3403 sg4385 - -lemma sg17235 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13676 - -lemma sg17236 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13677 - -lemma sg17237 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg13678 - -lemma sg17238 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg13 sg13679 - -lemma sg17239 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg3402 sg4386 - -lemma sg17240 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg3403 sg4386 - -lemma sg17241 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg3405 sg4379 - -lemma sg17242 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,4] := by - exact rowSquare_join (by decide) sg2644 sg4949 - -lemma sg17243 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg3402 sg4388 - -lemma sg17244 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg14 sg13654 - -lemma sg17245 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg3406 sg4377 - -lemma sg17246 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by - exact rowSquare_join (by decide) sg13 sg13689 - -lemma sg17247 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg3553 sg4307 - -lemma sg17248 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg3557 sg4304 - -lemma sg17249 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by - exact rowSquare_join (by decide) sg3406 sg4379 - -lemma sg17250 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3582 sg4190 - -lemma sg17251 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg3325 sg4473 - -lemma sg17252 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg3403 sg4389 - -lemma sg17253 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13690 - -lemma sg17254 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13691 - -lemma sg17255 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13692 - -lemma sg17256 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg13693 - -lemma sg17257 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg3402 sg4390 - -lemma sg17258 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2,2] := by - exact rowSquare_join (by decide) sg3403 sg4390 - -lemma sg17259 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,3,1] := by - exact rowSquare_join (by decide) sg3576 sg4193 - -lemma sg17260 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13694 - -lemma sg17261 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13695 - -lemma sg17262 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13696 - -lemma sg17263 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13697 - -lemma sg17264 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13698 - -lemma sg17265 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg13699 - -lemma sg17266 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg13700 - -lemma sg17267 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by - exact rowSquare_join (by decide) sg3576 sg4194 - -lemma sg17268 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by - exact rowSquare_join (by decide) sg3675 sg4111 - -lemma sg17269 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3552 sg4311 - -lemma sg17270 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13701 - -lemma sg17271 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13702 - -lemma sg17272 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13703 - -lemma sg17273 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13704 - -lemma sg17274 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by - exact rowSquare_join (by decide) sg13 sg13705 - -lemma sg17275 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg13706 - -lemma sg17276 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by - exact rowSquare_join (by decide) sg13 sg13707 - -lemma sg17277 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by - exact rowSquare_join (by decide) sg13 sg13708 - -lemma sg17278 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg3556 sg4307 - -lemma sg17279 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg13711 - -lemma sg17280 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg14 sg13656 - -lemma sg17281 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg14 sg13657 - -lemma sg17282 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg14 sg13658 - -lemma sg17283 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3404 sg4387 - -lemma sg17284 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by - exact rowSquare_join (by decide) sg2640 sg4956 - -lemma sg17285 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2642 sg4953 - -lemma sg17286 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3573 sg4196 - -lemma sg17287 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13717 - -lemma sg17288 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13718 - -lemma sg17289 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13719 - -lemma sg17290 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13720 - -lemma sg17291 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg13721 - -lemma sg17292 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg13722 - -lemma sg17293 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg14 sg13671 - -lemma sg17294 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by - exact rowSquare_join (by decide) sg3679 sg4111 - -lemma sg17295 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4474 - -lemma sg17296 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg3329 sg4467 - -lemma sg17297 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4475 - -lemma sg17298 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3573 sg4199 - -lemma sg17299 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3553 sg4310 - -lemma sg17300 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg3329 sg4468 - -lemma sg17301 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,3] := by - exact rowSquare_join (by decide) sg3332 sg4466 - -lemma sg17302 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3573 sg4200 - -lemma sg17303 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13727 - -lemma sg17304 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13728 - -lemma sg17305 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13729 - -lemma sg17306 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13730 - -lemma sg17307 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by - exact rowSquare_join (by decide) sg13 sg13731 - -lemma sg17308 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg13732 - -lemma sg17309 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by - exact rowSquare_join (by decide) sg13 sg13733 - -lemma sg17310 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by - exact rowSquare_join (by decide) sg3556 sg4309 - -lemma sg17311 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1675 sg6519 - -lemma sg17312 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13734 - -lemma sg17313 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13735 - -lemma sg17314 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13736 - -lemma sg17315 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by - exact rowSquare_join (by decide) sg13 sg13737 - -lemma sg17316 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by - exact rowSquare_join (by decide) sg13 sg13738 - -lemma sg17317 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by - exact rowSquare_join (by decide) sg13 sg13739 - -lemma sg17318 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3354 sg4434 - -lemma sg17319 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3574 sg4197 - -lemma sg17320 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2889 sg4880 - -lemma sg17321 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3571 sg4212 - -lemma sg17322 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3574 sg4198 - -lemma sg17323 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13740 - -lemma sg17324 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3574 sg4199 - -lemma sg17325 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3593 sg4190 - -lemma sg17326 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,2] := by - exact rowSquare_join (by decide) sg3576 sg4197 - -lemma sg17327 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,3,1] := by - exact rowSquare_join (by decide) sg3332 sg4467 - -lemma sg17328 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3574 sg4200 - -lemma sg17329 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13741 - -lemma sg17330 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13742 - -lemma sg17331 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13743 - -lemma sg17332 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13744 - -lemma sg17333 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg13745 - -lemma sg17334 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by - exact rowSquare_join (by decide) sg3576 sg4199 - -lemma sg17335 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by - exact rowSquare_join (by decide) sg3332 sg4468 - -lemma sg17336 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1756 sg6496 - -lemma sg17337 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13746 - -lemma sg17338 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13747 - -lemma sg17339 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13748 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes29 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes30 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes35 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes33 + +namespace OAI + +/-! Semigroup Nodes 41. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg16940 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by + exact rowSquare_join (by decide) sg74 sg12403 + +lemma sg16941 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by + exact rowSquare_join (by decide) sg74 sg12404 + +lemma sg16942 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg12405 + +lemma sg16943 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg12406 + +lemma sg16944 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by + exact rowSquare_join (by decide) sg74 sg12407 + +lemma sg16945 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg75 sg12358 + +lemma sg16946 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by + exact rowSquare_join (by decide) sg142 sg11555 + +lemma sg16947 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg13812 + +lemma sg16948 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg12408 + +lemma sg16949 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg75 sg12360 + +lemma sg16950 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by + exact rowSquare_join (by decide) sg142 sg11556 + +lemma sg16951 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by + exact rowSquare_join (by decide) sg142 sg11557 + +lemma sg16952 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by + exact rowSquare_join (by decide) sg75 sg12363 + +lemma sg16953 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg56 sg12442 + +lemma sg16954 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by + exact rowSquare_join (by decide) sg142 sg11558 + +lemma sg16955 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by + exact rowSquare_join (by decide) sg142 sg11559 + +lemma sg16956 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by + exact rowSquare_join (by decide) sg75 sg12365 + +lemma sg16957 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg10 sg13780 + +lemma sg16958 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg22 sg12821 + +lemma sg16959 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg26 sg12797 + +lemma sg16960 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg26 sg12798 + +lemma sg16961 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg74 sg12409 + +lemma sg16962 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by + exact rowSquare_join (by decide) sg74 sg12410 + +lemma sg16963 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg27 sg12794 + +lemma sg16964 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg12411 + +lemma sg16965 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg26 sg12799 + +lemma sg16966 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg12412 + +lemma sg16967 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by + exact rowSquare_join (by decide) sg74 sg12413 + +lemma sg16968 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg75 sg12366 + +lemma sg16969 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by + exact rowSquare_join (by decide) sg142 sg11560 + +lemma sg16970 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg13812 + +lemma sg16971 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg12414 + +lemma sg16972 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg56 sg12443 + +lemma sg16973 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by + exact rowSquare_join (by decide) sg142 sg11561 + +lemma sg16974 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by + exact rowSquare_join (by decide) sg142 sg11562 + +lemma sg16975 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by + exact rowSquare_join (by decide) sg75 sg12370 + +lemma sg16976 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg12415 + +lemma sg16977 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg12416 + +lemma sg16978 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg13849 + +lemma sg16979 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg12417 + +lemma sg16980 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg75 sg12371 + +lemma sg16981 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by + exact rowSquare_join (by decide) sg142 sg11563 + +lemma sg16982 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by + exact rowSquare_join (by decide) sg142 sg11564 + +lemma sg16983 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg75 sg12374 + +lemma sg16984 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by + exact rowSquare_join (by decide) sg142 sg11565 + +lemma sg16985 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by + exact rowSquare_join (by decide) sg142 sg11566 + +lemma sg16986 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by + exact rowSquare_join (by decide) sg143 sg11557 + +lemma sg16987 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg56 sg12444 + +lemma sg16988 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by + exact rowSquare_join (by decide) sg142 sg11567 + +lemma sg16989 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by + exact rowSquare_join (by decide) sg143 sg11559 + +lemma sg16990 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg23 sg12821 + +lemma sg16991 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg12418 + +lemma sg16992 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg12419 + +lemma sg16993 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by + exact rowSquare_join (by decide) sg74 sg12420 + +lemma sg16994 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg29 sg12786 + +lemma sg16995 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,2] := by + exact rowSquare_join (by decide) sg142 sg11569 + +lemma sg16996 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg12421 + +lemma sg16997 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg12422 + +lemma sg16998 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg13849 + +lemma sg16999 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg12423 + +lemma sg17000 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg75 sg12380 + +lemma sg17001 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,2] := by + exact rowSquare_join (by decide) sg142 sg11570 + +lemma sg17002 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,4,1] := by + exact rowSquare_join (by decide) sg142 sg11571 + +lemma sg17003 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg26 sg12800 + +lemma sg17004 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,2] := by + exact rowSquare_join (by decide) sg142 sg11572 + +lemma sg17005 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,3,1] := by + exact rowSquare_join (by decide) sg142 sg11573 + +lemma sg17006 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,4] := by + exact rowSquare_join (by decide) sg143 sg11562 + +lemma sg17007 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg13860 + +lemma sg17008 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg123 sg11595 + +lemma sg17009 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg75 sg12385 + +lemma sg17010 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,2] := by + exact rowSquare_join (by decide) sg142 sg11574 + +lemma sg17011 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg123 sg11596 + +lemma sg17012 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,2] := by + exact rowSquare_join (by decide) sg142 sg11575 + +lemma sg17013 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,3,1] := by + exact rowSquare_join (by decide) sg142 sg11576 + +lemma sg17014 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,4] := by + exact rowSquare_join (by decide) sg143 sg11564 + +lemma sg17015 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg123 sg11597 + +lemma sg17016 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,2,1] := by + exact rowSquare_join (by decide) sg142 sg11577 + +lemma sg17017 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,3] := by + exact rowSquare_join (by decide) sg143 sg11566 + +lemma sg17018 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,6,1,1] := by + exact rowSquare_join (by decide) sg142 sg11578 + +lemma sg17019 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,6,2] := by + exact rowSquare_join (by decide) sg143 sg11567 + +lemma sg17020 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg10 sg13871 + +lemma sg17021 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg10 sg13872 + +lemma sg17022 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg12424 + +lemma sg17023 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by + exact rowSquare_join (by decide) sg74 sg12425 + +lemma sg17024 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3686 sg4102 + +lemma sg17025 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg12426 + +lemma sg17026 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg10 sg13881 + +lemma sg17027 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,2] := by + exact rowSquare_join (by decide) sg74 sg12427 + +lemma sg17028 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,4,1] := by + exact rowSquare_join (by decide) sg143 sg11569 + +lemma sg17029 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3 sg14668 + +lemma sg17030 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3 sg14669 + +lemma sg17031 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg5 sg14643 + +lemma sg17032 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3 sg14670 + +lemma sg17033 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg9 sg13899 + +lemma sg17034 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8 sg14082 + +lemma sg17035 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8 sg14083 + +lemma sg17036 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg6 sg14641 + +lemma sg17037 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8 sg14084 + +lemma sg17038 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg12 sg13678 + +lemma sg17039 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg12 sg13679 + +lemma sg17040 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3 sg14671 + +lemma sg17041 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg10 sg13899 + +lemma sg17042 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3 sg14672 + +lemma sg17043 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg9 sg13902 + +lemma sg17044 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg13904 + +lemma sg17045 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg9 sg13906 + +lemma sg17046 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg11 sg13766 + +lemma sg17047 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg11 sg13768 + +lemma sg17048 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg26 sg12801 + +lemma sg17049 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg11 sg13772 + +lemma sg17050 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg24 sg12820 + +lemma sg17051 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg74 sg12428 + +lemma sg17052 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg74 sg12429 + +lemma sg17053 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg26 sg12802 + +lemma sg17054 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg12430 + +lemma sg17055 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg74 sg12431 + +lemma sg17056 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg12432 + +lemma sg17057 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg12803 + +lemma sg17058 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg26 sg12804 + +lemma sg17059 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg12433 + +lemma sg17060 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg74 sg12434 + +lemma sg17061 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg142 sg11579 + +lemma sg17062 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg12805 + +lemma sg17063 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg26 sg12806 + +lemma sg17064 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg12435 + +lemma sg17065 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg142 sg11580 + +lemma sg17066 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg56 sg12445 + +lemma sg17067 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg142 sg11581 + +lemma sg17068 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg142 sg11582 + +lemma sg17069 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3 sg14674 + +lemma sg17070 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg10 sg13902 + +lemma sg17071 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg13904 + +lemma sg17072 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg10 sg13906 + +lemma sg17073 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg26 sg12807 + +lemma sg17074 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg12436 + +lemma sg17075 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg27 sg12801 + +lemma sg17076 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg12437 + +lemma sg17077 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg12808 + +lemma sg17078 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg26 sg12809 + +lemma sg17079 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg12438 + +lemma sg17080 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg27 sg12802 + +lemma sg17081 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg12439 + +lemma sg17082 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg27 sg12803 + +lemma sg17083 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg27 sg12804 + +lemma sg17084 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg12810 + +lemma sg17085 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg26 sg12811 + +lemma sg17086 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg75 sg12399 + +lemma sg17087 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg12812 + +lemma sg17088 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg75 sg12401 + +lemma sg17089 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,5] := by + exact rowSquare_join (by decide) sg143 sg11582 + +lemma sg17090 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg12440 + +lemma sg17091 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg12813 + +lemma sg17092 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg56 sg12446 + +lemma sg17093 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg12814 + +lemma sg17094 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg123 sg11599 + +lemma sg17095 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg123 sg11600 + +lemma sg17096 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,4] := by + exact rowSquare_join (by decide) sg145 sg11557 + +lemma sg17097 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg56 sg12447 + +lemma sg17098 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,6,3] := by + exact rowSquare_join (by decide) sg145 sg11559 + +lemma sg17099 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg27 sg12809 + +lemma sg17100 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg26 sg12815 + +lemma sg17101 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg75 sg12409 + +lemma sg17102 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg29 sg12797 + +lemma sg17103 : RowSquare [6,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg56 sg12448 + +lemma sg17104 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1461 sg7812 + +lemma sg17105 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1075 sg8780 + +lemma sg17106 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1464 sg7812 + +lemma sg17107 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1076 sg8780 + +lemma sg17108 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1461 sg7813 + +lemma sg17109 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1077 sg8780 + +lemma sg17110 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1468 sg7812 + +lemma sg17111 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1078 sg8780 + +lemma sg17112 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1469 sg7812 + +lemma sg17113 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [5,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1464 sg7815 + +lemma sg17114 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1470 sg7812 + +lemma sg17115 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1079 sg8780 + +lemma sg17116 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1471 sg7812 + +lemma sg17117 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1465 sg7813 + +lemma sg17118 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1080 sg8780 + +lemma sg17119 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1472 sg7812 + +lemma sg17120 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1467 sg7813 + +lemma sg17121 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1081 sg8780 + +lemma sg17122 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1082 sg8780 + +lemma sg17123 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1468 sg7813 + +lemma sg17124 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1473 sg7812 + +lemma sg17125 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1468 sg7814 + +lemma sg17126 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1078 sg8781 + +lemma sg17127 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1468 sg7815 + +lemma sg17128 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1474 sg7812 + +lemma sg17129 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1083 sg8780 + +lemma sg17130 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1475 sg7812 + +lemma sg17131 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1470 sg7813 + +lemma sg17132 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1084 sg8780 + +lemma sg17133 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1471 sg7813 + +lemma sg17134 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1085 sg8780 + +lemma sg17135 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1472 sg7813 + +lemma sg17136 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1086 sg8780 + +lemma sg17137 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1476 sg7812 + +lemma sg17138 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1468 sg7823 + +lemma sg17139 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1087 sg8780 + +lemma sg17140 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1477 sg7812 + +lemma sg17141 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1474 sg7813 + +lemma sg17142 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1088 sg8780 + +lemma sg17143 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1475 sg7813 + +lemma sg17144 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1089 sg8780 + +lemma sg17145 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [10,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1090 sg8780 + +lemma sg17146 : RowSquare [6,6,3,2,2,2,2,2,2,2,1,1] [11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1091 sg8780 + +lemma sg17147 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1754 sg6492 + +lemma sg17148 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2626 sg4947 + +lemma sg17149 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1754 sg6494 + +lemma sg17150 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2626 sg4949 + +lemma sg17151 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3325 sg4463 + +lemma sg17152 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg2632 sg4945 + +lemma sg17153 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2630 sg4949 + +lemma sg17154 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg2632 sg4947 + +lemma sg17155 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg2633 sg4947 + +lemma sg17156 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3353 sg4434 + +lemma sg17157 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg2631 sg4949 + +lemma sg17158 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg2633 sg4948 + +lemma sg17159 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg2632 sg4949 + +lemma sg17160 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg2633 sg4949 + +lemma sg17161 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2640 sg4942 + +lemma sg17162 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg3402 sg4376 + +lemma sg17163 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg3402 sg4377 + +lemma sg17164 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg3403 sg4377 + +lemma sg17165 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3401 sg4378 + +lemma sg17166 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg2632 sg4951 + +lemma sg17167 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg3325 sg4464 + +lemma sg17168 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13652 + +lemma sg17169 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13653 + +lemma sg17170 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg3402 sg4378 + +lemma sg17171 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,2] := by + exact rowSquare_join (by decide) sg13 sg13654 + +lemma sg17172 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3404 sg4374 + +lemma sg17173 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg3552 sg4304 + +lemma sg17174 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg2635 sg4948 + +lemma sg17175 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg3402 sg4379 + +lemma sg17176 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,3,2] := by + exact rowSquare_join (by decide) sg3403 sg4379 + +lemma sg17177 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,5,5,5,5,4,1] := by + exact rowSquare_join (by decide) sg2636 sg4949 + +lemma sg17178 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2640 sg4943 + +lemma sg17179 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2632 sg4954 + +lemma sg17180 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg2633 sg4954 + +lemma sg17181 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg2632 sg4956 + +lemma sg17182 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg2633 sg4956 + +lemma sg17183 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg2633 sg4957 + +lemma sg17184 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13656 + +lemma sg17185 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg13658 + +lemma sg17186 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg3353 sg4435 + +lemma sg17187 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg3553 sg4304 + +lemma sg17188 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg2633 sg4958 + +lemma sg17189 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg2639 sg4949 + +lemma sg17190 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,4] := by + exact rowSquare_join (by decide) sg2640 sg4949 + +lemma sg17191 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg13661 + +lemma sg17192 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3323 sg4468 + +lemma sg17193 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4468 + +lemma sg17194 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2632 sg4960 + +lemma sg17195 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3,2] := by + exact rowSquare_join (by decide) sg3554 sg4302 + +lemma sg17196 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg13662 + +lemma sg17197 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2631 sg4962 + +lemma sg17198 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13663 + +lemma sg17199 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg13664 + +lemma sg17200 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg3353 sg4436 + +lemma sg17201 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,2,1] := by + exact rowSquare_join (by decide) sg3554 sg4304 + +lemma sg17202 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,3] := by + exact rowSquare_join (by decide) sg2641 sg4949 + +lemma sg17203 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1675 sg6518 + +lemma sg17204 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg1757 sg6495 + +lemma sg17205 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13666 + +lemma sg17206 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13667 + +lemma sg17207 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13668 + +lemma sg17208 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13669 + +lemma sg17209 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg13670 + +lemma sg17210 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by + exact rowSquare_join (by decide) sg3555 sg4303 + +lemma sg17211 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg13671 + +lemma sg17212 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by + exact rowSquare_join (by decide) sg3555 sg4304 + +lemma sg17213 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by + exact rowSquare_join (by decide) sg3556 sg4304 + +lemma sg17214 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2365 sg5734 + +lemma sg17215 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg2272 sg5751 + +lemma sg17216 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg2273 sg5751 + +lemma sg17217 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg2644 sg4942 + +lemma sg17218 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg3402 sg4380 + +lemma sg17219 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg3402 sg4381 + +lemma sg17220 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,4,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg3403 sg4381 + +lemma sg17221 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14865 + +lemma sg17222 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg3402 sg4382 + +lemma sg17223 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg3403 sg4382 + +lemma sg17224 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg3325 sg4469 + +lemma sg17225 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13672 + +lemma sg17226 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13673 + +lemma sg17227 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg2635 sg4950 + +lemma sg17228 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg3325 sg4470 + +lemma sg17229 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg3403 sg4383 + +lemma sg17230 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg3402 sg4384 + +lemma sg17231 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg3403 sg4384 + +lemma sg17232 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13674 + +lemma sg17233 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13675 + +lemma sg17234 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg3403 sg4385 + +lemma sg17235 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13676 + +lemma sg17236 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13677 + +lemma sg17237 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg13678 + +lemma sg17238 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg13 sg13679 + +lemma sg17239 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg3402 sg4386 + +lemma sg17240 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg3403 sg4386 + +lemma sg17241 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg3405 sg4379 + +lemma sg17242 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,4] := by + exact rowSquare_join (by decide) sg2644 sg4949 + +lemma sg17243 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg3402 sg4388 + +lemma sg17244 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg14 sg13654 + +lemma sg17245 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg3406 sg4377 + +lemma sg17246 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by + exact rowSquare_join (by decide) sg13 sg13689 + +lemma sg17247 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg3553 sg4307 + +lemma sg17248 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg3557 sg4304 + +lemma sg17249 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by + exact rowSquare_join (by decide) sg3406 sg4379 + +lemma sg17250 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3582 sg4190 + +lemma sg17251 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg3325 sg4473 + +lemma sg17252 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg3403 sg4389 + +lemma sg17253 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13690 + +lemma sg17254 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13691 + +lemma sg17255 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13692 + +lemma sg17256 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg13693 + +lemma sg17257 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg3402 sg4390 + +lemma sg17258 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2,2] := by + exact rowSquare_join (by decide) sg3403 sg4390 + +lemma sg17259 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,3,1] := by + exact rowSquare_join (by decide) sg3576 sg4193 + +lemma sg17260 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13694 + +lemma sg17261 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13695 + +lemma sg17262 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13696 + +lemma sg17263 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13697 + +lemma sg17264 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13698 + +lemma sg17265 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg13699 + +lemma sg17266 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg13700 + +lemma sg17267 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by + exact rowSquare_join (by decide) sg3576 sg4194 + +lemma sg17268 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by + exact rowSquare_join (by decide) sg3675 sg4111 + +lemma sg17269 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3552 sg4311 + +lemma sg17270 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13701 + +lemma sg17271 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13702 + +lemma sg17272 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13703 + +lemma sg17273 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13704 + +lemma sg17274 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by + exact rowSquare_join (by decide) sg13 sg13705 + +lemma sg17275 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg13706 + +lemma sg17276 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by + exact rowSquare_join (by decide) sg13 sg13707 + +lemma sg17277 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by + exact rowSquare_join (by decide) sg13 sg13708 + +lemma sg17278 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg3556 sg4307 + +lemma sg17279 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg13711 + +lemma sg17280 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg14 sg13656 + +lemma sg17281 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg14 sg13657 + +lemma sg17282 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg14 sg13658 + +lemma sg17283 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3404 sg4387 + +lemma sg17284 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by + exact rowSquare_join (by decide) sg2640 sg4956 + +lemma sg17285 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2642 sg4953 + +lemma sg17286 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3573 sg4196 + +lemma sg17287 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13717 + +lemma sg17288 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13718 + +lemma sg17289 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13719 + +lemma sg17290 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13720 + +lemma sg17291 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg13721 + +lemma sg17292 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg13722 + +lemma sg17293 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg14 sg13671 + +lemma sg17294 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by + exact rowSquare_join (by decide) sg3679 sg4111 + +lemma sg17295 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4474 + +lemma sg17296 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg3329 sg4467 + +lemma sg17297 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4475 + +lemma sg17298 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3573 sg4199 + +lemma sg17299 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3553 sg4310 + +lemma sg17300 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg3329 sg4468 + +lemma sg17301 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,3] := by + exact rowSquare_join (by decide) sg3332 sg4466 + +lemma sg17302 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3573 sg4200 + +lemma sg17303 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13727 + +lemma sg17304 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13728 + +lemma sg17305 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13729 + +lemma sg17306 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13730 + +lemma sg17307 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by + exact rowSquare_join (by decide) sg13 sg13731 + +lemma sg17308 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg13732 + +lemma sg17309 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by + exact rowSquare_join (by decide) sg13 sg13733 + +lemma sg17310 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by + exact rowSquare_join (by decide) sg3556 sg4309 + +lemma sg17311 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1675 sg6519 + +lemma sg17312 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13734 + +lemma sg17313 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13735 + +lemma sg17314 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13736 + +lemma sg17315 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by + exact rowSquare_join (by decide) sg13 sg13737 + +lemma sg17316 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by + exact rowSquare_join (by decide) sg13 sg13738 + +lemma sg17317 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by + exact rowSquare_join (by decide) sg13 sg13739 + +lemma sg17318 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3354 sg4434 + +lemma sg17319 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3574 sg4197 + +lemma sg17320 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2889 sg4880 + +lemma sg17321 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3571 sg4212 + +lemma sg17322 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3574 sg4198 + +lemma sg17323 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13740 + +lemma sg17324 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3574 sg4199 + +lemma sg17325 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3593 sg4190 + +lemma sg17326 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,2] := by + exact rowSquare_join (by decide) sg3576 sg4197 + +lemma sg17327 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,3,1] := by + exact rowSquare_join (by decide) sg3332 sg4467 + +lemma sg17328 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3574 sg4200 + +lemma sg17329 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13741 + +lemma sg17330 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13742 + +lemma sg17331 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13743 + +lemma sg17332 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13744 + +lemma sg17333 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg13745 + +lemma sg17334 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by + exact rowSquare_join (by decide) sg3576 sg4199 + +lemma sg17335 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by + exact rowSquare_join (by decide) sg3332 sg4468 + +lemma sg17336 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1756 sg6496 + +lemma sg17337 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13746 + +lemma sg17338 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13747 + +lemma sg17339 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13748 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes42.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes42.lean index 2d0ee1aca698238bf6510aa667d05897cadef77b..6de4c27cb5eff710d902da40fedc9ff7a8e9f257 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes42.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes42.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes36 - -namespace OAI - -/-! Semigroup Nodes 42. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg17340 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg13749 - -lemma sg17341 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg13750 - -lemma sg17342 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg3556 sg4310 - -lemma sg17343 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13751 - -lemma sg17344 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13752 - -lemma sg17345 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg13753 - -lemma sg17346 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by - exact rowSquare_join (by decide) sg13 sg13754 - -lemma sg17347 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by - exact rowSquare_join (by decide) sg13 sg13755 - -lemma sg17348 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13756 - -lemma sg17349 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by - exact rowSquare_join (by decide) sg13 sg13757 - -lemma sg17350 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by - exact rowSquare_join (by decide) sg13 sg13758 - -lemma sg17351 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg14866 - -lemma sg17352 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14867 - -lemma sg17353 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg14868 - -lemma sg17354 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14869 - -lemma sg17355 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3579 sg4192 - -lemma sg17356 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg13759 - -lemma sg17357 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg14870 - -lemma sg17358 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg14871 - -lemma sg17359 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg3325 sg4476 - -lemma sg17360 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14872 - -lemma sg17361 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg1 sg14873 - -lemma sg17362 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg3403 sg4391 - -lemma sg17363 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14874 - -lemma sg17364 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg14875 - -lemma sg17365 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14876 - -lemma sg17366 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg14877 - -lemma sg17367 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg14878 - -lemma sg17368 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14879 - -lemma sg17369 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg14880 - -lemma sg17370 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13760 - -lemma sg17371 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13761 - -lemma sg17372 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg14881 - -lemma sg17373 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14882 - -lemma sg17374 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14883 - -lemma sg17375 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg14884 - -lemma sg17376 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg3403 sg4392 - -lemma sg17377 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1 sg14885 - -lemma sg17378 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg1 sg14886 - -lemma sg17379 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14887 - -lemma sg17380 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg14888 - -lemma sg17381 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg14889 - -lemma sg17382 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg14890 - -lemma sg17383 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13762 - -lemma sg17384 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13763 - -lemma sg17385 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14891 - -lemma sg17386 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13764 - -lemma sg17387 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg13765 - -lemma sg17388 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14892 - -lemma sg17389 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg14893 - -lemma sg17390 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg14894 - -lemma sg17391 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg1 sg14895 - -lemma sg17392 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg1 sg14896 - -lemma sg17393 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13766 - -lemma sg17394 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13767 - -lemma sg17395 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13768 - -lemma sg17396 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13769 - -lemma sg17397 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13770 - -lemma sg17398 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg13771 - -lemma sg17399 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13772 - -lemma sg17400 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13773 - -lemma sg17401 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg13774 - -lemma sg17402 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg13775 - -lemma sg17403 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg13 sg13776 - -lemma sg17404 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14898 - -lemma sg17405 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg1 sg14899 - -lemma sg17406 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg1 sg14900 - -lemma sg17407 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14901 - -lemma sg17408 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3587 sg4192 - -lemma sg17409 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg14902 - -lemma sg17410 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14903 - -lemma sg17411 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg14904 - -lemma sg17412 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg13672 - -lemma sg17413 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg14 sg13673 - -lemma sg17414 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13777 - -lemma sg17415 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13778 - -lemma sg17416 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14905 - -lemma sg17417 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13779 - -lemma sg17418 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg13780 - -lemma sg17419 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14906 - -lemma sg17420 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg13676 - -lemma sg17421 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg14 sg13677 - -lemma sg17422 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg14 sg13678 - -lemma sg17423 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg14 sg13679 - -lemma sg17424 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14907 - -lemma sg17425 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg14908 - -lemma sg17426 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14909 - -lemma sg17427 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14910 - -lemma sg17428 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg14911 - -lemma sg17429 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg14912 - -lemma sg17430 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13781 - -lemma sg17431 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13782 - -lemma sg17432 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13783 - -lemma sg17433 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13784 - -lemma sg17434 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13785 - -lemma sg17435 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg13786 - -lemma sg17436 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14913 - -lemma sg17437 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg14914 - -lemma sg17438 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg14915 - -lemma sg17439 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg14916 - -lemma sg17440 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg14917 - -lemma sg17441 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13787 - -lemma sg17442 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13788 - -lemma sg17443 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13789 - -lemma sg17444 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13790 - -lemma sg17445 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13791 - -lemma sg17446 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13792 - -lemma sg17447 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13793 - -lemma sg17448 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg13794 - -lemma sg17449 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg13795 - -lemma sg17450 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1 sg14918 - -lemma sg17451 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg1 sg14919 - -lemma sg17452 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13796 - -lemma sg17453 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13797 - -lemma sg17454 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14920 - -lemma sg17455 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg14921 - -lemma sg17456 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg14922 - -lemma sg17457 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg14923 - -lemma sg17458 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13798 - -lemma sg17459 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13799 - -lemma sg17460 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13800 - -lemma sg17461 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13801 - -lemma sg17462 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13802 - -lemma sg17463 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13803 - -lemma sg17464 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14924 - -lemma sg17465 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg1 sg14925 - -lemma sg17466 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by - exact rowSquare_join (by decide) sg1 sg14926 - -lemma sg17467 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13804 - -lemma sg17468 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13805 - -lemma sg17469 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13806 - -lemma sg17470 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13807 - -lemma sg17471 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13808 - -lemma sg17472 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by - exact rowSquare_join (by decide) sg13 sg13809 - -lemma sg17473 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg13810 - -lemma sg17474 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by - exact rowSquare_join (by decide) sg13 sg13811 - -lemma sg17475 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by - exact rowSquare_join (by decide) sg1 sg14927 - -lemma sg17476 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13812 - -lemma sg17477 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13813 - -lemma sg17478 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13814 - -lemma sg17479 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13815 - -lemma sg17480 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by - exact rowSquare_join (by decide) sg13 sg13816 - -lemma sg17481 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by - exact rowSquare_join (by decide) sg13 sg13817 - -lemma sg17482 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by - exact rowSquare_join (by decide) sg13 sg13818 - -lemma sg17483 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3573 sg4201 - -lemma sg17484 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4477 - -lemma sg17485 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg13680 - -lemma sg17486 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg14 sg13681 - -lemma sg17487 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3574 sg4201 - -lemma sg17488 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg3552 sg4313 - -lemma sg17489 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg13682 - -lemma sg17490 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4478 - -lemma sg17491 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg14 sg13683 - -lemma sg17492 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg13684 - -lemma sg17493 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13819 - -lemma sg17494 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13820 - -lemma sg17495 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13821 - -lemma sg17496 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13822 - -lemma sg17497 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13823 - -lemma sg17498 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg13824 - -lemma sg17499 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3552 sg4314 - -lemma sg17500 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg13686 - -lemma sg17501 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg14 sg13687 - -lemma sg17502 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg14 sg13688 - -lemma sg17503 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by - exact rowSquare_join (by decide) sg14 sg13689 - -lemma sg17504 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13825 - -lemma sg17505 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13826 - -lemma sg17506 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4479 - -lemma sg17507 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg13691 - -lemma sg17508 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg14 sg13692 - -lemma sg17509 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg13693 - -lemma sg17510 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13827 - -lemma sg17511 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13828 - -lemma sg17512 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13829 - -lemma sg17513 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13830 - -lemma sg17514 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13831 - -lemma sg17515 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13832 - -lemma sg17516 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg13698 - -lemma sg17517 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg14 sg13699 - -lemma sg17518 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by - exact rowSquare_join (by decide) sg14 sg13700 - -lemma sg17519 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13833 - -lemma sg17520 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13834 - -lemma sg17521 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13835 - -lemma sg17522 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13836 - -lemma sg17523 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13837 - -lemma sg17524 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by - exact rowSquare_join (by decide) sg13 sg13838 - -lemma sg17525 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg13839 - -lemma sg17526 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by - exact rowSquare_join (by decide) sg13 sg13840 - -lemma sg17527 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by - exact rowSquare_join (by decide) sg14 sg13708 - -lemma sg17528 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3574 sg4202 - -lemma sg17529 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3673 sg4113 - -lemma sg17530 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13841 - -lemma sg17531 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13842 - -lemma sg17532 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3552 sg4315 - -lemma sg17533 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3402 sg4393 - -lemma sg17534 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg3403 sg4393 - -lemma sg17535 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg3329 sg4473 - -lemma sg17536 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13843 - -lemma sg17537 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13844 - -lemma sg17538 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13845 - -lemma sg17539 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13846 - -lemma sg17540 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13847 - -lemma sg17541 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg13848 - -lemma sg17542 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg3576 sg4203 - -lemma sg17543 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by - exact rowSquare_join (by decide) sg3332 sg4472 - -lemma sg17544 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13849 - -lemma sg17545 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13850 - -lemma sg17546 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13851 - -lemma sg17547 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13852 - -lemma sg17548 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg13853 - -lemma sg17549 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg13854 - -lemma sg17550 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by - exact rowSquare_join (by decide) sg3556 sg4312 - -lemma sg17551 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13855 - -lemma sg17552 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13856 - -lemma sg17553 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg13857 - -lemma sg17554 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by - exact rowSquare_join (by decide) sg13 sg13858 - -lemma sg17555 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by - exact rowSquare_join (by decide) sg13 sg13859 - -lemma sg17556 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,7,5,4] := by - exact rowSquare_join (by decide) sg83 sg12343 - -lemma sg17557 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,7,6,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13861 - -lemma sg17558 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,7,6,2,1] := by - exact rowSquare_join (by decide) sg13 sg13862 - -lemma sg17559 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,7,6,3] := by - exact rowSquare_join (by decide) sg13 sg13863 - -lemma sg17560 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,7,7,1,1] := by - exact rowSquare_join (by decide) sg13 sg13864 - -lemma sg17561 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,7,7,2] := by - exact rowSquare_join (by decide) sg13 sg13865 - -lemma sg17562 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3671 sg4116 - -lemma sg17563 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3335 sg4465 - -lemma sg17564 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13866 - -lemma sg17565 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3573 sg4204 - -lemma sg17566 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg3587 sg4195 - -lemma sg17567 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg13709 - -lemma sg17568 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4480 - -lemma sg17569 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg14 sg13710 - -lemma sg17570 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg13711 - -lemma sg17571 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3573 sg4205 - -lemma sg17572 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13867 - -lemma sg17573 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4481 - -lemma sg17574 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg13713 - -lemma sg17575 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg14 sg13714 - -lemma sg17576 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg13715 - -lemma sg17577 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13868 - -lemma sg17578 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3573 sg4206 - -lemma sg17579 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13869 - -lemma sg17580 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3573 sg4207 - -lemma sg17581 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13870 - -lemma sg17582 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13871 - -lemma sg17583 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13872 - -lemma sg17584 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg13720 - -lemma sg17585 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg14 sg13721 - -lemma sg17586 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by - exact rowSquare_join (by decide) sg14 sg13722 - -lemma sg17587 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3574 sg4205 - -lemma sg17588 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg13723 - -lemma sg17589 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4482 - -lemma sg17590 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13873 - -lemma sg17591 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3574 sg4207 - -lemma sg17592 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg13724 - -lemma sg17593 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg13725 - -lemma sg17594 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg14 sg13726 - -lemma sg17595 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3573 sg4208 - -lemma sg17596 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13874 - -lemma sg17597 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13875 - -lemma sg17598 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13876 - -lemma sg17599 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13877 - -lemma sg17600 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg13878 - -lemma sg17601 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg14 sg13732 - -lemma sg17602 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,2] := by - exact rowSquare_join (by decide) sg14 sg13733 - -lemma sg17603 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3573 sg4209 - -lemma sg17604 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13879 - -lemma sg17605 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13880 - -lemma sg17606 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13881 - -lemma sg17607 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg13882 - -lemma sg17608 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg13883 - -lemma sg17609 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,5] := by - exact rowSquare_join (by decide) sg14 sg13739 - -lemma sg17610 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4483 - -lemma sg17611 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg55 sg12475 - -lemma sg17612 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3573 sg4210 - -lemma sg17613 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg55 sg12476 - -lemma sg17614 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg55 sg12477 - -lemma sg17615 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg55 sg12478 - -lemma sg17616 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg14 sg13744 - -lemma sg17617 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg13745 - -lemma sg17618 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3573 sg4211 - -lemma sg17619 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13884 - -lemma sg17620 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg55 sg12479 - -lemma sg17621 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg55 sg12480 - -lemma sg17622 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg13885 - -lemma sg17623 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,4,1] := by - exact rowSquare_join (by decide) sg83 sg12344 - -lemma sg17624 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13886 - -lemma sg17625 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13887 - -lemma sg17626 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,2] := by - exact rowSquare_join (by decide) sg13 sg13888 - -lemma sg17627 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,3,1] := by - exact rowSquare_join (by decide) sg13 sg13889 - -lemma sg17628 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,4] := by - exact rowSquare_join (by decide) sg13 sg13890 - -lemma sg17629 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13891 - -lemma sg17630 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by - exact rowSquare_join (by decide) sg13 sg13892 - -lemma sg17631 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,3] := by - exact rowSquare_join (by decide) sg13 sg13893 - -lemma sg17632 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,4,4] := by - exact rowSquare_join (by decide) sg83 sg12346 - -lemma sg17633 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,5,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13894 - -lemma sg17634 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,5,2,1] := by - exact rowSquare_join (by decide) sg83 sg12347 - -lemma sg17635 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,5,3] := by - exact rowSquare_join (by decide) sg83 sg12348 - -lemma sg17636 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,6,1,1] := by - exact rowSquare_join (by decide) sg13 sg13895 - -lemma sg17637 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,6,2] := by - exact rowSquare_join (by decide) sg13 sg13896 - -lemma sg17638 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,7,1] := by - exact rowSquare_join (by decide) sg13 sg13897 - -lemma sg17639 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,3,2,1,1] := by - exact rowSquare_join (by decide) sg55 sg12487 - -lemma sg17640 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,3,2,2] := by - exact rowSquare_join (by decide) sg55 sg12488 - -lemma sg17641 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,3,3,1] := by - exact rowSquare_join (by decide) sg83 sg12349 - -lemma sg17642 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,4,1,1,1] := by - exact rowSquare_join (by decide) sg55 sg12489 - -lemma sg17643 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,4,2,1] := by - exact rowSquare_join (by decide) sg83 sg12350 - -lemma sg17644 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,4,3] := by - exact rowSquare_join (by decide) sg83 sg12351 - -lemma sg17645 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,5,1,1] := by - exact rowSquare_join (by decide) sg83 sg12352 - -lemma sg17646 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,5,2] := by - exact rowSquare_join (by decide) sg83 sg12353 - -lemma sg17647 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,6,1] := by - exact rowSquare_join (by decide) sg83 sg12354 - -lemma sg17648 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,7] := by - exact rowSquare_join (by decide) sg13 sg13898 - -lemma sg17649 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg14928 - -lemma sg17650 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14929 - -lemma sg17651 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg14930 - -lemma sg17652 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14931 - -lemma sg17653 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg14932 - -lemma sg17654 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg14933 - -lemma sg17655 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8 sg14121 - -lemma sg17656 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13899 - -lemma sg17657 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13900 - -lemma sg17658 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13901 - -lemma sg17659 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg14934 - -lemma sg17660 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg13652 - -lemma sg17661 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14935 - -lemma sg17662 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg15 sg13653 - -lemma sg17663 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg3403 sg4394 - -lemma sg17664 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1 sg14936 - -lemma sg17665 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg15 sg13654 - -lemma sg17666 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14937 - -lemma sg17667 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg14938 - -lemma sg17668 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg13759 - -lemma sg17669 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8 sg14122 - -lemma sg17670 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg14939 - -lemma sg17671 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg14940 - -lemma sg17672 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg14941 - -lemma sg17673 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13902 - -lemma sg17674 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13903 - -lemma sg17675 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13904 - -lemma sg17676 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13905 - -lemma sg17677 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg13906 - -lemma sg17678 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14942 - -lemma sg17679 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg15 sg13655 - -lemma sg17680 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg15 sg13656 - -lemma sg17681 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg15 sg13657 - -lemma sg17682 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg15 sg13658 - -lemma sg17683 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8 sg14123 - -lemma sg17684 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg14943 - -lemma sg17685 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg13659 - -lemma sg17686 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14944 - -lemma sg17687 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg15 sg13660 - -lemma sg17688 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg15 sg13661 - -lemma sg17689 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13907 - -lemma sg17690 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13908 - -lemma sg17691 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13909 - -lemma sg17692 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13910 - -lemma sg17693 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13911 - -lemma sg17694 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg13912 - -lemma sg17695 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14945 - -lemma sg17696 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg15 sg13663 - -lemma sg17697 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg15 sg13664 - -lemma sg17698 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg15 sg13665 - -lemma sg17699 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg14946 - -lemma sg17700 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13913 - -lemma sg17701 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13914 - -lemma sg17702 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13915 - -lemma sg17703 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13916 - -lemma sg17704 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13917 - -lemma sg17705 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13918 - -lemma sg17706 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13919 - -lemma sg17707 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg13920 - -lemma sg17708 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg13921 - -lemma sg17709 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg15 sg13671 - -lemma sg17710 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1 sg14947 - -lemma sg17711 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14948 - -lemma sg17712 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg14949 - -lemma sg17713 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg13760 - -lemma sg17714 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg14 sg13761 - -lemma sg17715 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14950 - -lemma sg17716 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg13762 - -lemma sg17717 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg13763 - -lemma sg17718 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14951 - -lemma sg17719 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg14 sg13764 - -lemma sg17720 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg13765 - -lemma sg17721 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13922 - -lemma sg17722 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13923 - -lemma sg17723 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13924 - -lemma sg17724 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13925 - -lemma sg17725 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13926 - -lemma sg17726 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg13927 - -lemma sg17727 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg13772 - -lemma sg17728 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg13773 - -lemma sg17729 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg14 sg13774 - -lemma sg17730 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg14 sg13775 - -lemma sg17731 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg14 sg13776 - -lemma sg17732 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13928 - -lemma sg17733 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13929 - -lemma sg17734 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14952 - -lemma sg17735 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg14953 - -lemma sg17736 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg14954 - -lemma sg17737 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg14955 - -lemma sg17738 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13930 - -lemma sg17739 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13931 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes36 + +namespace OAI + +/-! Semigroup Nodes 42. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg17340 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg13749 + +lemma sg17341 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg13750 + +lemma sg17342 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg3556 sg4310 + +lemma sg17343 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13751 + +lemma sg17344 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13752 + +lemma sg17345 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg13753 + +lemma sg17346 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by + exact rowSquare_join (by decide) sg13 sg13754 + +lemma sg17347 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by + exact rowSquare_join (by decide) sg13 sg13755 + +lemma sg17348 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13756 + +lemma sg17349 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by + exact rowSquare_join (by decide) sg13 sg13757 + +lemma sg17350 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by + exact rowSquare_join (by decide) sg13 sg13758 + +lemma sg17351 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg14866 + +lemma sg17352 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14867 + +lemma sg17353 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg14868 + +lemma sg17354 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14869 + +lemma sg17355 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3579 sg4192 + +lemma sg17356 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg13759 + +lemma sg17357 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg14870 + +lemma sg17358 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg14871 + +lemma sg17359 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg3325 sg4476 + +lemma sg17360 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14872 + +lemma sg17361 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg1 sg14873 + +lemma sg17362 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg3403 sg4391 + +lemma sg17363 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14874 + +lemma sg17364 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg14875 + +lemma sg17365 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14876 + +lemma sg17366 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg14877 + +lemma sg17367 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg14878 + +lemma sg17368 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14879 + +lemma sg17369 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg14880 + +lemma sg17370 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13760 + +lemma sg17371 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13761 + +lemma sg17372 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg14881 + +lemma sg17373 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14882 + +lemma sg17374 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14883 + +lemma sg17375 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg14884 + +lemma sg17376 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg3403 sg4392 + +lemma sg17377 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1 sg14885 + +lemma sg17378 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg1 sg14886 + +lemma sg17379 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14887 + +lemma sg17380 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg14888 + +lemma sg17381 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg14889 + +lemma sg17382 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg14890 + +lemma sg17383 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13762 + +lemma sg17384 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13763 + +lemma sg17385 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14891 + +lemma sg17386 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13764 + +lemma sg17387 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg13765 + +lemma sg17388 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14892 + +lemma sg17389 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg14893 + +lemma sg17390 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg14894 + +lemma sg17391 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg1 sg14895 + +lemma sg17392 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg1 sg14896 + +lemma sg17393 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13766 + +lemma sg17394 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13767 + +lemma sg17395 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13768 + +lemma sg17396 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13769 + +lemma sg17397 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13770 + +lemma sg17398 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg13771 + +lemma sg17399 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13772 + +lemma sg17400 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13773 + +lemma sg17401 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg13774 + +lemma sg17402 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg13775 + +lemma sg17403 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg13 sg13776 + +lemma sg17404 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14898 + +lemma sg17405 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg1 sg14899 + +lemma sg17406 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg1 sg14900 + +lemma sg17407 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14901 + +lemma sg17408 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3587 sg4192 + +lemma sg17409 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg14902 + +lemma sg17410 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14903 + +lemma sg17411 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg14904 + +lemma sg17412 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg13672 + +lemma sg17413 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg14 sg13673 + +lemma sg17414 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13777 + +lemma sg17415 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13778 + +lemma sg17416 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14905 + +lemma sg17417 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13779 + +lemma sg17418 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg13780 + +lemma sg17419 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14906 + +lemma sg17420 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg13676 + +lemma sg17421 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg14 sg13677 + +lemma sg17422 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg14 sg13678 + +lemma sg17423 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg14 sg13679 + +lemma sg17424 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14907 + +lemma sg17425 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg14908 + +lemma sg17426 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14909 + +lemma sg17427 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14910 + +lemma sg17428 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg14911 + +lemma sg17429 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg14912 + +lemma sg17430 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13781 + +lemma sg17431 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13782 + +lemma sg17432 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13783 + +lemma sg17433 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13784 + +lemma sg17434 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13785 + +lemma sg17435 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg13786 + +lemma sg17436 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14913 + +lemma sg17437 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg14914 + +lemma sg17438 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg14915 + +lemma sg17439 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg14916 + +lemma sg17440 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg14917 + +lemma sg17441 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13787 + +lemma sg17442 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13788 + +lemma sg17443 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13789 + +lemma sg17444 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13790 + +lemma sg17445 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13791 + +lemma sg17446 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13792 + +lemma sg17447 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13793 + +lemma sg17448 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg13794 + +lemma sg17449 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg13795 + +lemma sg17450 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1 sg14918 + +lemma sg17451 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg1 sg14919 + +lemma sg17452 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13796 + +lemma sg17453 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13797 + +lemma sg17454 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14920 + +lemma sg17455 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg14921 + +lemma sg17456 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg14922 + +lemma sg17457 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg14923 + +lemma sg17458 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13798 + +lemma sg17459 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13799 + +lemma sg17460 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13800 + +lemma sg17461 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13801 + +lemma sg17462 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13802 + +lemma sg17463 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13803 + +lemma sg17464 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14924 + +lemma sg17465 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg1 sg14925 + +lemma sg17466 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by + exact rowSquare_join (by decide) sg1 sg14926 + +lemma sg17467 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13804 + +lemma sg17468 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13805 + +lemma sg17469 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13806 + +lemma sg17470 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13807 + +lemma sg17471 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13808 + +lemma sg17472 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by + exact rowSquare_join (by decide) sg13 sg13809 + +lemma sg17473 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg13810 + +lemma sg17474 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by + exact rowSquare_join (by decide) sg13 sg13811 + +lemma sg17475 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by + exact rowSquare_join (by decide) sg1 sg14927 + +lemma sg17476 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13812 + +lemma sg17477 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13813 + +lemma sg17478 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13814 + +lemma sg17479 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13815 + +lemma sg17480 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by + exact rowSquare_join (by decide) sg13 sg13816 + +lemma sg17481 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by + exact rowSquare_join (by decide) sg13 sg13817 + +lemma sg17482 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by + exact rowSquare_join (by decide) sg13 sg13818 + +lemma sg17483 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3573 sg4201 + +lemma sg17484 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4477 + +lemma sg17485 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg13680 + +lemma sg17486 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg14 sg13681 + +lemma sg17487 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3574 sg4201 + +lemma sg17488 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg3552 sg4313 + +lemma sg17489 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg13682 + +lemma sg17490 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4478 + +lemma sg17491 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg14 sg13683 + +lemma sg17492 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg13684 + +lemma sg17493 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13819 + +lemma sg17494 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13820 + +lemma sg17495 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13821 + +lemma sg17496 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13822 + +lemma sg17497 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13823 + +lemma sg17498 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg13824 + +lemma sg17499 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3552 sg4314 + +lemma sg17500 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg13686 + +lemma sg17501 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg14 sg13687 + +lemma sg17502 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg14 sg13688 + +lemma sg17503 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by + exact rowSquare_join (by decide) sg14 sg13689 + +lemma sg17504 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13825 + +lemma sg17505 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13826 + +lemma sg17506 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4479 + +lemma sg17507 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg13691 + +lemma sg17508 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg14 sg13692 + +lemma sg17509 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg13693 + +lemma sg17510 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13827 + +lemma sg17511 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13828 + +lemma sg17512 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13829 + +lemma sg17513 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13830 + +lemma sg17514 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13831 + +lemma sg17515 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13832 + +lemma sg17516 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg13698 + +lemma sg17517 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg14 sg13699 + +lemma sg17518 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by + exact rowSquare_join (by decide) sg14 sg13700 + +lemma sg17519 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13833 + +lemma sg17520 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13834 + +lemma sg17521 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13835 + +lemma sg17522 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13836 + +lemma sg17523 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13837 + +lemma sg17524 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by + exact rowSquare_join (by decide) sg13 sg13838 + +lemma sg17525 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg13839 + +lemma sg17526 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by + exact rowSquare_join (by decide) sg13 sg13840 + +lemma sg17527 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by + exact rowSquare_join (by decide) sg14 sg13708 + +lemma sg17528 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3574 sg4202 + +lemma sg17529 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3673 sg4113 + +lemma sg17530 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13841 + +lemma sg17531 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13842 + +lemma sg17532 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3552 sg4315 + +lemma sg17533 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3402 sg4393 + +lemma sg17534 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg3403 sg4393 + +lemma sg17535 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg3329 sg4473 + +lemma sg17536 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13843 + +lemma sg17537 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13844 + +lemma sg17538 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13845 + +lemma sg17539 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13846 + +lemma sg17540 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13847 + +lemma sg17541 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg13848 + +lemma sg17542 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg3576 sg4203 + +lemma sg17543 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by + exact rowSquare_join (by decide) sg3332 sg4472 + +lemma sg17544 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13849 + +lemma sg17545 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13850 + +lemma sg17546 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13851 + +lemma sg17547 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13852 + +lemma sg17548 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg13853 + +lemma sg17549 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg13854 + +lemma sg17550 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by + exact rowSquare_join (by decide) sg3556 sg4312 + +lemma sg17551 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13855 + +lemma sg17552 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13856 + +lemma sg17553 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg13857 + +lemma sg17554 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by + exact rowSquare_join (by decide) sg13 sg13858 + +lemma sg17555 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by + exact rowSquare_join (by decide) sg13 sg13859 + +lemma sg17556 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,7,5,4] := by + exact rowSquare_join (by decide) sg83 sg12343 + +lemma sg17557 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,7,6,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13861 + +lemma sg17558 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,7,6,2,1] := by + exact rowSquare_join (by decide) sg13 sg13862 + +lemma sg17559 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,7,6,3] := by + exact rowSquare_join (by decide) sg13 sg13863 + +lemma sg17560 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,7,7,1,1] := by + exact rowSquare_join (by decide) sg13 sg13864 + +lemma sg17561 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,7,7,2] := by + exact rowSquare_join (by decide) sg13 sg13865 + +lemma sg17562 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3671 sg4116 + +lemma sg17563 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3335 sg4465 + +lemma sg17564 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13866 + +lemma sg17565 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3573 sg4204 + +lemma sg17566 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg3587 sg4195 + +lemma sg17567 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg13709 + +lemma sg17568 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4480 + +lemma sg17569 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg14 sg13710 + +lemma sg17570 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg13711 + +lemma sg17571 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3573 sg4205 + +lemma sg17572 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13867 + +lemma sg17573 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4481 + +lemma sg17574 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg13713 + +lemma sg17575 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg14 sg13714 + +lemma sg17576 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg13715 + +lemma sg17577 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13868 + +lemma sg17578 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3573 sg4206 + +lemma sg17579 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13869 + +lemma sg17580 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3573 sg4207 + +lemma sg17581 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13870 + +lemma sg17582 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13871 + +lemma sg17583 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13872 + +lemma sg17584 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg13720 + +lemma sg17585 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg14 sg13721 + +lemma sg17586 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by + exact rowSquare_join (by decide) sg14 sg13722 + +lemma sg17587 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3574 sg4205 + +lemma sg17588 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg13723 + +lemma sg17589 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4482 + +lemma sg17590 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13873 + +lemma sg17591 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3574 sg4207 + +lemma sg17592 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg13724 + +lemma sg17593 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg13725 + +lemma sg17594 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg14 sg13726 + +lemma sg17595 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3573 sg4208 + +lemma sg17596 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13874 + +lemma sg17597 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13875 + +lemma sg17598 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13876 + +lemma sg17599 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13877 + +lemma sg17600 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg13878 + +lemma sg17601 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg14 sg13732 + +lemma sg17602 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,2] := by + exact rowSquare_join (by decide) sg14 sg13733 + +lemma sg17603 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3573 sg4209 + +lemma sg17604 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13879 + +lemma sg17605 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13880 + +lemma sg17606 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13881 + +lemma sg17607 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg13882 + +lemma sg17608 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg13883 + +lemma sg17609 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,5] := by + exact rowSquare_join (by decide) sg14 sg13739 + +lemma sg17610 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4483 + +lemma sg17611 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg55 sg12475 + +lemma sg17612 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3573 sg4210 + +lemma sg17613 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg55 sg12476 + +lemma sg17614 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg55 sg12477 + +lemma sg17615 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg55 sg12478 + +lemma sg17616 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg14 sg13744 + +lemma sg17617 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg13745 + +lemma sg17618 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3573 sg4211 + +lemma sg17619 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13884 + +lemma sg17620 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg55 sg12479 + +lemma sg17621 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg55 sg12480 + +lemma sg17622 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg13885 + +lemma sg17623 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,4,1] := by + exact rowSquare_join (by decide) sg83 sg12344 + +lemma sg17624 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13886 + +lemma sg17625 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13887 + +lemma sg17626 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,2] := by + exact rowSquare_join (by decide) sg13 sg13888 + +lemma sg17627 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,3,1] := by + exact rowSquare_join (by decide) sg13 sg13889 + +lemma sg17628 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,5,4] := by + exact rowSquare_join (by decide) sg13 sg13890 + +lemma sg17629 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13891 + +lemma sg17630 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by + exact rowSquare_join (by decide) sg13 sg13892 + +lemma sg17631 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,6,3] := by + exact rowSquare_join (by decide) sg13 sg13893 + +lemma sg17632 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,4,4] := by + exact rowSquare_join (by decide) sg83 sg12346 + +lemma sg17633 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,5,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13894 + +lemma sg17634 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,5,2,1] := by + exact rowSquare_join (by decide) sg83 sg12347 + +lemma sg17635 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,5,3] := by + exact rowSquare_join (by decide) sg83 sg12348 + +lemma sg17636 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,6,1,1] := by + exact rowSquare_join (by decide) sg13 sg13895 + +lemma sg17637 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,6,2] := by + exact rowSquare_join (by decide) sg13 sg13896 + +lemma sg17638 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,7,7,1] := by + exact rowSquare_join (by decide) sg13 sg13897 + +lemma sg17639 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,3,2,1,1] := by + exact rowSquare_join (by decide) sg55 sg12487 + +lemma sg17640 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,3,2,2] := by + exact rowSquare_join (by decide) sg55 sg12488 + +lemma sg17641 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,3,3,1] := by + exact rowSquare_join (by decide) sg83 sg12349 + +lemma sg17642 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,4,1,1,1] := by + exact rowSquare_join (by decide) sg55 sg12489 + +lemma sg17643 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,4,2,1] := by + exact rowSquare_join (by decide) sg83 sg12350 + +lemma sg17644 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,4,3] := by + exact rowSquare_join (by decide) sg83 sg12351 + +lemma sg17645 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,5,1,1] := by + exact rowSquare_join (by decide) sg83 sg12352 + +lemma sg17646 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,5,2] := by + exact rowSquare_join (by decide) sg83 sg12353 + +lemma sg17647 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,6,1] := by + exact rowSquare_join (by decide) sg83 sg12354 + +lemma sg17648 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,8,7] := by + exact rowSquare_join (by decide) sg13 sg13898 + +lemma sg17649 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg14928 + +lemma sg17650 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14929 + +lemma sg17651 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg14930 + +lemma sg17652 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14931 + +lemma sg17653 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg14932 + +lemma sg17654 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg14933 + +lemma sg17655 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8 sg14121 + +lemma sg17656 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13899 + +lemma sg17657 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13900 + +lemma sg17658 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13901 + +lemma sg17659 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg14934 + +lemma sg17660 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg13652 + +lemma sg17661 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14935 + +lemma sg17662 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg15 sg13653 + +lemma sg17663 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg3403 sg4394 + +lemma sg17664 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1 sg14936 + +lemma sg17665 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg15 sg13654 + +lemma sg17666 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14937 + +lemma sg17667 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg14938 + +lemma sg17668 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg13759 + +lemma sg17669 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8 sg14122 + +lemma sg17670 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg14939 + +lemma sg17671 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg14940 + +lemma sg17672 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg14941 + +lemma sg17673 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13902 + +lemma sg17674 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13903 + +lemma sg17675 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13904 + +lemma sg17676 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13905 + +lemma sg17677 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg13906 + +lemma sg17678 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14942 + +lemma sg17679 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg15 sg13655 + +lemma sg17680 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg15 sg13656 + +lemma sg17681 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg15 sg13657 + +lemma sg17682 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg15 sg13658 + +lemma sg17683 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8 sg14123 + +lemma sg17684 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg14943 + +lemma sg17685 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg13659 + +lemma sg17686 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14944 + +lemma sg17687 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg15 sg13660 + +lemma sg17688 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg15 sg13661 + +lemma sg17689 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13907 + +lemma sg17690 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13908 + +lemma sg17691 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13909 + +lemma sg17692 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13910 + +lemma sg17693 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13911 + +lemma sg17694 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg13912 + +lemma sg17695 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14945 + +lemma sg17696 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg15 sg13663 + +lemma sg17697 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg15 sg13664 + +lemma sg17698 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg15 sg13665 + +lemma sg17699 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg14946 + +lemma sg17700 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13913 + +lemma sg17701 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13914 + +lemma sg17702 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13915 + +lemma sg17703 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13916 + +lemma sg17704 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13917 + +lemma sg17705 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13918 + +lemma sg17706 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13919 + +lemma sg17707 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg13920 + +lemma sg17708 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg13921 + +lemma sg17709 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg15 sg13671 + +lemma sg17710 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1 sg14947 + +lemma sg17711 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14948 + +lemma sg17712 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg14949 + +lemma sg17713 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg13760 + +lemma sg17714 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg14 sg13761 + +lemma sg17715 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14950 + +lemma sg17716 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg13762 + +lemma sg17717 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg13763 + +lemma sg17718 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14951 + +lemma sg17719 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg14 sg13764 + +lemma sg17720 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg13765 + +lemma sg17721 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13922 + +lemma sg17722 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13923 + +lemma sg17723 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13924 + +lemma sg17724 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13925 + +lemma sg17725 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13926 + +lemma sg17726 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg13927 + +lemma sg17727 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg13772 + +lemma sg17728 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg13773 + +lemma sg17729 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg14 sg13774 + +lemma sg17730 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg14 sg13775 + +lemma sg17731 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg14 sg13776 + +lemma sg17732 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13928 + +lemma sg17733 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13929 + +lemma sg17734 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14952 + +lemma sg17735 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg14953 + +lemma sg17736 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg14954 + +lemma sg17737 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg14955 + +lemma sg17738 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13930 + +lemma sg17739 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13931 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes43.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes43.lean index b442d434396286eca9e3c4146bcb3da14a215b23..791b9bdfe2ed9b660f8563be28fdd7bcde396013 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes43.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes43.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 - -namespace OAI - -/-! Semigroup Nodes 43. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg17740 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13932 - -lemma sg17741 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13933 - -lemma sg17742 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13934 - -lemma sg17743 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13935 - -lemma sg17744 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14956 - -lemma sg17745 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg1 sg14957 - -lemma sg17746 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg1 sg14958 - -lemma sg17747 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13936 - -lemma sg17748 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13937 - -lemma sg17749 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13938 - -lemma sg17750 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13939 - -lemma sg17751 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg13 sg13940 - -lemma sg17752 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg13941 - -lemma sg17753 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by - exact rowSquare_join (by decide) sg13 sg13942 - -lemma sg17754 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by - exact rowSquare_join (by decide) sg1 sg14959 - -lemma sg17755 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg14960 - -lemma sg17756 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13943 - -lemma sg17757 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14961 - -lemma sg17758 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg14962 - -lemma sg17759 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg14963 - -lemma sg17760 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13944 - -lemma sg17761 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg56 sg12469 - -lemma sg17762 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg13945 - -lemma sg17763 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg13946 - -lemma sg17764 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg1 sg14964 - -lemma sg17765 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by - exact rowSquare_join (by decide) sg83 sg12355 - -lemma sg17766 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13947 - -lemma sg17767 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg56 sg12470 - -lemma sg17768 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg56 sg12471 - -lemma sg17769 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg13948 - -lemma sg17770 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by - exact rowSquare_join (by decide) sg84 sg12341 - -lemma sg17771 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by - exact rowSquare_join (by decide) sg1 sg14965 - -lemma sg17772 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13949 - -lemma sg17773 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by - exact rowSquare_join (by decide) sg56 sg12472 - -lemma sg17774 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by - exact rowSquare_join (by decide) sg84 sg12342 - -lemma sg17775 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by - exact rowSquare_join (by decide) sg84 sg12343 - -lemma sg17776 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14966 - -lemma sg17777 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg13777 - -lemma sg17778 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14967 - -lemma sg17779 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg13780 - -lemma sg17780 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13950 - -lemma sg17781 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg13783 - -lemma sg17782 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg13786 - -lemma sg17783 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13951 - -lemma sg17784 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13952 - -lemma sg17785 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg13953 - -lemma sg17786 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg13954 - -lemma sg17787 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by - exact rowSquare_join (by decide) sg14 sg13795 - -lemma sg17788 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg13796 - -lemma sg17789 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13955 - -lemma sg17790 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg13800 - -lemma sg17791 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13956 - -lemma sg17792 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg13957 - -lemma sg17793 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg14 sg13810 - -lemma sg17794 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by - exact rowSquare_join (by decide) sg14 sg13811 - -lemma sg17795 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13958 - -lemma sg17796 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg56 sg12480 - -lemma sg17797 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg13959 - -lemma sg17798 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by - exact rowSquare_join (by decide) sg84 sg12344 - -lemma sg17799 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by - exact rowSquare_join (by decide) sg14 sg13818 - -lemma sg17800 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14968 - -lemma sg17801 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13960 - -lemma sg17802 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg14969 - -lemma sg17803 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13961 - -lemma sg17804 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg56 sg12483 - -lemma sg17805 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by - exact rowSquare_join (by decide) sg83 sg12356 - -lemma sg17806 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by - exact rowSquare_join (by decide) sg83 sg12357 - -lemma sg17807 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13962 - -lemma sg17808 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by - exact rowSquare_join (by decide) sg56 sg12484 - -lemma sg17809 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by - exact rowSquare_join (by decide) sg84 sg12345 - -lemma sg17810 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by - exact rowSquare_join (by decide) sg84 sg12346 - -lemma sg17811 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13963 - -lemma sg17812 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by - exact rowSquare_join (by decide) sg84 sg12347 - -lemma sg17813 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by - exact rowSquare_join (by decide) sg84 sg12348 - -lemma sg17814 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg13829 - -lemma sg17815 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13964 - -lemma sg17816 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg13965 - -lemma sg17817 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg14 sg13839 - -lemma sg17818 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,2] := by - exact rowSquare_join (by decide) sg14 sg13840 - -lemma sg17819 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg13848 - -lemma sg17820 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg57 sg12480 - -lemma sg17821 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg13966 - -lemma sg17822 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,4,1] := by - exact rowSquare_join (by decide) sg14 sg13854 - -lemma sg17823 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg13967 - -lemma sg17824 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,2] := by - exact rowSquare_join (by decide) sg13 sg13968 - -lemma sg17825 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,3,1] := by - exact rowSquare_join (by decide) sg13 sg13969 - -lemma sg17826 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,4] := by - exact rowSquare_join (by decide) sg13 sg13970 - -lemma sg17827 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg83 sg12366 - -lemma sg17828 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,2] := by - exact rowSquare_join (by decide) sg83 sg12367 - -lemma sg17829 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg55 sg12492 - -lemma sg17830 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,2] := by - exact rowSquare_join (by decide) sg83 sg12368 - -lemma sg17831 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,3,1] := by - exact rowSquare_join (by decide) sg83 sg12369 - -lemma sg17832 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,4] := by - exact rowSquare_join (by decide) sg83 sg12370 - -lemma sg17833 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13971 - -lemma sg17834 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,2,1] := by - exact rowSquare_join (by decide) sg13 sg13972 - -lemma sg17835 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,3] := by - exact rowSquare_join (by decide) sg13 sg13973 - -lemma sg17836 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,6,1,1] := by - exact rowSquare_join (by decide) sg13 sg13974 - -lemma sg17837 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,6,2] := by - exact rowSquare_join (by decide) sg13 sg13975 - -lemma sg17838 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3676 sg4117 - -lemma sg17839 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg13867 - -lemma sg17840 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13976 - -lemma sg17841 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3676 sg4118 - -lemma sg17842 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg13870 - -lemma sg17843 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg13871 - -lemma sg17844 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg14 sg13872 - -lemma sg17845 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4484 - -lemma sg17846 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13977 - -lemma sg17847 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg13978 - -lemma sg17848 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg14 sg13877 - -lemma sg17849 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg13878 - -lemma sg17850 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13979 - -lemma sg17851 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg13980 - -lemma sg17852 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg13981 - -lemma sg17853 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg13982 - -lemma sg17854 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,4,1] := by - exact rowSquare_join (by decide) sg14 sg13883 - -lemma sg17855 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14970 - -lemma sg17856 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg14971 - -lemma sg17857 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8 sg14125 - -lemma sg17858 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13983 - -lemma sg17859 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14972 - -lemma sg17860 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg15 sg13679 - -lemma sg17861 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8 sg14126 - -lemma sg17862 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8 sg14127 - -lemma sg17863 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14973 - -lemma sg17864 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13985 - -lemma sg17865 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14974 - -lemma sg17866 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg15 sg13689 - -lemma sg17867 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg14975 - -lemma sg17868 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13987 - -lemma sg17869 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13988 - -lemma sg17870 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg15 sg13700 - -lemma sg17871 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg13991 - -lemma sg17872 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg13 sg13992 - -lemma sg17873 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg13993 - -lemma sg17874 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg84 sg12355 - -lemma sg17875 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg15 sg13708 - -lemma sg17876 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,4,4,3] := by - exact rowSquare_join (by decide) sg14 sg13921 - -lemma sg17877 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg13997 - -lemma sg17878 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg15 sg13732 - -lemma sg17879 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,4,4,2] := by - exact rowSquare_join (by decide) sg15 sg13733 - -lemma sg17880 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg56 sg12490 - -lemma sg17881 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,3,2] := by - exact rowSquare_join (by decide) sg84 sg12356 - -lemma sg17882 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,4,1] := by - exact rowSquare_join (by decide) sg84 sg12357 - -lemma sg17883 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,5] := by - exact rowSquare_join (by decide) sg15 sg13739 - -lemma sg17884 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,3,3,3] := by - exact rowSquare_join (by decide) sg83 sg12394 - -lemma sg17885 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg84 sg12358 - -lemma sg17886 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,4,3,2] := by - exact rowSquare_join (by decide) sg84 sg12359 - -lemma sg17887 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,4,4,1] := by - exact rowSquare_join (by decide) sg83 sg12396 - -lemma sg17888 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12360 - -lemma sg17889 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,2,2] := by - exact rowSquare_join (by decide) sg84 sg12361 - -lemma sg17890 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,3,1] := by - exact rowSquare_join (by decide) sg84 sg12362 - -lemma sg17891 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,4] := by - exact rowSquare_join (by decide) sg84 sg12363 - -lemma sg17892 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg56 sg12491 - -lemma sg17893 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,6,2,1] := by - exact rowSquare_join (by decide) sg84 sg12364 - -lemma sg17894 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,6,3] := by - exact rowSquare_join (by decide) sg84 sg12365 - -lemma sg17895 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,4,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg13999 - -lemma sg17896 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg14 sg13941 - -lemma sg17897 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,4,4,4,2] := by - exact rowSquare_join (by decide) sg14 sg13942 - -lemma sg17898 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,3,3,3] := by - exact rowSquare_join (by decide) sg83 sg12397 - -lemma sg17899 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg84 sg12366 - -lemma sg17900 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,4,3,2] := by - exact rowSquare_join (by decide) sg84 sg12367 - -lemma sg17901 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,4,4,1] := by - exact rowSquare_join (by decide) sg85 sg12341 - -lemma sg17902 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg56 sg12492 - -lemma sg17903 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,5,2,2] := by - exact rowSquare_join (by decide) sg84 sg12368 - -lemma sg17904 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,5,3,1] := by - exact rowSquare_join (by decide) sg84 sg12369 - -lemma sg17905 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,5,4] := by - exact rowSquare_join (by decide) sg84 sg12370 - -lemma sg17906 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg83 sg12399 - -lemma sg17907 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,3,3,2] := by - exact rowSquare_join (by decide) sg295 sg11062 - -lemma sg17908 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12371 - -lemma sg17909 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,4,2,2] := by - exact rowSquare_join (by decide) sg295 sg11063 - -lemma sg17910 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,4,3,1] := by - exact rowSquare_join (by decide) sg295 sg11064 - -lemma sg17911 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,4,4] := by - exact rowSquare_join (by decide) sg83 sg12404 - -lemma sg17912 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12374 - -lemma sg17913 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,5,2,1] := by - exact rowSquare_join (by decide) sg295 sg11065 - -lemma sg17914 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,5,3] := by - exact rowSquare_join (by decide) sg84 sg12376 - -lemma sg17915 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,6,1,1] := by - exact rowSquare_join (by decide) sg295 sg11066 - -lemma sg17916 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,6,2] := by - exact rowSquare_join (by decide) sg84 sg12378 - -lemma sg17917 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,4,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg13957 - -lemma sg17918 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg56 sg12495 - -lemma sg17919 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,4,4,3,2] := by - exact rowSquare_join (by decide) sg84 sg12379 - -lemma sg17920 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,4,4,4,1] := by - exact rowSquare_join (by decide) sg85 sg12344 - -lemma sg17921 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg83 sg12409 - -lemma sg17922 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,3,3,2] := by - exact rowSquare_join (by decide) sg295 sg11067 - -lemma sg17923 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12380 - -lemma sg17924 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,4,2,2] := by - exact rowSquare_join (by decide) sg295 sg11068 - -lemma sg17925 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,4,3,1] := by - exact rowSquare_join (by decide) sg295 sg11069 - -lemma sg17926 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,4,4] := by - exact rowSquare_join (by decide) sg57 sg12493 - -lemma sg17927 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg56 sg12496 - -lemma sg17928 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,5,2,1] := by - exact rowSquare_join (by decide) sg295 sg11070 - -lemma sg17929 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,5,3] := by - exact rowSquare_join (by decide) sg84 sg12384 - -lemma sg17930 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12385 - -lemma sg17931 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,3,2,2] := by - exact rowSquare_join (by decide) sg295 sg11071 - -lemma sg17932 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,3,3,1] := by - exact rowSquare_join (by decide) sg295 sg11072 - -lemma sg17933 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12387 - -lemma sg17934 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,4,2,1] := by - exact rowSquare_join (by decide) sg295 sg11073 - -lemma sg17935 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,4,3] := by - exact rowSquare_join (by decide) sg296 sg11069 - -lemma sg17936 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,5,1,1] := by - exact rowSquare_join (by decide) sg295 sg11074 - -lemma sg17937 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,5,2] := by - exact rowSquare_join (by decide) sg296 sg11070 - -lemma sg17938 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,6,1] := by - exact rowSquare_join (by decide) sg297 sg11070 - -lemma sg17939 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,3,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg13965 - -lemma sg17940 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg57 sg12495 - -lemma sg17941 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,4,3,3,2] := by - exact rowSquare_join (by decide) sg295 sg11076 - -lemma sg17942 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14000 - -lemma sg17943 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,4,4,2,2] := by - exact rowSquare_join (by decide) sg295 sg11077 - -lemma sg17944 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,4,4,3,1] := by - exact rowSquare_join (by decide) sg295 sg11078 - -lemma sg17945 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,4,4,4] := by - exact rowSquare_join (by decide) sg14 sg13970 - -lemma sg17946 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg13978 - -lemma sg17947 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14001 - -lemma sg17948 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg14 sg13981 - -lemma sg17949 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,3,3,3,2] := by - exact rowSquare_join (by decide) sg295 sg11080 - -lemma sg17950 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg55 sg12505 - -lemma sg17951 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14002 - -lemma sg17952 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,3,2,2] := by - exact rowSquare_join (by decide) sg295 sg11081 - -lemma sg17953 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,3,3,1] := by - exact rowSquare_join (by decide) sg295 sg11082 - -lemma sg17954 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14003 - -lemma sg17955 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,4,2,1] := by - exact rowSquare_join (by decide) sg295 sg11083 - -lemma sg17956 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,4,3] := by - exact rowSquare_join (by decide) sg13 sg14004 - -lemma sg17957 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg15 sg13765 - -lemma sg17958 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg14005 - -lemma sg17959 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg15 sg13774 - -lemma sg17960 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg15 sg13775 - -lemma sg17961 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg15 sg13776 - -lemma sg17962 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg13984 - -lemma sg17963 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg15 sg13786 - -lemma sg17964 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14006 - -lemma sg17965 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg14007 - -lemma sg17966 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg15 sg13794 - -lemma sg17967 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg15 sg13795 - -lemma sg17968 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg15 sg13802 - -lemma sg17969 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg15 sg13803 - -lemma sg17970 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg56 sg12497 - -lemma sg17971 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg84 sg12393 - -lemma sg17972 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,4,3,3] := by - exact rowSquare_join (by decide) sg84 sg12394 - -lemma sg17973 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg15 sg13810 - -lemma sg17974 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,4,4,2] := by - exact rowSquare_join (by decide) sg15 sg13811 - -lemma sg17975 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg56 sg12498 - -lemma sg17976 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg56 sg12499 - -lemma sg17977 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,5,3,2] := by - exact rowSquare_join (by decide) sg84 sg12395 - -lemma sg17978 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,5,4,1] := by - exact rowSquare_join (by decide) sg84 sg12396 - -lemma sg17979 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,5,5] := by - exact rowSquare_join (by decide) sg15 sg13818 - -lemma sg17980 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg13986 - -lemma sg17981 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg13989 - -lemma sg17982 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg14 sg13990 - -lemma sg17983 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg56 sg12500 - -lemma sg17984 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg14008 - -lemma sg17985 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,4,3,3] := by - exact rowSquare_join (by decide) sg84 sg12397 - -lemma sg17986 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg14 sg13993 - -lemma sg17987 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,4,4,2] := by - exact rowSquare_join (by decide) sg85 sg12355 - -lemma sg17988 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg56 sg12501 - -lemma sg17989 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg83 sg12428 - -lemma sg17990 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,3,3,3] := by - exact rowSquare_join (by decide) sg295 sg11085 - -lemma sg17991 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg84 sg12398 - -lemma sg17992 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg84 sg12399 - -lemma sg17993 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,4,3,2] := by - exact rowSquare_join (by decide) sg295 sg11086 - -lemma sg17994 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,4,4,1] := by - exact rowSquare_join (by decide) sg295 sg11087 - -lemma sg17995 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12401 - -lemma sg17996 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,5,2,2] := by - exact rowSquare_join (by decide) sg295 sg11088 - -lemma sg17997 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,5,3,1] := by - exact rowSquare_join (by decide) sg295 sg11089 - -lemma sg17998 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,5,4] := by - exact rowSquare_join (by decide) sg84 sg12404 - -lemma sg17999 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg239 sg11140 - -lemma sg18000 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg239 sg11141 - -lemma sg18001 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg239 sg11142 - -lemma sg18002 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,3,3,2] := by - exact rowSquare_join (by decide) sg298 sg11062 - -lemma sg18003 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12406 - -lemma sg18004 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,4,2,2] := by - exact rowSquare_join (by decide) sg298 sg11063 - -lemma sg18005 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,4,3,1] := by - exact rowSquare_join (by decide) sg298 sg11064 - -lemma sg18006 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,4,4] := by - exact rowSquare_join (by decide) sg762 sg8020 - -lemma sg18007 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12408 - -lemma sg18008 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,5,2,1] := by - exact rowSquare_join (by decide) sg298 sg11065 - -lemma sg18009 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,5,3] := by - exact rowSquare_join (by decide) sg762 sg8021 - -lemma sg18010 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,6,1,1] := by - exact rowSquare_join (by decide) sg298 sg11066 - -lemma sg18011 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,6,2] := by - exact rowSquare_join (by decide) sg762 sg8022 - -lemma sg18012 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg13994 - -lemma sg18013 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg14 sg13995 - -lemma sg18014 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg56 sg12502 - -lemma sg18015 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg14 sg13996 - -lemma sg18016 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,3,3,3] := by - exact rowSquare_join (by decide) sg295 sg11090 - -lemma sg18017 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg56 sg12503 - -lemma sg18018 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg84 sg12409 - -lemma sg18019 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,4,3,2] := by - exact rowSquare_join (by decide) sg295 sg11091 - -lemma sg18020 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,4,4,1] := by - exact rowSquare_join (by decide) sg295 sg11092 - -lemma sg18021 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,8,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg56 sg12504 - -lemma sg18022 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,8,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg14 sg13998 - -lemma sg18023 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,8,3,3,3,3] := by - exact rowSquare_join (by decide) sg295 sg11093 - -lemma sg18024 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,8,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg239 sg11146 - -lemma sg18025 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,8,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg240 sg11144 - -lemma sg18026 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,8,4,4,4] := by - exact rowSquare_join (by decide) sg762 sg8023 - -lemma sg18027 : RowSquare [6,6,3,3,2,2,2,2,2,2,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg993 sg8780 - -lemma sg18028 : RowSquare [6,6,3,3,2,2,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg993 sg8781 - -lemma sg18029 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg14013 - -lemma sg18030 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by - exact rowSquare_join (by decide) sg2624 sg4949 - -lemma sg18031 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by - exact rowSquare_join (by decide) sg3318 sg4438 - -lemma sg18032 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by - exact rowSquare_join (by decide) sg3554 sg4186 - -lemma sg18033 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by - exact rowSquare_join (by decide) sg3675 sg4034 - -lemma sg18034 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by - exact rowSquare_join (by decide) sg26 sg12822 - -lemma sg18035 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by - exact rowSquare_join (by decide) sg13 sg14016 - -lemma sg18036 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by - exact rowSquare_join (by decide) sg13 sg14017 - -lemma sg18037 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg3556 sg4186 - -lemma sg18038 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg14 sg14013 - -lemma sg18039 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by - exact rowSquare_join (by decide) sg3679 sg4034 - -lemma sg18040 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by - exact rowSquare_join (by decide) sg13 sg14019 - -lemma sg18041 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by - exact rowSquare_join (by decide) sg3556 sg4187 - -lemma sg18042 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by - exact rowSquare_join (by decide) sg13 sg14020 - -lemma sg18043 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by - exact rowSquare_join (by decide) sg13 sg14021 - -lemma sg18044 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by - exact rowSquare_join (by decide) sg13 sg14022 - -lemma sg18045 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by - exact rowSquare_join (by decide) sg55 sg12509 - -lemma sg18046 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by - exact rowSquare_join (by decide) sg3319 sg4438 - -lemma sg18047 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg55 sg12514 - -lemma sg18048 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg1757 sg6491 - -lemma sg18049 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by - exact rowSquare_join (by decide) sg1675 sg6507 - -lemma sg18050 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg15 sg14010 - -lemma sg18051 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg1 sg14986 - -lemma sg18052 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg1 sg14987 - -lemma sg18053 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg26 sg12823 - -lemma sg18054 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg1 sg14988 - -lemma sg18055 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg13 sg14023 - -lemma sg18056 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg1 sg14989 - -lemma sg18057 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg1 sg14990 - -lemma sg18058 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg14024 - -lemma sg18059 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg14 sg14014 - -lemma sg18060 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg27 sg12823 - -lemma sg18061 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg14991 - -lemma sg18062 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by - exact rowSquare_join (by decide) sg26 sg12824 - -lemma sg18063 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1 sg14992 - -lemma sg18064 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg1 sg14993 - -lemma sg18065 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by - exact rowSquare_join (by decide) sg1 sg14994 - -lemma sg18066 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by - exact rowSquare_join (by decide) sg26 sg12825 - -lemma sg18067 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by - exact rowSquare_join (by decide) sg165 sg11584 - -lemma sg18068 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by - exact rowSquare_join (by decide) sg56 sg12514 - -lemma sg18069 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg14015 - -lemma sg18070 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg26 sg12826 - -lemma sg18071 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by - exact rowSquare_join (by decide) sg2640 sg4934 - -lemma sg18072 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by - exact rowSquare_join (by decide) sg27 sg12824 - -lemma sg18073 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by - exact rowSquare_join (by decide) sg26 sg12827 - -lemma sg18074 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by - exact rowSquare_join (by decide) sg26 sg12828 - -lemma sg18075 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by - exact rowSquare_join (by decide) sg165 sg11585 - -lemma sg18076 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by - exact rowSquare_join (by decide) sg55 sg12521 - -lemma sg18077 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by - exact rowSquare_join (by decide) sg166 sg11584 - -lemma sg18078 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg14018 - -lemma sg18079 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg27 sg12826 - -lemma sg18080 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14025 - -lemma sg18081 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg14026 - -lemma sg18082 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by - exact rowSquare_join (by decide) sg3679 sg4035 - -lemma sg18083 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg15 sg14011 - -lemma sg18084 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg15 sg14012 - -lemma sg18085 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg26 sg12829 - -lemma sg18086 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg1 sg14995 - -lemma sg18087 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg28 sg12823 - -lemma sg18088 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg14996 - -lemma sg18089 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg26 sg12830 - -lemma sg18090 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg15 sg14013 - -lemma sg18091 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg165 sg11586 - -lemma sg18092 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg27 sg12829 - -lemma sg18093 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg14 sg14023 - -lemma sg18094 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg27 sg12830 - -lemma sg18095 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg56 sg12521 - -lemma sg18096 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by - exact rowSquare_join (by decide) sg165 sg11587 - -lemma sg18097 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by - exact rowSquare_join (by decide) sg55 sg12535 - -lemma sg18098 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by - exact rowSquare_join (by decide) sg168 sg11584 - -lemma sg18099 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg14024 - -lemma sg18100 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by - exact rowSquare_join (by decide) sg29 sg12824 - -lemma sg18101 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by - exact rowSquare_join (by decide) sg166 sg11587 - -lemma sg18102 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,4,1] := by - exact rowSquare_join (by decide) sg295 sg11097 - -lemma sg18103 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg26 sg12831 - -lemma sg18104 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by - exact rowSquare_join (by decide) sg3556 sg3992 - -lemma sg18105 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg165 sg11588 - -lemma sg18106 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg3556 sg3993 - -lemma sg18107 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [8,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3 sg14699 - -lemma sg18108 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg1 sg15003 - -lemma sg18109 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg165 sg11590 - -lemma sg18110 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by - exact rowSquare_join (by decide) sg165 sg11592 - -lemma sg18111 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg14030 - -lemma sg18112 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4918 - -lemma sg18113 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2704 sg4918 - -lemma sg18114 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4924 - -lemma sg18115 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg5755 - -lemma sg18116 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2252 sg5755 - -lemma sg18117 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3622 sg4164 - -lemma sg18118 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg3623 sg4167 - -lemma sg18119 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg3615 sg4168 - -lemma sg18120 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3626 sg4166 - -lemma sg18121 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3630 sg4162 - -lemma sg18122 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by - exact rowSquare_join (by decide) sg3620 sg4173 - -lemma sg18123 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14647 - -lemma sg18124 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,2,1] := by - exact rowSquare_join (by decide) sg4 sg14648 - -lemma sg18125 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,3] := by - exact rowSquare_join (by decide) sg3620 sg4174 - -lemma sg18126 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14031 - -lemma sg18127 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14032 - -lemma sg18128 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg3622 sg4171 - -lemma sg18129 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,2,1] := by - exact rowSquare_join (by decide) sg3621 sg4172 - -lemma sg18130 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by - exact rowSquare_join (by decide) sg13 sg14033 - -lemma sg18131 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by - exact rowSquare_join (by decide) sg3622 sg4172 - -lemma sg18132 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by - exact rowSquare_join (by decide) sg13 sg14034 - -lemma sg18133 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by - exact rowSquare_join (by decide) sg3622 sg4174 - -lemma sg18134 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,4] := by - exact rowSquare_join (by decide) sg0 sg15551 - -lemma sg18135 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by - exact rowSquare_join (by decide) sg0 sg15552 - -lemma sg18136 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by - exact rowSquare_join (by decide) sg0 sg15553 - -lemma sg18137 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg4 sg14651 - -lemma sg18138 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,2,1] := by - exact rowSquare_join (by decide) sg39 sg12766 - -lemma sg18139 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg14036 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 + +namespace OAI + +/-! Semigroup Nodes 43. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg17740 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13932 + +lemma sg17741 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13933 + +lemma sg17742 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13934 + +lemma sg17743 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13935 + +lemma sg17744 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14956 + +lemma sg17745 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg1 sg14957 + +lemma sg17746 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg1 sg14958 + +lemma sg17747 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13936 + +lemma sg17748 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13937 + +lemma sg17749 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13938 + +lemma sg17750 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13939 + +lemma sg17751 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg13 sg13940 + +lemma sg17752 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg13941 + +lemma sg17753 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by + exact rowSquare_join (by decide) sg13 sg13942 + +lemma sg17754 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by + exact rowSquare_join (by decide) sg1 sg14959 + +lemma sg17755 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg14960 + +lemma sg17756 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13943 + +lemma sg17757 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14961 + +lemma sg17758 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg14962 + +lemma sg17759 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg14963 + +lemma sg17760 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13944 + +lemma sg17761 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg56 sg12469 + +lemma sg17762 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg13945 + +lemma sg17763 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg13946 + +lemma sg17764 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg1 sg14964 + +lemma sg17765 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by + exact rowSquare_join (by decide) sg83 sg12355 + +lemma sg17766 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13947 + +lemma sg17767 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg56 sg12470 + +lemma sg17768 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg56 sg12471 + +lemma sg17769 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg13948 + +lemma sg17770 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by + exact rowSquare_join (by decide) sg84 sg12341 + +lemma sg17771 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by + exact rowSquare_join (by decide) sg1 sg14965 + +lemma sg17772 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13949 + +lemma sg17773 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by + exact rowSquare_join (by decide) sg56 sg12472 + +lemma sg17774 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by + exact rowSquare_join (by decide) sg84 sg12342 + +lemma sg17775 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by + exact rowSquare_join (by decide) sg84 sg12343 + +lemma sg17776 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14966 + +lemma sg17777 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg13777 + +lemma sg17778 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14967 + +lemma sg17779 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg13780 + +lemma sg17780 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13950 + +lemma sg17781 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg13783 + +lemma sg17782 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg13786 + +lemma sg17783 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13951 + +lemma sg17784 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13952 + +lemma sg17785 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg13953 + +lemma sg17786 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg13954 + +lemma sg17787 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by + exact rowSquare_join (by decide) sg14 sg13795 + +lemma sg17788 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg13796 + +lemma sg17789 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13955 + +lemma sg17790 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg13800 + +lemma sg17791 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13956 + +lemma sg17792 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg13957 + +lemma sg17793 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg14 sg13810 + +lemma sg17794 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by + exact rowSquare_join (by decide) sg14 sg13811 + +lemma sg17795 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13958 + +lemma sg17796 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg56 sg12480 + +lemma sg17797 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg13959 + +lemma sg17798 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by + exact rowSquare_join (by decide) sg84 sg12344 + +lemma sg17799 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by + exact rowSquare_join (by decide) sg14 sg13818 + +lemma sg17800 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14968 + +lemma sg17801 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13960 + +lemma sg17802 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg14969 + +lemma sg17803 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13961 + +lemma sg17804 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg56 sg12483 + +lemma sg17805 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by + exact rowSquare_join (by decide) sg83 sg12356 + +lemma sg17806 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by + exact rowSquare_join (by decide) sg83 sg12357 + +lemma sg17807 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13962 + +lemma sg17808 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by + exact rowSquare_join (by decide) sg56 sg12484 + +lemma sg17809 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by + exact rowSquare_join (by decide) sg84 sg12345 + +lemma sg17810 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by + exact rowSquare_join (by decide) sg84 sg12346 + +lemma sg17811 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13963 + +lemma sg17812 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by + exact rowSquare_join (by decide) sg84 sg12347 + +lemma sg17813 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by + exact rowSquare_join (by decide) sg84 sg12348 + +lemma sg17814 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg13829 + +lemma sg17815 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13964 + +lemma sg17816 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg13965 + +lemma sg17817 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg14 sg13839 + +lemma sg17818 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,2] := by + exact rowSquare_join (by decide) sg14 sg13840 + +lemma sg17819 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg13848 + +lemma sg17820 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg57 sg12480 + +lemma sg17821 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg13966 + +lemma sg17822 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,4,4,1] := by + exact rowSquare_join (by decide) sg14 sg13854 + +lemma sg17823 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg13967 + +lemma sg17824 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,2] := by + exact rowSquare_join (by decide) sg13 sg13968 + +lemma sg17825 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,3,1] := by + exact rowSquare_join (by decide) sg13 sg13969 + +lemma sg17826 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,5,5,4] := by + exact rowSquare_join (by decide) sg13 sg13970 + +lemma sg17827 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg83 sg12366 + +lemma sg17828 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,2] := by + exact rowSquare_join (by decide) sg83 sg12367 + +lemma sg17829 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg55 sg12492 + +lemma sg17830 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,2] := by + exact rowSquare_join (by decide) sg83 sg12368 + +lemma sg17831 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,3,1] := by + exact rowSquare_join (by decide) sg83 sg12369 + +lemma sg17832 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,4,4] := by + exact rowSquare_join (by decide) sg83 sg12370 + +lemma sg17833 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13971 + +lemma sg17834 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,2,1] := by + exact rowSquare_join (by decide) sg13 sg13972 + +lemma sg17835 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,5,3] := by + exact rowSquare_join (by decide) sg13 sg13973 + +lemma sg17836 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,6,1,1] := by + exact rowSquare_join (by decide) sg13 sg13974 + +lemma sg17837 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,8,6,6,2] := by + exact rowSquare_join (by decide) sg13 sg13975 + +lemma sg17838 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3676 sg4117 + +lemma sg17839 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg13867 + +lemma sg17840 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13976 + +lemma sg17841 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3676 sg4118 + +lemma sg17842 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg13870 + +lemma sg17843 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg13871 + +lemma sg17844 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg14 sg13872 + +lemma sg17845 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4484 + +lemma sg17846 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13977 + +lemma sg17847 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg13978 + +lemma sg17848 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg14 sg13877 + +lemma sg17849 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg13878 + +lemma sg17850 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13979 + +lemma sg17851 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg13980 + +lemma sg17852 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg13981 + +lemma sg17853 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg13982 + +lemma sg17854 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,4,1] := by + exact rowSquare_join (by decide) sg14 sg13883 + +lemma sg17855 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14970 + +lemma sg17856 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg14971 + +lemma sg17857 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8 sg14125 + +lemma sg17858 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13983 + +lemma sg17859 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14972 + +lemma sg17860 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg15 sg13679 + +lemma sg17861 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8 sg14126 + +lemma sg17862 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8 sg14127 + +lemma sg17863 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14973 + +lemma sg17864 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13985 + +lemma sg17865 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14974 + +lemma sg17866 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg15 sg13689 + +lemma sg17867 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg14975 + +lemma sg17868 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13987 + +lemma sg17869 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13988 + +lemma sg17870 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg15 sg13700 + +lemma sg17871 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg13991 + +lemma sg17872 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg13 sg13992 + +lemma sg17873 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg13993 + +lemma sg17874 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg84 sg12355 + +lemma sg17875 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg15 sg13708 + +lemma sg17876 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,4,4,4,3] := by + exact rowSquare_join (by decide) sg14 sg13921 + +lemma sg17877 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg13997 + +lemma sg17878 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg15 sg13732 + +lemma sg17879 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,4,4,2] := by + exact rowSquare_join (by decide) sg15 sg13733 + +lemma sg17880 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg56 sg12490 + +lemma sg17881 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,3,2] := by + exact rowSquare_join (by decide) sg84 sg12356 + +lemma sg17882 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,4,1] := by + exact rowSquare_join (by decide) sg84 sg12357 + +lemma sg17883 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,5,5,5] := by + exact rowSquare_join (by decide) sg15 sg13739 + +lemma sg17884 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,3,3,3] := by + exact rowSquare_join (by decide) sg83 sg12394 + +lemma sg17885 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg84 sg12358 + +lemma sg17886 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,4,3,2] := by + exact rowSquare_join (by decide) sg84 sg12359 + +lemma sg17887 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,4,4,1] := by + exact rowSquare_join (by decide) sg83 sg12396 + +lemma sg17888 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12360 + +lemma sg17889 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,2,2] := by + exact rowSquare_join (by decide) sg84 sg12361 + +lemma sg17890 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,3,1] := by + exact rowSquare_join (by decide) sg84 sg12362 + +lemma sg17891 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,5,4] := by + exact rowSquare_join (by decide) sg84 sg12363 + +lemma sg17892 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg56 sg12491 + +lemma sg17893 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,6,2,1] := by + exact rowSquare_join (by decide) sg84 sg12364 + +lemma sg17894 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,6,6,6,3] := by + exact rowSquare_join (by decide) sg84 sg12365 + +lemma sg17895 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,4,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg13999 + +lemma sg17896 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg14 sg13941 + +lemma sg17897 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,4,4,4,2] := by + exact rowSquare_join (by decide) sg14 sg13942 + +lemma sg17898 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,3,3,3] := by + exact rowSquare_join (by decide) sg83 sg12397 + +lemma sg17899 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg84 sg12366 + +lemma sg17900 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,4,3,2] := by + exact rowSquare_join (by decide) sg84 sg12367 + +lemma sg17901 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,4,4,1] := by + exact rowSquare_join (by decide) sg85 sg12341 + +lemma sg17902 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg56 sg12492 + +lemma sg17903 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,5,2,2] := by + exact rowSquare_join (by decide) sg84 sg12368 + +lemma sg17904 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,5,3,1] := by + exact rowSquare_join (by decide) sg84 sg12369 + +lemma sg17905 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,5,5,4] := by + exact rowSquare_join (by decide) sg84 sg12370 + +lemma sg17906 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg83 sg12399 + +lemma sg17907 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,3,3,2] := by + exact rowSquare_join (by decide) sg295 sg11062 + +lemma sg17908 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12371 + +lemma sg17909 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,4,2,2] := by + exact rowSquare_join (by decide) sg295 sg11063 + +lemma sg17910 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,4,3,1] := by + exact rowSquare_join (by decide) sg295 sg11064 + +lemma sg17911 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,4,4] := by + exact rowSquare_join (by decide) sg83 sg12404 + +lemma sg17912 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12374 + +lemma sg17913 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,5,2,1] := by + exact rowSquare_join (by decide) sg295 sg11065 + +lemma sg17914 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,5,3] := by + exact rowSquare_join (by decide) sg84 sg12376 + +lemma sg17915 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,6,1,1] := by + exact rowSquare_join (by decide) sg295 sg11066 + +lemma sg17916 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,7,6,6,2] := by + exact rowSquare_join (by decide) sg84 sg12378 + +lemma sg17917 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,4,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg13957 + +lemma sg17918 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg56 sg12495 + +lemma sg17919 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,4,4,3,2] := by + exact rowSquare_join (by decide) sg84 sg12379 + +lemma sg17920 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,4,4,4,1] := by + exact rowSquare_join (by decide) sg85 sg12344 + +lemma sg17921 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg83 sg12409 + +lemma sg17922 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,3,3,2] := by + exact rowSquare_join (by decide) sg295 sg11067 + +lemma sg17923 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12380 + +lemma sg17924 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,4,2,2] := by + exact rowSquare_join (by decide) sg295 sg11068 + +lemma sg17925 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,4,3,1] := by + exact rowSquare_join (by decide) sg295 sg11069 + +lemma sg17926 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,4,4] := by + exact rowSquare_join (by decide) sg57 sg12493 + +lemma sg17927 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg56 sg12496 + +lemma sg17928 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,5,2,1] := by + exact rowSquare_join (by decide) sg295 sg11070 + +lemma sg17929 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,5,5,3] := by + exact rowSquare_join (by decide) sg84 sg12384 + +lemma sg17930 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12385 + +lemma sg17931 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,3,2,2] := by + exact rowSquare_join (by decide) sg295 sg11071 + +lemma sg17932 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,3,3,1] := by + exact rowSquare_join (by decide) sg295 sg11072 + +lemma sg17933 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12387 + +lemma sg17934 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,4,2,1] := by + exact rowSquare_join (by decide) sg295 sg11073 + +lemma sg17935 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,4,3] := by + exact rowSquare_join (by decide) sg296 sg11069 + +lemma sg17936 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,5,1,1] := by + exact rowSquare_join (by decide) sg295 sg11074 + +lemma sg17937 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,5,2] := by + exact rowSquare_join (by decide) sg296 sg11070 + +lemma sg17938 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,8,6,6,1] := by + exact rowSquare_join (by decide) sg297 sg11070 + +lemma sg17939 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,3,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg13965 + +lemma sg17940 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg57 sg12495 + +lemma sg17941 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,4,3,3,2] := by + exact rowSquare_join (by decide) sg295 sg11076 + +lemma sg17942 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14000 + +lemma sg17943 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,4,4,2,2] := by + exact rowSquare_join (by decide) sg295 sg11077 + +lemma sg17944 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,4,4,3,1] := by + exact rowSquare_join (by decide) sg295 sg11078 + +lemma sg17945 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,9,4,4,4] := by + exact rowSquare_join (by decide) sg14 sg13970 + +lemma sg17946 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg13978 + +lemma sg17947 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14001 + +lemma sg17948 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg14 sg13981 + +lemma sg17949 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,3,3,3,2] := by + exact rowSquare_join (by decide) sg295 sg11080 + +lemma sg17950 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg55 sg12505 + +lemma sg17951 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14002 + +lemma sg17952 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,3,2,2] := by + exact rowSquare_join (by decide) sg295 sg11081 + +lemma sg17953 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,3,3,1] := by + exact rowSquare_join (by decide) sg295 sg11082 + +lemma sg17954 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14003 + +lemma sg17955 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,4,2,1] := by + exact rowSquare_join (by decide) sg295 sg11083 + +lemma sg17956 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [10,10,4,4,3] := by + exact rowSquare_join (by decide) sg13 sg14004 + +lemma sg17957 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg15 sg13765 + +lemma sg17958 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg14005 + +lemma sg17959 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg15 sg13774 + +lemma sg17960 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg15 sg13775 + +lemma sg17961 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg15 sg13776 + +lemma sg17962 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg13984 + +lemma sg17963 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg15 sg13786 + +lemma sg17964 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14006 + +lemma sg17965 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg14007 + +lemma sg17966 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg15 sg13794 + +lemma sg17967 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg15 sg13795 + +lemma sg17968 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg15 sg13802 + +lemma sg17969 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg15 sg13803 + +lemma sg17970 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg56 sg12497 + +lemma sg17971 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg84 sg12393 + +lemma sg17972 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,4,3,3] := by + exact rowSquare_join (by decide) sg84 sg12394 + +lemma sg17973 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg15 sg13810 + +lemma sg17974 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,4,4,2] := by + exact rowSquare_join (by decide) sg15 sg13811 + +lemma sg17975 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg56 sg12498 + +lemma sg17976 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg56 sg12499 + +lemma sg17977 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,5,3,2] := by + exact rowSquare_join (by decide) sg84 sg12395 + +lemma sg17978 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,5,4,1] := by + exact rowSquare_join (by decide) sg84 sg12396 + +lemma sg17979 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,5,5,5,5] := by + exact rowSquare_join (by decide) sg15 sg13818 + +lemma sg17980 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg13986 + +lemma sg17981 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg13989 + +lemma sg17982 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg14 sg13990 + +lemma sg17983 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg56 sg12500 + +lemma sg17984 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg14008 + +lemma sg17985 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,4,3,3] := by + exact rowSquare_join (by decide) sg84 sg12397 + +lemma sg17986 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg14 sg13993 + +lemma sg17987 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,4,4,4,2] := by + exact rowSquare_join (by decide) sg85 sg12355 + +lemma sg17988 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg56 sg12501 + +lemma sg17989 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg83 sg12428 + +lemma sg17990 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,3,3,3] := by + exact rowSquare_join (by decide) sg295 sg11085 + +lemma sg17991 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg84 sg12398 + +lemma sg17992 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg84 sg12399 + +lemma sg17993 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,4,3,2] := by + exact rowSquare_join (by decide) sg295 sg11086 + +lemma sg17994 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,4,4,1] := by + exact rowSquare_join (by decide) sg295 sg11087 + +lemma sg17995 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12401 + +lemma sg17996 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,5,2,2] := by + exact rowSquare_join (by decide) sg295 sg11088 + +lemma sg17997 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,5,3,1] := by + exact rowSquare_join (by decide) sg295 sg11089 + +lemma sg17998 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,5,5,4] := by + exact rowSquare_join (by decide) sg84 sg12404 + +lemma sg17999 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg239 sg11140 + +lemma sg18000 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg239 sg11141 + +lemma sg18001 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg239 sg11142 + +lemma sg18002 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,3,3,2] := by + exact rowSquare_join (by decide) sg298 sg11062 + +lemma sg18003 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12406 + +lemma sg18004 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,4,2,2] := by + exact rowSquare_join (by decide) sg298 sg11063 + +lemma sg18005 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,4,3,1] := by + exact rowSquare_join (by decide) sg298 sg11064 + +lemma sg18006 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,4,4] := by + exact rowSquare_join (by decide) sg762 sg8020 + +lemma sg18007 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12408 + +lemma sg18008 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,5,2,1] := by + exact rowSquare_join (by decide) sg298 sg11065 + +lemma sg18009 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,5,3] := by + exact rowSquare_join (by decide) sg762 sg8021 + +lemma sg18010 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,6,1,1] := by + exact rowSquare_join (by decide) sg298 sg11066 + +lemma sg18011 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,6,6,6,2] := by + exact rowSquare_join (by decide) sg762 sg8022 + +lemma sg18012 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg13994 + +lemma sg18013 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg14 sg13995 + +lemma sg18014 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg56 sg12502 + +lemma sg18015 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg14 sg13996 + +lemma sg18016 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,3,3,3] := by + exact rowSquare_join (by decide) sg295 sg11090 + +lemma sg18017 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg56 sg12503 + +lemma sg18018 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg84 sg12409 + +lemma sg18019 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,4,3,2] := by + exact rowSquare_join (by decide) sg295 sg11091 + +lemma sg18020 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,7,4,4,4,1] := by + exact rowSquare_join (by decide) sg295 sg11092 + +lemma sg18021 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,8,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg56 sg12504 + +lemma sg18022 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,8,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg14 sg13998 + +lemma sg18023 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,8,3,3,3,3] := by + exact rowSquare_join (by decide) sg295 sg11093 + +lemma sg18024 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,8,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg239 sg11146 + +lemma sg18025 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,8,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg240 sg11144 + +lemma sg18026 : RowSquare [6,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [11,8,4,4,4] := by + exact rowSquare_join (by decide) sg762 sg8023 + +lemma sg18027 : RowSquare [6,6,3,3,2,2,2,2,2,2,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg993 sg8780 + +lemma sg18028 : RowSquare [6,6,3,3,2,2,2,2,2,2,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg993 sg8781 + +lemma sg18029 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg14013 + +lemma sg18030 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by + exact rowSquare_join (by decide) sg2624 sg4949 + +lemma sg18031 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by + exact rowSquare_join (by decide) sg3318 sg4438 + +lemma sg18032 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by + exact rowSquare_join (by decide) sg3554 sg4186 + +lemma sg18033 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by + exact rowSquare_join (by decide) sg3675 sg4034 + +lemma sg18034 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by + exact rowSquare_join (by decide) sg26 sg12822 + +lemma sg18035 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by + exact rowSquare_join (by decide) sg13 sg14016 + +lemma sg18036 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by + exact rowSquare_join (by decide) sg13 sg14017 + +lemma sg18037 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg3556 sg4186 + +lemma sg18038 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg14 sg14013 + +lemma sg18039 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by + exact rowSquare_join (by decide) sg3679 sg4034 + +lemma sg18040 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by + exact rowSquare_join (by decide) sg13 sg14019 + +lemma sg18041 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by + exact rowSquare_join (by decide) sg3556 sg4187 + +lemma sg18042 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by + exact rowSquare_join (by decide) sg13 sg14020 + +lemma sg18043 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by + exact rowSquare_join (by decide) sg13 sg14021 + +lemma sg18044 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by + exact rowSquare_join (by decide) sg13 sg14022 + +lemma sg18045 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by + exact rowSquare_join (by decide) sg55 sg12509 + +lemma sg18046 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by + exact rowSquare_join (by decide) sg3319 sg4438 + +lemma sg18047 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg55 sg12514 + +lemma sg18048 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg1757 sg6491 + +lemma sg18049 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by + exact rowSquare_join (by decide) sg1675 sg6507 + +lemma sg18050 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg15 sg14010 + +lemma sg18051 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg1 sg14986 + +lemma sg18052 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg1 sg14987 + +lemma sg18053 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg26 sg12823 + +lemma sg18054 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg1 sg14988 + +lemma sg18055 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg13 sg14023 + +lemma sg18056 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg1 sg14989 + +lemma sg18057 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg1 sg14990 + +lemma sg18058 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg14024 + +lemma sg18059 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg14 sg14014 + +lemma sg18060 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg27 sg12823 + +lemma sg18061 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg14991 + +lemma sg18062 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by + exact rowSquare_join (by decide) sg26 sg12824 + +lemma sg18063 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1 sg14992 + +lemma sg18064 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg1 sg14993 + +lemma sg18065 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by + exact rowSquare_join (by decide) sg1 sg14994 + +lemma sg18066 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by + exact rowSquare_join (by decide) sg26 sg12825 + +lemma sg18067 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by + exact rowSquare_join (by decide) sg165 sg11584 + +lemma sg18068 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by + exact rowSquare_join (by decide) sg56 sg12514 + +lemma sg18069 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg14015 + +lemma sg18070 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg26 sg12826 + +lemma sg18071 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by + exact rowSquare_join (by decide) sg2640 sg4934 + +lemma sg18072 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by + exact rowSquare_join (by decide) sg27 sg12824 + +lemma sg18073 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by + exact rowSquare_join (by decide) sg26 sg12827 + +lemma sg18074 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by + exact rowSquare_join (by decide) sg26 sg12828 + +lemma sg18075 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by + exact rowSquare_join (by decide) sg165 sg11585 + +lemma sg18076 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by + exact rowSquare_join (by decide) sg55 sg12521 + +lemma sg18077 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by + exact rowSquare_join (by decide) sg166 sg11584 + +lemma sg18078 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg14018 + +lemma sg18079 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg27 sg12826 + +lemma sg18080 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14025 + +lemma sg18081 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg14026 + +lemma sg18082 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by + exact rowSquare_join (by decide) sg3679 sg4035 + +lemma sg18083 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg15 sg14011 + +lemma sg18084 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg15 sg14012 + +lemma sg18085 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg26 sg12829 + +lemma sg18086 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg1 sg14995 + +lemma sg18087 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg28 sg12823 + +lemma sg18088 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg14996 + +lemma sg18089 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg26 sg12830 + +lemma sg18090 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg15 sg14013 + +lemma sg18091 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg165 sg11586 + +lemma sg18092 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg27 sg12829 + +lemma sg18093 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg14 sg14023 + +lemma sg18094 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg27 sg12830 + +lemma sg18095 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg56 sg12521 + +lemma sg18096 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by + exact rowSquare_join (by decide) sg165 sg11587 + +lemma sg18097 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by + exact rowSquare_join (by decide) sg55 sg12535 + +lemma sg18098 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by + exact rowSquare_join (by decide) sg168 sg11584 + +lemma sg18099 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg14024 + +lemma sg18100 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by + exact rowSquare_join (by decide) sg29 sg12824 + +lemma sg18101 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by + exact rowSquare_join (by decide) sg166 sg11587 + +lemma sg18102 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,4,1] := by + exact rowSquare_join (by decide) sg295 sg11097 + +lemma sg18103 : RowSquare [6,6,4,3,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg26 sg12831 + +lemma sg18104 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by + exact rowSquare_join (by decide) sg3556 sg3992 + +lemma sg18105 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg165 sg11588 + +lemma sg18106 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg3556 sg3993 + +lemma sg18107 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [8,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3 sg14699 + +lemma sg18108 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg1 sg15003 + +lemma sg18109 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg165 sg11590 + +lemma sg18110 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by + exact rowSquare_join (by decide) sg165 sg11592 + +lemma sg18111 : RowSquare [6,6,4,3,3,2,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg14030 + +lemma sg18112 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4918 + +lemma sg18113 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2704 sg4918 + +lemma sg18114 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4924 + +lemma sg18115 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg5755 + +lemma sg18116 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2252 sg5755 + +lemma sg18117 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3622 sg4164 + +lemma sg18118 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg3623 sg4167 + +lemma sg18119 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg3615 sg4168 + +lemma sg18120 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3626 sg4166 + +lemma sg18121 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3630 sg4162 + +lemma sg18122 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by + exact rowSquare_join (by decide) sg3620 sg4173 + +lemma sg18123 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14647 + +lemma sg18124 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,2,1] := by + exact rowSquare_join (by decide) sg4 sg14648 + +lemma sg18125 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,3] := by + exact rowSquare_join (by decide) sg3620 sg4174 + +lemma sg18126 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14031 + +lemma sg18127 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14032 + +lemma sg18128 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg3622 sg4171 + +lemma sg18129 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,2,1] := by + exact rowSquare_join (by decide) sg3621 sg4172 + +lemma sg18130 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by + exact rowSquare_join (by decide) sg13 sg14033 + +lemma sg18131 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by + exact rowSquare_join (by decide) sg3622 sg4172 + +lemma sg18132 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by + exact rowSquare_join (by decide) sg13 sg14034 + +lemma sg18133 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by + exact rowSquare_join (by decide) sg3622 sg4174 + +lemma sg18134 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,4] := by + exact rowSquare_join (by decide) sg0 sg15551 + +lemma sg18135 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by + exact rowSquare_join (by decide) sg0 sg15552 + +lemma sg18136 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by + exact rowSquare_join (by decide) sg0 sg15553 + +lemma sg18137 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg4 sg14651 + +lemma sg18138 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,2,1] := by + exact rowSquare_join (by decide) sg39 sg12766 + +lemma sg18139 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg14036 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes44.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes44.lean index a8b9244b0771b57f1e5c60e1209aea2abb4c8f9d..2875bd60060f0695508d979a892a13ca903c2b4b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes44.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes44.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 - -namespace OAI - -/-! Semigroup Nodes 44. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg18140 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by - exact rowSquare_join (by decide) sg16 sg13671 - -lemma sg18141 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by - exact rowSquare_join (by decide) sg4 sg14652 - -lemma sg18142 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14037 - -lemma sg18143 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15554 - -lemma sg18144 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,2,1] := by - exact rowSquare_join (by decide) sg39 sg12768 - -lemma sg18145 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by - exact rowSquare_join (by decide) sg13 sg14038 - -lemma sg18146 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by - exact rowSquare_join (by decide) sg39 sg12769 - -lemma sg18147 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by - exact rowSquare_join (by decide) sg39 sg12770 - -lemma sg18148 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by - exact rowSquare_join (by decide) sg39 sg12771 - -lemma sg18149 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg0 sg15555 - -lemma sg18150 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by - exact rowSquare_join (by decide) sg4 sg14653 - -lemma sg18151 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14040 - -lemma sg18152 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg14041 - -lemma sg18153 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg17 sg13671 - -lemma sg18154 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by - exact rowSquare_join (by decide) sg14 sg14034 - -lemma sg18155 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg12765 - -lemma sg18156 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,3] := by - exact rowSquare_join (by decide) sg4 sg14654 - -lemma sg18157 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14042 - -lemma sg18158 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14043 - -lemma sg18159 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14044 - -lemma sg18160 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg12767 - -lemma sg18161 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by - exact rowSquare_join (by decide) sg13 sg14045 - -lemma sg18162 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg40 sg12769 - -lemma sg18163 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by - exact rowSquare_join (by decide) sg40 sg12770 - -lemma sg18164 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by - exact rowSquare_join (by decide) sg40 sg12771 - -lemma sg18165 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14046 - -lemma sg18166 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14047 - -lemma sg18167 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14048 - -lemma sg18168 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by - exact rowSquare_join (by decide) sg13 sg14049 - -lemma sg18169 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by - exact rowSquare_join (by decide) sg13 sg14050 - -lemma sg18170 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by - exact rowSquare_join (by decide) sg13 sg14051 - -lemma sg18171 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3631 sg4164 - -lemma sg18172 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14656 - -lemma sg18173 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg14657 - -lemma sg18174 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3631 sg4167 - -lemma sg18175 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14052 - -lemma sg18176 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14053 - -lemma sg18177 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14658 - -lemma sg18178 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg14659 - -lemma sg18179 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,2] := by - exact rowSquare_join (by decide) sg4 sg14660 - -lemma sg18180 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg14661 - -lemma sg18181 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14054 - -lemma sg18182 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14055 - -lemma sg18183 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14056 - -lemma sg18184 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14057 - -lemma sg18185 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg14058 - -lemma sg18186 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg14059 - -lemma sg18187 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by - exact rowSquare_join (by decide) sg4 sg14662 - -lemma sg18188 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by - exact rowSquare_join (by decide) sg4 sg14663 - -lemma sg18189 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14060 - -lemma sg18190 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14664 - -lemma sg18191 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14061 - -lemma sg18192 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14062 - -lemma sg18193 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg14063 - -lemma sg18194 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg14064 - -lemma sg18195 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg4 sg14665 - -lemma sg18196 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14666 - -lemma sg18197 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14065 - -lemma sg18198 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg14066 - -lemma sg18199 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by - exact rowSquare_join (by decide) sg13 sg14067 - -lemma sg18200 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by - exact rowSquare_join (by decide) sg13 sg14068 - -lemma sg18201 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by - exact rowSquare_join (by decide) sg13 sg14069 - -lemma sg18202 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by - exact rowSquare_join (by decide) sg13 sg14070 - -lemma sg18203 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg14869 - -lemma sg18204 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14669 - -lemma sg18205 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg14649 - -lemma sg18206 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14071 - -lemma sg18207 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14072 - -lemma sg18208 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg2 sg14897 - -lemma sg18209 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg2 sg14900 - -lemma sg18210 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg14650 - -lemma sg18211 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14073 - -lemma sg18212 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14672 - -lemma sg18213 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14673 - -lemma sg18214 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg16 sg13689 - -lemma sg18215 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14074 - -lemma sg18216 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by - exact rowSquare_join (by decide) sg39 sg12775 - -lemma sg18217 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg5 sg14652 - -lemma sg18218 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14075 - -lemma sg18219 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14674 - -lemma sg18220 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14035 - -lemma sg18221 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by - exact rowSquare_join (by decide) sg17 sg13689 - -lemma sg18222 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg23 sg12861 - -lemma sg18223 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by - exact rowSquare_join (by decide) sg40 sg12775 - -lemma sg18224 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14076 - -lemma sg18225 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by - exact rowSquare_join (by decide) sg39 sg12785 - -lemma sg18226 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by - exact rowSquare_join (by decide) sg39 sg12787 - -lemma sg18227 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by - exact rowSquare_join (by decide) sg42 sg12771 - -lemma sg18228 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14675 - -lemma sg18229 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg14039 - -lemma sg18230 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg13709 - -lemma sg18231 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg17 sg13711 - -lemma sg18232 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14676 - -lemma sg18233 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14077 - -lemma sg18234 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg14669 - -lemma sg18235 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14078 - -lemma sg18236 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14677 - -lemma sg18237 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg13772 - -lemma sg18238 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14079 - -lemma sg18239 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14080 - -lemma sg18240 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg14071 - -lemma sg18241 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg13772 - -lemma sg18242 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg656 sg10867 - -lemma sg18243 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg658 sg10867 - -lemma sg18244 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg661 sg10867 - -lemma sg18245 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg662 sg10867 - -lemma sg18246 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg658 sg10871 - -lemma sg18247 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg658 sg10873 - -lemma sg18248 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg663 sg10867 - -lemma sg18249 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg664 sg10867 - -lemma sg18250 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg659 sg10868 - -lemma sg18251 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg665 sg10867 - -lemma sg18252 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg660 sg10868 - -lemma sg18253 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg661 sg10868 - -lemma sg18254 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg659 sg10869 - -lemma sg18255 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg666 sg10867 - -lemma sg18256 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg662 sg10868 - -lemma sg18257 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg661 sg10869 - -lemma sg18258 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg662 sg10869 - -lemma sg18259 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg667 sg10867 - -lemma sg18260 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg668 sg10867 - -lemma sg18261 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg663 sg10868 - -lemma sg18262 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg664 sg10868 - -lemma sg18263 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg669 sg10867 - -lemma sg18264 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg665 sg10868 - -lemma sg18265 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg664 sg10869 - -lemma sg18266 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg666 sg10868 - -lemma sg18267 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg665 sg10869 - -lemma sg18268 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg661 sg10875 - -lemma sg18269 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg666 sg10869 - -lemma sg18270 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg666 sg10870 - -lemma sg18271 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg662 sg10875 - -lemma sg18272 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg670 sg10867 - -lemma sg18273 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg671 sg10867 - -lemma sg18274 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg672 sg10867 - -lemma sg18275 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2626 sg4937 - -lemma sg18276 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2629 sg4940 - -lemma sg18277 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3354 sg4421 - -lemma sg18278 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14085 - -lemma sg18279 : RowSquare [7,6,3,2,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg11533 - -lemma sg18280 : RowSquare [7,6,3,2,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg11534 - -lemma sg18281 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2626 sg4877 - -lemma sg18282 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2626 sg4878 - -lemma sg18283 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3320 sg4162 - -lemma sg18284 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3320 sg4165 - -lemma sg18285 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2628 sg4877 - -lemma sg18286 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2628 sg4878 - -lemma sg18287 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3325 sg4163 - -lemma sg18288 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2635 sg4876 - -lemma sg18289 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg0 sg15597 - -lemma sg18290 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [6,6,5,5,5,4] := by - exact rowSquare_join (by decide) sg2640 sg4879 - -lemma sg18291 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,4,4,4,1] := by - exact rowSquare_join (by decide) sg4 sg14700 - -lemma sg18292 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by - exact rowSquare_join (by decide) sg3332 sg4173 - -lemma sg18293 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by - exact rowSquare_join (by decide) sg3732 sg3858 - -lemma sg18294 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg4 sg14702 - -lemma sg18295 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg0 sg15598 - -lemma sg18296 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,6,6,5] := by - exact rowSquare_join (by decide) sg13 sg14110 - -lemma sg18297 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg762 sg8076 - -lemma sg18298 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg271 sg11152 - -lemma sg18299 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,7,6,4] := by - exact rowSquare_join (by decide) sg762 sg8077 - -lemma sg18300 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by - exact rowSquare_join (by decide) sg271 sg11153 - -lemma sg18301 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by - exact rowSquare_join (by decide) sg490 sg8898 - -lemma sg18302 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,7,7,3] := by - exact rowSquare_join (by decide) sg490 sg8899 - -lemma sg18303 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg15 sg14089 - -lemma sg18304 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg14699 - -lemma sg18305 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg13 sg14112 - -lemma sg18306 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg4 sg14703 - -lemma sg18307 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,6,6,6,5] := by - exact rowSquare_join (by decide) sg762 sg8080 - -lemma sg18308 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by - exact rowSquare_join (by decide) sg14 sg14109 - -lemma sg18309 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,6,5,5] := by - exact rowSquare_join (by decide) sg762 sg8084 - -lemma sg18310 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,6,6,4] := by - exact rowSquare_join (by decide) sg762 sg8085 - -lemma sg18311 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,7,5,4] := by - exact rowSquare_join (by decide) sg841 sg8026 - -lemma sg18312 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,7,6,1,1,1] := by - exact rowSquare_join (by decide) sg839 sg8028 - -lemma sg18313 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,7,6,2,1] := by - exact rowSquare_join (by decide) sg840 sg8027 - -lemma sg18314 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,7,6,3] := by - exact rowSquare_join (by decide) sg841 sg8027 - -lemma sg18315 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,7,7,1,1] := by - exact rowSquare_join (by decide) sg840 sg8028 - -lemma sg18316 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,7,7,2] := by - exact rowSquare_join (by decide) sg841 sg8028 - -lemma sg18317 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,5,5,5] := by - exact rowSquare_join (by decide) sg762 sg8090 - -lemma sg18318 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,6,5,4] := by - exact rowSquare_join (by decide) sg841 sg8030 - -lemma sg18319 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg271 sg11160 - -lemma sg18320 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by - exact rowSquare_join (by decide) sg840 sg8031 - -lemma sg18321 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,6,6,3] := by - exact rowSquare_join (by decide) sg841 sg8031 - -lemma sg18322 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,4,4] := by - exact rowSquare_join (by decide) sg841 sg8032 - -lemma sg18323 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,5,1,1,1] := by - exact rowSquare_join (by decide) sg839 sg8034 - -lemma sg18324 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,5,2,1] := by - exact rowSquare_join (by decide) sg840 sg8033 - -lemma sg18325 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,5,3] := by - exact rowSquare_join (by decide) sg841 sg8033 - -lemma sg18326 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,6,1,1] := by - exact rowSquare_join (by decide) sg840 sg8034 - -lemma sg18327 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,6,2] := by - exact rowSquare_join (by decide) sg841 sg8034 - -lemma sg18328 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,7,1] := by - exact rowSquare_join (by decide) sg490 sg8903 - -lemma sg18329 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12465 - -lemma sg18330 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg11593 - -lemma sg18331 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg496 sg8896 - -lemma sg18332 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,2,2,2,1] := by - exact rowSquare_join (by decide) sg839 sg8035 - -lemma sg18333 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg496 sg8897 - -lemma sg18334 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,3,2,1,1] := by - exact rowSquare_join (by decide) sg839 sg8036 - -lemma sg18335 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,3,2,2] := by - exact rowSquare_join (by decide) sg840 sg8035 - -lemma sg18336 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,3,3,1] := by - exact rowSquare_join (by decide) sg841 sg8035 - -lemma sg18337 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,4,1,1,1] := by - exact rowSquare_join (by decide) sg839 sg8037 - -lemma sg18338 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,4,2,1] := by - exact rowSquare_join (by decide) sg840 sg8036 - -lemma sg18339 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,4,3] := by - exact rowSquare_join (by decide) sg841 sg8036 - -lemma sg18340 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,5,1,1] := by - exact rowSquare_join (by decide) sg840 sg8037 - -lemma sg18341 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,5,2] := by - exact rowSquare_join (by decide) sg841 sg8037 - -lemma sg18342 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,6,1] := by - exact rowSquare_join (by decide) sg490 sg8904 - -lemma sg18343 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,7] := by - exact rowSquare_join (by decide) sg271 sg11161 - -lemma sg18344 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg15 sg14090 - -lemma sg18345 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg15 sg14091 - -lemma sg18346 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg14092 - -lemma sg18347 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg43 sg12834 - -lemma sg18348 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg15 sg14093 - -lemma sg18349 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg14094 - -lemma sg18350 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg41 sg12837 - -lemma sg18351 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg41 sg12838 - -lemma sg18352 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg41 sg12839 - -lemma sg18353 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14116 - -lemma sg18354 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg84 sg12459 - -lemma sg18355 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12460 - -lemma sg18356 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg272 sg11154 - -lemma sg18357 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg39 sg12854 - -lemma sg18358 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg44 sg12833 - -lemma sg18359 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg14095 - -lemma sg18360 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg14096 - -lemma sg18361 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg15 sg14097 - -lemma sg18362 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg1 sg15058 - -lemma sg18363 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg6 sg14701 - -lemma sg18364 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg15 sg14098 - -lemma sg18365 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg14111 - -lemma sg18366 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg42 sg12837 - -lemma sg18367 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg42 sg12838 - -lemma sg18368 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg42 sg12839 - -lemma sg18369 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14117 - -lemma sg18370 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg40 sg12852 - -lemma sg18371 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg12853 - -lemma sg18372 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg272 sg11155 - -lemma sg18373 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg40 sg12854 - -lemma sg18374 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg116 sg11724 - -lemma sg18375 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12461 - -lemma sg18376 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg273 sg11154 - -lemma sg18377 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12462 - -lemma sg18378 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg272 sg11156 - -lemma sg18379 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg39 sg12856 - -lemma sg18380 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg12835 - -lemma sg18381 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg43 sg12836 - -lemma sg18382 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg15 sg14099 - -lemma sg18383 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg15 sg14100 - -lemma sg18384 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg15 sg14101 - -lemma sg18385 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg110 sg11727 - -lemma sg18386 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg242 sg11167 - -lemma sg18387 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg83 sg12466 - -lemma sg18388 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg455 sg8923 - -lemma sg18389 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12467 - -lemma sg18390 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg460 sg8912 - -lemma sg18391 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg41 sg12843 - -lemma sg18392 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1131 sg6707 - -lemma sg18393 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg456 sg8923 - -lemma sg18394 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg11594 - -lemma sg18395 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg455 sg8924 - -lemma sg18396 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg489 sg8905 - -lemma sg18397 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg460 sg8913 - -lemma sg18398 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg12844 - -lemma sg18399 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg762 sg8091 - -lemma sg18400 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg41 sg12845 - -lemma sg18401 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg41 sg12846 - -lemma sg18402 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg4 sg14704 - -lemma sg18403 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg11168 - -lemma sg18404 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg456 sg8924 - -lemma sg18405 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg11169 - -lemma sg18406 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg490 sg8905 - -lemma sg18407 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg277 sg11150 - -lemma sg18408 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg460 sg8914 - -lemma sg18409 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg762 sg8092 - -lemma sg18410 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg762 sg8093 - -lemma sg18411 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg84 sg12463 - -lemma sg18412 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg762 sg8094 - -lemma sg18413 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg15 sg14102 - -lemma sg18414 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14118 - -lemma sg18415 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg42 sg12840 - -lemma sg18416 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg42 sg12841 - -lemma sg18417 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg272 sg11157 - -lemma sg18418 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg42 sg12842 - -lemma sg18419 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg111 sg11727 - -lemma sg18420 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg240 sg11170 - -lemma sg18421 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg85 sg12453 - -lemma sg18422 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg455 sg8925 - -lemma sg18423 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg12855 - -lemma sg18424 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg460 sg8915 - -lemma sg18425 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg40 sg12856 - -lemma sg18426 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg116 sg11725 - -lemma sg18427 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg456 sg8925 - -lemma sg18428 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12464 - -lemma sg18429 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg457 sg8924 - -lemma sg18430 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg460 sg8916 - -lemma sg18431 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg460 sg8917 - -lemma sg18432 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg85 sg12454 - -lemma sg18433 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg762 sg8095 - -lemma sg18434 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg85 sg12455 - -lemma sg18435 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg85 sg12456 - -lemma sg18436 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg14 sg14112 - -lemma sg18437 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg239 sg11171 - -lemma sg18438 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg239 sg11172 - -lemma sg18439 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg458 sg8923 - -lemma sg18440 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12468 - -lemma sg18441 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg455 sg8926 - -lemma sg18442 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg838 sg8038 - -lemma sg18443 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg460 sg8918 - -lemma sg18444 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1131 sg6708 - -lemma sg18445 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1131 sg6709 - -lemma sg18446 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg243 sg11169 - -lemma sg18447 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8039 - -lemma sg18448 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg455 sg8927 - -lemma sg18449 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg489 sg8906 - -lemma sg18450 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg8040 - -lemma sg18451 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg762 sg8096 - -lemma sg18452 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg40 sg12857 - -lemma sg18453 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg11589 - -lemma sg18454 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8041 - -lemma sg18455 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg456 sg8927 - -lemma sg18456 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg8042 - -lemma sg18457 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg491 sg8900 - -lemma sg18458 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg491 sg8901 - -lemma sg18459 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg762 sg8097 - -lemma sg18460 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by - exact rowSquare_join (by decide) sg762 sg8098 - -lemma sg18461 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by - exact rowSquare_join (by decide) sg762 sg8099 - -lemma sg18462 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg239 sg11173 - -lemma sg18463 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg459 sg8923 - -lemma sg18464 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg11174 - -lemma sg18465 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg462 sg8912 - -lemma sg18466 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg11175 - -lemma sg18467 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg842 sg8024 - -lemma sg18468 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg455 sg8928 - -lemma sg18469 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg839 sg8038 - -lemma sg18470 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1131 sg6710 - -lemma sg18471 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg842 sg8025 - -lemma sg18472 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg1131 sg6711 - -lemma sg18473 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg842 sg8026 - -lemma sg18474 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg839 sg8039 - -lemma sg18475 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by - exact rowSquare_join (by decide) sg840 sg8038 - -lemma sg18476 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg839 sg8040 - -lemma sg18477 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by - exact rowSquare_join (by decide) sg763 sg8078 - -lemma sg18478 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1131 sg6712 - -lemma sg18479 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg842 sg8027 - -lemma sg18480 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg1131 sg6713 - -lemma sg18481 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg1131 sg6714 - -lemma sg18482 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by - exact rowSquare_join (by decide) sg840 sg8039 - -lemma sg18483 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by - exact rowSquare_join (by decide) sg840 sg8040 - -lemma sg18484 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,5] := by - exact rowSquare_join (by decide) sg841 sg8040 - -lemma sg18485 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg842 sg8028 - -lemma sg18486 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg764 sg8079 - -lemma sg18487 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by - exact rowSquare_join (by decide) sg840 sg8041 - -lemma sg18488 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by - exact rowSquare_join (by decide) sg840 sg8042 - -lemma sg18489 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,6,4] := by - exact rowSquare_join (by decide) sg841 sg8042 - -lemma sg18490 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg14113 - -lemma sg18491 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg241 sg11170 - -lemma sg18492 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg85 sg12457 - -lemma sg18493 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg457 sg8925 - -lemma sg18494 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg12847 - -lemma sg18495 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg272 sg11158 - -lemma sg18496 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg42 sg12848 - -lemma sg18497 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg239 sg11177 - -lemma sg18498 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg240 sg11172 - -lemma sg18499 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg458 sg8925 - -lemma sg18500 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg85 sg12458 - -lemma sg18501 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg455 sg8929 - -lemma sg18502 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg838 sg8043 - -lemma sg18503 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg272 sg11159 - -lemma sg18504 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg244 sg11168 - -lemma sg18505 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg456 sg8929 - -lemma sg18506 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg244 sg11169 - -lemma sg18507 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8044 - -lemma sg18508 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg457 sg8927 - -lemma sg18509 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg491 sg8902 - -lemma sg18510 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg8045 - -lemma sg18511 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg762 sg8100 - -lemma sg18512 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by - exact rowSquare_join (by decide) sg42 sg12849 - -lemma sg18513 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg239 sg11178 - -lemma sg18514 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg459 sg8925 - -lemma sg18515 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg11179 - -lemma sg18516 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg458 sg8926 - -lemma sg18517 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg11180 - -lemma sg18518 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8046 - -lemma sg18519 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg455 sg8930 - -lemma sg18520 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg839 sg8043 - -lemma sg18521 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg11176 - -lemma sg18522 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1131 sg6715 - -lemma sg18523 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg456 sg8930 - -lemma sg18524 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg8047 - -lemma sg18525 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg839 sg8044 - -lemma sg18526 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by - exact rowSquare_join (by decide) sg840 sg8043 - -lemma sg18527 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg839 sg8045 - -lemma sg18528 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by - exact rowSquare_join (by decide) sg763 sg8082 - -lemma sg18529 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg11591 - -lemma sg18530 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg8048 - -lemma sg18531 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg765 sg8079 - -lemma sg18532 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg762 sg8101 - -lemma sg18533 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by - exact rowSquare_join (by decide) sg840 sg8044 - -lemma sg18534 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by - exact rowSquare_join (by decide) sg840 sg8045 - -lemma sg18535 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,5] := by - exact rowSquare_join (by decide) sg841 sg8045 - -lemma sg18536 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg11181 - -lemma sg18537 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg838 sg8049 - -lemma sg18538 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg11182 - -lemma sg18539 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8050 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 + +namespace OAI + +/-! Semigroup Nodes 44. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg18140 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by + exact rowSquare_join (by decide) sg16 sg13671 + +lemma sg18141 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by + exact rowSquare_join (by decide) sg4 sg14652 + +lemma sg18142 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14037 + +lemma sg18143 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15554 + +lemma sg18144 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,2,1] := by + exact rowSquare_join (by decide) sg39 sg12768 + +lemma sg18145 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by + exact rowSquare_join (by decide) sg13 sg14038 + +lemma sg18146 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by + exact rowSquare_join (by decide) sg39 sg12769 + +lemma sg18147 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by + exact rowSquare_join (by decide) sg39 sg12770 + +lemma sg18148 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by + exact rowSquare_join (by decide) sg39 sg12771 + +lemma sg18149 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg0 sg15555 + +lemma sg18150 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by + exact rowSquare_join (by decide) sg4 sg14653 + +lemma sg18151 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14040 + +lemma sg18152 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg14041 + +lemma sg18153 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg17 sg13671 + +lemma sg18154 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by + exact rowSquare_join (by decide) sg14 sg14034 + +lemma sg18155 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg12765 + +lemma sg18156 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,3] := by + exact rowSquare_join (by decide) sg4 sg14654 + +lemma sg18157 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14042 + +lemma sg18158 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14043 + +lemma sg18159 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14044 + +lemma sg18160 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg12767 + +lemma sg18161 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by + exact rowSquare_join (by decide) sg13 sg14045 + +lemma sg18162 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg40 sg12769 + +lemma sg18163 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by + exact rowSquare_join (by decide) sg40 sg12770 + +lemma sg18164 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by + exact rowSquare_join (by decide) sg40 sg12771 + +lemma sg18165 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14046 + +lemma sg18166 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14047 + +lemma sg18167 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14048 + +lemma sg18168 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by + exact rowSquare_join (by decide) sg13 sg14049 + +lemma sg18169 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by + exact rowSquare_join (by decide) sg13 sg14050 + +lemma sg18170 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by + exact rowSquare_join (by decide) sg13 sg14051 + +lemma sg18171 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3631 sg4164 + +lemma sg18172 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14656 + +lemma sg18173 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg14657 + +lemma sg18174 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3631 sg4167 + +lemma sg18175 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14052 + +lemma sg18176 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14053 + +lemma sg18177 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14658 + +lemma sg18178 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg14659 + +lemma sg18179 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,2] := by + exact rowSquare_join (by decide) sg4 sg14660 + +lemma sg18180 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg14661 + +lemma sg18181 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14054 + +lemma sg18182 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14055 + +lemma sg18183 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14056 + +lemma sg18184 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14057 + +lemma sg18185 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg14058 + +lemma sg18186 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg14059 + +lemma sg18187 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by + exact rowSquare_join (by decide) sg4 sg14662 + +lemma sg18188 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by + exact rowSquare_join (by decide) sg4 sg14663 + +lemma sg18189 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14060 + +lemma sg18190 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14664 + +lemma sg18191 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14061 + +lemma sg18192 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14062 + +lemma sg18193 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg14063 + +lemma sg18194 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg14064 + +lemma sg18195 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg4 sg14665 + +lemma sg18196 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14666 + +lemma sg18197 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14065 + +lemma sg18198 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg14066 + +lemma sg18199 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by + exact rowSquare_join (by decide) sg13 sg14067 + +lemma sg18200 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by + exact rowSquare_join (by decide) sg13 sg14068 + +lemma sg18201 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by + exact rowSquare_join (by decide) sg13 sg14069 + +lemma sg18202 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by + exact rowSquare_join (by decide) sg13 sg14070 + +lemma sg18203 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg14869 + +lemma sg18204 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14669 + +lemma sg18205 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg14649 + +lemma sg18206 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14071 + +lemma sg18207 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14072 + +lemma sg18208 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg2 sg14897 + +lemma sg18209 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg2 sg14900 + +lemma sg18210 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg14650 + +lemma sg18211 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14073 + +lemma sg18212 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14672 + +lemma sg18213 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14673 + +lemma sg18214 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg16 sg13689 + +lemma sg18215 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14074 + +lemma sg18216 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by + exact rowSquare_join (by decide) sg39 sg12775 + +lemma sg18217 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg5 sg14652 + +lemma sg18218 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14075 + +lemma sg18219 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14674 + +lemma sg18220 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14035 + +lemma sg18221 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by + exact rowSquare_join (by decide) sg17 sg13689 + +lemma sg18222 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg23 sg12861 + +lemma sg18223 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by + exact rowSquare_join (by decide) sg40 sg12775 + +lemma sg18224 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14076 + +lemma sg18225 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by + exact rowSquare_join (by decide) sg39 sg12785 + +lemma sg18226 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by + exact rowSquare_join (by decide) sg39 sg12787 + +lemma sg18227 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by + exact rowSquare_join (by decide) sg42 sg12771 + +lemma sg18228 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14675 + +lemma sg18229 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg14039 + +lemma sg18230 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg13709 + +lemma sg18231 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg17 sg13711 + +lemma sg18232 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14676 + +lemma sg18233 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14077 + +lemma sg18234 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg14669 + +lemma sg18235 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14078 + +lemma sg18236 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14677 + +lemma sg18237 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg13772 + +lemma sg18238 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14079 + +lemma sg18239 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14080 + +lemma sg18240 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg14071 + +lemma sg18241 : RowSquare [7,5,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg13772 + +lemma sg18242 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg656 sg10867 + +lemma sg18243 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg658 sg10867 + +lemma sg18244 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg661 sg10867 + +lemma sg18245 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg662 sg10867 + +lemma sg18246 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg658 sg10871 + +lemma sg18247 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg658 sg10873 + +lemma sg18248 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg663 sg10867 + +lemma sg18249 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg664 sg10867 + +lemma sg18250 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg659 sg10868 + +lemma sg18251 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg665 sg10867 + +lemma sg18252 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg660 sg10868 + +lemma sg18253 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg661 sg10868 + +lemma sg18254 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg659 sg10869 + +lemma sg18255 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg666 sg10867 + +lemma sg18256 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg662 sg10868 + +lemma sg18257 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg661 sg10869 + +lemma sg18258 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [6,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg662 sg10869 + +lemma sg18259 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg667 sg10867 + +lemma sg18260 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg668 sg10867 + +lemma sg18261 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg663 sg10868 + +lemma sg18262 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg664 sg10868 + +lemma sg18263 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg669 sg10867 + +lemma sg18264 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg665 sg10868 + +lemma sg18265 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg664 sg10869 + +lemma sg18266 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg666 sg10868 + +lemma sg18267 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg665 sg10869 + +lemma sg18268 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg661 sg10875 + +lemma sg18269 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg666 sg10869 + +lemma sg18270 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg666 sg10870 + +lemma sg18271 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [7,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg662 sg10875 + +lemma sg18272 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg670 sg10867 + +lemma sg18273 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [9,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg671 sg10867 + +lemma sg18274 : RowSquare [7,6,2,2,2,2,2,2,2,2,1,1] [10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg672 sg10867 + +lemma sg18275 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2626 sg4937 + +lemma sg18276 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2629 sg4940 + +lemma sg18277 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3354 sg4421 + +lemma sg18278 : RowSquare [7,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14085 + +lemma sg18279 : RowSquare [7,6,3,2,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg11533 + +lemma sg18280 : RowSquare [7,6,3,2,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg11534 + +lemma sg18281 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2626 sg4877 + +lemma sg18282 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2626 sg4878 + +lemma sg18283 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3320 sg4162 + +lemma sg18284 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3320 sg4165 + +lemma sg18285 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2628 sg4877 + +lemma sg18286 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2628 sg4878 + +lemma sg18287 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3325 sg4163 + +lemma sg18288 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2635 sg4876 + +lemma sg18289 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [6,4,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg0 sg15597 + +lemma sg18290 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [6,6,5,5,5,4] := by + exact rowSquare_join (by decide) sg2640 sg4879 + +lemma sg18291 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,4,4,4,1] := by + exact rowSquare_join (by decide) sg4 sg14700 + +lemma sg18292 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by + exact rowSquare_join (by decide) sg3332 sg4173 + +lemma sg18293 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by + exact rowSquare_join (by decide) sg3732 sg3858 + +lemma sg18294 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg4 sg14702 + +lemma sg18295 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg0 sg15598 + +lemma sg18296 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,6,6,5] := by + exact rowSquare_join (by decide) sg13 sg14110 + +lemma sg18297 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg762 sg8076 + +lemma sg18298 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg271 sg11152 + +lemma sg18299 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,7,6,4] := by + exact rowSquare_join (by decide) sg762 sg8077 + +lemma sg18300 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by + exact rowSquare_join (by decide) sg271 sg11153 + +lemma sg18301 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by + exact rowSquare_join (by decide) sg490 sg8898 + +lemma sg18302 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [7,7,7,7,3] := by + exact rowSquare_join (by decide) sg490 sg8899 + +lemma sg18303 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg15 sg14089 + +lemma sg18304 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg14699 + +lemma sg18305 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg13 sg14112 + +lemma sg18306 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg4 sg14703 + +lemma sg18307 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,6,6,6,5] := by + exact rowSquare_join (by decide) sg762 sg8080 + +lemma sg18308 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by + exact rowSquare_join (by decide) sg14 sg14109 + +lemma sg18309 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,6,5,5] := by + exact rowSquare_join (by decide) sg762 sg8084 + +lemma sg18310 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,6,6,4] := by + exact rowSquare_join (by decide) sg762 sg8085 + +lemma sg18311 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,7,5,4] := by + exact rowSquare_join (by decide) sg841 sg8026 + +lemma sg18312 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,7,6,1,1,1] := by + exact rowSquare_join (by decide) sg839 sg8028 + +lemma sg18313 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,7,6,2,1] := by + exact rowSquare_join (by decide) sg840 sg8027 + +lemma sg18314 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,7,6,3] := by + exact rowSquare_join (by decide) sg841 sg8027 + +lemma sg18315 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,7,7,1,1] := by + exact rowSquare_join (by decide) sg840 sg8028 + +lemma sg18316 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,7,7,7,2] := by + exact rowSquare_join (by decide) sg841 sg8028 + +lemma sg18317 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,5,5,5] := by + exact rowSquare_join (by decide) sg762 sg8090 + +lemma sg18318 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,6,5,4] := by + exact rowSquare_join (by decide) sg841 sg8030 + +lemma sg18319 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg271 sg11160 + +lemma sg18320 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by + exact rowSquare_join (by decide) sg840 sg8031 + +lemma sg18321 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,6,6,3] := by + exact rowSquare_join (by decide) sg841 sg8031 + +lemma sg18322 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,4,4] := by + exact rowSquare_join (by decide) sg841 sg8032 + +lemma sg18323 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,5,1,1,1] := by + exact rowSquare_join (by decide) sg839 sg8034 + +lemma sg18324 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,5,2,1] := by + exact rowSquare_join (by decide) sg840 sg8033 + +lemma sg18325 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,5,3] := by + exact rowSquare_join (by decide) sg841 sg8033 + +lemma sg18326 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,6,1,1] := by + exact rowSquare_join (by decide) sg840 sg8034 + +lemma sg18327 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,6,2] := by + exact rowSquare_join (by decide) sg841 sg8034 + +lemma sg18328 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,7,7,1] := by + exact rowSquare_join (by decide) sg490 sg8903 + +lemma sg18329 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12465 + +lemma sg18330 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg11593 + +lemma sg18331 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg496 sg8896 + +lemma sg18332 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,2,2,2,1] := by + exact rowSquare_join (by decide) sg839 sg8035 + +lemma sg18333 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg496 sg8897 + +lemma sg18334 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,3,2,1,1] := by + exact rowSquare_join (by decide) sg839 sg8036 + +lemma sg18335 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,3,2,2] := by + exact rowSquare_join (by decide) sg840 sg8035 + +lemma sg18336 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,3,3,1] := by + exact rowSquare_join (by decide) sg841 sg8035 + +lemma sg18337 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,4,1,1,1] := by + exact rowSquare_join (by decide) sg839 sg8037 + +lemma sg18338 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,4,2,1] := by + exact rowSquare_join (by decide) sg840 sg8036 + +lemma sg18339 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,4,3] := by + exact rowSquare_join (by decide) sg841 sg8036 + +lemma sg18340 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,5,1,1] := by + exact rowSquare_join (by decide) sg840 sg8037 + +lemma sg18341 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,5,2] := by + exact rowSquare_join (by decide) sg841 sg8037 + +lemma sg18342 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,6,1] := by + exact rowSquare_join (by decide) sg490 sg8904 + +lemma sg18343 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [8,8,8,7] := by + exact rowSquare_join (by decide) sg271 sg11161 + +lemma sg18344 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg15 sg14090 + +lemma sg18345 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg15 sg14091 + +lemma sg18346 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg14092 + +lemma sg18347 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg43 sg12834 + +lemma sg18348 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg15 sg14093 + +lemma sg18349 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg14094 + +lemma sg18350 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg41 sg12837 + +lemma sg18351 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg41 sg12838 + +lemma sg18352 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg41 sg12839 + +lemma sg18353 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14116 + +lemma sg18354 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg84 sg12459 + +lemma sg18355 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12460 + +lemma sg18356 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg272 sg11154 + +lemma sg18357 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg39 sg12854 + +lemma sg18358 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg44 sg12833 + +lemma sg18359 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg14095 + +lemma sg18360 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg14096 + +lemma sg18361 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg15 sg14097 + +lemma sg18362 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg1 sg15058 + +lemma sg18363 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg6 sg14701 + +lemma sg18364 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg15 sg14098 + +lemma sg18365 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg14111 + +lemma sg18366 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg42 sg12837 + +lemma sg18367 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg42 sg12838 + +lemma sg18368 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg42 sg12839 + +lemma sg18369 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14117 + +lemma sg18370 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg40 sg12852 + +lemma sg18371 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg12853 + +lemma sg18372 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg272 sg11155 + +lemma sg18373 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg40 sg12854 + +lemma sg18374 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg116 sg11724 + +lemma sg18375 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12461 + +lemma sg18376 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg273 sg11154 + +lemma sg18377 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12462 + +lemma sg18378 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg272 sg11156 + +lemma sg18379 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg39 sg12856 + +lemma sg18380 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg12835 + +lemma sg18381 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg43 sg12836 + +lemma sg18382 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg15 sg14099 + +lemma sg18383 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg15 sg14100 + +lemma sg18384 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg15 sg14101 + +lemma sg18385 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg110 sg11727 + +lemma sg18386 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg242 sg11167 + +lemma sg18387 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg83 sg12466 + +lemma sg18388 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg455 sg8923 + +lemma sg18389 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12467 + +lemma sg18390 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg460 sg8912 + +lemma sg18391 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg41 sg12843 + +lemma sg18392 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1131 sg6707 + +lemma sg18393 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg456 sg8923 + +lemma sg18394 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg11594 + +lemma sg18395 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg455 sg8924 + +lemma sg18396 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg489 sg8905 + +lemma sg18397 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg460 sg8913 + +lemma sg18398 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg12844 + +lemma sg18399 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg762 sg8091 + +lemma sg18400 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg41 sg12845 + +lemma sg18401 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg41 sg12846 + +lemma sg18402 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg4 sg14704 + +lemma sg18403 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg11168 + +lemma sg18404 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg456 sg8924 + +lemma sg18405 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg11169 + +lemma sg18406 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg490 sg8905 + +lemma sg18407 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg277 sg11150 + +lemma sg18408 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg460 sg8914 + +lemma sg18409 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg762 sg8092 + +lemma sg18410 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg762 sg8093 + +lemma sg18411 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg84 sg12463 + +lemma sg18412 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg762 sg8094 + +lemma sg18413 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg15 sg14102 + +lemma sg18414 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14118 + +lemma sg18415 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg42 sg12840 + +lemma sg18416 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg42 sg12841 + +lemma sg18417 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg272 sg11157 + +lemma sg18418 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg42 sg12842 + +lemma sg18419 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg111 sg11727 + +lemma sg18420 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg240 sg11170 + +lemma sg18421 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg85 sg12453 + +lemma sg18422 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg455 sg8925 + +lemma sg18423 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg12855 + +lemma sg18424 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg460 sg8915 + +lemma sg18425 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg40 sg12856 + +lemma sg18426 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg116 sg11725 + +lemma sg18427 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg456 sg8925 + +lemma sg18428 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12464 + +lemma sg18429 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg457 sg8924 + +lemma sg18430 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg460 sg8916 + +lemma sg18431 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg460 sg8917 + +lemma sg18432 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg85 sg12454 + +lemma sg18433 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg762 sg8095 + +lemma sg18434 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg85 sg12455 + +lemma sg18435 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg85 sg12456 + +lemma sg18436 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg14 sg14112 + +lemma sg18437 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg239 sg11171 + +lemma sg18438 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg239 sg11172 + +lemma sg18439 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg458 sg8923 + +lemma sg18440 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12468 + +lemma sg18441 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg455 sg8926 + +lemma sg18442 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg838 sg8038 + +lemma sg18443 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg460 sg8918 + +lemma sg18444 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1131 sg6708 + +lemma sg18445 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1131 sg6709 + +lemma sg18446 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg243 sg11169 + +lemma sg18447 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8039 + +lemma sg18448 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg455 sg8927 + +lemma sg18449 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg489 sg8906 + +lemma sg18450 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg8040 + +lemma sg18451 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg762 sg8096 + +lemma sg18452 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg40 sg12857 + +lemma sg18453 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg11589 + +lemma sg18454 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8041 + +lemma sg18455 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg456 sg8927 + +lemma sg18456 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg8042 + +lemma sg18457 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg491 sg8900 + +lemma sg18458 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg491 sg8901 + +lemma sg18459 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg762 sg8097 + +lemma sg18460 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by + exact rowSquare_join (by decide) sg762 sg8098 + +lemma sg18461 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by + exact rowSquare_join (by decide) sg762 sg8099 + +lemma sg18462 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg239 sg11173 + +lemma sg18463 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg459 sg8923 + +lemma sg18464 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg11174 + +lemma sg18465 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg462 sg8912 + +lemma sg18466 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg11175 + +lemma sg18467 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg842 sg8024 + +lemma sg18468 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg455 sg8928 + +lemma sg18469 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg839 sg8038 + +lemma sg18470 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1131 sg6710 + +lemma sg18471 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg842 sg8025 + +lemma sg18472 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg1131 sg6711 + +lemma sg18473 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg842 sg8026 + +lemma sg18474 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg839 sg8039 + +lemma sg18475 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by + exact rowSquare_join (by decide) sg840 sg8038 + +lemma sg18476 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg839 sg8040 + +lemma sg18477 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by + exact rowSquare_join (by decide) sg763 sg8078 + +lemma sg18478 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1131 sg6712 + +lemma sg18479 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg842 sg8027 + +lemma sg18480 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg1131 sg6713 + +lemma sg18481 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg1131 sg6714 + +lemma sg18482 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by + exact rowSquare_join (by decide) sg840 sg8039 + +lemma sg18483 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by + exact rowSquare_join (by decide) sg840 sg8040 + +lemma sg18484 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,5,5] := by + exact rowSquare_join (by decide) sg841 sg8040 + +lemma sg18485 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg842 sg8028 + +lemma sg18486 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg764 sg8079 + +lemma sg18487 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by + exact rowSquare_join (by decide) sg840 sg8041 + +lemma sg18488 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by + exact rowSquare_join (by decide) sg840 sg8042 + +lemma sg18489 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,6,6,6,4] := by + exact rowSquare_join (by decide) sg841 sg8042 + +lemma sg18490 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg14113 + +lemma sg18491 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg241 sg11170 + +lemma sg18492 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg85 sg12457 + +lemma sg18493 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg457 sg8925 + +lemma sg18494 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg12847 + +lemma sg18495 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg272 sg11158 + +lemma sg18496 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg42 sg12848 + +lemma sg18497 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg239 sg11177 + +lemma sg18498 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg240 sg11172 + +lemma sg18499 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg458 sg8925 + +lemma sg18500 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg85 sg12458 + +lemma sg18501 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg455 sg8929 + +lemma sg18502 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg838 sg8043 + +lemma sg18503 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg272 sg11159 + +lemma sg18504 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg244 sg11168 + +lemma sg18505 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg456 sg8929 + +lemma sg18506 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg244 sg11169 + +lemma sg18507 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8044 + +lemma sg18508 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg457 sg8927 + +lemma sg18509 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg491 sg8902 + +lemma sg18510 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg8045 + +lemma sg18511 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg762 sg8100 + +lemma sg18512 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by + exact rowSquare_join (by decide) sg42 sg12849 + +lemma sg18513 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg239 sg11178 + +lemma sg18514 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg459 sg8925 + +lemma sg18515 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg11179 + +lemma sg18516 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg458 sg8926 + +lemma sg18517 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg11180 + +lemma sg18518 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8046 + +lemma sg18519 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg455 sg8930 + +lemma sg18520 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg839 sg8043 + +lemma sg18521 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg11176 + +lemma sg18522 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1131 sg6715 + +lemma sg18523 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg456 sg8930 + +lemma sg18524 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg8047 + +lemma sg18525 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg839 sg8044 + +lemma sg18526 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by + exact rowSquare_join (by decide) sg840 sg8043 + +lemma sg18527 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg839 sg8045 + +lemma sg18528 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by + exact rowSquare_join (by decide) sg763 sg8082 + +lemma sg18529 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg11591 + +lemma sg18530 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg8048 + +lemma sg18531 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg765 sg8079 + +lemma sg18532 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg762 sg8101 + +lemma sg18533 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by + exact rowSquare_join (by decide) sg840 sg8044 + +lemma sg18534 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by + exact rowSquare_join (by decide) sg840 sg8045 + +lemma sg18535 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,5,5,5] := by + exact rowSquare_join (by decide) sg841 sg8045 + +lemma sg18536 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg11181 + +lemma sg18537 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg838 sg8049 + +lemma sg18538 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg11182 + +lemma sg18539 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8050 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes45.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes45.lean index b9d3b5ef1e20824872841cde6c46776ef262188f..bee5ca73b9315ad7b65b9037a4c93d1a2901d025 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes45.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes45.lean @@ -1,1224 +1,1224 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes26 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes29 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes30 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes34 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes33 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 - -namespace OAI - -/-! Semigroup Nodes 45. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg18540 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg458 sg8928 - -lemma sg18541 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6523 - -lemma sg18542 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg839 sg8046 - -lemma sg18543 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by - exact rowSquare_join (by decide) sg763 sg8083 - -lemma sg18544 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg11183 - -lemma sg18545 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6524 - -lemma sg18546 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg1131 sg6716 - -lemma sg18547 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg839 sg8047 - -lemma sg18548 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by - exact rowSquare_join (by decide) sg840 sg8046 - -lemma sg18549 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by - exact rowSquare_join (by decide) sg763 sg8084 - -lemma sg18550 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6525 - -lemma sg18551 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg839 sg8048 - -lemma sg18552 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by - exact rowSquare_join (by decide) sg1131 sg6717 - -lemma sg18553 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by - exact rowSquare_join (by decide) sg1131 sg6718 - -lemma sg18554 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,5,4] := by - exact rowSquare_join (by decide) sg841 sg8047 - -lemma sg18555 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg843 sg8028 - -lemma sg18556 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by - exact rowSquare_join (by decide) sg840 sg8048 - -lemma sg18557 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,6,3] := by - exact rowSquare_join (by decide) sg841 sg8048 - -lemma sg18558 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg14114 - -lemma sg18559 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg240 sg11177 - -lemma sg18560 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg241 sg11172 - -lemma sg18561 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg275 sg11157 - -lemma sg18562 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg12850 - -lemma sg18563 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg457 sg8929 - -lemma sg18564 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg838 sg8051 - -lemma sg18565 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg42 sg12851 - -lemma sg18566 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg240 sg11178 - -lemma sg18567 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg276 sg11157 - -lemma sg18568 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg11179 - -lemma sg18569 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg458 sg8929 - -lemma sg18570 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg11180 - -lemma sg18571 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8052 - -lemma sg18572 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg455 sg8931 - -lemma sg18573 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg839 sg8051 - -lemma sg18574 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg11176 - -lemma sg18575 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8053 - -lemma sg18576 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg456 sg8931 - -lemma sg18577 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg8054 - -lemma sg18578 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg765 sg8081 - -lemma sg18579 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by - exact rowSquare_join (by decide) sg840 sg8051 - -lemma sg18580 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg762 sg8102 - -lemma sg18581 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,4,2] := by - exact rowSquare_join (by decide) sg765 sg8082 - -lemma sg18582 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg11181 - -lemma sg18583 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg838 sg8055 - -lemma sg18584 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg11182 - -lemma sg18585 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8056 - -lemma sg18586 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg458 sg8930 - -lemma sg18587 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6526 - -lemma sg18588 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg839 sg8052 - -lemma sg18589 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,3,3,3] := by - exact rowSquare_join (by decide) sg763 sg8088 - -lemma sg18590 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg11183 - -lemma sg18591 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6527 - -lemma sg18592 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg839 sg8053 - -lemma sg18593 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg839 sg8054 - -lemma sg18594 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,4,3,2] := by - exact rowSquare_join (by decide) sg840 sg8052 - -lemma sg18595 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,4,4,1] := by - exact rowSquare_join (by decide) sg763 sg8090 - -lemma sg18596 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6528 - -lemma sg18597 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg843 sg8031 - -lemma sg18598 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,5,2,2] := by - exact rowSquare_join (by decide) sg840 sg8053 - -lemma sg18599 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,5,3,1] := by - exact rowSquare_join (by decide) sg840 sg8054 - -lemma sg18600 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,5,4] := by - exact rowSquare_join (by decide) sg841 sg8054 - -lemma sg18601 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg11184 - -lemma sg18602 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8057 - -lemma sg18603 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg839 sg8055 - -lemma sg18604 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg11185 - -lemma sg18605 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6529 - -lemma sg18606 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg839 sg8056 - -lemma sg18607 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg1203 sg6526 - -lemma sg18608 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,3,3,2] := by - exact rowSquare_join (by decide) sg844 sg8029 - -lemma sg18609 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6530 - -lemma sg18610 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg1203 sg6527 - -lemma sg18611 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,4,2,2] := by - exact rowSquare_join (by decide) sg840 sg8056 - -lemma sg18612 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,4,3,1] := by - exact rowSquare_join (by decide) sg1204 sg6526 - -lemma sg18613 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,4,4] := by - exact rowSquare_join (by decide) sg1205 sg6526 - -lemma sg18614 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg1203 sg6528 - -lemma sg18615 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,5,2,1] := by - exact rowSquare_join (by decide) sg1204 sg6527 - -lemma sg18616 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,5,3] := by - exact rowSquare_join (by decide) sg1205 sg6527 - -lemma sg18617 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,6,1,1] := by - exact rowSquare_join (by decide) sg1204 sg6528 - -lemma sg18618 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,6,2] := by - exact rowSquare_join (by decide) sg1205 sg6528 - -lemma sg18619 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14115 - -lemma sg18620 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg241 sg11177 - -lemma sg18621 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg241 sg11178 - -lemma sg18622 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg281 sg11151 - -lemma sg18623 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14119 - -lemma sg18624 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg11179 - -lemma sg18625 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg275 sg11158 - -lemma sg18626 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg11180 - -lemma sg18627 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8058 - -lemma sg18628 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg457 sg8931 - -lemma sg18629 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg765 sg8087 - -lemma sg18630 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg11181 - -lemma sg18631 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg838 sg8059 - -lemma sg18632 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg11182 - -lemma sg18633 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8060 - -lemma sg18634 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg458 sg8931 - -lemma sg18635 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg8061 - -lemma sg18636 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg839 sg8058 - -lemma sg18637 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by - exact rowSquare_join (by decide) sg765 sg8088 - -lemma sg18638 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg11183 - -lemma sg18639 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg8062 - -lemma sg18640 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg765 sg8089 - -lemma sg18641 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg762 sg8103 - -lemma sg18642 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,4,3,2] := by - exact rowSquare_join (by decide) sg840 sg8058 - -lemma sg18643 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,4,4,1] := by - exact rowSquare_join (by decide) sg765 sg8090 - -lemma sg18644 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg14103 - -lemma sg18645 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg44 sg12834 - -lemma sg18646 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg15 sg14104 - -lemma sg18647 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg14105 - -lemma sg18648 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg43 sg12837 - -lemma sg18649 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg43 sg12838 - -lemma sg18650 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg43 sg12839 - -lemma sg18651 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg110 sg11728 - -lemma sg18652 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg41 sg12852 - -lemma sg18653 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg41 sg12853 - -lemma sg18654 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg460 sg8923 - -lemma sg18655 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg41 sg12854 - -lemma sg18656 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg242 sg11170 - -lemma sg18657 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12466 - -lemma sg18658 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg277 sg11154 - -lemma sg18659 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12467 - -lemma sg18660 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg460 sg8924 - -lemma sg18661 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg39 sg12860 - -lemma sg18662 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg12835 - -lemma sg18663 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg86 sg12452 - -lemma sg18664 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg15 sg14106 - -lemma sg18665 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg15 sg14107 - -lemma sg18666 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg15 sg14108 - -lemma sg18667 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg111 sg11728 - -lemma sg18668 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg85 sg12459 - -lemma sg18669 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg85 sg12460 - -lemma sg18670 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg460 sg8925 - -lemma sg18671 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg42 sg12854 - -lemma sg18672 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg110 sg11729 - -lemma sg18673 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg242 sg11171 - -lemma sg18674 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg12858 - -lemma sg18675 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg455 sg8934 - -lemma sg18676 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg12859 - -lemma sg18677 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg460 sg8926 - -lemma sg18678 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg40 sg12860 - -lemma sg18679 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1132 sg6707 - -lemma sg18680 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg456 sg8934 - -lemma sg18681 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg208 sg11594 - -lemma sg18682 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg461 sg8924 - -lemma sg18683 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg838 sg8063 - -lemma sg18684 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg1588 sg5821 - -lemma sg18685 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg12844 - -lemma sg18686 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8064 - -lemma sg18687 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg43 sg12845 - -lemma sg18688 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg43 sg12846 - -lemma sg18689 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg15 sg14109 - -lemma sg18690 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg239 sg11188 - -lemma sg18691 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1133 sg6707 - -lemma sg18692 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg462 sg8923 - -lemma sg18693 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg11594 - -lemma sg18694 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg455 sg8935 - -lemma sg18695 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg842 sg8038 - -lemma sg18696 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg1589 sg5821 - -lemma sg18697 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1131 sg6719 - -lemma sg18698 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1131 sg6720 - -lemma sg18699 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg11175 - -lemma sg18700 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg842 sg8039 - -lemma sg18701 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg1590 sg5821 - -lemma sg18702 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg839 sg8063 - -lemma sg18703 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg842 sg8040 - -lemma sg18704 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg839 sg8064 - -lemma sg18705 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg41 sg12857 - -lemma sg18706 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg11176 - -lemma sg18707 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg842 sg8041 - -lemma sg18708 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg1591 sg5821 - -lemma sg18709 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg842 sg8042 - -lemma sg18710 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg764 sg8093 - -lemma sg18711 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg840 sg8063 - -lemma sg18712 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg762 sg8104 - -lemma sg18713 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg840 sg8064 - -lemma sg18714 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg841 sg8064 - -lemma sg18715 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg111 sg11729 - -lemma sg18716 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg242 sg11177 - -lemma sg18717 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg85 sg12461 - -lemma sg18718 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg457 sg8934 - -lemma sg18719 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg85 sg12462 - -lemma sg18720 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg460 sg8929 - -lemma sg18721 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg42 sg12856 - -lemma sg18722 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg239 sg11190 - -lemma sg18723 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1134 sg6707 - -lemma sg18724 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg458 sg8934 - -lemma sg18725 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg11594 - -lemma sg18726 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg455 sg8937 - -lemma sg18727 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg838 sg8065 - -lemma sg18728 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg460 sg8930 - -lemma sg18729 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1132 sg6708 - -lemma sg18730 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1132 sg6709 - -lemma sg18731 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg242 sg11180 - -lemma sg18732 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8066 - -lemma sg18733 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg457 sg8936 - -lemma sg18734 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1588 sg5822 - -lemma sg18735 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg8067 - -lemma sg18736 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg765 sg8094 - -lemma sg18737 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,4,3] := by - exact rowSquare_join (by decide) sg85 sg12463 - -lemma sg18738 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1135 sg6707 - -lemma sg18739 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg838 sg8068 - -lemma sg18740 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1133 sg6708 - -lemma sg18741 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1133 sg6709 - -lemma sg18742 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg11192 - -lemma sg18743 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6531 - -lemma sg18744 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg455 sg8938 - -lemma sg18745 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg1589 sg5822 - -lemma sg18746 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1131 sg6721 - -lemma sg18747 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6532 - -lemma sg18748 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg1131 sg6722 - -lemma sg18749 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6533 - -lemma sg18750 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg1588 sg5823 - -lemma sg18751 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,3,3] := by - exact rowSquare_join (by decide) sg840 sg8065 - -lemma sg18752 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg839 sg8067 - -lemma sg18753 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,4,2] := by - exact rowSquare_join (by decide) sg763 sg8099 - -lemma sg18754 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1132 sg6712 - -lemma sg18755 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6534 - -lemma sg18756 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg1588 sg5824 - -lemma sg18757 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg1132 sg6714 - -lemma sg18758 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,3,2] := by - exact rowSquare_join (by decide) sg840 sg8066 - -lemma sg18759 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,4,1] := by - exact rowSquare_join (by decide) sg840 sg8067 - -lemma sg18760 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,5] := by - exact rowSquare_join (by decide) sg841 sg8067 - -lemma sg18761 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg489 sg8907 - -lemma sg18762 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg842 sg8049 - -lemma sg18763 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1133 sg6710 - -lemma sg18764 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg842 sg8050 - -lemma sg18765 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg1133 sg6711 - -lemma sg18766 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1209 sg6523 - -lemma sg18767 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg1589 sg5823 - -lemma sg18768 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,3,3,3] := by - exact rowSquare_join (by decide) sg844 sg8038 - -lemma sg18769 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1131 sg6723 - -lemma sg18770 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1209 sg6524 - -lemma sg18771 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg1589 sg5824 - -lemma sg18772 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg1590 sg5823 - -lemma sg18773 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,4,3,2] := by - exact rowSquare_join (by decide) sg1204 sg6531 - -lemma sg18774 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,4,4,1] := by - exact rowSquare_join (by decide) sg1205 sg6531 - -lemma sg18775 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg1209 sg6525 - -lemma sg18776 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg1590 sg5824 - -lemma sg18777 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,5,2,2] := by - exact rowSquare_join (by decide) sg1204 sg6532 - -lemma sg18778 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,5,3,1] := by - exact rowSquare_join (by decide) sg1204 sg6533 - -lemma sg18779 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,5,4] := by - exact rowSquare_join (by decide) sg1205 sg6533 - -lemma sg18780 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg1591 sg5824 - -lemma sg18781 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,6,2,1] := by - exact rowSquare_join (by decide) sg1204 sg6534 - -lemma sg18782 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,6,3] := by - exact rowSquare_join (by decide) sg1205 sg6534 - -lemma sg18783 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg14118 - -lemma sg18784 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg240 sg11190 - -lemma sg18785 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg241 sg11189 - -lemma sg18786 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg463 sg8925 - -lemma sg18787 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg85 sg12464 - -lemma sg18788 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg457 sg8937 - -lemma sg18789 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg838 sg8069 - -lemma sg18790 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg460 sg8931 - -lemma sg18791 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg239 sg11194 - -lemma sg18792 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg838 sg8070 - -lemma sg18793 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1134 sg6708 - -lemma sg18794 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1134 sg6709 - -lemma sg18795 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg240 sg11192 - -lemma sg18796 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6535 - -lemma sg18797 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg455 sg8939 - -lemma sg18798 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg839 sg8069 - -lemma sg18799 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg244 sg11176 - -lemma sg18800 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6536 - -lemma sg18801 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg456 sg8939 - -lemma sg18802 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6537 - -lemma sg18803 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg843 sg8044 - -lemma sg18804 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,3,3] := by - exact rowSquare_join (by decide) sg1588 sg5825 - -lemma sg18805 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg843 sg8045 - -lemma sg18806 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,4,2] := by - exact rowSquare_join (by decide) sg765 sg8099 - -lemma sg18807 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1135 sg6708 - -lemma sg18808 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1135 sg6709 - -lemma sg18809 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1134 sg6710 - -lemma sg18810 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6538 - -lemma sg18811 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg1134 sg6711 - -lemma sg18812 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6539 - -lemma sg18813 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg1203 sg6535 - -lemma sg18814 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,3,3,3] := by - exact rowSquare_join (by decide) sg1589 sg5825 - -lemma sg18815 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1131 sg6724 - -lemma sg18816 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6540 - -lemma sg18817 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg1203 sg6536 - -lemma sg18818 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg1203 sg6537 - -lemma sg18819 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,4,3,2] := by - exact rowSquare_join (by decide) sg1588 sg5826 - -lemma sg18820 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,4,4,1] := by - exact rowSquare_join (by decide) sg1205 sg6535 - -lemma sg18821 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6541 - -lemma sg18822 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg1206 sg6534 - -lemma sg18823 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,5,2,2] := by - exact rowSquare_join (by decide) sg1588 sg5827 - -lemma sg18824 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,5,3,1] := by - exact rowSquare_join (by decide) sg1204 sg6537 - -lemma sg18825 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,5,4] := by - exact rowSquare_join (by decide) sg1205 sg6537 - -lemma sg18826 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1135 sg6710 - -lemma sg18827 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6542 - -lemma sg18828 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg1135 sg6711 - -lemma sg18829 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1131 sg6725 - -lemma sg18830 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6543 - -lemma sg18831 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg1203 sg6538 - -lemma sg18832 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg1203 sg6539 - -lemma sg18833 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,3,3,2] := by - exact rowSquare_join (by decide) sg1589 sg5826 - -lemma sg18834 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6544 - -lemma sg18835 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg1203 sg6540 - -lemma sg18836 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,4,2,2] := by - exact rowSquare_join (by decide) sg1589 sg5827 - -lemma sg18837 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,4,3,1] := by - exact rowSquare_join (by decide) sg1588 sg5828 - -lemma sg18838 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,4,4] := by - exact rowSquare_join (by decide) sg1205 sg6539 - -lemma sg18839 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg1203 sg6541 - -lemma sg18840 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,5,2,1] := by - exact rowSquare_join (by decide) sg1588 sg5829 - -lemma sg18841 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,5,3] := by - exact rowSquare_join (by decide) sg1205 sg6540 - -lemma sg18842 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,6,1,1] := by - exact rowSquare_join (by decide) sg1588 sg5830 - -lemma sg18843 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,6,2] := by - exact rowSquare_join (by decide) sg1205 sg6541 - -lemma sg18844 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg241 sg11190 - -lemma sg18845 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg240 sg11194 - -lemma sg18846 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg838 sg8071 - -lemma sg18847 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg11191 - -lemma sg18848 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg463 sg8929 - -lemma sg18849 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg11192 - -lemma sg18850 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6545 - -lemma sg18851 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg457 sg8939 - -lemma sg18852 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg843 sg8051 - -lemma sg18853 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg489 sg8908 - -lemma sg18854 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg838 sg8072 - -lemma sg18855 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg490 sg8908 - -lemma sg18856 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6546 - -lemma sg18857 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg458 sg8939 - -lemma sg18858 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6547 - -lemma sg18859 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg1203 sg6545 - -lemma sg18860 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,3,3,3] := by - exact rowSquare_join (by decide) sg844 sg8051 - -lemma sg18861 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg241 sg11193 - -lemma sg18862 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6548 - -lemma sg18863 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1206 sg6536 - -lemma sg18864 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1206 sg6537 - -lemma sg18865 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,4,3,2] := by - exact rowSquare_join (by decide) sg1204 sg6545 - -lemma sg18866 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,4,4,1] := by - exact rowSquare_join (by decide) sg1205 sg6545 - -lemma sg18867 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg11195 - -lemma sg18868 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6549 - -lemma sg18869 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg839 sg8072 - -lemma sg18870 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg11196 - -lemma sg18871 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6550 - -lemma sg18872 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg1203 sg6546 - -lemma sg18873 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg1203 sg6547 - -lemma sg18874 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,3,3,2] := by - exact rowSquare_join (by decide) sg844 sg8052 - -lemma sg18875 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1202 sg6551 - -lemma sg18876 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg1203 sg6548 - -lemma sg18877 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,4,2,2] := by - exact rowSquare_join (by decide) sg1204 sg6546 - -lemma sg18878 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,4,3,1] := by - exact rowSquare_join (by decide) sg1204 sg6547 - -lemma sg18879 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,4,4] := by - exact rowSquare_join (by decide) sg1205 sg6547 - -lemma sg18880 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg1206 sg6541 - -lemma sg18881 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,5,2,1] := by - exact rowSquare_join (by decide) sg1204 sg6548 - -lemma sg18882 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,5,3] := by - exact rowSquare_join (by decide) sg1205 sg6548 - -lemma sg18883 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg239 sg11197 - -lemma sg18884 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg1235 sg6520 - -lemma sg18885 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg1235 sg6521 - -lemma sg18886 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,3,2,2] := by - exact rowSquare_join (by decide) sg1236 sg6520 - -lemma sg18887 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,3,3,1] := by - exact rowSquare_join (by decide) sg1211 sg6526 - -lemma sg18888 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg1235 sg6522 - -lemma sg18889 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,4,2,1] := by - exact rowSquare_join (by decide) sg1236 sg6521 - -lemma sg18890 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,4,3] := by - exact rowSquare_join (by decide) sg1237 sg6521 - -lemma sg18891 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,5,1,1] := by - exact rowSquare_join (by decide) sg1236 sg6522 - -lemma sg18892 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,5,2] := by - exact rowSquare_join (by decide) sg1237 sg6522 - -lemma sg18893 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,6,1] := by - exact rowSquare_join (by decide) sg1207 sg6541 - -lemma sg18894 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg463 sg8931 - -lemma sg18895 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1206 sg6545 - -lemma sg18896 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,3,3,3,3] := by - exact rowSquare_join (by decide) sg846 sg8051 - -lemma sg18897 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg839 sg8073 - -lemma sg18898 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1203 sg6552 - -lemma sg18899 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1203 sg6553 - -lemma sg18900 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,3,3,2] := by - exact rowSquare_join (by decide) sg844 sg8058 - -lemma sg18901 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1206 sg6548 - -lemma sg18902 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,4,2,2] := by - exact rowSquare_join (by decide) sg1204 sg6552 - -lemma sg18903 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,4,3,1] := by - exact rowSquare_join (by decide) sg1204 sg6553 - -lemma sg18904 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,4,4] := by - exact rowSquare_join (by decide) sg1205 sg6553 - -lemma sg18905 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,10,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg839 sg8074 - -lemma sg18906 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,10,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1206 sg6552 - -lemma sg18907 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,10,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1206 sg6553 - -lemma sg18908 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,10,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg1206 sg6554 - -lemma sg18909 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1754 sg6468 - -lemma sg18910 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4868 - -lemma sg18911 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1754 sg6469 - -lemma sg18912 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4869 - -lemma sg18913 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1754 sg6470 - -lemma sg18914 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1754 sg6471 - -lemma sg18915 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1755 sg6468 - -lemma sg18916 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2704 sg4868 - -lemma sg18917 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2704 sg4869 - -lemma sg18918 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14120 - -lemma sg18919 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4872 - -lemma sg18920 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg5731 - -lemma sg18921 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14124 - -lemma sg18922 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg2712 sg4901 - -lemma sg18923 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14131 - -lemma sg18924 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14132 - -lemma sg18925 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14133 - -lemma sg18926 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14134 - -lemma sg18927 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14136 - -lemma sg18928 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg3348 sg4422 - -lemma sg18929 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14137 - -lemma sg18930 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14138 - -lemma sg18931 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by - exact rowSquare_join (by decide) sg2714 sg4900 - -lemma sg18932 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by - exact rowSquare_join (by decide) sg2714 sg4901 - -lemma sg18933 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14139 - -lemma sg18934 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg14140 - -lemma sg18935 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by - exact rowSquare_join (by decide) sg13 sg14141 - -lemma sg18936 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by - exact rowSquare_join (by decide) sg13 sg14142 - -lemma sg18937 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by - exact rowSquare_join (by decide) sg13 sg14143 - -lemma sg18938 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by - exact rowSquare_join (by decide) sg13 sg14144 - -lemma sg18939 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3533 sg4276 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes26 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes29 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes30 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes34 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes33 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 + +namespace OAI + +/-! Semigroup Nodes 45. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg18540 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg458 sg8928 + +lemma sg18541 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6523 + +lemma sg18542 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg839 sg8046 + +lemma sg18543 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by + exact rowSquare_join (by decide) sg763 sg8083 + +lemma sg18544 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg11183 + +lemma sg18545 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6524 + +lemma sg18546 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg1131 sg6716 + +lemma sg18547 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg839 sg8047 + +lemma sg18548 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by + exact rowSquare_join (by decide) sg840 sg8046 + +lemma sg18549 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by + exact rowSquare_join (by decide) sg763 sg8084 + +lemma sg18550 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6525 + +lemma sg18551 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg839 sg8048 + +lemma sg18552 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by + exact rowSquare_join (by decide) sg1131 sg6717 + +lemma sg18553 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by + exact rowSquare_join (by decide) sg1131 sg6718 + +lemma sg18554 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,5,4] := by + exact rowSquare_join (by decide) sg841 sg8047 + +lemma sg18555 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg843 sg8028 + +lemma sg18556 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by + exact rowSquare_join (by decide) sg840 sg8048 + +lemma sg18557 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,7,6,6,3] := by + exact rowSquare_join (by decide) sg841 sg8048 + +lemma sg18558 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg14114 + +lemma sg18559 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg240 sg11177 + +lemma sg18560 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg241 sg11172 + +lemma sg18561 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg275 sg11157 + +lemma sg18562 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg12850 + +lemma sg18563 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg457 sg8929 + +lemma sg18564 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg838 sg8051 + +lemma sg18565 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg42 sg12851 + +lemma sg18566 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg240 sg11178 + +lemma sg18567 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg276 sg11157 + +lemma sg18568 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg11179 + +lemma sg18569 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg458 sg8929 + +lemma sg18570 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg11180 + +lemma sg18571 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8052 + +lemma sg18572 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg455 sg8931 + +lemma sg18573 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg839 sg8051 + +lemma sg18574 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg11176 + +lemma sg18575 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8053 + +lemma sg18576 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg456 sg8931 + +lemma sg18577 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg8054 + +lemma sg18578 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg765 sg8081 + +lemma sg18579 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by + exact rowSquare_join (by decide) sg840 sg8051 + +lemma sg18580 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg762 sg8102 + +lemma sg18581 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,4,4,4,2] := by + exact rowSquare_join (by decide) sg765 sg8082 + +lemma sg18582 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg11181 + +lemma sg18583 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg838 sg8055 + +lemma sg18584 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg11182 + +lemma sg18585 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8056 + +lemma sg18586 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg458 sg8930 + +lemma sg18587 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6526 + +lemma sg18588 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg839 sg8052 + +lemma sg18589 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,3,3,3] := by + exact rowSquare_join (by decide) sg763 sg8088 + +lemma sg18590 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg11183 + +lemma sg18591 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6527 + +lemma sg18592 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg839 sg8053 + +lemma sg18593 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg839 sg8054 + +lemma sg18594 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,4,3,2] := by + exact rowSquare_join (by decide) sg840 sg8052 + +lemma sg18595 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,4,4,1] := by + exact rowSquare_join (by decide) sg763 sg8090 + +lemma sg18596 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6528 + +lemma sg18597 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg843 sg8031 + +lemma sg18598 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,5,2,2] := by + exact rowSquare_join (by decide) sg840 sg8053 + +lemma sg18599 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,5,3,1] := by + exact rowSquare_join (by decide) sg840 sg8054 + +lemma sg18600 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,5,5,4] := by + exact rowSquare_join (by decide) sg841 sg8054 + +lemma sg18601 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg11184 + +lemma sg18602 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8057 + +lemma sg18603 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg839 sg8055 + +lemma sg18604 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg11185 + +lemma sg18605 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6529 + +lemma sg18606 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg839 sg8056 + +lemma sg18607 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg1203 sg6526 + +lemma sg18608 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,3,3,2] := by + exact rowSquare_join (by decide) sg844 sg8029 + +lemma sg18609 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6530 + +lemma sg18610 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg1203 sg6527 + +lemma sg18611 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,4,2,2] := by + exact rowSquare_join (by decide) sg840 sg8056 + +lemma sg18612 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,4,3,1] := by + exact rowSquare_join (by decide) sg1204 sg6526 + +lemma sg18613 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,4,4] := by + exact rowSquare_join (by decide) sg1205 sg6526 + +lemma sg18614 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg1203 sg6528 + +lemma sg18615 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,5,2,1] := by + exact rowSquare_join (by decide) sg1204 sg6527 + +lemma sg18616 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,5,3] := by + exact rowSquare_join (by decide) sg1205 sg6527 + +lemma sg18617 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,6,1,1] := by + exact rowSquare_join (by decide) sg1204 sg6528 + +lemma sg18618 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,8,6,6,2] := by + exact rowSquare_join (by decide) sg1205 sg6528 + +lemma sg18619 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14115 + +lemma sg18620 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg241 sg11177 + +lemma sg18621 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg241 sg11178 + +lemma sg18622 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg281 sg11151 + +lemma sg18623 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14119 + +lemma sg18624 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg11179 + +lemma sg18625 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg275 sg11158 + +lemma sg18626 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg11180 + +lemma sg18627 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8058 + +lemma sg18628 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg457 sg8931 + +lemma sg18629 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg765 sg8087 + +lemma sg18630 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg11181 + +lemma sg18631 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg838 sg8059 + +lemma sg18632 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg11182 + +lemma sg18633 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8060 + +lemma sg18634 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg458 sg8931 + +lemma sg18635 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg8061 + +lemma sg18636 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg839 sg8058 + +lemma sg18637 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by + exact rowSquare_join (by decide) sg765 sg8088 + +lemma sg18638 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg11183 + +lemma sg18639 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg8062 + +lemma sg18640 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg765 sg8089 + +lemma sg18641 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg762 sg8103 + +lemma sg18642 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,4,3,2] := by + exact rowSquare_join (by decide) sg840 sg8058 + +lemma sg18643 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [9,9,4,4,4,1] := by + exact rowSquare_join (by decide) sg765 sg8090 + +lemma sg18644 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg14103 + +lemma sg18645 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg44 sg12834 + +lemma sg18646 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg15 sg14104 + +lemma sg18647 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg14105 + +lemma sg18648 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg43 sg12837 + +lemma sg18649 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg43 sg12838 + +lemma sg18650 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg43 sg12839 + +lemma sg18651 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg110 sg11728 + +lemma sg18652 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg41 sg12852 + +lemma sg18653 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg41 sg12853 + +lemma sg18654 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg460 sg8923 + +lemma sg18655 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg41 sg12854 + +lemma sg18656 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg242 sg11170 + +lemma sg18657 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12466 + +lemma sg18658 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg277 sg11154 + +lemma sg18659 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12467 + +lemma sg18660 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg460 sg8924 + +lemma sg18661 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg39 sg12860 + +lemma sg18662 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg12835 + +lemma sg18663 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg86 sg12452 + +lemma sg18664 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg15 sg14106 + +lemma sg18665 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg15 sg14107 + +lemma sg18666 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg15 sg14108 + +lemma sg18667 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg111 sg11728 + +lemma sg18668 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg85 sg12459 + +lemma sg18669 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg85 sg12460 + +lemma sg18670 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg460 sg8925 + +lemma sg18671 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg42 sg12854 + +lemma sg18672 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg110 sg11729 + +lemma sg18673 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg242 sg11171 + +lemma sg18674 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg12858 + +lemma sg18675 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg455 sg8934 + +lemma sg18676 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg12859 + +lemma sg18677 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg460 sg8926 + +lemma sg18678 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg40 sg12860 + +lemma sg18679 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1132 sg6707 + +lemma sg18680 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg456 sg8934 + +lemma sg18681 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg208 sg11594 + +lemma sg18682 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg461 sg8924 + +lemma sg18683 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg838 sg8063 + +lemma sg18684 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg1588 sg5821 + +lemma sg18685 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg12844 + +lemma sg18686 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8064 + +lemma sg18687 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg43 sg12845 + +lemma sg18688 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg43 sg12846 + +lemma sg18689 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg15 sg14109 + +lemma sg18690 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg239 sg11188 + +lemma sg18691 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1133 sg6707 + +lemma sg18692 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg462 sg8923 + +lemma sg18693 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg11594 + +lemma sg18694 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg455 sg8935 + +lemma sg18695 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg842 sg8038 + +lemma sg18696 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg1589 sg5821 + +lemma sg18697 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1131 sg6719 + +lemma sg18698 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1131 sg6720 + +lemma sg18699 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg11175 + +lemma sg18700 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg842 sg8039 + +lemma sg18701 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg1590 sg5821 + +lemma sg18702 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg839 sg8063 + +lemma sg18703 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg842 sg8040 + +lemma sg18704 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg839 sg8064 + +lemma sg18705 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg41 sg12857 + +lemma sg18706 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg11176 + +lemma sg18707 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg842 sg8041 + +lemma sg18708 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg1591 sg5821 + +lemma sg18709 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg842 sg8042 + +lemma sg18710 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg764 sg8093 + +lemma sg18711 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg840 sg8063 + +lemma sg18712 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg762 sg8104 + +lemma sg18713 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg840 sg8064 + +lemma sg18714 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg841 sg8064 + +lemma sg18715 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg111 sg11729 + +lemma sg18716 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg242 sg11177 + +lemma sg18717 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg85 sg12461 + +lemma sg18718 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg457 sg8934 + +lemma sg18719 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg85 sg12462 + +lemma sg18720 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg460 sg8929 + +lemma sg18721 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg42 sg12856 + +lemma sg18722 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg239 sg11190 + +lemma sg18723 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1134 sg6707 + +lemma sg18724 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg458 sg8934 + +lemma sg18725 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg11594 + +lemma sg18726 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg455 sg8937 + +lemma sg18727 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg838 sg8065 + +lemma sg18728 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg460 sg8930 + +lemma sg18729 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1132 sg6708 + +lemma sg18730 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1132 sg6709 + +lemma sg18731 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg242 sg11180 + +lemma sg18732 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8066 + +lemma sg18733 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg457 sg8936 + +lemma sg18734 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1588 sg5822 + +lemma sg18735 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg8067 + +lemma sg18736 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg765 sg8094 + +lemma sg18737 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,4,4,4,3] := by + exact rowSquare_join (by decide) sg85 sg12463 + +lemma sg18738 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1135 sg6707 + +lemma sg18739 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg838 sg8068 + +lemma sg18740 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1133 sg6708 + +lemma sg18741 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1133 sg6709 + +lemma sg18742 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg11192 + +lemma sg18743 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6531 + +lemma sg18744 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg455 sg8938 + +lemma sg18745 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg1589 sg5822 + +lemma sg18746 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1131 sg6721 + +lemma sg18747 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6532 + +lemma sg18748 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg1131 sg6722 + +lemma sg18749 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6533 + +lemma sg18750 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg1588 sg5823 + +lemma sg18751 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,3,3] := by + exact rowSquare_join (by decide) sg840 sg8065 + +lemma sg18752 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg839 sg8067 + +lemma sg18753 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,4,4,2] := by + exact rowSquare_join (by decide) sg763 sg8099 + +lemma sg18754 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1132 sg6712 + +lemma sg18755 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6534 + +lemma sg18756 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg1588 sg5824 + +lemma sg18757 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg1132 sg6714 + +lemma sg18758 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,3,2] := by + exact rowSquare_join (by decide) sg840 sg8066 + +lemma sg18759 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,4,1] := by + exact rowSquare_join (by decide) sg840 sg8067 + +lemma sg18760 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,5,5,5] := by + exact rowSquare_join (by decide) sg841 sg8067 + +lemma sg18761 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg489 sg8907 + +lemma sg18762 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg842 sg8049 + +lemma sg18763 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1133 sg6710 + +lemma sg18764 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg842 sg8050 + +lemma sg18765 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg1133 sg6711 + +lemma sg18766 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1209 sg6523 + +lemma sg18767 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg1589 sg5823 + +lemma sg18768 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,3,3,3] := by + exact rowSquare_join (by decide) sg844 sg8038 + +lemma sg18769 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1131 sg6723 + +lemma sg18770 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1209 sg6524 + +lemma sg18771 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg1589 sg5824 + +lemma sg18772 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg1590 sg5823 + +lemma sg18773 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,4,3,2] := by + exact rowSquare_join (by decide) sg1204 sg6531 + +lemma sg18774 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,4,4,1] := by + exact rowSquare_join (by decide) sg1205 sg6531 + +lemma sg18775 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg1209 sg6525 + +lemma sg18776 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg1590 sg5824 + +lemma sg18777 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,5,2,2] := by + exact rowSquare_join (by decide) sg1204 sg6532 + +lemma sg18778 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,5,3,1] := by + exact rowSquare_join (by decide) sg1204 sg6533 + +lemma sg18779 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,5,4] := by + exact rowSquare_join (by decide) sg1205 sg6533 + +lemma sg18780 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg1591 sg5824 + +lemma sg18781 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,6,2,1] := by + exact rowSquare_join (by decide) sg1204 sg6534 + +lemma sg18782 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,6,6,6,3] := by + exact rowSquare_join (by decide) sg1205 sg6534 + +lemma sg18783 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg14118 + +lemma sg18784 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg240 sg11190 + +lemma sg18785 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg241 sg11189 + +lemma sg18786 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg463 sg8925 + +lemma sg18787 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg85 sg12464 + +lemma sg18788 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg457 sg8937 + +lemma sg18789 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg838 sg8069 + +lemma sg18790 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg460 sg8931 + +lemma sg18791 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg239 sg11194 + +lemma sg18792 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg838 sg8070 + +lemma sg18793 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1134 sg6708 + +lemma sg18794 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1134 sg6709 + +lemma sg18795 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg240 sg11192 + +lemma sg18796 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6535 + +lemma sg18797 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg455 sg8939 + +lemma sg18798 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg839 sg8069 + +lemma sg18799 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg244 sg11176 + +lemma sg18800 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6536 + +lemma sg18801 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg456 sg8939 + +lemma sg18802 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6537 + +lemma sg18803 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg843 sg8044 + +lemma sg18804 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,3,3] := by + exact rowSquare_join (by decide) sg1588 sg5825 + +lemma sg18805 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg843 sg8045 + +lemma sg18806 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,4,4,4,2] := by + exact rowSquare_join (by decide) sg765 sg8099 + +lemma sg18807 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1135 sg6708 + +lemma sg18808 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1135 sg6709 + +lemma sg18809 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1134 sg6710 + +lemma sg18810 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6538 + +lemma sg18811 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg1134 sg6711 + +lemma sg18812 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6539 + +lemma sg18813 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg1203 sg6535 + +lemma sg18814 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,3,3,3] := by + exact rowSquare_join (by decide) sg1589 sg5825 + +lemma sg18815 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1131 sg6724 + +lemma sg18816 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6540 + +lemma sg18817 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg1203 sg6536 + +lemma sg18818 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg1203 sg6537 + +lemma sg18819 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,4,3,2] := by + exact rowSquare_join (by decide) sg1588 sg5826 + +lemma sg18820 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,4,4,1] := by + exact rowSquare_join (by decide) sg1205 sg6535 + +lemma sg18821 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6541 + +lemma sg18822 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg1206 sg6534 + +lemma sg18823 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,5,2,2] := by + exact rowSquare_join (by decide) sg1588 sg5827 + +lemma sg18824 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,5,3,1] := by + exact rowSquare_join (by decide) sg1204 sg6537 + +lemma sg18825 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,5,5,4] := by + exact rowSquare_join (by decide) sg1205 sg6537 + +lemma sg18826 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1135 sg6710 + +lemma sg18827 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6542 + +lemma sg18828 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg1135 sg6711 + +lemma sg18829 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1131 sg6725 + +lemma sg18830 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6543 + +lemma sg18831 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg1203 sg6538 + +lemma sg18832 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg1203 sg6539 + +lemma sg18833 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,3,3,2] := by + exact rowSquare_join (by decide) sg1589 sg5826 + +lemma sg18834 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6544 + +lemma sg18835 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg1203 sg6540 + +lemma sg18836 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,4,2,2] := by + exact rowSquare_join (by decide) sg1589 sg5827 + +lemma sg18837 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,4,3,1] := by + exact rowSquare_join (by decide) sg1588 sg5828 + +lemma sg18838 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,4,4] := by + exact rowSquare_join (by decide) sg1205 sg6539 + +lemma sg18839 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg1203 sg6541 + +lemma sg18840 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,5,2,1] := by + exact rowSquare_join (by decide) sg1588 sg5829 + +lemma sg18841 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,5,3] := by + exact rowSquare_join (by decide) sg1205 sg6540 + +lemma sg18842 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,6,1,1] := by + exact rowSquare_join (by decide) sg1588 sg5830 + +lemma sg18843 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,7,6,6,2] := by + exact rowSquare_join (by decide) sg1205 sg6541 + +lemma sg18844 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg241 sg11190 + +lemma sg18845 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg240 sg11194 + +lemma sg18846 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg838 sg8071 + +lemma sg18847 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg11191 + +lemma sg18848 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg463 sg8929 + +lemma sg18849 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg11192 + +lemma sg18850 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6545 + +lemma sg18851 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg457 sg8939 + +lemma sg18852 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg843 sg8051 + +lemma sg18853 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg489 sg8908 + +lemma sg18854 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg838 sg8072 + +lemma sg18855 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg490 sg8908 + +lemma sg18856 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6546 + +lemma sg18857 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg458 sg8939 + +lemma sg18858 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6547 + +lemma sg18859 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg1203 sg6545 + +lemma sg18860 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,3,3,3] := by + exact rowSquare_join (by decide) sg844 sg8051 + +lemma sg18861 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg241 sg11193 + +lemma sg18862 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6548 + +lemma sg18863 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1206 sg6536 + +lemma sg18864 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1206 sg6537 + +lemma sg18865 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,4,3,2] := by + exact rowSquare_join (by decide) sg1204 sg6545 + +lemma sg18866 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,4,4,4,1] := by + exact rowSquare_join (by decide) sg1205 sg6545 + +lemma sg18867 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg11195 + +lemma sg18868 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6549 + +lemma sg18869 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg839 sg8072 + +lemma sg18870 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg11196 + +lemma sg18871 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6550 + +lemma sg18872 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg1203 sg6546 + +lemma sg18873 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg1203 sg6547 + +lemma sg18874 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,3,3,2] := by + exact rowSquare_join (by decide) sg844 sg8052 + +lemma sg18875 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1202 sg6551 + +lemma sg18876 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg1203 sg6548 + +lemma sg18877 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,4,2,2] := by + exact rowSquare_join (by decide) sg1204 sg6546 + +lemma sg18878 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,4,3,1] := by + exact rowSquare_join (by decide) sg1204 sg6547 + +lemma sg18879 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,4,4] := by + exact rowSquare_join (by decide) sg1205 sg6547 + +lemma sg18880 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg1206 sg6541 + +lemma sg18881 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,5,2,1] := by + exact rowSquare_join (by decide) sg1204 sg6548 + +lemma sg18882 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,5,5,3] := by + exact rowSquare_join (by decide) sg1205 sg6548 + +lemma sg18883 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg239 sg11197 + +lemma sg18884 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg1235 sg6520 + +lemma sg18885 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg1235 sg6521 + +lemma sg18886 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,3,2,2] := by + exact rowSquare_join (by decide) sg1236 sg6520 + +lemma sg18887 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,3,3,1] := by + exact rowSquare_join (by decide) sg1211 sg6526 + +lemma sg18888 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg1235 sg6522 + +lemma sg18889 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,4,2,1] := by + exact rowSquare_join (by decide) sg1236 sg6521 + +lemma sg18890 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,4,3] := by + exact rowSquare_join (by decide) sg1237 sg6521 + +lemma sg18891 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,5,1,1] := by + exact rowSquare_join (by decide) sg1236 sg6522 + +lemma sg18892 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,5,2] := by + exact rowSquare_join (by decide) sg1237 sg6522 + +lemma sg18893 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,8,6,6,1] := by + exact rowSquare_join (by decide) sg1207 sg6541 + +lemma sg18894 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg463 sg8931 + +lemma sg18895 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1206 sg6545 + +lemma sg18896 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,3,3,3,3] := by + exact rowSquare_join (by decide) sg846 sg8051 + +lemma sg18897 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg839 sg8073 + +lemma sg18898 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1203 sg6552 + +lemma sg18899 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1203 sg6553 + +lemma sg18900 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,3,3,2] := by + exact rowSquare_join (by decide) sg844 sg8058 + +lemma sg18901 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1206 sg6548 + +lemma sg18902 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,4,2,2] := by + exact rowSquare_join (by decide) sg1204 sg6552 + +lemma sg18903 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,4,3,1] := by + exact rowSquare_join (by decide) sg1204 sg6553 + +lemma sg18904 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,9,4,4,4] := by + exact rowSquare_join (by decide) sg1205 sg6553 + +lemma sg18905 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,10,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg839 sg8074 + +lemma sg18906 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,10,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1206 sg6552 + +lemma sg18907 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,10,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1206 sg6553 + +lemma sg18908 : RowSquare [7,6,3,3,3,2,1,1,1,1,1,1,1] [10,10,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg1206 sg6554 + +lemma sg18909 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1754 sg6468 + +lemma sg18910 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4868 + +lemma sg18911 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1754 sg6469 + +lemma sg18912 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4869 + +lemma sg18913 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1754 sg6470 + +lemma sg18914 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1754 sg6471 + +lemma sg18915 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1755 sg6468 + +lemma sg18916 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2704 sg4868 + +lemma sg18917 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2704 sg4869 + +lemma sg18918 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14120 + +lemma sg18919 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4872 + +lemma sg18920 : RowSquare [7,6,4,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg5731 + +lemma sg18921 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14124 + +lemma sg18922 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg2712 sg4901 + +lemma sg18923 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14131 + +lemma sg18924 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14132 + +lemma sg18925 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14133 + +lemma sg18926 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14134 + +lemma sg18927 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14136 + +lemma sg18928 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg3348 sg4422 + +lemma sg18929 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14137 + +lemma sg18930 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14138 + +lemma sg18931 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by + exact rowSquare_join (by decide) sg2714 sg4900 + +lemma sg18932 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by + exact rowSquare_join (by decide) sg2714 sg4901 + +lemma sg18933 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14139 + +lemma sg18934 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg14140 + +lemma sg18935 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by + exact rowSquare_join (by decide) sg13 sg14141 + +lemma sg18936 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by + exact rowSquare_join (by decide) sg13 sg14142 + +lemma sg18937 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by + exact rowSquare_join (by decide) sg13 sg14143 + +lemma sg18938 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by + exact rowSquare_join (by decide) sg13 sg14144 + +lemma sg18939 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3533 sg4276 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes46.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes46.lean index 03f39ee060377a3f9a0ff062e8859cc241af9418..8df3c4909de8591ab4e5f4d9714d27cea57a3d2b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes46.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes46.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes36 - -namespace OAI - -/-! Semigroup Nodes 46. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg18940 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg3382 sg4366 - -lemma sg18941 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3533 sg4277 - -lemma sg18942 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg3383 sg4366 - -lemma sg18943 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14145 - -lemma sg18944 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3533 sg4278 - -lemma sg18945 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3537 sg4267 - -lemma sg18946 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg3534 sg4278 - -lemma sg18947 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4279 - -lemma sg18948 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg3534 sg4279 - -lemma sg18949 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14146 - -lemma sg18950 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3533 sg4280 - -lemma sg18951 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3381 sg4369 - -lemma sg18952 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3534 sg4280 - -lemma sg18953 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14147 - -lemma sg18954 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg15059 - -lemma sg18955 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg3536 sg4268 - -lemma sg18956 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg3534 sg4281 - -lemma sg18957 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4282 - -lemma sg18958 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg3663 sg4152 - -lemma sg18959 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg3534 sg4282 - -lemma sg18960 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg3537 sg4269 - -lemma sg18961 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14148 - -lemma sg18962 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14149 - -lemma sg18963 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15060 - -lemma sg18964 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg15061 - -lemma sg18965 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg3534 sg4283 - -lemma sg18966 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg4902 - -lemma sg18967 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4284 - -lemma sg18968 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg3534 sg4284 - -lemma sg18969 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg15062 - -lemma sg18970 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg2710 sg4903 - -lemma sg18971 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3533 sg4285 - -lemma sg18972 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg3534 sg4285 - -lemma sg18973 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14150 - -lemma sg18974 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg3533 sg4286 - -lemma sg18975 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg3537 sg4270 - -lemma sg18976 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3534 sg4286 - -lemma sg18977 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14151 - -lemma sg18978 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4287 - -lemma sg18979 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg2881 sg4888 - -lemma sg18980 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg3534 sg4287 - -lemma sg18981 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4288 - -lemma sg18982 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg3663 sg4153 - -lemma sg18983 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg3534 sg4288 - -lemma sg18984 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg3537 sg4271 - -lemma sg18985 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg15063 - -lemma sg18986 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14152 - -lemma sg18987 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg15064 - -lemma sg18988 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3350 sg4422 - -lemma sg18989 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg3534 sg4289 - -lemma sg18990 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14153 - -lemma sg18991 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14154 - -lemma sg18992 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4290 - -lemma sg18993 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg15065 - -lemma sg18994 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg3534 sg4290 - -lemma sg18995 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg3537 sg4272 - -lemma sg18996 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4291 - -lemma sg18997 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg3534 sg4291 - -lemma sg18998 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg15066 - -lemma sg18999 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg3537 sg4273 - -lemma sg19000 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14155 - -lemma sg19001 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14156 - -lemma sg19002 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14157 - -lemma sg19003 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg15067 - -lemma sg19004 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg3669 sg4151 - -lemma sg19005 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg4904 - -lemma sg19006 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg3663 sg4154 - -lemma sg19007 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg2710 sg4905 - -lemma sg19008 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg15068 - -lemma sg19009 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14158 - -lemma sg19010 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14159 - -lemma sg19011 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15069 - -lemma sg19012 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg15070 - -lemma sg19013 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3534 sg4292 - -lemma sg19014 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg4906 - -lemma sg19015 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14160 - -lemma sg19016 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14161 - -lemma sg19017 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14162 - -lemma sg19018 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg15071 - -lemma sg19019 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg15072 - -lemma sg19020 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,3,1] := by - exact rowSquare_join (by decide) sg3537 sg4274 - -lemma sg19021 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3536 sg4275 - -lemma sg19022 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg1 sg15073 - -lemma sg19023 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14163 - -lemma sg19024 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14164 - -lemma sg19025 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14165 - -lemma sg19026 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg15074 - -lemma sg19027 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg1 sg15075 - -lemma sg19028 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by - exact rowSquare_join (by decide) sg2714 sg4903 - -lemma sg19029 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14166 - -lemma sg19030 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14167 - -lemma sg19031 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14168 - -lemma sg19032 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by - exact rowSquare_join (by decide) sg1 sg15076 - -lemma sg19033 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by - exact rowSquare_join (by decide) sg1 sg15077 - -lemma sg19034 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14169 - -lemma sg19035 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2710 sg4907 - -lemma sg19036 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg14127 - -lemma sg19037 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4293 - -lemma sg19038 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14170 - -lemma sg19039 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4294 - -lemma sg19040 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4295 - -lemma sg19041 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg3539 sg4271 - -lemma sg19042 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg2710 sg4908 - -lemma sg19043 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14171 - -lemma sg19044 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4296 - -lemma sg19045 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg4909 - -lemma sg19046 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14172 - -lemma sg19047 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14173 - -lemma sg19048 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg3347 sg4427 - -lemma sg19049 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg4910 - -lemma sg19050 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg3347 sg4428 - -lemma sg19051 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14174 - -lemma sg19052 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14175 - -lemma sg19053 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg2710 sg4911 - -lemma sg19054 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg2712 sg4905 - -lemma sg19055 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3381 sg4370 - -lemma sg19056 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14176 - -lemma sg19057 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4297 - -lemma sg19058 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg3347 sg4429 - -lemma sg19059 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg4912 - -lemma sg19060 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14177 - -lemma sg19061 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14178 - -lemma sg19062 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg3347 sg4430 - -lemma sg19063 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg3539 sg4275 - -lemma sg19064 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by - exact rowSquare_join (by decide) sg3540 sg4273 - -lemma sg19065 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14179 - -lemma sg19066 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14180 - -lemma sg19067 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14181 - -lemma sg19068 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by - exact rowSquare_join (by decide) sg2714 sg4904 - -lemma sg19069 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by - exact rowSquare_join (by decide) sg2714 sg4905 - -lemma sg19070 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14182 - -lemma sg19071 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg14183 - -lemma sg19072 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by - exact rowSquare_join (by decide) sg13 sg14184 - -lemma sg19073 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by - exact rowSquare_join (by decide) sg13 sg14185 - -lemma sg19074 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg14128 - -lemma sg19075 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2707 sg4913 - -lemma sg19076 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14186 - -lemma sg19077 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2707 sg4914 - -lemma sg19078 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg2708 sg4914 - -lemma sg19079 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14188 - -lemma sg19080 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14189 - -lemma sg19081 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg2708 sg4915 - -lemma sg19082 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg2625 sg4939 - -lemma sg19083 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg2712 sg4908 - -lemma sg19084 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg14129 - -lemma sg19085 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14190 - -lemma sg19086 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14130 - -lemma sg19087 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14191 - -lemma sg19088 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14193 - -lemma sg19089 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14135 - -lemma sg19090 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14194 - -lemma sg19091 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14195 - -lemma sg19092 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg3537 sg4279 - -lemma sg19093 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg3537 sg4281 - -lemma sg19094 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg15078 - -lemma sg19095 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg3537 sg4282 - -lemma sg19096 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg15079 - -lemma sg19097 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg3537 sg4283 - -lemma sg19098 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg1 sg15080 - -lemma sg19099 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg3537 sg4287 - -lemma sg19100 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg15081 - -lemma sg19101 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg3537 sg4288 - -lemma sg19102 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg3537 sg4289 - -lemma sg19103 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg15082 - -lemma sg19104 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg3537 sg4290 - -lemma sg19105 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg1 sg15083 - -lemma sg19106 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14196 - -lemma sg19107 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg15084 - -lemma sg19108 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg1 sg15085 - -lemma sg19109 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by - exact rowSquare_join (by decide) sg3388 sg4367 - -lemma sg19110 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg15086 - -lemma sg19111 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg3537 sg4292 - -lemma sg19112 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg84 sg12469 - -lemma sg19113 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg15087 - -lemma sg19114 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg1 sg15088 - -lemma sg19115 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by - exact rowSquare_join (by decide) sg1 sg15089 - -lemma sg19116 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg84 sg12470 - -lemma sg19117 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg84 sg12471 - -lemma sg19118 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by - exact rowSquare_join (by decide) sg1 sg15090 - -lemma sg19119 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by - exact rowSquare_join (by decide) sg1 sg15091 - -lemma sg19120 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14197 - -lemma sg19121 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by - exact rowSquare_join (by decide) sg84 sg12472 - -lemma sg19122 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by - exact rowSquare_join (by decide) sg84 sg12473 - -lemma sg19123 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by - exact rowSquare_join (by decide) sg84 sg12474 - -lemma sg19124 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg3537 sg4293 - -lemma sg19125 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg3539 sg4287 - -lemma sg19126 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg3537 sg4294 - -lemma sg19127 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg3537 sg4295 - -lemma sg19128 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg15092 - -lemma sg19129 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg3537 sg4296 - -lemma sg19130 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg84 sg12477 - -lemma sg19131 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg15093 - -lemma sg19132 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by - exact rowSquare_join (by decide) sg401 sg11553 - -lemma sg19133 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg1 sg15094 - -lemma sg19134 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by - exact rowSquare_join (by decide) sg3540 sg4288 - -lemma sg19135 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg84 sg12479 - -lemma sg19136 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg84 sg12480 - -lemma sg19137 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by - exact rowSquare_join (by decide) sg1 sg15095 - -lemma sg19138 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by - exact rowSquare_join (by decide) sg1 sg15096 - -lemma sg19139 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg84 sg12481 - -lemma sg19140 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg15097 - -lemma sg19141 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by - exact rowSquare_join (by decide) sg706 sg11058 - -lemma sg19142 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg84 sg12482 - -lemma sg19143 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg84 sg12483 - -lemma sg19144 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by - exact rowSquare_join (by decide) sg1 sg15098 - -lemma sg19145 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by - exact rowSquare_join (by decide) sg1 sg15099 - -lemma sg19146 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14198 - -lemma sg19147 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by - exact rowSquare_join (by decide) sg84 sg12484 - -lemma sg19148 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by - exact rowSquare_join (by decide) sg84 sg12485 - -lemma sg19149 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by - exact rowSquare_join (by decide) sg84 sg12486 - -lemma sg19150 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14199 - -lemma sg19151 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by - exact rowSquare_join (by decide) sg13 sg14200 - -lemma sg19152 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by - exact rowSquare_join (by decide) sg13 sg14201 - -lemma sg19153 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg4913 - -lemma sg19154 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg3347 sg4433 - -lemma sg19155 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg4914 - -lemma sg19156 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14202 - -lemma sg19157 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg3539 sg4294 - -lemma sg19158 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by - exact rowSquare_join (by decide) sg402 sg11553 - -lemma sg19159 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg3539 sg4295 - -lemma sg19160 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,2] := by - exact rowSquare_join (by decide) sg2715 sg4908 - -lemma sg19161 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg14187 - -lemma sg19162 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14203 - -lemma sg19163 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg2708 sg4916 - -lemma sg19164 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg2712 sg4913 - -lemma sg19165 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg424 sg11548 - -lemma sg19166 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg83 sg12494 - -lemma sg19167 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14204 - -lemma sg19168 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14205 - -lemma sg19169 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14192 - -lemma sg19170 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg2712 sg4914 - -lemma sg19171 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by - exact rowSquare_join (by decide) sg228 sg12339 - -lemma sg19172 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14206 - -lemma sg19173 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14207 - -lemma sg19174 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14208 - -lemma sg19175 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,2] := by - exact rowSquare_join (by decide) sg2716 sg4908 - -lemma sg19176 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg3537 sg4298 - -lemma sg19177 : RowSquare [7,7,2,2,2,2,2,2,2,2,1] [5,5,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg11799 - -lemma sg19178 : RowSquare [7,7,2,2,2,2,2,2,2,2,1] [5,5,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg210 sg11800 - -lemma sg19179 : RowSquare [7,7,2,2,2,2,2,2,2,2,1] [5,5,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg210 sg11801 - -lemma sg19180 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg2256 sg5750 - -lemma sg19181 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg2622 sg4938 - -lemma sg19182 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg2623 sg4938 - -lemma sg19183 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg3537 sg4173 - -lemma sg19184 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg3534 sg4178 - -lemma sg19185 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg1 sg15103 - -lemma sg19186 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg1 sg15104 - -lemma sg19187 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg3539 sg4172 - -lemma sg19188 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg3539 sg4173 - -lemma sg19189 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg3539 sg4174 - -lemma sg19190 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2,2] := by - exact rowSquare_join (by decide) sg3315 sg4423 - -lemma sg19191 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,3,1] := by - exact rowSquare_join (by decide) sg3540 sg4170 - -lemma sg19192 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14220 - -lemma sg19193 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg14221 - -lemma sg19194 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg14223 - -lemma sg19195 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by - exact rowSquare_join (by decide) sg3540 sg4173 - -lemma sg19196 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by - exact rowSquare_join (by decide) sg3316 sg4423 - -lemma sg19197 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by - exact rowSquare_join (by decide) sg3540 sg4174 - -lemma sg19198 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14224 - -lemma sg19199 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14225 - -lemma sg19200 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg14226 - -lemma sg19201 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by - exact rowSquare_join (by decide) sg13 sg14227 - -lemma sg19202 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg14228 - -lemma sg19203 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by - exact rowSquare_join (by decide) sg13 sg14229 - -lemma sg19204 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by - exact rowSquare_join (by decide) sg13 sg14230 - -lemma sg19205 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg2712 sg4894 - -lemma sg19206 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14231 - -lemma sg19207 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14232 - -lemma sg19208 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14233 - -lemma sg19209 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg14234 - -lemma sg19210 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14235 - -lemma sg19211 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg14236 - -lemma sg19212 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14237 - -lemma sg19213 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg14238 - -lemma sg19214 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg2712 sg4895 - -lemma sg19215 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14239 - -lemma sg19216 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg14240 - -lemma sg19217 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by - exact rowSquare_join (by decide) sg13 sg14241 - -lemma sg19218 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg14242 - -lemma sg19219 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by - exact rowSquare_join (by decide) sg13 sg14243 - -lemma sg19220 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by - exact rowSquare_join (by decide) sg74 sg12722 - -lemma sg19221 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14244 - -lemma sg19222 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14245 - -lemma sg19223 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14246 - -lemma sg19224 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by - exact rowSquare_join (by decide) sg13 sg14247 - -lemma sg19225 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by - exact rowSquare_join (by decide) sg13 sg14248 - -lemma sg19226 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by - exact rowSquare_join (by decide) sg13 sg14249 - -lemma sg19227 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,2] := by - exact rowSquare_join (by decide) sg83 sg12506 - -lemma sg19228 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,2] := by - exact rowSquare_join (by decide) sg83 sg12507 - -lemma sg19229 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,2,1] := by - exact rowSquare_join (by decide) sg83 sg12508 - -lemma sg19230 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg14250 - -lemma sg19231 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by - exact rowSquare_join (by decide) sg83 sg12509 - -lemma sg19232 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by - exact rowSquare_join (by decide) sg2714 sg4895 - -lemma sg19233 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by - exact rowSquare_join (by decide) sg83 sg12510 - -lemma sg19234 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by - exact rowSquare_join (by decide) sg83 sg12511 - -lemma sg19235 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by - exact rowSquare_join (by decide) sg83 sg12512 - -lemma sg19236 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by - exact rowSquare_join (by decide) sg83 sg12513 - -lemma sg19237 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg83 sg12514 - -lemma sg19238 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14251 - -lemma sg19239 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg14252 - -lemma sg19240 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by - exact rowSquare_join (by decide) sg13 sg14253 - -lemma sg19241 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by - exact rowSquare_join (by decide) sg13 sg14254 - -lemma sg19242 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by - exact rowSquare_join (by decide) sg13 sg14255 - -lemma sg19243 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by - exact rowSquare_join (by decide) sg13 sg14256 - -lemma sg19244 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3547 sg4166 - -lemma sg19245 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg3547 sg4167 - -lemma sg19246 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg14212 - -lemma sg19247 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg3541 sg4168 - -lemma sg19248 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg3548 sg4167 - -lemma sg19249 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3535 sg4175 - -lemma sg19250 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg3542 sg4168 - -lemma sg19251 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg3533 sg4181 - -lemma sg19252 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg15105 - -lemma sg19253 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg3534 sg4181 - -lemma sg19254 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg3536 sg4175 - -lemma sg19255 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg3534 sg4182 - -lemma sg19256 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg3314 sg4425 - -lemma sg19257 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg14213 - -lemma sg19258 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg3543 sg4168 - -lemma sg19259 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg3549 sg4167 - -lemma sg19260 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg15106 - -lemma sg19261 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg3544 sg4168 - -lemma sg19262 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14257 - -lemma sg19263 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg3538 sg4175 - -lemma sg19264 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg3663 sg4061 - -lemma sg19265 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15107 - -lemma sg19266 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg15108 - -lemma sg19267 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg3314 sg4426 - -lemma sg19268 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg3534 sg4183 - -lemma sg19269 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg3537 sg4176 - -lemma sg19270 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg15109 - -lemma sg19271 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg15110 - -lemma sg19272 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14258 - -lemma sg19273 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14259 - -lemma sg19274 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg14260 - -lemma sg19275 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg15111 - -lemma sg19276 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg15112 - -lemma sg19277 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg15113 - -lemma sg19278 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg1 sg15114 - -lemma sg19279 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg3537 sg4177 - -lemma sg19280 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14261 - -lemma sg19281 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14262 - -lemma sg19282 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14263 - -lemma sg19283 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg15115 - -lemma sg19284 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14264 - -lemma sg19285 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg15116 - -lemma sg19286 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg15117 - -lemma sg19287 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg3663 sg4062 - -lemma sg19288 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg1 sg15118 - -lemma sg19289 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg1 sg15119 - -lemma sg19290 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg15120 - -lemma sg19291 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg3546 sg4168 - -lemma sg19292 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg14214 - -lemma sg19293 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg15121 - -lemma sg19294 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14265 - -lemma sg19295 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14266 - -lemma sg19296 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg14267 - -lemma sg19297 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg15122 - -lemma sg19298 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg15123 - -lemma sg19299 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg15124 - -lemma sg19300 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg1 sg15125 - -lemma sg19301 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg3537 sg4180 - -lemma sg19302 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg15126 - -lemma sg19303 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15127 - -lemma sg19304 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg15128 - -lemma sg19305 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg3314 sg4429 - -lemma sg19306 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg26 sg12869 - -lemma sg19307 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14268 - -lemma sg19308 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14269 - -lemma sg19309 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg14270 - -lemma sg19310 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg15129 - -lemma sg19311 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg15130 - -lemma sg19312 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg15131 - -lemma sg19313 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14271 - -lemma sg19314 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14272 - -lemma sg19315 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14273 - -lemma sg19316 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg14274 - -lemma sg19317 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14275 - -lemma sg19318 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg14276 - -lemma sg19319 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by - exact rowSquare_join (by decide) sg1 sg15132 - -lemma sg19320 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1 sg15133 - -lemma sg19321 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg1 sg15134 - -lemma sg19322 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14277 - -lemma sg19323 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg83 sg12515 - -lemma sg19324 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg15135 - -lemma sg19325 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg165 sg11604 - -lemma sg19326 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg83 sg12516 - -lemma sg19327 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg83 sg12517 - -lemma sg19328 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg84 sg12506 - -lemma sg19329 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,3,1] := by - exact rowSquare_join (by decide) sg165 sg11605 - -lemma sg19330 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12518 - -lemma sg19331 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg165 sg11606 - -lemma sg19332 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by - exact rowSquare_join (by decide) sg1 sg15136 - -lemma sg19333 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg26 sg12873 - -lemma sg19334 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg84 sg12507 - -lemma sg19335 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg12874 - -lemma sg19336 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,2,1] := by - exact rowSquare_join (by decide) sg84 sg12508 - -lemma sg19337 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by - exact rowSquare_join (by decide) sg165 sg11607 - -lemma sg19338 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg84 sg12509 - -lemma sg19339 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by - exact rowSquare_join (by decide) sg165 sg11608 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes36 + +namespace OAI + +/-! Semigroup Nodes 46. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg18940 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg3382 sg4366 + +lemma sg18941 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3533 sg4277 + +lemma sg18942 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg3383 sg4366 + +lemma sg18943 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14145 + +lemma sg18944 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3533 sg4278 + +lemma sg18945 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3537 sg4267 + +lemma sg18946 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg3534 sg4278 + +lemma sg18947 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4279 + +lemma sg18948 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg3534 sg4279 + +lemma sg18949 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14146 + +lemma sg18950 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3533 sg4280 + +lemma sg18951 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3381 sg4369 + +lemma sg18952 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3534 sg4280 + +lemma sg18953 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14147 + +lemma sg18954 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg15059 + +lemma sg18955 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg3536 sg4268 + +lemma sg18956 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg3534 sg4281 + +lemma sg18957 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4282 + +lemma sg18958 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg3663 sg4152 + +lemma sg18959 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg3534 sg4282 + +lemma sg18960 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg3537 sg4269 + +lemma sg18961 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14148 + +lemma sg18962 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14149 + +lemma sg18963 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15060 + +lemma sg18964 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg15061 + +lemma sg18965 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg3534 sg4283 + +lemma sg18966 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg4902 + +lemma sg18967 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4284 + +lemma sg18968 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg3534 sg4284 + +lemma sg18969 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg15062 + +lemma sg18970 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg2710 sg4903 + +lemma sg18971 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3533 sg4285 + +lemma sg18972 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg3534 sg4285 + +lemma sg18973 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14150 + +lemma sg18974 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg3533 sg4286 + +lemma sg18975 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg3537 sg4270 + +lemma sg18976 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3534 sg4286 + +lemma sg18977 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14151 + +lemma sg18978 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4287 + +lemma sg18979 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg2881 sg4888 + +lemma sg18980 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg3534 sg4287 + +lemma sg18981 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4288 + +lemma sg18982 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg3663 sg4153 + +lemma sg18983 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg3534 sg4288 + +lemma sg18984 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg3537 sg4271 + +lemma sg18985 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg15063 + +lemma sg18986 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14152 + +lemma sg18987 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg15064 + +lemma sg18988 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3350 sg4422 + +lemma sg18989 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg3534 sg4289 + +lemma sg18990 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14153 + +lemma sg18991 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14154 + +lemma sg18992 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4290 + +lemma sg18993 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg15065 + +lemma sg18994 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg3534 sg4290 + +lemma sg18995 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg3537 sg4272 + +lemma sg18996 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4291 + +lemma sg18997 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg3534 sg4291 + +lemma sg18998 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg15066 + +lemma sg18999 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg3537 sg4273 + +lemma sg19000 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14155 + +lemma sg19001 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14156 + +lemma sg19002 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14157 + +lemma sg19003 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg15067 + +lemma sg19004 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg3669 sg4151 + +lemma sg19005 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg4904 + +lemma sg19006 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg3663 sg4154 + +lemma sg19007 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg2710 sg4905 + +lemma sg19008 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg15068 + +lemma sg19009 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14158 + +lemma sg19010 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14159 + +lemma sg19011 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15069 + +lemma sg19012 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg15070 + +lemma sg19013 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3534 sg4292 + +lemma sg19014 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg4906 + +lemma sg19015 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14160 + +lemma sg19016 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14161 + +lemma sg19017 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14162 + +lemma sg19018 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg15071 + +lemma sg19019 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg15072 + +lemma sg19020 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,3,1] := by + exact rowSquare_join (by decide) sg3537 sg4274 + +lemma sg19021 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3536 sg4275 + +lemma sg19022 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg1 sg15073 + +lemma sg19023 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14163 + +lemma sg19024 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14164 + +lemma sg19025 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14165 + +lemma sg19026 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg15074 + +lemma sg19027 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg1 sg15075 + +lemma sg19028 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by + exact rowSquare_join (by decide) sg2714 sg4903 + +lemma sg19029 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14166 + +lemma sg19030 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14167 + +lemma sg19031 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14168 + +lemma sg19032 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by + exact rowSquare_join (by decide) sg1 sg15076 + +lemma sg19033 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by + exact rowSquare_join (by decide) sg1 sg15077 + +lemma sg19034 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14169 + +lemma sg19035 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2710 sg4907 + +lemma sg19036 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg14127 + +lemma sg19037 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4293 + +lemma sg19038 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14170 + +lemma sg19039 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4294 + +lemma sg19040 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4295 + +lemma sg19041 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg3539 sg4271 + +lemma sg19042 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg2710 sg4908 + +lemma sg19043 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14171 + +lemma sg19044 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4296 + +lemma sg19045 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg4909 + +lemma sg19046 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14172 + +lemma sg19047 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14173 + +lemma sg19048 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg3347 sg4427 + +lemma sg19049 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg4910 + +lemma sg19050 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg3347 sg4428 + +lemma sg19051 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14174 + +lemma sg19052 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14175 + +lemma sg19053 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg2710 sg4911 + +lemma sg19054 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg2712 sg4905 + +lemma sg19055 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3381 sg4370 + +lemma sg19056 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14176 + +lemma sg19057 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4297 + +lemma sg19058 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg3347 sg4429 + +lemma sg19059 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg4912 + +lemma sg19060 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14177 + +lemma sg19061 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14178 + +lemma sg19062 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg3347 sg4430 + +lemma sg19063 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg3539 sg4275 + +lemma sg19064 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by + exact rowSquare_join (by decide) sg3540 sg4273 + +lemma sg19065 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14179 + +lemma sg19066 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14180 + +lemma sg19067 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14181 + +lemma sg19068 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by + exact rowSquare_join (by decide) sg2714 sg4904 + +lemma sg19069 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by + exact rowSquare_join (by decide) sg2714 sg4905 + +lemma sg19070 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14182 + +lemma sg19071 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg14183 + +lemma sg19072 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by + exact rowSquare_join (by decide) sg13 sg14184 + +lemma sg19073 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by + exact rowSquare_join (by decide) sg13 sg14185 + +lemma sg19074 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg14128 + +lemma sg19075 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2707 sg4913 + +lemma sg19076 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14186 + +lemma sg19077 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2707 sg4914 + +lemma sg19078 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg2708 sg4914 + +lemma sg19079 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14188 + +lemma sg19080 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14189 + +lemma sg19081 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg2708 sg4915 + +lemma sg19082 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg2625 sg4939 + +lemma sg19083 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg2712 sg4908 + +lemma sg19084 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg14129 + +lemma sg19085 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14190 + +lemma sg19086 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14130 + +lemma sg19087 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14191 + +lemma sg19088 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14193 + +lemma sg19089 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14135 + +lemma sg19090 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14194 + +lemma sg19091 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14195 + +lemma sg19092 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg3537 sg4279 + +lemma sg19093 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg3537 sg4281 + +lemma sg19094 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg15078 + +lemma sg19095 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg3537 sg4282 + +lemma sg19096 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg15079 + +lemma sg19097 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg3537 sg4283 + +lemma sg19098 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg1 sg15080 + +lemma sg19099 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg3537 sg4287 + +lemma sg19100 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg15081 + +lemma sg19101 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg3537 sg4288 + +lemma sg19102 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg3537 sg4289 + +lemma sg19103 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg15082 + +lemma sg19104 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg3537 sg4290 + +lemma sg19105 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg1 sg15083 + +lemma sg19106 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14196 + +lemma sg19107 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg15084 + +lemma sg19108 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg1 sg15085 + +lemma sg19109 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by + exact rowSquare_join (by decide) sg3388 sg4367 + +lemma sg19110 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg15086 + +lemma sg19111 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg3537 sg4292 + +lemma sg19112 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg84 sg12469 + +lemma sg19113 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg15087 + +lemma sg19114 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg1 sg15088 + +lemma sg19115 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by + exact rowSquare_join (by decide) sg1 sg15089 + +lemma sg19116 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg84 sg12470 + +lemma sg19117 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg84 sg12471 + +lemma sg19118 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by + exact rowSquare_join (by decide) sg1 sg15090 + +lemma sg19119 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by + exact rowSquare_join (by decide) sg1 sg15091 + +lemma sg19120 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14197 + +lemma sg19121 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by + exact rowSquare_join (by decide) sg84 sg12472 + +lemma sg19122 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by + exact rowSquare_join (by decide) sg84 sg12473 + +lemma sg19123 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by + exact rowSquare_join (by decide) sg84 sg12474 + +lemma sg19124 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg3537 sg4293 + +lemma sg19125 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg3539 sg4287 + +lemma sg19126 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg3537 sg4294 + +lemma sg19127 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg3537 sg4295 + +lemma sg19128 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg15092 + +lemma sg19129 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg3537 sg4296 + +lemma sg19130 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg84 sg12477 + +lemma sg19131 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg15093 + +lemma sg19132 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by + exact rowSquare_join (by decide) sg401 sg11553 + +lemma sg19133 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg1 sg15094 + +lemma sg19134 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by + exact rowSquare_join (by decide) sg3540 sg4288 + +lemma sg19135 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg84 sg12479 + +lemma sg19136 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg84 sg12480 + +lemma sg19137 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by + exact rowSquare_join (by decide) sg1 sg15095 + +lemma sg19138 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by + exact rowSquare_join (by decide) sg1 sg15096 + +lemma sg19139 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg84 sg12481 + +lemma sg19140 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg15097 + +lemma sg19141 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by + exact rowSquare_join (by decide) sg706 sg11058 + +lemma sg19142 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg84 sg12482 + +lemma sg19143 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg84 sg12483 + +lemma sg19144 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by + exact rowSquare_join (by decide) sg1 sg15098 + +lemma sg19145 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by + exact rowSquare_join (by decide) sg1 sg15099 + +lemma sg19146 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14198 + +lemma sg19147 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by + exact rowSquare_join (by decide) sg84 sg12484 + +lemma sg19148 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by + exact rowSquare_join (by decide) sg84 sg12485 + +lemma sg19149 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by + exact rowSquare_join (by decide) sg84 sg12486 + +lemma sg19150 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14199 + +lemma sg19151 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by + exact rowSquare_join (by decide) sg13 sg14200 + +lemma sg19152 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by + exact rowSquare_join (by decide) sg13 sg14201 + +lemma sg19153 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg4913 + +lemma sg19154 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg3347 sg4433 + +lemma sg19155 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg4914 + +lemma sg19156 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14202 + +lemma sg19157 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg3539 sg4294 + +lemma sg19158 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by + exact rowSquare_join (by decide) sg402 sg11553 + +lemma sg19159 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg3539 sg4295 + +lemma sg19160 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,2] := by + exact rowSquare_join (by decide) sg2715 sg4908 + +lemma sg19161 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg14187 + +lemma sg19162 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14203 + +lemma sg19163 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg2708 sg4916 + +lemma sg19164 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg2712 sg4913 + +lemma sg19165 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg424 sg11548 + +lemma sg19166 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg83 sg12494 + +lemma sg19167 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14204 + +lemma sg19168 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14205 + +lemma sg19169 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14192 + +lemma sg19170 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg2712 sg4914 + +lemma sg19171 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by + exact rowSquare_join (by decide) sg228 sg12339 + +lemma sg19172 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14206 + +lemma sg19173 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14207 + +lemma sg19174 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14208 + +lemma sg19175 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,2] := by + exact rowSquare_join (by decide) sg2716 sg4908 + +lemma sg19176 : RowSquare [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg3537 sg4298 + +lemma sg19177 : RowSquare [7,7,2,2,2,2,2,2,2,2,1] [5,5,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg11799 + +lemma sg19178 : RowSquare [7,7,2,2,2,2,2,2,2,2,1] [5,5,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg210 sg11800 + +lemma sg19179 : RowSquare [7,7,2,2,2,2,2,2,2,2,1] [5,5,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg210 sg11801 + +lemma sg19180 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg2256 sg5750 + +lemma sg19181 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg2622 sg4938 + +lemma sg19182 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg2623 sg4938 + +lemma sg19183 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg3537 sg4173 + +lemma sg19184 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg3534 sg4178 + +lemma sg19185 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg1 sg15103 + +lemma sg19186 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg1 sg15104 + +lemma sg19187 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg3539 sg4172 + +lemma sg19188 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg3539 sg4173 + +lemma sg19189 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg3539 sg4174 + +lemma sg19190 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,2,2] := by + exact rowSquare_join (by decide) sg3315 sg4423 + +lemma sg19191 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,4,4,3,1] := by + exact rowSquare_join (by decide) sg3540 sg4170 + +lemma sg19192 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14220 + +lemma sg19193 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg14221 + +lemma sg19194 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg14223 + +lemma sg19195 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by + exact rowSquare_join (by decide) sg3540 sg4173 + +lemma sg19196 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by + exact rowSquare_join (by decide) sg3316 sg4423 + +lemma sg19197 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by + exact rowSquare_join (by decide) sg3540 sg4174 + +lemma sg19198 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14224 + +lemma sg19199 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14225 + +lemma sg19200 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg14226 + +lemma sg19201 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by + exact rowSquare_join (by decide) sg13 sg14227 + +lemma sg19202 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg14228 + +lemma sg19203 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by + exact rowSquare_join (by decide) sg13 sg14229 + +lemma sg19204 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by + exact rowSquare_join (by decide) sg13 sg14230 + +lemma sg19205 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg2712 sg4894 + +lemma sg19206 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14231 + +lemma sg19207 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14232 + +lemma sg19208 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14233 + +lemma sg19209 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg14234 + +lemma sg19210 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14235 + +lemma sg19211 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg14236 + +lemma sg19212 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14237 + +lemma sg19213 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg14238 + +lemma sg19214 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg2712 sg4895 + +lemma sg19215 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14239 + +lemma sg19216 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg14240 + +lemma sg19217 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by + exact rowSquare_join (by decide) sg13 sg14241 + +lemma sg19218 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg14242 + +lemma sg19219 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by + exact rowSquare_join (by decide) sg13 sg14243 + +lemma sg19220 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by + exact rowSquare_join (by decide) sg74 sg12722 + +lemma sg19221 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14244 + +lemma sg19222 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14245 + +lemma sg19223 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14246 + +lemma sg19224 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by + exact rowSquare_join (by decide) sg13 sg14247 + +lemma sg19225 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by + exact rowSquare_join (by decide) sg13 sg14248 + +lemma sg19226 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by + exact rowSquare_join (by decide) sg13 sg14249 + +lemma sg19227 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,2] := by + exact rowSquare_join (by decide) sg83 sg12506 + +lemma sg19228 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,2,2,2] := by + exact rowSquare_join (by decide) sg83 sg12507 + +lemma sg19229 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,2,1] := by + exact rowSquare_join (by decide) sg83 sg12508 + +lemma sg19230 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg14250 + +lemma sg19231 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by + exact rowSquare_join (by decide) sg83 sg12509 + +lemma sg19232 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by + exact rowSquare_join (by decide) sg2714 sg4895 + +lemma sg19233 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by + exact rowSquare_join (by decide) sg83 sg12510 + +lemma sg19234 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by + exact rowSquare_join (by decide) sg83 sg12511 + +lemma sg19235 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by + exact rowSquare_join (by decide) sg83 sg12512 + +lemma sg19236 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by + exact rowSquare_join (by decide) sg83 sg12513 + +lemma sg19237 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg83 sg12514 + +lemma sg19238 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14251 + +lemma sg19239 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg14252 + +lemma sg19240 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by + exact rowSquare_join (by decide) sg13 sg14253 + +lemma sg19241 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by + exact rowSquare_join (by decide) sg13 sg14254 + +lemma sg19242 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by + exact rowSquare_join (by decide) sg13 sg14255 + +lemma sg19243 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by + exact rowSquare_join (by decide) sg13 sg14256 + +lemma sg19244 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3547 sg4166 + +lemma sg19245 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg3547 sg4167 + +lemma sg19246 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg14212 + +lemma sg19247 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg3541 sg4168 + +lemma sg19248 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg3548 sg4167 + +lemma sg19249 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3535 sg4175 + +lemma sg19250 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg3542 sg4168 + +lemma sg19251 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg3533 sg4181 + +lemma sg19252 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg15105 + +lemma sg19253 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg3534 sg4181 + +lemma sg19254 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg3536 sg4175 + +lemma sg19255 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg3534 sg4182 + +lemma sg19256 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg3314 sg4425 + +lemma sg19257 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg14213 + +lemma sg19258 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg3543 sg4168 + +lemma sg19259 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg3549 sg4167 + +lemma sg19260 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg15106 + +lemma sg19261 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg3544 sg4168 + +lemma sg19262 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14257 + +lemma sg19263 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg3538 sg4175 + +lemma sg19264 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg3663 sg4061 + +lemma sg19265 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15107 + +lemma sg19266 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg15108 + +lemma sg19267 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg3314 sg4426 + +lemma sg19268 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg3534 sg4183 + +lemma sg19269 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg3537 sg4176 + +lemma sg19270 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg15109 + +lemma sg19271 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg15110 + +lemma sg19272 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14258 + +lemma sg19273 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14259 + +lemma sg19274 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg14260 + +lemma sg19275 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg15111 + +lemma sg19276 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg15112 + +lemma sg19277 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg15113 + +lemma sg19278 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg1 sg15114 + +lemma sg19279 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg3537 sg4177 + +lemma sg19280 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14261 + +lemma sg19281 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14262 + +lemma sg19282 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14263 + +lemma sg19283 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg15115 + +lemma sg19284 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14264 + +lemma sg19285 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg15116 + +lemma sg19286 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg15117 + +lemma sg19287 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg3663 sg4062 + +lemma sg19288 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg1 sg15118 + +lemma sg19289 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg1 sg15119 + +lemma sg19290 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg15120 + +lemma sg19291 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg3546 sg4168 + +lemma sg19292 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg14214 + +lemma sg19293 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg15121 + +lemma sg19294 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14265 + +lemma sg19295 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14266 + +lemma sg19296 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg14267 + +lemma sg19297 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg15122 + +lemma sg19298 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg15123 + +lemma sg19299 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg15124 + +lemma sg19300 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg1 sg15125 + +lemma sg19301 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg3537 sg4180 + +lemma sg19302 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg15126 + +lemma sg19303 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15127 + +lemma sg19304 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg15128 + +lemma sg19305 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg3314 sg4429 + +lemma sg19306 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg26 sg12869 + +lemma sg19307 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14268 + +lemma sg19308 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14269 + +lemma sg19309 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg14270 + +lemma sg19310 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg15129 + +lemma sg19311 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg15130 + +lemma sg19312 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg15131 + +lemma sg19313 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14271 + +lemma sg19314 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14272 + +lemma sg19315 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14273 + +lemma sg19316 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg14274 + +lemma sg19317 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14275 + +lemma sg19318 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg14276 + +lemma sg19319 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by + exact rowSquare_join (by decide) sg1 sg15132 + +lemma sg19320 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1 sg15133 + +lemma sg19321 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg1 sg15134 + +lemma sg19322 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14277 + +lemma sg19323 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg83 sg12515 + +lemma sg19324 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg15135 + +lemma sg19325 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg165 sg11604 + +lemma sg19326 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg83 sg12516 + +lemma sg19327 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg83 sg12517 + +lemma sg19328 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg84 sg12506 + +lemma sg19329 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,3,1] := by + exact rowSquare_join (by decide) sg165 sg11605 + +lemma sg19330 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12518 + +lemma sg19331 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg165 sg11606 + +lemma sg19332 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by + exact rowSquare_join (by decide) sg1 sg15136 + +lemma sg19333 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg26 sg12873 + +lemma sg19334 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg84 sg12507 + +lemma sg19335 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg12874 + +lemma sg19336 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,2,1] := by + exact rowSquare_join (by decide) sg84 sg12508 + +lemma sg19337 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by + exact rowSquare_join (by decide) sg165 sg11607 + +lemma sg19338 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg84 sg12509 + +lemma sg19339 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by + exact rowSquare_join (by decide) sg165 sg11608 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes47.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes47.lean index d1afad3790644dd4a295237fdd9dedd22b65e845..0fa71e01af93dfad96826729eba2854111755e62 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes47.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes47.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 - -namespace OAI - -/-! Semigroup Nodes 47. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg19340 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by - exact rowSquare_join (by decide) sg165 sg11609 - -lemma sg19341 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14278 - -lemma sg19342 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg84 sg12510 - -lemma sg19343 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg84 sg12511 - -lemma sg19344 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by - exact rowSquare_join (by decide) sg84 sg12512 - -lemma sg19345 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by - exact rowSquare_join (by decide) sg84 sg12513 - -lemma sg19346 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by - exact rowSquare_join (by decide) sg84 sg12514 - -lemma sg19347 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg14215 - -lemma sg19348 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg3546 sg4169 - -lemma sg19349 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg14216 - -lemma sg19350 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg14 sg14217 - -lemma sg19351 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg3314 sg4431 - -lemma sg19352 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14279 - -lemma sg19353 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14280 - -lemma sg19354 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14281 - -lemma sg19355 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg14282 - -lemma sg19356 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg14218 - -lemma sg19357 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg3539 sg4179 - -lemma sg19358 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg3539 sg4180 - -lemma sg19359 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg26 sg12877 - -lemma sg19360 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg83 sg12519 - -lemma sg19361 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg14 sg14219 - -lemma sg19362 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg165 sg11610 - -lemma sg19363 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg26 sg12879 - -lemma sg19364 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14283 - -lemma sg19365 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14284 - -lemma sg19366 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg165 sg11611 - -lemma sg19367 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14222 - -lemma sg19368 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg165 sg11612 - -lemma sg19369 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by - exact rowSquare_join (by decide) sg3540 sg4180 - -lemma sg19370 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14285 - -lemma sg19371 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14286 - -lemma sg19372 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg14287 - -lemma sg19373 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by - exact rowSquare_join (by decide) sg165 sg11613 - -lemma sg19374 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg14288 - -lemma sg19375 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by - exact rowSquare_join (by decide) sg165 sg11614 - -lemma sg19376 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by - exact rowSquare_join (by decide) sg165 sg11615 - -lemma sg19377 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg165 sg11616 - -lemma sg19378 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12520 - -lemma sg19379 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg166 sg11605 - -lemma sg19380 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by - exact rowSquare_join (by decide) sg165 sg11617 - -lemma sg19381 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg166 sg11606 - -lemma sg19382 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by - exact rowSquare_join (by decide) sg165 sg11618 - -lemma sg19383 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg12884 - -lemma sg19384 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg26 sg12885 - -lemma sg19385 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg26 sg12886 - -lemma sg19386 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by - exact rowSquare_join (by decide) sg166 sg11607 - -lemma sg19387 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by - exact rowSquare_join (by decide) sg166 sg11608 - -lemma sg19388 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by - exact rowSquare_join (by decide) sg166 sg11609 - -lemma sg19389 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14289 - -lemma sg19390 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14290 - -lemma sg19391 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg14291 - -lemma sg19392 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by - exact rowSquare_join (by decide) sg13 sg14292 - -lemma sg19393 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by - exact rowSquare_join (by decide) sg13 sg14293 - -lemma sg19394 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg14294 - -lemma sg19395 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14235 - -lemma sg19396 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg14 sg14236 - -lemma sg19397 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg83 sg12526 - -lemma sg19398 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14295 - -lemma sg19399 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg166 sg11611 - -lemma sg19400 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg14296 - -lemma sg19401 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg166 sg11612 - -lemma sg19402 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,2] := by - exact rowSquare_join (by decide) sg14 sg14243 - -lemma sg19403 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14297 - -lemma sg19404 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14298 - -lemma sg19405 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14299 - -lemma sg19406 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,2] := by - exact rowSquare_join (by decide) sg166 sg11613 - -lemma sg19407 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,4,1] := by - exact rowSquare_join (by decide) sg166 sg11614 - -lemma sg19408 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,5] := by - exact rowSquare_join (by decide) sg166 sg11615 - -lemma sg19409 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12527 - -lemma sg19410 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg166 sg11616 - -lemma sg19411 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,3] := by - exact rowSquare_join (by decide) sg83 sg12528 - -lemma sg19412 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12529 - -lemma sg19413 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg167 sg11611 - -lemma sg19414 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg167 sg11612 - -lemma sg19415 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,2] := by - exact rowSquare_join (by decide) sg166 sg11617 - -lemma sg19416 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,4,4,1] := by - exact rowSquare_join (by decide) sg166 sg11618 - -lemma sg19417 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14300 - -lemma sg19418 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14301 - -lemma sg19419 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,2] := by - exact rowSquare_join (by decide) sg167 sg11613 - -lemma sg19420 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,5,3,1] := by - exact rowSquare_join (by decide) sg167 sg11614 - -lemma sg19421 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,5,4] := by - exact rowSquare_join (by decide) sg167 sg11615 - -lemma sg19422 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14302 - -lemma sg19423 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by - exact rowSquare_join (by decide) sg13 sg14303 - -lemma sg19424 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,3] := by - exact rowSquare_join (by decide) sg13 sg14304 - -lemma sg19425 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg3537 sg4183 - -lemma sg19426 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg15137 - -lemma sg19427 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg165 sg11628 - -lemma sg19428 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12518 - -lemma sg19429 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg165 sg11629 - -lemma sg19430 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg1 sg15138 - -lemma sg19431 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg1 sg15139 - -lemma sg19432 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg1 sg15140 - -lemma sg19433 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg15141 - -lemma sg19434 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg391 sg11553 - -lemma sg19435 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg165 sg11636 - -lemma sg19436 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg166 sg11627 - -lemma sg19437 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg165 sg11637 - -lemma sg19438 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg1 sg15142 - -lemma sg19439 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12520 - -lemma sg19440 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg166 sg11628 - -lemma sg19441 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg165 sg11638 - -lemma sg19442 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg166 sg11629 - -lemma sg19443 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by - exact rowSquare_join (by decide) sg165 sg11639 - -lemma sg19444 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by - exact rowSquare_join (by decide) sg165 sg11640 - -lemma sg19445 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg165 sg11642 - -lemma sg19446 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg167 sg11627 - -lemma sg19447 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg165 sg11644 - -lemma sg19448 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by - exact rowSquare_join (by decide) sg165 sg11645 - -lemma sg19449 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg168 sg11606 - -lemma sg19450 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by - exact rowSquare_join (by decide) sg165 sg11646 - -lemma sg19451 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12522 - -lemma sg19452 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg165 sg11647 - -lemma sg19453 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg167 sg11629 - -lemma sg19454 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by - exact rowSquare_join (by decide) sg165 sg11648 - -lemma sg19455 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by - exact rowSquare_join (by decide) sg165 sg11649 - -lemma sg19456 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by - exact rowSquare_join (by decide) sg168 sg11609 - -lemma sg19457 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12523 - -lemma sg19458 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12524 - -lemma sg19459 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by - exact rowSquare_join (by decide) sg165 sg11650 - -lemma sg19460 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by - exact rowSquare_join (by decide) sg165 sg11651 - -lemma sg19461 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by - exact rowSquare_join (by decide) sg84 sg12525 - -lemma sg19462 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg165 sg11655 - -lemma sg19463 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg166 sg11633 - -lemma sg19464 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg165 sg11656 - -lemma sg19465 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by - exact rowSquare_join (by decide) sg1 sg15143 - -lemma sg19466 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg165 sg11658 - -lemma sg19467 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg167 sg11633 - -lemma sg19468 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg165 sg11660 - -lemma sg19469 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by - exact rowSquare_join (by decide) sg165 sg11661 - -lemma sg19470 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg166 sg11637 - -lemma sg19471 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by - exact rowSquare_join (by decide) sg165 sg11662 - -lemma sg19472 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12529 - -lemma sg19473 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg165 sg11663 - -lemma sg19474 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg84 sg12530 - -lemma sg19475 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by - exact rowSquare_join (by decide) sg165 sg11664 - -lemma sg19476 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by - exact rowSquare_join (by decide) sg165 sg11665 - -lemma sg19477 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by - exact rowSquare_join (by decide) sg166 sg11640 - -lemma sg19478 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg166 sg11641 - -lemma sg19479 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg165 sg11666 - -lemma sg19480 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by - exact rowSquare_join (by decide) sg165 sg11667 - -lemma sg19481 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg166 sg11643 - -lemma sg19482 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg165 sg11668 - -lemma sg19483 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg166 sg11644 - -lemma sg19484 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by - exact rowSquare_join (by decide) sg165 sg11669 - -lemma sg19485 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by - exact rowSquare_join (by decide) sg165 sg11670 - -lemma sg19486 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12531 - -lemma sg19487 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg166 sg11647 - -lemma sg19488 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by - exact rowSquare_join (by decide) sg165 sg11671 - -lemma sg19489 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by - exact rowSquare_join (by decide) sg165 sg11672 - -lemma sg19490 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by - exact rowSquare_join (by decide) sg166 sg11649 - -lemma sg19491 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12532 - -lemma sg19492 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by - exact rowSquare_join (by decide) sg166 sg11650 - -lemma sg19493 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by - exact rowSquare_join (by decide) sg166 sg11651 - -lemma sg19494 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg165 sg11676 - -lemma sg19495 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14305 - -lemma sg19496 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg165 sg11678 - -lemma sg19497 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by - exact rowSquare_join (by decide) sg165 sg11679 - -lemma sg19498 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg166 sg11656 - -lemma sg19499 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,2] := by - exact rowSquare_join (by decide) sg165 sg11680 - -lemma sg19500 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg166 sg11657 - -lemma sg19501 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg165 sg11681 - -lemma sg19502 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,3] := by - exact rowSquare_join (by decide) sg165 sg11682 - -lemma sg19503 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg166 sg11659 - -lemma sg19504 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg165 sg11683 - -lemma sg19505 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg166 sg11660 - -lemma sg19506 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,2] := by - exact rowSquare_join (by decide) sg165 sg11684 - -lemma sg19507 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,4,1] := by - exact rowSquare_join (by decide) sg165 sg11685 - -lemma sg19508 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg12907 - -lemma sg19509 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg166 sg11663 - -lemma sg19510 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,2] := by - exact rowSquare_join (by decide) sg165 sg11686 - -lemma sg19511 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,3,1] := by - exact rowSquare_join (by decide) sg165 sg11687 - -lemma sg19512 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,4] := by - exact rowSquare_join (by decide) sg166 sg11665 - -lemma sg19513 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg167 sg11657 - -lemma sg19514 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg165 sg11688 - -lemma sg19515 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg166 sg11666 - -lemma sg19516 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,2] := by - exact rowSquare_join (by decide) sg165 sg11689 - -lemma sg19517 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg167 sg11659 - -lemma sg19518 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg166 sg11668 - -lemma sg19519 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,2] := by - exact rowSquare_join (by decide) sg165 sg11690 - -lemma sg19520 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,3,1] := by - exact rowSquare_join (by decide) sg165 sg11691 - -lemma sg19521 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,4] := by - exact rowSquare_join (by decide) sg166 sg11670 - -lemma sg19522 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg167 sg11663 - -lemma sg19523 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,5,2,1] := by - exact rowSquare_join (by decide) sg165 sg11692 - -lemma sg19524 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,5,3] := by - exact rowSquare_join (by decide) sg364 sg11094 - -lemma sg19525 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,6,1,1] := by - exact rowSquare_join (by decide) sg165 sg11693 - -lemma sg19526 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,6,2] := by - exact rowSquare_join (by decide) sg364 sg11095 - -lemma sg19527 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg14 sg14294 - -lemma sg19528 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg166 sg11675 - -lemma sg19529 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg166 sg11676 - -lemma sg19530 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg14296 - -lemma sg19531 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg166 sg11677 - -lemma sg19532 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14306 - -lemma sg19533 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg166 sg11678 - -lemma sg19534 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,2] := by - exact rowSquare_join (by decide) sg166 sg11679 - -lemma sg19535 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,4,1] := by - exact rowSquare_join (by decide) sg166 sg11680 - -lemma sg19536 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg3551 sg4167 - -lemma sg19537 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg3550 sg4168 - -lemma sg19538 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg165 sg11694 - -lemma sg19539 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg15144 - -lemma sg19540 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg84 sg12533 - -lemma sg19541 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg165 sg11695 - -lemma sg19542 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg15145 - -lemma sg19543 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg15146 - -lemma sg19544 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg15147 - -lemma sg19545 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg1 sg15148 - -lemma sg19546 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg3537 sg4184 - -lemma sg19547 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg165 sg11696 - -lemma sg19548 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg15149 - -lemma sg19549 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg166 sg11694 - -lemma sg19550 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg165 sg11697 - -lemma sg19551 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg15150 - -lemma sg19552 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg84 sg12534 - -lemma sg19553 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg166 sg11695 - -lemma sg19554 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg165 sg11698 - -lemma sg19555 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg165 sg11699 - -lemma sg19556 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg165 sg11700 - -lemma sg19557 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg3 sg14733 - -lemma sg19558 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg15151 - -lemma sg19559 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg697 sg11058 - -lemma sg19560 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg167 sg11694 - -lemma sg19561 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg168 sg11625 - -lemma sg19562 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg165 sg11701 - -lemma sg19563 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg489 sg8909 - -lemma sg19564 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg167 sg11695 - -lemma sg19565 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg165 sg11702 - -lemma sg19566 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg490 sg8909 - -lemma sg19567 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg489 sg8910 - -lemma sg19568 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg168 sg11627 - -lemma sg19569 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg165 sg11703 - -lemma sg19570 : RowSquare [7,7,3,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg12673 - -lemma sg19571 : RowSquare [7,7,3,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg101 sg12674 - -lemma sg19572 : RowSquare [7,7,3,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg202 sg11799 - -lemma sg19573 : RowSquare [7,7,3,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg102 sg12674 - -lemma sg19574 : RowSquare [7,7,3,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg103 sg12669 - -lemma sg19575 : RowSquare [7,7,3,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3311 sg4167 - -lemma sg19576 : RowSquare [7,7,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1748 sg6469 - -lemma sg19577 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by - exact rowSquare_join (by decide) sg3578 sg4158 - -lemma sg19578 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by - exact rowSquare_join (by decide) sg3309 sg4466 - -lemma sg19579 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg3309 sg4468 - -lemma sg19580 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14314 - -lemma sg19581 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3468 sg4350 - -lemma sg19582 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3462 sg4351 - -lemma sg19583 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3469 sg4350 - -lemma sg19584 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3463 sg4351 - -lemma sg19585 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3672 sg4051 - -lemma sg19586 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3464 sg4351 - -lemma sg19587 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg3275 sg4517 - -lemma sg19588 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3676 sg4051 - -lemma sg19589 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3465 sg4351 - -lemma sg19590 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg3275 sg4518 - -lemma sg19591 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3466 sg4351 - -lemma sg19592 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg3581 sg4158 - -lemma sg19593 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by - exact rowSquare_join (by decide) sg401 sg11550 - -lemma sg19594 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by - exact rowSquare_join (by decide) sg3675 sg4053 - -lemma sg19595 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by - exact rowSquare_join (by decide) sg3309 sg4471 - -lemma sg19596 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3467 sg4351 - -lemma sg19597 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg3277 sg4518 - -lemma sg19598 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by - exact rowSquare_join (by decide) sg402 sg11550 - -lemma sg19599 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by - exact rowSquare_join (by decide) sg3578 sg4159 - -lemma sg19600 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by - exact rowSquare_join (by decide) sg3679 sg4053 - -lemma sg19601 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by - exact rowSquare_join (by decide) sg401 sg11552 - -lemma sg19602 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by - exact rowSquare_join (by decide) sg3309 sg4472 - -lemma sg19603 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg11549 - -lemma sg19604 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg707 sg11056 - -lemma sg19605 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14315 - -lemma sg19606 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg402 sg11551 - -lemma sg19607 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by - exact rowSquare_join (by decide) sg3309 sg4438 - -lemma sg19608 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg3556 sg4158 - -lemma sg19609 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14317 - -lemma sg19610 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14318 - -lemma sg19611 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg391 sg11550 - -lemma sg19612 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg391 sg11552 - -lemma sg19613 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by - exact rowSquare_join (by decide) sg193 sg12340 - -lemma sg19614 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by - exact rowSquare_join (by decide) sg14 sg14316 - -lemma sg19615 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg697 sg11057 - -lemma sg19616 : RowSquare [8,6,3,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2134 sg5739 - -lemma sg19617 : RowSquare [8,6,3,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15608 - -lemma sg19618 : RowSquare [8,6,3,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2134 sg5740 - -lemma sg19619 : RowSquare [8,6,3,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2134 sg5741 - -lemma sg19620 : RowSquare [8,6,3,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14319 - -lemma sg19621 : RowSquare [8,6,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg15616 - -lemma sg19622 : RowSquare [8,6,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg888 sg8892 - -lemma sg19623 : RowSquare [8,6,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg8891 - -lemma sg19624 : RowSquare [8,6,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg889 sg8892 - -lemma sg19625 : RowSquare [8,6,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg12916 - -lemma sg19626 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg2708 sg4890 - -lemma sg19627 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3384 sg4351 - -lemma sg19628 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg3533 sg4158 - -lemma sg19629 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by - exact rowSquare_join (by decide) sg3309 sg4423 - -lemma sg19630 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by - exact rowSquare_join (by decide) sg39 sg13504 - -lemma sg19631 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg14321 - -lemma sg19632 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by - exact rowSquare_join (by decide) sg39 sg13505 - -lemma sg19633 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by - exact rowSquare_join (by decide) sg39 sg13506 - -lemma sg19634 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14323 - -lemma sg19635 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14324 - -lemma sg19636 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3385 sg4354 - -lemma sg19637 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by - exact rowSquare_join (by decide) sg40 sg13504 - -lemma sg19638 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg14325 - -lemma sg19639 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by - exact rowSquare_join (by decide) sg40 sg13505 - -lemma sg19640 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by - exact rowSquare_join (by decide) sg40 sg13506 - -lemma sg19641 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14728 - -lemma sg19642 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3385 sg4355 - -lemma sg19643 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14729 - -lemma sg19644 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg14730 - -lemma sg19645 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,3,1] := by - exact rowSquare_join (by decide) sg97 sg12720 - -lemma sg19646 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by - exact rowSquare_join (by decide) sg97 sg12721 - -lemma sg19647 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by - exact rowSquare_join (by decide) sg4 sg14731 - -lemma sg19648 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by - exact rowSquare_join (by decide) sg4 sg14732 - -lemma sg19649 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14326 - -lemma sg19650 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14327 - -lemma sg19651 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14328 - -lemma sg19652 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg14329 - -lemma sg19653 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg14330 - -lemma sg19654 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14331 - -lemma sg19655 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg14332 - -lemma sg19656 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by - exact rowSquare_join (by decide) sg13 sg14333 - -lemma sg19657 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by - exact rowSquare_join (by decide) sg13 sg14334 - -lemma sg19658 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3661 sg4057 - -lemma sg19659 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3386 sg4351 - -lemma sg19660 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg15159 - -lemma sg19661 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg0 sg15619 - -lemma sg19662 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg3663 sg4051 - -lemma sg19663 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg0 sg15620 - -lemma sg19664 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3387 sg4351 - -lemma sg19665 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg15160 - -lemma sg19666 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg39 sg12866 - -lemma sg19667 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg3307 sg4424 - -lemma sg19668 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg3388 sg4351 - -lemma sg19669 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg39 sg12867 - -lemma sg19670 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3389 sg4351 - -lemma sg19671 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15161 - -lemma sg19672 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg1 sg15162 - -lemma sg19673 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14336 - -lemma sg19674 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg15163 - -lemma sg19675 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15164 - -lemma sg19676 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg1 sg15165 - -lemma sg19677 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg15166 - -lemma sg19678 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg3537 sg4158 - -lemma sg19679 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg15167 - -lemma sg19680 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg39 sg12868 - -lemma sg19681 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3390 sg4351 - -lemma sg19682 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15168 - -lemma sg19683 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg40 sg12867 - -lemma sg19684 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3391 sg4351 - -lemma sg19685 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14338 - -lemma sg19686 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15169 - -lemma sg19687 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12870 - -lemma sg19688 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12871 - -lemma sg19689 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14734 - -lemma sg19690 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12536 - -lemma sg19691 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12537 - -lemma sg19692 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12872 - -lemma sg19693 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by - exact rowSquare_join (by decide) sg98 sg12721 - -lemma sg19694 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by - exact rowSquare_join (by decide) sg4 sg14735 - -lemma sg19695 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by - exact rowSquare_join (by decide) sg3540 sg4158 - -lemma sg19696 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by - exact rowSquare_join (by decide) sg13 sg14343 - -lemma sg19697 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by - exact rowSquare_join (by decide) sg13 sg14344 - -lemma sg19698 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by - exact rowSquare_join (by decide) sg39 sg13507 - -lemma sg19699 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg39 sg12875 - -lemma sg19700 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg40 sg12868 - -lemma sg19701 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3393 sg4351 - -lemma sg19702 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14345 - -lemma sg19703 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3528 sg4295 - -lemma sg19704 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14320 - -lemma sg19705 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12878 - -lemma sg19706 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12880 - -lemma sg19707 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12881 - -lemma sg19708 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by - exact rowSquare_join (by decide) sg39 sg13508 - -lemma sg19709 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by - exact rowSquare_join (by decide) sg3308 sg4428 - -lemma sg19710 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by - exact rowSquare_join (by decide) sg3309 sg4428 - -lemma sg19711 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12543 - -lemma sg19712 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12544 - -lemma sg19713 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12882 - -lemma sg19714 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by - exact rowSquare_join (by decide) sg227 sg12335 - -lemma sg19715 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by - exact rowSquare_join (by decide) sg4 sg14737 - -lemma sg19716 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12883 - -lemma sg19717 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg14351 - -lemma sg19718 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg14352 - -lemma sg19719 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by - exact rowSquare_join (by decide) sg40 sg13507 - -lemma sg19720 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg14353 - -lemma sg19721 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by - exact rowSquare_join (by decide) sg13 sg14354 - -lemma sg19722 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by - exact rowSquare_join (by decide) sg13 sg14355 - -lemma sg19723 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,7,5,4] := by - exact rowSquare_join (by decide) sg207 sg11609 - -lemma sg19724 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,7,6,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14357 - -lemma sg19725 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,7,6,2,1] := by - exact rowSquare_join (by decide) sg39 sg12887 - -lemma sg19726 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,7,6,3] := by - exact rowSquare_join (by decide) sg39 sg12888 - -lemma sg19727 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3523 sg4299 - -lemma sg19728 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg40 sg12875 - -lemma sg19729 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3523 sg4300 - -lemma sg19730 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14358 - -lemma sg19731 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg3530 sg4271 - -lemma sg19732 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg424 sg11544 - -lemma sg19733 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg12876 - -lemma sg19734 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14322 - -lemma sg19735 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg228 sg12334 - -lemma sg19736 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14359 - -lemma sg19737 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14360 - -lemma sg19738 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg2580 sg4991 - -lemma sg19739 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,5] := by - exact rowSquare_join (by decide) sg17 sg14551 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 + +namespace OAI + +/-! Semigroup Nodes 47. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg19340 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by + exact rowSquare_join (by decide) sg165 sg11609 + +lemma sg19341 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14278 + +lemma sg19342 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg84 sg12510 + +lemma sg19343 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg84 sg12511 + +lemma sg19344 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by + exact rowSquare_join (by decide) sg84 sg12512 + +lemma sg19345 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by + exact rowSquare_join (by decide) sg84 sg12513 + +lemma sg19346 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by + exact rowSquare_join (by decide) sg84 sg12514 + +lemma sg19347 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg14215 + +lemma sg19348 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg3546 sg4169 + +lemma sg19349 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg14216 + +lemma sg19350 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg14 sg14217 + +lemma sg19351 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg3314 sg4431 + +lemma sg19352 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14279 + +lemma sg19353 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14280 + +lemma sg19354 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14281 + +lemma sg19355 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg14282 + +lemma sg19356 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg14218 + +lemma sg19357 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg3539 sg4179 + +lemma sg19358 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg3539 sg4180 + +lemma sg19359 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg26 sg12877 + +lemma sg19360 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg83 sg12519 + +lemma sg19361 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg14 sg14219 + +lemma sg19362 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg165 sg11610 + +lemma sg19363 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg26 sg12879 + +lemma sg19364 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14283 + +lemma sg19365 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14284 + +lemma sg19366 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg165 sg11611 + +lemma sg19367 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14222 + +lemma sg19368 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg165 sg11612 + +lemma sg19369 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by + exact rowSquare_join (by decide) sg3540 sg4180 + +lemma sg19370 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14285 + +lemma sg19371 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14286 + +lemma sg19372 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg14287 + +lemma sg19373 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by + exact rowSquare_join (by decide) sg165 sg11613 + +lemma sg19374 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg14288 + +lemma sg19375 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by + exact rowSquare_join (by decide) sg165 sg11614 + +lemma sg19376 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by + exact rowSquare_join (by decide) sg165 sg11615 + +lemma sg19377 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg165 sg11616 + +lemma sg19378 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12520 + +lemma sg19379 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg166 sg11605 + +lemma sg19380 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by + exact rowSquare_join (by decide) sg165 sg11617 + +lemma sg19381 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg166 sg11606 + +lemma sg19382 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by + exact rowSquare_join (by decide) sg165 sg11618 + +lemma sg19383 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg12884 + +lemma sg19384 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg26 sg12885 + +lemma sg19385 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg26 sg12886 + +lemma sg19386 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by + exact rowSquare_join (by decide) sg166 sg11607 + +lemma sg19387 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by + exact rowSquare_join (by decide) sg166 sg11608 + +lemma sg19388 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by + exact rowSquare_join (by decide) sg166 sg11609 + +lemma sg19389 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14289 + +lemma sg19390 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14290 + +lemma sg19391 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg14291 + +lemma sg19392 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by + exact rowSquare_join (by decide) sg13 sg14292 + +lemma sg19393 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by + exact rowSquare_join (by decide) sg13 sg14293 + +lemma sg19394 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg14294 + +lemma sg19395 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14235 + +lemma sg19396 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg14 sg14236 + +lemma sg19397 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg83 sg12526 + +lemma sg19398 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14295 + +lemma sg19399 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg166 sg11611 + +lemma sg19400 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg14296 + +lemma sg19401 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg166 sg11612 + +lemma sg19402 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,4,4,2] := by + exact rowSquare_join (by decide) sg14 sg14243 + +lemma sg19403 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14297 + +lemma sg19404 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14298 + +lemma sg19405 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14299 + +lemma sg19406 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,3,2] := by + exact rowSquare_join (by decide) sg166 sg11613 + +lemma sg19407 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,4,1] := by + exact rowSquare_join (by decide) sg166 sg11614 + +lemma sg19408 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,5] := by + exact rowSquare_join (by decide) sg166 sg11615 + +lemma sg19409 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12527 + +lemma sg19410 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg166 sg11616 + +lemma sg19411 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,3,3,3] := by + exact rowSquare_join (by decide) sg83 sg12528 + +lemma sg19412 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12529 + +lemma sg19413 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg167 sg11611 + +lemma sg19414 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg167 sg11612 + +lemma sg19415 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,4,3,2] := by + exact rowSquare_join (by decide) sg166 sg11617 + +lemma sg19416 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,4,4,1] := by + exact rowSquare_join (by decide) sg166 sg11618 + +lemma sg19417 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14300 + +lemma sg19418 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14301 + +lemma sg19419 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,5,2,2] := by + exact rowSquare_join (by decide) sg167 sg11613 + +lemma sg19420 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,5,3,1] := by + exact rowSquare_join (by decide) sg167 sg11614 + +lemma sg19421 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,5,4] := by + exact rowSquare_join (by decide) sg167 sg11615 + +lemma sg19422 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14302 + +lemma sg19423 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by + exact rowSquare_join (by decide) sg13 sg14303 + +lemma sg19424 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,3] := by + exact rowSquare_join (by decide) sg13 sg14304 + +lemma sg19425 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg3537 sg4183 + +lemma sg19426 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg15137 + +lemma sg19427 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg165 sg11628 + +lemma sg19428 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12518 + +lemma sg19429 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg165 sg11629 + +lemma sg19430 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg1 sg15138 + +lemma sg19431 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg1 sg15139 + +lemma sg19432 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg1 sg15140 + +lemma sg19433 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg15141 + +lemma sg19434 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg391 sg11553 + +lemma sg19435 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg165 sg11636 + +lemma sg19436 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg166 sg11627 + +lemma sg19437 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg165 sg11637 + +lemma sg19438 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg1 sg15142 + +lemma sg19439 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12520 + +lemma sg19440 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg166 sg11628 + +lemma sg19441 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg165 sg11638 + +lemma sg19442 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg166 sg11629 + +lemma sg19443 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by + exact rowSquare_join (by decide) sg165 sg11639 + +lemma sg19444 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by + exact rowSquare_join (by decide) sg165 sg11640 + +lemma sg19445 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg165 sg11642 + +lemma sg19446 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg167 sg11627 + +lemma sg19447 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg165 sg11644 + +lemma sg19448 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by + exact rowSquare_join (by decide) sg165 sg11645 + +lemma sg19449 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg168 sg11606 + +lemma sg19450 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by + exact rowSquare_join (by decide) sg165 sg11646 + +lemma sg19451 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12522 + +lemma sg19452 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg165 sg11647 + +lemma sg19453 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg167 sg11629 + +lemma sg19454 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by + exact rowSquare_join (by decide) sg165 sg11648 + +lemma sg19455 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by + exact rowSquare_join (by decide) sg165 sg11649 + +lemma sg19456 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by + exact rowSquare_join (by decide) sg168 sg11609 + +lemma sg19457 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12523 + +lemma sg19458 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12524 + +lemma sg19459 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by + exact rowSquare_join (by decide) sg165 sg11650 + +lemma sg19460 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by + exact rowSquare_join (by decide) sg165 sg11651 + +lemma sg19461 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by + exact rowSquare_join (by decide) sg84 sg12525 + +lemma sg19462 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg165 sg11655 + +lemma sg19463 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg166 sg11633 + +lemma sg19464 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg165 sg11656 + +lemma sg19465 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by + exact rowSquare_join (by decide) sg1 sg15143 + +lemma sg19466 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg165 sg11658 + +lemma sg19467 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg167 sg11633 + +lemma sg19468 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg165 sg11660 + +lemma sg19469 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by + exact rowSquare_join (by decide) sg165 sg11661 + +lemma sg19470 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg166 sg11637 + +lemma sg19471 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by + exact rowSquare_join (by decide) sg165 sg11662 + +lemma sg19472 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12529 + +lemma sg19473 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg165 sg11663 + +lemma sg19474 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg84 sg12530 + +lemma sg19475 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by + exact rowSquare_join (by decide) sg165 sg11664 + +lemma sg19476 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by + exact rowSquare_join (by decide) sg165 sg11665 + +lemma sg19477 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by + exact rowSquare_join (by decide) sg166 sg11640 + +lemma sg19478 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg166 sg11641 + +lemma sg19479 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg165 sg11666 + +lemma sg19480 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by + exact rowSquare_join (by decide) sg165 sg11667 + +lemma sg19481 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg166 sg11643 + +lemma sg19482 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg165 sg11668 + +lemma sg19483 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg166 sg11644 + +lemma sg19484 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by + exact rowSquare_join (by decide) sg165 sg11669 + +lemma sg19485 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by + exact rowSquare_join (by decide) sg165 sg11670 + +lemma sg19486 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12531 + +lemma sg19487 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg166 sg11647 + +lemma sg19488 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by + exact rowSquare_join (by decide) sg165 sg11671 + +lemma sg19489 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by + exact rowSquare_join (by decide) sg165 sg11672 + +lemma sg19490 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by + exact rowSquare_join (by decide) sg166 sg11649 + +lemma sg19491 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12532 + +lemma sg19492 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by + exact rowSquare_join (by decide) sg166 sg11650 + +lemma sg19493 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by + exact rowSquare_join (by decide) sg166 sg11651 + +lemma sg19494 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg165 sg11676 + +lemma sg19495 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14305 + +lemma sg19496 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg165 sg11678 + +lemma sg19497 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by + exact rowSquare_join (by decide) sg165 sg11679 + +lemma sg19498 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg166 sg11656 + +lemma sg19499 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,2] := by + exact rowSquare_join (by decide) sg165 sg11680 + +lemma sg19500 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg166 sg11657 + +lemma sg19501 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg165 sg11681 + +lemma sg19502 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,3] := by + exact rowSquare_join (by decide) sg165 sg11682 + +lemma sg19503 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg166 sg11659 + +lemma sg19504 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg165 sg11683 + +lemma sg19505 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg166 sg11660 + +lemma sg19506 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,2] := by + exact rowSquare_join (by decide) sg165 sg11684 + +lemma sg19507 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,4,1] := by + exact rowSquare_join (by decide) sg165 sg11685 + +lemma sg19508 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg12907 + +lemma sg19509 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg166 sg11663 + +lemma sg19510 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,2] := by + exact rowSquare_join (by decide) sg165 sg11686 + +lemma sg19511 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,3,1] := by + exact rowSquare_join (by decide) sg165 sg11687 + +lemma sg19512 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,4] := by + exact rowSquare_join (by decide) sg166 sg11665 + +lemma sg19513 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg167 sg11657 + +lemma sg19514 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg165 sg11688 + +lemma sg19515 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg166 sg11666 + +lemma sg19516 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,2] := by + exact rowSquare_join (by decide) sg165 sg11689 + +lemma sg19517 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg167 sg11659 + +lemma sg19518 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg166 sg11668 + +lemma sg19519 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,2] := by + exact rowSquare_join (by decide) sg165 sg11690 + +lemma sg19520 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,3,1] := by + exact rowSquare_join (by decide) sg165 sg11691 + +lemma sg19521 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,4] := by + exact rowSquare_join (by decide) sg166 sg11670 + +lemma sg19522 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg167 sg11663 + +lemma sg19523 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,5,2,1] := by + exact rowSquare_join (by decide) sg165 sg11692 + +lemma sg19524 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,5,3] := by + exact rowSquare_join (by decide) sg364 sg11094 + +lemma sg19525 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,6,1,1] := by + exact rowSquare_join (by decide) sg165 sg11693 + +lemma sg19526 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,6,2] := by + exact rowSquare_join (by decide) sg364 sg11095 + +lemma sg19527 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg14 sg14294 + +lemma sg19528 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg166 sg11675 + +lemma sg19529 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg166 sg11676 + +lemma sg19530 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg14296 + +lemma sg19531 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg166 sg11677 + +lemma sg19532 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14306 + +lemma sg19533 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg166 sg11678 + +lemma sg19534 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,2] := by + exact rowSquare_join (by decide) sg166 sg11679 + +lemma sg19535 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,4,1] := by + exact rowSquare_join (by decide) sg166 sg11680 + +lemma sg19536 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg3551 sg4167 + +lemma sg19537 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg3550 sg4168 + +lemma sg19538 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg165 sg11694 + +lemma sg19539 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg15144 + +lemma sg19540 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg84 sg12533 + +lemma sg19541 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg165 sg11695 + +lemma sg19542 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg15145 + +lemma sg19543 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg15146 + +lemma sg19544 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg15147 + +lemma sg19545 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg1 sg15148 + +lemma sg19546 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg3537 sg4184 + +lemma sg19547 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg165 sg11696 + +lemma sg19548 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg15149 + +lemma sg19549 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg166 sg11694 + +lemma sg19550 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg165 sg11697 + +lemma sg19551 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg15150 + +lemma sg19552 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg84 sg12534 + +lemma sg19553 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg166 sg11695 + +lemma sg19554 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg165 sg11698 + +lemma sg19555 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg165 sg11699 + +lemma sg19556 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg165 sg11700 + +lemma sg19557 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg3 sg14733 + +lemma sg19558 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg15151 + +lemma sg19559 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg697 sg11058 + +lemma sg19560 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg167 sg11694 + +lemma sg19561 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg168 sg11625 + +lemma sg19562 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg165 sg11701 + +lemma sg19563 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg489 sg8909 + +lemma sg19564 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg167 sg11695 + +lemma sg19565 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg165 sg11702 + +lemma sg19566 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg490 sg8909 + +lemma sg19567 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg489 sg8910 + +lemma sg19568 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg168 sg11627 + +lemma sg19569 : RowSquare [7,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg165 sg11703 + +lemma sg19570 : RowSquare [7,7,3,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg12673 + +lemma sg19571 : RowSquare [7,7,3,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg101 sg12674 + +lemma sg19572 : RowSquare [7,7,3,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg202 sg11799 + +lemma sg19573 : RowSquare [7,7,3,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg102 sg12674 + +lemma sg19574 : RowSquare [7,7,3,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg103 sg12669 + +lemma sg19575 : RowSquare [7,7,3,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3311 sg4167 + +lemma sg19576 : RowSquare [7,7,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1748 sg6469 + +lemma sg19577 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by + exact rowSquare_join (by decide) sg3578 sg4158 + +lemma sg19578 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by + exact rowSquare_join (by decide) sg3309 sg4466 + +lemma sg19579 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg3309 sg4468 + +lemma sg19580 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14314 + +lemma sg19581 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3468 sg4350 + +lemma sg19582 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3462 sg4351 + +lemma sg19583 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3469 sg4350 + +lemma sg19584 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3463 sg4351 + +lemma sg19585 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3672 sg4051 + +lemma sg19586 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3464 sg4351 + +lemma sg19587 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg3275 sg4517 + +lemma sg19588 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3676 sg4051 + +lemma sg19589 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3465 sg4351 + +lemma sg19590 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg3275 sg4518 + +lemma sg19591 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3466 sg4351 + +lemma sg19592 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg3581 sg4158 + +lemma sg19593 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by + exact rowSquare_join (by decide) sg401 sg11550 + +lemma sg19594 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by + exact rowSquare_join (by decide) sg3675 sg4053 + +lemma sg19595 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by + exact rowSquare_join (by decide) sg3309 sg4471 + +lemma sg19596 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3467 sg4351 + +lemma sg19597 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg3277 sg4518 + +lemma sg19598 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by + exact rowSquare_join (by decide) sg402 sg11550 + +lemma sg19599 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by + exact rowSquare_join (by decide) sg3578 sg4159 + +lemma sg19600 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by + exact rowSquare_join (by decide) sg3679 sg4053 + +lemma sg19601 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by + exact rowSquare_join (by decide) sg401 sg11552 + +lemma sg19602 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by + exact rowSquare_join (by decide) sg3309 sg4472 + +lemma sg19603 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg11549 + +lemma sg19604 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg707 sg11056 + +lemma sg19605 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14315 + +lemma sg19606 : RowSquare [8,6,2,2,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg402 sg11551 + +lemma sg19607 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by + exact rowSquare_join (by decide) sg3309 sg4438 + +lemma sg19608 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg3556 sg4158 + +lemma sg19609 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14317 + +lemma sg19610 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14318 + +lemma sg19611 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg391 sg11550 + +lemma sg19612 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg391 sg11552 + +lemma sg19613 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by + exact rowSquare_join (by decide) sg193 sg12340 + +lemma sg19614 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by + exact rowSquare_join (by decide) sg14 sg14316 + +lemma sg19615 : RowSquare [8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg697 sg11057 + +lemma sg19616 : RowSquare [8,6,3,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2134 sg5739 + +lemma sg19617 : RowSquare [8,6,3,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15608 + +lemma sg19618 : RowSquare [8,6,3,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2134 sg5740 + +lemma sg19619 : RowSquare [8,6,3,3,2,2,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2134 sg5741 + +lemma sg19620 : RowSquare [8,6,3,3,2,2,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14319 + +lemma sg19621 : RowSquare [8,6,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg15616 + +lemma sg19622 : RowSquare [8,6,4,3,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg888 sg8892 + +lemma sg19623 : RowSquare [8,6,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg8891 + +lemma sg19624 : RowSquare [8,6,4,3,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg889 sg8892 + +lemma sg19625 : RowSquare [8,6,4,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg12916 + +lemma sg19626 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg2708 sg4890 + +lemma sg19627 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3384 sg4351 + +lemma sg19628 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg3533 sg4158 + +lemma sg19629 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,1,1] := by + exact rowSquare_join (by decide) sg3309 sg4423 + +lemma sg19630 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,3,3] := by + exact rowSquare_join (by decide) sg39 sg13504 + +lemma sg19631 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg14321 + +lemma sg19632 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,4,2] := by + exact rowSquare_join (by decide) sg39 sg13505 + +lemma sg19633 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,5,1] := by + exact rowSquare_join (by decide) sg39 sg13506 + +lemma sg19634 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14323 + +lemma sg19635 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14324 + +lemma sg19636 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3385 sg4354 + +lemma sg19637 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,3,3] := by + exact rowSquare_join (by decide) sg40 sg13504 + +lemma sg19638 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg14325 + +lemma sg19639 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,4,2] := by + exact rowSquare_join (by decide) sg40 sg13505 + +lemma sg19640 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,5,5,1] := by + exact rowSquare_join (by decide) sg40 sg13506 + +lemma sg19641 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14728 + +lemma sg19642 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3385 sg4355 + +lemma sg19643 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14729 + +lemma sg19644 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg14730 + +lemma sg19645 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,3,1] := by + exact rowSquare_join (by decide) sg97 sg12720 + +lemma sg19646 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,3,3] := by + exact rowSquare_join (by decide) sg97 sg12721 + +lemma sg19647 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,1,1] := by + exact rowSquare_join (by decide) sg4 sg14731 + +lemma sg19648 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,2] := by + exact rowSquare_join (by decide) sg4 sg14732 + +lemma sg19649 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14326 + +lemma sg19650 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14327 + +lemma sg19651 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14328 + +lemma sg19652 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg14329 + +lemma sg19653 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg14330 + +lemma sg19654 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14331 + +lemma sg19655 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg14332 + +lemma sg19656 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,3,1] := by + exact rowSquare_join (by decide) sg13 sg14333 + +lemma sg19657 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,4] := by + exact rowSquare_join (by decide) sg13 sg14334 + +lemma sg19658 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3661 sg4057 + +lemma sg19659 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3386 sg4351 + +lemma sg19660 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg15159 + +lemma sg19661 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg0 sg15619 + +lemma sg19662 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg3663 sg4051 + +lemma sg19663 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg0 sg15620 + +lemma sg19664 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3387 sg4351 + +lemma sg19665 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg15160 + +lemma sg19666 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg39 sg12866 + +lemma sg19667 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg3307 sg4424 + +lemma sg19668 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg3388 sg4351 + +lemma sg19669 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg39 sg12867 + +lemma sg19670 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3389 sg4351 + +lemma sg19671 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15161 + +lemma sg19672 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg1 sg15162 + +lemma sg19673 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14336 + +lemma sg19674 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg15163 + +lemma sg19675 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15164 + +lemma sg19676 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg1 sg15165 + +lemma sg19677 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg15166 + +lemma sg19678 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg3537 sg4158 + +lemma sg19679 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg15167 + +lemma sg19680 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg39 sg12868 + +lemma sg19681 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3390 sg4351 + +lemma sg19682 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15168 + +lemma sg19683 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg40 sg12867 + +lemma sg19684 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3391 sg4351 + +lemma sg19685 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14338 + +lemma sg19686 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15169 + +lemma sg19687 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12870 + +lemma sg19688 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12871 + +lemma sg19689 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14734 + +lemma sg19690 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12536 + +lemma sg19691 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12537 + +lemma sg19692 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12872 + +lemma sg19693 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,3,3] := by + exact rowSquare_join (by decide) sg98 sg12721 + +lemma sg19694 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,4,2] := by + exact rowSquare_join (by decide) sg4 sg14735 + +lemma sg19695 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,5,5,1] := by + exact rowSquare_join (by decide) sg3540 sg4158 + +lemma sg19696 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,3,2] := by + exact rowSquare_join (by decide) sg13 sg14343 + +lemma sg19697 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,4,1] := by + exact rowSquare_join (by decide) sg13 sg14344 + +lemma sg19698 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,5] := by + exact rowSquare_join (by decide) sg39 sg13507 + +lemma sg19699 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg39 sg12875 + +lemma sg19700 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg40 sg12868 + +lemma sg19701 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3393 sg4351 + +lemma sg19702 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14345 + +lemma sg19703 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3528 sg4295 + +lemma sg19704 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14320 + +lemma sg19705 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12878 + +lemma sg19706 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12880 + +lemma sg19707 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12881 + +lemma sg19708 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,3,3] := by + exact rowSquare_join (by decide) sg39 sg13508 + +lemma sg19709 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,4,2] := by + exact rowSquare_join (by decide) sg3308 sg4428 + +lemma sg19710 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,5,5,5,1] := by + exact rowSquare_join (by decide) sg3309 sg4428 + +lemma sg19711 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12543 + +lemma sg19712 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12544 + +lemma sg19713 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12882 + +lemma sg19714 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,3,3] := by + exact rowSquare_join (by decide) sg227 sg12335 + +lemma sg19715 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,4,4,2] := by + exact rowSquare_join (by decide) sg4 sg14737 + +lemma sg19716 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12883 + +lemma sg19717 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg14351 + +lemma sg19718 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg14352 + +lemma sg19719 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,5,5] := by + exact rowSquare_join (by decide) sg40 sg13507 + +lemma sg19720 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg14353 + +lemma sg19721 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,3,1] := by + exact rowSquare_join (by decide) sg13 sg14354 + +lemma sg19722 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,6,6,4] := by + exact rowSquare_join (by decide) sg13 sg14355 + +lemma sg19723 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,7,5,4] := by + exact rowSquare_join (by decide) sg207 sg11609 + +lemma sg19724 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,7,6,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14357 + +lemma sg19725 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,7,6,2,1] := by + exact rowSquare_join (by decide) sg39 sg12887 + +lemma sg19726 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,7,7,6,3] := by + exact rowSquare_join (by decide) sg39 sg12888 + +lemma sg19727 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3523 sg4299 + +lemma sg19728 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg40 sg12875 + +lemma sg19729 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3523 sg4300 + +lemma sg19730 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14358 + +lemma sg19731 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg3530 sg4271 + +lemma sg19732 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg424 sg11544 + +lemma sg19733 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg12876 + +lemma sg19734 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14322 + +lemma sg19735 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg228 sg12334 + +lemma sg19736 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14359 + +lemma sg19737 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14360 + +lemma sg19738 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg2580 sg4991 + +lemma sg19739 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,5,5,5] := by + exact rowSquare_join (by decide) sg17 sg14551 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes48.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes48.lean index 57d545e88a02a4bb9b0a2e44f9d44294d2a3a9c4..cbfdf5b211a647163dffd1f62c7eeb19a7824d92 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes48.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes48.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 - -namespace OAI - -/-! Semigroup Nodes 48. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg19740 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,5,4] := by - exact rowSquare_join (by decide) sg207 sg11615 - -lemma sg19741 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14362 - -lemma sg19742 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by - exact rowSquare_join (by decide) sg13 sg14363 - -lemma sg19743 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,3] := by - exact rowSquare_join (by decide) sg13 sg14364 - -lemma sg19744 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,4,4] := by - exact rowSquare_join (by decide) sg83 sg12562 - -lemma sg19745 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,5,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14365 - -lemma sg19746 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,5,2,1] := by - exact rowSquare_join (by decide) sg40 sg12887 - -lemma sg19747 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,5,3] := by - exact rowSquare_join (by decide) sg40 sg12888 - -lemma sg19748 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,6,1,1] := by - exact rowSquare_join (by decide) sg13 sg14366 - -lemma sg19749 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,6,2] := by - exact rowSquare_join (by decide) sg13 sg14367 - -lemma sg19750 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12563 - -lemma sg19751 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14738 - -lemma sg19752 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,2,2,2,1] := by - exact rowSquare_join (by decide) sg83 sg12564 - -lemma sg19753 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14368 - -lemma sg19754 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,3,2,1,1] := by - exact rowSquare_join (by decide) sg207 sg11619 - -lemma sg19755 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,3,2,2] := by - exact rowSquare_join (by decide) sg83 sg12565 - -lemma sg19756 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,3,3,1] := by - exact rowSquare_join (by decide) sg83 sg12566 - -lemma sg19757 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,4,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg11620 - -lemma sg19758 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,4,2,1] := by - exact rowSquare_join (by decide) sg207 sg11621 - -lemma sg19759 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,4,3] := by - exact rowSquare_join (by decide) sg207 sg11622 - -lemma sg19760 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,5,1,1] := by - exact rowSquare_join (by decide) sg207 sg11623 - -lemma sg19761 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,5,2] := by - exact rowSquare_join (by decide) sg207 sg11624 - -lemma sg19762 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3661 sg4059 - -lemma sg19763 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3399 sg4350 - -lemma sg19764 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg3394 sg4351 - -lemma sg19765 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg3400 sg4350 - -lemma sg19766 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg270 sg11202 - -lemma sg19767 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg15170 - -lemma sg19768 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3664 sg4051 - -lemma sg19769 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg271 sg11202 - -lemma sg19770 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg15171 - -lemma sg19771 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg15172 - -lemma sg19772 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg15173 - -lemma sg19773 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg3665 sg4051 - -lemma sg19774 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg15174 - -lemma sg19775 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg15621 - -lemma sg19776 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg3395 sg4351 - -lemma sg19777 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg15175 - -lemma sg19778 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg3275 sg4510 - -lemma sg19779 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg0 sg15622 - -lemma sg19780 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg15176 - -lemma sg19781 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg15177 - -lemma sg19782 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3667 sg4051 - -lemma sg19783 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg39 sg12889 - -lemma sg19784 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg270 sg11203 - -lemma sg19785 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg15178 - -lemma sg19786 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg15179 - -lemma sg19787 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg3668 sg4051 - -lemma sg19788 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg271 sg11203 - -lemma sg19789 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14369 - -lemma sg19790 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg15180 - -lemma sg19791 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3662 sg4057 - -lemma sg19792 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg15181 - -lemma sg19793 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg3275 sg4511 - -lemma sg19794 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15182 - -lemma sg19795 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg15183 - -lemma sg19796 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg15184 - -lemma sg19797 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg1 sg15185 - -lemma sg19798 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg41 sg12867 - -lemma sg19799 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg84 sg12538 - -lemma sg19800 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg270 sg11204 - -lemma sg19801 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg15186 - -lemma sg19802 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3396 sg4351 - -lemma sg19803 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg15187 - -lemma sg19804 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg271 sg11204 - -lemma sg19805 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg39 sg12890 - -lemma sg19806 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg270 sg11205 - -lemma sg19807 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14370 - -lemma sg19808 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg15188 - -lemma sg19809 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg15189 - -lemma sg19810 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg270 sg11206 - -lemma sg19811 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg15190 - -lemma sg19812 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg4 sg14739 - -lemma sg19813 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg15191 - -lemma sg19814 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg271 sg11205 - -lemma sg19815 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14371 - -lemma sg19816 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg271 sg11206 - -lemma sg19817 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14372 - -lemma sg19818 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14373 - -lemma sg19819 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg15192 - -lemma sg19820 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15193 - -lemma sg19821 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg6 sg14727 - -lemma sg19822 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg3666 sg4053 - -lemma sg19823 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg39 sg12891 - -lemma sg19824 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg15194 - -lemma sg19825 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg15195 - -lemma sg19826 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg15196 - -lemma sg19827 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg40 sg12889 - -lemma sg19828 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg84 sg12539 - -lemma sg19829 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg14335 - -lemma sg19830 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg270 sg11207 - -lemma sg19831 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3397 sg4351 - -lemma sg19832 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg15197 - -lemma sg19833 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12540 - -lemma sg19834 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg271 sg11207 - -lemma sg19835 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14374 - -lemma sg19836 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14375 - -lemma sg19837 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg15198 - -lemma sg19838 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg15199 - -lemma sg19839 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15200 - -lemma sg19840 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg15201 - -lemma sg19841 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg5 sg14733 - -lemma sg19842 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg15202 - -lemma sg19843 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg83 sg12567 - -lemma sg19844 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12541 - -lemma sg19845 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg84 sg12542 - -lemma sg19846 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14740 - -lemma sg19847 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg270 sg11208 - -lemma sg19848 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg15203 - -lemma sg19849 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg15204 - -lemma sg19850 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12543 - -lemma sg19851 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg271 sg11208 - -lemma sg19852 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12544 - -lemma sg19853 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg270 sg11209 - -lemma sg19854 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14376 - -lemma sg19855 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg15205 - -lemma sg19856 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg270 sg11210 - -lemma sg19857 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg4 sg14741 - -lemma sg19858 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12892 - -lemma sg19859 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg271 sg11209 - -lemma sg19860 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14377 - -lemma sg19861 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg271 sg11210 - -lemma sg19862 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg14378 - -lemma sg19863 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg229 sg12335 - -lemma sg19864 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg13 sg14379 - -lemma sg19865 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by - exact rowSquare_join (by decide) sg5 sg14735 - -lemma sg19866 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by - exact rowSquare_join (by decide) sg3545 sg4158 - -lemma sg19867 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg83 sg12568 - -lemma sg19868 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg83 sg12569 - -lemma sg19869 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12545 - -lemma sg19870 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg207 sg11625 - -lemma sg19871 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12570 - -lemma sg19872 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg14742 - -lemma sg19873 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg270 sg11211 - -lemma sg19874 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg15206 - -lemma sg19875 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12546 - -lemma sg19876 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg207 sg11626 - -lemma sg19877 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg271 sg11211 - -lemma sg19878 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg11627 - -lemma sg19879 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg270 sg11212 - -lemma sg19880 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by - exact rowSquare_join (by decide) sg229 sg12336 - -lemma sg19881 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg270 sg11213 - -lemma sg19882 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by - exact rowSquare_join (by decide) sg4 sg14743 - -lemma sg19883 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12547 - -lemma sg19884 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12893 - -lemma sg19885 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg271 sg11212 - -lemma sg19886 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg271 sg11213 - -lemma sg19887 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by - exact rowSquare_join (by decide) sg270 sg11214 - -lemma sg19888 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by - exact rowSquare_join (by decide) sg270 sg11215 - -lemma sg19889 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by - exact rowSquare_join (by decide) sg270 sg11216 - -lemma sg19890 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14380 - -lemma sg19891 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14381 - -lemma sg19892 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by - exact rowSquare_join (by decide) sg271 sg11214 - -lemma sg19893 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by - exact rowSquare_join (by decide) sg271 sg11215 - -lemma sg19894 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by - exact rowSquare_join (by decide) sg271 sg11216 - -lemma sg19895 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg40 sg12891 - -lemma sg19896 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg84 sg12548 - -lemma sg19897 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg14337 - -lemma sg19898 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg15207 - -lemma sg19899 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3398 sg4351 - -lemma sg19900 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg1 sg15208 - -lemma sg19901 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg83 sg12571 - -lemma sg19902 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg84 sg12549 - -lemma sg19903 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg84 sg12550 - -lemma sg19904 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14338 - -lemma sg19905 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg14339 - -lemma sg19906 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg1 sg15209 - -lemma sg19907 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg0 sg15623 - -lemma sg19908 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12551 - -lemma sg19909 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg84 sg12552 - -lemma sg19910 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12895 - -lemma sg19911 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14382 - -lemma sg19912 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14383 - -lemma sg19913 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg4891 - -lemma sg19914 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15624 - -lemma sg19915 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg5 sg14736 - -lemma sg19916 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg83 sg12572 - -lemma sg19917 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg83 sg12573 - -lemma sg19918 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12553 - -lemma sg19919 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg207 sg11630 - -lemma sg19920 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12574 - -lemma sg19921 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg14340 - -lemma sg19922 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg14341 - -lemma sg19923 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg0 sg15625 - -lemma sg19924 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12554 - -lemma sg19925 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg207 sg11631 - -lemma sg19926 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg207 sg11632 - -lemma sg19927 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg11633 - -lemma sg19928 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg14384 - -lemma sg19929 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by - exact rowSquare_join (by decide) sg228 sg12337 - -lemma sg19930 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg14 sg14342 - -lemma sg19931 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by - exact rowSquare_join (by decide) sg4 sg14744 - -lemma sg19932 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12555 - -lemma sg19933 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12896 - -lemma sg19934 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg84 sg12556 - -lemma sg19935 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg84 sg12557 - -lemma sg19936 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by - exact rowSquare_join (by decide) sg13 sg14385 - -lemma sg19937 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by - exact rowSquare_join (by decide) sg13 sg14386 - -lemma sg19938 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by - exact rowSquare_join (by decide) sg3309 sg4432 - -lemma sg19939 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12575 - -lemma sg19940 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg83 sg12576 - -lemma sg19941 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12558 - -lemma sg19942 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg207 sg11634 - -lemma sg19943 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg207 sg11635 - -lemma sg19944 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12577 - -lemma sg19945 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg4 sg14745 - -lemma sg19946 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by - exact rowSquare_join (by decide) sg422 sg11546 - -lemma sg19947 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12559 - -lemma sg19948 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12560 - -lemma sg19949 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg207 sg11636 - -lemma sg19950 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg207 sg11637 - -lemma sg19951 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg14387 - -lemma sg19952 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by - exact rowSquare_join (by decide) sg4 sg14746 - -lemma sg19953 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12561 - -lemma sg19954 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg12897 - -lemma sg19955 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by - exact rowSquare_join (by decide) sg207 sg11638 - -lemma sg19956 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by - exact rowSquare_join (by decide) sg207 sg11639 - -lemma sg19957 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by - exact rowSquare_join (by decide) sg207 sg11640 - -lemma sg19958 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14388 - -lemma sg19959 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by - exact rowSquare_join (by decide) sg39 sg12898 - -lemma sg19960 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by - exact rowSquare_join (by decide) sg39 sg12899 - -lemma sg19961 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg42 sg12875 - -lemma sg19962 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg40 sg12894 - -lemma sg19963 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg12900 - -lemma sg19964 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14389 - -lemma sg19965 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14345 - -lemma sg19966 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg14346 - -lemma sg19967 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg15626 - -lemma sg19968 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg2710 sg4892 - -lemma sg19969 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg83 sg12578 - -lemma sg19970 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg83 sg12579 - -lemma sg19971 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12901 - -lemma sg19972 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg207 sg11652 - -lemma sg19973 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg12895 - -lemma sg19974 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg14 sg14347 - -lemma sg19975 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg14348 - -lemma sg19976 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg2710 sg4893 - -lemma sg19977 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12902 - -lemma sg19978 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg12903 - -lemma sg19979 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg39 sg12904 - -lemma sg19980 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14390 - -lemma sg19981 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg14391 - -lemma sg19982 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by - exact rowSquare_join (by decide) sg230 sg12335 - -lemma sg19983 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg14 sg14349 - -lemma sg19984 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,2] := by - exact rowSquare_join (by decide) sg3310 sg4428 - -lemma sg19985 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12580 - -lemma sg19986 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg83 sg12581 - -lemma sg19987 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12582 - -lemma sg19988 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg207 sg11653 - -lemma sg19989 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg207 sg11654 - -lemma sg19990 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12583 - -lemma sg19991 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg14 sg14350 - -lemma sg19992 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,3] := by - exact rowSquare_join (by decide) sg423 sg11546 - -lemma sg19993 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12905 - -lemma sg19994 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12906 - -lemma sg19995 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg207 sg11655 - -lemma sg19996 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg207 sg11656 - -lemma sg19997 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg14392 - -lemma sg19998 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,4,1] := by - exact rowSquare_join (by decide) sg14 sg14352 - -lemma sg19999 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12907 - -lemma sg20000 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg12908 - -lemma sg20001 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,2] := by - exact rowSquare_join (by decide) sg208 sg11613 - -lemma sg20002 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,3,1] := by - exact rowSquare_join (by decide) sg208 sg11614 - -lemma sg20003 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,4] := by - exact rowSquare_join (by decide) sg208 sg11615 - -lemma sg20004 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12584 - -lemma sg20005 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg209 sg11610 - -lemma sg20006 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12585 - -lemma sg20007 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg207 sg11658 - -lemma sg20008 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg209 sg11612 - -lemma sg20009 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg14356 - -lemma sg20010 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg11659 - -lemma sg20011 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg364 sg11100 - -lemma sg20012 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,2] := by - exact rowSquare_join (by decide) sg207 sg11661 - -lemma sg20013 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,3,1] := by - exact rowSquare_join (by decide) sg207 sg11662 - -lemma sg20014 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,4] := by - exact rowSquare_join (by decide) sg209 sg11615 - -lemma sg20015 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11101 - -lemma sg20016 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,5,2,1] := by - exact rowSquare_join (by decide) sg364 sg11102 - -lemma sg20017 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,5,3] := by - exact rowSquare_join (by decide) sg364 sg11103 - -lemma sg20018 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,6,1,1] := by - exact rowSquare_join (by decide) sg364 sg11104 - -lemma sg20019 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,6,2] := by - exact rowSquare_join (by decide) sg364 sg11105 - -lemma sg20020 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3523 sg4301 - -lemma sg20021 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3392 sg4356 - -lemma sg20022 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg424 sg11545 - -lemma sg20023 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg207 sg11674 - -lemma sg20024 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg14 sg14361 - -lemma sg20025 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by - exact rowSquare_join (by decide) sg424 sg11546 - -lemma sg20026 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14395 - -lemma sg20027 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14396 - -lemma sg20028 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg14397 - -lemma sg20029 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,4,1] := by - exact rowSquare_join (by decide) sg17 sg14552 - -lemma sg20030 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg3275 sg4512 - -lemma sg20031 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg1 sg15210 - -lemma sg20032 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg3275 sg4514 - -lemma sg20033 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg15211 - -lemma sg20034 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg5 sg14739 - -lemma sg20035 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg15212 - -lemma sg20036 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg489 sg8944 - -lemma sg20037 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg490 sg8944 - -lemma sg20038 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg489 sg8946 - -lemma sg20039 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg489 sg8947 - -lemma sg20040 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14398 - -lemma sg20041 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg490 sg8946 - -lemma sg20042 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg272 sg11214 - -lemma sg20043 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg490 sg8947 - -lemma sg20044 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg272 sg11215 - -lemma sg20045 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg272 sg11216 - -lemma sg20046 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg3275 sg4515 - -lemma sg20047 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg15213 - -lemma sg20048 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14399 - -lemma sg20049 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg15214 - -lemma sg20050 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg5 sg14741 - -lemma sg20051 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg270 sg11223 - -lemma sg20052 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg489 sg8948 - -lemma sg20053 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg271 sg11223 - -lemma sg20054 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg490 sg8948 - -lemma sg20055 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,4,3,3] := by - exact rowSquare_join (by decide) sg489 sg8949 - -lemma sg20056 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg270 sg11225 - -lemma sg20057 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,4,4,2] := by - exact rowSquare_join (by decide) sg489 sg8950 - -lemma sg20058 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg271 sg11224 - -lemma sg20059 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg271 sg11225 - -lemma sg20060 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,5,3,2] := by - exact rowSquare_join (by decide) sg490 sg8949 - -lemma sg20061 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,5,4,1] := by - exact rowSquare_join (by decide) sg490 sg8950 - -lemma sg20062 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,5,5] := by - exact rowSquare_join (by decide) sg273 sg11216 - -lemma sg20063 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg274 sg11211 - -lemma sg20064 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg489 sg8951 - -lemma sg20065 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,3,3,3] := by - exact rowSquare_join (by decide) sg422 sg11547 - -lemma sg20066 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg489 sg8952 - -lemma sg20067 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg490 sg8951 - -lemma sg20068 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,4,3,2] := by - exact rowSquare_join (by decide) sg489 sg8953 - -lemma sg20069 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,4,4,1] := by - exact rowSquare_join (by decide) sg489 sg8954 - -lemma sg20070 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11108 - -lemma sg20071 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg490 sg8952 - -lemma sg20072 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,5,2,2] := by - exact rowSquare_join (by decide) sg489 sg8955 - -lemma sg20073 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,5,3,1] := by - exact rowSquare_join (by decide) sg489 sg8956 - -lemma sg20074 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,5,4] := by - exact rowSquare_join (by decide) sg490 sg8954 - -lemma sg20075 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11109 - -lemma sg20076 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,6,2,1] := by - exact rowSquare_join (by decide) sg490 sg8955 - -lemma sg20077 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,6,3] := by - exact rowSquare_join (by decide) sg490 sg8956 - -lemma sg20078 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg15215 - -lemma sg20079 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg14376 - -lemma sg20080 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg15216 - -lemma sg20081 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg208 sg11632 - -lemma sg20082 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg14400 - -lemma sg20083 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,4,3,3] := by - exact rowSquare_join (by decide) sg229 sg12338 - -lemma sg20084 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg14 sg14379 - -lemma sg20085 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,4,4,2] := by - exact rowSquare_join (by decide) sg5 sg14744 - -lemma sg20086 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg275 sg11211 - -lemma sg20087 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg270 sg11226 - -lemma sg20088 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg15217 - -lemma sg20089 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg364 sg11110 - -lemma sg20090 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg275 sg11213 - -lemma sg20091 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,4,3,2] := by - exact rowSquare_join (by decide) sg270 sg11227 - -lemma sg20092 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,4,4,1] := by - exact rowSquare_join (by decide) sg270 sg11228 - -lemma sg20093 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11111 - -lemma sg20094 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg364 sg11112 - -lemma sg20095 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,5,2,2] := by - exact rowSquare_join (by decide) sg364 sg11113 - -lemma sg20096 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,5,3,1] := by - exact rowSquare_join (by decide) sg364 sg11114 - -lemma sg20097 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,5,4] := by - exact rowSquare_join (by decide) sg275 sg11216 - -lemma sg20098 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg276 sg11211 - -lemma sg20099 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg276 sg11212 - -lemma sg20100 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg270 sg11229 - -lemma sg20101 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,3,3,2] := by - exact rowSquare_join (by decide) sg4 sg14747 - -lemma sg20102 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11115 - -lemma sg20103 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg270 sg11230 - -lemma sg20104 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,4,2,2] := by - exact rowSquare_join (by decide) sg364 sg11116 - -lemma sg20105 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,4,3,1] := by - exact rowSquare_join (by decide) sg270 sg11231 - -lemma sg20106 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,4,4] := by - exact rowSquare_join (by decide) sg270 sg11232 - -lemma sg20107 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11117 - -lemma sg20108 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,5,2,1] := by - exact rowSquare_join (by decide) sg270 sg11233 - -lemma sg20109 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,5,3] := by - exact rowSquare_join (by decide) sg270 sg11234 - -lemma sg20110 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,6,1,1] := by - exact rowSquare_join (by decide) sg364 sg11118 - -lemma sg20111 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,6,2] := by - exact rowSquare_join (by decide) sg364 sg11119 - -lemma sg20112 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg14383 - -lemma sg20113 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg15218 - -lemma sg20114 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg207 sg11704 - -lemma sg20115 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg14 sg14384 - -lemma sg20116 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg15219 - -lemma sg20117 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg364 sg11120 - -lemma sg20118 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg208 sg11656 - -lemma sg20119 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,4,3,2] := by - exact rowSquare_join (by decide) sg13 sg14401 - -lemma sg20120 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,4,4,1] := by - exact rowSquare_join (by decide) sg14 sg14386 - -lemma sg20121 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg209 sg11654 - -lemma sg20122 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg207 sg11705 - -lemma sg20123 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg209 sg11656 - -lemma sg20124 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg14387 - -lemma sg20125 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11121 - -lemma sg20126 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg364 sg11122 - -lemma sg20127 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,4,2,2] := by - exact rowSquare_join (by decide) sg364 sg11123 - -lemma sg20128 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,4,3,1] := by - exact rowSquare_join (by decide) sg207 sg11706 - -lemma sg20129 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,4,4] := by - exact rowSquare_join (by decide) sg210 sg11640 - -lemma sg20130 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11124 - -lemma sg20131 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,5,2,1] := by - exact rowSquare_join (by decide) sg364 sg11125 - -lemma sg20132 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,5,3] := by - exact rowSquare_join (by decide) sg364 sg11126 - -lemma sg20133 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg209 sg11658 - -lemma sg20134 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11127 - -lemma sg20135 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg365 sg11098 - -lemma sg20136 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,3,2,2] := by - exact rowSquare_join (by decide) sg207 sg11707 - -lemma sg20137 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,3,3,1] := by - exact rowSquare_join (by decide) sg209 sg11662 - -lemma sg20138 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11128 - -lemma sg20139 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,4,2,1] := by - exact rowSquare_join (by decide) sg364 sg11129 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 + +namespace OAI + +/-! Semigroup Nodes 48. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg19740 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,5,4] := by + exact rowSquare_join (by decide) sg207 sg11615 + +lemma sg19741 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14362 + +lemma sg19742 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,1] := by + exact rowSquare_join (by decide) sg13 sg14363 + +lemma sg19743 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,3] := by + exact rowSquare_join (by decide) sg13 sg14364 + +lemma sg19744 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,4,4] := by + exact rowSquare_join (by decide) sg83 sg12562 + +lemma sg19745 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,5,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14365 + +lemma sg19746 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,5,2,1] := by + exact rowSquare_join (by decide) sg40 sg12887 + +lemma sg19747 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,5,3] := by + exact rowSquare_join (by decide) sg40 sg12888 + +lemma sg19748 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,6,1,1] := by + exact rowSquare_join (by decide) sg13 sg14366 + +lemma sg19749 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,6,2] := by + exact rowSquare_join (by decide) sg13 sg14367 + +lemma sg19750 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12563 + +lemma sg19751 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14738 + +lemma sg19752 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,2,2,2,1] := by + exact rowSquare_join (by decide) sg83 sg12564 + +lemma sg19753 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14368 + +lemma sg19754 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,3,2,1,1] := by + exact rowSquare_join (by decide) sg207 sg11619 + +lemma sg19755 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,3,2,2] := by + exact rowSquare_join (by decide) sg83 sg12565 + +lemma sg19756 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,3,3,1] := by + exact rowSquare_join (by decide) sg83 sg12566 + +lemma sg19757 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,4,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg11620 + +lemma sg19758 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,4,2,1] := by + exact rowSquare_join (by decide) sg207 sg11621 + +lemma sg19759 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,4,3] := by + exact rowSquare_join (by decide) sg207 sg11622 + +lemma sg19760 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,5,1,1] := by + exact rowSquare_join (by decide) sg207 sg11623 + +lemma sg19761 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,5,2] := by + exact rowSquare_join (by decide) sg207 sg11624 + +lemma sg19762 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3661 sg4059 + +lemma sg19763 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3399 sg4350 + +lemma sg19764 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg3394 sg4351 + +lemma sg19765 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg3400 sg4350 + +lemma sg19766 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg270 sg11202 + +lemma sg19767 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg15170 + +lemma sg19768 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3664 sg4051 + +lemma sg19769 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg271 sg11202 + +lemma sg19770 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg15171 + +lemma sg19771 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg15172 + +lemma sg19772 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg15173 + +lemma sg19773 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg3665 sg4051 + +lemma sg19774 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg15174 + +lemma sg19775 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg15621 + +lemma sg19776 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg3395 sg4351 + +lemma sg19777 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg15175 + +lemma sg19778 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg3275 sg4510 + +lemma sg19779 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg0 sg15622 + +lemma sg19780 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg15176 + +lemma sg19781 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg15177 + +lemma sg19782 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3667 sg4051 + +lemma sg19783 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg39 sg12889 + +lemma sg19784 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg270 sg11203 + +lemma sg19785 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg15178 + +lemma sg19786 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg15179 + +lemma sg19787 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg3668 sg4051 + +lemma sg19788 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg271 sg11203 + +lemma sg19789 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14369 + +lemma sg19790 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg15180 + +lemma sg19791 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3662 sg4057 + +lemma sg19792 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg15181 + +lemma sg19793 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg3275 sg4511 + +lemma sg19794 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15182 + +lemma sg19795 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg15183 + +lemma sg19796 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg15184 + +lemma sg19797 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg1 sg15185 + +lemma sg19798 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg41 sg12867 + +lemma sg19799 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg84 sg12538 + +lemma sg19800 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg270 sg11204 + +lemma sg19801 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg15186 + +lemma sg19802 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3396 sg4351 + +lemma sg19803 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg15187 + +lemma sg19804 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg271 sg11204 + +lemma sg19805 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg39 sg12890 + +lemma sg19806 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg270 sg11205 + +lemma sg19807 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14370 + +lemma sg19808 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg15188 + +lemma sg19809 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg15189 + +lemma sg19810 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg270 sg11206 + +lemma sg19811 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg15190 + +lemma sg19812 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg4 sg14739 + +lemma sg19813 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg15191 + +lemma sg19814 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg271 sg11205 + +lemma sg19815 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14371 + +lemma sg19816 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg271 sg11206 + +lemma sg19817 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14372 + +lemma sg19818 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14373 + +lemma sg19819 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg15192 + +lemma sg19820 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15193 + +lemma sg19821 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg6 sg14727 + +lemma sg19822 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg3666 sg4053 + +lemma sg19823 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg39 sg12891 + +lemma sg19824 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg15194 + +lemma sg19825 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg15195 + +lemma sg19826 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg15196 + +lemma sg19827 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg40 sg12889 + +lemma sg19828 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg84 sg12539 + +lemma sg19829 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg14335 + +lemma sg19830 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg270 sg11207 + +lemma sg19831 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3397 sg4351 + +lemma sg19832 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg15197 + +lemma sg19833 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12540 + +lemma sg19834 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg271 sg11207 + +lemma sg19835 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14374 + +lemma sg19836 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14375 + +lemma sg19837 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg15198 + +lemma sg19838 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg15199 + +lemma sg19839 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15200 + +lemma sg19840 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg15201 + +lemma sg19841 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg5 sg14733 + +lemma sg19842 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg15202 + +lemma sg19843 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg83 sg12567 + +lemma sg19844 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12541 + +lemma sg19845 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg84 sg12542 + +lemma sg19846 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14740 + +lemma sg19847 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg270 sg11208 + +lemma sg19848 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg15203 + +lemma sg19849 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg15204 + +lemma sg19850 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12543 + +lemma sg19851 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg271 sg11208 + +lemma sg19852 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12544 + +lemma sg19853 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg270 sg11209 + +lemma sg19854 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14376 + +lemma sg19855 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg15205 + +lemma sg19856 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg270 sg11210 + +lemma sg19857 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg4 sg14741 + +lemma sg19858 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12892 + +lemma sg19859 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg271 sg11209 + +lemma sg19860 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14377 + +lemma sg19861 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg271 sg11210 + +lemma sg19862 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg14378 + +lemma sg19863 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg229 sg12335 + +lemma sg19864 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg13 sg14379 + +lemma sg19865 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,4,2] := by + exact rowSquare_join (by decide) sg5 sg14735 + +lemma sg19866 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,5,5,5,1] := by + exact rowSquare_join (by decide) sg3545 sg4158 + +lemma sg19867 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg83 sg12568 + +lemma sg19868 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg83 sg12569 + +lemma sg19869 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12545 + +lemma sg19870 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg207 sg11625 + +lemma sg19871 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12570 + +lemma sg19872 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg14742 + +lemma sg19873 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg270 sg11211 + +lemma sg19874 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg15206 + +lemma sg19875 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12546 + +lemma sg19876 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg207 sg11626 + +lemma sg19877 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg271 sg11211 + +lemma sg19878 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg11627 + +lemma sg19879 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg270 sg11212 + +lemma sg19880 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,3,3] := by + exact rowSquare_join (by decide) sg229 sg12336 + +lemma sg19881 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg270 sg11213 + +lemma sg19882 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,4,4,2] := by + exact rowSquare_join (by decide) sg4 sg14743 + +lemma sg19883 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12547 + +lemma sg19884 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12893 + +lemma sg19885 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg271 sg11212 + +lemma sg19886 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg271 sg11213 + +lemma sg19887 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,3,2] := by + exact rowSquare_join (by decide) sg270 sg11214 + +lemma sg19888 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,4,1] := by + exact rowSquare_join (by decide) sg270 sg11215 + +lemma sg19889 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,5,5] := by + exact rowSquare_join (by decide) sg270 sg11216 + +lemma sg19890 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14380 + +lemma sg19891 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14381 + +lemma sg19892 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,2,2] := by + exact rowSquare_join (by decide) sg271 sg11214 + +lemma sg19893 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,3,1] := by + exact rowSquare_join (by decide) sg271 sg11215 + +lemma sg19894 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,6,6,6,4] := by + exact rowSquare_join (by decide) sg271 sg11216 + +lemma sg19895 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg40 sg12891 + +lemma sg19896 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg84 sg12548 + +lemma sg19897 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg14337 + +lemma sg19898 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg15207 + +lemma sg19899 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3398 sg4351 + +lemma sg19900 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg1 sg15208 + +lemma sg19901 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg83 sg12571 + +lemma sg19902 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg84 sg12549 + +lemma sg19903 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg84 sg12550 + +lemma sg19904 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14338 + +lemma sg19905 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg14339 + +lemma sg19906 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg1 sg15209 + +lemma sg19907 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg0 sg15623 + +lemma sg19908 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12551 + +lemma sg19909 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg84 sg12552 + +lemma sg19910 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12895 + +lemma sg19911 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14382 + +lemma sg19912 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14383 + +lemma sg19913 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg4891 + +lemma sg19914 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15624 + +lemma sg19915 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg5 sg14736 + +lemma sg19916 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg83 sg12572 + +lemma sg19917 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg83 sg12573 + +lemma sg19918 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12553 + +lemma sg19919 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg207 sg11630 + +lemma sg19920 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12574 + +lemma sg19921 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg14340 + +lemma sg19922 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg14341 + +lemma sg19923 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg0 sg15625 + +lemma sg19924 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12554 + +lemma sg19925 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg207 sg11631 + +lemma sg19926 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg207 sg11632 + +lemma sg19927 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg11633 + +lemma sg19928 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg14384 + +lemma sg19929 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,3,3] := by + exact rowSquare_join (by decide) sg228 sg12337 + +lemma sg19930 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg14 sg14342 + +lemma sg19931 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,4,4,2] := by + exact rowSquare_join (by decide) sg4 sg14744 + +lemma sg19932 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12555 + +lemma sg19933 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12896 + +lemma sg19934 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg84 sg12556 + +lemma sg19935 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg84 sg12557 + +lemma sg19936 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,3,2] := by + exact rowSquare_join (by decide) sg13 sg14385 + +lemma sg19937 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,4,1] := by + exact rowSquare_join (by decide) sg13 sg14386 + +lemma sg19938 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,5,5,5] := by + exact rowSquare_join (by decide) sg3309 sg4432 + +lemma sg19939 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12575 + +lemma sg19940 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg83 sg12576 + +lemma sg19941 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12558 + +lemma sg19942 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg207 sg11634 + +lemma sg19943 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg207 sg11635 + +lemma sg19944 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12577 + +lemma sg19945 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg4 sg14745 + +lemma sg19946 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by + exact rowSquare_join (by decide) sg422 sg11546 + +lemma sg19947 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12559 + +lemma sg19948 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12560 + +lemma sg19949 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg207 sg11636 + +lemma sg19950 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg207 sg11637 + +lemma sg19951 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg14387 + +lemma sg19952 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,4,4,1] := by + exact rowSquare_join (by decide) sg4 sg14746 + +lemma sg19953 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12561 + +lemma sg19954 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg12897 + +lemma sg19955 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,2,2] := by + exact rowSquare_join (by decide) sg207 sg11638 + +lemma sg19956 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,3,1] := by + exact rowSquare_join (by decide) sg207 sg11639 + +lemma sg19957 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,5,4] := by + exact rowSquare_join (by decide) sg207 sg11640 + +lemma sg19958 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14388 + +lemma sg19959 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,6,2,1] := by + exact rowSquare_join (by decide) sg39 sg12898 + +lemma sg19960 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,7,6,6,3] := by + exact rowSquare_join (by decide) sg39 sg12899 + +lemma sg19961 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg42 sg12875 + +lemma sg19962 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg40 sg12894 + +lemma sg19963 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg12900 + +lemma sg19964 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14389 + +lemma sg19965 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14345 + +lemma sg19966 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg14346 + +lemma sg19967 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg15626 + +lemma sg19968 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg2710 sg4892 + +lemma sg19969 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg83 sg12578 + +lemma sg19970 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg83 sg12579 + +lemma sg19971 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12901 + +lemma sg19972 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg207 sg11652 + +lemma sg19973 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg12895 + +lemma sg19974 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg14 sg14347 + +lemma sg19975 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg14348 + +lemma sg19976 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg2710 sg4893 + +lemma sg19977 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12902 + +lemma sg19978 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg12903 + +lemma sg19979 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg39 sg12904 + +lemma sg19980 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14390 + +lemma sg19981 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg14391 + +lemma sg19982 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,3,3] := by + exact rowSquare_join (by decide) sg230 sg12335 + +lemma sg19983 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg14 sg14349 + +lemma sg19984 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,4,4,4,2] := by + exact rowSquare_join (by decide) sg3310 sg4428 + +lemma sg19985 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12580 + +lemma sg19986 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg83 sg12581 + +lemma sg19987 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12582 + +lemma sg19988 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg207 sg11653 + +lemma sg19989 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg207 sg11654 + +lemma sg19990 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12583 + +lemma sg19991 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg14 sg14350 + +lemma sg19992 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,3,3,3] := by + exact rowSquare_join (by decide) sg423 sg11546 + +lemma sg19993 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12905 + +lemma sg19994 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12906 + +lemma sg19995 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg207 sg11655 + +lemma sg19996 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg207 sg11656 + +lemma sg19997 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg14392 + +lemma sg19998 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,4,4,1] := by + exact rowSquare_join (by decide) sg14 sg14352 + +lemma sg19999 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12907 + +lemma sg20000 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg12908 + +lemma sg20001 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,2,2] := by + exact rowSquare_join (by decide) sg208 sg11613 + +lemma sg20002 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,3,1] := by + exact rowSquare_join (by decide) sg208 sg11614 + +lemma sg20003 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,5,5,4] := by + exact rowSquare_join (by decide) sg208 sg11615 + +lemma sg20004 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12584 + +lemma sg20005 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg209 sg11610 + +lemma sg20006 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12585 + +lemma sg20007 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg207 sg11658 + +lemma sg20008 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg209 sg11612 + +lemma sg20009 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg14356 + +lemma sg20010 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg11659 + +lemma sg20011 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg364 sg11100 + +lemma sg20012 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,2,2] := by + exact rowSquare_join (by decide) sg207 sg11661 + +lemma sg20013 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,3,1] := by + exact rowSquare_join (by decide) sg207 sg11662 + +lemma sg20014 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,4,4] := by + exact rowSquare_join (by decide) sg209 sg11615 + +lemma sg20015 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11101 + +lemma sg20016 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,5,2,1] := by + exact rowSquare_join (by decide) sg364 sg11102 + +lemma sg20017 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,5,3] := by + exact rowSquare_join (by decide) sg364 sg11103 + +lemma sg20018 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,6,1,1] := by + exact rowSquare_join (by decide) sg364 sg11104 + +lemma sg20019 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,8,6,6,2] := by + exact rowSquare_join (by decide) sg364 sg11105 + +lemma sg20020 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3523 sg4301 + +lemma sg20021 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3392 sg4356 + +lemma sg20022 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg424 sg11545 + +lemma sg20023 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg207 sg11674 + +lemma sg20024 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg14 sg14361 + +lemma sg20025 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,3,3] := by + exact rowSquare_join (by decide) sg424 sg11546 + +lemma sg20026 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14395 + +lemma sg20027 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14396 + +lemma sg20028 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg14397 + +lemma sg20029 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,4,1] := by + exact rowSquare_join (by decide) sg17 sg14552 + +lemma sg20030 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg3275 sg4512 + +lemma sg20031 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg1 sg15210 + +lemma sg20032 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg3275 sg4514 + +lemma sg20033 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg15211 + +lemma sg20034 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg5 sg14739 + +lemma sg20035 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg15212 + +lemma sg20036 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg489 sg8944 + +lemma sg20037 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg490 sg8944 + +lemma sg20038 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg489 sg8946 + +lemma sg20039 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg489 sg8947 + +lemma sg20040 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14398 + +lemma sg20041 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg490 sg8946 + +lemma sg20042 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg272 sg11214 + +lemma sg20043 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg490 sg8947 + +lemma sg20044 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg272 sg11215 + +lemma sg20045 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg272 sg11216 + +lemma sg20046 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg3275 sg4515 + +lemma sg20047 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg15213 + +lemma sg20048 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14399 + +lemma sg20049 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg15214 + +lemma sg20050 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg5 sg14741 + +lemma sg20051 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg270 sg11223 + +lemma sg20052 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg489 sg8948 + +lemma sg20053 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg271 sg11223 + +lemma sg20054 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg490 sg8948 + +lemma sg20055 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,4,3,3] := by + exact rowSquare_join (by decide) sg489 sg8949 + +lemma sg20056 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg270 sg11225 + +lemma sg20057 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,4,4,2] := by + exact rowSquare_join (by decide) sg489 sg8950 + +lemma sg20058 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg271 sg11224 + +lemma sg20059 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg271 sg11225 + +lemma sg20060 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,5,3,2] := by + exact rowSquare_join (by decide) sg490 sg8949 + +lemma sg20061 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,5,4,1] := by + exact rowSquare_join (by decide) sg490 sg8950 + +lemma sg20062 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,5,5,5] := by + exact rowSquare_join (by decide) sg273 sg11216 + +lemma sg20063 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg274 sg11211 + +lemma sg20064 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg489 sg8951 + +lemma sg20065 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,3,3,3] := by + exact rowSquare_join (by decide) sg422 sg11547 + +lemma sg20066 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg489 sg8952 + +lemma sg20067 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg490 sg8951 + +lemma sg20068 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,4,3,2] := by + exact rowSquare_join (by decide) sg489 sg8953 + +lemma sg20069 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,4,4,1] := by + exact rowSquare_join (by decide) sg489 sg8954 + +lemma sg20070 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11108 + +lemma sg20071 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg490 sg8952 + +lemma sg20072 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,5,2,2] := by + exact rowSquare_join (by decide) sg489 sg8955 + +lemma sg20073 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,5,3,1] := by + exact rowSquare_join (by decide) sg489 sg8956 + +lemma sg20074 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,5,4] := by + exact rowSquare_join (by decide) sg490 sg8954 + +lemma sg20075 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11109 + +lemma sg20076 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,6,2,1] := by + exact rowSquare_join (by decide) sg490 sg8955 + +lemma sg20077 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,6,6,6,3] := by + exact rowSquare_join (by decide) sg490 sg8956 + +lemma sg20078 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg15215 + +lemma sg20079 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg14376 + +lemma sg20080 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg15216 + +lemma sg20081 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg208 sg11632 + +lemma sg20082 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg14400 + +lemma sg20083 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,4,3,3] := by + exact rowSquare_join (by decide) sg229 sg12338 + +lemma sg20084 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg14 sg14379 + +lemma sg20085 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,4,4,4,2] := by + exact rowSquare_join (by decide) sg5 sg14744 + +lemma sg20086 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg275 sg11211 + +lemma sg20087 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg270 sg11226 + +lemma sg20088 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg15217 + +lemma sg20089 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg364 sg11110 + +lemma sg20090 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg275 sg11213 + +lemma sg20091 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,4,3,2] := by + exact rowSquare_join (by decide) sg270 sg11227 + +lemma sg20092 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,4,4,1] := by + exact rowSquare_join (by decide) sg270 sg11228 + +lemma sg20093 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11111 + +lemma sg20094 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg364 sg11112 + +lemma sg20095 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,5,2,2] := by + exact rowSquare_join (by decide) sg364 sg11113 + +lemma sg20096 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,5,3,1] := by + exact rowSquare_join (by decide) sg364 sg11114 + +lemma sg20097 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,5,5,4] := by + exact rowSquare_join (by decide) sg275 sg11216 + +lemma sg20098 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg276 sg11211 + +lemma sg20099 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg276 sg11212 + +lemma sg20100 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg270 sg11229 + +lemma sg20101 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,3,3,2] := by + exact rowSquare_join (by decide) sg4 sg14747 + +lemma sg20102 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11115 + +lemma sg20103 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg270 sg11230 + +lemma sg20104 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,4,2,2] := by + exact rowSquare_join (by decide) sg364 sg11116 + +lemma sg20105 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,4,3,1] := by + exact rowSquare_join (by decide) sg270 sg11231 + +lemma sg20106 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,4,4] := by + exact rowSquare_join (by decide) sg270 sg11232 + +lemma sg20107 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11117 + +lemma sg20108 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,5,2,1] := by + exact rowSquare_join (by decide) sg270 sg11233 + +lemma sg20109 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,5,3] := by + exact rowSquare_join (by decide) sg270 sg11234 + +lemma sg20110 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,6,1,1] := by + exact rowSquare_join (by decide) sg364 sg11118 + +lemma sg20111 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,7,6,6,2] := by + exact rowSquare_join (by decide) sg364 sg11119 + +lemma sg20112 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg14383 + +lemma sg20113 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg15218 + +lemma sg20114 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg207 sg11704 + +lemma sg20115 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg14 sg14384 + +lemma sg20116 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg15219 + +lemma sg20117 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg364 sg11120 + +lemma sg20118 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg208 sg11656 + +lemma sg20119 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,4,3,2] := by + exact rowSquare_join (by decide) sg13 sg14401 + +lemma sg20120 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,4,4,4,1] := by + exact rowSquare_join (by decide) sg14 sg14386 + +lemma sg20121 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg209 sg11654 + +lemma sg20122 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg207 sg11705 + +lemma sg20123 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg209 sg11656 + +lemma sg20124 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg14387 + +lemma sg20125 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11121 + +lemma sg20126 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg364 sg11122 + +lemma sg20127 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,4,2,2] := by + exact rowSquare_join (by decide) sg364 sg11123 + +lemma sg20128 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,4,3,1] := by + exact rowSquare_join (by decide) sg207 sg11706 + +lemma sg20129 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,4,4] := by + exact rowSquare_join (by decide) sg210 sg11640 + +lemma sg20130 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11124 + +lemma sg20131 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,5,2,1] := by + exact rowSquare_join (by decide) sg364 sg11125 + +lemma sg20132 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,5,5,3] := by + exact rowSquare_join (by decide) sg364 sg11126 + +lemma sg20133 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg209 sg11658 + +lemma sg20134 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11127 + +lemma sg20135 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg365 sg11098 + +lemma sg20136 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,3,2,2] := by + exact rowSquare_join (by decide) sg207 sg11707 + +lemma sg20137 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,3,3,1] := by + exact rowSquare_join (by decide) sg209 sg11662 + +lemma sg20138 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11128 + +lemma sg20139 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,4,2,1] := by + exact rowSquare_join (by decide) sg364 sg11129 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes49.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes49.lean index b906485c60d2e36c3ca0f5751e3a9262b37434e1..9db01bff24cbb238477616f852e7346e58066f77 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes49.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes49.lean @@ -1,1221 +1,1221 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 - -namespace OAI - -/-! Semigroup Nodes 49. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg20140 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,4,3] := by - exact rowSquare_join (by decide) sg365 sg11099 - -lemma sg20141 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,5,1,1] := by - exact rowSquare_join (by decide) sg364 sg11130 - -lemma sg20142 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,5,2] := by - exact rowSquare_join (by decide) sg364 sg11131 - -lemma sg20143 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,6,1] := by - exact rowSquare_join (by decide) sg364 sg11132 - -lemma sg20144 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg208 sg11674 - -lemma sg20145 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg14 sg14391 - -lemma sg20146 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,3,3,3,3] := by - exact rowSquare_join (by decide) sg715 sg11050 - -lemma sg20147 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg209 sg11674 - -lemma sg20148 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg207 sg11708 - -lemma sg20149 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg210 sg11656 - -lemma sg20150 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg14392 - -lemma sg20151 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11133 - -lemma sg20152 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg364 sg11134 - -lemma sg20153 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,4,2,2] := by - exact rowSquare_join (by decide) sg364 sg11135 - -lemma sg20154 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,4,3,1] := by - exact rowSquare_join (by decide) sg208 sg11680 - -lemma sg20155 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,4,4] := by - exact rowSquare_join (by decide) sg213 sg11615 - -lemma sg20156 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14393 - -lemma sg20157 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg14394 - -lemma sg20158 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg12909 - -lemma sg20159 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg210 sg11673 - -lemma sg20160 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg210 sg11674 - -lemma sg20161 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14402 - -lemma sg20162 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14403 - -lemma sg20163 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14404 - -lemma sg20164 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg14 sg14396 - -lemma sg20165 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,3,2] := by - exact rowSquare_join (by decide) sg14 sg14397 - -lemma sg20166 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12586 - -lemma sg20167 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg11675 - -lemma sg20168 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg210 sg11676 - -lemma sg20169 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg11709 - -lemma sg20170 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg365 sg11106 - -lemma sg20171 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,3,2,2] := by - exact rowSquare_join (by decide) sg207 sg11710 - -lemma sg20172 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,3,3,1] := by - exact rowSquare_join (by decide) sg210 sg11680 - -lemma sg20173 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11136 - -lemma sg20174 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,4,2,1] := by - exact rowSquare_join (by decide) sg364 sg11137 - -lemma sg20175 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,4,3] := by - exact rowSquare_join (by decide) sg365 sg11107 - -lemma sg20176 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg277 sg11202 - -lemma sg20177 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg272 sg11217 - -lemma sg20178 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3670 sg4051 - -lemma sg20179 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg278 sg11202 - -lemma sg20180 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg273 sg11217 - -lemma sg20181 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg491 sg8940 - -lemma sg20182 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg272 sg11219 - -lemma sg20183 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg838 sg8105 - -lemma sg20184 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg279 sg11202 - -lemma sg20185 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg274 sg11217 - -lemma sg20186 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg492 sg8940 - -lemma sg20187 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg270 sg11235 - -lemma sg20188 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg489 sg8957 - -lemma sg20189 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg489 sg8958 - -lemma sg20190 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg839 sg8105 - -lemma sg20191 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg493 sg8940 - -lemma sg20192 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg271 sg11235 - -lemma sg20193 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg490 sg8957 - -lemma sg20194 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg490 sg8958 - -lemma sg20195 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg272 sg11221 - -lemma sg20196 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg840 sg8105 - -lemma sg20197 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg277 sg11206 - -lemma sg20198 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg272 sg11222 - -lemma sg20199 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg841 sg8105 - -lemma sg20200 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg1 sg15220 - -lemma sg20201 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg280 sg11202 - -lemma sg20202 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg275 sg11217 - -lemma sg20203 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg494 sg8940 - -lemma sg20204 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg273 sg11219 - -lemma sg20205 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg491 sg8941 - -lemma sg20206 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg838 sg8106 - -lemma sg20207 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg3275 sg4516 - -lemma sg20208 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg276 sg11217 - -lemma sg20209 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg495 sg8940 - -lemma sg20210 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg274 sg11219 - -lemma sg20211 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg489 sg8959 - -lemma sg20212 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg838 sg8107 - -lemma sg20213 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg489 sg8960 - -lemma sg20214 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg839 sg8106 - -lemma sg20215 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg491 sg8945 - -lemma sg20216 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg838 sg8108 - -lemma sg20217 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg490 sg8959 - -lemma sg20218 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg490 sg8960 - -lemma sg20219 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg490 sg8961 - -lemma sg20220 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg840 sg8106 - -lemma sg20221 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg273 sg11222 - -lemma sg20222 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg841 sg8106 - -lemma sg20223 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg3284 sg4513 - -lemma sg20224 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg496 sg8940 - -lemma sg20225 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg209 sg11694 - -lemma sg20226 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg489 sg8962 - -lemma sg20227 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg274 sg11220 - -lemma sg20228 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg492 sg8943 - -lemma sg20229 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg489 sg8963 - -lemma sg20230 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg839 sg8107 - -lemma sg20231 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg489 sg8964 - -lemma sg20232 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg490 sg8962 - -lemma sg20233 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg489 sg8965 - -lemma sg20234 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg839 sg8108 - -lemma sg20235 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg490 sg8963 - -lemma sg20236 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg840 sg8107 - -lemma sg20237 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,3,3] := by - exact rowSquare_join (by decide) sg489 sg8966 - -lemma sg20238 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg841 sg8107 - -lemma sg20239 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,4,2] := by - exact rowSquare_join (by decide) sg489 sg8967 - -lemma sg20240 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg493 sg8945 - -lemma sg20241 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg490 sg8965 - -lemma sg20242 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg840 sg8108 - -lemma sg20243 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg841 sg8108 - -lemma sg20244 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,3,2] := by - exact rowSquare_join (by decide) sg490 sg8966 - -lemma sg20245 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,4,1] := by - exact rowSquare_join (by decide) sg490 sg8967 - -lemma sg20246 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,5] := by - exact rowSquare_join (by decide) sg277 sg11216 - -lemma sg20247 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg281 sg11202 - -lemma sg20248 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg280 sg11203 - -lemma sg20249 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg275 sg11218 - -lemma sg20250 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg275 sg11219 - -lemma sg20251 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg494 sg8941 - -lemma sg20252 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg494 sg8942 - -lemma sg20253 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg838 sg8109 - -lemma sg20254 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg15221 - -lemma sg20255 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg276 sg11218 - -lemma sg20256 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg276 sg11219 - -lemma sg20257 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg489 sg8968 - -lemma sg20258 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg495 sg8942 - -lemma sg20259 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg494 sg8943 - -lemma sg20260 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8110 - -lemma sg20261 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg494 sg8944 - -lemma sg20262 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg839 sg8109 - -lemma sg20263 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg490 sg8968 - -lemma sg20264 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg838 sg8111 - -lemma sg20265 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg271 sg11236 - -lemma sg20266 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg490 sg8969 - -lemma sg20267 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg490 sg8970 - -lemma sg20268 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,3,3] := by - exact rowSquare_join (by decide) sg840 sg8109 - -lemma sg20269 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg494 sg8947 - -lemma sg20270 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,4,2] := by - exact rowSquare_join (by decide) sg841 sg8109 - -lemma sg20271 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg489 sg8971 - -lemma sg20272 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg496 sg8942 - -lemma sg20273 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg490 sg8971 - -lemma sg20274 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg489 sg8972 - -lemma sg20275 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg495 sg8944 - -lemma sg20276 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg8112 - -lemma sg20277 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg839 sg8110 - -lemma sg20278 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,3,3,3] := by - exact rowSquare_join (by decide) sg489 sg8974 - -lemma sg20279 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg495 sg8945 - -lemma sg20280 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg8113 - -lemma sg20281 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg839 sg8111 - -lemma sg20282 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg490 sg8973 - -lemma sg20283 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,4,3,2] := by - exact rowSquare_join (by decide) sg840 sg8110 - -lemma sg20284 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,4,4,1] := by - exact rowSquare_join (by decide) sg841 sg8110 - -lemma sg20285 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg838 sg8114 - -lemma sg20286 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg490 sg8975 - -lemma sg20287 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,5,2,2] := by - exact rowSquare_join (by decide) sg840 sg8111 - -lemma sg20288 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,5,3,1] := by - exact rowSquare_join (by decide) sg841 sg8111 - -lemma sg20289 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,5,4] := by - exact rowSquare_join (by decide) sg490 sg8976 - -lemma sg20290 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg496 sg8943 - -lemma sg20291 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg496 sg8944 - -lemma sg20292 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg496 sg8945 - -lemma sg20293 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg489 sg8977 - -lemma sg20294 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg839 sg8112 - -lemma sg20295 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,3,3,2] := by - exact rowSquare_join (by decide) sg489 sg8978 - -lemma sg20296 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg839 sg8113 - -lemma sg20297 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,4,2,2] := by - exact rowSquare_join (by decide) sg489 sg8979 - -lemma sg20298 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,4,3,1] := by - exact rowSquare_join (by decide) sg840 sg8112 - -lemma sg20299 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,4,4] := by - exact rowSquare_join (by decide) sg841 sg8112 - -lemma sg20300 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg839 sg8114 - -lemma sg20301 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,5,2,1] := by - exact rowSquare_join (by decide) sg840 sg8113 - -lemma sg20302 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,5,3] := by - exact rowSquare_join (by decide) sg841 sg8113 - -lemma sg20303 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,6,1,1] := by - exact rowSquare_join (by decide) sg840 sg8114 - -lemma sg20304 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,6,2] := by - exact rowSquare_join (by decide) sg841 sg8114 - -lemma sg20305 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,7,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg14 sg14399 - -lemma sg20306 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1 sg15222 - -lemma sg20307 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,7,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg275 sg11223 - -lemma sg20308 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,7,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg494 sg8948 - -lemma sg20309 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,7,4,3,3,3] := by - exact rowSquare_join (by decide) sg489 sg8980 - -lemma sg20310 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg364 sg11138 - -lemma sg20311 : RowSquare [8,7,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg12954 - -lemma sg20312 : RowSquare [8,7,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg43 sg12955 - -lemma sg20313 : RowSquare [8,7,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg43 sg12956 - -lemma sg20314 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2251 sg5737 - -lemma sg20315 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2251 sg5738 - -lemma sg20316 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2251 sg5739 - -lemma sg20317 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg5740 - -lemma sg20318 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg5741 - -lemma sg20319 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg2252 sg5740 - -lemma sg20320 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg2252 sg5741 - -lemma sg20321 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3523 sg4165 - -lemma sg20322 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg5742 - -lemma sg20323 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3524 sg4165 - -lemma sg20324 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg5743 - -lemma sg20325 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3524 sg4167 - -lemma sg20326 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg5746 - -lemma sg20327 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2256 sg5738 - -lemma sg20328 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15628 - -lemma sg20329 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg2256 sg5745 - -lemma sg20330 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15629 - -lemma sg20331 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,2,2] := by - exact rowSquare_join (by decide) sg13 sg14417 - -lemma sg20332 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg14418 - -lemma sg20333 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,2,1] := by - exact rowSquare_join (by decide) sg4 sg14756 - -lemma sg20334 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,3] := by - exact rowSquare_join (by decide) sg4 sg14757 - -lemma sg20335 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg14419 - -lemma sg20336 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,2,1] := by - exact rowSquare_join (by decide) sg13 sg14420 - -lemma sg20337 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by - exact rowSquare_join (by decide) sg13 sg14421 - -lemma sg20338 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by - exact rowSquare_join (by decide) sg13 sg14422 - -lemma sg20339 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by - exact rowSquare_join (by decide) sg13 sg14423 - -lemma sg20340 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by - exact rowSquare_join (by decide) sg32 sg13506 - -lemma sg20341 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by - exact rowSquare_join (by decide) sg5 sg14757 - -lemma sg20342 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by - exact rowSquare_join (by decide) sg4 sg14758 - -lemma sg20343 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14425 - -lemma sg20344 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg32 sg13507 - -lemma sg20345 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg14 sg14418 - -lemma sg20346 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg14427 - -lemma sg20347 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg14 sg14422 - -lemma sg20348 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by - exact rowSquare_join (by decide) sg14 sg14423 - -lemma sg20349 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,3] := by - exact rowSquare_join (by decide) sg4 sg14759 - -lemma sg20350 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14428 - -lemma sg20351 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14429 - -lemma sg20352 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14430 - -lemma sg20353 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg14431 - -lemma sg20354 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by - exact rowSquare_join (by decide) sg13 sg14432 - -lemma sg20355 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by - exact rowSquare_join (by decide) sg13 sg14433 - -lemma sg20356 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by - exact rowSquare_join (by decide) sg13 sg14434 - -lemma sg20357 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12589 - -lemma sg20358 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg83 sg12590 - -lemma sg20359 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14435 - -lemma sg20360 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by - exact rowSquare_join (by decide) sg13 sg14436 - -lemma sg20361 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14437 - -lemma sg20362 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by - exact rowSquare_join (by decide) sg13 sg14438 - -lemma sg20363 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by - exact rowSquare_join (by decide) sg13 sg14439 - -lemma sg20364 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg15227 - -lemma sg20365 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg1 sg15228 - -lemma sg20366 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15631 - -lemma sg20367 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg0 sg15632 - -lemma sg20368 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg14440 - -lemma sg20369 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg0 sg15633 - -lemma sg20370 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg4 sg14760 - -lemma sg20371 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg14441 - -lemma sg20372 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg6 sg14757 - -lemma sg20373 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15634 - -lemma sg20374 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg2260 sg5748 - -lemma sg20375 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg2265 sg5747 - -lemma sg20376 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg14442 - -lemma sg20377 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg5 sg14758 - -lemma sg20378 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg165 sg11719 - -lemma sg20379 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by - exact rowSquare_join (by decide) sg4 sg14761 - -lemma sg20380 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12589 - -lemma sg20381 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg3531 sg4169 - -lemma sg20382 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg165 sg11720 - -lemma sg20383 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by - exact rowSquare_join (by decide) sg14 sg14424 - -lemma sg20384 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg165 sg11721 - -lemma sg20385 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,7,7,1,1] := by - exact rowSquare_join (by decide) sg39 sg12914 - -lemma sg20386 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,7,7,2] := by - exact rowSquare_join (by decide) sg39 sg12915 - -lemma sg20387 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg3532 sg4169 - -lemma sg20388 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg74 sg12592 - -lemma sg20389 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg14443 - -lemma sg20390 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg14 sg14426 - -lemma sg20391 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by - exact rowSquare_join (by decide) sg14 sg14427 - -lemma sg20392 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,7,7,1] := by - exact rowSquare_join (by decide) sg13 sg14444 - -lemma sg20393 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,8,6,1] := by - exact rowSquare_join (by decide) sg207 sg11712 - -lemma sg20394 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,8,7] := by - exact rowSquare_join (by decide) sg207 sg11713 - -lemma sg20395 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg3537 sg4156 - -lemma sg20396 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg4 sg14762 - -lemma sg20397 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg14445 - -lemma sg20398 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg15 sg14423 - -lemma sg20399 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg14 sg14441 - -lemma sg20400 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg356 sg11140 - -lemma sg20401 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg4 sg14763 - -lemma sg20402 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg165 sg11722 - -lemma sg20403 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15635 - -lemma sg20404 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg356 sg11143 - -lemma sg20405 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by - exact rowSquare_join (by decide) sg14 sg14442 - -lemma sg20406 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg356 sg11145 - -lemma sg20407 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by - exact rowSquare_join (by decide) sg165 sg11723 - -lemma sg20408 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg356 sg11146 - -lemma sg20409 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg356 sg11147 - -lemma sg20410 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg356 sg11148 - -lemma sg20411 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg207 sg11714 - -lemma sg20412 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg356 sg11149 - -lemma sg20413 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg15 sg14424 - -lemma sg20414 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [10,6,4,4,4,3] := by - exact rowSquare_join (by decide) sg14 sg14445 - -lemma sg20415 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [11,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg561 sg8911 - -lemma sg20416 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2119 sg5737 - -lemma sg20417 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1663 sg6487 - -lemma sg20418 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg5669 - -lemma sg20419 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1667 sg6487 - -lemma sg20420 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by - exact rowSquare_join (by decide) sg74 sg12719 - -lemma sg20421 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg1667 sg6489 - -lemma sg20422 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3259 sg4347 - -lemma sg20423 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3260 sg4347 - -lemma sg20424 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3260 sg4348 - -lemma sg20425 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3264 sg4347 - -lemma sg20426 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg3264 sg4349 - -lemma sg20427 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg3264 sg4350 - -lemma sg20428 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3265 sg4349 - -lemma sg20429 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15238 - -lemma sg20430 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3264 sg4351 - -lemma sg20431 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg3377 sg4025 - -lemma sg20432 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg3376 sg4026 - -lemma sg20433 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg3377 sg4026 - -lemma sg20434 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3525 sg3985 - -lemma sg20435 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg3376 sg4027 - -lemma sg20436 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg3377 sg4027 - -lemma sg20437 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3523 sg3986 - -lemma sg20438 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg3263 sg4354 - -lemma sg20439 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg3264 sg4354 - -lemma sg20440 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14448 - -lemma sg20441 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg3265 sg4353 - -lemma sg20442 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14449 - -lemma sg20443 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3525 sg3987 - -lemma sg20444 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14550 - -lemma sg20445 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1] := by - exact rowSquare_join (by decide) sg364 sg11162 - -lemma sg20446 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by - exact rowSquare_join (by decide) sg13 sg14450 - -lemma sg20447 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by - exact rowSquare_join (by decide) sg13 sg14451 - -lemma sg20448 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3268 sg4351 - -lemma sg20449 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg3377 sg4028 - -lemma sg20450 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg3377 sg4029 - -lemma sg20451 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg3378 sg4025 - -lemma sg20452 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg3378 sg4026 - -lemma sg20453 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg3377 sg4030 - -lemma sg20454 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg74 sg12710 - -lemma sg20455 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg193 sg12331 - -lemma sg20456 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by - exact rowSquare_join (by decide) sg74 sg12711 - -lemma sg20457 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by - exact rowSquare_join (by decide) sg74 sg12712 - -lemma sg20458 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg74 sg12713 - -lemma sg20459 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg14452 - -lemma sg20460 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by - exact rowSquare_join (by decide) sg3379 sg4027 - -lemma sg20461 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg792 sg8213 - -lemma sg20462 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14453 - -lemma sg20463 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by - exact rowSquare_join (by decide) sg74 sg12714 - -lemma sg20464 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg364 sg11163 - -lemma sg20465 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg14454 - -lemma sg20466 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by - exact rowSquare_join (by decide) sg14 sg14451 - -lemma sg20467 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,4,4,3] := by - exact rowSquare_join (by decide) sg74 sg12715 - -lemma sg20468 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14455 - -lemma sg20469 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg364 sg11164 - -lemma sg20470 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by - exact rowSquare_join (by decide) sg580 sg8919 - -lemma sg20471 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by - exact rowSquare_join (by decide) sg580 sg8920 - -lemma sg20472 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by - exact rowSquare_join (by decide) sg166 sg11730 - -lemma sg20473 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3270 sg4347 - -lemma sg20474 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg83 sg12593 - -lemma sg20475 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11165 - -lemma sg20476 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by - exact rowSquare_join (by decide) sg580 sg8921 - -lemma sg20477 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by - exact rowSquare_join (by decide) sg580 sg8922 - -lemma sg20478 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15239 - -lemma sg20479 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg3269 sg4351 - -lemma sg20480 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg1 sg15240 - -lemma sg20481 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg1 sg15241 - -lemma sg20482 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg3263 sg4357 - -lemma sg20483 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg3378 sg4029 - -lemma sg20484 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg74 sg12716 - -lemma sg20485 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg74 sg12717 - -lemma sg20486 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg3378 sg4030 - -lemma sg20487 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg193 sg12332 - -lemma sg20488 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by - exact rowSquare_join (by decide) sg13 sg14456 - -lemma sg20489 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg3380 sg4027 - -lemma sg20490 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by - exact rowSquare_join (by decide) sg74 sg12718 - -lemma sg20491 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by - exact rowSquare_join (by decide) sg14 sg14452 - -lemma sg20492 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg391 sg11536 - -lemma sg20493 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg15242 - -lemma sg20494 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [10,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg15243 - -lemma sg20495 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [11,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg1 sg15244 - -lemma sg20496 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2156 sg5761 - -lemma sg20497 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2156 sg5762 - -lemma sg20498 : RowSquare [9,7,2,2,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4846 - -lemma sg20499 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4834 - -lemma sg20500 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4835 - -lemma sg20501 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4836 - -lemma sg20502 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2879 sg4776 - -lemma sg20503 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2879 sg4777 - -lemma sg20504 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4837 - -lemma sg20505 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2704 sg4834 - -lemma sg20506 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4838 - -lemma sg20507 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2704 sg4835 - -lemma sg20508 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg5661 - -lemma sg20509 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14766 - -lemma sg20510 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14767 - -lemma sg20511 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg14768 - -lemma sg20512 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14769 - -lemma sg20513 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg12594 - -lemma sg20514 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2705 sg4835 - -lemma sg20515 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg5662 - -lemma sg20516 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14770 - -lemma sg20517 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2706 sg4834 - -lemma sg20518 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4840 - -lemma sg20519 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg12595 - -lemma sg20520 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4841 - -lemma sg20521 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2251 sg5663 - -lemma sg20522 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2707 sg4834 - -lemma sg20523 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4842 - -lemma sg20524 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2074 sg5759 - -lemma sg20525 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2708 sg4834 - -lemma sg20526 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2074 sg5760 - -lemma sg20527 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14771 - -lemma sg20528 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2880 sg4776 - -lemma sg20529 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2879 sg4779 - -lemma sg20530 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg2880 sg4777 - -lemma sg20531 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg14770 - -lemma sg20532 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2709 sg4834 - -lemma sg20533 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2075 sg5760 - -lemma sg20534 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2251 sg5664 - -lemma sg20535 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2704 sg4837 - -lemma sg20536 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg4843 - -lemma sg20537 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg12596 - -lemma sg20538 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1188 sg8000 - -lemma sg20539 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5 sg14771 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 + +namespace OAI + +/-! Semigroup Nodes 49. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg20140 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,4,3] := by + exact rowSquare_join (by decide) sg365 sg11099 + +lemma sg20141 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,5,1,1] := by + exact rowSquare_join (by decide) sg364 sg11130 + +lemma sg20142 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,5,2] := by + exact rowSquare_join (by decide) sg364 sg11131 + +lemma sg20143 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,8,6,6,1] := by + exact rowSquare_join (by decide) sg364 sg11132 + +lemma sg20144 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg208 sg11674 + +lemma sg20145 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg14 sg14391 + +lemma sg20146 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,3,3,3,3] := by + exact rowSquare_join (by decide) sg715 sg11050 + +lemma sg20147 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg209 sg11674 + +lemma sg20148 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg207 sg11708 + +lemma sg20149 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg210 sg11656 + +lemma sg20150 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg14392 + +lemma sg20151 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11133 + +lemma sg20152 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg364 sg11134 + +lemma sg20153 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,4,2,2] := by + exact rowSquare_join (by decide) sg364 sg11135 + +lemma sg20154 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,4,3,1] := by + exact rowSquare_join (by decide) sg208 sg11680 + +lemma sg20155 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,9,4,4,4] := by + exact rowSquare_join (by decide) sg213 sg11615 + +lemma sg20156 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14393 + +lemma sg20157 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg14394 + +lemma sg20158 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg12909 + +lemma sg20159 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg210 sg11673 + +lemma sg20160 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg210 sg11674 + +lemma sg20161 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14402 + +lemma sg20162 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14403 + +lemma sg20163 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14404 + +lemma sg20164 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg14 sg14396 + +lemma sg20165 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,3,2] := by + exact rowSquare_join (by decide) sg14 sg14397 + +lemma sg20166 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12586 + +lemma sg20167 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg11675 + +lemma sg20168 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg210 sg11676 + +lemma sg20169 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg11709 + +lemma sg20170 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg365 sg11106 + +lemma sg20171 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,3,2,2] := by + exact rowSquare_join (by decide) sg207 sg11710 + +lemma sg20172 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,3,3,1] := by + exact rowSquare_join (by decide) sg210 sg11680 + +lemma sg20173 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11136 + +lemma sg20174 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,4,2,1] := by + exact rowSquare_join (by decide) sg364 sg11137 + +lemma sg20175 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,4,3] := by + exact rowSquare_join (by decide) sg365 sg11107 + +lemma sg20176 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg277 sg11202 + +lemma sg20177 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg272 sg11217 + +lemma sg20178 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3670 sg4051 + +lemma sg20179 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg278 sg11202 + +lemma sg20180 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg273 sg11217 + +lemma sg20181 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg491 sg8940 + +lemma sg20182 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg272 sg11219 + +lemma sg20183 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg838 sg8105 + +lemma sg20184 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg279 sg11202 + +lemma sg20185 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg274 sg11217 + +lemma sg20186 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg492 sg8940 + +lemma sg20187 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg270 sg11235 + +lemma sg20188 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg489 sg8957 + +lemma sg20189 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg489 sg8958 + +lemma sg20190 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg839 sg8105 + +lemma sg20191 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg493 sg8940 + +lemma sg20192 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg271 sg11235 + +lemma sg20193 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg490 sg8957 + +lemma sg20194 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg490 sg8958 + +lemma sg20195 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg272 sg11221 + +lemma sg20196 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg840 sg8105 + +lemma sg20197 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg277 sg11206 + +lemma sg20198 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg272 sg11222 + +lemma sg20199 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg841 sg8105 + +lemma sg20200 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg1 sg15220 + +lemma sg20201 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg280 sg11202 + +lemma sg20202 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg275 sg11217 + +lemma sg20203 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg494 sg8940 + +lemma sg20204 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg273 sg11219 + +lemma sg20205 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg491 sg8941 + +lemma sg20206 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg838 sg8106 + +lemma sg20207 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg3275 sg4516 + +lemma sg20208 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg276 sg11217 + +lemma sg20209 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg495 sg8940 + +lemma sg20210 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg274 sg11219 + +lemma sg20211 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg489 sg8959 + +lemma sg20212 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg838 sg8107 + +lemma sg20213 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg489 sg8960 + +lemma sg20214 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg839 sg8106 + +lemma sg20215 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg491 sg8945 + +lemma sg20216 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg838 sg8108 + +lemma sg20217 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg490 sg8959 + +lemma sg20218 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg490 sg8960 + +lemma sg20219 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg490 sg8961 + +lemma sg20220 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg840 sg8106 + +lemma sg20221 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg273 sg11222 + +lemma sg20222 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg841 sg8106 + +lemma sg20223 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg3284 sg4513 + +lemma sg20224 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg496 sg8940 + +lemma sg20225 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg209 sg11694 + +lemma sg20226 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg489 sg8962 + +lemma sg20227 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg274 sg11220 + +lemma sg20228 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg492 sg8943 + +lemma sg20229 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg489 sg8963 + +lemma sg20230 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg839 sg8107 + +lemma sg20231 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg489 sg8964 + +lemma sg20232 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg490 sg8962 + +lemma sg20233 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg489 sg8965 + +lemma sg20234 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg839 sg8108 + +lemma sg20235 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg490 sg8963 + +lemma sg20236 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg840 sg8107 + +lemma sg20237 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,3,3] := by + exact rowSquare_join (by decide) sg489 sg8966 + +lemma sg20238 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg841 sg8107 + +lemma sg20239 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,4,4,2] := by + exact rowSquare_join (by decide) sg489 sg8967 + +lemma sg20240 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg493 sg8945 + +lemma sg20241 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg490 sg8965 + +lemma sg20242 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg840 sg8108 + +lemma sg20243 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg841 sg8108 + +lemma sg20244 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,3,2] := by + exact rowSquare_join (by decide) sg490 sg8966 + +lemma sg20245 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,4,1] := by + exact rowSquare_join (by decide) sg490 sg8967 + +lemma sg20246 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,5,5,5,5] := by + exact rowSquare_join (by decide) sg277 sg11216 + +lemma sg20247 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg281 sg11202 + +lemma sg20248 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg280 sg11203 + +lemma sg20249 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg275 sg11218 + +lemma sg20250 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg275 sg11219 + +lemma sg20251 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg494 sg8941 + +lemma sg20252 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg494 sg8942 + +lemma sg20253 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg838 sg8109 + +lemma sg20254 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg15221 + +lemma sg20255 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg276 sg11218 + +lemma sg20256 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg276 sg11219 + +lemma sg20257 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg489 sg8968 + +lemma sg20258 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg495 sg8942 + +lemma sg20259 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg494 sg8943 + +lemma sg20260 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8110 + +lemma sg20261 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg494 sg8944 + +lemma sg20262 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg839 sg8109 + +lemma sg20263 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg490 sg8968 + +lemma sg20264 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg838 sg8111 + +lemma sg20265 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg271 sg11236 + +lemma sg20266 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg490 sg8969 + +lemma sg20267 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg490 sg8970 + +lemma sg20268 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,3,3] := by + exact rowSquare_join (by decide) sg840 sg8109 + +lemma sg20269 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg494 sg8947 + +lemma sg20270 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,4,4,4,2] := by + exact rowSquare_join (by decide) sg841 sg8109 + +lemma sg20271 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg489 sg8971 + +lemma sg20272 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg496 sg8942 + +lemma sg20273 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg490 sg8971 + +lemma sg20274 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg489 sg8972 + +lemma sg20275 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg495 sg8944 + +lemma sg20276 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg8112 + +lemma sg20277 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg839 sg8110 + +lemma sg20278 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,3,3,3] := by + exact rowSquare_join (by decide) sg489 sg8974 + +lemma sg20279 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg495 sg8945 + +lemma sg20280 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg8113 + +lemma sg20281 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg839 sg8111 + +lemma sg20282 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg490 sg8973 + +lemma sg20283 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,4,3,2] := by + exact rowSquare_join (by decide) sg840 sg8110 + +lemma sg20284 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,4,4,1] := by + exact rowSquare_join (by decide) sg841 sg8110 + +lemma sg20285 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg838 sg8114 + +lemma sg20286 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg490 sg8975 + +lemma sg20287 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,5,2,2] := by + exact rowSquare_join (by decide) sg840 sg8111 + +lemma sg20288 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,5,3,1] := by + exact rowSquare_join (by decide) sg841 sg8111 + +lemma sg20289 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,5,5,4] := by + exact rowSquare_join (by decide) sg490 sg8976 + +lemma sg20290 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg496 sg8943 + +lemma sg20291 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg496 sg8944 + +lemma sg20292 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg496 sg8945 + +lemma sg20293 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg489 sg8977 + +lemma sg20294 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg839 sg8112 + +lemma sg20295 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,3,3,2] := by + exact rowSquare_join (by decide) sg489 sg8978 + +lemma sg20296 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg839 sg8113 + +lemma sg20297 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,4,2,2] := by + exact rowSquare_join (by decide) sg489 sg8979 + +lemma sg20298 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,4,3,1] := by + exact rowSquare_join (by decide) sg840 sg8112 + +lemma sg20299 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,4,4] := by + exact rowSquare_join (by decide) sg841 sg8112 + +lemma sg20300 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg839 sg8114 + +lemma sg20301 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,5,2,1] := by + exact rowSquare_join (by decide) sg840 sg8113 + +lemma sg20302 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,5,3] := by + exact rowSquare_join (by decide) sg841 sg8113 + +lemma sg20303 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,6,1,1] := by + exact rowSquare_join (by decide) sg840 sg8114 + +lemma sg20304 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,6,6,6,2] := by + exact rowSquare_join (by decide) sg841 sg8114 + +lemma sg20305 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,7,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg14 sg14399 + +lemma sg20306 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1 sg15222 + +lemma sg20307 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,7,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg275 sg11223 + +lemma sg20308 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,7,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg494 sg8948 + +lemma sg20309 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,7,4,3,3,3] := by + exact rowSquare_join (by decide) sg489 sg8980 + +lemma sg20310 : RowSquare [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1] [11,7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg364 sg11138 + +lemma sg20311 : RowSquare [8,7,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg12954 + +lemma sg20312 : RowSquare [8,7,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg43 sg12955 + +lemma sg20313 : RowSquare [8,7,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg43 sg12956 + +lemma sg20314 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2251 sg5737 + +lemma sg20315 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2251 sg5738 + +lemma sg20316 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2251 sg5739 + +lemma sg20317 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg5740 + +lemma sg20318 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg5741 + +lemma sg20319 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg2252 sg5740 + +lemma sg20320 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg2252 sg5741 + +lemma sg20321 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3523 sg4165 + +lemma sg20322 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg5742 + +lemma sg20323 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3524 sg4165 + +lemma sg20324 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg5743 + +lemma sg20325 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3524 sg4167 + +lemma sg20326 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg5746 + +lemma sg20327 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2256 sg5738 + +lemma sg20328 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15628 + +lemma sg20329 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg2256 sg5745 + +lemma sg20330 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15629 + +lemma sg20331 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,2,2] := by + exact rowSquare_join (by decide) sg13 sg14417 + +lemma sg20332 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg14418 + +lemma sg20333 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,2,1] := by + exact rowSquare_join (by decide) sg4 sg14756 + +lemma sg20334 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,3] := by + exact rowSquare_join (by decide) sg4 sg14757 + +lemma sg20335 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg14419 + +lemma sg20336 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,2,1] := by + exact rowSquare_join (by decide) sg13 sg14420 + +lemma sg20337 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by + exact rowSquare_join (by decide) sg13 sg14421 + +lemma sg20338 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,1,1] := by + exact rowSquare_join (by decide) sg13 sg14422 + +lemma sg20339 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by + exact rowSquare_join (by decide) sg13 sg14423 + +lemma sg20340 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1] := by + exact rowSquare_join (by decide) sg32 sg13506 + +lemma sg20341 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by + exact rowSquare_join (by decide) sg5 sg14757 + +lemma sg20342 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by + exact rowSquare_join (by decide) sg4 sg14758 + +lemma sg20343 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14425 + +lemma sg20344 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg32 sg13507 + +lemma sg20345 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg14 sg14418 + +lemma sg20346 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg14427 + +lemma sg20347 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg14 sg14422 + +lemma sg20348 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by + exact rowSquare_join (by decide) sg14 sg14423 + +lemma sg20349 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,3] := by + exact rowSquare_join (by decide) sg4 sg14759 + +lemma sg20350 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14428 + +lemma sg20351 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14429 + +lemma sg20352 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14430 + +lemma sg20353 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg14431 + +lemma sg20354 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by + exact rowSquare_join (by decide) sg13 sg14432 + +lemma sg20355 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by + exact rowSquare_join (by decide) sg13 sg14433 + +lemma sg20356 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by + exact rowSquare_join (by decide) sg13 sg14434 + +lemma sg20357 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12589 + +lemma sg20358 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg83 sg12590 + +lemma sg20359 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14435 + +lemma sg20360 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,6,2,2] := by + exact rowSquare_join (by decide) sg13 sg14436 + +lemma sg20361 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14437 + +lemma sg20362 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by + exact rowSquare_join (by decide) sg13 sg14438 + +lemma sg20363 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by + exact rowSquare_join (by decide) sg13 sg14439 + +lemma sg20364 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg15227 + +lemma sg20365 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg1 sg15228 + +lemma sg20366 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15631 + +lemma sg20367 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg0 sg15632 + +lemma sg20368 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg14440 + +lemma sg20369 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg0 sg15633 + +lemma sg20370 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg4 sg14760 + +lemma sg20371 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg14441 + +lemma sg20372 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg6 sg14757 + +lemma sg20373 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15634 + +lemma sg20374 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg2260 sg5748 + +lemma sg20375 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg2265 sg5747 + +lemma sg20376 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg14442 + +lemma sg20377 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg5 sg14758 + +lemma sg20378 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg165 sg11719 + +lemma sg20379 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,6,4,4,3] := by + exact rowSquare_join (by decide) sg4 sg14761 + +lemma sg20380 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,6,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12589 + +lemma sg20381 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg3531 sg4169 + +lemma sg20382 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg165 sg11720 + +lemma sg20383 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by + exact rowSquare_join (by decide) sg14 sg14424 + +lemma sg20384 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg165 sg11721 + +lemma sg20385 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,7,7,1,1] := by + exact rowSquare_join (by decide) sg39 sg12914 + +lemma sg20386 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,7,7,7,2] := by + exact rowSquare_join (by decide) sg39 sg12915 + +lemma sg20387 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg3532 sg4169 + +lemma sg20388 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg74 sg12592 + +lemma sg20389 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg14443 + +lemma sg20390 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg14 sg14426 + +lemma sg20391 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,3] := by + exact rowSquare_join (by decide) sg14 sg14427 + +lemma sg20392 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,7,7,1] := by + exact rowSquare_join (by decide) sg13 sg14444 + +lemma sg20393 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,8,6,1] := by + exact rowSquare_join (by decide) sg207 sg11712 + +lemma sg20394 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [8,8,8,7] := by + exact rowSquare_join (by decide) sg207 sg11713 + +lemma sg20395 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg3537 sg4156 + +lemma sg20396 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg4 sg14762 + +lemma sg20397 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg14445 + +lemma sg20398 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg15 sg14423 + +lemma sg20399 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg14 sg14441 + +lemma sg20400 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg356 sg11140 + +lemma sg20401 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg4 sg14763 + +lemma sg20402 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg165 sg11722 + +lemma sg20403 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15635 + +lemma sg20404 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,7,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg356 sg11143 + +lemma sg20405 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by + exact rowSquare_join (by decide) sg14 sg14442 + +lemma sg20406 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,7,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg356 sg11145 + +lemma sg20407 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,7,6,3,3,3] := by + exact rowSquare_join (by decide) sg165 sg11723 + +lemma sg20408 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,8,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg356 sg11146 + +lemma sg20409 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,8,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg356 sg11147 + +lemma sg20410 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,9,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg356 sg11148 + +lemma sg20411 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,9,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg207 sg11714 + +lemma sg20412 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg356 sg11149 + +lemma sg20413 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [10,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg15 sg14424 + +lemma sg20414 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [10,6,4,4,4,3] := by + exact rowSquare_join (by decide) sg14 sg14445 + +lemma sg20415 : RowSquare [8,7,3,2,1,1,1,1,1,1,1,1,1,1,1] [11,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg561 sg8911 + +lemma sg20416 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2119 sg5737 + +lemma sg20417 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1663 sg6487 + +lemma sg20418 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg5669 + +lemma sg20419 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1667 sg6487 + +lemma sg20420 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by + exact rowSquare_join (by decide) sg74 sg12719 + +lemma sg20421 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg1667 sg6489 + +lemma sg20422 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3259 sg4347 + +lemma sg20423 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3260 sg4347 + +lemma sg20424 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3260 sg4348 + +lemma sg20425 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3264 sg4347 + +lemma sg20426 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg3264 sg4349 + +lemma sg20427 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg3264 sg4350 + +lemma sg20428 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3265 sg4349 + +lemma sg20429 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15238 + +lemma sg20430 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3264 sg4351 + +lemma sg20431 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg3377 sg4025 + +lemma sg20432 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg3376 sg4026 + +lemma sg20433 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg3377 sg4026 + +lemma sg20434 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3525 sg3985 + +lemma sg20435 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg3376 sg4027 + +lemma sg20436 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg3377 sg4027 + +lemma sg20437 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3523 sg3986 + +lemma sg20438 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg3263 sg4354 + +lemma sg20439 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg3264 sg4354 + +lemma sg20440 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14448 + +lemma sg20441 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg3265 sg4353 + +lemma sg20442 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14449 + +lemma sg20443 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3525 sg3987 + +lemma sg20444 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14550 + +lemma sg20445 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1] := by + exact rowSquare_join (by decide) sg364 sg11162 + +lemma sg20446 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,4,3] := by + exact rowSquare_join (by decide) sg13 sg14450 + +lemma sg20447 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,5,2] := by + exact rowSquare_join (by decide) sg13 sg14451 + +lemma sg20448 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3268 sg4351 + +lemma sg20449 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,5,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg3377 sg4028 + +lemma sg20450 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg3377 sg4029 + +lemma sg20451 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg3378 sg4025 + +lemma sg20452 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg3378 sg4026 + +lemma sg20453 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg3377 sg4030 + +lemma sg20454 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg74 sg12710 + +lemma sg20455 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg193 sg12331 + +lemma sg20456 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by + exact rowSquare_join (by decide) sg74 sg12711 + +lemma sg20457 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,5,5,5,3] := by + exact rowSquare_join (by decide) sg74 sg12712 + +lemma sg20458 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg74 sg12713 + +lemma sg20459 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,6,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg14452 + +lemma sg20460 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,6,5,5,2] := by + exact rowSquare_join (by decide) sg3379 sg4027 + +lemma sg20461 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg792 sg8213 + +lemma sg20462 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14453 + +lemma sg20463 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by + exact rowSquare_join (by decide) sg74 sg12714 + +lemma sg20464 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg364 sg11163 + +lemma sg20465 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg14454 + +lemma sg20466 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,5,5,5,2] := by + exact rowSquare_join (by decide) sg14 sg14451 + +lemma sg20467 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,4,4,3] := by + exact rowSquare_join (by decide) sg74 sg12715 + +lemma sg20468 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14455 + +lemma sg20469 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg364 sg11164 + +lemma sg20470 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,3,2] := by + exact rowSquare_join (by decide) sg580 sg8919 + +lemma sg20471 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,4,1] := by + exact rowSquare_join (by decide) sg580 sg8920 + +lemma sg20472 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by + exact rowSquare_join (by decide) sg166 sg11730 + +lemma sg20473 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3270 sg4347 + +lemma sg20474 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg83 sg12593 + +lemma sg20475 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11165 + +lemma sg20476 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by + exact rowSquare_join (by decide) sg580 sg8921 + +lemma sg20477 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by + exact rowSquare_join (by decide) sg580 sg8922 + +lemma sg20478 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15239 + +lemma sg20479 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg3269 sg4351 + +lemma sg20480 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg1 sg15240 + +lemma sg20481 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg1 sg15241 + +lemma sg20482 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg3263 sg4357 + +lemma sg20483 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg3378 sg4029 + +lemma sg20484 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg74 sg12716 + +lemma sg20485 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg74 sg12717 + +lemma sg20486 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,6,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg3378 sg4030 + +lemma sg20487 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg193 sg12332 + +lemma sg20488 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,6,5,5,4,3] := by + exact rowSquare_join (by decide) sg13 sg14456 + +lemma sg20489 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg3380 sg4027 + +lemma sg20490 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,7,4,4,4,4] := by + exact rowSquare_join (by decide) sg74 sg12718 + +lemma sg20491 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [8,7,5,4,4,3] := by + exact rowSquare_join (by decide) sg14 sg14452 + +lemma sg20492 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg391 sg11536 + +lemma sg20493 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg15242 + +lemma sg20494 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [10,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg15243 + +lemma sg20495 : RowSquare [8,8,3,2,2,1,1,1,1,1,1,1,1] [11,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg1 sg15244 + +lemma sg20496 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2156 sg5761 + +lemma sg20497 : RowSquare [9,7,2,2,1,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2156 sg5762 + +lemma sg20498 : RowSquare [9,7,2,2,2,2,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4846 + +lemma sg20499 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4834 + +lemma sg20500 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [3,3,3,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4835 + +lemma sg20501 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4836 + +lemma sg20502 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2879 sg4776 + +lemma sg20503 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2879 sg4777 + +lemma sg20504 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4837 + +lemma sg20505 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2704 sg4834 + +lemma sg20506 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4838 + +lemma sg20507 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2704 sg4835 + +lemma sg20508 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg5661 + +lemma sg20509 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14766 + +lemma sg20510 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14767 + +lemma sg20511 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg14768 + +lemma sg20512 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14769 + +lemma sg20513 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg12594 + +lemma sg20514 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2705 sg4835 + +lemma sg20515 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg5662 + +lemma sg20516 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14770 + +lemma sg20517 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2706 sg4834 + +lemma sg20518 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4840 + +lemma sg20519 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg12595 + +lemma sg20520 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4841 + +lemma sg20521 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2251 sg5663 + +lemma sg20522 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2707 sg4834 + +lemma sg20523 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4842 + +lemma sg20524 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2074 sg5759 + +lemma sg20525 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2708 sg4834 + +lemma sg20526 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2074 sg5760 + +lemma sg20527 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14771 + +lemma sg20528 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2880 sg4776 + +lemma sg20529 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2879 sg4779 + +lemma sg20530 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg2880 sg4777 + +lemma sg20531 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg14770 + +lemma sg20532 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2709 sg4834 + +lemma sg20533 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2075 sg5760 + +lemma sg20534 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2251 sg5664 + +lemma sg20535 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2704 sg4837 + +lemma sg20536 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg4843 + +lemma sg20537 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg12596 + +lemma sg20538 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1188 sg8000 + +lemma sg20539 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5 sg14771 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes5.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes5.lean index 6a5bb225df550e2ae95b09f48f0f2439bb548b69..f474a60b91d5391e960d66ff0ebfab945135e0be 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes5.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes5.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes4 - -namespace OAI - -/-! Semigroup Nodes 5. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg2493 : RowSquare [3,2,2,2,1,1,1,1,1] [5,4,4,1] := by - exact rowSquare_join (by decide) sg207 sg220 - -lemma sg2494 : RowSquare [3,2,2,2,1,1,1,1,1] [5,5,4] := by - exact rowSquare_join (by decide) sg97 sg395 - -lemma sg2495 : RowSquare [3,3,1,1,1,1,1,1,1,1] [6,2,2,2,2] := by - exact rowSquare_join (by decide) sg218 sg218 - -lemma sg2496 : RowSquare [3,3,1,1,1,1,1,1,1,1] [6,3,3,1,1] := by - exact rowSquare_join (by decide) sg218 sg220 - -lemma sg2497 : RowSquare [3,3,1,1,1,1,1,1,1,1] [6,4,4] := by - exact rowSquare_join (by decide) sg220 sg220 - -lemma sg2498 : RowSquare [3,3,1,1,1,1,1,1,1,1] [7,5,1,1] := by - exact rowSquare_join (by decide) sg219 sg223 - -lemma sg2499 : RowSquare [3,3,2,1,1,1,1,1,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg88 sg390 - -lemma sg2500 : RowSquare [3,3,2,1,1,1,1,1,1] [5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg193 sg219 - -lemma sg2501 : RowSquare [3,3,2,1,1,1,1,1,1] [5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg220 - -lemma sg2502 : RowSquare [3,3,2,1,1,1,1,1,1] [5,3,3,3] := by - exact rowSquare_join (by decide) sg90 sg390 - -lemma sg2503 : RowSquare [3,3,2,1,1,1,1,1,1] [5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg636 - -lemma sg2504 : RowSquare [3,3,2,2,1,1,1,1] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg193 sg193 - -lemma sg2505 : RowSquare [3,3,3,2,1,1,1] [7,7] := by - exact rowSquare_join (by decide) sg92 sg311 - -lemma sg2506 : RowSquare [3,3,3,2,1,1,1] [9,5] := by - exact rowSquare_join (by decide) sg3 sg1130 - -lemma sg2507 : RowSquare [3,3,3,2,1,1,1] [11,3] := by - exact rowSquare_join (by decide) sg128 sg109 - -lemma sg2508 : RowSquare [4,2,1,1,1,1,1,1,1,1] [6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg231 - -lemma sg2509 : RowSquare [4,2,1,1,1,1,1,1,1,1] [6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg232 - -lemma sg2510 : RowSquare [4,2,1,1,1,1,1,1,1,1] [6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg104 sg371 - -lemma sg2511 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg108 sg330 - -lemma sg2512 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg233 - -lemma sg2513 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg231 - -lemma sg2514 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,2,2,2,1] := by - exact rowSquare_join (by decide) sg49 sg616 - -lemma sg2515 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg232 - -lemma sg2516 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,3,2,1,1] := by - exact rowSquare_join (by decide) sg180 sg231 - -lemma sg2517 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,3,2,2] := by - exact rowSquare_join (by decide) sg106 sg373 - -lemma sg2518 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,3,3,1] := by - exact rowSquare_join (by decide) sg181 sg231 - -lemma sg2519 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,4,1,1,1] := by - exact rowSquare_join (by decide) sg180 sg232 - -lemma sg2520 : RowSquare [4,2,2,1,1,1,1,1,1] [4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg227 - -lemma sg2521 : RowSquare [4,3,1,1,1,1,1,1,1] [6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg940 - -lemma sg2522 : RowSquare [4,3,1,1,1,1,1,1,1] [6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg224 - -lemma sg2523 : RowSquare [4,3,1,1,1,1,1,1,1] [6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg225 - -lemma sg2524 : RowSquare [4,3,1,1,1,1,1,1,1] [7,7] := by - exact rowSquare_join (by decide) sg92 sg383 - -lemma sg2525 : RowSquare [4,3,1,1,1,1,1,1,1] [8,6] := by - exact rowSquare_join (by decide) sg0 sg2031 - -lemma sg2526 : RowSquare [4,3,1,1,1,1,1,1,1] [9,5] := by - exact rowSquare_join (by decide) sg5 sg1122 - -lemma sg2527 : RowSquare [4,3,1,1,1,1,1,1,1] [10,4] := by - exact rowSquare_join (by decide) sg14 sg719 - -lemma sg2528 : RowSquare [4,3,2,1,1,1,1,1] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg194 - -lemma sg2529 : RowSquare [4,3,2,1,1,1,1,1] [3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg371 - -lemma sg2530 : RowSquare [4,3,2,1,1,1,1,1] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg195 - -lemma sg2531 : RowSquare [4,3,2,1,1,1,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg616 - -lemma sg2532 : RowSquare [4,3,2,1,1,1,1,1] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg193 sg179 - -lemma sg2533 : RowSquare [4,3,2,1,1,1,1,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg194 sg180 - -lemma sg2534 : RowSquare [4,3,2,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg849 - -lemma sg2535 : RowSquare [4,3,2,1,1,1,1,1] [7,7] := by - exact rowSquare_join (by decide) sg92 sg342 - -lemma sg2536 : RowSquare [4,3,2,1,1,1,1,1] [8,6] := by - exact rowSquare_join (by decide) sg10 sg722 - -lemma sg2537 : RowSquare [4,3,2,1,1,1,1,1] [9,5] := by - exact rowSquare_join (by decide) sg10 sg724 - -lemma sg2538 : RowSquare [4,3,2,1,1,1,1,1] [10,4] := by - exact rowSquare_join (by decide) sg29 sg429 - -lemma sg2539 : RowSquare [4,3,2,1,1,1,1,1] [11,3] := by - exact rowSquare_join (by decide) sg80 sg235 - -lemma sg2540 : RowSquare [4,3,2,1,1,1,1,1] [12,2] := by - exact rowSquare_join (by decide) sg81 sg235 - -lemma sg2541 : RowSquare [4,3,2,1,1,1,1,1] [13,1] := by - exact rowSquare_join (by decide) sg82 sg235 - -lemma sg2542 : RowSquare [4,3,2,2,1,1,1] [5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg849 - -lemma sg2543 : RowSquare [4,3,2,2,2,1] [5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg849 - -lemma sg2544 : RowSquare [4,3,2,2,2,1] [6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg850 - -lemma sg2545 : RowSquare [4,3,3,2,1,1] [2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1232 - -lemma sg2546 : RowSquare [4,4,1,1,1,1,1,1] [2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg178 - -lemma sg2547 : RowSquare [4,4,1,1,1,1,1,1] [3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg179 - -lemma sg2548 : RowSquare [4,4,1,1,1,1,1,1] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg180 - -lemma sg2549 : RowSquare [4,4,1,1,1,1,1,1] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg181 - -lemma sg2550 : RowSquare [4,4,1,1,1,1,1,1] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg179 sg179 - -lemma sg2551 : RowSquare [4,4,1,1,1,1,1,1] [4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg179 sg180 - -lemma sg2552 : RowSquare [4,4,1,1,1,1,1,1] [4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg179 sg181 - -lemma sg2553 : RowSquare [4,4,1,1,1,1,1,1] [4,3,3,2,2] := by - exact rowSquare_join (by decide) sg66 sg372 - -lemma sg2554 : RowSquare [4,4,1,1,1,1,1,1] [4,3,3,3,1] := by - exact rowSquare_join (by decide) sg66 sg373 - -lemma sg2555 : RowSquare [4,4,1,1,1,1,1,1] [4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg185 - -lemma sg2556 : RowSquare [4,4,1,1,1,1,1,1] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg67 sg371 - -lemma sg2557 : RowSquare [4,4,1,1,1,1,1,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg180 sg180 - -lemma sg2558 : RowSquare [4,4,1,1,1,1,1,1] [4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg371 - -lemma sg2559 : RowSquare [4,4,1,1,1,1,1,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg67 sg373 - -lemma sg2560 : RowSquare [4,4,1,1,1,1,1,1] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg68 sg372 - -lemma sg2561 : RowSquare [4,4,1,1,1,1,1,1] [4,4,4,2] := by - exact rowSquare_join (by decide) sg181 sg181 - -lemma sg2562 : RowSquare [4,4,1,1,1,1,1,1] [5,3,3,3] := by - exact rowSquare_join (by decide) sg69 sg373 - -lemma sg2563 : RowSquare [4,4,1,1,1,1,1,1] [5,5,4] := by - exact rowSquare_join (by decide) sg68 sg378 - -lemma sg2564 : RowSquare [4,4,1,1,1,1,1,1] [6,3,3,2] := by - exact rowSquare_join (by decide) sg181 sg186 - -lemma sg2565 : RowSquare [4,4,1,1,1,1,1,1] [7,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg721 - -lemma sg2566 : RowSquare [4,4,1,1,1,1,1,1] [7,7] := by - exact rowSquare_join (by decide) sg71 sg383 - -lemma sg2567 : RowSquare [4,4,1,1,1,1,1,1] [8,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg723 - -lemma sg2568 : RowSquare [4,4,1,1,1,1,1,1] [8,6] := by - exact rowSquare_join (by decide) sg14 sg722 - -lemma sg2569 : RowSquare [4,4,1,1,1,1,1,1] [9,5] := by - exact rowSquare_join (by decide) sg14 sg724 - -lemma sg2570 : RowSquare [4,4,1,1,1,1,1,1] [10,4] := by - exact rowSquare_join (by decide) sg14 sg725 - -lemma sg2571 : RowSquare [4,4,1,1,1,1,1,1] [12,2] := by - exact rowSquare_join (by decide) sg85 sg235 - -lemma sg2572 : RowSquare [4,4,1,1,1,1,1,1] [13,1] := by - exact rowSquare_join (by decide) sg15 sg726 - -lemma sg2574 : RowSquare [4,4,2,2,1,1] [4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1651 - -lemma sg2575 : RowSquare [5,1,1,1,1,1,1,1,1,1] [8,4,2] := by - exact rowSquare_join (by decide) sg20 sg1016 - -lemma sg2576 : RowSquare [5,3,1,1,1,1,1,1] [2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg586 - -lemma sg2577 : RowSquare [5,3,1,1,1,1,1,1] [3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg586 - -lemma sg2578 : RowSquare [5,3,1,1,1,1,1,1] [3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg587 - -lemma sg2579 : RowSquare [5,3,1,1,1,1,1,1] [3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg34 sg586 - -lemma sg2580 : RowSquare [5,3,1,1,1,1,1,1] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg588 - -lemma sg2581 : RowSquare [5,3,1,1,1,1,1,1] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg589 - -lemma sg2582 : RowSquare [5,3,1,1,1,1,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg590 - -lemma sg2583 : RowSquare [5,3,1,1,1,1,1,1] [4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg35 sg586 - -lemma sg2584 : RowSquare [5,3,1,1,1,1,1,1] [4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg587 - -lemma sg2585 : RowSquare [5,3,1,1,1,1,1,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg36 sg586 - -lemma sg2586 : RowSquare [5,3,1,1,1,1,1,1] [4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg998 - -lemma sg2587 : RowSquare [5,3,1,1,1,1,1,1] [5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg37 sg586 - -lemma sg2588 : RowSquare [5,3,2,1,1,1,1] [3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg2074 - -lemma sg2589 : RowSquare [5,3,2,1,1,1,1] [3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg313 - -lemma sg2590 : RowSquare [5,3,2,1,1,1,1] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg2075 - -lemma sg2591 : RowSquare [5,3,2,2,1,1] [4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg1687 - -lemma sg2592 : RowSquare [5,4,1,1,1,1,1] [4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg22 sg586 - -lemma sg2593 : RowSquare [5,4,1,1,1,1,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg23 sg586 - -lemma sg2594 : RowSquare [5,4,1,1,1,1,1] [5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg586 - -lemma sg2595 : RowSquare [5,4,1,1,1,1,1] [7,7] := by - exact rowSquare_join (by decide) sg14 sg748 - -lemma sg2597 : RowSquare [5,4,2,2,1] [2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg153 sg122 - -lemma sg2598 : RowSquare [5,4,2,2,1] [2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg152 sg122 - -lemma sg2599 : RowSquare [5,4,2,2,1] [2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg151 sg122 - -lemma sg2600 : RowSquare [5,4,2,2,1] [2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg151 sg121 - -lemma sg2601 : RowSquare [5,4,2,2,1] [2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg151 sg120 - -lemma sg2602 : RowSquare [5,4,2,2,1] [2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg761 - -lemma sg2603 : RowSquare [5,4,2,2,1] [3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg150 sg122 - -lemma sg2604 : RowSquare [5,4,2,2,1] [3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg122 - -lemma sg2605 : RowSquare [5,4,2,2,1] [3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg120 - -lemma sg2606 : RowSquare [5,4,2,2,1] [3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg148 sg118 - -lemma sg2607 : RowSquare [5,4,2,2,1] [3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg147 sg122 - -lemma sg2608 : RowSquare [5,4,2,2,1] [3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg147 sg121 - -lemma sg2609 : RowSquare [5,4,2,2,1] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg147 sg118 - -lemma sg2610 : RowSquare [5,4,2,2,1] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg2106 - -lemma sg2611 : RowSquare [5,4,2,2,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg144 sg122 - -lemma sg2612 : RowSquare [5,4,2,2,1] [7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg21 sg561 - -lemma sg2613 : RowSquare [5,4,2,2,1] [7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg21 sg562 - -lemma sg2614 : RowSquare [5,4,3,2] [3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2110 - -lemma sg2615 : RowSquare [5,4,3,2] [3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg2111 - -lemma sg2616 : RowSquare [5,4,3,2] [4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1181 - -lemma sg2617 : RowSquare [5,4,3,2] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2113 - -lemma sg2618 : RowSquare [6,1,1,1,1,1,1,1,1] [8,5,1] := by - exact rowSquare_join (by decide) sg7 sg1358 - -lemma sg2619 : RowSquare [6,2,1,1,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1327 - -lemma sg2620 : RowSquare [6,2,1,1,1,1,1,1] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg1332 - -lemma sg2621 : RowSquare [6,2,1,1,1,1,1,1] [4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg1332 - -lemma sg2622 : RowSquare [6,2,2,1,1,1,1] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg891 - -lemma sg2623 : RowSquare [6,2,2,1,1,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg892 - -lemma sg2624 : RowSquare [6,2,2,2,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg809 - -lemma sg2625 : RowSquare [6,3,1,1,1,1,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg10 sg892 - -lemma sg2627 : RowSquare [6,3,2,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg205 sg113 - -lemma sg2628 : RowSquare [6,3,2,1,1,1] [2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg204 sg113 - -lemma sg2629 : RowSquare [6,3,2,1,1,1] [2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg202 sg113 - -lemma sg2630 : RowSquare [6,3,2,1,1,1] [2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg202 sg112 - -lemma sg2631 : RowSquare [6,3,2,1,1,1] [2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg202 sg111 - -lemma sg2632 : RowSquare [6,3,2,1,1,1] [2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg92 sg244 - -lemma sg2633 : RowSquare [6,3,2,1,1,1] [2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg92 sg241 - -lemma sg2634 : RowSquare [6,3,2,1,1,1] [3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg199 sg112 - -lemma sg2635 : RowSquare [6,3,2,1,1,1] [3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg199 sg111 - -lemma sg2636 : RowSquare [6,3,2,1,1,1] [3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg91 sg241 - -lemma sg2637 : RowSquare [6,3,2,1,1,1] [3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg198 sg113 - -lemma sg2638 : RowSquare [6,3,2,1,1,1] [3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg198 sg111 - -lemma sg2639 : RowSquare [6,3,2,1,1,1] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg89 sg244 - -lemma sg2640 : RowSquare [6,3,2,1,1,1] [3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg89 sg241 - -lemma sg2641 : RowSquare [6,3,2,1,1,1] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg89 sg240 - -lemma sg2642 : RowSquare [6,3,2,1,1,1] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg89 sg239 - -lemma sg2643 : RowSquare [6,3,2,1,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg34 sg459 - -lemma sg2644 : RowSquare [6,3,2,1,1,1] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg2135 - -lemma sg2645 : RowSquare [6,3,3,1,1] [3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2139 - -lemma sg2646 : RowSquare [6,3,3,1,1] [3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2140 - -lemma sg2647 : RowSquare [6,3,3,1,1] [3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg2141 - -lemma sg2648 : RowSquare [6,3,3,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg476 - -lemma sg2649 : RowSquare [6,3,3,1,1] [4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2142 - -lemma sg2650 : RowSquare [6,3,3,1,1] [4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg2143 - -lemma sg2651 : RowSquare [6,3,3,1,1] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg2144 - -lemma sg2652 : RowSquare [6,3,3,1,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2145 - -lemma sg2653 : RowSquare [6,3,3,1,1] [4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg826 - -lemma sg2654 : RowSquare [6,3,3,1,1] [4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg826 - -lemma sg2655 : RowSquare [6,3,3,1,1] [5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg1648 - -lemma sg2656 : RowSquare [6,3,3,2] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg481 - -lemma sg2657 : RowSquare [6,3,3,2] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg483 - -lemma sg2658 : RowSquare [6,3,3,2] [5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg22 sg548 - -lemma sg2659 : RowSquare [6,3,3,2] [5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg23 sg548 - -lemma sg2660 : RowSquare [6,3,3,2] [6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg1181 - -lemma sg2661 : RowSquare [6,4,2,2] [5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg56 sg331 - -lemma sg2662 : RowSquare [6,4,3,1] [2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1232 - -lemma sg2663 : RowSquare [6,4,3,1] [3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1233 - -lemma sg2664 : RowSquare [6,4,4] [2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg516 - -lemma sg2665 : RowSquare [6,5,2,1] [2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg849 - -lemma sg2666 : RowSquare [6,5,2,1] [3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg850 - -lemma sg2667 : RowSquare [6,5,2,1] [3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg849 - -lemma sg2668 : RowSquare [6,5,2,1] [3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg851 - -lemma sg2669 : RowSquare [6,5,2,1] [3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg295 - -lemma sg2670 : RowSquare [6,5,2,1] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg852 - -lemma sg2671 : RowSquare [6,5,2,1] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg296 - -lemma sg2672 : RowSquare [6,5,2,1] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg74 sg297 - -lemma sg2673 : RowSquare [6,5,2,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg854 - -lemma sg2674 : RowSquare [6,5,2,1] [4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg510 - -lemma sg2675 : RowSquare [6,5,2,1] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg165 sg142 - -lemma sg2676 : RowSquare [6,5,2,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg850 - -lemma sg2677 : RowSquare [6,5,2,1] [4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg510 - -lemma sg2678 : RowSquare [6,5,2,1] [4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg9 sg877 - -lemma sg2679 : RowSquare [6,5,2,1] [4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg165 sg144 - -lemma sg2680 : RowSquare [6,5,2,1] [4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg851 - -lemma sg2681 : RowSquare [6,5,2,1] [4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg511 - -lemma sg2682 : RowSquare [6,5,2,1] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg300 - -lemma sg2683 : RowSquare [6,5,2,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg166 sg143 - -lemma sg2684 : RowSquare [6,5,2,1] [4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg301 - -lemma sg2685 : RowSquare [6,5,2,1] [4,4,3,2,1] := by - exact rowSquare_join (by decide) sg166 sg144 - -lemma sg2686 : RowSquare [6,5,2,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg76 sg297 - -lemma sg2687 : RowSquare [6,5,2,1] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg83 sg286 - -lemma sg2688 : RowSquare [6,5,2,1] [4,4,4,2] := by - exact rowSquare_join (by decide) sg207 sg123 - -lemma sg2689 : RowSquare [6,5,2,1] [5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg849 - -lemma sg2690 : RowSquare [6,5,3] [2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg306 - -lemma sg2691 : RowSquare [6,5,3] [3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg308 - -lemma sg2692 : RowSquare [6,5,3] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg309 - -lemma sg2693 : RowSquare [6,6,1,1] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg877 - -lemma sg2694 : RowSquare [6,6,1,1] [4,3,3,3,1] := by - exact rowSquare_join (by decide) sg13 sg883 - -lemma sg2695 : RowSquare [6,6,1,1] [4,4,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg885 - -lemma sg2696 : RowSquare [6,6,1,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg886 - -lemma sg2697 : RowSquare [6,6,1,1] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg83 sg296 - -lemma sg2698 : RowSquare [6,6,1,1] [4,4,4,2] := by - exact rowSquare_join (by decide) sg83 sg297 - -lemma sg2699 : RowSquare [7,1,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2251 - -lemma sg2700 : RowSquare [7,1,1,1,1,1,1,1] [3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2252 - -lemma sg2701 : RowSquare [7,1,1,1,1,1,1,1] [3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2256 - -lemma sg2703 : RowSquare [7,2,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg233 sg109 - -lemma sg2704 : RowSquare [7,2,1,1,1,1,1] [2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg232 sg109 - -lemma sg2705 : RowSquare [7,2,1,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg105 sg237 - -lemma sg2706 : RowSquare [7,2,1,1,1,1,1] [2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg105 sg236 - -lemma sg2707 : RowSquare [7,2,1,1,1,1,1] [2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg451 - -lemma sg2708 : RowSquare [7,2,1,1,1,1,1] [2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg806 - -lemma sg2709 : RowSquare [7,2,1,1,1,1,1] [3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg806 - -lemma sg2710 : RowSquare [7,2,1,1,1,1,1] [3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg1256 - -lemma sg2711 : RowSquare [7,2,1,1,1,1,1] [3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg449 - -lemma sg2712 : RowSquare [7,2,1,1,1,1,1] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg804 - -lemma sg2713 : RowSquare [7,2,1,1,1,1,1] [3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg449 - -lemma sg2714 : RowSquare [7,2,1,1,1,1,1] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg1254 - -lemma sg2715 : RowSquare [7,2,1,1,1,1,1] [4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg1253 - -lemma sg2716 : RowSquare [7,2,1,1,1,1,1] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg801 - -lemma sg2717 : RowSquare [7,2,2,2,1] [4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg22 sg586 - -lemma sg2718 : RowSquare [7,2,2,2,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg23 sg586 - -lemma sg2719 : RowSquare [7,2,2,2,1] [5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg586 - -lemma sg2720 : RowSquare [7,3,1,1,1,1] [3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg888 - -lemma sg2721 : RowSquare [7,3,1,1,1,1] [3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg889 - -lemma sg2722 : RowSquare [7,3,1,1,1,1] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg890 - -lemma sg2723 : RowSquare [7,3,1,1,1,1] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg891 - -lemma sg2724 : RowSquare [7,3,1,1,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg892 - -lemma sg2725 : RowSquare [7,3,1,1,1,1] [4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1258 - -lemma sg2726 : RowSquare [7,3,1,1,1,1] [4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg1758 - -lemma sg2727 : RowSquare [7,3,1,1,1,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg888 - -lemma sg2728 : RowSquare [7,3,1,1,1,1] [4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg894 - -lemma sg2729 : RowSquare [7,3,1,1,1,1] [4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg807 - -lemma sg2730 : RowSquare [7,3,1,1,1,1] [4,3,3,2,2] := by - exact rowSquare_join (by decide) sg16 sg809 - -lemma sg2731 : RowSquare [7,3,1,1,1,1] [4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg889 - -lemma sg2732 : RowSquare [7,3,1,1,1,1] [4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg807 - -lemma sg2733 : RowSquare [7,3,1,1,1,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg809 - -lemma sg2734 : RowSquare [7,3,1,1,1,1] [4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1261 - -lemma sg2735 : RowSquare [7,3,1,1,1,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg899 - -lemma sg2736 : RowSquare [7,3,1,1,1,1] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg4 sg1262 - -lemma sg2737 : RowSquare [7,3,1,1,1,1] [5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg1762 - -lemma sg2738 : RowSquare [7,3,1,1,1,1] [5,3,2,2,2] := by - exact rowSquare_join (by decide) sg18 sg809 - -lemma sg2739 : RowSquare [7,3,1,1,1,1] [5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg814 - -lemma sg2740 : RowSquare [7,3,1,1,1,1] [6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg521 - -lemma sg2741 : RowSquare [7,3,2,1,1] [3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg586 - -lemma sg2742 : RowSquare [7,3,2,1,1] [3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg534 - -lemma sg2743 : RowSquare [7,3,2,1,1] [3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg312 - -lemma sg2744 : RowSquare [7,3,2,1,1] [3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg27 sg586 - -lemma sg2745 : RowSquare [7,3,2,1,1] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg535 - -lemma sg2746 : RowSquare [7,3,2,1,1] [3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg313 - -lemma sg2747 : RowSquare [7,3,2,1,1] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg314 - -lemma sg2748 : RowSquare [7,3,2,1,1] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg74 sg315 - -lemma sg2749 : RowSquare [7,3,2,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg537 - -lemma sg2750 : RowSquare [7,3,2,1,1] [4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg28 sg586 - -lemma sg2751 : RowSquare [7,3,2,1,1] [4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg75 sg312 - -lemma sg2752 : RowSquare [7,3,2,1,1] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg316 - -lemma sg2753 : RowSquare [7,3,2,1,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg29 sg586 - -lemma sg2754 : RowSquare [7,3,2,1,1] [4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg317 - -lemma sg2755 : RowSquare [7,3,2,1,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg541 - -lemma sg2756 : RowSquare [7,3,2,1,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg88 sg271 - -lemma sg2757 : RowSquare [7,3,2,1,1] [5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg30 sg586 - -lemma sg2758 : RowSquare [7,3,2,1,1] [6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg31 sg586 - -lemma sg2759 : RowSquare [7,3,2,2] [3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg66 sg330 - -lemma sg2760 : RowSquare [7,3,2,2] [3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg67 sg330 - -lemma sg2761 : RowSquare [7,3,2,2] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg143 - -lemma sg2762 : RowSquare [7,3,2,2] [3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg330 - -lemma sg2763 : RowSquare [7,3,2,2] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg144 - -lemma sg2764 : RowSquare [7,3,2,2] [4,3,3,3,1] := by - exact rowSquare_join (by decide) sg66 sg334 - -lemma sg2765 : RowSquare [7,3,2,2] [4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg71 sg330 - -lemma sg2766 : RowSquare [7,3,2,2] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg180 sg143 - -lemma sg2767 : RowSquare [7,3,2,2] [4,4,3,3] := by - exact rowSquare_join (by decide) sg67 sg334 - -lemma sg2768 : RowSquare [7,3,2,2] [5,4,2,2,1] := by - exact rowSquare_join (by decide) sg180 sg146 - -lemma sg2769 : RowSquare [7,3,3,1] [3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg154 - -lemma sg2770 : RowSquare [7,3,3,1] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg155 - -lemma sg2771 : RowSquare [7,3,3,1] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg156 - -lemma sg2772 : RowSquare [7,3,3,1] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg550 - -lemma sg2773 : RowSquare [7,3,3,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg551 - -lemma sg2774 : RowSquare [7,3,3,1] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg154 sg179 - -lemma sg2775 : RowSquare [7,3,3,1] [4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg154 sg180 - -lemma sg2776 : RowSquare [7,3,3,1] [4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg940 - -lemma sg2777 : RowSquare [7,3,3,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg155 sg180 - -lemma sg2778 : RowSquare [7,3,3,1] [4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg285 - -lemma sg2779 : RowSquare [7,3,3,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg88 sg287 - -lemma sg2780 : RowSquare [7,3,3,1] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg89 sg286 - -lemma sg2781 : RowSquare [7,3,3,1] [4,4,4,2] := by - exact rowSquare_join (by decide) sg156 sg181 - -lemma sg2782 : RowSquare [7,3,3,1] [5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg154 sg184 - -lemma sg2783 : RowSquare [7,4,1,1,1] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg914 - -lemma sg2784 : RowSquare [7,4,1,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg915 - -lemma sg2785 : RowSquare [7,4,1,1,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg911 - -lemma sg2786 : RowSquare [7,4,1,1,1] [4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg534 - -lemma sg2787 : RowSquare [7,4,1,1,1] [4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg312 - -lemma sg2788 : RowSquare [7,4,1,1,1] [4,3,3,2,2] := by - exact rowSquare_join (by decide) sg16 sg841 - -lemma sg2789 : RowSquare [7,4,1,1,1] [4,3,3,3,1] := by - exact rowSquare_join (by decide) sg39 sg537 - -lemma sg2790 : RowSquare [7,4,1,1,1] [4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg838 - -lemma sg2791 : RowSquare [7,4,1,1,1] [4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg535 - -lemma sg2792 : RowSquare [7,4,1,1,1] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg920 - -lemma sg2793 : RowSquare [7,4,1,1,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg841 - -lemma sg2794 : RowSquare [7,4,1,1,1] [4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg313 - -lemma sg2795 : RowSquare [7,4,1,1,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg922 - -lemma sg2796 : RowSquare [7,4,1,1,1] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg97 sg270 - -lemma sg2797 : RowSquare [7,4,1,1,1] [5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg846 - -lemma sg2798 : RowSquare [7,4,2,1] [2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg330 - -lemma sg2799 : RowSquare [7,4,2,1] [3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg165 - -lemma sg2800 : RowSquare [7,4,2,1] [3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg76 sg330 - -lemma sg2801 : RowSquare [7,4,2,1] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg166 - -lemma sg2802 : RowSquare [7,4,2,1] [3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg332 - -lemma sg2803 : RowSquare [7,4,2,1] [3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg77 sg330 - -lemma sg2804 : RowSquare [7,4,2,1] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg167 - -lemma sg2805 : RowSquare [7,4,2,1] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg333 - -lemma sg2806 : RowSquare [7,4,2,1] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg74 sg334 - -lemma sg2807 : RowSquare [7,4,2,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg564 - -lemma sg2808 : RowSquare [7,4,2,1] [4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg850 - -lemma sg2809 : RowSquare [7,4,2,1] [4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg168 - -lemma sg2810 : RowSquare [7,4,2,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg850 - -lemma sg2811 : RowSquare [7,4,2,1] [4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg169 - -lemma sg2812 : RowSquare [7,4,2,1] [4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg170 - -lemma sg2813 : RowSquare [7,4,2,1] [4,3,3,2,2] := by - exact rowSquare_join (by decide) sg87 sg296 - -lemma sg2814 : RowSquare [7,4,2,1] [4,3,3,3,1] := by - exact rowSquare_join (by decide) sg87 sg297 - -lemma sg2815 : RowSquare [7,4,2,1] [4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg330 - -lemma sg2816 : RowSquare [7,4,2,1] [4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg171 - -lemma sg2817 : RowSquare [7,4,2,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg194 sg143 - -lemma sg2818 : RowSquare [7,4,2,1] [4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg339 - -lemma sg2819 : RowSquare [7,4,2,1] [4,4,3,2,1] := by - exact rowSquare_join (by decide) sg194 sg144 - -lemma sg2820 : RowSquare [7,4,2,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg88 sg297 - -lemma sg2821 : RowSquare [7,4,2,1] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg97 sg286 - -lemma sg2822 : RowSquare [7,4,2,1] [4,4,4,2] := by - exact rowSquare_join (by decide) sg195 sg144 - -lemma sg2823 : RowSquare [7,4,2,1] [5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg850 - -lemma sg2824 : RowSquare [7,4,2,1] [5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg172 - -lemma sg2825 : RowSquare [7,4,2,1] [5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg173 - -lemma sg2826 : RowSquare [7,4,2,1] [5,3,2,2,2] := by - exact rowSquare_join (by decide) sg194 sg145 - -lemma sg2827 : RowSquare [7,4,2,1] [5,3,3,3] := by - exact rowSquare_join (by decide) sg98 sg287 - -lemma sg2828 : RowSquare [7,4,2,1] [5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg174 - -lemma sg2829 : RowSquare [7,4,2,1] [5,4,3,2] := by - exact rowSquare_join (by decide) sg195 sg146 - -lemma sg2830 : RowSquare [7,4,2,1] [5,5,2,2] := by - exact rowSquare_join (by decide) sg88 sg300 - -lemma sg2831 : RowSquare [7,4,2,1] [6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg850 - -lemma sg2832 : RowSquare [7,4,2,1] [6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg175 - -lemma sg2833 : RowSquare [7,4,2,1] [6,2,2,2,2] := by - exact rowSquare_join (by decide) sg196 sg145 - -lemma sg2834 : RowSquare [7,4,2,1] [6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg176 - -lemma sg2835 : RowSquare [7,4,2,1] [6,6,1,1] := by - exact rowSquare_join (by decide) sg88 sg302 - -lemma sg2836 : RowSquare [7,4,2,1] [7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg177 - -lemma sg2837 : RowSquare [7,4,3] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg577 - -lemma sg2838 : RowSquare [7,4,3] [3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg348 - -lemma sg2839 : RowSquare [7,4,3] [3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg306 - -lemma sg2840 : RowSquare [7,4,3] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg74 sg350 - -lemma sg2841 : RowSquare [7,4,3] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg578 - -lemma sg2842 : RowSquare [7,4,3] [4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg516 - -lemma sg2843 : RowSquare [7,4,3] [4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg87 sg307 - -lemma sg2844 : RowSquare [7,4,3] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg193 sg154 - -lemma sg2845 : RowSquare [7,4,3] [4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg88 sg307 - -lemma sg2846 : RowSquare [7,4,3] [4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg193 sg155 - -lemma sg2847 : RowSquare [7,4,3] [4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg307 - -lemma sg2848 : RowSquare [7,4,3] [4,3,3,2,2] := by - exact rowSquare_join (by decide) sg87 sg309 - -lemma sg2849 : RowSquare [7,4,3] [4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg34 sg577 - -lemma sg2850 : RowSquare [7,4,3] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg194 sg155 - -lemma sg2851 : RowSquare [7,4,3] [4,4,3,2,1] := by - exact rowSquare_join (by decide) sg194 sg156 - -lemma sg2852 : RowSquare [7,4,3] [4,4,3,3] := by - exact rowSquare_join (by decide) sg88 sg310 - -lemma sg2853 : RowSquare [7,4,3] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg89 sg309 - -lemma sg2854 : RowSquare [7,4,3] [5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg90 sg307 - -lemma sg2855 : RowSquare [7,4,3] [5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg193 sg157 - -lemma sg2856 : RowSquare [7,4,3] [5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg91 sg307 - -lemma sg2857 : RowSquare [7,4,3] [5,3,2,2,2] := by - exact rowSquare_join (by decide) sg194 sg157 - -lemma sg2858 : RowSquare [7,4,3] [5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg159 - -lemma sg2859 : RowSquare [7,4,3] [5,3,3,3] := by - exact rowSquare_join (by decide) sg90 sg310 - -lemma sg2860 : RowSquare [7,4,3] [5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg307 - -lemma sg2861 : RowSquare [7,4,3] [5,4,3,1,1] := by - exact rowSquare_join (by decide) sg194 sg159 - -lemma sg2862 : RowSquare [7,4,3] [6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg93 sg307 - -lemma sg2863 : RowSquare [7,4,3] [6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg94 sg307 - -lemma sg2864 : RowSquare [7,4,3] [6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg162 - -lemma sg2865 : RowSquare [7,4,3] [6,3,3,1,1] := by - exact rowSquare_join (by decide) sg196 sg159 - -lemma sg2866 : RowSquare [7,4,3] [7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg95 sg307 - -lemma sg2867 : RowSquare [7,5,1,1] [3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg958 - -lemma sg2868 : RowSquare [7,5,1,1] [3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg330 - -lemma sg2869 : RowSquare [7,5,1,1] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg959 - -lemma sg2870 : RowSquare [7,5,1,1] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg960 - -lemma sg2871 : RowSquare [7,5,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg961 - -lemma sg2872 : RowSquare [7,5,1,1] [4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg330 - -lemma sg2873 : RowSquare [7,5,1,1] [4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg562 - -lemma sg2874 : RowSquare [7,5,1,1] [4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg331 - -lemma sg2875 : RowSquare [7,5,1,1] [4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg142 sg207 - -lemma sg2876 : RowSquare [7,5,1,1] [4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg562 - -lemma sg2877 : RowSquare [7,6,1] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg83 sg357 - -lemma sg2878 : RowSquare [7,6,1] [4,4,4,2] := by - exact rowSquare_join (by decide) sg207 sg167 - -lemma sg2879 : RowSquare [8,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2251 - -lemma sg2880 : RowSquare [8,1,1,1,1,1,1] [3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2252 - -lemma sg2881 : RowSquare [8,1,1,1,1,1,1] [3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2256 - -lemma sg2882 : RowSquare [8,1,1,1,1,1,1] [4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg2260 - -lemma sg2883 : RowSquare [8,1,1,1,1,1,1] [4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2262 - -lemma sg2884 : RowSquare [8,1,1,1,1,1,1] [4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2263 - -lemma sg2885 : RowSquare [8,1,1,1,1,1,1] [5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2264 - -lemma sg2886 : RowSquare [8,1,1,1,1,1,1] [5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2267 - -lemma sg2887 : RowSquare [8,2,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1327 - -lemma sg2888 : RowSquare [8,2,1,1,1,1] [3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1329 - -lemma sg2889 : RowSquare [8,2,1,1,1,1] [3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1330 - -lemma sg2890 : RowSquare [8,2,1,1,1,1] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1331 - -lemma sg2891 : RowSquare [8,2,1,1,1,1] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg1332 - -lemma sg2892 : RowSquare [8,2,1,1,1,1] [4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg1758 - -lemma sg2893 : RowSquare [8,2,1,1,1,1] [4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg1332 - -lemma sg2894 : RowSquare [8,2,1,1,1,1] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg891 - -lemma sg2895 : RowSquare [8,2,1,1,1,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg892 - -lemma sg2896 : RowSquare [8,2,1,1,1,1] [5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg893 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes4 + +namespace OAI + +/-! Semigroup Nodes 5. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg2493 : RowSquare [3,2,2,2,1,1,1,1,1] [5,4,4,1] := by + exact rowSquare_join (by decide) sg207 sg220 + +lemma sg2494 : RowSquare [3,2,2,2,1,1,1,1,1] [5,5,4] := by + exact rowSquare_join (by decide) sg97 sg395 + +lemma sg2495 : RowSquare [3,3,1,1,1,1,1,1,1,1] [6,2,2,2,2] := by + exact rowSquare_join (by decide) sg218 sg218 + +lemma sg2496 : RowSquare [3,3,1,1,1,1,1,1,1,1] [6,3,3,1,1] := by + exact rowSquare_join (by decide) sg218 sg220 + +lemma sg2497 : RowSquare [3,3,1,1,1,1,1,1,1,1] [6,4,4] := by + exact rowSquare_join (by decide) sg220 sg220 + +lemma sg2498 : RowSquare [3,3,1,1,1,1,1,1,1,1] [7,5,1,1] := by + exact rowSquare_join (by decide) sg219 sg223 + +lemma sg2499 : RowSquare [3,3,2,1,1,1,1,1,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg88 sg390 + +lemma sg2500 : RowSquare [3,3,2,1,1,1,1,1,1] [5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg193 sg219 + +lemma sg2501 : RowSquare [3,3,2,1,1,1,1,1,1] [5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg220 + +lemma sg2502 : RowSquare [3,3,2,1,1,1,1,1,1] [5,3,3,3] := by + exact rowSquare_join (by decide) sg90 sg390 + +lemma sg2503 : RowSquare [3,3,2,1,1,1,1,1,1] [5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg636 + +lemma sg2504 : RowSquare [3,3,2,2,1,1,1,1] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg193 sg193 + +lemma sg2505 : RowSquare [3,3,3,2,1,1,1] [7,7] := by + exact rowSquare_join (by decide) sg92 sg311 + +lemma sg2506 : RowSquare [3,3,3,2,1,1,1] [9,5] := by + exact rowSquare_join (by decide) sg3 sg1130 + +lemma sg2507 : RowSquare [3,3,3,2,1,1,1] [11,3] := by + exact rowSquare_join (by decide) sg128 sg109 + +lemma sg2508 : RowSquare [4,2,1,1,1,1,1,1,1,1] [6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg231 + +lemma sg2509 : RowSquare [4,2,1,1,1,1,1,1,1,1] [6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg232 + +lemma sg2510 : RowSquare [4,2,1,1,1,1,1,1,1,1] [6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg104 sg371 + +lemma sg2511 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg108 sg330 + +lemma sg2512 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg233 + +lemma sg2513 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg231 + +lemma sg2514 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,2,2,2,1] := by + exact rowSquare_join (by decide) sg49 sg616 + +lemma sg2515 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg232 + +lemma sg2516 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,3,2,1,1] := by + exact rowSquare_join (by decide) sg180 sg231 + +lemma sg2517 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,3,2,2] := by + exact rowSquare_join (by decide) sg106 sg373 + +lemma sg2518 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,3,3,1] := by + exact rowSquare_join (by decide) sg181 sg231 + +lemma sg2519 : RowSquare [4,2,1,1,1,1,1,1,1,1] [7,4,1,1,1] := by + exact rowSquare_join (by decide) sg180 sg232 + +lemma sg2520 : RowSquare [4,2,2,1,1,1,1,1,1] [4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg227 + +lemma sg2521 : RowSquare [4,3,1,1,1,1,1,1,1] [6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg940 + +lemma sg2522 : RowSquare [4,3,1,1,1,1,1,1,1] [6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg224 + +lemma sg2523 : RowSquare [4,3,1,1,1,1,1,1,1] [6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg225 + +lemma sg2524 : RowSquare [4,3,1,1,1,1,1,1,1] [7,7] := by + exact rowSquare_join (by decide) sg92 sg383 + +lemma sg2525 : RowSquare [4,3,1,1,1,1,1,1,1] [8,6] := by + exact rowSquare_join (by decide) sg0 sg2031 + +lemma sg2526 : RowSquare [4,3,1,1,1,1,1,1,1] [9,5] := by + exact rowSquare_join (by decide) sg5 sg1122 + +lemma sg2527 : RowSquare [4,3,1,1,1,1,1,1,1] [10,4] := by + exact rowSquare_join (by decide) sg14 sg719 + +lemma sg2528 : RowSquare [4,3,2,1,1,1,1,1] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg194 + +lemma sg2529 : RowSquare [4,3,2,1,1,1,1,1] [3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg371 + +lemma sg2530 : RowSquare [4,3,2,1,1,1,1,1] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg195 + +lemma sg2531 : RowSquare [4,3,2,1,1,1,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg616 + +lemma sg2532 : RowSquare [4,3,2,1,1,1,1,1] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg193 sg179 + +lemma sg2533 : RowSquare [4,3,2,1,1,1,1,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg194 sg180 + +lemma sg2534 : RowSquare [4,3,2,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg849 + +lemma sg2535 : RowSquare [4,3,2,1,1,1,1,1] [7,7] := by + exact rowSquare_join (by decide) sg92 sg342 + +lemma sg2536 : RowSquare [4,3,2,1,1,1,1,1] [8,6] := by + exact rowSquare_join (by decide) sg10 sg722 + +lemma sg2537 : RowSquare [4,3,2,1,1,1,1,1] [9,5] := by + exact rowSquare_join (by decide) sg10 sg724 + +lemma sg2538 : RowSquare [4,3,2,1,1,1,1,1] [10,4] := by + exact rowSquare_join (by decide) sg29 sg429 + +lemma sg2539 : RowSquare [4,3,2,1,1,1,1,1] [11,3] := by + exact rowSquare_join (by decide) sg80 sg235 + +lemma sg2540 : RowSquare [4,3,2,1,1,1,1,1] [12,2] := by + exact rowSquare_join (by decide) sg81 sg235 + +lemma sg2541 : RowSquare [4,3,2,1,1,1,1,1] [13,1] := by + exact rowSquare_join (by decide) sg82 sg235 + +lemma sg2542 : RowSquare [4,3,2,2,1,1,1] [5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg849 + +lemma sg2543 : RowSquare [4,3,2,2,2,1] [5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg849 + +lemma sg2544 : RowSquare [4,3,2,2,2,1] [6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg850 + +lemma sg2545 : RowSquare [4,3,3,2,1,1] [2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1232 + +lemma sg2546 : RowSquare [4,4,1,1,1,1,1,1] [2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg178 + +lemma sg2547 : RowSquare [4,4,1,1,1,1,1,1] [3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg179 + +lemma sg2548 : RowSquare [4,4,1,1,1,1,1,1] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg180 + +lemma sg2549 : RowSquare [4,4,1,1,1,1,1,1] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg181 + +lemma sg2550 : RowSquare [4,4,1,1,1,1,1,1] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg179 sg179 + +lemma sg2551 : RowSquare [4,4,1,1,1,1,1,1] [4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg179 sg180 + +lemma sg2552 : RowSquare [4,4,1,1,1,1,1,1] [4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg179 sg181 + +lemma sg2553 : RowSquare [4,4,1,1,1,1,1,1] [4,3,3,2,2] := by + exact rowSquare_join (by decide) sg66 sg372 + +lemma sg2554 : RowSquare [4,4,1,1,1,1,1,1] [4,3,3,3,1] := by + exact rowSquare_join (by decide) sg66 sg373 + +lemma sg2555 : RowSquare [4,4,1,1,1,1,1,1] [4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg185 + +lemma sg2556 : RowSquare [4,4,1,1,1,1,1,1] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg67 sg371 + +lemma sg2557 : RowSquare [4,4,1,1,1,1,1,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg180 sg180 + +lemma sg2558 : RowSquare [4,4,1,1,1,1,1,1] [4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg371 + +lemma sg2559 : RowSquare [4,4,1,1,1,1,1,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg67 sg373 + +lemma sg2560 : RowSquare [4,4,1,1,1,1,1,1] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg68 sg372 + +lemma sg2561 : RowSquare [4,4,1,1,1,1,1,1] [4,4,4,2] := by + exact rowSquare_join (by decide) sg181 sg181 + +lemma sg2562 : RowSquare [4,4,1,1,1,1,1,1] [5,3,3,3] := by + exact rowSquare_join (by decide) sg69 sg373 + +lemma sg2563 : RowSquare [4,4,1,1,1,1,1,1] [5,5,4] := by + exact rowSquare_join (by decide) sg68 sg378 + +lemma sg2564 : RowSquare [4,4,1,1,1,1,1,1] [6,3,3,2] := by + exact rowSquare_join (by decide) sg181 sg186 + +lemma sg2565 : RowSquare [4,4,1,1,1,1,1,1] [7,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg721 + +lemma sg2566 : RowSquare [4,4,1,1,1,1,1,1] [7,7] := by + exact rowSquare_join (by decide) sg71 sg383 + +lemma sg2567 : RowSquare [4,4,1,1,1,1,1,1] [8,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg723 + +lemma sg2568 : RowSquare [4,4,1,1,1,1,1,1] [8,6] := by + exact rowSquare_join (by decide) sg14 sg722 + +lemma sg2569 : RowSquare [4,4,1,1,1,1,1,1] [9,5] := by + exact rowSquare_join (by decide) sg14 sg724 + +lemma sg2570 : RowSquare [4,4,1,1,1,1,1,1] [10,4] := by + exact rowSquare_join (by decide) sg14 sg725 + +lemma sg2571 : RowSquare [4,4,1,1,1,1,1,1] [12,2] := by + exact rowSquare_join (by decide) sg85 sg235 + +lemma sg2572 : RowSquare [4,4,1,1,1,1,1,1] [13,1] := by + exact rowSquare_join (by decide) sg15 sg726 + +lemma sg2574 : RowSquare [4,4,2,2,1,1] [4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1651 + +lemma sg2575 : RowSquare [5,1,1,1,1,1,1,1,1,1] [8,4,2] := by + exact rowSquare_join (by decide) sg20 sg1016 + +lemma sg2576 : RowSquare [5,3,1,1,1,1,1,1] [2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg586 + +lemma sg2577 : RowSquare [5,3,1,1,1,1,1,1] [3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg586 + +lemma sg2578 : RowSquare [5,3,1,1,1,1,1,1] [3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg587 + +lemma sg2579 : RowSquare [5,3,1,1,1,1,1,1] [3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg34 sg586 + +lemma sg2580 : RowSquare [5,3,1,1,1,1,1,1] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg588 + +lemma sg2581 : RowSquare [5,3,1,1,1,1,1,1] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg589 + +lemma sg2582 : RowSquare [5,3,1,1,1,1,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg590 + +lemma sg2583 : RowSquare [5,3,1,1,1,1,1,1] [4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg35 sg586 + +lemma sg2584 : RowSquare [5,3,1,1,1,1,1,1] [4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg587 + +lemma sg2585 : RowSquare [5,3,1,1,1,1,1,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg36 sg586 + +lemma sg2586 : RowSquare [5,3,1,1,1,1,1,1] [4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg998 + +lemma sg2587 : RowSquare [5,3,1,1,1,1,1,1] [5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg37 sg586 + +lemma sg2588 : RowSquare [5,3,2,1,1,1,1] [3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg2074 + +lemma sg2589 : RowSquare [5,3,2,1,1,1,1] [3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg313 + +lemma sg2590 : RowSquare [5,3,2,1,1,1,1] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg2075 + +lemma sg2591 : RowSquare [5,3,2,2,1,1] [4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg1687 + +lemma sg2592 : RowSquare [5,4,1,1,1,1,1] [4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg22 sg586 + +lemma sg2593 : RowSquare [5,4,1,1,1,1,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg23 sg586 + +lemma sg2594 : RowSquare [5,4,1,1,1,1,1] [5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg586 + +lemma sg2595 : RowSquare [5,4,1,1,1,1,1] [7,7] := by + exact rowSquare_join (by decide) sg14 sg748 + +lemma sg2597 : RowSquare [5,4,2,2,1] [2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg153 sg122 + +lemma sg2598 : RowSquare [5,4,2,2,1] [2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg152 sg122 + +lemma sg2599 : RowSquare [5,4,2,2,1] [2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg151 sg122 + +lemma sg2600 : RowSquare [5,4,2,2,1] [2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg151 sg121 + +lemma sg2601 : RowSquare [5,4,2,2,1] [2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg151 sg120 + +lemma sg2602 : RowSquare [5,4,2,2,1] [2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg761 + +lemma sg2603 : RowSquare [5,4,2,2,1] [3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg150 sg122 + +lemma sg2604 : RowSquare [5,4,2,2,1] [3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg122 + +lemma sg2605 : RowSquare [5,4,2,2,1] [3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg120 + +lemma sg2606 : RowSquare [5,4,2,2,1] [3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg148 sg118 + +lemma sg2607 : RowSquare [5,4,2,2,1] [3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg147 sg122 + +lemma sg2608 : RowSquare [5,4,2,2,1] [3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg147 sg121 + +lemma sg2609 : RowSquare [5,4,2,2,1] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg147 sg118 + +lemma sg2610 : RowSquare [5,4,2,2,1] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg2106 + +lemma sg2611 : RowSquare [5,4,2,2,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg144 sg122 + +lemma sg2612 : RowSquare [5,4,2,2,1] [7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg21 sg561 + +lemma sg2613 : RowSquare [5,4,2,2,1] [7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg21 sg562 + +lemma sg2614 : RowSquare [5,4,3,2] [3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2110 + +lemma sg2615 : RowSquare [5,4,3,2] [3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg2111 + +lemma sg2616 : RowSquare [5,4,3,2] [4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1181 + +lemma sg2617 : RowSquare [5,4,3,2] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2113 + +lemma sg2618 : RowSquare [6,1,1,1,1,1,1,1,1] [8,5,1] := by + exact rowSquare_join (by decide) sg7 sg1358 + +lemma sg2619 : RowSquare [6,2,1,1,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1327 + +lemma sg2620 : RowSquare [6,2,1,1,1,1,1,1] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg1332 + +lemma sg2621 : RowSquare [6,2,1,1,1,1,1,1] [4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg1332 + +lemma sg2622 : RowSquare [6,2,2,1,1,1,1] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg891 + +lemma sg2623 : RowSquare [6,2,2,1,1,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg892 + +lemma sg2624 : RowSquare [6,2,2,2,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg809 + +lemma sg2625 : RowSquare [6,3,1,1,1,1,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg10 sg892 + +lemma sg2627 : RowSquare [6,3,2,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg205 sg113 + +lemma sg2628 : RowSquare [6,3,2,1,1,1] [2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg204 sg113 + +lemma sg2629 : RowSquare [6,3,2,1,1,1] [2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg202 sg113 + +lemma sg2630 : RowSquare [6,3,2,1,1,1] [2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg202 sg112 + +lemma sg2631 : RowSquare [6,3,2,1,1,1] [2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg202 sg111 + +lemma sg2632 : RowSquare [6,3,2,1,1,1] [2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg92 sg244 + +lemma sg2633 : RowSquare [6,3,2,1,1,1] [2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg92 sg241 + +lemma sg2634 : RowSquare [6,3,2,1,1,1] [3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg199 sg112 + +lemma sg2635 : RowSquare [6,3,2,1,1,1] [3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg199 sg111 + +lemma sg2636 : RowSquare [6,3,2,1,1,1] [3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg91 sg241 + +lemma sg2637 : RowSquare [6,3,2,1,1,1] [3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg198 sg113 + +lemma sg2638 : RowSquare [6,3,2,1,1,1] [3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg198 sg111 + +lemma sg2639 : RowSquare [6,3,2,1,1,1] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg89 sg244 + +lemma sg2640 : RowSquare [6,3,2,1,1,1] [3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg89 sg241 + +lemma sg2641 : RowSquare [6,3,2,1,1,1] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg89 sg240 + +lemma sg2642 : RowSquare [6,3,2,1,1,1] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg89 sg239 + +lemma sg2643 : RowSquare [6,3,2,1,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg34 sg459 + +lemma sg2644 : RowSquare [6,3,2,1,1,1] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg2135 + +lemma sg2645 : RowSquare [6,3,3,1,1] [3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2139 + +lemma sg2646 : RowSquare [6,3,3,1,1] [3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2140 + +lemma sg2647 : RowSquare [6,3,3,1,1] [3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg2141 + +lemma sg2648 : RowSquare [6,3,3,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg476 + +lemma sg2649 : RowSquare [6,3,3,1,1] [4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2142 + +lemma sg2650 : RowSquare [6,3,3,1,1] [4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg2143 + +lemma sg2651 : RowSquare [6,3,3,1,1] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg2144 + +lemma sg2652 : RowSquare [6,3,3,1,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2145 + +lemma sg2653 : RowSquare [6,3,3,1,1] [4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg826 + +lemma sg2654 : RowSquare [6,3,3,1,1] [4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg826 + +lemma sg2655 : RowSquare [6,3,3,1,1] [5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg1648 + +lemma sg2656 : RowSquare [6,3,3,2] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg481 + +lemma sg2657 : RowSquare [6,3,3,2] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg483 + +lemma sg2658 : RowSquare [6,3,3,2] [5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg22 sg548 + +lemma sg2659 : RowSquare [6,3,3,2] [5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg23 sg548 + +lemma sg2660 : RowSquare [6,3,3,2] [6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg1181 + +lemma sg2661 : RowSquare [6,4,2,2] [5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg56 sg331 + +lemma sg2662 : RowSquare [6,4,3,1] [2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1232 + +lemma sg2663 : RowSquare [6,4,3,1] [3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1233 + +lemma sg2664 : RowSquare [6,4,4] [2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg516 + +lemma sg2665 : RowSquare [6,5,2,1] [2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg849 + +lemma sg2666 : RowSquare [6,5,2,1] [3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg850 + +lemma sg2667 : RowSquare [6,5,2,1] [3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg849 + +lemma sg2668 : RowSquare [6,5,2,1] [3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg851 + +lemma sg2669 : RowSquare [6,5,2,1] [3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg295 + +lemma sg2670 : RowSquare [6,5,2,1] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg852 + +lemma sg2671 : RowSquare [6,5,2,1] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg296 + +lemma sg2672 : RowSquare [6,5,2,1] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg74 sg297 + +lemma sg2673 : RowSquare [6,5,2,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg854 + +lemma sg2674 : RowSquare [6,5,2,1] [4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg510 + +lemma sg2675 : RowSquare [6,5,2,1] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg165 sg142 + +lemma sg2676 : RowSquare [6,5,2,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg850 + +lemma sg2677 : RowSquare [6,5,2,1] [4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg510 + +lemma sg2678 : RowSquare [6,5,2,1] [4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg9 sg877 + +lemma sg2679 : RowSquare [6,5,2,1] [4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg165 sg144 + +lemma sg2680 : RowSquare [6,5,2,1] [4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg851 + +lemma sg2681 : RowSquare [6,5,2,1] [4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg511 + +lemma sg2682 : RowSquare [6,5,2,1] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg300 + +lemma sg2683 : RowSquare [6,5,2,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg166 sg143 + +lemma sg2684 : RowSquare [6,5,2,1] [4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg301 + +lemma sg2685 : RowSquare [6,5,2,1] [4,4,3,2,1] := by + exact rowSquare_join (by decide) sg166 sg144 + +lemma sg2686 : RowSquare [6,5,2,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg76 sg297 + +lemma sg2687 : RowSquare [6,5,2,1] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg83 sg286 + +lemma sg2688 : RowSquare [6,5,2,1] [4,4,4,2] := by + exact rowSquare_join (by decide) sg207 sg123 + +lemma sg2689 : RowSquare [6,5,2,1] [5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg849 + +lemma sg2690 : RowSquare [6,5,3] [2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg306 + +lemma sg2691 : RowSquare [6,5,3] [3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg308 + +lemma sg2692 : RowSquare [6,5,3] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg309 + +lemma sg2693 : RowSquare [6,6,1,1] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg877 + +lemma sg2694 : RowSquare [6,6,1,1] [4,3,3,3,1] := by + exact rowSquare_join (by decide) sg13 sg883 + +lemma sg2695 : RowSquare [6,6,1,1] [4,4,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg885 + +lemma sg2696 : RowSquare [6,6,1,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg886 + +lemma sg2697 : RowSquare [6,6,1,1] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg83 sg296 + +lemma sg2698 : RowSquare [6,6,1,1] [4,4,4,2] := by + exact rowSquare_join (by decide) sg83 sg297 + +lemma sg2699 : RowSquare [7,1,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2251 + +lemma sg2700 : RowSquare [7,1,1,1,1,1,1,1] [3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2252 + +lemma sg2701 : RowSquare [7,1,1,1,1,1,1,1] [3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2256 + +lemma sg2703 : RowSquare [7,2,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg233 sg109 + +lemma sg2704 : RowSquare [7,2,1,1,1,1,1] [2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg232 sg109 + +lemma sg2705 : RowSquare [7,2,1,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg105 sg237 + +lemma sg2706 : RowSquare [7,2,1,1,1,1,1] [2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg105 sg236 + +lemma sg2707 : RowSquare [7,2,1,1,1,1,1] [2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg451 + +lemma sg2708 : RowSquare [7,2,1,1,1,1,1] [2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg806 + +lemma sg2709 : RowSquare [7,2,1,1,1,1,1] [3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg806 + +lemma sg2710 : RowSquare [7,2,1,1,1,1,1] [3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg1256 + +lemma sg2711 : RowSquare [7,2,1,1,1,1,1] [3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg449 + +lemma sg2712 : RowSquare [7,2,1,1,1,1,1] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg804 + +lemma sg2713 : RowSquare [7,2,1,1,1,1,1] [3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg449 + +lemma sg2714 : RowSquare [7,2,1,1,1,1,1] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg1254 + +lemma sg2715 : RowSquare [7,2,1,1,1,1,1] [4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg1253 + +lemma sg2716 : RowSquare [7,2,1,1,1,1,1] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg801 + +lemma sg2717 : RowSquare [7,2,2,2,1] [4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg22 sg586 + +lemma sg2718 : RowSquare [7,2,2,2,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg23 sg586 + +lemma sg2719 : RowSquare [7,2,2,2,1] [5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg586 + +lemma sg2720 : RowSquare [7,3,1,1,1,1] [3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg888 + +lemma sg2721 : RowSquare [7,3,1,1,1,1] [3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg889 + +lemma sg2722 : RowSquare [7,3,1,1,1,1] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg890 + +lemma sg2723 : RowSquare [7,3,1,1,1,1] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg891 + +lemma sg2724 : RowSquare [7,3,1,1,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg892 + +lemma sg2725 : RowSquare [7,3,1,1,1,1] [4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1258 + +lemma sg2726 : RowSquare [7,3,1,1,1,1] [4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg1758 + +lemma sg2727 : RowSquare [7,3,1,1,1,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg888 + +lemma sg2728 : RowSquare [7,3,1,1,1,1] [4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg894 + +lemma sg2729 : RowSquare [7,3,1,1,1,1] [4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg807 + +lemma sg2730 : RowSquare [7,3,1,1,1,1] [4,3,3,2,2] := by + exact rowSquare_join (by decide) sg16 sg809 + +lemma sg2731 : RowSquare [7,3,1,1,1,1] [4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg889 + +lemma sg2732 : RowSquare [7,3,1,1,1,1] [4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg807 + +lemma sg2733 : RowSquare [7,3,1,1,1,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg809 + +lemma sg2734 : RowSquare [7,3,1,1,1,1] [4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1261 + +lemma sg2735 : RowSquare [7,3,1,1,1,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg899 + +lemma sg2736 : RowSquare [7,3,1,1,1,1] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg4 sg1262 + +lemma sg2737 : RowSquare [7,3,1,1,1,1] [5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg1762 + +lemma sg2738 : RowSquare [7,3,1,1,1,1] [5,3,2,2,2] := by + exact rowSquare_join (by decide) sg18 sg809 + +lemma sg2739 : RowSquare [7,3,1,1,1,1] [5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg814 + +lemma sg2740 : RowSquare [7,3,1,1,1,1] [6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg521 + +lemma sg2741 : RowSquare [7,3,2,1,1] [3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg586 + +lemma sg2742 : RowSquare [7,3,2,1,1] [3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg534 + +lemma sg2743 : RowSquare [7,3,2,1,1] [3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg312 + +lemma sg2744 : RowSquare [7,3,2,1,1] [3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg27 sg586 + +lemma sg2745 : RowSquare [7,3,2,1,1] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg535 + +lemma sg2746 : RowSquare [7,3,2,1,1] [3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg313 + +lemma sg2747 : RowSquare [7,3,2,1,1] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg314 + +lemma sg2748 : RowSquare [7,3,2,1,1] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg74 sg315 + +lemma sg2749 : RowSquare [7,3,2,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg537 + +lemma sg2750 : RowSquare [7,3,2,1,1] [4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg28 sg586 + +lemma sg2751 : RowSquare [7,3,2,1,1] [4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg75 sg312 + +lemma sg2752 : RowSquare [7,3,2,1,1] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg316 + +lemma sg2753 : RowSquare [7,3,2,1,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg29 sg586 + +lemma sg2754 : RowSquare [7,3,2,1,1] [4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg317 + +lemma sg2755 : RowSquare [7,3,2,1,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg541 + +lemma sg2756 : RowSquare [7,3,2,1,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg88 sg271 + +lemma sg2757 : RowSquare [7,3,2,1,1] [5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg30 sg586 + +lemma sg2758 : RowSquare [7,3,2,1,1] [6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg31 sg586 + +lemma sg2759 : RowSquare [7,3,2,2] [3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg66 sg330 + +lemma sg2760 : RowSquare [7,3,2,2] [3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg67 sg330 + +lemma sg2761 : RowSquare [7,3,2,2] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg143 + +lemma sg2762 : RowSquare [7,3,2,2] [3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg330 + +lemma sg2763 : RowSquare [7,3,2,2] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg144 + +lemma sg2764 : RowSquare [7,3,2,2] [4,3,3,3,1] := by + exact rowSquare_join (by decide) sg66 sg334 + +lemma sg2765 : RowSquare [7,3,2,2] [4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg71 sg330 + +lemma sg2766 : RowSquare [7,3,2,2] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg180 sg143 + +lemma sg2767 : RowSquare [7,3,2,2] [4,4,3,3] := by + exact rowSquare_join (by decide) sg67 sg334 + +lemma sg2768 : RowSquare [7,3,2,2] [5,4,2,2,1] := by + exact rowSquare_join (by decide) sg180 sg146 + +lemma sg2769 : RowSquare [7,3,3,1] [3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg154 + +lemma sg2770 : RowSquare [7,3,3,1] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg155 + +lemma sg2771 : RowSquare [7,3,3,1] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg156 + +lemma sg2772 : RowSquare [7,3,3,1] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg550 + +lemma sg2773 : RowSquare [7,3,3,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg551 + +lemma sg2774 : RowSquare [7,3,3,1] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg154 sg179 + +lemma sg2775 : RowSquare [7,3,3,1] [4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg154 sg180 + +lemma sg2776 : RowSquare [7,3,3,1] [4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg940 + +lemma sg2777 : RowSquare [7,3,3,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg155 sg180 + +lemma sg2778 : RowSquare [7,3,3,1] [4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg285 + +lemma sg2779 : RowSquare [7,3,3,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg88 sg287 + +lemma sg2780 : RowSquare [7,3,3,1] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg89 sg286 + +lemma sg2781 : RowSquare [7,3,3,1] [4,4,4,2] := by + exact rowSquare_join (by decide) sg156 sg181 + +lemma sg2782 : RowSquare [7,3,3,1] [5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg154 sg184 + +lemma sg2783 : RowSquare [7,4,1,1,1] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg914 + +lemma sg2784 : RowSquare [7,4,1,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg915 + +lemma sg2785 : RowSquare [7,4,1,1,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg911 + +lemma sg2786 : RowSquare [7,4,1,1,1] [4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg534 + +lemma sg2787 : RowSquare [7,4,1,1,1] [4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg312 + +lemma sg2788 : RowSquare [7,4,1,1,1] [4,3,3,2,2] := by + exact rowSquare_join (by decide) sg16 sg841 + +lemma sg2789 : RowSquare [7,4,1,1,1] [4,3,3,3,1] := by + exact rowSquare_join (by decide) sg39 sg537 + +lemma sg2790 : RowSquare [7,4,1,1,1] [4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg838 + +lemma sg2791 : RowSquare [7,4,1,1,1] [4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg535 + +lemma sg2792 : RowSquare [7,4,1,1,1] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg920 + +lemma sg2793 : RowSquare [7,4,1,1,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg841 + +lemma sg2794 : RowSquare [7,4,1,1,1] [4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg313 + +lemma sg2795 : RowSquare [7,4,1,1,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg922 + +lemma sg2796 : RowSquare [7,4,1,1,1] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg97 sg270 + +lemma sg2797 : RowSquare [7,4,1,1,1] [5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg846 + +lemma sg2798 : RowSquare [7,4,2,1] [2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg330 + +lemma sg2799 : RowSquare [7,4,2,1] [3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg165 + +lemma sg2800 : RowSquare [7,4,2,1] [3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg76 sg330 + +lemma sg2801 : RowSquare [7,4,2,1] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg166 + +lemma sg2802 : RowSquare [7,4,2,1] [3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg332 + +lemma sg2803 : RowSquare [7,4,2,1] [3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg77 sg330 + +lemma sg2804 : RowSquare [7,4,2,1] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg167 + +lemma sg2805 : RowSquare [7,4,2,1] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg333 + +lemma sg2806 : RowSquare [7,4,2,1] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg74 sg334 + +lemma sg2807 : RowSquare [7,4,2,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg564 + +lemma sg2808 : RowSquare [7,4,2,1] [4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg850 + +lemma sg2809 : RowSquare [7,4,2,1] [4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg168 + +lemma sg2810 : RowSquare [7,4,2,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg850 + +lemma sg2811 : RowSquare [7,4,2,1] [4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg169 + +lemma sg2812 : RowSquare [7,4,2,1] [4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg170 + +lemma sg2813 : RowSquare [7,4,2,1] [4,3,3,2,2] := by + exact rowSquare_join (by decide) sg87 sg296 + +lemma sg2814 : RowSquare [7,4,2,1] [4,3,3,3,1] := by + exact rowSquare_join (by decide) sg87 sg297 + +lemma sg2815 : RowSquare [7,4,2,1] [4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg330 + +lemma sg2816 : RowSquare [7,4,2,1] [4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg171 + +lemma sg2817 : RowSquare [7,4,2,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg194 sg143 + +lemma sg2818 : RowSquare [7,4,2,1] [4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg339 + +lemma sg2819 : RowSquare [7,4,2,1] [4,4,3,2,1] := by + exact rowSquare_join (by decide) sg194 sg144 + +lemma sg2820 : RowSquare [7,4,2,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg88 sg297 + +lemma sg2821 : RowSquare [7,4,2,1] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg97 sg286 + +lemma sg2822 : RowSquare [7,4,2,1] [4,4,4,2] := by + exact rowSquare_join (by decide) sg195 sg144 + +lemma sg2823 : RowSquare [7,4,2,1] [5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg850 + +lemma sg2824 : RowSquare [7,4,2,1] [5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg172 + +lemma sg2825 : RowSquare [7,4,2,1] [5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg173 + +lemma sg2826 : RowSquare [7,4,2,1] [5,3,2,2,2] := by + exact rowSquare_join (by decide) sg194 sg145 + +lemma sg2827 : RowSquare [7,4,2,1] [5,3,3,3] := by + exact rowSquare_join (by decide) sg98 sg287 + +lemma sg2828 : RowSquare [7,4,2,1] [5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg174 + +lemma sg2829 : RowSquare [7,4,2,1] [5,4,3,2] := by + exact rowSquare_join (by decide) sg195 sg146 + +lemma sg2830 : RowSquare [7,4,2,1] [5,5,2,2] := by + exact rowSquare_join (by decide) sg88 sg300 + +lemma sg2831 : RowSquare [7,4,2,1] [6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg850 + +lemma sg2832 : RowSquare [7,4,2,1] [6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg175 + +lemma sg2833 : RowSquare [7,4,2,1] [6,2,2,2,2] := by + exact rowSquare_join (by decide) sg196 sg145 + +lemma sg2834 : RowSquare [7,4,2,1] [6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg176 + +lemma sg2835 : RowSquare [7,4,2,1] [6,6,1,1] := by + exact rowSquare_join (by decide) sg88 sg302 + +lemma sg2836 : RowSquare [7,4,2,1] [7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg177 + +lemma sg2837 : RowSquare [7,4,3] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg577 + +lemma sg2838 : RowSquare [7,4,3] [3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg348 + +lemma sg2839 : RowSquare [7,4,3] [3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg306 + +lemma sg2840 : RowSquare [7,4,3] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg74 sg350 + +lemma sg2841 : RowSquare [7,4,3] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg578 + +lemma sg2842 : RowSquare [7,4,3] [4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg516 + +lemma sg2843 : RowSquare [7,4,3] [4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg87 sg307 + +lemma sg2844 : RowSquare [7,4,3] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg193 sg154 + +lemma sg2845 : RowSquare [7,4,3] [4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg88 sg307 + +lemma sg2846 : RowSquare [7,4,3] [4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg193 sg155 + +lemma sg2847 : RowSquare [7,4,3] [4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg307 + +lemma sg2848 : RowSquare [7,4,3] [4,3,3,2,2] := by + exact rowSquare_join (by decide) sg87 sg309 + +lemma sg2849 : RowSquare [7,4,3] [4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg34 sg577 + +lemma sg2850 : RowSquare [7,4,3] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg194 sg155 + +lemma sg2851 : RowSquare [7,4,3] [4,4,3,2,1] := by + exact rowSquare_join (by decide) sg194 sg156 + +lemma sg2852 : RowSquare [7,4,3] [4,4,3,3] := by + exact rowSquare_join (by decide) sg88 sg310 + +lemma sg2853 : RowSquare [7,4,3] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg89 sg309 + +lemma sg2854 : RowSquare [7,4,3] [5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg90 sg307 + +lemma sg2855 : RowSquare [7,4,3] [5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg193 sg157 + +lemma sg2856 : RowSquare [7,4,3] [5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg91 sg307 + +lemma sg2857 : RowSquare [7,4,3] [5,3,2,2,2] := by + exact rowSquare_join (by decide) sg194 sg157 + +lemma sg2858 : RowSquare [7,4,3] [5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg159 + +lemma sg2859 : RowSquare [7,4,3] [5,3,3,3] := by + exact rowSquare_join (by decide) sg90 sg310 + +lemma sg2860 : RowSquare [7,4,3] [5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg307 + +lemma sg2861 : RowSquare [7,4,3] [5,4,3,1,1] := by + exact rowSquare_join (by decide) sg194 sg159 + +lemma sg2862 : RowSquare [7,4,3] [6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg93 sg307 + +lemma sg2863 : RowSquare [7,4,3] [6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg94 sg307 + +lemma sg2864 : RowSquare [7,4,3] [6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg162 + +lemma sg2865 : RowSquare [7,4,3] [6,3,3,1,1] := by + exact rowSquare_join (by decide) sg196 sg159 + +lemma sg2866 : RowSquare [7,4,3] [7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg95 sg307 + +lemma sg2867 : RowSquare [7,5,1,1] [3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg958 + +lemma sg2868 : RowSquare [7,5,1,1] [3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg330 + +lemma sg2869 : RowSquare [7,5,1,1] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg959 + +lemma sg2870 : RowSquare [7,5,1,1] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg960 + +lemma sg2871 : RowSquare [7,5,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg961 + +lemma sg2872 : RowSquare [7,5,1,1] [4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg330 + +lemma sg2873 : RowSquare [7,5,1,1] [4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg562 + +lemma sg2874 : RowSquare [7,5,1,1] [4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg331 + +lemma sg2875 : RowSquare [7,5,1,1] [4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg142 sg207 + +lemma sg2876 : RowSquare [7,5,1,1] [4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg562 + +lemma sg2877 : RowSquare [7,6,1] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg83 sg357 + +lemma sg2878 : RowSquare [7,6,1] [4,4,4,2] := by + exact rowSquare_join (by decide) sg207 sg167 + +lemma sg2879 : RowSquare [8,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2251 + +lemma sg2880 : RowSquare [8,1,1,1,1,1,1] [3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2252 + +lemma sg2881 : RowSquare [8,1,1,1,1,1,1] [3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2256 + +lemma sg2882 : RowSquare [8,1,1,1,1,1,1] [4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg2260 + +lemma sg2883 : RowSquare [8,1,1,1,1,1,1] [4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2262 + +lemma sg2884 : RowSquare [8,1,1,1,1,1,1] [4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2263 + +lemma sg2885 : RowSquare [8,1,1,1,1,1,1] [5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2264 + +lemma sg2886 : RowSquare [8,1,1,1,1,1,1] [5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2267 + +lemma sg2887 : RowSquare [8,2,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1327 + +lemma sg2888 : RowSquare [8,2,1,1,1,1] [3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1329 + +lemma sg2889 : RowSquare [8,2,1,1,1,1] [3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1330 + +lemma sg2890 : RowSquare [8,2,1,1,1,1] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1331 + +lemma sg2891 : RowSquare [8,2,1,1,1,1] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg1332 + +lemma sg2892 : RowSquare [8,2,1,1,1,1] [4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg1758 + +lemma sg2893 : RowSquare [8,2,1,1,1,1] [4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg1332 + +lemma sg2894 : RowSquare [8,2,1,1,1,1] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg891 + +lemma sg2895 : RowSquare [8,2,1,1,1,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg892 + +lemma sg2896 : RowSquare [8,2,1,1,1,1] [5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg893 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes50.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes50.lean index c77308beefa7e5e7c0c387c28065f65204a8c5f2..a5366ea763607e890a9dfa2130bbf62771476793 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes50.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes50.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 - -namespace OAI - -/-! Semigroup Nodes 50. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg20540 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg14770 - -lemma sg20541 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,4,1] := by - exact rowSquare_join (by decide) sg2710 sg4842 - -lemma sg20542 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg74 sg12703 - -lemma sg20543 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg2712 sg4841 - -lemma sg20544 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg2712 sg4842 - -lemma sg20545 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,5,4] := by - exact rowSquare_join (by decide) sg74 sg12704 - -lemma sg20546 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,4,4,4,1] := by - exact rowSquare_join (by decide) sg74 sg12705 - -lemma sg20547 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by - exact rowSquare_join (by decide) sg74 sg12706 - -lemma sg20548 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14549 - -lemma sg20549 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,2] := by - exact rowSquare_join (by decide) sg13 sg14458 - -lemma sg20550 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,4] := by - exact rowSquare_join (by decide) sg74 sg12708 - -lemma sg20551 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,6,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg4 sg14772 - -lemma sg20552 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by - exact rowSquare_join (by decide) sg0 sg15649 - -lemma sg20553 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by - exact rowSquare_join (by decide) sg0 sg15650 - -lemma sg20554 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg841 sg8174 - -lemma sg20555 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg74 sg12709 - -lemma sg20556 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by - exact rowSquare_join (by decide) sg4 sg14773 - -lemma sg20557 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by - exact rowSquare_join (by decide) sg194 sg11730 - -lemma sg20558 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg982 sg8076 - -lemma sg20559 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by - exact rowSquare_join (by decide) sg390 sg11535 - -lemma sg20560 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by - exact rowSquare_join (by decide) sg644 sg8921 - -lemma sg20561 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by - exact rowSquare_join (by decide) sg644 sg8922 - -lemma sg20562 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [8,7,7,7,1,1] := by - exact rowSquare_join (by decide) sg981 sg8086 - -lemma sg20563 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [8,7,7,7,2] := by - exact rowSquare_join (by decide) sg982 sg8086 - -lemma sg20564 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [8,8,7,7,1] := by - exact rowSquare_join (by decide) sg644 sg8933 - -lemma sg20565 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [8,8,8,6,1] := by - exact rowSquare_join (by decide) sg1075 sg8075 - -lemma sg20566 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [8,8,8,7] := by - exact rowSquare_join (by decide) sg364 sg11166 - -lemma sg20567 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg842 sg8175 - -lemma sg20568 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg838 sg8178 - -lemma sg20569 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg842 sg8176 - -lemma sg20570 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg15 sg14457 - -lemma sg20571 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg1224 sg6709 - -lemma sg20572 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg1688 sg5822 - -lemma sg20573 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg1275 sg6561 - -lemma sg20574 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg4 sg14774 - -lemma sg20575 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg791 sg8408 - -lemma sg20576 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg792 sg8408 - -lemma sg20577 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg1274 sg6562 - -lemma sg20578 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg1275 sg6562 - -lemma sg20579 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg1688 sg5825 - -lemma sg20580 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg1688 sg5826 - -lemma sg20581 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg843 sg8177 - -lemma sg20582 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by - exact rowSquare_join (by decide) sg794 sg8407 - -lemma sg20583 : RowSquare [9,7,4,3,2,2,2,1,1] [8,8,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg3739 - -lemma sg20584 : RowSquare [9,7,4,3,2,2,2,1,1] [8,8,8,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3241 sg3950 - -lemma sg20585 : RowSquare [9,7,4,3,2,2,2,1,1] [9,7,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3513 sg3740 - -lemma sg20586 : RowSquare [9,7,4,3,2,2,2,1,1] [9,8,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3513 sg3743 - -lemma sg20587 : RowSquare [9,7,4,3,2,2,2,1,1] [9,8,7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg3740 - -lemma sg20588 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3240 sg3955 - -lemma sg20589 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3272 sg3917 - -lemma sg20590 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3206 sg3970 - -lemma sg20591 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3206 sg3971 - -lemma sg20592 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg3741 - -lemma sg20593 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg3742 - -lemma sg20594 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg3743 - -lemma sg20595 : RowSquare [9,7,4,3,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3242 sg3954 - -lemma sg20596 : RowSquare [9,7,4,3,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3206 sg3972 - -lemma sg20597 : RowSquare [9,7,4,3,2,2,2,1,1] [10,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg3297 sg3849 - -lemma sg20598 : RowSquare [9,7,4,3,2,2,2,1,1] [10,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg3273 sg3915 - -lemma sg20599 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3293 sg3852 - -lemma sg20600 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3207 sg3969 - -lemma sg20601 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3206 sg3973 - -lemma sg20602 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3296 sg3851 - -lemma sg20603 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3293 sg3853 - -lemma sg20604 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3271 sg3918 - -lemma sg20605 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3206 sg3974 - -lemma sg20606 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3293 sg3854 - -lemma sg20607 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3271 sg3919 - -lemma sg20608 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3206 sg3975 - -lemma sg20609 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3206 sg3976 - -lemma sg20610 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3295 sg3852 - -lemma sg20611 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3208 sg3969 - -lemma sg20612 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3271 sg3920 - -lemma sg20613 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3206 sg3977 - -lemma sg20614 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg3295 sg3854 - -lemma sg20615 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3272 sg3918 - -lemma sg20616 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3271 sg3921 - -lemma sg20617 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3206 sg3978 - -lemma sg20618 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3271 sg3922 - -lemma sg20619 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3206 sg3979 - -lemma sg20620 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3293 sg3856 - -lemma sg20621 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3271 sg3923 - -lemma sg20622 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3206 sg3980 - -lemma sg20623 : RowSquare [9,7,4,3,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3295 sg3855 - -lemma sg20624 : RowSquare [9,7,4,3,2,2,2,1,1] [10,6,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3272 sg3920 - -lemma sg20625 : RowSquare [9,7,4,3,2,2,2,1,1] [10,6,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3271 sg3925 - -lemma sg20626 : RowSquare [9,7,4,3,2,2,2,1,1] [10,6,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3206 sg3981 - -lemma sg20627 : RowSquare [9,7,4,3,2,2,2,1,1] [10,6,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3272 sg3921 - -lemma sg20628 : RowSquare [9,7,4,3,2,2,2,1,1] [10,6,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3271 sg3926 - -lemma sg20629 : RowSquare [9,7,4,3,2,2,2,1,1] [10,7,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3295 sg3857 - -lemma sg20630 : RowSquare [9,7,4,3,2,2,2,1,1] [10,7,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3272 sg3925 - -lemma sg20631 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3375 sg4023 - -lemma sg20632 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3964 - -lemma sg20633 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3523 sg3964 - -lemma sg20634 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2546 sg4931 - -lemma sg20635 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3524 sg3964 - -lemma sg20636 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2546 sg4933 - -lemma sg20637 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3966 - -lemma sg20638 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3526 sg3964 - -lemma sg20639 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3967 - -lemma sg20640 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3523 sg3966 - -lemma sg20641 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3527 sg3964 - -lemma sg20642 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2699 sg4847 - -lemma sg20643 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3524 sg3966 - -lemma sg20644 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2699 sg4848 - -lemma sg20645 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3523 sg3967 - -lemma sg20646 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3524 sg3967 - -lemma sg20647 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3256 sg4348 - -lemma sg20648 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2040 sg5760 - -lemma sg20649 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3258 sg4346 - -lemma sg20650 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2548 sg4933 - -lemma sg20651 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3309 sg4155 - -lemma sg20652 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2044 sg5758 - -lemma sg20653 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3258 sg4348 - -lemma sg20654 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15657 - -lemma sg20655 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3526 sg3966 - -lemma sg20656 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3529 sg3964 - -lemma sg20657 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3256 sg4352 - -lemma sg20658 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3258 sg4352 - -lemma sg20659 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15250 - -lemma sg20660 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by - exact rowSquare_join (by decide) sg841 sg8213 - -lemma sg20661 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by - exact rowSquare_join (by decide) sg13 sg14548 - -lemma sg20662 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,7,7,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14776 - -lemma sg20663 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by - exact rowSquare_join (by decide) sg4 sg14812 - -lemma sg20664 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by - exact rowSquare_join (by decide) sg364 sg11186 - -lemma sg20665 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by - exact rowSquare_join (by decide) sg364 sg11187 - -lemma sg20666 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [8,7,7,7,1,1] := by - exact rowSquare_join (by decide) sg656 sg8921 - -lemma sg20667 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [8,7,7,7,2] := by - exact rowSquare_join (by decide) sg656 sg8922 - -lemma sg20668 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [8,8,7,7,1] := by - exact rowSquare_join (by decide) sg364 sg11198 - -lemma sg20669 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [8,8,8,6,1] := by - exact rowSquare_join (by decide) sg364 sg11200 - -lemma sg20670 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [8,8,8,7] := by - exact rowSquare_join (by decide) sg364 sg11201 - -lemma sg20671 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg842 sg8214 - -lemma sg20672 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg838 sg8216 - -lemma sg20673 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg842 sg8215 - -lemma sg20674 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg838 sg8217 - -lemma sg20675 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg1235 sg6711 - -lemma sg20676 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg497 sg9653 - -lemma sg20677 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg497 sg9654 - -lemma sg20678 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg838 sg8218 - -lemma sg20679 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg839 sg8218 - -lemma sg20680 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg489 sg9656 - -lemma sg20681 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg15659 - -lemma sg20682 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by - exact rowSquare_join (by decide) sg491 sg9655 - -lemma sg20683 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14459 - -lemma sg20684 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg14777 - -lemma sg20685 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14460 - -lemma sg20686 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg2699 sg4834 - -lemma sg20687 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg12598 - -lemma sg20688 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg14459 - -lemma sg20689 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14461 - -lemma sg20690 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14462 - -lemma sg20691 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14463 - -lemma sg20692 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg123 sg11748 - -lemma sg20693 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14464 - -lemma sg20694 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14465 - -lemma sg20695 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14466 - -lemma sg20696 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14467 - -lemma sg20697 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14468 - -lemma sg20698 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14469 - -lemma sg20699 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14470 - -lemma sg20700 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14471 - -lemma sg20701 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg14777 - -lemma sg20702 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14778 - -lemma sg20703 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15660 - -lemma sg20704 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg75 sg12598 - -lemma sg20705 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15661 - -lemma sg20706 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2699 sg4836 - -lemma sg20707 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg142 sg11738 - -lemma sg20708 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg14460 - -lemma sg20709 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3948 - -lemma sg20710 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3949 - -lemma sg20711 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15662 - -lemma sg20712 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg12599 - -lemma sg20713 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3951 - -lemma sg20714 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14779 - -lemma sg20715 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg165 sg11733 - -lemma sg20716 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14780 - -lemma sg20717 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14472 - -lemma sg20718 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14473 - -lemma sg20719 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3522 sg3952 - -lemma sg20720 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14474 - -lemma sg20721 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2699 sg4841 - -lemma sg20722 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2701 sg4834 - -lemma sg20723 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14461 - -lemma sg20724 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg14462 - -lemma sg20725 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14475 - -lemma sg20726 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14476 - -lemma sg20727 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg14477 - -lemma sg20728 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14467 - -lemma sg20729 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14468 - -lemma sg20730 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14470 - -lemma sg20731 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14471 - -lemma sg20732 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg55 sg12638 - -lemma sg20733 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg123 sg11751 - -lemma sg20734 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg27 sg12925 - -lemma sg20735 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2529 sg4931 - -lemma sg20736 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14478 - -lemma sg20737 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14479 - -lemma sg20738 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14480 - -lemma sg20739 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14481 - -lemma sg20740 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14482 - -lemma sg20741 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2528 sg4933 - -lemma sg20742 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2529 sg4933 - -lemma sg20743 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg55 sg12639 - -lemma sg20744 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg55 sg12640 - -lemma sg20745 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg55 sg12641 - -lemma sg20746 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg55 sg12642 - -lemma sg20747 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg123 sg11753 - -lemma sg20748 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg167 sg11733 - -lemma sg20749 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg12600 - -lemma sg20750 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14483 - -lemma sg20751 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14484 - -lemma sg20752 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2530 sg4933 - -lemma sg20753 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg12601 - -lemma sg20754 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg12602 - -lemma sg20755 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14485 - -lemma sg20756 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14486 - -lemma sg20757 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14487 - -lemma sg20758 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14488 - -lemma sg20759 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2531 sg4933 - -lemma sg20760 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg15 sg14459 - -lemma sg20761 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15663 - -lemma sg20762 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15251 - -lemma sg20763 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15664 - -lemma sg20764 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg14780 - -lemma sg20765 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14475 - -lemma sg20766 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg14476 - -lemma sg20767 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg14477 - -lemma sg20768 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2533 sg4933 - -lemma sg20769 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg15252 - -lemma sg20770 : RowSquare [9,8,3,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3292 sg3934 - -lemma sg20771 : RowSquare [9,8,3,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3292 sg3932 - -lemma sg20772 : RowSquare [9,8,3,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3292 sg3931 - -lemma sg20773 : RowSquare [9,8,3,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3292 sg3930 - -lemma sg20774 : RowSquare [9,8,3,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3292 sg3928 - -lemma sg20775 : RowSquare [9,8,3,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3292 sg3927 - -lemma sg20776 : RowSquare [9,8,3,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3291 sg3933 - -lemma sg20777 : RowSquare [9,8,3,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3291 sg3932 - -lemma sg20778 : RowSquare [9,8,3,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3291 sg3931 - -lemma sg20779 : RowSquare [9,8,3,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3291 sg3930 - -lemma sg20780 : RowSquare [9,8,3,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3291 sg3928 - -lemma sg20781 : RowSquare [9,8,3,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3291 sg3927 - -lemma sg20782 : RowSquare [9,8,3,2,2,2,2,2,1] [4,4,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3288 sg3929 - -lemma sg20783 : RowSquare [9,8,3,2,2,2,2,2,1] [4,4,4,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3290 sg3924 - -lemma sg20784 : RowSquare [9,8,3,2,2,2,2,2,1] [5,5,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg2557 sg4783 - -lemma sg20785 : RowSquare [9,8,3,2,2,2,2,2,1] [5,5,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg3196 sg3997 - -lemma sg20786 : RowSquare [9,8,3,2,2,2,2,2,1] [5,5,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg3196 sg3996 - -lemma sg20787 : RowSquare [9,8,3,2,2,2,2,2,1] [5,5,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg1324 sg6555 - -lemma sg20788 : RowSquare [9,8,3,2,2,2,2,2,1] [5,5,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg982 sg8115 - -lemma sg20789 : RowSquare [9,9,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14490 - -lemma sg20790 : RowSquare [9,9,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14491 - -lemma sg20791 : RowSquare [9,9,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14492 - -lemma sg20792 : RowSquare [10,8,1,1,1,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14781 - -lemma sg20793 : RowSquare [10,8,1,1,1,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg14489 - -lemma sg20794 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg142 sg11748 - -lemma sg20795 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg143 sg11748 - -lemma sg20796 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg144 sg11748 - -lemma sg20797 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg145 sg11748 - -lemma sg20798 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg142 sg11749 - -lemma sg20799 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg142 sg11750 - -lemma sg20800 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg146 sg11748 - -lemma sg20801 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg143 sg11749 - -lemma sg20802 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg143 sg11750 - -lemma sg20803 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg295 sg11425 - -lemma sg20804 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg147 sg11748 - -lemma sg20805 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg144 sg11749 - -lemma sg20806 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg144 sg11750 - -lemma sg20807 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg142 sg11753 - -lemma sg20808 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12924 - -lemma sg20809 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg297 sg11425 - -lemma sg20810 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg12925 - -lemma sg20811 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12926 - -lemma sg20812 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg142 sg11754 - -lemma sg20813 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg12927 - -lemma sg20814 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg148 sg11748 - -lemma sg20815 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg143 sg11751 - -lemma sg20816 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg295 sg11426 - -lemma sg20817 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg12922 - -lemma sg20818 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg40 sg12923 - -lemma sg20819 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg295 sg11427 - -lemma sg20820 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg12927 - -lemma sg20821 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg295 sg11428 - -lemma sg20822 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg295 sg11429 - -lemma sg20823 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg14782 - -lemma sg20824 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg11733 - -lemma sg20825 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg297 sg11427 - -lemma sg20826 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg296 sg11428 - -lemma sg20827 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg296 sg11429 - -lemma sg20828 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg297 sg11428 - -lemma sg20829 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg297 sg11429 - -lemma sg20830 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg149 sg11748 - -lemma sg20831 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg15256 - -lemma sg20832 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg145 sg11749 - -lemma sg20833 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg298 sg11425 - -lemma sg20834 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg142 sg11756 - -lemma sg20835 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg150 sg11748 - -lemma sg20836 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg146 sg11749 - -lemma sg20837 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg15680 - -lemma sg20838 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg295 sg11430 - -lemma sg20839 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg147 sg11749 - -lemma sg20840 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg151 sg11748 - -lemma sg20841 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg11749 - -lemma sg20842 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg148 sg11750 - -lemma sg20843 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg11751 - -lemma sg20844 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12607 - -lemma sg20845 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12608 - -lemma sg20846 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg12600 - -lemma sg20847 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11237 - -lemma sg20848 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12606 - -lemma sg20849 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg57 sg12679 - -lemma sg20850 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg12928 - -lemma sg20851 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg165 sg11748 - -lemma sg20852 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg166 sg11748 - -lemma sg20853 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12635 - -lemma sg20854 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg83 sg12636 - -lemma sg20855 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg167 sg11748 - -lemma sg20856 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg12635 - -lemma sg20857 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg84 sg12636 - -lemma sg20858 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg168 sg11748 - -lemma sg20859 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg165 sg11749 - -lemma sg20860 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg165 sg11750 - -lemma sg20861 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg12933 - -lemma sg20862 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg40 sg12934 - -lemma sg20863 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg169 sg11748 - -lemma sg20864 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg166 sg11749 - -lemma sg20865 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg166 sg11750 - -lemma sg20866 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg165 sg11751 - -lemma sg20867 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg170 sg11748 - -lemma sg20868 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14525 - -lemma sg20869 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg167 sg11749 - -lemma sg20870 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg165 sg11753 - -lemma sg20871 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg358 sg11255 - -lemma sg20872 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg165 sg11754 - -lemma sg20873 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg171 sg11748 - -lemma sg20874 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg166 sg11751 - -lemma sg20875 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12637 - -lemma sg20876 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12638 - -lemma sg20877 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg167 sg11752 - -lemma sg20878 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12639 - -lemma sg20879 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12640 - -lemma sg20880 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg83 sg12641 - -lemma sg20881 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12643 - -lemma sg20882 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12644 - -lemma sg20883 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12645 - -lemma sg20884 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12646 - -lemma sg20885 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg41 sg12934 - -lemma sg20886 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg172 sg11748 - -lemma sg20887 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg168 sg11749 - -lemma sg20888 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg168 sg11750 - -lemma sg20889 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg85 sg12636 - -lemma sg20890 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg174 sg11748 - -lemma sg20891 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg12647 - -lemma sg20892 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg14787 - -lemma sg20893 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg12933 - -lemma sg20894 : RowSquare [5,5,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg3408 sg4898 - -lemma sg20895 : RowSquare [5,5,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1682 sg8014 - -lemma sg20896 : RowSquare [5,5,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,4] := by - exact rowSquare_join (by decide) sg1688 sg8012 - -lemma sg20897 : RowSquare [5,5,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,2] := by - exact rowSquare_join (by decide) sg1688 sg8013 - -lemma sg20898 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3691 sg4865 - -lemma sg20899 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2626 sg5767 - -lemma sg20900 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3691 sg4866 - -lemma sg20901 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3691 sg4867 - -lemma sg20902 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg3688 sg4870 - -lemma sg20903 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg2632 sg5766 - -lemma sg20904 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,4] := by - exact rowSquare_join (by decide) sg1688 sg8011 - -lemma sg20905 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1,1] := by - exact rowSquare_join (by decide) sg3691 sg4871 - -lemma sg20906 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg4319 sg4358 - -lemma sg20907 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,4] := by - exact rowSquare_join (by decide) sg4488 sg4035 - -lemma sg20908 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,3] := by - exact rowSquare_join (by decide) sg4488 sg4036 - -lemma sg20909 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1,1] := by - exact rowSquare_join (by decide) sg3963 sg4539 - -lemma sg20910 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,2] := by - exact rowSquare_join (by decide) sg4378 sg4226 - -lemma sg20911 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,7,1] := by - exact rowSquare_join (by decide) sg270 sg11554 - -lemma sg20912 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,8] := by - exact rowSquare_join (by decide) sg271 sg11554 - -lemma sg20913 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,7,7,1] := by - exact rowSquare_join (by decide) sg273 sg11554 - -lemma sg20914 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,8,6,1] := by - exact rowSquare_join (by decide) sg476 sg11061 - -lemma sg20915 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,8,7] := by - exact rowSquare_join (by decide) sg271 sg11568 - -lemma sg20916 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,7,7,7,1] := by - exact rowSquare_join (by decide) sg476 sg11066 - -lemma sg20917 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,7,6,1] := by - exact rowSquare_join (by decide) sg476 sg11074 - -lemma sg20918 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,7,7] := by - exact rowSquare_join (by decide) sg456 sg11096 - -lemma sg20919 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,8,5,1] := by - exact rowSquare_join (by decide) sg476 sg11075 - -lemma sg20920 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,8,6] := by - exact rowSquare_join (by decide) sg477 sg11061 - -lemma sg20921 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,9,6,6,1] := by - exact rowSquare_join (by decide) sg476 sg11079 - -lemma sg20922 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,10,6,5,1] := by - exact rowSquare_join (by decide) sg476 sg11084 - -lemma sg20923 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,10,6,6] := by - exact rowSquare_join (by decide) sg271 sg11583 - -lemma sg20924 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [11,8,6,6,1] := by - exact rowSquare_join (by decide) sg751 sg8895 - -lemma sg20925 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1461 sg8780 - -lemma sg20926 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1845 sg7812 - -lemma sg20927 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg7813 - -lemma sg20928 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [4,4,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg7817 - -lemma sg20929 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [4,4,4,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg1844 sg7821 - -lemma sg20930 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [5,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1845 sg7813 - -lemma sg20931 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1468 sg8780 - -lemma sg20932 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [5,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1847 sg7814 - -lemma sg20933 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1469 sg8780 - -lemma sg20934 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [5,5,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg7838 - -lemma sg20935 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1470 sg8780 - -lemma sg20936 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1471 sg8780 - -lemma sg20937 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1472 sg8780 - -lemma sg20938 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1473 sg8780 - -lemma sg20939 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1468 sg8781 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 + +namespace OAI + +/-! Semigroup Nodes 50. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg20540 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg14770 + +lemma sg20541 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,5,5,5,5,4,1] := by + exact rowSquare_join (by decide) sg2710 sg4842 + +lemma sg20542 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg74 sg12703 + +lemma sg20543 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg2712 sg4841 + +lemma sg20544 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg2712 sg4842 + +lemma sg20545 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,5,5,5,4] := by + exact rowSquare_join (by decide) sg74 sg12704 + +lemma sg20546 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,4,4,4,1] := by + exact rowSquare_join (by decide) sg74 sg12705 + +lemma sg20547 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,5,4,4] := by + exact rowSquare_join (by decide) sg74 sg12706 + +lemma sg20548 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14549 + +lemma sg20549 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [6,6,6,6,3,2,2] := by + exact rowSquare_join (by decide) sg13 sg14458 + +lemma sg20550 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,5,5,5,5,4] := by + exact rowSquare_join (by decide) sg74 sg12708 + +lemma sg20551 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,6,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg4 sg14772 + +lemma sg20552 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,6,5,5,4,4] := by + exact rowSquare_join (by decide) sg0 sg15649 + +lemma sg20553 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,6,6,4,4,4] := by + exact rowSquare_join (by decide) sg0 sg15650 + +lemma sg20554 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg841 sg8174 + +lemma sg20555 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg74 sg12709 + +lemma sg20556 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,5,4,4,4] := by + exact rowSquare_join (by decide) sg4 sg14773 + +lemma sg20557 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by + exact rowSquare_join (by decide) sg194 sg11730 + +lemma sg20558 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg982 sg8076 + +lemma sg20559 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1] := by + exact rowSquare_join (by decide) sg390 sg11535 + +lemma sg20560 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by + exact rowSquare_join (by decide) sg644 sg8921 + +lemma sg20561 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by + exact rowSquare_join (by decide) sg644 sg8922 + +lemma sg20562 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [8,7,7,7,1,1] := by + exact rowSquare_join (by decide) sg981 sg8086 + +lemma sg20563 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [8,7,7,7,2] := by + exact rowSquare_join (by decide) sg982 sg8086 + +lemma sg20564 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [8,8,7,7,1] := by + exact rowSquare_join (by decide) sg644 sg8933 + +lemma sg20565 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [8,8,8,6,1] := by + exact rowSquare_join (by decide) sg1075 sg8075 + +lemma sg20566 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [8,8,8,7] := by + exact rowSquare_join (by decide) sg364 sg11166 + +lemma sg20567 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg842 sg8175 + +lemma sg20568 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg838 sg8178 + +lemma sg20569 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg842 sg8176 + +lemma sg20570 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg15 sg14457 + +lemma sg20571 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg1224 sg6709 + +lemma sg20572 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg1688 sg5822 + +lemma sg20573 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg1275 sg6561 + +lemma sg20574 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg4 sg14774 + +lemma sg20575 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg791 sg8408 + +lemma sg20576 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg792 sg8408 + +lemma sg20577 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg1274 sg6562 + +lemma sg20578 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg1275 sg6562 + +lemma sg20579 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg1688 sg5825 + +lemma sg20580 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg1688 sg5826 + +lemma sg20581 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg843 sg8177 + +lemma sg20582 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by + exact rowSquare_join (by decide) sg794 sg8407 + +lemma sg20583 : RowSquare [9,7,4,3,2,2,2,1,1] [8,8,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg3739 + +lemma sg20584 : RowSquare [9,7,4,3,2,2,2,1,1] [8,8,8,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3241 sg3950 + +lemma sg20585 : RowSquare [9,7,4,3,2,2,2,1,1] [9,7,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3513 sg3740 + +lemma sg20586 : RowSquare [9,7,4,3,2,2,2,1,1] [9,8,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3513 sg3743 + +lemma sg20587 : RowSquare [9,7,4,3,2,2,2,1,1] [9,8,7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg3740 + +lemma sg20588 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3240 sg3955 + +lemma sg20589 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3272 sg3917 + +lemma sg20590 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3206 sg3970 + +lemma sg20591 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3206 sg3971 + +lemma sg20592 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg3741 + +lemma sg20593 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg3742 + +lemma sg20594 : RowSquare [9,7,4,3,2,2,2,1,1] [9,9,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg3743 + +lemma sg20595 : RowSquare [9,7,4,3,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3242 sg3954 + +lemma sg20596 : RowSquare [9,7,4,3,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3206 sg3972 + +lemma sg20597 : RowSquare [9,7,4,3,2,2,2,1,1] [10,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg3297 sg3849 + +lemma sg20598 : RowSquare [9,7,4,3,2,2,2,1,1] [10,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg3273 sg3915 + +lemma sg20599 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3293 sg3852 + +lemma sg20600 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3207 sg3969 + +lemma sg20601 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3206 sg3973 + +lemma sg20602 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3296 sg3851 + +lemma sg20603 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3293 sg3853 + +lemma sg20604 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3271 sg3918 + +lemma sg20605 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3206 sg3974 + +lemma sg20606 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3293 sg3854 + +lemma sg20607 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3271 sg3919 + +lemma sg20608 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3206 sg3975 + +lemma sg20609 : RowSquare [9,7,4,3,2,2,2,1,1] [10,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3206 sg3976 + +lemma sg20610 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3295 sg3852 + +lemma sg20611 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3208 sg3969 + +lemma sg20612 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3271 sg3920 + +lemma sg20613 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3206 sg3977 + +lemma sg20614 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg3295 sg3854 + +lemma sg20615 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3272 sg3918 + +lemma sg20616 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3271 sg3921 + +lemma sg20617 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3206 sg3978 + +lemma sg20618 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3271 sg3922 + +lemma sg20619 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3206 sg3979 + +lemma sg20620 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3293 sg3856 + +lemma sg20621 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3271 sg3923 + +lemma sg20622 : RowSquare [9,7,4,3,2,2,2,1,1] [10,5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3206 sg3980 + +lemma sg20623 : RowSquare [9,7,4,3,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3295 sg3855 + +lemma sg20624 : RowSquare [9,7,4,3,2,2,2,1,1] [10,6,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3272 sg3920 + +lemma sg20625 : RowSquare [9,7,4,3,2,2,2,1,1] [10,6,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3271 sg3925 + +lemma sg20626 : RowSquare [9,7,4,3,2,2,2,1,1] [10,6,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3206 sg3981 + +lemma sg20627 : RowSquare [9,7,4,3,2,2,2,1,1] [10,6,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3272 sg3921 + +lemma sg20628 : RowSquare [9,7,4,3,2,2,2,1,1] [10,6,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3271 sg3926 + +lemma sg20629 : RowSquare [9,7,4,3,2,2,2,1,1] [10,7,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3295 sg3857 + +lemma sg20630 : RowSquare [9,7,4,3,2,2,2,1,1] [10,7,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3272 sg3925 + +lemma sg20631 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3375 sg4023 + +lemma sg20632 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3964 + +lemma sg20633 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [4,4,3,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3523 sg3964 + +lemma sg20634 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2546 sg4931 + +lemma sg20635 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3524 sg3964 + +lemma sg20636 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [4,4,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2546 sg4933 + +lemma sg20637 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3966 + +lemma sg20638 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3526 sg3964 + +lemma sg20639 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3967 + +lemma sg20640 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3523 sg3966 + +lemma sg20641 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3527 sg3964 + +lemma sg20642 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2699 sg4847 + +lemma sg20643 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3524 sg3966 + +lemma sg20644 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2699 sg4848 + +lemma sg20645 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3523 sg3967 + +lemma sg20646 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3524 sg3967 + +lemma sg20647 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3256 sg4348 + +lemma sg20648 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2040 sg5760 + +lemma sg20649 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3258 sg4346 + +lemma sg20650 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2548 sg4933 + +lemma sg20651 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3309 sg4155 + +lemma sg20652 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2044 sg5758 + +lemma sg20653 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3258 sg4348 + +lemma sg20654 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15657 + +lemma sg20655 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3526 sg3966 + +lemma sg20656 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3529 sg3964 + +lemma sg20657 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [6,6,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3256 sg4352 + +lemma sg20658 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3258 sg4352 + +lemma sg20659 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15250 + +lemma sg20660 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,6,6,6,6] := by + exact rowSquare_join (by decide) sg841 sg8213 + +lemma sg20661 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,7,6,6,5] := by + exact rowSquare_join (by decide) sg13 sg14548 + +lemma sg20662 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,7,7,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14776 + +lemma sg20663 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,7,7,5,5] := by + exact rowSquare_join (by decide) sg4 sg14812 + +lemma sg20664 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,2,1] := by + exact rowSquare_join (by decide) sg364 sg11186 + +lemma sg20665 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [7,7,7,7,3] := by + exact rowSquare_join (by decide) sg364 sg11187 + +lemma sg20666 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [8,7,7,7,1,1] := by + exact rowSquare_join (by decide) sg656 sg8921 + +lemma sg20667 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [8,7,7,7,2] := by + exact rowSquare_join (by decide) sg656 sg8922 + +lemma sg20668 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [8,8,7,7,1] := by + exact rowSquare_join (by decide) sg364 sg11198 + +lemma sg20669 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [8,8,8,6,1] := by + exact rowSquare_join (by decide) sg364 sg11200 + +lemma sg20670 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [8,8,8,7] := by + exact rowSquare_join (by decide) sg364 sg11201 + +lemma sg20671 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg842 sg8214 + +lemma sg20672 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg838 sg8216 + +lemma sg20673 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg842 sg8215 + +lemma sg20674 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg838 sg8217 + +lemma sg20675 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg1235 sg6711 + +lemma sg20676 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg497 sg9653 + +lemma sg20677 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg497 sg9654 + +lemma sg20678 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,6,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg838 sg8218 + +lemma sg20679 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg839 sg8218 + +lemma sg20680 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg489 sg9656 + +lemma sg20681 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,7,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg15659 + +lemma sg20682 : RowSquare [9,8,2,2,2,1,1,1,1,1,1,1,1] [9,7,4,4,4,3] := by + exact rowSquare_join (by decide) sg491 sg9655 + +lemma sg20683 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14459 + +lemma sg20684 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg14777 + +lemma sg20685 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14460 + +lemma sg20686 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg2699 sg4834 + +lemma sg20687 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg12598 + +lemma sg20688 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg14459 + +lemma sg20689 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14461 + +lemma sg20690 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14462 + +lemma sg20691 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14463 + +lemma sg20692 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg123 sg11748 + +lemma sg20693 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14464 + +lemma sg20694 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14465 + +lemma sg20695 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14466 + +lemma sg20696 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14467 + +lemma sg20697 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14468 + +lemma sg20698 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14469 + +lemma sg20699 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14470 + +lemma sg20700 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14471 + +lemma sg20701 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg14777 + +lemma sg20702 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14778 + +lemma sg20703 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15660 + +lemma sg20704 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg75 sg12598 + +lemma sg20705 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15661 + +lemma sg20706 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2699 sg4836 + +lemma sg20707 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg142 sg11738 + +lemma sg20708 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg14460 + +lemma sg20709 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3948 + +lemma sg20710 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3949 + +lemma sg20711 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15662 + +lemma sg20712 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg12599 + +lemma sg20713 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3951 + +lemma sg20714 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14779 + +lemma sg20715 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg165 sg11733 + +lemma sg20716 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14780 + +lemma sg20717 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14472 + +lemma sg20718 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14473 + +lemma sg20719 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3522 sg3952 + +lemma sg20720 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14474 + +lemma sg20721 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2699 sg4841 + +lemma sg20722 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2701 sg4834 + +lemma sg20723 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14461 + +lemma sg20724 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg14462 + +lemma sg20725 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14475 + +lemma sg20726 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14476 + +lemma sg20727 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg14477 + +lemma sg20728 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14467 + +lemma sg20729 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14468 + +lemma sg20730 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14470 + +lemma sg20731 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14471 + +lemma sg20732 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg55 sg12638 + +lemma sg20733 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg123 sg11751 + +lemma sg20734 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg27 sg12925 + +lemma sg20735 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2529 sg4931 + +lemma sg20736 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14478 + +lemma sg20737 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14479 + +lemma sg20738 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14480 + +lemma sg20739 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14481 + +lemma sg20740 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14482 + +lemma sg20741 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2528 sg4933 + +lemma sg20742 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2529 sg4933 + +lemma sg20743 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg55 sg12639 + +lemma sg20744 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg55 sg12640 + +lemma sg20745 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg55 sg12641 + +lemma sg20746 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg55 sg12642 + +lemma sg20747 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg123 sg11753 + +lemma sg20748 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg167 sg11733 + +lemma sg20749 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg12600 + +lemma sg20750 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14483 + +lemma sg20751 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14484 + +lemma sg20752 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2530 sg4933 + +lemma sg20753 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg12601 + +lemma sg20754 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg12602 + +lemma sg20755 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14485 + +lemma sg20756 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14486 + +lemma sg20757 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14487 + +lemma sg20758 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14488 + +lemma sg20759 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2531 sg4933 + +lemma sg20760 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg15 sg14459 + +lemma sg20761 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15663 + +lemma sg20762 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15251 + +lemma sg20763 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15664 + +lemma sg20764 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg14780 + +lemma sg20765 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14475 + +lemma sg20766 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg14476 + +lemma sg20767 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,6,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg14477 + +lemma sg20768 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2533 sg4933 + +lemma sg20769 : RowSquare [9,8,3,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg15252 + +lemma sg20770 : RowSquare [9,8,3,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3292 sg3934 + +lemma sg20771 : RowSquare [9,8,3,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3292 sg3932 + +lemma sg20772 : RowSquare [9,8,3,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3292 sg3931 + +lemma sg20773 : RowSquare [9,8,3,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3292 sg3930 + +lemma sg20774 : RowSquare [9,8,3,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3292 sg3928 + +lemma sg20775 : RowSquare [9,8,3,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3292 sg3927 + +lemma sg20776 : RowSquare [9,8,3,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3291 sg3933 + +lemma sg20777 : RowSquare [9,8,3,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3291 sg3932 + +lemma sg20778 : RowSquare [9,8,3,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3291 sg3931 + +lemma sg20779 : RowSquare [9,8,3,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3291 sg3930 + +lemma sg20780 : RowSquare [9,8,3,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3291 sg3928 + +lemma sg20781 : RowSquare [9,8,3,2,2,2,2,2,1] [3,3,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3291 sg3927 + +lemma sg20782 : RowSquare [9,8,3,2,2,2,2,2,1] [4,4,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3288 sg3929 + +lemma sg20783 : RowSquare [9,8,3,2,2,2,2,2,1] [4,4,4,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3290 sg3924 + +lemma sg20784 : RowSquare [9,8,3,2,2,2,2,2,1] [5,5,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg2557 sg4783 + +lemma sg20785 : RowSquare [9,8,3,2,2,2,2,2,1] [5,5,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg3196 sg3997 + +lemma sg20786 : RowSquare [9,8,3,2,2,2,2,2,1] [5,5,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg3196 sg3996 + +lemma sg20787 : RowSquare [9,8,3,2,2,2,2,2,1] [5,5,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg1324 sg6555 + +lemma sg20788 : RowSquare [9,8,3,2,2,2,2,2,1] [5,5,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg982 sg8115 + +lemma sg20789 : RowSquare [9,9,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14490 + +lemma sg20790 : RowSquare [9,9,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14491 + +lemma sg20791 : RowSquare [9,9,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14492 + +lemma sg20792 : RowSquare [10,8,1,1,1,1,1,1,1,1,1,1,1,1,1] [4,4,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14781 + +lemma sg20793 : RowSquare [10,8,1,1,1,1,1,1,1,1,1,1,1,1,1] [5,4,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg14489 + +lemma sg20794 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg142 sg11748 + +lemma sg20795 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg143 sg11748 + +lemma sg20796 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg144 sg11748 + +lemma sg20797 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg145 sg11748 + +lemma sg20798 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg142 sg11749 + +lemma sg20799 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg142 sg11750 + +lemma sg20800 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg146 sg11748 + +lemma sg20801 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg143 sg11749 + +lemma sg20802 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg143 sg11750 + +lemma sg20803 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg295 sg11425 + +lemma sg20804 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg147 sg11748 + +lemma sg20805 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg144 sg11749 + +lemma sg20806 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg144 sg11750 + +lemma sg20807 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg142 sg11753 + +lemma sg20808 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12924 + +lemma sg20809 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg297 sg11425 + +lemma sg20810 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg12925 + +lemma sg20811 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12926 + +lemma sg20812 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg142 sg11754 + +lemma sg20813 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg12927 + +lemma sg20814 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg148 sg11748 + +lemma sg20815 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg143 sg11751 + +lemma sg20816 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg295 sg11426 + +lemma sg20817 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg12922 + +lemma sg20818 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg40 sg12923 + +lemma sg20819 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg295 sg11427 + +lemma sg20820 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg12927 + +lemma sg20821 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg295 sg11428 + +lemma sg20822 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg295 sg11429 + +lemma sg20823 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg14782 + +lemma sg20824 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg11733 + +lemma sg20825 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg297 sg11427 + +lemma sg20826 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg296 sg11428 + +lemma sg20827 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg296 sg11429 + +lemma sg20828 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg297 sg11428 + +lemma sg20829 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg297 sg11429 + +lemma sg20830 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg149 sg11748 + +lemma sg20831 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg15256 + +lemma sg20832 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg145 sg11749 + +lemma sg20833 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg298 sg11425 + +lemma sg20834 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg142 sg11756 + +lemma sg20835 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,4,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg150 sg11748 + +lemma sg20836 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg146 sg11749 + +lemma sg20837 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg15680 + +lemma sg20838 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,4,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg295 sg11430 + +lemma sg20839 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg147 sg11749 + +lemma sg20840 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg151 sg11748 + +lemma sg20841 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg11749 + +lemma sg20842 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,5,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg148 sg11750 + +lemma sg20843 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,6,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg11751 + +lemma sg20844 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12607 + +lemma sg20845 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12608 + +lemma sg20846 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg12600 + +lemma sg20847 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11237 + +lemma sg20848 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [7,3,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12606 + +lemma sg20849 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [7,4,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg57 sg12679 + +lemma sg20850 : RowSquare [10,8,2,2,1,1,1,1,1,1,1,1,1] [7,5,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg12928 + +lemma sg20851 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [4,3,3,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg165 sg11748 + +lemma sg20852 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [4,4,3,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg166 sg11748 + +lemma sg20853 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12635 + +lemma sg20854 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg83 sg12636 + +lemma sg20855 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg167 sg11748 + +lemma sg20856 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg12635 + +lemma sg20857 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg84 sg12636 + +lemma sg20858 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg168 sg11748 + +lemma sg20859 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg165 sg11749 + +lemma sg20860 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,3,3,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg165 sg11750 + +lemma sg20861 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg12933 + +lemma sg20862 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg40 sg12934 + +lemma sg20863 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg169 sg11748 + +lemma sg20864 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg166 sg11749 + +lemma sg20865 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg166 sg11750 + +lemma sg20866 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg165 sg11751 + +lemma sg20867 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg170 sg11748 + +lemma sg20868 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14525 + +lemma sg20869 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg167 sg11749 + +lemma sg20870 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg165 sg11753 + +lemma sg20871 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg358 sg11255 + +lemma sg20872 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg165 sg11754 + +lemma sg20873 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg171 sg11748 + +lemma sg20874 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg166 sg11751 + +lemma sg20875 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12637 + +lemma sg20876 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12638 + +lemma sg20877 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg167 sg11752 + +lemma sg20878 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12639 + +lemma sg20879 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12640 + +lemma sg20880 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg83 sg12641 + +lemma sg20881 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12643 + +lemma sg20882 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12644 + +lemma sg20883 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12645 + +lemma sg20884 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12646 + +lemma sg20885 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg41 sg12934 + +lemma sg20886 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg172 sg11748 + +lemma sg20887 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg168 sg11749 + +lemma sg20888 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,3,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg168 sg11750 + +lemma sg20889 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg85 sg12636 + +lemma sg20890 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,5,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg174 sg11748 + +lemma sg20891 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg12647 + +lemma sg20892 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg14787 + +lemma sg20893 : RowSquare [10,9,2,1,1,1,1,1,1,1,1,1,1] [7,3,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg12933 + +lemma sg20894 : RowSquare [5,5,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg3408 sg4898 + +lemma sg20895 : RowSquare [5,5,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1682 sg8014 + +lemma sg20896 : RowSquare [5,5,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,4] := by + exact rowSquare_join (by decide) sg1688 sg8012 + +lemma sg20897 : RowSquare [5,5,4,4,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,2] := by + exact rowSquare_join (by decide) sg1688 sg8013 + +lemma sg20898 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3691 sg4865 + +lemma sg20899 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2626 sg5767 + +lemma sg20900 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3691 sg4866 + +lemma sg20901 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3691 sg4867 + +lemma sg20902 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg3688 sg4870 + +lemma sg20903 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg2632 sg5766 + +lemma sg20904 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,4] := by + exact rowSquare_join (by decide) sg1688 sg8011 + +lemma sg20905 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1,1] := by + exact rowSquare_join (by decide) sg3691 sg4871 + +lemma sg20906 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg4319 sg4358 + +lemma sg20907 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,4] := by + exact rowSquare_join (by decide) sg4488 sg4035 + +lemma sg20908 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,3] := by + exact rowSquare_join (by decide) sg4488 sg4036 + +lemma sg20909 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1,1] := by + exact rowSquare_join (by decide) sg3963 sg4539 + +lemma sg20910 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,2] := by + exact rowSquare_join (by decide) sg4378 sg4226 + +lemma sg20911 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,7,1] := by + exact rowSquare_join (by decide) sg270 sg11554 + +lemma sg20912 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,8] := by + exact rowSquare_join (by decide) sg271 sg11554 + +lemma sg20913 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,7,7,1] := by + exact rowSquare_join (by decide) sg273 sg11554 + +lemma sg20914 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,8,6,1] := by + exact rowSquare_join (by decide) sg476 sg11061 + +lemma sg20915 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [9,8,8,7] := by + exact rowSquare_join (by decide) sg271 sg11568 + +lemma sg20916 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,7,7,7,1] := by + exact rowSquare_join (by decide) sg476 sg11066 + +lemma sg20917 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,7,6,1] := by + exact rowSquare_join (by decide) sg476 sg11074 + +lemma sg20918 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,7,7] := by + exact rowSquare_join (by decide) sg456 sg11096 + +lemma sg20919 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,8,5,1] := by + exact rowSquare_join (by decide) sg476 sg11075 + +lemma sg20920 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,8,8,6] := by + exact rowSquare_join (by decide) sg477 sg11061 + +lemma sg20921 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,9,6,6,1] := by + exact rowSquare_join (by decide) sg476 sg11079 + +lemma sg20922 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,10,6,5,1] := by + exact rowSquare_join (by decide) sg476 sg11084 + +lemma sg20923 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [10,10,6,6] := by + exact rowSquare_join (by decide) sg271 sg11583 + +lemma sg20924 : RowSquare [6,5,4,3,3,2,1,1,1,1,1,1,1,1,1] [11,8,6,6,1] := by + exact rowSquare_join (by decide) sg751 sg8895 + +lemma sg20925 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1461 sg8780 + +lemma sg20926 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1845 sg7812 + +lemma sg20927 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg7813 + +lemma sg20928 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [4,4,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg7817 + +lemma sg20929 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [4,4,4,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg1844 sg7821 + +lemma sg20930 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [5,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1845 sg7813 + +lemma sg20931 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1468 sg8780 + +lemma sg20932 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [5,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1847 sg7814 + +lemma sg20933 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1469 sg8780 + +lemma sg20934 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [5,5,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg7838 + +lemma sg20935 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1470 sg8780 + +lemma sg20936 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1471 sg8780 + +lemma sg20937 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1472 sg8780 + +lemma sg20938 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1473 sg8780 + +lemma sg20939 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1468 sg8781 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes51.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes51.lean index a55b80c2629e9fd955b498116b30503d1ac8283b..81ff92f50b6a7a9ded43c51ba64f934d5acff606 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes51.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes51.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes50 - -namespace OAI - -/-! Semigroup Nodes 51. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg20940 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1474 sg8780 - -lemma sg20941 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1475 sg8780 - -lemma sg20942 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1476 sg8780 - -lemma sg20943 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2626 sg5764 - -lemma sg20944 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2626 sg5765 - -lemma sg20945 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3334 sg4941 - -lemma sg20946 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4949 - -lemma sg20947 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3323 sg4958 - -lemma sg20948 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3332 sg4944 - -lemma sg20949 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg3332 sg4945 - -lemma sg20950 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,4] := by - exact rowSquare_join (by decide) sg3332 sg4949 - -lemma sg20951 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1,1] := by - exact rowSquare_join (by decide) sg3334 sg4948 - -lemma sg20952 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,4] := by - exact rowSquare_join (by decide) sg3332 sg4956 - -lemma sg20953 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,6] := by - exact rowSquare_join (by decide) sg3732 sg4844 - -lemma sg20954 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3407 sg4897 - -lemma sg20955 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3330 sg4959 - -lemma sg20956 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg3324 sg4963 - -lemma sg20957 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3332 sg4959 - -lemma sg20958 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,3] := by - exact rowSquare_join (by decide) sg3332 sg4960 - -lemma sg20959 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1,1] := by - exact rowSquare_join (by decide) sg1757 sg8002 - -lemma sg20960 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,8] := by - exact rowSquare_join (by decide) sg1675 sg8015 - -lemma sg20961 : RowSquare [7,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg4167 sg4402 - -lemma sg20962 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg658 sg11531 - -lemma sg20963 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg984 sg10868 - -lemma sg20964 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg661 sg11531 - -lemma sg20965 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg662 sg11531 - -lemma sg20966 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg985 sg10869 - -lemma sg20967 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg991 sg10867 - -lemma sg20968 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg663 sg11531 - -lemma sg20969 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg992 sg10867 - -lemma sg20970 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg987 sg10868 - -lemma sg20971 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg664 sg11531 - -lemma sg20972 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg988 sg10868 - -lemma sg20973 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg665 sg11531 - -lemma sg20974 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg989 sg10868 - -lemma sg20975 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg666 sg11531 - -lemma sg20976 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg993 sg10867 - -lemma sg20977 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg667 sg11531 - -lemma sg20978 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg994 sg10867 - -lemma sg20979 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg991 sg10868 - -lemma sg20980 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg668 sg11531 - -lemma sg20981 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg992 sg10868 - -lemma sg20982 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg669 sg11531 - -lemma sg20983 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3332 sg4935 - -lemma sg20984 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3593 sg4875 - -lemma sg20985 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,4] := by - exact rowSquare_join (by decide) sg4378 sg4173 - -lemma sg20986 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,4] := by - exact rowSquare_join (by decide) sg13 sg14653 - -lemma sg20987 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,3] := by - exact rowSquare_join (by decide) sg13 sg14655 - -lemma sg20988 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,2] := by - exact rowSquare_join (by decide) sg13 sg14667 - -lemma sg20989 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,4] := by - exact rowSquare_join (by decide) sg14 sg14653 - -lemma sg20990 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,3] := by - exact rowSquare_join (by decide) sg295 sg11598 - -lemma sg20991 : RowSquare [7,6,4,3,3,2,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg271 sg11715 - -lemma sg20992 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg402 sg11798 - -lemma sg20993 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg402 sg11799 - -lemma sg20994 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg402 sg11800 - -lemma sg20995 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg403 sg11799 - -lemma sg20996 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg403 sg11800 - -lemma sg20997 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg11798 - -lemma sg20998 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg11799 - -lemma sg20999 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg407 sg11800 - -lemma sg21000 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg408 sg11795 - -lemma sg21001 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg409 sg11795 - -lemma sg21002 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg408 sg11796 - -lemma sg21003 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg408 sg11797 - -lemma sg21004 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg410 sg11795 - -lemma sg21005 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg409 sg11796 - -lemma sg21006 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg409 sg11797 - -lemma sg21007 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg404 sg11803 - -lemma sg21008 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg405 sg11803 - -lemma sg21009 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg405 sg11804 - -lemma sg21010 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg410 sg11796 - -lemma sg21011 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg410 sg11797 - -lemma sg21012 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg410 sg11798 - -lemma sg21013 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg406 sg11803 - -lemma sg21014 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg11802 - -lemma sg21015 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg402 sg11812 - -lemma sg21016 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg11803 - -lemma sg21017 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg11804 - -lemma sg21018 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg11806 - -lemma sg21019 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg11807 - -lemma sg21020 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg11808 - -lemma sg21021 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg411 sg11795 - -lemma sg21022 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg412 sg11795 - -lemma sg21023 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg411 sg11796 - -lemma sg21024 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg411 sg11797 - -lemma sg21025 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg408 sg11803 - -lemma sg21026 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg412 sg11796 - -lemma sg21027 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg412 sg11797 - -lemma sg21028 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg409 sg11803 - -lemma sg21029 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg410 sg11803 - -lemma sg21030 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg410 sg11804 - -lemma sg21031 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,5,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg410 sg11805 - -lemma sg21032 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg11812 - -lemma sg21033 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg11813 - -lemma sg21034 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,8,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg11815 - -lemma sg21035 : RowSquare [7,7,3,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3316 sg4936 - -lemma sg21036 : RowSquare [7,7,3,2,2,2,2,2,2,2,1] [7,7,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg363 sg11809 - -lemma sg21037 : RowSquare [7,7,3,2,2,2,2,2,2,2,1] [7,7,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg363 sg11810 - -lemma sg21038 : RowSquare [7,7,3,2,2,2,2,2,2,2,1] [8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg363 sg11814 - -lemma sg21039 : RowSquare [7,7,3,2,2,2,2,2,2,2,1] [8,8,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg363 sg11815 - -lemma sg21040 : RowSquare [7,7,3,3,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg5749 - -lemma sg21041 : RowSquare [8,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14705 - -lemma sg21042 : RowSquare [8,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14706 - -lemma sg21043 : RowSquare [8,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14707 - -lemma sg21044 : RowSquare [8,6,3,3,3,2,1,1,1,1,1,1,1] [6,5,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg2135 sg6488 - -lemma sg21045 : RowSquare [8,6,4,3,2,2,1,1,1,1,1,1,1] [6,5,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg74 sg12863 - -lemma sg21046 : RowSquare [8,6,4,3,2,2,1,1,1,1,1,1,1] [6,6,5,5,5,5] := by - exact rowSquare_join (by decide) sg74 sg12864 - -lemma sg21047 : RowSquare [8,6,4,3,2,2,1,1,1,1,1,1,1] [7,5,5,5,5,5] := by - exact rowSquare_join (by decide) sg74 sg12865 - -lemma sg21048 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg5744 - -lemma sg21049 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg5745 - -lemma sg21050 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2707 sg5737 - -lemma sg21051 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2708 sg5738 - -lemma sg21052 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2710 sg5738 - -lemma sg21053 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,4] := by - exact rowSquare_join (by decide) sg74 sg13504 - -lemma sg21054 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,4] := by - exact rowSquare_join (by decide) sg74 sg13508 - -lemma sg21055 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg14709 - -lemma sg21056 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,3] := by - exact rowSquare_join (by decide) sg13 sg14710 - -lemma sg21057 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14711 - -lemma sg21058 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,2] := by - exact rowSquare_join (by decide) sg13 sg14712 - -lemma sg21059 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg14713 - -lemma sg21060 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,2] := by - exact rowSquare_join (by decide) sg358 sg11613 - -lemma sg21061 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,7,1,1] := by - exact rowSquare_join (by decide) sg364 sg11601 - -lemma sg21062 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,8] := by - exact rowSquare_join (by decide) sg364 sg11602 - -lemma sg21063 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,3] := by - exact rowSquare_join (by decide) sg356 sg11679 - -lemma sg21064 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg281 sg11726 - -lemma sg21065 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg356 sg11709 - -lemma sg21066 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,3,3] := by - exact rowSquare_join (by decide) sg356 sg11710 - -lemma sg21067 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11603 - -lemma sg21068 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,4,2,2] := by - exact rowSquare_join (by decide) sg356 sg11711 - -lemma sg21069 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg14530 - -lemma sg21070 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg14531 - -lemma sg21071 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg43 sg14532 - -lemma sg21072 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg14529 - -lemma sg21073 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg14530 - -lemma sg21074 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg14531 - -lemma sg21075 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg44 sg14532 - -lemma sg21076 : RowSquare [8,7,3,3,2,2,1,1,1,1,1,1,1] [5,5,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2589 sg5738 - -lemma sg21077 : RowSquare [8,8,3,2,2,2,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg364 sg11715 - -lemma sg21078 : RowSquare [8,8,3,2,2,2,1,1,1,1,1,1,1] [7,7,7,7,1,1,1,1] := by - exact rowSquare_join (by decide) sg364 sg11716 - -lemma sg21079 : RowSquare [8,8,3,2,2,2,1,1,1,1,1,1,1] [8,8,8,8] := by - exact rowSquare_join (by decide) sg364 sg11717 - -lemma sg21080 : RowSquare [9,7,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg14808 - -lemma sg21081 : RowSquare [9,7,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg14809 - -lemma sg21082 : RowSquare [9,7,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg15 sg14810 - -lemma sg21083 : RowSquare [9,7,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg14811 - -lemma sg21084 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2590 sg5760 - -lemma sg21085 : RowSquare [9,7,3,3,2,1,1,1,1,1,1,1,1] [7,7,7,7,2,2] := by - exact rowSquare_join (by decide) sg960 sg8921 - -lemma sg21086 : RowSquare [9,7,3,3,2,1,1,1,1,1,1,1,1] [8,8,6,6,2,2] := by - exact rowSquare_join (by decide) sg960 sg8932 - -lemma sg21087 : RowSquare [9,7,3,3,2,1,1,1,1,1,1,1,1] [8,8,7,7,1,1] := by - exact rowSquare_join (by decide) sg960 sg8933 - -lemma sg21088 : RowSquare [9,7,3,3,2,1,1,1,1,1,1,1,1] [8,8,8,3,3,2] := by - exact rowSquare_join (by decide) sg563 sg11199 - -lemma sg21089 : RowSquare [9,7,3,3,2,1,1,1,1,1,1,1,1] [8,8,8,8] := by - exact rowSquare_join (by decide) sg364 sg11718 - -lemma sg21090 : RowSquare [9,8,2,2,2,2,1,1,1,1,1,1,1] [4,4,4,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2546 sg5760 - -lemma sg21091 : RowSquare [9,8,3,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2529 sg5760 - -lemma sg21092 : RowSquare [9,9,2,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg14775 - -lemma sg21093 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3220 sg4816 - -lemma sg21094 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3220 sg4812 - -lemma sg21095 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3220 sg4815 - -lemma sg21096 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3220 sg4811 - -lemma sg21097 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3220 sg4813 - -lemma sg21098 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3225 sg4810 - -lemma sg21099 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3223 sg4810 - -lemma sg21100 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3220 sg4810 - -lemma sg21101 : RowSquare [10,8,2,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4060 sg3910 - -lemma sg21102 : RowSquare [10,8,2,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4060 sg3909 - -lemma sg21103 : RowSquare [10,8,2,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4060 sg3908 - -lemma sg21104 : RowSquare [10,8,2,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4060 sg3907 - -lemma sg21105 : RowSquare [10,8,2,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4060 sg3906 - -lemma sg21106 : RowSquare [10,8,2,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4060 sg3905 - -lemma sg21107 : RowSquare [7,6,3,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg991 sg11531 - -lemma sg21108 : RowSquare [7,6,3,3,2,2,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg993 sg11531 - -lemma sg21109 : RowSquare [7,6,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg990 sg11532 - -lemma sg21110 : RowSquare [7,6,3,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg994 sg11531 - -lemma sg21111 : RowSquare [7,6,3,3,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg993 sg11532 - -lemma sg21112 : RowSquare [7,6,4,3,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg12649 - -lemma sg21113 : RowSquare [7,6,4,3,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg12650 - -lemma sg21114 : RowSquare [7,6,4,3,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg12651 - -lemma sg21115 : RowSquare [7,6,4,3,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg12652 - -lemma sg21116 : RowSquare [7,6,4,3,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg367 sg12653 - -lemma sg21117 : RowSquare [7,6,4,4,3,2,1,1,1,1,1,1,1] [6,6,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg3702 sg5301 - -lemma sg21118 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg403 sg12671 - -lemma sg21119 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg403 sg12673 - -lemma sg21120 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg403 sg12674 - -lemma sg21121 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg647 sg11799 - -lemma sg21122 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg647 sg11800 - -lemma sg21123 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg648 sg11795 - -lemma sg21124 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [6,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg648 sg11796 - -lemma sg21125 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg12672 - -lemma sg21126 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg651 sg11795 - -lemma sg21127 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg408 sg12669 - -lemma sg21128 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg408 sg12670 - -lemma sg21129 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg648 sg11803 - -lemma sg21130 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg651 sg11798 - -lemma sg21131 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg648 sg11804 - -lemma sg21132 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg12675 - -lemma sg21133 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg402 sg12678 - -lemma sg21134 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg12676 - -lemma sg21135 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg12677 - -lemma sg21136 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [8,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg411 sg12669 - -lemma sg21137 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg412 sg12669 - -lemma sg21138 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg412 sg12670 - -lemma sg21139 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg12678 - -lemma sg21140 : RowSquare [7,7,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2589 sg6503 - -lemma sg21141 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,4,4,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg12954 - -lemma sg21142 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,4,4,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg209 sg12955 - -lemma sg21143 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,4,4,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg209 sg12956 - -lemma sg21144 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg12952 - -lemma sg21145 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg12954 - -lemma sg21146 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg210 sg12955 - -lemma sg21147 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg210 sg12956 - -lemma sg21148 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg211 sg12950 - -lemma sg21149 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,3,3,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg211 sg12954 - -lemma sg21150 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,3,3,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg211 sg12955 - -lemma sg21151 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,3,3,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg211 sg12956 - -lemma sg21152 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,4,3,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg212 sg12954 - -lemma sg21153 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,4,3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg212 sg12955 - -lemma sg21154 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,4,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg212 sg12956 - -lemma sg21155 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg213 sg12952 - -lemma sg21156 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg213 sg12954 - -lemma sg21157 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg213 sg12955 - -lemma sg21158 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg213 sg12956 - -lemma sg21159 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg214 sg12950 - -lemma sg21160 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg214 sg12951 - -lemma sg21161 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg214 sg12954 - -lemma sg21162 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg214 sg12955 - -lemma sg21163 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg214 sg12956 - -lemma sg21164 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg215 sg12950 - -lemma sg21165 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg215 sg12954 - -lemma sg21166 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg215 sg12955 - -lemma sg21167 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg215 sg12956 - -lemma sg21168 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg216 sg12948 - -lemma sg21169 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg216 sg12949 - -lemma sg21170 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg216 sg12950 - -lemma sg21171 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg216 sg12951 - -lemma sg21172 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg214 sg12957 - -lemma sg21173 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg214 sg12958 - -lemma sg21174 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg214 sg12959 - -lemma sg21175 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg215 sg12957 - -lemma sg21176 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg215 sg12958 - -lemma sg21177 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg215 sg12959 - -lemma sg21178 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg12969 - -lemma sg21179 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,8,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg12970 - -lemma sg21180 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg217 sg12948 - -lemma sg21181 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg217 sg12949 - -lemma sg21182 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg217 sg12950 - -lemma sg21183 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg217 sg12951 - -lemma sg21184 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg216 sg12957 - -lemma sg21185 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg216 sg12958 - -lemma sg21186 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg216 sg12959 - -lemma sg21187 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg6488 - -lemma sg21188 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2702 sg6489 - -lemma sg21189 : RowSquare [8,7,3,3,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg14533 - -lemma sg21190 : RowSquare [8,7,3,3,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg14534 - -lemma sg21191 : RowSquare [8,7,3,3,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg14535 - -lemma sg21192 : RowSquare [8,7,3,3,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg80 sg14536 - -lemma sg21193 : RowSquare [8,7,3,3,3,2,1,1,1,1,1,1,1] [6,5,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg2588 sg6488 - -lemma sg21194 : RowSquare [8,7,3,3,3,2,1,1,1,1,1,1,1] [6,6,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg2589 sg6488 - -lemma sg21195 : RowSquare [8,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg15262 - -lemma sg21196 : RowSquare [8,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg15263 - -lemma sg21197 : RowSquare [8,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg15264 - -lemma sg21198 : RowSquare [8,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19 sg15265 - -lemma sg21199 : RowSquare [9,7,3,3,2,2,1,1,1,1,1,1,1] [5,5,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg4165 sg4842 - -lemma sg21200 : RowSquare [9,7,3,3,2,2,1,1,1,1,1,1,1] [6,6,6,6,5,4] := by - exact rowSquare_join (by decide) sg4173 sg4842 - -lemma sg21201 : RowSquare [9,7,3,3,2,2,1,1,1,1,1,1,1] [6,6,6,6,6,3] := by - exact rowSquare_join (by decide) sg4174 sg4842 - -lemma sg21202 : RowSquare [9,8,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3264 sg5760 - -lemma sg21203 : RowSquare [9,9,3,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3927 sg4821 - -lemma sg21204 : RowSquare [9,9,3,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3927 sg4820 - -lemma sg21205 : RowSquare [9,9,3,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3927 sg4819 - -lemma sg21206 : RowSquare [9,9,3,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3927 sg4818 - -lemma sg21207 : RowSquare [9,9,3,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3927 sg4817 - -lemma sg21208 : RowSquare [9,9,3,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3927 sg4814 - -lemma sg21209 : RowSquare [10,9,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3839 sg4932 - -lemma sg21210 : RowSquare [7,6,4,3,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg658 sg12650 - -lemma sg21211 : RowSquare [7,6,4,3,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg658 sg12651 - -lemma sg21212 : RowSquare [7,6,4,3,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg658 sg12652 - -lemma sg21213 : RowSquare [7,6,4,3,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg658 sg12653 - -lemma sg21214 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg14529 - -lemma sg21215 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg14530 - -lemma sg21216 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg14531 - -lemma sg21217 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg210 sg14532 - -lemma sg21218 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg361 sg12952 - -lemma sg21219 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg361 sg12954 - -lemma sg21220 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg361 sg12955 - -lemma sg21221 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg361 sg12956 - -lemma sg21222 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,5,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg357 sg12965 - -lemma sg21223 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,3,3,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg362 sg12956 - -lemma sg21224 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg213 sg14530 - -lemma sg21225 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg213 sg14531 - -lemma sg21226 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg213 sg14532 - -lemma sg21227 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg363 sg12952 - -lemma sg21228 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg363 sg12953 - -lemma sg21229 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg363 sg12954 - -lemma sg21230 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg363 sg12955 - -lemma sg21231 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg363 sg12956 - -lemma sg21232 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg356 sg12967 - -lemma sg21233 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg356 sg12968 - -lemma sg21234 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg214 sg14527 - -lemma sg21235 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg214 sg14530 - -lemma sg21236 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg214 sg14531 - -lemma sg21237 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg214 sg14532 - -lemma sg21238 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg215 sg14530 - -lemma sg21239 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg215 sg14531 - -lemma sg21240 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg215 sg14532 - -lemma sg21241 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg363 sg12960 - -lemma sg21242 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg360 sg12966 - -lemma sg21243 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg363 sg12961 - -lemma sg21244 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg363 sg12962 - -lemma sg21245 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg363 sg12963 - -lemma sg21246 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg363 sg12964 - -lemma sg21247 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg216 sg14527 - -lemma sg21248 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg216 sg14528 - -lemma sg21249 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg216 sg14532 - -lemma sg21250 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg363 sg12966 - -lemma sg21251 : RowSquare [8,7,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4165 sg5738 - -lemma sg21252 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [5,5,5,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg97 sg14795 - -lemma sg21253 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg100 sg14791 - -lemma sg21254 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg100 sg14792 - -lemma sg21255 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg100 sg14793 - -lemma sg21256 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg100 sg14794 - -lemma sg21257 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg14791 - -lemma sg21258 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg14792 - -lemma sg21259 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg101 sg14793 - -lemma sg21260 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg101 sg14794 - -lemma sg21261 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg102 sg14791 - -lemma sg21262 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg102 sg14792 - -lemma sg21263 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg102 sg14793 - -lemma sg21264 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg102 sg14794 - -lemma sg21265 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg103 sg14788 - -lemma sg21266 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg103 sg14789 - -lemma sg21267 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg103 sg14790 - -lemma sg21268 : RowSquare [8,8,3,3,3,2,1,1,1,1,1,1,1] [6,6,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg3263 sg6488 - -lemma sg21269 : RowSquare [8,8,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,5,5,5,1] := by - exact rowSquare_join (by decide) sg3264 sg6488 - -lemma sg21270 : RowSquare [9,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4025 sg5760 - -lemma sg21271 : RowSquare [9,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4026 sg5760 - -lemma sg21272 : RowSquare [9,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4029 sg5760 - -lemma sg21273 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg20772 - -lemma sg21274 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg20773 - -lemma sg21275 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg20774 - -lemma sg21276 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6 sg20775 - -lemma sg21277 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg15685 - -lemma sg21278 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg15686 - -lemma sg21279 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg15687 - -lemma sg21280 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg12 sg15688 - -lemma sg21281 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg12 sg15689 - -lemma sg21282 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4814 sg4775 - -lemma sg21283 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4814 sg4774 - -lemma sg21284 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4814 sg4773 - -lemma sg21285 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4814 sg4772 - -lemma sg21286 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4814 sg4771 - -lemma sg21287 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4814 sg4770 - -lemma sg21288 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3982 sg5600 - -lemma sg21289 : RowSquare [7,7,4,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg14493 - -lemma sg21290 : RowSquare [7,7,4,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg14494 - -lemma sg21291 : RowSquare [7,7,4,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg14495 - -lemma sg21292 : RowSquare [7,7,4,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg14496 - -lemma sg21293 : RowSquare [7,7,4,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg407 sg14497 - -lemma sg21294 : RowSquare [8,7,3,3,2,2,2,2,2,2,1,1] [6,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg362 sg14529 - -lemma sg21295 : RowSquare [8,7,3,3,2,2,2,2,2,2,1,1] [6,6,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg356 sg14537 - -lemma sg21296 : RowSquare [8,7,3,3,2,2,2,2,2,2,1,1] [6,6,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg356 sg14538 - -lemma sg21297 : RowSquare [8,7,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,5,1] := by - exact rowSquare_join (by decide) sg4173 sg6488 - -lemma sg21298 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg199 sg14790 - -lemma sg21299 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg199 sg14791 - -lemma sg21300 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg199 sg14792 - -lemma sg21301 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg199 sg14793 - -lemma sg21302 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg199 sg14794 - -lemma sg21303 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg100 sg15262 - -lemma sg21304 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg100 sg15263 - -lemma sg21305 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg100 sg15264 - -lemma sg21306 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg100 sg15265 - -lemma sg21307 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg15262 - -lemma sg21308 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg15263 - -lemma sg21309 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg15264 - -lemma sg21310 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg101 sg15265 - -lemma sg21311 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg202 sg14790 - -lemma sg21312 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg202 sg14791 - -lemma sg21313 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg202 sg14792 - -lemma sg21314 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg202 sg14793 - -lemma sg21315 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg202 sg14794 - -lemma sg21316 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg14798 - -lemma sg21317 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,5,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg193 sg14799 - -lemma sg21318 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg102 sg15262 - -lemma sg21319 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg102 sg15263 - -lemma sg21320 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg102 sg15264 - -lemma sg21321 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg102 sg15265 - -lemma sg21322 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,5,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg4852 sg5732 - -lemma sg21323 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,5,5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg3281 sg7993 - -lemma sg21324 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,5,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg3994 sg6485 - -lemma sg21325 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,5,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg14800 - -lemma sg21326 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,5,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg193 sg14801 - -lemma sg21327 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,5,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg3275 sg7994 - -lemma sg21328 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg103 sg15260 - -lemma sg21329 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg103 sg15261 - -lemma sg21330 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg103 sg15262 - -lemma sg21331 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg103 sg15263 - -lemma sg21332 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg103 sg15264 - -lemma sg21333 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg103 sg15265 - -lemma sg21334 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg15685 - -lemma sg21335 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg15686 - -lemma sg21336 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg15687 - -lemma sg21337 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg43 sg15688 - -lemma sg21338 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg43 sg15689 - -lemma sg21339 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg15684 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes50 + +namespace OAI + +/-! Semigroup Nodes 51. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg20940 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1474 sg8780 + +lemma sg20941 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1475 sg8780 + +lemma sg20942 : RowSquare [6,6,3,3,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1476 sg8780 + +lemma sg20943 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2626 sg5764 + +lemma sg20944 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2626 sg5765 + +lemma sg20945 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3334 sg4941 + +lemma sg20946 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4949 + +lemma sg20947 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3323 sg4958 + +lemma sg20948 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3332 sg4944 + +lemma sg20949 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg3332 sg4945 + +lemma sg20950 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,5,5,4] := by + exact rowSquare_join (by decide) sg3332 sg4949 + +lemma sg20951 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,6,1,1] := by + exact rowSquare_join (by decide) sg3334 sg4948 + +lemma sg20952 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,4,4,4] := by + exact rowSquare_join (by decide) sg3332 sg4956 + +lemma sg20953 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,6] := by + exact rowSquare_join (by decide) sg3732 sg4844 + +lemma sg20954 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3407 sg4897 + +lemma sg20955 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3330 sg4959 + +lemma sg20956 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg3324 sg4963 + +lemma sg20957 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3332 sg4959 + +lemma sg20958 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,4,4,3] := by + exact rowSquare_join (by decide) sg3332 sg4960 + +lemma sg20959 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1,1] := by + exact rowSquare_join (by decide) sg1757 sg8002 + +lemma sg20960 : RowSquare [6,6,3,3,3,2,1,1,1,1,1,1,1,1,1] [8,8,8,8] := by + exact rowSquare_join (by decide) sg1675 sg8015 + +lemma sg20961 : RowSquare [7,5,4,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg4167 sg4402 + +lemma sg20962 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg658 sg11531 + +lemma sg20963 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg984 sg10868 + +lemma sg20964 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg661 sg11531 + +lemma sg20965 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg662 sg11531 + +lemma sg20966 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [5,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg985 sg10869 + +lemma sg20967 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg991 sg10867 + +lemma sg20968 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg663 sg11531 + +lemma sg20969 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg992 sg10867 + +lemma sg20970 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg987 sg10868 + +lemma sg20971 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg664 sg11531 + +lemma sg20972 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg988 sg10868 + +lemma sg20973 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg665 sg11531 + +lemma sg20974 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg989 sg10868 + +lemma sg20975 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg666 sg11531 + +lemma sg20976 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg993 sg10867 + +lemma sg20977 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg667 sg11531 + +lemma sg20978 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg994 sg10867 + +lemma sg20979 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg991 sg10868 + +lemma sg20980 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg668 sg11531 + +lemma sg20981 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg992 sg10868 + +lemma sg20982 : RowSquare [7,6,3,2,2,2,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg669 sg11531 + +lemma sg20983 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3332 sg4935 + +lemma sg20984 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3593 sg4875 + +lemma sg20985 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,4] := by + exact rowSquare_join (by decide) sg4378 sg4173 + +lemma sg20986 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,4] := by + exact rowSquare_join (by decide) sg13 sg14653 + +lemma sg20987 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,3] := by + exact rowSquare_join (by decide) sg13 sg14655 + +lemma sg20988 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,2] := by + exact rowSquare_join (by decide) sg13 sg14667 + +lemma sg20989 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [8,8,4,4,4,4] := by + exact rowSquare_join (by decide) sg14 sg14653 + +lemma sg20990 : RowSquare [7,6,3,3,2,2,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,3] := by + exact rowSquare_join (by decide) sg295 sg11598 + +lemma sg20991 : RowSquare [7,6,4,3,3,2,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg271 sg11715 + +lemma sg20992 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg402 sg11798 + +lemma sg20993 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg402 sg11799 + +lemma sg20994 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg402 sg11800 + +lemma sg20995 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg403 sg11799 + +lemma sg20996 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg403 sg11800 + +lemma sg20997 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg11798 + +lemma sg20998 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg11799 + +lemma sg20999 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg407 sg11800 + +lemma sg21000 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg408 sg11795 + +lemma sg21001 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg409 sg11795 + +lemma sg21002 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg408 sg11796 + +lemma sg21003 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg408 sg11797 + +lemma sg21004 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg410 sg11795 + +lemma sg21005 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg409 sg11796 + +lemma sg21006 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg409 sg11797 + +lemma sg21007 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg404 sg11803 + +lemma sg21008 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg405 sg11803 + +lemma sg21009 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg405 sg11804 + +lemma sg21010 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg410 sg11796 + +lemma sg21011 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg410 sg11797 + +lemma sg21012 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg410 sg11798 + +lemma sg21013 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg406 sg11803 + +lemma sg21014 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg11802 + +lemma sg21015 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg402 sg11812 + +lemma sg21016 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg11803 + +lemma sg21017 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg11804 + +lemma sg21018 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg11806 + +lemma sg21019 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg11807 + +lemma sg21020 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg11808 + +lemma sg21021 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg411 sg11795 + +lemma sg21022 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg412 sg11795 + +lemma sg21023 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg411 sg11796 + +lemma sg21024 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg411 sg11797 + +lemma sg21025 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg408 sg11803 + +lemma sg21026 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg412 sg11796 + +lemma sg21027 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg412 sg11797 + +lemma sg21028 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg409 sg11803 + +lemma sg21029 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg410 sg11803 + +lemma sg21030 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg410 sg11804 + +lemma sg21031 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,5,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg410 sg11805 + +lemma sg21032 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg11812 + +lemma sg21033 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg11813 + +lemma sg21034 : RowSquare [7,7,2,2,2,2,2,2,2,2,1,1] [8,8,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg11815 + +lemma sg21035 : RowSquare [7,7,3,2,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3316 sg4936 + +lemma sg21036 : RowSquare [7,7,3,2,2,2,2,2,2,2,1] [7,7,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg363 sg11809 + +lemma sg21037 : RowSquare [7,7,3,2,2,2,2,2,2,2,1] [7,7,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg363 sg11810 + +lemma sg21038 : RowSquare [7,7,3,2,2,2,2,2,2,2,1] [8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg363 sg11814 + +lemma sg21039 : RowSquare [7,7,3,2,2,2,2,2,2,2,1] [8,8,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg363 sg11815 + +lemma sg21040 : RowSquare [7,7,3,3,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg5749 + +lemma sg21041 : RowSquare [8,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14705 + +lemma sg21042 : RowSquare [8,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14706 + +lemma sg21043 : RowSquare [8,6,3,2,2,2,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14707 + +lemma sg21044 : RowSquare [8,6,3,3,3,2,1,1,1,1,1,1,1] [6,5,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg2135 sg6488 + +lemma sg21045 : RowSquare [8,6,4,3,2,2,1,1,1,1,1,1,1] [6,5,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg74 sg12863 + +lemma sg21046 : RowSquare [8,6,4,3,2,2,1,1,1,1,1,1,1] [6,6,5,5,5,5] := by + exact rowSquare_join (by decide) sg74 sg12864 + +lemma sg21047 : RowSquare [8,6,4,3,2,2,1,1,1,1,1,1,1] [7,5,5,5,5,5] := by + exact rowSquare_join (by decide) sg74 sg12865 + +lemma sg21048 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg5744 + +lemma sg21049 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg5745 + +lemma sg21050 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2707 sg5737 + +lemma sg21051 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2708 sg5738 + +lemma sg21052 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2710 sg5738 + +lemma sg21053 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,6,6,4,4] := by + exact rowSquare_join (by decide) sg74 sg13504 + +lemma sg21054 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,5,5,4,4] := by + exact rowSquare_join (by decide) sg74 sg13508 + +lemma sg21055 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg14709 + +lemma sg21056 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,6,6,3,3] := by + exact rowSquare_join (by decide) sg13 sg14710 + +lemma sg21057 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14711 + +lemma sg21058 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [7,7,7,7,2,2] := by + exact rowSquare_join (by decide) sg13 sg14712 + +lemma sg21059 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg14713 + +lemma sg21060 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,6,6,2,2] := by + exact rowSquare_join (by decide) sg358 sg11613 + +lemma sg21061 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,7,7,1,1] := by + exact rowSquare_join (by decide) sg364 sg11601 + +lemma sg21062 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [8,8,8,8] := by + exact rowSquare_join (by decide) sg364 sg11602 + +lemma sg21063 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [9,9,4,4,3,3] := by + exact rowSquare_join (by decide) sg356 sg11679 + +lemma sg21064 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg281 sg11726 + +lemma sg21065 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg356 sg11709 + +lemma sg21066 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,3,3,3,3] := by + exact rowSquare_join (by decide) sg356 sg11710 + +lemma sg21067 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11603 + +lemma sg21068 : RowSquare [8,7,3,2,2,1,1,1,1,1,1,1,1,1,1] [10,10,4,4,2,2] := by + exact rowSquare_join (by decide) sg356 sg11711 + +lemma sg21069 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg14530 + +lemma sg21070 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg14531 + +lemma sg21071 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg43 sg14532 + +lemma sg21072 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg14529 + +lemma sg21073 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg14530 + +lemma sg21074 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg14531 + +lemma sg21075 : RowSquare [8,7,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg44 sg14532 + +lemma sg21076 : RowSquare [8,7,3,3,2,2,1,1,1,1,1,1,1] [5,5,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2589 sg5738 + +lemma sg21077 : RowSquare [8,8,3,2,2,2,1,1,1,1,1,1,1] [6,6,6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg364 sg11715 + +lemma sg21078 : RowSquare [8,8,3,2,2,2,1,1,1,1,1,1,1] [7,7,7,7,1,1,1,1] := by + exact rowSquare_join (by decide) sg364 sg11716 + +lemma sg21079 : RowSquare [8,8,3,2,2,2,1,1,1,1,1,1,1] [8,8,8,8] := by + exact rowSquare_join (by decide) sg364 sg11717 + +lemma sg21080 : RowSquare [9,7,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg14808 + +lemma sg21081 : RowSquare [9,7,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg14809 + +lemma sg21082 : RowSquare [9,7,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg15 sg14810 + +lemma sg21083 : RowSquare [9,7,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg14811 + +lemma sg21084 : RowSquare [9,7,3,2,2,1,1,1,1,1,1,1,1,1] [6,4,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2590 sg5760 + +lemma sg21085 : RowSquare [9,7,3,3,2,1,1,1,1,1,1,1,1] [7,7,7,7,2,2] := by + exact rowSquare_join (by decide) sg960 sg8921 + +lemma sg21086 : RowSquare [9,7,3,3,2,1,1,1,1,1,1,1,1] [8,8,6,6,2,2] := by + exact rowSquare_join (by decide) sg960 sg8932 + +lemma sg21087 : RowSquare [9,7,3,3,2,1,1,1,1,1,1,1,1] [8,8,7,7,1,1] := by + exact rowSquare_join (by decide) sg960 sg8933 + +lemma sg21088 : RowSquare [9,7,3,3,2,1,1,1,1,1,1,1,1] [8,8,8,3,3,2] := by + exact rowSquare_join (by decide) sg563 sg11199 + +lemma sg21089 : RowSquare [9,7,3,3,2,1,1,1,1,1,1,1,1] [8,8,8,8] := by + exact rowSquare_join (by decide) sg364 sg11718 + +lemma sg21090 : RowSquare [9,8,2,2,2,2,1,1,1,1,1,1,1] [4,4,4,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2546 sg5760 + +lemma sg21091 : RowSquare [9,8,3,2,2,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2529 sg5760 + +lemma sg21092 : RowSquare [9,9,2,2,1,1,1,1,1,1,1,1,1,1] [3,3,3,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg14775 + +lemma sg21093 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3220 sg4816 + +lemma sg21094 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3220 sg4812 + +lemma sg21095 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3220 sg4815 + +lemma sg21096 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3220 sg4811 + +lemma sg21097 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3220 sg4813 + +lemma sg21098 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3225 sg4810 + +lemma sg21099 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3223 sg4810 + +lemma sg21100 : RowSquare [9,9,2,2,2,2,2,2,2] [4,4,4,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3220 sg4810 + +lemma sg21101 : RowSquare [10,8,2,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4060 sg3910 + +lemma sg21102 : RowSquare [10,8,2,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4060 sg3909 + +lemma sg21103 : RowSquare [10,8,2,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4060 sg3908 + +lemma sg21104 : RowSquare [10,8,2,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4060 sg3907 + +lemma sg21105 : RowSquare [10,8,2,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4060 sg3906 + +lemma sg21106 : RowSquare [10,8,2,2,2,2,2,2,1,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4060 sg3905 + +lemma sg21107 : RowSquare [7,6,3,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg991 sg11531 + +lemma sg21108 : RowSquare [7,6,3,3,2,2,2,2,2,2,1,1] [6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg993 sg11531 + +lemma sg21109 : RowSquare [7,6,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg990 sg11532 + +lemma sg21110 : RowSquare [7,6,3,3,2,2,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg994 sg11531 + +lemma sg21111 : RowSquare [7,6,3,3,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg993 sg11532 + +lemma sg21112 : RowSquare [7,6,4,3,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg12649 + +lemma sg21113 : RowSquare [7,6,4,3,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg12650 + +lemma sg21114 : RowSquare [7,6,4,3,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg12651 + +lemma sg21115 : RowSquare [7,6,4,3,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg12652 + +lemma sg21116 : RowSquare [7,6,4,3,2,2,2,2,2,2,1] [6,6,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg367 sg12653 + +lemma sg21117 : RowSquare [7,6,4,4,3,2,1,1,1,1,1,1,1] [6,6,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg3702 sg5301 + +lemma sg21118 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg403 sg12671 + +lemma sg21119 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg403 sg12673 + +lemma sg21120 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg403 sg12674 + +lemma sg21121 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg647 sg11799 + +lemma sg21122 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg647 sg11800 + +lemma sg21123 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg648 sg11795 + +lemma sg21124 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [6,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg648 sg11796 + +lemma sg21125 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg12672 + +lemma sg21126 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg651 sg11795 + +lemma sg21127 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg408 sg12669 + +lemma sg21128 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg408 sg12670 + +lemma sg21129 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg648 sg11803 + +lemma sg21130 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg651 sg11798 + +lemma sg21131 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg648 sg11804 + +lemma sg21132 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg12675 + +lemma sg21133 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg402 sg12678 + +lemma sg21134 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg12676 + +lemma sg21135 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg12677 + +lemma sg21136 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [8,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg411 sg12669 + +lemma sg21137 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg412 sg12669 + +lemma sg21138 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg412 sg12670 + +lemma sg21139 : RowSquare [7,7,3,2,2,2,2,2,2,2,1,1] [8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg12678 + +lemma sg21140 : RowSquare [7,7,3,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2589 sg6503 + +lemma sg21141 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,4,4,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg12954 + +lemma sg21142 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,4,4,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg209 sg12955 + +lemma sg21143 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,4,4,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg209 sg12956 + +lemma sg21144 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg12952 + +lemma sg21145 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg12954 + +lemma sg21146 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg210 sg12955 + +lemma sg21147 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg210 sg12956 + +lemma sg21148 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg211 sg12950 + +lemma sg21149 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,3,3,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg211 sg12954 + +lemma sg21150 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,3,3,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg211 sg12955 + +lemma sg21151 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,3,3,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg211 sg12956 + +lemma sg21152 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,4,3,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg212 sg12954 + +lemma sg21153 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,4,3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg212 sg12955 + +lemma sg21154 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,4,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg212 sg12956 + +lemma sg21155 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg213 sg12952 + +lemma sg21156 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg213 sg12954 + +lemma sg21157 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg213 sg12955 + +lemma sg21158 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg213 sg12956 + +lemma sg21159 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg214 sg12950 + +lemma sg21160 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg214 sg12951 + +lemma sg21161 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg214 sg12954 + +lemma sg21162 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg214 sg12955 + +lemma sg21163 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg214 sg12956 + +lemma sg21164 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg215 sg12950 + +lemma sg21165 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg215 sg12954 + +lemma sg21166 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg215 sg12955 + +lemma sg21167 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg215 sg12956 + +lemma sg21168 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg216 sg12948 + +lemma sg21169 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg216 sg12949 + +lemma sg21170 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg216 sg12950 + +lemma sg21171 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg216 sg12951 + +lemma sg21172 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg214 sg12957 + +lemma sg21173 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg214 sg12958 + +lemma sg21174 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg214 sg12959 + +lemma sg21175 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg215 sg12957 + +lemma sg21176 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg215 sg12958 + +lemma sg21177 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg215 sg12959 + +lemma sg21178 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg12969 + +lemma sg21179 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [8,8,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg12970 + +lemma sg21180 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg217 sg12948 + +lemma sg21181 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg217 sg12949 + +lemma sg21182 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg217 sg12950 + +lemma sg21183 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg217 sg12951 + +lemma sg21184 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg216 sg12957 + +lemma sg21185 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg216 sg12958 + +lemma sg21186 : RowSquare [8,7,2,2,2,2,2,2,2,2,1,1] [9,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg216 sg12959 + +lemma sg21187 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg6488 + +lemma sg21188 : RowSquare [8,7,3,3,2,1,1,1,1,1,1,1,1,1,1] [5,4,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2702 sg6489 + +lemma sg21189 : RowSquare [8,7,3,3,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg14533 + +lemma sg21190 : RowSquare [8,7,3,3,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg14534 + +lemma sg21191 : RowSquare [8,7,3,3,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg14535 + +lemma sg21192 : RowSquare [8,7,3,3,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg80 sg14536 + +lemma sg21193 : RowSquare [8,7,3,3,3,2,1,1,1,1,1,1,1] [6,5,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg2588 sg6488 + +lemma sg21194 : RowSquare [8,7,3,3,3,2,1,1,1,1,1,1,1] [6,6,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg2589 sg6488 + +lemma sg21195 : RowSquare [8,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg15262 + +lemma sg21196 : RowSquare [8,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg15263 + +lemma sg21197 : RowSquare [8,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg15264 + +lemma sg21198 : RowSquare [8,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19 sg15265 + +lemma sg21199 : RowSquare [9,7,3,3,2,2,1,1,1,1,1,1,1] [5,5,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg4165 sg4842 + +lemma sg21200 : RowSquare [9,7,3,3,2,2,1,1,1,1,1,1,1] [6,6,6,6,5,4] := by + exact rowSquare_join (by decide) sg4173 sg4842 + +lemma sg21201 : RowSquare [9,7,3,3,2,2,1,1,1,1,1,1,1] [6,6,6,6,6,3] := by + exact rowSquare_join (by decide) sg4174 sg4842 + +lemma sg21202 : RowSquare [9,8,3,2,2,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3264 sg5760 + +lemma sg21203 : RowSquare [9,9,3,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3927 sg4821 + +lemma sg21204 : RowSquare [9,9,3,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3927 sg4820 + +lemma sg21205 : RowSquare [9,9,3,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3927 sg4819 + +lemma sg21206 : RowSquare [9,9,3,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3927 sg4818 + +lemma sg21207 : RowSquare [9,9,3,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3927 sg4817 + +lemma sg21208 : RowSquare [9,9,3,2,2,2,2,2,2] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3927 sg4814 + +lemma sg21209 : RowSquare [10,9,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3839 sg4932 + +lemma sg21210 : RowSquare [7,6,4,3,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg658 sg12650 + +lemma sg21211 : RowSquare [7,6,4,3,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg658 sg12651 + +lemma sg21212 : RowSquare [7,6,4,3,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg658 sg12652 + +lemma sg21213 : RowSquare [7,6,4,3,2,2,2,2,2,2,1,1] [5,5,5,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg658 sg12653 + +lemma sg21214 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg14529 + +lemma sg21215 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg14530 + +lemma sg21216 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg14531 + +lemma sg21217 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg210 sg14532 + +lemma sg21218 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg361 sg12952 + +lemma sg21219 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg361 sg12954 + +lemma sg21220 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg361 sg12955 + +lemma sg21221 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,4,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg361 sg12956 + +lemma sg21222 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [5,5,5,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg357 sg12965 + +lemma sg21223 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,3,3,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg362 sg12956 + +lemma sg21224 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg213 sg14530 + +lemma sg21225 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg213 sg14531 + +lemma sg21226 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg213 sg14532 + +lemma sg21227 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg363 sg12952 + +lemma sg21228 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg363 sg12953 + +lemma sg21229 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg363 sg12954 + +lemma sg21230 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg363 sg12955 + +lemma sg21231 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg363 sg12956 + +lemma sg21232 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg356 sg12967 + +lemma sg21233 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [6,6,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg356 sg12968 + +lemma sg21234 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg214 sg14527 + +lemma sg21235 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg214 sg14530 + +lemma sg21236 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg214 sg14531 + +lemma sg21237 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,3,3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg214 sg14532 + +lemma sg21238 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg215 sg14530 + +lemma sg21239 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg215 sg14531 + +lemma sg21240 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,4,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg215 sg14532 + +lemma sg21241 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg363 sg12960 + +lemma sg21242 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg360 sg12966 + +lemma sg21243 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg363 sg12961 + +lemma sg21244 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg363 sg12962 + +lemma sg21245 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg363 sg12963 + +lemma sg21246 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [7,7,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg363 sg12964 + +lemma sg21247 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg216 sg14527 + +lemma sg21248 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg216 sg14528 + +lemma sg21249 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [8,3,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg216 sg14532 + +lemma sg21250 : RowSquare [8,7,3,2,2,2,2,2,2,2,1,1] [8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg363 sg12966 + +lemma sg21251 : RowSquare [8,7,3,3,2,2,1,1,1,1,1,1,1,1,1] [4,4,4,4,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4165 sg5738 + +lemma sg21252 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [5,5,5,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg97 sg14795 + +lemma sg21253 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg100 sg14791 + +lemma sg21254 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg100 sg14792 + +lemma sg21255 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg100 sg14793 + +lemma sg21256 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg100 sg14794 + +lemma sg21257 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg14791 + +lemma sg21258 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg14792 + +lemma sg21259 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg101 sg14793 + +lemma sg21260 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg101 sg14794 + +lemma sg21261 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg102 sg14791 + +lemma sg21262 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg102 sg14792 + +lemma sg21263 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg102 sg14793 + +lemma sg21264 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg102 sg14794 + +lemma sg21265 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg103 sg14788 + +lemma sg21266 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg103 sg14789 + +lemma sg21267 : RowSquare [8,8,2,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg103 sg14790 + +lemma sg21268 : RowSquare [8,8,3,3,3,2,1,1,1,1,1,1,1] [6,6,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg3263 sg6488 + +lemma sg21269 : RowSquare [8,8,3,3,3,2,1,1,1,1,1,1,1] [6,6,6,5,5,5,1] := by + exact rowSquare_join (by decide) sg3264 sg6488 + +lemma sg21270 : RowSquare [9,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4025 sg5760 + +lemma sg21271 : RowSquare [9,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4026 sg5760 + +lemma sg21272 : RowSquare [9,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4029 sg5760 + +lemma sg21273 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg20772 + +lemma sg21274 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg20773 + +lemma sg21275 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg20774 + +lemma sg21276 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6 sg20775 + +lemma sg21277 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg15685 + +lemma sg21278 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg15686 + +lemma sg21279 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg15687 + +lemma sg21280 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg12 sg15688 + +lemma sg21281 : RowSquare [9,8,3,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg12 sg15689 + +lemma sg21282 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4814 sg4775 + +lemma sg21283 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4814 sg4774 + +lemma sg21284 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4814 sg4773 + +lemma sg21285 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4814 sg4772 + +lemma sg21286 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4814 sg4771 + +lemma sg21287 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4814 sg4770 + +lemma sg21288 : RowSquare [10,9,2,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3982 sg5600 + +lemma sg21289 : RowSquare [7,7,4,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg14493 + +lemma sg21290 : RowSquare [7,7,4,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg14494 + +lemma sg21291 : RowSquare [7,7,4,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg14495 + +lemma sg21292 : RowSquare [7,7,4,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg14496 + +lemma sg21293 : RowSquare [7,7,4,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg407 sg14497 + +lemma sg21294 : RowSquare [8,7,3,3,2,2,2,2,2,2,1,1] [6,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg362 sg14529 + +lemma sg21295 : RowSquare [8,7,3,3,2,2,2,2,2,2,1,1] [6,6,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg356 sg14537 + +lemma sg21296 : RowSquare [8,7,3,3,2,2,2,2,2,2,1,1] [6,6,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg356 sg14538 + +lemma sg21297 : RowSquare [8,7,3,3,3,2,1,1,1,1,1,1,1,1,1] [6,6,6,6,5,5,1] := by + exact rowSquare_join (by decide) sg4173 sg6488 + +lemma sg21298 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg199 sg14790 + +lemma sg21299 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg199 sg14791 + +lemma sg21300 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg199 sg14792 + +lemma sg21301 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg199 sg14793 + +lemma sg21302 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [5,5,3,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg199 sg14794 + +lemma sg21303 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg100 sg15262 + +lemma sg21304 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg100 sg15263 + +lemma sg21305 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg100 sg15264 + +lemma sg21306 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,3,3,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg100 sg15265 + +lemma sg21307 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg15262 + +lemma sg21308 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg15263 + +lemma sg21309 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg15264 + +lemma sg21310 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,4,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg101 sg15265 + +lemma sg21311 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg202 sg14790 + +lemma sg21312 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg202 sg14791 + +lemma sg21313 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg202 sg14792 + +lemma sg21314 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg202 sg14793 + +lemma sg21315 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg202 sg14794 + +lemma sg21316 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg14798 + +lemma sg21317 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [6,5,5,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg193 sg14799 + +lemma sg21318 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg102 sg15262 + +lemma sg21319 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg102 sg15263 + +lemma sg21320 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg102 sg15264 + +lemma sg21321 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,3,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg102 sg15265 + +lemma sg21322 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,5,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg4852 sg5732 + +lemma sg21323 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,5,5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg3281 sg7993 + +lemma sg21324 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,5,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg3994 sg6485 + +lemma sg21325 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,5,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg14800 + +lemma sg21326 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,5,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg193 sg14801 + +lemma sg21327 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [7,5,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg3275 sg7994 + +lemma sg21328 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg103 sg15260 + +lemma sg21329 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg103 sg15261 + +lemma sg21330 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg103 sg15262 + +lemma sg21331 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg103 sg15263 + +lemma sg21332 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg103 sg15264 + +lemma sg21333 : RowSquare [8,8,3,2,2,2,2,2,2,2,1,1] [8,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg103 sg15265 + +lemma sg21334 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg15685 + +lemma sg21335 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg15686 + +lemma sg21336 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg15687 + +lemma sg21337 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg43 sg15688 + +lemma sg21338 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg43 sg15689 + +lemma sg21339 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg15684 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes52.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes52.lean index 4f47602dc315928ef375bc0421a4dca62d0b3a48..70821b8b56e360583232d6b916d93f8bfd13e77e 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes52.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes52.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 - -namespace OAI - -/-! Semigroup Nodes 52. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg21340 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg15685 - -lemma sg21341 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg15686 - -lemma sg21342 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg15687 - -lemma sg21343 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg44 sg15688 - -lemma sg21344 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg44 sg15689 - -lemma sg21345 : RowSquare [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3264 sg8009 - -lemma sg21346 : RowSquare [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg15294 - -lemma sg21347 : RowSquare [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3268 sg8009 - -lemma sg21348 : RowSquare [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3264 sg8010 - -lemma sg21349 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,7,7,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5440 - -lemma sg21350 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,7,7,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4829 sg5348 - -lemma sg21351 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,6,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5447 - -lemma sg21352 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4789 sg5428 - -lemma sg21353 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4826 sg5350 - -lemma sg21354 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5445 - -lemma sg21355 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5448 - -lemma sg21356 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5446 - -lemma sg21357 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5449 - -lemma sg21358 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5450 - -lemma sg21359 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5447 - -lemma sg21360 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,8,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg3984 sg6123 - -lemma sg21361 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,8,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5448 - -lemma sg21362 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,8,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4831 sg5347 - -lemma sg21363 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,8,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5449 - -lemma sg21364 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,8,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4929 sg5011 - -lemma sg21365 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,6,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5467 - -lemma sg21366 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4854 sg5261 - -lemma sg21367 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4827 sg5350 - -lemma sg21368 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5626 - -lemma sg21369 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5471 - -lemma sg21370 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5472 - -lemma sg21371 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4851 sg5269 - -lemma sg21372 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4851 sg5270 - -lemma sg21373 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4929 sg5012 - -lemma sg21374 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4854 sg5264 - -lemma sg21375 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4826 sg5353 - -lemma sg21376 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5627 - -lemma sg21377 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5479 - -lemma sg21378 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5480 - -lemma sg21379 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5469 - -lemma sg21380 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5470 - -lemma sg21381 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4853 sg5267 - -lemma sg21382 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,7,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5628 - -lemma sg21383 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,7,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5481 - -lemma sg21384 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,7,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5471 - -lemma sg21385 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,7,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5472 - -lemma sg21386 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,7,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4929 sg5013 - -lemma sg21387 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,8,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5482 - -lemma sg21388 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,8,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5471 - -lemma sg21389 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,8,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4929 sg5014 - -lemma sg21390 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4788 sg5441 - -lemma sg21391 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4825 sg5354 - -lemma sg21392 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5473 - -lemma sg21393 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg4830 sg5349 - -lemma sg21394 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5629 - -lemma sg21395 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4788 sg5442 - -lemma sg21396 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5473 - -lemma sg21397 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4825 sg5355 - -lemma sg21398 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5630 - -lemma sg21399 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4788 sg5443 - -lemma sg21400 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5631 - -lemma sg21401 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5474 - -lemma sg21402 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5475 - -lemma sg21403 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4788 sg5444 - -lemma sg21404 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5632 - -lemma sg21405 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5476 - -lemma sg21406 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5474 - -lemma sg21407 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5477 - -lemma sg21408 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5478 - -lemma sg21409 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5633 - -lemma sg21410 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,6,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5476 - -lemma sg21411 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,6,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5479 - -lemma sg21412 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,6,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5480 - -lemma sg21413 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,6,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5478 - -lemma sg21414 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4788 sg5448 - -lemma sg21415 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5481 - -lemma sg21416 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4929 sg5015 - -lemma sg21417 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,8,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5482 - -lemma sg21418 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,8,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4929 sg5016 - -lemma sg21419 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,9,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4929 sg5017 - -lemma sg21420 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg25 sg15651 - -lemma sg21421 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg25 sg15652 - -lemma sg21422 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg15653 - -lemma sg21423 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg24 sg15654 - -lemma sg21424 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg24 sg15655 - -lemma sg21425 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg11731 - -lemma sg21426 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg72 sg15245 - -lemma sg21427 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg72 sg15246 - -lemma sg21428 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4755 sg5524 - -lemma sg21429 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5451 - -lemma sg21430 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4719 sg5621 - -lemma sg21431 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3935 sg6357 - -lemma sg21432 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4756 sg5524 - -lemma sg21433 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5452 - -lemma sg21434 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4790 sg5431 - -lemma sg21435 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4720 sg5617 - -lemma sg21436 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4757 sg5524 - -lemma sg21437 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5453 - -lemma sg21438 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4790 sg5432 - -lemma sg21439 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4793 sg5424 - -lemma sg21440 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4722 sg5615 - -lemma sg21441 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5454 - -lemma sg21442 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4790 sg5433 - -lemma sg21443 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4793 sg5425 - -lemma sg21444 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg4795 sg5414 - -lemma sg21445 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4857 sg5240 - -lemma sg21446 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4795 sg5415 - -lemma sg21447 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg3988 sg6118 - -lemma sg21448 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg4739 sg5525 - -lemma sg21449 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg11732 - -lemma sg21450 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg73 sg15245 - -lemma sg21451 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg73 sg15246 - -lemma sg21452 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4758 sg5524 - -lemma sg21453 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5455 - -lemma sg21454 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4719 sg5622 - -lemma sg21455 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3935 sg6358 - -lemma sg21456 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4759 sg5524 - -lemma sg21457 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5456 - -lemma sg21458 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4790 sg5434 - -lemma sg21459 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4720 sg5618 - -lemma sg21460 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4760 sg5524 - -lemma sg21461 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5457 - -lemma sg21462 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4738 sg5578 - -lemma sg21463 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4791 sg5431 - -lemma sg21464 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4721 sg5617 - -lemma sg21465 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4761 sg5524 - -lemma sg21466 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5458 - -lemma sg21467 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4738 sg5579 - -lemma sg21468 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4791 sg5432 - -lemma sg21469 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4794 sg5424 - -lemma sg21470 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4738 sg5580 - -lemma sg21471 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4855 sg5258 - -lemma sg21472 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4794 sg5425 - -lemma sg21473 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg4718 sg5634 - -lemma sg21474 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4858 sg5240 - -lemma sg21475 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg4796 sg5415 - -lemma sg21476 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4762 sg5524 - -lemma sg21477 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5459 - -lemma sg21478 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4790 sg5435 - -lemma sg21479 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4720 sg5619 - -lemma sg21480 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4763 sg5524 - -lemma sg21481 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5460 - -lemma sg21482 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4735 sg5588 - -lemma sg21483 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4793 sg5426 - -lemma sg21484 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4722 sg5616 - -lemma sg21485 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4764 sg5524 - -lemma sg21486 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5461 - -lemma sg21487 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4735 sg5589 - -lemma sg21488 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4734 sg5595 - -lemma sg21489 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4873 sg5128 - -lemma sg21490 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5462 - -lemma sg21491 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4735 sg5590 - -lemma sg21492 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4849 sg5271 - -lemma sg21493 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4792 sg5432 - -lemma sg21494 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg4784 sg5483 - -lemma sg21495 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4849 sg5272 - -lemma sg21496 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4873 sg5129 - -lemma sg21497 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg4718 sg5635 - -lemma sg21498 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg4859 sg5240 - -lemma sg21499 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4765 sg5524 - -lemma sg21500 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5463 - -lemma sg21501 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4790 sg5436 - -lemma sg21502 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4736 sg5588 - -lemma sg21503 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4795 sg5421 - -lemma sg21504 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4766 sg5524 - -lemma sg21505 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5464 - -lemma sg21506 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4790 sg5437 - -lemma sg21507 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4734 sg5596 - -lemma sg21508 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4737 sg5588 - -lemma sg21509 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4822 sg5357 - -lemma sg21510 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4790 sg5438 - -lemma sg21511 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4736 sg5590 - -lemma sg21512 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4850 sg5271 - -lemma sg21513 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg4784 sg5484 - -lemma sg21514 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4850 sg5272 - -lemma sg21515 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5636 - -lemma sg21516 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5465 - -lemma sg21517 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4790 sg5439 - -lemma sg21518 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4734 sg5597 - -lemma sg21519 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4737 sg5589 - -lemma sg21520 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4822 sg5358 - -lemma sg21521 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4734 sg5598 - -lemma sg21522 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4737 sg5590 - -lemma sg21523 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5485 - -lemma sg21524 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5637 - -lemma sg21525 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4723 sg5615 - -lemma sg21526 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5638 - -lemma sg21527 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4767 sg5524 - -lemma sg21528 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5466 - -lemma sg21529 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4719 sg5623 - -lemma sg21530 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg3935 sg6359 - -lemma sg21531 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg4784 sg5486 - -lemma sg21532 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg4718 sg5639 - -lemma sg21533 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg4860 sg5240 - -lemma sg21534 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4785 sg5483 - -lemma sg21535 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg4784 sg5487 - -lemma sg21536 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5640 - -lemma sg21537 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4823 sg5357 - -lemma sg21538 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4785 sg5484 - -lemma sg21539 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5488 - -lemma sg21540 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5641 - -lemma sg21541 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5485 - -lemma sg21542 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5642 - -lemma sg21543 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5489 - -lemma sg21544 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4786 sg5483 - -lemma sg21545 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4822 sg5361 - -lemma sg21546 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5490 - -lemma sg21547 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5643 - -lemma sg21548 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4786 sg5484 - -lemma sg21549 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4851 sg5273 - -lemma sg21550 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5644 - -lemma sg21551 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5645 - -lemma sg21552 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5491 - -lemma sg21553 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4856 sg5259 - -lemma sg21554 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5646 - -lemma sg21555 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5492 - -lemma sg21556 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5493 - -lemma sg21557 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4851 sg5274 - -lemma sg21558 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4768 sg5524 - -lemma sg21559 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4787 sg5468 - -lemma sg21560 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4790 sg5441 - -lemma sg21561 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg3935 sg6360 - -lemma sg21562 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4785 sg5486 - -lemma sg21563 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg4784 sg5494 - -lemma sg21564 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5647 - -lemma sg21565 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4786 sg5486 - -lemma sg21566 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4785 sg5487 - -lemma sg21567 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5495 - -lemma sg21568 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5648 - -lemma sg21569 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4823 sg5360 - -lemma sg21570 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5488 - -lemma sg21571 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5649 - -lemma sg21572 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5650 - -lemma sg21573 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5496 - -lemma sg21574 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4824 sg5359 - -lemma sg21575 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4786 sg5487 - -lemma sg21576 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5490 - -lemma sg21577 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5651 - -lemma sg21578 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5488 - -lemma sg21579 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5652 - -lemma sg21580 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5497 - -lemma sg21581 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5498 - -lemma sg21582 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5653 - -lemma sg21583 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4824 sg5361 - -lemma sg21584 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5490 - -lemma sg21585 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5654 - -lemma sg21586 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5499 - -lemma sg21587 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5655 - -lemma sg21588 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4823 sg5362 - -lemma sg21589 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4785 sg5494 - -lemma sg21590 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4784 sg5500 - -lemma sg21591 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5656 - -lemma sg21592 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4824 sg5362 - -lemma sg21593 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4786 sg5494 - -lemma sg21594 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5495 - -lemma sg21595 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5657 - -lemma sg21596 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4853 sg5275 - -lemma sg21597 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5658 - -lemma sg21598 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4824 sg5363 - -lemma sg21599 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5495 - -lemma sg21600 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4718 sg5659 - -lemma sg21601 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4854 sg5276 - -lemma sg21602 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4788 sg5466 - -lemma sg21603 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4823 sg5364 - -lemma sg21604 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4785 sg5500 - -lemma sg21605 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4824 sg5364 - -lemma sg21606 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4786 sg5500 - -lemma sg21607 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4828 sg5354 - -lemma sg21608 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4788 sg5468 - -lemma sg21609 : RowSquare [10,9,3,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4814 sg5506 - -lemma sg21610 : RowSquare [10,9,3,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4814 sg5505 - -lemma sg21611 : RowSquare [10,9,3,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4814 sg5504 - -lemma sg21612 : RowSquare [10,9,3,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4814 sg5503 - -lemma sg21613 : RowSquare [10,9,3,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg4814 sg5502 - -lemma sg21614 : RowSquare [10,9,3,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4814 sg5501 - -lemma sg21615 : RowSquare [8,8,3,3,2,2,2,2,2,2,1,1] [6,5,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg15266 - -lemma sg21616 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg20771 - -lemma sg21617 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg20772 - -lemma sg21618 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg20773 - -lemma sg21619 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg20774 - -lemma sg21620 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg43 sg20775 - -lemma sg21621 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [6,6,6,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg15692 - -lemma sg21622 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg20770 - -lemma sg21623 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg20771 - -lemma sg21624 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg20772 - -lemma sg21625 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg20773 - -lemma sg21626 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg20774 - -lemma sg21627 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg44 sg20775 - -lemma sg21628 : RowSquare [10,8,2,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg21101 - -lemma sg21629 : RowSquare [10,8,2,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg21102 - -lemma sg21630 : RowSquare [10,8,2,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg21103 - -lemma sg21631 : RowSquare [10,8,2,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg21104 - -lemma sg21632 : RowSquare [10,8,2,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg15 sg21105 - -lemma sg21633 : RowSquare [10,8,2,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg15 sg21106 - -lemma sg21634 : RowSquare [10,9,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3949 sg8009 - -lemma sg21635 : RowSquare [10,9,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3952 sg8009 - -lemma sg21636 : RowSquare [10,9,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3956 sg8009 - -lemma sg21637 : RowSquare [11,9,2,2,2,2,2,2,2,1,1] [3,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5671 sg5413 - -lemma sg21638 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg20776 - -lemma sg21639 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg20777 - -lemma sg21640 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg20778 - -lemma sg21641 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg20779 - -lemma sg21642 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg20780 - -lemma sg21643 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg80 sg20781 - -lemma sg21644 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,6,5,5,5,4] := by - exact rowSquare_join (by decide) sg4782 sg7993 - -lemma sg21645 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,6,6,6,3,2,2] := by - exact rowSquare_join (by decide) sg74 sg20784 - -lemma sg21646 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,6,6,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg20785 - -lemma sg21647 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,6,6,6,5,1,1] := by - exact rowSquare_join (by decide) sg74 sg20786 - -lemma sg21648 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,6,6,6,5,2] := by - exact rowSquare_join (by decide) sg74 sg20787 - -lemma sg21649 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,6,6,6,6,1] := by - exact rowSquare_join (by decide) sg74 sg20788 - -lemma sg21650 : RowSquare [9,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg21203 - -lemma sg21651 : RowSquare [9,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg21204 - -lemma sg21652 : RowSquare [9,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg21205 - -lemma sg21653 : RowSquare [9,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg21206 - -lemma sg21654 : RowSquare [9,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg21207 - -lemma sg21655 : RowSquare [9,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19 sg21208 - -lemma sg21656 : RowSquare [10,9,4,3,2,2,2,2,2,1] [10,10,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5606 sg6122 - -lemma sg21657 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg21609 - -lemma sg21658 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg21610 - -lemma sg21659 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg21611 - -lemma sg21660 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg21612 - -lemma sg21661 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg21613 - -lemma sg21662 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6 sg21614 - -lemma sg21663 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg21282 - -lemma sg21664 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg21283 - -lemma sg21665 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg21284 - -lemma sg21666 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg21285 - -lemma sg21667 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg12 sg21286 - -lemma sg21668 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg12 sg21287 - -lemma sg21669 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg12 sg21288 - -lemma sg21670 : RowSquare [11,9,3,2,2,2,2,2,2,2,1,1] [6,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3 sg21637 - -lemma sg21671 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [7,7,7,7,7,1,1,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6788 - -lemma sg21672 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [7,7,7,7,7,2,1,1] := by - exact rowSquare_join (by decide) sg5509 sg8626 - -lemma sg21673 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,4,4,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg6151 sg7540 - -lemma sg21674 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7542 - -lemma sg21675 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg6151 sg7543 - -lemma sg21676 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7545 - -lemma sg21677 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7546 - -lemma sg21678 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg6414 sg6768 - -lemma sg21679 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7547 - -lemma sg21680 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7548 - -lemma sg21681 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7549 - -lemma sg21682 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg6414 sg6769 - -lemma sg21683 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg5605 sg8409 - -lemma sg21684 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7550 - -lemma sg21685 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7551 - -lemma sg21686 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg6303 sg7303 - -lemma sg21687 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg6303 sg7304 - -lemma sg21688 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg5605 sg8410 - -lemma sg21689 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7492 - -lemma sg21690 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg6180 sg7486 - -lemma sg21691 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg4696 sg10842 - -lemma sg21692 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg6480 sg6629 - -lemma sg21693 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg4696 sg10843 - -lemma sg21694 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg4806 sg9652 - -lemma sg21695 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,4,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7553 - -lemma sg21696 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7554 - -lemma sg21697 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg6297 sg7316 - -lemma sg21698 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7556 - -lemma sg21699 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7557 - -lemma sg21700 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7558 - -lemma sg21701 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7317 - -lemma sg21702 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg6418 sg6768 - -lemma sg21703 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7559 - -lemma sg21704 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7560 - -lemma sg21705 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7561 - -lemma sg21706 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7318 - -lemma sg21707 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7319 - -lemma sg21708 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg6418 sg6769 - -lemma sg21709 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7562 - -lemma sg21710 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7320 - -lemma sg21711 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7563 - -lemma sg21712 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7321 - -lemma sg21713 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,4,3,3] := by - exact rowSquare_join (by decide) sg6305 sg7303 - -lemma sg21714 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6632 - -lemma sg21715 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,2] := by - exact rowSquare_join (by decide) sg6305 sg7304 - -lemma sg21716 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg6177 sg7492 - -lemma sg21717 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6633 - -lemma sg21718 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,2] := by - exact rowSquare_join (by decide) sg6182 sg7486 - -lemma sg21719 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,5,4,1] := by - exact rowSquare_join (by decide) sg6482 sg6629 - -lemma sg21720 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6176 sg7494 - -lemma sg21721 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7564 - -lemma sg21722 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7565 - -lemma sg21723 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg6414 sg6779 - -lemma sg21724 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6780 - -lemma sg21725 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg6423 sg6768 - -lemma sg21726 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7566 - -lemma sg21727 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7567 - -lemma sg21728 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg6414 sg6782 - -lemma sg21729 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7568 - -lemma sg21730 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6783 - -lemma sg21731 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg6425 sg6768 - -lemma sg21732 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6650 - -lemma sg21733 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg6154 sg7546 - -lemma sg21734 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7569 - -lemma sg21735 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6784 - -lemma sg21736 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg6426 sg6768 - -lemma sg21737 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg6303 sg7313 - -lemma sg21738 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6652 - -lemma sg21739 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,2] := by - exact rowSquare_join (by decide) sg6475 sg6631 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 + +namespace OAI + +/-! Semigroup Nodes 52. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg21340 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg15685 + +lemma sg21341 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg15686 + +lemma sg21342 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg15687 + +lemma sg21343 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg44 sg15688 + +lemma sg21344 : RowSquare [9,8,2,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg44 sg15689 + +lemma sg21345 : RowSquare [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3264 sg8009 + +lemma sg21346 : RowSquare [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg15294 + +lemma sg21347 : RowSquare [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,5,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3268 sg8009 + +lemma sg21348 : RowSquare [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3264 sg8010 + +lemma sg21349 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,7,7,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5440 + +lemma sg21350 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,7,7,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4829 sg5348 + +lemma sg21351 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,6,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5447 + +lemma sg21352 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4789 sg5428 + +lemma sg21353 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4826 sg5350 + +lemma sg21354 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5445 + +lemma sg21355 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5448 + +lemma sg21356 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5446 + +lemma sg21357 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5449 + +lemma sg21358 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5450 + +lemma sg21359 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,7,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5447 + +lemma sg21360 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,8,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg3984 sg6123 + +lemma sg21361 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,8,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5448 + +lemma sg21362 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,8,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4831 sg5347 + +lemma sg21363 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,8,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5449 + +lemma sg21364 : RowSquare [10,8,4,3,2,2,2,2,1,1] [8,8,8,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4929 sg5011 + +lemma sg21365 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,6,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5467 + +lemma sg21366 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4854 sg5261 + +lemma sg21367 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4827 sg5350 + +lemma sg21368 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5626 + +lemma sg21369 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5471 + +lemma sg21370 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5472 + +lemma sg21371 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4851 sg5269 + +lemma sg21372 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4851 sg5270 + +lemma sg21373 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,7,7,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4929 sg5012 + +lemma sg21374 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4854 sg5264 + +lemma sg21375 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4826 sg5353 + +lemma sg21376 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5627 + +lemma sg21377 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5479 + +lemma sg21378 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5480 + +lemma sg21379 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5469 + +lemma sg21380 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5470 + +lemma sg21381 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4853 sg5267 + +lemma sg21382 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,7,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5628 + +lemma sg21383 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,7,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5481 + +lemma sg21384 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,7,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5471 + +lemma sg21385 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,7,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5472 + +lemma sg21386 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,7,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4929 sg5013 + +lemma sg21387 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,8,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5482 + +lemma sg21388 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,8,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5471 + +lemma sg21389 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,8,8,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4929 sg5014 + +lemma sg21390 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4788 sg5441 + +lemma sg21391 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4825 sg5354 + +lemma sg21392 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5473 + +lemma sg21393 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg4830 sg5349 + +lemma sg21394 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5629 + +lemma sg21395 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4788 sg5442 + +lemma sg21396 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5473 + +lemma sg21397 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4825 sg5355 + +lemma sg21398 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5630 + +lemma sg21399 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4788 sg5443 + +lemma sg21400 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5631 + +lemma sg21401 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5474 + +lemma sg21402 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5475 + +lemma sg21403 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4788 sg5444 + +lemma sg21404 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5632 + +lemma sg21405 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5476 + +lemma sg21406 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5474 + +lemma sg21407 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5477 + +lemma sg21408 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5478 + +lemma sg21409 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5633 + +lemma sg21410 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,6,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5476 + +lemma sg21411 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,6,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5479 + +lemma sg21412 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,6,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5480 + +lemma sg21413 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,6,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5478 + +lemma sg21414 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4788 sg5448 + +lemma sg21415 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5481 + +lemma sg21416 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4929 sg5015 + +lemma sg21417 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,8,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5482 + +lemma sg21418 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,8,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4929 sg5016 + +lemma sg21419 : RowSquare [10,8,4,3,2,2,2,2,1,1] [9,9,9,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4929 sg5017 + +lemma sg21420 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg25 sg15651 + +lemma sg21421 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg25 sg15652 + +lemma sg21422 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg15653 + +lemma sg21423 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg24 sg15654 + +lemma sg21424 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg24 sg15655 + +lemma sg21425 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg11731 + +lemma sg21426 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg72 sg15245 + +lemma sg21427 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg72 sg15246 + +lemma sg21428 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4755 sg5524 + +lemma sg21429 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5451 + +lemma sg21430 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4719 sg5621 + +lemma sg21431 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3935 sg6357 + +lemma sg21432 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4756 sg5524 + +lemma sg21433 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5452 + +lemma sg21434 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4790 sg5431 + +lemma sg21435 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4720 sg5617 + +lemma sg21436 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4757 sg5524 + +lemma sg21437 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5453 + +lemma sg21438 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4790 sg5432 + +lemma sg21439 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4793 sg5424 + +lemma sg21440 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4722 sg5615 + +lemma sg21441 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5454 + +lemma sg21442 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4790 sg5433 + +lemma sg21443 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4793 sg5425 + +lemma sg21444 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg4795 sg5414 + +lemma sg21445 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4857 sg5240 + +lemma sg21446 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4795 sg5415 + +lemma sg21447 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg3988 sg6118 + +lemma sg21448 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg4739 sg5525 + +lemma sg21449 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg11732 + +lemma sg21450 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg73 sg15245 + +lemma sg21451 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg73 sg15246 + +lemma sg21452 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4758 sg5524 + +lemma sg21453 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5455 + +lemma sg21454 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4719 sg5622 + +lemma sg21455 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3935 sg6358 + +lemma sg21456 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4759 sg5524 + +lemma sg21457 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5456 + +lemma sg21458 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4790 sg5434 + +lemma sg21459 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4720 sg5618 + +lemma sg21460 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4760 sg5524 + +lemma sg21461 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5457 + +lemma sg21462 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4738 sg5578 + +lemma sg21463 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4791 sg5431 + +lemma sg21464 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4721 sg5617 + +lemma sg21465 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4761 sg5524 + +lemma sg21466 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5458 + +lemma sg21467 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4738 sg5579 + +lemma sg21468 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4791 sg5432 + +lemma sg21469 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4794 sg5424 + +lemma sg21470 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4738 sg5580 + +lemma sg21471 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4855 sg5258 + +lemma sg21472 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4794 sg5425 + +lemma sg21473 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg4718 sg5634 + +lemma sg21474 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4858 sg5240 + +lemma sg21475 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg4796 sg5415 + +lemma sg21476 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4762 sg5524 + +lemma sg21477 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5459 + +lemma sg21478 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4790 sg5435 + +lemma sg21479 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4720 sg5619 + +lemma sg21480 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4763 sg5524 + +lemma sg21481 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5460 + +lemma sg21482 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4735 sg5588 + +lemma sg21483 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4793 sg5426 + +lemma sg21484 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4722 sg5616 + +lemma sg21485 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4764 sg5524 + +lemma sg21486 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5461 + +lemma sg21487 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4735 sg5589 + +lemma sg21488 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4734 sg5595 + +lemma sg21489 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4873 sg5128 + +lemma sg21490 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5462 + +lemma sg21491 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4735 sg5590 + +lemma sg21492 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4849 sg5271 + +lemma sg21493 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4792 sg5432 + +lemma sg21494 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg4784 sg5483 + +lemma sg21495 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4849 sg5272 + +lemma sg21496 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4873 sg5129 + +lemma sg21497 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg4718 sg5635 + +lemma sg21498 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg4859 sg5240 + +lemma sg21499 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4765 sg5524 + +lemma sg21500 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5463 + +lemma sg21501 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4790 sg5436 + +lemma sg21502 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4736 sg5588 + +lemma sg21503 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4795 sg5421 + +lemma sg21504 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4766 sg5524 + +lemma sg21505 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5464 + +lemma sg21506 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4790 sg5437 + +lemma sg21507 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4734 sg5596 + +lemma sg21508 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4737 sg5588 + +lemma sg21509 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4822 sg5357 + +lemma sg21510 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4790 sg5438 + +lemma sg21511 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4736 sg5590 + +lemma sg21512 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4850 sg5271 + +lemma sg21513 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg4784 sg5484 + +lemma sg21514 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4850 sg5272 + +lemma sg21515 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5636 + +lemma sg21516 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5465 + +lemma sg21517 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4790 sg5439 + +lemma sg21518 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4734 sg5597 + +lemma sg21519 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4737 sg5589 + +lemma sg21520 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4822 sg5358 + +lemma sg21521 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4734 sg5598 + +lemma sg21522 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4737 sg5590 + +lemma sg21523 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5485 + +lemma sg21524 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5637 + +lemma sg21525 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4723 sg5615 + +lemma sg21526 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,4,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5638 + +lemma sg21527 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4767 sg5524 + +lemma sg21528 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5466 + +lemma sg21529 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4719 sg5623 + +lemma sg21530 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg3935 sg6359 + +lemma sg21531 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg4784 sg5486 + +lemma sg21532 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg4718 sg5639 + +lemma sg21533 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg4860 sg5240 + +lemma sg21534 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4785 sg5483 + +lemma sg21535 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg4784 sg5487 + +lemma sg21536 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5640 + +lemma sg21537 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4823 sg5357 + +lemma sg21538 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4785 sg5484 + +lemma sg21539 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5488 + +lemma sg21540 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5641 + +lemma sg21541 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5485 + +lemma sg21542 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5642 + +lemma sg21543 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5489 + +lemma sg21544 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4786 sg5483 + +lemma sg21545 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4822 sg5361 + +lemma sg21546 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5490 + +lemma sg21547 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5643 + +lemma sg21548 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4786 sg5484 + +lemma sg21549 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4851 sg5273 + +lemma sg21550 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5644 + +lemma sg21551 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5645 + +lemma sg21552 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5491 + +lemma sg21553 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4856 sg5259 + +lemma sg21554 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5646 + +lemma sg21555 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5492 + +lemma sg21556 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5493 + +lemma sg21557 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4851 sg5274 + +lemma sg21558 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4768 sg5524 + +lemma sg21559 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4787 sg5468 + +lemma sg21560 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4790 sg5441 + +lemma sg21561 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg3935 sg6360 + +lemma sg21562 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4785 sg5486 + +lemma sg21563 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg4784 sg5494 + +lemma sg21564 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5647 + +lemma sg21565 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4786 sg5486 + +lemma sg21566 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4785 sg5487 + +lemma sg21567 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5495 + +lemma sg21568 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5648 + +lemma sg21569 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4823 sg5360 + +lemma sg21570 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5488 + +lemma sg21571 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5649 + +lemma sg21572 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5650 + +lemma sg21573 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5496 + +lemma sg21574 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4824 sg5359 + +lemma sg21575 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4786 sg5487 + +lemma sg21576 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5490 + +lemma sg21577 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5651 + +lemma sg21578 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5488 + +lemma sg21579 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5652 + +lemma sg21580 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5497 + +lemma sg21581 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5498 + +lemma sg21582 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5653 + +lemma sg21583 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4824 sg5361 + +lemma sg21584 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5490 + +lemma sg21585 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5654 + +lemma sg21586 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5499 + +lemma sg21587 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,6,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5655 + +lemma sg21588 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4823 sg5362 + +lemma sg21589 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4785 sg5494 + +lemma sg21590 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4784 sg5500 + +lemma sg21591 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5656 + +lemma sg21592 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4824 sg5362 + +lemma sg21593 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4786 sg5494 + +lemma sg21594 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5495 + +lemma sg21595 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5657 + +lemma sg21596 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4853 sg5275 + +lemma sg21597 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5658 + +lemma sg21598 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4824 sg5363 + +lemma sg21599 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5495 + +lemma sg21600 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4718 sg5659 + +lemma sg21601 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4854 sg5276 + +lemma sg21602 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4788 sg5466 + +lemma sg21603 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4823 sg5364 + +lemma sg21604 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4785 sg5500 + +lemma sg21605 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4824 sg5364 + +lemma sg21606 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4786 sg5500 + +lemma sg21607 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4828 sg5354 + +lemma sg21608 : RowSquare [10,8,4,3,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4788 sg5468 + +lemma sg21609 : RowSquare [10,9,3,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4814 sg5506 + +lemma sg21610 : RowSquare [10,9,3,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4814 sg5505 + +lemma sg21611 : RowSquare [10,9,3,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4814 sg5504 + +lemma sg21612 : RowSquare [10,9,3,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4814 sg5503 + +lemma sg21613 : RowSquare [10,9,3,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg4814 sg5502 + +lemma sg21614 : RowSquare [10,9,3,2,2,2,2,2,2,1] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4814 sg5501 + +lemma sg21615 : RowSquare [8,8,3,3,2,2,2,2,2,2,1,1] [6,5,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg15266 + +lemma sg21616 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg20771 + +lemma sg21617 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg20772 + +lemma sg21618 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg20773 + +lemma sg21619 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg20774 + +lemma sg21620 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [6,3,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg43 sg20775 + +lemma sg21621 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [6,6,6,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg15692 + +lemma sg21622 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg20770 + +lemma sg21623 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg20771 + +lemma sg21624 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg20772 + +lemma sg21625 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg20773 + +lemma sg21626 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg20774 + +lemma sg21627 : RowSquare [9,8,3,2,2,2,2,2,2,2,1,1] [7,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg44 sg20775 + +lemma sg21628 : RowSquare [10,8,2,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg21101 + +lemma sg21629 : RowSquare [10,8,2,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg21102 + +lemma sg21630 : RowSquare [10,8,2,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg21103 + +lemma sg21631 : RowSquare [10,8,2,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg21104 + +lemma sg21632 : RowSquare [10,8,2,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg15 sg21105 + +lemma sg21633 : RowSquare [10,8,2,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg15 sg21106 + +lemma sg21634 : RowSquare [10,9,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,4,4,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3949 sg8009 + +lemma sg21635 : RowSquare [10,9,3,2,2,1,1,1,1,1,1,1,1,1,1] [5,5,5,5,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3952 sg8009 + +lemma sg21636 : RowSquare [10,9,3,2,2,1,1,1,1,1,1,1,1,1,1] [6,6,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3956 sg8009 + +lemma sg21637 : RowSquare [11,9,2,2,2,2,2,2,2,1,1] [3,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5671 sg5413 + +lemma sg21638 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg20776 + +lemma sg21639 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg20777 + +lemma sg21640 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg20778 + +lemma sg21641 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg20779 + +lemma sg21642 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg20780 + +lemma sg21643 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg80 sg20781 + +lemma sg21644 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,6,5,5,5,4] := by + exact rowSquare_join (by decide) sg4782 sg7993 + +lemma sg21645 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,6,6,6,3,2,2] := by + exact rowSquare_join (by decide) sg74 sg20784 + +lemma sg21646 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,6,6,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg20785 + +lemma sg21647 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,6,6,6,5,1,1] := by + exact rowSquare_join (by decide) sg74 sg20786 + +lemma sg21648 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,6,6,6,5,2] := by + exact rowSquare_join (by decide) sg74 sg20787 + +lemma sg21649 : RowSquare [9,8,3,3,2,2,2,2,2,2,1,1] [6,6,6,6,6,6,1] := by + exact rowSquare_join (by decide) sg74 sg20788 + +lemma sg21650 : RowSquare [9,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg21203 + +lemma sg21651 : RowSquare [9,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg21204 + +lemma sg21652 : RowSquare [9,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg21205 + +lemma sg21653 : RowSquare [9,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg21206 + +lemma sg21654 : RowSquare [9,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg21207 + +lemma sg21655 : RowSquare [9,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19 sg21208 + +lemma sg21656 : RowSquare [10,9,4,3,2,2,2,2,2,1] [10,10,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5606 sg6122 + +lemma sg21657 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg21609 + +lemma sg21658 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg21610 + +lemma sg21659 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg21611 + +lemma sg21660 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg21612 + +lemma sg21661 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg21613 + +lemma sg21662 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [5,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6 sg21614 + +lemma sg21663 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg21282 + +lemma sg21664 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg21283 + +lemma sg21665 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg21284 + +lemma sg21666 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg21285 + +lemma sg21667 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg12 sg21286 + +lemma sg21668 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg12 sg21287 + +lemma sg21669 : RowSquare [10,9,3,2,2,2,2,2,2,2,1,1] [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg12 sg21288 + +lemma sg21670 : RowSquare [11,9,3,2,2,2,2,2,2,2,1,1] [6,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3 sg21637 + +lemma sg21671 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [7,7,7,7,7,1,1,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6788 + +lemma sg21672 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [7,7,7,7,7,2,1,1] := by + exact rowSquare_join (by decide) sg5509 sg8626 + +lemma sg21673 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,4,4,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg6151 sg7540 + +lemma sg21674 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7542 + +lemma sg21675 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg6151 sg7543 + +lemma sg21676 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7545 + +lemma sg21677 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7546 + +lemma sg21678 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg6414 sg6768 + +lemma sg21679 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7547 + +lemma sg21680 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7548 + +lemma sg21681 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7549 + +lemma sg21682 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg6414 sg6769 + +lemma sg21683 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg5605 sg8409 + +lemma sg21684 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7550 + +lemma sg21685 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7551 + +lemma sg21686 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg6303 sg7303 + +lemma sg21687 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg6303 sg7304 + +lemma sg21688 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg5605 sg8410 + +lemma sg21689 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7492 + +lemma sg21690 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg6180 sg7486 + +lemma sg21691 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg4696 sg10842 + +lemma sg21692 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg6480 sg6629 + +lemma sg21693 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg4696 sg10843 + +lemma sg21694 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg4806 sg9652 + +lemma sg21695 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,4,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7553 + +lemma sg21696 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7554 + +lemma sg21697 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg6297 sg7316 + +lemma sg21698 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7556 + +lemma sg21699 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7557 + +lemma sg21700 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7558 + +lemma sg21701 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7317 + +lemma sg21702 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg6418 sg6768 + +lemma sg21703 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7559 + +lemma sg21704 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7560 + +lemma sg21705 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7561 + +lemma sg21706 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7318 + +lemma sg21707 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7319 + +lemma sg21708 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg6418 sg6769 + +lemma sg21709 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7562 + +lemma sg21710 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7320 + +lemma sg21711 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7563 + +lemma sg21712 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7321 + +lemma sg21713 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,4,3,3] := by + exact rowSquare_join (by decide) sg6305 sg7303 + +lemma sg21714 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6632 + +lemma sg21715 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,2] := by + exact rowSquare_join (by decide) sg6305 sg7304 + +lemma sg21716 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg6177 sg7492 + +lemma sg21717 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6633 + +lemma sg21718 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,2] := by + exact rowSquare_join (by decide) sg6182 sg7486 + +lemma sg21719 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,5,5,5,5,4,1] := by + exact rowSquare_join (by decide) sg6482 sg6629 + +lemma sg21720 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6176 sg7494 + +lemma sg21721 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7564 + +lemma sg21722 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7565 + +lemma sg21723 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg6414 sg6779 + +lemma sg21724 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6780 + +lemma sg21725 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg6423 sg6768 + +lemma sg21726 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7566 + +lemma sg21727 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7567 + +lemma sg21728 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg6414 sg6782 + +lemma sg21729 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7568 + +lemma sg21730 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6783 + +lemma sg21731 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg6425 sg6768 + +lemma sg21732 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6650 + +lemma sg21733 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg6154 sg7546 + +lemma sg21734 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7569 + +lemma sg21735 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6784 + +lemma sg21736 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg6426 sg6768 + +lemma sg21737 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg6303 sg7313 + +lemma sg21738 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6652 + +lemma sg21739 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,2] := by + exact rowSquare_join (by decide) sg6475 sg6631 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes53.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes53.lean index 2f757754ee1b66b467676058d7c15351b9e56778..037d9995a3536b0390db4d0770fb0a3ee0cc99e3 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes53.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes53.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 - -namespace OAI - -/-! Semigroup Nodes 53. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg21740 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg6475 sg6632 - -lemma sg21741 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6653 - -lemma sg21742 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg6162 sg7522 - -lemma sg21743 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg6475 sg6633 - -lemma sg21744 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7570 - -lemma sg21745 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6303 sg7314 - -lemma sg21746 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7571 - -lemma sg21747 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6785 - -lemma sg21748 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,3,3,3] := by - exact rowSquare_join (by decide) sg5605 sg8411 - -lemma sg21749 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6786 - -lemma sg21750 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6794 - -lemma sg21751 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,2] := by - exact rowSquare_join (by decide) sg6154 sg7548 - -lemma sg21752 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,4,4,1] := by - exact rowSquare_join (by decide) sg6154 sg7549 - -lemma sg21753 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7572 - -lemma sg21754 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6787 - -lemma sg21755 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6794 - -lemma sg21756 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,2] := by - exact rowSquare_join (by decide) sg6154 sg7550 - -lemma sg21757 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg6300 sg7321 - -lemma sg21758 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,4,2,2] := by - exact rowSquare_join (by decide) sg6309 sg7303 - -lemma sg21759 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,4,3,1] := by - exact rowSquare_join (by decide) sg6154 sg7551 - -lemma sg21760 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg6178 sg7492 - -lemma sg21761 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,5,2,1] := by - exact rowSquare_join (by decide) sg6186 sg7486 - -lemma sg21762 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6788 - -lemma sg21763 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg6301 sg7321 - -lemma sg21764 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,3,2,2] := by - exact rowSquare_join (by decide) sg6310 sg7303 - -lemma sg21765 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,3,3,1] := by - exact rowSquare_join (by decide) sg6310 sg7304 - -lemma sg21766 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg6179 sg7492 - -lemma sg21767 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,4,2,1] := by - exact rowSquare_join (by decide) sg6187 sg7486 - -lemma sg21768 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,5,1,1] := by - exact rowSquare_join (by decide) sg6162 sg7525 - -lemma sg21769 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,4,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7574 - -lemma sg21770 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,4,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7575 - -lemma sg21771 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7576 - -lemma sg21772 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7322 - -lemma sg21773 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg6418 sg6771 - -lemma sg21774 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7577 - -lemma sg21775 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7578 - -lemma sg21776 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7579 - -lemma sg21777 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7323 - -lemma sg21778 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7324 - -lemma sg21779 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg6418 sg6773 - -lemma sg21780 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7580 - -lemma sg21781 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7581 - -lemma sg21782 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7325 - -lemma sg21783 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7582 - -lemma sg21784 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7326 - -lemma sg21785 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg6418 sg6775 - -lemma sg21786 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6634 - -lemma sg21787 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg6418 sg6776 - -lemma sg21788 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7583 - -lemma sg21789 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7327 - -lemma sg21790 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg6418 sg6777 - -lemma sg21791 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7328 - -lemma sg21792 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6635 - -lemma sg21793 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,2] := by - exact rowSquare_join (by decide) sg6305 sg7308 - -lemma sg21794 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg6313 sg7304 - -lemma sg21795 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg6343 sg7286 - -lemma sg21796 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg6162 sg7528 - -lemma sg21797 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg6189 sg7486 - -lemma sg21798 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6176 sg7495 - -lemma sg21799 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7584 - -lemma sg21800 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7585 - -lemma sg21801 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7331 - -lemma sg21802 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7586 - -lemma sg21803 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7332 - -lemma sg21804 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg6418 sg6779 - -lemma sg21805 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6656 - -lemma sg21806 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg6418 sg6780 - -lemma sg21807 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7587 - -lemma sg21808 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7333 - -lemma sg21809 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7588 - -lemma sg21810 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7334 - -lemma sg21811 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg6418 sg6782 - -lemma sg21812 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7335 - -lemma sg21813 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6658 - -lemma sg21814 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg6418 sg6783 - -lemma sg21815 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg6154 sg7558 - -lemma sg21816 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7589 - -lemma sg21817 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7336 - -lemma sg21818 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6659 - -lemma sg21819 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg6418 sg6784 - -lemma sg21820 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6660 - -lemma sg21821 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg6305 sg7313 - -lemma sg21822 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg6475 sg6635 - -lemma sg21823 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg6162 sg7530 - -lemma sg21824 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg6344 sg7286 - -lemma sg21825 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7590 - -lemma sg21826 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7337 - -lemma sg21827 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,3,3,3,3] := by - exact rowSquare_join (by decide) sg6305 sg7314 - -lemma sg21828 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7591 - -lemma sg21829 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7338 - -lemma sg21830 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6639 - -lemma sg21831 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,2] := by - exact rowSquare_join (by decide) sg6418 sg6785 - -lemma sg21832 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6640 - -lemma sg21833 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,4,2,2] := by - exact rowSquare_join (by decide) sg6418 sg6786 - -lemma sg21834 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,4,3,1] := by - exact rowSquare_join (by decide) sg6154 sg7561 - -lemma sg21835 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7339 - -lemma sg21836 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6641 - -lemma sg21837 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,5,3,2,2] := by - exact rowSquare_join (by decide) sg6418 sg6787 - -lemma sg21838 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,5,3,3,1] := by - exact rowSquare_join (by decide) sg6154 sg7562 - -lemma sg21839 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg6300 sg7328 - -lemma sg21840 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,5,4,2,1] := by - exact rowSquare_join (by decide) sg6154 sg7563 - -lemma sg21841 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6416 sg6788 - -lemma sg21842 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6417 sg6788 - -lemma sg21843 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6642 - -lemma sg21844 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,6,2,2,2] := by - exact rowSquare_join (by decide) sg6418 sg6788 - -lemma sg21845 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg6301 sg7328 - -lemma sg21846 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6176 sg7496 - -lemma sg21847 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7497 - -lemma sg21848 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6435 sg6768 - -lemma sg21849 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7498 - -lemma sg21850 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg6472 sg6661 - -lemma sg21851 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg6436 sg6768 - -lemma sg21852 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg6422 sg6779 - -lemma sg21853 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6662 - -lemma sg21854 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg6423 sg6779 - -lemma sg21855 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg6475 sg6636 - -lemma sg21856 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7499 - -lemma sg21857 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6472 sg6663 - -lemma sg21858 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg6437 sg6768 - -lemma sg21859 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7500 - -lemma sg21860 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg6409 sg6797 - -lemma sg21861 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6664 - -lemma sg21862 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg6154 sg7564 - -lemma sg21863 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6665 - -lemma sg21864 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg6425 sg6779 - -lemma sg21865 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg6154 sg7565 - -lemma sg21866 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg6410 sg6797 - -lemma sg21867 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6666 - -lemma sg21868 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg6426 sg6779 - -lemma sg21869 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg6475 sg6638 - -lemma sg21870 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg6306 sg7313 - -lemma sg21871 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7644 - -lemma sg21872 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7099 - -lemma sg21873 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7501 - -lemma sg21874 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7337 - -lemma sg21875 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6409 sg6799 - -lemma sg21876 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6667 - -lemma sg21877 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg6154 sg7566 - -lemma sg21878 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7334 - -lemma sg21879 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg6410 sg6799 - -lemma sg21880 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7338 - -lemma sg21881 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6668 - -lemma sg21882 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg6425 sg6782 - -lemma sg21883 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6801 - -lemma sg21884 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7339 - -lemma sg21885 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6669 - -lemma sg21886 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg6426 sg6782 - -lemma sg21887 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6802 - -lemma sg21888 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6421 sg6788 - -lemma sg21889 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg6474 sg6642 - -lemma sg21890 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6307 sg7314 - -lemma sg21891 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7502 - -lemma sg21892 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7337 - -lemma sg21893 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6308 sg7314 - -lemma sg21894 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6424 sg6786 - -lemma sg21895 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6803 - -lemma sg21896 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,3,3,2,2] := by - exact rowSquare_join (by decide) sg6309 sg7314 - -lemma sg21897 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7338 - -lemma sg21898 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6803 - -lemma sg21899 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,4,2,2,2] := by - exact rowSquare_join (by decide) sg6310 sg7314 - -lemma sg21900 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6804 - -lemma sg21901 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7339 - -lemma sg21902 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6805 - -lemma sg21903 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6805 - -lemma sg21904 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6165 sg7514 - -lemma sg21905 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg6297 sg7340 - -lemma sg21906 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg6428 sg6770 - -lemma sg21907 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7341 - -lemma sg21908 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7342 - -lemma sg21909 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg6429 sg6771 - -lemma sg21910 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6166 sg7514 - -lemma sg21911 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6297 sg7344 - -lemma sg21912 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg6407 sg6806 - -lemma sg21913 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7345 - -lemma sg21914 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg6428 sg6772 - -lemma sg21915 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7346 - -lemma sg21916 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg6432 sg6771 - -lemma sg21917 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6671 - -lemma sg21918 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg6429 sg6773 - -lemma sg21919 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6433 sg6770 - -lemma sg21920 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7347 - -lemma sg21921 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg6409 sg6806 - -lemma sg21922 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7348 - -lemma sg21923 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg6434 sg6771 - -lemma sg21924 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7349 - -lemma sg21925 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6807 - -lemma sg21926 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg6154 sg7575 - -lemma sg21927 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg6410 sg6806 - -lemma sg21928 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7350 - -lemma sg21929 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6807 - -lemma sg21930 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg6429 sg6777 - -lemma sg21931 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg6312 sg7308 - -lemma sg21932 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg6373 sg7036 - -lemma sg21933 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg6345 sg7286 - -lemma sg21934 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6297 sg7351 - -lemma sg21935 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6407 sg6809 - -lemma sg21936 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7352 - -lemma sg21937 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg6428 sg6778 - -lemma sg21938 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7353 - -lemma sg21939 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg6436 sg6771 - -lemma sg21940 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7354 - -lemma sg21941 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6673 - -lemma sg21942 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg6429 sg6779 - -lemma sg21943 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6409 sg6809 - -lemma sg21944 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7355 - -lemma sg21945 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg6437 sg6771 - -lemma sg21946 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg6410 sg6809 - -lemma sg21947 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7356 - -lemma sg21948 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6675 - -lemma sg21949 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg6154 sg7578 - -lemma sg21950 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6676 - -lemma sg21951 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg6432 sg6775 - -lemma sg21952 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7357 - -lemma sg21953 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6677 - -lemma sg21954 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg6432 sg6777 - -lemma sg21955 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg6312 sg7313 - -lemma sg21956 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2499 sg12696 - -lemma sg21957 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6233 sg7481 - -lemma sg21958 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5294 sg8787 - -lemma sg21959 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7658 - -lemma sg21960 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6408 sg6810 - -lemma sg21961 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7658 - -lemma sg21962 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5295 sg8787 - -lemma sg21963 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7093 - -lemma sg21964 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6408 sg6811 - -lemma sg21965 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7347 - -lemma sg21966 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6433 sg6774 - -lemma sg21967 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7093 - -lemma sg21968 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7358 - -lemma sg21969 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7358 - -lemma sg21970 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6476 sg6634 - -lemma sg21971 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg6154 sg7580 - -lemma sg21972 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7094 - -lemma sg21973 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7094 - -lemma sg21974 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7359 - -lemma sg21975 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7359 - -lemma sg21976 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7349 - -lemma sg21977 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6811 - -lemma sg21978 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6812 - -lemma sg21979 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6427 sg6788 - -lemma sg21980 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7350 - -lemma sg21981 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6811 - -lemma sg21982 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6813 - -lemma sg21983 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6371 sg7044 - -lemma sg21984 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg6428 sg6788 - -lemma sg21985 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6315 sg7305 - -lemma sg21986 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6298 sg7351 - -lemma sg21987 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7360 - -lemma sg21988 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6407 sg6814 - -lemma sg21989 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7360 - -lemma sg21990 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6315 sg7306 - -lemma sg21991 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6299 sg7351 - -lemma sg21992 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7352 - -lemma sg21993 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6409 sg6814 - -lemma sg21994 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7361 - -lemma sg21995 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7361 - -lemma sg21996 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg5508 sg8637 - -lemma sg21997 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6315 sg7307 - -lemma sg21998 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg6410 sg6814 - -lemma sg21999 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7362 - -lemma sg22000 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7362 - -lemma sg22001 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6678 - -lemma sg22002 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg6436 sg6773 - -lemma sg22003 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7354 - -lemma sg22004 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6679 - -lemma sg22005 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6372 sg7039 - -lemma sg22006 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7352 - -lemma sg22007 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6431 sg6781 - -lemma sg22008 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7363 - -lemma sg22009 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7363 - -lemma sg22010 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6680 - -lemma sg22011 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7364 - -lemma sg22012 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7364 - -lemma sg22013 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7356 - -lemma sg22014 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6681 - -lemma sg22015 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6815 - -lemma sg22016 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7357 - -lemma sg22017 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6682 - -lemma sg22018 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6815 - -lemma sg22019 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6314 sg7314 - -lemma sg22020 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6433 sg6781 - -lemma sg22021 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7365 - -lemma sg22022 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7365 - -lemma sg22023 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7358 - -lemma sg22024 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6683 - -lemma sg22025 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7359 - -lemma sg22026 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6684 - -lemma sg22027 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6816 - -lemma sg22028 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7357 - -lemma sg22029 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6817 - -lemma sg22030 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6817 - -lemma sg22031 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6464 sg6703 - -lemma sg22032 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6177 sg7502 - -lemma sg22033 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7358 - -lemma sg22034 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6476 sg6639 - -lemma sg22035 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6818 - -lemma sg22036 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7359 - -lemma sg22037 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6819 - -lemma sg22038 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6819 - -lemma sg22039 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4344 sg11139 - -lemma sg22040 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6315 sg7309 - -lemma sg22041 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7360 - -lemma sg22042 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg5603 sg8412 - -lemma sg22043 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6315 sg7310 - -lemma sg22044 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6472 sg6685 - -lemma sg22045 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg554 sg15627 - -lemma sg22046 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6315 sg7311 - -lemma sg22047 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7360 - -lemma sg22048 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6435 sg6778 - -lemma sg22049 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7361 - -lemma sg22050 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6300 sg7360 - -lemma sg22051 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6686 - -lemma sg22052 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6315 sg7312 - -lemma sg22053 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg6301 sg7360 - -lemma sg22054 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7362 - -lemma sg22055 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6687 - -lemma sg22056 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg5603 sg8413 - -lemma sg22057 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6315 sg7314 - -lemma sg22058 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6435 sg6781 - -lemma sg22059 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7361 - -lemma sg22060 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6477 sg6637 - -lemma sg22061 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7363 - -lemma sg22062 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6688 - -lemma sg22063 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7364 - -lemma sg22064 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6689 - -lemma sg22065 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6821 - -lemma sg22066 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6315 sg7315 - -lemma sg22067 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6821 - -lemma sg22068 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6464 sg6704 - -lemma sg22069 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6316 sg7314 - -lemma sg22070 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7365 - -lemma sg22071 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6690 - -lemma sg22072 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6822 - -lemma sg22073 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7364 - -lemma sg22074 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6823 - -lemma sg22075 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6823 - -lemma sg22076 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6447 sg6766 - -lemma sg22077 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,7,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6407 sg6825 - -lemma sg22078 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7365 - -lemma sg22079 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,7,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6824 - -lemma sg22080 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,7,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6824 - -lemma sg22081 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,8,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5756 sg8019 - -lemma sg22082 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,8,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6409 sg6825 - -lemma sg22083 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,8,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6410 sg6825 - -lemma sg22084 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7593 - -lemma sg22085 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg6151 sg7594 - -lemma sg22086 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,4,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7596 - -lemma sg22087 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7597 - -lemma sg22088 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg6297 sg7366 - -lemma sg22089 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7599 - -lemma sg22090 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7600 - -lemma sg22091 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7601 - -lemma sg22092 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg6414 sg6791 - -lemma sg22093 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7602 - -lemma sg22094 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7603 - -lemma sg22095 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7604 - -lemma sg22096 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg6414 sg6793 - -lemma sg22097 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6794 - -lemma sg22098 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7605 - -lemma sg22099 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg6414 sg6795 - -lemma sg22100 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7606 - -lemma sg22101 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg6303 sg7321 - -lemma sg22102 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg6480 sg6632 - -lemma sg22103 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg6180 sg7492 - -lemma sg22104 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg6480 sg6633 - -lemma sg22105 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,4,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7607 - -lemma sg22106 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,4,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7608 - -lemma sg22107 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7609 - -lemma sg22108 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7367 - -lemma sg22109 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7610 - -lemma sg22110 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7611 - -lemma sg22111 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7612 - -lemma sg22112 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7368 - -lemma sg22113 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7369 - -lemma sg22114 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7613 - -lemma sg22115 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7614 - -lemma sg22116 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7370 - -lemma sg22117 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7615 - -lemma sg22118 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7371 - -lemma sg22119 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6650 - -lemma sg22120 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7616 - -lemma sg22121 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7372 - -lemma sg22122 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7373 - -lemma sg22123 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6652 - -lemma sg22124 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6653 - -lemma sg22125 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6176 sg7504 - -lemma sg22126 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7617 - -lemma sg22127 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7618 - -lemma sg22128 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg6414 sg6797 - -lemma sg22129 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7619 - -lemma sg22130 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6798 - -lemma sg22131 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6691 - -lemma sg22132 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7620 - -lemma sg22133 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6414 sg6799 - -lemma sg22134 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7621 - -lemma sg22135 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6800 - -lemma sg22136 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6801 - -lemma sg22137 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6692 - -lemma sg22138 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7622 - -lemma sg22139 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6802 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 + +namespace OAI + +/-! Semigroup Nodes 53. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg21740 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg6475 sg6632 + +lemma sg21741 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6653 + +lemma sg21742 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg6162 sg7522 + +lemma sg21743 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg6475 sg6633 + +lemma sg21744 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7570 + +lemma sg21745 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6303 sg7314 + +lemma sg21746 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7571 + +lemma sg21747 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6785 + +lemma sg21748 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,3,3,3] := by + exact rowSquare_join (by decide) sg5605 sg8411 + +lemma sg21749 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6786 + +lemma sg21750 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6794 + +lemma sg21751 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,2] := by + exact rowSquare_join (by decide) sg6154 sg7548 + +lemma sg21752 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,4,4,4,1] := by + exact rowSquare_join (by decide) sg6154 sg7549 + +lemma sg21753 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7572 + +lemma sg21754 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6787 + +lemma sg21755 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6794 + +lemma sg21756 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,2] := by + exact rowSquare_join (by decide) sg6154 sg7550 + +lemma sg21757 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg6300 sg7321 + +lemma sg21758 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,4,2,2] := by + exact rowSquare_join (by decide) sg6309 sg7303 + +lemma sg21759 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,4,3,1] := by + exact rowSquare_join (by decide) sg6154 sg7551 + +lemma sg21760 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg6178 sg7492 + +lemma sg21761 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,5,5,2,1] := by + exact rowSquare_join (by decide) sg6186 sg7486 + +lemma sg21762 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6788 + +lemma sg21763 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg6301 sg7321 + +lemma sg21764 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,3,2,2] := by + exact rowSquare_join (by decide) sg6310 sg7303 + +lemma sg21765 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,3,3,1] := by + exact rowSquare_join (by decide) sg6310 sg7304 + +lemma sg21766 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg6179 sg7492 + +lemma sg21767 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,4,2,1] := by + exact rowSquare_join (by decide) sg6187 sg7486 + +lemma sg21768 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,6,6,6,6,5,1,1] := by + exact rowSquare_join (by decide) sg6162 sg7525 + +lemma sg21769 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,4,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7574 + +lemma sg21770 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,4,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7575 + +lemma sg21771 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7576 + +lemma sg21772 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7322 + +lemma sg21773 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg6418 sg6771 + +lemma sg21774 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7577 + +lemma sg21775 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7578 + +lemma sg21776 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7579 + +lemma sg21777 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7323 + +lemma sg21778 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7324 + +lemma sg21779 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg6418 sg6773 + +lemma sg21780 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7580 + +lemma sg21781 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7581 + +lemma sg21782 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7325 + +lemma sg21783 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7582 + +lemma sg21784 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7326 + +lemma sg21785 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg6418 sg6775 + +lemma sg21786 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6634 + +lemma sg21787 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg6418 sg6776 + +lemma sg21788 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7583 + +lemma sg21789 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7327 + +lemma sg21790 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg6418 sg6777 + +lemma sg21791 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7328 + +lemma sg21792 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6635 + +lemma sg21793 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,2] := by + exact rowSquare_join (by decide) sg6305 sg7308 + +lemma sg21794 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg6313 sg7304 + +lemma sg21795 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg6343 sg7286 + +lemma sg21796 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg6162 sg7528 + +lemma sg21797 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,5,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg6189 sg7486 + +lemma sg21798 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6176 sg7495 + +lemma sg21799 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7584 + +lemma sg21800 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7585 + +lemma sg21801 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7331 + +lemma sg21802 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7586 + +lemma sg21803 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7332 + +lemma sg21804 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg6418 sg6779 + +lemma sg21805 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6656 + +lemma sg21806 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg6418 sg6780 + +lemma sg21807 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7587 + +lemma sg21808 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7333 + +lemma sg21809 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7588 + +lemma sg21810 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7334 + +lemma sg21811 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg6418 sg6782 + +lemma sg21812 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7335 + +lemma sg21813 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6658 + +lemma sg21814 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg6418 sg6783 + +lemma sg21815 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg6154 sg7558 + +lemma sg21816 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7589 + +lemma sg21817 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7336 + +lemma sg21818 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6659 + +lemma sg21819 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg6418 sg6784 + +lemma sg21820 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6660 + +lemma sg21821 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg6305 sg7313 + +lemma sg21822 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg6475 sg6635 + +lemma sg21823 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg6162 sg7530 + +lemma sg21824 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg6344 sg7286 + +lemma sg21825 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7590 + +lemma sg21826 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7337 + +lemma sg21827 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,3,3,3,3] := by + exact rowSquare_join (by decide) sg6305 sg7314 + +lemma sg21828 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7591 + +lemma sg21829 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7338 + +lemma sg21830 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6639 + +lemma sg21831 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,2] := by + exact rowSquare_join (by decide) sg6418 sg6785 + +lemma sg21832 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6640 + +lemma sg21833 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,4,2,2] := by + exact rowSquare_join (by decide) sg6418 sg6786 + +lemma sg21834 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,4,4,3,1] := by + exact rowSquare_join (by decide) sg6154 sg7561 + +lemma sg21835 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7339 + +lemma sg21836 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6641 + +lemma sg21837 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,5,3,2,2] := by + exact rowSquare_join (by decide) sg6418 sg6787 + +lemma sg21838 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,5,3,3,1] := by + exact rowSquare_join (by decide) sg6154 sg7562 + +lemma sg21839 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg6300 sg7328 + +lemma sg21840 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,5,4,2,1] := by + exact rowSquare_join (by decide) sg6154 sg7563 + +lemma sg21841 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6416 sg6788 + +lemma sg21842 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6417 sg6788 + +lemma sg21843 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6642 + +lemma sg21844 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,6,2,2,2] := by + exact rowSquare_join (by decide) sg6418 sg6788 + +lemma sg21845 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,6,6,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg6301 sg7328 + +lemma sg21846 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6176 sg7496 + +lemma sg21847 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7497 + +lemma sg21848 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6435 sg6768 + +lemma sg21849 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7498 + +lemma sg21850 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg6472 sg6661 + +lemma sg21851 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg6436 sg6768 + +lemma sg21852 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg6422 sg6779 + +lemma sg21853 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6662 + +lemma sg21854 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg6423 sg6779 + +lemma sg21855 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg6475 sg6636 + +lemma sg21856 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7499 + +lemma sg21857 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6472 sg6663 + +lemma sg21858 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg6437 sg6768 + +lemma sg21859 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7500 + +lemma sg21860 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg6409 sg6797 + +lemma sg21861 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6664 + +lemma sg21862 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg6154 sg7564 + +lemma sg21863 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6665 + +lemma sg21864 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg6425 sg6779 + +lemma sg21865 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg6154 sg7565 + +lemma sg21866 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg6410 sg6797 + +lemma sg21867 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6666 + +lemma sg21868 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg6426 sg6779 + +lemma sg21869 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg6475 sg6638 + +lemma sg21870 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg6306 sg7313 + +lemma sg21871 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7644 + +lemma sg21872 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7099 + +lemma sg21873 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7501 + +lemma sg21874 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7337 + +lemma sg21875 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6409 sg6799 + +lemma sg21876 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6667 + +lemma sg21877 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg6154 sg7566 + +lemma sg21878 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7334 + +lemma sg21879 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg6410 sg6799 + +lemma sg21880 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7338 + +lemma sg21881 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6668 + +lemma sg21882 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg6425 sg6782 + +lemma sg21883 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6801 + +lemma sg21884 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7339 + +lemma sg21885 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6669 + +lemma sg21886 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg6426 sg6782 + +lemma sg21887 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6802 + +lemma sg21888 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6421 sg6788 + +lemma sg21889 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg6474 sg6642 + +lemma sg21890 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6307 sg7314 + +lemma sg21891 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7502 + +lemma sg21892 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7337 + +lemma sg21893 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6308 sg7314 + +lemma sg21894 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6424 sg6786 + +lemma sg21895 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6803 + +lemma sg21896 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,3,3,2,2] := by + exact rowSquare_join (by decide) sg6309 sg7314 + +lemma sg21897 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7338 + +lemma sg21898 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6803 + +lemma sg21899 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,4,2,2,2] := by + exact rowSquare_join (by decide) sg6310 sg7314 + +lemma sg21900 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6804 + +lemma sg21901 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7339 + +lemma sg21902 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6805 + +lemma sg21903 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,7,7,7,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6805 + +lemma sg21904 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6165 sg7514 + +lemma sg21905 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg6297 sg7340 + +lemma sg21906 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg6428 sg6770 + +lemma sg21907 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7341 + +lemma sg21908 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7342 + +lemma sg21909 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg6429 sg6771 + +lemma sg21910 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6166 sg7514 + +lemma sg21911 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6297 sg7344 + +lemma sg21912 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg6407 sg6806 + +lemma sg21913 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7345 + +lemma sg21914 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg6428 sg6772 + +lemma sg21915 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7346 + +lemma sg21916 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg6432 sg6771 + +lemma sg21917 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6671 + +lemma sg21918 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg6429 sg6773 + +lemma sg21919 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6433 sg6770 + +lemma sg21920 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7347 + +lemma sg21921 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg6409 sg6806 + +lemma sg21922 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7348 + +lemma sg21923 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg6434 sg6771 + +lemma sg21924 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7349 + +lemma sg21925 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6807 + +lemma sg21926 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg6154 sg7575 + +lemma sg21927 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg6410 sg6806 + +lemma sg21928 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7350 + +lemma sg21929 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6807 + +lemma sg21930 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg6429 sg6777 + +lemma sg21931 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg6312 sg7308 + +lemma sg21932 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg6373 sg7036 + +lemma sg21933 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg6345 sg7286 + +lemma sg21934 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6297 sg7351 + +lemma sg21935 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6407 sg6809 + +lemma sg21936 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7352 + +lemma sg21937 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg6428 sg6778 + +lemma sg21938 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7353 + +lemma sg21939 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg6436 sg6771 + +lemma sg21940 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7354 + +lemma sg21941 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6673 + +lemma sg21942 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg6429 sg6779 + +lemma sg21943 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6409 sg6809 + +lemma sg21944 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7355 + +lemma sg21945 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg6437 sg6771 + +lemma sg21946 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg6410 sg6809 + +lemma sg21947 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7356 + +lemma sg21948 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6675 + +lemma sg21949 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg6154 sg7578 + +lemma sg21950 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6676 + +lemma sg21951 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg6432 sg6775 + +lemma sg21952 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7357 + +lemma sg21953 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6677 + +lemma sg21954 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg6432 sg6777 + +lemma sg21955 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg6312 sg7313 + +lemma sg21956 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2499 sg12696 + +lemma sg21957 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6233 sg7481 + +lemma sg21958 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5294 sg8787 + +lemma sg21959 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7658 + +lemma sg21960 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6408 sg6810 + +lemma sg21961 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7658 + +lemma sg21962 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5295 sg8787 + +lemma sg21963 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7093 + +lemma sg21964 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6408 sg6811 + +lemma sg21965 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7347 + +lemma sg21966 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6433 sg6774 + +lemma sg21967 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7093 + +lemma sg21968 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7358 + +lemma sg21969 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7358 + +lemma sg21970 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6476 sg6634 + +lemma sg21971 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg6154 sg7580 + +lemma sg21972 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7094 + +lemma sg21973 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7094 + +lemma sg21974 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7359 + +lemma sg21975 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7359 + +lemma sg21976 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7349 + +lemma sg21977 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6811 + +lemma sg21978 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6812 + +lemma sg21979 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6427 sg6788 + +lemma sg21980 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7350 + +lemma sg21981 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6811 + +lemma sg21982 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6813 + +lemma sg21983 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6371 sg7044 + +lemma sg21984 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,6,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg6428 sg6788 + +lemma sg21985 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6315 sg7305 + +lemma sg21986 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6298 sg7351 + +lemma sg21987 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7360 + +lemma sg21988 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6407 sg6814 + +lemma sg21989 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7360 + +lemma sg21990 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6315 sg7306 + +lemma sg21991 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6299 sg7351 + +lemma sg21992 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7352 + +lemma sg21993 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6409 sg6814 + +lemma sg21994 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7361 + +lemma sg21995 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7361 + +lemma sg21996 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg5508 sg8637 + +lemma sg21997 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6315 sg7307 + +lemma sg21998 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg6410 sg6814 + +lemma sg21999 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7362 + +lemma sg22000 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7362 + +lemma sg22001 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6678 + +lemma sg22002 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg6436 sg6773 + +lemma sg22003 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7354 + +lemma sg22004 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6679 + +lemma sg22005 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6372 sg7039 + +lemma sg22006 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7352 + +lemma sg22007 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6431 sg6781 + +lemma sg22008 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7363 + +lemma sg22009 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7363 + +lemma sg22010 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6680 + +lemma sg22011 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7364 + +lemma sg22012 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7364 + +lemma sg22013 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7356 + +lemma sg22014 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6681 + +lemma sg22015 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6815 + +lemma sg22016 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7357 + +lemma sg22017 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6682 + +lemma sg22018 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6815 + +lemma sg22019 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6314 sg7314 + +lemma sg22020 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6433 sg6781 + +lemma sg22021 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7365 + +lemma sg22022 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7365 + +lemma sg22023 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7358 + +lemma sg22024 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6683 + +lemma sg22025 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7359 + +lemma sg22026 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6684 + +lemma sg22027 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6816 + +lemma sg22028 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7357 + +lemma sg22029 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6817 + +lemma sg22030 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6817 + +lemma sg22031 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6464 sg6703 + +lemma sg22032 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6177 sg7502 + +lemma sg22033 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7358 + +lemma sg22034 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6476 sg6639 + +lemma sg22035 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6818 + +lemma sg22036 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7359 + +lemma sg22037 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6819 + +lemma sg22038 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,7,7,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6819 + +lemma sg22039 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4344 sg11139 + +lemma sg22040 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6315 sg7309 + +lemma sg22041 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7360 + +lemma sg22042 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg5603 sg8412 + +lemma sg22043 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6315 sg7310 + +lemma sg22044 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6472 sg6685 + +lemma sg22045 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg554 sg15627 + +lemma sg22046 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6315 sg7311 + +lemma sg22047 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7360 + +lemma sg22048 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6435 sg6778 + +lemma sg22049 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7361 + +lemma sg22050 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6300 sg7360 + +lemma sg22051 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6686 + +lemma sg22052 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6315 sg7312 + +lemma sg22053 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg6301 sg7360 + +lemma sg22054 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7362 + +lemma sg22055 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6687 + +lemma sg22056 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg5603 sg8413 + +lemma sg22057 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6315 sg7314 + +lemma sg22058 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6435 sg6781 + +lemma sg22059 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7361 + +lemma sg22060 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6477 sg6637 + +lemma sg22061 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7363 + +lemma sg22062 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6688 + +lemma sg22063 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7364 + +lemma sg22064 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6689 + +lemma sg22065 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6821 + +lemma sg22066 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6315 sg7315 + +lemma sg22067 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6821 + +lemma sg22068 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6464 sg6704 + +lemma sg22069 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6316 sg7314 + +lemma sg22070 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7365 + +lemma sg22071 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6690 + +lemma sg22072 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6822 + +lemma sg22073 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7364 + +lemma sg22074 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6823 + +lemma sg22075 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6823 + +lemma sg22076 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6447 sg6766 + +lemma sg22077 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,7,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6407 sg6825 + +lemma sg22078 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7365 + +lemma sg22079 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,7,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6824 + +lemma sg22080 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,7,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6824 + +lemma sg22081 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,8,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5756 sg8019 + +lemma sg22082 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,8,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6409 sg6825 + +lemma sg22083 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [8,8,8,8,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6410 sg6825 + +lemma sg22084 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7593 + +lemma sg22085 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg6151 sg7594 + +lemma sg22086 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,4,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7596 + +lemma sg22087 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7597 + +lemma sg22088 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg6297 sg7366 + +lemma sg22089 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7599 + +lemma sg22090 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7600 + +lemma sg22091 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7601 + +lemma sg22092 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg6414 sg6791 + +lemma sg22093 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7602 + +lemma sg22094 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7603 + +lemma sg22095 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7604 + +lemma sg22096 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg6414 sg6793 + +lemma sg22097 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6794 + +lemma sg22098 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7605 + +lemma sg22099 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg6414 sg6795 + +lemma sg22100 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7606 + +lemma sg22101 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg6303 sg7321 + +lemma sg22102 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg6480 sg6632 + +lemma sg22103 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg6180 sg7492 + +lemma sg22104 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,5,5,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg6480 sg6633 + +lemma sg22105 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,4,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7607 + +lemma sg22106 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,4,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7608 + +lemma sg22107 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7609 + +lemma sg22108 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7367 + +lemma sg22109 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7610 + +lemma sg22110 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7611 + +lemma sg22111 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7612 + +lemma sg22112 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7368 + +lemma sg22113 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7369 + +lemma sg22114 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7613 + +lemma sg22115 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7614 + +lemma sg22116 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7370 + +lemma sg22117 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7615 + +lemma sg22118 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7371 + +lemma sg22119 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6650 + +lemma sg22120 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7616 + +lemma sg22121 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7372 + +lemma sg22122 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7373 + +lemma sg22123 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6652 + +lemma sg22124 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,5,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6653 + +lemma sg22125 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6176 sg7504 + +lemma sg22126 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7617 + +lemma sg22127 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7618 + +lemma sg22128 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg6414 sg6797 + +lemma sg22129 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7619 + +lemma sg22130 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6798 + +lemma sg22131 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6691 + +lemma sg22132 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7620 + +lemma sg22133 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6414 sg6799 + +lemma sg22134 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7621 + +lemma sg22135 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6800 + +lemma sg22136 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6801 + +lemma sg22137 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6692 + +lemma sg22138 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7622 + +lemma sg22139 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6802 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes54.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes54.lean index 5e0cf0a5eface7daea908bccab4d223371fcde3d..7574f90c5d706950133d766a0182565a208d07ce 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes54.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes54.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 - -namespace OAI - -/-! Semigroup Nodes 54. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg22140 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6693 - -lemma sg22141 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6694 - -lemma sg22142 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg6474 sg6653 - -lemma sg22143 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7623 - -lemma sg22144 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6803 - -lemma sg22145 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7624 - -lemma sg22146 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6804 - -lemma sg22147 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg6480 sg6639 - -lemma sg22148 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg6480 sg6640 - -lemma sg22149 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6805 - -lemma sg22150 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg6480 sg6641 - -lemma sg22151 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg6300 sg7373 - -lemma sg22152 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6479 sg6642 - -lemma sg22153 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6439 sg6788 - -lemma sg22154 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg6480 sg6642 - -lemma sg22155 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7626 - -lemma sg22156 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7627 - -lemma sg22157 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7628 - -lemma sg22158 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7374 - -lemma sg22159 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7375 - -lemma sg22160 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7629 - -lemma sg22161 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7630 - -lemma sg22162 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7631 - -lemma sg22163 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7377 - -lemma sg22164 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7632 - -lemma sg22165 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7378 - -lemma sg22166 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6695 - -lemma sg22167 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7633 - -lemma sg22168 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7379 - -lemma sg22169 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7634 - -lemma sg22170 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7380 - -lemma sg22171 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7381 - -lemma sg22172 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6658 - -lemma sg22173 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7635 - -lemma sg22174 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7382 - -lemma sg22175 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6659 - -lemma sg22176 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6660 - -lemma sg22177 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7636 - -lemma sg22178 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7637 - -lemma sg22179 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7384 - -lemma sg22180 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7638 - -lemma sg22181 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7385 - -lemma sg22182 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7386 - -lemma sg22183 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6696 - -lemma sg22184 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7639 - -lemma sg22185 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7387 - -lemma sg22186 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7640 - -lemma sg22187 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7388 - -lemma sg22188 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6697 - -lemma sg22189 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6698 - -lemma sg22190 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7389 - -lemma sg22191 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6699 - -lemma sg22192 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7699 - -lemma sg22193 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7151 - -lemma sg22194 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7641 - -lemma sg22195 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7390 - -lemma sg22196 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7390 - -lemma sg22197 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6473 sg6667 - -lemma sg22198 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7391 - -lemma sg22199 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7391 - -lemma sg22200 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6417 sg6804 - -lemma sg22201 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6417 sg6805 - -lemma sg22202 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6441 sg6788 - -lemma sg22203 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6421 sg6796 - -lemma sg22204 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6298 sg7383 - -lemma sg22205 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7152 - -lemma sg22206 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7505 - -lemma sg22207 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6303 sg7360 - -lemma sg22208 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6424 sg6796 - -lemma sg22209 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7700 - -lemma sg22210 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7153 - -lemma sg22211 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7506 - -lemma sg22212 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6820 - -lemma sg22213 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6820 - -lemma sg22214 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7154 - -lemma sg22215 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7642 - -lemma sg22216 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6821 - -lemma sg22217 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6821 - -lemma sg22218 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg6472 sg6700 - -lemma sg22219 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7386 - -lemma sg22220 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7701 - -lemma sg22221 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7155 - -lemma sg22222 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7643 - -lemma sg22223 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6822 - -lemma sg22224 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6822 - -lemma sg22225 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6823 - -lemma sg22226 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6823 - -lemma sg22227 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7388 - -lemma sg22228 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7389 - -lemma sg22229 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7156 - -lemma sg22230 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7644 - -lemma sg22231 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6824 - -lemma sg22232 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6824 - -lemma sg22233 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7390 - -lemma sg22234 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7391 - -lemma sg22235 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7389 - -lemma sg22236 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6825 - -lemma sg22237 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,7,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6414 sg6825 - -lemma sg22238 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7390 - -lemma sg22239 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7391 - -lemma sg22240 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6151 sg7645 - -lemma sg22241 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7646 - -lemma sg22242 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7647 - -lemma sg22243 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7393 - -lemma sg22244 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7648 - -lemma sg22245 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7394 - -lemma sg22246 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6151 sg7649 - -lemma sg22247 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7650 - -lemma sg22248 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7395 - -lemma sg22249 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7651 - -lemma sg22250 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7396 - -lemma sg22251 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7397 - -lemma sg22252 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7652 - -lemma sg22253 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7398 - -lemma sg22254 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7653 - -lemma sg22255 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7399 - -lemma sg22256 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7400 - -lemma sg22257 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6421 sg6808 - -lemma sg22258 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7706 - -lemma sg22259 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7166 - -lemma sg22260 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7654 - -lemma sg22261 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6297 sg7401 - -lemma sg22262 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6424 sg6808 - -lemma sg22263 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7707 - -lemma sg22264 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7167 - -lemma sg22265 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7655 - -lemma sg22266 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7402 - -lemma sg22267 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7402 - -lemma sg22268 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7168 - -lemma sg22269 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7656 - -lemma sg22270 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7403 - -lemma sg22271 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7403 - -lemma sg22272 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7397 - -lemma sg22273 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7708 - -lemma sg22274 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7169 - -lemma sg22275 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7657 - -lemma sg22276 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7404 - -lemma sg22277 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7405 - -lemma sg22278 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7399 - -lemma sg22279 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7400 - -lemma sg22280 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7170 - -lemma sg22281 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6151 sg7658 - -lemma sg22282 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7406 - -lemma sg22283 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6417 sg6818 - -lemma sg22284 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6417 sg6819 - -lemma sg22285 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7400 - -lemma sg22286 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6314 sg7329 - -lemma sg22287 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7709 - -lemma sg22288 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7171 - -lemma sg22289 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7507 - -lemma sg22290 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7407 - -lemma sg22291 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6297 sg7407 - -lemma sg22292 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7710 - -lemma sg22293 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7172 - -lemma sg22294 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7508 - -lemma sg22295 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7408 - -lemma sg22296 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7409 - -lemma sg22297 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7403 - -lemma sg22298 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7173 - -lemma sg22299 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7509 - -lemma sg22300 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7410 - -lemma sg22301 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7404 - -lemma sg22302 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7405 - -lemma sg22303 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6421 sg6817 - -lemma sg22304 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7411 - -lemma sg22305 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7406 - -lemma sg22306 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7405 - -lemma sg22307 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6417 sg6825 - -lemma sg22308 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7406 - -lemma sg22309 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6315 sg7329 - -lemma sg22310 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6315 sg7330 - -lemma sg22311 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6295 sg7430 - -lemma sg22312 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7510 - -lemma sg22313 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7407 - -lemma sg22314 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6295 sg7431 - -lemma sg22315 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6176 sg7511 - -lemma sg22316 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7407 - -lemma sg22317 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7408 - -lemma sg22318 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7409 - -lemma sg22319 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6424 sg6820 - -lemma sg22320 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7410 - -lemma sg22321 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7409 - -lemma sg22322 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7411 - -lemma sg22323 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7410 - -lemma sg22324 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7411 - -lemma sg22325 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,8,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6424 sg6825 - -lemma sg22326 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg985 sg15055 - -lemma sg22327 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg562 sg15606 - -lemma sg22328 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg15154 - -lemma sg22329 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg21189 - -lemma sg22330 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg21190 - -lemma sg22331 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg21191 - -lemma sg22332 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg80 sg21192 - -lemma sg22333 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6296 sg7412 - -lemma sg22334 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7711 - -lemma sg22335 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6169 sg7514 - -lemma sg22336 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6298 sg7412 - -lemma sg22337 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7712 - -lemma sg22338 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6377 sg7036 - -lemma sg22339 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6297 sg7413 - -lemma sg22340 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6299 sg7412 - -lemma sg22341 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7713 - -lemma sg22342 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7414 - -lemma sg22343 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6446 sg6770 - -lemma sg22344 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7714 - -lemma sg22345 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6371 sg7078 - -lemma sg22346 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg6428 sg6806 - -lemma sg22347 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7415 - -lemma sg22348 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7416 - -lemma sg22349 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6371 sg7079 - -lemma sg22350 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7715 - -lemma sg22351 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7417 - -lemma sg22352 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6407 sg6854 - -lemma sg22353 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6372 sg7077 - -lemma sg22354 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7716 - -lemma sg22355 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7414 - -lemma sg22356 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6409 sg6854 - -lemma sg22357 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7418 - -lemma sg22358 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6371 sg7081 - -lemma sg22359 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg6410 sg6854 - -lemma sg22360 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7419 - -lemma sg22361 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7416 - -lemma sg22362 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7717 - -lemma sg22363 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7414 - -lemma sg22364 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7420 - -lemma sg22365 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7421 - -lemma sg22366 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7416 - -lemma sg22367 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6371 sg7085 - -lemma sg22368 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6372 sg7079 - -lemma sg22369 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7718 - -lemma sg22370 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7417 - -lemma sg22371 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6428 sg6814 - -lemma sg22372 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7422 - -lemma sg22373 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7719 - -lemma sg22374 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7417 - -lemma sg22375 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7423 - -lemma sg22376 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7424 - -lemma sg22377 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7419 - -lemma sg22378 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6372 sg7083 - -lemma sg22379 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7425 - -lemma sg22380 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7420 - -lemma sg22381 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7421 - -lemma sg22382 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6371 sg7092 - -lemma sg22383 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7426 - -lemma sg22384 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7420 - -lemma sg22385 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7421 - -lemma sg22386 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6315 sg7343 - -lemma sg22387 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6372 sg7086 - -lemma sg22388 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6311 sg7360 - -lemma sg22389 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7427 - -lemma sg22390 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6372 sg7087 - -lemma sg22391 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7428 - -lemma sg22392 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7423 - -lemma sg22393 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7424 - -lemma sg22394 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7429 - -lemma sg22395 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7425 - -lemma sg22396 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7424 - -lemma sg22397 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7426 - -lemma sg22398 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7425 - -lemma sg22399 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7426 - -lemma sg22400 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6315 sg7351 - -lemma sg22401 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6314 sg7360 - -lemma sg22402 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7430 - -lemma sg22403 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7427 - -lemma sg22404 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7431 - -lemma sg22405 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7428 - -lemma sg22406 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6315 sg7357 - -lemma sg22407 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7429 - -lemma sg22408 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7428 - -lemma sg22409 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7429 - -lemma sg22410 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6021 sg7811 - -lemma sg22411 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6315 sg7360 - -lemma sg22412 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6315 sg7361 - -lemma sg22413 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7430 - -lemma sg22414 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7431 - -lemma sg22415 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7430 - -lemma sg22416 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6299 sg7431 - -lemma sg22417 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6022 sg7811 - -lemma sg22418 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg25 sg21273 - -lemma sg22419 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg25 sg21274 - -lemma sg22420 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg25 sg21275 - -lemma sg22421 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg25 sg21276 - -lemma sg22422 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg21277 - -lemma sg22423 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg21278 - -lemma sg22424 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg21279 - -lemma sg22425 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg24 sg21280 - -lemma sg22426 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg24 sg21281 - -lemma sg22427 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg14753 - -lemma sg22428 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg72 sg21195 - -lemma sg22429 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg72 sg21196 - -lemma sg22430 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg72 sg21197 - -lemma sg22431 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg72 sg21198 - -lemma sg22432 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg14748 - -lemma sg22433 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg14410 - -lemma sg22434 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg126 sg21080 - -lemma sg22435 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg126 sg21081 - -lemma sg22436 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg126 sg21082 - -lemma sg22437 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg126 sg21083 - -lemma sg22438 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg962 sg15153 - -lemma sg22439 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg145 sg21072 - -lemma sg22440 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg15223 - -lemma sg22441 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg145 sg21073 - -lemma sg22442 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg145 sg21074 - -lemma sg22443 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg145 sg21075 - -lemma sg22444 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg967 sg15152 - -lemma sg22445 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1309 sg14714 - -lemma sg22446 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6234 sg7483 - -lemma sg22447 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7100 - -lemma sg22448 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7539 - -lemma sg22449 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5510 sg8627 - -lemma sg22450 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5298 sg8784 - -lemma sg22451 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg331 sg19574 - -lemma sg22452 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6235 sg7483 - -lemma sg22453 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7101 - -lemma sg22454 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7045 - -lemma sg22455 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7519 - -lemma sg22456 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5511 sg8620 - -lemma sg22457 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7102 - -lemma sg22458 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7046 - -lemma sg22459 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7028 - -lemma sg22460 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6170 sg7513 - -lemma sg22461 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg5513 sg8616 - -lemma sg22462 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7029 - -lemma sg22463 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6385 sg7025 - -lemma sg22464 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6174 sg7512 - -lemma sg22465 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg5665 sg8271 - -lemma sg22466 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg5514 sg8615 - -lemma sg22467 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg14754 - -lemma sg22468 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg73 sg21195 - -lemma sg22469 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg73 sg21196 - -lemma sg22470 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg73 sg21197 - -lemma sg22471 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg73 sg21198 - -lemma sg22472 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg14749 - -lemma sg22473 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg14411 - -lemma sg22474 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg127 sg21080 - -lemma sg22475 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg127 sg21081 - -lemma sg22476 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg127 sg21082 - -lemma sg22477 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg127 sg21083 - -lemma sg22478 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1290 sg14748 - -lemma sg22479 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg14406 - -lemma sg22480 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg14412 - -lemma sg22481 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg146 sg21073 - -lemma sg22482 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg146 sg21074 - -lemma sg22483 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg146 sg21075 - -lemma sg22484 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg963 sg15153 - -lemma sg22485 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1309 sg14716 - -lemma sg22486 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6236 sg7483 - -lemma sg22487 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7103 - -lemma sg22488 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7541 - -lemma sg22489 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5510 sg8628 - -lemma sg22490 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5298 sg8785 - -lemma sg22491 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg987 sg15054 - -lemma sg22492 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1310 sg14714 - -lemma sg22493 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6237 sg7483 - -lemma sg22494 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7104 - -lemma sg22495 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7047 - -lemma sg22496 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7520 - -lemma sg22497 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5511 sg8621 - -lemma sg22498 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6238 sg7483 - -lemma sg22499 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7105 - -lemma sg22500 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7048 - -lemma sg22501 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7045 - -lemma sg22502 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6168 sg7519 - -lemma sg22503 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5512 sg8620 - -lemma sg22504 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7049 - -lemma sg22505 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7046 - -lemma sg22506 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6379 sg7028 - -lemma sg22507 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6171 sg7513 - -lemma sg22508 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6379 sg7029 - -lemma sg22509 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6386 sg7025 - -lemma sg22510 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6175 sg7512 - -lemma sg22511 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg5666 sg8271 - -lemma sg22512 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1309 sg14717 - -lemma sg22513 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg14407 - -lemma sg22514 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg14413 - -lemma sg22515 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg147 sg21073 - -lemma sg22516 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg147 sg21074 - -lemma sg22517 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg147 sg21075 - -lemma sg22518 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1302 sg14720 - -lemma sg22519 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1703 sg14410 - -lemma sg22520 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6239 sg7483 - -lemma sg22521 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7106 - -lemma sg22522 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7544 - -lemma sg22523 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5510 sg8629 - -lemma sg22524 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5298 sg8786 - -lemma sg22525 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg983 sg15056 - -lemma sg22526 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1302 sg14721 - -lemma sg22527 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6240 sg7483 - -lemma sg22528 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7107 - -lemma sg22529 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7050 - -lemma sg22530 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7521 - -lemma sg22531 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5511 sg8622 - -lemma sg22532 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1311 sg14714 - -lemma sg22533 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6241 sg7483 - -lemma sg22534 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7108 - -lemma sg22535 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7051 - -lemma sg22536 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7031 - -lemma sg22537 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6170 sg7515 - -lemma sg22538 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5513 sg8617 - -lemma sg22539 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7109 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 + +namespace OAI + +/-! Semigroup Nodes 54. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg22140 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6693 + +lemma sg22141 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6694 + +lemma sg22142 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg6474 sg6653 + +lemma sg22143 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7623 + +lemma sg22144 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6803 + +lemma sg22145 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7624 + +lemma sg22146 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6804 + +lemma sg22147 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg6480 sg6639 + +lemma sg22148 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg6480 sg6640 + +lemma sg22149 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6805 + +lemma sg22150 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg6480 sg6641 + +lemma sg22151 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg6300 sg7373 + +lemma sg22152 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6479 sg6642 + +lemma sg22153 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6439 sg6788 + +lemma sg22154 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,6,6,6,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg6480 sg6642 + +lemma sg22155 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7626 + +lemma sg22156 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7627 + +lemma sg22157 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7628 + +lemma sg22158 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7374 + +lemma sg22159 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7375 + +lemma sg22160 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7629 + +lemma sg22161 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7630 + +lemma sg22162 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7631 + +lemma sg22163 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7377 + +lemma sg22164 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7632 + +lemma sg22165 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7378 + +lemma sg22166 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6695 + +lemma sg22167 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7633 + +lemma sg22168 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7379 + +lemma sg22169 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7634 + +lemma sg22170 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7380 + +lemma sg22171 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7381 + +lemma sg22172 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6658 + +lemma sg22173 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7635 + +lemma sg22174 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7382 + +lemma sg22175 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6659 + +lemma sg22176 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,5,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6660 + +lemma sg22177 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7636 + +lemma sg22178 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7637 + +lemma sg22179 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7384 + +lemma sg22180 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7638 + +lemma sg22181 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7385 + +lemma sg22182 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7386 + +lemma sg22183 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6696 + +lemma sg22184 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7639 + +lemma sg22185 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7387 + +lemma sg22186 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7640 + +lemma sg22187 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7388 + +lemma sg22188 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6697 + +lemma sg22189 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6698 + +lemma sg22190 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7389 + +lemma sg22191 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6699 + +lemma sg22192 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7699 + +lemma sg22193 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7151 + +lemma sg22194 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7641 + +lemma sg22195 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7390 + +lemma sg22196 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7390 + +lemma sg22197 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6473 sg6667 + +lemma sg22198 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7391 + +lemma sg22199 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7391 + +lemma sg22200 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6417 sg6804 + +lemma sg22201 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6417 sg6805 + +lemma sg22202 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,6,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6441 sg6788 + +lemma sg22203 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6421 sg6796 + +lemma sg22204 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6298 sg7383 + +lemma sg22205 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7152 + +lemma sg22206 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7505 + +lemma sg22207 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6303 sg7360 + +lemma sg22208 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6424 sg6796 + +lemma sg22209 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7700 + +lemma sg22210 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7153 + +lemma sg22211 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7506 + +lemma sg22212 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6820 + +lemma sg22213 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6820 + +lemma sg22214 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7154 + +lemma sg22215 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7642 + +lemma sg22216 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6821 + +lemma sg22217 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6821 + +lemma sg22218 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg6472 sg6700 + +lemma sg22219 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7386 + +lemma sg22220 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7701 + +lemma sg22221 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7155 + +lemma sg22222 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7643 + +lemma sg22223 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6822 + +lemma sg22224 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6822 + +lemma sg22225 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6823 + +lemma sg22226 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6823 + +lemma sg22227 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7388 + +lemma sg22228 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7389 + +lemma sg22229 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7156 + +lemma sg22230 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7644 + +lemma sg22231 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6824 + +lemma sg22232 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6824 + +lemma sg22233 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7390 + +lemma sg22234 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7391 + +lemma sg22235 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7389 + +lemma sg22236 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6825 + +lemma sg22237 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,7,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6414 sg6825 + +lemma sg22238 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7390 + +lemma sg22239 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,7,7,7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7391 + +lemma sg22240 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6151 sg7645 + +lemma sg22241 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7646 + +lemma sg22242 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7647 + +lemma sg22243 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7393 + +lemma sg22244 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7648 + +lemma sg22245 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7394 + +lemma sg22246 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6151 sg7649 + +lemma sg22247 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7650 + +lemma sg22248 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7395 + +lemma sg22249 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7651 + +lemma sg22250 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7396 + +lemma sg22251 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7397 + +lemma sg22252 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7652 + +lemma sg22253 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7398 + +lemma sg22254 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7653 + +lemma sg22255 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7399 + +lemma sg22256 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7400 + +lemma sg22257 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6421 sg6808 + +lemma sg22258 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7706 + +lemma sg22259 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7166 + +lemma sg22260 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7654 + +lemma sg22261 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6297 sg7401 + +lemma sg22262 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6424 sg6808 + +lemma sg22263 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7707 + +lemma sg22264 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7167 + +lemma sg22265 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7655 + +lemma sg22266 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7402 + +lemma sg22267 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7402 + +lemma sg22268 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7168 + +lemma sg22269 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7656 + +lemma sg22270 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7403 + +lemma sg22271 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7403 + +lemma sg22272 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7397 + +lemma sg22273 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7708 + +lemma sg22274 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7169 + +lemma sg22275 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7657 + +lemma sg22276 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7404 + +lemma sg22277 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7405 + +lemma sg22278 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7399 + +lemma sg22279 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7400 + +lemma sg22280 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7170 + +lemma sg22281 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6151 sg7658 + +lemma sg22282 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7406 + +lemma sg22283 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6417 sg6818 + +lemma sg22284 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6417 sg6819 + +lemma sg22285 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7400 + +lemma sg22286 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6314 sg7329 + +lemma sg22287 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7709 + +lemma sg22288 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7171 + +lemma sg22289 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7507 + +lemma sg22290 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7407 + +lemma sg22291 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6297 sg7407 + +lemma sg22292 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7710 + +lemma sg22293 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7172 + +lemma sg22294 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7508 + +lemma sg22295 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7408 + +lemma sg22296 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7409 + +lemma sg22297 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7403 + +lemma sg22298 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7173 + +lemma sg22299 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7509 + +lemma sg22300 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7410 + +lemma sg22301 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7404 + +lemma sg22302 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7405 + +lemma sg22303 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6421 sg6817 + +lemma sg22304 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7411 + +lemma sg22305 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7406 + +lemma sg22306 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7405 + +lemma sg22307 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6417 sg6825 + +lemma sg22308 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,7,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7406 + +lemma sg22309 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6315 sg7329 + +lemma sg22310 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6315 sg7330 + +lemma sg22311 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6295 sg7430 + +lemma sg22312 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7510 + +lemma sg22313 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7407 + +lemma sg22314 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6295 sg7431 + +lemma sg22315 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6176 sg7511 + +lemma sg22316 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7407 + +lemma sg22317 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7408 + +lemma sg22318 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7409 + +lemma sg22319 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6424 sg6820 + +lemma sg22320 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7410 + +lemma sg22321 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7409 + +lemma sg22322 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7411 + +lemma sg22323 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7410 + +lemma sg22324 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7411 + +lemma sg22325 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,8,8,8,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6424 sg6825 + +lemma sg22326 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg985 sg15055 + +lemma sg22327 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg562 sg15606 + +lemma sg22328 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg15154 + +lemma sg22329 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg21189 + +lemma sg22330 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg21190 + +lemma sg22331 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg21191 + +lemma sg22332 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg80 sg21192 + +lemma sg22333 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6296 sg7412 + +lemma sg22334 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7711 + +lemma sg22335 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6169 sg7514 + +lemma sg22336 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6298 sg7412 + +lemma sg22337 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7712 + +lemma sg22338 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6377 sg7036 + +lemma sg22339 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6297 sg7413 + +lemma sg22340 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6299 sg7412 + +lemma sg22341 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7713 + +lemma sg22342 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7414 + +lemma sg22343 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6446 sg6770 + +lemma sg22344 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7714 + +lemma sg22345 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6371 sg7078 + +lemma sg22346 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg6428 sg6806 + +lemma sg22347 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7415 + +lemma sg22348 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7416 + +lemma sg22349 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6371 sg7079 + +lemma sg22350 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7715 + +lemma sg22351 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7417 + +lemma sg22352 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6407 sg6854 + +lemma sg22353 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6372 sg7077 + +lemma sg22354 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7716 + +lemma sg22355 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7414 + +lemma sg22356 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6409 sg6854 + +lemma sg22357 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7418 + +lemma sg22358 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6371 sg7081 + +lemma sg22359 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg6410 sg6854 + +lemma sg22360 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7419 + +lemma sg22361 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7416 + +lemma sg22362 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7717 + +lemma sg22363 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7414 + +lemma sg22364 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7420 + +lemma sg22365 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7421 + +lemma sg22366 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7416 + +lemma sg22367 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6371 sg7085 + +lemma sg22368 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6372 sg7079 + +lemma sg22369 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7718 + +lemma sg22370 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7417 + +lemma sg22371 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6428 sg6814 + +lemma sg22372 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7422 + +lemma sg22373 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7719 + +lemma sg22374 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7417 + +lemma sg22375 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7423 + +lemma sg22376 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7424 + +lemma sg22377 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7419 + +lemma sg22378 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6372 sg7083 + +lemma sg22379 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7425 + +lemma sg22380 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7420 + +lemma sg22381 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7421 + +lemma sg22382 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6371 sg7092 + +lemma sg22383 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7426 + +lemma sg22384 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7420 + +lemma sg22385 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,6,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7421 + +lemma sg22386 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6315 sg7343 + +lemma sg22387 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6372 sg7086 + +lemma sg22388 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6311 sg7360 + +lemma sg22389 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7427 + +lemma sg22390 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6372 sg7087 + +lemma sg22391 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7428 + +lemma sg22392 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7423 + +lemma sg22393 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7424 + +lemma sg22394 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7429 + +lemma sg22395 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7425 + +lemma sg22396 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7424 + +lemma sg22397 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7426 + +lemma sg22398 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7425 + +lemma sg22399 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,7,7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7426 + +lemma sg22400 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6315 sg7351 + +lemma sg22401 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6314 sg7360 + +lemma sg22402 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7430 + +lemma sg22403 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7427 + +lemma sg22404 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7431 + +lemma sg22405 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7428 + +lemma sg22406 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6315 sg7357 + +lemma sg22407 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7429 + +lemma sg22408 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7428 + +lemma sg22409 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7429 + +lemma sg22410 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,8,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6021 sg7811 + +lemma sg22411 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6315 sg7360 + +lemma sg22412 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6315 sg7361 + +lemma sg22413 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7430 + +lemma sg22414 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7431 + +lemma sg22415 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7430 + +lemma sg22416 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6299 sg7431 + +lemma sg22417 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [9,9,9,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6022 sg7811 + +lemma sg22418 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg25 sg21273 + +lemma sg22419 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg25 sg21274 + +lemma sg22420 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg25 sg21275 + +lemma sg22421 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg25 sg21276 + +lemma sg22422 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg21277 + +lemma sg22423 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg21278 + +lemma sg22424 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg21279 + +lemma sg22425 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg24 sg21280 + +lemma sg22426 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg24 sg21281 + +lemma sg22427 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg14753 + +lemma sg22428 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg72 sg21195 + +lemma sg22429 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg72 sg21196 + +lemma sg22430 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg72 sg21197 + +lemma sg22431 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg72 sg21198 + +lemma sg22432 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg14748 + +lemma sg22433 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg14410 + +lemma sg22434 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg126 sg21080 + +lemma sg22435 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg126 sg21081 + +lemma sg22436 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg126 sg21082 + +lemma sg22437 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg126 sg21083 + +lemma sg22438 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg962 sg15153 + +lemma sg22439 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg145 sg21072 + +lemma sg22440 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg15223 + +lemma sg22441 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg145 sg21073 + +lemma sg22442 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg145 sg21074 + +lemma sg22443 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg145 sg21075 + +lemma sg22444 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg967 sg15152 + +lemma sg22445 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1309 sg14714 + +lemma sg22446 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6234 sg7483 + +lemma sg22447 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7100 + +lemma sg22448 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7539 + +lemma sg22449 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5510 sg8627 + +lemma sg22450 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5298 sg8784 + +lemma sg22451 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg331 sg19574 + +lemma sg22452 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6235 sg7483 + +lemma sg22453 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7101 + +lemma sg22454 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7045 + +lemma sg22455 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7519 + +lemma sg22456 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5511 sg8620 + +lemma sg22457 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7102 + +lemma sg22458 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7046 + +lemma sg22459 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7028 + +lemma sg22460 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6170 sg7513 + +lemma sg22461 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg5513 sg8616 + +lemma sg22462 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7029 + +lemma sg22463 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6385 sg7025 + +lemma sg22464 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6174 sg7512 + +lemma sg22465 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg5665 sg8271 + +lemma sg22466 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg5514 sg8615 + +lemma sg22467 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg14754 + +lemma sg22468 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg73 sg21195 + +lemma sg22469 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg73 sg21196 + +lemma sg22470 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg73 sg21197 + +lemma sg22471 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg73 sg21198 + +lemma sg22472 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg14749 + +lemma sg22473 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg14411 + +lemma sg22474 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg127 sg21080 + +lemma sg22475 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg127 sg21081 + +lemma sg22476 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg127 sg21082 + +lemma sg22477 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg127 sg21083 + +lemma sg22478 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1290 sg14748 + +lemma sg22479 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg14406 + +lemma sg22480 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg14412 + +lemma sg22481 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg146 sg21073 + +lemma sg22482 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg146 sg21074 + +lemma sg22483 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg146 sg21075 + +lemma sg22484 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg963 sg15153 + +lemma sg22485 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1309 sg14716 + +lemma sg22486 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6236 sg7483 + +lemma sg22487 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7103 + +lemma sg22488 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7541 + +lemma sg22489 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5510 sg8628 + +lemma sg22490 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5298 sg8785 + +lemma sg22491 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg987 sg15054 + +lemma sg22492 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1310 sg14714 + +lemma sg22493 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6237 sg7483 + +lemma sg22494 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7104 + +lemma sg22495 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7047 + +lemma sg22496 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7520 + +lemma sg22497 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5511 sg8621 + +lemma sg22498 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6238 sg7483 + +lemma sg22499 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7105 + +lemma sg22500 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7048 + +lemma sg22501 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7045 + +lemma sg22502 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6168 sg7519 + +lemma sg22503 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5512 sg8620 + +lemma sg22504 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7049 + +lemma sg22505 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7046 + +lemma sg22506 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6379 sg7028 + +lemma sg22507 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6171 sg7513 + +lemma sg22508 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6379 sg7029 + +lemma sg22509 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6386 sg7025 + +lemma sg22510 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6175 sg7512 + +lemma sg22511 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg5666 sg8271 + +lemma sg22512 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1309 sg14717 + +lemma sg22513 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg14407 + +lemma sg22514 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg14413 + +lemma sg22515 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg147 sg21073 + +lemma sg22516 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg147 sg21074 + +lemma sg22517 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg147 sg21075 + +lemma sg22518 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1302 sg14720 + +lemma sg22519 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1703 sg14410 + +lemma sg22520 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6239 sg7483 + +lemma sg22521 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7106 + +lemma sg22522 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7544 + +lemma sg22523 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5510 sg8629 + +lemma sg22524 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5298 sg8786 + +lemma sg22525 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg983 sg15056 + +lemma sg22526 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1302 sg14721 + +lemma sg22527 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6240 sg7483 + +lemma sg22528 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7107 + +lemma sg22529 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7050 + +lemma sg22530 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7521 + +lemma sg22531 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5511 sg8622 + +lemma sg22532 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1311 sg14714 + +lemma sg22533 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6241 sg7483 + +lemma sg22534 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7108 + +lemma sg22535 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7051 + +lemma sg22536 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7031 + +lemma sg22537 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6170 sg7515 + +lemma sg22538 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5513 sg8617 + +lemma sg22539 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7109 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes55.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes55.lean index 93b8de851d0be8898f1b67f0e61b18b671984332..b61c45a5f9c6605783a2aa536a2e6b577b24c6e4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes55.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes55.lean @@ -1,1221 +1,1221 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 - -namespace OAI - -/-! Semigroup Nodes 55. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg22540 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7052 - -lemma sg22541 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7032 - -lemma sg22542 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6643 - -lemma sg22543 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6147 sg7720 - -lemma sg22544 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7522 - -lemma sg22545 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6376 sg7046 - -lemma sg22546 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6448 sg6767 - -lemma sg22547 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6172 sg7513 - -lemma sg22548 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6380 sg7029 - -lemma sg22549 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6387 sg7025 - -lemma sg22550 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg5667 sg8271 - -lemma sg22551 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1303 sg14720 - -lemma sg22552 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1727 sg14405 - -lemma sg22553 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6242 sg7483 - -lemma sg22554 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7110 - -lemma sg22555 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7053 - -lemma sg22556 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7523 - -lemma sg22557 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5511 sg8623 - -lemma sg22558 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1304 sg14720 - -lemma sg22559 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1303 sg14721 - -lemma sg22560 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6243 sg7483 - -lemma sg22561 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7111 - -lemma sg22562 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7054 - -lemma sg22563 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7033 - -lemma sg22564 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6170 sg7516 - -lemma sg22565 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5513 sg8618 - -lemma sg22566 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6244 sg7483 - -lemma sg22567 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7112 - -lemma sg22568 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7055 - -lemma sg22569 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7034 - -lemma sg22570 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6385 sg7026 - -lemma sg22571 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6149 sg7659 - -lemma sg22572 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7549 - -lemma sg22573 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7524 - -lemma sg22574 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6170 sg7517 - -lemma sg22575 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7721 - -lemma sg22576 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6150 sg7659 - -lemma sg22577 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6203 sg7490 - -lemma sg22578 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6438 sg6789 - -lemma sg22579 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6449 sg6767 - -lemma sg22580 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6381 sg7029 - -lemma sg22581 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6148 sg7721 - -lemma sg22582 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2021 sg12941 - -lemma sg22583 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6245 sg7483 - -lemma sg22584 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7113 - -lemma sg22585 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7056 - -lemma sg22586 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7035 - -lemma sg22587 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6385 sg7027 - -lemma sg22588 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6156 sg7592 - -lemma sg22589 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3221 sg11743 - -lemma sg22590 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7551 - -lemma sg22591 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7525 - -lemma sg22592 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6170 sg7518 - -lemma sg22593 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7174 - -lemma sg22594 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6157 sg7592 - -lemma sg22595 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6283 sg7480 - -lemma sg22596 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6484 sg6628 - -lemma sg22597 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7722 - -lemma sg22598 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6150 sg7660 - -lemma sg22599 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6411 sg6827 - -lemma sg22600 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6465 sg6705 - -lemma sg22601 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6365 sg7174 - -lemma sg22602 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6148 sg7722 - -lemma sg22603 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3221 sg11744 - -lemma sg22604 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4808 sg9651 - -lemma sg22605 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5299 sg8784 - -lemma sg22606 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7175 - -lemma sg22607 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6412 sg6826 - -lemma sg22608 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6484 sg6629 - -lemma sg22609 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7723 - -lemma sg22610 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7661 - -lemma sg22611 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg6413 sg6826 - -lemma sg22612 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6412 sg6827 - -lemma sg22613 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7723 - -lemma sg22614 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7724 - -lemma sg22615 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7662 - -lemma sg22616 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7724 - -lemma sg22617 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7176 - -lemma sg22618 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg14750 - -lemma sg22619 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg14414 - -lemma sg22620 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg128 sg21080 - -lemma sg22621 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg128 sg21081 - -lemma sg22622 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg128 sg21082 - -lemma sg22623 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg128 sg21083 - -lemma sg22624 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1290 sg14749 - -lemma sg22625 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg14408 - -lemma sg22626 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg14415 - -lemma sg22627 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg21073 - -lemma sg22628 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg21074 - -lemma sg22629 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg148 sg21075 - -lemma sg22630 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1310 sg14715 - -lemma sg22631 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1710 sg14406 - -lemma sg22632 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6246 sg7483 - -lemma sg22633 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7114 - -lemma sg22634 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7552 - -lemma sg22635 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5510 sg8630 - -lemma sg22636 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5298 sg8787 - -lemma sg22637 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg985 sg15056 - -lemma sg22638 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1310 sg14716 - -lemma sg22639 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6247 sg7483 - -lemma sg22640 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7115 - -lemma sg22641 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7057 - -lemma sg22642 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7526 - -lemma sg22643 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5511 sg8624 - -lemma sg22644 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1313 sg14714 - -lemma sg22645 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6248 sg7483 - -lemma sg22646 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7116 - -lemma sg22647 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7058 - -lemma sg22648 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7047 - -lemma sg22649 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6168 sg7520 - -lemma sg22650 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5512 sg8621 - -lemma sg22651 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7117 - -lemma sg22652 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7059 - -lemma sg22653 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7048 - -lemma sg22654 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6643 - -lemma sg22655 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6147 sg7725 - -lemma sg22656 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7049 - -lemma sg22657 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6379 sg7030 - -lemma sg22658 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6450 sg6767 - -lemma sg22659 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6173 sg7513 - -lemma sg22660 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6382 sg7029 - -lemma sg22661 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6388 sg7025 - -lemma sg22662 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg5668 sg8271 - -lemma sg22663 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1302 sg14722 - -lemma sg22664 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1703 sg14411 - -lemma sg22665 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6249 sg7483 - -lemma sg22666 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7118 - -lemma sg22667 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7555 - -lemma sg22668 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5510 sg8631 - -lemma sg22669 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5298 sg8788 - -lemma sg22670 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1303 sg14722 - -lemma sg22671 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1704 sg14410 - -lemma sg22672 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6250 sg7483 - -lemma sg22673 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7119 - -lemma sg22674 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7060 - -lemma sg22675 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7529 - -lemma sg22676 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5511 sg8625 - -lemma sg22677 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1304 sg14722 - -lemma sg22678 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1305 sg14721 - -lemma sg22679 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6251 sg7483 - -lemma sg22680 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7120 - -lemma sg22681 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7061 - -lemma sg22682 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7050 - -lemma sg22683 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6168 sg7521 - -lemma sg22684 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5512 sg8622 - -lemma sg22685 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6252 sg7483 - -lemma sg22686 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7121 - -lemma sg22687 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7062 - -lemma sg22688 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7051 - -lemma sg22689 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6644 - -lemma sg22690 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6149 sg7663 - -lemma sg22691 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7063 - -lemma sg22692 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7052 - -lemma sg22693 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6376 sg7048 - -lemma sg22694 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7726 - -lemma sg22695 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6150 sg7663 - -lemma sg22696 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6645 - -lemma sg22697 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6440 sg6789 - -lemma sg22698 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6451 sg6767 - -lemma sg22699 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6383 sg7029 - -lemma sg22700 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6148 sg7726 - -lemma sg22701 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1306 sg14720 - -lemma sg22702 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1705 sg14410 - -lemma sg22703 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6253 sg7483 - -lemma sg22704 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7122 - -lemma sg22705 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7064 - -lemma sg22706 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7053 - -lemma sg22707 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6168 sg7523 - -lemma sg22708 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5512 sg8623 - -lemma sg22709 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2021 sg12942 - -lemma sg22710 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6254 sg7483 - -lemma sg22711 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7123 - -lemma sg22712 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7065 - -lemma sg22713 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7054 - -lemma sg22714 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6379 sg7033 - -lemma sg22715 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6152 sg7659 - -lemma sg22716 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7124 - -lemma sg22717 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7066 - -lemma sg22718 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7055 - -lemma sg22719 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6379 sg7034 - -lemma sg22720 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7177 - -lemma sg22721 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6340 sg7289 - -lemma sg22722 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7532 - -lemma sg22723 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6483 sg6630 - -lemma sg22724 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7727 - -lemma sg22725 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6150 sg7664 - -lemma sg22726 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6415 sg6827 - -lemma sg22727 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6466 sg6705 - -lemma sg22728 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6365 sg7177 - -lemma sg22729 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6148 sg7727 - -lemma sg22730 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6255 sg7483 - -lemma sg22731 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7125 - -lemma sg22732 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7067 - -lemma sg22733 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7056 - -lemma sg22734 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6379 sg7035 - -lemma sg22735 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7174 - -lemma sg22736 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6159 sg7592 - -lemma sg22737 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7563 - -lemma sg22738 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7533 - -lemma sg22739 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6483 sg6631 - -lemma sg22740 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7178 - -lemma sg22741 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6367 sg7174 - -lemma sg22742 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6483 sg6632 - -lemma sg22743 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7728 - -lemma sg22744 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7665 - -lemma sg22745 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6296 sg7432 - -lemma sg22746 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6416 sg6827 - -lemma sg22747 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7728 - -lemma sg22748 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4809 sg9651 - -lemma sg22749 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6483 sg6633 - -lemma sg22750 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7179 - -lemma sg22751 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7175 - -lemma sg22752 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg6417 sg6826 - -lemma sg22753 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7729 - -lemma sg22754 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7666 - -lemma sg22755 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7729 - -lemma sg22756 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7179 - -lemma sg22757 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7667 - -lemma sg22758 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7180 - -lemma sg22759 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1311 sg14717 - -lemma sg22760 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1711 sg14407 - -lemma sg22761 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1812 sg14307 - -lemma sg22762 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7126 - -lemma sg22763 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2173 sg12912 - -lemma sg22764 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5510 sg8632 - -lemma sg22765 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4697 sg10841 - -lemma sg22766 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1312 sg14717 - -lemma sg22767 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1712 sg14407 - -lemma sg22768 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6256 sg7483 - -lemma sg22769 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7127 - -lemma sg22770 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7068 - -lemma sg22771 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5510 sg8633 - -lemma sg22772 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5365 sg8709 - -lemma sg22773 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4729 sg10576 - -lemma sg22774 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2021 sg12943 - -lemma sg22775 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6257 sg7483 - -lemma sg22776 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7128 - -lemma sg22777 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7069 - -lemma sg22778 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7037 - -lemma sg22779 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6646 - -lemma sg22780 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6156 sg7598 - -lemma sg22781 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7129 - -lemma sg22782 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7070 - -lemma sg22783 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7534 - -lemma sg22784 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6376 sg7051 - -lemma sg22785 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7181 - -lemma sg22786 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6157 sg7598 - -lemma sg22787 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7038 - -lemma sg22788 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6647 - -lemma sg22789 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7730 - -lemma sg22790 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6150 sg7668 - -lemma sg22791 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6419 sg6827 - -lemma sg22792 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6467 sg6705 - -lemma sg22793 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6365 sg7181 - -lemma sg22794 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6148 sg7730 - -lemma sg22795 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1308 sg14720 - -lemma sg22796 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1707 sg14410 - -lemma sg22797 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6258 sg7483 - -lemma sg22798 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7130 - -lemma sg22799 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7071 - -lemma sg22800 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7039 - -lemma sg22801 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6648 - -lemma sg22802 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6153 sg7659 - -lemma sg22803 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6259 sg7483 - -lemma sg22804 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7131 - -lemma sg22805 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7072 - -lemma sg22806 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7535 - -lemma sg22807 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6376 sg7054 - -lemma sg22808 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6411 sg6829 - -lemma sg22809 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6341 sg7289 - -lemma sg22810 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7073 - -lemma sg22811 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7040 - -lemma sg22812 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6649 - -lemma sg22813 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7182 - -lemma sg22814 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6412 sg6829 - -lemma sg22815 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6650 - -lemma sg22816 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7731 - -lemma sg22817 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7669 - -lemma sg22818 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6413 sg6829 - -lemma sg22819 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6420 sg6827 - -lemma sg22820 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7731 - -lemma sg22821 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7132 - -lemma sg22822 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7074 - -lemma sg22823 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7041 - -lemma sg22824 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6651 - -lemma sg22825 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6411 sg6830 - -lemma sg22826 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6406 sg6856 - -lemma sg22827 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7536 - -lemma sg22828 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6652 - -lemma sg22829 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7183 - -lemma sg22830 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6412 sg6830 - -lemma sg22831 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6298 sg7432 - -lemma sg22832 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7732 - -lemma sg22833 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7670 - -lemma sg22834 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7732 - -lemma sg22835 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7183 - -lemma sg22836 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6653 - -lemma sg22837 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7733 - -lemma sg22838 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6412 sg6831 - -lemma sg22839 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7733 - -lemma sg22840 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7671 - -lemma sg22841 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7184 - -lemma sg22842 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6832 - -lemma sg22843 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1708 sg14410 - -lemma sg22844 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6260 sg7483 - -lemma sg22845 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7133 - -lemma sg22846 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7570 - -lemma sg22847 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6242 sg7484 - -lemma sg22848 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6205 sg7490 - -lemma sg22849 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6438 sg6792 - -lemma sg22850 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6342 sg7289 - -lemma sg22851 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7134 - -lemma sg22852 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7075 - -lemma sg22853 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6167 sg7537 - -lemma sg22854 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6206 sg7490 - -lemma sg22855 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6411 sg6833 - -lemma sg22856 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6479 sg6648 - -lemma sg22857 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7042 - -lemma sg22858 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6207 sg7490 - -lemma sg22859 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7185 - -lemma sg22860 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6412 sg6833 - -lemma sg22861 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6439 sg6792 - -lemma sg22862 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7734 - -lemma sg22863 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7672 - -lemma sg22864 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7734 - -lemma sg22865 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7185 - -lemma sg22866 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7076 - -lemma sg22867 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7043 - -lemma sg22868 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6208 sg7490 - -lemma sg22869 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6411 sg6834 - -lemma sg22870 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6465 sg6706 - -lemma sg22871 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6299 sg7432 - -lemma sg22872 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6244 sg7485 - -lemma sg22873 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7735 - -lemma sg22874 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6412 sg6834 - -lemma sg22875 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7735 - -lemma sg22876 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7673 - -lemma sg22877 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7186 - -lemma sg22878 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7187 - -lemma sg22879 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7674 - -lemma sg22880 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7187 - -lemma sg22881 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6835 - -lemma sg22882 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6378 sg7044 - -lemma sg22883 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6245 sg7485 - -lemma sg22884 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7736 - -lemma sg22885 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6479 sg6651 - -lemma sg22886 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7736 - -lemma sg22887 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7188 - -lemma sg22888 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7675 - -lemma sg22889 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7188 - -lemma sg22890 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6836 - -lemma sg22891 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6157 sg7606 - -lemma sg22892 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg6302 sg7373 - -lemma sg22893 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg6347 sg7287 - -lemma sg22894 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1290 sg14750 - -lemma sg22895 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg14409 - -lemma sg22896 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg14416 - -lemma sg22897 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg151 sg21069 - -lemma sg22898 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg151 sg21070 - -lemma sg22899 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg151 sg21071 - -lemma sg22900 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1302 sg14723 - -lemma sg22901 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1703 sg14414 - -lemma sg22902 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6261 sg7483 - -lemma sg22903 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7135 - -lemma sg22904 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7573 - -lemma sg22905 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5510 sg8634 - -lemma sg22906 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg293 sg20313 - -lemma sg22907 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1303 sg14723 - -lemma sg22908 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1714 sg14406 - -lemma sg22909 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6262 sg7483 - -lemma sg22910 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7136 - -lemma sg22911 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7077 - -lemma sg22912 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5510 sg8635 - -lemma sg22913 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg338 sg19573 - -lemma sg22914 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1304 sg14723 - -lemma sg22915 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1313 sg14716 - -lemma sg22916 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6263 sg7483 - -lemma sg22917 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7137 - -lemma sg22918 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7574 - -lemma sg22919 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7057 - -lemma sg22920 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6168 sg7526 - -lemma sg22921 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5512 sg8624 - -lemma sg22922 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6264 sg7483 - -lemma sg22923 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7138 - -lemma sg22924 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7078 - -lemma sg22925 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7058 - -lemma sg22926 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6644 - -lemma sg22927 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6149 sg7676 - -lemma sg22928 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7576 - -lemma sg22929 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7059 - -lemma sg22930 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6168 sg7527 - -lemma sg22931 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7737 - -lemma sg22932 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6150 sg7676 - -lemma sg22933 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6645 - -lemma sg22934 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6443 sg6789 - -lemma sg22935 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6452 sg6767 - -lemma sg22936 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6384 sg7029 - -lemma sg22937 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg6148 sg7737 - -lemma sg22938 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1305 sg14722 - -lemma sg22939 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1704 sg14411 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 + +namespace OAI + +/-! Semigroup Nodes 55. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg22540 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7052 + +lemma sg22541 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7032 + +lemma sg22542 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6643 + +lemma sg22543 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6147 sg7720 + +lemma sg22544 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7522 + +lemma sg22545 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6376 sg7046 + +lemma sg22546 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6448 sg6767 + +lemma sg22547 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6172 sg7513 + +lemma sg22548 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6380 sg7029 + +lemma sg22549 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6387 sg7025 + +lemma sg22550 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg5667 sg8271 + +lemma sg22551 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1303 sg14720 + +lemma sg22552 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1727 sg14405 + +lemma sg22553 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6242 sg7483 + +lemma sg22554 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7110 + +lemma sg22555 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7053 + +lemma sg22556 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7523 + +lemma sg22557 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5511 sg8623 + +lemma sg22558 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1304 sg14720 + +lemma sg22559 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1303 sg14721 + +lemma sg22560 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6243 sg7483 + +lemma sg22561 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7111 + +lemma sg22562 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7054 + +lemma sg22563 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7033 + +lemma sg22564 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6170 sg7516 + +lemma sg22565 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5513 sg8618 + +lemma sg22566 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6244 sg7483 + +lemma sg22567 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7112 + +lemma sg22568 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7055 + +lemma sg22569 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7034 + +lemma sg22570 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6385 sg7026 + +lemma sg22571 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6149 sg7659 + +lemma sg22572 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7549 + +lemma sg22573 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7524 + +lemma sg22574 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6170 sg7517 + +lemma sg22575 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7721 + +lemma sg22576 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6150 sg7659 + +lemma sg22577 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6203 sg7490 + +lemma sg22578 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6438 sg6789 + +lemma sg22579 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6449 sg6767 + +lemma sg22580 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6381 sg7029 + +lemma sg22581 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6148 sg7721 + +lemma sg22582 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2021 sg12941 + +lemma sg22583 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6245 sg7483 + +lemma sg22584 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7113 + +lemma sg22585 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7056 + +lemma sg22586 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7035 + +lemma sg22587 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6385 sg7027 + +lemma sg22588 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6156 sg7592 + +lemma sg22589 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3221 sg11743 + +lemma sg22590 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7551 + +lemma sg22591 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7525 + +lemma sg22592 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6170 sg7518 + +lemma sg22593 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7174 + +lemma sg22594 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6157 sg7592 + +lemma sg22595 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6283 sg7480 + +lemma sg22596 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6484 sg6628 + +lemma sg22597 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7722 + +lemma sg22598 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6150 sg7660 + +lemma sg22599 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6411 sg6827 + +lemma sg22600 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6465 sg6705 + +lemma sg22601 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6365 sg7174 + +lemma sg22602 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6148 sg7722 + +lemma sg22603 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3221 sg11744 + +lemma sg22604 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4808 sg9651 + +lemma sg22605 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5299 sg8784 + +lemma sg22606 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7175 + +lemma sg22607 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6412 sg6826 + +lemma sg22608 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6484 sg6629 + +lemma sg22609 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7723 + +lemma sg22610 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7661 + +lemma sg22611 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg6413 sg6826 + +lemma sg22612 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6412 sg6827 + +lemma sg22613 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7723 + +lemma sg22614 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7724 + +lemma sg22615 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7662 + +lemma sg22616 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7724 + +lemma sg22617 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7176 + +lemma sg22618 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg14750 + +lemma sg22619 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg14414 + +lemma sg22620 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg128 sg21080 + +lemma sg22621 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg128 sg21081 + +lemma sg22622 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg128 sg21082 + +lemma sg22623 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg128 sg21083 + +lemma sg22624 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1290 sg14749 + +lemma sg22625 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg14408 + +lemma sg22626 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg14415 + +lemma sg22627 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg21073 + +lemma sg22628 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg21074 + +lemma sg22629 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg148 sg21075 + +lemma sg22630 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1310 sg14715 + +lemma sg22631 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1710 sg14406 + +lemma sg22632 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6246 sg7483 + +lemma sg22633 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7114 + +lemma sg22634 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7552 + +lemma sg22635 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5510 sg8630 + +lemma sg22636 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5298 sg8787 + +lemma sg22637 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg985 sg15056 + +lemma sg22638 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1310 sg14716 + +lemma sg22639 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6247 sg7483 + +lemma sg22640 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7115 + +lemma sg22641 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7057 + +lemma sg22642 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7526 + +lemma sg22643 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5511 sg8624 + +lemma sg22644 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1313 sg14714 + +lemma sg22645 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6248 sg7483 + +lemma sg22646 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7116 + +lemma sg22647 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7058 + +lemma sg22648 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7047 + +lemma sg22649 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6168 sg7520 + +lemma sg22650 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5512 sg8621 + +lemma sg22651 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7117 + +lemma sg22652 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7059 + +lemma sg22653 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7048 + +lemma sg22654 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6643 + +lemma sg22655 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6147 sg7725 + +lemma sg22656 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7049 + +lemma sg22657 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6379 sg7030 + +lemma sg22658 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6450 sg6767 + +lemma sg22659 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6173 sg7513 + +lemma sg22660 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6382 sg7029 + +lemma sg22661 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6388 sg7025 + +lemma sg22662 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg5668 sg8271 + +lemma sg22663 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1302 sg14722 + +lemma sg22664 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1703 sg14411 + +lemma sg22665 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6249 sg7483 + +lemma sg22666 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7118 + +lemma sg22667 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7555 + +lemma sg22668 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5510 sg8631 + +lemma sg22669 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5298 sg8788 + +lemma sg22670 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1303 sg14722 + +lemma sg22671 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1704 sg14410 + +lemma sg22672 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6250 sg7483 + +lemma sg22673 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7119 + +lemma sg22674 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7060 + +lemma sg22675 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7529 + +lemma sg22676 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5511 sg8625 + +lemma sg22677 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1304 sg14722 + +lemma sg22678 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1305 sg14721 + +lemma sg22679 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6251 sg7483 + +lemma sg22680 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7120 + +lemma sg22681 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7061 + +lemma sg22682 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7050 + +lemma sg22683 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6168 sg7521 + +lemma sg22684 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5512 sg8622 + +lemma sg22685 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6252 sg7483 + +lemma sg22686 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7121 + +lemma sg22687 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7062 + +lemma sg22688 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7051 + +lemma sg22689 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6644 + +lemma sg22690 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6149 sg7663 + +lemma sg22691 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7063 + +lemma sg22692 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7052 + +lemma sg22693 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6376 sg7048 + +lemma sg22694 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7726 + +lemma sg22695 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6150 sg7663 + +lemma sg22696 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6645 + +lemma sg22697 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6440 sg6789 + +lemma sg22698 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6451 sg6767 + +lemma sg22699 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6383 sg7029 + +lemma sg22700 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6148 sg7726 + +lemma sg22701 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1306 sg14720 + +lemma sg22702 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1705 sg14410 + +lemma sg22703 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6253 sg7483 + +lemma sg22704 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7122 + +lemma sg22705 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7064 + +lemma sg22706 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7053 + +lemma sg22707 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6168 sg7523 + +lemma sg22708 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5512 sg8623 + +lemma sg22709 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2021 sg12942 + +lemma sg22710 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6254 sg7483 + +lemma sg22711 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7123 + +lemma sg22712 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7065 + +lemma sg22713 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7054 + +lemma sg22714 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6379 sg7033 + +lemma sg22715 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6152 sg7659 + +lemma sg22716 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7124 + +lemma sg22717 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7066 + +lemma sg22718 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7055 + +lemma sg22719 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6379 sg7034 + +lemma sg22720 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7177 + +lemma sg22721 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6340 sg7289 + +lemma sg22722 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7532 + +lemma sg22723 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6483 sg6630 + +lemma sg22724 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7727 + +lemma sg22725 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6150 sg7664 + +lemma sg22726 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6415 sg6827 + +lemma sg22727 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6466 sg6705 + +lemma sg22728 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6365 sg7177 + +lemma sg22729 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6148 sg7727 + +lemma sg22730 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6255 sg7483 + +lemma sg22731 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7125 + +lemma sg22732 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7067 + +lemma sg22733 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7056 + +lemma sg22734 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6379 sg7035 + +lemma sg22735 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7174 + +lemma sg22736 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6159 sg7592 + +lemma sg22737 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7563 + +lemma sg22738 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7533 + +lemma sg22739 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6483 sg6631 + +lemma sg22740 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7178 + +lemma sg22741 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6367 sg7174 + +lemma sg22742 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6483 sg6632 + +lemma sg22743 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7728 + +lemma sg22744 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7665 + +lemma sg22745 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6296 sg7432 + +lemma sg22746 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6416 sg6827 + +lemma sg22747 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7728 + +lemma sg22748 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4809 sg9651 + +lemma sg22749 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6483 sg6633 + +lemma sg22750 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7179 + +lemma sg22751 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7175 + +lemma sg22752 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg6417 sg6826 + +lemma sg22753 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7729 + +lemma sg22754 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7666 + +lemma sg22755 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7729 + +lemma sg22756 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7179 + +lemma sg22757 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7667 + +lemma sg22758 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7180 + +lemma sg22759 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1311 sg14717 + +lemma sg22760 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1711 sg14407 + +lemma sg22761 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1812 sg14307 + +lemma sg22762 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7126 + +lemma sg22763 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2173 sg12912 + +lemma sg22764 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5510 sg8632 + +lemma sg22765 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4697 sg10841 + +lemma sg22766 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1312 sg14717 + +lemma sg22767 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1712 sg14407 + +lemma sg22768 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6256 sg7483 + +lemma sg22769 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7127 + +lemma sg22770 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7068 + +lemma sg22771 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5510 sg8633 + +lemma sg22772 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5365 sg8709 + +lemma sg22773 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4729 sg10576 + +lemma sg22774 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2021 sg12943 + +lemma sg22775 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6257 sg7483 + +lemma sg22776 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7128 + +lemma sg22777 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7069 + +lemma sg22778 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7037 + +lemma sg22779 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6646 + +lemma sg22780 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6156 sg7598 + +lemma sg22781 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7129 + +lemma sg22782 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7070 + +lemma sg22783 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7534 + +lemma sg22784 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6376 sg7051 + +lemma sg22785 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7181 + +lemma sg22786 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6157 sg7598 + +lemma sg22787 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7038 + +lemma sg22788 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6647 + +lemma sg22789 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7730 + +lemma sg22790 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6150 sg7668 + +lemma sg22791 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6419 sg6827 + +lemma sg22792 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6467 sg6705 + +lemma sg22793 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6365 sg7181 + +lemma sg22794 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6148 sg7730 + +lemma sg22795 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1308 sg14720 + +lemma sg22796 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1707 sg14410 + +lemma sg22797 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6258 sg7483 + +lemma sg22798 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7130 + +lemma sg22799 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7071 + +lemma sg22800 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7039 + +lemma sg22801 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6648 + +lemma sg22802 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6153 sg7659 + +lemma sg22803 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6259 sg7483 + +lemma sg22804 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7131 + +lemma sg22805 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7072 + +lemma sg22806 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7535 + +lemma sg22807 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6376 sg7054 + +lemma sg22808 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6411 sg6829 + +lemma sg22809 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6341 sg7289 + +lemma sg22810 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7073 + +lemma sg22811 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7040 + +lemma sg22812 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6649 + +lemma sg22813 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7182 + +lemma sg22814 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6412 sg6829 + +lemma sg22815 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6650 + +lemma sg22816 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7731 + +lemma sg22817 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7669 + +lemma sg22818 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6413 sg6829 + +lemma sg22819 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6420 sg6827 + +lemma sg22820 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7731 + +lemma sg22821 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7132 + +lemma sg22822 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7074 + +lemma sg22823 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7041 + +lemma sg22824 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6651 + +lemma sg22825 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6411 sg6830 + +lemma sg22826 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6406 sg6856 + +lemma sg22827 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7536 + +lemma sg22828 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6652 + +lemma sg22829 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7183 + +lemma sg22830 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6412 sg6830 + +lemma sg22831 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6298 sg7432 + +lemma sg22832 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7732 + +lemma sg22833 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7670 + +lemma sg22834 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7732 + +lemma sg22835 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7183 + +lemma sg22836 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6653 + +lemma sg22837 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7733 + +lemma sg22838 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6412 sg6831 + +lemma sg22839 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7733 + +lemma sg22840 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7671 + +lemma sg22841 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7184 + +lemma sg22842 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6832 + +lemma sg22843 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1708 sg14410 + +lemma sg22844 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6260 sg7483 + +lemma sg22845 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7133 + +lemma sg22846 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7570 + +lemma sg22847 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6242 sg7484 + +lemma sg22848 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6205 sg7490 + +lemma sg22849 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6438 sg6792 + +lemma sg22850 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6342 sg7289 + +lemma sg22851 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7134 + +lemma sg22852 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7075 + +lemma sg22853 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6167 sg7537 + +lemma sg22854 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6206 sg7490 + +lemma sg22855 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6411 sg6833 + +lemma sg22856 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6479 sg6648 + +lemma sg22857 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7042 + +lemma sg22858 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6207 sg7490 + +lemma sg22859 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7185 + +lemma sg22860 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6412 sg6833 + +lemma sg22861 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6439 sg6792 + +lemma sg22862 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7734 + +lemma sg22863 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7672 + +lemma sg22864 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7734 + +lemma sg22865 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7185 + +lemma sg22866 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7076 + +lemma sg22867 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7043 + +lemma sg22868 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6208 sg7490 + +lemma sg22869 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6411 sg6834 + +lemma sg22870 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6465 sg6706 + +lemma sg22871 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6299 sg7432 + +lemma sg22872 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6244 sg7485 + +lemma sg22873 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7735 + +lemma sg22874 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6412 sg6834 + +lemma sg22875 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7735 + +lemma sg22876 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7673 + +lemma sg22877 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7186 + +lemma sg22878 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7187 + +lemma sg22879 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7674 + +lemma sg22880 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7187 + +lemma sg22881 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6835 + +lemma sg22882 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6378 sg7044 + +lemma sg22883 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6245 sg7485 + +lemma sg22884 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7736 + +lemma sg22885 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6479 sg6651 + +lemma sg22886 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7736 + +lemma sg22887 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7188 + +lemma sg22888 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7675 + +lemma sg22889 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7188 + +lemma sg22890 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6836 + +lemma sg22891 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6157 sg7606 + +lemma sg22892 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg6302 sg7373 + +lemma sg22893 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,5,5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg6347 sg7287 + +lemma sg22894 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1290 sg14750 + +lemma sg22895 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg14409 + +lemma sg22896 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg14416 + +lemma sg22897 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg151 sg21069 + +lemma sg22898 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg151 sg21070 + +lemma sg22899 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg151 sg21071 + +lemma sg22900 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1302 sg14723 + +lemma sg22901 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1703 sg14414 + +lemma sg22902 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6261 sg7483 + +lemma sg22903 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7135 + +lemma sg22904 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7573 + +lemma sg22905 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5510 sg8634 + +lemma sg22906 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg293 sg20313 + +lemma sg22907 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1303 sg14723 + +lemma sg22908 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1714 sg14406 + +lemma sg22909 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6262 sg7483 + +lemma sg22910 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7136 + +lemma sg22911 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7077 + +lemma sg22912 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5510 sg8635 + +lemma sg22913 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg338 sg19573 + +lemma sg22914 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1304 sg14723 + +lemma sg22915 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1313 sg14716 + +lemma sg22916 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6263 sg7483 + +lemma sg22917 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7137 + +lemma sg22918 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7574 + +lemma sg22919 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7057 + +lemma sg22920 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6168 sg7526 + +lemma sg22921 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5512 sg8624 + +lemma sg22922 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6264 sg7483 + +lemma sg22923 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7138 + +lemma sg22924 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7078 + +lemma sg22925 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7058 + +lemma sg22926 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6644 + +lemma sg22927 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6149 sg7676 + +lemma sg22928 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7576 + +lemma sg22929 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7059 + +lemma sg22930 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6168 sg7527 + +lemma sg22931 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7737 + +lemma sg22932 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6150 sg7676 + +lemma sg22933 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6645 + +lemma sg22934 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6443 sg6789 + +lemma sg22935 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6452 sg6767 + +lemma sg22936 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6384 sg7029 + +lemma sg22937 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg6148 sg7737 + +lemma sg22938 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1305 sg14722 + +lemma sg22939 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1704 sg14411 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes56.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes56.lean index 2a0a77cde8d64a4e72220070f3297317a086e564..c771194a2299e0a76d4e2d7fb4215b2e17bb747c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes56.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes56.lean @@ -1,1220 +1,1220 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 - -namespace OAI - -/-! Semigroup Nodes 56. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg22940 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6265 sg7483 - -lemma sg22941 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7139 - -lemma sg22942 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7079 - -lemma sg22943 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5510 sg8636 - -lemma sg22944 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg339 sg19573 - -lemma sg22945 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1306 sg14722 - -lemma sg22946 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1705 sg14411 - -lemma sg22947 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6266 sg7483 - -lemma sg22948 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7140 - -lemma sg22949 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7080 - -lemma sg22950 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7060 - -lemma sg22951 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6168 sg7529 - -lemma sg22952 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg5512 sg8625 - -lemma sg22953 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1713 sg14408 - -lemma sg22954 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6267 sg7483 - -lemma sg22955 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7141 - -lemma sg22956 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7081 - -lemma sg22957 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7061 - -lemma sg22958 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6376 sg7057 - -lemma sg22959 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6152 sg7663 - -lemma sg22960 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7142 - -lemma sg22961 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7082 - -lemma sg22962 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7062 - -lemma sg22963 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6376 sg7058 - -lemma sg22964 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7189 - -lemma sg22965 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6340 sg7290 - -lemma sg22966 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7063 - -lemma sg22967 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6654 - -lemma sg22968 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7738 - -lemma sg22969 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6150 sg7677 - -lemma sg22970 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6370 sg7102 - -lemma sg22971 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6444 sg6789 - -lemma sg22972 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6365 sg7189 - -lemma sg22973 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6148 sg7738 - -lemma sg22974 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1315 sg14715 - -lemma sg22975 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2022 sg12942 - -lemma sg22976 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6268 sg7483 - -lemma sg22977 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7143 - -lemma sg22978 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7083 - -lemma sg22979 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7064 - -lemma sg22980 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6648 - -lemma sg22981 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6158 sg7595 - -lemma sg22982 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6269 sg7483 - -lemma sg22983 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7144 - -lemma sg22984 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6164 sg7581 - -lemma sg22985 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7065 - -lemma sg22986 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6168 sg7531 - -lemma sg22987 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7177 - -lemma sg22988 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6159 sg7595 - -lemma sg22989 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7084 - -lemma sg22990 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7066 - -lemma sg22991 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6649 - -lemma sg22992 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7190 - -lemma sg22993 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6367 sg7177 - -lemma sg22994 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6650 - -lemma sg22995 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7739 - -lemma sg22996 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7678 - -lemma sg22997 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6296 sg7433 - -lemma sg22998 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6427 sg6827 - -lemma sg22999 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7739 - -lemma sg23000 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7145 - -lemma sg23001 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7085 - -lemma sg23002 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7067 - -lemma sg23003 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6651 - -lemma sg23004 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7178 - -lemma sg23005 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6416 sg6828 - -lemma sg23006 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6285 sg7480 - -lemma sg23007 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6652 - -lemma sg23008 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7191 - -lemma sg23009 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7178 - -lemma sg23010 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6417 sg6828 - -lemma sg23011 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7740 - -lemma sg23012 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7679 - -lemma sg23013 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7740 - -lemma sg23014 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7191 - -lemma sg23015 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6653 - -lemma sg23016 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7741 - -lemma sg23017 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7179 - -lemma sg23018 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7741 - -lemma sg23019 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7680 - -lemma sg23020 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7192 - -lemma sg23021 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7434 - -lemma sg23022 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1307 sg14722 - -lemma sg23023 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1706 sg14411 - -lemma sg23024 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6270 sg7483 - -lemma sg23025 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7146 - -lemma sg23026 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7086 - -lemma sg23027 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg3850 sg11506 - -lemma sg23028 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5365 sg8712 - -lemma sg23029 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4729 sg10578 - -lemma sg23030 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1308 sg14722 - -lemma sg23031 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2022 sg12943 - -lemma sg23032 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6271 sg7483 - -lemma sg23033 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7147 - -lemma sg23034 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7087 - -lemma sg23035 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7068 - -lemma sg23036 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6376 sg7060 - -lemma sg23037 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6153 sg7663 - -lemma sg23038 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6272 sg7483 - -lemma sg23039 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7148 - -lemma sg23040 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7088 - -lemma sg23041 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7069 - -lemma sg23042 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6376 sg7061 - -lemma sg23043 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7181 - -lemma sg23044 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6341 sg7290 - -lemma sg23045 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7089 - -lemma sg23046 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7070 - -lemma sg23047 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6655 - -lemma sg23048 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7193 - -lemma sg23049 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6367 sg7181 - -lemma sg23050 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6656 - -lemma sg23051 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7742 - -lemma sg23052 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7681 - -lemma sg23053 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6296 sg7435 - -lemma sg23054 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6430 sg6827 - -lemma sg23055 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7742 - -lemma sg23056 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1708 sg14411 - -lemma sg23057 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6273 sg7483 - -lemma sg23058 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7149 - -lemma sg23059 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7090 - -lemma sg23060 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7071 - -lemma sg23061 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6376 sg7064 - -lemma sg23062 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6368 sg7177 - -lemma sg23063 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6342 sg7290 - -lemma sg23064 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7150 - -lemma sg23065 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7091 - -lemma sg23066 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7072 - -lemma sg23067 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6657 - -lemma sg23068 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7182 - -lemma sg23069 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6406 sg6857 - -lemma sg23070 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7073 - -lemma sg23071 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6658 - -lemma sg23072 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7194 - -lemma sg23073 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7182 - -lemma sg23074 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6298 sg7433 - -lemma sg23075 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7743 - -lemma sg23076 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7682 - -lemma sg23077 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7743 - -lemma sg23078 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7194 - -lemma sg23079 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7092 - -lemma sg23080 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7074 - -lemma sg23081 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6659 - -lemma sg23082 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7183 - -lemma sg23083 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6406 sg6858 - -lemma sg23084 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6421 sg6828 - -lemma sg23085 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6660 - -lemma sg23086 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7744 - -lemma sg23087 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7183 - -lemma sg23088 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7744 - -lemma sg23089 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7683 - -lemma sg23090 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7195 - -lemma sg23091 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7196 - -lemma sg23092 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7684 - -lemma sg23093 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7196 - -lemma sg23094 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7436 - -lemma sg23095 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6274 sg7483 - -lemma sg23096 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7151 - -lemma sg23097 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7093 - -lemma sg23098 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5900 sg7860 - -lemma sg23099 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6212 sg7490 - -lemma sg23100 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6415 sg6833 - -lemma sg23101 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6408 sg6857 - -lemma sg23102 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7094 - -lemma sg23103 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7075 - -lemma sg23104 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6483 sg6639 - -lemma sg23105 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7185 - -lemma sg23106 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6416 sg6833 - -lemma sg23107 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6299 sg7433 - -lemma sg23108 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6483 sg6640 - -lemma sg23109 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7745 - -lemma sg23110 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7185 - -lemma sg23111 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7745 - -lemma sg23112 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7685 - -lemma sg23113 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7197 - -lemma sg23114 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7076 - -lemma sg23115 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6483 sg6641 - -lemma sg23116 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7746 - -lemma sg23117 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6416 sg6834 - -lemma sg23118 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7746 - -lemma sg23119 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7198 - -lemma sg23120 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7686 - -lemma sg23121 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7198 - -lemma sg23122 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7437 - -lemma sg23123 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7187 - -lemma sg23124 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7438 - -lemma sg23125 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6483 sg6642 - -lemma sg23126 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7199 - -lemma sg23127 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7687 - -lemma sg23128 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7199 - -lemma sg23129 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7188 - -lemma sg23130 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7439 - -lemma sg23131 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg6304 sg7373 - -lemma sg23132 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1316 sg14717 - -lemma sg23133 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2023 sg12943 - -lemma sg23134 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1817 sg14307 - -lemma sg23135 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7152 - -lemma sg23136 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3796 sg11537 - -lemma sg23137 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6284 sg7482 - -lemma sg23138 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5296 sg8789 - -lemma sg23139 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6160 sg7598 - -lemma sg23140 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1718 sg14407 - -lemma sg23141 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1818 sg14307 - -lemma sg23142 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7153 - -lemma sg23143 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7095 - -lemma sg23144 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5909 sg7859 - -lemma sg23145 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6376 sg7068 - -lemma sg23146 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6368 sg7181 - -lemma sg23147 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6161 sg7598 - -lemma sg23148 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7154 - -lemma sg23149 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7096 - -lemma sg23150 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6214 sg7489 - -lemma sg23151 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6661 - -lemma sg23152 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6411 sg6840 - -lemma sg23153 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6406 sg6859 - -lemma sg23154 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6215 sg7489 - -lemma sg23155 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6662 - -lemma sg23156 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7200 - -lemma sg23157 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6412 sg6840 - -lemma sg23158 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6298 sg7435 - -lemma sg23159 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7747 - -lemma sg23160 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7688 - -lemma sg23161 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7747 - -lemma sg23162 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7200 - -lemma sg23163 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1819 sg14307 - -lemma sg23164 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7155 - -lemma sg23165 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7097 - -lemma sg23166 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6216 sg7489 - -lemma sg23167 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6663 - -lemma sg23168 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6368 sg7182 - -lemma sg23169 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6408 sg6859 - -lemma sg23170 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7098 - -lemma sg23171 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6217 sg7489 - -lemma sg23172 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6664 - -lemma sg23173 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6411 sg6841 - -lemma sg23174 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6406 sg6860 - -lemma sg23175 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6299 sg7435 - -lemma sg23176 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6665 - -lemma sg23177 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7748 - -lemma sg23178 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6412 sg6841 - -lemma sg23179 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7748 - -lemma sg23180 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7689 - -lemma sg23181 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7201 - -lemma sg23182 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6218 sg7489 - -lemma sg23183 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6666 - -lemma sg23184 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7749 - -lemma sg23185 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6406 sg6861 - -lemma sg23186 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7749 - -lemma sg23187 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7202 - -lemma sg23188 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7690 - -lemma sg23189 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7202 - -lemma sg23190 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6842 - -lemma sg23191 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6412 sg6843 - -lemma sg23192 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6843 - -lemma sg23193 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7156 - -lemma sg23194 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6374 sg7099 - -lemma sg23195 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6219 sg7489 - -lemma sg23196 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6667 - -lemma sg23197 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6368 sg7185 - -lemma sg23198 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6408 sg6860 - -lemma sg23199 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6424 sg6829 - -lemma sg23200 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6220 sg7489 - -lemma sg23201 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6668 - -lemma sg23202 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7750 - -lemma sg23203 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6406 sg6862 - -lemma sg23204 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7750 - -lemma sg23205 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7203 - -lemma sg23206 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7691 - -lemma sg23207 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7203 - -lemma sg23208 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6844 - -lemma sg23209 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6669 - -lemma sg23210 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7204 - -lemma sg23211 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7692 - -lemma sg23212 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7204 - -lemma sg23213 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6412 sg6845 - -lemma sg23214 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6845 - -lemma sg23215 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7438 - -lemma sg23216 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6411 sg6846 - -lemma sg23217 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6412 sg6846 - -lemma sg23218 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6846 - -lemma sg23219 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6298 sg7439 - -lemma sg23220 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3795 sg11538 - -lemma sg23221 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6260 sg7484 - -lemma sg23222 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6219 sg7490 - -lemma sg23223 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7751 - -lemma sg23224 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6408 sg6862 - -lemma sg23225 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7751 - -lemma sg23226 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6220 sg7490 - -lemma sg23227 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7205 - -lemma sg23228 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7693 - -lemma sg23229 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7205 - -lemma sg23230 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6412 sg6847 - -lemma sg23231 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6847 - -lemma sg23232 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6411 sg6848 - -lemma sg23233 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6412 sg6848 - -lemma sg23234 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6848 - -lemma sg23235 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6479 sg6669 - -lemma sg23236 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1310 sg14718 - -lemma sg23237 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1710 sg14409 - -lemma sg23238 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6275 sg7483 - -lemma sg23239 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7157 - -lemma sg23240 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg294 sg20311 - -lemma sg23241 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg294 sg20312 - -lemma sg23242 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg294 sg20313 - -lemma sg23243 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1305 sg14723 - -lemma sg23244 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1704 sg14414 - -lemma sg23245 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6276 sg7483 - -lemma sg23246 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7158 - -lemma sg23247 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2173 sg12913 - -lemma sg23248 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg341 sg19570 - -lemma sg23249 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg341 sg19571 - -lemma sg23250 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1306 sg14723 - -lemma sg23251 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1705 sg14414 - -lemma sg23252 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6277 sg7483 - -lemma sg23253 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7159 - -lemma sg23254 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6221 sg7488 - -lemma sg23255 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7077 - -lemma sg23256 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5366 sg8710 - -lemma sg23257 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4730 sg10577 - -lemma sg23258 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1713 sg14409 - -lemma sg23259 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6278 sg7483 - -lemma sg23260 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3212 sg11746 - -lemma sg23261 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6222 sg7488 - -lemma sg23262 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6209 sg7491 - -lemma sg23263 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5366 sg8711 - -lemma sg23264 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6152 sg7676 - -lemma sg23265 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7160 - -lemma sg23266 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6223 sg7488 - -lemma sg23267 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7078 - -lemma sg23268 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6188 sg7503 - -lemma sg23269 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7206 - -lemma sg23270 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6340 sg7291 - -lemma sg23271 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6210 sg7491 - -lemma sg23272 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6654 - -lemma sg23273 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7752 - -lemma sg23274 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6150 sg7694 - -lemma sg23275 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6443 sg6790 - -lemma sg23276 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6445 sg6789 - -lemma sg23277 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg6365 sg7206 - -lemma sg23278 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg6148 sg7752 - -lemma sg23279 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1307 sg14723 - -lemma sg23280 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1706 sg14414 - -lemma sg23281 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6279 sg7483 - -lemma sg23282 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7161 - -lemma sg23283 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6224 sg7488 - -lemma sg23284 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7079 - -lemma sg23285 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5365 sg8713 - -lemma sg23286 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4729 sg10579 - -lemma sg23287 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1308 sg14723 - -lemma sg23288 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1707 sg14414 - -lemma sg23289 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6280 sg7483 - -lemma sg23290 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7162 - -lemma sg23291 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6225 sg7488 - -lemma sg23292 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7080 - -lemma sg23293 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6376 sg7077 - -lemma sg23294 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6153 sg7676 - -lemma sg23295 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6281 sg7483 - -lemma sg23296 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7163 - -lemma sg23297 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6226 sg7488 - -lemma sg23298 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7081 - -lemma sg23299 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6190 sg7503 - -lemma sg23300 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7189 - -lemma sg23301 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6341 sg7291 - -lemma sg23302 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6227 sg7488 - -lemma sg23303 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7082 - -lemma sg23304 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6670 - -lemma sg23305 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7207 - -lemma sg23306 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6367 sg7189 - -lemma sg23307 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6478 sg6671 - -lemma sg23308 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7753 - -lemma sg23309 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7695 - -lemma sg23310 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6296 sg7440 - -lemma sg23311 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6444 sg6790 - -lemma sg23312 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7753 - -lemma sg23313 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2024 sg12942 - -lemma sg23314 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6282 sg7483 - -lemma sg23315 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7164 - -lemma sg23316 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6228 sg7488 - -lemma sg23317 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7083 - -lemma sg23318 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6193 sg7503 - -lemma sg23319 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6415 sg6837 - -lemma sg23320 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6342 sg7291 - -lemma sg23321 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6369 sg7165 - -lemma sg23322 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6229 sg7488 - -lemma sg23323 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6213 sg7491 - -lemma sg23324 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6657 - -lemma sg23325 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7190 - -lemma sg23326 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6416 sg6837 - -lemma sg23327 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7084 - -lemma sg23328 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6658 - -lemma sg23329 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7208 - -lemma sg23330 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7190 - -lemma sg23331 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6417 sg6837 - -lemma sg23332 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7754 - -lemma sg23333 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7696 - -lemma sg23334 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7754 - -lemma sg23335 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7208 - -lemma sg23336 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6230 sg7488 - -lemma sg23337 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6375 sg7085 - -lemma sg23338 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6659 - -lemma sg23339 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7191 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 + +namespace OAI + +/-! Semigroup Nodes 56. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg22940 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6265 sg7483 + +lemma sg22941 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7139 + +lemma sg22942 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7079 + +lemma sg22943 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5510 sg8636 + +lemma sg22944 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg339 sg19573 + +lemma sg22945 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1306 sg14722 + +lemma sg22946 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1705 sg14411 + +lemma sg22947 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6266 sg7483 + +lemma sg22948 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7140 + +lemma sg22949 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7080 + +lemma sg22950 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7060 + +lemma sg22951 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6168 sg7529 + +lemma sg22952 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg5512 sg8625 + +lemma sg22953 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1713 sg14408 + +lemma sg22954 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6267 sg7483 + +lemma sg22955 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7141 + +lemma sg22956 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7081 + +lemma sg22957 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7061 + +lemma sg22958 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6376 sg7057 + +lemma sg22959 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6152 sg7663 + +lemma sg22960 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7142 + +lemma sg22961 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7082 + +lemma sg22962 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7062 + +lemma sg22963 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6376 sg7058 + +lemma sg22964 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7189 + +lemma sg22965 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6340 sg7290 + +lemma sg22966 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7063 + +lemma sg22967 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6654 + +lemma sg22968 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7738 + +lemma sg22969 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6150 sg7677 + +lemma sg22970 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6370 sg7102 + +lemma sg22971 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6444 sg6789 + +lemma sg22972 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6365 sg7189 + +lemma sg22973 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6148 sg7738 + +lemma sg22974 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1315 sg14715 + +lemma sg22975 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2022 sg12942 + +lemma sg22976 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6268 sg7483 + +lemma sg22977 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7143 + +lemma sg22978 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7083 + +lemma sg22979 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7064 + +lemma sg22980 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6648 + +lemma sg22981 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6158 sg7595 + +lemma sg22982 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6269 sg7483 + +lemma sg22983 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7144 + +lemma sg22984 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6164 sg7581 + +lemma sg22985 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7065 + +lemma sg22986 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6168 sg7531 + +lemma sg22987 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7177 + +lemma sg22988 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6159 sg7595 + +lemma sg22989 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7084 + +lemma sg22990 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7066 + +lemma sg22991 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6649 + +lemma sg22992 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7190 + +lemma sg22993 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6367 sg7177 + +lemma sg22994 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6650 + +lemma sg22995 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7739 + +lemma sg22996 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7678 + +lemma sg22997 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6296 sg7433 + +lemma sg22998 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6427 sg6827 + +lemma sg22999 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7739 + +lemma sg23000 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7145 + +lemma sg23001 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7085 + +lemma sg23002 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7067 + +lemma sg23003 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6651 + +lemma sg23004 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7178 + +lemma sg23005 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6416 sg6828 + +lemma sg23006 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6285 sg7480 + +lemma sg23007 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6652 + +lemma sg23008 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7191 + +lemma sg23009 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7178 + +lemma sg23010 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6417 sg6828 + +lemma sg23011 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7740 + +lemma sg23012 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7679 + +lemma sg23013 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7740 + +lemma sg23014 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7191 + +lemma sg23015 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6653 + +lemma sg23016 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7741 + +lemma sg23017 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7179 + +lemma sg23018 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7741 + +lemma sg23019 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7680 + +lemma sg23020 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7192 + +lemma sg23021 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7434 + +lemma sg23022 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1307 sg14722 + +lemma sg23023 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1706 sg14411 + +lemma sg23024 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6270 sg7483 + +lemma sg23025 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7146 + +lemma sg23026 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7086 + +lemma sg23027 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg3850 sg11506 + +lemma sg23028 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5365 sg8712 + +lemma sg23029 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4729 sg10578 + +lemma sg23030 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1308 sg14722 + +lemma sg23031 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2022 sg12943 + +lemma sg23032 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6271 sg7483 + +lemma sg23033 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7147 + +lemma sg23034 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7087 + +lemma sg23035 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7068 + +lemma sg23036 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6376 sg7060 + +lemma sg23037 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6153 sg7663 + +lemma sg23038 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6272 sg7483 + +lemma sg23039 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7148 + +lemma sg23040 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7088 + +lemma sg23041 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7069 + +lemma sg23042 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6376 sg7061 + +lemma sg23043 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7181 + +lemma sg23044 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6341 sg7290 + +lemma sg23045 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7089 + +lemma sg23046 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7070 + +lemma sg23047 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6655 + +lemma sg23048 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7193 + +lemma sg23049 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6367 sg7181 + +lemma sg23050 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6656 + +lemma sg23051 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7742 + +lemma sg23052 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7681 + +lemma sg23053 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6296 sg7435 + +lemma sg23054 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6430 sg6827 + +lemma sg23055 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7742 + +lemma sg23056 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1708 sg14411 + +lemma sg23057 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6273 sg7483 + +lemma sg23058 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7149 + +lemma sg23059 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7090 + +lemma sg23060 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7071 + +lemma sg23061 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6376 sg7064 + +lemma sg23062 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6368 sg7177 + +lemma sg23063 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6342 sg7290 + +lemma sg23064 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7150 + +lemma sg23065 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7091 + +lemma sg23066 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7072 + +lemma sg23067 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6657 + +lemma sg23068 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7182 + +lemma sg23069 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6406 sg6857 + +lemma sg23070 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7073 + +lemma sg23071 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6658 + +lemma sg23072 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7194 + +lemma sg23073 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7182 + +lemma sg23074 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6298 sg7433 + +lemma sg23075 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7743 + +lemma sg23076 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7682 + +lemma sg23077 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7743 + +lemma sg23078 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7194 + +lemma sg23079 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7092 + +lemma sg23080 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7074 + +lemma sg23081 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6659 + +lemma sg23082 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7183 + +lemma sg23083 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6406 sg6858 + +lemma sg23084 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6421 sg6828 + +lemma sg23085 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6660 + +lemma sg23086 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7744 + +lemma sg23087 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7183 + +lemma sg23088 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7744 + +lemma sg23089 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7683 + +lemma sg23090 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7195 + +lemma sg23091 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7196 + +lemma sg23092 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7684 + +lemma sg23093 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7196 + +lemma sg23094 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7436 + +lemma sg23095 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6274 sg7483 + +lemma sg23096 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7151 + +lemma sg23097 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7093 + +lemma sg23098 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5900 sg7860 + +lemma sg23099 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6212 sg7490 + +lemma sg23100 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6415 sg6833 + +lemma sg23101 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6408 sg6857 + +lemma sg23102 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7094 + +lemma sg23103 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7075 + +lemma sg23104 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6483 sg6639 + +lemma sg23105 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7185 + +lemma sg23106 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6416 sg6833 + +lemma sg23107 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6299 sg7433 + +lemma sg23108 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6483 sg6640 + +lemma sg23109 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7745 + +lemma sg23110 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7185 + +lemma sg23111 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7745 + +lemma sg23112 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7685 + +lemma sg23113 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7197 + +lemma sg23114 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7076 + +lemma sg23115 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6483 sg6641 + +lemma sg23116 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7746 + +lemma sg23117 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6416 sg6834 + +lemma sg23118 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7746 + +lemma sg23119 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7198 + +lemma sg23120 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7686 + +lemma sg23121 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7198 + +lemma sg23122 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7437 + +lemma sg23123 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7187 + +lemma sg23124 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7438 + +lemma sg23125 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6483 sg6642 + +lemma sg23126 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7199 + +lemma sg23127 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7687 + +lemma sg23128 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7199 + +lemma sg23129 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7188 + +lemma sg23130 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7439 + +lemma sg23131 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg6304 sg7373 + +lemma sg23132 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1316 sg14717 + +lemma sg23133 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2023 sg12943 + +lemma sg23134 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1817 sg14307 + +lemma sg23135 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7152 + +lemma sg23136 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3796 sg11537 + +lemma sg23137 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6284 sg7482 + +lemma sg23138 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5296 sg8789 + +lemma sg23139 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6160 sg7598 + +lemma sg23140 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1718 sg14407 + +lemma sg23141 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1818 sg14307 + +lemma sg23142 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7153 + +lemma sg23143 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7095 + +lemma sg23144 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5909 sg7859 + +lemma sg23145 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6376 sg7068 + +lemma sg23146 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6368 sg7181 + +lemma sg23147 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6161 sg7598 + +lemma sg23148 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7154 + +lemma sg23149 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7096 + +lemma sg23150 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6214 sg7489 + +lemma sg23151 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6661 + +lemma sg23152 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6411 sg6840 + +lemma sg23153 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6406 sg6859 + +lemma sg23154 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6215 sg7489 + +lemma sg23155 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6662 + +lemma sg23156 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7200 + +lemma sg23157 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6412 sg6840 + +lemma sg23158 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6298 sg7435 + +lemma sg23159 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7747 + +lemma sg23160 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7688 + +lemma sg23161 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7747 + +lemma sg23162 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7200 + +lemma sg23163 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1819 sg14307 + +lemma sg23164 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7155 + +lemma sg23165 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7097 + +lemma sg23166 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6216 sg7489 + +lemma sg23167 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6663 + +lemma sg23168 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6368 sg7182 + +lemma sg23169 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6408 sg6859 + +lemma sg23170 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7098 + +lemma sg23171 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6217 sg7489 + +lemma sg23172 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6664 + +lemma sg23173 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6411 sg6841 + +lemma sg23174 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6406 sg6860 + +lemma sg23175 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6299 sg7435 + +lemma sg23176 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6665 + +lemma sg23177 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7748 + +lemma sg23178 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6412 sg6841 + +lemma sg23179 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7748 + +lemma sg23180 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7689 + +lemma sg23181 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7201 + +lemma sg23182 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6218 sg7489 + +lemma sg23183 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6666 + +lemma sg23184 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7749 + +lemma sg23185 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6406 sg6861 + +lemma sg23186 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7749 + +lemma sg23187 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7202 + +lemma sg23188 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7690 + +lemma sg23189 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7202 + +lemma sg23190 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6842 + +lemma sg23191 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6412 sg6843 + +lemma sg23192 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6843 + +lemma sg23193 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7156 + +lemma sg23194 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6374 sg7099 + +lemma sg23195 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6219 sg7489 + +lemma sg23196 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6667 + +lemma sg23197 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6368 sg7185 + +lemma sg23198 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6408 sg6860 + +lemma sg23199 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6424 sg6829 + +lemma sg23200 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6220 sg7489 + +lemma sg23201 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6668 + +lemma sg23202 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7750 + +lemma sg23203 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6406 sg6862 + +lemma sg23204 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7750 + +lemma sg23205 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7203 + +lemma sg23206 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7691 + +lemma sg23207 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7203 + +lemma sg23208 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6844 + +lemma sg23209 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6669 + +lemma sg23210 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7204 + +lemma sg23211 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7692 + +lemma sg23212 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7204 + +lemma sg23213 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6412 sg6845 + +lemma sg23214 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6845 + +lemma sg23215 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7438 + +lemma sg23216 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6411 sg6846 + +lemma sg23217 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6412 sg6846 + +lemma sg23218 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6846 + +lemma sg23219 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6298 sg7439 + +lemma sg23220 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3795 sg11538 + +lemma sg23221 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6260 sg7484 + +lemma sg23222 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6219 sg7490 + +lemma sg23223 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7751 + +lemma sg23224 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6408 sg6862 + +lemma sg23225 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7751 + +lemma sg23226 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6220 sg7490 + +lemma sg23227 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7205 + +lemma sg23228 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7693 + +lemma sg23229 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7205 + +lemma sg23230 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6412 sg6847 + +lemma sg23231 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6847 + +lemma sg23232 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6411 sg6848 + +lemma sg23233 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6412 sg6848 + +lemma sg23234 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6848 + +lemma sg23235 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,6,6,6,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6479 sg6669 + +lemma sg23236 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1310 sg14718 + +lemma sg23237 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1710 sg14409 + +lemma sg23238 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6275 sg7483 + +lemma sg23239 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7157 + +lemma sg23240 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg294 sg20311 + +lemma sg23241 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg294 sg20312 + +lemma sg23242 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg294 sg20313 + +lemma sg23243 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1305 sg14723 + +lemma sg23244 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1704 sg14414 + +lemma sg23245 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6276 sg7483 + +lemma sg23246 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7158 + +lemma sg23247 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2173 sg12913 + +lemma sg23248 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg341 sg19570 + +lemma sg23249 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg341 sg19571 + +lemma sg23250 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1306 sg14723 + +lemma sg23251 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1705 sg14414 + +lemma sg23252 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6277 sg7483 + +lemma sg23253 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7159 + +lemma sg23254 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6221 sg7488 + +lemma sg23255 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7077 + +lemma sg23256 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5366 sg8710 + +lemma sg23257 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4730 sg10577 + +lemma sg23258 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1713 sg14409 + +lemma sg23259 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6278 sg7483 + +lemma sg23260 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3212 sg11746 + +lemma sg23261 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6222 sg7488 + +lemma sg23262 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6209 sg7491 + +lemma sg23263 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5366 sg8711 + +lemma sg23264 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6152 sg7676 + +lemma sg23265 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7160 + +lemma sg23266 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6223 sg7488 + +lemma sg23267 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7078 + +lemma sg23268 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6188 sg7503 + +lemma sg23269 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7206 + +lemma sg23270 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6340 sg7291 + +lemma sg23271 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6210 sg7491 + +lemma sg23272 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6654 + +lemma sg23273 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7752 + +lemma sg23274 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6150 sg7694 + +lemma sg23275 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6443 sg6790 + +lemma sg23276 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6445 sg6789 + +lemma sg23277 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg6365 sg7206 + +lemma sg23278 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg6148 sg7752 + +lemma sg23279 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1307 sg14723 + +lemma sg23280 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1706 sg14414 + +lemma sg23281 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6279 sg7483 + +lemma sg23282 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7161 + +lemma sg23283 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6224 sg7488 + +lemma sg23284 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7079 + +lemma sg23285 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5365 sg8713 + +lemma sg23286 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4729 sg10579 + +lemma sg23287 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1308 sg14723 + +lemma sg23288 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1707 sg14414 + +lemma sg23289 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6280 sg7483 + +lemma sg23290 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7162 + +lemma sg23291 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6225 sg7488 + +lemma sg23292 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7080 + +lemma sg23293 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6376 sg7077 + +lemma sg23294 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6153 sg7676 + +lemma sg23295 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6281 sg7483 + +lemma sg23296 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7163 + +lemma sg23297 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6226 sg7488 + +lemma sg23298 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7081 + +lemma sg23299 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6190 sg7503 + +lemma sg23300 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7189 + +lemma sg23301 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6341 sg7291 + +lemma sg23302 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6227 sg7488 + +lemma sg23303 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7082 + +lemma sg23304 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6670 + +lemma sg23305 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7207 + +lemma sg23306 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6367 sg7189 + +lemma sg23307 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6478 sg6671 + +lemma sg23308 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7753 + +lemma sg23309 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7695 + +lemma sg23310 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6296 sg7440 + +lemma sg23311 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6444 sg6790 + +lemma sg23312 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7753 + +lemma sg23313 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2024 sg12942 + +lemma sg23314 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6282 sg7483 + +lemma sg23315 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7164 + +lemma sg23316 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6228 sg7488 + +lemma sg23317 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7083 + +lemma sg23318 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6193 sg7503 + +lemma sg23319 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6415 sg6837 + +lemma sg23320 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6342 sg7291 + +lemma sg23321 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6369 sg7165 + +lemma sg23322 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6229 sg7488 + +lemma sg23323 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6213 sg7491 + +lemma sg23324 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6657 + +lemma sg23325 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7190 + +lemma sg23326 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6416 sg6837 + +lemma sg23327 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7084 + +lemma sg23328 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6658 + +lemma sg23329 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7208 + +lemma sg23330 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7190 + +lemma sg23331 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6417 sg6837 + +lemma sg23332 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7754 + +lemma sg23333 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7696 + +lemma sg23334 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7754 + +lemma sg23335 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7208 + +lemma sg23336 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6230 sg7488 + +lemma sg23337 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6375 sg7085 + +lemma sg23338 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6659 + +lemma sg23339 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7191 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes57.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes57.lean index 10810df53928b0b0cc5139a3ade77cdb2c1d1556..64b3c4531ccebdbeed602a0bbcb32452d503ae74 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes57.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes57.lean @@ -1,1225 +1,1225 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 - -namespace OAI - -/-! Semigroup Nodes 57. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg23340 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6416 sg6838 - -lemma sg23341 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6371 sg7103 - -lemma sg23342 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6660 - -lemma sg23343 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7755 - -lemma sg23344 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7191 - -lemma sg23345 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7755 - -lemma sg23346 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7697 - -lemma sg23347 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7209 - -lemma sg23348 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7210 - -lemma sg23349 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7698 - -lemma sg23350 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7210 - -lemma sg23351 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7441 - -lemma sg23352 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6298 sg7440 - -lemma sg23353 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7756 - -lemma sg23354 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7211 - -lemma sg23355 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6299 sg7440 - -lemma sg23356 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7757 - -lemma sg23357 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7212 - -lemma sg23358 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7758 - -lemma sg23359 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7213 - -lemma sg23360 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7442 - -lemma sg23361 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7443 - -lemma sg23362 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6424 sg6837 - -lemma sg23363 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7759 - -lemma sg23364 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7214 - -lemma sg23365 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7444 - -lemma sg23366 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7215 - -lemma sg23367 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7445 - -lemma sg23368 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7446 - -lemma sg23369 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6421 sg6839 - -lemma sg23370 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7760 - -lemma sg23371 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7216 - -lemma sg23372 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6424 sg6839 - -lemma sg23373 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7761 - -lemma sg23374 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7217 - -lemma sg23375 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7447 - -lemma sg23376 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7218 - -lemma sg23377 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6296 sg7448 - -lemma sg23378 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7762 - -lemma sg23379 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7219 - -lemma sg23380 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7220 - -lemma sg23381 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6442 sg6796 - -lemma sg23382 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7763 - -lemma sg23383 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7221 - -lemma sg23384 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6413 sg6852 - -lemma sg23385 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7764 - -lemma sg23386 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7222 - -lemma sg23387 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7223 - -lemma sg23388 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1313 sg14718 - -lemma sg23389 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1714 sg14409 - -lemma sg23390 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg14308 - -lemma sg23391 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg14751 - -lemma sg23392 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg14755 - -lemma sg23393 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg19570 - -lemma sg23394 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg342 sg19571 - -lemma sg23395 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1314 sg14718 - -lemma sg23396 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1715 sg14409 - -lemma sg23397 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1815 sg14308 - -lemma sg23398 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2178 sg12910 - -lemma sg23399 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg14752 - -lemma sg23400 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg12587 - -lemma sg23401 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5365 sg8717 - -lemma sg23402 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4729 sg10580 - -lemma sg23403 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1315 sg14718 - -lemma sg23404 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1716 sg14409 - -lemma sg23405 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1816 sg14308 - -lemma sg23406 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3214 sg11746 - -lemma sg23407 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2222 sg12862 - -lemma sg23408 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6221 sg7491 - -lemma sg23409 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5366 sg8714 - -lemma sg23410 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6158 sg7625 - -lemma sg23411 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1461 sg14698 - -lemma sg23412 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3215 sg11746 - -lemma sg23413 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3212 sg11747 - -lemma sg23414 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6222 sg7491 - -lemma sg23415 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6209 sg7493 - -lemma sg23416 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7206 - -lemma sg23417 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6159 sg7625 - -lemma sg23418 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3790 sg11539 - -lemma sg23419 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6223 sg7491 - -lemma sg23420 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6670 - -lemma sg23421 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7224 - -lemma sg23422 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6367 sg7206 - -lemma sg23423 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6671 - -lemma sg23424 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7765 - -lemma sg23425 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7702 - -lemma sg23426 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6296 sg7449 - -lemma sg23427 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg6445 sg6790 - -lemma sg23428 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7765 - -lemma sg23429 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1316 sg14718 - -lemma sg23430 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1717 sg14409 - -lemma sg23431 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1817 sg14308 - -lemma sg23432 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3216 sg11746 - -lemma sg23433 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2178 sg12911 - -lemma sg23434 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6224 sg7491 - -lemma sg23435 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5366 sg8715 - -lemma sg23436 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6160 sg7625 - -lemma sg23437 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1718 sg14409 - -lemma sg23438 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1818 sg14308 - -lemma sg23439 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3217 sg11746 - -lemma sg23440 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3791 sg11539 - -lemma sg23441 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6225 sg7491 - -lemma sg23442 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6211 sg7493 - -lemma sg23443 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6368 sg7206 - -lemma sg23444 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6161 sg7625 - -lemma sg23445 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3218 sg11746 - -lemma sg23446 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3792 sg11539 - -lemma sg23447 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6226 sg7491 - -lemma sg23448 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6672 - -lemma sg23449 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7207 - -lemma sg23450 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6406 sg6863 - -lemma sg23451 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6227 sg7491 - -lemma sg23452 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6673 - -lemma sg23453 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7225 - -lemma sg23454 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7207 - -lemma sg23455 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6298 sg7449 - -lemma sg23456 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7766 - -lemma sg23457 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7703 - -lemma sg23458 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7766 - -lemma sg23459 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7225 - -lemma sg23460 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1819 sg14308 - -lemma sg23461 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3219 sg11746 - -lemma sg23462 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3793 sg11539 - -lemma sg23463 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6228 sg7491 - -lemma sg23464 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6674 - -lemma sg23465 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6415 sg6850 - -lemma sg23466 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6408 sg6863 - -lemma sg23467 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3794 sg11539 - -lemma sg23468 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6229 sg7491 - -lemma sg23469 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6675 - -lemma sg23470 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6366 sg7208 - -lemma sg23471 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6416 sg6850 - -lemma sg23472 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6299 sg7449 - -lemma sg23473 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6676 - -lemma sg23474 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7767 - -lemma sg23475 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7208 - -lemma sg23476 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7767 - -lemma sg23477 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7704 - -lemma sg23478 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7226 - -lemma sg23479 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6230 sg7491 - -lemma sg23480 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6481 sg6677 - -lemma sg23481 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6147 sg7768 - -lemma sg23482 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6416 sg6851 - -lemma sg23483 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7768 - -lemma sg23484 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6364 sg7227 - -lemma sg23485 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6150 sg7705 - -lemma sg23486 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7227 - -lemma sg23487 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6367 sg7210 - -lemma sg23488 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6421 sg6849 - -lemma sg23489 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7769 - -lemma sg23490 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7228 - -lemma sg23491 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6424 sg6849 - -lemma sg23492 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7770 - -lemma sg23493 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7229 - -lemma sg23494 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7230 - -lemma sg23495 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7771 - -lemma sg23496 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6372 sg7118 - -lemma sg23497 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,6,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7772 - -lemma sg23498 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg6365 sg7231 - -lemma sg23499 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,6,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7773 - -lemma sg23500 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6315 sg7376 - -lemma sg23501 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,7,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7774 - -lemma sg23502 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,8,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6315 sg7383 - -lemma sg23503 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1317 sg14718 - -lemma sg23504 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1719 sg14409 - -lemma sg23505 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg963 sg15154 - -lemma sg23506 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg14309 - -lemma sg23507 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg19572 - -lemma sg23508 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg12588 - -lemma sg23509 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5366 sg8717 - -lemma sg23510 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg4730 sg10580 - -lemma sg23511 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6417 sg6853 - -lemma sg23512 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7775 - -lemma sg23513 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6421 sg6853 - -lemma sg23514 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7776 - -lemma sg23515 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6424 sg6853 - -lemma sg23516 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7777 - -lemma sg23517 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6372 sg7135 - -lemma sg23518 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6148 sg7778 - -lemma sg23519 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6315 sg7392 - -lemma sg23520 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg990 sg15055 - -lemma sg23521 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1317 sg14719 - -lemma sg23522 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg985 sg15057 - -lemma sg23523 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3224 sg11745 - -lemma sg23524 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg15155 - -lemma sg23525 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6275 sg7487 - -lemma sg23526 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5297 sg8790 - -lemma sg23527 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6348 sg7288 - -lemma sg23528 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6371 sg7157 - -lemma sg23529 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6372 sg7157 - -lemma sg23530 : RowSquare [6,6,3,3,3,3,2,2,2,2,2,2,2,1,1] [5,5,5,5,5,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7817 sg8007 - -lemma sg23531 : RowSquare [8,8,3,3,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg14796 - -lemma sg23532 : RowSquare [8,8,3,3,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg14797 - -lemma sg23533 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [6,5,5,5,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg7809 sg8210 - -lemma sg23534 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [8,8,8,8,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1868 sg14846 - -lemma sg23535 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [8,8,8,8,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7786 sg8273 - -lemma sg23536 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [8,8,8,8,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7254 sg8619 - -lemma sg23537 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [8,8,8,8,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7787 sg8273 - -lemma sg23538 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [9,9,8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg7232 sg8639 - -lemma sg23539 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [9,9,9,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1723 sg15101 - -lemma sg23540 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,8,8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg7232 sg8640 - -lemma sg23541 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,9,7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg7232 sg8641 - -lemma sg23542 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,9,8,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg7232 sg8642 - -lemma sg23543 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg990 sg18027 - -lemma sg23544 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1317 sg15596 - -lemma sg23545 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg985 sg18028 - -lemma sg23546 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg562 sg21038 - -lemma sg23547 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg21112 - -lemma sg23548 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg21113 - -lemma sg23549 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg21114 - -lemma sg23550 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg367 sg21115 - -lemma sg23551 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg367 sg21116 - -lemma sg23552 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1322 sg15595 - -lemma sg23553 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1725 sg15100 - -lemma sg23554 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1325 sg15557 - -lemma sg23555 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1744 sg15047 - -lemma sg23556 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2237 sg14696 - -lemma sg23557 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2680 sg14209 - -lemma sg23558 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg871 sg19177 - -lemma sg23559 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg14210 - -lemma sg23560 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg871 sg19178 - -lemma sg23561 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg871 sg19179 - -lemma sg23562 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg986 sg18028 - -lemma sg23563 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1746 sg15045 - -lemma sg23564 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1849 sg14977 - -lemma sg23565 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2223 sg14697 - -lemma sg23566 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg887 sg18279 - -lemma sg23567 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6221 sg10105 - -lemma sg23568 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg887 sg18280 - -lemma sg23569 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6891 sg8717 - -lemma sg23570 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1325 sg15558 - -lemma sg23571 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2246 sg14695 - -lemma sg23572 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg562 sg21039 - -lemma sg23573 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6222 sg10105 - -lemma sg23574 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg569 sg21036 - -lemma sg23575 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7255 sg8624 - -lemma sg23576 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg569 sg21037 - -lemma sg23577 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1854 sg14976 - -lemma sg23578 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6223 sg10105 - -lemma sg23579 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5242 sg11507 - -lemma sg23580 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7780 sg8281 - -lemma sg23581 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg7239 sg8638 - -lemma sg23582 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5243 sg11507 - -lemma sg23583 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6900 sg8707 - -lemma sg23584 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg7512 sg8404 - -lemma sg23585 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg7232 sg8643 - -lemma sg23586 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg7240 sg8638 - -lemma sg23587 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1726 sg15100 - -lemma sg23588 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1746 sg15046 - -lemma sg23589 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2151 sg14708 - -lemma sg23590 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2238 sg14696 - -lemma sg23591 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2681 sg14209 - -lemma sg23592 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1326 sg15556 - -lemma sg23593 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6224 sg10105 - -lemma sg23594 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg14211 - -lemma sg23595 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6892 sg8717 - -lemma sg23596 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1745 sg15047 - -lemma sg23597 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2239 sg14696 - -lemma sg23598 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2682 sg14209 - -lemma sg23599 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2693 sg14086 - -lemma sg23600 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6225 sg10105 - -lemma sg23601 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1238 sg15601 - -lemma sg23602 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7791 sg8275 - -lemma sg23603 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1238 sg15602 - -lemma sg23604 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2683 sg14209 - -lemma sg23605 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2249 sg14678 - -lemma sg23606 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6226 sg10105 - -lemma sg23607 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5912 sg10861 - -lemma sg23608 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7783 sg8281 - -lemma sg23609 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg7792 sg8275 - -lemma sg23610 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6227 sg10105 - -lemma sg23611 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5913 sg10861 - -lemma sg23612 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7780 sg8282 - -lemma sg23613 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7512 sg8405 - -lemma sg23614 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg7232 sg8644 - -lemma sg23615 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7798 sg8272 - -lemma sg23616 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg7781 sg8282 - -lemma sg23617 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1868 sg14847 - -lemma sg23618 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3169 sg12947 - -lemma sg23619 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3777 sg12701 - -lemma sg23620 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6228 sg10105 - -lemma sg23621 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5246 sg11507 - -lemma sg23622 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7786 sg8281 - -lemma sg23623 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg7242 sg8638 - -lemma sg23624 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3778 sg12701 - -lemma sg23625 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6229 sg10105 - -lemma sg23626 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5919 sg10852 - -lemma sg23627 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6891 sg8718 - -lemma sg23628 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7512 sg8406 - -lemma sg23629 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg7232 sg8645 - -lemma sg23630 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5248 sg11507 - -lemma sg23631 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7780 sg8283 - -lemma sg23632 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7243 sg8638 - -lemma sg23633 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg7781 sg8283 - -lemma sg23634 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6230 sg10105 - -lemma sg23635 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5920 sg10852 - -lemma sg23636 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6900 sg8708 - -lemma sg23637 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7526 sg8400 - -lemma sg23638 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7780 sg8284 - -lemma sg23639 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7781 sg8284 - -lemma sg23640 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6893 sg8717 - -lemma sg23641 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg7232 sg8646 - -lemma sg23642 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,5,5,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6883 sg8719 - -lemma sg23643 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,5,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7808 sg8211 - -lemma sg23644 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,5,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7780 sg8286 - -lemma sg23645 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,5,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7780 sg8287 - -lemma sg23646 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,5,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7805 sg8212 - -lemma sg23647 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7790 sg8276 - -lemma sg23648 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7790 sg8277 - -lemma sg23649 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7784 sg8286 - -lemma sg23650 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7790 sg8278 - -lemma sg23651 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7784 sg8287 - -lemma sg23652 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4652 sg11786 - -lemma sg23653 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,6,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6124 sg10575 - -lemma sg23654 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7786 sg8285 - -lemma sg23655 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7790 sg8279 - -lemma sg23656 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7790 sg8280 - -lemma sg23657 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7797 sg8274 - -lemma sg23658 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,8,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7780 sg8289 - -lemma sg23659 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,5,5,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7790 sg8286 - -lemma sg23660 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,5,5,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7790 sg8287 - -lemma sg23661 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7780 sg8291 - -lemma sg23662 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,5,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7780 sg8292 - -lemma sg23663 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,5,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7780 sg8293 - -lemma sg23664 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7790 sg8288 - -lemma sg23665 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4652 sg11787 - -lemma sg23666 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6855 sg8769 - -lemma sg23667 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7786 sg8290 - -lemma sg23668 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6901 sg8716 - -lemma sg23669 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6855 sg8770 - -lemma sg23670 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,6,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6701 sg8887 - -lemma sg23671 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7779 sg8294 - -lemma sg23672 : RowSquare [11,10,4,3,2,2,2,2,2,2,1,1] [7,5,5,5,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg23533 - -lemma sg23673 : RowSquare [9,8,3,3,2,2,2,2,2,2,2,2,2,1,1] [7,6,6,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2247 sg15690 - -lemma sg23674 : RowSquare [9,8,3,3,2,2,2,2,2,2,2,2,2,1,1] [7,6,6,6,6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2247 sg15691 - -lemma sg23675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,6,6,6,6,6,6] := by - exact rowSquare_join (by decide) sg74 sg21649 - -lemma sg23676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,6,6,6,6,5] := by - exact rowSquare_join (by decide) sg74 sg21648 - -lemma sg23677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,6,6,5,5] := by - exact rowSquare_join (by decide) sg8432 sg10195 - -lemma sg23678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,6,6,6,4] := by - exact rowSquare_join (by decide) sg74 sg21644 - -lemma sg23679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,5,5,5] := by - exact rowSquare_join (by decide) sg8432 sg10193 - -lemma sg23680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,6,5,4] := by - exact rowSquare_join (by decide) sg8432 sg10194 - -lemma sg23681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7247 sg11435 - -lemma sg23682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8748 sg9444 - -lemma sg23683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9468 - -lemma sg23684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7235 sg11448 - -lemma sg23685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,2,2,2,2] := by - exact rowSquare_join (by decide) sg7247 sg11437 - -lemma sg23686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8428 sg10195 - -lemma sg23687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4747 sg12931 - -lemma sg23688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,3,2,2,1] := by - exact rowSquare_join (by decide) sg7247 sg11438 - -lemma sg23689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,3,3,1,1] := by - exact rowSquare_join (by decide) sg6398 sg11736 - -lemma sg23690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,3,3,2] := by - exact rowSquare_join (by decide) sg4747 sg12932 - -lemma sg23691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10195 - -lemma sg23692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,4,2,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10195 - -lemma sg23693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,4,2,2] := by - exact rowSquare_join (by decide) sg74 sg21645 - -lemma sg23694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,4,3,1] := by - exact rowSquare_join (by decide) sg7451 sg11286 - -lemma sg23695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,5,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg21646 - -lemma sg23696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,5,2,1] := by - exact rowSquare_join (by decide) sg8431 sg10195 - -lemma sg23697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,6,1,1] := by - exact rowSquare_join (by decide) sg74 sg21647 - -lemma sg23698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,4,4,4,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8494 sg10167 - -lemma sg23699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,4,4,4,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10245 - -lemma sg23700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,4,4,4,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10196 - -lemma sg23701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,4,4,4,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10246 - -lemma sg23702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,4,4,4,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10247 - -lemma sg23703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,4,4,4,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg8648 sg9684 - -lemma sg23704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8498 sg10167 - -lemma sg23705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10248 - -lemma sg23706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10198 - -lemma sg23707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10249 - -lemma sg23708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9683 - -lemma sg23709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10250 - -lemma sg23710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9686 - -lemma sg23711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10200 - -lemma sg23712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg8648 sg9687 - -lemma sg23713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8499 sg10167 - -lemma sg23714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10251 - -lemma sg23715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10201 - -lemma sg23716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10252 - -lemma sg23717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9445 - -lemma sg23718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10253 - -lemma sg23719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9689 - -lemma sg23720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10254 - -lemma sg23721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10203 - -lemma sg23722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9690 - -lemma sg23723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8798 sg9160 - -lemma sg23724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10255 - -lemma sg23725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10204 - -lemma sg23726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10256 - -lemma sg23727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9447 - -lemma sg23728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10257 - -lemma sg23729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9692 - -lemma sg23730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8750 sg9443 - -lemma sg23731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10258 - -lemma sg23732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10206 - -lemma sg23733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9693 - -lemma sg23734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10615 - -lemma sg23735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9694 - -lemma sg23736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9161 - -lemma sg23737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg8830 sg9158 - -lemma sg23738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9448 - -lemma sg23739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10259 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 + +namespace OAI + +/-! Semigroup Nodes 57. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg23340 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6416 sg6838 + +lemma sg23341 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6371 sg7103 + +lemma sg23342 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6660 + +lemma sg23343 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7755 + +lemma sg23344 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7191 + +lemma sg23345 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7755 + +lemma sg23346 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7697 + +lemma sg23347 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7209 + +lemma sg23348 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7210 + +lemma sg23349 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7698 + +lemma sg23350 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7210 + +lemma sg23351 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7441 + +lemma sg23352 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6298 sg7440 + +lemma sg23353 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7756 + +lemma sg23354 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7211 + +lemma sg23355 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6299 sg7440 + +lemma sg23356 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7757 + +lemma sg23357 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7212 + +lemma sg23358 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7758 + +lemma sg23359 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7213 + +lemma sg23360 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7442 + +lemma sg23361 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7443 + +lemma sg23362 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6424 sg6837 + +lemma sg23363 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7759 + +lemma sg23364 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7214 + +lemma sg23365 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7444 + +lemma sg23366 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7215 + +lemma sg23367 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7445 + +lemma sg23368 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7446 + +lemma sg23369 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6421 sg6839 + +lemma sg23370 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7760 + +lemma sg23371 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7216 + +lemma sg23372 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6424 sg6839 + +lemma sg23373 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7761 + +lemma sg23374 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7217 + +lemma sg23375 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7447 + +lemma sg23376 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7218 + +lemma sg23377 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6296 sg7448 + +lemma sg23378 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7762 + +lemma sg23379 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7219 + +lemma sg23380 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7220 + +lemma sg23381 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6442 sg6796 + +lemma sg23382 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7763 + +lemma sg23383 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7221 + +lemma sg23384 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6413 sg6852 + +lemma sg23385 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7764 + +lemma sg23386 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7222 + +lemma sg23387 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,7,7,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7223 + +lemma sg23388 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1313 sg14718 + +lemma sg23389 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1714 sg14409 + +lemma sg23390 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg14308 + +lemma sg23391 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg14751 + +lemma sg23392 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg14755 + +lemma sg23393 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg19570 + +lemma sg23394 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg342 sg19571 + +lemma sg23395 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1314 sg14718 + +lemma sg23396 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1715 sg14409 + +lemma sg23397 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1815 sg14308 + +lemma sg23398 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2178 sg12910 + +lemma sg23399 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg14752 + +lemma sg23400 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg12587 + +lemma sg23401 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5365 sg8717 + +lemma sg23402 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4729 sg10580 + +lemma sg23403 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1315 sg14718 + +lemma sg23404 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1716 sg14409 + +lemma sg23405 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1816 sg14308 + +lemma sg23406 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3214 sg11746 + +lemma sg23407 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2222 sg12862 + +lemma sg23408 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6221 sg7491 + +lemma sg23409 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5366 sg8714 + +lemma sg23410 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6158 sg7625 + +lemma sg23411 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1461 sg14698 + +lemma sg23412 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3215 sg11746 + +lemma sg23413 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3212 sg11747 + +lemma sg23414 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6222 sg7491 + +lemma sg23415 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6209 sg7493 + +lemma sg23416 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7206 + +lemma sg23417 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6159 sg7625 + +lemma sg23418 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3790 sg11539 + +lemma sg23419 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6223 sg7491 + +lemma sg23420 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6670 + +lemma sg23421 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7224 + +lemma sg23422 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6367 sg7206 + +lemma sg23423 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6671 + +lemma sg23424 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7765 + +lemma sg23425 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7702 + +lemma sg23426 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6296 sg7449 + +lemma sg23427 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg6445 sg6790 + +lemma sg23428 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7765 + +lemma sg23429 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1316 sg14718 + +lemma sg23430 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1717 sg14409 + +lemma sg23431 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1817 sg14308 + +lemma sg23432 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3216 sg11746 + +lemma sg23433 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2178 sg12911 + +lemma sg23434 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6224 sg7491 + +lemma sg23435 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5366 sg8715 + +lemma sg23436 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6160 sg7625 + +lemma sg23437 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1718 sg14409 + +lemma sg23438 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1818 sg14308 + +lemma sg23439 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3217 sg11746 + +lemma sg23440 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3791 sg11539 + +lemma sg23441 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6225 sg7491 + +lemma sg23442 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6211 sg7493 + +lemma sg23443 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6368 sg7206 + +lemma sg23444 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6161 sg7625 + +lemma sg23445 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3218 sg11746 + +lemma sg23446 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3792 sg11539 + +lemma sg23447 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6226 sg7491 + +lemma sg23448 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6672 + +lemma sg23449 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7207 + +lemma sg23450 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6406 sg6863 + +lemma sg23451 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6227 sg7491 + +lemma sg23452 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6673 + +lemma sg23453 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7225 + +lemma sg23454 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7207 + +lemma sg23455 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6298 sg7449 + +lemma sg23456 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7766 + +lemma sg23457 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7703 + +lemma sg23458 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7766 + +lemma sg23459 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7225 + +lemma sg23460 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1819 sg14308 + +lemma sg23461 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3219 sg11746 + +lemma sg23462 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3793 sg11539 + +lemma sg23463 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6228 sg7491 + +lemma sg23464 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6674 + +lemma sg23465 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6415 sg6850 + +lemma sg23466 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6408 sg6863 + +lemma sg23467 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3794 sg11539 + +lemma sg23468 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6229 sg7491 + +lemma sg23469 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6675 + +lemma sg23470 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6366 sg7208 + +lemma sg23471 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6416 sg6850 + +lemma sg23472 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6299 sg7449 + +lemma sg23473 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6676 + +lemma sg23474 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7767 + +lemma sg23475 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7208 + +lemma sg23476 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7767 + +lemma sg23477 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7704 + +lemma sg23478 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7226 + +lemma sg23479 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6230 sg7491 + +lemma sg23480 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6481 sg6677 + +lemma sg23481 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6147 sg7768 + +lemma sg23482 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6416 sg6851 + +lemma sg23483 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7768 + +lemma sg23484 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6364 sg7227 + +lemma sg23485 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6150 sg7705 + +lemma sg23486 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7227 + +lemma sg23487 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6367 sg7210 + +lemma sg23488 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6421 sg6849 + +lemma sg23489 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7769 + +lemma sg23490 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7228 + +lemma sg23491 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6424 sg6849 + +lemma sg23492 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7770 + +lemma sg23493 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7229 + +lemma sg23494 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7230 + +lemma sg23495 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7771 + +lemma sg23496 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6372 sg7118 + +lemma sg23497 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,6,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7772 + +lemma sg23498 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg6365 sg7231 + +lemma sg23499 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,6,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7773 + +lemma sg23500 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6315 sg7376 + +lemma sg23501 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,7,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7774 + +lemma sg23502 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,8,8,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6315 sg7383 + +lemma sg23503 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1317 sg14718 + +lemma sg23504 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1719 sg14409 + +lemma sg23505 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg963 sg15154 + +lemma sg23506 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg14309 + +lemma sg23507 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg19572 + +lemma sg23508 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg12588 + +lemma sg23509 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5366 sg8717 + +lemma sg23510 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg4730 sg10580 + +lemma sg23511 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6417 sg6853 + +lemma sg23512 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7775 + +lemma sg23513 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6421 sg6853 + +lemma sg23514 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7776 + +lemma sg23515 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6424 sg6853 + +lemma sg23516 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7777 + +lemma sg23517 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6372 sg7135 + +lemma sg23518 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6148 sg7778 + +lemma sg23519 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6315 sg7392 + +lemma sg23520 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg990 sg15055 + +lemma sg23521 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1317 sg14719 + +lemma sg23522 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg985 sg15057 + +lemma sg23523 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3224 sg11745 + +lemma sg23524 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg15155 + +lemma sg23525 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6275 sg7487 + +lemma sg23526 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5297 sg8790 + +lemma sg23527 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6348 sg7288 + +lemma sg23528 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6371 sg7157 + +lemma sg23529 : RowSquare [11,9,4,3,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6372 sg7157 + +lemma sg23530 : RowSquare [6,6,3,3,3,3,2,2,2,2,2,2,2,1,1] [5,5,5,5,5,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7817 sg8007 + +lemma sg23531 : RowSquare [8,8,3,3,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg14796 + +lemma sg23532 : RowSquare [8,8,3,3,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg14797 + +lemma sg23533 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [6,5,5,5,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg7809 sg8210 + +lemma sg23534 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [8,8,8,8,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1868 sg14846 + +lemma sg23535 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [8,8,8,8,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7786 sg8273 + +lemma sg23536 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [8,8,8,8,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7254 sg8619 + +lemma sg23537 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [8,8,8,8,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7787 sg8273 + +lemma sg23538 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [9,9,8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg7232 sg8639 + +lemma sg23539 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [9,9,9,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1723 sg15101 + +lemma sg23540 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,8,8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg7232 sg8640 + +lemma sg23541 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,9,7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg7232 sg8641 + +lemma sg23542 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,9,8,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg7232 sg8642 + +lemma sg23543 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg990 sg18027 + +lemma sg23544 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1317 sg15596 + +lemma sg23545 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg985 sg18028 + +lemma sg23546 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg562 sg21038 + +lemma sg23547 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg21112 + +lemma sg23548 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg21113 + +lemma sg23549 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg21114 + +lemma sg23550 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg367 sg21115 + +lemma sg23551 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg367 sg21116 + +lemma sg23552 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1322 sg15595 + +lemma sg23553 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1725 sg15100 + +lemma sg23554 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1325 sg15557 + +lemma sg23555 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1744 sg15047 + +lemma sg23556 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2237 sg14696 + +lemma sg23557 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2680 sg14209 + +lemma sg23558 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg871 sg19177 + +lemma sg23559 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg14210 + +lemma sg23560 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg871 sg19178 + +lemma sg23561 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg871 sg19179 + +lemma sg23562 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg986 sg18028 + +lemma sg23563 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1746 sg15045 + +lemma sg23564 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1849 sg14977 + +lemma sg23565 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2223 sg14697 + +lemma sg23566 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg887 sg18279 + +lemma sg23567 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6221 sg10105 + +lemma sg23568 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg887 sg18280 + +lemma sg23569 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6891 sg8717 + +lemma sg23570 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1325 sg15558 + +lemma sg23571 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2246 sg14695 + +lemma sg23572 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg562 sg21039 + +lemma sg23573 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6222 sg10105 + +lemma sg23574 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg569 sg21036 + +lemma sg23575 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7255 sg8624 + +lemma sg23576 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg569 sg21037 + +lemma sg23577 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1854 sg14976 + +lemma sg23578 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6223 sg10105 + +lemma sg23579 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5242 sg11507 + +lemma sg23580 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7780 sg8281 + +lemma sg23581 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg7239 sg8638 + +lemma sg23582 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5243 sg11507 + +lemma sg23583 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6900 sg8707 + +lemma sg23584 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg7512 sg8404 + +lemma sg23585 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg7232 sg8643 + +lemma sg23586 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg7240 sg8638 + +lemma sg23587 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1726 sg15100 + +lemma sg23588 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1746 sg15046 + +lemma sg23589 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2151 sg14708 + +lemma sg23590 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2238 sg14696 + +lemma sg23591 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2681 sg14209 + +lemma sg23592 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1326 sg15556 + +lemma sg23593 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6224 sg10105 + +lemma sg23594 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg14211 + +lemma sg23595 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6892 sg8717 + +lemma sg23596 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1745 sg15047 + +lemma sg23597 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2239 sg14696 + +lemma sg23598 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2682 sg14209 + +lemma sg23599 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2693 sg14086 + +lemma sg23600 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6225 sg10105 + +lemma sg23601 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1238 sg15601 + +lemma sg23602 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7791 sg8275 + +lemma sg23603 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1238 sg15602 + +lemma sg23604 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2683 sg14209 + +lemma sg23605 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2249 sg14678 + +lemma sg23606 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6226 sg10105 + +lemma sg23607 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5912 sg10861 + +lemma sg23608 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7783 sg8281 + +lemma sg23609 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg7792 sg8275 + +lemma sg23610 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6227 sg10105 + +lemma sg23611 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5913 sg10861 + +lemma sg23612 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7780 sg8282 + +lemma sg23613 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7512 sg8405 + +lemma sg23614 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg7232 sg8644 + +lemma sg23615 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7798 sg8272 + +lemma sg23616 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg7781 sg8282 + +lemma sg23617 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1868 sg14847 + +lemma sg23618 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3169 sg12947 + +lemma sg23619 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3777 sg12701 + +lemma sg23620 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6228 sg10105 + +lemma sg23621 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5246 sg11507 + +lemma sg23622 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7786 sg8281 + +lemma sg23623 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg7242 sg8638 + +lemma sg23624 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3778 sg12701 + +lemma sg23625 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6229 sg10105 + +lemma sg23626 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5919 sg10852 + +lemma sg23627 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6891 sg8718 + +lemma sg23628 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7512 sg8406 + +lemma sg23629 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg7232 sg8645 + +lemma sg23630 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5248 sg11507 + +lemma sg23631 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7780 sg8283 + +lemma sg23632 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7243 sg8638 + +lemma sg23633 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg7781 sg8283 + +lemma sg23634 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6230 sg10105 + +lemma sg23635 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5920 sg10852 + +lemma sg23636 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6900 sg8708 + +lemma sg23637 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7526 sg8400 + +lemma sg23638 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7780 sg8284 + +lemma sg23639 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7781 sg8284 + +lemma sg23640 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6893 sg8717 + +lemma sg23641 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [10,10,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg7232 sg8646 + +lemma sg23642 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,5,5,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6883 sg8719 + +lemma sg23643 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,5,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7808 sg8211 + +lemma sg23644 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,5,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7780 sg8286 + +lemma sg23645 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,5,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7780 sg8287 + +lemma sg23646 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,5,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7805 sg8212 + +lemma sg23647 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7790 sg8276 + +lemma sg23648 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7790 sg8277 + +lemma sg23649 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7784 sg8286 + +lemma sg23650 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7790 sg8278 + +lemma sg23651 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7784 sg8287 + +lemma sg23652 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4652 sg11786 + +lemma sg23653 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,6,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6124 sg10575 + +lemma sg23654 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7786 sg8285 + +lemma sg23655 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7790 sg8279 + +lemma sg23656 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7790 sg8280 + +lemma sg23657 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,6,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7797 sg8274 + +lemma sg23658 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [11,8,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7780 sg8289 + +lemma sg23659 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,5,5,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7790 sg8286 + +lemma sg23660 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,5,5,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7790 sg8287 + +lemma sg23661 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7780 sg8291 + +lemma sg23662 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,5,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7780 sg8292 + +lemma sg23663 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,5,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7780 sg8293 + +lemma sg23664 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7790 sg8288 + +lemma sg23665 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4652 sg11787 + +lemma sg23666 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6855 sg8769 + +lemma sg23667 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7786 sg8290 + +lemma sg23668 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6901 sg8716 + +lemma sg23669 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6855 sg8770 + +lemma sg23670 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,6,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6701 sg8887 + +lemma sg23671 : RowSquare [11,10,4,3,2,2,2,2,2,2,1] [12,6,6,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7779 sg8294 + +lemma sg23672 : RowSquare [11,10,4,3,2,2,2,2,2,2,1,1] [7,5,5,5,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg23533 + +lemma sg23673 : RowSquare [9,8,3,3,2,2,2,2,2,2,2,2,2,1,1] [7,6,6,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2247 sg15690 + +lemma sg23674 : RowSquare [9,8,3,3,2,2,2,2,2,2,2,2,2,1,1] [7,6,6,6,6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2247 sg15691 + +lemma sg23675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,6,6,6,6,6,6] := by + exact rowSquare_join (by decide) sg74 sg21649 + +lemma sg23676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,6,6,6,6,5] := by + exact rowSquare_join (by decide) sg74 sg21648 + +lemma sg23677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,6,6,5,5] := by + exact rowSquare_join (by decide) sg8432 sg10195 + +lemma sg23678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,6,6,6,4] := by + exact rowSquare_join (by decide) sg74 sg21644 + +lemma sg23679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,5,5,5] := by + exact rowSquare_join (by decide) sg8432 sg10193 + +lemma sg23680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,6,5,4] := by + exact rowSquare_join (by decide) sg8432 sg10194 + +lemma sg23681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7247 sg11435 + +lemma sg23682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8748 sg9444 + +lemma sg23683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9468 + +lemma sg23684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7235 sg11448 + +lemma sg23685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,2,2,2,2] := by + exact rowSquare_join (by decide) sg7247 sg11437 + +lemma sg23686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8428 sg10195 + +lemma sg23687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4747 sg12931 + +lemma sg23688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,3,2,2,1] := by + exact rowSquare_join (by decide) sg7247 sg11438 + +lemma sg23689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,3,3,1,1] := by + exact rowSquare_join (by decide) sg6398 sg11736 + +lemma sg23690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,3,3,2] := by + exact rowSquare_join (by decide) sg4747 sg12932 + +lemma sg23691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10195 + +lemma sg23692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,4,2,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10195 + +lemma sg23693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,4,2,2] := by + exact rowSquare_join (by decide) sg74 sg21645 + +lemma sg23694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,4,3,1] := by + exact rowSquare_join (by decide) sg7451 sg11286 + +lemma sg23695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,5,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg21646 + +lemma sg23696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,5,2,1] := by + exact rowSquare_join (by decide) sg8431 sg10195 + +lemma sg23697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [7,7,7,7,7,6,1,1] := by + exact rowSquare_join (by decide) sg74 sg21647 + +lemma sg23698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,4,4,4,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8494 sg10167 + +lemma sg23699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,4,4,4,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10245 + +lemma sg23700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,4,4,4,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10196 + +lemma sg23701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,4,4,4,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10246 + +lemma sg23702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,4,4,4,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10247 + +lemma sg23703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,4,4,4,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg8648 sg9684 + +lemma sg23704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8498 sg10167 + +lemma sg23705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10248 + +lemma sg23706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10198 + +lemma sg23707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10249 + +lemma sg23708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9683 + +lemma sg23709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10250 + +lemma sg23710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9686 + +lemma sg23711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10200 + +lemma sg23712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,4,4,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg8648 sg9687 + +lemma sg23713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8499 sg10167 + +lemma sg23714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10251 + +lemma sg23715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10201 + +lemma sg23716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10252 + +lemma sg23717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9445 + +lemma sg23718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10253 + +lemma sg23719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9689 + +lemma sg23720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10254 + +lemma sg23721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10203 + +lemma sg23722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9690 + +lemma sg23723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,4,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8798 sg9160 + +lemma sg23724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10255 + +lemma sg23725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10204 + +lemma sg23726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10256 + +lemma sg23727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9447 + +lemma sg23728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10257 + +lemma sg23729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9692 + +lemma sg23730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8750 sg9443 + +lemma sg23731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10258 + +lemma sg23732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10206 + +lemma sg23733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9693 + +lemma sg23734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10615 + +lemma sg23735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9694 + +lemma sg23736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9161 + +lemma sg23737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg8830 sg9158 + +lemma sg23738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9448 + +lemma sg23739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10259 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes58.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes58.lean index 8d633bfda1d957655fdbaa077b06e27481b00fe2..7c502e2f2c6da72b64447dcc92b619bade34d51a 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes58.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes58.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes57 - -namespace OAI - -/-! Semigroup Nodes 58. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg23740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9695 - -lemma sg23741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8472 sg10172 - -lemma sg23742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10260 - -lemma sg23743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10208 - -lemma sg23744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9696 - -lemma sg23745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8872 sg8981 - -lemma sg23746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10617 - -lemma sg23747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9697 - -lemma sg23748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8653 sg9661 - -lemma sg23749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8353 sg10601 - -lemma sg23750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8354 sg10601 - -lemma sg23751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg8873 sg8982 - -lemma sg23752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8500 sg10167 - -lemma sg23753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8481 sg10168 - -lemma sg23754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10099 - -lemma sg23755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg8451 sg10174 - -lemma sg23756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg8530 sg10084 - -lemma sg23757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10100 - -lemma sg23758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg8452 sg10174 - -lemma sg23759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8529 sg10085 - -lemma sg23760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10085 - -lemma sg23761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,3,3] := by - exact rowSquare_join (by decide) sg8873 sg8983 - -lemma sg23762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg7236 sg11439 - -lemma sg23763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,4,2] := by - exact rowSquare_join (by decide) sg7237 sg11439 - -lemma sg23764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg8529 sg10086 - -lemma sg23765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10086 - -lemma sg23766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg0 sg23672 - -lemma sg23767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,3,2] := by - exact rowSquare_join (by decide) sg6392 sg11737 - -lemma sg23768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,4,1] := by - exact rowSquare_join (by decide) sg5526 sg12627 - -lemma sg23769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,5] := by - exact rowSquare_join (by decide) sg5531 sg12619 - -lemma sg23770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8502 sg10167 - -lemma sg23771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10261 - -lemma sg23772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10209 - -lemma sg23773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10262 - -lemma sg23774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9685 - -lemma sg23775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10263 - -lemma sg23776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9699 - -lemma sg23777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10264 - -lemma sg23778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10211 - -lemma sg23779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9700 - -lemma sg23780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8423 sg10200 - -lemma sg23781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8503 sg10167 - -lemma sg23782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10265 - -lemma sg23783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10212 - -lemma sg23784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10266 - -lemma sg23785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9688 - -lemma sg23786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10267 - -lemma sg23787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9703 - -lemma sg23788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9470 - -lemma sg23789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10268 - -lemma sg23790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10214 - -lemma sg23791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9704 - -lemma sg23792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10215 - -lemma sg23793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9705 - -lemma sg23794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10203 - -lemma sg23795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg8792 sg9174 - -lemma sg23796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10216 - -lemma sg23797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10269 - -lemma sg23798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9691 - -lemma sg23799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10270 - -lemma sg23800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9707 - -lemma sg23801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9447 - -lemma sg23802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10271 - -lemma sg23803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10218 - -lemma sg23804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9708 - -lemma sg23805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10272 - -lemma sg23806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10219 - -lemma sg23807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9709 - -lemma sg23808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10206 - -lemma sg23809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9694 - -lemma sg23810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10615 - -lemma sg23811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg8861 sg8984 - -lemma sg23812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9448 - -lemma sg23813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10273 - -lemma sg23814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10220 - -lemma sg23815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9710 - -lemma sg23816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8477 sg10172 - -lemma sg23817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10274 - -lemma sg23818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10221 - -lemma sg23819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9711 - -lemma sg23820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10208 - -lemma sg23821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10625 - -lemma sg23822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9712 - -lemma sg23823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9697 - -lemma sg23824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10617 - -lemma sg23825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg8861 sg8985 - -lemma sg23826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8356 sg10601 - -lemma sg23827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg8861 sg8986 - -lemma sg23828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8484 sg10168 - -lemma sg23829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10102 - -lemma sg23830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg8462 sg10174 - -lemma sg23831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10099 - -lemma sg23832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10090 - -lemma sg23833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg8861 sg8987 - -lemma sg23834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10100 - -lemma sg23835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10091 - -lemma sg23836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10085 - -lemma sg23837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,4,3,2] := by - exact rowSquare_join (by decide) sg8861 sg8988 - -lemma sg23838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg7238 sg11439 - -lemma sg23839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg8531 sg10086 - -lemma sg23840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10086 - -lemma sg23841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg8533 sg10086 - -lemma sg23842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg6394 sg11737 - -lemma sg23843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,5,4] := by - exact rowSquare_join (by decide) sg5531 sg12623 - -lemma sg23844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8673 sg9657 - -lemma sg23845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8524 sg10103 - -lemma sg23846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8667 sg9658 - -lemma sg23847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9457 - -lemma sg23848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8345 sg10626 - -lemma sg23849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9714 - -lemma sg23850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9471 - -lemma sg23851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10275 - -lemma sg23852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10627 - -lemma sg23853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9715 - -lemma sg23854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10276 - -lemma sg23855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10222 - -lemma sg23856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9716 - -lemma sg23857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9167 - -lemma sg23858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9458 - -lemma sg23859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9458 - -lemma sg23860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg8860 sg9008 - -lemma sg23861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9459 - -lemma sg23862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8345 sg10629 - -lemma sg23863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9717 - -lemma sg23864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9473 - -lemma sg23865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10277 - -lemma sg23866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10630 - -lemma sg23867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9718 - -lemma sg23868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9471 - -lemma sg23869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10278 - -lemma sg23870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10223 - -lemma sg23871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9719 - -lemma sg23872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9169 - -lemma sg23873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10224 - -lemma sg23874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9720 - -lemma sg23875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9460 - -lemma sg23876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9460 - -lemma sg23877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9010 - -lemma sg23878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8655 sg9659 - -lemma sg23879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg8860 sg9011 - -lemma sg23880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9448 - -lemma sg23881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10279 - -lemma sg23882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10225 - -lemma sg23883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9721 - -lemma sg23884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9170 - -lemma sg23885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10280 - -lemma sg23886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10226 - -lemma sg23887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9722 - -lemma sg23888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9462 - -lemma sg23889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9462 - -lemma sg23890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9013 - -lemma sg23891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9463 - -lemma sg23892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9463 - -lemma sg23893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8358 sg10601 - -lemma sg23894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9014 - -lemma sg23895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg8862 sg8986 - -lemma sg23896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10104 - -lemma sg23897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1465 sg20929 - -lemma sg23898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8529 sg10094 - -lemma sg23899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10094 - -lemma sg23900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg8451 sg10178 - -lemma sg23901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9015 - -lemma sg23902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8526 sg10100 - -lemma sg23903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg8535 sg10085 - -lemma sg23904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9016 - -lemma sg23905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg8862 sg8988 - -lemma sg23906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg5531 sg12624 - -lemma sg23907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg8535 sg10086 - -lemma sg23908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg8536 sg10086 - -lemma sg23909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg5533 sg12619 - -lemma sg23910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8756 sg9443 - -lemma sg23911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8529 sg10095 - -lemma sg23912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10635 - -lemma sg23913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8530 sg10095 - -lemma sg23914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9473 - -lemma sg23915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10281 - -lemma sg23916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10636 - -lemma sg23917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9723 - -lemma sg23918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9171 - -lemma sg23919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10282 - -lemma sg23920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10227 - -lemma sg23921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9724 - -lemma sg23922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9464 - -lemma sg23923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9464 - -lemma sg23924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8834 sg9158 - -lemma sg23925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9465 - -lemma sg23926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9465 - -lemma sg23927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8655 sg9660 - -lemma sg23928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8350 sg10614 - -lemma sg23929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8350 sg10615 - -lemma sg23930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9473 - -lemma sg23931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10283 - -lemma sg23932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10228 - -lemma sg23933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9725 - -lemma sg23934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9466 - -lemma sg23935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9466 - -lemma sg23936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg8835 sg9158 - -lemma sg23937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10229 - -lemma sg23938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9726 - -lemma sg23939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9467 - -lemma sg23940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9467 - -lemma sg23941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8360 sg10601 - -lemma sg23942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg8350 sg10616 - -lemma sg23943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8537 sg10086 - -lemma sg23944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8656 sg9660 - -lemma sg23945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg8430 sg10206 - -lemma sg23946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10617 - -lemma sg23947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,4,4] := by - exact rowSquare_join (by decide) sg8361 sg10601 - -lemma sg23948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8529 sg10098 - -lemma sg23949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10098 - -lemma sg23950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8527 sg10100 - -lemma sg23951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg8538 sg10085 - -lemma sg23952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg8863 sg8987 - -lemma sg23953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg8352 sg10615 - -lemma sg23954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg8538 sg10086 - -lemma sg23955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg8863 sg8988 - -lemma sg23956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,4,3] := by - exact rowSquare_join (by decide) sg5535 sg12619 - -lemma sg23957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg8539 sg10086 - -lemma sg23958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,5,2] := by - exact rowSquare_join (by decide) sg330 sg21322 - -lemma sg23959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10284 - -lemma sg23960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10230 - -lemma sg23961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9727 - -lemma sg23962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9468 - -lemma sg23963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9468 - -lemma sg23964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8362 sg10601 - -lemma sg23965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,3,3,3,2] := by - exact rowSquare_join (by decide) sg8881 sg8982 - -lemma sg23966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8435 sg10195 - -lemma sg23967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8436 sg10195 - -lemma sg23968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8528 sg10100 - -lemma sg23969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8540 sg10085 - -lemma sg23970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,3,2,2] := by - exact rowSquare_join (by decide) sg8430 sg10208 - -lemma sg23971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,3,3,1] := by - exact rowSquare_join (by decide) sg8363 sg10601 - -lemma sg23972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8540 sg10086 - -lemma sg23973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,4,2,1] := by - exact rowSquare_join (by decide) sg8351 sg10617 - -lemma sg23974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,4,3] := by - exact rowSquare_join (by decide) sg8364 sg10601 - -lemma sg23975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8481 sg10172 - -lemma sg23976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg8451 sg10182 - -lemma sg23977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,2,2,2] := by - exact rowSquare_join (by decide) sg8352 sg10616 - -lemma sg23978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg8452 sg10182 - -lemma sg23979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,3,2,1] := by - exact rowSquare_join (by decide) sg8352 sg10617 - -lemma sg23980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,3,3] := by - exact rowSquare_join (by decide) sg8365 sg10601 - -lemma sg23981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,4,1,1] := by - exact rowSquare_join (by decide) sg8541 sg10086 - -lemma sg23982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,4,2] := by - exact rowSquare_join (by decide) sg330 sg21323 - -lemma sg23983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,5,1] := by - exact rowSquare_join (by decide) sg330 sg21324 - -lemma sg23984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg21615 - -lemma sg23985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg331 sg21316 - -lemma sg23986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,6,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg21325 - -lemma sg23987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,6,3,1,1] := by - exact rowSquare_join (by decide) sg331 sg21317 - -lemma sg23988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,6,3,2] := by - exact rowSquare_join (by decide) sg330 sg21326 - -lemma sg23989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,6,4,1] := by - exact rowSquare_join (by decide) sg330 sg21327 - -lemma sg23990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8504 sg10167 - -lemma sg23991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10285 - -lemma sg23992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10231 - -lemma sg23993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10286 - -lemma sg23994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9698 - -lemma sg23995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10287 - -lemma sg23996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9729 - -lemma sg23997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9450 - -lemma sg23998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10288 - -lemma sg23999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10232 - -lemma sg24000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8419 sg10232 - -lemma sg24001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10106 - -lemma sg24002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9730 - -lemma sg24003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10211 - -lemma sg24004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg8804 sg9162 - -lemma sg24005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10289 - -lemma sg24006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10233 - -lemma sg24007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10290 - -lemma sg24008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9702 - -lemma sg24009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10291 - -lemma sg24010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9733 - -lemma sg24011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9475 - -lemma sg24012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10292 - -lemma sg24013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10234 - -lemma sg24014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9734 - -lemma sg24015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10293 - -lemma sg24016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10235 - -lemma sg24017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9735 - -lemma sg24018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10214 - -lemma sg24019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9705 - -lemma sg24020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10215 - -lemma sg24021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg8860 sg9017 - -lemma sg24022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9706 - -lemma sg24023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10294 - -lemma sg24024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9736 - -lemma sg24025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9454 - -lemma sg24026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10295 - -lemma sg24027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10236 - -lemma sg24028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8419 sg10236 - -lemma sg24029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9475 - -lemma sg24030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10296 - -lemma sg24031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10107 - -lemma sg24032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9737 - -lemma sg24033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10218 - -lemma sg24034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10237 - -lemma sg24035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8419 sg10237 - -lemma sg24036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9709 - -lemma sg24037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10219 - -lemma sg24038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg8861 sg8990 - -lemma sg24039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8654 sg9669 - -lemma sg24040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg8533 sg10089 - -lemma sg24041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8736 sg9448 - -lemma sg24042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10297 - -lemma sg24043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10647 - -lemma sg24044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9738 - -lemma sg24045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10220 - -lemma sg24046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10298 - -lemma sg24047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10238 - -lemma sg24048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9739 - -lemma sg24049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9711 - -lemma sg24050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10221 - -lemma sg24051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg8861 sg8992 - -lemma sg24052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9712 - -lemma sg24053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10625 - -lemma sg24054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8654 sg9671 - -lemma sg24055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg8861 sg8993 - -lemma sg24056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg8368 sg10601 - -lemma sg24057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10108 - -lemma sg24058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg1467 sg20929 - -lemma sg24059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10102 - -lemma sg24060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg8352 sg10619 - -lemma sg24061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10090 - -lemma sg24062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg8533 sg10090 - -lemma sg24063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8531 sg10091 - -lemma sg24064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10091 - -lemma sg24065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg8861 sg8994 - -lemma sg24066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg8543 sg10085 - -lemma sg24067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,4,4] := by - exact rowSquare_join (by decide) sg7240 sg11439 - -lemma sg24068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg8432 sg10210 - -lemma sg24069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg8543 sg10086 - -lemma sg24070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,5,3] := by - exact rowSquare_join (by decide) sg6401 sg11735 - -lemma sg24071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8524 sg10109 - -lemma sg24072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8648 sg9740 - -lemma sg24073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9713 - -lemma sg24074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8345 sg10648 - -lemma sg24075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg7232 sg11451 - -lemma sg24076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9476 - -lemma sg24077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10299 - -lemma sg24078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10110 - -lemma sg24079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9741 - -lemma sg24080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9452 - -lemma sg24081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10300 - -lemma sg24082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10239 - -lemma sg24083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9742 - -lemma sg24084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8347 sg10627 - -lemma sg24085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10111 - -lemma sg24086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9743 - -lemma sg24087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9716 - -lemma sg24088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10222 - -lemma sg24089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9018 - -lemma sg24090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10215 - -lemma sg24091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg8860 sg9019 - -lemma sg24092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9477 - -lemma sg24093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10301 - -lemma sg24094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10650 - -lemma sg24095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9744 - -lemma sg24096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9476 - -lemma sg24097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10302 - -lemma sg24098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10240 - -lemma sg24099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9745 - -lemma sg24100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8347 sg10630 - -lemma sg24101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10303 - -lemma sg24102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10241 - -lemma sg24103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9746 - -lemma sg24104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9719 - -lemma sg24105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10223 - -lemma sg24106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9020 - -lemma sg24107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9720 - -lemma sg24108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10224 - -lemma sg24109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10219 - -lemma sg24110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9021 - -lemma sg24111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8350 sg10622 - -lemma sg24112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9476 - -lemma sg24113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10304 - -lemma sg24114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10112 - -lemma sg24115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9747 - -lemma sg24116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9721 - -lemma sg24117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10225 - -lemma sg24118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9022 - -lemma sg24119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10242 - -lemma sg24120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9748 - -lemma sg24121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9722 - -lemma sg24122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10226 - -lemma sg24123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10221 - -lemma sg24124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9023 - -lemma sg24125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9479 - -lemma sg24126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9463 - -lemma sg24127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9024 - -lemma sg24128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg8862 sg8993 - -lemma sg24129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg5540 sg12619 - -lemma sg24130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10104 - -lemma sg24131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg8352 sg10621 - -lemma sg24132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8526 sg10102 - -lemma sg24133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10094 - -lemma sg24134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9025 - -lemma sg24135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg8536 sg10090 - -lemma sg24136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg8535 sg10091 - -lemma sg24137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg8862 sg8994 - -lemma sg24138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg8546 sg10085 - -lemma sg24139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg8545 sg10086 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes57 + +namespace OAI + +/-! Semigroup Nodes 58. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg23740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9695 + +lemma sg23741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8472 sg10172 + +lemma sg23742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10260 + +lemma sg23743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10208 + +lemma sg23744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9696 + +lemma sg23745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8872 sg8981 + +lemma sg23746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10617 + +lemma sg23747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9697 + +lemma sg23748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8653 sg9661 + +lemma sg23749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8353 sg10601 + +lemma sg23750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8354 sg10601 + +lemma sg23751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg8873 sg8982 + +lemma sg23752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8500 sg10167 + +lemma sg23753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8481 sg10168 + +lemma sg23754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10099 + +lemma sg23755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg8451 sg10174 + +lemma sg23756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg8530 sg10084 + +lemma sg23757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10100 + +lemma sg23758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg8452 sg10174 + +lemma sg23759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8529 sg10085 + +lemma sg23760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10085 + +lemma sg23761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,3,3] := by + exact rowSquare_join (by decide) sg8873 sg8983 + +lemma sg23762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg7236 sg11439 + +lemma sg23763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,4,4,2] := by + exact rowSquare_join (by decide) sg7237 sg11439 + +lemma sg23764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg8529 sg10086 + +lemma sg23765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10086 + +lemma sg23766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg0 sg23672 + +lemma sg23767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,3,2] := by + exact rowSquare_join (by decide) sg6392 sg11737 + +lemma sg23768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,4,1] := by + exact rowSquare_join (by decide) sg5526 sg12627 + +lemma sg23769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,5,5,5,5,5,5,5] := by + exact rowSquare_join (by decide) sg5531 sg12619 + +lemma sg23770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8502 sg10167 + +lemma sg23771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10261 + +lemma sg23772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10209 + +lemma sg23773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10262 + +lemma sg23774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9685 + +lemma sg23775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10263 + +lemma sg23776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9699 + +lemma sg23777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10264 + +lemma sg23778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10211 + +lemma sg23779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9700 + +lemma sg23780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,4,4,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8423 sg10200 + +lemma sg23781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8503 sg10167 + +lemma sg23782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10265 + +lemma sg23783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10212 + +lemma sg23784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10266 + +lemma sg23785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9688 + +lemma sg23786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10267 + +lemma sg23787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9703 + +lemma sg23788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9470 + +lemma sg23789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10268 + +lemma sg23790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10214 + +lemma sg23791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9704 + +lemma sg23792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10215 + +lemma sg23793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9705 + +lemma sg23794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10203 + +lemma sg23795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,4,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg8792 sg9174 + +lemma sg23796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10216 + +lemma sg23797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10269 + +lemma sg23798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9691 + +lemma sg23799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10270 + +lemma sg23800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9707 + +lemma sg23801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9447 + +lemma sg23802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10271 + +lemma sg23803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10218 + +lemma sg23804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9708 + +lemma sg23805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10272 + +lemma sg23806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10219 + +lemma sg23807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9709 + +lemma sg23808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10206 + +lemma sg23809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9694 + +lemma sg23810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10615 + +lemma sg23811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg8861 sg8984 + +lemma sg23812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9448 + +lemma sg23813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10273 + +lemma sg23814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10220 + +lemma sg23815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9710 + +lemma sg23816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8477 sg10172 + +lemma sg23817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10274 + +lemma sg23818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10221 + +lemma sg23819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9711 + +lemma sg23820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10208 + +lemma sg23821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10625 + +lemma sg23822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9712 + +lemma sg23823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9697 + +lemma sg23824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10617 + +lemma sg23825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg8861 sg8985 + +lemma sg23826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8356 sg10601 + +lemma sg23827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg8861 sg8986 + +lemma sg23828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8484 sg10168 + +lemma sg23829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10102 + +lemma sg23830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg8462 sg10174 + +lemma sg23831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10099 + +lemma sg23832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10090 + +lemma sg23833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg8861 sg8987 + +lemma sg23834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10100 + +lemma sg23835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10091 + +lemma sg23836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10085 + +lemma sg23837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,4,3,2] := by + exact rowSquare_join (by decide) sg8861 sg8988 + +lemma sg23838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg7238 sg11439 + +lemma sg23839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg8531 sg10086 + +lemma sg23840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10086 + +lemma sg23841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg8533 sg10086 + +lemma sg23842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg6394 sg11737 + +lemma sg23843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,5,5,5,5,5,4] := by + exact rowSquare_join (by decide) sg5531 sg12623 + +lemma sg23844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8673 sg9657 + +lemma sg23845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8524 sg10103 + +lemma sg23846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8667 sg9658 + +lemma sg23847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9457 + +lemma sg23848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8345 sg10626 + +lemma sg23849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9714 + +lemma sg23850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9471 + +lemma sg23851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10275 + +lemma sg23852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10627 + +lemma sg23853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9715 + +lemma sg23854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10276 + +lemma sg23855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10222 + +lemma sg23856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9716 + +lemma sg23857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9167 + +lemma sg23858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9458 + +lemma sg23859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9458 + +lemma sg23860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg8860 sg9008 + +lemma sg23861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9459 + +lemma sg23862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8345 sg10629 + +lemma sg23863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9717 + +lemma sg23864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9473 + +lemma sg23865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10277 + +lemma sg23866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10630 + +lemma sg23867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9718 + +lemma sg23868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9471 + +lemma sg23869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10278 + +lemma sg23870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10223 + +lemma sg23871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9719 + +lemma sg23872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9169 + +lemma sg23873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10224 + +lemma sg23874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9720 + +lemma sg23875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9460 + +lemma sg23876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9460 + +lemma sg23877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9010 + +lemma sg23878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8655 sg9659 + +lemma sg23879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg8860 sg9011 + +lemma sg23880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9448 + +lemma sg23881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10279 + +lemma sg23882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10225 + +lemma sg23883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9721 + +lemma sg23884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9170 + +lemma sg23885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10280 + +lemma sg23886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10226 + +lemma sg23887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9722 + +lemma sg23888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9462 + +lemma sg23889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9462 + +lemma sg23890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9013 + +lemma sg23891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9463 + +lemma sg23892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9463 + +lemma sg23893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8358 sg10601 + +lemma sg23894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9014 + +lemma sg23895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg8862 sg8986 + +lemma sg23896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10104 + +lemma sg23897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1465 sg20929 + +lemma sg23898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8529 sg10094 + +lemma sg23899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10094 + +lemma sg23900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg8451 sg10178 + +lemma sg23901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9015 + +lemma sg23902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8526 sg10100 + +lemma sg23903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg8535 sg10085 + +lemma sg23904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9016 + +lemma sg23905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg8862 sg8988 + +lemma sg23906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg5531 sg12624 + +lemma sg23907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg8535 sg10086 + +lemma sg23908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg8536 sg10086 + +lemma sg23909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg5533 sg12619 + +lemma sg23910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8756 sg9443 + +lemma sg23911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8529 sg10095 + +lemma sg23912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10635 + +lemma sg23913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8530 sg10095 + +lemma sg23914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9473 + +lemma sg23915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10281 + +lemma sg23916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10636 + +lemma sg23917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9723 + +lemma sg23918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9171 + +lemma sg23919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10282 + +lemma sg23920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10227 + +lemma sg23921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9724 + +lemma sg23922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9464 + +lemma sg23923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9464 + +lemma sg23924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8834 sg9158 + +lemma sg23925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9465 + +lemma sg23926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9465 + +lemma sg23927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8655 sg9660 + +lemma sg23928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8350 sg10614 + +lemma sg23929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8350 sg10615 + +lemma sg23930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9473 + +lemma sg23931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10283 + +lemma sg23932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10228 + +lemma sg23933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9725 + +lemma sg23934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9466 + +lemma sg23935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9466 + +lemma sg23936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg8835 sg9158 + +lemma sg23937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10229 + +lemma sg23938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9726 + +lemma sg23939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9467 + +lemma sg23940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9467 + +lemma sg23941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8360 sg10601 + +lemma sg23942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg8350 sg10616 + +lemma sg23943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8537 sg10086 + +lemma sg23944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8656 sg9660 + +lemma sg23945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg8430 sg10206 + +lemma sg23946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10617 + +lemma sg23947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,4,4,4] := by + exact rowSquare_join (by decide) sg8361 sg10601 + +lemma sg23948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8529 sg10098 + +lemma sg23949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10098 + +lemma sg23950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8527 sg10100 + +lemma sg23951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg8538 sg10085 + +lemma sg23952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg8863 sg8987 + +lemma sg23953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg8352 sg10615 + +lemma sg23954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg8538 sg10086 + +lemma sg23955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg8863 sg8988 + +lemma sg23956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,4,3] := by + exact rowSquare_join (by decide) sg5535 sg12619 + +lemma sg23957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg8539 sg10086 + +lemma sg23958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,5,5,5,2] := by + exact rowSquare_join (by decide) sg330 sg21322 + +lemma sg23959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10284 + +lemma sg23960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10230 + +lemma sg23961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9727 + +lemma sg23962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9468 + +lemma sg23963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9468 + +lemma sg23964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8362 sg10601 + +lemma sg23965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,3,3,3,2] := by + exact rowSquare_join (by decide) sg8881 sg8982 + +lemma sg23966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8435 sg10195 + +lemma sg23967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8436 sg10195 + +lemma sg23968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8528 sg10100 + +lemma sg23969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8540 sg10085 + +lemma sg23970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,3,2,2] := by + exact rowSquare_join (by decide) sg8430 sg10208 + +lemma sg23971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,3,3,1] := by + exact rowSquare_join (by decide) sg8363 sg10601 + +lemma sg23972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8540 sg10086 + +lemma sg23973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,4,2,1] := by + exact rowSquare_join (by decide) sg8351 sg10617 + +lemma sg23974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,4,4,3] := by + exact rowSquare_join (by decide) sg8364 sg10601 + +lemma sg23975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8481 sg10172 + +lemma sg23976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg8451 sg10182 + +lemma sg23977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,2,2,2] := by + exact rowSquare_join (by decide) sg8352 sg10616 + +lemma sg23978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg8452 sg10182 + +lemma sg23979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,3,2,1] := by + exact rowSquare_join (by decide) sg8352 sg10617 + +lemma sg23980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,3,3] := by + exact rowSquare_join (by decide) sg8365 sg10601 + +lemma sg23981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,4,1,1] := by + exact rowSquare_join (by decide) sg8541 sg10086 + +lemma sg23982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,4,2] := by + exact rowSquare_join (by decide) sg330 sg21323 + +lemma sg23983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,5,5,1] := by + exact rowSquare_join (by decide) sg330 sg21324 + +lemma sg23984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg21615 + +lemma sg23985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg331 sg21316 + +lemma sg23986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,6,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg21325 + +lemma sg23987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,6,3,1,1] := by + exact rowSquare_join (by decide) sg331 sg21317 + +lemma sg23988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,6,3,2] := by + exact rowSquare_join (by decide) sg330 sg21326 + +lemma sg23989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,6,6,6,6,6,4,1] := by + exact rowSquare_join (by decide) sg330 sg21327 + +lemma sg23990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8504 sg10167 + +lemma sg23991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10285 + +lemma sg23992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10231 + +lemma sg23993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10286 + +lemma sg23994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9698 + +lemma sg23995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10287 + +lemma sg23996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9729 + +lemma sg23997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9450 + +lemma sg23998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10288 + +lemma sg23999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10232 + +lemma sg24000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8419 sg10232 + +lemma sg24001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10106 + +lemma sg24002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9730 + +lemma sg24003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10211 + +lemma sg24004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,4,4,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg8804 sg9162 + +lemma sg24005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10289 + +lemma sg24006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10233 + +lemma sg24007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10290 + +lemma sg24008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9702 + +lemma sg24009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10291 + +lemma sg24010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9733 + +lemma sg24011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9475 + +lemma sg24012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10292 + +lemma sg24013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10234 + +lemma sg24014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9734 + +lemma sg24015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10293 + +lemma sg24016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10235 + +lemma sg24017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9735 + +lemma sg24018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10214 + +lemma sg24019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9705 + +lemma sg24020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10215 + +lemma sg24021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg8860 sg9017 + +lemma sg24022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9706 + +lemma sg24023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10294 + +lemma sg24024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9736 + +lemma sg24025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9454 + +lemma sg24026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10295 + +lemma sg24027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10236 + +lemma sg24028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8419 sg10236 + +lemma sg24029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9475 + +lemma sg24030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10296 + +lemma sg24031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10107 + +lemma sg24032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9737 + +lemma sg24033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10218 + +lemma sg24034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10237 + +lemma sg24035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8419 sg10237 + +lemma sg24036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9709 + +lemma sg24037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10219 + +lemma sg24038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg8861 sg8990 + +lemma sg24039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8654 sg9669 + +lemma sg24040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg8533 sg10089 + +lemma sg24041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8736 sg9448 + +lemma sg24042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10297 + +lemma sg24043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10647 + +lemma sg24044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9738 + +lemma sg24045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10220 + +lemma sg24046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10298 + +lemma sg24047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10238 + +lemma sg24048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9739 + +lemma sg24049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9711 + +lemma sg24050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10221 + +lemma sg24051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg8861 sg8992 + +lemma sg24052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9712 + +lemma sg24053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10625 + +lemma sg24054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8654 sg9671 + +lemma sg24055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg8861 sg8993 + +lemma sg24056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg8368 sg10601 + +lemma sg24057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10108 + +lemma sg24058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg1467 sg20929 + +lemma sg24059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10102 + +lemma sg24060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg8352 sg10619 + +lemma sg24061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10090 + +lemma sg24062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg8533 sg10090 + +lemma sg24063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8531 sg10091 + +lemma sg24064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10091 + +lemma sg24065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg8861 sg8994 + +lemma sg24066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg8543 sg10085 + +lemma sg24067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,4,4] := by + exact rowSquare_join (by decide) sg7240 sg11439 + +lemma sg24068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg8432 sg10210 + +lemma sg24069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg8543 sg10086 + +lemma sg24070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,5,5,5,5,5,3] := by + exact rowSquare_join (by decide) sg6401 sg11735 + +lemma sg24071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8524 sg10109 + +lemma sg24072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8648 sg9740 + +lemma sg24073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9713 + +lemma sg24074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8345 sg10648 + +lemma sg24075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg7232 sg11451 + +lemma sg24076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9476 + +lemma sg24077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10299 + +lemma sg24078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10110 + +lemma sg24079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9741 + +lemma sg24080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9452 + +lemma sg24081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10300 + +lemma sg24082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10239 + +lemma sg24083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9742 + +lemma sg24084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8347 sg10627 + +lemma sg24085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10111 + +lemma sg24086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9743 + +lemma sg24087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9716 + +lemma sg24088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10222 + +lemma sg24089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9018 + +lemma sg24090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10215 + +lemma sg24091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg8860 sg9019 + +lemma sg24092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9477 + +lemma sg24093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10301 + +lemma sg24094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10650 + +lemma sg24095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9744 + +lemma sg24096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9476 + +lemma sg24097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10302 + +lemma sg24098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10240 + +lemma sg24099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9745 + +lemma sg24100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8347 sg10630 + +lemma sg24101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10303 + +lemma sg24102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10241 + +lemma sg24103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9746 + +lemma sg24104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9719 + +lemma sg24105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10223 + +lemma sg24106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9020 + +lemma sg24107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9720 + +lemma sg24108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10224 + +lemma sg24109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10219 + +lemma sg24110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9021 + +lemma sg24111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8350 sg10622 + +lemma sg24112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9476 + +lemma sg24113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10304 + +lemma sg24114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10112 + +lemma sg24115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9747 + +lemma sg24116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9721 + +lemma sg24117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10225 + +lemma sg24118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9022 + +lemma sg24119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10242 + +lemma sg24120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9748 + +lemma sg24121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9722 + +lemma sg24122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10226 + +lemma sg24123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10221 + +lemma sg24124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9023 + +lemma sg24125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9479 + +lemma sg24126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9463 + +lemma sg24127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9024 + +lemma sg24128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg8862 sg8993 + +lemma sg24129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg5540 sg12619 + +lemma sg24130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10104 + +lemma sg24131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg8352 sg10621 + +lemma sg24132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8526 sg10102 + +lemma sg24133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10094 + +lemma sg24134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9025 + +lemma sg24135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg8536 sg10090 + +lemma sg24136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg8535 sg10091 + +lemma sg24137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg8862 sg8994 + +lemma sg24138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg8546 sg10085 + +lemma sg24139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg8545 sg10086 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes59.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes59.lean index 266a1a7b782bcbc912bcc1e2eb3d5217b925038a..058cfc1365f8cf497f5dbcc3eeb7b3b4f0738bd4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes59.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes59.lean @@ -1,1221 +1,1221 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 - -namespace OAI - -/-! Semigroup Nodes 59. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg24140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg8546 sg10086 - -lemma sg24141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9477 - -lemma sg24142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10305 - -lemma sg24143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10113 - -lemma sg24144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9749 - -lemma sg24145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8347 sg10635 - -lemma sg24146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9477 - -lemma sg24147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10306 - -lemma sg24148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10243 - -lemma sg24149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9750 - -lemma sg24150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9723 - -lemma sg24151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10636 - -lemma sg24152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8861 sg8999 - -lemma sg24153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10114 - -lemma sg24154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9751 - -lemma sg24155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9724 - -lemma sg24156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10227 - -lemma sg24157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9464 - -lemma sg24158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8533 sg10097 - -lemma sg24159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8727 sg9465 - -lemma sg24160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9465 - -lemma sg24161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8442 sg10193 - -lemma sg24162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10623 - -lemma sg24163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,4,4] := by - exact rowSquare_join (by decide) sg8655 sg9669 - -lemma sg24164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10307 - -lemma sg24165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10244 - -lemma sg24166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9752 - -lemma sg24167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9725 - -lemma sg24168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10228 - -lemma sg24169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9466 - -lemma sg24170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg8861 sg9000 - -lemma sg24171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9726 - -lemma sg24172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10229 - -lemma sg24173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8727 sg9467 - -lemma sg24174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9467 - -lemma sg24175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9001 - -lemma sg24176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10624 - -lemma sg24177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8432 sg10217 - -lemma sg24178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10625 - -lemma sg24179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,4,3] := by - exact rowSquare_join (by decide) sg8655 sg9671 - -lemma sg24180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8531 sg10098 - -lemma sg24181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10098 - -lemma sg24182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg8533 sg10098 - -lemma sg24183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg8538 sg10091 - -lemma sg24184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg8539 sg10090 - -lemma sg24185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,3,3] := by - exact rowSquare_join (by decide) sg7243 sg11439 - -lemma sg24186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg8863 sg8994 - -lemma sg24187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,4,2] := by - exact rowSquare_join (by decide) sg8431 sg10219 - -lemma sg24188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,5,1] := by - exact rowSquare_join (by decide) sg8549 sg10086 - -lemma sg24189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5260 sg12681 - -lemma sg24190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10230 - -lemma sg24191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8385 sg10597 - -lemma sg24192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8757 sg9444 - -lemma sg24193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10115 - -lemma sg24194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8735 sg9456 - -lemma sg24195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8438 sg10195 - -lemma sg24196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9727 - -lemma sg24197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9727 - -lemma sg24198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10230 - -lemma sg24199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8727 sg9468 - -lemma sg24200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9468 - -lemma sg24201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9002 - -lemma sg24202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg8371 sg10601 - -lemma sg24203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8439 sg10195 - -lemma sg24204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8440 sg10195 - -lemma sg24205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8441 sg10195 - -lemma sg24206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg8442 sg10195 - -lemma sg24207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8540 sg10091 - -lemma sg24208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg8430 sg10221 - -lemma sg24209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,3,3] := by - exact rowSquare_join (by decide) sg7244 sg11439 - -lemma sg24210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg8351 sg10625 - -lemma sg24211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,4,2] := by - exact rowSquare_join (by decide) sg8656 sg9671 - -lemma sg24212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8484 sg10172 - -lemma sg24213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg8462 sg10182 - -lemma sg24214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg8352 sg10624 - -lemma sg24215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg8352 sg10625 - -lemma sg24216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,5,3,2] := by - exact rowSquare_join (by decide) sg8431 sg10221 - -lemma sg24217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,5,4,1] := by - exact rowSquare_join (by decide) sg8550 sg10086 - -lemma sg24218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg332 sg21316 - -lemma sg24219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg332 sg21317 - -lemma sg24220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,6,2,2] := by - exact rowSquare_join (by decide) sg561 sg21232 - -lemma sg24221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,6,3,1] := by - exact rowSquare_join (by decide) sg561 sg21233 - -lemma sg24222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8758 sg9441 - -lemma sg24223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8524 sg10116 - -lemma sg24224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg7232 sg11452 - -lemma sg24225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9481 - -lemma sg24226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8742 sg9446 - -lemma sg24227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10117 - -lemma sg24228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8839 sg9157 - -lemma sg24229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9457 - -lemma sg24230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8720 sg9482 - -lemma sg24231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10118 - -lemma sg24232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9753 - -lemma sg24233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8820 sg9160 - -lemma sg24234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8808 sg9166 - -lemma sg24235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10119 - -lemma sg24236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9754 - -lemma sg24237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8730 sg9458 - -lemma sg24238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8810 sg9166 - -lemma sg24239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9026 - -lemma sg24240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9483 - -lemma sg24241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8809 sg9167 - -lemma sg24242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10222 - -lemma sg24243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9027 - -lemma sg24244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8447 sg10190 - -lemma sg24245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9481 - -lemma sg24246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8720 sg9484 - -lemma sg24247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10120 - -lemma sg24248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9755 - -lemma sg24249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8823 sg9160 - -lemma sg24250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9481 - -lemma sg24251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8721 sg9482 - -lemma sg24252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10121 - -lemma sg24253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9756 - -lemma sg24254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8733 sg9458 - -lemma sg24255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8820 sg9161 - -lemma sg24256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9028 - -lemma sg24257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10122 - -lemma sg24258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9757 - -lemma sg24259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9485 - -lemma sg24260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8809 sg9169 - -lemma sg24261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10223 - -lemma sg24262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9029 - -lemma sg24263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9486 - -lemma sg24264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10224 - -lemma sg24265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9030 - -lemma sg24266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10628 - -lemma sg24267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg8449 sg10190 - -lemma sg24268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8722 sg9482 - -lemma sg24269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10123 - -lemma sg24270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9758 - -lemma sg24271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9487 - -lemma sg24272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8809 sg9170 - -lemma sg24273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10225 - -lemma sg24274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9031 - -lemma sg24275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8730 sg9462 - -lemma sg24276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8352 sg10626 - -lemma sg24277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9488 - -lemma sg24278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10226 - -lemma sg24279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9032 - -lemma sg24280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg8862 sg8996 - -lemma sg24281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8731 sg9463 - -lemma sg24282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg8862 sg8997 - -lemma sg24283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg8450 sg10190 - -lemma sg24284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8526 sg10104 - -lemma sg24285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg8365 sg10606 - -lemma sg24286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9033 - -lemma sg24287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg8535 sg10094 - -lemma sg24288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg8862 sg8998 - -lemma sg24289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg8451 sg10190 - -lemma sg24290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg8117 sg11052 - -lemma sg24291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg8431 sg10222 - -lemma sg24292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,5,1] := by - exact rowSquare_join (by decide) sg8551 sg10086 - -lemma sg24293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2236 sg15512 - -lemma sg24294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3874 sg14500 - -lemma sg24295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2870 sg14849 - -lemma sg24296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5548 sg12618 - -lemma sg24297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4621 sg12946 - -lemma sg24298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8244 sg10845 - -lemma sg24299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9189 - -lemma sg24300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8732 sg9459 - -lemma sg24301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2871 sg14849 - -lemma sg24302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5549 sg12618 - -lemma sg24303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5967 sg11829 - -lemma sg24304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8577 sg10081 - -lemma sg24305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9194 - -lemma sg24306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9717 - -lemma sg24307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8733 sg9459 - -lemma sg24308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5968 sg11829 - -lemma sg24309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10227 - -lemma sg24310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9191 - -lemma sg24311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10699 - -lemma sg24312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8721 sg9484 - -lemma sg24313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9192 - -lemma sg24314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9759 - -lemma sg24315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10124 - -lemma sg24316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9759 - -lemma sg24317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8655 sg9674 - -lemma sg24318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8823 sg9161 - -lemma sg24319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9034 - -lemma sg24320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5550 sg12618 - -lemma sg24321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5969 sg11829 - -lemma sg24322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10228 - -lemma sg24323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9195 - -lemma sg24324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10700 - -lemma sg24325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8722 sg9484 - -lemma sg24326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10229 - -lemma sg24327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9196 - -lemma sg24328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9760 - -lemma sg24329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10125 - -lemma sg24330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9760 - -lemma sg24331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9720 - -lemma sg24332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9489 - -lemma sg24333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8809 sg9171 - -lemma sg24334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8374 sg10601 - -lemma sg24335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9035 - -lemma sg24336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10600 - -lemma sg24337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9724 - -lemma sg24338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9485 - -lemma sg24339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8813 sg9169 - -lemma sg24340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9490 - -lemma sg24341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10227 - -lemma sg24342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9036 - -lemma sg24343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10631 - -lemma sg24344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10224 - -lemma sg24345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10632 - -lemma sg24346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,4,3] := by - exact rowSquare_join (by decide) sg8655 sg9676 - -lemma sg24347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5971 sg11828 - -lemma sg24348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10230 - -lemma sg24349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9197 - -lemma sg24350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9761 - -lemma sg24351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10126 - -lemma sg24352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9761 - -lemma sg24353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8444 sg10195 - -lemma sg24354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9725 - -lemma sg24355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9487 - -lemma sg24356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8813 sg9170 - -lemma sg24357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9491 - -lemma sg24358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10228 - -lemma sg24359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9037 - -lemma sg24360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10633 - -lemma sg24361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9726 - -lemma sg24362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9492 - -lemma sg24363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10229 - -lemma sg24364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9038 - -lemma sg24365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10226 - -lemma sg24366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10634 - -lemma sg24367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,3,3] := by - exact rowSquare_join (by decide) sg8449 sg10192 - -lemma sg24368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10224 - -lemma sg24369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,4,2] := by - exact rowSquare_join (by decide) sg8655 sg9678 - -lemma sg24370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8527 sg10104 - -lemma sg24371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg8535 sg10098 - -lemma sg24372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg8536 sg10098 - -lemma sg24373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg8863 sg8998 - -lemma sg24374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,5,3,2] := by - exact rowSquare_join (by decide) sg8431 sg10223 - -lemma sg24375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,5,4,1] := by - exact rowSquare_join (by decide) sg8431 sg10224 - -lemma sg24376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8582 sg10080 - -lemma sg24377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8559 sg10082 - -lemma sg24378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8729 sg9468 - -lemma sg24379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9487 - -lemma sg24380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8814 sg9170 - -lemma sg24381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9727 - -lemma sg24382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9493 - -lemma sg24383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10230 - -lemma sg24384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9039 - -lemma sg24385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8731 sg9468 - -lemma sg24386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg8862 sg9002 - -lemma sg24387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,3,3] := by - exact rowSquare_join (by decide) sg5550 sg12619 - -lemma sg24388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8445 sg10195 - -lemma sg24389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8446 sg10195 - -lemma sg24390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg8447 sg10195 - -lemma sg24391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10226 - -lemma sg24392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,4,3,2] := by - exact rowSquare_join (by decide) sg8431 sg10225 - -lemma sg24393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,4,4,1] := by - exact rowSquare_join (by decide) sg8656 sg9678 - -lemma sg24394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg333 sg21316 - -lemma sg24395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg8352 sg10634 - -lemma sg24396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,5,2,2] := by - exact rowSquare_join (by decide) sg8451 sg10192 - -lemma sg24397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,5,3,1] := by - exact rowSquare_join (by decide) sg8431 sg10226 - -lemma sg24398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg142 sg21621 - -lemma sg24399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14500 - -lemma sg24400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2694 sg15004 - -lemma sg24401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5551 sg12618 - -lemma sg24402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14501 - -lemma sg24403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7254 sg11431 - -lemma sg24404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9194 - -lemma sg24405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7786 sg11247 - -lemma sg24406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8505 sg10167 - -lemma sg24407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5552 sg12618 - -lemma sg24408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5970 sg11829 - -lemma sg24409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8579 sg10081 - -lemma sg24410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9195 - -lemma sg24411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8349 sg10635 - -lemma sg24412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8537 sg10095 - -lemma sg24413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8580 sg10081 - -lemma sg24414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9196 - -lemma sg24415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8732 sg9464 - -lemma sg24416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10127 - -lemma sg24417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8538 sg10095 - -lemma sg24418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8732 sg9465 - -lemma sg24419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8760 sg9443 - -lemma sg24420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8539 sg10095 - -lemma sg24421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg7794 sg11243 - -lemma sg24422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8350 sg10635 - -lemma sg24423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5971 sg11829 - -lemma sg24424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8581 sg10081 - -lemma sg24425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9197 - -lemma sg24426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9723 - -lemma sg24427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10128 - -lemma sg24428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8540 sg10095 - -lemma sg24429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8379 sg10600 - -lemma sg24430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9724 - -lemma sg24431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9489 - -lemma sg24432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8813 sg9171 - -lemma sg24433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8733 sg9465 - -lemma sg24434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8672 sg9660 - -lemma sg24435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8351 sg10635 - -lemma sg24436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10636 - -lemma sg24437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8761 sg9442 - -lemma sg24438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9490 - -lemma sg24439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8734 sg9464 - -lemma sg24440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8352 sg10635 - -lemma sg24441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10227 - -lemma sg24442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10637 - -lemma sg24443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,3,3] := by - exact rowSquare_join (by decide) sg8655 sg9679 - -lemma sg24444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8448 sg10193 - -lemma sg24445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,4,2] := by - exact rowSquare_join (by decide) sg8449 sg10193 - -lemma sg24446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8582 sg10081 - -lemma sg24447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8559 sg10083 - -lemma sg24448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9725 - -lemma sg24449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9489 - -lemma sg24450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8814 sg9171 - -lemma sg24451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9726 - -lemma sg24452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9491 - -lemma sg24453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8734 sg9466 - -lemma sg24454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg8363 sg10610 - -lemma sg24455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10228 - -lemma sg24456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10638 - -lemma sg24457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,3,3] := by - exact rowSquare_join (by decide) sg8655 sg9680 - -lemma sg24458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9492 - -lemma sg24459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10229 - -lemma sg24460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10639 - -lemma sg24461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10227 - -lemma sg24462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,4,3,2] := by - exact rowSquare_join (by decide) sg8655 sg9681 - -lemma sg24463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,4,4,1] := by - exact rowSquare_join (by decide) sg8450 sg10193 - -lemma sg24464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg8538 sg10098 - -lemma sg24465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg8539 sg10098 - -lemma sg24466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,5,2,2] := by - exact rowSquare_join (by decide) sg7246 sg11439 - -lemma sg24467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8385 sg10599 - -lemma sg24468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9727 - -lemma sg24469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9491 - -lemma sg24470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8735 sg9466 - -lemma sg24471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg8841 sg9158 - -lemma sg24472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9493 - -lemma sg24473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10230 - -lemma sg24474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10640 - -lemma sg24475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10228 - -lemma sg24476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,3,3,2] := by - exact rowSquare_join (by decide) sg8655 sg9682 - -lemma sg24477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10229 - -lemma sg24478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10229 - -lemma sg24479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,4,2,2] := by - exact rowSquare_join (by decide) sg8449 sg10195 - -lemma sg24480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg8352 sg10639 - -lemma sg24481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8762 sg9444 - -lemma sg24482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9493 - -lemma sg24483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8735 sg9468 - -lemma sg24484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,2,2,2,1] := by - exact rowSquare_join (by decide) sg8882 sg8982 - -lemma sg24485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10230 - -lemma sg24486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,3,2,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10230 - -lemma sg24487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,3,2,2] := by - exact rowSquare_join (by decide) sg7247 sg11439 - -lemma sg24488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,4,1,1,1] := by - exact rowSquare_join (by decide) sg8352 sg10640 - -lemma sg24489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,3,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8506 sg10167 - -lemma sg24490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10308 - -lemma sg24491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8485 sg10169 - -lemma sg24492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg7232 sg11454 - -lemma sg24493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8422 sg10231 - -lemma sg24494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10309 - -lemma sg24495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg7232 sg11455 - -lemma sg24496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8736 sg9450 - -lemma sg24497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8650 sg9729 - -lemma sg24498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8455 sg10184 - -lemma sg24499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg7232 sg11456 - -lemma sg24500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10310 - -lemma sg24501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8422 sg10232 - -lemma sg24502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8658 sg9662 - -lemma sg24503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10232 - -lemma sg24504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9730 - -lemma sg24505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8659 sg9662 - -lemma sg24506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg8457 sg10184 - -lemma sg24507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8486 sg10169 - -lemma sg24508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg7232 sg11457 - -lemma sg24509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9732 - -lemma sg24510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10311 - -lemma sg24511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg7232 sg11458 - -lemma sg24512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9495 - -lemma sg24513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10312 - -lemma sg24514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8817 sg9162 - -lemma sg24515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8347 sg10643 - -lemma sg24516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8736 sg9452 - -lemma sg24517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10313 - -lemma sg24518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9734 - -lemma sg24519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8661 sg9662 - -lemma sg24520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10234 - -lemma sg24521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9497 - -lemma sg24522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8658 sg9665 - -lemma sg24523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9735 - -lemma sg24524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10235 - -lemma sg24525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9041 - -lemma sg24526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8662 sg9662 - -lemma sg24527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg8860 sg9042 - -lemma sg24528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9450 - -lemma sg24529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8650 sg9736 - -lemma sg24530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8819 sg9162 - -lemma sg24531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg7232 sg11459 - -lemma sg24532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9495 - -lemma sg24533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10314 - -lemma sg24534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8422 sg10236 - -lemma sg24535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8663 sg9662 - -lemma sg24536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10236 - -lemma sg24537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8721 sg9496 - -lemma sg24538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9497 - -lemma sg24539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8658 sg9668 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 + +namespace OAI + +/-! Semigroup Nodes 59. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg24140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg8546 sg10086 + +lemma sg24141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9477 + +lemma sg24142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10305 + +lemma sg24143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10113 + +lemma sg24144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9749 + +lemma sg24145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8347 sg10635 + +lemma sg24146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9477 + +lemma sg24147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10306 + +lemma sg24148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10243 + +lemma sg24149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9750 + +lemma sg24150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9723 + +lemma sg24151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10636 + +lemma sg24152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8861 sg8999 + +lemma sg24153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10114 + +lemma sg24154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9751 + +lemma sg24155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9724 + +lemma sg24156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10227 + +lemma sg24157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9464 + +lemma sg24158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8533 sg10097 + +lemma sg24159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8727 sg9465 + +lemma sg24160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9465 + +lemma sg24161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8442 sg10193 + +lemma sg24162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10623 + +lemma sg24163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,4,4,4,4] := by + exact rowSquare_join (by decide) sg8655 sg9669 + +lemma sg24164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10307 + +lemma sg24165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10244 + +lemma sg24166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9752 + +lemma sg24167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9725 + +lemma sg24168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10228 + +lemma sg24169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9466 + +lemma sg24170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg8861 sg9000 + +lemma sg24171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9726 + +lemma sg24172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10229 + +lemma sg24173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8727 sg9467 + +lemma sg24174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9467 + +lemma sg24175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9001 + +lemma sg24176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10624 + +lemma sg24177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8432 sg10217 + +lemma sg24178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10625 + +lemma sg24179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,4,4,3] := by + exact rowSquare_join (by decide) sg8655 sg9671 + +lemma sg24180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8531 sg10098 + +lemma sg24181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10098 + +lemma sg24182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg8533 sg10098 + +lemma sg24183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg8538 sg10091 + +lemma sg24184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg8539 sg10090 + +lemma sg24185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,3,3] := by + exact rowSquare_join (by decide) sg7243 sg11439 + +lemma sg24186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg8863 sg8994 + +lemma sg24187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,4,2] := by + exact rowSquare_join (by decide) sg8431 sg10219 + +lemma sg24188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,5,5,5,1] := by + exact rowSquare_join (by decide) sg8549 sg10086 + +lemma sg24189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5260 sg12681 + +lemma sg24190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10230 + +lemma sg24191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8385 sg10597 + +lemma sg24192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8757 sg9444 + +lemma sg24193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10115 + +lemma sg24194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8735 sg9456 + +lemma sg24195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8438 sg10195 + +lemma sg24196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9727 + +lemma sg24197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9727 + +lemma sg24198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10230 + +lemma sg24199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8727 sg9468 + +lemma sg24200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9468 + +lemma sg24201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9002 + +lemma sg24202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg8371 sg10601 + +lemma sg24203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8439 sg10195 + +lemma sg24204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8440 sg10195 + +lemma sg24205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8441 sg10195 + +lemma sg24206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg8442 sg10195 + +lemma sg24207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8540 sg10091 + +lemma sg24208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg8430 sg10221 + +lemma sg24209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,3,3] := by + exact rowSquare_join (by decide) sg7244 sg11439 + +lemma sg24210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg8351 sg10625 + +lemma sg24211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,4,4,2] := by + exact rowSquare_join (by decide) sg8656 sg9671 + +lemma sg24212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8484 sg10172 + +lemma sg24213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg8462 sg10182 + +lemma sg24214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg8352 sg10624 + +lemma sg24215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg8352 sg10625 + +lemma sg24216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,5,3,2] := by + exact rowSquare_join (by decide) sg8431 sg10221 + +lemma sg24217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,5,4,1] := by + exact rowSquare_join (by decide) sg8550 sg10086 + +lemma sg24218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg332 sg21316 + +lemma sg24219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg332 sg21317 + +lemma sg24220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,6,2,2] := by + exact rowSquare_join (by decide) sg561 sg21232 + +lemma sg24221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,6,6,6,6,3,1] := by + exact rowSquare_join (by decide) sg561 sg21233 + +lemma sg24222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8758 sg9441 + +lemma sg24223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8524 sg10116 + +lemma sg24224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg7232 sg11452 + +lemma sg24225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9481 + +lemma sg24226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8742 sg9446 + +lemma sg24227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10117 + +lemma sg24228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8839 sg9157 + +lemma sg24229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9457 + +lemma sg24230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8720 sg9482 + +lemma sg24231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10118 + +lemma sg24232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9753 + +lemma sg24233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8820 sg9160 + +lemma sg24234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8808 sg9166 + +lemma sg24235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10119 + +lemma sg24236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9754 + +lemma sg24237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8730 sg9458 + +lemma sg24238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8810 sg9166 + +lemma sg24239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9026 + +lemma sg24240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9483 + +lemma sg24241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8809 sg9167 + +lemma sg24242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10222 + +lemma sg24243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9027 + +lemma sg24244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8447 sg10190 + +lemma sg24245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9481 + +lemma sg24246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8720 sg9484 + +lemma sg24247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10120 + +lemma sg24248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9755 + +lemma sg24249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8823 sg9160 + +lemma sg24250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9481 + +lemma sg24251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8721 sg9482 + +lemma sg24252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10121 + +lemma sg24253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9756 + +lemma sg24254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8733 sg9458 + +lemma sg24255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8820 sg9161 + +lemma sg24256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9028 + +lemma sg24257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10122 + +lemma sg24258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9757 + +lemma sg24259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9485 + +lemma sg24260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8809 sg9169 + +lemma sg24261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10223 + +lemma sg24262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9029 + +lemma sg24263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9486 + +lemma sg24264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10224 + +lemma sg24265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9030 + +lemma sg24266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10628 + +lemma sg24267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg8449 sg10190 + +lemma sg24268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8722 sg9482 + +lemma sg24269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10123 + +lemma sg24270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9758 + +lemma sg24271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9487 + +lemma sg24272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8809 sg9170 + +lemma sg24273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10225 + +lemma sg24274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9031 + +lemma sg24275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8730 sg9462 + +lemma sg24276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8352 sg10626 + +lemma sg24277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9488 + +lemma sg24278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10226 + +lemma sg24279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9032 + +lemma sg24280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg8862 sg8996 + +lemma sg24281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8731 sg9463 + +lemma sg24282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg8862 sg8997 + +lemma sg24283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg8450 sg10190 + +lemma sg24284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8526 sg10104 + +lemma sg24285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg8365 sg10606 + +lemma sg24286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9033 + +lemma sg24287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg8535 sg10094 + +lemma sg24288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg8862 sg8998 + +lemma sg24289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg8451 sg10190 + +lemma sg24290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg8117 sg11052 + +lemma sg24291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg8431 sg10222 + +lemma sg24292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,5,5,5,5,1] := by + exact rowSquare_join (by decide) sg8551 sg10086 + +lemma sg24293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2236 sg15512 + +lemma sg24294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3874 sg14500 + +lemma sg24295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2870 sg14849 + +lemma sg24296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5548 sg12618 + +lemma sg24297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4621 sg12946 + +lemma sg24298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8244 sg10845 + +lemma sg24299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9189 + +lemma sg24300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8732 sg9459 + +lemma sg24301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2871 sg14849 + +lemma sg24302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5549 sg12618 + +lemma sg24303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5967 sg11829 + +lemma sg24304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8577 sg10081 + +lemma sg24305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9194 + +lemma sg24306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9717 + +lemma sg24307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8733 sg9459 + +lemma sg24308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5968 sg11829 + +lemma sg24309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10227 + +lemma sg24310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9191 + +lemma sg24311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10699 + +lemma sg24312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8721 sg9484 + +lemma sg24313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9192 + +lemma sg24314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9759 + +lemma sg24315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10124 + +lemma sg24316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9759 + +lemma sg24317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8655 sg9674 + +lemma sg24318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8823 sg9161 + +lemma sg24319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9034 + +lemma sg24320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5550 sg12618 + +lemma sg24321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5969 sg11829 + +lemma sg24322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10228 + +lemma sg24323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9195 + +lemma sg24324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10700 + +lemma sg24325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8722 sg9484 + +lemma sg24326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10229 + +lemma sg24327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9196 + +lemma sg24328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9760 + +lemma sg24329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10125 + +lemma sg24330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9760 + +lemma sg24331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9720 + +lemma sg24332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9489 + +lemma sg24333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8809 sg9171 + +lemma sg24334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8374 sg10601 + +lemma sg24335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9035 + +lemma sg24336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10600 + +lemma sg24337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9724 + +lemma sg24338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9485 + +lemma sg24339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8813 sg9169 + +lemma sg24340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9490 + +lemma sg24341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10227 + +lemma sg24342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9036 + +lemma sg24343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10631 + +lemma sg24344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10224 + +lemma sg24345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10632 + +lemma sg24346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,4,4,4,3] := by + exact rowSquare_join (by decide) sg8655 sg9676 + +lemma sg24347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5971 sg11828 + +lemma sg24348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10230 + +lemma sg24349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9197 + +lemma sg24350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9761 + +lemma sg24351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10126 + +lemma sg24352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9761 + +lemma sg24353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8444 sg10195 + +lemma sg24354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9725 + +lemma sg24355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9487 + +lemma sg24356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8813 sg9170 + +lemma sg24357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9491 + +lemma sg24358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10228 + +lemma sg24359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9037 + +lemma sg24360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10633 + +lemma sg24361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9726 + +lemma sg24362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9492 + +lemma sg24363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10229 + +lemma sg24364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9038 + +lemma sg24365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10226 + +lemma sg24366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10634 + +lemma sg24367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,3,3] := by + exact rowSquare_join (by decide) sg8449 sg10192 + +lemma sg24368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10224 + +lemma sg24369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,4,4,2] := by + exact rowSquare_join (by decide) sg8655 sg9678 + +lemma sg24370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8527 sg10104 + +lemma sg24371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg8535 sg10098 + +lemma sg24372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg8536 sg10098 + +lemma sg24373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg8863 sg8998 + +lemma sg24374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,5,3,2] := by + exact rowSquare_join (by decide) sg8431 sg10223 + +lemma sg24375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,5,5,4,1] := by + exact rowSquare_join (by decide) sg8431 sg10224 + +lemma sg24376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8582 sg10080 + +lemma sg24377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8559 sg10082 + +lemma sg24378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8729 sg9468 + +lemma sg24379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9487 + +lemma sg24380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8814 sg9170 + +lemma sg24381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9727 + +lemma sg24382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9493 + +lemma sg24383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10230 + +lemma sg24384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9039 + +lemma sg24385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8731 sg9468 + +lemma sg24386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg8862 sg9002 + +lemma sg24387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,3,3,3] := by + exact rowSquare_join (by decide) sg5550 sg12619 + +lemma sg24388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8445 sg10195 + +lemma sg24389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8446 sg10195 + +lemma sg24390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg8447 sg10195 + +lemma sg24391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10226 + +lemma sg24392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,4,3,2] := by + exact rowSquare_join (by decide) sg8431 sg10225 + +lemma sg24393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,4,4,1] := by + exact rowSquare_join (by decide) sg8656 sg9678 + +lemma sg24394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg333 sg21316 + +lemma sg24395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg8352 sg10634 + +lemma sg24396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,5,2,2] := by + exact rowSquare_join (by decide) sg8451 sg10192 + +lemma sg24397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,5,3,1] := by + exact rowSquare_join (by decide) sg8431 sg10226 + +lemma sg24398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg142 sg21621 + +lemma sg24399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14500 + +lemma sg24400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2694 sg15004 + +lemma sg24401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5551 sg12618 + +lemma sg24402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14501 + +lemma sg24403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7254 sg11431 + +lemma sg24404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9194 + +lemma sg24405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7786 sg11247 + +lemma sg24406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8505 sg10167 + +lemma sg24407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5552 sg12618 + +lemma sg24408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5970 sg11829 + +lemma sg24409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8579 sg10081 + +lemma sg24410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9195 + +lemma sg24411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8349 sg10635 + +lemma sg24412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8537 sg10095 + +lemma sg24413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8580 sg10081 + +lemma sg24414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9196 + +lemma sg24415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8732 sg9464 + +lemma sg24416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10127 + +lemma sg24417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8538 sg10095 + +lemma sg24418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8732 sg9465 + +lemma sg24419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8760 sg9443 + +lemma sg24420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8539 sg10095 + +lemma sg24421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg7794 sg11243 + +lemma sg24422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8350 sg10635 + +lemma sg24423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5971 sg11829 + +lemma sg24424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8581 sg10081 + +lemma sg24425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9197 + +lemma sg24426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9723 + +lemma sg24427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10128 + +lemma sg24428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8540 sg10095 + +lemma sg24429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8379 sg10600 + +lemma sg24430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9724 + +lemma sg24431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9489 + +lemma sg24432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8813 sg9171 + +lemma sg24433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8733 sg9465 + +lemma sg24434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8672 sg9660 + +lemma sg24435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8351 sg10635 + +lemma sg24436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10636 + +lemma sg24437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8761 sg9442 + +lemma sg24438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9490 + +lemma sg24439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8734 sg9464 + +lemma sg24440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8352 sg10635 + +lemma sg24441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10227 + +lemma sg24442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10637 + +lemma sg24443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,3,3] := by + exact rowSquare_join (by decide) sg8655 sg9679 + +lemma sg24444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8448 sg10193 + +lemma sg24445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,4,4,4,2] := by + exact rowSquare_join (by decide) sg8449 sg10193 + +lemma sg24446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8582 sg10081 + +lemma sg24447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8559 sg10083 + +lemma sg24448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9725 + +lemma sg24449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9489 + +lemma sg24450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8814 sg9171 + +lemma sg24451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9726 + +lemma sg24452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9491 + +lemma sg24453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8734 sg9466 + +lemma sg24454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg8363 sg10610 + +lemma sg24455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10228 + +lemma sg24456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10638 + +lemma sg24457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,3,3,3] := by + exact rowSquare_join (by decide) sg8655 sg9680 + +lemma sg24458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9492 + +lemma sg24459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10229 + +lemma sg24460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10639 + +lemma sg24461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10227 + +lemma sg24462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,4,3,2] := by + exact rowSquare_join (by decide) sg8655 sg9681 + +lemma sg24463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,4,4,1] := by + exact rowSquare_join (by decide) sg8450 sg10193 + +lemma sg24464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg8538 sg10098 + +lemma sg24465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg8539 sg10098 + +lemma sg24466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,5,5,2,2] := by + exact rowSquare_join (by decide) sg7246 sg11439 + +lemma sg24467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8385 sg10599 + +lemma sg24468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9727 + +lemma sg24469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9491 + +lemma sg24470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8735 sg9466 + +lemma sg24471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg8841 sg9158 + +lemma sg24472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9493 + +lemma sg24473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10230 + +lemma sg24474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10640 + +lemma sg24475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10228 + +lemma sg24476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,3,3,2] := by + exact rowSquare_join (by decide) sg8655 sg9682 + +lemma sg24477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10229 + +lemma sg24478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10229 + +lemma sg24479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,4,2,2] := by + exact rowSquare_join (by decide) sg8449 sg10195 + +lemma sg24480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg8352 sg10639 + +lemma sg24481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8762 sg9444 + +lemma sg24482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9493 + +lemma sg24483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8735 sg9468 + +lemma sg24484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,2,2,2,1] := by + exact rowSquare_join (by decide) sg8882 sg8982 + +lemma sg24485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10230 + +lemma sg24486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,3,2,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10230 + +lemma sg24487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,3,2,2] := by + exact rowSquare_join (by decide) sg7247 sg11439 + +lemma sg24488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,7,7,7,7,4,1,1,1] := by + exact rowSquare_join (by decide) sg8352 sg10640 + +lemma sg24489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,3,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8506 sg10167 + +lemma sg24490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10308 + +lemma sg24491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8485 sg10169 + +lemma sg24492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg7232 sg11454 + +lemma sg24493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8422 sg10231 + +lemma sg24494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10309 + +lemma sg24495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg7232 sg11455 + +lemma sg24496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8736 sg9450 + +lemma sg24497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8650 sg9729 + +lemma sg24498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8455 sg10184 + +lemma sg24499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg7232 sg11456 + +lemma sg24500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10310 + +lemma sg24501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8422 sg10232 + +lemma sg24502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8658 sg9662 + +lemma sg24503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10232 + +lemma sg24504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9730 + +lemma sg24505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8659 sg9662 + +lemma sg24506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,4,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg8457 sg10184 + +lemma sg24507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8486 sg10169 + +lemma sg24508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg7232 sg11457 + +lemma sg24509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9732 + +lemma sg24510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10311 + +lemma sg24511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg7232 sg11458 + +lemma sg24512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9495 + +lemma sg24513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10312 + +lemma sg24514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8817 sg9162 + +lemma sg24515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8347 sg10643 + +lemma sg24516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8736 sg9452 + +lemma sg24517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10313 + +lemma sg24518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9734 + +lemma sg24519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8661 sg9662 + +lemma sg24520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10234 + +lemma sg24521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9497 + +lemma sg24522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8658 sg9665 + +lemma sg24523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9735 + +lemma sg24524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10235 + +lemma sg24525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9041 + +lemma sg24526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8662 sg9662 + +lemma sg24527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg8860 sg9042 + +lemma sg24528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9450 + +lemma sg24529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8650 sg9736 + +lemma sg24530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8819 sg9162 + +lemma sg24531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg7232 sg11459 + +lemma sg24532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9495 + +lemma sg24533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10314 + +lemma sg24534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8422 sg10236 + +lemma sg24535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8663 sg9662 + +lemma sg24536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10236 + +lemma sg24537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8721 sg9496 + +lemma sg24538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9497 + +lemma sg24539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8658 sg9668 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes6.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes6.lean index 088d7fb8ba1714ee0cde056407fe6c09e9760179..a6792f2e08e2e02e886f932741f96ba0949838ed 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes6.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes6.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes5 - -namespace OAI - -/-! Semigroup Nodes 6. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg2897 : RowSquare [8,2,1,1,1,1] [5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg1331 - -lemma sg2898 : RowSquare [8,2,1,1,1,1] [5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6 sg1332 - -lemma sg2899 : RowSquare [8,2,1,1,1,1] [5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg893 - -lemma sg2900 : RowSquare [8,2,1,1,1,1] [5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg897 - -lemma sg2901 : RowSquare [8,2,1,1,1,1] [7,7] := by - exact rowSquare_join (by decide) sg17 sg909 - -lemma sg2902 : RowSquare [8,2,2,1,1] [2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg586 - -lemma sg2903 : RowSquare [8,2,2,1,1] [3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg586 - -lemma sg2904 : RowSquare [8,2,2,1,1] [3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg587 - -lemma sg2905 : RowSquare [8,2,2,1,1] [3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg34 sg586 - -lemma sg2906 : RowSquare [8,2,2,1,1] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg588 - -lemma sg2907 : RowSquare [8,2,2,1,1] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg589 - -lemma sg2908 : RowSquare [8,2,2,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg590 - -lemma sg2909 : RowSquare [8,2,2,1,1] [4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg35 sg586 - -lemma sg2910 : RowSquare [8,2,2,1,1] [4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg587 - -lemma sg2911 : RowSquare [8,2,2,1,1] [4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg87 sg312 - -lemma sg2912 : RowSquare [8,2,2,1,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg36 sg586 - -lemma sg2913 : RowSquare [8,2,2,1,1] [4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg34 sg587 - -lemma sg2914 : RowSquare [8,2,2,1,1] [4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg88 sg312 - -lemma sg2915 : RowSquare [8,2,2,1,1] [4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg313 - -lemma sg2916 : RowSquare [8,2,2,1,1] [4,3,3,3,1] := by - exact rowSquare_join (by decide) sg87 sg315 - -lemma sg2917 : RowSquare [8,2,2,1,1] [4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg998 - -lemma sg2918 : RowSquare [8,2,2,1,1] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg88 sg313 - -lemma sg2919 : RowSquare [8,2,2,1,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg595 - -lemma sg2920 : RowSquare [8,2,2,1,1] [4,4,3,2,1] := by - exact rowSquare_join (by decide) sg88 sg314 - -lemma sg2921 : RowSquare [8,2,2,1,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg88 sg315 - -lemma sg2922 : RowSquare [8,2,2,1,1] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg89 sg314 - -lemma sg2923 : RowSquare [8,2,2,1,1] [4,4,4,2] := by - exact rowSquare_join (by decide) sg89 sg315 - -lemma sg2924 : RowSquare [8,2,2,1,1] [5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg313 - -lemma sg2925 : RowSquare [8,2,2,2] [2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg178 - -lemma sg2926 : RowSquare [8,2,2,2] [3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg179 - -lemma sg2927 : RowSquare [8,2,2,2] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg180 - -lemma sg2928 : RowSquare [8,2,2,2] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg181 - -lemma sg2929 : RowSquare [8,2,2,2] [4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg182 - -lemma sg2930 : RowSquare [8,2,2,2] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg179 sg179 - -lemma sg2931 : RowSquare [8,2,2,2] [4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg179 sg180 - -lemma sg2932 : RowSquare [8,2,2,2] [4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg179 sg181 - -lemma sg2933 : RowSquare [8,2,2,2] [4,3,3,2,2] := by - exact rowSquare_join (by decide) sg66 sg372 - -lemma sg2934 : RowSquare [8,2,2,2] [4,3,3,3,1] := by - exact rowSquare_join (by decide) sg66 sg373 - -lemma sg2935 : RowSquare [8,2,2,2] [4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg185 - -lemma sg2936 : RowSquare [8,2,2,2] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg67 sg371 - -lemma sg2937 : RowSquare [8,2,2,2] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg180 sg180 - -lemma sg2938 : RowSquare [8,2,2,2] [4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg371 - -lemma sg2939 : RowSquare [8,2,2,2] [4,4,3,2,1] := by - exact rowSquare_join (by decide) sg180 sg181 - -lemma sg2940 : RowSquare [8,2,2,2] [4,4,3,3] := by - exact rowSquare_join (by decide) sg67 sg373 - -lemma sg2941 : RowSquare [8,2,2,2] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg68 sg372 - -lemma sg2942 : RowSquare [8,2,2,2] [4,4,4,2] := by - exact rowSquare_join (by decide) sg181 sg181 - -lemma sg2943 : RowSquare [8,2,2,2] [5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg179 sg182 - -lemma sg2944 : RowSquare [8,2,2,2] [5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg179 sg183 - -lemma sg2945 : RowSquare [8,2,2,2] [5,3,2,2,2] := by - exact rowSquare_join (by decide) sg180 sg182 - -lemma sg2946 : RowSquare [8,2,2,2] [5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg184 - -lemma sg2947 : RowSquare [8,2,2,2] [5,3,3,2,1] := by - exact rowSquare_join (by decide) sg182 sg181 - -lemma sg2948 : RowSquare [8,2,2,2] [5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg185 - -lemma sg2949 : RowSquare [8,2,2,2] [5,4,2,2,1] := by - exact rowSquare_join (by decide) sg180 sg183 - -lemma sg2950 : RowSquare [8,2,2,2] [5,4,3,2] := by - exact rowSquare_join (by decide) sg181 sg183 - -lemma sg2951 : RowSquare [8,2,2,2] [5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg71 sg371 - -lemma sg2952 : RowSquare [8,2,2,2] [5,5,2,1,1] := by - exact rowSquare_join (by decide) sg180 sg185 - -lemma sg2953 : RowSquare [8,2,2,2] [5,5,2,2] := by - exact rowSquare_join (by decide) sg67 sg377 - -lemma sg2954 : RowSquare [8,2,2,2] [6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg179 sg186 - -lemma sg2955 : RowSquare [8,2,2,2] [6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg187 - -lemma sg2956 : RowSquare [8,2,2,2] [6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg188 - -lemma sg2957 : RowSquare [8,3,1,1,1] [3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg586 - -lemma sg2958 : RowSquare [8,3,1,1,1] [3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg586 - -lemma sg2959 : RowSquare [8,3,1,1,1] [3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg998 - -lemma sg2960 : RowSquare [8,3,1,1,1] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg999 - -lemma sg2961 : RowSquare [8,3,1,1,1] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg1000 - -lemma sg2962 : RowSquare [8,3,1,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg1001 - -lemma sg2963 : RowSquare [8,3,1,1,1] [4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg586 - -lemma sg2964 : RowSquare [8,3,1,1,1] [4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg587 - -lemma sg2965 : RowSquare [8,3,1,1,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg586 - -lemma sg2966 : RowSquare [8,3,1,1,1] [4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg587 - -lemma sg2967 : RowSquare [8,3,1,1,1] [4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg588 - -lemma sg2968 : RowSquare [8,3,1,1,1] [4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg312 - -lemma sg2969 : RowSquare [8,3,1,1,1] [4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg589 - -lemma sg2970 : RowSquare [8,3,1,1,1] [4,3,3,2,2] := by - exact rowSquare_join (by decide) sg16 sg915 - -lemma sg2971 : RowSquare [8,3,1,1,1] [4,3,3,3,1] := by - exact rowSquare_join (by decide) sg39 sg590 - -lemma sg2972 : RowSquare [8,3,1,1,1] [4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg912 - -lemma sg2973 : RowSquare [8,3,1,1,1] [4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg588 - -lemma sg2974 : RowSquare [8,3,1,1,1] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg1006 - -lemma sg2975 : RowSquare [8,3,1,1,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg915 - -lemma sg2976 : RowSquare [8,3,1,1,1] [4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg313 - -lemma sg2977 : RowSquare [8,3,1,1,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg13 sg1008 - -lemma sg2978 : RowSquare [8,3,1,1,1] [4,4,4,2] := by - exact rowSquare_join (by decide) sg97 sg315 - -lemma sg2979 : RowSquare [8,3,1,1,1] [5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg586 - -lemma sg2980 : RowSquare [8,3,1,1,1] [5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg534 - -lemma sg2981 : RowSquare [8,3,1,1,1] [5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg98 sg312 - -lemma sg2982 : RowSquare [8,3,1,1,1] [5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg534 - -lemma sg2983 : RowSquare [8,3,1,1,1] [5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg99 sg312 - -lemma sg2984 : RowSquare [8,3,1,1,1] [5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg98 sg313 - -lemma sg2985 : RowSquare [8,3,1,1,1] [5,3,2,2,2] := by - exact rowSquare_join (by decide) sg18 sg915 - -lemma sg2986 : RowSquare [8,3,1,1,1] [5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg316 - -lemma sg2987 : RowSquare [8,3,1,1,1] [5,3,3,2,1] := by - exact rowSquare_join (by decide) sg98 sg314 - -lemma sg2988 : RowSquare [8,3,1,1,1] [5,3,3,3] := by - exact rowSquare_join (by decide) sg98 sg315 - -lemma sg2989 : RowSquare [8,3,1,1,1] [5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg535 - -lemma sg2990 : RowSquare [8,3,1,1,1] [5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg99 sg313 - -lemma sg2991 : RowSquare [8,3,1,1,1] [5,4,2,2,1] := by - exact rowSquare_join (by decide) sg39 sg595 - -lemma sg2992 : RowSquare [8,3,1,1,1] [5,4,3,1,1] := by - exact rowSquare_join (by decide) sg97 sg317 - -lemma sg2993 : RowSquare [8,3,1,1,1] [5,4,3,2] := by - exact rowSquare_join (by decide) sg99 sg315 - -lemma sg2994 : RowSquare [8,3,1,1,1] [5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg920 - -lemma sg2995 : RowSquare [8,3,1,1,1] [5,5,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg595 - -lemma sg2996 : RowSquare [8,3,1,1,1] [5,5,2,2] := by - exact rowSquare_join (by decide) sg13 sg1015 - -lemma sg2997 : RowSquare [8,3,1,1,1] [5,5,3,1] := by - exact rowSquare_join (by decide) sg97 sg319 - -lemma sg2998 : RowSquare [8,3,1,1,1] [6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg312 - -lemma sg2999 : RowSquare [8,3,1,1,1] [6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg101 sg313 - -lemma sg3000 : RowSquare [8,3,2,1] [3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg87 sg330 - -lemma sg3001 : RowSquare [8,3,2,1] [3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg193 - -lemma sg3002 : RowSquare [8,3,2,1] [3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg88 sg330 - -lemma sg3003 : RowSquare [8,3,2,1] [3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg194 - -lemma sg3004 : RowSquare [8,3,2,1] [3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg371 - -lemma sg3005 : RowSquare [8,3,2,1] [3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg330 - -lemma sg3006 : RowSquare [8,3,2,1] [3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg195 - -lemma sg3007 : RowSquare [8,3,2,1] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg372 - -lemma sg3008 : RowSquare [8,3,2,1] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg74 sg373 - -lemma sg3009 : RowSquare [8,3,2,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg616 - -lemma sg3010 : RowSquare [8,3,2,1] [4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg90 sg330 - -lemma sg3011 : RowSquare [8,3,2,1] [4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg196 - -lemma sg3012 : RowSquare [8,3,2,1] [4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg193 sg179 - -lemma sg3013 : RowSquare [8,3,2,1] [4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg91 sg330 - -lemma sg3014 : RowSquare [8,3,2,1] [4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg197 - -lemma sg3015 : RowSquare [8,3,2,1] [4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg193 sg180 - -lemma sg3016 : RowSquare [8,3,2,1] [4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg198 - -lemma sg3017 : RowSquare [8,3,2,1] [4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg193 sg181 - -lemma sg3018 : RowSquare [8,3,2,1] [4,3,3,2,2] := by - exact rowSquare_join (by decide) sg87 sg333 - -lemma sg3019 : RowSquare [8,3,2,1] [4,3,3,3,1] := by - exact rowSquare_join (by decide) sg87 sg334 - -lemma sg3020 : RowSquare [8,3,2,1] [4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg330 - -lemma sg3021 : RowSquare [8,3,2,1] [4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg199 - -lemma sg3022 : RowSquare [8,3,2,1] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg377 - -lemma sg3023 : RowSquare [8,3,2,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg194 sg180 - -lemma sg3024 : RowSquare [8,3,2,1] [4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg378 - -lemma sg3025 : RowSquare [8,3,2,1] [4,4,3,2,1] := by - exact rowSquare_join (by decide) sg194 sg181 - -lemma sg3026 : RowSquare [8,3,2,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg88 sg334 - -lemma sg3027 : RowSquare [8,3,2,1] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg89 sg333 - -lemma sg3028 : RowSquare [8,3,2,1] [4,4,4,2] := by - exact rowSquare_join (by decide) sg195 sg181 - -lemma sg3029 : RowSquare [8,3,2,1] [5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg93 sg330 - -lemma sg3030 : RowSquare [8,3,2,1] [5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg200 - -lemma sg3031 : RowSquare [8,3,2,1] [5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg193 sg182 - -lemma sg3032 : RowSquare [8,3,2,1] [5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg94 sg330 - -lemma sg3033 : RowSquare [8,3,2,1] [5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg201 - -lemma sg3034 : RowSquare [8,3,2,1] [5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg193 sg183 - -lemma sg3035 : RowSquare [8,3,2,1] [5,3,2,2,2] := by - exact rowSquare_join (by decide) sg194 sg182 - -lemma sg3036 : RowSquare [8,3,2,1] [5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg184 - -lemma sg3037 : RowSquare [8,3,2,1] [5,3,3,2,1] := by - exact rowSquare_join (by decide) sg218 sg144 - -lemma sg3038 : RowSquare [8,3,2,1] [5,3,3,3] := by - exact rowSquare_join (by decide) sg90 sg334 - -lemma sg3039 : RowSquare [8,3,2,1] [5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg202 - -lemma sg3040 : RowSquare [8,3,2,1] [5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg185 - -lemma sg3041 : RowSquare [8,3,2,1] [5,4,2,2,1] := by - exact rowSquare_join (by decide) sg194 sg183 - -lemma sg3042 : RowSquare [8,3,2,1] [5,4,3,1,1] := by - exact rowSquare_join (by decide) sg194 sg184 - -lemma sg3043 : RowSquare [8,3,2,1] [5,4,3,2] := by - exact rowSquare_join (by decide) sg195 sg183 - -lemma sg3044 : RowSquare [8,3,2,1] [5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg383 - -lemma sg3045 : RowSquare [8,3,2,1] [5,5,2,1,1] := by - exact rowSquare_join (by decide) sg194 sg185 - -lemma sg3046 : RowSquare [8,3,2,1] [5,5,2,2] := by - exact rowSquare_join (by decide) sg88 sg338 - -lemma sg3047 : RowSquare [8,3,2,1] [5,5,3,1] := by - exact rowSquare_join (by decide) sg195 sg185 - -lemma sg3048 : RowSquare [8,3,2,1] [6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg850 - -lemma sg3049 : RowSquare [8,3,2,1] [6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg95 sg330 - -lemma sg3050 : RowSquare [8,3,2,1] [6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg203 - -lemma sg3051 : RowSquare [8,3,2,1] [6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg193 sg186 - -lemma sg3052 : RowSquare [8,3,2,1] [6,2,2,2,2] := by - exact rowSquare_join (by decide) sg218 sg145 - -lemma sg3053 : RowSquare [8,3,2,1] [6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg204 - -lemma sg3054 : RowSquare [8,3,2,1] [6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg187 - -lemma sg3055 : RowSquare [8,3,2,1] [6,3,2,2,1] := by - exact rowSquare_join (by decide) sg194 sg186 - -lemma sg3056 : RowSquare [8,3,2,1] [6,3,3,1,1] := by - exact rowSquare_join (by decide) sg218 sg147 - -lemma sg3057 : RowSquare [8,3,2,1] [6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg188 - -lemma sg3058 : RowSquare [8,3,2,1] [6,6,1,1] := by - exact rowSquare_join (by decide) sg88 sg342 - -lemma sg3059 : RowSquare [8,3,2,1] [7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg205 - -lemma sg3060 : RowSquare [8,3,2,1] [7,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg189 - -lemma sg3061 : RowSquare [8,3,2,1] [7,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg190 - -lemma sg3062 : RowSquare [8,3,2,1] [7,3,2,1,1] := by - exact rowSquare_join (by decide) sg194 sg189 - -lemma sg3063 : RowSquare [8,3,2,1] [7,4,1,1,1] := by - exact rowSquare_join (by decide) sg194 sg190 - -lemma sg3064 : RowSquare [8,3,2,1] [7,7] := by - exact rowSquare_join (by decide) sg92 sg342 - -lemma sg3065 : RowSquare [8,3,2,1] [8,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg206 - -lemma sg3066 : RowSquare [8,3,2,1] [8,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg191 - -lemma sg3067 : RowSquare [8,3,2,1] [8,3,1,1,1] := by - exact rowSquare_join (by decide) sg194 sg191 - -lemma sg3068 : RowSquare [8,3,3] [3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg636 - -lemma sg3069 : RowSquare [8,3,3] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg637 - -lemma sg3070 : RowSquare [8,3,3] [4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg348 - -lemma sg3071 : RowSquare [8,3,3] [4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg33 sg636 - -lemma sg3072 : RowSquare [8,3,3] [4,3,3,2,2] := by - exact rowSquare_join (by decide) sg87 sg349 - -lemma sg3073 : RowSquare [8,3,3] [4,3,3,3,1] := by - exact rowSquare_join (by decide) sg87 sg350 - -lemma sg3074 : RowSquare [8,3,3] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg88 sg348 - -lemma sg3075 : RowSquare [8,3,3] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg639 - -lemma sg3076 : RowSquare [8,3,3] [4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg348 - -lemma sg3077 : RowSquare [8,3,3] [4,4,3,2,1] := by - exact rowSquare_join (by decide) sg88 sg349 - -lemma sg3078 : RowSquare [8,3,3] [4,4,3,3] := by - exact rowSquare_join (by decide) sg88 sg350 - -lemma sg3079 : RowSquare [8,3,3] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg89 sg349 - -lemma sg3080 : RowSquare [8,3,3] [4,4,4,2] := by - exact rowSquare_join (by decide) sg89 sg350 - -lemma sg3081 : RowSquare [8,3,3] [5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg154 sg218 - -lemma sg3082 : RowSquare [8,3,3] [5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg154 sg219 - -lemma sg3083 : RowSquare [8,3,3] [5,3,2,2,2] := by - exact rowSquare_join (by decide) sg155 sg218 - -lemma sg3084 : RowSquare [8,3,3] [5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg154 sg220 - -lemma sg3085 : RowSquare [8,3,3] [5,3,3,3] := by - exact rowSquare_join (by decide) sg90 sg350 - -lemma sg3086 : RowSquare [8,3,3] [5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg91 sg348 - -lemma sg3087 : RowSquare [8,3,3] [5,4,2,2,1] := by - exact rowSquare_join (by decide) sg155 sg219 - -lemma sg3088 : RowSquare [8,3,3] [5,4,3,2] := by - exact rowSquare_join (by decide) sg156 sg219 - -lemma sg3089 : RowSquare [8,3,3] [5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg348 - -lemma sg3090 : RowSquare [8,3,3] [5,5,2,2] := by - exact rowSquare_join (by decide) sg88 sg352 - -lemma sg3091 : RowSquare [8,3,3] [5,5,3,1] := by - exact rowSquare_join (by decide) sg88 sg353 - -lemma sg3092 : RowSquare [8,3,3] [6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg874 - -lemma sg3093 : RowSquare [8,3,3] [6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg154 sg221 - -lemma sg3094 : RowSquare [8,3,3] [6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg154 sg222 - -lemma sg3095 : RowSquare [8,3,3] [6,3,3,2] := by - exact rowSquare_join (by decide) sg156 sg221 - -lemma sg3096 : RowSquare [8,3,3] [6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg154 sg223 - -lemma sg3097 : RowSquare [8,3,3] [6,4,2,2] := by - exact rowSquare_join (by decide) sg219 sg158 - -lemma sg3098 : RowSquare [8,3,3] [6,6,1,1] := by - exact rowSquare_join (by decide) sg88 sg354 - -lemma sg3099 : RowSquare [8,4,1,1] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg1032 - -lemma sg3100 : RowSquare [8,4,1,1] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg1033 - -lemma sg3101 : RowSquare [8,4,1,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg961 - -lemma sg3102 : RowSquare [8,4,2] [3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg74 sg390 - -lemma sg3103 : RowSquare [8,4,2] [3,3,3,3,2] := by - exact rowSquare_join (by decide) sg32 sg644 - -lemma sg3104 : RowSquare [8,4,2] [4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg975 - -lemma sg3105 : RowSquare [8,4,2] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg194 sg194 - -lemma sg3107 : RowSquare [9,1,1,1,1,1] [5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg1330 - -lemma sg3108 : RowSquare [9,1,1,1,1,1] [5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg7 sg1332 - -lemma sg3109 : RowSquare [9,1,1,1,1,1] [6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg890 - -lemma sg3110 : RowSquare [9,2,1,1,1] [4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg586 - -lemma sg3111 : RowSquare [9,2,1,1,1] [4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg586 - -lemma sg3112 : RowSquare [9,2,1,1,1] [4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg998 - -lemma sg3113 : RowSquare [9,2,1,1,1] [4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg999 - -lemma sg3114 : RowSquare [9,2,1,1,1] [4,3,3,2,2] := by - exact rowSquare_join (by decide) sg16 sg1001 - -lemma sg3115 : RowSquare [9,2,1,1,1] [4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg998 - -lemma sg3116 : RowSquare [9,2,1,1,1] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg1000 - -lemma sg3117 : RowSquare [9,2,1,1,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg1001 - -lemma sg3118 : RowSquare [9,2,1,1,1] [5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg47 sg586 - -lemma sg3119 : RowSquare [9,2,2,1] [4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg218 - -lemma sg3120 : RowSquare [9,2,2,1] [4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg219 - -lemma sg3121 : RowSquare [9,2,2,1] [4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg87 sg371 - -lemma sg3122 : RowSquare [9,2,2,1] [4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg220 - -lemma sg3123 : RowSquare [9,2,2,1] [4,3,3,2,2] := by - exact rowSquare_join (by decide) sg87 sg372 - -lemma sg3124 : RowSquare [9,2,2,1] [4,3,3,3,1] := by - exact rowSquare_join (by decide) sg87 sg373 - -lemma sg3125 : RowSquare [9,2,2,1] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg88 sg371 - -lemma sg3126 : RowSquare [9,2,2,1] [4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg371 - -lemma sg3127 : RowSquare [9,2,2,1] [4,4,3,2,1] := by - exact rowSquare_join (by decide) sg88 sg372 - -lemma sg3128 : RowSquare [9,2,2,1] [4,4,3,3] := by - exact rowSquare_join (by decide) sg88 sg373 - -lemma sg3129 : RowSquare [9,2,2,1] [4,4,4,1,1] := by - exact rowSquare_join (by decide) sg89 sg372 - -lemma sg3130 : RowSquare [9,2,2,1] [4,4,4,2] := by - exact rowSquare_join (by decide) sg89 sg373 - -lemma sg3131 : RowSquare [9,2,2,1] [5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg221 - -lemma sg3132 : RowSquare [9,2,2,1] [5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg179 sg218 - -lemma sg3133 : RowSquare [9,2,2,1] [5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg222 - -lemma sg3134 : RowSquare [9,2,2,1] [5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg179 sg219 - -lemma sg3135 : RowSquare [9,2,2,1] [5,3,2,2,2] := by - exact rowSquare_join (by decide) sg180 sg218 - -lemma sg3136 : RowSquare [9,2,2,1] [5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg220 - -lemma sg3137 : RowSquare [9,2,2,1] [5,3,3,2,1] := by - exact rowSquare_join (by decide) sg218 sg181 - -lemma sg3138 : RowSquare [9,2,2,1] [5,3,3,3] := by - exact rowSquare_join (by decide) sg90 sg373 - -lemma sg3139 : RowSquare [9,2,2,1] [5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg223 - -lemma sg3140 : RowSquare [9,2,2,1] [5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg91 sg371 - -lemma sg3141 : RowSquare [9,2,2,1] [5,4,2,2,1] := by - exact rowSquare_join (by decide) sg180 sg219 - -lemma sg3142 : RowSquare [9,2,2,1] [5,4,3,1,1] := by - exact rowSquare_join (by decide) sg180 sg220 - -lemma sg3143 : RowSquare [9,2,2,1] [5,4,3,2] := by - exact rowSquare_join (by decide) sg181 sg219 - -lemma sg3144 : RowSquare [9,2,2,1] [5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg371 - -lemma sg3145 : RowSquare [9,2,2,1] [6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg179 sg221 - -lemma sg3146 : RowSquare [9,2,2,1] [6,2,2,2,2] := by - exact rowSquare_join (by decide) sg218 sg182 - -lemma sg3147 : RowSquare [9,3,1,1] [4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg228 - -lemma sg3148 : RowSquare [9,3,1,1] [4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg17 sg1032 - -lemma sg3149 : RowSquare [9,3,1,1] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg17 sg1033 - -lemma sg3150 : RowSquare [9,3,1,1] [5,5,2,2] := by - exact rowSquare_join (by decide) sg17 sg1040 - -lemma sg3151 : RowSquare [9,3,2] [4,4,2,2,2] := by - exact rowSquare_join (by decide) sg32 sg694 - -lemma sg3152 : RowSquare [9,3,2] [4,4,3,3] := by - exact rowSquare_join (by decide) sg88 sg390 - -lemma sg3153 : RowSquare [9,3,2] [5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1063 - -lemma sg3154 : RowSquare [9,4,1] [5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg424 - -lemma sg3155 : RowSquare [10,1,1,1,1] [6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg586 - -lemma sg3156 : RowSquare [10,1,1,1,1] [6,2,2,2,2] := by - exact rowSquare_join (by decide) sg20 sg1001 - -lemma sg3157 : RowSquare [3,2,2,2,1,1,1,1,1,1] [5,4,4,1,1] := by - exact rowSquare_join (by decide) sg227 sg389 - -lemma sg3158 : RowSquare [3,2,2,2,1,1,1,1,1,1] [5,4,4,2] := by - exact rowSquare_join (by decide) sg227 sg390 - -lemma sg3159 : RowSquare [3,2,2,2,1,1,1,1,1,1] [5,5,3,1,1] := by - exact rowSquare_join (by decide) sg228 sg389 - -lemma sg3160 : RowSquare [3,2,2,2,1,1,1,1,1,1] [5,5,5] := by - exact rowSquare_join (by decide) sg97 sg696 - -lemma sg3161 : RowSquare [3,2,2,2,2,2,1,1] [4,4,4,3] := by - exact rowSquare_join (by decide) sg207 sg358 - -lemma sg3162 : RowSquare [3,3,1,1,1,1,1,1,1,1,1] [9,3,3] := by - exact rowSquare_join (by decide) sg220 sg419 - -lemma sg3163 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,3,3,3,1] := by - exact rowSquare_join (by decide) sg218 sg390 - -lemma sg3164 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,4,2,2,2] := by - exact rowSquare_join (by decide) sg87 sg694 - -lemma sg3165 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,4,3,2,1] := by - exact rowSquare_join (by decide) sg219 sg389 - -lemma sg3166 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,4,3,3] := by - exact rowSquare_join (by decide) sg219 sg390 - -lemma sg3167 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,4,4,1,1] := by - exact rowSquare_join (by decide) sg220 sg389 - -lemma sg3168 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,4,4,2] := by - exact rowSquare_join (by decide) sg220 sg390 - -lemma sg3169 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,5,2,2,1] := by - exact rowSquare_join (by decide) sg88 sg694 - -lemma sg3170 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,5,3,1,1] := by - exact rowSquare_join (by decide) sg89 sg694 - -lemma sg3171 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,5,3,2] := by - exact rowSquare_join (by decide) sg88 sg695 - -lemma sg3172 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,5,4,1] := by - exact rowSquare_join (by decide) sg88 sg696 - -lemma sg3173 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,5,5] := by - exact rowSquare_join (by decide) sg89 sg696 - -lemma sg3174 : RowSquare [3,3,2,1,1,1,1,1,1,1] [6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg193 sg413 - -lemma sg3175 : RowSquare [3,3,2,1,1,1,1,1,1,1] [6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg193 sg414 - -lemma sg3176 : RowSquare [3,3,2,1,1,1,1,1,1,1] [6,3,2,2,2] := by - exact rowSquare_join (by decide) sg194 sg413 - -lemma sg3177 : RowSquare [3,3,2,1,1,1,1,1,1,1] [6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg415 - -lemma sg3178 : RowSquare [3,3,2,1,1,1,1,1,1,1] [6,6,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg694 - -lemma sg3179 : RowSquare [3,3,2,2,1,1,1,1,1] [4,4,4,2,1] := by - exact rowSquare_join (by decide) sg195 sg389 - -lemma sg3180 : RowSquare [3,3,2,2,1,1,1,1,1] [4,4,4,3] := by - exact rowSquare_join (by decide) sg195 sg390 - -lemma sg3181 : RowSquare [3,3,2,2,1,1,1,1,1] [5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg193 sg391 - -lemma sg3182 : RowSquare [3,3,2,2,1,1,1,1,1] [5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg975 - -lemma sg3183 : RowSquare [3,3,2,2,2,2,1] [4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg209 sg306 - -lemma sg3184 : RowSquare [3,3,2,2,2,2,1] [4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg210 sg306 - -lemma sg3185 : RowSquare [3,3,2,2,2,2,1] [5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg211 sg306 - -lemma sg3186 : RowSquare [4,3,1,1,1,1,1,1,1,1] [5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg413 - -lemma sg3187 : RowSquare [4,3,1,1,1,1,1,1,1,1] [5,4,4,1,1] := by - exact rowSquare_join (by decide) sg220 sg372 - -lemma sg3188 : RowSquare [4,3,1,1,1,1,1,1,1,1] [5,4,4,2] := by - exact rowSquare_join (by decide) sg220 sg373 - -lemma sg3189 : RowSquare [4,3,1,1,1,1,1,1,1,1] [6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg179 sg413 - -lemma sg3190 : RowSquare [4,3,1,1,1,1,1,1,1,1] [6,4,4,1] := by - exact rowSquare_join (by decide) sg181 sg415 - -lemma sg3191 : RowSquare [4,3,1,1,1,1,1,1,1,1] [6,5,3,1] := by - exact rowSquare_join (by decide) sg219 sg378 - -lemma sg3192 : RowSquare [4,3,1,1,1,1,1,1,1,1] [6,5,4] := by - exact rowSquare_join (by decide) sg220 sg378 - -lemma sg3193 : RowSquare [4,3,1,1,1,1,1,1,1,1] [7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg940 - -lemma sg3194 : RowSquare [4,3,1,1,1,1,1,1,1,1] [7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg419 - -lemma sg3195 : RowSquare [4,3,1,1,1,1,1,1,1,1] [7,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg417 - -lemma sg3196 : RowSquare [4,3,2,1,1,1,1,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg1033 - -lemma sg3197 : RowSquare [4,3,2,1,1,1,1,1,1] [4,4,4,3] := by - exact rowSquare_join (by decide) sg195 sg373 - -lemma sg3198 : RowSquare [4,3,2,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg849 - -lemma sg3199 : RowSquare [4,3,2,2,1,1,1,1] [5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg47 sg849 - -lemma sg3200 : RowSquare [4,3,2,2,2,1,1] [4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg849 - -lemma sg3201 : RowSquare [4,3,2,2,2,1,1] [4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg850 - -lemma sg3202 : RowSquare [4,3,2,2,2,1,1] [4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg849 - -lemma sg3203 : RowSquare [4,3,2,2,2,1,1] [4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg850 - -lemma sg3204 : RowSquare [4,3,2,2,2,1,1] [5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg43 sg849 - -lemma sg3205 : RowSquare [4,3,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg44 sg849 - -lemma sg3206 : RowSquare [4,3,3,2,1,1,1] [2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg849 - -lemma sg3207 : RowSquare [4,3,3,2,1,1,1] [3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg849 - -lemma sg3208 : RowSquare [4,3,3,2,1,1,1] [3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg34 sg849 - -lemma sg3209 : RowSquare [4,4,1,1,1,1,1,1,1] [3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg371 - -lemma sg3210 : RowSquare [4,4,1,1,1,1,1,1,1] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg373 - -lemma sg3211 : RowSquare [4,4,1,1,1,1,1,1,1] [4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg374 - -lemma sg3212 : RowSquare [4,4,1,1,1,1,1,1,1] [4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg375 - -lemma sg3213 : RowSquare [4,4,1,1,1,1,1,1,1] [4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg179 sg371 - -lemma sg3214 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg377 - -lemma sg3215 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg180 sg371 - -lemma sg3216 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg378 - -lemma sg3217 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg181 sg371 - -lemma sg3218 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,3,2,2] := by - exact rowSquare_join (by decide) sg180 sg372 - -lemma sg3219 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,3,3,1] := by - exact rowSquare_join (by decide) sg180 sg373 - -lemma sg3220 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,4,3] := by - exact rowSquare_join (by decide) sg181 sg373 - -lemma sg3221 : RowSquare [4,4,1,1,1,1,1,1,1] [5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg179 sg374 - -lemma sg3222 : RowSquare [4,4,1,1,1,1,1,1,1] [5,3,3,3,1] := by - exact rowSquare_join (by decide) sg182 sg373 - -lemma sg3223 : RowSquare [4,4,1,1,1,1,1,1,1] [5,4,3,3] := by - exact rowSquare_join (by decide) sg183 sg373 - -lemma sg3224 : RowSquare [4,4,1,1,1,1,1,1,1] [5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg383 - -lemma sg3225 : RowSquare [4,4,1,1,1,1,1,1,1] [6,3,3,3] := by - exact rowSquare_join (by decide) sg186 sg373 - -lemma sg3226 : RowSquare [4,4,1,1,1,1,1,1,1] [8,7] := by - exact rowSquare_join (by decide) sg188 sg383 - -lemma sg3227 : RowSquare [4,4,1,1,1,1,1,1,1] [9,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg1123 - -lemma sg3228 : RowSquare [4,4,1,1,1,1,1,1,1] [9,6] := by - exact rowSquare_join (by decide) sg14 sg1122 - -lemma sg3229 : RowSquare [4,4,1,1,1,1,1,1,1] [10,5] := by - exact rowSquare_join (by decide) sg14 sg1124 - -lemma sg3230 : RowSquare [4,4,1,1,1,1,1,1,1] [11,4] := by - exact rowSquare_join (by decide) sg14 sg1125 - -lemma sg3231 : RowSquare [4,4,1,1,1,1,1,1,1] [13,2] := by - exact rowSquare_join (by decide) sg85 sg427 - -lemma sg3232 : RowSquare [4,4,2,1,1,1,1,1] [2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg330 - -lemma sg3233 : RowSquare [4,4,2,1,1,1,1,1] [6,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg2035 - -lemma sg3234 : RowSquare [4,4,2,1,1,1,1,1] [8,7] := by - exact rowSquare_join (by decide) sg14 sg1127 - -lemma sg3235 : RowSquare [4,4,2,1,1,1,1,1] [9,6] := by - exact rowSquare_join (by decide) sg29 sg722 - -lemma sg3236 : RowSquare [4,4,2,1,1,1,1,1] [10,5] := by - exact rowSquare_join (by decide) sg29 sg724 - -lemma sg3237 : RowSquare [4,4,2,1,1,1,1,1] [11,4] := by - exact rowSquare_join (by decide) sg29 sg725 - -lemma sg3238 : RowSquare [4,4,2,1,1,1,1,1] [13,2] := by - exact rowSquare_join (by decide) sg176 sg235 - -lemma sg3240 : RowSquare [4,4,2,2,1,1,1] [5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg302 - -lemma sg3241 : RowSquare [4,4,2,2,1,1,1] [5,5,5] := by - exact rowSquare_join (by decide) sg97 sg484 - -lemma sg3242 : RowSquare [4,4,2,2,1,1,1] [6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg1655 - -lemma sg3243 : RowSquare [4,4,2,2,2,1] [4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg1650 - -lemma sg3244 : RowSquare [4,4,2,2,2,1] [5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg1651 - -lemma sg3245 : RowSquare [4,4,2,2,2,1] [5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg1656 - -lemma sg3246 : RowSquare [4,4,2,2,2,1] [6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg1655 - -lemma sg3247 : RowSquare [4,4,2,2,2,1] [6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg1657 - -lemma sg3248 : RowSquare [4,4,2,2,2,1] [7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg1657 - -lemma sg3249 : RowSquare [4,4,3,2,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg796 - -lemma sg3250 : RowSquare [4,4,3,2,2] [4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg2111 - -lemma sg3251 : RowSquare [4,4,4,3] [2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg130 sg257 - -lemma sg3252 : RowSquare [4,4,4,3] [3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg125 sg259 - -lemma sg3253 : RowSquare [4,4,4,3] [3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg124 sg259 - -lemma sg3254 : RowSquare [4,4,4,3] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg129 sg256 - -lemma sg3255 : RowSquare [5,3,1,1,1,1,1,1,1] [3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg88 sg586 - -lemma sg3256 : RowSquare [5,3,1,1,1,1,1,1,1] [3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg998 - -lemma sg3257 : RowSquare [5,3,1,1,1,1,1,1,1] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg586 - -lemma sg3258 : RowSquare [5,3,1,1,1,1,1,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg1001 - -lemma sg3259 : RowSquare [5,3,2,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg910 - -lemma sg3260 : RowSquare [5,3,2,1,1,1,1,1] [2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg586 - -lemma sg3261 : RowSquare [5,3,2,1,1,1,1,1] [3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg910 - -lemma sg3262 : RowSquare [5,3,2,1,1,1,1,1] [3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg587 - -lemma sg3263 : RowSquare [5,3,2,1,1,1,1,1] [3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg588 - -lemma sg3264 : RowSquare [5,3,2,1,1,1,1,1] [3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg589 - -lemma sg3265 : RowSquare [5,3,2,1,1,1,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg915 - -lemma sg3266 : RowSquare [5,3,2,1,1,1,1,1] [4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg1682 - -lemma sg3267 : RowSquare [5,3,2,1,1,1,1,1] [4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg36 sg910 - -lemma sg3268 : RowSquare [5,3,2,1,1,1,1,1] [4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg2529 - -lemma sg3269 : RowSquare [5,3,2,1,1,1,1,1] [5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg2532 - -lemma sg3270 : RowSquare [5,3,2,1,1,1,1,1] [5,5,5] := by - exact rowSquare_join (by decide) sg4 sg1586 - -lemma sg3271 : RowSquare [5,3,2,2,1,1,1] [3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg910 - -lemma sg3272 : RowSquare [5,3,2,2,1,1,1] [3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg27 sg910 - -lemma sg3273 : RowSquare [5,3,2,2,1,1,1] [6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2542 - -lemma sg3274 : RowSquare [5,4,1,1,1,1,1,1] [3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg66 sg586 - -lemma sg3275 : RowSquare [5,4,1,1,1,1,1,1] [3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg2546 - -lemma sg3276 : RowSquare [5,4,1,1,1,1,1,1] [3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg67 sg586 - -lemma sg3277 : RowSquare [5,4,1,1,1,1,1,1] [3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg313 - -lemma sg3278 : RowSquare [5,4,1,1,1,1,1,1] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg586 - -lemma sg3279 : RowSquare [5,4,1,1,1,1,1,1] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg315 - -lemma sg3280 : RowSquare [5,4,1,1,1,1,1,1] [4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg69 sg586 - -lemma sg3281 : RowSquare [5,4,1,1,1,1,1,1] [4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg66 sg587 - -lemma sg3282 : RowSquare [5,4,1,1,1,1,1,1] [4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg70 sg586 - -lemma sg3283 : RowSquare [5,4,1,1,1,1,1,1] [4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg67 sg587 - -lemma sg3284 : RowSquare [5,4,1,1,1,1,1,1] [4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg179 sg313 - -lemma sg3285 : RowSquare [5,4,1,1,1,1,1,1] [4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg587 - -lemma sg3286 : RowSquare [5,4,1,1,1,1,1,1] [4,3,3,3,2] := by - exact rowSquare_join (by decide) sg66 sg590 - -lemma sg3287 : RowSquare [5,4,1,1,1,1,1,1] [4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg71 sg586 - -lemma sg3288 : RowSquare [5,4,1,1,1,1,1,1] [4,4,4,3] := by - exact rowSquare_join (by decide) sg181 sg315 - -lemma sg3289 : RowSquare [5,4,1,1,1,1,1,1] [5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg69 sg587 - -lemma sg3290 : RowSquare [5,4,1,1,1,1,1,1] [6,3,3,3] := by - exact rowSquare_join (by decide) sg13 sg1137 - -lemma sg3291 : RowSquare [5,4,1,1,1,1,1,1] [7,6,2] := by - exact rowSquare_join (by decide) sg14 sg1139 - -lemma sg3292 : RowSquare [5,4,1,1,1,1,1,1] [8,7] := by - exact rowSquare_join (by decide) sg14 sg1141 - -lemma sg3293 : RowSquare [5,4,2,1,1,1,1] [4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg22 sg910 - -lemma sg3294 : RowSquare [5,4,2,1,1,1,1] [4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg2074 - -lemma sg3295 : RowSquare [5,4,2,1,1,1,1] [4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg23 sg910 - -lemma sg3296 : RowSquare [5,4,2,1,1,1,1] [5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg910 - -lemma sg3297 : RowSquare [5,4,2,1,1,1,1] [6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg2077 - -lemma sg3298 : RowSquare [5,4,3,1,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg759 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes5 + +namespace OAI + +/-! Semigroup Nodes 6. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg2897 : RowSquare [8,2,1,1,1,1] [5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg1331 + +lemma sg2898 : RowSquare [8,2,1,1,1,1] [5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6 sg1332 + +lemma sg2899 : RowSquare [8,2,1,1,1,1] [5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg893 + +lemma sg2900 : RowSquare [8,2,1,1,1,1] [5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg897 + +lemma sg2901 : RowSquare [8,2,1,1,1,1] [7,7] := by + exact rowSquare_join (by decide) sg17 sg909 + +lemma sg2902 : RowSquare [8,2,2,1,1] [2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg586 + +lemma sg2903 : RowSquare [8,2,2,1,1] [3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg586 + +lemma sg2904 : RowSquare [8,2,2,1,1] [3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg587 + +lemma sg2905 : RowSquare [8,2,2,1,1] [3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg34 sg586 + +lemma sg2906 : RowSquare [8,2,2,1,1] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg588 + +lemma sg2907 : RowSquare [8,2,2,1,1] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg589 + +lemma sg2908 : RowSquare [8,2,2,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg590 + +lemma sg2909 : RowSquare [8,2,2,1,1] [4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg35 sg586 + +lemma sg2910 : RowSquare [8,2,2,1,1] [4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg587 + +lemma sg2911 : RowSquare [8,2,2,1,1] [4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg87 sg312 + +lemma sg2912 : RowSquare [8,2,2,1,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg36 sg586 + +lemma sg2913 : RowSquare [8,2,2,1,1] [4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg34 sg587 + +lemma sg2914 : RowSquare [8,2,2,1,1] [4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg88 sg312 + +lemma sg2915 : RowSquare [8,2,2,1,1] [4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg313 + +lemma sg2916 : RowSquare [8,2,2,1,1] [4,3,3,3,1] := by + exact rowSquare_join (by decide) sg87 sg315 + +lemma sg2917 : RowSquare [8,2,2,1,1] [4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg998 + +lemma sg2918 : RowSquare [8,2,2,1,1] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg88 sg313 + +lemma sg2919 : RowSquare [8,2,2,1,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg595 + +lemma sg2920 : RowSquare [8,2,2,1,1] [4,4,3,2,1] := by + exact rowSquare_join (by decide) sg88 sg314 + +lemma sg2921 : RowSquare [8,2,2,1,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg88 sg315 + +lemma sg2922 : RowSquare [8,2,2,1,1] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg89 sg314 + +lemma sg2923 : RowSquare [8,2,2,1,1] [4,4,4,2] := by + exact rowSquare_join (by decide) sg89 sg315 + +lemma sg2924 : RowSquare [8,2,2,1,1] [5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg313 + +lemma sg2925 : RowSquare [8,2,2,2] [2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg178 + +lemma sg2926 : RowSquare [8,2,2,2] [3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg179 + +lemma sg2927 : RowSquare [8,2,2,2] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg180 + +lemma sg2928 : RowSquare [8,2,2,2] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg181 + +lemma sg2929 : RowSquare [8,2,2,2] [4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg182 + +lemma sg2930 : RowSquare [8,2,2,2] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg179 sg179 + +lemma sg2931 : RowSquare [8,2,2,2] [4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg179 sg180 + +lemma sg2932 : RowSquare [8,2,2,2] [4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg179 sg181 + +lemma sg2933 : RowSquare [8,2,2,2] [4,3,3,2,2] := by + exact rowSquare_join (by decide) sg66 sg372 + +lemma sg2934 : RowSquare [8,2,2,2] [4,3,3,3,1] := by + exact rowSquare_join (by decide) sg66 sg373 + +lemma sg2935 : RowSquare [8,2,2,2] [4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg185 + +lemma sg2936 : RowSquare [8,2,2,2] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg67 sg371 + +lemma sg2937 : RowSquare [8,2,2,2] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg180 sg180 + +lemma sg2938 : RowSquare [8,2,2,2] [4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg371 + +lemma sg2939 : RowSquare [8,2,2,2] [4,4,3,2,1] := by + exact rowSquare_join (by decide) sg180 sg181 + +lemma sg2940 : RowSquare [8,2,2,2] [4,4,3,3] := by + exact rowSquare_join (by decide) sg67 sg373 + +lemma sg2941 : RowSquare [8,2,2,2] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg68 sg372 + +lemma sg2942 : RowSquare [8,2,2,2] [4,4,4,2] := by + exact rowSquare_join (by decide) sg181 sg181 + +lemma sg2943 : RowSquare [8,2,2,2] [5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg179 sg182 + +lemma sg2944 : RowSquare [8,2,2,2] [5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg179 sg183 + +lemma sg2945 : RowSquare [8,2,2,2] [5,3,2,2,2] := by + exact rowSquare_join (by decide) sg180 sg182 + +lemma sg2946 : RowSquare [8,2,2,2] [5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg184 + +lemma sg2947 : RowSquare [8,2,2,2] [5,3,3,2,1] := by + exact rowSquare_join (by decide) sg182 sg181 + +lemma sg2948 : RowSquare [8,2,2,2] [5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg185 + +lemma sg2949 : RowSquare [8,2,2,2] [5,4,2,2,1] := by + exact rowSquare_join (by decide) sg180 sg183 + +lemma sg2950 : RowSquare [8,2,2,2] [5,4,3,2] := by + exact rowSquare_join (by decide) sg181 sg183 + +lemma sg2951 : RowSquare [8,2,2,2] [5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg71 sg371 + +lemma sg2952 : RowSquare [8,2,2,2] [5,5,2,1,1] := by + exact rowSquare_join (by decide) sg180 sg185 + +lemma sg2953 : RowSquare [8,2,2,2] [5,5,2,2] := by + exact rowSquare_join (by decide) sg67 sg377 + +lemma sg2954 : RowSquare [8,2,2,2] [6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg179 sg186 + +lemma sg2955 : RowSquare [8,2,2,2] [6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg187 + +lemma sg2956 : RowSquare [8,2,2,2] [6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg188 + +lemma sg2957 : RowSquare [8,3,1,1,1] [3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg586 + +lemma sg2958 : RowSquare [8,3,1,1,1] [3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg586 + +lemma sg2959 : RowSquare [8,3,1,1,1] [3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg998 + +lemma sg2960 : RowSquare [8,3,1,1,1] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg999 + +lemma sg2961 : RowSquare [8,3,1,1,1] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg1000 + +lemma sg2962 : RowSquare [8,3,1,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg1001 + +lemma sg2963 : RowSquare [8,3,1,1,1] [4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg586 + +lemma sg2964 : RowSquare [8,3,1,1,1] [4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg587 + +lemma sg2965 : RowSquare [8,3,1,1,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg586 + +lemma sg2966 : RowSquare [8,3,1,1,1] [4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg587 + +lemma sg2967 : RowSquare [8,3,1,1,1] [4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg588 + +lemma sg2968 : RowSquare [8,3,1,1,1] [4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg312 + +lemma sg2969 : RowSquare [8,3,1,1,1] [4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg589 + +lemma sg2970 : RowSquare [8,3,1,1,1] [4,3,3,2,2] := by + exact rowSquare_join (by decide) sg16 sg915 + +lemma sg2971 : RowSquare [8,3,1,1,1] [4,3,3,3,1] := by + exact rowSquare_join (by decide) sg39 sg590 + +lemma sg2972 : RowSquare [8,3,1,1,1] [4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg912 + +lemma sg2973 : RowSquare [8,3,1,1,1] [4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg588 + +lemma sg2974 : RowSquare [8,3,1,1,1] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg1006 + +lemma sg2975 : RowSquare [8,3,1,1,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg915 + +lemma sg2976 : RowSquare [8,3,1,1,1] [4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg313 + +lemma sg2977 : RowSquare [8,3,1,1,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg13 sg1008 + +lemma sg2978 : RowSquare [8,3,1,1,1] [4,4,4,2] := by + exact rowSquare_join (by decide) sg97 sg315 + +lemma sg2979 : RowSquare [8,3,1,1,1] [5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg586 + +lemma sg2980 : RowSquare [8,3,1,1,1] [5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg534 + +lemma sg2981 : RowSquare [8,3,1,1,1] [5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg98 sg312 + +lemma sg2982 : RowSquare [8,3,1,1,1] [5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg534 + +lemma sg2983 : RowSquare [8,3,1,1,1] [5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg99 sg312 + +lemma sg2984 : RowSquare [8,3,1,1,1] [5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg98 sg313 + +lemma sg2985 : RowSquare [8,3,1,1,1] [5,3,2,2,2] := by + exact rowSquare_join (by decide) sg18 sg915 + +lemma sg2986 : RowSquare [8,3,1,1,1] [5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg316 + +lemma sg2987 : RowSquare [8,3,1,1,1] [5,3,3,2,1] := by + exact rowSquare_join (by decide) sg98 sg314 + +lemma sg2988 : RowSquare [8,3,1,1,1] [5,3,3,3] := by + exact rowSquare_join (by decide) sg98 sg315 + +lemma sg2989 : RowSquare [8,3,1,1,1] [5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg535 + +lemma sg2990 : RowSquare [8,3,1,1,1] [5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg99 sg313 + +lemma sg2991 : RowSquare [8,3,1,1,1] [5,4,2,2,1] := by + exact rowSquare_join (by decide) sg39 sg595 + +lemma sg2992 : RowSquare [8,3,1,1,1] [5,4,3,1,1] := by + exact rowSquare_join (by decide) sg97 sg317 + +lemma sg2993 : RowSquare [8,3,1,1,1] [5,4,3,2] := by + exact rowSquare_join (by decide) sg99 sg315 + +lemma sg2994 : RowSquare [8,3,1,1,1] [5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg920 + +lemma sg2995 : RowSquare [8,3,1,1,1] [5,5,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg595 + +lemma sg2996 : RowSquare [8,3,1,1,1] [5,5,2,2] := by + exact rowSquare_join (by decide) sg13 sg1015 + +lemma sg2997 : RowSquare [8,3,1,1,1] [5,5,3,1] := by + exact rowSquare_join (by decide) sg97 sg319 + +lemma sg2998 : RowSquare [8,3,1,1,1] [6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg312 + +lemma sg2999 : RowSquare [8,3,1,1,1] [6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg101 sg313 + +lemma sg3000 : RowSquare [8,3,2,1] [3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg87 sg330 + +lemma sg3001 : RowSquare [8,3,2,1] [3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg193 + +lemma sg3002 : RowSquare [8,3,2,1] [3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg88 sg330 + +lemma sg3003 : RowSquare [8,3,2,1] [3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg194 + +lemma sg3004 : RowSquare [8,3,2,1] [3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg371 + +lemma sg3005 : RowSquare [8,3,2,1] [3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg330 + +lemma sg3006 : RowSquare [8,3,2,1] [3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg195 + +lemma sg3007 : RowSquare [8,3,2,1] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg372 + +lemma sg3008 : RowSquare [8,3,2,1] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg74 sg373 + +lemma sg3009 : RowSquare [8,3,2,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg616 + +lemma sg3010 : RowSquare [8,3,2,1] [4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg90 sg330 + +lemma sg3011 : RowSquare [8,3,2,1] [4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg196 + +lemma sg3012 : RowSquare [8,3,2,1] [4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg193 sg179 + +lemma sg3013 : RowSquare [8,3,2,1] [4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg91 sg330 + +lemma sg3014 : RowSquare [8,3,2,1] [4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg197 + +lemma sg3015 : RowSquare [8,3,2,1] [4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg193 sg180 + +lemma sg3016 : RowSquare [8,3,2,1] [4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg198 + +lemma sg3017 : RowSquare [8,3,2,1] [4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg193 sg181 + +lemma sg3018 : RowSquare [8,3,2,1] [4,3,3,2,2] := by + exact rowSquare_join (by decide) sg87 sg333 + +lemma sg3019 : RowSquare [8,3,2,1] [4,3,3,3,1] := by + exact rowSquare_join (by decide) sg87 sg334 + +lemma sg3020 : RowSquare [8,3,2,1] [4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg330 + +lemma sg3021 : RowSquare [8,3,2,1] [4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg199 + +lemma sg3022 : RowSquare [8,3,2,1] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg377 + +lemma sg3023 : RowSquare [8,3,2,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg194 sg180 + +lemma sg3024 : RowSquare [8,3,2,1] [4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg378 + +lemma sg3025 : RowSquare [8,3,2,1] [4,4,3,2,1] := by + exact rowSquare_join (by decide) sg194 sg181 + +lemma sg3026 : RowSquare [8,3,2,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg88 sg334 + +lemma sg3027 : RowSquare [8,3,2,1] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg89 sg333 + +lemma sg3028 : RowSquare [8,3,2,1] [4,4,4,2] := by + exact rowSquare_join (by decide) sg195 sg181 + +lemma sg3029 : RowSquare [8,3,2,1] [5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg93 sg330 + +lemma sg3030 : RowSquare [8,3,2,1] [5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg200 + +lemma sg3031 : RowSquare [8,3,2,1] [5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg193 sg182 + +lemma sg3032 : RowSquare [8,3,2,1] [5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg94 sg330 + +lemma sg3033 : RowSquare [8,3,2,1] [5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg201 + +lemma sg3034 : RowSquare [8,3,2,1] [5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg193 sg183 + +lemma sg3035 : RowSquare [8,3,2,1] [5,3,2,2,2] := by + exact rowSquare_join (by decide) sg194 sg182 + +lemma sg3036 : RowSquare [8,3,2,1] [5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg184 + +lemma sg3037 : RowSquare [8,3,2,1] [5,3,3,2,1] := by + exact rowSquare_join (by decide) sg218 sg144 + +lemma sg3038 : RowSquare [8,3,2,1] [5,3,3,3] := by + exact rowSquare_join (by decide) sg90 sg334 + +lemma sg3039 : RowSquare [8,3,2,1] [5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg202 + +lemma sg3040 : RowSquare [8,3,2,1] [5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg185 + +lemma sg3041 : RowSquare [8,3,2,1] [5,4,2,2,1] := by + exact rowSquare_join (by decide) sg194 sg183 + +lemma sg3042 : RowSquare [8,3,2,1] [5,4,3,1,1] := by + exact rowSquare_join (by decide) sg194 sg184 + +lemma sg3043 : RowSquare [8,3,2,1] [5,4,3,2] := by + exact rowSquare_join (by decide) sg195 sg183 + +lemma sg3044 : RowSquare [8,3,2,1] [5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg383 + +lemma sg3045 : RowSquare [8,3,2,1] [5,5,2,1,1] := by + exact rowSquare_join (by decide) sg194 sg185 + +lemma sg3046 : RowSquare [8,3,2,1] [5,5,2,2] := by + exact rowSquare_join (by decide) sg88 sg338 + +lemma sg3047 : RowSquare [8,3,2,1] [5,5,3,1] := by + exact rowSquare_join (by decide) sg195 sg185 + +lemma sg3048 : RowSquare [8,3,2,1] [6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg850 + +lemma sg3049 : RowSquare [8,3,2,1] [6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg95 sg330 + +lemma sg3050 : RowSquare [8,3,2,1] [6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg203 + +lemma sg3051 : RowSquare [8,3,2,1] [6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg193 sg186 + +lemma sg3052 : RowSquare [8,3,2,1] [6,2,2,2,2] := by + exact rowSquare_join (by decide) sg218 sg145 + +lemma sg3053 : RowSquare [8,3,2,1] [6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg204 + +lemma sg3054 : RowSquare [8,3,2,1] [6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg187 + +lemma sg3055 : RowSquare [8,3,2,1] [6,3,2,2,1] := by + exact rowSquare_join (by decide) sg194 sg186 + +lemma sg3056 : RowSquare [8,3,2,1] [6,3,3,1,1] := by + exact rowSquare_join (by decide) sg218 sg147 + +lemma sg3057 : RowSquare [8,3,2,1] [6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg188 + +lemma sg3058 : RowSquare [8,3,2,1] [6,6,1,1] := by + exact rowSquare_join (by decide) sg88 sg342 + +lemma sg3059 : RowSquare [8,3,2,1] [7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg205 + +lemma sg3060 : RowSquare [8,3,2,1] [7,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg189 + +lemma sg3061 : RowSquare [8,3,2,1] [7,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg190 + +lemma sg3062 : RowSquare [8,3,2,1] [7,3,2,1,1] := by + exact rowSquare_join (by decide) sg194 sg189 + +lemma sg3063 : RowSquare [8,3,2,1] [7,4,1,1,1] := by + exact rowSquare_join (by decide) sg194 sg190 + +lemma sg3064 : RowSquare [8,3,2,1] [7,7] := by + exact rowSquare_join (by decide) sg92 sg342 + +lemma sg3065 : RowSquare [8,3,2,1] [8,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg206 + +lemma sg3066 : RowSquare [8,3,2,1] [8,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg191 + +lemma sg3067 : RowSquare [8,3,2,1] [8,3,1,1,1] := by + exact rowSquare_join (by decide) sg194 sg191 + +lemma sg3068 : RowSquare [8,3,3] [3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg636 + +lemma sg3069 : RowSquare [8,3,3] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg637 + +lemma sg3070 : RowSquare [8,3,3] [4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg348 + +lemma sg3071 : RowSquare [8,3,3] [4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg33 sg636 + +lemma sg3072 : RowSquare [8,3,3] [4,3,3,2,2] := by + exact rowSquare_join (by decide) sg87 sg349 + +lemma sg3073 : RowSquare [8,3,3] [4,3,3,3,1] := by + exact rowSquare_join (by decide) sg87 sg350 + +lemma sg3074 : RowSquare [8,3,3] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg88 sg348 + +lemma sg3075 : RowSquare [8,3,3] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg639 + +lemma sg3076 : RowSquare [8,3,3] [4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg348 + +lemma sg3077 : RowSquare [8,3,3] [4,4,3,2,1] := by + exact rowSquare_join (by decide) sg88 sg349 + +lemma sg3078 : RowSquare [8,3,3] [4,4,3,3] := by + exact rowSquare_join (by decide) sg88 sg350 + +lemma sg3079 : RowSquare [8,3,3] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg89 sg349 + +lemma sg3080 : RowSquare [8,3,3] [4,4,4,2] := by + exact rowSquare_join (by decide) sg89 sg350 + +lemma sg3081 : RowSquare [8,3,3] [5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg154 sg218 + +lemma sg3082 : RowSquare [8,3,3] [5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg154 sg219 + +lemma sg3083 : RowSquare [8,3,3] [5,3,2,2,2] := by + exact rowSquare_join (by decide) sg155 sg218 + +lemma sg3084 : RowSquare [8,3,3] [5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg154 sg220 + +lemma sg3085 : RowSquare [8,3,3] [5,3,3,3] := by + exact rowSquare_join (by decide) sg90 sg350 + +lemma sg3086 : RowSquare [8,3,3] [5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg91 sg348 + +lemma sg3087 : RowSquare [8,3,3] [5,4,2,2,1] := by + exact rowSquare_join (by decide) sg155 sg219 + +lemma sg3088 : RowSquare [8,3,3] [5,4,3,2] := by + exact rowSquare_join (by decide) sg156 sg219 + +lemma sg3089 : RowSquare [8,3,3] [5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg348 + +lemma sg3090 : RowSquare [8,3,3] [5,5,2,2] := by + exact rowSquare_join (by decide) sg88 sg352 + +lemma sg3091 : RowSquare [8,3,3] [5,5,3,1] := by + exact rowSquare_join (by decide) sg88 sg353 + +lemma sg3092 : RowSquare [8,3,3] [6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg874 + +lemma sg3093 : RowSquare [8,3,3] [6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg154 sg221 + +lemma sg3094 : RowSquare [8,3,3] [6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg154 sg222 + +lemma sg3095 : RowSquare [8,3,3] [6,3,3,2] := by + exact rowSquare_join (by decide) sg156 sg221 + +lemma sg3096 : RowSquare [8,3,3] [6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg154 sg223 + +lemma sg3097 : RowSquare [8,3,3] [6,4,2,2] := by + exact rowSquare_join (by decide) sg219 sg158 + +lemma sg3098 : RowSquare [8,3,3] [6,6,1,1] := by + exact rowSquare_join (by decide) sg88 sg354 + +lemma sg3099 : RowSquare [8,4,1,1] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg1032 + +lemma sg3100 : RowSquare [8,4,1,1] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg1033 + +lemma sg3101 : RowSquare [8,4,1,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg961 + +lemma sg3102 : RowSquare [8,4,2] [3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg74 sg390 + +lemma sg3103 : RowSquare [8,4,2] [3,3,3,3,2] := by + exact rowSquare_join (by decide) sg32 sg644 + +lemma sg3104 : RowSquare [8,4,2] [4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg975 + +lemma sg3105 : RowSquare [8,4,2] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg194 sg194 + +lemma sg3107 : RowSquare [9,1,1,1,1,1] [5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg1330 + +lemma sg3108 : RowSquare [9,1,1,1,1,1] [5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg7 sg1332 + +lemma sg3109 : RowSquare [9,1,1,1,1,1] [6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg890 + +lemma sg3110 : RowSquare [9,2,1,1,1] [4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg586 + +lemma sg3111 : RowSquare [9,2,1,1,1] [4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg586 + +lemma sg3112 : RowSquare [9,2,1,1,1] [4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg998 + +lemma sg3113 : RowSquare [9,2,1,1,1] [4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg999 + +lemma sg3114 : RowSquare [9,2,1,1,1] [4,3,3,2,2] := by + exact rowSquare_join (by decide) sg16 sg1001 + +lemma sg3115 : RowSquare [9,2,1,1,1] [4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg998 + +lemma sg3116 : RowSquare [9,2,1,1,1] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg1000 + +lemma sg3117 : RowSquare [9,2,1,1,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg1001 + +lemma sg3118 : RowSquare [9,2,1,1,1] [5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg47 sg586 + +lemma sg3119 : RowSquare [9,2,2,1] [4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg218 + +lemma sg3120 : RowSquare [9,2,2,1] [4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg219 + +lemma sg3121 : RowSquare [9,2,2,1] [4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg87 sg371 + +lemma sg3122 : RowSquare [9,2,2,1] [4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg220 + +lemma sg3123 : RowSquare [9,2,2,1] [4,3,3,2,2] := by + exact rowSquare_join (by decide) sg87 sg372 + +lemma sg3124 : RowSquare [9,2,2,1] [4,3,3,3,1] := by + exact rowSquare_join (by decide) sg87 sg373 + +lemma sg3125 : RowSquare [9,2,2,1] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg88 sg371 + +lemma sg3126 : RowSquare [9,2,2,1] [4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg371 + +lemma sg3127 : RowSquare [9,2,2,1] [4,4,3,2,1] := by + exact rowSquare_join (by decide) sg88 sg372 + +lemma sg3128 : RowSquare [9,2,2,1] [4,4,3,3] := by + exact rowSquare_join (by decide) sg88 sg373 + +lemma sg3129 : RowSquare [9,2,2,1] [4,4,4,1,1] := by + exact rowSquare_join (by decide) sg89 sg372 + +lemma sg3130 : RowSquare [9,2,2,1] [4,4,4,2] := by + exact rowSquare_join (by decide) sg89 sg373 + +lemma sg3131 : RowSquare [9,2,2,1] [5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg221 + +lemma sg3132 : RowSquare [9,2,2,1] [5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg179 sg218 + +lemma sg3133 : RowSquare [9,2,2,1] [5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg222 + +lemma sg3134 : RowSquare [9,2,2,1] [5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg179 sg219 + +lemma sg3135 : RowSquare [9,2,2,1] [5,3,2,2,2] := by + exact rowSquare_join (by decide) sg180 sg218 + +lemma sg3136 : RowSquare [9,2,2,1] [5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg220 + +lemma sg3137 : RowSquare [9,2,2,1] [5,3,3,2,1] := by + exact rowSquare_join (by decide) sg218 sg181 + +lemma sg3138 : RowSquare [9,2,2,1] [5,3,3,3] := by + exact rowSquare_join (by decide) sg90 sg373 + +lemma sg3139 : RowSquare [9,2,2,1] [5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg223 + +lemma sg3140 : RowSquare [9,2,2,1] [5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg91 sg371 + +lemma sg3141 : RowSquare [9,2,2,1] [5,4,2,2,1] := by + exact rowSquare_join (by decide) sg180 sg219 + +lemma sg3142 : RowSquare [9,2,2,1] [5,4,3,1,1] := by + exact rowSquare_join (by decide) sg180 sg220 + +lemma sg3143 : RowSquare [9,2,2,1] [5,4,3,2] := by + exact rowSquare_join (by decide) sg181 sg219 + +lemma sg3144 : RowSquare [9,2,2,1] [5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg371 + +lemma sg3145 : RowSquare [9,2,2,1] [6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg179 sg221 + +lemma sg3146 : RowSquare [9,2,2,1] [6,2,2,2,2] := by + exact rowSquare_join (by decide) sg218 sg182 + +lemma sg3147 : RowSquare [9,3,1,1] [4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg228 + +lemma sg3148 : RowSquare [9,3,1,1] [4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg17 sg1032 + +lemma sg3149 : RowSquare [9,3,1,1] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg17 sg1033 + +lemma sg3150 : RowSquare [9,3,1,1] [5,5,2,2] := by + exact rowSquare_join (by decide) sg17 sg1040 + +lemma sg3151 : RowSquare [9,3,2] [4,4,2,2,2] := by + exact rowSquare_join (by decide) sg32 sg694 + +lemma sg3152 : RowSquare [9,3,2] [4,4,3,3] := by + exact rowSquare_join (by decide) sg88 sg390 + +lemma sg3153 : RowSquare [9,3,2] [5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1063 + +lemma sg3154 : RowSquare [9,4,1] [5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg424 + +lemma sg3155 : RowSquare [10,1,1,1,1] [6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg586 + +lemma sg3156 : RowSquare [10,1,1,1,1] [6,2,2,2,2] := by + exact rowSquare_join (by decide) sg20 sg1001 + +lemma sg3157 : RowSquare [3,2,2,2,1,1,1,1,1,1] [5,4,4,1,1] := by + exact rowSquare_join (by decide) sg227 sg389 + +lemma sg3158 : RowSquare [3,2,2,2,1,1,1,1,1,1] [5,4,4,2] := by + exact rowSquare_join (by decide) sg227 sg390 + +lemma sg3159 : RowSquare [3,2,2,2,1,1,1,1,1,1] [5,5,3,1,1] := by + exact rowSquare_join (by decide) sg228 sg389 + +lemma sg3160 : RowSquare [3,2,2,2,1,1,1,1,1,1] [5,5,5] := by + exact rowSquare_join (by decide) sg97 sg696 + +lemma sg3161 : RowSquare [3,2,2,2,2,2,1,1] [4,4,4,3] := by + exact rowSquare_join (by decide) sg207 sg358 + +lemma sg3162 : RowSquare [3,3,1,1,1,1,1,1,1,1,1] [9,3,3] := by + exact rowSquare_join (by decide) sg220 sg419 + +lemma sg3163 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,3,3,3,1] := by + exact rowSquare_join (by decide) sg218 sg390 + +lemma sg3164 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,4,2,2,2] := by + exact rowSquare_join (by decide) sg87 sg694 + +lemma sg3165 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,4,3,2,1] := by + exact rowSquare_join (by decide) sg219 sg389 + +lemma sg3166 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,4,3,3] := by + exact rowSquare_join (by decide) sg219 sg390 + +lemma sg3167 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,4,4,1,1] := by + exact rowSquare_join (by decide) sg220 sg389 + +lemma sg3168 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,4,4,2] := by + exact rowSquare_join (by decide) sg220 sg390 + +lemma sg3169 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,5,2,2,1] := by + exact rowSquare_join (by decide) sg88 sg694 + +lemma sg3170 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,5,3,1,1] := by + exact rowSquare_join (by decide) sg89 sg694 + +lemma sg3171 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,5,3,2] := by + exact rowSquare_join (by decide) sg88 sg695 + +lemma sg3172 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,5,4,1] := by + exact rowSquare_join (by decide) sg88 sg696 + +lemma sg3173 : RowSquare [3,3,2,1,1,1,1,1,1,1] [5,5,5] := by + exact rowSquare_join (by decide) sg89 sg696 + +lemma sg3174 : RowSquare [3,3,2,1,1,1,1,1,1,1] [6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg193 sg413 + +lemma sg3175 : RowSquare [3,3,2,1,1,1,1,1,1,1] [6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg193 sg414 + +lemma sg3176 : RowSquare [3,3,2,1,1,1,1,1,1,1] [6,3,2,2,2] := by + exact rowSquare_join (by decide) sg194 sg413 + +lemma sg3177 : RowSquare [3,3,2,1,1,1,1,1,1,1] [6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg415 + +lemma sg3178 : RowSquare [3,3,2,1,1,1,1,1,1,1] [6,6,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg694 + +lemma sg3179 : RowSquare [3,3,2,2,1,1,1,1,1] [4,4,4,2,1] := by + exact rowSquare_join (by decide) sg195 sg389 + +lemma sg3180 : RowSquare [3,3,2,2,1,1,1,1,1] [4,4,4,3] := by + exact rowSquare_join (by decide) sg195 sg390 + +lemma sg3181 : RowSquare [3,3,2,2,1,1,1,1,1] [5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg193 sg391 + +lemma sg3182 : RowSquare [3,3,2,2,1,1,1,1,1] [5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg975 + +lemma sg3183 : RowSquare [3,3,2,2,2,2,1] [4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg209 sg306 + +lemma sg3184 : RowSquare [3,3,2,2,2,2,1] [4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg210 sg306 + +lemma sg3185 : RowSquare [3,3,2,2,2,2,1] [5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg211 sg306 + +lemma sg3186 : RowSquare [4,3,1,1,1,1,1,1,1,1] [5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg413 + +lemma sg3187 : RowSquare [4,3,1,1,1,1,1,1,1,1] [5,4,4,1,1] := by + exact rowSquare_join (by decide) sg220 sg372 + +lemma sg3188 : RowSquare [4,3,1,1,1,1,1,1,1,1] [5,4,4,2] := by + exact rowSquare_join (by decide) sg220 sg373 + +lemma sg3189 : RowSquare [4,3,1,1,1,1,1,1,1,1] [6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg179 sg413 + +lemma sg3190 : RowSquare [4,3,1,1,1,1,1,1,1,1] [6,4,4,1] := by + exact rowSquare_join (by decide) sg181 sg415 + +lemma sg3191 : RowSquare [4,3,1,1,1,1,1,1,1,1] [6,5,3,1] := by + exact rowSquare_join (by decide) sg219 sg378 + +lemma sg3192 : RowSquare [4,3,1,1,1,1,1,1,1,1] [6,5,4] := by + exact rowSquare_join (by decide) sg220 sg378 + +lemma sg3193 : RowSquare [4,3,1,1,1,1,1,1,1,1] [7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg940 + +lemma sg3194 : RowSquare [4,3,1,1,1,1,1,1,1,1] [7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg419 + +lemma sg3195 : RowSquare [4,3,1,1,1,1,1,1,1,1] [7,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg417 + +lemma sg3196 : RowSquare [4,3,2,1,1,1,1,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg1033 + +lemma sg3197 : RowSquare [4,3,2,1,1,1,1,1,1] [4,4,4,3] := by + exact rowSquare_join (by decide) sg195 sg373 + +lemma sg3198 : RowSquare [4,3,2,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg849 + +lemma sg3199 : RowSquare [4,3,2,2,1,1,1,1] [5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg47 sg849 + +lemma sg3200 : RowSquare [4,3,2,2,2,1,1] [4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg849 + +lemma sg3201 : RowSquare [4,3,2,2,2,1,1] [4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg850 + +lemma sg3202 : RowSquare [4,3,2,2,2,1,1] [4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg849 + +lemma sg3203 : RowSquare [4,3,2,2,2,1,1] [4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg850 + +lemma sg3204 : RowSquare [4,3,2,2,2,1,1] [5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg43 sg849 + +lemma sg3205 : RowSquare [4,3,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg44 sg849 + +lemma sg3206 : RowSquare [4,3,3,2,1,1,1] [2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg849 + +lemma sg3207 : RowSquare [4,3,3,2,1,1,1] [3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg849 + +lemma sg3208 : RowSquare [4,3,3,2,1,1,1] [3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg34 sg849 + +lemma sg3209 : RowSquare [4,4,1,1,1,1,1,1,1] [3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg371 + +lemma sg3210 : RowSquare [4,4,1,1,1,1,1,1,1] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg373 + +lemma sg3211 : RowSquare [4,4,1,1,1,1,1,1,1] [4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg374 + +lemma sg3212 : RowSquare [4,4,1,1,1,1,1,1,1] [4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg375 + +lemma sg3213 : RowSquare [4,4,1,1,1,1,1,1,1] [4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg179 sg371 + +lemma sg3214 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg377 + +lemma sg3215 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg180 sg371 + +lemma sg3216 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg378 + +lemma sg3217 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg181 sg371 + +lemma sg3218 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,3,2,2] := by + exact rowSquare_join (by decide) sg180 sg372 + +lemma sg3219 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,3,3,1] := by + exact rowSquare_join (by decide) sg180 sg373 + +lemma sg3220 : RowSquare [4,4,1,1,1,1,1,1,1] [4,4,4,3] := by + exact rowSquare_join (by decide) sg181 sg373 + +lemma sg3221 : RowSquare [4,4,1,1,1,1,1,1,1] [5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg179 sg374 + +lemma sg3222 : RowSquare [4,4,1,1,1,1,1,1,1] [5,3,3,3,1] := by + exact rowSquare_join (by decide) sg182 sg373 + +lemma sg3223 : RowSquare [4,4,1,1,1,1,1,1,1] [5,4,3,3] := by + exact rowSquare_join (by decide) sg183 sg373 + +lemma sg3224 : RowSquare [4,4,1,1,1,1,1,1,1] [5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg383 + +lemma sg3225 : RowSquare [4,4,1,1,1,1,1,1,1] [6,3,3,3] := by + exact rowSquare_join (by decide) sg186 sg373 + +lemma sg3226 : RowSquare [4,4,1,1,1,1,1,1,1] [8,7] := by + exact rowSquare_join (by decide) sg188 sg383 + +lemma sg3227 : RowSquare [4,4,1,1,1,1,1,1,1] [9,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg1123 + +lemma sg3228 : RowSquare [4,4,1,1,1,1,1,1,1] [9,6] := by + exact rowSquare_join (by decide) sg14 sg1122 + +lemma sg3229 : RowSquare [4,4,1,1,1,1,1,1,1] [10,5] := by + exact rowSquare_join (by decide) sg14 sg1124 + +lemma sg3230 : RowSquare [4,4,1,1,1,1,1,1,1] [11,4] := by + exact rowSquare_join (by decide) sg14 sg1125 + +lemma sg3231 : RowSquare [4,4,1,1,1,1,1,1,1] [13,2] := by + exact rowSquare_join (by decide) sg85 sg427 + +lemma sg3232 : RowSquare [4,4,2,1,1,1,1,1] [2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg330 + +lemma sg3233 : RowSquare [4,4,2,1,1,1,1,1] [6,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg2035 + +lemma sg3234 : RowSquare [4,4,2,1,1,1,1,1] [8,7] := by + exact rowSquare_join (by decide) sg14 sg1127 + +lemma sg3235 : RowSquare [4,4,2,1,1,1,1,1] [9,6] := by + exact rowSquare_join (by decide) sg29 sg722 + +lemma sg3236 : RowSquare [4,4,2,1,1,1,1,1] [10,5] := by + exact rowSquare_join (by decide) sg29 sg724 + +lemma sg3237 : RowSquare [4,4,2,1,1,1,1,1] [11,4] := by + exact rowSquare_join (by decide) sg29 sg725 + +lemma sg3238 : RowSquare [4,4,2,1,1,1,1,1] [13,2] := by + exact rowSquare_join (by decide) sg176 sg235 + +lemma sg3240 : RowSquare [4,4,2,2,1,1,1] [5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg302 + +lemma sg3241 : RowSquare [4,4,2,2,1,1,1] [5,5,5] := by + exact rowSquare_join (by decide) sg97 sg484 + +lemma sg3242 : RowSquare [4,4,2,2,1,1,1] [6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg1655 + +lemma sg3243 : RowSquare [4,4,2,2,2,1] [4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg1650 + +lemma sg3244 : RowSquare [4,4,2,2,2,1] [5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg1651 + +lemma sg3245 : RowSquare [4,4,2,2,2,1] [5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg1656 + +lemma sg3246 : RowSquare [4,4,2,2,2,1] [6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg1655 + +lemma sg3247 : RowSquare [4,4,2,2,2,1] [6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg1657 + +lemma sg3248 : RowSquare [4,4,2,2,2,1] [7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg1657 + +lemma sg3249 : RowSquare [4,4,3,2,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg796 + +lemma sg3250 : RowSquare [4,4,3,2,2] [4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg2111 + +lemma sg3251 : RowSquare [4,4,4,3] [2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg130 sg257 + +lemma sg3252 : RowSquare [4,4,4,3] [3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg125 sg259 + +lemma sg3253 : RowSquare [4,4,4,3] [3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg124 sg259 + +lemma sg3254 : RowSquare [4,4,4,3] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg129 sg256 + +lemma sg3255 : RowSquare [5,3,1,1,1,1,1,1,1] [3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg88 sg586 + +lemma sg3256 : RowSquare [5,3,1,1,1,1,1,1,1] [3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg998 + +lemma sg3257 : RowSquare [5,3,1,1,1,1,1,1,1] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg586 + +lemma sg3258 : RowSquare [5,3,1,1,1,1,1,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg1001 + +lemma sg3259 : RowSquare [5,3,2,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg910 + +lemma sg3260 : RowSquare [5,3,2,1,1,1,1,1] [2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg586 + +lemma sg3261 : RowSquare [5,3,2,1,1,1,1,1] [3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg910 + +lemma sg3262 : RowSquare [5,3,2,1,1,1,1,1] [3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg587 + +lemma sg3263 : RowSquare [5,3,2,1,1,1,1,1] [3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg588 + +lemma sg3264 : RowSquare [5,3,2,1,1,1,1,1] [3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg589 + +lemma sg3265 : RowSquare [5,3,2,1,1,1,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg915 + +lemma sg3266 : RowSquare [5,3,2,1,1,1,1,1] [4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg1682 + +lemma sg3267 : RowSquare [5,3,2,1,1,1,1,1] [4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg36 sg910 + +lemma sg3268 : RowSquare [5,3,2,1,1,1,1,1] [4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg2529 + +lemma sg3269 : RowSquare [5,3,2,1,1,1,1,1] [5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg2532 + +lemma sg3270 : RowSquare [5,3,2,1,1,1,1,1] [5,5,5] := by + exact rowSquare_join (by decide) sg4 sg1586 + +lemma sg3271 : RowSquare [5,3,2,2,1,1,1] [3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg910 + +lemma sg3272 : RowSquare [5,3,2,2,1,1,1] [3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg27 sg910 + +lemma sg3273 : RowSquare [5,3,2,2,1,1,1] [6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2542 + +lemma sg3274 : RowSquare [5,4,1,1,1,1,1,1] [3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg66 sg586 + +lemma sg3275 : RowSquare [5,4,1,1,1,1,1,1] [3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg2546 + +lemma sg3276 : RowSquare [5,4,1,1,1,1,1,1] [3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg67 sg586 + +lemma sg3277 : RowSquare [5,4,1,1,1,1,1,1] [3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg313 + +lemma sg3278 : RowSquare [5,4,1,1,1,1,1,1] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg586 + +lemma sg3279 : RowSquare [5,4,1,1,1,1,1,1] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg315 + +lemma sg3280 : RowSquare [5,4,1,1,1,1,1,1] [4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg69 sg586 + +lemma sg3281 : RowSquare [5,4,1,1,1,1,1,1] [4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg66 sg587 + +lemma sg3282 : RowSquare [5,4,1,1,1,1,1,1] [4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg70 sg586 + +lemma sg3283 : RowSquare [5,4,1,1,1,1,1,1] [4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg67 sg587 + +lemma sg3284 : RowSquare [5,4,1,1,1,1,1,1] [4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg179 sg313 + +lemma sg3285 : RowSquare [5,4,1,1,1,1,1,1] [4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg587 + +lemma sg3286 : RowSquare [5,4,1,1,1,1,1,1] [4,3,3,3,2] := by + exact rowSquare_join (by decide) sg66 sg590 + +lemma sg3287 : RowSquare [5,4,1,1,1,1,1,1] [4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg71 sg586 + +lemma sg3288 : RowSquare [5,4,1,1,1,1,1,1] [4,4,4,3] := by + exact rowSquare_join (by decide) sg181 sg315 + +lemma sg3289 : RowSquare [5,4,1,1,1,1,1,1] [5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg69 sg587 + +lemma sg3290 : RowSquare [5,4,1,1,1,1,1,1] [6,3,3,3] := by + exact rowSquare_join (by decide) sg13 sg1137 + +lemma sg3291 : RowSquare [5,4,1,1,1,1,1,1] [7,6,2] := by + exact rowSquare_join (by decide) sg14 sg1139 + +lemma sg3292 : RowSquare [5,4,1,1,1,1,1,1] [8,7] := by + exact rowSquare_join (by decide) sg14 sg1141 + +lemma sg3293 : RowSquare [5,4,2,1,1,1,1] [4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg22 sg910 + +lemma sg3294 : RowSquare [5,4,2,1,1,1,1] [4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg2074 + +lemma sg3295 : RowSquare [5,4,2,1,1,1,1] [4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg23 sg910 + +lemma sg3296 : RowSquare [5,4,2,1,1,1,1] [5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg910 + +lemma sg3297 : RowSquare [5,4,2,1,1,1,1] [6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg2077 + +lemma sg3298 : RowSquare [5,4,3,1,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg759 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes60.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes60.lean index e4b93124fdb83701c652865adc2a6b074dd1a5c0..c4931e4c4ec35c842679c30ffec16859d0e42da6 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes60.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes60.lean @@ -1,1224 +1,1224 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 60. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg24540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9737 - -lemma sg24541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8659 sg9668 - -lemma sg24542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8460 sg10184 - -lemma sg24543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8422 sg10237 - -lemma sg24544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10237 - -lemma sg24545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9669 - -lemma sg24546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8350 sg10642 - -lemma sg24547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8659 sg9669 - -lemma sg24548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9495 - -lemma sg24549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10315 - -lemma sg24550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9497 - -lemma sg24551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8658 sg9670 - -lemma sg24552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9738 - -lemma sg24553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10647 - -lemma sg24554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg8461 sg10184 - -lemma sg24555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8455 sg10189 - -lemma sg24556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg7452 sg11275 - -lemma sg24557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9739 - -lemma sg24558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10238 - -lemma sg24559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8665 sg9662 - -lemma sg24560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg8457 sg10189 - -lemma sg24561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8432 sg10231 - -lemma sg24562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9671 - -lemma sg24563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg8430 sg10232 - -lemma sg24564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg8659 sg9671 - -lemma sg24565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,4,4] := by - exact rowSquare_join (by decide) sg7806 sg11239 - -lemma sg24566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10108 - -lemma sg24567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg5569 sg12616 - -lemma sg24568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8542 sg10091 - -lemma sg24569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg7239 sg11444 - -lemma sg24570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg8352 sg10642 - -lemma sg24571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg8543 sg10090 - -lemma sg24572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg5538 sg12622 - -lemma sg24573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg8543 sg10091 - -lemma sg24574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,4,3] := by - exact rowSquare_join (by decide) sg7806 sg11240 - -lemma sg24575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg8432 sg10232 - -lemma sg24576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,5,2] := by - exact rowSquare_join (by decide) sg6402 sg11735 - -lemma sg24577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9740 - -lemma sg24578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8845 sg9157 - -lemma sg24579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg7232 sg11460 - -lemma sg24580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9500 - -lemma sg24581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10316 - -lemma sg24582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8464 sg10184 - -lemma sg24583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8347 sg10648 - -lemma sg24584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8736 sg9457 - -lemma sg24585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8720 sg9501 - -lemma sg24586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9741 - -lemma sg24587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8668 sg9662 - -lemma sg24588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8820 sg9162 - -lemma sg24589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10317 - -lemma sg24590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9502 - -lemma sg24591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8367 sg10606 - -lemma sg24592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9742 - -lemma sg24593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10239 - -lemma sg24594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9043 - -lemma sg24595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9743 - -lemma sg24596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8658 sg9673 - -lemma sg24597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10235 - -lemma sg24598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9044 - -lemma sg24599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8457 sg10190 - -lemma sg24600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9500 - -lemma sg24601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10318 - -lemma sg24602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9744 - -lemma sg24603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8670 sg9662 - -lemma sg24604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8347 sg10650 - -lemma sg24605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9500 - -lemma sg24606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10319 - -lemma sg24607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9504 - -lemma sg24608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8367 sg10607 - -lemma sg24609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9745 - -lemma sg24610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10240 - -lemma sg24611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9046 - -lemma sg24612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9502 - -lemma sg24613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8661 sg9668 - -lemma sg24614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9746 - -lemma sg24615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10241 - -lemma sg24616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8661 sg9669 - -lemma sg24617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9047 - -lemma sg24618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9505 - -lemma sg24619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10237 - -lemma sg24620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9048 - -lemma sg24621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10644 - -lemma sg24622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,4,4] := by - exact rowSquare_join (by decide) sg8662 sg9669 - -lemma sg24623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8722 sg9501 - -lemma sg24624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9461 - -lemma sg24625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8661 sg9670 - -lemma sg24626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9747 - -lemma sg24627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8658 sg9677 - -lemma sg24628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8662 sg9670 - -lemma sg24629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9049 - -lemma sg24630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9748 - -lemma sg24631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10242 - -lemma sg24632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9507 - -lemma sg24633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10238 - -lemma sg24634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9050 - -lemma sg24635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg8457 sg10192 - -lemma sg24636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9678 - -lemma sg24637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg8659 sg9678 - -lemma sg24638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,4,3] := by - exact rowSquare_join (by decide) sg8662 sg9671 - -lemma sg24639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8526 sg10108 - -lemma sg24640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg7239 sg11446 - -lemma sg24641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9051 - -lemma sg24642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg8372 sg10605 - -lemma sg24643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg8543 sg10094 - -lemma sg24644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,3,3] := by - exact rowSquare_join (by decide) sg8546 sg10090 - -lemma sg24645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg8864 sg8994 - -lemma sg24646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,4,2] := by - exact rowSquare_join (by decide) sg8546 sg10091 - -lemma sg24647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1868 sg16187 - -lemma sg24648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2227 sg15519 - -lemma sg24649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2870 sg14850 - -lemma sg24650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5577 sg12612 - -lemma sg24651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5246 sg12687 - -lemma sg24652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8590 sg10081 - -lemma sg24653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9203 - -lemma sg24654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8739 sg9453 - -lemma sg24655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2871 sg14850 - -lemma sg24656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5551 sg12620 - -lemma sg24657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5247 sg12687 - -lemma sg24658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8591 sg10081 - -lemma sg24659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9204 - -lemma sg24660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9736 - -lemma sg24661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9454 - -lemma sg24662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5248 sg12687 - -lemma sg24663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8556 sg10087 - -lemma sg24664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9205 - -lemma sg24665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8740 sg9453 - -lemma sg24666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8721 sg9503 - -lemma sg24667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9206 - -lemma sg24668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9749 - -lemma sg24669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8819 sg9165 - -lemma sg24670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8179 sg10857 - -lemma sg24671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9749 - -lemma sg24672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8543 sg10095 - -lemma sg24673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8826 sg9162 - -lemma sg24674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5552 sg12620 - -lemma sg24675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5249 sg12687 - -lemma sg24676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10320 - -lemma sg24677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8377 sg10602 - -lemma sg24678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8426 sg10236 - -lemma sg24679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10320 - -lemma sg24680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8558 sg10087 - -lemma sg24681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8190 sg10852 - -lemma sg24682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9737 - -lemma sg24683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9504 - -lemma sg24684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8663 sg9668 - -lemma sg24685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9750 - -lemma sg24686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9750 - -lemma sg24687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10243 - -lemma sg24688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9669 - -lemma sg24689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8350 sg10645 - -lemma sg24690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6893 sg11495 - -lemma sg24691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9751 - -lemma sg24692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9751 - -lemma sg24693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8740 sg9455 - -lemma sg24694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9505 - -lemma sg24695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9679 - -lemma sg24696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8865 sg8990 - -lemma sg24697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8659 sg9679 - -lemma sg24698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10237 - -lemma sg24699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10646 - -lemma sg24700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,4,3] := by - exact rowSquare_join (by decide) sg8664 sg9669 - -lemma sg24701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5265 sg12681 - -lemma sg24702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10244 - -lemma sg24703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8378 sg10602 - -lemma sg24704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9738 - -lemma sg24705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9504 - -lemma sg24706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8663 sg9670 - -lemma sg24707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8379 sg10602 - -lemma sg24708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9752 - -lemma sg24709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9752 - -lemma sg24710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10244 - -lemma sg24711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9505 - -lemma sg24712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9680 - -lemma sg24713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg8430 sg10236 - -lemma sg24714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10647 - -lemma sg24715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8747 sg9449 - -lemma sg24716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9507 - -lemma sg24717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8665 sg9668 - -lemma sg24718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg8352 sg10645 - -lemma sg24719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10238 - -lemma sg24720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg8659 sg9681 - -lemma sg24721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,3,3] := by - exact rowSquare_join (by decide) sg8665 sg9669 - -lemma sg24722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10237 - -lemma sg24723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,4,2] := by - exact rowSquare_join (by decide) sg8866 sg8993 - -lemma sg24724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8527 sg10108 - -lemma sg24725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg5544 sg12622 - -lemma sg24726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg8543 sg10098 - -lemma sg24727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg8352 sg10646 - -lemma sg24728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,5,3,2] := by - exact rowSquare_join (by decide) sg8549 sg10090 - -lemma sg24729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7247 sg11440 - -lemma sg24730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7252 sg11435 - -lemma sg24731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9682 - -lemma sg24732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10115 - -lemma sg24733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8741 sg9456 - -lemma sg24734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8454 sg10195 - -lemma sg24735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9468 - -lemma sg24736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8665 sg9670 - -lemma sg24737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg8461 sg10189 - -lemma sg24738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9682 - -lemma sg24739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg8659 sg9682 - -lemma sg24740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,3,3] := by - exact rowSquare_join (by decide) sg7806 sg11241 - -lemma sg24741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8455 sg10195 - -lemma sg24742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8456 sg10195 - -lemma sg24743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg8457 sg10195 - -lemma sg24744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10238 - -lemma sg24745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,4,3,2] := by - exact rowSquare_join (by decide) sg8665 sg9671 - -lemma sg24746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg356 sg21295 - -lemma sg24747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg8462 sg10189 - -lemma sg24748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,5,2,2] := by - exact rowSquare_join (by decide) sg8550 sg10090 - -lemma sg24749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,6,1,1,1] := by - exact rowSquare_join (by decide) sg356 sg21296 - -lemma sg24750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1319 sg20962 - -lemma sg24751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1722 sg18243 - -lemma sg24752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1464 sg20933 - -lemma sg24753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1817 sg17112 - -lemma sg24754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2224 sg15520 - -lemma sg24755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1857 sg16195 - -lemma sg24756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg571 sg21218 - -lemma sg24757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg14680 - -lemma sg24758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg571 sg21219 - -lemma sg24759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg571 sg21220 - -lemma sg24760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg571 sg21221 - -lemma sg24761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1830 sg17105 - -lemma sg24762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2197 sg15561 - -lemma sg24763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2225 sg15520 - -lemma sg24764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2670 sg15014 - -lemma sg24765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2867 sg14852 - -lemma sg24766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg966 sg21118 - -lemma sg24767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2665 sg15023 - -lemma sg24768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg966 sg21119 - -lemma sg24769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg966 sg21120 - -lemma sg24770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2226 sg15520 - -lemma sg24771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2671 sg15014 - -lemma sg24772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1815 sg17113 - -lemma sg24773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3894 sg14498 - -lemma sg24774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1293 sg20995 - -lemma sg24775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6119 sg11763 - -lemma sg24776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1293 sg20996 - -lemma sg24777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8666 sg9663 - -lemma sg24778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1850 sg16200 - -lemma sg24779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5574 sg12613 - -lemma sg24780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4622 sg12944 - -lemma sg24781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8228 sg10847 - -lemma sg24782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9166 - -lemma sg24783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8651 sg9740 - -lemma sg24784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5266 sg12680 - -lemma sg24785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8551 sg10088 - -lemma sg24786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9167 - -lemma sg24787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9665 - -lemma sg24788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9508 - -lemma sg24789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8181 sg10854 - -lemma sg24790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9666 - -lemma sg24791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8525 sg10116 - -lemma sg24792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8219 sg10850 - -lemma sg24793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8847 sg9157 - -lemma sg24794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2198 sg15561 - -lemma sg24795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2227 sg15520 - -lemma sg24796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2672 sg15014 - -lemma sg24797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2869 sg14851 - -lemma sg24798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3895 sg14498 - -lemma sg24799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1294 sg20995 - -lemma sg24800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7245 sg11442 - -lemma sg24801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1294 sg20996 - -lemma sg24802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8666 sg9667 - -lemma sg24803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2673 sg15014 - -lemma sg24804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2180 sg15565 - -lemma sg24805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5546 sg12621 - -lemma sg24806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5244 sg12688 - -lemma sg24807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8229 sg10847 - -lemma sg24808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9207 - -lemma sg24809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8652 sg9740 - -lemma sg24810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5547 sg12621 - -lemma sg24811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5245 sg12688 - -lemma sg24812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10239 - -lemma sg24813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9169 - -lemma sg24814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8348 sg10648 - -lemma sg24815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9508 - -lemma sg24816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8553 sg10088 - -lemma sg24817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8182 sg10854 - -lemma sg24818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8660 sg9673 - -lemma sg24819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8720 sg9509 - -lemma sg24820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8458 sg10190 - -lemma sg24821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10117 - -lemma sg24822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg7232 sg11461 - -lemma sg24823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8847 sg9158 - -lemma sg24824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2360 sg15482 - -lemma sg24825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5576 sg12613 - -lemma sg24826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5251 sg12686 - -lemma sg24827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8554 sg10088 - -lemma sg24828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9208 - -lemma sg24829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9670 - -lemma sg24830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9508 - -lemma sg24831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5252 sg12686 - -lemma sg24832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8555 sg10088 - -lemma sg24833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9209 - -lemma sg24834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9741 - -lemma sg24835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8817 sg9166 - -lemma sg24836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9210 - -lemma sg24837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9753 - -lemma sg24838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9510 - -lemma sg24839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8820 sg9163 - -lemma sg24840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9753 - -lemma sg24841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8820 sg9164 - -lemma sg24842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9052 - -lemma sg24843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7253 sg11433 - -lemma sg24844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8394 sg10598 - -lemma sg24845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9742 - -lemma sg24846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8669 sg9664 - -lemma sg24847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8818 sg9166 - -lemma sg24848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9754 - -lemma sg24849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9754 - -lemma sg24850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8818 sg9167 - -lemma sg24851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10239 - -lemma sg24852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9053 - -lemma sg24853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9511 - -lemma sg24854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8822 sg9163 - -lemma sg24855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9054 - -lemma sg24856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8738 sg9458 - -lemma sg24857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg8459 sg10190 - -lemma sg24858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2241 sg15512 - -lemma sg24859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2685 sg15011 - -lemma sg24860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2870 sg14851 - -lemma sg24861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5548 sg12621 - -lemma sg24862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5246 sg12688 - -lemma sg24863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8250 sg10845 - -lemma sg24864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9207 - -lemma sg24865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8660 sg9674 - -lemma sg24866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2871 sg14851 - -lemma sg24867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5549 sg12621 - -lemma sg24868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5247 sg12688 - -lemma sg24869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10240 - -lemma sg24870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9211 - -lemma sg24871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8349 sg10648 - -lemma sg24872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8737 sg9459 - -lemma sg24873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5248 sg12688 - -lemma sg24874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10241 - -lemma sg24875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9209 - -lemma sg24876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9744 - -lemma sg24877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8721 sg9509 - -lemma sg24878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9210 - -lemma sg24879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9755 - -lemma sg24880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9512 - -lemma sg24881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8823 sg9163 - -lemma sg24882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9755 - -lemma sg24883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8823 sg9164 - -lemma sg24884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9055 - -lemma sg24885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5550 sg12621 - -lemma sg24886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5249 sg12688 - -lemma sg24887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8557 sg10088 - -lemma sg24888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9212 - -lemma sg24889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9741 - -lemma sg24890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8722 sg9509 - -lemma sg24891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10242 - -lemma sg24892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9213 - -lemma sg24893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9745 - -lemma sg24894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9510 - -lemma sg24895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8818 sg9168 - -lemma sg24896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9756 - -lemma sg24897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9756 - -lemma sg24898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8663 sg9673 - -lemma sg24899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10240 - -lemma sg24900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9056 - -lemma sg24901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10603 - -lemma sg24902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9757 - -lemma sg24903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9757 - -lemma sg24904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8818 sg9169 - -lemma sg24905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9513 - -lemma sg24906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10241 - -lemma sg24907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9057 - -lemma sg24908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10649 - -lemma sg24909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8869 sg8989 - -lemma sg24910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8738 sg9460 - -lemma sg24911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,4,3] := by - exact rowSquare_join (by decide) sg8662 sg9676 - -lemma sg24912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5255 sg12686 - -lemma sg24913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8559 sg10088 - -lemma sg24914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9214 - -lemma sg24915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8745 sg9451 - -lemma sg24916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9510 - -lemma sg24917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8668 sg9670 - -lemma sg24918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8395 sg10598 - -lemma sg24919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9758 - -lemma sg24920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9758 - -lemma sg24921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8818 sg9170 - -lemma sg24922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9514 - -lemma sg24923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8668 sg9671 - -lemma sg24924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9058 - -lemma sg24925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg8741 sg9458 - -lemma sg24926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9748 - -lemma sg24927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9515 - -lemma sg24928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10242 - -lemma sg24929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9059 - -lemma sg24930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8661 sg9678 - -lemma sg24931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg8430 sg10239 - -lemma sg24932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,3,3] := by - exact rowSquare_join (by decide) sg8459 sg10192 - -lemma sg24933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg8864 sg8997 - -lemma sg24934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,4,2] := by - exact rowSquare_join (by decide) sg8662 sg9678 - -lemma sg24935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10604 - -lemma sg24936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg8372 sg10606 - -lemma sg24937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg8352 sg10649 - -lemma sg24938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg8864 sg8998 - -lemma sg24939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,5,3,2] := by - exact rowSquare_join (by decide) sg8546 sg10094 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 60. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg24540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9737 + +lemma sg24541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8659 sg9668 + +lemma sg24542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8460 sg10184 + +lemma sg24543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8422 sg10237 + +lemma sg24544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10237 + +lemma sg24545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9669 + +lemma sg24546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8350 sg10642 + +lemma sg24547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8659 sg9669 + +lemma sg24548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9495 + +lemma sg24549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10315 + +lemma sg24550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9497 + +lemma sg24551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8658 sg9670 + +lemma sg24552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9738 + +lemma sg24553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10647 + +lemma sg24554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg8461 sg10184 + +lemma sg24555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8455 sg10189 + +lemma sg24556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg7452 sg11275 + +lemma sg24557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9739 + +lemma sg24558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10238 + +lemma sg24559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8665 sg9662 + +lemma sg24560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg8457 sg10189 + +lemma sg24561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8432 sg10231 + +lemma sg24562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9671 + +lemma sg24563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg8430 sg10232 + +lemma sg24564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg8659 sg9671 + +lemma sg24565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,4,4,4] := by + exact rowSquare_join (by decide) sg7806 sg11239 + +lemma sg24566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10108 + +lemma sg24567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg5569 sg12616 + +lemma sg24568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8542 sg10091 + +lemma sg24569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg7239 sg11444 + +lemma sg24570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg8352 sg10642 + +lemma sg24571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg8543 sg10090 + +lemma sg24572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg5538 sg12622 + +lemma sg24573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg8543 sg10091 + +lemma sg24574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,4,3] := by + exact rowSquare_join (by decide) sg7806 sg11240 + +lemma sg24575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg8432 sg10232 + +lemma sg24576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,5,5,5,5,5,2] := by + exact rowSquare_join (by decide) sg6402 sg11735 + +lemma sg24577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9740 + +lemma sg24578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8845 sg9157 + +lemma sg24579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg7232 sg11460 + +lemma sg24580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9500 + +lemma sg24581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10316 + +lemma sg24582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8464 sg10184 + +lemma sg24583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8347 sg10648 + +lemma sg24584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8736 sg9457 + +lemma sg24585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8720 sg9501 + +lemma sg24586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9741 + +lemma sg24587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8668 sg9662 + +lemma sg24588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8820 sg9162 + +lemma sg24589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10317 + +lemma sg24590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9502 + +lemma sg24591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8367 sg10606 + +lemma sg24592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9742 + +lemma sg24593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10239 + +lemma sg24594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9043 + +lemma sg24595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9743 + +lemma sg24596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8658 sg9673 + +lemma sg24597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10235 + +lemma sg24598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9044 + +lemma sg24599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8457 sg10190 + +lemma sg24600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9500 + +lemma sg24601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10318 + +lemma sg24602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9744 + +lemma sg24603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8670 sg9662 + +lemma sg24604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8347 sg10650 + +lemma sg24605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9500 + +lemma sg24606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10319 + +lemma sg24607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9504 + +lemma sg24608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8367 sg10607 + +lemma sg24609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9745 + +lemma sg24610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10240 + +lemma sg24611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9046 + +lemma sg24612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9502 + +lemma sg24613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8661 sg9668 + +lemma sg24614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9746 + +lemma sg24615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10241 + +lemma sg24616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8661 sg9669 + +lemma sg24617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9047 + +lemma sg24618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9505 + +lemma sg24619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10237 + +lemma sg24620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9048 + +lemma sg24621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10644 + +lemma sg24622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,4,4,4,4] := by + exact rowSquare_join (by decide) sg8662 sg9669 + +lemma sg24623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8722 sg9501 + +lemma sg24624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9461 + +lemma sg24625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8661 sg9670 + +lemma sg24626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9747 + +lemma sg24627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8658 sg9677 + +lemma sg24628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8662 sg9670 + +lemma sg24629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9049 + +lemma sg24630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9748 + +lemma sg24631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10242 + +lemma sg24632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9507 + +lemma sg24633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10238 + +lemma sg24634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9050 + +lemma sg24635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg8457 sg10192 + +lemma sg24636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9678 + +lemma sg24637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg8659 sg9678 + +lemma sg24638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,4,4,3] := by + exact rowSquare_join (by decide) sg8662 sg9671 + +lemma sg24639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8526 sg10108 + +lemma sg24640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg7239 sg11446 + +lemma sg24641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9051 + +lemma sg24642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg8372 sg10605 + +lemma sg24643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg8543 sg10094 + +lemma sg24644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,3,3] := by + exact rowSquare_join (by decide) sg8546 sg10090 + +lemma sg24645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg8864 sg8994 + +lemma sg24646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,5,5,5,4,2] := by + exact rowSquare_join (by decide) sg8546 sg10091 + +lemma sg24647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1868 sg16187 + +lemma sg24648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2227 sg15519 + +lemma sg24649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2870 sg14850 + +lemma sg24650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5577 sg12612 + +lemma sg24651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5246 sg12687 + +lemma sg24652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8590 sg10081 + +lemma sg24653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9203 + +lemma sg24654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8739 sg9453 + +lemma sg24655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2871 sg14850 + +lemma sg24656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5551 sg12620 + +lemma sg24657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5247 sg12687 + +lemma sg24658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8591 sg10081 + +lemma sg24659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9204 + +lemma sg24660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9736 + +lemma sg24661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9454 + +lemma sg24662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5248 sg12687 + +lemma sg24663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8556 sg10087 + +lemma sg24664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9205 + +lemma sg24665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8740 sg9453 + +lemma sg24666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8721 sg9503 + +lemma sg24667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9206 + +lemma sg24668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9749 + +lemma sg24669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8819 sg9165 + +lemma sg24670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8179 sg10857 + +lemma sg24671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9749 + +lemma sg24672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8543 sg10095 + +lemma sg24673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8826 sg9162 + +lemma sg24674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5552 sg12620 + +lemma sg24675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5249 sg12687 + +lemma sg24676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10320 + +lemma sg24677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8377 sg10602 + +lemma sg24678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8426 sg10236 + +lemma sg24679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10320 + +lemma sg24680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8558 sg10087 + +lemma sg24681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8190 sg10852 + +lemma sg24682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9737 + +lemma sg24683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9504 + +lemma sg24684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8663 sg9668 + +lemma sg24685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9750 + +lemma sg24686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9750 + +lemma sg24687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10243 + +lemma sg24688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9669 + +lemma sg24689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8350 sg10645 + +lemma sg24690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6893 sg11495 + +lemma sg24691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9751 + +lemma sg24692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9751 + +lemma sg24693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8740 sg9455 + +lemma sg24694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9505 + +lemma sg24695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9679 + +lemma sg24696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8865 sg8990 + +lemma sg24697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8659 sg9679 + +lemma sg24698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10237 + +lemma sg24699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10646 + +lemma sg24700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,4,4,4,3] := by + exact rowSquare_join (by decide) sg8664 sg9669 + +lemma sg24701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5265 sg12681 + +lemma sg24702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10244 + +lemma sg24703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8378 sg10602 + +lemma sg24704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9738 + +lemma sg24705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9504 + +lemma sg24706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8663 sg9670 + +lemma sg24707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8379 sg10602 + +lemma sg24708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9752 + +lemma sg24709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9752 + +lemma sg24710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10244 + +lemma sg24711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9505 + +lemma sg24712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9680 + +lemma sg24713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg8430 sg10236 + +lemma sg24714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10647 + +lemma sg24715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8747 sg9449 + +lemma sg24716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9507 + +lemma sg24717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8665 sg9668 + +lemma sg24718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg8352 sg10645 + +lemma sg24719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10238 + +lemma sg24720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg8659 sg9681 + +lemma sg24721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,3,3] := by + exact rowSquare_join (by decide) sg8665 sg9669 + +lemma sg24722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10237 + +lemma sg24723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,4,4,2] := by + exact rowSquare_join (by decide) sg8866 sg8993 + +lemma sg24724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8527 sg10108 + +lemma sg24725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg5544 sg12622 + +lemma sg24726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg8543 sg10098 + +lemma sg24727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg8352 sg10646 + +lemma sg24728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,5,5,3,2] := by + exact rowSquare_join (by decide) sg8549 sg10090 + +lemma sg24729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7247 sg11440 + +lemma sg24730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7252 sg11435 + +lemma sg24731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9682 + +lemma sg24732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10115 + +lemma sg24733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8741 sg9456 + +lemma sg24734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8454 sg10195 + +lemma sg24735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9468 + +lemma sg24736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8665 sg9670 + +lemma sg24737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg8461 sg10189 + +lemma sg24738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9682 + +lemma sg24739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg8659 sg9682 + +lemma sg24740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,3,3,3] := by + exact rowSquare_join (by decide) sg7806 sg11241 + +lemma sg24741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8455 sg10195 + +lemma sg24742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8456 sg10195 + +lemma sg24743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg8457 sg10195 + +lemma sg24744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10238 + +lemma sg24745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,4,3,2] := by + exact rowSquare_join (by decide) sg8665 sg9671 + +lemma sg24746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg356 sg21295 + +lemma sg24747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg8462 sg10189 + +lemma sg24748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,5,2,2] := by + exact rowSquare_join (by decide) sg8550 sg10090 + +lemma sg24749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,6,6,6,6,1,1,1] := by + exact rowSquare_join (by decide) sg356 sg21296 + +lemma sg24750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1319 sg20962 + +lemma sg24751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1722 sg18243 + +lemma sg24752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1464 sg20933 + +lemma sg24753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1817 sg17112 + +lemma sg24754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2224 sg15520 + +lemma sg24755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1857 sg16195 + +lemma sg24756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg571 sg21218 + +lemma sg24757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg14680 + +lemma sg24758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg571 sg21219 + +lemma sg24759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg571 sg21220 + +lemma sg24760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg571 sg21221 + +lemma sg24761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1830 sg17105 + +lemma sg24762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2197 sg15561 + +lemma sg24763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2225 sg15520 + +lemma sg24764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2670 sg15014 + +lemma sg24765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2867 sg14852 + +lemma sg24766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg966 sg21118 + +lemma sg24767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2665 sg15023 + +lemma sg24768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg966 sg21119 + +lemma sg24769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg966 sg21120 + +lemma sg24770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2226 sg15520 + +lemma sg24771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2671 sg15014 + +lemma sg24772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1815 sg17113 + +lemma sg24773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3894 sg14498 + +lemma sg24774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1293 sg20995 + +lemma sg24775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6119 sg11763 + +lemma sg24776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1293 sg20996 + +lemma sg24777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8666 sg9663 + +lemma sg24778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1850 sg16200 + +lemma sg24779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5574 sg12613 + +lemma sg24780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4622 sg12944 + +lemma sg24781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8228 sg10847 + +lemma sg24782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9166 + +lemma sg24783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8651 sg9740 + +lemma sg24784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5266 sg12680 + +lemma sg24785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8551 sg10088 + +lemma sg24786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9167 + +lemma sg24787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9665 + +lemma sg24788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9508 + +lemma sg24789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8181 sg10854 + +lemma sg24790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9666 + +lemma sg24791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8525 sg10116 + +lemma sg24792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8219 sg10850 + +lemma sg24793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8847 sg9157 + +lemma sg24794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2198 sg15561 + +lemma sg24795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2227 sg15520 + +lemma sg24796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2672 sg15014 + +lemma sg24797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2869 sg14851 + +lemma sg24798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3895 sg14498 + +lemma sg24799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1294 sg20995 + +lemma sg24800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7245 sg11442 + +lemma sg24801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1294 sg20996 + +lemma sg24802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8666 sg9667 + +lemma sg24803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2673 sg15014 + +lemma sg24804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2180 sg15565 + +lemma sg24805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5546 sg12621 + +lemma sg24806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5244 sg12688 + +lemma sg24807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8229 sg10847 + +lemma sg24808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9207 + +lemma sg24809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8652 sg9740 + +lemma sg24810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5547 sg12621 + +lemma sg24811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5245 sg12688 + +lemma sg24812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10239 + +lemma sg24813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9169 + +lemma sg24814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8348 sg10648 + +lemma sg24815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9508 + +lemma sg24816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8553 sg10088 + +lemma sg24817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8182 sg10854 + +lemma sg24818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8660 sg9673 + +lemma sg24819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8720 sg9509 + +lemma sg24820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8458 sg10190 + +lemma sg24821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10117 + +lemma sg24822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg7232 sg11461 + +lemma sg24823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8847 sg9158 + +lemma sg24824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2360 sg15482 + +lemma sg24825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5576 sg12613 + +lemma sg24826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5251 sg12686 + +lemma sg24827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8554 sg10088 + +lemma sg24828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9208 + +lemma sg24829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9670 + +lemma sg24830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9508 + +lemma sg24831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5252 sg12686 + +lemma sg24832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8555 sg10088 + +lemma sg24833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9209 + +lemma sg24834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9741 + +lemma sg24835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8817 sg9166 + +lemma sg24836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9210 + +lemma sg24837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9753 + +lemma sg24838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9510 + +lemma sg24839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8820 sg9163 + +lemma sg24840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9753 + +lemma sg24841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8820 sg9164 + +lemma sg24842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9052 + +lemma sg24843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7253 sg11433 + +lemma sg24844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8394 sg10598 + +lemma sg24845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9742 + +lemma sg24846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8669 sg9664 + +lemma sg24847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8818 sg9166 + +lemma sg24848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9754 + +lemma sg24849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9754 + +lemma sg24850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8818 sg9167 + +lemma sg24851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10239 + +lemma sg24852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9053 + +lemma sg24853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9511 + +lemma sg24854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8822 sg9163 + +lemma sg24855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9054 + +lemma sg24856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8738 sg9458 + +lemma sg24857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg8459 sg10190 + +lemma sg24858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2241 sg15512 + +lemma sg24859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2685 sg15011 + +lemma sg24860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2870 sg14851 + +lemma sg24861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5548 sg12621 + +lemma sg24862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5246 sg12688 + +lemma sg24863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8250 sg10845 + +lemma sg24864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9207 + +lemma sg24865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8660 sg9674 + +lemma sg24866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2871 sg14851 + +lemma sg24867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5549 sg12621 + +lemma sg24868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5247 sg12688 + +lemma sg24869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10240 + +lemma sg24870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9211 + +lemma sg24871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8349 sg10648 + +lemma sg24872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8737 sg9459 + +lemma sg24873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5248 sg12688 + +lemma sg24874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10241 + +lemma sg24875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9209 + +lemma sg24876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9744 + +lemma sg24877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8721 sg9509 + +lemma sg24878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9210 + +lemma sg24879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9755 + +lemma sg24880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9512 + +lemma sg24881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8823 sg9163 + +lemma sg24882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9755 + +lemma sg24883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8823 sg9164 + +lemma sg24884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9055 + +lemma sg24885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5550 sg12621 + +lemma sg24886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5249 sg12688 + +lemma sg24887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8557 sg10088 + +lemma sg24888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9212 + +lemma sg24889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9741 + +lemma sg24890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8722 sg9509 + +lemma sg24891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10242 + +lemma sg24892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9213 + +lemma sg24893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9745 + +lemma sg24894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9510 + +lemma sg24895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8818 sg9168 + +lemma sg24896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9756 + +lemma sg24897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9756 + +lemma sg24898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8663 sg9673 + +lemma sg24899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10240 + +lemma sg24900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9056 + +lemma sg24901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10603 + +lemma sg24902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9757 + +lemma sg24903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9757 + +lemma sg24904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8818 sg9169 + +lemma sg24905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9513 + +lemma sg24906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10241 + +lemma sg24907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9057 + +lemma sg24908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10649 + +lemma sg24909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8869 sg8989 + +lemma sg24910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8738 sg9460 + +lemma sg24911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,4,4,4,3] := by + exact rowSquare_join (by decide) sg8662 sg9676 + +lemma sg24912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5255 sg12686 + +lemma sg24913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8559 sg10088 + +lemma sg24914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9214 + +lemma sg24915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8745 sg9451 + +lemma sg24916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9510 + +lemma sg24917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8668 sg9670 + +lemma sg24918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8395 sg10598 + +lemma sg24919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9758 + +lemma sg24920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9758 + +lemma sg24921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8818 sg9170 + +lemma sg24922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9514 + +lemma sg24923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8668 sg9671 + +lemma sg24924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9058 + +lemma sg24925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg8741 sg9458 + +lemma sg24926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9748 + +lemma sg24927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9515 + +lemma sg24928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10242 + +lemma sg24929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9059 + +lemma sg24930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8661 sg9678 + +lemma sg24931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg8430 sg10239 + +lemma sg24932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,3,3] := by + exact rowSquare_join (by decide) sg8459 sg10192 + +lemma sg24933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg8864 sg8997 + +lemma sg24934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,4,4,2] := by + exact rowSquare_join (by decide) sg8662 sg9678 + +lemma sg24935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10604 + +lemma sg24936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg8372 sg10606 + +lemma sg24937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg8352 sg10649 + +lemma sg24938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg8864 sg8998 + +lemma sg24939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,5,5,5,3,2] := by + exact rowSquare_join (by decide) sg8546 sg10094 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes61.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes61.lean index 427863ffa60a6d7c9b6eadfe47053d81c2df52e1..7c7ee3e346220f977022eb0d4ab958093a832320 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes61.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes61.lean @@ -1,1224 +1,1224 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 61. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg24940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2686 sg15011 - -lemma sg24941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2695 sg15004 - -lemma sg24942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5551 sg12621 - -lemma sg24943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5253 sg12687 - -lemma sg24944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8595 sg10081 - -lemma sg24945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9211 - -lemma sg24946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8670 sg9667 - -lemma sg24947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9459 - -lemma sg24948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5552 sg12621 - -lemma sg24949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5254 sg12687 - -lemma sg24950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10243 - -lemma sg24951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9215 - -lemma sg24952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9744 - -lemma sg24953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8544 sg10095 - -lemma sg24954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8596 sg10081 - -lemma sg24955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9213 - -lemma sg24956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9749 - -lemma sg24957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9512 - -lemma sg24958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8180 sg10857 - -lemma sg24959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9759 - -lemma sg24960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9759 - -lemma sg24961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8823 sg9165 - -lemma sg24962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8670 sg9669 - -lemma sg24963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9060 - -lemma sg24964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5255 sg12687 - -lemma sg24965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10244 - -lemma sg24966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9216 - -lemma sg24967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9745 - -lemma sg24968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9512 - -lemma sg24969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8370 sg10607 - -lemma sg24970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9217 - -lemma sg24971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9760 - -lemma sg24972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9760 - -lemma sg24973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8818 sg9171 - -lemma sg24974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9516 - -lemma sg24975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10243 - -lemma sg24976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9061 - -lemma sg24977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10651 - -lemma sg24978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9751 - -lemma sg24979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9517 - -lemma sg24980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8661 sg9679 - -lemma sg24981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9062 - -lemma sg24982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10241 - -lemma sg24983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10652 - -lemma sg24984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,3,3] := by - exact rowSquare_join (by decide) sg8662 sg9679 - -lemma sg24985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8738 sg9465 - -lemma sg24986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,4,2] := by - exact rowSquare_join (by decide) sg8459 sg10193 - -lemma sg24987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8599 sg10080 - -lemma sg24988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9218 - -lemma sg24989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9761 - -lemma sg24990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9761 - -lemma sg24991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8663 sg9677 - -lemma sg24992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9752 - -lemma sg24993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9518 - -lemma sg24994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10244 - -lemma sg24995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9063 - -lemma sg24996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9678 - -lemma sg24997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg8430 sg10240 - -lemma sg24998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,3,3] := by - exact rowSquare_join (by decide) sg8662 sg9680 - -lemma sg24999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9515 - -lemma sg25000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10242 - -lemma sg25001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg8352 sg10651 - -lemma sg25002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10241 - -lemma sg25003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,4,3,2] := by - exact rowSquare_join (by decide) sg8662 sg9681 - -lemma sg25004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg6893 sg11498 - -lemma sg25005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg8545 sg10098 - -lemma sg25006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7247 sg11443 - -lemma sg25007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8748 sg9451 - -lemma sg25008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8526 sg10115 - -lemma sg25009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8745 sg9456 - -lemma sg25010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9064 - -lemma sg25011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9515 - -lemma sg25012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8661 sg9682 - -lemma sg25013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg8741 sg9462 - -lemma sg25014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,3,3,1,1] := by - exact rowSquare_join (by decide) sg8864 sg9002 - -lemma sg25015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10242 - -lemma sg25016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,4,2,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10242 - -lemma sg25017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,5,1,1,1] := by - exact rowSquare_join (by decide) sg1462 sg20934 - -lemma sg25018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2696 sg15004 - -lemma sg25019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5577 sg12614 - -lemma sg25020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5256 sg12687 - -lemma sg25021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8597 sg10081 - -lemma sg25022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9215 - -lemma sg25023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7786 sg11248 - -lemma sg25024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8547 sg10095 - -lemma sg25025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5257 sg12687 - -lemma sg25026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8598 sg10081 - -lemma sg25027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9216 - -lemma sg25028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9749 - -lemma sg25029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8819 sg9171 - -lemma sg25030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg7242 sg11447 - -lemma sg25031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9217 - -lemma sg25032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8746 sg9453 - -lemma sg25033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10127 - -lemma sg25034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8548 sg10095 - -lemma sg25035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8739 sg9465 - -lemma sg25036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8549 sg10095 - -lemma sg25037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8870 sg8990 - -lemma sg25038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8189 sg10853 - -lemma sg25039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8599 sg10081 - -lemma sg25040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9218 - -lemma sg25041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9750 - -lemma sg25042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10128 - -lemma sg25043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8370 sg10610 - -lemma sg25044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9751 - -lemma sg25045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9516 - -lemma sg25046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9679 - -lemma sg25047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8865 sg8999 - -lemma sg25048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10243 - -lemma sg25049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10653 - -lemma sg25050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,3,3] := by - exact rowSquare_join (by decide) sg8672 sg9669 - -lemma sg25051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9517 - -lemma sg25052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8746 sg9455 - -lemma sg25053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8740 sg9464 - -lemma sg25054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8740 sg9465 - -lemma sg25055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8396 sg10599 - -lemma sg25056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9752 - -lemma sg25057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9516 - -lemma sg25058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9680 - -lemma sg25059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg8371 sg10610 - -lemma sg25060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9518 - -lemma sg25061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10244 - -lemma sg25062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg8865 sg9000 - -lemma sg25063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10243 - -lemma sg25064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8747 sg9455 - -lemma sg25065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg8352 sg10653 - -lemma sg25066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg8548 sg10098 - -lemma sg25067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8767 sg9444 - -lemma sg25068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8527 sg10115 - -lemma sg25069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9682 - -lemma sg25070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg8741 sg9466 - -lemma sg25071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10244 - -lemma sg25072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10244 - -lemma sg25073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg8460 sg10195 - -lemma sg25074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8528 sg10115 - -lemma sg25075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,7,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8748 sg9456 - -lemma sg25076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,7,2,2,1,1] := by - exact rowSquare_join (by decide) sg8741 sg9468 - -lemma sg25077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,7,3,1,1,1] := by - exact rowSquare_join (by decide) sg8461 sg10195 - -lemma sg25078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1723 sg18243 - -lemma sg25079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1831 sg17105 - -lemma sg25080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1831 sg17106 - -lemma sg25081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1850 sg16201 - -lemma sg25082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2224 sg15521 - -lemma sg25083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2868 sg14852 - -lemma sg25084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg658 sg21210 - -lemma sg25085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg658 sg21211 - -lemma sg25086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg658 sg21212 - -lemma sg25087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg658 sg21213 - -lemma sg25088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2199 sg15561 - -lemma sg25089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1851 sg16201 - -lemma sg25090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2225 sg15521 - -lemma sg25091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2869 sg14852 - -lemma sg25092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3515 sg14680 - -lemma sg25093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg966 sg21121 - -lemma sg25094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg6294 sg11742 - -lemma sg25095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg966 sg21122 - -lemma sg25096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6361 sg11739 - -lemma sg25097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2226 sg15521 - -lemma sg25098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1817 sg17113 - -lemma sg25099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4692 sg12937 - -lemma sg25100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4622 sg12945 - -lemma sg25101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6734 sg11508 - -lemma sg25102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8183 sg10854 - -lemma sg25103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8666 sg9672 - -lemma sg25104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3516 sg14680 - -lemma sg25105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5268 sg12680 - -lemma sg25106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1706 sg18246 - -lemma sg25107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8228 sg10848 - -lemma sg25108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1706 sg18247 - -lemma sg25109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8507 sg10167 - -lemma sg25110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6914 sg11470 - -lemma sg25111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8184 sg10854 - -lemma sg25112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9673 - -lemma sg25113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8526 sg10116 - -lemma sg25114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8463 sg10190 - -lemma sg25115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8488 sg10170 - -lemma sg25116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg554 sg21252 - -lemma sg25117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8860 sg9065 - -lemma sg25118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2242 sg15512 - -lemma sg25119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2687 sg15011 - -lemma sg25120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2870 sg14852 - -lemma sg25121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4680 sg12939 - -lemma sg25122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5250 sg12688 - -lemma sg25123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6735 sg11508 - -lemma sg25124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8185 sg10854 - -lemma sg25125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8666 sg9674 - -lemma sg25126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2871 sg14852 - -lemma sg25127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4681 sg12939 - -lemma sg25128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5251 sg12688 - -lemma sg25129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2877 sg14819 - -lemma sg25130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9219 - -lemma sg25131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2173 sg15575 - -lemma sg25132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8742 sg9457 - -lemma sg25133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5252 sg12688 - -lemma sg25134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6915 sg11470 - -lemma sg25135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8186 sg10854 - -lemma sg25136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9675 - -lemma sg25137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8527 sg10116 - -lemma sg25138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8187 sg10854 - -lemma sg25139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9676 - -lemma sg25140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9519 - -lemma sg25141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg7232 sg11462 - -lemma sg25142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8742 sg9458 - -lemma sg25143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg7245 sg11445 - -lemma sg25144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9066 - -lemma sg25145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4692 sg12938 - -lemma sg25146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5268 sg12681 - -lemma sg25147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8254 sg10844 - -lemma sg25148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8188 sg10854 - -lemma sg25149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9677 - -lemma sg25150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8528 sg10116 - -lemma sg25151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8255 sg10844 - -lemma sg25152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9220 - -lemma sg25153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9753 - -lemma sg25154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8669 sg9672 - -lemma sg25155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8820 sg9166 - -lemma sg25156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9678 - -lemma sg25157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9520 - -lemma sg25158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8820 sg9167 - -lemma sg25159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg571 sg21222 - -lemma sg25160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9067 - -lemma sg25161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8398 sg10598 - -lemma sg25162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9754 - -lemma sg25163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8489 sg10170 - -lemma sg25164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8821 sg9166 - -lemma sg25165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9521 - -lemma sg25166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8822 sg9166 - -lemma sg25167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9068 - -lemma sg25168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8465 sg10190 - -lemma sg25169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg7785 sg11249 - -lemma sg25170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8822 sg9167 - -lemma sg25171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg8743 sg9458 - -lemma sg25172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2688 sg15011 - -lemma sg25173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2697 sg15004 - -lemma sg25174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4682 sg12939 - -lemma sg25175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5253 sg12688 - -lemma sg25176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2878 sg14819 - -lemma sg25177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9219 - -lemma sg25178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg4929 sg12816 - -lemma sg25179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8742 sg9459 - -lemma sg25180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4683 sg12939 - -lemma sg25181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5254 sg12688 - -lemma sg25182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8254 sg10845 - -lemma sg25183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6120 sg11767 - -lemma sg25184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7783 sg11250 - -lemma sg25185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8668 sg9674 - -lemma sg25186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8255 sg10845 - -lemma sg25187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9220 - -lemma sg25188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9755 - -lemma sg25189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9519 - -lemma sg25190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8823 sg9166 - -lemma sg25191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8463 sg10193 - -lemma sg25192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9522 - -lemma sg25193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8823 sg9167 - -lemma sg25194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8466 sg10190 - -lemma sg25195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9069 - -lemma sg25196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5255 sg12688 - -lemma sg25197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8257 sg10844 - -lemma sg25198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9221 - -lemma sg25199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9753 - -lemma sg25200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9519 - -lemma sg25201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8820 sg9168 - -lemma sg25202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9222 - -lemma sg25203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9756 - -lemma sg25204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9520 - -lemma sg25205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8820 sg9169 - -lemma sg25206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9523 - -lemma sg25207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8668 sg9676 - -lemma sg25208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9070 - -lemma sg25209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8467 sg10190 - -lemma sg25210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9757 - -lemma sg25211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9524 - -lemma sg25212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8824 sg9166 - -lemma sg25213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9071 - -lemma sg25214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8553 sg10092 - -lemma sg25215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8669 sg9676 - -lemma sg25216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg8744 sg9458 - -lemma sg25217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8869 sg8995 - -lemma sg25218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8258 sg10844 - -lemma sg25219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9223 - -lemma sg25220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9682 - -lemma sg25221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9520 - -lemma sg25222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8820 sg9170 - -lemma sg25223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9758 - -lemma sg25224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9525 - -lemma sg25225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8373 sg10609 - -lemma sg25226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9072 - -lemma sg25227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8668 sg9678 - -lemma sg25228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg8822 sg9170 - -lemma sg25229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg8745 sg9458 - -lemma sg25230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8489 sg10172 - -lemma sg25231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8375 sg10606 - -lemma sg25232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg8867 sg8996 - -lemma sg25233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg8867 sg8997 - -lemma sg25234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10606 - -lemma sg25235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg8867 sg8998 - -lemma sg25236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2698 sg15004 - -lemma sg25237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4684 sg12939 - -lemma sg25238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5256 sg12688 - -lemma sg25239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8256 sg10845 - -lemma sg25240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6121 sg11767 - -lemma sg25241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7786 sg11250 - -lemma sg25242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8670 sg9674 - -lemma sg25243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5257 sg12688 - -lemma sg25244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8257 sg10845 - -lemma sg25245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9224 - -lemma sg25246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9755 - -lemma sg25247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8671 sg9674 - -lemma sg25248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8183 sg10857 - -lemma sg25249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9222 - -lemma sg25250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9759 - -lemma sg25251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9522 - -lemma sg25252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8823 sg9169 - -lemma sg25253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9526 - -lemma sg25254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8670 sg9676 - -lemma sg25255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9073 - -lemma sg25256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg7453 sg11281 - -lemma sg25257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8258 sg10845 - -lemma sg25258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9225 - -lemma sg25259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9756 - -lemma sg25260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9522 - -lemma sg25261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8820 sg9171 - -lemma sg25262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9760 - -lemma sg25263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9527 - -lemma sg25264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8668 sg9679 - -lemma sg25265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9074 - -lemma sg25266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8670 sg9678 - -lemma sg25267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8671 sg9676 - -lemma sg25268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9524 - -lemma sg25269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8556 sg10092 - -lemma sg25270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8669 sg9679 - -lemma sg25271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8465 sg10193 - -lemma sg25272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9226 - -lemma sg25273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9761 - -lemma sg25274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9528 - -lemma sg25275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8668 sg9680 - -lemma sg25276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9075 - -lemma sg25277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9525 - -lemma sg25278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8668 sg9681 - -lemma sg25279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg8867 sg9000 - -lemma sg25280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg8868 sg8997 - -lemma sg25281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10607 - -lemma sg25282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg8867 sg9001 - -lemma sg25283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10608 - -lemma sg25284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8768 sg9444 - -lemma sg25285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9525 - -lemma sg25286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8668 sg9682 - -lemma sg25287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg8825 sg9170 - -lemma sg25288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8559 sg10092 - -lemma sg25289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,3,2,1,1] := by - exact rowSquare_join (by decide) sg8867 sg9002 - -lemma sg25290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,4,1,1,1] := by - exact rowSquare_join (by decide) sg8465 sg10195 - -lemma sg25291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14502 - -lemma sg25292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4623 sg12946 - -lemma sg25293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8259 sg10845 - -lemma sg25294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9224 - -lemma sg25295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7450 sg11351 - -lemma sg25296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8189 sg10855 - -lemma sg25297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8185 sg10857 - -lemma sg25298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8260 sg10845 - -lemma sg25299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9227 - -lemma sg25300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9759 - -lemma sg25301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8672 sg9674 - -lemma sg25302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8823 sg9171 - -lemma sg25303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8769 sg9442 - -lemma sg25304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9529 - -lemma sg25305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8670 sg9679 - -lemma sg25306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9076 - -lemma sg25307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8466 sg10193 - -lemma sg25308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8189 sg10856 - -lemma sg25309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9228 - -lemma sg25310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9760 - -lemma sg25311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9530 - -lemma sg25312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8670 sg9680 - -lemma sg25313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9077 - -lemma sg25314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9527 - -lemma sg25315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8670 sg9681 - -lemma sg25316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8671 sg9679 - -lemma sg25317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8467 sg10193 - -lemma sg25318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg7788 sg11251 - -lemma sg25319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8870 sg8998 - -lemma sg25320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9761 - -lemma sg25321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9528 - -lemma sg25322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8670 sg9682 - -lemma sg25323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg8868 sg9000 - -lemma sg25324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8466 sg10195 - -lemma sg25325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg8868 sg9001 - -lemma sg25326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10610 - -lemma sg25327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9528 - -lemma sg25328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8559 sg10093 - -lemma sg25329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,6,2,2,1,1] := by - exact rowSquare_join (by decide) sg8868 sg9002 - -lemma sg25330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,6,3,1,1,1] := by - exact rowSquare_join (by decide) sg8467 sg10195 - -lemma sg25331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,7,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7789 sg11252 - -lemma sg25332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,7,2,1,1,1] := by - exact rowSquare_join (by decide) sg8748 sg9461 - -lemma sg25333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1868 sg16188 - -lemma sg25334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7254 sg11434 - -lemma sg25335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9227 - -lemma sg25336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7786 sg11253 - -lemma sg25337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7794 sg11244 - -lemma sg25338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8189 sg10857 - -lemma sg25339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9228 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 61. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg24940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2686 sg15011 + +lemma sg24941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2695 sg15004 + +lemma sg24942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5551 sg12621 + +lemma sg24943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5253 sg12687 + +lemma sg24944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8595 sg10081 + +lemma sg24945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9211 + +lemma sg24946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8670 sg9667 + +lemma sg24947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9459 + +lemma sg24948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5552 sg12621 + +lemma sg24949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5254 sg12687 + +lemma sg24950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10243 + +lemma sg24951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9215 + +lemma sg24952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9744 + +lemma sg24953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8544 sg10095 + +lemma sg24954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8596 sg10081 + +lemma sg24955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9213 + +lemma sg24956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9749 + +lemma sg24957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9512 + +lemma sg24958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8180 sg10857 + +lemma sg24959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9759 + +lemma sg24960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9759 + +lemma sg24961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8823 sg9165 + +lemma sg24962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8670 sg9669 + +lemma sg24963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9060 + +lemma sg24964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5255 sg12687 + +lemma sg24965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10244 + +lemma sg24966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9216 + +lemma sg24967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9745 + +lemma sg24968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9512 + +lemma sg24969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8370 sg10607 + +lemma sg24970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9217 + +lemma sg24971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9760 + +lemma sg24972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9760 + +lemma sg24973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8818 sg9171 + +lemma sg24974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9516 + +lemma sg24975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10243 + +lemma sg24976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9061 + +lemma sg24977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10651 + +lemma sg24978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9751 + +lemma sg24979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9517 + +lemma sg24980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8661 sg9679 + +lemma sg24981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9062 + +lemma sg24982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10241 + +lemma sg24983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10652 + +lemma sg24984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,3,3] := by + exact rowSquare_join (by decide) sg8662 sg9679 + +lemma sg24985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8738 sg9465 + +lemma sg24986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,4,4,4,2] := by + exact rowSquare_join (by decide) sg8459 sg10193 + +lemma sg24987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8599 sg10080 + +lemma sg24988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9218 + +lemma sg24989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9761 + +lemma sg24990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9761 + +lemma sg24991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8663 sg9677 + +lemma sg24992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9752 + +lemma sg24993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9518 + +lemma sg24994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10244 + +lemma sg24995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9063 + +lemma sg24996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9678 + +lemma sg24997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg8430 sg10240 + +lemma sg24998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,3,3,3] := by + exact rowSquare_join (by decide) sg8662 sg9680 + +lemma sg24999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9515 + +lemma sg25000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10242 + +lemma sg25001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg8352 sg10651 + +lemma sg25002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10241 + +lemma sg25003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,4,3,2] := by + exact rowSquare_join (by decide) sg8662 sg9681 + +lemma sg25004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg6893 sg11498 + +lemma sg25005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg8545 sg10098 + +lemma sg25006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7247 sg11443 + +lemma sg25007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8748 sg9451 + +lemma sg25008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8526 sg10115 + +lemma sg25009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8745 sg9456 + +lemma sg25010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9064 + +lemma sg25011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9515 + +lemma sg25012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8661 sg9682 + +lemma sg25013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg8741 sg9462 + +lemma sg25014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,3,3,1,1] := by + exact rowSquare_join (by decide) sg8864 sg9002 + +lemma sg25015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10242 + +lemma sg25016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,4,2,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10242 + +lemma sg25017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,6,6,5,1,1,1] := by + exact rowSquare_join (by decide) sg1462 sg20934 + +lemma sg25018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2696 sg15004 + +lemma sg25019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5577 sg12614 + +lemma sg25020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5256 sg12687 + +lemma sg25021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8597 sg10081 + +lemma sg25022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9215 + +lemma sg25023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7786 sg11248 + +lemma sg25024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8547 sg10095 + +lemma sg25025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5257 sg12687 + +lemma sg25026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8598 sg10081 + +lemma sg25027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9216 + +lemma sg25028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9749 + +lemma sg25029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8819 sg9171 + +lemma sg25030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg7242 sg11447 + +lemma sg25031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9217 + +lemma sg25032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8746 sg9453 + +lemma sg25033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10127 + +lemma sg25034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8548 sg10095 + +lemma sg25035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8739 sg9465 + +lemma sg25036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8549 sg10095 + +lemma sg25037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8870 sg8990 + +lemma sg25038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8189 sg10853 + +lemma sg25039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8599 sg10081 + +lemma sg25040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9218 + +lemma sg25041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9750 + +lemma sg25042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10128 + +lemma sg25043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8370 sg10610 + +lemma sg25044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9751 + +lemma sg25045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9516 + +lemma sg25046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9679 + +lemma sg25047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8865 sg8999 + +lemma sg25048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10243 + +lemma sg25049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10653 + +lemma sg25050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,3,3,3] := by + exact rowSquare_join (by decide) sg8672 sg9669 + +lemma sg25051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9517 + +lemma sg25052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8746 sg9455 + +lemma sg25053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8740 sg9464 + +lemma sg25054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8740 sg9465 + +lemma sg25055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8396 sg10599 + +lemma sg25056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9752 + +lemma sg25057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9516 + +lemma sg25058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9680 + +lemma sg25059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg8371 sg10610 + +lemma sg25060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9518 + +lemma sg25061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10244 + +lemma sg25062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg8865 sg9000 + +lemma sg25063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10243 + +lemma sg25064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8747 sg9455 + +lemma sg25065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg8352 sg10653 + +lemma sg25066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg8548 sg10098 + +lemma sg25067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8767 sg9444 + +lemma sg25068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8527 sg10115 + +lemma sg25069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9682 + +lemma sg25070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg8741 sg9466 + +lemma sg25071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10244 + +lemma sg25072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10244 + +lemma sg25073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg8460 sg10195 + +lemma sg25074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8528 sg10115 + +lemma sg25075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,7,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8748 sg9456 + +lemma sg25076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,7,2,2,1,1] := by + exact rowSquare_join (by decide) sg8741 sg9468 + +lemma sg25077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,7,7,7,3,1,1,1] := by + exact rowSquare_join (by decide) sg8461 sg10195 + +lemma sg25078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1723 sg18243 + +lemma sg25079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1831 sg17105 + +lemma sg25080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1831 sg17106 + +lemma sg25081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1850 sg16201 + +lemma sg25082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2224 sg15521 + +lemma sg25083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2868 sg14852 + +lemma sg25084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg658 sg21210 + +lemma sg25085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg658 sg21211 + +lemma sg25086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg658 sg21212 + +lemma sg25087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg658 sg21213 + +lemma sg25088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2199 sg15561 + +lemma sg25089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1851 sg16201 + +lemma sg25090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2225 sg15521 + +lemma sg25091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2869 sg14852 + +lemma sg25092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3515 sg14680 + +lemma sg25093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg966 sg21121 + +lemma sg25094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg6294 sg11742 + +lemma sg25095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg966 sg21122 + +lemma sg25096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6361 sg11739 + +lemma sg25097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2226 sg15521 + +lemma sg25098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1817 sg17113 + +lemma sg25099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4692 sg12937 + +lemma sg25100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4622 sg12945 + +lemma sg25101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6734 sg11508 + +lemma sg25102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8183 sg10854 + +lemma sg25103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8666 sg9672 + +lemma sg25104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3516 sg14680 + +lemma sg25105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5268 sg12680 + +lemma sg25106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1706 sg18246 + +lemma sg25107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8228 sg10848 + +lemma sg25108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1706 sg18247 + +lemma sg25109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8507 sg10167 + +lemma sg25110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6914 sg11470 + +lemma sg25111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8184 sg10854 + +lemma sg25112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9673 + +lemma sg25113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8526 sg10116 + +lemma sg25114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8463 sg10190 + +lemma sg25115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8488 sg10170 + +lemma sg25116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg554 sg21252 + +lemma sg25117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8860 sg9065 + +lemma sg25118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2242 sg15512 + +lemma sg25119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2687 sg15011 + +lemma sg25120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2870 sg14852 + +lemma sg25121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4680 sg12939 + +lemma sg25122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5250 sg12688 + +lemma sg25123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6735 sg11508 + +lemma sg25124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8185 sg10854 + +lemma sg25125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8666 sg9674 + +lemma sg25126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2871 sg14852 + +lemma sg25127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4681 sg12939 + +lemma sg25128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5251 sg12688 + +lemma sg25129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2877 sg14819 + +lemma sg25130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9219 + +lemma sg25131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2173 sg15575 + +lemma sg25132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8742 sg9457 + +lemma sg25133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5252 sg12688 + +lemma sg25134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6915 sg11470 + +lemma sg25135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8186 sg10854 + +lemma sg25136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9675 + +lemma sg25137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8527 sg10116 + +lemma sg25138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8187 sg10854 + +lemma sg25139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9676 + +lemma sg25140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9519 + +lemma sg25141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg7232 sg11462 + +lemma sg25142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8742 sg9458 + +lemma sg25143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg7245 sg11445 + +lemma sg25144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9066 + +lemma sg25145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4692 sg12938 + +lemma sg25146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5268 sg12681 + +lemma sg25147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8254 sg10844 + +lemma sg25148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8188 sg10854 + +lemma sg25149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9677 + +lemma sg25150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8528 sg10116 + +lemma sg25151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8255 sg10844 + +lemma sg25152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9220 + +lemma sg25153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9753 + +lemma sg25154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8669 sg9672 + +lemma sg25155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8820 sg9166 + +lemma sg25156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9678 + +lemma sg25157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9520 + +lemma sg25158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8820 sg9167 + +lemma sg25159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg571 sg21222 + +lemma sg25160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9067 + +lemma sg25161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8398 sg10598 + +lemma sg25162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9754 + +lemma sg25163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8489 sg10170 + +lemma sg25164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8821 sg9166 + +lemma sg25165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9521 + +lemma sg25166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8822 sg9166 + +lemma sg25167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9068 + +lemma sg25168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8465 sg10190 + +lemma sg25169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg7785 sg11249 + +lemma sg25170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8822 sg9167 + +lemma sg25171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg8743 sg9458 + +lemma sg25172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2688 sg15011 + +lemma sg25173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2697 sg15004 + +lemma sg25174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4682 sg12939 + +lemma sg25175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5253 sg12688 + +lemma sg25176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2878 sg14819 + +lemma sg25177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9219 + +lemma sg25178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg4929 sg12816 + +lemma sg25179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8742 sg9459 + +lemma sg25180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4683 sg12939 + +lemma sg25181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5254 sg12688 + +lemma sg25182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8254 sg10845 + +lemma sg25183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6120 sg11767 + +lemma sg25184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7783 sg11250 + +lemma sg25185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8668 sg9674 + +lemma sg25186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8255 sg10845 + +lemma sg25187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9220 + +lemma sg25188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9755 + +lemma sg25189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9519 + +lemma sg25190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8823 sg9166 + +lemma sg25191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8463 sg10193 + +lemma sg25192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9522 + +lemma sg25193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8823 sg9167 + +lemma sg25194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8466 sg10190 + +lemma sg25195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9069 + +lemma sg25196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5255 sg12688 + +lemma sg25197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8257 sg10844 + +lemma sg25198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9221 + +lemma sg25199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9753 + +lemma sg25200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9519 + +lemma sg25201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8820 sg9168 + +lemma sg25202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9222 + +lemma sg25203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9756 + +lemma sg25204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9520 + +lemma sg25205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8820 sg9169 + +lemma sg25206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9523 + +lemma sg25207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8668 sg9676 + +lemma sg25208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9070 + +lemma sg25209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8467 sg10190 + +lemma sg25210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9757 + +lemma sg25211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9524 + +lemma sg25212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8824 sg9166 + +lemma sg25213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9071 + +lemma sg25214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8553 sg10092 + +lemma sg25215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8669 sg9676 + +lemma sg25216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg8744 sg9458 + +lemma sg25217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8869 sg8995 + +lemma sg25218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8258 sg10844 + +lemma sg25219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9223 + +lemma sg25220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9682 + +lemma sg25221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9520 + +lemma sg25222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8820 sg9170 + +lemma sg25223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9758 + +lemma sg25224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9525 + +lemma sg25225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8373 sg10609 + +lemma sg25226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9072 + +lemma sg25227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8668 sg9678 + +lemma sg25228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg8822 sg9170 + +lemma sg25229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg8745 sg9458 + +lemma sg25230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8489 sg10172 + +lemma sg25231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8375 sg10606 + +lemma sg25232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg8867 sg8996 + +lemma sg25233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg8867 sg8997 + +lemma sg25234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10606 + +lemma sg25235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg8867 sg8998 + +lemma sg25236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2698 sg15004 + +lemma sg25237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4684 sg12939 + +lemma sg25238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5256 sg12688 + +lemma sg25239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8256 sg10845 + +lemma sg25240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6121 sg11767 + +lemma sg25241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7786 sg11250 + +lemma sg25242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8670 sg9674 + +lemma sg25243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5257 sg12688 + +lemma sg25244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8257 sg10845 + +lemma sg25245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9224 + +lemma sg25246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9755 + +lemma sg25247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8671 sg9674 + +lemma sg25248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8183 sg10857 + +lemma sg25249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9222 + +lemma sg25250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9759 + +lemma sg25251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9522 + +lemma sg25252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8823 sg9169 + +lemma sg25253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9526 + +lemma sg25254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8670 sg9676 + +lemma sg25255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9073 + +lemma sg25256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg7453 sg11281 + +lemma sg25257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8258 sg10845 + +lemma sg25258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9225 + +lemma sg25259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9756 + +lemma sg25260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9522 + +lemma sg25261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8820 sg9171 + +lemma sg25262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9760 + +lemma sg25263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9527 + +lemma sg25264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8668 sg9679 + +lemma sg25265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9074 + +lemma sg25266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8670 sg9678 + +lemma sg25267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8671 sg9676 + +lemma sg25268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9524 + +lemma sg25269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8556 sg10092 + +lemma sg25270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8669 sg9679 + +lemma sg25271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8465 sg10193 + +lemma sg25272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9226 + +lemma sg25273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9761 + +lemma sg25274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9528 + +lemma sg25275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8668 sg9680 + +lemma sg25276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9075 + +lemma sg25277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9525 + +lemma sg25278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8668 sg9681 + +lemma sg25279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg8867 sg9000 + +lemma sg25280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg8868 sg8997 + +lemma sg25281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10607 + +lemma sg25282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg8867 sg9001 + +lemma sg25283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10608 + +lemma sg25284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8768 sg9444 + +lemma sg25285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9525 + +lemma sg25286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8668 sg9682 + +lemma sg25287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg8825 sg9170 + +lemma sg25288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8559 sg10092 + +lemma sg25289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,3,2,1,1] := by + exact rowSquare_join (by decide) sg8867 sg9002 + +lemma sg25290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,6,6,4,1,1,1] := by + exact rowSquare_join (by decide) sg8465 sg10195 + +lemma sg25291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14502 + +lemma sg25292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4623 sg12946 + +lemma sg25293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8259 sg10845 + +lemma sg25294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9224 + +lemma sg25295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7450 sg11351 + +lemma sg25296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8189 sg10855 + +lemma sg25297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8185 sg10857 + +lemma sg25298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8260 sg10845 + +lemma sg25299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9227 + +lemma sg25300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9759 + +lemma sg25301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8672 sg9674 + +lemma sg25302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8823 sg9171 + +lemma sg25303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8769 sg9442 + +lemma sg25304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9529 + +lemma sg25305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8670 sg9679 + +lemma sg25306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9076 + +lemma sg25307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8466 sg10193 + +lemma sg25308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8189 sg10856 + +lemma sg25309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9228 + +lemma sg25310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9760 + +lemma sg25311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9530 + +lemma sg25312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8670 sg9680 + +lemma sg25313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9077 + +lemma sg25314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9527 + +lemma sg25315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8670 sg9681 + +lemma sg25316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8671 sg9679 + +lemma sg25317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8467 sg10193 + +lemma sg25318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg7788 sg11251 + +lemma sg25319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8870 sg8998 + +lemma sg25320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9761 + +lemma sg25321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9528 + +lemma sg25322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8670 sg9682 + +lemma sg25323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg8868 sg9000 + +lemma sg25324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8466 sg10195 + +lemma sg25325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg8868 sg9001 + +lemma sg25326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10610 + +lemma sg25327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9528 + +lemma sg25328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8559 sg10093 + +lemma sg25329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,6,2,2,1,1] := by + exact rowSquare_join (by decide) sg8868 sg9002 + +lemma sg25330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,6,3,1,1,1] := by + exact rowSquare_join (by decide) sg8467 sg10195 + +lemma sg25331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,7,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7789 sg11252 + +lemma sg25332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,7,7,2,1,1,1] := by + exact rowSquare_join (by decide) sg8748 sg9461 + +lemma sg25333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1868 sg16188 + +lemma sg25334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7254 sg11434 + +lemma sg25335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9227 + +lemma sg25336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7786 sg11253 + +lemma sg25337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7794 sg11244 + +lemma sg25338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8189 sg10857 + +lemma sg25339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9228 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes62.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes62.lean index 607241671173fa9a8c71d61ed9a969edc715a6b1..42a99c94bc9c82fa28c90623621aa8dde62fa3e1 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes62.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes62.lean @@ -1,1221 +1,1221 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 - -namespace OAI - -/-! Semigroup Nodes 62. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg25340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8770 sg9442 - -lemma sg25341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8770 sg9443 - -lemma sg25342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7254 sg11436 - -lemma sg25343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8870 sg8999 - -lemma sg25344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9529 - -lemma sg25345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8556 sg10095 - -lemma sg25346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8189 sg10858 - -lemma sg25347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14503 - -lemma sg25348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8770 sg9444 - -lemma sg25349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9530 - -lemma sg25350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8557 sg10095 - -lemma sg25351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8870 sg9000 - -lemma sg25352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8558 sg10095 - -lemma sg25353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8870 sg9001 - -lemma sg25354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg7795 sg11245 - -lemma sg25355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9530 - -lemma sg25356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8559 sg10095 - -lemma sg25357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg8870 sg9002 - -lemma sg25358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg8379 sg10610 - -lemma sg25359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7789 sg11254 - -lemma sg25360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,6,2,1,1,1] := by - exact rowSquare_join (by decide) sg8559 sg10096 - -lemma sg25361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,7,1,1,1,1] := by - exact rowSquare_join (by decide) sg7796 sg11246 - -lemma sg25362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8511 sg10167 - -lemma sg25363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10321 - -lemma sg25364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10245 - -lemma sg25365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10322 - -lemma sg25366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9469 - -lemma sg25367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10323 - -lemma sg25368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9763 - -lemma sg25369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10247 - -lemma sg25370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg8648 sg9764 - -lemma sg25371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8513 sg10167 - -lemma sg25372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10324 - -lemma sg25373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10248 - -lemma sg25374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10325 - -lemma sg25375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9762 - -lemma sg25376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10326 - -lemma sg25377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9767 - -lemma sg25378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10327 - -lemma sg25379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10250 - -lemma sg25380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9768 - -lemma sg25381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8423 sg10247 - -lemma sg25382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8514 sg10167 - -lemma sg25383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10328 - -lemma sg25384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10251 - -lemma sg25385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10329 - -lemma sg25386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9471 - -lemma sg25387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10330 - -lemma sg25388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9770 - -lemma sg25389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9532 - -lemma sg25390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10331 - -lemma sg25391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10253 - -lemma sg25392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9771 - -lemma sg25393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10254 - -lemma sg25394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9772 - -lemma sg25395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9175 - -lemma sg25396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg8860 sg9078 - -lemma sg25397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10255 - -lemma sg25398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10332 - -lemma sg25399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9473 - -lemma sg25400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10333 - -lemma sg25401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9774 - -lemma sg25402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8750 sg9447 - -lemma sg25403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10334 - -lemma sg25404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10257 - -lemma sg25405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9775 - -lemma sg25406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10335 - -lemma sg25407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10258 - -lemma sg25408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9776 - -lemma sg25409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9177 - -lemma sg25410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9178 - -lemma sg25411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9178 - -lemma sg25412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg8873 sg8984 - -lemma sg25413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8750 sg9448 - -lemma sg25414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10336 - -lemma sg25415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10259 - -lemma sg25416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9777 - -lemma sg25417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8494 sg10172 - -lemma sg25418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10337 - -lemma sg25419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10260 - -lemma sg25420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9778 - -lemma sg25421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8653 sg9696 - -lemma sg25422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10660 - -lemma sg25423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9779 - -lemma sg25424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9474 - -lemma sg25425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9474 - -lemma sg25426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,3,3] := by - exact rowSquare_join (by decide) sg8873 sg8985 - -lemma sg25427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8381 sg10601 - -lemma sg25428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,4,2] := by - exact rowSquare_join (by decide) sg8873 sg8986 - -lemma sg25429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8500 sg10168 - -lemma sg25430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10129 - -lemma sg25431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg8481 sg10174 - -lemma sg25432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8529 sg10099 - -lemma sg25433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10099 - -lemma sg25434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,3,3,3] := by - exact rowSquare_join (by decide) sg8873 sg8987 - -lemma sg25435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8529 sg10100 - -lemma sg25436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10100 - -lemma sg25437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg8561 sg10085 - -lemma sg25438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,4,3,2] := by - exact rowSquare_join (by decide) sg8873 sg8988 - -lemma sg25439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,4,4,1] := by - exact rowSquare_join (by decide) sg7248 sg11439 - -lemma sg25440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg8560 sg10086 - -lemma sg25441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,5,2,1,1] := by - exact rowSquare_join (by decide) sg8561 sg10086 - -lemma sg25442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,5,2,2] := by - exact rowSquare_join (by decide) sg8562 sg10086 - -lemma sg25443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,5,3,1] := by - exact rowSquare_join (by decide) sg6400 sg11737 - -lemma sg25444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8515 sg10167 - -lemma sg25445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10338 - -lemma sg25446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10261 - -lemma sg25447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10339 - -lemma sg25448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9766 - -lemma sg25449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10340 - -lemma sg25450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9781 - -lemma sg25451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9470 - -lemma sg25452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10341 - -lemma sg25453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10263 - -lemma sg25454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9782 - -lemma sg25455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10264 - -lemma sg25456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9783 - -lemma sg25457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10250 - -lemma sg25458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,4,4] := by - exact rowSquare_join (by decide) sg8804 sg9174 - -lemma sg25459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10342 - -lemma sg25460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10265 - -lemma sg25461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10343 - -lemma sg25462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9769 - -lemma sg25463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10344 - -lemma sg25464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9786 - -lemma sg25465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9534 - -lemma sg25466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10345 - -lemma sg25467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10267 - -lemma sg25468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9787 - -lemma sg25469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10346 - -lemma sg25470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10268 - -lemma sg25471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9788 - -lemma sg25472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10253 - -lemma sg25473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9772 - -lemma sg25474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10254 - -lemma sg25475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg8860 sg9079 - -lemma sg25476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9773 - -lemma sg25477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10347 - -lemma sg25478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9789 - -lemma sg25479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9473 - -lemma sg25480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10348 - -lemma sg25481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10270 - -lemma sg25482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9790 - -lemma sg25483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9534 - -lemma sg25484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10349 - -lemma sg25485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10271 - -lemma sg25486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9791 - -lemma sg25487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10257 - -lemma sg25488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10272 - -lemma sg25489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9792 - -lemma sg25490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9776 - -lemma sg25491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10258 - -lemma sg25492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg8861 sg9010 - -lemma sg25493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9178 - -lemma sg25494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg8861 sg9011 - -lemma sg25495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8753 sg9448 - -lemma sg25496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10350 - -lemma sg25497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10273 - -lemma sg25498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9793 - -lemma sg25499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10259 - -lemma sg25500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10351 - -lemma sg25501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10274 - -lemma sg25502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9794 - -lemma sg25503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9778 - -lemma sg25504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10260 - -lemma sg25505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,3,3,3] := by - exact rowSquare_join (by decide) sg8861 sg9013 - -lemma sg25506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9779 - -lemma sg25507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10660 - -lemma sg25508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9474 - -lemma sg25509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,4,3,2] := by - exact rowSquare_join (by decide) sg8861 sg9014 - -lemma sg25510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,4,4,1] := by - exact rowSquare_join (by decide) sg8876 sg8986 - -lemma sg25511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10130 - -lemma sg25512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg8484 sg10174 - -lemma sg25513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10129 - -lemma sg25514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10102 - -lemma sg25515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10099 - -lemma sg25516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,3,3,2] := by - exact rowSquare_join (by decide) sg8861 sg9015 - -lemma sg25517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8531 sg10100 - -lemma sg25518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10100 - -lemma sg25519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,4,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9016 - -lemma sg25520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,4,3,1] := by - exact rowSquare_join (by decide) sg8876 sg8988 - -lemma sg25521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg8563 sg10086 - -lemma sg25522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,5,2,1] := by - exact rowSquare_join (by decide) sg8564 sg10086 - -lemma sg25523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8524 sg10131 - -lemma sg25524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8838 sg9159 - -lemma sg25525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9481 - -lemma sg25526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8345 sg10668 - -lemma sg25527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9796 - -lemma sg25528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9536 - -lemma sg25529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10352 - -lemma sg25530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10669 - -lemma sg25531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9797 - -lemma sg25532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9471 - -lemma sg25533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10353 - -lemma sg25534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10275 - -lemma sg25535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9798 - -lemma sg25536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9187 - -lemma sg25537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10276 - -lemma sg25538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9799 - -lemma sg25539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9188 - -lemma sg25540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9188 - -lemma sg25541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9080 - -lemma sg25542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10254 - -lemma sg25543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg8860 sg9081 - -lemma sg25544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9537 - -lemma sg25545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10354 - -lemma sg25546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10672 - -lemma sg25547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9800 - -lemma sg25548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9536 - -lemma sg25549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10355 - -lemma sg25550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10277 - -lemma sg25551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9801 - -lemma sg25552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9190 - -lemma sg25553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10356 - -lemma sg25554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10278 - -lemma sg25555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9802 - -lemma sg25556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9191 - -lemma sg25557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9191 - -lemma sg25558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9082 - -lemma sg25559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9192 - -lemma sg25560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9192 - -lemma sg25561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10258 - -lemma sg25562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9083 - -lemma sg25563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8350 sg10657 - -lemma sg25564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9536 - -lemma sg25565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10357 - -lemma sg25566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10279 - -lemma sg25567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9803 - -lemma sg25568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9193 - -lemma sg25569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9193 - -lemma sg25570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9084 - -lemma sg25571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10280 - -lemma sg25572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9804 - -lemma sg25573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9488 - -lemma sg25574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9488 - -lemma sg25575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10260 - -lemma sg25576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9085 - -lemma sg25577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9539 - -lemma sg25578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8751 sg9463 - -lemma sg25579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9086 - -lemma sg25580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg8862 sg9014 - -lemma sg25581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8529 sg10104 - -lemma sg25582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10104 - -lemma sg25583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8526 sg10129 - -lemma sg25584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg8561 sg10094 - -lemma sg25585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9087 - -lemma sg25586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg8862 sg9015 - -lemma sg25587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg8535 sg10100 - -lemma sg25588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg8862 sg9016 - -lemma sg25589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg8566 sg10086 - -lemma sg25590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9537 - -lemma sg25591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10358 - -lemma sg25592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10677 - -lemma sg25593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9805 - -lemma sg25594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9194 - -lemma sg25595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9537 - -lemma sg25596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10359 - -lemma sg25597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10281 - -lemma sg25598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9806 - -lemma sg25599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9195 - -lemma sg25600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9195 - -lemma sg25601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8873 sg8999 - -lemma sg25602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10282 - -lemma sg25603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9807 - -lemma sg25604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9196 - -lemma sg25605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9196 - -lemma sg25606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8751 sg9464 - -lemma sg25607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8752 sg9464 - -lemma sg25608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8750 sg9465 - -lemma sg25609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8751 sg9465 - -lemma sg25610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8752 sg9465 - -lemma sg25611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10658 - -lemma sg25612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10360 - -lemma sg25613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10283 - -lemma sg25614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9808 - -lemma sg25615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9197 - -lemma sg25616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9197 - -lemma sg25617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8751 sg9466 - -lemma sg25618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg8873 sg9000 - -lemma sg25619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9492 - -lemma sg25620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9492 - -lemma sg25621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8872 sg9001 - -lemma sg25622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8751 sg9467 - -lemma sg25623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg8873 sg9001 - -lemma sg25624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10659 - -lemma sg25625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8568 sg10086 - -lemma sg25626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10660 - -lemma sg25627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8560 sg10098 - -lemma sg25628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg8561 sg10098 - -lemma sg25629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg8562 sg10098 - -lemma sg25630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg8538 sg10100 - -lemma sg25631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg8863 sg9015 - -lemma sg25632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg8863 sg9016 - -lemma sg25633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6919 sg11472 - -lemma sg25634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10284 - -lemma sg25635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10284 - -lemma sg25636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9809 - -lemma sg25637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10284 - -lemma sg25638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9809 - -lemma sg25639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10230 - -lemma sg25640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8723 sg9493 - -lemma sg25641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9493 - -lemma sg25642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9493 - -lemma sg25643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8872 sg9002 - -lemma sg25644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8751 sg9468 - -lemma sg25645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,3,2,2] := by - exact rowSquare_join (by decide) sg8873 sg9002 - -lemma sg25646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,3,3,1] := by - exact rowSquare_join (by decide) sg8881 sg8986 - -lemma sg25647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8471 sg10195 - -lemma sg25648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8472 sg10195 - -lemma sg25649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8473 sg10195 - -lemma sg25650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,2,2,2] := by - exact rowSquare_join (by decide) sg8474 sg10195 - -lemma sg25651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8540 sg10100 - -lemma sg25652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,3,2,1] := by - exact rowSquare_join (by decide) sg8430 sg10260 - -lemma sg25653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,4,1,1] := by - exact rowSquare_join (by decide) sg8351 sg10660 - -lemma sg25654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8500 sg10172 - -lemma sg25655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg8481 sg10182 - -lemma sg25656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,5,2,2,1] := by - exact rowSquare_join (by decide) sg8352 sg10659 - -lemma sg25657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,5,3,1,1] := by - exact rowSquare_join (by decide) sg8352 sg10660 - -lemma sg25658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg335 sg21316 - -lemma sg25659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,6,2,1,1] := by - exact rowSquare_join (by decide) sg331 sg21325 - -lemma sg25660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,3,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8516 sg10167 - -lemma sg25661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10361 - -lemma sg25662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10285 - -lemma sg25663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10362 - -lemma sg25664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9780 - -lemma sg25665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10363 - -lemma sg25666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9812 - -lemma sg25667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9475 - -lemma sg25668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10364 - -lemma sg25669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10287 - -lemma sg25670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9813 - -lemma sg25671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10365 - -lemma sg25672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10288 - -lemma sg25673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9814 - -lemma sg25674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10263 - -lemma sg25675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9783 - -lemma sg25676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10264 - -lemma sg25677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,4,3] := by - exact rowSquare_join (by decide) sg8861 sg9017 - -lemma sg25678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10289 - -lemma sg25679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10366 - -lemma sg25680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9785 - -lemma sg25681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10367 - -lemma sg25682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9816 - -lemma sg25683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9541 - -lemma sg25684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10368 - -lemma sg25685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10291 - -lemma sg25686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9817 - -lemma sg25687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9475 - -lemma sg25688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10369 - -lemma sg25689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10292 - -lemma sg25690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9818 - -lemma sg25691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10267 - -lemma sg25692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10293 - -lemma sg25693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9819 - -lemma sg25694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9788 - -lemma sg25695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10268 - -lemma sg25696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9088 - -lemma sg25697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10264 - -lemma sg25698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg8860 sg9089 - -lemma sg25699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9477 - -lemma sg25700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10370 - -lemma sg25701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10294 - -lemma sg25702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9820 - -lemma sg25703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9541 - -lemma sg25704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10371 - -lemma sg25705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10295 - -lemma sg25706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9821 - -lemma sg25707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10270 - -lemma sg25708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10372 - -lemma sg25709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10296 - -lemma sg25710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9822 - -lemma sg25711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9791 - -lemma sg25712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10271 - -lemma sg25713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8861 sg9020 - -lemma sg25714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9792 - -lemma sg25715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10272 - -lemma sg25716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9185 - -lemma sg25717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8861 sg9021 - -lemma sg25718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8350 sg10662 - -lemma sg25719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9541 - -lemma sg25720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10373 - -lemma sg25721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10297 - -lemma sg25722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9823 - -lemma sg25723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9793 - -lemma sg25724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10273 - -lemma sg25725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,3,3,3,3] := by - exact rowSquare_join (by decide) sg8861 sg9022 - -lemma sg25726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10298 - -lemma sg25727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9824 - -lemma sg25728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9794 - -lemma sg25729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10274 - -lemma sg25730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9478 - -lemma sg25731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,3,3,2] := by - exact rowSquare_join (by decide) sg8861 sg9023 - -lemma sg25732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8727 sg9479 - -lemma sg25733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9479 - -lemma sg25734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,4,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9024 - -lemma sg25735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,4,3,1] := by - exact rowSquare_join (by decide) sg8659 sg9697 - -lemma sg25736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10130 - -lemma sg25737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10108 - -lemma sg25738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8531 sg10102 - -lemma sg25739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10102 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 + +namespace OAI + +/-! Semigroup Nodes 62. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg25340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8770 sg9442 + +lemma sg25341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8770 sg9443 + +lemma sg25342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7254 sg11436 + +lemma sg25343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8870 sg8999 + +lemma sg25344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9529 + +lemma sg25345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8556 sg10095 + +lemma sg25346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8189 sg10858 + +lemma sg25347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14503 + +lemma sg25348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8770 sg9444 + +lemma sg25349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9530 + +lemma sg25350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8557 sg10095 + +lemma sg25351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8870 sg9000 + +lemma sg25352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8558 sg10095 + +lemma sg25353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8870 sg9001 + +lemma sg25354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg7795 sg11245 + +lemma sg25355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9530 + +lemma sg25356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8559 sg10095 + +lemma sg25357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg8870 sg9002 + +lemma sg25358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg8379 sg10610 + +lemma sg25359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7789 sg11254 + +lemma sg25360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,6,2,1,1,1] := by + exact rowSquare_join (by decide) sg8559 sg10096 + +lemma sg25361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [8,8,8,8,7,1,1,1,1] := by + exact rowSquare_join (by decide) sg7796 sg11246 + +lemma sg25362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8511 sg10167 + +lemma sg25363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10321 + +lemma sg25364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10245 + +lemma sg25365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10322 + +lemma sg25366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9469 + +lemma sg25367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10323 + +lemma sg25368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9763 + +lemma sg25369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10247 + +lemma sg25370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,4,4,4,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg8648 sg9764 + +lemma sg25371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8513 sg10167 + +lemma sg25372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10324 + +lemma sg25373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10248 + +lemma sg25374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10325 + +lemma sg25375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9762 + +lemma sg25376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10326 + +lemma sg25377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9767 + +lemma sg25378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10327 + +lemma sg25379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10250 + +lemma sg25380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9768 + +lemma sg25381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,4,4,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8423 sg10247 + +lemma sg25382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8514 sg10167 + +lemma sg25383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10328 + +lemma sg25384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10251 + +lemma sg25385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10329 + +lemma sg25386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9471 + +lemma sg25387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10330 + +lemma sg25388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9770 + +lemma sg25389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9532 + +lemma sg25390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10331 + +lemma sg25391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10253 + +lemma sg25392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9771 + +lemma sg25393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10254 + +lemma sg25394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9772 + +lemma sg25395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9175 + +lemma sg25396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,4,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg8860 sg9078 + +lemma sg25397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10255 + +lemma sg25398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10332 + +lemma sg25399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9473 + +lemma sg25400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10333 + +lemma sg25401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9774 + +lemma sg25402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8750 sg9447 + +lemma sg25403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10334 + +lemma sg25404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10257 + +lemma sg25405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9775 + +lemma sg25406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10335 + +lemma sg25407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10258 + +lemma sg25408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9776 + +lemma sg25409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9177 + +lemma sg25410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9178 + +lemma sg25411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9178 + +lemma sg25412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg8873 sg8984 + +lemma sg25413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8750 sg9448 + +lemma sg25414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10336 + +lemma sg25415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10259 + +lemma sg25416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9777 + +lemma sg25417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8494 sg10172 + +lemma sg25418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10337 + +lemma sg25419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10260 + +lemma sg25420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9778 + +lemma sg25421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8653 sg9696 + +lemma sg25422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10660 + +lemma sg25423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9779 + +lemma sg25424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9474 + +lemma sg25425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9474 + +lemma sg25426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,3,3] := by + exact rowSquare_join (by decide) sg8873 sg8985 + +lemma sg25427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8381 sg10601 + +lemma sg25428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,4,4,4,2] := by + exact rowSquare_join (by decide) sg8873 sg8986 + +lemma sg25429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8500 sg10168 + +lemma sg25430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10129 + +lemma sg25431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg8481 sg10174 + +lemma sg25432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8529 sg10099 + +lemma sg25433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10099 + +lemma sg25434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,3,3,3] := by + exact rowSquare_join (by decide) sg8873 sg8987 + +lemma sg25435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8529 sg10100 + +lemma sg25436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10100 + +lemma sg25437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg8561 sg10085 + +lemma sg25438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,4,3,2] := by + exact rowSquare_join (by decide) sg8873 sg8988 + +lemma sg25439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,4,4,1] := by + exact rowSquare_join (by decide) sg7248 sg11439 + +lemma sg25440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg8560 sg10086 + +lemma sg25441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,5,2,1,1] := by + exact rowSquare_join (by decide) sg8561 sg10086 + +lemma sg25442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,5,2,2] := by + exact rowSquare_join (by decide) sg8562 sg10086 + +lemma sg25443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,5,5,5,5,5,5,3,1] := by + exact rowSquare_join (by decide) sg6400 sg11737 + +lemma sg25444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8515 sg10167 + +lemma sg25445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10338 + +lemma sg25446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10261 + +lemma sg25447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10339 + +lemma sg25448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9766 + +lemma sg25449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10340 + +lemma sg25450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9781 + +lemma sg25451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9470 + +lemma sg25452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10341 + +lemma sg25453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10263 + +lemma sg25454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9782 + +lemma sg25455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10264 + +lemma sg25456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9783 + +lemma sg25457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10250 + +lemma sg25458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,4,4,4,4,4,4,4] := by + exact rowSquare_join (by decide) sg8804 sg9174 + +lemma sg25459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10342 + +lemma sg25460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10265 + +lemma sg25461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10343 + +lemma sg25462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9769 + +lemma sg25463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10344 + +lemma sg25464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9786 + +lemma sg25465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9534 + +lemma sg25466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10345 + +lemma sg25467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10267 + +lemma sg25468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9787 + +lemma sg25469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10346 + +lemma sg25470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10268 + +lemma sg25471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9788 + +lemma sg25472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10253 + +lemma sg25473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9772 + +lemma sg25474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10254 + +lemma sg25475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg8860 sg9079 + +lemma sg25476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9773 + +lemma sg25477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10347 + +lemma sg25478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9789 + +lemma sg25479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9473 + +lemma sg25480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10348 + +lemma sg25481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10270 + +lemma sg25482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9790 + +lemma sg25483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9534 + +lemma sg25484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10349 + +lemma sg25485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10271 + +lemma sg25486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9791 + +lemma sg25487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10257 + +lemma sg25488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10272 + +lemma sg25489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9792 + +lemma sg25490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9776 + +lemma sg25491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10258 + +lemma sg25492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg8861 sg9010 + +lemma sg25493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9178 + +lemma sg25494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg8861 sg9011 + +lemma sg25495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8753 sg9448 + +lemma sg25496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10350 + +lemma sg25497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10273 + +lemma sg25498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9793 + +lemma sg25499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10259 + +lemma sg25500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10351 + +lemma sg25501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10274 + +lemma sg25502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9794 + +lemma sg25503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9778 + +lemma sg25504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10260 + +lemma sg25505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,3,3,3] := by + exact rowSquare_join (by decide) sg8861 sg9013 + +lemma sg25506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9779 + +lemma sg25507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10660 + +lemma sg25508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9474 + +lemma sg25509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,4,3,2] := by + exact rowSquare_join (by decide) sg8861 sg9014 + +lemma sg25510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,4,4,4,1] := by + exact rowSquare_join (by decide) sg8876 sg8986 + +lemma sg25511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10130 + +lemma sg25512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg8484 sg10174 + +lemma sg25513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10129 + +lemma sg25514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10102 + +lemma sg25515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10099 + +lemma sg25516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,3,3,2] := by + exact rowSquare_join (by decide) sg8861 sg9015 + +lemma sg25517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8531 sg10100 + +lemma sg25518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10100 + +lemma sg25519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,4,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9016 + +lemma sg25520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,4,3,1] := by + exact rowSquare_join (by decide) sg8876 sg8988 + +lemma sg25521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg8563 sg10086 + +lemma sg25522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,5,5,5,5,5,2,1] := by + exact rowSquare_join (by decide) sg8564 sg10086 + +lemma sg25523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8524 sg10131 + +lemma sg25524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8838 sg9159 + +lemma sg25525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9481 + +lemma sg25526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8345 sg10668 + +lemma sg25527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9796 + +lemma sg25528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9536 + +lemma sg25529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10352 + +lemma sg25530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10669 + +lemma sg25531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9797 + +lemma sg25532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9471 + +lemma sg25533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10353 + +lemma sg25534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10275 + +lemma sg25535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9798 + +lemma sg25536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9187 + +lemma sg25537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10276 + +lemma sg25538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9799 + +lemma sg25539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9188 + +lemma sg25540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9188 + +lemma sg25541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9080 + +lemma sg25542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10254 + +lemma sg25543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg8860 sg9081 + +lemma sg25544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9537 + +lemma sg25545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10354 + +lemma sg25546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10672 + +lemma sg25547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9800 + +lemma sg25548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9536 + +lemma sg25549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10355 + +lemma sg25550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10277 + +lemma sg25551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9801 + +lemma sg25552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9190 + +lemma sg25553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10356 + +lemma sg25554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10278 + +lemma sg25555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9802 + +lemma sg25556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9191 + +lemma sg25557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9191 + +lemma sg25558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9082 + +lemma sg25559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9192 + +lemma sg25560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9192 + +lemma sg25561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10258 + +lemma sg25562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9083 + +lemma sg25563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8350 sg10657 + +lemma sg25564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9536 + +lemma sg25565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10357 + +lemma sg25566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10279 + +lemma sg25567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9803 + +lemma sg25568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9193 + +lemma sg25569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9193 + +lemma sg25570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9084 + +lemma sg25571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10280 + +lemma sg25572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9804 + +lemma sg25573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9488 + +lemma sg25574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9488 + +lemma sg25575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10260 + +lemma sg25576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9085 + +lemma sg25577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9539 + +lemma sg25578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8751 sg9463 + +lemma sg25579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9086 + +lemma sg25580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg8862 sg9014 + +lemma sg25581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8529 sg10104 + +lemma sg25582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10104 + +lemma sg25583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8526 sg10129 + +lemma sg25584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg8561 sg10094 + +lemma sg25585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9087 + +lemma sg25586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg8862 sg9015 + +lemma sg25587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg8535 sg10100 + +lemma sg25588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg8862 sg9016 + +lemma sg25589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg8566 sg10086 + +lemma sg25590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9537 + +lemma sg25591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10358 + +lemma sg25592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10677 + +lemma sg25593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9805 + +lemma sg25594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9194 + +lemma sg25595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9537 + +lemma sg25596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10359 + +lemma sg25597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10281 + +lemma sg25598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9806 + +lemma sg25599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9195 + +lemma sg25600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9195 + +lemma sg25601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8873 sg8999 + +lemma sg25602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10282 + +lemma sg25603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9807 + +lemma sg25604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9196 + +lemma sg25605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9196 + +lemma sg25606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8751 sg9464 + +lemma sg25607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8752 sg9464 + +lemma sg25608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8750 sg9465 + +lemma sg25609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8751 sg9465 + +lemma sg25610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8752 sg9465 + +lemma sg25611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10658 + +lemma sg25612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10360 + +lemma sg25613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10283 + +lemma sg25614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9808 + +lemma sg25615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9197 + +lemma sg25616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9197 + +lemma sg25617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8751 sg9466 + +lemma sg25618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg8873 sg9000 + +lemma sg25619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9492 + +lemma sg25620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9492 + +lemma sg25621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8872 sg9001 + +lemma sg25622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8751 sg9467 + +lemma sg25623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg8873 sg9001 + +lemma sg25624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10659 + +lemma sg25625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8568 sg10086 + +lemma sg25626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10660 + +lemma sg25627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8560 sg10098 + +lemma sg25628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg8561 sg10098 + +lemma sg25629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg8562 sg10098 + +lemma sg25630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg8538 sg10100 + +lemma sg25631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg8863 sg9015 + +lemma sg25632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg8863 sg9016 + +lemma sg25633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6919 sg11472 + +lemma sg25634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10284 + +lemma sg25635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10284 + +lemma sg25636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9809 + +lemma sg25637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10284 + +lemma sg25638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9809 + +lemma sg25639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10230 + +lemma sg25640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8723 sg9493 + +lemma sg25641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9493 + +lemma sg25642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9493 + +lemma sg25643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8872 sg9002 + +lemma sg25644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8751 sg9468 + +lemma sg25645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,3,2,2] := by + exact rowSquare_join (by decide) sg8873 sg9002 + +lemma sg25646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,3,3,3,1] := by + exact rowSquare_join (by decide) sg8881 sg8986 + +lemma sg25647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8471 sg10195 + +lemma sg25648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8472 sg10195 + +lemma sg25649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8473 sg10195 + +lemma sg25650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,2,2,2] := by + exact rowSquare_join (by decide) sg8474 sg10195 + +lemma sg25651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8540 sg10100 + +lemma sg25652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,3,2,1] := by + exact rowSquare_join (by decide) sg8430 sg10260 + +lemma sg25653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,4,4,1,1] := by + exact rowSquare_join (by decide) sg8351 sg10660 + +lemma sg25654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8500 sg10172 + +lemma sg25655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg8481 sg10182 + +lemma sg25656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,5,2,2,1] := by + exact rowSquare_join (by decide) sg8352 sg10659 + +lemma sg25657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,5,3,1,1] := by + exact rowSquare_join (by decide) sg8352 sg10660 + +lemma sg25658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg335 sg21316 + +lemma sg25659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,6,6,6,6,6,2,1,1] := by + exact rowSquare_join (by decide) sg331 sg21325 + +lemma sg25660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,3,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8516 sg10167 + +lemma sg25661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10361 + +lemma sg25662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10285 + +lemma sg25663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10362 + +lemma sg25664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9780 + +lemma sg25665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10363 + +lemma sg25666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9812 + +lemma sg25667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9475 + +lemma sg25668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10364 + +lemma sg25669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10287 + +lemma sg25670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9813 + +lemma sg25671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10365 + +lemma sg25672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10288 + +lemma sg25673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9814 + +lemma sg25674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10263 + +lemma sg25675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9783 + +lemma sg25676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10264 + +lemma sg25677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,4,4,4,4,4,4,3] := by + exact rowSquare_join (by decide) sg8861 sg9017 + +lemma sg25678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10289 + +lemma sg25679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10366 + +lemma sg25680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9785 + +lemma sg25681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10367 + +lemma sg25682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9816 + +lemma sg25683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9541 + +lemma sg25684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10368 + +lemma sg25685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10291 + +lemma sg25686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9817 + +lemma sg25687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9475 + +lemma sg25688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10369 + +lemma sg25689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10292 + +lemma sg25690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9818 + +lemma sg25691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10267 + +lemma sg25692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10293 + +lemma sg25693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9819 + +lemma sg25694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9788 + +lemma sg25695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10268 + +lemma sg25696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9088 + +lemma sg25697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10264 + +lemma sg25698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg8860 sg9089 + +lemma sg25699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9477 + +lemma sg25700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10370 + +lemma sg25701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10294 + +lemma sg25702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9820 + +lemma sg25703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9541 + +lemma sg25704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10371 + +lemma sg25705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10295 + +lemma sg25706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9821 + +lemma sg25707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10270 + +lemma sg25708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10372 + +lemma sg25709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10296 + +lemma sg25710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9822 + +lemma sg25711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9791 + +lemma sg25712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10271 + +lemma sg25713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8861 sg9020 + +lemma sg25714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9792 + +lemma sg25715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10272 + +lemma sg25716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9185 + +lemma sg25717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8861 sg9021 + +lemma sg25718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8350 sg10662 + +lemma sg25719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9541 + +lemma sg25720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10373 + +lemma sg25721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10297 + +lemma sg25722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9823 + +lemma sg25723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9793 + +lemma sg25724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10273 + +lemma sg25725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,3,3,3,3] := by + exact rowSquare_join (by decide) sg8861 sg9022 + +lemma sg25726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10298 + +lemma sg25727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9824 + +lemma sg25728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9794 + +lemma sg25729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10274 + +lemma sg25730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9478 + +lemma sg25731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,3,3,2] := by + exact rowSquare_join (by decide) sg8861 sg9023 + +lemma sg25732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8727 sg9479 + +lemma sg25733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9479 + +lemma sg25734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,4,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9024 + +lemma sg25735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,4,4,3,1] := by + exact rowSquare_join (by decide) sg8659 sg9697 + +lemma sg25736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10130 + +lemma sg25737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10108 + +lemma sg25738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8531 sg10102 + +lemma sg25739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10102 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes63.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes63.lean index 2cddb00c902b64ce26276bf567d9b451ff315fc5..e340bdd9341e7154b60903f35d04d951150ddbb4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes63.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes63.lean @@ -1,1223 +1,1223 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 63. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg25740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,3,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9025 - -lemma sg25741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,3,3,1] := by - exact rowSquare_join (by decide) sg8543 sg10099 - -lemma sg25742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg8179 sg10859 - -lemma sg25743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,4,2,1] := by - exact rowSquare_join (by decide) sg8543 sg10100 - -lemma sg25744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,5,1,1] := by - exact rowSquare_join (by decide) sg8571 sg10086 - -lemma sg25745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9795 - -lemma sg25746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8345 sg10690 - -lemma sg25747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9825 - -lemma sg25748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9543 - -lemma sg25749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10374 - -lemma sg25750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10691 - -lemma sg25751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9826 - -lemma sg25752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9476 - -lemma sg25753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10375 - -lemma sg25754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10299 - -lemma sg25755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9827 - -lemma sg25756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8347 sg10669 - -lemma sg25757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10376 - -lemma sg25758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10300 - -lemma sg25759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9828 - -lemma sg25760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9798 - -lemma sg25761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10275 - -lemma sg25762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9090 - -lemma sg25763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9799 - -lemma sg25764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10276 - -lemma sg25765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10268 - -lemma sg25766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9091 - -lemma sg25767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8862 sg9019 - -lemma sg25768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9543 - -lemma sg25769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10377 - -lemma sg25770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10301 - -lemma sg25771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9829 - -lemma sg25772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8347 sg10672 - -lemma sg25773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9543 - -lemma sg25774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10378 - -lemma sg25775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10302 - -lemma sg25776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9830 - -lemma sg25777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9801 - -lemma sg25778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10277 - -lemma sg25779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9092 - -lemma sg25780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10303 - -lemma sg25781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9831 - -lemma sg25782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9802 - -lemma sg25783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10278 - -lemma sg25784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10271 - -lemma sg25785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9093 - -lemma sg25786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9544 - -lemma sg25787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10272 - -lemma sg25788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9094 - -lemma sg25789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10663 - -lemma sg25790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10379 - -lemma sg25791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10304 - -lemma sg25792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9832 - -lemma sg25793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9803 - -lemma sg25794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10279 - -lemma sg25795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10273 - -lemma sg25796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9095 - -lemma sg25797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9804 - -lemma sg25798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10280 - -lemma sg25799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9545 - -lemma sg25800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10274 - -lemma sg25801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9096 - -lemma sg25802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg8862 sg9023 - -lemma sg25803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8731 sg9479 - -lemma sg25804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg8862 sg9024 - -lemma sg25805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8526 sg10130 - -lemma sg25806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10104 - -lemma sg25807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9097 - -lemma sg25808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg8535 sg10102 - -lemma sg25809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg8862 sg9025 - -lemma sg25810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,5,4,1,1] := by - exact rowSquare_join (by decide) sg8864 sg9016 - -lemma sg25811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2236 sg15514 - -lemma sg25812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3887 sg14500 - -lemma sg25813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3872 sg14508 - -lemma sg25814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5564 sg12618 - -lemma sg25815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5986 sg11829 - -lemma sg25816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9194 - -lemma sg25817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9243 - -lemma sg25818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8732 sg9477 - -lemma sg25819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3163 sg14802 - -lemma sg25820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6941 sg11468 - -lemma sg25821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5987 sg11829 - -lemma sg25822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9215 - -lemma sg25823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9194 - -lemma sg25824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9789 - -lemma sg25825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8733 sg9477 - -lemma sg25826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6917 sg11474 - -lemma sg25827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10380 - -lemma sg25828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9215 - -lemma sg25829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10709 - -lemma sg25830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10380 - -lemma sg25831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10305 - -lemma sg25832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9833 - -lemma sg25833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10305 - -lemma sg25834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9833 - -lemma sg25835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9805 - -lemma sg25836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10677 - -lemma sg25837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8861 sg9034 - -lemma sg25838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6942 sg11468 - -lemma sg25839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6918 sg11474 - -lemma sg25840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10381 - -lemma sg25841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9195 - -lemma sg25842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10710 - -lemma sg25843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10381 - -lemma sg25844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10306 - -lemma sg25845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10306 - -lemma sg25846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9834 - -lemma sg25847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10306 - -lemma sg25848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9834 - -lemma sg25849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9806 - -lemma sg25850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9806 - -lemma sg25851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10281 - -lemma sg25852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9195 - -lemma sg25853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8861 sg9035 - -lemma sg25854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9217 - -lemma sg25855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9807 - -lemma sg25856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9807 - -lemma sg25857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10282 - -lemma sg25858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9196 - -lemma sg25859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9196 - -lemma sg25860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9036 - -lemma sg25861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10664 - -lemma sg25862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10272 - -lemma sg25863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10665 - -lemma sg25864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6919 sg11474 - -lemma sg25865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10307 - -lemma sg25866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10307 - -lemma sg25867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9835 - -lemma sg25868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10307 - -lemma sg25869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9835 - -lemma sg25870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9218 - -lemma sg25871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9808 - -lemma sg25872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9808 - -lemma sg25873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10283 - -lemma sg25874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9197 - -lemma sg25875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9197 - -lemma sg25876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9037 - -lemma sg25877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10666 - -lemma sg25878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8726 sg9492 - -lemma sg25879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8727 sg9492 - -lemma sg25880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9492 - -lemma sg25881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9038 - -lemma sg25882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10274 - -lemma sg25883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10667 - -lemma sg25884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10272 - -lemma sg25885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8527 sg10130 - -lemma sg25886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg8563 sg10098 - -lemma sg25887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg8564 sg10098 - -lemma sg25888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg8863 sg9025 - -lemma sg25889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10284 - -lemma sg25890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8438 sg10230 - -lemma sg25891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9809 - -lemma sg25892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9809 - -lemma sg25893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10284 - -lemma sg25894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8726 sg9493 - -lemma sg25895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8727 sg9493 - -lemma sg25896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9493 - -lemma sg25897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,3,2,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9039 - -lemma sg25898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8754 sg9468 - -lemma sg25899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,3,3,2,1] := by - exact rowSquare_join (by decide) sg8876 sg9002 - -lemma sg25900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8477 sg10195 - -lemma sg25901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8478 sg10195 - -lemma sg25902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,4,2,2,1] := by - exact rowSquare_join (by decide) sg8479 sg10195 - -lemma sg25903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,4,3,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10274 - -lemma sg25904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg8484 sg10182 - -lemma sg25905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,5,2,1,1] := by - exact rowSquare_join (by decide) sg8352 sg10667 - -lemma sg25906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1321 sg20962 - -lemma sg25907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1724 sg18243 - -lemma sg25908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1825 sg17109 - -lemma sg25909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2191 sg15563 - -lemma sg25910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2224 sg15529 - -lemma sg25911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2228 sg15521 - -lemma sg25912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15572 - -lemma sg25913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3517 sg14680 - -lemma sg25914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg867 sg21141 - -lemma sg25915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg867 sg21142 - -lemma sg25916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg867 sg21143 - -lemma sg25917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1826 sg17109 - -lemma sg25918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2192 sg15563 - -lemma sg25919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2225 sg15529 - -lemma sg25920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2670 sg15016 - -lemma sg25921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2872 sg14852 - -lemma sg25922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5591 sg12609 - -lemma sg25923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3513 sg14683 - -lemma sg25924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5626 sg12603 - -lemma sg25925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg5591 sg12610 - -lemma sg25926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2226 sg15529 - -lemma sg25927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2671 sg15016 - -lemma sg25928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2224 sg15530 - -lemma sg25929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5261 sg12683 - -lemma sg25930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15573 - -lemma sg25931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9186 - -lemma sg25932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5624 sg12604 - -lemma sg25933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8729 sg9480 - -lemma sg25934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2177 sg15572 - -lemma sg25935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6937 sg11469 - -lemma sg25936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5241 sg12691 - -lemma sg25937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9187 - -lemma sg25938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8833 sg9166 - -lemma sg25939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8651 sg9795 - -lemma sg25940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6914 sg11475 - -lemma sg25941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9188 - -lemma sg25942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8877 sg8995 - -lemma sg25943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9689 - -lemma sg25944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9546 - -lemma sg25945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8480 sg10190 - -lemma sg25946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9690 - -lemma sg25947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8529 sg10116 - -lemma sg25948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10133 - -lemma sg25949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8530 sg10116 - -lemma sg25950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2193 sg15563 - -lemma sg25951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2227 sg15529 - -lemma sg25952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2672 sg15016 - -lemma sg25953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2869 sg14853 - -lemma sg25954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5250 sg12689 - -lemma sg25955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15021 - -lemma sg25956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9189 - -lemma sg25957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5625 sg12604 - -lemma sg25958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8732 sg9480 - -lemma sg25959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3873 sg14506 - -lemma sg25960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2671 sg15017 - -lemma sg25961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6938 sg11469 - -lemma sg25962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5965 sg11832 - -lemma sg25963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9219 - -lemma sg25964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9248 - -lemma sg25965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8652 sg9795 - -lemma sg25966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6939 sg11469 - -lemma sg25967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6915 sg11475 - -lemma sg25968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10275 - -lemma sg25969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9219 - -lemma sg25970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9796 - -lemma sg25971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9546 - -lemma sg25972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10276 - -lemma sg25973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9188 - -lemma sg25974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10711 - -lemma sg25975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8720 sg9547 - -lemma sg25976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9836 - -lemma sg25977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10134 - -lemma sg25978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9836 - -lemma sg25979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9219 - -lemma sg25980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3873 sg14507 - -lemma sg25981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6940 sg11469 - -lemma sg25982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6916 sg11475 - -lemma sg25983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9193 - -lemma sg25984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9249 - -lemma sg25985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8807 sg9186 - -lemma sg25986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9546 - -lemma sg25987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5990 sg11828 - -lemma sg25988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9220 - -lemma sg25989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9250 - -lemma sg25990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10712 - -lemma sg25991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8808 sg9186 - -lemma sg25992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9251 - -lemma sg25993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9837 - -lemma sg25994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10695 - -lemma sg25995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9837 - -lemma sg25996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9520 - -lemma sg25997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9520 - -lemma sg25998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9098 - -lemma sg25999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8255 sg10846 - -lemma sg26000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9220 - -lemma sg26001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9838 - -lemma sg26002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10135 - -lemma sg26003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9838 - -lemma sg26004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9220 - -lemma sg26005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9220 - -lemma sg26006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9220 - -lemma sg26007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10275 - -lemma sg26008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9099 - -lemma sg26009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9548 - -lemma sg26010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10276 - -lemma sg26011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9100 - -lemma sg26012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8862 sg9027 - -lemma sg26013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2236 sg15515 - -lemma sg26014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3874 sg14506 - -lemma sg26015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2870 sg14853 - -lemma sg26016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5548 sg12626 - -lemma sg26017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5989 sg11829 - -lemma sg26018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9194 - -lemma sg26019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9248 - -lemma sg26020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8732 sg9481 - -lemma sg26021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3873 sg14508 - -lemma sg26022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6941 sg11469 - -lemma sg26023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5967 sg11832 - -lemma sg26024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10277 - -lemma sg26025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9252 - -lemma sg26026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9796 - -lemma sg26027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8733 sg9481 - -lemma sg26028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6917 sg11475 - -lemma sg26029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10278 - -lemma sg26030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9250 - -lemma sg26031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10713 - -lemma sg26032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8721 sg9547 - -lemma sg26033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9251 - -lemma sg26034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9839 - -lemma sg26035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10696 - -lemma sg26036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9839 - -lemma sg26037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9522 - -lemma sg26038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9522 - -lemma sg26039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9101 - -lemma sg26040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6942 sg11469 - -lemma sg26041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6918 sg11475 - -lemma sg26042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10382 - -lemma sg26043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9253 - -lemma sg26044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10714 - -lemma sg26045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10382 - -lemma sg26046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9222 - -lemma sg26047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9221 - -lemma sg26048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9840 - -lemma sg26049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10697 - -lemma sg26050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9840 - -lemma sg26051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9221 - -lemma sg26052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9221 - -lemma sg26053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9221 - -lemma sg26054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10277 - -lemma sg26055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9102 - -lemma sg26056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9222 - -lemma sg26057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9222 - -lemma sg26058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9222 - -lemma sg26059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9222 - -lemma sg26060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9549 - -lemma sg26061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10278 - -lemma sg26062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9103 - -lemma sg26063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10670 - -lemma sg26064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10276 - -lemma sg26065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10671 - -lemma sg26066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6919 sg11475 - -lemma sg26067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9223 - -lemma sg26068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9255 - -lemma sg26069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9841 - -lemma sg26070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10698 - -lemma sg26071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9841 - -lemma sg26072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9223 - -lemma sg26073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9223 - -lemma sg26074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9223 - -lemma sg26075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9223 - -lemma sg26076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9550 - -lemma sg26077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10279 - -lemma sg26078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9104 - -lemma sg26079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg8862 sg9031 - -lemma sg26080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9804 - -lemma sg26081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9551 - -lemma sg26082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10280 - -lemma sg26083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9105 - -lemma sg26084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8731 sg9488 - -lemma sg26085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg8862 sg9032 - -lemma sg26086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,4,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10276 - -lemma sg26087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8534 sg10104 - -lemma sg26088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg8535 sg10104 - -lemma sg26089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg8862 sg9033 - -lemma sg26090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,5,3,1,1] := by - exact rowSquare_join (by decide) sg8879 sg8998 - -lemma sg26091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14506 - -lemma sg26092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3874 sg14508 - -lemma sg26093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5551 sg12626 - -lemma sg26094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5991 sg11829 - -lemma sg26095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8601 sg10081 - -lemma sg26096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9252 - -lemma sg26097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9189 - -lemma sg26098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8756 sg9459 - -lemma sg26099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5552 sg12626 - -lemma sg26100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5970 sg11832 - -lemma sg26101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10383 - -lemma sg26102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9256 - -lemma sg26103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10715 - -lemma sg26104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10383 - -lemma sg26105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10282 - -lemma sg26106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9224 - -lemma sg26107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9842 - -lemma sg26108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10699 - -lemma sg26109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9842 - -lemma sg26110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9224 - -lemma sg26111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9224 - -lemma sg26112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9224 - -lemma sg26113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8823 sg9178 - -lemma sg26114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9106 - -lemma sg26115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5971 sg11832 - -lemma sg26116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9225 - -lemma sg26117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9257 - -lemma sg26118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9843 - -lemma sg26119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10700 - -lemma sg26120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9843 - -lemma sg26121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9225 - -lemma sg26122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9225 - -lemma sg26123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9225 - -lemma sg26124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9225 - -lemma sg26125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9552 - -lemma sg26126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10281 - -lemma sg26127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9107 - -lemma sg26128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10673 - -lemma sg26129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9807 - -lemma sg26130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9553 - -lemma sg26131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10282 - -lemma sg26132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9108 - -lemma sg26133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10278 - -lemma sg26134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10674 - -lemma sg26135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8863 sg9030 - -lemma sg26136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9226 - -lemma sg26137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9226 - -lemma sg26138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9226 - -lemma sg26139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9226 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 63. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg25740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,3,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9025 + +lemma sg25741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,3,3,1] := by + exact rowSquare_join (by decide) sg8543 sg10099 + +lemma sg25742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg8179 sg10859 + +lemma sg25743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,4,2,1] := by + exact rowSquare_join (by decide) sg8543 sg10100 + +lemma sg25744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,5,5,5,5,5,1,1] := by + exact rowSquare_join (by decide) sg8571 sg10086 + +lemma sg25745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9795 + +lemma sg25746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8345 sg10690 + +lemma sg25747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9825 + +lemma sg25748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9543 + +lemma sg25749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10374 + +lemma sg25750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10691 + +lemma sg25751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9826 + +lemma sg25752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9476 + +lemma sg25753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10375 + +lemma sg25754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10299 + +lemma sg25755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9827 + +lemma sg25756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8347 sg10669 + +lemma sg25757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10376 + +lemma sg25758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10300 + +lemma sg25759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9828 + +lemma sg25760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9798 + +lemma sg25761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10275 + +lemma sg25762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9090 + +lemma sg25763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9799 + +lemma sg25764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10276 + +lemma sg25765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10268 + +lemma sg25766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9091 + +lemma sg25767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8862 sg9019 + +lemma sg25768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9543 + +lemma sg25769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10377 + +lemma sg25770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10301 + +lemma sg25771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9829 + +lemma sg25772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8347 sg10672 + +lemma sg25773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9543 + +lemma sg25774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10378 + +lemma sg25775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10302 + +lemma sg25776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9830 + +lemma sg25777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9801 + +lemma sg25778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10277 + +lemma sg25779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9092 + +lemma sg25780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10303 + +lemma sg25781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9831 + +lemma sg25782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9802 + +lemma sg25783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10278 + +lemma sg25784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10271 + +lemma sg25785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9093 + +lemma sg25786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9544 + +lemma sg25787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10272 + +lemma sg25788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9094 + +lemma sg25789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10663 + +lemma sg25790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10379 + +lemma sg25791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10304 + +lemma sg25792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9832 + +lemma sg25793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9803 + +lemma sg25794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10279 + +lemma sg25795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10273 + +lemma sg25796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9095 + +lemma sg25797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9804 + +lemma sg25798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10280 + +lemma sg25799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9545 + +lemma sg25800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10274 + +lemma sg25801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9096 + +lemma sg25802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg8862 sg9023 + +lemma sg25803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8731 sg9479 + +lemma sg25804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg8862 sg9024 + +lemma sg25805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8526 sg10130 + +lemma sg25806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10104 + +lemma sg25807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9097 + +lemma sg25808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg8535 sg10102 + +lemma sg25809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg8862 sg9025 + +lemma sg25810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,5,5,5,4,1,1] := by + exact rowSquare_join (by decide) sg8864 sg9016 + +lemma sg25811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2236 sg15514 + +lemma sg25812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3887 sg14500 + +lemma sg25813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3872 sg14508 + +lemma sg25814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5564 sg12618 + +lemma sg25815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5986 sg11829 + +lemma sg25816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9194 + +lemma sg25817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9243 + +lemma sg25818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8732 sg9477 + +lemma sg25819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3163 sg14802 + +lemma sg25820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6941 sg11468 + +lemma sg25821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5987 sg11829 + +lemma sg25822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9215 + +lemma sg25823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9194 + +lemma sg25824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9789 + +lemma sg25825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8733 sg9477 + +lemma sg25826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6917 sg11474 + +lemma sg25827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10380 + +lemma sg25828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9215 + +lemma sg25829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10709 + +lemma sg25830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10380 + +lemma sg25831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10305 + +lemma sg25832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9833 + +lemma sg25833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10305 + +lemma sg25834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9833 + +lemma sg25835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9805 + +lemma sg25836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10677 + +lemma sg25837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8861 sg9034 + +lemma sg25838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6942 sg11468 + +lemma sg25839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6918 sg11474 + +lemma sg25840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10381 + +lemma sg25841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9195 + +lemma sg25842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10710 + +lemma sg25843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10381 + +lemma sg25844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10306 + +lemma sg25845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10306 + +lemma sg25846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9834 + +lemma sg25847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10306 + +lemma sg25848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9834 + +lemma sg25849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9806 + +lemma sg25850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9806 + +lemma sg25851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10281 + +lemma sg25852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9195 + +lemma sg25853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8861 sg9035 + +lemma sg25854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9217 + +lemma sg25855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9807 + +lemma sg25856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9807 + +lemma sg25857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10282 + +lemma sg25858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9196 + +lemma sg25859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9196 + +lemma sg25860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9036 + +lemma sg25861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10664 + +lemma sg25862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10272 + +lemma sg25863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10665 + +lemma sg25864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6919 sg11474 + +lemma sg25865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10307 + +lemma sg25866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10307 + +lemma sg25867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9835 + +lemma sg25868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10307 + +lemma sg25869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9835 + +lemma sg25870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9218 + +lemma sg25871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9808 + +lemma sg25872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9808 + +lemma sg25873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10283 + +lemma sg25874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9197 + +lemma sg25875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9197 + +lemma sg25876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9037 + +lemma sg25877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10666 + +lemma sg25878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8726 sg9492 + +lemma sg25879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8727 sg9492 + +lemma sg25880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9492 + +lemma sg25881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9038 + +lemma sg25882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10274 + +lemma sg25883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10667 + +lemma sg25884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10272 + +lemma sg25885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8527 sg10130 + +lemma sg25886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg8563 sg10098 + +lemma sg25887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg8564 sg10098 + +lemma sg25888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg8863 sg9025 + +lemma sg25889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10284 + +lemma sg25890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8438 sg10230 + +lemma sg25891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9809 + +lemma sg25892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9809 + +lemma sg25893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10284 + +lemma sg25894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8726 sg9493 + +lemma sg25895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8727 sg9493 + +lemma sg25896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9493 + +lemma sg25897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,3,2,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9039 + +lemma sg25898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8754 sg9468 + +lemma sg25899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,3,3,2,1] := by + exact rowSquare_join (by decide) sg8876 sg9002 + +lemma sg25900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8477 sg10195 + +lemma sg25901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8478 sg10195 + +lemma sg25902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,4,2,2,1] := by + exact rowSquare_join (by decide) sg8479 sg10195 + +lemma sg25903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,4,3,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10274 + +lemma sg25904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg8484 sg10182 + +lemma sg25905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,6,6,6,5,2,1,1] := by + exact rowSquare_join (by decide) sg8352 sg10667 + +lemma sg25906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1321 sg20962 + +lemma sg25907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1724 sg18243 + +lemma sg25908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1825 sg17109 + +lemma sg25909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2191 sg15563 + +lemma sg25910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2224 sg15529 + +lemma sg25911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2228 sg15521 + +lemma sg25912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15572 + +lemma sg25913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3517 sg14680 + +lemma sg25914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg867 sg21141 + +lemma sg25915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg867 sg21142 + +lemma sg25916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg867 sg21143 + +lemma sg25917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1826 sg17109 + +lemma sg25918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2192 sg15563 + +lemma sg25919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2225 sg15529 + +lemma sg25920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2670 sg15016 + +lemma sg25921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2872 sg14852 + +lemma sg25922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5591 sg12609 + +lemma sg25923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3513 sg14683 + +lemma sg25924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5626 sg12603 + +lemma sg25925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg5591 sg12610 + +lemma sg25926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2226 sg15529 + +lemma sg25927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2671 sg15016 + +lemma sg25928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2224 sg15530 + +lemma sg25929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5261 sg12683 + +lemma sg25930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15573 + +lemma sg25931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9186 + +lemma sg25932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5624 sg12604 + +lemma sg25933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8729 sg9480 + +lemma sg25934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2177 sg15572 + +lemma sg25935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6937 sg11469 + +lemma sg25936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5241 sg12691 + +lemma sg25937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9187 + +lemma sg25938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8833 sg9166 + +lemma sg25939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8651 sg9795 + +lemma sg25940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6914 sg11475 + +lemma sg25941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9188 + +lemma sg25942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8877 sg8995 + +lemma sg25943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9689 + +lemma sg25944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9546 + +lemma sg25945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8480 sg10190 + +lemma sg25946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9690 + +lemma sg25947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8529 sg10116 + +lemma sg25948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10133 + +lemma sg25949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8530 sg10116 + +lemma sg25950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2193 sg15563 + +lemma sg25951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2227 sg15529 + +lemma sg25952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2672 sg15016 + +lemma sg25953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2869 sg14853 + +lemma sg25954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5250 sg12689 + +lemma sg25955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15021 + +lemma sg25956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9189 + +lemma sg25957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5625 sg12604 + +lemma sg25958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8732 sg9480 + +lemma sg25959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3873 sg14506 + +lemma sg25960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2671 sg15017 + +lemma sg25961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6938 sg11469 + +lemma sg25962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5965 sg11832 + +lemma sg25963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9219 + +lemma sg25964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9248 + +lemma sg25965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8652 sg9795 + +lemma sg25966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6939 sg11469 + +lemma sg25967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6915 sg11475 + +lemma sg25968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10275 + +lemma sg25969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9219 + +lemma sg25970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9796 + +lemma sg25971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9546 + +lemma sg25972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10276 + +lemma sg25973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9188 + +lemma sg25974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10711 + +lemma sg25975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8720 sg9547 + +lemma sg25976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9836 + +lemma sg25977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10134 + +lemma sg25978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9836 + +lemma sg25979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9219 + +lemma sg25980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3873 sg14507 + +lemma sg25981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6940 sg11469 + +lemma sg25982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6916 sg11475 + +lemma sg25983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9193 + +lemma sg25984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9249 + +lemma sg25985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8807 sg9186 + +lemma sg25986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9546 + +lemma sg25987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5990 sg11828 + +lemma sg25988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9220 + +lemma sg25989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9250 + +lemma sg25990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10712 + +lemma sg25991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8808 sg9186 + +lemma sg25992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9251 + +lemma sg25993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9837 + +lemma sg25994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10695 + +lemma sg25995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9837 + +lemma sg25996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9520 + +lemma sg25997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9520 + +lemma sg25998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9098 + +lemma sg25999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8255 sg10846 + +lemma sg26000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9220 + +lemma sg26001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9838 + +lemma sg26002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10135 + +lemma sg26003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9838 + +lemma sg26004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9220 + +lemma sg26005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9220 + +lemma sg26006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9220 + +lemma sg26007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10275 + +lemma sg26008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9099 + +lemma sg26009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9548 + +lemma sg26010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10276 + +lemma sg26011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9100 + +lemma sg26012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8862 sg9027 + +lemma sg26013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2236 sg15515 + +lemma sg26014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3874 sg14506 + +lemma sg26015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2870 sg14853 + +lemma sg26016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5548 sg12626 + +lemma sg26017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5989 sg11829 + +lemma sg26018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9194 + +lemma sg26019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9248 + +lemma sg26020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8732 sg9481 + +lemma sg26021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3873 sg14508 + +lemma sg26022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6941 sg11469 + +lemma sg26023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5967 sg11832 + +lemma sg26024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10277 + +lemma sg26025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9252 + +lemma sg26026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9796 + +lemma sg26027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8733 sg9481 + +lemma sg26028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6917 sg11475 + +lemma sg26029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10278 + +lemma sg26030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9250 + +lemma sg26031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10713 + +lemma sg26032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8721 sg9547 + +lemma sg26033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9251 + +lemma sg26034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9839 + +lemma sg26035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10696 + +lemma sg26036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9839 + +lemma sg26037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9522 + +lemma sg26038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9522 + +lemma sg26039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9101 + +lemma sg26040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6942 sg11469 + +lemma sg26041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6918 sg11475 + +lemma sg26042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10382 + +lemma sg26043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9253 + +lemma sg26044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10714 + +lemma sg26045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10382 + +lemma sg26046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9222 + +lemma sg26047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9221 + +lemma sg26048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9840 + +lemma sg26049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10697 + +lemma sg26050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9840 + +lemma sg26051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9221 + +lemma sg26052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9221 + +lemma sg26053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9221 + +lemma sg26054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10277 + +lemma sg26055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9102 + +lemma sg26056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9222 + +lemma sg26057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9222 + +lemma sg26058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9222 + +lemma sg26059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9222 + +lemma sg26060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9549 + +lemma sg26061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10278 + +lemma sg26062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9103 + +lemma sg26063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10670 + +lemma sg26064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10276 + +lemma sg26065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10671 + +lemma sg26066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6919 sg11475 + +lemma sg26067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9223 + +lemma sg26068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9255 + +lemma sg26069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9841 + +lemma sg26070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10698 + +lemma sg26071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9841 + +lemma sg26072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9223 + +lemma sg26073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9223 + +lemma sg26074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9223 + +lemma sg26075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9223 + +lemma sg26076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9550 + +lemma sg26077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10279 + +lemma sg26078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9104 + +lemma sg26079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg8862 sg9031 + +lemma sg26080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9804 + +lemma sg26081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9551 + +lemma sg26082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10280 + +lemma sg26083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9105 + +lemma sg26084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8731 sg9488 + +lemma sg26085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg8862 sg9032 + +lemma sg26086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,4,4,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10276 + +lemma sg26087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8534 sg10104 + +lemma sg26088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg8535 sg10104 + +lemma sg26089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg8862 sg9033 + +lemma sg26090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,5,5,5,3,1,1] := by + exact rowSquare_join (by decide) sg8879 sg8998 + +lemma sg26091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14506 + +lemma sg26092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3874 sg14508 + +lemma sg26093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5551 sg12626 + +lemma sg26094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5991 sg11829 + +lemma sg26095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8601 sg10081 + +lemma sg26096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9252 + +lemma sg26097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9189 + +lemma sg26098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8756 sg9459 + +lemma sg26099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5552 sg12626 + +lemma sg26100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5970 sg11832 + +lemma sg26101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10383 + +lemma sg26102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9256 + +lemma sg26103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10715 + +lemma sg26104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10383 + +lemma sg26105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10282 + +lemma sg26106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9224 + +lemma sg26107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9842 + +lemma sg26108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10699 + +lemma sg26109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9842 + +lemma sg26110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9224 + +lemma sg26111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9224 + +lemma sg26112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9224 + +lemma sg26113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8823 sg9178 + +lemma sg26114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9106 + +lemma sg26115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5971 sg11832 + +lemma sg26116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9225 + +lemma sg26117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9257 + +lemma sg26118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9843 + +lemma sg26119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10700 + +lemma sg26120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9843 + +lemma sg26121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9225 + +lemma sg26122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9225 + +lemma sg26123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9225 + +lemma sg26124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9225 + +lemma sg26125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9552 + +lemma sg26126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10281 + +lemma sg26127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9107 + +lemma sg26128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10673 + +lemma sg26129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9807 + +lemma sg26130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9553 + +lemma sg26131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10282 + +lemma sg26132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9108 + +lemma sg26133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10278 + +lemma sg26134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10674 + +lemma sg26135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8863 sg9030 + +lemma sg26136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9226 + +lemma sg26137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9226 + +lemma sg26138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9226 + +lemma sg26139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9226 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes64.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes64.lean index b241df61dc95a23e5eedd8d27fed47326ad5fbc8..124b6ab45825fc7e5a1c04cc655ae5fe6abd78be 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes64.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes64.lean @@ -1,1223 +1,1223 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 64. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg26140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9226 - -lemma sg26141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9808 - -lemma sg26142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9554 - -lemma sg26143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10283 - -lemma sg26144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9109 - -lemma sg26145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10279 - -lemma sg26146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10675 - -lemma sg26147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9551 - -lemma sg26148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10280 - -lemma sg26149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10676 - -lemma sg26150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,4,3,1,1] := by - exact rowSquare_join (by decide) sg8430 sg10278 - -lemma sg26151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg8538 sg10104 - -lemma sg26152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9260 - -lemma sg26153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9809 - -lemma sg26154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9555 - -lemma sg26155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10284 - -lemma sg26156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9110 - -lemma sg26157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8730 sg9493 - -lemma sg26158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8731 sg9493 - -lemma sg26159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,3,2,2,1] := by - exact rowSquare_join (by decide) sg8862 sg9039 - -lemma sg26160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10280 - -lemma sg26161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14508 - -lemma sg26162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5565 sg12618 - -lemma sg26163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5992 sg11829 - -lemma sg26164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10384 - -lemma sg26165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9256 - -lemma sg26166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9194 - -lemma sg26167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10384 - -lemma sg26168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5993 sg11829 - -lemma sg26169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9227 - -lemma sg26170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9257 - -lemma sg26171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9805 - -lemma sg26172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10136 - -lemma sg26173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8568 sg10095 - -lemma sg26174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9227 - -lemma sg26175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9227 - -lemma sg26176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9227 - -lemma sg26177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9227 - -lemma sg26178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8756 sg9465 - -lemma sg26179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8569 sg10095 - -lemma sg26180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8863 sg9034 - -lemma sg26181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10677 - -lemma sg26182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9228 - -lemma sg26183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9228 - -lemma sg26184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9228 - -lemma sg26185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9228 - -lemma sg26186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9228 - -lemma sg26187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9807 - -lemma sg26188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9552 - -lemma sg26189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8813 sg9195 - -lemma sg26190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8363 sg10635 - -lemma sg26191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10281 - -lemma sg26192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10678 - -lemma sg26193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9553 - -lemma sg26194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10282 - -lemma sg26195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10679 - -lemma sg26196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9260 - -lemma sg26197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9808 - -lemma sg26198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9552 - -lemma sg26199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8814 sg9195 - -lemma sg26200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg8881 sg8999 - -lemma sg26201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9554 - -lemma sg26202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10283 - -lemma sg26203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10680 - -lemma sg26204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10282 - -lemma sg26205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9809 - -lemma sg26206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9555 - -lemma sg26207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10284 - -lemma sg26208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,6,2,2,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10681 - -lemma sg26209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10283 - -lemma sg26210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9555 - -lemma sg26211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,7,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10284 - -lemma sg26212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,3,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10385 - -lemma sg26213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10308 - -lemma sg26214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10386 - -lemma sg26215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9811 - -lemma sg26216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10387 - -lemma sg26217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9846 - -lemma sg26218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9495 - -lemma sg26219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10388 - -lemma sg26220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10309 - -lemma sg26221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8419 sg10309 - -lemma sg26222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8736 sg9475 - -lemma sg26223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10389 - -lemma sg26224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10137 - -lemma sg26225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9847 - -lemma sg26226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10287 - -lemma sg26227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10310 - -lemma sg26228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8419 sg10310 - -lemma sg26229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9814 - -lemma sg26230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10288 - -lemma sg26231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,3,3] := by - exact rowSquare_join (by decide) sg8861 sg9041 - -lemma sg26232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9498 - -lemma sg26233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,4,2] := by - exact rowSquare_join (by decide) sg8861 sg9042 - -lemma sg26234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9815 - -lemma sg26235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10390 - -lemma sg26236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9848 - -lemma sg26237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9557 - -lemma sg26238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10391 - -lemma sg26239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10311 - -lemma sg26240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9849 - -lemma sg26241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9495 - -lemma sg26242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10392 - -lemma sg26243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10312 - -lemma sg26244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9850 - -lemma sg26245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10291 - -lemma sg26246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10393 - -lemma sg26247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10313 - -lemma sg26248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9851 - -lemma sg26249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9818 - -lemma sg26250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10292 - -lemma sg26251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9111 - -lemma sg26252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9819 - -lemma sg26253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10293 - -lemma sg26254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10288 - -lemma sg26255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9112 - -lemma sg26256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8862 sg9042 - -lemma sg26257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9557 - -lemma sg26258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10394 - -lemma sg26259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10138 - -lemma sg26260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9852 - -lemma sg26261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10294 - -lemma sg26262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9557 - -lemma sg26263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10395 - -lemma sg26264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10314 - -lemma sg26265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9853 - -lemma sg26266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9821 - -lemma sg26267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10295 - -lemma sg26268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8861 sg9046 - -lemma sg26269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10139 - -lemma sg26270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9854 - -lemma sg26271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9822 - -lemma sg26272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10296 - -lemma sg26273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9205 - -lemma sg26274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8861 sg9047 - -lemma sg26275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9206 - -lemma sg26276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9206 - -lemma sg26277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9048 - -lemma sg26278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10683 - -lemma sg26279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10396 - -lemma sg26280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10315 - -lemma sg26281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9855 - -lemma sg26282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9823 - -lemma sg26283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10297 - -lemma sg26284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9506 - -lemma sg26285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,3,3,3,2] := by - exact rowSquare_join (by decide) sg8861 sg9049 - -lemma sg26286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9824 - -lemma sg26287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10298 - -lemma sg26288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8727 sg9507 - -lemma sg26289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9507 - -lemma sg26290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,3,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9050 - -lemma sg26291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,3,3,1] := by - exact rowSquare_join (by decide) sg8659 sg9711 - -lemma sg26292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9712 - -lemma sg26293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,4,2,1] := by - exact rowSquare_join (by decide) sg8659 sg9712 - -lemma sg26294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8531 sg10108 - -lemma sg26295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10108 - -lemma sg26296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,5,2,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9051 - -lemma sg26297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg8179 sg10860 - -lemma sg26298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,5,3,2,1] := by - exact rowSquare_join (by decide) sg8543 sg10102 - -lemma sg26299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1319 sg20964 - -lemma sg26300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1722 sg18244 - -lemma sg26301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1825 sg17111 - -lemma sg26302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2191 sg15564 - -lemma sg26303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2224 sg15534 - -lemma sg26304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2677 sg15014 - -lemma sg26305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15574 - -lemma sg26306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg14681 - -lemma sg26307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg867 sg21145 - -lemma sg26308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg867 sg21146 - -lemma sg26309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg867 sg21147 - -lemma sg26310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1826 sg17111 - -lemma sg26311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2192 sg15564 - -lemma sg26312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2225 sg15534 - -lemma sg26313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2670 sg15018 - -lemma sg26314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2867 sg14855 - -lemma sg26315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5539 sg12628 - -lemma sg26316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg14682 - -lemma sg26317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10289 - -lemma sg26318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8369 sg10620 - -lemma sg26319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2226 sg15534 - -lemma sg26320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3871 sg14510 - -lemma sg26321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2224 sg15535 - -lemma sg26322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6944 sg11469 - -lemma sg26323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5587 sg12611 - -lemma sg26324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9200 - -lemma sg26325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8544 sg10101 - -lemma sg26326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8729 sg9499 - -lemma sg26327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2669 sg15020 - -lemma sg26328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6945 sg11469 - -lemma sg26329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5961 sg11834 - -lemma sg26330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9201 - -lemma sg26331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9182 - -lemma sg26332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8651 sg9815 - -lemma sg26333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6563 sg11541 - -lemma sg26334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10397 - -lemma sg26335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9183 - -lemma sg26336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9825 - -lemma sg26337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9558 - -lemma sg26338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9184 - -lemma sg26339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10716 - -lemma sg26340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10397 - -lemma sg26341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10140 - -lemma sg26342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9856 - -lemma sg26343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2193 sg15564 - -lemma sg26344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2227 sg15534 - -lemma sg26345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3872 sg14510 - -lemma sg26346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2869 sg14854 - -lemma sg26347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6946 sg11469 - -lemma sg26348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5539 sg12629 - -lemma sg26349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10290 - -lemma sg26350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8444 sg10233 - -lemma sg26351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8732 sg9499 - -lemma sg26352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3873 sg14509 - -lemma sg26353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2671 sg15019 - -lemma sg26354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6949 sg11468 - -lemma sg26355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5963 sg11834 - -lemma sg26356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10291 - -lemma sg26357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9264 - -lemma sg26358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8652 sg9815 - -lemma sg26359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6947 sg11469 - -lemma sg26360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6564 sg11541 - -lemma sg26361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10316 - -lemma sg26362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9201 - -lemma sg26363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9816 - -lemma sg26364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9558 - -lemma sg26365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10398 - -lemma sg26366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10316 - -lemma sg26367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10717 - -lemma sg26368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10398 - -lemma sg26369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9857 - -lemma sg26370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10316 - -lemma sg26371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9857 - -lemma sg26372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8347 sg10691 - -lemma sg26373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3766 sg14539 - -lemma sg26374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6948 sg11469 - -lemma sg26375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6565 sg11541 - -lemma sg26376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10299 - -lemma sg26377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9265 - -lemma sg26378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8807 sg9200 - -lemma sg26379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9558 - -lemma sg26380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5995 sg11828 - -lemma sg26381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10399 - -lemma sg26382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9266 - -lemma sg26383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10718 - -lemma sg26384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10399 - -lemma sg26385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9267 - -lemma sg26386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9858 - -lemma sg26387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10141 - -lemma sg26388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9858 - -lemma sg26389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9827 - -lemma sg26390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10299 - -lemma sg26391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9113 - -lemma sg26392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10317 - -lemma sg26393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10317 - -lemma sg26394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9859 - -lemma sg26395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10317 - -lemma sg26396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9859 - -lemma sg26397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9828 - -lemma sg26398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9828 - -lemma sg26399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10300 - -lemma sg26400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10292 - -lemma sg26401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9114 - -lemma sg26402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9559 - -lemma sg26403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10293 - -lemma sg26404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9115 - -lemma sg26405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8862 sg9044 - -lemma sg26406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2236 sg15517 - -lemma sg26407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3874 sg14509 - -lemma sg26408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2870 sg14854 - -lemma sg26409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6950 sg11468 - -lemma sg26410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5994 sg11829 - -lemma sg26411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10294 - -lemma sg26412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9264 - -lemma sg26413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8732 sg9500 - -lemma sg26414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3767 sg14539 - -lemma sg26415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6951 sg11468 - -lemma sg26416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5967 sg11833 - -lemma sg26417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10301 - -lemma sg26418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9268 - -lemma sg26419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9816 - -lemma sg26420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8733 sg9500 - -lemma sg26421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6566 sg11541 - -lemma sg26422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10400 - -lemma sg26423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9266 - -lemma sg26424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10719 - -lemma sg26425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10400 - -lemma sg26426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10318 - -lemma sg26427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9860 - -lemma sg26428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10318 - -lemma sg26429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9860 - -lemma sg26430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9829 - -lemma sg26431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10301 - -lemma sg26432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9116 - -lemma sg26433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6952 sg11468 - -lemma sg26434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6567 sg11541 - -lemma sg26435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10401 - -lemma sg26436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9269 - -lemma sg26437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10720 - -lemma sg26438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10401 - -lemma sg26439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10319 - -lemma sg26440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10319 - -lemma sg26441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9861 - -lemma sg26442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10319 - -lemma sg26443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9861 - -lemma sg26444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9830 - -lemma sg26445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9830 - -lemma sg26446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10302 - -lemma sg26447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10295 - -lemma sg26448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9117 - -lemma sg26449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10618 - -lemma sg26450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9831 - -lemma sg26451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9831 - -lemma sg26452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10303 - -lemma sg26453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9560 - -lemma sg26454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10296 - -lemma sg26455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9118 - -lemma sg26456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10684 - -lemma sg26457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10293 - -lemma sg26458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10685 - -lemma sg26459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6568 sg11541 - -lemma sg26460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10304 - -lemma sg26461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9271 - -lemma sg26462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9862 - -lemma sg26463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10142 - -lemma sg26464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9862 - -lemma sg26465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8438 sg10242 - -lemma sg26466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9832 - -lemma sg26467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9832 - -lemma sg26468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10304 - -lemma sg26469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9561 - -lemma sg26470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10297 - -lemma sg26471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9119 - -lemma sg26472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,3,3,1] := by - exact rowSquare_join (by decide) sg8862 sg9049 - -lemma sg26473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9824 - -lemma sg26474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9562 - -lemma sg26475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10298 - -lemma sg26476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9120 - -lemma sg26477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8731 sg9507 - -lemma sg26478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,4,3,2,1] := by - exact rowSquare_join (by decide) sg8862 sg9050 - -lemma sg26479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8534 sg10108 - -lemma sg26480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg8535 sg10108 - -lemma sg26481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,5,2,2,1] := by - exact rowSquare_join (by decide) sg8862 sg9051 - -lemma sg26482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14509 - -lemma sg26483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3768 sg14539 - -lemma sg26484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6953 sg11468 - -lemma sg26485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5996 sg11829 - -lemma sg26486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9215 - -lemma sg26487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9268 - -lemma sg26488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9203 - -lemma sg26489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9477 - -lemma sg26490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6954 sg11468 - -lemma sg26491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5970 sg11833 - -lemma sg26492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10402 - -lemma sg26493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9215 - -lemma sg26494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10721 - -lemma sg26495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10402 - -lemma sg26496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9217 - -lemma sg26497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9270 - -lemma sg26498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9863 - -lemma sg26499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10143 - -lemma sg26500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9863 - -lemma sg26501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9833 - -lemma sg26502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9833 - -lemma sg26503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10305 - -lemma sg26504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9215 - -lemma sg26505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8861 sg9060 - -lemma sg26506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5971 sg11833 - -lemma sg26507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10320 - -lemma sg26508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10320 - -lemma sg26509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9864 - -lemma sg26510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10320 - -lemma sg26511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9864 - -lemma sg26512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9217 - -lemma sg26513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9834 - -lemma sg26514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9834 - -lemma sg26515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10306 - -lemma sg26516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9216 - -lemma sg26517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9216 - -lemma sg26518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9061 - -lemma sg26519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10686 - -lemma sg26520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9217 - -lemma sg26521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9217 - -lemma sg26522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9217 - -lemma sg26523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9062 - -lemma sg26524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10296 - -lemma sg26525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10687 - -lemma sg26526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10307 - -lemma sg26527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9218 - -lemma sg26528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9835 - -lemma sg26529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9835 - -lemma sg26530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10307 - -lemma sg26531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9218 - -lemma sg26532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9218 - -lemma sg26533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9218 - -lemma sg26534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9063 - -lemma sg26535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10297 - -lemma sg26536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10688 - -lemma sg26537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9562 - -lemma sg26538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10298 - -lemma sg26539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,4,2,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10689 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 64. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg26140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9226 + +lemma sg26141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9808 + +lemma sg26142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9554 + +lemma sg26143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10283 + +lemma sg26144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9109 + +lemma sg26145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10279 + +lemma sg26146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10675 + +lemma sg26147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9551 + +lemma sg26148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10280 + +lemma sg26149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10676 + +lemma sg26150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,4,3,1,1] := by + exact rowSquare_join (by decide) sg8430 sg10278 + +lemma sg26151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg8538 sg10104 + +lemma sg26152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9260 + +lemma sg26153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9809 + +lemma sg26154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9555 + +lemma sg26155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10284 + +lemma sg26156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9110 + +lemma sg26157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8730 sg9493 + +lemma sg26158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8731 sg9493 + +lemma sg26159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,3,2,2,1] := by + exact rowSquare_join (by decide) sg8862 sg9039 + +lemma sg26160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,6,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10280 + +lemma sg26161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14508 + +lemma sg26162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5565 sg12618 + +lemma sg26163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5992 sg11829 + +lemma sg26164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10384 + +lemma sg26165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9256 + +lemma sg26166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9194 + +lemma sg26167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10384 + +lemma sg26168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5993 sg11829 + +lemma sg26169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9227 + +lemma sg26170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9257 + +lemma sg26171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9805 + +lemma sg26172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10136 + +lemma sg26173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8568 sg10095 + +lemma sg26174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9227 + +lemma sg26175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9227 + +lemma sg26176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9227 + +lemma sg26177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9227 + +lemma sg26178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8756 sg9465 + +lemma sg26179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8569 sg10095 + +lemma sg26180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8863 sg9034 + +lemma sg26181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10677 + +lemma sg26182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9228 + +lemma sg26183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9228 + +lemma sg26184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9228 + +lemma sg26185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9228 + +lemma sg26186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9228 + +lemma sg26187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9807 + +lemma sg26188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9552 + +lemma sg26189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8813 sg9195 + +lemma sg26190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8363 sg10635 + +lemma sg26191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10281 + +lemma sg26192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10678 + +lemma sg26193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9553 + +lemma sg26194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10282 + +lemma sg26195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10679 + +lemma sg26196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9260 + +lemma sg26197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9808 + +lemma sg26198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9552 + +lemma sg26199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8814 sg9195 + +lemma sg26200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg8881 sg8999 + +lemma sg26201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9554 + +lemma sg26202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10283 + +lemma sg26203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10680 + +lemma sg26204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10282 + +lemma sg26205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9809 + +lemma sg26206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9555 + +lemma sg26207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10284 + +lemma sg26208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,6,2,2,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10681 + +lemma sg26209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10283 + +lemma sg26210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9555 + +lemma sg26211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,7,7,7,7,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10284 + +lemma sg26212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,3,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10385 + +lemma sg26213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10308 + +lemma sg26214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10386 + +lemma sg26215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9811 + +lemma sg26216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10387 + +lemma sg26217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9846 + +lemma sg26218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9495 + +lemma sg26219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10388 + +lemma sg26220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10309 + +lemma sg26221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8419 sg10309 + +lemma sg26222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8736 sg9475 + +lemma sg26223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10389 + +lemma sg26224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10137 + +lemma sg26225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9847 + +lemma sg26226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10287 + +lemma sg26227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10310 + +lemma sg26228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8419 sg10310 + +lemma sg26229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9814 + +lemma sg26230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10288 + +lemma sg26231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,3,3] := by + exact rowSquare_join (by decide) sg8861 sg9041 + +lemma sg26232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9498 + +lemma sg26233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,4,4,4,4,4,4,2] := by + exact rowSquare_join (by decide) sg8861 sg9042 + +lemma sg26234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9815 + +lemma sg26235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10390 + +lemma sg26236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9848 + +lemma sg26237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9557 + +lemma sg26238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10391 + +lemma sg26239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10311 + +lemma sg26240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9849 + +lemma sg26241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9495 + +lemma sg26242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10392 + +lemma sg26243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10312 + +lemma sg26244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9850 + +lemma sg26245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10291 + +lemma sg26246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10393 + +lemma sg26247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10313 + +lemma sg26248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9851 + +lemma sg26249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9818 + +lemma sg26250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10292 + +lemma sg26251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9111 + +lemma sg26252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9819 + +lemma sg26253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10293 + +lemma sg26254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10288 + +lemma sg26255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9112 + +lemma sg26256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8862 sg9042 + +lemma sg26257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9557 + +lemma sg26258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10394 + +lemma sg26259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10138 + +lemma sg26260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9852 + +lemma sg26261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10294 + +lemma sg26262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9557 + +lemma sg26263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10395 + +lemma sg26264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10314 + +lemma sg26265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9853 + +lemma sg26266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9821 + +lemma sg26267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10295 + +lemma sg26268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8861 sg9046 + +lemma sg26269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10139 + +lemma sg26270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9854 + +lemma sg26271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9822 + +lemma sg26272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10296 + +lemma sg26273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9205 + +lemma sg26274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8861 sg9047 + +lemma sg26275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9206 + +lemma sg26276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9206 + +lemma sg26277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9048 + +lemma sg26278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10683 + +lemma sg26279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10396 + +lemma sg26280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10315 + +lemma sg26281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9855 + +lemma sg26282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9823 + +lemma sg26283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10297 + +lemma sg26284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9506 + +lemma sg26285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,3,3,3,2] := by + exact rowSquare_join (by decide) sg8861 sg9049 + +lemma sg26286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9824 + +lemma sg26287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10298 + +lemma sg26288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8727 sg9507 + +lemma sg26289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9507 + +lemma sg26290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,3,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9050 + +lemma sg26291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,3,3,1] := by + exact rowSquare_join (by decide) sg8659 sg9711 + +lemma sg26292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9712 + +lemma sg26293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,4,4,2,1] := by + exact rowSquare_join (by decide) sg8659 sg9712 + +lemma sg26294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8531 sg10108 + +lemma sg26295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10108 + +lemma sg26296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,5,2,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9051 + +lemma sg26297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg8179 sg10860 + +lemma sg26298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,5,5,5,5,3,2,1] := by + exact rowSquare_join (by decide) sg8543 sg10102 + +lemma sg26299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1319 sg20964 + +lemma sg26300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1722 sg18244 + +lemma sg26301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1825 sg17111 + +lemma sg26302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2191 sg15564 + +lemma sg26303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2224 sg15534 + +lemma sg26304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2677 sg15014 + +lemma sg26305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15574 + +lemma sg26306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg14681 + +lemma sg26307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg867 sg21145 + +lemma sg26308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg867 sg21146 + +lemma sg26309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg867 sg21147 + +lemma sg26310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1826 sg17111 + +lemma sg26311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2192 sg15564 + +lemma sg26312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2225 sg15534 + +lemma sg26313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2670 sg15018 + +lemma sg26314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2867 sg14855 + +lemma sg26315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5539 sg12628 + +lemma sg26316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg14682 + +lemma sg26317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10289 + +lemma sg26318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8369 sg10620 + +lemma sg26319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2226 sg15534 + +lemma sg26320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3871 sg14510 + +lemma sg26321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2224 sg15535 + +lemma sg26322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6944 sg11469 + +lemma sg26323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5587 sg12611 + +lemma sg26324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9200 + +lemma sg26325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8544 sg10101 + +lemma sg26326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8729 sg9499 + +lemma sg26327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2669 sg15020 + +lemma sg26328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6945 sg11469 + +lemma sg26329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5961 sg11834 + +lemma sg26330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9201 + +lemma sg26331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9182 + +lemma sg26332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8651 sg9815 + +lemma sg26333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6563 sg11541 + +lemma sg26334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10397 + +lemma sg26335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9183 + +lemma sg26336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9825 + +lemma sg26337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9558 + +lemma sg26338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9184 + +lemma sg26339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10716 + +lemma sg26340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10397 + +lemma sg26341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10140 + +lemma sg26342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9856 + +lemma sg26343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2193 sg15564 + +lemma sg26344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2227 sg15534 + +lemma sg26345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3872 sg14510 + +lemma sg26346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2869 sg14854 + +lemma sg26347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6946 sg11469 + +lemma sg26348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5539 sg12629 + +lemma sg26349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10290 + +lemma sg26350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8444 sg10233 + +lemma sg26351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8732 sg9499 + +lemma sg26352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3873 sg14509 + +lemma sg26353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2671 sg15019 + +lemma sg26354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6949 sg11468 + +lemma sg26355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5963 sg11834 + +lemma sg26356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10291 + +lemma sg26357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9264 + +lemma sg26358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8652 sg9815 + +lemma sg26359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6947 sg11469 + +lemma sg26360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6564 sg11541 + +lemma sg26361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10316 + +lemma sg26362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9201 + +lemma sg26363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9816 + +lemma sg26364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9558 + +lemma sg26365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10398 + +lemma sg26366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10316 + +lemma sg26367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10717 + +lemma sg26368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10398 + +lemma sg26369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9857 + +lemma sg26370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10316 + +lemma sg26371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9857 + +lemma sg26372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8347 sg10691 + +lemma sg26373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3766 sg14539 + +lemma sg26374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6948 sg11469 + +lemma sg26375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6565 sg11541 + +lemma sg26376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10299 + +lemma sg26377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9265 + +lemma sg26378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8807 sg9200 + +lemma sg26379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9558 + +lemma sg26380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5995 sg11828 + +lemma sg26381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10399 + +lemma sg26382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9266 + +lemma sg26383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10718 + +lemma sg26384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10399 + +lemma sg26385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9267 + +lemma sg26386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9858 + +lemma sg26387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10141 + +lemma sg26388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9858 + +lemma sg26389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9827 + +lemma sg26390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10299 + +lemma sg26391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9113 + +lemma sg26392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10317 + +lemma sg26393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10317 + +lemma sg26394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9859 + +lemma sg26395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10317 + +lemma sg26396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9859 + +lemma sg26397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9828 + +lemma sg26398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9828 + +lemma sg26399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10300 + +lemma sg26400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10292 + +lemma sg26401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9114 + +lemma sg26402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9559 + +lemma sg26403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10293 + +lemma sg26404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9115 + +lemma sg26405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8862 sg9044 + +lemma sg26406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2236 sg15517 + +lemma sg26407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3874 sg14509 + +lemma sg26408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2870 sg14854 + +lemma sg26409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6950 sg11468 + +lemma sg26410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5994 sg11829 + +lemma sg26411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10294 + +lemma sg26412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9264 + +lemma sg26413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8732 sg9500 + +lemma sg26414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3767 sg14539 + +lemma sg26415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6951 sg11468 + +lemma sg26416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5967 sg11833 + +lemma sg26417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10301 + +lemma sg26418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9268 + +lemma sg26419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9816 + +lemma sg26420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8733 sg9500 + +lemma sg26421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6566 sg11541 + +lemma sg26422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10400 + +lemma sg26423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9266 + +lemma sg26424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10719 + +lemma sg26425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10400 + +lemma sg26426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10318 + +lemma sg26427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9860 + +lemma sg26428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10318 + +lemma sg26429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9860 + +lemma sg26430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9829 + +lemma sg26431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10301 + +lemma sg26432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9116 + +lemma sg26433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6952 sg11468 + +lemma sg26434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6567 sg11541 + +lemma sg26435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10401 + +lemma sg26436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9269 + +lemma sg26437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10720 + +lemma sg26438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10401 + +lemma sg26439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10319 + +lemma sg26440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10319 + +lemma sg26441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9861 + +lemma sg26442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10319 + +lemma sg26443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9861 + +lemma sg26444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9830 + +lemma sg26445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9830 + +lemma sg26446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10302 + +lemma sg26447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10295 + +lemma sg26448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9117 + +lemma sg26449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10618 + +lemma sg26450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9831 + +lemma sg26451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9831 + +lemma sg26452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10303 + +lemma sg26453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9560 + +lemma sg26454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10296 + +lemma sg26455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9118 + +lemma sg26456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10684 + +lemma sg26457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10293 + +lemma sg26458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10685 + +lemma sg26459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6568 sg11541 + +lemma sg26460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10304 + +lemma sg26461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9271 + +lemma sg26462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9862 + +lemma sg26463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10142 + +lemma sg26464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9862 + +lemma sg26465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8438 sg10242 + +lemma sg26466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9832 + +lemma sg26467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9832 + +lemma sg26468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10304 + +lemma sg26469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9561 + +lemma sg26470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10297 + +lemma sg26471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9119 + +lemma sg26472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,3,3,3,1] := by + exact rowSquare_join (by decide) sg8862 sg9049 + +lemma sg26473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9824 + +lemma sg26474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9562 + +lemma sg26475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10298 + +lemma sg26476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9120 + +lemma sg26477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8731 sg9507 + +lemma sg26478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,4,3,2,1] := by + exact rowSquare_join (by decide) sg8862 sg9050 + +lemma sg26479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8534 sg10108 + +lemma sg26480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg8535 sg10108 + +lemma sg26481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,5,5,5,2,2,1] := by + exact rowSquare_join (by decide) sg8862 sg9051 + +lemma sg26482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14509 + +lemma sg26483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3768 sg14539 + +lemma sg26484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6953 sg11468 + +lemma sg26485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5996 sg11829 + +lemma sg26486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9215 + +lemma sg26487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9268 + +lemma sg26488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9203 + +lemma sg26489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9477 + +lemma sg26490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6954 sg11468 + +lemma sg26491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5970 sg11833 + +lemma sg26492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10402 + +lemma sg26493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9215 + +lemma sg26494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10721 + +lemma sg26495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10402 + +lemma sg26496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9217 + +lemma sg26497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9270 + +lemma sg26498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9863 + +lemma sg26499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10143 + +lemma sg26500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9863 + +lemma sg26501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9833 + +lemma sg26502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9833 + +lemma sg26503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10305 + +lemma sg26504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9215 + +lemma sg26505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8861 sg9060 + +lemma sg26506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5971 sg11833 + +lemma sg26507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10320 + +lemma sg26508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10320 + +lemma sg26509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9864 + +lemma sg26510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10320 + +lemma sg26511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9864 + +lemma sg26512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9217 + +lemma sg26513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9834 + +lemma sg26514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9834 + +lemma sg26515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10306 + +lemma sg26516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9216 + +lemma sg26517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9216 + +lemma sg26518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9061 + +lemma sg26519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10686 + +lemma sg26520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9217 + +lemma sg26521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9217 + +lemma sg26522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9217 + +lemma sg26523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9062 + +lemma sg26524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10296 + +lemma sg26525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10687 + +lemma sg26526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10307 + +lemma sg26527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9218 + +lemma sg26528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9835 + +lemma sg26529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9835 + +lemma sg26530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10307 + +lemma sg26531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9218 + +lemma sg26532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9218 + +lemma sg26533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9218 + +lemma sg26534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9063 + +lemma sg26535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10297 + +lemma sg26536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10688 + +lemma sg26537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9562 + +lemma sg26538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10298 + +lemma sg26539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,4,2,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10689 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes65.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes65.lean index 64fae308e684711088be980b0e8c4435963cba59..11958dbb1d7beba6bbe67769494a26f5090ac54b 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes65.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes65.lean @@ -1,1224 +1,1224 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 65. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg26540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg8538 sg10108 - -lemma sg26541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8385 sg10602 - -lemma sg26542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9727 - -lemma sg26543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8531 sg10115 - -lemma sg26544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10115 - -lemma sg26545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,2,2,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9064 - -lemma sg26546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9493 - -lemma sg26547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9727 - -lemma sg26548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10298 - -lemma sg26549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1723 sg18244 - -lemma sg26550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1830 sg17109 - -lemma sg26551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2197 sg15563 - -lemma sg26552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2234 sg15520 - -lemma sg26553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2678 sg15014 - -lemma sg26554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2868 sg14855 - -lemma sg26555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3518 sg14680 - -lemma sg26556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg14683 - -lemma sg26557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5628 sg12603 - -lemma sg26558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg971 sg21120 - -lemma sg26559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2198 sg15563 - -lemma sg26560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2235 sg15520 - -lemma sg26561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2679 sg15014 - -lemma sg26562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2869 sg14855 - -lemma sg26563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5250 sg12690 - -lemma sg26564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15023 - -lemma sg26565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9207 - -lemma sg26566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1296 sg20996 - -lemma sg26567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8666 sg9701 - -lemma sg26568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3873 sg14510 - -lemma sg26569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2671 sg15020 - -lemma sg26570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6949 sg11469 - -lemma sg26571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5965 sg11834 - -lemma sg26572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9208 - -lemma sg26573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9272 - -lemma sg26574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8729 sg9508 - -lemma sg26575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5547 sg12628 - -lemma sg26576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5966 sg11834 - -lemma sg26577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9209 - -lemma sg26578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9187 - -lemma sg26579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9825 - -lemma sg26580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9508 - -lemma sg26581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9210 - -lemma sg26582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9188 - -lemma sg26583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10722 - -lemma sg26584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8720 sg9563 - -lemma sg26585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9865 - -lemma sg26586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10144 - -lemma sg26587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9865 - -lemma sg26588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8847 sg9160 - -lemma sg26589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2236 sg15520 - -lemma sg26590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3874 sg14510 - -lemma sg26591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2870 sg14855 - -lemma sg26592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6950 sg11469 - -lemma sg26593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5997 sg11829 - -lemma sg26594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9219 - -lemma sg26595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9272 - -lemma sg26596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8732 sg9508 - -lemma sg26597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3766 sg14540 - -lemma sg26598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6951 sg11469 - -lemma sg26599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5967 sg11834 - -lemma sg26600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10299 - -lemma sg26601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9273 - -lemma sg26602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9825 - -lemma sg26603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8733 sg9508 - -lemma sg26604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5968 sg11834 - -lemma sg26605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10300 - -lemma sg26606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9209 - -lemma sg26607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10723 - -lemma sg26608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8721 sg9563 - -lemma sg26609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9210 - -lemma sg26610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9866 - -lemma sg26611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10145 - -lemma sg26612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9866 - -lemma sg26613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9836 - -lemma sg26614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8803 sg9219 - -lemma sg26615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9121 - -lemma sg26616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6952 sg11469 - -lemma sg26617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5969 sg11834 - -lemma sg26618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9214 - -lemma sg26619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9274 - -lemma sg26620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10724 - -lemma sg26621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8722 sg9563 - -lemma sg26622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8443 sg10242 - -lemma sg26623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9275 - -lemma sg26624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9867 - -lemma sg26625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10146 - -lemma sg26626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9867 - -lemma sg26627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9837 - -lemma sg26628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9837 - -lemma sg26629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10695 - -lemma sg26630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10299 - -lemma sg26631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9122 - -lemma sg26632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10620 - -lemma sg26633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9838 - -lemma sg26634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9838 - -lemma sg26635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8818 sg9187 - -lemma sg26636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9564 - -lemma sg26637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10300 - -lemma sg26638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9123 - -lemma sg26639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8862 sg9053 - -lemma sg26640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9210 - -lemma sg26641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8862 sg9054 - -lemma sg26642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14510 - -lemma sg26643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3767 sg14540 - -lemma sg26644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6953 sg11469 - -lemma sg26645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5998 sg11829 - -lemma sg26646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10301 - -lemma sg26647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9273 - -lemma sg26648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9207 - -lemma sg26649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9481 - -lemma sg26650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6954 sg11469 - -lemma sg26651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5970 sg11834 - -lemma sg26652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10302 - -lemma sg26653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9276 - -lemma sg26654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10725 - -lemma sg26655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8812 sg9207 - -lemma sg26656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10303 - -lemma sg26657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9275 - -lemma sg26658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9868 - -lemma sg26659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10147 - -lemma sg26660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9868 - -lemma sg26661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9839 - -lemma sg26662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9839 - -lemma sg26663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10696 - -lemma sg26664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10301 - -lemma sg26665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9124 - -lemma sg26666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5971 sg11834 - -lemma sg26667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10304 - -lemma sg26668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9277 - -lemma sg26669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9869 - -lemma sg26670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10148 - -lemma sg26671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9869 - -lemma sg26672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9278 - -lemma sg26673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9840 - -lemma sg26674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9840 - -lemma sg26675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10697 - -lemma sg26676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9565 - -lemma sg26677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10302 - -lemma sg26678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9125 - -lemma sg26679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10692 - -lemma sg26680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9831 - -lemma sg26681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9566 - -lemma sg26682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10303 - -lemma sg26683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9126 - -lemma sg26684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10300 - -lemma sg26685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8350 sg10693 - -lemma sg26686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8582 sg10088 - -lemma sg26687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9279 - -lemma sg26688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9841 - -lemma sg26689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9841 - -lemma sg26690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10698 - -lemma sg26691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9832 - -lemma sg26692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9567 - -lemma sg26693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10304 - -lemma sg26694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9127 - -lemma sg26695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9214 - -lemma sg26696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,3,3,2,1] := by - exact rowSquare_join (by decide) sg8862 sg9058 - -lemma sg26697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8730 sg9515 - -lemma sg26698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8731 sg9515 - -lemma sg26699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10621 - -lemma sg26700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3768 sg14540 - -lemma sg26701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5565 sg12621 - -lemma sg26702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5999 sg11829 - -lemma sg26703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10305 - -lemma sg26704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9276 - -lemma sg26705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10726 - -lemma sg26706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8819 sg9189 - -lemma sg26707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6000 sg11829 - -lemma sg26708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10306 - -lemma sg26709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9280 - -lemma sg26710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9870 - -lemma sg26711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10149 - -lemma sg26712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9870 - -lemma sg26713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9278 - -lemma sg26714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9842 - -lemma sg26715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9842 - -lemma sg26716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10699 - -lemma sg26717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9568 - -lemma sg26718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10305 - -lemma sg26719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9128 - -lemma sg26720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8350 sg10694 - -lemma sg26721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10307 - -lemma sg26722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9281 - -lemma sg26723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9843 - -lemma sg26724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9843 - -lemma sg26725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10700 - -lemma sg26726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9834 - -lemma sg26727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9569 - -lemma sg26728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10306 - -lemma sg26729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9129 - -lemma sg26730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10302 - -lemma sg26731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9566 - -lemma sg26732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10303 - -lemma sg26733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9282 - -lemma sg26734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9835 - -lemma sg26735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9570 - -lemma sg26736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10307 - -lemma sg26737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9130 - -lemma sg26738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9567 - -lemma sg26739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10304 - -lemma sg26740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10303 - -lemma sg26741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8762 sg9451 - -lemma sg26742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8534 sg10115 - -lemma sg26743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8535 sg10115 - -lemma sg26744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10304 - -lemma sg26745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5577 sg12618 - -lemma sg26746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6001 sg11829 - -lemma sg26747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9227 - -lemma sg26748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9280 - -lemma sg26749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9215 - -lemma sg26750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10150 - -lemma sg26751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8573 sg10095 - -lemma sg26752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9228 - -lemma sg26753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9227 - -lemma sg26754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9833 - -lemma sg26755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10136 - -lemma sg26756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8370 sg10635 - -lemma sg26757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9227 - -lemma sg26758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9227 - -lemma sg26759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9227 - -lemma sg26760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9076 - -lemma sg26761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10305 - -lemma sg26762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9228 - -lemma sg26763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9228 - -lemma sg26764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9228 - -lemma sg26765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9228 - -lemma sg26766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8861 sg9077 - -lemma sg26767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9569 - -lemma sg26768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10306 - -lemma sg26769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8813 sg9217 - -lemma sg26770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9835 - -lemma sg26771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9570 - -lemma sg26772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10307 - -lemma sg26773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10306 - -lemma sg26774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9570 - -lemma sg26775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10307 - -lemma sg26776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,7,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8540 sg10115 - -lemma sg26777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1831 sg17109 - -lemma sg26778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2199 sg15563 - -lemma sg26779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1853 sg16201 - -lemma sg26780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2234 sg15521 - -lemma sg26781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2874 sg14852 - -lemma sg26782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3519 sg14680 - -lemma sg26783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg971 sg21121 - -lemma sg26784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5482 sg12648 - -lemma sg26785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg971 sg21122 - -lemma sg26786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6362 sg11739 - -lemma sg26787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2242 sg15515 - -lemma sg26788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2687 sg15012 - -lemma sg26789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2875 sg14852 - -lemma sg26790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4680 sg12940 - -lemma sg26791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5250 sg12691 - -lemma sg26792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9219 - -lemma sg26793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8193 sg10854 - -lemma sg26794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8666 sg9713 - -lemma sg26795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3766 sg14541 - -lemma sg26796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5268 sg12683 - -lemma sg26797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6002 sg11828 - -lemma sg26798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6756 sg11508 - -lemma sg26799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9283 - -lemma sg26800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9714 - -lemma sg26801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8758 sg9457 - -lemma sg26802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5252 sg12691 - -lemma sg26803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9220 - -lemma sg26804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8242 sg10848 - -lemma sg26805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9715 - -lemma sg26806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8534 sg10116 - -lemma sg26807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8243 sg10848 - -lemma sg26808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9716 - -lemma sg26809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10151 - -lemma sg26810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8535 sg10116 - -lemma sg26811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8758 sg9458 - -lemma sg26812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8862 sg9065 - -lemma sg26813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9131 - -lemma sg26814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2688 sg15012 - -lemma sg26815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3767 sg14541 - -lemma sg26816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5268 sg12684 - -lemma sg26817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6002 sg11829 - -lemma sg26818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6757 sg11508 - -lemma sg26819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9283 - -lemma sg26820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9717 - -lemma sg26821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8742 sg9481 - -lemma sg26822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5269 sg12683 - -lemma sg26823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6003 sg11828 - -lemma sg26824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9221 - -lemma sg26825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9284 - -lemma sg26826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8807 sg9219 - -lemma sg26827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8537 sg10116 - -lemma sg26828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9222 - -lemma sg26829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9220 - -lemma sg26830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9836 - -lemma sg26831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10152 - -lemma sg26832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8538 sg10116 - -lemma sg26833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9720 - -lemma sg26834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9571 - -lemma sg26835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8809 sg9219 - -lemma sg26836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8759 sg9458 - -lemma sg26837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9132 - -lemma sg26838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6004 sg11828 - -lemma sg26839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9223 - -lemma sg26840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9285 - -lemma sg26841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9871 - -lemma sg26842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10153 - -lemma sg26843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9871 - -lemma sg26844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9286 - -lemma sg26845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9837 - -lemma sg26846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8730 sg9520 - -lemma sg26847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8820 sg9187 - -lemma sg26848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9572 - -lemma sg26849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8731 sg9520 - -lemma sg26850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9133 - -lemma sg26851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8862 sg9067 - -lemma sg26852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9838 - -lemma sg26853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9573 - -lemma sg26854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8840 sg9166 - -lemma sg26855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9134 - -lemma sg26856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9220 - -lemma sg26857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3768 sg14541 - -lemma sg26858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5269 sg12684 - -lemma sg26859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6003 sg11829 - -lemma sg26860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9224 - -lemma sg26861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9284 - -lemma sg26862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9219 - -lemma sg26863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8742 sg9484 - -lemma sg26864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6004 sg11829 - -lemma sg26865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9225 - -lemma sg26866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9287 - -lemma sg26867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9872 - -lemma sg26868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10154 - -lemma sg26869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9872 - -lemma sg26870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9286 - -lemma sg26871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9839 - -lemma sg26872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9571 - -lemma sg26873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8813 sg9219 - -lemma sg26874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9574 - -lemma sg26875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8731 sg9522 - -lemma sg26876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9135 - -lemma sg26877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9226 - -lemma sg26878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9288 - -lemma sg26879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9837 - -lemma sg26880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9571 - -lemma sg26881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8814 sg9219 - -lemma sg26882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9840 - -lemma sg26883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9575 - -lemma sg26884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8734 sg9520 - -lemma sg26885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9136 - -lemma sg26886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9221 - -lemma sg26887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9573 - -lemma sg26888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9222 - -lemma sg26889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9289 - -lemma sg26890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9841 - -lemma sg26891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9576 - -lemma sg26892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8735 sg9520 - -lemma sg26893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9137 - -lemma sg26894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8808 sg9223 - -lemma sg26895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9223 - -lemma sg26896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10626 - -lemma sg26897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5270 sg12684 - -lemma sg26898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6005 sg11829 - -lemma sg26899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9227 - -lemma sg26900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9287 - -lemma sg26901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9873 - -lemma sg26902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10155 - -lemma sg26903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9873 - -lemma sg26904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9228 - -lemma sg26905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9290 - -lemma sg26906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9839 - -lemma sg26907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8733 sg9522 - -lemma sg26908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8820 sg9194 - -lemma sg26909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9842 - -lemma sg26910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9577 - -lemma sg26911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8734 sg9522 - -lemma sg26912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9138 - -lemma sg26913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9224 - -lemma sg26914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9291 - -lemma sg26915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9843 - -lemma sg26916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9578 - -lemma sg26917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8735 sg9522 - -lemma sg26918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9139 - -lemma sg26919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9575 - -lemma sg26920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9225 - -lemma sg26921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8813 sg9222 - -lemma sg26922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9841 - -lemma sg26923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9576 - -lemma sg26924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9226 - -lemma sg26925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8813 sg9223 - -lemma sg26926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9576 - -lemma sg26927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8814 sg9223 - -lemma sg26928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6006 sg11829 - -lemma sg26929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8265 sg10845 - -lemma sg26930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9290 - -lemma sg26931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9224 - -lemma sg26932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8760 sg9459 - -lemma sg26933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8823 sg9194 - -lemma sg26934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9292 - -lemma sg26935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9842 - -lemma sg26936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9579 - -lemma sg26937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8823 sg9195 - -lemma sg26938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9140 - -lemma sg26939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9577 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 65. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg26540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg8538 sg10108 + +lemma sg26541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8385 sg10602 + +lemma sg26542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9727 + +lemma sg26543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8531 sg10115 + +lemma sg26544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10115 + +lemma sg26545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,2,2,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9064 + +lemma sg26546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9493 + +lemma sg26547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9727 + +lemma sg26548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,6,6,6,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10298 + +lemma sg26549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1723 sg18244 + +lemma sg26550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1830 sg17109 + +lemma sg26551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2197 sg15563 + +lemma sg26552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2234 sg15520 + +lemma sg26553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2678 sg15014 + +lemma sg26554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2868 sg14855 + +lemma sg26555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3518 sg14680 + +lemma sg26556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg14683 + +lemma sg26557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5628 sg12603 + +lemma sg26558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg971 sg21120 + +lemma sg26559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2198 sg15563 + +lemma sg26560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2235 sg15520 + +lemma sg26561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2679 sg15014 + +lemma sg26562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2869 sg14855 + +lemma sg26563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5250 sg12690 + +lemma sg26564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15023 + +lemma sg26565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9207 + +lemma sg26566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1296 sg20996 + +lemma sg26567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8666 sg9701 + +lemma sg26568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3873 sg14510 + +lemma sg26569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2671 sg15020 + +lemma sg26570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6949 sg11469 + +lemma sg26571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5965 sg11834 + +lemma sg26572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9208 + +lemma sg26573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9272 + +lemma sg26574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8729 sg9508 + +lemma sg26575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5547 sg12628 + +lemma sg26576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5966 sg11834 + +lemma sg26577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9209 + +lemma sg26578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9187 + +lemma sg26579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9825 + +lemma sg26580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9508 + +lemma sg26581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9210 + +lemma sg26582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9188 + +lemma sg26583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10722 + +lemma sg26584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8720 sg9563 + +lemma sg26585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9865 + +lemma sg26586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10144 + +lemma sg26587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9865 + +lemma sg26588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8847 sg9160 + +lemma sg26589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2236 sg15520 + +lemma sg26590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3874 sg14510 + +lemma sg26591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2870 sg14855 + +lemma sg26592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6950 sg11469 + +lemma sg26593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5997 sg11829 + +lemma sg26594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9219 + +lemma sg26595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9272 + +lemma sg26596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8732 sg9508 + +lemma sg26597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3766 sg14540 + +lemma sg26598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6951 sg11469 + +lemma sg26599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5967 sg11834 + +lemma sg26600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10299 + +lemma sg26601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9273 + +lemma sg26602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9825 + +lemma sg26603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8733 sg9508 + +lemma sg26604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5968 sg11834 + +lemma sg26605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10300 + +lemma sg26606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9209 + +lemma sg26607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10723 + +lemma sg26608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8721 sg9563 + +lemma sg26609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9210 + +lemma sg26610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9866 + +lemma sg26611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10145 + +lemma sg26612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9866 + +lemma sg26613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9836 + +lemma sg26614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8803 sg9219 + +lemma sg26615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9121 + +lemma sg26616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6952 sg11469 + +lemma sg26617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5969 sg11834 + +lemma sg26618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9214 + +lemma sg26619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9274 + +lemma sg26620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10724 + +lemma sg26621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8722 sg9563 + +lemma sg26622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8443 sg10242 + +lemma sg26623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9275 + +lemma sg26624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9867 + +lemma sg26625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10146 + +lemma sg26626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9867 + +lemma sg26627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9837 + +lemma sg26628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9837 + +lemma sg26629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10695 + +lemma sg26630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10299 + +lemma sg26631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9122 + +lemma sg26632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10620 + +lemma sg26633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9838 + +lemma sg26634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9838 + +lemma sg26635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8818 sg9187 + +lemma sg26636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9564 + +lemma sg26637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10300 + +lemma sg26638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9123 + +lemma sg26639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8862 sg9053 + +lemma sg26640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9210 + +lemma sg26641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8862 sg9054 + +lemma sg26642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14510 + +lemma sg26643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3767 sg14540 + +lemma sg26644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6953 sg11469 + +lemma sg26645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5998 sg11829 + +lemma sg26646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10301 + +lemma sg26647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9273 + +lemma sg26648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9207 + +lemma sg26649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9481 + +lemma sg26650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6954 sg11469 + +lemma sg26651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5970 sg11834 + +lemma sg26652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10302 + +lemma sg26653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9276 + +lemma sg26654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10725 + +lemma sg26655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8812 sg9207 + +lemma sg26656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10303 + +lemma sg26657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9275 + +lemma sg26658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9868 + +lemma sg26659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10147 + +lemma sg26660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9868 + +lemma sg26661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9839 + +lemma sg26662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9839 + +lemma sg26663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10696 + +lemma sg26664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10301 + +lemma sg26665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9124 + +lemma sg26666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5971 sg11834 + +lemma sg26667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10304 + +lemma sg26668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9277 + +lemma sg26669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9869 + +lemma sg26670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10148 + +lemma sg26671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9869 + +lemma sg26672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9278 + +lemma sg26673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9840 + +lemma sg26674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9840 + +lemma sg26675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10697 + +lemma sg26676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9565 + +lemma sg26677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10302 + +lemma sg26678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9125 + +lemma sg26679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10692 + +lemma sg26680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9831 + +lemma sg26681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9566 + +lemma sg26682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10303 + +lemma sg26683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9126 + +lemma sg26684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10300 + +lemma sg26685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8350 sg10693 + +lemma sg26686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8582 sg10088 + +lemma sg26687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9279 + +lemma sg26688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9841 + +lemma sg26689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9841 + +lemma sg26690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10698 + +lemma sg26691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9832 + +lemma sg26692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9567 + +lemma sg26693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10304 + +lemma sg26694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9127 + +lemma sg26695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9214 + +lemma sg26696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,3,3,2,1] := by + exact rowSquare_join (by decide) sg8862 sg9058 + +lemma sg26697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8730 sg9515 + +lemma sg26698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8731 sg9515 + +lemma sg26699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10621 + +lemma sg26700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3768 sg14540 + +lemma sg26701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5565 sg12621 + +lemma sg26702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5999 sg11829 + +lemma sg26703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10305 + +lemma sg26704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9276 + +lemma sg26705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10726 + +lemma sg26706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8819 sg9189 + +lemma sg26707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6000 sg11829 + +lemma sg26708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10306 + +lemma sg26709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9280 + +lemma sg26710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9870 + +lemma sg26711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10149 + +lemma sg26712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9870 + +lemma sg26713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9278 + +lemma sg26714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9842 + +lemma sg26715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9842 + +lemma sg26716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10699 + +lemma sg26717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9568 + +lemma sg26718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10305 + +lemma sg26719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9128 + +lemma sg26720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8350 sg10694 + +lemma sg26721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10307 + +lemma sg26722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9281 + +lemma sg26723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9843 + +lemma sg26724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9843 + +lemma sg26725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10700 + +lemma sg26726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9834 + +lemma sg26727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9569 + +lemma sg26728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10306 + +lemma sg26729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9129 + +lemma sg26730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10302 + +lemma sg26731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9566 + +lemma sg26732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10303 + +lemma sg26733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9282 + +lemma sg26734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9835 + +lemma sg26735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9570 + +lemma sg26736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10307 + +lemma sg26737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9130 + +lemma sg26738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9567 + +lemma sg26739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10304 + +lemma sg26740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10303 + +lemma sg26741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8762 sg9451 + +lemma sg26742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8534 sg10115 + +lemma sg26743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8535 sg10115 + +lemma sg26744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,6,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10304 + +lemma sg26745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5577 sg12618 + +lemma sg26746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6001 sg11829 + +lemma sg26747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9227 + +lemma sg26748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9280 + +lemma sg26749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9215 + +lemma sg26750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10150 + +lemma sg26751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8573 sg10095 + +lemma sg26752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9228 + +lemma sg26753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9227 + +lemma sg26754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9833 + +lemma sg26755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10136 + +lemma sg26756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8370 sg10635 + +lemma sg26757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9227 + +lemma sg26758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9227 + +lemma sg26759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9227 + +lemma sg26760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9076 + +lemma sg26761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10305 + +lemma sg26762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9228 + +lemma sg26763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9228 + +lemma sg26764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9228 + +lemma sg26765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9228 + +lemma sg26766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8861 sg9077 + +lemma sg26767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9569 + +lemma sg26768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10306 + +lemma sg26769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8813 sg9217 + +lemma sg26770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9835 + +lemma sg26771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9570 + +lemma sg26772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10307 + +lemma sg26773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10306 + +lemma sg26774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9570 + +lemma sg26775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10307 + +lemma sg26776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,7,7,7,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8540 sg10115 + +lemma sg26777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1831 sg17109 + +lemma sg26778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2199 sg15563 + +lemma sg26779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1853 sg16201 + +lemma sg26780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2234 sg15521 + +lemma sg26781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2874 sg14852 + +lemma sg26782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3519 sg14680 + +lemma sg26783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg971 sg21121 + +lemma sg26784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5482 sg12648 + +lemma sg26785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg971 sg21122 + +lemma sg26786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6362 sg11739 + +lemma sg26787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2242 sg15515 + +lemma sg26788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2687 sg15012 + +lemma sg26789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2875 sg14852 + +lemma sg26790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4680 sg12940 + +lemma sg26791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5250 sg12691 + +lemma sg26792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9219 + +lemma sg26793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8193 sg10854 + +lemma sg26794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8666 sg9713 + +lemma sg26795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3766 sg14541 + +lemma sg26796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5268 sg12683 + +lemma sg26797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6002 sg11828 + +lemma sg26798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6756 sg11508 + +lemma sg26799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9283 + +lemma sg26800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9714 + +lemma sg26801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8758 sg9457 + +lemma sg26802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5252 sg12691 + +lemma sg26803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9220 + +lemma sg26804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8242 sg10848 + +lemma sg26805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9715 + +lemma sg26806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8534 sg10116 + +lemma sg26807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8243 sg10848 + +lemma sg26808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9716 + +lemma sg26809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10151 + +lemma sg26810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8535 sg10116 + +lemma sg26811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8758 sg9458 + +lemma sg26812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8862 sg9065 + +lemma sg26813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9131 + +lemma sg26814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2688 sg15012 + +lemma sg26815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3767 sg14541 + +lemma sg26816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5268 sg12684 + +lemma sg26817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6002 sg11829 + +lemma sg26818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6757 sg11508 + +lemma sg26819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9283 + +lemma sg26820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9717 + +lemma sg26821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8742 sg9481 + +lemma sg26822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5269 sg12683 + +lemma sg26823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6003 sg11828 + +lemma sg26824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9221 + +lemma sg26825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9284 + +lemma sg26826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8807 sg9219 + +lemma sg26827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8537 sg10116 + +lemma sg26828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9222 + +lemma sg26829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9220 + +lemma sg26830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9836 + +lemma sg26831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10152 + +lemma sg26832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8538 sg10116 + +lemma sg26833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9720 + +lemma sg26834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9571 + +lemma sg26835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8809 sg9219 + +lemma sg26836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8759 sg9458 + +lemma sg26837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9132 + +lemma sg26838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6004 sg11828 + +lemma sg26839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9223 + +lemma sg26840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9285 + +lemma sg26841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9871 + +lemma sg26842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10153 + +lemma sg26843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9871 + +lemma sg26844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9286 + +lemma sg26845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9837 + +lemma sg26846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8730 sg9520 + +lemma sg26847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8820 sg9187 + +lemma sg26848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9572 + +lemma sg26849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8731 sg9520 + +lemma sg26850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9133 + +lemma sg26851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8862 sg9067 + +lemma sg26852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9838 + +lemma sg26853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9573 + +lemma sg26854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8840 sg9166 + +lemma sg26855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9134 + +lemma sg26856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9220 + +lemma sg26857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3768 sg14541 + +lemma sg26858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5269 sg12684 + +lemma sg26859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6003 sg11829 + +lemma sg26860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9224 + +lemma sg26861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9284 + +lemma sg26862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9219 + +lemma sg26863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8742 sg9484 + +lemma sg26864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6004 sg11829 + +lemma sg26865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9225 + +lemma sg26866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9287 + +lemma sg26867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9872 + +lemma sg26868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10154 + +lemma sg26869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9872 + +lemma sg26870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9286 + +lemma sg26871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9839 + +lemma sg26872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9571 + +lemma sg26873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8813 sg9219 + +lemma sg26874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9574 + +lemma sg26875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8731 sg9522 + +lemma sg26876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9135 + +lemma sg26877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9226 + +lemma sg26878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9288 + +lemma sg26879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9837 + +lemma sg26880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9571 + +lemma sg26881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8814 sg9219 + +lemma sg26882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9840 + +lemma sg26883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9575 + +lemma sg26884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8734 sg9520 + +lemma sg26885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9136 + +lemma sg26886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9221 + +lemma sg26887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9573 + +lemma sg26888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9222 + +lemma sg26889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9289 + +lemma sg26890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9841 + +lemma sg26891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9576 + +lemma sg26892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8735 sg9520 + +lemma sg26893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9137 + +lemma sg26894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8808 sg9223 + +lemma sg26895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9223 + +lemma sg26896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10626 + +lemma sg26897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5270 sg12684 + +lemma sg26898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6005 sg11829 + +lemma sg26899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9227 + +lemma sg26900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9287 + +lemma sg26901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9873 + +lemma sg26902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10155 + +lemma sg26903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9873 + +lemma sg26904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9228 + +lemma sg26905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9290 + +lemma sg26906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9839 + +lemma sg26907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8733 sg9522 + +lemma sg26908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8820 sg9194 + +lemma sg26909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9842 + +lemma sg26910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9577 + +lemma sg26911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8734 sg9522 + +lemma sg26912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9138 + +lemma sg26913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9224 + +lemma sg26914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9291 + +lemma sg26915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9843 + +lemma sg26916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9578 + +lemma sg26917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8735 sg9522 + +lemma sg26918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9139 + +lemma sg26919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9575 + +lemma sg26920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9225 + +lemma sg26921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8813 sg9222 + +lemma sg26922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9841 + +lemma sg26923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9576 + +lemma sg26924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9226 + +lemma sg26925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8813 sg9223 + +lemma sg26926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9576 + +lemma sg26927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,6,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8814 sg9223 + +lemma sg26928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6006 sg11829 + +lemma sg26929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8265 sg10845 + +lemma sg26930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9290 + +lemma sg26931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9224 + +lemma sg26932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8760 sg9459 + +lemma sg26933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8823 sg9194 + +lemma sg26934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9292 + +lemma sg26935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9842 + +lemma sg26936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9579 + +lemma sg26937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8823 sg9195 + +lemma sg26938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9140 + +lemma sg26939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9577 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes66.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes66.lean index 4323c0e1d02678275659e63ee46ec35f1b4f4d32..bf28afa3f4e117fa7a2da3cbc646297c4a3d62aa 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes66.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes66.lean @@ -1,1224 +1,1224 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 66. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg26940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9227 - -lemma sg26941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9843 - -lemma sg26942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9578 - -lemma sg26943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9228 - -lemma sg26944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8813 sg9225 - -lemma sg26945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9578 - -lemma sg26946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8813 sg9226 - -lemma sg26947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8814 sg9226 - -lemma sg26948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7810 sg11238 - -lemma sg26949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9292 - -lemma sg26950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9227 - -lemma sg26951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8776 sg9443 - -lemma sg26952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8194 sg10857 - -lemma sg26953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8870 sg9034 - -lemma sg26954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9228 - -lemma sg26955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9579 - -lemma sg26956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8579 sg10095 - -lemma sg26957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8813 sg9227 - -lemma sg26958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9579 - -lemma sg26959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8813 sg9228 - -lemma sg26960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8814 sg9228 - -lemma sg26961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg985 sg21108 - -lemma sg26962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg562 sg21241 - -lemma sg26963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg21132 - -lemma sg26964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg21638 - -lemma sg26965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg21639 - -lemma sg26966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg21640 - -lemma sg26967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg21641 - -lemma sg26968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg21642 - -lemma sg26969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg80 sg21643 - -lemma sg26970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1317 sg20965 - -lemma sg26971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1719 sg18245 - -lemma sg26972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg959 sg21132 - -lemma sg26973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg17124 - -lemma sg26974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg21298 - -lemma sg26975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg15022 - -lemma sg26976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg21299 - -lemma sg26977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg21300 - -lemma sg26978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg342 sg21301 - -lemma sg26979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg342 sg21302 - -lemma sg26980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg986 sg21108 - -lemma sg26981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1306 sg20976 - -lemma sg26982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg981 sg21111 - -lemma sg26983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg562 sg21242 - -lemma sg26984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg21133 - -lemma sg26985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg402 sg21289 - -lemma sg26986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg402 sg21290 - -lemma sg26987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg402 sg21291 - -lemma sg26988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg402 sg21292 - -lemma sg26989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg402 sg21293 - -lemma sg26990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1468 sg20931 - -lemma sg26991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1827 sg17110 - -lemma sg26992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg562 sg21243 - -lemma sg26993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg17125 - -lemma sg26994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg569 sg21227 - -lemma sg26995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg569 sg21228 - -lemma sg26996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg569 sg21229 - -lemma sg26997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg569 sg21230 - -lemma sg26998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg569 sg21231 - -lemma sg26999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1854 sg16198 - -lemma sg27000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2237 sg15516 - -lemma sg27001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg21134 - -lemma sg27002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5592 sg12609 - -lemma sg27003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg964 sg21125 - -lemma sg27004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8542 sg10105 - -lemma sg27005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6879 sg11505 - -lemma sg27006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg562 sg21244 - -lemma sg27007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5583 sg12612 - -lemma sg27008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg562 sg21245 - -lemma sg27009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7255 sg11432 - -lemma sg27010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg562 sg21246 - -lemma sg27011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8649 sg9844 - -lemma sg27012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg21135 - -lemma sg27013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8543 sg10105 - -lemma sg27014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7234 sg11453 - -lemma sg27015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8650 sg9844 - -lemma sg27016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9162 - -lemma sg27017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg7455 sg11270 - -lemma sg27018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8506 sg10169 - -lemma sg27019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg7232 sg11463 - -lemma sg27020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1318 sg20965 - -lemma sg27021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1720 sg18245 - -lemma sg27022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1827 sg17111 - -lemma sg27023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2194 sg15564 - -lemma sg27024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg17126 - -lemma sg27025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg575 sg21214 - -lemma sg27026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg21178 - -lemma sg27027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg575 sg21215 - -lemma sg27028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg575 sg21216 - -lemma sg27029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg575 sg21217 - -lemma sg27030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1721 sg18245 - -lemma sg27031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1463 sg20938 - -lemma sg27032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1816 sg17124 - -lemma sg27033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2223 sg15536 - -lemma sg27034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2668 sg15022 - -lemma sg27035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg868 sg21144 - -lemma sg27036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg14684 - -lemma sg27037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg868 sg21145 - -lemma sg27038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg868 sg21146 - -lemma sg27039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg868 sg21147 - -lemma sg27040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1828 sg17110 - -lemma sg27041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1854 sg16199 - -lemma sg27042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2237 sg15518 - -lemma sg27043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg17127 - -lemma sg27044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5536 sg12630 - -lemma sg27045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg21179 - -lemma sg27046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10308 - -lemma sg27047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8366 sg10641 - -lemma sg27048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2669 sg15022 - -lemma sg27049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1292 sg20997 - -lemma sg27050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5537 sg12630 - -lemma sg27051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1292 sg20998 - -lemma sg27052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7239 sg11449 - -lemma sg27053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1292 sg20999 - -lemma sg27054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8651 sg9844 - -lemma sg27055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5538 sg12630 - -lemma sg27056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5236 sg12695 - -lemma sg27057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10403 - -lemma sg27058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9163 - -lemma sg27059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8649 sg9845 - -lemma sg27060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8546 sg10105 - -lemma sg27061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9164 - -lemma sg27062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8674 sg9662 - -lemma sg27063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9845 - -lemma sg27064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10727 - -lemma sg27065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10403 - -lemma sg27066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg7232 sg11464 - -lemma sg27067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg986 sg21109 - -lemma sg27068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1829 sg17110 - -lemma sg27069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1849 sg16206 - -lemma sg27070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2223 sg15537 - -lemma sg27071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2867 sg14856 - -lemma sg27072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5593 sg12609 - -lemma sg27073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg965 sg21125 - -lemma sg27074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8547 sg10105 - -lemma sg27075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6882 sg11505 - -lemma sg27076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1463 sg20939 - -lemma sg27077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2239 sg15516 - -lemma sg27078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1297 sg20992 - -lemma sg27079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5567 sg12620 - -lemma sg27080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1297 sg20993 - -lemma sg27081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7249 sg11440 - -lemma sg27082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1297 sg20994 - -lemma sg27083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8652 sg9844 - -lemma sg27084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1849 sg16207 - -lemma sg27085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5584 sg12612 - -lemma sg27086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5237 sg12695 - -lemma sg27087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8548 sg10105 - -lemma sg27088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9198 - -lemma sg27089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8721 sg9580 - -lemma sg27090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5238 sg12695 - -lemma sg27091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8549 sg10105 - -lemma sg27092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9199 - -lemma sg27093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9846 - -lemma sg27094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8763 sg9450 - -lemma sg27095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7240 sg11450 - -lemma sg27096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8659 sg9728 - -lemma sg27097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8650 sg9846 - -lemma sg27098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8843 sg9162 - -lemma sg27099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg7232 sg11465 - -lemma sg27100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1468 sg20932 - -lemma sg27101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1317 sg20966 - -lemma sg27102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5568 sg12620 - -lemma sg27103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5239 sg12695 - -lemma sg27104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10309 - -lemma sg27105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8387 sg10602 - -lemma sg27106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8454 sg10231 - -lemma sg27107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5569 sg12620 - -lemma sg27108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5262 sg12685 - -lemma sg27109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8550 sg10105 - -lemma sg27110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8388 sg10602 - -lemma sg27111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9729 - -lemma sg27112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8736 sg9495 - -lemma sg27113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10404 - -lemma sg27114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8389 sg10602 - -lemma sg27115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10728 - -lemma sg27116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10404 - -lemma sg27117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9730 - -lemma sg27118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8422 sg10309 - -lemma sg27119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8675 sg9662 - -lemma sg27120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10309 - -lemma sg27121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5263 sg12685 - -lemma sg27122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8602 sg10079 - -lemma sg27123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7250 sg11441 - -lemma sg27124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8764 sg9449 - -lemma sg27125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8736 sg9496 - -lemma sg27126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8401 sg10597 - -lemma sg27127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9847 - -lemma sg27128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9497 - -lemma sg27129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8658 sg9729 - -lemma sg27130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9847 - -lemma sg27131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8659 sg9729 - -lemma sg27132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8844 sg9162 - -lemma sg27133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8421 sg10310 - -lemma sg27134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8422 sg10310 - -lemma sg27135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10310 - -lemma sg27136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9730 - -lemma sg27137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8457 sg10232 - -lemma sg27138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1319 sg20965 - -lemma sg27139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1722 sg18245 - -lemma sg27140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1828 sg17111 - -lemma sg27141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2195 sg15564 - -lemma sg27142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2224 sg15536 - -lemma sg27143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2680 sg15014 - -lemma sg27144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg869 sg21144 - -lemma sg27145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg14685 - -lemma sg27146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg869 sg21145 - -lemma sg27147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg869 sg21146 - -lemma sg27148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg869 sg21147 - -lemma sg27149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1829 sg17111 - -lemma sg27150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2196 sg15564 - -lemma sg27151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2225 sg15536 - -lemma sg27152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2670 sg15022 - -lemma sg27153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2867 sg14857 - -lemma sg27154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5539 sg12630 - -lemma sg27155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2665 sg15035 - -lemma sg27156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10308 - -lemma sg27157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8369 sg10641 - -lemma sg27158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2226 sg15536 - -lemma sg27159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2671 sg15022 - -lemma sg27160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1815 sg17127 - -lemma sg27161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5540 sg12630 - -lemma sg27162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1293 sg20998 - -lemma sg27163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7241 sg11449 - -lemma sg27164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1293 sg20999 - -lemma sg27165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8657 sg9731 - -lemma sg27166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2361 sg15481 - -lemma sg27167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5541 sg12630 - -lemma sg27168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5242 sg12693 - -lemma sg27169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8453 sg10234 - -lemma sg27170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9198 - -lemma sg27171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8651 sg9845 - -lemma sg27172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6563 sg11542 - -lemma sg27173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10405 - -lemma sg27174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9199 - -lemma sg27175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9848 - -lemma sg27176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9581 - -lemma sg27177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8181 sg10861 - -lemma sg27178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10729 - -lemma sg27179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10405 - -lemma sg27180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8845 sg9162 - -lemma sg27181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8347 sg10702 - -lemma sg27182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1819 sg17124 - -lemma sg27183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2227 sg15536 - -lemma sg27184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2672 sg15022 - -lemma sg27185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2869 sg14856 - -lemma sg27186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5542 sg12630 - -lemma sg27187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1294 sg20998 - -lemma sg27188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7242 sg11449 - -lemma sg27189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1294 sg20999 - -lemma sg27190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8660 sg9728 - -lemma sg27191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2673 sg15022 - -lemma sg27192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2359 sg15483 - -lemma sg27193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5543 sg12630 - -lemma sg27194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5244 sg12692 - -lemma sg27195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10311 - -lemma sg27196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9293 - -lemma sg27197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8652 sg9845 - -lemma sg27198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5544 sg12630 - -lemma sg27199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6564 sg11542 - -lemma sg27200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8552 sg10105 - -lemma sg27201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9201 - -lemma sg27202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9846 - -lemma sg27203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9581 - -lemma sg27204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10406 - -lemma sg27205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9202 - -lemma sg27206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10730 - -lemma sg27207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10406 - -lemma sg27208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8660 sg9730 - -lemma sg27209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9849 - -lemma sg27210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8676 sg9662 - -lemma sg27211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10311 - -lemma sg27212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2360 sg15483 - -lemma sg27213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5545 sg12630 - -lemma sg27214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6565 sg11542 - -lemma sg27215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10312 - -lemma sg27216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9294 - -lemma sg27217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9733 - -lemma sg27218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9581 - -lemma sg27219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5263 sg12686 - -lemma sg27220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10407 - -lemma sg27221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9295 - -lemma sg27222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10731 - -lemma sg27223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10407 - -lemma sg27224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9296 - -lemma sg27225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9850 - -lemma sg27226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9583 - -lemma sg27227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8658 sg9733 - -lemma sg27228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9850 - -lemma sg27229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10312 - -lemma sg27230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9141 - -lemma sg27231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8604 sg10079 - -lemma sg27232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8372 sg10641 - -lemma sg27233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9847 - -lemma sg27234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9502 - -lemma sg27235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8818 sg9198 - -lemma sg27236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9851 - -lemma sg27237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9851 - -lemma sg27238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10313 - -lemma sg27239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8661 sg9730 - -lemma sg27240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9142 - -lemma sg27241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9584 - -lemma sg27242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10310 - -lemma sg27243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9143 - -lemma sg27244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1868 sg16189 - -lemma sg27245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2227 sg15537 - -lemma sg27246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2870 sg14856 - -lemma sg27247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5586 sg12612 - -lemma sg27248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5246 sg12692 - -lemma sg27249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8590 sg10087 - -lemma sg27250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9293 - -lemma sg27251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8739 sg9494 - -lemma sg27252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3169 sg14802 - -lemma sg27253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5572 sg12620 - -lemma sg27254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5247 sg12692 - -lemma sg27255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8591 sg10087 - -lemma sg27256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9294 - -lemma sg27257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9846 - -lemma sg27258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9495 - -lemma sg27259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6566 sg11542 - -lemma sg27260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8556 sg10105 - -lemma sg27261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9295 - -lemma sg27262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8740 sg9494 - -lemma sg27263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8721 sg9582 - -lemma sg27264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9296 - -lemma sg27265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9852 - -lemma sg27266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8819 sg9199 - -lemma sg27267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8658 sg9736 - -lemma sg27268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9852 - -lemma sg27269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8659 sg9736 - -lemma sg27270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8846 sg9162 - -lemma sg27271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5573 sg12620 - -lemma sg27272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6567 sg11542 - -lemma sg27273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10408 - -lemma sg27274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8390 sg10602 - -lemma sg27275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10732 - -lemma sg27276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10408 - -lemma sg27277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8558 sg10105 - -lemma sg27278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8391 sg10602 - -lemma sg27279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9847 - -lemma sg27280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9583 - -lemma sg27281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8663 sg9729 - -lemma sg27282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9853 - -lemma sg27283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9853 - -lemma sg27284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10314 - -lemma sg27285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9730 - -lemma sg27286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8350 sg10701 - -lemma sg27287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6893 sg11503 - -lemma sg27288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9854 - -lemma sg27289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9854 - -lemma sg27290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8865 sg9040 - -lemma sg27291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9584 - -lemma sg27292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9737 - -lemma sg27293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8865 sg9041 - -lemma sg27294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10310 - -lemma sg27295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6568 sg11542 - -lemma sg27296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10315 - -lemma sg27297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8392 sg10602 - -lemma sg27298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9738 - -lemma sg27299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9583 - -lemma sg27300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8675 sg9670 - -lemma sg27301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8393 sg10602 - -lemma sg27302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9855 - -lemma sg27303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9855 - -lemma sg27304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10315 - -lemma sg27305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9584 - -lemma sg27306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9738 - -lemma sg27307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,3,2,2] := by - exact rowSquare_join (by decide) sg8430 sg10309 - -lemma sg27308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8766 sg9449 - -lemma sg27309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9507 - -lemma sg27310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8665 sg9729 - -lemma sg27311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,4,2,2,2] := by - exact rowSquare_join (by decide) sg8352 sg10701 - -lemma sg27312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9739 - -lemma sg27313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8542 sg10108 - -lemma sg27314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg8179 sg10862 - -lemma sg27315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1723 sg18245 - -lemma sg27316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1830 sg17111 - -lemma sg27317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2197 sg15564 - -lemma sg27318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2238 sg15520 - -lemma sg27319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2681 sg15014 - -lemma sg27320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2868 sg14857 - -lemma sg27321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5594 sg12609 - -lemma sg27322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg15023 - -lemma sg27323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8586 sg10088 - -lemma sg27324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6892 sg11504 - -lemma sg27325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2198 sg15564 - -lemma sg27326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2239 sg15520 - -lemma sg27327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2682 sg15014 - -lemma sg27328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2869 sg14857 - -lemma sg27329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5570 sg12621 - -lemma sg27330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1298 sg20995 - -lemma sg27331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7245 sg11449 - -lemma sg27332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1298 sg20996 - -lemma sg27333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8660 sg9731 - -lemma sg27334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2683 sg15014 - -lemma sg27335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2180 sg15574 - -lemma sg27336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5546 sg12630 - -lemma sg27337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5244 sg12693 - -lemma sg27338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8587 sg10088 - -lemma sg27339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9297 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 66. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg26940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9227 + +lemma sg26941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9843 + +lemma sg26942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9578 + +lemma sg26943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9228 + +lemma sg26944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8813 sg9225 + +lemma sg26945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9578 + +lemma sg26946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8813 sg9226 + +lemma sg26947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,7,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8814 sg9226 + +lemma sg26948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7810 sg11238 + +lemma sg26949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9292 + +lemma sg26950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9227 + +lemma sg26951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8776 sg9443 + +lemma sg26952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8194 sg10857 + +lemma sg26953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8870 sg9034 + +lemma sg26954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9228 + +lemma sg26955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9579 + +lemma sg26956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8579 sg10095 + +lemma sg26957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8813 sg9227 + +lemma sg26958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9579 + +lemma sg26959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8813 sg9228 + +lemma sg26960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,8,8,8,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8814 sg9228 + +lemma sg26961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg985 sg21108 + +lemma sg26962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg562 sg21241 + +lemma sg26963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg21132 + +lemma sg26964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg21638 + +lemma sg26965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg21639 + +lemma sg26966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg21640 + +lemma sg26967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg21641 + +lemma sg26968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg21642 + +lemma sg26969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg80 sg21643 + +lemma sg26970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1317 sg20965 + +lemma sg26971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1719 sg18245 + +lemma sg26972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg959 sg21132 + +lemma sg26973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg17124 + +lemma sg26974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg21298 + +lemma sg26975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg15022 + +lemma sg26976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg21299 + +lemma sg26977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg21300 + +lemma sg26978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg342 sg21301 + +lemma sg26979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg342 sg21302 + +lemma sg26980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg986 sg21108 + +lemma sg26981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1306 sg20976 + +lemma sg26982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg981 sg21111 + +lemma sg26983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg562 sg21242 + +lemma sg26984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg21133 + +lemma sg26985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg402 sg21289 + +lemma sg26986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg402 sg21290 + +lemma sg26987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg402 sg21291 + +lemma sg26988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg402 sg21292 + +lemma sg26989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg402 sg21293 + +lemma sg26990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1468 sg20931 + +lemma sg26991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1827 sg17110 + +lemma sg26992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg562 sg21243 + +lemma sg26993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg17125 + +lemma sg26994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg569 sg21227 + +lemma sg26995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg569 sg21228 + +lemma sg26996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg569 sg21229 + +lemma sg26997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg569 sg21230 + +lemma sg26998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg569 sg21231 + +lemma sg26999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1854 sg16198 + +lemma sg27000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2237 sg15516 + +lemma sg27001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg21134 + +lemma sg27002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5592 sg12609 + +lemma sg27003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg964 sg21125 + +lemma sg27004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8542 sg10105 + +lemma sg27005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6879 sg11505 + +lemma sg27006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg562 sg21244 + +lemma sg27007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5583 sg12612 + +lemma sg27008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg562 sg21245 + +lemma sg27009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7255 sg11432 + +lemma sg27010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg562 sg21246 + +lemma sg27011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8649 sg9844 + +lemma sg27012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg21135 + +lemma sg27013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8543 sg10105 + +lemma sg27014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7234 sg11453 + +lemma sg27015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8650 sg9844 + +lemma sg27016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9162 + +lemma sg27017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg7455 sg11270 + +lemma sg27018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8506 sg10169 + +lemma sg27019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,3,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg7232 sg11463 + +lemma sg27020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1318 sg20965 + +lemma sg27021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1720 sg18245 + +lemma sg27022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1827 sg17111 + +lemma sg27023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2194 sg15564 + +lemma sg27024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg17126 + +lemma sg27025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg575 sg21214 + +lemma sg27026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg21178 + +lemma sg27027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg575 sg21215 + +lemma sg27028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg575 sg21216 + +lemma sg27029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg575 sg21217 + +lemma sg27030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1721 sg18245 + +lemma sg27031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1463 sg20938 + +lemma sg27032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1816 sg17124 + +lemma sg27033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2223 sg15536 + +lemma sg27034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2668 sg15022 + +lemma sg27035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg868 sg21144 + +lemma sg27036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg14684 + +lemma sg27037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg868 sg21145 + +lemma sg27038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg868 sg21146 + +lemma sg27039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg868 sg21147 + +lemma sg27040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1828 sg17110 + +lemma sg27041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1854 sg16199 + +lemma sg27042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2237 sg15518 + +lemma sg27043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg17127 + +lemma sg27044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5536 sg12630 + +lemma sg27045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg21179 + +lemma sg27046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10308 + +lemma sg27047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8366 sg10641 + +lemma sg27048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2669 sg15022 + +lemma sg27049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1292 sg20997 + +lemma sg27050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5537 sg12630 + +lemma sg27051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1292 sg20998 + +lemma sg27052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7239 sg11449 + +lemma sg27053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1292 sg20999 + +lemma sg27054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8651 sg9844 + +lemma sg27055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5538 sg12630 + +lemma sg27056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5236 sg12695 + +lemma sg27057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10403 + +lemma sg27058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9163 + +lemma sg27059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8649 sg9845 + +lemma sg27060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8546 sg10105 + +lemma sg27061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9164 + +lemma sg27062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8674 sg9662 + +lemma sg27063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9845 + +lemma sg27064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10727 + +lemma sg27065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10403 + +lemma sg27066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg7232 sg11464 + +lemma sg27067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg986 sg21109 + +lemma sg27068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1829 sg17110 + +lemma sg27069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1849 sg16206 + +lemma sg27070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2223 sg15537 + +lemma sg27071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2867 sg14856 + +lemma sg27072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5593 sg12609 + +lemma sg27073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg965 sg21125 + +lemma sg27074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8547 sg10105 + +lemma sg27075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6882 sg11505 + +lemma sg27076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1463 sg20939 + +lemma sg27077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2239 sg15516 + +lemma sg27078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1297 sg20992 + +lemma sg27079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5567 sg12620 + +lemma sg27080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1297 sg20993 + +lemma sg27081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7249 sg11440 + +lemma sg27082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1297 sg20994 + +lemma sg27083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8652 sg9844 + +lemma sg27084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1849 sg16207 + +lemma sg27085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5584 sg12612 + +lemma sg27086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5237 sg12695 + +lemma sg27087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8548 sg10105 + +lemma sg27088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9198 + +lemma sg27089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8721 sg9580 + +lemma sg27090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5238 sg12695 + +lemma sg27091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8549 sg10105 + +lemma sg27092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9199 + +lemma sg27093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9846 + +lemma sg27094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8763 sg9450 + +lemma sg27095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7240 sg11450 + +lemma sg27096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8659 sg9728 + +lemma sg27097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8650 sg9846 + +lemma sg27098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8843 sg9162 + +lemma sg27099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg7232 sg11465 + +lemma sg27100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1468 sg20932 + +lemma sg27101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1317 sg20966 + +lemma sg27102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5568 sg12620 + +lemma sg27103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5239 sg12695 + +lemma sg27104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10309 + +lemma sg27105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8387 sg10602 + +lemma sg27106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8454 sg10231 + +lemma sg27107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5569 sg12620 + +lemma sg27108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5262 sg12685 + +lemma sg27109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8550 sg10105 + +lemma sg27110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8388 sg10602 + +lemma sg27111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9729 + +lemma sg27112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8736 sg9495 + +lemma sg27113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10404 + +lemma sg27114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8389 sg10602 + +lemma sg27115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10728 + +lemma sg27116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10404 + +lemma sg27117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9730 + +lemma sg27118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8422 sg10309 + +lemma sg27119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8675 sg9662 + +lemma sg27120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10309 + +lemma sg27121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5263 sg12685 + +lemma sg27122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8602 sg10079 + +lemma sg27123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7250 sg11441 + +lemma sg27124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8764 sg9449 + +lemma sg27125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8736 sg9496 + +lemma sg27126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8401 sg10597 + +lemma sg27127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9847 + +lemma sg27128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9497 + +lemma sg27129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8658 sg9729 + +lemma sg27130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9847 + +lemma sg27131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8659 sg9729 + +lemma sg27132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8844 sg9162 + +lemma sg27133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8421 sg10310 + +lemma sg27134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8422 sg10310 + +lemma sg27135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10310 + +lemma sg27136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9730 + +lemma sg27137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,4,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8457 sg10232 + +lemma sg27138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1319 sg20965 + +lemma sg27139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1722 sg18245 + +lemma sg27140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1828 sg17111 + +lemma sg27141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2195 sg15564 + +lemma sg27142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2224 sg15536 + +lemma sg27143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2680 sg15014 + +lemma sg27144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg869 sg21144 + +lemma sg27145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg14685 + +lemma sg27146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg869 sg21145 + +lemma sg27147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg869 sg21146 + +lemma sg27148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg869 sg21147 + +lemma sg27149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1829 sg17111 + +lemma sg27150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2196 sg15564 + +lemma sg27151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2225 sg15536 + +lemma sg27152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2670 sg15022 + +lemma sg27153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2867 sg14857 + +lemma sg27154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5539 sg12630 + +lemma sg27155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2665 sg15035 + +lemma sg27156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10308 + +lemma sg27157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8369 sg10641 + +lemma sg27158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2226 sg15536 + +lemma sg27159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2671 sg15022 + +lemma sg27160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1815 sg17127 + +lemma sg27161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5540 sg12630 + +lemma sg27162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1293 sg20998 + +lemma sg27163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7241 sg11449 + +lemma sg27164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1293 sg20999 + +lemma sg27165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8657 sg9731 + +lemma sg27166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2361 sg15481 + +lemma sg27167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5541 sg12630 + +lemma sg27168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5242 sg12693 + +lemma sg27169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8453 sg10234 + +lemma sg27170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9198 + +lemma sg27171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8651 sg9845 + +lemma sg27172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6563 sg11542 + +lemma sg27173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10405 + +lemma sg27174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9199 + +lemma sg27175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9848 + +lemma sg27176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9581 + +lemma sg27177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8181 sg10861 + +lemma sg27178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10729 + +lemma sg27179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10405 + +lemma sg27180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8845 sg9162 + +lemma sg27181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8347 sg10702 + +lemma sg27182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1819 sg17124 + +lemma sg27183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2227 sg15536 + +lemma sg27184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2672 sg15022 + +lemma sg27185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2869 sg14856 + +lemma sg27186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5542 sg12630 + +lemma sg27187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1294 sg20998 + +lemma sg27188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7242 sg11449 + +lemma sg27189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1294 sg20999 + +lemma sg27190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8660 sg9728 + +lemma sg27191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2673 sg15022 + +lemma sg27192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2359 sg15483 + +lemma sg27193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5543 sg12630 + +lemma sg27194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5244 sg12692 + +lemma sg27195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10311 + +lemma sg27196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9293 + +lemma sg27197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8652 sg9845 + +lemma sg27198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5544 sg12630 + +lemma sg27199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6564 sg11542 + +lemma sg27200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8552 sg10105 + +lemma sg27201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9201 + +lemma sg27202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9846 + +lemma sg27203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9581 + +lemma sg27204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10406 + +lemma sg27205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9202 + +lemma sg27206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10730 + +lemma sg27207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10406 + +lemma sg27208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8660 sg9730 + +lemma sg27209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9849 + +lemma sg27210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8676 sg9662 + +lemma sg27211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10311 + +lemma sg27212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2360 sg15483 + +lemma sg27213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5545 sg12630 + +lemma sg27214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6565 sg11542 + +lemma sg27215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10312 + +lemma sg27216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9294 + +lemma sg27217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9733 + +lemma sg27218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9581 + +lemma sg27219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5263 sg12686 + +lemma sg27220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10407 + +lemma sg27221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9295 + +lemma sg27222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10731 + +lemma sg27223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10407 + +lemma sg27224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9296 + +lemma sg27225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9850 + +lemma sg27226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9583 + +lemma sg27227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8658 sg9733 + +lemma sg27228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9850 + +lemma sg27229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10312 + +lemma sg27230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9141 + +lemma sg27231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8604 sg10079 + +lemma sg27232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8372 sg10641 + +lemma sg27233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9847 + +lemma sg27234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9502 + +lemma sg27235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8818 sg9198 + +lemma sg27236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9851 + +lemma sg27237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9851 + +lemma sg27238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10313 + +lemma sg27239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8661 sg9730 + +lemma sg27240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9142 + +lemma sg27241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9584 + +lemma sg27242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10310 + +lemma sg27243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9143 + +lemma sg27244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1868 sg16189 + +lemma sg27245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2227 sg15537 + +lemma sg27246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2870 sg14856 + +lemma sg27247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5586 sg12612 + +lemma sg27248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5246 sg12692 + +lemma sg27249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8590 sg10087 + +lemma sg27250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9293 + +lemma sg27251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8739 sg9494 + +lemma sg27252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3169 sg14802 + +lemma sg27253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5572 sg12620 + +lemma sg27254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5247 sg12692 + +lemma sg27255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8591 sg10087 + +lemma sg27256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9294 + +lemma sg27257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9846 + +lemma sg27258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9495 + +lemma sg27259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6566 sg11542 + +lemma sg27260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8556 sg10105 + +lemma sg27261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9295 + +lemma sg27262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8740 sg9494 + +lemma sg27263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8721 sg9582 + +lemma sg27264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9296 + +lemma sg27265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9852 + +lemma sg27266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8819 sg9199 + +lemma sg27267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8658 sg9736 + +lemma sg27268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9852 + +lemma sg27269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8659 sg9736 + +lemma sg27270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8846 sg9162 + +lemma sg27271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5573 sg12620 + +lemma sg27272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6567 sg11542 + +lemma sg27273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10408 + +lemma sg27274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8390 sg10602 + +lemma sg27275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10732 + +lemma sg27276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10408 + +lemma sg27277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8558 sg10105 + +lemma sg27278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8391 sg10602 + +lemma sg27279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9847 + +lemma sg27280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9583 + +lemma sg27281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8663 sg9729 + +lemma sg27282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9853 + +lemma sg27283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9853 + +lemma sg27284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10314 + +lemma sg27285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9730 + +lemma sg27286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8350 sg10701 + +lemma sg27287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6893 sg11503 + +lemma sg27288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9854 + +lemma sg27289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9854 + +lemma sg27290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8865 sg9040 + +lemma sg27291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9584 + +lemma sg27292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9737 + +lemma sg27293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8865 sg9041 + +lemma sg27294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10310 + +lemma sg27295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6568 sg11542 + +lemma sg27296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10315 + +lemma sg27297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8392 sg10602 + +lemma sg27298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9738 + +lemma sg27299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9583 + +lemma sg27300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8675 sg9670 + +lemma sg27301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8393 sg10602 + +lemma sg27302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9855 + +lemma sg27303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9855 + +lemma sg27304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10315 + +lemma sg27305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9584 + +lemma sg27306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9738 + +lemma sg27307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,3,3,2,2] := by + exact rowSquare_join (by decide) sg8430 sg10309 + +lemma sg27308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8766 sg9449 + +lemma sg27309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9507 + +lemma sg27310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8665 sg9729 + +lemma sg27311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,4,2,2,2] := by + exact rowSquare_join (by decide) sg8352 sg10701 + +lemma sg27312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9739 + +lemma sg27313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8542 sg10108 + +lemma sg27314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,5,5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg8179 sg10862 + +lemma sg27315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1723 sg18245 + +lemma sg27316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1830 sg17111 + +lemma sg27317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2197 sg15564 + +lemma sg27318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2238 sg15520 + +lemma sg27319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2681 sg15014 + +lemma sg27320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2868 sg14857 + +lemma sg27321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5594 sg12609 + +lemma sg27322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg15023 + +lemma sg27323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8586 sg10088 + +lemma sg27324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6892 sg11504 + +lemma sg27325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2198 sg15564 + +lemma sg27326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2239 sg15520 + +lemma sg27327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2682 sg15014 + +lemma sg27328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2869 sg14857 + +lemma sg27329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5570 sg12621 + +lemma sg27330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1298 sg20995 + +lemma sg27331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7245 sg11449 + +lemma sg27332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1298 sg20996 + +lemma sg27333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8660 sg9731 + +lemma sg27334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2683 sg15014 + +lemma sg27335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2180 sg15574 + +lemma sg27336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5546 sg12630 + +lemma sg27337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5244 sg12693 + +lemma sg27338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8587 sg10088 + +lemma sg27339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9297 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes67.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes67.lean index b5a9a6ff784e1d6cb15f43a1d3f04d40b7b0d4d1..42125ae32e26d086efe076e9b9934b98d6f2b07c 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes67.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes67.lean @@ -1,1222 +1,1222 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 - -namespace OAI - -/-! Semigroup Nodes 67. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg27340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8657 sg9740 - -lemma sg27341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5547 sg12630 - -lemma sg27342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5245 sg12693 - -lemma sg27343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8453 sg10239 - -lemma sg27344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9201 - -lemma sg27345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9848 - -lemma sg27346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8736 sg9508 - -lemma sg27347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8589 sg10088 - -lemma sg27348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9202 - -lemma sg27349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9856 - -lemma sg27350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8720 sg9585 - -lemma sg27351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9730 - -lemma sg27352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9856 - -lemma sg27353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8677 sg9662 - -lemma sg27354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8847 sg9162 - -lemma sg27355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2241 sg15517 - -lemma sg27356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2685 sg15013 - -lemma sg27357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2870 sg14857 - -lemma sg27358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5548 sg12630 - -lemma sg27359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5246 sg12693 - -lemma sg27360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10311 - -lemma sg27361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9297 - -lemma sg27362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8660 sg9732 - -lemma sg27363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3766 sg14542 - -lemma sg27364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5549 sg12630 - -lemma sg27365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5247 sg12693 - -lemma sg27366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10316 - -lemma sg27367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9298 - -lemma sg27368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9848 - -lemma sg27369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8737 sg9500 - -lemma sg27370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5248 sg12693 - -lemma sg27371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10409 - -lemma sg27372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9209 - -lemma sg27373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10733 - -lemma sg27374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10409 - -lemma sg27375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9210 - -lemma sg27376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9857 - -lemma sg27377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9586 - -lemma sg27378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8367 sg10648 - -lemma sg27379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9857 - -lemma sg27380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10316 - -lemma sg27381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9144 - -lemma sg27382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5550 sg12630 - -lemma sg27383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5249 sg12693 - -lemma sg27384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8593 sg10088 - -lemma sg27385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9299 - -lemma sg27386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9741 - -lemma sg27387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8722 sg9585 - -lemma sg27388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10317 - -lemma sg27389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9300 - -lemma sg27390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9850 - -lemma sg27391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9510 - -lemma sg27392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8818 sg9200 - -lemma sg27393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9858 - -lemma sg27394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9858 - -lemma sg27395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8658 sg9741 - -lemma sg27396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10312 - -lemma sg27397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9145 - -lemma sg27398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10641 - -lemma sg27399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9859 - -lemma sg27400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9859 - -lemma sg27401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10317 - -lemma sg27402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9587 - -lemma sg27403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10313 - -lemma sg27404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9146 - -lemma sg27405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9743 - -lemma sg27406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2686 sg15013 - -lemma sg27407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3767 sg14542 - -lemma sg27408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5551 sg12630 - -lemma sg27409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5253 sg12692 - -lemma sg27410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8595 sg10087 - -lemma sg27411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9298 - -lemma sg27412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8660 sg9736 - -lemma sg27413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9500 - -lemma sg27414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5552 sg12630 - -lemma sg27415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5254 sg12692 - -lemma sg27416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10410 - -lemma sg27417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9301 - -lemma sg27418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9849 - -lemma sg27419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10410 - -lemma sg27420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8596 sg10087 - -lemma sg27421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9300 - -lemma sg27422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9852 - -lemma sg27423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9586 - -lemma sg27424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8818 sg9203 - -lemma sg27425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9860 - -lemma sg27426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9860 - -lemma sg27427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10318 - -lemma sg27428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8670 sg9730 - -lemma sg27429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9147 - -lemma sg27430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5255 sg12692 - -lemma sg27431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10319 - -lemma sg27432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9302 - -lemma sg27433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9850 - -lemma sg27434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9586 - -lemma sg27435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8663 sg9733 - -lemma sg27436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9303 - -lemma sg27437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9861 - -lemma sg27438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9861 - -lemma sg27439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10319 - -lemma sg27440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9588 - -lemma sg27441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10314 - -lemma sg27442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9148 - -lemma sg27443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9854 - -lemma sg27444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9589 - -lemma sg27445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8818 sg9205 - -lemma sg27446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9149 - -lemma sg27447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10313 - -lemma sg27448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8605 sg10080 - -lemma sg27449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9304 - -lemma sg27450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9862 - -lemma sg27451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9862 - -lemma sg27452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8675 sg9677 - -lemma sg27453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9855 - -lemma sg27454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9590 - -lemma sg27455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10315 - -lemma sg27456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,3,2,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9150 - -lemma sg27457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9747 - -lemma sg27458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9515 - -lemma sg27459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9748 - -lemma sg27460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg8180 sg10862 - -lemma sg27461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3768 sg14542 - -lemma sg27462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5577 sg12620 - -lemma sg27463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5256 sg12692 - -lemma sg27464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8597 sg10087 - -lemma sg27465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9301 - -lemma sg27466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8765 sg9453 - -lemma sg27467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8819 sg9203 - -lemma sg27468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5257 sg12692 - -lemma sg27469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8598 sg10087 - -lemma sg27470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9302 - -lemma sg27471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9852 - -lemma sg27472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8819 sg9204 - -lemma sg27473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8663 sg9736 - -lemma sg27474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9303 - -lemma sg27475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9863 - -lemma sg27476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9863 - -lemma sg27477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8865 sg9045 - -lemma sg27478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8819 sg9206 - -lemma sg27479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9749 - -lemma sg27480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8870 sg9041 - -lemma sg27481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10320 - -lemma sg27482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9304 - -lemma sg27483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9864 - -lemma sg27484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9864 - -lemma sg27485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10320 - -lemma sg27486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9854 - -lemma sg27487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9588 - -lemma sg27488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9737 - -lemma sg27489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10314 - -lemma sg27490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9589 - -lemma sg27491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9751 - -lemma sg27492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8396 sg10602 - -lemma sg27493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9855 - -lemma sg27494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9588 - -lemma sg27495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9738 - -lemma sg27496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9590 - -lemma sg27497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10315 - -lemma sg27498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8747 sg9496 - -lemma sg27499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8778 sg9444 - -lemma sg27500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8542 sg10115 - -lemma sg27501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,6,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8675 sg9682 - -lemma sg27502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,6,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10315 - -lemma sg27503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8179 sg10863 - -lemma sg27504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8847 sg9164 - -lemma sg27505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8860 sg9151 - -lemma sg27506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8818 sg9207 - -lemma sg27507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8179 sg10864 - -lemma sg27508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10316 - -lemma sg27509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9152 - -lemma sg27510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8820 sg9200 - -lemma sg27511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8818 sg9208 - -lemma sg27512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9753 - -lemma sg27513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8860 sg9153 - -lemma sg27514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10317 - -lemma sg27515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9754 - -lemma sg27516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8370 sg10648 - -lemma sg27517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8818 sg9211 - -lemma sg27518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10318 - -lemma sg27519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8663 sg9741 - -lemma sg27520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10319 - -lemma sg27521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9756 - -lemma sg27522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10317 - -lemma sg27523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8668 sg9738 - -lemma sg27524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9758 - -lemma sg27525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10317 - -lemma sg27526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8823 sg9203 - -lemma sg27527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8663 sg9744 - -lemma sg27528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8818 sg9215 - -lemma sg27529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10318 - -lemma sg27530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10320 - -lemma sg27531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10319 - -lemma sg27532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8818 sg9217 - -lemma sg27533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9761 - -lemma sg27534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10319 - -lemma sg27535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,6,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8748 sg9501 - -lemma sg27536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8870 sg9045 - -lemma sg27537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9749 - -lemma sg27538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8179 sg10865 - -lemma sg27539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10320 - -lemma sg27540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9751 - -lemma sg27541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8429 sg10320 - -lemma sg27542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8883 sg8991 - -lemma sg27543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8180 sg10863 - -lemma sg27544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8847 sg9167 - -lemma sg27545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8487 sg10190 - -lemma sg27546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8860 sg9154 - -lemma sg27547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8820 sg9207 - -lemma sg27548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8818 sg9219 - -lemma sg27549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8677 sg9676 - -lemma sg27550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8820 sg9208 - -lemma sg27551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8661 sg9753 - -lemma sg27552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8820 sg9210 - -lemma sg27553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8818 sg9220 - -lemma sg27554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8823 sg9207 - -lemma sg27555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8820 sg9211 - -lemma sg27556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8661 sg9755 - -lemma sg27557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8823 sg9210 - -lemma sg27558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9753 - -lemma sg27559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8818 sg9221 - -lemma sg27560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8818 sg9222 - -lemma sg27561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8820 sg9214 - -lemma sg27562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8818 sg9223 - -lemma sg27563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8823 sg9211 - -lemma sg27564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9755 - -lemma sg27565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8818 sg9224 - -lemma sg27566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9756 - -lemma sg27567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8818 sg9225 - -lemma sg27568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8818 sg9226 - -lemma sg27569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,6,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8884 sg8991 - -lemma sg27570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8823 sg9215 - -lemma sg27571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9759 - -lemma sg27572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8818 sg9227 - -lemma sg27573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8818 sg9228 - -lemma sg27574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8663 sg9761 - -lemma sg27575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,8,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8597 sg10095 - -lemma sg27576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,8,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8173 sg11048 - -lemma sg27577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,8,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8173 sg11049 - -lemma sg27578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8183 sg10863 - -lemma sg27579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8867 sg9065 - -lemma sg27580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8551 sg10116 - -lemma sg27581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8185 sg10863 - -lemma sg27582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8820 sg9219 - -lemma sg27583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8552 sg10116 - -lemma sg27584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8869 sg9065 - -lemma sg27585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8668 sg9753 - -lemma sg27586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8820 sg9220 - -lemma sg27587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8848 sg9166 - -lemma sg27588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8823 sg9219 - -lemma sg27589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8668 sg9755 - -lemma sg27590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8823 sg9220 - -lemma sg27591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8820 sg9221 - -lemma sg27592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8820 sg9222 - -lemma sg27593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8820 sg9223 - -lemma sg27594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8670 sg9755 - -lemma sg27595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8820 sg9224 - -lemma sg27596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8823 sg9222 - -lemma sg27597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8820 sg9225 - -lemma sg27598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8820 sg9226 - -lemma sg27599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8823 sg9224 - -lemma sg27600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8820 sg9227 - -lemma sg27601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8820 sg9228 - -lemma sg27602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,8,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8823 sg9227 - -lemma sg27603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,8,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8823 sg9228 - -lemma sg27604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,9,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8208 sg10857 - -lemma sg27605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg25 sg21657 - -lemma sg27606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg25 sg21658 - -lemma sg27607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg25 sg21659 - -lemma sg27608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg25 sg21660 - -lemma sg27609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg25 sg21661 - -lemma sg27610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg25 sg21662 - -lemma sg27611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg21663 - -lemma sg27612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg21664 - -lemma sg27613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg21665 - -lemma sg27614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg21666 - -lemma sg27615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg21667 - -lemma sg27616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg24 sg21668 - -lemma sg27617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg24 sg21669 - -lemma sg27618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21021 - -lemma sg27619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg72 sg21650 - -lemma sg27620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg72 sg21651 - -lemma sg27621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg72 sg21652 - -lemma sg27622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg72 sg21653 - -lemma sg27623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg72 sg21654 - -lemma sg27624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg72 sg21655 - -lemma sg27625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21000 - -lemma sg27626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18259 - -lemma sg27627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg126 sg21628 - -lemma sg27628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg126 sg21629 - -lemma sg27629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg126 sg21630 - -lemma sg27630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg126 sg21631 - -lemma sg27631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg126 sg21632 - -lemma sg27632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg126 sg21633 - -lemma sg27633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg962 sg21126 - -lemma sg27634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg145 sg21622 - -lemma sg27635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg21180 - -lemma sg27636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg145 sg21623 - -lemma sg27637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg145 sg21624 - -lemma sg27638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg145 sg21625 - -lemma sg27639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg145 sg21626 - -lemma sg27640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg145 sg21627 - -lemma sg27641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg967 sg21123 - -lemma sg27642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1309 sg20967 - -lemma sg27643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg288 sg21339 - -lemma sg27644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg21181 - -lemma sg27645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg288 sg21340 - -lemma sg27646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg288 sg21341 - -lemma sg27647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg288 sg21342 - -lemma sg27648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg288 sg21343 - -lemma sg27649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg288 sg21344 - -lemma sg27650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg331 sg21328 - -lemma sg27651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg548 sg21265 - -lemma sg27652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg331 sg21329 - -lemma sg27653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg21182 - -lemma sg27654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg331 sg21330 - -lemma sg27655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg331 sg21331 - -lemma sg27656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg331 sg21332 - -lemma sg27657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg331 sg21333 - -lemma sg27658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg548 sg21266 - -lemma sg27659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg548 sg21267 - -lemma sg27660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg21183 - -lemma sg27661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10196 - -lemma sg27662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11287 - -lemma sg27663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11486 - -lemma sg27664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6124 sg11758 - -lemma sg27665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8 sg21670 - -lemma sg27666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10197 - -lemma sg27667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10173 - -lemma sg27668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11261 - -lemma sg27669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6903 sg11481 - -lemma sg27670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10174 - -lemma sg27671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8508 sg10168 - -lemma sg27672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg7458 sg11257 - -lemma sg27673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg6125 sg11757 - -lemma sg27674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8517 sg10167 - -lemma sg27675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg7460 sg11256 - -lemma sg27676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg6363 sg11739 - -lemma sg27677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21022 - -lemma sg27678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg73 sg21650 - -lemma sg27679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg73 sg21651 - -lemma sg27680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg73 sg21652 - -lemma sg27681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg73 sg21653 - -lemma sg27682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg73 sg21654 - -lemma sg27683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg73 sg21655 - -lemma sg27684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21001 - -lemma sg27685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18260 - -lemma sg27686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg127 sg21628 - -lemma sg27687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg127 sg21629 - -lemma sg27688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg127 sg21630 - -lemma sg27689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg127 sg21631 - -lemma sg27690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg127 sg21632 - -lemma sg27691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg127 sg21633 - -lemma sg27692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1290 sg21000 - -lemma sg27693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg18248 - -lemma sg27694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18261 - -lemma sg27695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg146 sg21623 - -lemma sg27696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg146 sg21624 - -lemma sg27697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg146 sg21625 - -lemma sg27698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg146 sg21626 - -lemma sg27699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg146 sg21627 - -lemma sg27700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg963 sg21126 - -lemma sg27701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1309 sg20969 - -lemma sg27702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg850 sg21168 - -lemma sg27703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg21184 - -lemma sg27704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg289 sg21340 - -lemma sg27705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg289 sg21341 - -lemma sg27706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg289 sg21342 - -lemma sg27707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg289 sg21343 - -lemma sg27708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg289 sg21344 - -lemma sg27709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg987 sg21107 - -lemma sg27710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1310 sg20967 - -lemma sg27711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1309 sg20970 - -lemma sg27712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg850 sg21169 - -lemma sg27713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg21185 - -lemma sg27714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg332 sg21330 - -lemma sg27715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg332 sg21331 - -lemma sg27716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg332 sg21332 - -lemma sg27717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg332 sg21333 - -lemma sg27718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg549 sg21265 - -lemma sg27719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg561 sg21247 - -lemma sg27720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg850 sg21170 - -lemma sg27721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg849 sg21186 - -lemma sg27722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10198 - -lemma sg27723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11288 - -lemma sg27724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11487 - -lemma sg27725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6124 sg11759 - -lemma sg27726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg561 sg21248 - -lemma sg27727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg850 sg21171 - -lemma sg27728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10199 - -lemma sg27729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10175 - -lemma sg27730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11262 - -lemma sg27731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6903 sg11482 - -lemma sg27732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10200 - -lemma sg27733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10176 - -lemma sg27734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10173 - -lemma sg27735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7457 sg11261 - -lemma sg27736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg6904 sg11481 - -lemma sg27737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10174 - -lemma sg27738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8509 sg10168 - -lemma sg27739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg7459 sg11257 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 + +namespace OAI + +/-! Semigroup Nodes 67. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg27340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8657 sg9740 + +lemma sg27341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5547 sg12630 + +lemma sg27342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5245 sg12693 + +lemma sg27343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8453 sg10239 + +lemma sg27344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9201 + +lemma sg27345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9848 + +lemma sg27346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8736 sg9508 + +lemma sg27347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8589 sg10088 + +lemma sg27348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9202 + +lemma sg27349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9856 + +lemma sg27350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8720 sg9585 + +lemma sg27351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9730 + +lemma sg27352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9856 + +lemma sg27353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8677 sg9662 + +lemma sg27354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8847 sg9162 + +lemma sg27355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2241 sg15517 + +lemma sg27356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2685 sg15013 + +lemma sg27357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2870 sg14857 + +lemma sg27358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5548 sg12630 + +lemma sg27359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5246 sg12693 + +lemma sg27360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10311 + +lemma sg27361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9297 + +lemma sg27362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8660 sg9732 + +lemma sg27363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3766 sg14542 + +lemma sg27364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5549 sg12630 + +lemma sg27365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5247 sg12693 + +lemma sg27366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10316 + +lemma sg27367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9298 + +lemma sg27368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9848 + +lemma sg27369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8737 sg9500 + +lemma sg27370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5248 sg12693 + +lemma sg27371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10409 + +lemma sg27372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9209 + +lemma sg27373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10733 + +lemma sg27374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10409 + +lemma sg27375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9210 + +lemma sg27376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9857 + +lemma sg27377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9586 + +lemma sg27378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8367 sg10648 + +lemma sg27379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9857 + +lemma sg27380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10316 + +lemma sg27381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9144 + +lemma sg27382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5550 sg12630 + +lemma sg27383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5249 sg12693 + +lemma sg27384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8593 sg10088 + +lemma sg27385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9299 + +lemma sg27386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9741 + +lemma sg27387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8722 sg9585 + +lemma sg27388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10317 + +lemma sg27389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9300 + +lemma sg27390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9850 + +lemma sg27391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9510 + +lemma sg27392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8818 sg9200 + +lemma sg27393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9858 + +lemma sg27394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9858 + +lemma sg27395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8658 sg9741 + +lemma sg27396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10312 + +lemma sg27397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9145 + +lemma sg27398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10641 + +lemma sg27399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9859 + +lemma sg27400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9859 + +lemma sg27401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10317 + +lemma sg27402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9587 + +lemma sg27403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10313 + +lemma sg27404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9146 + +lemma sg27405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9743 + +lemma sg27406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2686 sg15013 + +lemma sg27407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3767 sg14542 + +lemma sg27408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5551 sg12630 + +lemma sg27409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5253 sg12692 + +lemma sg27410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8595 sg10087 + +lemma sg27411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9298 + +lemma sg27412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8660 sg9736 + +lemma sg27413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9500 + +lemma sg27414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5552 sg12630 + +lemma sg27415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5254 sg12692 + +lemma sg27416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10410 + +lemma sg27417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9301 + +lemma sg27418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9849 + +lemma sg27419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10410 + +lemma sg27420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8596 sg10087 + +lemma sg27421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9300 + +lemma sg27422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9852 + +lemma sg27423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9586 + +lemma sg27424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8818 sg9203 + +lemma sg27425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9860 + +lemma sg27426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9860 + +lemma sg27427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10318 + +lemma sg27428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8670 sg9730 + +lemma sg27429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9147 + +lemma sg27430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5255 sg12692 + +lemma sg27431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10319 + +lemma sg27432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9302 + +lemma sg27433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9850 + +lemma sg27434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9586 + +lemma sg27435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8663 sg9733 + +lemma sg27436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9303 + +lemma sg27437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9861 + +lemma sg27438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9861 + +lemma sg27439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10319 + +lemma sg27440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9588 + +lemma sg27441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10314 + +lemma sg27442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9148 + +lemma sg27443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9854 + +lemma sg27444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9589 + +lemma sg27445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8818 sg9205 + +lemma sg27446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9149 + +lemma sg27447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10313 + +lemma sg27448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8605 sg10080 + +lemma sg27449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9304 + +lemma sg27450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9862 + +lemma sg27451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9862 + +lemma sg27452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8675 sg9677 + +lemma sg27453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9855 + +lemma sg27454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9590 + +lemma sg27455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10315 + +lemma sg27456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,3,2,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9150 + +lemma sg27457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9747 + +lemma sg27458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9515 + +lemma sg27459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9748 + +lemma sg27460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,5,5,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg8180 sg10862 + +lemma sg27461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3768 sg14542 + +lemma sg27462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5577 sg12620 + +lemma sg27463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5256 sg12692 + +lemma sg27464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8597 sg10087 + +lemma sg27465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9301 + +lemma sg27466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8765 sg9453 + +lemma sg27467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8819 sg9203 + +lemma sg27468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5257 sg12692 + +lemma sg27469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8598 sg10087 + +lemma sg27470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9302 + +lemma sg27471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9852 + +lemma sg27472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8819 sg9204 + +lemma sg27473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8663 sg9736 + +lemma sg27474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9303 + +lemma sg27475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9863 + +lemma sg27476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9863 + +lemma sg27477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8865 sg9045 + +lemma sg27478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8819 sg9206 + +lemma sg27479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9749 + +lemma sg27480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8870 sg9041 + +lemma sg27481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10320 + +lemma sg27482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9304 + +lemma sg27483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9864 + +lemma sg27484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9864 + +lemma sg27485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10320 + +lemma sg27486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9854 + +lemma sg27487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9588 + +lemma sg27488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9737 + +lemma sg27489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10314 + +lemma sg27490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9589 + +lemma sg27491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9751 + +lemma sg27492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8396 sg10602 + +lemma sg27493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9855 + +lemma sg27494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9588 + +lemma sg27495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9738 + +lemma sg27496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9590 + +lemma sg27497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10315 + +lemma sg27498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8747 sg9496 + +lemma sg27499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8778 sg9444 + +lemma sg27500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8542 sg10115 + +lemma sg27501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,6,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8675 sg9682 + +lemma sg27502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,6,6,6,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10315 + +lemma sg27503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8179 sg10863 + +lemma sg27504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8847 sg9164 + +lemma sg27505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8860 sg9151 + +lemma sg27506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8818 sg9207 + +lemma sg27507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8179 sg10864 + +lemma sg27508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10316 + +lemma sg27509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9152 + +lemma sg27510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8820 sg9200 + +lemma sg27511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8818 sg9208 + +lemma sg27512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9753 + +lemma sg27513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8860 sg9153 + +lemma sg27514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10317 + +lemma sg27515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9754 + +lemma sg27516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8370 sg10648 + +lemma sg27517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8818 sg9211 + +lemma sg27518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10318 + +lemma sg27519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8663 sg9741 + +lemma sg27520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10319 + +lemma sg27521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9756 + +lemma sg27522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10317 + +lemma sg27523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8668 sg9738 + +lemma sg27524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9758 + +lemma sg27525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10317 + +lemma sg27526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8823 sg9203 + +lemma sg27527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8663 sg9744 + +lemma sg27528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8818 sg9215 + +lemma sg27529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10318 + +lemma sg27530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10320 + +lemma sg27531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10319 + +lemma sg27532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8818 sg9217 + +lemma sg27533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9761 + +lemma sg27534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10319 + +lemma sg27535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,6,6,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8748 sg9501 + +lemma sg27536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8870 sg9045 + +lemma sg27537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9749 + +lemma sg27538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8179 sg10865 + +lemma sg27539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10320 + +lemma sg27540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9751 + +lemma sg27541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8429 sg10320 + +lemma sg27542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,7,7,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8883 sg8991 + +lemma sg27543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8180 sg10863 + +lemma sg27544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8847 sg9167 + +lemma sg27545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8487 sg10190 + +lemma sg27546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8860 sg9154 + +lemma sg27547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8820 sg9207 + +lemma sg27548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8818 sg9219 + +lemma sg27549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8677 sg9676 + +lemma sg27550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8820 sg9208 + +lemma sg27551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8661 sg9753 + +lemma sg27552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8820 sg9210 + +lemma sg27553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8818 sg9220 + +lemma sg27554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8823 sg9207 + +lemma sg27555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8820 sg9211 + +lemma sg27556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8661 sg9755 + +lemma sg27557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8823 sg9210 + +lemma sg27558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9753 + +lemma sg27559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8818 sg9221 + +lemma sg27560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8818 sg9222 + +lemma sg27561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8820 sg9214 + +lemma sg27562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8818 sg9223 + +lemma sg27563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8823 sg9211 + +lemma sg27564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9755 + +lemma sg27565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8818 sg9224 + +lemma sg27566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9756 + +lemma sg27567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8818 sg9225 + +lemma sg27568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8818 sg9226 + +lemma sg27569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,6,6,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8884 sg8991 + +lemma sg27570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8823 sg9215 + +lemma sg27571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9759 + +lemma sg27572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8818 sg9227 + +lemma sg27573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8818 sg9228 + +lemma sg27574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8663 sg9761 + +lemma sg27575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,8,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8597 sg10095 + +lemma sg27576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,8,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8173 sg11048 + +lemma sg27577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,8,8,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8173 sg11049 + +lemma sg27578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8183 sg10863 + +lemma sg27579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8867 sg9065 + +lemma sg27580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8551 sg10116 + +lemma sg27581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8185 sg10863 + +lemma sg27582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8820 sg9219 + +lemma sg27583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8552 sg10116 + +lemma sg27584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8869 sg9065 + +lemma sg27585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8668 sg9753 + +lemma sg27586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8820 sg9220 + +lemma sg27587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8848 sg9166 + +lemma sg27588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8823 sg9219 + +lemma sg27589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8668 sg9755 + +lemma sg27590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8823 sg9220 + +lemma sg27591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8820 sg9221 + +lemma sg27592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8820 sg9222 + +lemma sg27593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8820 sg9223 + +lemma sg27594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8670 sg9755 + +lemma sg27595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8820 sg9224 + +lemma sg27596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8823 sg9222 + +lemma sg27597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8820 sg9225 + +lemma sg27598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8820 sg9226 + +lemma sg27599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8823 sg9224 + +lemma sg27600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8820 sg9227 + +lemma sg27601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8820 sg9228 + +lemma sg27602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,8,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8823 sg9227 + +lemma sg27603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,8,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8823 sg9228 + +lemma sg27604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [9,9,9,9,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8208 sg10857 + +lemma sg27605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg25 sg21657 + +lemma sg27606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg25 sg21658 + +lemma sg27607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg25 sg21659 + +lemma sg27608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg25 sg21660 + +lemma sg27609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg25 sg21661 + +lemma sg27610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg25 sg21662 + +lemma sg27611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg21663 + +lemma sg27612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg21664 + +lemma sg27613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg21665 + +lemma sg27614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg21666 + +lemma sg27615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg21667 + +lemma sg27616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg24 sg21668 + +lemma sg27617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg24 sg21669 + +lemma sg27618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21021 + +lemma sg27619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg72 sg21650 + +lemma sg27620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg72 sg21651 + +lemma sg27621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg72 sg21652 + +lemma sg27622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg72 sg21653 + +lemma sg27623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg72 sg21654 + +lemma sg27624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg72 sg21655 + +lemma sg27625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21000 + +lemma sg27626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18259 + +lemma sg27627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg126 sg21628 + +lemma sg27628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg126 sg21629 + +lemma sg27629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg126 sg21630 + +lemma sg27630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg126 sg21631 + +lemma sg27631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg126 sg21632 + +lemma sg27632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg126 sg21633 + +lemma sg27633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg962 sg21126 + +lemma sg27634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg145 sg21622 + +lemma sg27635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg21180 + +lemma sg27636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg145 sg21623 + +lemma sg27637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg145 sg21624 + +lemma sg27638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg145 sg21625 + +lemma sg27639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg145 sg21626 + +lemma sg27640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg145 sg21627 + +lemma sg27641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg967 sg21123 + +lemma sg27642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1309 sg20967 + +lemma sg27643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg288 sg21339 + +lemma sg27644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg21181 + +lemma sg27645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg288 sg21340 + +lemma sg27646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg288 sg21341 + +lemma sg27647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg288 sg21342 + +lemma sg27648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg288 sg21343 + +lemma sg27649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg288 sg21344 + +lemma sg27650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg331 sg21328 + +lemma sg27651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg548 sg21265 + +lemma sg27652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg331 sg21329 + +lemma sg27653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg21182 + +lemma sg27654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg331 sg21330 + +lemma sg27655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg331 sg21331 + +lemma sg27656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg331 sg21332 + +lemma sg27657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg331 sg21333 + +lemma sg27658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg548 sg21266 + +lemma sg27659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg548 sg21267 + +lemma sg27660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg21183 + +lemma sg27661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10196 + +lemma sg27662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11287 + +lemma sg27663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11486 + +lemma sg27664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6124 sg11758 + +lemma sg27665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8 sg21670 + +lemma sg27666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10197 + +lemma sg27667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10173 + +lemma sg27668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11261 + +lemma sg27669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6903 sg11481 + +lemma sg27670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10174 + +lemma sg27671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8508 sg10168 + +lemma sg27672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg7458 sg11257 + +lemma sg27673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg6125 sg11757 + +lemma sg27674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8517 sg10167 + +lemma sg27675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg7460 sg11256 + +lemma sg27676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,3,3,3,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg6363 sg11739 + +lemma sg27677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21022 + +lemma sg27678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg73 sg21650 + +lemma sg27679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg73 sg21651 + +lemma sg27680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg73 sg21652 + +lemma sg27681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg73 sg21653 + +lemma sg27682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg73 sg21654 + +lemma sg27683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg73 sg21655 + +lemma sg27684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21001 + +lemma sg27685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18260 + +lemma sg27686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg127 sg21628 + +lemma sg27687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg127 sg21629 + +lemma sg27688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg127 sg21630 + +lemma sg27689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg127 sg21631 + +lemma sg27690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg127 sg21632 + +lemma sg27691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg127 sg21633 + +lemma sg27692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1290 sg21000 + +lemma sg27693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg18248 + +lemma sg27694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18261 + +lemma sg27695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg146 sg21623 + +lemma sg27696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg146 sg21624 + +lemma sg27697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg146 sg21625 + +lemma sg27698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg146 sg21626 + +lemma sg27699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg146 sg21627 + +lemma sg27700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg963 sg21126 + +lemma sg27701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1309 sg20969 + +lemma sg27702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg850 sg21168 + +lemma sg27703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg21184 + +lemma sg27704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg289 sg21340 + +lemma sg27705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg289 sg21341 + +lemma sg27706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg289 sg21342 + +lemma sg27707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg289 sg21343 + +lemma sg27708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg289 sg21344 + +lemma sg27709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg987 sg21107 + +lemma sg27710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1310 sg20967 + +lemma sg27711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1309 sg20970 + +lemma sg27712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg850 sg21169 + +lemma sg27713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg21185 + +lemma sg27714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg332 sg21330 + +lemma sg27715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg332 sg21331 + +lemma sg27716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg332 sg21332 + +lemma sg27717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg332 sg21333 + +lemma sg27718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg549 sg21265 + +lemma sg27719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg561 sg21247 + +lemma sg27720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg850 sg21170 + +lemma sg27721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg849 sg21186 + +lemma sg27722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10198 + +lemma sg27723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11288 + +lemma sg27724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11487 + +lemma sg27725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6124 sg11759 + +lemma sg27726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg561 sg21248 + +lemma sg27727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg850 sg21171 + +lemma sg27728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10199 + +lemma sg27729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10175 + +lemma sg27730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11262 + +lemma sg27731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6903 sg11482 + +lemma sg27732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10200 + +lemma sg27733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10176 + +lemma sg27734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10173 + +lemma sg27735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7457 sg11261 + +lemma sg27736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg6904 sg11481 + +lemma sg27737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10174 + +lemma sg27738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8509 sg10168 + +lemma sg27739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg7459 sg11257 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes68.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes68.lean index 922a1285b9ce1652ec7afd61739f43b2253a430f..8b1c6f1450b9a8b92336c262b7d0437bd7d3afe8 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes68.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes68.lean @@ -1,1223 +1,1223 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 68. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg27740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8518 sg10167 - -lemma sg27741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg7461 sg11256 - -lemma sg27742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1309 sg20971 - -lemma sg27743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg18249 - -lemma sg27744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18262 - -lemma sg27745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg147 sg21623 - -lemma sg27746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg147 sg21624 - -lemma sg27747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg147 sg21625 - -lemma sg27748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg147 sg21626 - -lemma sg27749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg147 sg21627 - -lemma sg27750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1302 sg20977 - -lemma sg27751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1703 sg18259 - -lemma sg27752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg18250 - -lemma sg27753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2173 sg15586 - -lemma sg27754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg290 sg21340 - -lemma sg27755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg290 sg21341 - -lemma sg27756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg290 sg21342 - -lemma sg27757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg290 sg21343 - -lemma sg27758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg290 sg21344 - -lemma sg27759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg983 sg21110 - -lemma sg27760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1302 sg20978 - -lemma sg27761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1309 sg20972 - -lemma sg27762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg850 sg21172 - -lemma sg27763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21023 - -lemma sg27764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg333 sg21330 - -lemma sg27765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg333 sg21331 - -lemma sg27766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg333 sg21332 - -lemma sg27767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg333 sg21333 - -lemma sg27768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1311 sg20967 - -lemma sg27769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1302 sg20979 - -lemma sg27770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1812 sg17128 - -lemma sg27771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg850 sg21173 - -lemma sg27772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21024 - -lemma sg27773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10201 - -lemma sg27774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11289 - -lemma sg27775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11488 - -lemma sg27776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6124 sg11760 - -lemma sg27777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg565 sg21234 - -lemma sg27778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg855 sg21159 - -lemma sg27779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg850 sg21174 - -lemma sg27780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10202 - -lemma sg27781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10177 - -lemma sg27782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11263 - -lemma sg27783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6903 sg11483 - -lemma sg27784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg855 sg21160 - -lemma sg27785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10203 - -lemma sg27786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10178 - -lemma sg27787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8508 sg10170 - -lemma sg27788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7458 sg11258 - -lemma sg27789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6023 sg11788 - -lemma sg27790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8219 sg10851 - -lemma sg27791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11264 - -lemma sg27792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8492 sg10173 - -lemma sg27793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8343 sg10734 - -lemma sg27794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8849 sg9159 - -lemma sg27795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8510 sg10168 - -lemma sg27796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg7799 sg11242 - -lemma sg27797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8519 sg10167 - -lemma sg27798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1303 sg20977 - -lemma sg27799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1727 sg18242 - -lemma sg27800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1811 sg17139 - -lemma sg27801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2200 sg15562 - -lemma sg27802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2185 sg15567 - -lemma sg27803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg334 sg21330 - -lemma sg27804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg334 sg21331 - -lemma sg27805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg334 sg21332 - -lemma sg27806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg334 sg21333 - -lemma sg27807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1304 sg20977 - -lemma sg27808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1303 sg20978 - -lemma sg27809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1320 sg20963 - -lemma sg27810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1811 sg17140 - -lemma sg27811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21002 - -lemma sg27812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21025 - -lemma sg27813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10204 - -lemma sg27814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11290 - -lemma sg27815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11489 - -lemma sg27816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6124 sg11761 - -lemma sg27817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1460 sg20940 - -lemma sg27818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1813 sg17128 - -lemma sg27819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1811 sg17141 - -lemma sg27820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21003 - -lemma sg27821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10205 - -lemma sg27822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10179 - -lemma sg27823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11265 - -lemma sg27824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6903 sg11484 - -lemma sg27825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg863 sg21148 - -lemma sg27826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg962 sg21127 - -lemma sg27827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10206 - -lemma sg27828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10180 - -lemma sg27829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8508 sg10171 - -lemma sg27830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7458 sg11259 - -lemma sg27831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg863 sg21151 - -lemma sg27832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg962 sg21128 - -lemma sg27833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11291 - -lemma sg27834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11266 - -lemma sg27835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8469 sg10196 - -lemma sg27836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8344 sg10703 - -lemma sg27837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11490 - -lemma sg27838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8827 sg9172 - -lemma sg27839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8493 sg10173 - -lemma sg27840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8343 sg10735 - -lemma sg27841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8850 sg9159 - -lemma sg27842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8679 sg9657 - -lemma sg27843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8520 sg10167 - -lemma sg27844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1304 sg20978 - -lemma sg27845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1474 sg20925 - -lemma sg27846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1839 sg17104 - -lemma sg27847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1832 sg17108 - -lemma sg27848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg362 sg21294 - -lemma sg27849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10207 - -lemma sg27850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10181 - -lemma sg27851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11267 - -lemma sg27852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6903 sg11485 - -lemma sg27853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1474 sg20926 - -lemma sg27854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg967 sg21124 - -lemma sg27855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg962 sg21129 - -lemma sg27856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10208 - -lemma sg27857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10182 - -lemma sg27858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8508 sg10172 - -lemma sg27859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7458 sg11260 - -lemma sg27860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg572 sg21223 - -lemma sg27861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3866 sg14511 - -lemma sg27862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg962 sg21130 - -lemma sg27863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11292 - -lemma sg27864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11268 - -lemma sg27865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10411 - -lemma sg27866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8871 sg9003 - -lemma sg27867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6956 sg11467 - -lemma sg27868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11492 - -lemma sg27869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9229 - -lemma sg27870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8470 sg10196 - -lemma sg27871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8647 sg9874 - -lemma sg27872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9230 - -lemma sg27873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8871 sg9004 - -lemma sg27874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8343 sg10736 - -lemma sg27875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8851 sg9159 - -lemma sg27876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10411 - -lemma sg27877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1474 sg20927 - -lemma sg27878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3876 sg14504 - -lemma sg27879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg962 sg21131 - -lemma sg27880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5553 sg12625 - -lemma sg27881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5972 sg11830 - -lemma sg27882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10321 - -lemma sg27883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8380 sg10611 - -lemma sg27884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3866 sg14512 - -lemma sg27885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5554 sg12625 - -lemma sg27886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5973 sg11830 - -lemma sg27887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10412 - -lemma sg27888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10321 - -lemma sg27889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8723 sg9531 - -lemma sg27890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5974 sg11830 - -lemma sg27891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10323 - -lemma sg27892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9229 - -lemma sg27893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8647 sg9875 - -lemma sg27894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9230 - -lemma sg27895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10737 - -lemma sg27896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10321 - -lemma sg27897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10412 - -lemma sg27898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5580 sg12617 - -lemma sg27899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6008 sg11826 - -lemma sg27900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10413 - -lemma sg27901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10322 - -lemma sg27902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8723 sg9532 - -lemma sg27903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10414 - -lemma sg27904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10323 - -lemma sg27905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9876 - -lemma sg27906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9532 - -lemma sg27907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10738 - -lemma sg27908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10413 - -lemma sg27909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9876 - -lemma sg27910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8403 sg10595 - -lemma sg27911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10739 - -lemma sg27912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10414 - -lemma sg27913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10323 - -lemma sg27914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,4,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9877 - -lemma sg27915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,4,4,1] := by - exact rowSquare_join (by decide) sg8798 sg9230 - -lemma sg27916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21004 - -lemma sg27917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18263 - -lemma sg27918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg128 sg21628 - -lemma sg27919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg128 sg21629 - -lemma sg27920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg128 sg21630 - -lemma sg27921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg128 sg21631 - -lemma sg27922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg128 sg21632 - -lemma sg27923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg128 sg21633 - -lemma sg27924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1290 sg21001 - -lemma sg27925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg18251 - -lemma sg27926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18264 - -lemma sg27927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg21623 - -lemma sg27928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg21624 - -lemma sg27929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg21625 - -lemma sg27930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg148 sg21626 - -lemma sg27931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg148 sg21627 - -lemma sg27932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1310 sg20968 - -lemma sg27933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1710 sg18248 - -lemma sg27934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg18252 - -lemma sg27935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2174 sg15576 - -lemma sg27936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg291 sg21340 - -lemma sg27937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg291 sg21341 - -lemma sg27938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg291 sg21342 - -lemma sg27939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg291 sg21343 - -lemma sg27940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg291 sg21344 - -lemma sg27941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg985 sg21110 - -lemma sg27942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1310 sg20969 - -lemma sg27943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1309 sg20974 - -lemma sg27944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg850 sg21175 - -lemma sg27945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21026 - -lemma sg27946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg336 sg21318 - -lemma sg27947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg336 sg21319 - -lemma sg27948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg336 sg21320 - -lemma sg27949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg336 sg21321 - -lemma sg27950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1313 sg20967 - -lemma sg27951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1310 sg20970 - -lemma sg27952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg17128 - -lemma sg27953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg850 sg21176 - -lemma sg27954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21027 - -lemma sg27955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10209 - -lemma sg27956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11293 - -lemma sg27957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11493 - -lemma sg27958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6124 sg11762 - -lemma sg27959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg562 sg21247 - -lemma sg27960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg851 sg21170 - -lemma sg27961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg850 sg21177 - -lemma sg27962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10210 - -lemma sg27963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10183 - -lemma sg27964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11269 - -lemma sg27965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg562 sg21249 - -lemma sg27966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg851 sg21171 - -lemma sg27967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10211 - -lemma sg27968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11294 - -lemma sg27969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10175 - -lemma sg27970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7457 sg11262 - -lemma sg27971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6904 sg11482 - -lemma sg27972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10184 - -lemma sg27973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10176 - -lemma sg27974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8496 sg10173 - -lemma sg27975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8343 sg10740 - -lemma sg27976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8852 sg9159 - -lemma sg27977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8512 sg10168 - -lemma sg27978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg7800 sg11242 - -lemma sg27979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8521 sg10167 - -lemma sg27980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1302 sg20980 - -lemma sg27981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1703 sg18260 - -lemma sg27982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg18253 - -lemma sg27983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2173 sg15587 - -lemma sg27984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg292 sg21340 - -lemma sg27985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg292 sg21341 - -lemma sg27986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg292 sg21342 - -lemma sg27987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg292 sg21343 - -lemma sg27988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg292 sg21344 - -lemma sg27989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1303 sg20980 - -lemma sg27990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1704 sg18259 - -lemma sg27991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1811 sg17142 - -lemma sg27992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15576 - -lemma sg27993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2173 sg15588 - -lemma sg27994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg337 sg21318 - -lemma sg27995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg337 sg21319 - -lemma sg27996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg337 sg21320 - -lemma sg27997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg337 sg21321 - -lemma sg27998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1304 sg20980 - -lemma sg27999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1305 sg20978 - -lemma sg28000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1302 sg20981 - -lemma sg28001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1812 sg17130 - -lemma sg28002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21005 - -lemma sg28003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21028 - -lemma sg28004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10212 - -lemma sg28005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11295 - -lemma sg28006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11494 - -lemma sg28007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6124 sg11763 - -lemma sg28008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1462 sg20940 - -lemma sg28009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1815 sg17128 - -lemma sg28010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1812 sg17131 - -lemma sg28011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21006 - -lemma sg28012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10213 - -lemma sg28013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10185 - -lemma sg28014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11271 - -lemma sg28015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6124 sg11764 - -lemma sg28016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg852 sg21170 - -lemma sg28017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg21136 - -lemma sg28018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10214 - -lemma sg28019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11296 - -lemma sg28020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10177 - -lemma sg28021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7457 sg11263 - -lemma sg28022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6904 sg11483 - -lemma sg28023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10215 - -lemma sg28024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10186 - -lemma sg28025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10178 - -lemma sg28026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8475 sg10196 - -lemma sg28027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8344 sg10704 - -lemma sg28028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11272 - -lemma sg28029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8831 sg9172 - -lemma sg28030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8497 sg10173 - -lemma sg28031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8343 sg10741 - -lemma sg28032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8853 sg9159 - -lemma sg28033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8680 sg9657 - -lemma sg28034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8522 sg10167 - -lemma sg28035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1306 sg20977 - -lemma sg28036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1705 sg18259 - -lemma sg28037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1813 sg17129 - -lemma sg28038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2176 sg15576 - -lemma sg28039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2186 sg15567 - -lemma sg28040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2665 sg15036 - -lemma sg28041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10216 - -lemma sg28042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11297 - -lemma sg28043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11495 - -lemma sg28044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6124 sg11765 - -lemma sg28045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1713 sg18248 - -lemma sg28046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1460 sg20941 - -lemma sg28047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1813 sg17130 - -lemma sg28048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1811 sg17143 - -lemma sg28049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21007 - -lemma sg28050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10217 - -lemma sg28051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10187 - -lemma sg28052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11273 - -lemma sg28053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg564 sg21249 - -lemma sg28054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2177 sg15576 - -lemma sg28055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1813 sg17131 - -lemma sg28056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2222 sg15538 - -lemma sg28057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10218 - -lemma sg28058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11298 - -lemma sg28059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10179 - -lemma sg28060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7457 sg11265 - -lemma sg28061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6904 sg11484 - -lemma sg28062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3866 sg14513 - -lemma sg28063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10219 - -lemma sg28064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10188 - -lemma sg28065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10180 - -lemma sg28066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10415 - -lemma sg28067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8874 sg9003 - -lemma sg28068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11299 - -lemma sg28069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11274 - -lemma sg28070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9229 - -lemma sg28071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8476 sg10196 - -lemma sg28072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8647 sg9878 - -lemma sg28073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9230 - -lemma sg28074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8874 sg9004 - -lemma sg28075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8343 sg10742 - -lemma sg28076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8854 sg9159 - -lemma sg28077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10415 - -lemma sg28078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1461 sg20941 - -lemma sg28079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1840 sg17104 - -lemma sg28080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1833 sg17108 - -lemma sg28081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2243 sg15513 - -lemma sg28082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10220 - -lemma sg28083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11300 - -lemma sg28084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10181 - -lemma sg28085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7457 sg11267 - -lemma sg28086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6904 sg11485 - -lemma sg28087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1470 sg20930 - -lemma sg28088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3867 sg14511 - -lemma sg28089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10221 - -lemma sg28090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10189 - -lemma sg28091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10182 - -lemma sg28092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10324 - -lemma sg28093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8871 sg9005 - -lemma sg28094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3866 sg14514 - -lemma sg28095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11301 - -lemma sg28096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11276 - -lemma sg28097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10416 - -lemma sg28098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10324 - -lemma sg28099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8649 sg9874 - -lemma sg28100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11496 - -lemma sg28101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10323 - -lemma sg28102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9229 - -lemma sg28103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8647 sg9879 - -lemma sg28104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9230 - -lemma sg28105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10743 - -lemma sg28106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10324 - -lemma sg28107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10416 - -lemma sg28108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3878 sg14504 - -lemma sg28109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3867 sg14512 - -lemma sg28110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5555 sg12625 - -lemma sg28111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5976 sg11830 - -lemma sg28112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10325 - -lemma sg28113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10248 - -lemma sg28114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8726 sg9531 - -lemma sg28115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5556 sg12625 - -lemma sg28116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5977 sg11830 - -lemma sg28117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10417 - -lemma sg28118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10325 - -lemma sg28119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8649 sg9875 - -lemma sg28120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10327 - -lemma sg28121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9231 - -lemma sg28122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9880 - -lemma sg28123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9875 - -lemma sg28124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10744 - -lemma sg28125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10417 - -lemma sg28126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9880 - -lemma sg28127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6009 sg11826 - -lemma sg28128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10418 - -lemma sg28129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10326 - -lemma sg28130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9876 - -lemma sg28131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9532 - -lemma sg28132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10327 - -lemma sg28133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10745 - -lemma sg28134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10418 - -lemma sg28135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10326 - -lemma sg28136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9881 - -lemma sg28137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9882 - -lemma sg28138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10327 - -lemma sg28139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,4,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9882 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 68. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg27740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8518 sg10167 + +lemma sg27741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,3,3,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg7461 sg11256 + +lemma sg27742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1309 sg20971 + +lemma sg27743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg18249 + +lemma sg27744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18262 + +lemma sg27745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg147 sg21623 + +lemma sg27746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg147 sg21624 + +lemma sg27747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg147 sg21625 + +lemma sg27748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg147 sg21626 + +lemma sg27749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg147 sg21627 + +lemma sg27750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1302 sg20977 + +lemma sg27751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1703 sg18259 + +lemma sg27752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg18250 + +lemma sg27753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2173 sg15586 + +lemma sg27754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg290 sg21340 + +lemma sg27755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg290 sg21341 + +lemma sg27756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg290 sg21342 + +lemma sg27757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg290 sg21343 + +lemma sg27758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg290 sg21344 + +lemma sg27759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg983 sg21110 + +lemma sg27760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1302 sg20978 + +lemma sg27761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1309 sg20972 + +lemma sg27762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg850 sg21172 + +lemma sg27763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21023 + +lemma sg27764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg333 sg21330 + +lemma sg27765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg333 sg21331 + +lemma sg27766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg333 sg21332 + +lemma sg27767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg333 sg21333 + +lemma sg27768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1311 sg20967 + +lemma sg27769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1302 sg20979 + +lemma sg27770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1812 sg17128 + +lemma sg27771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg850 sg21173 + +lemma sg27772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21024 + +lemma sg27773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10201 + +lemma sg27774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11289 + +lemma sg27775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11488 + +lemma sg27776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6124 sg11760 + +lemma sg27777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg565 sg21234 + +lemma sg27778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg855 sg21159 + +lemma sg27779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg850 sg21174 + +lemma sg27780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10202 + +lemma sg27781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10177 + +lemma sg27782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11263 + +lemma sg27783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6903 sg11483 + +lemma sg27784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg855 sg21160 + +lemma sg27785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10203 + +lemma sg27786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10178 + +lemma sg27787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8508 sg10170 + +lemma sg27788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7458 sg11258 + +lemma sg27789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6023 sg11788 + +lemma sg27790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8219 sg10851 + +lemma sg27791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11264 + +lemma sg27792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8492 sg10173 + +lemma sg27793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8343 sg10734 + +lemma sg27794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8849 sg9159 + +lemma sg27795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8510 sg10168 + +lemma sg27796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg7799 sg11242 + +lemma sg27797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,3,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8519 sg10167 + +lemma sg27798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1303 sg20977 + +lemma sg27799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1727 sg18242 + +lemma sg27800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1811 sg17139 + +lemma sg27801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2200 sg15562 + +lemma sg27802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2185 sg15567 + +lemma sg27803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg334 sg21330 + +lemma sg27804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg334 sg21331 + +lemma sg27805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg334 sg21332 + +lemma sg27806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg334 sg21333 + +lemma sg27807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1304 sg20977 + +lemma sg27808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1303 sg20978 + +lemma sg27809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1320 sg20963 + +lemma sg27810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1811 sg17140 + +lemma sg27811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21002 + +lemma sg27812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21025 + +lemma sg27813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10204 + +lemma sg27814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11290 + +lemma sg27815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11489 + +lemma sg27816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6124 sg11761 + +lemma sg27817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1460 sg20940 + +lemma sg27818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1813 sg17128 + +lemma sg27819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1811 sg17141 + +lemma sg27820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21003 + +lemma sg27821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10205 + +lemma sg27822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10179 + +lemma sg27823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11265 + +lemma sg27824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6903 sg11484 + +lemma sg27825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg863 sg21148 + +lemma sg27826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg962 sg21127 + +lemma sg27827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10206 + +lemma sg27828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10180 + +lemma sg27829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8508 sg10171 + +lemma sg27830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7458 sg11259 + +lemma sg27831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg863 sg21151 + +lemma sg27832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg962 sg21128 + +lemma sg27833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11291 + +lemma sg27834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11266 + +lemma sg27835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8469 sg10196 + +lemma sg27836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8344 sg10703 + +lemma sg27837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11490 + +lemma sg27838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8827 sg9172 + +lemma sg27839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8493 sg10173 + +lemma sg27840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8343 sg10735 + +lemma sg27841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8850 sg9159 + +lemma sg27842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8679 sg9657 + +lemma sg27843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8520 sg10167 + +lemma sg27844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1304 sg20978 + +lemma sg27845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1474 sg20925 + +lemma sg27846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1839 sg17104 + +lemma sg27847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1832 sg17108 + +lemma sg27848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg362 sg21294 + +lemma sg27849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10207 + +lemma sg27850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10181 + +lemma sg27851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11267 + +lemma sg27852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6903 sg11485 + +lemma sg27853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1474 sg20926 + +lemma sg27854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg967 sg21124 + +lemma sg27855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg962 sg21129 + +lemma sg27856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10208 + +lemma sg27857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10182 + +lemma sg27858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8508 sg10172 + +lemma sg27859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7458 sg11260 + +lemma sg27860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg572 sg21223 + +lemma sg27861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3866 sg14511 + +lemma sg27862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg962 sg21130 + +lemma sg27863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11292 + +lemma sg27864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11268 + +lemma sg27865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10411 + +lemma sg27866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8871 sg9003 + +lemma sg27867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6956 sg11467 + +lemma sg27868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11492 + +lemma sg27869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9229 + +lemma sg27870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8470 sg10196 + +lemma sg27871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8647 sg9874 + +lemma sg27872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9230 + +lemma sg27873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8871 sg9004 + +lemma sg27874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8343 sg10736 + +lemma sg27875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8851 sg9159 + +lemma sg27876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10411 + +lemma sg27877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1474 sg20927 + +lemma sg27878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3876 sg14504 + +lemma sg27879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg962 sg21131 + +lemma sg27880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5553 sg12625 + +lemma sg27881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5972 sg11830 + +lemma sg27882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10321 + +lemma sg27883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8380 sg10611 + +lemma sg27884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3866 sg14512 + +lemma sg27885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5554 sg12625 + +lemma sg27886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5973 sg11830 + +lemma sg27887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10412 + +lemma sg27888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10321 + +lemma sg27889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8723 sg9531 + +lemma sg27890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5974 sg11830 + +lemma sg27891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10323 + +lemma sg27892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9229 + +lemma sg27893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8647 sg9875 + +lemma sg27894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9230 + +lemma sg27895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10737 + +lemma sg27896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10321 + +lemma sg27897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10412 + +lemma sg27898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5580 sg12617 + +lemma sg27899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6008 sg11826 + +lemma sg27900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10413 + +lemma sg27901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10322 + +lemma sg27902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8723 sg9532 + +lemma sg27903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10414 + +lemma sg27904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10323 + +lemma sg27905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9876 + +lemma sg27906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9532 + +lemma sg27907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10738 + +lemma sg27908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10413 + +lemma sg27909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9876 + +lemma sg27910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8403 sg10595 + +lemma sg27911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10739 + +lemma sg27912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10414 + +lemma sg27913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10323 + +lemma sg27914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,4,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9877 + +lemma sg27915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,4,4,4,4,4,4,4,4,1] := by + exact rowSquare_join (by decide) sg8798 sg9230 + +lemma sg27916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21004 + +lemma sg27917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18263 + +lemma sg27918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg128 sg21628 + +lemma sg27919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg128 sg21629 + +lemma sg27920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg128 sg21630 + +lemma sg27921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg128 sg21631 + +lemma sg27922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg128 sg21632 + +lemma sg27923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,2,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg128 sg21633 + +lemma sg27924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1290 sg21001 + +lemma sg27925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg18251 + +lemma sg27926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18264 + +lemma sg27927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg21623 + +lemma sg27928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg21624 + +lemma sg27929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg21625 + +lemma sg27930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg148 sg21626 + +lemma sg27931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg148 sg21627 + +lemma sg27932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1310 sg20968 + +lemma sg27933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1710 sg18248 + +lemma sg27934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg18252 + +lemma sg27935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2174 sg15576 + +lemma sg27936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg291 sg21340 + +lemma sg27937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg291 sg21341 + +lemma sg27938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg291 sg21342 + +lemma sg27939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg291 sg21343 + +lemma sg27940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg291 sg21344 + +lemma sg27941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg985 sg21110 + +lemma sg27942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1310 sg20969 + +lemma sg27943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1309 sg20974 + +lemma sg27944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg850 sg21175 + +lemma sg27945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21026 + +lemma sg27946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg336 sg21318 + +lemma sg27947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg336 sg21319 + +lemma sg27948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg336 sg21320 + +lemma sg27949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg336 sg21321 + +lemma sg27950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1313 sg20967 + +lemma sg27951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1310 sg20970 + +lemma sg27952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg17128 + +lemma sg27953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg850 sg21176 + +lemma sg27954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21027 + +lemma sg27955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10209 + +lemma sg27956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11293 + +lemma sg27957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11493 + +lemma sg27958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6124 sg11762 + +lemma sg27959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg562 sg21247 + +lemma sg27960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg851 sg21170 + +lemma sg27961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg850 sg21177 + +lemma sg27962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10210 + +lemma sg27963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10183 + +lemma sg27964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11269 + +lemma sg27965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg562 sg21249 + +lemma sg27966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg851 sg21171 + +lemma sg27967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10211 + +lemma sg27968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11294 + +lemma sg27969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10175 + +lemma sg27970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7457 sg11262 + +lemma sg27971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6904 sg11482 + +lemma sg27972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10184 + +lemma sg27973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10176 + +lemma sg27974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8496 sg10173 + +lemma sg27975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8343 sg10740 + +lemma sg27976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8852 sg9159 + +lemma sg27977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8512 sg10168 + +lemma sg27978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg7800 sg11242 + +lemma sg27979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,3,3,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8521 sg10167 + +lemma sg27980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1302 sg20980 + +lemma sg27981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1703 sg18260 + +lemma sg27982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg18253 + +lemma sg27983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2173 sg15587 + +lemma sg27984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg292 sg21340 + +lemma sg27985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg292 sg21341 + +lemma sg27986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg292 sg21342 + +lemma sg27987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg292 sg21343 + +lemma sg27988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg292 sg21344 + +lemma sg27989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1303 sg20980 + +lemma sg27990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1704 sg18259 + +lemma sg27991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1811 sg17142 + +lemma sg27992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15576 + +lemma sg27993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2173 sg15588 + +lemma sg27994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg337 sg21318 + +lemma sg27995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg337 sg21319 + +lemma sg27996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg337 sg21320 + +lemma sg27997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg337 sg21321 + +lemma sg27998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1304 sg20980 + +lemma sg27999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1305 sg20978 + +lemma sg28000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1302 sg20981 + +lemma sg28001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1812 sg17130 + +lemma sg28002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21005 + +lemma sg28003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21028 + +lemma sg28004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10212 + +lemma sg28005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11295 + +lemma sg28006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11494 + +lemma sg28007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6124 sg11763 + +lemma sg28008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1462 sg20940 + +lemma sg28009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1815 sg17128 + +lemma sg28010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1812 sg17131 + +lemma sg28011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21006 + +lemma sg28012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10213 + +lemma sg28013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10185 + +lemma sg28014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11271 + +lemma sg28015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6124 sg11764 + +lemma sg28016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg852 sg21170 + +lemma sg28017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg21136 + +lemma sg28018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10214 + +lemma sg28019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11296 + +lemma sg28020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10177 + +lemma sg28021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7457 sg11263 + +lemma sg28022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6904 sg11483 + +lemma sg28023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10215 + +lemma sg28024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10186 + +lemma sg28025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10178 + +lemma sg28026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8475 sg10196 + +lemma sg28027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8344 sg10704 + +lemma sg28028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11272 + +lemma sg28029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8831 sg9172 + +lemma sg28030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8497 sg10173 + +lemma sg28031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8343 sg10741 + +lemma sg28032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8853 sg9159 + +lemma sg28033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8680 sg9657 + +lemma sg28034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8522 sg10167 + +lemma sg28035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1306 sg20977 + +lemma sg28036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1705 sg18259 + +lemma sg28037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1813 sg17129 + +lemma sg28038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2176 sg15576 + +lemma sg28039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2186 sg15567 + +lemma sg28040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2665 sg15036 + +lemma sg28041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10216 + +lemma sg28042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11297 + +lemma sg28043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11495 + +lemma sg28044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6124 sg11765 + +lemma sg28045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1713 sg18248 + +lemma sg28046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1460 sg20941 + +lemma sg28047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1813 sg17130 + +lemma sg28048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1811 sg17143 + +lemma sg28049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21007 + +lemma sg28050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10217 + +lemma sg28051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10187 + +lemma sg28052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11273 + +lemma sg28053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg564 sg21249 + +lemma sg28054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2177 sg15576 + +lemma sg28055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1813 sg17131 + +lemma sg28056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2222 sg15538 + +lemma sg28057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10218 + +lemma sg28058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11298 + +lemma sg28059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10179 + +lemma sg28060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7457 sg11265 + +lemma sg28061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6904 sg11484 + +lemma sg28062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3866 sg14513 + +lemma sg28063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10219 + +lemma sg28064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10188 + +lemma sg28065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10180 + +lemma sg28066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10415 + +lemma sg28067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8874 sg9003 + +lemma sg28068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11299 + +lemma sg28069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11274 + +lemma sg28070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9229 + +lemma sg28071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8476 sg10196 + +lemma sg28072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8647 sg9878 + +lemma sg28073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9230 + +lemma sg28074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8874 sg9004 + +lemma sg28075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8343 sg10742 + +lemma sg28076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8854 sg9159 + +lemma sg28077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10415 + +lemma sg28078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1461 sg20941 + +lemma sg28079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1840 sg17104 + +lemma sg28080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1833 sg17108 + +lemma sg28081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2243 sg15513 + +lemma sg28082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10220 + +lemma sg28083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11300 + +lemma sg28084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10181 + +lemma sg28085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7457 sg11267 + +lemma sg28086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6904 sg11485 + +lemma sg28087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1470 sg20930 + +lemma sg28088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3867 sg14511 + +lemma sg28089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10221 + +lemma sg28090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10189 + +lemma sg28091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10182 + +lemma sg28092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10324 + +lemma sg28093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8871 sg9005 + +lemma sg28094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3866 sg14514 + +lemma sg28095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11301 + +lemma sg28096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11276 + +lemma sg28097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10416 + +lemma sg28098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10324 + +lemma sg28099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8649 sg9874 + +lemma sg28100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11496 + +lemma sg28101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10323 + +lemma sg28102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9229 + +lemma sg28103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8647 sg9879 + +lemma sg28104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9230 + +lemma sg28105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10743 + +lemma sg28106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10324 + +lemma sg28107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10416 + +lemma sg28108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3878 sg14504 + +lemma sg28109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3867 sg14512 + +lemma sg28110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5555 sg12625 + +lemma sg28111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5976 sg11830 + +lemma sg28112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10325 + +lemma sg28113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10248 + +lemma sg28114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8726 sg9531 + +lemma sg28115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5556 sg12625 + +lemma sg28116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5977 sg11830 + +lemma sg28117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10417 + +lemma sg28118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10325 + +lemma sg28119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8649 sg9875 + +lemma sg28120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10327 + +lemma sg28121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9231 + +lemma sg28122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9880 + +lemma sg28123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9875 + +lemma sg28124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10744 + +lemma sg28125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10417 + +lemma sg28126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9880 + +lemma sg28127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6009 sg11826 + +lemma sg28128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10418 + +lemma sg28129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10326 + +lemma sg28130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9876 + +lemma sg28131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9532 + +lemma sg28132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10327 + +lemma sg28133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10745 + +lemma sg28134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10418 + +lemma sg28135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10326 + +lemma sg28136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9881 + +lemma sg28137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9882 + +lemma sg28138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10327 + +lemma sg28139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,4,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9882 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes69.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes69.lean index 406ddf1c3d565d5b3c576b0ac1c0ef90e6c139a1..99b777ce145f40cc2973b81c20dd3ac857d14a74 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes69.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes69.lean @@ -1,1224 +1,1224 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 69. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg28140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,4,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10323 - -lemma sg28141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1311 sg20971 - -lemma sg28142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1711 sg18249 - -lemma sg28143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1812 sg17132 - -lemma sg28144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15577 - -lemma sg28145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2173 sg15589 - -lemma sg28146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg340 sg21303 - -lemma sg28147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg340 sg21304 - -lemma sg28148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg340 sg21305 - -lemma sg28149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg340 sg21306 - -lemma sg28150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1312 sg20971 - -lemma sg28151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1712 sg18249 - -lemma sg28152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1813 sg17132 - -lemma sg28153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2176 sg15577 - -lemma sg28154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15578 - -lemma sg28155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2665 sg15037 - -lemma sg28156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg556 sg21253 - -lemma sg28157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg556 sg21254 - -lemma sg28158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg556 sg21255 - -lemma sg28159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg556 sg21256 - -lemma sg28160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1713 sg18249 - -lemma sg28161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1465 sg20936 - -lemma sg28162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1820 sg17116 - -lemma sg28163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1812 sg17133 - -lemma sg28164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21008 - -lemma sg28165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18265 - -lemma sg28166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11302 - -lemma sg28167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg567 sg21236 - -lemma sg28168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6124 sg11766 - -lemma sg28169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2177 sg15577 - -lemma sg28170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1820 sg17117 - -lemma sg28171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2228 sg15522 - -lemma sg28172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21009 - -lemma sg28173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11303 - -lemma sg28174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11277 - -lemma sg28175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5351 sg12654 - -lemma sg28176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6023 sg11790 - -lemma sg28177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3866 sg14515 - -lemma sg28178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10222 - -lemma sg28179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11304 - -lemma sg28180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11497 - -lemma sg28181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10419 - -lemma sg28182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8877 sg9003 - -lemma sg28183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10190 - -lemma sg28184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11278 - -lemma sg28185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9229 - -lemma sg28186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8480 sg10196 - -lemma sg28187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8647 sg9883 - -lemma sg28188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9230 - -lemma sg28189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8877 sg9004 - -lemma sg28190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8343 sg10746 - -lemma sg28191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8855 sg9159 - -lemma sg28192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10419 - -lemma sg28193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1308 sg20977 - -lemma sg28194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1707 sg18259 - -lemma sg28195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1821 sg17115 - -lemma sg28196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2187 sg15566 - -lemma sg28197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2222 sg15539 - -lemma sg28198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15024 - -lemma sg28199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2665 sg15038 - -lemma sg28200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11305 - -lemma sg28201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg568 sg21236 - -lemma sg28202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6124 sg11767 - -lemma sg28203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1822 sg17115 - -lemma sg28204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2188 sg15566 - -lemma sg28205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1813 sg17133 - -lemma sg28206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2222 sg15540 - -lemma sg28207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg18254 - -lemma sg28208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11306 - -lemma sg28209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11279 - -lemma sg28210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5351 sg12655 - -lemma sg28211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6023 sg11791 - -lemma sg28212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2177 sg15578 - -lemma sg28213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3876 sg14506 - -lemma sg28214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10223 - -lemma sg28215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11307 - -lemma sg28216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11498 - -lemma sg28217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10328 - -lemma sg28218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8348 sg10703 - -lemma sg28219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10224 - -lemma sg28220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10191 - -lemma sg28221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11280 - -lemma sg28222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10420 - -lemma sg28223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10328 - -lemma sg28224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8723 sg9535 - -lemma sg28225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11281 - -lemma sg28226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10323 - -lemma sg28227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9229 - -lemma sg28228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8647 sg9884 - -lemma sg28229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9230 - -lemma sg28230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10747 - -lemma sg28231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10328 - -lemma sg28232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10420 - -lemma sg28233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1822 sg17116 - -lemma sg28234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1858 sg16196 - -lemma sg28235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3868 sg14511 - -lemma sg28236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10225 - -lemma sg28237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11308 - -lemma sg28238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11499 - -lemma sg28239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8433 sg10251 - -lemma sg28240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8871 sg9006 - -lemma sg28241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3897 sg14499 - -lemma sg28242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10226 - -lemma sg28243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10192 - -lemma sg28244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11282 - -lemma sg28245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10329 - -lemma sg28246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10251 - -lemma sg28247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8651 sg9874 - -lemma sg28248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11309 - -lemma sg28249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8116 sg11053 - -lemma sg28250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10421 - -lemma sg28251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10329 - -lemma sg28252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8723 sg9536 - -lemma sg28253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9234 - -lemma sg28254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9324 - -lemma sg28255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9885 - -lemma sg28256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9536 - -lemma sg28257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10748 - -lemma sg28258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10421 - -lemma sg28259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9885 - -lemma sg28260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1858 sg16197 - -lemma sg28261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5557 sg12625 - -lemma sg28262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5979 sg11830 - -lemma sg28263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10330 - -lemma sg28264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9232 - -lemma sg28265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8651 sg9875 - -lemma sg28266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8117 sg11053 - -lemma sg28267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10422 - -lemma sg28268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10330 - -lemma sg28269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9232 - -lemma sg28270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9595 - -lemma sg28271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9234 - -lemma sg28272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10749 - -lemma sg28273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10422 - -lemma sg28274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10330 - -lemma sg28275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9886 - -lemma sg28276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10423 - -lemma sg28277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10331 - -lemma sg28278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10750 - -lemma sg28279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10423 - -lemma sg28280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9887 - -lemma sg28281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10331 - -lemma sg28282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9887 - -lemma sg28283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9233 - -lemma sg28284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9234 - -lemma sg28285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9234 - -lemma sg28286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1708 sg18259 - -lemma sg28287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1834 sg17107 - -lemma sg28288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2201 sg15562 - -lemma sg28289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2229 sg15523 - -lemma sg28290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2674 sg15015 - -lemma sg28291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15025 - -lemma sg28292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3513 sg14686 - -lemma sg28293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg864 sg21149 - -lemma sg28294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg864 sg21150 - -lemma sg28295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg864 sg21151 - -lemma sg28296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2202 sg15562 - -lemma sg28297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2188 sg15567 - -lemma sg28298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3896 sg14500 - -lemma sg28299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2222 sg15542 - -lemma sg28300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6925 sg11471 - -lemma sg28301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6007 sg11829 - -lemma sg28302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8433 sg10255 - -lemma sg28303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8871 sg9009 - -lemma sg28304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3897 sg14500 - -lemma sg28305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10227 - -lemma sg28306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11310 - -lemma sg28307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11500 - -lemma sg28308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10332 - -lemma sg28309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10255 - -lemma sg28310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8749 sg9472 - -lemma sg28311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10193 - -lemma sg28312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11283 - -lemma sg28313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10424 - -lemma sg28314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10332 - -lemma sg28315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8723 sg9537 - -lemma sg28316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8827 sg9178 - -lemma sg28317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9324 - -lemma sg28318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9888 - -lemma sg28319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9537 - -lemma sg28320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10751 - -lemma sg28321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10424 - -lemma sg28322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9888 - -lemma sg28323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1852 sg16202 - -lemma sg28324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2244 sg15513 - -lemma sg28325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10228 - -lemma sg28326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11311 - -lemma sg28327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11501 - -lemma sg28328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9235 - -lemma sg28329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8470 sg10204 - -lemma sg28330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8652 sg9874 - -lemma sg28331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10229 - -lemma sg28332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10194 - -lemma sg28333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11284 - -lemma sg28334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10333 - -lemma sg28335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9235 - -lemma sg28336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8749 sg9473 - -lemma sg28337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11285 - -lemma sg28338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10425 - -lemma sg28339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10333 - -lemma sg28340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9235 - -lemma sg28341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8750 sg9473 - -lemma sg28342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8871 sg9011 - -lemma sg28343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10752 - -lemma sg28344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10425 - -lemma sg28345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10333 - -lemma sg28346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9889 - -lemma sg28347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5559 sg12625 - -lemma sg28348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5981 sg11830 - -lemma sg28349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10334 - -lemma sg28350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9236 - -lemma sg28351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8828 sg9176 - -lemma sg28352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9595 - -lemma sg28353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10426 - -lemma sg28354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10334 - -lemma sg28355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10753 - -lemma sg28356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10426 - -lemma sg28357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9890 - -lemma sg28358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10334 - -lemma sg28359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9890 - -lemma sg28360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9236 - -lemma sg28361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10335 - -lemma sg28362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9891 - -lemma sg28363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10335 - -lemma sg28364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9891 - -lemma sg28365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9237 - -lemma sg28366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9237 - -lemma sg28367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8829 sg9178 - -lemma sg28368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2245 sg15513 - -lemma sg28369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10230 - -lemma sg28370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11312 - -lemma sg28371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6901 sg11502 - -lemma sg28372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9238 - -lemma sg28373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8871 sg9012 - -lemma sg28374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8771 sg9448 - -lemma sg28375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10195 - -lemma sg28376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11286 - -lemma sg28377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10336 - -lemma sg28378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9238 - -lemma sg28379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8828 sg9179 - -lemma sg28380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8772 sg9448 - -lemma sg28381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10427 - -lemma sg28382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10336 - -lemma sg28383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10754 - -lemma sg28384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10427 - -lemma sg28385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9892 - -lemma sg28386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10336 - -lemma sg28387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9892 - -lemma sg28388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9238 - -lemma sg28389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5982 sg11830 - -lemma sg28390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10428 - -lemma sg28391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10260 - -lemma sg28392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10755 - -lemma sg28393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10428 - -lemma sg28394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10337 - -lemma sg28395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9893 - -lemma sg28396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10337 - -lemma sg28397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9893 - -lemma sg28398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9538 - -lemma sg28399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9538 - -lemma sg28400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8723 sg9539 - -lemma sg28401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9539 - -lemma sg28402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9539 - -lemma sg28403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8751 sg9474 - -lemma sg28404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1474 sg20928 - -lemma sg28405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8382 sg10611 - -lemma sg28406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8365 sg10655 - -lemma sg28407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10156 - -lemma sg28408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,2,2,2,2] := by - exact rowSquare_join (by decide) sg8500 sg10174 - -lemma sg28409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8382 sg10612 - -lemma sg28410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8529 sg10129 - -lemma sg28411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,3,2,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10129 - -lemma sg28412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,3,3,1,1] := by - exact rowSquare_join (by decide) sg8561 sg10099 - -lemma sg28413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8872 sg9016 - -lemma sg28414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,4,2,1,1] := by - exact rowSquare_join (by decide) sg8561 sg10100 - -lemma sg28415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,5,1,1,1] := by - exact rowSquare_join (by decide) sg8600 sg10086 - -lemma sg28416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1290 sg21004 - -lemma sg28417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg18255 - -lemma sg28418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18266 - -lemma sg28419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg151 sg21616 - -lemma sg28420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg151 sg21617 - -lemma sg28421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg151 sg21618 - -lemma sg28422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg151 sg21619 - -lemma sg28423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg151 sg21620 - -lemma sg28424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1302 sg20982 - -lemma sg28425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1703 sg18263 - -lemma sg28426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg18256 - -lemma sg28427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2173 sg15590 - -lemma sg28428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg293 sg21334 - -lemma sg28429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg293 sg21335 - -lemma sg28430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg293 sg21336 - -lemma sg28431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg293 sg21337 - -lemma sg28432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg293 sg21338 - -lemma sg28433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1303 sg20982 - -lemma sg28434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1714 sg18248 - -lemma sg28435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1811 sg17144 - -lemma sg28436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2186 sg15568 - -lemma sg28437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2174 sg15580 - -lemma sg28438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg338 sg21318 - -lemma sg28439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg338 sg21319 - -lemma sg28440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg338 sg21320 - -lemma sg28441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg338 sg21321 - -lemma sg28442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1304 sg20982 - -lemma sg28443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1313 sg20969 - -lemma sg28444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1310 sg20974 - -lemma sg28445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg17130 - -lemma sg28446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21010 - -lemma sg28447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21029 - -lemma sg28448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10231 - -lemma sg28449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11313 - -lemma sg28450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg552 sg21263 - -lemma sg28451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg552 sg21264 - -lemma sg28452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1467 sg20935 - -lemma sg28453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1823 sg17114 - -lemma sg28454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg17131 - -lemma sg28455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21011 - -lemma sg28456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21030 - -lemma sg28457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11314 - -lemma sg28458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg566 sg21239 - -lemma sg28459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg566 sg21240 - -lemma sg28460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg856 sg21164 - -lemma sg28461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg21137 - -lemma sg28462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10232 - -lemma sg28463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11315 - -lemma sg28464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10183 - -lemma sg28465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7457 sg11269 - -lemma sg28466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6025 sg11789 - -lemma sg28467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg21138 - -lemma sg28468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11316 - -lemma sg28469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21031 - -lemma sg28470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8482 sg10196 - -lemma sg28471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8344 sg10705 - -lemma sg28472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10184 - -lemma sg28473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8836 sg9172 - -lemma sg28474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8501 sg10173 - -lemma sg28475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8343 sg10756 - -lemma sg28476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8856 sg9159 - -lemma sg28477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8681 sg9657 - -lemma sg28478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8523 sg10167 - -lemma sg28479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1305 sg20980 - -lemma sg28480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1704 sg18260 - -lemma sg28481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1812 sg17134 - -lemma sg28482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15579 - -lemma sg28483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2173 sg15591 - -lemma sg28484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg339 sg21318 - -lemma sg28485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg339 sg21319 - -lemma sg28486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg339 sg21320 - -lemma sg28487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg339 sg21321 - -lemma sg28488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1306 sg20980 - -lemma sg28489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1705 sg18260 - -lemma sg28490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1813 sg17134 - -lemma sg28491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2176 sg15579 - -lemma sg28492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15580 - -lemma sg28493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2665 sg15039 - -lemma sg28494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10233 - -lemma sg28495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11317 - -lemma sg28496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg553 sg21263 - -lemma sg28497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg553 sg21264 - -lemma sg28498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1713 sg18251 - -lemma sg28499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1462 sg20941 - -lemma sg28500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1815 sg17130 - -lemma sg28501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1812 sg17135 - -lemma sg28502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21013 - -lemma sg28503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18267 - -lemma sg28504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11318 - -lemma sg28505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg567 sg21239 - -lemma sg28506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg567 sg21240 - -lemma sg28507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2177 sg15579 - -lemma sg28508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1815 sg17131 - -lemma sg28509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2228 sg15526 - -lemma sg28510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10234 - -lemma sg28511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11319 - -lemma sg28512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10185 - -lemma sg28513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7457 sg11271 - -lemma sg28514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6023 sg11792 - -lemma sg28515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3866 sg14517 - -lemma sg28516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10235 - -lemma sg28517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11320 - -lemma sg28518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5956 sg11837 - -lemma sg28519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10429 - -lemma sg28520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8346 sg10704 - -lemma sg28521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11321 - -lemma sg28522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10186 - -lemma sg28523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8453 sg10246 - -lemma sg28524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8483 sg10196 - -lemma sg28525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8647 sg9894 - -lemma sg28526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8453 sg10247 - -lemma sg28527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8837 sg9172 - -lemma sg28528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8343 sg10757 - -lemma sg28529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8857 sg9159 - -lemma sg28530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10429 - -lemma sg28531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1315 sg20968 - -lemma sg28532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1716 sg18248 - -lemma sg28533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1816 sg17129 - -lemma sg28534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2179 sg15576 - -lemma sg28535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2222 sg15543 - -lemma sg28536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15026 - -lemma sg28537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2665 sg15040 - -lemma sg28538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg568 sg21238 - -lemma sg28539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg568 sg21239 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 69. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg28140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,4,4,4,4,4,4,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10323 + +lemma sg28141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1311 sg20971 + +lemma sg28142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1711 sg18249 + +lemma sg28143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1812 sg17132 + +lemma sg28144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15577 + +lemma sg28145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2173 sg15589 + +lemma sg28146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg340 sg21303 + +lemma sg28147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg340 sg21304 + +lemma sg28148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg340 sg21305 + +lemma sg28149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg340 sg21306 + +lemma sg28150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1312 sg20971 + +lemma sg28151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1712 sg18249 + +lemma sg28152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1813 sg17132 + +lemma sg28153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2176 sg15577 + +lemma sg28154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15578 + +lemma sg28155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2665 sg15037 + +lemma sg28156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg556 sg21253 + +lemma sg28157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg556 sg21254 + +lemma sg28158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg556 sg21255 + +lemma sg28159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg556 sg21256 + +lemma sg28160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1713 sg18249 + +lemma sg28161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1465 sg20936 + +lemma sg28162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1820 sg17116 + +lemma sg28163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1812 sg17133 + +lemma sg28164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21008 + +lemma sg28165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18265 + +lemma sg28166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11302 + +lemma sg28167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg567 sg21236 + +lemma sg28168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6124 sg11766 + +lemma sg28169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2177 sg15577 + +lemma sg28170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1820 sg17117 + +lemma sg28171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2228 sg15522 + +lemma sg28172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21009 + +lemma sg28173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11303 + +lemma sg28174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11277 + +lemma sg28175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5351 sg12654 + +lemma sg28176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6023 sg11790 + +lemma sg28177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3866 sg14515 + +lemma sg28178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10222 + +lemma sg28179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11304 + +lemma sg28180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11497 + +lemma sg28181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10419 + +lemma sg28182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8877 sg9003 + +lemma sg28183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10190 + +lemma sg28184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11278 + +lemma sg28185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9229 + +lemma sg28186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8480 sg10196 + +lemma sg28187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8647 sg9883 + +lemma sg28188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9230 + +lemma sg28189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8877 sg9004 + +lemma sg28190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8343 sg10746 + +lemma sg28191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8855 sg9159 + +lemma sg28192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10419 + +lemma sg28193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1308 sg20977 + +lemma sg28194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1707 sg18259 + +lemma sg28195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1821 sg17115 + +lemma sg28196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2187 sg15566 + +lemma sg28197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2222 sg15539 + +lemma sg28198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15024 + +lemma sg28199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2665 sg15038 + +lemma sg28200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11305 + +lemma sg28201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg568 sg21236 + +lemma sg28202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6124 sg11767 + +lemma sg28203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1822 sg17115 + +lemma sg28204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2188 sg15566 + +lemma sg28205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1813 sg17133 + +lemma sg28206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2222 sg15540 + +lemma sg28207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg18254 + +lemma sg28208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11306 + +lemma sg28209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11279 + +lemma sg28210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5351 sg12655 + +lemma sg28211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6023 sg11791 + +lemma sg28212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2177 sg15578 + +lemma sg28213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3876 sg14506 + +lemma sg28214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10223 + +lemma sg28215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11307 + +lemma sg28216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11498 + +lemma sg28217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10328 + +lemma sg28218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8348 sg10703 + +lemma sg28219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10224 + +lemma sg28220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10191 + +lemma sg28221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11280 + +lemma sg28222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10420 + +lemma sg28223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10328 + +lemma sg28224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8723 sg9535 + +lemma sg28225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11281 + +lemma sg28226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10323 + +lemma sg28227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9229 + +lemma sg28228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8647 sg9884 + +lemma sg28229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9230 + +lemma sg28230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10747 + +lemma sg28231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10328 + +lemma sg28232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10420 + +lemma sg28233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1822 sg17116 + +lemma sg28234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1858 sg16196 + +lemma sg28235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3868 sg14511 + +lemma sg28236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10225 + +lemma sg28237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11308 + +lemma sg28238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11499 + +lemma sg28239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8433 sg10251 + +lemma sg28240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8871 sg9006 + +lemma sg28241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3897 sg14499 + +lemma sg28242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10226 + +lemma sg28243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10192 + +lemma sg28244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11282 + +lemma sg28245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10329 + +lemma sg28246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10251 + +lemma sg28247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8651 sg9874 + +lemma sg28248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11309 + +lemma sg28249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8116 sg11053 + +lemma sg28250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10421 + +lemma sg28251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10329 + +lemma sg28252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8723 sg9536 + +lemma sg28253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9234 + +lemma sg28254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9324 + +lemma sg28255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9885 + +lemma sg28256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9536 + +lemma sg28257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10748 + +lemma sg28258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10421 + +lemma sg28259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9885 + +lemma sg28260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1858 sg16197 + +lemma sg28261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5557 sg12625 + +lemma sg28262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5979 sg11830 + +lemma sg28263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10330 + +lemma sg28264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9232 + +lemma sg28265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8651 sg9875 + +lemma sg28266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8117 sg11053 + +lemma sg28267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10422 + +lemma sg28268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10330 + +lemma sg28269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9232 + +lemma sg28270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9595 + +lemma sg28271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9234 + +lemma sg28272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10749 + +lemma sg28273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10422 + +lemma sg28274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10330 + +lemma sg28275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9886 + +lemma sg28276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10423 + +lemma sg28277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10331 + +lemma sg28278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10750 + +lemma sg28279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10423 + +lemma sg28280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9887 + +lemma sg28281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10331 + +lemma sg28282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9887 + +lemma sg28283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9233 + +lemma sg28284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9234 + +lemma sg28285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9234 + +lemma sg28286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1708 sg18259 + +lemma sg28287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1834 sg17107 + +lemma sg28288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2201 sg15562 + +lemma sg28289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2229 sg15523 + +lemma sg28290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2674 sg15015 + +lemma sg28291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15025 + +lemma sg28292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3513 sg14686 + +lemma sg28293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg864 sg21149 + +lemma sg28294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg864 sg21150 + +lemma sg28295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg864 sg21151 + +lemma sg28296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2202 sg15562 + +lemma sg28297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2188 sg15567 + +lemma sg28298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3896 sg14500 + +lemma sg28299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2222 sg15542 + +lemma sg28300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6925 sg11471 + +lemma sg28301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6007 sg11829 + +lemma sg28302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8433 sg10255 + +lemma sg28303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8871 sg9009 + +lemma sg28304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3897 sg14500 + +lemma sg28305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10227 + +lemma sg28306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11310 + +lemma sg28307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11500 + +lemma sg28308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10332 + +lemma sg28309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10255 + +lemma sg28310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8749 sg9472 + +lemma sg28311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10193 + +lemma sg28312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11283 + +lemma sg28313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10424 + +lemma sg28314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10332 + +lemma sg28315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8723 sg9537 + +lemma sg28316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8827 sg9178 + +lemma sg28317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9324 + +lemma sg28318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9888 + +lemma sg28319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9537 + +lemma sg28320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10751 + +lemma sg28321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10424 + +lemma sg28322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9888 + +lemma sg28323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1852 sg16202 + +lemma sg28324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2244 sg15513 + +lemma sg28325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10228 + +lemma sg28326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11311 + +lemma sg28327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11501 + +lemma sg28328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9235 + +lemma sg28329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8470 sg10204 + +lemma sg28330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8652 sg9874 + +lemma sg28331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10229 + +lemma sg28332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10194 + +lemma sg28333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11284 + +lemma sg28334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10333 + +lemma sg28335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9235 + +lemma sg28336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8749 sg9473 + +lemma sg28337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11285 + +lemma sg28338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10425 + +lemma sg28339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10333 + +lemma sg28340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9235 + +lemma sg28341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8750 sg9473 + +lemma sg28342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8871 sg9011 + +lemma sg28343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10752 + +lemma sg28344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10425 + +lemma sg28345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10333 + +lemma sg28346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9889 + +lemma sg28347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5559 sg12625 + +lemma sg28348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5981 sg11830 + +lemma sg28349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10334 + +lemma sg28350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9236 + +lemma sg28351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8828 sg9176 + +lemma sg28352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9595 + +lemma sg28353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10426 + +lemma sg28354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10334 + +lemma sg28355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10753 + +lemma sg28356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10426 + +lemma sg28357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9890 + +lemma sg28358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10334 + +lemma sg28359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9890 + +lemma sg28360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9236 + +lemma sg28361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10335 + +lemma sg28362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9891 + +lemma sg28363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10335 + +lemma sg28364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9891 + +lemma sg28365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9237 + +lemma sg28366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9237 + +lemma sg28367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8829 sg9178 + +lemma sg28368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2245 sg15513 + +lemma sg28369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10230 + +lemma sg28370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11312 + +lemma sg28371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6901 sg11502 + +lemma sg28372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9238 + +lemma sg28373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8871 sg9012 + +lemma sg28374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8771 sg9448 + +lemma sg28375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10195 + +lemma sg28376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11286 + +lemma sg28377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10336 + +lemma sg28378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9238 + +lemma sg28379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8828 sg9179 + +lemma sg28380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8772 sg9448 + +lemma sg28381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10427 + +lemma sg28382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10336 + +lemma sg28383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10754 + +lemma sg28384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10427 + +lemma sg28385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9892 + +lemma sg28386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10336 + +lemma sg28387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9892 + +lemma sg28388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9238 + +lemma sg28389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5982 sg11830 + +lemma sg28390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10428 + +lemma sg28391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10260 + +lemma sg28392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10755 + +lemma sg28393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10428 + +lemma sg28394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10337 + +lemma sg28395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9893 + +lemma sg28396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10337 + +lemma sg28397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9893 + +lemma sg28398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9538 + +lemma sg28399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9538 + +lemma sg28400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8723 sg9539 + +lemma sg28401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9539 + +lemma sg28402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9539 + +lemma sg28403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8751 sg9474 + +lemma sg28404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1474 sg20928 + +lemma sg28405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8382 sg10611 + +lemma sg28406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8365 sg10655 + +lemma sg28407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10156 + +lemma sg28408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,2,2,2,2] := by + exact rowSquare_join (by decide) sg8500 sg10174 + +lemma sg28409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8382 sg10612 + +lemma sg28410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8529 sg10129 + +lemma sg28411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,3,2,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10129 + +lemma sg28412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,3,3,1,1] := by + exact rowSquare_join (by decide) sg8561 sg10099 + +lemma sg28413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8872 sg9016 + +lemma sg28414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,4,2,1,1] := by + exact rowSquare_join (by decide) sg8561 sg10100 + +lemma sg28415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,5,5,5,5,5,5,1,1,1] := by + exact rowSquare_join (by decide) sg8600 sg10086 + +lemma sg28416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1290 sg21004 + +lemma sg28417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg18255 + +lemma sg28418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18266 + +lemma sg28419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg151 sg21616 + +lemma sg28420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg151 sg21617 + +lemma sg28421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg151 sg21618 + +lemma sg28422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg151 sg21619 + +lemma sg28423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,2,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg151 sg21620 + +lemma sg28424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1302 sg20982 + +lemma sg28425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1703 sg18263 + +lemma sg28426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg18256 + +lemma sg28427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2173 sg15590 + +lemma sg28428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg293 sg21334 + +lemma sg28429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg293 sg21335 + +lemma sg28430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg293 sg21336 + +lemma sg28431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg293 sg21337 + +lemma sg28432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg293 sg21338 + +lemma sg28433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1303 sg20982 + +lemma sg28434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1714 sg18248 + +lemma sg28435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1811 sg17144 + +lemma sg28436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2186 sg15568 + +lemma sg28437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2174 sg15580 + +lemma sg28438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg338 sg21318 + +lemma sg28439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg338 sg21319 + +lemma sg28440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg338 sg21320 + +lemma sg28441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg338 sg21321 + +lemma sg28442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1304 sg20982 + +lemma sg28443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1313 sg20969 + +lemma sg28444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1310 sg20974 + +lemma sg28445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg17130 + +lemma sg28446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21010 + +lemma sg28447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21029 + +lemma sg28448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10231 + +lemma sg28449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11313 + +lemma sg28450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg552 sg21263 + +lemma sg28451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg552 sg21264 + +lemma sg28452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1467 sg20935 + +lemma sg28453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1823 sg17114 + +lemma sg28454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg17131 + +lemma sg28455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21011 + +lemma sg28456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21030 + +lemma sg28457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11314 + +lemma sg28458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg566 sg21239 + +lemma sg28459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg566 sg21240 + +lemma sg28460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg856 sg21164 + +lemma sg28461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg21137 + +lemma sg28462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10232 + +lemma sg28463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11315 + +lemma sg28464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10183 + +lemma sg28465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7457 sg11269 + +lemma sg28466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6025 sg11789 + +lemma sg28467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg21138 + +lemma sg28468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11316 + +lemma sg28469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21031 + +lemma sg28470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8482 sg10196 + +lemma sg28471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8344 sg10705 + +lemma sg28472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10184 + +lemma sg28473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8836 sg9172 + +lemma sg28474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8501 sg10173 + +lemma sg28475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8343 sg10756 + +lemma sg28476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8856 sg9159 + +lemma sg28477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8681 sg9657 + +lemma sg28478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,3,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8523 sg10167 + +lemma sg28479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1305 sg20980 + +lemma sg28480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1704 sg18260 + +lemma sg28481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1812 sg17134 + +lemma sg28482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15579 + +lemma sg28483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2173 sg15591 + +lemma sg28484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg339 sg21318 + +lemma sg28485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg339 sg21319 + +lemma sg28486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg339 sg21320 + +lemma sg28487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg339 sg21321 + +lemma sg28488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1306 sg20980 + +lemma sg28489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1705 sg18260 + +lemma sg28490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1813 sg17134 + +lemma sg28491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2176 sg15579 + +lemma sg28492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15580 + +lemma sg28493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2665 sg15039 + +lemma sg28494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10233 + +lemma sg28495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11317 + +lemma sg28496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg553 sg21263 + +lemma sg28497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg553 sg21264 + +lemma sg28498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1713 sg18251 + +lemma sg28499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1462 sg20941 + +lemma sg28500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1815 sg17130 + +lemma sg28501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1812 sg17135 + +lemma sg28502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21013 + +lemma sg28503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18267 + +lemma sg28504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11318 + +lemma sg28505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg567 sg21239 + +lemma sg28506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg567 sg21240 + +lemma sg28507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2177 sg15579 + +lemma sg28508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1815 sg17131 + +lemma sg28509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2228 sg15526 + +lemma sg28510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10234 + +lemma sg28511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11319 + +lemma sg28512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10185 + +lemma sg28513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7457 sg11271 + +lemma sg28514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6023 sg11792 + +lemma sg28515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3866 sg14517 + +lemma sg28516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10235 + +lemma sg28517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11320 + +lemma sg28518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5956 sg11837 + +lemma sg28519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10429 + +lemma sg28520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8346 sg10704 + +lemma sg28521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11321 + +lemma sg28522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10186 + +lemma sg28523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8453 sg10246 + +lemma sg28524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8483 sg10196 + +lemma sg28525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8647 sg9894 + +lemma sg28526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8453 sg10247 + +lemma sg28527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8837 sg9172 + +lemma sg28528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8343 sg10757 + +lemma sg28529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8857 sg9159 + +lemma sg28530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10429 + +lemma sg28531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1315 sg20968 + +lemma sg28532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1716 sg18248 + +lemma sg28533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1816 sg17129 + +lemma sg28534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2179 sg15576 + +lemma sg28535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2222 sg15543 + +lemma sg28536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15026 + +lemma sg28537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2665 sg15040 + +lemma sg28538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg568 sg21238 + +lemma sg28539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg568 sg21239 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes7.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes7.lean index 93850efeae15e715ddab099d746fa1b96063a585..05e6ecfc640e76f7ab71ab6eda31f90ce86e27aa 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes7.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes7.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes5 - -namespace OAI - -/-! Semigroup Nodes 7. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg3307 : RowSquare [6,3,1,1,1,1,1,1] [3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg889 - -lemma sg3308 : RowSquare [6,3,1,1,1,1,1,1] [3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg32 sg891 - -lemma sg3309 : RowSquare [6,3,1,1,1,1,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg892 - -lemma sg3310 : RowSquare [6,3,1,1,1,1,1,1] [4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg897 - -lemma sg3311 : RowSquare [6,3,2,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2626 - -lemma sg3312 : RowSquare [6,3,2,1,1,1,1] [3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2627 - -lemma sg3313 : RowSquare [6,3,2,1,1,1,1] [3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg2632 - -lemma sg3314 : RowSquare [6,3,2,1,1,1,1] [3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg2633 - -lemma sg3315 : RowSquare [6,3,2,1,1,1,1] [3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg807 - -lemma sg3316 : RowSquare [6,3,2,1,1,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg809 - -lemma sg3317 : RowSquare [6,3,2,1,1,1,1] [4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg2589 - -lemma sg3318 : RowSquare [6,3,2,2,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg762 - -lemma sg3319 : RowSquare [6,3,2,2,1,1] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1629 - -lemma sg3320 : RowSquare [6,3,3,1,1,1] [2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg164 sg269 - -lemma sg3321 : RowSquare [6,3,3,1,1,1] [2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg163 sg269 - -lemma sg3322 : RowSquare [6,3,3,1,1,1] [2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg163 sg268 - -lemma sg3323 : RowSquare [6,3,3,1,1,1] [2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg163 sg267 - -lemma sg3324 : RowSquare [6,3,3,1,1,1] [2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg163 sg265 - -lemma sg3325 : RowSquare [6,3,3,1,1,1] [2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg92 sg442 - -lemma sg3326 : RowSquare [6,3,3,1,1,1] [3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg160 sg265 - -lemma sg3327 : RowSquare [6,3,3,1,1,1] [3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg92 sg441 - -lemma sg3328 : RowSquare [6,3,3,1,1,1] [3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg159 sg267 - -lemma sg3329 : RowSquare [6,3,3,1,1,1] [3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg89 sg442 - -lemma sg3330 : RowSquare [6,3,3,1,1,1] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg159 sg266 - -lemma sg3331 : RowSquare [6,3,3,1,1,1] [3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg159 sg264 - -lemma sg3332 : RowSquare [6,3,3,1,1,1] [3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg89 sg441 - -lemma sg3333 : RowSquare [6,3,3,1,1,1] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg159 sg262 - -lemma sg3334 : RowSquare [6,3,3,1,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg89 sg440 - -lemma sg3335 : RowSquare [6,3,3,1,1,1] [4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg161 sg263 - -lemma sg3336 : RowSquare [6,3,3,1,1,1] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg63 sg520 - -lemma sg3337 : RowSquare [6,3,3,2,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg759 - -lemma sg3338 : RowSquare [6,3,3,3] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg254 - -lemma sg3339 : RowSquare [6,3,3,3] [4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg66 sg480 - -lemma sg3340 : RowSquare [6,3,3,3] [4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg179 sg254 - -lemma sg3341 : RowSquare [6,3,3,3] [4,3,3,3,2] := by - exact rowSquare_join (by decide) sg66 sg481 - -lemma sg3342 : RowSquare [6,3,3,3] [4,4,3,3,1] := by - exact rowSquare_join (by decide) sg180 sg254 - -lemma sg3343 : RowSquare [6,3,3,3] [4,4,4,2,1] := by - exact rowSquare_join (by decide) sg68 sg481 - -lemma sg3344 : RowSquare [6,3,3,3] [4,4,4,3] := by - exact rowSquare_join (by decide) sg181 sg254 - -lemma sg3345 : RowSquare [6,3,3,3] [5,3,3,3,1] := by - exact rowSquare_join (by decide) sg182 sg254 - -lemma sg3346 : RowSquare [6,3,3,3] [5,4,3,3] := by - exact rowSquare_join (by decide) sg183 sg254 - -lemma sg3347 : RowSquare [6,4,1,1,1,1,1] [3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg1632 - -lemma sg3348 : RowSquare [6,4,1,1,1,1,1] [4,4,4,3] := by - exact rowSquare_join (by decide) sg13 sg1191 - -lemma sg3349 : RowSquare [6,4,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8 sg1327 - -lemma sg3350 : RowSquare [6,4,1,1,1,1,1] [5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1637 - -lemma sg3351 : RowSquare [6,4,1,1,1,1,1] [5,5,5] := by - exact rowSquare_join (by decide) sg4 sg1641 - -lemma sg3352 : RowSquare [6,4,2,1,1,1] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg1196 - -lemma sg3353 : RowSquare [6,4,2,1,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg762 - -lemma sg3354 : RowSquare [6,4,2,1,1,1] [5,5,5] := by - exact rowSquare_join (by decide) sg97 sg440 - -lemma sg3355 : RowSquare [6,4,2,2,1] [3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg2602 - -lemma sg3356 : RowSquare [6,4,2,2,1] [3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg4 sg1616 - -lemma sg3357 : RowSquare [6,4,3,1,1] [3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg790 - -lemma sg3358 : RowSquare [6,4,3,1,1] [3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg475 - -lemma sg3359 : RowSquare [6,4,3,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg792 - -lemma sg3360 : RowSquare [6,4,3,2] [3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg480 - -lemma sg3361 : RowSquare [6,4,3,2] [3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg481 - -lemma sg3362 : RowSquare [6,4,3,2] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg796 - -lemma sg3363 : RowSquare [6,4,3,2] [4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2110 - -lemma sg3364 : RowSquare [6,4,3,2] [4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg142 sg285 - -lemma sg3365 : RowSquare [6,4,3,2] [4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg123 sg331 - -lemma sg3366 : RowSquare [6,4,3,2] [4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg143 sg285 - -lemma sg3367 : RowSquare [6,4,3,2] [4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg511 - -lemma sg3368 : RowSquare [6,4,3,2] [4,4,4,3] := by - exact rowSquare_join (by decide) sg195 sg254 - -lemma sg3369 : RowSquare [6,4,3,2] [5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg124 sg331 - -lemma sg3370 : RowSquare [6,4,3,2] [5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg125 sg331 - -lemma sg3371 : RowSquare [6,4,3,2] [5,4,4,2] := by - exact rowSquare_join (by decide) sg144 sg290 - -lemma sg3372 : RowSquare [6,4,3,2] [5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg71 sg511 - -lemma sg3373 : RowSquare [6,4,3,2] [6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg127 sg331 - -lemma sg3374 : RowSquare [6,4,3,2] [6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg128 sg331 - -lemma sg3375 : RowSquare [7,2,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2702 - -lemma sg3376 : RowSquare [7,2,1,1,1,1,1,1] [3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2707 - -lemma sg3377 : RowSquare [7,2,1,1,1,1,1,1] [3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg2708 - -lemma sg3378 : RowSquare [7,2,1,1,1,1,1,1] [4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg2710 - -lemma sg3379 : RowSquare [7,2,1,1,1,1,1,1] [4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg2620 - -lemma sg3380 : RowSquare [7,2,1,1,1,1,1,1] [5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg2621 - -lemma sg3381 : RowSquare [7,3,1,1,1,1,1] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1663 - -lemma sg3382 : RowSquare [7,3,1,1,1,1,1] [4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg1240 - -lemma sg3383 : RowSquare [7,3,1,1,1,1,1] [4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1664 - -lemma sg3384 : RowSquare [7,3,1,1,1,1,1] [4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg13 sg1243 - -lemma sg3385 : RowSquare [7,3,1,1,1,1,1] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1667 - -lemma sg3386 : RowSquare [7,3,1,1,1,1,1] [5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1668 - -lemma sg3387 : RowSquare [7,3,1,1,1,1,1] [5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg1240 - -lemma sg3388 : RowSquare [7,3,1,1,1,1,1] [5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg2 sg2123 - -lemma sg3389 : RowSquare [7,3,1,1,1,1,1] [5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg1247 - -lemma sg3390 : RowSquare [7,3,1,1,1,1,1] [5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg1249 - -lemma sg3391 : RowSquare [7,3,1,1,1,1,1] [5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg1189 - -lemma sg3392 : RowSquare [7,3,1,1,1,1,1] [5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1188 - -lemma sg3393 : RowSquare [7,3,1,1,1,1,1] [5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1189 - -lemma sg3394 : RowSquare [7,3,1,1,1,1,1] [6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg1668 - -lemma sg3395 : RowSquare [7,3,1,1,1,1,1] [6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg7 sg1634 - -lemma sg3396 : RowSquare [7,3,1,1,1,1,1] [6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg1193 - -lemma sg3397 : RowSquare [7,3,1,1,1,1,1] [6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg800 - -lemma sg3398 : RowSquare [7,3,1,1,1,1,1] [6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1194 - -lemma sg3399 : RowSquare [7,3,1,1,1,1,1] [7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg1240 - -lemma sg3400 : RowSquare [7,3,1,1,1,1,1] [7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg1192 - -lemma sg3401 : RowSquare [7,3,2,1,1,1] [3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2630 - -lemma sg3402 : RowSquare [7,3,2,1,1,1] [3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg2632 - -lemma sg3403 : RowSquare [7,3,2,1,1,1] [3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg2633 - -lemma sg3404 : RowSquare [7,3,2,1,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg809 - -lemma sg3405 : RowSquare [7,3,2,1,1,1] [4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg517 - -lemma sg3406 : RowSquare [7,3,2,1,1,1] [4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg518 - -lemma sg3407 : RowSquare [7,3,2,1,1,1] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1673 - -lemma sg3408 : RowSquare [7,3,2,2,1] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg55 sg586 - -lemma sg3409 : RowSquare [7,3,3,1,1] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg62 sg586 - -lemma sg3410 : RowSquare [7,3,3,1,1] [3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg32 sg828 - -lemma sg3411 : RowSquare [7,3,3,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg829 - -lemma sg3412 : RowSquare [7,3,3,1,1] [4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg154 sg312 - -lemma sg3413 : RowSquare [7,3,3,1,1] [4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg154 sg313 - -lemma sg3414 : RowSquare [7,3,3,1,1] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg475 - -lemma sg3415 : RowSquare [7,3,3,1,1] [5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg157 sg312 - -lemma sg3416 : RowSquare [7,3,3,1,1] [5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg154 sg316 - -lemma sg3417 : RowSquare [7,3,3,2] [3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg286 - -lemma sg3418 : RowSquare [7,3,3,2] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg287 - -lemma sg3419 : RowSquare [7,3,3,2] [3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg32 sg833 - -lemma sg3420 : RowSquare [7,3,3,2] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg834 - -lemma sg3421 : RowSquare [7,3,3,2] [4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg66 sg548 - -lemma sg3422 : RowSquare [7,3,3,2] [4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg67 sg548 - -lemma sg3423 : RowSquare [7,3,3,2] [4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg179 sg285 - -lemma sg3424 : RowSquare [7,3,3,2] [4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg548 - -lemma sg3425 : RowSquare [7,3,3,2] [4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg179 sg286 - -lemma sg3426 : RowSquare [7,3,3,2] [4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg179 sg287 - -lemma sg3427 : RowSquare [7,3,3,2] [4,3,3,3,2] := by - exact rowSquare_join (by decide) sg87 sg481 - -lemma sg3428 : RowSquare [7,3,3,2] [4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg180 sg285 - -lemma sg3429 : RowSquare [7,3,3,2] [4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg181 sg285 - -lemma sg3430 : RowSquare [7,3,3,2] [4,4,3,2,2] := by - exact rowSquare_join (by decide) sg180 sg286 - -lemma sg3431 : RowSquare [7,3,3,2] [4,4,3,3,1] := by - exact rowSquare_join (by decide) sg180 sg287 - -lemma sg3432 : RowSquare [7,3,3,2] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg480 - -lemma sg3433 : RowSquare [7,3,3,2] [4,4,4,2,1] := by - exact rowSquare_join (by decide) sg181 sg286 - -lemma sg3434 : RowSquare [7,3,3,2] [4,4,4,3] := by - exact rowSquare_join (by decide) sg181 sg287 - -lemma sg3435 : RowSquare [7,3,3,2] [5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg69 sg548 - -lemma sg3436 : RowSquare [7,3,3,2] [5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg179 sg288 - -lemma sg3437 : RowSquare [7,3,3,2] [5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg70 sg548 - -lemma sg3438 : RowSquare [7,3,3,2] [5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg179 sg289 - -lemma sg3439 : RowSquare [7,3,3,2] [5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg179 sg290 - -lemma sg3440 : RowSquare [7,3,3,2] [5,3,3,2,2] := by - exact rowSquare_join (by decide) sg182 sg286 - -lemma sg3441 : RowSquare [7,3,3,2] [5,3,3,3,1] := by - exact rowSquare_join (by decide) sg218 sg254 - -lemma sg3442 : RowSquare [7,3,3,2] [5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg71 sg548 - -lemma sg3443 : RowSquare [7,3,3,2] [5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg179 sg291 - -lemma sg3444 : RowSquare [7,3,3,2] [5,4,2,2,2] := by - exact rowSquare_join (by decide) sg180 sg289 - -lemma sg3445 : RowSquare [7,3,3,2] [5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg292 - -lemma sg3446 : RowSquare [7,3,3,2] [5,4,3,2,1] := by - exact rowSquare_join (by decide) sg180 sg290 - -lemma sg3447 : RowSquare [7,3,3,2] [5,4,3,3] := by - exact rowSquare_join (by decide) sg219 sg254 - -lemma sg3448 : RowSquare [7,3,3,2] [5,4,4,1,1] := by - exact rowSquare_join (by decide) sg184 sg286 - -lemma sg3449 : RowSquare [7,3,3,2] [5,4,4,2] := by - exact rowSquare_join (by decide) sg181 sg290 - -lemma sg3450 : RowSquare [7,3,3,2] [5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg294 - -lemma sg3451 : RowSquare [7,3,3,2] [5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg185 sg285 - -lemma sg3452 : RowSquare [7,3,3,2] [5,5,2,2,1] := by - exact rowSquare_join (by decide) sg180 sg291 - -lemma sg3453 : RowSquare [7,3,3,2] [5,5,3,1,1] := by - exact rowSquare_join (by decide) sg180 sg292 - -lemma sg3454 : RowSquare [7,3,3,2] [5,5,3,2] := by - exact rowSquare_join (by decide) sg181 sg291 - -lemma sg3455 : RowSquare [7,3,3,2] [5,5,4,1] := by - exact rowSquare_join (by decide) sg181 sg292 - -lemma sg3456 : RowSquare [7,4,1,1,1,1] [4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg1259 - -lemma sg3457 : RowSquare [7,4,1,1,1,1] [4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg39 sg808 - -lemma sg3458 : RowSquare [7,4,1,1,1,1] [4,3,3,3,2] := by - exact rowSquare_join (by decide) sg39 sg809 - -lemma sg3459 : RowSquare [7,4,1,1,1,1] [4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg807 - -lemma sg3460 : RowSquare [7,4,1,1,1,1] [4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg808 - -lemma sg3461 : RowSquare [7,4,1,1,1,1] [4,4,3,2,2] := by - exact rowSquare_join (by decide) sg40 sg809 - -lemma sg3462 : RowSquare [7,4,1,1,1,1] [5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1678 - -lemma sg3463 : RowSquare [7,4,1,1,1,1] [5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg1258 - -lemma sg3464 : RowSquare [7,4,1,1,1,1] [5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg812 - -lemma sg3465 : RowSquare [7,4,1,1,1,1] [5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg814 - -lemma sg3466 : RowSquare [7,4,1,1,1,1] [5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg518 - -lemma sg3467 : RowSquare [7,4,1,1,1,1] [5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg814 - -lemma sg3468 : RowSquare [7,4,1,1,1,1] [6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg1678 - -lemma sg3469 : RowSquare [7,4,1,1,1,1] [6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg517 - -lemma sg3470 : RowSquare [7,4,2,1,1] [3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg534 - -lemma sg3471 : RowSquare [7,4,2,1,1] [3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg838 - -lemma sg3472 : RowSquare [7,4,2,1,1] [3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg535 - -lemma sg3473 : RowSquare [7,4,2,1,1] [3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg839 - -lemma sg3474 : RowSquare [7,4,2,1,1] [3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg536 - -lemma sg3475 : RowSquare [7,4,2,1,1] [3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg537 - -lemma sg3476 : RowSquare [7,4,2,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg841 - -lemma sg3477 : RowSquare [7,4,2,1,1] [4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg26 sg911 - -lemma sg3478 : RowSquare [7,4,2,1,1] [4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg165 sg312 - -lemma sg3479 : RowSquare [7,4,2,1,1] [4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg27 sg911 - -lemma sg3480 : RowSquare [7,4,2,1,1] [4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg166 sg312 - -lemma sg3481 : RowSquare [7,4,2,1,1] [4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg165 sg313 - -lemma sg3482 : RowSquare [7,4,2,1,1] [4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg193 sg270 - -lemma sg3483 : RowSquare [7,4,2,1,1] [4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg166 sg313 - -lemma sg3484 : RowSquare [7,4,2,1,1] [4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg77 sg535 - -lemma sg3485 : RowSquare [7,4,2,1,1] [4,4,3,2,2] := by - exact rowSquare_join (by decide) sg194 sg270 - -lemma sg3486 : RowSquare [7,4,2,1,1] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg543 - -lemma sg3487 : RowSquare [7,4,2,1,1] [5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg28 sg911 - -lemma sg3488 : RowSquare [7,4,2,1,1] [5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg168 sg312 - -lemma sg3489 : RowSquare [7,4,2,1,1] [5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg193 sg272 - -lemma sg3490 : RowSquare [7,4,2,1,1] [5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg29 sg911 - -lemma sg3491 : RowSquare [7,4,2,1,1] [5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg193 sg273 - -lemma sg3492 : RowSquare [7,4,2,1,1] [5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg170 sg312 - -lemma sg3493 : RowSquare [7,4,2,1,1] [5,3,3,2,2] := by - exact rowSquare_join (by decide) sg196 sg270 - -lemma sg3494 : RowSquare [7,4,2,1,1] [5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg276 - -lemma sg3495 : RowSquare [7,4,2,1,1] [5,4,4,1,1] := by - exact rowSquare_join (by decide) sg198 sg270 - -lemma sg3496 : RowSquare [7,4,2,1,1] [6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg30 sg911 - -lemma sg3497 : RowSquare [7,4,2,1,1] [6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg193 sg277 - -lemma sg3498 : RowSquare [7,4,2,1,1] [6,3,2,2,2] := by - exact rowSquare_join (by decide) sg194 sg277 - -lemma sg3499 : RowSquare [7,4,2,1,1] [6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg279 - -lemma sg3500 : RowSquare [7,4,2,2] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg297 - -lemma sg3501 : RowSquare [7,4,3,1] [2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg306 - -lemma sg3502 : RowSquare [7,4,3,1] [3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg850 - -lemma sg3503 : RowSquare [7,4,3,1] [3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1232 - -lemma sg3504 : RowSquare [7,4,3,1] [3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg308 - -lemma sg3505 : RowSquare [7,4,3,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg854 - -lemma sg3506 : RowSquare [7,4,3,1] [4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg850 - -lemma sg3507 : RowSquare [7,4,3,1] [4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg34 sg850 - -lemma sg3508 : RowSquare [7,4,3,1] [4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1233 - -lemma sg3509 : RowSquare [7,4,3,1] [5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg798 - -lemma sg3510 : RowSquare [7,4,3,1] [5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg193 sg288 - -lemma sg3511 : RowSquare [7,4,3,1] [5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg798 - -lemma sg3512 : RowSquare [7,4,4] [3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg88 sg516 - -lemma sg3513 : RowSquare [7,5,2,1] [3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg849 - -lemma sg3514 : RowSquare [7,5,2,1] [3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg849 - -lemma sg3515 : RowSquare [7,5,2,1] [3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg167 sg330 - -lemma sg3516 : RowSquare [7,5,2,1] [3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg563 - -lemma sg3517 : RowSquare [7,5,2,1] [4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg41 sg849 - -lemma sg3518 : RowSquare [7,5,2,1] [4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg850 - -lemma sg3519 : RowSquare [7,5,2,1] [4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg170 sg330 - -lemma sg3520 : RowSquare [7,6,2] [3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg306 - -lemma sg3522 : RowSquare [8,1,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg108 sg430 - -lemma sg3523 : RowSquare [8,1,1,1,1,1,1,1] [2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg108 sg429 - -lemma sg3524 : RowSquare [8,1,1,1,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg733 - -lemma sg3525 : RowSquare [8,1,1,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg1662 - -lemma sg3526 : RowSquare [8,1,1,1,1,1,1,1] [3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2699 - -lemma sg3527 : RowSquare [8,1,1,1,1,1,1,1] [3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg49 sg732 - -lemma sg3528 : RowSquare [8,1,1,1,1,1,1,1] [3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2155 - -lemma sg3529 : RowSquare [8,1,1,1,1,1,1,1] [4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2700 - -lemma sg3530 : RowSquare [8,1,1,1,1,1,1,1] [4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg1182 - -lemma sg3531 : RowSquare [8,1,1,1,1,1,1,1] [5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2154 - -lemma sg3532 : RowSquare [8,1,1,1,1,1,1,1] [5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7 sg1659 - -lemma sg3533 : RowSquare [8,2,1,1,1,1,1] [3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2707 - -lemma sg3534 : RowSquare [8,2,1,1,1,1,1] [3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg2708 - -lemma sg3535 : RowSquare [8,2,1,1,1,1,1] [4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg2255 - -lemma sg3536 : RowSquare [8,2,1,1,1,1,1] [4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg2256 - -lemma sg3537 : RowSquare [8,2,1,1,1,1,1] [4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg2710 - -lemma sg3538 : RowSquare [8,2,1,1,1,1,1] [4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg2711 - -lemma sg3539 : RowSquare [8,2,1,1,1,1,1] [4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg0 sg2712 - -lemma sg3540 : RowSquare [8,2,1,1,1,1,1] [4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg1750 - -lemma sg3541 : RowSquare [8,2,1,1,1,1,1] [5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg1240 - -lemma sg3542 : RowSquare [8,2,1,1,1,1,1] [5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2157 - -lemma sg3543 : RowSquare [8,2,1,1,1,1,1] [5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1240 - -lemma sg3544 : RowSquare [8,2,1,1,1,1,1] [5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg1241 - -lemma sg3545 : RowSquare [8,2,1,1,1,1,1] [5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg1750 - -lemma sg3546 : RowSquare [8,2,1,1,1,1,1] [5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1241 - -lemma sg3547 : RowSquare [8,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg1240 - -lemma sg3548 : RowSquare [8,2,1,1,1,1,1] [6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg1245 - -lemma sg3549 : RowSquare [8,2,1,1,1,1,1] [6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1245 - -lemma sg3550 : RowSquare [8,2,1,1,1,1,1] [7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg1245 - -lemma sg3551 : RowSquare [8,2,1,1,1,1,1] [8,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg1192 - -lemma sg3552 : RowSquare [8,2,2,1,1,1] [3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg888 - -lemma sg3553 : RowSquare [8,2,2,1,1,1] [3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg889 - -lemma sg3554 : RowSquare [8,2,2,1,1,1] [3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg890 - -lemma sg3555 : RowSquare [8,2,2,1,1,1] [3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg32 sg891 - -lemma sg3556 : RowSquare [8,2,2,1,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg892 - -lemma sg3557 : RowSquare [8,2,2,1,1,1] [4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg894 - -lemma sg3558 : RowSquare [8,2,2,1,1,1] [4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg10 sg1329 - -lemma sg3559 : RowSquare [8,2,2,2,1] [3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg66 sg586 - -lemma sg3560 : RowSquare [8,2,2,2,1] [3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg312 - -lemma sg3561 : RowSquare [8,2,2,2,1] [3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg67 sg586 - -lemma sg3562 : RowSquare [8,2,2,2,1] [3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg313 - -lemma sg3563 : RowSquare [8,2,2,2,1] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg586 - -lemma sg3564 : RowSquare [8,2,2,2,1] [3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg314 - -lemma sg3565 : RowSquare [8,2,2,2,1] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg315 - -lemma sg3566 : RowSquare [8,2,2,2,1] [4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg70 sg586 - -lemma sg3567 : RowSquare [8,2,2,2,1] [4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg179 sg313 - -lemma sg3568 : RowSquare [8,2,2,2,1] [4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg71 sg586 - -lemma sg3569 : RowSquare [8,2,2,2,1] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg589 - -lemma sg3570 : RowSquare [8,2,2,2,1] [4,4,4,3] := by - exact rowSquare_join (by decide) sg181 sg315 - -lemma sg3571 : RowSquare [8,3,1,1,1,1] [2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg1327 - -lemma sg3572 : RowSquare [8,3,1,1,1,1] [3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg1327 - -lemma sg3573 : RowSquare [8,3,1,1,1,1] [3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg1329 - -lemma sg3574 : RowSquare [8,3,1,1,1,1] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1756 - -lemma sg3575 : RowSquare [8,3,1,1,1,1] [3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg1330 - -lemma sg3576 : RowSquare [8,3,1,1,1,1] [3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg4 sg1758 - -lemma sg3577 : RowSquare [8,3,1,1,1,1] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg1331 - -lemma sg3578 : RowSquare [8,3,1,1,1,1] [3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg13 sg1332 - -lemma sg3579 : RowSquare [8,3,1,1,1,1] [4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg888 - -lemma sg3580 : RowSquare [8,3,1,1,1,1] [4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg888 - -lemma sg3581 : RowSquare [8,3,1,1,1,1] [4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5 sg1758 - -lemma sg3582 : RowSquare [8,3,1,1,1,1] [4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1760 - -lemma sg3583 : RowSquare [8,3,1,1,1,1] [4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg890 - -lemma sg3584 : RowSquare [8,3,1,1,1,1] [4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg4 sg1762 - -lemma sg3585 : RowSquare [8,3,1,1,1,1] [4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg39 sg891 - -lemma sg3586 : RowSquare [8,3,1,1,1,1] [4,3,3,3,2] := by - exact rowSquare_join (by decide) sg39 sg892 - -lemma sg3587 : RowSquare [8,3,1,1,1,1] [4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg1329 - -lemma sg3588 : RowSquare [8,3,1,1,1,1] [4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg1338 - -lemma sg3589 : RowSquare [8,3,1,1,1,1] [4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg14 sg1332 - -lemma sg3590 : RowSquare [8,3,1,1,1,1] [4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg890 - -lemma sg3591 : RowSquare [8,3,1,1,1,1] [4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg40 sg891 - -lemma sg3592 : RowSquare [8,3,1,1,1,1] [4,4,3,2,2] := by - exact rowSquare_join (by decide) sg40 sg892 - -lemma sg3593 : RowSquare [8,3,1,1,1,1] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg1766 - -lemma sg3594 : RowSquare [8,3,1,1,1,1] [5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg893 - -lemma sg3595 : RowSquare [8,3,1,1,1,1] [5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg6 sg1758 - -lemma sg3596 : RowSquare [8,3,1,1,1,1] [5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg888 - -lemma sg3597 : RowSquare [8,3,1,1,1,1] [5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg893 - -lemma sg3598 : RowSquare [8,3,1,1,1,1] [5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg39 sg894 - -lemma sg3599 : RowSquare [8,3,1,1,1,1] [5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg5 sg1762 - -lemma sg3600 : RowSquare [8,3,1,1,1,1] [5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg517 - -lemma sg3601 : RowSquare [8,3,1,1,1,1] [5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg895 - -lemma sg3602 : RowSquare [8,3,1,1,1,1] [5,3,3,2,2] := by - exact rowSquare_join (by decide) sg45 sg809 - -lemma sg3603 : RowSquare [8,3,1,1,1,1] [5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg42 sg889 - -lemma sg3604 : RowSquare [8,3,1,1,1,1] [5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg894 - -lemma sg3605 : RowSquare [8,3,1,1,1,1] [5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg39 sg897 - -lemma sg3606 : RowSquare [8,3,1,1,1,1] [5,4,2,2,2] := by - exact rowSquare_join (by decide) sg46 sg809 - -lemma sg3607 : RowSquare [8,3,1,1,1,1] [5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg518 - -lemma sg3608 : RowSquare [8,3,1,1,1,1] [5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg1338 - -lemma sg3609 : RowSquare [8,3,1,1,1,1] [5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg40 sg897 - -lemma sg3610 : RowSquare [8,3,1,1,1,1] [6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg15 sg1332 - -lemma sg3611 : RowSquare [8,3,1,1,1,1] [6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg811 - -lemma sg3612 : RowSquare [8,3,1,1,1,1] [6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg46 sg814 - -lemma sg3613 : RowSquare [8,3,2,1,1] [2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg910 - -lemma sg3614 : RowSquare [8,3,2,1,1] [2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg586 - -lemma sg3615 : RowSquare [8,3,2,1,1] [3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg587 - -lemma sg3616 : RowSquare [8,3,2,1,1] [3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg76 sg586 - -lemma sg3617 : RowSquare [8,3,2,1,1] [3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg588 - -lemma sg3618 : RowSquare [8,3,2,1,1] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg77 sg586 - -lemma sg3619 : RowSquare [8,3,2,1,1] [3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg913 - -lemma sg3620 : RowSquare [8,3,2,1,1] [3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg589 - -lemma sg3621 : RowSquare [8,3,2,1,1] [3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg74 sg590 - -lemma sg3622 : RowSquare [8,3,2,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg915 - -lemma sg3623 : RowSquare [8,3,2,1,1] [4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg87 sg534 - -lemma sg3624 : RowSquare [8,3,2,1,1] [4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg534 - -lemma sg3625 : RowSquare [8,3,2,1,1] [4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg193 sg314 - -lemma sg3626 : RowSquare [8,3,2,1,1] [4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg80 sg586 - -lemma sg3627 : RowSquare [8,3,2,1,1] [4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg535 - -lemma sg3628 : RowSquare [8,3,2,1,1] [4,4,3,2,2] := by - exact rowSquare_join (by decide) sg194 sg314 - -lemma sg3629 : RowSquare [8,3,2,1,1] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg536 - -lemma sg3630 : RowSquare [8,3,2,1,1] [4,4,4,3] := by - exact rowSquare_join (by decide) sg195 sg315 - -lemma sg3631 : RowSquare [8,3,2,1,1] [5,5,5] := by - exact rowSquare_join (by decide) sg89 sg543 - -lemma sg3632 : RowSquare [8,3,2,2] [2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg330 - -lemma sg3633 : RowSquare [8,3,2,2] [3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg179 sg330 - -lemma sg3634 : RowSquare [8,3,2,2] [3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg331 - -lemma sg3635 : RowSquare [8,3,2,2] [3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg180 sg330 - -lemma sg3636 : RowSquare [8,3,2,2] [3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg181 sg330 - -lemma sg3637 : RowSquare [8,3,2,2] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg334 - -lemma sg3638 : RowSquare [8,3,2,2] [4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg182 sg330 - -lemma sg3639 : RowSquare [8,3,2,2] [4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg183 sg330 - -lemma sg3640 : RowSquare [8,3,2,2] [4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg184 sg330 - -lemma sg3641 : RowSquare [8,3,2,2] [4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg185 sg330 - -lemma sg3642 : RowSquare [8,3,2,2] [4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg180 sg332 - -lemma sg3643 : RowSquare [8,3,2,2] [4,4,3,2,2] := by - exact rowSquare_join (by decide) sg180 sg333 - -lemma sg3644 : RowSquare [8,3,2,2] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg615 - -lemma sg3645 : RowSquare [8,3,2,2] [4,4,4,3] := by - exact rowSquare_join (by decide) sg181 sg334 - -lemma sg3646 : RowSquare [8,3,2,2] [5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg342 - -lemma sg3647 : RowSquare [8,3,3,1] [3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg348 - -lemma sg3648 : RowSquare [8,3,3,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg943 - -lemma sg3649 : RowSquare [8,3,3,1] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg550 - -lemma sg3650 : RowSquare [8,4,1,1,1] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg586 - -lemma sg3651 : RowSquare [8,4,1,1,1] [4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg534 - -lemma sg3652 : RowSquare [8,4,1,1,1] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg536 - -lemma sg3653 : RowSquare [8,4,2,1] [3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg356 - -lemma sg3654 : RowSquare [8,4,2,1] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg358 - -lemma sg3655 : RowSquare [8,4,2,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg961 - -lemma sg3656 : RowSquare [8,4,3] [3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg975 - -lemma sg3657 : RowSquare [8,4,3] [3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg636 - -lemma sg3658 : RowSquare [8,4,3] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg977 - -lemma sg3659 : RowSquare [8,4,3] [4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg33 sg975 - -lemma sg3660 : RowSquare [8,4,3] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg74 sg641 - -lemma sg3661 : RowSquare [9,1,1,1,1,1,1] [3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2251 - -lemma sg3662 : RowSquare [9,1,1,1,1,1,1] [4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2255 - -lemma sg3663 : RowSquare [9,1,1,1,1,1,1] [4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2256 - -lemma sg3664 : RowSquare [9,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2258 - -lemma sg3665 : RowSquare [9,1,1,1,1,1,1] [5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2259 - -lemma sg3666 : RowSquare [9,1,1,1,1,1,1] [5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2 sg2260 - -lemma sg3667 : RowSquare [9,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2261 - -lemma sg3668 : RowSquare [9,1,1,1,1,1,1] [5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2262 - -lemma sg3669 : RowSquare [9,1,1,1,1,1,1] [5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2263 - -lemma sg3670 : RowSquare [9,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg1240 - -lemma sg3671 : RowSquare [9,2,1,1,1,1] [3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1327 - -lemma sg3672 : RowSquare [9,2,1,1,1,1] [4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg1329 - -lemma sg3673 : RowSquare [9,2,1,1,1,1] [4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg1330 - -lemma sg3674 : RowSquare [9,2,1,1,1,1] [4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg1331 - -lemma sg3675 : RowSquare [9,2,1,1,1,1] [4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg16 sg1332 - -lemma sg3676 : RowSquare [9,2,1,1,1,1] [4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1329 - -lemma sg3677 : RowSquare [9,2,1,1,1,1] [4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1330 - -lemma sg3678 : RowSquare [9,2,1,1,1,1] [4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1331 - -lemma sg3679 : RowSquare [9,2,1,1,1,1] [4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg17 sg1332 - -lemma sg3680 : RowSquare [9,2,1,1,1,1] [5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7 sg1758 - -lemma sg3681 : RowSquare [9,2,1,1,1,1] [5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg18 sg1332 - -lemma sg3682 : RowSquare [9,2,1,1,1,1] [6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg1331 - -lemma sg3683 : RowSquare [9,2,1,1,1,1] [6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19 sg1332 - -lemma sg3684 : RowSquare [9,2,1,1,1,1] [6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg45 sg894 - -lemma sg3685 : RowSquare [9,2,2,1,1] [3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg87 sg586 - -lemma sg3686 : RowSquare [9,2,2,1,1] [3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg88 sg586 - -lemma sg3687 : RowSquare [9,2,2,1,1] [3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg998 - -lemma sg3688 : RowSquare [9,2,2,1,1] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg586 - -lemma sg3689 : RowSquare [9,2,2,1,1] [3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg32 sg999 - -lemma sg3690 : RowSquare [9,2,2,1,1] [3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg32 sg1000 - -lemma sg3691 : RowSquare [9,2,2,1,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg1001 - -lemma sg3692 : RowSquare [9,2,2,1,1] [4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg90 sg586 - -lemma sg3693 : RowSquare [9,2,2,1,1] [4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg91 sg586 - -lemma sg3694 : RowSquare [9,2,2,1,1] [4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg33 sg1000 - -lemma sg3695 : RowSquare [9,2,2,1,1] [4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg586 - -lemma sg3696 : RowSquare [9,2,2,1,1] [4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg88 sg588 - -lemma sg3697 : RowSquare [9,2,2,1,1] [4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg1006 - -lemma sg3698 : RowSquare [9,2,2,1,1] [4,4,3,3,1] := by - exact rowSquare_join (by decide) sg88 sg590 - -lemma sg3699 : RowSquare [9,2,2,1,1] [4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg589 - -lemma sg3700 : RowSquare [9,2,2,1,1] [5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg93 sg586 - -lemma sg3701 : RowSquare [9,2,2,2] [3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg370 - -lemma sg3702 : RowSquare [9,2,2,2] [3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg371 - -lemma sg3703 : RowSquare [9,2,2,2] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg373 - -lemma sg3704 : RowSquare [9,2,2,2] [4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg179 sg371 - -lemma sg3705 : RowSquare [9,2,2,2] [4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg179 sg372 - -lemma sg3706 : RowSquare [9,2,2,2] [4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg179 sg373 - -lemma sg3707 : RowSquare [9,2,2,2] [4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg180 sg371 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes5 + +namespace OAI + +/-! Semigroup Nodes 7. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg3307 : RowSquare [6,3,1,1,1,1,1,1] [3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg889 + +lemma sg3308 : RowSquare [6,3,1,1,1,1,1,1] [3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg32 sg891 + +lemma sg3309 : RowSquare [6,3,1,1,1,1,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg892 + +lemma sg3310 : RowSquare [6,3,1,1,1,1,1,1] [4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg897 + +lemma sg3311 : RowSquare [6,3,2,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2626 + +lemma sg3312 : RowSquare [6,3,2,1,1,1,1] [3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2627 + +lemma sg3313 : RowSquare [6,3,2,1,1,1,1] [3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg2632 + +lemma sg3314 : RowSquare [6,3,2,1,1,1,1] [3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg2633 + +lemma sg3315 : RowSquare [6,3,2,1,1,1,1] [3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg807 + +lemma sg3316 : RowSquare [6,3,2,1,1,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg809 + +lemma sg3317 : RowSquare [6,3,2,1,1,1,1] [4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg2589 + +lemma sg3318 : RowSquare [6,3,2,2,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg762 + +lemma sg3319 : RowSquare [6,3,2,2,1,1] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1629 + +lemma sg3320 : RowSquare [6,3,3,1,1,1] [2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg164 sg269 + +lemma sg3321 : RowSquare [6,3,3,1,1,1] [2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg163 sg269 + +lemma sg3322 : RowSquare [6,3,3,1,1,1] [2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg163 sg268 + +lemma sg3323 : RowSquare [6,3,3,1,1,1] [2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg163 sg267 + +lemma sg3324 : RowSquare [6,3,3,1,1,1] [2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg163 sg265 + +lemma sg3325 : RowSquare [6,3,3,1,1,1] [2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg92 sg442 + +lemma sg3326 : RowSquare [6,3,3,1,1,1] [3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg160 sg265 + +lemma sg3327 : RowSquare [6,3,3,1,1,1] [3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg92 sg441 + +lemma sg3328 : RowSquare [6,3,3,1,1,1] [3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg159 sg267 + +lemma sg3329 : RowSquare [6,3,3,1,1,1] [3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg89 sg442 + +lemma sg3330 : RowSquare [6,3,3,1,1,1] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg159 sg266 + +lemma sg3331 : RowSquare [6,3,3,1,1,1] [3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg159 sg264 + +lemma sg3332 : RowSquare [6,3,3,1,1,1] [3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg89 sg441 + +lemma sg3333 : RowSquare [6,3,3,1,1,1] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg159 sg262 + +lemma sg3334 : RowSquare [6,3,3,1,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg89 sg440 + +lemma sg3335 : RowSquare [6,3,3,1,1,1] [4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg161 sg263 + +lemma sg3336 : RowSquare [6,3,3,1,1,1] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg63 sg520 + +lemma sg3337 : RowSquare [6,3,3,2,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg759 + +lemma sg3338 : RowSquare [6,3,3,3] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg254 + +lemma sg3339 : RowSquare [6,3,3,3] [4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg66 sg480 + +lemma sg3340 : RowSquare [6,3,3,3] [4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg179 sg254 + +lemma sg3341 : RowSquare [6,3,3,3] [4,3,3,3,2] := by + exact rowSquare_join (by decide) sg66 sg481 + +lemma sg3342 : RowSquare [6,3,3,3] [4,4,3,3,1] := by + exact rowSquare_join (by decide) sg180 sg254 + +lemma sg3343 : RowSquare [6,3,3,3] [4,4,4,2,1] := by + exact rowSquare_join (by decide) sg68 sg481 + +lemma sg3344 : RowSquare [6,3,3,3] [4,4,4,3] := by + exact rowSquare_join (by decide) sg181 sg254 + +lemma sg3345 : RowSquare [6,3,3,3] [5,3,3,3,1] := by + exact rowSquare_join (by decide) sg182 sg254 + +lemma sg3346 : RowSquare [6,3,3,3] [5,4,3,3] := by + exact rowSquare_join (by decide) sg183 sg254 + +lemma sg3347 : RowSquare [6,4,1,1,1,1,1] [3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg1632 + +lemma sg3348 : RowSquare [6,4,1,1,1,1,1] [4,4,4,3] := by + exact rowSquare_join (by decide) sg13 sg1191 + +lemma sg3349 : RowSquare [6,4,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8 sg1327 + +lemma sg3350 : RowSquare [6,4,1,1,1,1,1] [5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1637 + +lemma sg3351 : RowSquare [6,4,1,1,1,1,1] [5,5,5] := by + exact rowSquare_join (by decide) sg4 sg1641 + +lemma sg3352 : RowSquare [6,4,2,1,1,1] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg1196 + +lemma sg3353 : RowSquare [6,4,2,1,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg762 + +lemma sg3354 : RowSquare [6,4,2,1,1,1] [5,5,5] := by + exact rowSquare_join (by decide) sg97 sg440 + +lemma sg3355 : RowSquare [6,4,2,2,1] [3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg2602 + +lemma sg3356 : RowSquare [6,4,2,2,1] [3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg4 sg1616 + +lemma sg3357 : RowSquare [6,4,3,1,1] [3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg790 + +lemma sg3358 : RowSquare [6,4,3,1,1] [3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg475 + +lemma sg3359 : RowSquare [6,4,3,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg792 + +lemma sg3360 : RowSquare [6,4,3,2] [3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg480 + +lemma sg3361 : RowSquare [6,4,3,2] [3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg481 + +lemma sg3362 : RowSquare [6,4,3,2] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg796 + +lemma sg3363 : RowSquare [6,4,3,2] [4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2110 + +lemma sg3364 : RowSquare [6,4,3,2] [4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg142 sg285 + +lemma sg3365 : RowSquare [6,4,3,2] [4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg123 sg331 + +lemma sg3366 : RowSquare [6,4,3,2] [4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg143 sg285 + +lemma sg3367 : RowSquare [6,4,3,2] [4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg511 + +lemma sg3368 : RowSquare [6,4,3,2] [4,4,4,3] := by + exact rowSquare_join (by decide) sg195 sg254 + +lemma sg3369 : RowSquare [6,4,3,2] [5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg124 sg331 + +lemma sg3370 : RowSquare [6,4,3,2] [5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg125 sg331 + +lemma sg3371 : RowSquare [6,4,3,2] [5,4,4,2] := by + exact rowSquare_join (by decide) sg144 sg290 + +lemma sg3372 : RowSquare [6,4,3,2] [5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg71 sg511 + +lemma sg3373 : RowSquare [6,4,3,2] [6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg127 sg331 + +lemma sg3374 : RowSquare [6,4,3,2] [6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg128 sg331 + +lemma sg3375 : RowSquare [7,2,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2702 + +lemma sg3376 : RowSquare [7,2,1,1,1,1,1,1] [3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2707 + +lemma sg3377 : RowSquare [7,2,1,1,1,1,1,1] [3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg2708 + +lemma sg3378 : RowSquare [7,2,1,1,1,1,1,1] [4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg2710 + +lemma sg3379 : RowSquare [7,2,1,1,1,1,1,1] [4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg2620 + +lemma sg3380 : RowSquare [7,2,1,1,1,1,1,1] [5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg2621 + +lemma sg3381 : RowSquare [7,3,1,1,1,1,1] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1663 + +lemma sg3382 : RowSquare [7,3,1,1,1,1,1] [4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg1240 + +lemma sg3383 : RowSquare [7,3,1,1,1,1,1] [4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1664 + +lemma sg3384 : RowSquare [7,3,1,1,1,1,1] [4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg13 sg1243 + +lemma sg3385 : RowSquare [7,3,1,1,1,1,1] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1667 + +lemma sg3386 : RowSquare [7,3,1,1,1,1,1] [5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1668 + +lemma sg3387 : RowSquare [7,3,1,1,1,1,1] [5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg1240 + +lemma sg3388 : RowSquare [7,3,1,1,1,1,1] [5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg2 sg2123 + +lemma sg3389 : RowSquare [7,3,1,1,1,1,1] [5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg1247 + +lemma sg3390 : RowSquare [7,3,1,1,1,1,1] [5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg1249 + +lemma sg3391 : RowSquare [7,3,1,1,1,1,1] [5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg1189 + +lemma sg3392 : RowSquare [7,3,1,1,1,1,1] [5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1188 + +lemma sg3393 : RowSquare [7,3,1,1,1,1,1] [5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1189 + +lemma sg3394 : RowSquare [7,3,1,1,1,1,1] [6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg1668 + +lemma sg3395 : RowSquare [7,3,1,1,1,1,1] [6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg7 sg1634 + +lemma sg3396 : RowSquare [7,3,1,1,1,1,1] [6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg1193 + +lemma sg3397 : RowSquare [7,3,1,1,1,1,1] [6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg800 + +lemma sg3398 : RowSquare [7,3,1,1,1,1,1] [6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1194 + +lemma sg3399 : RowSquare [7,3,1,1,1,1,1] [7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg1240 + +lemma sg3400 : RowSquare [7,3,1,1,1,1,1] [7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg1192 + +lemma sg3401 : RowSquare [7,3,2,1,1,1] [3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2630 + +lemma sg3402 : RowSquare [7,3,2,1,1,1] [3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg2632 + +lemma sg3403 : RowSquare [7,3,2,1,1,1] [3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg2633 + +lemma sg3404 : RowSquare [7,3,2,1,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg809 + +lemma sg3405 : RowSquare [7,3,2,1,1,1] [4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg517 + +lemma sg3406 : RowSquare [7,3,2,1,1,1] [4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg518 + +lemma sg3407 : RowSquare [7,3,2,1,1,1] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1673 + +lemma sg3408 : RowSquare [7,3,2,2,1] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg55 sg586 + +lemma sg3409 : RowSquare [7,3,3,1,1] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg62 sg586 + +lemma sg3410 : RowSquare [7,3,3,1,1] [3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg32 sg828 + +lemma sg3411 : RowSquare [7,3,3,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg829 + +lemma sg3412 : RowSquare [7,3,3,1,1] [4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg154 sg312 + +lemma sg3413 : RowSquare [7,3,3,1,1] [4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg154 sg313 + +lemma sg3414 : RowSquare [7,3,3,1,1] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg475 + +lemma sg3415 : RowSquare [7,3,3,1,1] [5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg157 sg312 + +lemma sg3416 : RowSquare [7,3,3,1,1] [5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg154 sg316 + +lemma sg3417 : RowSquare [7,3,3,2] [3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg286 + +lemma sg3418 : RowSquare [7,3,3,2] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg287 + +lemma sg3419 : RowSquare [7,3,3,2] [3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg32 sg833 + +lemma sg3420 : RowSquare [7,3,3,2] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg834 + +lemma sg3421 : RowSquare [7,3,3,2] [4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg66 sg548 + +lemma sg3422 : RowSquare [7,3,3,2] [4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg67 sg548 + +lemma sg3423 : RowSquare [7,3,3,2] [4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg179 sg285 + +lemma sg3424 : RowSquare [7,3,3,2] [4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg548 + +lemma sg3425 : RowSquare [7,3,3,2] [4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg179 sg286 + +lemma sg3426 : RowSquare [7,3,3,2] [4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg179 sg287 + +lemma sg3427 : RowSquare [7,3,3,2] [4,3,3,3,2] := by + exact rowSquare_join (by decide) sg87 sg481 + +lemma sg3428 : RowSquare [7,3,3,2] [4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg180 sg285 + +lemma sg3429 : RowSquare [7,3,3,2] [4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg181 sg285 + +lemma sg3430 : RowSquare [7,3,3,2] [4,4,3,2,2] := by + exact rowSquare_join (by decide) sg180 sg286 + +lemma sg3431 : RowSquare [7,3,3,2] [4,4,3,3,1] := by + exact rowSquare_join (by decide) sg180 sg287 + +lemma sg3432 : RowSquare [7,3,3,2] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg480 + +lemma sg3433 : RowSquare [7,3,3,2] [4,4,4,2,1] := by + exact rowSquare_join (by decide) sg181 sg286 + +lemma sg3434 : RowSquare [7,3,3,2] [4,4,4,3] := by + exact rowSquare_join (by decide) sg181 sg287 + +lemma sg3435 : RowSquare [7,3,3,2] [5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg69 sg548 + +lemma sg3436 : RowSquare [7,3,3,2] [5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg179 sg288 + +lemma sg3437 : RowSquare [7,3,3,2] [5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg70 sg548 + +lemma sg3438 : RowSquare [7,3,3,2] [5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg179 sg289 + +lemma sg3439 : RowSquare [7,3,3,2] [5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg179 sg290 + +lemma sg3440 : RowSquare [7,3,3,2] [5,3,3,2,2] := by + exact rowSquare_join (by decide) sg182 sg286 + +lemma sg3441 : RowSquare [7,3,3,2] [5,3,3,3,1] := by + exact rowSquare_join (by decide) sg218 sg254 + +lemma sg3442 : RowSquare [7,3,3,2] [5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg71 sg548 + +lemma sg3443 : RowSquare [7,3,3,2] [5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg179 sg291 + +lemma sg3444 : RowSquare [7,3,3,2] [5,4,2,2,2] := by + exact rowSquare_join (by decide) sg180 sg289 + +lemma sg3445 : RowSquare [7,3,3,2] [5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg292 + +lemma sg3446 : RowSquare [7,3,3,2] [5,4,3,2,1] := by + exact rowSquare_join (by decide) sg180 sg290 + +lemma sg3447 : RowSquare [7,3,3,2] [5,4,3,3] := by + exact rowSquare_join (by decide) sg219 sg254 + +lemma sg3448 : RowSquare [7,3,3,2] [5,4,4,1,1] := by + exact rowSquare_join (by decide) sg184 sg286 + +lemma sg3449 : RowSquare [7,3,3,2] [5,4,4,2] := by + exact rowSquare_join (by decide) sg181 sg290 + +lemma sg3450 : RowSquare [7,3,3,2] [5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg294 + +lemma sg3451 : RowSquare [7,3,3,2] [5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg185 sg285 + +lemma sg3452 : RowSquare [7,3,3,2] [5,5,2,2,1] := by + exact rowSquare_join (by decide) sg180 sg291 + +lemma sg3453 : RowSquare [7,3,3,2] [5,5,3,1,1] := by + exact rowSquare_join (by decide) sg180 sg292 + +lemma sg3454 : RowSquare [7,3,3,2] [5,5,3,2] := by + exact rowSquare_join (by decide) sg181 sg291 + +lemma sg3455 : RowSquare [7,3,3,2] [5,5,4,1] := by + exact rowSquare_join (by decide) sg181 sg292 + +lemma sg3456 : RowSquare [7,4,1,1,1,1] [4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg1259 + +lemma sg3457 : RowSquare [7,4,1,1,1,1] [4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg39 sg808 + +lemma sg3458 : RowSquare [7,4,1,1,1,1] [4,3,3,3,2] := by + exact rowSquare_join (by decide) sg39 sg809 + +lemma sg3459 : RowSquare [7,4,1,1,1,1] [4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg807 + +lemma sg3460 : RowSquare [7,4,1,1,1,1] [4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg808 + +lemma sg3461 : RowSquare [7,4,1,1,1,1] [4,4,3,2,2] := by + exact rowSquare_join (by decide) sg40 sg809 + +lemma sg3462 : RowSquare [7,4,1,1,1,1] [5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1678 + +lemma sg3463 : RowSquare [7,4,1,1,1,1] [5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg1258 + +lemma sg3464 : RowSquare [7,4,1,1,1,1] [5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg812 + +lemma sg3465 : RowSquare [7,4,1,1,1,1] [5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg814 + +lemma sg3466 : RowSquare [7,4,1,1,1,1] [5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg518 + +lemma sg3467 : RowSquare [7,4,1,1,1,1] [5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg814 + +lemma sg3468 : RowSquare [7,4,1,1,1,1] [6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg1678 + +lemma sg3469 : RowSquare [7,4,1,1,1,1] [6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg517 + +lemma sg3470 : RowSquare [7,4,2,1,1] [3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg534 + +lemma sg3471 : RowSquare [7,4,2,1,1] [3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg838 + +lemma sg3472 : RowSquare [7,4,2,1,1] [3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg535 + +lemma sg3473 : RowSquare [7,4,2,1,1] [3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg839 + +lemma sg3474 : RowSquare [7,4,2,1,1] [3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg536 + +lemma sg3475 : RowSquare [7,4,2,1,1] [3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg537 + +lemma sg3476 : RowSquare [7,4,2,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg841 + +lemma sg3477 : RowSquare [7,4,2,1,1] [4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg26 sg911 + +lemma sg3478 : RowSquare [7,4,2,1,1] [4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg165 sg312 + +lemma sg3479 : RowSquare [7,4,2,1,1] [4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg27 sg911 + +lemma sg3480 : RowSquare [7,4,2,1,1] [4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg166 sg312 + +lemma sg3481 : RowSquare [7,4,2,1,1] [4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg165 sg313 + +lemma sg3482 : RowSquare [7,4,2,1,1] [4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg193 sg270 + +lemma sg3483 : RowSquare [7,4,2,1,1] [4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg166 sg313 + +lemma sg3484 : RowSquare [7,4,2,1,1] [4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg77 sg535 + +lemma sg3485 : RowSquare [7,4,2,1,1] [4,4,3,2,2] := by + exact rowSquare_join (by decide) sg194 sg270 + +lemma sg3486 : RowSquare [7,4,2,1,1] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg543 + +lemma sg3487 : RowSquare [7,4,2,1,1] [5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg28 sg911 + +lemma sg3488 : RowSquare [7,4,2,1,1] [5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg168 sg312 + +lemma sg3489 : RowSquare [7,4,2,1,1] [5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg193 sg272 + +lemma sg3490 : RowSquare [7,4,2,1,1] [5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg29 sg911 + +lemma sg3491 : RowSquare [7,4,2,1,1] [5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg193 sg273 + +lemma sg3492 : RowSquare [7,4,2,1,1] [5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg170 sg312 + +lemma sg3493 : RowSquare [7,4,2,1,1] [5,3,3,2,2] := by + exact rowSquare_join (by decide) sg196 sg270 + +lemma sg3494 : RowSquare [7,4,2,1,1] [5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg276 + +lemma sg3495 : RowSquare [7,4,2,1,1] [5,4,4,1,1] := by + exact rowSquare_join (by decide) sg198 sg270 + +lemma sg3496 : RowSquare [7,4,2,1,1] [6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg30 sg911 + +lemma sg3497 : RowSquare [7,4,2,1,1] [6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg193 sg277 + +lemma sg3498 : RowSquare [7,4,2,1,1] [6,3,2,2,2] := by + exact rowSquare_join (by decide) sg194 sg277 + +lemma sg3499 : RowSquare [7,4,2,1,1] [6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg279 + +lemma sg3500 : RowSquare [7,4,2,2] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg297 + +lemma sg3501 : RowSquare [7,4,3,1] [2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg306 + +lemma sg3502 : RowSquare [7,4,3,1] [3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg850 + +lemma sg3503 : RowSquare [7,4,3,1] [3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1232 + +lemma sg3504 : RowSquare [7,4,3,1] [3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg308 + +lemma sg3505 : RowSquare [7,4,3,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg854 + +lemma sg3506 : RowSquare [7,4,3,1] [4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg850 + +lemma sg3507 : RowSquare [7,4,3,1] [4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg34 sg850 + +lemma sg3508 : RowSquare [7,4,3,1] [4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1233 + +lemma sg3509 : RowSquare [7,4,3,1] [5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg798 + +lemma sg3510 : RowSquare [7,4,3,1] [5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg193 sg288 + +lemma sg3511 : RowSquare [7,4,3,1] [5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg798 + +lemma sg3512 : RowSquare [7,4,4] [3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg88 sg516 + +lemma sg3513 : RowSquare [7,5,2,1] [3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg849 + +lemma sg3514 : RowSquare [7,5,2,1] [3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg849 + +lemma sg3515 : RowSquare [7,5,2,1] [3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg167 sg330 + +lemma sg3516 : RowSquare [7,5,2,1] [3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg563 + +lemma sg3517 : RowSquare [7,5,2,1] [4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg41 sg849 + +lemma sg3518 : RowSquare [7,5,2,1] [4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg850 + +lemma sg3519 : RowSquare [7,5,2,1] [4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg170 sg330 + +lemma sg3520 : RowSquare [7,6,2] [3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg306 + +lemma sg3522 : RowSquare [8,1,1,1,1,1,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg108 sg430 + +lemma sg3523 : RowSquare [8,1,1,1,1,1,1,1] [2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg108 sg429 + +lemma sg3524 : RowSquare [8,1,1,1,1,1,1,1] [2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg733 + +lemma sg3525 : RowSquare [8,1,1,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg1662 + +lemma sg3526 : RowSquare [8,1,1,1,1,1,1,1] [3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2699 + +lemma sg3527 : RowSquare [8,1,1,1,1,1,1,1] [3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg49 sg732 + +lemma sg3528 : RowSquare [8,1,1,1,1,1,1,1] [3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2155 + +lemma sg3529 : RowSquare [8,1,1,1,1,1,1,1] [4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2700 + +lemma sg3530 : RowSquare [8,1,1,1,1,1,1,1] [4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg1182 + +lemma sg3531 : RowSquare [8,1,1,1,1,1,1,1] [5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2154 + +lemma sg3532 : RowSquare [8,1,1,1,1,1,1,1] [5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7 sg1659 + +lemma sg3533 : RowSquare [8,2,1,1,1,1,1] [3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2707 + +lemma sg3534 : RowSquare [8,2,1,1,1,1,1] [3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg2708 + +lemma sg3535 : RowSquare [8,2,1,1,1,1,1] [4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg2255 + +lemma sg3536 : RowSquare [8,2,1,1,1,1,1] [4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg2256 + +lemma sg3537 : RowSquare [8,2,1,1,1,1,1] [4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg2710 + +lemma sg3538 : RowSquare [8,2,1,1,1,1,1] [4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg2711 + +lemma sg3539 : RowSquare [8,2,1,1,1,1,1] [4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg0 sg2712 + +lemma sg3540 : RowSquare [8,2,1,1,1,1,1] [4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg1750 + +lemma sg3541 : RowSquare [8,2,1,1,1,1,1] [5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg1240 + +lemma sg3542 : RowSquare [8,2,1,1,1,1,1] [5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2157 + +lemma sg3543 : RowSquare [8,2,1,1,1,1,1] [5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1240 + +lemma sg3544 : RowSquare [8,2,1,1,1,1,1] [5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg1241 + +lemma sg3545 : RowSquare [8,2,1,1,1,1,1] [5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg1750 + +lemma sg3546 : RowSquare [8,2,1,1,1,1,1] [5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1241 + +lemma sg3547 : RowSquare [8,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg1240 + +lemma sg3548 : RowSquare [8,2,1,1,1,1,1] [6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg1245 + +lemma sg3549 : RowSquare [8,2,1,1,1,1,1] [6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1245 + +lemma sg3550 : RowSquare [8,2,1,1,1,1,1] [7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg1245 + +lemma sg3551 : RowSquare [8,2,1,1,1,1,1] [8,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg1192 + +lemma sg3552 : RowSquare [8,2,2,1,1,1] [3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg888 + +lemma sg3553 : RowSquare [8,2,2,1,1,1] [3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg889 + +lemma sg3554 : RowSquare [8,2,2,1,1,1] [3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg890 + +lemma sg3555 : RowSquare [8,2,2,1,1,1] [3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg32 sg891 + +lemma sg3556 : RowSquare [8,2,2,1,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg892 + +lemma sg3557 : RowSquare [8,2,2,1,1,1] [4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg894 + +lemma sg3558 : RowSquare [8,2,2,1,1,1] [4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg10 sg1329 + +lemma sg3559 : RowSquare [8,2,2,2,1] [3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg66 sg586 + +lemma sg3560 : RowSquare [8,2,2,2,1] [3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg312 + +lemma sg3561 : RowSquare [8,2,2,2,1] [3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg67 sg586 + +lemma sg3562 : RowSquare [8,2,2,2,1] [3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg313 + +lemma sg3563 : RowSquare [8,2,2,2,1] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg586 + +lemma sg3564 : RowSquare [8,2,2,2,1] [3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg314 + +lemma sg3565 : RowSquare [8,2,2,2,1] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg315 + +lemma sg3566 : RowSquare [8,2,2,2,1] [4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg70 sg586 + +lemma sg3567 : RowSquare [8,2,2,2,1] [4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg179 sg313 + +lemma sg3568 : RowSquare [8,2,2,2,1] [4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg71 sg586 + +lemma sg3569 : RowSquare [8,2,2,2,1] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg589 + +lemma sg3570 : RowSquare [8,2,2,2,1] [4,4,4,3] := by + exact rowSquare_join (by decide) sg181 sg315 + +lemma sg3571 : RowSquare [8,3,1,1,1,1] [2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg1327 + +lemma sg3572 : RowSquare [8,3,1,1,1,1] [3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg1327 + +lemma sg3573 : RowSquare [8,3,1,1,1,1] [3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg1329 + +lemma sg3574 : RowSquare [8,3,1,1,1,1] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1756 + +lemma sg3575 : RowSquare [8,3,1,1,1,1] [3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg1330 + +lemma sg3576 : RowSquare [8,3,1,1,1,1] [3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg4 sg1758 + +lemma sg3577 : RowSquare [8,3,1,1,1,1] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg1331 + +lemma sg3578 : RowSquare [8,3,1,1,1,1] [3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg13 sg1332 + +lemma sg3579 : RowSquare [8,3,1,1,1,1] [4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg888 + +lemma sg3580 : RowSquare [8,3,1,1,1,1] [4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg888 + +lemma sg3581 : RowSquare [8,3,1,1,1,1] [4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5 sg1758 + +lemma sg3582 : RowSquare [8,3,1,1,1,1] [4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1760 + +lemma sg3583 : RowSquare [8,3,1,1,1,1] [4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg890 + +lemma sg3584 : RowSquare [8,3,1,1,1,1] [4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg4 sg1762 + +lemma sg3585 : RowSquare [8,3,1,1,1,1] [4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg39 sg891 + +lemma sg3586 : RowSquare [8,3,1,1,1,1] [4,3,3,3,2] := by + exact rowSquare_join (by decide) sg39 sg892 + +lemma sg3587 : RowSquare [8,3,1,1,1,1] [4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg1329 + +lemma sg3588 : RowSquare [8,3,1,1,1,1] [4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg1338 + +lemma sg3589 : RowSquare [8,3,1,1,1,1] [4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg14 sg1332 + +lemma sg3590 : RowSquare [8,3,1,1,1,1] [4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg890 + +lemma sg3591 : RowSquare [8,3,1,1,1,1] [4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg40 sg891 + +lemma sg3592 : RowSquare [8,3,1,1,1,1] [4,4,3,2,2] := by + exact rowSquare_join (by decide) sg40 sg892 + +lemma sg3593 : RowSquare [8,3,1,1,1,1] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg1766 + +lemma sg3594 : RowSquare [8,3,1,1,1,1] [5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg893 + +lemma sg3595 : RowSquare [8,3,1,1,1,1] [5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg6 sg1758 + +lemma sg3596 : RowSquare [8,3,1,1,1,1] [5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg888 + +lemma sg3597 : RowSquare [8,3,1,1,1,1] [5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg893 + +lemma sg3598 : RowSquare [8,3,1,1,1,1] [5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg39 sg894 + +lemma sg3599 : RowSquare [8,3,1,1,1,1] [5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg5 sg1762 + +lemma sg3600 : RowSquare [8,3,1,1,1,1] [5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg517 + +lemma sg3601 : RowSquare [8,3,1,1,1,1] [5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg895 + +lemma sg3602 : RowSquare [8,3,1,1,1,1] [5,3,3,2,2] := by + exact rowSquare_join (by decide) sg45 sg809 + +lemma sg3603 : RowSquare [8,3,1,1,1,1] [5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg42 sg889 + +lemma sg3604 : RowSquare [8,3,1,1,1,1] [5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg894 + +lemma sg3605 : RowSquare [8,3,1,1,1,1] [5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg39 sg897 + +lemma sg3606 : RowSquare [8,3,1,1,1,1] [5,4,2,2,2] := by + exact rowSquare_join (by decide) sg46 sg809 + +lemma sg3607 : RowSquare [8,3,1,1,1,1] [5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg518 + +lemma sg3608 : RowSquare [8,3,1,1,1,1] [5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg1338 + +lemma sg3609 : RowSquare [8,3,1,1,1,1] [5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg40 sg897 + +lemma sg3610 : RowSquare [8,3,1,1,1,1] [6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg15 sg1332 + +lemma sg3611 : RowSquare [8,3,1,1,1,1] [6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg811 + +lemma sg3612 : RowSquare [8,3,1,1,1,1] [6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg46 sg814 + +lemma sg3613 : RowSquare [8,3,2,1,1] [2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg910 + +lemma sg3614 : RowSquare [8,3,2,1,1] [2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg586 + +lemma sg3615 : RowSquare [8,3,2,1,1] [3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg587 + +lemma sg3616 : RowSquare [8,3,2,1,1] [3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg76 sg586 + +lemma sg3617 : RowSquare [8,3,2,1,1] [3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg588 + +lemma sg3618 : RowSquare [8,3,2,1,1] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg77 sg586 + +lemma sg3619 : RowSquare [8,3,2,1,1] [3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg913 + +lemma sg3620 : RowSquare [8,3,2,1,1] [3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg589 + +lemma sg3621 : RowSquare [8,3,2,1,1] [3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg74 sg590 + +lemma sg3622 : RowSquare [8,3,2,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg915 + +lemma sg3623 : RowSquare [8,3,2,1,1] [4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg87 sg534 + +lemma sg3624 : RowSquare [8,3,2,1,1] [4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg534 + +lemma sg3625 : RowSquare [8,3,2,1,1] [4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg193 sg314 + +lemma sg3626 : RowSquare [8,3,2,1,1] [4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg80 sg586 + +lemma sg3627 : RowSquare [8,3,2,1,1] [4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg535 + +lemma sg3628 : RowSquare [8,3,2,1,1] [4,4,3,2,2] := by + exact rowSquare_join (by decide) sg194 sg314 + +lemma sg3629 : RowSquare [8,3,2,1,1] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg536 + +lemma sg3630 : RowSquare [8,3,2,1,1] [4,4,4,3] := by + exact rowSquare_join (by decide) sg195 sg315 + +lemma sg3631 : RowSquare [8,3,2,1,1] [5,5,5] := by + exact rowSquare_join (by decide) sg89 sg543 + +lemma sg3632 : RowSquare [8,3,2,2] [2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg330 + +lemma sg3633 : RowSquare [8,3,2,2] [3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg179 sg330 + +lemma sg3634 : RowSquare [8,3,2,2] [3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg331 + +lemma sg3635 : RowSquare [8,3,2,2] [3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg180 sg330 + +lemma sg3636 : RowSquare [8,3,2,2] [3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg181 sg330 + +lemma sg3637 : RowSquare [8,3,2,2] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg334 + +lemma sg3638 : RowSquare [8,3,2,2] [4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg182 sg330 + +lemma sg3639 : RowSquare [8,3,2,2] [4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg183 sg330 + +lemma sg3640 : RowSquare [8,3,2,2] [4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg184 sg330 + +lemma sg3641 : RowSquare [8,3,2,2] [4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg185 sg330 + +lemma sg3642 : RowSquare [8,3,2,2] [4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg180 sg332 + +lemma sg3643 : RowSquare [8,3,2,2] [4,4,3,2,2] := by + exact rowSquare_join (by decide) sg180 sg333 + +lemma sg3644 : RowSquare [8,3,2,2] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg615 + +lemma sg3645 : RowSquare [8,3,2,2] [4,4,4,3] := by + exact rowSquare_join (by decide) sg181 sg334 + +lemma sg3646 : RowSquare [8,3,2,2] [5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg342 + +lemma sg3647 : RowSquare [8,3,3,1] [3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg348 + +lemma sg3648 : RowSquare [8,3,3,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg943 + +lemma sg3649 : RowSquare [8,3,3,1] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg550 + +lemma sg3650 : RowSquare [8,4,1,1,1] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg586 + +lemma sg3651 : RowSquare [8,4,1,1,1] [4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg534 + +lemma sg3652 : RowSquare [8,4,1,1,1] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg536 + +lemma sg3653 : RowSquare [8,4,2,1] [3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg356 + +lemma sg3654 : RowSquare [8,4,2,1] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg358 + +lemma sg3655 : RowSquare [8,4,2,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg961 + +lemma sg3656 : RowSquare [8,4,3] [3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg975 + +lemma sg3657 : RowSquare [8,4,3] [3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg636 + +lemma sg3658 : RowSquare [8,4,3] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg977 + +lemma sg3659 : RowSquare [8,4,3] [4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg33 sg975 + +lemma sg3660 : RowSquare [8,4,3] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg74 sg641 + +lemma sg3661 : RowSquare [9,1,1,1,1,1,1] [3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2251 + +lemma sg3662 : RowSquare [9,1,1,1,1,1,1] [4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2255 + +lemma sg3663 : RowSquare [9,1,1,1,1,1,1] [4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2256 + +lemma sg3664 : RowSquare [9,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2258 + +lemma sg3665 : RowSquare [9,1,1,1,1,1,1] [5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2259 + +lemma sg3666 : RowSquare [9,1,1,1,1,1,1] [5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2 sg2260 + +lemma sg3667 : RowSquare [9,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2261 + +lemma sg3668 : RowSquare [9,1,1,1,1,1,1] [5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2262 + +lemma sg3669 : RowSquare [9,1,1,1,1,1,1] [5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2263 + +lemma sg3670 : RowSquare [9,1,1,1,1,1,1] [7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg1240 + +lemma sg3671 : RowSquare [9,2,1,1,1,1] [3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1327 + +lemma sg3672 : RowSquare [9,2,1,1,1,1] [4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg1329 + +lemma sg3673 : RowSquare [9,2,1,1,1,1] [4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg1330 + +lemma sg3674 : RowSquare [9,2,1,1,1,1] [4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg1331 + +lemma sg3675 : RowSquare [9,2,1,1,1,1] [4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg16 sg1332 + +lemma sg3676 : RowSquare [9,2,1,1,1,1] [4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1329 + +lemma sg3677 : RowSquare [9,2,1,1,1,1] [4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1330 + +lemma sg3678 : RowSquare [9,2,1,1,1,1] [4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1331 + +lemma sg3679 : RowSquare [9,2,1,1,1,1] [4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg17 sg1332 + +lemma sg3680 : RowSquare [9,2,1,1,1,1] [5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7 sg1758 + +lemma sg3681 : RowSquare [9,2,1,1,1,1] [5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg18 sg1332 + +lemma sg3682 : RowSquare [9,2,1,1,1,1] [6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg1331 + +lemma sg3683 : RowSquare [9,2,1,1,1,1] [6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19 sg1332 + +lemma sg3684 : RowSquare [9,2,1,1,1,1] [6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg45 sg894 + +lemma sg3685 : RowSquare [9,2,2,1,1] [3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg87 sg586 + +lemma sg3686 : RowSquare [9,2,2,1,1] [3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg88 sg586 + +lemma sg3687 : RowSquare [9,2,2,1,1] [3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg998 + +lemma sg3688 : RowSquare [9,2,2,1,1] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg586 + +lemma sg3689 : RowSquare [9,2,2,1,1] [3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg32 sg999 + +lemma sg3690 : RowSquare [9,2,2,1,1] [3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg32 sg1000 + +lemma sg3691 : RowSquare [9,2,2,1,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg1001 + +lemma sg3692 : RowSquare [9,2,2,1,1] [4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg90 sg586 + +lemma sg3693 : RowSquare [9,2,2,1,1] [4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg91 sg586 + +lemma sg3694 : RowSquare [9,2,2,1,1] [4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg33 sg1000 + +lemma sg3695 : RowSquare [9,2,2,1,1] [4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg586 + +lemma sg3696 : RowSquare [9,2,2,1,1] [4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg88 sg588 + +lemma sg3697 : RowSquare [9,2,2,1,1] [4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg1006 + +lemma sg3698 : RowSquare [9,2,2,1,1] [4,4,3,3,1] := by + exact rowSquare_join (by decide) sg88 sg590 + +lemma sg3699 : RowSquare [9,2,2,1,1] [4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg589 + +lemma sg3700 : RowSquare [9,2,2,1,1] [5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg93 sg586 + +lemma sg3701 : RowSquare [9,2,2,2] [3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg370 + +lemma sg3702 : RowSquare [9,2,2,2] [3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg371 + +lemma sg3703 : RowSquare [9,2,2,2] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg373 + +lemma sg3704 : RowSquare [9,2,2,2] [4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg179 sg371 + +lemma sg3705 : RowSquare [9,2,2,2] [4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg179 sg372 + +lemma sg3706 : RowSquare [9,2,2,2] [4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg179 sg373 + +lemma sg3707 : RowSquare [9,2,2,2] [4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg180 sg371 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes70.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes70.lean index 53539f7bb6de2a1d7c75e7853775cad49e878512..1a0347c467f2bb161c075348ba1f25af2573dd55 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes70.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes70.lean @@ -1,1224 +1,1224 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 70. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg28540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg568 sg21240 - -lemma sg28541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1822 sg17118 - -lemma sg28542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2180 sg15576 - -lemma sg28543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1813 sg17135 - -lemma sg28544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2222 sg15544 - -lemma sg28545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10236 - -lemma sg28546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11322 - -lemma sg28547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10187 - -lemma sg28548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg7457 sg11273 - -lemma sg28549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6025 sg11791 - -lemma sg28550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2177 sg15580 - -lemma sg28551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3867 sg14513 - -lemma sg28552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2222 sg15545 - -lemma sg28553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11323 - -lemma sg28554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5957 sg11835 - -lemma sg28555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10338 - -lemma sg28556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8874 sg9005 - -lemma sg28557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10237 - -lemma sg28558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11324 - -lemma sg28559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10188 - -lemma sg28560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10430 - -lemma sg28561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10338 - -lemma sg28562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8649 sg9878 - -lemma sg28563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6910 sg11477 - -lemma sg28564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9231 - -lemma sg28565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9229 - -lemma sg28566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8647 sg9895 - -lemma sg28567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9230 - -lemma sg28568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10758 - -lemma sg28569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10338 - -lemma sg28570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10430 - -lemma sg28571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1822 sg17119 - -lemma sg28572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1860 sg16196 - -lemma sg28573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3877 sg14505 - -lemma sg28574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2230 sg15525 - -lemma sg28575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6909 sg11478 - -lemma sg28576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5975 sg11831 - -lemma sg28577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10324 - -lemma sg28578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8366 sg10654 - -lemma sg28579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3870 sg14511 - -lemma sg28580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10238 - -lemma sg28581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11325 - -lemma sg28582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10189 - -lemma sg28583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10339 - -lemma sg28584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10261 - -lemma sg28585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8726 sg9533 - -lemma sg28586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11326 - -lemma sg28587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8116 sg11054 - -lemma sg28588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10431 - -lemma sg28589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10339 - -lemma sg28590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8649 sg9879 - -lemma sg28591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10327 - -lemma sg28592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9231 - -lemma sg28593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9896 - -lemma sg28594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9879 - -lemma sg28595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10759 - -lemma sg28596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10431 - -lemma sg28597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9896 - -lemma sg28598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3870 sg14512 - -lemma sg28599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5561 sg12625 - -lemma sg28600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5984 sg11830 - -lemma sg28601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10340 - -lemma sg28602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9239 - -lemma sg28603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8726 sg9534 - -lemma sg28604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8117 sg11054 - -lemma sg28605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10432 - -lemma sg28606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10340 - -lemma sg28607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9880 - -lemma sg28608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9534 - -lemma sg28609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9240 - -lemma sg28610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10760 - -lemma sg28611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10432 - -lemma sg28612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10340 - -lemma sg28613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9897 - -lemma sg28614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10433 - -lemma sg28615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10341 - -lemma sg28616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10761 - -lemma sg28617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10433 - -lemma sg28618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9898 - -lemma sg28619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10341 - -lemma sg28620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9898 - -lemma sg28621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10326 - -lemma sg28622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9882 - -lemma sg28623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,4,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10327 - -lemma sg28624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1307 sg20980 - -lemma sg28625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1706 sg18260 - -lemma sg28626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1815 sg17132 - -lemma sg28627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2178 sg15577 - -lemma sg28628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15581 - -lemma sg28629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2689 sg15014 - -lemma sg28630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg554 sg21261 - -lemma sg28631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg554 sg21262 - -lemma sg28632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg554 sg21263 - -lemma sg28633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg554 sg21264 - -lemma sg28634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1308 sg20980 - -lemma sg28635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1707 sg18260 - -lemma sg28636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1816 sg17132 - -lemma sg28637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2179 sg15577 - -lemma sg28638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2222 sg15546 - -lemma sg28639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15027 - -lemma sg28640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2665 sg15041 - -lemma sg28641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11327 - -lemma sg28642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg570 sg21236 - -lemma sg28643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg570 sg21237 - -lemma sg28644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1822 sg17121 - -lemma sg28645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2180 sg15577 - -lemma sg28646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1815 sg17133 - -lemma sg28647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2228 sg15528 - -lemma sg28648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg18257 - -lemma sg28649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18268 - -lemma sg28650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg860 sg21161 - -lemma sg28651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5351 sg12657 - -lemma sg28652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6023 sg11793 - -lemma sg28653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2177 sg15581 - -lemma sg28654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3867 sg14515 - -lemma sg28655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10239 - -lemma sg28656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11328 - -lemma sg28657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5957 sg11836 - -lemma sg28658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10342 - -lemma sg28659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8877 sg9005 - -lemma sg28660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3866 sg14519 - -lemma sg28661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11329 - -lemma sg28662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6907 sg11479 - -lemma sg28663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10434 - -lemma sg28664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10342 - -lemma sg28665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8649 sg9883 - -lemma sg28666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10190 - -lemma sg28667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9231 - -lemma sg28668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9229 - -lemma sg28669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8647 sg9899 - -lemma sg28670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9230 - -lemma sg28671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10762 - -lemma sg28672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10342 - -lemma sg28673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10434 - -lemma sg28674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1708 sg18260 - -lemma sg28675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1818 sg17129 - -lemma sg28676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2182 sg15576 - -lemma sg28677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2223 sg15539 - -lemma sg28678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2668 sg15024 - -lemma sg28679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15028 - -lemma sg28680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3513 sg14687 - -lemma sg28681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg861 sg21161 - -lemma sg28682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5351 sg12658 - -lemma sg28683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6023 sg11794 - -lemma sg28684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2183 sg15576 - -lemma sg28685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2180 sg15578 - -lemma sg28686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3868 sg14513 - -lemma sg28687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10240 - -lemma sg28688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11330 - -lemma sg28689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5958 sg11835 - -lemma sg28690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10328 - -lemma sg28691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8874 sg9006 - -lemma sg28692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3878 sg14506 - -lemma sg28693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10241 - -lemma sg28694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11331 - -lemma sg28695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6908 sg11479 - -lemma sg28696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10343 - -lemma sg28697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10265 - -lemma sg28698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8651 sg9878 - -lemma sg28699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11332 - -lemma sg28700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10191 - -lemma sg28701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10435 - -lemma sg28702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10343 - -lemma sg28703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8649 sg9884 - -lemma sg28704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10327 - -lemma sg28705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9231 - -lemma sg28706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9900 - -lemma sg28707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9884 - -lemma sg28708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10763 - -lemma sg28709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10435 - -lemma sg28710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9900 - -lemma sg28711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1852 sg16204 - -lemma sg28712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3871 sg14511 - -lemma sg28713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3868 sg14514 - -lemma sg28714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11333 - -lemma sg28715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6909 sg11479 - -lemma sg28716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10329 - -lemma sg28717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8438 sg10251 - -lemma sg28718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8729 sg9533 - -lemma sg28719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10242 - -lemma sg28720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11334 - -lemma sg28721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10192 - -lemma sg28722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10344 - -lemma sg28723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9241 - -lemma sg28724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8651 sg9879 - -lemma sg28725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8120 sg11053 - -lemma sg28726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10436 - -lemma sg28727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10344 - -lemma sg28728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9885 - -lemma sg28729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9596 - -lemma sg28730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9325 - -lemma sg28731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10764 - -lemma sg28732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10436 - -lemma sg28733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10344 - -lemma sg28734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9901 - -lemma sg28735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5563 sg12625 - -lemma sg28736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8121 sg11053 - -lemma sg28737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10345 - -lemma sg28738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9242 - -lemma sg28739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9880 - -lemma sg28740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9534 - -lemma sg28741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10437 - -lemma sg28742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10345 - -lemma sg28743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10765 - -lemma sg28744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10437 - -lemma sg28745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9902 - -lemma sg28746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10345 - -lemma sg28747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9902 - -lemma sg28748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10330 - -lemma sg28749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10346 - -lemma sg28750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9903 - -lemma sg28751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10346 - -lemma sg28752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9903 - -lemma sg28753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9887 - -lemma sg28754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10331 - -lemma sg28755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10327 - -lemma sg28756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1819 sg17129 - -lemma sg28757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2184 sg15576 - -lemma sg28758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2232 sg15523 - -lemma sg28759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3869 sg14513 - -lemma sg28760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2867 sg14858 - -lemma sg28761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6933 sg11471 - -lemma sg28762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5959 sg11835 - -lemma sg28763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8437 sg10255 - -lemma sg28764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8874 sg9009 - -lemma sg28765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2233 sg15523 - -lemma sg28766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3898 sg14500 - -lemma sg28767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10243 - -lemma sg28768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11335 - -lemma sg28769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6925 sg11474 - -lemma sg28770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10332 - -lemma sg28771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8438 sg10255 - -lemma sg28772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8652 sg9878 - -lemma sg28773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3878 sg14508 - -lemma sg28774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11336 - -lemma sg28775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6912 sg11477 - -lemma sg28776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10347 - -lemma sg28777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9243 - -lemma sg28778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8726 sg9537 - -lemma sg28779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10193 - -lemma sg28780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10438 - -lemma sg28781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10347 - -lemma sg28782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9888 - -lemma sg28783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9537 - -lemma sg28784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9325 - -lemma sg28785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10766 - -lemma sg28786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10438 - -lemma sg28787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10347 - -lemma sg28788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9904 - -lemma sg28789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2233 sg15524 - -lemma sg28790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10244 - -lemma sg28791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11337 - -lemma sg28792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6913 sg11477 - -lemma sg28793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10333 - -lemma sg28794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9235 - -lemma sg28795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8652 sg9879 - -lemma sg28796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11338 - -lemma sg28797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10194 - -lemma sg28798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10348 - -lemma sg28799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9244 - -lemma sg28800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9235 - -lemma sg28801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9596 - -lemma sg28802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10439 - -lemma sg28803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10348 - -lemma sg28804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10767 - -lemma sg28805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10439 - -lemma sg28806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9905 - -lemma sg28807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10348 - -lemma sg28808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9905 - -lemma sg28809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10333 - -lemma sg28810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5988 sg11830 - -lemma sg28811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10440 - -lemma sg28812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9245 - -lemma sg28813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10768 - -lemma sg28814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10440 - -lemma sg28815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10349 - -lemma sg28816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9906 - -lemma sg28817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10349 - -lemma sg28818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9906 - -lemma sg28819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9890 - -lemma sg28820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10334 - -lemma sg28821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9891 - -lemma sg28822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9891 - -lemma sg28823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10335 - -lemma sg28824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9237 - -lemma sg28825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4571 sg13499 - -lemma sg28826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6973 sg11467 - -lemma sg28827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6936 sg11472 - -lemma sg28828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10336 - -lemma sg28829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9238 - -lemma sg28830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8832 sg9179 - -lemma sg28831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9596 - -lemma sg28832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10195 - -lemma sg28833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10441 - -lemma sg28834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9247 - -lemma sg28835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10769 - -lemma sg28836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10441 - -lemma sg28837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10350 - -lemma sg28838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9907 - -lemma sg28839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10350 - -lemma sg28840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9907 - -lemma sg28841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9892 - -lemma sg28842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10336 - -lemma sg28843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10351 - -lemma sg28844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10351 - -lemma sg28845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9908 - -lemma sg28846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10351 - -lemma sg28847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9908 - -lemma sg28848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9893 - -lemma sg28849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9893 - -lemma sg28850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10337 - -lemma sg28851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9538 - -lemma sg28852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8727 sg9539 - -lemma sg28853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9539 - -lemma sg28854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8384 sg10611 - -lemma sg28855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8372 sg10655 - -lemma sg28856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8525 sg10156 - -lemma sg28857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,2,2,2,1] := by - exact rowSquare_join (by decide) sg8530 sg10130 - -lemma sg28858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8531 sg10129 - -lemma sg28859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,3,2,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10129 - -lemma sg28860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,4,1,1,1] := by - exact rowSquare_join (by decide) sg8563 sg10100 - -lemma sg28861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1316 sg20971 - -lemma sg28862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1717 sg18249 - -lemma sg28863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1817 sg17132 - -lemma sg28864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2181 sg15577 - -lemma sg28865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2228 sg15529 - -lemma sg28866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15582 - -lemma sg28867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2173 sg15592 - -lemma sg28868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg571 sg21235 - -lemma sg28869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg571 sg21236 - -lemma sg28870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg571 sg21237 - -lemma sg28871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1718 sg18249 - -lemma sg28872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1818 sg17132 - -lemma sg28873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2182 sg15577 - -lemma sg28874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2229 sg15529 - -lemma sg28875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2674 sg15016 - -lemma sg28876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15029 - -lemma sg28877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3513 sg14688 - -lemma sg28878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg862 sg21161 - -lemma sg28879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg862 sg21162 - -lemma sg28880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg862 sg21163 - -lemma sg28881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2183 sg15577 - -lemma sg28882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2188 sg15570 - -lemma sg28883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3868 sg14515 - -lemma sg28884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2228 sg15530 - -lemma sg28885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6959 sg11469 - -lemma sg28886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5958 sg11836 - -lemma sg28887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8443 sg10251 - -lemma sg28888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8877 sg9006 - -lemma sg28889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2675 sg15016 - -lemma sg28890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2224 sg15541 - -lemma sg28891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11339 - -lemma sg28892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6923 sg11475 - -lemma sg28893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9232 - -lemma sg28894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8480 sg10201 - -lemma sg28895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8651 sg9883 - -lemma sg28896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11340 - -lemma sg28897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8122 sg11053 - -lemma sg28898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9233 - -lemma sg28899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8877 sg9007 - -lemma sg28900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8723 sg9546 - -lemma sg28901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9234 - -lemma sg28902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8877 sg9008 - -lemma sg28903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9909 - -lemma sg28904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8724 sg9546 - -lemma sg28905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10770 - -lemma sg28906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8345 sg10706 - -lemma sg28907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9909 - -lemma sg28908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1819 sg17132 - -lemma sg28909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2184 sg15577 - -lemma sg28910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2225 sg15539 - -lemma sg28911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3869 sg14515 - -lemma sg28912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2872 sg14853 - -lemma sg28913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6962 sg11469 - -lemma sg28914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5959 sg11836 - -lemma sg28915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10328 - -lemma sg28916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8877 sg9009 - -lemma sg28917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2226 sg15539 - -lemma sg28918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3880 sg14506 - -lemma sg28919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3868 sg14516 - -lemma sg28920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11341 - -lemma sg28921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6925 sg11475 - -lemma sg28922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9248 - -lemma sg28923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8444 sg10251 - -lemma sg28924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8652 sg9883 - -lemma sg28925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2675 sg15017 - -lemma sg28926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11342 - -lemma sg28927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6926 sg11475 - -lemma sg28928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10330 - -lemma sg28929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9248 - -lemma sg28930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8651 sg9884 - -lemma sg28931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8123 sg11053 - -lemma sg28932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10442 - -lemma sg28933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9233 - -lemma sg28934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9248 - -lemma sg28935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9597 - -lemma sg28936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9234 - -lemma sg28937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10771 - -lemma sg28938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10442 - -lemma sg28939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10707 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 70. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg28540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg568 sg21240 + +lemma sg28541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1822 sg17118 + +lemma sg28542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2180 sg15576 + +lemma sg28543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1813 sg17135 + +lemma sg28544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2222 sg15544 + +lemma sg28545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10236 + +lemma sg28546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11322 + +lemma sg28547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10187 + +lemma sg28548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg7457 sg11273 + +lemma sg28549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6025 sg11791 + +lemma sg28550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2177 sg15580 + +lemma sg28551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3867 sg14513 + +lemma sg28552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2222 sg15545 + +lemma sg28553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11323 + +lemma sg28554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5957 sg11835 + +lemma sg28555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10338 + +lemma sg28556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8874 sg9005 + +lemma sg28557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10237 + +lemma sg28558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11324 + +lemma sg28559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10188 + +lemma sg28560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10430 + +lemma sg28561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10338 + +lemma sg28562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8649 sg9878 + +lemma sg28563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6910 sg11477 + +lemma sg28564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9231 + +lemma sg28565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9229 + +lemma sg28566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8647 sg9895 + +lemma sg28567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9230 + +lemma sg28568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10758 + +lemma sg28569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10338 + +lemma sg28570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10430 + +lemma sg28571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1822 sg17119 + +lemma sg28572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1860 sg16196 + +lemma sg28573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3877 sg14505 + +lemma sg28574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2230 sg15525 + +lemma sg28575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6909 sg11478 + +lemma sg28576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5975 sg11831 + +lemma sg28577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10324 + +lemma sg28578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8366 sg10654 + +lemma sg28579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3870 sg14511 + +lemma sg28580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10238 + +lemma sg28581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11325 + +lemma sg28582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10189 + +lemma sg28583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10339 + +lemma sg28584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10261 + +lemma sg28585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8726 sg9533 + +lemma sg28586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11326 + +lemma sg28587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8116 sg11054 + +lemma sg28588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10431 + +lemma sg28589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10339 + +lemma sg28590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8649 sg9879 + +lemma sg28591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10327 + +lemma sg28592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9231 + +lemma sg28593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9896 + +lemma sg28594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9879 + +lemma sg28595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10759 + +lemma sg28596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10431 + +lemma sg28597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9896 + +lemma sg28598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3870 sg14512 + +lemma sg28599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5561 sg12625 + +lemma sg28600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5984 sg11830 + +lemma sg28601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10340 + +lemma sg28602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9239 + +lemma sg28603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8726 sg9534 + +lemma sg28604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8117 sg11054 + +lemma sg28605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10432 + +lemma sg28606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10340 + +lemma sg28607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9880 + +lemma sg28608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9534 + +lemma sg28609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9240 + +lemma sg28610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10760 + +lemma sg28611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10432 + +lemma sg28612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10340 + +lemma sg28613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9897 + +lemma sg28614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10433 + +lemma sg28615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10341 + +lemma sg28616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10761 + +lemma sg28617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10433 + +lemma sg28618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9898 + +lemma sg28619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10341 + +lemma sg28620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9898 + +lemma sg28621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10326 + +lemma sg28622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9882 + +lemma sg28623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,4,4,4,4,4,4,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10327 + +lemma sg28624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1307 sg20980 + +lemma sg28625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1706 sg18260 + +lemma sg28626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1815 sg17132 + +lemma sg28627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2178 sg15577 + +lemma sg28628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15581 + +lemma sg28629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2689 sg15014 + +lemma sg28630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg554 sg21261 + +lemma sg28631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg554 sg21262 + +lemma sg28632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg554 sg21263 + +lemma sg28633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg554 sg21264 + +lemma sg28634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1308 sg20980 + +lemma sg28635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1707 sg18260 + +lemma sg28636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1816 sg17132 + +lemma sg28637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2179 sg15577 + +lemma sg28638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2222 sg15546 + +lemma sg28639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15027 + +lemma sg28640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2665 sg15041 + +lemma sg28641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11327 + +lemma sg28642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg570 sg21236 + +lemma sg28643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg570 sg21237 + +lemma sg28644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1822 sg17121 + +lemma sg28645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2180 sg15577 + +lemma sg28646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1815 sg17133 + +lemma sg28647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2228 sg15528 + +lemma sg28648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg18257 + +lemma sg28649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18268 + +lemma sg28650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg860 sg21161 + +lemma sg28651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5351 sg12657 + +lemma sg28652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6023 sg11793 + +lemma sg28653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2177 sg15581 + +lemma sg28654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3867 sg14515 + +lemma sg28655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10239 + +lemma sg28656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11328 + +lemma sg28657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5957 sg11836 + +lemma sg28658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10342 + +lemma sg28659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8877 sg9005 + +lemma sg28660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3866 sg14519 + +lemma sg28661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11329 + +lemma sg28662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6907 sg11479 + +lemma sg28663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10434 + +lemma sg28664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10342 + +lemma sg28665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8649 sg9883 + +lemma sg28666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10190 + +lemma sg28667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9231 + +lemma sg28668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9229 + +lemma sg28669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8647 sg9899 + +lemma sg28670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9230 + +lemma sg28671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10762 + +lemma sg28672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10342 + +lemma sg28673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10434 + +lemma sg28674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1708 sg18260 + +lemma sg28675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1818 sg17129 + +lemma sg28676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2182 sg15576 + +lemma sg28677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2223 sg15539 + +lemma sg28678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2668 sg15024 + +lemma sg28679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15028 + +lemma sg28680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3513 sg14687 + +lemma sg28681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg861 sg21161 + +lemma sg28682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5351 sg12658 + +lemma sg28683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6023 sg11794 + +lemma sg28684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2183 sg15576 + +lemma sg28685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2180 sg15578 + +lemma sg28686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3868 sg14513 + +lemma sg28687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10240 + +lemma sg28688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11330 + +lemma sg28689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5958 sg11835 + +lemma sg28690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10328 + +lemma sg28691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8874 sg9006 + +lemma sg28692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3878 sg14506 + +lemma sg28693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10241 + +lemma sg28694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11331 + +lemma sg28695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6908 sg11479 + +lemma sg28696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10343 + +lemma sg28697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10265 + +lemma sg28698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8651 sg9878 + +lemma sg28699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11332 + +lemma sg28700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10191 + +lemma sg28701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10435 + +lemma sg28702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10343 + +lemma sg28703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8649 sg9884 + +lemma sg28704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10327 + +lemma sg28705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9231 + +lemma sg28706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9900 + +lemma sg28707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9884 + +lemma sg28708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10763 + +lemma sg28709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10435 + +lemma sg28710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9900 + +lemma sg28711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1852 sg16204 + +lemma sg28712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3871 sg14511 + +lemma sg28713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3868 sg14514 + +lemma sg28714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11333 + +lemma sg28715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6909 sg11479 + +lemma sg28716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10329 + +lemma sg28717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8438 sg10251 + +lemma sg28718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8729 sg9533 + +lemma sg28719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10242 + +lemma sg28720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11334 + +lemma sg28721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10192 + +lemma sg28722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10344 + +lemma sg28723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9241 + +lemma sg28724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8651 sg9879 + +lemma sg28725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8120 sg11053 + +lemma sg28726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10436 + +lemma sg28727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10344 + +lemma sg28728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9885 + +lemma sg28729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9596 + +lemma sg28730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9325 + +lemma sg28731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10764 + +lemma sg28732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10436 + +lemma sg28733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10344 + +lemma sg28734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9901 + +lemma sg28735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5563 sg12625 + +lemma sg28736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8121 sg11053 + +lemma sg28737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10345 + +lemma sg28738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9242 + +lemma sg28739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9880 + +lemma sg28740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9534 + +lemma sg28741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10437 + +lemma sg28742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10345 + +lemma sg28743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10765 + +lemma sg28744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10437 + +lemma sg28745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9902 + +lemma sg28746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10345 + +lemma sg28747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9902 + +lemma sg28748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10330 + +lemma sg28749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10346 + +lemma sg28750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9903 + +lemma sg28751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10346 + +lemma sg28752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9903 + +lemma sg28753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9887 + +lemma sg28754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10331 + +lemma sg28755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10327 + +lemma sg28756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1819 sg17129 + +lemma sg28757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2184 sg15576 + +lemma sg28758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2232 sg15523 + +lemma sg28759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3869 sg14513 + +lemma sg28760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2867 sg14858 + +lemma sg28761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6933 sg11471 + +lemma sg28762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5959 sg11835 + +lemma sg28763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8437 sg10255 + +lemma sg28764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8874 sg9009 + +lemma sg28765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2233 sg15523 + +lemma sg28766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3898 sg14500 + +lemma sg28767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10243 + +lemma sg28768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11335 + +lemma sg28769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6925 sg11474 + +lemma sg28770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10332 + +lemma sg28771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8438 sg10255 + +lemma sg28772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8652 sg9878 + +lemma sg28773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3878 sg14508 + +lemma sg28774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11336 + +lemma sg28775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6912 sg11477 + +lemma sg28776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10347 + +lemma sg28777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9243 + +lemma sg28778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8726 sg9537 + +lemma sg28779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10193 + +lemma sg28780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10438 + +lemma sg28781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10347 + +lemma sg28782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9888 + +lemma sg28783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9537 + +lemma sg28784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9325 + +lemma sg28785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10766 + +lemma sg28786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10438 + +lemma sg28787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10347 + +lemma sg28788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9904 + +lemma sg28789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2233 sg15524 + +lemma sg28790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10244 + +lemma sg28791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11337 + +lemma sg28792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6913 sg11477 + +lemma sg28793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10333 + +lemma sg28794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9235 + +lemma sg28795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8652 sg9879 + +lemma sg28796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11338 + +lemma sg28797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10194 + +lemma sg28798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10348 + +lemma sg28799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9244 + +lemma sg28800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9235 + +lemma sg28801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9596 + +lemma sg28802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10439 + +lemma sg28803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10348 + +lemma sg28804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10767 + +lemma sg28805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10439 + +lemma sg28806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9905 + +lemma sg28807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10348 + +lemma sg28808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9905 + +lemma sg28809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10333 + +lemma sg28810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5988 sg11830 + +lemma sg28811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10440 + +lemma sg28812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9245 + +lemma sg28813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10768 + +lemma sg28814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10440 + +lemma sg28815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10349 + +lemma sg28816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9906 + +lemma sg28817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10349 + +lemma sg28818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9906 + +lemma sg28819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9890 + +lemma sg28820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10334 + +lemma sg28821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9891 + +lemma sg28822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9891 + +lemma sg28823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10335 + +lemma sg28824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9237 + +lemma sg28825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4571 sg13499 + +lemma sg28826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6973 sg11467 + +lemma sg28827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6936 sg11472 + +lemma sg28828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10336 + +lemma sg28829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9238 + +lemma sg28830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8832 sg9179 + +lemma sg28831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9596 + +lemma sg28832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10195 + +lemma sg28833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10441 + +lemma sg28834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9247 + +lemma sg28835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10769 + +lemma sg28836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10441 + +lemma sg28837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10350 + +lemma sg28838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9907 + +lemma sg28839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10350 + +lemma sg28840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9907 + +lemma sg28841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9892 + +lemma sg28842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10336 + +lemma sg28843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10351 + +lemma sg28844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10351 + +lemma sg28845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9908 + +lemma sg28846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10351 + +lemma sg28847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9908 + +lemma sg28848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9893 + +lemma sg28849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9893 + +lemma sg28850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10337 + +lemma sg28851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9538 + +lemma sg28852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8727 sg9539 + +lemma sg28853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9539 + +lemma sg28854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8384 sg10611 + +lemma sg28855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8372 sg10655 + +lemma sg28856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8525 sg10156 + +lemma sg28857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,2,2,2,1] := by + exact rowSquare_join (by decide) sg8530 sg10130 + +lemma sg28858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8531 sg10129 + +lemma sg28859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,3,2,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10129 + +lemma sg28860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,5,5,5,5,4,1,1,1] := by + exact rowSquare_join (by decide) sg8563 sg10100 + +lemma sg28861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1316 sg20971 + +lemma sg28862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1717 sg18249 + +lemma sg28863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1817 sg17132 + +lemma sg28864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2181 sg15577 + +lemma sg28865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2228 sg15529 + +lemma sg28866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15582 + +lemma sg28867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2173 sg15592 + +lemma sg28868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg571 sg21235 + +lemma sg28869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg571 sg21236 + +lemma sg28870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg571 sg21237 + +lemma sg28871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1718 sg18249 + +lemma sg28872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1818 sg17132 + +lemma sg28873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2182 sg15577 + +lemma sg28874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2229 sg15529 + +lemma sg28875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2674 sg15016 + +lemma sg28876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15029 + +lemma sg28877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3513 sg14688 + +lemma sg28878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg862 sg21161 + +lemma sg28879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg862 sg21162 + +lemma sg28880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg862 sg21163 + +lemma sg28881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2183 sg15577 + +lemma sg28882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2188 sg15570 + +lemma sg28883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3868 sg14515 + +lemma sg28884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2228 sg15530 + +lemma sg28885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6959 sg11469 + +lemma sg28886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5958 sg11836 + +lemma sg28887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8443 sg10251 + +lemma sg28888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8877 sg9006 + +lemma sg28889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2675 sg15016 + +lemma sg28890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2224 sg15541 + +lemma sg28891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11339 + +lemma sg28892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6923 sg11475 + +lemma sg28893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9232 + +lemma sg28894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8480 sg10201 + +lemma sg28895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8651 sg9883 + +lemma sg28896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11340 + +lemma sg28897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8122 sg11053 + +lemma sg28898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9233 + +lemma sg28899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8877 sg9007 + +lemma sg28900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8723 sg9546 + +lemma sg28901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9234 + +lemma sg28902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8877 sg9008 + +lemma sg28903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9909 + +lemma sg28904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8724 sg9546 + +lemma sg28905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10770 + +lemma sg28906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8345 sg10706 + +lemma sg28907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9909 + +lemma sg28908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1819 sg17132 + +lemma sg28909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2184 sg15577 + +lemma sg28910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2225 sg15539 + +lemma sg28911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3869 sg14515 + +lemma sg28912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2872 sg14853 + +lemma sg28913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6962 sg11469 + +lemma sg28914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5959 sg11836 + +lemma sg28915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10328 + +lemma sg28916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8877 sg9009 + +lemma sg28917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2226 sg15539 + +lemma sg28918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3880 sg14506 + +lemma sg28919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3868 sg14516 + +lemma sg28920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11341 + +lemma sg28921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6925 sg11475 + +lemma sg28922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9248 + +lemma sg28923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8444 sg10251 + +lemma sg28924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8652 sg9883 + +lemma sg28925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2675 sg15017 + +lemma sg28926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11342 + +lemma sg28927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6926 sg11475 + +lemma sg28928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10330 + +lemma sg28929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9248 + +lemma sg28930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8651 sg9884 + +lemma sg28931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8123 sg11053 + +lemma sg28932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10442 + +lemma sg28933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9233 + +lemma sg28934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9248 + +lemma sg28935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9597 + +lemma sg28936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9234 + +lemma sg28937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10771 + +lemma sg28938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10442 + +lemma sg28939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10707 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes71.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes71.lean index ca06b1b74beabdeb121fc26bfd72b20f0c971668..362cdef6a63fe245340ddb2510db7be36b5ae5be 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes71.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes71.lean @@ -1,1224 +1,1224 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 71. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg28940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9910 - -lemma sg28941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3873 sg14511 - -lemma sg28942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4569 sg13501 - -lemma sg28943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11343 - -lemma sg28944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8124 sg11053 - -lemma sg28945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9249 - -lemma sg28946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9326 - -lemma sg28947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8729 sg9536 - -lemma sg28948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11344 - -lemma sg28949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8125 sg11053 - -lemma sg28950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10352 - -lemma sg28951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9249 - -lemma sg28952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9885 - -lemma sg28953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9536 - -lemma sg28954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10443 - -lemma sg28955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10352 - -lemma sg28956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10772 - -lemma sg28957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10443 - -lemma sg28958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9911 - -lemma sg28959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10352 - -lemma sg28960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9911 - -lemma sg28961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9249 - -lemma sg28962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5990 sg11830 - -lemma sg28963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10444 - -lemma sg28964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9250 - -lemma sg28965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10773 - -lemma sg28966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10444 - -lemma sg28967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10353 - -lemma sg28968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9912 - -lemma sg28969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10353 - -lemma sg28970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9912 - -lemma sg28971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9250 - -lemma sg28972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9250 - -lemma sg28973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9251 - -lemma sg28974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9251 - -lemma sg28975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9251 - -lemma sg28976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10331 - -lemma sg28977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2193 sg15566 - -lemma sg28978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2227 sg15539 - -lemma sg28979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3881 sg14506 - -lemma sg28980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3869 sg14516 - -lemma sg28981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5558 sg12626 - -lemma sg28982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5980 sg11832 - -lemma sg28983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10332 - -lemma sg28984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8444 sg10255 - -lemma sg28985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8732 sg9535 - -lemma sg28986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3899 sg14500 - -lemma sg28987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4573 sg13499 - -lemma sg28988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11345 - -lemma sg28989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8126 sg11053 - -lemma sg28990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9252 - -lemma sg28991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9327 - -lemma sg28992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8652 sg9884 - -lemma sg28993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11346 - -lemma sg28994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8127 sg11053 - -lemma sg28995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10354 - -lemma sg28996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9252 - -lemma sg28997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9888 - -lemma sg28998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9597 - -lemma sg28999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10445 - -lemma sg29000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10354 - -lemma sg29001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10774 - -lemma sg29002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10445 - -lemma sg29003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9913 - -lemma sg29004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10354 - -lemma sg29005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9913 - -lemma sg29006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9252 - -lemma sg29007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4574 sg13499 - -lemma sg29008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11347 - -lemma sg29009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8128 sg11053 - -lemma sg29010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9253 - -lemma sg29011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9328 - -lemma sg29012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9885 - -lemma sg29013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9597 - -lemma sg29014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6939 sg11472 - -lemma sg29015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10446 - -lemma sg29016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9253 - -lemma sg29017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10775 - -lemma sg29018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10446 - -lemma sg29019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10355 - -lemma sg29020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9914 - -lemma sg29021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10355 - -lemma sg29022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9914 - -lemma sg29023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9253 - -lemma sg29024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9253 - -lemma sg29025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10356 - -lemma sg29026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10356 - -lemma sg29027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9915 - -lemma sg29028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10356 - -lemma sg29029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9915 - -lemma sg29030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9254 - -lemma sg29031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9254 - -lemma sg29032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9254 - -lemma sg29033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10334 - -lemma sg29034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9598 - -lemma sg29035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10335 - -lemma sg29036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11348 - -lemma sg29037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6940 sg11472 - -lemma sg29038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10447 - -lemma sg29039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9329 - -lemma sg29040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10776 - -lemma sg29041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10447 - -lemma sg29042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10357 - -lemma sg29043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10357 - -lemma sg29044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9916 - -lemma sg29045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10357 - -lemma sg29046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9916 - -lemma sg29047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9255 - -lemma sg29048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9255 - -lemma sg29049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9255 - -lemma sg29050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10336 - -lemma sg29051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10280 - -lemma sg29052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8723 sg9551 - -lemma sg29053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8724 sg9551 - -lemma sg29054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8725 sg9551 - -lemma sg29055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9599 - -lemma sg29056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10337 - -lemma sg29057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8731 sg9539 - -lemma sg29058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10655 - -lemma sg29059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8526 sg10156 - -lemma sg29060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg8561 sg10104 - -lemma sg29061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg8535 sg10129 - -lemma sg29062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2236 sg15523 - -lemma sg29063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3900 sg14500 - -lemma sg29064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3881 sg14508 - -lemma sg29065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5581 sg12618 - -lemma sg29066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6010 sg11829 - -lemma sg29067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8827 sg9194 - -lemma sg29068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9327 - -lemma sg29069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8732 sg9537 - -lemma sg29070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4575 sg13499 - -lemma sg29071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6941 sg11471 - -lemma sg29072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6011 sg11829 - -lemma sg29073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9256 - -lemma sg29074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8871 sg9034 - -lemma sg29075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9888 - -lemma sg29076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8733 sg9537 - -lemma sg29077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6917 sg11477 - -lemma sg29078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10448 - -lemma sg29079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9256 - -lemma sg29080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10777 - -lemma sg29081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10448 - -lemma sg29082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10358 - -lemma sg29083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9917 - -lemma sg29084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10358 - -lemma sg29085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9917 - -lemma sg29086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9256 - -lemma sg29087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9256 - -lemma sg29088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6942 sg11471 - -lemma sg29089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6918 sg11477 - -lemma sg29090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10449 - -lemma sg29091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8871 sg9035 - -lemma sg29092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10778 - -lemma sg29093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10449 - -lemma sg29094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10359 - -lemma sg29095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10359 - -lemma sg29096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9918 - -lemma sg29097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10359 - -lemma sg29098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9918 - -lemma sg29099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9257 - -lemma sg29100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9257 - -lemma sg29101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9257 - -lemma sg29102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8829 sg9195 - -lemma sg29103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9258 - -lemma sg29104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9258 - -lemma sg29105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9258 - -lemma sg29106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9258 - -lemma sg29107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8872 sg9036 - -lemma sg29108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8829 sg9196 - -lemma sg29109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10335 - -lemma sg29110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6919 sg11477 - -lemma sg29111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10360 - -lemma sg29112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10360 - -lemma sg29113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9919 - -lemma sg29114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10360 - -lemma sg29115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9919 - -lemma sg29116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9259 - -lemma sg29117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9259 - -lemma sg29118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9259 - -lemma sg29119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9259 - -lemma sg29120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8872 sg9037 - -lemma sg29121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8829 sg9197 - -lemma sg29122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8749 sg9492 - -lemma sg29123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8872 sg9038 - -lemma sg29124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8751 sg9492 - -lemma sg29125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10337 - -lemma sg29126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8527 sg10156 - -lemma sg29127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg8600 sg10098 - -lemma sg29128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9260 - -lemma sg29129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9260 - -lemma sg29130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9260 - -lemma sg29131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9260 - -lemma sg29132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9260 - -lemma sg29133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8749 sg9493 - -lemma sg29134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8872 sg9039 - -lemma sg29135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8751 sg9493 - -lemma sg29136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8888 sg9002 - -lemma sg29137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8494 sg10195 - -lemma sg29138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8495 sg10195 - -lemma sg29139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg8500 sg10182 - -lemma sg29140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1310 sg20975 - -lemma sg29141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1710 sg18255 - -lemma sg29142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21014 - -lemma sg29143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2174 sg15583 - -lemma sg29144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg294 sg21334 - -lemma sg29145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg294 sg21335 - -lemma sg29146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg294 sg21336 - -lemma sg29147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg294 sg21337 - -lemma sg29148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg294 sg21338 - -lemma sg29149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1305 sg20982 - -lemma sg29150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1704 sg18263 - -lemma sg29151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1812 sg17136 - -lemma sg29152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15583 - -lemma sg29153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2173 sg15593 - -lemma sg29154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg341 sg21307 - -lemma sg29155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg341 sg21308 - -lemma sg29156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg341 sg21309 - -lemma sg29157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg341 sg21310 - -lemma sg29158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1306 sg20982 - -lemma sg29159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1705 sg18263 - -lemma sg29160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1813 sg17136 - -lemma sg29161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2176 sg15583 - -lemma sg29162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21015 - -lemma sg29163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2665 sg15042 - -lemma sg29164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg557 sg21257 - -lemma sg29165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg557 sg21258 - -lemma sg29166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg557 sg21259 - -lemma sg29167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg557 sg21260 - -lemma sg29168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1713 sg18255 - -lemma sg29169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1467 sg20937 - -lemma sg29170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1823 sg17119 - -lemma sg29171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg17135 - -lemma sg29172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21016 - -lemma sg29173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18269 - -lemma sg29174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg569 sg21238 - -lemma sg29175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg569 sg21239 - -lemma sg29176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg569 sg21240 - -lemma sg29177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2177 sg15583 - -lemma sg29178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1823 sg17120 - -lemma sg29179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2230 sg15526 - -lemma sg29180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21017 - -lemma sg29181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18270 - -lemma sg29182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg859 sg21165 - -lemma sg29183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5352 sg12656 - -lemma sg29184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6025 sg11792 - -lemma sg29185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3866 sg14520 - -lemma sg29186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1290 sg21012 - -lemma sg29187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6921 sg11476 - -lemma sg29188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5956 sg11838 - -lemma sg29189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10450 - -lemma sg29190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8346 sg10705 - -lemma sg29191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6910 sg11478 - -lemma sg29192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6906 sg11480 - -lemma sg29193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8836 sg9173 - -lemma sg29194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8501 sg10175 - -lemma sg29195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8647 sg9920 - -lemma sg29196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8836 sg9174 - -lemma sg29197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9172 - -lemma sg29198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8343 sg10779 - -lemma sg29199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8858 sg9159 - -lemma sg29200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8415 sg10450 - -lemma sg29201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1307 sg20982 - -lemma sg29202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1706 sg18263 - -lemma sg29203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1815 sg17134 - -lemma sg29204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2178 sg15579 - -lemma sg29205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15584 - -lemma sg29206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg15027 - -lemma sg29207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg558 sg21257 - -lemma sg29208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg558 sg21258 - -lemma sg29209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg558 sg21259 - -lemma sg29210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg558 sg21260 - -lemma sg29211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1308 sg20982 - -lemma sg29212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1707 sg18263 - -lemma sg29213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1816 sg17134 - -lemma sg29214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2179 sg15579 - -lemma sg29215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2222 sg15547 - -lemma sg29216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15030 - -lemma sg29217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2665 sg15043 - -lemma sg29218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg570 sg21238 - -lemma sg29219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg570 sg21239 - -lemma sg29220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg570 sg21240 - -lemma sg29221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1822 sg17122 - -lemma sg29222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2180 sg15579 - -lemma sg29223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1815 sg17135 - -lemma sg29224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2228 sg15532 - -lemma sg29225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1709 sg18258 - -lemma sg29226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1702 sg18271 - -lemma sg29227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg860 sg21165 - -lemma sg29228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5352 sg12657 - -lemma sg29229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6025 sg11793 - -lemma sg29230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2177 sg15584 - -lemma sg29231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3867 sg14517 - -lemma sg29232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2228 sg15533 - -lemma sg29233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6923 sg11476 - -lemma sg29234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5957 sg11837 - -lemma sg29235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10361 - -lemma sg29236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8348 sg10705 - -lemma sg29237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1291 sg21012 - -lemma sg29238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6911 sg11478 - -lemma sg29239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6907 sg11480 - -lemma sg29240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10451 - -lemma sg29241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10361 - -lemma sg29242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8649 sg9894 - -lemma sg29243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6910 sg11479 - -lemma sg29244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8453 sg10250 - -lemma sg29245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8837 sg9173 - -lemma sg29246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8647 sg9921 - -lemma sg29247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8837 sg9174 - -lemma sg29248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10780 - -lemma sg29249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10361 - -lemma sg29250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10451 - -lemma sg29251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1708 sg18263 - -lemma sg29252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1824 sg17118 - -lemma sg29253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2189 sg15568 - -lemma sg29254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2223 sg15543 - -lemma sg29255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2668 sg15026 - -lemma sg29256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15031 - -lemma sg29257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3513 sg14689 - -lemma sg29258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg861 sg21165 - -lemma sg29259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5352 sg12658 - -lemma sg29260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg6025 sg11794 - -lemma sg29261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2190 sg15568 - -lemma sg29262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2180 sg15580 - -lemma sg29263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3877 sg14509 - -lemma sg29264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2222 sg15548 - -lemma sg29265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6925 sg11476 - -lemma sg29266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5975 sg11833 - -lemma sg29267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10338 - -lemma sg29268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8349 sg10705 - -lemma sg29269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3870 sg14513 - -lemma sg29270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3867 sg14518 - -lemma sg29271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6912 sg11478 - -lemma sg29272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6908 sg11480 - -lemma sg29273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10362 - -lemma sg29274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10285 - -lemma sg29275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8726 sg9540 - -lemma sg29276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6967 sg11468 - -lemma sg29277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8118 sg11054 - -lemma sg29278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10452 - -lemma sg29279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10362 - -lemma sg29280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8649 sg9895 - -lemma sg29281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9240 - -lemma sg29282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9231 - -lemma sg29283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9922 - -lemma sg29284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9895 - -lemma sg29285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10781 - -lemma sg29286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10452 - -lemma sg29287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9922 - -lemma sg29288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1852 sg16205 - -lemma sg29289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3883 sg14505 - -lemma sg29290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2237 sg15525 - -lemma sg29291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6913 sg11478 - -lemma sg29292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6909 sg11480 - -lemma sg29293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10339 - -lemma sg29294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8438 sg10261 - -lemma sg29295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8657 sg9765 - -lemma sg29296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3870 sg14514 - -lemma sg29297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6983 sg11467 - -lemma sg29298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8119 sg11054 - -lemma sg29299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10363 - -lemma sg29300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9261 - -lemma sg29301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8726 sg9541 - -lemma sg29302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8120 sg11054 - -lemma sg29303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10453 - -lemma sg29304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10363 - -lemma sg29305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9896 - -lemma sg29306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9541 - -lemma sg29307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9240 - -lemma sg29308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10782 - -lemma sg29309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10453 - -lemma sg29310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10363 - -lemma sg29311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9923 - -lemma sg29312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5569 sg12625 - -lemma sg29313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8121 sg11054 - -lemma sg29314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10364 - -lemma sg29315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9262 - -lemma sg29316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9239 - -lemma sg29317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8736 sg9534 - -lemma sg29318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10454 - -lemma sg29319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10364 - -lemma sg29320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10783 - -lemma sg29321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10454 - -lemma sg29322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9924 - -lemma sg29323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10364 - -lemma sg29324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9924 - -lemma sg29325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10340 - -lemma sg29326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10365 - -lemma sg29327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9925 - -lemma sg29328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10365 - -lemma sg29329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9925 - -lemma sg29330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9898 - -lemma sg29331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10341 - -lemma sg29332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,4,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9240 - -lemma sg29333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1316 sg20973 - -lemma sg29334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1717 sg18251 - -lemma sg29335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1817 sg17134 - -lemma sg29336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2181 sg15579 - -lemma sg29337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2178 sg15581 - -lemma sg29338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2676 sg15016 - -lemma sg29339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg15029 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 71. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg28940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9910 + +lemma sg28941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3873 sg14511 + +lemma sg28942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4569 sg13501 + +lemma sg28943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11343 + +lemma sg28944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8124 sg11053 + +lemma sg28945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9249 + +lemma sg28946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9326 + +lemma sg28947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8729 sg9536 + +lemma sg28948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11344 + +lemma sg28949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8125 sg11053 + +lemma sg28950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10352 + +lemma sg28951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9249 + +lemma sg28952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9885 + +lemma sg28953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9536 + +lemma sg28954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10443 + +lemma sg28955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10352 + +lemma sg28956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10772 + +lemma sg28957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10443 + +lemma sg28958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9911 + +lemma sg28959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10352 + +lemma sg28960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9911 + +lemma sg28961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9249 + +lemma sg28962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5990 sg11830 + +lemma sg28963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10444 + +lemma sg28964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9250 + +lemma sg28965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10773 + +lemma sg28966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10444 + +lemma sg28967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10353 + +lemma sg28968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9912 + +lemma sg28969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10353 + +lemma sg28970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9912 + +lemma sg28971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9250 + +lemma sg28972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9250 + +lemma sg28973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9251 + +lemma sg28974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9251 + +lemma sg28975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9251 + +lemma sg28976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10331 + +lemma sg28977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2193 sg15566 + +lemma sg28978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2227 sg15539 + +lemma sg28979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3881 sg14506 + +lemma sg28980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3869 sg14516 + +lemma sg28981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5558 sg12626 + +lemma sg28982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5980 sg11832 + +lemma sg28983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10332 + +lemma sg28984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8444 sg10255 + +lemma sg28985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8732 sg9535 + +lemma sg28986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3899 sg14500 + +lemma sg28987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4573 sg13499 + +lemma sg28988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11345 + +lemma sg28989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8126 sg11053 + +lemma sg28990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9252 + +lemma sg28991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9327 + +lemma sg28992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8652 sg9884 + +lemma sg28993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11346 + +lemma sg28994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8127 sg11053 + +lemma sg28995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10354 + +lemma sg28996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9252 + +lemma sg28997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9888 + +lemma sg28998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9597 + +lemma sg28999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10445 + +lemma sg29000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10354 + +lemma sg29001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10774 + +lemma sg29002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10445 + +lemma sg29003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9913 + +lemma sg29004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10354 + +lemma sg29005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9913 + +lemma sg29006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9252 + +lemma sg29007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4574 sg13499 + +lemma sg29008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11347 + +lemma sg29009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8128 sg11053 + +lemma sg29010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9253 + +lemma sg29011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9328 + +lemma sg29012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9885 + +lemma sg29013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9597 + +lemma sg29014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6939 sg11472 + +lemma sg29015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10446 + +lemma sg29016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9253 + +lemma sg29017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10775 + +lemma sg29018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10446 + +lemma sg29019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10355 + +lemma sg29020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9914 + +lemma sg29021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10355 + +lemma sg29022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9914 + +lemma sg29023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9253 + +lemma sg29024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9253 + +lemma sg29025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10356 + +lemma sg29026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10356 + +lemma sg29027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9915 + +lemma sg29028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10356 + +lemma sg29029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9915 + +lemma sg29030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9254 + +lemma sg29031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9254 + +lemma sg29032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9254 + +lemma sg29033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10334 + +lemma sg29034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9598 + +lemma sg29035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10335 + +lemma sg29036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11348 + +lemma sg29037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6940 sg11472 + +lemma sg29038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10447 + +lemma sg29039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9329 + +lemma sg29040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10776 + +lemma sg29041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10447 + +lemma sg29042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10357 + +lemma sg29043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10357 + +lemma sg29044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9916 + +lemma sg29045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10357 + +lemma sg29046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9916 + +lemma sg29047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9255 + +lemma sg29048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9255 + +lemma sg29049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9255 + +lemma sg29050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10336 + +lemma sg29051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10280 + +lemma sg29052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8723 sg9551 + +lemma sg29053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8724 sg9551 + +lemma sg29054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8725 sg9551 + +lemma sg29055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9599 + +lemma sg29056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10337 + +lemma sg29057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8731 sg9539 + +lemma sg29058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10655 + +lemma sg29059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8526 sg10156 + +lemma sg29060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg8561 sg10104 + +lemma sg29061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg8535 sg10129 + +lemma sg29062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2236 sg15523 + +lemma sg29063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3900 sg14500 + +lemma sg29064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3881 sg14508 + +lemma sg29065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5581 sg12618 + +lemma sg29066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6010 sg11829 + +lemma sg29067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8827 sg9194 + +lemma sg29068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9327 + +lemma sg29069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8732 sg9537 + +lemma sg29070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4575 sg13499 + +lemma sg29071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6941 sg11471 + +lemma sg29072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6011 sg11829 + +lemma sg29073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9256 + +lemma sg29074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8871 sg9034 + +lemma sg29075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9888 + +lemma sg29076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8733 sg9537 + +lemma sg29077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6917 sg11477 + +lemma sg29078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10448 + +lemma sg29079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9256 + +lemma sg29080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10777 + +lemma sg29081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10448 + +lemma sg29082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10358 + +lemma sg29083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9917 + +lemma sg29084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10358 + +lemma sg29085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9917 + +lemma sg29086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9256 + +lemma sg29087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9256 + +lemma sg29088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6942 sg11471 + +lemma sg29089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6918 sg11477 + +lemma sg29090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10449 + +lemma sg29091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8871 sg9035 + +lemma sg29092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10778 + +lemma sg29093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10449 + +lemma sg29094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10359 + +lemma sg29095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10359 + +lemma sg29096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9918 + +lemma sg29097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10359 + +lemma sg29098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9918 + +lemma sg29099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9257 + +lemma sg29100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9257 + +lemma sg29101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9257 + +lemma sg29102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8829 sg9195 + +lemma sg29103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9258 + +lemma sg29104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9258 + +lemma sg29105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9258 + +lemma sg29106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9258 + +lemma sg29107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8872 sg9036 + +lemma sg29108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8829 sg9196 + +lemma sg29109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10335 + +lemma sg29110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6919 sg11477 + +lemma sg29111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10360 + +lemma sg29112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10360 + +lemma sg29113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9919 + +lemma sg29114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10360 + +lemma sg29115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9919 + +lemma sg29116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9259 + +lemma sg29117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9259 + +lemma sg29118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9259 + +lemma sg29119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9259 + +lemma sg29120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8872 sg9037 + +lemma sg29121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8829 sg9197 + +lemma sg29122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8749 sg9492 + +lemma sg29123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8872 sg9038 + +lemma sg29124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8751 sg9492 + +lemma sg29125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10337 + +lemma sg29126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8527 sg10156 + +lemma sg29127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg8600 sg10098 + +lemma sg29128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9260 + +lemma sg29129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9260 + +lemma sg29130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9260 + +lemma sg29131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9260 + +lemma sg29132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9260 + +lemma sg29133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8749 sg9493 + +lemma sg29134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8872 sg9039 + +lemma sg29135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8751 sg9493 + +lemma sg29136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8888 sg9002 + +lemma sg29137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8494 sg10195 + +lemma sg29138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8495 sg10195 + +lemma sg29139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,6,6,6,6,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg8500 sg10182 + +lemma sg29140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1310 sg20975 + +lemma sg29141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1710 sg18255 + +lemma sg29142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21014 + +lemma sg29143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2174 sg15583 + +lemma sg29144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg294 sg21334 + +lemma sg29145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg294 sg21335 + +lemma sg29146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg294 sg21336 + +lemma sg29147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg294 sg21337 + +lemma sg29148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,2,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg294 sg21338 + +lemma sg29149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1305 sg20982 + +lemma sg29150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1704 sg18263 + +lemma sg29151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1812 sg17136 + +lemma sg29152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15583 + +lemma sg29153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2173 sg15593 + +lemma sg29154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg341 sg21307 + +lemma sg29155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg341 sg21308 + +lemma sg29156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg341 sg21309 + +lemma sg29157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg341 sg21310 + +lemma sg29158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1306 sg20982 + +lemma sg29159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1705 sg18263 + +lemma sg29160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1813 sg17136 + +lemma sg29161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2176 sg15583 + +lemma sg29162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21015 + +lemma sg29163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2665 sg15042 + +lemma sg29164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg557 sg21257 + +lemma sg29165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg557 sg21258 + +lemma sg29166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg557 sg21259 + +lemma sg29167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg557 sg21260 + +lemma sg29168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1713 sg18255 + +lemma sg29169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1467 sg20937 + +lemma sg29170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1823 sg17119 + +lemma sg29171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg17135 + +lemma sg29172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21016 + +lemma sg29173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18269 + +lemma sg29174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg569 sg21238 + +lemma sg29175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg569 sg21239 + +lemma sg29176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg569 sg21240 + +lemma sg29177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2177 sg15583 + +lemma sg29178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1823 sg17120 + +lemma sg29179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2230 sg15526 + +lemma sg29180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21017 + +lemma sg29181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18270 + +lemma sg29182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg859 sg21165 + +lemma sg29183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5352 sg12656 + +lemma sg29184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6025 sg11792 + +lemma sg29185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3866 sg14520 + +lemma sg29186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1290 sg21012 + +lemma sg29187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6921 sg11476 + +lemma sg29188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5956 sg11838 + +lemma sg29189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10450 + +lemma sg29190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8346 sg10705 + +lemma sg29191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6910 sg11478 + +lemma sg29192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6906 sg11480 + +lemma sg29193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8836 sg9173 + +lemma sg29194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8501 sg10175 + +lemma sg29195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8647 sg9920 + +lemma sg29196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8836 sg9174 + +lemma sg29197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9172 + +lemma sg29198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8343 sg10779 + +lemma sg29199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8858 sg9159 + +lemma sg29200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,3,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8415 sg10450 + +lemma sg29201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1307 sg20982 + +lemma sg29202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1706 sg18263 + +lemma sg29203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1815 sg17134 + +lemma sg29204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2178 sg15579 + +lemma sg29205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15584 + +lemma sg29206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg15027 + +lemma sg29207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg558 sg21257 + +lemma sg29208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg558 sg21258 + +lemma sg29209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg558 sg21259 + +lemma sg29210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg558 sg21260 + +lemma sg29211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1308 sg20982 + +lemma sg29212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1707 sg18263 + +lemma sg29213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1816 sg17134 + +lemma sg29214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2179 sg15579 + +lemma sg29215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2222 sg15547 + +lemma sg29216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15030 + +lemma sg29217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2665 sg15043 + +lemma sg29218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg570 sg21238 + +lemma sg29219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg570 sg21239 + +lemma sg29220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg570 sg21240 + +lemma sg29221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1822 sg17122 + +lemma sg29222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2180 sg15579 + +lemma sg29223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1815 sg17135 + +lemma sg29224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2228 sg15532 + +lemma sg29225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1709 sg18258 + +lemma sg29226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1702 sg18271 + +lemma sg29227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg860 sg21165 + +lemma sg29228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5352 sg12657 + +lemma sg29229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6025 sg11793 + +lemma sg29230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2177 sg15584 + +lemma sg29231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3867 sg14517 + +lemma sg29232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2228 sg15533 + +lemma sg29233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6923 sg11476 + +lemma sg29234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5957 sg11837 + +lemma sg29235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10361 + +lemma sg29236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8348 sg10705 + +lemma sg29237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1291 sg21012 + +lemma sg29238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6911 sg11478 + +lemma sg29239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6907 sg11480 + +lemma sg29240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10451 + +lemma sg29241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10361 + +lemma sg29242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8649 sg9894 + +lemma sg29243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6910 sg11479 + +lemma sg29244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8453 sg10250 + +lemma sg29245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8837 sg9173 + +lemma sg29246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8647 sg9921 + +lemma sg29247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8837 sg9174 + +lemma sg29248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10780 + +lemma sg29249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10361 + +lemma sg29250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10451 + +lemma sg29251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1708 sg18263 + +lemma sg29252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1824 sg17118 + +lemma sg29253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2189 sg15568 + +lemma sg29254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2223 sg15543 + +lemma sg29255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2668 sg15026 + +lemma sg29256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15031 + +lemma sg29257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3513 sg14689 + +lemma sg29258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg861 sg21165 + +lemma sg29259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5352 sg12658 + +lemma sg29260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg6025 sg11794 + +lemma sg29261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2190 sg15568 + +lemma sg29262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2180 sg15580 + +lemma sg29263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3877 sg14509 + +lemma sg29264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2222 sg15548 + +lemma sg29265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6925 sg11476 + +lemma sg29266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5975 sg11833 + +lemma sg29267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10338 + +lemma sg29268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8349 sg10705 + +lemma sg29269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3870 sg14513 + +lemma sg29270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3867 sg14518 + +lemma sg29271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6912 sg11478 + +lemma sg29272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6908 sg11480 + +lemma sg29273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10362 + +lemma sg29274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10285 + +lemma sg29275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8726 sg9540 + +lemma sg29276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6967 sg11468 + +lemma sg29277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8118 sg11054 + +lemma sg29278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10452 + +lemma sg29279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10362 + +lemma sg29280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8649 sg9895 + +lemma sg29281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9240 + +lemma sg29282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9231 + +lemma sg29283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9922 + +lemma sg29284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9895 + +lemma sg29285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10781 + +lemma sg29286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10452 + +lemma sg29287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9922 + +lemma sg29288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1852 sg16205 + +lemma sg29289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3883 sg14505 + +lemma sg29290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2237 sg15525 + +lemma sg29291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6913 sg11478 + +lemma sg29292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6909 sg11480 + +lemma sg29293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10339 + +lemma sg29294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8438 sg10261 + +lemma sg29295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8657 sg9765 + +lemma sg29296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3870 sg14514 + +lemma sg29297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6983 sg11467 + +lemma sg29298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8119 sg11054 + +lemma sg29299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10363 + +lemma sg29300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9261 + +lemma sg29301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8726 sg9541 + +lemma sg29302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8120 sg11054 + +lemma sg29303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10453 + +lemma sg29304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10363 + +lemma sg29305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9896 + +lemma sg29306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9541 + +lemma sg29307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9240 + +lemma sg29308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10782 + +lemma sg29309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10453 + +lemma sg29310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10363 + +lemma sg29311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9923 + +lemma sg29312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5569 sg12625 + +lemma sg29313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8121 sg11054 + +lemma sg29314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10364 + +lemma sg29315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9262 + +lemma sg29316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9239 + +lemma sg29317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8736 sg9534 + +lemma sg29318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10454 + +lemma sg29319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10364 + +lemma sg29320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10783 + +lemma sg29321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10454 + +lemma sg29322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9924 + +lemma sg29323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10364 + +lemma sg29324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9924 + +lemma sg29325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10340 + +lemma sg29326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10365 + +lemma sg29327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9925 + +lemma sg29328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10365 + +lemma sg29329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9925 + +lemma sg29330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9898 + +lemma sg29331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10341 + +lemma sg29332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,4,4,4,4,4,4,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9240 + +lemma sg29333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1316 sg20973 + +lemma sg29334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1717 sg18251 + +lemma sg29335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1817 sg17134 + +lemma sg29336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2181 sg15579 + +lemma sg29337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2178 sg15581 + +lemma sg29338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2676 sg15016 + +lemma sg29339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg15029 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes72.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes72.lean index 1b6147149c840387b26c55f8d5a46dcdf099d6de..0c5ff55bea4512156a59941e40d13009c2389b33 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes72.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes72.lean @@ -1,1223 +1,1223 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 72. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg29340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg571 sg21238 - -lemma sg29341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg571 sg21239 - -lemma sg29342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg571 sg21240 - -lemma sg29343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1718 sg18251 - -lemma sg29344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1818 sg17134 - -lemma sg29345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2182 sg15579 - -lemma sg29346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2223 sg15546 - -lemma sg29347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2668 sg15027 - -lemma sg29348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15032 - -lemma sg29349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3513 sg14690 - -lemma sg29350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg862 sg21165 - -lemma sg29351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg862 sg21166 - -lemma sg29352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg862 sg21167 - -lemma sg29353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2183 sg15579 - -lemma sg29354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2180 sg15581 - -lemma sg29355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3868 sg14517 - -lemma sg29356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2228 sg15535 - -lemma sg29357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6930 sg11473 - -lemma sg29358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5958 sg11837 - -lemma sg29359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10342 - -lemma sg29360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8357 sg10661 - -lemma sg29361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3870 sg14515 - -lemma sg29362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3867 sg14519 - -lemma sg29363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6931 sg11473 - -lemma sg29364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6928 sg11475 - -lemma sg29365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10366 - -lemma sg29366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10289 - -lemma sg29367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8651 sg9894 - -lemma sg29368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6914 sg11478 - -lemma sg29369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8122 sg11054 - -lemma sg29370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10455 - -lemma sg29371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10366 - -lemma sg29372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8649 sg9899 - -lemma sg29373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9240 - -lemma sg29374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9231 - -lemma sg29375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9926 - -lemma sg29376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9899 - -lemma sg29377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10784 - -lemma sg29378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10455 - -lemma sg29379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9926 - -lemma sg29380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1819 sg17134 - -lemma sg29381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2184 sg15579 - -lemma sg29382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2225 sg15543 - -lemma sg29383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3869 sg14517 - -lemma sg29384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2867 sg14859 - -lemma sg29385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6933 sg11473 - -lemma sg29386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5959 sg11837 - -lemma sg29387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10338 - -lemma sg29388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8359 sg10661 - -lemma sg29389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2226 sg15543 - -lemma sg29390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3871 sg14513 - -lemma sg29391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3868 sg14518 - -lemma sg29392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6934 sg11473 - -lemma sg29393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6930 sg11474 - -lemma sg29394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10343 - -lemma sg29395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8438 sg10265 - -lemma sg29396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8652 sg9894 - -lemma sg29397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3870 sg14516 - -lemma sg29398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6915 sg11478 - -lemma sg29399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6912 sg11479 - -lemma sg29400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10367 - -lemma sg29401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9264 - -lemma sg29402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8651 sg9895 - -lemma sg29403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8123 sg11054 - -lemma sg29404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10456 - -lemma sg29405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10367 - -lemma sg29406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9900 - -lemma sg29407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9600 - -lemma sg29408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9240 - -lemma sg29409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10785 - -lemma sg29410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10456 - -lemma sg29411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10367 - -lemma sg29412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9927 - -lemma sg29413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3886 sg14505 - -lemma sg29414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3871 sg14514 - -lemma sg29415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6916 sg11478 - -lemma sg29416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8124 sg11054 - -lemma sg29417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10344 - -lemma sg29418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9330 - -lemma sg29419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8729 sg9541 - -lemma sg29420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6986 sg11467 - -lemma sg29421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8125 sg11054 - -lemma sg29422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10368 - -lemma sg29423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9265 - -lemma sg29424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9896 - -lemma sg29425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9541 - -lemma sg29426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10457 - -lemma sg29427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10368 - -lemma sg29428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10786 - -lemma sg29429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10457 - -lemma sg29430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9928 - -lemma sg29431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10368 - -lemma sg29432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9928 - -lemma sg29433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10344 - -lemma sg29434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5995 sg11830 - -lemma sg29435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10458 - -lemma sg29436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9266 - -lemma sg29437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10787 - -lemma sg29438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10458 - -lemma sg29439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10369 - -lemma sg29440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9929 - -lemma sg29441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10369 - -lemma sg29442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9929 - -lemma sg29443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9902 - -lemma sg29444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10345 - -lemma sg29445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9903 - -lemma sg29446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9903 - -lemma sg29447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10346 - -lemma sg29448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10341 - -lemma sg29449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2193 sg15568 - -lemma sg29450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2227 sg15543 - -lemma sg29451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3872 sg14513 - -lemma sg29452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3869 sg14518 - -lemma sg29453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6946 sg11471 - -lemma sg29454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6933 sg11474 - -lemma sg29455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9243 - -lemma sg29456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8476 sg10216 - -lemma sg29457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8732 sg9540 - -lemma sg29458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3901 sg14500 - -lemma sg29459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4570 sg13500 - -lemma sg29460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6972 sg11468 - -lemma sg29461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8126 sg11054 - -lemma sg29462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10347 - -lemma sg29463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9243 - -lemma sg29464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8652 sg9895 - -lemma sg29465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6917 sg11478 - -lemma sg29466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8127 sg11054 - -lemma sg29467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10370 - -lemma sg29468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9268 - -lemma sg29469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9243 - -lemma sg29470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9600 - -lemma sg29471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10459 - -lemma sg29472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10370 - -lemma sg29473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10788 - -lemma sg29474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10459 - -lemma sg29475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9930 - -lemma sg29476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10370 - -lemma sg29477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9930 - -lemma sg29478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10347 - -lemma sg29479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4571 sg13500 - -lemma sg29480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6918 sg11478 - -lemma sg29481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8128 sg11054 - -lemma sg29482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10348 - -lemma sg29483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9244 - -lemma sg29484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9896 - -lemma sg29485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9600 - -lemma sg29486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6947 sg11472 - -lemma sg29487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10460 - -lemma sg29488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9269 - -lemma sg29489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10789 - -lemma sg29490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10460 - -lemma sg29491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10371 - -lemma sg29492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9931 - -lemma sg29493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10371 - -lemma sg29494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9931 - -lemma sg29495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9905 - -lemma sg29496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10348 - -lemma sg29497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10372 - -lemma sg29498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10372 - -lemma sg29499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9932 - -lemma sg29500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10372 - -lemma sg29501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9932 - -lemma sg29502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9906 - -lemma sg29503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9906 - -lemma sg29504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10349 - -lemma sg29505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9245 - -lemma sg29506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9246 - -lemma sg29507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9246 - -lemma sg29508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6919 sg11478 - -lemma sg29509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6948 sg11472 - -lemma sg29510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10461 - -lemma sg29511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9247 - -lemma sg29512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10790 - -lemma sg29513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10461 - -lemma sg29514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10373 - -lemma sg29515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10373 - -lemma sg29516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9933 - -lemma sg29517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10373 - -lemma sg29518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9933 - -lemma sg29519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9907 - -lemma sg29520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9907 - -lemma sg29521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10350 - -lemma sg29522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9247 - -lemma sg29523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10298 - -lemma sg29524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9908 - -lemma sg29525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9908 - -lemma sg29526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10351 - -lemma sg29527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8727 sg9545 - -lemma sg29528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9545 - -lemma sg29529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8658 sg9779 - -lemma sg29530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8384 sg10613 - -lemma sg29531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8531 sg10130 - -lemma sg29532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg8532 sg10130 - -lemma sg29533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg8179 sg10866 - -lemma sg29534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1319 sg20971 - -lemma sg29535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1722 sg18249 - -lemma sg29536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1825 sg17121 - -lemma sg29537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2191 sg15569 - -lemma sg29538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2224 sg15546 - -lemma sg29539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2677 sg15016 - -lemma sg29540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2175 sg15585 - -lemma sg29541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg14688 - -lemma sg29542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg867 sg21152 - -lemma sg29543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg867 sg21153 - -lemma sg29544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg867 sg21154 - -lemma sg29545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1826 sg17121 - -lemma sg29546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2192 sg15569 - -lemma sg29547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2225 sg15546 - -lemma sg29548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3879 sg14510 - -lemma sg29549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2867 sg14860 - -lemma sg29550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6968 sg11469 - -lemma sg29551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5978 sg11834 - -lemma sg29552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10342 - -lemma sg29553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8369 sg10656 - -lemma sg29554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2226 sg15546 - -lemma sg29555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3871 sg14515 - -lemma sg29556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3868 sg14519 - -lemma sg29557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6969 sg11469 - -lemma sg29558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6930 sg11475 - -lemma sg29559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9272 - -lemma sg29560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8480 sg10212 - -lemma sg29561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8729 sg9542 - -lemma sg29562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2669 sg15029 - -lemma sg29563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6937 sg11473 - -lemma sg29564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6931 sg11475 - -lemma sg29565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9242 - -lemma sg29566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9272 - -lemma sg29567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8651 sg9899 - -lemma sg29568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6914 sg11479 - -lemma sg29569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10462 - -lemma sg29570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9233 - -lemma sg29571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9909 - -lemma sg29572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9601 - -lemma sg29573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9234 - -lemma sg29574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10791 - -lemma sg29575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10462 - -lemma sg29576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10708 - -lemma sg29577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9934 - -lemma sg29578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2193 sg15569 - -lemma sg29579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2227 sg15546 - -lemma sg29580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3872 sg14515 - -lemma sg29581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3869 sg14519 - -lemma sg29582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6971 sg11469 - -lemma sg29583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6933 sg11475 - -lemma sg29584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10343 - -lemma sg29585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8444 sg10265 - -lemma sg29586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8732 sg9542 - -lemma sg29587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3873 sg14513 - -lemma sg29588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4570 sg13501 - -lemma sg29589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6938 sg11473 - -lemma sg29590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6934 sg11475 - -lemma sg29591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9273 - -lemma sg29592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9331 - -lemma sg29593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8652 sg9899 - -lemma sg29594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6939 sg11473 - -lemma sg29595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6915 sg11479 - -lemma sg29596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10374 - -lemma sg29597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9273 - -lemma sg29598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9900 - -lemma sg29599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9601 - -lemma sg29600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10463 - -lemma sg29601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10374 - -lemma sg29602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10792 - -lemma sg29603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10463 - -lemma sg29604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9935 - -lemma sg29605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10374 - -lemma sg29606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9935 - -lemma sg29607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8347 sg10707 - -lemma sg29608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4571 sg13501 - -lemma sg29609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6940 sg11473 - -lemma sg29610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6916 sg11479 - -lemma sg29611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10352 - -lemma sg29612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9332 - -lemma sg29613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8807 sg9241 - -lemma sg29614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9601 - -lemma sg29615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5982 sg11834 - -lemma sg29616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10464 - -lemma sg29617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9274 - -lemma sg29618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10793 - -lemma sg29619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10464 - -lemma sg29620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10375 - -lemma sg29621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9936 - -lemma sg29622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10375 - -lemma sg29623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9936 - -lemma sg29624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9911 - -lemma sg29625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10352 - -lemma sg29626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10376 - -lemma sg29627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10376 - -lemma sg29628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9937 - -lemma sg29629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10376 - -lemma sg29630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9937 - -lemma sg29631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9912 - -lemma sg29632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9912 - -lemma sg29633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10353 - -lemma sg29634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10345 - -lemma sg29635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9602 - -lemma sg29636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10346 - -lemma sg29637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2236 sg15527 - -lemma sg29638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3874 sg14513 - -lemma sg29639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4573 sg13500 - -lemma sg29640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6950 sg11471 - -lemma sg29641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5986 sg11832 - -lemma sg29642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10347 - -lemma sg29643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9331 - -lemma sg29644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8732 sg9543 - -lemma sg29645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4574 sg13500 - -lemma sg29646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6941 sg11473 - -lemma sg29647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6938 sg11474 - -lemma sg29648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10354 - -lemma sg29649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9333 - -lemma sg29650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9900 - -lemma sg29651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8733 sg9543 - -lemma sg29652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6917 sg11479 - -lemma sg29653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10465 - -lemma sg29654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9276 - -lemma sg29655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10794 - -lemma sg29656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10465 - -lemma sg29657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10377 - -lemma sg29658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9938 - -lemma sg29659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10377 - -lemma sg29660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9938 - -lemma sg29661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9913 - -lemma sg29662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10354 - -lemma sg29663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6942 sg11473 - -lemma sg29664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6918 sg11479 - -lemma sg29665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10466 - -lemma sg29666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9334 - -lemma sg29667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10795 - -lemma sg29668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10466 - -lemma sg29669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10378 - -lemma sg29670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10378 - -lemma sg29671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9939 - -lemma sg29672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10378 - -lemma sg29673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9939 - -lemma sg29674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9914 - -lemma sg29675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9914 - -lemma sg29676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10355 - -lemma sg29677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10348 - -lemma sg29678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9278 - -lemma sg29679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9915 - -lemma sg29680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9915 - -lemma sg29681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10356 - -lemma sg29682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9603 - -lemma sg29683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10349 - -lemma sg29684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10346 - -lemma sg29685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6919 sg11479 - -lemma sg29686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10379 - -lemma sg29687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10379 - -lemma sg29688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9940 - -lemma sg29689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10379 - -lemma sg29690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9940 - -lemma sg29691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9279 - -lemma sg29692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9916 - -lemma sg29693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9916 - -lemma sg29694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10357 - -lemma sg29695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9604 - -lemma sg29696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10350 - -lemma sg29697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9908 - -lemma sg29698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9605 - -lemma sg29699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10351 - -lemma sg29700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8731 sg9545 - -lemma sg29701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8534 sg10130 - -lemma sg29702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,5,2,1,1,1] := by - exact rowSquare_join (by decide) sg8535 sg10130 - -lemma sg29703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14513 - -lemma sg29704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4575 sg13500 - -lemma sg29705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6953 sg11471 - -lemma sg29706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6012 sg11829 - -lemma sg29707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9256 - -lemma sg29708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9333 - -lemma sg29709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9243 - -lemma sg29710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9537 - -lemma sg29711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6954 sg11471 - -lemma sg29712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6941 sg11474 - -lemma sg29713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10467 - -lemma sg29714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9256 - -lemma sg29715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10796 - -lemma sg29716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10467 - -lemma sg29717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10380 - -lemma sg29718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10380 - -lemma sg29719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9941 - -lemma sg29720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10380 - -lemma sg29721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9941 - -lemma sg29722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9917 - -lemma sg29723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9917 - -lemma sg29724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10358 - -lemma sg29725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9256 - -lemma sg29726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6942 sg11474 - -lemma sg29727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10381 - -lemma sg29728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10381 - -lemma sg29729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9942 - -lemma sg29730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10381 - -lemma sg29731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9942 - -lemma sg29732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9281 - -lemma sg29733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9918 - -lemma sg29734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9918 - -lemma sg29735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10359 - -lemma sg29736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9257 - -lemma sg29737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9257 - -lemma sg29738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9258 - -lemma sg29739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9258 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 72. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg29340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg571 sg21238 + +lemma sg29341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg571 sg21239 + +lemma sg29342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg571 sg21240 + +lemma sg29343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1718 sg18251 + +lemma sg29344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1818 sg17134 + +lemma sg29345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2182 sg15579 + +lemma sg29346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2223 sg15546 + +lemma sg29347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2668 sg15027 + +lemma sg29348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15032 + +lemma sg29349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3513 sg14690 + +lemma sg29350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg862 sg21165 + +lemma sg29351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg862 sg21166 + +lemma sg29352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg862 sg21167 + +lemma sg29353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2183 sg15579 + +lemma sg29354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2180 sg15581 + +lemma sg29355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3868 sg14517 + +lemma sg29356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2228 sg15535 + +lemma sg29357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6930 sg11473 + +lemma sg29358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5958 sg11837 + +lemma sg29359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10342 + +lemma sg29360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8357 sg10661 + +lemma sg29361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3870 sg14515 + +lemma sg29362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3867 sg14519 + +lemma sg29363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6931 sg11473 + +lemma sg29364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6928 sg11475 + +lemma sg29365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10366 + +lemma sg29366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10289 + +lemma sg29367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8651 sg9894 + +lemma sg29368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6914 sg11478 + +lemma sg29369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8122 sg11054 + +lemma sg29370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10455 + +lemma sg29371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10366 + +lemma sg29372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8649 sg9899 + +lemma sg29373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9240 + +lemma sg29374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9231 + +lemma sg29375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9926 + +lemma sg29376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9899 + +lemma sg29377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10784 + +lemma sg29378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10455 + +lemma sg29379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9926 + +lemma sg29380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1819 sg17134 + +lemma sg29381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2184 sg15579 + +lemma sg29382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2225 sg15543 + +lemma sg29383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3869 sg14517 + +lemma sg29384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2867 sg14859 + +lemma sg29385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6933 sg11473 + +lemma sg29386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5959 sg11837 + +lemma sg29387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10338 + +lemma sg29388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8359 sg10661 + +lemma sg29389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2226 sg15543 + +lemma sg29390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3871 sg14513 + +lemma sg29391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3868 sg14518 + +lemma sg29392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6934 sg11473 + +lemma sg29393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6930 sg11474 + +lemma sg29394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10343 + +lemma sg29395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8438 sg10265 + +lemma sg29396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8652 sg9894 + +lemma sg29397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3870 sg14516 + +lemma sg29398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6915 sg11478 + +lemma sg29399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6912 sg11479 + +lemma sg29400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10367 + +lemma sg29401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9264 + +lemma sg29402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8651 sg9895 + +lemma sg29403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8123 sg11054 + +lemma sg29404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10456 + +lemma sg29405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10367 + +lemma sg29406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9900 + +lemma sg29407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9600 + +lemma sg29408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9240 + +lemma sg29409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10785 + +lemma sg29410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10456 + +lemma sg29411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10367 + +lemma sg29412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9927 + +lemma sg29413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3886 sg14505 + +lemma sg29414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3871 sg14514 + +lemma sg29415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6916 sg11478 + +lemma sg29416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8124 sg11054 + +lemma sg29417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10344 + +lemma sg29418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9330 + +lemma sg29419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8729 sg9541 + +lemma sg29420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6986 sg11467 + +lemma sg29421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8125 sg11054 + +lemma sg29422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10368 + +lemma sg29423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9265 + +lemma sg29424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9896 + +lemma sg29425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9541 + +lemma sg29426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10457 + +lemma sg29427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10368 + +lemma sg29428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10786 + +lemma sg29429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10457 + +lemma sg29430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9928 + +lemma sg29431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10368 + +lemma sg29432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9928 + +lemma sg29433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10344 + +lemma sg29434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5995 sg11830 + +lemma sg29435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10458 + +lemma sg29436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9266 + +lemma sg29437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10787 + +lemma sg29438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10458 + +lemma sg29439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10369 + +lemma sg29440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9929 + +lemma sg29441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10369 + +lemma sg29442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9929 + +lemma sg29443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9902 + +lemma sg29444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10345 + +lemma sg29445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9903 + +lemma sg29446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9903 + +lemma sg29447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10346 + +lemma sg29448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10341 + +lemma sg29449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2193 sg15568 + +lemma sg29450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2227 sg15543 + +lemma sg29451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3872 sg14513 + +lemma sg29452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3869 sg14518 + +lemma sg29453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6946 sg11471 + +lemma sg29454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6933 sg11474 + +lemma sg29455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9243 + +lemma sg29456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8476 sg10216 + +lemma sg29457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8732 sg9540 + +lemma sg29458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3901 sg14500 + +lemma sg29459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4570 sg13500 + +lemma sg29460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6972 sg11468 + +lemma sg29461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8126 sg11054 + +lemma sg29462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10347 + +lemma sg29463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9243 + +lemma sg29464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8652 sg9895 + +lemma sg29465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6917 sg11478 + +lemma sg29466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8127 sg11054 + +lemma sg29467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10370 + +lemma sg29468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9268 + +lemma sg29469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9243 + +lemma sg29470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9600 + +lemma sg29471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10459 + +lemma sg29472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10370 + +lemma sg29473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10788 + +lemma sg29474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10459 + +lemma sg29475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9930 + +lemma sg29476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10370 + +lemma sg29477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9930 + +lemma sg29478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10347 + +lemma sg29479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4571 sg13500 + +lemma sg29480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6918 sg11478 + +lemma sg29481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8128 sg11054 + +lemma sg29482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10348 + +lemma sg29483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9244 + +lemma sg29484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9896 + +lemma sg29485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9600 + +lemma sg29486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6947 sg11472 + +lemma sg29487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10460 + +lemma sg29488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9269 + +lemma sg29489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10789 + +lemma sg29490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10460 + +lemma sg29491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10371 + +lemma sg29492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9931 + +lemma sg29493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10371 + +lemma sg29494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9931 + +lemma sg29495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9905 + +lemma sg29496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10348 + +lemma sg29497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10372 + +lemma sg29498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10372 + +lemma sg29499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9932 + +lemma sg29500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10372 + +lemma sg29501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9932 + +lemma sg29502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9906 + +lemma sg29503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9906 + +lemma sg29504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10349 + +lemma sg29505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9245 + +lemma sg29506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9246 + +lemma sg29507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9246 + +lemma sg29508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6919 sg11478 + +lemma sg29509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6948 sg11472 + +lemma sg29510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10461 + +lemma sg29511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9247 + +lemma sg29512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10790 + +lemma sg29513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10461 + +lemma sg29514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10373 + +lemma sg29515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10373 + +lemma sg29516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9933 + +lemma sg29517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10373 + +lemma sg29518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9933 + +lemma sg29519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9907 + +lemma sg29520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9907 + +lemma sg29521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10350 + +lemma sg29522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9247 + +lemma sg29523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10298 + +lemma sg29524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9908 + +lemma sg29525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9908 + +lemma sg29526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10351 + +lemma sg29527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8727 sg9545 + +lemma sg29528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9545 + +lemma sg29529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8658 sg9779 + +lemma sg29530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8384 sg10613 + +lemma sg29531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8531 sg10130 + +lemma sg29532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg8532 sg10130 + +lemma sg29533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,5,5,5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg8179 sg10866 + +lemma sg29534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1319 sg20971 + +lemma sg29535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1722 sg18249 + +lemma sg29536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1825 sg17121 + +lemma sg29537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2191 sg15569 + +lemma sg29538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2224 sg15546 + +lemma sg29539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2677 sg15016 + +lemma sg29540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2175 sg15585 + +lemma sg29541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg14688 + +lemma sg29542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg867 sg21152 + +lemma sg29543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg867 sg21153 + +lemma sg29544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg867 sg21154 + +lemma sg29545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1826 sg17121 + +lemma sg29546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2192 sg15569 + +lemma sg29547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2225 sg15546 + +lemma sg29548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3879 sg14510 + +lemma sg29549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2867 sg14860 + +lemma sg29550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6968 sg11469 + +lemma sg29551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5978 sg11834 + +lemma sg29552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10342 + +lemma sg29553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8369 sg10656 + +lemma sg29554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2226 sg15546 + +lemma sg29555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3871 sg14515 + +lemma sg29556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3868 sg14519 + +lemma sg29557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6969 sg11469 + +lemma sg29558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6930 sg11475 + +lemma sg29559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9272 + +lemma sg29560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8480 sg10212 + +lemma sg29561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8729 sg9542 + +lemma sg29562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2669 sg15029 + +lemma sg29563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6937 sg11473 + +lemma sg29564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6931 sg11475 + +lemma sg29565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9242 + +lemma sg29566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9272 + +lemma sg29567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8651 sg9899 + +lemma sg29568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6914 sg11479 + +lemma sg29569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10462 + +lemma sg29570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9233 + +lemma sg29571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9909 + +lemma sg29572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9601 + +lemma sg29573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9234 + +lemma sg29574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10791 + +lemma sg29575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10462 + +lemma sg29576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10708 + +lemma sg29577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9934 + +lemma sg29578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2193 sg15569 + +lemma sg29579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2227 sg15546 + +lemma sg29580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3872 sg14515 + +lemma sg29581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3869 sg14519 + +lemma sg29582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6971 sg11469 + +lemma sg29583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6933 sg11475 + +lemma sg29584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10343 + +lemma sg29585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8444 sg10265 + +lemma sg29586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8732 sg9542 + +lemma sg29587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3873 sg14513 + +lemma sg29588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4570 sg13501 + +lemma sg29589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6938 sg11473 + +lemma sg29590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6934 sg11475 + +lemma sg29591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9273 + +lemma sg29592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9331 + +lemma sg29593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8652 sg9899 + +lemma sg29594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6939 sg11473 + +lemma sg29595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6915 sg11479 + +lemma sg29596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10374 + +lemma sg29597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9273 + +lemma sg29598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9900 + +lemma sg29599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9601 + +lemma sg29600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10463 + +lemma sg29601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10374 + +lemma sg29602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10792 + +lemma sg29603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10463 + +lemma sg29604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9935 + +lemma sg29605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10374 + +lemma sg29606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9935 + +lemma sg29607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8347 sg10707 + +lemma sg29608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4571 sg13501 + +lemma sg29609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6940 sg11473 + +lemma sg29610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6916 sg11479 + +lemma sg29611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10352 + +lemma sg29612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9332 + +lemma sg29613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8807 sg9241 + +lemma sg29614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9601 + +lemma sg29615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5982 sg11834 + +lemma sg29616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10464 + +lemma sg29617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9274 + +lemma sg29618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10793 + +lemma sg29619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10464 + +lemma sg29620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10375 + +lemma sg29621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9936 + +lemma sg29622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10375 + +lemma sg29623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9936 + +lemma sg29624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9911 + +lemma sg29625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10352 + +lemma sg29626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10376 + +lemma sg29627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10376 + +lemma sg29628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9937 + +lemma sg29629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10376 + +lemma sg29630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9937 + +lemma sg29631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9912 + +lemma sg29632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9912 + +lemma sg29633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10353 + +lemma sg29634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10345 + +lemma sg29635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9602 + +lemma sg29636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10346 + +lemma sg29637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2236 sg15527 + +lemma sg29638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3874 sg14513 + +lemma sg29639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4573 sg13500 + +lemma sg29640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6950 sg11471 + +lemma sg29641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5986 sg11832 + +lemma sg29642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10347 + +lemma sg29643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9331 + +lemma sg29644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8732 sg9543 + +lemma sg29645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4574 sg13500 + +lemma sg29646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6941 sg11473 + +lemma sg29647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6938 sg11474 + +lemma sg29648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10354 + +lemma sg29649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9333 + +lemma sg29650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9900 + +lemma sg29651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8733 sg9543 + +lemma sg29652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6917 sg11479 + +lemma sg29653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10465 + +lemma sg29654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9276 + +lemma sg29655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10794 + +lemma sg29656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10465 + +lemma sg29657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10377 + +lemma sg29658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9938 + +lemma sg29659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10377 + +lemma sg29660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9938 + +lemma sg29661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9913 + +lemma sg29662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10354 + +lemma sg29663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6942 sg11473 + +lemma sg29664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6918 sg11479 + +lemma sg29665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10466 + +lemma sg29666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9334 + +lemma sg29667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10795 + +lemma sg29668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10466 + +lemma sg29669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10378 + +lemma sg29670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10378 + +lemma sg29671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9939 + +lemma sg29672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10378 + +lemma sg29673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9939 + +lemma sg29674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9914 + +lemma sg29675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9914 + +lemma sg29676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10355 + +lemma sg29677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10348 + +lemma sg29678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9278 + +lemma sg29679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9915 + +lemma sg29680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9915 + +lemma sg29681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10356 + +lemma sg29682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9603 + +lemma sg29683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10349 + +lemma sg29684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10346 + +lemma sg29685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6919 sg11479 + +lemma sg29686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10379 + +lemma sg29687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10379 + +lemma sg29688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9940 + +lemma sg29689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10379 + +lemma sg29690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9940 + +lemma sg29691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9279 + +lemma sg29692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9916 + +lemma sg29693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9916 + +lemma sg29694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10357 + +lemma sg29695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9604 + +lemma sg29696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10350 + +lemma sg29697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9908 + +lemma sg29698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9605 + +lemma sg29699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10351 + +lemma sg29700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8731 sg9545 + +lemma sg29701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8534 sg10130 + +lemma sg29702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,5,5,5,2,1,1,1] := by + exact rowSquare_join (by decide) sg8535 sg10130 + +lemma sg29703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14513 + +lemma sg29704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4575 sg13500 + +lemma sg29705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6953 sg11471 + +lemma sg29706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6012 sg11829 + +lemma sg29707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9256 + +lemma sg29708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9333 + +lemma sg29709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9243 + +lemma sg29710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9537 + +lemma sg29711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6954 sg11471 + +lemma sg29712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6941 sg11474 + +lemma sg29713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10467 + +lemma sg29714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9256 + +lemma sg29715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10796 + +lemma sg29716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10467 + +lemma sg29717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10380 + +lemma sg29718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10380 + +lemma sg29719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9941 + +lemma sg29720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10380 + +lemma sg29721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9941 + +lemma sg29722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9917 + +lemma sg29723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9917 + +lemma sg29724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10358 + +lemma sg29725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9256 + +lemma sg29726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6942 sg11474 + +lemma sg29727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10381 + +lemma sg29728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10381 + +lemma sg29729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9942 + +lemma sg29730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10381 + +lemma sg29731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9942 + +lemma sg29732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9281 + +lemma sg29733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9918 + +lemma sg29734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9918 + +lemma sg29735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10359 + +lemma sg29736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9257 + +lemma sg29737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9257 + +lemma sg29738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9258 + +lemma sg29739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9258 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes73.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes73.lean index cb9079c83b739af17c5c7d66e7e4c96c7c6eba06..0f517c952dd1f4a799d4c934e35f45f8311e03f4 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes73.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes73.lean @@ -1,1224 +1,1224 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 73. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg29740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9258 - -lemma sg29741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10349 - -lemma sg29742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10360 - -lemma sg29743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9282 - -lemma sg29744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9919 - -lemma sg29745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9919 - -lemma sg29746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10360 - -lemma sg29747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9259 - -lemma sg29748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9259 - -lemma sg29749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9259 - -lemma sg29750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10350 - -lemma sg29751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9605 - -lemma sg29752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10351 - -lemma sg29753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9260 - -lemma sg29754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9260 - -lemma sg29755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9260 - -lemma sg29756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,6,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9260 - -lemma sg29757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8875 sg9039 - -lemma sg29758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1723 sg18249 - -lemma sg29759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1835 sg17109 - -lemma sg29760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2203 sg15563 - -lemma sg29761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2234 sg15529 - -lemma sg29762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2678 sg15016 - -lemma sg29763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2868 sg14860 - -lemma sg29764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4769 sg12929 - -lemma sg29765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3517 sg14683 - -lemma sg29766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5660 sg12603 - -lemma sg29767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg4769 sg12930 - -lemma sg29768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2204 sg15563 - -lemma sg29769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2235 sg15529 - -lemma sg29770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2679 sg15016 - -lemma sg29771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2869 sg14860 - -lemma sg29772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5250 sg12694 - -lemma sg29773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5591 sg12611 - -lemma sg29774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9248 - -lemma sg29775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5626 sg12604 - -lemma sg29776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8755 sg9480 - -lemma sg29777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3873 sg14515 - -lemma sg29778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4572 sg13501 - -lemma sg29779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6974 sg11469 - -lemma sg29780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6576 sg11540 - -lemma sg29781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9283 - -lemma sg29782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9335 - -lemma sg29783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8729 sg9546 - -lemma sg29784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6975 sg11469 - -lemma sg29785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6937 sg11475 - -lemma sg29786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9250 - -lemma sg29787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9283 - -lemma sg29788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9909 - -lemma sg29789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9546 - -lemma sg29790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9251 - -lemma sg29791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8877 sg9027 - -lemma sg29792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10797 - -lemma sg29793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8720 sg9606 - -lemma sg29794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9943 - -lemma sg29795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10157 - -lemma sg29796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9943 - -lemma sg29797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8798 sg9283 - -lemma sg29798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2236 sg15529 - -lemma sg29799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3874 sg14515 - -lemma sg29800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4573 sg13501 - -lemma sg29801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6976 sg11469 - -lemma sg29802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6578 sg11540 - -lemma sg29803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8827 sg9219 - -lemma sg29804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9335 - -lemma sg29805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8732 sg9546 - -lemma sg29806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4574 sg13501 - -lemma sg29807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6977 sg11469 - -lemma sg29808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6938 sg11475 - -lemma sg29809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9284 - -lemma sg29810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9336 - -lemma sg29811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9909 - -lemma sg29812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8733 sg9546 - -lemma sg29813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6939 sg11475 - -lemma sg29814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10353 - -lemma sg29815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9284 - -lemma sg29816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10798 - -lemma sg29817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8721 sg9606 - -lemma sg29818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9251 - -lemma sg29819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9944 - -lemma sg29820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10711 - -lemma sg29821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9944 - -lemma sg29822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9284 - -lemma sg29823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9284 - -lemma sg29824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6978 sg11469 - -lemma sg29825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6940 sg11475 - -lemma sg29826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9285 - -lemma sg29827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9337 - -lemma sg29828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10799 - -lemma sg29829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8722 sg9606 - -lemma sg29830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9286 - -lemma sg29831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9285 - -lemma sg29832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9945 - -lemma sg29833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10712 - -lemma sg29834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9945 - -lemma sg29835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9285 - -lemma sg29836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9285 - -lemma sg29837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9285 - -lemma sg29838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10352 - -lemma sg29839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9286 - -lemma sg29840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9286 - -lemma sg29841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9286 - -lemma sg29842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9286 - -lemma sg29843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9607 - -lemma sg29844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10353 - -lemma sg29845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9251 - -lemma sg29846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14515 - -lemma sg29847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4575 sg13501 - -lemma sg29848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6979 sg11469 - -lemma sg29849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6582 sg11540 - -lemma sg29850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10354 - -lemma sg29851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9336 - -lemma sg29852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9248 - -lemma sg29853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8756 sg9481 - -lemma sg29854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6980 sg11469 - -lemma sg29855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6941 sg11475 - -lemma sg29856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10468 - -lemma sg29857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9338 - -lemma sg29858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10800 - -lemma sg29859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10468 - -lemma sg29860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10356 - -lemma sg29861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9287 - -lemma sg29862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9946 - -lemma sg29863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10713 - -lemma sg29864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9946 - -lemma sg29865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9287 - -lemma sg29866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9287 - -lemma sg29867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9287 - -lemma sg29868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10354 - -lemma sg29869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6942 sg11475 - -lemma sg29870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10382 - -lemma sg29871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10382 - -lemma sg29872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9947 - -lemma sg29873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10382 - -lemma sg29874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9947 - -lemma sg29875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9288 - -lemma sg29876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9288 - -lemma sg29877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9288 - -lemma sg29878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9288 - -lemma sg29879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9608 - -lemma sg29880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10355 - -lemma sg29881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9915 - -lemma sg29882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9609 - -lemma sg29883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10356 - -lemma sg29884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg8427 sg10353 - -lemma sg29885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9289 - -lemma sg29886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9289 - -lemma sg29887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9289 - -lemma sg29888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9289 - -lemma sg29889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9289 - -lemma sg29890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9916 - -lemma sg29891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9610 - -lemma sg29892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10357 - -lemma sg29893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8809 sg9255 - -lemma sg29894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8730 sg9551 - -lemma sg29895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14516 - -lemma sg29896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5565 sg12626 - -lemma sg29897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5992 sg11832 - -lemma sg29898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10469 - -lemma sg29899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9338 - -lemma sg29900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10801 - -lemma sg29901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10469 - -lemma sg29902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5993 sg11832 - -lemma sg29903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10383 - -lemma sg29904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10383 - -lemma sg29905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9948 - -lemma sg29906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10383 - -lemma sg29907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9948 - -lemma sg29908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9290 - -lemma sg29909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9290 - -lemma sg29910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9290 - -lemma sg29911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9290 - -lemma sg29912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9611 - -lemma sg29913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10358 - -lemma sg29914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9291 - -lemma sg29915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9291 - -lemma sg29916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9291 - -lemma sg29917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9291 - -lemma sg29918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9291 - -lemma sg29919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9918 - -lemma sg29920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9612 - -lemma sg29921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10359 - -lemma sg29922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9609 - -lemma sg29923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9342 - -lemma sg29924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9919 - -lemma sg29925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9613 - -lemma sg29926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,5,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10360 - -lemma sg29927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9610 - -lemma sg29928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8807 sg9260 - -lemma sg29929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8808 sg9260 - -lemma sg29930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5582 sg12618 - -lemma sg29931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6013 sg11829 - -lemma sg29932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10384 - -lemma sg29933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10384 - -lemma sg29934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9949 - -lemma sg29935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10384 - -lemma sg29936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9949 - -lemma sg29937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9292 - -lemma sg29938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9292 - -lemma sg29939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9292 - -lemma sg29940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9292 - -lemma sg29941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9292 - -lemma sg29942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8828 sg9227 - -lemma sg29943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8872 sg9076 - -lemma sg29944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8829 sg9227 - -lemma sg29945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8871 sg9077 - -lemma sg29946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8828 sg9228 - -lemma sg29947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8872 sg9077 - -lemma sg29948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8829 sg9228 - -lemma sg29949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9612 - -lemma sg29950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9919 - -lemma sg29951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9613 - -lemma sg29952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9613 - -lemma sg29953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1313 sg20975 - -lemma sg29954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1714 sg18255 - -lemma sg29955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg17136 - -lemma sg29956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21018 - -lemma sg29957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21032 - -lemma sg29958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg21307 - -lemma sg29959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg21308 - -lemma sg29960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg21309 - -lemma sg29961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg342 sg21310 - -lemma sg29962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1314 sg20975 - -lemma sg29963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1715 sg18255 - -lemma sg29964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1815 sg17136 - -lemma sg29965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2178 sg15583 - -lemma sg29966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21019 - -lemma sg29967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg15030 - -lemma sg29968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg559 sg21257 - -lemma sg29969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg559 sg21258 - -lemma sg29970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg559 sg21259 - -lemma sg29971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg559 sg21260 - -lemma sg29972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1315 sg20975 - -lemma sg29973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1716 sg18255 - -lemma sg29974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1816 sg17136 - -lemma sg29975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2179 sg15583 - -lemma sg29976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2222 sg15549 - -lemma sg29977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15033 - -lemma sg29978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2665 sg15044 - -lemma sg29979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg573 sg21224 - -lemma sg29980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg573 sg21225 - -lemma sg29981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg573 sg21226 - -lemma sg29982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1461 sg20942 - -lemma sg29983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2180 sg15583 - -lemma sg29984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1823 sg17123 - -lemma sg29985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2230 sg15532 - -lemma sg29986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1289 sg21020 - -lemma sg29987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21033 - -lemma sg29988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg865 sg21156 - -lemma sg29989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg865 sg21157 - -lemma sg29990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg865 sg21158 - -lemma sg29991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1854 sg16203 - -lemma sg29992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3867 sg14520 - -lemma sg29993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2230 sg15533 - -lemma sg29994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6928 sg11476 - -lemma sg29995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5957 sg11838 - -lemma sg29996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10385 - -lemma sg29997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8355 sg10682 - -lemma sg29998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1295 sg20997 - -lemma sg29999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6929 sg11476 - -lemma sg30000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5527 sg12634 - -lemma sg30001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10470 - -lemma sg30002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10385 - -lemma sg30003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8649 sg9920 - -lemma sg30004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6910 sg11480 - -lemma sg30005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8836 sg9181 - -lemma sg30006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9173 - -lemma sg30007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8647 sg9950 - -lemma sg30008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9174 - -lemma sg30009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10802 - -lemma sg30010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8418 sg10385 - -lemma sg30011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8415 sg10470 - -lemma sg30012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1316 sg20975 - -lemma sg30013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1717 sg18255 - -lemma sg30014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1817 sg17136 - -lemma sg30015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2181 sg15583 - -lemma sg30016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2178 sg15584 - -lemma sg30017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2676 sg15018 - -lemma sg30018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg15032 - -lemma sg30019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg574 sg21224 - -lemma sg30020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg574 sg21225 - -lemma sg30021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg574 sg21226 - -lemma sg30022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1718 sg18255 - -lemma sg30023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1818 sg17136 - -lemma sg30024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2182 sg15583 - -lemma sg30025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2223 sg15547 - -lemma sg30026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2668 sg15030 - -lemma sg30027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2666 sg15034 - -lemma sg30028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3513 sg14691 - -lemma sg30029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg866 sg21156 - -lemma sg30030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg866 sg21157 - -lemma sg30031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg866 sg21158 - -lemma sg30032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2183 sg15583 - -lemma sg30033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2180 sg15584 - -lemma sg30034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3868 sg14520 - -lemma sg30035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2230 sg15535 - -lemma sg30036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6930 sg11476 - -lemma sg30037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5958 sg11838 - -lemma sg30038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10361 - -lemma sg30039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8357 sg10682 - -lemma sg30040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3870 sg14517 - -lemma sg30041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2231 sg15533 - -lemma sg30042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6931 sg11476 - -lemma sg30043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5528 sg12634 - -lemma sg30044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10386 - -lemma sg30045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10308 - -lemma sg30046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8651 sg9920 - -lemma sg30047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6932 sg11476 - -lemma sg30048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6911 sg11480 - -lemma sg30049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10471 - -lemma sg30050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10386 - -lemma sg30051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8649 sg9921 - -lemma sg30052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8453 sg10264 - -lemma sg30053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8837 sg9181 - -lemma sg30054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9951 - -lemma sg30055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9921 - -lemma sg30056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10803 - -lemma sg30057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10471 - -lemma sg30058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9951 - -lemma sg30059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1819 sg17136 - -lemma sg30060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2184 sg15583 - -lemma sg30061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2232 sg15531 - -lemma sg30062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3869 sg14520 - -lemma sg30063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2867 sg14861 - -lemma sg30064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6933 sg11476 - -lemma sg30065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5959 sg11838 - -lemma sg30066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8437 sg10285 - -lemma sg30067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8359 sg10682 - -lemma sg30068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2233 sg15531 - -lemma sg30069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3883 sg14509 - -lemma sg30070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2223 sg15548 - -lemma sg30071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6934 sg11476 - -lemma sg30072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5529 sg12634 - -lemma sg30073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10362 - -lemma sg30074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8438 sg10285 - -lemma sg30075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8652 sg9920 - -lemma sg30076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3870 sg14518 - -lemma sg30077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6935 sg11476 - -lemma sg30078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6912 sg11480 - -lemma sg30079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10387 - -lemma sg30080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9293 - -lemma sg30081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8726 sg9557 - -lemma sg30082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6569 sg11542 - -lemma sg30083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10472 - -lemma sg30084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10387 - -lemma sg30085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9922 - -lemma sg30086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8727 sg9557 - -lemma sg30087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9240 - -lemma sg30088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10804 - -lemma sg30089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10472 - -lemma sg30090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10387 - -lemma sg30091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9952 - -lemma sg30092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3164 sg14803 - -lemma sg30093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3770 sg14539 - -lemma sg30094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6936 sg11476 - -lemma sg30095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6913 sg11480 - -lemma sg30096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10363 - -lemma sg30097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9261 - -lemma sg30098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8657 sg9780 - -lemma sg30099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6995 sg11467 - -lemma sg30100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5960 sg11838 - -lemma sg30101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10388 - -lemma sg30102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9294 - -lemma sg30103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9261 - -lemma sg30104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8736 sg9541 - -lemma sg30105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10473 - -lemma sg30106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10388 - -lemma sg30107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10805 - -lemma sg30108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10473 - -lemma sg30109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9953 - -lemma sg30110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10388 - -lemma sg30111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9953 - -lemma sg30112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10363 - -lemma sg30113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6014 sg11827 - -lemma sg30114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10474 - -lemma sg30115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9295 - -lemma sg30116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10806 - -lemma sg30117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10474 - -lemma sg30118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10389 - -lemma sg30119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9954 - -lemma sg30120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10389 - -lemma sg30121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9954 - -lemma sg30122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9924 - -lemma sg30123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10364 - -lemma sg30124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9925 - -lemma sg30125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9925 - -lemma sg30126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,4,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10365 - -lemma sg30127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,4,3,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9263 - -lemma sg30128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1319 sg20973 - -lemma sg30129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1722 sg18251 - -lemma sg30130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1825 sg17122 - -lemma sg30131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2191 sg15571 - -lemma sg30132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2224 sg15547 - -lemma sg30133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2677 sg15018 - -lemma sg30134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2676 sg15020 - -lemma sg30135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg14690 - -lemma sg30136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg867 sg21156 - -lemma sg30137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg867 sg21157 - -lemma sg30138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg867 sg21158 - -lemma sg30139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1826 sg17122 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 73. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg29740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9258 + +lemma sg29741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10349 + +lemma sg29742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10360 + +lemma sg29743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9282 + +lemma sg29744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9919 + +lemma sg29745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9919 + +lemma sg29746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10360 + +lemma sg29747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9259 + +lemma sg29748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9259 + +lemma sg29749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9259 + +lemma sg29750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10350 + +lemma sg29751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9605 + +lemma sg29752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,5,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10351 + +lemma sg29753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9260 + +lemma sg29754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9260 + +lemma sg29755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9260 + +lemma sg29756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,6,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9260 + +lemma sg29757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,6,6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8875 sg9039 + +lemma sg29758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1723 sg18249 + +lemma sg29759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1835 sg17109 + +lemma sg29760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2203 sg15563 + +lemma sg29761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2234 sg15529 + +lemma sg29762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2678 sg15016 + +lemma sg29763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2868 sg14860 + +lemma sg29764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4769 sg12929 + +lemma sg29765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3517 sg14683 + +lemma sg29766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5660 sg12603 + +lemma sg29767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg4769 sg12930 + +lemma sg29768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2204 sg15563 + +lemma sg29769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2235 sg15529 + +lemma sg29770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2679 sg15016 + +lemma sg29771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2869 sg14860 + +lemma sg29772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5250 sg12694 + +lemma sg29773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5591 sg12611 + +lemma sg29774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9248 + +lemma sg29775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5626 sg12604 + +lemma sg29776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8755 sg9480 + +lemma sg29777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3873 sg14515 + +lemma sg29778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4572 sg13501 + +lemma sg29779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6974 sg11469 + +lemma sg29780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6576 sg11540 + +lemma sg29781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9283 + +lemma sg29782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9335 + +lemma sg29783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8729 sg9546 + +lemma sg29784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6975 sg11469 + +lemma sg29785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6937 sg11475 + +lemma sg29786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9250 + +lemma sg29787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9283 + +lemma sg29788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9909 + +lemma sg29789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9546 + +lemma sg29790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9251 + +lemma sg29791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8877 sg9027 + +lemma sg29792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10797 + +lemma sg29793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8720 sg9606 + +lemma sg29794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9943 + +lemma sg29795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10157 + +lemma sg29796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9943 + +lemma sg29797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8798 sg9283 + +lemma sg29798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2236 sg15529 + +lemma sg29799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3874 sg14515 + +lemma sg29800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4573 sg13501 + +lemma sg29801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6976 sg11469 + +lemma sg29802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6578 sg11540 + +lemma sg29803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8827 sg9219 + +lemma sg29804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9335 + +lemma sg29805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8732 sg9546 + +lemma sg29806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4574 sg13501 + +lemma sg29807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6977 sg11469 + +lemma sg29808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6938 sg11475 + +lemma sg29809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9284 + +lemma sg29810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9336 + +lemma sg29811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9909 + +lemma sg29812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8733 sg9546 + +lemma sg29813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6939 sg11475 + +lemma sg29814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10353 + +lemma sg29815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9284 + +lemma sg29816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10798 + +lemma sg29817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8721 sg9606 + +lemma sg29818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9251 + +lemma sg29819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9944 + +lemma sg29820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10711 + +lemma sg29821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9944 + +lemma sg29822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9284 + +lemma sg29823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9284 + +lemma sg29824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6978 sg11469 + +lemma sg29825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6940 sg11475 + +lemma sg29826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9285 + +lemma sg29827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9337 + +lemma sg29828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10799 + +lemma sg29829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8722 sg9606 + +lemma sg29830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9286 + +lemma sg29831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9285 + +lemma sg29832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9945 + +lemma sg29833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10712 + +lemma sg29834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9945 + +lemma sg29835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9285 + +lemma sg29836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9285 + +lemma sg29837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9285 + +lemma sg29838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10352 + +lemma sg29839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9286 + +lemma sg29840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9286 + +lemma sg29841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9286 + +lemma sg29842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9286 + +lemma sg29843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9607 + +lemma sg29844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10353 + +lemma sg29845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,4,4,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9251 + +lemma sg29846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14515 + +lemma sg29847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4575 sg13501 + +lemma sg29848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6979 sg11469 + +lemma sg29849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6582 sg11540 + +lemma sg29850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10354 + +lemma sg29851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9336 + +lemma sg29852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9248 + +lemma sg29853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8756 sg9481 + +lemma sg29854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6980 sg11469 + +lemma sg29855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6941 sg11475 + +lemma sg29856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10468 + +lemma sg29857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9338 + +lemma sg29858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10800 + +lemma sg29859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10468 + +lemma sg29860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10356 + +lemma sg29861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9287 + +lemma sg29862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9946 + +lemma sg29863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10713 + +lemma sg29864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9946 + +lemma sg29865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9287 + +lemma sg29866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9287 + +lemma sg29867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9287 + +lemma sg29868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10354 + +lemma sg29869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6942 sg11475 + +lemma sg29870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10382 + +lemma sg29871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10382 + +lemma sg29872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9947 + +lemma sg29873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10382 + +lemma sg29874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9947 + +lemma sg29875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9288 + +lemma sg29876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9288 + +lemma sg29877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9288 + +lemma sg29878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9288 + +lemma sg29879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9608 + +lemma sg29880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10355 + +lemma sg29881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9915 + +lemma sg29882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9609 + +lemma sg29883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10356 + +lemma sg29884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg8427 sg10353 + +lemma sg29885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9289 + +lemma sg29886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9289 + +lemma sg29887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9289 + +lemma sg29888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9289 + +lemma sg29889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9289 + +lemma sg29890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9916 + +lemma sg29891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9610 + +lemma sg29892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10357 + +lemma sg29893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8809 sg9255 + +lemma sg29894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8730 sg9551 + +lemma sg29895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14516 + +lemma sg29896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5565 sg12626 + +lemma sg29897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5992 sg11832 + +lemma sg29898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10469 + +lemma sg29899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9338 + +lemma sg29900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10801 + +lemma sg29901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10469 + +lemma sg29902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5993 sg11832 + +lemma sg29903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10383 + +lemma sg29904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10383 + +lemma sg29905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9948 + +lemma sg29906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10383 + +lemma sg29907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9948 + +lemma sg29908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9290 + +lemma sg29909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9290 + +lemma sg29910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9290 + +lemma sg29911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9290 + +lemma sg29912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9611 + +lemma sg29913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10358 + +lemma sg29914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9291 + +lemma sg29915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9291 + +lemma sg29916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9291 + +lemma sg29917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9291 + +lemma sg29918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9291 + +lemma sg29919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9918 + +lemma sg29920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9612 + +lemma sg29921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10359 + +lemma sg29922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9609 + +lemma sg29923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9342 + +lemma sg29924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9919 + +lemma sg29925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9613 + +lemma sg29926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,5,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10360 + +lemma sg29927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9610 + +lemma sg29928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8807 sg9260 + +lemma sg29929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,6,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8808 sg9260 + +lemma sg29930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5582 sg12618 + +lemma sg29931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6013 sg11829 + +lemma sg29932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10384 + +lemma sg29933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10384 + +lemma sg29934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9949 + +lemma sg29935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10384 + +lemma sg29936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9949 + +lemma sg29937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9292 + +lemma sg29938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9292 + +lemma sg29939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9292 + +lemma sg29940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9292 + +lemma sg29941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9292 + +lemma sg29942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8828 sg9227 + +lemma sg29943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8872 sg9076 + +lemma sg29944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8829 sg9227 + +lemma sg29945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8871 sg9077 + +lemma sg29946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8828 sg9228 + +lemma sg29947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8872 sg9077 + +lemma sg29948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8829 sg9228 + +lemma sg29949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9612 + +lemma sg29950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9919 + +lemma sg29951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9613 + +lemma sg29952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,7,7,7,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9613 + +lemma sg29953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1313 sg20975 + +lemma sg29954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1714 sg18255 + +lemma sg29955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg17136 + +lemma sg29956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21018 + +lemma sg29957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21032 + +lemma sg29958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg21307 + +lemma sg29959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg21308 + +lemma sg29960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg21309 + +lemma sg29961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,2,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg342 sg21310 + +lemma sg29962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1314 sg20975 + +lemma sg29963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1715 sg18255 + +lemma sg29964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1815 sg17136 + +lemma sg29965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2178 sg15583 + +lemma sg29966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21019 + +lemma sg29967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg15030 + +lemma sg29968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg559 sg21257 + +lemma sg29969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg559 sg21258 + +lemma sg29970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg559 sg21259 + +lemma sg29971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg559 sg21260 + +lemma sg29972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1315 sg20975 + +lemma sg29973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1716 sg18255 + +lemma sg29974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1816 sg17136 + +lemma sg29975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2179 sg15583 + +lemma sg29976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2222 sg15549 + +lemma sg29977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15033 + +lemma sg29978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2665 sg15044 + +lemma sg29979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg573 sg21224 + +lemma sg29980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg573 sg21225 + +lemma sg29981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg573 sg21226 + +lemma sg29982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1461 sg20942 + +lemma sg29983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2180 sg15583 + +lemma sg29984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1823 sg17123 + +lemma sg29985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2230 sg15532 + +lemma sg29986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1289 sg21020 + +lemma sg29987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21033 + +lemma sg29988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg865 sg21156 + +lemma sg29989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg865 sg21157 + +lemma sg29990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg865 sg21158 + +lemma sg29991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1854 sg16203 + +lemma sg29992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3867 sg14520 + +lemma sg29993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2230 sg15533 + +lemma sg29994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6928 sg11476 + +lemma sg29995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5957 sg11838 + +lemma sg29996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10385 + +lemma sg29997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8355 sg10682 + +lemma sg29998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1295 sg20997 + +lemma sg29999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6929 sg11476 + +lemma sg30000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5527 sg12634 + +lemma sg30001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10470 + +lemma sg30002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10385 + +lemma sg30003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8649 sg9920 + +lemma sg30004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6910 sg11480 + +lemma sg30005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8836 sg9181 + +lemma sg30006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9173 + +lemma sg30007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8647 sg9950 + +lemma sg30008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9174 + +lemma sg30009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10802 + +lemma sg30010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8418 sg10385 + +lemma sg30011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,3,3,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8415 sg10470 + +lemma sg30012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1316 sg20975 + +lemma sg30013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1717 sg18255 + +lemma sg30014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1817 sg17136 + +lemma sg30015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2181 sg15583 + +lemma sg30016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2178 sg15584 + +lemma sg30017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2676 sg15018 + +lemma sg30018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg15032 + +lemma sg30019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg574 sg21224 + +lemma sg30020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg574 sg21225 + +lemma sg30021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg574 sg21226 + +lemma sg30022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1718 sg18255 + +lemma sg30023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1818 sg17136 + +lemma sg30024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2182 sg15583 + +lemma sg30025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2223 sg15547 + +lemma sg30026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2668 sg15030 + +lemma sg30027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2666 sg15034 + +lemma sg30028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3513 sg14691 + +lemma sg30029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg866 sg21156 + +lemma sg30030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg866 sg21157 + +lemma sg30031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg866 sg21158 + +lemma sg30032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2183 sg15583 + +lemma sg30033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2180 sg15584 + +lemma sg30034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3868 sg14520 + +lemma sg30035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2230 sg15535 + +lemma sg30036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6930 sg11476 + +lemma sg30037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5958 sg11838 + +lemma sg30038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10361 + +lemma sg30039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8357 sg10682 + +lemma sg30040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3870 sg14517 + +lemma sg30041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2231 sg15533 + +lemma sg30042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6931 sg11476 + +lemma sg30043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5528 sg12634 + +lemma sg30044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10386 + +lemma sg30045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10308 + +lemma sg30046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8651 sg9920 + +lemma sg30047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6932 sg11476 + +lemma sg30048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6911 sg11480 + +lemma sg30049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10471 + +lemma sg30050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10386 + +lemma sg30051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8649 sg9921 + +lemma sg30052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8453 sg10264 + +lemma sg30053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8837 sg9181 + +lemma sg30054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9951 + +lemma sg30055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9921 + +lemma sg30056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10803 + +lemma sg30057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10471 + +lemma sg30058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9951 + +lemma sg30059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1819 sg17136 + +lemma sg30060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2184 sg15583 + +lemma sg30061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2232 sg15531 + +lemma sg30062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3869 sg14520 + +lemma sg30063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2867 sg14861 + +lemma sg30064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6933 sg11476 + +lemma sg30065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5959 sg11838 + +lemma sg30066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8437 sg10285 + +lemma sg30067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8359 sg10682 + +lemma sg30068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2233 sg15531 + +lemma sg30069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3883 sg14509 + +lemma sg30070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2223 sg15548 + +lemma sg30071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6934 sg11476 + +lemma sg30072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5529 sg12634 + +lemma sg30073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10362 + +lemma sg30074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8438 sg10285 + +lemma sg30075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8652 sg9920 + +lemma sg30076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3870 sg14518 + +lemma sg30077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6935 sg11476 + +lemma sg30078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6912 sg11480 + +lemma sg30079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10387 + +lemma sg30080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9293 + +lemma sg30081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8726 sg9557 + +lemma sg30082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6569 sg11542 + +lemma sg30083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10472 + +lemma sg30084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10387 + +lemma sg30085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9922 + +lemma sg30086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8727 sg9557 + +lemma sg30087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9240 + +lemma sg30088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10804 + +lemma sg30089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10472 + +lemma sg30090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10387 + +lemma sg30091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9952 + +lemma sg30092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3164 sg14803 + +lemma sg30093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3770 sg14539 + +lemma sg30094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6936 sg11476 + +lemma sg30095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6913 sg11480 + +lemma sg30096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10363 + +lemma sg30097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9261 + +lemma sg30098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8657 sg9780 + +lemma sg30099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6995 sg11467 + +lemma sg30100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5960 sg11838 + +lemma sg30101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10388 + +lemma sg30102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9294 + +lemma sg30103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9261 + +lemma sg30104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8736 sg9541 + +lemma sg30105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10473 + +lemma sg30106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10388 + +lemma sg30107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10805 + +lemma sg30108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10473 + +lemma sg30109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9953 + +lemma sg30110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10388 + +lemma sg30111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9953 + +lemma sg30112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10363 + +lemma sg30113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6014 sg11827 + +lemma sg30114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10474 + +lemma sg30115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9295 + +lemma sg30116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10806 + +lemma sg30117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10474 + +lemma sg30118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10389 + +lemma sg30119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9954 + +lemma sg30120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10389 + +lemma sg30121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9954 + +lemma sg30122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9924 + +lemma sg30123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10364 + +lemma sg30124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9925 + +lemma sg30125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9925 + +lemma sg30126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,4,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10365 + +lemma sg30127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,4,4,4,4,4,3,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9263 + +lemma sg30128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1319 sg20973 + +lemma sg30129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1722 sg18251 + +lemma sg30130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1825 sg17122 + +lemma sg30131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2191 sg15571 + +lemma sg30132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2224 sg15547 + +lemma sg30133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2677 sg15018 + +lemma sg30134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2676 sg15020 + +lemma sg30135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg14690 + +lemma sg30136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg867 sg21156 + +lemma sg30137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg867 sg21157 + +lemma sg30138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg867 sg21158 + +lemma sg30139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1826 sg17122 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes74.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes74.lean index d9b56534c29a0cb0c71a43af27dadc6c2daf98f8..2f05ccacfbb81cc584b24d97ad3f6571ae459425 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes74.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes74.lean @@ -1,1222 +1,1222 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 74. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg30140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2192 sg15571 - -lemma sg30141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2225 sg15547 - -lemma sg30142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3882 sg14510 - -lemma sg30143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2867 sg14862 - -lemma sg30144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6981 sg11469 - -lemma sg30145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5983 sg11834 - -lemma sg30146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10361 - -lemma sg30147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8369 sg10661 - -lemma sg30148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2226 sg15547 - -lemma sg30149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3871 sg14517 - -lemma sg30150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2224 sg15548 - -lemma sg30151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6944 sg11473 - -lemma sg30152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5532 sg12633 - -lemma sg30153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10366 - -lemma sg30154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8438 sg10289 - -lemma sg30155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8729 sg9556 - -lemma sg30156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3870 sg14519 - -lemma sg30157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6937 sg11476 - -lemma sg30158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6572 sg11541 - -lemma sg30159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10390 - -lemma sg30160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9297 - -lemma sg30161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8651 sg9921 - -lemma sg30162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6914 sg11480 - -lemma sg30163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10475 - -lemma sg30164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10390 - -lemma sg30165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9926 - -lemma sg30166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9614 - -lemma sg30167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9240 - -lemma sg30168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10807 - -lemma sg30169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10475 - -lemma sg30170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10390 - -lemma sg30171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9955 - -lemma sg30172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2193 sg15571 - -lemma sg30173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2227 sg15547 - -lemma sg30174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3872 sg14517 - -lemma sg30175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2869 sg14861 - -lemma sg30176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6946 sg11473 - -lemma sg30177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5534 sg12633 - -lemma sg30178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10362 - -lemma sg30179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8444 sg10285 - -lemma sg30180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8732 sg9556 - -lemma sg30181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3886 sg14509 - -lemma sg30182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3871 sg14518 - -lemma sg30183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6938 sg11476 - -lemma sg30184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6944 sg11474 - -lemma sg30185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10367 - -lemma sg30186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9343 - -lemma sg30187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8652 sg9921 - -lemma sg30188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6939 sg11476 - -lemma sg30189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6915 sg11480 - -lemma sg30190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10391 - -lemma sg30191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9298 - -lemma sg30192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9922 - -lemma sg30193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9614 - -lemma sg30194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10476 - -lemma sg30195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10391 - -lemma sg30196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10808 - -lemma sg30197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10476 - -lemma sg30198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9956 - -lemma sg30199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10391 - -lemma sg30200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9956 - -lemma sg30201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10367 - -lemma sg30202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3772 sg14539 - -lemma sg30203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6940 sg11476 - -lemma sg30204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6916 sg11480 - -lemma sg30205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10368 - -lemma sg30206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9344 - -lemma sg30207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8807 sg9261 - -lemma sg30208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9614 - -lemma sg30209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5995 sg11831 - -lemma sg30210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10477 - -lemma sg30211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9299 - -lemma sg30212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10809 - -lemma sg30213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10477 - -lemma sg30214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10392 - -lemma sg30215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9957 - -lemma sg30216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10392 - -lemma sg30217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9957 - -lemma sg30218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9928 - -lemma sg30219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10368 - -lemma sg30220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10393 - -lemma sg30221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10393 - -lemma sg30222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9958 - -lemma sg30223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10393 - -lemma sg30224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9958 - -lemma sg30225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9929 - -lemma sg30226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9929 - -lemma sg30227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10369 - -lemma sg30228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10364 - -lemma sg30229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9615 - -lemma sg30230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,4,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10365 - -lemma sg30231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2236 sg15531 - -lemma sg30232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3887 sg14509 - -lemma sg30233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3872 sg14518 - -lemma sg30234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6987 sg11468 - -lemma sg30235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6946 sg11474 - -lemma sg30236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9268 - -lemma sg30237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9343 - -lemma sg30238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8732 sg9557 - -lemma sg30239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3769 sg14542 - -lemma sg30240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6941 sg11476 - -lemma sg30241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5987 sg11833 - -lemma sg30242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10370 - -lemma sg30243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9268 - -lemma sg30244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9922 - -lemma sg30245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8733 sg9557 - -lemma sg30246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6917 sg11480 - -lemma sg30247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10478 - -lemma sg30248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9301 - -lemma sg30249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10810 - -lemma sg30250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10478 - -lemma sg30251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10394 - -lemma sg30252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9959 - -lemma sg30253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10394 - -lemma sg30254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9959 - -lemma sg30255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9930 - -lemma sg30256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10370 - -lemma sg30257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6942 sg11476 - -lemma sg30258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6918 sg11480 - -lemma sg30259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10479 - -lemma sg30260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9269 - -lemma sg30261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10811 - -lemma sg30262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10479 - -lemma sg30263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10395 - -lemma sg30264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10395 - -lemma sg30265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9960 - -lemma sg30266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10395 - -lemma sg30267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9960 - -lemma sg30268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9931 - -lemma sg30269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9931 - -lemma sg30270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10371 - -lemma sg30271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9269 - -lemma sg30272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9303 - -lemma sg30273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9932 - -lemma sg30274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9932 - -lemma sg30275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10372 - -lemma sg30276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9270 - -lemma sg30277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9270 - -lemma sg30278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6919 sg11480 - -lemma sg30279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10396 - -lemma sg30280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10396 - -lemma sg30281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9961 - -lemma sg30282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10396 - -lemma sg30283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9961 - -lemma sg30284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9304 - -lemma sg30285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9933 - -lemma sg30286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9933 - -lemma sg30287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10373 - -lemma sg30288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9271 - -lemma sg30289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9271 - -lemma sg30290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8726 sg9562 - -lemma sg30291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8727 sg9562 - -lemma sg30292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8728 sg9562 - -lemma sg30293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8542 sg10130 - -lemma sg30294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1723 sg18251 - -lemma sg30295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1830 sg17121 - -lemma sg30296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2197 sg15569 - -lemma sg30297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2234 sg15534 - -lemma sg30298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3884 sg14510 - -lemma sg30299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2868 sg14862 - -lemma sg30300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6984 sg11469 - -lemma sg30301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5985 sg11834 - -lemma sg30302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8443 sg10289 - -lemma sg30303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8383 sg10620 - -lemma sg30304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2198 sg15569 - -lemma sg30305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2235 sg15534 - -lemma sg30306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3885 sg14510 - -lemma sg30307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2869 sg14862 - -lemma sg30308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6985 sg11469 - -lemma sg30309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5539 sg12631 - -lemma sg30310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10366 - -lemma sg30311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8444 sg10289 - -lemma sg30312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8660 sg9784 - -lemma sg30313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3873 sg14517 - -lemma sg30314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3871 sg14519 - -lemma sg30315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6949 sg11473 - -lemma sg30316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6576 sg11541 - -lemma sg30317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9305 - -lemma sg30318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9345 - -lemma sg30319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8729 sg9558 - -lemma sg30320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6986 sg11469 - -lemma sg30321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6577 sg11541 - -lemma sg30322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10397 - -lemma sg30323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9305 - -lemma sg30324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9926 - -lemma sg30325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9558 - -lemma sg30326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10480 - -lemma sg30327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10397 - -lemma sg30328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10812 - -lemma sg30329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10480 - -lemma sg30330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9962 - -lemma sg30331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10397 - -lemma sg30332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9962 - -lemma sg30333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8347 sg10708 - -lemma sg30334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2236 sg15534 - -lemma sg30335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3874 sg14517 - -lemma sg30336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3872 sg14519 - -lemma sg30337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6950 sg11473 - -lemma sg30338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6578 sg11541 - -lemma sg30339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10367 - -lemma sg30340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9345 - -lemma sg30341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8732 sg9558 - -lemma sg30342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3769 sg14543 - -lemma sg30343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6951 sg11473 - -lemma sg30344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6579 sg11541 - -lemma sg30345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10374 - -lemma sg30346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9346 - -lemma sg30347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9926 - -lemma sg30348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8733 sg9558 - -lemma sg30349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6580 sg11541 - -lemma sg30350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10481 - -lemma sg30351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9306 - -lemma sg30352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10813 - -lemma sg30353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10481 - -lemma sg30354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10398 - -lemma sg30355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9963 - -lemma sg30356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10398 - -lemma sg30357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9963 - -lemma sg30358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9935 - -lemma sg30359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10374 - -lemma sg30360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6952 sg11473 - -lemma sg30361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6581 sg11541 - -lemma sg30362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10482 - -lemma sg30363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9347 - -lemma sg30364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10814 - -lemma sg30365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10482 - -lemma sg30366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10399 - -lemma sg30367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10399 - -lemma sg30368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9964 - -lemma sg30369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10399 - -lemma sg30370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9964 - -lemma sg30371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9936 - -lemma sg30372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9936 - -lemma sg30373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10375 - -lemma sg30374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10368 - -lemma sg30375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9307 - -lemma sg30376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9937 - -lemma sg30377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9937 - -lemma sg30378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10376 - -lemma sg30379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9616 - -lemma sg30380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10369 - -lemma sg30381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14517 - -lemma sg30382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3874 sg14518 - -lemma sg30383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6953 sg11473 - -lemma sg30384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6582 sg11541 - -lemma sg30385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10370 - -lemma sg30386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9346 - -lemma sg30387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9264 - -lemma sg30388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9543 - -lemma sg30389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6954 sg11473 - -lemma sg30390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6583 sg11541 - -lemma sg30391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10483 - -lemma sg30392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9348 - -lemma sg30393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10815 - -lemma sg30394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10483 - -lemma sg30395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10400 - -lemma sg30396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10400 - -lemma sg30397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9965 - -lemma sg30398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10400 - -lemma sg30399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9965 - -lemma sg30400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9938 - -lemma sg30401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9938 - -lemma sg30402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10377 - -lemma sg30403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10370 - -lemma sg30404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6584 sg11541 - -lemma sg30405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10401 - -lemma sg30406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10401 - -lemma sg30407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9966 - -lemma sg30408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10401 - -lemma sg30409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9966 - -lemma sg30410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9308 - -lemma sg30411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9939 - -lemma sg30412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9939 - -lemma sg30413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10378 - -lemma sg30414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9617 - -lemma sg30415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10371 - -lemma sg30416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9932 - -lemma sg30417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9618 - -lemma sg30418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10372 - -lemma sg30419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10379 - -lemma sg30420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9309 - -lemma sg30421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9940 - -lemma sg30422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9940 - -lemma sg30423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10379 - -lemma sg30424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9933 - -lemma sg30425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9619 - -lemma sg30426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10373 - -lemma sg30427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8730 sg9562 - -lemma sg30428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14518 - -lemma sg30429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6993 sg11468 - -lemma sg30430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6953 sg11474 - -lemma sg30431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10484 - -lemma sg30432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9348 - -lemma sg30433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10816 - -lemma sg30434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10484 - -lemma sg30435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6954 sg11474 - -lemma sg30436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10402 - -lemma sg30437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10402 - -lemma sg30438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9967 - -lemma sg30439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10402 - -lemma sg30440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9967 - -lemma sg30441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9310 - -lemma sg30442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9941 - -lemma sg30443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9941 - -lemma sg30444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10380 - -lemma sg30445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9280 - -lemma sg30446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8803 sg9280 - -lemma sg30447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10381 - -lemma sg30448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9311 - -lemma sg30449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9942 - -lemma sg30450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9942 - -lemma sg30451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10381 - -lemma sg30452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9281 - -lemma sg30453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9281 - -lemma sg30454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9618 - -lemma sg30455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9282 - -lemma sg30456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9282 - -lemma sg30457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9282 - -lemma sg30458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9619 - -lemma sg30459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9809 - -lemma sg30460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9555 - -lemma sg30461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1831 sg17121 - -lemma sg30462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2199 sg15569 - -lemma sg30463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2240 sg15529 - -lemma sg30464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2684 sg15016 - -lemma sg30465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2874 sg14855 - -lemma sg30466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5261 sg12690 - -lemma sg30467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3518 sg14683 - -lemma sg30468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9272 - -lemma sg30469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5628 sg12604 - -lemma sg30470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8666 sg9784 - -lemma sg30471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2241 sg15529 - -lemma sg30472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3888 sg14510 - -lemma sg30473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3771 sg14541 - -lemma sg30474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6989 sg11469 - -lemma sg30475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5989 sg11834 - -lemma sg30476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9283 - -lemma sg30477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9272 - -lemma sg30478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8660 sg9795 - -lemma sg30479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3873 sg14519 - -lemma sg30480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6990 sg11469 - -lemma sg30481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6949 sg11475 - -lemma sg30482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9312 - -lemma sg30483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9351 - -lemma sg30484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8807 sg9272 - -lemma sg30485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8737 sg9546 - -lemma sg30486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6594 sg11540 - -lemma sg30487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9275 - -lemma sg30488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9312 - -lemma sg30489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10817 - -lemma sg30490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8808 sg9272 - -lemma sg30491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9251 - -lemma sg30492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9968 - -lemma sg30493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10722 - -lemma sg30494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9968 - -lemma sg30495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9943 - -lemma sg30496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9312 - -lemma sg30497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3889 sg14510 - -lemma sg30498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3874 sg14519 - -lemma sg30499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6991 sg11469 - -lemma sg30500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6950 sg11475 - -lemma sg30501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10374 - -lemma sg30502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9351 - -lemma sg30503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9272 - -lemma sg30504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9546 - -lemma sg30505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6992 sg11469 - -lemma sg30506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6951 sg11475 - -lemma sg30507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10485 - -lemma sg30508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9352 - -lemma sg30509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10818 - -lemma sg30510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10485 - -lemma sg30511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10376 - -lemma sg30512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9313 - -lemma sg30513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9969 - -lemma sg30514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10723 - -lemma sg30515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9969 - -lemma sg30516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9944 - -lemma sg30517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9944 - -lemma sg30518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10711 - -lemma sg30519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10374 - -lemma sg30520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6952 sg11475 - -lemma sg30521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9314 - -lemma sg30522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9353 - -lemma sg30523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9970 - -lemma sg30524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10724 - -lemma sg30525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9970 - -lemma sg30526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9314 - -lemma sg30527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9945 - -lemma sg30528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9945 - -lemma sg30529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10712 - -lemma sg30530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9620 - -lemma sg30531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8425 sg10375 - -lemma sg30532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9937 - -lemma sg30533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9621 - -lemma sg30534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14519 - -lemma sg30535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6993 sg11469 - -lemma sg30536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6953 sg11475 - -lemma sg30537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10486 - -lemma sg30538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9352 - -lemma sg30539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10819 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 74. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg30140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2192 sg15571 + +lemma sg30141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2225 sg15547 + +lemma sg30142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3882 sg14510 + +lemma sg30143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2867 sg14862 + +lemma sg30144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6981 sg11469 + +lemma sg30145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5983 sg11834 + +lemma sg30146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10361 + +lemma sg30147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8369 sg10661 + +lemma sg30148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2226 sg15547 + +lemma sg30149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3871 sg14517 + +lemma sg30150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2224 sg15548 + +lemma sg30151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6944 sg11473 + +lemma sg30152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5532 sg12633 + +lemma sg30153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10366 + +lemma sg30154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8438 sg10289 + +lemma sg30155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8729 sg9556 + +lemma sg30156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3870 sg14519 + +lemma sg30157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6937 sg11476 + +lemma sg30158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6572 sg11541 + +lemma sg30159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10390 + +lemma sg30160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9297 + +lemma sg30161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8651 sg9921 + +lemma sg30162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6914 sg11480 + +lemma sg30163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10475 + +lemma sg30164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10390 + +lemma sg30165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9926 + +lemma sg30166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9614 + +lemma sg30167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9240 + +lemma sg30168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10807 + +lemma sg30169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10475 + +lemma sg30170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10390 + +lemma sg30171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9955 + +lemma sg30172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2193 sg15571 + +lemma sg30173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2227 sg15547 + +lemma sg30174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3872 sg14517 + +lemma sg30175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2869 sg14861 + +lemma sg30176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6946 sg11473 + +lemma sg30177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5534 sg12633 + +lemma sg30178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10362 + +lemma sg30179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8444 sg10285 + +lemma sg30180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8732 sg9556 + +lemma sg30181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3886 sg14509 + +lemma sg30182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3871 sg14518 + +lemma sg30183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6938 sg11476 + +lemma sg30184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6944 sg11474 + +lemma sg30185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10367 + +lemma sg30186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9343 + +lemma sg30187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8652 sg9921 + +lemma sg30188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6939 sg11476 + +lemma sg30189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6915 sg11480 + +lemma sg30190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10391 + +lemma sg30191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9298 + +lemma sg30192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9922 + +lemma sg30193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9614 + +lemma sg30194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10476 + +lemma sg30195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10391 + +lemma sg30196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10808 + +lemma sg30197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10476 + +lemma sg30198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9956 + +lemma sg30199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10391 + +lemma sg30200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9956 + +lemma sg30201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10367 + +lemma sg30202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3772 sg14539 + +lemma sg30203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6940 sg11476 + +lemma sg30204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6916 sg11480 + +lemma sg30205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10368 + +lemma sg30206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9344 + +lemma sg30207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8807 sg9261 + +lemma sg30208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9614 + +lemma sg30209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5995 sg11831 + +lemma sg30210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10477 + +lemma sg30211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9299 + +lemma sg30212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10809 + +lemma sg30213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10477 + +lemma sg30214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10392 + +lemma sg30215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9957 + +lemma sg30216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10392 + +lemma sg30217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9957 + +lemma sg30218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9928 + +lemma sg30219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10368 + +lemma sg30220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10393 + +lemma sg30221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10393 + +lemma sg30222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9958 + +lemma sg30223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10393 + +lemma sg30224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9958 + +lemma sg30225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9929 + +lemma sg30226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9929 + +lemma sg30227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10369 + +lemma sg30228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10364 + +lemma sg30229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9615 + +lemma sg30230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,4,4,4,4,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10365 + +lemma sg30231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2236 sg15531 + +lemma sg30232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3887 sg14509 + +lemma sg30233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3872 sg14518 + +lemma sg30234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6987 sg11468 + +lemma sg30235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6946 sg11474 + +lemma sg30236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9268 + +lemma sg30237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9343 + +lemma sg30238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8732 sg9557 + +lemma sg30239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3769 sg14542 + +lemma sg30240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6941 sg11476 + +lemma sg30241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5987 sg11833 + +lemma sg30242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10370 + +lemma sg30243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9268 + +lemma sg30244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9922 + +lemma sg30245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8733 sg9557 + +lemma sg30246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6917 sg11480 + +lemma sg30247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10478 + +lemma sg30248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9301 + +lemma sg30249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10810 + +lemma sg30250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10478 + +lemma sg30251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10394 + +lemma sg30252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9959 + +lemma sg30253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10394 + +lemma sg30254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9959 + +lemma sg30255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9930 + +lemma sg30256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10370 + +lemma sg30257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6942 sg11476 + +lemma sg30258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6918 sg11480 + +lemma sg30259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10479 + +lemma sg30260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9269 + +lemma sg30261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10811 + +lemma sg30262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10479 + +lemma sg30263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10395 + +lemma sg30264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10395 + +lemma sg30265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9960 + +lemma sg30266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10395 + +lemma sg30267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9960 + +lemma sg30268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9931 + +lemma sg30269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9931 + +lemma sg30270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10371 + +lemma sg30271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9269 + +lemma sg30272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9303 + +lemma sg30273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9932 + +lemma sg30274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9932 + +lemma sg30275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10372 + +lemma sg30276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9270 + +lemma sg30277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9270 + +lemma sg30278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6919 sg11480 + +lemma sg30279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10396 + +lemma sg30280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10396 + +lemma sg30281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9961 + +lemma sg30282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10396 + +lemma sg30283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9961 + +lemma sg30284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9304 + +lemma sg30285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9933 + +lemma sg30286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9933 + +lemma sg30287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10373 + +lemma sg30288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9271 + +lemma sg30289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9271 + +lemma sg30290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8726 sg9562 + +lemma sg30291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8727 sg9562 + +lemma sg30292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8728 sg9562 + +lemma sg30293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,5,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8542 sg10130 + +lemma sg30294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1723 sg18251 + +lemma sg30295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1830 sg17121 + +lemma sg30296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2197 sg15569 + +lemma sg30297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2234 sg15534 + +lemma sg30298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3884 sg14510 + +lemma sg30299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2868 sg14862 + +lemma sg30300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6984 sg11469 + +lemma sg30301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5985 sg11834 + +lemma sg30302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8443 sg10289 + +lemma sg30303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8383 sg10620 + +lemma sg30304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2198 sg15569 + +lemma sg30305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2235 sg15534 + +lemma sg30306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3885 sg14510 + +lemma sg30307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2869 sg14862 + +lemma sg30308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6985 sg11469 + +lemma sg30309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5539 sg12631 + +lemma sg30310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10366 + +lemma sg30311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8444 sg10289 + +lemma sg30312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8660 sg9784 + +lemma sg30313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3873 sg14517 + +lemma sg30314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3871 sg14519 + +lemma sg30315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6949 sg11473 + +lemma sg30316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6576 sg11541 + +lemma sg30317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9305 + +lemma sg30318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9345 + +lemma sg30319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8729 sg9558 + +lemma sg30320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6986 sg11469 + +lemma sg30321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6577 sg11541 + +lemma sg30322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10397 + +lemma sg30323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9305 + +lemma sg30324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9926 + +lemma sg30325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9558 + +lemma sg30326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10480 + +lemma sg30327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10397 + +lemma sg30328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10812 + +lemma sg30329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10480 + +lemma sg30330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9962 + +lemma sg30331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10397 + +lemma sg30332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9962 + +lemma sg30333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8347 sg10708 + +lemma sg30334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2236 sg15534 + +lemma sg30335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3874 sg14517 + +lemma sg30336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3872 sg14519 + +lemma sg30337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6950 sg11473 + +lemma sg30338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6578 sg11541 + +lemma sg30339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10367 + +lemma sg30340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9345 + +lemma sg30341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8732 sg9558 + +lemma sg30342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3769 sg14543 + +lemma sg30343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6951 sg11473 + +lemma sg30344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6579 sg11541 + +lemma sg30345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10374 + +lemma sg30346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9346 + +lemma sg30347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9926 + +lemma sg30348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8733 sg9558 + +lemma sg30349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6580 sg11541 + +lemma sg30350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10481 + +lemma sg30351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9306 + +lemma sg30352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10813 + +lemma sg30353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10481 + +lemma sg30354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10398 + +lemma sg30355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9963 + +lemma sg30356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10398 + +lemma sg30357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9963 + +lemma sg30358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9935 + +lemma sg30359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10374 + +lemma sg30360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6952 sg11473 + +lemma sg30361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6581 sg11541 + +lemma sg30362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10482 + +lemma sg30363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9347 + +lemma sg30364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10814 + +lemma sg30365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10482 + +lemma sg30366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10399 + +lemma sg30367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10399 + +lemma sg30368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9964 + +lemma sg30369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10399 + +lemma sg30370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9964 + +lemma sg30371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9936 + +lemma sg30372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9936 + +lemma sg30373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10375 + +lemma sg30374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10368 + +lemma sg30375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9307 + +lemma sg30376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9937 + +lemma sg30377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9937 + +lemma sg30378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10376 + +lemma sg30379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9616 + +lemma sg30380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,4,4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10369 + +lemma sg30381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14517 + +lemma sg30382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3874 sg14518 + +lemma sg30383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6953 sg11473 + +lemma sg30384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6582 sg11541 + +lemma sg30385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10370 + +lemma sg30386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9346 + +lemma sg30387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9264 + +lemma sg30388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9543 + +lemma sg30389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6954 sg11473 + +lemma sg30390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6583 sg11541 + +lemma sg30391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10483 + +lemma sg30392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9348 + +lemma sg30393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10815 + +lemma sg30394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10483 + +lemma sg30395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10400 + +lemma sg30396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10400 + +lemma sg30397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9965 + +lemma sg30398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10400 + +lemma sg30399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9965 + +lemma sg30400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9938 + +lemma sg30401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9938 + +lemma sg30402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10377 + +lemma sg30403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10370 + +lemma sg30404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6584 sg11541 + +lemma sg30405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10401 + +lemma sg30406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10401 + +lemma sg30407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9966 + +lemma sg30408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10401 + +lemma sg30409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9966 + +lemma sg30410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9308 + +lemma sg30411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9939 + +lemma sg30412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9939 + +lemma sg30413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10378 + +lemma sg30414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9617 + +lemma sg30415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10371 + +lemma sg30416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9932 + +lemma sg30417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9618 + +lemma sg30418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10372 + +lemma sg30419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10379 + +lemma sg30420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9309 + +lemma sg30421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9940 + +lemma sg30422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9940 + +lemma sg30423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10379 + +lemma sg30424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9933 + +lemma sg30425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9619 + +lemma sg30426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10373 + +lemma sg30427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8730 sg9562 + +lemma sg30428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14518 + +lemma sg30429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6993 sg11468 + +lemma sg30430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6953 sg11474 + +lemma sg30431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10484 + +lemma sg30432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9348 + +lemma sg30433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10816 + +lemma sg30434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10484 + +lemma sg30435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6954 sg11474 + +lemma sg30436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10402 + +lemma sg30437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10402 + +lemma sg30438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9967 + +lemma sg30439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10402 + +lemma sg30440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9967 + +lemma sg30441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9310 + +lemma sg30442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9941 + +lemma sg30443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9941 + +lemma sg30444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10380 + +lemma sg30445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9280 + +lemma sg30446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8803 sg9280 + +lemma sg30447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10381 + +lemma sg30448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9311 + +lemma sg30449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9942 + +lemma sg30450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9942 + +lemma sg30451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10381 + +lemma sg30452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9281 + +lemma sg30453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9281 + +lemma sg30454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9618 + +lemma sg30455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9282 + +lemma sg30456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9282 + +lemma sg30457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9282 + +lemma sg30458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9619 + +lemma sg30459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9809 + +lemma sg30460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,6,6,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9555 + +lemma sg30461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1831 sg17121 + +lemma sg30462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2199 sg15569 + +lemma sg30463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2240 sg15529 + +lemma sg30464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2684 sg15016 + +lemma sg30465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2874 sg14855 + +lemma sg30466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5261 sg12690 + +lemma sg30467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3518 sg14683 + +lemma sg30468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9272 + +lemma sg30469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5628 sg12604 + +lemma sg30470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8666 sg9784 + +lemma sg30471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2241 sg15529 + +lemma sg30472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3888 sg14510 + +lemma sg30473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3771 sg14541 + +lemma sg30474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6989 sg11469 + +lemma sg30475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5989 sg11834 + +lemma sg30476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9283 + +lemma sg30477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9272 + +lemma sg30478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8660 sg9795 + +lemma sg30479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3873 sg14519 + +lemma sg30480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6990 sg11469 + +lemma sg30481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6949 sg11475 + +lemma sg30482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9312 + +lemma sg30483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9351 + +lemma sg30484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8807 sg9272 + +lemma sg30485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8737 sg9546 + +lemma sg30486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6594 sg11540 + +lemma sg30487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9275 + +lemma sg30488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9312 + +lemma sg30489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10817 + +lemma sg30490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8808 sg9272 + +lemma sg30491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9251 + +lemma sg30492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9968 + +lemma sg30493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10722 + +lemma sg30494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9968 + +lemma sg30495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9943 + +lemma sg30496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9312 + +lemma sg30497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3889 sg14510 + +lemma sg30498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3874 sg14519 + +lemma sg30499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6991 sg11469 + +lemma sg30500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6950 sg11475 + +lemma sg30501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10374 + +lemma sg30502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9351 + +lemma sg30503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9272 + +lemma sg30504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9546 + +lemma sg30505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6992 sg11469 + +lemma sg30506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6951 sg11475 + +lemma sg30507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10485 + +lemma sg30508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9352 + +lemma sg30509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10818 + +lemma sg30510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10485 + +lemma sg30511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10376 + +lemma sg30512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9313 + +lemma sg30513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9969 + +lemma sg30514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10723 + +lemma sg30515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9969 + +lemma sg30516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9944 + +lemma sg30517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9944 + +lemma sg30518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10711 + +lemma sg30519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10374 + +lemma sg30520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6952 sg11475 + +lemma sg30521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9314 + +lemma sg30522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9353 + +lemma sg30523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9970 + +lemma sg30524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10724 + +lemma sg30525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9970 + +lemma sg30526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9314 + +lemma sg30527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9945 + +lemma sg30528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9945 + +lemma sg30529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10712 + +lemma sg30530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9620 + +lemma sg30531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8425 sg10375 + +lemma sg30532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9937 + +lemma sg30533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9621 + +lemma sg30534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14519 + +lemma sg30535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6993 sg11469 + +lemma sg30536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6953 sg11475 + +lemma sg30537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10486 + +lemma sg30538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9352 + +lemma sg30539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10819 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes75.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes75.lean index a1cde2a04cbf07a8cd98b7ae576cdc25eb85646c..3822572f4b2cca45ef3227feafb6e80c1efd6396 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes75.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes75.lean @@ -1,1224 +1,1224 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 75. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg30540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10486 - -lemma sg30541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6954 sg11475 - -lemma sg30542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9315 - -lemma sg30543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9355 - -lemma sg30544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9971 - -lemma sg30545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10725 - -lemma sg30546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9971 - -lemma sg30547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9315 - -lemma sg30548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9946 - -lemma sg30549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9946 - -lemma sg30550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10713 - -lemma sg30551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9622 - -lemma sg30552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10382 - -lemma sg30553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9316 - -lemma sg30554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9947 - -lemma sg30555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9947 - -lemma sg30556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10382 - -lemma sg30557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9939 - -lemma sg30558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9623 - -lemma sg30559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9621 - -lemma sg30560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9357 - -lemma sg30561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9940 - -lemma sg30562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9624 - -lemma sg30563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8808 sg9279 - -lemma sg30564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5577 sg12626 - -lemma sg30565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6001 sg11832 - -lemma sg30566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10380 - -lemma sg30567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9355 - -lemma sg30568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9972 - -lemma sg30569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8345 sg10726 - -lemma sg30570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9972 - -lemma sg30571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10383 - -lemma sg30572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9317 - -lemma sg30573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9948 - -lemma sg30574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9948 - -lemma sg30575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10383 - -lemma sg30576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9941 - -lemma sg30577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9625 - -lemma sg30578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9359 - -lemma sg30579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9942 - -lemma sg30580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9626 - -lemma sg30581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9623 - -lemma sg30582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9940 - -lemma sg30583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9624 - -lemma sg30584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9624 - -lemma sg30585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6015 sg11829 - -lemma sg30586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10384 - -lemma sg30587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9318 - -lemma sg30588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9949 - -lemma sg30589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9949 - -lemma sg30590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10384 - -lemma sg30591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9292 - -lemma sg30592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9292 - -lemma sg30593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9292 - -lemma sg30594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9625 - -lemma sg30595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9942 - -lemma sg30596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9626 - -lemma sg30597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9626 - -lemma sg30598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2205 sg15563 - -lemma sg30599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2242 sg15529 - -lemma sg30600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3167 sg14804 - -lemma sg30601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3774 sg14541 - -lemma sg30602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5277 sg12682 - -lemma sg30603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5261 sg12691 - -lemma sg30604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9283 - -lemma sg30605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8877 sg9065 - -lemma sg30606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8666 sg9795 - -lemma sg30607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3168 sg14804 - -lemma sg30608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3775 sg14541 - -lemma sg30609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5268 sg12689 - -lemma sg30610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6600 sg11540 - -lemma sg30611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9284 - -lemma sg30612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9283 - -lemma sg30613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8666 sg9796 - -lemma sg30614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8742 sg9546 - -lemma sg30615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5850 sg11839 - -lemma sg30616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6601 sg11540 - -lemma sg30617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9319 - -lemma sg30618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9360 - -lemma sg30619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8807 sg9283 - -lemma sg30620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8878 sg9065 - -lemma sg30621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9286 - -lemma sg30622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9319 - -lemma sg30623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9943 - -lemma sg30624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10158 - -lemma sg30625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8565 sg10116 - -lemma sg30626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9319 - -lemma sg30627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9319 - -lemma sg30628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9319 - -lemma sg30629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8773 sg9458 - -lemma sg30630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3776 sg14541 - -lemma sg30631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5851 sg11839 - -lemma sg30632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6602 sg11540 - -lemma sg30633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9287 - -lemma sg30634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9360 - -lemma sg30635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9283 - -lemma sg30636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8880 sg9065 - -lemma sg30637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6603 sg11540 - -lemma sg30638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9320 - -lemma sg30639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9361 - -lemma sg30640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9973 - -lemma sg30641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10159 - -lemma sg30642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9973 - -lemma sg30643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9320 - -lemma sg30644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9320 - -lemma sg30645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9320 - -lemma sg30646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9320 - -lemma sg30647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9627 - -lemma sg30648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9321 - -lemma sg30649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9321 - -lemma sg30650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9321 - -lemma sg30651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9321 - -lemma sg30652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9321 - -lemma sg30653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9945 - -lemma sg30654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9628 - -lemma sg30655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8808 sg9286 - -lemma sg30656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5852 sg11839 - -lemma sg30657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6604 sg11540 - -lemma sg30658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9290 - -lemma sg30659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9361 - -lemma sg30660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9974 - -lemma sg30661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10160 - -lemma sg30662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9974 - -lemma sg30663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9322 - -lemma sg30664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9322 - -lemma sg30665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9322 - -lemma sg30666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9322 - -lemma sg30667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9322 - -lemma sg30668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9946 - -lemma sg30669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9629 - -lemma sg30670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9362 - -lemma sg30671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9947 - -lemma sg30672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9630 - -lemma sg30673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9628 - -lemma sg30674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8807 sg9289 - -lemma sg30675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8808 sg9289 - -lemma sg30676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6605 sg11540 - -lemma sg30677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9323 - -lemma sg30678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9323 - -lemma sg30679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9323 - -lemma sg30680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9323 - -lemma sg30681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8798 sg9323 - -lemma sg30682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9363 - -lemma sg30683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9948 - -lemma sg30684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9631 - -lemma sg30685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9629 - -lemma sg30686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9947 - -lemma sg30687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9630 - -lemma sg30688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9630 - -lemma sg30689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10384 - -lemma sg30690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9364 - -lemma sg30691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9949 - -lemma sg30692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9632 - -lemma sg30693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9948 - -lemma sg30694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9631 - -lemma sg30695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9631 - -lemma sg30696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,8,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9364 - -lemma sg30697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,8,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9949 - -lemma sg30698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,8,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9632 - -lemma sg30699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,8,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9632 - -lemma sg30700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1317 sg20975 - -lemma sg30701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1719 sg18255 - -lemma sg30702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg963 sg21132 - -lemma sg30703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg17137 - -lemma sg30704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg21311 - -lemma sg30705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg15033 - -lemma sg30706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg21312 - -lemma sg30707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg21313 - -lemma sg30708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg342 sg21314 - -lemma sg30709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg342 sg21315 - -lemma sg30710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1318 sg20975 - -lemma sg30711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1720 sg18255 - -lemma sg30712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1827 sg17122 - -lemma sg30713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2194 sg15571 - -lemma sg30714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2230 sg15536 - -lemma sg30715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2676 sg15022 - -lemma sg30716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg15034 - -lemma sg30717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg575 sg21224 - -lemma sg30718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg575 sg21225 - -lemma sg30719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg575 sg21226 - -lemma sg30720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1721 sg18255 - -lemma sg30721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1463 sg20942 - -lemma sg30722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1816 sg17137 - -lemma sg30723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2223 sg15549 - -lemma sg30724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2668 sg15033 - -lemma sg30725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg868 sg21155 - -lemma sg30726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3513 sg14694 - -lemma sg30727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg868 sg21156 - -lemma sg30728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg868 sg21157 - -lemma sg30729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg868 sg21158 - -lemma sg30730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1836 sg17110 - -lemma sg30731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1854 sg16205 - -lemma sg30732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2237 sg15532 - -lemma sg30733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1814 sg17138 - -lemma sg30734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5536 sg12632 - -lemma sg30735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1288 sg21034 - -lemma sg30736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10385 - -lemma sg30737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8366 sg10682 - -lemma sg30738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3870 sg14520 - -lemma sg30739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2237 sg15533 - -lemma sg30740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6943 sg11476 - -lemma sg30741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5592 sg12611 - -lemma sg30742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8836 sg9198 - -lemma sg30743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8542 sg10132 - -lemma sg30744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8726 sg9580 - -lemma sg30745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5834 sg11840 - -lemma sg30746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6571 sg11542 - -lemma sg30747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10487 - -lemma sg30748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9180 - -lemma sg30749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8649 sg9950 - -lemma sg30750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8572 sg10105 - -lemma sg30751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9181 - -lemma sg30752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9975 - -lemma sg30753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8650 sg9950 - -lemma sg30754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10820 - -lemma sg30755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10487 - -lemma sg30756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg8648 sg9975 - -lemma sg30757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1319 sg20975 - -lemma sg30758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1722 sg18255 - -lemma sg30759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1828 sg17122 - -lemma sg30760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2195 sg15571 - -lemma sg30761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2224 sg15549 - -lemma sg30762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2677 sg15022 - -lemma sg30763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg850 sg21178 - -lemma sg30764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg14691 - -lemma sg30765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg869 sg21156 - -lemma sg30766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg869 sg21157 - -lemma sg30767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg869 sg21158 - -lemma sg30768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1829 sg17122 - -lemma sg30769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2196 sg15571 - -lemma sg30770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2225 sg15549 - -lemma sg30771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2670 sg15033 - -lemma sg30772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2867 sg14863 - -lemma sg30773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5539 sg12632 - -lemma sg30774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg14692 - -lemma sg30775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10385 - -lemma sg30776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8369 sg10682 - -lemma sg30777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2226 sg15549 - -lemma sg30778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3871 sg14520 - -lemma sg30779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2237 sg15535 - -lemma sg30780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6944 sg11476 - -lemma sg30781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5536 sg12633 - -lemma sg30782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10386 - -lemma sg30783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8438 sg10308 - -lemma sg30784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8729 sg9580 - -lemma sg30785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2669 sg15034 - -lemma sg30786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6945 sg11476 - -lemma sg30787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6572 sg11542 - -lemma sg30788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10403 - -lemma sg30789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8837 sg9198 - -lemma sg30790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8651 sg9950 - -lemma sg30791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6573 sg11542 - -lemma sg30792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10488 - -lemma sg30793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10403 - -lemma sg30794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9951 - -lemma sg30795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8720 sg9633 - -lemma sg30796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9184 - -lemma sg30797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10821 - -lemma sg30798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10488 - -lemma sg30799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10403 - -lemma sg30800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg8648 sg9976 - -lemma sg30801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1819 sg17137 - -lemma sg30802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2227 sg15549 - -lemma sg30803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3872 sg14520 - -lemma sg30804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2873 sg14856 - -lemma sg30805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6946 sg11476 - -lemma sg30806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5593 sg12611 - -lemma sg30807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9293 - -lemma sg30808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8547 sg10132 - -lemma sg30809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8732 sg9580 - -lemma sg30810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3164 sg14805 - -lemma sg30811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3770 sg14542 - -lemma sg30812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5543 sg12632 - -lemma sg30813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5963 sg11838 - -lemma sg30814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10387 - -lemma sg30815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9293 - -lemma sg30816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8652 sg9950 - -lemma sg30817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6947 sg11476 - -lemma sg30818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6574 sg11542 - -lemma sg30819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9295 - -lemma sg30820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9262 - -lemma sg30821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9293 - -lemma sg30822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8721 sg9633 - -lemma sg30823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10489 - -lemma sg30824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9263 - -lemma sg30825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10822 - -lemma sg30826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10489 - -lemma sg30827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9977 - -lemma sg30828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10161 - -lemma sg30829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9977 - -lemma sg30830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10387 - -lemma sg30831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3778 sg14539 - -lemma sg30832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6948 sg11476 - -lemma sg30833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6575 sg11542 - -lemma sg30834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10388 - -lemma sg30835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9294 - -lemma sg30836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9812 - -lemma sg30837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8722 sg9633 - -lemma sg30838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6016 sg11827 - -lemma sg30839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10490 - -lemma sg30840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9295 - -lemma sg30841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10823 - -lemma sg30842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10490 - -lemma sg30843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10404 - -lemma sg30844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9978 - -lemma sg30845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10404 - -lemma sg30846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9978 - -lemma sg30847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9953 - -lemma sg30848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10388 - -lemma sg30849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8610 sg10079 - -lemma sg30850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8372 sg10682 - -lemma sg30851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9979 - -lemma sg30852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10162 - -lemma sg30853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9979 - -lemma sg30854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9954 - -lemma sg30855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9954 - -lemma sg30856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10389 - -lemma sg30857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9296 - -lemma sg30858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1723 sg18255 - -lemma sg30859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1830 sg17122 - -lemma sg30860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2197 sg15571 - -lemma sg30861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2234 sg15536 - -lemma sg30862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2678 sg15022 - -lemma sg30863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2868 sg14863 - -lemma sg30864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5562 sg12630 - -lemma sg30865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg14693 - -lemma sg30866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8443 sg10308 - -lemma sg30867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8383 sg10641 - -lemma sg30868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2198 sg15571 - -lemma sg30869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2235 sg15536 - -lemma sg30870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3890 sg14510 - -lemma sg30871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2869 sg14863 - -lemma sg30872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6994 sg11469 - -lemma sg30873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5539 sg12633 - -lemma sg30874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10386 - -lemma sg30875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8444 sg10308 - -lemma sg30876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8660 sg9810 - -lemma sg30877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3873 sg14520 - -lemma sg30878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3770 sg14543 - -lemma sg30879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6949 sg11476 - -lemma sg30880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6576 sg11542 - -lemma sg30881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10390 - -lemma sg30882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9365 - -lemma sg30883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8729 sg9581 - -lemma sg30884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6995 sg11469 - -lemma sg30885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6577 sg11542 - -lemma sg30886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10405 - -lemma sg30887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9262 - -lemma sg30888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9951 - -lemma sg30889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8730 sg9581 - -lemma sg30890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10491 - -lemma sg30891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10405 - -lemma sg30892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10824 - -lemma sg30893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10491 - -lemma sg30894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9980 - -lemma sg30895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10405 - -lemma sg30896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9980 - -lemma sg30897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg8423 sg10390 - -lemma sg30898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2236 sg15536 - -lemma sg30899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3874 sg14520 - -lemma sg30900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3771 sg14542 - -lemma sg30901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6950 sg11476 - -lemma sg30902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6578 sg11542 - -lemma sg30903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10387 - -lemma sg30904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9365 - -lemma sg30905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8732 sg9581 - -lemma sg30906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3772 sg14542 - -lemma sg30907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6951 sg11476 - -lemma sg30908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6579 sg11542 - -lemma sg30909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10391 - -lemma sg30910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9366 - -lemma sg30911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9951 - -lemma sg30912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8733 sg9581 - -lemma sg30913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6580 sg11542 - -lemma sg30914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10492 - -lemma sg30915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9295 - -lemma sg30916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10825 - -lemma sg30917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10492 - -lemma sg30918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10406 - -lemma sg30919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9981 - -lemma sg30920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10406 - -lemma sg30921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9981 - -lemma sg30922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9956 - -lemma sg30923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10391 - -lemma sg30924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6952 sg11476 - -lemma sg30925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6581 sg11542 - -lemma sg30926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10493 - -lemma sg30927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9367 - -lemma sg30928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10826 - -lemma sg30929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10493 - -lemma sg30930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10407 - -lemma sg30931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10407 - -lemma sg30932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9982 - -lemma sg30933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10407 - -lemma sg30934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9982 - -lemma sg30935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9957 - -lemma sg30936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9957 - -lemma sg30937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10392 - -lemma sg30938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8376 sg10682 - -lemma sg30939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9958 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 75. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg30540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10486 + +lemma sg30541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6954 sg11475 + +lemma sg30542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9315 + +lemma sg30543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9355 + +lemma sg30544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9971 + +lemma sg30545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10725 + +lemma sg30546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9971 + +lemma sg30547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9315 + +lemma sg30548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9946 + +lemma sg30549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9946 + +lemma sg30550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10713 + +lemma sg30551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9622 + +lemma sg30552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10382 + +lemma sg30553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9316 + +lemma sg30554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9947 + +lemma sg30555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9947 + +lemma sg30556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10382 + +lemma sg30557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9939 + +lemma sg30558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9623 + +lemma sg30559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9621 + +lemma sg30560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9357 + +lemma sg30561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9940 + +lemma sg30562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9624 + +lemma sg30563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8808 sg9279 + +lemma sg30564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5577 sg12626 + +lemma sg30565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6001 sg11832 + +lemma sg30566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10380 + +lemma sg30567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9355 + +lemma sg30568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9972 + +lemma sg30569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8345 sg10726 + +lemma sg30570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9972 + +lemma sg30571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10383 + +lemma sg30572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9317 + +lemma sg30573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9948 + +lemma sg30574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9948 + +lemma sg30575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10383 + +lemma sg30576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9941 + +lemma sg30577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9625 + +lemma sg30578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9359 + +lemma sg30579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9942 + +lemma sg30580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9626 + +lemma sg30581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9623 + +lemma sg30582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9940 + +lemma sg30583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9624 + +lemma sg30584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9624 + +lemma sg30585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6015 sg11829 + +lemma sg30586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10384 + +lemma sg30587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9318 + +lemma sg30588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9949 + +lemma sg30589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9949 + +lemma sg30590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10384 + +lemma sg30591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9292 + +lemma sg30592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9292 + +lemma sg30593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9292 + +lemma sg30594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9625 + +lemma sg30595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9942 + +lemma sg30596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9626 + +lemma sg30597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,7,7,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9626 + +lemma sg30598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2205 sg15563 + +lemma sg30599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2242 sg15529 + +lemma sg30600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3167 sg14804 + +lemma sg30601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3774 sg14541 + +lemma sg30602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5277 sg12682 + +lemma sg30603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5261 sg12691 + +lemma sg30604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9283 + +lemma sg30605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8877 sg9065 + +lemma sg30606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8666 sg9795 + +lemma sg30607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3168 sg14804 + +lemma sg30608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3775 sg14541 + +lemma sg30609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5268 sg12689 + +lemma sg30610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6600 sg11540 + +lemma sg30611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9284 + +lemma sg30612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9283 + +lemma sg30613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8666 sg9796 + +lemma sg30614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8742 sg9546 + +lemma sg30615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5850 sg11839 + +lemma sg30616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6601 sg11540 + +lemma sg30617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9319 + +lemma sg30618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9360 + +lemma sg30619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8807 sg9283 + +lemma sg30620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8878 sg9065 + +lemma sg30621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9286 + +lemma sg30622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9319 + +lemma sg30623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9943 + +lemma sg30624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10158 + +lemma sg30625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8565 sg10116 + +lemma sg30626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9319 + +lemma sg30627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9319 + +lemma sg30628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9319 + +lemma sg30629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8773 sg9458 + +lemma sg30630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3776 sg14541 + +lemma sg30631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5851 sg11839 + +lemma sg30632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6602 sg11540 + +lemma sg30633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9287 + +lemma sg30634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9360 + +lemma sg30635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9283 + +lemma sg30636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8880 sg9065 + +lemma sg30637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6603 sg11540 + +lemma sg30638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9320 + +lemma sg30639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9361 + +lemma sg30640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9973 + +lemma sg30641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10159 + +lemma sg30642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9973 + +lemma sg30643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9320 + +lemma sg30644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9320 + +lemma sg30645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9320 + +lemma sg30646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9320 + +lemma sg30647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9627 + +lemma sg30648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9321 + +lemma sg30649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9321 + +lemma sg30650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9321 + +lemma sg30651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9321 + +lemma sg30652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9321 + +lemma sg30653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9945 + +lemma sg30654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9628 + +lemma sg30655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8808 sg9286 + +lemma sg30656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5852 sg11839 + +lemma sg30657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6604 sg11540 + +lemma sg30658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9290 + +lemma sg30659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9361 + +lemma sg30660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9974 + +lemma sg30661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10160 + +lemma sg30662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9974 + +lemma sg30663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9322 + +lemma sg30664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9322 + +lemma sg30665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9322 + +lemma sg30666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9322 + +lemma sg30667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9322 + +lemma sg30668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9946 + +lemma sg30669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9629 + +lemma sg30670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9362 + +lemma sg30671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9947 + +lemma sg30672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9630 + +lemma sg30673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9628 + +lemma sg30674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8807 sg9289 + +lemma sg30675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8808 sg9289 + +lemma sg30676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6605 sg11540 + +lemma sg30677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9323 + +lemma sg30678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9323 + +lemma sg30679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9323 + +lemma sg30680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9323 + +lemma sg30681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8798 sg9323 + +lemma sg30682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9363 + +lemma sg30683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9948 + +lemma sg30684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9631 + +lemma sg30685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9629 + +lemma sg30686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9947 + +lemma sg30687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9630 + +lemma sg30688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,6,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9630 + +lemma sg30689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10384 + +lemma sg30690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9364 + +lemma sg30691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9949 + +lemma sg30692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9632 + +lemma sg30693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9948 + +lemma sg30694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9631 + +lemma sg30695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9631 + +lemma sg30696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,8,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9364 + +lemma sg30697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,8,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9949 + +lemma sg30698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,8,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9632 + +lemma sg30699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,8,8,8,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9632 + +lemma sg30700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1317 sg20975 + +lemma sg30701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1719 sg18255 + +lemma sg30702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg963 sg21132 + +lemma sg30703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg17137 + +lemma sg30704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg21311 + +lemma sg30705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg15033 + +lemma sg30706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg21312 + +lemma sg30707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg21313 + +lemma sg30708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg342 sg21314 + +lemma sg30709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,2,2,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg342 sg21315 + +lemma sg30710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1318 sg20975 + +lemma sg30711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1720 sg18255 + +lemma sg30712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1827 sg17122 + +lemma sg30713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2194 sg15571 + +lemma sg30714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2230 sg15536 + +lemma sg30715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2676 sg15022 + +lemma sg30716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg15034 + +lemma sg30717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg575 sg21224 + +lemma sg30718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg575 sg21225 + +lemma sg30719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg575 sg21226 + +lemma sg30720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1721 sg18255 + +lemma sg30721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1463 sg20942 + +lemma sg30722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1816 sg17137 + +lemma sg30723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2223 sg15549 + +lemma sg30724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2668 sg15033 + +lemma sg30725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg868 sg21155 + +lemma sg30726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3513 sg14694 + +lemma sg30727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg868 sg21156 + +lemma sg30728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg868 sg21157 + +lemma sg30729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg868 sg21158 + +lemma sg30730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1836 sg17110 + +lemma sg30731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1854 sg16205 + +lemma sg30732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2237 sg15532 + +lemma sg30733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1814 sg17138 + +lemma sg30734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5536 sg12632 + +lemma sg30735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1288 sg21034 + +lemma sg30736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10385 + +lemma sg30737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8366 sg10682 + +lemma sg30738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3870 sg14520 + +lemma sg30739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2237 sg15533 + +lemma sg30740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6943 sg11476 + +lemma sg30741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5592 sg12611 + +lemma sg30742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8836 sg9198 + +lemma sg30743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8542 sg10132 + +lemma sg30744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8726 sg9580 + +lemma sg30745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5834 sg11840 + +lemma sg30746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6571 sg11542 + +lemma sg30747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10487 + +lemma sg30748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9180 + +lemma sg30749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8649 sg9950 + +lemma sg30750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8572 sg10105 + +lemma sg30751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9181 + +lemma sg30752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9975 + +lemma sg30753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8650 sg9950 + +lemma sg30754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10820 + +lemma sg30755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10487 + +lemma sg30756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,3,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg8648 sg9975 + +lemma sg30757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1319 sg20975 + +lemma sg30758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1722 sg18255 + +lemma sg30759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1828 sg17122 + +lemma sg30760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2195 sg15571 + +lemma sg30761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2224 sg15549 + +lemma sg30762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2677 sg15022 + +lemma sg30763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg850 sg21178 + +lemma sg30764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg14691 + +lemma sg30765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg869 sg21156 + +lemma sg30766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg869 sg21157 + +lemma sg30767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg869 sg21158 + +lemma sg30768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1829 sg17122 + +lemma sg30769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2196 sg15571 + +lemma sg30770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2225 sg15549 + +lemma sg30771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2670 sg15033 + +lemma sg30772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2867 sg14863 + +lemma sg30773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5539 sg12632 + +lemma sg30774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg14692 + +lemma sg30775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10385 + +lemma sg30776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8369 sg10682 + +lemma sg30777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2226 sg15549 + +lemma sg30778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3871 sg14520 + +lemma sg30779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2237 sg15535 + +lemma sg30780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6944 sg11476 + +lemma sg30781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5536 sg12633 + +lemma sg30782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10386 + +lemma sg30783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8438 sg10308 + +lemma sg30784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8729 sg9580 + +lemma sg30785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2669 sg15034 + +lemma sg30786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6945 sg11476 + +lemma sg30787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6572 sg11542 + +lemma sg30788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10403 + +lemma sg30789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8837 sg9198 + +lemma sg30790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8651 sg9950 + +lemma sg30791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6573 sg11542 + +lemma sg30792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10488 + +lemma sg30793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10403 + +lemma sg30794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9951 + +lemma sg30795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8720 sg9633 + +lemma sg30796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9184 + +lemma sg30797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10821 + +lemma sg30798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10488 + +lemma sg30799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10403 + +lemma sg30800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg8648 sg9976 + +lemma sg30801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1819 sg17137 + +lemma sg30802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2227 sg15549 + +lemma sg30803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3872 sg14520 + +lemma sg30804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2873 sg14856 + +lemma sg30805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6946 sg11476 + +lemma sg30806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5593 sg12611 + +lemma sg30807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9293 + +lemma sg30808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8547 sg10132 + +lemma sg30809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8732 sg9580 + +lemma sg30810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3164 sg14805 + +lemma sg30811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3770 sg14542 + +lemma sg30812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5543 sg12632 + +lemma sg30813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5963 sg11838 + +lemma sg30814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10387 + +lemma sg30815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9293 + +lemma sg30816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8652 sg9950 + +lemma sg30817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6947 sg11476 + +lemma sg30818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6574 sg11542 + +lemma sg30819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9295 + +lemma sg30820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9262 + +lemma sg30821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9293 + +lemma sg30822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8721 sg9633 + +lemma sg30823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10489 + +lemma sg30824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9263 + +lemma sg30825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10822 + +lemma sg30826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10489 + +lemma sg30827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9977 + +lemma sg30828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10161 + +lemma sg30829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9977 + +lemma sg30830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10387 + +lemma sg30831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3778 sg14539 + +lemma sg30832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6948 sg11476 + +lemma sg30833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6575 sg11542 + +lemma sg30834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10388 + +lemma sg30835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9294 + +lemma sg30836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9812 + +lemma sg30837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8722 sg9633 + +lemma sg30838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6016 sg11827 + +lemma sg30839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10490 + +lemma sg30840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9295 + +lemma sg30841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10823 + +lemma sg30842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10490 + +lemma sg30843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10404 + +lemma sg30844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9978 + +lemma sg30845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10404 + +lemma sg30846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9978 + +lemma sg30847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9953 + +lemma sg30848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10388 + +lemma sg30849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8610 sg10079 + +lemma sg30850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8372 sg10682 + +lemma sg30851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9979 + +lemma sg30852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10162 + +lemma sg30853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9979 + +lemma sg30854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9954 + +lemma sg30855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9954 + +lemma sg30856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10389 + +lemma sg30857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,4,4,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9296 + +lemma sg30858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1723 sg18255 + +lemma sg30859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1830 sg17122 + +lemma sg30860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2197 sg15571 + +lemma sg30861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2234 sg15536 + +lemma sg30862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2678 sg15022 + +lemma sg30863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2868 sg14863 + +lemma sg30864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5562 sg12630 + +lemma sg30865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg14693 + +lemma sg30866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8443 sg10308 + +lemma sg30867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8383 sg10641 + +lemma sg30868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2198 sg15571 + +lemma sg30869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2235 sg15536 + +lemma sg30870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3890 sg14510 + +lemma sg30871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2869 sg14863 + +lemma sg30872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6994 sg11469 + +lemma sg30873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5539 sg12633 + +lemma sg30874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10386 + +lemma sg30875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8444 sg10308 + +lemma sg30876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8660 sg9810 + +lemma sg30877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3873 sg14520 + +lemma sg30878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3770 sg14543 + +lemma sg30879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6949 sg11476 + +lemma sg30880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6576 sg11542 + +lemma sg30881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10390 + +lemma sg30882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9365 + +lemma sg30883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8729 sg9581 + +lemma sg30884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6995 sg11469 + +lemma sg30885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6577 sg11542 + +lemma sg30886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10405 + +lemma sg30887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9262 + +lemma sg30888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9951 + +lemma sg30889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8730 sg9581 + +lemma sg30890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10491 + +lemma sg30891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10405 + +lemma sg30892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10824 + +lemma sg30893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10491 + +lemma sg30894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9980 + +lemma sg30895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10405 + +lemma sg30896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9980 + +lemma sg30897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,3,3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg8423 sg10390 + +lemma sg30898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2236 sg15536 + +lemma sg30899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3874 sg14520 + +lemma sg30900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3771 sg14542 + +lemma sg30901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6950 sg11476 + +lemma sg30902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6578 sg11542 + +lemma sg30903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10387 + +lemma sg30904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9365 + +lemma sg30905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8732 sg9581 + +lemma sg30906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3772 sg14542 + +lemma sg30907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6951 sg11476 + +lemma sg30908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6579 sg11542 + +lemma sg30909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10391 + +lemma sg30910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9366 + +lemma sg30911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9951 + +lemma sg30912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8733 sg9581 + +lemma sg30913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6580 sg11542 + +lemma sg30914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10492 + +lemma sg30915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9295 + +lemma sg30916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10825 + +lemma sg30917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10492 + +lemma sg30918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10406 + +lemma sg30919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9981 + +lemma sg30920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10406 + +lemma sg30921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9981 + +lemma sg30922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9956 + +lemma sg30923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10391 + +lemma sg30924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6952 sg11476 + +lemma sg30925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6581 sg11542 + +lemma sg30926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10493 + +lemma sg30927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9367 + +lemma sg30928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10826 + +lemma sg30929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10493 + +lemma sg30930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10407 + +lemma sg30931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10407 + +lemma sg30932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9982 + +lemma sg30933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10407 + +lemma sg30934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9982 + +lemma sg30935 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9957 + +lemma sg30936 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9957 + +lemma sg30937 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10392 + +lemma sg30938 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8376 sg10682 + +lemma sg30939 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9958 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes76.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes76.lean index ca5767a67bca66b6e1f87bdc94208fd2e2886a59..053c39a30b08980fcc4d0c781716446759071953 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes76.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes76.lean @@ -1,1224 +1,1224 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 - -namespace OAI - -/-! Semigroup Nodes 76. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg30940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9958 - -lemma sg30941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10393 - -lemma sg30942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9634 - -lemma sg30943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14520 - -lemma sg30944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3773 sg14542 - -lemma sg30945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6953 sg11476 - -lemma sg30946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6582 sg11542 - -lemma sg30947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9301 - -lemma sg30948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9366 - -lemma sg30949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9293 - -lemma sg30950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9557 - -lemma sg30951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6954 sg11476 - -lemma sg30952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6583 sg11542 - -lemma sg30953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10494 - -lemma sg30954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9301 - -lemma sg30955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10827 - -lemma sg30956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10494 - -lemma sg30957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9303 - -lemma sg30958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9368 - -lemma sg30959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9983 - -lemma sg30960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10163 - -lemma sg30961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9983 - -lemma sg30962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9959 - -lemma sg30963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9959 - -lemma sg30964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10394 - -lemma sg30965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6584 sg11542 - -lemma sg30966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10408 - -lemma sg30967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10408 - -lemma sg30968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9984 - -lemma sg30969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10408 - -lemma sg30970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9984 - -lemma sg30971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9303 - -lemma sg30972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9960 - -lemma sg30973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9960 - -lemma sg30974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10395 - -lemma sg30975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9302 - -lemma sg30976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9303 - -lemma sg30977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9303 - -lemma sg30978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10396 - -lemma sg30979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9304 - -lemma sg30980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9961 - -lemma sg30981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9961 - -lemma sg30982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10396 - -lemma sg30983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9304 - -lemma sg30984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9304 - -lemma sg30985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9562 - -lemma sg30986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1831 sg17122 - -lemma sg30987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2199 sg15571 - -lemma sg30988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2240 sg15534 - -lemma sg30989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3891 sg14510 - -lemma sg30990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2874 sg14857 - -lemma sg30991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6996 sg11469 - -lemma sg30992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5594 sg12611 - -lemma sg30993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8805 sg9297 - -lemma sg30994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8586 sg10101 - -lemma sg30995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8666 sg9810 - -lemma sg30996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2241 sg15534 - -lemma sg30997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3892 sg14510 - -lemma sg30998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3771 sg14543 - -lemma sg30999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6997 sg11469 - -lemma sg31000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5994 sg11834 - -lemma sg31001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10390 - -lemma sg31002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8806 sg9297 - -lemma sg31003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8660 sg9815 - -lemma sg31004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3766 sg14544 - -lemma sg31005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6998 sg11469 - -lemma sg31006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6593 sg11541 - -lemma sg31007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10397 - -lemma sg31008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9369 - -lemma sg31009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8807 sg9297 - -lemma sg31010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8737 sg9558 - -lemma sg31011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6594 sg11541 - -lemma sg31012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10495 - -lemma sg31013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9266 - -lemma sg31014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10828 - -lemma sg31015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10495 - -lemma sg31016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9267 - -lemma sg31017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9985 - -lemma sg31018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10164 - -lemma sg31019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9985 - -lemma sg31020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9962 - -lemma sg31021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10397 - -lemma sg31022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3893 sg14510 - -lemma sg31023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3767 sg14544 - -lemma sg31024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6999 sg11469 - -lemma sg31025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6595 sg11541 - -lemma sg31026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10391 - -lemma sg31027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9369 - -lemma sg31028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9297 - -lemma sg31029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9558 - -lemma sg31030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7000 sg11469 - -lemma sg31031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6596 sg11541 - -lemma sg31032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10496 - -lemma sg31033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9370 - -lemma sg31034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10829 - -lemma sg31035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10496 - -lemma sg31036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10409 - -lemma sg31037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10409 - -lemma sg31038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9986 - -lemma sg31039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10409 - -lemma sg31040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9986 - -lemma sg31041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9963 - -lemma sg31042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9963 - -lemma sg31043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10398 - -lemma sg31044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6597 sg11541 - -lemma sg31045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10399 - -lemma sg31046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9371 - -lemma sg31047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9987 - -lemma sg31048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10165 - -lemma sg31049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9987 - -lemma sg31050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9372 - -lemma sg31051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9964 - -lemma sg31052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9964 - -lemma sg31053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8423 sg10399 - -lemma sg31054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9635 - -lemma sg31055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9958 - -lemma sg31056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9636 - -lemma sg31057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3768 sg14544 - -lemma sg31058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7002 sg11468 - -lemma sg31059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6598 sg11541 - -lemma sg31060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10497 - -lemma sg31061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9370 - -lemma sg31062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10830 - -lemma sg31063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10497 - -lemma sg31064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6599 sg11541 - -lemma sg31065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10410 - -lemma sg31066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10410 - -lemma sg31067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9988 - -lemma sg31068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10410 - -lemma sg31069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9988 - -lemma sg31070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9372 - -lemma sg31071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9965 - -lemma sg31072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9965 - -lemma sg31073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9637 - -lemma sg31074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10401 - -lemma sg31075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9374 - -lemma sg31076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9966 - -lemma sg31077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9966 - -lemma sg31078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9960 - -lemma sg31079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9638 - -lemma sg31080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9636 - -lemma sg31081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9375 - -lemma sg31082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9961 - -lemma sg31083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9639 - -lemma sg31084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8808 sg9304 - -lemma sg31085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7003 sg11468 - -lemma sg31086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6001 sg11833 - -lemma sg31087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9310 - -lemma sg31088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9373 - -lemma sg31089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9989 - -lemma sg31090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8524 sg10166 - -lemma sg31091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9989 - -lemma sg31092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10402 - -lemma sg31093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9310 - -lemma sg31094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9967 - -lemma sg31095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9967 - -lemma sg31096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9310 - -lemma sg31097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9310 - -lemma sg31098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9311 - -lemma sg31099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9311 - -lemma sg31100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8802 sg9311 - -lemma sg31101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9638 - -lemma sg31102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9961 - -lemma sg31103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9639 - -lemma sg31104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9639 - -lemma sg31105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,7,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9990 - -lemma sg31106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,7,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8347 sg10722 - -lemma sg31107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,7,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9991 - -lemma sg31108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,7,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9992 - -lemma sg31109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,8,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9993 - -lemma sg31110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,8,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8648 sg9994 - -lemma sg31111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,9,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8193 sg10863 - -lemma sg31112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg990 sg21108 - -lemma sg31113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1317 sg20976 - -lemma sg31114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg985 sg21111 - -lemma sg31115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg562 sg21250 - -lemma sg31116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg958 sg21139 - -lemma sg31117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg21289 - -lemma sg31118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg21290 - -lemma sg31119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg21291 - -lemma sg31120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg407 sg21292 - -lemma sg31121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg407 sg21293 - -lemma sg31122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1322 sg20965 - -lemma sg31123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1725 sg18245 - -lemma sg31124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1468 sg20938 - -lemma sg31125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1827 sg17124 - -lemma sg31126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2237 sg15536 - -lemma sg31127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2680 sg15022 - -lemma sg31128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg871 sg21144 - -lemma sg31129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3514 sg14694 - -lemma sg31130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg871 sg21145 - -lemma sg31131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg871 sg21146 - -lemma sg31132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg871 sg21147 - -lemma sg31133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg986 sg21111 - -lemma sg31134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1837 sg17110 - -lemma sg31135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1849 sg16208 - -lemma sg31136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2223 sg15550 - -lemma sg31137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2867 sg14864 - -lemma sg31138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5599 sg12609 - -lemma sg31139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg972 sg21125 - -lemma sg31140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8583 sg10105 - -lemma sg31141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg6891 sg11505 - -lemma sg31142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1468 sg20939 - -lemma sg31143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2246 sg15516 - -lemma sg31144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1297 sg20997 - -lemma sg31145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5583 sg12620 - -lemma sg31146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1297 sg20998 - -lemma sg31147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7255 sg11440 - -lemma sg31148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1297 sg20999 - -lemma sg31149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8657 sg9844 - -lemma sg31150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1854 sg16207 - -lemma sg31151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5844 sg11840 - -lemma sg31152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6585 sg11542 - -lemma sg31153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8584 sg10105 - -lemma sg31154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9198 - -lemma sg31155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8736 sg9580 - -lemma sg31156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6586 sg11542 - -lemma sg31157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8585 sg10105 - -lemma sg31158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9199 - -lemma sg31159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9975 - -lemma sg31160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8777 sg9450 - -lemma sg31161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7240 sg11453 - -lemma sg31162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8659 sg9844 - -lemma sg31163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg8650 sg9975 - -lemma sg31164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg8859 sg9162 - -lemma sg31165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,3,3,2] := by - exact rowSquare_join (by decide) sg7232 sg11466 - -lemma sg31166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1726 sg18245 - -lemma sg31167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1837 sg17111 - -lemma sg31168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2206 sg15564 - -lemma sg31169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2238 sg15536 - -lemma sg31170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2681 sg15022 - -lemma sg31171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2868 sg14864 - -lemma sg31172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5566 sg12630 - -lemma sg31173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2667 sg15035 - -lemma sg31174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8453 sg10308 - -lemma sg31175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8386 sg10641 - -lemma sg31176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1829 sg17124 - -lemma sg31177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2239 sg15536 - -lemma sg31178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2682 sg15022 - -lemma sg31179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2869 sg14864 - -lemma sg31180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5567 sg12630 - -lemma sg31181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1298 sg20998 - -lemma sg31182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7249 sg11449 - -lemma sg31183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1298 sg20999 - -lemma sg31184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8660 sg9844 - -lemma sg31185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2683 sg15022 - -lemma sg31186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2361 sg15483 - -lemma sg31187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5845 sg11840 - -lemma sg31188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6587 sg11542 - -lemma sg31189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10403 - -lemma sg31190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9380 - -lemma sg31191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8657 sg9845 - -lemma sg31192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5846 sg11840 - -lemma sg31193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6588 sg11542 - -lemma sg31194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8588 sg10105 - -lemma sg31195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9201 - -lemma sg31196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9975 - -lemma sg31197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8736 sg9581 - -lemma sg31198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10498 - -lemma sg31199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9202 - -lemma sg31200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10831 - -lemma sg31201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10498 - -lemma sg31202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8674 sg9730 - -lemma sg31203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9976 - -lemma sg31204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg8678 sg9662 - -lemma sg31205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1868 sg16190 - -lemma sg31206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3169 sg14805 - -lemma sg31207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3777 sg14542 - -lemma sg31208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5847 sg11840 - -lemma sg31209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6589 sg11542 - -lemma sg31210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8590 sg10105 - -lemma sg31211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9380 - -lemma sg31212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8739 sg9580 - -lemma sg31213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3778 sg14542 - -lemma sg31214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5584 sg12620 - -lemma sg31215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6590 sg11542 - -lemma sg31216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8591 sg10105 - -lemma sg31217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9294 - -lemma sg31218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9975 - -lemma sg31219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8763 sg9495 - -lemma sg31220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6591 sg11542 - -lemma sg31221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8592 sg10105 - -lemma sg31222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9295 - -lemma sg31223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8740 sg9580 - -lemma sg31224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8721 sg9640 - -lemma sg31225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9296 - -lemma sg31226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9977 - -lemma sg31227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8843 sg9199 - -lemma sg31228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8658 sg9846 - -lemma sg31229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9977 - -lemma sg31230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5585 sg12620 - -lemma sg31231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6592 sg11542 - -lemma sg31232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10499 - -lemma sg31233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8400 sg10602 - -lemma sg31234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10832 - -lemma sg31235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10499 - -lemma sg31236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8594 sg10105 - -lemma sg31237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8401 sg10602 - -lemma sg31238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9847 - -lemma sg31239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9583 - -lemma sg31240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8675 sg9729 - -lemma sg31241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9978 - -lemma sg31242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9978 - -lemma sg31243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6893 sg11505 - -lemma sg31244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9979 - -lemma sg31245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9979 - -lemma sg31246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9584 - -lemma sg31247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1838 sg17111 - -lemma sg31248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2207 sg15564 - -lemma sg31249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2240 sg15536 - -lemma sg31250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2684 sg15022 - -lemma sg31251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2876 sg14857 - -lemma sg31252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5570 sg12630 - -lemma sg31253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1299 sg20998 - -lemma sg31254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg7251 sg11449 - -lemma sg31255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1299 sg20999 - -lemma sg31256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8666 sg9844 - -lemma sg31257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2241 sg15536 - -lemma sg31258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3169 sg14806 - -lemma sg31259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3777 sg14543 - -lemma sg31260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5571 sg12630 - -lemma sg31261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5250 sg12695 - -lemma sg31262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10403 - -lemma sg31263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9297 - -lemma sg31264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8660 sg9845 - -lemma sg31265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3766 sg14545 - -lemma sg31266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5848 sg11840 - -lemma sg31267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6593 sg11542 - -lemma sg31268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10405 - -lemma sg31269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9381 - -lemma sg31270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9848 - -lemma sg31271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8737 sg9581 - -lemma sg31272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6594 sg11542 - -lemma sg31273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10500 - -lemma sg31274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9295 - -lemma sg31275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10833 - -lemma sg31276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10500 - -lemma sg31277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9296 - -lemma sg31278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9980 - -lemma sg31279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9641 - -lemma sg31280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg8658 sg9848 - -lemma sg31281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9980 - -lemma sg31282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3171 sg14805 - -lemma sg31283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3767 sg14545 - -lemma sg31284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5849 sg11840 - -lemma sg31285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6595 sg11542 - -lemma sg31286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8595 sg10105 - -lemma sg31287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9381 - -lemma sg31288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8660 sg9846 - -lemma sg31289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8739 sg9581 - -lemma sg31290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5573 sg12630 - -lemma sg31291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6596 sg11542 - -lemma sg31292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10501 - -lemma sg31293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9382 - -lemma sg31294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10834 - -lemma sg31295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10501 - -lemma sg31296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8596 sg10105 - -lemma sg31297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9300 - -lemma sg31298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9977 - -lemma sg31299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9641 - -lemma sg31300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8818 sg9293 - -lemma sg31301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9981 - -lemma sg31302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9981 - -lemma sg31303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6597 sg11542 - -lemma sg31304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10407 - -lemma sg31305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9383 - -lemma sg31306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9850 - -lemma sg31307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9641 - -lemma sg31308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8675 sg9733 - -lemma sg31309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9384 - -lemma sg31310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9982 - -lemma sg31311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9982 - -lemma sg31312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9642 - -lemma sg31313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9979 - -lemma sg31314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9643 - -lemma sg31315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3768 sg14545 - -lemma sg31316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5586 sg12620 - -lemma sg31317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6598 sg11542 - -lemma sg31318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8597 sg10105 - -lemma sg31319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9382 - -lemma sg31320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8765 sg9494 - -lemma sg31321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8819 sg9293 - -lemma sg31322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6599 sg11542 - -lemma sg31323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8598 sg10105 - -lemma sg31324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9383 - -lemma sg31325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9977 - -lemma sg31326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8819 sg9294 - -lemma sg31327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9384 - -lemma sg31328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9983 - -lemma sg31329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9983 - -lemma sg31330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8819 sg9296 - -lemma sg31331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10408 - -lemma sg31332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9304 - -lemma sg31333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9984 - -lemma sg31334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9984 - -lemma sg31335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9979 - -lemma sg31336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9642 - -lemma sg31337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9643 - -lemma sg31338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8402 sg10602 - -lemma sg31339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9855 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes51 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 + +namespace OAI + +/-! Semigroup Nodes 76. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg30940 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9958 + +lemma sg30941 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10393 + +lemma sg30942 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9634 + +lemma sg30943 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14520 + +lemma sg30944 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3773 sg14542 + +lemma sg30945 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6953 sg11476 + +lemma sg30946 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6582 sg11542 + +lemma sg30947 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9301 + +lemma sg30948 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9366 + +lemma sg30949 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9293 + +lemma sg30950 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9557 + +lemma sg30951 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6954 sg11476 + +lemma sg30952 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6583 sg11542 + +lemma sg30953 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10494 + +lemma sg30954 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9301 + +lemma sg30955 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10827 + +lemma sg30956 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10494 + +lemma sg30957 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9303 + +lemma sg30958 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9368 + +lemma sg30959 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9983 + +lemma sg30960 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10163 + +lemma sg30961 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9983 + +lemma sg30962 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9959 + +lemma sg30963 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9959 + +lemma sg30964 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10394 + +lemma sg30965 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6584 sg11542 + +lemma sg30966 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10408 + +lemma sg30967 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10408 + +lemma sg30968 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9984 + +lemma sg30969 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10408 + +lemma sg30970 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9984 + +lemma sg30971 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9303 + +lemma sg30972 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9960 + +lemma sg30973 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9960 + +lemma sg30974 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10395 + +lemma sg30975 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9302 + +lemma sg30976 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9303 + +lemma sg30977 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9303 + +lemma sg30978 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10396 + +lemma sg30979 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9304 + +lemma sg30980 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9961 + +lemma sg30981 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9961 + +lemma sg30982 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10396 + +lemma sg30983 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9304 + +lemma sg30984 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9304 + +lemma sg30985 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,5,5,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9562 + +lemma sg30986 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1831 sg17122 + +lemma sg30987 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2199 sg15571 + +lemma sg30988 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2240 sg15534 + +lemma sg30989 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3891 sg14510 + +lemma sg30990 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2874 sg14857 + +lemma sg30991 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6996 sg11469 + +lemma sg30992 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5594 sg12611 + +lemma sg30993 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8805 sg9297 + +lemma sg30994 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8586 sg10101 + +lemma sg30995 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8666 sg9810 + +lemma sg30996 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2241 sg15534 + +lemma sg30997 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3892 sg14510 + +lemma sg30998 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3771 sg14543 + +lemma sg30999 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6997 sg11469 + +lemma sg31000 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5994 sg11834 + +lemma sg31001 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10390 + +lemma sg31002 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8806 sg9297 + +lemma sg31003 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8660 sg9815 + +lemma sg31004 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3766 sg14544 + +lemma sg31005 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6998 sg11469 + +lemma sg31006 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6593 sg11541 + +lemma sg31007 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10397 + +lemma sg31008 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9369 + +lemma sg31009 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8807 sg9297 + +lemma sg31010 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8737 sg9558 + +lemma sg31011 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6594 sg11541 + +lemma sg31012 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10495 + +lemma sg31013 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9266 + +lemma sg31014 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10828 + +lemma sg31015 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10495 + +lemma sg31016 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9267 + +lemma sg31017 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9985 + +lemma sg31018 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10164 + +lemma sg31019 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9985 + +lemma sg31020 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9962 + +lemma sg31021 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,3,3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10397 + +lemma sg31022 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3893 sg14510 + +lemma sg31023 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3767 sg14544 + +lemma sg31024 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6999 sg11469 + +lemma sg31025 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6595 sg11541 + +lemma sg31026 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10391 + +lemma sg31027 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9369 + +lemma sg31028 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9297 + +lemma sg31029 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9558 + +lemma sg31030 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7000 sg11469 + +lemma sg31031 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6596 sg11541 + +lemma sg31032 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10496 + +lemma sg31033 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9370 + +lemma sg31034 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10829 + +lemma sg31035 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10496 + +lemma sg31036 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10409 + +lemma sg31037 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10409 + +lemma sg31038 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9986 + +lemma sg31039 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10409 + +lemma sg31040 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9986 + +lemma sg31041 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9963 + +lemma sg31042 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9963 + +lemma sg31043 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10398 + +lemma sg31044 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6597 sg11541 + +lemma sg31045 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10399 + +lemma sg31046 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9371 + +lemma sg31047 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9987 + +lemma sg31048 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10165 + +lemma sg31049 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9987 + +lemma sg31050 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9372 + +lemma sg31051 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9964 + +lemma sg31052 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9964 + +lemma sg31053 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8423 sg10399 + +lemma sg31054 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9635 + +lemma sg31055 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9958 + +lemma sg31056 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9636 + +lemma sg31057 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3768 sg14544 + +lemma sg31058 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7002 sg11468 + +lemma sg31059 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6598 sg11541 + +lemma sg31060 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10497 + +lemma sg31061 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9370 + +lemma sg31062 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10830 + +lemma sg31063 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10497 + +lemma sg31064 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6599 sg11541 + +lemma sg31065 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10410 + +lemma sg31066 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10410 + +lemma sg31067 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9988 + +lemma sg31068 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10410 + +lemma sg31069 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9988 + +lemma sg31070 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9372 + +lemma sg31071 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9965 + +lemma sg31072 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9965 + +lemma sg31073 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9637 + +lemma sg31074 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10401 + +lemma sg31075 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9374 + +lemma sg31076 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9966 + +lemma sg31077 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9966 + +lemma sg31078 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9960 + +lemma sg31079 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9638 + +lemma sg31080 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9636 + +lemma sg31081 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9375 + +lemma sg31082 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9961 + +lemma sg31083 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9639 + +lemma sg31084 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8808 sg9304 + +lemma sg31085 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7003 sg11468 + +lemma sg31086 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6001 sg11833 + +lemma sg31087 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9310 + +lemma sg31088 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9373 + +lemma sg31089 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9989 + +lemma sg31090 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8524 sg10166 + +lemma sg31091 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9989 + +lemma sg31092 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10402 + +lemma sg31093 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9310 + +lemma sg31094 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9967 + +lemma sg31095 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9967 + +lemma sg31096 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9310 + +lemma sg31097 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9310 + +lemma sg31098 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9311 + +lemma sg31099 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9311 + +lemma sg31100 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8802 sg9311 + +lemma sg31101 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9638 + +lemma sg31102 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9961 + +lemma sg31103 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9639 + +lemma sg31104 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,6,6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9639 + +lemma sg31105 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,7,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9990 + +lemma sg31106 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,7,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8347 sg10722 + +lemma sg31107 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,7,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9991 + +lemma sg31108 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,7,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9992 + +lemma sg31109 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,8,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9993 + +lemma sg31110 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,8,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8648 sg9994 + +lemma sg31111 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,9,9,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8193 sg10863 + +lemma sg31112 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg990 sg21108 + +lemma sg31113 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1317 sg20976 + +lemma sg31114 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg985 sg21111 + +lemma sg31115 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg562 sg21250 + +lemma sg31116 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg958 sg21139 + +lemma sg31117 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg21289 + +lemma sg31118 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg21290 + +lemma sg31119 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg21291 + +lemma sg31120 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg407 sg21292 + +lemma sg31121 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,2,2,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg407 sg21293 + +lemma sg31122 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1322 sg20965 + +lemma sg31123 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1725 sg18245 + +lemma sg31124 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1468 sg20938 + +lemma sg31125 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1827 sg17124 + +lemma sg31126 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2237 sg15536 + +lemma sg31127 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2680 sg15022 + +lemma sg31128 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg871 sg21144 + +lemma sg31129 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3514 sg14694 + +lemma sg31130 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg871 sg21145 + +lemma sg31131 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg871 sg21146 + +lemma sg31132 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg871 sg21147 + +lemma sg31133 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg986 sg21111 + +lemma sg31134 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1837 sg17110 + +lemma sg31135 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1849 sg16208 + +lemma sg31136 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2223 sg15550 + +lemma sg31137 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2867 sg14864 + +lemma sg31138 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5599 sg12609 + +lemma sg31139 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg972 sg21125 + +lemma sg31140 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8583 sg10105 + +lemma sg31141 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg6891 sg11505 + +lemma sg31142 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1468 sg20939 + +lemma sg31143 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2246 sg15516 + +lemma sg31144 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1297 sg20997 + +lemma sg31145 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5583 sg12620 + +lemma sg31146 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1297 sg20998 + +lemma sg31147 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7255 sg11440 + +lemma sg31148 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1297 sg20999 + +lemma sg31149 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8657 sg9844 + +lemma sg31150 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1854 sg16207 + +lemma sg31151 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5844 sg11840 + +lemma sg31152 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6585 sg11542 + +lemma sg31153 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8584 sg10105 + +lemma sg31154 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9198 + +lemma sg31155 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8736 sg9580 + +lemma sg31156 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6586 sg11542 + +lemma sg31157 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8585 sg10105 + +lemma sg31158 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9199 + +lemma sg31159 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9975 + +lemma sg31160 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8777 sg9450 + +lemma sg31161 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7240 sg11453 + +lemma sg31162 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8659 sg9844 + +lemma sg31163 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg8650 sg9975 + +lemma sg31164 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg8859 sg9162 + +lemma sg31165 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,3,3,3,3,3,3,3,2] := by + exact rowSquare_join (by decide) sg7232 sg11466 + +lemma sg31166 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1726 sg18245 + +lemma sg31167 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1837 sg17111 + +lemma sg31168 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2206 sg15564 + +lemma sg31169 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2238 sg15536 + +lemma sg31170 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2681 sg15022 + +lemma sg31171 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2868 sg14864 + +lemma sg31172 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5566 sg12630 + +lemma sg31173 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2667 sg15035 + +lemma sg31174 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8453 sg10308 + +lemma sg31175 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,2,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8386 sg10641 + +lemma sg31176 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1829 sg17124 + +lemma sg31177 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2239 sg15536 + +lemma sg31178 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2682 sg15022 + +lemma sg31179 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2869 sg14864 + +lemma sg31180 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5567 sg12630 + +lemma sg31181 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1298 sg20998 + +lemma sg31182 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7249 sg11449 + +lemma sg31183 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1298 sg20999 + +lemma sg31184 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8660 sg9844 + +lemma sg31185 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2683 sg15022 + +lemma sg31186 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2361 sg15483 + +lemma sg31187 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5845 sg11840 + +lemma sg31188 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6587 sg11542 + +lemma sg31189 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10403 + +lemma sg31190 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9380 + +lemma sg31191 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8657 sg9845 + +lemma sg31192 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5846 sg11840 + +lemma sg31193 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6588 sg11542 + +lemma sg31194 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8588 sg10105 + +lemma sg31195 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9201 + +lemma sg31196 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9975 + +lemma sg31197 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8736 sg9581 + +lemma sg31198 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10498 + +lemma sg31199 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9202 + +lemma sg31200 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10831 + +lemma sg31201 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10498 + +lemma sg31202 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8674 sg9730 + +lemma sg31203 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9976 + +lemma sg31204 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,3,3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg8678 sg9662 + +lemma sg31205 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1868 sg16190 + +lemma sg31206 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3169 sg14805 + +lemma sg31207 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3777 sg14542 + +lemma sg31208 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5847 sg11840 + +lemma sg31209 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6589 sg11542 + +lemma sg31210 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8590 sg10105 + +lemma sg31211 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9380 + +lemma sg31212 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8739 sg9580 + +lemma sg31213 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3778 sg14542 + +lemma sg31214 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5584 sg12620 + +lemma sg31215 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6590 sg11542 + +lemma sg31216 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8591 sg10105 + +lemma sg31217 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9294 + +lemma sg31218 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9975 + +lemma sg31219 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8763 sg9495 + +lemma sg31220 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6591 sg11542 + +lemma sg31221 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8592 sg10105 + +lemma sg31222 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9295 + +lemma sg31223 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8740 sg9580 + +lemma sg31224 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8721 sg9640 + +lemma sg31225 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9296 + +lemma sg31226 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9977 + +lemma sg31227 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8843 sg9199 + +lemma sg31228 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8658 sg9846 + +lemma sg31229 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9977 + +lemma sg31230 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5585 sg12620 + +lemma sg31231 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6592 sg11542 + +lemma sg31232 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10499 + +lemma sg31233 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8400 sg10602 + +lemma sg31234 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10832 + +lemma sg31235 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10499 + +lemma sg31236 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8594 sg10105 + +lemma sg31237 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8401 sg10602 + +lemma sg31238 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9847 + +lemma sg31239 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9583 + +lemma sg31240 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8675 sg9729 + +lemma sg31241 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9978 + +lemma sg31242 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9978 + +lemma sg31243 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6893 sg11505 + +lemma sg31244 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9979 + +lemma sg31245 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9979 + +lemma sg31246 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,4,4,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9584 + +lemma sg31247 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1838 sg17111 + +lemma sg31248 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2207 sg15564 + +lemma sg31249 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2240 sg15536 + +lemma sg31250 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2684 sg15022 + +lemma sg31251 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2876 sg14857 + +lemma sg31252 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5570 sg12630 + +lemma sg31253 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1299 sg20998 + +lemma sg31254 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg7251 sg11449 + +lemma sg31255 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1299 sg20999 + +lemma sg31256 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8666 sg9844 + +lemma sg31257 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2241 sg15536 + +lemma sg31258 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3169 sg14806 + +lemma sg31259 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3777 sg14543 + +lemma sg31260 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5571 sg12630 + +lemma sg31261 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5250 sg12695 + +lemma sg31262 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10403 + +lemma sg31263 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9297 + +lemma sg31264 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8660 sg9845 + +lemma sg31265 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3766 sg14545 + +lemma sg31266 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5848 sg11840 + +lemma sg31267 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6593 sg11542 + +lemma sg31268 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10405 + +lemma sg31269 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9381 + +lemma sg31270 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9848 + +lemma sg31271 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8737 sg9581 + +lemma sg31272 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6594 sg11542 + +lemma sg31273 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10500 + +lemma sg31274 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9295 + +lemma sg31275 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10833 + +lemma sg31276 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10500 + +lemma sg31277 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9296 + +lemma sg31278 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9980 + +lemma sg31279 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9641 + +lemma sg31280 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg8658 sg9848 + +lemma sg31281 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,3,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9980 + +lemma sg31282 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3171 sg14805 + +lemma sg31283 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3767 sg14545 + +lemma sg31284 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5849 sg11840 + +lemma sg31285 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6595 sg11542 + +lemma sg31286 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8595 sg10105 + +lemma sg31287 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9381 + +lemma sg31288 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8660 sg9846 + +lemma sg31289 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8739 sg9581 + +lemma sg31290 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5573 sg12630 + +lemma sg31291 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6596 sg11542 + +lemma sg31292 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10501 + +lemma sg31293 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9382 + +lemma sg31294 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10834 + +lemma sg31295 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10501 + +lemma sg31296 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8596 sg10105 + +lemma sg31297 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9300 + +lemma sg31298 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9977 + +lemma sg31299 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9641 + +lemma sg31300 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8818 sg9293 + +lemma sg31301 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9981 + +lemma sg31302 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9981 + +lemma sg31303 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6597 sg11542 + +lemma sg31304 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10407 + +lemma sg31305 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9383 + +lemma sg31306 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9850 + +lemma sg31307 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9641 + +lemma sg31308 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8675 sg9733 + +lemma sg31309 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9384 + +lemma sg31310 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9982 + +lemma sg31311 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9982 + +lemma sg31312 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9642 + +lemma sg31313 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9979 + +lemma sg31314 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9643 + +lemma sg31315 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3768 sg14545 + +lemma sg31316 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5586 sg12620 + +lemma sg31317 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6598 sg11542 + +lemma sg31318 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8597 sg10105 + +lemma sg31319 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9382 + +lemma sg31320 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8765 sg9494 + +lemma sg31321 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8819 sg9293 + +lemma sg31322 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6599 sg11542 + +lemma sg31323 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8598 sg10105 + +lemma sg31324 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9383 + +lemma sg31325 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9977 + +lemma sg31326 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8819 sg9294 + +lemma sg31327 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9384 + +lemma sg31328 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9983 + +lemma sg31329 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9983 + +lemma sg31330 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8819 sg9296 + +lemma sg31331 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10408 + +lemma sg31332 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9304 + +lemma sg31333 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9984 + +lemma sg31334 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9984 + +lemma sg31335 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9979 + +lemma sg31336 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9642 + +lemma sg31337 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9643 + +lemma sg31338 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8402 sg10602 + +lemma sg31339 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9855 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes77.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes77.lean index 2d7c8ba93be200f3677e0fbc28ebbf06370f38f7..a45b9cddfa2a6973d93f06f75d06ba01d9354acd 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes77.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes77.lean @@ -1,1222 +1,1222 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 - -namespace OAI - -/-! Semigroup Nodes 77. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg31340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9642 - -lemma sg31341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9590 - -lemma sg31342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2208 sg15564 - -lemma sg31343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2242 sg15536 - -lemma sg31344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3170 sg14806 - -lemma sg31345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3779 sg14543 - -lemma sg31346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5574 sg12630 - -lemma sg31347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5264 sg12693 - -lemma sg31348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8603 sg10088 - -lemma sg31349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9297 - -lemma sg31350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8666 sg9845 - -lemma sg31351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3171 sg14806 - -lemma sg31352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3780 sg14543 - -lemma sg31353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5575 sg12630 - -lemma sg31354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6600 sg11542 - -lemma sg31355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10405 - -lemma sg31356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9305 - -lemma sg31357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8660 sg9848 - -lemma sg31358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8742 sg9581 - -lemma sg31359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5850 sg11840 - -lemma sg31360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6601 sg11542 - -lemma sg31361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8254 sg10849 - -lemma sg31362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9385 - -lemma sg31363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9856 - -lemma sg31364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8817 sg9297 - -lemma sg31365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8453 sg10317 - -lemma sg31366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8816 sg9300 - -lemma sg31367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9980 - -lemma sg31368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9591 - -lemma sg31369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg8818 sg9297 - -lemma sg31370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9985 - -lemma sg31371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9985 - -lemma sg31372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3781 sg14543 - -lemma sg31373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5851 sg11840 - -lemma sg31374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6602 sg11542 - -lemma sg31375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10502 - -lemma sg31376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9385 - -lemma sg31377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8660 sg9849 - -lemma sg31378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10502 - -lemma sg31379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6603 sg11542 - -lemma sg31380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10409 - -lemma sg31381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9386 - -lemma sg31382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9980 - -lemma sg31383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8817 sg9298 - -lemma sg31384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8815 sg9307 - -lemma sg31385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9986 - -lemma sg31386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9986 - -lemma sg31387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9644 - -lemma sg31388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8258 sg10849 - -lemma sg31389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9387 - -lemma sg31390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9987 - -lemma sg31391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9987 - -lemma sg31392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9982 - -lemma sg31393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9645 - -lemma sg31394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9592 - -lemma sg31395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5852 sg11840 - -lemma sg31396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6604 sg11542 - -lemma sg31397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8259 sg10849 - -lemma sg31398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9386 - -lemma sg31399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8660 sg9852 - -lemma sg31400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8819 sg9298 - -lemma sg31401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10410 - -lemma sg31402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9388 - -lemma sg31403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9988 - -lemma sg31404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9988 - -lemma sg31405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9983 - -lemma sg31406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9646 - -lemma sg31407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9389 - -lemma sg31408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9984 - -lemma sg31409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9647 - -lemma sg31410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9645 - -lemma sg31411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8657 sg9862 - -lemma sg31412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8736 sg9593 - -lemma sg31413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6605 sg11542 - -lemma sg31414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8606 sg10087 - -lemma sg31415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9388 - -lemma sg31416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9989 - -lemma sg31417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9989 - -lemma sg31418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9389 - -lemma sg31419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9983 - -lemma sg31420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8819 sg9302 - -lemma sg31421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9646 - -lemma sg31422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg9984 - -lemma sg31423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9647 - -lemma sg31424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8722 sg9647 - -lemma sg31425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,5,5,5,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10428 - -lemma sg31426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,5,5,5,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9995 - -lemma sg31427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,5,5,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8399 sg10611 - -lemma sg31428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,5,5,5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8382 sg10655 - -lemma sg31429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,5,5,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8529 sg10156 - -lemma sg31430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10440 - -lemma sg31431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9997 - -lemma sg31432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10441 - -lemma sg31433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9998 - -lemma sg31434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10351 - -lemma sg31435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9995 - -lemma sg31436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9995 - -lemma sg31437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8384 sg10655 - -lemma sg31438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8531 sg10156 - -lemma sg31439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10444 - -lemma sg31440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg9999 - -lemma sg31441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10446 - -lemma sg31442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10000 - -lemma sg31443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9339 - -lemma sg31444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9339 - -lemma sg31445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9339 - -lemma sg31446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10447 - -lemma sg31447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10001 - -lemma sg31448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9340 - -lemma sg31449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9340 - -lemma sg31450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9340 - -lemma sg31451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9995 - -lemma sg31452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9648 - -lemma sg31453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8534 sg10156 - -lemma sg31454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14521 - -lemma sg31455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11349 - -lemma sg31456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8827 sg9256 - -lemma sg31457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9327 - -lemma sg31458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10448 - -lemma sg31459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10002 - -lemma sg31460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10449 - -lemma sg31461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10003 - -lemma sg31462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9341 - -lemma sg31463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9341 - -lemma sg31464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9341 - -lemma sg31465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8828 sg9258 - -lemma sg31466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8872 sg9108 - -lemma sg31467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9342 - -lemma sg31468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9342 - -lemma sg31469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9342 - -lemma sg31470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8797 sg9342 - -lemma sg31471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8828 sg9259 - -lemma sg31472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8872 sg9109 - -lemma sg31473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8721 sg9648 - -lemma sg31474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8871 sg9110 - -lemma sg31475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8828 sg9260 - -lemma sg31476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8872 sg9110 - -lemma sg31477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10458 - -lemma sg31478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10004 - -lemma sg31479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10460 - -lemma sg31480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10005 - -lemma sg31481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9349 - -lemma sg31482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9997 - -lemma sg31483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9997 - -lemma sg31484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10461 - -lemma sg31485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10006 - -lemma sg31486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9350 - -lemma sg31487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9998 - -lemma sg31488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9998 - -lemma sg31489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8726 sg9605 - -lemma sg31490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8727 sg9605 - -lemma sg31491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10464 - -lemma sg31492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10007 - -lemma sg31493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9354 - -lemma sg31494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg9999 - -lemma sg31495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg9999 - -lemma sg31496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14522 - -lemma sg31497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11350 - -lemma sg31498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10438 - -lemma sg31499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9331 - -lemma sg31500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10465 - -lemma sg31501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10008 - -lemma sg31502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10466 - -lemma sg31503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10009 - -lemma sg31504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9356 - -lemma sg31505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10000 - -lemma sg31506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg10000 - -lemma sg31507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9997 - -lemma sg31508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9649 - -lemma sg31509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10447 - -lemma sg31510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9357 - -lemma sg31511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10001 - -lemma sg31512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg10001 - -lemma sg31513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg9998 - -lemma sg31514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8720 sg9650 - -lemma sg31515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4576 sg13500 - -lemma sg31516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6993 sg11471 - -lemma sg31517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6953 sg11477 - -lemma sg31518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10523 - -lemma sg31519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9393 - -lemma sg31520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10835 - -lemma sg31521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10523 - -lemma sg31522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10467 - -lemma sg31523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10010 - -lemma sg31524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9358 - -lemma sg31525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10002 - -lemma sg31526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg10002 - -lemma sg31527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10449 - -lemma sg31528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9359 - -lemma sg31529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10003 - -lemma sg31530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg10003 - -lemma sg31531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9341 - -lemma sg31532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9342 - -lemma sg31533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9342 - -lemma sg31534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8832 sg9260 - -lemma sg31535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10474 - -lemma sg31536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,4,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10012 - -lemma sg31537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10477 - -lemma sg31538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10013 - -lemma sg31539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9372 - -lemma sg31540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10004 - -lemma sg31541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,4,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg10004 - -lemma sg31542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3875 sg14523 - -lemma sg31543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6953 sg11478 - -lemma sg31544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9348 - -lemma sg31545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9343 - -lemma sg31546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10478 - -lemma sg31547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10014 - -lemma sg31548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10479 - -lemma sg31549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10015 - -lemma sg31550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9374 - -lemma sg31551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10005 - -lemma sg31552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg10005 - -lemma sg31553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9349 - -lemma sg31554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10461 - -lemma sg31555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9375 - -lemma sg31556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10006 - -lemma sg31557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg10006 - -lemma sg31558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9350 - -lemma sg31559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3889 sg14517 - -lemma sg31560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6602 sg11543 - -lemma sg31561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10456 - -lemma sg31562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9345 - -lemma sg31563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10481 - -lemma sg31564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10016 - -lemma sg31565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10482 - -lemma sg31566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10017 - -lemma sg31567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9376 - -lemma sg31568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10007 - -lemma sg31569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8650 sg10007 - -lemma sg31570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg10004 - -lemma sg31571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4577 sg13500 - -lemma sg31572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6604 sg11543 - -lemma sg31573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8166 sg11054 - -lemma sg31574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10531 - -lemma sg31575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9402 - -lemma sg31576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10836 - -lemma sg31577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg8415 sg10531 - -lemma sg31578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10483 - -lemma sg31579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10018 - -lemma sg31580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9377 - -lemma sg31581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10008 - -lemma sg31582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10466 - -lemma sg31583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9378 - -lemma sg31584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10009 - -lemma sg31585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg10005 - -lemma sg31586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9405 - -lemma sg31587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg10006 - -lemma sg31588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6605 sg11543 - -lemma sg31589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8167 sg11054 - -lemma sg31590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10484 - -lemma sg31591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10484 - -lemma sg31592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10019 - -lemma sg31593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8418 sg10484 - -lemma sg31594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10467 - -lemma sg31595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9379 - -lemma sg31596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10010 - -lemma sg31597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9358 - -lemma sg31598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9359 - -lemma sg31599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9359 - -lemma sg31600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8652 sg10006 - -lemma sg31601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,9,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10490 - -lemma sg31602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,9,4,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10020 - -lemma sg31603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,9,4,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9384 - -lemma sg31604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,9,4,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10012 - -lemma sg31605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3893 sg14520 - -lemma sg31606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6999 sg11476 - -lemma sg31607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9382 - -lemma sg31608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9380 - -lemma sg31609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9384 - -lemma sg31610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10021 - -lemma sg31611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10499 - -lemma sg31612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10022 - -lemma sg31613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9384 - -lemma sg31614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10020 - -lemma sg31615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8801 sg9384 - -lemma sg31616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10504 - -lemma sg31617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10023 - -lemma sg31618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10505 - -lemma sg31619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10024 - -lemma sg31620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8434 sg10428 - -lemma sg31621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8723 sg9648 - -lemma sg31622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8399 sg10655 - -lemma sg31623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10507 - -lemma sg31624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10025 - -lemma sg31625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10508 - -lemma sg31626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10026 - -lemma sg31627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9394 - -lemma sg31628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10023 - -lemma sg31629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10509 - -lemma sg31630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10027 - -lemma sg31631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9395 - -lemma sg31632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10024 - -lemma sg31633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8726 sg9648 - -lemma sg31634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10510 - -lemma sg31635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10028 - -lemma sg31636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9396 - -lemma sg31637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9396 - -lemma sg31638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5144 sg12697 - -lemma sg31639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8769 sg9594 - -lemma sg31640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10503 - -lemma sg31641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9390 - -lemma sg31642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10511 - -lemma sg31643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10029 - -lemma sg31644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10512 - -lemma sg31645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10030 - -lemma sg31646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9397 - -lemma sg31647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9397 - -lemma sg31648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg10023 - -lemma sg31649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9398 - -lemma sg31650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9398 - -lemma sg31651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9398 - -lemma sg31652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8651 sg10024 - -lemma sg31653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10384 - -lemma sg31654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8770 sg9594 - -lemma sg31655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7456 sg11349 - -lemma sg31656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10549 - -lemma sg31657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9423 - -lemma sg31658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10837 - -lemma sg31659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10513 - -lemma sg31660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10031 - -lemma sg31661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9399 - -lemma sg31662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9399 - -lemma sg31663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9400 - -lemma sg31664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9400 - -lemma sg31665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8796 sg9400 - -lemma sg31666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8871 sg9155 - -lemma sg31667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10515 - -lemma sg31668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,4,4,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10032 - -lemma sg31669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10517 - -lemma sg31670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10033 - -lemma sg31671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9403 - -lemma sg31672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,4,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10025 - -lemma sg31673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5144 sg12698 - -lemma sg31674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11352 - -lemma sg31675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9393 - -lemma sg31676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9391 - -lemma sg31677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10518 - -lemma sg31678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10034 - -lemma sg31679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10519 - -lemma sg31680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10035 - -lemma sg31681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9404 - -lemma sg31682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10026 - -lemma sg31683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10509 - -lemma sg31684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9405 - -lemma sg31685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10027 - -lemma sg31686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3889 sg14522 - -lemma sg31687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11353 - -lemma sg31688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10506 - -lemma sg31689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9392 - -lemma sg31690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10520 - -lemma sg31691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10036 - -lemma sg31692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10521 - -lemma sg31693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10037 - -lemma sg31694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9406 - -lemma sg31695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8649 sg10028 - -lemma sg31696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4576 sg13502 - -lemma sg31697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11354 - -lemma sg31698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8166 sg11055 - -lemma sg31699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10552 - -lemma sg31700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9426 - -lemma sg31701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10838 - -lemma sg31702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10522 - -lemma sg31703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10038 - -lemma sg31704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9407 - -lemma sg31705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10512 - -lemma sg31706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9408 - -lemma sg31707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9429 - -lemma sg31708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11355 - -lemma sg31709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8167 sg11055 - -lemma sg31710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10523 - -lemma sg31711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10523 - -lemma sg31712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10039 - -lemma sg31713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10513 - -lemma sg31714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9409 - -lemma sg31715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9400 - -lemma sg31716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10525 - -lemma sg31717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,4,4,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10040 - -lemma sg31718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,4,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9412 - -lemma sg31719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3889 sg14523 - -lemma sg31720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11356 - -lemma sg31721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10514 - -lemma sg31722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9401 - -lemma sg31723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10526 - -lemma sg31724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10041 - -lemma sg31725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10527 - -lemma sg31726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10042 - -lemma sg31727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9413 - -lemma sg31728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4576 sg13503 - -lemma sg31729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11357 - -lemma sg31730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8168 sg11054 - -lemma sg31731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10556 - -lemma sg31732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9434 - -lemma sg31733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10839 - -lemma sg31734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10528 - -lemma sg31735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9414 - -lemma sg31736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10519 - -lemma sg31737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9415 - -lemma sg31738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9405 - -lemma sg31739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3895 sg14522 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes32 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes37 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes21 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes24 + +namespace OAI + +/-! Semigroup Nodes 77. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg31340 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9642 + +lemma sg31341 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,5,5,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9590 + +lemma sg31342 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2208 sg15564 + +lemma sg31343 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2242 sg15536 + +lemma sg31344 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3170 sg14806 + +lemma sg31345 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3779 sg14543 + +lemma sg31346 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5574 sg12630 + +lemma sg31347 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5264 sg12693 + +lemma sg31348 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8603 sg10088 + +lemma sg31349 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9297 + +lemma sg31350 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8666 sg9845 + +lemma sg31351 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3171 sg14806 + +lemma sg31352 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3780 sg14543 + +lemma sg31353 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5575 sg12630 + +lemma sg31354 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6600 sg11542 + +lemma sg31355 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10405 + +lemma sg31356 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9305 + +lemma sg31357 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8660 sg9848 + +lemma sg31358 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8742 sg9581 + +lemma sg31359 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5850 sg11840 + +lemma sg31360 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6601 sg11542 + +lemma sg31361 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8254 sg10849 + +lemma sg31362 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9385 + +lemma sg31363 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9856 + +lemma sg31364 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8817 sg9297 + +lemma sg31365 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8453 sg10317 + +lemma sg31366 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8816 sg9300 + +lemma sg31367 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9980 + +lemma sg31368 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9591 + +lemma sg31369 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg8818 sg9297 + +lemma sg31370 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9985 + +lemma sg31371 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9985 + +lemma sg31372 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3781 sg14543 + +lemma sg31373 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5851 sg11840 + +lemma sg31374 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6602 sg11542 + +lemma sg31375 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10502 + +lemma sg31376 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9385 + +lemma sg31377 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8660 sg9849 + +lemma sg31378 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10502 + +lemma sg31379 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6603 sg11542 + +lemma sg31380 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10409 + +lemma sg31381 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9386 + +lemma sg31382 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9980 + +lemma sg31383 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8817 sg9298 + +lemma sg31384 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8815 sg9307 + +lemma sg31385 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9986 + +lemma sg31386 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9986 + +lemma sg31387 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9644 + +lemma sg31388 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8258 sg10849 + +lemma sg31389 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9387 + +lemma sg31390 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9987 + +lemma sg31391 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9987 + +lemma sg31392 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9982 + +lemma sg31393 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9645 + +lemma sg31394 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9592 + +lemma sg31395 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5852 sg11840 + +lemma sg31396 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6604 sg11542 + +lemma sg31397 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8259 sg10849 + +lemma sg31398 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9386 + +lemma sg31399 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8660 sg9852 + +lemma sg31400 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8819 sg9298 + +lemma sg31401 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10410 + +lemma sg31402 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9388 + +lemma sg31403 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9988 + +lemma sg31404 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9988 + +lemma sg31405 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9983 + +lemma sg31406 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9646 + +lemma sg31407 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9389 + +lemma sg31408 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9984 + +lemma sg31409 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9647 + +lemma sg31410 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9645 + +lemma sg31411 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8657 sg9862 + +lemma sg31412 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8736 sg9593 + +lemma sg31413 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6605 sg11542 + +lemma sg31414 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8606 sg10087 + +lemma sg31415 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9388 + +lemma sg31416 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9989 + +lemma sg31417 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9989 + +lemma sg31418 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9389 + +lemma sg31419 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9983 + +lemma sg31420 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8819 sg9302 + +lemma sg31421 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9646 + +lemma sg31422 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg9984 + +lemma sg31423 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9647 + +lemma sg31424 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [10,10,6,6,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8722 sg9647 + +lemma sg31425 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,5,5,5,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10428 + +lemma sg31426 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,5,5,5,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9995 + +lemma sg31427 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,5,5,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8399 sg10611 + +lemma sg31428 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,5,5,5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8382 sg10655 + +lemma sg31429 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,5,5,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8529 sg10156 + +lemma sg31430 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10440 + +lemma sg31431 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9997 + +lemma sg31432 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10441 + +lemma sg31433 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9998 + +lemma sg31434 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10351 + +lemma sg31435 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9995 + +lemma sg31436 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9995 + +lemma sg31437 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8384 sg10655 + +lemma sg31438 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,5,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8531 sg10156 + +lemma sg31439 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10444 + +lemma sg31440 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg9999 + +lemma sg31441 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10446 + +lemma sg31442 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10000 + +lemma sg31443 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9339 + +lemma sg31444 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9339 + +lemma sg31445 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9339 + +lemma sg31446 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10447 + +lemma sg31447 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10001 + +lemma sg31448 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9340 + +lemma sg31449 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9340 + +lemma sg31450 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9340 + +lemma sg31451 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9995 + +lemma sg31452 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9648 + +lemma sg31453 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,5,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8534 sg10156 + +lemma sg31454 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14521 + +lemma sg31455 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11349 + +lemma sg31456 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8827 sg9256 + +lemma sg31457 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9327 + +lemma sg31458 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10448 + +lemma sg31459 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10002 + +lemma sg31460 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10449 + +lemma sg31461 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10003 + +lemma sg31462 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9341 + +lemma sg31463 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9341 + +lemma sg31464 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9341 + +lemma sg31465 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8828 sg9258 + +lemma sg31466 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8872 sg9108 + +lemma sg31467 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9342 + +lemma sg31468 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9342 + +lemma sg31469 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9342 + +lemma sg31470 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8797 sg9342 + +lemma sg31471 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8828 sg9259 + +lemma sg31472 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8872 sg9109 + +lemma sg31473 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8721 sg9648 + +lemma sg31474 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8871 sg9110 + +lemma sg31475 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8828 sg9260 + +lemma sg31476 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,6,6,6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8872 sg9110 + +lemma sg31477 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10458 + +lemma sg31478 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10004 + +lemma sg31479 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10460 + +lemma sg31480 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10005 + +lemma sg31481 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9349 + +lemma sg31482 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9997 + +lemma sg31483 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9997 + +lemma sg31484 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10461 + +lemma sg31485 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10006 + +lemma sg31486 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9350 + +lemma sg31487 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9998 + +lemma sg31488 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9998 + +lemma sg31489 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8726 sg9605 + +lemma sg31490 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,5,5,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8727 sg9605 + +lemma sg31491 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10464 + +lemma sg31492 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10007 + +lemma sg31493 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9354 + +lemma sg31494 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg9999 + +lemma sg31495 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg9999 + +lemma sg31496 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14522 + +lemma sg31497 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11350 + +lemma sg31498 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10438 + +lemma sg31499 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9331 + +lemma sg31500 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10465 + +lemma sg31501 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10008 + +lemma sg31502 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10466 + +lemma sg31503 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10009 + +lemma sg31504 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9356 + +lemma sg31505 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10000 + +lemma sg31506 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg10000 + +lemma sg31507 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9997 + +lemma sg31508 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9649 + +lemma sg31509 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10447 + +lemma sg31510 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9357 + +lemma sg31511 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10001 + +lemma sg31512 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg10001 + +lemma sg31513 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg9998 + +lemma sg31514 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,5,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8720 sg9650 + +lemma sg31515 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4576 sg13500 + +lemma sg31516 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6993 sg11471 + +lemma sg31517 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6953 sg11477 + +lemma sg31518 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10523 + +lemma sg31519 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9393 + +lemma sg31520 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10835 + +lemma sg31521 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10523 + +lemma sg31522 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10467 + +lemma sg31523 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10010 + +lemma sg31524 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9358 + +lemma sg31525 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10002 + +lemma sg31526 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg10002 + +lemma sg31527 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10449 + +lemma sg31528 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9359 + +lemma sg31529 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10003 + +lemma sg31530 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg10003 + +lemma sg31531 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9341 + +lemma sg31532 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9342 + +lemma sg31533 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9342 + +lemma sg31534 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,7,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8832 sg9260 + +lemma sg31535 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10474 + +lemma sg31536 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,4,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10012 + +lemma sg31537 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10477 + +lemma sg31538 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10013 + +lemma sg31539 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9372 + +lemma sg31540 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10004 + +lemma sg31541 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,4,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg10004 + +lemma sg31542 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3875 sg14523 + +lemma sg31543 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6953 sg11478 + +lemma sg31544 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9348 + +lemma sg31545 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9343 + +lemma sg31546 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10478 + +lemma sg31547 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10014 + +lemma sg31548 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10479 + +lemma sg31549 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10015 + +lemma sg31550 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9374 + +lemma sg31551 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10005 + +lemma sg31552 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg10005 + +lemma sg31553 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9349 + +lemma sg31554 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10461 + +lemma sg31555 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9375 + +lemma sg31556 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10006 + +lemma sg31557 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg10006 + +lemma sg31558 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,5,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9350 + +lemma sg31559 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3889 sg14517 + +lemma sg31560 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6602 sg11543 + +lemma sg31561 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10456 + +lemma sg31562 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9345 + +lemma sg31563 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10481 + +lemma sg31564 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10016 + +lemma sg31565 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10482 + +lemma sg31566 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10017 + +lemma sg31567 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9376 + +lemma sg31568 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10007 + +lemma sg31569 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8650 sg10007 + +lemma sg31570 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg10004 + +lemma sg31571 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4577 sg13500 + +lemma sg31572 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6604 sg11543 + +lemma sg31573 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8166 sg11054 + +lemma sg31574 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10531 + +lemma sg31575 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9402 + +lemma sg31576 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10836 + +lemma sg31577 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg8415 sg10531 + +lemma sg31578 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10483 + +lemma sg31579 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10018 + +lemma sg31580 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9377 + +lemma sg31581 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10008 + +lemma sg31582 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10466 + +lemma sg31583 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9378 + +lemma sg31584 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10009 + +lemma sg31585 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg10005 + +lemma sg31586 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9405 + +lemma sg31587 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,5,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg10006 + +lemma sg31588 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6605 sg11543 + +lemma sg31589 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8167 sg11054 + +lemma sg31590 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10484 + +lemma sg31591 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10484 + +lemma sg31592 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10019 + +lemma sg31593 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8418 sg10484 + +lemma sg31594 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10467 + +lemma sg31595 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9379 + +lemma sg31596 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10010 + +lemma sg31597 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9358 + +lemma sg31598 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9359 + +lemma sg31599 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9359 + +lemma sg31600 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,8,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8652 sg10006 + +lemma sg31601 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,9,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10490 + +lemma sg31602 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,9,4,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10020 + +lemma sg31603 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,9,4,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9384 + +lemma sg31604 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,9,4,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10012 + +lemma sg31605 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3893 sg14520 + +lemma sg31606 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6999 sg11476 + +lemma sg31607 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9382 + +lemma sg31608 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9380 + +lemma sg31609 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9384 + +lemma sg31610 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10021 + +lemma sg31611 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10499 + +lemma sg31612 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10022 + +lemma sg31613 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9384 + +lemma sg31614 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10020 + +lemma sg31615 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [11,10,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8801 sg9384 + +lemma sg31616 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10504 + +lemma sg31617 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10023 + +lemma sg31618 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10505 + +lemma sg31619 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10024 + +lemma sg31620 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8434 sg10428 + +lemma sg31621 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8723 sg9648 + +lemma sg31622 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,5,5,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8399 sg10655 + +lemma sg31623 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10507 + +lemma sg31624 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10025 + +lemma sg31625 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10508 + +lemma sg31626 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10026 + +lemma sg31627 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9394 + +lemma sg31628 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10023 + +lemma sg31629 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10509 + +lemma sg31630 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10027 + +lemma sg31631 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9395 + +lemma sg31632 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10024 + +lemma sg31633 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,5,5,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8726 sg9648 + +lemma sg31634 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10510 + +lemma sg31635 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10028 + +lemma sg31636 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9396 + +lemma sg31637 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9396 + +lemma sg31638 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5144 sg12697 + +lemma sg31639 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8769 sg9594 + +lemma sg31640 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10503 + +lemma sg31641 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9390 + +lemma sg31642 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10511 + +lemma sg31643 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10029 + +lemma sg31644 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10512 + +lemma sg31645 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10030 + +lemma sg31646 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9397 + +lemma sg31647 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9397 + +lemma sg31648 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg10023 + +lemma sg31649 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9398 + +lemma sg31650 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9398 + +lemma sg31651 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9398 + +lemma sg31652 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,5,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8651 sg10024 + +lemma sg31653 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10384 + +lemma sg31654 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8770 sg9594 + +lemma sg31655 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7456 sg11349 + +lemma sg31656 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10549 + +lemma sg31657 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9423 + +lemma sg31658 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10837 + +lemma sg31659 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10513 + +lemma sg31660 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10031 + +lemma sg31661 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9399 + +lemma sg31662 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9399 + +lemma sg31663 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9400 + +lemma sg31664 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9400 + +lemma sg31665 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8796 sg9400 + +lemma sg31666 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,6,6,6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8871 sg9155 + +lemma sg31667 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10515 + +lemma sg31668 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,4,4,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10032 + +lemma sg31669 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10517 + +lemma sg31670 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10033 + +lemma sg31671 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9403 + +lemma sg31672 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,4,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10025 + +lemma sg31673 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5144 sg12698 + +lemma sg31674 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11352 + +lemma sg31675 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9393 + +lemma sg31676 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9391 + +lemma sg31677 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10518 + +lemma sg31678 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10034 + +lemma sg31679 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10519 + +lemma sg31680 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10035 + +lemma sg31681 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9404 + +lemma sg31682 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10026 + +lemma sg31683 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10509 + +lemma sg31684 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9405 + +lemma sg31685 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,5,5,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10027 + +lemma sg31686 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3889 sg14522 + +lemma sg31687 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11353 + +lemma sg31688 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10506 + +lemma sg31689 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9392 + +lemma sg31690 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10520 + +lemma sg31691 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10036 + +lemma sg31692 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10521 + +lemma sg31693 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10037 + +lemma sg31694 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9406 + +lemma sg31695 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8649 sg10028 + +lemma sg31696 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4576 sg13502 + +lemma sg31697 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11354 + +lemma sg31698 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8166 sg11055 + +lemma sg31699 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10552 + +lemma sg31700 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9426 + +lemma sg31701 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10838 + +lemma sg31702 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10522 + +lemma sg31703 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10038 + +lemma sg31704 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9407 + +lemma sg31705 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10512 + +lemma sg31706 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9408 + +lemma sg31707 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9429 + +lemma sg31708 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11355 + +lemma sg31709 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8167 sg11055 + +lemma sg31710 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10523 + +lemma sg31711 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10523 + +lemma sg31712 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10039 + +lemma sg31713 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10513 + +lemma sg31714 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9409 + +lemma sg31715 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,7,6,6,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9400 + +lemma sg31716 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10525 + +lemma sg31717 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,4,4,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10040 + +lemma sg31718 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,4,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9412 + +lemma sg31719 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3889 sg14523 + +lemma sg31720 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11356 + +lemma sg31721 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10514 + +lemma sg31722 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9401 + +lemma sg31723 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10526 + +lemma sg31724 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10041 + +lemma sg31725 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10527 + +lemma sg31726 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10042 + +lemma sg31727 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9413 + +lemma sg31728 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4576 sg13503 + +lemma sg31729 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11357 + +lemma sg31730 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8168 sg11054 + +lemma sg31731 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10556 + +lemma sg31732 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9434 + +lemma sg31733 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10839 + +lemma sg31734 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10528 + +lemma sg31735 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9414 + +lemma sg31736 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10519 + +lemma sg31737 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9415 + +lemma sg31738 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,5,5,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9405 + +lemma sg31739 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3895 sg14522 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes78.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes78.lean index 3c70a6478e7a43505e25da0a710f871c9924e3da..2a73ad052900e84089a83b1862d1f9072e12d8ae 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes78.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes78.lean @@ -1,1224 +1,1224 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes57 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 - -namespace OAI - -/-! Semigroup Nodes 78. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg31740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11358 - -lemma sg31741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10516 - -lemma sg31742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8660 sg9996 - -lemma sg31743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10529 - -lemma sg31744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,3,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8647 sg10043 - -lemma sg31745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4577 sg13502 - -lemma sg31746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11359 - -lemma sg31747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8169 sg11054 - -lemma sg31748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10557 - -lemma sg31749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9435 - -lemma sg31750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8343 sg10840 - -lemma sg31751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10530 - -lemma sg31752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9416 - -lemma sg31753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10521 - -lemma sg31754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9417 - -lemma sg31755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11360 - -lemma sg31756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8170 sg11054 - -lemma sg31757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10531 - -lemma sg31758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10531 - -lemma sg31759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10522 - -lemma sg31760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9418 - -lemma sg31761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8791 sg9436 - -lemma sg31762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8171 sg11054 - -lemma sg31763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,6,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10523 - -lemma sg31764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,6,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9419 - -lemma sg31765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,6,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8800 sg9409 - -lemma sg31766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3893 sg14523 - -lemma sg31767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6999 sg11478 - -lemma sg31768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9411 - -lemma sg31769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8811 sg9410 - -lemma sg31770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10533 - -lemma sg31771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10534 - -lemma sg31772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9420 - -lemma sg31773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3902 sg14520 - -lemma sg31774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7013 sg11476 - -lemma sg31775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10532 - -lemma sg31776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,3,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg8660 sg10011 - -lemma sg31777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10536 - -lemma sg31778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3893 sg14524 - -lemma sg31779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7014 sg11476 - -lemma sg31780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6999 sg11480 - -lemma sg31781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10558 - -lemma sg31782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9437 - -lemma sg31783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10537 - -lemma sg31784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9421 - -lemma sg31785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10534 - -lemma sg31786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9422 - -lemma sg31787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1728 sg18255 - -lemma sg31788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,11,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1837 sg17137 - -lemma sg31789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,11,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3903 sg14520 - -lemma sg31790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,11,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7016 sg11476 - -lemma sg31791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,11,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8836 sg9380 - -lemma sg31792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,11,2,2,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg8774 sg9580 - -lemma sg31793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg993 sg21111 - -lemma sg31794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1841 sg17124 - -lemma sg31795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1935 sg16123 - -lemma sg31796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3178 sg14807 - -lemma sg31797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3786 sg14545 - -lemma sg31798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5889 sg11840 - -lemma sg31799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6626 sg11542 - -lemma sg31800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,2,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8611 sg10105 - -lemma sg31801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg8842 sg9380 - -lemma sg31802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,5,5,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10539 - -lemma sg31803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,5,5,5,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10540 - -lemma sg31804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,5,5,5,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9424 - -lemma sg31805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,5,5,5,5,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10541 - -lemma sg31806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,5,5,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9425 - -lemma sg31807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10542 - -lemma sg31808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10543 - -lemma sg31809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,4,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9427 - -lemma sg31810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5144 sg12699 - -lemma sg31811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10380 - -lemma sg31812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9423 - -lemma sg31813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10544 - -lemma sg31814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10545 - -lemma sg31815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9428 - -lemma sg31816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8420 sg10541 - -lemma sg31817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9429 - -lemma sg31818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5158 sg12697 - -lemma sg31819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8775 sg9594 - -lemma sg31820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10538 - -lemma sg31821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10546 - -lemma sg31822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10547 - -lemma sg31823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,4,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8795 sg9430 - -lemma sg31824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10469 - -lemma sg31825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10383 - -lemma sg31826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8885 sg9156 - -lemma sg31827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10569 - -lemma sg31828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8793 sg9438 - -lemma sg31829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10548 - -lemma sg31830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,4,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9431 - -lemma sg31831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10384 - -lemma sg31832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,6,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8886 sg9156 - -lemma sg31833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,6,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10549 - -lemma sg31834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,6,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8417 sg10549 - -lemma sg31835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,6,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9432 - -lemma sg31836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,7,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10550 - -lemma sg31837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5162 sg12698 - -lemma sg31838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,8,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11361 - -lemma sg31839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,8,4,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9434 - -lemma sg31840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,8,4,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10554 - -lemma sg31841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,8,4,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10555 - -lemma sg31842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1728 sg18263 - -lemma sg31843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2210 sg15583 - -lemma sg31844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3903 sg14523 - -lemma sg31845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,10,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7016 sg11478 - -lemma sg31846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,10,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8836 sg9410 - -lemma sg31847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,4,4,4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10560 - -lemma sg31848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10562 - -lemma sg31849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5144 sg12700 - -lemma sg31850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10448 - -lemma sg31851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,5,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8827 sg9423 - -lemma sg31852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,5,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10563 - -lemma sg31853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,5,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10564 - -lemma sg31854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,5,5,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8794 sg9439 - -lemma sg31855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,4,4,4,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10565 - -lemma sg31856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5023 sg12702 - -lemma sg31857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10465 - -lemma sg31858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10559 - -lemma sg31859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,4,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10566 - -lemma sg31860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,4,4,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10567 - -lemma sg31861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10523 - -lemma sg31862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10467 - -lemma sg31863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,5,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10448 - -lemma sg31864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,5,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10573 - -lemma sg31865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5024 sg12702 - -lemma sg31866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8779 sg9594 - -lemma sg31867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10561 - -lemma sg31868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,3,3,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8416 sg10568 - -lemma sg31869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10524 - -lemma sg31870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10468 - -lemma sg31871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8889 sg9156 - -lemma sg31872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,4,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8414 sg10574 - -lemma sg31873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10469 - -lemma sg31874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,5,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8508 sg10383 - -lemma sg31875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,6,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8508 sg10384 - -lemma sg31876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5026 sg12702 - -lemma sg31877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,7,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10478 - -lemma sg31878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,7,4,4,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8799 sg9440 - -lemma sg31879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5179 sg12698 - -lemma sg31880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,8,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10492 - -lemma sg31881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,8,4,3,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8424 sg10570 - -lemma sg31882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10535 - -lemma sg31883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,8,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10494 - -lemma sg31884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,8,4,4,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8491 sg10478 - -lemma sg31885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1728 sg18272 - -lemma sg31886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,9,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2498 sg15279 - -lemma sg31887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5180 sg12698 - -lemma sg31888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11362 - -lemma sg31889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,9,2,2,2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg8836 sg9433 - -lemma sg31890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1841 sg17144 - -lemma sg31891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2211 sg15590 - -lemma sg31892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2486 sg15292 - -lemma sg31893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3904 sg14523 - -lemma sg31894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4578 sg13503 - -lemma sg31895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg7454 sg11363 - -lemma sg31896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,2,2,2,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8172 sg11054 - -lemma sg31897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [15,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5162 sg12700 - -lemma sg31898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [15,6,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10518 - -lemma sg31899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [15,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1728 sg18273 - -lemma sg31900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [15,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2498 sg15280 - -lemma sg31901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [15,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5039 sg12702 - -lemma sg31902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [15,8,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10532 - -lemma sg31903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5174 sg12700 - -lemma sg31904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10544 - -lemma sg31905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5179 sg12700 - -lemma sg31906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10551 - -lemma sg31907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10571 - -lemma sg31908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1728 sg18274 - -lemma sg31909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2498 sg15281 - -lemma sg31910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5180 sg12700 - -lemma sg31911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8490 sg10553 - -lemma sg31912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1841 sg17145 - -lemma sg31913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2487 sg15293 - -lemma sg31914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2498 sg15282 - -lemma sg31915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5045 sg12702 - -lemma sg31916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8468 sg10572 - -lemma sg31917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [17,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5187 sg12700 - -lemma sg31918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [17,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1729 sg18274 - -lemma sg31919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [17,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3752 sg14546 - -lemma sg31920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [17,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5190 sg12700 - -lemma sg31921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5195 sg12700 - -lemma sg31922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1730 sg18274 - -lemma sg31923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3753 sg14546 - -lemma sg31924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5196 sg12700 - -lemma sg31925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1842 sg17146 - -lemma sg31926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3754 sg14546 - -lemma sg31927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3752 sg14547 - -lemma sg31928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [19,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1731 sg18274 - -lemma sg31929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [19,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3755 sg14546 - -lemma sg31930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [20,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1732 sg18274 - -lemma sg31931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [20,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg3756 sg14546 - -lemma sg31932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [20,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1843 sg17146 - -lemma sg31933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [21,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1733 sg18274 - -lemma sg31934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [22,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1734 sg18274 - -lemma sg31935 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2690 sg15690 - -lemma sg31936 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg2690 sg15691 - -lemma sg31937 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [7,6,6,6,6,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2247 sg20782 - -lemma sg31938 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [7,6,6,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2247 sg20783 - -lemma sg31939 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [7,7,6,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2691 sg15690 - -lemma sg31940 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [7,7,6,6,6,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2691 sg15691 - -lemma sg31941 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [7,7,7,6,6,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2692 sg15691 - -lemma sg31942 : RowSquare [9,8,4,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,5,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg2665 sg15691 - -lemma sg31943 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,5,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg21093 - -lemma sg31944 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,5,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg21094 - -lemma sg31945 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg21095 - -lemma sg31946 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg21096 - -lemma sg31947 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg21097 - -lemma sg31948 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg21098 - -lemma sg31949 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg21099 - -lemma sg31950 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1844 sg21100 - -lemma sg31951 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5670 sg23531 - -lemma sg31952 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5670 sg23532 - -lemma sg31953 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12591 sg21202 - -lemma sg31954 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15255 sg15048 - -lemma sg31955 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15267 sg14997 - -lemma sg31956 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15283 sg14848 - -lemma sg31957 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg14785 sg15559 - -lemma sg31958 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15267 sg14998 - -lemma sg31959 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15286 sg14814 - -lemma sg31960 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg15278 sg14978 - -lemma sg31961 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15290 sg14813 - -lemma sg31962 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15273 sg14980 - -lemma sg31963 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15267 sg14999 - -lemma sg31964 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15286 sg14815 - -lemma sg31965 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15158 sg15235 - -lemma sg31966 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15273 sg14981 - -lemma sg31967 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15272 sg14982 - -lemma sg31968 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15273 sg14982 - -lemma sg31969 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15247 sg15156 - -lemma sg31970 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12919 sg21084 - -lemma sg31971 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15247 sg15157 - -lemma sg31972 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15277 sg14979 - -lemma sg31973 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15274 sg14983 - -lemma sg31974 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15287 sg14816 - -lemma sg31975 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg15275 sg14983 - -lemma sg31976 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15276 sg14983 - -lemma sg31977 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15288 sg14816 - -lemma sg31978 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg15289 sg14816 - -lemma sg31979 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15268 sg15000 - -lemma sg31980 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15269 sg15000 - -lemma sg31981 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15258 sg15005 - -lemma sg31982 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15270 sg14985 - -lemma sg31983 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15271 sg14985 - -lemma sg31984 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15254 sg15049 - -lemma sg31985 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15285 sg14818 - -lemma sg31986 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15254 sg15050 - -lemma sg31987 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15158 sg15236 - -lemma sg31988 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15267 sg15001 - -lemma sg31989 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15290 sg14814 - -lemma sg31990 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg15284 sg14848 - -lemma sg31991 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15267 sg15002 - -lemma sg31992 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15286 sg14817 - -lemma sg31993 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15291 sg14814 - -lemma sg31994 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15273 sg14984 - -lemma sg31995 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15286 sg14818 - -lemma sg31996 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15273 sg14985 - -lemma sg31997 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15158 sg15237 - -lemma sg31998 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [12,9,7,7,7,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15253 sg15051 - -lemma sg31999 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [13,8,7,7,7,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15253 sg15052 - -lemma sg32000 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15253 sg15053 - -lemma sg32001 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15259 sg15006 - -lemma sg32002 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15257 sg15007 - -lemma sg32003 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15257 sg15008 - -lemma sg32004 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [14,7,7,7,6,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15257 sg15009 - -lemma sg32005 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15257 sg15010 - -lemma sg32007 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg11059 sg23530 - -lemma sg32008 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg14310 sg21346 - -lemma sg32009 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg5696 sg31942 - -lemma sg32010 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5670 sg31943 - -lemma sg32011 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14470 sg21297 - -lemma sg32012 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5670 sg31944 - -lemma sg32013 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg15612 sg21051 - -lemma sg32014 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14471 sg21297 - -lemma sg32015 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17154 - -lemma sg32016 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17155 - -lemma sg32017 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17159 - -lemma sg32018 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15672 sg20946 - -lemma sg32019 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg15102 sg21199 - -lemma sg32020 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17160 - -lemma sg32021 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17159 - -lemma sg32022 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17157 - -lemma sg32023 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17159 - -lemma sg32024 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17160 - -lemma sg32025 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17160 - -lemma sg32026 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16656 - -lemma sg32027 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,8,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5670 sg31945 - -lemma sg32028 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,8,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5731 sg31935 - -lemma sg32029 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,8,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5670 sg31946 - -lemma sg32030 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,8,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5670 sg31947 - -lemma sg32031 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,8,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17159 - -lemma sg32032 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,8,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17160 - -lemma sg32033 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,9,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5670 sg31948 - -lemma sg32034 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,9,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5670 sg31949 - -lemma sg32035 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,9,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg5731 sg31936 - -lemma sg32036 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,9,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5670 sg31950 - -lemma sg32037 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14311 sg21345 - -lemma sg32038 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20430 - -lemma sg32039 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18116 sg20426 - -lemma sg32040 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15229 sg21188 - -lemma sg32041 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20431 - -lemma sg32042 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18116 sg20427 - -lemma sg32043 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17152 - -lemma sg32044 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15224 sg21193 - -lemma sg32045 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17163 - -lemma sg32046 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17164 - -lemma sg32047 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17170 - -lemma sg32048 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20432 - -lemma sg32049 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17153 - -lemma sg32050 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17177 - -lemma sg32051 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16227 - -lemma sg32052 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17177 - -lemma sg32053 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17170 - -lemma sg32054 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16227 - -lemma sg32055 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20541 - -lemma sg32056 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16658 - -lemma sg32057 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,8,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12863 sg21635 - -lemma sg32058 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,8,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20433 - -lemma sg32059 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,8,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14724 sg21271 - -lemma sg32060 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,8,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15225 sg21193 - -lemma sg32061 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,8,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17170 - -lemma sg32062 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,8,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17171 - -lemma sg32063 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17278 - -lemma sg32064 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18295 - -lemma sg32065 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17278 - -lemma sg32066 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20315 sg18295 - -lemma sg32067 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18281 sg20344 - -lemma sg32068 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18295 - -lemma sg32069 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg16649 sg20660 - -lemma sg32070 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18282 sg20344 - -lemma sg32071 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18295 - -lemma sg32072 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg17147 sg20554 - -lemma sg32073 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18295 - -lemma sg32074 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg16650 sg20660 - -lemma sg32075 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17213 - -lemma sg32076 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20794 sg16159 - -lemma sg32077 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16267 - -lemma sg32078 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16690 - -lemma sg32079 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17213 - -lemma sg32080 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20496 sg18104 - -lemma sg32081 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19575 sg19607 - -lemma sg32082 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17213 - -lemma sg32083 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20319 sg18293 - -lemma sg32084 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20320 sg18293 - -lemma sg32085 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17174 - -lemma sg32086 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20721 sg16219 - -lemma sg32087 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16659 - -lemma sg32088 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17174 - -lemma sg32089 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17174 - -lemma sg32090 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg18288 sg20329 - -lemma sg32091 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17173 - -lemma sg32092 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20434 - -lemma sg32093 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20533 sg17156 - -lemma sg32094 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17175 - -lemma sg32095 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17173 - -lemma sg32096 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17172 - -lemma sg32097 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17175 - -lemma sg32098 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17175 - -lemma sg32099 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17176 - -lemma sg32100 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17176 - -lemma sg32101 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17176 - -lemma sg32102 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17174 - -lemma sg32103 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20644 sg16655 - -lemma sg32104 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20532 sg17158 - -lemma sg32105 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17175 - -lemma sg32106 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20435 - -lemma sg32107 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18116 sg20428 - -lemma sg32108 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17177 - -lemma sg32109 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17177 - -lemma sg32110 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17177 - -lemma sg32111 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17175 - -lemma sg32112 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17176 - -lemma sg32113 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17176 - -lemma sg32114 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16660 - -lemma sg32115 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17177 - -lemma sg32116 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20436 - -lemma sg32117 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17157 - -lemma sg32118 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17177 - -lemma sg32119 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17177 - -lemma sg32120 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16661 - -lemma sg32121 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,8,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5731 sg31937 - -lemma sg32122 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,8,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6459 sg23673 - -lemma sg32123 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,8,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17159 - -lemma sg32124 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,8,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17177 - -lemma sg32125 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,9,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5731 sg31938 - -lemma sg32126 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,9,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6459 sg23674 - -lemma sg32127 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12864 sg21634 - -lemma sg32128 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15248 sg21140 - -lemma sg32129 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg14773 sg21251 - -lemma sg32130 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15231 sg21187 - -lemma sg32131 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20438 - -lemma sg32132 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17178 - -lemma sg32133 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg15603 sg21076 - -lemma sg32134 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14764 sg21268 - -lemma sg32135 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17179 - -lemma sg32136 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17180 - -lemma sg32137 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17190 - -lemma sg32138 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20322 sg18290 - -lemma sg32139 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17190 - -lemma sg32140 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16670 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes57 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 + +namespace OAI + +/-! Semigroup Nodes 78. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg31740 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11358 + +lemma sg31741 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10516 + +lemma sg31742 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8660 sg9996 + +lemma sg31743 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10529 + +lemma sg31744 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,3,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8647 sg10043 + +lemma sg31745 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4577 sg13502 + +lemma sg31746 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11359 + +lemma sg31747 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8169 sg11054 + +lemma sg31748 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10557 + +lemma sg31749 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9435 + +lemma sg31750 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8343 sg10840 + +lemma sg31751 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10530 + +lemma sg31752 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9416 + +lemma sg31753 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10521 + +lemma sg31754 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9417 + +lemma sg31755 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11360 + +lemma sg31756 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8170 sg11054 + +lemma sg31757 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10531 + +lemma sg31758 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10531 + +lemma sg31759 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10522 + +lemma sg31760 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9418 + +lemma sg31761 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,5,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8791 sg9436 + +lemma sg31762 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8171 sg11054 + +lemma sg31763 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,6,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10523 + +lemma sg31764 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,6,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9419 + +lemma sg31765 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,8,6,6,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8800 sg9409 + +lemma sg31766 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3893 sg14523 + +lemma sg31767 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6999 sg11478 + +lemma sg31768 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9411 + +lemma sg31769 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8811 sg9410 + +lemma sg31770 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10533 + +lemma sg31771 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10534 + +lemma sg31772 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,9,4,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9420 + +lemma sg31773 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3902 sg14520 + +lemma sg31774 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7013 sg11476 + +lemma sg31775 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10532 + +lemma sg31776 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,3,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg8660 sg10011 + +lemma sg31777 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10536 + +lemma sg31778 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3893 sg14524 + +lemma sg31779 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7014 sg11476 + +lemma sg31780 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6999 sg11480 + +lemma sg31781 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10558 + +lemma sg31782 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9437 + +lemma sg31783 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10537 + +lemma sg31784 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9421 + +lemma sg31785 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10534 + +lemma sg31786 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,10,4,4,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9422 + +lemma sg31787 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1728 sg18255 + +lemma sg31788 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,11,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1837 sg17137 + +lemma sg31789 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,11,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3903 sg14520 + +lemma sg31790 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,11,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7016 sg11476 + +lemma sg31791 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,11,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8836 sg9380 + +lemma sg31792 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,11,2,2,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg8774 sg9580 + +lemma sg31793 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg993 sg21111 + +lemma sg31794 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1841 sg17124 + +lemma sg31795 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1935 sg16123 + +lemma sg31796 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3178 sg14807 + +lemma sg31797 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3786 sg14545 + +lemma sg31798 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5889 sg11840 + +lemma sg31799 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6626 sg11542 + +lemma sg31800 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,2,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8611 sg10105 + +lemma sg31801 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [12,12,2,2,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg8842 sg9380 + +lemma sg31802 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,5,5,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10539 + +lemma sg31803 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,5,5,5,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10540 + +lemma sg31804 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,5,5,5,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9424 + +lemma sg31805 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,5,5,5,5,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10541 + +lemma sg31806 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,5,5,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9425 + +lemma sg31807 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10542 + +lemma sg31808 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10543 + +lemma sg31809 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,4,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9427 + +lemma sg31810 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5144 sg12699 + +lemma sg31811 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10380 + +lemma sg31812 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9423 + +lemma sg31813 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10544 + +lemma sg31814 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10545 + +lemma sg31815 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9428 + +lemma sg31816 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8420 sg10541 + +lemma sg31817 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,5,5,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9429 + +lemma sg31818 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5158 sg12697 + +lemma sg31819 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8775 sg9594 + +lemma sg31820 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10538 + +lemma sg31821 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10546 + +lemma sg31822 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10547 + +lemma sg31823 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,4,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8795 sg9430 + +lemma sg31824 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10469 + +lemma sg31825 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10383 + +lemma sg31826 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8885 sg9156 + +lemma sg31827 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10569 + +lemma sg31828 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8793 sg9438 + +lemma sg31829 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10548 + +lemma sg31830 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,5,4,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9431 + +lemma sg31831 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10384 + +lemma sg31832 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,6,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8886 sg9156 + +lemma sg31833 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,6,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10549 + +lemma sg31834 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,6,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8417 sg10549 + +lemma sg31835 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,6,6,6,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9432 + +lemma sg31836 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,7,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10550 + +lemma sg31837 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5162 sg12698 + +lemma sg31838 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,8,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11361 + +lemma sg31839 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,8,4,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9434 + +lemma sg31840 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,8,4,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10554 + +lemma sg31841 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,8,4,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10555 + +lemma sg31842 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1728 sg18263 + +lemma sg31843 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2210 sg15583 + +lemma sg31844 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3903 sg14523 + +lemma sg31845 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,10,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7016 sg11478 + +lemma sg31846 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [13,10,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8836 sg9410 + +lemma sg31847 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,4,4,4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10560 + +lemma sg31848 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10562 + +lemma sg31849 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5144 sg12700 + +lemma sg31850 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,5,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10448 + +lemma sg31851 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,5,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8827 sg9423 + +lemma sg31852 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,5,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10563 + +lemma sg31853 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,5,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10564 + +lemma sg31854 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,5,5,5,5,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8794 sg9439 + +lemma sg31855 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,4,4,4,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10565 + +lemma sg31856 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5023 sg12702 + +lemma sg31857 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10465 + +lemma sg31858 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10559 + +lemma sg31859 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,4,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10566 + +lemma sg31860 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,4,4,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10567 + +lemma sg31861 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10523 + +lemma sg31862 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,5,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10467 + +lemma sg31863 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,5,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10448 + +lemma sg31864 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,5,5,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10573 + +lemma sg31865 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5024 sg12702 + +lemma sg31866 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8779 sg9594 + +lemma sg31867 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10561 + +lemma sg31868 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,3,3,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8416 sg10568 + +lemma sg31869 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10524 + +lemma sg31870 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10468 + +lemma sg31871 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8889 sg9156 + +lemma sg31872 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,4,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8414 sg10574 + +lemma sg31873 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,5,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10469 + +lemma sg31874 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,5,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8508 sg10383 + +lemma sg31875 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,6,6,6,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8508 sg10384 + +lemma sg31876 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,7,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5026 sg12702 + +lemma sg31877 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,7,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10478 + +lemma sg31878 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,7,4,4,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8799 sg9440 + +lemma sg31879 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,8,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5179 sg12698 + +lemma sg31880 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,8,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10492 + +lemma sg31881 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,8,4,3,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8424 sg10570 + +lemma sg31882 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,8,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10535 + +lemma sg31883 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,8,4,4,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10494 + +lemma sg31884 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,8,4,4,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8491 sg10478 + +lemma sg31885 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1728 sg18272 + +lemma sg31886 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,9,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2498 sg15279 + +lemma sg31887 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,9,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5180 sg12698 + +lemma sg31888 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,9,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11362 + +lemma sg31889 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,9,2,2,2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg8836 sg9433 + +lemma sg31890 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1841 sg17144 + +lemma sg31891 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2211 sg15590 + +lemma sg31892 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2486 sg15292 + +lemma sg31893 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3904 sg14523 + +lemma sg31894 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4578 sg13503 + +lemma sg31895 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,2,2,2,2,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg7454 sg11363 + +lemma sg31896 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [14,10,2,2,2,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8172 sg11054 + +lemma sg31897 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [15,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5162 sg12700 + +lemma sg31898 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [15,6,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10518 + +lemma sg31899 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [15,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1728 sg18273 + +lemma sg31900 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [15,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2498 sg15280 + +lemma sg31901 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [15,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5039 sg12702 + +lemma sg31902 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [15,8,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10532 + +lemma sg31903 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,5,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5174 sg12700 + +lemma sg31904 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,5,4,4,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10544 + +lemma sg31905 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,6,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5179 sg12700 + +lemma sg31906 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,6,4,3,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10551 + +lemma sg31907 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,6,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10571 + +lemma sg31908 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1728 sg18274 + +lemma sg31909 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,7,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2498 sg15281 + +lemma sg31910 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,7,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5180 sg12700 + +lemma sg31911 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,7,2,2,2,2,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8490 sg10553 + +lemma sg31912 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1841 sg17145 + +lemma sg31913 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,8,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2487 sg15293 + +lemma sg31914 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,8,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2498 sg15282 + +lemma sg31915 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,8,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5045 sg12702 + +lemma sg31916 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [16,8,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8468 sg10572 + +lemma sg31917 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [17,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5187 sg12700 + +lemma sg31918 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [17,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1729 sg18274 + +lemma sg31919 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [17,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3752 sg14546 + +lemma sg31920 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [17,6,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5190 sg12700 + +lemma sg31921 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5195 sg12700 + +lemma sg31922 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1730 sg18274 + +lemma sg31923 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,5,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3753 sg14546 + +lemma sg31924 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,5,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5196 sg12700 + +lemma sg31925 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1842 sg17146 + +lemma sg31926 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,6,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3754 sg14546 + +lemma sg31927 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [18,6,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3752 sg14547 + +lemma sg31928 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [19,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1731 sg18274 + +lemma sg31929 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [19,4,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3755 sg14546 + +lemma sg31930 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [20,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1732 sg18274 + +lemma sg31931 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [20,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg3756 sg14546 + +lemma sg31932 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [20,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1843 sg17146 + +lemma sg31933 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [21,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1733 sg18274 + +lemma sg31934 : RowSquare [12,10,4,3,2,2,2,2,2,2,1,1] [22,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1734 sg18274 + +lemma sg31935 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2690 sg15690 + +lemma sg31936 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg2690 sg15691 + +lemma sg31937 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [7,6,6,6,6,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2247 sg20782 + +lemma sg31938 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [7,6,6,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2247 sg20783 + +lemma sg31939 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [7,7,6,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2691 sg15690 + +lemma sg31940 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [7,7,6,6,6,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2691 sg15691 + +lemma sg31941 : RowSquare [9,8,3,3,3,2,2,2,2,2,2,2,2,1,1] [7,7,7,6,6,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2692 sg15691 + +lemma sg31942 : RowSquare [9,8,4,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,5,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg2665 sg15691 + +lemma sg31943 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,5,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg21093 + +lemma sg31944 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,5,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg21094 + +lemma sg31945 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg21095 + +lemma sg31946 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg21096 + +lemma sg31947 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg21097 + +lemma sg31948 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg21098 + +lemma sg31949 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg21099 + +lemma sg31950 : RowSquare [9,9,3,3,2,2,2,2,2,2,2,2,2,1,1] [6,6,6,6,6,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1844 sg21100 + +lemma sg31951 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5670 sg23531 + +lemma sg31952 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5670 sg23532 + +lemma sg31953 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12591 sg21202 + +lemma sg31954 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15255 sg15048 + +lemma sg31955 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15267 sg14997 + +lemma sg31956 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15283 sg14848 + +lemma sg31957 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg14785 sg15559 + +lemma sg31958 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15267 sg14998 + +lemma sg31959 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15286 sg14814 + +lemma sg31960 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg15278 sg14978 + +lemma sg31961 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15290 sg14813 + +lemma sg31962 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15273 sg14980 + +lemma sg31963 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15267 sg14999 + +lemma sg31964 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15286 sg14815 + +lemma sg31965 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15158 sg15235 + +lemma sg31966 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15273 sg14981 + +lemma sg31967 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15272 sg14982 + +lemma sg31968 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15273 sg14982 + +lemma sg31969 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15247 sg15156 + +lemma sg31970 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12919 sg21084 + +lemma sg31971 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15247 sg15157 + +lemma sg31972 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15277 sg14979 + +lemma sg31973 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15274 sg14983 + +lemma sg31974 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15287 sg14816 + +lemma sg31975 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg15275 sg14983 + +lemma sg31976 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15276 sg14983 + +lemma sg31977 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15288 sg14816 + +lemma sg31978 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg15289 sg14816 + +lemma sg31979 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15268 sg15000 + +lemma sg31980 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15269 sg15000 + +lemma sg31981 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15258 sg15005 + +lemma sg31982 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15270 sg14985 + +lemma sg31983 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15271 sg14985 + +lemma sg31984 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15254 sg15049 + +lemma sg31985 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15285 sg14818 + +lemma sg31986 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15254 sg15050 + +lemma sg31987 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15158 sg15236 + +lemma sg31988 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15267 sg15001 + +lemma sg31989 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15290 sg14814 + +lemma sg31990 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg15284 sg14848 + +lemma sg31991 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15267 sg15002 + +lemma sg31992 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15286 sg14817 + +lemma sg31993 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15291 sg14814 + +lemma sg31994 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15273 sg14984 + +lemma sg31995 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15286 sg14818 + +lemma sg31996 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15273 sg14985 + +lemma sg31997 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15158 sg15237 + +lemma sg31998 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [12,9,7,7,7,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15253 sg15051 + +lemma sg31999 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [13,8,7,7,7,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15253 sg15052 + +lemma sg32000 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [13,9,7,7,7,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15253 sg15053 + +lemma sg32001 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [13,9,7,7,7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15259 sg15006 + +lemma sg32002 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [14,7,6,6,6,6,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15257 sg15007 + +lemma sg32003 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [14,7,7,6,6,6,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15257 sg15008 + +lemma sg32004 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [14,7,7,7,6,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15257 sg15009 + +lemma sg32005 : RowSquare [14,12,6,5,4,3,2,2,2,2,2,2,1,1] [14,7,7,7,6,6,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15257 sg15010 + +lemma sg32007 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg11059 sg23530 + +lemma sg32008 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg14310 sg21346 + +lemma sg32009 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg5696 sg31942 + +lemma sg32010 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5670 sg31943 + +lemma sg32011 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14470 sg21297 + +lemma sg32012 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5670 sg31944 + +lemma sg32013 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg15612 sg21051 + +lemma sg32014 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14471 sg21297 + +lemma sg32015 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17154 + +lemma sg32016 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,8,8,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17155 + +lemma sg32017 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17159 + +lemma sg32018 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15672 sg20946 + +lemma sg32019 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg15102 sg21199 + +lemma sg32020 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17160 + +lemma sg32021 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17159 + +lemma sg32022 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17157 + +lemma sg32023 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17159 + +lemma sg32024 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17160 + +lemma sg32025 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17160 + +lemma sg32026 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16656 + +lemma sg32027 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,8,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5670 sg31945 + +lemma sg32028 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,8,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5731 sg31935 + +lemma sg32029 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,8,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5670 sg31946 + +lemma sg32030 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,8,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5670 sg31947 + +lemma sg32031 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,8,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17159 + +lemma sg32032 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,8,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17160 + +lemma sg32033 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,9,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5670 sg31948 + +lemma sg32034 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,9,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5670 sg31949 + +lemma sg32035 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,9,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg5731 sg31936 + +lemma sg32036 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [9,9,9,9,9,9,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5670 sg31950 + +lemma sg32037 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14311 sg21345 + +lemma sg32038 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20430 + +lemma sg32039 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18116 sg20426 + +lemma sg32040 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15229 sg21188 + +lemma sg32041 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20431 + +lemma sg32042 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18116 sg20427 + +lemma sg32043 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17152 + +lemma sg32044 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15224 sg21193 + +lemma sg32045 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17163 + +lemma sg32046 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,8,8,8,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17164 + +lemma sg32047 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17170 + +lemma sg32048 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20432 + +lemma sg32049 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17153 + +lemma sg32050 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17177 + +lemma sg32051 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16227 + +lemma sg32052 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17177 + +lemma sg32053 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17170 + +lemma sg32054 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16227 + +lemma sg32055 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20541 + +lemma sg32056 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16658 + +lemma sg32057 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,8,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12863 sg21635 + +lemma sg32058 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,8,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20433 + +lemma sg32059 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,8,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14724 sg21271 + +lemma sg32060 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,8,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15225 sg21193 + +lemma sg32061 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,8,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17170 + +lemma sg32062 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,8,8,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17171 + +lemma sg32063 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17278 + +lemma sg32064 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18295 + +lemma sg32065 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17278 + +lemma sg32066 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20315 sg18295 + +lemma sg32067 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18281 sg20344 + +lemma sg32068 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18295 + +lemma sg32069 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg16649 sg20660 + +lemma sg32070 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18282 sg20344 + +lemma sg32071 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18295 + +lemma sg32072 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg17147 sg20554 + +lemma sg32073 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18295 + +lemma sg32074 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg16650 sg20660 + +lemma sg32075 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17213 + +lemma sg32076 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20794 sg16159 + +lemma sg32077 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16267 + +lemma sg32078 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16690 + +lemma sg32079 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17213 + +lemma sg32080 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20496 sg18104 + +lemma sg32081 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19575 sg19607 + +lemma sg32082 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17213 + +lemma sg32083 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20319 sg18293 + +lemma sg32084 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20320 sg18293 + +lemma sg32085 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17174 + +lemma sg32086 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20721 sg16219 + +lemma sg32087 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16659 + +lemma sg32088 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17174 + +lemma sg32089 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17174 + +lemma sg32090 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg18288 sg20329 + +lemma sg32091 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17173 + +lemma sg32092 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20434 + +lemma sg32093 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20533 sg17156 + +lemma sg32094 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17175 + +lemma sg32095 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17173 + +lemma sg32096 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17172 + +lemma sg32097 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17175 + +lemma sg32098 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17175 + +lemma sg32099 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17176 + +lemma sg32100 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17176 + +lemma sg32101 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17176 + +lemma sg32102 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17174 + +lemma sg32103 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20644 sg16655 + +lemma sg32104 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20532 sg17158 + +lemma sg32105 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17175 + +lemma sg32106 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20435 + +lemma sg32107 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18116 sg20428 + +lemma sg32108 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17177 + +lemma sg32109 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17177 + +lemma sg32110 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17177 + +lemma sg32111 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17175 + +lemma sg32112 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17176 + +lemma sg32113 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17176 + +lemma sg32114 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16660 + +lemma sg32115 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17177 + +lemma sg32116 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20436 + +lemma sg32117 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17157 + +lemma sg32118 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17177 + +lemma sg32119 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17177 + +lemma sg32120 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16661 + +lemma sg32121 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,8,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5731 sg31937 + +lemma sg32122 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,8,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6459 sg23673 + +lemma sg32123 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,8,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17159 + +lemma sg32124 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,8,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17177 + +lemma sg32125 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,9,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5731 sg31938 + +lemma sg32126 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,9,9,9,9,9,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6459 sg23674 + +lemma sg32127 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12864 sg21634 + +lemma sg32128 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15248 sg21140 + +lemma sg32129 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg14773 sg21251 + +lemma sg32130 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15231 sg21187 + +lemma sg32131 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20438 + +lemma sg32132 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17178 + +lemma sg32133 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg15603 sg21076 + +lemma sg32134 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14764 sg21268 + +lemma sg32135 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17179 + +lemma sg32136 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,8,8,8,8,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17180 + +lemma sg32137 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17190 + +lemma sg32138 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20322 sg18290 + +lemma sg32139 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17190 + +lemma sg32140 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16670 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes79.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes79.lean index 51dffd85a18d2940f028d6f7add41c73ebe6038c..688dc86bc4570cc315bcdeff39eb26957db0dcf5 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes79.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes79.lean @@ -1,1221 +1,1221 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes78 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 - -namespace OAI - -/-! Semigroup Nodes 79. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg32141 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17190 - -lemma sg32142 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16670 - -lemma sg32143 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17190 - -lemma sg32144 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17182 - -lemma sg32145 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17182 - -lemma sg32146 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16663 - -lemma sg32147 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,8,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14312 sg21345 - -lemma sg32148 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,8,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20439 - -lemma sg32149 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,8,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg14310 sg21348 - -lemma sg32150 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,8,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15224 sg21194 - -lemma sg32151 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,8,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17181 - -lemma sg32152 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,8,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17182 - -lemma sg32153 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15644 sg20985 - -lemma sg32154 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20440 - -lemma sg32155 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg15610 sg21053 - -lemma sg32156 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17185 - -lemma sg32157 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16232 - -lemma sg32158 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17185 - -lemma sg32159 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg15611 sg21053 - -lemma sg32160 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16232 - -lemma sg32161 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20542 - -lemma sg32162 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17183 - -lemma sg32163 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17317 - -lemma sg32164 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18296 - -lemma sg32165 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17317 - -lemma sg32166 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20315 sg18296 - -lemma sg32167 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18281 sg20356 - -lemma sg32168 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18296 - -lemma sg32169 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg16649 sg20661 - -lemma sg32170 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18282 sg20356 - -lemma sg32171 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18296 - -lemma sg32172 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg17147 sg20557 - -lemma sg32173 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18296 - -lemma sg32174 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg16650 sg20661 - -lemma sg32175 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17212 - -lemma sg32176 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20795 sg16158 - -lemma sg32177 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20505 sg17212 - -lemma sg32178 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17211 - -lemma sg32179 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18284 sg20338 - -lemma sg32180 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20507 sg17211 - -lemma sg32181 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16234 - -lemma sg32182 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16234 - -lemma sg32183 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17187 - -lemma sg32184 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17186 - -lemma sg32185 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18029 - -lemma sg32186 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16688 - -lemma sg32187 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18285 sg20338 - -lemma sg32188 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17211 - -lemma sg32189 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18286 sg20338 - -lemma sg32190 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20647 sg16654 - -lemma sg32191 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17212 - -lemma sg32192 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18284 sg20339 - -lemma sg32193 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20507 sg17212 - -lemma sg32194 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18030 - -lemma sg32195 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16689 - -lemma sg32196 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18285 sg20339 - -lemma sg32197 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17212 - -lemma sg32198 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18286 sg20339 - -lemma sg32199 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17188 - -lemma sg32200 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16235 - -lemma sg32201 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17188 - -lemma sg32202 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19180 - -lemma sg32203 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16235 - -lemma sg32204 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20543 - -lemma sg32205 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16237 - -lemma sg32206 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16237 - -lemma sg32207 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17190 - -lemma sg32208 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17189 - -lemma sg32209 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16236 - -lemma sg32210 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17189 - -lemma sg32211 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17184 - -lemma sg32212 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16236 - -lemma sg32213 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20544 - -lemma sg32214 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16665 - -lemma sg32215 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17190 - -lemma sg32216 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16237 - -lemma sg32217 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17190 - -lemma sg32218 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16237 - -lemma sg32219 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20545 - -lemma sg32220 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16666 - -lemma sg32221 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,8,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12864 sg21635 - -lemma sg32222 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,8,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15225 sg21194 - -lemma sg32223 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,8,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15604 sg21076 - -lemma sg32224 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,8,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17185 - -lemma sg32225 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20649 sg16652 - -lemma sg32226 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg15665 sg20953 - -lemma sg32227 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17213 - -lemma sg32228 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20795 sg16159 - -lemma sg32229 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20505 sg17213 - -lemma sg32230 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17186 - -lemma sg32231 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg15666 sg20951 - -lemma sg32232 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20741 sg16217 - -lemma sg32233 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20649 sg16654 - -lemma sg32234 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17186 - -lemma sg32235 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg15671 sg20947 - -lemma sg32236 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17186 - -lemma sg32237 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17213 - -lemma sg32238 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18284 sg20340 - -lemma sg32239 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20507 sg17213 - -lemma sg32240 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18031 - -lemma sg32241 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16690 - -lemma sg32242 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18285 sg20340 - -lemma sg32243 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17213 - -lemma sg32244 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18286 sg20340 - -lemma sg32245 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17188 - -lemma sg32246 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17188 - -lemma sg32247 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17188 - -lemma sg32248 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20650 sg16654 - -lemma sg32249 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17187 - -lemma sg32250 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20441 - -lemma sg32251 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20742 sg16218 - -lemma sg32252 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17189 - -lemma sg32253 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17189 - -lemma sg32254 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17189 - -lemma sg32255 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17187 - -lemma sg32256 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17188 - -lemma sg32257 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17188 - -lemma sg32258 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16668 - -lemma sg32259 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17190 - -lemma sg32260 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17190 - -lemma sg32261 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17190 - -lemma sg32262 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17189 - -lemma sg32263 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17189 - -lemma sg32264 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16669 - -lemma sg32265 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17190 - -lemma sg32266 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17190 - -lemma sg32267 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17190 - -lemma sg32268 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16670 - -lemma sg32269 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,8,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5731 sg31939 - -lemma sg32270 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,8,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17190 - -lemma sg32271 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,9,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5731 sg31940 - -lemma sg32272 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18275 sg20420 - -lemma sg32273 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18122 - -lemma sg32274 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20323 sg18292 - -lemma sg32275 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16677 - -lemma sg32276 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20324 sg18292 - -lemma sg32277 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16677 - -lemma sg32278 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20325 sg18292 - -lemma sg32279 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16245 - -lemma sg32280 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20546 - -lemma sg32281 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17191 - -lemma sg32282 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17342 - -lemma sg32283 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18297 - -lemma sg32284 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17342 - -lemma sg32285 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20315 sg18297 - -lemma sg32286 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18281 sg20358 - -lemma sg32287 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18297 - -lemma sg32288 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg16649 sg20663 - -lemma sg32289 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18282 sg20358 - -lemma sg32290 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18297 - -lemma sg32291 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg17147 sg20558 - -lemma sg32292 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18297 - -lemma sg32293 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg16650 sg20663 - -lemma sg32294 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17192 - -lemma sg32295 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20425 sg18117 - -lemma sg32296 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20754 sg16209 - -lemma sg32297 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17201 - -lemma sg32298 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18124 - -lemma sg32299 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17201 - -lemma sg32300 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17200 - -lemma sg32301 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18123 - -lemma sg32302 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17200 - -lemma sg32303 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17193 - -lemma sg32304 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16678 - -lemma sg32305 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20883 sg15698 - -lemma sg32306 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16671 - -lemma sg32307 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17200 - -lemma sg32308 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16678 - -lemma sg32309 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17200 - -lemma sg32310 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17202 - -lemma sg32311 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18125 - -lemma sg32312 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17202 - -lemma sg32313 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17201 - -lemma sg32314 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18124 - -lemma sg32315 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17201 - -lemma sg32316 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17194 - -lemma sg32317 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17194 - -lemma sg32318 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16679 - -lemma sg32319 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17201 - -lemma sg32320 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16679 - -lemma sg32321 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17201 - -lemma sg32322 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20883 sg15699 - -lemma sg32323 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20884 sg15699 - -lemma sg32324 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17202 - -lemma sg32325 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18125 - -lemma sg32326 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17202 - -lemma sg32327 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16680 - -lemma sg32328 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17202 - -lemma sg32329 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16680 - -lemma sg32330 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17202 - -lemma sg32331 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17195 - -lemma sg32332 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17195 - -lemma sg32333 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16672 - -lemma sg32334 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17150 sg20546 - -lemma sg32335 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18920 sg19626 - -lemma sg32336 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg15668 sg20950 - -lemma sg32337 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20326 sg18291 - -lemma sg32338 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20327 sg18291 - -lemma sg32339 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16673 - -lemma sg32340 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,8,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14313 sg21345 - -lemma sg32341 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,8,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14765 sg21269 - -lemma sg32342 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,8,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15613 sg21051 - -lemma sg32343 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,8,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14725 sg21270 - -lemma sg32344 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17347 - -lemma sg32345 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18299 - -lemma sg32346 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17347 - -lemma sg32347 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg19657 - -lemma sg32348 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg19657 - -lemma sg32349 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18299 - -lemma sg32350 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18911 sg19657 - -lemma sg32351 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg19657 - -lemma sg32352 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18299 - -lemma sg32353 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg18913 sg19657 - -lemma sg32354 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18299 - -lemma sg32355 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg18914 sg19657 - -lemma sg32356 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20691 sg16266 - -lemma sg32357 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20796 sg16158 - -lemma sg32358 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20509 sg17212 - -lemma sg32359 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17209 - -lemma sg32360 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18129 - -lemma sg32361 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17209 - -lemma sg32362 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17208 - -lemma sg32363 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18128 - -lemma sg32364 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17208 - -lemma sg32365 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17197 - -lemma sg32366 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16249 - -lemma sg32367 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16249 - -lemma sg32368 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17199 - -lemma sg32369 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17208 - -lemma sg32370 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16685 - -lemma sg32371 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17208 - -lemma sg32372 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17210 - -lemma sg32373 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18130 - -lemma sg32374 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17210 - -lemma sg32375 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17209 - -lemma sg32376 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18129 - -lemma sg32377 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17209 - -lemma sg32378 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16248 - -lemma sg32379 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17198 - -lemma sg32380 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16686 - -lemma sg32381 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17209 - -lemma sg32382 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16686 - -lemma sg32383 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17209 - -lemma sg32384 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16249 - -lemma sg32385 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20331 - -lemma sg32386 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17210 - -lemma sg32387 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18130 - -lemma sg32388 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17210 - -lemma sg32389 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16687 - -lemma sg32390 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17210 - -lemma sg32391 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16687 - -lemma sg32392 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17210 - -lemma sg32393 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16250 - -lemma sg32394 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20332 - -lemma sg32395 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16674 - -lemma sg32396 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17148 sg20547 - -lemma sg32397 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16251 - -lemma sg32398 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20424 sg18122 - -lemma sg32399 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16251 - -lemma sg32400 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20547 - -lemma sg32401 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17196 - -lemma sg32402 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20791 sg16191 - -lemma sg32403 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20827 sg16128 - -lemma sg32404 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20691 sg16267 - -lemma sg32405 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20796 sg16159 - -lemma sg32406 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20509 sg17213 - -lemma sg32407 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17211 - -lemma sg32408 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18131 - -lemma sg32409 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17211 - -lemma sg32410 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16252 - -lemma sg32411 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16252 - -lemma sg32412 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17200 - -lemma sg32413 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17197 - -lemma sg32414 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17212 - -lemma sg32415 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18132 - -lemma sg32416 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17212 - -lemma sg32417 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17211 - -lemma sg32418 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18131 - -lemma sg32419 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17211 - -lemma sg32420 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16252 - -lemma sg32421 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17200 - -lemma sg32422 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16688 - -lemma sg32423 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17211 - -lemma sg32424 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16688 - -lemma sg32425 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17211 - -lemma sg32426 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17212 - -lemma sg32427 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18132 - -lemma sg32428 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17212 - -lemma sg32429 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16689 - -lemma sg32430 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17212 - -lemma sg32431 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16689 - -lemma sg32432 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17212 - -lemma sg32433 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16253 - -lemma sg32434 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20333 - -lemma sg32435 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16675 - -lemma sg32436 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17202 - -lemma sg32437 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16254 - -lemma sg32438 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17202 - -lemma sg32439 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16254 - -lemma sg32440 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20334 - -lemma sg32441 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16676 - -lemma sg32442 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17150 sg20547 - -lemma sg32443 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20326 sg18292 - -lemma sg32444 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20327 sg18292 - -lemma sg32445 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16677 - -lemma sg32446 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,8,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14313 sg21346 - -lemma sg32447 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,8,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14725 sg21271 - -lemma sg32448 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15683 sg20898 - -lemma sg32449 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20827 sg16130 - -lemma sg32450 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg15682 sg20901 - -lemma sg32451 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17213 - -lemma sg32452 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18133 - -lemma sg32453 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17213 - -lemma sg32454 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17200 - -lemma sg32455 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20827 sg16131 - -lemma sg32456 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg15667 sg20951 - -lemma sg32457 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17200 - -lemma sg32458 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17200 - -lemma sg32459 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17213 - -lemma sg32460 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18133 - -lemma sg32461 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17213 - -lemma sg32462 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16690 - -lemma sg32463 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17213 - -lemma sg32464 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16690 - -lemma sg32465 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17213 - -lemma sg32466 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20651 sg16655 - -lemma sg32467 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16678 - -lemma sg32468 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17202 - -lemma sg32469 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17202 - -lemma sg32470 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17202 - -lemma sg32471 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17201 - -lemma sg32472 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17201 - -lemma sg32473 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16679 - -lemma sg32474 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17202 - -lemma sg32475 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17202 - -lemma sg32476 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17202 - -lemma sg32477 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16680 - -lemma sg32478 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15672 sg20950 - -lemma sg32479 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17202 - -lemma sg32480 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,8,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5731 sg31941 - -lemma sg32481 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18300 - -lemma sg32482 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16255 - -lemma sg32483 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg20698 sg16255 - -lemma sg32484 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20828 sg16126 - -lemma sg32485 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17348 - -lemma sg32486 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20315 sg18300 - -lemma sg32487 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16255 - -lemma sg32488 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16256 - -lemma sg32489 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16256 - -lemma sg32490 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16256 - -lemma sg32491 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18281 sg20361 - -lemma sg32492 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18300 - -lemma sg32493 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20756 sg16210 - -lemma sg32494 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18282 sg20361 - -lemma sg32495 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18300 - -lemma sg32496 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg17147 sg20559 - -lemma sg32497 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18300 - -lemma sg32498 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg20756 sg16211 - -lemma sg32499 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15608 sg21057 - -lemma sg32500 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15599 sg21078 - -lemma sg32501 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg15642 sg20991 - -lemma sg32502 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg15638 sg21041 - -lemma sg32503 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16384 - -lemma sg32504 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18301 - -lemma sg32505 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17203 - -lemma sg32506 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20757 sg16210 - -lemma sg32507 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17203 - -lemma sg32508 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16258 - -lemma sg32509 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16258 - -lemma sg32510 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16258 - -lemma sg32511 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17349 - -lemma sg32512 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20315 sg18301 - -lemma sg32513 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18281 sg20362 - -lemma sg32514 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18301 - -lemma sg32515 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg16649 sg20664 - -lemma sg32516 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18282 sg20362 - -lemma sg32517 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18301 - -lemma sg32518 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg17147 sg20560 - -lemma sg32519 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18301 - -lemma sg32520 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg16650 sg20664 - -lemma sg32521 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16260 - -lemma sg32522 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16260 - -lemma sg32523 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16260 - -lemma sg32524 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16257 - -lemma sg32525 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16257 - -lemma sg32526 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17204 - -lemma sg32527 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20756 sg16213 - -lemma sg32528 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15637 sg21042 - -lemma sg32529 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg15656 sg20961 - -lemma sg32530 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15607 sg21058 - -lemma sg32531 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20442 - -lemma sg32532 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg15594 sg21085 - -lemma sg32533 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16261 - -lemma sg32534 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16261 - -lemma sg32535 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16261 - -lemma sg32536 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15608 sg21058 - -lemma sg32537 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16256 - -lemma sg32538 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg15677 sg20903 - -lemma sg32539 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20424 sg18126 - -lemma sg32540 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17204 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes78 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 + +namespace OAI + +/-! Semigroup Nodes 79. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg32141 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17190 + +lemma sg32142 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16670 + +lemma sg32143 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17190 + +lemma sg32144 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17182 + +lemma sg32145 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17182 + +lemma sg32146 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16663 + +lemma sg32147 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,8,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14312 sg21345 + +lemma sg32148 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,8,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20439 + +lemma sg32149 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,8,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg14310 sg21348 + +lemma sg32150 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,8,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15224 sg21194 + +lemma sg32151 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,8,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17181 + +lemma sg32152 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,8,8,8,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17182 + +lemma sg32153 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15644 sg20985 + +lemma sg32154 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20440 + +lemma sg32155 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg15610 sg21053 + +lemma sg32156 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17185 + +lemma sg32157 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16232 + +lemma sg32158 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17185 + +lemma sg32159 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg15611 sg21053 + +lemma sg32160 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16232 + +lemma sg32161 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20542 + +lemma sg32162 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17183 + +lemma sg32163 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17317 + +lemma sg32164 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18296 + +lemma sg32165 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17317 + +lemma sg32166 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20315 sg18296 + +lemma sg32167 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18281 sg20356 + +lemma sg32168 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18296 + +lemma sg32169 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg16649 sg20661 + +lemma sg32170 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18282 sg20356 + +lemma sg32171 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18296 + +lemma sg32172 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg17147 sg20557 + +lemma sg32173 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18296 + +lemma sg32174 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg16650 sg20661 + +lemma sg32175 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17212 + +lemma sg32176 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20795 sg16158 + +lemma sg32177 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20505 sg17212 + +lemma sg32178 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17211 + +lemma sg32179 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18284 sg20338 + +lemma sg32180 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20507 sg17211 + +lemma sg32181 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16234 + +lemma sg32182 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16234 + +lemma sg32183 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17187 + +lemma sg32184 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17186 + +lemma sg32185 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18029 + +lemma sg32186 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16688 + +lemma sg32187 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18285 sg20338 + +lemma sg32188 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17211 + +lemma sg32189 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18286 sg20338 + +lemma sg32190 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20647 sg16654 + +lemma sg32191 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17212 + +lemma sg32192 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18284 sg20339 + +lemma sg32193 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20507 sg17212 + +lemma sg32194 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18030 + +lemma sg32195 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16689 + +lemma sg32196 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18285 sg20339 + +lemma sg32197 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17212 + +lemma sg32198 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18286 sg20339 + +lemma sg32199 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17188 + +lemma sg32200 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16235 + +lemma sg32201 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17188 + +lemma sg32202 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19180 + +lemma sg32203 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16235 + +lemma sg32204 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20543 + +lemma sg32205 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16237 + +lemma sg32206 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16237 + +lemma sg32207 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17190 + +lemma sg32208 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17189 + +lemma sg32209 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16236 + +lemma sg32210 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17189 + +lemma sg32211 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17184 + +lemma sg32212 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16236 + +lemma sg32213 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20544 + +lemma sg32214 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16665 + +lemma sg32215 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17190 + +lemma sg32216 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16237 + +lemma sg32217 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17190 + +lemma sg32218 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16237 + +lemma sg32219 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20545 + +lemma sg32220 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16666 + +lemma sg32221 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,8,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12864 sg21635 + +lemma sg32222 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,8,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15225 sg21194 + +lemma sg32223 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,8,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15604 sg21076 + +lemma sg32224 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,8,8,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17185 + +lemma sg32225 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20649 sg16652 + +lemma sg32226 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg15665 sg20953 + +lemma sg32227 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17213 + +lemma sg32228 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20795 sg16159 + +lemma sg32229 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20505 sg17213 + +lemma sg32230 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17186 + +lemma sg32231 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg15666 sg20951 + +lemma sg32232 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20741 sg16217 + +lemma sg32233 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20649 sg16654 + +lemma sg32234 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17186 + +lemma sg32235 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg15671 sg20947 + +lemma sg32236 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17186 + +lemma sg32237 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17213 + +lemma sg32238 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18284 sg20340 + +lemma sg32239 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20507 sg17213 + +lemma sg32240 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18031 + +lemma sg32241 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16690 + +lemma sg32242 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18285 sg20340 + +lemma sg32243 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17213 + +lemma sg32244 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18286 sg20340 + +lemma sg32245 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17188 + +lemma sg32246 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17188 + +lemma sg32247 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17188 + +lemma sg32248 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20650 sg16654 + +lemma sg32249 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17187 + +lemma sg32250 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20441 + +lemma sg32251 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20742 sg16218 + +lemma sg32252 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17189 + +lemma sg32253 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17189 + +lemma sg32254 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17189 + +lemma sg32255 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17187 + +lemma sg32256 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17188 + +lemma sg32257 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17188 + +lemma sg32258 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16668 + +lemma sg32259 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17190 + +lemma sg32260 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17190 + +lemma sg32261 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17190 + +lemma sg32262 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17189 + +lemma sg32263 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17189 + +lemma sg32264 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16669 + +lemma sg32265 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17190 + +lemma sg32266 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17190 + +lemma sg32267 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17190 + +lemma sg32268 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16670 + +lemma sg32269 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,8,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5731 sg31939 + +lemma sg32270 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,8,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17190 + +lemma sg32271 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,9,9,9,9,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5731 sg31940 + +lemma sg32272 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18275 sg20420 + +lemma sg32273 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18122 + +lemma sg32274 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20323 sg18292 + +lemma sg32275 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16677 + +lemma sg32276 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20324 sg18292 + +lemma sg32277 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16677 + +lemma sg32278 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20325 sg18292 + +lemma sg32279 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16245 + +lemma sg32280 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20546 + +lemma sg32281 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17191 + +lemma sg32282 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17342 + +lemma sg32283 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18297 + +lemma sg32284 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17342 + +lemma sg32285 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20315 sg18297 + +lemma sg32286 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18281 sg20358 + +lemma sg32287 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18297 + +lemma sg32288 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg16649 sg20663 + +lemma sg32289 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18282 sg20358 + +lemma sg32290 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18297 + +lemma sg32291 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg17147 sg20558 + +lemma sg32292 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18297 + +lemma sg32293 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg16650 sg20663 + +lemma sg32294 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17192 + +lemma sg32295 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20425 sg18117 + +lemma sg32296 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20754 sg16209 + +lemma sg32297 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17201 + +lemma sg32298 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18124 + +lemma sg32299 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17201 + +lemma sg32300 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17200 + +lemma sg32301 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18123 + +lemma sg32302 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17200 + +lemma sg32303 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17193 + +lemma sg32304 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16678 + +lemma sg32305 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20883 sg15698 + +lemma sg32306 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16671 + +lemma sg32307 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17200 + +lemma sg32308 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16678 + +lemma sg32309 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17200 + +lemma sg32310 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17202 + +lemma sg32311 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18125 + +lemma sg32312 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17202 + +lemma sg32313 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17201 + +lemma sg32314 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18124 + +lemma sg32315 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17201 + +lemma sg32316 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17194 + +lemma sg32317 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17194 + +lemma sg32318 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16679 + +lemma sg32319 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17201 + +lemma sg32320 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16679 + +lemma sg32321 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17201 + +lemma sg32322 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20883 sg15699 + +lemma sg32323 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20884 sg15699 + +lemma sg32324 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17202 + +lemma sg32325 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18125 + +lemma sg32326 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17202 + +lemma sg32327 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16680 + +lemma sg32328 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17202 + +lemma sg32329 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16680 + +lemma sg32330 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17202 + +lemma sg32331 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17195 + +lemma sg32332 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17195 + +lemma sg32333 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16672 + +lemma sg32334 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17150 sg20546 + +lemma sg32335 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18920 sg19626 + +lemma sg32336 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg15668 sg20950 + +lemma sg32337 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20326 sg18291 + +lemma sg32338 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20327 sg18291 + +lemma sg32339 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16673 + +lemma sg32340 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,8,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14313 sg21345 + +lemma sg32341 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,8,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14765 sg21269 + +lemma sg32342 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,8,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15613 sg21051 + +lemma sg32343 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,8,8,8,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14725 sg21270 + +lemma sg32344 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17347 + +lemma sg32345 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18299 + +lemma sg32346 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17347 + +lemma sg32347 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg19657 + +lemma sg32348 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg19657 + +lemma sg32349 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18299 + +lemma sg32350 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18911 sg19657 + +lemma sg32351 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg19657 + +lemma sg32352 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18299 + +lemma sg32353 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg18913 sg19657 + +lemma sg32354 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18299 + +lemma sg32355 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg18914 sg19657 + +lemma sg32356 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20691 sg16266 + +lemma sg32357 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20796 sg16158 + +lemma sg32358 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20509 sg17212 + +lemma sg32359 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17209 + +lemma sg32360 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18129 + +lemma sg32361 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17209 + +lemma sg32362 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17208 + +lemma sg32363 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18128 + +lemma sg32364 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17208 + +lemma sg32365 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17197 + +lemma sg32366 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16249 + +lemma sg32367 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16249 + +lemma sg32368 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17199 + +lemma sg32369 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17208 + +lemma sg32370 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16685 + +lemma sg32371 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17208 + +lemma sg32372 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17210 + +lemma sg32373 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18130 + +lemma sg32374 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17210 + +lemma sg32375 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17209 + +lemma sg32376 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18129 + +lemma sg32377 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17209 + +lemma sg32378 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16248 + +lemma sg32379 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17198 + +lemma sg32380 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16686 + +lemma sg32381 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17209 + +lemma sg32382 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16686 + +lemma sg32383 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17209 + +lemma sg32384 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16249 + +lemma sg32385 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20331 + +lemma sg32386 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17210 + +lemma sg32387 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18130 + +lemma sg32388 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17210 + +lemma sg32389 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16687 + +lemma sg32390 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17210 + +lemma sg32391 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16687 + +lemma sg32392 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17210 + +lemma sg32393 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16250 + +lemma sg32394 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20332 + +lemma sg32395 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16674 + +lemma sg32396 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17148 sg20547 + +lemma sg32397 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16251 + +lemma sg32398 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20424 sg18122 + +lemma sg32399 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16251 + +lemma sg32400 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20547 + +lemma sg32401 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,7,7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17196 + +lemma sg32402 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20791 sg16191 + +lemma sg32403 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20827 sg16128 + +lemma sg32404 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20691 sg16267 + +lemma sg32405 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20796 sg16159 + +lemma sg32406 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20509 sg17213 + +lemma sg32407 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17211 + +lemma sg32408 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18131 + +lemma sg32409 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17211 + +lemma sg32410 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16252 + +lemma sg32411 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16252 + +lemma sg32412 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17200 + +lemma sg32413 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17197 + +lemma sg32414 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17212 + +lemma sg32415 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18132 + +lemma sg32416 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17212 + +lemma sg32417 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17211 + +lemma sg32418 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18131 + +lemma sg32419 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17211 + +lemma sg32420 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16252 + +lemma sg32421 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17200 + +lemma sg32422 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16688 + +lemma sg32423 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17211 + +lemma sg32424 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16688 + +lemma sg32425 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17211 + +lemma sg32426 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17212 + +lemma sg32427 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18132 + +lemma sg32428 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17212 + +lemma sg32429 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16689 + +lemma sg32430 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17212 + +lemma sg32431 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16689 + +lemma sg32432 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17212 + +lemma sg32433 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16253 + +lemma sg32434 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20333 + +lemma sg32435 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16675 + +lemma sg32436 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17202 + +lemma sg32437 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16254 + +lemma sg32438 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17202 + +lemma sg32439 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16254 + +lemma sg32440 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20334 + +lemma sg32441 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16676 + +lemma sg32442 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17150 sg20547 + +lemma sg32443 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20326 sg18292 + +lemma sg32444 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20327 sg18292 + +lemma sg32445 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16677 + +lemma sg32446 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,8,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14313 sg21346 + +lemma sg32447 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,8,8,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14725 sg21271 + +lemma sg32448 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15683 sg20898 + +lemma sg32449 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20827 sg16130 + +lemma sg32450 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg15682 sg20901 + +lemma sg32451 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17213 + +lemma sg32452 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18133 + +lemma sg32453 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17213 + +lemma sg32454 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17200 + +lemma sg32455 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20827 sg16131 + +lemma sg32456 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg15667 sg20951 + +lemma sg32457 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17200 + +lemma sg32458 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17200 + +lemma sg32459 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17213 + +lemma sg32460 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18133 + +lemma sg32461 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17213 + +lemma sg32462 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16690 + +lemma sg32463 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17213 + +lemma sg32464 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16690 + +lemma sg32465 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17213 + +lemma sg32466 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20651 sg16655 + +lemma sg32467 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16678 + +lemma sg32468 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17202 + +lemma sg32469 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17202 + +lemma sg32470 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17202 + +lemma sg32471 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17201 + +lemma sg32472 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17201 + +lemma sg32473 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16679 + +lemma sg32474 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17202 + +lemma sg32475 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17202 + +lemma sg32476 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17202 + +lemma sg32477 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16680 + +lemma sg32478 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15672 sg20950 + +lemma sg32479 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17202 + +lemma sg32480 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,9,9,8,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5731 sg31941 + +lemma sg32481 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18300 + +lemma sg32482 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16255 + +lemma sg32483 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg20698 sg16255 + +lemma sg32484 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20828 sg16126 + +lemma sg32485 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17348 + +lemma sg32486 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20315 sg18300 + +lemma sg32487 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16255 + +lemma sg32488 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16256 + +lemma sg32489 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16256 + +lemma sg32490 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16256 + +lemma sg32491 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18281 sg20361 + +lemma sg32492 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18300 + +lemma sg32493 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20756 sg16210 + +lemma sg32494 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18282 sg20361 + +lemma sg32495 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18300 + +lemma sg32496 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg17147 sg20559 + +lemma sg32497 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18300 + +lemma sg32498 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg20756 sg16211 + +lemma sg32499 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15608 sg21057 + +lemma sg32500 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15599 sg21078 + +lemma sg32501 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg15642 sg20991 + +lemma sg32502 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg15638 sg21041 + +lemma sg32503 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16384 + +lemma sg32504 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18301 + +lemma sg32505 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17203 + +lemma sg32506 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20757 sg16210 + +lemma sg32507 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17203 + +lemma sg32508 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16258 + +lemma sg32509 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16258 + +lemma sg32510 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16258 + +lemma sg32511 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17349 + +lemma sg32512 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20315 sg18301 + +lemma sg32513 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18281 sg20362 + +lemma sg32514 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18301 + +lemma sg32515 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg16649 sg20664 + +lemma sg32516 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18282 sg20362 + +lemma sg32517 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18301 + +lemma sg32518 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg17147 sg20560 + +lemma sg32519 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18301 + +lemma sg32520 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg16650 sg20664 + +lemma sg32521 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16260 + +lemma sg32522 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16260 + +lemma sg32523 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16260 + +lemma sg32524 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16257 + +lemma sg32525 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16257 + +lemma sg32526 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17204 + +lemma sg32527 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20756 sg16213 + +lemma sg32528 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15637 sg21042 + +lemma sg32529 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg15656 sg20961 + +lemma sg32530 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15607 sg21058 + +lemma sg32531 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20442 + +lemma sg32532 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg15594 sg21085 + +lemma sg32533 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16261 + +lemma sg32534 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16261 + +lemma sg32535 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16261 + +lemma sg32536 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15608 sg21058 + +lemma sg32537 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16256 + +lemma sg32538 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg15677 sg20903 + +lemma sg32539 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20424 sg18126 + +lemma sg32540 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17204 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes8.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes8.lean index 79fab4a19f64d4d706949ac20ca9d725f6292f74..18e0fcc477b93b6ab5d6934cf9f17f30106af842 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes8.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes8.lean @@ -1,1219 +1,1219 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes6 - -namespace OAI - -/-! Semigroup Nodes 8. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg3708 : RowSquare [9,2,2,2] [4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg181 sg371 - -lemma sg3709 : RowSquare [9,2,2,2] [4,4,3,2,2] := by - exact rowSquare_join (by decide) sg180 sg372 - -lemma sg3710 : RowSquare [9,2,2,2] [4,4,3,3,1] := by - exact rowSquare_join (by decide) sg180 sg373 - -lemma sg3711 : RowSquare [9,2,2,2] [4,4,4,2,1] := by - exact rowSquare_join (by decide) sg181 sg372 - -lemma sg3712 : RowSquare [9,2,2,2] [4,4,4,3] := by - exact rowSquare_join (by decide) sg181 sg373 - -lemma sg3713 : RowSquare [9,2,2,2] [5,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg179 sg374 - -lemma sg3714 : RowSquare [9,2,2,2] [5,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg179 sg375 - -lemma sg3715 : RowSquare [9,2,2,2] [5,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg179 sg376 - -lemma sg3716 : RowSquare [9,2,2,2] [5,3,3,3,1] := by - exact rowSquare_join (by decide) sg182 sg373 - -lemma sg3717 : RowSquare [9,2,2,2] [5,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg179 sg377 - -lemma sg3718 : RowSquare [9,2,2,2] [5,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg378 - -lemma sg3719 : RowSquare [9,2,2,2] [5,4,3,3] := by - exact rowSquare_join (by decide) sg183 sg373 - -lemma sg3720 : RowSquare [9,2,2,2] [5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg383 - -lemma sg3721 : RowSquare [9,3,1,1,1] [3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg97 sg586 - -lemma sg3722 : RowSquare [9,3,1,1,1] [4,4,3,2,2] := by - exact rowSquare_join (by decide) sg40 sg1001 - -lemma sg3723 : RowSquare [9,3,2,1] [3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg389 - -lemma sg3724 : RowSquare [9,3,2,1] [3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg390 - -lemma sg3725 : RowSquare [9,3,2,1] [3,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg32 sg1032 - -lemma sg3726 : RowSquare [9,3,2,1] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg1033 - -lemma sg3727 : RowSquare [9,3,2,1] [4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg218 sg330 - -lemma sg3728 : RowSquare [9,3,2,1] [4,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg193 sg371 - -lemma sg3729 : RowSquare [9,3,2,1] [4,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg193 sg373 - -lemma sg3730 : RowSquare [9,3,2,1] [4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg194 sg371 - -lemma sg3731 : RowSquare [9,3,2,1] [4,4,4,3] := by - exact rowSquare_join (by decide) sg195 sg373 - -lemma sg3732 : RowSquare [9,3,3] [3,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg1061 - -lemma sg3733 : RowSquare [9,3,3] [4,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg32 sg1063 - -lemma sg3734 : RowSquare [9,3,3] [4,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg88 sg636 - -lemma sg3735 : RowSquare [9,3,3] [4,4,3,3,1] := by - exact rowSquare_join (by decide) sg88 sg637 - -lemma sg3736 : RowSquare [9,3,3] [5,5,5] := by - exact rowSquare_join (by decide) sg89 sg641 - -lemma sg3737 : RowSquare [9,4,1,1] [4,4,3,2,2] := by - exact rowSquare_join (by decide) sg40 sg1033 - -lemma sg3738 : RowSquare [9,4,1,1] [5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg407 - -lemma sg3741 : RowSquare [2,2,2,2,2,2,2,1,1] [6,6,2,2] := by - exact rowSquare_join (by decide) sg364 sg407 - -lemma sg3744 : RowSquare [3,2,2,2,2,2,2,1] [4,4,4,4] := by - exact rowSquare_join (by decide) sg364 sg358 - -lemma sg3745 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2] := by - exact rowSquare_join (by decide) sg413 sg413 - -lemma sg3746 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,1] := by - exact rowSquare_join (by decide) sg413 sg414 - -lemma sg3747 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [8,3,3,1,1] := by - exact rowSquare_join (by decide) sg413 sg415 - -lemma sg3748 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [8,4,2,2] := by - exact rowSquare_join (by decide) sg414 sg414 - -lemma sg3749 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [8,4,3,1] := by - exact rowSquare_join (by decide) sg414 sg415 - -lemma sg3750 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [9,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg234 sg636 - -lemma sg3751 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [9,3,2,2] := by - exact rowSquare_join (by decide) sg414 sg416 - -lemma sg3752 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [9,5,1,1] := by - exact rowSquare_join (by decide) sg414 sg418 - -lemma sg3753 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [10,4,1,1] := by - exact rowSquare_join (by decide) sg414 sg420 - -lemma sg3754 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [10,5,1] := by - exact rowSquare_join (by decide) sg417 sg418 - -lemma sg3755 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [11,3,1,1] := by - exact rowSquare_join (by decide) sg352 sg426 - -lemma sg3756 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [12,2,1,1] := by - exact rowSquare_join (by decide) sg414 sg421 - -lemma sg3757 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,3,3,2,2] := by - exact rowSquare_join (by decide) sg389 sg413 - -lemma sg3758 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,1] := by - exact rowSquare_join (by decide) sg413 sg390 - -lemma sg3759 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,4,2,2,2] := by - exact rowSquare_join (by decide) sg218 sg694 - -lemma sg3760 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,4,3,2,1] := by - exact rowSquare_join (by decide) sg389 sg414 - -lemma sg3761 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,4,3,3] := by - exact rowSquare_join (by decide) sg390 sg414 - -lemma sg3762 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,4,4,1,1] := by - exact rowSquare_join (by decide) sg389 sg415 - -lemma sg3763 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,4,4,2] := by - exact rowSquare_join (by decide) sg390 sg415 - -lemma sg3764 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,5,5] := by - exact rowSquare_join (by decide) sg220 sg696 - -lemma sg3765 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,6,4] := by - exact rowSquare_join (by decide) sg89 sg1110 - -lemma sg3766 : RowSquare [3,3,2,2,1,1,1,1,1,1] [4,4,4,2,2] := by - exact rowSquare_join (by decide) sg389 sg389 - -lemma sg3767 : RowSquare [3,3,2,2,1,1,1,1,1,1] [4,4,4,3,1] := by - exact rowSquare_join (by decide) sg389 sg390 - -lemma sg3768 : RowSquare [3,3,2,2,1,1,1,1,1,1] [4,4,4,4] := by - exact rowSquare_join (by decide) sg390 sg390 - -lemma sg3769 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,3,3,3,2] := by - exact rowSquare_join (by decide) sg218 sg644 - -lemma sg3770 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg193 sg694 - -lemma sg3771 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg193 sg695 - -lemma sg3772 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,3,2,2] := by - exact rowSquare_join (by decide) sg389 sg392 - -lemma sg3773 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,3,3,1] := by - exact rowSquare_join (by decide) sg392 sg390 - -lemma sg3774 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,4,1,1,1] := by - exact rowSquare_join (by decide) sg193 sg696 - -lemma sg3775 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,4,2,1] := by - exact rowSquare_join (by decide) sg389 sg393 - -lemma sg3776 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,4,3] := by - exact rowSquare_join (by decide) sg390 sg393 - -lemma sg3777 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg1109 - -lemma sg3778 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,2,2,2] := by - exact rowSquare_join (by decide) sg194 sg694 - -lemma sg3779 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg228 sg636 - -lemma sg3780 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,3,2,1] := by - exact rowSquare_join (by decide) sg389 sg394 - -lemma sg3781 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,3,3] := by - exact rowSquare_join (by decide) sg390 sg394 - -lemma sg3782 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,4,1,1] := by - exact rowSquare_join (by decide) sg389 sg395 - -lemma sg3783 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,4,2] := by - exact rowSquare_join (by decide) sg390 sg395 - -lemma sg3784 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,5,1] := by - exact rowSquare_join (by decide) sg195 sg696 - -lemma sg3785 : RowSquare [3,3,2,2,1,1,1,1,1,1] [6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg391 sg391 - -lemma sg3786 : RowSquare [3,3,2,2,1,1,1,1,1,1] [6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg348 sg424 - -lemma sg3787 : RowSquare [3,3,2,2,1,1,1,1,1,1] [6,6,2,2] := by - exact rowSquare_join (by decide) sg390 sg396 - -lemma sg3788 : RowSquare [3,3,2,2,2,2,1,1] [4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg306 sg403 - -lemma sg3789 : RowSquare [3,3,2,2,2,2,2] [8,8] := by - exact rowSquare_join (by decide) sg367 sg311 - -lemma sg3790 : RowSquare [3,3,3,2,1,1,1,1,1] [4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg1063 - -lemma sg3791 : RowSquare [3,3,3,2,1,1,1,1,1] [4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg88 sg975 - -lemma sg3792 : RowSquare [3,3,3,2,1,1,1,1,1] [4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg348 sg389 - -lemma sg3793 : RowSquare [3,3,3,2,1,1,1,1,1] [4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg348 sg390 - -lemma sg3794 : RowSquare [3,3,3,2,1,1,1,1,1] [4,4,3,3,2] := by - exact rowSquare_join (by decide) sg194 sg637 - -lemma sg3795 : RowSquare [3,3,3,2,1,1,1,1,1] [4,4,4,4] := by - exact rowSquare_join (by decide) sg390 sg350 - -lemma sg3796 : RowSquare [3,3,3,2,1,1,1,1,1] [5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg306 sg415 - -lemma sg3797 : RowSquare [4,2,2,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg422 - -lemma sg3798 : RowSquare [4,2,2,2,2,2,1,1] [4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg207 sg561 - -lemma sg3799 : RowSquare [4,2,2,2,2,2,1,1] [4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg365 - -lemma sg3800 : RowSquare [4,2,2,2,2,2,1,1] [4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg958 - -lemma sg3801 : RowSquare [4,2,2,2,2,2,1,1] [4,4,4,3,1] := by - exact rowSquare_join (by decide) sg333 sg364 - -lemma sg3802 : RowSquare [4,2,2,2,2,2,1,1] [4,4,4,4] := by - exact rowSquare_join (by decide) sg364 sg334 - -lemma sg3803 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg413 - -lemma sg3804 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg414 - -lemma sg3805 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg413 - -lemma sg3806 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg415 - -lemma sg3807 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,3,3,2,2] := by - exact rowSquare_join (by decide) sg372 sg413 - -lemma sg3808 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,3,3,3,1] := by - exact rowSquare_join (by decide) sg413 sg373 - -lemma sg3809 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg415 - -lemma sg3810 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,4,3,3] := by - exact rowSquare_join (by decide) sg373 sg414 - -lemma sg3811 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,4,4,1,1] := by - exact rowSquare_join (by decide) sg372 sg415 - -lemma sg3812 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,4,4,2] := by - exact rowSquare_join (by decide) sg373 sg415 - -lemma sg3813 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg416 - -lemma sg3814 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg374 sg413 - -lemma sg3815 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg417 - -lemma sg3816 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg371 sg416 - -lemma sg3817 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,3,2,2,2] := by - exact rowSquare_join (by decide) sg375 sg413 - -lemma sg3818 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg374 sg415 - -lemma sg3819 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,3,3,2,1] := by - exact rowSquare_join (by decide) sg372 sg416 - -lemma sg3820 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,3,3,3] := by - exact rowSquare_join (by decide) sg373 sg416 - -lemma sg3821 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg418 - -lemma sg3822 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg417 - -lemma sg3823 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,4,2,2,1] := by - exact rowSquare_join (by decide) sg375 sg414 - -lemma sg3824 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,4,3,1,1] := by - exact rowSquare_join (by decide) sg372 sg417 - -lemma sg3825 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,4,3,2] := by - exact rowSquare_join (by decide) sg373 sg417 - -lemma sg3826 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,4,4,1] := by - exact rowSquare_join (by decide) sg376 sg415 - -lemma sg3827 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg418 - -lemma sg3828 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,5,2,1,1] := by - exact rowSquare_join (by decide) sg372 sg418 - -lemma sg3829 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,5,2,2] := by - exact rowSquare_join (by decide) sg373 sg418 - -lemma sg3830 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,5,3,1] := by - exact rowSquare_join (by decide) sg377 sg415 - -lemma sg3831 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,5,4] := by - exact rowSquare_join (by decide) sg378 sg415 - -lemma sg3832 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg389 - -lemma sg3833 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg390 - -lemma sg3834 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,3,3,3,2,1] := by - exact rowSquare_join (by decide) sg87 sg1032 - -lemma sg3835 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,3,3,3,3] := by - exact rowSquare_join (by decide) sg87 sg1033 - -lemma sg3836 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg694 - -lemma sg3837 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg695 - -lemma sg3838 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg696 - -lemma sg3839 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,4,4,4] := by - exact rowSquare_join (by decide) sg390 sg373 - -lemma sg3840 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg413 - -lemma sg3841 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg414 - -lemma sg3842 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg391 - -lemma sg3843 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg415 - -lemma sg3844 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg391 sg373 - -lemma sg3845 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,3,3,3,2] := by - exact rowSquare_join (by decide) sg218 sg616 - -lemma sg3846 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg392 - -lemma sg3847 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg701 - -lemma sg3848 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,5,5,1] := by - exact rowSquare_join (by decide) sg181 sg696 - -lemma sg3849 : RowSquare [4,3,2,2,1,1,1,1,1] [4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg391 - -lemma sg3850 : RowSquare [4,3,2,2,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg104 sg849 - -lemma sg3851 : RowSquare [4,3,2,2,1,1,1,1,1] [5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg370 sg359 - -lemma sg3852 : RowSquare [4,3,2,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg106 sg849 - -lemma sg3853 : RowSquare [4,3,2,2,1,1,1,1,1] [6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg104 sg850 - -lemma sg3854 : RowSquare [4,3,2,2,1,1,1,1,1] [6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg3181 - -lemma sg3855 : RowSquare [4,3,2,2,1,1,1,1,1] [6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg105 sg850 - -lemma sg3856 : RowSquare [4,3,2,2,1,1,1,1,1] [6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg0 sg3182 - -lemma sg3857 : RowSquare [4,3,2,2,1,1,1,1,1] [6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg399 - -lemma sg3858 : RowSquare [4,3,2,2,2,2,1] [3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg879 - -lemma sg3859 : RowSquare [4,3,2,2,2,2,1] [4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg849 - -lemma sg3860 : RowSquare [4,3,2,2,2,2,1] [4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg165 sg561 - -lemma sg3861 : RowSquare [4,3,2,2,2,2,1] [4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg83 sg850 - -lemma sg3862 : RowSquare [4,3,2,2,2,2,1] [5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg84 sg850 - -lemma sg3863 : RowSquare [4,3,2,2,2,2,1] [5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg85 sg849 - -lemma sg3864 : RowSquare [4,3,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg86 sg849 - -lemma sg3865 : RowSquare [4,3,3,2,1,1,1,1] [7,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg96 sg849 - -lemma sg3866 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg370 sg370 - -lemma sg3867 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg370 sg371 - -lemma sg3868 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg372 - -lemma sg3869 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg373 - -lemma sg3870 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg371 - -lemma sg3871 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,4,3,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg372 - -lemma sg3872 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg371 sg373 - -lemma sg3873 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,4,4,2,2] := by - exact rowSquare_join (by decide) sg372 sg372 - -lemma sg3874 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,4,4,3,1] := by - exact rowSquare_join (by decide) sg372 sg373 - -lemma sg3875 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,4,4,4] := by - exact rowSquare_join (by decide) sg373 sg373 - -lemma sg3876 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg370 sg374 - -lemma sg3877 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg375 - -lemma sg3878 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg371 sg374 - -lemma sg3879 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg376 - -lemma sg3880 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg374 sg372 - -lemma sg3881 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,3,3,3,1,1] := by - exact rowSquare_join (by decide) sg374 sg373 - -lemma sg3882 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg377 - -lemma sg3883 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,2,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg375 - -lemma sg3884 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg378 - -lemma sg3885 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,3,2,1,1] := by - exact rowSquare_join (by decide) sg371 sg376 - -lemma sg3886 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,3,2,2] := by - exact rowSquare_join (by decide) sg372 sg375 - -lemma sg3887 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,3,3,1] := by - exact rowSquare_join (by decide) sg375 sg373 - -lemma sg3888 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,4,2,1] := by - exact rowSquare_join (by decide) sg372 sg376 - -lemma sg3889 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,4,3] := by - exact rowSquare_join (by decide) sg373 sg376 - -lemma sg3890 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg371 sg377 - -lemma sg3891 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,5,3,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg378 - -lemma sg3892 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,5,3,2,1] := by - exact rowSquare_join (by decide) sg372 sg377 - -lemma sg3893 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,5,3,3] := by - exact rowSquare_join (by decide) sg373 sg377 - -lemma sg3894 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,5,4,1,1] := by - exact rowSquare_join (by decide) sg372 sg378 - -lemma sg3895 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,5,4,2] := by - exact rowSquare_join (by decide) sg373 sg378 - -lemma sg3896 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg370 sg379 - -lemma sg3897 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg374 sg374 - -lemma sg3898 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg371 sg379 - -lemma sg3899 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,3,3,2,2] := by - exact rowSquare_join (by decide) sg372 sg379 - -lemma sg3900 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,3,3,3,1] := by - exact rowSquare_join (by decide) sg379 sg373 - -lemma sg3901 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,4,2,2,2] := by - exact rowSquare_join (by decide) sg375 sg375 - -lemma sg3902 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,5,3,2] := by - exact rowSquare_join (by decide) sg373 sg382 - -lemma sg3903 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg383 - -lemma sg3904 : RowSquare [4,4,1,1,1,1,1,1,1,1] [7,6,1,1,1] := by - exact rowSquare_join (by decide) sg375 sg383 - -lemma sg3905 : RowSquare [4,4,1,1,1,1,1,1,1,1] [8,8] := by - exact rowSquare_join (by decide) sg383 sg383 - -lemma sg3906 : RowSquare [4,4,1,1,1,1,1,1,1,1] [9,7] := by - exact rowSquare_join (by decide) sg383 sg386 - -lemma sg3907 : RowSquare [4,4,1,1,1,1,1,1,1,1] [10,6] := by - exact rowSquare_join (by decide) sg14 sg1577 - -lemma sg3908 : RowSquare [4,4,1,1,1,1,1,1,1,1] [11,5] := by - exact rowSquare_join (by decide) sg14 sg1578 - -lemma sg3909 : RowSquare [4,4,1,1,1,1,1,1,1,1] [12,4] := by - exact rowSquare_join (by decide) sg14 sg1579 - -lemma sg3910 : RowSquare [4,4,1,1,1,1,1,1,1,1] [13,3] := by - exact rowSquare_join (by decide) sg14 sg1580 - -lemma sg3911 : RowSquare [4,4,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg330 sg370 - -lemma sg3912 : RowSquare [4,4,2,1,1,1,1,1,1] [3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg330 sg371 - -lemma sg3913 : RowSquare [4,4,2,1,1,1,1,1,1] [3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg372 - -lemma sg3914 : RowSquare [4,4,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg373 - -lemma sg3915 : RowSquare [4,4,2,1,1,1,1,1,1] [4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg370 sg331 - -lemma sg3916 : RowSquare [4,4,2,1,1,1,1,1,1] [4,4,4,4] := by - exact rowSquare_join (by decide) sg373 sg334 - -lemma sg3917 : RowSquare [4,4,2,1,1,1,1,1,1] [6,6,1,1,1,1] := by - exact rowSquare_join (by decide) sg371 sg342 - -lemma sg3918 : RowSquare [4,4,2,1,1,1,1,1,1] [7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg387 - -lemma sg3919 : RowSquare [4,4,2,1,1,1,1,1,1] [7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg343 - -lemma sg3920 : RowSquare [4,4,2,1,1,1,1,1,1] [7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg388 - -lemma sg3921 : RowSquare [4,4,2,1,1,1,1,1,1] [7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg344 - -lemma sg3922 : RowSquare [4,4,2,1,1,1,1,1,1] [7,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg2500 - -lemma sg3923 : RowSquare [4,4,2,1,1,1,1,1,1] [7,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg2501 - -lemma sg3924 : RowSquare [4,4,2,1,1,1,1,1,1] [7,3,3,3] := by - exact rowSquare_join (by decide) sg1 sg2502 - -lemma sg3925 : RowSquare [4,4,2,1,1,1,1,1,1] [7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg370 sg345 - -lemma sg3926 : RowSquare [4,4,2,1,1,1,1,1,1] [7,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg2503 - -lemma sg3927 : RowSquare [4,4,2,1,1,1,1,1,1] [8,8] := by - exact rowSquare_join (by decide) sg14 sg1581 - -lemma sg3928 : RowSquare [4,4,2,1,1,1,1,1,1] [9,7] := by - exact rowSquare_join (by decide) sg14 sg1582 - -lemma sg3929 : RowSquare [4,4,2,1,1,1,1,1,1] [10,2,2,2] := by - exact rowSquare_join (by decide) sg26 sg1123 - -lemma sg3930 : RowSquare [4,4,2,1,1,1,1,1,1] [10,6] := by - exact rowSquare_join (by decide) sg29 sg1122 - -lemma sg3931 : RowSquare [4,4,2,1,1,1,1,1,1] [11,5] := by - exact rowSquare_join (by decide) sg29 sg1124 - -lemma sg3932 : RowSquare [4,4,2,1,1,1,1,1,1] [12,4] := by - exact rowSquare_join (by decide) sg29 sg1125 - -lemma sg3933 : RowSquare [4,4,2,1,1,1,1,1,1] [13,3] := by - exact rowSquare_join (by decide) sg174 sg427 - -lemma sg3934 : RowSquare [4,4,2,1,1,1,1,1,1] [14,2] := by - exact rowSquare_join (by decide) sg176 sg427 - -lemma sg3935 : RowSquare [4,4,2,2,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg1650 - -lemma sg3936 : RowSquare [4,4,2,2,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg1651 - -lemma sg3937 : RowSquare [4,4,2,2,2,1,1] [4,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg1650 - -lemma sg3938 : RowSquare [4,4,2,2,2,1,1] [4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg16 sg1651 - -lemma sg3939 : RowSquare [4,4,2,2,2,1,1] [4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1651 - -lemma sg3940 : RowSquare [4,4,2,2,2,1,1] [4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17 sg1652 - -lemma sg3941 : RowSquare [4,4,2,2,2,1,1] [4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg332 sg295 - -lemma sg3942 : RowSquare [4,4,2,2,2,1,1] [5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg1650 - -lemma sg3943 : RowSquare [4,4,2,2,2,1,1] [5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18 sg1651 - -lemma sg3944 : RowSquare [4,4,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19 sg1651 - -lemma sg3945 : RowSquare [5,3,1,1,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg224 sg586 - -lemma sg3946 : RowSquare [5,3,1,1,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg225 sg586 - -lemma sg3947 : RowSquare [5,3,1,1,1,1,1,1,1,1] [6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg223 sg587 - -lemma sg3948 : RowSquare [5,3,2,1,1,1,1,1,1] [3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg194 sg586 - -lemma sg3949 : RowSquare [5,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg998 - -lemma sg3950 : RowSquare [5,3,2,1,1,1,1,1,1] [3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg89 sg910 - -lemma sg3951 : RowSquare [5,3,2,1,1,1,1,1,1] [3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg999 - -lemma sg3952 : RowSquare [5,3,2,1,1,1,1,1,1] [3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg74 sg1000 - -lemma sg3953 : RowSquare [5,3,2,1,1,1,1,1,1] [3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg1001 - -lemma sg3954 : RowSquare [5,3,2,1,1,1,1,1,1] [4,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg90 sg910 - -lemma sg3955 : RowSquare [5,3,2,1,1,1,1,1,1] [4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg92 sg910 - -lemma sg3956 : RowSquare [5,3,2,1,1,1,1,1,1] [4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg1006 - -lemma sg3957 : RowSquare [5,3,2,1,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20 sg1682 - -lemma sg3958 : RowSquare [5,3,2,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg94 sg910 - -lemma sg3959 : RowSquare [5,3,2,2,2,1,1] [4,4,4,4] := by - exact rowSquare_join (by decide) sg358 sg271 - -lemma sg3960 : RowSquare [5,3,2,2,2,1,1] [5,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg1682 - -lemma sg3961 : RowSquare [5,3,2,2,2,1,1] [5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14 sg1689 - -lemma sg3962 : RowSquare [5,3,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15 sg1683 - -lemma sg3963 : RowSquare [5,3,3,2,2,1] [3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg306 sg271 - -lemma sg3964 : RowSquare [5,4,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg178 sg586 - -lemma sg3965 : RowSquare [5,4,1,1,1,1,1,1,1] [3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg179 sg586 - -lemma sg3966 : RowSquare [5,4,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg178 sg587 - -lemma sg3967 : RowSquare [5,4,1,1,1,1,1,1,1] [3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg178 sg588 - -lemma sg3968 : RowSquare [5,4,1,1,1,1,1,1,1] [4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg179 sg589 - -lemma sg3969 : RowSquare [5,4,1,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg191 sg586 - -lemma sg3970 : RowSquare [5,4,1,1,1,1,1,1,1] [7,7,1,1] := by - exact rowSquare_join (by decide) sg377 sg324 - -lemma sg3971 : RowSquare [5,4,1,1,1,1,1,1,1] [7,7,2] := by - exact rowSquare_join (by decide) sg378 sg324 - -lemma sg3972 : RowSquare [5,4,1,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg192 sg586 - -lemma sg3973 : RowSquare [5,4,1,1,1,1,1,1,1] [8,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg2521 - -lemma sg3974 : RowSquare [5,4,1,1,1,1,1,1,1] [8,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg2522 - -lemma sg3975 : RowSquare [5,4,1,1,1,1,1,1,1] [8,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg13 sg1584 - -lemma sg3976 : RowSquare [5,4,1,1,1,1,1,1,1] [8,2,2,2,2] := by - exact rowSquare_join (by decide) sg6 sg2021 - -lemma sg3977 : RowSquare [5,4,1,1,1,1,1,1,1] [8,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg2523 - -lemma sg3978 : RowSquare [5,4,1,1,1,1,1,1,1] [8,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg2026 - -lemma sg3979 : RowSquare [5,4,1,1,1,1,1,1,1] [8,3,2,2,1] := by - exact rowSquare_join (by decide) sg13 sg1585 - -lemma sg3980 : RowSquare [5,4,1,1,1,1,1,1,1] [8,3,3,1,1] := by - exact rowSquare_join (by decide) sg4 sg2027 - -lemma sg3981 : RowSquare [5,4,1,1,1,1,1,1,1] [8,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg2025 - -lemma sg3982 : RowSquare [5,4,1,1,1,1,1,1,1] [8,8] := by - exact rowSquare_join (by decide) sg383 sg324 - -lemma sg3983 : RowSquare [5,4,2,1,1,1,1,1] [3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg67 sg910 - -lemma sg3984 : RowSquare [5,4,2,1,1,1,1,1] [3,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg68 sg910 - -lemma sg3985 : RowSquare [5,4,2,1,1,1,1,1] [4,3,3,3,3] := by - exact rowSquare_join (by decide) sg66 sg915 - -lemma sg3986 : RowSquare [5,4,2,1,1,1,1,1] [4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg71 sg910 - -lemma sg3987 : RowSquare [5,4,2,1,1,1,1,1] [4,4,4,4] := by - exact rowSquare_join (by decide) sg373 sg271 - -lemma sg3988 : RowSquare [5,4,2,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg2534 - -lemma sg3989 : RowSquare [5,4,2,2,2,1] [5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg1 sg2605 - -lemma sg3990 : RowSquare [5,4,2,2,2,1] [5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg1 sg2606 - -lemma sg3991 : RowSquare [5,4,2,2,2,1] [5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg2609 - -lemma sg3992 : RowSquare [5,4,3,2,1,1] [3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg759 - -lemma sg3993 : RowSquare [5,4,3,2,1,1] [4,3,3,3,3] := by - exact rowSquare_join (by decide) sg0 sg3249 - -lemma sg3994 : RowSquare [5,5,1,1,1,1,1,1] [4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg1 sg2546 - -lemma sg3995 : RowSquare [5,5,1,1,1,1,1,1] [4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg313 sg313 - -lemma sg3996 : RowSquare [5,5,1,1,1,1,1,1] [5,3,3,3,2] := by - exact rowSquare_join (by decide) sg13 sg1592 - -lemma sg3997 : RowSquare [5,5,1,1,1,1,1,1] [6,3,3,2,2] := by - exact rowSquare_join (by decide) sg1 sg2553 - -lemma sg3999 : RowSquare [5,5,2,2,2] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg121 sg509 - -lemma sg4000 : RowSquare [5,5,2,2,2] [2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg120 sg509 - -lemma sg4001 : RowSquare [5,5,2,2,2] [2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg118 sg509 - -lemma sg4002 : RowSquare [5,5,2,2,2] [2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg118 sg507 - -lemma sg4003 : RowSquare [5,5,2,2,2] [2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg118 sg506 - -lemma sg4004 : RowSquare [5,5,2,2,2] [2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg118 sg503 - -lemma sg4005 : RowSquare [5,5,2,2,2] [2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg14 sg1617 - -lemma sg4006 : RowSquare [5,5,2,2,2] [3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg119 sg509 - -lemma sg4007 : RowSquare [5,5,2,2,2] [3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg117 sg509 - -lemma sg4008 : RowSquare [5,5,2,2,2] [3,2,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg115 sg508 - -lemma sg4009 : RowSquare [5,5,2,2,2] [3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg115 sg507 - -lemma sg4010 : RowSquare [5,5,2,2,2] [3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg115 sg506 - -lemma sg4011 : RowSquare [5,5,2,2,2] [3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg115 sg503 - -lemma sg4012 : RowSquare [5,5,2,2,2] [3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg114 sg509 - -lemma sg4013 : RowSquare [5,5,2,2,2] [3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg114 sg508 - -lemma sg4014 : RowSquare [5,5,2,2,2] [3,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg114 sg507 - -lemma sg4015 : RowSquare [5,5,2,2,2] [3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg114 sg506 - -lemma sg4016 : RowSquare [5,5,2,2,2] [3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg115 sg500 - -lemma sg4017 : RowSquare [5,5,2,2,2] [3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg114 sg505 - -lemma sg4018 : RowSquare [5,5,2,2,2] [4,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg116 sg509 - -lemma sg4019 : RowSquare [5,5,2,2,2] [4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg116 sg503 - -lemma sg4020 : RowSquare [5,5,2,2,2] [4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg13 sg1617 - -lemma sg4021 : RowSquare [5,5,2,2,2] [4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg116 sg504 - -lemma sg4022 : RowSquare [5,5,2,2,2] [5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg120 sg501 - -lemma sg4023 : RowSquare [6,3,1,1,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg32 sg1327 - -lemma sg4024 : RowSquare [6,3,2,1,1,1,1,1] [3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg74 sg889 - -lemma sg4025 : RowSquare [6,3,2,1,1,1,1,1] [3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg74 sg890 - -lemma sg4026 : RowSquare [6,3,2,1,1,1,1,1] [3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg74 sg891 - -lemma sg4027 : RowSquare [6,3,2,1,1,1,1,1] [3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg892 - -lemma sg4028 : RowSquare [6,3,2,1,1,1,1,1] [4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg0 sg3263 - -lemma sg4029 : RowSquare [6,3,2,1,1,1,1,1] [4,3,3,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg3264 - -lemma sg4030 : RowSquare [6,3,2,1,1,1,1,1] [4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg897 - -lemma sg4031 : RowSquare [6,3,2,2,2,1] [3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg74 sg762 - -lemma sg4032 : RowSquare [6,3,2,2,2,1] [4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg765 - -lemma sg4033 : RowSquare [6,3,2,2,2,1] [4,4,3,3,2] := by - exact rowSquare_join (by decide) sg76 sg762 - -lemma sg4034 : RowSquare [6,3,3,2,1,1] [3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg1178 - -lemma sg4035 : RowSquare [6,3,3,2,1,1] [4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg752 - -lemma sg4036 : RowSquare [6,3,3,2,1,1] [4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg74 sg754 - -lemma sg4037 : RowSquare [6,3,3,2,1,1] [4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg440 - -lemma sg4038 : RowSquare [6,3,3,2,1,1] [4,4,4,2,2] := by - exact rowSquare_join (by decide) sg32 sg1144 - -lemma sg4039 : RowSquare [6,3,3,2,1,1] [4,4,4,3,1] := by - exact rowSquare_join (by decide) sg32 sg1145 - -lemma sg4040 : RowSquare [6,3,3,3,1] [4,4,3,3,1,1] := by - exact rowSquare_join (by decide) sg313 sg254 - -lemma sg4041 : RowSquare [6,3,3,3,1] [4,4,3,3,2] := by - exact rowSquare_join (by decide) sg67 sg759 - -lemma sg4042 : RowSquare [6,3,3,3,1] [4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg178 sg446 - -lemma sg4043 : RowSquare [6,3,3,3,1] [4,4,4,2,2] := by - exact rowSquare_join (by decide) sg68 sg759 - -lemma sg4044 : RowSquare [6,3,3,3,1] [4,4,4,3,1] := by - exact rowSquare_join (by decide) sg314 sg254 - -lemma sg4045 : RowSquare [6,3,3,3,1] [4,4,4,4] := by - exact rowSquare_join (by decide) sg254 sg315 - -lemma sg4046 : RowSquare [6,3,3,3,1] [5,5,2,2,1,1] := by - exact rowSquare_join (by decide) sg313 sg255 - -lemma sg4047 : RowSquare [6,3,3,3,1] [5,5,2,2,2] := by - exact rowSquare_join (by decide) sg71 sg759 - -lemma sg4048 : RowSquare [6,3,3,3,1] [5,5,3,2,1] := by - exact rowSquare_join (by decide) sg314 sg255 - -lemma sg4049 : RowSquare [6,3,3,3,1] [5,5,3,3] := by - exact rowSquare_join (by decide) sg254 sg319 - -lemma sg4050 : RowSquare [6,4,1,1,1,1,1,1] [4,2,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg22 sg1327 - -lemma sg4051 : RowSquare [6,4,1,1,1,1,1,1] [4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg2546 - -lemma sg4052 : RowSquare [6,4,1,1,1,1,1,1] [4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg23 sg1327 - -lemma sg4053 : RowSquare [6,4,1,1,1,1,1,1] [4,3,3,3,3] := by - exact rowSquare_join (by decide) sg66 sg892 - -lemma sg4054 : RowSquare [6,4,1,1,1,1,1,1] [5,2,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg24 sg1327 - -lemma sg4055 : RowSquare [6,4,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg22 sg1328 - -lemma sg4056 : RowSquare [6,4,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg23 sg1328 - -lemma sg4057 : RowSquare [6,4,1,1,1,1,1,1] [5,3,2,2,2,2] := by - exact rowSquare_join (by decide) sg0 sg3284 - -lemma sg4058 : RowSquare [6,4,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg25 sg1327 - -lemma sg4059 : RowSquare [6,4,1,1,1,1,1,1] [6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg2 sg2550 - -lemma sg4060 : RowSquare [6,4,1,1,1,1,1,1] [8,8] := by - exact rowSquare_join (by decide) sg17 sg1606 - -lemma sg4061 : RowSquare [6,4,2,1,1,1,1] [4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg2073 - -lemma sg4062 : RowSquare [6,4,2,1,1,1,1] [4,3,3,3,3] := by - exact rowSquare_join (by decide) sg32 sg1146 - -lemma sg4064 : RowSquare [6,4,2,2,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg347 sg248 - -lemma sg4065 : RowSquare [6,4,2,2,1,1] [2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg346 sg248 - -lemma sg4066 : RowSquare [6,4,2,2,1,1] [2,2,2,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg345 sg248 - -lemma sg4067 : RowSquare [6,4,2,2,1,1] [2,2,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg247 - -lemma sg4068 : RowSquare [6,4,2,2,1,1] [2,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg342 sg246 - -lemma sg4069 : RowSquare [6,4,2,2,1,1] [2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg342 sg244 - -lemma sg4070 : RowSquare [6,4,2,2,1,1] [2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg342 sg241 - -lemma sg4071 : RowSquare [6,4,2,2,1,1] [3,2,1,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg344 sg248 - -lemma sg4072 : RowSquare [6,4,2,2,1,1] [3,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg341 sg246 - -lemma sg4073 : RowSquare [6,4,2,2,1,1] [3,3,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg340 sg248 - -lemma sg4074 : RowSquare [6,4,2,2,1,1] [3,3,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg339 sg248 - -lemma sg4075 : RowSquare [6,4,2,2,1,1] [3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg339 sg246 - -lemma sg4076 : RowSquare [6,4,2,2,1,1] [3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg339 sg241 - -lemma sg4077 : RowSquare [6,4,2,2,1,1] [3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg13 sg1628 - -lemma sg4078 : RowSquare [6,4,2,2,1,1] [3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg339 sg239 - -lemma sg4079 : RowSquare [6,4,2,2,1,1] [3,3,3,3,2,2] := by - exact rowSquare_join (by decide) sg148 sg459 - -lemma sg4080 : RowSquare [6,4,2,2,1,1] [4,3,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg337 sg248 - -lemma sg4081 : RowSquare [6,4,2,2,1,1] [4,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg334 sg248 - -lemma sg4082 : RowSquare [6,4,2,2,1,1] [4,4,4,3,1] := by - exact rowSquare_join (by decide) sg13 sg1630 - -lemma sg4083 : RowSquare [6,4,2,2,1,1] [4,4,4,4] := by - exact rowSquare_join (by decide) sg13 sg1631 - -lemma sg4084 : RowSquare [6,4,2,2,1,1] [5,5,3,3] := by - exact rowSquare_join (by decide) sg67 sg767 - -lemma sg4085 : RowSquare [6,4,2,2,1,1] [5,5,4,2] := by - exact rowSquare_join (by decide) sg144 sg458 - -lemma sg4086 : RowSquare [6,4,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg2 sg2574 - -lemma sg4087 : RowSquare [6,4,2,2,1,1] [6,2,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg2079 - -lemma sg4088 : RowSquare [6,4,2,2,1,1] [6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg4 sg2081 - -lemma sg4089 : RowSquare [6,4,2,2,1,1] [6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg242 - -lemma sg4090 : RowSquare [6,4,2,2,1,1] [6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg1 sg2591 - -lemma sg4091 : RowSquare [6,4,2,2,1,1] [6,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg142 sg460 - -lemma sg4092 : RowSquare [6,4,2,2,1,1] [6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg2080 - -lemma sg4093 : RowSquare [6,4,2,2,1,1] [6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg243 - -lemma sg4094 : RowSquare [6,4,2,2,1,1] [6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg56 sg811 - -lemma sg4095 : RowSquare [6,4,2,2,1,1] [6,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg295 sg260 - -lemma sg4096 : RowSquare [6,4,2,2,1,1] [6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg331 sg239 - -lemma sg4097 : RowSquare [6,4,2,2,1,1] [6,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg142 sg462 - -lemma sg4098 : RowSquare [6,4,2,2,1,1] [6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg244 - -lemma sg4099 : RowSquare [6,4,2,2,1,1] [6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg331 sg240 - -lemma sg4100 : RowSquare [6,4,2,2,1,1] [6,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg295 sg261 - -lemma sg4101 : RowSquare [6,4,2,2,1,1] [6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg331 sg241 - -lemma sg4102 : RowSquare [6,4,2,2,1,1] [6,6,2,2] := by - exact rowSquare_join (by decide) sg334 sg241 - -lemma sg4103 : RowSquare [6,4,2,2,1,1] [7,1,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6 sg2079 - -lemma sg4104 : RowSquare [6,4,2,2,1,1] [7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg5 sg2081 - -lemma sg4105 : RowSquare [6,4,2,2,1,1] [7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg245 - -lemma sg4106 : RowSquare [6,4,2,2,1,1] [7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg331 sg242 - -lemma sg4107 : RowSquare [6,4,2,2,1,1] [7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg246 - -lemma sg4108 : RowSquare [6,4,2,2,1,1] [7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg331 sg243 - -lemma sg4109 : RowSquare [6,4,2,2,1,1] [8,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg8 sg1678 - -lemma sg4110 : RowSquare [6,4,2,2,1,1] [8,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg330 sg247 - -lemma sg4111 : RowSquare [6,4,3,1,1,1] [3,3,3,3,3,1] := by - exact rowSquare_join (by decide) sg32 sg1178 - -lemma sg4112 : RowSquare [6,4,3,1,1,1] [4,4,2,2,2,2] := by - exact rowSquare_join (by decide) sg74 sg752 - -lemma sg4113 : RowSquare [6,4,3,1,1,1] [4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg27 sg1195 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes6 + +namespace OAI + +/-! Semigroup Nodes 8. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg3708 : RowSquare [9,2,2,2] [4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg181 sg371 + +lemma sg3709 : RowSquare [9,2,2,2] [4,4,3,2,2] := by + exact rowSquare_join (by decide) sg180 sg372 + +lemma sg3710 : RowSquare [9,2,2,2] [4,4,3,3,1] := by + exact rowSquare_join (by decide) sg180 sg373 + +lemma sg3711 : RowSquare [9,2,2,2] [4,4,4,2,1] := by + exact rowSquare_join (by decide) sg181 sg372 + +lemma sg3712 : RowSquare [9,2,2,2] [4,4,4,3] := by + exact rowSquare_join (by decide) sg181 sg373 + +lemma sg3713 : RowSquare [9,2,2,2] [5,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg179 sg374 + +lemma sg3714 : RowSquare [9,2,2,2] [5,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg179 sg375 + +lemma sg3715 : RowSquare [9,2,2,2] [5,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg179 sg376 + +lemma sg3716 : RowSquare [9,2,2,2] [5,3,3,3,1] := by + exact rowSquare_join (by decide) sg182 sg373 + +lemma sg3717 : RowSquare [9,2,2,2] [5,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg179 sg377 + +lemma sg3718 : RowSquare [9,2,2,2] [5,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg378 + +lemma sg3719 : RowSquare [9,2,2,2] [5,4,3,3] := by + exact rowSquare_join (by decide) sg183 sg373 + +lemma sg3720 : RowSquare [9,2,2,2] [5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg383 + +lemma sg3721 : RowSquare [9,3,1,1,1] [3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg97 sg586 + +lemma sg3722 : RowSquare [9,3,1,1,1] [4,4,3,2,2] := by + exact rowSquare_join (by decide) sg40 sg1001 + +lemma sg3723 : RowSquare [9,3,2,1] [3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg389 + +lemma sg3724 : RowSquare [9,3,2,1] [3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg390 + +lemma sg3725 : RowSquare [9,3,2,1] [3,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg32 sg1032 + +lemma sg3726 : RowSquare [9,3,2,1] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg1033 + +lemma sg3727 : RowSquare [9,3,2,1] [4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg218 sg330 + +lemma sg3728 : RowSquare [9,3,2,1] [4,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg193 sg371 + +lemma sg3729 : RowSquare [9,3,2,1] [4,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg193 sg373 + +lemma sg3730 : RowSquare [9,3,2,1] [4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg194 sg371 + +lemma sg3731 : RowSquare [9,3,2,1] [4,4,4,3] := by + exact rowSquare_join (by decide) sg195 sg373 + +lemma sg3732 : RowSquare [9,3,3] [3,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg1061 + +lemma sg3733 : RowSquare [9,3,3] [4,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg32 sg1063 + +lemma sg3734 : RowSquare [9,3,3] [4,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg88 sg636 + +lemma sg3735 : RowSquare [9,3,3] [4,4,3,3,1] := by + exact rowSquare_join (by decide) sg88 sg637 + +lemma sg3736 : RowSquare [9,3,3] [5,5,5] := by + exact rowSquare_join (by decide) sg89 sg641 + +lemma sg3737 : RowSquare [9,4,1,1] [4,4,3,2,2] := by + exact rowSquare_join (by decide) sg40 sg1033 + +lemma sg3738 : RowSquare [9,4,1,1] [5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg407 + +lemma sg3741 : RowSquare [2,2,2,2,2,2,2,1,1] [6,6,2,2] := by + exact rowSquare_join (by decide) sg364 sg407 + +lemma sg3744 : RowSquare [3,2,2,2,2,2,2,1] [4,4,4,4] := by + exact rowSquare_join (by decide) sg364 sg358 + +lemma sg3745 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [8,2,2,2,2] := by + exact rowSquare_join (by decide) sg413 sg413 + +lemma sg3746 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [8,3,2,2,1] := by + exact rowSquare_join (by decide) sg413 sg414 + +lemma sg3747 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [8,3,3,1,1] := by + exact rowSquare_join (by decide) sg413 sg415 + +lemma sg3748 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [8,4,2,2] := by + exact rowSquare_join (by decide) sg414 sg414 + +lemma sg3749 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [8,4,3,1] := by + exact rowSquare_join (by decide) sg414 sg415 + +lemma sg3750 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [9,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg234 sg636 + +lemma sg3751 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [9,3,2,2] := by + exact rowSquare_join (by decide) sg414 sg416 + +lemma sg3752 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [9,5,1,1] := by + exact rowSquare_join (by decide) sg414 sg418 + +lemma sg3753 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [10,4,1,1] := by + exact rowSquare_join (by decide) sg414 sg420 + +lemma sg3754 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [10,5,1] := by + exact rowSquare_join (by decide) sg417 sg418 + +lemma sg3755 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [11,3,1,1] := by + exact rowSquare_join (by decide) sg352 sg426 + +lemma sg3756 : RowSquare [3,3,1,1,1,1,1,1,1,1,1,1] [12,2,1,1] := by + exact rowSquare_join (by decide) sg414 sg421 + +lemma sg3757 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,3,3,2,2] := by + exact rowSquare_join (by decide) sg389 sg413 + +lemma sg3758 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,3,3,3,1] := by + exact rowSquare_join (by decide) sg413 sg390 + +lemma sg3759 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,4,2,2,2] := by + exact rowSquare_join (by decide) sg218 sg694 + +lemma sg3760 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,4,3,2,1] := by + exact rowSquare_join (by decide) sg389 sg414 + +lemma sg3761 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,4,3,3] := by + exact rowSquare_join (by decide) sg390 sg414 + +lemma sg3762 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,4,4,1,1] := by + exact rowSquare_join (by decide) sg389 sg415 + +lemma sg3763 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,4,4,2] := by + exact rowSquare_join (by decide) sg390 sg415 + +lemma sg3764 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,5,5] := by + exact rowSquare_join (by decide) sg220 sg696 + +lemma sg3765 : RowSquare [3,3,2,1,1,1,1,1,1,1,1] [6,6,4] := by + exact rowSquare_join (by decide) sg89 sg1110 + +lemma sg3766 : RowSquare [3,3,2,2,1,1,1,1,1,1] [4,4,4,2,2] := by + exact rowSquare_join (by decide) sg389 sg389 + +lemma sg3767 : RowSquare [3,3,2,2,1,1,1,1,1,1] [4,4,4,3,1] := by + exact rowSquare_join (by decide) sg389 sg390 + +lemma sg3768 : RowSquare [3,3,2,2,1,1,1,1,1,1] [4,4,4,4] := by + exact rowSquare_join (by decide) sg390 sg390 + +lemma sg3769 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,3,3,3,2] := by + exact rowSquare_join (by decide) sg218 sg644 + +lemma sg3770 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg193 sg694 + +lemma sg3771 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg193 sg695 + +lemma sg3772 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,3,2,2] := by + exact rowSquare_join (by decide) sg389 sg392 + +lemma sg3773 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,3,3,1] := by + exact rowSquare_join (by decide) sg392 sg390 + +lemma sg3774 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,4,1,1,1] := by + exact rowSquare_join (by decide) sg193 sg696 + +lemma sg3775 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,4,2,1] := by + exact rowSquare_join (by decide) sg389 sg393 + +lemma sg3776 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,4,4,3] := by + exact rowSquare_join (by decide) sg390 sg393 + +lemma sg3777 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg1109 + +lemma sg3778 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,2,2,2] := by + exact rowSquare_join (by decide) sg194 sg694 + +lemma sg3779 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg228 sg636 + +lemma sg3780 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,3,2,1] := by + exact rowSquare_join (by decide) sg389 sg394 + +lemma sg3781 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,3,3] := by + exact rowSquare_join (by decide) sg390 sg394 + +lemma sg3782 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,4,1,1] := by + exact rowSquare_join (by decide) sg389 sg395 + +lemma sg3783 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,4,2] := by + exact rowSquare_join (by decide) sg390 sg395 + +lemma sg3784 : RowSquare [3,3,2,2,1,1,1,1,1,1] [5,5,5,1] := by + exact rowSquare_join (by decide) sg195 sg696 + +lemma sg3785 : RowSquare [3,3,2,2,1,1,1,1,1,1] [6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg391 sg391 + +lemma sg3786 : RowSquare [3,3,2,2,1,1,1,1,1,1] [6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg348 sg424 + +lemma sg3787 : RowSquare [3,3,2,2,1,1,1,1,1,1] [6,6,2,2] := by + exact rowSquare_join (by decide) sg390 sg396 + +lemma sg3788 : RowSquare [3,3,2,2,2,2,1,1] [4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg306 sg403 + +lemma sg3789 : RowSquare [3,3,2,2,2,2,2] [8,8] := by + exact rowSquare_join (by decide) sg367 sg311 + +lemma sg3790 : RowSquare [3,3,3,2,1,1,1,1,1] [4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg1063 + +lemma sg3791 : RowSquare [3,3,3,2,1,1,1,1,1] [4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg88 sg975 + +lemma sg3792 : RowSquare [3,3,3,2,1,1,1,1,1] [4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg348 sg389 + +lemma sg3793 : RowSquare [3,3,3,2,1,1,1,1,1] [4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg348 sg390 + +lemma sg3794 : RowSquare [3,3,3,2,1,1,1,1,1] [4,4,3,3,2] := by + exact rowSquare_join (by decide) sg194 sg637 + +lemma sg3795 : RowSquare [3,3,3,2,1,1,1,1,1] [4,4,4,4] := by + exact rowSquare_join (by decide) sg390 sg350 + +lemma sg3796 : RowSquare [3,3,3,2,1,1,1,1,1] [5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg306 sg415 + +lemma sg3797 : RowSquare [4,2,2,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg422 + +lemma sg3798 : RowSquare [4,2,2,2,2,2,1,1] [4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg207 sg561 + +lemma sg3799 : RowSquare [4,2,2,2,2,2,1,1] [4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg365 + +lemma sg3800 : RowSquare [4,2,2,2,2,2,1,1] [4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg958 + +lemma sg3801 : RowSquare [4,2,2,2,2,2,1,1] [4,4,4,3,1] := by + exact rowSquare_join (by decide) sg333 sg364 + +lemma sg3802 : RowSquare [4,2,2,2,2,2,1,1] [4,4,4,4] := by + exact rowSquare_join (by decide) sg364 sg334 + +lemma sg3803 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg413 + +lemma sg3804 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg414 + +lemma sg3805 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg413 + +lemma sg3806 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg415 + +lemma sg3807 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,3,3,2,2] := by + exact rowSquare_join (by decide) sg372 sg413 + +lemma sg3808 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,3,3,3,1] := by + exact rowSquare_join (by decide) sg413 sg373 + +lemma sg3809 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg415 + +lemma sg3810 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,4,3,3] := by + exact rowSquare_join (by decide) sg373 sg414 + +lemma sg3811 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,4,4,1,1] := by + exact rowSquare_join (by decide) sg372 sg415 + +lemma sg3812 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [6,4,4,2] := by + exact rowSquare_join (by decide) sg373 sg415 + +lemma sg3813 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg416 + +lemma sg3814 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg374 sg413 + +lemma sg3815 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg417 + +lemma sg3816 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg371 sg416 + +lemma sg3817 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,3,2,2,2] := by + exact rowSquare_join (by decide) sg375 sg413 + +lemma sg3818 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg374 sg415 + +lemma sg3819 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,3,3,2,1] := by + exact rowSquare_join (by decide) sg372 sg416 + +lemma sg3820 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,3,3,3] := by + exact rowSquare_join (by decide) sg373 sg416 + +lemma sg3821 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg418 + +lemma sg3822 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg417 + +lemma sg3823 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,4,2,2,1] := by + exact rowSquare_join (by decide) sg375 sg414 + +lemma sg3824 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,4,3,1,1] := by + exact rowSquare_join (by decide) sg372 sg417 + +lemma sg3825 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,4,3,2] := by + exact rowSquare_join (by decide) sg373 sg417 + +lemma sg3826 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,4,4,1] := by + exact rowSquare_join (by decide) sg376 sg415 + +lemma sg3827 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,5,1,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg418 + +lemma sg3828 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,5,2,1,1] := by + exact rowSquare_join (by decide) sg372 sg418 + +lemma sg3829 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,5,2,2] := by + exact rowSquare_join (by decide) sg373 sg418 + +lemma sg3830 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,5,3,1] := by + exact rowSquare_join (by decide) sg377 sg415 + +lemma sg3831 : RowSquare [4,3,1,1,1,1,1,1,1,1,1] [7,5,4] := by + exact rowSquare_join (by decide) sg378 sg415 + +lemma sg3832 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg389 + +lemma sg3833 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg390 + +lemma sg3834 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,3,3,3,2,1] := by + exact rowSquare_join (by decide) sg87 sg1032 + +lemma sg3835 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,3,3,3,3] := by + exact rowSquare_join (by decide) sg87 sg1033 + +lemma sg3836 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg694 + +lemma sg3837 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg695 + +lemma sg3838 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg696 + +lemma sg3839 : RowSquare [4,3,2,1,1,1,1,1,1,1] [4,4,4,4] := by + exact rowSquare_join (by decide) sg390 sg373 + +lemma sg3840 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg413 + +lemma sg3841 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg414 + +lemma sg3842 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg391 + +lemma sg3843 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg415 + +lemma sg3844 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg391 sg373 + +lemma sg3845 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,3,3,3,2] := by + exact rowSquare_join (by decide) sg218 sg616 + +lemma sg3846 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg392 + +lemma sg3847 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg701 + +lemma sg3848 : RowSquare [4,3,2,1,1,1,1,1,1,1] [5,5,5,1] := by + exact rowSquare_join (by decide) sg181 sg696 + +lemma sg3849 : RowSquare [4,3,2,2,1,1,1,1,1] [4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg391 + +lemma sg3850 : RowSquare [4,3,2,2,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg104 sg849 + +lemma sg3851 : RowSquare [4,3,2,2,1,1,1,1,1] [5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg370 sg359 + +lemma sg3852 : RowSquare [4,3,2,2,1,1,1,1,1] [6,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg106 sg849 + +lemma sg3853 : RowSquare [4,3,2,2,1,1,1,1,1] [6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg104 sg850 + +lemma sg3854 : RowSquare [4,3,2,2,1,1,1,1,1] [6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg3181 + +lemma sg3855 : RowSquare [4,3,2,2,1,1,1,1,1] [6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg105 sg850 + +lemma sg3856 : RowSquare [4,3,2,2,1,1,1,1,1] [6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg0 sg3182 + +lemma sg3857 : RowSquare [4,3,2,2,1,1,1,1,1] [6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg399 + +lemma sg3858 : RowSquare [4,3,2,2,2,2,1] [3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg879 + +lemma sg3859 : RowSquare [4,3,2,2,2,2,1] [4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg849 + +lemma sg3860 : RowSquare [4,3,2,2,2,2,1] [4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg165 sg561 + +lemma sg3861 : RowSquare [4,3,2,2,2,2,1] [4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg83 sg850 + +lemma sg3862 : RowSquare [4,3,2,2,2,2,1] [5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg84 sg850 + +lemma sg3863 : RowSquare [4,3,2,2,2,2,1] [5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg85 sg849 + +lemma sg3864 : RowSquare [4,3,2,2,2,2,1] [7,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg86 sg849 + +lemma sg3865 : RowSquare [4,3,3,2,1,1,1,1] [7,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg96 sg849 + +lemma sg3866 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg370 sg370 + +lemma sg3867 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg370 sg371 + +lemma sg3868 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg372 + +lemma sg3869 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg373 + +lemma sg3870 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg371 + +lemma sg3871 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,4,3,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg372 + +lemma sg3872 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg371 sg373 + +lemma sg3873 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,4,4,2,2] := by + exact rowSquare_join (by decide) sg372 sg372 + +lemma sg3874 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,4,4,3,1] := by + exact rowSquare_join (by decide) sg372 sg373 + +lemma sg3875 : RowSquare [4,4,1,1,1,1,1,1,1,1] [4,4,4,4] := by + exact rowSquare_join (by decide) sg373 sg373 + +lemma sg3876 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg370 sg374 + +lemma sg3877 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg375 + +lemma sg3878 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg371 sg374 + +lemma sg3879 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg376 + +lemma sg3880 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg374 sg372 + +lemma sg3881 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,3,3,3,1,1] := by + exact rowSquare_join (by decide) sg374 sg373 + +lemma sg3882 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg377 + +lemma sg3883 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,2,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg375 + +lemma sg3884 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg378 + +lemma sg3885 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,3,2,1,1] := by + exact rowSquare_join (by decide) sg371 sg376 + +lemma sg3886 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,3,2,2] := by + exact rowSquare_join (by decide) sg372 sg375 + +lemma sg3887 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,3,3,1] := by + exact rowSquare_join (by decide) sg375 sg373 + +lemma sg3888 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,4,2,1] := by + exact rowSquare_join (by decide) sg372 sg376 + +lemma sg3889 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,4,4,3] := by + exact rowSquare_join (by decide) sg373 sg376 + +lemma sg3890 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg371 sg377 + +lemma sg3891 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,5,3,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg378 + +lemma sg3892 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,5,3,2,1] := by + exact rowSquare_join (by decide) sg372 sg377 + +lemma sg3893 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,5,3,3] := by + exact rowSquare_join (by decide) sg373 sg377 + +lemma sg3894 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,5,4,1,1] := by + exact rowSquare_join (by decide) sg372 sg378 + +lemma sg3895 : RowSquare [4,4,1,1,1,1,1,1,1,1] [5,5,4,2] := by + exact rowSquare_join (by decide) sg373 sg378 + +lemma sg3896 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg370 sg379 + +lemma sg3897 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg374 sg374 + +lemma sg3898 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg371 sg379 + +lemma sg3899 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,3,3,2,2] := by + exact rowSquare_join (by decide) sg372 sg379 + +lemma sg3900 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,3,3,3,1] := by + exact rowSquare_join (by decide) sg379 sg373 + +lemma sg3901 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,4,2,2,2] := by + exact rowSquare_join (by decide) sg375 sg375 + +lemma sg3902 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,5,3,2] := by + exact rowSquare_join (by decide) sg373 sg382 + +lemma sg3903 : RowSquare [4,4,1,1,1,1,1,1,1,1] [6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg383 + +lemma sg3904 : RowSquare [4,4,1,1,1,1,1,1,1,1] [7,6,1,1,1] := by + exact rowSquare_join (by decide) sg375 sg383 + +lemma sg3905 : RowSquare [4,4,1,1,1,1,1,1,1,1] [8,8] := by + exact rowSquare_join (by decide) sg383 sg383 + +lemma sg3906 : RowSquare [4,4,1,1,1,1,1,1,1,1] [9,7] := by + exact rowSquare_join (by decide) sg383 sg386 + +lemma sg3907 : RowSquare [4,4,1,1,1,1,1,1,1,1] [10,6] := by + exact rowSquare_join (by decide) sg14 sg1577 + +lemma sg3908 : RowSquare [4,4,1,1,1,1,1,1,1,1] [11,5] := by + exact rowSquare_join (by decide) sg14 sg1578 + +lemma sg3909 : RowSquare [4,4,1,1,1,1,1,1,1,1] [12,4] := by + exact rowSquare_join (by decide) sg14 sg1579 + +lemma sg3910 : RowSquare [4,4,1,1,1,1,1,1,1,1] [13,3] := by + exact rowSquare_join (by decide) sg14 sg1580 + +lemma sg3911 : RowSquare [4,4,2,1,1,1,1,1,1] [3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg330 sg370 + +lemma sg3912 : RowSquare [4,4,2,1,1,1,1,1,1] [3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg330 sg371 + +lemma sg3913 : RowSquare [4,4,2,1,1,1,1,1,1] [3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg372 + +lemma sg3914 : RowSquare [4,4,2,1,1,1,1,1,1] [3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg373 + +lemma sg3915 : RowSquare [4,4,2,1,1,1,1,1,1] [4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg370 sg331 + +lemma sg3916 : RowSquare [4,4,2,1,1,1,1,1,1] [4,4,4,4] := by + exact rowSquare_join (by decide) sg373 sg334 + +lemma sg3917 : RowSquare [4,4,2,1,1,1,1,1,1] [6,6,1,1,1,1] := by + exact rowSquare_join (by decide) sg371 sg342 + +lemma sg3918 : RowSquare [4,4,2,1,1,1,1,1,1] [7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg387 + +lemma sg3919 : RowSquare [4,4,2,1,1,1,1,1,1] [7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg343 + +lemma sg3920 : RowSquare [4,4,2,1,1,1,1,1,1] [7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg388 + +lemma sg3921 : RowSquare [4,4,2,1,1,1,1,1,1] [7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg344 + +lemma sg3922 : RowSquare [4,4,2,1,1,1,1,1,1] [7,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg2500 + +lemma sg3923 : RowSquare [4,4,2,1,1,1,1,1,1] [7,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg2501 + +lemma sg3924 : RowSquare [4,4,2,1,1,1,1,1,1] [7,3,3,3] := by + exact rowSquare_join (by decide) sg1 sg2502 + +lemma sg3925 : RowSquare [4,4,2,1,1,1,1,1,1] [7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg370 sg345 + +lemma sg3926 : RowSquare [4,4,2,1,1,1,1,1,1] [7,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg2503 + +lemma sg3927 : RowSquare [4,4,2,1,1,1,1,1,1] [8,8] := by + exact rowSquare_join (by decide) sg14 sg1581 + +lemma sg3928 : RowSquare [4,4,2,1,1,1,1,1,1] [9,7] := by + exact rowSquare_join (by decide) sg14 sg1582 + +lemma sg3929 : RowSquare [4,4,2,1,1,1,1,1,1] [10,2,2,2] := by + exact rowSquare_join (by decide) sg26 sg1123 + +lemma sg3930 : RowSquare [4,4,2,1,1,1,1,1,1] [10,6] := by + exact rowSquare_join (by decide) sg29 sg1122 + +lemma sg3931 : RowSquare [4,4,2,1,1,1,1,1,1] [11,5] := by + exact rowSquare_join (by decide) sg29 sg1124 + +lemma sg3932 : RowSquare [4,4,2,1,1,1,1,1,1] [12,4] := by + exact rowSquare_join (by decide) sg29 sg1125 + +lemma sg3933 : RowSquare [4,4,2,1,1,1,1,1,1] [13,3] := by + exact rowSquare_join (by decide) sg174 sg427 + +lemma sg3934 : RowSquare [4,4,2,1,1,1,1,1,1] [14,2] := by + exact rowSquare_join (by decide) sg176 sg427 + +lemma sg3935 : RowSquare [4,4,2,2,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg1650 + +lemma sg3936 : RowSquare [4,4,2,2,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg1651 + +lemma sg3937 : RowSquare [4,4,2,2,2,1,1] [4,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg1650 + +lemma sg3938 : RowSquare [4,4,2,2,2,1,1] [4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg16 sg1651 + +lemma sg3939 : RowSquare [4,4,2,2,2,1,1] [4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1651 + +lemma sg3940 : RowSquare [4,4,2,2,2,1,1] [4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17 sg1652 + +lemma sg3941 : RowSquare [4,4,2,2,2,1,1] [4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg332 sg295 + +lemma sg3942 : RowSquare [4,4,2,2,2,1,1] [5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg1650 + +lemma sg3943 : RowSquare [4,4,2,2,2,1,1] [5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18 sg1651 + +lemma sg3944 : RowSquare [4,4,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19 sg1651 + +lemma sg3945 : RowSquare [5,3,1,1,1,1,1,1,1,1] [6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg224 sg586 + +lemma sg3946 : RowSquare [5,3,1,1,1,1,1,1,1,1] [6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg225 sg586 + +lemma sg3947 : RowSquare [5,3,1,1,1,1,1,1,1,1] [6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg223 sg587 + +lemma sg3948 : RowSquare [5,3,2,1,1,1,1,1,1] [3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg194 sg586 + +lemma sg3949 : RowSquare [5,3,2,1,1,1,1,1,1] [3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg998 + +lemma sg3950 : RowSquare [5,3,2,1,1,1,1,1,1] [3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg89 sg910 + +lemma sg3951 : RowSquare [5,3,2,1,1,1,1,1,1] [3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg999 + +lemma sg3952 : RowSquare [5,3,2,1,1,1,1,1,1] [3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg74 sg1000 + +lemma sg3953 : RowSquare [5,3,2,1,1,1,1,1,1] [3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg1001 + +lemma sg3954 : RowSquare [5,3,2,1,1,1,1,1,1] [4,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg90 sg910 + +lemma sg3955 : RowSquare [5,3,2,1,1,1,1,1,1] [4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg92 sg910 + +lemma sg3956 : RowSquare [5,3,2,1,1,1,1,1,1] [4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg1006 + +lemma sg3957 : RowSquare [5,3,2,1,1,1,1,1,1] [5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20 sg1682 + +lemma sg3958 : RowSquare [5,3,2,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg94 sg910 + +lemma sg3959 : RowSquare [5,3,2,2,2,1,1] [4,4,4,4] := by + exact rowSquare_join (by decide) sg358 sg271 + +lemma sg3960 : RowSquare [5,3,2,2,2,1,1] [5,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg1682 + +lemma sg3961 : RowSquare [5,3,2,2,2,1,1] [5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14 sg1689 + +lemma sg3962 : RowSquare [5,3,2,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15 sg1683 + +lemma sg3963 : RowSquare [5,3,3,2,2,1] [3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg306 sg271 + +lemma sg3964 : RowSquare [5,4,1,1,1,1,1,1,1] [2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg178 sg586 + +lemma sg3965 : RowSquare [5,4,1,1,1,1,1,1,1] [3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg179 sg586 + +lemma sg3966 : RowSquare [5,4,1,1,1,1,1,1,1] [3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg178 sg587 + +lemma sg3967 : RowSquare [5,4,1,1,1,1,1,1,1] [3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg178 sg588 + +lemma sg3968 : RowSquare [5,4,1,1,1,1,1,1,1] [4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg179 sg589 + +lemma sg3969 : RowSquare [5,4,1,1,1,1,1,1,1] [7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg191 sg586 + +lemma sg3970 : RowSquare [5,4,1,1,1,1,1,1,1] [7,7,1,1] := by + exact rowSquare_join (by decide) sg377 sg324 + +lemma sg3971 : RowSquare [5,4,1,1,1,1,1,1,1] [7,7,2] := by + exact rowSquare_join (by decide) sg378 sg324 + +lemma sg3972 : RowSquare [5,4,1,1,1,1,1,1,1] [8,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg192 sg586 + +lemma sg3973 : RowSquare [5,4,1,1,1,1,1,1,1] [8,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg2521 + +lemma sg3974 : RowSquare [5,4,1,1,1,1,1,1,1] [8,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg2522 + +lemma sg3975 : RowSquare [5,4,1,1,1,1,1,1,1] [8,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg13 sg1584 + +lemma sg3976 : RowSquare [5,4,1,1,1,1,1,1,1] [8,2,2,2,2] := by + exact rowSquare_join (by decide) sg6 sg2021 + +lemma sg3977 : RowSquare [5,4,1,1,1,1,1,1,1] [8,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg2523 + +lemma sg3978 : RowSquare [5,4,1,1,1,1,1,1,1] [8,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg2026 + +lemma sg3979 : RowSquare [5,4,1,1,1,1,1,1,1] [8,3,2,2,1] := by + exact rowSquare_join (by decide) sg13 sg1585 + +lemma sg3980 : RowSquare [5,4,1,1,1,1,1,1,1] [8,3,3,1,1] := by + exact rowSquare_join (by decide) sg4 sg2027 + +lemma sg3981 : RowSquare [5,4,1,1,1,1,1,1,1] [8,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg2025 + +lemma sg3982 : RowSquare [5,4,1,1,1,1,1,1,1] [8,8] := by + exact rowSquare_join (by decide) sg383 sg324 + +lemma sg3983 : RowSquare [5,4,2,1,1,1,1,1] [3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg67 sg910 + +lemma sg3984 : RowSquare [5,4,2,1,1,1,1,1] [3,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg68 sg910 + +lemma sg3985 : RowSquare [5,4,2,1,1,1,1,1] [4,3,3,3,3] := by + exact rowSquare_join (by decide) sg66 sg915 + +lemma sg3986 : RowSquare [5,4,2,1,1,1,1,1] [4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg71 sg910 + +lemma sg3987 : RowSquare [5,4,2,1,1,1,1,1] [4,4,4,4] := by + exact rowSquare_join (by decide) sg373 sg271 + +lemma sg3988 : RowSquare [5,4,2,1,1,1,1,1] [7,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg2534 + +lemma sg3989 : RowSquare [5,4,2,2,2,1] [5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg1 sg2605 + +lemma sg3990 : RowSquare [5,4,2,2,2,1] [5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg1 sg2606 + +lemma sg3991 : RowSquare [5,4,2,2,2,1] [5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg2609 + +lemma sg3992 : RowSquare [5,4,3,2,1,1] [3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg759 + +lemma sg3993 : RowSquare [5,4,3,2,1,1] [4,3,3,3,3] := by + exact rowSquare_join (by decide) sg0 sg3249 + +lemma sg3994 : RowSquare [5,5,1,1,1,1,1,1] [4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg1 sg2546 + +lemma sg3995 : RowSquare [5,5,1,1,1,1,1,1] [4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg313 sg313 + +lemma sg3996 : RowSquare [5,5,1,1,1,1,1,1] [5,3,3,3,2] := by + exact rowSquare_join (by decide) sg13 sg1592 + +lemma sg3997 : RowSquare [5,5,1,1,1,1,1,1] [6,3,3,2,2] := by + exact rowSquare_join (by decide) sg1 sg2553 + +lemma sg3999 : RowSquare [5,5,2,2,2] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg121 sg509 + +lemma sg4000 : RowSquare [5,5,2,2,2] [2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg120 sg509 + +lemma sg4001 : RowSquare [5,5,2,2,2] [2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg118 sg509 + +lemma sg4002 : RowSquare [5,5,2,2,2] [2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg118 sg507 + +lemma sg4003 : RowSquare [5,5,2,2,2] [2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg118 sg506 + +lemma sg4004 : RowSquare [5,5,2,2,2] [2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg118 sg503 + +lemma sg4005 : RowSquare [5,5,2,2,2] [2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg14 sg1617 + +lemma sg4006 : RowSquare [5,5,2,2,2] [3,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg119 sg509 + +lemma sg4007 : RowSquare [5,5,2,2,2] [3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg117 sg509 + +lemma sg4008 : RowSquare [5,5,2,2,2] [3,2,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg115 sg508 + +lemma sg4009 : RowSquare [5,5,2,2,2] [3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg115 sg507 + +lemma sg4010 : RowSquare [5,5,2,2,2] [3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg115 sg506 + +lemma sg4011 : RowSquare [5,5,2,2,2] [3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg115 sg503 + +lemma sg4012 : RowSquare [5,5,2,2,2] [3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg114 sg509 + +lemma sg4013 : RowSquare [5,5,2,2,2] [3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg114 sg508 + +lemma sg4014 : RowSquare [5,5,2,2,2] [3,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg114 sg507 + +lemma sg4015 : RowSquare [5,5,2,2,2] [3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg114 sg506 + +lemma sg4016 : RowSquare [5,5,2,2,2] [3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg115 sg500 + +lemma sg4017 : RowSquare [5,5,2,2,2] [3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg114 sg505 + +lemma sg4018 : RowSquare [5,5,2,2,2] [4,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg116 sg509 + +lemma sg4019 : RowSquare [5,5,2,2,2] [4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg116 sg503 + +lemma sg4020 : RowSquare [5,5,2,2,2] [4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg13 sg1617 + +lemma sg4021 : RowSquare [5,5,2,2,2] [4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg116 sg504 + +lemma sg4022 : RowSquare [5,5,2,2,2] [5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg120 sg501 + +lemma sg4023 : RowSquare [6,3,1,1,1,1,1,1,1] [2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg32 sg1327 + +lemma sg4024 : RowSquare [6,3,2,1,1,1,1,1] [3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg74 sg889 + +lemma sg4025 : RowSquare [6,3,2,1,1,1,1,1] [3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg74 sg890 + +lemma sg4026 : RowSquare [6,3,2,1,1,1,1,1] [3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg74 sg891 + +lemma sg4027 : RowSquare [6,3,2,1,1,1,1,1] [3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg892 + +lemma sg4028 : RowSquare [6,3,2,1,1,1,1,1] [4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg0 sg3263 + +lemma sg4029 : RowSquare [6,3,2,1,1,1,1,1] [4,3,3,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg3264 + +lemma sg4030 : RowSquare [6,3,2,1,1,1,1,1] [4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg897 + +lemma sg4031 : RowSquare [6,3,2,2,2,1] [3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg74 sg762 + +lemma sg4032 : RowSquare [6,3,2,2,2,1] [4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg765 + +lemma sg4033 : RowSquare [6,3,2,2,2,1] [4,4,3,3,2] := by + exact rowSquare_join (by decide) sg76 sg762 + +lemma sg4034 : RowSquare [6,3,3,2,1,1] [3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg1178 + +lemma sg4035 : RowSquare [6,3,3,2,1,1] [4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg752 + +lemma sg4036 : RowSquare [6,3,3,2,1,1] [4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg74 sg754 + +lemma sg4037 : RowSquare [6,3,3,2,1,1] [4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg440 + +lemma sg4038 : RowSquare [6,3,3,2,1,1] [4,4,4,2,2] := by + exact rowSquare_join (by decide) sg32 sg1144 + +lemma sg4039 : RowSquare [6,3,3,2,1,1] [4,4,4,3,1] := by + exact rowSquare_join (by decide) sg32 sg1145 + +lemma sg4040 : RowSquare [6,3,3,3,1] [4,4,3,3,1,1] := by + exact rowSquare_join (by decide) sg313 sg254 + +lemma sg4041 : RowSquare [6,3,3,3,1] [4,4,3,3,2] := by + exact rowSquare_join (by decide) sg67 sg759 + +lemma sg4042 : RowSquare [6,3,3,3,1] [4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg178 sg446 + +lemma sg4043 : RowSquare [6,3,3,3,1] [4,4,4,2,2] := by + exact rowSquare_join (by decide) sg68 sg759 + +lemma sg4044 : RowSquare [6,3,3,3,1] [4,4,4,3,1] := by + exact rowSquare_join (by decide) sg314 sg254 + +lemma sg4045 : RowSquare [6,3,3,3,1] [4,4,4,4] := by + exact rowSquare_join (by decide) sg254 sg315 + +lemma sg4046 : RowSquare [6,3,3,3,1] [5,5,2,2,1,1] := by + exact rowSquare_join (by decide) sg313 sg255 + +lemma sg4047 : RowSquare [6,3,3,3,1] [5,5,2,2,2] := by + exact rowSquare_join (by decide) sg71 sg759 + +lemma sg4048 : RowSquare [6,3,3,3,1] [5,5,3,2,1] := by + exact rowSquare_join (by decide) sg314 sg255 + +lemma sg4049 : RowSquare [6,3,3,3,1] [5,5,3,3] := by + exact rowSquare_join (by decide) sg254 sg319 + +lemma sg4050 : RowSquare [6,4,1,1,1,1,1,1] [4,2,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg22 sg1327 + +lemma sg4051 : RowSquare [6,4,1,1,1,1,1,1] [4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg2546 + +lemma sg4052 : RowSquare [6,4,1,1,1,1,1,1] [4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg23 sg1327 + +lemma sg4053 : RowSquare [6,4,1,1,1,1,1,1] [4,3,3,3,3] := by + exact rowSquare_join (by decide) sg66 sg892 + +lemma sg4054 : RowSquare [6,4,1,1,1,1,1,1] [5,2,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg24 sg1327 + +lemma sg4055 : RowSquare [6,4,1,1,1,1,1,1] [5,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg22 sg1328 + +lemma sg4056 : RowSquare [6,4,1,1,1,1,1,1] [5,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg23 sg1328 + +lemma sg4057 : RowSquare [6,4,1,1,1,1,1,1] [5,3,2,2,2,2] := by + exact rowSquare_join (by decide) sg0 sg3284 + +lemma sg4058 : RowSquare [6,4,1,1,1,1,1,1] [6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg25 sg1327 + +lemma sg4059 : RowSquare [6,4,1,1,1,1,1,1] [6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg2 sg2550 + +lemma sg4060 : RowSquare [6,4,1,1,1,1,1,1] [8,8] := by + exact rowSquare_join (by decide) sg17 sg1606 + +lemma sg4061 : RowSquare [6,4,2,1,1,1,1] [4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg2073 + +lemma sg4062 : RowSquare [6,4,2,1,1,1,1] [4,3,3,3,3] := by + exact rowSquare_join (by decide) sg32 sg1146 + +lemma sg4064 : RowSquare [6,4,2,2,1,1] [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg347 sg248 + +lemma sg4065 : RowSquare [6,4,2,2,1,1] [2,2,1,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg346 sg248 + +lemma sg4066 : RowSquare [6,4,2,2,1,1] [2,2,2,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg345 sg248 + +lemma sg4067 : RowSquare [6,4,2,2,1,1] [2,2,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg247 + +lemma sg4068 : RowSquare [6,4,2,2,1,1] [2,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg342 sg246 + +lemma sg4069 : RowSquare [6,4,2,2,1,1] [2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg342 sg244 + +lemma sg4070 : RowSquare [6,4,2,2,1,1] [2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg342 sg241 + +lemma sg4071 : RowSquare [6,4,2,2,1,1] [3,2,1,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg344 sg248 + +lemma sg4072 : RowSquare [6,4,2,2,1,1] [3,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg341 sg246 + +lemma sg4073 : RowSquare [6,4,2,2,1,1] [3,3,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg340 sg248 + +lemma sg4074 : RowSquare [6,4,2,2,1,1] [3,3,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg339 sg248 + +lemma sg4075 : RowSquare [6,4,2,2,1,1] [3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg339 sg246 + +lemma sg4076 : RowSquare [6,4,2,2,1,1] [3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg339 sg241 + +lemma sg4077 : RowSquare [6,4,2,2,1,1] [3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg13 sg1628 + +lemma sg4078 : RowSquare [6,4,2,2,1,1] [3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg339 sg239 + +lemma sg4079 : RowSquare [6,4,2,2,1,1] [3,3,3,3,2,2] := by + exact rowSquare_join (by decide) sg148 sg459 + +lemma sg4080 : RowSquare [6,4,2,2,1,1] [4,3,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg337 sg248 + +lemma sg4081 : RowSquare [6,4,2,2,1,1] [4,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg334 sg248 + +lemma sg4082 : RowSquare [6,4,2,2,1,1] [4,4,4,3,1] := by + exact rowSquare_join (by decide) sg13 sg1630 + +lemma sg4083 : RowSquare [6,4,2,2,1,1] [4,4,4,4] := by + exact rowSquare_join (by decide) sg13 sg1631 + +lemma sg4084 : RowSquare [6,4,2,2,1,1] [5,5,3,3] := by + exact rowSquare_join (by decide) sg67 sg767 + +lemma sg4085 : RowSquare [6,4,2,2,1,1] [5,5,4,2] := by + exact rowSquare_join (by decide) sg144 sg458 + +lemma sg4086 : RowSquare [6,4,2,2,1,1] [6,1,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg2 sg2574 + +lemma sg4087 : RowSquare [6,4,2,2,1,1] [6,2,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg2079 + +lemma sg4088 : RowSquare [6,4,2,2,1,1] [6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg4 sg2081 + +lemma sg4089 : RowSquare [6,4,2,2,1,1] [6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg242 + +lemma sg4090 : RowSquare [6,4,2,2,1,1] [6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg1 sg2591 + +lemma sg4091 : RowSquare [6,4,2,2,1,1] [6,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg142 sg460 + +lemma sg4092 : RowSquare [6,4,2,2,1,1] [6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg2080 + +lemma sg4093 : RowSquare [6,4,2,2,1,1] [6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg243 + +lemma sg4094 : RowSquare [6,4,2,2,1,1] [6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg56 sg811 + +lemma sg4095 : RowSquare [6,4,2,2,1,1] [6,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg295 sg260 + +lemma sg4096 : RowSquare [6,4,2,2,1,1] [6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg331 sg239 + +lemma sg4097 : RowSquare [6,4,2,2,1,1] [6,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg142 sg462 + +lemma sg4098 : RowSquare [6,4,2,2,1,1] [6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg244 + +lemma sg4099 : RowSquare [6,4,2,2,1,1] [6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg331 sg240 + +lemma sg4100 : RowSquare [6,4,2,2,1,1] [6,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg295 sg261 + +lemma sg4101 : RowSquare [6,4,2,2,1,1] [6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg331 sg241 + +lemma sg4102 : RowSquare [6,4,2,2,1,1] [6,6,2,2] := by + exact rowSquare_join (by decide) sg334 sg241 + +lemma sg4103 : RowSquare [6,4,2,2,1,1] [7,1,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6 sg2079 + +lemma sg4104 : RowSquare [6,4,2,2,1,1] [7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg5 sg2081 + +lemma sg4105 : RowSquare [6,4,2,2,1,1] [7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg245 + +lemma sg4106 : RowSquare [6,4,2,2,1,1] [7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg331 sg242 + +lemma sg4107 : RowSquare [6,4,2,2,1,1] [7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg246 + +lemma sg4108 : RowSquare [6,4,2,2,1,1] [7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg331 sg243 + +lemma sg4109 : RowSquare [6,4,2,2,1,1] [8,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg8 sg1678 + +lemma sg4110 : RowSquare [6,4,2,2,1,1] [8,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg330 sg247 + +lemma sg4111 : RowSquare [6,4,3,1,1,1] [3,3,3,3,3,1] := by + exact rowSquare_join (by decide) sg32 sg1178 + +lemma sg4112 : RowSquare [6,4,3,1,1,1] [4,4,2,2,2,2] := by + exact rowSquare_join (by decide) sg74 sg752 + +lemma sg4113 : RowSquare [6,4,3,1,1,1] [4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg27 sg1195 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes80.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes80.lean index f16f2f9527d0ecc272329f4d89c4d5ee7427e045..7a2167f45351e6a4879eb41f9bcedfb595134759 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes80.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes80.lean @@ -1,1226 +1,1226 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes57 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 - -namespace OAI - -/-! Semigroup Nodes 80. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg32541 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16256 - -lemma sg32542 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20756 sg16214 - -lemma sg32543 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16257 - -lemma sg32544 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17204 - -lemma sg32545 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg15643 sg20991 - -lemma sg32546 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15614 sg21048 - -lemma sg32547 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16257 - -lemma sg32548 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20756 sg16215 - -lemma sg32549 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20548 - -lemma sg32550 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17350 - -lemma sg32551 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18302 - -lemma sg32552 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17350 - -lemma sg32553 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20315 sg18302 - -lemma sg32554 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18281 sg20363 - -lemma sg32555 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18302 - -lemma sg32556 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg16649 sg20665 - -lemma sg32557 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18282 sg20363 - -lemma sg32558 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18302 - -lemma sg32559 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg17147 sg20561 - -lemma sg32560 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18302 - -lemma sg32561 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg16650 sg20665 - -lemma sg32562 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18114 sg20443 - -lemma sg32563 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20828 sg16129 - -lemma sg32564 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20758 sg16212 - -lemma sg32565 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16263 - -lemma sg32566 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16263 - -lemma sg32567 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16263 - -lemma sg32568 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16259 - -lemma sg32569 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16259 - -lemma sg32570 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17205 - -lemma sg32571 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20424 sg18127 - -lemma sg32572 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16260 - -lemma sg32573 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16260 - -lemma sg32574 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17206 - -lemma sg32575 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17204 - -lemma sg32576 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17204 - -lemma sg32577 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg15600 sg21077 - -lemma sg32578 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16264 - -lemma sg32579 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16264 - -lemma sg32580 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16264 - -lemma sg32581 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16261 - -lemma sg32582 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16261 - -lemma sg32583 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17207 - -lemma sg32584 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16259 - -lemma sg32585 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17205 - -lemma sg32586 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17206 - -lemma sg32587 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16260 - -lemma sg32588 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17206 - -lemma sg32589 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19181 - -lemma sg32590 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16260 - -lemma sg32591 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20549 - -lemma sg32592 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15676 sg20904 - -lemma sg32593 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20444 - -lemma sg32594 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg15677 sg20904 - -lemma sg32595 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17207 - -lemma sg32596 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16261 - -lemma sg32597 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17207 - -lemma sg32598 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg15679 sg20903 - -lemma sg32599 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16261 - -lemma sg32600 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20335 - -lemma sg32601 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15560 sg21090 - -lemma sg32602 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20652 sg16652 - -lemma sg32603 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20829 sg16128 - -lemma sg32604 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20652 sg16653 - -lemma sg32605 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20828 sg16130 - -lemma sg32606 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20758 sg16216 - -lemma sg32607 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16265 - -lemma sg32608 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16265 - -lemma sg32609 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16265 - -lemma sg32610 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16262 - -lemma sg32611 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16262 - -lemma sg32612 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17208 - -lemma sg32613 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19625 sg18921 - -lemma sg32614 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16266 - -lemma sg32615 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16266 - -lemma sg32616 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16266 - -lemma sg32617 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16263 - -lemma sg32618 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16263 - -lemma sg32619 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17209 - -lemma sg32620 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16262 - -lemma sg32621 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17208 - -lemma sg32622 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17206 - -lemma sg32623 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17206 - -lemma sg32624 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17206 - -lemma sg32625 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19182 - -lemma sg32626 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16264 - -lemma sg32627 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16264 - -lemma sg32628 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17210 - -lemma sg32629 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17209 - -lemma sg32630 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16263 - -lemma sg32631 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17209 - -lemma sg32632 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17205 - -lemma sg32633 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16263 - -lemma sg32634 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20336 - -lemma sg32635 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16683 - -lemma sg32636 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17210 - -lemma sg32637 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16264 - -lemma sg32638 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17210 - -lemma sg32639 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16264 - -lemma sg32640 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20337 - -lemma sg32641 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16684 - -lemma sg32642 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15645 sg20985 - -lemma sg32643 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20445 - -lemma sg32644 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15679 sg20904 - -lemma sg32645 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17207 - -lemma sg32646 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15683 sg20899 - -lemma sg32647 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20829 sg16130 - -lemma sg32648 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20759 sg16216 - -lemma sg32649 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16267 - -lemma sg32650 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16267 - -lemma sg32651 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16267 - -lemma sg32652 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16265 - -lemma sg32653 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16265 - -lemma sg32654 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17211 - -lemma sg32655 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17208 - -lemma sg32656 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17208 - -lemma sg32657 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16266 - -lemma sg32658 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16266 - -lemma sg32659 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17212 - -lemma sg32660 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17211 - -lemma sg32661 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16265 - -lemma sg32662 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17211 - -lemma sg32663 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17208 - -lemma sg32664 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16265 - -lemma sg32665 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20338 - -lemma sg32666 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17212 - -lemma sg32667 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16266 - -lemma sg32668 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17212 - -lemma sg32669 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16266 - -lemma sg32670 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20339 - -lemma sg32671 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16686 - -lemma sg32672 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17210 - -lemma sg32673 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17210 - -lemma sg32674 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17210 - -lemma sg32675 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16687 - -lemma sg32676 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20446 - -lemma sg32677 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17210 - -lemma sg32678 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,8,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14726 sg21271 - -lemma sg32679 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15640 sg21040 - -lemma sg32680 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg15683 sg20900 - -lemma sg32681 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20759 sg16217 - -lemma sg32682 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16267 - -lemma sg32683 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16267 - -lemma sg32684 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17213 - -lemma sg32685 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17211 - -lemma sg32686 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17211 - -lemma sg32687 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17211 - -lemma sg32688 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20653 sg16654 - -lemma sg32689 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17213 - -lemma sg32690 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16267 - -lemma sg32691 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17213 - -lemma sg32692 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16267 - -lemma sg32693 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20340 - -lemma sg32694 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16688 - -lemma sg32695 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17212 - -lemma sg32696 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17212 - -lemma sg32697 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17212 - -lemma sg32698 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16689 - -lemma sg32699 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20447 - -lemma sg32700 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17212 - -lemma sg32701 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15102 sg21200 - -lemma sg32702 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15615 sg21049 - -lemma sg32703 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15615 sg21050 - -lemma sg32704 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg15683 sg20901 - -lemma sg32705 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17213 - -lemma sg32706 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17213 - -lemma sg32707 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17213 - -lemma sg32708 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15670 sg20951 - -lemma sg32709 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15671 sg20951 - -lemma sg32710 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17213 - -lemma sg32711 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17213 - -lemma sg32712 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17213 - -lemma sg32713 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16690 - -lemma sg32714 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15693 sg20897 - -lemma sg32715 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17213 - -lemma sg32716 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15102 sg21201 - -lemma sg32717 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15617 sg21046 - -lemma sg32718 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20448 - -lemma sg32719 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17161 - -lemma sg32720 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15249 sg21117 - -lemma sg32721 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20449 - -lemma sg32722 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17221 - -lemma sg32723 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17162 - -lemma sg32724 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15630 sg21044 - -lemma sg32725 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17222 - -lemma sg32726 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17223 - -lemma sg32727 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17242 - -lemma sg32728 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18134 - -lemma sg32729 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17242 - -lemma sg32730 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16700 - -lemma sg32731 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17242 - -lemma sg32732 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16700 - -lemma sg32733 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17242 - -lemma sg32734 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20716 sg16227 - -lemma sg32735 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20643 sg16661 - -lemma sg32736 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16694 - -lemma sg32737 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,8,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15230 sg21188 - -lemma sg32738 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,8,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20450 - -lemma sg32739 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,8,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18116 sg20430 - -lemma sg32740 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,8,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20451 - -lemma sg32741 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,8,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17230 - -lemma sg32742 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,8,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17231 - -lemma sg32743 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20719 sg16223 - -lemma sg32744 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18920 sg19627 - -lemma sg32745 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17165 - -lemma sg32746 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17238 - -lemma sg32747 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16273 - -lemma sg32748 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17238 - -lemma sg32749 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20813 sg16136 - -lemma sg32750 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16273 - -lemma sg32751 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19183 - -lemma sg32752 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20720 sg16224 - -lemma sg32753 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17482 - -lemma sg32754 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18307 - -lemma sg32755 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17482 - -lemma sg32756 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg19698 - -lemma sg32757 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg19698 - -lemma sg32758 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18307 - -lemma sg32759 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18911 sg19698 - -lemma sg32760 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg19698 - -lemma sg32761 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18307 - -lemma sg32762 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg18913 sg19698 - -lemma sg32763 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18307 - -lemma sg32764 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg18914 sg19698 - -lemma sg32765 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17277 - -lemma sg32766 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15755 - -lemma sg32767 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16313 - -lemma sg32768 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16730 - -lemma sg32769 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17277 - -lemma sg32770 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19576 sg19577 - -lemma sg32771 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19204 - -lemma sg32772 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17277 - -lemma sg32773 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg19618 sg19204 - -lemma sg32774 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19619 sg19204 - -lemma sg32775 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16688 - -lemma sg32776 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20638 sg16688 - -lemma sg32777 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20528 sg17211 - -lemma sg32778 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17211 - -lemma sg32779 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20530 sg17211 - -lemma sg32780 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20722 sg16222 - -lemma sg32781 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16266 - -lemma sg32782 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20798 sg16158 - -lemma sg32783 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20799 sg16158 - -lemma sg32784 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16689 - -lemma sg32785 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20638 sg16689 - -lemma sg32786 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20528 sg17212 - -lemma sg32787 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17212 - -lemma sg32788 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20530 sg17212 - -lemma sg32789 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17240 - -lemma sg32790 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16275 - -lemma sg32791 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17240 - -lemma sg32792 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19184 - -lemma sg32793 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16275 - -lemma sg32794 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19185 - -lemma sg32795 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16277 - -lemma sg32796 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16277 - -lemma sg32797 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17242 - -lemma sg32798 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17241 - -lemma sg32799 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16276 - -lemma sg32800 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17241 - -lemma sg32801 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17236 - -lemma sg32802 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16276 - -lemma sg32803 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19186 - -lemma sg32804 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16696 - -lemma sg32805 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17242 - -lemma sg32806 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16277 - -lemma sg32807 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17242 - -lemma sg32808 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16277 - -lemma sg32809 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20550 - -lemma sg32810 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16697 - -lemma sg32811 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,8,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12865 sg21635 - -lemma sg32812 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,8,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20452 - -lemma sg32813 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,8,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17170 - -lemma sg32814 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,8,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17238 - -lemma sg32815 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16731 - -lemma sg32816 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16314 - -lemma sg32817 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17278 - -lemma sg32818 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15756 - -lemma sg32819 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16314 - -lemma sg32820 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16731 - -lemma sg32821 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17278 - -lemma sg32822 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20496 sg18106 - -lemma sg32823 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19575 sg19608 - -lemma sg32824 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17278 - -lemma sg32825 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20319 sg18295 - -lemma sg32826 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20320 sg18295 - -lemma sg32827 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20705 sg16267 - -lemma sg32828 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20798 sg16159 - -lemma sg32829 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20799 sg16159 - -lemma sg32830 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20637 sg16690 - -lemma sg32831 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20638 sg16690 - -lemma sg32832 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20528 sg17213 - -lemma sg32833 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20529 sg17213 - -lemma sg32834 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20530 sg17213 - -lemma sg32835 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17240 - -lemma sg32836 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17240 - -lemma sg32837 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17240 - -lemma sg32838 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20722 sg16225 - -lemma sg32839 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17239 - -lemma sg32840 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18920 sg19628 - -lemma sg32841 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17172 - -lemma sg32842 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17241 - -lemma sg32843 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17241 - -lemma sg32844 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17241 - -lemma sg32845 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17239 - -lemma sg32846 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17240 - -lemma sg32847 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17240 - -lemma sg32848 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16698 - -lemma sg32849 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17242 - -lemma sg32850 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17242 - -lemma sg32851 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17242 - -lemma sg32852 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17241 - -lemma sg32853 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17241 - -lemma sg32854 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16699 - -lemma sg32855 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17242 - -lemma sg32856 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17242 - -lemma sg32857 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17242 - -lemma sg32858 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16700 - -lemma sg32859 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,8,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6460 sg23673 - -lemma sg32860 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,8,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17242 - -lemma sg32861 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,9,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg6460 sg23674 - -lemma sg32862 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16237 - -lemma sg32863 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20711 sg16237 - -lemma sg32864 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20712 sg16237 - -lemma sg32865 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16670 - -lemma sg32866 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20640 sg16670 - -lemma sg32867 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20641 sg16670 - -lemma sg32868 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20531 sg17190 - -lemma sg32869 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20731 sg16227 - -lemma sg32870 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20538 sg17177 - -lemma sg32871 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16702 - -lemma sg32872 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,8,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15231 sg21188 - -lemma sg32873 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,8,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20453 - -lemma sg32874 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,8,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17178 - -lemma sg32875 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,8,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20454 - -lemma sg32876 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,8,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17243 - -lemma sg32877 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,8,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17244 - -lemma sg32878 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17246 - -lemma sg32879 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18135 - -lemma sg32880 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17246 - -lemma sg32881 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16708 - -lemma sg32882 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17246 - -lemma sg32883 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16708 - -lemma sg32884 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17246 - -lemma sg32885 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16281 - -lemma sg32886 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20551 - -lemma sg32887 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20720 sg16228 - -lemma sg32888 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17550 - -lemma sg32889 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18309 - -lemma sg32890 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17550 - -lemma sg32891 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg19719 - -lemma sg32892 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg19719 - -lemma sg32893 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18309 - -lemma sg32894 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18911 sg19719 - -lemma sg32895 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg19719 - -lemma sg32896 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18309 - -lemma sg32897 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg18913 sg19719 - -lemma sg32898 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18309 - -lemma sg32899 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg18914 sg19719 - -lemma sg32900 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17310 - -lemma sg32901 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15769 - -lemma sg32902 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16347 - -lemma sg32903 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16756 - -lemma sg32904 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17310 - -lemma sg32905 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19576 sg19578 - -lemma sg32906 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19220 - -lemma sg32907 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17310 - -lemma sg32908 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg19618 sg19220 - -lemma sg32909 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19619 sg19220 - -lemma sg32910 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18032 - -lemma sg32911 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16721 - -lemma sg32912 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18916 sg19629 - -lemma sg32913 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17267 - -lemma sg32914 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18917 sg19629 - -lemma sg32915 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17247 - -lemma sg32916 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17268 - -lemma sg32917 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18284 sg20342 - -lemma sg32918 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20507 sg17268 - -lemma sg32919 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18033 - -lemma sg32920 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16722 - -lemma sg32921 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18285 sg20342 - -lemma sg32922 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17268 - -lemma sg32923 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18286 sg20342 - -lemma sg32924 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16709 - -lemma sg32925 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17248 - -lemma sg32926 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16709 - -lemma sg32927 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17248 - -lemma sg32928 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20716 sg16235 - -lemma sg32929 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20643 sg16668 - -lemma sg32930 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17249 - -lemma sg32931 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18136 - -lemma sg32932 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17249 - -lemma sg32933 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16710 - -lemma sg32934 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17249 - -lemma sg32935 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16710 - -lemma sg32936 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17249 - -lemma sg32937 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20716 sg16236 - -lemma sg32938 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20643 sg16669 - -lemma sg32939 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16703 - -lemma sg32940 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20713 sg16237 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes57 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 + +namespace OAI + +/-! Semigroup Nodes 80. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg32541 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16256 + +lemma sg32542 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20756 sg16214 + +lemma sg32543 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16257 + +lemma sg32544 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17204 + +lemma sg32545 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg15643 sg20991 + +lemma sg32546 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15614 sg21048 + +lemma sg32547 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16257 + +lemma sg32548 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20756 sg16215 + +lemma sg32549 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20548 + +lemma sg32550 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17350 + +lemma sg32551 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18302 + +lemma sg32552 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17350 + +lemma sg32553 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20315 sg18302 + +lemma sg32554 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18281 sg20363 + +lemma sg32555 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18302 + +lemma sg32556 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg16649 sg20665 + +lemma sg32557 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18282 sg20363 + +lemma sg32558 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18302 + +lemma sg32559 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg17147 sg20561 + +lemma sg32560 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18302 + +lemma sg32561 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg16650 sg20665 + +lemma sg32562 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18114 sg20443 + +lemma sg32563 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20828 sg16129 + +lemma sg32564 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20758 sg16212 + +lemma sg32565 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16263 + +lemma sg32566 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16263 + +lemma sg32567 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16263 + +lemma sg32568 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16259 + +lemma sg32569 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16259 + +lemma sg32570 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17205 + +lemma sg32571 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20424 sg18127 + +lemma sg32572 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16260 + +lemma sg32573 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16260 + +lemma sg32574 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17206 + +lemma sg32575 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17204 + +lemma sg32576 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17204 + +lemma sg32577 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg15600 sg21077 + +lemma sg32578 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16264 + +lemma sg32579 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16264 + +lemma sg32580 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16264 + +lemma sg32581 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16261 + +lemma sg32582 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16261 + +lemma sg32583 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17207 + +lemma sg32584 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16259 + +lemma sg32585 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17205 + +lemma sg32586 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17206 + +lemma sg32587 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16260 + +lemma sg32588 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17206 + +lemma sg32589 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19181 + +lemma sg32590 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16260 + +lemma sg32591 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20549 + +lemma sg32592 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15676 sg20904 + +lemma sg32593 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20444 + +lemma sg32594 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg15677 sg20904 + +lemma sg32595 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17207 + +lemma sg32596 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16261 + +lemma sg32597 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17207 + +lemma sg32598 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg15679 sg20903 + +lemma sg32599 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16261 + +lemma sg32600 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20335 + +lemma sg32601 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15560 sg21090 + +lemma sg32602 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20652 sg16652 + +lemma sg32603 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20829 sg16128 + +lemma sg32604 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20652 sg16653 + +lemma sg32605 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20828 sg16130 + +lemma sg32606 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20758 sg16216 + +lemma sg32607 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16265 + +lemma sg32608 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16265 + +lemma sg32609 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16265 + +lemma sg32610 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16262 + +lemma sg32611 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16262 + +lemma sg32612 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17208 + +lemma sg32613 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19625 sg18921 + +lemma sg32614 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16266 + +lemma sg32615 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16266 + +lemma sg32616 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16266 + +lemma sg32617 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16263 + +lemma sg32618 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16263 + +lemma sg32619 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17209 + +lemma sg32620 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16262 + +lemma sg32621 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17208 + +lemma sg32622 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17206 + +lemma sg32623 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17206 + +lemma sg32624 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17206 + +lemma sg32625 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19182 + +lemma sg32626 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16264 + +lemma sg32627 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16264 + +lemma sg32628 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17210 + +lemma sg32629 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17209 + +lemma sg32630 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16263 + +lemma sg32631 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17209 + +lemma sg32632 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17205 + +lemma sg32633 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16263 + +lemma sg32634 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20336 + +lemma sg32635 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16683 + +lemma sg32636 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17210 + +lemma sg32637 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16264 + +lemma sg32638 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17210 + +lemma sg32639 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16264 + +lemma sg32640 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20337 + +lemma sg32641 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16684 + +lemma sg32642 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15645 sg20985 + +lemma sg32643 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20445 + +lemma sg32644 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15679 sg20904 + +lemma sg32645 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,7,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17207 + +lemma sg32646 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15683 sg20899 + +lemma sg32647 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20829 sg16130 + +lemma sg32648 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20759 sg16216 + +lemma sg32649 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16267 + +lemma sg32650 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16267 + +lemma sg32651 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16267 + +lemma sg32652 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16265 + +lemma sg32653 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16265 + +lemma sg32654 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17211 + +lemma sg32655 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17208 + +lemma sg32656 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17208 + +lemma sg32657 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16266 + +lemma sg32658 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16266 + +lemma sg32659 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17212 + +lemma sg32660 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17211 + +lemma sg32661 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16265 + +lemma sg32662 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17211 + +lemma sg32663 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17208 + +lemma sg32664 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16265 + +lemma sg32665 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20338 + +lemma sg32666 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17212 + +lemma sg32667 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16266 + +lemma sg32668 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17212 + +lemma sg32669 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16266 + +lemma sg32670 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20339 + +lemma sg32671 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16686 + +lemma sg32672 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17210 + +lemma sg32673 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17210 + +lemma sg32674 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17210 + +lemma sg32675 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16687 + +lemma sg32676 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20446 + +lemma sg32677 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17210 + +lemma sg32678 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,8,8,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14726 sg21271 + +lemma sg32679 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15640 sg21040 + +lemma sg32680 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg15683 sg20900 + +lemma sg32681 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20759 sg16217 + +lemma sg32682 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16267 + +lemma sg32683 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16267 + +lemma sg32684 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17213 + +lemma sg32685 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17211 + +lemma sg32686 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17211 + +lemma sg32687 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17211 + +lemma sg32688 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20653 sg16654 + +lemma sg32689 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17213 + +lemma sg32690 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16267 + +lemma sg32691 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17213 + +lemma sg32692 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16267 + +lemma sg32693 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20340 + +lemma sg32694 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16688 + +lemma sg32695 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17212 + +lemma sg32696 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17212 + +lemma sg32697 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17212 + +lemma sg32698 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16689 + +lemma sg32699 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20447 + +lemma sg32700 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17212 + +lemma sg32701 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,9,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15102 sg21200 + +lemma sg32702 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15615 sg21049 + +lemma sg32703 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15615 sg21050 + +lemma sg32704 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg15683 sg20901 + +lemma sg32705 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17213 + +lemma sg32706 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17213 + +lemma sg32707 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17213 + +lemma sg32708 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15670 sg20951 + +lemma sg32709 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15671 sg20951 + +lemma sg32710 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17213 + +lemma sg32711 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17213 + +lemma sg32712 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17213 + +lemma sg32713 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16690 + +lemma sg32714 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15693 sg20897 + +lemma sg32715 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17213 + +lemma sg32716 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [10,10,10,10,10,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15102 sg21201 + +lemma sg32717 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15617 sg21046 + +lemma sg32718 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20448 + +lemma sg32719 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17161 + +lemma sg32720 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15249 sg21117 + +lemma sg32721 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20449 + +lemma sg32722 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17221 + +lemma sg32723 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17162 + +lemma sg32724 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15630 sg21044 + +lemma sg32725 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17222 + +lemma sg32726 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,8,8,8,8,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17223 + +lemma sg32727 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17242 + +lemma sg32728 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18134 + +lemma sg32729 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17242 + +lemma sg32730 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16700 + +lemma sg32731 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17242 + +lemma sg32732 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16700 + +lemma sg32733 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17242 + +lemma sg32734 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20716 sg16227 + +lemma sg32735 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20643 sg16661 + +lemma sg32736 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16694 + +lemma sg32737 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,8,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15230 sg21188 + +lemma sg32738 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,8,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20450 + +lemma sg32739 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,8,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18116 sg20430 + +lemma sg32740 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,8,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20451 + +lemma sg32741 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,8,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17230 + +lemma sg32742 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,8,8,8,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17231 + +lemma sg32743 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20719 sg16223 + +lemma sg32744 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18920 sg19627 + +lemma sg32745 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17165 + +lemma sg32746 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17238 + +lemma sg32747 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16273 + +lemma sg32748 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17238 + +lemma sg32749 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20813 sg16136 + +lemma sg32750 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16273 + +lemma sg32751 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19183 + +lemma sg32752 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20720 sg16224 + +lemma sg32753 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17482 + +lemma sg32754 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18307 + +lemma sg32755 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17482 + +lemma sg32756 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg19698 + +lemma sg32757 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg19698 + +lemma sg32758 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18307 + +lemma sg32759 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18911 sg19698 + +lemma sg32760 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg19698 + +lemma sg32761 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18307 + +lemma sg32762 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg18913 sg19698 + +lemma sg32763 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18307 + +lemma sg32764 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg18914 sg19698 + +lemma sg32765 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17277 + +lemma sg32766 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15755 + +lemma sg32767 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16313 + +lemma sg32768 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16730 + +lemma sg32769 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17277 + +lemma sg32770 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19576 sg19577 + +lemma sg32771 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19204 + +lemma sg32772 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17277 + +lemma sg32773 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg19618 sg19204 + +lemma sg32774 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19619 sg19204 + +lemma sg32775 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16688 + +lemma sg32776 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20638 sg16688 + +lemma sg32777 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20528 sg17211 + +lemma sg32778 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17211 + +lemma sg32779 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20530 sg17211 + +lemma sg32780 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20722 sg16222 + +lemma sg32781 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16266 + +lemma sg32782 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20798 sg16158 + +lemma sg32783 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20799 sg16158 + +lemma sg32784 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16689 + +lemma sg32785 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20638 sg16689 + +lemma sg32786 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20528 sg17212 + +lemma sg32787 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17212 + +lemma sg32788 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20530 sg17212 + +lemma sg32789 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17240 + +lemma sg32790 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16275 + +lemma sg32791 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17240 + +lemma sg32792 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19184 + +lemma sg32793 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16275 + +lemma sg32794 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19185 + +lemma sg32795 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16277 + +lemma sg32796 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16277 + +lemma sg32797 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17242 + +lemma sg32798 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17241 + +lemma sg32799 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16276 + +lemma sg32800 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17241 + +lemma sg32801 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17236 + +lemma sg32802 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16276 + +lemma sg32803 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19186 + +lemma sg32804 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16696 + +lemma sg32805 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17242 + +lemma sg32806 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16277 + +lemma sg32807 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17242 + +lemma sg32808 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16277 + +lemma sg32809 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20550 + +lemma sg32810 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16697 + +lemma sg32811 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,8,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12865 sg21635 + +lemma sg32812 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,8,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20452 + +lemma sg32813 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,8,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17170 + +lemma sg32814 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,8,8,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17238 + +lemma sg32815 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16731 + +lemma sg32816 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16314 + +lemma sg32817 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17278 + +lemma sg32818 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15756 + +lemma sg32819 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16314 + +lemma sg32820 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16731 + +lemma sg32821 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17278 + +lemma sg32822 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20496 sg18106 + +lemma sg32823 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19575 sg19608 + +lemma sg32824 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17278 + +lemma sg32825 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20319 sg18295 + +lemma sg32826 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20320 sg18295 + +lemma sg32827 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20705 sg16267 + +lemma sg32828 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20798 sg16159 + +lemma sg32829 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20799 sg16159 + +lemma sg32830 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20637 sg16690 + +lemma sg32831 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20638 sg16690 + +lemma sg32832 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20528 sg17213 + +lemma sg32833 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20529 sg17213 + +lemma sg32834 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20530 sg17213 + +lemma sg32835 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17240 + +lemma sg32836 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17240 + +lemma sg32837 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17240 + +lemma sg32838 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20722 sg16225 + +lemma sg32839 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17239 + +lemma sg32840 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18920 sg19628 + +lemma sg32841 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17172 + +lemma sg32842 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17241 + +lemma sg32843 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17241 + +lemma sg32844 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17241 + +lemma sg32845 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17239 + +lemma sg32846 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17240 + +lemma sg32847 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17240 + +lemma sg32848 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16698 + +lemma sg32849 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17242 + +lemma sg32850 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17242 + +lemma sg32851 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17242 + +lemma sg32852 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17241 + +lemma sg32853 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17241 + +lemma sg32854 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16699 + +lemma sg32855 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17242 + +lemma sg32856 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17242 + +lemma sg32857 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17242 + +lemma sg32858 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16700 + +lemma sg32859 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,8,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6460 sg23673 + +lemma sg32860 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,8,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17242 + +lemma sg32861 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,9,9,9,9,9,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg6460 sg23674 + +lemma sg32862 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16237 + +lemma sg32863 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20711 sg16237 + +lemma sg32864 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20712 sg16237 + +lemma sg32865 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16670 + +lemma sg32866 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20640 sg16670 + +lemma sg32867 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20641 sg16670 + +lemma sg32868 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20531 sg17190 + +lemma sg32869 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20731 sg16227 + +lemma sg32870 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20538 sg17177 + +lemma sg32871 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16702 + +lemma sg32872 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,8,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15231 sg21188 + +lemma sg32873 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,8,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20453 + +lemma sg32874 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,8,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17178 + +lemma sg32875 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,8,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20454 + +lemma sg32876 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,8,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17243 + +lemma sg32877 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,8,8,8,8,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17244 + +lemma sg32878 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17246 + +lemma sg32879 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18135 + +lemma sg32880 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17246 + +lemma sg32881 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16708 + +lemma sg32882 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17246 + +lemma sg32883 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16708 + +lemma sg32884 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17246 + +lemma sg32885 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16281 + +lemma sg32886 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20551 + +lemma sg32887 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20720 sg16228 + +lemma sg32888 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17550 + +lemma sg32889 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18309 + +lemma sg32890 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17550 + +lemma sg32891 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg19719 + +lemma sg32892 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg19719 + +lemma sg32893 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18309 + +lemma sg32894 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18911 sg19719 + +lemma sg32895 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg19719 + +lemma sg32896 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18309 + +lemma sg32897 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg18913 sg19719 + +lemma sg32898 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18309 + +lemma sg32899 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg18914 sg19719 + +lemma sg32900 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17310 + +lemma sg32901 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15769 + +lemma sg32902 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16347 + +lemma sg32903 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16756 + +lemma sg32904 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17310 + +lemma sg32905 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19576 sg19578 + +lemma sg32906 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19220 + +lemma sg32907 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17310 + +lemma sg32908 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg19618 sg19220 + +lemma sg32909 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19619 sg19220 + +lemma sg32910 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18032 + +lemma sg32911 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16721 + +lemma sg32912 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18916 sg19629 + +lemma sg32913 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17267 + +lemma sg32914 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18917 sg19629 + +lemma sg32915 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17247 + +lemma sg32916 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17268 + +lemma sg32917 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18284 sg20342 + +lemma sg32918 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20507 sg17268 + +lemma sg32919 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18033 + +lemma sg32920 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16722 + +lemma sg32921 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18285 sg20342 + +lemma sg32922 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17268 + +lemma sg32923 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18286 sg20342 + +lemma sg32924 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16709 + +lemma sg32925 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17248 + +lemma sg32926 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16709 + +lemma sg32927 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17248 + +lemma sg32928 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20716 sg16235 + +lemma sg32929 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20643 sg16668 + +lemma sg32930 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17249 + +lemma sg32931 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18136 + +lemma sg32932 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17249 + +lemma sg32933 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16710 + +lemma sg32934 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17249 + +lemma sg32935 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16710 + +lemma sg32936 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17249 + +lemma sg32937 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20716 sg16236 + +lemma sg32938 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20643 sg16669 + +lemma sg32939 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16703 + +lemma sg32940 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20713 sg16237 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes81.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes81.lean index a18dab7fc70ac560291bf644cc02e94498529eb6..d7e2725f8a7f8482b533827ceb881a48bd9b4ca2 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes81.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes81.lean @@ -1,1230 +1,1230 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 - -namespace OAI - -/-! Semigroup Nodes 81. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg32941 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20714 sg16237 - -lemma sg32942 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20715 sg16237 - -lemma sg32943 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20716 sg16237 - -lemma sg32944 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20643 sg16670 - -lemma sg32945 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16704 - -lemma sg32946 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,8,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14313 sg21347 - -lemma sg32947 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,8,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20455 - -lemma sg32948 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,8,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17181 - -lemma sg32949 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,8,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17245 - -lemma sg32950 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17555 - -lemma sg32951 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18310 - -lemma sg32952 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17555 - -lemma sg32953 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg19722 - -lemma sg32954 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg19722 - -lemma sg32955 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18310 - -lemma sg32956 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18911 sg19722 - -lemma sg32957 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg19722 - -lemma sg32958 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18310 - -lemma sg32959 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg18913 sg19722 - -lemma sg32960 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18310 - -lemma sg32961 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg18914 sg19722 - -lemma sg32962 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17316 - -lemma sg32963 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15773 - -lemma sg32964 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16353 - -lemma sg32965 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16762 - -lemma sg32966 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17316 - -lemma sg32967 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19616 sg19225 - -lemma sg32968 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19225 - -lemma sg32969 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17316 - -lemma sg32970 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg19618 sg19225 - -lemma sg32971 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19619 sg19225 - -lemma sg32972 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18034 - -lemma sg32973 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16728 - -lemma sg32974 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18916 sg19631 - -lemma sg32975 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17275 - -lemma sg32976 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18917 sg19631 - -lemma sg32977 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20531 sg17208 - -lemma sg32978 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17276 - -lemma sg32979 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19632 - -lemma sg32980 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20507 sg17276 - -lemma sg32981 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18035 - -lemma sg32982 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16729 - -lemma sg32983 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18916 sg19632 - -lemma sg32984 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17276 - -lemma sg32985 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18917 sg19632 - -lemma sg32986 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16686 - -lemma sg32987 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20640 sg16686 - -lemma sg32988 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20641 sg16686 - -lemma sg32989 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20531 sg17209 - -lemma sg32990 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16283 - -lemma sg32991 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19187 - -lemma sg32992 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16264 - -lemma sg32993 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20803 sg16156 - -lemma sg32994 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20712 sg16264 - -lemma sg32995 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16687 - -lemma sg32996 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20640 sg16687 - -lemma sg32997 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20641 sg16687 - -lemma sg32998 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20531 sg17210 - -lemma sg32999 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16284 - -lemma sg33000 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19188 - -lemma sg33001 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16705 - -lemma sg33002 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17246 - -lemma sg33003 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16285 - -lemma sg33004 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17246 - -lemma sg33005 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16285 - -lemma sg33006 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20552 - -lemma sg33007 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20720 sg16232 - -lemma sg33008 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16763 - -lemma sg33009 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16354 - -lemma sg33010 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17317 - -lemma sg33011 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15774 - -lemma sg33012 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16354 - -lemma sg33013 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16763 - -lemma sg33014 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17317 - -lemma sg33015 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19616 sg19226 - -lemma sg33016 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19226 - -lemma sg33017 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17317 - -lemma sg33018 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg19618 sg19226 - -lemma sg33019 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19619 sg19226 - -lemma sg33020 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17277 - -lemma sg33021 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19633 - -lemma sg33022 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20507 sg17277 - -lemma sg33023 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18036 - -lemma sg33024 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16730 - -lemma sg33025 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18916 sg19633 - -lemma sg33026 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17277 - -lemma sg33027 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18917 sg19633 - -lemma sg33028 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16688 - -lemma sg33029 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20640 sg16688 - -lemma sg33030 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20641 sg16688 - -lemma sg33031 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20531 sg17211 - -lemma sg33032 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16266 - -lemma sg33033 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20803 sg16158 - -lemma sg33034 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20712 sg16266 - -lemma sg33035 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16689 - -lemma sg33036 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20640 sg16689 - -lemma sg33037 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20641 sg16689 - -lemma sg33038 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20531 sg17212 - -lemma sg33039 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16286 - -lemma sg33040 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19189 - -lemma sg33041 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16706 - -lemma sg33042 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17249 - -lemma sg33043 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16287 - -lemma sg33044 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17249 - -lemma sg33045 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16287 - -lemma sg33046 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20341 - -lemma sg33047 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16707 - -lemma sg33048 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17246 - -lemma sg33049 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17246 - -lemma sg33050 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17246 - -lemma sg33051 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16708 - -lemma sg33052 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,8,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20456 - -lemma sg33053 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,8,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17246 - -lemma sg33054 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17278 - -lemma sg33055 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg15756 - -lemma sg33056 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20505 sg17278 - -lemma sg33057 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17278 - -lemma sg33058 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18284 sg20344 - -lemma sg33059 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20507 sg17278 - -lemma sg33060 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18037 - -lemma sg33061 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16731 - -lemma sg33062 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18285 sg20344 - -lemma sg33063 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17278 - -lemma sg33064 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18286 sg20344 - -lemma sg33065 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20710 sg16267 - -lemma sg33066 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20803 sg16159 - -lemma sg33067 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20712 sg16267 - -lemma sg33068 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20639 sg16690 - -lemma sg33069 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20640 sg16690 - -lemma sg33070 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20641 sg16690 - -lemma sg33071 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20531 sg17213 - -lemma sg33072 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20721 sg16235 - -lemma sg33073 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20722 sg16235 - -lemma sg33074 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17249 - -lemma sg33075 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17249 - -lemma sg33076 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17249 - -lemma sg33077 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17248 - -lemma sg33078 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17248 - -lemma sg33079 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16709 - -lemma sg33080 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17249 - -lemma sg33081 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17249 - -lemma sg33082 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17249 - -lemma sg33083 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16710 - -lemma sg33084 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20457 - -lemma sg33085 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17249 - -lemma sg33086 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,8,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17190 - -lemma sg33087 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18275 sg20421 - -lemma sg33088 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18137 - -lemma sg33089 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20323 sg18294 - -lemma sg33090 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16715 - -lemma sg33091 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20324 sg18294 - -lemma sg33092 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16715 - -lemma sg33093 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20325 sg18294 - -lemma sg33094 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20716 sg16245 - -lemma sg33095 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20643 sg16673 - -lemma sg33096 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17252 - -lemma sg33097 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17556 - -lemma sg33098 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18311 - -lemma sg33099 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17556 - -lemma sg33100 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg19723 - -lemma sg33101 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg19723 - -lemma sg33102 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18311 - -lemma sg33103 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18911 sg19723 - -lemma sg33104 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg19723 - -lemma sg33105 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18311 - -lemma sg33106 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg18913 sg19723 - -lemma sg33107 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18311 - -lemma sg33108 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg18914 sg19723 - -lemma sg33109 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17341 - -lemma sg33110 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15790 - -lemma sg33111 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16375 - -lemma sg33112 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16785 - -lemma sg33113 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17341 - -lemma sg33114 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19621 sg18932 - -lemma sg33115 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19236 - -lemma sg33116 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17341 - -lemma sg33117 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg19618 sg19236 - -lemma sg33118 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19622 sg18932 - -lemma sg33119 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16291 - -lemma sg33120 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16291 - -lemma sg33121 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17258 - -lemma sg33122 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17264 - -lemma sg33123 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16718 - -lemma sg33124 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17264 - -lemma sg33125 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17266 - -lemma sg33126 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18139 - -lemma sg33127 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17266 - -lemma sg33128 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17265 - -lemma sg33129 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18138 - -lemma sg33130 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17265 - -lemma sg33131 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16290 - -lemma sg33132 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17257 - -lemma sg33133 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16719 - -lemma sg33134 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17265 - -lemma sg33135 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16719 - -lemma sg33136 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17265 - -lemma sg33137 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16291 - -lemma sg33138 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19190 - -lemma sg33139 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17266 - -lemma sg33140 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18139 - -lemma sg33141 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17266 - -lemma sg33142 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16720 - -lemma sg33143 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17266 - -lemma sg33144 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16720 - -lemma sg33145 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17266 - -lemma sg33146 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16292 - -lemma sg33147 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19191 - -lemma sg33148 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16712 - -lemma sg33149 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg17148 sg20553 - -lemma sg33150 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16293 - -lemma sg33151 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20424 sg18137 - -lemma sg33152 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16293 - -lemma sg33153 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20553 - -lemma sg33154 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20720 sg16245 - -lemma sg33155 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16786 - -lemma sg33156 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16376 - -lemma sg33157 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17342 - -lemma sg33158 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15791 - -lemma sg33159 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16376 - -lemma sg33160 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16786 - -lemma sg33161 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17342 - -lemma sg33162 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19576 sg19579 - -lemma sg33163 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19237 - -lemma sg33164 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17342 - -lemma sg33165 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg19618 sg19237 - -lemma sg33166 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19619 sg19237 - -lemma sg33167 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17268 - -lemma sg33168 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18141 - -lemma sg33169 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17268 - -lemma sg33170 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17267 - -lemma sg33171 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18140 - -lemma sg33172 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17267 - -lemma sg33173 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20870 sg15710 - -lemma sg33174 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20715 sg16252 - -lemma sg33175 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16721 - -lemma sg33176 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17267 - -lemma sg33177 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16721 - -lemma sg33178 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17267 - -lemma sg33179 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17268 - -lemma sg33180 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18141 - -lemma sg33181 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17268 - -lemma sg33182 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16722 - -lemma sg33183 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17268 - -lemma sg33184 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16722 - -lemma sg33185 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17268 - -lemma sg33186 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20716 sg16253 - -lemma sg33187 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20643 sg16679 - -lemma sg33188 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16713 - -lemma sg33189 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20713 sg16254 - -lemma sg33190 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20807 sg16151 - -lemma sg33191 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20715 sg16254 - -lemma sg33192 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20716 sg16254 - -lemma sg33193 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20643 sg16680 - -lemma sg33194 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16714 - -lemma sg33195 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18114 sg20458 - -lemma sg33196 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20326 sg18294 - -lemma sg33197 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20327 sg18294 - -lemma sg33198 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16715 - -lemma sg33199 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,8,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20458 - -lemma sg33200 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,8,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15613 sg21052 - -lemma sg33201 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18312 - -lemma sg33202 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg15750 - -lemma sg33203 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg20698 sg16294 - -lemma sg33204 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16379 - -lemma sg33205 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17557 - -lemma sg33206 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg19724 - -lemma sg33207 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15792 - -lemma sg33208 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16295 - -lemma sg33209 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16295 - -lemma sg33210 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16295 - -lemma sg33211 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg19724 - -lemma sg33212 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18312 - -lemma sg33213 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18911 sg19724 - -lemma sg33214 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg19724 - -lemma sg33215 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18312 - -lemma sg33216 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg18913 sg19724 - -lemma sg33217 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18312 - -lemma sg33218 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg18914 sg19724 - -lemma sg33219 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19575 sg19609 - -lemma sg33220 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17343 - -lemma sg33221 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,4,2,2,1,1] := by - exact rowSquare_join (by decide) sg20319 sg18298 - -lemma sg33222 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,4,3,1,1,1] := by - exact rowSquare_join (by decide) sg20320 sg18298 - -lemma sg33223 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16469 - -lemma sg33224 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18313 - -lemma sg33225 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16788 - -lemma sg33226 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16378 - -lemma sg33227 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg15752 - -lemma sg33228 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17269 - -lemma sg33229 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18142 - -lemma sg33230 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17269 - -lemma sg33231 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17558 - -lemma sg33232 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg19725 - -lemma sg33233 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg19725 - -lemma sg33234 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18313 - -lemma sg33235 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18911 sg19725 - -lemma sg33236 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg19725 - -lemma sg33237 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18313 - -lemma sg33238 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg18913 sg19725 - -lemma sg33239 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18313 - -lemma sg33240 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg18914 sg19725 - -lemma sg33241 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16788 - -lemma sg33242 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17344 - -lemma sg33243 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19621 sg18933 - -lemma sg33244 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19238 - -lemma sg33245 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17344 - -lemma sg33246 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg19618 sg19238 - -lemma sg33247 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19622 sg18933 - -lemma sg33248 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20718 sg16246 - -lemma sg33249 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg20789 sg16192 - -lemma sg33250 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17345 - -lemma sg33251 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15794 - -lemma sg33252 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16379 - -lemma sg33253 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16789 - -lemma sg33254 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17345 - -lemma sg33255 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19621 sg18934 - -lemma sg33256 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19239 - -lemma sg33257 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17345 - -lemma sg33258 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg19618 sg19239 - -lemma sg33259 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19622 sg18934 - -lemma sg33260 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17271 - -lemma sg33261 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18143 - -lemma sg33262 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17271 - -lemma sg33263 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17270 - -lemma sg33264 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16723 - -lemma sg33265 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17270 - -lemma sg33266 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16724 - -lemma sg33267 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17271 - -lemma sg33268 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,5,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16724 - -lemma sg33269 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,5,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17271 - -lemma sg33270 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17559 - -lemma sg33271 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18314 - -lemma sg33272 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17559 - -lemma sg33273 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg19726 - -lemma sg33274 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg19726 - -lemma sg33275 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18314 - -lemma sg33276 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18911 sg19726 - -lemma sg33277 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg19726 - -lemma sg33278 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18314 - -lemma sg33279 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg18913 sg19726 - -lemma sg33280 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18314 - -lemma sg33281 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg18914 sg19726 - -lemma sg33282 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17346 - -lemma sg33283 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15795 - -lemma sg33284 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16380 - -lemma sg33285 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16790 - -lemma sg33286 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17346 - -lemma sg33287 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19621 sg18935 - -lemma sg33288 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19240 - -lemma sg33289 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17346 - -lemma sg33290 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg19618 sg19240 - -lemma sg33291 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19622 sg18935 - -lemma sg33292 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16298 - -lemma sg33293 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16298 - -lemma sg33294 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17262 - -lemma sg33295 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17272 - -lemma sg33296 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16725 - -lemma sg33297 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17272 - -lemma sg33298 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17274 - -lemma sg33299 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18145 - -lemma sg33300 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17274 - -lemma sg33301 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17273 - -lemma sg33302 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18144 - -lemma sg33303 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17273 - -lemma sg33304 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16297 - -lemma sg33305 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17261 - -lemma sg33306 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16726 - -lemma sg33307 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17273 - -lemma sg33308 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16726 - -lemma sg33309 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17273 - -lemma sg33310 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16298 - -lemma sg33311 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19192 - -lemma sg33312 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17274 - -lemma sg33313 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18145 - -lemma sg33314 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17274 - -lemma sg33315 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16727 - -lemma sg33316 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17274 - -lemma sg33317 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16727 - -lemma sg33318 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17274 - -lemma sg33319 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16299 - -lemma sg33320 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19193 - -lemma sg33321 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20720 sg16247 - -lemma sg33322 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16791 - -lemma sg33323 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16381 - -lemma sg33324 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17347 - -lemma sg33325 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15796 - -lemma sg33326 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16381 - -lemma sg33327 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16791 - -lemma sg33328 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17347 - -lemma sg33329 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19621 sg18936 - -lemma sg33330 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19241 - -lemma sg33331 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17347 - -lemma sg33332 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg19618 sg19241 - -lemma sg33333 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19622 sg18936 - -lemma sg33334 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17276 - -lemma sg33335 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18147 - -lemma sg33336 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17276 - -lemma sg33337 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17275 - -lemma sg33338 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18146 - -lemma sg33339 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17275 - -lemma sg33340 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16300 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 + +namespace OAI + +/-! Semigroup Nodes 81. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg32941 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20714 sg16237 + +lemma sg32942 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20715 sg16237 + +lemma sg32943 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20716 sg16237 + +lemma sg32944 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20643 sg16670 + +lemma sg32945 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16704 + +lemma sg32946 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,8,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14313 sg21347 + +lemma sg32947 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,8,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20455 + +lemma sg32948 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,8,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17181 + +lemma sg32949 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,8,8,8,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17245 + +lemma sg32950 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17555 + +lemma sg32951 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18310 + +lemma sg32952 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17555 + +lemma sg32953 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg19722 + +lemma sg32954 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg19722 + +lemma sg32955 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18310 + +lemma sg32956 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18911 sg19722 + +lemma sg32957 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg19722 + +lemma sg32958 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18310 + +lemma sg32959 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg18913 sg19722 + +lemma sg32960 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18310 + +lemma sg32961 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg18914 sg19722 + +lemma sg32962 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17316 + +lemma sg32963 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15773 + +lemma sg32964 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16353 + +lemma sg32965 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16762 + +lemma sg32966 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17316 + +lemma sg32967 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19616 sg19225 + +lemma sg32968 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19225 + +lemma sg32969 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17316 + +lemma sg32970 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg19618 sg19225 + +lemma sg32971 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19619 sg19225 + +lemma sg32972 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18034 + +lemma sg32973 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16728 + +lemma sg32974 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18916 sg19631 + +lemma sg32975 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17275 + +lemma sg32976 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18917 sg19631 + +lemma sg32977 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20531 sg17208 + +lemma sg32978 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17276 + +lemma sg32979 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19632 + +lemma sg32980 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20507 sg17276 + +lemma sg32981 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18035 + +lemma sg32982 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16729 + +lemma sg32983 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18916 sg19632 + +lemma sg32984 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17276 + +lemma sg32985 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18917 sg19632 + +lemma sg32986 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16686 + +lemma sg32987 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20640 sg16686 + +lemma sg32988 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20641 sg16686 + +lemma sg32989 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20531 sg17209 + +lemma sg32990 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16283 + +lemma sg32991 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19187 + +lemma sg32992 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16264 + +lemma sg32993 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20803 sg16156 + +lemma sg32994 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20712 sg16264 + +lemma sg32995 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16687 + +lemma sg32996 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20640 sg16687 + +lemma sg32997 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20641 sg16687 + +lemma sg32998 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20531 sg17210 + +lemma sg32999 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16284 + +lemma sg33000 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19188 + +lemma sg33001 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16705 + +lemma sg33002 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17246 + +lemma sg33003 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16285 + +lemma sg33004 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17246 + +lemma sg33005 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16285 + +lemma sg33006 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20552 + +lemma sg33007 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,7,7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20720 sg16232 + +lemma sg33008 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16763 + +lemma sg33009 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16354 + +lemma sg33010 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17317 + +lemma sg33011 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15774 + +lemma sg33012 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16354 + +lemma sg33013 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16763 + +lemma sg33014 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17317 + +lemma sg33015 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19616 sg19226 + +lemma sg33016 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19226 + +lemma sg33017 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17317 + +lemma sg33018 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg19618 sg19226 + +lemma sg33019 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19619 sg19226 + +lemma sg33020 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17277 + +lemma sg33021 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19633 + +lemma sg33022 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20507 sg17277 + +lemma sg33023 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18036 + +lemma sg33024 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16730 + +lemma sg33025 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18916 sg19633 + +lemma sg33026 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17277 + +lemma sg33027 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18917 sg19633 + +lemma sg33028 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16688 + +lemma sg33029 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20640 sg16688 + +lemma sg33030 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20641 sg16688 + +lemma sg33031 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20531 sg17211 + +lemma sg33032 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16266 + +lemma sg33033 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20803 sg16158 + +lemma sg33034 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20712 sg16266 + +lemma sg33035 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16689 + +lemma sg33036 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20640 sg16689 + +lemma sg33037 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20641 sg16689 + +lemma sg33038 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20531 sg17212 + +lemma sg33039 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16286 + +lemma sg33040 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19189 + +lemma sg33041 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16706 + +lemma sg33042 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17249 + +lemma sg33043 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16287 + +lemma sg33044 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17249 + +lemma sg33045 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16287 + +lemma sg33046 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20341 + +lemma sg33047 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16707 + +lemma sg33048 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17246 + +lemma sg33049 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17246 + +lemma sg33050 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17246 + +lemma sg33051 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16708 + +lemma sg33052 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,8,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20456 + +lemma sg33053 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,8,8,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17246 + +lemma sg33054 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17278 + +lemma sg33055 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg15756 + +lemma sg33056 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20505 sg17278 + +lemma sg33057 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17278 + +lemma sg33058 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18284 sg20344 + +lemma sg33059 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20507 sg17278 + +lemma sg33060 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18037 + +lemma sg33061 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16731 + +lemma sg33062 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18285 sg20344 + +lemma sg33063 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17278 + +lemma sg33064 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18286 sg20344 + +lemma sg33065 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20710 sg16267 + +lemma sg33066 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20803 sg16159 + +lemma sg33067 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20712 sg16267 + +lemma sg33068 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20639 sg16690 + +lemma sg33069 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20640 sg16690 + +lemma sg33070 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20641 sg16690 + +lemma sg33071 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20531 sg17213 + +lemma sg33072 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20721 sg16235 + +lemma sg33073 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20722 sg16235 + +lemma sg33074 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17249 + +lemma sg33075 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17249 + +lemma sg33076 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17249 + +lemma sg33077 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17248 + +lemma sg33078 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17248 + +lemma sg33079 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16709 + +lemma sg33080 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17249 + +lemma sg33081 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17249 + +lemma sg33082 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17249 + +lemma sg33083 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16710 + +lemma sg33084 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20457 + +lemma sg33085 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17249 + +lemma sg33086 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,9,9,9,8,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17190 + +lemma sg33087 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18275 sg20421 + +lemma sg33088 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18137 + +lemma sg33089 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20323 sg18294 + +lemma sg33090 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16715 + +lemma sg33091 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20324 sg18294 + +lemma sg33092 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16715 + +lemma sg33093 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20325 sg18294 + +lemma sg33094 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20716 sg16245 + +lemma sg33095 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20643 sg16673 + +lemma sg33096 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,7,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17252 + +lemma sg33097 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17556 + +lemma sg33098 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18311 + +lemma sg33099 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17556 + +lemma sg33100 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg19723 + +lemma sg33101 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg19723 + +lemma sg33102 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18311 + +lemma sg33103 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18911 sg19723 + +lemma sg33104 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg19723 + +lemma sg33105 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18311 + +lemma sg33106 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg18913 sg19723 + +lemma sg33107 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18311 + +lemma sg33108 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg18914 sg19723 + +lemma sg33109 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17341 + +lemma sg33110 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15790 + +lemma sg33111 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16375 + +lemma sg33112 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16785 + +lemma sg33113 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17341 + +lemma sg33114 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19621 sg18932 + +lemma sg33115 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19236 + +lemma sg33116 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17341 + +lemma sg33117 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg19618 sg19236 + +lemma sg33118 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19622 sg18932 + +lemma sg33119 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16291 + +lemma sg33120 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16291 + +lemma sg33121 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17258 + +lemma sg33122 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17264 + +lemma sg33123 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16718 + +lemma sg33124 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17264 + +lemma sg33125 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17266 + +lemma sg33126 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18139 + +lemma sg33127 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17266 + +lemma sg33128 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17265 + +lemma sg33129 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18138 + +lemma sg33130 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17265 + +lemma sg33131 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16290 + +lemma sg33132 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17257 + +lemma sg33133 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16719 + +lemma sg33134 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17265 + +lemma sg33135 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16719 + +lemma sg33136 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17265 + +lemma sg33137 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16291 + +lemma sg33138 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19190 + +lemma sg33139 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17266 + +lemma sg33140 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18139 + +lemma sg33141 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17266 + +lemma sg33142 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16720 + +lemma sg33143 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17266 + +lemma sg33144 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16720 + +lemma sg33145 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17266 + +lemma sg33146 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16292 + +lemma sg33147 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19191 + +lemma sg33148 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16712 + +lemma sg33149 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg17148 sg20553 + +lemma sg33150 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16293 + +lemma sg33151 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20424 sg18137 + +lemma sg33152 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16293 + +lemma sg33153 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20553 + +lemma sg33154 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,7,7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20720 sg16245 + +lemma sg33155 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16786 + +lemma sg33156 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16376 + +lemma sg33157 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17342 + +lemma sg33158 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15791 + +lemma sg33159 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16376 + +lemma sg33160 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16786 + +lemma sg33161 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17342 + +lemma sg33162 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19576 sg19579 + +lemma sg33163 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19237 + +lemma sg33164 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17342 + +lemma sg33165 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg19618 sg19237 + +lemma sg33166 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19619 sg19237 + +lemma sg33167 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17268 + +lemma sg33168 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18141 + +lemma sg33169 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17268 + +lemma sg33170 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17267 + +lemma sg33171 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18140 + +lemma sg33172 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17267 + +lemma sg33173 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20870 sg15710 + +lemma sg33174 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20715 sg16252 + +lemma sg33175 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16721 + +lemma sg33176 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17267 + +lemma sg33177 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16721 + +lemma sg33178 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17267 + +lemma sg33179 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17268 + +lemma sg33180 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18141 + +lemma sg33181 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17268 + +lemma sg33182 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16722 + +lemma sg33183 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17268 + +lemma sg33184 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16722 + +lemma sg33185 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17268 + +lemma sg33186 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20716 sg16253 + +lemma sg33187 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20643 sg16679 + +lemma sg33188 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16713 + +lemma sg33189 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20713 sg16254 + +lemma sg33190 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20807 sg16151 + +lemma sg33191 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20715 sg16254 + +lemma sg33192 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20716 sg16254 + +lemma sg33193 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20643 sg16680 + +lemma sg33194 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16714 + +lemma sg33195 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18114 sg20458 + +lemma sg33196 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20326 sg18294 + +lemma sg33197 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20327 sg18294 + +lemma sg33198 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16715 + +lemma sg33199 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,8,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20458 + +lemma sg33200 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,8,8,8,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15613 sg21052 + +lemma sg33201 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18312 + +lemma sg33202 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg15750 + +lemma sg33203 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg20698 sg16294 + +lemma sg33204 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16379 + +lemma sg33205 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17557 + +lemma sg33206 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg19724 + +lemma sg33207 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15792 + +lemma sg33208 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16295 + +lemma sg33209 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16295 + +lemma sg33210 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16295 + +lemma sg33211 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg19724 + +lemma sg33212 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18312 + +lemma sg33213 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18911 sg19724 + +lemma sg33214 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg19724 + +lemma sg33215 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18312 + +lemma sg33216 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg18913 sg19724 + +lemma sg33217 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18312 + +lemma sg33218 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg18914 sg19724 + +lemma sg33219 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19575 sg19609 + +lemma sg33220 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17343 + +lemma sg33221 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,4,2,2,1,1] := by + exact rowSquare_join (by decide) sg20319 sg18298 + +lemma sg33222 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,4,4,4,4,3,1,1,1] := by + exact rowSquare_join (by decide) sg20320 sg18298 + +lemma sg33223 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16469 + +lemma sg33224 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18313 + +lemma sg33225 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16788 + +lemma sg33226 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16378 + +lemma sg33227 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg15752 + +lemma sg33228 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17269 + +lemma sg33229 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18142 + +lemma sg33230 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17269 + +lemma sg33231 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17558 + +lemma sg33232 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg19725 + +lemma sg33233 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg19725 + +lemma sg33234 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18313 + +lemma sg33235 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18911 sg19725 + +lemma sg33236 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg19725 + +lemma sg33237 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18313 + +lemma sg33238 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg18913 sg19725 + +lemma sg33239 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18313 + +lemma sg33240 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg18914 sg19725 + +lemma sg33241 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16788 + +lemma sg33242 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17344 + +lemma sg33243 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19621 sg18933 + +lemma sg33244 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19238 + +lemma sg33245 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17344 + +lemma sg33246 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg19618 sg19238 + +lemma sg33247 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19622 sg18933 + +lemma sg33248 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20718 sg16246 + +lemma sg33249 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg20789 sg16192 + +lemma sg33250 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17345 + +lemma sg33251 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15794 + +lemma sg33252 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16379 + +lemma sg33253 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16789 + +lemma sg33254 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17345 + +lemma sg33255 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19621 sg18934 + +lemma sg33256 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19239 + +lemma sg33257 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17345 + +lemma sg33258 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg19618 sg19239 + +lemma sg33259 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19622 sg18934 + +lemma sg33260 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17271 + +lemma sg33261 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18143 + +lemma sg33262 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17271 + +lemma sg33263 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17270 + +lemma sg33264 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16723 + +lemma sg33265 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17270 + +lemma sg33266 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16724 + +lemma sg33267 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17271 + +lemma sg33268 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,5,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16724 + +lemma sg33269 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,5,5,5,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17271 + +lemma sg33270 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17559 + +lemma sg33271 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18314 + +lemma sg33272 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17559 + +lemma sg33273 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg19726 + +lemma sg33274 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg19726 + +lemma sg33275 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18314 + +lemma sg33276 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18911 sg19726 + +lemma sg33277 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg19726 + +lemma sg33278 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18314 + +lemma sg33279 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg18913 sg19726 + +lemma sg33280 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18314 + +lemma sg33281 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg18914 sg19726 + +lemma sg33282 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17346 + +lemma sg33283 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15795 + +lemma sg33284 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16380 + +lemma sg33285 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16790 + +lemma sg33286 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17346 + +lemma sg33287 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19621 sg18935 + +lemma sg33288 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19240 + +lemma sg33289 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17346 + +lemma sg33290 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg19618 sg19240 + +lemma sg33291 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19622 sg18935 + +lemma sg33292 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16298 + +lemma sg33293 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16298 + +lemma sg33294 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17262 + +lemma sg33295 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17272 + +lemma sg33296 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16725 + +lemma sg33297 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17272 + +lemma sg33298 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17274 + +lemma sg33299 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18145 + +lemma sg33300 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17274 + +lemma sg33301 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17273 + +lemma sg33302 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18144 + +lemma sg33303 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17273 + +lemma sg33304 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16297 + +lemma sg33305 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17261 + +lemma sg33306 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16726 + +lemma sg33307 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17273 + +lemma sg33308 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16726 + +lemma sg33309 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17273 + +lemma sg33310 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16298 + +lemma sg33311 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19192 + +lemma sg33312 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17274 + +lemma sg33313 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18145 + +lemma sg33314 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17274 + +lemma sg33315 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16727 + +lemma sg33316 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17274 + +lemma sg33317 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16727 + +lemma sg33318 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17274 + +lemma sg33319 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16299 + +lemma sg33320 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19193 + +lemma sg33321 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,6,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20720 sg16247 + +lemma sg33322 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16791 + +lemma sg33323 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16381 + +lemma sg33324 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17347 + +lemma sg33325 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15796 + +lemma sg33326 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16381 + +lemma sg33327 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16791 + +lemma sg33328 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17347 + +lemma sg33329 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19621 sg18936 + +lemma sg33330 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19241 + +lemma sg33331 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17347 + +lemma sg33332 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg19618 sg19241 + +lemma sg33333 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19622 sg18936 + +lemma sg33334 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17276 + +lemma sg33335 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18147 + +lemma sg33336 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17276 + +lemma sg33337 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17275 + +lemma sg33338 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18146 + +lemma sg33339 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17275 + +lemma sg33340 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16300 + +end UniversalTensorSquare +end +end + +end OAI diff --git a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes82.lean b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes82.lean index 3e543e98f0bec7c514654518783068958fd3b2dd..f72069d40443240c5abde8ffcad73cacfe299af1 100644 --- a/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes82.lean +++ b/lean/OAI/RepresentationTheory/UniversalSquare/Semigroup/SemigroupNodes82.lean @@ -1,1231 +1,1231 @@ -import Mathlib -import OAI.RepresentationTheory.Saxl.Main -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 -import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 - -namespace OAI - -/-! Semigroup Nodes 82. -/ - -section - -noncomputable section -namespace UniversalTensorSquare -open Saxl Saxl.Columns Saxl.Balance - -lemma sg33341 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17264 - -lemma sg33342 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16728 - -lemma sg33343 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17275 - -lemma sg33344 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16728 - -lemma sg33345 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17275 - -lemma sg33346 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17276 - -lemma sg33347 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18147 - -lemma sg33348 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17276 - -lemma sg33349 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16729 - -lemma sg33350 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17276 - -lemma sg33351 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16729 - -lemma sg33352 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17276 - -lemma sg33353 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16301 - -lemma sg33354 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19194 - -lemma sg33355 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16716 - -lemma sg33356 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17266 - -lemma sg33357 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16302 - -lemma sg33358 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17266 - -lemma sg33359 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16302 - -lemma sg33360 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19195 - -lemma sg33361 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16717 - -lemma sg33362 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,7,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20719 sg16251 - -lemma sg33363 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,7,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20812 sg16150 - -lemma sg33364 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,7,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20813 sg16150 - -lemma sg33365 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,7,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20720 sg16251 - -lemma sg33366 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20691 sg16314 - -lemma sg33367 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20855 sg15756 - -lemma sg33368 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20509 sg17278 - -lemma sg33369 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17277 - -lemma sg33370 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18148 - -lemma sg33371 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17277 - -lemma sg33372 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16303 - -lemma sg33373 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16303 - -lemma sg33374 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17267 - -lemma sg33375 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17264 - -lemma sg33376 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17264 - -lemma sg33377 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17277 - -lemma sg33378 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18148 - -lemma sg33379 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17277 - -lemma sg33380 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16730 - -lemma sg33381 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17277 - -lemma sg33382 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16730 - -lemma sg33383 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17277 - -lemma sg33384 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16303 - -lemma sg33385 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19196 - -lemma sg33386 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17268 - -lemma sg33387 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16304 - -lemma sg33388 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17268 - -lemma sg33389 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16304 - -lemma sg33390 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19197 - -lemma sg33391 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16719 - -lemma sg33392 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17266 - -lemma sg33393 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17266 - -lemma sg33394 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17266 - -lemma sg33395 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16720 - -lemma sg33396 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20459 - -lemma sg33397 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17266 - -lemma sg33398 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,8,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg14726 sg21272 - -lemma sg33399 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20510 sg17278 - -lemma sg33400 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20422 sg18149 - -lemma sg33401 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20511 sg17278 - -lemma sg33402 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17278 - -lemma sg33403 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18149 - -lemma sg33404 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17278 - -lemma sg33405 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16731 - -lemma sg33406 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17278 - -lemma sg33407 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16731 - -lemma sg33408 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17278 - -lemma sg33409 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20713 sg16267 - -lemma sg33410 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20807 sg16159 - -lemma sg33411 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20715 sg16267 - -lemma sg33412 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20716 sg16267 - -lemma sg33413 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20643 sg16690 - -lemma sg33414 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16721 - -lemma sg33415 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17268 - -lemma sg33416 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17268 - -lemma sg33417 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17268 - -lemma sg33418 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16722 - -lemma sg33419 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20460 - -lemma sg33420 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17268 - -lemma sg33421 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17202 - -lemma sg33422 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,3,3,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20685 sg16382 - -lemma sg33423 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,3,3,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20717 sg16255 - -lemma sg33424 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,3,3,3,3,3,3,3] := by - exact rowSquare_join (by decide) sg20871 sg15711 - -lemma sg33425 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,2,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20683 sg16470 - -lemma sg33426 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18315 - -lemma sg33427 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16792 - -lemma sg33428 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16382 - -lemma sg33429 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20718 sg16255 - -lemma sg33430 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16305 - -lemma sg33431 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16305 - -lemma sg33432 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,3,3,3,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16305 - -lemma sg33433 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17560 - -lemma sg33434 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20315 sg18315 - -lemma sg33435 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18281 sg20385 - -lemma sg33436 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18315 - -lemma sg33437 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg16649 sg20666 - -lemma sg33438 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18282 sg20385 - -lemma sg33439 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18315 - -lemma sg33440 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg17147 sg20562 - -lemma sg33441 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18315 - -lemma sg33442 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg16650 sg20666 - -lemma sg33443 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16792 - -lemma sg33444 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17348 - -lemma sg33445 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19576 sg19580 - -lemma sg33446 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19575 sg19610 - -lemma sg33447 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17348 - -lemma sg33448 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20319 sg18300 - -lemma sg33449 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20320 sg18300 - -lemma sg33450 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15609 sg21057 - -lemma sg33451 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,4,2,1,1,1] := by - exact rowSquare_join (by decide) sg15636 sg21043 - -lemma sg33452 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17561 - -lemma sg33453 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18316 - -lemma sg33454 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17561 - -lemma sg33455 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20315 sg18316 - -lemma sg33456 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18281 sg20386 - -lemma sg33457 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18316 - -lemma sg33458 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg16649 sg20667 - -lemma sg33459 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18282 sg20386 - -lemma sg33460 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18316 - -lemma sg33461 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg17147 sg20563 - -lemma sg33462 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18316 - -lemma sg33463 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg16650 sg20667 - -lemma sg33464 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17349 - -lemma sg33465 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15798 - -lemma sg33466 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16383 - -lemma sg33467 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16793 - -lemma sg33468 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17349 - -lemma sg33469 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19621 sg18937 - -lemma sg33470 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19242 - -lemma sg33471 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17349 - -lemma sg33472 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg19618 sg19242 - -lemma sg33473 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19622 sg18937 - -lemma sg33474 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16307 - -lemma sg33475 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16307 - -lemma sg33476 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17271 - -lemma sg33477 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20718 sg16257 - -lemma sg33478 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20811 sg16153 - -lemma sg33479 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg15658 sg20961 - -lemma sg33480 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16310 - -lemma sg33481 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16310 - -lemma sg33482 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16310 - -lemma sg33483 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20808 sg16155 - -lemma sg33484 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20809 sg16155 - -lemma sg33485 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20810 sg16155 - -lemma sg33486 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16306 - -lemma sg33487 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17270 - -lemma sg33488 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17271 - -lemma sg33489 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16307 - -lemma sg33490 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17271 - -lemma sg33491 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19198 - -lemma sg33492 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16307 - -lemma sg33493 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20343 - -lemma sg33494 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,2,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20631 sg16794 - -lemma sg33495 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,2,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20686 sg16384 - -lemma sg33496 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20501 sg17350 - -lemma sg33497 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20851 sg15799 - -lemma sg33498 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20687 sg16384 - -lemma sg33499 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20632 sg16794 - -lemma sg33500 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20502 sg17350 - -lemma sg33501 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg19621 sg18938 - -lemma sg33502 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19617 sg19243 - -lemma sg33503 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20503 sg17350 - -lemma sg33504 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg19618 sg19243 - -lemma sg33505 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg19622 sg18938 - -lemma sg33506 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16312 - -lemma sg33507 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16312 - -lemma sg33508 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16312 - -lemma sg33509 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16309 - -lemma sg33510 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16309 - -lemma sg33511 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17273 - -lemma sg33512 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16308 - -lemma sg33513 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17272 - -lemma sg33514 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17271 - -lemma sg33515 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17271 - -lemma sg33516 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17271 - -lemma sg33517 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19199 - -lemma sg33518 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16310 - -lemma sg33519 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16310 - -lemma sg33520 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17274 - -lemma sg33521 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17273 - -lemma sg33522 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16309 - -lemma sg33523 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17273 - -lemma sg33524 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17270 - -lemma sg33525 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16309 - -lemma sg33526 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19200 - -lemma sg33527 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16724 - -lemma sg33528 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,6,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17274 - -lemma sg33529 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,6,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16310 - -lemma sg33530 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,6,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17274 - -lemma sg33531 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,6,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16310 - -lemma sg33532 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,6,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19201 - -lemma sg33533 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,6,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20720 sg16261 - -lemma sg33534 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,2,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20652 sg16659 - -lemma sg33535 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20829 sg16135 - -lemma sg33536 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20759 sg16221 - -lemma sg33537 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16313 - -lemma sg33538 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16313 - -lemma sg33539 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16313 - -lemma sg33540 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16311 - -lemma sg33541 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16311 - -lemma sg33542 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17275 - -lemma sg33543 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17272 - -lemma sg33544 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17272 - -lemma sg33545 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16312 - -lemma sg33546 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16312 - -lemma sg33547 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17276 - -lemma sg33548 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17275 - -lemma sg33549 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16311 - -lemma sg33550 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17275 - -lemma sg33551 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17272 - -lemma sg33552 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16311 - -lemma sg33553 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19202 - -lemma sg33554 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,5,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17276 - -lemma sg33555 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,5,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16312 - -lemma sg33556 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,5,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17276 - -lemma sg33557 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,5,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16312 - -lemma sg33558 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,5,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19203 - -lemma sg33559 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,5,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16726 - -lemma sg33560 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,6,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17274 - -lemma sg33561 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,6,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17274 - -lemma sg33562 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,6,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17274 - -lemma sg33563 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,6,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16727 - -lemma sg33564 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,7,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18920 sg19630 - -lemma sg33565 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,7,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17274 - -lemma sg33566 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,2,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20693 sg16314 - -lemma sg33567 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20694 sg16314 - -lemma sg33568 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20695 sg16314 - -lemma sg33569 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16313 - -lemma sg33570 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16313 - -lemma sg33571 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17277 - -lemma sg33572 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17275 - -lemma sg33573 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17275 - -lemma sg33574 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17275 - -lemma sg33575 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20722 sg16262 - -lemma sg33576 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,4,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17277 - -lemma sg33577 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,4,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16313 - -lemma sg33578 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,4,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17277 - -lemma sg33579 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,4,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16313 - -lemma sg33580 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,4,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19204 - -lemma sg33581 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,4,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16728 - -lemma sg33582 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,5,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17276 - -lemma sg33583 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,5,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17276 - -lemma sg33584 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,5,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17276 - -lemma sg33585 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,5,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16729 - -lemma sg33586 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,6,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18920 sg19632 - -lemma sg33587 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,6,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17276 - -lemma sg33588 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,7,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17210 - -lemma sg33589 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,2,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20696 sg16314 - -lemma sg33590 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20697 sg16314 - -lemma sg33591 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20517 sg17278 - -lemma sg33592 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,3,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17278 - -lemma sg33593 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16314 - -lemma sg33594 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17278 - -lemma sg33595 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16314 - -lemma sg33596 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18287 sg20344 - -lemma sg33597 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,4,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17277 - -lemma sg33598 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17277 - -lemma sg33599 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17277 - -lemma sg33600 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16730 - -lemma sg33601 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,5,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18920 sg19633 - -lemma sg33602 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,5,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17277 - -lemma sg33603 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,6,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17212 - -lemma sg33604 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,2,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20520 sg17278 - -lemma sg33605 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20521 sg17278 - -lemma sg33606 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20522 sg17278 - -lemma sg33607 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,3,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20523 sg17278 - -lemma sg33608 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20524 sg17278 - -lemma sg33609 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17278 - -lemma sg33610 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16731 - -lemma sg33611 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20461 - -lemma sg33612 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17278 - -lemma sg33613 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20533 sg17213 - -lemma sg33614 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15644 sg20986 - -lemma sg33615 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18115 sg20462 - -lemma sg33616 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg15610 sg21054 - -lemma sg33617 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20518 sg17282 - -lemma sg33618 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20699 sg16319 - -lemma sg33619 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17282 - -lemma sg33620 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg15611 sg21054 - -lemma sg33621 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16319 - -lemma sg33622 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17149 sg20555 - -lemma sg33623 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17279 - -lemma sg33624 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17609 - -lemma sg33625 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18317 - -lemma sg33626 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17609 - -lemma sg33627 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg19739 - -lemma sg33628 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg19739 - -lemma sg33629 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18317 - -lemma sg33630 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18911 sg19739 - -lemma sg33631 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg19739 - -lemma sg33632 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18317 - -lemma sg33633 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg18913 sg19739 - -lemma sg33634 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18317 - -lemma sg33635 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg18914 sg19739 - -lemma sg33636 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17294 - -lemma sg33637 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg15765 - -lemma sg33638 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20505 sg17294 - -lemma sg33639 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17293 - -lemma sg33640 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18284 sg20347 - -lemma sg33641 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20507 sg17293 - -lemma sg33642 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20728 sg16234 - -lemma sg33643 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20874 sg15702 - -lemma sg33644 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20535 sg17187 - -lemma sg33645 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20537 sg17186 - -lemma sg33646 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18038 - -lemma sg33647 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16743 - -lemma sg33648 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18285 sg20347 - -lemma sg33649 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17293 - -lemma sg33650 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18286 sg20347 - -lemma sg33651 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20657 sg16654 - -lemma sg33652 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17294 - -lemma sg33653 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18284 sg20348 - -lemma sg33654 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20507 sg17294 - -lemma sg33655 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18039 - -lemma sg33656 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16744 - -lemma sg33657 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18285 sg20348 - -lemma sg33658 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17294 - -lemma sg33659 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18286 sg20348 - -lemma sg33660 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20536 sg17188 - -lemma sg33661 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20816 sg16142 - -lemma sg33662 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20537 sg17188 - -lemma sg33663 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20538 sg17187 - -lemma sg33664 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20731 sg16235 - -lemma sg33665 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20538 sg17188 - -lemma sg33666 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20728 sg16237 - -lemma sg33667 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20729 sg16237 - -lemma sg33668 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20535 sg17190 - -lemma sg33669 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20536 sg17189 - -lemma sg33670 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20816 sg16143 - -lemma sg33671 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20537 sg17189 - -lemma sg33672 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20525 sg17280 - -lemma sg33673 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20731 sg16236 - -lemma sg33674 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20538 sg17189 - -lemma sg33675 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16733 - -lemma sg33676 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,7,2,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20536 sg17190 - -lemma sg33677 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,7,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20730 sg16237 - -lemma sg33678 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,7,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20537 sg17190 - -lemma sg33679 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,7,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20731 sg16237 - -lemma sg33680 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,7,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20538 sg17190 - -lemma sg33681 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,7,4,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20636 sg16734 - -lemma sg33682 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,8,1,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg12864 sg21636 - -lemma sg33683 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,8,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg15226 sg21194 - -lemma sg33684 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,8,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg15605 sg21076 - -lemma sg33685 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,8,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20526 sg17282 - -lemma sg33686 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17284 - -lemma sg33687 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18150 - -lemma sg33688 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17284 - -lemma sg33689 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,3,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16738 - -lemma sg33690 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17284 - -lemma sg33691 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16738 - -lemma sg33692 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17284 - -lemma sg33693 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,4,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20731 sg16245 - -lemma sg33694 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,4,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg17151 sg20546 - -lemma sg33695 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,5,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20646 sg16663 - -lemma sg33696 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,2,2,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20499 sg17628 - -lemma sg33697 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,2,2,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20314 sg18318 - -lemma sg33698 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,2,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20500 sg17628 - -lemma sg33699 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,2,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg18909 sg19740 - -lemma sg33700 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg18910 sg19740 - -lemma sg33701 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20316 sg18318 - -lemma sg33702 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg18911 sg19740 - -lemma sg33703 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,3,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg18912 sg19740 - -lemma sg33704 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,3,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20317 sg18318 - -lemma sg33705 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,3,2,2,2,1] := by - exact rowSquare_join (by decide) sg18913 sg19740 - -lemma sg33706 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,3,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20318 sg18318 - -lemma sg33707 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,3,3,2,1,1] := by - exact rowSquare_join (by decide) sg18914 sg19740 - -lemma sg33708 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,2,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20504 sg17309 - -lemma sg33709 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,2,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20852 sg15768 - -lemma sg33710 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,2,2,2,2,2,2] := by - exact rowSquare_join (by decide) sg20505 sg17309 - -lemma sg33711 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17308 - -lemma sg33712 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19638 - -lemma sg33713 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20507 sg17308 - -lemma sg33714 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,3,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17290 - -lemma sg33715 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,3,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18151 - -lemma sg33716 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,3,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17290 - -lemma sg33717 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,3,3,1,1,1] := by - exact rowSquare_join (by decide) sg20519 sg17283 - -lemma sg33718 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,4,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg19623 sg18922 - -lemma sg33719 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,4,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16754 - -lemma sg33720 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,4,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18916 sg19638 - -lemma sg33721 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,4,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17308 - -lemma sg33722 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,4,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg19624 sg18922 - -lemma sg33723 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,4,4,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17290 - -lemma sg33724 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,2,2,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20506 sg17309 - -lemma sg33725 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,2,2,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg18915 sg19639 - -lemma sg33726 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,2,2,2,2,2,1] := by - exact rowSquare_join (by decide) sg20507 sg17309 - -lemma sg33727 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,3,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20498 sg18040 - -lemma sg33728 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,3,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20633 sg16755 - -lemma sg33729 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,3,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg18916 sg19639 - -lemma sg33730 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,3,3,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20508 sg17309 - -lemma sg33731 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,3,3,2,1,1,1] := by - exact rowSquare_join (by decide) sg18917 sg19639 - -lemma sg33732 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,4,1,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20634 sg16741 - -lemma sg33733 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,4,2,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20515 sg17291 - -lemma sg33734 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,4,2,2,1,1,1] := by - exact rowSquare_join (by decide) sg20635 sg16741 - -lemma sg33735 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,4,3,1,1,1,1] := by - exact rowSquare_join (by decide) sg20516 sg17291 - -lemma sg33736 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,5,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20700 sg16321 - -lemma sg33737 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,5,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg19620 sg19205 - -lemma sg33738 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,6,2,2,1,1,1,1,1,1] := by - exact rowSquare_join (by decide) sg20512 sg17292 - -lemma sg33739 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,6,2,2,2,1,1,1,1] := by - exact rowSquare_join (by decide) sg20423 sg18152 - -lemma sg33740 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,6,2,2,2,2,1,1] := by - exact rowSquare_join (by decide) sg20513 sg17292 - -end UniversalTensorSquare -end -end - -end OAI +import Mathlib +import OAI.RepresentationTheory.Saxl.Main +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes52 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes47 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes49 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes43 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes44 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes46 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes39 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes41 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes38 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes40 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes42 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes45 +import OAI.RepresentationTheory.UniversalSquare.Semigroup.SemigroupNodes48 + +namespace OAI + +/-! Semigroup Nodes 82. -/ + +section + +noncomputable section +namespace UniversalTensorSquare +open Saxl Saxl.Columns Saxl.Balance + +lemma sg33341 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17264 + +lemma sg33342 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16728 + +lemma sg33343 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17275 + +lemma sg33344 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16728 + +lemma sg33345 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17275 + +lemma sg33346 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17276 + +lemma sg33347 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18147 + +lemma sg33348 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17276 + +lemma sg33349 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16729 + +lemma sg33350 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17276 + +lemma sg33351 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16729 + +lemma sg33352 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17276 + +lemma sg33353 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16301 + +lemma sg33354 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19194 + +lemma sg33355 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16716 + +lemma sg33356 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17266 + +lemma sg33357 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16302 + +lemma sg33358 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17266 + +lemma sg33359 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16302 + +lemma sg33360 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19195 + +lemma sg33361 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16717 + +lemma sg33362 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,7,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20719 sg16251 + +lemma sg33363 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,7,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20812 sg16150 + +lemma sg33364 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,7,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20813 sg16150 + +lemma sg33365 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,7,7,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20720 sg16251 + +lemma sg33366 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20691 sg16314 + +lemma sg33367 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20855 sg15756 + +lemma sg33368 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20509 sg17278 + +lemma sg33369 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17277 + +lemma sg33370 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18148 + +lemma sg33371 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17277 + +lemma sg33372 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16303 + +lemma sg33373 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16303 + +lemma sg33374 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17267 + +lemma sg33375 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17264 + +lemma sg33376 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17264 + +lemma sg33377 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17277 + +lemma sg33378 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18148 + +lemma sg33379 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17277 + +lemma sg33380 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16730 + +lemma sg33381 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17277 + +lemma sg33382 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16730 + +lemma sg33383 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17277 + +lemma sg33384 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16303 + +lemma sg33385 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19196 + +lemma sg33386 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17268 + +lemma sg33387 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16304 + +lemma sg33388 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17268 + +lemma sg33389 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16304 + +lemma sg33390 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19197 + +lemma sg33391 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16719 + +lemma sg33392 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17266 + +lemma sg33393 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17266 + +lemma sg33394 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17266 + +lemma sg33395 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16720 + +lemma sg33396 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20459 + +lemma sg33397 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17266 + +lemma sg33398 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,8,8,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg14726 sg21272 + +lemma sg33399 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20510 sg17278 + +lemma sg33400 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20422 sg18149 + +lemma sg33401 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20511 sg17278 + +lemma sg33402 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17278 + +lemma sg33403 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18149 + +lemma sg33404 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17278 + +lemma sg33405 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16731 + +lemma sg33406 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17278 + +lemma sg33407 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16731 + +lemma sg33408 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17278 + +lemma sg33409 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20713 sg16267 + +lemma sg33410 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20807 sg16159 + +lemma sg33411 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20715 sg16267 + +lemma sg33412 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20716 sg16267 + +lemma sg33413 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20643 sg16690 + +lemma sg33414 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16721 + +lemma sg33415 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17268 + +lemma sg33416 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17268 + +lemma sg33417 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17268 + +lemma sg33418 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16722 + +lemma sg33419 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20460 + +lemma sg33420 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17268 + +lemma sg33421 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,9,9,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17202 + +lemma sg33422 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,3,3,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20685 sg16382 + +lemma sg33423 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,3,3,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20717 sg16255 + +lemma sg33424 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,3,3,3,3,3,3,3] := by + exact rowSquare_join (by decide) sg20871 sg15711 + +lemma sg33425 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,2,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20683 sg16470 + +lemma sg33426 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18315 + +lemma sg33427 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16792 + +lemma sg33428 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16382 + +lemma sg33429 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20718 sg16255 + +lemma sg33430 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16305 + +lemma sg33431 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16305 + +lemma sg33432 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,3,3,3,3,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16305 + +lemma sg33433 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17560 + +lemma sg33434 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20315 sg18315 + +lemma sg33435 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18281 sg20385 + +lemma sg33436 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18315 + +lemma sg33437 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg16649 sg20666 + +lemma sg33438 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18282 sg20385 + +lemma sg33439 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18315 + +lemma sg33440 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg17147 sg20562 + +lemma sg33441 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18315 + +lemma sg33442 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg16650 sg20666 + +lemma sg33443 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16792 + +lemma sg33444 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17348 + +lemma sg33445 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19576 sg19580 + +lemma sg33446 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19575 sg19610 + +lemma sg33447 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17348 + +lemma sg33448 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20319 sg18300 + +lemma sg33449 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20320 sg18300 + +lemma sg33450 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15609 sg21057 + +lemma sg33451 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,4,4,4,4,2,1,1,1] := by + exact rowSquare_join (by decide) sg15636 sg21043 + +lemma sg33452 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17561 + +lemma sg33453 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18316 + +lemma sg33454 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17561 + +lemma sg33455 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20315 sg18316 + +lemma sg33456 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18281 sg20386 + +lemma sg33457 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18316 + +lemma sg33458 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg16649 sg20667 + +lemma sg33459 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18282 sg20386 + +lemma sg33460 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18316 + +lemma sg33461 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg17147 sg20563 + +lemma sg33462 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18316 + +lemma sg33463 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg16650 sg20667 + +lemma sg33464 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17349 + +lemma sg33465 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15798 + +lemma sg33466 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16383 + +lemma sg33467 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16793 + +lemma sg33468 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17349 + +lemma sg33469 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19621 sg18937 + +lemma sg33470 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19242 + +lemma sg33471 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17349 + +lemma sg33472 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg19618 sg19242 + +lemma sg33473 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19622 sg18937 + +lemma sg33474 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16307 + +lemma sg33475 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16307 + +lemma sg33476 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17271 + +lemma sg33477 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20718 sg16257 + +lemma sg33478 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20811 sg16153 + +lemma sg33479 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg15658 sg20961 + +lemma sg33480 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16310 + +lemma sg33481 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16310 + +lemma sg33482 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16310 + +lemma sg33483 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20808 sg16155 + +lemma sg33484 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20809 sg16155 + +lemma sg33485 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20810 sg16155 + +lemma sg33486 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16306 + +lemma sg33487 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17270 + +lemma sg33488 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17271 + +lemma sg33489 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16307 + +lemma sg33490 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17271 + +lemma sg33491 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19198 + +lemma sg33492 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16307 + +lemma sg33493 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,5,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20343 + +lemma sg33494 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,2,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20631 sg16794 + +lemma sg33495 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,2,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20686 sg16384 + +lemma sg33496 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20501 sg17350 + +lemma sg33497 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20851 sg15799 + +lemma sg33498 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20687 sg16384 + +lemma sg33499 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20632 sg16794 + +lemma sg33500 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20502 sg17350 + +lemma sg33501 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg19621 sg18938 + +lemma sg33502 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19617 sg19243 + +lemma sg33503 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20503 sg17350 + +lemma sg33504 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg19618 sg19243 + +lemma sg33505 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,3,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg19622 sg18938 + +lemma sg33506 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16312 + +lemma sg33507 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16312 + +lemma sg33508 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16312 + +lemma sg33509 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16309 + +lemma sg33510 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16309 + +lemma sg33511 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17273 + +lemma sg33512 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16308 + +lemma sg33513 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17272 + +lemma sg33514 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17271 + +lemma sg33515 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17271 + +lemma sg33516 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17271 + +lemma sg33517 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,4,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19199 + +lemma sg33518 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16310 + +lemma sg33519 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16310 + +lemma sg33520 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17274 + +lemma sg33521 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17273 + +lemma sg33522 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16309 + +lemma sg33523 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17273 + +lemma sg33524 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17270 + +lemma sg33525 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16309 + +lemma sg33526 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19200 + +lemma sg33527 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,5,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16724 + +lemma sg33528 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,6,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17274 + +lemma sg33529 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,6,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16310 + +lemma sg33530 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,6,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17274 + +lemma sg33531 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,6,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16310 + +lemma sg33532 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,6,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19201 + +lemma sg33533 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,6,6,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20720 sg16261 + +lemma sg33534 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,2,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20652 sg16659 + +lemma sg33535 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20829 sg16135 + +lemma sg33536 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20759 sg16221 + +lemma sg33537 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16313 + +lemma sg33538 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16313 + +lemma sg33539 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16313 + +lemma sg33540 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16311 + +lemma sg33541 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16311 + +lemma sg33542 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17275 + +lemma sg33543 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17272 + +lemma sg33544 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,3,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17272 + +lemma sg33545 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16312 + +lemma sg33546 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16312 + +lemma sg33547 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17276 + +lemma sg33548 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17275 + +lemma sg33549 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16311 + +lemma sg33550 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17275 + +lemma sg33551 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17272 + +lemma sg33552 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16311 + +lemma sg33553 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,4,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19202 + +lemma sg33554 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,5,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17276 + +lemma sg33555 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,5,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16312 + +lemma sg33556 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,5,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17276 + +lemma sg33557 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,5,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16312 + +lemma sg33558 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,5,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19203 + +lemma sg33559 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,5,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16726 + +lemma sg33560 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,6,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17274 + +lemma sg33561 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,6,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17274 + +lemma sg33562 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,6,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17274 + +lemma sg33563 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,6,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16727 + +lemma sg33564 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,7,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18920 sg19630 + +lemma sg33565 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,7,7,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17274 + +lemma sg33566 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,2,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20693 sg16314 + +lemma sg33567 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20694 sg16314 + +lemma sg33568 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20695 sg16314 + +lemma sg33569 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16313 + +lemma sg33570 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16313 + +lemma sg33571 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17277 + +lemma sg33572 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17275 + +lemma sg33573 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17275 + +lemma sg33574 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17275 + +lemma sg33575 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20722 sg16262 + +lemma sg33576 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,4,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17277 + +lemma sg33577 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,4,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16313 + +lemma sg33578 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,4,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17277 + +lemma sg33579 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,4,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16313 + +lemma sg33580 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,4,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19204 + +lemma sg33581 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,4,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16728 + +lemma sg33582 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,5,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17276 + +lemma sg33583 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,5,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17276 + +lemma sg33584 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,5,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17276 + +lemma sg33585 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,5,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16729 + +lemma sg33586 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,6,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18920 sg19632 + +lemma sg33587 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,6,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17276 + +lemma sg33588 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,8,7,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17210 + +lemma sg33589 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,2,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20696 sg16314 + +lemma sg33590 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20697 sg16314 + +lemma sg33591 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20517 sg17278 + +lemma sg33592 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,3,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17278 + +lemma sg33593 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16314 + +lemma sg33594 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17278 + +lemma sg33595 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16314 + +lemma sg33596 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18287 sg20344 + +lemma sg33597 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,4,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17277 + +lemma sg33598 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17277 + +lemma sg33599 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17277 + +lemma sg33600 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16730 + +lemma sg33601 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,5,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18920 sg19633 + +lemma sg33602 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,5,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17277 + +lemma sg33603 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,9,6,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17212 + +lemma sg33604 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,2,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20520 sg17278 + +lemma sg33605 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20521 sg17278 + +lemma sg33606 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20522 sg17278 + +lemma sg33607 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,3,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20523 sg17278 + +lemma sg33608 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20524 sg17278 + +lemma sg33609 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17278 + +lemma sg33610 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16731 + +lemma sg33611 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20461 + +lemma sg33612 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17278 + +lemma sg33613 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,10,10,10,10,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20533 sg17213 + +lemma sg33614 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15644 sg20986 + +lemma sg33615 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18115 sg20462 + +lemma sg33616 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg15610 sg21054 + +lemma sg33617 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20518 sg17282 + +lemma sg33618 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20699 sg16319 + +lemma sg33619 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17282 + +lemma sg33620 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg15611 sg21054 + +lemma sg33621 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16319 + +lemma sg33622 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17149 sg20555 + +lemma sg33623 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17279 + +lemma sg33624 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17609 + +lemma sg33625 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18317 + +lemma sg33626 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17609 + +lemma sg33627 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg19739 + +lemma sg33628 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg19739 + +lemma sg33629 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18317 + +lemma sg33630 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18911 sg19739 + +lemma sg33631 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg19739 + +lemma sg33632 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18317 + +lemma sg33633 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg18913 sg19739 + +lemma sg33634 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18317 + +lemma sg33635 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg18914 sg19739 + +lemma sg33636 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17294 + +lemma sg33637 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg15765 + +lemma sg33638 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20505 sg17294 + +lemma sg33639 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17293 + +lemma sg33640 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18284 sg20347 + +lemma sg33641 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20507 sg17293 + +lemma sg33642 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20728 sg16234 + +lemma sg33643 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20874 sg15702 + +lemma sg33644 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20535 sg17187 + +lemma sg33645 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20537 sg17186 + +lemma sg33646 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18038 + +lemma sg33647 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16743 + +lemma sg33648 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18285 sg20347 + +lemma sg33649 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17293 + +lemma sg33650 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18286 sg20347 + +lemma sg33651 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20657 sg16654 + +lemma sg33652 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17294 + +lemma sg33653 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18284 sg20348 + +lemma sg33654 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20507 sg17294 + +lemma sg33655 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18039 + +lemma sg33656 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16744 + +lemma sg33657 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18285 sg20348 + +lemma sg33658 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17294 + +lemma sg33659 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18286 sg20348 + +lemma sg33660 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20536 sg17188 + +lemma sg33661 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20816 sg16142 + +lemma sg33662 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20537 sg17188 + +lemma sg33663 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20538 sg17187 + +lemma sg33664 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20731 sg16235 + +lemma sg33665 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20538 sg17188 + +lemma sg33666 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20728 sg16237 + +lemma sg33667 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20729 sg16237 + +lemma sg33668 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20535 sg17190 + +lemma sg33669 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20536 sg17189 + +lemma sg33670 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20816 sg16143 + +lemma sg33671 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20537 sg17189 + +lemma sg33672 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20525 sg17280 + +lemma sg33673 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20731 sg16236 + +lemma sg33674 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20538 sg17189 + +lemma sg33675 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,6,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16733 + +lemma sg33676 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,7,2,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20536 sg17190 + +lemma sg33677 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,7,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20730 sg16237 + +lemma sg33678 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,7,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20537 sg17190 + +lemma sg33679 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,7,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20731 sg16237 + +lemma sg33680 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,7,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20538 sg17190 + +lemma sg33681 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,7,4,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20636 sg16734 + +lemma sg33682 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,8,1,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg12864 sg21636 + +lemma sg33683 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,8,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg15226 sg21194 + +lemma sg33684 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,8,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg15605 sg21076 + +lemma sg33685 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,8,8,8,8,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20526 sg17282 + +lemma sg33686 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17284 + +lemma sg33687 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18150 + +lemma sg33688 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17284 + +lemma sg33689 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,3,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16738 + +lemma sg33690 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17284 + +lemma sg33691 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16738 + +lemma sg33692 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17284 + +lemma sg33693 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,4,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20731 sg16245 + +lemma sg33694 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,4,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg17151 sg20546 + +lemma sg33695 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,7,7,7,5,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20646 sg16663 + +lemma sg33696 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,2,2,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20499 sg17628 + +lemma sg33697 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,2,2,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20314 sg18318 + +lemma sg33698 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,2,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20500 sg17628 + +lemma sg33699 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,2,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg18909 sg19740 + +lemma sg33700 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg18910 sg19740 + +lemma sg33701 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20316 sg18318 + +lemma sg33702 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg18911 sg19740 + +lemma sg33703 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,3,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg18912 sg19740 + +lemma sg33704 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,3,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20317 sg18318 + +lemma sg33705 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,3,2,2,2,1] := by + exact rowSquare_join (by decide) sg18913 sg19740 + +lemma sg33706 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,3,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20318 sg18318 + +lemma sg33707 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,3,3,3,3,2,1,1] := by + exact rowSquare_join (by decide) sg18914 sg19740 + +lemma sg33708 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,2,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20504 sg17309 + +lemma sg33709 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,2,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20852 sg15768 + +lemma sg33710 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,2,2,2,2,2,2] := by + exact rowSquare_join (by decide) sg20505 sg17309 + +lemma sg33711 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17308 + +lemma sg33712 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19638 + +lemma sg33713 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20507 sg17308 + +lemma sg33714 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,3,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17290 + +lemma sg33715 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,3,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18151 + +lemma sg33716 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,3,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17290 + +lemma sg33717 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,3,3,3,1,1,1] := by + exact rowSquare_join (by decide) sg20519 sg17283 + +lemma sg33718 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,4,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg19623 sg18922 + +lemma sg33719 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,4,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16754 + +lemma sg33720 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,4,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18916 sg19638 + +lemma sg33721 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,4,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17308 + +lemma sg33722 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,4,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg19624 sg18922 + +lemma sg33723 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,4,4,4,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17290 + +lemma sg33724 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,2,2,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20506 sg17309 + +lemma sg33725 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,2,2,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg18915 sg19639 + +lemma sg33726 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,2,2,2,2,2,1] := by + exact rowSquare_join (by decide) sg20507 sg17309 + +lemma sg33727 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,3,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20498 sg18040 + +lemma sg33728 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,3,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20633 sg16755 + +lemma sg33729 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,3,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg18916 sg19639 + +lemma sg33730 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,3,3,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20508 sg17309 + +lemma sg33731 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,3,3,2,1,1,1] := by + exact rowSquare_join (by decide) sg18917 sg19639 + +lemma sg33732 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,4,1,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20634 sg16741 + +lemma sg33733 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,4,2,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20515 sg17291 + +lemma sg33734 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,4,2,2,1,1,1] := by + exact rowSquare_join (by decide) sg20635 sg16741 + +lemma sg33735 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,4,3,1,1,1,1] := by + exact rowSquare_join (by decide) sg20516 sg17291 + +lemma sg33736 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,5,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20700 sg16321 + +lemma sg33737 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,5,5,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg19620 sg19205 + +lemma sg33738 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,6,2,2,1,1,1,1,1,1] := by + exact rowSquare_join (by decide) sg20512 sg17292 + +lemma sg33739 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,6,2,2,2,1,1,1,1] := by + exact rowSquare_join (by decide) sg20423 sg18152 + +lemma sg33740 : RowSquare [15,13,6,5,4,3,2,2,2,2,2,2,2,1,1] [11,11,9,8,7,6,2,2,2,2,1,1] := by + exact rowSquare_join (by decide) sg20513 sg17292 + +end UniversalTensorSquare +end +end + +end OAI